Crooked Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⢄⠀⠈⢀⣠⠾⠃⠄⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠁⠀⠀⠀⠈⠳⣤⡟⡁⠀⠀⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣤⡾⠋⠳⣧⡀⢰⣿⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠳⣤⣴⣿⠁⠀⠄⢈⣷⡟⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢸⣿⢎⠀⢠⣠⣾⠿⠉⠁⠀⠀⠀⡀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠘⡀⢠⠂⠀⠀⣿⣿⣷⣿⣿⣵⣶⠾⠿⠿⢦⣤⣁⣵⠃⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢣⣟⠀⠀⢀⠘⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⠿⠶⠶⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣷⣄⠀⠙⣿⣯⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣶⣿⣿⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⡠⠁⠙⣿⣿⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣴⣿⣿⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣯⣿⣫⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣪⣿⠗⠋⢵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⡏⢴⡾⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣅⣿⣇⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⡟⠛⢛⣿⡟⠙⠓⢺⣿⣿⣿⡦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠉

⣇⣈⣿⣿⠀⠉⠐⠚⢶⣿⠀⠀⠈⣿⣧⠀⠀⠀⣿⠁⡀⠰⢼⣇⠈⠁⢳⣾⡿⠈⣆⠀⣷⣰⡷⠾⣣⣖⠢⠤⣼⣿⠤⠐⢾⣷⡀⠘⡄⠘⣦⠃⢸
⣧⠜⣿⣿⣦⠤⠂⠀⠀⣿⠀⢀⠀⣿⣿⠀⠀⣸⡿⡆⠈⢿⢸⡿⡀⠀⡎⢀⣿⠀⠀⣿⣿⠋⠀⣀⣯⠈⠁⠀⣿⣏⣠⠜⠩⣯⢿⣟⡟⢹⠟⢳⣾
⣿⠀⣿⣿⡅⠄⢀⡀⠀⣿⠋⠁⠀⣿⡟⠀⢠⡿⠀⣷⡀⣸⣾⣧⡧⣀⡷⢻⣿⠋⢁⣿⡏⠀⠀⠈⣿⡤⠔⠀⣿⣿⡅⠀⠐⡇⠀⠀⠙⣾⣶⠉⠘
⣿⠀⣿⣿⣇⢀⡠⠽⠛⣿⠀⠀⠀⣿⡷⢠⣿⣇⠠⢸⡆⡉⣿⡿⣄⡟⢉⣿⣏⠀⢸⣿⡇⠀⠀⠀⣿⠀⠀⢰⣿⠃⢿⣀⣠⣧⣤⣤⠄⢸⣿
⣿⢀⣿⣿⣏⢡⡔⠘⠒⣿⡶⠂⠘⣿⡇⣼⡇⠈⠁⢨⣏⠀⣽⡇⢹⣿⠑⢿⣧⠔⢸⣿⡇⠀⠀⠉⣿⣀⣀⣼⡿⠀⠸⣯⣽⢹⣿⡇⠀⢸⣿⠀⢀
⡿⢸⣿⣿⡟⠉⠙⡇⠀⣿⡇⠀⠀⣿⣿⣿⠁⠸⣦⠃⢹⣄⣿⡗⣿⡿⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⣿⣁⣠⣿⠇⠀⠀⢹⣿⠘⠿⠃⠀⢸⣿⠀⢸
⡇⢸⣿⣿⣿⠀⠀⠇⢀⣿⡇⠀⠀⣿⣿⡷⢄⣀⣷⡀⢀⣿⣿⢠⣿⠇⠀⣾⡟⠀⢸⣿⡇⠂⠀⠙⣿⠋⣼⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢸
⡇⢸⣿⡟⣿⠀⠰⡏⠀⣿⡇⠀⠐⣿⣿⠁⠀⢁⡈⣿⡟⢹⣿⣸⣿⠀⠀⣿⡇⠀⣾⣿⠁⠀⠀⠀⣿⡆⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡀⢸
⡇⢸⣿⣿⣿⡦⢄⡇⠀⣿⣧⠔⠀⣿⣿⠀⠀⠀⠈⣿⡇⣾⣿⣿⡇⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⣿⣧⣿⡟⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⣼
⡇⢸⣿⣿⣿⡇⠘⡇⠠⣿⣧⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⠀⠀⣿⣧⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿⡇⢸
⡇⢸⣿⣿⣿⡇⢠⣿⠔⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⡃⣿⣿⣿⠃⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⢸
⡇⠀⣿⣿⣿⣷⠈⡇⠀⣿⣿⠀⢀⣿⣿⠀⠀⠀⢰⣿⡏⣿⣿⡿⠀⠀⢠⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⣸
⡇⠀⣿⣿⣿⣿⢸⡇⠀⣿⣿⠋⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢀⠔⣿⣇⣿
⡇⠀⣻⣿⣿⣿⢸⣇⠄⢻⣿⡇⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠀⣿⣿⣿
⣇⣄⣿⣿⣿⣿⣸⡇⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣼⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢰⣿⣇⠈⢀⠀⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣿⣿⣿⣀⣀⣠⣤⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠓⠶⣤⣤⠴⠚⠛⠛⠓⠦⣄
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣄⣀⣀⣀⣀⡤⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣤⠤⠶⢤⣄⡀
⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡞⠀⢀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠶⠛⠋⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⣀⣤⠤⠤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⠤⠤⣤⣤⣄⣀⣀
⠶⠋⠉⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡾⠁⠀⢻⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢰⡏⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠲⣄⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⣼⠁⠀⠀⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠻⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⠟⠀⠀⠀⠀⠹⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⢳⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣶⣤⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢀⣴⣿⣿⣿⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠋⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠆⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠛⠉⣁⣠⣤⣶⠆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣶⠶⠿⠛⠉⠀⢀⣠⣴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠾⠟⠉⠀⠀⢀⣠⣴⣶⣶⣶⣤⣀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⢀⣀⣀⡉⠛⠿⣶⣄⠈⣿⡀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⣾⣿⣿⣿⣟⠻⣶⡌⠉⠀⣿⠿⣷⡄
⠀⠀⢀⣴⡿⠻⣿⠀⢀⣴⡶⠶⠿⠿⠻⠿⠶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣼⡿⣿⣿⡿⣻⣿⣴⠟⠀⠀⢰⣿⣴⣿⡇
⠀⠀⢸⣿⣤⣤⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣷⣦⣬⡛⢷⣤⠀⠀⠀⠀⠀⢀⣿⠀⣿⣧⣈⣹⣿⡿⠛⠁⠀⠀⠀⢸⣿⠏⣿⡇
⠀⠀⢸⡿⠀⠈⣿⡇⠀⠺⣷⣄⠸⣿⣿⣟⣿⡏⢙⣿⡆⠹⣧⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣏⡀⣿⡇
⠀⠀⢸⣇⣴⣶⣾⣿⠀⠀⠀⠙⢷⣮⣿⣿⣥⣴⠟⠋⠀⠀⢹⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⡇
⠀⠀⢸⣿⣿⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠈⠻⠿⣿⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠐⣿⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠻⣧⡸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠻⣷⣦⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡈⠻⣿⣿⡆⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣿⣿⣇⠀⣶⠟⠛⠉⠉⠉⢀⣀⣤⣼⣿⠇⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⣿⣦⣴⣶⣶⣿⣿⣿⣿⠟⠋⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⢹⣷⣾⣿⣿⠟⠛⠋⠀⠀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣝⢿⣯⣿⠟⠁⢀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⠾⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⡖⣇⠀⢄⡀⠰⡌⠙⣇⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣊⡡⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣑⡜⣉⡙⡲⣧⢦⡷⣀⢿⡡⣠⠄⢠⠄⠀⠀⠀⠀⠀⠀⢸⣁⠀⠈⡀⠂⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⡈⠹⢦⣈⡙⠮⣽⢷⣼⡎⢻⡿⡅⠢⡎⠀⠀⠀⠀⠀⠀⠀⢺⡄⠄⢀⡇⠀⠀⢰⠀⠀⠀⠀⢤⠂
⠀⠀⠀⠀⠀⠈⠁⠐⠃⠁⠒⠦⢵⠖⠳⡄⠈⠙⣿⣱⡧⡉⠳⠀⠀⠀⠀⠀⠀⠐⣸⣆⣒⡋⠁⡄⢀⢷⣀⠴⢠
⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⢀⡶⠚⠓⠦⡙⠶⠶⣧⡿⣠⠏⣰⠇⠀⠀⠀⡴⠒⣼⡏⢿⡁⠘⠋⣠⡴⢮⠟⠀⠦⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠋⠁⠀⠀⠀⡳⢦⣴⡟⣷⣯⣶⠏⠀⠀⠀⠐⣧⡶⠫⣴⣳⣗⣀⣠⠇⠈⠠⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⡠⢬⣿⡟⠁⠀⠀⠀⠀⠀⠀⣿⡴⠾⠶⢴⢀⠈⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⠟⠑⠀⠀⠀⠀⠀⠀⢻⣷⣶⣤⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠛⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⢽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⢊⣿⣿⡿⠻⣯⠷⠀⠀⠀⢀⣼⣏⣹⡧⣽⣟⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠛⣯⠿⣋⣸⢇⠞⠀⠀⠀⠸⠸⠧⣁⣹⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠠⡏⠁⠂⠀⠀⠀⠀⠀⠀⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⢋⡦⢭⣲⣤⣀⣀⣀⣀⡠⠴⢚⡟⡆⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⡤⠞⢁⠞⢱⡀⠀⠀⠀⠁⠀⣀⡤⢖⡿⠀⠘⠦⣀⣀⣀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡍⠓⠒⠋⠁⠀⣸⡟⠻⠭⠭⣉⠭⠤⠒⡹⢇⠀⠀⠀⠀⠀⣠⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⢆⠀⠀⣤⡰⠃⠸⡄⠀⠀⠀⠀⠀⡼⠁⢯⡦⣀⡀⣠⠞⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢻⣏⠉⠀⠀⠀⢹⡦⠿⠿⠖⣾⠁⠀⠀⠉⡡⢞⢿⠀⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⠇⠀⡇⢱⢦⣠⠔⣡⣿⣱⣎⡿⡝⣆⡠⢴⠋⠀⢸⢸⠀⠀⣇⢳
⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⡇⡼⠀⣯⠹⡟⢦⣽⣿⣖⢻⡟⠀⢺⠀⠀⢸⡘⡄⠀⠘⢆⢣
⠀⠀⠀⠑⠢⢴⣒⡽⠋⠉⠀⢀⣴⠟⠀⣠⣧⡼⢶⡽⢹⣟⣤⠟⡿⠲⠤⠷⢤⣀⣳⣱⣄⣀⣀⣙⣷⣤⠤⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠙⢏⠒⠚⠻⣗⠿⠟⠛⠁⣳⣎⠉⢻⢻⣈⣿⡜⠀⠀⠀⡰⢡⠞⠉⢀⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠈⣆⠀⢀⠜⠁⠈⠑⡟⠉⡇⠀⠙⢦⡀⠀⣧⠇⠀⢠⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠴⠓⠒⢤⡀⢰⠃⣀⠼⡤⠤⠤⢝⣦⣿⠀⠀⡞⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⢀⣠⣚⣡⣤⣀⠀⠀⢱⡼⠋⠀⠀⢳⠀⠀⠀⠀⠉⠳⢄⣣⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣰⠿⠷⠯⠥⠤⣄⡉⠛⢷⡄⢸⠃⣀⡤⠤⠤⢧⠀⣠⣴⡒⠒⠒⠛⠶⠽⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⣦⣷⠟⠛⠉⠉⠉⠛⢻⡛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠙⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡒⠋⣀⣿⣿⡿⣿⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠞⣣⣀⣙⣿⠋⢹⣭⣟⢻⣻⣿⣿⣆⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⢹⣷⣜⣿⣿⠿⣿⣿⣿⢿⣿⣿⣟⣉⣙⣯⣻⣿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠆⣿⣼⡿⣿⣟⣶⣿⣿⣽⣿⣿⣏⣿⣿⣯⣧⣷⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⢠⣶⡎⣰⣶⣿⣿⣷⣿⣿⣿⣿⣿⢋⣉⣿⣿⣿⣿⣿⣿⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢲⣾⣿⡛⣿⣿⣿⣿⡟⣼⣶⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⢀⣀⡀⢰⣟⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡉⣿⣿⣿⡋⣬⡿⠿⣿⣿⣇
⠀⠀⠀⢀⣿⢳⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⣿⠇⣨⠿⣿⣵⣾⡿⡿⠇
⠀⠀⠀⠘⡏⣹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠻⠛⠛⢻⣿⣿⣿⡾⠃⠀⠉⢛⣿⣿⣷⣾⣶⣤⣀⣀
⠀⠀⠀⠸⠗⣛⣿⣿⣿⣿⣋⣛⣷⣿⣼⣿⣇⠀⠀⠀⠀⢻⣿⣿⣄⣀⣰⣾⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣼⣿⣻⣿⡿⢿⣿⣿⠿⢿⣿⣿⣿⣶⡶⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠛⠋⠉⠀⢀⣽⣧⠀⡈⡉⠉⣿⣿⠁⠀⠀⠀⠀⠀⣨⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⢿⣿⣶⣿⣿⣾⠏⠉⠀⠀⠀⠀⠀⢸⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣶⡸⢿⣿⣿⣿⣿⡿⣿⡿⣧⡄⠀⠀⣴⣶⣶⠸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠙⠷⣞⣿⣿⣿⣽⡿⠋⠁⣩⣤⣤⣴⣿⣿⣯⣦⣧⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣡⣿⣾⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡟⢿⣿⣿⣿⡇⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⡿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠁⠙⠛⠁⠀⠀⢠⣭⣤⡿⠛⠻⣽⣭⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⡀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠐⠠⠂⠀⠀⣀⠀⠀⢁⠀⠰⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⣐⠋⠉⠓⠂⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠄⠀⢀⠀⡀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⣸⣟⣛⣿⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠨⠀⠄
⠀⠺⠔⠦⠎⠀⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠠⢠⣿⡄⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⣀⠀⣦⡀⠐⣿⣤⠀⣀⡀
⢸⡦⢸⡆⡼⠘⣀⣂⠴⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣧⠀⠀⠀⠀⠀⠀⢳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢬⣳⣶⡈⣿⡿⠙⣛
⢸⣧⡼⠃⣠⣾⣤⣌⠻⢾⡷⢤⣤⡀⠀⠀⠀⠀⠀⣰⣿⡇⢿⡆⠀⠀⠀⠀⠀⠀⠳⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⣦⡤⠀⠉⠙⣿⣷⢃⣴⣽⡷
⣰⠗⢡⠾⠯⣭⣵⡿⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⡴⢻⡏⠑⠚⢿⡄⠀⠀⠀⠀⣀⣀⣉⡧⠨⡉⢶⡄⠀⠀⡾⠒⣶⡰⣗⣳⡶⣠⡜⢟⣛⣿⣩⣥
⠃⠀⡟⢶⣴⣹⣥⣶⢴⣿⣛⣵⣦⠀⠀⢶⣄⡀⠉⣻⡇⠀⠀⠀⢹⣦⠶⠛⠛⠩⠽⢻⡏⠇⠘⢸⠇⠀⠀⢾⣷⣹⡃⢾⡉⢛⠒⣟⡞⢸⡿⣛⣫
⠀⣸⠟⢋⣥⣾⣹⠿⣿⣿⣯⣽⣿⡅⣷⡄⢹⡻⡎⣻⣃⡂⠀⠀⠀⣿⠀⠀⠂⠀⠀⣈⣧⣤⣤⣯⢞⣁⣙⠿⣿⠛⣗⣦⡻⣿⣧⣽⠀⣿⣽⣿⣿
⢠⠟⣤⡾⠿⠿⠄⢰⣿⣿⣯⠈⠻⣷⣿⣷⣈⣷⠞⠋⠉⠛⠛⠿⠷⢿⠶⠶⠿⠟⠛⠛⠉⢷⡇⣿⣤⣌⡱⢍⣲⠀⢹⣟⠝⠲⣤⠃⠀⣿⣻⢻⣿
⠀⠀⢸⣾⡿⠁⣠⣯⡿⣷⣿⠦⣔⣽⣷⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⠉⠀⠀⠹⠃⠀⣿⣾⣿⡿⠀⢀⡿⢻⣿⡿
⠀⠀⠘⣿⣂⢻⢹⣿⣻⣾⣿⣙⣻⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣨⣽⠯⢀⣱⡄⠀⢧⡾⣿⠃⠀⢸⣠⣟⣿⠷
⡀⠀⡠⢹⡃⠀⢸⣭⣿⣷⣶⢾⣿⣫⣛⣿⣿⡩⠉⠙⠛⠛⠶⠶⠦⣤⣤⣶⠶⠿⠛⠛⠛⠉⠉⣻⣿⣡⣐⣻⣿⡷⡀⡈⣷⠹⣆⠃⢘⢿⣋⣵⣼
⡇⠀⡇⠈⡇⠀⠀⣿⣿⣏⣠⣾⣿⣿⣿⣿⡏⠁⢠⠖⠲⢄⠀⠔⠀⣿⠃⠀⠀⠀⠀⠂⢠⠒⠀⢹⣷⣟⣹⢿⣿⠏⠉⣅⣿⠷⠿⡀⠈⠈⢻⡿⣿
⠃⠀⠱⣼⡇⠀⠀⠸⣿⣿⣗⣋⣽⣿⡿⣿⡇⠀⡇⠀⠀⠈⡆⠀⠀⣿⠀⢲⠐⠶⡆⠀⢸⠀⡀⣻⠿⡿⣿⣵⠏⠀⡀⢰⣯⣷⣦⡟⠀⠀⣞⣼⣿
⠀⠀⢠⡿⠷⠖⠉⠑⠻⠿⡿⠋⣵⠞⠓⠛⠧⣤⣇⠀⠀⢻⠁⠀⢸⡿⠀⠤⠀⠐⠃⠀⣀⣀⡰⠷⠦⣁⡈⠙⠢⢀⠤⠾⣿⣽⣯⣧⢠⠀⠙⠏⣿
⢠⠀⢸⠇⡀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠉⠒⠢⠀⣈⠋⠓⠺⠤⢤⣼⣧⠤⠴⠲⠂⠉⠁⣈⣤⠤⠐⠊⠁⠀⠀⡀⠁⠀⠀⠈⠻⠉⠙⣼⡇⠀⡃⣹
⢸⠀⡸⡇⢨⠂⠀⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⢔⠋⡛⡷⠲⢤⣀⣈⣀⡀⣤⡶⣶⣿⣿⡟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⡅⠟
⢸⠀⠁⢳⠈⠢⠀⠀⠀⠀⠀⠀⠁⢃⡀⡀⣰⣆⣾⠵⡮⣄⠤⠴⠭⡤⠤⢤⣙⣷⣿⢸⡧⠠⣀⣀⢀⡀⢑⠀⠀⠀⠀⠀⠀⠀⢠⣯⠁⠀⠀⣷
⢸⡄⠀⡈⡆⠀⣀⠴⠀⠀⠐⠒⠂⠀⠀⠀⠀⠙⠾⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠏⠀⠀⠀⠀⠀⠀⠁⠉⠓⠂⠒⠤⣤⣠⠞⢁⠀⢀⡄⢿⠖
⠘⠇⠀⢳⡸⣤⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡭⠖⠲⡃⣄⠈⣥⠺⡗
⠀⢰⠀⠘⡅⢈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡶⠃⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠙⠂⠈
⣠⣿⠂⢀⠟⠬⠆⠉⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣙⠫⠶⠔⠉⠁⠉
⠁⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠛⠛⠛⠋⠻⠻⢿⣿
⠀⠀⠀⠀⢀⣠⣿⡿⠟⠉⠉⠈⠉⢻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣰⣾⣿⡀⠁⠀⠀⠀⠀⠀⠠⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣠⣶⡿⠿⠿⣿⣷⣄⢀
⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠸⠶⢶⠟⠃⠀⠀⠀⣿⣆⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠈⢻⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣅⣀⣸⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⢀⣠⣾⣿
⠀⠀⠀⠀⠈⢻⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠹⢿⣦⣤⣤⣴⣾⢛⣽⡟
⠀⠀⠀⠀⠀⠀⢿⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⣡⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣻⣿⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣻⣿⣿⣿⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠿⠯⢭⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠙⡿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠈⠻⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣟⠃⣀⣤⣶⣵⣵⣿⣭⢶⡦⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣤⣶⡶⢏⣀⠀⣠⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⢁⣿⣿
⠀⠀⠀⣾⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠋⢱⣄⠉⠀⠉⣩⣎⠀⠀⠀⢶⣿⣿⣿⣿⣿⡄⠀⠀⠠⣸⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣹⣿⣿⣶⣾⣿⣿⣶⡄⠀⠘⠻⢿⣿⠿⠛⠁⠀⠐⢢⣿⣻⣿
⢀⣶⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⣯⣀⠀⡀⡀⣻⣭⢿⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡿⢿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠠⡿⣯⡄⠉⠉⠁⠀⢲⣧⣿⢼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠷⢿⢻⡿⠇⠀⢼⣿⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡈⣿⣿⡁⠀⠀⢠⡑⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣾⣧⡀⠀⢸⣿⠀⢘⣿⣿⣿⣿⣿⣿⣷⣿⣇⣾⣷⠁⠀⠀⠞⢳⣼⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡄⠀⠐⠉⡀⠈⣿⣿⣿⣿⣿⣿⣷⢸⣿⠚⠁⠀⠠⠵⣺⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠇⠀⠐⢾⡇⠀⢹⣿⣿⢿⣻⣿⡷⢤⡋⢁⠀⠀⠄⡺⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⢶⡗⡚⣿⡏⠽⡥⣿⣷⣺⣱⣻⠇⠀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣬⣿⣛⣭⣼⣿⡏⠀⡉⢹⡿⣼⣭⠁⠀⠀⠉⠿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢩⡿⢤⣴⣿⣿⠛⠛⢻⡟⠀⣷⠀⠀⢸⡗⢩⠏⠀⠀⠀⠀⣠⡈⣣⣼⣿⣋⣽⣿⢿⣾
⣌⠻⣿⣿⣿⣿⣋⣀⣈⣣⠈⠈⠁⢸⣯⣿⣄⣤⣴⣿⣿⠓⢈⡇⢂⢸⡗⠺⣿⣿⣤⠀⣴⣾⣿⣿⣿⣿⣿⠿⢷⣿⣿
⣿⣷⣽⣿⣿⣿⣿⢻⣿⣿⣇⣴⣿⣾⣿⣿⣥⣄⣈⣹⣀⣀⣼⣷⠊⢸⣿⠀⠀⢀⣉⣀⡈⣉⣿⡿⣿⣍⡙⠒⢛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣻⣏⣉⠉⢙⣟⣿⣿⣿⣤⣾⣿⣦⣄⣙⠿⠿⠯⣿⣿⡇⢋⣻⣇⣾⡿⣿⣷
⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷⢷⡟⠻⠟⢍⣿⣿⣿⣿⣤⣼⣿⣿⣧⡣⣠⣤⣀⣸⡖⣰⣿⠟⢹⣿⣷⣿⣿
⠛⠋⠁⢙⣷⡿⢿⡿⣿⣿⣿⣿⡗⢶⣶⣾⣦⣤⣴⣾⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣃⣰⣤⣽⣿⣿⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡆⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢷⠇⣭⠀⢄⠘⠦⠀⠶⠬⣦⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡫⠀⣀⠔⣟⢣⣿⣾⠀⠙⢦⣈⠀⡀⠀⠈⢂⡇⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣾⠖⢉⣤⣴⠥⣞⡻⣙⢶⡆⠀⠈⢷⣇⠀⢦⠀⢣⠀⢈
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠏⠀⢠⡞⣡⡴⣩⠊⣷⣼⠋⠲⢬⡓⢿⣆⡰⣠⣌⣳⣴⠀⢸⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⡿⢁⡾⠳⢿⣴⠇⡴⠾⣧⢀⠂⠀⠹⣧⡹⣷⡀⡍⠋⢿⡀⢿⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠑⡄⠀⡆⠀⠀⢳⣼⡁⠹⣾⣷⣴⡁⠘⣿⣯⠀⠀⠆⢸⡇⢻⡿⠸⣶⠚⡟⣾⡀⠸⡀⡼
⠀⠀⠀⠀⠀⠈⢲⡇⠀⠀⠀⢻⣇⠀⢹⡏⡿⣇⡀⠈⢺⣢⡀⠘⢾⡇⣸⣿⠀⡿⢒⣿⠿⡁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠿⢄⡀⠀⠀⠹⣦⣀⣷⡘⣼⢧⣀⠀⣿⣇⣀⣻⣥⣽⣿⡿⠖⠋⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠋⠉⠙⠻⣷⣜⠳⡟⢿⣿⣿⡟⣿⣿⡷⣶⡶⢶⡶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⡆⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⣯⣿⣿⣷⣤⣴⣷⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣿⣿⣽⣿⣵⢿⣿⣿⣿⡼⢿⢛⣻⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⢿⣿⠙⢸⣿⣿⠿⣞⠻⢶⡿⣿⣦⡾⢫⣥⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⡜⢟⢯⣿⣿⠿⢦⣿⣷⡾⣿⣿⣿⣿⣿⢿⣩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠌⢻⠾⠷⠯⣽⣭⣿⣫⣽⣶⣿⣦⣼⣿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⣱⣟⣟⢹⠻⣿⡝⣧⡜⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢻⡽⢞⡆⡰⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠈⠓⠢⠁⢠⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠗⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⠳⣄
⠀⠀⠀⠀⢘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣰⠏⢀⠈⠻⣤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⠋⢠⣿⣷⠆⠘⣷⣄
⠀⡀⠀⠀⠹⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠿⠿⡟⠀⠀⠈⢿⣦
⣴⢁⠀⣠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⢀⣦⣤⣤⣤⣤⣴⣶⡀
⣿⣇⣼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣸⣷⣿⣿⣿⣷⣿⣿⣷⠀⠀⢀⠀⣄⣿
⣿⣿⣿⣿⣿⠿⣿⣿⣷⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠛⡉⠉⠉⠀⢀⣠⣾⣿⣿
⣿⣿⡿⣻⢿⣃⣿⣿⣿⣿⣾⣅⣶⡄⢀⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⣆⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣷⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣤⣈⠀⢀⠀⣠⡀⠀⢀⣜⣆⣀⢀⣠⣰⡶⠀⡀⠀⢀⡜⠁⠀⠈⠷⠀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡶⠘⣰⣿⣿⣶⡇⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⡇⠀⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢠⣿⣿⠟⣠⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⡿⠀⠛⠋⠁⢸⢻⣿⣿⣿⢸⣸⣿⣿⢿⣿⡟
⣤⣈⠛⠿⡟⠁⣰⣿⣿⠘⣿⡿⡿⢿⠃⡀⡙⠻⠟⠛⠋⠉⠀⡱⠥⠾⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⠀⣾⠸⠿⠿⠛⢤⣿⣿⠃⢸⣿⣇
⣿⣿⣷⠆⢀⡈⠻⣿⡏⢰⠃⠀⠀⠀⠈⡿⢀⣶⣶⠖⠀⠀⠀⠁⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⢀⣤⡾⠟⠉⠁⣰⣿⣿⣿
⣿⣿⠏⢠⣾⣿⣦⡈⠣⠈⠀⠀⠀⢀⠸⣷⡘⢿⡇⠀⠀⠀⣠⣾⠇⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠋⠁⠀⠐⠛⠁⠀⠴⠂⣠⣿⣿⣿⣿
⣿⣿⠀⢸⣿⣿⣿⣿⣦⡀⠐⠀⢀⡀⢺⣿⢡⠈⢳⡀⠀⠀⠋⠈⠁⣴⣦⠀⢠⣶⣿⣿⡟⢻⣷⣤⡤⠀⣀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠙⠛⠀⠸⢿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣈⡉⠉⠀⠈⠓⠀⠀⠀⠀⠈⠙⠏⠀⠙⢿⣿⡿⠃⠰⠟⢉⣴⣿⣿⣿⠀⠀⠀⠀⠈⠛⠿⢿⣧
⣶⣾⠀⢰⣤⣀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣷⣶⣦⣤⣴⠀⠀⢠⣤⣤⡄⣠⣤⠀⢠⣴⣿⣿⣿⣿⣿⠆
⢻⣿⣿⣼⣿⣿⣿⣷⣶⣤⡈⠛⢿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⠇⣠⣾⣿⣿⣿⣇⣿⡿⠀⣼⣿⣿⣿⣿⠿⠃⢠⣾⣷⣤⣠⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠛⢿⣿⣷⠀⢸⣿⣿⠋⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⣿⡿⠟⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡙⠃⠀⠸⠿⠟⠓⠒⠂⠉⠛⠋⠻⠿⠟⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡄⢠⣤⣶⣶⣶⣿⣶⣶⣶⣶⡶⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡩⠃⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⣈⣤⣦⠀⠀⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⡀⠀⢄⣀⣬⡴⢶⣛⣉⣫⣥⣤⣦⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠒⠒⠒⠒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡴⠶⠟⠛⠛⢟⢻⣚⣋⣭⣥⣴⣶⣶⠂⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣛⣻⠿⡿⢉⣁⣀⣀⣠⣤⣴⠶⠾⠃⡂⠈⣫⣭⡭⣥⣤⡤⠠⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠄⠎⠷⠶⠛⠛⠆⠉⣭⣥⡤⠤⠶⠀⣀⣨⡤⠴⠖⣂⣙⡛⠻⠶⣦⣄⣂⠀⠀⢭⣍⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡶⠖⣲⣀⣉⠘⠛⠂⠀⠂⣁⣠⣥⡴⠶⢛⣛⣭⣤⡶⢆⣿⣯⣭⣿⠿⠳⣶⣦⣭⣝⡓⠲⠬⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⣴⠶⠟⢋⣉⣡⣤⢴⣶⣛⣻⣩⡅⣶⣿⣿⠘⢻⢈⣐⠀⣼⣿⣿⣿⡇⠀⡎⡠⠁⠀⠉⣼⣿⠛⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠒⠚⣿⣿⢿⠞⣿⣿⣏⠉⡅⠄⣿⣿⣿⣦⠍⠈⠈⣼⡿⠿⠿⢿⠑⠈⠀⠃⠌⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣲⢎⣿⣿⣧⡾⠗⠃⠿⠛⠛⣛⡀⠀⠡⠀⠰⠐⠀⠠⣀⡀⠀⠉⢀⣾⣿⡏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢛⣉⡀⠩⠁⡀⠶⠀⠀⠀⢃⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠈⠀⠄⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠈⠋⠀⠘⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠐⠴⠦⠤⢤⣤⣄⣰⣀⡀⠀⠀⠀⠀⠈⠁⡀⢠⣤⠠⣤⡤⢤⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠒⠚⠛⠷⠷⠼⢧⣸⣯⣷⣿⣀⣟⣷⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠶⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⢀⣄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢼⣟⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠄

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⣀⢀⢀⡄
⠀⠀⠀⠀⡦⠀⢨⠌⠀⠀⡎⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⣀⠄⠘⡚⠌⠛⠆
⠀⠀⠀⠀⠍⠒⣁⢠⣒⣆⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠁⠀⠈⠦⠀⠀⠟⠉
⠀⠀⠠⣔⢁⣔⡨⡭⣿⡫⠠⠤⠄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⡁⠀⠀⠏⢤⡀
⠀⠀⠀⠀⠀⠠⠄⢁⠋⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠁
⠀⠀⠀⠐⠋⠀⢐⣨⠤⠠⡄⠀⠒⠀⠀⠀⠀⠀⠀⠀⢒⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⠁⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣴⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠔⠀⢐⡾⡿⠣⠈⠦⢤⠤⠄⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠱⡈⠘⠋⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠰⠀⠀⠀⠢⢐⡀
⠀⠀⠀⠀⠀⠀⢀⠐⢃⡀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠠⡴⠂⠀⠀⠀⠉⠀⠀⠀⢠⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⡁⠀⡼⠃⠡⡃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠁⠇⠀⠀⢂⠀⣀⡖
⠀⠀⠀⠀⠁⠈⠖⠫⡔⣇⢢⡨⠶⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣄⠘⣉⡉⢄⠋⢀⠣⠄
⠀⠀⠀⠀⠀⠄⢨⠴⢮⠉⡜⠳⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡄⠠⣾⠃⠈⠁
⠀⠀⠀⠀⠀⡴⡁⠀⡤⠀⠘⠆⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⠌⠐⠀⠎⠉⠲⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⡥⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⠐⠀⠢⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⡁⣸⢰⣿⢯⣓⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⡑⣻⣣⡿⠃⠀⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡞⣡⠶⠯⠿⠟⠁⠀⠀⠀⢸⣹⠁⠀⠀⠀⣠⣤⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠳⣿⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⣈⣥⣤⣤⣤⣞⣽⣿⣿⡿⣿⣟⠿⢯⣍⡓⠂
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠏⠀⠀⣠⡤⠶⠚⠛⠉⠉⠠⠚⠉⠿⡦⠀⠀⢉⣭⠭⢟⡓⠶⢿⣷⣤⣉⠑⠂
⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠃⣀⡴⠛⠁⠀⠀⠀⠀⣤⠶⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠘⢻⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀
⠀⠘⢿⢿⣿⣿⣿⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠈⢻⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠶⠛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠴⠚⣋⣭⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⠦⠈⠙⠚⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣂⡀
⠀⠀⠀⠀⠀⠘⠚⠉⡽⠁⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠙⣆⠀⢻⠉⠳⠬⣷⠲⢤⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣸⠀⠀⠀⠀⠠⢔⣀⡉⠙⠒⠤⠤⣘⣯⡉⠙⢲⠒⠦⠬⣷⣦⡀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⠀⠀⠀⢀⡞⠉⠈⠉⠓⢄⠀⠀⠀⣀⣰⣤⠈⢧
⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡏⡼⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⢷⣰⠋⠀⠀⠈⡆⠈⢧⣀⡀
⠀⠀⠀⠀⡞⢉⣀⣉⠑⢾⡼⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣷⠀⠳⠆⠺⡄
⠀⠀⠀⠀⢇⠀⠈⠳⠻⠄⠁⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣠⣀⣸⢠⢴⣄⠀⢀⡇⠀⠘⢯⡍⡣
⠀⠀⠀⠀⠀⠑⠲⠤⠴⢶⡀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣳⣿⠋⠻⠿⠯⠤⠚⣠⠖⠒⡄⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠒⠲⠖⠛⠁⠀⠀⠀⠀⠀⠀⠁⢀⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠄⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⡠⢀⡴⠒⣒⡧⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡸⢀⠆⠀⠀⠀⢸⠉⣉⣹⠭⠼⠧⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⢱⠓⢺⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢖⡓⠄⠛⠀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠤⠤⠴⠃⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⡖⠒⠒⠒⢻⢹⡉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠼⢾⠷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⢾⠒⠲⣍⣹⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣢⠤⠤⠾⠷⢓⣚⡪⠽⠛⠉⠀⠀⠀⢀⣠⣤⣤⣤⠄⠍⠉⠉⠉⠛⠛⠳⠶⠶⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠿⠯⠭⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠻⠎⠙⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠠⠐⠀⠁⠀⠀⠀⠈⠉⠒⠦⢀⣠⠞⠀⠀⠀⠀⠀⠒⠈⢷⣄⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣀⣠⡤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠀⠀⠀⠈⣇⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢉⡥⠤⠄⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⠀⠀⠀⢰⠋⠀⣠⣴⡆⠈⢳⠀⠀⠀⠀⡴⢉⣤⣤⠀⠈⢢⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⡶⢸⡇⠀⠀⢰⠀⣿⣿⣷⣶⠀⠀⡇⠀⠀⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⠀⠀⠘⠲⠤⢌⢛⠋⣁⠜⠀⠀⠀⠀⠣⠙⠛⣛⢋⢀⡼⠁⠀⠀⠀⢀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣄⡀
⠀⠀⠀⠀⠈⢧⡈⠙⠦⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡤⠖⠋⣠⠟
⠀⣠⠤⠤⠶⠶⠞⠓⠀⠈⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠙⠂⠀⠀⠀⠀⣠⢞⡟⠉⠀⡀⠛⠷⠶⠤⢤⢤⡀
⣾⣃⣈⠭⠅⠀⠀⠈⠉⠙⡆⣜⠀⠀⠉⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⢘⡇⡔⠉⠉⠀⠀⠀⢭⣭⣁⣙
⢯⠁⣀⣀⣀⣀⣀⣠⣤⠴⠃⢹⡀⠀⠀⠀⠀⡽⠓⣶⢤⣤⣄⣀⣀⣀⣤⣤⡴⠶⣏⠁⠀⠀⠀⣸⠃⠳⢤⣤⣄⣀⣀⣀⣀⡀⢨
⠈⠉⠉⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣀⣀⣠⠞⠁⠀⣿⢢⡀⠴⣿⣿⡷⢄⡌⣿⠀⠙⢦⣄⣀⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠀⠀⣠⠞⣯⠀⠀⠀⢨⣽⡀⠀⠀⢸⣦⡀⠀⠀⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠤⠖⠚⠁⠀⡃⠀⠀⠀⠈⠛⣇⠀⠀⠈⡇⠉⠓⠦⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡿⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠒⢲⡆⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢰⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢯⡀⠀⠀⠀⠀⡹⠂⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣦⣤⣤⣷⣄⣀⣠⣾⣥⣤⣤⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢿⡟⠙⢿⣁⣹⣏⣈⣿⣀⣸⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢤⣜⠋⢾⡋⠙⣏⣉⣿⣅⣈⣿⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢾⣿⣷⣶⣶⣶⡶⢻⣆⣀⡿⣶⠞⢻⡟⠛⣿⠉⣿⠉⠉⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡿⠞⠋⠉⠉⠙⠛⢿⣷⡎⢉⣿⣠⡼⣧⡾⢷⡶⠻⣿⠛⢿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⡷⠋⢀⣤⣶⣦⠤⣤⣤⣿⣧⠟⢿⡁⣻⣀⣸⣧⣼⢧⣤⡿⣦⣼⣿⡟⠀⡆
⠀⠀⠀⠀⢀⣤⣾⣟⣻⡿⠟⣵⢶⣿⠷⠿⠓⠷⠶⡿⠿⠻⢶⠊⢻⣅⣹⣄⣸⣧⣀⣿⣀⣸⣇⣀⡇⣀⠁
⠀⠀⡠⢺⣿⡿⠟⠋⠁⢀⣠⣿⠏⠁⣀⣤⣀⣀⡀⢲⣼⣧⡼⢿⠋⢻⠉⢻⡏⢉⡏⠈⣿⠁⢹⣿⡇⡿⡀
⢀⣾⡿⠛⠉⢀⣠⣶⣿⣿⡿⢟⣥⣿⣿⣿⠿⣽⣿⣿⣯⣸⣦⡼⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠂⡇
⠸⡟⠁⣠⣾⣿⡿⠿⠋⠀⠀⣘⡿⠉⠀⣀⣀⠀⠈⣩⣝⠉⠖⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠤⣶⣶⡆⠀⡇
⠀⢡⣰⣿⠟⢁⣀⣸⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣷⣾⣿⢐⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠃⠀⣿
⠀⢸⣟⣡⣴⣿⣿⣿⡍⠀⠉⢽⡿⠋⢁⣀⠀⠈⠛⢛⣣⡏⠴⢃⣀⣤⣤⣤⣤⣤⣤⡤⠀⣤⣤⣶⡆
⠀⠀⢻⡟⠋⢀⣐⣿⣶⣿⣷⣿⣟⣻⣿⢭⣷⣶⣤⣸⣿⣷⣀⠻⠿⠿⠿⠿⠻⠟⠛⠓⠂⠛⠛⠛⡇⡀⣬
⠀⠀⣨⣴⣶⣿⣿⡉⠉⠉⢩⣽⣏⠁⠀⠈⠉⠙⠛⣛⣿⠋⣅⠀⣀⣀⣀⣠⣤⣤⣀⣠⣤⣤⣵⣴⡇⠁⣷
⠀⣼⠟⠋⣀⣺⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣶⣬⣿⣿⣶⣺⣿⣿⣿⣿⠿⠿⠿⠿⠿⠶⠿⠿⠿⡂⠀⡗
⠀⣧⣶⣿⡿⣿⣧⡀⠈⢉⣽⠟⣡⡀⠀⠈⠙⠛⣻⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠁
⠀⣿⢁⣀⣼⣿⠿⣿⣿⣾⣿⣶⣿⣿⣿⣷⣶⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢠
⢠⣿⠿⠿⣿⣟⡀⠀⣽⣿⠟⠉⠀⠀⠉⠛⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢸
⢸⣁⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⡿⠿⠿⠇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢾⠏⠉⢻⣷⡄
⠀⠀⠀⠀⣿⡁⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠙⠋⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠑⠦⣄⠀⠀⠈⢯⠳⢄⡀⠀⢀⡀⠀⠀⠀⠀⣀⡛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣴⣶⠀⠀⠀⠠⣤⣤⣤⠼⠀⠀⠀⠉⠒⠒⠋⠀⠀⠙⠦⠼⠏⠲⣄⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣈⣢⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠉⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡏⠀⠀⠀⠈⢳⡀⢠⠒⠒⢢⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡇⠀⠀⢸⡀⠀⠀⠀⠀⣸⡇⢻⠉⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣬⡓⠋⠀⠀⠀⠈⢇⠀⠀⠀⠀⣹⠁⠈⠳⠤⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠖⣆⠀⠀⠀⠀⠈⠣⣄⣀⡴⠃⠀⠀⠀⠐⢦⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠒⠐⠋⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠦⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠈⠙⠒⣦⢤⣄⣀⣁⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠦⡴⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠺⠟⠀⢰⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠭⠀⣀⣯⣀⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⢨⡭⠉⣹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠙⡟⢒⣶⣶⡾⠖⢺⠟⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠭⠭⠟⠋⠉⠑⠛⠭⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠀⠀⣠⠄⠀⣀⠤⣦⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡠⠀⢼⣤⣾⢟⡦⠄⠤⠜⠻⢷⠛⣷⣶⣄⠀⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⡯⠐⡚⠛⣻⢖⠈⠁⠂⠒⠦⠐⣎⡁⠾⡖⢩⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⠶⢗⠀⠠⡎⠉⠀⢀⣀⣤⣄⣀⠀⠁⠠⠓⣷⣀⡹⠶⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠀⣑⠀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋⡰⠂⠀⣀⣁⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢄⡶⣿⣼⠃⠀⠀⠸⠿⠿⠟⠀⠀⢹⣿⣿⠀⠸⣀⠄⠸⡄⠈⠉⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⡿⣃⡀⠀⢤⠀⠀⠤⢀⡔⠀⣠⣿⣿⡟⠀⠐⠋⢓⠸⣀⣀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡅⠀⣦⠀⡰⠋⠠⡟⠍⢀⣾⣿⣿⠟⠀⠀⡀⢠⡎⠈⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢁⣀⡭⣦⣳⠸⣏⠀⠀⣾⣿⣿⠋⠀⠀⠰⠛⢻⠷⡄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⠂⠀⠻⣼⣋⣀⠀⠉⠉⢉⠤⣠⡒⠒⢢⠁⠹⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⡄⠊⣱⣿⣿⡁⠀⣿⣿⣿⠀⠈⣕⣦⠬⠀⠀⠈⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⢀⡧⢰⡟⣷⡿⢷⠀⠉⠉⢉⣠⢼⡥⢤⠵⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠞⠛⠀⠤⠉⠌⢉⡀⠀⠀⠰⠄⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠤⠄⠀⡤⠤⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠿⠂⠀⠀⠷⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⣴⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢲⢰⠃⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⣏⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⣤⣶⣦⡄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⠋⠉⠻⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⡿⠋⢿⣿⣿⠏⠻⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⢀⣴⣄⠀⠀⢀⣦⡀⠈⠻⣿⣿⣿
⠀⠀⠀⠻⠿⣿⣷⣶⣤⣭⣥⣴⣶⣿⡿⠿⠃⠀⠀⠀⣿⣿⣿⣧⣀⡀⠈⠉⠛⠓⠚⠛⠋⠁⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⡀⢉⣿⣿⣿⣿⣿⣏⠁⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡼⠉⠉⠀⠀⢸⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣾⣿⣿⣿⣷⡹⣿⣿⣿
⠀⠀⠀⣼⣧⣤⣒⣒⣒⣼⣔⣒⣒⣢⣤⣿⡄⠀⠀⠀⣿⣿⣿⡟⠸⠿⠿⠭⠭⠟⠹⠭⠭⠿⠿⡇⢹⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠟⠛⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣃⠀⠀⠀⣀⣀⡀⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⣽⡃⠀⠉⣭⠁⠀⠉⠛⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠩⠍⠐⡒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠢⡀⠀⠀⠀⣠⢤⣤⡤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣠⠿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠛⠃
⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣻⣏⣙⢂⠀⠀⠀⠠⠤⠤⠀⠒⠂⠁⠀⠀⠀⣠⡤⠤⣤
⢸⠀⠐⠀⠒⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⡀⠀⠀⠐⢻⡅⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀
⢸⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⣴⠀⠀⠀⠀⢀⡴⠒⢲⡇⠀⠐⠒⠒⠒⡖⠛⠛⠛⠁⢀⡟⠉⠉⠻⣦⡀⠀⠀⢿⣀⡾⠁⠀⠀⠀⠀⠀⠀⢠⡏
⠘⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠘⣿⠛⠛⠛⠛⠛⠀⠀⠠⡕
⡄⠀⢠⡿⠒⠒⠲⢾⡇⠀⠀⠀⣿⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠈
⡇⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣴⠀⠀⠀⢙⡷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢿⣄⠀⢀⡾⠁⠀⠀⠀⠀⠛⠀⠀⠀⡠⠂
⡇⠀⠸⠃⠀⠀⠀⢸⠇⠀⠀⢰⡿⠀⠀⠀⠿⢶⣤⣤⠞⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⣀⡀⠠⠄⠂⠉
⠧⠀⠐⢆⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣤⠤⠤⠤⠀⠐⠒⠒⠒⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠡⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⢸⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⢸⠀⠀⠔⠜⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⢀⠀⡇⠀⠀⠀⢸⠠⠀⠀⠀⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠂⠸⠧⢤⡬⠐⢠⠄⠉⠁⠂⠨⠁
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡄⠀⣸⣹⡆⢢⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡁⠛⠛⠛⠧⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠂⠀⢀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠀⠀⢀⠖⣶⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣄⢀⣴⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢉⠉⠉⠉⣵⣶⣾⣿⣿⣿⣿⣿⡁⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠃⠀⠀⠡⠠⠸⠂⠀⣠⣾⣿⣿⣿⠿⠋

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⡇⢸⢸⠷⣿⢸⠉⠁⡿⠉⢸⢭⡇⢹⡏⢰⣿⡄⣿⢸⢧⡇⢉⡏⠈⢳⠋⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠉⠁⠈⠀⠉⠈⠉⠁⠉⠉⠈⠀⠁⠈⠁⠉⠀⠁⠉⠈⠀⠁⠀⠁⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠆⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠀⣰⣫⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⢻⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⣆⠀⠀⣀⣀⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠼⣶⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣤⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⢿⡟⠏⠉⣻⠉⠳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⢀⣠⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢠⣿⣿⢟⣷⣿⣿⣿⣿⣿⡄⠀⠈⠙⠧⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⠿⠛⠋⣿⣿⣿⣿⠀⠀⠀⠈⢹⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣄⠀⣼⣿⣿⣿⣿⠀⠀⢀⠀⠈⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣦⣻⣿⣿⣿⣿⢿⣿⣯⣭⢻⢿⣿⣿⣿⢛⡟⣿⡄⠘⢿⣿⣿⣿⠁⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠾⣽⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣦⣤⣤⣿⠏⢸⠃⣿⣿⣤⣿⡿⣿⣿⣧⣀⡀⢀⣠⣴⠀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡘⠿⠶⢿⣷⣿⡇⠀⠀⠀⠉⢻⣿⣿⣿⡟⠀⡾⢀⡇⢿⣿⣿⢃⣿⡧⠀⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣷⣶⣿⣿⡗⠀⠀⠀⠀⣼⣿⣿⣿⠃⣼⠁⢸⠓⢸⣿⣿⣿⣿⢃⣨⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡹⣿⣿⢿⢿⣿⠀⠀⠀⢠⡿⢹⣿⡏⠀⠁⠀⠀⠀⣼⣻⣿⣿⢡⡿⠋⢀⣤⣶⡀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡘⢿⣾⡛⣿⡆⠀⠀⠸⠅⣼⡿⠀⠀⠀⠀⠁⣰⢯⣿⡿⠃⣾⣾⣟⢃⣶⣄⠃⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣎⠻⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣾⣿⣇⡸⣿⠁⠀⠈⢉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣏⢿⣧⡄⢸⡇⠀⢀⡀⠀⠀⠀⠀⠀⡀⣰⣿⣶⣿⣷⣿⡗⣶⡛⠛⠢⠞⢴⠶⢴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠙⠳⠿⠇⢸⣷⣾⣿⣟⣿⡏⠀⠀⣸⣆⣻⣷⣿⣿⣿⣿⣿⣘⡇⠈⠁⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣶⣄⣀⣿⠏⠙⢿⣿⣿⣷⣀⣰⣿⣿⢿⡋⠉⠈⠿⠿⢻⣯⣿⣤⣤⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⠿⣿⡿⣻⣷⢟⣽⢟⡗⠘⠻⠻⠿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣷⣬⣴⣾⣿⣿⣿⡆⠀⠀⠀⠉⠉⠛⣿⡿⠟⠀⠈⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣴⣿⣿⣯⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠀⢤⣄⠄⠀⠛⠻⠿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠄⣾⢻⠎⠒⠁⠀⠀⢻⣷⣶⠆
⠀⠀⣠⣴⣶⣾⣿⣏⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠚⠛⠛⠛⠚⠷⠆⣀⢰⣿⠟
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣿⠛⠛⠛⢁⣬⡠⣦⠀⠀⠨⠾⠿⠚⠛⠛⠉
⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⡽⠶⣔⠺⣿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡉⠓⠀⠂⠘⢆⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣾⣿⣭⣿⣛⡿⣶⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣷⣶⣶⣶⣿⣭⣝⣻⢿⣿⣷⣼⣿⡯⢾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣷⣮⣙⢷⣻⣶⣿⣿⣾⣝⢿⠞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢷⣿⣟⣿⣿⣫⣷⡿⢿⣛⡿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⢿⣿⣻⣿⣸⣿⣟⣿⣿⢱⣿⣿⣿⣷⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⣿⣷⡻⠯⢿⣧⣻⣿⢹⣿⡛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠢⡀⠀⠴⠟⠋⣉⠉⠉⠀⠀⠀⠀⠈⠹⣿⣿⣶⣝⣵⢟⣾⣿⣿⣐⣯⡻⣳⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠓⠃⠀⠀⠐⠋⠹⢻⠗⠒⠀⠀⠀⠀⠀⢻⡿⣷⢯⣷⣿⡿⣻⣵⣿⣽⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣧⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⢿⣿⡇⣿⣿⣿⡿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣹⣿⣿⡟⣽⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⢿⣳⣿⣟⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢫⣵⢞⣯⣭⣿⣾⣿⣿⣏⣿⣏⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠤⠄⠐⠀⠀⠀⣿⣎⢿⣟⣿⣿⣿⣿⣿⣿⡿⣸⣿⣮⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⣿⣿⣼⣿⡼⣿⣿⡿⣛⣭⡾⣟⣵⡿⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠐⠀⠀⠀⠐⠀⠀⠀⠹⢟⣛⣛⣟⣯⣥⣿⣿⡜⢿⡏⣾⣿⠽⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠿⢇⣿⣿⡿⢎⣷⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⣿⡿⣣⣿⡟⣡⣾⣿⠟⠼⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣫⣿⡿⣣⣿⣿⠁⠟⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⡿⣻⡽⠾⠛⠛⠉⠀⠀⠀⠀⢀⡤⠒⠉⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣏⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣫⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⡐⣄⠊⢧⡲⡀
⠀⠀⠀⡠⠔⠉⠀⠀⠀⠙⢦⣠⠵⠌⠃⠀⠁⠘⠄⠀⠀⢀⣀⣀⡀
⠀⣠⠎⠀⠀⠀⠀⠀⠀⢠⠎⠁⢀⣀⡀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣰⠁⠀⠀⠀⠀⠀⡴⠋⠈⠆⠴⠛⠛⠃⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄
⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢣⡀
⠹⢄⡀⢀⡠⠞⠀⠀⠀⡀⠀⣀⠀⡱⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢳⠀⠰⠀⢢
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣣⡘⠿⢷⠀⢀⣤⡀⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠇⠀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣽⣿⣿⡆⠌⣛⠕⠁⠀⠀⢻⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⡀⠀⡇
⠀⡎⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠑⣄⠀⠀⠘⡗⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣸⠁⠠⠁⢀
⠀⢣⡀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠄⠀⠀⠀⠀⠘⡄⠀⠀⠘⢦⡀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠶⠊⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠁⠒⠖⢲⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠉⠒⢤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⡿⠟⠛⠛⠿⠶⣶⣶⣾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠤⠜⠛⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢇
⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠀⢀⣀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡌⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⢦⡀⢀⡴⠁⠀⠀⢳⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠹⣄⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡗⠲⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠃⠀⠀⡙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠠⠚⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⠄⢀⠀⠀⠀⠀⠀⡿⢤⠄⠋⠁⠀⠀⠀⠉⠒⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠞⠉⠉⠉⠉⠛⠛⠒⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠂⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⣿⣦⠀⠀⠀⠀⠀⠹⠿⠿⠛⠻⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣠⡤⠴⠶⠶⠦⠤⠤⠄⣀⣀⣀⡀⠀⠀⠀⢉⣠⠾⠁⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠙⣦⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠒⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠴⣞⣽⣃⣶⠀⠀⠀⠀⠰⣟⣛⣻⣿⣿⡑⡄⠀⠀⠀⣿⣉⠀⢊⠁⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠊⠉⠉⠉⠈⠀⠙⡄⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⣿⣀⠄⠉⣰⣇⡀⠀⠀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⠠⣤⣤⣄⠀⢸⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⠀⠈⢷⡀⣸⠋⠈⢳⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⠀⠀⠀⠈⠉⠉⠀⡌⠀⠀⠀⠑⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣧⠃⡴⠀⢘⠀⠀⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⡀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠐⠀⡟⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠋⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠶⠀⠀⠀⠒⠒⠻⢧⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠸⠤⠔⠒⠒⠒⠒⠂⢐⠂⠘⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢰⠲⣄⠀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣠⣤⣤⣤⡬⣷⡌⠳⣄⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡼⠁⢀⠀⡀
⠀⠀⣾⠿⠶⠾⠀⠀⠀⠴⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⣾⠛⢛⠛⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡙⠁⠉⠿⠽⣟⣷⡀
⠀⠀⠳⠤⠤⢤⣤⣀⣀⣀⣠⠷⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠏⣠⣎⠁⠀⢀⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣘⠁⠀⠀⠀⢀⣁⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡅⠀⢀⡽⣄⠀⠀⠀⠀⢀⡴⢿⠀⠃⠘⢻⣿⡿⠆⠴⠋⠀⠀⠉⡿⢦⠀⠀⠀⠀⠀⠀⣠⠋⠀⠉⠳⠚⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡁⠀⠈⠳⣄⠀⣠⠞⠁⢹⠀⡀⢠⣾⣿⡇⠔⠀⠀⠀⠀⣸⠃⠈⢳⡄⠀⠀⠀⠴⠉⠑⢢⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢹⠋⠀⠀⢰⢀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣰⢦⡀⠀⠀⠙⢦⡞⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣾⠀⣀⡴⢻⡆⠄⢸⣿⠃⠀⠀⠀⠀⢰⠏⠀⠙⢦⡀⠀⢸⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠚⠉⠀⠘⡇⠀⢠⠁⡠⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣌⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⡅⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⠻⣄⣀⣀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠲⡍⠉⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠄⠘⣷⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢤⣀⠀⣷⣶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠁⠀⣀⡈⣻⠋⠠⠀⢹⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⣒⡚⠙⠁⠀⢀⠡⣦⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢠⢄⡴⠀⠀⣀⣸⡐⠀⠀⠀⣸⠀⢏⠀⠉⠀⠀⠀⠑⢉⠂⠀⢄
⠀⠀⠀⠀⣀⣤⠠⢀⠀⡀⠙⠉⠠⠀⠀⠀⠀⣜⡈⠀⢂⠂⠈⠙⡏⠀⠀⠀⠀⡙⢀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠹⣴⡈⠃⠀⠀⠀⠀⠀⠈⡁⢐⣀⡀
⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠉⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠋⠀⢀⠀⠨⣠⠄⢀⠌⠀⠀⠙
⠀⠀⠀⠀⢐⢀⠀⡐⠃⢀⢔⣂⡴⠇⠀⠀⠀⠀⠀⠀⣀⣙⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠖⠀⠲⠤⡄⢠⠄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⢀⠈⠁⠄⠒⠘⢺⡇⠀⠀⠀⢆⠀⠖⠀⠃⠒⠂⣦⠀⠀⠀⠀⢀⠄⠀⠠⠀⠄⠒⢀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠐⠢
⠀⠀⠀⠀⠀⢸⠧⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⠀⠐⠀⠀⠀⠀⣏⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁⠀⠀⠡
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⣌⡠⠀⢀⠁⠀⠀⠀⠀⠈⠀⠀⠠⡠⠀⠀⡈⠀⠀⠀⠀⠀⢠⠀⣀⠀⠌⠁⣰⣁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⢀⣀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⡀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢢⠀⠀⠀⠀⠠⢐⣆⡀⠀⢀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠐⠠⠀⠤⣀⠘⠀⠀⠀⠀⡄⠀⠐⠒⠐⠂⠐⢈⠀⠀⠀⠀⣶⠛⡒⠑⢻⠻⣤⣤⡖
⠀⠀⠀⠀⠀⢀⠻⠁⢐⠀⠀⠈⠀⠘⠐⠀⠀⡴⠆⠐⣂⠀⢐⠀⠈⡇⠀⠀⠀⠀⠻⠀⠤⠀⠀⠀⠀⡎⠂⠀⠀⠀⠈⠀⠄⠀⠀⠀⢀⣩⠁
⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⢀⡀⠀⠨⠀⠀⠀⠁⠆⠀⠀⠄⠀⠀⠀⠗⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⠐⠂⠀⢀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠉⠉⡀⠔⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠢⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⡀⠀⠀⠀⠠⠂⠀⠀⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠄
⠀⠀⠀⠀⠀⢀⣀⡴⠶⠂⡴⠴⢠⢀⠀⠀⠀⠀⠀⣴⣐⠶⢤⣤⡤⡄⡀⠀⠀⠀⢶⠀⢀⠀⠀⢁⠀⣄⡳⠀⠀⠀⢰⠘⠡⠜⠸⢄⣠⣄⡨
⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⢂⠀⠀⡄⢤⡃⠀⠀⠰⠍⠰⠀⠀⠂⠀⠐⠃⠀⠀⠀⢠⠀⢘⠀⠐⠃⠀⠸⢓⠀⠀⠀⠀⡀⠀⠂⠀⠈⠀⢹⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠄⠀⠈⠀⠀⠀⠀⠀⠡⠀⠠⡒⠂⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠴⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⢨⡆⢀⠀⠀⠀⢀⠊⠈⠁⠀⡈⠉⡓⠄⠀⠀⠀⠀⢀⡔⠲⠄⣠⠀⢰⠀⠀⠀⡍⠀⠝⠛⠂⠰⢘⢲⡙
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠁⠀⢱⣼⠃⠀⠀⠘⠠⠀⠀⠀⠀⠀⢑⢬⠀⠀⠀⢠⠾⠃⠀⠈⠀⠀⢉⠄⠀⢀⠀⣊⠀⠀⠀⠀⠀⠘⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣏⠄⠀⠀⢏⠁⠀⢡⠀⠃⠀⢀⡄⠀⠀⠀⠘⡁⠀⢈⡀⡖⠀⡀⠀⠀⠀⠣⡌⠀⢀⠀⡀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠂⠂⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠔⠀⠀⠀⠀⠀⠂⢄⡀⢉⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢠⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⠛⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠈⠁⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠰⣦⡆⠠⠄⠀⠠⡂⠀⠀⠀⠀⠔⠀⠂⣼⣤⣌⠀⣤⡶⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⡀⠉⠠⣿⣿⣶⣾⣿⣿⣿⢰⣌⡀
⠀⠀⠀⠀⠉⢁⠀⠄⠠⢀⠀⠚⢅⣀⣀⣄⡀⠉⠷⠍⢵⣿⣿⣿⣿⡿⠿⠛⠋⠉⢁⠀⢰⣶⡀⠰⠆
⠀⠀⠀⠀⠀⠙⠢⠀⠈⣀⠒⠉⠉⢁⣀⠐⠄⠑⠂⠻⣿⡿⠟⠋⠁⠀⠀⠀⣨⣞⠁⢞⣾⣿⡇
⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⠿⠷⢾⣿⣷⣶⣶⣶⣶⣀⡐⠒⢀⣤⡶⠾⠟⠛⡀⣿⢿⣿⣿
⠀⠀⠀⠀⠽⠟⠋⠉⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠠⠶⠋⠁⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢈⣿⡟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⡎⢿⣯⣷⠶⠶⠆⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⢿⣿⣮⣿⣿⣿⣾⣾⣿⣿⣷⡰⣼⣾⣿⣿⣾⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣇⣻⣿⣿⣿⣿⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⡻⣿⣿⡀⠙⠻⠿⢿⡿⣿⣿⡿⠿⣿⣿⣿⡿⠟⠛⠋⠁⢰⣿⣏⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣿⣿⣶⣼⣿⣿⣷⠀⠀⠀⠎⣴⢿⡟⠁⠀⠀⠹⣿⢿⡦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣍⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠺⠁⡾⠀⠀⠀⠀⠀⠸⡆⢣⠀⠀⢀⡤⠍⢻⣿⣿⣿⣿⢯⡉⠋⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡋⠀⠒⠒⠢⣤⡀⠀⠇⠀⠀⠀⠀⢀⠄⠻⠀⣠⡾⣋⣠⠤⣶⣽⣿⣿⠿⣦⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡟⠀⠀⠛⠙⠓⠶⢿⣿⠶⠤⣄⣀⡀⢈⣡⣴⠞⠻⠛⠛⠀⠀⠊⢁⣿⠘⢧⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠈⠀⠉⢾⣷⠦⠤⠀⠀⠀⠀⠀⢰⢸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢠⡴⠆⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⡏⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣉⠹⠇⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⣤⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⠌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠁⠀⢀

⠀⢸⣿⣿⣆⣼⣿⣿⣿⣿⡿⣿⣿⡏⣿⣿⡇⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢫⣿⣿⠛⠻⠿⠿⠟⢋⣴⣿⠟
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢹⣿⣷⠀⠀⢀⣾⣿⣿⡿⠟⢉⡉⣡⣴⣾⣿⣿⢿⣷⣶⣴⣶⣶⣿⣿⡏
⠰⣿⣿⣿⠟⣿⣿⣩⣿⣿⠉⠻⣿⣆⠘⣿⡿⢀⣴⣿⡿⠛⠋⠀⣀⣿⣿⣿⠿⠛⢻⣿⣿⣿⡿⠿⢻⣿⡿⠿⣿⣦⡀⠀⠀⢀⣀
⠀⣿⣿⣷⣤⣿⣿⣿⣿⠃⠀⠀⠾⠟⠀⠈⠁⠘⠛⠋⠀⠀⠀⠺⠿⠟⠋⠀⠀⢀⣀⣹⣿⣿⣀⣠⣿⡿⠁⠀⠈⠻⣿⣿⣿⣿⣿
⠀⢹⣿⢿⣿⡟⠛⠋⠁⢀⣀⣀⠤⠒⠒⠋⠉⠉⠉⠒⠒⠤⢄⠀⠀⠀⠀⠰⣾⣿⠿⠿⠛⠻⠿⣿⣿⣧⣀⣀⣀⣤⣤⣶⣿⡿⠟
⣾⣿⣿⣄⠈⠀⠀⠀⠀⣏⣩⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣙⣻⠿⢿⣿⣿⣏⠁
⠉⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠿⣿⣿⠿⣿⣿⠿⠿⣿⣿⣿⠻⣿⣦⣀⡀
⠀⠀⢀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣴⣿⠟⢿⣷⣬⣿⣿⣿
⠀⢰⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠴⠒⠛⠉⠉⠉⠙⠓⠓⠦⣄⡀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣥⣤⣴⣾⣿⣿⣏⠁
⢸⣧⡙⢿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⢀⣀⣀⣠⣤⣤⠴⠦⢤⣄⣈⡇⠀⠀⠙⠛⠉⠙⣿⣿⣿⣿⠛⠛⠉⠙⣿⡆
⣼⣿⣷⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⢴⡞⠽⢛⠀⠈⢉⣥⠀⠀⠈⡇⠀⢱⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⣀⣤⣿⣿
⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⣇⠀⠙⠃⠀⠀⠁⠀⣀⡸⠁⠀⠀⠘⡄⠀⠀⠀⣀⣀⣻⣿⣿⡟⠻⢿⣿⣿⢿
⠀⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣁⠀⠀⠈⠓⠦⠤⢤⠖⢲⠞⠉⠀⠀⠀⠀⠀⠘⣆⠀⠀⠻⠿⠿⠿⢿⣿⣦⣿⣿⣿
⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⣯⣴⠀⠀⠀⠀⠀⠈⣉⣡⣤⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠉⢻⣯⠘⣿⣷
⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠹⣅⡠⠞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣤⣿⣿⡄⠀⢻⣷⣿⣿
⠛⠋⠉⠙⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⣸⣿⣿⣿⣶⣴⣿⠟⠉
⠀⣠⣴⣶⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠀⣿⡿⣿⣿⣏⠉⠁
⢸⣿⠛⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡴⠃⠀⠀⠀⣀⣄⢻⣧⡙⢿⣿⣷⣴⣾⣷
⠀⠀⠀⣹⣿⣷⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠾⣤⢦⡀⢠⣄⢰⠤⠜⠁⠀⠀⠀⠀⢸⣿⣿⠀⠙⢿⣷⡈⢻⣿⠈⢿
⣤⣤⣾⣿⠿⣿⣿⣿⣟⣥⣤⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⢀⣤⣦⡄⢀⣠⣿⣿⠀⢀⣼⣿⣇⣸⣿⠃⠈
⢿⣿⡿⠣⢰⣿⣿⢫⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⡆⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⢠⣿⣿⣯⣄⣾⣿⣿⣿⣶⣿⣿⠿⢿⣿⣿⣦
⠄⠀⣠⣴⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⡟⢙⣿⣷⣤⣴⣿⣿⣿⣿⣿⠆⠀⣠⣾⣿⣿⡿⢫⣿⡿⣿⣿⣿⡟⠁⢀⣾⡿⠻⣿⣧
⡶⢧⢙⡻⢿⣯⣀⣻⣿⣿⣿⣿⠙⢿⣿⣷⣬⣿⣿⣿⣿⣿⡿⠋⣿⣿⣀⣾⣿⠟⣿⣿⡇⠈⣿⡇⠹⣿⣿⣄⠀⢘⣿⡁⠀⣿⣿
⣿⣾⡎⠀⠁⢙⣿⣿⣿⣿⣿⣿⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢿⣿⣿⣯⣤⣿⣿⡇⠀⠹⣿⣆⠈⠛⠻⠿⣿⣿⠏⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡤⣶⣵⢻⣿⣿⣶⣶⣦⣶⣶⡶⠿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⣄⠑⣿⣾⣿⣤⣿⣿⣿⣻⣆⠀⣄⡀⠀⠀⡱⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⣠⠀⢠⠀⣘⠆
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢿⣿⣀⠀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠠⢇⣠⡧⣀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣈⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠀⠀⢠⣄⡹⠟⠹⠃
⠀⠀⠀⠀⠈⠀⢀⢀⡀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⠟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠙⠀⠈⢡⠾⠉⠁⠀⠀⡈
⠀⠀⠀⠀⠄⠀⠨⠤⠄⠀⠀⠀⠀⠀⠈⠛⠻⣶⣷⣯⠀⣀⣴⣿⣿⣿⢿⣻⣿⣿⣿⣿⣷⣠⣤⡼⠋
⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⢀⠀⠀⠄⠶⠄
⠀⠀⠀⠀⠤⠀⠒⠒⠀⠀⠀⠀⠀⣽⠀⠀⠘⠾⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡴⠐⠃⢿⠷⠆⠀⡆
⠀⠀⠀⠀⠂⠀⠠⠐⠀⠀⠀⠀⢠⠐⠀⣰⣄⠀⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣡⣞⣷⠃⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣷⣶⣌⡄⢉⣿⣿⣿⣅⡛⠛⢯⣽⣿⣿⣿⣿⣿⣿⣤⠻⣿⣿⣷⡮⠄⠀⡀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠊⠸⠀⠀⠀⠀⠀⠈⠛⠋⠀⢊⣿⣼⣧⠀⢹⣶⡋⢹⣿⣿⣿⣿⣿⣿⣛⣿⣿⢿⣿⣧⣠⡄⢋⠚⠰⣿
⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⡶⠇⠐⣻⣀⣹⣠⣿⣿⣿⣿⣿⣿⣿⣶⡩⢿⣿⣿⣧⣤⡏⢀⣤⡿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⠋⠁⠠⠊⠝⢩⣿⣿⣟⢏⣿⠿⣾⣿⣿⣧⣌⠈⣻⠋⢿⣿⣿⣏⡿⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢠⣦⣷⠹⠋⠀⢠⠖⠀⣠⡾⢻⣿⣯⢿⢃⠀⠻⣿⣿⣿⣿⣧⣉⠛⠴⣟⣿⡟⠀⠐
⠀⠀⠀⠀⣄⠀⢐⣐⠆⠀⠀⠀⠀⠁⠛⣿⡇⠀⣤⠂⠀⢐⣿⢡⣿⣿⠛⠀⡘⡀⡀⠈⠛⢻⣿⣿⣷⣦⠀⢸⣅⢟⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣟⠁⠀⢹⣄⣴⣯⢭⠟⡁⠀⠤⠐⠁⠀⠀⠊⠮⠀⣹⣿⣿⣿⠀⠘⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠈⠀⠁⠀⠀⠀⢠⡄⢻⣋⠀⠀⠁⠀⢇⡺⠆⣠⡶⠛⠛⢶⣄⠀⠀⣴⣿⣿⣿⣿⠿⠀⠀⢈⣉⠀⠂
⠀⠀⠀⠀⠐⠀⢀⣘⠀⠀⠀⠀⠀⣈⢠⢼⣿⡆⠀⠀⠐⠘⢁⠀⣿⠀⠐⠃⠀⢻⠆⣸⣿⣿⣿⡟⠁⠀⣀⣀⢙⣿⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣿⠄⠄⠀⢀⢀⣤⡀⠹⢦⣄⣀⣴⠿⣴⣿⣿⣿⠛⣶⣴⣿⣶⣽⣿⣿⠋⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣎⡔⣀⡀⠸⢿⣿⣦⡀⣹⣿⣿⣿⣿⣿⣿⣿⣦⡉⠿⣿⣿⣿⠉⢹⣾⣿⣇
⠀⠀⠀⠀⠍⠀⠀⠶⠀⠀⠀⢸⣿⣶⣤⣤⣿⣿⣿⣭⣿⣶⣿⣿⡿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣯⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣾⠛⠋⠀⠉⢍⣛⣵⢶⣾⣿⣿⣿⣷⣾⣿⡿⢿⣿⡟⠛⠋⣹⣿⣿⣿⡛⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⣻⣷⣷⣀⡀⢀⣾⣻⣿⢘⡿⣿⣿⣿⣿⣿⣌⣛⠛⠦⣄⡂⣶⠟⣿⣿⣿⣟⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣄⠻⣿⡧⠼⢿⣽⣿⣽⣿⣷⣿⣿⣿⣷⣶⣤⣼⣇⣀⡀⠀⠈⢙⣿⣿⡟⣴⣿⣆
⠀⠀⠀⠬⠭⠭⠭⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⢿⡯⠉⠉⠉⠉⠍⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣟⣉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠⡏⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣀⠀⠀⣀⣀⣠⠤⠴⠼⠮⣍⠒⠃⠋⠁⠚⠐⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠼⠦⠬⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣛⠂
⠀⠀⠀⠀⠀⠀⠶⣶⠦⠴⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣤⣤⣤⣤⣀⠈⠙⣆
⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡘⢾⡜⣡⠖⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀⠑⢄
⠀⠀⠀⠙⠓⠒⣦⠖⠁⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠙⢾⡟⠁⢀⣄⣀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢳⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⠳⣤⠀⠀⠀⠀⡇⠀⠀⢻⠁
⠀⠀⠀⢠⣣⢴⠆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠉⠳⣎⠁⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠋⠁⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣄⣀⡀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⡋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢍⡁⢀⡇
⠀⠀⠀⠀⠀⢸⠈⠩⠭⣷⠀⠒⢶⠶⠶⠾⠟⠛⠋⠉⠀⠘⠿⠂⠀⠘⠗⠀⠀⠀⠀⠀⢠⡿⠀⢠⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣾⠀⠀⠀⡾
⠀⠀⠀⠀⢀⣀⣸⡄⠀⠈⡆⠀⠀⠈⠛⢦⣤⣀⣀⣤⣤⡶⠂⠀⠀⣀⠀⠀⠀⠴⢾⡯⠀⠀⠀⣇⠀⣀⠴⠗⢒⢶⡄
⠀⠀⠀⣴⠋⠉⢀⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠠⠴⠿⠋⠀⠀⠀⠘⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⢾⡉⠀⢹⡄
⠀⠀⠀⣇⠀⠞⢩⡿⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢻⠇⠀⢸⡇
⠀⠀⠀⠹⣄⠀⠘⠀⠹⠀⣧⠀⠀⠀⠀⢀⣤⣖⡋⠉⠉⠉⠉⠀⠀⠈⠉⠉⢙⣶⣄⠀⠀⠀⠀⢀⣷⣄⠀⠉⠀⣀⡾⠁
⠀⠀⠀⠀⠈⠳⠦⣤⡤⠞⠹⡆⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣶⣶⣿⣿⣿⣇⠀⠀⠀⣼⠃⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢟⣿⠿⠿⠭⢌⣙⣉⣩⠿⠿⠟⠻⣿⣿⠏⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠒⠦⠤⠤⣄⣀⣠⣤⣤⠤⠖⠋⠁⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣦⣴⣶⣾⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠇⠀⣀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⢐⣫⡍⠀⠀⠙⠛⠛⣻⢿⣿⣿⣿⡿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⠿⠇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⢠⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⣿⣿⣿⣿⣿⣿⡿⠟⡉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣾⣿⣷⣦⢈⣹⣿⣿⣿⣿⣿⣿⣿⡒⠈⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⣿⡿⠟⢣⣶⡟⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣛⢥⣠⣾⣿⣿⣿⣿⡿⠗⣰⣿⡿⠛⠁⠀⠀⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣛⣭⣶⣿⣿⣿⣿⣷⣮⠁⢠⣾⣿⣧⣥⣤⣤⣤⡄⣤⣤⣭⣥⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡦⣰⣆⠀⠙⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⢏⣽⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⣴⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠟⠋⠉⠹⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠛⠿⠟⠉⠉⠉⠉⠹⢿⡿⡿⠿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢲⡀⠰⣦⠀⣰⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣆⠀⣸⣷⠀⡏⢷⠋⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠿⠋⠘⠛⠀⠘⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⣳⣾⣟⣿⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠈⠹⣿⣷⣄⠀⠈⢻⣿⣇
⠀⠀⠀⠀⠀⣶⣦⣼⣿⣿⣇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠈⢿⣿⣤⡄
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠘⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠀⠀⢸⡇⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⣀⠀⠘⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡽⠀⠀⠈⠉⠉⠀⠀⣴⡄⣤⠀⣀⠀⠀⢤⠀⠀⢸⡇
⠀⠤⠄⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣷⠃⠀⢀⠤⢸⡷⣦⡇⢹⢙⡿⠉⡷⣿⣿⡄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⣄⣿⠚⢾⡇⢹⡀⣸⣈⣇⣀⣇⣇⣏⣏⣻⡏
⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣿⣯⡽⣴⠾⢿⠛⠛⣿⠙⠉⣿⢙⣹⢩⣸⡏⠉⠉⠐⠒⠒
⠀⠀⣆⣠⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣧⢘⡄⢼⣇⠀⣿⣎⣡⣿⡞⢻⠁⣿⠁
⠀⠀⣯⣛⣕⠒⣄⠀⠈⠉⠀⠀⢿⡿⣿⣿⣏⠻⠓⠾⠙⢧⣿⠛⣩⡏⠀⠀⣸⠇
⠀⠀⠉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠈⢻⣿⣿⡟⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄⣀⡐⠋⠁⠀⣰⡟⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣽⣿⣯⡻⣎⣻⣿⣿⢿⣿⣿⡶⠿⠋⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿⣿⣏⠫⣙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠛⠛⠋⠉⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣿⣿⣿⣿⣸⢶⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠻⣿⣙⣿⣿⣿⣿⣿⣿⡄⠪⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣹⡿⠁
⢀⣠⣤⣤⣀⣤⡶⣿⣿⣿⣿⡿⠻⣷⣟⢮⡻⢿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣯⣿⠟⠁
⣿⣿⣿⡿⣻⣧⣿⣿⣿⣿⣿⣿⣦⣌⡻⣦⡑⡌⣿⣟⣱⣮⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⣽⣿⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⣿⣿⣤⣾⣫⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠙⠻⠿⠷⣦⣀
⣿⣽⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣤⠀⠉⠀⠁⠀⢠⡾⢛⠿
⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣯⣭⣝⣻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⡇⣿⣿⣶⣄⣿⣥⣷⣶⠛⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣭⣤⣶⣾⣿⣍⢻⣹⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣦⡷⠖⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢂⠠⠂⢂⠀⠀⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠉⠀⢇⠈⠄⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣎⠢⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠂⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠉⠰⠛⡏⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⢁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠠⠤⢧⡀⠀⠲⣄⠘⡀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⣴⠃⠀⠀⠀⠈⠢⢀⠈⠳⠵⣄⣀⠀⠘⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⡀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠒⢀⡀⠀⠀⠑⠦⡀⠀⠀⠀⠀⣰⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠔⠈⣿⣿⣿⣿⣿⣷⣤⣴⡿⠁⠀⠢⣀⠀⠈⠢⡀⠀⣰⣿⡟⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⠀⠀⡌⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠂⠁⢸⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠁⠀⡐⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡰⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠐⠁⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⡗⠈⠈⠁⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡋⠁⠐⠒⠒⠒⠚⢁⡀⠀⠔⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡟⠉⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⢼⣁⠀⠙⡙⠋⠙⠉⠉⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢀⡠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⡤⠤⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢀⡲⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠉⠉⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⣀⠜⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡬⠂⠀⠀⠀⠀⠀⠀⠀⡃⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠉⠁⠒⠒⡆⠀⠀⠀⠀⠀⡝⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡨⠀⠀⠀⠀⢀⣤⣄⡅⠀⠀⠀⠀⠀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠹⠀⠀⠀⢀⠨⣀⠨⡄⠀⠀⠀⠀⠀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠢⡀⠀⠀⠀⢀⣀⢀⡞⠉⡗⠀⠀⡁⠀⠀⠀⠀⠸⡶⠅⢪
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠠⠉⠐⠐⠶⣚⠁⠀⠀⠀⠈⠉⠉⠀⠈⠛⢻⣻⠃⠀⠀⠀⠀⠀⣫⣁⡯⣀
⠀⠀⠀⠀⠀⠀⠀⠅⡠⡍⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠣⠄⠀⠠⠔⣊⢙⣯⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠒⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠉⠘⣼⣻⠀⠀⣷⠘
⠀⠀⠀⠀⠀⠀⠀⡘⠶⣤⡞⢉⡱⠈⠉⣽⡄⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠜⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠘⢄⢠⠄⠀⠈⠓⠒⠦⠏⠢⡜⠗⠊⠙⡀⠀⡔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠚⠈⠉⠀⠀⢁⠀⢠⠐⠉⠀⠀⠀⠀⠈⢱⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢉⠉⠉⣤⣹
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠖⠛⠀⠈⢄⡤⠶⡄⢀⣀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⡟⠋
⠀⠀⠀⠎⠉⢒⣁⠀⠀⣠⣬⡓⠈⢁⠀⠈⢡⠐⠁⢺⠀⣥⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⡅
⠀⠀⠀⠣⠤⠏⠉⠀⠘⣇⡀⣹⣤⠼⠀⠀⠈⢄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣘⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠒⠒⠒⠂⠐⠚⠛⠛⠓⠂⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⣀⠀⠀⠀⠀⠀⠀⣀⠤⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢇⠀⠈⠉⠐⠂⠈⠉⠀⢰⠁⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠐⡶⡒⠂⠉⠁⠀⠀⠀⢀⡴⢹⠉⠑⠒⠒⠊⠉⡝⠱⣄⡔⣶⣶⣾⢇⠒⠒⣠⡤
⠀⠀⠀⠀⠀⠀⢱⠈⠑⠤⣀⣀⡠⠔⠉⠀⢠⢷⠂⠤⠤⠄⢺⢇⠀⠈⠓⠿⣉⡀⣈⠴⠊⢱⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠓⢄⣀⠠⠔⠁⢈⡦⠀⢀⢤⡇⠀⠑⠤⢀⣀⠤⢻⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡜⠀⠀⡉⠲⣤⠔⠃⠼⡂⠀⡾⢈⠒⢤⡤⠊⠅⠀⠸⡀⠀⠀⠈⢆
⠀⠀⠀⠀⡠⠊⠀⠀⠀⡰⠁⠀⡸⠀⠀⠇⠙⢣⣔⢫⢸⢓⡤⠛⠁⢆⠀⠰⡀⠀⠣⡀⠀⠀⠈⠢⡀
⠀⠀⠶⣞⠒⠒⠒⠒⢾⡒⠒⠾⡒⠒⢾⠲⡗⠶⢒⣿⣿⡗⢲⠖⡷⢺⠖⠒⡳⠖⠒⡷⠶⠲⠶⠶⢺⠷
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⡄⠀⠱⠀⠀⡃⡠⢜⠃⡼⢸⡌⠛⣦⣀⠆⠀⡰⠁⠀⡜⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢡⠀⢀⣡⠔⠉⠒⢄⡹⠒⠀⢷⢁⠔⠊⠑⢤⣆⠀⢰⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡔⠋⠈⠉⠢⡀⢠⠋⠉⠉⠙⢇⢀⡤⠊⠉⠉⢑⣼⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡸⢀⠴⠊⠀⠈⠉⠒⢄⠀⠈⡾⠒⠂⠐⠒⠺⡎⠀⣠⠔⠋⠁⠀⠈⠑⠤⡘⡄
⠀⠀⠀⠀⠀⠐⠛⠃⠢⠤⣀⠀⠀⠀⠀⠱⣼⡠⠤⠤⠠⠤⠤⣱⡔⠁⠀⠀⠀⣀⠤⠒⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠇⣀⠤⠤⠠⠀⠤⠤⣀⠘⡄⡜

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⢦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠑⠤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢡⡴⠄⠛⠃⠀⣀⢐⠄⣠⣶⣶⣤⣹⡧⠀⠀⠃⣀⡀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢀⣴⣾⣥⣤⡤⠴⠶⠾⢷⣿⣿⣿⣿⣿⣿⡿⣷⣶⣿⢷⣄⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣶⣿⣿⣿⣥⣤⣴⣶⠖⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡤⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠻⠋⠻⣿⠿⢿⣀⣱⣦⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠊⠀⠉⠘⠚⠋⠉⠀⠀⠀⠀⠛⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠙⢧⣤⣈⠙⠿⠿⢿⣿⣿⣿⠿⠖⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⠛⠻⢶⣶⣦⣿⣿⠆⠖⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠁⠉⠉⠙⢃⣄⠁⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠁⠙⠋⠻⠛⠃⢀⣴⠄⠐⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠈⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠛⠂⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠒⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⢦⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠒⠒⠲⣄
⠀⠀⠀⠀⠈⡦⠀⢀⡤⠼⣗⠉⠁⠀⠀⠔⠀⠀⣠⠂⢀⡈⣥⣤⠇⠀⠀⣶⡄⠀⠈⡇⢀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠀⣠⠐⠈⠉⠉⠀⠈⠙⠫⡗⠁⠀⠀⠀⣸⠟⠀⠀⢀⣇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⢤⠀⢥⣀⠀⠀⠀⠋⠀⠀⠀⠙⡿⠿⠶⢿⡏⠾⡀⢁⣀
⠀⠀⠀⠀⠀⡄⠰⣄⡤⠛⠁⠀⠀⠀⡤⠒⠀⠀⢆⡀⠀⠀⠀⢱⠀⠾⠀⠀⠀⠀⣠⡧⠄⠼⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⣄⢸⠁⠀⣀⡀⠀⡇⠹⣄⡀⠀⠀⠀⠉⠣⠀⣰⣤⣀⣠⣤⣶⣿⠋⠀⠀⠀⠀⡀⢠⢰⣐⠀⡊⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢦⠀⠀⠉⠳⣇⠀⢹⡀⣀⡄⠲⠄⠁⢰⣿⣏⠙⠛⠉⣿⠉⢰⠢⣇⣟⣄⠈⡇⠸⠥⠳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠆⠀⠉⠁⠀⠀⠀⠀⣼⠀⠀⠑⠒⡖⠘⠀⡘⠀⠘⠁⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⠁⠈⠳⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⠴⠃⠀⠀⣠⠜⠂⡀⠀⠣⠀⠀⣤⣄⡀⠀⣀⠴⢳⡀
⠀⠀⠀⠀⡰⠊⠀⡞⠉⡗⠀⠀⠉⣟⠓⠤⠤⡤⠔⠋⠀⠀⠀⠀⢰⠇⠀⠀⠀⡘⠀⡀⠀⢸⠃⠚⠛⠀⣠⠜⠁
⠀⠀⠀⠀⠧⠀⠀⠁⠀⠇⢀⠀⠴⠯⠤⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⠀⠁⢈⠔⠂⠀⠢⠤⠄⠊
⠀⠀⠀⠀⠀⠹⢄⣀⣀⣀⢉⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⢙⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠊⠁⢀⡀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⡖⠀⠒⠒⠒⠉⠁⠀⠀⠀⡠⠚⡓⢄⡀⠀⠀⠈⠙⠓⠒⠲⠶⢶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢦⣀⣀⣀⣀⡠⠔⠒⠉⠀⢀⡇⠀⠉⠒⠢⠄⣀⣀⢀⣀⡴⠋⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⠙⢄⠀⠀⠀⠀⠀⣀⠤⠊⠙⠦⣀⠀⠀⠀⠀⠀⣠⠊⡇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡎⠀⠈⡷⣖⠒⠈⠉⠀⠀⢀⡀⠀⠀⠉⠑⠒⢲⢾⠁⠀⢹⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠞⠀⠀⢠⠃⠈⢢⣄⡀⠤⠖⠉⠉⠒⠤⢀⣀⡔⠁⠘⡄⠀⠀⠳⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠋⠀⠀⣠⠃⠀⠀⡰⠉⢦⡀⠀⠀⠀⠀⠀⡰⠋⢆⠀⠀⠘⣄⠀⠀⠙⢄⡀⠀⠈⠢⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠛⢇⠒⠒⢶⡯⠤⢤⣤⣞⣁⠀⣀⠔⠁⠀⠀⠑⢄⠀⠀⡠⠊⠀⠀⠈⢢⡀⠀⣈⡳⣤⡠⠤⠽⡶⠒⠒⡸⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠱⡀⠀⠈⢃⠀⠈⠙⡍⠉⠒⠒⠒⠤⣷⣾⡄⠒⠒⠂⠈⢉⠏⠁⠀⠰⠁⠀⢀⠎⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢣⠀⠀⠈⡀⠀⠀⡆⠀⢀⡤⠒⠉⡎⢱⠉⠒⢤⡀⠀⢸⠀⠀⠀⠃⠀⠀⡜⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⠀⠀⠀⡇⠀⣀⡴⣚⠁⠀⠀⡸⠀⠀⢇⠀⠀⠈⣑⣾⣀⠀⢸⠀⠀⠀⠇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⣠⣷⣊⠁⠀⠀⠑⢄⢠⠃⠀⠀⠘⡄⡠⠊⠀⠀⠈⢑⣾⣆⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣼⢔⠉⠀⠀⠈⠑⢦⡀⠀⠀⠟⠉⠉⠉⠉⠻⡀⠀⢀⡤⠊⠁⠀⠀⠉⡢⣧⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡚⠁⠀⠀⠈⠐⠄⡀⠀⠀⠙⢆⡐⢀⣀⣀⣀⣀⡀⢃⣠⠋⠀⠀⢀⠤⠂⠁⠀⠀⠈⢓⣼⣄
⠀⠀⠀⠀⠀⠀⢠⠴⠊⠁⠀⠈⠉⠒⢤⡀⠀⠀⠈⠢⡀⠀⢸⠋⠀⠀⠀⠀⠀⠈⠙⣇⠀⢀⠔⠁⠀⠀⢀⡤⠖⠋⠁⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠐⣠⣇⡠⠤⠤⠤⠤⠤⠤⢄⣸⣠⠋⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣔⡠⠄⠐⠒⠒⠂⠐⠒⠒⠂⠤⢄⣣⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠛⠉⠉⠁⠉⠉⠉⠙⠻⠿⠛⠉⠉⠉⠈⠉⠉⠛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⣤⡶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢁⣀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣀⡉⠁⠀⠀⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢠⠋⠁⠀⠉⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠉⢶⡀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⡆⠀⠀⢸⣷⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⣶⠂⠀⠀⡇⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢣⠀⠰⣾⡿⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⣷⠆⠀⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠈⠣⣤⣀⡴⠋⠀⢀⣀⣤⣤⣤⣤⣄⠀⠈⠳⣌⠁⣠⠞⠁⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡉⠁⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⠟⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠱⠶⠄⣀⠤⠶⠚⣁⠶⠋⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⠦⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠏⡱⠉⠀⠙⡟⠓⠠⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠦⠰⢾⠛⠁⠙⢦⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⡼⠁⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⢧⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢁⡼⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢷⡀⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⡞⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⢧⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⡼⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣦⠈⣿⣿⣿⣆
⠀⠀⠀⠀⣼⣿⣿⣿⡏⢸⠇⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⡆⠸⣿⣿⣿⣧
⠀⠀⠀⣸⣿⣿⣿⣿⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢸⠀⢹⣿⣿⣿⣆
⠀⠀⢰⣿⣿⣿⣿⡇⣼⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠈⣿⣿⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⢁⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⡀⢹⣿⣿⣿⣷
⠀⢰⣿⣿⣿⣿⡟⢸⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⣿⣿⣿⣿⡆
⠀⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿
⣸⣿⣿⣿⣿⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠘⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠇⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⣷⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣾⠀⠀⠀⠘⣿⣿⣿
⠸⣿⣿⡟⠀⠀⠀⢀⣼⡆⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⣧⠀⠀⠀⠀⠹⣿⣿
⠀⠘⠛⠧⠤⠤⠔⠋⠀⢱⡄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡎⠀⠓⠤⠤⠀⠤⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⢀⣤⠴⠶⠂⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠉⠻⢿⣶⣶⣦⡄⣤⣶⠶⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⠶⠦⣤⣄
⠀⠀⠀⢠⠞⠁⣠⠴⠒⠉⠉⠁⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠈⠉⠐⠶⢤⡈⠙⢦⡀
⠀⠀⠀⣾⣀⣜⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⠀⠘⢧⠀⣡
⠀⠀⠀⢿⣿⣿⣦⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⣠⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣤⣤⣶⣿⣿⣿⣷⣤⣤⣤⣶⣿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⡝⣜⢎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⢝⣮⣪⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣷⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⣠⣤⣴⣶⣦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡲⣝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣯⣭⡮⡢⡳⣌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣟⢿⣿⣷⣿⡽⡵⡽⡜⣦⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⡾⡏⡇⡟⡾⣼⣻⣿⣿⣿⣿⣿⡿⡫⣾⣯⣷⣿⣵⢹⣹⡘⡆⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢯⣇⡇⣇⡇⢧⢳⣳⣿⣿⣿⣿⣯⣪⣞⡵⣻⢽⣯⣟⡏⡇⣇⢻⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢹⢇⣿⣿⣼⣯⣷⣿⣿⣿⣿⡯⣚⠵⣫⠵⣻⢽⡧⡇⡇⣿⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣷⣿⣽⣿⣿⣿⣝⡯⣗⡯⢖⣛⣭⠯⣇⡇⡇⡿⢸⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡻⣷⣽⡇⡟⣼⣿⣿⣿⣿⡿⣗⡯⠵⣚⣭⠵⠖⣛⣸⢹⣃⡏⣼⠢⡯
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⢿⣿⡿⣧⣿⣾⢿⣿⣿⣿⣿⣟⣲⠭⣓⣺⡭⠵⠖⣚⣋⣭⣥⡿⣸⢥⡗⢼⡇
⠀⠀⠀⠀⠀⠀⢀⣾⣟⢯⢿⣳⣽⡽⡏⣧⣿⣿⣾⣿⡿⣿⢿⣟⣒⡯⠭⠵⢒⣚⣛⣩⣭⣥⡤⠶⠶⠏⣼⠢⣟
⠀⠀⠀⠀⠀⠀⡞⡞⡞⣎⣏⣏⣇⣧⣿⣯⠿⣷⣿⠽⣿⣏⣓⣒⣒⣛⣯⣭⣭⡭⠤⠴⠶⠶⠶⠶⠾⠟⠣⣽⠃
⠀⠀⠀⠀⠀⠚⠘⠘⠘⠚⠚⠛⠛⠛⠛⠚⠛⠻⠿⠾⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠤⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠨⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢁⠨⠤⠤⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⡔⠊⠁⠀⠀⠀⠀⠉⠑⠂⢄⠀⠀⠀⠀⠁⢂⠸⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠊⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⠀⢳⣦⠀⠀⠀⠀⠀⣅⢣⠀⠀⠀⠀⠀⡖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠀⢰⣫⡿⠛⠛⡆⠀⠀⠀⠈⣾⡇⠀⠀⠀⠀⡏⣺⣀⡀⠀⠠⠄⠆⠀⠀⠉⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡯⣗⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢠
⠀⠀⠀⠀⠀⠀⢀⠐⠩⣀⡀⠀⠤⡄⠀⠀⠈⠻⠿⠿⠟⠛⡡⠄⠒⠀⠀⠀⠀⢠⢳⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣤⣶⡥⠞⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠁⢃⡠⠊
⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣵⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠛⡏⠉⠉⠉⠀⠘⠀⡠⠋
⠀⠀⠀⠙⢄⡀⠀⠀⠃⠨⠀⠀⢈⣰⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡀⠅⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠈⠢⣀⠠⠐⠈⠉⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⣿⡦⠀⠀⠀⠀⠀⠀⢀⡀⠘⡂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣀⣻⣯⠀⠀⠀⠀⠀⢀⣐⡆⣰⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠂⠀⠀⠀⠀⠀⠀⠙⠻⠟⢓⣉⣀⣀⡀⡠⡤⠴⠄⣄⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣒⣒⣒⣒⣢⡯⠽⠻⢛⢚⠛⠔⠖⠒⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠂⠁⠀⠀⠀⠐⠒⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠥⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠂⡠⠁
⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⠀⡀⠄⠠⡀⢀⠀⠀⢄⠠⠀⢀⠠⢀⠀⡀⢈⠱⢶⠁⡀⠀⠀⠀⠀⠀⠀⡀⠔⡀⠀⠠⢀⠀⡀⢀⠄⡀⢄⠠⠀⢄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠈⠀⠁⠊⠐⠀⠀⠁⠂⠁⠈⠀⠈⠐⠈⠐⠁⠈⠀⠁⠈⠀⠈⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⢀⠤⡀
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⡆⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠔⠀⠈⠣⠀⢀⣀⣀⣀⡀⠤⢷⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡄⠀⠀⠈⠁⢀⠀⠀⢀⠄⠙⡂
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⢀⣦⠶⠒⠃
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠐⢾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢦⡠⠖⠤⠀⠢⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⢠⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⣄⠰⠀⠀⠐⠒⠄⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠁⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢐⠀⠀⠸⠁⠨⠑⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢸⠄⠒⠶⠂⢖⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠈⠀⢈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠤⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠀⠀⣀⢀⣀⡀
⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠄⠘⡇
⠀⠀⠀⡟⣆⠀⠁⠒⠒⠒⠂⠐⠂⠤⠄⢀⣀⣀⣀⡀⠀⠠⠤⠤⠤⠤⠤⠄⠀⢀⣀⣀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⣀⣀⣀⣠⠃
⠀⠀⠀⢣⣈⠓⠠⠤⠤⠤⠄⠤⠄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠁⠀⠀⢀⠎
⠀⠀⠀⠈⢦⡣⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠉⠲⣕⠄⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠜
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⣛⠛⠋⠀⠉⠉⠉⣉⡀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⣀⠀⠀⣴⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠿⠿⠟⢿⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢄⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣶⣷⣶⣶⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⢀⡠⠐⠈⠉⠁⠀⠉⠉⠛⠢⣀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢻⣁⣠⣔⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠶⠛⠉⠉⠀⠀⠀⠈⠉⠉⠓⠦⣀⠀⠀⠀⢸⠄⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣼⡄⢠⡀⣾⣦⣿⡘⢧⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣃⡀⠴⢋⣧⠞⢳⡟⠀⠈⢳⠘⡆⠀⠀⠀⠀⢀⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠀⠀⠀⠠⣦⣤⣀⡈⠁⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠘⠛⣛⣛⣉⡉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠀⠀⠀⣷⢸⡆⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡴⠋⠀⠀⠀⠀⡴⠋⠁⣀⣀⡉⠳⡄⠀⠀⠀⠀⢀⠔⠊⡉⠉⠓⢦⡀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⠀⠀⠀⠀⢸⠁⠀⣼⣿⣿⣤⡄⢹⠀⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⢳⠀⠀⠀⠀⢹⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⠀⠀⠀⠀⠀⠘⣀⠀⠘⠿⣿⠿⠁⣘⠀⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡸⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠞⠁⠀⠀⠀⠀⠘⠦⠤⠶⠶⠒⠚⠁⠀⠀⠀⢀⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢠⠴⢄⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⢦⣀⠙⠲⣄⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠖⠋⣙⡆
⢀⣤⣀⣒⣒⠂⠒⠉⢁⣀⠀⠘⣆⠈⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡔⠉⠁⠀⠴⣮⣉⣀
⣾⣩⡭⠭⠤⠀⠀⠀⠈⠉⢹⡄⡟⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⢸⢄⡶⠛⠛⠀⠀⠀⠩⠭⣽⣶⡄
⢻⣀⣀⣀⣀⣀⣀⣀⣠⡤⠾⠁⢿⠀⠀⠀⠀⠀⣠⠏⡿⠙⠛⢶⣖⠒⠒⣒⡿⠉⠹⡎⣧⠀⠀⠀⠀⢀⡟⠘⣧⣀⠀⠀⠀⠀⠘⠓⠶⢬⣿
⠈⠉⠉⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⣆⠀⠀⣀⡴⠃⢀⡇⠀⠀⠀⠈⣉⣉⡉⠀⠀⠀⢷⠈⠳⣄⣀⣠⠞⠀⠀⢀⡟⠉⠛⠓⠒⠶⢤⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠋⠁⠀⠀⣼⠃⠀⠀⠀⠈⠛⢻⣿⡆⠀⠀⢸⡆⠀⠀⠉⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣤⠴⠋⢹⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⣿⠲⠤⣤⣤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠶⠶⠶⠶⠶⠒⠒⠒⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠰⣶⠂⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠐⠒⠂⠂⠀⣻⠒⠲⠖⠦⠴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⡀⠀⣿⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠼⣯⡉⠉⠉⠉⠙⣧⡽⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢻⠀⠀⠀⣾⠁⠀⠀⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠯⡉⠛⠒⢤⡮⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠒⠛⠉⠁⠀⣠⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⣅⡏⠂⠀⡾⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣠⠴⠖⡻⠻⡀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠶⠒⣲⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⢧⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⠀⠀⡀⠀⠀⢀⣠⠶⠋⠉⠀⠀⢀⣠⠴⡾⠀⠀⠀⠀⠀⠐⠢⣄⣀⣀⣀⠴⠋⠀⠀⡏
⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⢹⣿⡞⠋⠀⠀⠀⠐⠒⠋⠉⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢟⡏⠀⠀⠀⠀⠁
⠀⠀⠈⠉⠛⠶⠦⢄⣀⣀⡄⠀⠀⢻⣆⣿⣶⡀⣠⡟⠁⠈⠳⣖⠒⠒⠚⠋⠉⡀⠀⠀⠀⠀⠰⣄⣀⣀⡠⠖⠉⠀⠸
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠉⠛⣿⣻⣿⣿⣿⣿⣿⢟⣁⣀⣠⡴⠼⠶⡖⠒⠖⠚⢁⠀⠐⢆⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣷⡴⣶⣿⣿⣿⣿⣿⣿⣟⠛⠻⠭⣵⣊⣀⣴⠂⢙⣓⡒⣄⡸⠶⠒⢊⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⣠⡴⠋⠉⢰⣿⣿⣿⣿⣿⣿⣿⣧⠠⡀⠀⠰⡄⠘⠯⡿⢿⠿⠛⠛⠑⠛⠒⡺⠗⠦⠤⠤⣧⣄⣀⣀⣀⡀⠀⠳⣄⠀⠀⠀⠈⠳⣄
⠀⠀⣠⠞⠁⠀⠀⠀⠘⢿⣿⣿⣿⡿⣻⠇⠈⢳⡇⡀⠜⠋⠀⢤⡸⠇⠀⢺⡠⠄⠈⠚⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⠒⠒⠒⠀⢈⣳⠤
⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡟⠀⡠⠾⠿⢆⠀⠀⠀⢸⣧⠔⠈⠀⠁⠀⠀⠀⠀⠀⠴⠾⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣸⣗⠈⠀⠀⠀⠀⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⡤⠒⠉⢸⡏⠉⠢⠀⠀⠀⠀⠀⢳⣄⣤⠄⠀⠀⢠⣻⠃⠀⠀⠀⠀⠀⠀⠀⢠⠤⢵⣿⣄
⠀⠀⢀⣠⡤⠾⠷⣾⣭⣭⣀⠀⠉⢸⠇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠈⠑⠲⢤⡀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠳⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠹⠀⣤⠔⠈⠀⠀⠀⠀⠉⠳⣞⡿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠮⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣴⡯⠖⠂⠀⠀⠀⠀⠀⠀⠀⠒⠤⢌⣧⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⢶⡤⠚⢦⡀⠀⠀⢀⡐⠳⣤⢰⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡙⠶⠚⢦⣋⠻⣌⢷⣄⠰⣯⠹⡇⢿⣘⠳⡎⣹⠥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣙⢲⡛⣮⣍⢳⣝⢲⣚⢳⡘⣇⡓⣦⣸⡒⣷⢙⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⠶⣍⣫⣙⠵⣌⠳⠭⣭⡽⣎⠷⣌⣓⢲⡌⡇⣿⢸⡁⣏
⠀⠀⠀⠀⠀⠀⡀⡟⣉⣙⡓⢚⡳⢓⠦⣭⠤⠖⢮⣓⡲⢶⠳⣝⠷⢦⢹⠸⣅⢧⡝⢦⡑⡮⢸⡇⣿⠈⣿
⠀⠀⠀⠀⠀⠈⢋⣛⣋⣬⣭⣍⡴⢋⡝⡲⠲⢋⣓⠬⢞⣫⣳⣭⡹⡘⠮⢷⣘⢢⢍⡞⣼⢡⣏⢼⣃⡞⢡⡞⠁
⠀⠀⠀⠀⠰⠶⠾⢡⠼⢴⠖⣒⡖⣫⠴⢩⣭⣉⡬⣝⣭⠤⠵⢦⠳⣭⡛⡆⡟⢸⡀⢧⠸⣄⢫⡚⣥⢟⣠⠗⣰⡆
⠀⠀⠀⠀⣠⠟⣛⣋⣰⢛⣸⢩⡭⠥⢖⡏⣴⢒⡶⣓⣒⢒⣛⢯⡓⢦⡝⡧⡽⣰⢣⢋⡞⣱⢚⡴⢋⡼⢃⣽⠙⣄
⠀⠀⠀⠀⠈⠰⣏⣥⠶⢚⣡⡞⣰⡏⡭⢔⣣⠟⣰⢋⡶⢋⡭⢭⡙⢧⡃⡇⢻⠘⣎⢷⣱⡇⣼⢸⣋⡖⣫⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⣡⢾⢩⡵⣞⣫⠞⣣⢿⡰⡏⣷⢫⡇⣏⠰⠆⣹⢸⣣⢿⣸⠎⣷⢫⡴⢋⡽⢞⣃⡷⢋⡀
⠀⠀⠀⠀⢀⡴⠞⣫⡼⣩⡇⡟⢸⢏⢷⡹⡄⣧⢸⢨⠳⣌⣓⢚⡡⠾⣡⠏⣴⢫⠕⣚⣰⠏⡴⢋⡥⠶⢛⣩⠆⡀
⠀⠀⠀⠀⠙⢀⣟⢡⡞⣩⠞⣡⢞⡼⣡⢣⠏⣞⢾⣘⠳⢬⣳⣭⠥⠭⢭⡼⠥⠟⣸⠵⢒⣚⣃⡏⣥⠏⣩⣭⣴⠋
⠀⠀⠀⠀⠸⠯⢴⠋⣵⢛⡮⢣⠘⡆⢳⡈⡇⣼⠸⣬⣛⢦⠳⢖⠒⣛⣕⡚⣉⣛⣃⠖⣫⡭⠭⠴⠗⡖⢃⡶⠶⠆
⠀⠀⠀⠀⠀⢀⡴⢃⡼⢫⡗⣹⢂⡟⡼⣑⠣⡍⢳⡲⡌⣎⣛⢯⣫⡵⡒⢭⣡⠤⠮⣜⣩⠞⣛⣛⡛⣫⣍⣡⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⢸⡇⣺⢌⠳⣜⢳⣙⡆⣇⠳⢦⡝⢦⠷⠮⣭⠳⡴⠒⢛⠲⢥⢬⡥⢬⣍⣉⣼⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢈⡇⣿⢸⡘⠧⢭⡙⢶⠹⣞⣛⣒⢦⡑⢖⣍⣫⣙⠶⠶⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣅⢿⠬⡍⠻⢬⢹⡌⢧⡭⠯⣝⢧⣙⡻⣬⠧⣍⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢒⣟⡸⢦⡍⣷⢸⣆⢻⠆⠙⢷⡙⣦⣩⠳⡬⠶⣌⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠇⠛⢦⠌⠁⠀⠀⠈⠳⡤⠚⠷⠅⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣀⠀⣤⡀
⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡰⣖⣿⣿⣿⣿⣿⡿⠁
⠀⢠⣄⣼⣿⣹⣷⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣄⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣶⡾⠃⠘⠿⠟⢹⣿⣿⠁
⠀⠘⢻⣿⣟⠛⠛⠂⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⢾⡟⠋⠉⢿⣀⣤⣶⣷⣟⡛⠛⠛⠻⠿⢿⣿⣿⣷⡤⣺⣷⣿⣇
⠀⠀⠀⣿⡟⠀⢀⣀⣸⣿⡿⠿⠖⣲⣤⣤⡀⢻⠋⠀⣹⠋⠀⠀⠀⠘⠃⠀⣰⡿⠟⢻⠎⣉⢻⣿⠦⠀⠀⠀⠀⠙⠟⠿⣿⣿⣭⠻⢿⠿
⠀⠀⠳⠟⠛⣳⣿⣿⠏⠃⠀⠀⣾⣿⠻⠟⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⢋⢀⣤⠀⠀⠈⢱⣀⡀⠀⠀⠀⢀⡀⣸⠋⢀⣤⡄⠀⠀⣠⣤⠾⠛⠛⠛⢲⣄⣀⠀⠀⠀⠀⢻⣿⣧⡀
⠀⠀⠀⢀⡼⠁⠀⠀⣀⣤⣀⣾⣄⣸⣿⣀⠀⠀⠸⡟⠀⠀⠀⣴⡿⢱⡇⢰⢿⡏⢀⣴⣾⡿⠁⢀⠀⢠⣄⢈⡉⢻⡄⠀⠀⠀⢺⣿⡝⠷
⠀⠀⠀⣼⣧⠀⠀⢸⠿⡿⠏⠙⣁⠈⠀⠈⢢⠀⠀⢻⣆⠀⢀⣿⣷⣿⢀⠂⣾⡁⢨⣿⣿⣥⠀⣼⣧⣾⣿⣴⢏⣤⣷⠀⠀⠀⢸⡟⠁
⠀⠀⠙⠛⡏⠁⠀⠅⢸⣟⠰⠟⠻⣧⠰⢿⠺⡆⠸⡿⣿⣶⣿⢿⣿⣯⢿⡆⡴⡟⠸⣿⢷⣦⡷⣿⡇⡠⣾⡟⢼⣿⣿⠀⠀⢠⣾⣷
⠀⠀⠀⠀⣿⣶⡄⠀⢸⣿⢷⣶⣾⣏⠀⠀⢰⣷⣤⠀⢸⣿⣿⣿⡾⠁⣸⣿⣷⣖⠀⢻⡇⣤⡄⠸⣿⣷⡈⣁⣻⣿⠃⠀⣠⣿⣿⡇
⠀⠀⠀⠈⠙⣧⣀⢀⡀⣡⣿⣿⣿⣿⣷⣠⣿⠃⠀⠀⢈⣿⣯⣷⣹⣿⣿⣿⣿⢯⣷⡄⢷⣏⣠⣴⣾⣿⣍⠉⠁⣩⣧⣠⣿⣿⡟⠇
⠀⠀⠀⠠⣴⣾⢿⡿⣤⣼⣯⣶⣿⢱⣨⣿⣿⣧⡄⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⡊⠉⠁⠈⣿⣿⣿⣿⡿⣿⣷⣦⣽⠿⢻⡁⣿⣿⣤⡀
⠀⠀⢀⣰⣿⡟⠈⠃⠈⢋⣿⣿⣿⣱⣿⣿⡿⣿⣷⢉⠙⢿⣿⣿⣿⣿⡿⠆⢸⣿⣆⠀⠀⢿⣿⣿⡌⢹⣿⣿⣿⣷⡄⠀⠀⠙⠻⠟⠛⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⣿⣾⣿⣧⣄⡈⠀⣠⣟⣽⣿⣠⣤⡴⣶⣿⣿⣿⣿⣄⡈⠻⣿⣷⣿⣿⣿⣯⣿⣁⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⠀⠀⠀⠉⠙⠻⡽⠿⠚⠛⢹⠩⣭⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠻⠛⠛⠛⠛⠉⠉⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣟⢛⣉⣹⣿⡟⠛⠻⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣞⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠄⠒⠒⠒⠒⠚⡗⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠤⠒⠉⠉⠹⡀⠀⠈⠑⣄⣎⡠⠤⢄⣀⣀⣠⡤⣖⠉⠉⡇⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠙⠢⢤⡶⡿⠛⠈⠉⠀⡠⠊⠁⠉⠉⠳⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢰⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⠎⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠼⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⡘⠀⠀⠀⢣⠀⠀⠀⢀⡿⠁⠀⣠⠧⠴⠒⠒⠒⠒⠢⣄⠉⠒⠊⢁⣸⠴⠆⠦⣖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠣⡀⠀⢸⢃⣴⠟⠁⠀⠀⠀⢀⠔⠉⠁⢸⠉⢢⡔⢩⠃⠀⠀⠀⡼⢢⢀⠤⠒⠉⠉⠑⢾⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣾⠉⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⢀⠏⣳⠃⣀⠤⠒⠢⡆⡼⠁⠀⠀⠀⠀⠀⡇⠙⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⢠⢃⣸⢖⡷⠊⠀⠀⠀⣸⣿⡿⠀⠤⢄⠀⠀⢠⠃⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠉⠁⠚⡖⠒⢲⠋⣡⠼⣡⠃⠀⠀⠀⡰⠋⡿⢆⠀⠀⠀⡇⢀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃⢡⠀⠀⠀⠀⠀⠀⠀⠈⡲⣁⠞⠁⢠⢇⠀⠀⡠⡾⢁⢼⠃⠈⠳⢄⠀⠇⡜⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⣠⠎⡰⠋⠁⡲⠃⠜⢖⠈⠀⡧⠋⠸⠀⠀⠀⠀⢹⠟⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠀⠀⠀⠱⣄⠀⡠⠚⠁⡐⠁⢀⠔⠁⠀⠀⢀⡱⢞⡇⠀⡇⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⡆⢀⣀⠤⠚⠛⢄⡀⣰⡡⠔⠁⠀⢀⡠⠖⠉⠀⠀⠟⠲⠂⠒⠒⠉⡸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠤⠄⠒⠒⠃⠉⠉⡛⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠢⡀⢀⠆⠀⠀⠀⢀⡠⠊
⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢈⠟⠒⠒⠒⠊⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠎
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣈⣢⣀⡠⠤⠒⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⡠⠔⠊

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠫⠙⠻⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠈⡿⣿⣿⣿⠀⢻⣿⣿⢸⣿⣿⡟⣿⣿⢣⣿⡿⠃⠀⡼⠋⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢷⡁⠈⢿⣿⠀⢸⡿⣿⢸⣿⣿⣿⡏⣿⡾⡿⠁⠀⠈⠀⠀⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⡇⣿⢸⢿⢹⢻⠁⣿⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢸⢸⢸⠟⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⢸⠘⠈⢸⠀⢈⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⣿⣧⠀⢸⠀⢸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⡏⡏⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠀⡇⠇⠀⢸⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡇⠀⣿⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⣇⣿⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠇⣿⡇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣇⢠⣿⡇⠀⠛⢰⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⠀⢠⡄⢀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢁⣴⣤⡈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣤⡾⠟⠉⠙⠻⣷⣄⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡾⠋⣠⣴⡿⢷⣦⣀⠙⣷⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⢁⡾⠛⢁⣤⣄⠉⠻⣧⢸⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢺⢁⣾⠟⠋⠛⢿⣆⢹⢺⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣸⢸⢃⣴⡿⣶⣄⢻⢸⢾⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⢹⣼⢸⠋⣠⡈⣿⢸⣼⡞⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣫⢵⣫⠽⣫⠽⣫⠽⣸⠛⣇⡻⢽⡻⢭⣓⢯⣑⠮⣙⡶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⢋⡶⢋⣴⠋⣰⡏⢠⣿⠁⠾⡷⢖⢾⡿⠀⢹⣧⠈⣷⡌⢻⣆⠙⣦⡙⢷⣄
⠀⠀⠀⠀⠀⢰⡿⠀⣿⠇⢸⡿⠀⣿⡇⠘⠿⣶⡶⢞⣽⣕⠦⣶⡾⠟⠀⣿⡇⠀⣿⡆⢸⣷⠀⣿⡆
⠀⠀⠀⠀⠀⣼⡇⢠⣿⠀⣸⣇⡀⠛⠿⢷⣦⡴⢚⡽⡻⢳⣝⡲⢤⣶⡿⠟⠃⣀⣿⡇⢸⣿⠀⢸⣷
⠀⠀⠀⠀⠀⣿⡇⢸⣿⣄⡈⠙⠻⢷⣦⣤⠴⣊⡭⡺⠃⠈⢷⢭⣓⢦⣤⣶⠿⠟⠋⣁⣤⣿⠄⢸⣿
⠀⠀⠀⠀⠀⢿⣷⣤⣈⠙⠻⠷⣶⣤⣤⠶⣊⡥⠚⠁⠀⠀⠈⠓⢭⣕⠦⣤⣤⣶⠿⠟⠋⣁⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣤⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⢻⢉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠢⠽⠞⠾⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠰⡉⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣠⠷⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠂⠉⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠉⠂⠘⣾⡀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣑⣲⡚⣧⣤⠀⢀⠔⠉⠀⠀⠀⠀⠀⠠⡊⠉⠉⢹⡆⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢿⡍⠉⠁⢸⡴⠃⠀⠀⢀⠁⠀⠀⠀⠀⡀⠒⢒⣋⣤⣄⣀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣧⣸⠟⠳⣀⠞⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠁⡴⠋⠀⠀⠀⠈⠑⢆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⢫⡀⠀⠀⠀⢻⠀⠀⠀⠀⢰⡄⠤⠤⡀⠀⠀⢰⠁⠀⢀⣄⠀⠀⠀⠈⢧⠈⣧
⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢧⠀⠀⠀⠐⠀⠀⠀⡇⠘⡦⠘⠓⠢⣼⠛⠇⠀⠀⠀⠈⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠘⡆⠀⠀⠸⠀⠀⡸⠀⠀⡇⠀⠀⠀⠈⢣⠀⠀⠀⠀⢀⡏⠀⢠⠀⠀⠄⠀⠀⣠⠖⠉
⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠆⠀⠀⢣⠐⠁⠀⢠⡁⠀⠀⠀⠶⢼⠒⠒⠒⣒⣉⡴⠃⢨⠎⠀⢀⡴⠚⠁⠀⠀⢰
⠀⠀⢸⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣄⠀⠈⢧⣀⠀⠈⠙⠦⠄⠀⠠⠎⠀⠀⠀⠉⠁⠀⡐⠁⠀⠘⠉⠀⠀⠀⠀⢀⡟
⠀⠀⠸⡄⠀⠀⣯⠙⡶⠶⠤⠤⢄⣀⣀⣀⣀⣰⠀⠀⣠⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠶⠶⠂⢀⡔⢹⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⡇⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⢀⣶⠀⡖⢄⠀⣀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⢁⠀⠀⠲⠷⣴⣤⠄⠀⠀⠀⠀⠀⠀⡇⠀⠟⠀⠀⣟⠸⠀⠇⠀⠑⠏⠱⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⢀⣠⡼⢦⣤⣄⣀⢷⣄⣀⣀⣀⡀⣀⣠⣀⢦⣀⣧⠀⠀⠋⠀⢠⠃⠀⠀⠀⠀⢷⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⡜⠉⠀⣠⠁⠨⠿⠓⢀⠿⣆⠀⣸⡧⢨⠔⢣⠀⠈⠹⠑⠦⠄⢰⠇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⢳⣤⣤⣼⣖⡢⠴⠂⠀⠀⠀⠈⠛⠳⠶⢶⠒⣠⣤⡾⠀⠀⠐⠷⠤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣥⠄
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⢤⣄⣀⣀⣀⣀⣀⣠⣤⠤⠖⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠂⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢶⣩⣿⣿⠻⡗⣶⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⠤⡤⠶⡶⡉⠁
⠀⠀⠀⠙⠚⠻⡶⣶⠶⣤⠶⠶⠶⣒⠒⠛⠛⠭⣳⣨⡟⢤⣯⣇⣧⠚⢫⣠⠋⠀⡰⠋⠁⢸⠀⣧⠇⢰⠃⠀⡇⣧
⠀⠀⠀⠀⠀⠀⢱⠈⢣⡉⠙⠲⠤⣈⢳⡀⠀⣠⠞⠉⠛⡟⢦⣇⡨⣶⠊⠉⠢⣀⡇⠀⢀⠇⡜⠈⣠⠃⠀⢰⢃⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠈⡷⣧⡾⣥⣄⠀⡸⠀⠀⣯⠀⠘⡄⣠⡶⠟⠣⡀⢸⡜⣠⠞⠁⠀⢠⠏⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡆⠀⢀⣠⣏⣁⡀⠈⠛⣷⣃⠤⠤⣿⠴⠒⠺⡏⠀⢀⠤⠬⠾⣷⠁⠀⠀⡴⠁⡜
⠀⠀⠀⠀⠀⠀⢠⠃⢠⣿⢁⠴⠋⠉⠉⠓⠫⣷⣄⠏⢀⣀⠀⢸⠀⣠⠤⢵⣰⠃⠀⠀⠀⠈⠳⣄⣸⠀⢸⡟
⠀⠀⠀⠀⠀⢀⡜⢀⣾⠿⠓⠒⠢⢤⡀⠀⠀⠀⡝⠋⠉⠈⠻⠿⡞⠀⠀⠀⢻⡀⣠⠖⣩⠭⠽⠛⠛⢤⣸⠇
⠀⠀⠀⠀⢀⣸⣷⣟⣉⠉⠉⠉⠉⠓⠿⣦⠀⢰⠁⣀⣀⣀⡀⠀⡇⠀⠀⢀⣀⢿⣡⠊⠀⠀⠀⡠⠾⠟⠙⠧⡀
⠀⠀⠀⠈⠉⠀⠈⠓⢌⠙⠢⣄⠀⠀⠀⠘⢷⡟⠋⠁⠀⠀⠉⠓⣷⠺⠏⠉⠀⠀⠻⡀⠀⠀⡞⠀⠀⠀⢀⠔⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠣⡀⠀⠀⣜⣠⠤⠔⠒⠢⢤⡀⢸⠀⠀⠀⠀⠀⠀⠳⡀⢸⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢱⡀⢰⠋⠀⣀⣠⣤⣀⡀⠈⢻⡀⢀⣴⡿⠒⠒⠒⢷⣽⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⣧⣧⠖⠉⠀⠀⠀⠀⠈⠳⣄⡇⡻⠋⣠⠔⠚⠉⠉⠹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣿⠕⠶⠛⠛⠛⠋⠒⠦⣄⠈⢿⢁⠞⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠈⠉⠉⠉⠉⠐⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⡀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⡜⠁⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢠⠋⢀⡤⠤⠒⠒⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⢃⡔⠁⠀⠎⠉⠉⠙⠢⡀⠀⠑⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡜⠀⠀⠀⠳⣄⣀⣀⡴⠃⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢽⡄⠀⢸⡇⠀⠀⢀⠤⠖⠀⠤⠤⣀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⣠⠖⠋⠑⢦⢀⠎⠀⠀⠀⠈⠳⢄⣷⡀⠀⡇⠀⠀⠀⠀⠀⠈⡆⠀⢀⡌⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⡜⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡰⠋⠉⠉⠓⠶⢀⡠⠤⠤⢀⡐⠛⠉⠉⠉⠙⢦⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢧⡀⠀⠀⢀⡤⠒⠉⠉⠐⢦⡀⡇⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠈⡇⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⢙⣦⡄⡜⠀⠀⠀⠀⠀⠀⠙⡳⣄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⣠⠶⠤⠶⠖⠐⠚⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⢠⠎⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⢀⠇⠀⠉⣱⠆⠀⠙⠢⣄⣀⣀⣀⡴⠋⠘⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠂⠻⡁
⠘⡄⠀⢀⡔⠊⠉⠉⠑⠢⣄⡤⠊⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⢢⡤⠔⠒⠒⠒⠒⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠙⢄⠘⡄⠀⠀⠀⠀⠀⠸⣀⠴⠛⠒⠺⡦⣀⠀⠀⠀⠀⣼⠓⣄⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⢠⠖⠒⠛⠷⠀⡠⠤⠤⢄⡀⠁⠀⠀⠀⠀⠹⣄⡝⣁⡠⠯⠺⠀⡵⠽⠒⠚⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⡇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡯⣙⢧⡀⠀⢀⠏⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⣤⡶⠮⠤⢯⣱⣌⠲⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠳⠦⢶⠆⠘⢦⡀⠀⠀⠀⡰⠃⠀⠀⠉⢲⡒⠲⣤⣍⡓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⡎⠀⠀⠀⠈⠉⠈⣩⡀⠀⠀⠀⠀⠀⣿⡝⠉⡇⠈⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠒⠢⢄⡀
⠀⠀⠀⠳⣄⠀⠀⠀⠀⢠⠃⠙⢄⠀⠀⠀⡰⢹⡇⢠⠀⠀⠀⠀⠑⠢⢤⣄⢀⣀⣀⣀⡀⣠⡤⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠉⡶⠒⠒⠁⠀⠀⠀⠑⠒⠊⠀⢸⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⠻⣮⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡓⢎⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣝⢬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠤⠴⠒⠊⠉

⠀⠉⠉⠛⠿⣟⠻⣿⡻⠿⠿⠿⣟⡿⠛⠻⡿⠛⠛⠉⠉⠛⢻⣿⣿⠉⠟⠉⠻⣿⠙⢿⣽⡿⢿⣿⣿⣿⠹⣿⢿⡿⠛⠉⢙⣏⠁⠈⡿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⢹⡏⠀⠀⠀⠘⣧⢸⡟⠀⠀⠙⢺⢹⡘⢃⡿⠀⠀⠀⠀⢿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠈⣾⡇⠀⠀⠀⣾⠈⠙⣼⠁⠀⠀⠀⠀⠈⣧⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣾⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⠸⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⡇⣧⢸⡀
⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⠀⣷⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢷⡀⠀⠀⠀⣰⢑⣿⠈⢳⡀⠀⢀
⠀⠀⠀⠀⢀⣴⣇⠀⠀⣸⡇⠀⣷⣷⠀⠀⣷⡀⠀⠀⠀⠀⠀⣠⡀⠸⠄⢸⡀⠀⠀⠀⠀⠺⠿⠒⢈⣷⣦⣤⣶⣷⣾⣿⣶⣾⣿⣷⣾⣷⣤⣶⣄
⢠⣶⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣟⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⡿⠿⣿⠿⣿⡿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢟⣛⣿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠛⠛⠋⠉⠩⠥⠀⠆⠀⠉⠀⠀⠐⠒⠃⠀⠀⠀⠰⠿⡅
⠀⠀⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠖⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠯⡉⠓⠲⢤⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠒⠋⠉⠀⢀⡄⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⣠⠏⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡤⠴⢚⡟⢣⠀⠀⠀⠉⠒⠒⠶⠶⠶⠶⠖⢒⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⡼⢅⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠎⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⣇⠘⠀⠀⡀⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⣠⠶⠟⠀⠀⠀⠀⠀⠐⢤⣄⣀⣀⣠⠖⠁⠀⢸⠁
⠀⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠠⣿⠀⠀⠀⢻⣷⡞⠋⠀⠀⠀⠐⠒⠉⠉⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⣻⠃⠀⠀⠀⠈
⠀⠀⠀⠉⠛⠖⠦⣄⣀⣀⣆⠀⠀⢻⣤⣿⣆⠀⣰⡏⠀⠈⠲⡒⠓⠒⠛⠉⠁⡀⠀⠀⠀⠀⠢⣄⣀⣀⠴⠊⠁⠀⠏
⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉⠻⣿⣻⣿⣿⣿⣿⣿⢟⣀⣀⣤⠶⠼⢶⠒⠒⠒⠉⡀⠀⠱⣄⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣧⠴⣶⣿⣿⣿⣿⣿⣿⡟⠛⠋⠭⢖⣁⣠⡴⠀⣹⣒⢲⣄⠽⠖⠒⢉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⣠⠶⠋⠉⢰⣿⣿⣿⣿⣿⣿⡿⣧⢠⠀⠀⢱⡄⠙⠠⡿⢿⢿⠛⠋⠝⠛⢒⠟⠒⠠⠤⠼⣦⠄⣀⣀⣀⣀⠈⢧⡀⠀⠀⠀⠘⢦⡀
⠀⠀⣠⠚⠁⠀⠀⠀⠘⢿⣿⣿⣿⠟⣿⠃⠈⢿⡃⡀⠘⠉⠀⣄⠹⠃⠀⢧⡤⠄⠐⠚⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠒⠒⠂⠀⣩⡦
⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡏⢀⡠⠞⠻⢄⠀⠀⠀⢸⡧⠒⠀⠀⠀⠀⠀⠀⠀⠠⠶⠧⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣼⣗⡁⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡞
⠀⠀⠀⠀⠀⠀⣠⠞⢀⣠⡴⡒⠁⢸⠏⠉⠂⠀⠀⠀⠀⠀⢷⢠⡤⠀⠀⠀⢬⡿⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⢿⣧⡀
⠀⠀⢀⣤⠤⠾⠷⠿⠭⢥⣀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠢⣄⡀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡸⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡙⠲⣄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⢀⡤⠂⠁⠀⠀⠀⠀⠙⠳⣻⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣼⠷⠛⠁⠀⠀⠀⠀⠀⠀⠁⠒⠤⢼⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀

⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⣀⡀
⠀⠰⣾⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠐⠲⠤⠀⠀⣠⠔⠋⡏⣀⢤⢒⡈⠁⣦⠘⢸⠇⡈⠉⢍⡋⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⠧
⠀⠀⠉⣀⠀⠀⠀⠙⠋⠁⠀⠀⠘⣦⡀⠀⡠⠚⠁⠀⠀⡟⡰⢎⣌⢁⡃⣐⠶⢸⡄⠂⠂⠽⠋⣠⠄⠀⠀⠉⠻⠏⠉⠀⣤⡀
⠀⠀⠼⠧⠀⢰⣶⣶⣶⣶⣶⣶⣶⣼⣷⣌⠳⣄⡀⠀⠀⡏⠱⠆⣁⢈⢋⣍⠰⢸⡇⠀⢀⣤⠞⣁⣀⣠⡤⣤⢤⣶⣤⠀⠈⠁
⠀⠀⠀⢀⣀⠈⠛⠙⠻⠙⠻⠿⠻⣷⠋⠁⠀⠈⠙⠦⣄⣿⠛⠀⠭⠠⠎⣁⠲⢸⡇⠘⢿⣿⠭⠿⢿⣯⣿⣹⣿⣿⣿⠀⠶⠒⠒
⠀⣰⣾⣿⣿⣶⣶⣶⣿⡄⠀⠀⠞⠁⢀⣤⣠⣤⣶⠶⠶⠿⠄⠀⠀⠀⠀⠀⠉⢉⡁⠀⠀⠙⣦⡀⠀⣀⠈⠉⠉⠙⠻
⠀⠈⠙⠛⠿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⣿⣿⣿⣶⡄⠈⢁⣾⣿⣤⣤⣤⣄⣀⣀⡀⡀
⠀⠀⠀⢀⣀⠀⠀⢶⣦⣤⢼⡏⣹⠟⠋⠀⣠⣤⣴⣖⣂⣀⣀⣀⣈⣁⡀⠉⠀⠛⠛⠋⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠇
⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠛⠁⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠉⠉⠉⠀⡀⠀⠀⠀⡀⠀⠠⣀⠈⠙⠂⠀⠀⢀⡀
⠀⢸⠿⠶⢶⣤⣄⣀⣈⣿⣷⣤⡀⠀⠀⠀⣠⣤⣴⣶⠯⠤⠤⠴⠶⠶⠿⠿⠿⠀⠀⠸⡷⠦⠤⠆⠑⠪⠇⠉⠉⠉⠀⠐⠚
⠀⢸⡇⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠉⠉⠛⠇⢀⣠⣴⣤⣤⠶⠶⠶⠦⠀⡀⠀⠀⠀⠀⠀⢀⡼⣃⣀⣤⣀⣀⣀⣀⡀
⠀⢸⣿⣤⣴⣶⣿⣿⠿⣿⣿⡿⠋⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⢉⣀⣀⡀⠀⠀⢤⣾⢷⣦⢲⣰⣠⡀⠻⣽⠾⠿⠸⠿⠿⠿⠟⠣
⠀⠾⠿⠛⠋⠉⠀⠀⠐⣿⠏⠀⠀⠈⠉⠙⠋⠁⠀⠀⢀⡀⠀⠈⠁⢀⡀⠀⠀⠀⠙⠇⠁⠈⢁⣩⠁⠀⠈⠂
⠀⠠⣤⣶⣯⣤⣤⠄⠀⠀⠠⡾⠶⠶⠶⠶⠆⠀⢀⣴⣿⣥⣤⣶⣾⡿⠗⠀⠀⠀⠀⠀⠀⠀⠻⣟⡛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⠦⠀⣀⣀⣀⠀⠙⠻⣿⠏⠁⠀⠀⠀⠀⠠⢶⣶⡿⠭⠀⠀⠀⠉⠀⠀⣤⣤⣄⣀⣐⣦⣄⡀
⠀⣠⣶⣦⣤⣴⣶⠀⠀⠈⠉⠈⠁⠀⠈⠙⠋⠉⣀⣤⣤⣤⣤⣀⣀⣀⣼⠳⣦⠀⠀⠉⠀⣀⡔⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠁
⠀⠙⠛⠿⠋⠉⢁⡀⠀⣀⡠⣤⣽⣿⣿⣦⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠁⠀⣀⠄⠘⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⣴⣠⢤
⠀⠀⠀⠀⠀⣰⠘⢛⣀⠀⠀⠈⠙⠛⠋⠉⠀⠾⠗⠒⠓⠀⠀⡤⣄⣀⠀⢦⡀⠈⠙⠻⠛⠛⠒⢒⡒⠃⠀⢀⠀⠀⠈⠛⠀⠈
⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⢀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣇⣈⣩⣿⣶⡿⠆⠀⠀⠀⠀⠀⠸⠤⠛⠛⠟⠁
⠀⠂⢀⣭⠷⠶⠆⠀⠀⠘⠛⠿⠛⠓⠒⠃⠀⠉⠛⠉⠀⠀⠀⠉⠁⠀⠀⠏⠀⠀⠀⢰⡶⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤
⠀⠀⠤⠤⠴⠀⣤⣴⣶⣦⣄⠀⠀⠀⠀⠠⣤⣦⠤⠤⠀⠀⠀⠀⣀⣀⡄⣠⣀⣶⣦⣾⡇⠀⠉⠳⢦⡀⠀⢻⠓⠛⠛⠉
⠀⠀⢀⡠⠀⢀⣀⠈⠉⠀⣀⣠⠴⠀⠀⠀⣀⣀⣀⡀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⠚⠀⠀⢀⡀⠐⠒⠒⡯⠷⠖
⠀⠈⠛⠶⢿⡟⠛⠁⠀⠈⠛⠻⠿⣭⠭⠭⠭⣭⣬⣷⠀⠀⠀⠀⠁⠛⠙⠛⠻⠿⠻⠟⣧⠴⠋⠀⠀⠀⠠⣾⣥⣤⣤⣤⠴⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⢸⡿⠀⠀⣿⡇⠹⣿⠿⢶⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣤⣴⡾⠛⣿⡟⠿⣶⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣤⡶⠟⢻⣿⣿⡄⠀⠀⠀⠸⣷⡀
⠀⣸⡇⠀⠀⣿⠁⠀⣹⣷⡀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⢀⣿⣦⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢠⣿⠃⠘⣷⡄⠀⠀⠀⠙⣷⣄
⢠⣿⠃⠀⢠⣿⠀⠀⢿⡿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⣿⡏⠻⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣷⠀⠀⠈⢿⣆⠀⠀⠀⠈⠙⠿
⡿⠁⠀⠀⣾⡇⠀⠀⢸⡇⠘⣿⡉⠙⠛⠛⠻⠷⠶⠶⠾⠿⠟⠋⠉⠀⠀⣿⡇⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠛⠛⢉⣿⠋⠻⣧⡀⠀⠀⠙⢷⣄
⠀⠀⠀⢀⣿⠀⠀⠀⢸⡏⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠘⢿⣄⠀⠀⠀⠙⢷⣦⣀
⠀⠀⠀⢸⡟⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⢶⣦⣤⣤⣤⣤⣶⠶⠾⠟⠋⠀⣿⡇⠈⠙⠛⠿⠶⣶⣶⣶⠶⠾⢟⣿⣿⡄⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠛⠿
⠀⠀⢀⣿⠁⠀⠀⠀⣿⠃⠀⠀⣿⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠈⠻⣶⣄⠀⠀⠀⠈⠻⣦⣀
⠀⢀⣾⠃⠀⠀⠀⣰⡟⠀⠀⠀⣿⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⣿⡿⣦⣄⣀⣀⣀⣀⣤⣴⠾⣿⣿⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠈⠛⢷⣤⣄⣀
⣠⡿⠃⠀⠀⠀⢠⡿⠁⠀⠀⢠⣿⢠⣿⠘⣿⡟⠛⠛⠻⠛⠛⠛⠁⠀⣠⣿⣧⠀⠉⠉⠉⠉⠉⠁⠀⣼⠏⢻⣧⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠉⠛
⠟⠁⠀⠀⠀⢀⣿⠃⠀⠀⠀⣾⠇⣸⡏⠀⣸⣿⣶⣤⣤⣤⣤⣤⣶⠿⠋⣿⡟⢷⣄⡀⠀⢀⣠⣴⣾⣿⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣶⣤⣄
⠀⠀⠀⠀⢀⣿⠇⠀⠀⢀⣾⠏⢠⣿⠃⠀⣿⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠛⠛⠛⠋⣽⡟⢻⣇⠀⠀⠈⠙⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣿
⠀⠀⠀⢀⣾⠇⠀⠀⢀⣾⠋⢀⣾⠇⠀⢰⣿⠀⢸⣿⣤⣄⣀⣀⣀⣠⣤⣿⣷⣤⣄⣀⣀⣤⣶⡟⠀⠀⠙⢷⣤⣀⠀⠀⠀⠉⠙⠛⠷⢶⣶⣶⡾⢻⡿⠁
⠀⠀⣠⡾⠃⠀⢀⣴⠟⠁⢀⣾⠏⠀⠀⣾⠇⠀⣿⠋⢿⡏⠉⠉⠉⠉⣠⣿⡇⠈⠉⠉⣉⣹⣿⣆⠀⠀⠀⠀⠉⠛⠻⠿⢶⡶⣶⣶⣶⠿⣿⡏⠀⣿⠁
⣶⣾⣟⡁⢀⣴⡿⠋⠀⢠⣾⠋⠀⠀⣼⡏⠀⣸⡟⠀⠈⣿⣦⣤⣤⣴⠟⣿⡿⢶⣶⡾⣿⣿⠈⠻⢷⣤⣀⣀⣀⠀⣀⢀⣠⡶⣿⡏⠀⢰⡟⠀⢸⣿⠀⢀
⢿⡍⠙⠻⣿⣿⣤⣤⣴⡟⠁⠀⢀⣴⠟⢀⣼⠟⠀⠀⠀⣿⢿⣍⠉⠁⢠⣿⡇⠀⢀⣰⡿⢻⣦⡀⠀⠈⠙⠛⢛⣿⣿⠟⠉⠀⣿⠀⠀⣾⡇⠀⢸⡟⠀⢸
⢸⡿⠀⠀⢻⡇⠈⠹⣿⠻⢶⣶⣿⣋⣰⡿⠋⠀⠀⢀⣼⠟⠈⣿⣷⠾⠟⣿⡿⠶⣿⣿⡁⠀⠙⠿⢶⣶⣶⡾⠛⢹⡟⠀⠀⠀⣿⡀⠀⣿⠀⠀⢸⣧⠀⠘
⣼⡇⠀⠀⣾⡇⠀⠀⢻⡇⠀⢻⡏⠻⣿⣷⣶⣿⣿⠛⠁⠀⢀⣿⢿⣶⣶⣿⡷⣾⡿⠉⠻⢷⣶⣶⠾⢿⡇⠀⠀⢸⡇⠀⠀⠀⢹⣇⠀⢿⡄⠀⠈⣿⡀
⣿⠀⠀⢀⣿⠁⠀⠀⢸⡧⠀⢸⣿⠀⠘⢷⡄⠉⠻⣿⡿⣾⣿⣁⣈⣿⣇⣹⣧⡿⢿⣶⣶⠿⣿⠁⠀⢸⣧⠀⠀⠘⣿⡀⠀⠀⠈⢿⡄⠈⢿⣄⠀⠸⣷⡀
⠃⠀⢀⣾⠇⠀⠀⠀⣾⡇⠀⢸⣿⠀⠀⠘⣷⠀⠀⢸⣇⠀⢹⡿⠛⢿⣿⣿⣿⣿⡟⢻⣯⣀⡙⣷⣦⣀⣙⣷⣦⣄⣸⣷⣄⣀⣀⣘⣿⣄⣈⣻⣦⣀⣹⣷
⠶⢶⣾⠿⠶⠶⣶⣿⠿⠷⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣟⣿⡟⠛⠛⣿⡿⠛⠛⠛⣿⠟⠛⣿⡿⢛⣿⠟⠉⣿⠟⠉⢉⣿⠟
⠀⠀⠻⣷⡀⠀⠈⠙⢷⣄⡀⠈⠙⠻⣶⣄⡀⠉⠻⣷⡙⢷⣄⣽⣿⣟⣹⣿⡟⣿⣿⠿⠿⢿⣦⣼⣿⠀⠀⢀⣾⠏⠀⣼⠏⢠⡾⠃⠀⣼⠏⠀⣰⡟⠁
⠀⠀⠀⠈⢿⣆⠀⠀⠀⠙⠻⣦⡀⠀⠀⠙⢿⣆⠀⠈⣿⣼⣿⢿⣯⣽⣿⣿⡿⠻⢿⣄⣠⡾⠟⠛⠛⢷⣶⣾⣏⠀⢸⣿⠀⣾⠃⠀⢀⣿⠀⠀⣿⠃
⢷⣄⠀⠀⠀⠻⣧⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢻⣧⢀⣿⡿⣷⣤⣈⣿⠿⣿⣷⡶⠾⣿⣿⠀⣠⣶⠿⠛⠛⠛⠛⣿⣾⣿⣄⣿⡄⠀⢸⣿⠀⠀⣿⡄
⠀⠙⢷⣄⠀⠀⠙⣷⡀⠀⠀⠀⠀⠹⣧⠀⠀⢰⣿⣿⣥⣄⠀⠈⣿⣿⢶⣾⡇⣠⣤⣬⣿⣾⡟⠀⠀⢀⣤⣾⠟⠋⠉⣈⣽⣿⣷⣦⣬⣿⡀⠀⢻⣇
⠀⠀⠈⢿⣆⠀⠀⠘⢿⡄⠀⠀⠀⠀⢹⡇⣠⡿⠋⠉⠉⠙⣷⣼⣿⣀⣀⣹⡿⠛⠉⠉⠉⠻⣧⠀⣠⡿⠋⠀⢀⣤⡾⠛⠉⠀⢀⣨⣽⣿⣿⣦⣌⣿⣆
⠀⠀⠀⠈⢿⡄⠀⠀⠈⢿⣆⠀⠀⢠⣿⣿⣿⣶⣶⣦⣤⡀⢸⡿⠉⠉⠙⣿⣧⣴⣶⣶⣶⣶⣿⣷⣿⠁⢠⣾⠟⠁⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⢉⣿⣿⣷
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠈⣿⡀⣠⣾⠋⠀⠀⠀⠀⠀⠙⣷⣿⠁⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠹⣿⡀⣾⠃⠀⠀⣰⡿⠉⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁
⣄⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿⣿⠿⠛⠛⠻⢶⣤⡀⠀⠀⣿⡿⠛⠛⠛⠿⣿⣷⠾⠿⠛⠛⠿⠿⢶⣼⣿⡏⠀⢀⣾⠟⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⣠
⠻⣦⡀⠀⠀⠀⢹⡇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠻⣦⣼⣿⣤⣤⣤⣤⣀⢹⡇⠀⣀⣀⣤⣤⣀⣄⣉⣛⣿⡄⣼⡏⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⢀⣾⠋
⠀⢹⣧⠀⠀⠀⣼⣿⣿⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠉⠀⠀⠀⠈⠻⣿⣿⠿⠋⠉⠉⠉⠉⠉⠉⠙⠻⣿⣿⡇⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⣠⡿⠁
⠀⠀⣿⡇⢀⣼⠟⠉⠉⠉⠛⠻⠷⣦⣄⡀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢠⣿⠃⠀⠀⠀⣰⡿
⠀⠀⣿⣷⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⣾⠃⣀⣀⣀⣀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣼⡇⠀⠀⠀⢰⡿⠁
⠀⣴⡿⠋⠉⠛⠛⠿⢶⣤⣄⡀⠀⠀⠀⠀⠈⣿⡿⠟⠋⠉⠉⠉⠉⠻⣷⣼⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⢻⣧⠀⣿⠀⠀⠀⠀⣾⡇
⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⢿⣷⣿⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀
⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢸⡏⠀⠀⠀⠀⣼
⠉⠉⠉⠙⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⢹⣿⣷⠿⠛⠛⠻⠿⠷⣦⣄⡀⠀⢸⡇⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⠘⣷⡀⠀⣾⡇⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣼⣧⣴⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣾⣿⡄⣿⡇⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⣼⡏⠀⢀⣀⣤⣠⣀⣀⣀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠙⢿⣿⡇⠀⠀⢸⡟
⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠘⣿⣰⣿⡶⠟⠛⠉⠉⠉⠉⠉⠛⠛⠷⣦⣄⣸⡧⠀⠀⢀⣠⣴⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⣾⣿⣆⠀⠀⣼⡇
⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣴⡾⠛⠋⠁⠀⣀⣤⣤⣶⠶⡶⣶⣤⣤⣄⣀⡀⠀⠈⠙⢿⣦⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡴⣀⢶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠉⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡌⠀⠀⠀⠀⢸⣀⣀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢦⠴⣄⠴⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡸
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠓⠂⣤⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡤⠤⠄⠐⠂⠉⠀⠀⣀⠜⠧⣄⠀⠀⠉⠓⠒⠦⠤⢴⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢦⡀⠀⠠⠄⠒⠉⠀⢀⡅⠀⠉⠒⠠⠄⠀⢀⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡍⠑⢄⡀⣀⡀⠤⠒⠁⠉⠒⠤⢄⣀⣀⡠⠊⢱⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡰⠁⠀⡘⠱⣄⠀⠀⣀⠴⠦⣀⠀⠀⣠⠎⢣⠀⠈⢇⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠜⠀⠀⡰⠁⠀⡸⠫⡁⠀⠀⠀⠀⢈⠝⠃⠀⠈⢆⠀⠈⠣⡀⠀⠙⢄⡀
⠀⠀⠉⠁⠚⢟⠒⠲⢶⠥⠤⣤⢊⣀⣀⡔⠁⠀⠈⢢⡀⢀⡔⠁⠀⠈⢢⣀⣀⡳⣤⠤⠬⡶⠖⠒⡻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢣⠀⠈⢇⠀⠈⠂⠀⠈⠍⠉⠉⠐⣒⢿⡿⣒⠀⠉⠉⢹⠁⠀⠰⠁⠀⡰⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠘⡄⠀⢸⠀⠀⢸⡠⠔⠊⢀⠎⠸⡀⠑⠢⢄⡆⠀⠀⡆⠀⢀⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⢸⡠⠐⠉⠒⢄⠀⡜⠀⠀⢣⠀⡠⠒⠉⠲⢄⣇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⣰⡥⠒⠉⠉⠒⢄⡀⠀⠱⠓⠒⠒⠚⠎⠀⠀⡠⠒⠈⠉⠓⢬⣆⠀⢸
⠀⠀⠀⠀⠀⠀⣠⣷⣊⠁⠀⠉⠀⢄⠀⠀⠙⣄⣃⣀⠀⠀⣀⣘⣠⠊⠀⠀⡠⠒⠉⠀⠀⣑⣺⣄
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠉⠲⢄⠀⠀⠀⢄⠀⡞⠁⠀⠀⠀⠀⠈⢻⠀⡠⠊⠀⠀⡠⠖⠉⠁⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣾⠔⠂⠉⠉⠉⠉⠐⠢⣷⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡠⠃⡀⠀⠤⠤⠤⠤⠀⢀⠘⣄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠶⠟⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣀⣤⠾⢿⣄⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠖⠒⠛⠉⠉⠀⠀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⣀⣤⣤⡶⠾⠛⢋⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣤⣶⣿⠿⠟⠛⠛⠛⣻⣿⠟⠛⠛⢛⣿⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣿⡎⢻⣇⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠉⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⣹⡇⠀⠀⠀⠀⢰⣿⡇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠙⠛⠛⠀⠀⠀⠀⠀⢸⣿⠀⠺⣿⣽⣻⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⠦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠰⢾⣯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⢰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⢿⣿⣷⣄⡀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⢀⣠⣴⡾⠟⢉⣿⡇⠀⠀⠀⠀⣰⠏⠀⢸⡟⡀⠀⣼⢿⡄⠀⠀⠀⡿⣧⠀⠀⣼⡇⠘⣿⣇⠙⢿⣦⣄⣀⠀⠀⢹⣷
⢀⣴⡾⠟⠋⠁⠀⠀⣸⣿⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠳⣴⡇⠈⢿⣄⠀⣼⠇⢸⣂⡴⢉⡇⠀⢹⣿⡄⠀⠈⠙⠻⢿⣶⣾⠟
⠛⠿⣶⣤⣀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⡀⠀⠀⢸⡇⠀⠙⠁⠀⠀⣹⣿⣇⠀⠈⠋⠀⢸⡇⠠⢴⣿⣧
⠀⠀⠀⠉⠻⣷⡄⢸⣿⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠏⠀⠙⣦⠀⠀⠀⢸⡇⠀⢰⢿⣿⡀
⠀⢀⡀⡀⠀⣼⡏⣼⡟⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⣼⠏⠀⠀⠀⠘⣷⡀⠀⢸⡇⢠⠟⠈⣿⡇
⠀⣼⣿⣿⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠘⣷⠀⢸⣷⠏⠀⠀⢻⣿
⠀⠀⠉⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢿⣦⣤⣀⣀⣀⣠⣴⠿⠃⢸⠃⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠸⠿⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣸⣆⣀⣀⣀⣉⠙⠛⠛⢉⣀⣀⣀⣿⣀⣀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⢻⣿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⢤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⡶⠶⢶⠶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⡆⠀⠀⢀⣀⠙⣷⡀⠀⠀⠀⠀⠀⠀⣴⠟⢉⣁⡀⠀⠀⠆⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠷⠾⠛⠋⣿⣄⣼⡷⠀⠀⠀⠀⠀⠘⢷⣤⣾⠏⠛⠛⠛⠛⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠱⣌⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⢧⠀⠀⠠⠙⣄⠀⠀⠈⠑⠲⠤⣄⣀⣀⣀⣀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠙⠒⠤⣄⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⣆⡠⢇⠀⠈⠳⢄⡀⠀⠀⠀⠀⣀⡠⠝⠋⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⠉⠓⠒⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠸⣆⠀⠣⣄⠀⠀⠉⢓⣴⡶⠋⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠉⠙⠒⠲⠤⣶⢭⣀⣀⣀⠀⠀⠀⠄⠘⡆⠀⣀⡭⡶⠊⠉⣸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢆⠀⠀⠉⠉⠉⠙⣛⡷⠾⡿⢧⣤⣅⣀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⣀⡠⠖⠋⠑⢠⡀⡇⡠⠙⢦⡈⠉⡻⠲⠤⣄⣀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣀⡴⠶⠯⣅⣀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠙⣶⠀⠀⠀⠀⠈⠉⠛⠲⠤⢤⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⡤⠒⠋⠁⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⡇⢀⡴⠂⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢀⡠⠴⠚⠉⠉⠉⠉⠙⠒⠒⠦⢄⣀⠀⠀⠀⠀⠑⣌⡧⠋⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠙⣾⡇⠀⣀⡤⠶⠒⠒⠒⠒⠒⠢⢜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠖⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠦⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣀⡤
⠀⠀⣾⡁⣀⡀⠲⠄⠀⠀⠢⠀⠀⠦⡀⠀⠀⠀⢀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠉⠁⡉⡀⠀⠀⠐⠀⠠⠀⠰⠀⢳⠄⠀⠞⠙⠀⠈⠋⠙⠀⠀⠈⠀⠠⠖⠲⡤⠆⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠒⠂⠀⠀⠄⠀⠒⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⠀⠀⢠⣂⠀⠀⠀⠃
⠀⠀⠀⡠⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠃
⠀⠀⠀⠁⠠⠀⠐⠂⠘⠀⠀⠀⠀⠁⠀⠀⠀⠲⠀⠀⠀⡐⠀⠀⠀⢄⠀⠀⠀⢠⠀⡀⠀⠄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠂⠴⠃
⠀⠀⠀⠠⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠁⠉⠀⠀⠉⠀⠀⠲⠄⠀⠀⢀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⣄⠀⠐⠀⠈⠀⠀⢰⠏⠀⠀⢰⠖⠀⠀⡀⠀⠀⠀⠀⡌⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⠀⠀⠀⠾⠦⠀⠄⣰⡢⠂⠀⠁⠀⠀⠄⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⠀⠀⡀⠀⠀⡀⡤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢤
⠀⢨⠇⠀⠀⠀⢰⠇⠐⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⡁⠑⠀⠀⠀⠀⠀⠀⠀⠄⠀⢘
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⣀⣠⡀
⠀⠀⠀⢀⡤⠠⠤⢀⠀⠀⢀⠀⠀⠁⢀⡠⠀⠀⠐⠀⠀⠆⡀⠀⠘⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠
⠀⠀⢠⠁⠄⠘⠀⠨⠀⠀⠈⠉⠃⠈⠀⠱⠀⠀⠀⠀⠀⠀⠡⠀⠀⠤
⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠙⢯⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠤⢼⠀⠀⠀⠈⡆⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢆⠀⠀⣰⣱⠃⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⠙⠋⠉⠀⢀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⡞⠒⠒⠒⠒⢲⠇⠀⢸⠒⠒⠒⠒⠒⠒⠒⡗⠀⠀⠀⠀⠀⠀⡇⠀⣀⡀⠉⠉⠉⠉⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⢀⠀⠉⠉⠉⠑⠒⠋⠉⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⠈⠉⠙⠒⠒⠒⠒⠒⠃⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠈⠲⠋⠣⠔⠒⢦⠔⢲⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡎⠀⠙⠒⠒⠤⠤⠤⠤⠒⠀⣼⠃
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠖⢦⡠⢦⣀⡤⣄⢀⣠⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢰⠃⠐⠲⠤⠤⢤⣤⡤⠤⠄⡸⡻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠀⠀⠀⡇⠀⠀⠀⠀⢀⡏⠀⠒⠢⠤⠤⣤⣤⠤⠄⣰⢃⠇
⠀⠀⠀⠀⠀⢰⠇⠀⠊⠈⠒⠋⠳⠖⠓⢤⠖⢢⡀⠀⠀⢰⠃⠀⠐⢶⣤⠾⠤⣀⣀⣀⠤⢤⡀⠀⠀⡰⠃⡜
⠀⠀⠀⠀⠀⢸⠀⢀⠴⣄⣠⣄⠀⣀⡀⠀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠯⣍⣑⣒⡒⠦⠤⠤⠿⠶⠊⠀⡰⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠁⠈⠉⠀⠙⠊⠉⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠙⠒⠲⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠻⡦⣀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠂⢣⠀⠉⠉⠋⠉⢡⠋
⠀⠀⠀⠀⠀⠀⠀⢲⡎⣁⠀⠀⠀⠀⠀⠈⠀⠈⢓⠠⠀⠤⢰⠏⠀⠀⠀⠑⠤⣀⠑⠠⣤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢫⠐⠢⠄⡀⠀⠀⠀⠜⠆⠀⠀⡞⠀⠀⠀⠀⣀⡤⠴⠛⠉⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠇⠀⠀⠈⠀⠐⠀⡀⠐⠀⡎⢀⡠⠴⡖⠉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⣻⡩⢄⡀⠀⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠂⣀⣤⡀⠀⠉⢢⠀⣀⠀⢱⠁⠀⠉⠚⠢⣄⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣼⣡⣔⠋⠉⠁⠀⠈⢣⠀⠀⡀⠁⠀⠈⢧⠀⡄⠈⠀⢀⡈⠡⠶⠦⣀⢧
⠀⠀⠀⠠⠀⠚⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⡇⢰⠗⠉⠉⠑⠺⡎⠀⡠⠊⠁⢀⡠⠖⠂⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢰⣀⠤⠤⣄⣀⡀⠸⣴⠃⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⣎⠤⠤⠀⠀⠀⣉⡙⢻⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⠤⠄⠠⠤⠄⢀⡀⠉⠓⢧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠒⠒⠒⠒⠒⠒⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠉⠉⠉⠉⠉⠐⠦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠁⠁⠀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢰⣶⣶⣶⣶⡆⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢶⣶⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠚⠛⠛⡟⠉⠁⠀⣴⣶⣶⣶⣶⣶⡄⠀⠀⢠⣶⣶⣶⣶⣶⡆⠀⠘⠛⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢰⠁⡐⠁⠀⡆⠀⠀⠀⠈⠉⢉⣭⡉⠉⠀⠀⠀⠀⠉⣩⣭⡉⠉⠁⠀⠀⠀⠑⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠱⢀⠀⡇⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠠⠀⠀⠿⣿⠏⠀⠀⠀⠀⢀⡠⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⣀⡇⠀⠀⠀⠠⡠⠠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⡀⡄⠀⢠⣀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠒⠂⠀⠀⠀⠤⠀⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠐⠒⠂⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣶⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠁⠈⠛⠉⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⣿⣧
⠀⠀⠠⣿⡟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⢿⣷⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⠟⠉⠉⢛⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⢀⣴⣿⣿⣄⠈⠻⣷⣄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣴⣿⣏⠀⠈⠻⣷⣄⠈⠻⣷⣄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠉⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣷⣄⠈⣿⡂
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠉⠻⣷⣄⠈⠻⣷⣄
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣿⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠿⣷⣤⣾⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⣠⣾⡿⠋⣠⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⠿⠿⢿⣷⣄⣨⣿⡿⠋⣠⣾⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⣠⣾⠟⠁⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣅⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁

⡿⠿⠿⠿⡿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄
⠀⠀⠀⠀⠀⠀⠉⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠙⢏⠛⠒⣼⠀⠀⠀⠀⢀⣀⡀⠤⠴⠚⠉⠁⢀⡄⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠃⢰⡼⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⡝⠹⠀⠀⠀⠉⠉⠉⠉⠉⣩⢿⠃⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠶⠒⠶⠀⠀⠀⣀⠤⠄⠐⠀⢀⡜⠀⠀⠀⠄⡀⠀⠀⠀⢀⠔⠁⡏⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣇⠀⠀⢦⣄⡴⠛⠁⢀⡠⠴⠚⠉⠁⠀⠀⠀⠀⠈⠓⣲⡶⠁⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠈⠙⠳⢦⣄⡀⠀⢠⠀⠸⡆⣿⡀⢀⡾⠙⢦⡤⠤⠤⠄⠒⠀⠀⠀⢀⡀⠀⢀⡤⠊⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢠⡉⠙⠻⣶⣶⣿⣿⣿⡿⢁⣀⣠⡵⡤⠤⠤⠚⠀⢠⡀⢀⡩⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣣⢴⣶⣿⣿⣿⣿⡟⠛⢭⣏⣁⡴⢘⣒⢲⡈⠷⠒⡛⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢀⡴⠊⠁⣼⣿⣿⣿⣿⡿⣇⡄⠀⢧⠈⠵⣻⠿⠛⠩⠋⢰⠟⠒⠢⠼⠦⠤⢀⣀⣀⣳⣀⠀⠀⠘⢦⡀⠀⠀⢸⣿⡇
⠀⠠⠊⠀⠀⠀⠘⠿⠿⠟⢹⠃⠘⣇⠀⠉⠀⢦⠋⠀⠡⠒⠀⠙⠀⠀⣰⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠠⠽⠂⠀⢸⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⠉⠣⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⡰⠁⢀⡠⠚⡿⠦⠀⠀⠀⠀⢤⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣀⣠⣾⣵⣚⡛⠒⠂⡇⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠹⠀⠀⠀⠀⠀⠀⠈⠩⠝⠛⠦⣀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠈⠐⢀⠁⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠦⡀⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⣠⠄⠈⠀⠀⠉⠳⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢽⣇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢇⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡼⠛⠉⠀⠀⠀⠀⠀⠈⠒⠾⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠦⠀⠀⠀⠰⢾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣷⣄⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⢀⣴⣿⣿⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠈⠻⣿⣿⣦⣤⠀⠀⠀⢠⣤⣾⣿⡿⠃⠙⢿⣿⣿⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⠀⣠⣄⣀⣀⣀⡀⣀⣀⣀⣀⣤⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⣀⣤⣤⡄⠚⣉⣿⣿⣿⣦⡠⣾⡿⠋⡍⠩⡏⢹⠉⣯⠙⡏⠹⡿⡄⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠙⠉⠉⠉⠛⠉⠀⠙⢿⡶⠽⠖⠻⠎⠶⠿⠶⠴⡾⠟⠀⠈⠻⣇⠀⠀⠀⠈⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣸⡋⠀⠀⠀⠀⠀⢀⡀
⠀⣠⣾⣿⣿⣦⡀⠀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣄⠀⠀⣠⣾⣿⣿⣦⠀⠀⣠⣾⣿⣿⣦⡀⠀⢀⣴⣿⣿⣦⡀
⠺⣿⣿⣿⣿⣿⡿⠺⣿⣿⣿⣿⣇⠀⠀⠀⠠⠄⠄⠀⠀⠀⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠗⠺⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⡿⠲⣿⣿⣿⣿⣿⡿
⠀⠈⠻⣿⡿⠋⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠈⠸⣿⡿⠋⠀⠀⠈⠻⣿⡿⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣼⣄⠀⠀⠀⠀⣀⣼⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⣠⣴⣾⣿⣧⣶⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠠⣾⣿⠋⢻⣧⡄⢠⡴⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠈⠻⡾⠟⠛⠻⠏⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢸⣿⣷⣀⠹⠋⠈⠺⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠀⠙⠿⠋⠀⠀⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⢿⣿⣿⣷⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣴⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠉⠒⠀⠀⠚⠀⠀⠐⠀⠀⠚⠃⠈⠀⠀⠛⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⠀⠀⣀⡀⠀⢀⡀⠀⢀⣀⠀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⡗⠀⡸⢻⡄⠀⢻⡄⠀⡞⣷⠀⢰⠇⠀⡟⢳⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⣰⠗⠚⢷⠀⠈⣧⣸⠁⢸⣇⡟⠀⠀⡇⠀⠙⢧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠆⠀⠀⠻⠀⠀⠘⠃⠀⠘⠇⠀⠀⠿⠁⠀⠀⠻⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣴⣆⢀⠠⠀⠑⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡉⠋⣹⢭⣿⣤⣦⠴⣦⡤⠬⢧⣄⣠⠄⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠊⠀⠼⣦⣶⣿⣋⣿⣾⠭⠶⣿⣹⠲⢊⠛⠩⣹⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠻⠌⠄⢰⠿⠟⢢⣶⣿⣿⣷⣽⣿⢷⣿⣿⡿⢷⣿⠛⣤⣤⡘⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣰⣾⣿⣉⢉⣽⣿⣿⣾⣚⣾⡿⣷⣶⣍⣯⠉⣼⣿⣯⡰⣤⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣸⡥⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠹⠭⣛⡛⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢃⠛⠀⣿⣥⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⢿⣶⠛⡟⣍⢻⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⢴⣿⣿⣿⠟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⣤⠇⣙⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠶⠀⠳⡌⢧⡹⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣁⡨⡝⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⢁⠀⠃⢈⣷⡘⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⢧⡿⣍⡴⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⢐⡊⠙⣿⣇⣲⣮⡿⣿⣿⣿⣿⣻⣯⣿⠟⠉⣱⣸⠿⠘⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⢷⣄⡈⣹⠟⠓⠂⠻⠿⠟⠛⠻⠛⣧⢚⣥⡿⠉⠐⡀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠛⢭⡋⠑⠒⢻⣥⢤⡤⠉⠀⠀⣨⠿⡨⠧⠤⣤⣥⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠾⠀⡾⢯⠋⠛⠯⠀⠬⠁⠆⠀⡛⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⢀⠓⠀⠀⠀⠄⠛⠳⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠤⠤⠤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠖⠊⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣀⡀⣀⡀⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠘⠞⣻⡟⢭⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠸⣤⣄⢀⡛⡁⠀⢸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⡃⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀⠀⠠⠖⠀⠀⠘⠦⣀⣀⣀⣀⠀⠀⠠⠤⠤⠄⠠⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠤


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠐⠒⠀⠐⠒⠀⠉⠀⠀⠘⠀⠈⠑⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢃⠀⠀⠀⠀⠀⢀⠠⠐⡗⢄⠀⠀⠀⠀⠀⠉⠉⢀⠜⢃
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⡠⠊⢣⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠒⠤⠄⠀⢀⡠⠂⠀⠈⢄
⠀⠀⠀⠶⢄⡉⠀⠀⠀⢀⡠⠂⠁⠀⠀⢣⣀⣀⡀⠠⠔⢺⠃⢄⠀⠀⠀⠀⢀⠊⠘⡀⠀⠀⠈⠢⡀
⠀⠀⠀⢘⠀⠈⢲⠆⡈⠀⠀⠀⠀⢀⠔⠁⢣⠀⠀⠀⠀⣸⡀⠀⠈⠁⢀⠜⠇⠀⠀⠐⢄⠀⠀⠀⠈⠑⠤⣀
⠀⠀⠀⡐⠀⠀⢨⠀⠀⠑⠤⢔⠂⠁⠀⠀⡰⢣⠀⠈⠁⠀⠈⠒⠂⣤⠂⠀⠈⢄⠀⠀⠀⠑⠤⣀⠀⣀⠠⠄⠸⠃
⠀⠀⢠⠁⠀⠀⡈⠀⠀⠀⠀⠀⠁⠲⢖⠉⠀⢀⠷⠀⠒⡇⠤⣠⠊⠀⠣⡀⠀⠀⠑⣢⡤⠄⠒⢈⠋⠀⠀⢠⠁
⠀⡠⠁⠀⠀⠔⠀⠀⠀⢀⠃⠀⠀⡸⠀⠈⡟⢥⡤⠳⢨⢁⠶⣁⠑⣄⠠⠘⠗⠈⠀⠰⠀⠀⠀⠈⠀⠀⠀⠈
⠺⡐⠂⠐⢪⠀⠀⠂⠰⡃⠀⠀⠰⡅⠀⠰⡄⠴⠤⢱⣷⡧⢂⣙⡁⢀⠀⠀⡄⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠈⠄⠀⠀⠱⡀⠀⠀⠘⡄⠀⠀⢰⠀⠀⣅⠔⠢⣡⠙⠉⣠⡎⢩⠚⠓⠂⡴⠄⢀⡀⢣⠀⠀⠈⢆⠀⠀⠀⢃
⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣔⠈⠀⠑⢦⠥⠌⣇⠤⠓⢆⠀⢠⠊⠀⠀⠀⡠⠘⠉⠐⠂⠀⣧⣄⣀⠀⠣⡀

⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡦⠐⠁⠀⠀⠑⢆⠠⠁⠀⠀⠀⠀⢀⣀⡱⣄⠀⠀⢀⠊⠀⠀⠀⢀⠔⠉⠀⠀⠀⢈⠡⠛
⠀⠀⠀⡄⠀⢀⣃⠄⠊⠁⠀⠉⠐⢄⠀⠀⢨⠋⠈⠀⠐⢰⠊⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡠⠊
⠀⠀⢀⡁⠔⠊⠀⠁⠒⢄⡀⠀⠀⠀⠱⣀⠃⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠠⠐⢦⠀⠀⡌⠀⠀⠀⢠⠊
⠀⠀⠈⠐⠒⠠⢀⠀⠀⠀⠈⢢⠀⠀⢀⠋⠁⠀⠀⠈⠁⠢⡤⠊⠀⠀⠀⠀⠀⠀⠑⢄⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠡⢀⠂⠀⣀⣀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠄⠐⠒⠀⠠⠷⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢀⠋⠁⠀⠀⠀⠀⠉⠐⠤⣘⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠂⣀⠀⠀⠀⠀⣀⠀⠀⠀⠈⡀⠀⠀⡀⠄⠒⠈⠉⠀⠀⠉⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⣃⠔⠈

⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⢀⣱⣄⠀⠀⠈⠑⠒⠂⢁⡠⠤⠶⠒⡇⠀⠀⠀⠙⠷⠞⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⠀⠀⠀⠉⠉
⠒⠀⠐⠢⢠⠁⠀⠀⠀⢿⡟⢙⡇⠀⠀⠀⡾⢿⣿⡇⠒⠤⢄⡴⠊⠁⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⣰⣦⠀⣀⣀⠀⠀⣀⣨⣄
⠀⠀⠀⠀⢘⡀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠳⠴⠟⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⡹⠛⠉⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠈
⠒⠂⠒⠒⠛⠧⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣈⣢⣄⡀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡦⠤
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⠦⣀⡀⢀⣠⠔⠁⠀⢀⠇⠀⠀⠀⢸⣿⠿⣷⠀⠀⠀⢰⡿⣿⣷⠈⠇⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣀⠤⠤⠶⠰⠦⢼⡀⠀⠀⠀⠘⢿⣤⠟⠀⠀⠀⠘⢦⣼⠟⢸⠀⠀⠀⢸⡿⠻⡇⠀⠀⠀⢋⡝⠁
⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠘⡖⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⡜⠀⠀⢀⣀⣀⣀
⠆⠀⠀⣿⡟⢻⣿⣿⠇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⠘⡄⠀⠀⠀⠀⢀⠴⠒⠒⠒⠢⣄⠀⠀⠀⢆⠀⠀⠀⠠⡀⠀⠀⠀⢠⠃⠀⠀⣿⣿⡿⠻
⠀⠀⠀⠈⠳⣾⠿⠋⠀⠀⠀⢸⠀⣀⡀⠀⠀⠀⣾⠿⣷⡘⢦⡀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠂⠀⢀⣨⠦⠤⠀⠤⠽⢦⡤⠤⠸⠀⠀⠀⠈⠻⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣼⣿⠿⡄⠀⠀⠙⠶⢟⡡⠔⠛⠊⠉⠉⠁⠒⠢⢄⡀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡇
⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⣼⠁⠘⠻⠶⠃⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢦
⠒⠒⠒⠊⠁⠀⠀⠀⣠⠞⠀⠈⠉⠒⠤⡀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀
⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠘⢦⠇⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⣀⣤⣄⠀⠀⠀⠘⡈⠙⠃⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠲⢄⣀
⣹⠟⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⣏⣹⠇⠀⠀⠀⡟⠻⣿⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⢸⣷⡄⠀⠀⠸
⠀⠀⠃⠀⠀⠰⣤⣤⠀⠀⠀⠀⣤⣴⠂⠀⠸⡀⠀⠀⠀⣀⣉⣥⣄⣀⡀⠀⠙⠞⠋⠀⠀⠀⠀⡏⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⢀⢿⣤⡟
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⠊⠉⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠗⠒⠒⠒⠦⠤⣀
⠢⡀⢱⡀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢀⡴⠛⠁⠀⠒⠒⠤⣀⣠⠖⠉
⠀⡸⠋⠑⢄⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⡰⠁⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⡸⠁⠀⠀⠀⠑⠢⠄⣀⣀⣀⣀⣤⡐⠉⡇⠀⠀⣿⣿⠛⣿⠇⠀⠘⣿⠛⣿⣿⠂⠀⠈⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⢣⣀⡀⠀⠀⠀⠀⣴⣶⣦
⠁⠀⠀⠀⣴⣿⣷⡄⠀⠀⢀⣾⣿⣿⡄⡇⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⢀⣧⣄⠀⠀⠀⣿⠛⣿⠀⠀⠀⠀⣿⢿⡆⠀⠀⠀⣟⠙⣿
⠀⠀⠀⠀⢿⣏⣸⠇⠀⠀⠀⠣⣤⡿⠁⠰⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣟⠛⡆⠀⠀⠈⠛⠋⠀⠀⠀⠀⣷⡴⠃⠀⠀⠀⠈⠛⠉
⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠓⠤⠤⠤⠖⠁⠀⠀⢀⠜⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣀⣀⡀⣤⡄
⢵⡀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢠⠎⠓⠤⣀⠀⠀⠀⠀⠀⢀⡠⠔⠙⢄⠀⠀⠀⠀⢀⣀⠤⠤⠤⠄⣀⣀⠎⠀⠻⢿⣷⣶⣶⣾⠟⣁
⠀⠱⣄⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⢀⠃⠀⠀⢀⣤⣍⠁⠁⠈⢉⣁⡀⠀⠀⠈⡆⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠈⢉⠝⠋⠁
⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⣀⡠⠔⢻⠀⠀⠀⢸⣟⢹⠆⠀⠀⠈⠉⠉⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡴⠁
⠀⠀⠀⢀⡄⠀⠉⡹⠟⠈⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣀⡀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠘
⠀⠀⠒⠛⠁⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠠⡀⠀⠀⠀⢀⠄⠀⠀⠀⡇⠀⠀⠀⣿⡿⢿⡀⠀⠀⢸⠛⣿⡇⠀⠀⠀⠀⠀⠠⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣠⣽⣧⣼⣷⣶⠶⠶⠛⠛⠛⠛⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠶⠞⠛⠛⠛⠻⣯⡉⠁⠀⠘⣷⡈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡴⠶⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢠⣄⠈⢿⣄⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠻⣦⠀⠻⣦⠙⣷⡀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠙⣷⡀⠹⣧⡈⢿⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢿⣤⣼⠇⠈⣿⡄⠀⠀⠀⠀⢻⡆
⣠⣤⣴⠶⠾⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⢸⡇
⢿⡄⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠸⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣿⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⠶⠶⠾⠛⠛⣋⣩⣭⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⣤⣴⠶⠶⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⣴⠶⠞⠛⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⡀⠘⡄⠙⠶⣤⣀⣀⡤⠔⡿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠹⣖⠒⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠆⠀⠀⠹⣆⠀⢀⠄⢱⠀⠀⠀⠀⠀⣰⠃⠀⠡⡀⠀⠀⠈⠓⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠃⠀⠀⠀⡄⠘⣯⠀⠀⢸⠀⠀⠀⠀⣰⠇⠀⠀⠀⠙⢦⣀⠀⠀⠀⢈⣡⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠘⣷⡀⢠⡕⠲⠤⢴⠏⠀⠢⡀⠀⠀⠀⣈⣭⠿⠛⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣴⠒⠋⠁⠀⠀⠀⡀⠘⣷⡀⡇⠀⢠⡏⠰⣄⢀⣨⣽⠟⠋⠉⡇⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⢲⢤⣤⡄⠊⠀⠀⠈⢷⡕⢰⡟⣀⣤⠾⠋⠁⢲⡀⠀⠀⠱⣄⠀⠀⢈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡰⠀⠈⠙⣓⣶⣤⣄⣼⣿⣿⡿⢫⠜⠂⠰⠒⠒⢛⡗⠂⠀⡙⠁⠁
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠤⠤⢤⠐⠛⠒⠐⠖⠂⠈⠉⠫⡉⠈⠣⣀⣤⡾⢛⣿⢻⡟⠛⡶⠦⣧⣄⣀⢸⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⢀⣇⡴⠞⠻⢤⣀⡿⠁⡎⠻⡾⠀⠀⣠⠞⠉⠙⠳⠶⢤⣄⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣤⠶⠿⣁⠀⠀⠀⠀⡿⠃⠀⢇⣀⢹⣄⡜⠁⠀⢀⠔⠀⠀⠀⢀⠝⠛⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⢋⠁⠀⠀⠈⠙⠦⡀⣼⢣⠤⠤⣽⠁⢀⠹⣇⠀⣰⠋⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠑⠠⡀⠀⠀⣽⣃⡠⣄⡀⢸⠈⠀⠀⢘⣶⡇⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠀⠀⠀⠀⢸⠀⣠⠖⠉⠈⢧⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⣸⠇⠐⠂⠀⠀⠐⠒⡞⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠏⢀⡠⠤⠤⠤⠤⠄⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⡾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⠿⠛⠉
⣧⠀⠀⠀⠀⢀⣤⡟⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣍
⣿⣷⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⢨⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣄
⣿⣿⣧⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⡆⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢠⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠋⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣿⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⢿
⠻⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣷⣦⣄⡀⠀⠀⠈⠻⣿⣿⣿⡿⠿⣷⣤⡀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠈⠻⣿⣿⣿⠀⠀⠀⠉⠛⠿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⣿⣯⠀⠀⢿⣿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⠶⢿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣻⣦⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣩⣿⣶⣤⣙⣿⣧⢸⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⠁⠀⢀⣀⣀⣠⣤⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠀⠀⢻⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀
⣿⣿⣶⣄⣀⣿⣿⣿⣿⣿⡿⠁⠈⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⠟⠁⠀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣀⣤⣤⣶⣾⣿⡿
⣿⣿⣿⣿⣿⠟⠛⠿⢿⣿⣃⠀⠀⠀⢀⣾⣿⣿⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⣀⣤⣼⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠋⠀⠀⠀⢀⣾⡿⠟⠋⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣧⢀⣠⣴⣾⣿⠿⣿⣿⠿⣿⣷⣀⣼⣿⣿⣾⣿⠟⠉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠻⣿⡿⠋⠀⣼⣿⡏⣀⡿⠛⢻⣿⣿⠟⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣧⣤
⣿⣿⣿⡃⢀⣠⣤⡾⠛⠉⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⣶⣾⠛⠉⣿⣿⣿⣀⣠⣿⣧⣄⣀⡀⣠⣼⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣿⣿
⠋⠉⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢘⣿⠋⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⠀⠀⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⣄⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣧⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠁⢸⣿⣿⣿⣿⣆⠀⠀⠀⢈⣹⣿⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣆⢀⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣾⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠋⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠛⠻
⠀⠈⢿⣿⣿⣿⠟⠋⠀⠀⠈⠙⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢀⣸⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣟⣉
⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⡟⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⡀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⣿⣿⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⣾⣿⣿⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠜⠀⠀⠞⣻⣿⣿⣿⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⢄⣀⣄⢀⣆⠼⡧⠒⠿⠒⡶⠃⠀⢀⣴⣾⣿⣿⣿⣿⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⠀⠈⠛⠃⠁⠀⠀⠀⣴⣾⣴⠂⠀⣵⣿⣿⣿⣿⣿⣿⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠺⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡹⣿⣿⣿⣿⣿⢨⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠿⠀⠀⠀⠀⡤⢤⣄⣀⠀⠀⠀⠀⠻⢿⣿⣿⣟⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠃⠀⠉⡂⠀⠀⠀⠊⠀⠴⠆⠀⠉⢤⡀⠆⣀⠀⠀⠈⠉⠙⣁⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡻⢶⠻⣶⣈⡟⠀⠀⢀⣀⣠⣶⠿⠿⠷⣶⠤⠀⣀⣀⠀⠀⠀⠀⠠⠭⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠐⢤⡿⠁⠀⠀⠀⣿⣿⠧⠤⠤⠚⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡧⠐⠁⠀⠀⠀⡼⠋⠑⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⢶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠓⠀⠀⢀⣀⠀⢀⡀⠀⢶⡽⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋⠀⠀⣀⠤⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡈⠓⢦⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⠒⢻⠃⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣝⢷⢦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⣤⡏⠀⠀⠀⠀⠀⣀⠔⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣧⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣬⠉⠒⠤⣤⣴⣚⣡⣴⣶⣿⣿⣿⣿⣷⡒⠤⣀⠀⠀⠀⠘⢦⣌⣻⢟⣆⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⢧⡀⠀⠁⠀⠀⠀⠈⢿⣿⡎⣿⣟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⡌⠇⠁⠈⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠈⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡀⢀⢹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡋⠻⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡘⡟⠇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣀⣀⡠⠶⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠰⠶⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠠⣾⡟⠉⠛⠙⠛⢧⣄⠀⠀⠀⠉⠙⠛⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠤⣤⣤⡤⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⣀⣀⠽⣷⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⢠⣄
⠠⣾⣿⠛⠶⠶⠀⠒⠀⠀⣀⣉⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠰⠆⠈⠙⢿⡀⠀⠀⠀⠀⠀⠈⠛⣏⠀⠀⠀⠺⠷⣀⠀⠀⣀⡀⠰⠂⠀⠀⠀⠀⠁⠰⠆
⠀⠈⠉⠀⠀⠀⠠⠄⠀⠈⠙⠛⠉⠁⢰⡿⢷⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠙⣀⡀⠀⠀⠀⠿⣿⡆⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢦⣄⠀⠀⠀⠀⠀⠀⠈⣶⣄⣠⣤⣤⠀⠘⢿⠟⠙⠁⠀⠀⠀⣼⡆
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⠀⠀⠈⠃⠀⠀⠉⢷⣤⣀⠐⠛⠓⠂⠈⠙⢧⡀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢣⣄⠀⠀⠀⠀⠀⠀⢾⡏⠀⠀⠀⣰⡶⠶⠖⠀⣶⠟⠻⣿⣷⠶⢄⣀⠀⠀⠈⠹⢶⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠈⣳⡤⠈⠉⠛⠁⠀⠀⣤⠀⠀⠀⠘⢃⣀⠈⠻⣷⣤⠠⣤⡴⠿⣶⣤⣀⣹⡿⠂⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣧⠀⠸⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡿⠃⠀⠉⠁⠀⠀⠀⠀⣀⠛⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣽⡇⠀⠀⠀⠀⠀⢿⣄⠀⠐⠀⠈⠁⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢉⣹⠶⠶⠖⠂⠀⠀⣠⡄⠐⠒⠖⠊⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠉⢿⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⡀⢀⣶⡆⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠁⠀⢶⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡄
⠀⢀⣴⠀⠀⠚⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠿⠿⠲⠂⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⢀⣀⣀⡠⠶⠶⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢷⣦⠄⠠⠾⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣤⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⠀⠀⠀⢀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠂⣀⣤⣀⡀⠀⠀⢀⣀⣀⡀⠘⠛⠃⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢄⣀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⢀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⡄⠀⠀⠈⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣀⠈⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠾⣿⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⢀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣠⣤⣄⣠⣤⣀⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⣾⣶⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢻⣿⣿⡇⠰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢸⣿⡿⠀⢠⣾⣿⣿⡇⢠⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠙⠿⣇⢀⣿⡿⠋⢀⡀⠀⠀⠀⢠⣶⣷⣆⣸⣇⢠⣶⠄⠀⠀⠀⠀⠀⠀⣰⣶⡄⠐⣿⡧⠀⣸⠃⠀⠀⠸⣿⣿⣿⣇⠀⢻⣿⣿⡿⠃
⠀⠀⠀⠀⢠⣶⣤⣿⣿⣿⣦⡶⠈⠁⠀⠀⣀⡀⠻⣿⣿⣿⣿⣿⣄⣀⣀⣠⣴⣶⠀⠀⠙⠻⠿⣶⣿⣤⣴⣋⡀⠀⠀⠀⠈⠉⠉⣻⣷⣾⣯⣀⢠⣶⡄
⠀⠀⠀⠀⠀⢉⣡⣿⣿⣿⣿⠷⣶⣶⡄⠀⠈⢠⣾⣿⣿⣿⣿⣿⡟⠉⠀⣴⠄⠀⢠⣶⣶⡶⠶⢿⣿⠿⣿⣿⣿⠀⠀⠀⣴⣶⣾⣿⠛⣿⣿⡿⠀⠉
⠀⠀⠀⢠⣾⣿⣿⠃⣼⣏⠛⠀⠈⠉⠀⠀⠀⠈⠻⢿⣿⣟⠻⢿⠿⠀⠀⠀⠀⠀⠘⠿⠟⠀⢠⣿⣿⠀⠈⠋⠁⠀⠀⠀⠹⣿⣿⠟⠀⢀⣉⣀
⠀⠀⠀⠸⢿⣿⡟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣻⣻⣻⣛⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣭⣿⣭⣿⣿⣿⣿⣭⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡗⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢩⡄⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡔⠻⣿⣦⡀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⣀⠀⠈⠻⣿⣆⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡴⢿⣿⣷⣦⣀⠈⠻⢷⣌⠣⠀⠀⠀⠀⠀⠀⣠⣤⣀⣴⣶⣆⣴⣶⣆⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠧⠀⠀⠈⠛⠿⢿⣷⣦⣀⠙⠷⣄⡀⢀⣾⡿⣾⡿⢋⡿⠟⢡⠿⠋⣱⠿⠛⣹⣾⡿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣶⣤⣄⣀⠀⠈⠙⠻⣟⠶⠳⡞⢿⠏⠸⠋⣠⠈⣠⡔⣀⣴⣆⣠⡤⠈⢁⡀⠾⠟⢻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠙⠛⠿⠿⢿⣿⣷⡖⣸⣻⠽⣇⣑⠈⠰⣤⡾⠷⢟⡉⣛⣉⠙⣛⠩⠿⢿⣯⣤⡤⠐⠛⢛⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠲⢲⣤⣤⣤⣤⣀⣀⡸⣏⣁⣩⣌⢹⠹⣦⣿⠁⠜⢺⡽⣭⣿⣈⢍⡹⠶⣖⣈⡉⣽⣶⡶⠀⠉⣛⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠒⠘⠛⠛⠛⠛⠛⠙⣇⣉⣩⣅⠻⠉⠁⣼⣿⡦⣿⣤⣶⣬⣧⡉⣧⡉⣧⣍⢽⣧⠄⠾⢿⠖⠈⠛⣻⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠘⣏⠂⢰⣶⣶⠾⠿⢛⡿⣹⣼⠋⠀⣠⣾⣿⠟⠀⢙⠁⢙⡁⣩⣅⣨⣧⢠⣷⠄⢾⡶⠐⠿⡟⠃⠙⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⣭⣥⠄⢀⣤⡴⠶⣿⣿⠟⢁⣠⡾⠟⠋⠀⣀⣴⣿⠶⣿⠋⢻⠃⣹⣁⣠⣷⠤⣾⠷⠐⢿⠟⠃⢚⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢸⣷⡝⣾⡧⠡⢶⠏⠛⢁⣴⠟⣋⣤⠶⠾⠿⠿⠟⠉⢠⣧⣴⡿⢺⠟⣡⣽⣤⣴⡷⠤⣶⠿⠓⢺⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⣾⣿⡏⠉⣘⣳⣺⠃⡶⣫⠴⣋⡵⠶⠶⠶⢶⣦⣤⣶⡿⣁⣅⣤⠍⣠⣝⣩⣾⠧⣶⡿⠟⠲⣿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⢠⣿⣿⠇⠀⢻⣿⡁⠹⣧⡈⠳⣦⣉⠛⢷⣦⣄⠉⠋⢉⡼⣫⡴⣤⣖⣭⠴⢠⡴⠶⠖⢠⣴⣶⠷⠄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀⣼⣿⣿⠀⠀⢸⣿⡇⠀⢻⣷⡀⠘⢿⣷⡀⠘⢿⣷⢾⡫⣚⡥⠾⠗⢣⠶⠾⠛⠲⣶⣶⣿⠧
⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⢠⣿⣿⡏⠀⠀⣼⣿⡇⠀⠈⣿⣷⠀⠈⣿⣷⣀⣀⣴⣭⠼⠶⠶⠚⠛⠛⢰⣶⣶⣾⣧
⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⣾⣿⣿⠃⠀⠀⣿⣿⣇⣀⡄⣿⡿⢶⠆⣹⣥⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠉⠛⠛⠉⠛⠋⠙⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⠀⠀⢀⡀⠤⠔⣢⡄⠀⠀⠀⣀⠤⠡⠡⢀⡄⠀⢀⢀⣀⣀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢄⡀⠊⣁⣀⡙⠀⠀⠁⣀⣤⣤⣄⠀⠀⠀⠀⠁⣀⣀⣀⣀⡀⠀⡈⢁⣀⣈⣁⠀⢠⠀⠈⠑⢢
⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠈⠁⠊⣙⣻⠍⠀⠀⠈⢀⠘⠞⠀⠁⠀⠀⠀⠈⠀⠐⠃⠁⠁⠀⡁⠃⠐⠛⠉⠀⢘⠀⠀⠒⢸
⠀⠀⠀⠀⠀⠄⠀⡇⠀⠂⠀⠆⠀⠀⠉⢀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠑⠄⠀⠁⠁⠀⠨⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠥⠄⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠄⠑⠆⠀⡀⠀⠀⠀⠀⢁⠀⠀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⡠⢀⠄⠀⠀⢰⠀⠀⠀⠀⠀⡰⢀⠔
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠳⡄⠀⢺⣄⢤⡀⠀⢀⡶⠒⠀⠀⠀⠀⠐⠀⡐⠁⠀⢠⣄⡷⠀⠀⡀⠋⠀⠀⡰⢁⠊
⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡐⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡜⢀⠄⡂⢀⠀⠐⠀⠀⠄⡀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣀⣀⡀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡙⠿⠕⡳⠋⢀⣠⣿⣟⠎⣠⡾⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠐⡧⡤⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠀⠈⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣾⣿⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠙⢋⣛⣷⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡞⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⡿⢿⣽⣶⣶⠄
⠀⠀⢀⣴⣿⣿⡟⠛⠛⢛⣻⣿⡿⠿⠟⠛⢿⣿⣿⣿⣿⡟⠛⢫⣿⢿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⢀⣽⣿⣪⣿⣵⣿⠻⢻⣿⠇
⠀⠀⠈⣿⣿⣿⣷⡾⠿⠛⠉⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⢀⣾⢟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡾⢯⡾⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠹⣿⣷⣠⣤⣦⡀⣴⣾⣿⣻⣿⣿⣿⣿⣧⡾⢿⣼⣿⣿⣿⡿⠃⠀⣠⣄⣀⣰⠟⠈⢻⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡟⠁⢀⣾⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⣷⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⡿⣳⣿⢯⠯⡿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⣰⣟⣼⣿⡧⢋⢴⣿⣿⣿⣿⣿⣦⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣴⢯⣼⠿⣋⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢡⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠙⠻⢿⣿⣿⣿⣿⣵⣅⣤⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣳⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠁⠀⠀⠀⠀⠈⠙⠻⠿⠏

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢠⠄⠀⠐⠀⠀⠠
⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡄⠀⠈⠡⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⡄⠀⠈⠁⠀⠀⠀⠘
⠀⠀⠦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠦⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢀⠀⠙⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⢀⠉⠘⠡
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠈
⡀⢀⡀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⡀⢀⡀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠤⠁⠀⠀⢠⡁⠀⠀⠔⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠤⠁
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⠀⠘⠓⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠘⠓⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠛⠀⠀⢀⠀⠀⠰⠆⠀⠀⠁⢠⡛⠀⠀⠀⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠰⠆⠀⠀⠁⢀
⠀⠀⡀⢠⡤⠀⠀⠀⠀⠐⠀⠙⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠀⠀⠀⠀⠐⠀⠙⠃
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⠰⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⠰⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠆⠐⠂⢀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⠖⠀⠀⠀⠆⠐⠂⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠢⠀⠀⣠⣀⠀⠠⠖⠄⠀⠀⠀⠀⠀⠀⠠⠲⠄⠀⣀⣄⠀⠀⠔⠋⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣘⣓⣈⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣁⣚⣃⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠉⠳⢄⣀⠀⠀⠈⠫⣛⠦⠬⠌⠳⣄⠀⠀⠀⠀⣠⠖⠡⠥⠴⣻⠝⠁⠀⠀⣀⡠⠞⢉⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠣⠀⠀⠈⠉⠑⠒⠲⠮⠽⠿⣿⣒⡢⣷⡀⢀⣼⢕⣒⣻⠿⠯⠥⠖⠒⠚⠉⠁⠀⠀⠜⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⢧⡾⢛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢚⠉⠑⠢⠤⣤⣔⠉⠙⠀⠀⠀⡠⠚⠉⡉⠉⠉⠉⠉⠉⡉⠓⢄⠀⠀⠀⠋⠉⣢⣤⠤⠔⠊⠉⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠈⠀⠀⠺⣉⣀⠀⠀⠀⣈⡹⠆⠀⠁⠀⠀⠀⢨⠄⠀⠀⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣉⡁⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠈⣉⣽⠀⠀⠸⣍⡉⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⢈⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⢀⣤⠊⠀⢻⡅⡄⠈⠓⠂⠀⠀⠀⠒⠛⢠⣪⡟⠀⠑⣤⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠊⠙⠶⡃⠀⠀⠰⡶⠾⣦⣄⣀⣠⣄⣀⣠⡴⡷⢶⠆⠀⠀⢘⠾⠋⠑⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠱⣄⠀⠈⠀⠀⠀⢶⡀⢰⣶⠀⠀⠀⠀⣶⡆⢀⡶⠀⠀⠀⠂⠀⣠⠞⠀⡶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠊⠀⠀⠀⠑⠀⠀⠀⠀⢤⣀⡴⢋⡅⠀⠀⢸⣹⢧⡀⡤⠀⠀⠀⠀⠊⠀⠀⠀⠑⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢀⠀⠀⢀⡔⠀⠀⠀⠚⠂⠠⢤⣜⠀⠀⠀⠀⢣⡤⠀⠐⠓⠀⠀⠀⠢⡀⠀⠀⡀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⢯⢀⣀⠀⢠⣤⠀⠀⠸⣟⠋⡁⢈⠙⣻⠇⠀⠀⣤⡤⠀⢀⡀⡽⣄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡳⠊⠀⠲⠃⠈⠁⠀⠀⠀⠀⠐⣾⣯⠁⠈⢹⣷⠂⠀⠀⠀⠀⠀⠁⠘⠖⠀⠑⢞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡤⠄⠀⠀⣠⠀⢀⡠⠀⠀⠠⠟⠉⠀⠀⠉⠛⠆⠀⠐⢄⡀⠀⢄⠀⠀⠠⢤⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⣀⠆⠀⠀⠁⠀⡠⠄⠀⠀⠀⢫⣻⣤⣤⣟⡕⠀⠀⠀⢠⢄⠀⠈⠀⠀⠰⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡠⠴⠀⣠⡙⠃⢀⡠⠚⠁⠀⠀⠀⠀⠈⠓⢤⡀⠘⢋⣄⠀⠤⢤⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠄⠀⢄⠘⠛⠿⣥⣤⠴⠒⣛⡒⢒⣛⠒⠦⣤⣬⠿⠛⠇⡠⢄⡠⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⢩⢠⠞⠁⠀⠱⢤⣀⠚⠻⣯⠉⠉⠉⠉⠉⠉⣭⠟⠓⣄⡤⠊⠀⠈⠳⡄⡍⠱⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠦⣄⣈⠒⠉⠳⠦⠈⠳⣄⠀⠀⣠⠞⠁⠴⠞⠉⠒⣀⣠⠴⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠈⢈⠂⠀⠘⠂⠀⠀⠈⠉⠉⠁⠀⠀⡐⠃⠀⠐⡁⠁⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠀⠀⠛⠒⠚⠁⠀⠄⠀⠀⠀⠀⠀⡀⠈⠓⠒⠚⠀⠀⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⡠