Japanese maple Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⣤⣴⣀⠀⢠⡄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠨⠉⠛⠛⠹⢿⣿⣿⣿⣑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣶⣶⣶⣿⣿⣿⣿⣯⣥⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣲⣶⣤⣮⣻⣟⣿⣿⡿⣿⣽⣿⣿⣿⣶⣶⣄⣀
⠀⠀⠀⠀⢀⣰⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⢻⣿⠳⠄⢀
⠀⠀⠀⠲⠟⠙⠋⠉⠋⠉⠛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣤⠄
⠀⠀⠀⠀⠠⢤⣦⣦⣤⣦⣀⣹⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠒⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠟⠛⠇⠉⠉⠋⠘⠛⠛⠻⢋⡙⠙⠿⠻⢿⣿⡤⢄
⠠⢔⣿⣿⣿⣿⠿⠿⣿⣾⣿⣏⣿⣯⣿⠋⠙⢿⣿⡃⠀⣄⡀
⠠⠼⠋⠉⠈⠀⣀⣿⠿⠛⠋⠀⠙⠁⠀⠀⠀⠀⠁⠹⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠶⠀⠀⠽⠢⠀⠂⠀⠒⠐⠂⠀⠐⠀⠀⢤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿
⠀⠀⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀
⠀⠀⠀⠀⠙⢟⡿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⡛⢻⣿⣶⣄⠀⠀⠀⣾⡟⠻⣿⠀⠀⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⣾⣿⡟⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣀⠉⠀⠙⢆⠀⢸⣏⠁⠠⣿⠀⠀⠀⠀⠀⢿⡍⢻⣷⡀⠀⣴⣿⣿⠁⢸⣿⠃⠀⠀⠀⣀⣀⣠⣠⣶⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⡀⢿⣦⣿⡇⠀⠀⠁⠀⣀⠔⠀⠀⠈⢿⣧⠙⣿⣦⢿⣿⡇⢠⣿⢏⣠⣴⣶⣿⡿⣿⣿⡿⠋
⣤⠀⠰⢶⡴⢶⣿⣿⣷⣶⣶⣤⡀⢻⣷⠀⡏⠀⠁⠀⠀⠀⠜⠟⠀⠀⠀⠑⠶⣿⡷⠈⠧⢘⣿⡇⢀⣽⣿⡿⣟⣫⣴⣿⣿⠋
⠀⠀⠺⠧⠠⠀⠘⠛⠻⠿⣿⢾⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⣿⡟⠋⠉⣭⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠠⣷⣿⣶⣀⣦⣄⣠⠀⠀⠀⠀⠀⠀⢀⠌⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠛⢻⣿⣯⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⡾⠋⠀⠀⠀⠀⢀⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⣷⡆⢸⣼⡿⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠈⠀⠀⠀⢠⡼⣿⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⠁⠀⢋⣩⡶⢾⣿⣹⣿⣿⣿⣿⣿⠶⠗⠒⠛⠂
⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣿⣿⠏⣾⠃⣀⡻⠋⠀⠀⠀⠀⣸⣿⠦⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡏⠂⠀⠉⣽⣄⣠⣾⣿⣿⠿⠟⡛⠁
⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⡷⠶⢿⣾⢯⣤⡉⠁⠀⠀⠀⠀⠀⠻⣇⠀⣰⡀⠀⠀⠀⠀⢿⡟⠛⣽⡇⢀⠀⠠⠦⣬⣉⠉⠉⣀⣤⠾⠁
⠀⠀⠀⠙⠛⢿⣿⣿⣿⣷⣿⢶⡾⠇⢴⠶⠀⠀⠀⠀⠀⠀⠀⠠⠿⣦⣘⣿⣿⠀⢀⣰⣾⡥⣼⣿⣧⢈⣽⣶⣶⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣿⣿⣧⡴⢂⠀⡆⠀⠀⠀⠀⠀⠣⠀⢻⣿⣿⢠⠜⠛⣿⠀⢨⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢿⣽⣿⡿⠃⣈⡄⠁⠀⠀⠀⠀⠀⠀⢀⡀⢹⣷⢾⠀⢸⡧⣾⣾⡿⣍⠛⠿⠋⣉⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡠⠿⠛⠋⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡠⢇⣻⣿⠟⠁⣼⢏⣀⣴⣾⣿⢿⣿
⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⣴⣦⣤⡴⢿⡇⠀⠀⢤⡆⠘⠁⡀⢹⡿⠛⢁⣾⡧
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠘⣻⣿⣿⣿⣿⡆⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⢉⣿⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡧⠀⢀⡾⠛⣤⡉⠹⣿⢻⡇⢀⠄⠀⠀⠀⠀⢀⣠⢴⣿⠇⠀⠀⠀⣀⠀⠒⣶⣶⣶⠶⠶⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⠃⣰⡿⠁⠀⠈⠻⡦⣿⣿⠀⠀⠀⠀⠻⣿⣆⠸⡇⠶⠋⡴⠄⠀⣴⣧⣤⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠇⣼⣿⠁⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠸⣿⣿⣏⠁⠀⠀⠀⠀⠀⣀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣉⣿⠞⢻⠿⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⠀⣴⣿⣿⣿⡿⢿⣿⣶⣶⣿⣿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠋⠙⣤⠝⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣯⡙⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠿⠋⠉⠀⠈⠁⣀⠀⢨⣄⠶⢄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⣻⣿⣤⣧⣬⣄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀
⠀⠘⢿⣿⣿⠉⢁⠀⣄⠀⠀⢀⡿⠃⣀⣤⡖⣾⣷⡈⢻⣦⢠⣧⠀⠀⠀⠀⢂⣼⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⢀⠘⠾⠈⢃⡄⠉⣴⣾⣿⣿⣿⣿⣿⣹⣯⠈⡷⡟⠀⠀⠀⠀⠀⠙⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠍⠙⣿⣿⣿⣿⣧⣍⡉⠛⠿⣿
⠀⠀⢀⣤⡟⣡⢦⢀⡶⠟⢀⣾⣿⣿⣿⣿⣿⡟⣿⣿⠏⢰⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠘
⠀⣴⣿⣧⣴⣿⠿⠋⢀⣴⣿⣿⣿⣿⡿⢛⣿⣷⣿⠏⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠂⠀⠀⣿⣿⣿⣏⠛⠟⠻⠛⠻⢶
⡷⢾⣿⠿⠛⠁⠀⣠⣾⣿⣿⡿⠟⠉⢀⣾⣿⣿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢦⡀⠀⠁⠀⠀⣨⠀⠀⠈⠸⢃⡈⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣼⣿⣯⣥⣤⣤⣤⣤⣿⣿⣿⣥⣤⣤⣤⣼⣥⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣼⣿⣦⣤⣤⣤⣽⣧⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣄⡀⠀⣿⣿⣿⣿⡗⠀⠀⣀⣤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣿⣿⣆⣿⣿⣿⣿⣧⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⡀⠀⣼⠇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡦⠟⠀⠀⢀⣀⣀⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣛⣁⡀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠟⠒⠂⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣦⣄⡀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⡰⠟⠋⠹⣶⣄⣹⣿⣿⣅⣠⣧⡀⠀⢠⣿⣿⡗⠀⠀⢀⣀⣤⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣼⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣦⣿⣿⣿⣣⣶⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣽⣿⣿⣿⣿⣥⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣿⠋⠙⠛⠉⠉⠀⠙⣿⣿⣿⣿⣭⣥⣄⡀
⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⢈⣿⣿⡿⢿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣴⣿⣿⣿⢟⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠛⣿⣿⡄⠈⠉⠙⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⣼⣿⡿⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠋⠀⠀⢹⡿⠃⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠈⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⣴⣤⣄⣦⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣦⣶⣶⣷⣄⣈⣿⣿⣟⣷⣼⣯⡿⠓⠂⠀⠀⠀⠀⠀⠀⡄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡁⠛⠛⠋⣿⣿⣿⣿⣧⣽⣿⣿⣷⣤⢀⣀⣠⡴⣾⣷⣿⣿⣿⣥⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⡀⢀⣰⣮⣻⣧⣄⠀⠄⠐⠂⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣶⣿⣿⣝⣻⣿⣹⡿⠍⠉
⠀⠀⠀⠀⠀⢠⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣴⣶⣫⣿⣿⣿⣿⠿⣿⣿⠟⢛⣿⣟⠛⣿⣷⣿⢟⣢⣤⠦
⠀⠀⣠⣄⣴⣾⡟⠋⠈⠿⠟⠟⠟⠛⠻⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣄⣹⣿⣷⣾⣿⣿⣼⣿⣿⣥⣤⡀⠸⣿⣴⣿⣿⡗⠂
⠐⠉⠛⠹⠋⠛⠀⠀⠀⠀⢴⣀⡀⠀⠀⣀⠩⣭⣙⢻⠿⠿⣿⡿⠿⠿⣿⣿⡟⠻⠿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⣿⣷⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣷⣾⡟⠛⠈⠙⠛⠀⠀⠀⠈⠁⠀⠀⠀⣽⡿⠀⠉⠈⠉⠋⣿⠛⠿⣿⣷⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠛⢿⣿⣧⣖⢀⣶⣴⣖⣀⡀⡀⢀⣠⣾⣿⣧⢀⡀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⢫⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢿⣿⣿⣿⣿⣷⣦⡤⣠⠄⠀⠀⠛⠿⡿⠿⠀⠂⠀⠉⠛⣿⣴⣦
⠀⠀⠀⠀⢀⣠⣄⣼⣷⣿⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠃⠀⠀⣿⣿⣿⣿⠿⢻⣿⣿⣿⣴⠀⠐⠿⢳⡄⠀⠀⠀⠀⠉⠁⠶
⠀⠀⠀⠐⠉⠋⠹⠋⠟⠉⢉⣭⣿⣿⣻⣿⡏⠀⠾⠀⠀⠀⢻⣿⡀⠀⠀⠈⠛⣿⠃⠀⠀⠀⠈⠙⠛⢷⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢋⣉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠛⠀⠀⠁⠀⡀⠀⠀⢀⣀⣤⡾⣿⣿⣧⣀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡄⠖⠒⠃⠀⠈⠉⠤⠀⡀
⠀⠀⠀⠀⠀⢐⡞⢐⠷⠖⣇⠐⢂⡠⡠⠀⠀⠀⠐⠒⣢⠴⠀⠘⠛⢓⣂⣀⡀⢤⠔⢉⠁
⠀⠀⠀⠀⠀⠃⠀⠸⡃⣤⠿⠠⣀⠠⠉⡤⠀⠀⠦⠦⣌⠖⠀⠀⠈⢿⡤⠤⠈⠑⠀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⢠⣔⡰⠟⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⣁⠉⠛⠛⠒⠈⣇⠀⠀⠄⠒⠓⠒⠣
⠀⠀⠀⠀⠀⠀⠊⠈⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣯⡂⠤⠖⠦⠀⠀⠐⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠋⠳⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⠲⠿⢀⣀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣏⣴⣿⠿⣸⣉⢋⣽⡀⠀⠀⡀⠀⠀⠀⠀⣀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠩⢿⣿⣰⠿⣿⣛⣛⠏⢀⢀⣀⣠⡄⠀⠀⠑⠒⠂⠂⢿⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡶⢦⣤⡄⢀⣤⡉⠉⣿⢿⢿⠉⠁⠀⡟⠻⠙⠑⠀⠀⠂⠀⠈⢃⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⣬⡽⠿⠞⢿⠻⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠀⠀⠉⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⡀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢻⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣧⠀⠀⠲⢶⣿⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⢦⣾⣿⣿⣿⣿⣿⠷⠄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⣿⡏⠉⢰⣿⣿⢻⣿⠄
⠀⠀⠀⠀⠒⠉⠈⠈⠁⠁⢸⣿⠿⠀⠙⠀⠀⠘⡿⠋⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀⡜⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣁⡀⠀⢀⠐⠀⠥⢀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣶⣯⣥⡀⠈⡈⠁⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⣆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢙⢹⡿⢻⡟⠿⠷⣿⣧⣠⡀⠀⠤⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠗⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣙⣳⠏⠀⠿⠿⢻⡟⠁⡠⠟⠚⢯⢁⣿⡷⡩⢀⠀⠰⠰⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣛⣿⣗⡏⠀⢠⣾⣸⠇⣴⠀⢶⡄⠀⠀⠀⠈⡧⢄⡀⢈⣿⣇⡀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⣠⣿⣽⣿⣿⠟⣃⣈⢺⡽⣡⡆⣣⠖⠤⠢⠀⠀⠀⠀⠁⠸⡏⠉⠀⣼⠟⠋⢘⣑⡃⠀⢤⡀⠐⠀⠚
⠀⠀⠀⠀⠀⠸⣧⣎⣘⣿⣯⣌⣿⣧⣴⣷⣿⣾⠬⣼⡚⠉⠀⠐⠀⠀⠀⠀⠉⠋⣳⠏⠀⠀⣈⢿⣷⠀⠀⠀⡰⠶⠶⣄⣠⡆
⠀⠀⠀⢠⣖⢺⡥⡾⢸⠿⠿⣿⣯⣽⣬⠹⢮⠹⣆⣿⡶⣿⣦⣤⡅⣁⠽⠈⢳⣟⡉⠀⠀⠀⡹⠻⣟⣦⠀⠀⢃
⠀⠀⣸⣿⣿⣿⣣⡶⠁⢀⡰⠆⢹⡝⡿⢤⡐⠀⠠⠉⣧⠙⠋⠉⠁⣬⣶⠎⠛⢈⢳⡆⠀⠀⠀⢠⡏⠉⡿⠇⢾⣜⠆⢀⠀⠀⢈⡦⠀⠀⠀⠀⢀
⠀⢠⣿⣿⣋⣹⣟⣒⣳⣿⣷⠄⣀⠀⠀⢀⠙⢦⡤⠒⠋⠠⠆⠀⠸⣿⠏⡹⠿⠋⢠⠀⢠⠀⠐⠈⢳⡾⣥⣠⡏⡾⣶⢿⠃⢰⣟⡇⠀⠀⠀⠀⠈
⣴⣾⣿⣿⣿⣿⣏⣻⢼⣿⣶⢦⠉⠀⠀⣸⡇⠀⣧⠀⢸⣿⡆⡀⠀⠠⡿⠛⣶⢽⣷⣄⡰⣴⠜⠀⠘⣆⠀⠹⣆⠀⢸⣟⠦⠙⠛⠀⠀⠀⠀⠀⠀⡀⡄
⢻⡿⣦⣽⣿⣿⣿⣿⡄⣿⣿⣷⠞⡏⠀⠛⢿⣴⣎⣉⡶⠼⠟⠋⠀⠒⠀⢄⡿⠈⠛⠉⠁⠀⠀⠀⢰⠋⠀⠀⣻⡧⣈⠡⠆⠀⠀⠾⠀⠀⠀⠐
⠘⣷⢿⣿⣹⣏⣿⣿⣿⢱⡏⣿⣿⣼⣷⡆⢺⣿⢛⣧⣂⣠⡀⠰⠜⠃⠀⠘⠻⢦⡄⠀⠀⠀⠀⠀⠈⢻⣶⠋⠀⠀⡟⣀⠀⠀⠀⠐⠀⠀⠠⣤⠁⢀
⠀⠂⠀⠿⢻⠏⠙⠿⣿⣿⣟⣿⡷⠐⠃⠄⣈⠻⢍⡉⠉⣹⣧⠀⠀⠀⠀⠀⢀⣾⣿⠿⠷⣦⡀⠀⠀⢸⣿⡄⠀⠀⠀⠈⠐⠛⠲⢠⠧⠀⠂⠀⢠⣄
⠀⠀⠀⠃⠀⠀⠀⠀⢨⣽⢻⡧⠈⠁⠠⠞⡿⣧⢮⣠⠋⠹⣿⣄⠀⠀⠀⠀⣾⡿⠁⠀⠀⠹⣷⣄⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠻⠿⣦⣄⣸⣿⠁⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣟⣓⣛⣉⣙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣶⣐⣒⣔⣂⡖⣆⡖⣘⣤⡖⡀⢸⡇⣧⣞⣰⣲⣼⣰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠏⠈⢹⠁⠀⠈⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⢹⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠏⡆⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⠾⣿⣼
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⠟⢣⣯⢽⣧⠀⠀⠀⣠⣾⡷⣿⣽⣻
⠀⠀⠀⠘⠻⣵⣶⣤⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢲⣯⣿⡷⡏⣟⣷⣽⣇⠀⣼⣭⣾⣹⣯⡿⣿
⠀⠀⠀⠀⠀⠈⠻⣗⢿⣧⣥⣼⣦⣤⣄⣀⠀⠀⢘⣾⣯⣛⣿⡝⣹⡞⣿⣿⡟⢻⣟⣽⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣭⣯⣿⣿⡿⣿⣦⣴⣿⣯⢻⣿⣯⣿⣿⣹⣻⣿⡿⣿⡟⣳⣾⡇⠀⠀⢀⣀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣽⣯⣿⣿⣿⡒⣧⣿⣿⣟⢿⡻⣭⣿⡿⣿⣹⢣⣽⣿⣿⣿⣿⡿⡷⢞⡿⣟⣺⣳⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢶⠽⡗⡏⣟⢾⣎⣿⡞⡻⡴⣍⣿⢮⢹⠿⡨⢯⠲⣿⠟⡿⣟⣿⣾⣟⣤⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣾⣶⣟⢿⢽⣦⡣⡳⣧⡹⣯⡭⣣⣜⠵⡻⣄⣶⢷⣿⢺⣱⡾⠎
⠀⠀⣠⣀⣀⣀⣀⡀⣀⣠⣤⣤⣴⣴⣿⣿⣟⣿⣾⡧⡕⣽⡳⣷⣛⣿⣝⡿⣾⣍⣾⣻⠯⡵⣀⠶⠋
⠀⠀⠀⠉⠛⠻⣿⡓⣾⣽⣧⣻⣜⣿⣿⣯⣻⣷⣹⣷⣿⡦⡼⢿⣿⣿⣾⣿⣿⣓⢧⡿⠻⠟⡿⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢫⣤⡭⡟⢏⣝⣿⠯⣺⡼⣵⣾⣾⣿⣿⠟⠉⢧⠙⠩⠿⠯⣿⢿⠿⠾⠻⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠛⠺⠾⠿⠿⢭⢷⡟⣪⠇⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⢹⡨⠚⠁⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠃
⠀⠀⠀⠀⠀⢀⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠒⠀⠀⠀⠀⠳⣀⣠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠺⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠙⠂⠠⠤⣤⣀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠀⠀⠀⠈⢿⠛⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠿⠉⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠂
⠀⠀⠀⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡠
⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠢⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡼⠁
⠀⠀⠀⠀⠀⠀⣒⠀⠉⠀⠠⠤⠤⠤⠶⣤⣿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠰⠂⠀⠠⠀⠐⠋⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⠀⠀⠀⠠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠈⠀⠆⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠈
⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⢄
⠀⠀⠀⠀⠀⠈⠉⢳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣈⣓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠀⠁⠈⠉⠀⠀⠀⠀⠀⠂
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡟⠀⢄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢞⠟⠁⠀⠐⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠
⢠⠀⠁⠀⠀⡀⠀⠀⠀⣤⡒⠂⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⢁⡄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠈⢂⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣴⣤⣄⣴⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⠀⠁⠁⠀⠀⠀⢀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣷⣶
⠓⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠄⠂⠀⠀⢹⡿⠃⠙⠉
⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠘⡁⠀⠂⠀⡐⢤⣄⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠈⠉⣺⣿⣿⣠⣿⣶⣾⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⠛⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⣰⠁⠀⠶
⠀⠁⢰⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠤⠀⣲⠞⠛⠻⣇⠐⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⢠⠋⠁⠊⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠶⢦⣤⡄
⠀⠁⠀⠀⡀⠀⠀⠀⠠⠤⣀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠉⢘⡄⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠆⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹⣄⣸⣦⣶⣾⠋
⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠋⠀⠀⣠⣖⠀⠀⠀⠀⠀⠀⢈⣿⣿⡛⠉
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⢄⡀⠀⠸⣿⣷⣤⡆⢠⣾⡿⠋⠄⠀⠀⠀⠐⠀⠈⠁⠀⠙⠦⣀⡒
⠁⠀⠀⠀⠀⠀⠀⢠⠀⠠⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⣙⠇⠀⡸⣿⠗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠔⠒⠊⠩⠛⠛⠛⡿⡿⢉⣤⢚⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆⠀⠀⠀⠀⠀⢀⠀⡈⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠛⡀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠤⣤⡁⠠⠊⠀⠀⠀⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦⣀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠓⠀⢢⢀⢐⠠⠀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠐⠂⢠⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡤⠈⢕⣣⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠈⠲⣄⠀⢀⡠⠀⠐⠀⢀⡀⠀⣠⣤⠵⣧⡔⠋⠉⢉⡓⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠈⠊⠁⢹⣿⣶⡗⠠⡀⠀⠀⠀⠐⠏⡀⢲⠀⠀⠁⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢩⡀⢀⣾⣿⠿⠁⠀⠈⠒⣄⠀⠠⠔⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠃⠀⠀⠀⠀⠘⡧⠈⠈⠀⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠛⠙⠀⣤⣞⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠐⠀⠀⠀⠒⠉⣀⣀⣠⠞⠁⡉⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣮⠇⢀⠈⢠⠀⢠⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠆⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠈⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⢆⠀⠀⠀⢦⠀⠠⠀⠀⠀⠀⣄⠀⠈⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢃⠐⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠉⢷⡛⣷⣦⠀⠀⠀⠀⠊⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠰⠀⠋⠀⠀⠀⡰⠻⢿⣿⠛⠉⠉⢀⠀⢀⡠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⡘⢠⠚⠂⠠⠀⣰⡾⠇⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⢀⠹⠆⠘⠁⠘⢆⠀⠀⢠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠣⡀⠀⠠⠀⠀⡌⠄⠀⠀⡷⠀⢀⣑⣶⠻⣦⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠤⢄⠀⢙⣄⣶⣠⠈⠀⠀⡠⠎⠀⠀⠈⠉⠙⣿⡅⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠀⠄⠄⠀⠙⣿⡋⠅⣽⡧⠒⠉⠐⠂⠠⢶⠀⠀⠐⠈⠇⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠘⠂⠀⠳⢐⣻⠤⠤⠀⠐⢿⣿⣾⠟⢿⡀⠂⠀⠀⠀⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⠈⠁⡌⢽⡀⢀⡠⠀⠀⡟⠈⢀⠀⠙⢄⠐⠂⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢠⠴⠾⡃⡠⠂⡆⠀⠸⠀⠦⠀⠈⢃⡀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠂⠀⠉⢀⡞⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠏⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⢀⣤⣄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠒⠺⠷⣼⢵⣶⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠦⠈⠀⢀⣶⣆⠀⠀⠀⣁⠸⢆⠀⠀⢀⡦⡽⣷⣤⣄⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⣗⠒⠖⠈⠛⠋⣤⣀⡀⢀⠀⠀⠑⢄⠀⠀⠀⠉⠖⠀⢉⠀⠶⠆⠀⠀⠠⡀⠀⠀⢼⡷⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣰⢛⣛⣁⣬⣈⣳⣶⠶⠿⠦⠤⠶⠲⢴⠿⣿⠦⠴⠿⠶⢤⣽⣤⢤⣀⡀⢀⣴⠆
⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠒⠒⠂⠛⢷⣌⠉⠉⠛⣦
⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⠂⢠⣤⣄⠘⠀⠀⠈⠾⠀⠀⠔⡆⠀⠀⠀⢀⣀⠰⡆⠀⠀⠀⢀⣀⣹⣶⣦⣾⠗⠢⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢛⠛⠁⠀⠐⢀⡂⠂⠒⠚⠒⠶⢦⡄⣘⠟⠗⠐⢃⡬⠛⠉⠁⢀⣠⡤⠶⠋⠙⠒⢦⣌⡂⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡰⠇⠀⠀⠀⠈⠁⠀⠰⢷⠄⠀⠋⠐⠊⠡⠄⠚⢩⣄⡤⠒⠈⣉⠋⠀⠀⠀⠀⠀⣀⣼⠿⠶⣌⡑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⢩⣥⡄⠀⠚⠢⠀⠀⠀⠀⠴⢾⠉⠀⠀⠀⠀⠉⠲⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⠿⠋⠰⣦⡄⠀⠁⠀⣦⡀⠛⠋⠀⠀⠀⠀⢀⡴⣿⠀⢰⣿⡇⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⣆⡙⣃⠀⣼⠟⠠⠂⢰⡉⠛⠀⠀⠀⠤⠀⠀⠀⣴⡤⣔⠾⠋⣱⡌⠳⢀⣥⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠀⠀⠉⠀⠀⠈⢤⠄⠀⠀⠀⠀⢀⠤⠔⠊⣻⠿⠁⠀⠀⠀⠀⠛⠸⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⢠⣿⠀⠈⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣤⣆⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠅


⠀⡄
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢠⣴⡀⡶⢰⣶⠶⡖⢾⣶⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠨⢫⠃
⠀⠈⢻⣳⠠⣿⢂⣷⠃⡼⠀⠀⠀⠀⠀⠀⢰⠰⡀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⠁⠀⠠⠔⠁⠬
⠀⠀⠀⢻⡆⣿⠼⣿⣼⠁⠀⠀⠀⠀⠀⢠⠈⠀⠈⠦⡀⠔⠉⠀⠆⠀⠀⠀⢀⠀⠐⠀⠀⠀⠅
⠀⠀⠀⠘⣝⠛⠀⠸⡩⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠈⠑⣦⠏⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⢠⣤⠀⡆⠾⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠠⠀⠠⡅
⠀⠀⢠⣭⠤⡇⣿⠂⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠃⡀
⠀⠀⠀⠿⢰⣇⣀⠀⠀⠀⠀⠀⠠⡆⠄⠀⠀⠀⢁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡸⠋
⠀⠠⣶⡁⡑⠊⢛⣦⠀⠀⠀⠀⠀⠘⠀⠐⢄⠀⠈⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⡰
⠀⢰⣦⠰⡄⡷⠦⢋⣀⠀⠀⠀⠀⠀⢁⠀⠀⠑⢀⠀⡰⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢂⠀⢨⣀
⠀⠠⠌⠀⠀⣦⠃⠈⠉⠀⠀⠀⠀⠀⠀⠢⠤⠀⠂⣹⢂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠛⠃⠂⢄⣀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠂⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⣄⠀⠸⡟⠹⠗⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠂⢀⡀⠀⣠⠆⠀⠀⢤
⠀⠀⠀⠉⠔⢂⣹⠀⠃⡛⢁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡤⠀⠱⠀⠢⠐⠄⡀
⠀⠀⠀⠘⠓⢹⠁⠣⡄⠀⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠰⠀⠀⠀⢀⠠⠀⠈⠀⢠⠀⠈⠀⠀⡀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠤⠠⠀⠄⠄⠀⠀⢧⠀⠀⠀⠀⠀⢰⠁⠀⠀⡖⠀⠘⢀⣄⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⢸⠠⠀⢰⠀⢐⠀⠴⠀⢆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡀⠀⠠⡿⠈⡇⢄⠀⢨⠀⠀⠀⠀⠈⠂⠀⡌⠀⡆⠨⢄⢠⡀
⠀⠶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⢼⡇⠀⢻⠈⠄⠀⠀⠀⠀⠀⢀⠄⠀⠁⢠⠁⠀⠈⡄⠐⡄
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⡘⢏⠂⠈⢧⠃⠀⠀⠀⠀⡴⠁⠀⠀⠀⡇⠀⠀⠀⠀⠲⠇
⠀⠀⠀⡠⠁⠀⠀⠀⡀⠚⠀⠁⢠⡁⠀⠃⠀⠓⣞⡚⡆⠀⠀⠀⢜⠁⠔⠁⠀⡇⠁⡀
⠀⠀⠀⠗⠀⠄⠰⠚⠇⠀⠂⠀⠐⠀⠘⠀⠀⠚⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣷⡀⠀⣧⣼⣃⠀⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢰⣆⣬⣿⣿⣿⣿⣦⣿⣿⣿⣷⣿⣿⣿⣏⣴⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠠⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡴⡞
⠀⠀⠀⠀⠀⠀⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣂⣠⣤
⠀⠀⠀⠀⠀⠀⢚⣿⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠈
⠀⠀⠀⠀⠘⣿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠻⣿⣿⡿⢟⣁
⠀⠀⠀⠀⠀⠁⠀⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣋⡀⠀⠙⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣊⣿⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠛⠁⠈⠋⠀⠀⠀⠀⠉⣿⣿⣿⡟⠻⠇⠀⠈⠉⠀⠙⢿⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠙⠀⢀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠠⡇⠀⠂⠀⠀⠀⠈⠃⠔⠀⠠⡔⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⢠⠀⠀⠀⠀⠀⠐⡀⠀⢠⠔⠁⠀⢈⠜⠏⠀⢀
⠀⠀⠀⠀⠀⠐⠢⡀⠁⠀⠈⠀⡀⠈⠠⠀⠀⠐⠄⠸⢀⠄⠈⠀⠘⠀⡀⠿⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡁⠈⠃⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⡡⢁⠊⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡁⠀⠀⠀⠈⢀⣂⠔⠁⠀⠓⠁⠀⠀⣀⠀⠀⡐⠢⢤⡤⠄
⠀⠀⠀⠀⠀⠰⠄⣀⣀⣀⠀⠈⠀⠱⡄⠀⠀⠂⠘⠁⠀⠀⠀⠀⢀⣀⠀⠁⢀⠠⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠐⠢⠀⡱⣐⠀⠄⠿⢀⠔⢀⡤⠴⠉⠀⠂⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡠⠳⢌⢆⠐⠎⣠⠔⣋⣀⣤⡄⡀⠠⠦⣄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢱⣶⡾⠃⠉⠁⠀⠂⠀⡀⢀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢂⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡗⢺⢣⠏⣠⡀⣀⢠⣠⢏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠀⠀⠈⠈⠀⢡⠏⠉⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⡀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⡘⠀⠰⠀⠀⠀⠀⠆⠀⢀⠀⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠁⠀⠀⢣⠀⠀⡜⠀⠀⠈⠉⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⡀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⢀⠄⠀⠃
⠀⠀⠀⢀⡤⢀⡀⠀⠀⠀⠀⢀⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡀⠀⠀⠀⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠆⠀⢉⠙⠲⠀⢤⠞⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠳⡄⠄⠂⠋⡉⠀⡰
⠀⠀⠀⠀⠘⡄⠈⠑⠦⡀⠀⠀⠀⠰⡀⠀⠑⠢⢄⡀⡠⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣄⠀⡠⠔⠋⠀⠀⠂⠀⠀⠀⢀⠴⠊⠁⢠⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠳⢄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡠⠞⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠱⢄⠘⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠤⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠠⡄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⡤
⠀⠀⠀⠀⠀⡀⠀⠂⠀⣀⡀⠀⠀⠀⠀⠈⢆⠀⠀⢰⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡆⠀⠀⡰⠃⠀⠀⠀⠀⠀⣀⠠⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠁⠒⠂⠤⠄⣀⣱⡀⠈⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠁⢀⣎⣀⠠⠤⠐⠒⠉⠁⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠇⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠁⢀⡀⠊⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⠀⠐⠒⠠⠤⠤⠄⢀⣀⣀⣱⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣏⣀⣀⡀⠠⠤⠤⠄⠒⠂⠀⣴⡁
⠀⠀⠀⠀⣀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄⣀
⣤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠉⠑⠒
⠀⠑⠢⣀⠀⠀⠀⠀⢀⣀⣀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣀⣀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⢉⣩⠟⠃⠀⠒⠒⠒⠒⠒⠂⠀⠀⠠⠄⢠⡷⢾⣤⠤⠄⠀⠀⠀⠐⠒⠒⠒⠒⠂⠘⠻⢍⡉⠁⠀⠀⠀⠀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣰⣆⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠎⠁⡌⠳⣄⠀⠑⢄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⡠⠊⢀⠴⠊⠀⠀⠀⡇⠀⠀⠑⠦⡀⠑⢄⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠔⣋⠤⠚⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠓⠤⣙⠢⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢡
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢀⠋
⠀⢀⡀⢀⣀⡀⣀⠀⡀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⢀⡤⠀⢺
⢿⣿⣷⠺⣿⣇⣿⡿⡟⢿⣟⠟⣿⢿⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠚⠛⢡⡄⠀⠀⠰⢋⡠⠀⣿
⠈⢿⡹⣆⠘⣼⣿⠀⣷⣸⠏⢰⡏⠜⠀⠀⠀⠀⠀⢸⣇⠹⣦⡀⠀⠀⠀⢀⣤⠞⠉⡏⠀⠀⠀⣸⠀⠈⠀⠁⡶⠋⠀⠀⠀⢍
⠀⠀⢱⣿⡀⣿⡟⣠⣿⡏⣰⠟⠁⠀⠀⠀⠀⠀⢀⡾⢋⠀⠉⠻⣦⣀⡴⠎⠀⠀⠀⡇⠀⠀⠀⢹⠀⠸⣧⡏⠉⣡⠔⠀⠀⢸
⠀⠀⠀⣿⣥⢻⡿⠿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡄⠀⣠⠀⠛⠀⡆⠀⠀⠀⡇⠀⠀⠀⢸⠀⢰⡯⠙⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡝⠿⢧⠀⣽⡟⣹⠀⠀⠀⠀⠀⠀⢸⠿⡀⠸⡇⠀⡏⠀⣠⣠⡇⠀⠀⠀⢱⠀⠀⠀⠀⣿⣏⡠⠜⠃⠀⠀⠀⣀⠈⣿
⠀⠀⠀⠈⠙⢶⣄⣀⣴⡶⠋⠀⠀⠀⠀⠀⢠⠷⠐⣇⠀⣿⣰⠃⠀⠀⢀⣽⠀⠀⠀⢸⡅⠀⠓⣶⠿⠀⠀⠀⠀⣀⡤⠊⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠙⢆⠸⡇⠀⠀⠀⠀⠙⡀⠀⠀⠀⣗⠈⣹⡇⠈⡀⣤⠶⠋⠁⠀⠀⢀⠔⣿
⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⢀⣿⠀⢷⠀⠈⠻⡇⠀⣠⠀⠉⠙⢣⠀⠀⠀⠙⣰⠯⠙⠋⠁⠀⠀⠀⠀⣠⣔⠁⠠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢧⡀⠀⢰⣶⠋⠀⠀⠀⠙⢧⠀⠈⣺⠋⠤⠀⠀⠀⠀⣠⠶⠞⣀⡀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⣀⠀⣤⣄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠻⣤⡀⣧⠀⠀⠀⠀⠀⠘⢧⣼⠏⠁⢀⣀⡤⠖⠛⠓⠀⠀⠀⠀⠀⢀⠴⠀⠛⠶⣦⣤⣶
⠀⠀⢴⣿⣶⡆⢻⡔⣻⠛⠁⠀⠀⠀⠀⢠⣗⠀⠀⠀⠀⠈⠑⢷⡄⠀⣤⠄⠠⠔⣺⠟⠒⠦⣉⠉⠁⠒⠒⠂⠀⠀⠀⠀⠠⠁⠀⡀⠄⠒⢉⡴⠋
⠀⠀⢠⣬⣈⣧⣬⡰⣿⡿⠀⠀⠀⠀⠀⠀⣽⠶⢦⡀⠀⠀⠀⠀⢡⡜⠀⢀⠀⢠⡟⠛⠛⠂⠈⠀⠀⠀⠀⡄⠀⠸⢀⣠⡦⠐⠈⠉⠐⣻⠏
⠀⠀⠈⣿⣿⢃⣿⡉⠋⠀⠀⠀⠀⠀⠀⠀⠈⣶⠦⠼⢦⡀⠀⠀⠘⡅⠀⠀⣉⡿⣉⠱⠆⠀⠀⠀⠀⠀⣘⣀⡴⠛⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⢈⡻⡀⣿⢯⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠄⢩⣦⣄⡀⢳⡀⠠⣾⠃⠒⠃⢀⠞⢠⣏⡀⠚⠉⠀⠈⠉⠀⠀⠀⠉⢠⡞⠁
⠀⠀⣶⣾⠉⡙⣿⠊⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠠⠤⠬⠱⣦⣔⣲⠃⣌⣀⠤⠾⠶⣉⡉⠀⠒⠒⠒⠀⠀⠒⠒⠀⣱⠏
⠀⢀⣉⠛⢰⣃⣹⣶⣞⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⠴⠞⣻⡿⣋⡁⠀⠀⠀⠀⠈⠉⠛⠢⠤⣤⠀⠠⠄⢠⡞⠁
⠀⠘⣿⡗⠻⣿⣸⡟⣏⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠸⠋⠳⢤⡄⢀⣄⠀⠀⠀⠀⣀⡁⣤⡼⠋
⠀⠠⡤⠷⢔⡇⠹⣧⠛⠦⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠘⠠⣃⠀⠠⠀⠙⣿⠶⣄⠤⢤⣌⣍⠁
⠀⠀⢶⣷⣾⢷⡀⣿⠀⣿⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠈⠓⠲⣤⣄⡟⣴⡼⠷⠞⠉⠁
⠀⠀⠈⠉⠀⠀⠈⢻⢾⣷⣌⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠙⠶⣤⡀
⠀⠀⠀⣤⣤⡀⠀⠘⣏⣋⡸⠿⠃⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡻⢏⡉⠙⣦⣤⣀
⠀⠀⠀⠙⠛⢓⣶⣆⣹⡟⠀⠻⢐⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⣄⢈⡋⠙⢄⠙⢻⢿⣦⣄
⠀⠀⠀⠀⣠⣮⡠⣶⣿⢿⣄⠀⣻⣗⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣷⠀⠀⣿⡉⠁⠀⠀⠙⠤⠀⢿⡿⠇
⠀⠀⠀⠀⠙⠛⠓⣼⣇⠈⢻⣾⠃⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⠀⢿⠧⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣦⡀⣀⣤⣤⡤⣤⣤⣄⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡠⠚⠗⠢⣼⢦⡘⡷⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⢿⣧⡀⠈⠂⠨⠤⣍⡉⠳⡄⠈⣿⠀⠀⠀⠀⠀⢀⣼⣥⠔⠻⡤⢿⣦⠈⣿⠛⠡
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠋⠈⠠⢄⡙⢿⣌⠃⣤⣀⣀⣈⣳⣤⡀⢻⡆⠀⠀⠀⣴⡿⢁⡽⠀⠀⣧⠈⠛⢿⣄⠙⠶⠈⢳⡦⣤⣀
⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⠒⣤⡤⠴⠚⠋⠛⢿⣍⠉⠀⣀⣤⣿⠋⢘⣿⢀⡀⢾⠻⠇⢈⢁⣤⣤⡏⠡⡀⠘⠿⢟⠀⠙⢆⠀⠚⠉⢳⠄
⠀⠀⣀⣤⠚⣁⠠⠶⠖⠂⠉⢀⡀⣠⠤⠔⠒⠐⠛⣳⣶⣋⢸⣿⠀⠀⣿⡌⢹⠾⠆⢒⣬⢇⣀⡜⠙⡄⢹⡳⣶⠚⠀⠀⠀⠑⠂⠾⠛⠁
⠀⠛⠳⠴⣤⡉⠀⠀⠀⠀⠐⠉⠁⡀⠀⠀⠠⡠⣞⠃⠀⠙⢻⣯⡀⡀⢸⣇⡘⡇⠰⠋⡅⠘⠁⢰⠤⣇⠘⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢈⡃⠈⣉⠶⠆⠘⠋⠙⡉⣲⠟⠁⠌⠀⠀⠀⣘⢿⡙⢦⣀⢻⣧⠙⣶⠏⠀⡀⢠⡏⢀⣿⡄⠀⣩⡯⠹⣆
⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢀⣤⢀⣤⠞⠱⠆⠀⠘⠀⠀⠀⠿⠈⠻⣆⣽⣦⢿⡆⢹⣀⡴⠁⠸⡇⠈⣋⣧⢰⠋⢉⣦⠻⡏⠲⢤⡀
⠀⠀⠀⠀⣠⠞⠀⠈⠁⠀⠠⣠⡖⠁⠀⠀⠀⠀⡾⠀⠀⢾⠀⠃⠀⢈⡿⣾⣿⣿⠀⠉⠀⠀⠀⠙⢦⣬⢿⡎⠀⠈⣇⣠⠋⢲⠞⠛⢦
⠀⠀⠀⠀⠙⠇⠐⠂⠀⣲⠞⢹⠀⠀⠰⠀⠀⢀⠟⠀⠠⡿⠀⠀⣠⠏⠀⠀⠹⣯⡀⠀⠀⠀⠀⠀⢀⠬⠘⡟⠢⣴⡇⠉⠀⠀⢶⡀⠀⢛⣄
⠀⠀⠀⠀⣸⠃⠀⣿⠏⠉⠀⠀⠀⠀⠃⠀⠀⠈⣀⠀⠐⠀⢀⡾⠃⠀⠖⣶⠀⣽⡇⠀⠀⠀⠀⣠⡾⠶⡞⢳⡴⣿⢷⠀⠆⠀⠀⠑⠲⢄⡙
⠀⠀⠀⢠⡏⠴⠋⣀⣀⣤⡤⢶⡤⠦⠐⠛⠋⠋⠡⣄⡀⣰⠏⠀⠀⣀⣾⣁⡀⠘⣿⠀⠀⠀⣰⣿⠛⡤⠀⠀⡟⣿⠘⣀⠆
⠀⠀⣠⣾⡷⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠉⠿⣍⠁⠀⢿⠆⠀⢰⣿⠈⢀⠃⠀⠀⣿⠙⡟⣿
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠀⠀⠀⠀⢺⣁⠀⠉⠀⠀⠀⠙⠆⠈⠛
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠁⠤⡤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⢘⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣦⠀⠈⠛⠃⠀⠉⠁⠸⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡒⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠄⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠄⠀⢀⣀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⢰⡆
⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠙⠀⠀⠀⠀⠀⠻⠀⠀⡀⠀⠀⠀⠀⠈⠋⠀⢀⠀⠊⠁
⠀⠁⠀⢄⡀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢂⣠⡀⠁
⠀⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡀⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⡉⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠄⠰⢿⡇⠠⡀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⡈⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⠠⠀⢀⢝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠌⠉⠁⠀⠀⠂⠀⠀⠀⠀⠙⠿⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣾⣿⠄⠀⠀⠐⠀⠀⢀⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⢴⣥⠀⠁⠠⠀⣤
⠀⠀⠀⢀⣄⠀⢦⠀⡀⠀⠈
⠀⠀⠀⠀⠘⠂⠈⠒⠠⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⣀⣠⡆⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣿⣿⣿⣿⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢹⣿⣷⣶⣦⣀⡀⠺⣿⣿⣿⣿⣻⣿⣿⣿⣿⠗⢀⣀⣤⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⡟⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢹⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣾⣟⣿⡇⣿⢿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⢸⠀⣄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠿⠛⠛⠉⣾⠈⠛⠛⠿⠿⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⣿⣿⣾⣿⣿⣇⣠⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢀⠀⠀⠀⠘⣿⣿⣿⣿⣇⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⣤⣦⡈⢻⣿⣿⣿⡅⣿⣿⣿⣿⠋⣠⣤⣴⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⣿⣿⣿⣦⣙⣿⣿⡇⣽⣿⣟⣡⣾⣿⣿⣿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣷⣼⢿⣿⣿⡇⢿⣿⣿⢿⣴⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣷⣯⣻⡇⣿⣫⣿⣿⣿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣭⣭⡿⢶⠾⣭⣯⣽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠋⠉⠁⠈⠀⢸⠀⠈⠀⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⣿⢧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⠀⣇⢀⡾⡆⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄⣀⣠⡗⠈⠀⢣⡾⢀⡽⠛⢁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢆⠈⠀⠉⢄⠀⠈⠋⠞⠁⠐⣈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠣⡀⠀⠀⠑⠘⡞⠀⣠⠎⡠⡎⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⢦⡀⣀⠀⠀⣰⢦⡀⠈⢻⣦⡉⠐⠠⡀⠀⠗⠊⠁⠀⢀⢋⡿⠀⠀⣠⡾⡇⠀⠀⡀⠀⣀⢠⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣆⠈⠈⡙⠶⠋⠀⠻⣄⠀⣿⠁⡀⠀⠈⠒⠀⠀⣀⣴⠋⢸⡇⢠⡞⡹⠠⠉⠑⠉⡈⢉⡵⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⢹⣆⢀⡇⠀⠀⠀⡀⠙⠛⢃⠀⠈⠠⡀⠀⠀⣷⠚⠁⠀⠈⠙⠋⢀⡇⠀⠀⠀⠀⣦⡽⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠓⠌⢿⣄⠀⠀⠀⢠⠀⠀⣄⠀⠀⠀⠀⠙⠺⡇⠢⡰⠀⡄⠌⠀⠘⠀⠀⠀⠰⣒⠼⠰⣯⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⡐⠦⠤⢬⠶⣄⡀⢸⠀⠀⢹⠀⠀⠑⢄⠀⢸⣿⡘⡐⠂⠐⠀⠀⢃⠀⠷⠛⠶⠀⠐⠋⠷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠇⠠⢤⣀⢤⠬⠟⠾⣀⠀⢸⠀⠀⡆⠀⠙⠺⣿⢰⠇⠀⠀⡦⠀⣨⠃⠄⠀⠠⠤⠀⠐⢋⢉⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣐⠬⣅⣀⢀⡀⣀⣀⣴⠾⠻⣾⡀⠀⣧⠀⠀⢀⣿⠞⠠⠀⠀⣆⡜⠁⠠⠀⠤⠤⠶⠴⢶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⡭⢁⠀⢀⠐⣀⣨⣷⣤⡏⠀⠀⢸⣿⡆⢀⠆⣰⠏⡀⠀⠀⠀⠀⣠⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠄⢬⠹⠀⠈⢰⣼⢿⡤⡀⢸⣷⡆⢊⡶⣻⣾⣄⣤⡴⠽⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠛⠓⠲⢤⡀⠀⢆⠘⠙⠿⣯⣿⣏⣴⠟⣱⡧⠚⠁⠀⠀⠀⠐⢛⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⢢⣤⡤⠴⢲⠟⠛⠉⣩⠞⠛⣿⣿⣿⣿⠿⠿⣤⣄⣠⢚⣁⢀⣔⣉⣈⣭⣛⣳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣖⢚⡟⠋⠀⢀⠐⠁⠀⠀⠔⢁⣠⠞⣻⠿⣴⠁⠉⠓⢦⡄⠀⠉⠙⠯⣉⠉⢉⡭⠿⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠖⠛⠛⡶⠾⠞⠋⠁⢠⡿⠀⠈⠙⢦⡠⢤⣙⢦⣀⣴⠒⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠱⡀⠙⠦⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠼⠀⠀⠀⢱⡀⠀⠀⠹⠶⡦⠀⠀⠀⢀⠀⠀⢀⣴⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠐⢤⡀⠀⠀⢣⠀⡇⠀⠀⣧⠀⠀⢠⠏⠓⠖⠉⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠈⠳⣄⠈⢷⡇⠀⠀⠘⢦⡴⠋⠀⡄⠀⣸⠁⠸⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠓⢾⣇⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⡤⣄⡀⢸⡄⠀⠀⠀⠀⠹⡄⠀⠀⢠⠀⠀⠀⣧⠏⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠸⡿⢍⡉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢳⠀⢠⠏⠀⠀⣰⢋⡤⠖⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠓⠤⣀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⢢⡀⠈⣧⠏⠀⠀⣰⠟⠉⠀⠀⢠⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠈⠉⠒⠦⢤⣀⣈⢣⡀⠀⠀⠀⠀⠙⢄⣸⡄⠀⣰⠃⠀⠀⠀⠀⠘⠒⠒⠋⠉⠩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⢉⡹⠿⠦⢄⣀⡀⠀⠀⠙⣇⣰⠃⠀⠀⢀⣠⣤⣒⣁⣀⠤⠤⠤⠜⣻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢦⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠈⠉⠙⠲⢤⣼⣧⡤⠔⠚⠛⠉⠉⠉⠀⢀⣀⡀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡴⢺⠟⣿⣍⠒⢤⣀⠀⠀⡴⠉⠁⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠙⣆⠀⠀⠀⠀⡠⠋⠀⡞⠀⠟⣇⠱⡄⢈⡑⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⣠⠞⠁⠀⢸⠃⢸⠀⢿⡀⠘⠏⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⣠⠞⠁⡴⢦⣄⠘⣠⠞⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡠⠊⠀⢀⠞⠀⠀⠸⣤⠃⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⠖⠒⠒⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣥⠄⠒⠾⢀⡼⠿⠷⠇⠀⠐⠃⠀⣤⣿⣿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠶⠶⠀⠀⢀⠀⠀⠀⡀⢀⣀⣄⣀⣤⡄⢒⡀⠀⠀⠀⠈⠹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⡶⠄⠐⠀⠠⣬⡶⣬⣬⡍⠁⠉⠉⠛⠛⠉⠋⠁⢰⣤⡤⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠙⠛⠇⠀⢀⠀⠀⠁⣠⣄⡀⠀⣤⣖⢀⠀⠀⠀⠀⠑⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠃⠁⢊⡀⢀⡀⠈⠁⠀⠄⠀⠀⠟⢿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡝⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠊⠉⠈⡀⠀⠀⠁⠀⠀⠀⢴⠤⠈⠁⠐⠀⠀⠁⠰⡶⡂⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣷⢿⣷⠄⠀⠀⠚⠃⠀⠀⠀⠂⢀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣋⠀⢁⠀⠀⠀⢡⠾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⣄⡀⠀⠀⠀⢸⡄⠘⣿⡉⠃⣈⢀⡀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠛⠀⣿⠇⠄⠉⠀⣠⡤⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣷⡤⠿⠋⠀⠠⠤⠀⠀⠀⠀⠀⠐⢠⣲⣄⠀⣶⣴⣦⣾⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠂⠀⠀⢨⣿⣿⠆⢀⠀⣼⣅⠀⢙⡿⣯⠭⡦⠁⠀⢠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢤⣰⠾⠻⢿⡀⠀⡠⢾⣿⣱⠟⠙⢻⡀⠁⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣶⣿⣗⡀⠉⠛⢙⠛⠛⠀⠘⣥⠐⠏⠙⠁
⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⣄⠀⠀⠀⠀⠉⠉⠱⣞⣟⡑⢀⣠⣤⣨⡇⠀⡄⠀⠰⠂
⠀⢀⣥⣾⣾⣿⣶⡆⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣅⢠⣾⣷⠀⡀⢶⡆
⠀⣾⣻⣿⣿⣿⣿⣏⣦⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠁⢠⣤⣄⣀⠈⣿⣿⣿⣿⣼⣿⡏⠀⠃⣤⡐⢀⡀⣄
⠀⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠠⢶⡆⠠⠚⠑⠠⣤⡀⠀⠀⢀⠰⠏⠉⠐⠒⢌⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⣀⣼⣀⣄⣰⣆⠀⠀⣈⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣎⢀⠀⠠⠤⡴⣿⡉⣄⢀⣿⣀⣶⠘⠃⠀⡌⢿⣿⡟⢻⠛⣦⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣾⣾⣿⣄
⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠿⠿⠿⠻⠛⣷⠺⣿⠙⠷⠶⠇⢾⡏⠃⠘⠒⠃⠐⠲⠲⠿⠿⠿⠻⠿⠟⠿⠛⠙⠛⠉⠁
⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠰⠟⠀⠀⠀⠀⢸⡇⣀⠀⠀⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠈⠁⠈⠉⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⢠⢀⠀⢠⡾⠟⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠾⠶⠖⠚⠟⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠉⠀⠐⠀⣀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿⢂⡀⠀⠀⣀⣀⡤⠤⠆⠈⣭⠥⠐⠚⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⠂⠀⢀⣻⣯⡅⠤⠖⠒⠛⠀⠀⠰⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠄⠀⠈⠈⣽⠀⠀⠀⠈⠀⠀⡀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠰⠁⠀⠀⠂⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠀⠀⢆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠆⡀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢾⡏⠀⠀⠔⠉⠀⠐⠠⣀⠐⠀⢀⡄⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠡⢀⡜⡴⠃⠀⠀⠀⠀⠀⢀⢠⣁⢀⠄⠂⢠⡴⠾⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⢶⣿⣰⡃⠀⠀⠀⠀⠀⠀⠈⠈⣃⣠⠴⠊⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠁⠙⡹⠋⢹⠾⣧⠁⠀⠀⠀⠁⠀⠂⠀⡀⢮⣤⠔⠒⠀⠐⠂⠄⠌⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠊⡀⠠⠘⠓⠺⣆⠘⢦⠀⠀⠀⢠⠀⠀⡈⠙⠢⢤⡈⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⡼⠋⠁⠀⠁⠀⠆⠀⠀⡅⠀⠘⡄⠀⠤⠀⠠⠂⠙⡀⠀⠀⠀⠉⠠⠀⡀⠀⠀⠀⠑⢄
⢀⠀⠀⠒⠐⠛⠻⠛⠓⣛⡇⠀⣀⣀⡀⠙⠒⠄⠠⠎⠀⠀⠈⢠⡀⡀⠀⠀⠀⠑⢀⡀⠀⠀⠀⠀⠑⠀⠦
⠏⠀⠀⠀⠀⠀⠀⣀⠄⢹⣿⡛⢭⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠀⠀⠀⠈⠀⠂⠒⢢⡀
⠀⠀⠀⠀⠀⢀⠊⠐⠀⠀⡴⠁⠀⠒⠾⡆⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠁⠀⠁⠐⠂⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠀⠀⠀⢼⠄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠛⡻⢉⠉⢄⠀⠀⠀⡀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠠⠠⠄⢡
⠀⠀⠀⠀⢠⠊⠀⠀⠈⠀⠈⠐⢲⢦⠀⠈⠀⠠⡀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣡⡞⢿⡿⣦⣄⠀⢄⠀⢄⠀⠀⠀⠀⠐⠢⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢼⡉⠘⠀⠘⠢⢴⠲⣄⡀⠀⠁⡀⠀⠄⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠄⠁⠈⢑⠀⢀⢴⠂⠀⠑⠊⠀⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠊⠀⠈⠁⠁⠀⠀⠀⠀⠀⠑⠌⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠐⠓⠇⠀⣠⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠦⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢀⠀⠀⢠⡰⣤⡀⠀⠀⠀⠀⠀⢀⢠⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠐⢿⠁⠽⠿⠀⠀⠀⢸⡽⠿⠛⠃⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⢶⣵⡀⠀⢠⡀⠀⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠳⡀⢰⡆⠀⠀⠀⠀⠀⠀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢀⣠⣤⡆⠀⠀⠀⠤⠴⠦⢤⣽⣶⣷⣸⠃⠀⠀⠀⠀⠀⠀⠺⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⣀⠌⢩⠉⠁⠚⠀⠀⠀⠀⠀⢀⡀⠉⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡈⠀⢠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡂⠀⠀⠈⠳⠁⠀⠠⣴⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡄⠀⠀⠀⣰⣾⡷⠀⣄⣀⡄⠀⢰⣿⠋⢁⣶⣄⠀⠀⡀⢠⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠁⠲⢬⣻⣿⣷⡀⢱⠈⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣘⣧⡀⠀⣷⠀⣄⢰⣶⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣄⣃⣧⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⡈⠙⢦⣘⡄⠸⠉⠙⠀⠀⠀⢴⣿⠇⠀⠠⢤⣙⣻⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠈⠑⠒⠽⣿⣦⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⢀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠚⠉⠉⠉⠁⢰⣾⠟⣄⠀⠀⠀⢀⣤⡤⠀⠈⠙⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⣶⣌⣦⡀⠀⡉⠡⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠿⣿⣦⣱⡀⢣⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠎⠀⢀⣉⣐⣠⣿⣿⣷⣬⣧⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣶⡆⠀⠤⠤⠒⠚⠉⠉⠙⠻⠷⠶⣤⣤⣤⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣻⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣛⣛⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢸⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠲⢷⣤⣦⡄⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣿⣿⣿⠀⠻⣿⡀⠀⠈⠃⠀⠀⠀⠉⠶⣀⡤⠀⠀⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢉⡉⢙⡄⣀⣿⡇⣄⠀⠀⠀⢸⠋⢃⣠⣿⡄⠐⠒⢿⠛⠋⠀⠀⡟⡁⠀⢀⠀⠀⠀⠠⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⣿⠿⣿⣿⣿⣿⣿⡇⠉⢀⠀⢠⡿⠀⠃⣉⡿⠃⠀⠀⢘⠀⠀⣾⠆⣾⡇⠀⠀⠀⠀⢀⡴⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠒⠿⢘⣷⣾⣿⣿⠄⡈⠀⠀⡿⠀⢾⣿⣿⡀⠀⠀⣨⠀⠈⡉⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠒⠁⡈⠛⠋⠀⠀⠈⢀⠀⡄⢻⣶⣺⣿⣅⠲⣶⡿⠁⣠⣿⠀⠀⠀⣰⣾⣿⡟⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡃⠘⠒⠀⢚⡋⠙⢻⣦⣾⣿⠟⣻⡏⠀⠀⡇⠀⣌⠁⢀⡰⠋⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠙⠻⣆⢰⣿⣽⣦⣿⣿⣿⣿⡌⠿⣷⡄⠐⠁⠀⠁⢀⡜⠀⠀⠀⠉⣂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣶⣤⡄⠀⠀⣷⣝⠳⣦⣀⠈⠻⠉⡿⠈⢳⣀⣁⢡⡀⠰⡇⠠⠒⢻⣦⠾⠶⠦⠀⠖⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣟⠿⣿⣷⣶⣀⡀⠀⠀⠷⢶⠦⠀⠈⠁⢠⠈⣩⣿⡄⠀⠄⠀⠀⠀⠈⠏⠀⠀⠀⠉⣉⣥⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣈⣁⡽⠀⢠⣬⣴⡴⢤⠀⠀⠀⠀⢀⠀⠀⠀⠙⠋⠉⠰⢤⠀⠄⠀⠠⣀⣾⢟⣿⣆⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⡌⠁⠀⠈⠋⠀⠀⠀⠀⠁⠀⢿⡄⠀⠀⢠⣄⢠⣹⣿⣷⣾⡿⠶⠚⣀⣠⣧⡈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣴⣿⣿⠿⠛⠁⠀⣉⣠⡶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠟⠁⠀⠀⠉⠁⠀⠀⢠⣴⣿⣿⡙⠃⣹⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⣠⠀⣾⣿⣾⠿⠛⠁⡼⠋⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠜⠁⣻⠁⠄⠀⠀⠇⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⡜⡰⢀⠀⠀⡀⠀⠉⠀⠀⠘⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠘⠁⠋⠈⠡⠀⠀⠀⠀⠀⠀⠀⠁




⣿⣿⡿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣵⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡄⠀⠀⢠⠛⠀⠘⠁⢇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠰⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⣤⠔⠀⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⡀⠈⠢⠀⠜⠀⢧⠀⠀⡸⠀⠀⠀⠐⠄⢠⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠢⣀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⡔⠀⠀⠀⢀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠠⠤⠬⢧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡀⠀⡠⠔⠁⠀⠃⠀⠰⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⢄⠀⠀⠀⠀⠈⢲⡅⠀⠀⢸⠀⠀⢄⠀⡦⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠤⠽⢆⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡀⠐⠀⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠯
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⡁⢀⣀⣠⣤⢄⣀⣈⣢⡀⠀⠘⢄⠀⠀⠀⠀⢠⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⡀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠄⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⢦⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⠀⢀⢤⠀⠀⠰⡀⠀⡀⠠⠤⡀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡪⠃⠀⠀⠀⠇⣰⠁⠀⠀⠈⠳⡄⢠⠂⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢴⣦⣤⣀⡀⠀⠀⠀⠀⠀⣠⠴⠂⠉⣉⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⢀⠀⠈⠙⢿⣶⣄⠀⣠⡿⠁⢠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣻⡿⣷⡏⢉⢭⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢬⣾⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠀⠀⠀⢠⠀⠀⠀⠀⠀⡼⠀⡔⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡀⣐⢦⠀⡎⠀⠀⠀⠀⢰⡇⢠⠃⡠⡇⢀⠖⡄⠞⢁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠒⠃⠀⠀⠀⠘⠁⠁⠙⠀⠑⠙⡞⠀⠈⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠐⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠄⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠁⠀⠡⡀⢀⠌⠀⠈⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠀⠀⠘⠃⠀⠀⠀⡠⠀⡇
⠀⠀⠀⠀⠀⠀⠒⠒⠠⢀⡀⠀⡀⠑⢄⠀⠀⠀⠀⢸⠀⠀⢢⠀⠀⠀⠀⠀⠀⡜⠀⠀⠃⠀⠀⠀⠀⡠⠊⢀⠀⢀⡀⠄⠒⡂
⠀⠀⠀⠀⠀⠀⠈⠄⠐⠠⡀⠀⠀⠀⡀⠑⠢⢄⡀⡸⠀⠀⠀⠡⡀⠀⠀⢀⠌⠀⠀⠀⢆⢀⡠⠔⠈⢀⠀⠀⠉⢀⠄⠂⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⠐⢄⠀⢡⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠊⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠘⠃⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡥⠊⠀⠀⠀⠠⡁
⠀⠀⠀⠀⠀⠀⠣⠀⠠⠀⠀⠀⠀⠀⠈⠢⡀⠀⢃⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡘⠀⢀⠔⠀⠀⠀⠀⠀⠀⠄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠉⠐⠂⠤⠀⣐⣄⠸⠀⠀⠀⠈⠆⠀⠀⠀⠀⠰⠁⠀⠀⠀⠃⣠⣂⠀⠤⠐⠂⠉⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠈⢆⠀⠀⡰⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠱⠎⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⡀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠉⠀⠀⠀⠉⠉⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠉⠁⠀⠀⠀⠙⠀⠀⠄⣀
⠀⠀⠀⢠⠐⠂⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠉⠐⠂⡄
⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠠⠤⠌⢦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⠠⠤⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⠔⠈⠀⠀⠀⠀⠀⠉⠉⠉⢉⠝⢛⡛⠫⡉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠢⠄⡀⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡠⠋⡗⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠔⡁⠔⠉⠀⠀⡇⠀⠑⠢⣈⠢⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠊⠔⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠑⠢⠵⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠰⠌⡁⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢆⠃⠙⠁⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢉⡐⠁⠀⠀⠀⠀⠀⢴⣤⣽⣏⢡⡿⣶⢿⡿⠀⠀⠀⣠⢴⡀⠀⡑⠆⡁⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠈⡇⠀⠁⠀⠀⠂⠀⠀⠀⢘⣇⣽⢿⣨⣾⣣⢿⡟⠀⠀⠀⣹⣅⣀⠄⠈⢊⠀⢴⡀⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⠄⣯⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛⠿⠿⠽⠿⠿⠟⠃⠀⠀⠀⠈⢩⣗⣀⡤⢸⣗⡂⠹⠎
⠀⠀⠀⠀⠀⠀⠉⠃⠀⡀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠰⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠳⢤⡼⠀⡀⠹⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠅⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⠓⢦⣄⣀⢀⣴⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⢸⡇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠠⠈⠉⠉⠀⢆⠛⠏⠉⠀⠀⠀⠈⠄⠀⠈⠛⠋⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠈⠢⠀⠀⠈⢧⡀⠈⠢⡀⠀⠀⠈⡄⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠭⢥⣀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡷⠀⠀⠀⠐⠀⠀⢸⠀⠀⢠⢆⠀⢸⠷⢤⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠊⠀⠉⠁⢀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣧⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⡦⠀⠀⠀⠀⠀⠀⠀⡠⠂⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠐⠒⠚⠋⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠃⠀⠀⠀⣀⠤⠖⠉⠀⠀⠓⣶⡆
⠀⠀⠀⠀⠀⢦⡴⠶⠖⠚⠁⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢀⣀⠂⢄⢠⢀⠄⠂⠉⠀⠠⠄⠀⠀⡠⠞⠉
⣀⣀⣤⣤⠴⠞⠁⠀⠀⢀⠠⠤⠤⠶⠂⠀⢀⣠⣤⣤⡀⠀⠀⠀⠈⠁⠸⠛⢳⡶⣶⣦⡤⣤⣤⣬⣵⡦⠄
⠈⠉⠉⠉⠉⠁⠲⠀⠀⠀⠀⠀⠘⠁⢠⠞⠉⠀⠀⢈⣿⠀⠀⠀⠴⠀⠀⠀⠀⢳⠈⠙⢯⡲⣄⡀
⠀⠀⠀⠀⠀⠀⡀⢀⠤⠒⠛⢷⢀⠖⠁⠀⠀⢀⣠⠾⠋⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠱⡄⠻⣆
⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠘⠋⠀⠀⠀⠐⠿⣧⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠹⡀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠀⠀⢠⠀⣠⠔⠁⠀⠀⠀⠀⠀⢧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣀⣠⡀⠈⠀⢀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⣧⠀⣰⠋⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⠀⢀⢀⡀⠀⠀⠀⠀⢩⣏⣴⣤⡾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢖⣻⡁⠀⢀⣯⡥⠀⠀⠀⠀⠚⢿⣿⡶⣿⣧⠀⣣⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⣵⠾⣿⣲⣶⣿⣷⣶⡶⣶⠂⠘⣷⣶⣿⣿⡿⢶⡾⠷⠖⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢩⣤⣬⣿⣿⣿⣿⣟⣿⣟⢰⣿⣿⣿⣿⣿⣶⣶⣿⣶⣠⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣿⣷⣿⡿⣿⣍⣿⣿⣿⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣼⡿⢻⢏⣽⣿⠣⣏⠘⢃⡀⣤⣴⠂⠸⣯⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡟⢻⣿⣿⣿⠑⣯⣿⣾⣻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⡟⢃⡞⢾⡛⠿⣿⡌⠶⡾⣿⠧⢙⣤⢼⣿⣛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⡿⣷⣺⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣠⢮⣿⣿⣿⣾⣯⢀⣠⣋⣽⣶⠟⣿⡿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⠸⢸⣿⣧⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣵⣿⣷⣭⣫⣾⣿⡍⡪⣻⣿⣿⣹⣾⣿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣤⡿⣿⣿⣿⣿⣿⣷⣿⣯⡿⣿⣿⣿⡋⢃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣽⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢧⣾⣿⣿⣿⠿⣿⣿⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣿⣯⠭⠷⢿⣿⣿⣿⣿⣿⠃⢠⣾⣷⡀⢀⡖⣰
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⢾⣿⣿⣇⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⣿⡶⢷⣾⣽⡶⢯⣁⣧⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⠿⣬⡗⠊⠁
⠀⢀⠀⠀⠀⠸⣣⡆⢀⣴⣆⠀⢉⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣯⣿⣿⣷⣼⡟⢀⣽⡿⠛⠀⡜⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢛⣿⠟⢦⣤⡀
⠀⡿⣦⡆⠀⠀⢼⣷⣿⣷⣿⣷⣤⣧⡽⣻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣏⡘⣿⣇⡼⠛⠷⣿⣾⣷⣷⣿⣿⢿⣿⣿⣿⡷⣻⣿⣾⣿⣷⣼⣿⠋
⠀⢸⡓⢾⣷⣾⣿⣿⣿⣿⣿⢟⣻⣿⢢⣿⣟⣩⣿⣿⣯⣝⣻⣟⣿⣟⡃⢹⣿⣧⣀⡸⡿⣿⣽⣿⠟⠻⠸⣇⣿⣉⣷⣟⢿⣿⣿⢿⡿⠉⠰⠄
⠀⢀⣫⣿⢈⣩⣿⡿⢿⡿⣿⣾⣿⣟⠑⢉⢹⣿⢿⣿⣻⡿⣿⣾⣿⣝⣧⣼⣿⡍⢩⣷⡾⣿⡿⡿⠋⣀⣎⣽⠿⢭⣿⣿⣿⣿⣿⣾⣷⣿⡔⣤
⠀⠈⠁⠀⢙⣿⣿⡷⢛⣿⣿⣾⣿⣎⣷⢺⡧⡉⠱⠝⠋⢴⣷⣿⣿⡿⣟⢿⣿⠅⣼⡟⢱⣿⣿⡿⣯⣿⣿⡔⣻⠷⣿⣿⣿⣿⡿⢺⣿⣿⣿⣿⠗⢢⣀⣠⣂
⠀⠀⣌⣾⣿⣿⣿⢷⣠⣿⣿⣿⢿⡙⢻⣿⡷⣿⣦⡀⣀⣺⣿⡿⣻⡟⠿⢾⣿⠀⠸⡇⠘⣿⣿⠟⢻⣿⣿⣿⣿⣽⣿⡶⠛⢽⢷⡰⢿⣛⣘⣇⣠⣿⡜⠓⠌
⠀⠀⠉⠿⠛⠳⠃⢴⣿⣿⡿⠛⣍⣛⣮⣹⠗⢴⣯⣿⣿⣿⣿⣷⡿⣄⠀⣿⣿⠀⢠⣧⡾⠛⠛⣿⣏⣿⣿⢟⡿⡿⢿⣶⣏⣾⣿⡶⣟⣋⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⣯⣵⠘⣊⢋⣉⣁⡽⠿⠻⢧⣄⠈⠻⣿⣿⣶⠿⠋⠀⠀⠌⣙⣻⣿⣿⣿⣶⣿⣿⣉⣻⣿⢾⣿⣿⣿⣿⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⢤⡌⣿⠛⠑⣏⢛⡛⣁⣄⠀⠀⠀⣈⠙⠦⣿⣿⡇⠀⣀⡤⠾⠛⢋⢹⣅⠈⣋⡉⡸⢷⣿⣿⣿⣿⣿⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠚⠛⠃⠠⢾⣿⣿⣟⣿⣝⡟⡴⠆⣃⡭⠀⣻⣿⡷⠞⣩⡴⢆⣀⣊⠀⠺⣿⠏⢠⣿⣦⣼⡿⡿⣷⣾⡿⣿⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠑⢿⣽⠟⠿⣄⣍⠛⠾⠵⣾⣽⣿⡇⠀⠀⠀⠉⠈⡉⠀⠛⢿⠘⣷⠟⠀⢿⣧⣖⣦⠀⠀⠃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⢏⡙⠷⠆⠠⢌⣹⣿⣷⠀⢤⠼⢳⡏⣭⠗⠂⠀⠀⠁⠀⠀⠉⠉⠣⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⠛⠃⠀⠀⠀⢸⣿⣿⠖⠛⣀⠒⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠗
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣁⣍⣻⣀⣍⣉⣽⣉⣨⣟⣩⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠃⠑⢄⣀⠀⡀⡠⢴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠖⢹⠣⡄
⠀⠀⠀⠀⠀⣤⣀⣀⡀⢀⠀⣄⠉⠀⢀⡀⠀⠉⠀⠍⠠⡬⠈⡏⢀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢏⠙⠤⡆⠀⢐⠊⠀⣼⡀⢇
⠀⠀⠀⠀⠀⠀⢇⠈⠑⣍⡑⢌⢢⡀⢈⣕⠀⠈⠤⠀⢠⠃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⣧⠀⠸⣀⠌⠀⠀⡗⠁⠰⠁⢀⣄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⣀⠆⠀⠐⢟⢊⡑⠰⠀⢥⡄⠀⠀⢀⠟⠀⠌⠤⠒⢓⣢⡶⠀⠀⠀⠀⠀⢇⠀⠈⢶⠀⠀⠀⢀⢸⠇⠀⠑⠒⠁⢀⡤⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠉⠙⠝⢤⠀⠘⡆⠀⢠⠋⠀⢀⣠⠔⠊⢫⠘⠃⠀⠠⣤⠊⠐⠀⠁⠀⠘⠦⠀⠀⠈⣿⠀⠀⠀⣠⡖⠋⢀⡔⠁
⠀⠀⠀⠀⢀⣠⣤⢆⣒⣀⣠⣠⣀⣀⣑⣢⣸⣴⡣⠐⠋⠋⠀⡠⠀⠐⠂⠀⡄⠀⠨⣊⠑⠲⣄⢀⠀⠙⢤⠄⢀⡇⠀⡠⠆⠁⠀⢀⠐⡚
⠀⠀⠀⠀⠀⠈⠩⢶⡀⣀⠈⠉⠀⢁⡠⠗⢙⡿⡍⢑⢒⡶⢤⣈⢲⡄⠀⣼⣇⠀⠀⢀⡅⠀⠈⠩⠷⢤⡈⠳⣸⢁⣜⣀⣄⣤⠤⠬⠄⢙⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠔⠴⡫⠐⠢⡄⢡⠸⠄⠀⠈⠚⠀⠛⢛⡘⢸⡇⠙⠀⠀⠀⠀⢀⣔⡀⠴⠖⠻⠟⠛⢝⣀⢠⢀⡤⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡇⠀⠢⡄⠀⠐⠋⠉⠓⠈⠈⠁⡇⠀⠈⠀⠉⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⣦⠤⣀⡀⠀⠠⠀⠐⡏⠀⠀⢆⠀⡠⠚⠧⠀⢒⢾⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⢹⢃⡈⠉⠒⠁⠀⢀⣷⡀⠀⠀⠀⠀⠀⣀⠔⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⠀⠑⢄⠀⠀⠀⠀⣹⡁⠀⠀⠐⡀⠼⠁⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⠈⠙⢆⠀⠀⠸⡇⠀⢈⠖⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠉⠙⢦⠀⣇⠰⠃⠀⣀⣠⣀⣁⣰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡥⠒⠂⠀⠚⠻⠒⠳⣿⠖⠋⠁⠁⢀⡀⣠⡭⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠆⠀⠐⠁⢹⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠈⠁⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠉⠑⠦⡄⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢰⠋⠉⠀⠀⠙⣄⡎⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣻⣄⡄⠀⣠⡴⠥⠀⠤⣀⠀⢸⠀⠀⠀⠀⢤⣽⣷⡀⠀⠀⠀⡇
⠀⠰⢬⣭⣭⣙⣒⣲⠤⣄⣀⢣⡀⠀⠀⠀⣀⣿⣻⣶⣿⠟⠀⠀⠄⠀⠀⢁⣨⠦⠴⢶⣶⣾⣿⠛⣷⣾⣶⠛⠒⢦
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⡿⠿⠛⣻⠿⢻⣿⣿⠟⢦⡄⠀⠀⠀⢠⣿⠀⠀⠀⠠⠚⠻⣿⢿⣿⣯⡉⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠁⠀⢸⠇⠘⠀⠀⠉⢦⠤⠔⠁⡟⠀⠀⠀⠀⢀⣴⠏⠈⠙⠛⢷⡀⠀⠀⡼⠀⠀⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣆⣀⡀⠉⠒⢲⡤⠔⢫⠃⠀⠀⠀⠀⠀⡿⠓⣺⡷⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠂⠤⠊⠀⢄⡀⣀⠀⠀⡔⠉⠉⠙⣟⠓⡻⠶⠤⠤⢷⣄⠀⠀⢀⣴⣁⣸⣿⡧⠔⠀⠚⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣺⣿⣿⣝⡛⠒⠀⠠⢕⠒⠋⠀⠀⠹⠉⢿⡀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠋⠃⠙⠢⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠈⡇⠀⠀⠀⠀⠈⡶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠠⠉⠉⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⡀⣀
⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⢻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⡔⠟⠽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⡄⢡⣺⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣼⠀⣸⣽⡶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣥⠏⠀⠀⢉⠾⢷⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄⠀⣾⡟⡏⠙⠜⠳⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⣿⠟⣁⣤⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⣴⡄⣶⣴⣦⠸⠷⠣⠀⠚⠁⠀⠛⢿⣾⣶⣭⡻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣿⡆⢸⡿⡙⣓⠀⠐⢂⠐⢿⣭⣟⡻⣦⡄⠈⠛⠿⢿⣿⣾⡧
⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⡀⣶⠿⠣⠄⢈⣿⠞⠉⢁⣀⡘⣇⢍⣂⢀⣬⠀⠀⠻⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣟⠛⣢⡀⠀⢸⡆⠸⣿⣶⣽⣦⣟⣿⣭⠋
⠀⠀⠀⠀⠀⠀⠘⢿⣿⢺⠟⠸⢦⣷⣶⣛⠁⠀⠀⠀⠈⠛⢿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣶⡝⢋⣶⣛⣯⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⡿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣴⣄⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⡟⠀⣀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⠋⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠚⣠⡟⣠⣾⣿⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⢀⡀⢀⣼⣿⣷⡿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⢠⣿⣿⣿⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡻⠏⢥⣤⣦⣤⣄⣀⠀⠀⠀⠀⣾⠀⠀⢠⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠸⣿⣿⣿⡿⣿⠀⠀⠀⣤⣿⠀⢠⣿⣿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢻⣿⡿⣥⠁⠀⠀⠀⠿⢋⣾⣿⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣬⠤⠂⠀⢀⣶⣿⣿⣿⢾⠯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠀⠀⢀⣴⣯⣽⡏⠙⠿⠧⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠊⠛⠁⢐⡦⣤⡁⢀⡀⡄⠀⠒⠚⠒⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠄⠀⠀⠀⣠⡄⠤⠒⠉⠑⠘⡆⠈⠀⠀⠀⠀⠀⠀⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠀⠘⠃⠀⠀⠀⠀⣠⠾⠁⠀⠀⠘⡄⠀⠀⠀⢰⣄⣦⣄⡀⠛⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⢀⣀⣀⣀⣾⠞⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠙⠛⠽⢿⢿⣮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⠑⠊⠓⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⡿⠞⢷⣿⠀⠀⠐⠀⠀⠀⠀⠠⣟⣿⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣴⣦⣬⣦⣤⣤⣤⣶⣿⣿⡿⣿⣿⡷⠀⢀⣼⠀⠀⠀⠀⠀⢣⡀⣾⣿⣿⣴⣦⠤
⠀⠀⠀⠀⠀⠀⣀⠆⠀⠚⠉⠉⠀⠀⠈⠀⠀⠀⠀⣰⠟⠁⠉⠁⠀⠀⠸⡿⠋⠀⠀⠸⣿⠀⠀⠀⡀⢀⠠⠈⡏⠻⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠈⠁⠑⠂⠀⡤⠶⠚⠉⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⢀⣿⠀⠀⠀⣤⣼⠛⣶⣅⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢀⣿⠀⠀⠀⠀⢀⣉⡗⠀⠀⠈⠿⠀⠀⠀⠀⠀⡀⣼⢿⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢀⠞⣿⢀⠂⠀⠀⠀⢹⡟⠀⠀⣺⣄⠀⠀⠀⠁⡼⠇⠘⣿⠳⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⡀⠚⢀⡏⠀⠈⠙⢅⢤⡰⣆⢸⠆⠀⠀⢹⣿⠀⠀⢲⠀⠀⢰⠀⠙⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣉⡀⠴⠒⠊⠀⠉⠁⠀⠀⠀⠀⠀⠉⠻⠿⠎⠀⠀⠀⣈⣿⠀⠀⠀⠀⢠⢏⠀⠈⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠈⠀⠀⠀⠸⠚⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣄⠈⠳⠆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠈⠛⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠶⢄⣀⡀⠀⢠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠒⠠⡶⣄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⣿⠁⠀⠀⡇⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢘⠁⠀⠀⠀⠈⠙⣦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⢸
⢶⣦⡀⢤⠀⠠⠈⠉⢘⡋⠀⣈⠀⠀⠀⠀⠀⠀⠈⢡⣦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠄⠀⡿
⠀⠘⢁⣤⡀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠳⡄⠀⠀⠀⠀⠀⢀⠐⡆⢸⡄⢠⠀⡾
⠀⠀⠦⠀⠀⠁⣤⣄⡀⠀⠁⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡼⠛⠓⠘⠷
⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⢀⣠⡀⠀⢀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⢃⡀⠐⠂⠐⠂⠀⠀⠉⠑⢠⣼⡀⠀⠀⠀⠈⢀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣄⠀⢀⠈⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠒⠈⠁⠀⠈⠐⠂⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠁⠀⠀⢰
⠀⠀⠀⢀⠚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠃⠶⣄⡀⠀⠈⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠞⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠛⢀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣦⣀⠀⠀⠀⠀⠹⡄⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣤⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠢⣤⣀⠀⠙⣀⠈⠀⡠⠊⠀⠀⠀⠀⣤⠀⠀⢀⡴⠿⣦⠄⠹⣿⠇⣼⠻⣯⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠦⠐⠛⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⣹⡖⠈⠀⠀⠀⠀⠰⠃⣠⠂⠲⠾⠁⠀⣏⠀⠀⡶⠀⠁⠾⠟⠙⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠦⠼⡿⢣⣄⠀⢠⠄⣀⡀⠀⠈⠀⢀⡀⠈⠋⢿⠷⣄⢀⣤⠀⠠⢾⢤⣄
⠀⠀⠀⠀⠀⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⡀⠄⠶⠦⠴⠞⠛⠛⠋⠁⠀⢠⡞⢀⠃⠀⠙⢧⠀⠀⠈⠀⢁⠀⢀⠘⠳⠆⣠⠿⠀⠀⠙⠁⠀⠳⢾⣶⡘
⠀⠀⠀⣀⡘⠋⠀⠀⠀⠶⠄⢠⠜⠛⠀⠚⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⣤⠀⠀⠀⠈⢳⣤⣢⠀⠀⠘⠀⣤⠀⠤⠛⠀⠘⢢⣀⣀⡠⠘⠏⠠⠇
⠀⠀⠀⠛⠓⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⣿⡇⣶⣀⠀⢻⠻⣟⠀⣀⠐⠂⠈⢦⠀⠀⠀⠀⠀⢻⠉⠀⣠⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⢰⣇⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠐⠀⠀⠛⢀⡉⠉⠉⠓⣄⣩⣄⣠⣄⣀⠀⠈⠆⠀⠀⠀⠀⢺⣀⡄⠋⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢀⠐⠃⠀⠛⣹⣶⠟⠈⠹⡇⠈⢦⡄⠀⠉⠙⠛⠃⣴⣀⠀⣠⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠀⠀⠀⠀⠘⠛⠆⠁⣀⣰⠃⢀⡞⢁⠀⠀⠀⠀⠀⠘⠃⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠴⠆⠲⠖⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡉⠄⠘⢥⠾⡄⠀⠀⠀⠀⠀⠂⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⣴⡞⠋⠉⠉⠉⠉⠛⠓⠤⣄⡀⠀⠀⠈⣧⠀⠀⠀⠀⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠚⠋⢀⡴⠂⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⢸⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⣰⠏⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢦⣤⣠⠞⠋⠁⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠠⡷⠀⠸⣿⡀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣀⠶⣄⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣥⣤⢤⣤⠂⠶⠸⡗⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⠂⠈⠦⡀⢀⡅
⠀⠀⠀⠀⠀⢀⣠⠞⠛⠈⠀⠀⠀⠘⠠⡀⢸⡇⠀⠀⣠⢾⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠐⠀⠹⠆⡇
⠀⠀⠀⢀⣴⠎⠹⠀⠀⠀⠄⠀⢀⠀⠀⠁⡀⠀⣠⠞⠁⣸⠃⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⠀⠀⣠⠀⠀⠀⠀⠒⠃⡀
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⢇⡰⠁⠀⠀⣿⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠘⢳⣄⡀⠀⠀⠱⡀
⠀⡼⠋⠘⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢰⡾⠁⠀⠀⠈⠇⠀⠀⠀⠀⠀⠙⠃⠀⠀⣱⣄⠀⠀⠀⢴⠋⠀⣀⡷⠤⠄⠋⠉⢳⣄⠀⠀⠻⡄
⣾⡇⡀⠀⠀⠀⠀⣠⠃⠀⠀⠀⡀⣠⣤⣿⠀⠀⣀⣤⣴⠦⠀⠀⠀⠀⡾⠁⠀⡀⠀⠀⠈⠑⢤⡀⠀⠀⠠⠏⢁⠀⠀⠠⠀⠀⠙⠳⢄⡀
⠿⠁⠀⠀⠀⣠⠞⠁⠀⠀⣠⠾⢛⠉⠩⠻⣾⢢⠏⠉⢹⠒⢢⣤⣴⠇⠀⠀⣤⠉⠐⠄⠉⠁⠀⠽⣦⣴⠂⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈⠛⢂
⠀⠐⠒⠒⠉⠁⠀⠀⢠⡞⠋⠀⠉⢁⡆⢠⡿⠁⢀⣤⣾⣀⠀⠈⢻⡄⢀⡞⠁⡄⠀⠀⠁⠀⠀⠀⠙⠙⣷⣄⠀⠐⡀⠀⠀⠀⠐⠀⠀⠀⠘⠿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠐⠙⡟⣿⢀⡴⠉⠀⠀⠛⠻⢷⣆⢠⡾⠀⠀⢣⡀⠀⠀⠐⡀⠀⠀⠀⠘⢻⣆⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⡄⠀⠀⡇⣿⡌⠁⠀⡆⠀⠀⠀⠀⢹⣿⣶⠁⠀⠀⠱⠀⠀⠀⠑⢄⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦
⠀⠀⠀⠀⢀⣼⠛⠀⠀⠀⣀⠀⠀⠀⢸⣿⡄⠀⠀⢃⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⡄⠀⠀⠀⠓⢤⡀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠚⠠⠤⠀⠁
⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⠟⠀⠀⠀⣼⠏⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣆⠀⠀⠀⢰⡄
⠀⠀⠀⣾⠃⠀⠀⠀⣰⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⣿⠇⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⣄⠀⠀⠀⠱
⠀⠀⠀⡏⠀⠀⢀⡴⠃⠀⠀⡄⠀⠈⣿⡄⠀⠀⠀⠸⠂⠀⠈⢀⠀⠀⠀⠈⣧⠀⢄⣀⡰⠀⠀⠘⢻⡆⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠁⠤⠔⠋⠀⠀⠀⠀⡇⠀⠀⠘⣷⣂⠀⢠⡇⠀⠀⠀⠈⢂⡀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠈⠛⠑⠉⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠋⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠁⢃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⣀⠇⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠢⠔⢢⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠢⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠉⠈⢆⣸⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠤⣀⠖⠦⠔⢊⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⣀⣆⣠⠀⠑⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⢠⠋⠻⠟⡆⠀⢰⠁⠛⠋⠆⠀⠀⠀⠀⠀⠀⢎
⠀⠀⠀⠀⠀⠠⡤⠤⠔⠢⠼⠀⠀⠀⠀⠓⠤⠐⠁⠀⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣐⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⣠⣀⠔⠊⢻⠐⠢⠤⠤⣀⡠⢀⣘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠊⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠈⠉⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⠄⠀⠀⠲⢭⡢⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢠⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣤⠀⡼⠁⠀⢠⠏⢀⣀⣠⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠠⣦⡀⠘⣆⡀⠦⡏⠠⢁⣄⣴⡡⠒⠋⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠲⠂⠀⣈⢦⣌⠟⢧⣱⠛⠂⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠤⠖⠒⣚⡒⣬⣟⣟⠿⣿⣿⣿⣖⣈⠀⢈⣁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡰⡷⠀⠀⠀⠉⠀⠐⠛⠛⡒⠙⡋⠏⠋⠉⠁⠻⡁⠈⠁⠈⠀⠀⠀⢀⣀⡤⠂⡸
⠀⠀⠀⠀⠀⡔⠀⠀⠉⠀⠀⠀⠈⢸⠁⠀⠀⠀⠀⠶⠂⠀⠀⢀⡸⢰⡌⢀⠉⠻⠻⢷⣶⣄⡀⢀⡠⠞⢉⣀⣠⠞⠁
⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢘⠀⠀⠱⠶⠀⠀⠈⠙⠻⢟⠛⠉⠉⠁
⠀⠀⠀⠊⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠈⠢⢤⣱⣤⣀⣀⣀⡠⠀⠀⣠⠜⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⢠⠀⠀⠀⠙⠯⣅⣀⡤⠞⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠏⣾⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡀⢽⢠⡿⣄⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠤⠴⡅⠀⠸⣟⣱⠏⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄⠀⠈⠢⢠⡧⠁⢀⠔⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⡄⠀⠀⠀⡠⡀⠀⢳⣌⠓⠀⡀⠀⠧⠔⠁⠀⠟⣿⠀⠀⣠⡆⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱⣌⠉⣙⠶⠋⠙⢦⡀⣿⢁⠀⠈⠳⠠⠀⣠⡞⠹⣇⣠⢞⠇⠉⠒⢋⠛⣉⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡿⣄⡅⠀⠀⠀⠈⠛⠫⠀⠀⠢⣠⢀⡷⠉⢀⠈⢩⠁⠸⠀⠀⠀⠰⠾⢏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡁⣉⠘⠳⣀⠀⠀⡇⠀⢲⠀⠀⡀⠈⢙⣧⡶⣃⠐⠂⠀⡆⢀⣂⡘⠛⣉⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠉⠉⢉⣳⣤⡇⠀⢸⠀⢠⠈⠢⣼⣿⣲⡁⠀⡀⠀⠠⢈⡁⢉⣀⠀⠬⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣫⣴⡈⡉⠉⠁⣀⣭⡶⣾⠀⢸⡀⠈⢀⣷⠏⠀⠀⣟⡔⠃⠡⢠⣤⣤⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢭⣬⡭⢉⠀⣐⣀⣨⣷⣼⠁⠀⢸⡿⠆⡄⢠⢟⠀⠠⢀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡒⠌⠃⠀⠲⣿⣧⣄⣸⡿⢊⣵⣻⣾⡶⠶⠛⠻⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠲⡉⠉⠉⣙⣢⣀⣥⣁⣬⣿⣿⣷⣟⣱⡟⠉⢀⡠⠀⢈⡭⠿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣤⣤⠾⠛⠉⠡⠉⠀⡨⠋⣠⢿⣿⣹⠛⠭⣛⡑⠛⠒⢶⠾⠶⠞⣻⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠮⠤⠴⠶⣦⡤⠶⠚⠁⣾⠁⠙⠢⣀⣈⣳⣄⣀⡤⠽⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠘⡟⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠔⠂⡟⠩⠷⣤⣴⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠉⠒⢖⠃⠇⣷⣰⠆⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠀⠀⢸⠑⢠⡿⢷⠴⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⢀⡤⣄⡀⠀⠀⣸⠀⢀⠀⠠⣱⢀⡇⢀⣠⣆⠀⢧⣀⣀⡴⠋⢛⣶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣝⠉⢀⠀⠉⠑⡒⠁⠀⠈⢂⢇⠈⢩⡃⠋⠉⠁⠉⣚⠯⢁⡬⠖⠉⠁⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣊⣨⠷⡦⣁⣇⠰⠂⠀⡠⣲⣀⠀⠊⣪⠁⡀⠀⠰⠟⣫⡶⠿⠗⢓⠗⠈⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⠴⢷⣋⢍⡳⠷⣦⡖⠧⢷⡄⠌⣟⠀⠁⣀⡠⢞⢥⠀⢀⡔⠃⢀⣀⣈⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠲⢤⡀⠴⣂⣀⡈⠈⠙⠓⢦⡉⢹⣃⡤⡶⠋⠀⣀⡀⠕⣛⣽⡏⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠙⠢⠀⠠⠀⡀⠉⢾⣧⣾⣿⣦⣿⣷⣶⣿⣿⣯⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣮⡤⠴⠒⠒⠊⠉⡉⠉⠉⢹⢿⣟⠻⠿⠀⢀⡐⠀⠀⢋⠉⠙⢺⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⢤⣀⡰⠶⠮⢄⣀⣔⣁⣾⡿⡄⠀⠀⠀⢈⠀⣐⣸⣆⡤⠴⠒⠒⠚⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢻⣩⠟⢸⡇⠹⡄⢠⠞⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⡘⡇⠀⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⡀⠀⠀⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⢀⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣦⠀⢠⣾⣧⣴⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣻⣿⡿⡿⢿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠐⠻⠿⠿⠛⠛⠉⢡⢀⣀⢘⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢧⣸⣆⠄⠀⠀⠀⠀⠀⠀⠈⠹⣿⠋⠁⠁⠈⢦⣽⣷⣿⣿⣿⡟⣁
⠀⣿⣶⡄⠀⠀⠀⠀⠀⢿⢾⢮⢟⣿⣀⣤⠀⠀⠀⠀⠀⠀⠉⢠⠒⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶
⠀⢼⣯⣄⡀⠀⠀⠀⠀⠀⠄⢤⠜⢑⠫⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⣾⣿⣟⣻⣽⣿⣿⣿⣿⣿⡿⠏⠁
⣶⣼⣿⡿⠻⠇⠉⢀⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠚⠉⠃
⣿⣥⣄⢀⣄⣷⢶⣿⢋⡍⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠿⠿⠿⠁
⣿⣿⣿⣶⣿⣑⣺⣿⡏⡁⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⣀⣀
⣿⣿⣿⣿⢿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠙⠻⠳⠦⡀⠀⣤⢤⢀⣀⠄
⠀⠉⠁⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣿⣿⣿⣶⣺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣴⠀⠀⣿⠀⣁⣽⣿⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⣠⣿⣽⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠾⠿⢻⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣸⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⣀⣀⣀⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠛⠛⠛⠋⠉⠉⢻⠋⠉⠉⠛⠛⠛⠛⠻⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣂⠐⢁⣰⠐⡐⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡮⠿⣧⠟⡈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠲⠊⠁⠘⠠⠢⠄⡖⠒⠆⢹⠊⠁⠈
⠀⠀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣄⠘⠓⢂⠀⠀⢀⡀⣾⣗⠦⢀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡴⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⠀⠀⠀⠘⣏⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣰⡦⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠉
⠀⠀⠀⠀⠀⣀⠩⠉⠀⣀⡿⡄⠀⠠⣤⡄⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⢠⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠤⠛⣿⡆⠀⣤⣾⣷⠟⡴⢾⣿⢀⣠⠾⠋⣠⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢈⣀⠀⠀⢀⡀⠂⠺⢃⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠊⠁⠀⠘⡂⠈⠡⠄

⠀⠀⠀⣀
⠀⠀⠀⠈⢏⠃⠂⠀⠤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⡆⠀⣄⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⢀⠄⠀⢧
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠐⠌⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠀⠁⠀⠀⠀⠐⠀⠀⠄
⠀⠐⠂⠄⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠓⠄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡄⠄⠐⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡁⠀⠀⢂⠀⠀⠘⠀⠀⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠂⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠁⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⢠⠀⣰⢀⣠⢀⢠⠀⡀⣰⡀⡀⡀⡀⠀⠀⠁⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠸⠁⠀⠀⢰⠋⢉⡆⣻⡷⢠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠎⠀⠃⠀⠀⠀⠀⠀⢈⣄⠲⢀⠠⠇⠀⠲⣠⠋
⠀⠀⠀⠀⠀⠀⢸⡷⣤⡖⢸⠎⡷⡰⢻⡿⡇⡼⡖⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠡⡁⢀⠀⡄⠀⠄⢈⠀⠀⠀⠁⠀⠀⠀⠀⠿⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⠀⠌⠀⠈⡠⠊⠀⠀⠀⠀⠀⣄⠀⠁⡀⠙⠒⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳⢀⢊⡴⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢡⠀⠈⢆⠀⠁⠢⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⣄⣀⠊⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⠂⠀⣀⡘⠂⠐⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠈⠁⠈⠄⡆⠀⠀⠀⠀⠀⡂⠀⠀⠀⢠⣃⠀⠀⠀⠇⠀⠀⠸⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠢⣁⠀⠀⠀⠀⠀⠁⠀⠀⠊⣠⠆⢈⠂⣀⠐⣀⡘⠀⡡⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⠀⠀⠀⠀⢀⠔⠀⠁⠀⠀⠀⠈⠒⡀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡠⠀⠀⠀⠰⠠⡀⠁⠀⠀⠁⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣸⣿⣿⣷⡀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣷⣦⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⡛⢿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⠏⠀⡇⠀⠁⠀⠈⠋⠻⠁⠀⠀⣀⣴⣿⢿⡟⠀⠀⠀⣀⣀⣤⡴
⠀⠀⠀⠲⣶⣤⣤⣄⣀⡀⢹⣿⣿⡿⣶⣄⠀⣿⣿⠟⠁⢀⡰⠆⠀⠀⠀⠀⠀⠐⠀⠀⠾⣿⡿⢿⣿⣷⣶⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠙⢿⣿⠿⠏⠙⠿⠟⠁⠀⠈⠛⠳⣿⠃⢀⡠⠊⠣⡀⣈⣁⣀⣀⣀⠖⠀⠀⠀⢱⡇⠀⠉⠻⠋⢁⠈⢻⠏
⠀⠀⠀⠀⠀⠈⠣⡀⢃⣄⣀⡀⠀⠀⠀⠀⠀⠀⣱⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠘⠀⠀⠀⠀⠀⠙⢤⡁
⠀⠀⠀⣀⡀⢤⣴⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣤⣤⣶⣾⣿⣶⣦⠄
⠀⠀⠀⠀⠉⠛⠿⢿⣿⠿⠿⠿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠀⢠⣀⣄⡀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢽⠀⢠⠞⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⡀⠤⠴⠚⠛⠛⠛⠛⠛⢻⣿⣿⠉⠋⠉⠒⠒⠒⠻⠤⠦⠤⣔⣛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢼⣿⠛⢹⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⢿⣞⠿⠿⠟⠠⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡃⢻⢀⡙⣷⢶⡀⢀⣴⠏⢋⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠖⣀⡀⠀⠠⠒⡏⠲⣅⠹⡼⣿⣟⠁⣠⠟⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢰⡟⢡⠗⡴⡈⠂⡧⠀⠙⢦⠁⠏⡷⡹⡍⠀⣠⢚⠟⢀⣤⠒⠋⡠⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡦⣰⢡⠏⠀⡏⠘⡵⠙⠀⠇⠀⣴⠞⣹⡢⡄⢡⠿⠊⠁⣈⠴⡏⠀⠀⢨⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⡏⠄⡀⠀⠀⠀⠐⠀⡀⠈⠁⠃⢀⠑⠹⠣⡀⠀⠈⠀⠀⠙⠄⠀⣿⡀⠐
⠀⠀⠀⠀⠀⠀⠉⠀⡠⣿⣧⣀⣇⢀⡇⢀⠀⢉⡇⢀⣤⠀⣿⡄⠀⢸⡇⠀⢸⡇⠒⡖⡀⢰⣿⠻⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣗⢬⡿⣸⡟⢨⣏⣺⡗⠄⣿⢀⣿⡧⣿⢹⣯⠀⣸⡇⢀⡇⠁⢽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣻⣿⢺⡇⢾⣯⣬⣿⢴⣿⣇⣿⣽⣟⣺⣿⣧⣼⡿⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⡖⣻⣟⠒⣟⡿⣿⢭⣿⣿⣯⣻⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠽⠛⠚⣿⠓⠛⠿⠿⠭⢿⠽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⡆⣤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢀⠔⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠐⠁⠀⠀⠘⠁⡀⠀⠒⠲⢄⢀⠠⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠣⣀⠂⠠⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⠈⣿⣵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠳⢄⠤⣤⣀⣁⠐⠤⠀⠐⢞⣻⠎⡁⠀⢭⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠠⠅⠀⣼⣿⡿⠀⠒⢄⠀⠀⠉⡆⠈⠀⠀⠉⠸
⠀⠀⠀⠀⢀⠄⠀⠀⠼⠀⠀⠀⠐⢇⠀⠋⠹⠁⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⡜⠒⢀⣤⡂⠀⠀⠀⢰⡀
⠀⠀⠀⠁⠀⠀⠁⢁⣤⣴⠊⢨⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠁⡾⠆⢀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠲⠀⠈⠀⠰⠀⠀⠀⠀⢰⠄⡃⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠈⠂⠤⣤⣷⣠⠀⠀⠀⢐⠂⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠰⠆⠀⠀⢀⢿⣾⡯⠓⠒⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠀⡀⢈⠠⠁⠀⡏⡐⠒⠠⢀⣰⠿⡐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠆⢘⠀⠳⡀⠀⣰⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⠴⠐⠀⢠⠃⠀⡬⣿⣹⠶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠁⠢⣤⡷⠛⣮⣀⠤⠚⡁⢀⡄⠀⠀⠻⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠄⠱⠤⢴⣀⡀⠠⢽⣷⣤⡿⣇⠀⠀⠀⢨⠃⢶⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡄⠒⠁⣘⢹⡀⢀⠀⠀⡘⠙⠀⠘⢆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣀⠠⢶⠻⠠⠂⣡⠀⡛⠰⠀⠈⢃⡀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠰⠦⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⣉⣄⣠⡀⠁⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⡏⠉⠉⠛⣷⡄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⢻⣦⣤⠄⠀⠘⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡿⢀⣴⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣟⠐⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣄⠀⣿⠁⠀⠘⠦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡁⢙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢠⣶⠿⠿⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢻⣏⠀⠀⢀⠹⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣈⠙⠛⠁⡰⠂⣿⠀⠀⠀⣠⡤⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⢰⡇⠓⠀⢀⡿⠀⣠⠟⣩⠖⠛⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠁⠂⠀⣾⠃⣼⣣⠞⡕⢺⠇⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠖⠁⠀⠈⠛⠀⠀⠈⣸⣾⣏
⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠦⠶⣤⣄⡀⠀⠀⠀⠙⣶⣦⣴⡿⠀⠀⠀⠀⠘⢃⣼⠟⠉⠀⠈⠳⢄
⠀⠀⠀⠀⠙⢿⣄⠰⣖⢛⡿⣶⢶⣬⣇⠀⠀⢀⣀⣽⣿⣿⡷⢦⣤⠶⠖⠋⠛⢿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⣷⡈⠫⡻⣄⡈⠉⢛⡷⠀⠉⠁⠉⢻⡏⠁⣾⠁⠀⠀⠐⠀⢼⣿⣆⣤⣤⣶⠷⠚⠓⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣌⠊⠗⣦⣌⠀⠀⠀⠀⠀⣈⡳⠂⠉⠀⠂⣤⣤⣴⣾⣿⣏⣹⣿⡿⠂⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠉⠘⢦⡀⠀⡀⣤⡿⠁⠀⠀⠀⠀⠁⠈⠙⠛⣻⣿⣿⣿⣷⣄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⢿⣿⣂⠠⠤⠤⢤⡁⢀⠊⠉⠁⠀⠙⢯⡀⠙⢣⣤⣜⣓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢚⣿⠶⣿⣏⡿⠀⠀⠀⠀⠙⢬⡄⠀⠀⠀⠀⠀⠉⠀⠀⠛⢉⠻⢿⠦⡙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢻⣌⡇⠀⠀⠀⠈⠀⣸⣷⠀⠀⠀⣀⡀⠂⠠⣶⣁⠦⠤⠴⠴⠙⣣⡘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣿⠗⣀⡀⣤⣤⣤⣼⣿⡷⢿⣾⠉⠀⠀⠀⠀⢩⣤⣥⣉⣉⣉⣉⣥⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⢻⡄⠀⠀⠀⣠⣳⠞⠉⠁⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢡⠉⠈⠉⠁⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⡼⣻⠟⠁⡋⢃⡤⡆⠀⠀⠀⠀⠀⠀⢸⡿⠁⢻⠿⣦⡀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡿⢱⣯⣴⠶⠟⡫⠜⣣⡀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠈⠟⡹⢿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠧⠖⠒⠒⣉⣡⣴⠞⠛⠁⠉⠒⠀⠂⠹⠀⠀⠀⠀⠀⠀⠈⡅⠉⢋⢷⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣤⣴⡶⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⢀⣤⣾⡓⢦⣈⡌⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⢷⣝⠦⣍⡃⣿⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣙⠛⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠉⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⠀⢆⢀⠔⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢪⠁
⠀⠀⠀⠀⠀⠀⠀⢩⠁⠂⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠦⠤⠂⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠠⡄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠄⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠑⠒⠂⠒⠄⣀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠉⠙⢦⡐⠀⠀⠀⣿⠀⠀⠀⠐⣠⠞⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣿⠀⠀⠀⡴⠃⠀⠀⠀⢀⢀⣀⡀⠀⠀⠈⠀⠀⡠⠊
⠀⣀⣀⡀⠤⠄⠒⠈⠉⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⠀⠈⢧⡀⣿⠀⣠⠞⣁⣠⠴⠖⠚⠉⠁⠀⠉⠂⣀⠀⠀⡼
⠀⠀⠉⠉⠀⠒⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⡲⠶⢿⣿⣾⠟⠋⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⢻⡗⠂⠤⣀⠀⠀⠀⠠⡁⠀⠀⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠀⠉⠉⠉⠱⠀⠀⠀⡀⠔⠈⠀⠀⠀⢸⡇⠀⠀⠀⠉⠐⠢⢄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⡠⠐⠋⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧

⠀⠀⠀⠀⠁⠀⢤⣧⣤⣀⡀⠀⠤⡃⠀⠿⣿⡷
⠀⠀⠀⠀⠀⠉⠿⢿⡿⠏⠀⠀⠐⠚⠁⠀⢸⡇
⠀⠠⡄⠰⡂⣠⠀⠀⠀⠀⠀⠈⠙
⠀⠈⠹⠀⠀⠨⠀⢰⡀⠆⠀⠉
⠀⢀⣰⣀⡀⠀⠀⢀⡡
⠐⢲⣿⣿⣿⠉⠀⠀⠸
⠀⠀⠀⠉⠀⠀⠀⠒⠆⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣤⣾⣇
⠀⡇⠀⡄⢠⡀⠐⠒⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠛⡆⠀⠀⣀⠄⠉⢻⡏
⠀⠀⠀⠉⠈⠠⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠎⠀⢀⡀⠸⠃
⠸⣿⣶⠯⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠈⠛
⢀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣠⣀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⡃⠀⠈⢐⣆⠘⡀⢴⡀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠉⢻⡇⠀⠀⠀⠸⠀⠀⠈⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠀⠸⠃⠈⠀⠠⣼⣤⣀⠀⠀⠠⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⡀⢄⠀⠀⠀⠈⢹⡿⣿⠿⠉⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢌⠀⠀⠀⠰⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠈⢀⣠⣐⣗⡁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠬⡶⠉⢽⠋⠘⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⣻⣦⠈⠁⡐⡄⠙⣆⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⢹⣶⢷⣏⣀⡀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣷⣼⣿⡟⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠉⢹⣿⣿⣿⡤⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢴⠃⠀⠀⣨⠀⠈⢾⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣀⠐⢀⡀⢀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⠀⢀⠁⣤⠐⡊⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⠈⢻⡦⡼⢡⠜⠁⠀⠀⠀⢠
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢨⡶⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡞⠃⠀⠀⠰⠷⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠼⠟⠁⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣸⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠿⠿⠟⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣸⣧⠖⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠶⠀⣀⣤⠀⠀⢰⣤⡿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣔⠂⢀⣸⣾⡧⣌⣉⢛⣋⣽⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣥⡀⠀⠃⠀⠀⠀⣀⡀⠈⠁⠀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⣱⣏⣈⣉⠂⠘⢿⣾⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⣆⡀⠀⣠⡾⢿⣷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠝⢉⣹⣷⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠉⠀⠸⣿⣿⡆⢰⡇⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣤⡿⣻⣿⣿⣿⢿⣿⣿⣿⣤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠠⡄⠀⠀⣴⠿⣿⡇⠀⢿⣾⠃
⠀⠀⠀⠀⠠⣤⣿⡴⣿⣿⠯⣠⣘⣿⢿⣽⣧⣾⣹⣿⣿⣿⣿⣿⣿⠚⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠿
⠀⠀⠀⠀⠘⠛⣿⣿⣨⣷⣿⣿⣏⣵⠂⢿⢿⣿⣿⣿⣿⣿⣏⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⡷⣿⣿⣷⣴⣾⣿⣿⣿⣿⣏⠛⠳⠖⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡀
⠀⠀⠀⠀⠀⢀⠉⢙⠛⣿⣿⢿⣩⣭⣿⢿⣿⣿⣟⡻⢂⣥⣤⠀⠀⠰⠄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗
⠀⠀⠀⠀⠀⠈⢱⣿⡵⣿⣿⣻⣷⣶⡽⣺⡏⠿⢻⡿⠟⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠶⠶⠿⠆
⠀⠀⠀⠀⠀⣴⢄⣽⣷⣿⣯⣴⣿⣿⣿⣷⣿⢲⣟⣲⣤⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟
⠀⠀⠀⠀⠀⠉⠈⢛⣿⣿⡞⠁⠉⡙⠉⢿⣿⠻⠿⢁⠀⠀⠈⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠷⣶⣆⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⠀⣰⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠈⠀⠙⣟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣀⡀⠀⠀⣿⠀⢀⠂⠣⠀⣠⡄
⠀⠀⠀⠀⠀⢀⣤⣤⣄⠰⠦⡄⢶⣧⣿⣿⣦⣀⡀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠁⠀⠀⡇⠀⠀⠻⢶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠈⠛⠈⠓⠉⠛⠛⠋⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠋⣥⡀⠰⢏⣲⣶⣾⣅⠀⠀⠀⢰⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣠⣀⠀⠚⠀⠀⢀⢙⣿⣟⡳⣬⣴⢮⣀⠰⣯⣤⣍⡠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢯⠉⠙⠛⠻⢾⠿⢿⣿⣤⡄⠻⡿⡴⢮⣽⢿⣿⣿⣟⠛⠛⠛⢲⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠉⠀⠀⢀⣀⡠⠔⣂⣝⣯⡿⡉⡀⠀⡀⠠⣴⣌⡹⣿⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠓⣀⡀⠼⢲⡿⣤⣠⡟⡠⠚⠁⠀⢻⡟⣿⡿⠶⣶⣶⣥⣿⣷⣿⣷⣿⣍⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡭⠠⠲⠟⡑⠛⣿⠊⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠛⢦⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠀⠀⠐⣻⣧⣄⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡀⠀⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡥⠈⠁⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠶⣄⠀⠀⢀⡤⠦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡰⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⡀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⢺⣷⠀⣠⠖⠋⠉⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⠤⡴⠤⠤⢀⡴⠀⢀⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢶⣂⡠⠖⠳⢿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡀⢀⠐⠁⠂⠑⠀⠆⢠⡀⠭⠃⡖
⠀⠀⠀⢀⠤⣤⡤⠀⣞⣀⣠⡴⣀⠸⠿⠾⠓⠚⠛⠛⡟⠿⣾⣛⣻⣉⣟⠷⠿⢷⣄⣰⠈⠁⠈⠢⡀⠀⠀⠀⠀⠈⠻⣦⣆⢸⡆⠀⠀⠜⠀⡰
⡀⠠⠒⢠⢿⣷⣴⣶⠞⠩⠀⡠⠊⢀⣔⣲⣂⠀⢠⠞⠛⠛⠛⠛⠛⠛⠻⠿⣷⣦⣝⠿⣦⣦⣤⣤⣀⣄⠀⠀⠀⠀⠀⠙⣿⡟⠉⠂⠼⢄⡠
⠑⠶⠚⢁⠸⣿⡭⢀⡃⠀⠞⠀⠀⠛⣼⡟⠉⣴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣮⡻⣿⣿⠏⣈⣧⠀⠀⠀⠀⠀⠸⣯⡂⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠋⣸⣷⡟⢀⣀⣴⣿⠉⣧⠈⣥⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡛⠋⠉⣁⣴⠀⣿⡇⠀⠀⠀⠀⠀⠙⠇⠤⡴
⠀⠀⢴⣢⠞⠱⠊⢙⣿⢟⣿⣿⣿⣿⠘⡇⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣈⠛⣿⡟⠦⣿⡇⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠻⠂⣠⠀⠙⠛⢻⣿⣿⣿⣿⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡀⠘⠣⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠉⠒⠒⢚⡽⠉⢿⡿⠋⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠂⡰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⡈⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿