Eyes biting lip Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⢚⣛⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢂⣨⣵⣶⣤⣾⣽⣾⣿⣿⣦⡈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⢁⣴⢟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢫⣾⣣⣿⣿⣿⣿⣿⡏⠉⢙⠏⢹⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣿⣷⣿⣿⣿⣏⠀⠀⠱⡀⠀⢀⠄⠿⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⣿⣿⡟⠈⢻⡁⢀⣠⠟⠈⠁⢀⠒⠒⣂⠊⢝⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠋⢻⣀⣴⣿⠋⠊⠀⢀⣠⠁⢠⣻⣿⣷⡮⢧⠸
⠀⠀⠀⠀⠀⠀⠀⢱⠁⣿⣿⣏⠀⠀⢿⣿⣏⠀⠀⠀⠀⢐⡀⠈⠻⢿⠟⢃⣝⡺⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣰⣿⣿⣿⣾⡀⢸⣿⣿⡀⠀⠀⠀⠁⠈⠒⠄⢤⠐⢪⣾⣿⣦⢿
⠀⠀⠀⠀⠀⠀⠀⡄⠹⣿⣏⣿⣿⣿⣿⣿⠿⢷⠀⠀⠀⠀⠀⠀⠀⣈⣴⣿⣿⢿⣿⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠻⣿⣿⣟⣉⣉⣄⣠⣤⣦⣾⠿⠟⢛⣻⣿⣿⣿⣿⣿⢸⡿⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⡻⢿⣿⣿⣭⣭⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⡴⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣄⠉⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣫⠴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠁⠀⠄⠉⠙⠻⣿⣞⠒⠒⠈⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣀⣄⣆⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣷⣼⣴⣤⣧⣤⡀⢀
⠀⠀⠀⠀⢠⣠⣵⣾⣿⣿⣿⢿⣿⣿⢿⣯⣴⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡷⢿⣟⢿⣿⣟⢿⠿⡿⢿⣷⣦⣎⠀⢀
⠀⠀⠑⠶⠿⢿⣟⠁⠈⠄⠳⣿⠿⢁⣿⠃⠈⢻⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠏⠀⠈⢿⣌⡛⠟⣋⠀⠁⢀⣽⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠉⠹⢳⡦⣤⣙⣒⣚⣻⠡⠖⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠂⢪⡭⡭⣥⢶⠺⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠘⠈⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠋⠀⠀⠀⠀⢰⣶⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⢴⣿⢁⡀⠀⢀⣀⡀⣾⡏⢰⡿⠀⠀⠀⢀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣷⢻⣿⢠⠏⣹⢇⣿⢡⣿⠃⣼⢿⡦⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⢿⣉⣡⢞⣿⠫⣿⠼⣧⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣿⣿⣽⣿⣯⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣿⣿⣿⢿⣯⣛⣿⣿⠿⠿⠿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢯⣸⣄⠀⠈⢙⡉⠁⢀⣤⣾⣿⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣾⣿⣿⣿⣿⠿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡿⠋⣳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠃

⠀⠀⠀⠀⠀⠀⠀⢀⡈⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣤⣤⣤⣤⠤⡀⠀⠀⠀⠀⢀⠤⣤⣤⣤⣤⣾⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣶⣦⣴⣤⣶⢘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⣟⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁

⣶⡖⡶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠛⠿⢿⣷⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⣹⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣤⣄⣀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⢀⣴⡿⣿⣯⣍⣻⣷⡀⠀⠀⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣄⣸⣿⣿⠇⢸⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⠆⣼⠇⠀⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⠻⣧⣀⠀⠈⠛⠿⠿⠶⠟⠁⠀⠀⣠⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠚⠋⠛⠓⠂⠄⠄⠀⠀⠀⠀⠀⠘⠃⠈⣉⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣤⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣥⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⠿⠿⠿⠿⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢹

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠐⠃⠀⠀⣷⣀⣀⣴⠿⠿⠿⠓⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⣄⣨⣤⣤⣦⠀⢠⣶⣿⣿⣿⣿⣧⣀⣑⣦⢄⡀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⢡⣿⣿⣿⣿⡿⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣴⣿⣿⣿⡟⠛⢧⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠖⠀⠑⡀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠈⢠⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣿⢛⣿⣿⣿⣟⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⣿⠿⠛⠋⠀⠤⠤⠃⠈⢟⠒⠀⣄⡀⠈⠀⠀⠀⠀⠙⢦⡘⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠂⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠱⣶⣇⣈⠰⢇⠀⠀⠘⡄⠀⣿⣄⠻⣿⣿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢛⣿⣆⠀⠐⢄⠀⢻⠀⠈⣯⣷⠹⣿⡋⣈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⠻⣦⡝⣿⡇⠀⠀⠀⣠⠀⠀⠸⣿⣇⢻⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⡛⠻⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠣⠙⠋⠾⠀⠀⠀⣽⣧⢱⡀⠄⠈⢀⠀⠀⢿⣿⡎⣧⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣙⠀⠁⠀⠀⢸⡆⠀⢸⡿⣷⡄⢘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡎⢻⠀⠀⠀⠀⠀⢧⠀⢸⣿⢏⣥⣾⣿
⣿⡿⢿⣿⠟⣿⡿⠟⠛⠻⣿⣯⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠙⢱⣤⠆⠀⠀⠀⠀⢸⠀⡩⠷⣺⣿⣿⣿
⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢈⣰⢾⠘⠆⠀⠀⠀⠀⠈⠀⠁⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣴⣦⣄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡞⣅⣠⠂⠀⠀⠀⠀⣰⣏⠀⢠⣿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣄⣠⣼⣿⣿⣿⡀⢘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣡⠵⢈⡘⠁⠀⠀⠀⠀⣴⡿⠇⢰⣿⣷⣿⣿⡟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢰⣿⣿⣿⣿⡿⣿⣷⣾⣿⡉⠓⢦⣄⠀⠀⠀⠀⡀⢴⣾⡧⣼⡧⠍⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣼⣿⣿⣿⡟⣴⣾
⣿⣿⣿⣿⣿⣿⠛⠁⢀⣠⡴⢾⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣇⡀⠀⠙⢞⡓⢾⣿⣴⣞⣿⣧⣿⣷⣿⡀⠀⠀⣀⣴⣾⡧⠀⠀⠀⠀⠛⠋⠻⢿⣶⣿⣿
⣿⣿⣷⡄⢉⣥⣶⡟⣾⣿⣦⣼⣿⣿⣿⣿⣿⣿⡇⡙⣿⣿⡏⢛⠓⠢⠤⠼⢾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢁⣈⣿⣿⣿
⣿⣿⡟⠁⠘⠿⢿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⡷⢀⠀⠀⠀⠀⠀⠈⠳⣿⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣄⠀⠀⠀⠀⠸⠿⣿⣿⣿
⣿⣿⣿⣦⣔⣶⣿⢀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⠈⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠞⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠃⢀⡖⠁⢠⣶⣿⣾⣿
⣽⣿⣿⣿⣿⣼⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⢿⣿⣿⣿⣿⣿⣿⣷⠆⠀⢰⡞⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣽⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⠿⠛⠁⠀⠄⢸⣧⣀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣶⣄⣀⣴⣶⣿⣟⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠣⡀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢙⣰⣦⣴⣶⣶⣦⣈⣹⠟⣻⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⠏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠙⠉⠛⠚⠛⠟⠛⠛⠋⠛⢿⡿⠿⣿⣿⣿⣿
⣿⡿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣎⢠⣿⡿⠷⠴⠄⢂⣀⣀⣄⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⠛⠃⠉⠻⣿
⣿⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣶⣶⣯⣴⣶⣿⣿⣷⣾⡿⠛⠋⠉⠻⠶⠶⠾⠿⠦⠀⠀⠀⠢⠶⠞⠋⠁⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣾⣿⣿⣿⣯⣿⣿⣶⡢⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⡯⢍⡏⢉⠉⠉⠀⠀⡰⢦⣤⣶⣿⠟⢿⣿⣿⣯⣭⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠂⠐⠶⠶⠾⠿⣶⠋⠁⢙⡴⠻⣿⠿⠛⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣍⣂⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⢂⠄⣀⢀⣀⣀⢀⣀⣀⣀⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣯⣠⣇⡏⠈⡁⢀⠉⣨⣝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣏⣸⣄⣥⣈⣨⣬⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⡿⠿⠦⠔⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣶⣶⣦⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣻⣿⣾⡏⠛⢷⡀
⠀⠀⠀⠀⠀⣰⣾⣿⣿⡟⠛⡏⠻⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠿⣿⢿⣿⢿⣿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠻⠿⣿⣿⣿⡄
⠀⠀⠀⠀⣾⣿⣿⣷⣴⣦⣤⣦⣤⣷⣾⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣮⣤⣅⣀⣤⣀⣈⣰⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⠀⠀⠹⣯⣻⣿⣥⣤⣴⣦⣤⣤⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣶⣾⣿⣿⡿⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣤⣭⣭⣭⣤⣿⣾⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⣦⣀⢠⢀⢀⣼⢏⣿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⠟⡿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣶⣠⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡤⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠛⠋⡏⠉⢻⠈⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⡿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣤⣦⣤⣧⣤⣴⣴⣷⣿⡄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⣶⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣯⣥⣤⣤⣤⣽⣽⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⡿⠋⠉⠉⠉⠉⠉⠙⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣟⣻⠋⠛⡛⠋⠻⡋⠙⢿⣆
⠀⠀⠀⠀⠸⣿⣿⣿⠟⠛⠉⠋⠉⠛⠻⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⡁⠈⠁⠈⠉⣔⣠⣦⣿⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣟⡷⢤⣄⣀⣀⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣧⡀⣀⢀⡀⣀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠻⠛⢿⣛⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣾⣯⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣗⡒⣶⢓⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⠿⠿⣿⣿⣶⣦⣄⡀⠀⢀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢋⣴⣿⣉⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢏⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣯⣭⣽⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⠟⠋⠉⠀⠈⣿⠀⠀⠀⠉⠹⡿⠿⣟⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠨⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⣀⣾⣦⣄⣀⣤⣤⣤⣾⣷⣦⣤⠦⠈⢻⠶⠆⠘⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠁⣸⣿⣿⣿⣿⡿⢿⣿⣿⣧⠀⠈⠀⠀⠑⢶⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡷⠃⠀⢹⣿⣿⣿⣿⣿⣶⣿⣿⣿⡅⠀⠀⠀⠔⠃⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⢶⡧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠳⠞⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣧⡏⣼⣿⠀⠀⠘⠛⠿⠿⠿⠛⠁⠀⠀⠀⢰⡆⢀⠆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡇⢻⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠰⠃⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡓⢦⠁⡈⠠⠀⠀⡴⠀⠀⠀⠈⠁⠀⡔⠀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣤⡃⢴⣀⣑⢛⣶⠐⠢⣴⢆⡤⠶⢛⣠⣾⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣵⡟⠉⢉⣭⣼⣥⣤⣾⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣴⣄⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠳⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠉⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⣷⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⠉⠀⠒⠒⠂⠠⠤⠄⣀⣀⣀⠀⠀⠀⡔⢡⠃
⠀⠀⠀⣼⠁⢠⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠂
⠀⠀⣰⡏⢀⣿⡇⢀⣠⡞⠀⠀⢸⣇⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢰⡟⠀⠘⢿⣿⡿⠟⠀⠀⠀⠘⣿⣶⣾⠟⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⢀⣿⠃⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⢀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⣼⡟⠀⠀⠀⠻⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠘⡆⠀⠀⠀⠀⠀⣰⠟
⣿⡃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⠀⠀⠀⠀⠀⢀⡾⠃
⣿⡇⠀⠀⠀⠀⠀⠤⣤⡤⠤⢤⠄⠀⢒⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡤⣈⣁⡠⠃⠀⠀⠀⠀⢠⠟
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠑⠢⣤⠷⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⢿⣄⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠛⠷⣦⣄⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⡤⠔⠊⠀⠀⢀⡷⠶⢦⣤⣤⣤⣀⣀⣀⢘⣇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⡤⠾⠃
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠛⠛⠶⠖⠛⠉⠛⠲⣤⠖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⣠⠴⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣄
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠈⠲⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⣠⣄⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠉⠙⠓⠒⠶⠖⠚⠋⠁⠀⢿⣄⠁⣿⠀⠀⠫⣤⡇⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠁⠀⠒⠀⠤⠄⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡆⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢿⣷⡾⠃⠀⠸⣷⣤⠞⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⠤⠠⠀⢄⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠈⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠤⡄⠠⡄⠀⠠⠀⠀⠀⠀⠀⠀⠠⠌⠁⠈⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢰⡤⣤⣄⣀⣀⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣿⡀⠀⠀⣸⠀⠀⠀⠀⠈⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣂⣤⣴⣶⣶⣿⣿⣶⣶⣦⣄⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⡿⠟⠛⠛⣿⡿⠻⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣧⠀⠀⠀⠈⠉⠛⠇⠙⠋⠁⠀⠀⠀⠙⠋⠁⠀⠀⡙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠛⠿⢿⣿⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠋⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡿⠿⠃
⠀⠀⠀⠀⠀⢀⡀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣿⣿⣁⣤⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡆⢠⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡏⠉⠙⢯⣠⢸⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⢸⡃⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆⠀⠀⣄⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣀⣀⣠⡎⠓⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣿⠀⠀⠀⠚⠗⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠁⠀⠀⣾⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⢙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⣀⣠⡤⠶⠋⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣿⠟⠳⢤⣄⣀⣀⣀⣀⡠⠖⠉⠙⠲⢶⡿⠿⠋⠉⢉⡡⠤⠶⠒⠉⠁⢨⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⢨⠋⠈⠈⠀⠀⠀⠀⠀⠀⠙⢦⡀⠾⢯⣤⣄⣠⣤⣌⡀⠪⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣭⣿⡾⠛⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡇⠀⠇⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠋⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⢿⣿⣿⠙⣿⣿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣇⡀⠘⢻⠃⢠⣿⣿⠏⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠋⠂⠘⠿⠏⣠⣿⣿⣿⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣛⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣤⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡅⠀⠀⠁⣀⣀⡉⠀⠀⠀⠔⢉⣄⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢛⡤⣹⠀⠀⠰⠛⠗⠀⠀⠀⠀⠀⠉⠊⠋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣼⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠋⠻⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣶⣿⣵⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣏⣩⣬⣹⡇⠀⢸⠟⠛⠁⠁⠀⢠
⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣴⣿⣷⣶⠀⠀⠀⠀⠀⣿⡟⠛⠻⣿⠁⢀⡿⠀⠀⠀⠙⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠋⠳⡤⠀⠀⠹⣇⠀⠀⣿⠀⠋⠀⠀⠂⠀⠑⠆⠐⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢻⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠀⠀⠀⡧⢤⡙⠳⠞⠋⣆⡐⠀⠀⠀⠀⠀⠀⣈⡴⠃⢀
⠀⠀⠀⠀⣀⣤⠾⠃⠀⠀⣰⡏⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⠞⠀⠀⠀⠀⠀⣠⡞⠁⠈⠈
⠀⠐⢀⣼⠋⠀⠀⠀⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⡷⣶⣀⣀⠀⠀⠀⠀⡙⠀⠙⠏⠀⠀⠀⠀⡠⠚⠙⢿⣆
⢂⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⢻⣇⢰⠏⠈⠉⠁⠀⢀⠞⠀⠀⠀⠠⠀⠀⠀⠈⢣⠀⠀⠀⠙⣧
⢾⡃⠀⠀⣠⠶⠛⠛⠛⠛⠲⠤⣀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⡆⠀⠀⠀⠈⣧
⠈⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡜⠀⠀⠀⠀⠀⡘⢣⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠹⡄⠀⠀⢠⡟
⠀⠀⠳⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡐⠀⠀⠀⠀⠀⢠⠁⠀⢣⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣆⠀⡾⣷
⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡀⡜⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢳⡄⠀⠀⣸⢻⠀⠀⠀⠀⠀⠘⢶⠃⠸⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠹⡆⢠⠃⠸⡆⠀⠀⠀⠀⠀⠈⢳⡀⠛
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⠠⠤⢶⣿⠀⢹⠃⠈⠺⡇⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢀⡟⠀⠘⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠁⠀⠀⠀⠈⢧
⡀⡀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⢀⣴⡄⠀⠀⢀⣴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡠⠍⠛⠯⠀⢿⠇⠨⠟⠋⠥⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠁⣤⡦⠀⠈⠀⠠⡦⡄⠉⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⠀⠮⠴⠀⠀⠀⠠⠬⠆⠀⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⠛⡛⠂⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠚⡛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠁⠀⢀⠀⠈⢳⣶⣦⣶⣶⠋⠀⢀⠀⠀⠡⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⢀⠀⠀⠈⢹⠉⠀⠀⢀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⣀⠀⢑⠐⠂⢩⢐⠂⠒⠁⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠄⣄⠀⢈⠀⠘⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠂⠀⢸⣿⣶⣅⣴⣾⣿⠀⠀⠚⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀⣈⠀⠸⠿⠛⠁⠙⠻⠿⠀⢈⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣭⣶⣷⠿⠿⠟⠛⠛⠻⠿⢿⣿⣿⣷⢦⡀⠀⠀⠔⠁
⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣉⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇⢿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢁⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡜⣷⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⢠⣿⣿⣿⣿⡏⠉⣉⣄⡚⣤⣀⣀⠶⠶⠶⠶⢄⡀⢸⣿⣧⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⢁⠀⠀⠀⣼⣿⣿⣿⣿⠀⠘⠛⠉⢃⡞⠉⡏⠀⠾⠛⠦⠀⢹⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⣀⡀⢠⣿⣿⣿⣿⡏⠓⠲⠤⠐⠋⠀⠀⠘⢄⣀⣀⣀⡠⠊⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠁⣿⣿⡞⣿⠁⠀⠀⠀⠀⠈⠁⠙⠀⠀⠈⠉⠁⠀⠀⢸⣿⣿⡏⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⢠⠀⠀⠀⢠⣶⠶⣦⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠀⠈⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠇⠈⢙⣿⣗⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⣾⣿⣿⣿⡇⠀⠀⠻⠀⠀⢿⣿⣿⣿⠃⠀⠀⢶⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⢿⡯⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣿⣿⡏
⢀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢡⣿⣿⣿⣿⣷⣶
⠀⡅⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⣾⣿⣿⣿⣿⣿⣿
⠐⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣵⣣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿
⠀⠇⠀⠀⠀⢈⣿⣿⣿⣿⣿⢿⣿⣿⣷⡸⡏⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⣿
⠠⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⢠⡿⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣿⣿⡻⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠂⠀⠈⠐⠒⠤⣀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣘⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⠠⢤⡴⣂⠤⠐⠒⠒⠒⠂⠤⠀⠀⠘⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⢠⠞⠊⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠈⡀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠤⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⡄⠈⢦⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠉⠑⢄⠀⡄⡠⠒⠒⢄⢀⣀⡀⠀⠀⠂⠀⠀⠀⠃⢸⠀⠀⣀⣈⡆⡎⠀⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠷⡀⠘⡄⢿⣧⠴⠦⠀⢧⠀⠀⠀⠀⠒⠛⠛⠛⠿⠀⠣⡎⢝⢀⡁⢨⠊⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣹⠀⢰⠀⠀⠃⡜⠀⢀⡤⠔⠒⢠⠄⠀⠀⠀⢀⡿⠑⠂⠀⠀⣀⠼⢁⠎⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢂⡑⠋⠈⠳⣊⣀⠣⠀⢣⠀⠸⣄⠀⠘⠁⠀⠀⠠⠁⠀⠀⠀⠀⢀⡔⠁⡠⠊⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠑⠢⠤⣉⠋⠀⠀⠀⣀⠀⠀⡀⠤⠶⣭⠶⠊⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠊⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠦⢄⣀⣀⡀⠤⠴⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠈⢏⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡇⠐⢢⡄⢸⡤⡔⠒⢰⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢪⣀⠉⡆⣸⡅⠀⠉⣧⠠⠼⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⠀⠀⠈⠳⡄⠉⠉⣽⠃⠐⣍⠗⡲⠶⠛⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⣒⠲⠠⠤⠴⠗⣒⠬⠋⠀⠀⢟⢼⣀⠀⠀⠀⠀⡨⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠑⠢⠍⡉⣉⡉⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠴⠶⠒⠶⠚⠰⠶⠖⠒⠂⠀⠀⠀⠘⠞⠧⠅⠂⠔⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⡠⢶⣟⡡⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣽⠞⡰⢋⡵⢟⣺⠿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠰⠀⠃⠀⠀⠴⢾⣷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠄⠂⠁⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⣶⠹⠀⠀⠠⠆⡈⢆⣴⠒⠂⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠽⣒⠀⠀⠀⠀⠘⢆⠹⠀⠀⠀⠁⠰⠀⡸⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠕⣋⠉⠀⠀⠀⠀⠀⠀⢡⠀⠂⠀⠔⠀⠐⠧⠒⠒⠉⠉⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠾⢓⣿⢵⢋⡤⡶⠀⠀⠎⠥⢃⠀⠀⠀⠀⠀⠈⠁⠒⠒⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠟⠁⢰⣱⠀⠀⠉⠋⠁⠀⠀⡀⠔⠒⡢⠤⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣸⢆⠐⠀⠀⠀⠀⣡⡉⡑⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠑⠀⠄⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⣀⣠⠀⢃⣠⣂⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡆⠚⣆⡄⠤⣬⠃⢘⡬⣁⣼⡥⠤⠤⠶⠖⣖⡠⢶⡬⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠽⡄⢗⡆⠀⢠⠃⠀⢴⠃⠀⠉⠀⠀⠀⠄⠀⠈⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⠠⡀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡏⣀⣽⣠⡧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠓⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠙⠢⡀⠈⠻⣷⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⡿⡽⢾⣷⣄⠈⠳⣄⠈⠻⣿⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⣧⣠⣦⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡟⢫⡳⡿⣧⣑⣜⣦⣳⣽⡕⣄⠈⢣⣀⡈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠈⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⢶⣖⣛⣻⣿⣶⣽⣦⣷⣿⠶⠶⡶⠶⠶⠶⠶⢾⠟⢹⠋⢉⣿⠿⣿⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡞⠳⣬⣇⠀⠀⠀⣞⣷⡶⠾⣛⣭⠵⠖⣛⣋⣩⣭⣥⠤⠶⣾⣷⣧⣧⣇⣀⣀⠀⠀⠀⠀⢠⠃⢠⠇⢠⣾⠋⠘⢛⣣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⣴⢶⣷⣿⣿⠿⣛⡭⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⠿⣿⣤⣋⣠⡿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣋⣬⢟⣫⠶⠋⠁⠰⣦⣀⣠⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⣭⢞⣫⠷⣋⠁⠀⠀⠀⠀⠹⡍⢉⣤⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣋⣥⠞⣋⡴⠛⠁⢰⣿⡀⠀⠀⠀⠀⠀⠛⠋⠈⠳⣼⠁
⠀⠀⢀⣀⡤⠶⠚⣋⣡⡴⠞⣉⡴⠞⠉⠀⠀⢀⣟⣈⠙⠛⣶⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢩⣥⠴⠞⢛⣩⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⣽⠁⠀⡟
⠀⠀⠀⠰⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠈⠀⠒⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠛⠛⠛⠛⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡿⣧⠟
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⡾⠃⠈⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⢠⡆⠀⠀⣠⡴⠞⠛⠛⢶⣄
⠀⠀⢀⣴⠞⢻⠇⠀⠀⠀⠀⢀⣠⠴⠋⠁⢸⡀⠀⠛⠀⠀⣼⠋⠀⠀⠀⠀⠀⠹⣇
⠀⣴⠟⠁⠀⠋⠀⠀⣠⣴⠞⠋⠁⠀⠀⠀⣨⠿⠛⠛⠳⣾⣟⣿⡆⠀⠀⠀⠀⠀⣿
⣼⠏⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢰⡏⠀⠀⠀⢾⡿⣿⠉⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠒⠒⠛
⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⢿⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢀⣠⣾⣥⣤⡴⠶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠘⢷⡀⠸⣇⠀⠀⠀⠀⢀⣾⣟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠈⢿⡄⠙⢷⣤⣤⣴⠿⢫⡏⠀⠀⠀⠐⠶⢿⣤⣤⣤⣤⣤⣤⡶⢶⡟⠋⠉
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣀⣠⣬⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣠⡞⠋⣁⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣿⠀⠞⠻⣤⠞⠁⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⠶⠟⠉⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⣤⠖⠂⠀⠀⣼⠏
⠀⠀⠀⢸⡏⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣴⠋⢿⠀⠀⠀⣼⠏
⠀⠀⠀⠸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣸⢛⣧⡾⠟⢃⣼⠃
⠀⠀⠀⠀⢿⡀⢸⣿⡆⠀⠀⠈⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡄⠀⡿⠟⠁⠀⢠⡾⠁
⠀⠀⠀⠀⠈⢳⣼⣏⢻⣄⠀⠀⠘⣏⠻⢶⣄⣀⠀⣀⡴⢿⠶⠶⣷⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠻⠶⢶⣿⠆⠀⠀⠉⠛⠋⠀⣸⣆⡳⣼⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠁⠈⢳⣀⣞⠳⡄⠀⠀⣀⣀⣴⠋⣩⣭⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⣤⠤⠀⢿⡏⢻⡿⠀⢸⡏⢻⡷⠾⣷⠞⠉⢀⡿⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠃⠈⣿⣄⠘⣷⡞⠁⠀⠻⠶⢺⡛⠓⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⠀⠘⢦⡀⠀⢸⡙⢦⡈⠙⡧⠀⣴⠖⡟⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⡄⠀⠀⠻⣶⡾⠃⢠⣿⣰⠃⢠⡟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡀⠀⠀⢈⣷⢠⣿⣿⡟⠀⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢣⡀⣠⣿⣿⣿⢦⣽⠇⢀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⠋⠀⠈⠙⣦⣄⣀⣸⡟⠳⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⢀⣀⣀⣤⡴⢿⡇⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠉⠉⠉⠉⠉⣁⡤⢴⡿⠳⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣀⣀⡀⠉⠀⠐⠋⠀⠀⠀⠀⠈⠙⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢋⡵⠟⠉⡉⠉⠛⠒⠶⠦⢤⣤⡤⠶⠶⠖⠺⢿⡛⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⣈⣷⠶⠋⠉⠙⠛⠓⠲⠶⠶⠶⠤⠤⣤⣤⠴⠾⠿⠶⠶⠞⠃

⣿⣿⣿⣷⢻⣎⠻⣮⣿⣆⠳⣌⠛⠷⣶⣶⣽⣿⣿⣿⣾⣿⢃⣴⣿⡿⢟⣫⣾⣧⣾⣿⢟⣠⣿⣵⠏⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡄⢻⣧⡀⠹⣿⣿⣿⣿⣶⣄⡈⠙⣿⡎⢻⣿⣿⣾⣿⣯⡾⣫⣭⣿⣿⣿⣿⣿⣿⠏⣠⣶⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢻⣷⠀⣿⢇⣤⣌⡙⠻⢿⣦⣹⣧⣾⣿⣿⣿⣿⣿⣴⣿⡿⠛⢉⣡⣤⣸⣿⣾⡿⠋⣠⡿⢣⣿⣹⣿
⣿⣿⣿⣿⢿⣷⡀⢻⣷⣿⣸⢳⣎⣙⢦⡀⠙⠿⠛⠋⠉⠉⠉⠙⠛⠿⠋⢀⡔⣋⣥⠸⡇⣿⡟⣠⣾⠟⠁⣼⢣⣿⣿
⣿⣯⢻⡟⣧⡹⣿⣌⣿⣏⣿⢸⣙⡾⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡰⣿⣿⡃⡇⣿⣿⠟⠁⣠⣾⣿⡿⣿⣿
⣿⣿⣎⢿⣌⠻⣿⣿⣿⣿⣾⡘⣛⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢣⣷⣿⣯⣴⣿⣿⢟⣩⣾⣿⣿
⣿⣷⣿⣾⣿⣦⣌⣻⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢟⣿⣿⣯⣶⣿⢟⣱⣿⣿
⣿⠶⢈⣙⣻⣿⣯⡉⠉⠁⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⣉⣽⣿⣿⣿⡿⠛⢻
⣿⣫⣭⣭⣿⣟⣛⣛⡶⡄⠀⠀⠀⠀⡞⠀⢰⡏⠳⡄⠀⠀⠀⢠⠞⣽⠀⠈⡧⠀⠀⠀⠀⠀⢾⣛⣿⣿⣿⣿⣿⣿⣻
⣿⡿⢟⣿⣿⣫⣭⠍⠁⠀⠀⠀⠀⠀⠸⡄⢸⡇⠀⡇⠀⠀⠀⢸⠀⢿⡇⣠⠃⠀⠀⠀⠀⠀⠈⠭⣭⣛⣿⣯⣟⡻⢿
⣿⣴⢟⣿⣿⠟⠁⢀⣀⣀⣀⠀⠀⠀⠀⠈⠚⠓⠊⠀⠀⡤⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⣀⣀⣀⡀⠈⠻⣿⣿⣷⣭⣻
⣿⣶⣿⣿⢇⡴⢋⣭⠿⠛⠉⣿⡷⢦⣄⡀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⠉⠙⠻⣍⠛⢦⣹⣿⡿⣿⣿
⣿⣾⣿⣿⡟⢀⡾⠁⠀⢠⠾⢫⡇⠀⠈⠙⠳⠦⠤⣤⢰⣿⣂⡤⠤⠴⠚⠋⠁⠀⢸⡙⠧⡀⠀⠈⠳⠀⢿⣿⣿⣿⢻
⣿⣿⡇⢹⣧⠸⠁⠀⠀⠀⠀⢚⣇⠀⠀⠀⠀⠀⠀⢀⡏⡇⢯⡀⠀⠀⠀⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣾
⣿⣿⣧⠈⢿⡄⢤⠀⠀⣀⡤⢟⣿⠀⠀⠀⠀⠀⢀⡞⣠⣿⡌⢧⠀⠀⠀⠀⠀⢸⣿⠳⢤⡀⠀⠀⡄⢠⡟⠟⢸⣿⣿
⣿⣿⣿⣷⡈⠳⠸⡷⠤⣤⣴⡿⢻⣷⠀⠀⠀⢀⡞⣰⠃⡇⠹⣌⢧⠀⠀⠀⢸⣾⠟⢷⣤⣤⠴⣾⠇⠟⠀⣠⣿⣿⣿
⣿⣿⣿⡿⢿⣷⣶⣿⣷⡿⢯⣤⡀⢿⣴⠀⠀⣼⡼⠁⠀⡇⢀⠘⢮⣧⠀⠈⣾⡟⢀⣤⡽⣿⣾⣷⣶⣶⡾⢿⣿⣿⣿
⣿⣮⠻⣷⡀⢠⣾⣿⣿⣿⣶⣌⢻⡌⣿⡀⠀⣿⣇⠀⡀⠟⠀⠀⣼⡿⠀⢀⣿⢠⡟⣡⣾⣿⣿⣿⣷⡄⢠⣿⢏⣵⣿
⣿⣿⣧⠘⣷⣿⣿⡸⣿⣼⣿⢿⣾⣇⣿⠙⢆⢸⣿⠀⠀⣤⠀⢀⣿⠇⡴⠋⣿⣾⣾⡿⣿⣷⣿⢡⣿⣿⣾⠃⣾⣿⣿
⣿⣿⣿⠀⢸⣿⠹⣿⣿⢿⣿⣸⣿⣿⠇⠀⠈⢿⣿⡆⡦⠀⠄⢸⣿⡾⠀⠀⢻⣿⣿⣅⣿⡿⣿⣿⠫⣿⡇⢠⣿⣿⢻
⣿⢻⣿⣇⠈⣿⣷⡿⣃⠘⣭⣿⣿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⣿⣿⣭⠁⡛⣿⣾⡿⠀⣼⣿⠏⣸
⣿⣶⣿⣿⣷⣬⣝⣛⣻⠿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⡿⠿⣛⣋⣭⣤⣾⣿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⢻⡿⠀⠀⠀⠀⠀⣀⠀⣠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢧⠚⠁⢠⢄⠀⠐⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⠉⠀⠀⠀⡠⠔⠒⢂⠎⣸⡖⠁⣴⢦⣄⠈⠙⣿⣿⣤⡀⠀⡌⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠩⣐⣚⡁⠀⡀⠠⠘⠁⠘⡄⠙⠚⠿⣿⠦⣼⠛⠿⠛⠀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣹⠇⡀⠄⢇⠀⢠⡁⣤⠔⠊⠀⢡⠈⡟⢂⠀⠀⡉⠀⠀⢠⡾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⡻⢃⡀⣴⡆⠱⡀⠀⠸⣉⠦⠒⠋⠺⠁⠺⣦⡐⠸⠀⢀⣩⣴⣿⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⠆⠻⢯⣬⣿⣾⣏⢀⣀⠃⠀⡀⡀⠀⢠⡀⠈⠈⢇⠀⠀⠀⠈⠻⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣂⢠⣠⡄⠐⠒⢩⠛⠉⣔⡄⠀⣉⠲⡄⠃⣀⣠⣤⠀⡠⢀⠉⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡁⡨⢣⡀⢰⠁⠀⠀⡽⠧⠛⠃⠀⡎⢁⡮⠛⠃⠪⢄⣨⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠅⠀⡋⠉⠲⠏⠉⠋⠀⣼⡀⡠⠒⠉⠉⠁⠲⡷⢃⢠⡕⡀⣧⠕⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⡀⠙⠢⢭⣳⠀⡄⠀⠰⠆⠀⢹⠀⠰⡆⡴⠶⠖⠘⠇⡸⠱⢡⣏⣀⡊⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠂⢐⡡⠚⡇⠀⢠⣤⣴⡄⠀⠀⡀⠄⠠⠀⣤⠀⠀⡟⠀⢀⠸⡃⡐⢍⢣⡊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣈⣏⣀⣈⣑⣉⣀⣀⣀⣇⣑⣘⣘⣛⣀⣀⣃⣀⣈⣀⣇⠠⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⣀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⠀⢀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⠀⠘⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠒⠒⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠛⠛⠛⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡾⠁⠀⢠⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⣸⠇⠀⢈⠏⢹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣿⠀⠀⠺⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠀⠀⠀⠀⣴⠞⠋⠉⠁⠀⠀⠈⠉⠉⠛⠶⣤⣀
⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣧⡴⠇⠀⣀⣀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠳⢼⡇⠀⠀⠺⠤⠜⠘⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠹⣆
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠳⣼⠁⢀⣤⣤⣄⣀⣀⣹⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⢄⢻⡄
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠋⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⠸⡇
⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡏⠓⢾⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠷⢤⡾⠀⠀⢀⡔⣶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⡾⠀⠀⢀⠀⠀⣸⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠐⠭⠇⠀⣿⠃⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣯⠤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣌⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉



⣶⣶⢶⠶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⡶⣶⣶⣶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⣰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣆⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢱⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⡎⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠈⠛⠉⠁⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠈⠉⠛⠁⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⣾⡿⠋⠁⠉⢻⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⡟⠉⠈⠙⢿⣷⡄⠀⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⢸⣿⡿⣆⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⢿⠀⠀⣹⣷⠟⠉⠉⣿⠇⠀⠀⠀⠀⠸⡇⠀⢈⣿⡾⠋⠉⢙⡿⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣧⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣅⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠛⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠲⠶⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⠛⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠉




⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⠶⠶⢶⣶⠶⢶⣶⠶⠶⢶⠶⠶⡶⠶⡶⢶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣾⠀⣠⠔⡿⢋⣀⣠⡅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣧⠞⢡⡾⢛⣥⣾⠥⢶⣦⠤⠀⠁
⠀⠀⠀⠀⠀⠐⠀⢠⡀⢰⠃⣾⠋⠀⠋⠰⣛⡭⠖⣛⣉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⣼⣧⡟⠰⠃⠀⠀⠀⠚⣛⡭⠿⠛⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠂⠀⢻⠘⠇⠀⠀⠀⣠⡖⠋⠁⣠⠀⠀⠐⠀⠈⠲⡄⠄
⠀⠀⠈⠀⠐⠶⣤⠬⣧⠀⠀⠀⣜⠁⠙⣄⢠⡔⠲⢤⡀⠀⣠⠔⠒⢦⠀⠁
⠀⠀⠠⠀⠚⠿⢭⣇⣀⠀⠀⡄⠁⠈⢰⡌⠻⡄⠀⠀⠈⢾⢁⣤⠀⢸⡇⢈⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠴⠾⢭⣥⠤⠀⠀⠀⠀⠀⠀⠑⣄⠱⣀⡠⠔⠚⡇⠉⠀⡼⠀⠀⣂⣀⡤⠤⠖⢒⡆⠠
⠀⠐⠀⢀⡴⢚⣩⠄⠀⠀⠀⠀⠀⠀⠀⢀⣈⡄⠈⠓⠶⣺⠋⠒⢚⠛⠋⠉⠉⠀⠀⣀⡴⠛⠀⠂
⠠⠀⡰⠿⢺⣟⢵⡞⢁⡤⣶⠂⠀⣰⠊⡅⠶⣀⠀⠀⠀⠁⠀⠀⠉⠁⠒⠒⠒⡺⠋⠁⠀⠀⠂
⠀⠀⠂⠀⠟⢁⣾⠞⠉⣰⢃⠀⠀⠘⠲⠶⠚⠙⡄⠀⢀⣠⡤⡄⣀⣀⡀⠀⡴⠁
⠀⠀⠀⠒⠀⠌⢁⠀⠀⡏⣿⠀⡆⠀⢀⠀⠀⠀⠁⢀⡯⡾⢴⢥⠏⠈⣡⠞⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣼⡟⣆⢸⠳⢄⡀⠀⠸⠴⠦⠧⡏⣠⠞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠈⠁⠈⠛⠀⡶⢭⡇⠀⠀⠀⡠⠞⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⣀⣐⡀⠈⠀⡟⢸⠀⣠⠔⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⠿⡇⠀⠉⠉⠛⢧⠀⢟⠻⠛⢛⠿⠥⠄⠀⠀⠀⢀⣤⠤⣲⣓⣢⣤⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠢⣖⣶⠾⠇⣀⠓⠚⠉⠉⡟⠀⠀⢸⠉⠒⢼⡟⠉⠉⠉⠉⠉⠉⠳⠴⢭⣻⠉⠍
⠀⠀⠀⠀⠀⠀⠯⢶⢫⠒⢢⠕⠀⠀⢸⠁⠀⠐⣏⠁⠀⠀⠀⠈⠐⠁⠐⠀⠁⠈⠀⠀⠁⢈⡃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⠀⡏⠀⠀⠀⠸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠳⢴⡚⠋⢁⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣇⠀⣹⠄⣻⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢽⠠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠏⠁⢨⣗⣐⣯⠤⣄⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣃⣽⣿⣉⡭⠗⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⡂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣤⢧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣀⡸⠲⢀⣤⣄⡲⡀⢢⠠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡏⠀⣴⣿⠟⠛⠻⢾⣾⣾⣏⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗⢠⣿⡇⠒⠀⢀⢄⠙⠿⣽⡿⠗⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠾⢿⠃⠀⠈⠈⢳⠀⣠⠤⡍⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢰⣦⣠⣿⣷⡈⠈⠁⢠⠒⢢⠈⣈⡃⢀⠇⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⢏⠃⣠⣄⠀⠀⠀⠈⠨⢀⡵⠊⢀⠜⠁⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢋⡕⠉⠑⢉⡭⠗⠤⢩⣤⣴⢮⢄⡀⠈⠀⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⣴⣿⣿⣶⣿⣿⣄⣀⠐⢒⡛⢡⡶⢾⣀⡅⠀⠤⠄⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⠻⢿⣿⣿⣿⠃⢀⠄⠉⠁⠘⠱⡀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⢈⠙⠋⠀⠐⠀⠀⢡⠐⢤⡇⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⠛⠀⠈⠀⠀⠀⠋⠀⠀⠰⣖⠠⠙⠋⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠤⠔⠂⠁⠀⠀⠀⠀⠀⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⢤⠤⢤⣤⣤⠀⢠⣄⣀⡀
⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⢉⣽⣿⣿⣿⣿⣿⣥⡀⣀⠦⣸⣻⣿
⠀⣴⡿⠟⠋⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⡿⣿⣿⣿⣿⠗⣺⣿⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⣣⡟⢿⢳⣿⠿⠿⠛⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⠤⣀⣀⢀⣀⣀⣀⣀⣀
⠀⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣕⣿⠹⣇⣷⢾⣿⣤⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣤⣄⣺⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⢹⣿⣸⡿⠿⢿⣿⣿⣿⣇⣀⡀⠀⠈⠉⠛⠙⠛⠿⠿⠿⢿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠙⠷⣾⡆⢿⣍⣁⢀⣀⡀⣙⣿⣿⣿⡿⠻⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣿⡄
⠀⠀⠀⠀⣀⣀⣀⣾⣿⣿⣿⣿⣴⣖⠿⣿⣶⡇⠀⠈⠉⠀⠛⠛⠛⠉⠛⠛⠛⣷⣟⣙⣛⣛⣶⣤⣄⣀⠀⠀⢸⣿⠁
⠀⠰⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣶⣦⣄⣤⣴⡶⣤⡀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢥⣀⡀⠐⢸⣶⠄⣧
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠻⠛⠛⠋⢉⣡⣽⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢯⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠿⠿⠿⠿⢿⣷⣿⣾⣿⣒⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⣾⠉⣷⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⢰⡏⠀⢻⡆⠀⠀⠀⣠⡾⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡀⢾⠁⠀⠘⣷⠀⣠⡾⠋⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣤⣀⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⡿⠋⠀⠀⢸⡏⠀⠀⠀⠀⣀⣀⣤⣴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡙⠛⠳⠶⡆⠻⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣴⠶⠞⠛⢋⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠹⣿⡯⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠐⠻⠿⢿⣭⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣭⡿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⡴⠶⠟⠛⠉⢉⡿⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢿⡍⠉⠛⠳⠶⢦⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡄⢸⣷⠀⠀⠀⣼⡇⣤⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣴⠟⠁⢸⣿⡄⠀⢠⣿⡇⠈⠻⣦⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⠟⠁⠀⠀⢸⣿⣧⠀⣾⣿⡇⠀⠀⠈⠛⠊⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢸⣿⣿⣤⣿⣿⡇⢠⣾⣿⣿⣷⣆⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡿⠿⠇⠿⠟⠛⠛⠛⠛⢀⠛⡛⢛⠛⠛⠻⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣶⣿⠆⣠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠆⠀⢴⣶⣶⣶⣶⡦⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣀⠉⢥⣾⣷⣌⠛⠿⠿⠛⣡⡄⠻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣷⣾⣿⣿⣿⣦⣌⣉⣉⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠈

⠀⠀⢰⣶⣶⣶⡶⠒⠀⠒⠶⣶⣶⠶⠀⠰⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⣤⣤⣤
⠀⠀⢸⣿⣿⣿⠠⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡦⠀⠐⢻⣷⡶⠎⠀⠀⠀⣶⣿
⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠉⠉⠁⠀⠀⠀⠈⠃⡀⠀⠀⠘⣿⣿
⠀⠀⢸⠁⠀⠀⠀⠀⠀⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢒⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣷⣤⣼⣿⣿
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠀⠀⠘⠛⣳⣷⢿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⢸⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡀⠇⢀⠀⢿⣿⣿⣶⡀⠀⠀⠀⠀⣤⠸⠟⠻⠀⠀⠀⣰⣿⠿⠿⣿
⠀⠀⢸⣷⣤⠀⠈⠁⠀⠀⠀⣀⣴⣄⠹⠀⠡⡄⠀⢷⠘⢿⣿⠙⠇⢀⠠⢠⣴⠟⠇⠹⠄⠀⠀⠁⠉⠉⠀⠀⢸
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⣸⡆⠀⠀⢠⡈⣟⣇⣸⣄⣀⣸⠿⡶⠀⣰⡐⢼⣀⡤⠀⠀⠀⠀⢸
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡠⠀⠀⢱⠰⠲⡿⣉⣙⣁⢠⣤⣔⣧⡤⣾⠛⠀⠀⠀⠀⠀⠠
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠻⠻⠛⢻⣄⠁⠀⠈⠁⠠⡐⠍⢿⣽⣿⣿⣿⣿⣾⣿⡖⢄⡶⠷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠒⢀⡒⡀⢼⣿⡘⡂⠒⠒⡄⡈⠠⠀⠹⣯⣝⣻⣿⣿⡿⢷⢦⡤⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⢀⣼⡇⡹⣿⡇⢱⠀⠀⠐⠀⡀⠘⠤⣟⡟⠛⠋⠀⠀⠓⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣠⢈⣹⠀⣿⠃⠡⡀⠈⠀⠙⠶⠀⢀⠈⠑⠢⢄⡘⠦⣀⣀⠲⡤⠐⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡢⡴⠛⠒⠒⠲⠸⣶⣏⣽⠔⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠁⠮⠓⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠀⠀⠰⠿⠿⠰⠶⠦⠀⠀⠤⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠆⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠉⠀⠀⠀⠀⠈⠉⠑⠢⢤⡀⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡡⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⢀⣀⠤⠤⠤⢄⣀⡀⠀⠀⠀⠳⠔⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡠⠔⠊⠉⣠⣫⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠴⠏⣠⡤⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠠⠶⣦⠀⠀⡼⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠦⣀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡴⠁⡸⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⠇⠀⠀⢀⡼⢄⡀⠀⠀⠀⣠⢤⡈⢳⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢋⡥⠤⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⢸⠀⠀⠀⠸⡄⠀⠙⣄⣄⣠⡇⠀⢹⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠞⠙⠲⡄⠀⡇⢀⡴⠒⠲⣄⠀⢀⡀⠀⠀⠀⡔⠉⠀⠀⠈⢳⠸⡆⠀⠀⠀⠈⢢⢰⠁⠀⡝⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣄⠀⠹⣀⣱⢺⣀⣀⣀⡈⢼⠁⠉⠆⠀⠀⠤⠶⠶⠶⢶⣾⠄⠳⣄⠊⡟⠉⠛⠘⠢⠞⠁⠀⣰⠃
⠀⠀⠀⡇⢀⠔⠒⢲⠃⠀⡝⠀⠀⡇⢀⠟⠋⠁⠀⢀⣈⠁⠀⠀⠀⠀⠀⠀⢠⣤⢄⡀⠀⠀⠏⠀⢳⡖⢲⠀⠳⠀⢠⠞⠁
⠀⠰⡀⣇⢸⡀⣠⠼⣄⢀⡇⢠⠀⠀⢸⠀⠀⡴⠋⠁⠀⡨⠝⠓⠲⠤⣤⠤⠖⠁⠀⠀⠀⠀⡰⠖⠋⣠⠃⠀⠀⠀⣾
⠀⠀⠳⡈⢦⠈⠀⠀⠈⠯⣤⡤⠑⠀⠘⣄⠀⠙⢤⣀⠈⠀⢀⣀⣠⠔⠁⠀⠀⠀⠀⠀⢀⡴⠁⢀⠜⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠙⠲⠤⣬⣉⣉⣉⣁⣀⣀⠠⠀⢠⡤⠖⠚⣧⡶⠖⠉⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠒⠒⠉⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠺⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡓⠤⣀⠀⠀⠀⢀⣀⡤⠔⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠦⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢢⡤⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⣄⡀⠀⡾⢷⠀⠀⠀⣀⣀⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢬⣇⠀⠉⣶⠇⢸⣖⣟⠉⠉⡽⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣧⣀⡈⣳⢀⣧⡀⠀⠀⢹⡤⠔⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠁⠀⠀⠈⠙⢦⠀⠈⠉⢩⡟⠁⠰⡋⠿⢄⣶⠶⠿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡓⠤⢀⣀⣀⠀⣠⣇⠠⢔⡻⠃⠀⠀⣿⣠⡋⠀⠀⠀⠀⠀⠀⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⠤⠤⠔⠒⠂⠉⠀⠀⠀⠀⠘⠪⣝⡒⠤⠤⠤⠴⠚⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠂⠒⠀⠀⠀⠀⠰⠀⠶⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠒⠰⠂⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⢠⢀⢈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡀⠒⡄⠉⠀⠈⠁⠉⢹⣧⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢠⡄⠀⠀⠰⠀⠀⠀⠸⡛⢉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⠠⠒⠚⠋⠁⠀⠀⠀⠀⠈⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠆⠀⠰⡀
⠀⠀⠀⣆⠀⠀⠀⠀⠀⡇⢀⡄⠀⠀⠀⠀⢀⡤⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠢⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⢀
⠀⠀⠀⢸⡄⣀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⣾⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⢠⠀⠀⠀⠀⢣⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡠⠀⠀⠀⠈⠀⠠⠊
⠀⠀⠀⠀⢷⣿⡀⠀⠀⡿⢹⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠀⠀⠀⠀⢀⠈⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊
⠀⠀⠀⠀⠈⠁⢳⠀⠀⠀⠘⠀⠀⠀⡼⠉⠁⢀⣤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠓⠑⣄⠄⡠⠊⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢁⡠⠚⣽⡧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠔⠏⠈⢀⠴⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠈⠁⠀⢀⠠⠔⣊⠷⠔⠒⠁⠀⠀⢺⡄⢀⡀⠀⠀⠀⡘⠃⠀⠐⠁⠰⢧⣆⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠐⠀⠀⠀⡀⠀⠀⠒⢆⠁⠀⠀⠀⠀⠀⡐⠒⠤⠐⠄⢳⠈⠙⠢⠤⠔⢁⡆⠁⠀⠀⡀⡀⠛⣄
⠀⠀⠀⠀⡆⠀⠀⠀⢠⣄⣠⡄⠉⢹⠀⠚⠀⠂⠈⠃⠀⠉⣉⣀⢸⡇⠸⡀⣀⠜⢦⡀⠡⡀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠘⡈⢆
⠀⠀⠀⠀⡇⠀⠰⠂⠓⠋⠈⠁⡄⠀⠓⠛⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠛⠓⠑⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠒⠒⠢⠦⢤⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠇
⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠘⡄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠘⠛⠛⠲⠦⢤⣄⣀⠀⠸⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢹⡄⣀⠀⠀⠀⢭⣽⣶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢠⠀⢀⣀⣀⣤⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⡀⠀⢳⣹⡄⠀⠀⠀⠀⠉⠙⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠨⠠⠐⣦⣴⡿⠟⠛⠋⢉⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢧⠀⠀⠻⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⣾⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⣀⡄⠀⠀⠙⡄⠀⠀⢀⣠⡤⠤⠤⠤⢄⣀⠀⠀⠀⠀⣼⣿⠿⠁⠀⠀⠀⢀⣾⣿⠏⣁⣠⠤⠐⠂⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⢷⡀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠒⠭⣒⠦⣼⣿⠃⠀⠀⠀⠀⣠⣼⡿⠟⣋⠥⠒⠈⠁⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⢀⠀⢀⡈⠉⠂⢽⡀⠀⠀⠀⠀⡹⣫⠔⠉⠀⠀⣀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠊⠁⠀⠀⠀⢸⡟⢁⠀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠉⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢹⢀⣀⠀⠀⣀⣠⡤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠤⠇⠀⠀⠀⠀⠈⠀⠀⠙⠊⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠢⣤⠴⠋⠉⠙⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⣀⠀⣀⡴⠃⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⣀⣠⡖⠚⠁⠉⠉⣠⠞⠛⠁⠀⠀⠀⠀⠀⠘⠛⠓⠆⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠚⠁⢀⡤⠶⠦⣄⡀⠀⢀⡴⠒⠒⠦⣄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠲⡏⠀⠀⠀⠀⠈⠳⡄⠀⠀⠹⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⣹⣔⣦⠀⠀⠀⢀⡇⠀⠀⠀⠘⣶⠹⣋⡭⠭⠉⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⢻⣏⡁⠀⢀⣠⠞⢁⡤⠶⢤⡀⠘⣯⡽⠆⢾⣉⣌⡟
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣸⠀⠀⠀⠀⠀⠀⢀⣨⠦⠤⢤⣄⣀⠀⢠⠞⠀⠉⠉⠉⠀⢠⠏⠀⠀⢈⡇⠀⠘⣦⠔⠋⡡⠋
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠩⢍⣳⣌⣉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⠀⠀⠀⠀⠀⠀⠂⢠⢀⡠⠞⠀⠀⠀⢿⠀⡎
⠀⠀⠀⠀⠀⠸⡆⠀⢀⡈⢳⣦⣸⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠹⡄⣸⠶⠯⣄⣀⣠⡤⠴⠖⢦⡀⠀⠀⠠⠚⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡇⣗⠀⢀⣤⠤⠤⠤⠴⠦⠂⠛⠓⠤⣄⡀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⣆⡴⠋⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣟⣀⣸⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⢻⡉⠁⠙⢆⠈⠳⣞⠉
⠀⠀⠀⠀⠀⠀⢸⣀⣈⣉⣉⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⣶⠦⠤⠤⢤⣤⣶⣧⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⣯⣇⣀⣠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⢤⣀⠀⢀⡟⠛⠋⠉⠉⠁⠀⠀⠳⣤⣀⣀⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣦⡀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠙⠒⠲⠦⣤⣤⣤⣄⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡜⠀⠀⠀⠀⠀⣀⣾⣰⠃⠀⢰⠃
⠀⠀⠀⠀⠀⠀⡞⠉⠀⡹⢍⢙⢓⣦⡤⣄⣉⣠⣏⣉⣁⣠⣾⢤⣤⠤⣀
⠀⠀⠀⠀⠀⠠⣷⣤⣀⣧⣠⣭⢭⣝⣶⠿⠛⠛⢶⣤⣮⡤⠤⠚⣦⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠋⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠷⡖⠯⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣷⡀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣴⣿⠛⠟⠛⠁⠒⠀⢀⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠀⠀⠀⠀⠀⠀⣀⡒⣒⠚⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣀⣠⡄⠀⠀⠀⠨⣥⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣤⠀⠀⠁⠈⠀⠀⠒⣂⣿⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠂⠀⠀⠀⠀⢦⣹⣃⠀⠀⠀⠀⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡌⠀⠠⠀⠐⢾⣻⡷⠀⠀⠄⠰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡄⢀⠀⠀⢙⣷⣄⡀⠄⠀⣹⣿⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠙⢄⠀⠶⠻⣿⣿⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠆⠻⢶⣿⣿⣿⠃⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⡀⠈⠉⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⠓⠚⡶⠿⢋⡶⣯⣷⣟⣣
⠒⠒⡾⠿⠿⠻⠿⠻⠿⠻⢟⠳⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠓⢶⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠔⢚⡇⠀⠀⠀⠈⠁⠂⠹⠂⠠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢰⠁⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⢸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢸⠀⢸⠀⢀⠀⢸⣤⡇⠀⠀⠀⡀⠀⣠⠀⠄⠄⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣦⣜⠦⠿⢷⠋⡠⠶⠆⠀⠐⠁⠘⠡⠾⡦⢀⠜⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢶⡛⠂⠀⠀⠘⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣀⣀⠈⡁⠀⠀⠀⢀⣄⣀⠀⠀⠀⢈⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⢉⠉⠻⠧⠀⠀⠀⠟⠋⢉⡈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠕⠒⠲⡄⠀⠀⢀⠴⠚⠓⢦⡀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⠀⠁⠀⠶⠀⠸⣵⠀⣮⠀⠴⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢳⠇⠢⣀⠀⢀⠼⡏⠀⢻⣆⣀⣀⠴⡄⢠⣧⠄⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠓⡾⠀⠘⠓⠒⠀⠈⠀⠀⠀⠙⠀⠀⠀⠀⠀⢳⠊⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠉⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⠀⠀⠀⢠⠊⠀⢄⠀⠀⠀⠲⡄⠀⠀⠀⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠘⠀⠿⠄⠀⢴⠿⠃⠀⠀⠀⢀⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⣯⣉⣉⣉⣛⣋⣉⣉⣉⣭⣭⣇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣏⣉⣉⠉⢉⣉⠉⠉⠉⢙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣆⠀⠤⠤⠤⠤⠄⣰⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡼⠁⠀⠀⠀⠸⢇⡴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠑⠤⡄⢀⣠⡴⠊⠀⠀⠈⠁⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⡶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣿⢀⣀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠼⠇⠀⠀⠀⠀⠉⠉⠉⠓⠚⠉⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠀⠐⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣀⡤⠊⠀⠒⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆⠀⠀⣠⠤⠞⠁⠀⠉⣠⠶⠛⠀⠀⠀⠀⠀⠀⠰⠶⠤⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡟⠁⠀⠀⠀⠠⠞⠁⢀⣀⣀⣀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠉⠢⣠⠊⠀⠀⠀⠀⠙⢦⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢆⣠⣄⠀⠀⠀⠈⡇⠀⠀⠀⠹⣤⢔⡶⢒⣒⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠸⢿⠞⠋⠀⠀⠀⡰⠁⢀⣀⡀⠀⠹⣦⢻⣍⣠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡞⠑⠂⠤⠖⠋⢀⡴⠋⠀⠙⡆⠀⠹⡏⣀⠼⠂⡰⠂
⠀⠀⠀⠀⠀⢠⠒⠀⠀⠒⠒⠲⢶⡒⠒⠶⢇⠀⠀⠀⠀⠀⠐⠚⠉⠁⠈⠈⠐⠢⢤⡚⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⣰⠃⠀⠀⢿⠁⠀⠊
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡉⠛⣟⣲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⢸⡄⠡
⠀⠀⠀⠀⠀⠀⠁⠀⠠⣀⣀⠉⠒⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⢠⠁⠀⠀⠒⠒⠂⠉⠀⠀⠀⣄⠀⠀⠀⠀⠉⠒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠀⣨⡆
⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢤⣀⠀⠀⠈⠉⠛⠲⠶⠤⢤⣄⣀⣀⡀⠀⡤⠤⠐⢶⠉⠂⣌⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠸⠤⠼⠧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠳⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠘⠇⠠⠤⠤⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⣏⣉⣉⣭⠭⠽⠛⠻⣄⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠴⢲⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠙⠲⢤⣄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⠄⠀⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠉⠓⢂⡶⢶⠦⠤⢤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣤⣼⡀⠀⠀⠀⠀⢠⣼⣥⣏⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡞⠁⠀⡨⠳⣀⣉⣳⡶⠦⣤⣤⡾⢤⣬⣤⠼⠷⣶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⣟⣦⣤⣷⣤⣤⣶⣒⡾⠿⠛⠉⠻⢶⣾⣗⡶⠖⠱⡄⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠿⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡷⠀⢉⣠⣽⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⣀⣤⡴⢶⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⣤⣔⠋⣁⣽⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣒⣦⣄⣴⣿⣿⣶⡟⠩⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢸⡇⠴⠮⣿⣬⡹⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢀⣤⣶⣶⠿⡟⠛⠉⠉⣯⣻⣿⣯⣽⣿⣻⡰⢻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠃⣿⢓⡏⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢀⣴⣿⣿⡿⠓⠀⠽⠖⢁⣴⣿⣿⣿⣿⣿⣿⣿⣧⣿⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⠀⠉⠁⠀⠀⠙⢿⣿⡟⣹⣿⣿⣦⡄
⠀⠀⣾⣿⣿⡏⠦⢠⣠⡴⢶⠿⣿⣿⣿⡏⠀⠙⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣷⠀⠀⠀⠀⠐⣻⣶⣴⣿⡿⠋⠙⣁⣀
⠀⣼⣿⣿⣿⢠⠀⣾⣿⣆⣐⣾⡿⢿⡻⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⢀⣠⣴⣴⣷⠿⢹⣿⠏⠀⣠⣾⠿⠹
⠀⠸⣿⣿⣿⡌⠀⠿⢿⣿⠋⠉⠁⢏⣩⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠋⠀⠀⠈⠈⠀⣰⣿
⠀⠀⠙⣿⣿⣵⢦⣿⣼⣿⡄⠀⠀⠈⠛⠄⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⡀⠀⠀⢀⡧⠰⣽⡃⠶⠆⡰⢿⡏
⠀⠀⠀⣟⣿⣹⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠃⠄⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣤⣾⠃⠀⠀⠀⠀⠩⠘⣦⣼⣿⣰⣿⡅⠈
⠀⠀⣠⣮⣿⡏⢿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣤⣤⣈⣀⠲⣥⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⣄⣀⡀⠀⠀⠀⠂⠀⣄⣐⠇⠀⢠⣄⠀⠀⢴⠒⠛⠛⠀⠑⢟⢷⡄⢻⣦
⠀⢸⣿⣿⣿⣿⣜⠻⠿⠿⣿⣿⣿⣿⣿⣟⣭⣟⣽⡟⠛⠛⠷⠤⠯⣽⡿⠃⣀⣤⣶⣶⣿⣿⠁⠀⠀⠀⠈⠙⢿⡿⠀⢘⡏⠸⣳⡦⡞⠁⠀⠀⢀⢳⡄⢻⣿⣯⣿
⠀⠀⠐⠶⣴⠲⠿⠻⠶⣻⡿⠉⠛⠛⠛⠛⠿⠿⠿⣧⣤⣤⣄⡀⠀⠀⠀⠈⠁⠀⠀⠡⠙⣿⡀⠀⠀⠀⠀⠀⠀⢠⠿⠖⠀⣮⡿⠈⠅⠀⠀⠈⠤⠆⠙⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⡀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠠⠀⠀⠄⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⠀⠀⠆⠄⠀⠆⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠶⣷⣄⠀⠀⠀⠀⢀⣈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⢶⣸⣿⠀⠐⣒⣃⣻⣏⣡⣯⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⣿⣟⡦⠀⣿⣷⣀⣍⠉⢛⡿⠠⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⡿⠉⢀⣤⠙⢻⣾⣿⢿⠛⣿⣶⣶⣿⣿⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡷⣽⠦⠘⠛⠚⢃⣜⣽⣿⣿⣿⠉⠳⠿⠓⠒⠠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣴⣾⡀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠐⠀⠋⠀⠘⢄⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠃⠀⠀⠰⣯⢿⢿⣿⠋⠀⣴⠀⢰⣶⠀⠀⠈⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⡎⣼⢠⣣⣞⡏⢰⠁⡿⠟⡀⠈⠀⢰⠀⢠⠸⡆⠰⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⡿⠀⣽⣿⠏⠋⣷⠘⠀⠀⠀⡏⠀⠀⠀⡄⢈⡆⢳⠀⢳⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⠁⢀⡘⠃⠀⣸⣿⠀⠠⣑⣴⠁⠀⠀⠀⠘⠺⣧⢸⡄⠈⣧⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡏⠀⣿⡘⣼⠀⡄⠠⣿⣿⠆⣴⠈⢻⣤⡀⣄⠀⠀⠘⠛⠀⡇⠀⢸⡀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⢈⠛⣿⡟⢰⡇⢰⣿⣟⡀⢺⠓⢜⣉⠁⡎⠀⠀⠀⢢⠀⣿⠀⢸⠁⠀⡀⠀⠠
⠀⠀⠀⠀⠚⠷⣤⡬⣽⣿⣦⠀⠀⠀⡀⢰⠠⣿⡇⢸⣧⣾⣿⡏⠁⠈⡄⠀⢿⣤⡁⠁⡀⠀⠀⠀⠀⡀⠀⠀⠀⢷⠹⣦⠢
⠀⠀⠀⠀⠀⠀⠹⣾⣿⠿⠛⠂⠀⠻⡀⠈⠸⣿⡇⠸⣿⣿⡟⠀⠀⢀⠐⠀⣾⣿⢣⢤⡇⠀⠀⠀⠀⠃⡇⠂⠀⠀⣷⡜⢳⣄⠓
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⢶⣶⣠⠀⠰⠄⣆⣿⣧⠀⣿⡿⣿⡟⠀⢪⣦⣄⡼⠙⠠⢾⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⢹⢛⢙⠛⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣰⣟⣾⣿⣿⣿⡆⣽⣷⣿⡇⠀⠠⠉⠛⠀⠀⠀⣾⠇⠀⠀⠀⠀⣀⠈⡀⠀⠇⢸⡃⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡶⠛⠿⠶⡦⢀⠀⢀⠋⠀⠀⠀⠀⠀⢹⡀⠃⠀⢴⢀⢣⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣧⣤⣸⠛⠠⣈⢡⡞⣓⡹⣛⣦⡀⢸⡸⡇⠰⠀⠈⠈⠈⠲⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠫⣽⣿⣿⣿⣿⣿⣶⣿⡀⠸⣿⣿⣿⣿⣟⠭⠀⡟⡀⡆⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⡿⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⠋⠀⣿⢱⡇⠀⢀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠔⠁⢀⣀⣀⢹⣿⣛⢿⣿⣿⣿⣿⣏⢢⢹⣻⣟⠄⠀⢠⣿⣾⣧⠀⠘⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠘⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣆⢁⠙⠋⠱⢸⣿⣿⢻⠀⠀⡄⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢀⢳⣴⢠⡆⠴⠗⠚⠁⠈⢷⣤⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣷⢄⠀⢸⣿⣯⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠃⡴⠀⠀⡀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⢈⠃⠀⠚⣿⡏⠃⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⣿⣿⣜⣷⣶⣣⣿⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⢻⣏⢯⡛⣿⡿⢿⣧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⣛⠛⢿⣿⡿⠟⠛⠛⠛⠻⠿⡁⠀⣈⣉⡩⠽⣿⠾⢿⣦⣣⡹⠷⠀⠈⠙⠄⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠰⠀⠀⠀⠀⣀⣀⡒⠛⠋⠁⠀⠀⠀⠐⠢⢀⠈⠙⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⡀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠛⠻⢿⣿⡿⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣿⣿⢁⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣤⡄⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠼⠿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣟⣀⣉⢩⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠰⠿⠶⡾⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡼⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢀⣠⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣣⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⢸⣿⡟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠉
⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣠⣿⣿⣿⣿⠋
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣴⣾⣿⣷⣶⣄
⠀⠀⠀⠙⠻⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⠁⠈⠻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠈⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋


⣿⠿⠿⡿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿

⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠘⡏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⢸⡇
⠀⠘⢿⠛⢹⠀⠉⢓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠙⢿⠢⣄⠰⡿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⢁⠔⠁⣼
⠀⠀⠈⢧⠈⣇⠀⠀⠈⠁⠒⠢⠬⢍⣛⠲⠤⣄⣠⣤⣈⣧⠈⠙⢧⠀⠉⠙⠛⠛⠛⠛⠛⠶⠶⢦⣤⡀⠀⠀⣠⡤⠶⠚⠋⠉⡀⠤⠐⠊⠀⠀⠀⣿
⠀⠀⠀⠈⣇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢬⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠲⠀⠉⠐⢋⠁⠀⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠸⡆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠹⡄⠣⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⢆⠑⢄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⢄⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠊⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡑⠦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠⠎⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠚⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠰⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠛⠛⠻⠿⠿⠿⠿⠿⠀⠛⠃⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠿⠿⠀⠛⠃⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀
⠀⠀⠀⠀⠀⢤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⣉⣳⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠴⢾⣭⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣙⣻⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠦⣄⡀⠀⠀⠐⠂⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠒⢒⡿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡠⠔⠊⢕⠒⠢⠤⣀⣀⠀⠀⣀⡀⠤⠴⠂⠀⠉⠓⠦⣀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣔⠉⠀⠀⠀⠀⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣀⣀⣀⣀⣠⡤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⢠⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠦⡀⠠⠀⠀⠀⠀⠒⠤⠌⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⢘⠀⠀⠂⠈⠄⠄⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠰⠀⠀⠰⢦⡀⠀⠠⠀⠀⠑⠤⢠⠁⡀⠃⠀⠘⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠈⢦
⠀⠀⠀⠀⠂⠀⠀⠀⢘⠀⠀⠈⠒⠀⠂⠀⠉⠀⠀⠑⢄⡀
⠾⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢠⠬⠲⣤⠢⠦⢂⣤⣄⠀⠀⠀⠈⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡟⠿⠃⠀⠀⠠⠏⠀⠀⠈⠛⠃⠈⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢃⠀⠀⠸⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠢⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡐⠢⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣊⣂⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀
⣿⣿⡟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣼⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⡟⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⠋⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣽⣆⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣿⣧⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢹⡾⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣗⡿⣾⣿⣄⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⡿⣿⣆⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠈⠛⣷⣞⣛⣿⣿⣿⣛⣶⣤⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠻⣷⣄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠈⠀⠉⠀⠈⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡗⠄⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⢘⢙⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⠐⠂⠀⠀⠀⠀⠀⠀⠀⠃⠂⠂⣳⣿⠿⠛⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⠀⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡄⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣬⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⠄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⣿⠋⠉⠉⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠈⣹⠋⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠐⢛⠇⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⣤⡤⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣻⣿⣿⠋⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠛⠃⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⢠⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣟⠛⠋⠉⠹⠿⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⠶⠶⠞⠛⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣥⠀⠀⠀⣴⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣶⡾⠛⠄⡈⢻⣿⠛⠛⠿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⣿⣿⣿⣶⣄⠙⢺⣿⣀⣀⣀⣠⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣷⣻⣟⡛⣿⣿⣿⣿⠋⢹⣿⣿⣦⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣅⡢⠀⢿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣤⣹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠏⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠈⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⢸⣿⣿⡏
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⢻⡄⠀⣿⣿⣀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣾⠇⠀⢉⣍⢻
⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠛⠋⠀⠀⢀⡀⣠
⠀⠀⠀⢠⣿⠁⠰⠛⠷⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠻⣦⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠛⣿⠿⢶⣄⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢹⡆⠀⢻⡄⠈⣿⡄⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀⠸⣇⠀⢻⡇⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠁⠀⠀⠀⢸⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠛⠛⠿⣷⣶⣶⣶⣾⡟⠀⠀⠀⠀⠀⣠⡿⠃⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣦⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣷⣄⠀⠀⠀⠸⣿⠁⣀⣤⡾⠟⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢿⡆⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠙⢿⣏⠁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠃⠀⠀⠀⠀⣸⣿⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠙⠧⠀⠀⠀⠸⣷
⢀⣤⣤⣤⣤⣤⣤⣶⡾⠋⠀⠀⠀⠀⣠⡾⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣿⠃
⠻⣦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⠾⠁
⠀⠸⣿⡉⠉⢉⣽⡿⣧⡀⠀⠀⢹⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠈⠛⠛⠛⠉⠀⠹⢷⣤⣶⠿⠃⠀⠀⢸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠋⢙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⣿⢻⣿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣤⣤⣤⣤⣴⣿⠸⣿⣤⣤⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢨⣿⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡚⠻⡏⢻⡿⠿⠿⠿⢿⡏⠀⣿⡿⠿⠿⠿⣾⠏⣹⠟⢲⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠈⠱⡛⠖⠛⠚⠁⠀⠀⠀⠘⣿⢀⣿⠀⠀⠀⠀⠘⠓⠛⠒⢿⠋⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠓⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠚⣿⢸⣿⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠚⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤
⣿⣿⣿⡿⠟⠻⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣠⣄⣠⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠲⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢠⢆⡴⣄⣤⠀⢀⣸⣁⢀⢔⣤⠀⠀⠀⠀⣴⡢⡀⣈⣇⡀⠀⣄⣠⢦⡴⡄
⠀⠀⠀⠀⠀⠀⢯⢻⡸⠧⠏⡜⠀⣯⡄⢸⠈⠁⣀⠀⠀⠀⠀⣀⠈⠁⡇⣠⣷⠀⢣⠻⡼⣧⡟⡽
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠚⡩⠞⣇⣻⠸⣄⣉⣁⠐⠂⠐⠀⣈⣉⣠⠃⣟⣸⠲⢝⠓⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⢺⠀⠀⠈⣹⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⡏⠀⠀⠀⡗⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠦⠤⠤⢾⠀⠀⠀⣶⣿⣶⣶⣿⣦⠀⠀⢀⡷⠤⠤⠴⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢰⠃⠳⣄⡀⠻⠿⠛⠛⠿⠟⢀⣠⠎⠱⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⡆⠀⠀⠀⠉⠓⠲⠶⠶⠖⠚⠉⠀⠀⠀⢠⠤⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠔⠤⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠄⢬⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢔⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⢸⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⠓⠒⠶⠶⠤⠼⠦⠤⠶⠶⠒⠚⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⡀⠀⢸⡇⠀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣴⣿⣥⣶⣶⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣾⣿⣿⡿⠛⢋⣭⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣏⡤⢶⣾⣏⠁⢈⣿⣿⣿⣿⣿⣿⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢨⠃⠀⣿⠏
⠀⠀⠀⠀⠀⡠⢀⠀⢠⣤⣄⢈⣿⣿⣿⣿⣵⣿⡿⢿⣿⡵⠿⢋⢻⣿⣿⣿⣿⣷⣤⢴⣾⣿⡏⠀⠀⣀⣤⣾⣷⡴⠒⠂⠁
⠀⠀⠀⠀⠈⠁⠀⢔⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢰⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁
⠀⠀⠀⠀⠀⠀⢾⠞⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠉⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡶
⠀⠀⠀⠀⠀⠀⡡⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠈⢻⣿⣿⣍⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⡠⠴⠂
⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⠿⠓⠂⠂⠀⣺⣥⣤⣤⣤⣉⣉⣉⢤⣤⣤⣤⣴⣶⡶⠶⠖⠶⠶⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⡿⠿⠛⠋⠉⠉⠉⠛⠛⠟⣛⣋⠻⠟⠛⠛⠛⠛⠃⠠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢆⣠⡄⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⠟⠛⠻⠷⣶⣤⡀⠀⠀⠀⠀⣠⣴⠾⠟⠻⠿⢿⣽⣿⣾⣷⣀⣠⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣠⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠙⢿⣿⣿⣿⣄
⠀⠀⠀⠀⣄⣾⣿⣿⠉⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄
⠀⠀⠀⠰⢻⣿⣿⠇⠀⠀⠀⠀⢰⣀⠴⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢠⡟⣿⣿⡖⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦
⠀⠀⠀⠀⣩⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣀⡠⠀⠴⠒⢐⡩⠋⠀⠀⠀⠀⢠⣿⣿⠫⡉
⠀⠀⠀⠀⠈⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠔⠒⠊⠉⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⠾⠃
⠀⠀⠀⠀⠀⠿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⢀⡀⢀⡀⠀⣶⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣁⡀⠤⠄⠒⠂⠈⠉⠀⡔⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⣶⡄⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣌⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠜⠻⡾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⣠⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢀⣠⢊⡵⠋⠙⠉⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⢸
⣿⠀⢀⠎⠸⡇⣾⡵⢒⠛⠉⢽⡇⠀⠀⠀⠀⠀⠀⢠⠊⠈⠈⣠⢖⠈⣧⠇⠀⣠⣴⣶⣷⣦⣰⣊⠐⠦⢄⠑⢠⠀⢸
⣿⠀⢈⠆⢸⣇⣿⠃⠀⠓⡘⢻⡇⠀⠀⠀⠀⠀⠀⠸⠀⢰⡒⠁⠇⠐⢅⠀⠸⣟⠉⢉⡈⢿⡯⠘⡁⢲⢄⠀⢄⢹⣸
⣿⠀⠻⠦⠎⠈⠛⢆⠀⠀⠅⡜⠀⠀⠀⠀⠀⠀⢤⣃⢆⣄⣥⡀⣷⠾⣿⠀⠠⡗⢂⠀⢀⠘⡇⣜⢧⣠⡎⢳⠀⢢⣹
⣿⠀⠀⠀⠀⢀⠠⣤⡟⠑⢯⢀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢯⣢⣸⠇⢀⠎⠀⢀⣧⣼⡟⢉⢼⡇⡏⣺⠕⢑⡹⢲⠴⢻
⣿⠀⠀⠀⢰⠋⡄⠸⡓⠚⢻⠀⣇⠀⠀⠀⠀⠀⣸⠀⠀⣠⠟⠁⣰⡇⠀⢀⠇⡆⢀⡗⠚⠀⣭⠉⡍⠐⢌⠑⠯⣄⣼
⣿⠀⠀⢠⠃⠀⢹⠀⠑⠴⠁⢰⢻⡀⠀⠀⠀⢠⠯⠷⠴⠧⢠⠚⣧⣧⠀⡿⠒⢁⠎⢀⡤⡀⣸⢴⣁⡇⠀⠑⠤⠴⢻
⣿⠀⠀⠈⠓⢲⠇⠀⠀⢀⠀⢸⢚⠀⠀⠀⠀⡞⠀⠰⠦⡁⠛⠋⢁⡗⠀⠓⠒⡇⠀⢰⣆⣈⣠⡴⡇⡿⡄⠠⣀⡀⢸
⣿⠀⠀⢰⠆⢸⠒⢲⠀⠀⠀⢸⢸⠀⠀⠀⢠⠇⠀⠀⠀⠉⠋⢹⠀⠀⠀⠀⣰⠳⠄⠀⠈⠀⠰⡇⡧⣇⣈⡀⢀⣀⣼
⣿⠀⠀⢸⢰⠸⣀⣸⠦⠞⡦⡾⣌⠆⠀⠀⢸⡴⠦⣄⠀⠀⡇⣸⠆⠀⠀⢀⡗⠒⠀⠤⠲⠶⢤⠷⡡⡇⠀⣉⠉⠁⢸
⣿⠀⠀⠈⠙⢦⠼⢛⠀⡀⡇⢧⢏⠀⠀⠀⠀⢧⠀⠉⠙⡷⠏⢹⠄⠀⠀⡜⠀⠀⡹⠛⡆⠀⠈⡆⠙⡇⠀⠈⡇⠀⢸
⣿⠀⠀⠀⠀⡇⡄⢸⠐⡇⡇⢸⢸⠀⠀⠀⠀⣇⠀⠀⢠⡇⠀⢨⠇⠀⢠⠇⠀⢠⠃⠀⡇⠀⠀⡇⢀⡇⠀⠀⡇⠀⢸
⣿⠀⠀⠀⠠⣇⡇⡾⠀⡇⢣⠈⣏⡇⠀⠀⠀⣾⠀⠀⢘⡧⠀⣸⠀⠀⢸⡄⠀⣿⠀⠀⣗⠀⢀⡇⠈⠓⡖⢶⢱⠖⢺
⠿⡤⠤⠤⠤⠬⢽⢿⠿⠷⡿⡿⠧⠤⠤⢤⠤⠧⠤⠤⠾⠤⠤⠽⠤⠤⠼⠤⢤⠼⠤⠴⠧⡤⠼⢧⠤⠤⠧⠼⠼⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠶⠶⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢠⢄⡴⣄⣄⠀⣀⣼⡀⢠⢐⣤⠀⠀⠀⢠⣔⢠⠀⣸⣄⠀⢀⣄⡴⣄⢤
⠀⠀⠀⠀⠀⠀⢏⢿⣼⢧⢏⡎⠀⣧⡀⠀⠉⢁⡀⠀⠀⠀⠀⡀⠉⠁⠀⣠⡇⠈⢎⢧⢿⣴⢏⠇
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢚⡩⠺⣅⣷⠰⣀⣉⣁⠐⠀⠐⢀⣈⣁⡰⢰⣇⡽⠺⣙⠂⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢾⠀⠀⠀⡽⠀⠀⠀⠉⠑⠂⠒⠉⠁⠀⠀⢸⡍⠀⠀⢸⠖⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠤⠤⠴⣧⠀⠀⢠⣾⣿⣶⣾⣿⣦⠀⠀⢠⠷⠤⠤⠼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠰⠉⠳⣄⠈⠻⠟⠋⠛⠿⠋⣀⡴⠋⢃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠆⠀⠀⠀⠉⠓⠲⠤⠴⠒⠋⠁⠀⠀⠀⠦⠤⠤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠓⠒⠲⠤⠤⠼⠤⠤⠴⠒⠒⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠐⢲⠒⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⠀⠀⣸⠀⠀⢀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠈⠉⠉⢹⠉⠉⠉⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠛⠓⠒⠒⠒⠒⠚⠃

⣿⡿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠇⢐⣦⡀⠀⠀⢀
⠀⠀⠀⣠⡄⠀⢰⣷⠰⣿⣼⣴⣾⣿⡇⠀⠘⠿⡀⠁⠀⠸⢦
⠀⢠⣿⣿⣿⣷⣾⣿⢰⣿⣿⣿⣿⣿⣷⠀⠀⣄⠁
⠀⠸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠃⠛⠁⠀⠉⣀⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣷⣷⣆
⠀⠀⠉⠛⠛⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⢛⣻⣦⣤⣥⢶⣾⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠹⠛⠛⣟⠀⠀⣀⠠⠐⣂⣬⣽⣿⣿⣧⣾⡿⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠒⠹⠿⠿⡿⠛⠋⠀⠉⠀⠋⠀⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣷⡤⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠻⠷⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⢛⣿⡟
⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢀⡠⠴⠊⠀⠀⡀⡀⢕⠢⡀⠀⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠹⣿⡖⠒⠊⠁⠀⠀⠀⠀⠀⠙⢄⠂⠁⡈⠢⠘⠈⢆⠀⠀⠀⠀⠀⠀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠳⡁⠈⠃⠀⠐⠢⠀⠁⠈⠢⡀⠀⠀⠀⠠⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢳⡀⠠⡀⠀⠹⣽⣇⠀⠀⠀⠀⠀⠀⠈⠢⣀⡈⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢀⣾⡟⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠙⢦⡀⢀⠀⠹⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⡑⣄⠂⠀⠀⠀⠀⠀⠀⠉⠐⠘⠿⢅⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠙⢦⠢⡀⢹⣿⠀⠀⠀⠀⠀⠀⠬⠤⠤⠬⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠑⠔⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣿⣷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣍⠙⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠡⡀⠠⢄⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠀⢸⣅⠀⠠⡄⢉⠉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣞⡏⠂⢳⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢐⣻⡆⠀⠀⣀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⣾⡀⠑⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠹⡄⠀⣀⠉⣀⠩⠤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⣽⣇⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠓⡦⢄⠉⠤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠀⢌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡿⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡠⢀⡀⢀⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠇⠹⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⠔⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢙⡒⠦⠤⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢠⠊⠉⢹⣷⣄⠀⠀⡰⠊⠈⢹⣷⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⣤⣤⠟⣿⣿⠀⠀⣷⣤⣴⣋⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠛⢿⡿⠟⠋⠀⠀⠘⠻⠿⠿⠛⠁⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠢⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⡤⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠀⠀⢠⣶⣶⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠋⠋⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿
⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡖⠂
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣶⠓⠓⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠚⠛⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣿⡴⣾⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢳⡄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠶⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣾⡴⠞⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⢒⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠴⠖⠛⠋⠉⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣡⣤⠤⠶⠖⠛⠋⠉⣡⠏⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⢈⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣄⣀⢀⣾⡆
⢻⣌⣉⡋⠁⢷⡀
⠀⠈⠉⠛⣦⠀⠳⣄⡀⠀⠀⠀⠀⢀⣴⠖⠓⠶⣄⡀
⠀⠀⠀⠀⠘⣧⠀⠈⠛⠓⠶⠦⠤⣼⡇⠀⠀⠀⣿⡟⠛⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⡀⢸⡇⠀⠀⣰⣿⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⢧⣤⡾⢻⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠃⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣰⣿⣿⡀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣰⠏⠉⠛⢿⣿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⢀⣠⠔⠋⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡟⣧⣀⣀⣤⡴⠶⠛⠋⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠉⣀⡴⠚⠉⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⣠⠴⠿⠿⠿⠿⣿⣿⣯⠀⠈⠉⠁⣠⣤⡶⠞⠛⠲⣤⣙
⠀⠀⠀⠀⠀⠀⠚⠻⠶⠤⠴⠾⠋⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠘⠉⠀⠀⢀⣀⣤⣤⣤⣤⣹⣷⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣤⡤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⡒⠉⠉⠉⠉⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠒⠒⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠈⣦⡀⠀⠀⠱⡄⢀
⠀⠀⠀⠀⠀⠀⣴⡿⠿⣿⣷⣄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢸⠈⠓⢦⡔⠉⠁⠉⠳
⠀⠀⠀⠀⠀⢰⣿⠁⡀⠈⠛⠿⣷⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⣈⠛⠓⠂⠀⠙⢿⠅⠉⠙⣿⡶⠒⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⢦⣀⡀⢀⣠
⠀⠀⠀⠀⠀⠀⢈⡿⠿⠟⠋⠀⠀⣀⣀⠀⠀⠀⠸⠇⠀⠀⢀⣀⣈⠉⠓⠶⢤⣀⠀⠀⢰⠃⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢠⣎⠀⠀⠀⠀⣰⠾⣛⡛⠃⠀⠀⠀⠀⠀⠀⠘⢛⣛⠷⡄⠀⠀⠀⢉⣻⡁
⠀⠀⠀⠀⡰⠛⠛⠛⠛⠃⠀⠀⡜⠁⠙⡆⠀⠀⠀⠀⠀⠀⡼⠁⠈⡇⠀⠀⠘⠛⠛⠛⠛⣄
⠀⠀⢠⣞⣁⠀⠀⠀⠀⠀⠀⠀⠱⠚⠛⠋⠀⠀⣠⣄⡀⠀⠛⠛⠓⠃⠀⠀⠀⠀⠀⠀⢀⣈⣷⡀
⠀⡠⠛⠻⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠚⠻⠿⠿⠿⠿⠟⠛⣆
⣸⠁⠀⠀⢀⡤⠖⠊⠉⠉⠙⠒⢤⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠴⠒⠉⠉⠉⠑⠲⢄⡀⠀⠀⠈⡆
⣿⠶⠆⢠⠋⠀⠀⠀⠀⠀⠀⠰⠀⠈⢿⣷⣶⣦⣤⣤⣴⣶⣾⡟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠶⠾⣿
⢇⠀⠀⢸⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⣈⠻⢿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢂⡴⠋⠀⠀⠀⠀⡇⠀⠀⡞
⠘⢆⠀⠘⣆⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠆⠀⠀⡀⠀⡾⠀⠀⠀⠀⠀⡸⠁⠀⡼⠁
⠀⠈⠳⣄⡈⢦⡀⠀⠀⠀⠈⢧⣀⠀⠘⠂⠀⣠⢾⠳⣄⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⢀⠞⢁⡤⠚
⠀⠀⠀⠀⠉⠓⠿⣦⣀⠀⠀⠀⠈⡏⠉⢩⠏⠀⣸⠀⢈⡏⠉⠉⢹⠁⠀⠀⠀⣀⡴⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠲⣤⣀⣇⠀⠸⡄⠀⣿⠀⢸⠀⠀⠀⣼⣀⣤⠒⠉⢹
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⡇⠈⠙⢦⣀⣇⠀⠈⠀⣸⣀⣠⠴⠋⠀⢸⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣰⣧⣄⠀⡾⠀⢠⣶⣦⣬⣉⠳⠤⠴⠋⣉⣤⣶⣶⡄⠈⣧⠀⣠⣼⡆
⠀⠀⠀⠀⠀⢠⠏⠉⠉⢱⠇⠀⢸⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⡇⠀⠸⡌⠉⠉⠹⡄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⠀⠀⢸⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⢳⡀
⠀⠀⠀⢀⣾⣦⣄⣀⣀⡇⠀⠀⠘⠿⠿⠛⠁⠀⠀⠀⠀⠈⠛⠿⠿⠃⠀⠀⢹⣀⣀⣤⣴⣷
⠀⠀⠀⡞⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⢧
⠀⠀⣸⠁⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠀⠀⠀⠘⡆
⠀⢠⡏⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻
⠀⢸⣿⣦⣤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣤⣶⣿⡇
⠀⠾⠛⠿⠿⠿⠿⠷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠾⠿⠿⠿⠿⠛⡇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣖⠋⠉⠉⠉⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠷⠶⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⢸⠓⢦⣀⢀⡼⠖⠒⠶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠻⣿⣷⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⢸⡄⠀⠈⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢿⣇⠀⢤⣄⣈⣙⠛⢿⣷⡶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣄⣉⠀⠀⠀⠙⠇⠀⠀⠈⣿⡏⠉⠙⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠦⢤⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⣠⠛⠛⠋⠁⠀⢀⣠⣤⣄⠀⠀⠀⠘⠁⠀⠀⢀⣤⣤⣀⠈⠉⠓⠦⢤⣀⠀⣠⠃
⠀⠀⠀⠀⠀⢀⣼⣁⣀⠀⠀⠀⠴⠟⣛⣙⡉⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⡛⠷⠄⠀⠀⣀⣈⣹⣅
⠀⠀⠀⠀⣠⠞⠛⠛⠛⠛⠁⠀⠀⢸⠁⠀⢱⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⠀⠀⠀⠘⠛⠛⠛⠛⢦⡀
⠀⠀⢀⣴⣃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠛⠛⠃⠀⢀⣀⣀⠀⠀⠙⠛⠓⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣄
⠀⣠⠞⠿⢿⣿⣿⣶⠶⠶⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠶⢶⣾⣿⣿⠿⠟⢦⡀
⢰⠃⠀⠀⠀⠀⣠⠴⠖⠒⠒⠲⢦⣄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⡤⠶⠒⠒⠒⠶⢤⣀⠀⠀⠀⠀⢳
⣿⣤⣄⠀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠙⢳⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⣤⣼⡇
⡏⠉⠁⢰⠃⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠒⠀⢀⡀⣠⠴⠀⠀⠀⠀⢻⠀⠉⠉⡇
⢹⡀⠀⠈⣇⠀⠀⠀⠀⠀⠙⡆⢠⠀⠀⠰⠂⠈⠛⠻⢿⠿⠛⠋⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡟⠀⠀⣸⠃
⠀⠱⣄⠀⠘⣆⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡀⠀⠀⠀⣼⡆⠀⠀⠉⠀⠀⠰⠀⣸⠁⠀⠀⠀⠀⢀⡼⠁⢀⡴⠃
⠀⠀⠈⠳⢤⣈⠣⡀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣤⠞⣻⠙⠦⣄⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⣠⢊⣀⠴⠋
⠀⠀⠀⠀⠀⠈⠙⠻⠶⣄⡀⠀⠀⠀⡿⠀⠀⣸⠀⠀⡿⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⣀⡴⠾⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⣻⠀⠀⢻⠀⠀⡇⠀⢸⠃⠀⠀⢸⣃⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣸⡄⠀⠁⠀⣸⢀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣈⠙⢦⣄⡴⠋⢉⣠⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠋⠀⠀⠀⠈⠛⠿⣿⣿⡿
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿