Mush Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⡶⠶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠿⣯⠀⠀⠀⠀⠀⢸⣧⠀⠀⠉⢹⣿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣹⡇⠀⠀⠀⣀⣀⡙⠻⠶⠿⠛⠁⢀⣼⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠻⢷⣤⣤⣴⠟⠁⠀⣠⡾⠛⠉⠻⣷⡀⠀⠀⠀⣼⡇⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢷⣤⣄⣤⣾⠟⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠈⣿⣄⣤⣤⣴⣶⣶⠶⢶⡶⠿⠿⣿⡿⠶⠿⣷⡶⣶⣤⣤⣤⣈⡉⠉⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣶⡿⣿⠛⠙⣏⠀⠸⡇⠀⠀⣇⠀⠀⢻⠀⠀⠀⣾⠀⠀⢠⡏⠉⠉⣿⠿⢶⣦⣄⡈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠁⠀⠙⢧⡀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠁⠀⣴⠟⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⡒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠠⣀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣾⣁⣀⠀⣼⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣧⠀⠀⢦⡀⣀⣷⣤⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣀⢸⣿⣾⣿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢸⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⡀⢸⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⢆⠎⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⢀⡞⠸⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⡼⠀⠇⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠐⠋⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⠶⢤⣠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠙⢳⣄⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⡤⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣤⠶⠓⠀⠑⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⢶⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣥⡀⠀⢠⣶⣵⠞⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠤⠤⠶⠶⠶⣶⣿⠇⠀⢻⣶⣿⣟⠩⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣠⠜⠛⠻⠟⠇⠀⢸⡿⠵⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠂⠉⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⡶⠿⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠀⢠⡞⠁⠀⠀⠀⠡⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢿⢲⡏⠳⣈⣰⣤⣠⡄⠀⠀⣰⣟⣀⠤⠀⠀⠠⠠⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠟⠉⠀⠈⠁⠀⠀⢟⡫⣀⣠⡴⠖⣤⣀⠼⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠃⠀⠸⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢱⠀⠀⠀⢸⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠧⠄⠤⠼⠁

⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣿⠿⣿⣛⡻⠛⢭⣚⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡤⢶⠚⠛⠛⠍⠹⠹⣿⢋⣉⣓⠒⢂⣶⠆⢀⣐⠀⠐⠂⠀⡙⠯⠙⠈⠉⠿⣛⡒⠻⠿⠿⡘⠁
⠀⠀⠀⠀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣛⣿⣝⣶⡾⠶⠿⠛⠟⠛⡿⠿⣿⣿⡿⣿⣽⠶⢻⣩⢀⣁⡠⠄⣓⣈⣀⣶⣦⣩⣬⣿⠟⠓⠊
⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⣴⣿⣵⣿⣷⣤⢐⣿⣶⢶⣿⣽⣽⢏⣛⡻⣻⡿⠟⠋
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡼⠗⠋⠁⠁
⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠸⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⣲⣆⣀⠀⠀⠈⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⢿⣷⣶⣶⡶⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣬⣿⣿⣿⡇⠀⣐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠘⣏⠀⠀⠂⠠⣼⣾⣿⣿⣿⣇⣀⣀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠁⠈⠈⠑⠋⠁⠈⠉⠉⠉⠉⠉⠙⠹⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠀⠀⠀⢔⠊⠁⠒⡌⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⢌⡩⠇⠀⠀⠀⠀⠈⠀⠒⠊⠁⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣠⠞⠕⠊⠉⠉⠑⡄⠀⠀⡠⠖⠒⠒⠒⠲⣄⠀⠀⢀⠔⠒⠒⠒⢤⠀⠳⡀
⠀⠀⠀⠀⢀⠞⠁⠐⠄⢠⠤⠤⠚⠁⠀⢸⠀⠀⠀⠀⢀⣠⠏⠀⠀⠈⠀⠀⠀⠀⢀⠇⠀⠙⢄
⠀⠀⠀⢠⠋⠀⠀⢀⣀⠠⠤⠄⣀⠀⠀⠈⠒⠂⠉⠉⠁⠀⢀⠠⢄⡈⠲⠤⠖⠚⠁⠀⠀⡠⢬⣣
⠀⠀⠀⡎⠀⠀⡞⠁⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠣⣀⠟⡇
⠀⠀⠀⡇⠀⠀⠣⠀⠀⠠⠤⠒⣉⡤⠤⠲⡖⠒⡖⠒⠒⢒⠚⡖⠒⡲⢲⠤⣄⠐⣅⠉⣢⠀⠀⠀⡇
⠀⠀⠀⢳⠀⢠⠤⣄⠀⣠⠔⠋⠤⣈⡐⢤⡈⢆⠇⠸⠀⣎⠜⣠⡪⢔⡡⢒⡡⠝⠢⡉⠁⢀⢤⣀⠇
⠀⠀⠀⠀⠑⢄⠀⠊⢰⠃⠀⠬⠵⣶⣬⣕⣚⡦⠗⠒⠓⠛⠺⠿⣞⣓⣪⣥⢴⠖⠄⢽⠀⢥⡼⠋
⠀⠀⠀⠀⠀⠀⠑⠦⣘⢯⡉⠭⠭⢍⡙⢿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣟⣒⣀⣈⣉⣤⠾⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⠀⠤⡀⠀⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⢀⢐⠂⠀⠀⠐⠈⠀⠈⠀⠠⢆⠉⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣀⡁⠤⠐⠒⢰⡆⡻⠸⢫⡙⠁⠒⠂⠬⢀⠂⡈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⠒⠠⠑⠊⠑⠠⣤⣾⡏⠻⢿⣿⣿⣶⣤⣆⡀⠀⠀⠁⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠉⡀⠀⠆⠚⠛⠹⡇⠀⠀⣿⣟⢟⢟⢅⠉⢀⡤⠚⡉⠩⠉⠛⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡗⠦⠤⠤⠤⢄⣀⢁⡀⠋⠀⠀⢸⢈⣈⠠⠤⢴⠋⢁⠀⠀⠀⠀⠄⠀⠀⢙⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠊⡉⠉⠉⠙⠒⢦⡤⣐⠠⠀⠄⠀⠃⠀⠀⣿⡀⠀⠀⡰⢋⣓⣪⣤⣶⣶⣾⣶⣶⣶⡲⠶⣮⣱
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⠂⠀⠂⠀⠀⠄⡠⠊⠀⠀⠹⢦⣄⣀⠃⠀⢠⣯⡷⡄⢪⠞⠩⠁⠉⠛⢻⡀⠀⡿⢿⣽⠗⠒⠛⠁
⠀⠀⠀⠀⢀⠴⠁⠀⠀⠒⠒⠄⠀⠀⠀⠠⡄⠀⠀⠘⠖⠊⠈⢇⠀⠀⢸⠙⠢⣱⠈⣉⣉⡿⠋⠈⣸⠂⢀⣧⠀⠈⢱⡀
⠀⠀⠀⠀⡦⠼⠀⠀⠀⠂⠈⠀⠀⠀⠑⠒⠁⠀⠀⣀⣀⡀⢀⠻⡀⡀⠘⡶⠞⠋⠉⠉⣽⡇⣴⡞⠁⠀⡾⣦⠄⠈⣹⠇
⠀⠀⠀⠀⠗⠂⠀⠀⢀⣀⣀⣠⣤⣤⠤⠴⠶⡾⡿⠛⠂⠀⡠⠋⠀⠀⠸⠀⣤⣴⣴⠷⣾⠷⠋⠈⡽⠚⢠⡛⠨⠒⠁
⠀⠀⠀⠀⠈⠠⠄⢉⠉⠀⠘⠋⣙⠀⠀⠀⠀⠙⠃⠈⠉⡁⡀⠀⠀⢀⡏⣉⠘⢛⡏⡼⠁⠀⡠⠎⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠡⠀⠇⠀⠀⠀⢨⣄⠄⠤⣠⠏⠀⢀⠞⢀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡆⠀⠀⠐⠒⠉⠀⡃⡇⠀⠀⣶⠡⢁⡸⠃⠀⢠⠊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢐⠸⡄⠀⠀⠀⠀⠈⢧⣇⡀⠀⢘⣷⠏⠀⠀⣴⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠓⠹⣄⠀⠀⠀⠀⠈⠛⠻⡞⠂⠨⠃⣠⣼⠃⡜⡰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣌⢑⡼⣦⠴⢤⡘⠀⠤⢲⡉⠈⣾⣿⠟⠳⠺⣏⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⠫⡽⠀⠧⠀⣤⠃⠀⠀⣨⡷⢷⣃⣀⣠⠔⠒⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⠃⠀⠀⠀⠈⢉⣹⢗⡁⠤⢄⠠⠼⠧⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣠⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⡿⠿⡿⠛⢿⠛⢿⢻⠻⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢛⡁⠀⠤⠠⣬⣔⣵⣄⣦⣄⣨⢞⠁⠂⡀⠉⠙⠛⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣤⣀⣈⣅⢀⣙⣿⢉⢬⠠⢉⣿⣿⣶⣟⣻⣶⣶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣛⠂⢀⠀⢹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⣶⡴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⡀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡞⠀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⡼⠁⠠⢀⣾⠀⠀⢸⡄⣠⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣷⠃⣼⠀⡞⡏⠀⢰⠿⡷⢁⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⢿⣿⣄⡿⣾⢡⣵⣧⣷⣾⠗⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠈⠟⠃⠛⠸⠏⠟⠁⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠃⠀⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⣤⠐⠃⡀⠀⣀⣀⣼⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠁⢁⢙⠋⡗⠐⡞⠿⣘⣂⣤⠟⠀⠠⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠨⢴⡀⢸⣀⣇⣜⠹⢠⣰⠍⢩⠜⣨⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠁⠀⠘⠙⣶⠷⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⢿⠘⠃⢲⣇⢠⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣡⠀⣬⣛⣬⣀⠁⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠘⠫⠀⠁⠀⠀⢠⣴⠒⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠤⡇⠗⢀⠠⠀⢩⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⢧⣧⡅⣀⠘⡳⠠⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠃⠀⠀⠀⢠⣖⠂⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣸⢛⠀⢈⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠋⠱⠂⠀⠂⠀⠠⣄⠴⠆⠸⣗⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣺⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢤⠀⠀⠀⠀⢀⠐⠁⠲⠳⢶⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡁⠀⠀⠀⢀⠊⠀⠀⠀⢀⠐⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠐⠂⠀⠤⠀⠀⠂⠀⠁⠀⠀⠚⠂⠠⠅⠀⠀⠀⠉⠂⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⢿⣿⡿⣿⣿⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠒⠂⠠⠖⠉⠉⠉⠛⠛⠻⣿⣿⣿⠿⠿⠿⠿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢦⡀
⠀⠀⠀⠀⢀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⢻⣿⣶⣿⣴⡄
⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⡀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣷⠀⠃⠘⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⡄⠀⠀⠛⠋⠀⣶⣾⡧⠀⠀⠀⠀⠀⣠⣶⣬⠿⣿⣿⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠉⣠⣴⠦⣽⣿⣿⠟⠋⠁⠀⠀⠀⣴⣶⣁⡀⠿⠿⣿⣥⡼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⢀⠿⣿⣿⠀⠀⠀⠀⠰⢿⡶⢟⡈⠁⠀⠀⠈⠁⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⡆⠀⠀⠀⠰⣷⠀⣈⡁⠀⠸⢦⠀⣰⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣹⣿⣷⠀⠀⠀⠀⠀⠈⠉⠀⢠⠄⠈⠃⠙⠃⣹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠟⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠰⠠⣤⡀⠀⠀⠈⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠉⠛⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣹⣿⣇⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡼⣿⣿⡄⠀⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣿⣿⣧⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢻⣿⣿⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣆⢾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⢐⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢫⡘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣶⡟⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠟⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣈⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠟⣛⡛⠛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⡀⠀⠀⠁⠀⠈⠁⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠿⢶⣦⣀
⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄
⠀⠀⢀⣤⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⣄⣤⣠⣤
⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡏⠀⠀⢿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣻⣿⣿⣿⣿⡄⠠⠘⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣽⣿⣿⣿⣧⠀⠀⠹⠿⠃⣤⣴⣏⠀⠀⠀⠀⠀⣠⣤⣻⣿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⢉⠙⠋⣠⣤⣶⣶⣶⡿⠟⠃⠀⠀⠀⣤⣮⡋⢹⡿⣿⣿⣥⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠻⡏⠁⡸⣿⣿⡀⠀⠀⠀⠰⣿⣼⣏⠉⠁⠀⠈⠉⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣚⣿⣇⠀⠀⠀⠴⣶⠀⣉⠁⠀⢶⣄⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢩⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠤⠀⢙⣈⠛⢩⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣳⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠐⠲⣦⡀⠀⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇⠀⠀⣀⠀⠀⠺⠟⠀⠀⠀⠈⠉⠛⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢟⣿⣷⠀⠠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⡇⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⣿⣿⣷⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣖⡟⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠾⠩⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⢟⡰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡿⣻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣮⡿⣸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣘⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣂⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⠀⢀⣤⠤⠴⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⡘⠛⠫⣉⠀⠀⠈⠉⠙⠛⠷⢶⣤⣄⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⠁⠀⠉⠙⠻⢦⣄⡑⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⢁⠤⡀⠀⠀⠀⠨⢿⠃⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠠⠴⠒⢠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠛⠛⠛⠛⠛⠶⢦⣜⡆⠀⠀⠀⠐⠋⠁⠠⠤⠀⠞⠐⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠶⢦⡀⠀⠀⠀⠀⢀⡠⠭⣿⠀⠀⣴⠿⠛⠛⠻⠿⠿⠷⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠽⡄⠀⠀⢰⣏⣤⡴⠶⠶⠶⠶⢧⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢷⣦⡀⠐⢤⠀⠀⢸⣿⣅⡀⠀⠀⠀⠀⠐⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡛⢷⣾⣷⠤⠬⠷⠭⠿⢄⡀⢀⡏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣫⠭⠖⠒⠊⠉⠉⢙⡿⣿⣿⣧⣤⡤⣤⣤⣀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⡊⠁⠀⠀⠀⠀⠀⠀⢀⣜⣾⠟⠉⠀⠀⠀⠀⠀⠉⠛⢿⣵⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⠧⠠⡀⠀⠀⠀⠀⠀⠀⣠⠤⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⢸⡆⠀⠀⠀⢠⡿⢧⣀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⢀⣀⣀⠎⠀⠀⠀⠀⡜⠀⢀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⣀⠀⠔⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠆⠈⠉⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠄⠐⠄⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⢀⣶⡀⠀⣀⣄⠀⣀⢀⣀⢂⠀⣀⡠⣀⣀⠀⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⠛⠛⠛⠋⠁⠒⡖⠀⠀⠀⠉⠁⢸⠉⠉⣉⣉⣉⠭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠒⢲⢃⣀⡰⣄⣠⡀⢸⠉⠉⠁⢀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢨⠉⠀⢀⣠⣤⣌⣈⣀⡀⠈⠑⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠸⡄⠀⢣⠔⠛⠶⢌⡙⠉⠉⡟⠓⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⠇⢀⢆⠀⠀⢀⣀⡈⣆⠀⣧⡥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⢀⠎⠀⡏⣁⣴⡊⠙⣆⢦⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠰⢃⡞⠀⠀⠻⣡⣙⡇⠀⢹⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠘⠈⣧⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⠴⠖⠃⠀⠀⠀⠀⠈⠋⠙⠛⠁⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣖⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣉⠅⠂⠉⠈⠉⠙⢢
⠀⠀⢀⣠⣴⣶⣶⣲⣾⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⡄⠀⠀⠀⡠⠖⠉⠭⢰⠮⠂⡠⠊⡁⠀⠀⠀⠙⠑⢢⠀⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡀⠀⠀⠀⠀⠀⡄
⠀⠀⢿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣻⣿⣿⣿⠟⠋⠀⠀⠀⠀⠘⡃⠀⡀⠀⠀⠀⠠⡄⠀⠿⠖⢈⠁⠀⠄
⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡀⠀⣀⠀⡘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣧⣀⡀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠉⠉⠛⢶⣤⡄⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣹⡿⣿⣾⣿⣿⣿⣗⣊⣽⣶⡄⠀⠀⠀⠀⠀⠸⠏⠉⠁⡒⢤⠀⠁⠀⠀⠈⠼⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢄⣀⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⢿⣿⠿⠿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠂⠀⠀⠤⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡄⠀⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⡀⠀⠀⡀⠀⠀⣿⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⡿⣿⢿⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣼⡅⢶⠀⡄⠀⠑⣌⣤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠘⠻⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⠽⠿⠿⢿⣧⡰⠋⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⠿⣿⠻⡇⠀⢰⣄⡀⠠⣠⣴⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠋⠁⠀⠈⠆⠀⠁⡀⠀⠙⠃⠀⡆⠀⠈⡁⡆⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠄⠀⠀⢀⣀⠀⠀⢹⣇⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠿⠄⣾⢿⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠹⡇⠸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠋⠛⠻⣯⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠛⠀⠀⠐⠒⠄⢀⠀⠀⠀⠀⠀⢠⡍⠀⠀⠁⠀⠀⢠⠀⣠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⠇⠘⠀⢠⡄⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⢀⠛⣄⡧
⠀⠀⠀⠀⠀⠀⢿⣤⠇⠈⢀⡆⠀⠘⠃⠀⠀⠀⠀⠀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⢀⣸⣿⡦⠁⠘⢣⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⣤⣠⣬⣎⣁⣄⡀⠀⡀⢸⠐⠀⢸⣿⣷
⠀⠀⠀⠀⠀⣾⣿⡇⠀⠰⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣈⣁⣤⣤⣶⣿⣻⡿⣟⠋⠀⠄⠐⠸⠃⠈⡇⠃⣾⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣛⠃⠐⠆⠀⠀⠀⠀⠀⠀⠀⡿⢻⡏⠉⢀⣤⣦⡤⢶⠖⢺⢻⣟⣿⣿⣿⠗⣩⠮⠗⠉⠀⠀⠀⠀⠐⠁⠀⡀⠁⠀⢾⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣀⣤⠾⠍⢾⣿⣿⣦⣵⣾⣿⣿⣿⣿⣛⣡⣤⣾⣥⣤⣀⣄⡠⠈⠀⠀⠀⠀⢸⣆⣸⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣧⠀⠆⠀⠀⠀⢠⣾⣿⣿⣿⡿⣢⡶⠾⢟⣛⠿⣻⡿⠟⠛⠋⠉⢀⣼⣿⣿⣿⣿⡽⠿⠋⠁⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⠠⡆⠀⠀⠀⣿⣿⣿⣿⣯⣅⠀⠀⡀⠈⣡⣼⣯⣶⣾⣿⡾⢶⢿⣿⣿⠿⠋⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠷⠤⠌⣶⠽⠟⠻⠿⠿⣿⢀⠀⠀⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢸⡮⠀⠀⠀⠀⠀⠻⡀⢸⡀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡕⠲⣄⠈⠂⢀⡀⠀⡀⠀⠀⠀⠀⠤⠄⠀⠁⠰⠀⣇⠀⠀⠀⣠⡔⠛⠀⠀⠀⠀⠀⢀⠐⣠⢦⣽⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⣬⠁⠤⡀⠙⠀⢑⠂⡆⠀⠀⠀⠀⠀⠱⡇⣀⣧⠄⠐⢰⣿⣿⣀⠀⠀⠀⠀⠀⠀⠛⠁⢸⡏⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⡸⠟⠠⣄⠆⣼⣿⡧⠀⣀⣀⠀⠐⠃⠁⠹⣷⡄⠈⢿⡿⣷⣤⣤⡀⠀⠀⠀⠀⢠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠙⣏⣤⣽⣷⢿⣿⣿⡿⠿⣿⣗⣤⠃⠀⠀⣿⠀⢀⡁⠁⣸⡿⢿⡍⠋⠉⣩⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢤⣿⣟⣿⣾⡛⢿⣶⡂⠉⢍⣿⣆⡀⢘⣡⠔⠂⠀⢠⡟⠀⣾⣷⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣰⡀⠀⣿⣿⣿⣿⣿⡏⣷⡄⢡⣶⣿⡧⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⡤⡶⡒⢻⡏⠉⢹⡟⡝⢟⢷⢶⣄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣾⢏⠎⡴⢱⢱⡇⠀⠘⡿⡘⡎⢦⢳⣽⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠻⠼⣥⣧⣼⡇⠀⠀⣧⠷⠿⣚⣫⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠓⢦⡀⠀⠀⠀⠀⠈⠙⠓⠒⠒⢺⡇⠀⠀⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⢀⡤⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⠀⠀⣠⠶⠚⠉⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⣴⣒⡒⣲⡖⠒⡶⠶⠦⣄⠀⢳⡀⠀⠀⠀⠀⡾⠀⠀⢠⡏⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⣛⣺⠀⢀⡷⠶⠿⢛⣡⠞⠀⠀⠀⠀⣼⠁⠀⠀⡼⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⣸⠃⠀⠀⣸⠃⠀⠀⠀⠀⠙⠲⣤⣄⣀⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⢠⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢹⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡼⠁⠀⡾⠀⠀⣀⡤⠴⠚⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢳⡀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡇⠀⠀⠀⠀⢠⡞⠀⠀⡼⠁⢰⠋⣁⣀⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠈⢧⠀⠀⠳⡄⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⠀⠀⢠⡟⠀⠀⡼⠁⠀⠘⢦⡻⣭⣹⠓⢲⣤⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠳⢤⡈⢧⠀⠀⠙⣦⠀⠀⡏⠀⠀⠀⣼⠀⠀⠀⢀⡟⠀⠀⣼⠁⠀⠀⠀⠀⠙⣳⠃⢀⣟⡶⠿⢂⡼
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣹⠈⢷⡀⠀⠈⢧⣰⡇⠀⠀⠀⢸⠀⠀⠀⣼⠁⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁⢠⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⣀⣤⠴⠚⠁⠀⠈⢧⠀⠀⠀⢻⡇⠀⠀⠀⢸⡄⠀⢠⡏⠀⠀⢸⠀⠀⢀⣤⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⣇⠀⠀⠀⠈⣧⠀⢸⠃⠀⠀⢸⣀⡴⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⢦⣀⣀⣀⡀⠸⡆⠀⠀⢹⡀⠀⠀⠀⠸⡆⢸⠀⠀⠀⢸⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⠀⠈⠉⠙⣧⢷⠀⠀⠀⢳⡀⠀⠀⢀⡗⢸⡄⠀⠀⢸⡇⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠤⠶⠃⠸⡆⠀⠀⢨⡟⠲⠶⠚⠁⠈⢧⡀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠴⠞⠁⠀⠀⠀⠀⠀⠈⠙⠛⠉

⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⣿⡑⢌⣠⢡⣝⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣫⡌⣄⡡⢊⡿
⠀⠘⣦⢻⡪⢙⣋⣙⡻⢯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⡼⢋⣋⣙⡋⢕⡗⣴⠃
⠀⠀⠘⣎⢧⣏⢲⡆⠀⠭⠟⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⠫⠩⠀⢰⡔⣹⡼⣱⠃
⠀⠀⠀⠸⡌⣎⠒⠬⢒⠤⡀⡀⠙⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⠏⠊⢀⠀⢤⣒⠥⠒⣱⢡⠇
⠀⠀⠀⠀⣿⢸⡗⠦⠔⢆⡈⠑⡓⠦⣌⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⣡⠴⢚⠈⢅⡐⠢⠴⢺⡇⡿
⠀⠀⠀⠀⢸⠨⡿⣓⣈⣀⢈⡁⠐⠤⠀⠙⠺⣿⡻⣦⠀⢀⡀⠀⣴⢟⣷⠗⠋⠀⠴⠃⢈⡁⣀⢁⡚⢿⠡⡇
⠀⠀⠀⠀⠘⣯⢇⣧⣤⣦⣀⣬⣨⣆⣠⠈⡂⠨⠻⣽⣇⣾⣷⣸⣯⠟⠁⢖⠁⣄⣰⣁⣥⣀⣤⣤⣼⡼⡽⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠄⠀⠉⠛⠲⢤⡈⣿⣿⣿⣿⣁⡤⠖⠋⠉⠀⠠⠀⠀⢀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡻⢣⠟⡟⣞⠗⠶⣾⣟⣽⣿⣿⣏⣻⣷⠶⠻⣳⢿⠻⡝⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⢸⠀⡇⣜⠤⠈⠹⢿⡿⢹⡏⣿⡿⠏⠁⠄⣣⢸⠀⡇⠀⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠠⠃⠨⡇⠸⡀⢇⡐⠀⣀⠇⣿⡇⠸⢀⠀⢂⡼⢀⠇⢸⠅⠘⠄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠹⣄⠙⢦⣈⢦⡞⠀⢹⡇⠀⢳⡔⣁⠴⠃⡰⠏⠀⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡌⢀⣀⡉⠓⠤⣤⠏⠀⠀⠘⠃⠀⠀⠹⣤⠤⠚⢉⣀⡀⢡⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⢦⢊⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡑⡴⠒⠾

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢽⡞⠛⢻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⠛⢑⡮⢭⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠏⣻⡍⠿⡽⠓⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⠚⢫⡾⢩⣟⠹⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢶⠯⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡽⡶⢺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡷⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠙⠶⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣗⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⡄⢰⡦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡒⣥⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡷⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⢿⣼⣷⡿⠂⠀⠀⠀⠠⠤⠤⣄⣀⡤⢾⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠋⣡⠃⠀⢀⠠⠀⠀⠀⢀⡜⣿⣿⠣⡀⠀⠀⠀⠄⡀⠀⠈⢌⠙⢭⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠂⠀⠀⠈⠁⡄⠀⢀⡠⠴⠁⠀⢻⡟⠀⠈⠢⢄⡀⠀⠀⡀⠉⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣥⠀⠀⠀⠀⠀⠐⠀⠋⠐⠀⠀⠀⠈⠃⠐⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⣤⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣇⣠⠀⠀⡀⠀⠠⠁⠀⠀⠀⠌⠀⢀⡆⠀⠡⠀⠀⠀⠈⢂⠀⠀⠀⠀⢄⣸⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣇⣠⠂⢀⡔⠀⣠⣀⣴⡟⠀⠀⠘⠃⠀⠀⠹⣦⣀⣄⠀⠢⡀⠑⣤⣈⣏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣾⣶⣞⣶⣪⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣕⣶⣟⣶⣿⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⣹⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣯⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⢷⡶⢤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠈⠀⠉⠒⠌⠀⠀⠉⡓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠘⠀⠀⠀⠀⠀⢀⣠⣶⠿⢛⡷⢾⣆⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃⠀⠀⠀⢀⣀⠤⠒⠻⠁⠈⠀⠀⠀⠜⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣠⣴⠦⠘⠫⠁⠀⠀⡖⠀⠀⠀⠀⠀⣀⣤⡶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢄⣿⠀⠀⠀⣴⣾⣿⡿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣀⡀⢀⣀⣤⣤⣤⣴⣾⡎⠙⢳⣤⣾⣿⣟⡃⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣉⠈⣀⣶⣿⣿⣿⡇⠀⢸⣿⣟⣩⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠒⠟⠺⡇⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⠘⢿⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡇⠀⠀⠀⠁⠀⠓⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣾⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⣠⡿⠉⠁⠻⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⣄⣦⣌⡗⠤⡀⠈⠄⠀⠀⠸⠀⣼⠏⠀⠀⠀⠀⠈⢅⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⣿⠁⠹⣶⣿⠷⢾⠞⠀⠀⣿⣿⡔⠊⠈⡁⠐⠐⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠈⠀⠀⠀⠀⠹⠜⡶⣶⡿⠉⢹⣶⣞⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⢠⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⡀⠀⠰⠀⠀⠀⠀⠀⠀⢰⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⢦⡀⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡇⠀⠀⠀⠀⣦⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢹⡀⠀⠀⢸⣧⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠦⠴⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢈⣡⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⡿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢤⡀⠒⠶⠾⢦⣔⢾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⣤⣤⣤⣈⠻⢶⣶⣦⣶⣶⣤⣄⣤⣤⣴⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⣿⣿⣿⣿⣧⡄⠀⠉⠛⢻⣿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠶⢂⣤⣴⣶⢶⣾⣶⣶⣦⣾⠀⢠⡿⠛⣻⣟⣠⣿⠷⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡌⢿⡿⠟⠀⠃⠀⠈⣠⣾⣩⣹⡿⠑⡆⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⣶⠄⠀⠀⠀⠀⠀⠿⠿⠻⠛⠏⠁⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢦⠀⠸⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⡰⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠬⣠⣶⣧⣄⠃⠀⠀⣸⣶⡀⢸⣄⠀⢀⣠⠎⠀⠊⠁
⠀⠀⠀⠀⠂⠀⢣⡀⣰⡈⠛⢹⣿⣯⠤⢦⣿⣿⣷⣼⣧⣖⣼⡃⠄
⠀⠀⠀⠀⠀⠀⠻⠋⠉⣿⣿⣻⣿⣿⣷⣄⣿⣿⢉⠙⡀⠟⠋
⠀⠀⠀⠀⠀⠀⠺⣟⠁⠈⢻⢛⣾⣿⠋⡙⣛⠋
⠀⠀⠀⠀⠀⠀⠈⠟⠓⠀⢠⠨⠅⠈⠁⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣸⣄⠀⢆⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⢀⡀⠀⣤⣤⡤⣤⣄⣀⣀⣉⡀⢀⣀⡀⣤⣴⣶⣎⣽⠿⣿⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⡤⢴⡖⠀⠀⠁⡶⠂⣘⣿⡟⣫⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣷⣌⣀⣀⡾⠛⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢤⣴⣶⣶⣶⣷⣾⣷⣴⡀⣼⡟⢿⣿⣃⠙⡼⡿⠻⣹⣷⠟⠻⠛⠟⣿⠿⢻⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣥⣠⡀⠀⠀⠀⠀⠀⠠⠄⢀⣴⣾⡟⢾⣿⠛⣿⡍⢻⣻⣟⣿⡋⠀⠉⣻⢇⠀⠀⠰⠁⠀⠀⠀⠐⢀⣿⣶⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡌⠂⠠⠄⠐⠆⢀⣤⣾⣿⣟⠛⡿⢿⣦⣈⣿⣦⡝⢿⠃⢁⡀⢠⣿⣿⡔⣠⣤⡄⣀⣤⢤⢴⣿⣿⣿⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣴⣿⣿⣿⠛⠯⠙⠝⠢⠴⣻⣿⣿⢿⣷⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣿⣟⡽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠉⠉⠻⠀⠀⡴⢦⡲⢤⣼⠿⣿⣿⣿⣿⣿⣷⡿⢿⡯⣿⣛⠛⠻⠿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠛⠛⠛⠛⢩⡿⣿⣛⣷⢿⣧⣬⣿⠻⢶⣴⣷⣤⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⢺⣶⡿⡟⠻⣿⠿⢻⣿⡦⢀⠀⠀⠀⠀⠀⠀⠈⢲⣿⡿⣿⠿⣿⣿⣏⣿⣦⣄⣤⣈⣿⡂⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⣏⣻⠿⢿⠇⣰⣧⡈⠳⢘⡁⠺⣆⠀⠀⢠⠀⠀⠀⠈⠉⣸⢷⣌⢨⣍⠻⣿⣤⣿⣛⠿⣿⠿⣣⣄⣰⣼⡆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠛⠳⣤⠀⣿⢹⣇⣧⣏⢀⡺⠋⠀⠀⠀⠀⠀⠀⠐⡿⠄⠸⣏⠰⣿⣷⡯⠿⢌⡛⢲⣶⣿⣭⡿⠟⣣⣈
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣯⡏⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠘⣄⠿⢆⣿⣿⣿⣷⣿⣴⣿⣫⠿⠛⠷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣯⣿⣿⣿⣿⣿⠟⠛⠛⢻⣿⣿⣶⣤⣀⠀⠉⠁⠀⠄⠐⡲⠾⠉⣳⡾⠁⢉⠻⢿⣿⣿⣿⡍⠀⠀⣠⠯⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠤⣮⣁⡁⠉⠉⠑⠀⠀⠀⠀⠀⠀⠋⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⢸⠏⠛⠛⢶⣶⣶⣶⣶⣦⣶⠆⠤⠶⠶⣦⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠻⠁⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠰⠀⠠⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⡀⠇⢀⠀⠀⠀⠀⠘⠉⠁⢐⣾⣄⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠂⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⡁⠈⣷⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣶⣭⣶⣿⣾⣶⣶⣶⣿⡀⠀⠀⠀⠀⠸⣄⠀⠃⠀⠀⠈⠒⠀⠠⠄⠀⠀⢘⣤⣌⣀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⠟⠛⣏⠙⠛⠃⠀⠀⠸⠿⠄⠈⠠⠀⠗⢀⡀⠰⠄⠀⠀⢀⡰⢻⠉⠉⠛⠙⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡴⠞⠀⠀⠀⢭⣉⡄⠀⢀⡀⡜⠉⢀⣀⣴⠦⠞⠀⡘⠀⣀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⢠⠐⠴⢇⣀⣬⣽⡇⠄⠈⠀⡉⠀⣿⣠⣴⣿⣿⣦⠈⠹⣷⡄⠀⠀⢠⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢤⡀⣤⣄⢀⡀⢶⡁⠈⡀⢀⡈⣫⠙⢡⢂⡠⠒⢸⡇⠀⣿⣿⣿⣿⣿⣿⡄⠀⢹⣷⡀⠀⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢤⣤⣱⣿⠸⠏⠀⢀⣁⣦⡟⣧⠀⣷⣄⣿⠞⠁⢠⠶⠀⡞⠿⢿⣿⣟⣿⣿⡇⠀⣼⡿⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠷⠆⠛⠍⣈⣳⣶⣈⣽⢟⣤⡖⠋⠀⢠⣴⣤⠘⣏⣹⡿⣿⣿⣥⠾⢋⡄⠀⣠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠛⠙⠛⠁⠀⠀⡜⠿⣿⠿⠿⠻⠿⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠻⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⡾⠃⠀⠀⠀⣰⡟⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠘⣷⡀⠀⠀⠀⠻⣦⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣿⠁⠠⣿⣉⣻⡇⠀⠀⣿⣋⣹⡧⠀⢹⡇⠀⠀⠀⠀⠈⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣦⠀⠀⣿⡄⠀⠙⠻⠛⠁⠀⠀⠙⠻⠛⠁⠀⣼⡇⠀⢀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠸⣷⡀⠀⠀⣤⡀⠀⠀⣠⡄⠀⠀⣰⡿⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠈⠛⠛⠛⠋⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⣿⠓⠀⠉⠛⠿⠶⠶⠶⠾⠟⠋⠀⠐⢻⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠿⠀⠀⠀⣤⣀⠀⠀⠀⢀⣤⡄⠀⠀⠸⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣤⣤⣤⣤⣤⣬⣽⣷⣦⣶⣿⣭⣤⣤⣤⣤⣤⣄⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⣦⣼⠿⣧⣤⡿⢿⣤⣼⠿⣧⣤⡿⢿⣤⣾⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⡿⠷⠶⠾⠿⠶⠶⠿⠷⠶⠾⠿⠶⠶⠿⣿⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⡾⢻⣷⠟⠻⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⣠⡾⠟⠁⠀⢘⣿⣀⠀⠀⠙⠿⣦⡀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣿⠿⠋⠀⠀⣀⣴⠟⠋⠛⢷⣄⡀⠀⠈⠻⢿⣇⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⠛⠁⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠙⠻⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣶⣶⣶⠆





⣿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣟⣿⣟⣛⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠚⠛⠛⠋⠙⠛⠛⠶⠒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠈⠱⡄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠒⠉⠀⠀⠀⠀⡴⠋⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⡤⠔⠒⠒⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⢤⡀⠘⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠹⡀⠘⣧
⠀⠀⣰⠃⣠⠖⠉⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢰⠁⠀⠸⣆
⠀⢠⡏⢰⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢄⠤⠖⠁⠀⠀⠀⢹⡀
⠀⣼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⢠⡇⠀⠈⢦⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠃⠀⠀⠀⠉⠒⠂⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞
⠘⣧⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⢳⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠈⠳⣤⣀⡀⠀⠀⣀⣈⣳⣤⡤⠤⠴⠶⠚⠛⠛⠛⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠛⠓⠒⠒⠶⠦⠶⢮⣤⣀⣠⣴⡋⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠉⠛⠻⠿⠭⢤⣤⣤⣤⡤⠤⠤⠤⠤⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠤⢤⣤⣤⡤⣤⣤⣤⣤⢤⠭⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⠿⠶⠤⣤⣤⣄⣀⣤⣤⠤⠞⠛⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⣀⣤⡤⠤⠶⣶⠦⠤⢤⣤⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⠾⢋⢉⠀⠀⣷⠀⠀⢸⣂⢠⠀⡈⢍⢻⡆⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠒⢦⡀⢧⠀⢿⣡⠃⠎⡼⢰⢻⠀⠀⢸⡄⡆⢣⣘⣬⠗⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠙⣎⠳⢦⣉⣛⠒⠓⠚⣾⠀⠀⢸⣟⣛⣩⡥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠉⠉⠉⠉⡿⠀⠀⢸⡏⠀⣠⡴⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⣴⠶⢶⡖⠒⢺⡶⠶⣤⣤⣀⠙⣆⠀⠀⢰⡇⠀⠀⣸⣠⠞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⡍⣄⡤⣼⡇⠀⢸⡇⢀⣤⢬⣿⠆⣿⠀⠀⣾⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⣻⣶⣶⡇⠀⢸⡷⠞⣿⣫⣵⠞⠁⠂⣸⠃⠀⠀⣸⢁⣀⣤⣤⡤⠤⢀⣀⣀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⢤⡀⠀⠉⠙⡇⠀⠘⡏⠉⠉⠁⠀⠀⠀⢰⠏⠀⠀⢠⡟⠿⣤⣟⣀⡇⠀⢸⡇⢈⣉⣳⠆⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠦⣄⠀⢿⠀⠀⢻⡀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡾⠙⠲⠤⢤⣩⠇⠀⢸⣏⣉⣩⡥⠴⠊
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣀⣀⣀⠀⠈⢧⠸⡇⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢿⠀⣶⣚⣻⣿⠀⢸⣟⣿⣿⠆⣸⠂⢻⡀⠀⠙⣦⠀⠀⣸⠃⠠⠀⢰⡏⠀⠀⠀⠀⣰⠃⠀⢐⣿⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠶⡭⣭⣿⠀⢸⡭⠴⠶⠛⠁⠀⠈⢧⠀⠀⢹⣆⢠⡏⠀⠀⠀⣼⠀⠀⠀⠀⣰⢏⡠⠞⠋⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⢷⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣾⠃⠀⠀⠀⡟⠀⠀⠀⡴⠃⡾⢁⣠⢤⣤⣄⣀⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢧⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠹⡄⠀⠈⢸⡇⠀⣠⠞⠁⠀⠙⣮⣓⠲⡿⠀⣸⣩⣷⠆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠳⣄⠀⠀⠀⠀⠀⢻⡀⠀⠀⢹⡀⠀⢸⣇⡼⠃⠀⠀⢀⡼⠁⠈⣽⠃⢠⠟⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠘⢧⡀⠀⠀⠀⠈⣧⠀⠀⠀⢳⠀⢸⡏⠀⠀⠀⣰⠏⠀⢀⡜⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣦⠀⠀⠀⢸⡆⠀⠀⠈⡇⠀⡇⠀⢀⡼⠁⢀⡴⠋⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⢳⡀⠀⠀⣇⠀⠀⠀⢻⠀⢹⣀⡞⠀⣠⠟⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⢸⠀⠀⢿⠀⣼⠃⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡀⡟⠀⠀⠀⣸⠀⠀⣸⣼⠇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⡾⠁⠳⣄⣀⣴⠷⠤⠴⠋⠸⣦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉

⠀⠀⣦⣤⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⣤⣴
⠀⠀⠸⣿⣶⣩⡟⠋⠻⢾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⠽⠛⠚⣯⣹⣽⡏
⠀⠀⠀⢫⡽⣤⢟⠋⢀⣙⡿⠄⣹⣫⣵⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣿⡁⢾⣏⣉⣉⢻⢧⡼⣿⠃
⠀⠀⠀⠈⢯⣏⣹⣟⠁⠉⡻⢶⣉⣁⣞⣷⣭⣳⣤⡀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⣠⣶⣫⣴⣿⣟⣉⣵⢻⡋⠉⢹⡿⢉⣿⠏
⠀⠀⠀⠀⠈⢻⣿⣽⡟⠻⣽⡏⠁⠈⠑⠀⠀⠈⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠈⠁⠀⢉⡿⡤⠛⣟⣶⣼⠋
⠀⠀⠀⠀⠀⠀⠹⣯⣧⢾⣽⣦⣦⡀⠀⠴⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⡄⠀⣠⣛⣿⣷⢴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣟⣽⡏⢿⡏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣧⠽⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⡾⣧⣄⠀⠤⠤⠴⠖⠛⠓⠀⠀⠀⠀⠈⠳⡄⢠⣤⠀⡴⠋⠀⠀⡀⠀⠐⠛⠒⠶⠤⠄⠄⢀⣴⠟⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⢤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⠀⢀⣴⣶⣶⣶⣶⣦⣤⣀⣤⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠅⠀⠉⠉⠉⠉⠓⠈⠀⠀⠂⠀⢀⠿⣿⣿⡿⣇⠁⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠈⢭⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡤⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⠔⠉⠀⢹⣿⠑⡈⠓⢤⡀⠀⠀⠀⠀⠆⠀⠀⠠⠤⣼⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣾⠁⠀⠀⠀⣠⠄⠀⣀⡤⠖⠋⠀⠀⡔⠀⢿⣿⠀⠐⡀⠀⠈⠳⣦⣄⣀⡀⣄⡀⠀⠀⠈⢻⣾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⠿⣶⠦⠀⠈⣉⠔⠉⠁⠀⠀⠀⠀⠈⢁⡄⢸⣿⠘⣆⠉⠀⠀⠀⢀⡀⠉⠀⢍⡉⠓⠶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣄⣠⡞⠁⠀⠀⠀⠀⠀⢠⠂⢰⡞⠀⠘⠟⠀⠘⣧⠀⢢⠀⠀⠠⠀⠀⠀⠹⣦⣀⣾⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⣛⣿⣦⣀⣀⣴⠃⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⡀⠀⢳⣄⣀⣠⣿⣋⡻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣿⣭⣿⣻⣶⢾⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣿⢶⣟⣹⣯⣿⣽⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆⠢⢸
⠀⠀⠀⠀⠀⠀⠀⡰⠉⢀⠐⠁⠀⠀⢠⠀⠉⠒⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢁⠀⠀⠀⢐⣀⡤⠰⢤⠱⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠒⠢⢄⡀
⠀⠀⠀⠀⠀⢀⠇⠀⠀⣈⡤⠴⠖⡛⢩⣴⣅⡴⡿⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄⠁⠀⢠⠀⠊⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠸⠀⣠⠊⣁⡠⠖⠈⠀⠀⠍⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡤⠴⡲⠊⢩⡶⠃
⠀⠀⠀⠀⠀⠀⠑⠛⠂⠐⠒⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⢀⡠⠔⡚⢋⠅⠀⠾⣷⠖⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⣤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣏⢒⢒⣊⣥⡀⠀⠈
⠀⠀⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⡃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡔⠤⠚⠙⠀⠀⠀⠀⠀⢀⡠⠒⠉⠠
⠈⠀⠀⠈⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⠀⠀⠀⠀⣀⠄⠒⠈⠀⠀⠈⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡤⠄⣀⣀
⠓⠦⠤⢤⡀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡔⠋⠀⠀⠐⠀⠀⠀⠀⠠⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⢳⢤⣈⣤
⠀⠑⠴⡤⠈⠲⣄⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢴⣋⠑⡲⠦⣄⡀⠀⠁⠀⠀⠠⠽⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠙⠋
⠠⡙⠓⠒⠖⠒⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢝⠶⣾⠷⠀⠍⠙⡒⠦⢄⡀⢀⣃
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣌⣒⣒⣒⣹⠄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢤⡀
⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠤⢤⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡠⠂⠉⡈⠈⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠐⠒⠀⠠⣄⡀
⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⠀⠐⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠀⠁⠀⠀⠀⠄⡈⠐⠤⡀
⠀⠀⠀⡼⠡⠀⠀⠀⠁⠀⣀⡤⡤⡖⢒⣶⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡀⠀⠀⠀⠀⠉⢐⣁⢤⠠⢤⡰
⠀⠀⢠⢃⠀⣠⡴⠖⠒⡉⠁⠰⣮⡶⢞⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣤⠴⠖⠚⢩⣶⣧⡴⡾⠊
⠀⠀⠸⡀⣞⠓⠀⢚⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⡅⢠⠒⠁⠤⠲⠊⠀⠀⠙⠉
⠀⠀⠀⠈⠃⠉⠉⠉⠉⠑⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠐⠚⠒⠒⠒⠛⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⢄⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡁⠀⠀⢃⠠⠀⢀⠀⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠠⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣄⠘⡔⠲⠤⣀⡀⠀⠄⠈⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠝⣻⠿⠃⠀⠢⣉⠙⠳⢦⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣍⠍⠁⢿⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⢠⣤⣤⣤⣀⡀
⠀⣮⣾⣾⣿⣴⣦⡉⠛⢶⡤⠀⡀
⠀⠻⣷⣿⣾⣿⣿⣟⣷⣶⣾⣿⣷⣦⣄⢀
⠀⠀⢸⣯⣇⣻⣿⣟⢛⠛⣯⣽⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢹⣿⡻⡟⢿⣍⣉⣹⡏⠀⠀⣠⣿⣿⣟⣷⡀⢄⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠈⢻⣿⠟⢻⣷⠤⠬⢿⡀⠰⣿⣿⠛⠉⠛⣝⢦⡁
⠀⠀⠀⠀⠘⢿⣿⢿⣿⣦⠴⠐⠚⠳⢬⡁⠀⣤⣿⣿⣷⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⡿⠶⠾⢿⡷⠒⠒⠒⠒⢿⣷⣮⣙⠻⡟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠐⢦⢿⡿⠿⢻⠦⠀⠀⠠⠶⣿⣿⣿⡟⠲⢄⡈⢻⣿⡄⠀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢙⣿⠻⢻⣴⠂⠀⠒⠒⠚⠻⠿⠷⢤⣀⣹⣿⣿⣷⣤⣞⣻⣿⡿⠃⠀⠀⠀⣀⣀⣤⣴⣦⣦⣤⣆⣴⣶⣒⡲⠶⠤⣤⣤⣀
⠀⠀⠀⠀⠀⣠⣼⠿⣿⠋⣉⣩⡷⠒⠚⠉⠉⠉⠙⠃⠐⠢⢭⣝⣻⣿⣿⣿⣿⣿⣧⡶⠾⠟⠛⠛⠛⠛⢛⣻⣶⡾⠒⢶⣷⣭⡍⣙⡛⠶⢦⣌⣹⣶⣤⣀
⠀⠀⠀⠀⠀⣼⣹⣷⢿⡋⠁⣞⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢙⣿⣿⣛⣿⣟⠿⢿⣿⡟⠿⠻⠶⠀⢤⣰⣿⠿⠃⢀⡽⣷⠇⠀⠈⢿⡗⠲⢶⣿⣿⣞⣛⢷⡆⡀
⠀⠀⠀⠀⢀⣼⣿⣤⣿⡟⢁⡼⠶⣤⣤⣤⣤⣶⠛⠁⠀⢀⡴⢪⣟⠦⣽⣿⡿⠋⠐⠈⡙⠢⣄⣀⣰⣾⣿⣿⣿⣲⢬⣿⣇⣀⣠⡤⡞⠑⢦⣴⣿⣽⣿⡟⣯⣅⣿
⠀⠀⠀⠀⠀⣿⣿⣱⣼⣿⡏⢀⣴⠁⠉⣡⠝⠁⠀⢀⣴⠟⣰⣿⣮⣿⡟⡀⠀⢰⡀⠀⠈⠲⣄⠙⠿⣿⡽⢏⡀⠁⠀⠉⠀⡈⠹⣦⣉⣷⣿⡛⢣⣭⢻⣧⡾⠟⠛
⠀⠀⠀⠀⠰⣿⣛⣫⣼⣿⣿⣿⣿⣤⣤⣧⣄⠀⣠⣾⠋⣰⣿⣿⣿⠏⣰⠇⠀⢰⣧⠀⠀⠀⠘⣿⠢⣬⣿⣶⣽⣆⣀⣶⣴⣼⣿⡟⣻⣞⣽⡷⡮⠟⠉⠉
⠀⠀⠀⠀⠀⣼⣿⡟⢫⣙⣿⡿⣻⣿⣿⣛⣿⡖⣷⠃⢰⣿⣿⠟⢁⡼⠋⠀⠀⢸⠟⣧⡀⠀⢀⡿⣦⣘⣷⣿⡿⣿⣿⣯⣽⣷⣾⣿⠟⠛⠋
⠀⠀⠀⠀⣸⢋⡔⠂⠀⣟⠿⠛⢿⡟⠘⠛⡟⣭⠏⠀⠘⠋⠁⡀⣺⠶⣶⣄⠀⣾⠀⢸⠉⠛⠈⣇⣸⡿⣶⣿⠇⠀⠉⠀⠉⠁⠀⠈
⠀⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⣠⠌⢿⡿⣸⣿⣀⡏⠀⣾⡀⣰⣶⡟⠻⣦⣿⣇
⠀⠀⠸⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⣠⣴⣿⣿⣿⣷⣴⣿⣿⣿⡋⢻⣤⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢙⣿⢿⣿⢣⣿⣀⣿⣷⣾⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡿⢷⣤⣿⣿⣿⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠳⣿⣿⡿⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⠔⠊⢹⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⢀⣀⢀⡜⠁⡰⠃⠀⠀⢸⠀⣠⠀⡰⠊⠉⠲⣄
⣴⡖⠤⠋⠈⠋⠀⠰⡁⠀⠀⠀⣸⡤⠄⠠⢇⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠓⠊⠉⡆⢀⡠⠤⣈⢧⠀⢼⡡⠤⠄⠒⢶⣸⢶⡖⣒⡇⠀⣀⣀⠤⠤⠤⠔⠲⠤⢄⡀⠀⠀⠀⠀⢾⡵⠒⣷⣄⣤⣄⣀⡀
⠀⠀⠀⠀⠉⠁⠀⣀⣈⣯⣷⠀⠉⠓⠒⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠸⡅
⠀⠀⠀⠀⠀⢀⣸⡁⠠⠶⠮⠁⠀⠀⢀⡀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡔⠛⢤⠀⠀⡟⠲⡁
⠀⠀⠀⠀⠀⠈⢧⢈⣲⠶⠒⢢⠀⠈⠙⡧⣄⠀⠀⠀⠀⠉⠂⠄⢀⡀⠀⠄⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢱⠸⠊⠀⠀⠈⡯⣉⣱
⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⢀⡜⢣⠀⠀⠹⡜⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⠤⢤⣤⣀⠠⠄⣶⠤⠒⠁⣀⠷⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠑⢤⣣⣀⡀⠈⠃⠀⠙⠂⠀⠀⣀⣀⣀⣀⡤⢄⣈⢻⠉⠓⠤⢀⠀⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡝⠀⠙⠢⠤⣄⣈⣉⠉⠉⠉⠁⠀⠀⡆⠀⠀⠉⠳⠝⠂⠀⠃⠉⠛⣢⣄⡀⠀⢀⣀⢠⣤⠤⠒⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠂⠃⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⠀⠤⠋⠁⠀⡠⠊⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⠌⡒⢄⠄⠀⢀⡞⠁⠀⣀⠄⣠⣞⠾⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡛⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⠞⠛⠂⠤⢾⣴⠊⢉⣼⡶⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢦⣕⡢⢄⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠑⠻⣁⠀⣀⡠⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠉⠓⠮⣕⣢⢄⣠⢎⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⠀⠀⢀⣀⠜⣹⠙⠓⠦⠭⣕⣢⣤⣄⣀⣀⣠⡯⠛⠉⡷⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠤⠖⣊⠭⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⢹⠀⠀⠀⡰⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠦⠒⣹⠁⠀⠀⣘⠤⠢⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠻⠔⣒⡺⠅⢴⣉⠦⢶⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣋⣽⣿⣧⠴⣶⣤⣀
⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⣰⣿⣆⣀⣠⣤⣁⣤⣠⣶⣄⣀⣄⣉⣈⠁⢀⣀⠐⠂⠈⠛⣦⣄
⠀⠀⠀⠀⣰⣏⡴⡛⠛⠉⠀⠈⠪⣻⠁⠙⡭⡹⢹⣹⢹⡙⡏⣉⢋⢋⠟⡯⢴⣦⣀⡉⡤⠈⢣⡀
⠀⠀⠀⠀⡟⠁⠀⠀⠄⢀⠂⠄⡐⠈⢶⣄⠌⣱⡾⣏⣧⣕⣼⣏⣡⣪⢊⡴⠓⠉⡹⠶⣗⣄⠀⢱⡀
⠀⠀⠀⠀⢷⡀⡀⠀⠀⠠⠬⣒⣬⣑⣦⣜⡷⠿⠷⢿⣿⣿⣿⣿⣥⣿⣥⢤⣴⣮⣴⣵⣮⠿⣌⣋⠡
⠀⠀⠀⠀⠀⠻⣤⠒⣒⠺⠷⢶⣬⣽⣻⣿⡇⠀⠀⢰⡟⢿⣿⣶⣦⣤⣄⣀⡤⠍⠉⢉⡬⠟⢻⣥⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢬⣥⠶⢒⣛⣻⣿⠀⠀⠀⢸⠀⢸⣧⣙⠡⡉⠙⡻⠽⢍⠛⡻⠶⠄⣼⡛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⠀⠀⠀⠀⡆⢻⣿⣿⡀⠀⠀⠈⠂⡀⣑⣌⣢⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡇⣼⠻⢽⣧⠴⠖⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠠⣶⣾⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⣠⠂⣤⡀⡻⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⣵⣿⣾⣿⣿⣷⣮⣬⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣀⡀⣤⣀⣼⠟⠋⠁⠸⠸⡟⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⣗⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⡏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⣀⣻⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⢶⣶⢶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠽⠟⠛⠛⠃⠀⠀⠒⠀⠀⠘⠛⠛⠿⢿⡷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⡯⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠿⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣄
⠀⠀⠀⠀⠀⠀⣴⣿⡯⠀⠀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠁⠀⠀⢿⣿
⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣴⣿⣿⣿⠉⣛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠙⡄⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡄⠄⠀⢸⣿⡋⢏⠸⠊⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢹⡏⡿⢿⣿⡆⠇⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣧⠘⠄⢸⣟⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⠧⣨⡑⠃⡈⣿⡇⠀⡀⠰⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠂⠛⠀⠀⠀⠀⠈⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠐⠁⠀⠀⠀⠿⠁⠠⠁⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣬⣙⣒⣒⣛⣀⣾⡏⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⢀⡀⠤⠀⠀⠀⣠⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⠓⢠⠁⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⡿⠳⢬⣽⣷⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠅⣸⠀⠀⠀⠀⠇⠀⠀⡄⢸⠀⢀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⠀⢸⠃⠀⡀⠀⠀⡆⠀⢸⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⢀⠀⠀⢠⠇⠀⡸⠀⢸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣇⡀⠀⠈⠀⠀⠸⠀⠀⡇⠀⠸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠓⠒⠒⠷⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢰⠂⣘⣀⣏⣠⠏⠤⠅⠤⠁⢠⣁⣰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⡸⢉⣯⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠂⣀
⠀⠀⠀⠀⠀⠀⢠⠄⣋⡼⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⡠⠚⣸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢰⣡⠏⠁⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⢠⡞⠁⠀⠀⠀⣀⠴⣞⠋⣿⠁⣧⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⢰⠉⡇⡲⢠⢄⠀⠀⠀⠘
⠀⠀⢸⠀⠀⠀⠀⡴⠻⣄⣹⣤⣿⣶⣿⠀⠀⡇⠀⠀⡄⠀⠀⢸⠀⠀⠀⠁⠘⣤⣧⣧⣮⡜⣱⠄
⠀⠀⢸⠀⠀⠀⢰⡙⢢⣾⣿⣿⣿⣿⣿⡀⠀⠀⢠⠀⡇⠀⡄⢸⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠆⠀⠀⠸⣍⣿⣿⠟⠁⠀⠈⠙⡇⠀⢸⠸⠀⠇⠀⡇⢸⠀⡇⠀⠇⠀⡟⠉⠀⠈⠙⣿⠇⢀⠂
⠀⠀⠀⠈⠢⡀⠀⠙⠻⠏⠀⠀⠀⠀⢠⡇⠀⠸⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢀⠀⠓⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠇⠀⠘⠀⠀⠀⠘⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡘⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠃⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠤⢄⣀⡀⣀⣀⡀⡀⣀⢠⠤⠴⡒⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠰⠠⠌⠤⠠⠤⠆⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠉⠀⠐⢁⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⠿⠿⠿⢿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠐⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣍⣁⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣔
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠋⠀⠁⠀⠂⠀⠀⠁⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⠟⠁⠀⣜⠐⢶⣶⡄⠀⠀⠰⠿⠛⠀⠇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⡀⠀⠰⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠄⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈⣷⣉⠛⣛⣿⣿⠿⠱⠿⣿⣍⣉⣤⣴⣶⣶⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠠⠄⢻⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⠏⢻⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠈⢿⠿⠷⠀⠀⠀⠀⠐⠛⠛⠿⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⢡⡀⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡩⠥⠎⠄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⠤⣌⠍⠲⣄⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⣝⣁⡼⢸⠀⢹⠀⠄⣢⢹⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠷⢄⠀⠐⠁⠀⠀⠆⢉⠁⡘⡇⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⣖⡒⢦⠢⠁⠀⠀⠀⠀⠐⡀⠒⠁⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠈⠫⠥⠞⡠⠁⠀⠀⠀⢄⠀⠀⠀⢚⠃⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠦⣄⠀⠀⢸⡧⣿⢀⠀⢄⢈⠀⠀⠀⠀⠀⠀⣑⣤⣷⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣛⣤⣼⣧⡀⠈⣷⢻⠘⡡⠜⠘⠀⠀⣀⠬⣴⣿⠟⠛⠛⠁⠀⠀⢀⣴⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡘⢿⠻⡻⣆⣷⡀⠘⢿⣧⣀⣠⠴⠒⠉⠀⠾⠛⠁⠀⠀⠀⠀⠀⢠⣿⡜⣅⠔⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⣋⣉⣾⣷⣽⡟⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠟⣳⡤⠚⣫⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣻⡄⢿⣟⠿⣧⠈⣇⣘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⡟⣩⢷⡂⢁⠷⣻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣽⠓⢢⣿⣗⠘⢧⣹⣿⣷⢹⠀⠹⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣓⢿⣿⡡⠞⣯⡠⠞⣹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⣿⡿⠯⠁⠀⠻⣿⠟⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⢴⠀⠀⠀⠸⠻⠳⠤⣧⣛⡤⠂⢉⣧⠔⠁⠾⡇
⠀⠀⠀⣀⣤⣤⣶⣤⣬⣝⣿⣇⠀⠀⠀⠈⠙⠆⢻⡇⢠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡷⠋⡷⣳⣯⡴⠚⠉⣹⡖⠁⠘⠓⢲⡀
⠀⢀⣞⣻⡟⢽⣿⡄⢟⣆⣹⣟⣿⢾⣵⢶⡄⢸⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡠⢠⠿⣿⡾⠛⠉⣉⠴⣮⡤⠀⠉⢙⣦
⠀⢸⡭⣝⠰⠶⠦⠼⣏⡁⠐⠬⠝⣺⣿⣓⣽⣶⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠇⢃⠂⠀⢠⣿⢾⠋⢁⡈⠩⢷⡶⠒⠚⠛⣦
⠀⠘⢗⣻⣇⡚⢃⣬⣉⡝⣻⣿⣯⣽⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣄⣠⠀⠀⠹⢾⣝⣇⣀⠀⢘⣷⣂⠀⠈⠙⢂⣤⣄⣀⡀
⠀⠀⠈⠓⠾⠧⠾⠷⠚⠋⠉⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⠶⠦⠤⣟⣼⣧⡤⠤⣼⣇⡀⢾⣙⣯⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⠉⠓⠶⣾⣁⢾⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⡀⠀⠈⠛⠒⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠙⢆⠀⠀⠀⣀⣠⣄⣀
⠀⠀⢀⣞⣿⣿⣿⣿⣿⣍⠻⣿⡄⠀⠀⡇⠀⠀⠀⠀⠈⢳⠀⠀⡼⠁⠀⣤⣶⣷⡄⠀⠀⢠⡃⠀⠀⠀⠀⡀⣴⣿⠀⣰⠋⠁⠀⣀⣈⢣
⠀⠀⢸⢹⣿⣿⠟⠉⠉⠙⠛⢿⡟⠀⠀⡼⠁⠀⡀⠀⢀⣼⠇⢰⡇⠀⠀⠀⠉⠻⠧⣄⡀⠈⢧⣀⢀⣂⠤⠐⣿⠃⠀⡇⠀⠀⢊⠥⠆⡼
⠀⠀⠸⣮⣿⣿⣿⣶⣶⠿⣶⣻⠇⢀⠜⠀⣤⣶⠟⠦⠤⠋⠀⠘⡿⡄⢰⣦⣄⡀⠀⠀⠙⠢⡄⠙⢻⠁⠀⠀⢿⠀⠀⠻⣦⣴⣿⡀⠀⠀⡀
⠀⠀⠀⠈⠙⠳⠶⠤⠴⠞⠋⠁⠰⣕⠢⣾⡟⠁⢀⣀⣀⠀⠀⠀⠘⢮⣬⣻⡼⠞⠓⢤⣀⠀⠹⣦⠀⢳⠀⠀⠘⢧⠀⠀⠀⠀⠘⢿⣄⠀⠑⡀
⠀⠀⠀⠀⠀⢀⣠⡤⠤⢤⣀⠀⠀⠈⠉⠉⢠⢎⠀⠈⠉⠉⢢⡀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠑⣀⡤⠞⠀⠀⢀⠀⠀⠀⢻⣤⣤⡗
⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢘⣼⣧⣄⠀⢀⠀⠱⡄⠀⠀⠀⣠⠖⣉⣍⡑⠢⢄⣀⠀⠀⠀⠈⠀⠀⠀⠂⢉⡠⠤⠠⢈⠉⠁
⠀⠀⠀⢸⣶⡶⣖⣂⣠⣴⢶⡟⠀⠀⠀⠀⡴⠃⠀⢹⣦⡀⠂⣀⣿⠀⢠⢞⣵⣿⣿⣿⣯⣿⣷⣶⠙⡀⠀⠀⠀⠁⠀⢘⢵⡴⠂⠀⠀⠁⡀
⠀⠀⠀⠈⠻⠭⢿⡇⠈⠉⣇⠀⠀⠀⠀⡼⠁⠀⣰⠿⣿⢃⣼⣿⠏⠀⡇⢿⣿⣿⣿⠉⠀⠈⣿⣿⣼⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⢷⡀⡀⠘⢆⠀⠀⢰⣃⣀⣸⡇⠀⠈⠙⠋⠁⠀⠀⠘⣎⠿⡿⣿⣷⣶⡾⢟⣿⠏⠀⠀⢀⡠⠖⠁⠀⢀⣠⡜⠿⢁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡶⣲⠗⠀⠘⠧⣬⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⣀⣴⠶⠞⠋⠀⠀⠐⢏⠀⠀⣠⠖⠋⠀⠙⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⣀⣤⡤⠤⢤⠤⠤⣤⣀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⢴⢋⢁⠀⠈⡇⠀⢸⡂⠀⠠⠨⡹⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢦⠳⡈⠣⣇⣆⡄⣀⡇⠀⠸⣇⣄⡦⠷⣛⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠳⣌⠓⠲⠤⠬⢭⡇⠀⢨⡗⠒⢚⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣠⡤⢤⡤⠤⣤⣤⣀⡀⠑⣄⠀⠀⢸⠁⠀⢸⢁⡴⠋⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠰⣯⠀⡀⢸⡇⠀⡇⠀⠀⢙⡆⢸⠀⠀⡏⠀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⢭⣓⣻⡅⠀⣗⣚⣚⡭⠔⠁⠀⡼⠀⠀⢰⣃⡤⠤⢤⠤⢠⡤⣀⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠓⠦⣀⠀⠘⡇⠀⢹⠀⠀⠀⠀⠀⣰⠃⠀⠀⣮⡙⠲⠦⢼⠀⢀⣧⣤⠬⠗⣠⠇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⡄⢳⠀⠘⡇⠀⠀⠀⢠⠇⠀⠀⡼⠁⠈⠉⠛⡏⠀⢸⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⣞⢀⡤⠖⢲⠂⠲⠒⣲⡄⣸⠘⡆⠀⠹⡄⠀⠀⡞⠀⠀⢰⠃⠀⠀⠀⣰⠃⠀⣼⣀⣀
⠀⠀⠀⠀⠀⠘⠲⠭⠭⣿⠀⢻⠭⠥⠒⠁⠀⠹⡄⠀⠹⡄⢸⠁⠀⠀⡞⠀⠀⠀⣰⢃⡤⠚⠉⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡆⠀⠀⠀⠀⠀⢳⡀⠀⠹⡏⠀⠀⢠⡇⠀⠀⡴⠃⡏⣠⠤⢤⠤⣄⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⣆⠀⠀⠀⠀⠀⢧⠀⠀⢱⡀⠀⢸⠀⣠⠞⠀⠀⢸⠮⢭⡟⠀⣶⣾⣓⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳⣄⠀⠀⠀⠘⡆⠀⠀⢣⠀⢸⡞⠁⠀⢀⡴⠁⢀⡜⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢦⡀⠀⠀⢹⠀⠀⠈⣇⠸⡄⠀⢠⠞⠀⡰⠋⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠹⣄⠀⠘⡇⠀⠀⢸⠀⢧⣰⠋⣠⠞⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣆⠀⡇⠀⠀⢸⠀⠘⡇⣰⠃⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢸⠄⡇⠀⠀⡼⠀⢀⠟⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠋⠀⠙⠲⠚⠉⠉⠉⠀⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁⠀⠀⠀⠀⠀⠈⡻⢿⠛⠀⠀⢿⣿⣿⣿⡷⠀⠐⢏⣉⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠄⡅⠀⠀⠀⠀⠀⢫⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠣⡤⠃⢹⠡⡔⠊⢂⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⡔⠀⠀⠀⢀⢎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⣸⣀⢼⠏⠈⠀⠀⡠⠊⢒⡦⠀⠀⠀⠉⠀⠀⠀⠐⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠀⠀⠀⠀⠀⠓⠚⡋⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣢⠀⠀⠀⠀⠀⠀⠰⠓⣠⡐⠒⢠⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡌⠆⢐⠝⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡘⠂⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠓⢒⠚⣄⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⢃⣴⣶⡄⠀⠀⠀⠀⡦⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠈⠙⠋⠀⠀⠀⠀⢰⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡂⠀⠀⠀⠀⠉⠀⢌⡆⠀⠀⠂⠀⠀⠀⠀⠀⢸⡀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠀⣀⣠⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⢾⢙⡈⠋
⠀⠀⠀⠀⠀⠀⠠⣠⠎⣀⠀⠀⡈⢆⡀⠀⠀⠀⠀⠀⠀⣀⠙⣆⣒⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡶⠁⠀⠀⠑⡾⢁⣄⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠒⠒⠋⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⡀⠀⢹⠩⡯⡯⢹⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⢚⣼⣯⡧⣄⠀⠀⠀⠀⢀⣿⡿⠿⢸⠿⠿⣦⠙⠶⠚⠳⠾⠃⠀⠛⣠⠾⢟
⠀⠀⠚⠟⠂⠸⢍⠻⡟⣛⠇⠀⠀⠀⠀⢸⡅⢉⣻⠏⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣸⢀⠀⣀⢣⢠⡄
⠀⠀⠀⠀⠀⠰⣶⢿⣯⡁⠶⠆⠀⠀⠀⠘⢷⣬⣙⣊⣡⣶⠏⠀⠀⠀⠀⠀⠀⠀⠘⠺⠦⠷⠊⠈⠁
⠀⠀⠀⠠⣶⣶⡌⠙⡿⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⡤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⣒⡮⠭⠭⠛⡒⢚⡉⠉⣉⠈⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣤⠀⠀⠀⢸⡸⡅⢲⣖⡶⠾⠿⠹⠿⠏⠉⠉⠀⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣄⠀⣵⡂⠀⠀⡇⡇⠈⡁⣄⣠⣰⡔⠖⠀⠀⠀⠀⡘⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠄⠰⠀⠐⠀⡚⠀⠀⢱⢡⢀⡉⢁⣁⣠⠀⢰⡶⠶⠾⠈⢁⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⣐⣀⡀⠓⠁⠀⠀⠘⡘⡜⠑⣉⣈⠥⠤⠤⣒⣒⣛⣉⠭⠥⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢧⡨⠥⠤⠖⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴

⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄
⠀⠀⠀⣸⠋⣀⣉⣐⡒⠨⢕⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⣂⣈⣀⡈⢳
⠀⠀⠀⢸⡍⡡⠤⠤⠭⣍⣒⡟⠚⠓⢄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⣠⠔⠛⠺⣖⣫⡭⠥⠤⢄⡉⣿
⠀⠀⠀⠀⢷⡀⠂⠒⠒⢒⣲⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⢗⣒⠒⠒⠂⠀⣼⠃
⠀⠀⠀⠀⠈⢷⡈⣉⣉⠀⠈⠩⣍⣳⣦⣀⡀⠑⣄⠀⡀⢀⠞⠁⣀⣤⣖⣉⡭⠉⠀⢈⣉⡁⣰⠃
⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠄⠠⠤⠤⠤⠤⣭⠷⢮⡶⢺⣧⠶⢯⡥⠤⠤⠤⠀⠒⢤⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⠛⠉⢙⣛⣛⣉⡩⢽⣷⣼⡿⢭⣉⢛⣛⣋⠉⠛⠛⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⠒⣉⠡⢤⠞⠉⠀⣠⠃⡿⢸⡏⢦⠀⠉⠑⢤⠤⢉⡑⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠁⡀⠔⣧⣀⣤⠞⠙⢰⠃⠆⢧⢠⠙⣦⣀⣨⡇⠄⡈⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠋⡠⠊⢀⠃⠘⠀⢠⡞⠐⠆⠸⡜⠀⠸⠀⢇⠈⠢⡈⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠁⢀⠂⠀⠀⠀⣸⠁⠀⠀⠀⢳⡀⢀⠀⠈⢆⠀⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠾⣤⣤⡼⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⢿⢿⠻⠏⠿⠿⢿⢿⣷⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⠛⣉⣡⣌⣤⣤⣤⣴⣶⣶⣄⣄⠁⠛⠙⠿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢋⣈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣬⣍⡻⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣟⠋⣟⠈⣋⠡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⢟⡀⣽⡧⠈⠘⠁⠴⢧⣬⣿⡿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣛⣽⣧⣶⣙⣿⣿⡆⢰⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠏⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣂⣉⣙⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠀⠁⢸⡟⠻⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿⠿⣿⣿⣿⠿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣤⣶⣶⣤⣄⣀⠢⡀
⠀⠀⣠⢔⣾⣿⡿⠋⢀⣉⣤⣶⣤⣴⣦⣴⣶⣤⣮⣙⡻⠆⠀⠀⠀⠀⠀⣧⠀⢠⣿⠀⠀⠀⠀⢀⣠⠀⠀⡰⠶⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⣷⣝⢢⡀
⠀⢰⣵⢿⣫⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇⠐⢸⣿⡀⠀⠀⠀⣿⣷⣶⣷⣶⣶⣶⣷⣶⣷⣶⣛⣿⣻⣗⣾⠶⠤⣬⡙⣆
⠀⡟⢋⣼⣿⣿⣿⣻⣻⣤⣬⣥⣿⣿⣾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⡁⠀⠀⠐⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⣖⠠
⠀⠰⣽⣿⣿⣿⠿⠿⠛⠉⠛⠻⡯⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⢹⡇⠀⠀⠀⢋⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠿⠟⢻⣿⣿⣿⣿⣷⣞⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢡⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠀⠀⡷⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠀⠉⢻⡾⡇⢰⣾⣧⣶⣿⣿⣿⣿⣿⣿⣆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⢸⣷⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠇⠸⠟⠉⠙⠻⠿⢿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣴⣾⣹⣟⡻⢿⣛⣿⣻⣦⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣣⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣾⡷⢿⡿⠿⣿⡿⢛⣿⣿⣛⣋⣋⠃⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⠠⠈⠳⡀⠀⠀⠀⠀⠠⢽⣠⠀⣷⣾⣿⣿⣿⠿⣿⠎⡿⣿⣿⡿⠿⠇⠀⠀⣿⡇⣀⠀⠀⠀⠀⢠⡀⣟⠉
⠀⠀⢸⠇⠃⣠⠀⠀⠀⠀⢒⠀⢁⠀⠘⣿⣧⠸⣗⠀⠀⠀⠀⢈⢻⣠⡄⣿⡙⣿⣿⣿⠀⣹⢷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢹⠄⠀⠀⠀⠘⡿⠟
⠀⠀⠠⡴⠆⠉⢀⣄⠀⠀⠘⠁⠀⠁⠀⠈⢿⣦⡙⡄⠀⠀⠀⢉⢹⣀⣀⣿⠃⠁⠋⢻⠀⣿⢸⠀⢠⣿⡀⠀⠀⢀⣾⡯⠀⡰⠀⠀⠐⣿⣾⣷
⠀⠀⠀⠀⣤⣤⣼⡍⠀⠀⠰⠡⠤⠁⢁⠀⠀⢻⡗⠈⢮⣂⠀⢉⣹⡅⠉⣿⠂⠀⠀⢸⠀⡿⢸⠀⠲⣿⡅⠀⢀⣾⡿⠁⢰⠃⢀⣤⣄⣸⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠛⠉⠀⣤⡖⠀⠀⣲⠀⠘⣀⠀⠀⢻⡀⠘⠿⢣⠈⠙⡧⠄⣿⠀⢸⠁⣼⢀⣷⡟⠀⣛⡇⠀⢀⣾⡏⢠⠰⡞⠀⠀⠀⣿⠛⢋⠀⠒⠡⡀
⠀⠀⠀⠀⠀⠀⠒⢃⡱⠁⠤⡄⠰⣂⢼⠿⠀⠀⣀⢷⠾⢤⡈⣷⣴⣧⣤⣿⢠⢺⣧⣿⣾⠃⡇⠀⠉⡟⢳⣿⠟⠀⠀⡘⠀⢸⣇⣠⡶⢀⡈⠛⡀⠒⠑
⠀⠀⠀⠐⠶⠀⠰⢣⠕⠀⣺⣏⠈⢛⠂⢀⣤⢀⣽⣷⠶⢼⡗⣼⢿⣿⣿⣯⡼⢸⣿⡹⡟⢠⡍⠙⢀⣧⣾⢏⡜⠀⡾⢠⡄⠾⣾⡇⠀⢺⠔⡠⢁⢀⡀
⠀⠀⠐⠷⠈⢠⡄⠉⢙⡚⣥⢾⡧⠰⢂⣌⢙⠉⣰⣟⠀⣺⣿⣸⣷⣿⣿⣿⡇⣿⣿⣷⢂⡼⢳⣾⣿⡟⢇⡾⠑⢸⠋⠀⡗⠀⠘⣇⣟⡀⢛⢀⡘⠚⠃
⠀⠀⠀⠀⠀⠛⢼⠧⠘⡻⠏⡄⢱⠀⠀⣻⢦⣤⣽⣯⠀⣿⠏⠁⠉⣿⣿⣿⣿⣿⠋⣡⣾⣧⣿⣿⡿⢀⢾⠃⢠⣾⣷⣴⣳⡾⢄⠈⠀⡟⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣁⢐⠀⢛⠀⡽⠃⣩⣤⣿⣿⣧⣠⣿⣦⣠⡀⣿⠋⠈⣿⡧⢾⣿⣿⣿⣿⣿⠃⠀⠠⢀⣼⣿⣿⣿⣿⣿⣾⣧⣼⣇⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣧⣶⣿⣿⣿⣻⣟⣹⣿⡉⠈⢷⣿⣆⣼⠏⠀⠀⢠⣾⣿⣿⣟⠀⠄⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡷⢦⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⣮⢹⣿⣠⣴⣶⣿⣿⣿⣿⣿⣤⣶⣿⡿⣿⣿⢿⣿⣿⡿⠿⠿⠋⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠛⠿⣿⣉⣻⡿⢿⣿⣿⡿⠧⣀⣀⣾⣎⠹⣯⣀⡀⢹⠈⠛⠛⠀⠈⠉⠋⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠁⠀⠉⠉⠁

⠀⠀⢀⣾⣟⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣆
⠀⠀⠀⢻⣯⣿⣿⣿⠿⠿⢶⣼⣿⣿⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢀⣠⣶⣿⣿⣿⡶⠾⠯⣿⣿⣯⣿⠋
⠀⠀⠀⠈⣿⣷⣿⣿⣶⠛⣿⣿⡇⠀⢈⣽⣿⣶⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣶⣿⡋⠁⠈⣻⣿⡿⠿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠙⣿⣼⣿⣿⡟⠋⣙⣻⣦⣿⣿⠏⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢿⣿⣧⣴⡛⠙⠛⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⠉⣉⣡⡽⠿⣆⣀⣠⣾⣿⣿⣦⡐⠀⠀⠀⢀⣴⣿⣿⣄⠀⢀⣼⣿⣉⠉⠙⢛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣯⣹⣿⣿⣿⡉⣀⡤⠶⠚⠛⢿⣿⣿⣿⣿⣷⣾⣿⣦⣿⣿⣿⣿⣿⠿⠿⠷⣤⣀⠉⣳⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⣀⠀⢀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⠀⣨⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣻⣿⣿⣿⢃⠠⠔⠚⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣍⠛⠛⠲⢤⣈⣸⣿⣿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⢿⣿⡆⠀⠤⠐⡘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⡌⠒⠠⢀⣼⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⡠⠐⢸⡇⢸⣿⣿⡿⣿⣿⢿⣿⣿⡇⠀⣿⠐⢄⢠⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣿⣿⣧⣔⠀⠛⢹⡿⣿⡇⣿⣿⡇⣿⣿⡟⢚⠣⠑⢤⣿⣿⣿⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣟⢻⣿⣿⣿⣷⣦⣼⣧⣼⣇⠸⡿⠁⣿⣧⣇⣤⣴⣿⣿⣿⣿⠿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⣟⣿⣿⣿⣿⣿⡻⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣽⣿⣯⣽⣿⣽⣷⡴⠁⠀⠀⠀⠑⣴⣿⣽⣿⣛⣻⣿⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠒⠉⠁⠀⠑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣼⣿⣄⣀⡀⠀⠀⠀⠰⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠀⠉⠙⠛⠿⢿⣿⢷⣶⣾⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠁⠹⡿⠯⠀⠀⠀⢈⡉⡤⠖⠈⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠨⣦⡀⠀⣠⣮⣄⣀⢣⠀⠀⣴⠚⠻⢿⣶⡦⠤⢤⡀⠀⠀⢷
⠀⠀⠀⠀⠀⣤⣤⣤⣶⣶⣶⣶⣶⠶⠯⢷⣄⠉⠃⠀⢹⢛⡠⠤⠌⡑⠦⣀⡽⠃⠀⣴⣿⣷⢤⣸⣆
⠀⠀⠀⠀⠀⠓⠀⠭⠟⢻⠁⢈⣗⠒⠚⠋⠁⢀⠀⠀⣼⠋⠀⠀⠀⠘⡄⣠⣇⠀⢠⠋⠤⠀⣀⣬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⡻⠀⠀⠠⡀⢸⠀⢠⣅⣀⣀⡀⠀⢀⡇⡹⠉⠑⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⣧⠀⠀⠀⣵⢸⠀⠀⣏⣿⣉⢹⠿⠟⢡⠁⠀⡘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡇⠸⣿⣛⣺⠃⢈⡀⠀⣧⠁⢘⠋⠅⡠⠃⠀⡰⠁⣼
⠀⠀⠀⠀⠈⣦⠸⡵⣎⠭⢧⣿⠀⢻⡁⠙⣴⣾⡇⢰⠇⠀⢸⣾⠏⠁⢀⣴⠁⠠⡋⠠
⠀⠀⠀⠀⡀⠈⢀⢼⣿⡀⠀⣿⣀⡈⣧⢠⠹⣿⣧⣿⡄⣲⣺⣤⣶⣶⣟⠁⢠⡄
⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣴⡞⠓⠢⡀
⠀⠀⠀⠀⣰⣿⣿⣿⠻⢿⢟⡻⠟⢛⢻⣏⢉⢻⣄⣀⣈⣙⠿⠽⣿⠿⠿⣿⣏⣾⣿⣷⡆⠉
⠀⠀⠀⠀⠊⠉⠁⠀⠀⠉⠉⠁⠈⠈⠉⠉⠉⠓⠛⠛⠀⠚⠛⠛⠻⠛⠛⠛⠛⠛⠋⠑⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⠛⠲⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⠦⡀⠀⠘⢦⠁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⢢⡀⢈⡟⠁⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⠋⠛⣟⠋⢿⡟⣶⠚⣿⢻⣿⡇⠀⠀⠀⢀⣠⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢧⣺⠃⣿⢀⣿⠈⡇⠉⠛⢻⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⣿⠀⢸⠂⡏⢀⡇⠀⢀⡞⢸⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⣿⢳⡞⠻⣽⠀⢸⢀⡇⢸⠁⠀⣜⣠⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⢸⡆⠀⢸⠀⢸⣸⠁⡾⢀⡾⢫⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣇⢸⡷⣶⢺⠁⣻⣟⣢⣷⣏⣘⣁⣰⣠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⡇⡿⠚⠩⠵⠂⢸⣿⣿⡏⠁⠖⠂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣯⢣⣀⠀⢠⡴⡫⡀⠙⢿⣆⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣼⣿⠉⢿⢧⠀⠀⠀⣸⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢿⣿⠀⢸⡌⣿⠛⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⢧⠀⠘⡇⣿⠀⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡀⠈⢷⠀⣿⣿⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣈⣇⡿⣿⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠉⠀⠄⠐⡌⢻⣿⣿⣯⣽⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠐⠀⠔⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⢹⣿⣿⣽⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠄⢹⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠈⢆⣿⣿⣿⣿⡋⣹⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⣀⣀⠤⠤⠤⢤⣤⣤⣾⣿⣿⣿⣿⣿⡿⣿⠟
⠀⠀⠀⠀⠀⡀⠀⠀⠠⠐⢊⣁⣭⠭⢿⠀⠀⠀⡏⠉⠙⠒⠓⠒⠶⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠈⠐⠓⠊⠉⠉⠀⠀⠀⠈⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡠⢬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⣈⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⠚⢹⣿⢻⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠐⠂⠤⠤⢤⠥⠀⠀⠀⠀⠀⠈⠀⢾⡇⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣙⠇⢀⢀⣠⣀⣠⠼⢷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⢻⣦⡀⠀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣄⡆⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢈⡏⢻⣿⠉⡇⠀⠀⠀⢃⣤⣵⣾⣥⣜⠃⠀⠈⠻⣾⢶⣶⢷⡞⠃⠀⠈⢿⡿⣦⣴⢿⣿⠃
⠀⠀⠀⢸⣮⠁⠁⢡⣟⠀⠀⠀⠺⠽⠋⠉⠯⠿⠀⠀⠀⠸⣿⠊⠁⢿⠟⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣦⣀⡸⠇⠀⢠⠀⠒⣢⣆⠒⠀⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠀⠈⠇⠀⠂⠀⠀⠀⢿⣰⡟⠻⣆⣽⠀⠀⠀⠙⢟⠻⢟⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠖⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣄⠂
⠀⠀⠀⠸⣲⠚⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠸⣯⣻⢟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠈⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠈⠮⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢘⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣀⣀⡡⠤⣀⠤⠄⠀⢀⣀⢀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⠩⢀⣀⣱⣤⣴⣤⣦⣤⣬⠄⠙⠛⢷⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣐⣒⠢⢽⣽⣿⡏⢸⣿⣿⣿⠿⣛⣛⣀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢈⣁⠤⠒⣡⢞⣿⠀⢸⡏⢿⡯⣑⠲⠀⠤⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠤⠤⣞⣁⡞⢹⠀⢸⡈⢀⡈⠢⠅⠒⢀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⢠⠿⠛⠀⠀⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠉⢦⣼⡄⢸⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⣡⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠈⣿⠀⠘⠀⠀⠀⠀⡜⢻⠂⠀⠀⠀⠸⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣀⣹⡄⠀⠀⠀⠀⣸⣭⢠⣬⣤⣤⣤⣽⡾⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢟⢻⠠⠃⠀⠀⠀⠀⠳⠤⢦⣟⡿⣿⣿⠂⣄⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡶⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⡇⠀⡸⠀⠀⠀⠀⢀⠜⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡚⡯⠀⠀⡇⠀⠀⠀⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠃⣀⡔⢀⣠⠴⠊⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣁⣀⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣠⡤⠖⠚⠛⡏⠁⠈⣯⠉⠉⡙⡳⢦⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠸⡄⢸⡍⡔⡰⠠⢀⣿⠀⠀⣷⢡⢡⠐⣘⣬⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢳⡙⢦⣙⠓⠷⠧⠴⣿⠀⠀⣿⠞⣚⣋⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠉⠙⠛⠛⡏⠀⠀⣿⠉⢁⡤⠴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣠⡴⠖⠒⡖⠒⢲⠶⠦⢤⣀⠈⢦⠀⠀⢰⠃⠀⠀⣇⡴⠋⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡸⣷⡀⡐⠀⡇⠀⢸⠄⡀⡔⣸⠇⣸⠀⠀⡞⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠭⢭⣝⡇⠀⢸⣟⣉⣭⠵⠚⠁⠀⡼⠁⠀⠀⣏⡤⠴⠶⡶⠒⢠⡤⢤⣀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠙⠢⣄⠀⠀⢷⠀⠈⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣍⡓⠷⠶⡝⠀⢸⣥⣤⠤⠟⢀⡜
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⢸⡄⠀⢹⡀⠀⠀⠀⢠⠇⠀⠀⢰⠇⠀⠉⠙⢒⡇⠀⢸⠖⠒⠒⠋⠁
⠀⠀⠀⠀⠀⢰⠃⢀⡤⠤⣴⠒⡶⠲⡶⡄⢘⡆⢧⠀⠀⢧⠀⠀⠀⡞⠀⠀⠀⡏⠀⠀⠀⠀⡼⠀⠀⡞
⠀⠀⠀⠀⠀⠈⠣⣌⣚⣒⣿⠀⣿⣛⣩⠥⠚⠀⠘⣆⠀⠈⢧⠀⢸⠁⠀⠀⣸⠁⠀⠀⠀⡼⢁⡠⠖⠋⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠸⡄⠀⠀⠀⠀⠀⠸⡄⠀⠈⢧⡏⠀⠀⠀⡏⠀⠀⢀⡼⢡⠏⣀⣀⣀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠱⡄⠀⠀⠀⠀⠀⢹⡀⠀⠈⢇⠀⠀⢰⡇⠀⣠⠎⠀⠈⢦⣓⠦⡿⠀⣝⣳⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠀⠀⢧⠀⠀⠘⣆⠀⢸⣇⡞⠁⠀⠀⣰⠋⠈⣹⠃⢠⠗⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠳⣄⠀⠀⠀⠘⡆⠀⠀⠸⡄⠸⡏⠀⠀⢀⡞⠁⢀⡜⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢳⡀⠀⠀⢻⠀⠀⠀⢳⠀⣇⠀⣠⠏⢀⡴⠋⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠹⣄⠀⢸⡆⠀⠀⢸⡀⠸⣴⠃⣠⠞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣆⢸⡇⠀⠀⢸⠇⠀⢳⢰⠏⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⢸⡄⠀⠀⣼⡀⣀⠟⢿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠙⠒⠋⠉⠉⠁⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⢦⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢰⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠸⡄⢀⡴⠛⠉⠀⠀⠀⠀⠀⠉⢩⢛⡰⠃⠀⠀⡆⠀⣠⣦⠄⠀⠀⠀⠀⣠⣀⠀⢸⡇
⠀⠀⠀⠀⠠⠄⠻⠀⢸⠀⠀⠀⠀⠀⡇⠀⠹⣀⠜⠀⠀⠀⠙⠈⠃⠃⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠳⣤⡹⠂⠀⠀⠀⠀⠈⢙⣿⠆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠤⠤⣄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣄⡀
⠀⠀⠀⠀⣀⡤⠶⠶⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠙⠛⠓⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⢀⠀⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢐⢶⡄⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⣴⠟⡆⠀⠀⠀⢠⠙⠧⢀⡜⠀⠀⠀⠀⠰⢟⠤⠆⠀⠀⠀⠀⣈⠀⠵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠸⣧⠀⠰⠁
⠀⠀⠀⠀⡻⠄⠇⠀⠀⠀⠸⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡟⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢄⠀⠜
⠀⠀⠀⠀⠀⠀⠈⠀⣆⣀⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠚⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⡘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠚⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⡀⡀⢠⠃⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠉⠓⠂⠈⠁⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⠂⠁⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠦⠀⠀⠀⠀⠘⡉⢙⠆⢀⠏⠀⠀⠰⡀⠀⠀⠀⣠⠖⠁⠀⠀⡞⢀⣤⣠⢄⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠂⠀⠀⠀⠀⠀⢇⠈⠃⠁⠀⠀⠀⠀⠙⠲⠤⣀⡳⢤⠀⠀⠈⡀⡿⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⠶⣔⠆⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠸⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣩⠔⠚⠓⠢⣍⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡥⠒⠉⢀⣠⣼⣦⣄⡀⠉⠲⢌⡙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⣈⠳⢤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⠴⢋⡠⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⣌⡙⠿⣿⣿⣿⡿⠟⢉⠤⠒⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠉⠒⠤⣉⣡⠔⠊⠁⠀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⣧⣠⣄⡀⠀⢸⠀⠀⠀⢠⠿⢄⡀⠙⠲⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⠀⠳⢄⡈⠑⡶⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⠃⢸⠀⠀⠀⠀⠀⣀⣘⠀⢁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢿⡿⣿⣶⣿⠿⣶⣄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⠟⠁⠀⢸⠀⠀⠀⢠⠛⢅⣉⠀⢸⠀⣿
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣛⣻⣿⡿⢟⣿⣻⢿⣿⣟⣿⡿⣷⣤⣀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⢄⡉⠀⠸⠀⣿⣶⣤⣄⡀
⠀⠀⠀⢰⣿⡿⣷⣾⣯⣿⣿⣯⡺⠿⠿⠿⢿⣪⣿⣿⣾⣟⣿⣿⢿⡆⠀⠉⠓⠦⣄⡀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿⣷⣿⣾⣿⣿⠿⠋⠁
⠀⠀⠀⢸⣿⣿⣷⣭⣻⢿⣭⣿⢿⣷⣾⣶⢿⣿⣭⣿⠿⣻⣽⣾⣿⣷⠀⠀⠀⠀⠀⠙⠳⢤⣸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⢸⡏⠻⣿⣿⣿⣷⣯⣛⠿⣿⣟⣻⡿⢟⣫⣷⣿⣿⡿⠿⠋⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡿⠟⠋⠁⠈⠁
⠀⠀⠀⠘⠳⣄⡀⠉⠙⠻⢿⣿⣿⣾⡍⣽⣾⣿⡿⠛⠁⠀⠀⣀⣤⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠙⠻⢿⣧⡿⠟⠁⠀⢀⣠⣴⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⢸⠀⣀⣤⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠒⠠⠤⠀⣙⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⡂⠈⠀⠀⠤⡄⡀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⢶⣪⣤
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢢⣤⣬⣁⡀⣉⣁⣀⠩⢀⡀⠁⣈⠉⠋⠁⠉⠙
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡰⠖⠶⠐⠀⠀⠐⠐⠀⡀⠀⠀⠀⢡⠀⠀⣬⣀⠈⠉⠻⢿⣿
⠀⠀⢀⠎⠀⠀⠀⠀⠀⣘⣳⡾⠋⠉⠉⢻⣿⡤⠀⡛⢄⠀⠀⠀⣇⠀⡾⠈⠈⢦⢤⣤⣼
⠀⠀⡜⠀⠀⠀⠀⠀⢠⡅⣯⠀⠀⠀⠀⠘⢿⡦⠀⣀⣹⠄⠀⠀⢹⠀⡄⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠠⣿⣲⣿⠀⠀⠀⠀⠀⠀⢿⡦⠄⢀⡇⠀⠀⢸⠀⠃⠀⠀⠀⠀⢰⡇
⠀⠀⠱⡀⠀⠀⠀⠀⠉⠿⣽⣅⠀⠈⠈⠀⣤⣾⠻⣥⠊⠀⠀⠀⠎⠀⠄⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠒⠶⠻⠀⠀⠀⠀⠀⢹⠉⠀⠀⢀⠀⠂⠀⠀⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠖⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠃⠀⠀⠀⠀⢀⡅⠀⠀⠀⠠⣄⠀⢠⡇⠀⠀⠀⠀⣼⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡜⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠸⢷⣾⡿⢀⠂⠀⡀⣻⢷⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡈⡴⣤⣱⣿⡜⠞⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡜⠁⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡜⣏⡄⡧⠄
⠀⠀⠀⠀⠀⢀⢀⢸⡇⠘⣄⠀⡄⠀⠀⣀⡌⣹⠒⠀⢠⡀⠀⠀⠀⠀⢀⣿⡙⡧⠉⠇⠁
⠀⠀⠀⠀⠀⠰⠈⠸⣤⡤⣼⣠⢰⠘⣇⣿⢱⡿⢀⠆⠀⠀⢀⣦⣠⡦⠏⢲⠙⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠏⠃⠈⠣⠆⠄⡴⢸⡾⣯⡩⠆⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⢠⠆⠀⠀⠀⠀⠠⡄⠀⠀⠰⢢⡖⠀⠀⠀⠀⠀⠀⢶⡴⠆⢰⡇⠂⠀⡀⠀⠀⡀⠐⠲⡷
⠀⠀⠀⠈⢦⣀⠀⣰⠀⢀⡠⠏⠀⠀⠀⣿⣰⢩⢄⡰⡍⣆⣻⠀⠀⠀⠈⠇⠀⠀⢠⡄⠀⠀⢾⠀⠀⠀⢳⠀⠀⠨⣶⡌⠀⠀⣺⠁
⠀⠀⠀⠀⣴⠀⠀⢼⠀⠀⢰⠄⠀⠀⠀⢩⣾⠘⣾⣷⠃⣷⣍⠀⠀⠀⠀⣠⡀⠀⠸⠇⠀⢠⡄⠀⠀⠀⠈⣳⢂⣴⢻⢲⣔⢲⠋
⠀⠀⠀⠀⠘⣷⠶⠖⠶⢶⡟⠀⠀⠀⠀⠈⢿⣇⠈⠁⣸⡿⠁⠀⠀⠀⠀⠙⢷⣤⡄⢠⣴⠿⠃⠀⠀⠀⠀⠹⣜⣱⠀⢸⣋⡼
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠀⠘⠁⠀⠈⠙⠀⣀
⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡂⠖⣤⡀⠀⠀⣠⠰⠂⡆⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⣆⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⣇⠀⠀⠀⣴⠀⠀⠀⣠⠃⠀⠀⢻⠙⠚⡘⣶⢚⠙⠚⣼⠁⠀⠘⡇⠀⠀⠀⣤⠀⠀⠀⣾⠁⠀⠀⠸⠟⠂⢰⠀⠚⠿
⠀⠀⠀⠈⣷⡀⠀⠹⠀⠀⣸⠏⠀⠀⠀⠨⣗⢆⡙⠻⠊⣠⢆⡏⠀⠀⠀⠻⡄⠀⠀⡟⠀⠀⣰⠋⠀⠀⠀⣆⠀⠀⠘⠀⠀⢀⠆
⠀⠀⠀⠀⠙⠿⠶⠀⠶⠾⠛⠀⠀⠀⠀⠀⠈⠣⠭⠀⠨⠵⠋⠀⠀⠀⠀⠀⠱⠤⠄⠀⠠⠴⠋⠀⠀⠀⠀⠘⢶⡤⠀⠠⣴⠟
⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⠀⡤
⠀⠀⠈⢷⡈⠊⠀⣀⠀⠙⠈⡼⠃⠀⠀⡀⠀⠀⠰⣿⡆⠀⠀⢀⡀⠀⠀⠐⢰⡆⠂⢀⠀⠂⣶⠐⠀⠀⠀⠀⠀⠠⣿⡆
⠀⠀⠀⠀⣙⠀⠀⢿⠀⠀⢚⠁⠀⠀⠈⠓⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢨⠃⠀⢻⠃⠀⢫⠀⠀⠀⠀⢀⣌⡓⣛⠒⣋⡄
⠀⠀⠀⠀⠘⠦⠦⠈⠰⠴⠛⠀⢤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⢠⣶⠯⢍⣩⣏⠭⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⣶⠖⣠⡄⠀⠀⠀⢠⣤⠲⣶⠄⠀⣶⣶⣤⡀⠀⠀⢀⣤⢶⣶⠀⠀⣶⣶⢄⠀⠀⠀⢠⣶⣶⠀⠠⣤⣄⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠹⠀⢿⠀⠀⣤⠀⠀⣿⠀⠘⠀⠀⢹⡀⢁⣞⢳⡞⢻⡈⢀⡏⠀⠀⢻⠀⠀⠡⣀⠊⠀⢨⡇⠀⠀⠸⣧⠀⠀⣤⠀⠀⢰⡟
⠀⠀⠀⠀⠘⢧⣀⣿⣀⣴⠋⠀⠀⠀⠀⠈⢓⠘⠏⠈⠁⠹⠃⣚⠁⠀⠀⠘⠦⠀⠀⡿⠀⠠⢴⠁⠀⠀⠀⢙⡗⠀⢹⠀⢰⡏
⠀⠀⠀⠀⢷⣦⣉⠀⢉⣥⡾⠀⠀⠀⠀⠀⠘⣦⡤⠀⠀⢤⣴⠃⠀⠀⠀⠀⢧⣤⠂⠁⠰⣤⡼⠀⠀⠀⠀⠈⢷⣴⠏⣧⡴⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⡾⣿⣿⣓⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢺⣿⣿⡟
⠹⣟⣿⣿⣅⣼⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⣿⣇⣴⣿⣿⣿
⠀⠹⣽⣿⣯⣈⠿⠀⢼⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣧⡠⠙⠓⣿⣿⣽⠃
⠀⠀⠹⡽⣿⣍⣁⠀⠸⣿⠀⣾⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⣠⠾⣿⡏⠀⣻⠏⠀⠶⣿⣿⢷⡏
⠀⠀⠀⢳⠻⣿⣦⣠⣀⠛⠢⣿⡇⠀⢹⣷⣄⠀⠑⢄⠀⠀⠀⠌⡠⣠⣾⣇⠀⠘⣿⠄⠁⠀⢬⣶⣿⣟⡿
⠀⠀⠀⠈⢷⠻⣿⣧⣤⣠⠀⠾⠃⠀⣿⣿⠙⣷⣌⠄⣿⣿⣄⣪⡾⠛⣿⣿⠀⢀⡛⠀⠀⢠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢷⣛⣿⣦⣤⡄⠀⠀⢀⣿⠋⠈⢾⣿⣷⣾⣿⣿⣿⠃⣀⣸⣿⣆⠀⠀⠠⢤⣴⣿⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢦⠄⠙⠁⢰⣆⠀⢹⣿⣿⣿⣿⡇⠈⢿⡇⢈⠩⣯⣜⠒⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠚⠀⢹⡀⠀⠐⣽⣿⢿⠁⠀⢸⠀⠈⡑⢿⣽⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⠀⢦⡀⠀⡧⠀⢧⢿⣿⡼⣇⠀⡟⠀⢠⡏⣿⡟⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⣿⣷⣤⠀⠅⠀⣷⢠⢸⠘⡟⢰⣄⢠⠃⠰⠋⣤⣼⢷⡟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⣿⣿⣰⡆⠀⢻⠈⣐⠀⠀⣸⠁⣸⠀⠰⣀⣬⡏⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⡿⣿⣵⣦⣾⣦⠶⠀⠀⠰⢆⣿⣷⣤⣾⣹⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣾⣋⣾⣥⣿⠋⠀⠀⠉⣟⣹⣟⣙⣏⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣹⣯⡞⠀⠀⠀⠀⠻⣽⣏⡙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣤⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠋⠁⣿⣿⣿⣍⡁⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⣀⠲⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⠃⠙⠃⠈⠉⠁⠀⢉⣌⠉⠹⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠉⣁⣀⣀⣠⡴⠿⢟⠻⣶⣶⡶⠾⣿⣦⢴⣿⣶⣿⣿⣷⣶⣦⣶⣴⣶⣶⣆⣀⣠⣤⡄⠀⠁⠀⠀⢤⠠⠿⢦⡀
⠀⠀⠀⠀⠀⠀⢰⣯⣠⣾⣋⠋⠉⠭⢀⡀⠠⣙⢮⡻⡀⠢⠙⢮⢆⡹⠈⣏⢹⠈⡇⢸⡁⢠⡸⢁⠏⢹⠟⢻⠶⢾⣷⣄⣀⡀⢠⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢠⡿⠟⠁⠀⠀⠈⠁⠲⠄⣀⠀⠀⣸⠙⢦⣀⠀⠈⠸⣡⡇⣿⠘⣦⠙⢦⢁⣼⢣⠎⡰⢋⡴⢋⣴⡋⠝⠛⢿⣤⣼⣇⡈⠀⠈⢣⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠒⠂⢄⠉⠲⢤⣁⠘⠿⢷⡜⠀⣿⣧⢹⣧⣽⣿⣶⣿⣷⣵⡮⢴⣯⡤⠞⠉⡠⠂⡴⠊⠈⠛⣶⣿⠀⢠⣤⣧
⠀⠀⠀⠀⠀⠈⢿⡈⢭⡍⠁⠒⠒⠪⠭⠴⢊⣥⠖⣨⣑⢦⣌⣿⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣶⢾⣥⣴⢶⣥⣶⣿⣦⣭⡶⣭⣴⠻⣦⡈⣁⡈⠆
⠀⠀⠀⠀⠀⠀⠈⠻⣖⣂⣤⠤⢤⣴⣶⣦⣭⣄⣛⡻⠿⣷⣮⡿⠀⠀⠀⠀⢨⣿⢿⣿⣿⣭⣤⠄⠀⠀⠀⠉⢐⣀⡚⠓⠚⠉⠀⢘⣷⠾⢟⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡖⢒⣠⠤⠍⠉⢛⣛⣛⣻⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⣿⡟⠿⣻⠿⢛⡿⣿⣿⣶⠤⣤⢤⣄⣘⣛⠋⠤⠄⣻⣿⣃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⢤⣾⠿⠛⣉⣩⣭⡽⣿⡇⠀⠀⠀⠀⢸⠀⠀⣿⣷⣦⡇⠰⡠⢈⠣⢍⠳⣛⠦⡈⠩⣙⠟⠛⠖⣠⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣽⣮⣿⣿⠇⠀⠀⠀⠀⠸⣄⠘⣿⣿⣿⣟⠢⡀⠀⠀⢀⠑⢌⠡⡈⠳⡌⠳⣌⣶⣿⣿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡿⢯⡶⠐⢀⣁⣀⣴⣤⣷⣼⠶⠾⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⣿⠀⡏⠙⠳⠿⠿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡠⠀⢀⣴⣤⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⡜⠛⠃⠈⢻⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⢀⢀⣾⠁⣸⣷⣄⡤⠹⣍⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣰⣏⣾⣷⣾⣿⣿⣿⣿⡿⣮⣵⣌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⢀⠀⠀⣼⣿⣿⠿⠋⠁⡷⢸⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡷⠶⠶⠒⠚⢧⣦⣾⠛⠁⠀⠀⠀⠈⠓⠸⡏⠉⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⡆⣼⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣠⢧⡈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢠⡞⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡦⣀⠀⠀⠐⡿⣋⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣭⣤⣤⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⣽⣦⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢰⠇⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣂⣈⣳⣾⡟⢾⣵⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢻⣄⠀⠘⠉⠈⠻⠃⠀⠀⠙⠛⠟⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠳⣶⣕⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠉⠉⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⣿⣦⣦⡄⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠛⠿⠿⣯⣴⣶⣿⣦⣶⣶⣶⠟⠙⢿⣿⣤⣤⡤⣴⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡴⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⢿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠁⢀⠀⠀⠀⠀⠀⣿⣿⣿⣅⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣟⣻⠷⠖⠊⠀⠀⠀⠀⠀⣿⣿⣿⡈⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣠⠖⠒⠂⠚⢿⣿⡆⠀⠀⠈⡀
⠀⠀⢀⠀⠀⠀⠀⢸⡿⡟⠁⢰⠿⢻⣿⣀⡀⠀⠀⠈⢿⡆⠁⠀⠀⢠
⢀⣾⡟⠀⠀⠀⣰⣿⡏⠀⠀⠸⠀⠀⣨⣿⠟⢿⣤⣤⣿⡥⣤⣄⠀⠀⠓
⠸⣿⠄⣀⣴⠞⢿⣿⣇⠀⠀⠀⣧⢰⡿⠃⠀⠀⢸⣿⡿⢀⣀⣙⠀⠀⠀⠀⠀⠀⠀⠆⡞
⠀⠙⠓⠙⣿⡀⢀⣹⣿⣿⣻⣶⣿⣿⣷⣶⣤⣰⣾⣿⣿⣮⡀⠈⢃⣀⣠⣤⣤⣀⠐⣘⡇⣘⣅⣄⡀⠀⡀
⠀⠀⠀⠀⠹⠿⠿⢛⠙⠁⢸⠟⠿⠟⠛⠻⠛⠻⠳⠛⠛⠻⡷⣷⠾⡿⡿⢿⣿⣿⣭⠿⠿⠋⠿⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⠟⠉⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣾⣿⠻⡆⠘⢿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⡿⠋⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⢱⣿⠿⠁⠀⠁⠀⠀⠻⣿
⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢸⣿⣿⣿⣿⣇⣾⣿⣿⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⢠⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡿⣿⣎⣿⣿⣿⣾⣿⡟⣸⣿⣿⣿⣿⠃⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡟⠻⡟⠀⠀⠀⠀⠀⡀⣤⡀⠠
⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣴⠏⠀⠀⠠⠂⠀⢀⣤⣠⣴⠞⣽⣿⣿⡏⠀⣴⡇⠀⠀⠀⠀⠀⡇⢹⡇
⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢠⡿⠃⠀⠀⠀⣠⣴⣾⣿⣿⣿⣣⣾⣿⣿⣿⠀⣼⣿⣧⣤⠀⠀⠀⠀⠁⢸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡆⡀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡿⣧⠃⠀⠀⠀⠸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⣼⣿⣿⣿⡿⢨⣿⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣧⠟⠀⠀⠀⡀⠀⠁
⣿⣿⣿⣿⣿⣿⣻⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣯⣾⣿⣿⣿⣿⡟⠁⢸⡞⣿⣿⣿⣿⣧⠀⠀⢠⣇
⣿⣿⣟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠿⣿⠟⠀⣿⣿⣿⡿⣿⠛⣿⣧⡄⠀⢇⠈⠻⢿⡇⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡟⠀⣠⢿⣿⣿⣿⣿⠀⠈⠻⣷⡀⠘⠆⠀⢸⣷⡀⠘⠀⠀⢻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠇⠀⡇⠈⣿⣿⣿⢹⡆⠀⠀⠹⣧⠀⠀⠀⢸⣿⣷⡤⠀⠀⠈⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣾⣿⣯⠇⠀⠀⠀⠙⡆⠀⠀⠀⢿⣿⣧⣇⠀⠀⢹⡆
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⠃⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⠀⠀⠀⠀⢰⡄⠀⠀⠈⢻⡿⣿⡀⠀⢼⠁
⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠟⠁⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠳⠀⠀⠀⠘⣇⣿⣧⠀⢸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣾⣿⡟⢸⣷⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣷⣀⠀⣀⣤⣴⣄⣀⣤⣴⣿⣿⠀⠸⡇⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⡗⠀⠀⣿⠟⠿⠛⠛⠻⠿⠿⠛⠛⠛⠉⠁⠀⢸⣿⡟⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⠸⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣟⠋⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⢦⣀⣀⣀⣀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⣰⡌⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡟⣿⣿⣿⡿⣟⡿⠛
⣿⣿⣿⣿⣷⡜⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⢿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⠂⣠⣤⣾⣿⣿⣿⣿⣿⠇⠿⣿⠿⠚⠉
⣿⣿⣿⣿⣿⣿⣞⢷⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⡖
⣿⣿⣿⣿⣿⣿⣿⣯⠻⣆⠈⠛⠿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣉⣉⣭⣿⣿⣿⣿⣿⠿⠟⠫⠐⠋⠁⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣷⣦⡀⠀⠉⠲⠬⣝⣛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢁⡀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠀⢈⣇⣀⡀⠀⠀⣎⣍⣑⡆⠀⠈⠃⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠁⣤⣤⣄⡀
⠀⠀⠀⠛⠃⠓⠀⠀⠈⠉⠈⠉⠀⠀⣉⢂⢠⡾⠶⣏⠉⠑⠒⢤⡀⢀⠀⠀⣀⣤⡀⠘⠒⢷⣶⡟⠋⠁⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠛⠂⢹⡶⠤⢤⣀⠀⠀⠁⠀⠉⠻⣹⢉⣠⡤⣤⠀⠌⠀⠀⠀⢀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠀⠀⠖⡍⠀⠀⠀⠀⠀⠀⡀⠀⠈⢑⠁⠀⢀⠀⠀⠀⠐⠦⠔⠠⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠀⠀⠀⣀⠀⠀⠀⠾⠗⠺⠿⠦⠴⠤
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠀⠀⠄⠒⠲⣤⣄⠀⠀⠀⠀⠀⠠⢤⣀⣄⠀⠀⠀⠀⠈
⠀⠀⠀⡀⣾⡾⢭⣵⣚⢻⣧⠀⠀⢀⠸⣏⢸⡿⠁⠀⠀⠀⠘⠛⠛⠲⡦⠼⠂⠀⠀⠀⠀⡤⠀⠀⣀⣰⠀⢀⡀⠀⠀⡀⠔⠀⠀⡠
⠀⠀⣿⡿⢎⣐⠀⠘⣾⠻⠟⠀⠀⢘⣷⣿⡿⠴⠀⠀⠀⠀⣀⡀⠀⢀⣷⣛⠛⣶⠀⡄⠀⠀⠀⠢⡦⡄⠠⠈⠑⠈⠈⠁⠀⠡⠀⠁
⠀⠀⠸⢻⢳⡒⣾⡄⠘⠃⡀⠀⠀⠘⣿⣿⣿⡎⠀⠀⠀⣿⣽⣿⠆⠀⠘⠋⠛⠉⠀⣐⠋⠀⠀⡶⠐⠈⢋⡄⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠈⠣⠝⠚⠁⢀⣄⠁⠀⠀⠀⢸⡾⢿⡥⠀⠀⣠⡀⠀⠀⡧⠖⠀⠀⠀⣠⠀⠁⠢⠤⠀⣅⠦⠖
⠀⠀⠀⢠⣤⡀⠀⢰⣽⣿⣦⠀⠀⠀⠘⠓⡛⠁⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⣀⣈⠉⠀⠀⠁
⠀⠀⠀⣼⣿⣟⣶⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⡀⠀⢠⠾⢫⡀⠱⡄⠀⠀⠀⠀⠀⠛⠋⠉⡉⢉⡛⠁⠁
⠀⠀⠀⢻⣿⣿⡿⢳⣿⣿⠿⣤⣶⣾⡀⠀⠀⠀⠠⠋⢀⢀⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠾⠐⠛⠃⠜⣶
⠀⠀⠀⠀⠁⠉⠀⠀⠁⠉⠘⢿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠄⠹⡀⠀⣄⣠⠀⢀⠀⠀⠀⠀⠀⠀⢔⠻⠆⣦⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠠⠤⠄⡼⠄⠴⠡⣬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠧⠀⠀⠙⠀⡈⠀⠀⠀⠀⠀⠀⠀⠙⣀⠁⠠⠤⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠒⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠘⠇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠤⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡀⠀⢀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡃⢻⡋⣿⣖⢒⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣩⠿⣧⡼⠻⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣞⢙⣶⡋⣳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣤⠿⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡉⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⡀⠙⠶⣄⡀⢠⡤⠈⢳⠀⠀⠸⣇⠘⢦⠴⣄⡤⣿⠀⢀⡄⠀⡀⢀⠺⣠⠖⠚⠉⠈⠙⢦⡀⠦⠀⣀⡤⢶⡎⠀⡆⠀⠒
⡃⠀⠀⣀⡽⠓⣦⠀⢸⡆⣤⡴⠏⠶⢄⠀⠀⣀⡼⠞⠉⠉⠛⠺⢧⡀⠇⠀⠀⠀⠉⠀⡀⠑⡄⠚⠁⠀⣉⠀⠀⠎⠀⠠⠄
⠛⢀⡾⠉⢀⣀⡸⠘⢫⠄⣀⡖⠀⣠⠼⠶⢦⡟⠁⠀⠚⠀⠠⣆⡤⠖⠉⠉⠙⠢⣄⠈⢁⡄⠥⠤⠠⣄⡀⢩⠶⡀⠀⠀⢀
⣀⡼⣣⡖⠛⠉⠙⠲⠠⣄⠴⢄⡾⠁⠀⡆⠈⢧⡀⠹⠤⠦⠀⠚⠀⢀⣀⣉⡀⣀⠈⢱⡉⠀⠀⠠⠄⠈⢣⡐⠲⠕⡶⠊⢍
⣯⣵⠋⠀⠰⠄⠀⡀⠀⢸⠂⢸⠀⠀⢄⡀⡀⢈⣱⠿⠿⠿⠿⠿⠿⠛⠛⠛⢻⣶⣶⡄⡇⠠⠄⠀⠀⠄⠀⢑⠀⢀⠈⠳⡄
⠼⡇⠰⢦⠀⠀⡄⡷⠀⢺⡀⢀⡱⠦⣈⠉⢨⣼⠛⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠂⠀⠀⢀⡼⠀⠀⠀⢀⡞
⣾⢿⡄⠀⠠⠴⠗⠀⢀⠀⢳⡌⠀⡦⠀⢸⣿⠁⠀⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⡇⠀⠉⠙⠢⣄⡀⠀⠀⠑⢤⡨
⣿⡀⠻⢦⣤⡴⠖⠛⣹⠋⣯⠁⢠⡀⢤⣾⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣶⠈⠀⠠⠀⠁⠄⠂⠒⠀⠉⡀
⠘⠷⠶⣤⢦⡦⣤⡀⢾⡁⣙⢦⣤⣈⢸⣿⠀⠀⠀⢠⣦⠀⠀⣶⣆⣀⣰⠿⠀⠀⠀⠀⢸⣿⢠⠀⠀⠀⠠⠃⠀⢀⣀⠀⠱
⠷⢦⣤⣤⣦⣄⡈⢯⢙⡜⠃⠀⠴⠉⠸⣿⣀⡀⠀⠀⠘⠿⠟⠃⠘⠛⠛⠀⢀⣀⣰⠶⠿⠩⠌⢀⡀⡀⠔⡀⠀⢀⠀⠉⠑
⠷⣤⡶⠾⣋⣙⣻⣯⠸⡀⠀⢆⡀⡀⠀⠀⠛⢳⣶⣶⣀⣀⡀⠀⠀⠀⠀⣤⡟⠛⠃⠀⠆⠀⠀⠠⠀⠀⢆⠈⣂
⠀⠀⠙⢶⡍⡉⠀⢠⡀⣙⢦⡀⠀⠈⠉⣀⣀⣰⠀⣀⠛⠛⢳⣆⠀⠀⣀⡿⠇⡈⠑⠜⠀⠡⠀⠀⠀⠄⠀⠃⠐⠀⠐
⠀⠋⠀⠀⣻⠀⠀⡀⠴⣃⡀⠗⢀⡴⠋⣭⠀⠰⠄⢸⡈⠁⡘⠛⣤⠀⣿⡇⣤⣭⣂⣀⡀⠜⠁⠀⠀⠀⠀⠈⠠⠀⠀⠄⢒
⠒⠀⣀⣼⣯⡒⣺⠗⠉⡉⠉⠛⠲⢤⠀⠏⣠⠤⠒⠓⠶⢤⣈⡠⠄⠻⠃⠀⢠⠀⠀⡀⠈⠒⡄⠢⢠⢀⡄
⣦⠞⠉⡀⢀⡟⠁⠀⠀⠃⠀⠴⠀⠀⢹⠄⠉⠀⠰⠂⠀⡄⠈⠳⣄⠾⠀⠀⠈⠀⠀⠁⠀⠀⠇⠀⢀⡄⡀⠈⢣⠀⠀⠀⠂
⠉⠀⠀⠁⠈⢧⡀⠘⠦⢶⣀⡀⠀⠀⢞⠀⠀⢲⣀⡄⠀⠁⠀⢀⡏⠰⣄⡀⠑⠊⠲⠈⠀⢀⡸⠀⠀⠀⢀⠀⠰⠀⠐⠀⢀
⣄⠈⠳⠖⠣⠬⠳⣆⠀⠀⠁⣀⣠⣤⠟⠘⢧⡀⠁⠘⠋⠁⠀⢈⡇⠀⠢⠝⢂⡀⠀⣠⠛⡉⠀⠀⢠⠀⠈⠀⠀⢀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢒⣿⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣗⣒⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⣤⡼⠿⢟⣬⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⠿⠿⢧⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⠤⠤⠬⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠤⠤⠤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠱⢤⡀⠉⢷⡄⠀⣀⠀⣰⠟⠁⣠⠴⠁⠤⠤⠤⢤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⠀⠀⠀⠀⠀⠈⠑⠠⠙⣾⣿⣞⠡⠐⠉⠀⠀⠀⠀⣀⣀⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⠿⠿⠶⠶⢲⣿⢸⣿⠖⠶⠿⠿⢿⠿⢻⣟⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⢰⠊⠁⢀⠔⠨⢿⣿⠿⠀⠀⠀⠈⠱⠀⠀⠀⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣈⣁⠠⠖⠁⡀⠀⢸⣿⡀⠀⠄⠈⠢⠄⣈⣀⠀⠠⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⢀⠌⢠⡞⠀⠌⠀⠠⢹⣿⠑⡀⠈⢆⠀⢦⠈⢂⠀⢢⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣎⣀⡌⢀⠌⢀⡔⠀⠀⠛⠀⠀⢆⠀⢂⠀⣅⣀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣦⠞⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠶⠾⠿⠿⠛⢻⠶⠶⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢿⠛⢇⠀⠀⣀⣀⣀⡌⠀⡀⠰⣉⠘⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⠐⠀⣤⣸⣶⣿⣿⣿⣿⣷⣾⣿⣿⣍⠁⢀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢈⡱⣶⣽⣿⡿⠿⠛⣿⣿⣿⣿⣶⣶⣾⡇⣾⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡀⠈⢣⣭⣿⣿⡇⠀⠀⣿⣿⣿⣉⡟⠛⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠉⠉⠀⠳⠟⢸⡇⠀⣰⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠒⣨⠻⢧⢤⣽⣿⣷⡹⠎⠙⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢤⠀⠀⣠⣶⣿⡛⣿⣙⢋⣭⣻⡛⣦⠀⣤⠆⢰⠞⢡⣿⣿⣿⣿⣿⣿⣿⡵⠂⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣾⡿⢿⣯⣿⣿⣿⣷⣿⡿⠿⠟⠉⣀⠀⠀⢤⠀⣄⣴⡿⢻⣛⣋⣩⣍⣿⣿⡷⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡼⠋⠡⢼⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠓⠂⠒⢀⠙⠀⠀⢀⣤⣿⣷⠿⢟⣿⣯⣁⡙⠟⠻⢿⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠲⢿⣿⣿⣿⢻⣿⣻⠆⠀⠀⠀⠀⠉⠀⠀⢀⠾⠏⣿⣿⣿⣿⣿⣿⣿⣷⣦⡠⠐⠊⢹⣿⣷⣿⣈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣭⣿⡗⠈⡿⠻⠄⠀⠀⠀⠀⢀⣶⣦⡈⠒⠈⣩⣿⣿⣿⡏⣿⣿⣿⡏⠀⠈⠁⣼⣿⣯⣭⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠀⠀⠀⠀⠀⣄⣤⣶⣿⣿⣿⣧⡀⠉⠀⠀⠀⣿⠁⣽⠏⠀⠂⠀⣠⣾⣿⣟⡛⠋⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠛⢫⣿⣿⣿⣿⠿⣿⡿⠖⢠⣤⡄⢨⡔⠋⢀⣤⣶⣾⣿⣿⣿⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠄⣹⠙⢿⣿⡏⠉⠁⠀⣼⡿⠀⠀⠀⠀⠀⠙⠿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠸⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣷⣦⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢼⡷⠀⠀⠀⠀⠠⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣾⣧⠀⠀⠀⠀⡄⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⠀⠀⠀⣾⢻⡇⣀⠀⢀⡺⠀⠀⠀⠀⠈⠙⠻⢿⠻⠯⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⢀⡀⠠⣄⢀⣿⣿⡷⠁⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠀⢀⣿⠀⣾⣇⣾⣏⢸⣿⣿⡇⣼⣿⠇⠀⠀⠀⠀⠀⠀⣤⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢨⣿⣧⢸⡿⢻⠉⣸⣿⡿⢲⣿⣿⣤⠌⠀⠀⠀⠀⠀⠀⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣧⡸⣷⣿⣿⢷⣿⣿⣿⡷⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣦⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣤⣼⣿⡽⠋⠙⢻⢿⡏⠈⣿⡏⠳⣼⡻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠿⠛⢛⣼⠿⢿⡏⢹⡏⠀⠙⡿⠛⢻⣿⠻⣿⣿⡿⣿⠋⢠⣞⠁⠀⢠⠁⢸⡇⠀⡿⡇⠀⠘⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠜⢫⠁⠀⢨⠗⣾⠀⠀⠐⠓⡀⠀⠻⡄⠘⣿⡀⠁⠀⠻⠋⠀⠀⡾⢿⠛⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠙⢃⠀⠀⠀⢠⡜⠢⠁⠀⡆⠀⠼⠉⠀⢰⠇⣤⠋⠹⠀⠀⡄⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠘⡄⠠⢃⡈⠑⠆⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠄⠒⠒⠒⠀⠉⠉⠉⠉⠉⠁⠁⠀⠒⠒⠂⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠠⢙⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠓⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠄⢐⠾⣧⣝⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠴⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠠⠀⠀⠀⠢⠈⠓⣿⣯⣠⡈⣷⣼⣛⣹⣦⡀
⠀⠀⠀⠀⠀⣠⠞⠿⠠⠄⠀⠀⠀⠀⠲⠞⢂⣠⡀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⠉⠁⢀⠀⠠⠀⡄⠙⠛⢊⢬⡟⠻⠇⡰⣿⣾⣿⣿⣷⡀
⠀⠀⠀⢀⣾⠁⡀⡌⠃⠁⠻⠓⠀⣄⠐⠀⠉⢡⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡀⢀⢠⢬⠴⠶⠎⠉⠉⠉⢉⢡⣵⡩⣀⡆⣽⡛⣻⣿⢿⣷⡀
⠀⠀⣠⣋⡽⣈⡙⢁⡀⠠⡀⠂⠃⢠⡟⢵⠃⠻⡆⠀⢀⡀⠀⠀⠀⡀⠀⠈⠀⠸⢻⣤⡀⠤⢤⣤⡧⢷⠾⣿⣿⣿⣧⣷⢿⣿⣟⣻⡼⣟⣷
⠀⢠⠟⣰⣷⣤⡝⠀⠈⠸⣯⠀⡀⢄⠉⠁⢀⠀⡄⠀⠀⠁⠀⠀⠀⠘⡶⡴⠶⠀⢠⢈⡳⠀⠀⢙⠁⠶⠞⠿⣨⣾⣧⣿⣷⣿⣻⣿⣿⣿⣿
⠀⣾⢸⢽⣯⣍⣸⡟⢠⣾⣷⣤⣇⠘⣿⡟⠠⡇⢠⢤⣄⢀⠀⠀⠀⣦⡗⠀⢀⢠⠀⠀⣄⢢⢰⠻⡿⠳⠾⡴⣿⣟⣿⣏⣿⡽⣿⣿⣿⣿⣿
⢰⢻⣼⣼⡿⣿⣿⣯⣸⠟⡏⣼⣿⠆⣹⣻⢻⢷⡟⠴⡍⠛⠛⠀⣀⣿⡗⣆⠀⣀⠀⠀⣨⣄⣬⢓⣿⣫⡞⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣾⣾⣿⡟⡸⠻⠿⡿⢇⡗⣿⢿⣻⠸⡈⠋⣗⡊⢣⣾⠧⣶⣠⡀⣿⠟⢻⡅⢃⢻⣦⣿⣿⣿⣿⣸⡿⢟⣧⣿⣼⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿
⣿⣽⢿⡗⣅⣫⣴⣥⣼⣴⠁⣶⠙⣴⢻⡞⣞⠿⣏⡼⣖⣻⢿⣟⠻⣶⣿⢷⣶⣿⣿⣿⣾⣿⣿⢿⣿⣟⡿⣿⣿⣿⡿⡏⠟⢈⠉⣈⠛⣿⠏
⣿⣿⣿⣷⣽⣍⣿⣏⣰⣿⢻⣇⣳⠟⣾⣧⡱⡷⡻⢶⣿⠩⡎⢷⣼⢶⢚⢷⣿⡟⣿⡯⡞⣿⡌⡾⣹⠞⢇⠞⣡⣧⡇⠀⢀⠨⢆⣹⡿⠋
⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠟⣿⣿⣟⣿⣿⣷⣱⡿⣧⢧⣴⣿⣿⢷⣾⠿⠿⢿⣿⣿⣿⠉⣿⣤⣿⢌⣿⠴⡛⣿⣠⢖⣤⣴⠶⠛⠉
⠘⣿⣙⣿⣟⢻⣿⣾⣟⣻⣮⡟⣤⣿⣟⣿⣿⣿⣿⣿⣿⡿⠾⠿⢋⠀⣈⡆⢘⣩⣉⢐⢾⣿⣿⣷⣶⣷⣿⣾⣷⡿⠛⠉
⠀⠘⣿⣿⣿⣷⣿⡿⣿⣿⢿⣿⣾⣿⣿⣾⣿⣿⣿⣛⣭⠗⠑⠚⠀⠀⠉⠛⠷⣴⣾⠿⠋⠉⠽⠋⡉⠁⢺⡿⠋
⠀⠀⠈⢻⣿⣿⣿⣳⣿⣿⣿⡛⠯⠛⠛⠋⡹⠤⠀⢁⣱⠢⢀⠈⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⣤⡁⣿⣿⠁
⠀⠀⠀⠀⠙⠿⣿⣿⣝⣳⣭⣤⣤⣸⣵⣶⢶⣿⣿⣯⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣧⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠛⣇⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣤⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⢸⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣔⣮⣼⣷⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣬⣧⣴⣶⣶⣶⣷⣶⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠴⠞⠁⢀⣤⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⢀⣶⣴⣿⣿⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇
⠀⠀⠀⠀⢀⣤⡤⠴⢖⣲⠟⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⡉⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢠⣾⢟⠅⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡇
⠀⠀⠸⣿⣍⣰⠇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⠀⠀⠀⠙⠻⣿⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠋⠀⡿⢿⣿⣿⣏⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⣄⣨⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣦⠀⠀⠁⠀⠀⠀⠤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠀⢀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡆⠀⣰⠀⠀⢀⠀⠀⠀⠀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣿⣆⣠⣾⡂⢠⣄⣠⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋


⣿⠿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠈⠁⠀⠉⠙⠛⠃⠀⠀⠑⠠⠀⡐⠉⠁⠀⠀⠡⡀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠈⠋⠐⠀⠐⠆⠘⠂⠒⠒⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⡄
⠀⠀⠈⢢⠀⡇⠈⠚⠉⠁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠀⠀⠀⠀⢀⢠⡀⠀⠀⡇⠰⠷⠒⠀⠲⠲⡇⠐⡀⡇
⠀⠀⠀⢦⣃⠈⠁⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⢆⠀⠀⠀⡀⠄⡵⠈⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢉⡥⣍⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠢⣈⡡⠚⡃⡅⠀⠀⠇⠀⠄
⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠁⠈⢆⢀⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⡀⢸⠀⠀⠀⠀⠀⠀⡠⢢⣉⡀⣸⠁⠀⠐⢀⣤⡀⠐⣤
⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⡀⠀⢀⡠⠸⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⠀⠀⠀⠀⡠⠊⠰⢿⣿⣿⣿⡿⠀⠄⠀⡸⠁
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢘⠀⠁⠀⣀⣤⢎⡶⣀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢄⣂⠘⡛⣛⣟⡅⠀⠀⢈⠃⠀⠒⠒⠂⠠
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠤⣀⡠⢴⡁⠀⣻⣧⡢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠊⢙⠀⠀⠀⠱⢼⡄⠤⠊⠀⠁⠐⠲⠂⠂
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⢸⣷⣾⠿⢿⠤⠴⠖⠡⠀⠀⠀⠀⠀⠀⡤⠤⠖⠃⠀⠀⠀⠀⠀⠀⠘⠀⡀⣀⡀⣀⠃⠀⠀⠰⠆⠰⠶
⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⡇⡄⠈⠙⢇⡞⠓⠀⠠⡄⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠀⠀⠀⠠⡤⠤
⢇⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠃⠈⢀⢡⡥⢤⠎⠀⣥⢀⣰⡒⣬⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⢰⣄⡃⢈⠀⠀⠀⠠⡤⠔⠤⠠⢤⡄
⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠺⠤⠤⠄⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⢌⠁⠀⠀⣀⡠
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⣄⣂⣉⡃⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⠉⠀⠀⠀⠖⠀⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠠⠤⡈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠑⠢⠀⠠⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠤⠴⠶⣤⡄⠀⠤⠞⠛⠂⠀⠀⡇⠀⠠⠐⠈⠉⠀⠀⠉⠉⠀⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⠀⠠⠒⠁⠂⠀⠀⠀⠀⠐⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡤⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⠀⠤⠒⠒⠒⠐⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⢀⡀⠲⠶⠦⠦⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡀⠀⠀⠀⠀⠉⢩⡉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠈⢳⠠⢄⣀⣀⡠⠓⡀⠉⢓⠲⠤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠤⠀⠰⠶⠴⢿⠛⠋⠙⠂⠋⠀⠀⠀⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠣⠆⠀⠀⠀⠀⠠⢀⣰⠒⠛⠃⠀⠀⠀⠔⠒⠀⠚⠀⣠⣄⣬⠀⠀⢂⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣹⠇⠀⠀⠚⣿⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠛⠆⢿⣷⠀⠀⢀⡀⠜⠳⢄⣀⡴⠖⠲⣄⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠠⠏⢠⣦⡄⠀⠀⠈⠀⠻⠿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣻⣍⣁⠀⠀⠀⠀⢀⣰⡆⠠⠆⠀⠀⠀⣤⣀⡀⠈⠉⠉⠠⣴⠐⠀⠠⣤⡤⠖⠒⠚⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠉⠈⢡⠉⠀⠀⠀⠀⠈⠁⣾⠤⠀⢠⡖⠛⠉⠛⠀⣁⣀⠀⠀⠁⠈⣷⣶⡏⠀⠀⠀⠀⠀⠙⡷
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢻⣶⣾⠋⠀⠀⠀⠠⣾⡥⠄⣤⠈⡴⢄⠀⠀⠀⠈⢃⡹⠂⢀⡸⠇⢀⠀⠚⢿⣿⠛⠀⢀⡸⠛⢀⣠⣴⣿⠐⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠋⣸⣆⠀⠀⠀⣤⠃⠘⣷⡘⠧⠀⠀⢦⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⣦⡟⠁⠀⠈⠁⣭⣤⣌⣀⠀⠀⠚⡂
⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⢀⣄⣈⣉⠇⠠⠾⡇⢠⡄⠘⠁⡈⠃⠀⠐⠊⠁⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠘⠛⠀⠀⠻⣄⠀⠀⠀⠀⠈⣹⣙⠉⠀⠐⡀⠉⠲⠶
⡀⣀⣰⣆⠀⠀⠀⠀⠁⠈⠿⢧⣄⠀⠀⠀⠀⠀⠀⣻⢾⡇⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠘⢻⠀⠀⠀⠀⠀⢳⣤⡄⣸⣷⠶⠖⠂⠈⠛⢀⣾⣿⣦⠀⠀⢀⡀
⠀⠀⠙⠟⠀⢀⠀⠀⠈⠀⠀⠀⣹⡄⠀⠀⠀⠀⢀⠣⠈⠁⠘⠲⣄⠙⣿⣶⠶⠖⠲⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⣾⠃⠀⠈⢙⠀⠀⠀⠀⢢⡈⠻⠛⠁⠀⠀⣼⡇
⠀⠀⠀⢦⣤⠾⣳⠴⢀⡀⠀⠀⠉⠁⠂⠐⠆⠀⠀⠐⠀⠀⣀⣼⣿⡄⠀⠀⠀⠀⠀⢰⡿⠰⢀⣠⣄⡄⠂⠐⠂⠛⢃⣉⠀⠈⠁⡟⠀⠀⣤⡄⠸⠻⠇⢠⡔⠉
⠀⠀⠀⠸⡇⠀⠀⠀⠘⠁⠀⡀⠀⠰⠓⠀⠀⣀⢠⠀⢤⣠⡈⢉⣿⣥⡀⠀⡀⠐⣦⠈⠀⠀⠀⢹⣿⣤⡀⠀⠀⢰⣦⠙⢶⡌⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣇⠀⠀⠂⠀⠄⣀⣽⠿⠇⠀⢰⣾⡟⢣⠀⠀⠉⠛⢀⣄⡙⠟⠈⢀⣸⣿⡇⠀⣠⣀⣠⣷⣄⢡⡀⣤⡈⠛⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠛⢇⣸⠀⠀⠀⠀⠸⣿⣇⠀⠀⢿⣿⡄⠀⠀⠉⠹⠾⠿⠛⡛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⠣⢀⣠⣿⣄⡀⠘⠀⠀⠀⠈⡃⢀⠶⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠙⣻⡀⢀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠔⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡁⠀⡉⠠⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣗⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣿⠀⠀⣀⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠂⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⡴⡶⢶⠛⢿⣻⣳⣶⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢷⣛⣴⣺⠁⢸⣿⣿⠿⣻⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⢲⡄⠀⠀⠈⠓⠒⠒⢾⠀⢸⠗⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠹⣆⠀⠀⠀⠀⢀⡏⠀⣸⠀⢀⣠⡴⠋⠉⢳⡄
⠀⠀⠀⠀⠀⠀⢸⠠⣶⣖⣶⢲⣶⣤⡌⢳⠀⠀⠀⡼⠀⢀⡇⢰⠏⠁⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠭⡇⢸⠭⠭⠵⠊⠀⠀⣰⠁⠀⡼⠀⠈⠳⢄⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⢠⠃⠀⢰⠃⠀⠀⠀⣠⠏⣿⠋⠋⠉⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⠀⠀⠀⠀⡞⠀⠀⡏⠀⠀⠀⡰⠃⢰⠃⡠⠴⠞⠉⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⠈⢇⠀⢳⡀⠀⢰⠇⠀⢸⠁⠀⠀⡼⠁⣠⠃⠘⢦⣿⣶⢦⣤⡈⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⠳⣌⢦⠀⠹⣄⢸⠀⠀⣸⠀⠀⣸⠁⢠⠇⠀⠀⠀⡹⠃⡼⠿⠯⠜⠁
⠀⠀⠀⠀⠈⠧⣀⣀⣀⣠⠴⠋⠈⢧⠀⠘⣿⡄⣤⣿⡀⢀⣿⡄⣾⠀⢀⡴⠊⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠳⣄⠀⠀⠈⣧⡄⢿⣟⡡⡿⣇⢸⣿⣷⢿⡞⠁⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠿⣷⣶⣼⡼⣊⣿⣚⠜⣹⢸⣇⣽⢼⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⣷⣃⣸⠟⠛⠋⠀⠳⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠁⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠁⠀⣤⣢⠀⠀⠀⠀⠃⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠻⠘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⠶⠂⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠾⠟⠛⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⢀⠀⠈⠉⠓⠒⠤⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠘⠳⢦⡀
⠀⠀⠀⠀⢠⣿⣏⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⣠⠦⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣿⠄
⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠋⣉⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⢶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠐⡲⠞⠉⣉⡴⠥⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣬⣉⣻⣯⣛⠙⠛⠻⣟⠛⠛⠛⠛⠛⢻⠻⠋⠉⢉⡭⣁⣠⢎⣡⣤⡴⠦⠅⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠶⢿⣷⣦⣤⣤⣤⣾⠆⠈⡴⠿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡠⠀⠀⣿⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⣮⣦⣄⣄⣠⠔⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢴⣧⣀⣰⢀⣄⣸⠷⢾⠋⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⢠⠀⢠⠀⠀⣿⣿⠛⠉⠁⠀⠀⠘⣇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢧⣸⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⡇⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⢣⢈⣿⣀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣼⠀⡴⠁⡿⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣇⢻⣇⠙⢿⣇⠀⠀⠀⠀⠀⢰⠀⠀⠈⠆⣿⢰⠇⢸⢇⡀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣧⣼⢻⣆⣾⣿⣆⠀⠀⠀⠀⡎⠀⠀⠀⠰⡏⣾⣠⡾⠋⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⠋⣿⣼⣿⢉⣿⠀⣀⠀⢠⠁⠀⢀⠃⠀⣷⡟⢠⡇⢠⡿⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢠⡇⣼⣿⢈⣿⠀⡏⠀⡎⠀⠀⠘⠀⠀⣿⠃⣾⠁⣼⠃⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣸⣇⣿⣿⢸⣿⣰⠁⢰⠁⢰⠀⠀⡆⢰⣿⣿⣡⣼⠿⠛⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣿⣿⣤⢿⣿⡀⢸⠀⢸⠀⡀⣿⣼⣿⣿⣿⡷⠞⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣷⣼⣧⣼⣦⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢳⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡞⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠽⢿⣛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⡿⠯⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠒⠲⢿⡟⠁⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡉⠈⢻⡿⠒⠒⢲⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⡒⠒⣚⣧⣰⣿⡿⢉⣿⣄⠀⠰⠀⠀⠆⠀⣠⣾⡉⢿⣿⣆⣼⣛⡚⢒⣾⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢉⣉⣉⢻⣿⡀⢸⣿⡿⣦⠘⡀⣠⠃⣼⢿⣿⡇⢀⣿⡯⣍⣁⡉⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣇⣀⢠⠤⠿⠟⣿⡿⢥⣹⣇⣿⣿⣸⣏⡬⢿⣿⠻⠿⠤⠤⢀⣸⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡤⠔⠒⠒⠒⢿⡟⠒⠦⣽⡇⢸⣯⠖⠒⢻⡿⠐⠒⠒⠂⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⡟⠛⢋⣉⣉⣽⠿⠛⣿⣇⣸⣿⠛⠿⣯⣍⣉⡉⠛⢻⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⡟⠋⡹⠋⢠⡿⢀⡼⣹⣿⣿⣏⢧⡀⢿⡄⠘⢏⠉⢻⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡷⠚⡇⠀⢘⣷⡾⢠⡇⢻⡟⠸⡄⢷⣾⡃⠀⢸⠓⢺⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣷⠞⣹⠒⡟⢻⣷⡿⠀⠀⠀⠀⢿⢺⡟⢻⠒⣏⠳⣿⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣍⣧⣧⣰⣧⣼⣽⡇⠀⠀⠀⠀⢸⣯⣧⣼⣦⣼⣼⣭⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣶⣿⣷⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣾⣿⣶⣿⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣽⡿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣯⡾⢿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣤⣤⣄⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⣾⣿⣿⣿⣿⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣞⢦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⡟⣭⡿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢸⣿⡇⣿⡇⣿⢱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢿⠇⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢞⡇⠀⠀⣿⠇
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⣿⣿⣿⣦⡀
⣿⣟⠀⣸⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣶⣷⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠄⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⢄⣀⡈⠢⡙⠦⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⠄⢙⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡈⠀⠄⢈⠘⠐⠣⠰⡀⢠⡀⠀⠀⠀⡄⠀⠀⠠⢀⢀⠀⠀⠀⠀⡐⣆⢀⢢⣎⣾⣇
⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠁⢰⣦⣤⣤⣉⢀⡁⢀⡁⣀⣀⡠⣀⣀⣀⣁⣈⠀⠉⢉⣈⣀⣉⠠⠃
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣤⠠⢠⠠⠆⠖⠠⠂⡴⢀⢄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⠉⠉⠘⠛⠷⢽⡍⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠗⡌⢠⣠⡦⡴⣤⣠⣦⡤⢂⠡⢢⢐⠀⠀⠀⠀⠀⢇⠀⠀⢸⡗⠦⠠⡀⠀⠘⠐⢟⡇
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠬⢥⡿⠟⠀⠀⠀⠀⠸⣿⡷⠖⠁⣀⡐⣀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠙⠖⠳⠞⣾⡟
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⡃⢽⡇⠀⠀⠀⠀⠀⠀⠻⣷⣆⠀⠀⠀⢰⡦⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⡼⠀⠀⠀⠀⠀⠀⠀⣰⣦⠥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠈⠉⠑⠻⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠹⢶⣮⢻⣿⠀⠀⠠⣄⣀⡀⠀⠀⣹⣦⡍⡉⣐⡛⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢟⢔⢿⣤⠀⠀⠀⠀⠈⢢⣾⣿⠝⠻⠦⠀⠀⠀⠀⠀⡼⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠌⡾⡆⡿⠀⠀⠀⠀⠀⠀⠀⢺⠂⠁⠀⠀⠀⢀⡠⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣆⡀⠤⠔⠂⠉⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⣀⠀⠀⢀⣀⡌⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠲⣤⡀⠆⢣⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⠀⠈⠀⠐⠨⣽⣼⣼⣿⠎⠰⠂⠀⢠⠀⢻⣿⣼⡅⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣣⠞⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡀⠸⢠⢀⠘⣀⣿⡁⠟⡄⡘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢀⠟⢸⡇⡿⠏⡷⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⢂⠀⠠⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⡀⡆⠙⡇⡇⢱⠂⠄
⠀⠀⠀⠀⠀⠀⠈⠀⡀⣿⢸⢸⡀⠀⠀⢰⠀⢀⠀⠀⢠⠀⢳⠂⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⠙⣇⠘⡃⣷⠘⠖
⠀⠀⠀⠀⠀⠀⣃⠐⠳⡜⣰⢸⠀⡇⠀⢻⠀⢨⠄⣶⡞⡀⣿⠀⠠⠀⠀⠃⠁⠂⡀⠀⠀⠀⣰⢃⡗⢃⠸⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠉⠈⠀⠓⡿⠞⡔⣇⢻⢸⣧⠉⣆⣿⠰⣿⡛⠃⠾⠀⠂⠀⡀⢠⣼⣤⡼⠛⠁⠀⢳⠁⠀⠀⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠁⠀⠇⠘⠀⡀⠃⠆⢬⠈⣸⠀⣿⢼⣇⣄⠼⠀⡀⡔⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠛⠛⠛⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢛⢉⢀⢀⠀⢿⣿⣿⣿⡄⢌⢢⡰⡑⠎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠸⣿⣇⠣⠇⡎⡞⢸⢸⣿⣿⣿⠈⡌⠆⣱⣨⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⠿⢶⣶⣷⣾⣾⣿⣿⣿⣷⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⣠⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠋⠉⢹⣿⣿⡏⠙⠛⠻⠿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡂⢀⢂⢀⢸⣿⣿⡿⠠⡐⡐⠕⣸⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢾⣾⣼⣿⣿⣷⣤⣵⣶⠾⠛⠁⠀⠀⣰⣿⣿⣿⣿⢟⢛⠛⠉⣿⣿⣿⠛⠛⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⡀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣦⣥⣂⣂⣿⣿⣿⠰⢀⣂⣡⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠉⠙⠛⢻⣿⣿⡿⠻⠟⠛⠛⠉
⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣿⣿⠟⠻⠿⣿⡆⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣇⣐⡐⢸⣿⣿⣀⣀⣩⡾⠃⠀⠀⢻⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⣿⣿⢃⣴⣾⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣰⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⠏⣾⡟⠛⠛⣿⣿⡿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⠋⠀⠈⠻⠶⣤⣿⣿⣁⣀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣿⣿⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠸⣿⣿⣿⡿⢿⣿⣿⠟⠀⠀⠸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢹⡿⣋⡟⢿⣤⢶⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⠟⣿⣻⡟
⠀⠀⠀⢻⢻⠗⢿⣤⡀⠨⢿⣿⠛⢷⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠟⢻⣿⠯⢤⣤⣼⠛⣿⣿⠃
⠀⠀⠀⠘⣿⣹⢯⣦⣤⠴⠞⣯⣁⡾⡞⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣻⣿⡿⣆⣩⣷⠶⢦⣤⣮⢽⣽⡟
⠀⠀⠀⠀⠙⣷⣴⣿⣦⣀⡠⣏⣹⠶⠶⣏⠛⠳⠾⢿⣦⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣠⣾⠷⠶⠿⢿⡷⠶⠾⣭⡧⣀⣠⣟⡃⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣳⣾⠉⢱⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⠈⢹⣾⣷⠏
⠀⠀⠀⠀⠀⠀⠈⣻⣾⡟⣳⣾⢾⡧⠄⠀⠞⠦⢄⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⡤⠿⠆⠀⠴⢭⣿⢿⡳⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⠝⢿⠁⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⠞⢯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣛⣧⣤⠤⠤⠤⠒⠒⠛⠙⠓⠀⠀⠀⠀⠈⠳⡄⢰⣶⠀⡴⠋⠀⠀⢀⠠⠐⠊⠉⠓⠒⠒⠠⠤⢤⣤⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢁⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⠤⣤⣤⣤⣤⣽⣿⣿⣿⣤⣤⣤⡀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣠⣾⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠍⠉⠉⠉⠉⠉⠻⠆⠁⠀⠤⠐⠀⢉⡿⣿⣿⣿⣏⠉⠐⠠⠤⠉⠛⠛⠉⠉⠉⠉⠀⠫⣍⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣀⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⠴⠋⠘⢹⣿⠹⡈⠳⢄⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⣸⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠊⠁⠀⠀⠀⡀⠀⠀⢀⣠⡴⠊⠁⠀⡰⠀⣾⣿⠆⠁⡀⠀⠉⠲⣤⣀⠀⠀⠠⡀⠀⠀⠀⠈⢻⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣷⣄⣀⠀⠐⠚⢁⠴⠛⠉⠁⠀⠀⠀⠸⠃⡀⢸⣿⠐⡄⠙⠄⠀⠀⠀⠉⠙⠳⢀⠛⠒⠤⢀⣀⣼⣿⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣬⣿⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⢠⡼⠁⢸⡿⠀⠹⣴⠀⢀⠀⠀⠀⡀⠀⠀⠑⢦⡀⠀⢹⣞⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣷⣾⡇⠀⠀⠀⡔⠀⠀⣠⠃⢀⡿⠁⠀⠀⠁⠀⠀⠹⡆⠀⢣⡀⠀⠐⡀⠀⠀⠀⣿⡶⣿⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣶⢿⣿⡶⣶⣾⣇⣀⣴⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⣄⣀⣿⣶⡶⣾⢿⢶⣮⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣿⣲⣻⣭⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣾⣯⣿⣷⣺⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉