Water pollution Emojis & Symbols

⠀⠀⠀⢸⡏⠻⠴⠟⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡟⠷⣾⠋⣿
⠀⠀⠀⢸⡇⢰⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣿
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⠀⣠⠶⠛⢻⡆⠀⠀⠀⠀⠀⠸⡇⠀⢸⠀⣿
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⠺⣥⣀⣤⠾⠃⠀⣀⡴⣦⠀⢸⡇⠀⢸⠀⣿
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⠀⠀⠉⢱⡟⢳⡌⡏⠀⢸⡆⢸⡇⠀⢸⠀⣿
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⢀⣤⠶⣮⣛⠋⠘⠷⣄⣼⠁⢸⡇⠀⢸⠀⣿
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⠙⢦⣀⠀⢹⡇⠀⠀⠀⠁⠀⢸⡇⠀⢸⠀⣿⠀⢻⡇⠛⠛⠒⠶⠦⣤⣀
⠀⠀⠀⢸⡇⢸⠀⠀⣿⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣿⠀⢸⡇⠀⠐⠶⠂⢠⣄⡉⠛⢦⣄
⠀⠀⠀⢸⡇⢸⣄⡀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⠀⣿⠐⠛⠃⠒⠲⢤⡀⠀⢈⠙⠶⣄⠙⢷⡀
⠀⠀⠀⠈⠓⠛⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠓⠋⠀⠀⠀⠀⠀⠀⠙⢧⡈⠳⣄⠘⢷⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡄⠈⢷⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⠀⠸⡇⠘⣇
⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⠀⠀⠀⢀⣠⠤⣤⣀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡋⠀⠀⠗⠀⣠⡤⢤⣄⡀
⠀⠀⠀⠠⠶⠛⠉⠀⠀⠀⠉⠳⠶⠶⠞⠉⠀⠀⠀⠉⠓⠶⠴⠞⠋⠀⠀⠀⠈⠛⠶⠴⠞⠋⠁⠀⠀⠈⠙⠶⠦⠖⠋⠁⠀⠀⠈⠙⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠶⣄⡀
⠀⠀⠀⠀⠀⢀⣤⠖⠛⠩⣍⠉⠉⠉⠛⠶⣤⣤⠞⣶⠀⠀⠀⠀⣀⡴⠖⠶⣄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣿⠀⢰⣶⡂⣹⠀⠀⠀⠀⠀⢈⡁⠀⣿⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠞⠳⠶⣄
⠀⠀⠀⠀⠀⠈⠛⠮⣤⣑⣋⣀⣀⣀⣤⠶⠛⠛⢦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⣛⠉⠉⠛⠓⠶⣤⣀⣴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢭⣭⡥⠶⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡿⣯⠘⡇⠀⠀⠀⠀⠀⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠉⠈⠙⠳⠦⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⡼⠃⠀⢀⣀⣤⠶⠛⢦⣼⠇
⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣿⣿⣿⣿⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣴⡖⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠘⣧⠀⠀⠀⣿⣧⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠈⢧⡀⢀⡟⢹⡄⠀⢻⡄⠀⠀⠴⠶⠦⣤⡴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢦⣤⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢷⠀⠈⠷⠞⠛⢋⠁⡾⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡇⠘⣇⠀⠀⠀⢀⣋⣘⣁⠀⠸⣇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠸⣏⢀⣤⠿⢤⣤⣤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⣤⣽⣤⡤⠞⠋⠉⠉⠉⠛⠦⣿⣄⣤⡴⠞⠉⠉⠉⠉⠳⢦⣤⣤⣤⠴⠛⡏⠀⠀⠀⢀⡈⢳⣤⣤⠶⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢳⡄⠀⠀⠀⠀⠀⠀⢼⣁⣀⣀⣀⣈⣷⣄⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡷⢾⡷⣏⣹⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠲⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠹⠇⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣄⡀⠀⠈⣀⣭⠶⠚⠛⠲⢦⣄⡀⠀⠀⣀⡴⠖⠛⠛⠲⢦⣀⠀⠀⢀⣠⡴⠚⠛⠓⠶⣤⣀⠀⠀⢀⣨⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⣤⣄⡀⠀⠀⠀⠀⢸⣛⡷⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠾⣷⠶⣿⡶⣿⠀⣹⠆⠀⠀⠀⠈⠉⠁⠀⢰⡏⠉⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡆⠀⠀⠀⠀⣠⠶⠦⣤⣀⠀⠀⠀⠈⠀⠈⠁⠐⠋⠀⠛⠛⠉⠀⢀⡀⠀⠀⣠⠶⠒⠋⠉⠓⣾⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⠋⢷⣄⠀⠉⠀⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢠⠆⢀⡀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣠⠄⠉⠳⢦⣀⠀⠰⣟⠻⢦⣄⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⡟⢠⡟⢀⣟⣠⣾⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⣴⠋⠀⠀⢀⣀⣉⠛⠦⣍⣓⠿⠿⣟⠶⣄⠀⠀⠀⠀⠉⠳⠦⣤⣬⠴⠞⠉⠁⠀⠈⠙⠳⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣼⠋⢳⡶⠛⢋⣭⠹⣇⠀⠀⠉⠙⠓⢻⡆⠈⣷⠀⠀⠀⣠⣄⠀⠀⠀⣀⣤⠀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡼⠃⠀⠀⣷⠰⣏⣹⠇⢻⡀⠀⠀⠀⣰⢿⡇⠰⠸⡇⠀⠘⠷⠾⠀⠀⠐⢯⣼⠿⣟⢻⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡄⠀⠀⠀⠀⠸⣦⣬⡵⠶⠛⠓⠶⠤⣴⠏⢸⡇⢰⡄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣏⣀⡾⠁⠀⠀⢀⣤⡤⠤⣤⣄⡀⠀⠀⠀⣴⣃⣤⣼⡃⠀⠁⠈⠳⣤⣀⣀⣀⣤⠤⢤⣤⡀⠀⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠚⠋⠀⠀⠀⠀⠈⠙⠲⠶⠾⠛⠉⠀⠘⠇⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠙⠓⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⡿⠀⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢠⡴⣼⣿⡗⠀⠀⠀⠀⢹⣿⣽⠀⠈⠳⣄⢀
⠀⠀⣠⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢱⣿⣸⣿⣿⣿⡗⠀⠀⠀⢠⣎⠻⠃⠀⠀⠀⢘⠁
⠀⠠⣿⣏⠠⢥⠄⠀⠀⠀⠀⠀⠀⠠⣀⣇⠐⠃⢸⠻⢫⠿⠁⠀⠀⠀⢸⣿⣷⡄⠀⠀⢦⣨
⠀⢶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠃⠀⠀⠀⢻⣿⠄
⠀⣾⣿⣋⣉⣈⣵⡦⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠋⠀⠀⠀⠰⢄⠀⡄⠤
⠀⠛⠿⣿⣿⣿⣡⣬⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠟⠛
⠀⠀⠀⠘⠿⣿⣿⣿⡗⢚⣅⠠⠀⠀⠀⠐⠿⠆⠀⠀⠀⢹⣿⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⣺⣿⡿⣿⠃⠘⠿⣷⣇⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠗
⠀⠀⠘⠛⠻⠿⠶⣶⣶⣶⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣏⣀⣀⠀⠀⠀⠀⢀⣤⡤⠀⣠⣤⣤⣶⣶⡿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣷⡄⢀⣴⣿⣿⣿⣿⣥⣤⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⢾⣷⣿⣿⠿⠿⠿⠿⠟⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠶⢤⡀⠀⣀⣀⣀⡀⠀⠀⢀⡴⢿⣿⠿⠁⠀⠀⠀⣠⣤⣴⠞⠋⠉⠈
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢠⠴⠒⠛⠓⢦⡴⠋⠉⠳⡄⡴⣵⠿⠂⠀⢀⡴⠋⠉⠀⠀⠀⠉⠳⡄⠘⣀⠤⠶⠶⠶⢤⣄⢸⠃
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡹⠊⠁⠀⠀⠀⠀⠀⢘⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠳⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⢦⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⣇⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠉⠁⢸⠀⣸⠀⠸⠷⠤⠴⠶⠤⠶⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⣠⡀⠀⠀⣀⣀
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⢸⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠷⠤⠤⠤⠞⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣷⠀⠈⠓⠀⠀⠀⠀⠀⠴⠶⠊⠁⠀⠀⠀⠰⣄⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠛⠷⠶
⠀⢤⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠙⠢⢄⡀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⣿⠀⢸⣦⡾⢳⡆⠀⠀⠀⠀⠀⢸⡇⣿⠀⢰⡏⠉⣉⣉⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡟⠀⢸⡟⠃⠸⣇⠀⣴⢿⡆⠀⢸⡇⢻⣶⣿⠀⢰⡛⠟⠀⠀⢿⣛⣉⣉⣉⣙⣉⣿
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⣀⣀⣀⣀⣠⡇⠀⢸⡇⠀⠀⠉⠉⠉⠸⣧⣤⣼⡇⣸⣿⡟⠀⠀⠉⠀⠀⠀⠸⣏⣉⣉⣀⣤⣤⣿
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⡏⠉⠉⠉⢹⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⡤⠤⠴⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠴⠶⠶⠶⣿
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠖⠒⠚⣻
⠀⠀⠀⠀⢀⣸⣇⣀⣀⣀⣤⣧⣤⣤⣤⣾⣤⣤⣤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣿⣄⣼⣅⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣟⣛⣛⣋⣿⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⣄⠀⠀⣠⣄⠀⠀⢀⣍⠉⠉⢉⣭⡉⠉⠉⣩⣄⠀⢀⣦⡀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠞⠛⢦⡴⠟⠛⠲⠶⠋⠙⠛⠛⠉⠛⠛⠋⠉⠛⠚⠋⠉⠛⠚⠋⠉⠛⠛⠛⠋⠉⠙⠉⠉⠙⠛⠋⠀⢉⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠀⢀⣶⠛⣿⠓⢦⡴⠆⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣟⠉⡏⣷⡄⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠿⣥⣯⠴⠋⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠒⢠⡶⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⢤⣄⠀⣤⠤⠤⠤⣄⠀⣿⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡿⠀⣇⣀⣀⣀⡿⠀⣿⢀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⡀⠀⣿⢀⣀⣀⣀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣧⠀⣇⠀⠀⠀⣿⠀⣿⢀⣀⣀⣀⣀⢸⣇⣀⣀⣀⣤⣠⠀⠰⢯⠇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⣿⠀⠉⠉⠉⠁⢸⡏⠉⠉⠉⣿⢹⠶⠦⣤⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣿⣸⡀⠂⢤⡙⢦⡀⠫⠝
⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠾⢷⡄⠀⠀⠉⢈⠙⡆⠀⠹⡆⢷
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠚⠁⢀⣀⠀⢸⡄⡿⠀⠁⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠽⠃⠈⠁⣿⠈⠠⠅⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⣒⡒⠒⠒⠛⠓⢒⣒⡒⠒⣒⣒⣛⣒⣒⣒⣚⡓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠤⠀⠀⢈⣀⢀⠀⠀⠘⠿⠇⠀⠀⢠⣤⣬⣭⣥⣬⣭⣭⠉⢭⣭⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣴⢶⣴⣦⣦⡄⠀⠀⠀⠯⡿⢿⠻⠟⠇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣄⠀⠀⠀⠀⢿⡷⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣤⣤⡴⠞⠋⠉⠙⠶⢤⣤⣤⠶⠋⠉⠉⠳⢦⣤⣤⠴⠞⠉⠉⠛⠶⣤⣤⣤⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠉⠓⠒⠒⠋⠁⠀⠀⠈⠙⠒⠒⠚⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣈⣀⣠⣴⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠎⣑⠉⢹⣇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡁⢲⣐⠣⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣶⢠⣞⡩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠚⣿⡶⠶⣴⣀⢀⡋⠀⣆⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡸⠃⠀⣼⠿⢶⣤⣧⣛⡵⠄⣉⣀⣤⠴⢋⡄⢠⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢠⡀⡅⢰⣧⠀⢠⣟⡀⠀⠈⠛⠛⠿⣾⡯⢟⡥⠞⠉⡇⣸⠙⢦⡑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣼⠗⠀⠀⠀⠀⠀⠈⣠⣴⠿⣉⢌⣾⣿⣿⣷⣾⣤⣀⠤⡫⠖⠉⠀⣦⠀⡇⡟⢠⡄⠉⠳⣕⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠉⠸⠃⢀⡇⠀⠀⢀⣴⣿⡿⠃⠀⠉⠉⠀⠉⠹⠿⡿⣟⠑⠈⠀⠀⠀⢰⣿⠀⢃⡇⣿⠇⠀⠀⠈⠑⢌⠢
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠃⣢⠀⢾⠀⠀⣠⢋⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⠀⠀⠈⠋⠀⢸⠃⠛⠀⠀⠀⠀⠀⠀⢸⠦⠂
⠀⠀⠀⠀⠀⠀⡐⠀⠀⢐⢁⠀⠀⠀⢸⡆⢀⢫⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢠⠇⠀⠀⡨⣯⠀⣀⠀⢸⣧⣳⣿⣿⡇⠀⠀⣠⠔⠀⠀⠀⠀⠀⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⣀⡜⠓⣦⣠⡐⢊⡁⠈⠁⢸⢃⡿⢸⣟⡇⠀⠰⠆⣀⠀⠀⠀⠈⠑⢮⡁⣶⠬⣧⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⠞⢀⠤
⠀⠈⠧⣈⡕⠹⢃⣿⡿⡁⠮⠙⠇⢠⡏⢸⡇⣼⣟⠣⣨⠰⢛⣉⡀⠀⡀⠀⠀⠀⠬⢉⢣⡈⠳⡤⠀⠀⠀⢸⡇⠀⠀⠀⠐⣠⣾⡖⠤⠰⣆⣀⢀
⠀⢰⣴⡞⠐⠂⠀⠀⢹⣁⣀⣶⣂⣘⡇⠹⠀⢿⡘⣄⣁⣈⣀⣉⣥⣀⣁⡀⠠⢄⢉⡀⡛⠰⣌⡻⠤⣀⠀⢸⠀⠀⠀⠰⢾⠁⠁⢤⡆⠀⠂⠀⠂
⠀⠛⢤⣻⣁⣄⠀⠀⣬⣧⠉⢛⣿⣯⣥⣖⡓⠶⢶⣿⣿⣾⠿⣷⣶⣾⣿⣷⣶⣶⡆⠐⡠⠉⠉⠉⠀⢼⣷⣿⣷⣶⣷⣋⣀⣂⣀⣒⣐⣊⣑⣐⣒⣀⡀
⠀⠀⠀⠀⢸⠏⠇⠈⢉⣴⠄⠰⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣭⣭⣥⣴⣾⡟⣿⣿⣿⣿⡿⠿⠿⠭⠘⠃⣤
⠀⠀⡠⠀⡸⠠⠸⠦⡤⠇⠈⠀⠀⠀⠀⠀⠀⠀⠁⠩⠥⠤⠍⠙⠛⠛⠛⠉⠻⢿⣿⣿⣯⣿⣯⡉⣉⠁⠀⠀⠀⠀⣾⣿⣋⣉⣉⣉⣀⣛⠛⣷⠈⠉
⠠⣞⡤⢀⠀⠀⣐⠀⢰⡎⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠀⢒⣈⡉⠩⠉⠙⠟⠓⠁⠶⡀⢀⡐⣋⠍⠛⣿⣍⠩⠭⠭⣥⣄
⠀⠀⠀⠘⠓⣀⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠿⢷⣶⡖⠒⠒⠀⠁⠈⠁

⠀⠀⠀⣠⣤⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣤
⠀⠀⠀⡇⢈⡉⠁⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⡇⢸
⠀⠀⠀⡇⢸⡇⠀⡇⠀⢀⣤⠴⢶⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸
⠀⠀⠀⡇⢸⡇⠀⡇⠀⢯⣀⣠⠾⠀⢀⣠⢤⡀⢸⡇⠀⡇⢸
⠀⠀⠀⡇⢸⡇⠀⡇⠀⠀⠈⢱⣏⣳⢸⠀⢸⡇⢸⡇⠀⡇⢸
⠀⠀⠀⡇⢸⠃⠀⡇⠀⡴⠛⠳⢭⠁⠈⠳⠾⠁⢸⡇⠀⡇⢸⠀⣀⡀⣀⣀⡀
⠀⠀⠀⡇⢸⡁⠀⡇⠀⠙⠳⢤⣼⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⢸⡇⠈⣉⡉⠉⠓⠶⣄⡀
⠀⠀⠀⡇⢸⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠃⢸⠀⠼⠇⢤⣄⡀⠈⠛⠦⣄⠙⢦⡀
⠀⠀⠀⠳⠾⠋⠳⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⠋⠳⠾⠀⠀⠀⠀⠈⠙⢦⡘⢦⡈⠳⡄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢷⠀⢹⡄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢈⡀⠀⣧⠈⠇
⠀⠀⠀⠀⣀⡴⠖⠒⠦⣄⡀⠀⣀⡴⠖⠒⠦⣄⡀⢀⣠⠴⠒⠒⠦⣄⡀⢀⣠⠴⠒⠲⢮⣁⠀⢋⣠⠴⠒⠲⢤⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣈⡉⠉⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⡤⠶⢒⠚⠓⠲⠦⣄⡀⣠⢤⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠲⠚⠁⠀⠙⠳⠆
⠀⠀⠀⠀⢼⡋⢠⣴⠈⡇⠀⠀⠀⠀⠉⠁⢸⠀⠀⠀⠚⠉⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⣄
⠀⠀⠀⠀⠈⠛⠮⣬⣘⣁⣀⣠⡤⠖⠋⠳⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⣏⠉⠙⠛⠲⢤⣠⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠚⠀⠀⠀⠀⠀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⢯⡀⠿⠇⢸⠀⠀⠀⠀⢀⣁⠀⣿
⠀⠀⠀⠀⠀⣀⡤⠖⠛⠲⢤⡀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠙⠲⠤⣭⣤⣤⠴⠖⠋⠉⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢴⡀⠀⢿⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠛⣿⠟⠿⢿⡿⠛⠛⢻⡿⠟⠛⠯⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣧⣤⣼⣶⣶⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⢙⠒⠋⠠⠄⡈⢁⣀⣀⡈⠁⢄⠩⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⣀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣤⣤⡤⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠐
⠀⠀⠀⠀⢿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠰⠳⠦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠠⠂⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀

⠀⠀⠀⠀⠀⡄⠀⢤⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢠
⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣻⣉⣛⣿⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣀⠀⠀⢄⢢⠀⠀⣰⠒⠂⠁⠀⢋⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡲⠴⠀⠀⠤⢀⠀⠀⠈⠀⠀⠀⠰⠀⠁⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣠⡤⠄⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠈⠙⣀⠠⠖⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⢠⠄⢠⠀⠀⠀⠀⠁⠈⠀⠀⣀⠀⠀⠀⠀⢢⣬⡀⠀⠙⠒⠐⠀⠐⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠐⡂⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠐⠀⠀⣀⠀⢀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠉⡀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⣀⠀⣀
⠠⡤⣄⠀⠀⠄⠀⠠⠄⠂⣴⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠤⠆⡀⠀⠀⠀⠐⠄⡠⠴⠀⣀⠀⠀⠀⠐⠫⠐⠢
⠆⠰⠀⠠⠀⠀⡄⡀⠀⠀⠠⠀⠒⠰⠞⡁⣀⠡⠅⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⡀⠠⢄⡀⢠⣄⢈⡹⠃⠀⠒⠀⠠
⢀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢀⠀⠀⠀⠨⠄⠡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡀⠁⠂⠐⠃⠀⠁⠪⠀⠐⠀⠢⢀⠈
⠀⠀⡀⠀⠀⠂⠀⢀⡀⠤⠈⠁⠀⠤⠠⡄⠀⢴⣅⠀⠘⠀⠀⠀⠉⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠐⠀⠁
⠀⠀⠠⠟⠉⠃⠀⠘⠁⠠⠀⣀⢀⠆⢑⣀⠀⠀⠀⠀⠛⠁⠀⠆⠀⠀⠀⠃⢀⠁⡀⠀⠀⠀⠖⠗⢲⠀⠀⡀⠀⠐⡀

⣾⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⡙⠢
⣿⠀⠀⠐⠖⠉⠈⠠⠔⠁⠂⡀⠀⢠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣉⠉⠊⠻⠓⠐⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠
⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠂⠀⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣿⠀⠀⠀⠀⠀⠘⠋⠉⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⠀⠀⢶⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠄
⣿⠀⡜⠈⠃⠀⠀⠀⠄⠀⠄⠀⡀⠀⠀⢈⠁⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⠈⠢⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⣿⠀⠀⠀⠉⠁⠀⠀⠀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿
⣿
⣿
⣿
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀
⠀⠀⠀⠀⠀⠠⠈⠒⢦⡀⠀⠀⠀⠀⠀⡰⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣄⠀⠀⠀⢀⣀⣀⠀⠀⣰⣿⣆⠀⢢⢷⡀
⠀⠀⠀⡄⠁⠀⠀⠀⠀⢘⢦⡀⠀⠀⢨⣥⣤⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⠁⡠⠙⠴⠏⠱⠏⠀⠀⠓⢶⣿⣿⣿⣿⣶⡾⠁
⠀⠀⢀⣧⡀⣀⣀⣠⣦⣵⣆⣙⣶⣦⣼⣿⣿⣿⣿⣿⣿⠀⢀⠔⠈⡄⠀⢀⠀⠀⠀⠀⢈⣣⣴⣾⡿⢿⣷⣀⠀⢀⣀⣀⠀⠘⢉⣉⣿⣿⣿⣶⣶⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣛⣻⣿⡇⠀⠀⠈⢆⣀⣀⣠⣤⣶⣿⣿⣿⣟⠀⠀⠉⠻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣀⣉⣉⣩⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⠿⢿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣛⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣩⡄
⠀⢨⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣯⣭⣵⣶⣿⡿⠿⡃
⠀⠘⠛⣩⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣋⡀
⠀⠀⣴⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣽⣟⣛⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠴⠠⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠉⢡⠎⠁⢰⡞⠋⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣗⠯⠵⣼⣇⣦⢀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠈⡷⠀⠉⢧⣠⠖⠒⢄⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⢪⡿⠀⠈⠉⠹⣿⠪⡃⢰⠂
⠀⠀⠀⠀⠀⠀⠀⢻⡟⠓⢷⣀⡶⠚⢧⡄⣠⠾⠇⡀⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠰⡰⢀⢐⣬⣤⠦⢧⢳⢻⠸⡇⣶
⠀⠀⠀⠀⠀⠀⣤⣬⣤⣠⣄⡟⠀⠀⢀⢹⠃⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⢱⣿⣥⢱⠏⢴⣟⢷⣼⡎⣇⢳⣧⣇⡆
⠀⠀⠀⠀⠀⠀⠏⠉⢹⡟⠉⠉⠻⡾⠋⠃⠲⣶⠟⠻⢿⡀⠀⠀⠀⠀⠀⠀⣼⣦⢻⡌⡟⠧⣼⣣⣾⣿⠳⣷⣐⣧⣼⡇⣾⣇
⠀⠀⠀⠀⠀⠀⠰⣤⣾⣁⠀⡰⠒⠁⢶⢠⣶⠫⣤⡄⠸⠃⠀⠀⠀⠀⠀⠀⠌⢿⣌⣧⠻⠄⠯⢿⠟⠿⡷⠜⠿⢛⠟⢠⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⢳⡇⣀⠀⠀⡿⠃⠀⢨⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡛⢇⠀⠰⠋⠀⠄⢸⡦⠀⣀⣴⡷⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠷⡄⠀⠿⢐⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣍⡳⠆⠀⠀⠈⠁⠈⠀⠨⢝⡫⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣴⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⡀⠀⠀⠀⣀⠦⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⠠⠀⠠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡟⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣋⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠐⠀⠠⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⢤⡆⢀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀⠀⣀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠰⠀⡈⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠏⠀⠻⢐⠂⡁⣤⣴⡿⠀⠀⢀⣀⣤⣤⣀⡠⠀⡀⠀⢀⣤⣤⣔⣂⣄⣃⡻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠸⣦⢁⣿⡟⢁⣶⣿⣿⣿⣿⣿⢿⣿⠄⠀⠤⣠⣾⣿⣿⣿⣿⡿⢿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⠐⢀⡄⢠⡟⠀⣼⣿⣿⣿⣿⣾⠁⠈⠈⡀⠀⠀⢄⣿⣿⣿⠛⡙⣆⠚⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠹⣦⠘⣋⣿⠇⠀⢻⡽⢿⡤⠊⠁⠀⠀⡰⠃⡐⠀⢸⡟⠿⣿⣿⠁⢌⣠⡜⣼⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢧⣄⠱⠤⡄⠀⠀⠛⠷⠶⠀⠂⠀⠀⢀⠈⣴⢿⣿⣽⣆⠘⠉⢀⡈⣉⢰⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠉⠳⢄⠓⠄⠀⢀⢀⣴⣶⣴⠀⠀⠀⢀⡿⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣳⣾⣤⡟⢦⣤⣾⣝⠉⠀⣸⠃⠀⠀⣾⣧⣸⣿⣿⡟⣻⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⣿⣿⣶⠀⣿⣷⡄⠘⠀⠀⠀⠙⡭⢉⣧⡴⠷⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣙⡟⢻⣆⠀⣿⠃⠀⠀⠄⠀⠀⠀⠸⠁⠀⠀⠸⣿⣿⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⡸⣿⢦⣄⠀⠀⠀⠀⠀⠐⠃⠀⠀⢁⠀⠀⢉⣹⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣷⡄⠀⠢⡉⠐⠂⡂⢋⠈⠁⠀⢀⠀⠈⢙⣻⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡙⢿⡅⠀⠀⠈⠁⠛⠓⠞⠐⡇⢻⢸⢸⠇⢾⡿⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡍⠐⠆⠀⠐⠀⠀⠀⠀⠁⠀⠚⢠⡿⠀⢘⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡀⠀⠘⠀⠀⠀⠀⠁⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠠⠰⠒⠒⠲⠟⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢴⣧⡐⠓⡿⢻⠚⢂⣼⡶⠴⠖⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣤⣤⣅⣰⣄⣠⣆⠨⣤⣤⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣥⠔⡨⢟⠩⠶⣛⡉⠉⠻⠟⠉⠋⣙⠲⠍⡻⢥⠂⣤⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡧⠁⢀⠴⠣⢤⣪⣴⠏⠘⢺⡛⠃⠘⣦⣕⡤⠌⠦⡀⠌⢸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡌⡴⣡⠖⢫⠷⣣⣵⡀⣈⠉⠉⣁⣀⣶⣜⠾⡯⠳⣌⢢⠰⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡜⡠⢉⣁⢾⣿⡟⠙⠟⠋⢀⡐⢂⡀⠉⠿⠋⢹⣿⡷⢈⡈⢄⢻⠠⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠛⠅⠈⡶⢸⡟⢠⠏⠀⠀⠈⠃⠌⠁⠀⠀⠸⡄⢻⣇⢰⠁⠨⠙⣧⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡦⣁⣣⡰⢀⠀⢿⡷⠃⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠘⢾⡿⠀⡀⢆⣜⣉⢴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠅⠟⡁⠠⢞⢇⠀⠀⠀⣠⠛⠤⠤⢛⣄⠀⠀⠀⡸⡳⠔⢈⠺⠨⣃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢺⠇⡈⢿⣉⠰⠉⢛⣍⡓⠛⣉⡵⠒⠒⢮⣉⠛⢚⣩⠛⡉⠆⣉⣿⢁⠨⡇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡶⢰⡁⠘⠛⢓⢙⠚⡁⠁⠁⠀⠠⠄⠠⠄⠂⠀⠨⢩⠙⣉⡚⠛⠁⠀⡆⢲⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡀⠳⣦⣤⣤⠀⡌⠁⠘⠀⣄⠀⠀⠀⠀⣠⠀⠛⠀⢣⡀⣤⣤⣴⠞⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠆⡀⠁⠿⢫⣀⣠⣀⣦⠄⠈⠘⠀⠀⠋⠁⠀⣶⣀⣤⣀⡜⠿⠀⢀⠰⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠀⣠⠂⣸⠋⠉⠟⢻⡄⡇⢠⠂⠰⡄⢸⢠⡟⠻⠉⠙⣇⠐⣆⣀⣥⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⡞⢁⠁⠀⡀⣀⠀⠷⢧⠀⢄⡠⡀⣴⠾⠁⣀⢀⡀⠈⠀⢳⡟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⡎⢰⠈⣰⠋⠄⠀⣧⢾⠃⠐⡷⣼⠀⠀⡘⣆⠁⡆⢱⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢁⢹⡈⣴⡄⠉⠀⠀⠀⠀⠉⢀⣤⢁⡏⡀⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣄⠛⡯⠁⣴⠶⡀⢀⠶⣦⡄⢻⠟⣠⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣠⠀⡃⣤⠙⠋⣤⠸⠀⣄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣇⣘⡆⢸⣂⣸⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠂⡤⠂⠀⣠⠀⢰⠀⠐⠂⡄⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢿⣎⡠⣊⠁⠀⠶⣬⡀⠊⠚⣯⣠⠾
⠀⠀⠀⡍⡶⣤⣶⣅⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠳⢶⠂⡙⠢⢌⠂⠱⣎⣏⢳⣇
⠀⠀⠀⠳⣤⠀⠛⠓⠾⢄⡀⠀⠈⠑⢲⣤⡄⠀⠀⠀⠈⠻⣆⠈⢻⡆⢸⡟⠀⣻⡀
⠀⠀⠈⣷⣤⠀⠀⠀⠀⠈⢻⣀⢀⠀⠀⠀⡠⠇⡀⠀⠀⢘⣿⠀⣿⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠿⠿⠛⠓⠒⢦⣤⣼⠉⠀⠀⠑⠒⢷⣦⣽⡄⠀⠘⣿⠀⣿⡇⢸⣷⠀⣿⡇
⠀⠀⠀⠀⡀⠀⠀⠀⡾⠟⠿⣷⠀⠀⠀⢀⣿⠛⠛⣿⠀⢸⣿⠀⣿⡇⢸⢿⠀⣿⡇
⠀⠀⠀⣟⣁⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⣿⡆⠈⣿⠀⣿⡇⢸⣿⠀⢹⡇
⠀⠀⠀⠀⠈⠳⡀⢸⠀⠀⠀⢿⡀⠀⠀⣸⠃⠀⠀⢻⡇⠀⣿⠀⣿⡇⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡸⠀⠀⠠⢸⡇⠀⢀⡏⠀⠀⠀⠘⣿⡶⠿⢴⣿⣷⣾⣿⣶⣿⣷⣶⡆
⠀⠀⠀⢀⡀⢸⣿⠵⠀⠀⠐⣸⣿⠀⡼⠀⠀⠀⠠⠞⣿⣷⣶⣶⣶⣤⡤⠈⠉⠑⠟⠛⠛⠀⠀⠂
⠀⠀⠀⢸⣇⣸⣿⣦⡀⣤⣤⣿⣿⣷⡕⢀⠀⠀⢀⠀⣹⣿⣇⣿⠿⣿⣻⣶⡶⠓⣶⣦⡴⣼⠒⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⢷⣴⢶⣶⣿⣾⣿⣿⠻⢶⡆⣿⡿⢭⠅⣾⣯⣽⣾⣿⣤⣤
⠀⠀⠀⣿⣿⡛⠛⣻⡿⠫⠭⠿⠨⠭⠿⠿⠁⣿⡟⠋⠙⠙⠀⣉⣀⣯⣀⣀⣀⠀⢀⠀⣼⣿⠿⠿
⠀⠀⠀⣉⣉⣉⣉⣙⣤⣖⣦⣀⣀⣀⣴⣶⣦⣏⣀⣄⣀⣸⣭⣿⣽⣧⣤⣼⣿⣷⣿⣟⣁⣀⣀⣀
⠀⠀⠀⠿⠿⠭⠽⠤⠤⠤⠤⠤⠽⠿⠷⠿⠥⠼⠷⠿⠶⠤⠤⠶⠤⠤⠴⠴⠽⠷⠤⠤⠽⠷⠿⠿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⠿⠂⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⡄⠂⠀⠀⠀⠀⣠⣼⡆⠀⠀⠀⠀⠀⢀⣴⣿⠿⠝⠿⣳⣴⡆
⠀⠀⠀⠀⠀⢀⣤⣷⣾⣷⣦⣤⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠁⠀⠀⣌⣀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⡀⠉⠁⠀⠐⠿⠿⠟
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⣿⣿⣿⠟⣶⣧⡼⢿⣿⣿⡿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠻⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣄⣛⣟⢁⣼⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣷⠉⠓⠀⠀⠀⠀⡄⠀⣿⣟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠿⣿⣶⡆⠀⢠⣾⣷⣶⣿⠏
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠘⣿⣿⣿⣟⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠻⡟⠉⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠂⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣀⣤
⠀⠀⠀⣠⢴⣞⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⢻⣛⣛⣛⣛⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠛⣙⣿⣿⣿⠇
⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⢹⣿⡿⣿⣿⣟⢹⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⡀⠀⠀⠉⠉⠙⠋⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣈⡀⠀⢀⣴⣿⣴⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠝⠋⠛⢛⠟⠋⡇⣀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⡷⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠀⠺⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⣿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⠋⠁⠀⠀⠀⠀⠀⣼⠂⠀⠉⠉⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿


⠀⠀⠀⣤⣶⣾⣿⣿⣶⣶⣄⠀⠀⠀⠀⢀⣠⣤⣤⣦⣵⣤⣤⣀⠀⠀⠀⠀⠀⣴⠶⠶⠚⠛⠛⠛⠛⠷⠶⢦⡄
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢈⢛⣟⣛⣛⣛⣛⣛⢛⡁⠀⠀⠀⠀⠸⠶⢶⣶⣤⣤⣴⣤⡶⠶⠾
⠀⠀⠀⢸⣿⣿⢛⠛⣿⣿⠀⠀⠀⠀⢏⣻⠐⡇⢸⡇⢸⠀⣿⢰⣏⡇⠀⠀⠀⠠⣴⣄⣄⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠠⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⢸⣿⠉⣿⠿⢙⣿⠀⠀⠀⠀⠀⢹⠈⡇⢸⡇⢸⠀⣿⢸⡇⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠉⠨⠀⣀⠀⠀⠀⠀⠀⢹⣶⣾⢻⣶⣾⣻⣷⣾⡟⣷⣶⡏
⠀⠀⠀⢸⣿⣷⣾⣶⣿⣿⠀⠀⠀⠀⠀⢸⡀⣷⢸⡇⢸⠀⣿⢸⠇⠀⠀⠀⠀⠀⢉⡋⠛⠛⠓⠛⠛⠉⣉⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⢹⣿⣿⡇⣿⣿⡇
⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⢸⣇⣿⢸⡇⣸⠀⣿⣸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣶⣶⣾⣿⡏⠀⠀⠀⠀⠀⠶⠿⠿⠾⠿⠿⠾⠿⠿⠷⠿⠿⠶
⠀⠀⠸⠟⠿⠿⠿⠿⠿⠟⠿⠀⠀⠀⠀⠀⠺⠭⠽⡧⡿⠭⠽⠒⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⠿⠿⠟⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣠⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣟⠁⣠⣿⣴⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠻⣿⡷⠀⠀⠀⠈⣷⠘⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠸⠷⠿⠀⢻⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⣿⣿⣿⠀⢀⡴⢛⡟⢻⠟⠉⠉⣿⠀⠀⠀⠀⠀⠰⣶⣾⡿⠋⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣩⡶⠿⠛⠉⣿⡴⠋⠀⠀⣰⠋⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⡵⠛⠉⠀⠀⠀⠀⣿⡀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⢁⡖⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣰⠃⠀⠀⠀⠀⠀⠀⣸⣇⣀⣠⣤⣀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⢀⡴⢷⡟⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⣠⠞⡩⠛⣿⣧⡈⢿⡷⣄⠀⠀⠰⣿⠿⣷⡀⠀⠀⠀⡀
⠀⠀⠀⠀⡞⠀⢾⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⡠⠞⡡⠋⠀⢀⣿⣿⡿⡌⢷⡘⢧⠀⠀⠀⠀⠘⣿⡀⠀⠀⡀
⠀⠀⠀⢸⠀⠀⢸⣷⣿⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡴⠋⠀⣼⠁⠀⠀⠈⣝⣿⣷⠹⣾⣇⠈⢳⡀⠀⠀⠀⢹⣷⣆⠰⠅
⠀⠀⠀⡼⠀⠀⣾⣿⣿⠟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣾⣤⠞⢶⣏⠀⠀⠀⠀⢹⡘⣿⡇⢹⣿⡀⠀⢻⡀⠀⠀⢸⣿⣿⣦
⠀⠀⢠⡇⠀⢸⣿⣿⠏⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⣾⣻⣿⡿⠉⠀⠀⠀⠹⣧⠀⠀⠀⠀⠑⠉⠀⠈⢿⣇⠀⠘⣧⠀⠀⣼⣿⣿⣿⡇
⠀⠀⢸⡇⢀⣿⣿⡟⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣼⢋⡟⣱⡟⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡄⣰⣿⣿⣿⣿⡇
⠀⠀⠈⢧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣠⣿⢃⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠋⣠⣿⣿⣿⣿⣿⡇
⠀⠀⣰⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⡸⢡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⢀⣀⠀⠀⡿⠀⠀⣰⠟⡿⣧⢻⣿⣿⡇
⠀⢀⣿⡄⠸⣿⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡿⢷⣾⣿⠻⡆⠀⣧⠀⣴⠏⠀⢹⣿⢸⣿⣿⡇
⠀⠀⢻⣇⠀⢻⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⣀⣀⡤⠞⠋⢰⣇⣿⣇⢻⡇⢻⡄⢿⣸⡏⠀⠀⠀⣿⠀⣿⣿⠁
⠀⠀⠀⠻⣧⡀⢻⣧⢻⡄⠀⠀⣤⡄⠀⠀⠀⠀⠸⣿⡇⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⢸⣿⠇⣿⢸⣷⠈⢻⣾⡿⠁⠀⠀⠀⡿⢰⣿⣿
⠀⠀⠀⠀⠈⢳⣄⠹⣿⣷⣴⠾⡟⠙⠶⣤⣄⡀⠀⣿⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⣿⣿⠀⠸⣿⠀⠀⠀⠀⢸⠇⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢦⡘⢿⣿⠀⣇⠀⠀⠀⠉⠛⢷⣿⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣷⠀⠀⠀⠀⣾⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⢻⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢛⡅⠀⣿⠀⠀⠀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡸⠃⠀⣿⢀⣀⣠⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣀⣀⣤⡴⠶⠖⠛⠛⠖⠻⠶⣾⣿⡿⠿⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⢀⣤⣴⣶⣦⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣞⣡⠴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠟⠛⣉⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣴⣿⣿⡿⠟⠋⠉⠀⠀⠉⠙⠛⠿⠿⠶⣶⡶⠒⠓⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⡴⣦⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠠⢿⡿⠛⠛⠻⠿⣿⣿⣿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣠⣶⠟⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣤⡄
⠀⣴⣿⠏⣠⠏⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⣿⣿⡶⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⣻⣿⠇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠁
⢠⡿⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⣟⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠹⣦⣀⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⠀⡀⣄⠀⠀⢀⡀
⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠷⠶⣆⡉⣒⡄⠀⠈⠻⢦⣄⣈⠉⠹⣧⡄⠸⡇
⠀⣬⢱⣷⣦⢾⡁⠐⠐⠂⠀⢀⠀⠀⡀⠀⣈⠈⠉⠸⡶⢛⣔⠀⢀⠻⡌⢶⣹⡇⢠⣿
⠀⠻⣆⣄⠈⠛⠢⠶⣤⣀⠀⠀⠈⠒⢠⠀⣈⠃⠀⠀⠀⠀⢹⣧⠀⠰⣿⠀⢹⡟⠀⢻⡆
⠀⣷⣌⣁⠀⠂⠠⠀⠘⢻⣇⡀⡀⠀⠈⠀⠈⢰⡄⠀⠀⠀⠘⣿⡇⢸⢿⠀⡟⣷⠀⠿⣷
⠀⢛⢿⣯⠤⣆⣤⣄⣀⡐⣿⠋⠑⠘⠦⠤⣄⣀⠒⣷⡀⠀⠀⣿⡇⢸⣿⠀⠃⣿⠀⡀⡿
⠀⠀⠁⠀⠀⠀⠀⣽⣿⣷⣿⡀⠀⠀⠀⠀⣬⣿⣿⣿⣧⠀⢠⣽⡇⢠⣽⠁⣆⣿⠀⡒⣇
⠀⠀⠀⢀⠀⠀⠀⠉⠉⠉⣽⡇⠀⠀⠀⠀⢸⠀⠀⢹⣿⠀⠘⢿⡅⠠⣿⠀⣃⣿⠀⡯⡟
⠀⠠⠀⡀⠂⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠐⠙⠀⠀⢸⣿⡄⠀⣿⡄⢸⣿⠀⡇⣿⠀⠅⡇
⠀⠀⠀⠀⢻⡀⠐⠀⠀⠀⠸⣿⠀⠀⠀⡀⡇⠀⠀⠀⣿⣇⠀⣻⡃⢸⣿⠀⣇⣿⠀⢄⡷
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡆⠀⢀⠀⠀⠀⠀⠀⢹⣿⡾⠿⢗⣿⣿⣷⣿⣿⣾⣿⣿⣿⣶⡆
⠀⠀⣀⠀⢸⣿⢰⠀⠀⠀⢆⣼⣧⠀⠀⡀⠀⠀⠀⡠⢺⣿⣷⣴⣶⣶⣤⣤⡄⠋⠋⠳⠿⠛⠛⠛⠂⠒⠐
⠀⠀⣿⡇⣼⣿⣆⠀⣀⣀⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠊⣿⣿⡍⣿⣿⣿⡷⢶⣤⡤⠶⢦⣦⣀⣄⣶⠴⠂
⠀⢶⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣇⣠⣀⣀⣴⣧⣾⣿⣿⣛⣩⣥⢸⣟⡜⠻⠃⢴⡿⣛⣯⣶⣿⣀⣀
⠀⣼⣿⣟⣻⡿⣿⣿⡿⠻⢿⠍⠽⢶⣷⣶⡎⣿⣽⣿⠟⠿⡿⠐⠲⠋⢼⠏⠁⠉⠙⠛⠛⠛⠻⣿⣿⣿⣿
⠀⢿⣿⣿⣤⣴⣾⠛⢉⡉⠉⠀⠉⠉⢉⣉⠁⣿⠟⠀⠀⠀⡠⢤⣴⠶⡾⠓⠒⣦⣶⣂⣤⣄⡾⠛⠋⠉⠉
⠀⣤⣤⣤⠤⡤⠼⠶⠯⠽⠶⠶⠶⠶⠾⠿⠷⠿⣦⠶⡤⠦⠷⠶⠿⠶⠷⠶⠶⠿⣿⡿⠿⠿⠶⡴⠦⢤⣤
⠀⠚⠚⠓⠒⠛⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠒⠛⠛⠛⠒⠒⠒⠛⠒⠒⠒⠒⠚⠒⠓⠒⠒⠒⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⡤⢴⣶⣶⣶⢦⣄⡤⠖⠛⣛⣛⠲⣄⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡫⢵⣾⠯⠿⢿⣡⠞⠛⢀⠈⠙⢦⠝⠁⠀⠚⠛⠛⠲⠬⠺⠿⣿⣯⣭⣭⣟⠙⠷⡆
⠀⠀⠀⠀⠀⠀⠀⡰⢫⡴⢿⣴⠥⡨⠋⠉⠀⠽⠚⠋⠚⠀⣄⠀⠀⠀⢠⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠈⠻⡅⠀⠿⠷⢶⣄⡀
⠀⠀⠀⠀⠀⢠⢞⢵⠏⠴⢖⡟⠀⠁⠀⡀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⡇⠀⢠⠁⠀⢠⠀⢀⠤⡀⠉⠀⠈⠙⠂⢳⠇
⠀⠀⠀⠀⠀⡇⣏⠄⣠⢠⠀⠠⡆⠀⡄⡇⠀⠀⡀⡇⠀⠀⢸⠆⠀⠀⠸⣄⣸⠇⠀⣼⠀⠀⡾⢰⠁⠀⡇⢀⣶⠀⠀⠀⠸⡝⣶⣄
⠀⠀⠀⠀⠀⠑⣼⣧⡌⢀⡀⠀⠘⣎⠀⠙⠄⢀⠇⠹⠐⢲⠤⠁⠁⠀⣠⣺⣁⠀⠀⠀⠀⠀⠃⠸⣀⠔⢁⠞⢸⠀⢀⡔⢠⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠣⣿⣛⠷⢉⠆⠀⠘⠆⠀⠀⠀⠀⠀⠀⢠⠀⢠⡀⢀⠯⠭⠿⠀⣰⣤⣄⠀⠘⠀⠀⠀⠉⠀⢸⡠⠋⢀⣴⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⡠⣠⡄⣠⣤⣄⣈⣈⣽⣷⣾⠨⢸⣿⡧⠀⠀⠀⣿⣿⣿⡿⠤⠤⢄⣀⣀⣀⢤⣌⣁⣰⣿⣿⢛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢽⣿⣿⠇⡾⡿⣏⠀⠀⡿⡟⠀⠘⡿⣇⣀⣀⡀⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣾⣟⠛⠻⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⠀⠀⣳⡇⠀⢀⣿⡇⠀⠀⠀⠿⢿⣤⡅⠀⠀⠈⢹⣿⣿⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢻⣿⣿⢀⠀⣿⡆⠀⠘⣿⡧⠐⠀⠀⠀⠨⠄⠃⠀⠀⠀⣸⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠀⣸⣿⠋⠀⢀⣿⠄⠤⠄⢫⣄⡀⡀⠀⠄⠀⠀⠀⠀⠀⠀⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠿⢿⡄⠀⣼⠃⠂⢠⣶⠁⠀⣁⢡⡜⠉⠤⠀⠀⢽⠀⠄⣿⠀⣀⠀⠀⣶⣦⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣽⣿⣿⣿⣦⣾⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣵⣼⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉
⠀⠀⢀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⠉⠀⠐⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠘⢆⠀⠀⠀⠀⠀⠈⠁⠘⠲⠦⢀⢄⡀⠀⠀⠀⠀⢠⡄⠀⠀⡄⠐⠂⠶⠖⠲⠂⠀⠉⠛⠋⠁⠰⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠋⠀⠀⠹
⠀⠀⠈⣄⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠶⠆⠠⠞⠋⠉⠁⠀⠀⠀⢀⣤⠖⡄
⠀⠀⠀⠙⣆⠘⣦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⡜
⠀⠀⠀⠀⠘⣧⠀⠽⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠘
⠀⠀⠀⠀⠀⢻⣆⠒⠂⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⣹⣿⡆
⠀⠀⠀⠀⠀⢸⡿⣷⣐⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢤⣿⡿⣽⠃
⠀⠀⠀⠀⠀⢹⣿⡾⢿⣿⣿⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠄⣸⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠓⠁⡀⠦⣭⡝⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⣿⠋⢀⡿⠀⡀
⠀⠀⠀⠀⣠⡄⠀⠀⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢣⠀⠈⠁⡾⠁
⠀⠀⠀⣀⡤⠀⠀⠀⢀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⠰⣦
⠀⠀⠀⠈⠙⠂⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⢳⡄
⠀⠀⠀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠛
⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠙⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠿⠿⠿⠿⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣶⣶⣶⣷⣶⣦⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢻⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⢉⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⢻⣿⣿⣿⡿⣾⡷⠀⠀⠀⠀⠀⠀⠀⣼⠿⠆
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠂⠀⠀⠀⠀⠀⠀⠀⡛⣷⣾⣾⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀⠀⣠⡇⠀⠘
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢰⡦⣿⡏⣱⣼⣿⣼⣗⣿⣿⣴⢠⡴⣦⣰⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⣠⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣦⣰⣮⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠃
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⠻⣯⣿⡟⢉⡽⣻⣿⡿⠻⡛⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢿⡟⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠉⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⠀⠀⠋⢸⠇⠀⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠈⣯⡀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣀⢢⠄⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣀⢴⡟⢠⣶⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠅⣰⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠘⢤⣦⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⣎⣿⡁⣟⣠⠉⠀⠐⠀⠀⡀⠀⠃⢈⡄⡠⡞⠀⠀⠀⠠⠀⠠⢠⠀⣄⢠⡅⣿⢧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⢧⠹⣞⠙⢢⡃⣴⠃⠘⠀⡀⢀⠘⣀⣼⣡⡞⢰⣤⠀⡀⣴⡯⣺⠃⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠛⢹⣾⠀⣙⡇⢼⡆⣿⡿⢋⡙⣟⢟⣱⣿⡟⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⠈⢷⠀⡁⠙⠡⣺⡿⠛⠛⠁⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣒⣶⣖⣒⣶⣖⣖⣲⣄⠀⠀⣤⣤⣤⣤⣤⣴⣖⣒⣒⣒⣒⣒⣒⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠇⠀⠘⣯⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠈⢿⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠀⠀⠉⠀⢰⡇⠀⠀⠀⠀⠈⣇⠀⠀⠁⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⣶⢲⣦⠀⠀⢸⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣿⠀⠀⠰⣷⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠸⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡇⠀⠀⠀⠀⠀⠀⠀⣏⣤⡀⠀⠀⠀⠀⢸⣧⣄⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⣧⡀⢀⠀⡀⢀⠀⣀⣿⠀⡇⠀⠀⠀⠀⡏⡔⢲⡽⡆⢀⠀⢀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⡼⠻⣧⣼⣤⣷⣬⣦⡽⠻⣤⠇⠀⠀⠀⠀⠳⣽⣯⣼⣧⣬⣦⣼⣦⡽⠃





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠠⠤⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣨⣧⣥⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣶⣶⣶⣶⣦⠀⠀⠀⠀⠰⢀⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⣿⡿⢿⣿⣿⡿⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣉⠛⠲⢿⡛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⡝⣿⣿⣄⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠘⡡⣾⣿⣿⣦⠀⠀⠀⠀⢀⢈⠉⠉⠀⡄⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠷⣿⣿⣿⣿⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣠⣤⣤⡐⠡⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠛⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣴⣖⢻⢛⠉⢰⣿⣿⣿⣿⣿⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣸⠏⢈⠄⠉⢀⡟⠻⠿⣿⣿⣁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⠀⠀⠀⠀⠀⠀⠠⣄⠰⡀⠀⡿⣻⣿⠇⠀⠁⠀⠈⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠃⠃⠀⠀⠀⠀⠰⠦⠾⠀⠃⠀⡠⠟⠁⠀⠀⠀⠀⡔⢠⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠠⠠⠠⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⣁⣀⡒⡀⠀⠀⠀⠀⣀⡠⠐⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣤⠖⢛⣉⠁⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⢠⡞⢁⡞⠋⠀⢀⡴⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣾⠀⢸⡇⠀⠠⡏⠀⠀⠀⠈⠉⠳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡖⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⢻⡄⠈⠳⣄⠀⠙⢦⠀⠀⠀⠀⣠⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠙⡆⠀⠈⢳⠀⢸⡇⠀⢀⡞⠁⠀⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⣼⠁⠀⢀⡞⠀⡼⠀⠀⢾⠀⠀⠀⠠⣄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢰⡇⠀⢀⡞⠀⢸⠃⠀⠀⠈⠳⠄⠀⠀⠈⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡏
⠀⠀⠀⠀⠈⣧⠀⠘⣇⠀⠈⠧⣄⡀⠀⠀⠀⣀⣠⡴⠃⢠⡏⠀⢀⣤⣤⣤⣤⡤⠴⠶⠶⠏⠀⠀⠀⠀⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠘⢦⡀⠈⠳⠦⠀⠀⠙⢦⠀⠀⠉⠀⣀⡴⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⢤⡄⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⢸⡷⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠘⢧⡀⠀⠀⠀⢸⣇⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠶⣤⣀⣀⠙⠶⠶⠖⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠈⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⣀⣀⣀⣠⡤⠶⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⣤⣤⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⣿⡀⢈⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⠛⠋⠁⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠂⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠄⠀⠀⠀⠀⠀⢤⣀⢀⣠⠄⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣁⡇⠀⣀⣀⣀⡀⠀⠈⠋⠀⢀⣀⣀⣀⠀⢰⣆⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⢃⣾⣿⣿⣿⣿⣆⠀⠀⢠⣿⣿⣿⣿⣿⡌⢿⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡇⢸⣿⣋⢙⣿⢏⠅⠀⠀⠈⡝⣿⡏⣙⣻⣿⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠃⠘⠷⠼⠿⠷⠯⠊⣾⣷⡑⠪⠞⠿⠯⠾⠃⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠉⠙⠒⠜⠇⢸⣿⣿⡇⠠⠣⠒⠛⠉⠉⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣶⡖⠀⡄⠀⠸⠾⠗⠄⠀⢠⡄⠐⣶⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠳⣘⠃⠀⠀⠀⠀⠀⠀⠈⣃⡜⡹⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠸⡄⠙⡻⠶⣦⣤⣦⣤⠶⠾⡛⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⣠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡙⠀⠀⠀⠀⠈⡀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠍⠀⠀⠀⠀⠈⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢶⡒⠒⠶⣶⡶⠞⠋⠉⠉⠉⠙⠓⠶⠦⣤⣤⠶⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⠀⠈⠷⠀⠀⠋⠀⠀⠰⡄⠀⠀⠀⠀⠀⠘⠋⠀⢀⡀⠀⠀⣿⣷⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣟⠳⢤⡈⠛⢦⣀⣴⢦⣤⡦⠶⣶⠿⣤⣄⡀⠀⠀⠠⠀⣠⠞⠀⢀⢠⡿⠉⢷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠉⢳⡦⠤⣤⣀⣿⠠⣞⠁⢤⡀⠸⣄⠀⢨⡟⠻⣟⠛⢾⡗⠶⢦⣾⠈⠁⠀⣠⡟⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⣴⠋⢤⠀⢀⡴⠋⠀⠀⠈⠉⢻⣤⡼⠷⢦⣍⣀⣈⣀⣼⣃⣀⢌⣉⣈⣉⣷⣀⣹⣟⣄⣠⣯⠀⠀⠄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢈⣤⠀⠀⠀⠀⣴⠟⠙⢧⢀⡀⠀⠉⠉⠉⠉⡿⠙⠻⠿⠿⢯⡍⠉⠉⠉⠀⠀⠻⡄⠀⠀⠀⠀⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠋⠀⠀⠀⠀⠚⠁⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠘⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠻⣆⠀⠀⠄⣤⠀⠀⡀⠀⣷⠀⠀⠣⠂⣤⠀⠀⠀⠀⠠⠀⠈⢧⠀⠀⣄⠀⠀⠀⠀⡆⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢤⡄⡇⠀⣈⣤⡤⣼⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⠞⣧⠀⣀⣤⠴⠦⣄⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⠟⠋⠉⠀⠀⠈⠛⠛⠛⠛⠓⠒⠒⠖⠖⠒⠋⠀⠀⠈⠉⠉⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠰⡂⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢿⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣼⢃⠀⠘⠉⠓⠶⡄⠀⠀⠀⢸⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⣟⠂⠀⠀⠀⠁⠀⢹⡄⠀⠀⠀⠻⣟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡇⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠙⠲⢦⡈⠂⠀⣠⡟⠀⠀⠀⠀⠀⠈⠳⢮⣟⡲⠦⢤⣤⣤⣤⣀⣀⣀⣠⣤⠴⠖⣛⣭⠞⠋⠀⣠⢶⠛⢻⠉⠉⠙⣇
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋⠀⣠⡴⠞⢦⡀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠤⠤⠤⠤⠶⠶⠚⠋⠉⠀⠀⠀⠀⣏⠈⠆⡀⠀⣈⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⡈⢿⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣤⣷⣋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡳⣤⣙⠀⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣍⣛⣻⡶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⠶⣶⣿⠿⣶⡾⢿⣶⣦⣶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣿⠋⣤⣶⣤⡙⢿⠀⠈⠁⠀⠈⠀⠈⠉⠀⢀⣿⠿⠛⣛⠛⠻⣷⣄
⠀⠀⠀⢠⣿⢿⡏⢸⣿⡿⠍⠁⣠⡴⠶⠶⠄⣾⠗⠛⠳⠆⠉⠰⠾⢿⣿⣿⡄⢸⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣦⣤⣄⣤⣀
⠀⠀⣴⣾⠟⠀⠻⠀⠀⠀⠀⠀⣡⡴⠶⠒⢶⣿⠞⠛⠳⢦⣄⡀⠀⠉⠻⠿⢀⣾⠟⢛⣿⣧⣤⠀⠀⣤⣶⣶⣾⣿⡛⠻⠿⠙⠻⣿⣿⣷⣦⣄⡀
⠀⣠⡿⠟⠛⠛⠀⠀⠀⠀⣀⣨⡵⠖⠛⠛⢲⡇⠲⠒⠒⠶⢤⡀⠀⠀⠀⠀⠈⠁⠀⠿⠛⣿⣿⣤⣶⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠙⣿⣿⣆
⠘⣿⡿⠛⠋⠀⠀⠀⠀⠀⠉⠁⢀⣠⠄⠶⢛⡛⠷⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⣷⡀
⢰⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠾⣿⣿⠿⠛⠛⠛⠿⢿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣷
⣸⣿⡟⣉⡀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣴⡿⣿⢿⣶⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡏⠁⠀⠀⠈⣿⣧⡀
⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⣼⠃⠠⢀⠻⢷⡷⠿⠋⠠⢀⡀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣿⣿⣦⣀⡀⢠⣤⣀⣠⣶⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠠⣿⣿⣷⠶⠀⠀⠀⠀⠰⠇⠐⠀⠂⣠⣾⣿⣦⡀⠋⠰⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠙⠛⠻⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣿
⠀⢹⣿⣧⡖⠀⠀⠀⠀⠀⠀⠛⠶⠻⡏⢸⡇⢈⡿⢦⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣘⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠈⠻⣿⣶⡿⣃⣀⠀⠀⠀⢠⡀⠀⠻⠶⡴⠟⠁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⠟⠉⠀⠀⠀⠀⠙⠷⢶⠾⣷⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⣦⣀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⢠⣿⡟⢿⣷⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢸⣿⡇⠀⠈⠉⢡⡿⢠⡖⣠⠄⢀⡄⠀⠀⠀⡀⠠⣆⣄⠘⣦⠀⣄⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢿⣇⠀⠀⠀⢿⠇⣿⣴⣿⠄⣼⣇⢸⡇⢠⣿⠈⣿⣿⠀⣿⢀⡟⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⣿⣦⠀⠀⠈⠀⠻⣿⢿⢸⡿⣿⣿⡇⠀⡿⠀⢿⡟⠀⠟⠈⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⢻⣟⠓⠀⠀⠀⠀⠘⠈⠘⣧⠉⣿⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣤⣤⣶⣶⣿⡿⠟⠋⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⢻⣿⡏⠉⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋
⠀⠀⠀⠀⠀⠸⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠹⣿⡟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⠋⣽⣿⠀⠀⠀⠀⠀⠈⢻⣿⣤⡀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⠀⠀⠉⠻⠷⢶⣶⣶⣶⣶⡶⠾⠟⠋⠁⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⢀⣸⣿⢹⣿⢷⡄⠀⠀⣤⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⠀⠀⠀⠀⠀⣀⣿⡟⢹⣧⠀⠀⠀⠀⠀⠀⢰⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠛⠃⢸⣿⠇⣼⣧⣤⣤⡄⢀⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣄⡀⠀⠀⠀⢻⣿⠁⠀⣿⡀⠀⠀⠀⠀⠀⣨⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣯⣴⣶⣆⣠⣾⢯⣾⢛⣁⢀⡀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⢠⣾⠟⡋⠉⠛⠃⠀⣰⡿⠋⠀⠀⣿⣷⡶⠦⡄⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁⠘⢿⣿⣷⣿⣷⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣾⣧⣴⣇⢀⣰⣿⠁⠀⠀⢸⣟⢀⡄⢀⡄⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠾⣿⣾⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⠁⠽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⢛⣒⣒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣥⣤⣴⣶⣾⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⢋⣤⣿⡟⢉⠀⠀⠙⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡿⣿⡿⠛⡻⠟⠉⠀⠀⠁⣹⣯⣿⡿⠿⢦⣤⠀⣠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡶⠾⠷⠈⠀⠀⠀⠀⠠⢞⡋⠉⠁⠀⠀⠀⠀⠛⢛⣋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⡶⠚⢻⣆⠈⠀⠀⠀⢀⡼⢤⣒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⠿⣿⡶⠖⠶⠖⠒⠒⢿⣦⠀⢀⣾⡿⠛⠬⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣟⣻⢻⣿⣿⣿⡷⠀⠀⠀⢀⠀⠈⣿⣷⣼⣇⠀⣤⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⢿⣷⠛⢷⡄⠻⣧⠘⠹⣷⠋⣿⡆⣽⡟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣽⣿⣿⣿⣿⡟⣿⡀⢸⡇⠀⣿⠀⠀⣿⠀⣿⠃⣽⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⣿⠀⠀⣿⠀⣿⠂⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⣿⠀⢀⡏⠀⣿⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⢸⡇⠀⣿⠀⢸⡇⢰⣿⢸⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢈⣿⠀⣿⡀⢸⡇⢸⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⢷⣼⣿⣿⣿⣿⣿⣯⣿⡍⣿⠀⢸⡇⢸⣧⢸⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⡇⢀⣿⢸⣯⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⢫⡿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡆⠈⡇⠈⣿⢸⡗⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠊⣴⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠁⠀⠟⢸⡧⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣿⣿⣿⣿⣿⣿⣛⣻⡿⠿⠸⠃⢠⡄⣀⣙⣨⡥⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣽⣿⣿⣿⡟⣿⣿⣿⣿⠿⠀⠀⠀⢰⣧⠈⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣟⣿⣿⣿⣿⣿⣆⡀⠀⠀⣸⣿⣤⣼⡷⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠈⠉⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠤⠄⠀⢰⣶⣦⠈⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠇⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⢄⡀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⠀⠤⠀⣬⢻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠈⠀⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠇⠶⠟⠓⠘⠛⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⡟⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡄⠄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠠⠄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿
⡇⠐⠒⠒⠛⠙⠃⠈⠀⠐⠛⠋⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠛⠻⠿⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣥⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠗⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣧⣄⣀⣀⣀⣀⣀⡀⡀⢀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣶⣶⣶⣤⣆⣀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠚⠋⣉⣉⡂⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣛⢙⡃⠀⠔⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠛⠛⡗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠰⠤⠤⠤⣾⡀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠙⡏⠙⠉⠉⠉⠉⠋⠉⠋⢹⠁⠀⠀⠀⠙⡋⠙⠉⠙⠉⠉⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠁⠄⠁⠄⠁⡇⠀⠀⠀⠨⠈⠠⠀⠠⠀⠁⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠁⠃⠁⠀⢱⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠅
⠀⠀⠀⠀⢰⠂⠀⠛⠁⠘⠀⠘⠁⠊⠃⠀⠑⠘⠋⠉⠀⠈⠉⠁⠘⠀⠘⠀⠈⠑⠈⠓⠈⠛⠀⢲
⠀⠀⠀⠀⢸⠀⠀⠀⣏⣀⣀⣈⠀⠀⠀⣇⣀⣀⣈⠀⠀⠀⠀⣏⣀⣀⣀⡇⠀⠀⣇⣀⣀⣈⡇⢸
⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⠀⢸⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢇⣀⣀⣀⠀⠀⠀⣇⣀⣀⡀⠀⠀⠀⠀⢇⣀⣀⣀⠇⠀⠀⣇⣀⣀⣠⠇⢸⣀⣀⣀⣀⣸⡀⠈⠳⡀
⠀⠀⠀⠀⢸⠀⠀⠀⡠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⡠⠄⠄⠤⡀⢸⠒⠒⠒⠦⠤⣘⡄⠀⢣
⠀⠀⠀⠀⢸⠀⠀⠀⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠃⢸⠆⢀⣤⣶⡄⠈⡇⠀⢸
⠀⠀⠀⠀⠘⠒⠂⠒⠀⠒⠒⠐⠂⠒⠐⠒⠒⠀⠐⠒⠀⠀⠐⠃⠀⠒⠒⠒⠂⠂⠐⠒⠀⠒⠂⠚⢰⠋⠀⠀⠘⠀⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠢⠤⠔⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣯⣭⣭⣭⣭⠙⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠉⠉⠠⠾⠛⠀⠀⠀⠀⠀⠀⠛⠧⠀⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣶⣤⣤⣤⣀⣐⣒⣒⣒⣒⣀⣀⣤⣤⣤⣶⣾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠟⣒⣲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣙⣛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠾⠿⠛⢛⣉⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⢻⣿⠛⠻⢷⣶⠶⠶⢶⣾⠟⠛⣿⡟⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡏⠀⠀⣿⡇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⠇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⠀⠀⢸⣿⠀⠀⣼⡇⠀⠀⣿⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⡄⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⣤⣼⣿⣀⣀⣿⣧⣤⣼⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣰⡾⠋⠀⠀⠉⠉⠉⠁⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠄⠒⠀⠐⠲⠊⠒⠒⠊⠐⠄
⠀⠀⠀⠀⣠⣾⣯⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠴⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣷⣶⣄⡤⠀⠀⠀⠠⠴⠷⡄⠀⠀⠱⣄
⠀⠀⠀⠈⣽⣍⠈⠀⠀⠨⣳⣇⣠⣶⢂⠀⠀⠀⣀⣤⣯⣀⠀⠀⠀⠀⠀⠀⢴⣾⠀⠸⣿⡿⢀⣠⡴⠂⣤⠶⠀⠈⣈⣃⡀⠙⡄
⠀⠀⠀⣨⠏⠀⠀⠀⠀⢀⣨⡿⠉⠿⠣⠄⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠸⠁⠀⠉⠥⠈⠀⢠⡆⠀⠀⢉⡁⠀⢁
⠀⠀⠀⣴⠂⠀⠀⠀⠚⠟⠛⣠⣄⠄⢀⢀⠶⠶⣂⠤⠃⢈⡽⠖⠂⠐⣿⡈⢻⠄⡀⠀⠀⠀⠀⢰⡀⠀⠀⠻⠿⢖⣦⣾⠃⠀⠸⠄
⠀⠀⠀⢽⢀⠤⠒⠂⠀⠀⠀⠀⠁⠀⢉⡉⠛⠛⠁⠀⠀⠘⠁⠀⠀⣰⠋⢻⡆⠀⠁⠀⠀⠀⠀⠀⠁⢴⢷⣶⣿⣟⡛⠋⠁⠀⠾
⠀⠀⠀⡲⠁⠀⠿⣭⡀⠀⠀⠀⠀⠀⠾⢿⡅⠀⠀⠀⠀⠀⢈⡧⠐⠉⠇⠸⣏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠛⠿⠳⠆⠀⢠⡇
⠀⠀⠀⠳⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⣻⣆⡀⠀⢠⣼⡄⠻⠄⠀⠰⠴⠀⠀⠀⠀⠀⢾
⠀⠀⠀⢀⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡄⠀⠀⠀⠀⢸⠅⠀⢰⠄⠐⠿⢿⣷⡐⠘⣏⠉⠀⠀⢀⣄⡀⠀⠀⠀⣦⡾
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣇⠀⢠⣾⠀⠀⠀⠀⣼⢀⢠⣄⠈⢈⣧⠀⠈⠀⠀⠀⠋⠉⠻⡻⢦⣤⣿⠟
⠀⠀⢼⣷⠀⠀⠀⠀⠀⠀⠉⢳⣭⠀⢀⣾⠈⡗⠀⠸⣿⢧⠀⠀⡄⠙⣿⠀⣿⣦⡈⠙⠻⣦⣄⡑⣌⣦⠀⠀⠀⢀⠈⡇
⠀⠀⠀⢿⡇⠀⠀⠀⠈⠉⠉⠉⠈⢻⠋⢻⢀⣿⣄⠀⣿⡈⢏⠀⢶⠄⣻⡀⢻⠘⢷⣆⣀⡈⠉⠛⢺⣿⣧⣷⡦⣮⠾⠃
⠀⠀⠀⠸⣇⢀⡀⠀⣀⠀⠀⠀⠀⠸⠀⢸⡿⣿⠿⢿⣧⣵⣿⣧⣼⣶⣾⡇⣸⠀⠀⠉⠻⠁⠀⠀⠀⠀⠉⡟⠁
⠀⠀⠀⠀⠉⠛⠻⣿⡟⢀⠀⠀⡰⠞⢁⡟⠀⠁⣴⠊⠀⠀⠀⠀⠀⠀⠈⢀⣌⠀⡀⠀⠀⠀⠀⡔⣲⠏⠔
⠀⠀⠀⠀⠀⠀⠀⠹⢻⠧⠏⢈⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⠉⡄⠀⣾⣰⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⢤⠚⠀⢸⣗⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡀⠀⠈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠋⠀⠀⠹⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠾⣿⠀⠴⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡂⠀⠀⠀⠄⠓⠲⠆⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠏⠠⣔⡽⠛⠶⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣂⣐⠒⠒⣢⢱⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡂⠁⠀⡠⠀⠀⡠⠂⠀⠀⠐⢄⠀⠠⢀⠀⠀⢂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⠁⠒⠂⠀⠀⠀⠤⠤⠬⠤⠤⠤⠤⠤⠤⠥⠤⠤⠀⠀⠐⠒⠒⠈⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠄⡀⠀⠀⣀⡀⠀⠀⠐⠀⠐⠂⠀⠀⣀⣀⠀⠀⢀⠤⢤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠂⢤⠀⠀⠀⡇⠀⠈⠀⠀⠇⠀⢸⠀⠀⠆⠀⠀⠀⠀⠃⠀⠀⠀⢠⠀⡤⠐⢂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢃⠈⠲⠀⡀⠀⡇⠀⠀⠀⠀⠄⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠖⠁⡘⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⢤⡀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠁⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡇⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⡇⠀⡁⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠤⠇⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠠⠄⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣁⠒⠤⠀⠁⠒⠁⠀⠀⠄⠸⠀⠀⠈⠒⠁⡀⠤⠒⣈⠤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢈⡑⠂⠀⠠⠌⠉⠉⠁⠈⠉⠉⠥⠄⠀⠐⢈⠡⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠦⠈⡁⢉⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠄⠲⣤⠀⡀⡤⢈⠕⠂⠠⣠⠞⠉⠉⠳⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡠⠄⢀⠠⠔⠉⠀⠁⠀⠀⠀⠶⢎⣽⠿⠾⠇⠐⢿⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⠀⠄⠐⠀⠐⠀⠀⠀⣠⢀⡳⢶⠖⠉⠃⠀⣤⣔⡻⠃⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⡏⠀⠀⣀⠤⠄⠀⠀⠉⢀⣤⣄⣀⣤⡀⠀⠀⢀⠦⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠷⠀⠀⠀⠀⠀⣀⠀⡢⢤⣾⣾⠁⠀⠐⠁⠁⠀⠀⠐⢶⣛⣿⡏⠛⠙⠻⠻⣶⢶⡿⡒⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣀⣠⠖⠾⠞⠁⠀⠀⠈⢹⡀⣠⣆⣴⣶⠶⠤⠿⠺⢾⣛⣩⡗⠂⠀⠐⠄⠀⠀⠀⠀⣠⣀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⢀⣽⣿⣷⣿⣿⣥⡄⠀⠀⠀⠀⠀⢀⣸⣧⣾⣿⣟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠋⠙⡏⠁⠀⠀⠀⠀⠀⢸⣿⡛⠟⠛⠛⠃⠀⠀⠀⠀⢀⡀⢠⠔⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠁⠀⣣⢀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⢉⡁
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢉⠘⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊⠑⠐⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣟⠃⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠆⠀⣸⠎
⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸⣿⠂⠈⠀⠀⠀⢀⠈⣸⣿⡇
⠀⠀⠀⠀⢰⣿⣿⡇⢦⡀⠀⠀⠀⠀⠄⢰⡀⢀⣿⣿⡀⠒⠀⠀⠀⠈⣁⢸⣿⡇⠀⣀⡀
⠀⠀⠀⠀⣾⣿⡻⠨⠑⠁⠀⠀⠀⠀⠀⣄⢣⣾⣿⣿⣷⡇⠀⠀⠀⠀⢰⣼⣿⡇⠀⣿⡇⠀⣀⣀⡀
⠀⠀⠀⣼⣿⣿⡇⣄⠀⣄⠀⠀⠀⠄⠀⢨⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣾⣿⣿⣿⣤⣿⣇⣀⣿⣽⣿⣀⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣷⣿⡓⣄⠀⡐⠠⡎⢿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣟⣾⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⢀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣭⠻⢕⠌⠳⢌⠘⠿⠿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣝⣛⣛⣿⣿⣻⠿⢿⣿⣷⣿⡓⠛⠘⢛⣃⣘⡂
⢸⣿⣿⠛⠛⠛⠛⢻⣿⣿⣿⣕⠄⠀⢀⣀⣁⣴⣶⣾⣾⣦⣾⣿⣿⣷⣿⣄⣀⡀⣷⣾⣿⣿⣿⣵⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠃
⠈⠋⠉⠀⠐⠐⠘⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠐⠒⠒⠒⠒⠒⠒⠲⣞⣛⣻⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠛⠛⢛⣻⣿⣛⣛⣛⠛⢛⣛⠛⠉⠉⠉⠉⠉
⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⡄⠠⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⠤⠶⠦⢄⣤⣤⠄⠀⠀⠀⠀⢀⡴⠟⠉⠀⣐⠓⠀⠐⠲⠈⠙⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣰⠦⡬⣤⣆⣦⣬⣦⢴⣀⠀⠀⣀⡼⢟⠀⠴⠀⡈⠁⢰⠴⠀⢨⠥⠴⠤⢎⠻⠆
⠀⠀⠀⠀⠀⠀⠀⣼⡛⠂⡈⠂⣩⣠⠠⢬⡥⠠⣈⡉⠨⡀⠘⢻⡄⠌⠀⠁⠠⠁⠀⠀⢀⢙⠦⠤⠀⢀⠺⠶⢠⢦
⠀⠀⠀⠀⠀⠀⢠⢋⠀⢀⠔⡺⣯⣅⡀⠋⠁⣀⣍⡽⡖⠬⠠⢈⣱⡄⠆⡀⠀⠀⠘⢃⣰⣤⣡⣬⣀⡘⠒⠰⢀⠘⠣
⠀⠀⠀⠀⠀⢰⢂⡎⠀⡅⢺⡟⡉⠋⠠⡄⡠⠈⠋⡙⣿⠃⡄⠀⣇⢐⣠⣀⡉⢰⠰⠋⠁⠀⠀⠀⠈⠉⠙⠶⣿⡀⢠⡇
⠀⠀⠀⠀⠀⣼⠛⢅⡀⠈⣾⡔⠁⠀⠀⢀⠀⠀⠀⠙⢼⡇⠁⢄⡞⢋⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⡹
⠀⠀⠀⠀⠀⢸⠈⢍⣃⠀⡺⣀⡀⢀⡜⠆⠜⣦⡀⢀⡸⡣⢀⡘⡽⠸⡇⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢢
⠀⠀⠀⠀⠀⣇⠃⠌⢷⣄⠄⠴⠭⠁⠚⠉⠙⠂⠉⠵⠤⠄⣴⠏⠀⢋⡗⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇
⠀⠀⠀⠀⠀⡎⠀⢢⣤⣀⢀⠈⠰⢀⠀⠀⠀⢀⠐⠁⢀⢁⣀⣤⠆⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢷⡖⠀⠈⢻⡤⣤⣶⢀⠉⡀⠈⢁⠰⣦⡤⢤⠛⠀⠀⢦⢏⡀⠀⠀⠀⠀⠀⢠⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠈⢻⣦⠟⠚⠀⠈⠸⣮⠀⡁⡁⢈⡼⠉⠀⠘⠒⢷⣾⠋⠀⠓⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼
⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⠈⡜⡀⢨⡴⠈⠱⢬⠀⡘⣆⢠⢀⡾⠀⠐⢦⠑⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⢣⣰⢀⢀⠀⢀⣀⠰⣡⠇⣄⡼⠁⠀⢀⠀⠣⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⡅⠸⢉⠲⢊⠙⠀⣡⠞⠉⠀⠀⠀⠀⢳⣀⠈⢢⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢶⣬⡆⣾⣴⠾⠃⡀⠀⠀⣀⡄⠈⣾⠙⠛⠺⣻⡿⠀⠀⠀⠀⠀⠀⡀⠈⢆⡎⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡦⠀⠻⣟⣤⠆⠀⠘⠄⠠⡔⠸⣾⠁⠀⠀⠀⠈⢁⠱⡄⠀⠀⠀⠀⠙⠀⣄⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣠⠉⡕⠠⠀⢄⡀⠆⢋⡜⠁⠀⠀⠀⠀⠀⠈⠣⡙⢦⡀⠀⡀⡁⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⡵⠀⠀⠀⠀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⢷⣤⣀⠃⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠇⠀⠀⠈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣇⠈⢢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢠⠈⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠠⢤⡁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⣶⣿⠻⣿⣿⡁⠀⠀⠈⢹⣿⣷⣦⣄⣀⠀⠄⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠋⠀⢛⣍⣿⣷⣽⣿⣻⣦⡀⠀⣹⣿⣿⣿⠿⠉⣭⡘⠉⠉⠉⠉⠩⣬⣥⣼⣿⣿⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣠⢏⣨⣧⠀⠀⠸⣿⣿⠟⢁⣸⣿⡻⣷⣤⠾⠿⠃⠀⠀⠀⣀⣤⣤⣤⠄⣴⢚⣲⡿⠿⠆
⠀⠀⠀⣀⠴⠇⠀⢀⣤⠦⡈⢻⡷⠿⣿⡋⣿⠟⠁⠀⠀⠈⢘⣟⣀⣠⢜⣻⣿⣤⡙⢲⣶⠷⣶⣶⣿⣿⡿⣿⢳⡊⠛⠛⠛⠁
⠀⠀⠐⠁⠀⠲⠶⠿⠋⠐⠓⠚⠃⢰⢃⣿⠃⠀⠀⠀⠀⣨⢿⣷⣾⣿⣿⣿⣶⣿⠿⣭⣿⣿⣿⣿⣿⣿⣥⡟⢽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡏⠊⠀⠀⠀⠀⠀⠙⣂⣶⣿⣟⡯⢶⣽⣋⣹⢿⣻⣿⣿⣿⣿⠋⣵⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣇⠀⠨⣴⣾⣷⣄⢺⣿⡿⢯⣶⣯⣭⣕⣺⣿⣿⣿⣿⣿⣿⣿⣤⣬⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡌⡛⣿⣿⣿⣿⣼⣿⣿⣿⣽⣟⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⡿⢛⣱⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⢿⣿⣷⣈⠙⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢤⣴⣿⣿⡟⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠭⣟⠳⣼⣿⣿⣿⣿⣷⡉⢿⣿⠿⢿⣿⣿⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⠈⢽⣿⣿⠃⠀⣠⠔⣣⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⣈⠛⠝⠛⠿⠿⠷⠌⠿⠆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣻⣯⣛⠛⠚⠛⠋⠚⢁⣀⣤⡼⠿⠶⠶⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡶⢶⣶⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣴⣾⣯⣭⣭⣍⣥⣴⡷⠀⠒⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣎⠙⠒⢺⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⡀⠀⠈⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⣶⣶⣶⣿⣿⣬⣭⢵⢶⢶⣦⡭⣽⣿⣶⣶⠶⢦⣤⣤⣀⡀
⠀⠀⠀⢠⡖⣊⠉⠁⠀⠒⠈⠙⢉⠉⠅⠊⠁⠂⡴⠁⢸⠀⠳⡌⠒⢍⠙⠶⣄⡠⢠⣒⡠⠍⣝⡒⠲⢦⡀
⠀⢀⠀⡿⣧⣴⣠⡄⠀⡀⠄⠈⠀⡠⠂⠁⢀⠊⠀⠀⢈⠀⠀⠙⣄⠀⠙⢦⡀⠉⠒⢤⡉⠑⠢⣀⣡⣾⣿⠠⡀
⠀⣾⣦⣜⣀⠨⠉⠛⠛⠳⠶⠶⣦⣤⣤⣤⣁⣀⣀⣀⣐⣀⣀⣀⣘⣆⣀⣀⣽⣦⣴⠶⠾⠿⠛⠛⠩⢝⣋⣼⣧⡀
⠀⠹⣤⡀⠉⠙⠓⠢⠤⣤⣄⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣀⣀⣤⡤⠶⠖⠛⠋⣉⣵⣮⡗
⠀⠀⠈⢹⡟⠶⢶⢤⣤⣀⣀⡈⢉⣉⣉⡙⠛⠓⠒⠒⠒⠒⠒⠒⠚⠛⠂⠉⠉⠉⠉⢀⣀⣠⣤⣴⣶⣿⠋⠉⠉
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠉⠉⢿⣶⠾⣿⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉⠁⠀⠸⢿⡿
⠀⠀⠀⠐⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇
⠀⠀⠀⠀⢸⠀⡟⠀⣤⠦⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠴⡔⢹⡏⢸⠇
⠀⠀⠀⠀⢸⠀⣿⠀⣿⠀⣻⡇⠈⠃⡞⠉⢀⢰⠞⠃⡄⡰⠛⠑⣠⡞⠉⢦⣾⠁⢻⡇⢰⡇⢰⡇⣿
⠀⠀⠀⠀⢸⠀⣿⠀⣿⠀⢸⡇⠀⣾⡇⠀⢸⡏⠀⠀⣿⡇⠀⠀⣿⠇⠀⢸⡇⠀⢻⡇⢈⡇⢸⠇⡟
⠀⠀⠀⠀⠀⡇⢸⠀⣿⠀⢸⣧⠀⠀⡇⠀⢸⡗⠀⠀⢿⡇⠀⠀⣿⡆⠀⢸⡇⠀⣹⡁⢸⠃⢸⢸⡇
⠀⠀⠀⠀⠀⡇⢸⡆⢻⠀⢸⡿⠀⠃⡇⠀⢸⣇⠀⠀⣸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣼⠄⢸⡆⣸⢸⠃
⠀⠀⠀⠀⠀⢡⢸⡇⢸⡆⢸⡇⠀⠸⡇⠀⢸⣿⠀⠀⣽⡇⠀⠀⣿⠀⠀⣸⠃⠀⣧⠀⣾⠁⡿⢸
⠀⠀⠀⠀⠀⢸⠘⡇⢸⡇⠈⣷⠀⢠⣿⠀⢸⣿⠀⠀⢿⡗⠀⢸⣿⠀⠀⣧⡀⢀⣿⠀⣿⠀⡇⡼
⠀⠀⠀⠀⠀⠸⡀⣷⢸⡇⢸⣯⠀⢸⣿⠀⠀⣿⠀⠀⢿⡇⠀⠈⣿⠀⠀⣿⠀⢠⡿⠀⣿⢠⡇⡇
⠀⠀⠀⠀⠀⠀⡀⣿⠈⡇⠀⣿⠀⠈⣧⠀⢠⣿⠀⠀⣿⡇⠀⢠⣿⠀⠀⣿⠀⢸⡇⠀⡏⢸⢃⡇
⠀⠀⠀⠀⠀⠀⡇⢻⠀⣷⠀⣿⡀⠘⣿⠀⢠⣿⠀⠀⣾⡇⠀⢸⣿⠀⢰⣿⠀⢸⡇⢸⡇⢸⢸⠁
⠀⠀⠀⠀⠀⠀⣥⢸⠄⣿⠀⢿⡃⠠⣿⠀⠘⣿⠀⠀⣼⡇⠀⢸⣿⠀⢸⣯⠀⣿⡇⢸⡇⣿⢸⠃
⠀⠀⠀⠀⠀⠀⢾⢸⡇⣿⠀⣹⡇⠀⣿⠀⠀⣿⠀⠀⢿⡇⠀⢸⣿⠀⢸⡟⠀⣿⠃⢺⠀⡟⣿
⠀⠀⠀⠀⠀⠀⢸⠸⡇⢸⠀⣿⡄⠀⣿⡀⠀⣿⠀⠀⢸⣧⠀⢸⣇⠀⢸⡇⠀⣿⠀⣿⢀⡇⣿
⠀⠀⠀⠀⠀⠀⢸⠇⣇⢸⡁⢹⡇⠀⣿⡀⠀⣿⡆⠀⢻⡇⠀⢸⡇⠀⢸⡇⠀⣿⠀⣿⢸⣧⡟
⠀⠀⠀⠀⠀⠀⢸⡆⣷⢸⡇⢸⡇⠀⣿⡇⠀⣿⡇⠀⢾⡆⠀⢸⡇⠀⣿⠇⢸⡿⠀⡇⢸⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⢿⢸⡇⢸⡇⠀⣿⡇⠀⣿⡅⠀⣾⡇⠀⣼⡇⠀⣿⠀⢸⡇⠐⡇⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣯⣸⠘⡇⢨⣧⠀⢻⡇⠀⣿⡆⠀⢸⡇⠀⣿⡇⠀⣿⠁⢸⡇⢠⡇⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⠣⠧⢨⣿⠀⢸⡇⠀⣿⡁⠀⣼⡇⠀⣿⡅⠀⣿⠀⢼⡇⢸⠗⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡉⠁⠺⠇⠄⢿⠇⢀⣽⡇⠀⣿⠇⠐⠟⠀⢉⡡⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠤⠀⠀⠀⠤⠤⠀⠀⠒⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣒⣻⣗⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣤⢠⡀
⠀⠀⠀⢀⠆⢿⡗⢹⡾⣦⣿⢻⡗⡀⠀⠀⠀⢀⣔⠠⡞⠁⠀⢩⣨⣇⣠⣠⠀⠀⠀⠀⢀⣤⡮⠙⠻⢿⠛⢻⡛⢷⣤⡀
⠀⠀⢰⣿⢠⢇⣰⢯⣽⣎⢿⣤⢸⣿⡆⠀⠀⠺⡏⠀⠰⠆⠐⠄⠀⠀⠉⢻⡀⠀⠀⣴⠋⡴⠘⡁⡠⠐⠒⠁⠀⢹⡌⢻⣆
⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣼⡇⡇⠀⠀⣧⣹⣀⠁⠀⠀⠘⠓⠐⣷⣿⠃⠀⢠⡟⢾⠁⠄⠉⠣⣀⠀⠈⠙⠏⢹⣾⣿
⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣼⣿⡵⡇⠀⠀⠙⣿⢿⣶⡴⠊⠀⢀⣴⡡⠋⠀⠀⢸⣇⡈⠾⣀⡀⠐⠉⠁⣄⣀⠼⢦⣿⣿⠄
⠀⠀⠘⣯⠛⠏⠉⠉⠛⠁⠈⠙⠛⣹⠃⠀⣰⣴⣀⣼⠛⠛⠛⠒⠋⠉⢀⠀⠀⠀⠠⣿⣧⣀⠤⠻⣀⠀⠀⣸⣀⣀⣼⢛⣿
⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⢀⡠⠞⠁⠀⠠⣯⣄⡾⠏⠀⠀⢀⣐⣲⣾⣷⣶⣚⣀⡀⠈⠳⢍⣄⣀⡜⠋⠚⡏⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⣴⠟⡏⣑⣺⣥⡒⢭⣯⣻⡆⠀⠀⠑⢟⠿⠶⠺⣟⣫⠉
⠀⠀⠀⠀⠀⠀⣦⣴⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣽⣼⣿⣿⣿⣿⣿⢻⣽⣅⠄⠀⠀⠈⢳⠿⢸⣧⠟
⠀⠀⠀⠀⠀⠀⠈⠙⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡟⣿⣿⣿⣿⣿⣿⣾⣿⠏⠀⠀⠀⠀⠸⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣿⡪⣿⣿⣿⣩⠟⣋⡿⠃⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠓⠛⠫⠝⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠳⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⣠⣦⡄⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⢀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠋⠀⠀⠀⣞⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠻⣄⣀⣀⣠⠟⠋⠁⠉⠛⠶⠶⠚⢻⡅⠀⠲⣄⣀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠉⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⢻⣄⠀⠀⢀⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡀⠀⠀⠀⠀⠙⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠶⠛⠛⠛⠲⣦⡀⠀⢸⡇⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡜⠁⠀⢾⡛⣿⠆⠀⢻⡄⢸⡇⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠠⡶⢾⣟⣷⢶⡆⠀⣿⠈⣧⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⣧⡀⠻⠾⠉⠻⠞⠁⣰⠇⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠻⢦⣄⣀⣀⣤⠾⠋⠀⠀⢸⣇⡟⠀⠀⠀⠀⢀⡴⠶⠶⠒⠛⠚⠛⠛⠛⠛⠒⠒⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢿⠇⢠⡤⣤⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡴⠞⣋⠛⠳⣦⠀⠀⠀⠀⠀⠀⠘⣇⠘⠶⣿⡿⠳⠒⠖⠒⠲⠶⠀⠄⠀⠐⠠⠿⠿⠾⠿⠿⠿⢿⣿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⠁⡞⠉⠁⠀⠘⣿⣿⠛⠛⠛⠛⠛⠛⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠸⣏⡛⣶⠀⣿⠛⣿⠛⢻⡟⠛⢻⡟⠻⣿⠛⣿⢠⡾⢛⣻⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠶⠄⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠋⠀⠈⠳⠿⣤⣼⣧⣤⣼⣧⣴⠷⠞⠁⠀⠙⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢀⡾⢡⡶⠛⢦⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⢤⢤⠤⡤⠤⢤⠤⣤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠹⣄⣀⣬⣉⣷⠀⢻⣦⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠸⣦⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠉⠀⢄⡀⠀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⣤⣶⣶⣂⣀⣠⣤⣤⣶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠿⢋⣽⡿⠛⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⡟⢛⠿⠛⠁⠀⢁⣿⣿⡿⠿⠦⣤⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣃⣀⠀⠀⠀⣐⣫⡉⠁⠀⠀⠀⠀⡋⠭⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣚⣿⣋⣻⣆⠀⠀⢠⣤⣽⡛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣿⢿⣿⣿⡿⢿⡉⠉⠉⠉⠉⢿⣆⣠⠟⠛⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣿⣿⣿⡤⢤⠠⢶⡄⠾⣿⠽⣷⠘⣷⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢥⣭⣿⣿⣿⢷⢻⡇⢸⡇⢸⡇⠀⢿⠀⣿⠂⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⣿⣿⣿⣿⣿⣧⢸⡇⢸⡇⠀⣿⠀⣿⢸⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⢸⡇⠈⡇⠀⣿⢀⣿⢸⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣭⣿⠼⡇⠀⡇⠀⣿⢰⣿⣼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⣿⣿⣿⣿⡶⣇⠀⣿⠀⣿⢸⡿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣿⠀⣿⢸⣷⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠤⢚⡿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣿⠀⢹⠀⣿⢸⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⡀⠈⠀⠿⢸⡧⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣟⣟⣿⠝⠁⠠⣀⣀⣭⡶⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠐⣿⡂⢸⣇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣿⣿⣿⣿⣿⣤⣤⣤⣿⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣠⣤⣴⣦⣤⣶⣿⣿⣿⣶⣶⣶⣷⣶⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⠿⠿⣿⣿⡟⠛⠻⢿⡿⠉⠻⠿⠟⠉⠿⡿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⢠⣴⣶⣦⣄⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⢋⣉⣁⣀⠉⠙⢿⣿⣿⣦
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⢠⣿⣿⣿⣟⠛⠇⠀⠉⣀⣤⣤⣤⡀⠀⣿⣷⡶⠶⣶⣤⡀⠛⠉⣠⣾⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣿⣿⠛⣿⣇⠘⣿⠿⠏⠉⠀⠀⢰⠟⠋⠉⣉⣉⣉⢰⣿⣁⣤⣤⣀⡀⠀⠀⠀⠈⠀⠰⠿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣾⣿⣿⠟⠂⠘⠿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⢿⣿⠟⠉⠉⠙⠛⠶⣦⣤⡄⠀⠀⠀⠉⠙⠋⢠⣿⡟⠉⢀⣼⣿⣿⣷⣦
⠀⠀⢘⣿⣿⣿⣿⣶⠦⠀⠀⠀⠀⠀⠀⠀⠘⢛⣩⣴⠶⠷⠶⠦⢸⡏⢠⡶⠶⠶⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢼⠿⠿⢿⣿⣿⡀
⠀⣴⣿⣿⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠟⠉⠀⠀⠀⢀⣠⣿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀
⠀⢻⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠀⢛⣋⣁⣉⣙⠛⠂⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⡀
⢠⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣷
⠘⣿⣿⣿⣯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⣀⣠⣤⣤⣤⣄⡀⠈⠙⢿⣿⣮⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣙⣻⣿⡿
⣰⣿⣿⡏⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⣸⣿⡟⢿⡟⢻⣿⡷⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣆
⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣀⠀⠘⢿⣷⣾⡧⣿⡿⠃⢠⡄⢀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣿⣿
⠈⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣀⠉⡐⠃⠀⣡⣿⣧⡀⠀⠀⣴⠀⣘⠁⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡏
⠀⢿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠉⠈⠉⣀⣼⡿⣿⡿⢿⣦⡀⠀⠀⠉⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣼⣿⣿⣷
⠀⠈⢻⣿⣿⣡⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⠿⣿⡏⠀⣿⠃⠀⣹⣿⣦⣤⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣈⣻⣿⣿⠟⠋
⠀⠀⠸⣿⣿⣿⣋⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡙⢀⣴⡿⠁⠈⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿
⠀⠀⠀⠈⢻⣿⣿⣿⣟⣡⣤⣤⠀⠀⠀⠀⠀⢶⣄⡀⠀⠈⠛⡻⠟⠋⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣾⣿⣿⣷⣶⣶⣾⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣀⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⣶⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣦⡀⠀⣿⣿⣾⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣶⡿⠀⣴⡟⢀⣴⠆⠀⣠⡄⠀⠀⠀⠀⣀⠀⠐⣷⡠⣄⠀⢿⣷⠀⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣇⣸⣿⣰⣿⣧⠀⢸⣿⡇⢸⣿⡄⢠⣿⣇⠀⣿⣇⣿⣆⢸⣿⣧⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣄⣿⣿⣧⣸⣿⡇⣸⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠛⠛⠛⠳⠔⠋⡡⠤⠐⠐⠶⠒⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠋⠉⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣟⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢮⡂⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⢄⠸⡆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡙⠒⢠⠶⣅⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⠄⠁⠀⢀⡆⠀⠀⠀⠀⠪⡉⠉⠁⠀⣾⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠰⡁⠀⣨⠀⢸⠁⠀⠀⠀⠈⡆⠑⡀⠀⠀⠘⣦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠃⠛⠛⠓⠒⠚⠒⠒⠂⠀⠤⠁⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠉⣿⠉⠀⠀⠀⠀⢀⡐⠃⢀⣿
⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠸⠀⢀⣴⢪⡀⠀⠀⠀⠈⠉⢀⣼⠛⠉
⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⠉⢻⣿⠀⠤⠤⠤⠤⠤⠤⠀⣾⣟⠙⣿⡷⠸⠖⠚⠻⠦⠽⣗⣰⡦⠖⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣸⢴⡁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠲⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠰⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡄⠀⠀⠀⠀⠀⢼⠁⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠤⠖⠦⢄⣀⡴⠋⢡⠃⢀⣠⡤⠤⡀⠈⠁⡞⢹⠁⠀⡠⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣆⠀⣀⡤⣄⡞⠁⠀⠀⢀⠔⠁⠀⠀⢸⠋⠁⡇⠀⠀⢹⣀⡠⠽⣄⠓⠤⣷⡤⠟⡆⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⠃⠘⢾⣁⠀⠀⠀⠀⡠⠖⠛⠒⠲⢄⡀⠸⣄⡤⠷⠀⢀⡼⠁⣀⣀⣨⣆⠀⠀⠀⠀⢳⠀⠀⢀⡜⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠆⢀⠏⠀⠀⠀⠈⠙⠢⡀⠘⠁⠀⠀⠀⠀⠀⠙⣤⠬⠟⠓⠛⠉⠐⠋⠁⠀⠀⠈⠳⡄⠀⠀⡾⠶⠦⣌⠁⠀⠀⢀⠯⣙⡆
⠀⠀⠀⠀⠀⠀⡏⢀⡎⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⣿⢢⡀⢀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠑⠆⠀⠘⣧⠖⠓⠃⢰⡋
⠀⠀⠀⠀⠀⢀⡸⠋⠋⠉⠉⠉⠙⠒⢤⠖⠉⠁⠀⠀⢩⠵⠒⠒⠒⠦⣄⠜⠉⢧⡻⡉⠀⠀⠀⠀⠀⢀⣠⠤⣤⣄⡀⠀⣰⠁⠀⠀⠀⠀⡇
⠀⠀⠀⢀⡔⠉⠀⢀⣠⠤⠄⠀⠀⠀⠀⠀⣀⡀⠀⡴⠒⢤⠀⠀⠀⠀⠈⢳⡤⠴⠷⠇⠀⠀⠀⠀⠀⠸⡏⠛⠉⢹⠡⠚⠉⠉⠉⠉⠒⣾⠷⠤⣄
⠀⠀⢀⠏⠀⢀⡴⠋⢀⡤⠤⠶⢤⣀⠐⠋⠉⠙⢦⣀⣀⡸⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣀⠀⠀⠀⠚⠉⠉⠑⢾⠀⠀⣠⠤⢤⣀⣀⣈⣀⡠⠜
⠀⠀⠘⠶⠶⠯⠖⠋⠙⠢⡀⢀⡤⠼⠣⠤⠤⠶⠶⠮⢭⣀⣀⢀⣀⠤⠖⠋⠉⠉⠁⠀⠀⠉⠉⠓⠢⢤⣀⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡀⢠⣦⢰⣿⣸⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗⣈⠀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⣿⡁⣺⡿⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⣀⣤⣴⣶⡿⠿⢻⣿⠀⠀⠀⢹⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⣾⣿⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠
⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣄⣠⣦⣿⣿⠀⡄⠀⣠⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⣷⣾⠟⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣾⣿
⣦⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡅⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡄⢸⣯⣿⣿⢹⣿⣧⣶⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣥⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣠⣼⣷⣾⣿⡌⢿⢸⣿⣿⣿⡞⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⣷⣾⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⣿⣿⣏⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠒⡾⢤⡀⠀⠀⠀⣀⣀⡤⡄⠀⠃⣸⠃⠞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⢺⠀⠉⢁⠀⢀⡔⢺⡈⠁⢸⠘⠀⣿⠌⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⣆⠀⠀⣀⡠⢼⡴⠻⡙⠄⠙⣶⢾⠉⠹⣯⣬⣙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠉⠂⠈⠓⠾⡟⠓⠉⠇⠀⠀⢀⡔⠁⠈⢤⠬⢄⣀⡔⢳⢀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠋⠓⢶⠀⠠⠗⠒⠀⣺⣶⠶⠤⠧⠤⠤⠤⢤⣐⣚⠯⠧⣄⢙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢰⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⡀⣤⡤⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠣⣀⡀⢉⡑⠃⠀⠀⠶⣶⠖⣺⢚⡯⡱⢰⣯⣼⠹⣻⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠤⣈⣉⡿⠯⠀⠀⠀⠿⠀⠙⠋⠉⠚⠉⠀⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠉⠒⠀⠀⠒⠒⡆⠀⠀⠀⠒⠒⠂⠄⠀⠐⠒⠈⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠉⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡁⡘⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠂⠙⡭⡝⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠋
⠀⠀⠀⠀⠀⢀⣀⣀⣬⠤⣀⠀⡀⠁⠈⠙⢤⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠄⣀
⠀⠀⠀⢰⠉⠉⣁⣀⠉⠉⠉⠂⠀⢸⣤⣀⣀⠬⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠸⠉⠉⠉⠉⡸⠛⢎⠉⠁
⠀⠀⠀⠘⡲⢞⠛⠀⠉⠋⠉⠈⠑⢬⣾⢨⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡙⠛⠛⠫⢭⣉⡩⢦⣄⣈⡢
⠀⢀⠤⠴⢡⢄⡰⡀⠀⠘⢆⠀⠐⠀⠟⢻⠀⢄⣀⠇⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠔⢈⡧⠬⣁⡒⠒⠋⠀⠛⠚⠤⢀⡉⠑
⢏⣁⣴⣋⣁⣀⠿⠚⢄⢀⣀⠧⣀⡀⠀⠾⠗⠲⣤⣤⣤⣀⣈⣉⣉⣀⣤⣤⡤⠶⠖⠋⠁⠀⠀⠈⠉⠓⠊⠉⠉⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⣀⠐⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣄⣄⢣⣠⠤⠄⠄⠀⠀⠀⢤⡄⠂⢉⡻⢒⣤⠱⠀⠀⠀⠀⠀⠀⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢾⣷⠿⠉⠀⠀⠀⡀⠀⠀⠀⠀⢀⠌⡤⢫⢀⡥⡹⢸⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣜⠳⣴⢏⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⢸⠀⠓⠠⢦⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠈⢠⠁⣾⢦⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⠄⢊⣆⠁⡀⠀⠀⠀⠀⠀⠀⡠⠤⣬⣶⣄⠈⠐⢁⠙⠄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⢈⠵⣊⢼⡇⣣⠎⠀⠀⠀⠀⠀⠀⢷⣮⣶⡌⠡⡉⠈⣆⡴⣄⡀⠀⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⣀⠰⣱⠇⠀⠀⠀⠃⢀⣢⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⢓⠴⢤⠃⠀⠀⠧⠄⡁
⠀⠀⠀⠀⢸⣼⡧⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠰⢃
⠀⠀⠀⠀⠸⣤⡀⡀⣸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠐⣄
⠀⠀⠀⠀⠀⠀⠁⢸⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠈
⠀⠀⠠⠄⠒⠠⠰⠌⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡕
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⡀⣦⡦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠠⠀⠠⠀⢳⠉⠀⠀⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠞⡏⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢡⡤⠀⠚⠃⠀⠀⠠⢄⣀⣒⣒⠉⠉⠁⡸⡄⠐⣀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡀⢀⠉⠀⠖⠉⠇⠀⠀⡐⠂⠤⠀⣠⡤⠬⣭⣷⠾⠃⢰⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠿⠶⠜⠁⠀⠰⠋⣉⣀⡀⠠⠿⠶⠄⠱⣖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣗⡠⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠋⠈⠩⢛⡶⣻⣇⣤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⡷⠁⠀⣀⡸⢟⣯⡿⠏⣿⣼⡟⢦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣭⡀⠀⣀⣴⣷⣾⡿⠫⠀⣰⡿⢻⣷⣿⣧⣥⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⡼⢿⣿⣯⣿⡵⡟⢿⠏⣴⣶⣿⣷⡾⠏⠱⣿⣿⣭⣭⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡴⣟⣳⣟⣻⡏⢱⢼⣿⢳⡿⣷⣷⣿⣿⣿⣿⢃⣼⣤⣼⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢴⡟⢾⡿⠃⣿⣙⠷⣼⢻⣿⣿⣱⣷⣾⣭⣚⣿⣿⣷⣿⣿⣦⡤⢸⡿⠿⢿⣿⠯⡀⢠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠏⠙⢿⣤⣇⡄⠠⣶⣿⣭⣟⣛⣿⣏⣭⣴⣨⣝⣻⡿⢝⣿⣿⢁⣀⣽⣇⠀⣾⠇⠀⠀⠀⣧⡼⢿⣿⣿⣦
⠀⠀⠀⠀⢠⣾⣛⡀⠀⣠⠞⢹⣿⡇⣿⣿⡿⢷⣶⣭⣿⡿⡌⠉⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣶⣤⣣⣿⠿⣴⣤⣭⠃
⠀⠀⠀⢠⣤⣿⣿⣿⣯⡋⢀⣨⡟⢳⣹⣿⣿⢿⣿⣷⣿⣿⡇⠀⠛⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣇⠂⠈⠿⣦⡀
⠀⠿⠻⠟⠿⠶⠶⠿⠟⠛⠛⠿⠗⠛⠛⠛⠁⠘⠙⠉⠉⠙⠈⠛⠐⠋⠛⠉⠻⠷⠾⠟⠻⠗⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠿⠿⠿⣿⣶⣦
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⣶⣶⠆⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⢸⣿⠟⠃⠀⢺⣿⣧⠤⢶⣶⣿⣿⣿⣷⣦⡀⠈⠿⠿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⢸⣿⣦⣄⠈⠛⣋⣀⣤⣤⣤⣤⣤⣀⠀⠉⠁⠀⠀⢲⣶⡦⠈⠙⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⠛⠃⠀⠘⠿⠷⠂
⠀⢘⠛⠋⠁⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠛⠋⠀⠀⠐⣿⣿⣿⣿⣿⣿⠟⠛⠁⠻⢿⣿⡿⠀⣴⣶⡄⠀⣴⣶⣄
⠀⠸⠀⠀⠰⠾⠶⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⠟⠛⠉⠀⠴⠤⠖⠀⢉⣁⣀⠀⣉⠀⠀⠘⠿⡇
⠀⢰⡤⠀⠀⣀⡀⣀⣀⡀⠀⠉⠛⠛⢿⣿⣿⣿⣿⠃⠀⠘⠛⠃⠀⠀⠠⣄⣀⠀⣶⣶⣄⠀⣰⣶⡄⠉⠛⠛⠛⠂⠀⠀⢀⣤⡀
⠀⠈⠁⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⣤⣤⣀⡀⠀⣀⣙⠉⠀⠹⣿⣯⠀⠉⠉⢀⣴⣶⣿⣿⣷⣦⣤⣤⣍⡀
⠀⠀⠀⢤⣾⠝⠛⢿⣿⡷⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣻⡿⢂⣤⣤⣶⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣶⡄⠀⠀⢠⣤⡁⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠈⣁⣼⣿⣿⣿⣿⣿⣶⡄⠀⢀⣤⡀⠉⢹⣿⣿⣿⣿⣿⣿
⠀⠘⠉⠀⠀⠐⠿⠟⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡁⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⢰⣶⣤⠄⠀⣶⣶⣶⣾⣿⣷⡦⠀⠀⠙⠛⠛⠛⠛⠋⠉⢀⣤⣤⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠉⠉⠉⠙⠿
⠀⠘⠛⠀⣀⠀⠀⠉⢹⣿⣿⠇⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⣭⣭⡙⠻⠿⢿⣿⡿⠃⠀⢠⣶⣶⣶⣤⠀⢾⣷
⠀⢀⣾⣿⣿⣷⣤⣀⠀⢀⣀⣤⣤⣄⡀⠈⠉⠉⣀⣀⡀⢠⣾⣿⡿⠿⠛⠀⠀⠀⠀⠀⢠⣤⡄⠀⠠⣶⣶⡞⠻⠿⠛⠋⠐⠿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⠻⣿⡄⠀⢀⣴⣿⣷⣤⡀⠀⠉⢀⣠⣤⣽⣅⡀⠐⣶⣶⠀⠀⣸⣿
⠀⠀⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠋⠁⠀⠺⠿⡿
⠀⠀⠀⣠⣤⣄⡀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⣯⣥⠀⠀⠠⣿⠆⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣴⣶⡀⠀⠀⣶
⠤⠄⠀⠋⠉⠙⠛⠁⠀⣀⣤⠭⠍⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣤⣶⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⢘⠠⠐⠀⠗⠂⢸⣿⡟⢡⣖⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠃⠀⠀⠀⠀⠀⠀⢐⣍⣿⣿⣷⣧⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⠺⢂⡄⠀⠀⠀⠀⠀⠉⠨⣿⣿⠋⣨⡿⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢷⠇⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⢀⠔⠃⠀⠀⠂⠀⠀⠐⠠⡀⠀⠀⠀⠀⠙⠦⠀⠐⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠋⠀⣼⣿⣇⠀⠀⠀⠀⠄⠀⠀⠑⠦⡀⠀⠀⠀⠀⠐⠀⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡕⠒⢟⡋⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠀⢀⡀⠀⠀⠈⠓⡀⠈⠂⠀⢻⡀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠈⠤⠀⠀⡸⠁⠀⠐⠀⡀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠠⠄⠁⠀⠀⢀⠀⠁⠀⠀⡄⠒⠲⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢤⡃⠀⠀⠀⠀⠀⠠⠄⠀⠀⡤⠀⠀⠠⠀⠀⠀⠘⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡌⠀⠠⠄⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⢘⡃⠠⠆
⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢘⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⢨⣁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡅⠀⠀⠈⠤⠁⠀⠀⠀⠀⠀⠀⠀⡀⢸⡃⢸⡀⢸⠀⢸⡁⢸⠀⢸⡇⢀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠀⠀⠀⠑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠁
⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢈⠀⠀⠀⠀⡇⠀⠇⠀⠇⠀⠇⠀⠇⠀⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣴⣧⣤⣶⣤⣾⣦⣴⣷⣤⣷⣼⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⢨⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⢀⠁⠈⢉⠉⠉⠉⠩⡉⠉⠍⡀⠀⢀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠊⠀⠀⠐⡁⢀⣀⣀⣀⡈⠂⠀⠀⠐⠀⠀⠀⠀⠉⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠐⢒⣒⣒⡀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡒⠂⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠤⠤⠤⠄⠄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡇⠈⠉⠁⠀⠀⠐⠀⠐⠀⠀⢠⠒⠒⡄⠀⠀⠂⠀⠂⠀⢰⠈⠉⠁⠸⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⠂⢌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⢸⡡⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⡆⠈⠀⠐⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠒⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠔⡁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⡇⠀⢸⠀⠀⠇⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠤⢂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⡐⠠⠀⢀⡑⠒⠀⠀⠀⠄⠰⠀⠀⠀⠀⢊⡀⠄⠄⢊⡁⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢌⡁⠂⠀⠤⠉⣁⣀⣀⡀⢀⣀⣀⡈⠡⠄⠀⠐⢈⠡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂⠀⠠⠤⠤⠤⠀⠀⠐⠒⠂⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠍⡉⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠲⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣶⡴⢶⡶⠶⢶⢤⣤⢤⣀⠀⠉⠳⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡟⠁⠁⠀⠀⠀⠀⠙⠀⢸⡇⠀⠀⠈⢇⠀⠹⣭⣉⣉⣉⠉⠉⠉⠙⢳⡄⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠇⠀⠀⠈⠀⠀⠀⢸⡇⠀⢸⣦⠘⣇⠀⢻⡤⠀⠤⠤⠤⠤⠤⠤⢷⡀⠸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⡇⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠘⣧⠘⡆⠀⢳⣶⣴⣤⣤⣤⣤⣤⣤⣷⡀⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠛⠚⠛⠐⠓⠒⠒⠒⠒⣺⡇⠀⣿⠀⢸⡄⠹⡀⠈⢿⢿⠉⠛⠛⠿⢿⣿⣿⣧⠀⠸⣧⠀⠀⠀⢀⡶⠶⠖⠲⠶⢶⡶⠲⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡇⢰⡿⠙⠇⠖⠖⠖⢶⡶⠶⣾⡇⠀⣿⠀⠘⡧⠀⠁⠀⠘⡞⣇⣶⢾⠦⣾⣿⣿⣿⡄⠐⢿⡆⠀⣀⣸⢨⡭⠉⣉⣙⣺⡼⡄⣻
⠀⠀⠀⠀⠀⢀⣶⣋⠤⠼⡇⢸⡇⠀⠀⡠⠀⠀⠈⠇⠆⢿⠁⠀⣿⠀⢰⡇⣤⠘⠀⠀⢳⠙⣧⠘⢱⡜⣿⣿⣿⡇⠀⣼⣧⣴⣿⢽⢺⡿⠭⠿⠶⠒⠛⠛⣿
⠀⠀⠀⠠⣶⣸⣿⠀⣶⣶⡇⠰⡇⠀⠀⠃⠇⠀⠀⠀⠀⢸⠀⠀⣿⠀⣿⢠⡟⡄⢤⠀⢸⢇⣿⢤⣤⣉⣻⡅⣸⠛⢾⣿⣤⠟⠋⠘⢿⢯⡀⠀⣰⢿⣧⠀⣿
⠀⠀⠀⠀⣿⢾⣿⣠⣷⣿⡇⠀⣧⣤⣤⣄⣀⣀⣀⡀⣀⣿⠀⠀⡟⢰⠇⣼⠀⡇⢸⠀⠀⣿⡀⢉⣤⠿⠈⢻⣿⣿⡟⠃⢻⡄⠀⠀⢸⣏⠹⢦⣿⣿⣥⡴⠛
⠀⠀⠀⣀⣴⣻⣿⣵⡿⠋⠇⠀⣀⡀⢤⠄⠠⡤⡤⡄⣤⣽⠀⠀⣇⡸⢀⡏⠀⣧⠘⠀⠀⢸⠛⡋⠠⢠⣴⡿⣷⣿⡇⠀⣼⡇⠀⠀⠀⠈⢷⠀⠀⠀⠀⠈⡿
⠀⠀⣴⠋⢀⡀⠀⣹⠀⠀⠀⠀⣧⠸⢠⠀⠀⠀⠁⠁⠙⢸⠀⠀⣿⡇⢸⣡⡴⠟⠀⠀⠀⠘⡿⠷⠺⠿⠿⠶⠾⢿⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⡇
⢀⣴⡇⠉⠁⠀⠀⢸⠀⢸⠀⠀⠘⠀⠈⠀⠀⠀⠀⢀⠀⢸⠀⠀⠋⠀⢉⣁⠄⢲⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⢠⣼⡇⠀⢺⡇⠀⠀⠀⠀⣸⠟⠃⠛⠻⢿⡇
⠈⢻⠁⠈⣴⣶⣆⢺⠀⢸⡆⠀⠀⠀⠀⢠⠖⠉⠁⢨⡤⢿⡀⠀⠀⠘⠉⠙⠓⠞⢰⠂⠀⠀⠧⠷⠾⠴⢦⠶⠿⣿⠇⠀⣻⡿⠀⠀⠀⠀⣿⢀⣠⣤⣤⣰⡇
⣤⣾⡀⣼⣿⣿⣿⣼⣦⣾⠷⢶⣶⣶⣶⣾⣔⣶⣄⣼⣳⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⠓⠒⠒⠒⠒⠒⠒⠶⠶⠶⠤⠤⠤⢼⡇⠀⠀⠀⠀⣟⠀⣻⠙⣯⢹⡇
⠻⠶⢿⣿⠰⢾⣿⠟⢻⣯⢼⢺⡏⣿⢶⢹⢻⡿⠿⠿⠟⢻⣿⠱⡎⣿⠃⡆⣹⣏⡿⠛⢻⣿⣿⣿⣿⣟⣿⣿⣿⣶⡾⠛⠛⠃⠀⠀⠀⠀⣿⠀⣿⠀⣿⠈⢷
⠀⠀⠀⠻⢷⣿⠟⠀⠘⢿⣶⣿⣷⢿⣶⣾⡿⠃⠀⠀⠀⠀⠿⣷⡾⢿⣷⣾⣿⠿⠁⠀⠀⠹⢿⣿⡿⠿⣿⣿⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⢹⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡟⠀⣸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣶⣶⣿⣯⣿⣿⣿⣯⣽⣶⣶⣖⣂⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣺⠯⢛⡈⣟⣋⡽⣿⡻⣾⣿⣻⣻⣽⣿⣿⠿⢬⣙⢇⣈⠛⢵⣂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⠻⣿⠉⣤⣌⢡⡜⣧⡶⣻⢿⣿⣿⣿⣿⣿⣿⢯⡙⢶⠟⡦⢁⣴⣄⠈⠙⠷⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠻⣤⠀⠀⠀⡎⣿⣿⠀⢰⠎⣻⢷⣎⣸⣉⡏⣏⣱⣈⣷⢟⡀⠶⠀⠸⣿⡏⠀⠀⠀⢠⡖⠋⠓⢤⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡴⠟⠀⠀⢠⣿⡿⠃⠀⠀⠀⠉⠀⣤⢉⣛⠛⢻⣏⠹⠆⠈⠁⠀⠀⠀⠙⠷⣄⡀⢀⡘⠷⣤⣀⠐⠛⣦⡀
⠀⠀⠀⠀⢀⡴⠛⣡⠾⠓⠒⠲⣶⠈⠉⠁⠀⠀⠀⠀⠀⢠⡖⣐⢦⠀⠉⠀⠀⠀⣠⢖⡍⣶⠀⠀⠀⠀⠀⠀⠉⠁⠰⠶⠀⠚⠻⠧⣉⠻⣆
⠀⠀⠀⢀⣾⣡⡞⢁⣲⡄⠀⠠⣜⣦⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣧⣳⡀⠀⠀⣰⣣⠟⠻⣋⡀⠀⠀⠀⠀⠀⠀⢠⣚⡦⠀⠀⣴⣒⠻⣷⣼⣆
⠀⠀⠀⣸⢧⣿⣀⠙⠟⢁⡤⣰⢻⡏⢠⣶⡄⠀⠀⠀⢸⣷⣾⡳⡨⣿⢃⠀⢀⢹⡿⡱⣩⣶⢻⠀⠀⠀⠀⣴⣶⠈⣿⢷⡔⣦⡙⠋⣀⡸⣷⢿⡀
⠀⠀⠀⣿⢶⣷⠯⠱⡄⢿⢾⡇⣿⢷⣸⡿⠁⠀⠀⠀⠈⠛⠿⢿⣵⣹⣷⠀⢸⣿⣽⣿⠿⠛⠁⠀⠀⠀⠀⠹⣟⣰⢿⠆⣿⣿⠃⡼⠉⡷⣶⢿⡇
⠀⠀⠀⣿⢻⣇⡈⠃⣿⡎⣿⣇⣿⠶⠋⠀⠀⠀⠀⠀⢰⣚⣳⠦⡙⢯⡏⠀⠈⣿⠛⡵⣞⣛⣳⠀⠀⠀⠀⠀⠈⠳⢻⣆⣿⡏⣿⡟⠋⡀⣾⣻⡇
⠀⠀⠀⣿⣹⠖⢬⣱⡿⣣⡿⠟⠁⠀⢀⡀⢠⡄⢠⡄⢀⡉⢛⡿⠺⣾⡇⠐⢠⣿⡾⢻⣍⠉⣁⠀⣤⠀⢤⠄⣀⠀⠀⠙⠻⣷⣹⣿⡩⠖⣿⣹⡇
⠀⠀⠀⣿⠍⣓⣤⢿⡵⠋⠀⠀⠀⠐⣈⣁⣀⣀⣀⠀⠘⠁⠤⠙⢧⣹⣧⣰⣴⡟⣠⠟⡡⠆⠉⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠈⠙⣬⡳⣞⡯⢾⡇
⠀⠀⠀⣿⢷⡿⣱⢏⣱⠖⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠁⣸⣿⣿⣿⣿⣿⣿⡀⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣑⢶⣍⢳⣽⣷⣽⡇
⠀⠀⠀⣿⣿⢵⣏⡾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣴⣿⣿⣿⠿⠿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣎⣿⣿⣿⡇
⠀⠀⠀⣿⡿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⢸⢰⣾⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡇
⠀⠀⠀⡟⢳⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢎⣭⣿⠠⣨⣯⣭⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣻⠷⡇
⠀⠀⠀⣿⢺⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢼⡇
⠀⠀⢀⣿⣾⡿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⢿⣿⣿⣿⣿⣿⣿⢻⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣾⣇
⢀⣴⢟⣛⡋⠀⠚⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⠃⣸⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⡌⠹⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡘⠀⠈⠿⣻⢳
⣾⣛⢚⡽⠆⠀⠀⠱⢊⣿⣿⣿⣿⣿⠿⠿⠋⠁⣻⣿⡆⢠⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⠀⣿⣿⣃⠉⠛⠛⠿⢿⣿⣿⡿⣏⠺⠀⠀⠀⠻⣌⢛
⢿⡍⠈⠀⡀⣀⠀⠀⠈⠁⠋⠉⣤⣴⣤⣴⣶⣿⣿⢯⠃⡎⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡆⢳⢿⣿⣿⢶⣦⣤⣤⡤⠉⠀⠉⠀⡀⢀⡀⡀⠀⢈
⠀⠙⣷⣦⠴⠈⢀⣃⠐⢠⠀⠀⢨⣍⢬⡻⣌⢣⢹⡜⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠈⣾⢱⢃⡾⣡⢤⣭⠀⠀⢠⠀⢀⣡⠈⠀⢴⣶⠟
⠀⠀⠘⡿⣷⣤⣾⣿⣿⣶⣶⠂⠀⠻⠺⣿⡇⢀⡿⠁⠀⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡆⠀⠙⢇⡀⢻⡟⠘⠃⠀⢲⣶⣾⣿⣿⣶⣶⡟⣿
⠀⠀⠀⢷⣝⣻⣭⣭⣭⣟⠻⣷⣤⢦⣀⡈⠀⣸⡆⠀⠀⢿⣆⠙⠛⢛⣁⠛⢁⣈⠛⢋⣡⣾⡇⠀⠀⢿⣀⠀⣀⣴⣾⣾⠟⣋⣭⣭⣭⣯⣯⡴⠃
⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠿⣷⣾⣿⡽⣿⣾⣿⣵⡆⠀⠘⠿⠻⡃⠈⠻⠃⠛⠋⠀⡛⠻⠋⠀⠀⢿⢿⣿⣿⢟⣽⣷⣾⡟⢿⡿⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠛⢷⡐⣷⣿⣿⣿⣿⣦⣿⣿⢧⡄⣼⢀⡇⠀⣱⠀⠀⣧⡇⠀⠸⡀⠈⣇⢸⡄⢴⣿⣿⣷⣾⣿⣿⣿⣿⡇⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣹⣾⣿⣿⣿⣿⣋⢮⢏⡼⠃⡾⠁⢴⠃⣀⡀⠛⢀⣀⡀⢳⠄⠹⡆⠻⣌⢯⣮⡻⣿⣿⣿⣯⣹⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣹⣿⣿⣿⠉⠛⣣⣈⡷⣤⡾⠛⢦⡾⠋⠙⢷⠏⠉⠙⣶⠟⠹⣦⡶⣦⣤⣙⣋⣹⣿⣿⣿⢹⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡻⣷⢿⣿⣿⡛⠟⡇⢹⡇⠈⠃⠀⢸⠃⠀⠀⢸⠀⠀⠀⢹⠀⠀⡉⠀⣿⠁⡟⡟⣻⣿⣏⢹⣛⣣⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣧⣿⠀⣿⣿⣷⣦⣼⣾⣧⡴⢧⣤⣼⣤⣤⣤⣼⡦⢤⣤⡾⢦⣴⠷⢦⡿⡾⣶⡶⣿⣿⡿⢻⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿⣿⠀⣿⡿⢿⣷⢱⠀⣸⠀⠀⣇⠀⢸⡇⠀⢸⠀⠀⣾⠀⢀⡏⠀⢸⠀⣰⢱⣷⠿⣿⣿⢸⣷⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣟⣰⣿⣿⣄⢻⠾⣧⡿⣦⣠⡿⣤⠾⠷⡴⠟⠷⠴⠛⠶⠾⢷⣤⠾⣧⡟⢻⢁⣶⣿⡿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⡇⠉⠙⣿⠸⠾⡀⢰⡄⠀⢶⡀⠀⣶⠀⢠⠀⣰⡇⠀⣴⠆⠀⡶⠀⡾⡞⢸⡟⠉⠀⣿⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢿⣧⠘⣠⠟⠀⠀⠁⠀⠃⠀⠈⠇⠀⠸⠇⠘⠀⠿⠀⠀⠃⠀⠀⠃⠀⠁⠀⠘⠷⡘⢠⣿⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⣆⡀⠀⣀⢴⣰⡆⣠⠀⠀⠀⠀⣤⣄⣾⢃⣤⡄⠀⠀⠀⢠⡄⣶⢴⢤⡀⢀⣠⢞⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢻⡏⣤⡴⢄⡡⢆⠀⠀⣀⠳⣾⣇⢿⡶⣁⡀⠀⣀⠓⣡⠴⢦⣌⡿⢋⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣭⣫⣄⣸⣧⣴⣄⠘⢭⣇⣼⢇⢿⣤⣯⠟⢀⣴⣦⣯⣤⣜⣮⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠭⢶⣦⣝⡳⢤⣉⣤⠾⠶⣬⡁⢖⣫⣵⡶⠶⠓⠊⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠛⠶⣄⢀⡴⢞⣩⠔⠀⠀⠀⠈⠛⢆⢀⣠⠴⢚⡻⠫⠭⢙⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠐⠊⠁⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⠀⠙⠖⠛⠛⠛⢛⣓⠲⣄
⠀⠀⠀⠀⠀⣠⢞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢾⢧
⠀⠀⠀⠀⢸⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢞⡆
⠀⠀⠀⠀⠸⣜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢀⣼⠗⠀⠀⠀⠀⠀⢀⣠⣀⠀⢰⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⡾⠀⢸⡇⠀⠙⠛⣲⠒⠲⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡲⣄
⠀⠀⠀⣰⠟⠁⠀⢀⣤⠶⢶⡄⣾⠀⠈⢷⠀⢷⠀⠀⠀⠀⣧⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⡏⠀⠀⠀⣼⠃⢀⡴⠒⢦⠀⠀⠀⠀⠀⠹⡌⢧
⠀⠀⣸⠃⠀⠀⠐⠙⣆⢀⠞⠀⢹⡄⠀⢸⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⣇⠀⡾⠀⠀⠀⢸⠇⠀⠀⢸⡟⠀⣾⠁⠀⢸⡇⠀⣤⠀⠀⠀⠀⢸⡄
⠀⠀⡏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠻⣤⠎⠀⠘⠓⠚⠛⠁⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠐⣿⠀⢀⡟⢁⡾⣿⠀⢠⠆⠀⢸⡇
⠀⠀⠻⣄⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⢀⡾⠁⢻⣦⡟⠀⠀⣾
⠀⠀⠀⠈⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⢀⣾⠏
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠁
⠀⠀⠀⠀⠀⠀⣷⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣬⣀⠀⢀⣀⡤⢶⡄⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠒⠒⠶⢒⣊⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠛⢄⠀⠀⠀⠀⠀⠁⠠⠤⣆⠀⢀⡀⢀⣀⣀⡀⠀⠀⣠⡾⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⣭⣭⣥⣤⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⣀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣈⡉⠙⠛⠻⠶⢶⣿⣅⣀⡀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢶⣤⣤⣀⣉⠉⠛⠛⠷⠿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⣶⣤⣄⣈⡉⠙⠛⠻⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣿⣷⣶⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⠀⠀⣶⠀⠀⣴⡄⠀⢰⡄⠀⢰⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⣿⡀⠀⣿⡇⠀⣼⡇⠀⣸⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢹⡇⠀⢻⡇⠀⣿⡇⠀⣿⠁⠀⣿⠁⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⢸⡇⠀⣿⡇⠀⣿⠀⢰⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡛⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⣿⡇⢠⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⢸⣇⠀⣿⡇⢸⣿⠀⣾⠇⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢹⡇⠘⣿⠀⢿⠇⢸⡟⠀⣿⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⢰⡇⠀⠀⣻⣷⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⠐⣁⣤⢼⡛⠋⠙⠛⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣼⢿⣿⠊⡁⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡷⠟⠛⠛⠿⣿⣿⣶⣬⣁⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠁⣠⣤⣤⣄⠀⠙⢧⡘⠉⠛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠉⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⣿⣿⣿⠇⠀⠀⠰⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣿⣿⣿⣿⣶⣾⣷⣾⣿⠿⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⠿⠿⢿⣿⠛⠿⠋⠀⠀⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣀⣀⣸⣿⣤⣀⣀⣀⣠⣶⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⢿⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⣦⣆⣄⡀⠀⠰⡀⠀⠈⢀⠈⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⣦⣽⣄⠀⠀⠀⠀⠀⠀⣠⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣁⣀⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⣆⡀⢠⣀⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣄⣀⣆⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠉⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⠛⠛⠟⠉⠋⠛⠛⠛⠛⠛⠻⠶⠶⠿⠷⠿⠶⠾⠻⠿⠿⢿⠿⠿⠿⠾⠿⠿⠿⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣖⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⣀⢀⠠⠤⠄⢠⡒⠒⠀⣤⣀⡀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⣔⡿⠀⢻⡄⠤⣔⣶⣷⣌⡛⠉⠩⠉⠓⣼⣯⡁⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠋⠉⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠤
⠀⠰⢘⢀⣴⣿⠀⠀⠀⠀⠾⣽⡄⠀⠀⠀⠀⠠⣌⣧⠠⡀⢤⣌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁
⠀⢼⡟⠉⠹⣿⡄⠀⠀⠀⠈⠛⣷⣤⠀⡀⣀⡀⠘⣿⣴⠋⠭⠙⠛⠥⡀⠀⣀⡀
⠀⢀⠀⠀⢠⣌⠿⠒⠶⠦⣤⣹⠟⠁⠀⠀⠀⠈⠉⠛⢿⡄⠀⠀⠀⠀⠀⡙⢿⣧⠡⡀
⢰⠿⣶⢀⣀⡏⠀⠀⠐⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠈⣙⣷⠀⠀⠀⠀⠑⣮⠷⠽⣦⣰⡀
⡆⠈⠈⢻⣿⡇⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⢀⠀⣈⣙⣧⠀⠀⠀⢤⣇⡈⠀⣪⣿⣇⣀⡄⠀⠀⣀⢤⢀⠀⣠⠀⠀⣀
⡇⠀⠁⣄⣹⣄⠀⠀⠀⠀⠀⠙⣧⠀⠀⣤⠚⠂⠛⠛⠓⠻⠿⣧⢀⡤⠞⣡⠴⠛⣩⡴⠖⠒⠀⢀⣁⡸⢞⡽⠂⣞⠠⠛⣫⣑⣀
⠀⡐⡦⠚⠁⠉⠉⠛⠦⢷⣤⣙⣿⣇⡞⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⡞⢉⠔⣋⡥⠶⣒⣫⣉⡤⠶⠚⣁⣞⣻⣽⣿⣶⠻⣥⡠⠤⡀
⠀⢹⣧⠀⠀⠀⠀⠀⠐⠀⠈⠉⠛⠻⣷⠀⠀⠀⠀⠠⠳⢠⡿⠡⣺⠏⡔⣡⣾⡩⠬⠍⠀⣦⣤⠶⢚⣫⠭⢽⣏⣉⡝⢙⣼⠏⣏⣥⠁
⠘⢷⣿⡄⣠⠰⠲⢦⣀⢀⠀⠀⠀⠑⢺⠀⠀⠀⠠⠁⣴⡋⣰⢱⠇⡌⣼⣛⣵⣶⡿⠿⠛⣋⠕⡮⠶⠀⢁⢲⢹⢟⡗⣻⠏⡼⠹⣯⡤
⠐⡀⠙⣿⡇⠀⠀⠠⠈⢙⠛⠿⢿⣷⣾⣆⠀⢀⠇⣸⡿⢀⡇⡞⣸⣿⡟⢉⠟⠉⠀⠙⠚⠷⣋⡴⢋⣵⢣⣤⣞⢸⡞⠅⣈⠑⣷⢣⠶⠆
⠀⠁⠀⠙⡇⠀⠀⠀⠀⠈⠑⠀⣤⠷⢶⣿⣦⡾⠀⣿⡇⢸⡇⡇⣏⣿⠇⠁⠀⠀⠁⠀⠀⠾⠗⠴⣿⢻⡿⢻⠷⡟⢀⢰⡏⠈⡟⢸⣊
⠀⠀⠐⢾⣿⣦⣤⣄⠀⠀⠤⢤⡄⠒⠀⠀⢨⡄⢸⡧⠀⠸⡇⣇⢻⣾⡄⠤⠀⠀⠀⠁⠀⠙⠂⠘⠀⠸⢰⢹⢸⡇⢁⠘⢁⢢⠁⣼⢹⠃
⠀⠀⠀⠀⠙⢷⡀⠉⠓⢤⣠⣴⡇⠀⠀⠀⠀⣷⠈⣷⠆⠀⢷⡘⢅⠉⠃⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠓⢻⢸⢸⡇⠆⡀⠌⡜⢠⢇⢚⠂
⠀⠀⠀⠀⠀⠀⠑⢄⡀⢀⣈⠙⠛⢶⣤⣤⣄⣹⡄⢻⣌⢌⢌⠻⠟⠁⠀⠀⠀⠈⠩⠀⢀⣀⠀⢀⢀⣴⡿⡌⣼⠃⣑⠏⠜⢠⣮⠎⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠿⠿⠛⠛⠛⠛⠋⣹⠀⠁⣀⣐⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠐⠂⢭⣭⣯⠜⣱⢃⢜⡀⠊⡪⠀⢂⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⣀⣠⣴⠟⠁⠐⠁⠺⠷⡀⠂⠀⠀⢦⢸⣷⠨⢙⠀⠒⠾⠿⢒⣫⣷⠕⢋⠤⡊⢄⣡⡾⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠝⠛⠀⠀⠀⠀⠀⢰⡯⢀⠶⠀⠠⣌⠢⣙⠻⠶⠦⠤⠴⠟⣛⠭⠖⢊⠥⡶⠻⣟⣩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⠅⠀⠀⠀⠀⠀⠀⡁⣀⡁⠶⠓⢮⣙⡶⠭⣭⣈⠩⢽⣇⣒⣠⠪⠑⠉⠔⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠢⢀⠠⢀⢀⣠⣾⣓⠗⠊⠑⠲⢐⠈⠉⢉⡛⠋⠉⡉⢉⡁⠀⠚⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣠⡕⣲⣿⠗⠋⠀⠀⠀⠀⠀⠀⠈⠘⠒⠂⠨⠭⠄⠐⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⠶⠶⢶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⣭⠴⢶⣒⣲⣶⣶⣐⣂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⡶⠿⠛⠛⠋⠉⣉⣉⣉⣙⣛⣛⣻⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣭⣶⠶⠾⠟⠛⠛⠛⠛⠋⠉⣉⡉⠙⠛⠛⠛⠿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⢏⠉⠀⢀⣠⣀⣀⣠⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣄⣀⣂⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣡⣤⣶⠾⠿⣿⣿⣿⣿⢿⣿⣽⠿⣷⣟⡝⣡⣋⣽⢿⣟⢿⣿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣏⠘⣛⣿⣶⣿⣿⡟⣇⣁⢹⣏⣷⡿⠛⣟⠛⢻⣷⣴⣶⣶⣿⣶⣥⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⢎⣸⣶⣿⣭⣶⣀⣙⣿⣥⣹⣾⣏⠹⣯⣵⢩⠙⢁⣦⣿⡿⢛⣋⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⢿⣿⠄⠀⠈⣉⣉⡉⠛⠛⣛⣻⣧⣬⣭⣽⣿⣿⡿⠛⠛⠟⡟⢻⡯⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢁⣠⣼⣿⠁⠿⢸⡿⣌⣿⠀⣸⡏⠙⣏⠀⢠⡖⢶⡄⠂⣰⢶⣦⠀⢸⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⣯⣤⣤⢸⡇⠀⣿⠀⣿⠇⠀⣿⠀⢸⠀⢸⣷⠀⣿⢸⣿⣶⠾⠿⠟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⠶⠿⢸⡇⠀⣿⠀⣿⠀⠀⣿⠀⢸⠀⢸⣿⠀⣿⠸⣿⠛⣷⡶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⢸⡇⠀⣿⠀⣿⠀⠀⡇⠀⢸⠀⢸⣿⠀⢹⠀⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡇⣺⡇⠀⣿⠀⣿⢠⡄⡇⠀⢸⠀⢸⣿⠀⢸⠀⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇⠀⣿⠀⣿⠀⠀⡇⠀⢸⠀⢸⣿⠀⢸⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⣿⡟⠀⡏⠀⣿⠀⠀⡇⠀⢸⠈⢸⣿⠀⣾⠄⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⠀⣿⡇⠀⡇⠀⣿⠀⠀⡇⠙⣿⠀⢸⣿⠀⣿⠀⣿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢰⡇⠀⣿⠠⢀⡇⠀⢿⠀⢘⣿⠀⣿⢰⡿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣄⡀⠈⠛⠋⠀⠀⢿⣀⣸⠃⠀⠸⣦⣼⠟⣀⡈⠋⠁⣸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣏⣽⠲⢽⣷⡦⣤⣝⣒⣀⣉⠀⠀⣀⣀⣀⣀⣬⡭⠵⣖⣻⢵⢛⣿⠀⠀⠀⢀⣤⣤⡀
⠀⠄⠀⠀⠀⢰⣿⣿⢶⠾⣤⣙⢷⣄⡒⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⢶⠶⠶⠚⠛⠉⣀⣬⣼⢏⣴⡾⢿⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣷⣮⡠⢎⠽⠿⣯⡛⠻⠿⢷⣦⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⡶⠶⢟⣛⠉⢿⣿⣛⣛⡹⣙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠜⢿⡔⢡⢖⣽⣫⣻⡆⠓⢀⣠⣤⣀⠈⠉⠉⣩⣿⣷⣶⣶⡆⢾⣿⣿⡗⠀⣍⢛⠛⡛⠛⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣾⣮⣵⠟⠀⠀⢿⣿⣻⣿⠆⠈⠉⠻⢷⣤⣤⡾⠇⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⡄
⠀⠀⠀⠀⠀⢰⢶⡶⡾⢷⠶⠶⠶⠿⠶⠶⣦⠀⠀⠀⠀⠀⣾⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣷⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿
⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⢸⣿⡟⢸⣿⡇⠀⠀⠀⠀⠀⢸⡀⢸⢷⠀⢸⡇⠀⣸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⢸⣿⡇⣸⣿⠁⠀⠀⠀⠀⠀⠘⡇⢸⣾⠀⢸⡇⠀⣯⡇⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡀⢸⡇⠀⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠘⣿⡇⢹⣿⢸⣿⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⠀⣟⡇⢸⡇⢸⢿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣿⢸⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡇⢸⡇⢸⡾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⣈⣁⣈⣁⣈⣁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⡀⢀⠀⣆⣄⣣⡤⠄⠀⠂⠐⠀⠀⢤⠔⠈⢩⡝⠀⣤⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠒⠀⠀⢪⢄⣾⡿⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⣠⡋⠴⡫⢀⠦⡔⠠⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⣦⢫⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⣸⢀⢳⠰⢦⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠉⠈⠰⠁⣯⣦⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⡠⢔⣁⣦⠀⡀⠀⠀⠀⠀⠀⠀⡤⠀⣼⣶⣄⡈⠜⢠⠹⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⠀⠀⠀⠨⢶⠁⣼⡎⣧⠃⠀⠀⠀⠀⠀⠀⢷⣵⣷⡎⠰⡉⠈⣀⡽⣤⡀
⠀⠀⠀⠀⢀⠀⡄⠸⡰⠃⠀⠀⠀⠃⣀⠵⢖⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢗⡶⠴⠃⠀⠘⠥⡇⡅
⠀⠀⠀⠀⢸⢼⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠿⠃
⠀⠀⠀⠀⠸⢤⡄⡔⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢬⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⠈
⠀⠀⠠⠄⠒⠂⠐⠎⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡗
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣄⣄⣀⡀⠀⠀⣀⣀⣀⡠⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠉⠉⠉⠁⠉⠉⠉⠉⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠟⠁⢀⣴⣄⠀⠙⠿⣿⣿⣿⣿⣿⠟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠉⠉⠉⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⡀⠀⠀⠀⠘⢿⠟⢿⠿⠀⠀⠀⠀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠃⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⣿⣉⣟⡉⣿⠉⢳⠋⢹⡏⣙⣏⣹⡿⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⠦⢯⣩⣿⣉⣹⣉⣹⣯⣩⠧⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣤⣤⠶⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠲⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡄⠀⠀⠀⠀⢰⣿⣼⡇⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠇⠀⢀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⡞⠀⠀⣾⣰⡿⠋⠁⠻⣷⡆⠀⠀⠀⠀⠸⣿⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⠃⠀⣴⣷⣿⠁⠀⠀⠀⠻⢿⣄⣀⠀⠀⠀⠈⠂⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⠇⢀⡼⠟⢋⣀⣀⠀⠀⠀⠀⢀⣭⣻⣷⡄⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢸⣿⣾⢋⣾⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⣿⡇⠸⣿⣿⣿⡿⠿⢿⡷⠠⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠙⢿⣄⡉⠛⠛⠋⠀⠋⢀⣤⠉⠙⠛⠹⠛⣇⢿⣦⡀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⢹⣆⠀⠀⠀⢀⣿⢹⡇⠀⠀⠀⠀⠉⣮⣿⣷⡄⠀⠀⠀⠘⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⢄⣀⣤⣶⣾⣿⣷⡄⠀⠀⠙⠈⠃⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣈⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢷⣼⢓⠀⠀⠀⠀⠀⠀⠙⢻⣾⡿⣿⣿⣿⣿⣿⣷⣦⠀⠘⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠙⠻⢿⣿⣿⠿⠿⣿⡇⠈⢻⠙⠉⠉⠀⠁⠀⠘⢛⡛⠉⢀⣿⣿⣿⣿⣿⣾⣿⣷⣦⡿⠋⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣽⣷⡈⠁⠉⠉⠋⠈⠈⠉⠊⠉⠁⠁⣼⣿⣟⡈⢓⣈⣽⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠢⣤⣀⠀⣀⣀⠀⣀⣠⡴⠞⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠐⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣢⣂⢀⣀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠠⠦⠀⠰⠶⠀⠐⠒⠊⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠧⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⢂⠀⠂⠁⠀⢸⠀⠀⣠⣤⢀⣤⣀⣠⣤⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⣻⠄⠀⠀⠈⠠⠴⠰⠴⠏⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣿⠀⣰⣶⢀⣐⡦⢀⣰⡶⠀⠠⣖⡆⢸⠉⠭⠤⠆⠅⠉⠁⠴⠧⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⡞⠻
⠀⠀⠀⠀⠀⠀⠈⠵⠶⠲⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⣷⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠀⠀⢲⡆⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⣧⢰
⠀⠀⠀⠀⠀⠚⠓⠒⠒⠒⠒⠒⠒⠸⠢⠠⠠⠄⠄⠼⠤⠤⠤⠤⠤⠼⠒⠲⠀⠘⠟⠋⠓⠚⠛⠛⠋⠋⠉⠉⠁