Communicator Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠛⠒⠲⢦⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⣤⣄⣀⣠⣤⠶⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠳⢴⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠛⠙⠻⢿⣷⡶⠋⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣭⣩⣉⣭⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠬⠭⠭⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⣶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⢀⡀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⡄⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠻⣄⣠⡇⠀⠀⢸⡇⠀⠀⣿⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣴⡇⠀⠀⢸⡇⠀⠀⢻⣤⡼⠃
⠀⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣼⣧⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠾⠧⠶⠞⠁

⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⠀⠐⠒⠒⠠⡀
⠀⠀⣰⡟⠁⠙⠃⡀⣀⠀⠤⠄⠒⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠈⠉⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⢱
⠀⢠⡿⠀⠀⠀⠀⠀⠀⣀⠠⠄⢂⣤⠀⣦⣤⡦⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠙⣄⣀⠠⠤⠌
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢦⣄⢸⡏⢸⡏⠀⢀⣾⢹⡇⠀⠀⠀⠀⠀⠀⢀⠔⠈⢉⡆⠀⠀⣀⣴⡇⣴⢿⣤⣤⣤⡾⢷⡀
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃⣾⠃⢠⡾⢣⡿⠀⠀⠀⠀⠀⠀⠀⠂⢠⠁⠀⠈⢂⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⣦
⠀⠀⠰⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠈⢵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠡⡀⠂⠀⠄⠾⠅⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⣧
⠀⠀⠀⠁⠜⢀⠈⣦⠀⠀⠀⠀⠔⠚⣡⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠟⠃⠀⠀⠀⠳⢤⣀⣀⣀⣤⠾⠃⠀⠀⠀⠀⢿⡀
⠀⠀⢀⠎⠀⠈⠀⠘⣷⣀⣀⣀⣂⣉⣥⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇
⠀⠀⠢⠤⠤⠤⠤⠠⣼⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠍⠀⠀⠀⠈⠕⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠌⠀⠀⠀⠀⠀⣈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇⢰⣦⡀⠀⢠⡴⠨⠤⠦⢬⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠀⠈⢁⣀⠀⣶⡀⠀⢸⠇⢀⣉⣉⠛⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡯⠭⠀⠁⠈⠙⢷⡿⠀⠀⠀⠀⠀⠹⡜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣶⠚⠋⠉⢹⡄⠸⣇⠀⡿⠀⠟⠀⠉⠉⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠝⠁⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⠀⣀⠀⣤⡴⠀⠉⠈⠁⠘⠿⠆⣤⣤⠀⣘⠁
⠀⠀⠀⠀⠀⠀⢸⣧⣦⠀⠀⠀⠀⠀⠀⠀⣻⠄⠀⠀⠀⠀⢠⢇⣿⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠛⠛⠀⠁⠀⡄⠸⣿⠀⠀⠀⠠⡄⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠸⣧⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇⣀⡀⠀⢂⡀⠟⠉⢰⡎⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢰⣻⡏⠀⠀⠀⠀⢿⡄⠀⠀⠈⣑⠇⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠓⣤⡤⠀⠀⠀⠀⠼⠃⠀⠈⠛⠛⠋⠀⣴⠟⠉⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠘⡧⠷⠀⠀⠀⠀⠘⡇⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣀⣠⡬⠑⠛⠶⠦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠶⠞⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠆⠀⠶⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣈⣀⣀⣀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣬⣿⣧⣽⣿⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⢶⡄⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⠞⢎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣿⣀⣀⠹⡄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡾⢁⣀⣸⡟⢦⡀
⠀⠀⠀⠀⠀⣀⢤⡤⠄⠊⠁⠀⢹⣇⠀⡁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡃⢀⣿⠁⠀⠉⠒⠤⣤⢄⡀
⠀⠀⠀⢴⠉⠀⠀⣷⠀⠀⠀⠀⠀⢻⢎⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢈⣾⠃⠀⠀⠀⠀⢰⡆⠀⠈⠱⠄
⠀⠀⠀⠆⢆⠀⠀⠘⢷⠄⠒⠂⠀⠀⠓⠥⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠠⠕⠃⠈⠀⠐⠢⢴⠏⠀⠀⢀⠆⠆
⠀⠀⠀⠈⠚⠢⠖⠲⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡙⠒⠆⠚⠊
⠀⠀⠀⠀⠀⠀⠘⠄⠘⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠑⢌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠔⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⣀⣠⡴⠓⢄⢠⠀⠀⠀⠀⠀⠀⢀⣤⣎⠁⣰⣪⣉⣩⡓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢶⣹⢲⠞⣹⡇⠀⠀⠀⠀⠀⢸⣯⣩⡟⠉⠁⠈⠀⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⠀⠀⠉⠸⡘⠟⠀⠀⠀⠀⠀⠀⠀⠉⢟⠁⠀⠁⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠱⣀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⢶⣄⠀⠀⠀⠀⠀⠀⢳⣀⡤⢤⠀⢠⠤⣀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠼⣄⡴⠛⠻⣦⠀⠀⠀⠀⠐⠀⠒⠈⡈⣇⢇⡉⣐⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠈⡇⠀⠀⢹⣆⠀⠀⠀⠀⢣⢛⡬⠁⢹⠀⠲⡍⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠀⢠⠷⠤⠤⢋⠿⡁⠀⠀⠀⠸⡌⠃⠀⣈⡧⠄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⡏⠡⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠂⢨⠈⠁⠐⠖⠆⠀⠀⠀⠀⠀⠌⢀⣠⢤⣀⠑⡀⠀⠀⠘⠀⠀⠀⠸⠀⡠⠶⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⡀⠀⢰⣸⣄⡀⠀⠀⠀⢸⢰⢫⡂⠀⡎⢆⢳⠀⠀⠀⡇⢀⢠⠀⡟⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⡷⣮⠀⠀⢤⡄⠀⠀⠀⠈⠸⠸⡃⠀⡇⠀⠌⠀⠀⠀⢹⠈⢏⣊⡧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠀⠂⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠴⠒⠶⠘⡦⢖⡢⣤⠀⠀⠀⣠⠎⠉⠑⢎⠁⣂⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⡓⠒⡷⢾⡁⠀⣠⠎⠀⡄⠴⠁⣀⣀⢀⠔⠛⠑⢎⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⡋⠀⠀⡹⠖⠁⠀⠀⠘⠓⠚⠀⠈⡏⠀⠒⡤⡸⠀⠀⠀⠐⠛⠒⠒⠒⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢐⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⢲
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⠀⠙⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡾
⠘⡄⠀⠀⠑⢪⡐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠤⠤⠤⠇
⠀⠙⢦⣀⠀⠀⣙⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⡿⢿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠅⠨⠨⠅
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⠀⠀⠀⢀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠘⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢺⠒⠚⡅⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠛⣆
⠀⠀⠀⠀⢀⡎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠒⢺⠓⠒⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⣠⠀⢸
⠀⠀⡀⠘⠞⠀⠈⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠺⠒⢲⣡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠉⠉⠓⢋
⠀⠀⠑⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣔⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢾⡀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀
⠀⠀⡴⠦⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠅⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡤⠃⠀⠀⠧⣤⠴⠁
⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠉⢢⠀⢀⠞⠉⠑⡄
⢠⡚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠭⠭⠭⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠷⠶⠐⢄⠈⡆
⠀⠀⠀⡀⢠⣀⣔⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡈
⠀⠆⠀⣴⠎⠈⢯⠉⠓⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠿⠷⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡅⠀⠀⠀⣜⠄
⡀⢰⣰⠃⠀⢀⣈⣧⡤⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠁⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡽⣄⠀⢀⣨⠆
⢡⠈⡿⢏⡉⠉⠁⠹⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⢀⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⠒⡋⠱⡈⠆
⠈⠣⣅⠀⠙⠿⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠤⠤⠤⠤⠜⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⣀⠄
⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⡞⠛⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠤⠤⠤⠤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣉⣉⣉⡉⠀⠀⣾⣿⣿⣿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡄⢠⠒⢉⠛⣰⠇⠀⠁
⠀⠀⠀⠘⢿⣿⢏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⡀⠀⢀⣿⣿⣿⠭⠭⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⢦⡁⠄⠰⠃⢠⡀
⠀⠀⠀⠀⠑⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⠀⠻⠿⣿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣄
⠀⠀⠀⠐⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠁





⠀⠀⠀⠀⣰⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣲⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⢄⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠢⠤⢤⡄
⠀⠀⠀⠀⠀⠀⡎⠛⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠄⠀⠀⠀⠹⠯⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣄⠀⢀⣤⠖⠊⠀⣿
⠀⠀⠀⡇⠀⠀⠛⠋⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠛⠉⠀⠙⢦⠀⡏
⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠭⠭⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠕⠒⠒⠋⠙⠛⠒⠲⠷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣤⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠁⠉⠉⠛⠋⠉⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣶⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣵⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣎⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢿⣿⣿⣼⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⠐⠂⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡠⢠⡀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠉⣭⡍⠀⠀⠀⠀⠈⢛⣿⣶⢻⡟⠃⠀⠀⠀⠀⠈⣶⢶⣶⡎⠰
⠀⠀⠀⠐⠀⡁⠔⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠈⠀⠀⠀⠀⠠⠣⠤⠤⠡


⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣼⣿⣿⣿⣷⠠⠀⠀⠀⠀⠨⠑⢄⡠⠊⣣⡄⠀⠀⠀⠀⠀⣿⣿⡆⠁⠀⠀⠀⠀⠀⠠⠀⡄⠘⣿⠃
⠀⠀⠈⠙⠿⠟⣡⠒⠀⠀⠀⠀⠰⠦⠤⢀⡾⠛⠃⠀⠀⠀⠀⠀⢿⣿⣇⡄⠀⠀⠀⠀⠀⠰⠼⠧⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⣿⡟⠻⣿⡇⠀⠀⠀⠀⠀⣶⡆⠀⢠⣶⠄⠀⠀⠀⠀⣴⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰
⠀⠀⠀⠿⠷⠾⠿⠇⠀⠀⠀⠀⣰⣾⣶⡀⣴⣷⣦⠀⠀⠀⠀⣿⣀⣐⣀⣐⡗⠀⠀⠀⠀⢸⣷⣼⣿⣤⣼
⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠁⠉⠉⠁


⠀⠀⠠⡆⠨⠧⠀⡦⠀⠀⠀⠀⠀⠀⠛⠛⠛⡆⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⡆⠀⠀⠀⠀⠰⠖⠒⠒⡲⡆
⠀⠀⠈⠉⢠⣤⠈⠉⠀⠀⠀⠀⠀⠀⠰⣶⡆⠁⠀⠀⠀⠀⠀⠀⠑⠁⣋⣁⠀⠀⠀⠀⠀⢀⡀⠁⠈⢴⡔
⠀⠀⠀⠀⠴⠷⠄⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠃⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠦⢤⡄
⠀⢠⡾⠉⠻⣦⣀⣀⣠⣤⡼⠧⠀⠙⢦⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠉⠀⣀⡀⠀⠀⠀⠀⢻⡄
⢀⣿⠁⠀⠀⠈⠛⣉⣁⣤⡤⣤⡄⢠⣀⣹⠂⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⢀⡤⠖⠊⠉⠉⠉⠙⢧⣀⣀⣤⣼⠃
⢸⡇⠀⠀⠀⠀⠀⠈⠻⣤⡀⣸⠃⣼⠉⠀⢰⣇⡷⠀⠀⠀⠀⠀⠀⢠⡶⢋⣹⡦⠀⠀⢀⣼⢁⡼⣧⣀⣀⣠⣿⡄
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢀⡿⠀⣰⠟⣼⠇⠀⠀⠀⠀⠀⠀⡏⢰⠋⠀⠙⢲⡿⠟⠛⠛⠃⠀⠉⠉⠁⠀⠛⠛⠛⠲⣄
⠀⢻⣆⢀⣤⡄⠀⠀⠀⠀⠀⠀⢻⣧⡀⢩⡾⠃⠀⠀⠀⠀⠀⠀⠀⢳⣈⠳⠤⠤⠿⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣧
⠀⠀⢻⡞⣁⠹⣆⠀⠀⠀⠀⠐⢋⡼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠛⠃⠀⠀⠈⠳⣤⣀⣀⣠⠴⠋⠀⠀⠀⠀⢸⡄
⠀⣰⡟⠀⠈⠀⠘⢧⣀⣀⣀⣈⣥⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⢠⣧
⠀⠿⠶⠶⠶⠶⠶⠾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡿⠁⠀⠀⠀⢹⡛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⣼⠁⠀⠀⠀⣀⡼⠧⢼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣠⠤⠶⢦⡀⠀⠀⣴⠶⠦⣤⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠀⠿⢶⣄⢠⡾⠋⠊⠉⠓⢮⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢉⣁⣤⣤⡄⠸⣇⠀⢸⡇⢰⠶⠤⣬⡉⠙⣷
⠀⠀⠀⠀⠀⠀⣰⠟⠛⠒⠀⠀⠀⠙⢿⡁⠀⠀⠀⠀⠀⢷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡏⠁⠀⠀⠃⠀⢻⠀⡿⢠⣉⡀⠀⠀⠅⢰⡇
⠀⠀⠀⠀⠀⣸⣏⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡸⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣩⣤⡆⠰⠾⠗⠸⣷⡇⠈⣉⡁⠘⠻⠂⣾
⠀⠀⠀⠀⠀⢻⡟⠇⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⢀⡴⣡⡿⣭⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⣁⡤⠤⠖⠒⠀⢿⡄⠀⠸⠏⢍⡆⢸⠇
⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⠀⠀⢀⡼⠉⠳⠦⡬⠵⠞⢋⣤⣼⠇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢷⢺⣀⠀⠀⠀⠈⣇⠀⠈⠀⢰⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣭⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⢿⡁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⡍⠀⠀⠀⠀⠀⢻⣦⣤⣄⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⣤⠶⠶⠛⠋⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠐⠂⠀⠀⠀⠐⠐⠀⠀⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠒⠀⢀⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠉⠻⠿⣿⣿⠋
⠀⠀⠀⠀⠀⢀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠀⠀⠀⠀⠀⠹⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⠀⠀⠀⠠⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡄⠀⠀⠀⢀⣴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠒⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠲⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣷⡄
⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢳⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⡇
⠀⠀⠀⠀⠙⢢⡄⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣭⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⣎⣀⡠⠤⠔⠒⠒⠫⢅⣀⡀⠀⠀⠀⠰⡊⠁⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠟⠛⠛⠉⠉⠐⠾⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠢⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠆

⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣖⣒⣲⣖⣲⣶⣶⣖⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣶⣋⣹⣶⣿⣋⣳⡆⠀⠀⠀⠀⠀⠀⢜⣹⠈⠐⢠⡤⣤⣄
⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡇⢸⠙⣶⠚⣿⠁⡇⠀⠀⠀⠀⠀⠀⢘⢿⠀⠀⣸⣇⣾⣿⠃
⠀⠀⠀⠠⣧⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠘⠿⠿⠶⣶⣾⡿⠿⠿⠟⠀⠀⠀⠀⠀⠉⠺⢄⣹⢀⣸⠤⠇⠀⠀⠀⠀⠀⠀⠈⠓⠈⠁⠀⠘⣥
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⢠⢴⡾⢻⡿⣶⢤⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣒⣲⠦⢤⡀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⣤⣤⣤
⠀⠀⢰⠏⣿⠛⢻⡛⢻⡏⢳⠀⠀⠀⠀⠀⠉⡤⠒⢉⣉⡙⠲⡌⠁⠀⠀⠀⠀⠀⢀⡥⠚⠙⣦⣴⣿⡇⠀⠀⠀⠀⢸⢰⣤⡄⡇⣀⠀⠿⠿⢿
⠀⠀⠸⡟⢿⠛⢻⡏⢹⡏⣻⠀⠀⠀⠀⠀⠀⠀⠊⣡⠬⣍⠃⠀⠀⠀⠀⠀⠀⠀⠺⣶⣾⣿⢟⣫⡞⠀⠀⠀⠀⠀⢸⠘⠛⠇⡇⠸⠶⠶⠆⢸
⠀⠀⠀⠙⢯⣿⣹⣿⣟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⣿⣄⠀⠀⠀⠀⠀⠸⠤⠤⠤⠥⠬⠤⠶⠦⠼
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⣤⣤⠤⢤⡀⠀⠀⠀⠀⠀⣠⠖⡾⣏⣉⣳⣖⢢⡀⠀⠀⠀⢀⠖⠉⠉⠉⠉⠉⠉⠑⢢
⠀⠀⠀⠀⣼⣿⣾⣾⣷⣄⠀⠀⠀⠀⠀⠀⡏⠑⣤⡀⠀⣠⡔⠋⡇⠀⠀⠀⠀⢰⡷⠾⢣⣽⣿⣅⢻⠶⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣧⠞⠁⠉⠉⠁⠙⣤⡇⠀⠀⠀⠀⢿⣣⣃⣙⣿⣿⣟⠈⡇⠀⠀⠀⠀⠈⠦⣀⡀⠀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⢷⢸⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠹⠟⠛⠛⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠽⠚⠁
⠀⠀⠀⠀⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⡶⢲⣶⣶⣶⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠃⢂⣄⠆⠃
⠀⢠⠃⠀⢩⣷⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠚⣃⠀⡟⠒⠒⡆⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠘⠢⠤⣿⠟⢀⠔⢁⣀⣀⣀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⣿⣡⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⡄
⠀⠀⠀⠀⠀⢰⣁⡤⡏⠀⠰⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢰⢤⣅⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠒⠒⠋⠀⠀⠀⠀⢧⢀⣀⣀⣀⣀⡼⠋⠀⠀⠀⠀⠀⠀⢿⣤⣼⣿⣶⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⡼⢼⡀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠡
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠒⠓⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢙⠁⡰⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⠀⠀⠀⢀⠀⠘⠀⠿⠀⠰⠀⠀⠀⠀⢀⢠⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡖⢸⠃⣟⠀⠀⠀⢃⠀⢈⠀⠛⠁⠃⠀⠀⠀⠀⠀⢸⡆⢘⡟
⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠐⠀⠀⠀⠀⠀⠂⠘⠀⠃⠘⠃⠚⠀⠏⠀⠀⠀⠀⠁⠙⠀⠄⠀⠀⠠⠂⠀⢦⠠⠀⢓⣠⠄⠂
⠀⠀⠀⠀⠐⠇⠀⠀⠄⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠂⠀⠀⢤⠄⠀⠀⠀⠀⠀⡤⠀⠆⠀⠀⠀⠠⠀⠜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢯⡅
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⣀⠄⠀⡳⠀⠂⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠄⢂⠀⠀⠀⠀⣀⡠⠀⠀⠄⠈⣉⠀⠨⠠
⠀⠀⠀⣀⡰⠃⠀⠰⡧⠐⠂⣾⡅⠐⠂⠀⢀⢀⣀⢀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠊⠤⠤⠂⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢉⣧⠆
⠀⠘⣇⡇⠀⠂⠀⠀⢁⡀⠀⠨⠷⡤⠁⠐⢋⢀⠁⠺⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⢻⠇⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢻⣋⡁⠀⠀⠒⠀⠀⠀⠴⠁⢀⠀⠠⠄⠒⠀⢀⠀⠀⠂⠀⠀⠸⡛⠱⠟⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠠⠀⠬⢀⡴⠀⠈⠒⠀⠀⠀⠀⠠⣬⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢹⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⡐⠁⠀⠀⣀⡠⠤⠰⠧⠄⢸⣿⡆⠀⡄⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠝⠲⢴⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣾⠉⠁⠀⠀⠀⢀⡌⢠⣾⣿⠇⠰⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠖⠇⠀⠈⣸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡑⠂⠄⢤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⣀⠀⣀⣀⣀⣀⣀⣀⡀⢀⣀⢀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⢠⣀⡀⢀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⡤⠤⢤⢠⣤⣭⣤⣤⣤⡄⢤⡄⢠⣤⣤⢤⣤⣤⡤⢡⣤⡄⠠⣤⣤⣤⣤⡄⣤⣄⣤⣤⣤⣤⡤⣤⣤⣤⡄⢤⡄⢠⣤⠤⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⠿⣒⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢛⣙⢻⣿⠟⣉⡻⣿⡿⣋⡙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣌⣋⣼⣿⣮⣛⣵⣿⣧⣙⣣⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⣿⣿⣿⣿⣿⣶⡍⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⣀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣷
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿
⣿⣿⣿⢋⣥⣦⣬⣭⣭⣭⣭⣭⣭⣭⣥⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿
⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣮⣭⣍⣛⣛⣛⡛⠿⣿⣿⣿⣿⠈⣿
⠈⢿⣷⣜⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡝⢿⣿⢰⣿
⠀⠀⠹⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡎⠟⣼⣿
⠀⠀⠀⠀⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⠿⢟⢱⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⠿⠸⢿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⣠⣶⣿⣿⣶⣮⣍⣛⠿⠏⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡘⠿⢛⣫⣭⣶⣿⣿⣷⣮⠉⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿
⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡧
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠓⠶⣄⡀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⣠⣀⣀⣀⣠⠴⠚⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡤⠖⠛⠛⠲⣼⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠻⢿⣷⡖⠋⠉⠙⠳⣄
⠀⠀⣾⠁⠀⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢸⡆
⠀⠀⢿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⢤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠞⠁
⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⢠⠄
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⢠⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⠀⠀⢸
⠳⣤⣾⠀⠀⢸⠀⠀⠀⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⡇⠀⠀⢸⠀⠀⢸⡦⠴
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠹⣄⠀⢸⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣼⣀⣀⡼⠁
⣶⣶⠶⠾⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⠀⡒⠄
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠉⠁⠑
⠠⠀⣴⠋⢫⠑⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡾⠷⠦⠶⠴⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⡉⠀⠀⡦
⡄⢷⡥⠤⠤⢷⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡤⠞
⠱⣌⠙⠶⠄⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⣀⡠⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠂⡈
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⢉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⡄
⠀⠀⢸⣿⣿⠱⠀⠀⠀⠀⠀⠀⢸⡇⠀⠨⠭⠅⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠁⠠⡠⠂⠙⡱⠃
⠀⠀⠈⢻⠿⠃⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢦⡀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⣆⣀⠁⠐
⠀⠀⠐⠚⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛



⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠁⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠊⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀
⠀⠀⠀⠀⣈⣓⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣀⡤⢖⠁⢸
⠀⠀⠧⠤⠬⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣛⣦⡚⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠤⠤⠤⠤⣱⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣶⣶⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⣿⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⠀⣿⡟⠛⢿⣦⠀⠀⠀⠀⠀⣀⣁
⠀⠀⠀⣴⡿⠛⠛⢿⣆⠀⠀⠀⣿⠀⠀⠈⠛⠀⠘⠃⠀⠛⠁⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣰⡿⠛⠛⢿⣦
⠀⠀⢸⣿⠀⠀⠀⢈⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⣿⠀⠀⠀⣿⡁⠀⠀⠀⣿⡇
⠀⠀⢀⣿⣷⣦⣴⣾⣯⡀⠀⠀⣿⣀⣴⢾⣷⠿⠿⠿⠿⠿⠷⠿⠿⠋⠀⠀⠀⣿⠀⠀⢀⣽⣷⣦⣴⣾⣿⡀
⠀⢰⣿⠃⠀⠈⠁⠀⠙⣿⡄⠀⣿⠟⠁⠀⠻⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣿⠀⢠⣿⠋⠀⠈⠁⠀⠘⣿⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⠻⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠻⠿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣀⣀⣀⣀⣤⣤⣶⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠐⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠷⣤⡈⠻⢦⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠙⠃
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⣠⣤⣤⠀⠀⣠⣤⣄⠀⠀⠀⢸⣇
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠻⣦⡾⠃⠀⠻⣤⡿⠀⠀⢿⣤⡿⠀⠀⠀⢸⣿
⣿⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣧⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠻⣆⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⣀⣀
⠀⠀⠙⠃⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⣠⡴⠟⢋⣡⣤⡶⠶⠛⠛⠛⠛⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣤⣀⣀⣀⣀⣀⣤⣴⠶⠛⠉⠀⢠⡾⠋⢠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠘⣷⣴⠟⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣴⠟⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢰⡟⢻⡆⠀⢰⡟⢳⡄⠀⣴⠟⢷⡄⠀⠀⠀⠀⠀⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⠛⠛⠁⠀⠈⠛⠛⠁⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣶⣦⠴⠶⠞⢷⣄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢐⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⢲
⢰⠀⠀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠑⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡞
⠈⢆⠀⠀⠈⢦⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⠛⠛⠁
⠀⠀⠑⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬



⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡧⠤⡧⢤⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⢳
⠀⠀⡀⢴⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣡⠤⠧⢤⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠒⠚⠦⢊
⠀⠀⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤
⠀⠀⠀⠀⣠⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣄⠀⠀⢀
⠀⠀⠀⠀⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠁
⠀⢀⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠀⠀⠣⣀⠜
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠙⠄⠀⠖⠉⠱
⠰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋

⢀⠔⠊⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠒⢄⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄
⡎⢀⡄⣄⣠⣠⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⢠⣀⡄⡄⠈⡆⠀⢰⣿⡟⣿⢿⢿⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡿⡿⢿⢿⣿
⢇⠀⠋⠉⠉⠈⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⠉⠉⠁⠋⢀⠆⠀⠸⣿⣯⣶⣶⣾⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣷⣶⣿⣽⣿
⠈⠳⢄⣀⣀⠠⣄⠱⡀⠀⠀⢀⠤⠒⠢⢄⠀⠀⠀⡰⢃⡤⢀⣀⣀⠴⠋⠀⠀⠀⠙⠿⣿⣿⣿⢿⣿⣆⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⣰⣿⡿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢈⠀⠀⠀⠈⡆⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⢰⠋⠉⠳⠀⠘⠦⣤⡤⠞⠀⢰⠋⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆⠀⠙⢿⣿⡿⠏⠀⣰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠈⢢⣤⠞⡴⠒⠀⠀⠀⠀⠲⡜⢢⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠋⣠⣴⣶⣶⣶⣦⣄⠙⢿⡿⠏
⠀⠀⠀⠀⠀⢠⠊⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣦⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⡇⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⠲⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡅⢎⡇
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠛⠀⠒⠒⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢊⠴⠁⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠸⠃⠀⠈⡆⡔
⠀⠠⠀⠀⠀⠀⣰⣁⡍⢀⡴⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠓⠒⠒⠒⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠀⠀⠀⠀⠀⡠⠂⠉⠉⡇⠢⡀⠀⠀⠀⠀⠀⡇⡤
⠀⠀⠀⠙⠔⠉⠉⠉⠉⠁⡜⢣⠈⠉⠉⠉⠉⠑⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢘⠀⠀⢀⡴⢆⠀⢸⠀⠀⠀⠀⢀⠈⡀
⠀⠀⢠⠖⠉⠉⢹⠙⠢⡀⠑⠊⠀⢀⠔⠋⠉⠉⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⢦⡀⠀⠈⢹⠈⠁⠀⠀⠸⠛⠀⠀⢀⠔⠁⠀⢈
⠀⢀⠁⠀⠀⢀⠾⡀⠀⢡⠀⠀⢀⠃⠀⠀⢀⠼⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⠦⣠⡈⢆⡀⠀⣀⠞⢸⡤⠔⠁⠀⢀⠴⠁
⠀⠀⠙⠂⠉⠁⠀⠈⢙⠈⠀⠀⠈⠛⡆⠈⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠉⠈⠉⠀⠁⠀⠀⢀⠔⠁
⠀⠀⠀⢆⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡔⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⡠⠒⠛⠂⠘⠓⠢⡀⠀⠀⠀⡤⠖⠛⠃⠘⠋⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠊⠙⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢣⠀⡴⣔⢉⢩⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡔⠒⢄⠀⠈⠁⠒⢄
⠀⠀⠰⠢⢄⠀⠀⡰⠛⢤⡣⠄⠃⠈⢣⠀⢀⠀⢀⡆⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠢⡊⠗⢄⠀⠀⠈
⠀⠀⢐⠀⠠⠃⠀⠑⠀⠲⡀⠁⡛⠀⠘⠀⠀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠙⠦⠴⠃⡀⠜
⢀⠄⣈⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠑⡲⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡀⠑⠄⣀⡠⠎⢠⠒⠄
⠣⠠⠆⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢦⠀⠀⠐⠒⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢬⣊⠀⠀⠀⠀⠀⠀⢈⡓⠅⢠⣄⡀
⠀⢠⠄⠤⡀⠀⠀⠠⣁⣀⡠⠚⠤⣀⡇⠀⠀⠀⡠⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢠⠀⠑⢄⠀⠀⠀⡰⠋⠀⠀⢠⠀⠉⢆
⠀⠸⡀⠀⠉⠢⡀⠀⢘⡀⠀⠀⠀⡇⠀⠀⡠⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⠴⠋⠢⣀⣈⠀⠀⠀⣇⣀⣀⠤⠊⠢⢀⣈
⠀⠀⠈⠢⡀⠀⠈⠒⠤⠵⠦⠤⠾⠤⠐⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⢨⠈
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⣀⣠⠃⠀⠀⠀⠀⡇⠑⣄⣀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠗⠉⠀⠀⠀⠀⠉⠲⡀
⣀⣀⣀⣀⣀⣀⣀⣘⣤⣄⣀⣤⣤⣤⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣤⣤⣤⣤⣤⣤⣤⣃⣀⣈⣀⣀⣀⣠⣄⣤⣤⣤⣃
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠉⠉⠉⠉⠑⠒⠢⠤⣠⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⣄
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⡜⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠘⡀⢰⠇⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⢹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢣⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⢠⠃⠈⣇⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⢀⡞
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏
⠀⠀⠀⠈⠓⢦⠀⠀⠀⠀⢀⣤⣤⣤⣤⡤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⣄⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⡸⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⠀⠀⢻⡀
⠀⠀⠀⢀⣴⣁⣤⣴⠯⣄⡀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⠬⢝⡲⠦⠵⠆
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠉⢢⠀⠀⣇⣴⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⡴⠋⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣼⣄⡤⠤⠴⠓⠦⣄⣇⠀⠘⠁⠈⠉⠓⠲⠶⠦⠤⠶⠖⠒⠋⠉⠀⠀⠀⣰⣅⣤⠤⠤⠒⠦⣄⣵
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⣀⣨⡗⠢⠤⠔⣾⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣵⠢⠤⠤⢺⣅⣀
⠀⢀⠔⠋⠁⠀⠈⠒⠒⠚⠁⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠓⠒⠒⠉⠀⠀⠉⠢⡀
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉
⠘⠦⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠣⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⣴⣴⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⠀⠒⠂⠋⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⣰⣶⣮⠁⠀⠀⠀⠀⠀⠀⠻⠷⠟⠀⡠⣤
⠀⠀⠀⠀⠀⡠⠀⠉⠁⠀⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡙⢿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠙⠛
⠀⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠡⠀⠑⡀⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢴⠛⠛⢿⣿⡆⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠁⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣵⣭⣴⣭⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣀⡀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠇⣾⣿⣿⡆⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃
⠀⠀⠀⠀⣠⣶⣮⣷⠶⣘⠻⢟⣑⢶⣮⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣈⣅⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣩⣡⣤⡀
⠀⠀⠀⠀⠛⠛⠛⢳⣿⣿⣿⣿⣿⣷⡙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡟⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠶⢤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣦⣶⣶⡄
⠀⠀⠀⠀⠀⢀⣴⣶⣴⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⡀⠀⠀⠀⠀⣘⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠘⠛⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⢿⣋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⢿⣿⡇⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣍⣛⣋⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣦⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣠⣦⣭⣶⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⡿⢏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠛⠛⠛⠛⠛⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠈⠉⠉⠉⠉⠁⠒⠢⠤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠉⢀⡀⠀⡇⠀⠀⢀⢴⠀⡘⠯⠀⠙⡆⠀⡠⠊⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⡫⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁⠀⠀⠀⢤⢰⣎⡇⠀⠇⠀⠀⠀⠸⠰⠀⠒⡈⠴⠁⢠⡃⠀⣼⣧⡾⣸⢿⠋⣴⠂⠀⡴⠀⠀⣠⣤⠀⣀⠣⠀⠈⠁
⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⡄⡾⢳⡜⠿⠉⢁⢴⠃⠀⠀⠀⢐⠂⠐⠐⢀⡜⠀⢸⠳⡀⠉⠀⠁⠙⠛⠚⠷⠶⠸⠧⠤⢾⣥⣽⢐⠃⠀⠀⢄
⠀⠀⠀⢀⠀⡀⠀⢰⡄⣧⣿⠙⠋⠀⢀⠔⠁⠀⠀⠀⠀⠈⠓⠂⠮⠕⠁⠀⠀⠀⠑⢌⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢄⡀⠀⢢
⠀⠀⠀⠈⠄⠰⠀⠀⠛⠁⠀⠀⢀⡴⠃⡠⠊⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠬⣉⡒⠒⠀⠲⠖⠀⠒⠐⣒⡨⠅⠢⣌⢦⡀⢡
⠀⠀⠀⠀⠐⠀⢃⠀⠀⠀⠀⡠⢊⠔⠊⠀⠀⢀⠔⡒⠒⠐⠊⠀⠀⠈⠐⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠢⠱⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⢊⠔⠁⠀⠀⡠⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⠡⠀⠐⠐⠂⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠱⣱⡀
⠀⠀⠀⠀⠀⠘⡀⢁⠀⠗⠁⠀⠀⠀⢀⠇⠀⠀⣀⢤⡀⢤⡀⢶⡀⢰⢲⠀⢹⠂⠀⠀⡡⠀⠀⠀⠀⠠⡄⢦⢰⣖⠐⣶⠂⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠀⠀⢠⠁⠀⠀⠀⣿⠀⡇⢠⡗⣦⠳⠸⠏⠇⢰⡄⠀⠐⡅⠀⠀⠀⠇⠀⡅⠸⠀⠻⠄⠘⠀⠸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠑⠲⠀⠀⠈⠘⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠂⠀⠀⠄⣀⠀⠄⣀
⠀⠀⠀⣀⠀⠀⠀⠰⠀⠳⠀⠀⠠⠀⠀⠡⢈⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠠⡀⡂⠀⠀⠀⠀⢀⠀⠀⠀⡌⠀⣤⢠⡄⠀⠀⠀⠀⡑⠠⠁
⠀⠀⠀⣀⠈⠢⡀⠀⠡⠁⠀⠀⠈⠐⠁⠀⠀⠀⠀⠉⠂⠂⠁⠂⠐⠉⠈⠉⠁⠀⠀⠀⠀⠙⠈⠀⠀⠀⠚⠁⠀⠀⢠⠁⢀⠌⣸⢇⠗⡷⠀⡐⠀⠁
⠀⠀⠠⢀⡈⠀⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠀⠀⠀⣀⠄⠀⠄⡀⠀⠀⠁⠈⠘⠁⢠
⠀⠀⠐⠀⠀⠙⠂⠀⠀⡠⠈⠀⣀⠀⢀⡄⣠⡠⣤⡤⢤⠀⢠⣄⣤⣠⠄⢀⡤⣠⢄⡄⠀⠠⠀⠀⡇⠀⠈⠔⣢⢀⠀⠀⠈⠀⠀⠄⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢄⣀⠀⠀⠈⠁⠉⠀⠉⠁⠈⠀⠀⠁⠉⠉⠁⠀⠉⢉⣀⣀⣀⠠⠤⠔⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⡀⣀⠤⠒⠒⠒⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⡀⠤⠁⠀⠐⠒⠂⠈⠉⠉⠨⠀⠀⠀⠀⠀⠀⠀⠠⠔⣊⠜⠉⠢⠤⠤⠰
⠀⠀⠀⠀⡚⣡⠊⠁⠀⠀⠀⣀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠇⣠⠀⢀⡀⣀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢐⡃⠀⠀⡖⢺⠋⠙⣺⠁⠀⠠⢆⠀⠀⠀⠀⢰⠀⠥⡖⠫⠚⠥⠓⡜⠀⡘⠀⠀⠀⠀⠀⡄⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠆
⠀⠀⠀⠀⡼⠁⠀⢀⣁⡈⢀⢀⢁⣀⠀⠀⠀⢳⠀⠀⠀⡈⠀⠂⢰⢰⠶⢱⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠡⠄⠒⢀⠀⣀⠀⠀⡎
⠀⠀⠀⠰⠁⠀⠀⠾⠂⠇⠾⠾⠿⠧⠀⠀⠀⡰⠀⠀⠀⠇⠀⠓⠙⠃⠘⠘⠓⠈⠀⠐⢄⠀⠀⠀⠠⡁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠠⡀
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⣀⡀⠀⠀⠤⠤⠄⠀⠐⠁⠑⠄⠆⠀⠀⠀⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠒⠉⠁
⠀⠀⠀⠀⠀⠉⠒⠶⢤⠄⢀⠰⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⡘⠀⠀⠀⠀⠀⠁⠀⠐⢠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡤⠒⠂⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠐⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠉⠉⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠃⠘⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⢛⣩⣴⣶⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣿⡟⣡⣾⣿⣿⣿⣿⠟⠉⠉⢻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠿⠟⣰⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠒⠚⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣉⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣶⣝⢿⣿⣤⣤⣤⣤⣤⣤⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠻⢿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠦⠤⠾⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠛⠉⠈⠉⠉⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠐
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢾⠸⢄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⣀⠠⠤⡀⠀⠀⡠⠒⠒⠈
⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠸⠀⠀⠀⠀⠡⠀⠠⠊⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠐⠃⠉⠍⡀⠀⠐
⠀⠀⠀⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡠⠀⠀⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠉⠀⢀⠌⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠓⠠⢴⠡⢀⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⢢⣀⠀⠁⢈⣁⣴⣀⣀⣀⣤⣤⣼⠶⣤⣤⣤⣴⣦⣶⣶⣤⣴⣤⣤⣶⣆⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠼⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠭⢥⠥⡭⠭⠽⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠀⠀⠚⠀⠀⠈⠀⠁⠀⠀⠐⠂⠀⡄⠀⠀⠰⠀⠆⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠜⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⡆⡆⠀⠖⠖⠀⠀⠂⠐⢠⠄⢴⠁⠀⠀⠀⡌⠀⠀⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡇⠁⠀⡀⡆⠀⠀⢠⢠⣌⡄⣧⣄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠞⡁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡆⠀⠀⡁⠀⠀⠀⠀⢧⡀⢰⣴⠀⠀⠈⠰⠠⡀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⢶⣤⣴⠢⢔⣄⡠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⡸⠆⡼⠙⢄⣠⢴⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢿⠾⠃⠁⠈⠁⠀⠀⠉⠙⠻⢀⢀
⠀⠀⠀⠀⠀⠈⢢⣄⣀⠟⢄⠴⠋⠒⠁⠀⠀⣾⣋⣀⢸⣼⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠀⠀⡀⠀⠠⠈⠂⠐⡀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢀⡅⠀⢀⣴⠶⠿⣟⣻⡆⣶⣤⡽⢿⡾⣿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⢤⠐⠦⠀⣀⠱⠀⣠⠈⣅⠃⠀⢼⣄
⠀⠀⠀⠀⠀⠈⠉⠲⠀⢸⣇⠀⢀⣿⠛⢶⡟⣙⢆⣘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡆⠀⠐⢦⡀⠑⡄⣀⡠⠧⠈⣀⠄⢀⡃⣾⡉⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡠⠤⡝⠛⠛⡍⡠⣨⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡅⠀⠓⠄⠔⠒⠡⠀⠠⠈⠘⠁⢀⡀⠛⠛⠓⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠋⠱⢿⠟⠠⠀⠹⠇⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣳⡦⡀⢀⣀⡀⠀⢀⣤⡤⡀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠊⠩⣝⠞⠋⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣸⠋⠉⢲⣆⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⡃⠀⠈⠿⠀⠀⠘⠇⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⡴⠛⠛⠷⠀⠀⠤⠠⠒⠔⠦⣠⡌⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢱⣟⣷⠄⠀⠀⠀⠀⠀⠀⠙⠆⠀⠻⡄⠀⠀⠀⠸⢧⡀⡀⠀⠐⡄⠀⠐⠊⠂⠙⠉⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡔⠈⠉⠱⢞⡴⣀⡀⢀⡀⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡼⠛⠃⠀⠁⠀⢰⣄⣠⣄⣦⣤⢋⠉⠀⢀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠐⠚⣷⣛⡾⣳⢱⡆⣦⢈⠀⠀⠀⠀⠀⠀⢧⡀⢈⣤⢨⣷⠿⠿⣿⡟⣉⠻⠀⢡⣆⠈⠀⠈
⠀⠀⠿⣇⡀⠀⠈⢱⡀⠀⠀⠀⠁⠈⠁⠉⠘⠀⢣⡏⠀⠀⠀⠀⠀⠀⠀⠉⠋⣏⠀⠁⣾⡇⠙⠀⣿⢆⠀⣆
⠀⠀⠀⠙⠷⠀⠀⠀⠛⠦⣄⢄⠀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠙⡟⢒⢚⠑⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠒⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠆⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣀⡐⠀⠀⠀⠀⠀⠰⠶⢐⡄⢀⣠⠞⠛⠉⠉⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⠟⠉⠉⠈⠉⠙⠆⠀⠀⠀⠀⠀⠀⠈⢀⣿⠁⠀⠀⠀⠀⠀⣀⢀⠀⠙⢠
⠀⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡽⠃⠀⠀⠀⣠⣄⣦⣶⡳⠀⣿⠤⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⣲⣀⡤⠀⠀⠂⠈⢱⡃
⠀⠘⠀⠀⠘⡈⣿⣷⣶⣄⠀⠀⣈⠤⠀⠀⠀⠀⠀⠀⠈⠇⢰⣶⡾⠽⠛⠋⠈⠀⢀⡶⠯⠤⠄⠀⠀⠀⠀⠀⠳⣀⠁⠈⢀⡠⢤⠀⠀⡶⠒⢋
⠀⠀⠀⠀⠐⠀⠙⠿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠁⠀⠀⡀⢀⣴⠴⠚⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠁⠀⠀⠃⣄⣧⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠶⠞⠃⠏⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠀⠰⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⢸⣿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⣿⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣤⡄⠀⠀⣿⡿⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⠀⠍⢻⣧⠀⠀⣤⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠙⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢹⣿⣿⠿⠛⠻⢿⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣇⠀⠀⠀⠀⠀⢀⣿⣷⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢈⣹⣦⣄⣀⣀⣤⣾⣉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣠⣤⣤⣶⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠋⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠠⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠑⠂⠰⠀⠐⠒⠉⢀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⣀⣀⣄⣀⣠⣀⠀⠐⠂⠂⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀⠀⠀⢈⠔⠒⠃⠈
⠀⠀⠀⠀⢀⠁⠀⡰⠀⠀⠀⣠⡆⣀⣒⢀⠄⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⡀⠠⡐⠀⠀⠀⠈⠄⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠂⠀⢈⢠⠟⠀⠀⠉⠉⠓⠺⡄⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠔⠅⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠼⠀⢀⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠐⠀⡼⠴⠀⠠⢬⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠀⠉⠀⠀⠈⠉⠁⡤⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠴⠦⠆⠀⠔⠋⠁⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠠⠄⠀⡆⠠⢸⡀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⢄⡀⠀⠀⡈⠀⡠⠂⢀⡀⠀⠀⠀⠀⠀⠙⢄⡁⠂⠀⣀⡄⢁⠀⡀⠳⣄⠈⠀⠁⡠⡞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠢⢄⣀⢥⠚⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠀⠀⠀⠆⠙⠒⠊⣩⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣁⠀⠁⠂⣤⠐⠈⢀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣤⠒⠓⢤⡀⠀⡠⠓⣥⠤⣇⠸
⠀⠀⠀⠀⠀⡄⠒⠉⠀⠀⠀⠙⠒⠚⠑⠙⠒⠉⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠁⠂⠤⠤⠅⠀⠈⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⡇⠀⠒⠀⢰⠀⠀⡖⡆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀⡠⠂⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠁⠊⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣠⣴⡾⠋⠉⠉⠉⠙⢿⠶⢦⣄⠀⠀⠀⠀⣠⣴⣾⡟⠋⠉⠉⠉⠉⠉⠉⠛⣲⣤⡀
⠀⠀⠀⢀⣾⠟⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⣸⡟⠈⢻⣄⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿⠇⠀⢻⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠋⠀⠀⠈⠻⢶⣶⠶⠾⠿⢿⣦⠀⣰⠟⠛⠋⠁
⠀⠀⠀⠀⠙⠷⢶⣶⠒⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⣁⣴⠏
⠀⠀⠀⠀⠀⢀⣸⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠿⠿⠿⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣦⣄
⠀⠀⠀⢠⣾⣯⡅⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣯⣀⡀⠀⠈⠹⣿⣶⣦⣄
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠇⠀⢻⣇⠀⠀⢠⣾⠟⠉⠉⠈⠉⠀⠀⢀⡿⠀⠈⢿⡆
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡿⠀⠀⣿⡇⠀⣀⣀⠄⠀⠀⠀⠈⠀⢀⠀⣸⡇
⠀⠀⠀⠀⠙⠿⣶⣶⡶⡞⠀⢸⣷⣦⣄⣠⣴⣦⣾⠃⠀⠀⠘⢿⣾⡟⠀⠀⠀⠀⠀⠀⢀⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣾⠃⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠹⣿⣤⣀⢀⣀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠒⠒⠂⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣭⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠤⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⢦⣄⡀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣴⣶⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⡀
⠀⡀⢀⠀⢀⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠃⠎⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣼⣿⠁⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀
⠀⠀⢠⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⣼
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⢃
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠖⠁
⠀⠐⡀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⢣⡑⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⡀⣠
⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠦⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠛⠛⢻⣦⣀⠀⠀⠀⢻⣆⢆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⢷⣦⣀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠻⢷⣦⣙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣷⣄⣀⣀⣀⣀⡀⠀⠀⡀
⠀⠀⢀⣴⣶⠿⠿⠟⠋⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠘⠛⠛⠛⠛⠿⠿⠿⣶⣤⡀
⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣀⣀⣀⣀⣀
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣦⡄
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⠀⠀⢀⣤⣶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣄⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⡿⠁⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠸⠿⠉⠿⢦⣶⠾⠿⠿⣶⡄⠀⠸⡿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣦⡀⠀⠀⠀⠀⢀⣶⠿⠿⠟⠛⠁
⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠙⢿⣦⡀⠀⠀⢸⣿
⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣄⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⡿
⠀⠀⠀⠀⣿⣤⣶⡾⠟⠋⠉⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⠏⢳⡄⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠛⠛⠛⠛⠛⠛⠂⠀⠀⣿
⠀⠀⠀⣀⣸⠃⠀⠀⠀⢸⡇⠀⠓⣲⡶⠒⠒⠲⡞⠛⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠀⠀⠀⣋⣛⣋⣉⣉⣛⡁⠀⠀⣿
⠀⢠⡟⠉⠉⢳⡄⠀⠀⢸⣇⠀⣼⠉⣾⠛⢳⡾⠛⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⢸⡁⠀⠀⢸⡇⠀⠀⠀⠙⡏⠁⠀⠙⠓⠋⠙⡶⠋⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣿⣄
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⢻⣄⠈⠉⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⡼⠋⠁⣠⡼⠟⠛⠳⣄⣺⠛⠻⣤⠈⠛⢦⡀
⣤⢸⡇⠀⠀⢸⡇⡤⠀⢀⣤⢤⣍⠓⠲⢶⣿⡁⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⣴⠋⠀⠀⣼⠃⠀⢀⡄⠀⠈⠻⠀⠀⠈⣧⠀⠀⠹⣆
⠙⣦⡙⠲⠖⣋⡼⢷⡞⠁⠀⠀⠙⠳⣄⣼⠁⢻⡀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⣼⠃⠀⠀⠀⢷⣀⠀⠈⣷⣀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⣇
⠀⠀⠉⢻⡟⠉⠀⠀⠙⠳⣤⣀⡀⠀⠈⠃⠀⠈⣧⣀⣤⠶⠋⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹
⠀⠀⡶⠾⠷⢶⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣸⡄⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠈⠛⠛⠛⠛⠀⠀⠀⢀⣤⠶⠚⠛⠉⠉⠉⠛⠛⠶⢤⣄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⢀⡿⠦⣤⡴⠏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣠⠶⠶⠶⠶⠶⠖⠶⢦⣌⠻⣦⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣠⢿⠛⠛⢉⡴⠶⢦⣄⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⠻⣄⠀⠀⠀⠘⣧⡀⠀⠀⠀⢰⠏⠘⣧⡴⠋⠀⠀⠀⠈⠳⣄⠀⢀⡼⠁
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⠀⠠⣤⣤⣤⣤⣤⣤⣤⠴⠋⠀⠀⠀⠹⡆⠀⠀⠀⠈⠳⣄⠀⠀⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣦⠟⠁
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⠀⠀⢰⠞⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⢾⣇⡀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢷⡴⠟⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠛⠛⠋⠉
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⣇⠀⠠⠤⠀⠙⠀⣿⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⠾⠁⠀⠀⢸⠛⠛⠛⠛⠛⠛⣷⡤⠤⠶⠚⢻⡆
⠀⠀⠀⠀⠀⠹⣆⠀⠀⣠⠶⠚⠛⢦⡈⠉⢩⡿⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢷⣞⠁⠀⠀⠀⠀⠙⢶⣾⠁⠘⣧⠀⠀⣸⡀⠀⠀⠀⠀⢀⣿⢤⣤⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠁⠀⢀⣹⡤⠞⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⢦⠎⠀⠀⠀⡷⠒⠖⠲⠗⠤⠤⠤⠤⠤⠤⠤⣀⢀⣭⡉⢸⠀⣸⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⡠⠤⠧⣼
⣤⣄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡟⠖⠁⢸⢸⠹⡀⠀⠀⠀⠈⠓⠤⢤⣤⣴⠃⠀⠀⠀⠈⢧⣠⣤
⠀⠀⡇⠀⠀⠀⣀⠞⠀⢀⠔⠊⠉⠉⠙⠒⠚⢡⠇⠀⠀⡇⠀⠀⢸⢸⠀⠉⠉⠉⡏⠉⢳⢰⣋⣁⣸⠀⠀⠀⠀⠀⣸⡇
⠀⠀⡧⠤⡀⢎⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⢸⠾⣄⣀⣀⣀⣧⠖⠹⡎⠀⠀⢸⡣⢄⣀⣠⠔⠁⡇
⠀⠀⢧⣄⠉⠛⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡧⣤⠤⠞⠀⠀⢧⣈⠁⡇⠀⠀⠁⠀⠀⠈⠀⠀⠀⢸⠀⠀⡇
⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠧⣇⠀⠀⠀⠀⡔⡩⠖⠚⠦⣄⡀⠀⠀⠀⠀⠀⡴⠓⢦⠀⡇
⠀⠀⡧⠤⠤⠤⠤⠤⠵⠤⣤⣀⣀⡀⠀⠀⢀⠞⠀⠀⠀⣠⡴⠃⠀⠲⢖⡛⠁⠀⠀⠀⢀⣉⣉⣉⠉⠉⠒⡡⢄⢀⠧⡇
⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠚⠁⠀⠀⠀⢠⠁⡆⠀⠀⠀⠀⡟⡆⠀⠀⠀⡏⠀⠀⠀⢹⡀⠀⠑⠋⡇⠀⣇⣀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠤⠤⠤⠤⠔⡣⠊⣧⠀⠀⠀⠀⡿⡇⠀⢲⠲⠃⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠈
⠀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⠤⠎⣠⡀⠰⣶⠲⠒⠁⠀⠻⠤⠤⠤⠤⠇⡇⠀⠀⠙⡆⠀⠀⠀⢸⠇⢠⠚⠉⠳⠤⣤⢤
⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⡰⠃⠙⣄⢈⣙⣢⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢠
⠤⠤⣄⡀⡎⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⡇⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⡀⠀⠀⠀⣠⠔⠓⠒⠺⡇⠀⠀⠀⢸⠤⠧⣄⠀⠀⡠⠚⠁
⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠀⠀⠀⣠⠔⣇⠀⠀⠀⡸⠀⠀⢸⠀⡜⠀⣀⣠
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⠀⠰⠁⠀⠀⠉⠉⠉⢣⠀⠀⢸⠀⡅⠀⡇
⠤⠤⠤⠤⢤⠭⠟⡹⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢣⡀⠳⠤
⣀⣀⡤⠖⠁⠀⠀⢇⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⢤⠤⡤⠤⢄⠀⡤⠤⠜⠀⠀⠱⢄⡀⠀⣀⡠⠋⠀⠀⠸⣄⠀⠑⢤
⠛⠒⠲⠤⣔⠒⠋⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠲⡇⠀⠀⠻⠀⢠⠖⠒⠒⠒⠒⢧⠟⠳⢦⡀⠀⠀⢀⡤⠛⢀⣼⣀
⠀⠀⠀⠀⠈⢣⠀⠀⠈⠓⠦⠤⠤⡠⠤⢄⠀⡞⠁⠀⠀⣇⠀⠀⣀⡤⠼⠶⠶⠦⣄⠀⠈⠀⠀⠀⡇⠀⠀⡸⠀⠀⡇⠘⠁
⣀⣀⣀⣠⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠂⠀⠀⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡗⠒⡎⠀⠀⠀⠙⣆⣀
⠀⠀⠀⠀⠙⠒⠒⢲⠄⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⡲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⣀⣠⠗⣏⣁⠀⠀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠺⢲⠁⠀⠀⡰⠒⠒⠒⠒⠒⠚⡃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⡴⠋⠁⠀⠀⠀⠀⠉⢢
⠤⠤⣄⠀⠀⡤⠤⠴⡊⠘⠯⣉⠁⠀⠀⠀⠀⠀⠀⠙⠦⢤⡀⢀⣤⠔⢺⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣿⣿⠿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠿⣿⣿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠉⠛⠛⢻⣿⣿⡟⠛⠛⠉⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠛⠛⠁⠀⢀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⠈⠛⠛⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⣄⣀⣠⣤⣾⣿⠗⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠐⠾⣿⣷⣤⣄⣀⣤⣴⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣴⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣦⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇







⣿⣷⣶⣾⣶⡷⢾⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⢷⡶⠾⠿⠶⢿⣶⠶⢶⠶⠶⢶⣾⠿⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⣷⡄⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢿⣧⠺⠗⣼⡿⠀⠀⠀⠀⠀⣿⣿⡏⣴⣿⣷⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣬⡛⠿⠿⢛⣥⣀⠀⠀⠀⠀⣿⣿⣷⣝⠛⣋⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⣠⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⡀⣿⡿⢫⣭⣭⣭⣍⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠛⠛⠛⠻⢻⣿⣿⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣧⡛⠃⠻⠻⠛⠿⠿⠈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠿⠛⡛⠿⣿⣿⣿⣿⣿⡿⢛⣛⣛⣛⣛⣃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⢿⡇⣿⣿⢡⣾⣿⣿⣷⡌⣿⣿⣿⣿⡇⣿⣿⣿⠿⣛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⣿⣿⣿⣿⣿⣶⣤⣿⣇⢸⣿⣿⣿⣿⡇⣼⣿⣿⣿⡇⣿⣿⡇⣾⣿⣿⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣛⣛⣫⣼⣿⣿⣿⣿⡇⣿⣿⣿⣬⣙⣭⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡟⣫⣭⣭⢩⡍⣭⣭⣝⢻⣿⣿⡇⣿⡟⢡⣶⣶⣶⣦⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡿⢸⡇⢿⣿⣿⡆⣿⣿⣧⣙⣃⣙⣛⣛⡛⠛⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣌⣡⣿⣿⣿⣧⣽⣿⡟⣩⣭⣭⣭⣭⣥⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇⣿⣿⣿⢛⣩⣛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠃⣿⣿⡇⢿⣿⣿⢂⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡿⠶⠭⠵⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⣿⡏⣰⣿⣿⣿⣷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠁⠈⠉⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⠑⢄⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠐⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡠⠤⡄⠀⢣⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠥⠀⠀⠬⠆⠈⡄⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⣍⠀⠂⠀⠄⠂⡘⠀⡇⠀⠀⠀⢸⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠈⢢⡀⠫⢃⡠⠃⡠⠃⠀⠀⠀⠗⠊⠁⠀⠑⢄⣀⠀⣀⡠⠞⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣤⠞⠀⠉⠹⠦⣒⠛⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠂⠤⠤⠤⠒⠁⠉⠢⡀⠀⠀⢀⠛⠉⢙⠏
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⣤⡤⡤⡄⠀⠀⠀⠘⡄⢀⠼⣀⡠⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡆⢀⠎⠀⠈⣿⠇⠀⢰⠀⠀⢈⠎⠀⠀⡏
⠀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠋⠁⠑⢢⠎⠁⠀⠀⢸⡄⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠇⠀⠊⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸⠈⠒⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⡴⠊⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢷⣶⣦⣤⣀⣠⣤⣶⣶⣶⣾⣿⣷⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⢾⠟⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣤⡀
⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢠⣾⡟⣀⣤⣤⣶⣶⣦⣤⣄⣀⣀⣀⣀⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⣿⡿⠿⠛⠛⠉⠁⠀⠉⠙⠛⠛⠻⠿⠿⠟⠁⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣤⡀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠙⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⠩⠀⠠⠑⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣾⣷⡆⠀⠀⠀⠀⠀⢠⣤⠶⡶⢶⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⠂⡒⠲
⠀⠀⠀⠀⡐⡄⣦⡄⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⡇⠀⠀⠀⠀⠀⠈⢩⣿⠩⡯⣻⣎⠉⢱⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⠀⢸
⠀⠀⠀⠀⠡⠁⠈⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢀⡇⠀⠀⠀⠀⠀⠀⠿⠿⠷⠾⠿⠿⠖⠃⠀⠀⠀⠀⠀⠀⡸⠅⠤⠤⠼⣀⠌
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣶⣾⣿⢶⣤⢀⠀⠀⠀⠀⠀⠀⢰⠶⡐⠂⠒⢂⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⢿⣿⣭⣿⣽⣿⠃⢱⠀⠀⠀⠀⠀⢸⠀⠈⠲⠞⠁⣠⣾⣎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⣀⣭⣯⣄
⠀⠀⠀⠀⠀⠿⠟⠫⣡⠒⠁⠀⠀⠀⠀⠀⠘⠏⠀⠠⢀⡸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡸⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠆⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃



⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⡄⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠠⠐⠒⣦⡀⠀⠀⠀⠀⠀⠀⡖⠂⠒⣀⠂⠒⢲
⠀⠀⠀⠀⣿⣿⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣘⣟⣁⠀⢃⣙⣟⣁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⣽⡇⠀⠀⠀⠀⠀⢀⡥⡄⠠⠿⠄⠀⢸
⠀⠀⠀⠀⣍⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠺⠿⠿⠿⠂⠀⠀⠀⠀⠀⠿⠷⠶⢤⡤⠤⢼⠅⠀⠀⠀⠀⠀⠸⣿⠟⡿⢿⠿⠟⠛



⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠰⡶⠀⠼⠧⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⡛⢍⠉⠉⣉⠝⡇
⠀⠀⠀⠈⠉⠀⣈⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡘⡐⢛⡘⢰⠀⠀⠀⠀⠀⠀⠀⠃⡀⠑⠚⢡⢖⡲⡄
⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣭⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠀⠂⡛⠛⣰⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠂⢣⣛⡓⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣤⠤⠴⠦⣤⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠙⠳⣦⡶⠋⠀⣀⣀⣀⠀⠉⢳⣤⠶⠛⠉⠉⠙⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣰⣄⠀⠀⣼⠁⠀⠀⣿⣁⣹⠇⠀⠀⢻⡀⢀⣤⡤⣤⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣰⠿⢿⣄⠀⣿⠀⠀⠀⣿⠉⣹⡆⠀⠀⣸⠃⢸⡁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠐⠋⠀⠀⠹⠂⠘⣧⡀⠀⠉⠉⠉⠀⠀⣰⡏⠀⠈⠳⠶⠞⠃⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⡾⠋⠙⠶⣄⠀⢠⡶⠛⠉⢷⡄⠀⠀⠀⢀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢦⣼⡇⠀⠀⠀⠹⣶⡟⠀⠀⠀⢸⣧⣴⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⣈⣀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢛⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⠂

⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⢳⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣶⣶⣶⣶⣶⣶⣶⡝⣿⣿
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣀⡀⣀⠀⡀⢀⡀⠀⢸⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⠿⢿⢿⣿⢿⡿⢿⣿⡇⣿⣿
⠀⠀⠀⡏⠁⠉⠉⠁⡁⠁⡉⠀⠀⢙⡏⠈⠋⠘⠁⠀⣸⠀⠀⠀⣿⣿⣿⢱⣿⣿⣿⣿⢿⣿⢿⣿⣿⣦⢰⣷⣾⣷⣾⣿⠇⣿⣿
⠀⠀⠀⡇⠀⠀⠀⢺⠟⣺⠓⠀⠀⢠⡏⠉⠉⠓⢦⣿⠁⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⡍⣬⠅⣬⣿⣿⣿⢰⣶⣶⣬⡛⠡⣾⣿⣿
⠀⠀⠀⡇⠀⠀⠘⠟⠹⠟⠁⠀⠀⠰⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⢸⣿⣟⣛⣰⣖⣰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⢦⡄⢀⣠⠦⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⣛⢻⣿⢍⣙⣉⣉⣉⣉⣩⣬⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠟⠉⠉⠉⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⠤⣤⣀⣀⣀⡠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⣀⣠⢊⣽⠥⡿⠭⠧⣀⡀⠀⠀⠀⠀⢠⠂⠀⠀⡆⠀⠀⠀⠀⠀⠀⡞⠁⠐⡍⠓⠲⠤⠤⠤⠤⠤⠤⠒⠚⠉⠁
⠀⠀⠀⠀⢀⣰⡅⠚⡀⠙⠄⠓⠀⠀⠀⠈⠑⢦⡀⠀⠀⢓⠶⠚⠁⠀⠀⠀⠀⠀⠀⢙⠒⠒⠁
⠀⠀⠀⠀⣷⠁⠑⠄⠈⠀⠀⢀⡀⠀⠀⡀⠀⠀⠙⢆⠀⠓⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠀⣦⣔⣪⣅⡠⠈⠀⡐⠤⣀⠀⠀⠔⠀⠉⠒⡄
⠀⠀⠀⢰⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠈⡎⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡔⠁⠀⠈⠁⠀⠀⠀⡌⡆⠈⠳⣍⣿⢍⠙⡄⢸
⠀⠀⠀⢸⢠⠤⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⠀⢀⡀⠀⠱⡘⣄⠀⣈⢧⠈⠀⣇⡇
⠀⠀⠀⠘⣌⠉⠀⠀⠀⠀⠀⠈⠢⡄⠠⠈⠀⠀⠀⣠⠃⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⠇⠀⠈⠀⠀⠀⠘⢮⡓⠬⡎⡄⠀⡟
⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⣀⠔⠁⠀⢈⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠈⠁⠐⡇⠀⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢄⢀⣀⠠⠤⡔⠊⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⠒⠛⠁⠀⠀⠀⠀⠀⠀⠬⠇⡸⢌⠂⠈⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠖⠃⡇⠳⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢓⠀⠀⠀⠉⠢⢀⠀⠀⠀⢀⣀⠀⣐⡠⠊⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡿⠀⠐⠒⠃⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡴⠐⢄⠜⢹⠏⠣⡉⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠁⢸⡇⠀⠈⠉⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⠀⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⣤⣀⠔⠋⠀⠀⠀⢹⡏⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⢀⡞
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠳⡎⠙⢞⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠀⠀⢹⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣠⠇⠀⠀⠉⢿⠄
⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠲⣤⣽⠆⠀⠀⠒⠲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠙⠋⠁⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⣋⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣟⣛⣛⠛⣛⣛⣛⡛⢋⣉⣤⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿
⠀⠀⣠⣤⣄⠛⣿⣿⣿⣿⠀⣿⣿⡏⣡⡾⢋⣙⠻⢋⣈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿
⠀⢰⣿⣿⣿⡇⢸⣿⣿⣿⣦⡙⢛⣡⣿⣇⠻⠟⢀⠸⠿⢃⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢨⣿⣿⣿⡇⢸⣿⣿⣿⣿⣧⢸⣿⡟⠛⣷⣾⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⠉⠙⠻⣿⡟⠉⠉⢉⣀⣀
⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣆⠻⢿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⣋⣴⣶⣿⣶⣈⠇⢸⣷⣦⡙⣿⣷⣄
⣦⠘⣿⣿⣿⡇⣸⠏⣿⡿⠟⢛⣙⠳⣶⣤⣤⠄⠺⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⣴⣿⣿⡟⢻⣿⣿⣧⣸⣿⣿⣷⠘⣿⣿⣷⡄
⠘⢷⣬⣉⣩⣴⠟⠀⠁⣴⣾⣿⣿⣷⣌⠻⡟⢰⣷⡘⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠻⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡄
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣤⣿⣿⣧⢹⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⢠⣤⣤⣤⣤⡄⢹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣭⣭⡌⠿⣿⣿⡿⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠿⠿⢛⣡⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⢋⣤⣶⣶⣶⣶⣶⣶⣶⣦⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⢡⡄⣿⣿⠟⢋⣴⣦⣌⡙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢡⣿⣧⠘⣡⣾⣿⣿⣿⣿⣿⣦⠹⣿⣿⠏
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⣋⣥⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣿⣿⡟⢋⣴⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣄⠻⠿⢃⣾⣿⣿⡏⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣘⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣷⣶⣾⣿⣿⡟⣠⣿⣿⣿⠟⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⣦⣍⣛⠛⣛⢡⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⢠⣤⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⣉⣴⣶⣶⣌⠻⢿⣿⠇⣴⡘⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⣿⣿⣷⣦⡙⢰⣿⣷⠘⣿⣿⣿⠸⣿⣿⡿⣿⣿⣿⡇⠈⠛⠛⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠋⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡋⢙⣿⠉⢹⣿⠉⢹⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣶⡦⠀⣶⡆⠠⣶⡆⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢦⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡹⣿⣿⣿
⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⢈⡇⠀⠀⢸⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡷⣹⣿⣿
⠀⠀⠀⢀⡴⠿⠋⠁⠐⢤⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⣿⣿⣿⣿⢋⣠⣴⣿⣏⡻⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠦⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣧⣙⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀⠀⠀⠀⣸⡇⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⢀⣤⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠋⠀⠈⠻⠿⠿⠿⠿⣶⣄⡀⣼⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⠻⣿⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⢷⣄⠀⠀⠀⠀⢠⣾⢿⣆⠀⠀⠀⠀⣰⡿⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⣿⠀⢀⣤⣶⠿⠃⠈⠻⢷⣦⣀⠀⣿⡁⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⣴⣿⡃⠀⠈⠛⠿⣶⡄⢀⣴⡾⠟⠉⠀⢙⣷⣦⣤⣶⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠉⠙⠻⣦⡀⠀⠀⠘⢿⣾⠏⠀⠀⢀⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠈⠉⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⢀⠀⠀⠀⣀⣀⣀⢀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠈⠁⠁⠁⠉⠀⠉⠉⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠀⠀⠀⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠘
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢨⣆⢳
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠋⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠮⠤⠐⠈
⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠀⠀⠉⢖⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡅⠀⠀⠀⠑⠢⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⣀⡠⢸⠤⡄⠀⠀⠀⡀⠀⠐⠒⢒⠒⠂⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠃
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠑⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢢⠀⠀⢈⡡⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⢀⠀⠀⢀⠔⠁⠀⡠⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠈⠁⠀⠀⡐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⣀⡠⢊⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠜⢄⠀⠀⠈⠢⠬⠟⢛⣠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡶⠤⠤⠵⠦⠤⠠⠤⠤⠾⠟⠒⠒⠒⠚⠿⠛⠛⠛⠛⠟⠻⠟⠛⠛⠛⠛⠿⠿⠟⠿⠛⠻⠛⠦⠄⠤⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⡏⠙⡋⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠃⠉⠊⠛⠉⠛⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⡏⠉⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠰⠄⠀⠐⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠰⠀⠀⠀⠀⢠⠀⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⠁⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⠄⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠍⢸⠀⠀⠅⠉⠀⠀⠀⠁⠉⢠⠏⢨⡏⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⡆⠃⠀⠀⠀⠀⢰⡧⢾⠸⠷⡶⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠐⠃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢇⡐⠀⡆⣦⠀⠀⠀⠃⠤⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠉⠒⠓⠛⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠛⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠷⣦⣀⣴⠾⠛⠟⢷⣦⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⣾⠋⠀⠀⠀⠀⠀⠈⠛⠁⠀⠐⠠⡱⡙⣷⣤⣤⣤⣤⣀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠻⠹⠱⡱⡹⢙⢷⣄⠈⠆
⠀⢀⡤⠖⠂⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠡⠁⠁⢃⠜⣻⡆
⠰⠁⣠⡶⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠛⠟⡷⣦⡀
⠁⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡐⠠⠊⣻
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣽
⠀⠀⠻⣦⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⢠⡟⠁⢠⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠸⣧⣸⣟⣗⣴⣼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠙⠿⣾⣮⣿⣧⣿⣮⡵⣡⡖⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣵⣟⣼⣱⣳⣷⣆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⢻⡆⠀⠀⠀⠀⣰⠟⠳⠶⠶⠶⠞⠉⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠋⢀⠴⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣤⡾⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠁⣀⠔⠉
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠷⠯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢀⡩⠗⠀⠀⠀⠧⣤⣤⣤⡤⠃⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⢿⡆⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⠘⢦⡀⢠
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⣾
⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠻⣀⡸⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡉⢢⡀⠀⠀⠀⠘⢇⣀⠇⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠸⣿⡿
⣰⠒⠒⠒⢲⠀⠀⠀⠸⡀⠀⠀⡔⣉⣉⣙⢃⠀⠀⢠⠖⠒⠒⠒⡄⠀⠀⠀⠀⣴⣶⣶⣶⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⣶⣶⣶⣶
⡇⠀⠀⠀⠀⡇⠀⠀⠀⠙⢢⣄⡣⢅⣉⡩⠊⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢻⡿⠷⢶⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿
⠙⠒⠒⠒⠚⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠈⠓⠒⠒⠒⠁⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋
⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⡴⠚⢢⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⢀⣶⣶⡆⠀⠀⠀⠀⡀⠀⡴⠂
⠀⠀⠀⠁⠙⢦⡀⠀⠀⠀⠀⣙⣲⣊⡀⠀⠀⠀⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠳⣄⠀⠀⠀⠀⢀⣛⣛⣁⠀⠀⠀⢰⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡎⠀⠀⠀⢹⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢘⠨⠋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠈⢙⠉⠑⠀⢸⠀⠀⠀⠀⠈⡀⠖⠰⠄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠈⢀⣀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠒⢀⠋⢢⠠⠀⢸⢆⠀⡀⠐⠋⠛⠄⢳⠲⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣦⠀⠈⠃⠀⡇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⠉⠔⠀⠀⣀⣀⢀⡀⢺⣧⡀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡩⣨⣡⠈⡹⠿⠀⠀⠂⣠⠉⠒⠠⣀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠩⢉⠉⢡⠂⠐⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠒⠒⢸⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⠶⠦⢤⡎⢈⠀⠒⠈⠀⡀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠀⢈⢘⡀⠂⢰⠀⠀⠀⠀⠸⠀⠀⠀⠂⢰⡄⠂⠀⠀⠀⠀⢡⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠘⢄⠀⠀⠀⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢐⠘⠊⠀⠁⡀⠀⠀⠀⠀⠀⡄⠀⢀⡴⠊⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⡈⠐⠠⠤⠤⠤⠂⠁
⠀⠀⠀⠀⠀⠁⠒⠲⠁⠀⠀⠀⠀⣏⠄⡁⠀⠀⠈⠐⠊⠁⠀⠇⠀⠀⠀⠀⠀⠁⠀⠐⠂⡠⠆⠀⠀⠀⡀⢀⣀⠇⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⠠⠐⠁⡰⠂⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠰⠀⠀⠀⠁⡶⠤⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠐⢊⠓⣿⡾⠃⡀⡠⠂⠀⡀⠀⠀⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⠐⠑⠀⠈⠑⠀⢠⡀⠿⡆⣄
⠀⠈⢆⠀⠚⣇⠌⣰⣛⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐⠒⠒⠀⠀⢌⠀⠤⡀⢐⢂⡤⠻⡀⠀⠀⠀⠀⠁⠠
⠀⠈⠂⠤⡶⠉⡜⠑⠠⡗⠂⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠑⠂⡈⠸⠀⡅⠀⢶⡄⡄⢐⠆
⡄⠠⡠⢎⣀⣞⠀⠀⠉⣃⠀⣀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢈⣀⣹⡆⠀⠈⠃⡆⢸⠂⠀⠁
⢈⠒⢂⢠⠀⠘⣤⣠⣴⠋⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢆⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⡅⠀⠀⠡
⠈⠈⠉⠀⡁⠀⠈⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠐⠔
⠀⠀⠀⢀⠀⠀⠐⢷⡴⠦⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠟⠶⠊⠀⢐
⠐⠊⠀⠉⠒⠴⠦⠤⠇⠀⠀⠀⠀⣤⠤⠓⠒⠀⠄⠀⠀⠀⠠⠄⠀⠉⠀⠁⠄⠀⠠⠀⠀⠸⠀⠀⠀⠀⠘⠀⢤⣤⣤⣤⠤⠤⠖⠦⠤⠤⠌⠂⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋⣰⣾⣿⣿⣷⣄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣠⣾⣿⣿⣷⣆⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢋⣤⣶⣦⣤⡙⢿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠃⣾⣿⣿⣿⣿⣷⠘⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉