Silly goofy Emojis & Symbols

⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢀⠀⢀⡀⢀
⠀⠀⡀⠠⠀⠐⠂⠄⠂⠀⠀⠀⠀⠂⠀⠀⠀⠉⠙⠉⠩⠉⠀⠀⢀⣀⣀⣀⠀⠈⠀⠃⠀⠀⠀⢀⠉⠁
⠀⠊⠂⠈⠐⠀⠆⠀⠐⠈⠀⠐⠀⠀⠀⠠⡀⠃⠆⠀⠶⠐⠀⠀⠈⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀
⠀⠐⠃⡀⠀⡤⠀⣀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀⠀⠘⡀⠒⠀⠂⠀⡀⠐⠄⠛⠁⠀⢀⠀⠠
⠀⠀⠀⠁⠀⠀⠄⠁⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠤⠧⠄⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⣅⠀⣈⠐⠀⠀⠀⢠⠄⠀⡄⠀⠠
⠀⠀⠀⠠⠖⠀⠳⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⡠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠿⠀⠻⠀⠀⠀⣶⠂⣴⡂⠐⠈
⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣩⠀⠀⠐⡂⠀⢐⠈⠀⠀⠄
⠀⢀⠀⣀⠁⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠁⡉⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣉⢈⠇⠀⠀⠄⣶⣴⡦
⠀⠀⠀⡀⠀⠈⠻⣦⠞⠃⠀⠀⠐⠀⢀⠀⠀⢀⣄⠀⠀⠀⠁⠀⠀⠴⠃⠀⠀⠀⠠⠩⠀⠡⠄⡀⢠⣤⡀
⠀⠀⠀⠀⠂⢠⡆⣀⢰⣏⠀⢶⠆⠀⠀⠀⢠⡀⠁⢠⡀⠀⠀⠀⡄⡂⢀⡀⠙⠋⠙⠀⠶⢀⣄⣉⣄
⠀⠀⠀⠂⠀⠛⢇⠛⠞⠛⠀⢠⠀⠄⠀⠀⢉⢠⠀⠄⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠁⣄⣀⠈⠀⠀⠀⠉⠀⠀⢆⢌⢠⠀⠀⢀⢀⠀⠀⢠⠀⠀⠄⠀⠀⠄⠀⠀⠀⢀⠂⠀⠀⠄
⠀⠀⠈⠛⠋⠛⢢⣀⠀⠈⠀⠈⣿⡄⠀⠀⠐⡀⠀⡀⠀⠀⠀⠒⡤⡀⠁⠠⠁⠔⠀⠀⠀⢀⠀⠅⠈
⠀⠦⠶⣤⠆⠀⠉⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⢀⡼⠁⠀⠀⡀⠀⠄⡀⠀⠙⠀⡁⠘⠁
⠀⠀⢼⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⠀⠀⢠⡄⠀⣤⠀⠒⠒⠋⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠠⠈⠃⠠⠉⠀⠀⠁⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⣤⡾⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣦⣶⠘⣧⣿⢣⣿⣱⡷⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡘⣼⣭⠾⣗⡿⠿⠲⢤⣿⡾⠋⣉⠁⠀⠀⠀⠀⠀⣀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡄⠀⠀⢀⣈⠛⠦⣧⣿⣽⠾⡁⠀⠀⠀⣀⡝⢷⣏⣥⣐⠀⠀⠀⠀⠀⢻⡆⡾⢁⣠⡄
⠀⠀⠀⠀⣄⡀⠈⢻⣄⣾⠁⠀⠀⣾⠭⢳⡜⣽⠟⣡⡀⠀⠀⠀⠈⣡⠴⢄⢻⣿⠽⠂⠀⠀⠠⣄⣸⣿⣷⠋⠁
⠀⠀⠀⠀⠈⠙⠲⣬⣿⠛⣧⠀⠀⠴⠖⡘⣼⠏⠰⣿⣿⠀⠀⠀⢸⢡⣶⠈⠈⣿⠀⠀⠀⠀⠀⠀⣿⣤⠟⠙⠛⠒
⠀⠀⠀⠀⠐⠺⠟⠉⣿⠾⢿⣦⡀⠀⠀⣿⡟⠀⠠⣈⣡⠂⠰⠆⠈⠢⠵⠃⠀⣻⣧⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠳⡙⢦⡀⢻⡗⡀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⢠⣿⡟⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣦⣿⣦⡹⡜⢦⡀⢰⣟⣫⣬⣼⡟⠀⣰⡿⠋⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠹⣮⣦⣝⣷⠮⣍⡉⢀⣴⠟⠋⣠⠾⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠉⠀⠙⣯⠛⠚⡿⠋⢷⣴⡿⠁⢀⣼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡄⠀⠈⠳⣾⠃⠀⠀⠉⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠉⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠻⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠯⣤⣀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⢀⣼⠻⣿⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣶⣾⠃⠀⣿⣧⣤⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠉⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠷⣄⣀⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡴⠚⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠴⠖⠋⢹⣿⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠳⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠂

⠀⠀⢠⡏⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢀
⠀⠀⠘⣄⣀⣞⣀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣠⠃⠀⢀⡇⠀⠀⠀⠀⠀⢀⣀⠀⠈⢦⠀⣾⠀⠀⠀⢀⡤⠖⠒
⠀⠀⡴⣫⠤⣄⠀⠉⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠒⠒⣲⠖⠊⠉⠉⠉⠉⠑⠦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠾⠼⠧⠤⣤⣤⣞⣠⡤⠤⠄
⠀⡜⠁⣅⣠⡼⢠⠖⢾⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢰⢳⠢⢰⡄⠀⠀⠀⡴⢒⢝⢷⠒⠦
⠀⢻⡀⠀⠁⡀⠻⠧⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡔⣐⢲⡀⠀⡤⠦⡄⠀⢹⠀⠀⠀⠀⠀⠈⠫⣲⣚⡁⠙⠒⠁⠑⠂⣊⠼
⠀⠀⠱⡀⠋⠉⠡⣞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣈⠣⠭⠞⠁⠀⠧⠥⠋⢀⡼⠀⠀⠀⠀⠀⠀⠳⣄⠀⡿⠀⠀⢻⠉⣉⡴
⢀⡤⢾⠃⠀⠀⠀⠀⠙⣍⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡖⠀⠐⠲⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⡟⠁
⠞⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢤⠀⠀⣠⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⠷⠚⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⣴⠃
⠀⠀⠘⢤⣀⡀⢀⣀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡖⠒⠶⢲⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢩⡇
⠀⠀⠀⠸⠃⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄
⠀⠀⠀⠲⢄⠀⠀⠀⣱⣄⣿⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠂⠒⢦⣀⡷⠒⣋⠁⢀⡤⣬⠙⡄⠀⠀⠀⠀⠀⠐⠓⢦⣈⣷⣠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠲⡤⠖⠛⠉⠉⠉⠉⠓⢯⡉⠁
⠈⠉⠙⢲⠋⢰⠻⠆⣳⠘⠮⠞⢀⠏⠀⠀⠀⠀⠀⢠⢢⣟⠳⡄⢀⣤⡊⡕⠀⠀⠀⠀⠀⠀⢰⣣⣞⢳⠌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠘⡇⠈⠓⠛⠱⠶⠛⢰⡏⠀⠀⠀⠀⠀⠀⣏⠸⠥⠞⠁⠘⢭⡴⠃⣧⠀⠀⠀⠀⠀⠸⣌⠉⠉⣶⣻⢆⡿⠛⢦⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡶⠙⢆⠀⠀⠀⠀⠀⠙⠲⡄⠀⠒⠂⠀⡀⠀⠹⡄⠀⠀⠀⠀⢀⠏⢹⡖⢾⠗⠋⠀⠀⡘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠃⠀⠻⣄⠀⠀⣰⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠐⢦⡀⢰⠃⠀⠀⣻⠀⠀⠀⠀⠀⡄⢨⡅⢸⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⡏
⠀⠀⠀⣯⠀⠀⠀⠈⠙⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠓⠈⠃⠀⠃⠀⣼⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠸⣄⡀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡦⠤⠶⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⣤⠚⠁
⠀⠀⠀⠀⠈⠹⡟⠋⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡤⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⡀⠀⣸⡀⢀⡤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠢⡤⠤
⠀⠀⠀⠀⣰⣧⣤⣾⣅⡤⠶⠆⠀⠀⠀⠀⠀⠀⠐⠉⠉⢓⡶⠺⣛⢯⣩⠽⢍⠉⠲⢤⠤⠦⡀⠀⠀⠀⠀⢋⣡⡧⡋⡉⣆⢀⠔⡒⡜⠦⡄
⠀⠀⢀⡴⠁⠀⠀⠀⠀⠉⠳⡗⠦⠀⠀⠀⠀⠀⢀⡤⢲⠏⠀⠓⠚⠃⠘⠢⠚⢀⣀⠈⣇⠀⠀⠀⠀⠀⠀⠚⢸⡇⠻⢥⠏⠘⠦⡡⠎⡆
⠀⠀⡞⠀⠀⣀⣀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠈⠉⠉⠉⠉⠉⢉⣉⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⣀⣀⠀⠀⠀⣧⡠
⠀⣴⠃⠀⣎⠱⢎⡧⠀⢾⡭⡾⣧⠀⠀⠀⠀⠀⠀⢀⡾⡄⠀⠀⠀⠀⠀⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣧⠀⠀⠉⠉⠀⠀⠀⢻
⠸⠙⣇⠀⠈⠉⢩⣠⣀⣈⠉⢡⠆⢳⠀⠀⠀⠀⠀⠚⠀⠙⣄⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢰⡀⠀⠀⠀⠀⠀⠀⣘
⠀⠀⠈⠳⡶⠦⠤⠤⠤⠖⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠤⢶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠤⠤⠤⣤⠴⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠖⣦⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⡾⠛⡆
⠀⣸⠆⠉⠰⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠂⠀⢸⣇⡀
⣾⠁⢠⡾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⡆⠈⢷
⢿⣄⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣼⠳⣤⡀⠀⢀⡼⠻⣦⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣠⡇⠀⣸
⠀⠙⣧⠀⠙⢷⠀⠀⠀⠀⠀⠀⢠⠏⠙⢷⣄⡼⠁⠀⠈⠻⣤⠞⠁⠀⠘⣧⢠⡟⠈⢷⡀⠀⠀⠀⡼⠋⢠⡾⠁
⠀⢠⠟⠀⢀⣼⠁⠀⣰⠿⢦⣠⠏⠀⠀⠀⠙⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⠋⠀⠀⠈⣧⠀⠀⠸⣇⠀⠸⣇
⢠⠏⠀⢰⠏⠀⠀⣰⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠘⢷⡄⠈⢻
⢸⡄⠀⢸⡄⢀⣀⣏⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠙⠙⡇⠀⠀⠀⣿⠀⢨
⠀⢷⣄⠀⠻⣼⡉⠉⠀⠀⠀⢀⡔⢉⡟⠉⠙⣳⠀⠀⠀⠀⠀⠀⡴⠋⡏⠉⠉⣷⡀⠀⠀⠸⢿⡆⢀⣴⠃⠀⣼
⠀⠀⠙⠳⣦⡌⠁⠀⠀⠀⠀⢸⠀⠀⠳⠶⠖⢩⡇⠀⠀⠀⠀⠀⡇⠀⠉⠓⠛⢹⠇⠀⠀⠀⠸⠷⠛⠁⣠⡾⠃
⠀⠀⠀⠀⠿⣅⡀⠀⠀⠘⣆⠘⣄⡀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠙⠦⣤⡤⠶⣋⠆⠀⠀⠀⢠⣴⠶⠛⠁
⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠈⠂⠀⠉⠉⣉⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⢸⣀⡞⠓⠚⠛⠻⣄⡞⠀⠀⣱⠀⠀⠀⠀⠀⠀⢠⣶⡛⠉
⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠘⢧⡀⠀⣠⠤⠤⣤⠴⠶⢤⡀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠸⢿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠶⢶⡇⠀⠀⣴⣤⠀⠀⠀⢀⣄⠀⠀⠀⢰⣤⠀⠀⢻⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠇⢿⡀⣠⠞⠋⠉⢷⡀⣠⡞⠘⣧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⠈⢷⠏⠀⠀⠀⠸⠟⠉⠀⠀⢸⡄⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠶⢾⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣤⣤⣤⣤⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⣀⠻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣈⣁⣀⡀⠀⠀⠀⠀⢻⡆⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠤⠒⠉⠉⠉⠀⠀⢀⣀⣀⠀⠰⣦⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠑⢄⠀⠤⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠔⡞⠋⠀⢀⠴⠒⠀⠀⠀⠀⠐⠌⠣⡀⠀⠑⣄⠀⠀⠀⠀⣠⠖⠉⠓⢄⠀⣀⠤⠄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡞⠀⢀⠀⡎⠀⠀⠀⠂⠀⠀⢀⠀⢀⠱⡀⢉⠇⠀⠀⢀⠔⢁⠖⢋⠑⡌⣯⠔⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢴⠋⠀⡇⠀⡤⠊⠉⠑⠶⠧⠀⠀⠰⠑⣬⠀⠀⢠⠎⡰⠉⠀⠀⡞⠙⠁⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢄⠰⠘⠀⠀⠀⠀⠰⡀⠀⠀⢠⠀⠸⣇⡴⢁⠜⣀⡠⠜⠉⠳⢤⡠⠤⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢉⣙⠒⠂⠤⢀⣱⣵⠁⠀⠤⠤⠛⠉⠐⠒⠁⡀⠀⠈⣠⠇⠐⠁⠀⠀⠀⠀⠀⠗⡤⠆⢀⠤⠼⡄⠀⠄
⠀⠀⠀⠀⠀⡤⠔⠒⢺⣀⠀⡏⠀⡏⠉⠒⠠⢬⣉⡀⠀⠀⡄⠀⠀⠀⠀⠀⠈⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢀⠆⠀⠀⢡⠀⠘⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠲⡷⠤⠦⠤⠼⠤⠭⢽⣶⡁⠀⠀⠀⠀⠀⢀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠰⡇⠟⠁⢀⠠⢄⠀⡆⠀⠃
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣀⣠⣴⠃⠀⠀⠀⠀⠀⠀⢾⣿⣷⣤⣤⣤⣤⣶⠿⠟⠛⠿⣄⠀⠀⠀⠀⠀⠀⢰⢠⡴⠊⣁⣀⠀⡷⠃⢀⡌
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⣜⣈⢢⠀⠀⠀⠀⠀⠀⠘⢿⡿⠛⠉⠉⢉⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⡎⠀⠀⠊⠁⠀⡠⠁⡠⠋
⠀⠀⠀⠀⠀⠀⢱⠀⢲⠶⢤⡀⠈⢳⠱⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣀⣀⡀⢀⣠⣞⣁⡀⣤⠤⢤⠎⢠⠏⠢⣤⠤⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠈⡄⠘⡄⠀⠱⠤⠞⠣⡈⠢⡀⠀⠀⠀⠘⣦⣄⣠⠔⠉⠀⠀⠈⠉⠓⠠⠥⢄⡠⠖⠁⣠⢋⠔⠊⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠱⠀⢱⠀⡴⠋⣉⢙⣛⠀⠈⠒⠖⣛⡉⣩⠖⠃⣠⠂⠀⠀⠀⢀⡠⠝⠓⠶⢤⠴⠚⠷⠁⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠳⡀⠹⠊⠁⠀⡙⠢⠤⣀⣈⡁⠴⠊⠀⠉⠁⠐⡏⠁⢱⡤⢤⠴⠁⠀⠀⠀⠹⡀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠬⣒⠀⠠⠚⠢⠤⣀⡀⠀⠀⡴⠒⠤⢄⠠⡔⢻⣀⡠⠟⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠞⠁⠑⣄⠀⢀⡠⠖⠀⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣀⠀⠀⠀⡜⠀⠀⠀⢸⡏⡇⠱⠤⣄⡌⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠦⡼⠀⠀⠀⠀⢸⢗⡏⠚⠀⢨⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠐⠁⠀⠀⠀⠀⣼⣱⠃⠀⢀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⡀⠀⣦⣿⡽⠀⠀⡎⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⡠⢴⠚⡅⠀⠀⠀⠀⡠⠊⢹⡔⣿⣿⡇⠀⡜⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠒⠖⠉⠉⠁⠀⠀⠘⡆⠘⡄⢀⡠⠊⠀⠀⠀⢻⢊⡿⢠⠎⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⣨⣤⢾⠉⠀⠀⠀⠀⠀⠀⠛⢷⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣵⣤⣀⣀⣀⣀⣠⣤⣚⣬⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢯⡛⠯⣯⣍⣛⣛⣿⣿⠷⡶⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⡍⠉⠀⠀⠀⠭⠭⠭⠝⠛⠛⢛⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠄⠀⠤⠤⠤⠀⠒⠒⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡢⣤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠛⠁⠀⠀⠨⠿⡶⣄⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⣀⣀⣀⣀⡠⠐⢀⠀⠈⢢⠀⡠⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢊⣉⡉⢥⡤⠀⠀⢀⡤⠀⣉⡑⢢⡇⠑⠀⡀⠀⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢾⣿⣿⣿⣶⡦⠰⣶⣾⣿⣿⣿⠂⣱⠀⠘⠴⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢒⡌⠻⣿⣿⡿⣁⣠⢻⣿⣿⠿⠋⣀⡘⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠆⠨⠁⠊⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠤⡳⢤⣀⣀⠀⠁⠀⢀⣀⡴⠋⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠠⡀⠀⠀⠍⠀⠀⠀⠀⢈⣶⠞⠻⢏⣉⡹⠟⠒⢦⢀⠄⠀⠄⢀⠀⠀⠀⡀⠤⠀⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠀⡀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⢄⠁⠀⢀⡈⠲⣤⣀⡀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠢⢀⢾⡄⠀⠀⢠⠂⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠿⠳⠈⠉⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠘⢀⣀⣀⣶⡀⣀⡴⢄⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠄⠀⠀⠀⠘⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⢁⠐⠉⠀⠀⠈⠉⠡⡀⠘⣾⠁⠀⠀⠀⠀⠀⠀⣇⡼⡟⠐⠈⠀⠭⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⡞⠀⠀⠀⠀⠀⠉⠀⢻⢿⣅⡀⠀⢀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡠⠴⢤⣁⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⠀⠀⢀⣿⠀⠀⠀⢸⡄⠉⠀⠘⠉⠀⠀⠀⠂⠈
⠀⠀⠀⢠⠊⠀⠀⠀⡈⢳⠀⠀⠀⠀⠀⠀⡠⢺⠁⠀⠀⢸⠸⡀⠀⠀⠀⣇⠠⠀⠀⠂⠈⠈⠐⠄
⠀⠀⠀⠰⡀⠀⠀⠀⠀⢹⠀⠀⠂⠒⠒⠊⠁⠛⡂⠀⠠⠞⠀⣇⣀⠀⠠⡼⠀⠀⠀⠂⠐⠀⠀⠆⡀
⠀⠀⠀⠀⠈⠃⠤⠤⠶⡹⠉⢉⠃⠁⠀⠀⠀⣠⣖⡄⢠⠀⠀⠀⠀⠀⢀⢴⡂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡈⠀⡠⣀⠐⠊⠀⠀⠀⣠⠴⠃⠎⠀⢀⠀⠀⠀⠀⠃⠉⢛⠙⠷⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠂⠐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡷⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠠⡢⠀⢀⠄⠠⡖⠐⢦⠤⢄⠀⠀⠀⢀⡐⡤⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⡠⠒⠆⠀⠘⢄⠀⢀⠄⠀⡰⡷⢎⣽⡎⢹⡯⠖⣢⡀
⠀⠀⠀⠀⠖⢑⠔⠈⠉⢉⡉⠢⣠⠦⡀⠀⠦⣁⠌⠀⠀⠀⠀⡖⣄⡘⠄⠿⠀⠏⣀⢀⣀⠙⠀⠀⠑⠀⠁⠰⢷⣶⣤⠚⡏⢩⠁⡩⠛⡍
⠀⠀⠀⡜⠉⠃⠀⢼⢹⣿⣽⡆⠐⣀⣄⠀⠀⠁⠀⡄⠐⠀⠀⢸⠼⢃⠁⡆⠀⡘⡧⠸⣧⢈⠀⠀⡁⠀⢀⣷⡶⢁⣀⢣⣰⣆⡬⠤⢐⡦
⠀⠀⠀⡘⠙⡀⠐⢨⠚⠫⠎⠅⢀⣅⡠⠂⢀⠀⠀⠐⠒⠁⠀⠀⠘⠄⢀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠈⣄⡥⠀⢒⣸⡇⠀⠱⡿⠋
⠀⠀⠀⠘⢰⠑⣄⠀⠑⠒⠀⡠⣎⣀⠅⠀⡄⠫⡳⠀⠀⠀⠀⠀⠁⠀⢁⢄⠀⠁⠀⢀⡀⠁⠀⠀⠁⠀⡀⠈⠉⠙⠛⠂⠙⡄⠀⠃⠀⠀⣲⠆
⠀⠀⠀⠀⢈⡒⠦⡈⣫⡁⢩⠤⠜⠀⠀⠀⠉⠁⠀⢀⠀⠀⢄⡥⠑⠀⠀⠀⠀⠀⠀⠡⡠⠁⢠⠄⣀⡔⠉⣆⡀⠤⠀⠀⠀⡄⠀⢸⠀⠎⡱
⠀⠀⠀⠀⢘⣻⡧⠤⢼⠉⣡⠪⢉⡜⠀⣀⠀⠀⠀⠡⠺⣇⠘⠳⡀⠀⠀⠀⠙⢶⠀⠀⠀⠀⢈⡖⢁⣄⢠⣤⡑⣼⠀⠀⢠⠀⠀⡸
⠀⠀⠀⡾⠽⢇⣀⠀⢀⡖⠁⠂⠁⢀⡎⡀⢑⡀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⡂⠀⠢⣁⠀⠳⠬⠑⠤⠃⢀⡈⠆⠀⠑⠂⠱⣲
⠀⠀⠀⠀⠀⠘⠭⠋⡸⠀⠀⠀⠀⡜⡗⣱⢫⠱⠀⠀⠀⠀⢀⠀⠡⠀⠀⠀⡀⢀⣀⡁⠄⠀⢀⠃⢁⠈⠥⢀⡠⠫⠀⠀⠀⠀⡂⢒⣸⠀⢢⡔
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠀⠀⡁⠑⠆⢚⡀⢃⠀⠀⢠⣏⢱⡖⠃⠀⠈⠐⢹⣧⠿⡀⠁⠈⠈⠉⠣⣀⠋⠉⠀⡠⠀⠀⢀⠀⠀⢰⢉⡢⠄
⠀⠀⠀⠒⠩⠀⠀⠁⠀⠀⠀⠀⠀⠑⢼⡟⠀⡿⠋⠀⢀⠔⡩⠀⠉⠄⠀⠐⠄⠁⠀⠀⠄⠀⢀⡀⠀⠀⠄⠀⠂⢰⠀⠀⠀⠀⠆⠐⠀⠠
⠀⠀⠀⠀⠀⠀⡀⢤⡊⠭⠑⣄⠀⠀⢀⠃⠀⡇⠀⠀⢶⡌⠀⠁⠊⠀⢀⢀⡄⣠⢀⠀⠀⠈⠂⠄⠀⠨⠀⠀⠀⠀⠆⠀⠀⠐
⠀⠀⠀⠀⡠⠺⣘⣰⣄⡙⣤⢉⠣⠀⠘⠄⠠⠃⠀⢀⠀⠀⠀⠀⠀⠠⠋⡤⣤⠴⣌⠓⣀⣀⠀⠀⠠⠀⠓⠀⠄⡀⣪⡉⠉⠣⣀⠀⠀⠚
⠀⠀⠀⠀⢻⣁⣲⡾⢪⡶⠭⢦⢺⠀⠀⠀⠀⠀⡰⠁⡆⠀⠀⠀⠀⢛⠀⠐⡿⠙⡿⢸⠈⡻⠀⠀⠆⠀⠀⠀⠠⣆⠿⠀⠀⠀⡱⠀⠀⠀⠀⠸
⠀⠀⠠⡢⠀⠠⠋⢀⠚⠛⠛⠓⠂⠀⠀⠒⡀⢨⠔⣶⣸⠀⡐⠀⠀⠸⡄⡀⢐⠀⡂⣨⠋⠁⠀⠀⠈⠂⠄⠀⠈⠈⢢⠤⠤⠔⠀⠁⠐⠠⠐⠁
⠀⠀⠀⠀⢀⠃⠀⡆⠀⠀⠀⠔⠤⢐⠀⠀⢈⠃⠜⠛⠛⠋⠀⠀⠀⠐⡁⠀⠀⡁⠈⠙⠀⠀⠔⡀⠀⢈⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠘⠄⠔⠁⠀⠀⠀⠈⠐⠁⠀⠀⠦⠐⠂⠙⠢⢬⠀⠀⠀⠀⠓⠉⠉⠉⠉⠃⠀⠘⠉⠙⠀⠀⠑⠀⠀⠚⡀⠀⠀⢀⠓⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣶⣉⣀⡬⠘⠷⣁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠖⣴⠟⠉⠈⠉⠁⠓⢾⡟⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⡠⣤⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⣑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠉⢐⠓⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⣿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠓⠒⠒⠢⡀⠀⠀⠀⠀⢀⣀⠤⢄⡀⠀⠀⠀⠀⢹⠀⠻⠄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣰⠋⢁⠀⠀⠘⢦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⢠⡖⠀⠀⠀⢸⠀⠀⢰⠇⢰⡏⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢇⠀⠘⠁⠀⠀⠀⡟⠀⠀⢹⡀⠀⠀⠀⠀⣠⠴⠃⠀⣠⠟⠛⠓⢦
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣇⣠⠆⠈⢷⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠘⠓⠒⢶⠖⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠉⠉⠛⠶⢄⣀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠈⠙⡦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠖⠛⠁⠀⠀⠀⠀⣟⡠⠒⠓⠒⠒⠲⠀⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠢⡄
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣋⣉⣉⣉⡙⣛⠛⠓⠒⠒⠒⠶⠶⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣊⣵⠶⠶⠖⠒⠂⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠦⠤⠤⠤⢬⣍⣉⣉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣟⠛⠭⠍⣐⡒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠒⠒⠒⠀⠤⠤⠤⣤⢻⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⡐⠒⢰⠏⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠙⠛⠛⠓⠒⠒⠲⠶⠶⠦⠤⠤⠤⣤⣤⣤⣀⣀⣀⣉⠉⣹⠏⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣷⢀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⣄⠀⠀⠀⢀⣤⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠛⠋⠻⡅⠀⡴⠁⠀⣀⣤⡙⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇
⠀⠀⠀⡴⢦⡀⠀⢠⠖⡳⠀⠀⠀⠀⠀⠀⢺⠀⢰⣿⣯⡷⠀⣇⠀⢸⣿⣿⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇
⡴⠒⠦⣷⡀⠱⡄⢸⡀⣅⠀⠀⠀⠀⠀⠀⠈⣷⢤⠽⠛⠁⠀⠈⠢⣤⣉⣽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇
⣨⠷⠤⢤⠉⠀⢈⡏⠀⠈⡇⠀⠀⠀⢀⣀⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇
⠙⠒⢒⡶⠂⡀⠀⠣⠀⣠⣝⣒⣚⣋⣩⡤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⡇⠸⢸⢸⡇
⠀⠀⢯⠴⠚⠉⠓⠒⠛⠁⠀⠈⠉⠉⠀⠀⠀⣿⠀⠀⢧⡀⠀⠀⠀⠀⠀⣨⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣄⠀⠀⡇⠀⢸⢸⡇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢶⠲⠴⠒⠋⢁⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⢤⣇⠸⠸⢘⡧⠏⢈⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢧⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣈⠙⠛⠏⠀⠘⣯⠔⠚⢉⣁⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⡇⠀⠀⠀⡸⠀⠈⣉⣁⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⣦⣄⣀⣠⡀⢰⣌⡉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣼⢻⡇⠀⠀⢣⣨⠆⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠙⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠋⠉⠉⠉⠙⠛⠛⠻⣟⠒⣶⠲⠶⠶⠶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⡀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⢄⡀⠀⠀⠀⢰⠇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⠓⠶⠴⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣍⣀⣤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡬⠿⣿⣿⣦⡀⠀⠀⣀⣤⣾⡿⠋⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢶⣤⡀⠙⣿⠛⣴⡾⠟⠛⠛⣦⡀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠲⣿⠀⣟⣀⣤⣴⠒⠉⢻⡄⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⣉⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠛⠛⠉⠀⣠⠟⠀⣿⣭⣿⣿⠂⠀⢸⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠙⢿⣿⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠨⠿⠶⠶⠾⠿⣶⣦⣿⣯⣉⣁⣀⣴⠟⠀⠀⠀⢸⣿⣦⣄
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣾⡇⠀⠀⠀⠀⠈⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣦⣄⣀⠀⢸⣿⡉⠙⣷
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣰⣿⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣾⣿⣇⠀⢿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⡇⠀⠀⠀⠀⣼⡟⣿⡇⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠁⠀⠀⠀⣸⣿⠀⢿⡇⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⢠⣿⡏⢀⠼⢿⣆⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⣸⡇⢸⡏⠀⠈⢻⣦⡀⠀⠀⠈⠛⠿⣿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⠀⠀⠀⢿⡟⠈⢣⢀⡰⠃⠙⠿⣦⡀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⣀⠀⢸⣧⠀⣠⠿⣄⠀⠀⠠⠘⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⠋⠁⠈⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⢿⡀⠀⠹⣿⣅⠀⠈⠛⠶⢦⣀⣠⣴⠿⠛⠿⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣿⣆⠈⢷⣄⠀⠈⠙⠛⠿⠟⠛⠛⠋⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣯⠙⣷⣄⠙⠷⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⣿⣿⣀⣀⠙⠿⣦⣄⡈⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⠈⣷⣀⣀⣀⣠⣤⣤⣶⣿⠿⠆⠀⣾⠁
⠀⠀⠀⠀⠀⠘⣿⡆⠀⠈⠉⠉⠛⠛⠿⠿⣶⣿⣿⡷⢶⣦⣤⣤⡞⠁⠀⠀⠀⠸⡇⠘⡅⢸⡟⠉⠉⠉⠉⠁⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⢻⣷⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠙⠻⣶⣤⡿⠋⠀⠀⠀⢰⡆⠀⣿⠀⣷⢸⣷⣤⣤⣤⣤⣤⣤⣴⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⠛⠛⠛⠛⠻⠷⢶⣄⠀⠿⠁⠀⠀⢀⣴⠿⣷⠀⠸⡄⣿⣾⠃⠀⠈⠉⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣤⣤⣶⠟⠉⡜⠻⡄⠀⣷⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⢹⡇⠀⢠⠋⠀⢹⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⡿⠀⢠⡟⠀⢀⡷⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢻⣅⣠⡟⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⣿⡉⠉⠉⠉⠉⢙⡿⠉⢹⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠸⣷⠀⠀⠀⢀⣾⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠹⣧⠀⠀⣼⠇⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⡿⠿⠿⠿⠛⠀⢹⣧⣰⡿⠀⠀⠚⠛⠻⠿⠶⠶⠶⠶⢶⣶⣦⣤⣤⣄⣀⡀⢀⣀⣤⡶⠿⠛⢻
⣶⢶⣄⣀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⠿⠟⠋⠁⠀⠀⣰⡿
⢻⡄⠈⠙⠻⠷⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣀⣾⠟⠁
⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣾⠟⢿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⣀⣠⣾⠟⠁
⠀⠀⠈⠛⠷⣶⣦⣤⣶⣶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁⠀⠀⢀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⢠⠁⢰⡇⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⡤⠤⣤⡀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⡃⠂⡐⠃⠠⣤⡀⠹⣄⠀⠀⠀⠀⠸⡄⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣀⣿⡇⠁⣀⣀⣼⣿⠀⢻⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⢃⡄⢿⣿⣿⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠈⠉⢁⠆⢳⡈⠻⠿⠋⠀⣸⡇⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠿⠛⠉⠀⠈⢷⣄⡀⣀⣴⡟⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣤⣄⣀⣀⠀⠙⠛⠛⠋⠀⠀⠀⣀⣿⣦⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠟⠛⠋⠉⠉⠙⠛⠛⠿⠿⠶⠶⠚⠛⠋⠉⠀⠙⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⡇⠀⠘⠛⠉⠁⠀⠀⢀⣀⣀⣀⣠⣤⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⢀⣴⠟⠋⣁⠤⣼⡇⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣿⠁⣀⣀⣤⣤⣿⡇⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⢀⣀⣠⠆⠀⠀⠀⢻⡄
⠀⠀⠘⠿⠛⠋⠉⠉⠁⣿⡇⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣶⣾⠿⠛⠁⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⡇⠀⠀⠀⠀⠀⣀⣀⣀⠉⠉⠉⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣴⡾⠛⠉⣀⢼⣿⠀⠀⠀⠀⣾⡿⠛⠛⠿⢶⣤⣄⣀⣀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⣴⡾⠋⠁⠀⠀⠁⣠⣼⣿⡀⠀⠀⠀⢻⣷⣀⠀⠀⠀⠈⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣾⣯⣀⣀⣤⣤⡶⠟⠋⠀⢿⣇⠀⠀⠀⠀⠙⢿⣷⣦⣤⣀⣀⣀⣤⣤⠶⠟⠛⠋⠁⣀⠀⠀⠀⠀⣼⡇
⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁⠀⠀⣀⣤⠶⠛⠁⠀⢀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠳⣄⡀⠙⢦⡀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢣⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡈⠙⢦⣄⠉⠳⢬⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄⣈⠙⠲⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⢶⣤⣤⣤⣤⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣧⠀⠀⠀⠸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠈⠙⠛⠛⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣦⣤⣤⣤⣴⠶⠛⠁
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢋⢀⣎⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢢⣀⣀⣄⠀⢸⠀⠀⠀⠀⢀⡀⠙⡄⣸⠀⠀⢀⡤⠒
⠀⠀⠀⠀⢠⠫⠒⡄⢀⣱⠦⠤⠀⠀⠀⠀⠈⢡⠊⠁⠀⠀⠈⠑⢇⠀⠀⠀⠀⢀⡜⢓⠛⠓⠒⢲⣯⣔⡒⠂
⠀⠀⠀⠀⢇⠘⠚⠡⢧⡼⠀⠀⠀⠀⠀⠀⠀⡆⣠⠤⡄⠀⡠⡀⠘⡂⠀⠀⠀⠸⣇⠼⠐⠤⠀⠽⣽⡇⠈
⠀⠀⠀⠀⠈⣂⠈⠉⠶⣁⣀⠀⠀⠀⠀⠀⠀⠣⣓⠑⠋⠀⠚⢊⡠⠃⠀⠀⠀⠀⠢⣨⠇⠀⢫⣡⠔
⠀⠀⠀⢠⠊⡇⠀⠀⠀⠘⢆⠑⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⢀⠀⡇⠀⠀⠀⠀⠀⠀⠞⠀⠀⢸⡅
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠱⠔⠁⢀⠂⠀⠀⠀⠀⠀⠀⠰⡀⢀⡼
⠀⠀⠀⠀⠀⠑⡤⠀⠄⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠩⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠐⢠⠀⢀⡳⠼⢴⡁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣋⡀⡀⣀
⠀⠀⠀⠀⠥⢍⡶⣫⣄⠄⢖⡶⢹⠀⠀⠀⠀⠀⣹⣖⠓⢓⣤⡀⠀⠀⠀⠀⣴⡩⡩⣟⠉⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⡇⠑⠑⠣⠴⢠⡋⠀⠀⠀⠀⡇⠯⠜⠀⠟⠼⢣⠀⠀⠀⠀⣏⠓⢣⣲⢰⠖⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⡖⠑⡄⠀⠀⠀⠙⢢⢀⠁⢀⠀⠘⡆⠀⠀⠀⠏⠹⢺⠛⠁⢀⠅⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢰⠁⠀⠑⠤⠐⠁⢀⠃⠀⠀⠀⠀⢸⡈⠁⠈⠀⢀⠇⠀⠀⠀⠠⠸⠀⠆⢀⡇⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠈⢦⣀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠑⢦⠄⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⡀⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⢀⡆⣀⠄⠤⠀⠀⠀⠀⠀⢀⠔⠒⠒⠂⢤⠤
⠀⠀⠀⠀⠀⠀⡰⠧⠾⠤⣖⣂⠀⠀⠀⠀⠈⠉⣹⢖⡫⡏⠝⢫⠉⠲⡖⠂⠀⠀⠀⢩⢾⢯⢹⡆⠊⢀⡓
⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠈⢣⠁⠀⠀⠀⠐⠉⡇⠠⠥⠒⠒⠓⠒⣀⠇⠀⠀⠀⠀⠀⠸⠈⠉⠀⠁⠉⢻⣠⠇
⠀⠀⠀⠀⣼⠀⢎⣿⡱⠀⣮⡾⣆⠀⠀⠀⠀⡰⢇⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⢠⠚⠀⠈⠉⠀⠀⢸
⠀⠀⠀⠘⠘⢦⣀⣀⣒⣒⣀⡴⠉⠃⠀⠀⠀⠁⠈⢢⡀⢀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡆⠀⠀⠀⠀⡠⠷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⠀⠀⠱⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠉⢝⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠈⠀⠀⠀⠀⣿⠙⢿⣷⣤⣀⠸⠀⠀⣀⣼⡄⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠛⠿⠿⠿⠿⠛⠻⢿⣶⣶⠿⢿⣿⠏⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⢿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠻⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⣠⠞⠋⠉⠉⠉⠙⢲⣾⡆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⠀⢀⣿⣆⣀⠀⠀⣤⢦⡄⠀⠀⠀⡇⠀⢹⣯⢂⣴⠾⢿⣶⣤⠿⢤⣧⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣦⣶⡶⠛⠉⠉⠉⠙⠲⣿⣿⠝⢦⡀⢸⠃⠀⠀⢿⣾⡁⢸⡍⠀⠀⠀⢸⣿⣀⣀⣷⠒
⠀⠀⢲⠒⠣⠀⠀⠀⠀⠀⢹⣿⡄⢀⣤⣶⣦⣄⠀⠈⢿⣁⠈⠳⣾⠀⢀⠀⠈⢿⡳⠬⠿⠟⠁⠀⡼⢹⡏⠀⢸⣦⣤⣤⣀
⠀⠀⠚⠒⠼⠀⠀⠀⠀⠀⣼⣿⣯⡟⠁⠀⠀⠹⡆⠀⠘⣗⣦⡀⠀⠀⢸⣧⠀⠘⣧⣀⣀⣀⣤⠞⣵⠞⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⡀⠀⠀⢠⠇⠀⢠⣿⣿⢷⣄⢀⡾⠸⣦⣴⠾⠛⠋⠉⠁⠘⣇⠀⠀⠀⠀⠠⡄⣀
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⡻⢿⣿⣷⡙⠓⠚⠉⠀⢀⣾⣿⣿⠆⠙⠛⠃⠀⠀⠀⠀⠐⣤⠶⡔⠶⠸⠦⠀⠀⠀⠘⢤⠼
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠞⠙⢿⣶⣤⣤⣤⡶⠿⣿⣅⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⠈⢣⡘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠴⠃⠀⠀⠘⠉⠈⠁⠀⠀⠀⠈⢻⡆⠀⢀⡴⠋⠀⣀⡈⠑⢦⠀⠀⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⣷⢠⡞⠀⡴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠍⠀⡑⠂⠀⠀⠀⠀⢹⡞⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠚⠲⠇⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠖⠀⠀⠀⠘⠿⣷⡀⠀⠀⢀⣀⣠⣿⣄⣀⣀⣠⣴⣶⣄⠀⠀⠀⠛⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⠊⠙⠛⠛⠛⠛⠻⣿⡿⠛⠛⠛⢷⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣠⣴⡦⠀⠈⠉⠉⠁⠀⠀⢶⣶⣄⠀⠀⠀⠀⢶⣶⣀⠈⠉⠙⢿⣿⣿⣤⣾⡿⣆⣀⣀
⠀⠀⠀⠀⢠⣤⠘⠛⠛⠁⣀⣼⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠙⠻⣷⣄⠈⠻⠿⣶⣤⡀
⠀⠀⣠⣶⠏⠁⠀⠀⣠⣾⠟⠁⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠶⠶⠤⢶⣶⣶⡄⠉⢻⣷⣄⡀⠈⠛⣿⣦
⣀⠸⠋⠀⠀⠀⣠⣾⡿⠟⠀⣀⠾⠿⠛⠉⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠉
⠿⠀⠀⠀⢠⡄⠻⣿⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋
⠀⠀⠀⣤⠛⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠋⠀⢸⡿⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⠴⠿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠖⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠈⠉⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠐⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠉⠛⠛⠛⠛⠃⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣠⣾⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢴⣿⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⢿⣿⣦⢤⣤⣴⣶⠖⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠈⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠁⠀⠀⠉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⢀⠀⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣆⡈⠟⠛⠙⢿⣇⠀⠀⠀⠀⠀⠈⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢹⡷⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠇⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠾⠗⠀⠙⠟⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⣿⣦⣴⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡄⠘⠛⠛⠃⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢿⣯⡉⠉⠉⠉⠉⠹⣿⡟⠋⠉⠉⠉⠉⠉⠀⠀⠀⣀⣠⣶⡏⠀⠀⠀⠀⣿⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⡿⢿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠚⠛⠀⠙⢷⣤⡀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⡄⠀⢻⡿⠛⣶⣶⣶⣶⣶⣶⣶⡶⠀⠉⠉⠁⠀⠀⠀⠀⠈⠙⠃⠀⠀⣿⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠀⠀⢀⣀⣀⡀⠒⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⡆⠀⢹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠉⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢠⠀⠀⠻⠃
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠀⣀⡀
⠀⠀⠀⠀⠀⠘⢿⣿⠆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⣀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠉⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⡿⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠘⣿⡇⠀⠀⠀⢀⡀⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠻⠿⠋⠉⠀⠂⠀⠘⠻⠿⠿⠷⣠⣤⣴⠟⠀⠀⠀⠙⠿⣷⣄⣀⣀⣀⣀⠀⠚⠿⠟⠋⠈⠉⠻⠿⢢⣤⣀
⠀⠀⠀⠀⢠⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶
⣀⣀⣀⣀⣠⣿⣶⣶⣾⣿⣷⣾⣿⣿⣷⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣷⣶⣶⣶⣤⣤⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⠉⢻⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠸⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠛⠉⠉⠉⣉⡵⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠦⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠒⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠂⠀⠀⠀⣀⠠⠤⠤⠤⠦⠤⠤⠤⢤⣀⣀⠀⠀⠀⢀⣀⣀⣤⠬⠭⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠔⢩⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⢄⠀⠀⣷⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⡆⢀⡇⠀⠀⣀⣀⣀⣈⣙⡛⠀⠀⠒⠋⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠤⠬⣍⠓⠾⠀⠀⠀⢸⠁⠀⠛⠀⢸⠍⣹⠈⠉⠉⠉⢣⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⠚⠲⢤⡀⣠⠞⠦⣅⣀⠀⢀⣠⠎⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠙⡇⠈⣹⢧⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⣀⠤⠤⣄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠁⢱⢤⡀⠀⠀⠀⠀⠀⠁⠀⢤⣀⣀⣀⡼⠀⣸⠁
⠀⠀⠀⠀⠀⢀⡠⠖⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡴⠁⢀⠏⠓⡦⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⢏⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⣠⣋⣀⣘⣁⣰⡭⠭⠟⠒⠂⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠀⠀⠀⠀⠉⠉⠁⠀⣀⣀⡤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠈⢦⣀⡤⡔⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣹⢃⣀⢿⡄⠀⠀⠀⠉⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡴⡊⠁⢀⡔⠐⠒⠒⠙⢷⠋⠀⠀⠀⢸⣤⠟
⠀⠀⠀⠀⠀⠀⠙⠲⠥⠞⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠸⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⣤⢤⡤⠴⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣸⣸⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡲⣾⣤⣤⣽⡤⢤⣷⡖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠧⠭⠟⠚⠉⠑⠺⠿⠾⠟⠃

⠀⠐⠂⠀⡄⢳⢄⠀⠀⠀⠀⠀⢼⠂⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⡴⠣⠁⣴⡇⠀⠀⠐⠀⠀⠠⣈⠞⠈⣆⠀⢸⢂⣼⣿⣿⣬⣀⣀
⠀⢀⠀⢰⡅⠘⡇⠈⠀⠀⠀⠀⣸⠀⢠⣾⡿⣿⡇⠀⠀⠀⠀⠀⡼⠃⠀⡰⢁⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⠀⣸⠜⣽⠟⣿⠻⣿⣿
⠀⢸⣧⡘⠀⢀⠙⡀⠀⠀⠀⠀⡏⣰⣿⠟⠁⣿⣇⣤⣶⣾⣿⣿⡷⣤⡐⠀⣸⢒⠠⠀⠀⠀⡔⡇⠀⠀⢀⡄⠀⣿⣼⡿⢀⡏⠀⠑⠘
⠀⠸⣿⣧⠀⡀⠀⠸⡀⠀⠀⠀⣳⣿⠏⠀⣠⣟⣻⣿⣿⢫⣬⣄⢩⣷⡟⣆⡧⠈⠀⠀⢀⠎⠀⠀⠀⠀⢸⣷⣴⣿⣿⠃⢸⡏
⠀⠀⠸⣿⡄⠀⠀⠉⢿⡄⠠⠀⣿⡟⠀⠘⣿⠐⣿⣿⣿⡈⣙⡋⠠⣭⠠⣿⡱⠀⠀⢠⠏⠀⠀⠀⠀⠰⠇⢀⡻⣿⠁⠀⣾⠁⠀⢡
⠀⠀⠁⣿⣧⠀⠀⠀⣸⣷⠀⠀⣿⡇⠀⠀⠙⣦⣽⣿⣿⣿⣿⣦⣠⠄⠂⢺⠄⠀⢠⠏⠀⠀⠀⠀⠀⣽⣾⣥⠔⠋⠀⢰⣿⠙⢶⢾⡇
⠀⠀⠀⢹⡏⣷⡀⠀⢸⣿⡅⢠⣿⡇⠀⣐⣶⣿⠿⠿⢿⣿⡟⠻⣿⣿⣿⡿⠀⣠⠋⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⢀⣿⣿⡆⠀⢠
⠀⠀⠀⢸⡇⣿⡇⠀⢰⣿⠃⠸⣿⠀⣸⣿⣿⣿⣶⣶⣿⣿⣿⣦⣤⣤⣿⣀⣰⠡⠴⣶⣾⣾⣿⣿⣿⣿⠏⠰⠀⢠⣾⡿⣷⠈⠀⠀⣻
⠀⠀⠀⣸⣷⣿⠂⠀⢸⣿⠀⢀⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣉⣩⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⢏⠅⠀⠀⢀⣾⡿⠁⠈⠀⢀⣼⣿
⠀⠀⢀⡟⣿⣿⠀⢀⣾⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣼⣿⠿⢡⠟⠁⠀⠀⣾⣿⠃⠀⠀⢠⣿⡿⢹
⠀⠀⢸⠁⣿⡏⣠⣾⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠒⠶⣶⣾⡿⠛⢀⡏⠀⠀⠀⣼⣿⠏⠀⠀⢠⣿⡟⡰⠿
⠀⢀⡏⠀⣿⣷⣿⢧⠤⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⢀⠀⡇⠀⠀⣴⣿⠏⠀⠀⣴⣿⠏⠀⠎
⠀⠸⠧⠄⣿⣿⡇⠘⣦⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣿⣿⣿⡆⢀⠂⣴⣶⣦⠀⠀⠀⠈⣃⠀⢠⡇⠀⣰⣿⠏⠀⣠⣾⡿⠃⠀⠁
⠀⠈⠀⠀⣿⣿⣿⠀⠹⡄⠀⠀⠀⣿⣿⣿⣿⡏⠀⢸⣿⣿⣧⢤⣾⣿⣿⣿⣿⣄⠀⠀⠑⢄⢸⠀⣴⣿⠏⢀⣾⣿⠟⠁
⠀⠰⠤⢀⣿⣿⣿⡄⠀⢳⠀⠀⠀⢿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢾⣿⢋⣴⣿⠟⠁⠀⠀⠀⠀⠀⡠⠚
⠀⢀⠀⢸⣿⣿⡿⠸⢄⠀⢇⠀⠀⠘⣿⣿⣿⣧⣠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠻⢷⣆⡀⠀⢱⣿⡿⠃⠀⠀⠀⠀⠀⢀⢞⠱⡀
⠀⠀⢀⣿⣿⣿⡇⠀⠀⢵⢼⡀⡈⠀⠙⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣦⣤⣤⠻⠿⢶⣶⣿⠛⠻⢶⣖⡂⠀⢀⡿⡘⡄⢳
⠀⠀⣿⣿⣿⣿⢇⠀⠀⠀⢧⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⣷⡀⠀⠀⠙⢧⡀⠀⠈⠉⠋⣿⠀⣡⠘⢉
⠀⢸⣿⣿⣿⡇⠘⣆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣟⠿⠿⣿⣿⢿⣷⣦⠀⠈⢻⣿⣿⣶⣄⣀⡀⠙⣷⣄⠀⣸⡿⣍⠀⠀⠈
⠀⣿⣿⣿⣿⠁⠀⠈⢧⡀⠀⠀⠀⢀⠀⠀⠀⡠⠞⠤⣈⡁⠀⠀⣰⣿⡇⠀⠀⣿⣷⡆⠈⣧⠙⢿⣿⣿⣿⣶⣌⣿⣿⣿⠃⠈⠳⢤
⠀⣿⣿⣿⡿⠀⠀⠀⠈⢐⢄⠀⠀⠀⠘⢦⡞⠁⠀⠂⠈⠃⢠⣾⠟⣼⠈⠃⠀⣿⣿⣷⡀⣷⠀⠀⢙⡿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢠⡝
⠀⢻⣿⣿⠀⠢⠀⠀⠀⠈⢢⠣⡀⢀⡴⠋⠀⠢⠀⠀⠄⣴⣿⡋⢸⠏⠒⠄⠀⠿⣿⣿⣧⢹⠀⠘⠁⠀⡈⣻⣿⣿⣿⣿⣿⣿⣷⣄⣱
⠀⣿⣿⣯⠀⢀⠀⡀⠀⠀⠀⢣⡸⠎⠀⠀⠀⠀⠀⢈⣼⠟⠁⣇⣾⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠂⣀⠞⠠⠃⠎⠳⣌⢉⠉⢻⠿⠿⢟
⠀⣾⣿⣿⠀⠈⠀⠛⠐⢂⠄⡟⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠠⢸⠇⠀⠀⠄⢀⡠⣾⣻⣿⣿⡁⠌⠡⠀⠀⠘⠀⠀⠟⣦⠹⣤⣀⢃⡘
⠀⢻⣿⣿⠀⠀⠀⢠⠜⠇⡄⠀⠀⠀⠀⠐⠀⢰⣿⠃⠀⠀⢀⡏⠀⢀⠤⠚⣡⠞⠁⣸⣿⣿⡗⠈⠀⠀⠀⠀⠀⠀⠀⠁⡷⡀⠈⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⢻⣿⣷⣶⣶⣶⡚⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⣰⣟⢿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⣠⣴⣾⣿⣿⣷⣿⣿⣿⣷⡠⣀⠀⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢃⣈⣹⣿⣿⣿⣿⣿⡿⠿⢿⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⣽⣿⣿⠟⠁⣁⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⣿⣿⣤⣦⣼⣃⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣶⣿⣿⠃⢠⣿⣿⠿⢿⣿⣿⡿⣶⡾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣾⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⡿⣿⣷⣔⣦⣰⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣽⣿⣯⡈⢙⣿⣿⣿⣿⣿⡟⢻⣿⣾⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡎⢻⣿⡇⣾⣿⣿⣿⣿⠏⠀⢸⣿⣿⠇⢸⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢺⡇⢸⣿⠁⣿⣿⣿⣿⣯⠀⢠⣿⣿⣿⡆⢺⣿⣧⠀⠀⢸⡄⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣚⡛⠂⣿⣿⣿⣿⡘⣇⢻⣿⣿⣿⠀⢸⣿⣟⡆⠙⣻⣷⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣴⣿⣿⣿⣿⣷⢻⣼⣿⣿⣿⢠⣿⣿⣿⣼⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠾⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⣠⠆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠛⠻⢷⣶⣾⣋⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⢿⣿⣿⣷⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣿⣷⣶⣿⣟⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⣿⣿⡛⠉⢻⣿⡟⠿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣃⠤⠄⠻⡧⠄⢼⡟⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣀⡀⠀⢠⣤⠀⡇⠀⠀⠀⠀⠀⢀⣀⡤⠿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣄⠸⣿⡇⣧⣠⠶⣢⡴⠋⣹⠏⠀⠀⠀⠉⠉⠁⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⣀⠉⠛⠿⠆⠛⡷⠟⣥⠞⠋⢠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣈⣙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠹⣿⣷⡌⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⢻⣿⣆⠀⠀⠀⠉⠛⠒⠒⠦⠶⠶⠶⣶⠖⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠉⠛⣷⠖⠛⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣷⣦⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢠⡾⠻⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠸⣤⡀⢹⣿⣿⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠲⣶⣞⠻⣦⡿⢿⣿⣷⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣶⣾⣿⣿⣿⣿⠀⠦⠀⢻⣿⣿⣆⠀⠛⠛⠛⠛⣿⢻⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⡟⠉⠉⠀⢿⣿⣿⣿⠇⠀⠀⠀⠛⠛⠿⣷⣦⣤⣤⣞⡋⢾⡝⢿⣿⣄
⠀⠀⠀⢀⣠⡴⠾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠀⠈⠁⠀⠻⢿⣷⡀
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣇⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⢀⢸⣿⣧⣾⣿⠿⠿⠟⠛⠛⠛⢻⣿⣿⣷⣦⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡆⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠘⠻⣷⡄
⠀⠀⠀⠀⠀⡈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣤⣄⣀⢀⣴⣾⣿⡿⣿⣿⣶⡀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠛⢻⣯⣿⣿⡇⠀⠀⠀⠀⠀⢹⡆
⢀⢀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⣿⣿⣿⣾⣍⣘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢆⠀⠀⢀⠐⡇
⠀⢆⣡⣄⣀⣀⣼⠷⠆⠀⠀⠀⠀⠀⢀⣾⣿⣤⢿⣿⣛⠀⠀⠉⠛⠻⠿⣾⣿⣿⣿⣿⣿⡟⠻⣿⡯⣿⣝⠛⠛⠋⠉⢀⡰⠋⠐⠃
⢀⠈⠛⠛⠉⠉⠀⠀⠀⠀⠀⣀⣀⣤⣾⣏⠀⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡟⢿⣦⢸⣿⡏⠀⠀⠃⢀⣤⠿⠋
⠘⢷⣄⣀⣀⠀⢀⣠⣴⡇⣻⣟⣉⣯⡉⠛⠷⣦⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⠀⠙⠃⠈⣿⣀⣴⠿⠋⠁
⠀⠀⠀⣉⣉⠛⠋⣡⡟⢻⣿⣿⣿⠿⣿⡿⣦⠈⠙⠿⣦⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣎⠀⣿⣶⣿⠋⠁
⠐⠳⢶⣌⠿⠻⠿⠿⠀⠸⣿⣿⣿⣷⣿⢿⢷⣆⠀⠀⠈⠙⠷⣶⣤⣶⣿⣿⣿⣿⡿⣿⢿⣧⡴⠾⠋⠁
⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣉⠃⠀⠉⠀⠀⠀⠀⠀⢤⣤⣤⣾⣿⠋⢻⡤⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠉⣤⣿⠁⠀⢷⡟⠋⠛⠶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣤⠿⠿⠀⠀⠈⢳⠉⠉⠉⠙⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠙⠲⠤⠤⠖⠒⠒⠛⠛⠛⠛⠋⠒⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠋⢸⣧⠴⠖⠛⠲⣄⠀⣄⣻⠉⠓⠲⠿⡍⠓⠲⠦⠿⠏⠛⠲⢦⣄⣀⠀⢦⣤⣀⠀⠑⠦⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠢⢾⡀⡮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢀⡞⠠⠌⠉⠓⠛⠀⠉⠓⠦⣌⣷
⠀⠀⠀⠈⠛⣟⣛⣒⣒⠒⠒⠠⠤⠤⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⠶⢦⠀⠉⠁⠀⠀⠀⣀⣀⠀⢀⠴⠒⠓⣄⢠⠞⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢀⡠⠔⣊⣁⣀⣀⡤⠤⣤⠤⣤⣤⡬⠍⠛⠛⢛⣿⡿⠶⠶⠶⠦⠈⠧⣄⣀⣀⣠⡄⠀⢠⡴⢋⡽⢩⠅⢰⠋⠀⠀⠀⡜⠈⣦⠄⠀⠀⣸
⠚⠋⠉⠉⠉⢻⡅⢠⠖⢾⠉⠹⡇⠀⣵⣔⣚⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢻⡉⣵⢻⠀⢾⠀⠀⠀⡰⠃⠀⠈⢟⠛⣛⡡⠤⣄
⠀⠀⠀⠀⠀⠀⠳⠜⠢⡀⢣⠀⡇⠐⢋⣁⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⣸⣿⠀⠀⠑⠒⠊⠁⢀⠀⠀⠨⠟⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠉⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠳⣼⡄⠀⠀⠀⠐⢦⠉⠄⠀⢀⣀⣀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣇⢠⣤⣤⣀⣀⡀⣀⡰⢛⣶⡤⢾⣿⡆⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣙⡆⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠒⠛⠋⠉⠉⠹⣄⣈⣉⢙⡄⠀⠀⠉⠀⠁⠸⡅⢀⣼⠉⠹⣆⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⡟⠉⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣏⡃⠀⠀⠀⠀⠀⠀⠘⠲⢋⡆⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢇⠀⠀⠀⠀⠀⠀⣎⠁⠀⠘⠛⠊⠁⠀⠀⠀⠀⠀⡀⠈⢧⣀⠀⠀⠙⠳⢤⣤⣤⣤⣤⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⡾⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⢀⣨⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⢶⢲⠊⡿⠀⠀⠀⠈⠓⠦⣄⣀⣀⡀⠀⣰⠁⣧⠔⣹⢿⣿⣤⡀⠀⣴⢮⣉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣦⠁⠀⠀⠀⠀⠀⢰⠃⡏⠉⢩⠏⠁⠀⠉⠀⠀⠀⠙⠦⣙⢺⢁⣤⡨⢏⡁⣹⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⣯⣄⡀⠀⠀⠀⠀⢿⠾⠗⠂⢺⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢰⡶⣄⣹⠁⠀⠀⠀⠀⠉⠉⠒⠒⠒⠀⠤⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⡜⠻⠏⡟⡿⡲⠶⡾⢶⣊⠻⠟⠻⠇⠉⢳⠀⣀⡠⠤⠒⠊⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⢀⣃⡤⢖⡽⠿⣧⡀⠈⢑⣲⣭⣛⣓⠶⢲⡏⣟⡓⠒⠶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣉⣴⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⠥⣶⣛⡃⢂⣴⡧⠯⢬⢤⠖⠒⢺⠻⡉⠁⠀⠈⠉⡿⠿⣷⣶⣶⣤⣤⣍⣉⣉⠒⠒⠲⠦⠤⢴⠋⣠⣾⠟⣋⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡸⠀⢸⠉⡏⠻⣳⠀⢸⠾⡆⠀⠀⡇⢧⠀⠀⠀⠀⢹⣤⣤⣤⣌⣉⣉⡛⠛⠻⠿⠿⢿⣶⣶⣶⠾⣋⡥⠊⢹⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠇⠀⢸⠰⡇⠀⠉⠀⠈⠉⠁⠀⠀⢳⠼⡄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢤⣄⣼⡧⠚⠁⠀⠀⢸⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⣠⣊⠁⠀⠀⠀⠀⠉⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠑⠀⠀⡤⠔⢒⠟⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠁⢸⠃⠐⡡⠂⠀⠀⠙⣿⠷⠐⠢⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢠⡀⠀⠈⠀⢢⡀⠀⠀⣸⡰⣿⣁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠛⡄⡠⢶⠀⠙⢲⡾⠛⠻⡟⠉⢳⡀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⡄⠀⡀⠀⢀⠝⠀⠀⣾⠁⠀⠀⠀⠀⠀⣯⡀
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠔⠑⠎⠀⢠⠊⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⣀⣶⠉⠀⠀⠀⠈⠀⠁⠀⢀⡾⣿⣧⠀⠀⣿⠀⡇⠀⢸⡿⠠⣄
⠀⠀⠔⠋⠀⢀⣾⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⠀⠀⣴⠟⡄⠉⠛⠀⢀⠸⠄⢃⠀⠈⠀⢠⣼
⠀⢨⠀⠈⠛⠛⠛⠛⠛⠉⠀⣠⠇⠀⠀⠀⠀⣠⣾⠏⠀⣤⠀⠂⠈⢠⣾⣿⣿⣿⡇⠀⠀⠀⠈⠓⠄
⠀⢈⠷⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⢀⣼⣿⠇⠀⠊⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⣿⣿⡟⠀⠀⢄⠀⠀⠀⠀⢀⣤⣶⣿⣿⡏⠀⠂⣶⡆⠁
⠀⠉⠀⠀⠠⠀⠀⠐⠚⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠁⢰⣄⣠⡔⠉⠻⠛⠻⠏⠀⣿⣿⣷
⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠠⠊⠀⢠⣇⠀⠀⠀⠀⢊⠀⢠⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣀⡀⠀⠙⠋⠃⠀⢀⠀⠀⠀⢸⣿⣿⡿
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠉⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠹⡀⠀⠀⠀⣀⣴⣄⡀⠀⠀⠀⠈⠛⠋
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⢉⣽⣿⠟⠁⠀⠁⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠶⠶⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢰⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡜⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢀⡴⠀⠀⠀⠀⠀⠈⣷⠀⢸⣿⣸
⠀⠀⠀⠀⠀⣀⠀⠈⢷⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢠⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣤⣿⣷⣼⣿⣿⠤⠤⣤⣀
⠀⠀⠀⢀⡾⢻⡿⣿⠟⢿⣿⣿⣿⣿⣍⡛⠷⣄⠀⠀⣿⣠⣤⣦⡀⠀⠀⢀⡤⢞⣿⡿⠋⣿⣿⣿⡻⢿⣿⣯⠙⣧
⠀⣰⣾⡿⠁⣿⡟⠀⠀⢸⣿⣿⡙⠿⣿⣿⣷⣿⣷⣤⣾⣿⢾⣿⣿⣦⣴⣯⣶⡿⠋⠀⣰⣿⣿⣿⡇⠀⠙⢿⡄⠹⣶⣤⣤
⢠⠏⡞⠀⠀⣿⡇⠀⠀⢸⣿⣿⣿⡒⠤⣈⣹⣿⣿⣿⡷⠀⠈⠁⠌⣀⣿⣿⣿⠿⠂⣾⣿⡿⢻⣿⡇⠀⠀⢸⡇⠀⠀⠂
⠋⠈⠀⠀⠀⣿⠁⠀⠀⢸⡇⢻⣿⣷⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢀⣾⡿⠋⠀⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡄⣽⣿⡆⢰⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡇⢀⣾⣿⣿⡇⠀⠀⣿⡇
⡀⠀⠀⠀⠀⢹⠀⠀⣀⣿⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠠⣤⣴⠂⠁⠀⠀⠘⠀⣿⢣⣾⣿⡏⣿⠃⢀⣾⣿⡇⠀⠀⠀⢰
⣧⠀⠀⠀⠀⣸⡆⣰⣿⢸⣿⣧⠻⣿⣿⣿⡀⠀⠀⠠⠤⠤⠍⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢸⣿⣷⣿⣿⣿⠃⠀⠀⠀⣮
⣹⣆⣧⠀⠀⣿⣇⣿⣿⣼⣿⣿⣧⣿⣿⣮⣷⣠⣤⣶⡿⠿⠿⠿⠿⠿⠿⠶⠂⢸⣿⣿⣿⠃⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣏
⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠀⢀⡀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣰⣿⣿⣿⣿⣿⠇⣴⡇⢠⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⠿⢃⣿⣿⣧⣿⣿⣿⣿⣿⣟⣼⡿⢁⣾⣿⣽
⢹⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠁⠀⠀⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢁⣾⢿⣽⣯
⣶⣿⣽⣿⡽⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⣿⣿⠇⠀⡀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⢿⣿⣧⠙⣿⣿⣽⣿⡟⢰⡑⠀⢸⣿⠟⣿⠀⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣦⣽⣿⣿⣿⣷⣿⣦⣤⣿⣿⣾⣷⣾⣿⣿⡿⠍⠁⠀⠀⠀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣿⣿⡿⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠀⠀⠀⠀⠀⣀⣠⣤⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⢀⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠦⠘⠓⢾⡿⠁⠀⠀⢀⠃⠀⡨⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢄⠀⢀⣸⣀⣬⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠘⣷⣿⠿⣿⣿⠟⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠈⠏⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠐⠀⠀⠀⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⡇⠀⠀⢀⣄⢠⣦⠀⠀⣿⣿⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡽⢁⣨⣿⣷⠀⠀⢸⣿⣾⣿⠀⠀⣿⠟⠣⡌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡼⢁⡞⠀⢹⡿⣆⠀⠈⣿⡯⠿⠤⠴⠋⢰⢰⣇⣀⡙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⢁⡞⣀⠤⠞⠳⠈⠓⡩⠥⣒⣂⣁⡀⠀⠉⠁⠀⠀⠈⡏⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢇⡞⢰⠁⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⡴⠃⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡅⠈⠧⣄⣀⠀⠀⠀⠉⠉⢉⣉⣁⣀⣠⡤⠴⠒⡏⠑⣄⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡢⠀⠀⢹⡉⠛⣛⣹⠟⠿⠿⠻⢿⣷⡶⡶⠚⠁⠀⠘⡆⠀⠸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠛⠶⣄⠀⠈⠙⡍⢣⠀⠀⠀⠀⢀⡼⣸⣷⡀⠀⠀⠀⢹⡀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠿⣻⠁⠀⠀⠈⣿⣦⡀⠘⢦⡉⠒⠒⠒⠋⣴⠛⣿⣇⠀⠀⠀⠀⢧⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣰⠃⠀⠀⠀⠀⣿⣿⡍⠳⣄⣙⠓⢦⡤⠒⠁⠀⢻⣿⠀⠀⠀⠀⠸⡆⠀⠀⠈⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡤⡿⣿⣿⣦⣀⣉⣩⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣼⠀⡇⢹⣿⣿⡿⢫⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣠⣠⠴⠊⣿⠀⠀⠀⠙⠿⠀⢸⠃⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⠤⣚⣩⠤⠤⠤⠼⢦⣤⣄⣀⡀⣠⠞⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⠛⠛⠂⠉⠉⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⠴⢋⠭⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠦⣖⠤⣴⡛⠉⠛⠓⠤⡉⠙⠳⣄⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⣡⠞⢁⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣿⣿⣦⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⢁⡴⠋⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⡿⠿⠿⢿⠀⠀⠀⠀⢸⣇⠀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠤⠤⠤⠖⠒⠉⠉⠈⠉⠁⠒⠒⠶⠶⠶⠚⠛⠓⠋⠑⠦⣤⣤⠤⠮⠶⠒⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠂⠘⠀⠛⠸⠄⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠁⠒⠂⢄⠀⡀⠤⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠠⢀⠀⠀⠄⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠓
⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⢉⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠃⢀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡐⠑⠃
⠀⠀⠀⠀⢁⠀⠀⠈⠋⠀⣌⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣆⠈⠁⠀⢀⠂⠀⠀⠀⠀⠀⢀⠀⢡⠀⠀⠀⠺⢫⠀⠀⠀⠀⠄
⠀⠐⠺⡇⠀⠁⠀⠀⠐⠈⠀⠉⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣉⡀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠩⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠈⡦⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠁
⠀⠀⠀⠀⠰⡄⠈⠀⠃⠀⠐⠃⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠘⢫⡉⠉⠉⠉⠙⠉⠉⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⠒⠂⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠐⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁⠈⠉⠉⠉⠉⠙⠃


⠀⠀⠀⠀⠀⠀⣠⠶⠶⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠂⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠤⡀⠀⣀⠠⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⡠⠀⠐⠛⠛⠂⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⣀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄⠱⢂⣅⣠⣌⢠
⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⡀⠻⣿⣿⡿⢃⠻⢿⣿⠟⢠⠀⠠⢤
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠔⠉⠢⠄⠤⠒⠁⠀⠀⠀⠀⠀⢱⠀⠀⠐⠀⠈⠉⠠⠊⠑⠤⠀⠔⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⢊⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢤⣠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢒⣀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣄
⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢃⣠⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⡀⠀⠀⠈⠙⠓
⠀⠀⠀⠉⠍⠉⠛⠿⣷⠶⣴⣦⢶⣿⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⡞⠉⢠⣤⡄⠀⠇⢤⣤⠀⠁⢱⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠲⠊⠀⠀⠀⠠
⠀⠀⠀⠀⠘⢄⠀⠀⠀⣠⠆⠑⢄⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⠦⢀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⢀⠛⠃⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⡠⠊⠒⠤⠀⠤⠊
⠀⠀⠀⠀⠀⠀⣀⡄⠒⠈⡇⠀⠈⠉⠁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢶⣄⣀
⠀⠀⠀⠀⢀⡞⠐⠒⢲⠐⠃⠀⡎⠁⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠸⡑⡄⠤⠘⠒⠒⠒⠓⠒⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠆
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⡦⠐⠀⣰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠈⢻⣿⢿⡿⠁⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⡀⠐⡈⣋⠂⠀⠀⠀⠀⣈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢻⣿⣿⣶⣄⠀⠀⠀⠀⢨⣴⣿⣿⡿⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠭⠿⡿⠟⠀⠀⠀⠀⠸⢿⡿⠯⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⣀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣴⣶⠆⠀⠀⠀⠀⠀⠘⢧⣁⣙⣛⣉⣵⠋⠀⠀⠀⠀⠀⠐⣶⣦⣌⢲⣀
⠀⠀⠀⠀⢦⡴⣶⣶⡄⠈⠸⠛⠛⠁⠀⠀⡀⠀⠀⠀⠀⠈⢿⣻⢟⡿⠁⠀⠀⠀⠀⢢⠀⠀⠈⠛⠛⠃⠉⢠⣴⣶⢦⣴
⠀⠀⠀⠀⠈⠾⠿⡿⢷⠀⠀⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⢋⠀⠀⠀⠀⠀⠀⠀⡾⢿⠿⠷⠃
⠀⠀⠀⠀⠀⠈⡖⢄⢸⣧⣴⡶⠂⢀⠀⠀⠸⢷⣦⡀⠀⢀⣀⢀⡀⢀⡀⠀⢀⣴⡾⠏⡀⠀⡀⠐⢶⣦⣼⡇⣀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⡬⣷⣟⡀⠀⠘⡦⡄⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⠘⡏⢀⢴⡃⠀⠀⣙⣶⠥⣼⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠙⢿⣤⣌⣿⣁⡴⠊⠀⢻⠀⠀⢈⠌⠉⠻⡿⠋⠁⡀⠀⠀⡟⠀⠙⢦⣈⣿⣁⣤⡿⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠈⠀⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠏⠀⠀⠀⠻⢿⣿⣿⡆⢰⣿⣿⣿⠟⠀⠀⠀⠘⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓


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

⣿⠋⠙⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⡿⡏⡌









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣩⣩⣭⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠻⡉⠉⣙⡛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣠⠤⠤⠤⠤⠤⣝⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢰⢄⠀⠀⠀⠀⠀⣀⣠⢶⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣄⠉⠉⠉⠉⠉⠉⣠⡎⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣿⣿⣶⣶⣶⣾⣿⠟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⣼⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣃⠀⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣄⣀⡀⠀⠀⢀⣀⣠⡶⠋⠀⠀⠙⠲⣄⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠉⠉⢉⣩⠟⠁⠈⠙⢦⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⠔⠊⠉⣄⠈⠉⣉⠓⠲⠤⢤⣤⠤⠶⠚⡿⠁⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⣷⡀
⡞⠲⠧⠴⣇⣀⣸⢧⡤⣾⣀⡀⢰⡖⠶⠶⠖⠒⠛⠛⠋⠉⠑⠄⠀⠀⠀⠀⠀⣠⡼⠋⢀⡠⠔⠋⠀⠀⠀⢹⡄⠀⠀⠤⠚⠀⢷
⠓⠶⠦⠤⠭⢭⣥⣄⣀⣀⣀⠉⠙⢷⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⡆⠭⣗⡶⢫⡀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⠀⠀⠉⠒⣽⡛⡻⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⢸⡇⢸⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀⠀⠀⠀⡇⠈⠳⠞⠁⠀⣀⣀⣀⣀⡠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢻⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢸⠇⡼⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡿⢀⡇⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠤⠤⣤⣤⣤⡤⠤⠖⠚⠉⠀⠀⠀⢀⡾⣅⣼⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣰⠋⠀⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠙⠓⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢩⠟⠛⠛⠛⠛⠛⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣖⠒⠶⠧⠿⣤⠖⠛⠲⣿⠀⠀⡀⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠽⣄⠀⠀⡾⠁⣠⢤⡀⢹⡙⠓⠻⠦⠤⠼⠷⠖⠛⠲⠶⠤⣤⣤⣀⣠⠴⠒⠦⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠙⠋⢙⠗⢾⡇⠐⣇⡼⠃⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡔⢢⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠋⠀⠘⣇⠀⠉⠀⢀⡾⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠶⢤⠤⢼⡇⠘⢦⠊⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣷⣄⣀⣀⣴⠏

⠀⠀⢀⠄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⠀⢀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠁⠣⢀⠀⠀⢀⡀⠀⠀⠀⣸⣤⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⡀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣶⣿⣶⣼⣿⣷⣧⣾⣼⣿⣷⢂⣤⡀⠀⠀⠀⠀⡠⠔⠋⠀⢠⠖⠋
⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⢤⡈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⡤⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣤⣞⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠂⡈⠁
⠀⠀⠀⠠⠤⠤⠴⠒⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠚⠙⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣱⣿⣿⣿⠻⠿⠋⠉⠿⢻⣿⠃⣼⣿⣿⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢈⣩⣽⡒⠀⠘⠋⠀⢘⣩⣤⣼⢿⣿⣿⠛⠁⠀⠀⠀⣀⠀⢈⡀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠈⠁⠛⠋⠀⠀⠀⠀⠉⠀⠛⠉⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣤⡤⠄⠀⠀⠠
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⡀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣦⣄⡑⠀⠠⠀⡀⠀⠀⠀⠀⠀⠈⠠⠀⣈⣤⣾⣷⣶⣤⣄⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣴⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⣠⠶⠛⠉⠉⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⡀⠀⠀⣀⣀⣀⠀⠘⣷⠞⠁⣀⣀⠀⠀⣀⣀⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠟⢻⣿⣷⣾⣿⣿⣿⣧⠀⠸⣇⣾⢋⣿⣿⣾⣿⣿⣿⡆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠀⢀⣀⣀⡀⠀⠀⠀⢻⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⡇⠘⠻⣿⣿⣿⣿⡿⠋⠀⠀⢀⡿⠀⠀⠀⠴⠞⢻⠷⣦
⠀⠰⠟⣿⡉⠉⠁⠀⠀⠈⢧⡀⠀⠀⠈⠛⠿⣿⣿⠿⠛⠁⠀⢀⡾⣧⡀⠀⠀⠉⠉⠁⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣼⠀⠈
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠈⠙⠶⣤⣄⣀⣀⣠⣤⠞⠋⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡛⠛⠛⠛⢛⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⡛⢦⣀⣀⣀⣀⣠⣞⡉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠀⠉⠉⠉⠉⠉⠘⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠐⠿⠽⠆⢠⡄⠘⠉⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠠⣤⠼⠧⡤⠄⠀⠀⠀⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⣴⠀⠀⠀⠀⣧⠖⠋⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⠀⡴⠚⠛⠛⠋⠉⣿⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡿⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⡼⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢀⣼⠈⢳⡀⠀⠀⠀⠀⠀⠀⣷⢰⠇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠐⣿⣀⡀⠈⠳⡄
⠀⠀⠀⠀⠐⠟⢃⣠⣴⣿⣴⣶⣿⠟⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠓⢿⣤⣶⡴⠿⠖⠲⠶⠶⠶⠖⠋⠁⠈⡿⠀⠀⡷
⠀⠀⠀⠀⠀⢰⣿⡿⣟⠛⠛⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠚⠛⠛⠛⠛⠛⠛⠛⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣾⢹⣦⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣀⣀⣤⠤⠤⠴⠶⠶⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣌⡓⠿⢶⣤⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣉⡽⠖⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⠁⠀⠀⠖⢂⡀⠁⡉⠉⢉⠁⠀⠀⢲⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣉⣉⡉⢙⡾⠁⠀⠀⠀⠀⣀⠤⠒⠋⠉⠁⢀⡏⣀⠀⠀⢰⠀⠀⠰⠆⠀⠀⠀⠶⠀⠀⠀⡄⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣹⡇⢰⡡⣤⠙⡞⠀⠀⠀⠀⣤⠚⠁⠀⢀⡠⠰⠂⣻⢀⡚⠀⠀⢸⠀⠀⠀⠀⢟⣛⠇⠀⠀⠀⣠⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠊⢈⡷⠴⠿⠷⠶⣇⡀⠀⢠⠞⠁⠀⢀⠶⡁⠱⠀⠆⣿⢑⠁⠀⠀⠀⠑⠂⠀⠐⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠜⢀⡜⠉⠀⢀⡤⠤⣄⠀⠙⢦⠏⠀⠀⡰⣓⣠⣌⣢⠓⠉⣿⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢞⡉⠉⠙⢍⠙⢛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⡞⠀⡜⠀⡞⠀⠀⠀⡇⠀⣤⢈⡇⠀⠀⢣⠴⠚⠉⠉⠀⠀⠉⠙⠓⢿⡪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠢⣀⡬⠶⠚⠓⠲⠼⡆
⠀⠀⠀⠀⠀⠀⣇⣠⣥⠼⠧⢤⣤⣀⡳⣄⡈⠉⠀⠀⢀⣼⠀⠀⠀⠰⢤⠀⠀⠀⠀⠀⠙⣄⠀⠀⣠⣤⠤⠤⣶⠀⢰⠋⠉⠁⠒⠢⣄⣰⠋
⠀⠀⠀⠀⢀⡞⠉⠀⣀⣀⣀⠀⠀⠀⠉⠓⢯⣉⣉⣉⣉⣾⣀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢸⡤⠤⢧⡄⠀⡰⠃⢀⡯⠤⢀⡀⠀⠀⢸⣃⣴⠚⠉⠙⢟⠢⡄
⠀⠀⠀⠀⡞⠀⢠⠞⠉⠀⡈⠳⡄⠀⠀⣠⠞⠉⠁⠀⠀⠀⠉⠑⢦⡀⠾⠟⠀⠀⠑⠀⠀⢸⣿⣿⢰⠇⠰⠧⠶⡞⠀⠀⠀⠈⠑⢄⡼⠋⠀⠈⠢⡀⠀⣃⣘⡆
⠀⠀⠀⢸⡇⠀⢸⠀⠀⣏⡙⣠⠇⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣼⣿⠏⠛⢻⣦⣤⡞⠃⠐⠢⢄⠀⡠⠊⠉⠉⠒⢤⠀⡵⠋⠉
⠀⠀⠀⠈⣇⠀⠘⢦⡀⠀⠉⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⡄⠀⠀⠀⠀⣰⣿⣿⣶⣿⣿⡿⠯⢀⡀⠀⠀⣠⠛⠉⠁⠒⠠⢄⠀⡿
⠀⠀⠀⠀⠘⢆⠀⠀⠉⠛⠒⠛⡉⢸⡀⠀⠀⠀⠀⢠⡞⠉⡠⣍⠙⢦⡀⣧⠀⠀⣀⣴⠿⠿⠿⠿⠿⠧⣤⣄⣀⡈⠑⣾⠃⠂⠂⠐⠢⢄⡀⢹⡇
⠀⠀⠀⠀⣀⡬⠷⠒⠋⠉⠉⠉⠉⠉⠓⠦⣄⠀⠀⠘⣆⡀⢁⡼⠀⢸⣇⡿⠒⠉⠁⠀⠀⠀⠀⠀⠀⡞⠁⣀⠀⠙⢆⡷⠋⠉⠉⠳⡄⠀⠉⣺⠁
⠀⠀⠀⡜⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢧⠀⠀⠀⠉⢉⣀⣴⠟⠁⠀⠀⢀⡀⢤⠐⠖⢶⢶⡶⠛⢤⡽⠂⠀⠘⠃⠀⠀⠀⠀⣳⣀⣴⠃
⠀⠀⢸⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣷⣾⣿⣿⣿⡟⠁⠀⠀⡠⠚⢍⠑⡄⢡⠈⡎⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⣆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀⢠⢎⡉⠢⠈⣢⠸⠖⠓⠙⡏⠀⠀⠀⣴⡦⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⢀⡟
⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢠⠓⠢⢈⠶⠋⣀⠴⠚⠋⠉⣳⣤⠄⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠘⠳⡄
⠀⠀⢸⠀⠀⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸⠿⢿⠷⠶⢲⠟⠛⡳⠞⠒⠾⡅⠀⣀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠈⠠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢸⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠰⡁⠤⠁⣼⠔⠁⢀⠔⠁⣠⠜⠁⣠⠊⢀⣿⠉⠁⠀⠈⠓⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⣤⣤⠤⠤⠶⠒⠋⠹⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠊⢁⡠⠚⠁⣠⠔⢁⠔⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣤⣄⠀⠀⠀⣶⠆⠀⠀⢳
⠀⠀⠘⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡼⠥⠤⠶⠬⠤⠴⠾⠴⠶⠷⠶⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⢄⠀⠀⣀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⣏⠉⠉⠉⢹⠀⠀⡇⠈⢇⠀⢀⣀⣀⢄⢀⡀⣀⡠⢄⠀⢸⠀⢰⣶⡒⡲⠀⠀⠀⢶⣷⣐⠀⢸⠀⠀⠀⢀⠀⠘⠆⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⡏⠀⠀⡇⠀⠘⡆⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠈⠳⣄⠀⠀⠀⠣⠴⠷⢤
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⢹⡀⠒⠑⠂⠉⠙⠉⠉⠀⢰⢧⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣠⣇⠀⠈⠓⠦⠤⠜⠈⠉⠉⢉⣉⡷⠞
⠀⠀⠀⢠⠒⠋⠀⠀⡼⠀⠀⠀⣇⠀⠀⠉⠓⡆⠀⢧⣀⣀⣀⣀⣀⣀⣀⣠⠟⠀⠉⠒⠒⠒⠒⠒⠲⠶⠶⠖⠚⠁⠈⠉⠛⠓⠒⠒⠊⠉⠉⠉⠉
⠀⠀⠀⠈⠓⠒⠒⠊⠁⠀⠀⠀⠈⠓⠒⠒⠋⠁⠀⠀⠉⠉⠉⠉⠉

⠀⢠⣤⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠾⠀⠀⠀⣀⡀
⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠉⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠰⠀⠀⠀⠀⠆⡀⠀⠀⠄⠀⠠⢶⢶⣤⣀⣠⣀⣠⣤⡶⠟⢻⠉⠀⠃⠀⠀⣀⠙⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠘
⠰⠀⠸⠇⠀⡇⠛⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠩⡁⠈⠁⢀⠌⠀⠀⠇⠀⠀⠿⢠⠙⠁⠀⠌⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠈
⠀⠑⠀⠀⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠒⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⢒⠀⠀⠀⢠⠴⠒⠀⠀⠐⠢
⠀⢀⣠⠾⠛⢁⡐⠳⣄⡀⠀⠀⢀⣤⣤⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⠂⠀⠀⠐⠂
⠐⡏⠁⣤⠄⠨⠄⡤⠀⠈⡃⠀⠀⠀⠀⠉⢻⡆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠
⠀⢳⠀⠀⠀⢠⡄⠀⠀⢠⠁⠀⠀⠖⠒⠬⣆⠀⠣⠘⠃⠀⠄⠀⠀⠡⡀⠀⣠⡄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠈⠁
⠀⠀⠑⠄⠀⠃⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣀
⠀⠀⠀⠐⠶⠐⠁⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠴⠂⡘⠛⠦⣄⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠀⠀⠀⠠⢡⣶⢦⡄⠁⣴⣶⠆⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠱⠆⠀⠀⡉
⠀⠐⠀⠀⠠⠇⠀⠀⠐⠖⠀⠀⠀⢀⠤⣿⡷⠀⡄⠭⢿⠟⠀⠀⠀⠆⠀⠒⢀⡆⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⣀
⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠄⡀⠀⠙⢛⡢⠀⠀⠀⢘⠩⠅⢀⠀⠈⠍⢃⠀⠀⠀⠀⠨⠀⠠⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠟⠛⠷⠆⠀⠀⢄⣀⣒⡂⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⢀⣤⢶⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣀
⠃⠀⠐⠛⠀⠰⠀⠘⠛⠉⣀⠂⠀⢠⠀⢉⡀⠀⣣⣼⡁⣰⡇⠀⠘⡀⠀⠈⠛⠸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠈⠣⣙⣋⠼⠓⠉⠉⠚⠀⠀⠀⠻⢄⢀⡴⠋⠲⠤⠚⠁⠀⠀⠀⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠠
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣤⠐⡀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣾⠁⠀⠀⣴⣿⣿⡟⠛⠳⡀⠀⠀⠀⢸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⢸⡇⠀⠀⢸⣿⡃⠀⠑⠀⠀⢡⠀⠀⠐⠹⣿⡿⠁⠑
⠀⠀⠀⠀⠀⠀⢄⡀⠌⠀⠐⠤⠓⣾⣿⣧⣀⠀⠀⣿⡄⠀⡀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⡘⢋⠋⠁⠀⠀⠀⢀⠖⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢣⡐⠪⢋⠀⠀⠀⠀⠀⡀⠴⠋⠈⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⢸⡷⣄⠀⠀⠀⠁⠃⠄⠊⠠⠁⠀⣆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⢀⣿⡇⠈⢿⣦⡀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⣸⣿⡃⣀⣘⢿⣿⣧⠠⣀⡀⠃⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⢻⠟⠁⠹⣧⠢⠉⠛⠂⢠⡈⠄⡁⠀⢀⡀⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⡠⠊⠀⠀⠀⢻⣇⠡⠀⣀⠰⠻⣦⠒⠀⠲⡀⠀⢀⢝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⡠⠊⠀⠀⠀⣠⠀⢸⣿⢀⠠⠄⠐⠀⠙⠓⠂⠄⡘⢭⣥⣾⠇⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠤⠤⠴⠠⢚⣠⢚⠋⠁⠀⠀⠀⠀⠂⠄⡀⠢⡈⠂⢝⠋⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⢠⣿⣷⡘⠄⣀⠀⠀⠀⣤⡀⠀⠈⠂⠌⢸⠄⢑⣂⣁⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠤⡀⣄⠈⡩⠁⠈⠉⠀⠀⠀⠀⠀⠀⠁⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⡒⢶⡿⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠖⠛⠁⠀⠐⠀⠀⣉⠀⠰⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣠⣾⢻⣤⠀⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⢦⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⡞⢡⠇⠀⠀⢠⡿⣤⣀⣠⡴⠖⠦⢤⣀⣠⣿⣆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⣠⣾⠋⢠⡇⠀⠳⡆⠈⢷⠈⠉⡴⠒⢀⠐⠦⠀⠀⡟⠀⠙⠖⠀⡀⠱
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠀⢀⣤⣾⡿⠁⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢉⠛⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⢀⡞⠉⠀⠀⠀⢀⣠⣶⣿⣿⠏⠀⠀⠀⠀⠀⠈⠳⢤⠀⠀⠉⠀⠀⢉⣭⡝⠂⢀⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠲⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠻⣿⣿⣿⠟⠉⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠘⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢱⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⠜⡑⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣼⠀⠀⠀⠀⠀⠀⠀⢸⣅⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⠆


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡖⠀⢀⣀⠀⠀⠀⣀⠄⡀
⠀⠀⢰⠉⠁⠀⢀⠀⠉⡣⠀⠀⠀⢰⡀⠀⠠⣎⣉⣩⠤⢄⣠⠇⠀⠀⠀⠀⣠⠤⠤⠤⣄⠀⠀⠘⠁⣀⠀⣜⣅⣠⣈⡲⠋⠀⠀⠘⣆
⠀⠀⢏⣀⡀⠀⢉⡁⢈⠇⠀⠰⢶⣿⣷⡞⠀⣀⠀⠈⠢⠤⠇⠀⢠⠄⠀⢸⢁⡀⠀⠀⡄⢡⠀⠀⠀⠪⢀⡾⠁⠀⠉⠀⠀⢄⡲⠟⢛⣿⡆
⠀⢀⠦⠀⢑⣒⠊⡈⠁⢶⡀⠀⠀⠏⠙⠷⠀⠛⠁⠀⢀⣦⠀⠀⠀⠀⠀⢸⠀⢦⣀⣠⠆⡼⠀⠀⣀⣀⠛⢷⠢⡀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⢆⠀⠱⠘⠋⠀⠿⠀⠈⠁⠀⠰⣦⠀⠀⢴⠆⠀⣰⢻⠁⢣⠀⡰⡆⠀⠀⠑⠤⠤⠤⠔⠁⠀⠀⠙⠛⠲⠶⠶⠊⠑⠂⠐⠊⠀⠀⠄
⠀⠈⠦⠀⣀⠀⢷⡀⠀⠀⢰⡄⠀⠈⠀⣤⡀⣠⢾⠓⢾⢤⣄⣧⠘⣼⠠⠀⠀⠀⠀⠀⠀⢀⡀⢰⠋⡋⠛⢲⡆
⠀⠀⣀⡰⢻⠀⠈⠁⠀⣾⠀⠙⢀⣀⡄⠘⠭⠝⠀⠆⣾⢀⠞⠉⠉⠁⠀⠐⡀⠀⠀⠠⢀⠙⠓⠀⡯⠉⠉⠋⠁⠀⠀⡀⠄⢀⠔⠑⢄
⠀⠈⣕⡀⡬⣆⠀⠀⢈⡇⠀⡰⠋⢰⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⡴⠋⣨⣍⣲⡀⠢⠀⡴⠒⠋⠀⠀⠀⣴⠀⠀⠠⠀⠂⣼⡤⣰⠌⡃
⠀⠈⠁⢱⠀⠀⠀⢀⡞⠁⢰⠁⠲⠄⡵⠂⠀⠀⣖⣶⣷⡦⠀⠀⠀⣷⠘⠿⠏⣄⡇⠀⠀⠓⠠⠤⠦⠤⠄⠊⠀⠀⠀⠀⢾⡾⢷⡟⢿⣳
⠀⠀⠀⠀⣴⣦⡀⠘⠳⣄⢸⠀⡖⠤⠕⠀⠀⠀⠀⣰⣤⣢⠀⠀⠀⠈⠲⠷⠤⠊⠀⢀⡀⠀⠀⠀⣄⡀⠀⡸⠓⢲⠀⣠⠃⢀⠀⠁⠀⢸
⠀⢰⣿⢾⡟⣻⡇⠀⠠⠘⠀⢦⠈⠒⠒⡄⠀⠀⠘⠼⠉⢢⣴⡆⠀⡤⡀⠀⠁⢠⠆⢫⣽⡬⢦⠈⠀⠁⠀⠈⠖⠚⠁⠁⠉⡹⠑⠉⡓⠉
⠀⠈⠛⠶⣤⡟⠀⢀⠤⡴⠒⡆⠙⠢⠤⠼⠀⠀⠀⠀⠀⠓⠃⣨⢻⠏⡁⠀⠀⠠⣋⡷⠴⢇⣹⠀⠀⠇⠀⢖⢲⢄⢀⠃⢀⣈⡒⠒⡁⠠
⠀⠀⠀⠀⠀⠑⡔⠺⡀⠰⢂⠇⠀⠀⠀⠀⣀⡠⣊⢿⢿⠂⠀⠈⢩⢠⣽⢎⡇⢀⢈⡓⠓⠜⠁⠀⠀⣀⠠⠈⠲⠾⣿⢺⠙⡠⠁⠐⢀⠐
⠀⠀⠀⣀⠀⠀⠘⢄⠈⠑⢊⠀⠀⠀⣠⣾⡟⠁⡣⠴⡃⠀⠀⠀⣀⣁⡮⢄⠀⣠⡀⠔⠀⣀⠤⡒⠲⣍⢣⠀⠀⠀⣼⠒⠉⠀⠀⡠⠠⠖⠆
⠀⠀⠸⡔⠁⠀⠀⠈⠀⠀⠠⠀⠤⠀⠉⠛⣤⡟⢅⣰⡿⠀⠀⠀⠁⢹⠉⢊⣴⠏⡀⣠⠚⠁⢀⣠⠔⠉⠀⠀⠀⡰⠀⠳⣀⡀⠀⠑⢤⣀⠇
⠀⠀⡠⠷⣀⡠⠤⢐⣒⣲⣤⣬⣄⠢⠁⠀⠉⠉⢻⡟⠁⠀⠀⠀⠀⠘⢠⣿⡿⠈⣇⡸⠒⠖⠉⠀⠀⠀⠀⢠⡎⠉⢢⡎⠀⠈⡆⢀⣀⡀
⠀⠀⠈⠊⠍⣶⡿⣛⠯⠉⠛⢮⣹⣧⡧⣀⠀⠀⠀⠀⡴⠊⠉⠒⢄⠀⠘⠟⠇⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠘⠧⠠⠜⠙⠂⠒⠀⡟⣯⣻⡄
⠀⠀⠀⠀⡸⠿⠷⢇⠀⠀⠀⢀⡁⠀⣀⠘⡄⠀⢠⠐⡀⠘⡘⠀⢸⠀⠐⠳⡀⠀⠀⡸⠃⠀⠀⡞⣦⠊⠑⢄⠀⠀⠀⢲⠥⠄⠀⢻⣿⣿⣿
⠀⠀⠀⠪⡀⠀⠁⣸⠀⠀⠀⠘⠦⠴⠦⢊⡐⠀⠀⢀⢱⠖⠀⣶⠁⠀⢀⣀⣨⣦⣼⣤⠤⢀⢀⣟⣁⣀⣀⢀⡱⠄⠁⠬⠀⢀⡀⠈⠁
⠀⠀⠂⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⢀⠜⠁⠈⢆⠀⠀⠘⡧⢤⠟⠀⠀⢸⣼⣿⣿⣿⣿⡇⡀⣤⠈⡀⡊⢱⡀⡄⠀⠀⠀⠀⣠⣈⠉⠵⠖⠂
⠀⠀⠄⠀⠀⠀⡰⠊⠳⡊⠉⠑⣤⢋⣤⢀⡄⣈⣆⠀⠀⠈⠋⠀⠀⠀⢸⢻⣿⣿⣿⣿⣷⣤⡏⠀⠧⠧⠤⠧⠃⠀⠀⡠⢚⠟⢦⡀
⠀⠀⠐⠀⠀⡜⠀⠀⠀⠙⣭⡴⠉⠁⠈⠋⠈⠁⠈⠆⠀⠀⡔⠲⡞⠂⠈⠂⠉⠉⠉⠋⠒⠒⠁⠀⠀⠀⡀⠄⠀⢀⣾⣦⣾⠀⢰⣼⢆⠀⠄
⠀⠀⠀⠃⣸⣀⣴⣀⣴⣦⣈⣧⠀⠀⠰⠶⠀⠀⠀⠙⡀⠀⡱⠒⢳⠳⡄⠀⢀⣴⢾⣽⠲⣦⡀⠀⢀⡶⠍⠀⠠⠧⣠⣀⣘⣿⣋⣀⣀⣳⡀
⠀⠀⠀⢰⣿⣿⡏⠉⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢱⠀⠘⠒⠚⠋⠀⠀⣾⡃⢰⠀⠡⠈⢷⠁⠀⢩⠀⠀⠰⡄⠲⠶⠆⠿⠤⠤⠤⠤⡷
⠀⠀⠀⠿⠿⠿⠛⠛⠛⠛⠛⠛⠿⠿⠂⠐⠒⠒⠒⠚⠁⠀⢀⠔⡲⠀⠀⠀⠙⣇⠘⡄⠀⣀⠎⠀⠀⢐⡃⠀⠀⠑⢬⣇⣀⣀⣀⣀⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢹⣟⣻⡏⣏⢩⣻⣟⣿⣟⠉⢹⡿⢿⣿⢻⣿⣿⣟⣿⣉⣿⡟⣿⣿⣛⣯⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠈
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠃⣀⣀⠻⢿⠟
⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄⢀
⠀⠐⠀⠀⠀⠠⡦⠀⠐⠀⠀⠀⠀⡤⢶⣶⠀⠃⢙⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠛⠣⠀⠀⠀⠀⢰⣇
⠀⠀⠑⢐⡿⠛⠉⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡬⠄⢤⠒⠀⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⢀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⢀⣤⣾⢿⣿⡏⣿⡿⢿⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠛⠁⣼⣿⠗⢿⣿⡜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⠀⠀⠤⠐⠊
⠀⠀⠀⠀⠀⢠⣿⣿⠀⢾⣿⣧⠀⠀⠀⠰⠚⢿⡃⡈⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠔⠒⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠛⠒
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⣿⠿⣿⣶⠿⣶⣿⢿⠿⡷⡿⢶⢶⡶⢶⠶⢶⠶⠶⠶⠶⢶⠶⠶⢶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠉⠙⠿⣿⣶⣤⣄⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣰⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠙⠻⢿⣷⣶⣶⣶⣶⣾⡿⠿⣿⣇
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⣼⣿⠟⠉⠁⠀⠀⠀⢻⣿
⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⣠⡆⠸⣿⡇
⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣷⡙⠻⣶⣤⣀⠀⠀⣀⣀⣠⣤⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⣾⣿⡇⠀⢿⣿
⠀⢸⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣷⡀⠈⡙⠿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠊⠁⠀⠀⠀⣀⣴⡿⠟⠁⠈⣿⡀⠘⣿⣇
⠀⠀⣿⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠻⣷⡀⠈⠳⣄⠉⠛⠿⣦⠹⣧⠀⠀⠀⠀⣀⣴⡾⢿⣉⡀⠀⢠⠀⠸⣧⠀⢹⣿⡄
⠀⠀⠸⣿⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢷⡀⠀⣿⡇⠈⠀⢠⣴⣾⠟⠋⢤⣬⢿⣿⣷⡏⠀⣀⣹⣧⠀⢻⣿
⠀⠀⠀⣿⣷⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⣸⣿⡆⣿⣇⠀⠀⣾⣿⠀⠀⠀⠀⠉⠂⠋⠉⠓⠀⠈⢿⣧⣀⣾⡟
⠀⠀⠀⢸⣿⡆⠀⠀⠈⣿⣿⠀⠀⠀⠀⢸⣷⡀⠀⠀⣙⣛⠁⢸⣿⠀⢀⣿⡏⠐⢦⡀⠀⢀⣰⣶⠦⠄⠀⠀⠀⠻⣿⡟
⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠹⣿⣄⠐⣿⠙⣧⢠⣿⠀⣸⣿⠇⠀⠈⢻⣶⡿⠻⣇⢠⣶⣄⠀⠀⠀⢻⣿⡀
⠀⣤⣶⠿⠟⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⠻⣷⣿⠀⣿⣿⠏⢰⣿⡟⠀⠀⠀⠸⠟⠁⠀⠈⣃⣈⡉⣷⣄⠀⢸⣿⡇
⢸⡿⢀⣤⣤⣤⣤⣤⣴⣿⣿⣧⣄⡀⠀⠀⠀⣿⡄⠘⠛⠀⣿⠇⣠⣿⡟⠀⠀⠀⠀⢀⣠⣴⣞⣛⣉⣍⣉⣻⣿⣷⣼⡿
⢸⢇⣾⠟⠛⠛⠉⠉⠉⢙⣻⣿⣿⣿⣷⣦⣄⠈⠿⣶⣶⡾⠋⡴⠟⣿⣷⠀⠀⠀⠀⠉⠉⠙⠓⠿⢬⣍⣋⣙⣹⢿⣧
⣼⡿⠃⠀⢀⣠⣴⣾⡿⠿⠿⠛⠛⠻⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠐⠶⢤⣤⣤⣈⣉⣁⣼⣿
⠁⢀⣴⣾⣿⣿⣭⣄⣀⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠻⣧⡀
⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠉⠛⢿⣧⡀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣶⣤⣀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⣄⡀⠀⠘⣦⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠙⢿⣿⣷⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣈⣻⣷⡀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣆
⣿⣷⠿⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣭⣹⣀⣢⡀
⠀⠀⠀⠀⣠⣤⡀⠀⢉⣬⡿⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⠿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠤⣿⣦⠴⠻⠟⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢿⢃⣼⣷⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣶⠔⠁⠀⠀⠀⠀⠀⠀⠤⢴⣴⠂⠀⠀⠒⢻⣿⡷
⠀⠸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢧⠀⠀⠀⠀⠀⠁
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⡷⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠁
⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⢤⢐⡂⠙⠏
⠀⠀⠚⢛⣿⡏⠈⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡯⠤⡇⠰⣽⠷⠀⠀⠀⠀⠀⠙⠀⠷⣾⣷⣄
⠀⢀⣴⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⣿⣿⣭⣭⣭⣽⣁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠹
⠠⠋⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁

⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤
⠀⢀⣸⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣤⠄⠀⢴⡔⠁⢀⣰⡀⠉⢦⠀⠀⠀⠀⠀⠀⣸⣷⠋⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⡄
⠀⠈⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣼⠀⠀⢈⣿⡉⠂⠀⡇⠀⠀⠀⠀⠀⢃⣿⡇⠘⡄⠀⠀⠀⠀⠀⢀⣵⣦⡴⢄⠀⠀⣿⡇
⠀⢸⣿⣿⠁⠘⠇⠀⠀⠀⠀⠀⠀⡼⢻⠀⠀⠀⢻⣀⣰⣋⣀⣹⣀⣀⡇⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠙⡆⠀⡞⠉⠙⢶⡀
⠀⠈⠁⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⣶⣶⡶⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⡾⠛⠓⣦⣼⣗⣤⣼⣿⣏⡛⢻⠿⣦⣆⠸⣿⣬⣿⡅⢀⣿⠟⠀⠉⠒⠉⠟⠋⠁⢀⣿⣿⣷⡄⢠⡄⢻⣍⠂⠠⠉⠀⠸⡿⢿⣴⠆⣤⠀⠺
⣿⠀⠀⠀⠀⣰⠿⡿⣿⠿⠿⣿⣿⢠⡾⠟⠀⠉⠀⠙⠃⠘⢿⣄⠀⠀⠀⣴⣀⣤⣼⣿⣿⣿⣿⡛⠋⠱⡿⠋⠻⣦⣄⣀⠀⠔⠀⢻⠀⠉⠦⢤
⠀⠀⠀⠀⠀⠹⢶⣾⣶⣿⣶⡿⢻⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣦⢠⠎⠀⢀⣰⠟⣋⣉⣹⣿⣦⣀⣰⠃⢀⠂⢀⣽⠟⠀⠀⠀⢸⠂⠸⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢷⣼⠿⠄⠀⠀⠼⠛⠛⠀⠀⠀⠘⣷⠁⠠⠒⠉⠁⠉⠙⢩⣙⢿⣧⡛⢻⡗⠾⣀⣺⡷⠋⠀⠀⣴⡿⠀⣴⠿⡀
⡤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣸⠿⠀⡅⠂⠀⠀⠀⠈⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠛⢛⣋⡱⢙⡡⠄⠀⠀⡇⣸⣅⣼⣇⣀⠈
⣄⢀⡀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣷⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢨⠍⠁⠈⠁⠰⣤⡞⣠⠋⠉⠁⠈⠿⢇
⡎⠙⢷⣤⣴⣅⣠⢾⣿⣿⣿⣿⣿⣿⠿⠂⣀⣀⣀⣀⣠⣤⡶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⡀⣏⢳⢦⠀⠀⠀⣻
⡁⢀⡄⢈⣴⠏⠁⠈⠙⠙⠛⠋⠛⠁⠀⠀⠿⠿⠿⠿⠟⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠋⠉⠀⠉⠛⢶⣇⠀⠳⣄⠰⡟
⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠸⣿⠁
⣿⡄⣸⡟⠷⠇⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢈⣉⣉⣉⣁⣤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣂⡼⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢻⡶⣤
⠉⠉⣻⣤⠀⠰⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⡟⣡⡦⢴⠖⠚⣏⠀⠉⢡⠐⢦⡤⣀⢀⢸⡷⢌
⠀⠰⣿⡿⠁⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣶⣶⡦⠀⠀⠀⠀⠀⢀⡀⠀⠈⣁⣀⡈⢻⡇⠹⠓⠚⠋⠙⠉⠉⠉⠉⠐⠒⠒⠡⢼⠈⣇
⢷⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡌⠉⠠⡀⠀⠀⠀⠀⠀⣠⢾⠉⠻⠞⠙⣿⣧⣾⣷⣴⣾⣿⣷⣦⠀⠀⠀⠀⠀⣠⣶⣿⣿⡇⣿⠈
⠀⠉⠀⠀⠀⠉⠀⢤⣠⣀⣀⣀⣀⣀⣠⣽⣿⣆⢀⣴⣆⣀⣤⡶⢚⣏⡰⡂⠁⠰⣾⣿⣿⣿⢸⣿⣋⠙⢿⡿⠀⠀⠀⠀⢰⣿⠟⢛⣿⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠟⠻⠿⠏⠛⠉⣿⣿⡏⢉⣿⣿⣁⣀⣾⠁⣠⣌⠀⠀⠈⢿⣿⢿⣘⣿⣿⣿⡿⠁⠐⢿⡖⠀⠈⢿⣿⣿⢟⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠒⠂⢀⣼⣿⣿⡆⢩⠟⣿⣯⢻⣿⣿⢉⢹⠏⠛⣷⡈⣿⡗⢻⣷⣬⡛⢤⣤⡀⢸⡄⢀⣀⡤⠋⣵⡏
⠀⠀⠀⠀⠀⢠⣴⣿⡿⠿⠛⠛⠛⠛⠻⣿⢹⡿⠇⢸⣶⣿⣿⠈⢿⣿⠈⡼⠀⠀⢿⢷⠸⣷⠋⢹⠟⠁⠀⠈⠑⣢⠤⡌⠁⠀⠀⠘⣷
⠿⠀⠀⠀⠀⠘⢧⡏⠀⠀⠀⠀⠈⠀⠀⠀⢿⣇⠘⣴⡿⠟⠛⠓⠾⡏⣴⠃⠀⠀⠋⠙⣧⢱⣤⢿⣴⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡼⣆
⠀⠉⠀⠀⠁⣀⠾⡇⢠⣄⠀⠀⠐⠀⣤⡶⣾⠻⣿⠋⠀⠀⠀⠀⠀⠸⣧⣀⣠⠇⠀⣀⠻⣆⣱⣿⡿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣦⡙⣦⡀
⢀⣤⡀⣠⠖⢡⡛⢧⡻⣍⠀⠁⣀⣀⡘⠷⢯⡷⡀⠀⠈⢁⠀⠀⠀⠂⠀⠩⠉⠀⢴⡟⢀⣿⣿⣬⡁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣿⣿⣟⠻
⣿⣡⣿⠃⠈⠉⢛⠸⣉⠀⠙⠿⠿⠛⣁⣠⡾⠀⠈⠀⢀⠀⠄⠀⠀⠀⢉⠀⠀⠀⠈⠛⢋⠛⣷⣿⠿⣷⣶⣦⣤⣤⣾⡤⣶⣶⣿⣿⣿⡽⠃
⠟⢹⣿⣶⣶⡦⢿⣴⡟⠁⢹⡆⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⠋⠉⠀⣿⡄⠜⠉⠉⠛⠛⠛⠋⠉⠉⠋⢀⣿⣶⣿⠄
⠀⡌⢻⡷⢹⠿⠛⠋⠉⠁⢀⠁⣃⠀⠀⠉⣄⠀⠀⠀⠀⠀⠀⠀⡀⢠⣈⡶⣶⣟⣿⠋⢶⡤⠐⠻⡇⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⢨⡏⠙⣿⣶
⡔⠑⠂⠀⠁⠀⠀⠲⠀⠀⠀⢹⡟⢧⡀⠀⠘⠆⠀⠀⠀⢠⡀⠀⠁⠀⠀⠅⠹⢿⣧⣥⠼⣶⡆⢠⣧⠀⠈⣻⠻⠛⠛⠻⢿⠉⠀⢸⡇⠀⠂
⡹⠁⠆⠀⠠⠀⠀⠀⢠⡀⠈⢹⠇⢸⡇⠀⠀⠀⠀⠀⠀⠿⠟⠀⢀⠀⣀⢻⣷⣦⣤⣤⣻⡌⠓⠀⣿⠀⠀⣟⡖⠠⠀⠠⢼⡄⠀⢸⡇
⡷⠄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠟⠓⠻⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣗⡝⢉⡽⠟⣩⣍⣩⣉⢢⣀⣬⠀⠀⡏⠀⠀⠀⠀⢰⡇⠀⢸⣥⡤⠴⠖
⠁⠀⡀⢂⠀⠀⠀⣀⠌⠁⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠐⢻⣍⣛⢩⣴⡬⢦⣬⣝⠻⣷⣉⣻⡆⠀⣇⠀⠀⠀⢀⣨⡇⠀⣿
⡙⠛⠃⠈⣀⠄⠚⠁⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠤⠀⡏⢀⡀⢿⡏⣳⣮⣍⣹⡇⢠⡟⠒⠚⠉⠁⢸⡇⢀⡿
⠑⣶⣦⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠀⠠⠀⠀⡀⢀⢀⡰⢎⠀⣿⣆⠱⠯⣭⡿⣸⡿⢿⣷⠀⠀⠀⠀⠘⣟⣛⡇
⠖⠳⣐⣤⣿⣟⠓⣤⣀⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢨⠁⣌⢀⢸⡿⠳⢄⡻⣀⢹⡿⣛⣷⠀⠀⠀⠀⢼⣛⣻⣇
⠐⣀⣿⣿⠋⡙⢶⣿⣏⣣⣿⡖⢻⣻⣄⣀⡀⠀⠀⠀⠀⠀⠈⢠⡀⠀⡗⢠⣿⣄⠢⡙⣦⠀⠈⣹⡟⢁⣼⣿⡇⠀⠀⠀⣾⢿⣗⣉⠷⣤⡀
⠂⡸⣿⣻⣄⣙⠼⢿⡏⣻⠼⣿⣟⡛⣯⡈⢳⣤⡤⠀⣀⡀⠀⠠⠀⠘⢃⣏⡿⠙⠷⣤⢈⣦⠾⠅⣠⣿⣏⣸⠇⠀⠀⠀⢾⡀⠽⣿⣦⠈⠉⠙
⣴⣟⠋⠿⠆⠁⠀⠈⠁⠻⡿⠻⣷⢾⡟⣷⣾⡉⠀⠙⣿⢹⡛⠢⠶⠀⢏⡿⣟⣆⣰⢋⣼⡁⠀⠀⠙⣯⣽⠇⠀⠀⠀⠀⠀⠙⠳⢬⣍⣀⣀⣀
⢨⡇⠘⢛⠘⠃⠀⠀⠀⠀⠀⠀⠙⠾⠿⠎⠀⢿⣤⣴⣾⣧⡌⣴⡇⢸⣼⡱⣜⣸⢛⠋⠈⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⢘⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠁⡞⢬⢳⡜⣧⠳⣵⣵⡟⢾
⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡷⢾⠁⡰⠊⣷⢹⣿⠛⠃
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢛⡐⠀⣦⠇⡏⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣛⣼⣜⣆⣀⣀⣠⣳⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣶⣦⣄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢛⡇⠀⠀⠀⠉⠻⢿⣦⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠻⣄⣀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢠⣼⣇⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣴⣿⣥⣴⣶⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⣘⣿⣿⣴⣃⣀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠛⠿⠟⠛⠛⢿⣶⣄⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠃⠀⣴⡿⠛⠳⣄⡴⠛⠻⣷⡄⠀⢻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠀⣼⡟⠀⠀⠀⠘⠁⠀⠀⠘⣿⡄⠈⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢻⣿⠁⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢹⣿⢻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠁⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠹⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⢸⣿⠀⢸⣿⠀⢰⣿⣷⠀⢰⣿⣷⠀⢸⣿⠀⢸⣿⠀⠀⠘⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⠀⢸⣿⠀⢸⣿⣿⡇⣿⣿⣿⠀⢸⣿⠀⢸⣿⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣴⡶⠶⣶⣤⣿⡇⠀⢿⣆⣈⣿⣿⣧⣿⣿⣏⣀⣾⠇⠀⣿⣇⣴⡶⠶⣶⣬⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁⠀⢀⣀⠈⠻⣧⣴⠾⠛⢋⣩⣭⣤⣭⣭⣉⠛⠻⢶⣤⡿⠋⠁⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣼⣿⣿⣿⣿⣿⢻⣿⠀⠾⢻⡉⠀⠐⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠓⠀⠀⣹⠻⠆⢸⣿⢻⣿⣿⣿⣿⣿⡄
⠀⣰⣿⣿⣿⣿⣿⡟⠀⠙⣦⣴⠾⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠳⢶⣤⡞⠁⠘⣿⣿⣿⣿⣿⣿⡀
⢠⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠻⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣿⣿⣿⣿⣿⣿⣇
⣸⣿⣿⣿⣿⣿⣿⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠻⣷⣤⣀⠀⠀⠀⢀⣀⣤⣶⡿⢿⣿⠁⠀⠀⢹⣿⠿⣷⣦⣄⣀⠀⠀⠀⢀⣀⣴⡿⠃⠈⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠻⣿⣿⠿⠟⠛⠉⠁⣀⣼⣿⣤⣤⣤⣼⣿⣆⡀⠉⠙⠛⠿⢿⣿⡿⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⣶⣿⡟⠋⠀⠀⠈⠙⠄⠈⠛⣿⣷⣶⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠃
⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⢿⣄⠀⠀⠀⠀⠀⢀⣼⠏⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠙⢷⣦⣤⣤⣶⠟⠁⢠⣾⡋⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠈⠉⢀⣠⣿⠇⠀⢈⣀⡁⢈⣀⣃⣈⣃⣄⣘⣀⣀⣀⣀⣘⡟

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠙⢲⡀⠀⣰⠞⠛⠛⠋⠙⠛⠛⠓⠲⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣔⣩⠤⣤⠀⠀⠀⠹⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠛⢉⡴⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⢀⢈⡗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠛⠁⠀⠀⠉⠓⠦⣄⣀⠐⢶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣄⡉⠳⣄
⠀⠀⠀⠀⢀⡀⠀⠀⢹⡄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣓⠮⣷⣄
⠀⣠⠶⠛⢉⢉⠙⠲⣼⠃⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠠⡀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠙⠂
⢰⡇⠀⠀⠉⠘⢳⠀⠹⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠻⣦⢹⡀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⢰⣤⣀⠀⠙⢷⡀
⠈⠛⠲⠤⠤⠤⢤⡄⠀⠀⠀⣀⣤⣴⠲⡖⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⣀⣀⠘⣆⠙⠳⢦⣽⣏⠓⢦⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⣾⣿⣿⣇⠀⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣇⠀⠀⢀⣀⣉⣉⣉⠀⠸⡆⠀⠀⠀⠉⠀⠀⠈⠛⢾
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⠀⠻⣇⣹⣾⠀⢹⣆⠀⠀⠀⢷⠀⠀⠀⠀⠀⣿⡴⠚⠉⠉⠀⠈⠉⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⢧⣈⡷⡁⢸⢦⡀⠀⠘⣆⡀⠀⢠⢀⣿⠘⠀⠀⠀⠀⢀⣠⠞⠀⠀⢧⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡄⠀⠀⠙⢦⣼⠧⣄⣹⢦⡀⠀⠉⠓⢶⡛⠙⠲⠴⠶⠖⠛⠉⠀⠀⢀⣠⠼⠛⠉⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠻⣦⡀⠀⠀⠻⣦⣼⠳⣦⣽⡷⣤⣜⡂⢃⠀⠤⠆⣀⠀⢠⠢⠀⢀⢤⣀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠀⠐⣿⠻⢦⡐⠈⠀⠙⠓⢾⣟⠛⢮⣿⠛⠶⣦⣌⣀⣁⠀⠈⠈⠀⢈⠉⠉⠙⡏⠁
⠀⠀⠀⠀⣠⠞⠀⠀⢰⠃⠀⠀⠸⣆⠀⠙⠦⣀⠀⠀⠀⠈⠙⠺⢤⣉⣳⠟⠤⢤⣼⣉⣉⡟⠉⠈⠀⠀⠀⣿
⠀⠀⠀⡴⠃⠀⠠⠽⡟⠀⠀⠀⠀⠙⢆⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠉⠙⠒⠾⠧⢤⣯⡀⠀⠀⠀⠀⣰⠇
⠀⠀⡼⠁⠀⠀⠀⣸⠃⢀⣠⣤⣶⣚⡿⠃⠀⠀⠀⠀⡼⠻⡝⠛⠲⠦⢤⣤⣀⣀⣀⣀⣈⣀⣀⣠⡤⠞⠋
⠀⡼⠁⠀⠀⠀⠀⣯⠶⢋⣿⡿⠟⠛⢦⣀⣠⠖⣲⠴⠗⠒⠛⠒⠶⡞⣽⣶⠀⠀⠈⠈⠉⠉⠁
⡼⠁⠀⠀⠀⠀⠀⠛⠋⠉⠀⠙⠦⣄⡀⠉⠉⠈⡉⠓⠶⣄⠀⠀⠀⡗⢙⠿⠶⣦
⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣧⠀⠠⡈⠓⢦⡼⠀⠀⠀⠈⠋⠙⢺⠃
⠀⠈⢳⡈⠙⠓⠶⠦⣤⣄⣀⣀⣀⠀⣼⢈⠳⣄⣸⠦⡼⠃⠀⠀⠀⠀⡴⠒⠻⡆
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢉⣉⠉⣿⢸⡀⠀⠁⠀⠀⠀⠀⠀⢰⡋⠙⢶⡞⠁
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠐⠀⠀⠀⠿⢿⡈⢧⠀⠀⠀⠀⠀⠀⠐⣺⡛⠛⠻⣄
⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠳⢄⠀⠀⠀⠀⠀⠹⡟⠲⠶⠋
⠀⠀⠀⠀⣼⢷⣶⢤⣤⣀⣀⣀⢀⣀⣠⣏⣀⣙⣦⣤⣀⣀⢀⣀⡴⢃
⠀⠀⠀⠀⠙⠶⢍⣛⠳⠤⣬⣭⣏⣁⣀⣀⣭⢿⣩⣃⣈⣉⡿⠁⢀⡾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡞⠁⠉⠳⠿⠛⠉⠉⠐⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠴⠦⡈⢻⠇⢀⣀⠀⠀⠀⣀⡀⠰⣷⠇⠇⢀⠀⠀⠃⠀⠂⢄⠀⠀⠀⣀⠀⠀⠤⠐⠈⠀⣰
⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠉⠁⠀⠐⠒⢈⠁⠀⠉⠁⠒⢄⡘⡎⢧⠈⠉⠉⠀⠉⠉⠀⣸⠇⡀⠀⠎⠀⠀⠀⠀⠀⠀⠙⢖⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⡰⠁⠀⠀⠀⢀⡠⠔⠒⠒⠒⠈⠉⡽⠀⠀⠀⠀⠐⡄⠱⣝⢎⠀⠀⠠⣀⠄⠀⢀⢈⢾⡀⡀⠀⡰⠀⠠⠂⢀⡄⠂⠀⠳⢤⣄⡀⠀⠀⢠⠏⠀⠀⢀
⠀⠀⢠⠁⠀⠀⢀⠔⠉⠳⠀⠀⠀⠀⠀⠄⣆⠀⠀⠀⠉⠀⠙⠀⠈⢎⢿⠂⠐⠀⠀⡰⠃⣸⢺⣄⡉⠩⡱⠖⠄⠔⡡⠀⠀⠀⠸⠀⠀⠉⠙⠒⠂⠀⠀⠈⡩
⠀⠀⢸⠀⢀⠜⢁⠄⠀⠀⠀⠀⠀⠀⢀⠠⠼⠦⣀⣀⣀⣀⠀⠀⠀⠈⢦⡣⠙⠀⠘⠁⠔⢁⣁⢺⡀⠀⠄⠐⢄⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠈⠔⠁⡀⠀⠀⠀⠀⠉⠤⡀⡎⠁⠀⠴⢆⠀⠀⠘⠇⠀⠀⠀⠀⠀⠙⢧⡀⠀⢘⡴⠋⠁⠘⠁⠀⠈⠀⠈⣳⣓⡆⠀⠐⠁⠀⠀⠀⢀⠠⠔⠊
⠀⠀⠀⠀⠐⠀⠀⠐⠄⠂⣠⠔⣧⠀⠀⠈⠀⠀⠝⣓⣊⡧⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡈⠉⠒⠢⠄⣄⠀⠓⠠⠤⣀⣀
⠀⠀⠀⠀⠀⡠⠖⠀⠀⢄⠀⠞⣠⡖⠊⠀⠀⠈⠉⠀⠀⡼⢆⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠐⠤⣀⠀⠈⠉⠉⢈⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⢁⠀⠀⠀⠀⠀⠀⠀⡜⢁⠜⡵⠢⣄⡀⢄⠠⠤⠻⢄⡀⠀⠀⠀⠀⣀⣴⢿⠘⣄⠀⠀⠀⣀⠴⢉⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠂⠀⠀⠀⠀⠤⡀⠰⢀⠞⡹⠁⠀⠙⠷⣦⣴⣤⣖⢢⣬⡭⠶⠆⠩⢙⠁⡘⠀⠘⢆⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⢠⠆⠀⠘⠀⣬⠎⡀⠀⠀⢀⠀⠀⠈⢳⣬⣉⡠⠤⢒⡀⠄⠀⠀⠑⠤⠤⠄⠁⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠠⠃⠀⠀⡞⠀⠀⡄⠟⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠆⠀⠀⣰⠃⠀⠀⡟⠀⠀⡎⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⣠⠞⠈⠀⠀⢰⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡰⠁⠀⠀⠀⢀⠟⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢊⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣈⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢶⣴⣶⣿⡅⢈⣿⡀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠡⠴⢶⣿⣄⢀⢹⡦⣿⣻⠿⠗⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⣧⣀⡂⣀⣿⣼⣿⣿⣿⣶⣶⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣿⣷⣿⣿⣿⣿⣿⣿⡟⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣾⣿⣿⣿⣿⡟⠯⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡻⠻⣿⣿⣿⡟⢿⣓⢄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣏⠄⠈⢹⣏⠙⣌⢲⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣤⣶⣼⣷⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠈⡟⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⠃⠀⡇⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢹⠀⠀⡇⡀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⣧⡇⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠸⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠀⠀⠀⠸⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⢳⠀⠸⣾
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⢤⣄⡀⠀⠀⠀⠈⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢸⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣣⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⡲⠞⣁⡴⠖⠛⠉⠉⠉⠉⠉⠛⠓⠦⣄⡀⠀⠀⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⣠⠖⠉⠀⠀⢀⣾⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡶⠒⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⣻⠁⣴⠷⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢿⡄⠀⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠋⠀⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠃⠀⠀⠀⢀⡿⢄⡀⠀⠀⠀⠀⢀⡠⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⢀⡀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠙⣦⠀⠀⠀⣾⠁⠈⢧⠀⠷
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠭⢍⡀⠀⠀⢿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠦⡀⢸⠀⠀⠀⠀⠈⠳⣄⠀⣼⠋⠉⢢⣏⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⢦⠀⢸⠀⡴⠋⠀⠀⠙⣆⢀⣤⢤⣄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⣠⣀⣤⣈⡄⣏⠀⢀⡏⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣷⡀⠀⠸⣇⠤⣇⢧⣠⣤⣤⣄⠀⢾⠀⠀⠘⠃⠀⠠⠴⠖⠛⠛⠛⠿⢿⡷⠀⠙⢦⡜⢡⡏⠀⠈⠁⢉⡒⠋⠀⠀⢀⡜
⠀⢰⡆⢀⡴⠞⠓⢶⠋⠀⢀⠙⠀⠀⣇⠀⢸⠛⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢸⠁⠈⢳⡖⠓⡆⠘⠃⠀⢠⡴⠋
⡄⠀⠀⢸⠀⠀⢀⣼⡀⠀⢹⡄⢠⠀⠉⠀⡇⠀⠀⢀⠔⠚⠉⠉⠉⣱⠶⠤⢄⣀⡀⢀⣀⡡⠏⠀⠉⠁⠀⠀⠀⣤⠤⠚⢀⡜⠀⠀⠀⠀⢸⠁
⢱⡀⠲⡀⠳⠖⠁⠀⠙⣶⠚⠀⠘⢦⠀⠀⣇⠀⠀⠻⡀⠀⠀⠰⠋⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠎⠀⠀⠀⠀⠀⡸
⠀⠹⢄⠙⠆⠀⠀⠀⠀⠈⠛⠒⡞⠀⠀⠀⠘⠦⣀⠀⠙⠲⠤⣀⣀⣀⠤⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⠉⠒⠶⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣰⠖⠒⠙⠋⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢀⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣐⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⠙⠲⠦⢤⣀⣠⠤⠤⠖⠛⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠲⣶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢤⣀⡀⠀⠀⠀⣘⢻⡀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡏⠉⠛⠶⣄⡟⠘⡇⣠⡴⠶⠖⠲⣞⣸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠳⣄⠀⠀⡟⠃⠀⠛⠒⣷⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⣤⣤⣬⠦⢤⣄⢸⡇⣸⡳⡄⠀⠀⠀⣷⠶⠚⠛⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⣭⡟⠁⠀⣎⠩⠷⠤⣒⡶⠾⠷⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠢⣤⡀⡀⠀⠀⠀⠀⣨⠇⣀⣠⠔⣫⠃⠀⠀⢸⣇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢌⣉⣑⣒⣒⣚⣉⣉⠭⠔⠊⠁⠀⠀⠀⠈⢯⡛⠧⣄⣀⠀⠀⠀⢀⣠⠼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⠉⠉⠉⠁⠀⣤⠖⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢳⠀⠀⠀⠀⠀⠀⡈⠒⠀⠀⠀⠀⠀⠀⠀⣿⠐⠂⠀⠀⠀⠀⠀⠀⠐⠏⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠆⠐⠐⠀⠐⠠⠀⠀⠁⠀⠁⠁⠀⠀⠡⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠁⠀⠆⠀⠄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⠀⠀⠀⠀⠀⣀⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠀⠀⠠⠘⠆⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⢢⠄⠤⠂⠲⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⡀⠨⠃
⠀⠀⠓⠀⠀⠀⠋⠀⠀⠀⠀⠃⡀⠀⣀⡀⠀⠀⠀⢠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠅⠀⠀⠀⠀⠁⠀⠀⠝⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠲⡀⠀⠀⠀⠀⠀⠀⡒⢲⡄⠀⠀⡀⣠⡔⠦⡄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠀⠠⢤⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠑⠀⣰⠀⠀⠀⠀⡀⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⡦
⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢠⠄⠀⠀⠀⠀⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀
⠀⠀⠀⡴⠢⠰⠀⠀⠀⠀⠀⠀⠐⠚⠲⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠀⠀⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠒⠂⠐⠒
⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢤⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠠⠀⠄⠀⠌⠁⠀⠀⠐⠀⠐⠀⠀⠂⠀⠚⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠀⠑⠖⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠢⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠈⢳⠀⠐⠖⠃⠘⠀⣸⢆⡸⠄⠀⠀⢀⠀⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡶⠓⠀⠿⠩⠀⠀⠂⠀⠀⠇⠘⠃⠘⠁⠀⠀⠚⡧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡾⠃⠢⠁⢄⣡⢾⡱⠀⠀⠀⠀⣾⠗⠀⢲⠚⠒⠀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⣲⣤⣾⣻⣄⠙⠧⠀⠀⠀⠀⠈⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡥⡏⠌⠳⠘⠖⠲⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣦⣤⠀⠀⠀⠛⠛⠀⠁⠈⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣿⡁⢀⠀⠀⠀⠀⠀⣴⠃⠀⣀⣤⢠⡀⠈⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣿⡧⢬⣏⡀⠀⠀⠠⠆⠘⠃⠀⢀⠀⠀⢹⠉⠉⠀⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢘⡵⣀⡈⠁⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠙⠶⠇⠐⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⣀⠀⠘⣦⣤⣀⣠⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⡐⠐⠄⣁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡄⢫⡀⠛⣃⠆⢀⣠⢤⣷⡆⠰⠎⢀⣀⠀⠀⠀⢀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠶⠻⢦⣾⠄⠀⠹⠤⢴⣤⣾⠻⠟⠀⠁⢨⣿⣧⣤⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠻⠿⢯⣼⣤⣎⣰⣄⠈⣿⣿⠀⠠⣆⣠⣿⣿⡉⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠂⠁⠉⠈⠙⢿⣿⣿⣏⠂⢀⠋⢫⠿⠛⠀⣽⠟⠀⠀⠀⠀⠀⢠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷⣦⠴⠁⢠⠄⠘⠛⣦⣄⣀⣀⣠⡴⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁⠀⠉⠰⢿⣯⠹⡅⠀⠀⠈⠓⠂⠂⠀⠈⠙⠿⠳⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠸⠶⢇⠀⠀⠀⠹⣷⣿⣿⠷⠈⠗⠂⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠁⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠛⢻⣄⢿⣿⣿⣂⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠴⣶⣀⣨⣀⣠⠈⠁⠀⠀⢰⣿⣶⠦⣴⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣶⠟⠙⠳⢶⣿⣄⠀⠀⢻⣯⣀⣁⣀⣒⡖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⣾⡟⠁⠀⠀⠀⠈⢿⣿⣧⣀⣀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢁⣆⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⢾⣻⣯⠀⠀⠀⠀⠖⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣦⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⢟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⢪⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠿⣦⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠳⠼⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠰⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣸⣿⣧⠀⠀⠀⠀⣀⣈⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡁
⠀⠀⠀⠀⢀⣾⠟⢉⡉⠙⢻⣿⠀⣤⣞⣋⠠⠤⠤⣤⣹⣿⣧⡀⠀⠀⠀⠀⣴⣿⠟⣉⣁⣉⣛⢶⣄⠀⠀⠀⢠⣾⠛⢉⣉⡛⣦
⠀⠀⠀⠀⣼⠃⠀⢀⣹⡆⠸⠟⢸⡏⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⣾⡿⠟⠛⠉⠉⠀⠀⠀⢛⡇⠀⠀⠀⠁⠀⣾⡟⠀⣼
⠀⠀⠀⠀⣿⡀⠀⢾⣯⣀⣠⡀⠈⢛⠲⠴⠤⠤⠤⠤⣼⣿⣿⠇⠀⠀⠀⣿⣦⣤⠀⢀⣀⣀⡠⠴⡟⠁⠀⢀⣀⣀⣀⣿⣷⢀⡿
⠀⠀⠀⠀⠸⠇⢀⣼⡿⠟⠋⢁⠀⠀⠘⠒⠂⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⣹⡿⠟⠛⠀⠩⠥⠄⠚⠀⠀⠀⠀⠉⠛⠿⣿⣧⡼⠃
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⣀⣀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣰⣦⣄⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⣾⠋⠀⠐⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠺⠶⠿⣦⣤⣠⣾⡿⠉⠛⠋⠀⠀⠀⠀⠀⣠⡶⠛⠉⠈⠉⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣴⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠉⠉⠉⢹⡇⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣀⣼⣷⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠛⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠼⠛⠉⠙⠛⠻⠷⢶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠛⠋⠉⠀⢠⡿⠁⠀⠈⠙⠻⣦⠀⠀⢻
⠀⠀⠀⣠⣴⠞⠋⠉⠉⠉⣀⣤⡶⠾⠶⣦⡀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣶⣶⣶⣶⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⡅⠀⢀⣀⣤⣄⣼⡇⠀⠘⣷⣤⣄⡀
⠀⢀⡾⠋⠀⠀⠀⠀⠀⢾⣏⣁⡀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠻⣦
⢰⣿⠗⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣷⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡄⢹
⣿⠃⢀⣴⠇⠀⣠⣤⣄⠀⠀⢀⣠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣠⣤⠖⢻⡇⠀⠀⠰⣆⠀⠈⣿⡿
⣿⠀⢸⡏⠀⠀⡏⠀⠙⠷⠾⠛⠋⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠀⠀⠸⠀⠀⠀⠀⣿⠀⣰⡟
⠸⣧⣼⡇⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣾⣿⡆⠀⢺⡆⠀⠀⣠⡿⠞⠋
⠀⠀⠈⠙⠶⣤⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣤⣿⡧⠀⠈⠻⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⠄⠐⠒⠒⠶⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⠉⠉⢹⡿⠉⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⠉⠙⠙⠛⠛⠛⠋⠉⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣀⣀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠉⠙⠛⠿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣤⣤⣤⣶⣶⡶⠟⠋
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⣠⠶⠛⠉⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠀⢹⢀⠠⣤⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢗⣺⣿⠀⠀⠀⢸⠻⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⠶⢶⢦⡄
⠀⡴⠛⣏⠉⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠳⣤⣀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⣠⣴⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⢻⡏⠉⠉⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⣿⣿⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣾⠿⠃⠀⠀⠈⠉⠙⢻⡟⢸⣟⠉⠁⠘⢧⣀⣸⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠻⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣄⣀⣀⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⢾⡟⠛⠉⠉⠉⠉⠉⠉⠉⣿⠙⠛⠛⠳⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣤⣶⣼⡿⠶⠶⠶⢶⣶⠶⠶⠶⠿⠷⠖⠛⠛⠛⠛⣿⡛⠛⠉⠉⠉⠉⠉⠉⠉⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⡴⠀⠀⣿⡇⠈⠻⣦⠀⠀⠀⠀⠀⣀⣀⣤⣿⣦⣶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⢶⣦⣤⣿⣇⣀
⠀⠀⠀⠀⠀⣷⠀⠀⠸⣷⡀⠀⢙⣷⣴⡶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠂
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠋⠁⠀⠀⠀⠉⠫⠭⠭⣛⡲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣋⠕⢪⣗⣉⣓⣒⣀⢀⠀⣶⡆⠀⠀⠈⠑⠪⣛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡫⠊⠁⠀⠈⣿⠟⢿⣶⣿⣟⡀⠉⣸⠀⠀⠀⠀⠀⠈⠑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠜⠁⠀⠀⠀⠀⣿⡲⣤⣈⣿⡿⢷⢿⣿⠗⠀⠀⠀⠀⠀⠀⠈⠣⡻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⢏⠎⠀⠀⠀⠀⢀⣼⣷⣿⣿⢿⣱⣾⣿⠿⢛⣂⣀⣄⣠⡏⠀⠀⠀⠀⠱⡹⡄
⠀⠀⠀⠀⠀⠀⠀⡟⡜⠀⠀⠀⠀⠀⣾⣧⣼⣿⣿⣿⡿⣿⣷⣶⣯⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢃⢻
⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠠⣿⠿⠻⠛⠛⣿⣿⣾⣿⣿⢿⡄⠀⠈⢿⣿⣆⠀⠀⣶⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⢛⡁⣿⣿⡊⢷⡀⠀⠈⣿⣷⣁⣼⡗⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⣼⠟⢸⡇⣿⣿⣳⣌⣿⠞⡒⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠓⠒⠚⠛⡃⠀⢸⣄⢻⣿⣿⡿⠬⣑⡀⠈⢿⣿⣿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⣿⣷⣶⠶⢶⠷⣤⣠⣝⣿⣿⣿⣿⣞⡈⠉⠀⠈⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻⣿⣷⡯⣷⣌⣺⣿⣿⠿⠿⣿⣿⣿⡿⣁⠀⠀⡀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⢾⣿⣿⣧⣿⣿⣸⣿⣿⣀⣠⣿⣿⣿⣏⠀⠉⢀⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡖⣷⣯⣿⣿⣿⣿⡿⡟⠉⠉⠉⢻⣿⣿⠡⢤⣈⢰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⣿⠇⢿⢻⣿⠀⠡⣷⢄⠤⠴⢿⣿⣟⠒⠀⠈⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⢀⠀⠹⡆⠀⢀⣸⣿⣟⣥⣦⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠷⣄⠀⣠⠶⣄⠀⠀⣀
⠀⢀⡤⣾⢻⡏⣷⣀⠀⠀⢀⣀⠀⢸⠉⠳⢤⡏⠀⠈⠛⠁⠀⠹⠞⠋⢹⠀⠀⠀⠀⠀⠀⠀⣀⣴⠳⣄⣤⡀
⠀⠸⣄⡈⠀⠀⣉⣹⠆⠀⢸⡍⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠘⠛⢹⠇⠀⠀⠀⢸⣍⠛⠀⠋⠼⠷⡄
⠀⠀⠈⢧⣀⠀⠻⣅⠀⢶⠤⠇⠀⢠⢎⠏⣯⢱⠀⠀⠀⠀⡏⣼⢹⢹⠀⠀⠛⢲⠆⠀⠀⣀⡾⠁⢀⣠⠤⠞⠁
⠀⠀⠀⠀⠉⢧⡀⠀⠙⠾⠇⠀⠀⠘⢾⣦⡯⠞⠀⠀⠀⠀⠑⠿⠾⠋⠀⠀⠴⠯⠶⠶⠛⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⢠⠴⣞⡿⠉⠉⠉⠹⠽⠋⠳⡀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡇⠀⠀⣀⣀⡀⣀⣤⣀⠀⠀⡇⠀⠀⢙⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠳⣄⣞⡁⠀⠉⠁⢀⣈⡦⠞⠁⠀⢘⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⢶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⡀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡇⠀⢤⣀⡤⣄⣀⡴⢶⠀⠀⣿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⠀⠈⠉⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⢀⠟⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠤⠭⠥⠤⠾⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠾⠃

⠀⠀⠀⠀⠀⠀⠤⠀⣀⡄⠀⠀⠄⠀⠀⠆⠀⢘⠃⠀⢀⠀⣄⠠⡤⢀⣀⠀⠀⢀⠀⣄⣍⠁⠀⠀⠀⢀⣀⣀⠀⢀⣀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⢲⡠⠂⢉⣒⡹⠇⣠⠊⠁⠠⢢⣶⣆⣀⢑⣜⢂⣉⡿⣿⣀⠻⠆⠀⠊⡽⠒⡸⠃⠀⠀⠈⠟⡓⠀⢀⠀⠀⠀⠀⡀⢿⠀⣀⡀⠀⠈
⠀⠀⠀⠀⠣⡀⣀⣉⠈⠁⢁⠀⠊⠀⠁⠀⢰⠀⠰⢎⣽⣼⣻⣾⠏⣿⣸⣧⡶⢠⡆⣾⠀⢰⡗⣏⣾⣿⡆⣰⡿⢀⠠⠀⠶⠄⣀⠀⠂⠑⠋⢀⢶⠁⢀
⠀⠀⠀⠀⠀⠀⠸⢀⠎⣵⣾⠀⠀⠀⠀⢀⡀⢐⠸⢫⣻⡷⣿⠟⠳⠄⠘⠿⠦⠴⠶⢆⠀⠤⣿⠛⠈⠋⠀⠀⠀⠶⠶⣦⠀⠚⠂⣁⠈⠉⡁⠤⠄⠀⠌
⠀⠀⠀⠀⠢⡀⠀⢿⣿⠾⡃⠀⣀⡀⢒⣚⢡⣾⡏⢁⡿⡿⠁⢀⡀⠄⠀⠀⢄⣀⠐⠄⠘⡀⠈⠇⠰⠠⣦⣶⣟⡂⣄⠀⠘⣣⠀⢉⣄⠀⣰⢒⣴⣦⡄
⠀⠀⠀⠀⠀⠠⠘⠃⠧⣺⠟⡁⠀⠀⠛⢿⣣⣉⣠⠘⠁⠀⠀⠛⢁⠠⢞⠢⢌⠁⠕⠀⠠⠁⣄⠀⠀⠸⠉⠁⣀⡀⠀⠀⢈⠟⡶⠶⠗⠊⠀⠈⠋⢉⡛
⠀⠀⠀⠀⠸⠄⠀⠀⠀⠈⡈⠓⠢⠗⠚⢈⡀⡭⢧⠐⠠⠐⠀⣰⣧⡷⠿⠳⣷⣵⡀⢀⡶⢆⡀⠀⣀⠔⣀⠞⢉⡿⣼⠷⠯⠀⢁⠾⠃⠂⢀⡄⠾⠦⠚⠇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡳⠦⠤⠤⡴⠿⡠⣶⡆⢠⠞⠛⠀⠙⠋⠀⢀⣠⡾⡟⢃⠟⠛⠊⠉⠉⡷⡆⢫⡀⠘⠲⠃⠃⠀⠠⠤⠴⠒⠊⢉⡷⡤⠶⠎
⠀⠀⠀⠀⠀⠈⠀⣐⠛⡿⠋⠀⢀⠐⠃⠀⢁⠈⠀⠀⠘⠛⢆⠀⠀⠐⢾⣁⠀⠱⡧⣦⣠⣤⡞⠶⢃⡤⢬⢣⡦⠀⣤⠠⡾⡿⠟⣥⡤⢠⡦⢱⢛⣿⠄
⠀⠀⠀⠀⠀⠀⢸⣛⡄⠛⠂⠀⠙⣿⣯⠠⡿⠶⠢⠤⣤⡄⡈⣀⢀⣶⡆⠿⣧⠀⠀⠀⣰⠋⢀⣠⣶⡀⣶⣦⠠⡄⠁⠋⠀⣠⠾⠰⢦⡤⠆⢎⣩⣥⡤⠄
⠀⠀⠀⠀⠀⠀⣼⣏⣹⣁⡀⠠⢾⣆⢀⣂⣀⡚⢲⠤⠊⡁⣥⠄⠀⠙⡁⢿⣦⠙⣶⣾⣿⢖⠻⣉⣥⡰⢸⣶⠂⡋⢈⣄⠀⠉⢁⡬⢸⣿⣇⠊⡘⠙⠁
⠀⠀⠀⠀⠀⠱⢟⣹⣿⣿⣗⣀⣤⣿⠷⠷⠚⢄⣉⣦⡌⠀⣆⡀⠀⠀⠀⣸⡿⢀⣿⣧⠧⢈⠀⠈⠿⠧⠀⠉⠙⠀⠸⣟⣠⣔⣀⣽⠁⠖⢩⡆⢹⢹⡇
⠀⠀⠀⠀⠀⠠⡼⣹⡏⢴⣮⠿⠈⠀⠁⠀⠈⢀⡽⠋⢴⣉⠈⢉⣡⣶⣾⣿⣇⠘⠉⠁⠀⢈⣆⠀⠳⠶⣤⣴⣾⡦⠀⠠⡬⣅⠈⡙⢰⣧⣈⣥⢲⡞⠁
⠀⠀⠀⠀⠀⠀⠶⡯⠁⠛⠓⠀⠴⢸⡇⡀⣷⣿⣾⣯⣼⣿⣶⣿⡷⣭⣄⠤⢛⢗⣦⣴⠴⠛⠋⡷⣄⡀⠀⠀⠀⠀⠶⠀⢀⠞⢒⣴⣷⡉⠃⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠘⠏⣩⣤⢬⠘⠈⠫⠀⠸⣿⡏⠉⠹⡾⣩⣤⣄⠈⠠⣽⠟⠓⠩⠄⠀⠀⠀⠀⠙⣶⠾⠻⠷⠶⠖⠐⠚⢛⠂⠙⠄⣩⣥⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠛⠺⠗⠺⠲⣷⠀⠀⠀⠀⠹⣧⣀⠀⠂⠻⣿⣿⡇⠀⠁⠈⠶⢶⣆⠀⠀⠀⠀⠀⠉⠙⢦⢀⣀⠀⠈⠀⠀⠴⣤⡶⠚⡠⢶⡜⣿⣤
⠀⠀⠀⠀⢠⣆⡀⠐⠀⢂⣠⠟⢀⡶⠦⠺⣀⠛⠉⡴⠲⠖⠛⡋⠁⠁⢀⠀⠐⠔⠋⠀⣶⣟⡂⠀⠙⢀⡇⠀⠀⠰⠀⠀⠀⡂⣨⠀⠛⣱⠟⠀⠻⣿⡆
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠹⡿⢡⣄⠤⠠⠘⢦⡤⡍⢀⣻⡄⢀⣠⠾⢧⢲⣄⠄⢀⡀⠀⠈⠋⠁⢤⡜⠁⠋⡼⡏⠖⠀⠃⢾⣯⡅⢴⠇⠠⣸⣇⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠉⠛⠕⠒⠳⠂⠐⠚⠀⠙⠿⠦⠔⠂⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣠⣶⡀⠀⣸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⢸⣈⠃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⣀⣄
⠀⠠⠀⣰⣿⡿⠋⠀⠀⠀⠀⠈⢿⣾⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠈⠀⠒⢺⣿⣿⠿⠂
⠀⠀⠀⠙⠟⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⠏⠀⠉⠣⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠁⠈⠙⢆⠀⣀⠀⠐⠀⠀⠀⠀⠀⠺⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⣤⣤⣄⠀⠘⣿⠋⠘⠁⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⣿⣿⣧⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠠⠄⠀⢂⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⠀⣀⣀⠀⠀⠀⠀⠀⣀⡠⡄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⣀⠉⠻⣿⠿⠿⠛⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠐⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⣼⣿⡟⠘⣧⠀⠀⠀⠀⠀⠀⢰⢁
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠸⢿⠟⠀⠀⠸⣷⣤⣀⣀⠐⠂⠀⠁
⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠀⠀⢾⣦⣄
⠀⠀⢠⠾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡅⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢿⣧⣄⣀⡀⣀⣀⡤⠖⠁⠈⠛⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⣠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣤⡀⠀⣾⠇⠰⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⢤⡄⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠈⠋⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⢀⠐⠿⣾⣿⣟⡂⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠷⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣷⡆⠤⢀⠺⠟⣿⡝⠃⣶⠄⠀⢀⡄
⠀⠀⠀⢠⣈⠓⠀⠀⠀⠀⠀⠀⠈⠀⠡⠄⠀⠀⠀⠀⠶⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠁
⠀⠀⢠⡈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢉⠁⠐⣦⠀⠀⣠⡀⠀⠀⠀⠁⠀⡤⠀⣼⣿⡿⢿⣿⣿⣷⡀⠀⠀⣀⠲⡆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠉⠀⠀⠈⢱⠆⠉⠁⢀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⠙⣿⣷⡀⠀⠹⢂
⠀⠀⠀⠀⠠⠀⠀⣀⣠⣤⣤⣶⡶⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠹⢹⡟⣿⢹⠁⠀⠀⠀⠀⢸⣿⡷⠀⠠⠤⠂⢹⣿⠿⠟⠋⠀⠀⠀⠀⠈⠙⠃⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠀⠀⠀⠁⠀⠀⠿⠏⠀⠀⡀⠢⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⠀⠈⢠⡎⠡⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⣧⠀⠈⡀
⠀⠀⠀⠀⠄⠈⢳⣦⣤⣄⠀⠠⠄⢀⣴⣶⣶⣦⣤⣄⣀⠀⢀⣀⣠⣴⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⡏
⠀⠀⠀⠀⢦⢀⣼⡿⢟⠁⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆
⠀⠀⠀⠄⠀⠼⠋⠂⠀⠀⠀⠀⠀⡠⠀⣀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠶⠀⠀⢰⣶⠶⠀⠃⠤⠐⣡⣿
⠀⠀⠀⠀⢀⡀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢄⠀⠀⠀⠶⠀⠀⠀⠀⡤⠀⠀⠀⡒⢄⣄⣠⢾⣟⡽
⠀⠀⠀⠀⣰⣿⣤⣾⣷⡄⠀⠀⠀⡀⠀⠀⠄⠀⠀⢀⡤⠀⣤⠀⠀⣠⠀⠀⢷⣦⣤⣶⡾⠿⡾⠋⠉
⠀⠀⠀⠀⠈⠛⠉⠛⠛⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠚⠳⠶⣤⣼⠃⠀⠀⠀⣀⠠⠴⠤⠄⠈⠃⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⣘⡅⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁⠀⠉⠀⠳⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣀⡴⠀⠀⠀⣠⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠾⢥⣀⠀⠀⠀⡹⠦⣄⡀⠹⡆⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳⡄⠤⠄⢀⡧⠚⠀⠀⠀⠙⡆⠀⡾⠁⠀⠀⠙⣦⢹⡖⠒⠲⠚⠁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⢻⡸⠃⠀⠀⠀⠀⢿⠈⣇⠀⠀⠀⢸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡄⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢾⣿⠀⠀⠠⢐⣀⣺⡇⣿⠀⠀⠀⣾⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⣯⡀⠀⠀⣰⣿⡛⣿⣿⠀⠀⣴⣿⣏⣿⡇⣿⡀⠀⠀⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⡇⠀⣰⣿⣿⣿⡿⢸⡆⢰⣿⣿⣿⣿⠃⡿⢣⠀⠀⠏⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⢀⡜⢣⢱⡄⢿⣿⣿⣿⣃⠀⢻⣿⣿⣿⣿⡟⢰⠇⠈⢦⡀⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢀⠔⠊⠀⠘⣄⠻⣿⡟⠟⢁⠈⠀⠀⠙⠛⠿⠟⢡⡟⠀⠀⠎⠩⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⣄⣠⣄⡀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⡇⠀⠀⠈⠳⣄⠀⠘⠀⠈⠉⢧⠀⠚⣧⠀⠀⡤⠚⢄⠀⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡆⠀⠀⠗⠈⠑⠆⠀⠈⠳⡇⠀⢀⠀⠀⡇⠀⣿⡤⠶⡀⠀⠐⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣷⠀⠀⢠⠀⠀⠐⠂⠀⡊⠳⢤⣶⣤⣿⡇⠀⣿⠀⠀⠄⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⢹⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠿⣿⣿⡇⢠⡏⠀⠀⠀⠀⠀⠀⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠋⢻⠀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢸⡀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢀⡴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⠿⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⠀⠀⠈⡄⢧⠀⠀⠀⠀⠀⠀⠀⠑⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡈⡠⢀⣈⠀⠳⣄⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢠⡿⠠⡇⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠈⠘⢁⠈⠙⢧⣄⠈⢧⡜⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⡘⠃⠈⠁⠀⠀⠀⢢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⡖⠉⠳⢶⣄⣉⠳⠄⠁⢀⠃⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠇⢀⠀⠦⠄⠀⠠⠖⠐⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠐⠒⠋⠀⢸⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡞⠀⢸⣀⣀⡀⠀⠀⠙⠉⠁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⠁⠀⠀⠀⠀⠈⠛⠒⠲⠶⠖⠁
⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⡿⠙⠒⢰⡖⡶⠒⠒⠒⠲⠶⠦⣾⠁⠀⠇
⠀⠀⣰⠚⠉⢻⡆⠰⡈⢳⡀⠀⠀⠀⢀⠞⣡⠬⡇⠀⠀⡛⠤⠠⠜⡰⠁⠀⠀⠀⠀⠀⢰⡏⠀⢸
⠀⠰⠃⠀⠀⢠⡇⠀⠩⡄⢳⣀⢀⡰⣡⠎⠀⠀⡶⠀⡼⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢾
⢀⠃⡄⢠⠀⠸⡀⠀⠀⠙⢄⣉⣩⠾⠁⠀⢠⣞⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠻⡀
⠘⠁⠁⣎⠘⣄⡙⠦⣀⡀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠒⠒⠲⣬
⠀⠀⠀⠉⠀⠈⠙⠓⠉⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡆⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠈⢳⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣘⣷⣤⣤⣴⣒⣚⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣳⣶⣶⣒⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⢛⣩⠭⠭⣭⣉⠉⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢴⠾⠿⠶⢶⣴⣾⣋⠁⠀⡔⠁⠀⠉⣳⣶⠾⣿⣿⡆⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡀⣠⡾⠋⠉⠛⠛⢾⠀⠀⣠⡎⠁⢠⡦⡼⠏⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠉⠙⠢⡀⠀⠀⠀⠈⡿⣼⠙⠃⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢿⠟⢶⣤⣀⣀⠘⢿⠦⢤⡀⠀⠀⠀⢸⠿⢷⣤⡀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⠀⠀⠹⣷⣻⣽⣶⣧⠀⠈⡛⣿⣿⠁⠀⠀⣙⣯⢢⣀⡀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠸⠀⠀⡠⣿⣿⠙⢿⣿⣿⣿⣮⣝⡻⣭⣁⣢⣌⣩⠀⠀⠘⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⣸⠀⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣶⣉⡿⢿⣿⡄⠀⠀⢳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢵⣷⣶⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⡟⠾⣿⣿⡇⢷⠈⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⡙⢳⣝⠝⣿⣿⣦⣸⣿⣿⠈⠻⢿⣿⣷⣄⠈⠛⢿⣼⡇⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠁⠀⣿⣄⡟⣽⣿⣿⡉⢻⣷⣄⠀⠙⢿⣿⣷⣄⠲⢹⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢤⠀⠀⠀⠀⠀⣿⣿⣷⠟⢹⣿⣿⣮⣿⣮⡳⣄⠃⢹⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⠀⠀⠀⣀⣼⡿⠛⢻⠀⢀⣺⣿⣿⣿⣿⣿⣦⣙⢿⠻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠖⠋⠁⠈⠛⠷⢾⣷⣤⣬⣭⣭⣿⣿⣿⣿⡿⠷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁



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

⠀⠲⡆⢠⠖⠢⠤⠠⡄⢀⡄⠐⠰⡦⠂⠀⢰⠦⣴⡂⠴⢠⡤⠀⠀⠄⡴⠐⣤⡄⠀⢠⡶⠀⠀⡄⠀⠀⠠⠀⡠⠄⠀⠀⠀⢀
⠀⠄⠃⣀⠑⢆⣄⣀⠉⠀⠙⠀⠚⠋⠀⠀⠀⣤⡼⠁⠀⢀⠀⠃⠀⠀⢄⠂⢀⠭⠤⠐⠓⠈⠋⠉⠓⠐⠄⢀⠁⠀⠀⢐⠔⠁⠀⡀
⠀⠀⠄⠀⠀⠾⠋⠉⡿⠐⠂⠀⠰⡌⠉⢀⠀⡉⠥⣤⡀⠀⠂⠐⠃⠀⢈⠴⠉⠀⡀⠄⠤⢒⠲⢄⠀⠀⠂⠀⠑⠀⠄⢁⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠁⠀⠉⢉⣹⡁⠀⠈⠀⢠⣃⠀⠀⠀⡘⠀⠀⣮⠀⠀⠩⡈⠀⠀⠀⠑⠂⠐⠀⢀⠀⠛⠵⠈⠉⠉
⠐⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⡎⡎⣠⠔⠒⠲⠘⠚⠃⠀⢐⡁⠀⠀⠀⠁⠀⠀⠀⠈⡀⠀⠀⠀⢆⡀⠘⠂⡠
⢀⠃⠀⠀⠀⠤⠀⠀⠈⠀⠀⣠⠀⠠⡞⡾⠅⣶⠶⡚⡃⠀⡀⠀⠀⠜⠒⠀⠀⢆⠁⠀⠀⠀⠀⠁⠂⡀⠂⠘⠛⣀⣄⠿⠓⠀⠀⢁⢢
⠸⡄⠀⠀⠀⡱⠒⠋⠐⠇⠀⠈⠴⠒⠀⠴⠦⠒⠆⡀⡀⠤⣄⠀⡇⠀⠀⠀⠀⠈⡆⠈⠉⠀⠀⠀⠈⠀⠀⠂⠀⢉⡻⢷⣆⠀⠀⠀⠟
⢀⡇⠀⠀⠻⡄⠛⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠀⠀⠉⠐⠚⠛⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⠀⢠⡄⢀⡃⠐⠒⠀⢀⠀⡀⠨
⠀⢣⡔⣀⠐⡆⠀⠀⠀⢠⠀⡆⢠⢘⠀⠀⣾⣿⡙⠁⠢⡤⡀⣀⢀⡆⠤⠤⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢀⠀⠈⢇⠀⣈
⠀⠉⠀⠀⠀⠁⠀⠀⠠⠈⠀⠘⠀⠀⡵⠔⠅⠙⡄⠶⠈⠀⠈⠳⡌⣣⠸⣀⡀⠀⠀⠀⠘⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠘
⠀⠀⠋⠀⠀⠀⠆⠀⠴⠂⠀⢀⠀⠀⠀⠒⠀⠘⠀⠙⠁⠀⢂⠏⠉⠉⢠⠴⢈⠀⠉⠁⠐⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⡆⠀⠁
⠀⠀⠀⠆⠌⢹⣐⣤⡀⠀⠁⠀⠂⠀⢀⠠⠐⠀⠀⢠⠀⠀⠷⠀⠀⠀⠀⠀⠈⡀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠉⠈
⠀⠀⠀⠀⠐⠒⠒⢍⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠐⢐⠂⠁⠀⢀⡈⠀⠂⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠡⠈⠂⣤⠀⠀⠀⠀⠀⠀⠀⢐⣂⣀⡐⢀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠄⠀⠀⠀⢀⣁⡈⠈⠀⠀⠠⠰⠹⠄⠘⠛⢰⠲⠀⠀⠀⠰
⠀⠀⠀⠀⢀⠀⠀⠉⡀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠁⠉⢀⡳⠀⢈⡔⠂⡄⠐⠀⠐⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠂⠀⡀⠀⠀⠀⡂
⠀⡔⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠂⠀⠉⠁⢀⠀⠀⠀⠈⢭⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡄⠀⠀⠀⠀⡤
⠀⠤⢐⣚⠍⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠰⣶⠀⠺⠀⠀⡄⠀⠀⠀⠁⠐⢀⡀⠀⠤
⠀⢠⡄⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠀⡂⠈⠁⠀⠠
⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢶⣄⠀⠀⠀⡀⠀⠀⠒⠀⡔⠀⡀⠋⠐⢀⣄⡄⠁⠄⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣸⡤⣀⣀⣀⠄⠀⠀⠀⠀⠈⠀⠄⠀⠀⢁⠀⠙⠂⠈⠀⠠⠋⠀⠠⠈⠁⠀⢉⣠⠀⠀⠉⢁⡂⠀⠀⠀⠘
⠀⡃⠀⠀⠀⠀⠈⡉⡧⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⣸⣮⠀⠀⠀⠀⠀⠀⠠⠀⢠
⠀⠦⠀⠄⠒⠀⢈⠁⠁⠀⠀⢀⡀⡀⠀⠀⠠⠆⡴⠀⠁⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣂⠀⣤⣼⠀⠀⠀⠃⠀⠀⠀⣤⣤⠼
⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡴⠷⠖⠃⢸⣤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣥⣤⣦⠄⠀⡀⠀⠀⠀⠀⠺⣄
⠀⠀⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠭⡀⠀⠀⠀⠖⠁⠐⠀⠙⡴⠱⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠘⠃⠀⠀⡀⠀⢠⡧⠄
⠀⠶⠶⠴⠾⠁⠀⠰⠦⠶⠶⠆⠀⠈⠒⠖⠊⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠞⠻⠖⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡞⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⢈⠙⠲⢤⡤⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣈⠳⣄⢢⡎⠉⣷⣶⣶⣶⣶⣿⣿⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⣆⣿⠦⠈⠛⠿⠿⣿⠿⠧⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣧⣤⣤⠀⠀⠀⠀⠀⣴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿⣿⣿⣿⠃⠘⣆⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣠⠿⠛⠉⣹⣿⣀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠀⠈⠿⠿⠋⠀⠀⢹⣄⡀⠀⠀⠀⣠⠋⢀⣠⠚⠁⠀⠀⢠⣿⣧⣿⣦⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣤⣄⣠⠃⣴⡟⠁⠀⢀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡀⠉⢾⡏⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠱⢤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠳⣠⡿⠟⠛⠛⠛⠛⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡰⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⡖⠒⠂⠀⡸⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡟⠀⣠⣶⡏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢹⠖⠒⠲⢶⣶⣾⣿⣿⣿⢿⡟⠀⠀⣿⣿⡇⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠋⠀⠀⠌⣼⠟⠉⡩⠋⠀⡼⠁⠀⢸⣿⣿⡗⠲⣄⠸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⠃⠀⠀⠀⠀⣰⠃⠀⠀⢸⣿⣿⣧⠀⠘⡇⠹⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⠀⠀⠀⠀⡰⠃⠀⠀⠀⣸⣿⣿⠏⠀⢠⡇⠀⠙⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠧⣤⡤⠞⣁⠖⠀⣀⡴⠋⠉⠁⠀⠀⠈⢹⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⠤⠞⠉⠊⠉⠳⣄⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠛⠿⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠦
⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⣤⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠶⣄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠋⠀⠀⣀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⣐⡊⠏⠉⢠⣾⣧
⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡰⢿⢷⠀⠀⠘⠟⠛
⠀⠈⠱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠀⠀⠀⠀⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⢀⠁⢂⠠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⡀⠈⠀⣠⠀⠠⠰⠀⣀
⠀⠀⠀⠀⠈⠀⢀⡀⠀⡀⠀⡈⠀⠀⠀⠀⠈⠀⠀⠈⠶⠉⠀⠀⠀⠀⢀⢀⡀⠀⠁⠀⠃⠀⠉⠃
⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⣠⡎⠀⣀
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡄⢀⠀⢀⣀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⠟⢣⡀⠀⠀⠀⠀⠴⠚⢛⣿⣿⣿⡎⠀⠀⢻⣆⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠇⠀⠀⡴⠁⢀⠤⠋⠁⢸⣿⠃⠀⠀⠈⣿⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠹⢆⡈⢠⡴⠁⠀⠀⣠⣿⣿⣇⣀⡀⠀⡿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠐⡄⠀⠀⠀⠀⠈⠙⢿⠁⢀⣴⣶⣿⣿⣿⠇⠀⠑⠒⠀⠀⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⢛⣛⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠉⠒⠂⠀⠀⠂⣀⡈⣤⡔⠉⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⣠⣴⡿⠋⠀⠘⢿⣄⠀⠀⠹⢿⣶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣠⠟⢳⣶⣿⣿⠛⢤⠀⠀⠀⠈⠻⣿⣦⣄⠀⠙⠻⢿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠈⠑⢦⡔⠋⠁⢀⣼⠏⠀⠙⠋⣭⠀⠀⠉⠒⠢⣄⡀⠀⠈⠻⣿⣿⣶⣤⡀⠈⠙⠻⠿⣿⣿⣿⣿⣦
⠀⠀⢀⠠⠤⠤⠤⠤⠤⠄⡠⠎⠀⠀⠀⠀⠀⠄⠀⢱⠀⢀⡾⠁⠈⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠔⢁⣀⣀⣀⣀⡀⢀⠜⠁⠀⠀⠀⠠⡀⠀⠀⢡⠀⣃⣾⠃⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠲⠶⠦⢠⣄
⢀⠊⠁⢀⣤⣤⡿⠙⠉⠀⠀⠀⠀⠀⠀⠈⠆⢀⡼⠊⢹⡇⠀⠀⠀⠀⠀⢸⣇⠀⢠⣤⣤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠈⢦⡀⠿⣿⣿⡇⠂⠀⠀⠀⠔⠃⠀⠀⣠⠾⡉⣀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠻⣦⠸⣿⣿⣆⠀⠈⠉⠘⠓⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠙⠢⠤⠉⠙⠒⠓⠒⠒⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠁⠀⠲⠆⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠉⠻⣿⡇⠀⠀⠀⠀⣀⠤⠀⢩⠒⣤⣤⣴⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠛⠢⡀⠙⠃⠀⠀⠀⡞⠁⠀⠀⠀⢄⠙⠛⠛⢁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠘⣃⢀⡀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⢈⠳⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠉⠉⠀⠀⠀⠀⢀⠴⠊⠁⠀⠘⢇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⣀⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠈⢣⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠲⠄⠰⠤⣀⠠⠄⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠐⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⢠⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡋⠈⠣⡄⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠀⠀⠸⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⣄⠘⢦⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠰⠃⡰⠉⠀⠒⠢⣄⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠈⠳⣄⠱⡄⠀⠀⠒⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢠⣾⣿⣶⣦⣄⠀⠀⠑⣄⠔⠁⠈⢣⡀⠀⠀⠀⠉⠁⠀⠈⠀⡱⣤⣄⣤⣤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⢠⠀⡁⠘⣿⣿⠋⠀⠈⢢⡄⠁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢦⡘⠻⠿⠃⢈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠤⢀⠈⡄⠱⡄⢹⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣄⡀⠀⠀⠀⠉⠀⠂⠈⠁⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢟⡄⠸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠂⠶⢦⣤⡤⠤⠤⣄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⣱⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⡠⠀⠀⢀⡀⡀⢀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⡇⠐⠂⠆⠀⠂⠀⠂⣼⠀⠀⠀⠀⠀⠀⡉⠑⠀⡉⠀⠀⠈⠀⠀⠀⡄⢈⠀⢉⡁⠀⠀⠈⠛⠈⡀⠉⠈⠀⡉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⡄⠀⠀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡁⠊⠀⢀⠀⠀⠀⠈⠀⠀⡃⠀⠰⠄⢰⠖⡂⢸⢤⡀⢀⡏⡼⢀⠠⠆⣠⠀⠂⠀⠀⡀⣈⠀⠀⠀⠄⢀⡅
⠀⠀⠐⢤⠅⠀⠀⠀⠀⠀⠀⠑⠐⠂⠠⠖⠄⠑⠢⠒⠁⠠⠹⠀⠀⠀⠡⠈⢰⠀⣾⠋⠁⣁⡞⣠⢀⡾⠀⠰⣫⣠⡘⠁⠸⠃⠂⠀⢙⣀⣆⠀⠄⢀⡀⡘⠁
⠀⠀⡸⠂⠀⠀⣸⣷⣶⣶⣏⠀⠀⠄⠀⠀⠀⠱⠀⠀⠁⠀⠀⠀⠄⠀⠀⠁⡀⠒⠋⢈⢉⠁⠈⢀⠈⠁⠙⠋⢉⢁⠐⠚⠀⠉⠀⠀⠈⠛⣿⣟⣛⣿⠟⠃
⠀⠀⠀⠀⡀⠀⣿⣭⣿⣯⣽⠇⠀⠀⡀⠀⠀⠘⠞⠚⠁⠀⠀⠀⠀⠀⣀⠐⠀⠈⠀⠀⠀⠄⠅⠀⠀⠀⠈⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣍
⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠠⠀⡀⢢⠁⠀⣠⣶⠀⢴⣦⡀⠀⡠⠀⠠⠀⠀⠀⠐⢶⣄⠀⠀⣴⡶⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠘⢅⡠⠀⠑⠁⠠⣌⠜⠀⢀⠀⠀⠀⠀⢀⠀⠀⠄⢤⠀⠀⠄⠀⠀⢀⡀⠙⢁⠊⠋⢐⣄⠀⠀⠀⠂⠀⠀⠀⠀⢈⠁⠰⠀⡀⠃⠇⠘⠘⠂⡀
⠀⠀⠰⠀⠀⠀⠀⣶⣶⣶⡆⢀⠀⠀⠀⡀⢐⡀⠐⡌⠀⡀⠄⡆⠉⠀⡦⠄⡄⠈⠀⠀⠠⠔⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⠀⢀⠁
⠀⠀⠀⠀⠠⢅⠠⢉⠁⡋⢡⡠⠄⠀⠒⣀⠠⠄⠀⠀⣠⣀⢄⡀⠒⠂⡀⠔⠁⠀⠀⡀⠈⠀⡀⠠⠀⠁⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠁⠀⠀⠐⠀⢒⠀⣀
⠀⠀⠀⠀⠀⠀⣼⡎⠁⢹⣷⡀⠀⠀⣾⡏⠙⠀⢀⠀⠀⠄⠀⣀⣨⣀⠠⣦⠀⢀⠀⢁⠄⢀⡀⠀⠀⠐⢷⣔⠒⢷⡿⠓⢂⣼⠟⠀⠀⠰⢠⠁⠀⠈
⠀⢀⠀⠈⠀⣈⠉⠁⠀⠈⢉⠉⠀⠀⠀⠀⠀⣠⠀⢋⡄⠀⠀⢆⡠⡀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠂⠐⠟⡁⠀⠀⠀⠸⠂⠀⠀⠆
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⡈⡐⠀⠈⠀⠀⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠒⠀⠠⠠⠠⠠⠾⠿⠦⠤⠀⠠⠆⠀⠀⠀⠀⠀⠄⢠
⠀⠀⢠⣤⣴⣶⣶⣶⣶⣬⣄⡀⠐⠀⠀⠀⠀⠉⠋⠀⠀⠐⠧⠅⠠⠺⠎⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⡂⠁⠌⠬⠀⠀⠀⠀⢘⡆
⠀⠀⣾⣻⣯⠭⢿⣿⣿⣿⡛⢛⡀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⡾⡷⠀⠃⠁⠀⠀⠚⠀⠈⠃⢸⡁
⠀⢘⣫⡵⢞⣫⡽⠿⠟⠛⠛⠈⠁⠈⠁⠀⠀⠀⠀⠀⠁⡃⠈⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠓⠒⠛⠁⠐⠃⠀⣀⠀⠈⢶⡷⠀⠍⢊⠀⠓⡃⠀⠘⢇⡾⠁
⠀⠀⠿⠞⠋⠁⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠘⡀⠤⠀⠀⠀⠀⠀⠲⠀⡄⠀⠀⠡⠀⠀⡀⡀⠀⠀⡀⠀⢀⠐⠀⠀⠀⠄⠀⠀⢜⠀⠀⠐⠤⠀⠐⠋⠀⡄⡀
⠀⠀⠀⠀⠀⠒⠀⢀⡆⠀⠀⣆⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠐⠀⡁⠀⠀⣿⡟⢿⣾⠟⣿⡇⠀⣀⠀⢀⡀⠀⠀⢠⡆⠁⠈⠀⡆⢠⠀⠀⠎⢙⢁
⠀⠀⡀⠀⡀⠀⠀⠚⠓⠀⡈⢙⠁⠀⠀⠀⡀⠀⠇⠈⠀⠈⠀⠋⠀⠉⢠⠉⠀⠀⠀⠈⠖⡶⢿⡶⠋⠀⠀⠀⠀⣀⣁⣀⣀⡻⣿⣶⣴⣶⡾⠃⠙⣆⠻⣿⡿
⠀⠀⠐⠀⠂⠀⠄⠀⠥⠈⠠⠄⠀⠆⠀⠀⠀⠀⠂⢀⠀⠀⢀⠂⠀⡀⢠⠆⠀⠂⠀⢀⡀⠐⢺⠂⠆⠀⠰⠠⠦⠾⠃⠞⠉⠀⠇⠀⡄⠀⡇⠀⠀⠘⢆⠈⡇
⠀⠀⠀⠄⠀⣠⡀⢈⠀⠂⠈⠅⠃⣠⡄⠀⠀⠀⠄⠀⠀⠘⠀⠄⠃⠐⠒⠃⠀⠂⠀⠃⢠⣤⣬⡤⢠⠂⠀⠑⠒⠒⠀⠠⠆⠀⠞⠻⠹⠛⠇⠀⣀⠤⠞⠃
⠀⠀⠀⠀⣄⠘⠀⣌⠂⠠⠀⢞⡁⠘⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⡤⠁⠀⠻⠏⠀⠈⡤⡀⠀⠀⠀⠀⠤⠀⠀⠀⡐⠒⡀⡀⠀⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⠀⣄⢠⢀⠄⠀⠀⠀⠀⠄⠠⠀⣶⡄⠀⢄⠄⠀⠀⠄⠐⠀⠀⠶⠀⢠⡀⢀⡤⠀⠓⠃⠀⠀⠀⠀⠄⢀⠘⠀⠀⠠⠆⡀⠀⠀⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠶⣭⠿⠂⠀⠀⠀⠀⠀⠀⠀⠨⠠⠂⠀⢀⡀⠀⡤⢀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⡀⠀⢈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⠆⠀⠈⠀⢨⣀⡈⣤⣐⠀⠈⠁⠀⠂⠀⠀⠀⠀⢀⣴⣤⣶⡶⢀⠉⠒⠀⠀⠀⣆⡆⢠⢰⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⣀⠀⣿
⠀⠐⠁⠀⠀⠀⠀⡈⡉⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠙⠘⡉⠉⠀⠀⠀⠀⠔⠙⠁⠸⠌⠦⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡼
⠀⠀⢈⠀⠀⠠⠆⠀⠅⠠⠬⠤⠅⠀⣆⡀⢰⠀⡅⠀⠀⡋⠁⠂⡘⠈⢁⠀⢠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠂⠀⠬⣄⠀⠀⠀⠀⠠⢀⠀⣀⠄⡃⠀⢠⡇
⠀⠀⡀⡀⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠯⠉⢹⠀⡋⠉⠀⡟⢡⠀⡆⠀⠐⠀⠀⠀⠀⠂⠄⠆⠀⠀⢀⠈⡠⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠐⠀⠁⠀⠁⠀⣰⠇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠙⠙⠙⠁

⠀⠀⠀⠀⠀⣠⣶⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⣠⠤⠶⠖
⠀⠀⠀⠀⣿⣿⡿⢿⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢞⣡⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠉⣵⣾⣿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⣿⣾⡿⢋⠔⠒⠢⢍⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⠻⣶⣄⡘⣿⣷⡧⢊⠭⣑⢄⠑⡜⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣿⣦⣶⠶⠿⠟⠛⠛⢛⣿⠿⠛⠿⢿⣿⠷⣶⣤⣦⡣⠈⠢⡙⢿⣆
⠀⠀⠀⣀⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣶⠦⢹⡆⠀⠈⠙⠻⣿⣢⡙⢦⢹⣷
⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣈⣡⡾⠁⠀⠀⠀⠀⠈⢿⣞⢸⢸⣿
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⣟⠣⠜
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢸⣿⣧⣿⣦⡀
⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣏⠁⠀⠀⣠⠾⠿⣿⣿⠿⠞
⠀⠀⠀⠉⠛⠿⠶⠶⣶⣦⣤⣤⣶⣶⡶⠶⠶⠀⠀⠀⢀⣴⠋⠀⢿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⣀⣠⣤⠶⠛⠁⠀⣠⣾⠀⠀⠀⠺⣶⣶⡿⠋⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⡄⠀⣀⣠⣾⠿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣿⠟⠋⢀⡼⠃⡀⠀⠀⠀⢸⡏⠀⠀⠀⢴⣿⣶⣾⣿⣾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠉⣀⣴⠏⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣼⡿⣿⠟⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⣤⣄⣀⣀⣀⡀⠀⠀⠈⠉⠀⢀⣀⣀⣰⡟⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠒⠲⠶⠦⠬⠭⣿⣤⣾⣉⣉⣉⣉⣉⣉⣿⣧⡶⠿⠛⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇
⠀⣰⠋⠙⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⢸⠇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣠⣿⢀⡞⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠷⠴⠚⠛⠻⠶⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⣶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠲⢦⣤⣤⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡾
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⢲⡀⠀⠠⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠶⠶⢺⠋⠀⠀⣤⡤⠄⠀⣀⠄⠆⣐⣠⢂⠠⢄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡘⠀⠀⠀⢳⣦⠤⠄⢀⡠⠔⢫⠸⠒⠁⠀⠀⠈⣗⢈⡆
⠀⠀⠀⠀⠀⠀⠈⠉⢁⣤⠾⠤⢤⢀⠞⠉⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠈⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠶⠿⠶⠷⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡤⠴⠖⠒⠒⠒⠒⠒⠶⠦⢼⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠔⠚⠛⡿⠻⠿⠿⢿⣿⣿⣶⣦⣤⣤⣀⣰⠀⢀⣠⣤⣶⣿⠿⠟⠛⠉⠁⣧⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠡⠿⠟⠉⠉⠉⠉⣿⠀⠈⠟⠿⠿⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠈⠢⢀⡀⠀⠀⢀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠠⡤⠀⠀⠀⠉⠒⠤⠤⠀⠠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠹⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢱⡀⢨⡗⠒⠶⠤⣤⣤⣤⠤⡤⣤⠤⠐⠒⠚⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁⠀⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠱⢦⡀⠀⣏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣧⠔⣆⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⣄⣀⡀⠀⠀⣷⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠃⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁

⠀⠀⢀⣴⣿⣿⣷⣦⠀⢀⠀⠀⠀⠄⢠⣶⣦⠀⠀⢠⣿⣿⣷⣤⣤⣤⠀⡀⠀⠀⢀⣀⡀⠰⠷⠀⢀⠤⠤⠤⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣇⢀⠃⡨⢀⠁⠀⠉⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⠁⠀⠈⠃⠀⡔⢁⣠⣄⡀⠀⠱⡀
⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡠⠀⠄⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⢆⠐⠀⡇⠠⢠⠋⢠⡆⣹⠀⢂⡇
⠀⠀⠀⠙⠿⣿⠿⠋⠀⠀⠀⠀⠘⡀⠀⠀⠐⠀⠀⢀⠙⠛⠉⠻⠿⠋⡛⠋⠐⠶⠀⠳⡀⠙⠄⣈⣦⣀⠉⢁⣠⡞
⠀⠠⣾⣶⠀⠊⠀⠘⠛⠀⠈⠢⢀⣈⡀⠤⠀⠒⠂⠈⠀⠐⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⢃⢀⢄⡀⢈⠭⠉⡥⠤⠟
⠀⢀⡉⠁⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠁⠰⠀⠀⠠⠀⠀⠀⠀⢀⡀⣦⠀⠁⠀⣉⣁⠀⠀⠀⣀
⠀⠀⠠⡄⠂⠠⠀⠀⠀⠀⠀⠀⠂⠘⠀⠁⠐⣻⣿⠄⠀⠀⠀⡠⠀⠀⠀⠀⠺⣦⡻⣜⡧⠀⡎⠀⠀⠙⠊⠀⠀⠙⡄
⠀⠠⠁⠁⠀⠀⠀⠀⠤⠀⠄⢀⡀⢠⠀⠐⣻⠿⠆⠀⠿⠂⠐⠀⠀⠀⠀⠘⠄⠈⠛⢀⣀⠀⢧⠀⠀⠀⠀⠀⠀⢀⠃
⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⣠⡀⠈⠀⣀⠠⢀⣀⠀⠨⠈⠀⠁⠈⠀⠃⠀⣠⣬⡉⠀⢀⡑⢦⡀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠐⠀⠐⠀⠈⠁⠈⠀⠈⠀⠀⠿⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠔⢆⠰⠁⠀⢹⠀⠉⠱⠀⠘⢎⣀⣀⣤⡀
⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀⠀⠀⠛⠈⢸⡧⠀⢀⠀⠀⢀⠀⠀⡌⠸⠀⠀⢸⡄⠁⡀⣴⡄⠸⣿⣿⡿⠃
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢾⣯⣀⡀⠀⠀⠀⢀⣀⣼⣿⡆⠘⠀⡀⠁⣲⠀⠀⠘⡦⠴⠁⣠⣴⣶⣦⣝
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡀⠉⠉⠛⠛⠛⠛⣛⣋⣍⠁⠀⠀⠀⠈⠀⢹⠀⠀⠀⠄⠀⣼⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣿⣶⡶⠀⢀⣴⣿⡟⠁⣿⣷⡄⠀⠀⠙⠃⠈⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠀⢠⣿⣿⡿⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠘⠋⠁⠉⠛⠀⢼⠿⢿⣇⠤⢄⣻⡿⢿⡇⣀⣀⠀⠀⠀⠀⣰⠃⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⠉⠀⡄⠀⠀⠑⠒⠁⠻⠂⠻⠏⡻⢹⡟⠋⠿
⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⢢⣤⣄⡀⠀⠀⠈⠁⠀⠰⠀⠀⠠⣄⣀⢰⣿⣀⣤⣶⠖⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⡀⠀⣀⢀⣀⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⢀⠀⢀⡈⠶⠆⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠙⠋⠙⠓⢦⣄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠄⣀⠀⣀⠀⡀⠀⣀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠌⡠⠤⡈⢋⠀⠀⠈⠃⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠀⠀⠈⠆⠀⠀⠑⡠⠀⠀⡄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢐⠈⣇⠀⠀⠸⠀⠆⠃⠀⡄⡼⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠔⢁⡀⠸⠀⢀⠀⠄⠤⠀⠰⠬⠸⣅⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠔⠉⢀⡀⠔⠐⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠎⢠⠂⠀⠀⠀⠀⠀⠐⠢⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⡀⠀⠀⠀⢀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⠀⠀⠈⠢⠀⠀⠀⠀⠤⡖⠉⠀⠀⠀⠀⡦⢨⡝⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣑⢴⠘⡄⠈⠂⠀⢢⠔⢀⢾⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡇⠀⠀⠀⣠⠖⠉⢀⠜⡄⠘⠄⠄⠀⠁⡠⠃⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡠⠃⠀⠀⠀⢹⡀⠀⠈⠂⠙⠦⣀⢀⠠⠊⠀⢰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡜⠁⠘⠀⠀⠀⣀⢀⡤⠊⠀⠀⠀⢸⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠈⠦⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠞⠀⠐⢂⣀⡀⢄⠀⠀⡀
⠀⠀⠀⠀⠀⣄⢠⣷⠾⠀⡀⠀⠐⠃
⠄⠀⠀⠠⡁⠀⠉⠉⠀⡠⠃⢄⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⡀⣦⡐⠀⠀⠂⣍⢹⠋⠀⡠⠋⣀⠈⠋⠸⠀⣠⣤⡜
⠉⠈⢘⠀⠀⠀⠀⡬⠀⠊⠀⢼⣶⣥⡠⢀⣶⣾⣿⡟
⠀⠀⠇⡀⠀⠘⢠⢃⠈⠀⠤⣶⠟⣡⣴⠟⠛⠉⠉⡉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠢
⡃⠘⡔⠁⢠⢁⣿⣤⠒⠒⡼⢷⡿⠋⠀⣠⠖⠒⢦⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀
⢀⡟⠀⠠⠃⣼⠉⠓⢁⡞⢠⠟⠀⠀⠀⠇⠀⣤⣼⠃⠀⡈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⠀⢸
⣸⠇⠀⢀⡜⠁⠀⢀⣾⢡⡟⠀⠀⠀⠀⢇⠈⠛⠤⠀⠂⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣴⣁⢀⡙
⡇⠀⠀⠬⠊⠐⠀⢸⠳⡈⣧⠀⠀⠀⠀⠈⠂⠠⠠⡤⢶⢧⡀⠀⡀⠀⠸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠻⡦⠈⠁⠀⠀⠈⢻
⡏⢀⠀⢀⡏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠒⠀⢁⠉⠀⠀⠀⢀⣠⣤⡄⠈⠉⠉⢴⣷⠴⣧⠄⢀⠀⠀⠘⢿⡿⠀⡠⠂
⣤⢠⡉⠸⠁⠀⠀⡂⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠈⢀⡳⠀⠀⡐⠉⢦⡠⠊⠀⠀⠀⠀⠈⠓⢄⠀⠈⠗⠀⠠⣄
⡟⠃⢇⠎⠀⠀⠀⢧⡀⠀⠀⢀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⢠⠦⠞⠉⠉⠑⢴⡋⠁⢘⡇⠀⠀⠀⠀⠀⢤⢂⣠⠇⠒
⡧⠀⡘⠀⠀⠠⠀⠸⣌⠢⠀⠀⠉⠒⠈⠓⢤⣄⣀⠀⠀⡀⣀⣠⡤⠴⠊⠉⠀⠀⠀⠀⡀⠀⠈⢥⡤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣷⠀⡀⠀⠀⠀⠀⠸⠳⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣁⠴⠒⠒⢤⡈⠇⠀⠀⠄
⡹⠞⠁⠀⠀⢰⠀⠈⡀⢹⣦⣙⣒⣂⠀⣀⠀⠀⠑⠲⢄⣀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠒⠲⣀⠁⡆⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⡀
⠀⠲⠀⠀⡂⠈⡀⡀⠁⠀⡰⠙⢦⣀⣈⠪⠀⠂⠰⢄⡠⠌⠁⠀⠀⣀⠔⡫⠀⠀⠀⠀⠀⠀⠽⣦⣷⠀⠀⠀⠉⢆⡉⠀⠐⠒⠀⢉⡀⠀⠀⠈⠢
⡀⠀⢰⠰⠀⠀⠀⠀⡄⠠⠑⢄⠀⠈⠙⠷⢦⣶⣴⣤⣤⠤⣤⠖⠉⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠳⣿⠀⠀⠉⢂⠀⠈⠀⠀⠀⣠⡤⣤⠁
⠀⠈⠘⣶⠀⠀⠀⠀⠈⠀⠑⠀⠁⠀⠀⠀⠠⠀⢀⠔⠀⡼⢁⠔⠀⠀⠉⠀⠄⠀⠀⠁⠀⣀⠠⠜⠷⢧⡀⣀⠀⠀⠀⣀⣐⡂⠠⠐⠒⠒⠲⢤⡀
⠀⠀⠀⠘⢷⣐⠂⠀⠀⡀⠀⠀⠐⠀⠀⠀⠐⠚⠁⠀⠐⠠⠈⠀⠀⠀⠀⠀⠁⢀⠀⠐⠉⢀⣀⠀⠀⠀⠀⢤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⡄⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁⢀⣀⠀⣠⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠙⡒⠶⠀⠴⠶⠆⠀⠒⠀⢦⡀
⠒⠒⠀⢄⠀⠀⠈⠛⢤⡀⠘⢆⠂⠑⠀⠀⠀⡀⣀⠈⠀⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⣀⠀⠀⠀⠠⠤⠀⠀⠀⡇
⠀⠀⠀⠀⠡⡐⢄⡀⠈⠉⢲⣮⣷⣦⣄⣉⣑⡢⠤⠬⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⠰⣾⡇⠀⠜⠁
⠀⠀⠀⠀⠠⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⡩⢇⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣷⣄⠀⣭⣿⣷⣿⢧⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢀⣾⣿⣿⣟⡂⠈⠛⠒⠿⣞⣿⣌⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⡼⣿⣿⣿⢿⠀⠀⠀⠀⠀⠸⣿⣿⣷⡙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⢋⣿⢠⡄⠛⠈⠻⢿⣶⣦⣤⠐⠂⠠⢿⣿⣿⡗⣜⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⡀⠹⣻⣶⡅⠀⠀⢀⠿⠶⠶⣿⣿⣿⣿⣿⣿⣿⡷⣻⣏⠁
⠀⠀⠀⠀⠀⣠⡖⣄⣻⣿⣧⣀⠈⠩⡷⣃⣴⣿⣶⠖⢠⣭⣿⠷⠶⢿⡿⠿⠷⠼⠿
⠀⠀⠀⠀⣞⣫⢿⣯⣿⢾⣿⣿⣧⣀⢀⣿⣟⡉⠀⢠⣾⣶⠛⢶⣶⠿⠟⠋
⠀⠀⠀⠀⠹⣖⣮⣿⡷⠟⠹⣿⣿⠿⠤⣭⢿⣿⠀⣾⢟⣹⣷⣸⡇⣠⣤⣤
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣾⣿⣿⣶⣿⣼⣿⠀⠁⠀⠔⣻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠉⠁⠉⠁⠉⠀⠀⠀⠀⠑⠻⢿⣿⡿⡿⣿⡟⢉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣀⠱⣖⠠⠤⢴⣦⠀⢠⣾⣿⣽⡿⣿⣿⠋⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣷⠈⢳⣶⡀⢀⣄⣾⣿⣿⡏⠀⣿⣿⠀⣆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠷⠘⠿⠇⠈⢻⣿⣿⣿⣧⢀⡿⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢠⡟⢲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡛⢛⣼⡏
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡟
⠀⠀⠀⠀⠀⣰⢟⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣟⡛⢛⣿⣿⣿⣿⣯⢸⣿⡇⡿
⠀⠀⠀⠀⣼⡿⠁⠀⠀⣠⣶⣷⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⢼⣿⢱⡇
⠀⠀⠀⣸⣏⣀⣀⣠⣾⠛⠋⠁⠶⢶⣾⣿⡿⠟⠋⢁⣾⡿⠃⡀⠀⢀⣿⡟⢸⡇
⠀⠀⢰⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⢹⣿⡷⠾⠿⠟⣋⠁⠾⠿⢦⣼⣿⠁⣿⡇
⠀⠀⠸⣿⣅⠀⢦⣀⣀⣠⣶⡿⠷⣛⣩⣴⣶⣿⣿⠿⠿⣿⣿⣿⣾⣿⡏⠀⣿
⠀⠀⠀⠙⠻⢿⣿⠿⠿⠿⠿⠿⠿⠷⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠻⣿⣃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠴⠶⢄
⠀⠀⠀⠀⠀⢀⡀⠀⢘⠀⡀⠀⣀⣠⡦⣦⠀⢠⣄⠈⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠤⠀⠉⠁⠒
⠀⠀⠀⠄⠀⠀⠀⠀⣤⣾⣧⡀⢙⡘⠃⢴⡄⠿⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣤⠀⠐
⠀⠀⠀⠄⠀⠀⠀⠈⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠈⠲⠂⠀⠀⠀⢠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠠⠀⠀⡧⠀⠀⠈⠃⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⡀⠠⠀⠀⢻⠿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄
⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡋⠀⠀⠀⠛⠋⠀⠀⢀⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⢠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠛⠀⠀⠀⠀⠀⣶⣦⡄⠀⠀⠀⠀⢿⡆⠀⠿⠆⠉
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠂⠀⡐⠈⠁⡀
⠀⠐⠀⠀⠀⣤⠀⠸⠃⠹⠄⠀⠄⣴⣿⠗⠀⠀⠀⠀⠀⡇⠘⠀⠀⠃⠀⠀⠃⠀⢠⠀⠈
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣴⠀⠀⠉⠀⠀⠀⠀⠀⣠⡇⠀⠀⢀⣤⠀⠀⢠⣶⡄⢄⠀⠀⠀⠀⠠⠆
⠀⠀⠈⠀⠘⠃⠀⣠⣤⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⠀⠀⠘⠟⠀⢀⠈⠛⠁⡾⠆⠰⠆⢀
⠀⠀⠂⠠⢴⡆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⡀⠀⠀⠀⠐⠖⠖⠀⢠⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠠⠠⠄⠡⢀⠀⠀⠀⠀⠀⠀⡠⠶⢾⠓⠶⠤⠀⠀⠃⠈⠢⡄⠄⣤⠀⠀⠀⠈⠀⠀⠠⠔⠀⠀⠈⡄
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡆⢀⡀⠙⠛⠃⠀⢀⠀⠀⠀⠀⡀⢀⡅⠀⣇⢰⡀⠀⡢⠃⢀⣤⣦⡄⠀⢠⠃
⠀⠀⠠⠄⠠⢴⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠈⠛⠃⠈⠀⣈⡀⠁⠀⠰⠏⠄⠃⢠⠂
⠀⢀⣠⣄⣀⡤⠀⠀⠐⠀⠀⠀⠀⠤⣠⠜⠁⣀⠀⠀⠉⢷⡖⠀⡀⠀⠀⠸⣿⣿⣧⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠈⠁⠀⠀⡄⠈⠁⢸⣿⣷⠀⠀⢈⠛⠁⠀⢠⡏
⠀⠀⠀⠀⣈⠀⢰⣶⡆⠀⢸⣿⠄⠀⠀⠀⠈⠙⠀⠈⠁⠾⠆⠀⠉⢉⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠨⠀⢴⡀⠀⠉⠀⠀⠀⠀⠄⣀⠀⠀⢀⡀⠀⠶⠁⠀⠀⡠⡄⡀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠈⠀⠀⠀⠀⠀⠙⠀⠈
⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠋⠀⠀⢶⡟⣠⡐⡄⡀⢠⡄⠂⠐⠞⠉⠓⠀⠀⠈⠢⠤⠂
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠁⠀⠀⠘
⠀⢀⡌⣴⡄⠀⠀⢠⡤⠤⣤⣦⠀⠀⠀⡀⠀⢾⡧⠤⠶⣶⠇⠀⠀⠼⠿⠀⠀⠹⠟⠀⠀⠀⠀⢠⠚⠂
⠀⢀⠀⠀⠠⠦⠀⠀⠀⢀⡀⠁⠀⢤⠈⠁⠀⠀⠁⠀⠀⢀⠀⠲⠛⠀⠈⣀⣀⣀⡀⠀⠠⣏⣀⣀⡐⠒⠂
⠀⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠖⠈⠀⢤⡤⠀⠠⠶⡾⠓⠀⢴⠋⠉⠉⠱⠆⠀⡉⠉⠉⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠐⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣠⡴⠾⢄⠐⣠⢦⡬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠘⡄⠀⢮⠀⢫⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠉⠁⠒⠒⠤⠤⠤⠀⠼⣧⠴⠤⠒⠒⢒⠒⡤⢯⣽⠛⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⣀⡀⣤⠤⠴⢶⣯⢹⡄⠀⠀⢈⡭⢤⣇⣾⠿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⣼⡥⡄⢀⠎⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡠⠾⠧⣄⡸⠈⠁⠀⠀⢹⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡏⠀⠙⡆⠀⠀⠜⠉⠉⠁⡜⣃⠀⠀⠀⢀⡎⠀⠀⠀⡜⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠙⢏⠲⡀⢸⠀⣀⠈⠒⠢⢴⡖⠉⠂⠐⠲⡏⠀⢀⡀⠀⢱⠀⡠⢫⠞⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠒⠌⠳⠇⢸⢸⠁⣈⢳⡤⠋⠀⠀⠀⠀⠐⡶⠊⣡⡘⠀⢀⠇⠧⠋⠔⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠒⠚⠀⠀⠜⠒⢊⡼⠋⠀⠀⠀⠀⠀⠀⠀⡇⠸⢍⡑⠲⠏⠀⠀⠈⣉⠉⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡠⠊⢱⡀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢆⠈⡇⠀⠀⠀⠹⡈⠳⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢰⠋⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢠⠤⠱⡟⢤⢀⡀⠴⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠚⠁⠀⡜⠀⢀⡗⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⢀⣀⣀⣼⡁⠀⣀⣄⠀⢰⠃⣠⠎⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⢀⡞⠉⠀⠀⡨⠷⠖⠁⠈⠓⢃⠞⠁⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢏⢧⡀⢸⡀⠀⣠⠎⠀⡆⠀⠀⠀⡰⠋⠀⠀⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⣉⠛⠁⠀⢀⡇⠀⢀⠞⠁⠀⠀⠀⠀⡼⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⠉⢦⣀⡀⣸⠀⢀⠋⠀⣀⢶⠷⢒⣪⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠁⠀⠀⠉⠹⢇⣀⡼⠉⠉⠁⢰⡶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⡀⠀⠀⠀⠸⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣑⠲⣄⠀⠀⠀⠀⡴⠲⣄⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠙⢤⠀⣈⣳⣄⠀⢸⠁⠀⠀⠑⢦⣜⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⠇⠨⣽⣞⠃⠀⠀⠀⠀⠀⠋⠈⠓⠦⢄⣀⠀⠀⠒⠦⠤⣀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣐⠢⡉⢳⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠏⡏⠉⠉⠉⢍⣁⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣄⣾⣿⢤⠀⠀⢸⠶⢄⠀⠀⢸⠰⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠋⠙⣍⠢⡳⣤⡜⠇⠀⠉⢻⠟⠻⠶⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠣⣙⣺⠋⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣠⣄⣀⣀⣈⣁⣀⣀⣀⠀⢠⡷⢶⣤⣤⣤⣤⡴⠤⠦⠾⠿⠟⠛⠻⡆⢉⠂⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠂⠉⠉⠀⠉⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠉⠐⠒⠒⠀⠤⠭⠍⠉⠍⠉⠉⠉⠭⠍⠩⠭⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠆⣰⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣋⣉⣹⠟⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⣴⡏⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⠋⢸⣿⣷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣠⣿⣿⣧⣤⣤⠄⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⡟⠁⠀⠘⠛⠛⣿⣿⣿⡇⢹⣿⣿⣿
⠀⠀⠀⠀⠸⡇⠀⠀⠐⠛⠛⢻⣿⣿⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣧⢸⣿⣿⣿⣤⣤⡄⠀⢀⣼⣿⣿⣿⡇⣸⣿⣿⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⡿⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⢦⣀⠀⢸⡟⠁⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⠿⣿⡏⢠⣿⣿⣿⠿⢋⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠏⠰⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣰⣏⣉⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠒⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⠀⣀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣃⣘⣻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⢈⠉⠉⠉⣩⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣼⣾⣿⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠉⠻⡿⠟⠁⠀⠀⠀⠀⠉⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⣴⣿⣿⣷⡀⣠⣤⡀⢠⣾⣿⣿⣆⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠀⠀⢿⣿⣿⣿⠣⣿⣿⣿⠸⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠙⢿⠀⠀⠀⠀⠉⠉⠀⠀⠙⠿⠋⠀⠈⠉⠁⠀⠀⠀⠠⠟⠉⢹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⢀⣠⣴⣶⣷⣶⣤⣤⣤⣤⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠟⠁⠀⠀⣾⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⠾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢵⣶⣿⣿⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠓⠀⠀⠀⠀⠀⢸⣿⣿⣯⣾⣿⣯⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠈⣽⣧⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⠟⠻⣿⣿⣿⣆⠀⠀⠀⠀⢿⢿⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠘⠛⠛⠛⠁

⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⢰⡟⡃⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣶⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⡟⣠⣇⠀⠀⠰⠶⢶⣾⣟⠙⣿⣿⣁⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⢹⡿⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡛⢛⣛⠃⣀⣸⣿⣶⡶⠶
⣀⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣯⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⠿⣶⠀⠀⠀⠀⠀⣿⣻⣟⠋⢻⡏⠛⣿⣿⣧⣀⠴⣷⣤⣾⣿⣿⣿⡿⠛⢿⡿⣿⣿⠀⠀⠀⠀⣴⠄
⠇⠀⡀⠀⠀⠀⠀⠀⠟⠙⢿⣷⣶⣿⣶⣽⣏⣽⡛⠺⣿⣿⣷⣿⣿⠽⣶⣴⣾⣽⣺⡇⠀⠀⠀⠀⢿⣦
⡶⠀⢧⠀⠀⠀⠀⠀⠰⣿⣿⣟⣿⢯⡃⡈⠹⣿⣿⣤⣿⣿⣿⢫⣥⣿⢞⣋⣼⣯⠹⡇⠀⠀⠀⠀⠀⢻⣷
⠁⣰⡿⠀⠀⠀⠀⠀⠀⢿⠓⣁⣸⣤⣽⣿⠿⢿⣿⣿⣛⣚⠿⢿⣿⣧⣾⣟⣚⣟⡓⣷⠄⠀⠀⠀⠀⠀⢻
⢠⣿⡇⢠⡄⠀⠀⠐⣷⣿⡛⢛⣿⡏⠀⣶⠓⠈⣛⣿⣿⣿⣤⣄⣈⣉⣿⣿⣿⣿⣷⣿⡦
⣼⣿⢣⣿⡏⠀⠀⠀⠉⠛⠿⣻⣿⡶⣶⣀⣿⣿⣿⣿⡿⠿⠟⠋⠈⠭⣉⣉⣬⣿⠟⠉⠁⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⠃⠀⠀⠀⣴⡆⠀⠈⢻⣿⣾⣿⣿⣿⣿⣯⣁⣀⣴⡟⣿⡿⣿⣿⠇⠰⣿⠆⠀⠀⠀⠀⠀⣐⣇
⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⠒⠀⢸⠈⠻⣿⣻⣿⢡⢻⡿⢹⣯⣶⣟⣸⣿⡇⠐⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠘⠃⠀⡂⢸⣀⣶⣿⣿⣿⣿⣼⠀⣼⣿⣿⣿⠁⢸⣧⣴⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠋⢠⣶⡌⠉⣿⣿⡿⣿⣿⠐⣿⡿⠛⠃⠀⢸⡏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣠⣾⣶⡀⠀⠀⠀⠀⠀⠛⡁⠀⣿⣿⡇⢸⣿⣿⢿⣀⣀⠄⠀⢸⠇⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⡇⠸⡏⠁⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⠻⢿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠁⠈⣠⠠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠁⠀⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣷⣶⣧⡶⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⡿⢛⠋⠉⢙⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⠇⠀⢸⣿⣿⡆⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⠛⠀⠀⠘⢹⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⡆⠙⢿⣿⣧⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠂⠁⠀⠀⠀⠀⠉⣹⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠙⠃⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢰⡿⠟⠀⠀⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠈⠘⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠄⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠂⠀⢸⣿⣧
⠀⠀⠀⠀⡀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣷⣄⠀⠀⠉⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠉⢋⡄
⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠉⢿⡻⠏⠆⠀⠀⣠⣶⣿⠁⠀⠐⣦⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⡀⠑⠀⠁⠀⢺⣿⣿⣿⣿⣶⠤⠍⠀⠀⠻⣿⣶⣦⡙⣶⠀⢀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⢀⠰⢴⣶⣶⣶⣾⡄⠀⠁⠀⠀⠙⠋⠀⠀⠉⠀⠠⢀⠀⠀⠀⠉⠉⠙⠀⠀⣿⣿⣿⣝⡋
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣽⣿⡿⠿⡇⠀⠀⣠⣀⠠⢰⠃⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⢋⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠰⠻⠇⠀⠀⠤⣄⡂⣛⣯⣴⣿⠀⠂⠀⠀⠀⣾⠀⠀⠀⠀⠓⢶⣶⣾⣧⣰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠙⢿⣿⡻⠇⠀⠐⠀⣆⠘⢉⣼⠀⠀⠉⠻⣾⣧⣤⣿⡿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢰⠀⠘⠀⡿⠙⢤⣀⠘⢿⣏⣀⣼⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣀⣀⠀⡀⣀⣠⣴⣾⡴⠀⠀⠀⠇⠀⠀⠉⠙⢋⣩⣿⠋⢀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⡷⠀⠘⠀⠀⠀⠀⠀⢀⡀⠋⠁⠶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡿⠀⠀⠀⠈⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁