Seaside Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢄⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣦⠀⣰⣿⠋⠀⣚⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢟⣩⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠄⠹⣧⣿⡃⢀⣾⢿⠇⠈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣾⣿⡿⢿⣿⣷⣷⢠⣤⣶⢂⣶⣦⣴⠖⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠔⠀⠄⠀⣘⣬⣡⣘⠁⢉⡀⠀⢉⠉⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠟⣁⣤⠬⢿⣿⣿⣾⣿⢻⣕⠋⠁⠀⠀⠀⠀⠀⢀⡴⠯⠿⠻⢟⡁⠈⠀⠲⠟⡿⠃⠘⣷⠘⠧⠈⠃⠈⠈⠛⠃⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣺⠋⡤⣶⣶⣾⣿⣿⣿⣿⢿⣭⠑⠦⣄⠀⠀⠀⠈⠀⠀⠀⠀⢸⡄⠀⠀⠁⢠⠇⠀⢸⡙⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣾⢃⣽⠟⣿⡿⢿⠿⢿⣧⡉⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠘⡇⠀⠁⠀⠈⠀⠀⢸⠆⠘⣇⠀⠀⠀⠀⠀⠀⢠⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⠟⠀⠀⣿⡃⡾⠁⠈⢿⡁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢼⡄⠀⠀⠃⠠⡇⠀⠀⢸⡄⠀⠰⠃⡄⠀⢸⡏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⢸⣿⡿⠁⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠇⠀⠀⠀⣶⠀⠀⡎⢠⠀⡾⠀⠘⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⡆⠀⡄⠌⢰⠇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠀⠃⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⡇
⠀⠀⠀⠀⢀⡀⢸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀⠀⠀⠀⠘⡇⠀⢰⡇⠀⠀⠄
⠀⠀⠀⠀⣼⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠒⡶⢻⡶⠴⣶⣺⣻⡀⢼⠅⠀⠀⠠
⠀⠐⢤⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⡡⢚⣙⢊⠴⢓⢃⡴⢚⣉⣡⣿⡆⣸⣃
⠀⠈⢩⣯⣿⣿⣾⣐⣤⣠⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠛⠱⢭⠇⢉⠠⠟⢍⡲⠂⣀⣾⣿⣷⣿⣿⣵⣀⣤
⠈⢉⣹⣿⣿⣿⣛⣿⠷⠬⢿⣶⣾⣿⣿⣶⣄⣀⠀⣼⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣭⣾⣖⣏⣩⣍⣀⣒⣒⣛⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⠶⠄
⠀⢸⣿⣿⣿⠏⠉⠉⠛⣫⣉⣿⣿⣿⡿⣿⡟⠁⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠹⠿⢿⣏⠹⣦⡄
⠀⠈⣿⡿⢃⣀⣤⣤⣤⣼⣿⣟⠟⣛⣿⢏⠁⠀⢀⡇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣀⢈⣉⣉⠛⢻⣿⣿⣿⣾⣿⣿⡿⠿⣿⡿⣿⣟⣿⣿⣷⡟⣿⣆⠀⠡⣄
⠀⢛⡽⠂⠈⠉⠘⢩⣽⠛⢁⣍⣀⠀⠈⣀⡀⠀⠀⡅⢸⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣼⣿⡿⢯⣿⣭⣬⣉⠳⠒⠛⠛⠉⠉⠉⠉⠀⠀⠀⢿⣆⠀⠙
⠺⠏⠀⠀⠀⠀⠀⠀⣀⡀⢉⣃⣠⡄⣈⣁⣀⠀⢈⣇⣿⢸⠁⠠⠀⠤⠤⠾⠟⠹⣯⠯⣭⣥⣶⡶⣿⣿⢌⡷⣟⣛⣷⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣏⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⠀⠀⢠⠠⠃
⠀⠀⠀⠀⠀⢠⠔⠉⠉⠑⠆⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢠⣤⠆⠁⠀⠀⠀⠤⢀
⠀⠀⠀⠀⢀⠸⣄⠀⢀⣀⠜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠱
⠀⠀⠀⠈⠀⠀⠈⠉⡉⠁⠀⠈⠢⠀⠰⠄⠄⠦⠀⢀⠴⡄⣀⡀⠤⠀⢠⣳⡠⠂⡠⡀⠤⠐⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠡⠀⠀⠀⢠⣏⣹⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⠗⠊⠀⠀⣹⠆⣐⡄⠀⠀⠠⠤⠄⢔⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠦⠊⠀⠀⠀⠀⠀⠈⢻⣀⠠⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠒⢒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡼⢤⡘⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠖⠁⠀⠀⠈⠐⠴⡉⠀⠈⠰⡶⠈⠐⢺⡇⠀⢠⣴⠀⠀⠠⢀⡴⠀⠀⠢⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠸⣧⠒⠐⠛⠠⢐⠂⡀⠀⠀⠀⠀⠃⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⣠⠀⠀⡤⠐⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠠⠗⠤⠀⠸⠅⡈⠾⠁
⠀⠀⢀⠄⠀⠐⠋⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⡀⠌⠉⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠂⢄
⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⡌⣫⠴⠒⠒⠒⠒⠠⡀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠉⠉⠒⢌⡆⠂⠘⠃⢉⠉⠉⠉⠀⠂⠠
⠀⣀⠀⠰⣆⢦⠄⠈⠁⠀⢉⣾⣤⡀⣀⣴⡄⢀⠀⠈⠁⠀⠵⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⣇⡀⣬⣿⡒⠚⠛⠛⠴⡏⠴⠣⠄⠀⠈⠂
⠀⠀⠀⡞⣼⠃⠀⢀⠀⠴⣿⠶⣏⠙⣧⢌⠆⠰⠂⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡸⣗⡿⠛⠳⢛⢿⡷⣴⠖⠁⠀⠀⠄⠐⠂⡁⠄⠀⡂
⠀⠀⢸⡳⠎⠀⠰⢎⠂⠀⠈⠀⣼⡶⠌⠋⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣠⣤⣶⠁⠈⣯⠞⢲⡯⠄⢐⠠⠀⠀⠀⠀⠱⠁
⠀⠀⠈⠀⠀⠀⢀⡈⠀⠀⠀⢰⣻⣇⣠⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⢠⠁⠀⠠⢟⣛⠈⡶
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⢀⡒⠀⠀⢠⣟⠁⠊⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡦⣴⠅⠷⡞⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠉⠐⠠⠄⠀⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠐⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠟⠃⠒⠃⠀⠉⢀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⢄⣠⣭⣀⠈⣉⣉⢉⣛⣛⣛⣛⠛⠛⢿⣛⣿⣋⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠈⠐⠀⠊⠀⠿⢯⠤⠤⣽⣤⡄⠀⠠⠠⠀⠀⠀⠐⠽⢬⢽⠀⠜⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⠂⠻⡆⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢂⠸⠄⠀⠀⠀⠀⢀⣠⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠠
⠀⠀⠀⢀⠄⠂⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠁
⠀⠠⡀⠂⠀⠀⠀⠀⡀⠀⠀⠀⢀⡶
⠀⠀⠁⠀⠀⠀⠀⠲⡇⠐⠟⢀⣾⣷⠂⠀⢠⣶
⠀⠂⡀⠀⠀⠀⡀⢀⠀⠀⣠⢞⣉⣦⡔⠀⠿⠄⠀⣀⡀⠐⠃⠀⠀⣀⣶⣄⡀
⠀⠀⡘⠁⠀⠀⢉⠀⠀⠀⠈⠀⠘⠙⠛⣽⣶⣆⠀⢴⠟⡿⠀⠀⠀⠈⠉⠛⢠⣤⡀
⠀⠀⠇⠸⠀⠐⠛⠂⠂⠀⠀⠀⠀⠀⡀⠈⡅⠁⠀⠋⠀⠀⠀⠀⠀⠀⠋⠀⢈⠙⠁
⠀⠀⠈⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⢀⡂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠐⠒⠁⠉⠁⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠂
⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⠟⠿⠿⠯⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠐⠠⠁⠀⠀⣤⣶⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠛⠈⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠤⣄⡀
⠀⠀⠠⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠀⠠
⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠒⠂⠒⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠤⡄⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣦⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣺⣿⣿⣗⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠘⠇⠀⠓⠠⠟⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠂⠀⠀⠀⡄⠐⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⠟⠃⠀⠀⠀⠀⠈⡀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡲⣤⣠⣤⣄⣷⣦⣞⣿⣿⣿⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⢛⡿⠛⠛⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⣀⡠⠤⠄⠀⠀⣀⡠⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠲⠖⠒⠒⠋⠉⠀⠂⢤⣄⣀⠀⠂
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⢀⣀⣠⠤⠶⠶⠖⠚⠁⡸⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢀⣀⡀⠤⠴⠶⣚⣩⣭⣤⠤⡶⣶⠶⠶⣶⣤⣤⣀⣀⣀⣤⣤⠴⠖⣋⣇⠀⢀⠠⠀⠈
⠀⠀⠀⠐⠒⠒⠒⠒⠒⠈⠉⠉⢀⣀⣀⡤⠤⠐⠂⠴⠒⠉⠀⣀⠤⠐⠉⠀⠀⠀⠀⠉⠀⣦⣠⣤⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠤⠒⠀⢀⣀⠤⠀⠂⠀⠘⠀⠀⠀⠀⠀⡠⢢⣴⡷⢖⣽⡋⢈⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠒⠁⠀⠀⠀⠈⠀⠁

⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣀⣀⠀⠀⣠⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣷⣶⠷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠦⠤⠤⣤⣤⣤⣤⣤⣤⣤
⠷⠶⠶⠶⠶⠿⠶⠿⠿⠒⠒⠒⠒⠒⠒⠒⠂⠀⠂⠒⠒⠂⠀⠉⠁⠈⠀⠀⣀⣤⣶⣿⣿⣿⡌⠉⠉⠉⠉
⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⠿⠟
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠛⠉⠉⠉⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣤⣤⣤⣐⣛⡓⠒⢒⣒⣶⣶⣶⣶⢚⣿⣿⣿⣿⣿⣿⣷⣖⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣐
⢿⣾⡟⣛⣿⡛⣛⣿⣿⣿⣿⣿⣿⠛⣛⣛⣉⣁⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣉⣉
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠝⠿⢿⡻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠉
⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣭⣍⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠶⠶⠶⠶⠶⠾⠿⢿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣍⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣿⣿⣿⣛⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣤⣤⣤⣤⣤⣉⡙⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⢀⣰⣄⣀⣶⣦⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⡿⡿⠿⣧⣉⠙⠿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⣄⣤⣠⣤⣥⣶⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⣆⠈⡄⢊⡁⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⡠⠄⠘⣾⢀⠈⣠⣀⢀⢐⠀⢄⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⠄⢁⠈⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠉⠉⠀⠃⠀⠀⠀⠰⠀⢨⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢤⠀⠀⣀⠀⠆⢤⡀⢈⠆⠀⠀⠀⠤⠀⢀⢴⠀⡒⠀⠠⣾⣧⢀⠹⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢳⠀⡀⠀⠀⢄⡠⠓⣇⠣⠤⠦⠄⠠⢬⡤⡇⣃⡠⠀⠀⠃⠋⠉⠈⠐⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠙⠻⠰⠅⠀⠀⠀⠀⠈⠷⡄⢀⣠⡴⠀⠀⠀⠛⠉⠨⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⡟⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡄⠀⢀⣴⢻⡋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⢰⠆⠀⠀⣸⣀⠀⠀⠀⣀⣴⣄
⠀⠁⠀⠈⠁⠘⠁⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⡗⠤⢼⢾⠀⢄⠛⠿⠳⠾⠿⠟⢻⡉⢀⠄⣸⠽⢻⣮
⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣈⠉⠁⠉⠀⠀⠀⠈⠀⠘⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠠⠤⠤
⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠂⢀⠀⣠⡀
⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⡄⢀⣤⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠇⡀⣀⣀⣀⣀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠦⢾⣿⣷⢟⣋⣄⣄⣀⡈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠊⠉⠈⠈⠁⠈⠁⠘⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⢿⡿⢯⡭⣭⣁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢫⢟⣴⡏⡏⠻⣄⠈⠛⢧⠰⡔⠀⠀⠀⠀⣀⣶⡴⠤⢤⡄⠀⠀⡄⠀⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢇⣀⡸⣿⡇⠸⢦⣿⣦⡀⠀⠀⠀⡀⠀⠰⣪⠿⣿⣅⠈⢲⣀⣤⠾⣿⡿⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⡹⠇⢻⡇⠀⠀⢹⡮⠃⠠⠀⠀⠁⠀⣸⠯⠁⢹⣟⣳⡄⢸⡟⢾⠋⠙⢶⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠃⠀⢠⡈⠓⢄⡀⠀⠀⠀⠀⠁⠀⠀⠈⠙⢿⡅⠀⠀⠈⠁⠀⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢦⣀⠀⠀⠈⠑⢦⡀⠀⠙⣦
⠀⠀⠀⠀⠀⢀⣀⣶⣶⣇⣠⣤⠄⠀⠘⠊⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣇⣀⠀⠀⠙⢿⣆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⣀⣤⠔⠒⠁⠀⢀⢤⠔⠂⠀⠠⠄⠀⠚⢷⣧⡄⠀⠈⢻⡇
⠀⠀⠀⠀⢀⡀⢀⡀⠀⣠⡤⠴⠶⠶⠶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠁⢢⣦⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⣻⣿⣦⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠶⠶⠶⠶⠶⠒⠠⠴⠒⠛⠛⠋⠉⣀⡜⠀⠀⠀⠀⢀⡴⠞⠛⠁⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⢚⣛⣭⠤⠶⠶⠖⠞⠿⠛⠚⠷⢶⡦⠤⠤⠤⣶⠶⠾⠋⠉⢀⣀⣤⠔⠚⠁⢄⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠐⠂⠀⠉⠉⠉⠉⠉⠀⠀⣀⡀⠤⠤⠔⠒⠈⠀⠚⠉⠀⢀⡤⠒⠈⠀⠀⠀⢀⡤⠊⣠⢷⡽⠶⣿⡉⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠖⠀⢀⣀⠤⠔⠂⡁⠀⠈⠀⠀⠀⠀⣠⡔⡻⢾⡟⠫⠾⠥⣤⠦⡄⠁⠀⠀⠀⠤⠰⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠉

⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠈⠉⠉⢉⣀⣀⣖⣒⣤⣄⣀⣤⣤⣤⡤⠈⡍⠍⡙⢍⣉⣙⣛⢩⠭⠭⠭⠴⠒⠶⠦⠤⠥⠤⠄
⠀⠀⣀⣚⣛⣋⣉⣉⣈⣉⣉⣍⣉⣁⠂⠐⠀⠤⠀⠠⡤⠤⡴⠶⠴⠮⠍⠭⠤⠤⠤⠤⠤⣖⣶⢶⡶⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢳⠀⣀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⡀⠺⠀⠈⠂⠐⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡉⠀⢠⣷⡂
⠀⠀⢀⣴⣄⣀⡁⠀⠈⣷⣼⣄⣲⣿⣴⣧⢸⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⡿⡾⣿⣿⠄
⠀⠃⠋⢉⢿⠟⠃⠀⠂⠛⠛⠛⠛⠻⠻⠛⠛⠛⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⢉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣲⣾⣿⣗⡀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠷⠀⠙⠀⠼⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠟⠛⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢤⣀⣤⣤⣸⣦⡴⣻⣿⣿⣶⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠛⠚⠛⠛⠛⠛⣛⣻⣛⡻⠿⠿⠿⠿⠿⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⢀⣀⠠⠄⠀⠀⢀⣀⠩⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠴⠶⠶⠶⠖⠚⠋⠁⠐⢀⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠒⠊⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⠤⠤⠴⠶⠖⠋⢉⠇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⢖⣛⣋⣭⣤⣤⣤⣤⠤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⠒⣫⠀⠀⡀⠀⠀⢁
⠀⠄⠤⠀⠀⠶⠶⠒⠒⠂⠈⠉⠉⠉⣀⣀⠠⠌⠀⠠⠖⠒⠉⢁⡉⠀⠒⠁⠀⠀⠈⠉⠁⢰⣀⣄⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⠄⠀⠀⢀⣀⠠⠀⠀⠐⠏⠀⠀⠀⠀⢀⠠⣠⣴⢶⣪⡟⠉⣙⡑
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠁⠀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠀⠈⠁⠀⠉⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⢤⣤⣄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⡀⢤⣤⠀⠤⢤⠤⢤⣤⣤⣤⣤⣀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤
⠩⢽⣛⣛⣻⣿⣽⣿⣿⣿⣽⣿⣿⣿⣭⡿⣿⣿⣷⠶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⠷⣒
⣬⡹⢟⣟⡛⣛⣛⣿⠿⢿⣿⡿⠛⢷⣾⣿⣿⣿⣿⡭⠽⠛⣙⡻⠿⠛⠛⠻⢿⣯⠉⠙⠛⠃⠰⠒⡋⠛⠒⠂⠀⠠⠤⠈⠉
⣉⠉⠁⠀⠁⠐⠒⠚⠒⢂⣀⡀⠙⠛⠛⠁⠄⠀⡀⠀⠤⠀⠀⠁⠒⠢⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⡀
⠉⠁⠀⠀⠀⠐⠂⠄⠈⠉⠉⠙⠀⠀⠀⠀⠤⣩⣁⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⠒⠚⠀⠀⠀⠀⠠⠄
⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣷⣶⣄⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⣀
⠿⠿⠛⠛⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠁⠀⠀⢰⣿⣿
⢠⣦⣄⠈⣹⡋⠁⠀⣠⣤⡃⠀⢼⣿⠇⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠙⠛⢓⣆⠐⠐⠂⠀⠀⠀⠐⠻⠿⠒⡂⢈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠺⠶⠄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⣸⣿⠄⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⠠⢄
⠀⠀⠀⣄⣻⣿⣠⠀⠀⠀⠀⠀⢸⣷⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⡀⠣⡀
⠀⠀⠀⠀⣽⣿⣋⠀⠀⠀⠀⠠⣽⣯⡀⠀⠀⢰⣿⡆⢀⡤⣤⠦⠐⠚⠉⠓⠦⡄⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⠑⠢⣀⣀⠀⠀⠀⠀⣸
⠀⠀⠐⣦⣿⣿⣿⠔⠙⢶⡋⢻⣿⣿⠟⡋⣷⣼⣿⣿⠁⠀⠀⠑⠢⡀⠀⠀⠀⠈⠲⠒⠤⠤⠀⠀⠴⠒⠉⠀⠐⠂⠀⠀⢠⠉⢂⡄⠀⣿⡆
⠀⠀⢸⣯⣿⣿⣿⡀⡀⣼⣧⣻⣿⣿⣿⣷⣿⣿⣛⠛⠒⠳⠦⠤⢤⣤⣠⣤⣶⡶⢦⠀⣷⢀⣤⠴⠒⠉⠈⠑⠒⢴⡦⠆⢾⡆⢺⣗⣪⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣤⡀⠀⠀⠀⠈⠻⣿⣿⡇⢾⣾⣿⣿⣧⣆⣠⡄⣀⣀⡄⣼⣷⣧⣾⣧⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠻⠆⠬⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢒⢺⣿⠒⡂⣿⣿⡿⣿⠭⢿⣿⠀⢸⣿⡟⣿⢻⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣼⣿⣤⣅⣿⣿⡇⡟⠥⠿⢿⠂⢸⡿⠒⠛⢸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠟
⠀⠀⠀⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣤⣼⢧⣤⢤⣘⣛⣻⣿⡿⠿⠿⣿⣿⣿⣿⣿⣭⣭⣭⣁⡀
⠀⠀⠀⠀⢹⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣉⡙⣛⠛⣛⣟⠳⢷⣤⣍⣉⣭⣭⣽⠿⠿⠟⠛⠛⠁⠠⡤⠤⡦⣀⠛⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣆⣽⠿⣛⣭⡛⠻⣿⣿⣿⣙⣛⣻⣿⣯⣍⣤⣁⣐⡒⠾⣉⡉⠓⠒⠲⠾⠤⣀⣤⣤⠤⠼⠛⠊⠉
⠀⠀⠀⠀⠀⠘⠇⠘⣿⣿⣿⣿⣿⣽⣿⣇⣾⣿⣿⣷⣄⢛⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣟⡛⢿⣟⣛⠛⢶⣤⡤⠶⣯⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⣴⡶⢹⡇⢻⣿⣷⣶⣿⣿⣿⣤⣷⣤⡀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠔⠋⠵⠛⠉⠽⢿⠿⢿⣿⣿⣿⣿⣿⣿⢧⣿⣶⣶⣿⡿⠯⠍⠉⠈⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠚⠋⠉⠉⠙⠈⠛⠛⠒



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡀⣰⡿⠉⢠⣽⠿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣋⣴⣾⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⢷⢿⡅⢠⡿⡛⠀⢈⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡿⠛⢻⣿⣿⣗⣶⣶⣏⢾⡷⠶⠋⠀⠀⠀⠀⠀⣠⣤⣴⣶⠖⠀⠀⢀⣬⡶⢶⡌⢀⡠⣄⡀⠄⣠⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢋⡴⠖⢒⣛⣿⣿⣿⣯⣿⡭⢀⠀⠀⠀⠀⠀⠰⠚⠚⠉⠋⡵⠀⠀⠘⠋⣿⠀⢨⣿⡈⠓⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⡎⢿⣿⣿⣿⣿⣿⣿⠿⣆⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠃⠀⢸⠈⢷⠀⠀⠀⠀⠀⠀⠀⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣵⠛⠁⣿⠋⡿⠉⢿⡇⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠘⢀⡄⠀⠀⠰⠀⡜⠀⠈⢇⠀⠀⣠⠀⠀⠀⣷⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⢰⣿⡴⠁⠀⠈⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢨⡇⠀⠀⠘⡀⠀⠁⠈⠀⢸⠃⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⠃⠀⠀⠀⠘⠛⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣧⠀⢘⠀⠃⡞⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⠀⢰⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣼
⠀⠀⠀⠀⡄⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢿⡀⠀⡏⠀⠀⠤
⠀⠀⠀⡠⣏⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠖⡾⢳⡦⠴⣶⣟⣇⠠⡇
⠀⠐⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣊⢚⣉⢊⠰⢓⣣⠔⢪⣉⣼⣷⢸⣇⡀
⢀⣈⣹⣯⣿⣷⣷⣦⠄⣀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡷⠚⠑⠣⣏⡉⠄⠛⢅⡒⢂⣰⣾⣿⣿⣿⣷⣆⡤⠄
⠀⢨⣽⣷⣿⣟⣿⣟⣗⣺⣿⣿⣿⣿⣷⣄⡄⢠⡏⠏⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣾⣖⣬⣥⣬⣤⣞⣋⣭⣿⣿⣷⣿⣿⣿⣿⣿⡶⠖⠂
⠀⢸⣿⣿⡟⠀⠈⠉⠩⣤⣿⣿⣿⣟⣿⡏⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣙⢛⣷⡈⠷⣦
⠀⣀⣿⠟⠤⡴⣶⣶⣾⡿⢿⠉⠽⢿⠣⠀⠀⠸⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠤⠰⠶⠌⣩⣿⣿⣿⣿⠿⢿⣟⢋⣿⣿⠿⠽⠿⠿⠿⠙⣷⠀⠐⢦
⣀⡵⠋⠀⠀⠀⠐⠚⠋⠤⣗⠐⠀⠠⡶⠈⠁⢸⢀⡇⡧⠀⠀⠀⠀⢀⣀⣀⣠⡴⢴⠖⣛⣛⣛⡿⢶⣶⣶⡍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠳
⠈⠁⠀⠀⠀⠀⠀⠒⠂⠐⠒⠘⠃⠔⠦⠤⠀⢸⢾⠇⡇⠀⠀⠉⠉⠉⠁⠈⠛⠛⠛⠻⠛⠻⠿⠭⠞⠛⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣟⣩⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠌⢅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⣀⢰⣄⠀⣿⡆⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢰⠂⢀⡴
⠀⠀⠀⠀⠀⠛⠷⣿⣧⣿⣧⣾⣯⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣆⣼⣧⣿⢁⣠⠴⠒
⠀⠀⠙⠛⠶⢶⣤⣿⣿⣿⣿⣿⣥⡶⢃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣦⣽⣿⣿⣿⣾⣿⣵⠶⠖⠛⠁
⠀⢀⣒⣚⣒⣒⣶⣿⣿⣿⣿⣿⣿⣾⣭⣥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⣾⣿⣿⣿⣿⣿⣧⣖⣒⠛⠒⠂
⠀⠈⠁⠀⢀⣠⠰⣛⣻⣿⣿⣟⠻⣎⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⢈⠺⢛⣿⣿⣿⣿⣿⣉⣙⠒
⠀⠀⠀⡴⠛⠁⠀⠔⣿⣿⣿⡧⠄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠹⢿⣿⣿⠁⠉⠋⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣷
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠘⠛⠉⢉⣭⠍⣀⣀⣰⠀⡤⣤⡬⣬⡖⢊⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠹⣶⢷⠀⣠⠄⣀
⠀⡤⣴⣂⢀⡾⠫⡤⢤⣶⠶⢦⣴⣦⡾⠋⢳⣾⣿⣷⣮⣿⣿⣿⣯⣡⣿⣼⣽⣦⠦⠴⢾⣶⣶⣾⣬⣌⢀⣤⣴⣿⣷⡄⠛⢉⠂⢀⣒⣤⣄
⣤⣬⣭⣤⣤⣤⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣭⣭⣭⣭⣭⣭⣥⣤⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣭⣥
⣿⣿⣩⣝⣫⣍⣉⣏⣩⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠅⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⢠⠝⠐⠋⠉⠀⠦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⡁⠤
⠀⠀⡀⠂⠀⠂⠐⠂⠀⠀⣿⡄⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⠄
⠀⠈⡄⠀⢀⠒⠀⠀⠀⠀⠡⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡁⠀⠀⠀⠈⠀⠀⠀⡴⠉⢀
⠀⠀⣀⠀⢀⠀⠗⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠂⠀⠠⠀⠀⠀⢠⣿⡐⠂⡀
⠀⠀⠟⠀⠈⠙⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⠀⠀⠀⡇⠀⠀⢀⠎
⠀⠀⢰⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⡎
⠀⠀⠸⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣷⢀⣸⣤⣤⣤⣶⡦
⢀⣠⡄⣧⡠⣤⣀⣿⠃⢄⡠⠤⢤⣤⣤⣤⣤⣤⢤⡤⣤⣀⠤⣤⣤⠤⡤⣤⣤⣤⣤⠤⠄⡀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⣠⡀
⢀⢎⣇⣿⣃⠌⡀⣿⡆⠀⠀⠀⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠦⠒⣠⡤⠀⠀⠀⠀⠀⠒⣂
⣏⣾⣿⣿⣿⣿⣿⣿⠁⣷⠅⣀⡀⠀⠐⠀⠀⠙⠷⠶⠦⢤⣤⣿⣿⣿⣾⣦⠰⠾⠶⠿⠿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣧⣪⣮⣜⣿⣿⣿⡿⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠿⠛⠻⠟⠉⠀⣿⡉⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡆
⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠔
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡈⣀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠸⠀⡀⣷⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡔⠘⣣⠀⠄⠀⢹⠐⠐⢿⠢⣁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢱⠀⣤⣦⣠⠀⠀⠐⠐⠟⠿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠄⠀⠂⠛⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠁⠀⠀⠀⠀⠀⣀⠀⠄⠀⣠⠀⢀
⠀⠤⠤⣤⣤⣤⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠋⣤⠼⣿⢘⡹⠿⡄⠐⡿⠇⣈⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠄⠚⠘⢷⠀⠱⡶⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⠃⠀⠰⠰⠅
⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠒



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣫⣌⣩⣯⣻⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⢶
⠀⠀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠒⠀⠀⠀⠀⠐⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠂
⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡠⠄⠤⠤⢀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡀⠐⠀⠄⣠⠀⠰⠆⠚⠓⠃
⠀⠀⠴⣄⡦⠀⠉⠉⣸⣯⣄⣠⣤⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⢀⣠⢠⣆⡠⣽⣗⠒⠓⠣⢖⠴⠦⢀⠈⠂
⠀⠀⣜⠾⠁⠀⡄⠺⠗⢻⡈⢷⡏⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠟⠙⢋⠝⣟⢶⢋⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠏⠁⠀⠉⠂⠀⠀⡸⡏⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢛⠏⠀⣸⡯⢹⡃⠐
⠀⠀⠀⠀⠀⠸⠀⠀⠀⡛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠀⠀⡘⠀⠀⣼⠋⠊⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠦⠶⠒⠞⠀⠀⡁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠀⠆⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⣠⠀⢰⡀⠀⠀⠀⠐⠐⠂⠐⡂
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠈⠀⠀⠀⠀⠀⠑⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣧⣤⢿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣿⣿⣿⣿⣿⣿⣿⡞⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠛⠛⠛⠿⠛⠛⠿⡿⠿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠈⠁⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣂⣠⣄⣤⣤⣶⣤⣤⣄⣀⣐⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⡟⠉⢙⡋⠉⠀⠈⣛⢉⡋⠀⢉⡉⣻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣛⣿⣿⣿⣉⣙⣿⣿⣿⣿⣿⣟⣉⣙⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢐⣿⣿⣿⠟⠉⠀⠀⠀⠉⠹⠿⣿⣿⣿⣯⣄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣴⣾⣿⣿⣤⣤⣤⣤⣄⢠⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣤⣤⣈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⡧⢹⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⡟⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢺⣿⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣄⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠰⠿⣿⣿⠛⠃⠀⠘⠛⠛⣿⣿⣿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⠆⠀⠀⠀⠴⣾⣿⣿⣿⡆⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⣿⠆⠀⠀⠀⠀⠀⣤⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⣿⣿⣧⠀⠀⠀⢀⣀⣨⣿⣿⣿⣭⣄⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⡀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣻⣿⣿⣿⠟⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⡷⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣿⣿⣿⡗⠂⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣉⣿⣋⡉⠀⠀⠀⠈⠉⠹⣿⣿⠟⣋⡉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣯⡄⠀⠀⠀⠀⠀⠠⣤⣤⣤⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢠⣬⣭⡅⠀⠀⠀⠀⠀⠀⠤⢶⣶⣶⣶⠤⠄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣭⠅⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡶⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣶⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣬⣭⣤⣤⣦⣤⣤⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⣿⣿⣿⣿⣿⠯⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣿⣿⣿⣿⣷⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣙⠻⠛⠉⠁⠀⠀⠈⠉⠛⠛⢛⣛⣛⣻⣭⣭⣭⣍⡉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠚⣋⠿⠖⠂⠀⠀⠀⠀⠀⠀⣀⣬⣭⣽⣿⣿⡶⠦⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠻⠿⠦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣭⣽⣿⣿⣷⠦⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠛⠷⠂⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠇⣶⣶⣿⣶⣷⣤⣄⠀⠀⠀⠀⣀⣀⣀⣀⣒⣒⣲⣶⣦⣤⣴⣤⣤⣤⡄⢸⣷
⠀⠀⠀⠀⠀⠀⢀⠏⢸⣿⣿⣿⣿⣿⣿⣧⠠⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠈⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠰⢿⢀⣿⣿⣿⣿⣿⣿⡟⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⣿⣧⢀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢻⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣤⣀⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣔⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⣀⠤⣠⣀⢀⠀⠀⠀⠀⣠⣴⠀⢤⣄⣀
⠀⠀⣘⣷⡄⢰⠉⣠⠒⠚⠢⠀⠔⠒⠢⡀⣴⣿⣯⣼⡁⠀⠀⠀⠀⢰⣿⣾⡛⠟⢷⡀⠀⠀⢰⡇⠸⣆⠀⡽⠿⢷
⠀⣾⣛⢧⣿⠜⣲⠧⠀⢀⣐⠆⠆⠀⠤⡇⢿⣯⣿⣿⢁⣤⠀⠀⢰⡸⣿⣽⣇⣉⣬⣷⠀⠀⢺⣿⣦⡈⠉⣳⣾⣿
⠀⢸⣿⡿⡟⠀⠙⣷⣾⣴⠋⠀⢴⣶⡶⠁⠘⣿⣳⡟⢛⣉⣀⣀⣸⠀⠻⣿⣯⣿⣼⠏⠀⠀⢸⣿⣿⣻⣷⣿⣿⡟
⠀⠘⣿⣿⠃⠀⠀⢿⣻⡍⠀⠀⠘⡝⠁⠀⠀⢿⣿⠇⠀⢿⣭⣼⠃⠀⠀⣠⣿⢹⣀⠀⠀⠀⠀⣇⠀⠈⡉⠈⣿
⠀⠀⢹⡇⠀⠀⠀⠈⣭⠃⢀⠀⠀⠑⠀⠀⠀⢸⣻⠀⠀⢸⣗⣿⠀⠀⠀⠉⠁⠈⢉⣴⠖⠂⠀⠻⣄⡀⣀⣠⡿
⠀⠀⢈⠁⠀⠀⣀⣀⡙⠀⣿⢯⣿⠀⡞⢻⡆⢀⣭⣤⣀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣨⣄⠀⠈⠉
⠀⠀⠈⠀⡄⢠⣿⣿⣽⡄⣿⣾⡟⠀⡃⢸⡇⣾⡏⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⢦⣤⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⢡⢸⣿⣿⡇⡁⣿⣽⣿⠀⡆⢸⡇⣿⡇⢈⣿⣿⠀⠀⠀⠀⠀⠀⢙⣇⣤⣶⣭⣁⡄
⠰⡟⠀⢬⣿⣾⣿⣿⡇⡅⣿⣿⣿⠀⡇⢸⡇⠻⣧⣠⣿⠏⢀⣀⣠⢤⣄⠀⢈⢻⣿⣿⣯⣿⠧⠄⣶⠀⠀⡀⡴⡄
⠀⠉⠉⠋⠉⠘⠻⠿⠓⠀⠙⠛⡏⠀⠳⠾⠃⠀⠀⠈⠀⣼⣿⣥⣿⣿⣿⠢⣀⣼⢀⣀⣘⣿⠀⣦⢸⣦⣶⣶⣶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠇⠀⠈⣻⠿⠿⣿⠁⠀⢸⣯⣻⣸⣟⢻⡬⡀
⠀⠊⠁⠉⢳⠀⢠⠖⠒⢤⡀⡠⠒⠒⢦⢀⡴⠒⠒⢆⢹⣶⣾⣿⣬⣿⡆⠀⠀⠉⡀⣠⠃⠀⠀⠘⣿⣷⠿⣿⢿⣿⠇
⠀⣷⠀⣀⣼⠆⣗⠀⠀⢰⠇⣷⠀⢀⣸⠘⣆⠀⣠⣾⠰⣟⠀⠀⢹⣯⠁⠀⠀⢞⡓⣻⡄⠀⠀⠀⠈⣿⢿⢻⣿⡇
⠀⠈⠉⠉⠉⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠂⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠑⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢂⡕⠉⠉⠑⡤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⢀⠤⠂⠁⠀⠀⠀⡠⠁⠸⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠐⠈⠀⠀⢀⡀⠄⠐⠈⠠⠂⢀⠥⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⠀⠠⠶⠠⠬⠄⠒⠀⠈⢉⠰⠂⠁⢀⢆⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠤⠂⠁⠀⠀⢀⠤⠐⠈⠀⢀⠠⠐⠁⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⢁⠀⠠⠐⠈⢁⠀⠠⠐⠂⠁⠀⠀⢀⠴⠄⠒⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⡀⠄⠂⠁⠀⠀⠀⣀⡀⠤⠀⠀⠁⠀⠀⡠⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠔⠉⠀⢠⣊⠀⠀⢀⠀⣀⢀⡄⠀⠁⠀⠀⠀⠄⠀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠠⡤⠀⢄⣄⠀⣀⡀⠀⠄⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⣀⠈⠙⠢⢀⡀⠀⠠⠒⠂⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠲⣀⠉⠉⠑⡠⠤⠊⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⢤⠄⠑⠒⠄⢀⣀⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⣈⠰⠤⢄⠈⠈⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠈⠑⠠⣀⡀⠠⠈⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠑⠌⡉⠀⠉⡀⠖⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠛⠃⠀⠒⠂⠉
⣿⣿⣻⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣯⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢉⣭⣿⣿⣿⣿⣭⡠⠀⢀⣲⣶⣷⣖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⠇⠡⣧⠀⠈⠹⡆⠈⣽⠟⡀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠃⢠⠀⠀⠀⠰⠁⠀⡇⠀⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡇⠐⢹⠟⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣥⢿⠟⢯⡍⠉⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣸⣧⡤⣧⣤⣀⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠙⣶⣤⣰⣴⣶⣦⣼⣟⣷⡝⢹⣿⣿⣷⣿⣽⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢶⣾⣿⡾⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠙⠒⠐⠲⠀⠤⢤⡄⠀⢈⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠒⠒⠒⠊⠁⠀⢀⣀⡤⠶⠾⠁⠒⠀⠀⣀⣠⡤⠔⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⢀⣂⣐⣒⣲⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣲⣶⡶⠾⠟⠛⠉⠀⣤⢀⠀⠀⠀⠘⠄⠶⠄
⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤⠭⠶⠶⠚⠛⡛⠛⠛⠭⠭⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠖⢶⠀⠀⠀⠢
⠀⠀⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣀⣒⡶⢖⡻⠿⠻⠟⠛⠋⠀⠀⡾⠁⠀⠀⢀⠠⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠟⠛⢋⣉⣉⣀⣠⣠⣤⣤⣄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⢋⡅⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠤⠄⠀⠉⠉⠛⠛⠒⣚⣛⣉⣉⣡⡴⡶⠟⠟⠟⠛⠉⠉⠛⠉⠏⠋⠉⢈⠛⢛⣛⡿⠟⠛⠓⠛⠓⣛⡿⠍⠕⠋⠓⠂⠾⢿⠤⠔⠒⠉⠁⠀⠀⠀⢣
⠒⠒⠒⠂⠊⠉⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⠚⡉⠭⠖⠛⡉⠄⠐⠈⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣷⢤⡔⣤⣟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠉⣁⣠⠤⠐⠈⠁⠀⠀⢀⣀⠤⠔⢀⠐⣯⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⢂⡐⣦⣦⠦⢙⡿⠂⠙⢛⡓⠂
⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠤⢄⣀⣤⣤⣤⠴⠖⠛⠉⠀⠀⣀⣤⡴⠞⠋⠉⠀⠠⠂⠁⠀⠀⠄⠠⠀⠀⠄⠀⠀⠶⢁⡼⠛⢛⣯⠉⠘⠿⠇⠠⠿⠿⠣⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⠻⣌⠀⠀⢀⠰⣾⠃⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣛⣛⣯⣟⣋⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣁⣤⣄⢠⣦⣐⡎⠀⠀⣴⣯⣬⠁⠀⠈⣧⠀⠀⣿⣿⣟⣭⣭⣿⡿⣻⡦
⠀⠀⢀⡴⠖⠛⠲⣤⡀⢛⣿⡏⠙⢉⣹⡿⠁⡴⠏⠁⠀⣀⡵⠶⠴⢿⣀⠀⢾⣿⣶⣤⣿⣶⣾⡉⠁⠀⢀⡿⣦⣀
⠀⢠⡏⠀⠀⠁⠀⢈⣷⠈⡿⣿⡿⣿⣿⠇⢰⡝⠂⠀⣼⠇⠀⠀⠀⠀⢈⡄⠸⣯⣏⣻⡟⢋⣿⡏⠀⠰⣏⣆⢻⣿⢳⡀
⠀⠈⢏⠀⠀⠀⣠⣬⣟⠀⢹⣿⡷⣾⢿⠀⠈⢹⢲⡴⣯⡀⢀⠀⠀⠀⠠⣾⠀⢹⣿⣟⣛⣿⡿⠀⠴⣴⠿⠼⣿⢘⣿⣧⡄
⠀⠀⢋⡀⢀⢠⣀⢢⡼⠀⠸⣿⡷⢮⣿⠀⠀⠺⣼⣗⠀⠣⣠⡀⠤⠤⢶⡋⠀⠀⣿⢹⣿⣿⡇⠀⠼⣯⣾⣱⠚⣜⣿⣹⠃
⠀⠀⢠⡾⣷⡾⡿⡾⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠈⢿⣿⣶⣶⣦⣴⡻⠉⠀⠀⠀⢽⢾⣤⣿⠃⠀⠀⢻⣿⣿⣾⣛⣿⡿
⠀⠀⠀⠜⣧⣻⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣧⠃⠀⠀⠀⠀⢸⣿⣩⣿⠀⠀⠀⠘⣟⣿⣹⣯⣽⠇
⠀⠀⠀⢸⣶⢋⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣖⡏⠀⠀⠀⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⢻⣿⣙⣯⣿
⠀⠀⠀⠈⡟⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣽⣩⠁⠀⠀⠀⠀⠀⠀⠹⢿⠇⠀⠀⠀⠀⠈⣿⡟⣿⠇
⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⡀⠀⠀⣄
⠀⠀⠀⢰⠂⠀⠀⠀⠀⠐⣴⠀⠀⠀⠁
⠀⠀⠀⠈⡇⠀⣀⣀⠀⠀⠨⡌⠙⢷⡁⢂⣠⠆
⠀⠀⠀⠀⡅⠀⠁⠈⢁⡀⠀⠀⢀⡈⣻⡗⢧⣄⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠁⡇⠀⡀⠩⡁⢺⠛⣦⣷⢶⣗⢠⣄⣠
⠀⠀⠀⢰⡇⠀⠀⠀⢠⢨⣷⣏⠈⠀⢈⣈⣽⠛⢂⡐⣻⠿⢷⠂
⠀⠀⠀⢸⡇⠀⠀⠀⣴⠛⠈⠁⠀⠀⡜⠛⠇⠈⠀⠀⠁⠆
⠀⠀⠀⣸⠀⠀⠀⠀⡟⠀⠰⠀⠀⢠⠁⠀⠀⠇⠀⠀⡸
⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⡬⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⣀⣀⣀⡀
⠀⠀⢸⡏⠀⠀⠀⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠈⠁
⠀⠀⣾⠃⣀⠀⠀⠀⠃
⠛⢲⡿⠀⠗
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠃
⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⢛⣥⣶⣵⡯⢒⣡⡤⠞⣁⣴⢞⣾⢿⣿⣿⢿⣾⡷⡟⠂⣬⠅⠐⠒⢂⠉⢩⣅⣒⢦⣤⡳⠾⣅⣀⡀⠛⠛⠛⠛⠷⢯⣷⣶⠦⣤⠆
⣿⣯⣾⣿⡯⠖⡩⣥⡶⢟⣻⠝⣫⠴⡿⢋⣾⣿⢯⣒⠨⠥⣄⣒⡒⠮⠭⢛⣓⠬⠙⣃⠤⠑⣀⠤⢉⣉⡉⢉⠛⡉⠰⠒⡬⢙⠳⢦⡋
⣿⣿⡿⣋⣄⣵⣿⡵⠞⣫⡴⢚⣥⢞⣵⣿⣿⣿⢿⣭⣍⠁⠠⠤⠶⠒⠋⢁⣤⠔⢋⡡⠂⣉⠴⢊⡥⠀⠀⠀⠀⠐⠒⠚⣤⣥⡔⠀⣉
⣯⣻⡞⣱⣿⣋⡥⣖⣯⠗⢚⣩⠶⢋⣵⣿⣋⠩⠤⠤⠐⠒⠒⠒⠒⠒⣉⠥⠔⣊⠥⣒⠭⠒⣉⠤⠒⣒⡀⠍⠁⡈⠉⠉⠄⠘⣻⣶⣄
⣿⡿⣰⣿⣿⡿⢛⣥⠶⢚⣉⣤⣶⣿⡿⠍⠉⠀⠐⠀⠀⠒⠒⠛⢋⣉⡠⠶⣛⠵⢚⣡⠖⢋⣡⣴⠿⠏⣉⣃⣤⣤⣤⣤⣀⡀⠤⢌⡙
⣿⢁⣿⣿⣯⡞⣉⣴⣾⣿⡿⠟⣛⣡⠖⠂⠬⣭⣉⣉⣉⣩⣭⣭⠴⠶⢚⣩⠴⢞⣩⣴⠾⢛⣩⣴⡾⠿⠿⠿⣿⣯⣁⠒⠭⠛⠷⠶⣤
⡟⣼⣿⣿⠏⣴⣿⣿⡷⠤⣀⡛⠩⢄⠛⠥⣒⠀⠤⠤⠤⠤⠤⠄⠒⣊⡬⢕⡶⠟⢋⣠⣾⣿⣿⣷⡶⣦⣖⣂⠤⢈⠉⠟⡶⠥⣦⡅⠂
⣳⢹⣿⣿⢠⣿⠟⠁⠀⠀⠀⠉⠲⣄⠙⠢⢤⡈⡉⠀⠀⣀⣉⣩⡽⠶⠛⣉⣤⣾⣿⣿⣿⣟⣻⣭⣭⣄⡐⢉⣙⠻⢾⣧⣤⡁⠀⠹⣿
⣟⢸⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⢈⣉⣉⣉⣉⣠⠤⠤⠚⠛⢿⡻⣿⢿⣿⣿⣉⠥⠼⠛⣙⡛⠷⣥⣛⠱⣊⢝⡻⡳⡢⠈
⡇⣼⡏⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣴⣫⣭⣙⠒⢦⢄⣀⠐⠦⣙⠷⣄⠰⣍⢦⢈⢶
⢱⣟⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣳⢖⡩⢟⡱⢎⣷⣌⠳⣄⠢⡑⢏
⣯⢿⡌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣭⠔⡣⠄⡙⢷⣌⡣⣈
⣿⣍⢷⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡄⠀⠰⡿⠿⡿⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢧⣤⡐⠈⠻⣿⣷
⣿⠋⣼⣾⠀⠀⠀⠀⠀⠀⣄⠀⠀⢾⠁⡀⠁⠄⢰⣷⣶⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡖⠀⡈⢟
⠏⢼⣿⠃⠀⠀⠀⠀⠀⠀⠈⡀⠀⣻⠃⠐⠀⠶⣾⡟⠿⡿⢿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠄⠉
⢎⣾⠟⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠋⠁⠀⠀⢉⡄⠀⠀⠀⠸⠁⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀
⣾⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠈⡇⠀⠀⠀⢀⠀⠀⡀⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠸⠆⠨⠃⡌⠀⡀⠆⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣿⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢀⡈⠀⠀⣶⠀⠀⠀⠀⠀⠂⠀⡇⢀⡀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡏⣼⠀⢀⣀⡟⢀⡀⠀⠀⠀⠹⡆⢱⡈⢀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡇⣿⢻⣾⢿⡿⢿⣿⣧⡄⠀⣴⠁⢸⡇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣧⣿⣾⡿⠞⢛⠛⠋⠿⠿⣿⣿⣧⣼⣇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡌
⣿⢸⣧⢸⠀⠀⠀⠀⠀⠀⠀⣬⠿⡿⠿⠟⠋⠀⠀⠉⣤⠀⠀⠀⠈⢿⡟⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠽⠁
⢻⠇⣹⡌⡄⠀⠀⠀⣀⡐⠻⠟⠀⠀⠛⠋⠀⣤⡀⠀⠈⠁⠀⠀⠠⠀⠀⠉⠉⠉⣹⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⠁⠀⠀⢔⣤
⡘⣤⢙⣧⠁⡀⠀⠀⠹⠿⢿⣷⣶⣾⣶⣿⣶⣾⣷⣶⣶⣦⣤⣤⣄⢀⣤⣬⣥⣤⣯⣥⣼⣿⣿⡿⠀⠀⠀⢀⣤⠊⡱⣓⣤⠖⠞⠉⠑
⣷⢀⠜⣻⡆⢡⠀⠀⠀⠀⠀⠙⣿⣿⣯⡿⣿⢿⣿⣿⠿⠿⣏⠉⣿⣾⣿⣿⣇⣹⢻⣏⣿⡿⠿⠁⠀⠀⣠⠪⣡⣾⡽⢋⠥⠒⡠⠔⠊
⣟⠀⠐⢹⣿⡀⢣⠀⠀⠀⠀⠀⠙⠿⡛⣷⢿⣿⣷⢹⡷⠾⣿⣿⣿⠿⣿⣿⣟⣿⠞⠋⢹⠀⠀⠀⢀⡴⣡⡞⠉⠉⠀⠀⠀⠈⠐⣠⣴
⣼⡆⠠⢁⢻⣿⡄⠳⡄⠀⠀⠀⠀⠈⠻⢾⣿⣾⣟⣿⣿⣾⣿⣯⣫⣾⢻⣿⣿⠁⠀⠀⠈⠀⢀⡴⢋⣴⠯⠗⠀⠀⣄⠔⢀⡀⠾⢋⡼
⡠⠶⠀⢂⠆⡹⢟⢦⠘⢆⠀⠀⠀⠀⠀⢀⡈⣻⣿⣿⣿⡟⢻⣿⣿⣿⣿⠇⣿⠀⠀⠀⢀⠴⡉⣰⠟⢁⣤⠆⡀⠀⣠⠒⠁⢀⡴⠋⠰
⣧⠞⢋⠌⠄⢱⣏⢾⡷⡌⢆⠀⠀⠀⠀⡟⠉⣿⢻⡿⠈⣧⣻⠙⣿⡿⠃⠀⠉⠀⡠⢚⡵⠊⡴⢋⡴⢛⡱⢊⣤⠊⠔⢁⠴⠋⠈⠁⠈
⠶⢛⡁⠄⠔⡀⢫⣆⠱⣞⡎⢦⡀⠀⠀⠃⠀⣯⠘⣿⠀⠛⡟⠀⣿⠀⠀⠀⣴⡾⠶⡋⢀⢄⠰⣫⡜⣡⡞⠻⢁⣤⠂⠁⠀⠀⠄⡠⢊
⡔⠙⢷⣈⢆⠱⣤⠻⣦⠈⢾⣦⠑⡄⠀⠀⠀⠋⠀⢿⠀⠀⠁⠀⠁⣠⣶⠿⡁⠄⢊⢀⡷⢋⡴⢋⣾⠟⠁⠀⢊⠀⠀⠀⢠⣎⠚⣠⢞
⠴⡀⠌⢿⡈⠵⡹⣣⠙⣧⠈⢿⣡⠘⡄⠀⠀⠀⠿⢸⠀⢀⣠⡴⠞⣩⠧⠀⠀⠢⠁⢈⡴⠋⣠⠞⠁⠀⠒⠁⡀⠀⣠⡾⠁⠀⠚⣡⡛
⠃⡥⠈⢊⣷⠀⣴⡹⣧⡘⢷⡈⢧⢣⠘⠆⠀⠀⣀⠌⠚⡉⢉⡤⠚⠁⠀⠀⢀⣤⡶⠋⠁⡐⠁⢀⢆⠀⠀⠀⣠⡾⠋⡠⠀⣰⣺⠋⠵
⢦⡹⣏⢄⠱⣿⡌⢸⣥⠻⣎⣷⣈⢆⠠⠘⣄⣼⠃⣠⠂⠔⠡⠀⠁⠐⡡⠞⡩⢊⠔⣠⠟⢀⢤⡀⠃⢀⣠⡾⠋⢄⣡⣶⠿⠊⠁⡠⢂
⠨⢷⡜⢮⡱⣌⠻⣦⡙⢷⡜⢿⣯⢺⣆⠰⢹⠧⣄⠄⢂⠀⢀⡢⢉⣀⠄⡣⢀⣤⠞⠁⢀⣮⢛⠀⣠⡾⢋⣤⡾⡛⠍⠡⡐⠄⢊⣔⡡
⢸⣧⣟⣦⡻⣎⠳⣌⢷⣄⠹⣮⣹⣧⡹⣷⣇⣿⠚⠠⡑⠀⢊⡴⠋⠑⣠⡴⢋⡁⢀⣴⡿⠑⣡⣾⣿⣼⠿⢋⣡⠶⠋⣁⢠⣼⠾⣌⡴
⠀⠿⣿⣿⢷⣌⢳⣌⠳⣝⢦⣄⠻⡿⣿⣎⣿⣿⣄⢁⣴⣶⠏⢦⡵⠚⠁⠔⡨⢾⡿⠋⣠⣾⢿⣿⡟⠥⣒⣩⣠⠶⢙⣪⠭⠖⠃⠁
⣶⣷⣾⣿⣷⣿⣷⣿⣷⣾⣷⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣿⣶⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠋⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠰⠌⠡⠈⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠃⠀⠀⠀⡀⠤⠖⠀⠩⡯⡄⢰⠦⠄⠌⠄⠐⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠐⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡈⠀⣸⡀⠠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣇⠙⠀⠀⠂⠈⢨⢲⢑⣁⣀⠀⠀⠡⢠⢪⠀⠀⡀⠌⠿⠗⠠⠨⣗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠘⠡⣿⢄⡁⠀⠀⠈⠉⢹⣘⠋⢁⣀⡄⠀⠀⠴⠀⢸⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⡿⠻⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⢀
⢀⡄⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠠⠀⠀⣀⠀⠀⠀⣸⠀⠀⢠⣅⠀⠁⠀⣀⣴⡀
⠀⠀⠀⠈⠀⠂⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⡿⠀⢼⢷⠀⡄⢛⠟⠲⠿⠛⠛⣝⢀⠆⡽⠽⢻⡾
⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠠

⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢
⠀⠀⠀⠀⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠪⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⣄⠀⠀⠀⢀⡀
⠀⠘⠷⣄⠂⠈⢽⣇⡕⠏⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠲⠄
⠀⢠⣄⠙⢻⡀⠱⢃⣴⣤⣧⣦⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⣀⡀
⠀⠀⠨⢧⠈⢥⣠⢀⣌⡀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⣣⠜⣉⡁⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡜⢲⠟⠛⠷⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⡆⠃⢀⢠⠇⡄⢠⠃⡄⢀⠄⠀⠀⠀⠀⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡰⣌⢆⠣⢱⣠⣘⣘⡰⠡⢃⠎⡰⢋⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⢀
⠀⠀⠀⠠⠔⠀⢀⠀⠈⣇⠀⠀⠀⠐⠦⣄⡐⠦⣀⠦⡑⢌⠾⠋⠉⠀⠀⠀⠉⠓⢮⢊⠴⣋⠴⠊⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⢈⠳⠀⡿⠒⠒⠒⠠⠤⣀⣉⠓⠬⡑⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠵⢚⣁
⠀⠀⠀⠀⠁⠀⠈⠂⢧⢈⡉⠓⠶⠆⠀⠠⠬⢭⡑⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠭⠤⠒⠒⠉⠁
⠀⠀⠀⠛⠀⠀⠀⠨⠶⢦⡉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈
⠀⠀⠐⠂⠀⠈

⠀⠀⡀⡀
⣤⣤⣉⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢴⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⢿⢎⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠀⠁
⠀⠀⡀⠀⣄⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠈
⠀⠀⠸⠁⠟⠲⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⢲⡆⠀⠀⠀⠆
⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⠀⡲⣦⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠇
⠀⠀⠀⠐⠂⠀⠀⢀⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⢄
⠈⠁⠀⠒⠠⣌⠋⢠⠄⠀⠀⠀⠀⠐⠶⠶⣦⣶⠶⢶⡴⠶⠶⢶⣶⣶⣦⣴⡤⠶⠶⠶⠶⠖⠂⢄⡤⣄⠀⠤⠐⠛⠛
⠒⠃⠀⠀⠲⠍⠀⠐⠀⠐⢀⡓⣀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠙⠋⠩⠥⠤⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⣠⢶⣀⣀⡀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠴⠆
⠀⠁⠀⠄⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠠⠶⠦⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣄⣴⠞⠛⠂⠀⠀⠀⠀⠀⠀⠁⢐⠂⠀⠀⠀⠈⠁⢠⡤⠀⠀⠀⠀⠀⢫⠍
⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠀⠀⠀⢀⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠒⠓⠒⠒⠈⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠾
⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⢨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⡀⠀⠀⠀⠘⢢⣤⣠⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢄⡀⠀⠀⠠⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠹⠂⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠔⠉⠰⠄⠀⠀⠀⠀⠈⠓⢶⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠘⠁⠀⠀⢀⣰⠂⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠂⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣿⣿⢟⠿⡟⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣏⣩⣭⣭⣭⣭⡤⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣥⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢠⣿⡆⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⠛⠛⠛⠛⡷
⣼⣿⣿⣷⣷⣶⣧⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣴⣧⣬⣯⣯⣿⣟⣰⣧⣨⣿⣯⣏⢹⣿⣿⣧⣦⡆⣤⣼⣿⣶⣶⣶⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣄⠀⠀⣀⣀⡀⢀⠀⠀⣢⢀⡴⠤⠆
⠀⠀⠀⣀⢀⠀⠀⠤⠤⢴⡾⠚⠉⠀⠀⠈⠉⠢⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⢺⣧⣀⣡⣤⠆⣠⢀⡀⠀⠀⢄
⠀⠂⢁⣝⣾⠃⠀⠀⢠⣖⣻⡟⣴⠺⡏⢂⡀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡂⣯⣼⢷⣦⣿⣿⣄⣀⠄⠈⠃⠙⠉⠠
⠀⠀⢸⣼⠃⠀⡔⠄⠉⠛⢘⣧⡈⠻⠁⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢁⣀⣠⠊⢸⣝⣇⣴⡂⠀⠀⠀⠀⠈⠐⡄
⠀⠀⠘⠀⠀⠀⠈⠁⠀⠀⣼⢿⠀⡀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⢩⠃⠀⢰⣿⠂⣯⠄⠈
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⡒⠀⠀⢸⡋⠑⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠦⡼⠔⢲⠃⠀⠀⡃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⣈⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢤⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠀⠒⢺⣿⡄⠸⣦⢄⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡄⣆⠀⠈⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠌⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠁⠀⠀⠀⠀⠀⠀⠛⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀
⠀⣿⣦⣀⣀
⠀⡏⠀⠀⠿⡃⠘⠒⢠
⠀⣏⠉⠀⠀⠀⠲⡄⢹⣷⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢊
⠀⠀⠀⠁⠀⠀⠀⠘⢆⢹⣿⠁⣠⣤⡈⠙⣦⠄⢀⣴⡖⣀⡼⠛⢶⠖⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡻⠧⡴⠯⡤⠀⠘⠢⣆⣄⠀⠈⠃⠀⢤⣀⠀⠀⠀⠈⢋⠀⠀⠄⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠺⡄⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠘⢷⠀⣘
⠀⠀⠀⠀⠀⠀⢰⡤⢶⡄⠈⣉⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⠶⠏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠷⠠⠨⢴⣤⠀⠀⠀⠁⠀⠀⠒⠋⠀⠀⠀⠈⠉⡈⠉⠀⠒⠁
⠀⢀⡀⠀⠀⠀⠀⠳⠴⠓⠀⠉⠻⠛⠃⠀⠀⠀⠀⠞⠀⠀⠀⠒⠂
⠀⠀⠙⢳⢄⠀⠀⠀⠀⠀⠐⠒⠘⠉
⠀⠀⠀⢘⣗⠀⣰⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⡾⢸⡇⣸⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢏⣰⡇⡏⠀⢹⠉⢻⢒
⠀⠀⠀⠀⠀⢰⣒⡲⢖⠖⠂⠐⣨⣭⣤⣦⣤⣤⣀⠀⠐⠻⠞⢩⣆⣿⣀⣚⣲⣖⣆⡀
⠀⠀⠀⠀⠈⢿⣿⠻⠏⡟⠋⠉⠧⠤⠤⢸⡚⡛⢹⣿⣿⣿⢻⣿⣝⣏⠉⢹⣹⢻⣯⢁⡀
⠀⠀⠀⠀⠀⠀⣏⣶⣔⢃⣀⡠⡀⠈⠉⠀⠺⠿⠶⣿⣿⣿⣼⡟⠋⠉⠁⠈⠙⢛⠓⠃
⠀⠀⠀⠀⠀⠀⢻⠉⠉⠋⠉⠁⠓⣶⠆⠀⠐⡂⠀⣿⣸⣇⣿⣄⣸⣸⢠⡆⢸⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠪⠉⠁⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣗⣿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠁⠀⠉⢐⡤
⠀⠀⠀⠀⠀⠁⠀⣠⠤⠤⠤⡀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠂⢀⡠⠋⠁
⠀⠀⠀⠀⠀⠀⣞⠁⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠠⠀⠘⠀⠀⢀⡷⠋⠀⠉⠀⠀⠀⠉⠐⢤
⠀⠀⠀⠀⡀⠄⠘⠤⣑⣰⡤⠚⠀⡀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠠⠃⠀⠀⠀⠀⠀⣄⢀⠠⠄⠐⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠢⠀⠓⠂⠊⠓⠀⠠⠔⠳⢤⠤⠄⠒⠂⢰⣼⣆⣊⡠⠢⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠐⠀⠁⠀⡠⣎⣩⠅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡠⠓⠉⠀⠀⢸⠦⢐⣳⠀⠀⠀⠠⠤⠄⡰⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠤⠊⠀⠀⠀⠀⠀⠈⠹⡇⠀⣄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠦⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⠄⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⡀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠂⠀⠠⣀⡠⠰⠀⠂⢄⣠⠄⠠⢜⣶⡒⠈⢁⢀⡠⠄⡀⠀⢀⡠⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠾⡠⠀⠀⠀⠀⠀⠈⠱⡂⠀⠀⠈⠫⠀⠀⠀⣹⣁⠠⢘⣷⠀⠀⡀⠁⠛⠉⠀⠀⠘⡅⠀⠈⠐⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠀⢠⡔⠡⢅⡤
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠒⠈⠉⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠀⣀⣀⠤⡤⠄⠀⠤⠀⠚⠕⠂⠀⠘⠒⠄⠘⠁⠀⢀⡀
⠀⡀⠠⠖⠀⠐⠈⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⢀⡠⠖⠚⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⢢⡀
⠼⠤⠐⠀⠀⠤⠐⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠉⠛⠀⠂⠀⠐⠀⠠⠤⠄⠀⠠⠄⠀⠀⠀⠀⠤⠤⠉⠁⠄⠀⠤⠄⠀⠄⠐⠀⠹⠤
⠀⠈⠈⣀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠒⠒⠒⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠒⠂⠀⠌
⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠀⠂⠒⠂⠐⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢡⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⠀⠈⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⡄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠄⠀⡀⠂⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢀⠎⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢛⡰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠹
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠉⢠⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠎⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⢀⡴⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⠀⠒⠉⠀⠀⠀⣀⠤⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠙⢶⡶⠠⢤⡴⠶⠚⠉⠛⣇⠀⠈⡙⠁⠈⠳⢄⡠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⢠⡀⡴⠀⠐⠀⠀⠈⠳⡄⠀⠀⠀⢀⠌⠁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠀⠘⡀⠳⡀⠀⠀⣠⠂⠈⠂⠀⡀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⢨⡇⠀⠀⠘⢠⠜⠁⠀⠀⢀⡜⠁⢄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠐⠄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠞⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜⠂⠀⠀⠀⠀⠉⠰⣄⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⠀⠆⠀⠀⠀⠀⣀⠝⠂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢀⡰⠊⠀⠀⠀⠀⣀⠞⠁⠀⢠⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠑⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠒⢆⠀⠀⢀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠈⡲⠊⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠈⠀⠀⠈⠐⠞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠠⢀⢀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡠⠉⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠶⠈⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠖⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠁

⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠟⡟⠓⡄⢺⠟⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠘⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣵⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡁⠀⠛⢀⡀⠩⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⠦⠴⠤⠴⠶⠖⠒⠚⠉⠠⢠⣀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠚⠋⣁⠃⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣒⣒⠛⠭⠷⠶⠚⠛⠛⠛⢛⣻⠶⠶⠶⠲⠖⠚⠋⠽⠆⡀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⠈⠉⠀⢀⡀⠀⠠⠖⠁⠀⠀⢀⣠⣠⣤⣽⠟⢛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠋⠉⠁⠠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠏⠘⠀⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣦⣤⡄
⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣷⣶⣶⣿⣿⣷⡦⠀⠀⠀⠀⠀⠠⢾⣿⣆⠀⣿⠏⠀⣠⡄
⠀⠀⠀⠊⢫⣣⢣⣀⡜⣸⡽⠓⠀⠀⠀⠀⠀⢸⣯⣽⣿⠋⣠⡈⢻⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣈⣛⡷⣯⢴⣿⣿⣧
⠀⠀⠀⠰⠋⠻⣿⣿⣿⠟⠋⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠙⢁⣼⣿⣿⣿⠀⠀⠀⠀⠀⢹⡿⠟⢋⣿⠹⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣄⣤⡶⢄⢀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣤⣤⣶⠏
⠀⠀⠀⠀⡾⢃⣤⠤⣤⡘⢻⡄⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⣥⡖⣺⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⡇
⠀⠀⠀⠐⣽⣿⡀⠀⠀⣽⣿⠂⠀⠀⠀⠀⠀⠀⠀⠟⠸⢷⠀⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣠⡾⠋⢻⣿⣟
⠀⠀⠀⠀⠡⠋⠉⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⡿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⠿⢿⠟⠿⢿
⠀⠀⠀⠀⢀⣰⣶⣿⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣁⠂⠀⠀⠀⢐⠐⠀⣾
⠀⠀⠀⠀⠉⣽⡿⠿⠶⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠺⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡀⠒⣤⢠⣀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣀⣀⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠈⠙⠛⠻⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣿⣿⣻⠋⢾⣿⣿⣟⠻⠀⣺⣿⣿⠣⣾⣿⣿⠀⠀⠀⣿⡿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⢯⡇⣺⣿⣿⣿⣿⠁⢈⣿⣿⡿⢘⣿⣿⡏⠀⠀⢰⣿⢣⣿⠏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣟⠎⢜⣾⣿⣿⣿⡏⠀⢐⣿⣿⡇⢼⣿⣿⠀⠀⠀⢸⡟⣾⠟⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⡙⢴⣾⣿⣿⣿⡟⠀⠀⢩⣿⣿⠁⣻⣿⠇⠀⠀⠀⠘⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⠿⠑⢼⣿⣿⣿⡿⠁⠀⠀⢼⣿⣿⠰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⡿⠁⣐⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⢠⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⡏⢙⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠛⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣿⣿⠏⠠⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⠂⢾⣽⣟⠏⠁
⠀⠀⠀⠀⣀⠀⣠⣴⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⣼⣿⡏
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⢰⢿⣿⣁⣷⣯⠛
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠟⠁⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⠄⠀⠟⢋⣙⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⡶⢖⣶⡶⣷⢶⣬⠛⠀⢠⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⣿⣿⣿⣿⢿⣛⠿⣻⣿⡿⣱⡿⣿⠇⢹⡎⢷⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣴⣿⣿⣿⣿⣿⣷⡀
⣿⣿⢿⣓⠂⣃⢸⠶⢶⣾⡿⣼⠟⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣤⣶⣦⣤
⡿⠛⢋⣴⠃⣿⣦⡙⠓⠋⣱⠃⠀⠀⠀⠀⠀⣰⡶⢞⢏⣉⣩⣑⡂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠻⣿⣿⠿⠿⠛⠀⠀⠲⣿⣿⣿⣿⣿
⠀⠀⠚⠁⠰⠇⠸⡟⠂⠠⡏⠀⠀⠀⠀⢀⡞⣁⣴⣶⢶⣿⠟⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⠁⠀⠀⠀⢀⢿⡿⡫⠟⣛⣛⣭⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣽⠀⠀⠀⠀⠀⠋⣾⣗⣛⣋⣙⣟⣉⣛⣆⣀⣀⣀⣀⣀⣀⣀⣀
⢀⣀⢀⣠⣤⣤⣴⡶⠀⠛⣶⣿⣿⣿⣶⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀
⣿⣍⡈⣽⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣋⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⡈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠶⠾⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⢉⣉⣁⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣦⣤⣭⣭⣍⣉⣛⣛⣛⣛⡛⠛⠛⠛⠛⣛⣛⣛⣛⣓⣢⣤⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣰⣷⣿⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⢿⣲⣄⣿⣿⣿⣿⣿⠿⠛⠙⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠈⠉⠁⠉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⡈⠠⢤⣄⡀⣠⣶⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠁⢰⣿⠟⠉⡟⠿⣿⣄⣤⣽⣿⣿⣿⣿⣝⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣼⡏⠀⠀⡇⠸⢿⡟⢉⣿⣿⣿⣿⣿⡛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠀⠀⠠⡇⠀⢸⠃⣼⠟⡜⣿⠇⠙⢷
⠀⠀⢤⣤⡀⠀⡀⡀⢀⡠⢀⣠⢘⠀⠀⠀⠩⡢⠀⣀⢸⣄⣀⣤⣀⡀⡜⠀⠈
⠀⠀⠛⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠙⠉⠉⡼⠉⠉⠉⢉⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⡿⡅⠂⠀⠀⠀⣼⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠰⠿⣷⡿⠟⣙⣭
⠀⠀⠀⠀⠀⠀⠀⠘⢊⣁⢨⣀⢀⣠⡀⡜⠀⠀⣰⣏⡉⠀⠈⠱⡄⠀⢰⣾⣿⣛⣛⣿⣿⢿⡄
⠀⠀⢀⡤⠔⠶⢤⡄⠘⢿⣿⠛⠚⢻⣿⠇⣠⠞⠉⠀⣉⣰⣤⢼⣇⠀⠨⣿⣯⣭⡭⣭⣶⡛⠃⠀⠀⣦⣄⡀
⠀⢠⠏⠀⠀⠀⠀⢹⡆⢹⢿⣷⣿⣿⡇⢠⡓⠂⠀⡼⠅⠀⠀⠀⠈⣣⠀⣿⡽⢻⡿⠛⣿⡟⠀⢠⣌⡞⣻⡟⣆
⠀⠈⣇⠀⠀⠀⡤⣽⡃⠘⣿⣳⢼⣿⠇⠈⢱⢢⡼⣧⡀⠀⠀⠀⠀⢼⡆⠈⣿⣟⣛⣿⡿⠁⢠⣴⠯⢼⡧⢰⣿⣤
⠀⠀⢁⠀⡀⢀⡀⣠⠇⠀⢿⡵⢾⣿⠀⠀⠸⣼⣗⢈⠣⣤⡠⠴⡶⡞⠁⠀⢹⡟⣿⣿⡇⠀⠰⣯⣾⣔⢻⣞⣯⡟
⠀⠀⢰⠟⣶⢻⢷⠇⠀⠀⠈⠓⠚⠋⠀⠀⠀⠈⢿⣿⣾⣶⡦⣾⠏⠁⠀⠀⢸⡟⣷⣿⠇⠀⠀⢻⣿⣿⣾⣹⣿⠇
⠀⠀⠀⣏⢤⣟⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠾⡞⠀⠀⠀⠀⠀⣿⣯⣿⠀⠀⠀⠈⣟⣯⣹⣦⣿
⠀⠀⠀⢹⣞⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣻⣽⠃⠀⠀⠀⠀⠀⢹⣭⣿⠀⠀⠀⠀⢻⣿⣭⣷⡏
⠀⠀⠀⠈⡉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢻⡎⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⣿⣛⡿
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠠⣬⣻⣿⡾⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣠⡾⠁⢀⣀⠤⠤⠀⠀⡀⣠⣼⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⣶⢆⣿⣟⣩⡷⠛⠉⠀⠀⠀⠀⠀⠀⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡻⠿⠉⠨⣿⡟⠛⣷⢸⣿⢲⣶⣽⡏⢀⠀⢀⢉⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠀⠀⠀⣸⣿⠀⠐⠀⠁⡨⣽⣾⢛⣿⣧⣵⠖⠂⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⢄⢸⠄⠸⡿⢫⣿⡏⠸⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣐⣶⡤⢶⣄⢶⣾⣶⠟⡝⣻⠴⠀⠀⡀⠘⠆⢺⡇⣿⣾⢂⡿⠆⡀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠫⡋⢽⣹⠋⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠉⠘⠀⠁⠠⠄⠸⠧⠄⣀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣁⠐⠤⣈⠀⠉⠀⠂⡐⠠⠄⠲⠀⣴⣦⣤⣤⣄⣄⣠⡄⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠈⠓⠦⠤⢀⡈⠀⠀⠂⠤⣈⡈⠉⠒⠠⠤⠀⠠⠀⠠⠀⠈⠉⠁⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠙⠢⢆⠀⠀⠀⠀⠁⠀⠀⠒⠐⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠛⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⢃⣤⣶⣿⣿⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣶⣤⣷⣿⣿⢉⣾⣿⣿⠿⣟⣿⠍⣃⠹⡃⠙⢷⡀
⠀⠀⠀⠀⠀⢰⡿⡿⡿⢿⣟⣿⣭⣭⡿⣮⣷⣿⣿⡿⣿⣿⣿⣿⣯⣵⣀⠈⠁
⠀⠀⠀⠀⠀⠉⢀⣴⣾⣿⢿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣶⣟⡿⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⣰⣿⣿⣿⢣⣿⣿⣿⢻⣿⣿⣻⣇⠟⢿⢿⣿⣗⠟⠛⢻⡿
⠀⠀⠀⠀⢰⣿⠿⠋⠋⣿⣿⡿⣿⣻⣿⣿⠏⢻⡄⠀⠸⣿⣿⠕
⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⡿⡷⠀⠀⣿⣏⠁⢸⡇⣠⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠑⠈⠀⠀⠙⢏⣥⣾⣿⠻⡿⣷⢶⡤⠤⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣞⠟⠑⠚⠣⣿⣀⣀⣘⢄⡛⢓⣀⠠⢝⡻⣭⣷⣤⣠⣤⣄⣀⡀
⠀⠀⠀⠠⠤⢤⣀⣉⡉⠍⠉⠉⠛⠛⠓⠿⣻⣶⣿⠠⠀⣍⠀⠙⠿⠉⠽⠼⡛⢋⣉⣉⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠛⠉⠉⠉⠀⠀⠀⢸⡟⢰⢆⣿⢀⣧⢞⠁⠀⣒⣲⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣛⠃⡹⣺⣈⣼⠳⣧⣷⣀⠀⠠⣿⠿⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⢉⠽⠋⠁⠀⠃⠹⠉⠃⠉⠛⠻⠻⠿⠿⠿⠛⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⡿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣯⠉⣨⣏⠉⢭⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⠰⢏⡉⠀⠀⡇⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡶⠷⢶⣾⣷⣶⡶⠷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡎⢡⡀⠀⠀⠀⠈⠉⡦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⣿⣧⣀⣀⣀⣐⡐⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠒⠈⠉⠉⠉⠉⠁⠒⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠋⠀⠀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣨⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠤⠤⢤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣶⣤⣤⣴⣛⣋⣉⣉⣉⣭⣭⣭⣤⣴⣶⡏⢀⠂⠶⠆⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣟⣿⣯⠭⠙⢛⡻⠿⠿⠿⣿⣷⣀
⠀⠀⠀⣠⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣤⡤⠶⢦⣤⣬⡇⢸⢸⣿⣷⠀⠀⠀⠀⠀⠀⢸⣯⣭⣭⣭⣴⣶⣷⣶⣤⣬⣤⣀⣈⣋⣉⣭⣤⡀
⠀⠀⢠⣤⣍⣉⣛⣛⣛⣛⣛⣛⣛⣯⣭⣵⣶⣾⣶⣦⣭⡇⢸⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣉⣉⣉⣛⣛⣛⡃
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣇⣸⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⡿⠻⠟⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠻⢿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠶⠶⠲⠶⣯⠉⠉⠉⠉⠛⢿⣷⣦⡀⠀⠀⠀⣷⣄⠒⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠷⠟⣯⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⣀⡿⠟⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣟⣛⡛⠛⠛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠾⠛⠉⠋⠓⠒⠒⠒⠒⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿