Living Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⢠⠀⠿⠿⠇⠀⠀⠀⠐
⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠵⠠⠀⠠⠀⠀⠀⠦⠠⠀⠠⠀⠈⠀⣶⠒⢲⠀⠀⠀⠄⠀⠐⠃⣸⣽
⠀⢀⢀⡀⠀⠀⠀⠀⠄⠀⣄⢠⡀⡀⣠⣠⠀⠀⠀⡀⠄⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠶⡟⠋
⠀⠈⠀⠀⢀⠀⠀⠀⣠⠀⠹⡘⠃⠈⠉⠉⠐⡀⡆⠉⠀⠃⠀⠀⠀⠸⠿⠷⠀⢀⡄⠀⠰⠀⠀⠀⠀⡈⠂
⠀⣀⠀⠀⠊⠉⠀⠈⠀⠄⠀⢁⣀⠠⠤⠔⠀⠀⠀⣀⡀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢰⠁
⠈⠉⠀⠀⠀⠠⠄⠒⠒⢉⠀⠐⠛⡒⠀⠀⠂⠠⠀⡁⠀⠈⠀⡀⠀⠠⠆⠀⠀⢀⡀⠀⠂⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠠⠤⠔⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠄⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗
⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⠀⢙⡷
⣖⣀⣠⣦⠄⠀⠀⠀⠂⢠⠄⠀⠀⡀⠀⣸⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠛⠟⢟
⠻⠿⣿⣿⣿⣴⠀⠀⠀⣠⠄⠀⠀⠀⠰⠅⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠀⠀⢡⡀⠀⢂⠀⣤⣤
⣤⠀⠀⠀⠸⣿⠀⠀⠰⠿⠋⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⣿⠀⠄⠀⠀⠀⠰⠂⠀⠀⠱⣿⣸⡇⢹⣿
⠛⠀⠀⠀⠀⢹⠃⠀⠐⣮⠀⢀⠰⠀⠉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠚⠛⠀⠫⡀⠀⠀⠁⠀⠀⠈⣿⠷⠼⣿
⠀⠀⠀⠀⢠⣿⣆⡄⠀⢻⣂⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣀⠀⠊⠀⠀⢠⣿⣀⠀⠹
⠀⠀⠀⢠⡿⠟⠛⠁⠄⠐⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣶⣿⠀⠀⢯⠀⠀⠀⣠⣿⣿⠿⠆
⠀⠀⡠⠈⠀⡀⠀⠀⠈⠾⣿⡆⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠿⠀⢠⡎⠀⠀⢶⣿⠏
⢀⡼⠃⠀⠀⠂⠀⠀⠀⠀⠘⠃⡀⢠⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠠⠟⠁⠀⣰⣾⠃
⠈⡀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⡇⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⢲⣴⡟⠀⠀⠀⠀⠰⠀⠄
⠾⣷⢂⣤⠆⠙⠮⠁⠈⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠀⠀⠉⠀⠀⢄⡄⠀⠀⠀⠠
⣾⣿⠟⠋⠉⠺⠠⠄⠀⠀⠁⠀⣀⠀⠀⠀⢀⣀⣀⡀⠀⣀⢀⠀⠀⠀⢀⣀⣠⣄⣀⣀⣀⣄⣤⣴⡄⠘⠒⠀⢀⠀⢀⠀⠠⢂⡀⢀
⠛⢁⠀⠀⠀⡀⢲⣿⣧⣼⣾⣿⣿⣿⡿⠛⠛⠙⠉⠙⠛⠛⠛⠓⠒⠻⠟⠻⠿⠿⠋⢙⡛⠛⠻⠿⣿⣦⣼⣽⡟⣋⠀⠀⠀⢩⣦⣼⢷
⣄⣠⡀⠨⣤⣴⡾⠋⠙⠛⠿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⣿⣾⣿⣶⣶⣤⣾⣿⣿⠿
⠛⠿⣷⣶⢿⣿⣿⣶⣦⣄⣀⣤⡾⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠷⠶⠾⠿⠿⠿⠟⠛⠋⠁⠀⠤⠖
⠀⠀⢿⢿⣶⣤⡭⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠥⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣥⣤⣉⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣤⣿⣶⣆⢠⡀⠻⣿⣶⣶⠆⢀⡄⣴⣿⣽⣿⣿⣟⠀⢀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢿⣿⣿⣿⡩⣅⠸⡿⢊⡴⣤⣦⡁⢾⠇⣡⠌⣿⣿⣿⣞⣿⣿⢯⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠚⠛⠿⠿⠷⠎⠳⠀⣸⣏⠻⣿⣇⠀⡞⠱⠞⠻⠻⠛⠛⠛⠉⠈⠀⢆⡀
⠀⠀⠀⡀⠀⣠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⢀⣼⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠲⡦⠅⠂⢄
⠀⠀⠐⠀⠀⡘⣧⣕⡠⠀⠀⠀⢀⠀⠠⠄⠀⠀⠸⣿⣾⣿⣿⣿⡇⠀⠂⠠⠄⠀⣀⠀⠀⠀⠄⣊⣶⣄⣠⣰⡌
⠀⠀⡄⠀⢸⣿⣯⣿⣿⣶⣦⡄⠀⠠⡴⣓⢤⣦⠤⢿⠏⠿⣿⡿⠤⣰⡦⠘⢦⡄⡀⢀⣠⣶⣾⣿⣿⣿⣿⠟⠃⠆
⠀⠀⢄⠀⠼⣿⣛⣿⣿⡿⢟⣁⣀⠪⣵⢿⠇⡼⢶⣥⣴⣶⣾⣯⡴⢧⠘⣿⡦⠑⣀⣬⣙⠉⢿⣻⣿⣿⡤⠀⡀
⠀⠀⠀⠙⠂⠈⠛⢋⣥⣶⠿⠛⠉⠑⠢⠉⣐⠃⣼⣁⣠⣶⣶⣿⣅⠀⣃⠉⠀⠀⠉⠛⠿⣿⣦⡈⠉⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⡟⣴⢹⣥⣤⣴⣾⣿⡍⣤⢻⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡠⠏⡄⣿⡀⢧⣀⣬⣿⡦⠰⣷⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡃⢟⣮⡌⠻⢿⢟⣡⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠛⠷⠞⠛⠋⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⡠⠚⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⣋⣉⡁⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢰⠏⠁⠀⠉⢳⡀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⠶⠶⠆⢻⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠙⠁⠘⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣥⠉⠉⠀⠀⠀⠙⠶⠤⠖⠋⠀⠀⠀⠀⠀⠀⣠⣾⠷⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣤⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡏⠀⠈⠣⣄⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣀⡤⠏⣼⠁⠘⢦⡀⠀⠀⠀⠀⠀⣠⢶⠏⠀⠈⣧⠀⠀⠀⠀⠙⢲⡄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⡞⠁⣠⣾⠁⠀⠀⠀⠙⠦⣄⠀⣠⠞⢱⠏⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠙⠦⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡴⠋⠀⠈⣡⠇⢀⡀⠀⠀⠀⠀⠈⣻⠧⡜⠉⠀⠀⣀⠀⢀⠀⠀⠀⠀⣾⡇⢴⡦⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠁⣠⣄⠀⠁⢘⣿⣟⠀⠀⠀⠀⣚⣿⣓⠙⣆⠀⢰⣿⠆⣿⡇⠀⣀⡤⠼⠧⠽⠯⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⢈⣽⣯⡡⣤⣐⣻⠓⠀⢀⣄⠀⠚⣿⠓⢀⡬⠷⠒⠛⠒⠛⠙⣛⣷⠄⠀⠀⣠⣧⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⢾⡷⠄⠀⣀⣩⠷⠆⣫⣯⡓⠉⠙⠛⠛⠓⠂⢀⡤⣶⣿⡿⠿⠋⣰⡀⢈⣩⣯⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⣓⠛⠉⠁⠀⠀⠀⠵⡿⠭⠀⠀⠀⠀⠀⢀⣸⠆⢳⢉⡳⡄⢉⣽⣍⠁⡴⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣿⡓⢀⣠⢤⣴⣞⠓⢷⡀⣠⠶⠒⣿⠉⠩⠴⠚⠿⢞⣳⠇⣩⣼⣭⡡⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⠈⠁⠀⠈⠉⣁⣈⣤⠟⢸⠣⣞⠉⣴⢢⠖⠋⠉⠀⠀⠤⢾⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠖⣻⠭⢗⣛⠀⣚⠉⢀⡨⢇⡼⠊⢳⡄⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⠃⡾⢉⡴⢋⡵⢚⣩⢖⡃⣠⠴⠋⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡇⢸⠇⡜⢠⠏⢠⠏⣸⠛⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠇⢰⢀⡇⡟⢰⢸⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠆⢸⠘⠃⡇⢾⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠘⣠⣧⣼⣸⡆⡇⣴⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⢷⣄⣠⠸⢃⣠⣬⡼⢷⡇⡾⠞⢳⡆⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢈⡅⠟⡋⠛⠳⠀⠠⠷⠞⠃⡀⣲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠹⠴⠦⠟⠲⠚⠓⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠀⠄⢀⣀⣀⢀⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⢀⡠⠄⠠⡀⠀⠀⠀⠈⠃⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⠉⠀⠀⠀⠈⢢⠀⠀⢠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣁⠈⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠣⡀⠀⠀⡠⠂⠐⠒⠀⠐⠁⠀⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣀⠤⠤⣀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠣⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠀⠀⠑⡀⠀⠈⢆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣎⢄⡀⠀⠀⠣⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⣰⠀⢀⡠⠜⠒⠒⠈⠁
⠀⠀⠀⠀⢀⠔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠀⠀⠀⡃⠈⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠂⠐⠒⠚⠢⠔⠊⠁⢱⠀⠀⡎⠀⠈⢆⠀⠀⠀⡠⠠⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢃⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠁
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠒⠀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠀⠒⠒⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠄⠠⠄⠀⠒⠒⠒⠀⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣤⣶⣶⣷⣿⣿⣶⣄
⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡈⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠁⠨⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠠⠔⠒⠉⠉⠉⠉⠁⠐⠠⢌⡀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠐⠤⣄⢀⠀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⠤⣤⣄⣀⣀⡀⠒⠦⠁⠀⠈⠂⢀⠹⣧⣾⢷⣾⣷⣤⣤⣄⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣷⣤⡶⢶⣄⣀⣘⠢⣴⣀⣀⣿⣿⣿⣿⣿⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣇⣤⣿⣿⣿⣿⣿⡛⡿⠿⠿⣰⣿⣿⣷⣸⣿⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡘⢶⣶⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠈⢿⣿⣷⣴⣿⣿⣿⠿⣷⣾⠛⠿⢻⡟⡟⢡⡈⢿⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣷⣦⣤⠀⠙⢿⣟⣵⣿⠏⠀⣾⣿⠀⠀⠈⠃⠁⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠈⠻⣿⣿⡿⣷⣿⡿⠁⢀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠹⣦⠔⠆⠀⠀⢀⠔⠀⠀⣀⣴⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣴⣩⣿⣿⡏⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠉⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⣿⠏⣿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⡿⠊⣡⢂⠀⡀⠀⡠⠔⠊⠈⠁⠀⠀⠉⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠿⠇⠸⢧⣾⣪⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢠⠔⠀⠀⠀⠀⠀⢻⣾⡇⠔⠊⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣻⣿⡍⠃⠀⠀⢀⠈⠀⣰⣿⣿⠿⠿⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠃⡠⠀⠀⣈⣴⣾⣿⣏⠙⠓⠂⠀⠠⠀⠀⠀⠉⠐⠒⠄⠀⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣝⣿⣿⣿⠟⠿⢿⣮⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡀⠈⠁⡾⢫⢯⠏⠸⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⠯⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢄⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⣎⣷⠀⠀⠀⠀⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠊⠀⠀⠀⠀⠀⠻⡅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣎⡀⣀⠀⡐⠣⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠾⡄⣁⣠⡈⠛⢁⡀⠀⢀⣀⣀⢹⣿⡬⠁⠀⠄⠶⡇⠀⠰⠐⠛⣰⢦⠀⣶⣿⠂
⠀⠀⠀⠀⠀⣀⣀⡘⢋⣼⣿⣀⣾⣿⡷⠛⠉⠉⢉⠇⠀⠀⢿⡄⢠⡷⠀⠧⠀⢀⠈⠈⠀⠙⠹⠀⡀
⠀⠀⠀⠀⠙⠛⠋⠐⠛⢿⣿⡿⣿⣿⠃⠀⠀⠀⣶⣿⠀⢠⡘⣠⡿⠁⠀⣴⣠⢱⡧⠀⠀⢨⠀⣦⠃
⠀⠀⠀⠀⠀⢶⣦⣾⣷⣶⡏⠀⣹⡟⠄⠀⢀⣠⠛⠻⠵⠿⠟⠋⠀⠀⠀⠈⢿⣮⠀⠀⠀⠘⡇⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣦⣼⠷⢛⡿⣯⣤⠾⠿⠿⠟⠱⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡧⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠈⢹⠏⠰⠀⠛⠛⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣊⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤
⠀⠀⠀⠀⠀⠀⢀⡈⠈⠛⣡⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠸⠿⠷⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠉⠾⠟⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠛⠛⠋⠀⠀⣀⠀⠀⠀⠘⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠛⠛⠉⠀⠀⣀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⣄⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠩⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠗⠣⠶⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠟⠣⠶⠂⠀⠀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠾⠤⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠋⡘⠒⠒⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⡐⠒⠖
⠀⠀⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢠⠖⠒⠒⠦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡅⣀⡄⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠠⠄⡀⠀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠠⢌⡀⠀⡃
⠆⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣖⡶⠂⠀⠀⠀⠘⠂⠠⠠⠔⠁⣀⡀⠀⡂⠈⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠰⠋⠘⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠙⢠⠆⠀⠀⢸⠐⠋⠘⠃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡍⠉
⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⡁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⡀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⠀⠀⢶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠄⠀⢲⣶⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⠀⠀⡀⠀⠀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⢀⠀⡀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⢠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣻⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣛⠀⠀⠀⠀⢶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠉⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠩⣦⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠕⠃⠶⠂⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠙⠁⠀⠀⠈⠟⠣⠶⠂⠀⢀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠰⠀⠋⡐⠖⠐⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢋⡐⠖⠚
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⢠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠖⠒⠒⠦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣆⠠⠌⠁⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡆⠠⠌⡉⠀⡃
⡆⠈⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠃⣀⡀⠀⠂⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠝⢰⠆⠀⠀⢘⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⡝⠙
⠀⠀⠀⠈⠷⠤⠤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⢦⡴⠞⠁⠀⢀⣀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⣦⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣤⠾⠛⠉⠉⠈⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠈⢿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠙⢿⡄⠀⢸⡇⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠿⠷⣤⣀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠉⢳⣤⣴⡶⠶⠺⣿⣷⣤⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⡏⠉⢻⣿⣿⡟⠛⢿⣿⣛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠋⠀⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⢸⣿⣿⣿⠇⠀⣾⣿⣿⡇⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢠⣿⣿⣿⡟⠀⢀⣿⣿⣿⠇⠀⣾⣿⣿⠃⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠻⣿⠃⠀⣠⣿⣿⣿⡟⠀⠀⣼⣿⣿⡿⠀⢰⣿⣿⡟⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿⠟⠀⠀⣼⣿⣿⡿⠁⢀⣿⣿⣿⠃⢀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡃⠀⣠⣾⣿⣿⡿⠁⢀⣾⣿⣿⠃⢠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣟⣀⣠⣿⣿⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣼⠏⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⣠⣴⠾⠋⠀⠀⠀⢀⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣴⡿⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⢀⣴⠟⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡀⠀⣰⡿⠁⠀⠀⢀⣀⣀⡀⠀⣴⠟⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⣀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠈⢻⣶⣿⣤⣴⠶⠟⠛⢻⡏⠻⢿⣯⣀⣀⣤⣴⠾⠛⢻⣿⠛⠷⢶⣶⡟⠋⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡟⠉⠁⠀⠀⠀⢸⡏⠀⠀⠀⣿⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢿⡄⠀⠀⠀⠘⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠘⣷⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣧⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⣼⡇⠀⢸⡏⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⢿⡆⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣦⣾⣧⣤⣤⣿⣄⣀⣀⣀⣴⣿⣤⣴⣿⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⣤⣄⠀⠈⢀⣯⠋⠋⣀⣄⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡋⠃⠀⠸⡿⠟⢉⣋⣭⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⣀⣼⣿⡆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠐⡟⠋⢉⣯⣿⠅⢀⡠⣄⣀⠐⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⢈⣹⠟⢀⡀
⣄⠀⠀⠀⠃⠀⠀⣠⣤⠖⠂⠁⠀⠴⠞⠋⠀⢀⠋⠀⢿⣿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠒⠛⠻⠻⢴⡾⠇
⠉⣦⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⢻⠟⠀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⣡⣾⣾⠟⠙⠋⠀⠀⠀⠀⠺⠿⣿⣦⣀⣀⡀⠀⠈⠀⠐⠆
⠀⠈⠳⡀⠀⢀⣈⣠⣶⡛⢤⡂⠀⠀⠀⠀⠀⠀⠀⡄⠈⠈⠃⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⠴⡾⠟⠀⣀⣠⣀⠀⠀⠀⠈⠉⣥⢿⣧⡟⣡⣿⡀⠀⢀⣷⣃
⠀⠀⣤⣤⡴⣯⣿⡻⠞⡀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠛⣻⠁⣀⠳⠒⠀⢦⣌⠉⣹⠟⣾⠃⠠⢀⡈⠃⡄
⣴⢿⢟⢯⠑⣯⠉⢧⣀⢘⣀⡙⢒⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⡠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣝⠛⡃⠐⣠⡇⠃⡻⢋⡟⠿⠛⠹⣧⠈⣸⣿⠀⣠⠟⡀
⣟⣣⣤⣌⣁⣘⣀⣾⣿⣿⣿⣥⣭⣼⡷⢄⣀⠠⣤⣠⡀⠀⣶⣿⠀⠀⠀⠀⠀⡐⠂⠴⡷⠾⠇⠘⢿⣷⣿⣤⣿⡏⢈⡼⠋⠉⡀⠀⠀⣿⣿⣿⣧⠞⠁⠀⢀⣄⣶
⣾⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⣯⣹⣿⣷⣾⣿⣦⣤⣿⣿⡆⣿⣿⣤⠶⠂⠀⠘⠋⢄⢂⠀⠐⢠⣶⣬⡟⣿⣼⣿⣿⣿⣅⣶⣤⠜⠋⢢⣿⣿⣿⣷⠶⢶⣿⣿⣿⣿
⣾⢿⠯⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣹⣟⡁⢀⢀⣀⠀⡀⠠⢀⣠⠞⢃⣾⣿⢷⣾⣿⣟⣿⣿⣿⠙⠛⡫⣥⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣥⣿⣿⣼⠏⣿⣟⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⠟⢻⣽⣿⣿⢯⣿⣷⣿⣻⣿⡽⠷⢤⡾⠿⣶⢿⡏⠘⣾⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣗⣾⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⢯⣽⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡟⠓⢴⣮⣿⣿⢿⣿⣾⠿⣿⡁⣠⣤⣼⣿⠦⡉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⡿⣿⣿⣿⡛⠻⢿⣿⣿
⣿⣿⣿⣶⣿⣷⣶⡿⣿⡟⡿⠿⣿⣿⣿⡿⠑⠿⢶⣿⣿⣭⣾⡇⣭⠳⣍⣿⠋⣡⣿⣿⠿⠿⠛⠛⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣥⣿⠷⣻⣵⣿⣧⠏⣉⠚⣷⣽⣿
⠉⠀⠀⠀⠀⠉⠻⠿⠟⠛⠛⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠙⠃⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠘⠛⠙⠺⠟⠋⠈⠛⠛⠛⠉⠙

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠒⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣻⣾⡷⠐⠀⠀⡶⠀⠀⠀⡴⠀⠀⠀⠀⠈⠀⣸⡩⢟⣖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠩⣽⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⡄⠀⠀⠀⠀⠿⠶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢫⡥⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠿⠃⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⡇⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠄⠀⠀⠀⣿⣤⢀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠃⢸⠀⠀⠀⢸⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⣿⣊⡥⠐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠲⣽⡆⣼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⣿⢃⡒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠛⣷⡾⠇⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡬⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣡⠀⠀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⢠⠴⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣦⠀⣾⡛⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⡹⠗
⠀⠀⠀⠀⠐⠀⠐⠊⠐⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣁
⠀⠀⠀⢲⣶⠎⠉⠉⠀⠀⠀⠀⣠⣤⡤⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣩⣤⣦⣴⢤⣄
⠀⠀⠲⢾⠃⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠋⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣿⣫⣴⣚⠁
⠀⠀⠘⢩⡏⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠃⠀⠀⠀⠸⣟⣋⠁
⠀⠀⠶⣶⡆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠂
⠀⠀⣚⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⢀⡀⠀⠀⠀⠠⠀⠀⠐⠶⡦⣀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠦⠀⠀⠀⠁⠀⠈⢉⠀⠀⠐⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠦⠤⢤⣠⣶⡿⠷⢤⡷⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡋⣁⡀⠀⢀⠀⠀⢻⣦⣾⣧⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⣒⣒⠛⢛⣋⡉⠭⢨⣟⢲⣿⡟⣿⡞⠋⠙⣷⠼⣿⣿⠟⣿⣦⠟⠉⠛⠛⠒⠶⠶⠶⠴⠖⢤⣄
⠀⠀⠀⠀⢀⡤⠒⡡⠊⠉⢑⠀⠠⡔⠀⠈⠁⠀⠛⠉⢀⣤⡾⠉⠾⣿⡿⣿⣶⣾⣿⣿⣷⠈⠿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⣠⣴⠞⢉⡞⣰⣇⠈⣿⣧⣙⢿⡿⣿⣿⡋⠀⠀⠘⡇
⠀⠀⠀⠀⠁⠀⠄⠀⠀⣀⣀⣀⣀⣠⠴⠺⢿⡿⠃⢠⣾⠅⢿⣿⣶⡍⠛⠿⣿⡞⠲⡏⠀⠀⣾⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⢿⣿⣄⠈⠣⠴⠛⢿⣦⠘⣿⣿⣏⣀⣀⣼⣷⠚⠉⣀⠞⠙⠛⢭⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣡⡀⠘⢿⣿⡀⠀⠀⢀⣼⡿⠷⢟⣿⢟⣟⠟⡼⣿⡷⠊⠁⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⢀⣠⠿⡭⠭⣯⡈⢿⣿⣷⡀⠙⢿⣦⠀⠘⣿⣀⡰⠋⢡⣾⣧⣾⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠋⠁⠀⠀⣬⣿⣿⡌⠻⣿⣷⡀⠘⣿⣿⡶⠋⢘⢷⣴⠟⠁⠽⠁⣿⠻⣟⡒⢢⣄⡀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡿⣿⣄⠙⣿⣿⣦⣘⡿⠅⠀⠉⠛⢳⣄⡔⠰⣺⠇⠀⠈⠻⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣌⢿⣷⣌⣿⣿⣿⠀⠀⠀⢀⡔⢣⠋⠀⢠⡏⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠉⠉⠉⣠⡏⠀⠠⠖⠉⢀⠄⠁⠶⡞⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⠀⠤⠐⠁⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠈⣀⠖⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠦⣠⠾⠒⠈

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢤⡀⢰⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⣂⠴⠚⠁
⠀⠀⢧⠀⠈⢦⣧⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣹⣶⣿⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣯⠠⠈
⠀⠀⠀⠙⠲⢄⣳⡍⢇⣀⠀⠀⠀⠀⡤⣊⡵⢆⠜⣷⠶⣿⠦⡱⢮⣑⢤⠀⠀⠀⠀⢾⣿⢀⡍⡔⣇⣦⡀
⠀⠀⠀⢠⣾⣇⡮⠇⠘⠟⠀⠀⠀⠈⠉⠛⠚⠁⠀⢘⡿⠍⠀⠈⠓⠛⠉⠁⠀⠀⠀⠠⠂⠈⡀⠸⡙⢟⠇
⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠨⠁⠂⠄⠀⣰⣆⠀⠠⠐⠈⡅⠀⠀⠤⣄⣀⡀⣠⠶⣤⢀⣀⣀⠤⠤⡀⢀⠤⠤⠄⣀⢠⣶⣄⢀⠀⠤⠤⣄
⠀⠀⠹⠛⠓⢿⠷⠾⡿⠚⠛⠏⠀⠀⠀⠀⠀⠀⠀⣽⠒⣿⠀⠀⡀⠄⠀⠀⠈⠒⠶⡒⣨⢿⠿⢿⢭⡐⡲⠖⠊
⠀⠀⠀⠀⠀⠈⢽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠉⠳⣄⢰⣄⡠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⢠⢢⢀⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡱⡎⠀⣀⣀⣀
⠀⠀⠈⠓⠒⠂⣡⣈⠒⠒⠚⠁⠀⠀⠀⠀⣏⠀⢀⣨⠞⠉⠀⠀⡷⠀⠀⠀⠀⠘⠤⣄⢈⣁⡷⢞⣉⠀⣤⠔⠁
⠀⠀⠀⠀⠀⠘⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⡝⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣯⣵⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠐⠲⣕⣦⡔⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡔⠉
⠀⠀⠀⠓⢒⣾⣿⣿⣶⡒⠚⠀⠀⠀⠀⠀⠀⣀⠴⣞⣙⣳⠤⡀⠀⠀⠀⠀⠀⠀⠂⠉⣩⣤⡼⣦⣬⣉⠁⠂
⠀⠀⠀⠚⠁⠐⣟⡿⠀⠉⠂⠀⠀⠀⠀⢀⠜⠁⡠⢧⠀⡼⣄⠈⢢⡀⠀⠀⠀⠀⠲⠟⠋⠐⣛⡛⠈⠛⠷⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠉⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣮⣄⣤⡤⠤⠶⠄⠀⠀⠈⠀⠀⢁⡉⡉⠀⢠⡄⠀⡄
⠀⠀⠧⠂⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠠⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠂⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢘⠀⠛⠛⠛⠁⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⣤⣤⠄⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠉⠁
⠀⠀⠀⠀⠀⢠⣴⠶⠀⣀⣀⡀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⡄⠻⠿⣾⣤⣤⣀
⠀⠀⡔⠂⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠀⡀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⢹⣾⡿⢻⣄⡀
⠀⠠⣇⠀⠀⠀⢸⡿⢻⡿⠟⢸⣿⣿⣸⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⣾⣿⣇⣿⣿⡇
⠀⠀⣶⣾⣴⣿⣹⡿⣿⣿⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠟⢹⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⠿⠿⠉⠁
⠀⠀⣛⡻⣿⣡⢨⡿⢫⣼⣿⣿⣿⡋⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢰
⠀⠀⣿⣿⣿⣿⡄⢰⣦⠁⣾⢿⣿⣏⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⠗⠀⠀⠀⠐⠤
⠀⠰⣿⣾⣿⡿⢁⡸⡟⢀⢻⣼⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⡄⢀⡒⠀⠄
⠀⢰⣿⡟⣽⣷⡞⢳⠛⡟⡏⣽⣛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡚⠋⠉⠁
⠀⢸⣿⣿⣍⣉⣈⣑⠚⢚⣛⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⠒⠒⠒⣷⣶
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣴⣦⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠛⠛⠋
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂

⣿⣿⣿⣿⣮⡑⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⣀⡀⣠⣷⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⠂⠀⡀⢸⣿⡇⠈⢽⣿⣿⣿⣿⣿⣿⡟⠈
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⠇⠀⠀⠀⠀⢾⢖⣼⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢺⡟⠂⡀⢬⣿⣿⠁⠀⠸⣿⣿⣿⣿⣿⣿⡃⣠⢠
⣿⣿⣿⣿⣿⣿⢀⠀⣠⠖⠛⠁⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢀⣤⡀⠀⠀⣴⣟⢴⣾⠃⠠⣈⢶⣿⠇⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⠈⠟⣯⡾⠿⣯⣶⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⢰⠻⠷⡷⣿⣏⣤⣾⣧⡀⡀⢮⠻⠜⠀⠀⠀⣆⢸⡿⣧⣿⣿⣿⡏⣿⣾
⣏⠛⠛⠻⣷⣶⣤⣠⣬⡉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣄⣀⣴⣿⣟⣭⣿⣿⡟⠿⡆⠃⢀⡇⠀⠀⢸⡜⠇⢹⢸⣿⣿⡇⡿⣁
⣤⡄⠀⠀⢈⠙⠟⢿⡯⠁⠀⠠⠀⠁⠀⠀⢤⡀⠀⠀⠀⠀⠂⢀⠸⡟⢉⣿⣿⣿⣿⣿⣿⣿⣦⢹⡆⢺⡇⠀⡉⠙⣧⢰⠘⠈⣿⣿⣇⣿⢋
⣿⣤⠀⠀⢸⣧⡠⡐⢩⠀⠀⣦⡄⡀⠀⠀⠀⣃⠀⠀⠀⠀⡀⣀⠀⢧⣸⣿⣿⣿⠟⣹⣿⣿⣿⠆⢃⢸⣇⠀⢇⠻⣿⣿⡄⠁⡇⣿⣿⣿⣿
⣽⣿⢄⣠⣘⣷⢷⠷⠀⠀⠀⠙⢡⡇⣾⠆⠀⠘⢳⣄⣀⢐⣿⡋⣀⣜⣿⣿⣿⣿⢸⣿⢿⡏⠉⠀⢨⣘⠥⠀⢀⣀⣿⡿⣷⠀⠀⣿⣿⣿⣻
⡏⣵⣿⣿⣿⣿⣄⡆⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠈⠹⣟⡋⣤⡿⠟⡅⢿⣿⣿⣿⣾⣿⣾⣧⣄⡀⡼⠘⣇⠀⠠⢉⣸⣷⣻⡄⢠⣿⣿⠋⡟
⢡⣿⣿⣿⣿⣿⣿⠀⠀⠘⣧⡀⠄⠸⠀⠀⠀⠀⠀⠀⡈⠇⢸⡦⠶⡆⠈⢻⣿⣿⣿⡿⢿⣿⣻⣧⣾⠀⣿⠀⠀⢸⡟⣿⣿⣷⢾⣿⡏
⡏⣿⣿⣻⣿⣿⠏⢀⢲⣆⠹⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⢼⠀⠷⠀⢿⣾⣿⣿⣿⣿⣷⣼⣿⣿⣻⣿⡄⢸⡄⢠⠘⣟⣿⡟⢻⣼⣻⡇⠀⠈
⣘⢽⣱⣿⣿⡿⠀⠘⣆⢿⡀⢹⣿⣿⣦⣴⠆⠀⠀⠀⠀⢀⣄⢸⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇⠸⡇⠈⠀⣿⣿⣧⢸⢿⣿⣇
⣠⢿⣽⣿⡿⠁⠀⢰⣿⣼⣷⣧⣿⣿⣟⢻⣶⣂⠑⢀⣠⣈⣻⡆⠻⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⣇⠀⡆⣿⣿⣿⣿⣼⣿⡟
⣯⣾⢟⡿⠃⠀⣠⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣯⡼⢫⣍⣿⣿⣧⣄⣀⣸⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠀⡇⢿⢻⢿⡈⢿⣿⠁⠀⢸
⣿⣿⣿⠁⠀⢀⡟⢿⣿⣤⣹⣿⣿⣿⣿⠿⠋⣨⣿⣿⣿⣿⣿⣿⡿⣟⠉⢹⡟⣿⡏⠙⠀⢻⣿⣿⣿⣿⡇⢸⠀⢰⣼⣾⣼⡇⢸⣿⠰⠀⠈
⣿⠟⠀⠁⣠⡞⣰⣿⣿⠿⣿⣿⣿⣿⡉⠠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⢻⣇⠩⣦⠀⢲⣿⣿⣿⣿⣿⡷⢸⡀⢸⣾⣿⣿⣧⡿⣿⣷
⡏⠀⠰⣴⡿⢠⣯⣿⣿⣦⡈⢹⡟⠻⣧⣄⠀⠉⠉⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣤⠈⡇⠈⣷⣷⣷⣶⢇⣿⣟⣤⣤
⠀⣨⣾⣿⠁⡾⣠⠌⣉⣭⣿⣾⣷⣾⡟⢯⣷⡋⣾⣬⣭⡀⣾⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⡆⠀⠃⠀⣿⣿⣥⣿⡾⢾⠚⠈⠁
⣼⡿⣿⢇⣸⢟⡛⣷⡈⠈⠉⠙⢿⣿⣿⣶⠈⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡴⠒⠻⣿⠀⢀⠀⠸⢟⣿⣾⣧⣿⢀⡠⡘
⣧⣽⡟⢠⣷⣾⣧⣼⣷⣾⣀⣹⣼⣿⡶⠘⠛⠿⣷⣿⣿⣿⣿⣿⠛⠛⠛⢛⣫⣭⣭⣙⣛⣻⣿⣦⣾⣿⣿⠀⢸⠀⢸⣿⣿⣿⡼⠁⣞⠀⣠
⠉⠛⠀⡾⠛⠟⠛⢯⣼⣿⣿⡿⣿⣟⢱⣷⣀⠀⢈⠁⠀⠀⠀⠉⠉⠉⢉⡉⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢺⡀⠘⣿⣿⣿⣿⣤⡇⢰⣿
⢁⠒⠲⣧⣠⣆⣸⠦⢼⣿⡿⣷⡾⠋⣿⣿⢿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢻⣿⣿⡿⠛⠟⠿⣿⣿⡿⢸⡇⣾⣿⣧⣿⣿⣯⡅⢸⣿
⣤⣀⣾⣿⣄⠁⣀⣼⡶⡿⢷⣿⡿⢛⠃⠀⠈⠙⡿⠗⠳⠂⠀⠀⠀⠀⠀⠘⠙⠞⠀⠁⠀⣀⠀⡀⠀⠻⣷⣾⣾⣷⣿⣿⡿⣿⣯⣾⢻⡈⢿
⠑⠀⠀⠀⠀⣿⣿⣿⡅⠀⡵⠿⠱⠾⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣢⡉⣠⡆⣀⢀⣤⣞⣻⣿⣿⣿⣿⣇⢸⣿⡿⣡⣶⣿
⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠊⠀⠁⣰⡿⢋⣡⣤⣿⣿⡻⡾⣸⣗⢿⠟⡋⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡩⣐⣻⡿⣛⣛⣻⠿⠿⣿⣿⣯⠿⠛⠛⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣌⣡⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠿⣿⣿⠿⣛⣛⠿⣿⣿⠿⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣝⡛⢿⡿⣛⣫⣝⣛⢿⡿⢛⣫⣝⣛⢿⡿⢛⣋⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣝⠻⢟⣭⣭⣭⣍⡻⢟⣩⣭⣭⣍⡻⠟⣫⣭⣭⣭⡻⠟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄
⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠄⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠃⠀⠂⠐⠈⠠⠀⠈⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⢠⠀⠂⠀⠐⠀⠂⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⢥⡿⠳
⠀⠀⠀⠀⢣⠀⠁⠀⠀⠈⠀⡰⠐⢆⠀⢩⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠩⠀⢘⣄⢀⠀⡰⢅
⠀⠀⠀⠀⠈⡄⠁⢸⠉⠑⠒⠁⠀⠈⠂⠔⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡀⠀⠀⠉⠈⠁⠠⠱⡀
⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣤⡦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⢤⡞⡻⠁⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡡⠊⡜⠀⠀⢇⠁⠚⠤⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢰⠁⢐⠁⠀⠀⠀⠳⡄⠀⠀⠻⡝⢧⡇⣐⢲⣄⣀⡤⡀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⡀⡤⠒⢺⡅⠀⢠⠀⠐⡆⠀⠀⠀⠀⢸⠀⠀⠀⣟⠻⠀⢏⠁⠈⢢⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⡀⡜⠑⠤⠌⢦⡀⠘⣦⣀⢀⡀⠜⠀⠔⠊⠇⠓⢖⠈⠙⢍⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠕⠒⢘⡛⠊⠍⣢⡠⠊⠢⡠⠚⠳⣠⠞⠒⠤⠒⢆⡤⠲⢖⡚⡳⣆⣞⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡹⠁⢙⠒⠶⠀⢵⠀⠀⢆⠀⠀⡆⠀⠀⠇⠀⣘⡠⠚⡉⠁⠄⠀⠀⠀⠠⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠘⡀⠘⡀⠀⡆⠀⢸⠀⠀⡇⠀⢸⠀⡠⠋⠀⢂⠀⠀⡤⠤⠊⠢⢄⡀⠁⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢱⣀⡵⠤⣰⠀⠘⡂⠀⠀⠀⡌⢠⠁⡀⠀⠀⢪⠝⠉⠈⠉⠈⢰⠇⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⠹⠆⠀⠺⡁⠈⠛⠀⠀⠈⡇⠀⠇⠀⠀⠀⠇⢰⣀⡀⢀⡁⠀⡑⠲⠄⠒⠒⠅⠀⠀⡘⠑⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⡌⠁⠘⣄⡠⠤⡀⠀⡤⠤⠰⠋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠠⠊⠑⠠⠄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⠈⠉⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡼⠁
⠀⠀⢀⠴⠒⠛⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⢀⡼⠟⠉⠉⠻⢧⡀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠛⠒⠦⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⣠⠏⠀⠀⠀⠀⠀⠀⠹⣄⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣤⣤⣤⣤⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⠟⠛⠛⠻⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⣴⡶⠶⠛⠋⠉⢠⣿⣶⣶⣶⣶⣿⡄⠉⠙⠛⠶⢶⣤⠤⠤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣠⠋⠉⠉⠉⠉⠉⠉⠛⣄⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠋⠈⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠃⠙⠲⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡘⠦⠈⡀⠶⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠹⣇⠈⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠂⣾⠀⠐⢶⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡕⢀⠠⠁⡄⢀⠀⠀⠀⣟⠡⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⣷⠺⣤⣼⡴⠀⠀⡟⢀⡐⡤⣤⢴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣷⠆⠀⠀⠀⠁⠚⠂⠀⠀⠀⠀⠀⠀⠀⣤⣤⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠋⠀⣿⢦⠐⢀⣿⢿⣿⡆⠀⡨⠱⣏⠃
⠀⠀⠐⠄⠠⡠⠤⠀⢰⣿⡏⡀⢀⡦⠐⢀⣴⠆⠀⢀⠀⠀⠀⠀⠀⠿⢹⡟⠂⠂⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢻⠀⠣⠁⠒⠸⠈⢳⠀⠁⣸⠈⠁
⠀⠀⠀⠀⠤⠀⠀⠄⢸⢿⣇⢠⣿⣴⡞⠛⢁⠀⠀⠈⠀⠂⠀⠀⠀⠀⡎⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⣼⡇⢸⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡧⢾⠏⠉⠠⠈⠀⠀⢈⠀⠀⠀⠀⠀⠺⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⡆⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢠⡿⡷⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⠄⠀⠀⢸⣀⠀⢺⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣉⠄⠀⠀⠘⠈⠁⠋⠉⠁⠈⠁⠀⠀⠀⠈⠉⠉⠈⠁⠁⠉⠁⠰⠄⠀⠀⠀⠸⡆⠀⠐⠀⠀⠀⢈⠧⠀⠀⠀⠄
⠀⠀⠀⠐⠋⣼⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣀⣠⣤⣤⡴⠶⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣳⠔⡂⡀⣀
⡄⠄⠀⠀⠰⣿⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⠛⠿⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠰⠒⣫⡉⠘⠈
⠀⢆⠈⠀⢾⣿⣿⣷⣦⠴⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃⠉⠉⠤⠿⠤⢥⣤⣶⣶⣶⣤⣤⣄⠴⠤⠠⢾⣿⠔⠂⠀⠚
⠀⠈⣀⠀⠈⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⣿⣿⣿⣦⣠⣤⣾⣵⣆⣀⣤⣤
⠀⠀⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠛⣿⣿⣿⡋⠛⣿⣿⣿
⠀⢀⣤⡄⣀⠀⠀⡀⠀⠀⣤⡀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣟⡙⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿
⣴⣿⣿⣽⣋⣂⣔⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠠⣤⣤⣶⣴⣾⡿⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⣶⣤⣤⡄⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣿⣿⣿⡷⠀⠀⠀⠀⠀⢠⣴⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⣶⣶
⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⠇⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠃
⠀⠀⠠⡄⠐⠀⠀⢠⣴⡴⠛⣡⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡇
⠀⠀⠀⠀⠐⠀⡋⠅⠨⠀⣙⣷⢿⡿⠛⢖⡤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠠⢈⣿⣿⠑⣒⠛⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠰⠆⢹⣍⢞⣓⡢⣆⣍⡍⣰⣰⣦⣤⡄⠀⠀⠀⠠⡤⠀⠀⢀⣀⣀⡀⢀⠀⣀⠀⣼⡾⣧⠮⢴⣨⣅⣰⣮⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢶⢘⣷⣿⡴⢋⠛⣮⣵⣷⡛⠀⠉⠉⠁⠀⠀⠀⣰⠌⠁⣉⣹⣶⠟⠀⠀⠀⢀⣠⣿⡟⣻⣿⣻⣭⡷⠿⢭⣭⣴⡻⣶⢭⡅
⠀⠀⠀⠀⠀⢀⣀⠈⠫⣤⣀⣼⣿⣯⣶⢛⠟⡻⢿⠛⣭⡐⠺⠀⠀⠁⠛⠀⡟⢿⣟⣟⣥⡞⠉⠀⠀⣳⣿⡯⠛⣡⣷⣿⠿⠀⣨⡀⡌⣷⡾⠿⠿⠋
⠀⠀⠀⠘⠛⠉⣉⣙⡓⠲⢿⣶⣤⣶⣷⣿⠈⣠⡟⢷⠘⠋⠀⠀⠀⠀⠀⠀⠠⡚⢛⣻⡟⠀⠀⠀⠀⠉⠉⠀⠀⠿⢟⣿⣤⣠⣿⣷⣿⣿⠷⠚⣓⠉⠉
⠀⠀⠀⠘⢲⣤⡌⣥⡄⣤⢠⣾⣷⣚⣙⣯⣛⣙⡏⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⣿⣟⣿⣏⣩⣿⠿⠿⠟⠓⠒⣀⡄
⠀⠀⠀⠀⡈⣀⠀⠀⠀⢉⣛⣋⣩⣿⣏⣉⣉⣭⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣴⣾⣿⡇⡀⢀⠀⣐⣩⣅⣽⡿⠃⠈⣻⠯⡍⢀⠀⢀⣰⣤⣾⠷⠚⠉
⠀⠀⠀⠀⠁⠛⢛⡁⠀⠀⣀⣀⣀⠉⣩⣛⣿⣿⣿⣴⠂⠀⢀⠀⠀⣀⠀⣼⣾⣽⣿⡏⠀⠀⠀⠀⠘⣿⣿⠟⠁⠃⣿⣶⣶⠶⠟⣋⣉⠩⢍⣁⣀⣠⠄
⠀⠀⠶⣤⠶⣤⣼⠧⢤⣄⠁⠀⢉⣝⣯⣿⠏⠉⠈⠀⠀⠀⠈⠘⠐⠀⠀⠀⠛⣿⣿⠧⠤⢄⡀⠠⠤⡿⣿⠖⠘⠣⣼⣌⠤⠀⠀⠀⠀⢀⡳⢌⡟⠉
⠀⠀⠀⠀⢨⡇⠹⠈⠳⠦⣤⡤⠀⠉⢻⡷⠀⠀⠀⠋⠀⠀⠀⠀⠒⠂⠦⠄⣄⣤⡠⠄⠀⠀⠤⣀⡀⠀⠈⠀⢀⣠⣈⣥⡤⠾⠧⡎⠛⠀⠸⣿⡉⠋⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠿⠁⠀⠀⠀⠒⠂⠀⠀⠁⠀⠁⠀⢀⢀⡄⠀⢀⠀⠀⠉⠁⠀⠀⠶⠐⠋⠛⠋⠀⠴⠶⠂⠙⠰⠆


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣄⠀⣿⢹⡿⠀⠙⠻⠛⠁⠀⠙⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠉⠉⠐⣩⠿⣇⢠⡟⠂⠤⠐⢷⣶⡿⠉⠙⢷⠀⠴⡰⠄⠀⠠⣄
⠀⠀⠁⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠘⣧⠠⠐⡳⣋⠠⠛⢻⠇⠀⠀⠀⠘⢿⡀⠀⠈⠁⡙⠤⠹⠇⣿⣃⣹⣆⠐⢀
⠀⠀⠀⠐⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⠃⡀⠛⠁⠀⠚⠀⠀⠀⠀⣀⣤⡲⠉⠀⠀⠀⣯⠀⠀⠀⠈⠁⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⣥⣤⠄⢀⢴⠂⣴⣶⠐⠈⠁⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⣾⣯⢐
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⢬⣄⢿⡤⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⢀⠙⠟⣾
⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠀⠈⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠨⣾⣷⣖⣿
⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢂⠀⠀⣦⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⡇⡹⣿
⠀⠀⠀⠇⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⣦⡀⢀⡈⠑⠟⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠐⠀⠀⠰⣽⣿
⠂⠀⠀⠀⠀⠀⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⢀⣶⠀⢋⢁⣈⣉⡡⠄⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⢹⢿
⡃⠀⠀⠀⠀⠀⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠰⣤⡀⠀⣿⣿⡇⠺⠋⠉⣀⠖⢀⠆⠀⠀⢠⣌⣛⠉⠀⠀⢀⣀⣰⡁⠀⠀⠀⠀⣠⠀⣶⣿⢴
⠇⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣠⠂⠀⠀⠀⠙⠶⣿⣿⡦⣀⡄⠈⢁⢰⡟⠀⠀⠀⠀⢸⣯⡀⠀⠒⠉⠉⠉⠉⠂⠀⠀⣴⣿⠀⡿⣿⠛
⣧⡀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢸⠃⠀⠀⣠⣾⣿⡿⢻⣿⣿⣿⣷⠀⠻⡌⣃⣶⠀⠀⠀⠻⡗⠉⠀⠀⠀⠀⠀⠀⠀⠰⣌⠋⢻⠀⣴⣿⠟
⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡞⠀⠀⢰⣿⠿⠋⢠⣿⣿⣿⣿⣿⣷⣄⡦⣿⡇⠀⠀⠀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠉⠁
⣿⡇⣀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠁⠀⠀⠚⠁⠀⠀⣿⣿⢹⣿⢻⣿⣿⡈⠁⣿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠼⢷⣶⡟
⣿⣿⡇⠀⠀⢀⡆⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⢿⠀⠙⣿⡆⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣻⠀⢸⣧⡜
⣿⡿⠃⢸⡇⢸⣷⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠀⠀⠇⠻⠀⠀⣂⠀⠆⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⢡⡀⣀⣼⡀⢸⢉⣿
⣻⠠⢞⣿⡇⣾⣿⡄⣿⣿⣿⣧⠀⠀⢀⣀⣠⣶⣄⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣧⢶⡄⠀⢈⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⣿⣿⣾⢋⣁⣛⠃⠈⢿⡿
⣷⣄⣿⣿⣻⣿⣿⡇⢿⣿⣿⣟⡀⠈⠉⠉⠉⢳⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⡀⡰⠂⡅⠀⢸⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢹⡏⠰⠁⡙⢿⡁⠀⣤⡄
⣿⢟⣿⢣⣿⣿⣿⡇⢸⣿⣿⣿⣿⣦⡀⢠⣤⠀⠃⠀⡀⠀⡆⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠐⢿⣿⡀⠀⠀⠀⢠⠂⢴⡇⢠⠇⠼⠛⠁⣠⡌⠁
⡿⠟⣡⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⢋⣥⣔⢆⣤⡐⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢃⠋⡆⠀⣼⡇⠀⠀⠀⣿⠏⠠⠀⡀⣈⣴⡳⠦⠛⡖⠳⠿⠈⠉⡟
⣴⣾⣿⠟⣿⣿⣿⣿⢸⣧⠙⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣰⡀⠀⣗⢃⢤⠄⢾⢧⡄⠈⠀⠡⡘⠈⠁⠢⠜⢝⡉⠀⠌⠦⡹
⡿⣿⠏⠀⣷⣿⣿⣿⠀⣿⡍⢻⣯⠛⢛⣛⡁⠀⠀⠀⠀⢃⠀⣼⠆⢠⡶⠀⠀⡇⢠⣄⠀⠀⢹⠃⠀⢿⢻⠸⡒⠲⢦⠘⣖⠁⠐⠣⠌⣋⡔⠦⠈⢀⠉⠈⠳⠦⠤
⣷⠎⠉⠂⣬⣿⣿⣟⠀⣿⣗⠀⢰⡾⣿⣿⣿⡀⠀⠀⠀⠘⣦⣾⠀⠀⢴⣶⣤⣀⠈⠚⢶⣄⠈⠁⣰⣶⣼⣇⢑⠟⣿⣿⠯⣧⠀⠛⠛⠉⠉⡅⠰⣤⠉⠀⢄
⣠⠀⠠⣠⣿⣿⣯⢹⡇⠹⣿⡄⠀⢻⣻⣿⡿⣧⠀⢠⣜⠦⣹⣿⢻⡏⠀⠉⠉⠻⡿⣗⣎⣻⣷⠄⠈⢳⣟⢶⢾⡇⣿⣿⣆⡀⠃⠀⠀⠀⠀⠀⠀⣳⠃⠀⠈⠱⡄
⠀⠰⢰⣿⣿⣿⢣⣿⣿⠀⢻⣟⠀⠀⠃⠟⢿⡘⠃⠀⢨⣿⣌⣿⣾⠽⠆⠀⠀⣤⣰⡏⣛⠏⣿⢀⣧⣄⢹⣿⣿⣿⣭⣭⣽⠃⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⣼⣿⠿⢫⣿⣿⣿⠀⠈⠿⠛⠀⠀⠀⠈⠀⠀⠀⠀⠈⢻⣏⠴⠲⡶⣠⡀⠀⠉⠀⢴⣶⠇⢈⣁⡩⢅⢉⣬⠻⣿⣧⡜⢿⡒⢛⣠⣤⣴⡶
⠀⠀⢿⣿⠀⣾⣿⣿⣇⠀⠀⠀⠀⣽⣾⣷⡀⠀⠀⠀⠀⠀⠘⣣⡛⣀⠀⠻⣿⣆⠂⣀⠀⠻⠀⣦⣭⣿⣾⣟⣷⠶⠂⣶⠛⢫⣾⣿⣿⣿⠛⠓⠂⠀⠀⠀⠀⠀⠑
⣆⠀⣾⠻⣇⣿⣯⣼⣿⠳⣆⠀⣿⣼⢿⣼⠗⠀⠀⠀⠀⠀⠀⣹⣯⣉⠑⢆⠸⣿⣴⣿⠿⠂⢀⠻⢿⣾⣿⣿⠋⠀⠀⠀⠀⠺⣿⡿⠋⠅⠐⡿⠀⠀⠀⠀⠀⢄
⣿⡀⣿⣀⠈⠻⠉⣿⠿⣟⣻⣦⣿⣋⠈⠉⠂⠀⠁⠀⠀⣤⡼⠿⠟⢷⣽⣎⣶⣛⣿⡏⠋⠀⠀⠻⡶⢿⢿⡏⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠁
⣽⣧⣿⣿⢶⡀⣮⣏⣠⣽⣿⣏⣽⣻⣶⣄⡀⠀⠀⢴⡶⡾⢃⣤⣤⣜⡿⣿⢿⣿⣿⣧⣤⣠⠀⢐⡿⣤⠀⢤⠀⢀⡄⠀⢀⣄⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⢤⡤⣤⡷⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⠬⡇⠀⠀⠀⠀⠀⠀⣠⠼⠁⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⡟⠲⠊⠙⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⣇⢀⣀⠀⢀⣀⠀⣸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢛⡏⠀⠀⠀⠀⠀⠀⠈⢻⡀⡍⢩⠄⡏⠁⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣇⡖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣄⣠⢧⡀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠱⡖⠁⠀⠀⠀⠀⠀⠀⢀⡤⠧⠾⢤
⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⡞⠛⠒⠛⠛⠛⠋⣻⠀⠀⠀⠀⠀⠰⣧⣠⢄⣤⣤⡷⠀⠀⠀⠀⠀⠀⠀⣸⠖⠦⠔⠺⡇
⠀⠀⠀⠀⠀⠘⠲⣍⣙⣚⣉⣙⣒⣋⡹⠚⠁⠀⠀⠀⡿⠿⠿⠿⠿⠝⠛⢿⠀⠀⠀⠀⠀⠀⠘⢦⣶⣤⡞⠀⠀⠀⠀⠀⠀⠐⢾⣛⣒⠒⠒⣓⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡗⢯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡔⣩⠥⠬⣝⢦⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠎⣡⠤⣍⠓⣄⠀⢳⠀⠀⠀⠀⠀⢸⢸⠁⡏⠵⣸⢀⡇⠀⠀⠀⠀⠀⢸⡁⢀⡀⢀⡀⢀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡁⣄⠈⡇⢸⡆⣸⠀⠀⠀⠀⠀⠈⢮⡳⢬⣯⡵⠾⠃⠀⠀⠀⠀⠀⣿⠙⣯⢹⡏⢹⡇⣹⠂⠀⠀⠀⠀⠀⣿⣿⣯⣍⣉⣽⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡳⣌⣙⣁⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢿⢸⡇⣼⢠⡏⠀⠀⠀⠀⠀⠐⡏⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠛⠛⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠠⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⢮⡹⣆⠀⠀⠀⠀⠀⠀⠀⢧⢠⡤⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠸⠁⠀⢀⠁⠀⢳⠀⠀⠀⠀⠀⠀⣰⢻⡄⢳⠀⡟⠋⠀⠀⠀⠀⠀⢰⡋⠚⠁⠀⠙⢋⣷⠀⠀⠀⠀⢰⢏⠀⢧⠀⠀⡼⠁⡹⡆
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠃⢀⡏⠀⠀⠀⠀⠰⣎⠳⣀⢣⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠰⡏⠀⠀⠀⠀⠀⠸⣄⢹⡚⠓⠚⢑⡟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡖⠛⠋⠀⠀⠀⠀⠀⠀⠘⠲⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠲⣄⠙⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⡀⠸⠄⢲⠾⠑⠀⠀⢤⡄⣠⡾⠳⠄⢀⡀⠊⠀⠠⠤⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣉⠡⣤⣰⢶⠠⢶⣤⣤⠶⠲⡿⠟⣻⣿⣿⣭⣴⣈⣴⣠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠺⣶⣤⣌⣿⠟⣤⢠⠀⣄⠰⣶⣯⣿⠟⣿⠁⡸⢿⠿⣿⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⣱⣿⣰⡞⢺⠃⢾⠀⠈⢀⣿⡿⡵⣇⠛⠀⠐⠚⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡐⠛⠛⣶⠘⢡⡼⠀⡌⠈⠀⠀⠀⢸⣿⡇⠂⠁⠀⠀⠀⠀⢻⡐⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⡤⢦⣄⠉⣦⣰⠅⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣵⣎⡭⠀⠀⢀⡠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⡄⠀⠐⢲⣦⣾⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⡀⠀⠀⢱⣾⡧⠀⠠⣁⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣬⠿⠃⣄⣴⣿⣿⢁⠔⢀⣶⣄⠀⠆⠀⢸⣿⡂⠋⠙⠆⠀⠀⠴⣷⣤⡸⠶⠚⣃⣨⡿⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡤⣴⡉⢀⣀⡙⢦⣄⣨⣿⠃⠀⢲⡾⢩⣿⣿⣄⠀⠀⠀⠙⠄⠀⠀⠀⠴⣶⣚⣻⣽⣿⣟⡛⠫⠁⠲⡿⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡝⠲⠋⢳⣦⡀⢿⣿⡿⣋⠁⡄⢠⣿⡾⠛⣿⣿⠡⡄⡀⢀⡀⡄⠀⠀⢰⣾⠿⢭⣴⣿⣗⠻⣷⠀⢀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⣿⡿⣿⡿⡼⠁⠐⠀⢸⣋⣴⣶⣾⡿⠀⠁⠁⠈⠁⠀⠀⠈⠀⡟⠀⠈⣿⣩⣿⣆⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣥⣾⠋⣩⣥⡾⠁⠀⠀⠀⠀⡯⡥⠀⢚⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠐⠋⠉⢚⣿⡇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣷⣯⡿⠁⠀⠀⠀⠀⠀⠶⠿⠶⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⠀⠤⠐⣡⢌⣵⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠺⣿⣀⣎⣿⠇⢀⠀⠀⠀⠀⣶⣶⠾⢛⣭⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠁⠀⠀⢈⣭⣼⣷⣶⡆⢁⣄⡏
⠀⠀⠀⠀⢴⡀⠀⠚⡛⠿⣆⣡⣴⠟⠿⠀⠚⠴⠀⠀⠀⣿⠇⣤⣾⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠂⣠⠶⣟⢛⡛⣹⡟⠃⠀⠿⠁
⠀⠀⠀⠀⠀⠁⣀⣀⣰⣿⣻⣿⣡⣠⣆⡠⣤⢀⠠⣦⣤⣶⣞⣿⡿⠿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣠⡄⠸⢉⣿⣷⣤⡀⠀⣲⡀
⠀⠀⠀⢀⣀⣆⣽⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣋⡿⠿⠧⠙⢿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⡴⢞⣡⣼⣿⠉⠃⢘⠛⢃
⠀⠀⠀⠀⣠⣼⢿⣿⣶⣿⡟⣸⠟⢶⣿⣿⣿⢡⡿⢿⣶⣿⣶⣾⡎⡗⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⠑⠯⠙⠻⢿⡀⢤⣀⢬⡻⡄
⠀⠠⣶⣾⡯⠻⠆⢻⣿⣿⡄⣃⢰⡟⡻⠿⡏⣼⠁⠘⢸⣿⢿⣿⡇⠅⠀⠘⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣀⣀⣀⣰⣾⡇⠀⠛⠈⢷⠱⡄
⠀⠀⠹⡇⠀⠀⠤⣸⡟⣸⠷⣼⣿⠁⠝⣿⠁⠏⠀⠀⣸⡿⣾⢿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢻⡿⠟⢋⣹⣄⠀⠀⠀⠈⠇⠸⠃
⠀⠀⠀⣧⠂⢰⣿⡿⣱⢆⡾⢏⠋⠀⠐⣡⢸⠀⢀⡄⣿⠢⠔⣶⣿⠂⠘⠂⠀⠹⠀⠀⠀⠀⠀⠀⢀⣠⡾⢿⣿⣏⣤⣾⣿⣿⣿⣷⠀⠀⠀⠘
⠀⠀⣰⣿⣄⣤⢿⠃⠁⣺⡇⠸⠁⠀⣰⡇⠀⠀⠙⠂⣿⣄⣄⡀⣿⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢰⣿⣤⣶⣾⠿⡿⠋⠀⠹⡏⠈⣷⣄
⠀⠹⠟⠋⠘⠿⠀⠀⡀⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣛⣿⣿⣿⠇⡶⠀⠀⠀⠀⢻⡇⠀⠀⣸⣿⡿⠉⠗⠈⡿⠁⠀⠀⠐⠏⠉⢨⣷
⠀⠀⠀⣤⣤⣘⠀⢀⢩⡇⠀⠀⠆⠀⣿⠅⠀⠀⣀⢸⡟⠋⠉⠰⣾⡀⠀⠀⠀⢀⣀⠘⡇⡀⢠⡟⣁⣠⣶⣀⣦⣀⣀⣀⠐⠀⣦⣲⣿⣿
⠀⠀⠀⠘⠲⡟⠀⠈⠈⠀⠀⠀⠀⢠⣿⠀⠀⣄⠁⠀⣿⡿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠁⠸⣿⣿⣿⣿⣯⢿⣿⣛⣿⡿⢺⣿⠾⠛⠟⣦⡀
⠀⠀⢰⡿⠿⠃⠀⠀⠀⠀⠀⢸⣇⢼⠟⢰⡔⠛⠀⠰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠇⠉⠘⠛⣁⣈⣿⡁⣀⣷⣿⣥⡀⠳⡄⣹⠊⢶⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠿⠻⠻⣿⠋⠉⠀⢬⣌⠛⣿⣿⣶⣿⠛⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣉⣁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠛⠶⠶⠞⠉⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⣷⡀⠀⠫⠙⠁⠰⠏⣿⣿⡗⠀⣄⡿⠦⢀⣤⠠⣽⣶⡖⣿⡟⠙⠘⢷⡦⠀⢠⢇⣦⡄⠀⠀⢴⣄
⠻⣷⡀⢠⠀⣠⣐⣹⠇⠈⣿⣸⣯⠇⠀⠀⢀⠀⠨⣽⣱⠋⠀⠀⠀⡮⠑⣄⠈⠸⢧⡅⢴⣦⠤⢿⡄⠀⢀⡀
⡀⠹⣷⠐⠂⣉⣬⣱⠄⠒⢈⡡⣞⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠁⠀⠀⠐⡌⠳⠂⠈⠇⢼⣧⡳⣄⣿⣦⠀⠙⢦
⢿⣦⡘⠆⠁⠀⠛⠁⠀⠆⠘⠁⠀⠀⠀⠀⠀⣠⢠⡤⣱⠍⠀⠀⠀⠀⠈⣽⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⣗⠀⠄
⠀⠉⢻⣦⣂⠀⠒⠀⠀⡀⣠⣤⠀⣨⣅⡰⠤⠉⠓⠋⠁⠀⠀⠄⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡝⠇⠦
⠀⠀⡶⠈⠻⠝⣯⡈⢁⡇⠓⠀⢠⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡆⢦
⠀⠀⢀⣀⠠⠔⠶⣶⢈⣫⠷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠀⠀⠀⠀⠀⠀⣀⣁⠹⠿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⠀⠀⠀⠀⠀⠀⢚⣲⣿⣶⡆⣿⣿
⠀⠈⠃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢡⡐⠀⠀⠀⠀⠈⣿⣿⠟⢴⣿⡟
⠀⠈⠀⠀⠱⠄⣀⡀⢹⣶⣀⢀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡀⠀⠐⠀⠉⢀⠀⠀⠀⠀⠈⠙⠁⣼⣿⣷
⠀⢘⢆⠀⢀⡀⠀⠙⠪⡗⣿⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠲⠀⠀⠀⢶⣼⣿⣿
⠀⢸⠜⠓⠀⠛⠚⠶⠀⠀⠁⠀⠀⠀⣀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢻⣿⣽
⠀⠀⣦⣤⣶⡶⠖⠛⣉⠍⡺⠲⠆⠀⠀⠀⢠⣤⡄⣤⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠚⠁⠀⢱⠀⠀⢀⣼⡏⢿
⡇⠀⠛⠉⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⣀⣶⣤⣝⠃⠀⠀⠀⠀⣀⣀⣠⣇⠀⠀⠀⠄⠀⠀⠀⣼⠀⢶⣿⣿⠱⣿
⣥⡄⠂⡀⠀⠚⠁⢠⣦⡏⠀⠀⠀⠀⠀⠐⢧⣍⡀⠀⠀⠴⠚⡉⠉⠋⠉⠛⠢⠀⠀⠀⣠⣴⣿⠀⢸⣿⣏⡾⡛
⣷⣾⣷⣏⠀⠀⣾⢸⢷⠀⣀⠀⠀⠀⠀⢐⣿⣟⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠻⣿⠀⠘⣡⣾⣦⣆
⣿⣿⣿⣿⣃⠀⠻⢺⢸⣰⣿⠀⠀⠀⠀⠉⠹⡇⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠢⠀⠀⣹⠀⠠⡟⣿⠙⠉
⣿⣿⣿⡿⣿⣧⡀⣾⢸⣿⡯⡄⠀⠀⠀⠀⡀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉
⣿⡻⣿⣿⣾⡏⠓⠜⢸⣽⠂⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⣾⣂⣀⣦⣧
⣿⡇⠹⣿⣿⣷⠀⠀⢈⠟⡀⢠⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⡇⠉⣿⠿⠳⣤
⢹⠁⠀⠈⢻⢿⡄⠀⠀⢹⢱⠸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⡅⠀⣿⣷⣤⢛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣠⣄⠠⣤⣤⠄⣀⣠⠄⣄⣤⣤⣤⠀⠀⢤⡄⠀⣠⡄⠀⠀⣀⡄⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠁⡎⣿⡁⢳⣿⠛⠀⣿⡿⢿⢻⠀⢰⡿⠛⠀⣼⡿⢂⢸⣿⢖⡟⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⠏⠸⡟⠰⠆⠘⣤⣠⠋⠀⢼⠿⠀⢳⠈⡇⠘⠈⣩⠾⠃⢀
⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⣀⠀⠁⡶⢵⠙⠉⠣⢄⡃⠀⠀⠈⣦⡃⠀⠠⠃⣠⣤⠊
⠀⠀⣰⣶⡀⠀⠘⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡆⠐⢷⠀⠀⠀⠑⠄⠀⠀⡟⠀⡠⠃⠸⡹⠋
⠀⠀⢹⣿⣿⣆⣀⡆⠹⣿⣿⣿⣿⣿⣓⠦⣀⠀⣀⢠⣐⡒⠢⠀⠀⠹⡀⠘⡄⠀⠀⠀⢇⠀⡴⠛⠉⠀⣠⠏⠀⠀⠀⢀⡀
⠀⠀⠘⠻⢿⣿⣿⣧⡀⣿⣿⣿⣿⣷⣌⡛⠆⢝⢷⣿⣿⠿⠷⣬⣦⠀⠈⠒⠷⠤⢤⣄⡈⣾⠁⠀⣠⣥⣏⣠⠄⣀⠁⣤⣢⡵
⠀⠀⠀⣶⣄⠉⠻⣿⣷⣿⣿⢿⣿⣿⣿⢟⢦⡑⠁⠘⢿⣷⣔⣽⠟⢳⠂⠤⢀⣀⠀⣀⠹⣧⠀⠸⣿⡟⢩⡑⣌⡀⣤⣾⡟⢲
⠀⠀⣠⣿⡓⠀⠀⠈⠛⢿⣿⣷⣍⢻⡿⣵⣷⡙⢦⡀⠀⢝⢿⣿⣿⣄⡀⠀⠀⠀⠹⡇⣰⣷⣤⣶⣿⣿⣾⢿⣿⣿⣿⣿⠟⠛
⠀⠀⣿⣿⣃⠀⠀⠀⡀⠀⣿⣿⣿⣅⠑⡈⠻⣿⣆⠳⣌⢈⢻⣿⣿⣾⠟⠿⠶⣤⣶⣿⣟⠉⠉⠉⠛⠛⢷⡀⠀⠀⠈⣿
⠀⠀⣿⣿⣻⣴⣀⣀⣷⡆⡿⠻⢿⣿⣻⣿⣦⡙⢞⢷⡙⣧⡰⡻⣿⣿⣿⣿⣵⣾⣿⣿⣯⣴⡢⠀⢀⣤⣸⣧⠀⣠⠂⣸⣄⠀⡀
⠀⠀⠻⠿⣿⣿⣿⣿⣿⣵⣆⡀⡀⢹⣿⣿⣿⣿⣌⣿⣷⣜⣷⣱⣻⣿⣿⣿⣿⣁⣽⣿⣿⣿⣧⠿⢿⣿⡿⠿⠚⠷⢏⠀⠀⠉⡁
⠀⢸⣀⠀⠀⠉⠉⠀⠈⠙⡿⠛⠓⠛⠛⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⡋⣧⣄⣀⠀⠀⠀⠀⠀⠈⣦⣤⣴⠇
⠀⢸⣿⣾⣆⠀⡀⠀⢨⣄⣿⡖⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⣿⣿⣿⣿⢿⠿⠃⠀⠀⠀⠀⠀⢿⣿⠇
⠀⢸⣿⣿⣿⣿⣿⡧⢘⣼⣿⣿⠀⠀⠀⠀⣀⡀⠀⢈⣿⣷⡮⣙⠛⢟⡻⢬⣭⡙⠻⠿⠿⣿⣿⡇⣳⣤⣀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⣿⠿⠿⠛⠛⠛⠻⣿⣿⣯⣀⠀⣶⣿⡿⣴⣶⣭⡻⢿⣿⣿⢧⣠⣌⠲⢌⡙⣷⡦⣀⡁⠛⢿⣾⣧⣿⣗⣄⡀⠀⠀⠈⡷
⠀⠀⠁⠟⢛⡀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣛⣜⢧⡉⠻⣿⠷⣽⡻⣓⠈⠋⠛⢦⡙⠷⣍⠀⢭⠢⣄⠈⠻⡿⣧⣴⣉⣿⡷⠞⠃
⠀⢸⢸⢿⡟⡒⠀⠀⠐⣿⣿⣿⣭⡇⠀⠈⢹⣷⣝⢧⡈⠳⠄⠙⢮⠳⣿⣦⡀⠙⠷⣌⠻⣦⡉⠀⠱⣄⠈⠪⣙⢿⡉
⠀⢸⣸⣴⣯⣅⠀⢀⡞⣿⣿⡛⢯⡓⠀⠀⠸⣿⣿⣅⡱⣄⢠⡀⠢⡑⢌⠻⣿⣦⠀⠘⢷⣌⠻⣦⡀⠪⡻⣄⠈⠳⣿⢦
⠀⢸⣺⣿⣿⣷⣯⡾⣣⣿⡏⢈⣧⡑⡄⠀⠀⢻⡿⠛⠳⠿⣿⣿⣄⠙⣦⠣⡈⢻⣷⠀⠰⣿⣷⡜⢿⣄⠙⣞⢷⡕⣌⢳⣷⣄
⠀⢸⣙⣻⣿⡿⠿⠋⠁⠙⢷⡀⠺⢳⣗⣦⠄⣸⣿⡤⠀⠀⠈⠙⠛⠂⠸⣷⡙⣆⠻⣦⠀⠘⣿⣿⣆⠙⢷⡈⢳⡻⣟⢦⠙⣧
⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠋⠉⠓⠒⠚⠛⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠛⠓⠘⠂⠙⠃⠀⠘⠛⠙⠃⠀⠑⠀⠛⠛⠋⠓⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁
⡝⠀⣰⡅⠀⠀⠀⠐⠦⠀⣀⠀⣴⣄⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⡀⠀⠀⢾⣦⣄⠀⠻⣀⠀⠀⠀⠠⠄⠀⠘⡠⠀⡀
⠀⠀⠹⢧⡀⠀⠲⢦⡀⠠⠤⢄⡀⠘⠄⠀⠀⠀⡇⠡⠄⠀⠀⠸⠇⠀⠀⠈⠉⡆⣶⠄⠠⣄⠀⢦⣠⠀⠀⠘⠃
⡀⠀⠀⠾⣿⣃⠀⠈⠁⠀⡤⡀⠈⠑⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⣦⠈⣯⡉⠑⠆⣴⠀⠀⠙⢃⣀⡄⠀⣄
⠀⠀⠀⠀⠉⠁⠙⠃⠀⠀⠹⠧⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠰⢰⡆⠃⠀⣿⠀⠈⠙⣦⠀⠙⣆⠀⠀⠀⢿⣷⡀⠀⢻
⠋⠈⠐⠠⡄⠀⠀⠀⠀⠲⣤⡄⠀⠀⠀⠀⠀⢰⡇⢂⠈⠀⠀⠸⠇⠀⠀⠉⠀⠀⠈⠈⣦⣠⠤⣀⠀⠀⠀⢩⠶⣤⡀
⣷⠀⠀⠀⢁⣾⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣙⠀⠀⠁⢀⠈⠁⢈⢈⠁⠀⠀⠀⢻⡃⠀⠈⠀⠀⠀⠀⣰⠏⠁
⠉⠀⠀⡠⠋⢙⡇⠀⢀⣉⡉⠀⠒⠒⠚⠉⠉⠩⠍⠉⠠⠠⠀⣼⠄⠀⠈⢸⡀⠀⠀⠀⠈⠱⠦⣀
⠀⠀⠀⠀⠀⠉⠛⠂⠈⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣄⣬⣥⣤⡤⠤⠚⢢⡀⠀⢀⡀⠀⠈⠰⣄
⠀⠆⠀⠀⠚⠛⠃⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠂⠀⠒⠓⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣵⣤⡀⠈⢁
⠀⠀⠀⢶⣤⣤⣀⢀⠀⠈⢀⠀⠀⢀⡀⠀⠀⢰⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁
⣨⣥⣤⣾⠿⠛⠛⠛⠛⠿⣿⣿⣿⣉⡀⠀⠀⠙⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⣠⣀⣤⣾⠿⠋⠉⢀⣀
⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣤⣄⣄⣀⣀⣠⣤⠴⢦⡴⠤⠤⠤⠴⠿⠛⠉⠁⠁⠀⠀⠀⠐⠛⠛⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⣤⠖⢿⠉⡟⢑⠦⣄⠀⠀⠀⠀⠀⠀⠀⡖⠒⢏⠉⠓⢦⡀⠀⠀⡞⢳⠞⢳⠞⢛⠖⢛⡖⢛⡆
⠀⠀⠀⠀⢀⠾⣀⠳⣸⣼⣡⣋⠴⠚⢧⠀⠀⠀⠀⠀⢠⠟⢦⡀⠑⢄⠀⢳⠀⠀⣇⡏⢀⡎⠀⡞⠀⡞⠀⡼⡇
⠀⠀⠀⠀⢸⠦⠬⢵⣿⣿⣿⣷⣚⣉⣙⡆⠀⠀⠀⠀⠈⣇⠀⠙⢦⡀⠑⡏⠀⠀⣟⣀⣜⣀⣼⣀⣼⣁⣸⣁⡇
⠀⠀⠀⠀⠸⡖⠒⣩⢿⢿⢿⢯⠲⢤⣹⠁⠀⠀⠀⣠⢞⡽⠓⠲⠶⠛⠒⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡽⣏⣠⠏⡼⠸⡆⢳⡴⠃⠀⠀⣠⢞⡵⠋⢀⣀⠤⣀⣀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠦⣄⠀⠀⠀⢠⠒⡿⠛⠛⠓⣦
⠀⠀⢀⡴⡫⠊⠀⠉⠓⠓⠒⠋⠁⠀⠀⠀⣞⡵⠋⠀⠀⡇⠀⠀⠈⢉⠇⠀⠀⣼⠁⢠⠖⠓⠂⠀⠘⡆⠀⠀⡞⠉⠛⠓⠒⠋⢹
⢀⡴⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡜⠀⠀⠀⠹⣄⠀⠁⠀⠀⠀⡰⠃⠀⠀⣇⠀⠀⠀⠀⠀⣀
⠻⠚⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣼⡅⠀⠀⠀⠀⠈⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢶⠲⢤⠋⠉⠉⠉⠈⠈⠙⡤⠖⡆⠀⠀⠀⡼⠉⠉⠉⢧⠀⠀⠀⠀⢠⠤⣄⣀⠔⠚⠉⠓⢦⣀⣠⠤⣤
⠀⠀⠀⠀⠀⢯⢀⣸⣄⠀⠀⠀⠀⠀⢠⣇⠀⡝⠀⠀⢰⠁⠀⠀⠀⠈⣇⠀⠀⠀⢞⠀⠀⡏⠀⠀⠀⠀⠀⡯⠀⠀⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠺⠤⠤⠤⠤⠤⠿⠀⠀⠀⠾⠴⠒⠛⢦⣀⣀⣀⠴⠋⠒⠮⠇
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⡅⡇⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⢸⢨⠆⠀⠀⠀⠀⡏⠀⢠⠃⠀⡼⠁⠀⡼⠁⠀⡼⠀⢈⡷⡄
⠀⠀⠀⠀⠀⠀⢘⡅⡇⠀⠀⡎⠁⠀⠀⠀⢹⠄⠀⢸⠠⡃⠀⠀⠀⠀⠈⠓⠛⠒⠚⠓⠒⠚⠓⠒⠚⠓⢲⠋⠀⢹
⠀⠀⠀⠀⠀⠀⢨⠆⡇⠀⠀⠈⠒⠶⠴⠒⠋⠀⠀⢸⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠚⠒⠋⡽
⠀⠀⠀⠀⠀⠀⠰⠷⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣓⡦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡈⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠑⡄⢻⡀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣄⠀⠑⠄⠹⡘⣇⠀⢀⡷⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣄⠢⡱⣽⣆⠸⣇⣀⣠⣄⢨⠇⢀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣿⣿⣷⣏⡉⠻⢿⣿⣶⡁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣶⣶⣆⡀⠀⢈⣿⣿⣿⣿⣿⣦⡀⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⢉⣀⣨⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠺⠿⠿⠛⠲⠦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣠⡴⠞⠛⢩⣿⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠉⠿⣿⣿⣿⠿⠋⠻⣿⡲⢍⣻⠻⠏⠍⡙⠻⠟⢛⢒⠢⡀
⠀⠀⣀⡤⠚⠙⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠘⠀⠀⢈⠁⠀⠀⠉⠉⢁⠀⠀⢨⠟
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣽⡆⠻⣿⠇⠀⠀⠀⠂⠙⢶⡦⣤⣀⡠⠨⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠙⢿⣿⣿⣿⣿⡿⠋⣿⠇⢸⡿⠀⠀⠀⠐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠲⠼⠿⠛⠉⢀⣼⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⠟⠁⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡧⠀⠀⠀⠀⠀⢀⣴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⢰⣿⣿⣧⡀⠀⠀⠀⠀⠼⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠐⠋⠽⢻⡿⣿⣶⣄⠀⠀⠀⠛⣻⣿⣇⠀⠀⠀⠀⢾⣿⡄⠀⠀⠀⣠⣾⣦⣉
⠆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⠿⠻⠀⠀⠀⠀⣹⣿⡉⠀⠀⠀⠰⠆⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⡟⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⠇⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠸⠿⠿⠦⠀⣷⣀
⠀⠀⠻⠷⣄⠀⠲⢤⠄⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠄⠄⢀⡈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⠖⠂⠀⠀⠀⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠊⠁⠀⢤⣤⡀⠁⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠓⠛⠻⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠢⠀⠀⠀⠀⠀⠀⠀⠒⠲⠦
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡀⠀⠀⡀
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠰⠶⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡀
⣤⠠⠙⠚⠢⢠⣶⣦⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠈⢐⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⢡⠄⠀⠀⠀⠀⠀⠘⠃
⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢠⠂⡄⠀⠀⢀⠄
⣰⢃⡀⣼⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠐⢄⣦⣀⢀⣾
⣴⣦⣵⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣴⣦⣧⣿⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⡤⠤⣤⡀⣀⡀⣶⣤⣤⣄
⠀⠀⠀⠀⠀⢠⡞⢸⡟⠀⣿⠁⢸⡏⠐⢻⣿⣿⣿⣿⣿⣿⣴⣦⡀
⠀⠀⠀⠀⢰⣾⡇⢸⣧⠀⣿⡀⠸⡇⠘⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠻⠀⢿⡗⣩⡥⢤⣻⠄⢨⠟⠳⢿⣿⢿⣿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⠀⠹⡗⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀
⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠔⠂⠀⠁⠀⠀⠀⠀⠀⣴⣿⣿⣯⡿⡷⠄⡀⡐⠒⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⣿⣿⣿⣷⣿⣿⣻⣿⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⠁⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠚⡿⣿⡿⠁⠹⡟⠋⠀⣿⠈⠛⣽⢿⡿⠟⠋⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠔⠁⠀⠀⠀⠁⢈⡇⠀⠀⠈⠃⠐⠁⠀⠀⣠⣾⣿⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣿⣿⣿⣿⡿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣬⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣾⣿⣟⣿⣿⣟⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢿⣭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⡋⠀⢸⣼⡧⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣽⢿⣿⠻⣿⣿⢏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣍⡛⠛⣋⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣧⣌⠉⠛⠛⠛⣩⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⠁⢮⣙⠛⠶⠶⢟⡯⢳⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣝⡛⠓⣛⡋⠁⠘⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣶⣶⣶⣶⣶⣖⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣒⣶⣶⣶⣶⣶⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣟⡿⣿⣿⠿⠿⠛⠛⠻⠟⠛⠛⠛⠛⠻⠿⠻⢿⢟⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⡄⠉⢳⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢐⡀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⠀⠀⢀⣠⣀⡈⢷⡄⠀⠐⠀⠀⣰⠃⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡃⢉⣿⠀⠙⠷⠶⠶⠚⣡⣏⡹⠈⠛⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⣙⣓⣿⠀⠀⠀⠀⠀⠐⣯⠢⡅⣢⠜⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢺⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡤⡤⠴⠋⠀⠠⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣇⡀⢸⣒⣔⣶⣘⣆⡠⡤⠀⠀⠀⠀⣰⣶⣶⣼⡆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣒⣻⣿⣿⣻⣶⣒⣦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠉⠉⠉⠹⠿⣛⢛⡛⠛⢛⣛⡛⣛⣛⣛⣛⣛⠛⠛⢻⠋⠋⠋⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⡉⠉⠉⢁⣀⣀⣀⣈⣉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇
⠀⠀⠀⠀⠐⣶⡀⠀⣹⣦⠀⣴⠁⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅
⠀⠀⠀⠀⠀⢻⣿⡷⣾⠗⣿⡿⡄⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣷⢸⢹⣿⠃⣇⣀⣀⣀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣮⣼⣿⠀⠠⠀⠀⡆⢰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣠⣤⣦⣤⣥⡼⠿⠻⠛⠻⢳⣶⣶⣶⣶⣶⣶⠶⠿⠾⠿⠿⢦⣷⣶⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢻⣯⣤⣤⣤⣤⣤⠜⠛⠛⠛⠛⠻⠛⢤⣤⣤⣤⣤⣤⡿⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⣀⣤⣶⣿⣟⢿⣻⣿⣿⣿⣿⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡏⠁⠀⠙⢻⠿⡿⣿⣿⣿⣷⡒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣙⠙⢷⡄⠀⡠⠣⢀⠀⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣀⣀⡤⢤⣤⡞⠀⠈⣿⡿⣄⠘⢇⠰⠁⣶⣾⣷⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠻⠃⠉⠀⠀⠀⠀⢹⣟⣃⠀⠀⠈⢻⣽⣣⢾⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⡇⠐⣆⠀⠀⡀⠤⠀⡀⠿⡽⣦⣀⠀⠘⠪⠀⠀⣸⠿⠟⠋⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⣾⡿⡀⢣⠈⠹⡄⠀⠀⠐⠀⠀⣄⡈⠋⠀⠀⠀⠀⠀⠰⣿⡄⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢀⡾⢿⣿⡱⡀⢂⠀⢘⠢⠀⠀⡀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠉
⠀⠀⠀⠀⣸⠷⢡⢻⣿⣽⢄⠀⡈⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡀⠀⠙⠑⢿⣷⣦⣈⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⢿⣿⣦⣴⣶⣷⡽⠿⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⢴⠻⠐⠚⠿⣤⡀⠀⠀⠀⠀⠀⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⣿⡇⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⢀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡀⢻⣿⢿⢠⢠⣀⣴⣿⠿⠇⠀⠀⣰⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣧⣀⣭⣿⣿⡟⡿⢿⣶⣷⣤⣀⣔⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡯⠈⠀⠀⠀⠈⠀⠈⠘⣷⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡻⣞⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡀⣐⣿⣡⣠⠂⢀⡀⠀⠀⠠⣦⣼⠿⢷⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣖⣒⣶⣊⠽⠏⠁⠒⡔⠸⠽⢿⣿⣷⣿⡷⣿⡷⣿⣿⢿⣛⡭⠤⠀⠀⠘⢯⣾⣲⠦⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠜⢠⡤⢴⡞⠛⠉⠍⠁⠫⠇⠉⢐⣶⣶⠤⡄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠇⠻⡎⠻⢦⣄⣀⢀⣀⣀⣤⠦⠾⠇⢉⠙⢓⠀⠀⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡀⠀⠀⢇⢸⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⢸⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⠁⠀⡀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠠⠀⣠⢿⡷⠤⠀⡀⠀⠀⠀⡀⢀⠠⠐⠰⢧⠈⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⣡⠟⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⡆⠀⠘⣎⠦⠰⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠃⠀⢻⣤⣦⠀⠀⠀⠀⠀⠀⢀⡛⢽⠇⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠉⠁⠁⡠⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⡤⣄⣀⣀⣀⣀⣤⡼⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠐⠈⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠟⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⡐⠃⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠃⠀⠀⠀⠀⠀⡄⠀⠀⣿⡿⠀⠀⠀⠀⠎⢀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣗⠀⠀⠀⢠⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⠒⠠⡀⠀⠀⣹⣏⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⠀⠀⠀⠁⠐⠀⠀⠀⠀⢀⣴⡆⠈⠘⢀⠞
⠀⠀⠀⠀⠀⠀⠑⣄⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⢆⠀⡆⠀⠀⢰⢀⣾⠟⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠐⠀⠙⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⡃⠉⠀⠀⣣⣾⣻⠂
⢀⢀⠀⠄⠀⠀⠀⠀⠹⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠉⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣧⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣄
⠀⣀⠀⢀⡄⠀⠀⠀⢨⡿⠈⠀⠀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⢰⠀⠂
⠀⠈⠒⢻⣧⡄⠀⠀⢸⣟⠴⡀⠀⣿⣿⣴⡶⠥⠤⠠⠶⠀⠀⣠⡄⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⠀⢀⠀⢀⠀⠀⠀⠂⢸⣿⣿⣅⡀⠸⡆⣸⣴⡞
⠘⠓⠀⠀⠀⠠⠄⠀⠀⠉⠘⠁⠃⠛⠙⠉⠁⠀⠀⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠂⠚⠛⠉⠉⠉⠁⠉
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣤⣠⣶⠆⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣒⢒⡈⢫⣍⠹⣤⠀⠀⠀⠄⡀⡀⣄⠈⠻⣿⣭⣭⣿⣥⣿⣴⡆⠀⢀⠷⣶⣶⣤⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠆⣤⣾⣿⣾⣧⣿⣿⣿⣿⣿⠀⢸⣷⠀⣧⠳⡼⠂⢠⣿⣿⣿⣿⣿⢛⣿⣶⣦⡠⣤⡞⠋⠁⡘⣡⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢈⡶⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠘⠛⠘⠻⠊⠀⢸⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣃⣿⣧⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢛⠟⣉⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⡇⠘⠀⠠⣴⠀⣿⣿⣿⣛⠋⣻⠿⠏⠓⠀⢸⣶⡿⠋⠉⠉⠉⠉⡉
⠀⠀⠀⠀⠀⠀⠀⢁⢄⣉⣉⣿⣿⣿⣿⣿⣻⣿⣿⡇⠸⡿⠁⠀⢀⢟⢿⣿⣿⣿⢛⣿⣿⣿⣦⣤⣴⡤⡤⠨⠟⠲⠒⠀⠈⣝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣋⠁⠁⠀⢉⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡶⢀⣴⢀⠶⣶⣾⣷⣷⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣤⢀⣜⣉⣹⣿⡟⠻⡿⢿⡇⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⣸⣾⣦⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣤⢶⣽⣿⣿⣽⡷⣼⣮⣷⡀⠈⢉⠿⠿⢟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⢿⡿⢿⣿⣿⣿⣿⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣽⣯⣿⣿⣿⣿⠿⣿⣿⣷⠉⢿⠛⠛⠁⠀⠈⢏⠙⣿⡙⠛⠛⠩⠿⢿⣧⢡⡔⢖⣶⣾⣿⡿⢾⣉⣫⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣿⣭⣽⣾⣿⣿⣤⣉⠙⢿⡁⢸⠄⠀⠀⢸⠀⣸⠀⠋⢱⠐⠀⠀⠀⠈⢛⣞⣿⡻⣟⡿⠙⣷⣾⣽⡿⠛
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⠿⣟⡟⢻⣿⣿⣷⣿⡅⢸⣆⠀⠀⢸⠀⡇⡇⡄⣼⡄⠀⠀⡀⠀⢹⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⢩⣤⣋⣛⣿⣿⣿⣿⣿⠀⢸⡟⣧⠀⢸⠀⡇⠁⣧⣿⣇⠀⠀⡇⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣶⠶⣿⣿⣿⣿⣿⣿⣿⠀⢸⣧⡇⠀⠸⠠⣷⡇⣿⣿⣿⠠⠀⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣷⣶⣿⣿⣿⡟⠀⠸⠿⠟⠀⣾⢐⣿⡇⢻⣿⣿⠀⠀⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠆
⠀⠀⠀⠀⠐⠒⠒⠒⠺⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠿⢿⣿⣿⣿⣿⣿⡎⠀⠐⣾⢢⡔⠲⠋⡇⢔⡀⠆⠀⠀⠄⢠⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠰⣃⠾⠋⡴⡦⠀⠲⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⣤⡄⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠯⣸⣲⠁⡀⠀⠀⠠⠄⠐⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⢀⠀⠀⠀⠀⢀⠁⡰⡬⠀⡬⠃⣘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠈⠁⠀⠰⢀⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠤⠋⠁⠢⡂⠀⠀⠀⠀⠐⠚⠣⠚⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⡈⢁⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠠⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣎⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠠⠄⠠⣀⠈
⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠉⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢣⣱⣧⡈⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠆⠀⠄⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢧⣞⠖⠀⠀⠀⠀⠀⠠⣬⢤⡄⣞⡄⠀⠑⠀⠀⠀⠜⣈⡒⠁⡀⠀⠀⠀⠀⡀⡑⠀⠀⠀⠀⠔⠀⠢⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠠⣀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠙⠾⡇⣻⢵⠔⠂⠀⠐⠄⡂⠓⣀⠁⠀⠀⠀⠀⠂⠀⠄⠐⠂⡈⠀⠀⠂⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡡⠈
⠀⠀⠀⠀⠀⠀⡀⠈⣦⡀⠀⠀⠀⠀⠀⠄⠈⠆⢸⠀⠀⠀⠄⠀⢃⠔⠀⢀⣃⠀⠰⡀⢿⡀⢠⠈⠑⠿⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠉⠃⠙⠃⢐⡀⠀⠤⣢⠀⠄⠙⠄⠈⢄⠁⠀⠨⠄⣄⠐⠈⠁⠀⣀⠍⣄⡁⣠⠓⠄⠀⢀⡄⠒⠃⠆⠰⠒⠋⠿⠂⠂⠆⢁⠋⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈

⠄⠀⠀⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡀⢀⢰⡀⠓⠃⡈⣛⣃⡀⣈⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⢀⠀⠄⢹⣿
⡇⠀⠀⠀⠀⠀⣿⣆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠠⣤⡈⠁⣾⣿⡇⠸⠛⠋⢉⡴⢂⡎⠉⠀⢀⣈⣻⠃⠁⠀⠀⠀⣠⠁⠀⠀⠊⠀⢀⠀⣤⣿⣨
⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⠄⠀⠀⠈⠻⢦⣽⣿⡥⡀⣀⠐⠋⢠⡾⠁⠀⠀⠀⠸⣯⡀⠀⠔⠛⠉⠋⠛⠂⠀⠀⣤⣿⠀⣿⢯⠾
⣧⡀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢰⡏⠀⠀⢀⣴⣾⣿⢿⣿⣿⣿⣷⠀⢺⣼⠃⣴⠀⠀⠀⠿⡗⠙⠀⠀⠀⠀⠀⠀⠀⢠⡄⠋⢻⠀⣰⣿⠿
⣿⡇⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠀⠀⢠⣿⣿⠟⢁⣿⣿⣿⣿⣿⣷⣄⣼⣾⣟⠀⠀⠀⠀⠃⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠋⠂
⣿⡇⢀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠞⠋⠀⠠⠁⠀⠀⠸⠋⠀⠀⣾⣿⠻⣿⢻⣿⣿⡉⠊⢹⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡴⢯⣤⡾
⢾⣿⣏⠀⠀⠀⡆⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠀⠙⣿⡇⠀⠰⡦⢡⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⢸⣯⣹
⣽⣿⠋⢰⡇⢠⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠀⠀⠗⠹⠀⠀⢳⠀⢆⠀⢼⠀⠀⠀⠀⠀⠀⠀⢀⣮⣣⡀⢀⣸⡅⢸⠟⣿
⢟⠁⡴⣿⡇⣸⣿⡇⣿⣿⣿⣯⠀⠀⠀⣀⣀⣶⣄⠀⠈⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣶⣴⡄⠀⢈⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⣾⣻⣼⠇⣉⢻⡇⠀⣿⡿
⣿⡤⣿⣿⢷⣿⣿⡇⢹⣿⣿⣿⡀⠐⠋⠋⠋⢳⡘⣿⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⡇⠀⠈⢠⠆⡃⠀⠸⡀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢻⡿⠰⠃⡹⢿⡇⠀⣆⡀
⣿⣿⣿⢯⣾⣿⣿⣿⢸⣿⣿⣿⣿⣦⠀⠠⣤⠈⠃⠁⠀⠀⠤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠧⠀⠀⠁⠀⠀⢿⣿⡀⠀⠀⠀⢠⠎⣼⡵⢀⡇⢱⠿⠇⣀⡌⠁
⣿⠾⣣⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⢟⣥⣤⠭⣄⡐⠂⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠈⠵⣇⠛⡇⠀⣸⡇⠀⠀⠀⣿⣇⠠⠀⡀⢈⣠⣦⡧⠞⡦⠶⢿⠀⠋⡿⠂
⣡⣶⣿⡟⣿⣿⣿⣿⢸⣷⡙⣿⣿⣿⣿⣿⣎⠉⠀⠀⠈⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡀⠀⣿⢳⢠⡄⢴⡗⡄⠂⡀⠱⡘⠈⠁⠆⠙⡻⢎⠀⢌⢆⢹
⣿⣿⠟⠀⣷⣿⣿⣿⠀⣿⡏⢹⣿⠿⠟⠛⠃⠀⠀⠀⠀⢇⠀⢸⡇⢀⣶⠄⠀⣇⢀⣄⠀⠀⠹⠇⠀⢿⢾⡬⡷⠶⠮⣘⣲⢈⠠⠣⠄⣟⢐⢦⠨⠁⠃⠎⠳⢦⣄
⣿⡎⠛⠲⣬⣿⣿⣿⠀⣿⣷⠀⢱⣶⣿⣿⣿⡀⠀⠀⠀⠈⣆⣼⠇⠈⢰⣶⣤⡀⠈⠛⢠⣄⠈⠃⢰⣶⣼⣇⢑⡖⣾⣷⡯⣣⠀⠑⠓⠛⠊⡁⠰⣌⠈⠀⢄
⢤⠀⣠⢠⣿⣿⣿⢋⣇⠸⣿⡄⠀⢻⡿⣿⡿⣷⠀⠀⣜⢦⣹⣿⢷⣞⠀⠉⠙⠹⣿⣷⣄⡻⣷⡄⠈⢧⣿⢶⣾⣷⣿⣻⣧⠉⠋⠀⠀⠀⠀⠁⠀⢷⠖⠀⠀⠱⡀
⠁⠀⢤⣿⣿⣿⢏⣾⣿⠀⢻⣿⠂⠀⠋⢿⢿⡙⠒⠀⠉⣷⣝⣿⣼⠽⠦⠀⠀⣄⣐⡾⢿⠏⣻⠀⣦⣄⢹⣿⣿⣿⣭⣭⣽⠇⣠⣶⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢸⣿⡿⢟⣾⣿⣿⠀⠈⠿⠟⠃⠀⠀⠈⠉⠀⠀⠀⠉⢻⠟⠡⠶⣦⢀⡀⠈⠉⠊⣸⣦⡏⢈⣋⠸⢕⠙⣩⢻⣿⣧⣽⠿⡺⠟⢁⣤⣤⡤
⠀⠀⢸⣿⠇⣼⣿⣿⣿⠀⠀⠈⠀⣽⣶⣷⡄⠀⠀⠀⠀⠀⠘⢏⡶⢂⠀⠻⣿⣆⠰⢀⠀⠻⠆⣴⣩⣿⣾⣿⣿⠶⠒⣶⡚⢪⣴⣿⣿⣿⣛⠻⠦⠌⠁⠀⠀⠀⠑
⣆⠀⣬⢻⣇⣿⣿⣹⣿⠳⣦⠀⣿⣽⢿⣽⠟⠄⠀⠀⠀⠀⠀⢺⣿⣛⠓⢆⠹⡿⣤⣿⡷⠆⠀⠹⢿⣿⣿⣿⠟⠁⠀⠈⠀⠰⣿⣿⠟⠭⠀⡾⠀⠀⠀⠀⠐⢄
⣿⡀⢿⣇⠈⠻⠉⣿⢿⣟⣻⣧⣿⣛⡀⠉⠂⠀⠁⠀⠀⣠⣴⠿⠟⠟⣽⡎⣶⣛⣿⡯⠓⠁⠀⠻⡶⢿⣿⣿⠀⠀⠀⠀⠀⠀⢽⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁
⣽⣷⣼⣿⡶⡀⣦⣟⣀⣽⣿⣏⣽⣻⣧⣄⡀⠉⠀⢠⣦⣽⢗⣤⣤⣘⣻⣿⠿⣿⣿⣷⣄⣀⣀⣰⣿⣄⠀⢡⠀⢀⡀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣤⣦⣤⣄⣠⣷⣼⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠻⢿⣿⡄⢀⡄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡅⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠾⠿⠿⠿⣿⣿⣿⣿⣯⣀⠀⠈⠹⣿⣿⡇⠀⠀⠀⢻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⣻⣿⡇⠀⠀⠀⠸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣿⢻⣿⣿⣷⣴⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡟⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⡿⣿⡇⣿⣿⣿⣿⣿⣈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠇⣿⣏⣿⣿⣿⣿⠟⠛⠉⠘⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠶⠶⠤⣌⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡁⢀⣀⣤⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠆⠀⣸⡿⠷⠶⣴⣿⡿⣿⣦⣤
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣤⣴⣷⣤⣶⣤⣄⣀⣠⣾⠛⠓⢶⠶⠿⢿⣷⠄
⠀⠀⠀⠀⠉⢁⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⠋⠉⠉⠉⠉⠉⠙⠻⠟⠻⢿⣿⣿⣿⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⠘⠉⠉⠉⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣿⢾⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠐⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢱⢀⠤⠒⠒⠀⢄⠀⠀⠀⠀⠀⠔⢆⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⡌⢀⢀⡃⡠⠊⠀⠀⠇
⠀⠀⠀⠄⠂⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⢩⡟⠒⠠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢱⠀⡼⠀⠀⠀⠀⠀⡈
⠀⠘⠀⠀⠀⠀⠀⠀⠠⠤⠖⠒⣽⣟⡾⢖⡁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠈⣴⡁⠀⠀⠖⣮⡗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡃⢸⢄⡃⠀⠃⢀⡀⠴⠓⠒⠂⠁⠐⠄⠀⡀⠉⢥⣁⠲⠉⡑⡟⠂⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⢙⠇⠀⡁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⡆⡀⠉⢣⡤⢉⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠠⡀⠀⣀⠠⠇⠀⠀⠘⠀⠀⠈⠳⢄⣀⣀⢀⠀⠀⠀⣀⣰⠡⠀⠀⠻⡀⠀⢫⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠉⠉⡩⡒⠅⠈⠀⠀⠀⠈⡗⣻⠀⠀⠀⠀⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⠦⣀⢀⡀⠤⠄⠒⠁⠀⣠⡫⠊⠀⠀⠀⠀⠀⠀⠀⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⢀⡀⠄⠈⠁⢠⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡀⠎⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠉
⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣺⠝⡎⣿⢟⡯⣑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢤⡀⡵⠚⠁⣸⢸⡇⢸⡆⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠞⣋⣁⡿⢭⣶⠛⠃⠛⡠⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠠⠂⠉⢀⣡⣤⣴⣶⡦⠥⣤⡤⣶⢿⣿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣠⠶⠛⢋⡉⠏⠤⢐⣒⠿⠩⢞⠟⣸⣿⡇⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡞⢁⡤⠊⢁⡠⠖⠋⢀⣀⠀⠤⠐⢒⣹⠟⣡⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⢿⡇⡎⠀⢠⠋⢀⡴⠊⠉⣠⠤⠐⢚⡩⠔⠉⢁⣰⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡷⢤⣀⠙⠻⢤⣽⣀⣾⢀⣴⣏⣁⣠⡴⣿⣗⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠁⠒⠂⢬⠭⠽⡭⢿⢿⠾⡷⢿⡛⣻⣹⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢸⠀⡏⡾⡇⣇⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⢹⢸⢈⢠⢇⣃⣹⢻⢳⣿⣿⣥⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣄⡆⣰⡀⠀⡄⢸⣼⣴⣸⣸⣷⣾⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠽⣿⣧⣠⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⡿⠿⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠄⠂⠂⢈⡀⠀⡉⠀⠀⠀⠢⢌⠔⠆⠩⠴⠇⠈⠢⠈⢀⠀⠐⠐⠠⢀⡠⠬⠤⠄⠀⠀⠀⢀⣄⣐
⠀⠀⠀⠀⠀⠉⢤⣤⣤⣥⡄⣤⣤⣤⣂⡠⣄⣅⣀⣀⣄⣠⡄⡐⠒⠂⠁⠄⠩⢄⠂⠀⡄⠀⢠⠐⠒⠀⠒⠀⠄⢀⠀⡀⠀⠑⠂⠐⠀⡀⠁⠀⠀⠠⣀⡤⠀⡀⢀
⠀⠂⠀⢀⣀⢀⠀⡉⡹⢛⢿⣚⡛⠳⡩⠷⡏⠉⡟⠻⢙⣿⡚⢷⣴⠶⣄⠲⣄⢺⣶⡆⡔⣠⣬⠼⣠⣰⣶⢴⡖⠰⣶⡶⢆⣶⣜⣶⣷⣿⣿⣲⣋⡛⣉⢀⡀⠴⠔
⠀⠀⠀⠈⠙⠺⣭⣏⡯⠟⠛⠉⠀⢠⠄⠀⠘⠒⠀⠀⠀⢸⢰⠈⠀⠀⠀⢹⠉⢷⠠⠈⠉⡉⠘⢫⠉⠉⠓⠸⣏⠎⠙⠓⡬⠋⠿⠙⠀⢟⠙⣯⣳⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠊⠙⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⢸⠀⠀⠀⠂⢰⡇⠀⠈⡄⠀⠀⢠⠋⠒⢛⣘⠀⠀⠀⠀⠀⠈⠂⠁⡷
⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⠻⠀⠀⠀⠀⠘⠄⣀⡠⠟⠈⣁⠀⠀⠀⠀⡀⠈⠀⡀⠘⣽⡀⡀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⢀⠁⠤⠐⠚⠀⠀⠀⠀⠉⠉⠂⠀⠐⠀⠀⠀⠐⠒⠄⢠⡿⢄⠁⠀⠀⠀⠌⠀⣤⣰⡚⣂⣀⣐⠀⢀⠐⠀⣄⣤⣄⣠
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⣎⣷⣤⣤⣀⣤⣄⣀⣶⣶⡆⠀⠐⠀⠀⠀⠀⠠⢴⣷⠊⣿⡦⣤⣴⣦⣴⣧⣤⣤⡜⠁⡿⣉⣋⣉⣿⡽⠻⠋⢻⠃
⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠈⢻⠿⠾⠳⣬⣟⡿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠀⠁⣈⠟⠁⠙⠤⠈⠳⢦⡤⠄⠂⡉⠋⠣⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠦⠀⡀⢀⣀⡦⢠⠆⠀⠀⢐⣏⠀⠘⢠⠂⡔⠀⠂⠐⠀⠀⠠⢀⡐⢠⡇⠀⠨⡀⠀⠀⠀⠀⠀⣀⡀⡧⠐⠀⢡⠄⣀⠀⠀⠐⠅
⠀⠀⠀⠀⠀⠀⢀⡀⡤⡌⣨⢄⣤⣠⠄⠀⢠⡜⠈⠀⠁⠘⠆⢄⢠⣡⡄⡀⢠⡀⣠⡄⣀⡄⠀⠈⡁⠤⠀⠄⣀⠀⠉⠀⡷⢶⠶⠸⠒⠛⠀⠀⢘⠂
⠀⠀⠀⠀⠀⠀⠀⡉⠙⠁⠂⠁⡁⢸⠀⠀⠀⣢⢀⢲⡄⠘⡇⠀⠉⠉⠛⢣⠚⠉⠀⡀⢰⡄⠈⢴⣶⢠⠶⠒⠂⠈⠀⠰⡅⢸⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⢀⠀⣰⣾⢳⢠⠀⣾⡗⢸⡄⠀⠔⡇⠐⡋⠡⢶⠳⡀⠀⠀⠢⣆⠀⠀⡼⡟⠈⣤⡄⠨⠀⠅⠀⠀⠀⠀⠀⢀⢀⢸⢀⠀⠀⢠⡀⠁⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⠯⠺⣁⠸⡟⠤⡀⡏⢁⣾⠋⠙⣴⠋⠁⢓⠀⠈⡅⡀⠅⠀⢀⣹⣶⠐⡆⢤⠀⢀⡊⢵⠀⠝⢻⠁⠀⠸⣆⠀⠀⠀⠀⠀⠵⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡷⠒⠠⡸⠉⠑⠀⠹⡖⠀⠉⠀⠀⠀⠀⠁⡥⢈⠴⠆⣸⠈⠐⠰⣧⡘⢰⣭⢷⣀⢡⡄⠘⡀⢨⢀⣫⠀⠩⣆⠀⠀⠌⣳
⠀⠀⠀⠀⠕⠈⠸⠆⠔⠠⣺⠟⠁⠀⠀⠣⠀⠁⠐⠇⢠⠁⠁⠷⠐⠋⠹⠰⠆⠈⠁⣠⣻⠄⠀⠁⣏⠁⠨⡙⠀⠙⠀⠀⢈⢒⡏⠇⠁⠳⡤⣸⠥⠘⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠲⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⡰⠄⠀⠙⠀⠣⠼⡆⠀⠀⣵⡃⠠⢄⣀⠋⢧⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠐⠀⠸⡁⢒⠠⠄⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢱⣤⣴⣶⣤⣇⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⣀⠀⠀⡴⢀
⠈⡄⠀⠱⣄⠁⠀⠀⢱⠀⠀⠀⠀⢻⣷⡀⢠⣿⣿⣿⠿⣿⣿⣧⠀⢸⡿⠀⡠⠐⢈⡇⠀⢀⣠⣖⠔⠁⡴
⠀⠘⢄⡀⠀⠙⢀⠒⠢⠅⠶⢄⡉⠢⠽⣿⡾⠉⣄⣄⣠⣤⣀⠉⠲⡿⠗⢁⡠⢐⠉⠒⣋⡡⠘⠁⠀⡰⠁
⠀⠀⠀⠩⣉⠀⠀⠩⠄⣐⣀⠠⠬⠥⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣯⣶⢭⡶⢂⡹⣿⠭⢊⠴⠂⣠⠞
⠀⠀⠀⠀⠈⠑⠠⢤⣤⡤⠤⡥⠤⠄⠛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⠒⢲⡚⠲⠶⢷⡒⠈
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢰⢁⡀⠀⡚⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢀⠁⠤⠬⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠄⠒⢩⣴⡟⠀⠈⠙⠛⡟⠋⠋⠉⠻⣿⣦⡉⠓⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣿⣥⣀⣀⣀⣀⣥⣀⣀⣀⣠⣽⣿⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠻⣿⡿⢿⣿⣿⣿⠿⢟⡿⣿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠈⠻⣾⡇⠀⠀⠀⢀⡤⠛⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠙⠓⠋⠉⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⡀⠀⠀⠀⠀⣠⠔⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢦⠀⠀⠈⠃⠀⠀⣠⠞⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠈⠉⠒⠂⢌⡣⡀⠀⡁⠀⣰⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢀⣀⣙⣮⡱⠆⢰⠇⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⢄⠀⠈⠇⣼⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠁⠀⠀⠀⠑⠒⠺⣇⣠⠔⠋⠀⣠
⠀⠀⠀⠀⠀⠀⢐⠲⢄⡀⠀⠀⠞⠁⠁⡰⠋⠀⠙⢆⠀⠀⣘⠀⠀⡰⠊⢡
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠲⣄⢦⡀⠀⢇⠁⠀⠀⢸⠆⢰⡟⠀⡼⠁⢀⠆⠀⠀⠀⣀⡀⠀⠎⣳
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⢆⡉⠀⠀⠙⠒⠒⠁⠀⢸⠡⡔⠇⣠⠎⠀⠀⢸⠋⠁⢨⠛⣯⣉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⢸⡈⠢⡀⢀⡤⠒⠒⠲⣇⠀⣿⠚⠁⠀⠀⠀⠘⣄⠴⢁⠜⡠⢷
⠀⠀⠀⠀⢀⣤⣤⡄⠠⠤⠄⠀⠀⠜⢶⣄⠀⠀⢠⠛⠄⠈⠁⢿⠀⠀⠀⠀⠀⠀⠈⠲⠧⠴⠱⠋
⠀⠀⠀⠀⠀⠑⠲⠤⣄⣀⣀⣀⣀⣠⡤⠞⠓⢄⠸⠀⣏⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢎⢱⠊⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡠⢿⠙⡍⢏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣶⠀⠀⠀⠀⠀⢀⣤⡔⢢
⠀⠀⠀⠀⠀⢰⡁⠀⢣⠘⣈⠿⢤⠄⠦⢄⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠀⠀⠀⢀⣽⠦⠷⣮⣀⡀
⠀⠀⠀⠀⠀⠀⠙⣲⠜⢛⡩⢀⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⠰⠀⠀⠀⠀⢈⠀⠸⢀⠃⠸⢫⠳⠖⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⡎⡀⠄⠀⢓⠀⢴⠁⠀⠀⠀⠀⠀⠀⢩⡄⡄⠀⠀⠀⡜⠣⣤⣬⣀⣴⣃⡀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢢⣀⠀⠱⣄⠀⣠⠆⠀⢘⠀⡴⠤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢧⡀⠀⠀⡞⢁⠀⠈⠆⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⣠⡄⠤⠊⠀⠈⢆⠀⠈⠑⢢⡀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠳⣀⣤⠴⠃⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠚⠉⣆⠀⠀⠀⠀⠀⠑⠦⢀⣀⠙⢼⡇⠀⢀⠔⢻⠣⣀⡀⣤⡀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠻⡇⣰⠃⠀⢸⠀⠀⠀⡆⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⡰⢻⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⡌⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠟⠲⢄⠀⠀⠀⠀⡇⠀⡜⠀⡦⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢦⡀⠀⡇⡜⠀⢀⠃⠀⠀⠀⠀⠀⠀⣯⠔⠁⢠⡀⠀⠀⡇⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠱⡄⢸⠆⠀⡼⠀⠀⣖⢤⡀⠀⠀⠁⠀⠀⠈⠱⡀⢀⠃⠀⣠⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢡⡜⠀⡜⠀⠀⠀⠘⢆⡈⢳⣐⡇⠀⠀⢃⠀⢣⢸⠀⡰⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣿⠎⠀⠀⠀⠀⠀⠀⠉⠒⢼⡇⠀⠀⠘⣄⠀⣟⠰⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢢⣿⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢻⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⣀⣀⣀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡿⠛⠛⠋⠙⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠶⠦⢷⡄⠀⠀⢠⣿⣿⣈⣷⠀⠀⠀⣸⣿⣠⣿⡷⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⡀⠸⣿⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⡏⢀⣀⣼⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣝⣿⣿⣿⣿⢷⡿⣿⣿⣿⣿⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⢿⠇⠀⠀⠀⠀⠉⣛⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢄⢬⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⠿⠿⣿⣿⣿⣿⣿⣿⣤⢀⡀⠀⠀⠀⠆⣾⣿⣿⣿⣿⣶⣶⣖⣰⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⡴⢛⠀⠁⣍⣩⣿⣿⡾⡷⠶⢦⠸⡞⢿⣫⣙⠉⠉⠙⢿⣍⠉⠉⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠟⠀⢀⣴⠟⠁⠈⣠⣾⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⣘⣿⣿⣿⣦⣀⠂⠻⣆⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣴⠟⠁⠀⠀⠀⣿⡿⢹⣿⣾⣷⣴⣶⣦⣾⣿⣿⣿⣿⣿⡟⢿⣿⠀⠀⠘⢦⡀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠠⢀⣿⡇⣿⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⢉⡇⠠⣿⣄⠀⠐⠌⠻⣦⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠄⠀⠀⠀⠀⣸⣿⠇⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⠀⢻⣿⡄⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⢸⡘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⢻⣿⠀⠈⢻⣷⣆⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣠⣿⠫⠁⠀⠀⠈⣿⣦⣶⣦⣴⣦⣠⣶⣾⣿⣿⣿⡇⠀⣴⡀⠉⠛⢷⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣴⡿⠋⢀⠄⠀⠀⠀⠀⠹⣮⣍⣉⡉⠛⣛⣋⣩⣭⣵⣿⠁⠀⠘⣛⠄⠀⠀⠙⢶⣦⡀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠠⡀⢀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠿⡿⡿⠿⠿⣿⠏⠀⠀⠀⠀⠂⠠⠀⡀⠈⠛⠁⠀⠀⠄⣧
⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣤⣴⣦⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠸⢧⡀⠘⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⢿⡇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠤⠤⢤⣀⣀⣀⣀⣠⡀⠒⣢⣤⡠⣴⣀⠘⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠁⠄⠸⠛⠀⠀⠀⠀⠀⠈⠙⠿⢾⣶⣄⡑⣄⢻⣷⣶⣇⠀⠀⠀⠀⠀⢀⣤⣤⣤⠤⠄⠘⠓⠦⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠉⠙⠻⣿⡾⢿⡷⠏⠀⠈⠁⠒⠰⣿⣿⣿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠠⠄⠖⠚⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⡓⣆⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡄⠀⠠⠋⠀⠀⠶⠶⠶⢦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣃⣀⡀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠃⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠎⠀⠁⠀⠀⠢⣀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈
⠀⠀⠀⠀⠀⠀⠈⠁⡏⡀⣶⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣀⠠
⠀⠀⠀⠀⠀⠀⢸⠘⠸⠁⢹⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⣧⠀⠀⡘⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⠙⠿⠟⠋⠉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣧⠀⢲⠁⢀⠀⠀⠸⣶⡶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠿⠀⠀⡇⡃⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⢸⠄⢀⡀⠀⠀⣀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣷⢀⣺⠚⠻⠿⠶⠿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠀⠀⠂⠀⠀⠀⠀⠀⣠⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠈⠒⠦⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠿⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠠⠈⠲⠶⠤⠀⠀⠀⠀⠠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⣀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡒⠀⠀⢀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⡄⠁⠙⠛⠃⠀⠀⠉⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⡀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠤⠒⠊⠋⣯⡿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠾⠷⠶⠶⠆⠀⠀⠀⠈⠑⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣠⣤⣴⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣛⣛⣛⣛⣛⣋⣉⣉⣉⣉⣙⣛⡛⠙⠛⠛⠛⢃⣠⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡼⠶⠋⠑⠚⢛⣋⣙⣫⣭⠭⠭⠭⠿⠭⠿⠿⠿⠿⠿⠶⠞⠓⠒⠂⠀⠀⠉⠁⠀⠐⠒⠒⠢⠤⠴⠦⠄⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⣒⣒⣒⣀⣀⣀⣒⣀⡀⠒⠒⠒⢒⣒⣒⣚⣓⣒⣒⣒⣒⣖⡒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡉⠉⠉⠛⠛⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⢹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⣴⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⣿⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢂⡀⡀⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢸⠟⠳⠁⠞⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡐⠀⠸⠤⠤⠤⠤⠤⠿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⣦⣭⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⣴⠆⠀⠐⠹⠃⠉⠀⠀⢀⣠⣀⡀⠻⠁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣀⡡⣽⡆⠀⠀⡆⠀⠀⢀⣴⠎⣹⣿⢰⠉⡆⠀⣆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⠨⠯⠴⠷⠿⣼⡤⠿⠶⠦⣾⣷⠶⠿⣿⡾⠦⠷⠾⠷⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣀⡀⢀⣈⣉⣉⣉⣁⣉⠉⠉⠉⠀⢀⠀⢀⠀⢠⣤⣼⡄⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣤⡤⠖⠋⠻⠙⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣷⡀⠀⠘⠆⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣠⠿⠛⠻⢦⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣶⠀⣿⣿⣿⢿⡿⣿⣿⣿⡿⣿⣻⣉⣀⣼⣦⣀⣤⡾⠃⠀⠀⠀⢀⣬⡉⠁⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣀⣀⡿⠀⣿⣿⣽⣉⣇⣶⣿⣌⣠⣷⠉⣿⣿⣿⡿⠿⢿⣱⡀⠀⠀⣀⣼⣿⣿⡄⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣟⣿⣟⣁⡀⠀⠀⠈⠙⠻⣿⣿⡇⣿⣿⣿⠊⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡤⠿⠷⡾⠓⠒⡶⠶⠶⠶⠒⢶⣿⣿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣿⣿⣿⣴⢿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠀⠠⠄⠀⠈⠭⠀⠠⠤⠂⠀⢿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⡏⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠫⠿⠭⠉⢉⣉⡙⠙⢋⡽⢻⣿⢟⣏⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠶⠶⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠳⢤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠟⠋⠉⠀⢀⡿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⣦⡀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⢤⣀⠻⣤⣈⡙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠋⣁⡰⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠉⢳⡘⢷⢮⣯⡹⣦⣤⣀⣀⣩⡭⠿⠿⠿⠭⣤⣤⣤⡴⠶⠞⣉⡴⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡆⠹⣟⠳⢦⣍⣉⣁⣀⣀⢀⣀⣀⣀⣀⣤⠤⠖⠛⠉⢀⡴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢰⡄⠈⡇⢹⡀⢸⡆⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢀⣀⣠⡤⠄⠀⠉⢠⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠃⠀⣧⠀⠀⠐⠒⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⣠⡴⠋⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⣼⠀⠀⡿⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⣠⠞⣽⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠇⡿⠀⢰⡗⠦⣄⣀⣀⣀⣩⡥⠶⠛⠒⠚⠛⠓⠶⠶⢛⣩⣾⡃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡿⢰⡇⠀⣾⠷⢦⣬⣉⣉⣉⣀⣀⠀⢀⣀⣀⣀⣤⣴⠾⠛⠉⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⠃⣼⠀⢸⠏⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⢀⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠏⣰⠇⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠚⠉⣠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢠⡞⢁⡼⠃⣰⠋⢠⡞⢣⡉⠓⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣞⣩⡴⢋⣠⠞⣁⡴⠋⠹⣦⡳⠶⣄⠀⢀⣈⣭⣙⣛⣛⣛⠛⠛⠛⠛⠋⣉⣤⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠠⠖⠛⠚⠋⠉⠀⠀⠀⠈⠛⠶⣬⣍⣉⡀⠀⠀⠀⠈⠙⠛⠛⠋⠉⢉⣉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠘⠿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣤⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣛⠻⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⡿⢛⡛⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡛⣣⣿⣿⣿⣇⢸⣿⡟⢩⣍⢻⣿⡇⢰⣿⣿⣿⣧⣙⣋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⠀⠹⣿⣿⣿⣿⡿⠿⣿⢸⣿⣿⣎⢡⣾⣿⡇⣼⡿⢿⣿⣿⣿⣿⠏⠀⣀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣏⠸⠷⣸⠘⣿⣿⡏⢸⣿⣿⠇⣏⠺⠗⣹⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣷⡸⣿⣇⢻⣿⡇⢸⣿⡿⣸⣿⡇⣾⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣧⠹⡿⠆⠻⠃⠘⠟⠱⢿⡟⣸⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣦⡙⣡⡰⣿⣿⣯⣸⣿⣿⠆⣀⢋⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⡇⢿⣿⣾⣿⣿⣿⣿⣿⣾⠟⣸⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣮⣍⣙⣛⣛⣋⣩⣵⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




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

⠸⡀⠀⠀⢸⠈⣇⠀⠀⠈⣾⠀⢲⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣀⠀⠀⠀⣸⠀⠀⣿⠙⣿⣷
⠀⠁⠀⠀⣤⠀⣤⠀⠀⠀⠻⠄⠸⠘⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡜⣿⡅⠖⢺⣿⡇⠀⢹⣤⣿⣿
⣼⠁⠀⢠⠿⠖⠻⡇⠀⠀⡤⡄⢀⠀⠠⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡿⢿⠀⡦⣀⣭⡅⠀⠘⡻⠛⠃
⠷⠀⠀⣀⢠⠞⡇⣇⠀⠀⠄⡃⢸⠀⠀⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⡸⡟⠀⠞⠀⣡⠻⣻⠁⠀⢰⣀⣠
⠀⠀⢀⠅⠘⠀⡁⣏⠀⠀⠀⡉⠸⠀⠀⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⡌⠁⣍⢫⠀⢈⡆⠑⣴⢿⠃⠀⢠⠉⠛
⠀⠀⢤⢀⡄⢀⣦⠊⠀⠀⣤⣤⢈⠀⢀⠏⢻⣿⣧⣀⡀⠀⠠⠀⢱⠃⢹⠸⡎⢠⣿⠁⣈⣡⣼⠀⣴⣿⣧⡀
⠀⡄⠈⠎⡏⡜⣘⡖⠀⠀⣼⢿⠘⠀⠨⠀⢸⣿⠿⠄⠔⠐⡤⡀⣦⣮⡼⠶⡃⠮⠩⡗⠋⡟⢗⠀⠈⠰⣟⠁
⠀⠀⠀⠀⡇⡇⣿⠀⠀⠀⣿⢸⡄⣀⣀⠰⢾⡷⣒⠀⠒⠀⡈⣆⠕⠈⠉⡅⣖⢉⢗⡯⣉⠫⢂⡌⢢⡀⢽⡀
⠀⠀⠀⠀⠀⠳⣿⡗⠀⢀⣿⢸⡇⢙⣤⣈⣁⡚⠁⡆⡄⠃⠄⣠⠇⠁⢴⣖⢀⣅⠚⠱⠬⢥⢢⢨⢦⣋⡎⠁⢀
⢹⡸⣦⠀⠀⠀⢨⡇⠀⠈⠛⠃⣷⠸⡍⠉⠹⢩⣃⢷⣳⡀⠁⢨⣝⢇⢪⡗⣻⢈⠂⠈⢆⡀⣀⠓⠀⠙⠽⠒⠏
⠈⠉⠏⢶⣆⡀⠀⠉⢀⣟⢿⣤⣿⣇⠑⡻⠕⣿⣿⣿⢦⣳⠀⢠⠋⠛⠋⠉⠃⢩⠀⠹⡦⡌⠁⠀⢦⡀
⡗⣶⢤⡈⢿⣿⣦⠀⠈⠫⣍⡼⣩⣨⡐⣷⡄⣿⣿⣿⡀⠉⠱⢛⠂⠀⠀⠀⠀⠈⠀⠀⡻⣴⠴⠀⠀⠙⢄
⢛⣘⣲⣾⣷⣽⣟⠃⢀⠀⠘⡷⢦⣻⣝⣿⣧⣿⢴⣿⣷⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠈⢳⡄
⣠⡟⠳⢉⠙⢀⣯⠀⣿⡿⣆⡘⢿⣏⣿⣿⣷⣶⣴⣵⡟⠃⣰⣼⣿⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠙⠀⠁⣹⣦⣼⠅⠀⡙⠁⢬⡙⠊⠛⣁⠹⡿⣿⠷⣨⡽⣿⠶⢭⡿⠁⣀⣤⣤⣤⡤
⠄⠀⠀⠉⢿⣟⠀⠀⢿⢛⣦⣈⣧⣶⣿⣀⣉⣉⢋⣍⣷⡠⢛⣴⣾⣴⣿⣿⣿⣿⣤⠀⠀⠤⠀⠀⠀⠀⠁⠢⣀
⠁⢢⣦⡀⠀⠑⠀⣿⣤⣿⢿⣿⣿⣧⣿⡍⠉⠀⢸⠦⠀⢱⢿⣿⣿⣿⣿⡯⠤⢈⡉⠉⠑⠀⠀⢀⡀⠀⠀⠀⠈
⣤⣿⣿⠿⡖⠀⠀⠙⢿⣿⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⢾⣿⣿⠟⠉⡆⠈⢿⡇⠀⠀⠀⠀⠀⠈⠢⣄
⣿⣿⠹⡆⠃⠀⠈⣷⣦⣭⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⣿⣿⡁⠀⠀⠀⡄⠀⢻⡍⠙⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠊⠁
⣿⣿⣧⣤⣤⢤⢤⢨⣟⢻⣦⡀⠀⣧⠀⠀⣠⠄⠤⠀⣠⣤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠃⠀⠀⢀⣴⠏
⠀⠀⠀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⣈⣿⣿⣿⣿⣁⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢼⣿⣿⣿⣿⣿⣿⡧⠀⣰⡿⠁⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠐⠤⡀⠀⠀⠈⢻⡷⠛⠉⠁⠀⠀⠈⠉⠛⢾⡟⠁⠀⠀⢀⠤⠒⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠶⣤⣼⣇⣀⣀⡄⢀⡀⢀⣀⣀⣸⣧⣤⠖⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⠂⠂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⣴⣿⢯⠛⠿⠿⠿⠛⣉⣉⠛⠿⠿⠿⠛⡽⣿⣦⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⠟⠁⠀⠐⠒⠶⠿⠿⡟⢻⡿⠿⠷⠓⠂⠀⠈⠻⣇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⢀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣼⣿⠀⠀⠀⠙⠓⠒⠶⠞⠛⠙⠲⠲⠲⠛⠃⠀⠀⠀⣿⣧⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⡇⠀⠀⠐⣤⣀⣀⢀⢀⣠⣀⡀⠀⣀⣀⣤⠃⠀⠀⢸⡇⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⢠⣴⣶⣶⣶⣤⣶⡶⢇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠆⢰⣿⣿⣿⣿⣶⣿⣿⣿⣿⢻⣿⣿⣶⣿⣿⣿⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣟⣏⣽⣿⣿⣷⣿⣿⣻⣿⣾⠛⠿⠟⠹⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠟⢻⣿⣿⣯⣿⣦⣍⣿⣿⣋⣿⣿⡿⠿⠟⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠌⠻⡿⠃⠙⠋⠙⣿⣿⣿⡟⠁⠀⠀⣠⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⢢⣤⣹⡆⠀⡽⣣⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⡌⠸⠟⠋⠉⠉
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⢀
⠀⠀⠀⠀⠀⠾⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣅⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠈⣛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠉⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⢹⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢠⠉⠙⠀⠀⠀⠀⠀⣸⣯⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⣿⠧⠀⠀⠀⠀⢀⣾⡿⣯⣿⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣤⡀⠀⠀⠀⠀⠈⢸⡇⣿⠉⠐⠛⠁
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠑⠀⣤⣄⡀⠀⠚⠀⣿⠀⡀
⠀⠀⠀⠀⠀⡤⠀⠀⣠⠀⠃⠀⡀⠀⠀⠀⠸⡟⠀⠈⣧⣀⠀⣿⣿⣧⠀⠀⠀⠀⣠⡁⠲⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⣿⠛⠐⢃⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠀⣥⢰⣆⠀⣦⠀⢀⣤⡤⣞⠁
⠀⠀⠀⠀⠀⣷⡄⢰⡏⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢄⡘⢦⠠⣼⠙⢷⠇⠀⠙⡏⠁⠉⡠⠶⢠⣀⡄
⠀⠀⠀⠀⠀⢹⣇⢠⣷⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⡉⠀⠀⣀⡀⠴⠋⠀⠀⡇⠀⠀⠀⢿⡆
⠀⠀⠐⠀⠀⠸⠟⠀⠻⡄⠀⢀⡀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⣾⣤⠉⠀⠀⠀⠀⠀⠘⠀⠀⢀⡛⣷
⠀⢂⣀⡄⠀⠐⠋⠀⠀⣾⣦⢾⠁⠀⠀⠆⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠿⣾
⠠⠀⣿⠀⠀⠀⠀⣠⡄⢿⣏⣿⠀⠀⠰⠆⣨⡃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠠⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⣏⣀⠀⡈⠀⠘⣷⣜⠿⢯⠀⠀⠀⣴⠈⣿⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⣄⣰⣿⠐⠋⠉⡀⠁⠀⣤⠇⠀⣀⣤⠀⠀⠀⡀⣴⣿
⠊⠀⠙⠏⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⢸⣿⣿⣿⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠠⡎⠀⣠⣴⣾⣿⣶⡄⢴⢡⡄⠀⠸⠇⠀⠀⠀⠀⢀⠻⡃⢹⡯
⠀⠀⠀⠀⠀⠀⠂⠀⢾⣿⣿⣿⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠠⠟⠀⠁⠐⠟⠋⣾⣿⣿⣿⠄⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⣠
⠀⢀⡀⠀⠀⠀⢀⢾⣶⣮⣁⡉⠀⠀⠈⣿⣿⣿⣿⠆⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⡏⢻⡄⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡏⢸⣍
⡴⠉⠁⠀⠀⠀⠀⠂⠙⠛⠿⠇⠀⠀⠀⣿⣿⣿⠋⣰⣇⣿⢹⣿⣧⠀⢀⣀⣄⠀⢢⠀⠀⠀⠀⠀⠀⢠⣄⠈⠀⠀⠀⠀⠀⠀⠀⣼⣷⢂⡇⠰⡾
⢥⡀⠁⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢻⣷⣿⣶⣿⣿⣿⣿⣿⣿⣄⠈⠁⠛⠛⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⣼⡆⠀⠀⠀⢿⠀⠨⡇⠀⠆
⠂⠀⠀⣨⢠⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⡿⢟⣿⣿⣿⣿⡿⣿⣿⣦⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⡗⠀⢸⡷⠀⢀⡀⠞⣸⠸⠂⠙⡆
⣶⣷⠀⣇⣰⠛⣷⣦⣤⠀⠀⠀⣄⠀⠀⠀⢀⣶⣿⠏⣽⣿⡏⣿⢻⡿⢿⡗⠀⠀⠠⢰⠀⡤⠀⠀⡀⠈⠲⠀⢧⡴⠿⣁⣐⠠⢀⣂⡀⠀⠀⠸⠁
⠙⠧⣤⡴⢧⣤⠛⣉⣤⣶⣄⣠⣄⣀⣀⠐⢻⡿⠃⠀⣼⣿⢧⢿⡆⢺⣿⣿⡄⢀⡀⣿⣤⠸⠶⢦⣌⢶⣄⠰⣿⢧⣏⣿⡛⠄⠉⠉⠀⢠⡀
⢿⡀⢿⣤⡞⠳⡶⠿⢿⡿⣾⢟⣛⣉⣉⣉⠈⠁⠀⣾⣿⣯⣿⠈⢿⡀⠘⠻⠋⠈⢿⣿⠞⠂⠀⠤⠞⡛⡏⢦⢸⠿⣿⣾⣧⣴⡆⠀⠀⠀⠀⠀⠘
⡟⠁⠀⠀⠈⢠⠀⠀⠀⢰⣐⣎⣻⣿⣿⣌⠀⠆⠀⣿⡇⣿⣿⡁⠀⢠⣴⡄⠀⠀⠀⢹⣆⡙⢶⡄⣀⠹⢡⣾⣦⣶⡾⢫⠟⣶⣾⡿⠧
⠃⠀⣴⣾⣷⣿⡇⠀⠀⠐⠉⠻⣿⣿⣿⣿⣷⣾⡀⣼⠻⠿⣿⣿⣦⣿⠻⠋⠀⠀⢀⣸⣿⣄⣀⣷⡿⠇⢠⣿⣿⡏⠀⠀⠀⢿⠋⠀⠃