Trash bin Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣀⣀⣀⣀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⠒⠒⠀⠒⠒⡒⠒⠐⠚⠒⠓⠐⠒⠒⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⠐⠈⠠⠔⠈⠀⡠⠊⠀⠀⠀⠀⠑⢄⠀⠁⠢⠀⠁⠂⠩⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡤⠭⠉⠉⠉⢀⡀⣐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣀⠀⠈⠉⠩⠥⢤⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠐⠒⠒⠒⠂⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠒⠒⠒⠒⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠭⠍⡉⠉⠁⣀⣀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀⣀⡀⠉⠉⢉⠭⠥⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠒⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⡇⢀⠠⠐⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢃⠉⠢⡅⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢨⠔⠉⡘⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠣⡀⠀⢸⠀⠀⡇⠀⠀⡄⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢀⠔⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⣙⠸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⣋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⢀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠂⠬⣀⠀⠀⠸⢀⠸⠀⠀⢀⠀⠀⡇⠀⠀⢄⡠⠇⠀⠀⣀⠥⠒⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡁⠒⠠⢍⡐⠐⠀⠀⠤⠤⠤⠁⠈⠤⠤⠤⠀⠀⠐⣂⡡⠄⠒⣈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⣉⡀⠒⠒⠀⠀⠀⠀⠀⠀⠒⢂⣈⡉⠄⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣼⣥⣤⣤⣼⣥⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⢶⡆
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⣸⡇⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠁⠀⣹⣿⡇⠀⢸⣇⣤⡶⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⢻⡇⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣼⡟⠁⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣼⣧⠀⢸⣿⣧⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣧⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠘⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣼⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⣧⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣉⡙⠛⠻⠿⠿⠿⠦⠴⠿⠿⠿⠟⠛⢋⣁⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⠤⠀⢀⣀⣀⣭⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⠿⠿⣛⣿⠟⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⠛⠹⠋⠁⠀⣸⣿⡿⠛⠦⢄⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣥⣄⠀⢠⣬⢥⡀⠀⠀⠀⠈⣙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⡿⢿⠿⠭⠽⠶⢿⡆⠀⣴⠟⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣽⣿⣦⡀⣀⢀⣄⢠⣿⡺⣇⢰⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣻⣿⣿⡾⣇⢸⡆⢹⠀⢸⡆⣿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢸⡇⢸⠀⢸⠁⣿⢸⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⣿⢸⡇⢸⡄⢸⠀⣿⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⡇⢸⡇⢸⢨⡟⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣻⣷⣿⣿⣿⣿⣻⡇⣇⢸⡇⢸⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⢾⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠇⢸⢸⣿⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢪⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠁⠘⢨⠆⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⣿⣿⣿⣿⣽⣝⠀⠀⢀⡄⢶⡂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣾⣿⣿⣇⠀⠀⢸⣇⣨⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠛⠻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠿⠿⠿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢓⠈⣷
⠀⠀⠀⠀⠀⠀⣸⡇⢀⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⢠⡿⠀⠐⡂⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣼⣧
⠀⠀⠀⠀⢸⣟⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣠⣤⣽⡇
⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣼⠇
⠀⠀⠀⠀⠀⠙⠛⠛⢻⡟⠛⠛⣿⠛⠋⣿⠋⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⣿⠉⠉⠉⠉⠉⠉⢹⡏⠀⢨⡏⠀⠉⠈⠈⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣦⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠿⠦⠾⠃⠀⠏⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⠀⠀⠀⠰⣿⡗⠒⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⢦⣄
⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⢆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢸⣿⡇⠀⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠹⢦⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⢿⣧⡾⠋
⠀⠈
⠀⠈
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣿⠛⠛⢲⡶⠚⠉⠉⠉⠉⠉⠛⠲⢶⣤⠶⠋⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢤⡀⠘⠃⠀⠈⠀⠀⠘⣆⠀⠀⠀⠀⠀⠉⠀⢀⡄⠀⠀⣿⣿⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢿⣙⠒⠄⠉⢧⡴⢛⡶⠟⠛⢻⠛⠲⢦⣄⣀⣀⣀⣰⣟⠀⢀⢴⠏⠀⢷⣀⣹⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡽⠛⠛⠶⢼⡇⠻⣄⡈⠦⠈⠳⠀⢸⠋⠙⠯⠝⠯⣍⠛⢿⣤⠀⢀⡾⠉⠁⠀⠙⣦
⠀⠀⠀⠀⠀⢸⡅⠘⠆⠐⠋⠀⠀⠀⠀⢀⡿⣿⠉⠙⠓⠶⠶⠶⠿⣤⢦⣴⣶⣶⠾⠷⠾⠷⠓⠚⣧⠀⠈⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢻⡀⢀⡴⠛⠀⠀⠀⠴⠋⠀⠈⢡⠆⠀⠀⠀⠀⢰⡇⠀⠈⠉⢉⠓⠀⠀⠀⠠⠆⠘⠂⠀⠀⠀⠔⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠶⡄⠀⠀⠀⡀⠀⠀⠀⢺⠀⠀⠄⡀⠀⠈⠃⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣈⢰⡇⠀⢐⣀⣸⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⣼⣧⠀⠉⣀⣤⣄⡘⣇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢿⠷⠛⠉⠁⠈⠻⠶⠶⠶⠶⠦⠤⠤⠤⠶⠋⠀⠈⠓⠋⠁⠀⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠠⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣰⠖⠲⣦⣄⣀⠀⠀⠀⠀⢷⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⢰⣏⠂⠀⠁⢠⠉⢷⡀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠘⢧⣀⠀⠄⠀⠀⣼⠇⠀⠀⠀⠙⢯⣗⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣫⡽⠃⠀⣠⣤⡤⠶⠶⣦
⠀⠀⠀⠀⠈⠻⢦⣤⠼⠋⠀⣀⣤⡄⠀⠀⠈⠙⠲⠮⣭⣉⣙⣛⣛⣛⣛⣛⣭⡥⠖⠋⠁⠀⠀⡞⢹⡀⠑⠀⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠹⡶⠶⢦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣰⡴⢖⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⢦⣀⠓⠈⠀⠈⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣛⣒⣲⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠀⠀⡀⠠⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠤⠄⡀⠀⠀⠈⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠑⣄⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠀⠒⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⢠⠀⠀⠈⠁⠀⠁⠏⠉⠉⠉⠉⠀⠀⠃⠀⠀⡀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⢄⡉⠀⠐⠂⠠⠤⠇⠀⡀⣄⠀⢀⣨⠀⡀⠸⠤⠄⠐⠂⠀⢉⡠⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠈⡃⠐⠒⠆⠀⠀⠤⠀⠀⠤⠀⠀⢰⠒⠂⠘⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠲⠄⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣀⠠⠖⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠐⠂⠀⢠⠀⣉⣉⠐⠒⠒⠒⠒⠒⠒⠂⣉⣉⠀⡄⠀⠐⠂⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⢉⠁⠉⠉⠁⠀⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠀⠘⠀⢀⠤⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠒⠂⠀⠘⠀⠀⠂⠀⠐⠒⠂⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠠⠤⠤⠤⠤⠄⠀⠂⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢰⣶⡄⠀⠀⢠⣶⡆⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡉⠉⠛⠛⠷⢶⣦⣴⣟⣉⠁⠈⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣦⣤⣀⣈⠉⠙⠛⠻⠶⣶⣽⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⢶⣤⣤⣀⡉⠉⠛⠛⠷⠶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢶⣦⣤⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡀⠀⠀⣀⠀⠀⣀⡀⠀⢀⡀⠀⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⣿⠀⠀⣿⡇⠀⢸⡇⠀⢸⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⠀⠀⣿⠀⠀⣿⡇⠀⣸⡇⠀⢸⡇⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⣿⡀⠀⣿⡇⠀⣿⡇⠀⣼⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⣿⡇⠀⣿⡇⠀⣿⠃⠀⣿⠁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢸⡇⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⣭⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡗⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⠀⢸⡇⠀⣿⡇⢀⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⠀⠸⠗⠀⠿⠇⠸⠿⠀⠾⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠛⠛⣉⣉⣉⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠿⠛⠛⣻⡿⠋⣰⠟⠛⠛⠛⣯⣸⡟⣿⡛⠛⠛⠳⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠿⠶⠿⣥⠤⣤⣤⣤⣤⠼⠷⠛⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠙⠻⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡴⠶⠛⠉⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣇⡙⠦⣄⣀⠀⠉⠉⠙⠛⠛⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⢀⡀⠤⠖⣋⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠹⣷⣦⣬⣉⣛⣒⡒⠶⢤⠤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⢖⣒⣒⠉⢩⡤⢶⡾⠿⠉⠈⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠿⣤⣄⣀⣈⠉⣁⣀⣩⣿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⡉⠉⠉⢩⠀⠀⠀⠀⣄⠀⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⡆⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣇⠀⢸⣧⠀⠀⠀⢹⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢰⣿⠀⠀⣸⡇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡆⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⢠⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⡇⠀⣿⡀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⢸⡿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⡇⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⣸⡇⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣷⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⠀⢹⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣯⠀⠀⣿⡇⠀⣼⣇⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣾⣧⣀⡀⢸⡇⠀⠀⠀⣿⠀⠀⢸⣇⢀⣀⣿⣦⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⣀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⢀⣀⡤⠤⠶⢖⣚⣿⡿⠿⣿⠷⠶⠲⢺⠒⡳⢖⠿⣿⡿⠛⠓⠶⠶⠤⣄⣀
⠀⠀⢀⣼⠭⠒⠀⠐⠉⠐⠈⠀⠂⠀⠀⠀⠔⠀⠸⠀⠘⣆⠁⠢⡈⠓⠬⣐⠢⢌⣐⠂⠍⢙⣶⡀
⠀⣴⠘⡟⠛⠷⢦⣤⣄⣀⣀⡀⠈⠀⠠⠂⠀⠀⢰⠀⠀⠈⢆⠀⠈⠢⣄⠀⣑⣢⣠⣥⡶⠾⣿⠇⣧
⠀⢿⠙⠒⠦⢤⣄⣀⡈⠉⠉⠛⠛⠛⠻⠶⠶⠶⠾⠶⠶⠶⠾⠷⠖⠛⠛⠛⠉⠉⣁⣀⣤⡽⠶⠞⣛⣦
⠀⠈⠛⣶⣤⣤⣀⡈⠉⠉⠓⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠶⠒⠚⠛⠋⠉⣁⣠⣤⡴⠟⠟⠃
⠀⠀⠀⢹⠀⠀⠁⠉⠙⠛⠒⣾⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠒⠛⠋⠋⢿⢿⡇
⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾
⠀⠀⠀⠀⡏⢸⠃⣠⠤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠤⡔⢸⡏⣿
⠀⠀⠀⠀⡇⢸⠀⣿⠀⢹⡇⠈⢰⡏⠁⣀⡞⠋⣄⡰⠋⢡⣴⠋⠹⣼⠃⢸⡏⢸⡇⢸⢰⡇
⠀⠀⠀⠀⢓⢸⡇⢸⠀⢸⡇⠀⢿⠇⠀⣿⠀⠀⣻⡇⠀⠈⣿⠀⠀⣿⠀⢸⡇⢠⡇⢸⢨⠇
⠀⠀⠀⠀⢸⠘⡇⢸⡇⢸⣇⠀⣾⡆⠀⡿⠀⠀⢹⡇⠀⢠⣿⠀⠀⣿⠀⢸⡇⢸⠀⣿⢸
⠀⠀⠀⠀⠸⠀⡇⢸⡇⢸⡏⠀⣸⠇⠀⣿⡄⠀⢸⡇⠀⢸⣿⠀⠀⡟⠀⣾⠃⢸⠀⡏⠈
⠀⠀⠀⠀⠀⡇⣧⢸⡇⠸⡇⠀⢹⡆⠀⣿⡇⠀⢺⣇⠀⢰⣿⠀⢰⠃⠀⣼⠀⣿⠀⡇⡴
⠀⠀⠀⠀⠀⡇⢻⠈⣧⢠⡇⠀⢸⡇⠀⢹⡇⠀⣸⡇⠀⠸⣿⠀⢸⡇⠀⣿⠀⣿⢀⢷⡇
⠀⠀⠀⠀⠀⠁⢸⠀⡇⠈⣿⠀⠸⡅⠀⣸⠁⠀⣸⡇⠀⢀⡏⠀⢸⡇⠀⡿⠀⡟⢸⢸⡇
⠀⠀⠀⠀⠀⢸⢸⡇⣿⠀⣿⠀⢸⡇⠀⣹⡄⠀⣸⡇⠀⣼⡇⠀⢸⡃⢰⡇⢠⡇⢸⢸⠁
⠀⠀⠀⠀⠀⢸⡘⡇⣿⠀⣿⠀⢠⡇⠀⢿⡇⠀⢨⡇⠀⢿⡇⠀⣾⡁⢸⡇⢸⡇⡿⣸
⠀⠀⠀⠀⠀⢰⡆⡇⢹⠀⣿⠄⢠⡇⠀⢸⡇⠀⢼⡇⠀⣾⡇⠀⣿⠁⢸⡇⢸⠁⡇⡟
⠀⠀⠀⠀⠀⠈⡇⡷⢸⡀⣿⡄⢸⣧⠀⢸⡇⠀⢰⣷⠀⣿⡇⠀⣿⠀⢸⠃⢾⢠⡇⡇
⠀⠀⠀⠀⠀⠀⡇⣿⢸⡅⢹⡇⠸⣧⠀⢸⡇⠀⢹⠇⠀⢹⡇⠀⣿⠀⣿⠀⣼⢸⢷⡇
⠀⠀⠀⠀⠀⠀⡇⢹⢸⡇⢸⡇⠠⣿⠀⢸⡇⠀⢻⡇⠀⣿⡇⢰⡟⠀⣿⠀⡿⢸⢸⡇
⠀⠀⠀⠀⠀⠀⣿⢸⡀⡇⢸⡇⠀⣿⠀⢸⡇⠀⢻⡇⠀⣿⠇⢸⣧⠀⣿⠀⡇⣼⣼⠁
⠀⠀⠀⠀⠀⠀⠘⣾⡇⡇⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⡟⠐⣇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣉⠘⠧⠀⣿⠀⢸⡇⠀⢺⡇⠀⣿⡀⢸⡧⠸⠟⣈⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠀⠀⢈⣁⠀⠉⠁⢀⡉⠀⠠⠄⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣦⣤⣤⣤⣤⣾⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢻⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢸⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⢰⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠈⣿⠇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠒⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⣀⠀⠒⠀⠀⣙⣓⣒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣷⣶⠾⣿⣿⠿⠻⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠿⠋⠨⢠⣾⣿⣥⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡯⣽⡇⠈⠁⠀⠀⢠⠞⠛⠋⠁⠈⠉⠶⢿⡫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣦⠀⡴⠖⠻⣦⠀⠀⠀⣀⡼⢔⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⣿⣿⣿⣿⣻⣗⠒⠒⠒⠊⢻⣷⠀⣴⠿⠋⠊⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣽⣿⣿⣏⣠⣄⢠⣄⢠⢿⣷⢿⡄⢶⣔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣙⣿⣿⣿⣷⣿⡄⢹⠀⢻⡀⠸⡇⢸⡇⣻⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣿⣾⡇⢸⠀⢸⠀⢰⡇⢸⡇⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⢸⠀⢸⡆⢸⡇⣸⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⢸⡆⢸⡇⢸⡇⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣿⣿⣿⣿⣿⣿⢸⡇⢸⡇⢸⡇⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣛⣽⣶⣿⣿⣿⣿⣿⣿⣿⡼⡇⠸⡇⢸⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⢚⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡧⣷⠀⡇⢸⡇⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠃⠘⡃⡿⠂⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣿⣿⣯⣏⠈⠀⢂⡤⠴⣞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⡅⠀⠀⢸⣯⣀⣯⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠷⠶⠿⠟⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⢶⡶⠶⠶⣶⠶⠶⠶⣆⠀⠀⠀⣴⡶⢶⣶⣴⣦⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⠀⠀⠹⣏⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡍⠉⢹⡏⠉⠉⠉⠉⡏⠉⠉⣿⠁⠀⠀⠀⠘⢿⣟⠉⠉⢹⡏⠉⠉⠉⠉⣿⠉⠉⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⠇⠀⠀⠀⠀⠇⠀⠀⡟⠀⠀⠀⠀⠀⠈⣿⡀⠀⠸⠇⠀⠀⠀⠀⠿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣐⠿⠋⠿⢗⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⣿⣁⠀⣀⣻⡷⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠟⠀⠿⠛⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢳⠀⠀⠀⠀⠀⣠⠟⣛⣛⢦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡷⡀⢰⠀⢦⠀⢆⠀⢦⣿⡇⢸⠀⠀⠀⠀⠀⣿⢸⣅⣽⢨⡇⠀⡄⠀⣄⠀⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠏⠳⠷⠶⠷⠾⠷⠾⠷⠾⠛⠷⠞⠀⠀⠀⠀⠀⠈⠳⠶⠶⠿⠿⠶⠿⠶⠾⠶⠾⠃





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⠞⠻⡆
⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡞⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⡴⠖⣲⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠁⢀⡴⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⠋⠀⠀⣿⣀⣀⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠘⠁⢀⡼⢧⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⠇⠀⢀⡴⠋⠁⢈⣷⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠚⠁⠀⢀⣠⠾⠋⠉⢹⠏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠛⠀⠀⠉⠀⠠⠞⠋⢉⣽⣷⣄⣴⣿⠿⢿⣛⠀⠀⠀⠀⠀⠀⠋⠁⣀⣠⡶⠋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠒⠛⠓⠂⠀⠚⠋⣿⣁⣸⣶⠞⠛⠓⠀⠀⠀⢀⣀⣀⣀⣉⣥⡴⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠋⢿⠉⢀⣹⢶⡀⠀⠀⢠⡞⠉⠁
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠠⠼⢷⡋⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⣰⠃⠀⠀⠸⣿⣶⣾⣿⠟⠀⠀⠀⠈⢿⣦⡀⠐⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⣼⣿⣿⣿⣷⠄⠀⠀⠀⠀⠻⣷⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⠀⢀⡿⠀⠀⣤⣄⣀⣀⣤⣤⡾⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠚⠁⠀⠀⠀⢀⣀⠀⠀⢀⣹⡄
⠀⠀⠀⠀⣿⣄⣠⣴⠞⠛⠉⠙⢳⡄⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⣤⡀⠀⠉⠉⠛⠉⣹⡇
⠀⠀⠀⠀⠈⠻⠿⠤⠤⢤⣤⡀⠀⣿⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⠀⣀⡽⠶⣄⣙⣛⠛⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡟⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⢿⡉⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠚⢻⡋⢯⡀⠐⣦⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣈⣳⣤⡬⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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


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


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

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

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠰⡯⠭⠭⠭⠭⣽⠀⠀⠀⠠⡤⠺⠤⠤⠼⠦⡤⠀⠀⠀⢲⡖⠛⠒⠒⠛⠒⡖⠀⠀⠀⠰⡆⠈⠀⠀⠁⠐⠆
⠀⠀⠀⡇⡆⢰⠀⡆⣼⠀⠀⠀⠀⡇⢰⠀⡆⢰⠀⡇⠀⠀⠀⠀⡇⢷⠐⡇⢸⢰⡇⠀⠀⠀⠀⠃
⠀⠀⠀⡇⣷⢸⠀⡇⡎⠀⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⠀⠀⠀⠀⡇⢸⠀⡇⣼⢸⠁⠀⠀⠀⠀⠁⢰⠀⠀⠀⠸
⠀⠀⠀⣇⠘⠸⠀⠇⡇⠀⠀⠀⠀⣇⠈⠀⠃⠈⢀⠇⠀⠀⠀⠀⣧⣈⣀⣁⣉⣸⠀⠀⠀⠀⠀⢃⣘⣀⣀⣁⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀
⠀⠀⢰⣶⣶⣿⣶⣶⡖⠀⠀⠀⠀⢶⣶⣿⣿⣷⣶⠆⠀⠀⠀⠠⣤⣼⣿⣿⣧⣤⠄⠀⠀⠀⠀⠀⠉⠻⢷⣽⡁
⠀⠀⠘⣏⣿⡏⣿⢹⡇⠀⠀⠀⠀⢸⡟⣿⢻⡟⣿⠀⠀⠀⠀⠀⣿⢿⣿⢻⡿⣿⠀⠀⠀⠀⠀⣤⣤⣤⣤⣬⡍
⠀⠀⠀⣿⢻⡇⣿⢸⡇⠀⠀⠀⠀⢸⡇⣿⢸⡇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣸⡇⣿⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⡇
⠀⠀⠀⣿⢸⡇⣿⢸⡇⠀⠀⠀⠀⢸⣇⣿⢸⡇⣿⠀⠀⠀⠀⠀⣿⣽⣿⣹⣇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠾⠿⠿⠿⠿⠿⠷⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⠃⠀⠀⠀⠀⣤⣾⣥⣬⣿⣤⠄⠀⠀⠀⠀⣻⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⣿⢸⡇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣤⣿⣼⣧⣿⠀⠀⠀⠀⢠⣾⣽⣿⣿⡿
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉
⠀⠀⠀⢰⡶⠶⢶⡄⠀⠀⠀⠀⠀⡠⠤⠶⠦⠤⡄⠀⠀⠀⠀⢀⣠⣴⣾⣷⣦⣤⡀⠀⠀⠀⠀⡤⠤⠶⠶⠤⣄
⠀⠈⣿⠉⠉⠉⠉⠉⡟⠁⠀⠀⠀⠓⠒⠂⢲⢰⡎⠀⠀⠀⠀⠘⣷⡒⠒⢒⢒⢺⠃⠀⠀⠀⠀⢳⠒⠒⠒⠒⡟
⠀⠀⣿⠀⡇⣗⣿⢀⡇⠀⠀⠀⠀⢰⡄⡀⠈⢸⠁⠀⠀⠀⠀⠀⣿⡇⠁⢸⢸⢸⠀⠀⠀⠀⠀⢸⢸⢺⢸⢸⡇
⠀⠀⢸⠀⠇⠗⠻⢸⡇⠀⠀⠀⠀⢸⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⣿⡇⠆⢸⢸⢸⠀⠀⠀⠀⠀⢸⢸⢻⢸⢸⠁
⠀⠀⠸⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠰⠧⠧⠤⠾⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠘⠾⠾⠾⠾
⣿⣿⠿⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠈⠁⠀⠀⠀⠀⡀⠀⠠⢄⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠈⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠃⠉⠀⠀⢀⠀⡄⠂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡃⡀⠀⠀⠀⠀⠐⣑⠀⠀⠀⠁⡫⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠐⠽⠀⠀⠀⠘⠑⠁
⠀⠀⠀⠀⠰⠒⠂⠒⠒⠂⠰⣦⣀⠔⠒⠒⠒⡄⠀⡠⠒⠲⠒⠒⠒⡖⠒⠀⠢⢔⠖⡠⠂⡔⠲⢦⡄
⠀⠀⠀⠀⡆⠀⠀⢖⠄⠀⠀⠀⠀⢀⣀⡀⠀⠈⠛⠀⠂⠀⠚⠂⠀⡇⠀⠀⠀⠨⣪⣾⣴⣬⡀⣊⢧
⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠐⠂⢠⠽⠊⠉⠂⠀⠀⠀⠀⠀⠀⢀⡴⠷⢄⠀⠌⣄⠕⢿⣁⠸⠦⡊⡂
⠀⠀⠀⠀⢀⢋⠃⠀⢠⠀⠀⠀⠀⠑⠒⠚⠀⠀⠃⠀⠀⠀⠀⠈⠓⢠⠾⠀⠀⡩⠉⠂⢂⡀⠔⡡⠄
⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠍⠑⠄⠀⠃⠀⠀⠄⠂⡀⢪⠖⠿⡔⡣⣘⢺⣡⡀
⠀⠀⠀⠘⡆⠀⣠⡤⡄⠀⠀⠀⠀⠀⠀⣼⠠⠀⢀⡀⡀⠀⢀⠴⢶⠷⡮⣮⡬⠓⠲⢋⣼⣇⡁⣨⠁
⠀⠀⠀⢸⠀⠀⠙⠤⠊⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠊⠀⠀⠸⣧⠀⢀⣀⢨⡎⢈⣐⣿⣱⠷⠀⣘
⠀⠀⠀⠘⡄⠀⠀⠀⣠⡤⢤⡀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠒⠒⠈⠕⡓⢉⢟⡵⣽⣿⢼⣀⣤⡤⠤⠤
⠀⠀⠀⡘⠁⠀⠀⣾⣱⣚⣉⣥⠀⠀⣀⢤⡀⠀⠀⠀⠀⠀⠓⠀⡘⣐⣗⣺⣵⣵⣵⣯⣝⠛⠿⢿⣖⠲⠶⠗⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡼⠮⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠙⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠔⡖⠀⠀⠀⠀⠀⠧⠀⡴⡶⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡴⠊⠉⠈⢉⡶⠊⠀⢰⡧⠔⡞⠉⠙⡆⠀⠸⡄⢣⡀⢾⡙⣿⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠹⣠⠚⠉⠙⠁⠀⢀⡤⠯⢄⡀⠀⠸⡀⢈⣧⠀⠀⡿⠚⠉⠉⣆⠈⠉⠉⠁⢧⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠈⢦⠀⣰⠁⠀⠈⠑⠢⣄⠀⠴⠁⠀⠀⠀⠈⠳⣄⣙⣧⠤⠴⠚⠡⠒⠉⠉⠙⠢⡀⠀⠀⣼⣀⣀⡘⠀⠀⠀⢰⡲⣄
⠀⠀⠀⠀⠀⢰⠃⢰⠃⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡶⣄⠀⠀⠀⠀⠀⠀⠀⠹⠒⠒⠣⠄⠀⢱⣠⠴⠶⠁⡟⠁
⠀⠀⠀⠀⠀⢈⡕⠛⠚⠋⠛⠓⠢⢤⠔⠊⠉⠉⠉⡣⠤⠖⠢⠤⣀⡼⠙⢎⢾⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⡼⠁⠀⠀⠀⢹
⠀⠀⠀⢠⠖⠉⠀⣀⡤⠤⠀⠀⠀⠀⠀⣀⠀⢀⠴⠦⡀⠀⠀⠀⠈⢣⡤⠬⠷⠇⠀⠀⠀⠀⠀⡟⠒⠚⢹⠡⠚⠉⠉⠉⠓⢦⡿⠤⣄
⠀⠀⢰⠃⠀⣠⠎⠁⡠⠤⠖⢦⣀⠐⠋⠉⠱⢄⣀⣀⠇⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⠀⠀⠐⠋⠉⠙⢺⠀⢀⡤⠤⢄⣀⣀⣁⡤⠼
⠀⠀⠘⠶⠾⠓⠋⠉⠑⢄⢀⡤⠜⠓⠲⠒⠒⠒⠢⢤⣀⣀⣠⠴⠒⠉⠉⠀⠀⠀⠀⠈⠉⠒⠦⠤⣤⡤⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠂⠠⢤⣢⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣄⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠀⠘⠁⠦⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠐⣛⠭⠥⢤⣀⠀⠀⠀⠀⠲⡮⠷⣤⠀⠀⠀⠀⢳⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣠⠖⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢸⠁⠀⠀⠀⠀⣀⣠⠏⠀⠀⠈⣉⠉⠒⠂⠀⠑⠦⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠏⠉⢢⠈⠦⣄⣀⣀⡼⠟⢡⣆⣉⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢫⠖⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣴⠁⠀⠀⠀⠣⣰⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠀⢀⡥⠧⠀⠀⠀⠠⠁⠜⠁⠀⢐⡆
⠀⠀⠀⡄⢀⠀⠀⡀⠠⠐⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⣄⢤⡉⠳⡄⠀⠀⠐⠐⠀⠀⠀⢀⡀⣠⠇⢨⠃
⠀⠰⣁⠘⠂⠓⢉⡴⣒⠒⢇⠀⠀⠀⣀⠃⠀⠈⠑⠢⠤⢄⣄⣀⣀⠤⠔⠚⠢⣄⣀⣀⣁⣠⠝⠢⠶⠀⠀⠀⠀⠀⠀⢏⢲⠋⡀⠸⣀
⠀⠀⢞⣉⠤⠒⠒⠤⠜⠃⠀⠓⠊⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⢞⠊⣉⠝⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢢⡑⢄⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠈⡁⠉⠉⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠰⡆⠀⠳⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⠀⢬⠇⠀⠀⣀⡇⠀⠀⠇⠀⠀⠀⠀⠰⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⢀⡀⠀⣀⣀⡀⠀⠀⢆⣀⡉⠁⠀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⢠⠤⠴⠶⠦⠤⡄⠀⠀⠀⢠⣤⣴⣴⣦⣤⡄⠀⠀⠀⠰⡀⠕⠂⠈⠀⠀⠀⠀⠀⢀⡤⠾⠛⠋⠉
⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠆⢠⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢠⠰⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠢⠠⠠⠌⠄⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠄⠄⠤⠤⠃⠀⠀⠀⠀⠘⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠉⠉⠉⠉⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡏⠀⢸⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⢾⣿⠶⠶⢾⣷⠶⠶⣿⡷⠶⣾⡇⠀⠀⠀⠀⣿⣿⣿⣿⠉⢻⣿⣿⣿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠃⠀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⡿⠿⢿⡿⠿⢿⣿⠿⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣻⡇⠀⣸⣇⠀⢸⣿⠀⣸⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢻⡟⠛⢻⡟⠛⢻⡟⠛⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣸⣷⣀⣸⣇⣀⣼⣇⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠙⣿⠋⢻⡟⠙⣿⠟⢻⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⡀⢸⡇⢀⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠈⠛⠛⠋

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





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

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂
⠀⠀⣀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣄
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣆⠀⠀⠀⠈⠀⠀⢂
⠀⠰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠠
⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠘⡀⠀⢸⢰⢢⣶⡄⡖⠀⣶⢰⣴⣦⡖⠂⡇⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⡇⠀⢸⠸⡼⡟⡆⣧⠤⠟⣿⢻⠎⢧⠄⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠁⠀⠈⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⡴⠟⠳⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀⠀⠈⠋⠀⣀⠐
⠀⠀⢠⠴⠧⣤⠀⠀⢀⡷⠂⠀⠀⠓⣆⠀⠀⣠⠴⠧⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢁
⠀⠀⢸⠀⠀⣿⠀⠀⠘⣧⣀⣀⢄⣠⡿⠀⠀⣿⠀⠀⣿⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠩⠁⠀⠀⠀⠀⠈
⠀⠀⢸⠀⠀⣿⠤⢄⣀⠈⠉⠑⠚⢉⣀⡀⠤⣿⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⡠
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢹⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⡀⠀⠀⠀⠀⠱⠊⠉⡹⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠑⠄⢤⡀⠀⠀⠀⠀⠉⠋⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡟⠉⡳⠤⠀⠀⠐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡷⠒⠒⠒⠦⣄⡀⠀⢀⠤⠒⠉⠉⢻⠀⢼⠀⠀⡤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡈⠉⠉⠙⠒⠤⣙⣾⣅⠀⠀⠀⠀⣟⠀⣨⠃⠈⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤⠤⠽⠶⠦⠄⠐⠒⠻⡍⠁⠀⣀⡠⠾⠁⢰⠥⠖⠒⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⣀⣀⣀⠠⠤⠊⠁⠀⠀⠙⠭⠉⠁⠀⠀⠀⣀⠐⠛⢋⡡⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⠀⢰⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠁⠀⠉⠑⠴⠂⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡠⠬⠦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣓⢾⠳⢌⣁⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠔⢆⠀⠀⠀⢀⠖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⣶⣂⠽⠀⠀⠈⠁⠢⣌⠀⠀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠈⠢⠄⠤⠊⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢆⠀⠤⠀⠀⠀⠀⠀⢳⡄⠀⢠⡻⢊⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡗⢻⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕⢄⡀⣠⡀⣤⢐⡳⢻⠴⠋⡠⠾⠤⠤⠤⠤⣤⡄⠀⠀⠀⠀⠀⡎⠙⡉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣝⡆⢠⡊⠀⠁⠐⠋⡤⢤⣀⠀⠀⡰⣭⠉⠉⠠⠤⠤⢜⡁⠻⠥⢼⠀⠀⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠞⠀⠀⠀⠀⣸⠁⠀⠀⠙⢲⠟⠁⠀⠀⠀⠀⠀⠀⠉⡟⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠤⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡤⠇⣣⡐⠤⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡀⠤⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣆⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣭⣼⣿⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢦⣾⣧⣤⣴⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣈⣿⣿⡿⢷⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠈⠙⣿⡁⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣯⣬⣭⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠶⢛⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢬⣭⠭⣭⣭⣭⣭⣭⣭⣭⣭⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠲⣷⠀⠰⠶⠀⠸⠿⠁⠹⠿⠂⠸⡿⠀⠺⠷⠞⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣹⠂⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⢻⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⢸⣿⠀⢸⣿⠀⣼⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣸⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣷⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣬⣉⣛⡛⠛⠒⠚⠛⣛⣋⣩⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠡⢄⠀⠀⡄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡀⠀⠱⠀⢡⠔⠉⠀⠀⠀⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠑⠢⡀⠈⠢⡀⢡⢸⠀⢀⠔⠊⢁⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡀⠀⠀⠘⠶⠠⣈⠲⠤⢖⢁⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢒⣀⡴⠟⠴⠰⠠⢎⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡐⠂⠂⠁⢠⠊⠀⠀⠡⠀⠁⠂⢌⡐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠀⠀⠀⡰⠁⠀⠀⠀⠀⠣⡀⠀⠀⠈⠐⠄⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠂⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠳⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠔⠁⠀⠀⠀⠀⠀⢰⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⣀⡀⠀⠈⠓⢄⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⠀⠐⠲⠶⠥⠤⠤⠤⠤⠤⠄⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠓⠂⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠉⠿⠻⣟⡉⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠠⠶⠆⠀⠉⠉⠈⠻⠷⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠲⠀⠀⠠⠊⠠⠄⠉⠀⠀⠀⠀⠑⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⣶⣷⠀⠀⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⠶⢤⡴⢆⡀⠀⠀⠿⠋⠀⠀⠿⠟⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠺⡿⠚⠛⠷⣄⠁⠘⠛⣠
⠀⠀⠀⢠⠀⠀⡀⠈⠉⢠⣿⠦⠤⠄⣀⠘⠀⠀⠉⣁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠀⢸⡄⠀⢷⣀⣀⣈⣿⣦⡀⠀⣽⣄⡠⠖⠀⠙⣷⠐⠶⢠⣄⣀⣀⠀⠴⠶⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡟⢹⡿⢿⠋⢤⠒⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣶⠄⠀⠀⢴⡆⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠘⢿⣆⡀⠂⠁⠀⠀⠉⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠃⡀⢛⡄⠀⠀⠙⠆⠀⠙⠛⠛⢲⡶⠠⠶⠚⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡀⢷⡌⠹⣦⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠙⢦⡼⠃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠿⠤⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠻⣦⣤⠖⠁⠀⠀⠀⠀⠀⠀⢀⣿⠉⡇
⠀⠀⠀⢠⠀⠠⣆⠀⠛⣠⣄⣺⠇⠸⣏⠀⣄⠀⠀⠀⠀⠀⠀⢠⡌⠻⠀⡇
⠀⠀⠀⠘⠀⠀⠈⠉⠉⢉⠛⡿⢧⣴⣿⠀⣿⠀⠀⠀⠀⠀⢰⠆⢹⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠖⠀⠈⠋⣿⡆⠛⡄⠀⠀⠀⢀⠇⢀⠈⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢏⠀⢰⣇⠀⠀⢀⠟⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠈⠀⠈⡟⠀⢀⠿⠀⠀⡌⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠸⠀⠀⢸⡇⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠘⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠛⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣤⣌⣠⣤⣼⡿⠃⠀⠀⠀⠀⠀⠈⠛⠛⣋⣤⣄⣀⣤⣾⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠁⠀⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⣤⣴⣤⣶⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⣰⣀⣀⣀⣐⣄⣡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡨⠅⠈⣀⠄⠀⠀⡠⠀⠀⠀⠀⢄⠀⠀⠤⡀⠀⠩⢁⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢊⣁⠐⣈⣁⣀⣐⡊⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⢑⣀⣀⣈⠑⠀⢉⠰⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠀⠠⠤⠤⠤⠤⠤⠀⠀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣀⡀⠀⠀⠀⠤⠤⠤⠤⠄⠀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠁⠈⠀⠘⠓⠐⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠒⠂⠀⠀⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡩⠭⢉⠉⠉⠁⢀⣀⣒⠐⠒⠒⠒⢒⡒⠒⠒⠒⠒⣀⣀⡀⠉⠉⢉⡍⠭⢍⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⢄⣸⠀⡇⠀⠀⡇⠀⠀⡇⠀⠈⡇⠀⠀⠊⠀⠈⡇⠀⠀⢸⠀⠀⢙⠀⠀⠈⠀⠀⠈⠀⣇⡠⠔⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏⠑⠢⣸⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠔⠊⠱⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⢆⡀⠈⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⣆⠀⠁⠀⡴⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⠠⡄⠀⠀⠀⡇⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⡇⢠⠔⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡜⢰⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠇⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⡇⠀⠀⢀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡇⠀⠀⠸⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡇⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡑⠒⠃⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠐⠒⢊⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⣈⠑⠢⠤⡀⣈⠓⠒⠁⠀⠀⠠⡀⡠⠇⠀⠀⠈⠒⠊⣀⣀⠤⠔⠊⣁⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡉⠑⠂⠤⢀⡈⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⣁⡀⠤⠐⠊⢁⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠠⠤⢀⣉⣉⡁⠀⠀⠀⠀⠀⣈⣉⣉⡁⠤⠤⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣀⣀⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠀⠖⠘⠀⠀⠀⠘⠂⠇⠠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢒⠩⠑⠂⢁⠄⠊⠁⡠⠊⠀⠀⠀⠈⠠⡀⠈⠐⠤⡈⠐⠊⠅⡐⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣉⡀⠀⠀⠂⠒⠒⠒⠂⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠒⠒⠒⠐⠂⠀⣈⣉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠬⠭⠭⠥⠀⠀⠉⠁⣉⣉⣀⣀⣀⣈⣉⣉⠉⠁⠀⠠⠬⠭⠭⠥⠄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⢒⣒⠒⠒⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⠀⠒⠒⣒⡂⠂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⣀⠘⠀⠀⠀⠈⠀⠀⠐⠁⠈⢢⠀⠀⡔⠀⠀⠆⠀⠀⡔⠁⠈⡆⠀⢰⠁⠀⢸⠀⠅⣀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠒⠤⣙⠀⡆⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⣋⠤⠂⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢢⡀⠈⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠁⢀⡔⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⠢⡄⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠇⠀⢸⠀⠀⠈⢨⠔⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⡃⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡀⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠣⠤⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠘⠤⠜⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢌⡐⠂⠤⣀⡀⠑⠠⠊⠀⠀⠸⡀⢀⠃⠀⠀⠑⠄⠂⢀⡀⠤⠐⢊⡡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢈⠑⠂⠤⠌⣉⠐⠒⠂⠂⠀⠀⠀⠀⠀⠀⠒⢂⣉⠡⠄⠐⢊⡡⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⢈⣉⣉⡀⠀⠀⣀⣀⣀⣉⣉⠠⠤⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⡶⠾⠷⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣦⣀
⠀⠀⠀⠀⢠⡾⠋⣹⡷⠛⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠈⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠀⢀⣀⡀⠀⠀⠈⠙⠳⢶⡾⠛⠛⠻⣆
⠀⠀⠀⣠⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣾⡷⠾⣿⠀⣿
⠀⠀⠀⢸⡗⠛⢺⣿⢿⣿⠛⠛⣛⣫⣛⡙⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣩⡽⠿⠶⠶⠟⠁
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⣴⠞⠋
⠀⠀⠀⠀⢿⣤⣤⣄⣠⣤⣤⣤⣀⣄⣠⣠⣀⣠⣀⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠶⢶⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠉⠉⠉⠹⣏⠉⢩⡟⠉⠉⠉⠉⠀⠈⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⣾⠁⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠳⠄⢿⣄⡾⠁⠀⠀⠀⠀⠀⠀⠘⢷⣤⠟⠀⠀⠀⠀⠶⠆⠹⣦⡾⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢟⣋⣭⡽⠿⠿⢿⣿⣿⠇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡾⠋⠉⠀⠀⠀⠀⠀⠈⠹⣧⡀
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣴⠏⠀⠀⣠⡴⠶⡶⢦⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢰⡏⣾⠛⢻⡇⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⡀⠀⠈⢻⣝⣛⣫⡽⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣛⣚⣓⣒⣒⣒⣒⣒⠒⠒⠒⠶⠤⠤⢴⣿⣌⣷⣄⠀⠀⠈⠉⠁⠀⢀⣠⠟⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⠶⠶⠶⠞⠛⠁
⠀⢰
⠀⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡷⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⣏⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣷⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠘⠛⠻⠿⠿⠿⠿


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠀⠙⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠉⠉⠙⠛⠂⠀⠀⠘⠋⠁⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠐⠛⢿⠃⠀⠀⠀⠀⠜⢿⠋⠃⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠴⠃⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡤⠀⢀⡔⠁⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠆⠀⠐⠁⠀⠀⠊⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠆⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠒⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣧⡌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡈⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⢿⣿⣶⣿⡶⣶⣦⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢲⣋⣩⣤⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡸⣿⠿⡍⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⢟⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣟⣿⣦
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⣼⣿⣭⢁⣿⣛⣛⡛⣾⣿⡿⢿⠻⣿⡟⠟⠛⢻⣿⣛⣛⡉⣿⣯⣭⣾⣷⣿⣾⡟⠉⣳⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣿⣹⣿⣛⣿⣿⣼⣿⣯⣯⣥⣿⣿⠿⣿⣟⣰⡯⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠠⡤⡶⣾⣿⣿⣿⣿⡵⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠒⠒⠒⠒⠒⠛⠛⠋⠹⣿⣥⣽⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⡏⣿⣿⣿⠻⣿⣿⣿⣿⢿⣇⠀⢀⠀⣠⡀⠀⠀⢠⣤⠀⠀⢸⡏⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⣿⠸⣿⠀⠸⠀⢸⡇⠀⠀⢸⣿⠀⠀⣿⡇⢸⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡀⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⣿⢈⣿⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿⡇⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢻⣿⣧⢹⣿⣿⡄⣿⣿⣿⣿⢨⣿⠀⠀⠀⢸⡇⠀⠀⣿⡏⠀⠀⣿⡇⣏⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⢰⣿⠀⠀⠀⢸⠁⠀⠀⣹⡇⠀⠀⣿⠁⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠈⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠀⣿⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⢸⣿⢀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠈⣿⣿⣸⣿⣿⡇⣿⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠸⣿⢸⣿⣧⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣿⣿⡇⣿⣿⡇⢻⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⢰⡿⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⢸⡇⢸⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⡇⣿⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠰⣿⠁⠀⢸⡇⢠⣿⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⡇⣿⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢼⡇⢟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⢸⣿⣿⢻⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⣿⣿⢸⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⣿⠁⢿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣿⢸⣿⣿⠸⣿⣿⣿⠀⣿⠀⠀⠀⣾⠀⠀⢸⣿⠀⠀⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⢸⣿⣿⠀⣿⣿⣿⠀⣿⠀⠀⠀⣇⠀⠀⢸⣿⠀⠀⣿⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣿⣿⣼⣿⣿⡆⣿⣿⣿⡄⣿⠀⠀⠀⡿⠀⠀⢸⡇⠀⢀⣿⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢸⣿⡏⣿⣿⡇⣿⣿⣿⠇⣿⠀⠀⠀⣷⠀⠀⢸⡇⠀⢸⡿⠘⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣧⣿⣿⡇⣿⣿⣿⡇⣿⠀⠀⠀⡏⠀⠀⢸⡇⢀⣸⣷⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠟⢇⠿⠶⠶⠀⡷⠶⡒⣻⣋⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠛⠒⠒⠛⠋⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣀⡀⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠄⠀⠶⠘⠀⠀⠀⠘⠂⠇⠀⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢒⠩⠐⠀⢁⠄⠊⠁⡠⠊⠀⠀⠀⠈⠣⡄⠈⠐⠠⡉⠀⠊⠅⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣉⡀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠀⠐⠒⠒⠒⠐⠀⠀⢈⣙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠬⠭⠭⠥⠄⠉⠉⠉⣉⣉⣁⣀⣈⣉⣉⡉⠁⠈⠉⠠⠬⠭⠭⠥⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⣒⣒⠒⠒⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠒⠒⣒⡒⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⣀⠸⠀⠁⠀⠈⠀⠀⢰⠁⠈⢢⠀⠀⡔⠀⠀⠆⠀⠀⡞⠁⠈⡆⠀⢰⠁⠀⢸⠀⠁⣀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠐⠤⣙⠀⡄⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⣋⠤⠂⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢢⡀⠈⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠁⢀⡔⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠢⡄⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠃⠀⢸⠀⠀⠈⢨⠔⢉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⡃⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡀⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⢠⠀⠀⡇⠀⠀⡇⠀⠸⠀⠀⢸⠄⢠⡇⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠠⠀⠀⢠⠄⠸⠇⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠂⢰⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠸⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠣⠤⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠘⠤⠜⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢌⡑⠢⠤⣀⡀⠑⠠⠊⠀⠀⠸⡀⢀⠇⠀⠀⠓⠄⠂⢀⡀⠤⠐⢊⡡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢌⠑⠂⠠⠌⣉⠐⠂⠐⠂⠒⠀⠀⠀⠂⠂⠒⢂⣉⠡⠄⠒⢊⡡⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠤⢀⣉⣉⣀⡀⠀⢀⣀⣈⣉⣉⠠⠤⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢙⣢⣄⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⣴⣶⡶⠂⠁⠈⠳⣶⡾⠒⠲⣶⠞⠀⠁⠀⠀⠀⠀⠀⠈⠀⣩⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⣿⠉⢙⠧⣠⠞⠁⠄⠀⢀⣀⣈⠟⢓⡸⠛⢿⣀⢠⣄⡚⡆⠀⠀⡔⠒⢏⡹⡟⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⡗⢄⡄⠁⢾⡀⢻⣤⢀⣤⠾⡁⣀⡠⠐⠛⠁⠐⢾⢍⡉⠛⡻⢄⢄⡴⣋⠶⣏⣠⣏⣹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣷⣤⣌⣭⠛⣚⢛⡇⢀⡀⠉⠖⣩⡤⢤⣤⠼⠄⠉⠧⠄⠠⠿⠤⠾⠛⠃⠀⠉⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠻⣿⣿⣏⠹⢿⣿⣷⠛⢛⣿⡿⠛⢻⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣿⠱⣟⣷⡟⢣⡘⣷⣛⡯⠙⣶⡋⠀⠙⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⢽⣷⡏⢉⡟⣭⠿⠒⢽⣷⠊⠀⠙⣤⠞⠀⢗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣸⠏⠱⣬⡜⠋⣳⣌⠾⡯⠳⣄⠞⠉⠳⣀⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⢿⣿⣶⠛⣄⠐⣼⠻⣇⣟⣵⠽⢦⢔⣶⠛⣶⢏⡁⠀⠀⠀⠀⠀⠀⣀⢤⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠉⠐⣬⣟⠀⠢⣼⣿⡋⢀⣼⣿⡀⠀⣼⢿⣗⣂⠀⠀⣀⡴⢮⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣴⡇⠱⣴⣋⠘⣷⣟⡏⠀⣳⣿⠁⡒⣻⡞⠁⠈⣽⣷⣢⣾⣿⣇⣈⢳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣧⡜⠙⣶⡴⢃⡹⢦⡟⢧⠹⣇⠾⠭⠙⢦⠞⣿⢹⣧⡟⠯⣷⣼⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣷⣠⠾⢇⠀⡠⠛⣦⡀⡴⠋⢳⣶⣶⣟⢷⣆⡷⠋⣧⣳⣾⢿⣡⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⡾⣏⢹⣹⣿⡵⠖⣤⠿⣞⣂⣩⠟⣴⡽⣷⡿⣖⠚⣿⠿⣿⣰⢿⣿⠀⠀⠀⣠⢾⠖⣾⣏⣹⠗⢚⣏⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⣿⣁⢸⣷⣛⠳⣿⣿⢉⡒⢪⣿⡛⠎⢙⣿⡿⠀⢈⢿⡷⢃⣿⡟⢿⣟⣀⡀⢼⠤⡶⠲⣅⠰⡆⣽⢁⡝⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⣧⣜⠤⠿⣴⠋⣈⢳⣶⠋⢈⠻⣴⠎⣱⠛⣴⢫⢘⣷⣞⢠⣿⡞⣻⠀⠘⠻⠶⣀⣦⠸⣄⣙⣛⡈⠒⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣷⣀⣼⡙⢶⣲⠞⠹⣧⣠⠟⣹⣟⣱⠊⠈⢧⣴⣏⠻⣿⢿⢷⡯⠀⠀⠀⢠⡀⠸⢃⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣫⢻⣄⢈⠝⠳⣷⢦⡜⠻⣌⣤⠼⠿⣤⣤⣿⡿⣇⣴⢛⣾⣾⡷⣊⣒⠤⢼⠏⢀⣥⠄⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠞⣦⡤⠟⠋⠉⣼⠘⡾⠿⡂⠁⡼⢯⡙⣁⡾⢧⣤⣄⡼⢧⡸⣷⡟⢳⣡⣾⣿⡏⠉⠉⠀⠀⣠⡿⢦⠊⠒⠁⣿⢽⠦
⠀⠀⠀⠒⠒⢈⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠒⣶⣿⣿⡅⠀⡹⢎⠀⠈⣿⣯⠖⠀⣹⣏⠣⢄⡿⢯⣿⣿⢿⣧⡿⠁⠀⠀⠀⠀⠙⠓⠫⢳⡴⠶⠆⠚⠃
⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⢀⡀⠔⠛⠻⢿⣯⣻⣾⡧⢤⣷⡞⢇⡉⣳⣞⣁⣨⡷⣿⡖⣾⣿⡷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⠾⠿⠿⠷⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡹⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠫⣱⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⣀⢤⠀⠀⠀⠀⠰⡁⢠⣤⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡔⠊⠉⠙⡶⠊⠀⣾⠤⡶⠋⠳⡄⠀⣇⠣⡀⢖⣺⣆⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⢠⠃⢧⡎⠉⠉⠀⢀⠤⠾⠤⣀⠀⢣⣀⠧⠀⢀⠗⢉⣉⣣⠈⠉⠉⢸⠀⠀⢈⠇
⠀⠀⠀⠀⠀⡱⢀⠎⠀⠀⠈⠑⢦⡀⠃⠀⠀⠀⠀⠱⡤⠝⠒⠚⠁⠚⠁⠀⠈⠑⣄⣀⣸⠶⠦⣌⠀⠀⣰⢯⡲
⠀⠀⠀⠀⠘⢅⣼⡠⠤⢄⣀⠀⣀⡧⠤⠤⠄⢀⣀⡀⠀⢀⡿⣳⡠⠄⠀⠀⠀⠀⠈⠉⠉⠓⠀⢸⠞⠉⠁⢻⡀
⠀⠀⠀⣠⠔⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⢀⣊⠁⠀⠈⠙⢮⣀⣙⣵⠀⠀⠀⠀⠰⡶⠤⠶⡆⡤⠿⠶⠦⢄⣼⣁⡀
⠀⠀⡰⠁⢀⠔⠉⣠⡤⢤⣀⠠⠒⠑⢦⡁⢀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠓⠒⠲⡇⠀⣀⣄⣀⠀⣁⣀⡹
⠀⠀⠳⠶⠗⠊⠉⠳⣀⡠⠴⠓⠄⠒⠒⠺⠥⣄⣀⠤⠔⠊⠉⠉⠀⠀⠉⠉⠒⠦⠤⠤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠭⠭⠽⠯⠭⠽⠯⠭⠭⠽⢦⠀⠀⢺⡿⣽⠿⠿⠿⠭⠭⠭⠭⠭⠭⠭⠭⠽⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠶⢶⡶⠶⠶⠶⢶⡶⠶⢶⡾⠀⠀⠀⠳⣾⡶⠶⠶⢶⠶⠶⠶⠶⢶⠶⠶⢶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⠙⣿⠄⠀⢸⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣿⠛⣿⠆⠀⠀⣾⠀⠀⠀⠀⠀⠀⢹⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰⣿⠂⠀⠀⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠿⠐⠿⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡇⠀⠀⠀⠀⣰⢫⡭⣝⢦⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣆⠸⡀⢣⡀⢦⠘⣾⣿⢸⡇⠀⠀⠀⠀⢿⡸⠦⢟⣼⡄⢰⡀⠰⡀⢱⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠘⠛⠁⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢐⡻⠞⠻⠾⠂⠁
⠀⠀⠀⠀⠀⠐⠒⣼⠋⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣧⣤⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡷⠦⡀
⠀⠀⠀⠀⣠⣤⡰⠷⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡧⠴⠿⠁⠀⡀⠀⠀⠀⠀⠴⠛⣀⡴⠚⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠷⢌⡣⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡀⠀⠀⠀⠈⢡⠀⠀⢀⣴⡷⢨⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡁⠀⠀⠀⣠⣤⣀⡀
⠀⠀⠀⠀⣀⠈⢠⡞⠃⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⡟⠋⠁⠀⠀⠀⠲⠀⠀⠀⠹⠶⢈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣍⠹⠀⠩⡁⠂⠉⠙
⠀⠀⠀⠈⠛⠦⠬⢉⣀⡼⠃⠀⠰⠀⠂⢺⡇⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢲⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡂⠀⠀⢁⣐
⠀⠀⠀⠀⠀⠀⠀⠊⣁⣀⣀⣀⣠⡦⠰⣾⠃⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⣀⣀⠀⠐⢊⠀⡇⠀⠀⠀⢸⡍⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢫⡤⠖⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢋⠉⠙⣷⣦⣄⠁⠀⠀⣟⢷⠒⣤⠂⠴⠓⠠⣾⣿⠂⠉⠁⠈⣤⣆⡀⠂⢀⡀⠀⠀⠀⠀⠸⠀⠀⣀⠀⠀⢢⣭⡄⢀⡻⠦⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠘⠲⠀⠻⢣⠟⠀⣀⢀⡻⢿⡽⠛⠛⠛⣿⣶⢏⠙⣶⣤⣼⡷⣿⠉⠙⠃⡉⢰⡆⠀⠀⠈⠀⠀⢎⠁⠀⠀⠀⠀⠈⠉⣱⠄⠛⣈⣤⠇
⠀⠀⠀⠀⠀⢀⠔⠙⠀⣷⠀⠀⠀⢹⡿⢂⢉⣉⣉⣁⣄⣀⣈⡁⢶⡟⣤⠳⠾⢡⡍⣤⠉⢹⡇⠀⠀⠙⠲⢀⠀⠰⠆⢠⡈⠂⠀⠀⠀⠀⣠⠶⣌⣡⠜⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢆⣴⠇⠀⢠⡦⢋⡴⢛⠧⠀⢧⡄⠉⢡⣼⣷⣾⠇⠀⠀⠴⠉⠀⠛⠄⢘⡇⠀⠀⠀⠀⡠⢺⣷⣤⡿⠁⡠⠄⣀⣤⠀⠉⠻⠷⢉⣷⣤⣴⢦⡀
⠀⡠⣠⡄⠀⡘⠀⠀⣁⡀⢰⠌⢀⣾⣧⣿⡀⢂⠠⢜⠷⣶⣯⣿⣁⡰⠦⠖⣦⠀⠀⠈⠒⠛⠁⠀⢠⠀⠠⣇⢀⣿⡏⠁⢀⣠⣦⡨⠋⡇⠀⣠⣤⣤⣋⡉⡀⣦⣽
⠿⣁⣿⡁⠰⣧⣤⠛⠁⠹⠃⢠⣿⣹⡷⣿⣷⡤⢷⡤⡶⢿⡿⠁⠀⠀⡀⠀⠀⣶⠀⣀⠐⠀⠀⡀⡾⠋⠙⠋⢀⣿⣇⠺⠟⢥⠈⠁⠔⠀⠀⠻⣶⡇⠀⠀⠀⠈
⠀⣀⣻⡽⠀⠉⠻⠀⠀⡄⠀⣾⠁⡈⠀⢙⡿⠷⠋⠀⢳⠈⡷⢐⡖⢠⡅⡀⠀⠛⠀⢛⡆⠀⢤⣇⡀⠀⠠⠈⣃⢸⡃⠀⠀⣄⣘⣦⠐⢦⣤⣤⣆⣼⠇
⠈⠫⠿⣤⠀⠀⠀⠂⢀⣧⠀⠻⢿⡧⠀⠈⠀⠰⠈⢀⠂⠰⡗⢨⠁⣼⣇⠑⠀⠀⠀⠀⠑⠳⠊⢁⠄⣀⡸⣆⣹⣏⣼⠟⢀⠀⠉⠿⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⡀⠀⢻⣆⠀⢦⠀⠀⡃⠀⡤⠀⠀⠐⠂⠿⠨⠐⣟⡹⠀⠀⣀⠐⣀⢠⣶⣼⠁⣴⣉⡟⠋⠉⡛⠃⣰⣃⠀⠉⡀⠀⠐⠐⢄⡀
⠀⠀⠀⠁⢴⡟⢲⣷⠀⢀⡙⢷⣼⠷⠚⠓⢤⣀⡂⠀⠀⠐⠀⠀⠈⢸⠁⢨⣾⠟⣿⠿⣦⣾⣿⡾⢳⠉⢀⠘⠋⠀⠒⡞⠉⠈⢹⡇⠙⠀⣷⣎⠁
⠀⠀⠀⠑⣈⠻⣿⣿⠏⠉⠙⠒⢀⡄⠐⠦⠀⠈⢳⡌⣠⡀⠀⠐⢶⣼⣷⣿⠛⠎⠀⣀⣀⣈⣽⠖⠈⠐⡍⢠⢀⡀⠀⣀⡀⠀⠛⠓⠀⠸⢷⠛⠚⠐⠢⡀
⠀⠀⠀⠀⠈⠐⣈⠻⠀⠀⠀⠀⢠⠺⠆⢼⣶⡶⣦⡉⠁⠈⠋⡙⠿⠋⢉⡙⠛⠛⠛⠛⣉⠉⢁⡀⠀⢾⡧⠈⣹⡄⣾⡌⢉⡗⠂⣠⣼⣣⡈⢴⠆⠁⠤⠉
⠀⠀⠀⠀⠀⢿⣄⡀⠀⠐⠀⠀⠶⡇⣰⣾⣏⠛⠚⣡⢮⣷⠶⠿⣿⡟⣤⡶⢺⣧⣾⣷⠿⡗⠋⣛⢷⠞⢷⣄⡀⣠⣿⣼⠋⠉⠉⠀⠀⣹⣏⢰
⠀⠀⠀⠀⠀⠈⢉⠇⠘⠀⠠⠰⣟⡦⠙⢛⣿⣗⠀⣴⢏⣹⣾⣿⠿⣿⣿⡏⠻⢿⡉⠉⣱⠀⣠⡀⢦⣤⣎⡛⢸⡇⠘⠢⠔⠉⠐⣆⠸⢌⣷⣽⠂
⠀⠀⠀⠀⠀⠰⠀⢀⠔⠀⢂⠀⠀⢀⣆⠾⢫⠛⠸⣧⣿⣦⣿⢀⡞⢻⣿⣿⡄⠀⠙⡎⢣⢀⡿⢻⣄⢹⣆⠹⡞⠛⠓⠚⠒⠛⠛⠛⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠤⢀⣼⢧⣴⣿⣩⣤⡈⠠⢀⠈⢷⣸⡁⠼⣛⡿⡿⠋⠀⠀⠀⡷⠀⠀⠀⠀⠀⠈⠉⠋⣡⣤⣤⣤⡤⠤⢀⣠⠔⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⢿⣿⣿⣿⣟⣁⣿⠀⠈⠛⠁⣀⣿⡵⠂⠀⠀⢱⠘⣷⠤⠂⢀⠀⡴⠄⠀⢸⣿⠟⠛⠁⢠⡆⠈⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠈⡉⠛⠻⠿⠿⠀⠀⠀⠾⠿⠋⠀⣠⡄⢠⠀⢴⠿⠶⣆⣠⢤⣄⠴⠘⠣⠀⠀⠈⣰⣼⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠢⠴⠄⢀⣐⣀⡀⠄⢀⡤⠔⠀⠞⠉⠉⠀⠀⠀⠀⠀⠈⠀⢀⣀⢦⣤⣤⠰⠖⠻⠉⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠈⠉⠙⠷⢀⣄⣤⠲⠿⠿⣶⡿⠖⠞⠲⠒⠂⠀⠙⠉⠉⠀⡀⢀⠁⢈⣦⢠⡷⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⢀⣤⠤⠖⢀⠀⠀⠀⠁⠀⠀⠁⡀⠀⢀⡀⠀⠀⠀⠐⣬⠶⠲⣄⠠⠁⢾⡉⠀⠛⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠰⢢⣄⣸⠁⡀⠀⠀⠃⠀⠀⠀⣀⢀⣾⠀⠘⠁⠈⡐⢀⡀⣰⠿⣠⠀⢈⡦⣑⣾⡉⠀⠀⠀⠀⢀⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣼⣿⣍⠁⠀⠀⠀⡿⣿⣦⠀⠉⢾⡷⠶⣾⠀⠀⣿⠼⣿⢿⣿⣧⠄⣿⣷⢿⣿⡟⢻⡇⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡏⠙⠿⠟⢣⣄⡠⣮⣼⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁⣾⣿⡏⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⣶⣦⣤⣏⣰⣏⢷⣿⡷⠀⠀⢻⡟⠛⠤⠀⠀⠻⣋⠾⣿⠦⠶⠂⣿⣿⢿⣿⣋⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⡟⢻⣿⣟⠉⠛⠻⠿⣿⣿⣦⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣄⣀⣀⠀⣤⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⠿⠟⠈⠁⠠⠤⡿⠛⠟⠉⠀⢛⡉⠩⠈⠀⠀⠙⠛⢹⣿⠙⠛⠈⣿⠛⢻⡟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⠀⠸⠂⠁⠀⠀⠀⠈⠀⠀⠀⢠⡄⠠⠀⠀⠀⠀⠀⢘⣥⡈⠉⠀⣕⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢨⣆⡉⠁⠀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⢠⠀⢹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠐⣍⣉⠀⠀⣷⢈⣾⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⢸⠁⣀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠐⠂⠀⠀⠀⠀⣘⢧⣈⠁⠀⣿⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⢈⠁⠀⠀⠀⠀⠀⠀⠁⠀⢘⠋⠉⠀⠀⠀⠀⠀⢨⡧⢈⠀⠀⡟⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠆⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠈⠁⠀⠀⠀⠀⢰⣧⢈⡀⠀⡿⠘⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠀⠀⠀⠀⠀⢸⡧⢀⡄⠀⢆⠰⣇⢸⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⠀⠑⣈⡀⠀⠰⠇⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⡧⣤⠀⢸⠃⠐⢋⣾⡁⠀⠈⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠐⠀⠈⠁⠀⠂⠀⠀⡔⠀⢸⡆⠀⠄⠀⢀⠀⠀⠸⢷⡄⣠⠮⠀⠀⡘⢡⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠓⠒⠠⠄⠀⠀⠀⠀⠛⠂⠤⠀⠃⠀⢠⣀⣡⠘⠡⠶⡈⠢⣤⣾⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠐⠂⠀⣲⣿⠛⠀⠀⠀⠈⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡴⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢠⣤⣄⠷⢊⣉⣀⢀⡤⠐⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠶⠾⠾⠿⠛⠋⢹⡿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⣰⠞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⣆
⠀⣀⣀⣠⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⢀⠀⣿⡀⣀⣀
⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿
⠉⠳⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠞
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⠳⠊⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⣠⡞⣉⣽⠖⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⣦⠈⠉⠈⠉⠓⠶⠶⠦⣤⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣄⣻⠀⠀⠀⠀⠀⢀⣴⠈⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣄⠉⠂⠀⠀⠀⡠⠚⢹⣦⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⢹⡇⢠⡞⠁⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⣤⣼⠇⠈⠳⣄⠀⢠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣠⡤⠦⣤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⠤⢤⣄
⠠⡏⠀⠀⠈⣳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣜⠀⠀⠀⢹
⠀⡇⠀⠀⠀⣽⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠀⠀⠀⢸
⠀⡇⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⢸
⠀⡇⠀⠀⠀⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⠀⠀⠀⢸
⠀⡇⠀⠀⠀⡿⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢿⠀⠀⠀⢸
⠀⡇⠀⠀⠀⣗⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⢸
⠀⡇⠀⠀⠀⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣼⠀⠀⠀⢸
⠀⣇⠀⠀⢀⡟⠀⠀⠙⠓⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠚⠋⠀⠀⢿⡀⠀⠀⣸
⣤⣬⣷⣶⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣾⣥
⣿⣿⣿⡟⠋⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣴⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠉⠀⢆⣀⠀⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⣤⣶⣶⣂⣀⣠⣤⣴⣾⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠿⢋⣽⡿⠛⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⡟⢻⠿⠛⠁⠀⢀⣿⣿⡿⠿⠦⣤⢀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣇⣁⠄⠀⠀⡐⣫⡉⠁⠀⠀⠀⠐⡋⠭⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣛⣋⣻⣆⠀⠀⢠⣴⣽⡻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣿⢿⣿⣿⣿⣿⠉⠉⠉⠉⠉⢿⣇⣠⡿⠋⢃⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⣾⣿⣿⣿⡤⢤⠠⢶⡀⠾⣿⠽⣷⠼⣷⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢵⣽⣿⣿⣿⣿⢿⡇⢸⡇⢸⡇⠀⢻⡄⣿⠂⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣧⢸⡇⢸⡇⠀⣿⠀⣿⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⡇⠈⡇⠀⣿⢀⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣭⣿⢼⡇⠀⡇⠀⣿⢸⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣖⣇⠀⣿⠀⣿⢸⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⠀⣿⠀⣿⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠠⣺⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⢹⠀⣿⢸⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠋⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠘⠀⠿⣸⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣟⣟⣿⠽⠁⢤⣀⣀⣭⡴⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠐⣿⡂⢸⣇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣍⡙⠓⠶⠤⣝⣢⡀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠉⠉⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠽⠷⣤⡀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⡉⠉⠀⠀⠀⠀⠀⢤⣝⣶⣄⠀⠀⠀⠀⠙⣆⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⡡⠔⠊⠉⠉⠉⠉⣦⠀⠀⠀⠀⠀⠑⢄⡉⠁⠀⠀⠀⠀⠘⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢠⠎⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠤⠤⠤⢤⣀⠙⠦⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⠤⢄⠀⢻⠀⠀⠀⠀⠰⣴⡶⠋⣀⠤⠄⠒⠒⠂⠀⠀⠀⠀⠈⢑⡤⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⡀⠀⢳⠀⠙⠲⠤⠴⠒⠉⠀⠛⠤⠤⢤⡀⠀⠀⠀⠀⠀⢠⣞⡁⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠜⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠞⠁⠀⠀⠀⢀⠀⠇⠀⠀⠀⢠⠰⠉⢹⠀⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣠⢿⡼⡀⠀⠀⠀⠈⢢⠗⢉⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠽⠶⠤⣤⣀⣀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⣀⡠⠞⠁⢠⡷⠇⠀⠀⠀⠤⠎⢰⢋⢽⡍⣉⠶
⠀⠀⡖⢦⠀⠀⢀⠠⠀⠇⠀⠀⠀⠀⠈⠳⢄⡀⠀⠙⠒⠉⠳⠀⠀⠀⠀⠀⠀⠀⠠⢤⡠⣄⠉⠲⡄⠸⠳⠒⠒⠒⠒⠒⠒⣌⢁⣴⠳⣨⠃
⢖⡐⠛⠂⠓⠊⡠⠔⠒⠺⡀⠀⠀⠀⢠⠇⠀⠈⠑⠲⠤⣄⣀⣀⣀⣀⡠⠤⠒⠢⣄⣀⣀⣈⣁⣀⠷⠤⠾⠀⠀⠀⠀⠀⠀⠘⡙⡾⠋⣀⣸⡀
⠀⡟⠋⣡⠴⠢⠤⠭⠗⠀⠑⠖⠒⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡗⡜⠒⡲⠺⢄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠘⣌⠫⡀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠒⠒⠒⠒⢰⠖⠶⠂⠀⠀⠒⠒⠒⠒⠒⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣘⣀⣸⡀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡔⢶⢧⡀⠀⠀⠈⢹⠉⠉⢹⠙⠂⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⡙⠞⠓⠋⠉⠒⠦⣼⠀⠀⠸⣄⣀⣀⡤⠴⠚⠣⠤⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠲⠾⠍⠉⠀⠀⠙⠀⠀⠀⠧⠤⣀⣀⣀⡀⠀⢀⡠⠖⠁

⠀⠀⠀⠀⠀⢀⠤⠤⠤⠀⠀⠒⠒⠀⠀⠀⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡎⠐⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡠⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡇⠀⠀⡈⢠⣄⡄⠀⢠⡄⣤⡀⡤⢠⢠⠄⢸⠀⢠⠀⢀⠀⠀⠒⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⢰⠀⠀⣁⢸⠟⡇⠀⣯⡇⡹⡀⡇⢸⠇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠘⡀⠀⠹⣘⣀⣓⣂⣃⣁⣙⣁⣁⣘⣘⣃⡼⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠇⠀⠀⣀⡄⠘⠉⠀⠀⡠
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠠⠊⠁⡤⠀⠀⠠⡞⣀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⢀⣣⡀⠀⠀⠀⠀⣎⡋⠀⠀⢟⣱⠀⠀⠀⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⢀⡠⠜⠁⠀⠀⠀⠈⠳⠶⠮⠃
⠀⠀⢸⠇⠀⠈⡇⠀⠀⢰⡏⠀⠀⠀⠀⢸⡆⠀⠀⡏⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⡃⠀⠀⡇⠀⠀⠀⠻⡦⢴⢲⡶⠟⠁⠀⠀⡇⠀⠀⣿⠀⠀⠠⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠁⠈⠀⠈⠁⠀⠀⠁⠀⠠⠤
⠀⠀⠸⣅⣀⣠⠟⠒⠂⠤⠤⠠⠤⠍⠀⠤⠄⠒⠉⣇⣀⣀⡝⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⠀⠀⠠⠀⢠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢆⠉⠁⠈⠉⠀⠀⠀⠈⠉⢩⡥⠤⢼⠀⠰⢦⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠔⡯⠿⢍⢑⠒⠤⢄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠒⠚⠷⠬⠑⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⣈⠦⠀⠀⠨⢉⡀⠀⠀⠁⠐⠒⠠⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡏⠑⠒⠒⠒⢓⣂⡩⠖⠀⠠⠄⢀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠀⠠⠄⠀⠀⣤⣤⡼
⠀⠀⠀⠀⠀⠀⡇⠀⢀⢠⠐⠫⠤⣭⡓⡄⠀⠉⠀⠀⠠⠤⠐⣒⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⡷
⠀⠀⠀⠀⠀⢠⡇⠎⠔⠹⠿⠿⠿⢯⡑⡇⠀⠀⡰⠊⠁⣀⢄⠘⣅⡀⠉⢹⠃⠐⢦⡀⠀⡽⠁
⠀⠀⠀⠀⠀⢠⡠⡄⢄⣀⣸⣀⣀⠴⣣⡇⠀⠀⡇⠀⠉⠀⠀⡶⠀⣅⡀⢸⠀⠀⠀⣱⠐⠁
⠀⠀⠀⠀⠀⢸⠇⠈⠓⠒⢶⠛⠒⠊⠀⡇⠀⠀⡇⠀⠀⠠⠀⡇⠀⠈⣇⡇⠀⠀⣠⠃⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠀⢠⡇⠀⢠⠁⠀⠀⢀⢸⠁⠀⢸⠀⠀⠀⣴⠃⣸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡌⡞⠀⠀⡏⠀⠀⢰⡏⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⡇⠀⢸⠃⠀⢀⢣⠇⢸⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⣸⠀⠀⡏⠀⠀⢠⢃⡇⠀⡞⠀⠀⡎⢸⠀⡞
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⢸⠀⡇⠀⠀⡇⠀⠀⡘⢸⠇⢠⠃⠀⣸⠁⡇⢀⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢀⡇⢸⠁⠀⢸⠇⠀⢠⠇⡞⠀⢸⠀⡰⠃⢸⠁⣸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⡸⠀⣼⠀⠀⢸⠀⢀⠎⢰⠃⠀⢸⠊⠀⢀⡏⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⡴⠁⢀⡇⠐⠃⠈⡗⠁⢀⡇⠀⠀⠘⢦⡤⠎⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠒⠤⣀⣀⠉⠛⠉⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⣀⣀⡠⢴⠃
⠀⠀⠀⠀⠀⠀⠑⠒⠲⠤⢭⣉⣐⡒⠒⠒⢒⣒⣒⣒⣒⣂⣉⣩⠭⠥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠂⠐⠒⠊⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠲⢴⠀⢓⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⠁⢀⠀⠀⣠⠛⠉⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠒⠊⠀⠀⠀⠀⢀⠞⠀⢰⠃⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢦⠀⠀⠀⠀⠧⣄⠀⠀⠀⠠⢊⠔⠒⠾⡀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢀⣽⠚⠀⠀⢀⣾⡳⠖⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⡌⢱⠀⠀⠈⠢⠤⠬⡿⠂⠤⠔⠛⠉⡁⢀⣀⡤⠞⠀⠀⠀⠘⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⣉⣉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⢳⠀⠀⠀⠀⠀⢴⡚⠉⡠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠚⠓⠋⢁⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⠼⠃⠑⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠖⠚⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡄⢀⣀⠞⠀⠀⠀⠀⣈⠣⡀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡏⠁⠀⠒⠋⠉⠙⢲⠀⠀⡀⣸⣡⠁⠀⢳⡌⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⢠⢠⡴⠀⠲⠼⠋⠀⡎⠉⠲⣌⡦⠀⠁⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠃⠀⠀⠀⠀⢸⠁⡞⠉⠀⠀⠀⠀⠀⠀⡃⠘⠟⢿⡦⡀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⢦⠀⢀⣠⠶⡏⢰⠗⠒⣟⣦⡠⠤⢒⠮⠒⠑⠦⠊⠑⠈⠁⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠣⣨⠃⣰⠃⡞⠀⠀⡿⡤⠒⠋⠁⠀⠀⠀⡇⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢳⣄⡝⢠⠓⠂⠤⡿⠁⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢆⢠⡿⢧⠃⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠁⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡯⠓⢄⢀⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⡇⢰⠆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣇⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣥⣤⣤⣍⣽⡭⣴⣷⣶⠖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⣼⣁⣬⡵⠟⠉⠻⢿⣭⣈⣆⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⣒⣉⣉⣉⡓⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡴⠛⠉⠉⠉⠉⠙⢦⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠀⠀⠀⠠⠰⠲⠀⠲⠒⠗⠲⠖⠶⠶⠰⠤⠾⠶⠞⠒⠒⠒⠒⠒⠒⠲⠖⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⡄⡄⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂⠀⠒⠒⠐⠀⠄⠐⠐⠀⠂⠀⠘⠐⠀⠀⠃⠂⠘⠀⠀⠂⠃⠀⠒⠂⠀⠒⠀⠃⠇⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡹⢋⠟⡹⢋⠟⢉⠏⡹⢋⠟⡹⢋⠟⢹⠛⠾⢋⡿⢋⠟⡹⠛⡹⠚⢘⠖⡰⠒⡶⢲⢖⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠉⠀⠁⠀⠁⠉⠀⠁⠈⠀⠁⠈⠠⠎⡴⢡⠞⢡⠞⢁⠔⣡⠞⡠⢊⠔⣡⢊⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⣦⠀⠀⢰⠶⡄⠀⠀⣴⢦⠀⠀⢠⡴⣄⠰⢁⣴⢥⡴⢁⢜⡥⡎⡰⢋⣼⣥⠊⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢺⢸⡀⠀⣿⠂⡇⠀⢠⡏⢸⠀⠀⢸⠅⠇⠀⣋⡿⢘⡖⣡⢾⠁⢟⡰⢛⡇⢰⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⣿⠀⠀⠀⢸⡇⢸⠀⠀⢸⡂⠀⠀⣡⣟⢀⠞⡡⢿⠀⣟⡴⣻⡇⣰⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⣟⠀⠀⠀⢸⡇⢸⠀⠀⢸⡃⠀⠀⡱⠿⠀⢟⡴⣿⠀⣏⠔⣹⡇⣴⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢹⡇⠀⣿⠀⠀⠀⢸⡃⢸⠀⠀⢸⠀⡁⠀⠔⣿⠀⣋⡔⣛⠀⣏⢞⣽⠂⣧⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠈⠃⠀⢹⡀⠀⠀⢸⡇⢸⠀⠀⢽⠁⡇⢠⠞⡯⠀⣋⠜⣟⠀⣧⠊⣸⠀⣧⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡁⠀⢸⠄⠀⠀⢸⡇⢸⠀⠀⢴⠄⡇⠠⢞⣟⠀⣥⢊⣿⠀⣧⠎⣹⠀⣧⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⢸⡁⠅⠀⢸⡇⢸⠀⠀⣾⠀⡇⠰⢋⣗⠀⣵⢋⡿⠀⣇⠞⣻⠀⣏⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⢸⡆⠀⠀⢸⡃⢸⠀⠀⢼⠀⡇⠐⢉⡧⠀⣷⠊⡯⠀⡏⣴⣻⠀⣯⠾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⡀⠇⠀⢸⡂⢰⠀⢸⡇⢸⠀⠀⢺⠀⡇⠀⢁⡟⠀⣥⠊⣿⠀⣯⢊⣽⠀⣧⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢸⡁⣤⠀⢸⡁⢸⠀⢸⠧⢸⠀⠀⢼⠤⡇⠘⠫⠿⠰⡿⢞⡿⠼⡿⠋⣿⠛⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⡅⠘⠀⢸⡂⢸⠀⠘⡇⢸⠀⠀⢺⢈⡇⠐⣠⣦⢀⡴⣪⣷⢤⡤⢂⣷⢤⣿⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢸⠅⠠⠀⢸⡂⢸⠀⢈⡆⢸⠀⠀⢼⢼⡇⠀⣡⣤⢠⡷⣠⣤⣠⡤⣠⣤⢠⣤⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⢸⡆⢘⠀⠸⡇⢸⠀⢸⡇⢸⠀⠀⣻⣀⡇⢈⡵⣏⠀⡟⡡⣾⠀⢟⡥⣿⠀⣟⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⠀⠀⡇⢸⠀⢸⡇⢸⠀⠀⣺⡀⡇⠀⠔⣏⠀⣯⢞⣽⠶⣯⣾⣿⠀⡟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢧⡴⠀⠀⣇⡸⠀⠀⣇⡸⠀⠀⢹⣀⡇⠀⢺⣇⣠⢗⡿⣻⣴⣫⢖⣿⣠⢏⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣠⣢⣀⡄⠄⠄⠀⠠⠀⠄⠠⠠⠠⠄⡞⠑⠋⡕⢫⠞⢡⡞⣱⢋⣞⣱⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠤⢖⠤⢒⡠⠔⣠⠄⣠⠴⢀⡠⢀⡠⢆⡠⠀⣀⢄⣠⠄⡠⢀⡠⢀⡠⢀⡠⢀⠄⣠⠄⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠒⠉⠔⠋⠐⠊⠁⠊⠁⠒⠉⠔⠊⠖⠉⠔⠩⠖⠡⠖⠡⠖⠡⠚⠱⠋⠔⠫⠖⠑⠋⠘⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣀⣴⡄⠀⠀⠀⠀⠀⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠀⠀⠀⠀⠿⠿⢿⣿⡟⣸⣿⣿⣿⣏⣚⣛⣛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⢡⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⢢⣿⣧⣬⣭⣭⢩⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢋⣵⢾⣿⣿⣷⢦⣝⢿⣿⣿⢸⣿⣿⣿⣿⡏⣾⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⣿⡐⢦⣝⢟⣵⢗⣽⣆⢻⡟⣴⣶⣶⣶⡶⣸⡿⣣⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣿⣿⢆⣿⣿⣅⢿⣿⣿⢸⡇⣿⣿⣿⣿⢣⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⡱⢟⣵⣦⡙⠇⣹⢏⣾⢱⣿⣿⣿⡏⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣛⠿⠿⠿⠿⢛⣡⣾⣿⢸⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⣴⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠻⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢿⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠂⣀⣠⣴⠶⠟⠋⠁⠀⠈⣷⡀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣤⣤⣤⠤⠶⠞⠛⠙⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣼⠇⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠈⠻⣧⠀⠀⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⢸⡇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢸⡇⠀⠀⠠⣴⠶⣾⣿⣷⠆⠀⠀⠀⠀⠰⣿⣿⠿⠷⠦⠄⠀⠀⠀⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⡇⠀⠀⠀⠀⠲⠛⠋⠁⠀⣴⠆⢀⡀⠀⠀⠙⢶⡄⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⢠⣾⠛⢹⣿⢰⡾⢷⣶⢦⠀⠀⠀⠀⠀⠀⠀⣈⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⣄⠀⠀⠀⠀⣾⠃⢰⡟⢛⣿⠀⢠⡷⢸⣷⡆⠀⠀⠀⠀⣰⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢹⡀⠈⠛⠛⠁⠀⠛⢵⣿⣿⡇⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠗⠈⠻⣦⡀⣸⡇⠀⠀⠀⠀⠀⠀⢈⣫⣿⣧⡴⠟⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⢀⣤⡿⠋⠀⠠⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣠⡾⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣟⣤⡾⣿⣿⠟⠋⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡿⢋⣼⠟⠁⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⡂⣿⡃⠀⠀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⠛⠛⠛⠛⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢸⠀⠀⠀⢐⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠶⣀⢸⣤⠞⠷⠸⠁⡀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠛⡏⠉⠶⠟⢀⠈⠃⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⡇⠀⠀⠀⣸⡇⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠛⢛⣛⣛⣋⣉⡉⠙⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⢰⣿⣛⣭⣭⣭⣽⣿⣿⣼⣧⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠾⠟⠛⣉⠉⣉⣀⣀⣀⣀⣀⣌⣉⣉⣙⣻⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣥⣶⡶⠾⠿⠟⠛⠛⠛⠛⠋⠉⠉⣉⡉⠉⠉⠛⠛⠛⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⡟⠉⠁⠀⢀⡀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡒⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⣁⣀⣤⣿⣶⣶⣾⣿⣿⣿⣿⡿⣻⣿⣿⣽⣿⣻⠏⡹⢻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣿⣥⣌⣿⣿⣿⣿⠋⠟⢿⣿⢧⣽⣿⣾⣦⣾⢿⣿⡋⣍⣓⣈⣿⣏⡽⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣩⠃⣆⣹⣼⠿⣻⠿⢿⣯⡬⠷⡆⣸⣿⢾⣿⡭⡈⡧⣄⡤⠛⢿⣿⣿⣿⣿⣿⣿⣷⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡯⢰⣃⣴⡿⠿⠿⣶⣷⣤⣤⣽⣷⣧⣾⣿⣧⢐⣻⣷⣯⣰⣀⣀⣼⣾⣿⣟⣡⣤⣿⣏⣽⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡿⢿⣿⡧⠀⠀⢀⣠⣤⣍⠉⠉⠉⣉⣹⣿⣶⣶⣶⣿⡿⠿⠿⠟⠛⠻⢏⡟⢹⣟⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⢁⣠⣼⣿⡏⢸⡇⣸⡏⣄⣹⡀⠀⣾⠏⠉⣿⠀⠀⣰⠖⢶⡄⠰⢀⡶⢷⡆⠀⢸⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⣁⣤⣄⢿⡇⠈⢹⡇⠀⣿⠀⠀⣿⠀⠀⣿⠀⢸⣷⠀⢸⡇⢸⣿⣴⣾⣿⣿⠎⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⣉⣉⣩⣭⡟⣾⡇⠀⢸⠀⢰⣿⠀⠀⣿⠀⠀⣿⠀⢸⣿⠀⢸⡇⢸⣿⢿⣧⣤⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⠉⠉⠁⣿⡇⠀⢸⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⢸⣿⠀⢸⡇⢸⣿⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⣿⡇⠀⢸⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⢸⣿⠀⢸⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠹⠂⣿⡇⠀⢸⠀⢸⣿⠰⠆⣿⠀⠀⣿⠀⢸⣿⠀⢸⡇⢸⣿⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⣿⡇⠀⣾⠀⢸⣿⠀⠀⣿⠀⠀⡟⢀⢸⣿⠀⢸⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡟⠀⣿⠀⢸⣿⠀⠀⣿⠀⠀⡧⠘⢸⣿⠀⢸⡧⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢤⡀⠀⣿⡇⠀⣿⠀⢸⣿⠀⠀⣿⠸⢦⡇⠀⢸⣿⠀⣺⡇⢸⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⣿⠀⢸⣿⠀⠀⣿⠀⠘⡇⠀⢸⣿⠀⢸⡇⢸⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡀⠀⠀⢿⣧⣴⠇⠀⠸⣿⢘⢠⡇⠀⠀⣷⠀⢸⣿⠀⠘⢧⡾⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡻⢦⣄⡀⠈⠀⢀⡀⠀⠿⡤⠾⠃⠀⠀⠙⠷⠾⢫⣤⣤⠀⢀⣠⡼⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣤⢸⣯⣴⡝⠳⠿⣿⣳⣶⣦⣭⣥⣀⣀⣀⣀⣀⣠⣤⣤⣤⠴⠶⠖⣛⣫⡵⢾⠋⣿⠁⠀⠀⠀⢠⣶⣶⣤
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⡿⢷⣦⣙⢷⣦⣐⠃⠀⠉⠉⠙⠛⠻⠿⠿⠿⠿⠿⠶⠶⣶⠶⠒⠛⠛⠉⠀⣀⣤⣴⡿⣠⣾⠟⢿⣾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣁⣤⠛⣻⠿⣯⣟⠻⠷⢾⣧⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣻⣀⣤⣤⣶⠶⠿⠛⠋⢿⣿⡟⠛⢛⠹⡛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣙⢿⣏⡰⢋⡤⣒⢿⡻⣷⠀⠦⠀⠉⠉⠉⠉⠙⠛⠛⠛⣻⣿⣭⣭⣭⡅⣰⣾⠿⣿⣦⠈⠙⠻⠿⠿⠷⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣧⡎⣸⣹⠷⣳⡿⠀⠀⣴⡿⣿⢿⣶⠀⠠⠆⣾⣿⣋⠋⠙⣹⣿⠈⠛⠛⠛⠁⠀⠙⠁⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠁⠀⠀⠙⠿⠷⠿⠟⠀⠀⠀⠀⠉⠛⠻⠟⠛⠁
⠀⠠
⠀⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠛⠛⠿⢶⣦⣤⣄⣀⣰⡾⠛⠛⠛⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⣦⣤⣄⣀⡈⠉⠙⠛⠿⠷⣶⣤⣤⣀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠷⣶⣤⣤⣀⣀⠉⠉⠛⠻⠿⢶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⣦⣤⣄⣀⡈⠉⠙⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣷⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠀⠀⢠⡄⠀⠀⣤⡀⠀⢠⣤⠀⠀⣠⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⡆⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡟⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠈⣿⠀⠀⣿⡇⠀⢸⡇⠀⢠⣿⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣷⠀⠀⣿⠀⠀⣿⡇⠀⢸⡇⠀⢸⡿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠈⣿⠀⠀⣿⠀⠀⣿⡇⠀⣼⡇⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⡀⠀⣿⡇⠀⣿⡇⠀⣾⡇⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⠇⠀⣿⠃⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢹⡇⠀⣿⡇⠀⣿⡇⠀⣿⠀⢀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⠀⢻⡇⠀⣿⡇⠀⣿⠀⢸⣿⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠋⠀⠘⠃⠀⠙⠁⠀⠛⠀⠈⠋⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠅
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠐⠈⠦⠄⡀⠦⢔⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠤⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠞⡛⠒⠒⠦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠈⠁⡡⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢀⠚⠃⡀
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠌⠁
⡠⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⠄
⠁⠐⠂⠀⠤⠲⠄⠠⠀⠐⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠄⠢⠀⠠⠂⠠⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢂⠈⠀⠠⠄⠄⠄⠀⠀⠀⠈⠤⠀⠠⠀⠈⠀⠒⡄
⠀⠀⠀⡠⠴⠚⣈⣤⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⡐⠐⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠒⢂⡀⣐
⠀⠀⠠⠤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⡄⠀⠂⠀⢀
⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠰⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠠⠀⠀⠁⢐⡂
⠀⠀⠀⠀⠀⠀⢺⡸⠗⣽⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠁⠀⠐⠀⠈⠀⠀⠀⠀⠅⠐⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣴⣶⣶⣶⣶⣾⣧⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⣿⡥⠴⠒⣒⣶⠖
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠉⠀⠀⠀⠉⠉⠉⣉⣭⡭⠝⠓⠂
⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣀⠼⠤⠄⣀⣀⣀⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣾⠥⠴⠶⠒⠒⠒⣺⣗⠒⠒⠒⢒⡿
⠀⠀⠀⡠⠊⣉⡉⠑⢾⠀⢀⡀⢭⡤⠌⠁⠒⠂⠉⠀⠀⠉⠉⢙⡵⠚⠉⣹⠆
⠀⠀⢸⠁⠈⠉⢉⠀⠠⣄⠀⠹⣄⠏⠓⡶⠤⡤⠤⣤⣤⠤⠀⠀⠀⠀⠉⠓⣄
⠀⠀⠈⠒⠒⠉⠀⠀⠀⠀⠑⢄⠈⠢⣰⠁⢠⠃⠀⣞⡀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⠉⠉⠉⠉⠀⠁⣀⣠⠤⠔⠒⠉⠀⠀⠀⠀⠀⢰⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠧⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡝⢿⣀⡴⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠉⢲⣸⠆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠈⠙⠀⠒⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡵⢾⡄⠀⠀⢣⢈⡂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡄⠀⢸⣄⡀⠀⣯⠬⠍⠉⠉⠉⠉⠭⠭⠭⠥⡀⢀⡜⠋⠳⡀⠳⡜⡄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢸⠀⠀⠀⡆⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠉⢱⠀⠀⡇⡰⠁⡸⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲⣶⠚⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡃⠀⢸⠀⢠⠁⣇⠀⠀⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠹⣤⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⣀⣼⠀⡎⠀⠋⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡺⢿⣄⡏⠙⡳⣤⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠁⠀⡇⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠰⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠰⠶⢶⠷⠇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠲⡇⠀⠀⠀⠀⠀⠑⢢
⠀⠀⠀⠀⣀⣀⣜⠁⠀⠀⠀⠀⡼⠀⠀⢸⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⡇⠀⠀⠀⠀⠀⣴⢶⡆
⠀⠠⣞⠉⠀⠈⣻⣽⣟⣫⠽⠟⠻⢿⣭⣽⣩⣏⣀⣀⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠙⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠇⠀⠀⠀⠀⠀⠀⠒⠚⠃

⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣲⢶⣶⣤⡀⠀⡀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠛⠃⢛⣫⣷⣿⠁
⠀⠀⠀⠀⢼⣀⡀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠀⠀⠘⠛⠛⠿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⡎⠛⠆⠀⠀⠀⠀⢀⠀⢈⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣼⣦⣄⡀⠀⢀⣴⣿⢠⣬⣭⡞
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠿⠇⠀⠘⢿⣿⠸⠟⠋
⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣯⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⢷
⠀⠀⠀⠀⠘⣟⣻⣍⣉⣉⣉⣭⡟⡟⠃⠀⠀⠀⠀⠀⠀⠀⠸⢿⠷⢶⣶⣶⣶⣶⣶⡶⠶⡿⠟
⠀⠀⠀⠀⠀⡏⢹⣿⠿⠿⠿⣿⡋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣄⣸⡀⢸⠀⠀⠀⣆⣀⣧⠇
⠀⠀⠀⠀⠀⡇⢺⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠉⡉⢹⠉⠋⠉⠋⢩⢀
⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢳⠶⡧⢼⠤⡦⠴⠶⠞⠛
⠀⠀⠀⠀⠀⡇⢸⣟⣛⣛⣛⣿⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣤⣧⣠⣀⣇⣠⣤⣷⡇
⠀⠀⠀⠀⠀⣇⠙⠛⠿⠿⠿⠛⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⢦⣤⣤⣤⣾⣟⣛⡉⠉⠻⢿⣶⠟⠋⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠛⣻⡿⠀⠀⠈⠻⠤⡀⢀⡀⠀⠈⣳⠌⠀⣇⠀⠂⣄⣈⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠺⠿⠶⠶⠶⠶⠴⠶⠷⠶⠶⠶⠶⠿⠶⠛⠛⠛⠛⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣲⠖⠒⠠⢤⡤⠤⣤⠤⠤⣤⠤⠀⠠⠤⢤⡤⠤⢤⡄⠖⠒⡶⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠓⢄⢀⡴⠋⠀⠀⠈⣱⠾⣁⠀⠀⠀⡴⠋⠀⠀⠀⠈⢲⠾⣁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⡠⠛⠦⣀⠀⢀⠜⠁⠀⠀⠑⡶⢎⡀⠀⠀⠀⢀⡴⠁⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠿⢄⠀⠀⢈⠗⠥⡀⠀⠀⢠⠞⠀⠀⠈⠓⢤⣤⡊⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠑⣶⡋⠀⠀⠈⠓⣶⣃⠀⠀⠀⠀⢀⠞⠁⠉⠓⠤⣀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡠⠊⠀⠙⢦⡀⢀⠞⠀⠈⠑⠦⣀⡴⠃⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⡸⠻⣄⠀⠀⠀⢀⠞⠙⠢⢄⡀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⠳⣄⣠⠎⠀⠀⠀⠑⢦⣠⠋⠀⠀⠀⠀⠉⠑⢲⠾⢥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⠞⠓⢄⠀⠀⠀⢀⠜⠉⠓⢤⡀⠀⠀⠀⡰⠋⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣅⠀⠀⠀⠑⢦⡔⠁⠀⠀⠀⠀⠈⠓⢤⣞⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠳⣄⣀⡴⠋⠙⠢⣀⠀⠀⠀⢀⡴⠁⠀⠉⣲⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠴⣿⣶⣤⣤⣤⣬⣱⣦⣴⣯⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⡀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡸⠀⠀⠀⡘⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⡆
⠀⠀⠀⢞⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣳⠀⣞⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣳⠀⢰⣃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠆
⠀⠀⠀⢸⢰⠒⠒⠂⠀⠉⠉⠉⠉⢹⠀⡇⠀⢸⢰⠒⠒⠂⠈⠉⠉⠉⠉⢹⠀⡇⠀⠈⡐⠒⠒⠂⠀⠉⠉⠉⠉⠉⡇⢸
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡗⠆⠀⠀⠀⠀⠀⠀⠀⢀⠁⡈
⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢠⠁⢸
⠀⠀⠀⢰⣺⣴⣶⣶⣶⣶⣶⣶⣮⣤⣞⣒⣒⣒⣲⣼⣶⣶⣶⣶⣶⣶⣮⣤⣖⣒⣒⣒⣚⣼⣶⣶⣶⣶⣶⣶⣾⣤⣼⣲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀
⠀⠀⠀⠀⠀⣤⣾⣶⣿⣼⣦⣶⣤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣽⣶⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣿⢹⣿⢹⣿⢻⡏⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢸⡿⢸⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣌⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢰⣧⢸⣧⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⠀⡉⡈⠀⠀⠀⠀⠀⠀⠀⣿⡃⢻⡟⠂⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢸⣿⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠄⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣧⣴⣿⣿⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣮⣿⣿⣳⣷⡿⣿⣯⡆⠀⠀⠀⠀⠀⢸⣿⠿⣴⣤⢿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡟⢹⡿⣿⣿
⠀⠀⠀⠀⠀⡇⣿⣷⣿⣯⣷⣿⠇⡇⠀⠀⠀⠀⠀⢸⣿⣄⣹⣍⣤⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣦⢻⣾⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣁⣻⠁⢹⡟
⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠛⠋⠓⠋⠛⠚⠛⠚⠃⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠁

⣶⣶⡶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠢⠤⣀⡀⠀⣯⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⣈⣉⣀⠇⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢳⠀⠀⢠⠞⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠓⢀⡤⡤⠞⠀⠠⣾⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠺⣁⠀⠀⣏⠀⠱⡀⡤⠦⢼⡀⣤⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣌⠣⡀⠙⡧⠤⠴⢸⡷⠛⠒⠒⠀⠀⠈⠉⣉⠖⠀⠀⠀⡠⠒⠒⠢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡱⡀⠱⢄⠀⣨⠁⠛⠒⠒⠒⡖⠋⠉⠀⠀⠀⠀⡸⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⡓⡃⠀⠀⠈⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⡴⣆⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠦⠀⠠⠀⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠈⢆⢀⡀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⢑⢦⠐⣏⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡇⠙⣄⠘⣶⠉⡟⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠦⣽⢦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⠾⣴⠀⠀⣎⠀⣀⠤⠲⡤⣤⣖⠶⠾⠛⠛⠳⣋⣼⢣⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡑⠚⢤⣼⠵⠍⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡖⠉⡏⣤⣗⣉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠢⠃⠙⠈⢏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣜⡑⣾⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢁⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠏⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣸⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣇⡵⡆⣄⣀⣀⠤⡕
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⣩⣧⡀⣪⢼⠁⠀⠀⡟⣒⠦⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡛⡤⢤⢀⣀⣀⡏⠛⠓⢁⣀⡉⡖⠩⢔⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡺⢶⣾⡁⠀⠐⠉⣋⢰⣧⠠⡀⠈⠑⠪⢑⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃⠉⠉⠉⠉⠉⠐⠛⠓⠉⠀⠀⠀⠀⢙⡤⡉⠲⠒⠈⣉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣁⢤⡴⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡹⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠫⢱⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⣀⢤⠀⠀⠀⠀⠰⡁⢠⣤⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡔⠊⠉⠙⡶⠊⠀⣮⠤⡶⠋⠳⡄⠀⣇⠣⡀⢞⣻⣆⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⢠⠃⢧⡊⠉⠉⠀⢀⠤⠮⠤⣀⠀⢣⣀⠧⠀⢀⠗⢉⣉⣣⠈⠉⠁⢸⠀⠀⢈⠇
⠀⠀⠀⠀⠀⡱⢀⠎⠀⠀⠈⠑⢦⡀⠃⠀⠀⠀⠀⠱⡤⠝⠒⠊⠁⠊⠁⠀⠈⠑⡄⠀⣸⠒⠢⣌⠀⠀⣰⢯⡲
⠀⠀⠀⠀⠘⢅⣼⡠⠤⢄⣀⠀⣀⠧⠤⠤⠄⢀⣀⡀⠀⢀⡿⣳⡠⠄⠀⠀⠀⠀⠈⠉⠉⠁⠀⢸⠎⠉⠁⢺
⠀⠀⠀⣠⠔⠃⠀⣀⠀⠀⠀⠉⠁⠀⠀⢀⣊⠁⠀⠈⠙⢪⣀⣙⣵⠀⠀⠀⠀⠠⡶⠭⠷⡆⡤⠧⠢⠤⢄⣸⣀⡀
⠀⠀⡰⠁⢀⠔⠉⣠⡠⢤⣀⠀⠒⠑⢦⡁⢀⡇⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠰⠓⠒⠲⡁⠀⣀⣄⣀⠀⢁⣀⡽
⠀⠀⠳⠶⠗⠊⠉⠳⣀⡠⠔⠓⠀⠒⠒⠚⠥⢄⣀⠤⠔⠊⠉⠉⠀⠀⠉⠉⠒⠢⠤⠤⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡀⠀⠀⠄⡠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⣠⠀⠄⠘⠀⢰⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣅⢀⣀⠀⠀⠀⠐⠈⠁⠺⠈⠀⠀⠀⠀⠀⢀⠀⠈⠹⠟⡈⠀⠀⠀⢀⣋⡀⠴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠰⠃⠀⠂⢏⡰⠀⠀⠀⠀⠀⡀⣸⡀⠀⠀⠀⠀⠒⠚⡃⠀⠀⠀⢭⢄⡀⠌⠁⠀⡛⠀⠸⠦⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢀⠸⠧⠀⢤⠀⠀⡋⠉⠉⢹⢦⠀⡄⣆⠘⠙⢣⣀⠀⠐⠃⠀⣴⣿⠆⠘⠁⠂⡀⠀⠉⠘⠇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠐⠁⠀⢀⠀⠀⠀⠒⠐⢉⢠⢔⠯⠋⠙⢌⡉⢹⣿⢢⡜⠛⠁⠁⣤⣄⡂⢀⣡⠤⠞⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡰⠀⠤⠷⣀⡀⠀⠀⠐⣤⣸⣾⡥⠃⠀⣈⣀⠀⠰⠭⢷⣶⠷⠶⠻⡄⢏⣁⣠⠗⡶⠇⠤⡀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠩⠁⠀⣀⡄⠀⣯⣣⢠⣎⡿⠃⠀⠀⠀⠿⣾⡶⢨⠖⠒⢚⡟⢿⡳⣶⣤⣸⢤⠜⠁⠀⡇⠀⢐⠢⣄⠑⢶⣤⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡉⣀⠀⠘⣍⠀⢬⠡⠦⢯⠄⠀⠀⠀⠀⢠⣟⣛⠋⢀⣠⣟⡮⢤⣒⣶⡴⠊⠉⠶⣧⠀⣡⠀⠈⠀⠌⢃⠀⠚⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠹⠟⣋⠔⠁⠀⠀⠘⢦⡒⢀⣠⠄⠀⡀⠠⢄⣶⣾⠷⡞⠻⠞⠁⡀⡂⠂⣌⠀⢀⡀⠖⠈⢲⡟⢄⢀⠀⢀⡠⠶⡶⢄⣨⣠
⠀⠀⠀⠀⠀⠀⠀⡔⡒⢾⡀⠀⠀⠀⠀⠀⠈⠗⡆⠻⠈⠆⢻⡳⠃⠀⠀⠀⠀⠲⠾⣤⣿⠓⠀⠛⠂⢀⠰⠊⠀⢾⡦⠈⠈⠳⠋⢀⠀⢀⡄⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣷⣄⢀⠄⠀⠀⠀⠀⢼⣧⣄⠁⢸⠀⡀⠀⠀⡀⡀⠀⠀⢀⣉⠀⠀⠀⠒⢨⢷⡠⢄⡸⠝⠧⠔⠢⡀⠀⠼⡃⠲⢈⣳⡈
⠀⠀⠀⠰⣌⠀⠀⠀⠀⡈⠻⡉⢑⠄⠀⠀⢀⣴⠂⠶⠧⠤⢤⣦⣀⠀⠁⠀⠐⠉⠈⠣⠹⠿⠽⣤⣨⢿⠾⠃⡄⣤⣦⣤⠆⠄⢀⠀⠀⡌⠛⠛⠉⠈
⠀⠀⡀⠀⠈⠓⣤⠆⡴⠴⣶⢷⡄⡀⠖⠖⡿⠟⣀⠀⠀⠀⠀⠐⠏⠃⠀⣀⡄⠀⠒⢠⢠⣴⠴⠤⠀⠀⢀⣱⣉⠉⠀⠀⠀⠀⠀⠀⠉⢿⣌⢂⠆⣴⡀
⠀⠀⠁⠒⠠⠄⠀⠤⠠⡄⠀⢈⣧⠦⡅⠀⣈⣁⢌⣉⡁⣠⣄⣀⣀⣀⣀⣀⣠⠫⠀⢀⡏⠠⠠⡄⠀⠀⠀⠟⡹⠇⠀⠠⠞⠂⠴⠔⠲⣆⣸⣧⣰⣿⠇⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠈⠁⠈⠋⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠒⠒⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠤⣧⠐⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠋⠀⢀⠀⠀⡼⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡸⠁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⢇⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⣷⠂⠀⠀⠀⠘⠠⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡙⢆⠀⠀⠙⢄⣀⡩⠗⠀⠀⠀⠈⠀⠀⠀⢀⡠⠋⠀⠀⠀⠚⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣈⢉⠉⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠈⠉⣇⠀⠀⠀⠀⠀⣴⠒⠉⣁⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠛⠐⠋⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⢀⣠⠽⠊⠣⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠉⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⠏⠀⠀⠀⠀⠘⢄⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⠛⢉⠿⣤⠀⠀⠀⡘⡹⠀⠙⢦⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⡶⠋⠠⠚⠓⢬⣑⡄⠀⠉⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⢲⠾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⠂⣸⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠈⠀⢸⠀⡇⠀⠀⣿⡤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠚⢅⠀⡇⢰⠆⠄⣀⣾⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢠⣮⣳⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠇⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳⡛⢄⡉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠁⠊⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠚⡏⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡇⡘⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠚⣟⢃⣀⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡿⠭⢟⣯⠟⠻⣾⣿⡛⠣⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠷⠞⠋⠁⠀⠀⠀⠉⠛⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠂⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣣⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠶⠉⠉⢳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⡈⠛⢏⢒⣒⣒⣒⣒⣂⣦⣤⣤⣤⣄⣀⣀⣀⡀⡤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡄⡀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⢢
⠀⠀⠀⠀⠀⠀⢀⠊⣰⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠃
⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠈⡀⠀⠀⠀⠀⠀⡀⠠⠄⠀⡠⠔⡆⠀⠀⠀⠀⠀⢞⡔⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠢⢤⡇⠀⠀⠀⢠⠊⠔⠁⠁⠀⠑⠄⠀⠄⢀⠀⠀⢸⡝
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣧⠀⠀⠘⡅⠈⠒⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⢈⣅⠀⠀⠀⠀⠀⠀⠀⡌⠰⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠣⡑⠄⢀⡰⠠⡠⠪⠒⠁⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠐⠀⠠⠀⢔⠀⠠⡊⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣈⣁⠀⠄⠀⠈⠀⠕⡠⢀⠔⠁⡨⠊⢀⠀⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣾⢏⡉⡑⢈⡆⠀⠐⡀⠀⠔⠀⠊⠀⠐⠁⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠐⠀⣁⢴⣇⠀⠀⠈⠐⠁⠊⠀⠀⠀⠂⠀⢿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠋⠀⠈⠙⠉⠛⠛⠙⠛⠛⠛⠛⠝⠗⠂⠚⠂⠀⠠⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢸⠀⠀⡇⡈⣍⣙⠓⢦⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠶⠤⠕⠀⠁⢹⣀⣀⣟⠠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠐⢅⡛⠍⡒⠵⢢⡈⠉⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠈⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠚⠑⠢⠀⠒⠤⢄⣀⠀⠀⠀⠈⠉⠉⠒⠲⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⠉⣉⣁⣒⠩⠄⢐⡂⠤⠀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠀⠠⠤⠤⠤⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⡔⠲⠧⠤⣬⡙⢦⠀⠀⠁⠀⠀⢲⠭⢍⣓⣂⡀⠀⠄⠀⠀⢀⣈⣉⡉⠉⠉⠛⣛⡆
⠀⠀⠀⠀⠀⠀⢸⡇⡔⡩⠒⠿⣿⣿⣶⣯⡙⣼⠀⠀⠀⣠⠒⠉⠀⣀⡀⢹⠁⠉⠉⠑⡖⢒⠲⣒⠒⠀⢨⠋⠁
⠀⠀⠀⠀⠀⠀⢸⢧⡁⣇⠀⠀⢸⠀⠀⣀⠇⣼⠀⠀⠀⡇⠀⠘⠊⡁⢱⣼⠉⡇⠀⢰⡇⠀⠀⠈⣧⢀⠋
⠀⠀⠀⠀⠀⠀⢸⠂⠳⢬⣙⣒⣛⣒⣚⠥⠚⢹⠀⠀⠀⡇⠀⠀⠀⡇⢸⠁⠀⠑⣦⢸⠀⠀⠀⢀⡟⡘
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢠⠃⠀⠀⠀⠇⣸⠀⠀⢠⡟⠞⠀⠀⢠⠎⢰⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢀⠀⡇⠀⠀⡼⠀⠀⠀⢸⡏⠀⡞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡇⠀⠀⡿⠀⠀⠀⢸⢸⠁⠀⢠⡇⠀⠀⢀⢿⠃⢠⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⣼⢸⠀⠀⢸⠁⠀⠀⡎⣼⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢀⠀⢸⠁⠀⠀⡇⠀⠀⠀⡇⣼⢀⢠⡏⠀⠀⡰⠀⡇⠀⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⢸⠀⡼⠀⠀⢠⠃⠀⠀⢰⠃⣇⠐⢸⠀⠀⢠⠇⢸⠁⢸⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⡟⢀⡇⠀⠀⢸⠀⠀⠀⡞⢰⠇⠀⣾⠀⢀⡞⠀⡏⠀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⢸⠁⢸⠃⠀⠀⢸⠀⠀⣸⠁⡞⠀⠀⣧⡴⠋⠀⣸⠃⢰⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⢀⠏⠀⡾⠀⠠⠄⢻⣀⡴⠁⢰⠃⠀⠀⢧⠀⠀⢠⠏⠀⢸
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠤⠌⢷⣋⣀⣠⠇⠈⠁⠀⠸⣅⠀⢀⠏⠀⠀⠀⠈⠳⠖⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⠑⠲⠤⣀⣀⡉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⠤⢖⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣍⣉⡉⠉⠒⠒⠒⠒⢒⣒⣒⣒⣉⣉⣉⣭⠥⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁