Ironing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠺⣿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠛⠀⠠⣵⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢸⣿⣯⠀⠀⠚⢀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡡⡆⢰⠈⢙⠁⠰⡘⣢⣼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⢠⣿⢈⠰⠶⣾⣿⣠⠻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣬⣷⠂⠀⠀⠠⠈⠁⢰⣧⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡯⠁⣤⣤⣄⡀⠉⣠⣾⡫⠺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠠⠀⠀⣠⠤⠀⠁⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⣤⡆⠀⢣⠀⣐⠏⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⢴⠃⡹⡄⠈⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡾⠀⠃⠈⢄⠰⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠀⠀⢆⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⡠⠄⠠⠄⠀⠦⠠⠖⠋⠀⠠⠒⣜⣀⠳⠏⡇⠀⠀⠴⠒⠒⠒⠰⠀⢡⠀⠠⠐⠒⠀⢤⠤⠤⠤⠤⠤⠤⠤
⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠁⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠐⡠⠘⠀⠀⡀⠀⠀⠈
⠁⠤⠤⠤⠤⠤⣤⠤⠤⠤⢤⢆⡠⠴⠦⡄⢀⠤⠄⢀⠤⢄⢀⡀⢀⢠⠤⠴⠦⠤⠶⠦⢖⡥⠈⢠⠈⣤⠤⠤⠶⠒⠒
⠀⠀⠀⠀⠀⠀⡗⠢⢄⡀⠈⠑⡦⣄⡄⡀⠀⠀⢸⡀⠀⢨⠹⡇⠀⠁⠀⠀⠀⣀⠤⠒⠉⢀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⢀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀⢠⠀⠈⠀⡔⠂⣀⠁⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠣⡀⠈⠂⠁⠀⢀⠀⠀⡠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⡀⠀⠀⡀⠊⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠫⡆⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣀⠀⣀⡿⠿⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠐⡅⠀⠀⠙⠈⠀⠊⠀⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠉⢀⠀⠀⠀⠀⠀⡠⠠⠖⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢡⠄⡀⠸⠠⠑⠄⠠⠂⠀⠀⠀⠀⠘⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠺⢅⣁⠀⠉⠁⠀⠁⢈⣄⠀⠀⠀⠀⠀⠀⢀⠥
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⢀⠀⠀⠚⣲⠂⠘⠈⠀⠠⠈⠀⠉⠀⠁⠀⢐⠂⠈⢈⠠⠀⠀⡀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⠀⣀⡀⠀⡺⠟⠁⠀⠀⠀⠀⠒⠓⠓⠁⢰⡖⠀⠛⠁⠉⠢⡀⠀⡀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣯⠅⠈⠁⠀⠐⠢⠀⢀⠀⡐⣀⣀⡴⠐⠁⠘⠆⢦⡀⠘⠀⢀⠄⠂⡈⠁⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠢⠔⠉⡀⣧⣄⡀⠩⡀⠀⠀⠀⡀⡘⠆⠁⢰⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡘⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠵⢬⡄⠛⠄⠉⠆⠁⠊⠈⠐⠁⠘⡄⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡑⢉⠀⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⢫⡀⠄⠂⠀⠈⠑⠢⡂⠈⠁⠂⠀⠘⠛⣧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢋⣿⣿⠿⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣡⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⣈⡛⠀⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠁⠀⠀⠛⠀⡔⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢿⡅⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⡠⠒⠚⠉⢹⠀⢠⠹⣆⠈⠛⣡⢧⣀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢿⡀⢀⡣⣿⣷⣊⣀⠂⠈⡽⢦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠈⠙⡂⠈⠟⠙⠀⠀⠌⠀⠀⠳⡄
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡌⠘⠀⠡⣀⢀⡰⠀⠐⣄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢹⠆⡶⢂⣤⣛⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠈⢻⡏⠁⠀⠙⢄⠀⠀⡀⠀⠀⠀⢀⡰⢷⣤⡶⠯⢿
⠀⠀⠀⠀⠀⠀⠸⡝⣆⠀⠀⠀⠑⢮⡀⠀⠀⢀⡞⠀⠈⠛⡄⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⡀⣧⠈⠒⠦⣀⠀⠀⠈⠢⡀⢁⠀⠀⠀⠀⠈⡄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⣈⠟⠼⣷⡀⠀⠀⠀⠒⢦⣄⡈⠳⠦⠤⠤⣄⠀⠘⣄⠀⠀⠐⡄
⠀⠀⠀⠀⠺⡗⠁⠀⡆⠉⠢⠀⠀⠀⠀⡀⠭⢷⣄⠀⠀⠈⡧⢤⠘⢦⠀⠀⠸⡄
⠀⠀⠀⠀⡜⠀⠀⢰⡇⠀⠀⠁⠀⠀⠀⠻⠸⠤⠭⠴⢶⡮⠿⠀⡇⠀⠳⡀⠀⢳⡀
⠀⠀⠀⣼⠁⠀⠀⠈⢰⠀⠀⠀⠀⠀⢠⠛⠐⠒⠒⠒⠒⠒⠒⠒⠻⣦⠀⠑⠀⠀⢣
⠀⠀⢰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⠸⡄⣄⡀⣷⣄
⡏⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠀⠀⠛⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⠛⠒⠛⠪⢮⠟⠒⠒⠒⠒⢲
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠇


⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣾⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠓⠒⠒⠚⢻⣹⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣁⠀⣀⠌⠈⢻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢜⡒⠋⣤⠖⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢳⠀⢳⠝⡶⠀⠀⢠⣛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠚⠻⣄⠉⠳⡄⢰⠳⡀⢠⠻⠋⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡩⠐⠂⠉⠀⠈⢣⠀⢀⠎⢢⠙⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣲⣖⡁⠀⠀⠀⠀⠀⠀⠀⢱⣬⢴⡀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠠⠤⡔⠒⠂⠒⠒⡿⠭⠅⠸⡏⠉⠫⡉⠉⠀⠀⡴⠁⢹⣇⡠⢼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⢄⠀⠀⠀⠀⠘⠄⡀⠀⠸⠵⠶⠒⠒⠛⠀⣀⣬⢓⡠⠊⠀⠀⢸⣿⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⣌⠢⣄⠀⠀⠀⠀⢉⣒⡤⠴⠖⣚⣛⠉⢤⡶⠋⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢹⡦⣹⢒⣈⠩⠭⠰⢖⠈⠹⡅⢀⣠⣾⣿⣷⣤⡀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠸⡜⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠏⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⡴⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠊⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢎⠴⡁⠀⠈⠉⠉⠉⢹⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠑⣷⠀⠀⠀⠀⠀⣌⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣷⣿⣷⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡄
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣤⡽⣿⣟⠙⠋⠡⣀⠉⠛⠛⣿⣿⣧
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠤⠐⠉⠀⢰⢫⠉⠀⠀⠘⠖⠁⣴⡟⠛⠛⠁
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠅⠀⠀⠀⢀⡰⠀⢸⠘⡀⣆⠀⢦⣴⣾⠋
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠥⣤⡶⠀⠀⠀⣸⠁⠀⠮⠤⣵⠈⡛⠞⢋⢻⡆
⣧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⣀⡀⠀⠐⡶⢀⣽⠃⠀⠀⠀⢹⠎⠙⠇⢘⣾⡇
⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠋⠀⠉⢳⠀⣿⠋⣡⠚⠦⡠⠤⣀⡀⠀⢀⣠⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠓⢻⠲⠀⠀⠘⣾⡁⣠⠇⠀⠀⠀⠀⠀⠈⠉⠁⡾⡸⡇
⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠁⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠰⠾⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠒⠶⢤⣄
⣺⠀⠀⠀⠀⠀⠀⠀⣴⢋⡟⠠⡀⠀⠀⠈⡏⠁⠀⠀⠀⠀⢀⣤⣾⣟⠇⡠⠄⠒⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⣤⣴⠏
⢻⠀⠀⠀⠀⠀⠀⣼⠃⠀⡆⠀⠱⡄⠀⠀⢱⠂⢀⣠⣴⠞⠋⠀⠹⠇⣾⠁⠀⠀⠀⠀⢀⠉⠉⠢⣠⡶⠶⣒⣒⣋⡉⠉⠉⠉⠀⣀⣀⣶⣾⠩⠤⠤⠤⣤⣄⣴⡾
⢸⠀⠀⠀⠀⠀⣼⣿⠀⠀⡇⠀⠀⠙⢦⠀⠀⢣⣄⣀⣸⡀⠀⠀⠀⠓⠮⡽⠟⠛⠛⠛⠉⠇⠀⠀⠈⠻⠷⢶⡶⠶⠶⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⢸⠀⠀⠀⠀⢠⣿⡿⠀⡄⠃⠀⠀⠀⠀⢳⠀⠁⠀⠈⠉⠹⡄⠀⠀⢀⣀⡴⠎⠀⠐⠒⠲⢾⠰⠒⢢⡠⣄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢊
⢸⠀⠀⠀⠀⣼⣿⡇⠀⡇⠰⠀⠀⠀⣀⣈⣹⣶⡆⠄⣆⣀⣽⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⠓⠀⠀⠑⠛⠛⠋⢤⣀⠀⠀⠀⠀⢀⣀⣀⠤⠔⣒⣫⠭⢴⣶⣿⣿
⢸⠀⠀⢀⡀⠿⠿⠷⠒⠋⠘⠀⠉⠁⠀⣀⣴⣿⡟⠻⠏⠙⠿⢃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⣀⣈⣽⡦⠖⣚⣫⠭⠴⠖⠚⠋⠉⠀⠀⠀⠀⠀⠉
⢸⠶⠖⠛⠋⠑⠦⣀⡀⠀⠀⠀⠀⠀⢸⣧⣤⡤⣴⣶⣶⣾⣿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣶⠯⠄⠒⣈⡩⠤⠔⢻⡟⠉
⢸⠀⠀⠀⣀⣀⡀⠀⠈⠓⠲⠤⣀⡀⠻⠿⠿⠧⠾⠿⠿⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⠀⣼⠧⠖⠒⠋⠉⠀⣧⠀⠀⠀⢀
⠘⠀⡠⢊⣿⣿⣿⣿⣿⠶⣄⠀⠀⠉⠙⠒⠠⣀⡀⠀⠀⠀⠀⠀⢀⠄⠀⡿⠁⠘⠁⠀⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠐⠘
⠐⢸⣷⣶⣴⣾⣾⣻⠿⠿⣾⣀⣠⡤⠤⠒⣚⣉⣿⣆⠀⠀⠀⠀⠘⠀⢠⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⣦⣀⣰
⣶⣤⣀⣀⣀⣠⡤⠶⠶⢛⣋⣭⡤⠶⠞⠋⠉⣝⣿⠋⠱⣄⠀⠀⠀⠀⠆⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢩⠀⡟⠒⠶⠦⣤⣄⣀⡀
⢶⣤⣉⣉⣩⣤⣶⠶⠛⠉⠁⠰⡀⠀⠀⢀⡾⢨⠋⠀⠀⠈⣷⠆⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠃⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⠤⣤⣀⡀
⣤⠀⠃⡼⢨⣿⣿⣦⠁⠀⠀⠀⡈⠆⢀⡞⢠⠏⠀⠀⠀⠀⢃⠸⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣸⠋⣸⠁⢸⣿⣿⡇⠑⡐⢄⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢸⣀⡏⣆⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⡆
⣹⠴⢷⢤⣼⣿⣿⣿⣿⣿⣆⠻⣷⡎⢠⠃⠀⠀⠀⠀⠀⢀⣼⡇⠀⠈⠳⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢱
⣩⡴⡐⡄⢸⣿⣿⣿⣿⣿⣿⣣⡍⢠⣿⣶⣶⣶⣶⣶⣶⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣨⠄
⡟⠀⠸⡔⣿⣿⣿⣿⣿⣿⣿⠏⣠⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⠖⠈⠁
⠻⠶⠶⠷⠾⠿⠿⠛⠟⠿⠟⠰⠿⠷⣾⣿⣿⢿⡿⡿⣿⢿⡿⢿⡤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⡤⣤⣤⣬⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣶⣤⣤⣤
⣿⣿⡿⠻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⠓⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠚⠛⠛⠛⠛⠛⠚⠛⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⠟⠛⠻⢿⣿⣿⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣋⠍⠋⢉⡿⠓⠀⠀⢭⠂⣠⡴⠿⠿⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠆⢸⠸⢠⡀⢠⣤⣴⠟⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣥⡴⠀⠀⢀⡏⠀⠸⠤⣇⢙⠒⠛⣛⡇
⡇⠀⠀⠀⠀⠀⠀⢀⣎⣀⡀⣀⡀⠰⣶⣨⠏⠀⠀⠀⠽⠊⠛⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⢸⣹⡏⠀⠀⢹⣠⠏⢀⠎⠑⠐⠒⠤⢀⣀⢴⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠉⣏⠁⠀⠀⣿⣤⡞⠀⠀⠀⠀⠀⠀⢀⡜⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⠀⠀⠀⠀⠀⠀⣠⢾⠟⡄⠀⠀⢸⠟⠃⠀⠀⠀⠀⢀⣠⢾⠈⢉⣉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⠁⠈⠉⠓
⣿⠀⠀⠀⠀⠀⣰⠏⢘⠀⠹⡀⠀⠀⣧⠄⡀⢀⡤⠚⠉⠿⢁⡌⠀⠀⠈⠉⠀⠒⠀⠀⡠⣤⠄⠠⠒⠒⠒⠚⠋⠉⢩⣽⣟⣉⣀⣀⣀⣀⣴
⣿⠀⠀⠀⠀⢰⣿⠀⢰⠀⠀⠘⢆⠀⠘⢄⡉⠘⠃⠀⠀⠀⠦⠑⠖⠖⠂⠒⠁⠀⠀⠈⠓⠶⠤⠤⠭⠿⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙
⣿⠀⠀⠀⢀⣿⡟⢰⠘⠀⠀⠀⠈⢳⠀⠀⠀⠀⠙⠀⠀⠀⠀⠰⠆⠀⠀⠐⠒⠠⠆⢢⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣚
⣿⠀⠀⠀⢸⣿⡇⢸⣀⣃⣀⡀⠠⠤⢿⣶⣐⣰⣤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠈⠐⣤⡀⠀⢀⣀⣠⠤⢔⣒⣩⠭⠒⠾⠿⢿
⢏⣀⣀⣤⣞⠛⠉⠉⠀⠀⠀⠀⢀⡤⠺⠟⠉⠋⣀⣫⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢂⣀⠤⠤⣶⣿⡭⠭⠒⠒⠉⠉
⣿⠉⠁⠀⠀⠉⠒⠤⣄⡀⠀⠀⢸⣿⣿⣛⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⣴⣛⣋⡭⠤⢲⡎⠉⠉⠇
⡿⠀⣠⣶⣶⣶⣦⣤⣄⡈⠁⠒⠠⢍⣉⠉⠉⠁⠀⠀⠀⢀⠀⢰⠂⢀⠂⢸⠋⠁⠀⠀⠀⠀⡇⠀⠀⢐
⡏⣼⣥⣭⣿⣿⣿⣿⣮⡇⣀⣀⣤⠤⠖⣻⣦⠀⠀⠀⠀⠸⠀⡙⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⢳⣀⠀⠃
⣧⣌⣁⣀⣠⡤⠤⠶⣚⣋⣭⠴⠖⠛⢩⣿⡟⠑⢄⠀⠀⠀⠰⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⣿⠋⠁⡗⠲⠦⢤⣄⣀⡀
⡷⢤⣬⣥⣴⣶⠚⠉⠉⠀⢆⠀⠀⢠⠏⡜⠁⠀⠀⡻⡆⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡀⠁⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⣤⣀
⣷⡘⢰⠃⣿⣿⡷⡀⡀⠀⠀⠁⢠⠏⡼⠁⠀⠀⠀⢡⢰⣄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈
⣿⢁⡇⠀⣿⣿⣧⣬⣎⢤⣄⣠⠏⡼⠁⠀⠀⠀⠀⢸⡶⠓⢇⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⡇
⠀⣉⢛⠛⣿⣿⣿⣿⣿⣦⣻⠃⣼⣄⣀⣀⣀⣀⣴⣿⡇⠀⠀⠑⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⢹
⡘⠈⢎⢼⣿⣿⣿⣿⣿⣿⠋⡼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⣤⠘⠋
⠷⠤⠼⠾⠿⠿⠿⠿⠿⠧⠾⠷⣼⡿⢿⣿⠿⣿⣿⡿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⢿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠟⠁⠀⣈⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣰⣶⣗⠃⠀⠰⠃⢀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠀⡇⠙⠻⠋⢠⠰⡄⣀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⠀⢀⣸⡆⠁⢀⣨⣦⣶⢃⠼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⠌⢿⣃⠀⠀⠀⠙⠙⠞⠀⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠿⠋⠀⠀⠀⠀⠤⠂⢰⣿⢏⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠗⡃⠒⠒⠲⠶⠤⠀⡼⠛⠗⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⠉⢀⣠⠴⠒⠁⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠪⣳⢣⠀⠈⡆⠠⡜⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢺⠃⢰⢦⠀⢱⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣾⠀⠇⠀⠣⠀⠇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡀⠀⠰⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠄⣀⠤⠛⠀⠀⠠⣌⣏⠐⢾⣛⠄⠈⠠⠤⠴⠖⠠⠄⡔⠀⡃⠀⠀⠤⠄⠠⢄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠊⠉⠉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠤⣀⠇⠀⠀⠀⠀⠀⠀⠇
⢎⣁⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⡊⠁⣀⣀⡀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⡁⢀⣠⠌⣡⠔⠠⠀⠈⢦⠀⣀⣀⣀⣀⣀
⠀⠈⠉⠉⠉⠉⢹⣉⠍⠉⠉⡯⢕⡣⢀⠀⠁⠒⠊⠀⣁⠊⠀⠱⢰⡆⠀⠒⠉⠉⠉⠉⠉⠉⣉⠭⠋⠀⢰⠁⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠉⠒⠤⡀⢀⡏⠓⠦⡂⢄⠀⠀⢻⠀⠀⠘⠀⣿⠀⠀⠀⠀⠀⠤⠒⠉⠀⣠⠬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢷⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⢠⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⡇⢸⠀⣀⣀⠤⢄⣠⣤⠤⠶⠒⢛⣋⡉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠄⢾⠀⠀⠀⢀⠘⡇⢸⠉⠀⠀⠀⠀⠈⠙⠲⢮⣡⠈⠠⠔⠒⢁⡀⠏⠑⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠖⠒⠈⠉⠀⠀⠀⠀⠈⢲⠀⠠⠞⠀⠀⣈⣁⣂⣄⣀⣀⢀⠀⠀⠀⠈⠙⠓⢦⡄⠀⠀⠀⠀⣀⠨
⠀⠀⠀⠀⠀⢀⣠⠤⠤⠒⠒⠉⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠒⠊⢁⠈⠉⠀⠈⡱⢤⠱⡠⠀⠀⠀⠀⢀⣹⠂⠉⠉
⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⡤⢴⠒⠒⠈⠉
⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠀⠸
⢧⣀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠐⠂⠀⠀⠀⣀⣀⡤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠒⢲⠒⠒⠉⠻⣌⠳⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⢌⠳⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⢄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⣄⣀⣄⡤⠖⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠜⠁⠀⠀⡇⠀⠀⠐⠀⢀⣀⡤⠞⠁⠀⢠⠤⢑⣦⡑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠋⠀⠀⠀⠀⢁⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠈⠐⠠⢌⡙⢦⡙⢦⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡔⠁⠀⠀⠀⠀⠀⠸⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠦⣍⡑⠢⢄⣀
⠀⠀⠀⠈⠢⢈⡑⠢⢄⡀⢀⡜⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣉⡲⢦
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢌⡙⠲⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣉⠒⠤⣄⡀

⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⢧⡏⡌⠑⣢⣀
⠀⠀⠀⢠⣻⠁⠇⠀⠳⣌⠙⡶⣄⡀
⠀⠀⠀⢸⣿⢰⠀⠀⠀⠀⠉⠉⢹⠉⠑⢆
⠀⠀⠀⡈⡇⢸⠀⠀⠀⠀⠀⠀⠸⡀⠀⢈⣖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣄⣀⣀⣀⣀
⠀⠀⠀⡏⡇⢸⠀⢠⠊⠑⠲⡤⣀⠈⡆⡇⢸⣋⣉⣉⣉⣉⣉⣉⣉⣉⠝⠻⡉⠛⢍⡩⠝⠋⡳⠒⢄
⠀⠀⠀⠹⡇⢸⠀⠘⢰⣿⡖⠴⣀⢱⠃⢱⠮⠤⠤⠤⠤⠤⠤⠤⣤⠃⠀⠀⠀⠁⠻⢸⠈⠉⠀⠀⠈⢢
⠀⠀⠀⠀⡇⠈⡀⢀⣸⡏⢸⠀⢸⣿⠀⠸⠒⠒⠒⠒⠒⠒⠒⢲⠁⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⡆⡇⠀⡇⢸⢸⣧⠌⠀⣸⣿⠀⣞⣙⣛⠒⠮⢀⡀⠀⣹⠤⠭⠭⠭⠭⠥⢽⢿⠭⠭⠭⠭⠭⠥⣼
⠀⠀⠀⠙⢷⢀⠃⠘⠾⢛⣛⠋⠽⠹⣀⠧⢀⣀⡈⢉⠲⣍⢢⣹⣤⣭⣭⣤⣤⣥⣽⣿⣤⣤⣤⣬⣭⣥⣼
⠀⠀⠀⠀⢠⡃⠀⠤⠤⠤⠤⠤⠤⠤⠙⣤⠀⢀⣽⣒⠂⢘⡸⢼⠦⠤⠀⠀⠀⠀⢺⣾⠀⠀⠀⠀⠠⠤⢾
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠚⠛⠒⠒⠒⠒⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣠⣶⠕⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠃⠀⢀⠠⠒⠀⠀⠀⠉⠑⢀⠀⠀⠈⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡰⠅⠀⠀⣆⣉⢉⣡⠖⢺⠀⠀⠀⠑⠀⠉⠁⠈⡧⠐⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠐⣀⣀⠠⠇⠀⠀⠀⢰
⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⡈⠈⠁⠒⠐⠁⠴⠒⢂⣀⣤⣤⠀⠀⠀⣀⣠⣤⡤⠤⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⠀⠀⠀⠀⠁⡠⠀⠁⠀⠀⠀⠀⠁⠀⠀⠰⠈⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠫⠁⠂⣀⠠⠀⢀⠀⠈⢆⢀⣀⣀⠰⠒⠐⠉⠒⣄⠀⢀⡀⠀⠀⠠⢤⡀⠀⠀⠀⠀⡥⠤⠀⠀⠠⢆⡮
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠲⡐⠆⠂⠀⠰⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⢹⠀⠀⠀⢀⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡃⡀⠀⡠⢊⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢌⠒⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢁⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⣸⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠡⠓⠄⠃⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀⢀⣴⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢟⠿⣿⣿⡿⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣴⠋⠻⢿⠏⠀⠀⠀⠀⠀⣠⣤⣶⣶⡄⠀⠀⢈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣶⣦⡀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⢻⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣤⣀⣀⡀⠀⠀⠀⣀⣠⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠉⠛⠿⢿⣿⣟⡛⢻⣿⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣴⠟⠛⢳⣄⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢹⣆⠀⠀⣿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢿⡄⢰⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢷⣼⡇⠀⢨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠈⠻⣿⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠈⠛⠿⣧⣄⣀⣤⣤⡶⣦⣶⠛⣫⣿⠋⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⢸⡏⠀⠀⠰⢶⣿⣿⣿⠃⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣿⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣤⣠⣿⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⣿
⢀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣀⣉⣻⣶⣤⣀⣀⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⣿⡀⣀⣀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⣿⣍⣻⣷⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠻⠶⢶⣄
⠘⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣈⡉⠉⠛⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⣿⣯⡙⢿⣿⠶⢶⡶⠟⠛⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠿⣶⡶⢶⣶⡶⣶⡶⠶⠶⠶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠻⣦⡙⢷⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠈⠻⣦⡙⠳⣄⡀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣼⠿⣿⢷⣌⠻⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣡⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣸⡏⠀⢿⡄⠙⢷⣌⠻⣧⡀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢰⡟⠀⠀⠘⣷⠀⠀⠙⢷⣌⠻⣦⡀⠀⢀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢠⡿⠀⠀⠀⠀⢹⡆⠀⠀⠀⢻⣷⣤⣿⠶⣿⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⢀⣿⠁⠀⠀⠀⠀⠈⣿⡀⠀⠀⢸⣧⡾⣧⣠⣼⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠛⠷⢾⣇⣀⣀⡀⠀⠀⠀⢸⣇⠀⣠⡾⢋⣴⣿⣿⠿⣦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⠀⠀⠀⠉⠉⠉⠛⢷⡄⠀⠀⣿⡾⢋⣴⠟⠉⠉⠀⠀⠈⠻⣦⡙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀⠀⢀⣤⣿⣴⣾⣧⣶⣿⣤⣄⣀⣀⣤⣴⠶⣾⣿⣿⣷⣼⣿⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⣈⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⢀⣀⣀⠀⠀⠀⣀⣤⣞⠧⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡴⠎⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⣍⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢒⠏⠂⠀⠀⠀⣀⠤⠀⠀⠒⠒⠒⠤⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠁⠀⠀⡠⠒⠉⠀⠀⡀⠤⠤⠤⡀⠀⢰⠀⠀⠀⠀⢓⡀⠀⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣼⠓⠒⠒⠀⢻⣤⣠⢀⣤⡺⠉⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⡗⠊⠉⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣶⠁⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠠⠤⠤⠤⠀⠐⠒⠀⠁⠀⠀⠀⠀⢸⠀⠆⠀⣀⣀⣀⡇⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⡠⠄⠒⠀⠀⠀⠀⠀⠀⠀⡔⡕⠛⠭⠍⣐⣒⠠⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠈⠉⡀⠤⠶⠒⢻⠭⠀⠈⠭⠭⠍⠬⠽⠛⠛⠙⠓⠳⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠑⠆⠀⠀⠐⠈⠁⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠉⠪⠍⣐⠂⠠⠄⠄⣀⣀⠀⠀⠙⡆⠀⠀⠀⣀⣀⠖⠂⠒⠉⠒⢢⡤⠤⠴⠆⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⢀⢨⡄⡤⠤⠤⠤⠤⠶⢒⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠠⢤⡌⢠⡉⣉⠉⢉⣡⡀⠀⠀⠀⠀⠀⠀⢫⠉⠉⠩⠭⠥⠤⠤⠤⠀⠘⡆⠀⠀⠀⠉⠸⡳⠒⠒⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠣⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣀⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠞⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡴⡣⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈⠳⣄⠀⠀⡠⢋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠓⣌⠢⡞⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡀⢰⠎⡠⠋⠈⠢⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠠⠀⠀⠀⣸⣇⢸⡞⠁⠀⠀⠀⠑⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠄⣣⠟⣤⠬⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣝⡻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢐⣫⡽⢳⣒⣛⡲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢾⣭⣿⣿⠃⢙⠏⠀⢀⣠⠴⠚⢁⡞⠀⢈⠀⠀⡥⠘⣏⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⠋⣟⠛⠛⠃⠀⣶⠞⢠⡖⣿⡇⠀⠀⢈⠗⠁⢸⢸⠁⡏⠢⣜⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠚⢻⢣⡀⠀⠀⠀⠀⢀⡀⣸⠄⡏⡇⡟⡇⠀⠀⠘⢦⡀⠘⡌⢰⠀⢀⠞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠈⢦⠈⡆⠳⡀⢀⣀⠀⢈⠏⠀⢀⢃⠇⡇⡇⠀⠀⠀⠀⠑⣄⢺⡟⣠⠋⡏⠉⠙⡆⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠞⢇⢸⠀⣽⣡⠀⠉⠋⠀⠀⢸⢸⠀⡇⡇⠀⠀⠀⠀⠀⢈⣋⠰⠃⠀⢇⠀⠀⠃⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣴⠛⠉⢉⡟⢧⡄⠘⡀⡿⣿⢟⣀⣀⣀⣀⣀⡎⢸⢰⡇⣧⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠀⠉⠁⠀⣜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢠⠏⣰⠆⠹⠄⡇⠇⢸⠈⣿⣿⣿⣿⣿⡇⢸⢸⡇⢻⠀⠀⠀⠀⠀⠠⣼⡄⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⡎⢀⡟⠀⢠⡄⣁⡇⡸⢰⠊⢿⣿⣿⣿⡇⣼⠀⡇⢸⠒⠒⠂⠀⠀⠀⣸⡇⠀⠀⠀⠐⠒⢒⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡞⠀⣸⠀⠀⣸⢹⠁⣇⡇⠈⢀⣀⡙⠻⣿⣇⣿⠀⡇⢸⠀⠀⠀⠀⠀⠈⡻⡏⠀⠀⠀⠀⠀⢸⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡀⡏⢀⡴⠃⢸⢀⣿⠓⠚⣩⡥⠴⠖⠀⠉⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢧⡷⠋⠀⢀⣼⣾⣿⣷⣦⣀⠀⠀⡇⠀⠀⠀⠀⢈⠟⠦⢀⣀⣀⣀⡴⣷⡞⠋⠲⢄⣀⣀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡶⠦⣞⣁⡀⢀⣾⣿⣿⣿⣿⣿⢿⣷⣦⣅⣀⡀⠀⢠⠏⠀⢠⢎⠝⠛⠛⠭⢭⣭⣅⣀⠀⠀⢀⡤⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⡜⠀⢀⡜⡩⠋⠉⠉⣁⡛⠃⢈⣙⣿⣿⠿⠟⠛⠛⠲⠤⠿⠼⠒⢲⡀⢤⡤⠤⠝⣋⣳⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣜⠀⢀⡾⣰⣇⡉⢁⣺⣿⣗⣯⢻⣿⠇⣍⠒⠦⣄⡤⠴⠒⠋⠀⠀⠀⠉⠐⠱⣀⣦⡯⠷⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡹⣉⡶⠋⠉⠹⠻⣽⠿⠄⡤⠴⠚⠉⠀⣳⡄⠀⠀⠀⠀⢀⣀⣠⠼⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠷⠶⢦⣤⣄⣄⣠⣤⡶⠟⠉⠓⠒⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣦⣶⣶⣦
⣿⣿⣍⣮⣫⣤⣍⣹⣽⣼⣏⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠟⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠁⠀⠀⠀⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠍⠀⠀⣫⣭⡀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠈⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⢠⣀⢠⠀⠀⠀⢀⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠁⠀⠀⠀⢀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠁⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠞⡼⣿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢠⣿⣿⠋⠀⠀⠀⠀⣸⣤⠿⣆⠀⠀⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣶⣿⡟⠙⡆⠀⠀⠀⢴⠇⢸⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠋⢚⠃⡀⢙⡦⠒⢡⡞⠀⡇⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⢻⡟⠛⠛⠛⠛⠃⠠⡇⠀⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠱⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠈⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⡀⠀⠁⠀⢠⡀⠀⠆⠀⠈⠄⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⠄⣀⠤⢀⡀⠤⠐⣢⢄⡸⠯⢄⣐⣄⣠⠤⢄⠀⢠⠀⠙⢶⡞⠸⠇⣸⣇⣧⠀⠐⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣥⣽⣆⣛⢱⣶⣛⣡⣶⣏⣉⣶⠚⠓⢻⣤⢤⡽⣷⣾⢃⡘⠂⢀⡠⠀⣲⡾⠓⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠀⠉⠋⠀⠹⠿⠟⠙⠟⠛⠀⠙⠳⠝⠏⠩⠇⠙⠛⡁⠉⢉⡀⠌⠤⠎⠉⠉⠀⠈⠓⢦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⡀⠀⠀⠀⠂⠐⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠤⢴⡶⣶⠟⠐⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠋⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣿⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⢿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⡗⡲⠿⠟⠉⠉⠉⠙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⣀⡀⠀⢀⣄⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⡿⠀⢫⣥⠦⠀⠈⠋⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠶⠀⠀⠀⠐⠢⠴⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠈⠒⠲⠦⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⢳⡀⠀⠀⠀⣿⠛⠢⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠹⠀⠀⠙⢄⠀⠀⠇⠀⢴⣼⡛⠛⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⣧⣤⣤⣤⠀⠰⡂⠄⢀⡾⠀⠁⠀⢰⠀⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠘⠋⠉⠉⠀⠈⠐⢌⣠⠋⠀⠀⠀⠀⢸⢀⡼⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢌⡄⠀⠀⠀⠀⢸⢸⠇⠀⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡜⠈⠀⠀⠀⠀⢀⣠⠂⠤⢀⣣⠀⠀⠀⠀⠘⣸⠀⢀⣰⢛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⢠⣾⣿⠇⠀⠔⢋⣁⠀⠩⠖⠀⠈⠉⠂⣤⠀⣰⡿⡶⢛⣁⡁⠉⢣⡀⢂
⠀⠀⠀⠀⠀⠀⠀⣶⠾⠭⠤⠄⣠⡟⠉⠻⣶⡤⢀⣀⣘⣆⣀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠙⢶⣭⣥⣤⡄⠁⢸
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⣀⡿⠁⠀⢶⠋⠁⢀⣼⣿⣿⣿⣿⣿⣶⣦⣟⣿⣿⡃⣠⢀⡀⠿⠿⠿⠛⠛⠛⡄
⠀⠀⠀⠀⠘⢇⣬⠴⠊⠁⠀⠀⠀⠀⠀⣬⡲⡾⣻⣿⣿⣿⣿⣿⣿⡟⠉⠭⠥⠤⠭⠝⣻⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⡤⠖⠋⠁⢈⡉⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⡤⠞⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠂⠒⠒⠛⠉⠁⠀⠀⠀⢀⠎⠛⠢⠤⠀⢐⢒⠀⠀⠸⣀⡀⠀⠀⣀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢠⣤⢾⣿⣶⡟⣻⣟⠛⢟⢫⣠⡉⢭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣵⠿⡿⣹⢁⡿⠃⢸⠈⣮⣿⢷⢸⣇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡠⠚⠣⠶⠄⣧⢈⡇⣦⠄⠀⠐⠛⠘⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⣼⡄⠀⠈⠁⠀⢸⢸⠇⣍⡀⠘⠛⠛⠛⠻⠿⠿⠿⠿⠶⠒⢁⡀⠀⣠⠞⣷⡐⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣓⠀⠀⠀⠀⣿⣿⢰⣿⡙⠛⠛⠲⠶⠶⠶⠦⠤⠶⠶⠖⠛⠁⠀⣧⣤⣤⡷⠶⢶⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣿⣧⣭⠄⠀⠀⢸⣿⣇⣾⣃⡄⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⣁⣀⣀⡇⠀⠀⡇⠀⢸⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⢀⡾⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠳⠶⠞⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠙⠿⠏⢁⠀⠀⠀⠀⠀⠙⠓⠶⠤⠤⢤⠤⠤⠴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠐⠒⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠴⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣠⡶⠚⠒⢤⡀⣀⡞⠉⠉⠉⠐⠚⠃⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⡴⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡃⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣧⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠶⢤⡾⠥⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⢀⣤⠤⠶⠚⠛⠛⠷⣤⡀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠎⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠰⠀⠀⠀⠀⠄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠶⢾⣇⠀⡠⠖⠉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠀⠀⢀⠀⠀⠀⠈⠂⡠⠊⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡤⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣤⣀⣀⡀⠀⣈⣀⡀⠤⠒⠉⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⢢⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢸⣀⠀⠀⢠⠀⠀⠀⠀⢀⢀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠁⠀⡠⠔⠊⢀⣠⡶⠛⠉⣷⠀⠀⠀⠀⡾⠋⠒⢤⡀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠉⠙⠛⠚⠒⠳⠶⠓⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠤⠔⠊⠁⢀⣤⡶⠛⠁⠀⠀⠀⣿⠀⠀⠀⠈⢳⣾⠃⠀⠈⠢⣼⡿
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠰⠏⠉⢳⣼⡃⢀⠟⠁
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠁⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠈
⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⡟⠂⠤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠤⠤⠄⠒⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠋⠉
⠀⠀⢷⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣶⣶⣤⣶⣾⣥⡄⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣿⣿⠏⠛⢿⣿⣿⣿⡿⣻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣾⠐⠃⠈⠉⠙⠻⠷⠛⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠉⣁⣀⡞⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⡴⢋⣩⡭⠶⠞⠋⠉⠹⡄⠀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⣉⠉⠛⠦⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⣁⣤⣶⡶⠞⠠⠄⣳⡼⢩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⢟⣻⠉⠀⠀⠀⠘⠻⠟⠇⠀⠀⣠⣌⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠉⣉⡩⡤⣶⣾⣏⢯⣗⣏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡿⠳⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⢸⣟⣽⣷⢺⡛⢏⡀⢺⡜⡞⡾⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⡛⡄⠀⠀⠀⠀⣀⣀⡀⠂⠼⢇⡾⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠆⢉⡼⡽⣌⣛⠻⢿⣾⣿⣼⣽⣷⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠙⣶⣯⣽⢣⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠁⢣⢻⡫⢈⡟⠋⢀⣻⣧⢣⢿⢧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⠀⠀⠀⠙⢦⣀⠀⠀⠉⣱⠋⣄⡠⠔⠢⡄⠀⠀⠀⠀⠀⠀⡏⠀⢃⡈⣇⢿⣿⣿⣷⢶⣿⣿⣏⣏⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⢧⡀⠀⠀⠀⠀⠈⢻⡗⢚⣱⣶⣆⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⡜⡜⣿⣿⣻⣹⣷⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⢠⡇⠀⠀⠙⠢⣄⠀⠀⠀⢸⣈⢢⠙⠌⠛⣆⠀⠈⠣⠤⠤⠀⠀⠀⠀⠀⢳⠀⠰⠃⢹⡿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠔⠋⠁⠀⢹⡄⣀⣴⡾⣟⢯⣢⡀⠀⠀⠀⠈⠀⢠⣞⣹⣛⡟⠛⠓⠒⠒⢲⡆⠀⠀⢀⡜⠀⠀⠀⠀⣼⠁⠀⢠⠃
⠀⠀⠀⢀⡈⢀⣴⣤⣤⡾⠛⢿⣳⣝⢮⢳⡽⣷⠀⠀⠀⣠⡶⢰⠶⣩⣭⠩⠭⠭⣭⠭⡏⠃⠀⣴⡏⠀⠀⠀⠀⢰⠇⠀⠀⡞
⢀⠔⢋⣡⣶⣿⣿⣿⣿⠃⠀⠀⠛⠻⢿⠳⣽⣎⠀⣠⣾⡋⢀⠴⢊⠴⢳⣶⣶⣶⡆⠀⣷⠀⠘⣹⡇⠀⠀⠀⢀⡏⠀⠀⠀⡇
⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⡟⢯⣤⣾⡻⠁⠔⣁⠴⠥⠤⢌⣽⣭⡛⡇⢠⣿⢠⡀⣹⣿⠀⠀⢀⡞⠀⠀⠀⢸
⠙⢆⠸⡔⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⠻⣿⣵⠠⡏⣁⠔⠊⣡⠤⠖⣯⣶⡇⢸⢻⠈⣷⣿⣿⠇⢀⠞⠀⠀⠀⠀⡌
⠀⠀⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢟⢿⣧⡉⠀⢰⣫⠔⠒⠀⠲⣧⣀⢸⣬⠀⠘⣿⠊⣱⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢧⣀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣮⣳⣵⠀⠀⠰⡎⠑⠒⠒⠒⠒⠚⠁⢀⣼⡿⣰⠃⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⠱⣼⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⡀⢉⡵⠋⠀⢀⡴⠃⠀⢀⣴⣿⡡⢊⣴⣿⠋⠀⠃⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢻⣿⠟⢉⡤⠖⠋⠉⠻⣿⣿⣿⡿⠁⠀⠀⢠⠎⠀⢀⠴⣫⡾⠋⣰⠟⠁⠘⢆⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠐⡏⣠⢖⠉⠀⠀⠀⠀⠀⣻⠟⠋⠀⠀⠀⢠⣿⣿⠟⢁⡴⠋⠀⢠⡏⠀⠀⠀⠀⠑⢤⡀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠘⠓⠚⢇⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡰⠛⠛⠁⠀⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣭⣭⣭⣭⣭⣭⣭⣉⣛⣛⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣧⡴⢾⣿⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣬⣭⣍⣽⠃⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣦⡹⣿⣿⣿⣿⣿⣿⡷⠟⠁⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡘⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢆⣿⣿⣿⣿⣿⣿⣧⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⢠⣴⣿⣿⡿⣣⣾⣿⣿⣀⣀⣀⣸⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠂⠉⠻⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡛⢠⣤⣿⣿⣟⣛⣛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡼⣧
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠿⠛⠛⠋⠉⠉⠁⠁⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡇⢻⡆
⠀⠀⢀⣠⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠶⠶⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⡇
⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠈⠛⠛⠒⠲⠶⠯⠭⠭⣭⡭⢝⣛⣛⣛⣛⣛⣛⣛⣒⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⢶⣾⣶⠚⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣀⣀⡀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣿⡿⢿⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠞⠛⠉⠁⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣉⣉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠋⠉⠉⠁⠀⠉⠉⠉⠉⠉⠛⠛⠻⠶⢶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠾⠛⠁
⠀⠀⠀⣰⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⢻⣿⣿⣿⣿⠏
⠀⠀⠙⠀⢉⡿⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣜⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠆⠿⠛⠉⠀⢷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⠀⡀⠀⠀⠀⢀⡈⢧⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⡦⢴⠀⠀⠀⠁⠀⢸⡁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⣷⣄⠀⠀⠀⣄⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠛⠹⠃⢀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠶⢃⣴⠛⡢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠀⢠⣶⡇⢀⡴⢿⣋⣱⣟⡺⡊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢠⣿⣿⠞⣉⣐⣸⣿⣿⣯⣾⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⣀⣿⡿⡟⣯⣽⠟⢻⡆
⠀⠀⠀⠀⠀⣰⠓⢛⠛⠓⣬⡿⣈⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣾⣫⡘⢣⣿⠆
⠀⠀⠀⠀⣀⠇⠄⠨⣄⣹⣭⢼⣿⢿⣖⢲⣤⠀⢤⣤⣄⣤⣀⣀⣤⡀⠀⠀⠀⠀⠀⣠⣿⡿⣉⡼⠿⣿⢿⣿
⠚⠷⠶⣿⣋⣿⣭⣽⣿⣻⣏⡀⠡⢴⠤⠶⣿⢟⣻⣾⣿⣿⣿⣿⣿⣷⣄⣀⣀⣤⣴⣿⣾⣟⣩⣗⠾⣵⢟⡃
⠀⠀⠀⠀⠈⠉⠙⠉⠉⠙⠛⠛⠓⣲⣂⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⢿⣿⢿⣿⣽⡿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣴⡿⠛⠁⢽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠿⢿⣿⣿⣿⣟⢿⣿⣷⠏⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠰⢶⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣾⡾⡇

⠀⠀⠀⠀⠀⠀⣠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⢀⣰⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠿⣿⣿
⠀⠀⠀⣠⡜⠟⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠈⠀⣀⢸⣿
⠀⢀⣼⢜⣁⠀⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣠⡉⠉⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠳⠂⠘
⠀⠸⠄⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢀⡄
⠀⠀⠀⠄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠐⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠳⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠓⠲⢄⠀⠀⠀⠀⠀⠀⠠⠶⣶⣄
⠀⠀⠀⠀⢀⣤⣠⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠚⠀⠀⠀⡄⠀⠀⠀⠀⠘⣻⣇
⠀⠀⠂⠀⢸⣽⠈⠳⠎⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣷⠀⠀⠐⠀⠀⢹⣿
⠀⠀⠉⣱⡦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠀⡀
⠀⠀⣭⡿⠏⠀⠀⣰⠀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⠃
⠀⠀⠉⠉⠆⠀⠐⠋⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣤⣦⡀
⠀⠀⠀⢠⡆⣿⠦⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⡇
⠀⠀⢠⣞⢷⡁⠀⠀⢰⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⡙⠆⠹⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡄⢸⣿⡇
⠀⣀⠻⠛⠈⠁⣤⣿⣪⠉⠄⢢⠀⠀⠀⠀⠀⠀⠾⡏⠉⣈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢀⡟⠁
⠀⣿⠰⠶⠛⢫⣿⣳⣿⡆⠀⢰⠀⠀⠀⠀⠀⠛⠀⠙⢺⠻⠁⠀⠀⠀⠀⠀⢤⢰⣶⣖⣒⣻⣿⡄⠄
⠀⡿⠀⠀⠤⢿⣿⠩⠙⣿⠁⠀⠀⠀⠀⠀⠻⠆⢲⣶⣿⠀⠀⠀⠀⠀⠀⠀⡼⠟⣿⣿⠟⣿⣾⣿⢇⢄⡀
⠀⠁⠀⠛⠛⠋⠙⠛⠐⠛⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠛⠛⠛⠛⠁⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣲⣥⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣶⣴⣿⠟⠛⣉⣼⣿⣿⣷⣶⣿⣿⣿⡟⢳⣄
⠀⠀⠀⠀⠀⢀⣤⣸⣷⣿⠿⠋⢀⣤⣾⢋⡟⢿⣿⣿⡏⢻⣿⣿⣏⡸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⣠⣿⣿⡟⠯⠟⠀⠉⠉⠁⢩⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠁⠀⠀⠀⠞⠓⠒⣒⡒⠼⠛
⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠰⣿⣿⣿⣿⢠⠶⠶⣤⡀⠀⠈⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠞⢻⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⢿⣿⣯⠁⢀⣠⣤⡀⠁⠀⠐⠛⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠒⠤⣀⣀⣤⡤⠤⠬⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠆⢿⡿⠇⠀⠈⠉⠛⠁⠈⠀⡀⢾⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣦⠁⠀⠀⠀⠀⠀⠀⠐⠀⢠⠄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡁⠀⠀⠀⠆⡤⠤⠶⠤⣤⡠⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠘⢷⣦⣴⡟⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⣰⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⠲⠴⢾⡛⣦⣀⡤⠊⠁⢄⠈⠳⠴⢦⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⣁⡈⠙⢶⣦⣀⠀⢻⡄⠀⠀⣩⠇⠁⠀⠈⣹⠖⠒⠒⠂⠀⠈⠃⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣏⠛⢷⣶⣿⣿⣿⣦⣷⡆⣰⡏⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣦⠀⠀⠀⠀⢺⡇⠂⠀⠀⠀⠙⠭⡻⣿⣿⣿⣿⣿⡏⠀⠀⡆⣼⣿⡀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣿⣷⡄⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠙⢮⣽⣿⣿⣿⣷⣤⣤⣇⣿⡟⠛⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⣿⣿⣿⣷⣶⡤⠠⠀⠀⠀⣀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣄⡙⠋
⠀⠀⠀⠀⠀⠀⢀⡔⠻⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⢠⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⢷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠳⡄⠀⠀⢿⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡹⢦⣤⠴⠞⠛⠙⡆⠀⢻⣽⣿⣿⣿⣿⣿⠀⢠⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢰⣧⣤⠤⠶⠶⢒⣠⣄⠀⡀⢿⣻⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⡬⠾⡄⠀⠀⣴⡾⠟⢋⣥⣾⣛⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢨⠀⠀⠀⠐⠠⠀⣀⣴⡟⠁⠈⠻⣷⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠋⠒⠠⡀⠀⣠⣬⣽⡆⠀⠀⠀⠈⠻⢟⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠉⣶⣿⠍⠉⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⡟⠂⣾⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠁⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠁⢀⣿⠟⢡⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⡎⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⠀⠸⠋⣴⠟⣋⣴⣿⣿⣿⣿⣿⠟⣿⣷⣤⣄⣀⣀
⢰⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⣋⣀⣴⠟⠙⣦⣽⡋⠙⢷
⡌⠀⠀⠀⠀⣾⣃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣟⣛⣉⣩⡤⠖⠛⠁⠈⠉⠀⠀⢹⡇⠀⠐⢾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣶⣶⣶⣾⡷⠀⠀⠘⠁⠀⠀⠘
⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠛⠻⠿⣷⣦⣍⡉⠉⠉⠉
⣈⣉⣙⣛⣓⣶⣶⣶⣶⣶⣶⣿⣿⣟⣛⣛⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡴⡵⠒⠪⡳⣄
⠀⠀⠀⠀⠀⠀⡜⡜⠀⠀⠀⢸⠞⠲⡄
⠀⠀⠀⠀⠀⡼⡼⠀⠀⠀⠀⠈⢧⠀⢱⣀
⠀⠀⠀⠀⢰⢳⠃⠀⠀⠀⡴⠚⠉⠣⠴⠃⠉⠙⠒⠦⢄⣀
⠀⠀⠀⢀⣏⡇⠀⠀⠀⢸⠁⠀⢰⠒⣤⣄⡀⠀⠀⠀⠀⠈⠙⠒⢼⠉⢱
⠀⠀⠀⡸⡼⠀⠀⠀⠀⡏⠀⠀⡏⢀⡇⠀⠈⠙⠲⠤⣄⡀⠀⠀⠸⠤⠼⠢⡀
⠀⠀⠀⠉⠁⠀⠀⠀⢰⠁⠀⢀⡇⠘⢇⡀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⡀⠀⠀⢉⡟⢩⠛⠻⢷⢦⡀⠀⠘⡆⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠑⠦⣄⣈⢧⣈⠑⠒⠒⠁⡷⠤⣀⣹⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣒⠚⠁⠀⠀⠹⡆⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡞⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠴⠃⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠈⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠉⠉⠓⠲⠤⠤⣄⣀⣀⠀⠀⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⢤⣀⣀⣀⣀⣀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠙⠛⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡄⢐⡀⠈⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠒⠁⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠓⠀⠀⠂⣸⣿⡖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄⠀⢀⣠⢿⣿⣧⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣲⣿⡟⠻⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠚⠈⢿⣿⣾⣿⣿⣿⣿⣿⡇⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⢄⡀⠀⠠⠀⠠⢀⠀⣠⣾⣿⣿⣿⣿⠁⢀⣴
⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠈⠃⠰⣖⠂⡚⠲⢿⣿⣿⣿⡿⠃⣰⣿⣿⣧
⠀⠀⠀⠀⡠⠒⠒⠁⠀⠀⠀⣀⣔⣺⣄⠀⠑⠹⠀⢦⣝⠿⢋⡀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠛⠁⠉⠳⢦⣀⣀⢠⡄⡻⣰⡤⠾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢩⡉⠙⠻⢅⠀⠀⡈⠛⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠙⢦⠀⠀⠁⠊⠀⠀⠀⠙⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠶⠚⣿⣟⠛⠛⠲⢤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡞⠁⢀⣼⡿⠉⠻⢦⣄⡀⠈⢷⡀⠀⠀⢸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡉⠉⠁
⠀⠀⢠⡟⠀⣠⢞⡿⠃⠀⣰⠋⠉⠛⡿⢷⣷⣄⡀⠀⠀⠀⢸⡷⢦⡄⠀⠀⢀⡤⠖⠒⠚⠁
⠀⣀⣸⡁⣾⡵⢻⠀⣠⠄⢹⡀⠚⠁⡰⠀⣿⢧⢻⠀⠀⠀⠺⠇⢠⣿⠀⠀⠀⠉⠙⠒⢢
⡜⢩⢭⡻⣿⠴⠚⢃⡀⠀⡠⢩⡒⠚⠁⢀⣿⡋⣸⠀⡐⠉⠦⠠⡄⠈⠀⠒⠛⠉⠉⠉⠁
⡇⣷⠆⣷⣿⣇⠀⠀⠀⠀⣄⠈⢀⠞⠀⣼⠃⠉⠁⠀⣇⡀⢀⢚⡇⠐⡼
⢷⠙⠛⠋⣼⣙⣦⣀⠀⠀⠈⠉⠁⣠⣾⠃⠰⣒⠦⠤⢤⡍⢉⣍⠀⠀⢀⣠⣿⣄
⠈⣑⡾⠟⠉⠁⢀⠉⠳⡖⠒⠒⠋⠉⢫⡙⢦⣸⠆⢸⣿⠂⠈⣯⠳⡴⠟⠓⠒⠺⢧⣴⣶⣶⡄
⢚⣿⠦⣤⣠⡞⣯⠀⠀⠘⣆⣀⣀⣠⠤⠽⢺⡉⠀⢸⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠈⠉⣯⠇⡷
⢾⡁⠀⠀⠙⠦⣼⡤⡄⠀⠀⠀⠀⠀⠀⠀⣸⠧⣀⣼⣀⡤⢾⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⡞⠋⢙⣿⣿⠂
⠀⠉⠙⠓⣒⣦⢄⣀⡟⠀⠀⠀⠀⣀⣤⠾⠋⠀⣾⣍⣀⣀⣀⣀⣉⣉⣉⣛⣛⣛⣛⣛⣛⣵⣾⣿⣿⡿
⠀⠀⢠⣾⣿⠉⠉⠋⠀⠀⠈⠁⠙⣿⣿⣦⠀⠀⢻⠀⠠⣶⡄⠀⢴⣦⠀⠠⣶⡆⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⢀⣼⣻⣿⣿⡆⠀⢸⡆⠀⣬⠤⠤⠤⠴⠶⠶⠶⠶⣦⠀⢹⣿⣿⣿⣿⡇
⠀⢰⢿⣿⣿⣷⣷⣦⣤⢤⣖⣻⣾⣿⣿⣿⣧⠀⠘⡇⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⡅⠈⠙⣿⡏⠉⠉⣿⠀⠀⠀⠀⠀⣿⠀⠈⠛⠛⠒⠒⠶⠶⠶⠾⠧⠀⢸⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢳⣀⣸⠇⢹⣆⣴⡃⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡿⠁
⠀⠀⠀⠀⠀⠀⠐⠿⠛⠳⠌⠛⠉⠛⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡒⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣠⠀⠀⠀⠀⠀⠀⢠⢞⣻⣿⣻⣧⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢸⠀⠀⠀⠀⠀⠀⠻⡟⢉⠀⡉⠟⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⣖⢰⡋⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡰⠹⡀⠈⠢⡀⠀⢀⣀⠀⣈⢀⢂⡀⣠⠔⠂⠂⠒⠒⠈⠉⠁⣀⠤⠋⢸⠀⢠⠀⢸⠀⠀⠀⠐⣲⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠉⠀⣀⡤⠖⠃⠀⠋⠶⠶⣤⣖⠒⠛⠛⠉⠁⠀⠀⠀⡖⠠⠋⡆⢸⠀⠀⠀⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⣀⠀⠈⠉⠉⣽⣅⣠⠴⢄⡀⠀⠀⢦⡀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠈⠂⠀⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⢀⡌⠀⡛⠁⠤⠀⠑⡆⠀⢨⠑⠦⣀⠀⠉⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⢹⡆⠤⠀⣀⡿⠀⣸⠀⠀⠈⠑⠲⠶⠴⠏⠸⠞⠲⢞⣛⡛⠛⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠋⢀⠠⠂⠀⢘⠂⢀⣅⡀⣀⣴⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡄⠒⠁⠀⠀⠀⠸⠀⠀⠀⠁⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠢⠀⠀⠀⣇⠀⠀⠀⠙⠀⠀⢁⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡈⠀⠀⠡⡀⠀⠈⠒⠒⠂⠀⠠⡀⢈⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⡀
⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠑⠤⠄⠀⣀⠀⠀⠀⣸⡟⠧⣄⠀⠀⠀⢠⢡⣾⣿⣷⡌⡆
⠀⠀⠀⠀⠐⠃⠉⠀⠀⠀⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠀⠘⠀⠀⠀⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠉⠀⠀⠀⠈⢄⠻⠿⠿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣟⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⣄⣀⣀⣉⣁⣁⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣫⡅⠀⠀⠐⣟⠁⠀⠈⠛⠀⠀⢠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠀⠸⢤⣤⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠂⠀⠀⢶⡄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡽⠛⡋⠀⠀⠀⠀⣶⣧⡀⠀⠀⠀⠀⠀⠀⣰⠅⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠈⠓⠀⠀⠠⠤⠏⠀⠀⠀⠀⠀⠄⠀⠄⢀⠀⠁⠀⠀⠸⠥⠜⠁⠀⠀⠀⠀⠂⢿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢈⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠉⠿⣿⣿⣟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢢⡄⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠑⠀⠀⠀⠀⠀⢀⢺⣿⣿⠟⠀⣀⠠⠀⠀⠀⢈⣠⡄⠈⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⣤⣴⣷⡀⠀⠀⢀⣾⡟⠁⠀⠀⣤⣾⣷⡄
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⠘⠻⠿⣿⣷⠖⠀⣼⣿⡇⢠⣠⣶⡿⠛⠛⠠
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⣷⣷⣟⢋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀⠂
⠀⠀⠀⠐⠶⢶⠿⠆⠰⠿⠥⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣶⡀
⠀⠀⠠⣭⣷⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷
⠀⠀⠀⢰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢻⣿⡇⠙⡇
⠀⠀⠀⠀⡇⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠘⠃⠃
⠀⠀⠀⠀⠙⠺⠤⠤⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠈⠉⠉⠉⠙⠓⠒⠦⠤⠤⠤⠤⠴⠊⠁⠀⠀⠀⣀⣬⠯⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⢼⣟⠁⠋⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠀⣀⣀⣈⣉⣙⣒⠒⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣰⠋⣠⡤⠴⢥⡤⠄⠉⠉⠉⠛⠛⠛⠛⠛⠓⠀⠀⡀⠐⢤⡀⠀⠊⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠃⠀⠀⢰⢋⣾⠋⠀⠀⠀⠉⠉⠚⠚⠿⠶⠶⠥⠶⣆⠁⠀⠀⠀⠙⣆⠙⣄⠀⠈⢈⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⣆⠸⡄⠀⢡⠃⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡀⣷⠀⠀⠐⢌⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠪⡔⠠⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠘⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠇⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⠀⠀⠀⢣⠙⠂⠀⠴⠒⣲⣿⣿⣿⢿⣷⣶⣶⣶⣤⡈⠓⠲⠭⠭⠭⠽⠿⠿⠷⠾⠿⠿⠿⠇⠉⠋⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠸⣿⣥⣾⣯⣼⣿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⣠⣤⡤⠤⠤⠶⠒⠒⠒⠋⠉⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡤⣤⣤⣶⣶⣾⣿⣟⡿⠾⠃⠀⠀⠀⠉⢉⠉⣉⣉⣉⣀⣤⠤⠤⠤⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠒⢀⣁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⠛⡍⠹⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣡⢤⣔⣚⠥⣗
⠀⠀⠀⠀⠀⠀⢀⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⣒⣻⠭⠟⠛⠋⠉⡁⢄⠠⣾
⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⡶⠿⠛⠓⡋⠉⢀⠀⠀⠀⠀⡰⣁⡴⠞⠛⠉
⠀⠀⠀⠀⣰⢸⡅⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⢤⠤⣖⣲⣶⠯⠭⠟⠓⠛⠋⠉⠉⠉⢉⢀⠀⠀⠀⢀⠀⣀⣐⣯⡴⠴⠒⠚⠉⠁
⠀⠀⠀⣰⠃⠐⠒⠚⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⠀⣀⠔⠠⠀⠀⣠⢏⣀⣤⣤⡴⠯⠔⠖⠚⠛⠉⠉⠁
⠀⠀⠀⡗⢀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠂⠀⠀⢀⣐⣁⣀⣥⣮⣤⠿⠷⠶⠛⠛⠋⠉⠉
⠀⠀⠀⠁⠉⠙⠓⠒⠒⠛⠓⠚⠒⠛⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠔⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠤⠔⠒⠒⠒⠒⠒⠒⠒⠦⠤⣼⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣴⠧⠚⠡⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠚⠁⠀⠀⡤⠒⠊⠉⠉⠉⠉⠉⠉⠓⠢⡄⠀⠧⣠⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣤⣾⣇⠀⠀⣀⢀⢀⢀⠀⠀⠀⣠⡇⠀⠀⠙⠃⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠔⠁⠀⠄⢙⣳⠾⠿⢾⡾⠶⠾⠲⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡀⣸⠃⠀⠀⢰⠃⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⣀⣀⣾⡿⠟⠀⠀⠀⠀⠠⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠐⠊⢳
⠀⠀⠀⠀⠀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠠⣭⣛⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣼⣏⣙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠉⠙⠛⠋⠩⠿⠶⣄⡘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡓⠆⠀⠀⢀⠀⠀⠀⠀⢼⠁⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣾⡟⠙⠂⠀⠀⢨⣍⠀⠀⠀⢾⠄⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⣾⠇⢨⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⢰⣦⣭⣿⡇⡖⠦⢄⡀⠀⠀⠀⢀⣀⡿⣡⡴⠿⢟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡻⢿⣿⣇⠙⠉⠋⠀⠀⠀⠀⢹⠿⠷⣿⠗⠐⢺⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠛⣿⣦⡄⠀⠀⠀⠀⠀⠘⣟⡻⠶⣶⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⣥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠋⠁⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⠈⣿⣉⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢋⠙⠛⠻⡻⣦⣔⢀⠀⠀⠉⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⣀⡀⠀⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠇
⠀⠐⠒⠒⠒⠒⠒⠀⠒⠒⣿⣒⣐⠒⠀⣂⣋⣿⠐⢛⣷⡄⠒⠀⠂⠀⠘⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢿⠿⣿⡟⠁⢰⡿⣿⡷⢄⡀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣳⣾⣶⣶⣗⣳⣄⠘⠧⡈⢛⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣞⡿⢻⠿⣾⣝⣿⢷⡄⢉⣬⠾⢷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣻⡾⠁⠀⠘⣇⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⣛⣛⣛⠛⡛⠛⠛⠛⢻⣿⡇⠀⠀⠀⢻⡀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠈⠛⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠛⠋⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⣿⣷⣤⣤⣀⣸⣶⣶⣿⣀⣤⣤⣴⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢶⡶⠛⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠘⣧⡀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣠⣤⡴⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠒⠲⠚⠋⠀⠀⠀⣴⠟⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⢙⣷⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠞⠋⢹⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠖⠒⠒⠲⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣏⠁⠀⠀⢸⠃⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⠒⠒⠒⣿⠀⠀⠀⠛⠒⢦⡀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⢀⣠⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⣤⡾⠋⠁⠀⠀⠀⠀⠉⠻⣦⣤⣤⡤⠴⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠷⠶⣄⣠
⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣯⣤⣤⣤⡤⢶⣶⣟⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠶⠶⠖⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡼⠿
⠀⢀⣼⠯⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠉⠉
⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠖⠛⠉
⣾⣛⣛⣛⣛⣛⣛⡛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⢷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠂⡙⢂⠓⣀⠂⠘⣀⠛⣘⠓⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⢁⣉⣴⣿⣿⣿⡿⠿⠯⣬⣅⡉⢀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⣾⣿⣭⠤⣄⠈⠛⢷⣟⢥⡄⢀⠀⠀⠀⠀⢀⡴⠎⠁⠠
⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢈⢻⡀⠲⠄⡶⠶⠖⠋⠉
⠀⠀⠩⠙⠲⠦⠤⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠋⠉⠉⠀⠀⠀⢹⣧⠀⡌⢇⣷⡄⠲⣿⡄⠀⠀⠠
⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠉⠒⠶⢤⣤⠴⠖⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⢴⣌⣾⣿⣔⣿⡇⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠦⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠋⡝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣤⠃⢀⠀⠀⠀⢸⡄⠀⣀⣀⠀⠀⠀⠀⢠⣶⣛⣀⠀⠀⠀⠉⠀⣤⡃
⠀⠐⠐⡐⠐⡀⠀⠀⠀⡐⢂⠀⠀⠀⢂⢲⡉⣱⠀⠀⠀⢃⠀⡨⢿⣿⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⢘⣠⣿⠂⢂⠀⡐⡐⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣂⣀⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠠⣬⣤⣴⣶⡾⠀⠀⠀⢠⣿⣿⣉⣀⣀⣾⡟⡀
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠀⠀⣀⠠⠀⠘⠛⠿⣦⡀⠈⠛⠛⠋⠀⠀⢀⣴⠟⣿⣿⡂⠀⠾⣿⡟⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠖⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⠴⠋⠁⠀⢸⣿⠆⠤⠟⠉⠀⠀⠀⡤⢄
⠀⠀⠄⠄⠀⠀⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⢦⡀⠀⣄⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀⢀⣼⡃⠈⠁
⠀⠤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣦⠀⠀⢹⡧⢀⣼⣆⣽⣶⠿⠟⠛⠉⠀⠀⠀⠀⠾⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠂⠂⠉⠉⠀⠀⠀⠀⠀⠀⠠⠟⠠⢠⣾⣿⣾⣿⡿⠗⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠡⠴⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⣠⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠀⠀⠛⠁⣤⣴⣆⠀⠁
⠀⠀⠠⠤⠤⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠤⠤⠤⠤⡀⠉⠀⠀⠐⠟⠀⠀⠘⠛⠀⠀⠈⠁⠀⣀⠀⠀⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣀⠀⠀⠠⣦⠀⠀⠈⠉⠀⣸⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⢀⡀⠈⠉⠀⠀⢠⡄⢠⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⡀⠀⢀⡨⠁⠸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢒⣒⣒⡒⢒⣒⣒⡒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⡞⠀⠙⠢⣄⡀⠀⠀⢀⡠⠔⠋⠈⢣⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠑⠢⢄⡀⠀⢈⡗⢏⠁⠀⢀⣀⠤⠚⠀⠀⢀⣘⣄
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⡆⢸⠉⠉⠁⠀⠀⠀⠀⠀⡎⡾⢹⠒⢤⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⡀⠀⠀⠀⠀⠀⠀⢀⢿⡇⡏⠀⠸⡍⠓⢦⣀
⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃⠀⠀⠀⠀⠀⠀⢸⣼⠀⡇⠀⠀⠈⠓⠺⠾⡿⠒⠤⡀
⠀⠀⡮⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣸⣀⣀⣀⣀⣀⣀⣀⡼⣿⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢱⣀
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢾⠀⠀⠀⠀⠀⠀⠀⡇⡏⢸⠀⠀⢀⠤⣀⡀⠀⠈⢢⠀⡞⢳⡇
⠀⠀⡮⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⣉⡉⢹⡃⣹⡉⢉⣉⡉⠉⢉⢉⡇⡇⢸⠀⢠⠇⣠⣀⡹⡕⠢⡈⡆⡇⡸⠁
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⡄⢸⠀⣷⡿⡍⠓⢦⣿⠀⢸
⠀⠀⠜⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢽⡧⢽⠭⠭⠭⠭⠭⠭⠭⡇⡇⠀⡇⢸⡤⣿⠀⡇⠀⣿⡏⠀⣘⣀
⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣸⣀⣀⣀⣀⣀⣀⣀⡇⣷⠀⡁⠀⡀⣿⣞⣁⣀⣿⡇⠀⠇⠤⠭⢉⣐⠢⢄
⠀⠀⢸⠒⠒⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠴⣧⣼⠦⠤⠤⠤⠤⠤⠤⠼⠿⣠⠃⠀⠛⠭⠭⠭⠥⠋⠣⣸⠢⠤⢄⡀⠀⠉⠢⡙⡄
⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢟⡻⠤⠤⠤⠤⠤⠤⠤⠤⠤⣓⡒⠒⠒⠒⠒⠒⠒⠒⠒⠛⡤⠤⠤⠬⢍⣒⣒⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⣀⠤⠀⣌⢙⡀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣰⠆⣄⢲⡀⠀⠀⠀⠀⠀⢠⡿⠾⣧⠠⠉⠀⠀⠀⠀⠘⠒⠒⠁⠀⠀⠀⠀⠀⢠⡶⣤⠐
⠀⠀⠀⠀⢹⣿⣛⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠉⠁⠨⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀
⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠆⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠺⠛⠻⠶⠗
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⣉⡣⠀⠀⠀⠀⠀⠀⠀⢠⣰⠦⠤⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠠⣦⡤⣦⣰⠄⠀⠀⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠆⣀⢤⡀⠀⠀⠀⠀⠀⠀⠐⠷⠾⠆
⠀⠀⠀⠹⠜⠠⠀⠀⠀⠀⠀⠀⠀⢠⡉⠹⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⣿⣟⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣄⢀⡄⠀⠀⠀⠀⠀⢀⡀⠀⡀⠠⠄⠀⠀⠀⠀⠀⡀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠴⠉⠁⠙⠄⠀⠀⠀⠀⠀⠀⢠⣥⣔⠀⠀⠀⠀⠀⠰⠿⠓⠒⠷⠇⠀⠀⠀⠀⠀⠀⠟⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠈⠉⠓⠦⣄⠀⢄⡀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠀⠀⠈⠙⢷⡈⠂
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠱⡄⠀⡀⠀⠀⢄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣄⡀⠄⠀⠀⠹⡎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠢⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠘⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢁⣾⣿⣯⣭⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠈⠛⠛⠉⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣨⣿⡿⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣹⡏⠈⠁⠀⣄⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⡤⠀⠐⢧⣬⣿⣷⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠦⠤⣌⣿⣿⣅⠀⠀⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⠿⢷⡄⡉⣩⣏⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣷⣾⣷⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡿⢿⣿⣿⠏⠀⠸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⢩⣿⣿⣿⣆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⢻⣿⣿⣿⡄⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣼⢿⣿⣿⣧⡀⠙⠻⢿⣷⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣞⣵⣾⡿⣸⡟⣧⠛⢤⣬⣥⣶⣧⣆
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠧⠿⠧⡿⢆⣍⠀⠀⣺⣧⠹⠤⠤⠤⠤⠤⠆⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠁⠀⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⠉⠛⠻⠿⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠘⠻⠇⠰⠄⠀⠀⡆⠀⠀⢀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠄⠀⠀⠀⠀⠀⠀⡀⠃⠀⡀⠀⠀⠀⠉⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⡈⠒⠂⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡒⠰⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠁⢰⡣
⠀⠀⠀⠀⠀⠀⣿⣙⣿⢸⣿⣿⢈⡍⣿⢿⣿⢸⣿⣻⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡣⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⢠⣝⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠠⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡆⠉⢈⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠓⠢⢾⡆⠀⢀⣀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⣀⣤⡖⢀⣾⡿⠀⠀⠀⠀⠀⠀⢹⠇⠀⢀⣸⠷⣄⣠⠾⣿⣿⠿⣿⡏⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣭⣥⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣟⣒⣻⣗⣒⣿⣟⣒⣻⠃⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⣻⣗⣒⣺⣗⣒⣿⣷⣒⣺⠀⠀⠀⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢾⣿⠀⣾⣷⠀⣿⡗⠀⣿⣤⣄⣀⣠⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣽⣯⣭⣽⣯⣬⣽⣯⣬⠟⠿⠿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠰⠒⣒⣶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣲⠖⡶⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠛⠀⠂