Immune system Emojis & Symbols

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠠⠂
⠀⠀⠀⢈⠲⣶⠁⡄⠀⠀⠀⠀⠀⢴⣦⡈⢳⡀⠀⠀⠀⠀⠀⠀⡔⠙⣆⠀⠀⠀⠀⠐⡄⢸⡁
⠀⠀⠀⠠⡄⡉⠂⡠⠍⠀⠀⠀⠀⢄⣙⡿⣾⣣⠀⠀⠀⠀⠀⠀⠷⠶⠟⠀⠀⠀⠀⠀⠁⡼
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃

⠀⠀⠤⠠⠀⠤⠄⠀⠀⠀⠀⠠⠄⠀⠤⠤⠄⠀⠀⠀⠀⠄⠀⠄⠀⠠⠀⠀⠀⠀⠄⠄⠠⠄

⠀⠀⠀⠀⠰⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣦
⠀⠀⠀⠀⠀⢀⣀⠏⠀⠀⠀⠀⠀⢸⣷⣤⠀⠀⠀⠀⠀⠀⠀⠐⠶⠇⠀⠀⠀⠀⠀⠀⠹⡆⢹⠆
⠀⠀⠀⠀⠀⢈⡡⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠹⣤⠼⠇⣼⠁⢀⣀⠀⠀⣀⣠⡤⠶⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⣴⠶⣤⠟⠀⢀⡀⠀⠈⠳⢋⣹⠟⠋⠉⠀⢀⣀⣤⣀⡀⠀⠉⠙⠳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠛⠲⡆⠀⠀⠈⠁⢀⠀⠀⣿⣁⣤⡴⠖⠛⠉⠁⠀⠈⠙⠛⠲⢦⣤⣀⡀⠈⠉⠻⡆
⠀⠀⠀⠀⠀⢠⡴⠗⡀⠀⠀⠀⠀⠀⢀⣬⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣿
⠀⠀⠀⠀⠀⠘⠶⠛⠛⣦⢀⣀⣤⡰⣯⠀⠉⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⣼⡇⠘⠧⠾⠁⠀⠀⣠⠴⠛⠉⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⢸⡍⠷⠾⠡⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠲⡆⠀⠀⠀⠙⢧⡀⠀⢼⣛⡛⠁⠠⠄⠀⠈⣥⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣻⠀⡗⠀⠀⠀⠀⠈⣧⠀⢀⣹⡇⠀⠀⠀⠂⠀⣘⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠰⣏⣉⣉⣉⠀⣉⣉⣉⣻⠀⠀⣿⠀⠘⠷⢾⣦⢄⣀⣄⢾⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢿⠀⠀⠈⠉⠉⣿⠀⡏⠉⠉⠁⠀⢀⡟⠀⠀⠀⣼⠻⠼⠃⠙⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⢷⡀⠀⠀⠀⠻⣤⠏⠀⠀⠀⢀⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢫⢷⣳⣿⣟⡑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⢠⣄⡀⠀⠀⠀⠀⠀⠀⠒⠀⠸⣿⣻⣿⣋⣠⣞⠃
⡦⣏⢸⣿⣿⣿⣞⣹⢓⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠯⢦⡀⠀⠀⠀⠀⠀⠀⠈⡟⣿⡟⡛⣭⣵
⠟⣩⠎⠻⣿⣿⣿⣙⣿⣶⣿⣟⣷⢲⣦⣤⣤⣄⣀⣀⡀⠀⠈⣰⡶⠆⣀⣀⠀⠀⠀⠄⢦⠀⠀⠀⠀⠀⠈⠣⣙⣽⣟⣩⡭
⣀⣡⡎⢐⡩⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⢻⣿⣯⣤⣾⡿⠿⣟⠛⣈⠷⢄⡀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠈⠁⣘⠻⠾
⣫⣽⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠋⠱⣤⣠⣿⠭⠌⠉⣀⣀⣬⢕⠢⣸⠂⣀⡀⢀⢀⣤⣍⢭⡐⠳
⣿⣿⣿⣿⣩⣵⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢛⡍⠹⣭⡟⠚⠳⡀⠘⠺⠧⠻⣤⢬⡘⠃⠙⢯⣳⣍⢻⣛⢿⣶
⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣏⡁⡼⣿⣿⣿⣿⠟⠒⠀⠀⣘⣃⣏⣀⣃⠒⢠⡏⠐⠪⠠⢁⠊⣹⣴⡫⢷⣽
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⡖⢛⠛⡋⢁⡀⠀⠀⠚⠋⢩⠛⣫⠑⠂⠀⠠⢿⡇⠰⡟⣢⢊⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⡳⢾⣿⣶⣶⣶⣶⣾⣶⣿⣷⣶⣶⣿⣾⣷⡔⠣⠚⢊⠤⡥⣼⣿⠯⠹⣾⣏⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⡉⣿⡻⢿⣿⣿⣶⣤⣌⡉⢩⣍⢉⡡⠠⠬⢎⣠⠴⠶⡎⣱⢂⠀⠊⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣘⠀⠠⠄⠉⠙⢛⢋⡡⠨⡄⠅⠨⣭⠼⠛⡖⣶⣷⡿⠧⠟⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⡪⣝⠷⣿⣿⣿⣷⣦⣤⣖⡞⠉⡡⠤⠊⠠⠂⠈⠉⢈⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⢿⣿⣿⣿⣮⣄⡐⠋⢉⠭⠍⣭⠄⠖⠙⡓⢠⡖⠊⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⣤⢄⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⢆⠟⡵⢃⡀
⠀⠀⠀⠀⠀⠀⡀⠔⠀⠑⢄⠛⣔⢀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣂⢞⠵⠊⠀⠄⡩⠃
⠀⠀⠀⠀⠀⠀⠈⠢⢔⠤⣀⠑⠬⡓⢵⣠⡶⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⢁⢓⡧⢚⠕⠁⢀⠐⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⡃⠀⡈⢲⢄⠳⣽⠄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⢀⢀⡶⢋⠔⠓⢔⢘⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⡃⢀⠉⠪⡑⢭⡠⡢⡈⠢⡀⠀⠀⠀⠀⠀⠀⡠⢋⡰⢐⡾⢋⠔⠁⢀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢕⠄⠈⠑⢍⡪⢦⡵⡮⡀⠀⠀⠀⠀⢀⢵⢍⡷⣏⠔⠁⡠⠐⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣙⢃⡄⢉⠆⠀⠈⢪⣆⠀⠀⣴⠑⠁⠀⠀⡁⠄⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⣠⣿⡀⠀⡻⣄⡀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⡯⢸⠀⡂⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣒⣿⢰⠀⠆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡂⢽⢸⠀⢥⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣟⢸⠀⢑⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡾⣟⢘⢬⢮⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠅⣺⢸⠀⣂⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢥⢿⢸⠀⡐⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢕⢽⢸⠀⡂⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡵⢾⠀⡆⡒⢵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠚⠁⠓⠚⠟
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠠⠠⢀⢄⠠⢀⠔⡠⢀⡠⢀⢄⠢⢀⠄⡂⢄⠤⡀⢔⠠⢂⠄⡢⢐⠄⡢⢐⠠⡂⠔⠀⡠⢀⢄⠠⡀⢄⠀⡠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠀⠁⠊⠀⠁⠈⠁⠊⠐⠁⠈⠀⠁⠈⠀⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠁⠈⠀⠁⠈⠈⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⣄⠀⠀⠀⠀⣠⠞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠳⣄⠈⢢⣄⣠⡜⠁⣠⠎⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠈⠳⡄⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⢸⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⣀⣤⣤⣄⣀⣠⡟⠀⣿⠀⠀⢀⣠⠴⠖⠛⠋⢹⡇⢸⡏⠙⠛⠲⠦⣄⡀⠀⠀⢸⠇⢸⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢯⣤⣀⣀⣀⣀⡀⠀⠹⣤⠞⠋⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⠀⠀⠀⠀⠙⠳⣄⡞⠀⠀⢉⣉⣉⣉⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣳⣄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⠚⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⢳⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⡴⠋⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢳⡀
⣴⠒⣤⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣤
⠙⢦⡈⠳⣄⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⡴⠋⢀
⠀⠀⠹⣄⠈⠳⠦⣼⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣇⣠⡴⠋⢀⡴⠃
⠀⠀⢀⡼⠃⢀⣀⣤⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣉⣉⣉⠀⠀⠰⣏
⠀⡰⠋⢀⡴⠋⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⠙⠲⣄⠘⢦⡀
⣞⣀⡴⠋⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠳⡄⠙
⠈⠉⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡴⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠳⣄⣠⠏
⠀⠀⠀⠀⣠⣤⣤⣤⣤⡤⠖⠋⢀⣴⠁⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠳⢤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠘⢧⣤⣤⣤⣤⣤⡀⢀⡟⠈⠳⢦⣀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣀⡴⠞⠉⣧⠀⢀⣀⣀⣀⣀⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⠀⠀⠀⠈⠙⠓⠲⠦⢼⡇⢸⡧⠤⠶⠚⠋⠁⠀⠀⠀⣿⠀⣿⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⡇⠀⠀⠀⠀⠀⠀⣠⠞⢁⣤⣄⡈⠳⣄⠀⠀⠀⠀⠀⠀⣧⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠞⠁⣠⠊⠁⠈⠳⣄⠈⠣⡀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⡾⢠⡀⡀⠀⠠⠄⠀⠀⠀⠀⠔⠑⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠄⠂⠄⠐⠒⠁⠀⠀⠀⠀⠀⠀⢂⠀⡧⢴⠀⣠⠔⡳
⠀⠀⠀⠀⠀⠀⢠⢞⡙⣆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢶⡏⠀⠀⠀⢻⠖⠋
⠀⠀⠀⠀⠀⠀⣨⠇⠈⠈⠨⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣞⡁⢀⢠⠀⣸⠗
⠀⠀⠀⠀⠀⢎⢀⣠⡀⣀⢄⣸⠀⠀⢷⢀⡄⣀⣀⡀⡠⠀⠀⠀⢀⣀⣀⢠⡀⣸⠀⠀⠘⠲⠭⠖⠮⣗⣦⠀⠀⠀⠒
⠀⠀⠀⢴⠂⠀⠁⠀⠉⠁⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠤⡄⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠀⠀⠀⢸⠀⡇⠀⠀⠆⠀⣿⣷⠀⠀⠀⠀⢰⠁⡇⠀⠀⠀⠓⣵⣀⠔⠉⣀⠇⠐
⠀⠀⠀⠀⠀⢀⢰⡛⠁⠀⠈⣷⠀⠀⢸⡆⡇⠀⣤⣤⣤⣿⣿⣤⣤⣄⠀⢸⠀⡇⠀⣠⢚⡡⠅⡈⢛⠉⠁⠀⠀⠀⢠⠒⡄
⠀⠀⠀⠀⠀⠈⠀⠺⣦⡤⣾⠁⠀⠀⠀⡇⢸⠀⠟⠛⠻⣿⣿⠛⠛⠛⠀⠸⢸⡇⠀⠍⠉⠀⡸⡏⠉⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡇⢸⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⡔⠘⡘⢆⠀⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⡀⠀⣠⠂⡟⠚⠱⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡜⠁⠀⠸⣀⠙⠒⠢⢤⡀⢀⡠⠴⠒⠊⣀⡟⠀⠀⠀⠈⠈⢷⠀⠁⠀⠂⠙⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠉⠀⠀⠀⠀⠈⠉⠙⠒⠦⣈⣁⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣦⡁⡚⣀⣰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠿⠀⠖⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠛⠳⢦⣄⠀⠀⠀⢸⡫⣙⣟⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠛⠀⢀⣴⠟⠁⠀⠀⠀⣠⣴⣤⣄⠀⠀⠀⠙⢷⣄⠀⠈⠛⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⠞⠁⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠻⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣤⡀⣠⡄⢤⣄⣠⣤⢠⡄⢠⡄⣤⡀⣤⢠⡄⠴⣤⠤⠠⣄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠙⢹⡇⣿⠙⠋⣿⠸⣇⣼⠃⣿⢻⣿⢸⡇⠀⣿⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⣄⣠⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠈⠳⡈⢁⠞⠁⠀⠀⠀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡷⢸⡄⣀⣤⣶⣶⡇⢸⣶⣶⣤⣀⢀⡇⢼⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠶⣄⠙⢿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠋⣠⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⣿⣿⣇⢀⣿⣿⣿⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⢦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡴⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⢈⣉⣉⣹⣿⣿⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⣉⣉⣉⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠞⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⣿⣿⡇⠈⠳⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣿⣿⣿⣿⣿⣦⣤⣴⡿⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠶⠋⣠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣷⣄⠙⠦⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⡗⢸⠁⠉⠛⠿⢿⡇⢸⠿⠿⠛⠉⠈⡇⢾⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⢀⡴⢃⡘⢦⡀⠀⠀⠀⠳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠋⠙⠦⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡦⠖⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡭⠤⠃⠹⣖⡲⠖⠘⡷⢟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠶⣄⠈⡠⢤⡤⢹⠚⠗⠀⠀⠀⠀⠀⣹⡧⠼⠛⢁⡈⠉⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡿⠊⡀⢷⠃⢃⡞⠀⠀⠀⠀⠀⠀⣼⢑⡀⠄⠀⠈⣗⣦⡤⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡦⠒⣤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⡇⠈⢻⢳⡄⠀⠀⠀⠀⠀⣜⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⠎⠀⢐⣫⠿⠖⠀⣹⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣰⣤⡀⠘⡃⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢄⣟⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣧⠖⠉⠉⠉⠁⠉⠓⣤⢀⣤⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠞⠁⠀⠀⢷⠦⡴⠂⠀⠘⢿⣻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠰⢿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠹⡝⡆⠀⠀⡤⠤⣥⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⠐⠟⢀⡀⠀⣷⠋⠀⠁⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣵⣀⣤⣠⠈⢀⣈⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠲⣽⠋⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⢿⣷⣄⠀⣀⣴⣾⡿⠟⠛⠉⠉⠀⢿⡿⠈⠉⠉⠛⠻⢿⣷⣦⣀⠀⣠⣾⡿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⠿⠇⠀⠀⠀⠀⠀⢀⣶⣿⠿⣿⣶⡀⠀⠀⠀⠀⠸⠿⠛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣼⣿⣥⣄⠀⠀⠀⢀⣴⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣧⣤⣤⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠛⠛⢻⣿⠛⠋⠀⠀⠀⢸⣿⣇⣨⣿⡇⠀⠀⠀⢠⣴⣿⡿⠿⣿⣶⣄⠀⠀⠀⠀⠙⠛⣿⡟⠛⠛⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣤⣤⣶⣿⠟⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢰⣶⣤⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⡿⠋⠀⠉⠻⢿⣷⣦⣤⣀⣀⠀⣾⣷⠀⣀⣀⣤⣴⣾⡿⠟⠋⠀⠙⢿⣷⣶⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠈⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⢸⣿⠟⠿⠿⠿⠿⠿⠿⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣥⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀⠠⡀⠀⠤⢠⠄⢸⡇⠀⢸⣿⠀⠀⠄⠀⠠⡄⡤⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⡷⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠛⠱⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠉⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣀⠀⠀⣀⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠛⠃⣀⣴⠟⠹⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠏⠻⣦⣀⠘⠛⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⡤⠶⠛⠉⣀⡴⠂⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣀⠉⠛⠶⢤⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢉⡠⠖⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⠃⠀⠲⢤⡉⠁⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢠⠖⠋⣀⠘⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠃⣀⠙⠲⡄⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠰⠛⣁⡄⠘⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣿⠃⢠⣈⠙⠆⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠚⣁⡤⠆⠘⣿⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⠃⠰⢤⣈⠓⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠉⠀⠀⠀⢨⣿⠂⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠐⣿⡅⠀⠀⠀⠉⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣀⣤⣾⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣷⣤⣀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡶⣿⡟⢿⡌⢿⣦⠀⠈⠻⠿⣶⣶⣶⣶⠿⠟⠁⠀⣴⡿⢩⡿⢻⣿⢶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢻⡌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⡟⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠘⣿⣆⢻⡌⢻⣧⠀⣀⡀⠀⠀⢀⣀⠀⣼⡿⢡⡟⣰⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡈⠉⠛⠛⠿⣶⣦⠀⠀⠘⢿⣆⢻⡄⢻⣿⢛⣿⡇⢸⣿⡛⣿⡟⢠⡟⣰⡿⠃⠀⠀⣴⣶⠿⠟⠛⠉⢁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⢀⡴⢻⣿⠀⠀⢠⣾⣿⡆⢻⣠⣵⡿⠋⠀⠀⠙⢿⣮⣄⡟⢰⣿⣷⡄⠀⠀⣿⡟⢦⡀⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡀⢀⣴⣯⣀⣸⣿⠀⠀⢿⣷⣶⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣾⡿⠀⠀⣿⡇⣀⣽⣦⡀⢀⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⠉⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⠿⠟⠛⠉⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣇⢠⡆⣰⡄⠉⣩⣍⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⡛⢛⣛⣛⣉⠉⡥⢤⡄⣶⡄⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⡾⢠⣧⣽⣸⡇⠈⢣⡏⠉⠓⣼⢸⢷⣸⡇⣼⢳⡈⢹⠁⢸⢸⡇⢀⡟⣿⠙⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣶⣬⣄⣈⡋⠓⠶⠋⠳⠤⠗⠿⠸⠀⠻⠧⠟⠛⠇⠸⠀⠘⠈⢛⣋⣠⣤⣶⡾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⡿⠟⠛⠻⢿⣿⣿⣷⣶⣤⣄⣀⡀
⣠⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣄
⣿⣿⡿⠿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣿⣿⣿⡿⠿⠛⠿⢿⣿⣿⣿⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⠁
⣿⣿⡇⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢠⣶⣶⣶⣶⣶⣶⡄
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠉⠙⣿⣿⠋⠉⠀⠀⠀⠀⢠⣤⡀
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⢀⣰⣿⣿⣄⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄
⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢿⣿⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣿⡿⢿⣿⣦
⢹⣿⣿⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⣿⣿⣿⣿⠉⠀⠈⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠀⠀⠈⠁
⠸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣷⡀
⠀⢿⣿⣷⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣷⠀⠀⠀⢰⣶
⠀⠈⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣴⣾⣿⡟⠻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿
⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⢿⣿⣇⢀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿
⠀⠀⠀⠈⣿⣿⣧⡀⠀⠀⠀⠀⠙⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡿⠋⠉⣿⣿⡟⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠛⠀⠀⠀⣀⡀⠀⠀⣾⣿⣿⣿⣿⣿⡋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⡿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⣿⣿⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣦⣄⣀⣠⣴⣶⣿⣿⡄⠀⠀⠀⠈⠛⠁⠀⠀⠀⢀⣀⣠⣿⣿⣄⣀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠃
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢀⣤⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠒⠊⠉⠊⢀⠒⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠠⠤⠓⠂⢒⣸⠓⠂⠀⠠⣭⣥⣤⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡠⠒⠀⢈⣩⡭⠭⠤⢈⡁⠈⠛⢍⠭⠉⠷⢻⠁⠀⠒⠂⠀⠀⠀⠐⢒⠂⣭
⠀⠀⠀⠀⠀⠛⠂⠀⠠⠬⠬⠉⠭⠭⠤⠀⠐⣁⡄⠀⣨⢾⡀⠀⠀⠀⠀⣜⢜⢕⠥⠪⠞
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⢔⠔⠐⠀⠀⢺⣠⣆⠠⠀⣹⠷⠲⠤⠴⠤⠷⠚⢶⡕⠄
⠀⠀⠀⠀⠀⠀⠃⣤⣀⡀⠐⠐⠅⠔⡕⣑⢹⣛⡙⠂⣠⢸⠁⠀⠈⠉⠉⠉⠉⠁⡀⢀⠀⡄
⠀⠀⠀⠀⠀⢀⠜⠉⣁⡈⠉⠉⠋⠉⠁⢋⠓⠷⡀⡄⠀⠈⠀⠀⠀⠀⠀⠠⠪⠦⠨⠘⣀⡇
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠉⢉⢉⢉⠄⢀⠤⠂⣇⡂⠀⡂⠀⢨⡉⠀⢒⠒⡒⢂⡉⣉⢰⡇
⠀⠀⠀⠀⠀⡟⠢⠤⢀⡀⠀⠁⠀⠀⠐⠉⣉⠁⡇⣀⠀⡇⠀⢸⡈⡄⠽⣘⠀⢀⠀⡏⢻⡅
⠀⠀⠀⠀⠀⣷⣴⡆⡄⠄⣉⠉⠉⡉⢉⠡⠂⠀⡇⠀⠎⡇⠀⢸⣹⣶⡠⠭⠂⠨⠄⠒⠚⠄
⠀⠀⠀⠀⠀⠯⣈⠁⢆⠸⣀⠠⠀⠑⣌⢈⡁⠀⡇⠀⡀⠅⠀⢸⠀⡫⠑⣋⣉⡀⠀⣒⠀⡆
⠀⠀⠀⠀⠀⣾⠶⣭⡒⢒⠂⠤⠤⡤⠄⢒⠊⠁⡖⠒⢛⡀⠀⠀⠲⣦⠍⡀⠂⠀⠀⣀⠤⡇
⠀⠀⠀⠀⠀⢲⣅⣒⠀⠈⠝⠉⠀⠇⢸⡗⠀⡆⡏⠉⠉⢙⠀⠀⠀⠀⢉⣒⣒⣎⠩⠀⠀⡏⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⡙⠪⢕⡀⠸⠓⠂⠀⠀⠈⠀⣀⠃⡧⠀⠀⠈⠢⡙⢤⣐⠛⡬⣍⣸⣶⠟⣸⣒⢒⣒⡂⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠁⡀⠀⠀⡉⠐⠒⢒⠂⢀⡊⣠⠂⣗⣒⡂⠀⠀⠈⠑⠪⢥⣬⣬⣬⣴⡛⠠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠘⢜⡦⣀⠨⠲⠃⠔⣤⢦⣴⠟⡾⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠪⢍⣊⠗⠒⠚⢉⢠⠚⣁⠀⠀⡀⠠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠉⠠⠤⠠⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠔⠴⠃⣀⣘⠴⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠴⠃⣤⡘⣅⣨⠇⢘⡦⡄⠑⠢
⠀⠀⠀⠀⠀⠀⢠⠄⠄⠤⡀⠀⠀⢧⣀⠀⡹⣅⢀⢔⠓⠘⣎⠜⠀⠀⠰⡁⠀⡠
⠀⠀⠀⠀⠀⢀⢼⡀⠀⢀⢇⡀⠀⠀⠸⡃⣓⠊⠑⠔⣁⢘⠄⠠⠤⣴⠫⡉⢑⠣⣀⢀⠄
⠀⠀⠀⠀⢠⠇⠤⠬⠭⠥⠤⢻⠀⠀⠀⠈⠈⠧⣀⠜⠀⠁⠀⠀⢀⣸⡀⢄⠈⠁⠈⠣⡀⠀⡀
⠀⠀⠀⠀⢸⠁⠀⣔⠙⣢⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣄⠀⢈⠀⠁⢹⠉
⠀⠀⠀⠀⠘⡦⠤⢈⣾⡠⠤⢼⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠘⠀⠑⣬⣀⣙⡼⠓⠒
⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠒⠁⠀⢠⢞⠁⠀⢀⣀⣀⣀⡈⠲⡀⠀⠀⠀⠀⠐⠁⠀⢹
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠃⠀⠉⠒⠚⠂⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠑⢷⠀⢸⠉⣩⠛⣍⢉⠇⠀⡷⠃⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠣⡀⠘⢟⢶⡻⠃⣠⠎⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠒⠒⠷⣿⡖⠐⠢⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⡠⠒⢒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠙⠲⣶⣶⣦⣀⢈⡿⠶⠴⠁⠀⠀⢻⣦⣤⣤⣄⣍⣑⠖⠀⣠⣤⡿⠋⠁⣠⡑⣀⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⠲⢶⣿⣀⠀⠈⢻⣿⢿⠟⠁⠀⠀⠀⠀⠀⠘⠿⢿⠿⠟⠻⡇⠀⣸⡿⠋⢀⣼⣿⡟⠋⢉⣁⣌⠃
⠀⠀⠀⢀⠊⢀⣼⣿⣶⣤⣤⣾⣿⣿⣷⣶⠾⢱⢺⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣦⣼⠘⠀⣠⣿⠇⠀⣸⣿⠏⠀⣰⣿⣿⣿⡀⠆
⠀⠀⠀⢘⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⡧⣼⡦⠤⣄⠀⠀⠀⠀⡖⠒⠀⠀⢺⠘⠶⠋⢰⠀⣰⣿⣿⣤⣾⣿⣿⣿⣟⣳⠈
⠀⠀⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠄⣰⠊⠀⠀⣠⠞⠀⠀⠀⠀⡆⠀⠁⠀⠙⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢡
⠀⠀⠀⢘⠈⠋⠹⢛⣿⣿⣿⣿⣿⢿⣿⣶⣯⣤⣴⡿⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣾⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡆
⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⢾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱
⠀⠀⠀⠠⠀⢿⣿⣿⣿⡟⣿⠁⣿⣿⣿⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠸⡆
⠀⠄⠀⠘⣣⣉⣿⣿⣿⣇⢻⡄⠻⡟⠋⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡘⡻⣿⣿⣿⣿⣿⣿⣯⣤⡈⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⢾⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⢉⣓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡤⠂⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠐⠣⣀⣘⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠙⠇⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡴⠛⡆⣠⠁⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⢀⡔⣁⠤⠼⠒⠲⠤⣄
⠀⠀⠀⢀⣞⣀⣠⡇⠘⢦⣀⣠⠞⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢰⣀⠞⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⣠⠊⠉⢰⠃⠀⠀⠀⣀⠯⠂⠀⠀⠈⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⡴⠁⠀⠀⢀⡱⠖⠂⠉⠀⣀⠀⣀⡄⠀⠀⠈⢆⠀⠈⠀⡗⠂⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⡼⠳⣶⠖⠈⠀⠀⠀⣀⠔⠊⠁⠙⠳⠇⠀⣏⠛⠢⢦⠀⠀⠛⠀⠀⠐⡎
⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⣦⠐⠀⠀⠈⠣⣀⠀⠀⠀⢀⠇⠀⠀⠂⠀⢸⡎
⣀⣀⡠⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡌⠂⢄⣀⡼⠓⠢⣀⡸⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠈⡦⡀⠀⠨⡃⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⢠⠃⠈⠢⢄⠘⠤⣀⢀⡎⠈⠒⢄⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⡼⠀⠀⠀⠀⠑⠒⠈⠉⠀⠀⠀⠀⠈⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⠺⡴⠂⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⢀⢔⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢔⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠄⣀⡄⢄⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠰⠀⡎⠀⠀⠀⠀⠀⠀⠀⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢑⣀⡀⠈⠢⡀⠀⠀⠣⡤⠶⢀⣨⠱⠀⢣⠐⡄⠀⠀⠀⠀⠀⠰⢘⡀⠤⠰
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡷⠊⠀⠀⠈⠲⡀⠑⠠⢂⠌⠀⠀⠀⣀⠈⠳⡤⠀⠘⠄⠀⠀⠀⠀⡇⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡀⠀⢈⠀⠘⠆⢀⡹⣀⣀⠄⠀⠀⢘⠀⠀⠀⢠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠢⢤⠂⠀⠁⠈⠉⠀⠀⠀⠘⡀⢀⡠⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠠⠄⢀⢀⠀⠀⠙⠌⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⢄⠀⠀⠀⡧⠂⠀⠀⡔⠃⠀⠀⠀⠀⠀⠱⠀⠀⠀⠸⠄⣤⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠙⢀⡊⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡎⠀⠀⠀⢀⢜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢈⠆⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠒⠒⠚⡁⣑⡈⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⠂⣀⠀⡀⠠⠐⠂⠀⠀⠀⢀⢴⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠚⠃⡈⠀⠀⠀⠀⠀⠀⢀⠀⡈⠉⠉⠑⠦⡀⠀⢠⡄⠒⠘⠛
⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠀⠀⢀⠆⢠⠃⠀⠀⠀⣤⠔⠘⠆⠀⡠⠚⠢⠀⡄⠀⠀⠀⠀⠈⠓⢤⡉⠒⠂⡐⡒⠔⠃
⠀⠀⠀⠀⠀⠀⠀⡼⠈⡢⠀⠄⠂⢀⠆⠀⠀⠀⠀⠁⠀⠀⡄⠘⠀⠀⡼⠋⢳⠀⠀⠀⠀⠀⠀⠀⠈⢢⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣠⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⢀⡔⡡⠖⠁⠠⡈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢁⡄
⠀⠀⠀⠀⠠⢊⠞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠐⠁
⠀⠀⣰⠏
⠀⢰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡀
⠀⠀⠀⠀⠀⣤⡄⠀⢠⣄⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⢿⣄
⠀⠀⠀⠀⠀⠙⣧⡤⢞⣛⣒⣚⣷⣤⣶⠆⠀⢀⠀⠀⠠⣿⣿⣿⡿⠄⠀⠀⠀⠀⢴⣄⢀⣞⣵⣿⠟⠁
⠀⠀⠀⠸⣷⠞⣵⣾⣿⣿⣀⣹⣿⣿⣿⣦⣤⠿⠗⠀⠀⠉⠟⠛⠀⠀⠀⠀⢀⡴⠋⠙⢷⣝⠟⠁
⠀⣶⣦⣠⢏⡾⢿⣧⣾⣿⣿⣿⣧⡿⠛⢻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⢦⡀⠀⣹⢷⠄
⠀⠀⠀⢸⢸⣧⣼⣿⣁⣨⣿⣋⣿⣷⣤⣼⣿⡟⠃⠀⠀⠀⠀⠀⢀⡴⢋⠀⠳⡄⠀⣠⠞⠁
⠀⠀⠻⠻⣼⣿⣏⣽⡟⢻⣿⣿⡿⢻⣿⣏⣿⠷⣶⣦⠀⠀⢀⡴⢋⡀⠈⠳⠀⣠⠞⠁
⠀⠀⣠⣤⠿⣿⣿⡟⣻⣿⡏⠀⢹⣿⣿⣿⣧⡀⠀⠀⢀⡴⠋⢤⡀⠙⠂⣠⠞⠁⢠⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠙⠃⠀⣼⡿⢿⣿⣿⣿⣿⣿⠿⣏⠀⠉⠀⢀⡴⢋⣄⠻⣿⣾⣿⠟⠁⠀⠀⣿⢸⡇⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠀⢀⣾⠉⠉⠿⠆⠀⠿⡷⢀⡴⢋⣴⣝⢿⣿⣿⠟⡁⠀⠀⠀⠀⠈⠛⡟⠛⠋⠉⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⡴⣯⣴⣦⣙⣿⣿⠟⠁⡜⡉⢆⠀⠀⠀⡠⠞⠁⠈⠉⠉⠁⠙⠲⡄
⠀⠐⢦⣰⣼⣡⡄⡀⠀⠀⠀⠀⠀⠀⡟⣵⣿⣿⣿⣿⠟⠁⠀⣸⢸⠁⠸⡄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠤⣽⢾⡿⣾⣟⢻⡅⠀⠀⠀⠀⠀⢤⣝⢿⣿⣿⠟⠁⠀⠀⠀⢯⠄⠀⢀⡇⠀⡇⠐⠀⠒⠒⠒⠒⠒⠒⠒⠂⡇
⢐⣻⣿⣿⡿⣿⣿⠲⠀⠀⠀⣀⣵⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⢫⡀⠀⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠈⠀⠛⡟⠻⠛⠌⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢃⣀⣀⡙⡄⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⡇⡇⡇⢻⠀⢿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⡇⡇⡇⣾⠀⣾⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣼⣿⣿⡇⡇⡇⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠿⠿⠿⢇⠇⢧⡙⠿⠿⠿⠿⠿⠿⠿⠟⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠠⠀⠭⠉⠉⠍⠩⠭⠭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣇⢰⡟⢠⡿⣷⠀⣼⠟⠛⠃⣾⠟⠛⠃⣿⠄⣿⣧⣸⡇⠀⣾⢿⡄⠛⣿⡟⠃⣿⢠⡾⠛⢻⣆⣿⣷⣄⣿
⠀⣻⣿⢀⣾⠛⢻⣧⠻⣷⣶⠆⠻⣶⣶⠆⣿⣂⣿⡈⢻⣇⣼⡟⠛⣿⡀⣿⡇⢀⣿⠈⢿⣦⣾⠃⣻⡇⢻⣿⡀
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠉⠉⠉⠉⠲⢄⡀⠀⠀⠀⠀⠀⣇⢠⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⡟⠋⠹⠬⡑⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⡀⢠⠀⢦⡀⢰⡄⢰⣄⠀⠀⠀⢣⠀⠀⠀⠀⠇⠀⣀⠀⠀⠀⠀⢣⠤⢤⠀⠈⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠦⠼⠙⠚⠈⠉⠉⠉⠉⠉⢤⡉⠉⠀⢈⠀⠀⠀⠀⣠⡀⢿⡇⣀⠤⢶⠁⠀⢸⠃⠀⢰⠀⠀⢰⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠐⠉⠁⠀⠀⠀⠀⠀⣀⠀⠁⠀⢰⡼⢄⠀⠀⠸⡀⠈⠉⠉⣀⠄⠸⠀⢰⡇⠀⠀⠘⠀⠀⢸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢾⣄⠀⠀⢾⣧⠀⠀⠀⠀⣿⡆⢀⡠⠚⠃⢨⠀⠀⠀⠑⡄⠉⠉⢀⡠⠀⢳⠆⠀⢸⠀⢸⠀⣠⢃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⡀⡗⠒⠚⣓⣊⡉⢉⣉⡉⠍⠀⢡⡰⠒⠁⠀⠀⠀⠀⠱⣈⠉⠁⢀⠴⠃⠀⢿⠈⣠⢆⡰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠤⠤⠤⡤⠤⠔⠒⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⡲⠀⣠⠚⢳⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠶⢖⣶⣖⣲⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⠟⢁⣠⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⡏⠉⠈⠙⡀⡠⢖⡒⣀⡶⠴⠤⡀⠀⠀⠀⠀⡜⣨⠃⢒⠁⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠖⣍⣭⣵⡀⣀⠷⣛⣩⣽⠋⠑⠢⠀⠀⡏⠑⠒⢴⡱⢁⢔⡥⠐⢦⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⣤⠁⠀⠈⠻⡓⢻⠁⠙⠯⠿⠖⠒⠉⠰⣅⡀⠀⣾⠔⡡⠊⠀⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠢⡀⠀⠀⠱⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢤⣤⡖⠘⠦⣀⠀⠀⢀⣀⡤⠤⠖⠒⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣯⢕⣂⠀⠀⠉⠁⢙⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⢦⠙⠒⠒⢎⠉⠧⠄⠒⠒⠂⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣎⡲⣴⢟⢦⣂⠄⠀⠀⣀⢤⣶⠃⣶⠀⡀⠀⠀⠀⢢⣴⣶⣾⣤⠂⣀
⠀⠀⠀⠀⢰⠷⠊⠃⠀⠀⠀⠀⠀⠀⠀⣀⣱⣾⣷⠐⢀⡫⣷⣃⠀⢰⣿⣿⣿⣍⣙⣿⣅⠀⢠⢨⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖⣯⣿⣿⣷⣶⣶⣻⡀⠀⠸⣿⣿⣾⣝⣶⣿⡟⠀⠠⢀⠹⣿⡅⠁⠀⠈⠀⠁
⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠊⡝⠿⡿⠷⡛⠃⠀⠀⠀⠘⠻⠿⠿⠿⠋⠀⠀⠀⠈⢠⠋⠀⠐⡌⠂
⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡩⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠀⠀⢸⣾⣷⡆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠁⠠⠂⣃⢁⡀⠁⢁
⠀⠀⠀⣤⢽⣿⣿⣯⣄⠀⠀⢐⣟⠂⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⢸⠛⣿⣿⣿⡇⠀⠠⠀⢠⡚⠡⢟⠈⠃⠀⡆
⠀⠀⠀⠀⠸⢹⣟⠇⠀⠀⠀⢀⣿⠇⠀⠀⠀⣾⡥⢿⣿⣭⡄⠀⠀⠀⠛⡶⠻⡿⠟⠃⠀⠀⠀⠀⢂⡀⠢⠖⢠⠙⠁
⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠆⣿⡄⠀⠀⠀⠸⠗⠾⠿⠟⠁⠀⠀⠀⡠⠋⠀⠹⠀⠀⠀⠀⠀⠂⠀⠄⠋⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⢸⡟⠃⠀⠀⠀⡊⣿⡆⠀⠀⠀⣂⣀⣀⣀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⡇⣿⡅⠀⠀⠸⡟⠛⠛⠿⠿⣟⠀⠀⢠⣶⣦⣖⣾⣷⣶⠀⠀⠀⢀⣀⣦⣴⣢⣶⠀⡀
⠀⠀⠀⠀⠀⢸⡋⠆⠀⠀⠀⠏⣯⡄⠀⠀⠰⠆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠉⠀⠈⠀⠀⠠⢤⣿⣿⡿⢏⢛⣎⡁
⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⣀⣦⣿⣇⣀⠀⠀⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢒⣯⣿⢕⡡⢁⣛⡒⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⣿⠀⠉⠀⠀⣇⣀⣀⣀⣼⣿⠀⠀⠀⣄⣀⠀⣀⣁⡀⠀⠀⠈⢉⢿⣿⣮⣥⡣⣟⠉
⠀⠀⠀⠀⠠⠟⠓⠀⠀⠀⠀⠾⠛⠦⠀⠀⠀⠋⠛⠻⠟⠛⠋⠀⠀⠀⠛⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠃⠘⠀⠁

⣶⣾⠿⣶⠶⢶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣰⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡿⠿⢿⣿⡿⣿⣦⡤⠀⠀⡴⣄⠀⢀⡽⣮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣀⣼⣿⣷⣿⣿⣇⠀⢀⡝⢮⡳⣏⠔⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⡏⠉⢹⠟⢁⠔⢁⠐⠀⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⠖⢁⠴⡉⠢⠀⠀⢀⡴⢋⣉⣁⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢁⠔⠁⠄⠈⠀⢀⡴⠋⢀⣾⡿⣿⣁⣹⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠁⠀⢀⡴⢋⠀⠀⠉⠹⣷⣾⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⡀⢀⡴⠋⠀⢻⣷⡒⠀⠈⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠊⣉⠉⣴⣷⣤⣾⣿⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣸⣿⣇⣀⣸⣿⣏⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡻⠿⣿⣿⠿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠠⣄⣼⣤⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⡾⠛⠻⡆⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠚⠓⠂
⠀⠀⢺⢿⡿⠋⠀⠀⢿⣿⣿⠗⠀⠀⠀⠁⠀⠀⠁⠀⠀⡰⠋⠀⣭⠀⠀⢠⣶⣷⡆⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⢆⢀⣰⡂⢀⠀⠀⠀⠀⠀⠀⣀⣤⣔⣦⡄⠀⠀⠀⠀⠀⠀⢀⡠⢴⡀⠠⡄⠀⠀⠀⠀⠀⠀⣠⠒⢒⠢⡀⠀⠀⠀⠀⠀⠀⣠⢄⣒⠐⢄
⠀⠀⠠⢤⠀⠀⣘⣇⠂⠀⠀⠀⠀⠀⣷⠃⠀⠀⣝⠇⠀⠀⠀⠀⠀⡅⠀⡋⠁⠀⢝⠀⠀⠀⠀⠀⢸⠀⠋⠀⢰⣘⠀⠀⠀⠀⠀⢠⠉⠙⡔⠉⢪⡁
⠀⠀⠠⡮⡲⠀⠂⡃⠀⠀⠀⠀⠀⠀⠯⣦⣴⣲⡻⠂⠀⠀⠀⠀⠀⠸⢄⣱⣎⣃⠎⠀⠀⠀⠀⠀⠘⢎⡐⠀⣁⠜⠀⠀⠀⠀⠀⠀⠲⣹⠬⢊⠵
⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⣤⠗⣓⠺⣄⠀⠀⠀⠀⠀⠀⣀⡨⠱⢤⣶⠀⠀⠀⠀⠀⠀⢀⡠⠟⠢⣤⡄⠀⠀⠀⠀⠀⠀⠠⣗⠓⡳⠀⠀⠀⠀⠀⠀⠀⡠⢒⣎⣉⢆
⠀⠀⠀⣿⠨⠀⢇⡿⠀⠀⠀⠀⠀⠀⢉⢎⡐⣨⢄⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⢨⠇⠀⠀⠀⠀⠀⢀⠤⠼⠹⠤⢤⠀⠀⠀⠀⠀⠐⡀⠀⠁⠛⠀⠇
⠀⠀⠀⠘⠓⠱⠛⠉⠀⠀⠀⠀⠀⠀⠁⠁⠘⠵⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠒⠚⠂⠀⠀⠀⠀⠀⠈⠉⠹⠏⠉⠁⠀⠀⠀⠀⠀⠀⠉⠢⠄⠤⠚


⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢰⢘⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠘⣦⢧⡀⠀⠀⠀⠀⠀⠈⣡⡀⠨⠢⠀⠀⠀⠀⠀⠀⠀⠊⡖⣠⠌⢳⠀⠀⠀⠀⠀⠀⣜⠁⣿⠈⢳⠄
⠀⠀⠀⠈⠙⠻⢕⢄⠀⠀⠀⠀⠀⠀⢻⠞⡆⠙⠒⠁⠀⠀⠀⠀⠀⢀⣐⢁⡀⣤⠀⠀⠀⠀⠀⠀⠀⣄⠙⠷⢀⡬⠀⠀⠀⠀⠀⠀⢫⡄⣿⢀⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⡤⠦⢤⡄⠀⠀⠀⠀⠀⠀⠶⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⢀⡀⢐⡂⢀⡀⠀⠀⠀⠀⠀⠀⡠⢔⡒⠤⣀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠲⢄
⠀⠀⠀⡟⠐⠉⡂⣏⠀⠀⠀⠀⠀⠀⠀⣈⡉⢠⠄⠀⠀⠀⠀⠀⠀⠈⢹⡏⢹⡏⠁⠀⠀⠀⠀⠀⢸⠌⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠁⢎⡹⢋⠎⡃
⠀⠀⠀⣱⢬⠬⡜⠣⠀⠀⠀⠀⠀⠀⣤⠥⠀⠰⠤⠀⠀⠀⠀⠀⠀⠘⠋⢹⡏⠙⠃⠀⠀⠀⠀⠀⠈⠪⣀⣃⠤⠚⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⠜



⠀⠀⠀⡜⠌⠖⠩⢣⠀⠀⠀⠀⠀⠀⣀⠤⡤⢠⣄⠀⠀⠀⠀⠀⠀⡆⠀⢞⡍⡱⡽⠀⠀⠀⠀⠀⢰⡫⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠏⠭⢝⢢⡀
⠀⠀⢠⠬⠎⠊⠴⡊⠄⠀⠀⠀⠀⠀⠫⠵⠝⢖⠀⡇⠀⠀⠀⠀⠀⠈⡒⡅⢆⣁⠇⠀⠀⠀⠀⠀⠀⠈⠺⣑⢵⣤⠀⠀⠀⠀⠀⠀⡤⢠⣄⣊⡜⠁
⠀⠀⠈⠒⠀⠁⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠼⠤⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠊⠀⠀⠀⠀⠀⠈⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⠀⣠⡶⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠹⣿⡋⠀⢀⣤⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣤⡶⢷⣄⠈⢻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣁⣴⠟⠙⠷⠀⣹⡇⠀⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⡾⠋⠻⠆⢀⣠⡾⠋⣠⡾⠋⠁⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣴⠟⠙⠷⠀⢀⣴⠟⢉⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⡾⠛⠻⠆⠀⣠⡾⠋⣡⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣾⠋⠀⣾⠛⠷⠀⢀⣴⠟⢋⣴⠾⠋
⠀⠀⠀⠀⠀⣀⣄⡀⠀⢰⣿⣷⠀⢴⣷⠄⢸⣿⣿⡿⠀⠀⠀⠀⢹⣧⡀⠙⢷⣤⡶⠟⣡⡶⠟⠁
⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠙⣿⠀⠘⡟⠀⢸⣿⠏⢰⣾⡆⢀⣶⠛⣉⣿⣦⡀⢉⣤⠾⠋
⠀⠀⠀⠀⢀⡀⠉⠙⢷⣄⣠⣼⣷⣶⣿⣶⣾⣧⣠⠟⠉⢀⡵⠛⠞⠋⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠿⢿⣦⣀⣼⣿⡿⠿⣿⣿⣏⣹⣿⣿⡿⢣⠔⠉⢀⣤⣤
⠀⢠⣤⣤⣄⠀⠀⣿⣿⣿⡀⠀⢸⣿⡟⠉⠈⠉⢠⣴⣿⡶⠿⠿⠟⠁
⠀⠘⠿⠿⠟⠻⢾⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⣀⣿⡟⢻⣿⠤⠴⢾⣿⠇
⢀⣶⣿⣶⣶⣦⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣶⣆
⠈⠻⠿⢟⣋⣁⣨⣿⣿⣿⣙⣿⣿⡟⠉⢹⣿⣧⣠⣿⣿⣇⡀⠉⠛⢿⡿⠏
⠀⠀⠐⢿⠿⠋⢀⣼⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠋⠈⠻⣿⣿⡆
⠀⠀⠀⢠⣾⣿⡿⠁⠀⢈⡿⠻⣿⣿⣿⡿⠿⡟⠉⠻⣦⣀⠀⠈⠉
⠀⠀⠀⠘⠛⠛⠁⢀⣴⣿⡇⣴⣇⢸⣿⡀⠀⢳⡀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠻⢛⣾⣿⣧⠀⢸⣿⡆⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⡄⠀⠀⡠⢀⣀⠀⡀⠀⢦⠹⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣶⠉⠀⠀⣈⣲⡇⢰⣏⣀⣀⣌⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡠⠀⣄⡼⠂⢻⣏⠉⠇⠻⠘⠃⠶⠀⢳⠀⣋⣀⣄⠀⢸⠒⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⣸⣎⢏⠀⠀⠐⢾⡶⠊⠀⣂⣠⠄⡈⠂⠞⠏⢉⣈⠛⣴⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡸⡵⢄⢀⡞⠉⠙⠧⢸⠀⢀⡀⠀⠀⠀⢦⠤⠒⠁⠂⢐⠂⡄⢄⠀⡰⠡⡇⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⡋⠜⣷⠀⠀⠙⠊⠀⠈⠀⠄⠠⠀⠀⠐⠂⠀⠀⣨⣍⣱⠔⠠⠶⠚⠶⠧⠄⢀⣉⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠺⠛⠀⠀⠠⠀⡀⠀⠓⣏⡩⠀⠀⠀⢆⡨⡀⠀⠀⠁⠂⠀⢠⡼⠁⡜⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣊⡰⠼⠢⣀⠘⠃⠀⡐⢺⣀⠄⠀⢀⡀⠀⡤⠀⠐⠒⠃⣀⢰⣁⠦⠀⠛⠦⡞⠂⢘⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠡⠛⢻⢤⣠⠓⣄⠀⠉⢁⣄⠀⠠⢧⠴⠀⠀⠀⠀⡀⠀⠈⠻⠴⠤⠀⠠⠄⠉⠭⣬⣤⡖⠲
⠀⠀⠀⠀⠀⠀⠠⣀⠀⢸⡀⠠⠾⠉⠠⠠⡀⡀⠀⠉⠊⠒⠃⠀⠀⠴⢳⠆⠀⠓⠀⢀⠁⠀⡂⢠⠦⣀⡇⠑⠁
⠀⠀⠀⠀⠀⠀⢳⢬⡤⠴⠶⡴⣂⠀⠐⠞⣦⠄⢀⡀⠀⠔⢀⠀⠀⠈⠁⠀⢀⣸⠞⡅⢄⠙⠶⡾⢴⢹
⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⡶⢄⣷⠖⣀⠏⠀⠂⠈⠁⠰⣉⠧⠔⠀⠂⡗⠲⢠⠘⡒⠓⠘⠀⣤⠑⢫⠿⣄⣺⡰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢲⡇⠀⢩⠺⡋⣷⠃⠀⠀⠀⡀⠐⣤⠠⠅⠝⠙⣧⡰⢶⠤⣔⠢⣀⡎⠀⠘⠥⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⠞⢇⠀⢉⡳⣎⠃⠀⢠⣾⠸⠆⠀⠀⠀⠁⢀⡿⠀⡦⠀⢙⡆⢀⢉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⠏⠀⠠⠟⠛⢠⡧⠁⠠⡕⠞⡹⠃⣰⠀⢀⠠⠆⠑⢁⣀⢴⠚⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠓⠶⣠⣀⣀⣠⡖⠛⡔⢃⢢⡤⠔⠚⠙⣆⠱⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠚⡀⣧⠀⠉⠉⠉⠣⠈⣻⢐⡀⠀⠀⠀⣏⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠀⠁⠀⠀⠀⠀⠴⡩⠄⠍


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠠⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠠⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⠡⠖⠒⠒⠒⠼⠭⠁⠉⠐⠀⢀⠄⠂⠀⠰⠺⠝⠶⠆⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢄⠀⡐⠁⠐⠀⡠⠂⢀⠈⠀⠀⠀⠀⠀⢠⠊⠀⢅⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢈⠂⠀⠀⠔⠀⠀⠀⠐⠲⠢⠄⠔⠖⠒⠆⠀⠢⡀⠀⡠⠒⠒⠂⠂⠂⠂⠂⢀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣱⣗⠦⣙⢤⡀⠀⡸⠄⠀⣀⠀⠀⠀⠀⠠⠀⡀⠆⢠⠁⠀⣀⠀⠀⠀⠀⢄⣀⡠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠪⠀⠀⠀⠑⠚⠂⡆⠐⠂⠀⠠⢨⡍⠁⠀⠀⡇⠀⢸⠀⠀⡀⠠⠄⠩⢅⡁⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡶⠡⠁⠀⠀⠀⠀⠀⠀⡇⠐⠀⢀⡀⠠⠄⠀⠈⠀⡇⠀⢈⠀⠀⠀⠠⡀⠢⠔⠰⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⠞⠔⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠛⠺⠀⠀⠀⠀⠀⠀⡇⢰⢸⠀⠀⠃⠀⡀⡅⠵⢈⠀⠀⠲
⠀⠀⠀⠀⣀⠀⠀⢀⠮⠰⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠣⢒⠭⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⠀⠀⠀⠁⠀⢀⡀⢀⡀⠬
⠀⠀⠀⠀⠐⠁⠢⢮⡒⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠒⠀⠠⠤⠠⠄⠀⠀⠃⢺⢸⠀⠀⢄⡀⠀⠁⠀⠐⠒⣒⠤
⠀⠀⠀⠀⠀⠀⠈⠒⢍⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠠⡠⠂⠈⢸⠀⠀⠀⠀⠀⠈⠉⠉⠩⡉⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠐⠀⠀⠂⠐⠂⠀⠀⠒⠈⠈⠗⠤⣀⡐⠀⠒⠀⣊⢁⡑⠋⠘⢤⣀⠀⠀⢀⢄⠀⡨⠒⢠⠞⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠂⠐⠀⠀⠁⠊⠝⠒⠒⠴⠢⠖⠀⠀⠐⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠿⢷⣦⣄⡀⣠⣴⡾⠟⠛⠛⠛⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⢉⣠⣴⣶⠾⠿⠿⠻⠿⠿⠷⣶⣤⣈⢙⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⣶⠟⠋⠁⠀⢀⣴⡶⣶⣄⠀⠀⠀⠉⢛⣿⠏⢀⣴⠿⠛⠻⣷⣾⠟⠛⢿⣦⡀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢠⣾⠟⠁⠀⠺⠇⠀⢸⡏⠀⠈⣿⠀⠀⠀⠀⢸⡿⠀⢸⣿⠀⠀⠀⢈⡁⠀⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣰⡿⠁⠀⠀⠀⠀⣀⣤⣼⡿⣶⣾⣿⣤⣄⡀⠀⢸⣷⠀⠈⠻⣦⡀⠘⢿⡿⠂⢀⣴⠟⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢰⣿⠁⠀⣀⡀⠰⡾⠛⣉⡀⠀⠀⠀⠀⠈⠙⢿⣆⠈⣿⡆⠀⠀⠙⢿⣦⡀⢀⣴⠟⠁⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣾⡇⠀⠀⠙⢁⣤⣤⣄⠙⠁⠀⠀⠀⠀⣤⡄⢸⣿⠀⠈⢿⣦⡀⠀⠀⠙⢿⡿⠃⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡃⠀⠿⠀⢸⣯⣼⡿⠀⠺⠃⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠙⠻⣶⣤⣤⣄⣠⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⣶⠄⢉⠉⠀⢴⡆⠀⠀⠀⠀⢹⡇⢸⣿⠀⢀⣄⠀⠀⠀⣸⡟⢉⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⣧⠀⠀⠀⠀⢸⣷⠀⣀⠀⠀⣀⡀⠀⢸⣇⢸⣿⠀⠈⠉⠀⠀⢀⣿⠇⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⣧⠀⠀⠀⠀⠛⠻⣿⠀⠀⣿⡇⠀⣸⡿⠛⠃⠀⠀⠺⠇⢀⣾⠏⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠻⣷⡀⠀⠻⠂⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⢴⡆⠀⠀⣠⣾⠋⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠈⠻⣦⣄⠀⠀⢻⡇⠀⣿⡇⠀⣿⠃⠀⠀⢀⣠⣾⠟⢁⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡈⠛⠿⣶⣾⣧⣀⣿⣇⣰⣿⣤⣴⡾⠟⠋⣠⣴⣿⠋⠀⢙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣈⣉⠉⠙⠛⠉⢉⣉⣡⣤⣶⠿⠛⠉⠻⣷⣴⡿⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠘⢿⣤⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⣄⠀⢠⣤⠄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⡠⠄⡂⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⡔⡂⠤⡀
⠀⠀⠀⣨⡍⠉⠉⢷⡱⠀⠀⠀⠀⠀⠀⣿⠏⠈⠉⢹⢣⠀⠀⠀⠀⠀⠀⡋⠀⢞⠁⠂⡸⠀⠀⠀⠀⠀⠀⡎⠰⠂⠉⢄⠹⠀⠀⠀⠀⠀⠀⡜⠓⠣⠕⠒⡼
⠀⠀⠀⢤⢣⡄⡬⠹⠁⠀⠀⠀⠀⠀⠀⣟⣄⢀⢤⣼⡇⠀⠀⠀⠀⠀⠀⢳⠐⢧⡔⠆⡸⠀⠀⠀⠀⠀⠀⢳⡈⠠⠠⢂⡽⠀⠀⠀⠀⠀⠀⠱⡖⣎⡳⠔⡱
⠀⠀⠀⠑⠊⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉


⠀⠀⠀⠀⢄⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⣹⢋⠖⢮⢻⡆⠀⠀⠀⠀⠀⠀⢶⡊⡈⡙⡗⠃⠀⠀⠀⠀⠀⠀⣰⡎⠉⠉⠻⡗⠀⠀⠀⠀⠀⠀⠀⠙⢢⢠⠋⠀⠀⠀⠀⠀⠀⠀⡐⠉⠴⣲⡆⠣
⠀⠀⠀⠞⣌⣲⣊⡼⠁⠀⠀⠀⠀⠀⠀⢤⡳⠤⣴⠛⠽⠀⠀⠀⠀⠀⠀⢈⣅⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⢶⣀⣇⣸⠆⠰⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⣠⠁
⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁


⠀⠀⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠌⡂⡃⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⡈⡷⠾⣆⠀⠀⠀⠀⠀⠀⠉⣥⡄⠠⠧⠀⠀⠀⠀⠀⠀⠀⢸⢡⡖⣲⡈⢳⠀⠀⠀⠀⠀⠀⢠⠋⢰⡆⠙⣧
⠀⠀⠀⠀⠉⠺⢯⡢⡄⠀⠀⠀⠀⠀⠀⢻⡾⣧⠘⠛⠋⠀⠀⠀⠀⠀⠀⢀⡐⢁⡀⣤⢄⠀⠀⠀⠀⠀⠀⢸⡈⠻⠗⢀⡼⠀⠀⠀⠀⠀⠀⠘⣅⠠⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠈⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠊⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋


⠀⠀⠀⠀⢄⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⠀⠀⣰⢎⠅⢭⢹⠆⠀⠀⠀⠀⠀⠀⠁⠰⠒⢀⡁⡀⠀⠀⠀⠀⠀⠀⠚⠶⠚⠛⣶⠗⠀⠀⠀⠀⠀⠀⠚⠛⠛⡷⠉⢻⡄⠀⠀⠀⠀⠀⣼⣫⠿⣾⣾⣽⡄
⠀⠀⠀⠼⡐⠆⢔⣼⠃⠀⠀⠀⠀⠀⠀⡈⠒⠂⢘⡁⡀⠀⠀⠀⠀⠀⠀⢤⡶⣶⣴⢿⣦⠀⠀⠀⠀⠀⠀⢶⣳⣼⡇⢀⣸⠇⠀⠀⠀⠀⠀⢿⡪⡟⣛⢛⣿⠇
⠀⠀⠀⠒⠉⠋⠙⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁


⠀⠀⠀⠀⡀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣌⡐⡙⡑⠊⡆⠀⠀⠀⠀⠀⠀⣤⡒⣆⠒⠦⡀⠀⠀⠀⠀⠀⠀⢇⠀⣣⠖⡜⡾⠀⠀⠀⠀⠀⠀⢮⣞⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠒⣌⢣
⠀⠀⠐⡦⡒⣘⢐⢋⣰⠀⠀⠀⠀⠀⠀⠃⠜⠪⠽⣒⡹⠀⠀⠀⠀⠀⠀⢠⠛⢄⡢⢅⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⢵⢦⠀⠀⠀⠀⠀⠀⡠⢐⣶⣶⡥⠎
⠀⠀⠀⠑⠲⠤⠜⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠊⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠶⠟⠳⢶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠉⠁⠀⣀⣠⣄⣀⠀⠉⠉⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣶⠛⠛⠉⠁⠉⠙⠛⠻⣶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⢠⢾⣅⣠⣴⣷⣤⣀⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⡄⠀⠀⠀⠀⢀⠀⢠⣿⣿⣶⣿⣿⣙⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⢻⣄⠀⠀⠀⢸⠷⢿⣹⣿⡋⣻⣿⣿⣿⡷⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠙⠳⣦⡴⠀⢀⠈⣿⣿⡿⣿⣿⣴⣟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⢀⣀⠈⠻⡅⠉⠙⣿⠋⠁⠽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣉⠻⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⡙⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣦⣈⠻⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣷⣤⡉⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⢀⣶⣦⡈⠛⢿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⣰⣿⣿⣿⣿⣷⣤⡉⠻⢿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⠻⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠀⠀⠙⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢃⡐⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⢃⣼⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⣰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⠟⠁⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⣠⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣙⠏⣰⣿⣿⠋⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣾⣿⠏⠀⠀⢀⣶⣶⣦⠀⠀⣀⣼⣿⣷⣿⣿⣶⣿⣧⣀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⣦⣾⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⣰⣿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢙⣛⣛⣻⣢⣾⣿⡿⢿⣿⣿⣿⣿⣧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠻⠿⠋⣰⣿⡿⠋⠀⠀⠀⠀⠀⣀⣄⡀⢀⣿⣿⣿⣻⣿⣿⣿⣟⣟⡀⢀⣹⣿⣿⣿⣿⣦⣤⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⠏⠀⠿⢷⣾⣿⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢿⣿⣿⣿⣷⣤⣼⣿⣿⡟⠁⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡿⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠙⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⢀⣹⣿⠛⠋⠉⠹⣿⡄⠀⠀⠀⠀⠙⠿⠿⠋
⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠈⢿⣿⡿⠁
⠀⠀⠀⠀⠈⠉