⠀⠀⠀⠀⠌⡸⢀⠅⠀⢐⠁⡂⠀⠀⢕⠀⠌⡆⠀⠀⠀⠀⡂⠁⠀⠌⠀⠀⠀⠠⠐⡀⠀⠨⠀⡃⠀⠀⠀⠆⠀⡊⠄⠀⠀⠀⠀⠡⡀⠀⢅⠀⠀⠀⠈⠄⠀⠅⢂⠀
⠀⠀⠀⠀⠁⡎⢰⠁⠀⢐⠀⡅⠀⠠⢑⠀⠌⡆⠀⠀⠀⢀⠪⠀⠠⠁⠀⠀⠀⢘⠀⡆⠀⡂⠅⢰⠀⠀⠀⠡⠀⡅⢃⠀⠀⠀⠀⠀⠢⠀⠈⠆⠀⠀⠀⠈⡀⠈⡂⡂
⠀⠀⠀⠀⢨⠂⡗⠀⠀⠠⠐⠄⠀⠐⠈⠄⠨⡂⠀⠀⠀⠀⠕⠀⢐⠀⠀⠀⠀⢀⡆⠅⠀⡂⢅⢸⠀⠀⠀⢸⠀⠆⠨⠀⠀⠀⠀⠀⠀⢅⠀⢘⠀⠀⠀⠀⠠⠀⠐⠌
⠀⠀⠀⠅⢰⢸⢘⠀⠀⠨⡀⠇⠀⠀⡁⡅⠨⡃⠀⠀⠀⠈⡪⠀⢜⠀⠀⠀⠀⢐⢄⠣⠀⠂⢅⠰⠀⠀⠀⢐⠀⢕⠀⡃⠀⠀⠀⠀⠀⠐⠄⠀⢅⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠨⠀⢌⢎⢸⠀⠀⠨⡂⡇⠀⠀⠅⢅⠈⣪⠀⠀⠀⠀⡪⡀⢕⠄⠀⠀⠀⠐⡈⡎⡀⡑⢔⠈⡂⠀⠀⠀⡆⡅⡂⠨⠀⠀⠀⠀⠀⠀⢱⠀⢐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡊⠀⡘⡮⡐⡢⠀⠀⠇⢆⠀⠀⢹⢐⠀⢞⡀⠀⠀⠀⢼⠄⢸⢀⠀⠀⠀⠀⡂⣱⠠⠢⡑⡁⡇⠀⠀⠐⡄⠆⠐⡈⡂⠀⠀⠀⠀⠀⠀⡆⠀⢅⠀⠀⠀⠐⠀⠄
⠀⠨⠀⠀⡪⡪⡂⢇⠨⠠⢹⢸⠀⠄⠐⡄⠅⢢⢃⢂⠀⠀⢘⡇⢸⢀⠀⠀⠀⠀⠇⠨⡆⢱⠀⠆⠅⠀⠀⠀⡆⠁⠀⡂⠸⠀⠀⠀⠀⠀⠀⢨⠀⢰⠀⠀⠀⠀⠁⢂
⠀⢌⠀⠐⡘⡆⡗⡕⡌⡐⠨⡧⣇⢂⠀⢣⢑⠈⢮⡂⠂⠄⠀⡯⡘⣖⠄⠀⠀⠀⢱⠈⢮⢸⠀⡇⠁⠀⠀⠀⡆⠀⠀⢜⠀⢇⠀⠀⠀⠀⠀⠀⡃⠐⡄⠀⠀⠀⠈⡐
⠀⡂⠀⠠⡃⠟⣜⡜⡜⣄⢅⣱⠸⡱⡠⢘⢇⢂⠑⣧⠡⠡⢀⢃⢣⠃⢗⡀⠀⠀⠨⡠⠘⣎⠀⡅⠀⠀⠀⠐⡄⠀⠀⢕⢡⢘⠀⠀⠀⠀⠀⠀⢘⠀⢂⠀⠀⠀⠀⡐
⢐⠀⠀⡪⢂⢹⢸⣿⣾⢾⣾⣶⣕⢔⢈⢑⠑⠌⠆⡕⠕⡌⡐⡘⡄⡏⡌⢧⠀⠀⠀⡢⠁⡇⠀⡅⠀⠀⠀⠐⡄⠀⠀⡇⢸⡆⡅⠀⠀⠀⠀⠀⠨⡂⠐⠀⠀⠀⠀⠄
⠌⠀⠰⡍⢂⠸⢸⢉⢧⠨⠸⣿⣿⣿⡐⠠⡈⠨⢐⠠⢁⠢⠨⢸⡾⡿⣾⣾⣶⣠⣀⣌⣂⡇⠀⡅⠀⠀⠀⢐⠀⠀⠐⡌⡸⠘⡌⡂⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠨
⠅⢠⡃⡇⢂⠕⡱⢁⠹⡀⠀⢻⣿⣿⡇⠀⠀⠀⠐⠈⠄⠈⠪⡉⡂⠁⡐⡸⣿⣿⣿⣿⣿⡃⠀⡂⠀⠀⠀⠰⠀⠀⠨⡂⠆⠀⢡⠱⠀⠀⠀⠀⠀⠸⡀⠀⠀⠠⠀⠀
⠀⡆⣳⠈⢄⢣⢃⠂⢅⢇⠣⢀⢙⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⢻⣿⡿⢿⣿⠀⠀⠄⠀⠀⠂⠨⠀⠀⡌⢐⠍⡂⠀⢃⠣⠀⠀⠀⠀⠐⢅⠀⠀⠐⠄⠀
⡸⢨⢸⠀⡕⡕⢐⢈⢆⢿⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢄⡀⡀⠈⠑⣋⢻⠀⠀⡁⠀⠠⠁⡁⠀⠀⠅⣸⢂⠈⢆⠈⢪⢀⠀⠀⠀⠈⢨⠀⠀⠀⢅⠀
⠭⠰⡸⠠⡣⢁⠂⢆⡊⠎⡂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠁⠈⠀⡇⠀⠀⡂⠀⡐⢨⠀⠀⢘⠠⡪⡂⡅⠈⢆⠌⡢⢀⠀⠀⠀⠂⡣⠀⠀⠢⠀
⠇⢸⢸⡘⠌⡐⡸⠰⡇⡇⢪⠀⠀⡸⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠄⠀⡂⡂⠀⠀⠅⡜⡗⠄⢌⢂⠈⠪⢌⢂⠄⠀⠀⠐⡘⠄⠀⠨⠀
⡑⢨⠎⡂⠅⡢⡱⠁⠇⡎⠸⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠨⡀⠠⢡⠂⠀⠈⣰⡇⠅⡇⠌⡢⢂⠀⠑⢌⢂⢂⠀⠀⡂⢣⠀⠀⠁
⢌⠊⡐⠄⡱⡑⠨⠨⡨⡊⠌⡚⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂⠀⠨⠂⢸⠐⠀⠀⢐⢼⢕⠨⢸⡐⡈⢢⠑⡡⠠⡑⢔⠠⡀⠌⠌⢆⠀⠅
⠌⠀⢐⢨⠪⠈⠌⢌⢜⢐⢐⠠⡏⡣⡄⠀⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠨⡀⡆⡑⠀⠨⡐⣿⣷⣌⢄⠱⡰⠡⠱⣐⡑⢄⢑⢂⠂⠅⠌⢢⠀⢘
⠀⠀⡰⡑⡁⠅⡡⢸⢸⠠⢐⠠⡇⡂⠌⠣⡀⣑⣟⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡐⠠⡃⢆⠐⡅⣓⡿⠛⠉⠀⠁⡀⠠⠐⠀⠄⢉⠒⠰⣑⠡⢁⠂⢕⢸
⠀⡐⢜⢀⠂⠅⡂⢕⡕⢈⠄⢢⡃⢂⠡⠡⢨⡂⡜⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠠⠀⠨⢸⢐⠅⡸⠌⠂⢀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠂⠙⢔⠈⠌⣾
⢐⢜⠌⠔⠨⢐⠸⢐⡇⠂⠌⣜⢐⠐⠨⢐⠅⠀⢨⠲⡀⠀⠀⡀⣠⠠⣢⣶⣿⣿⣿⢟⠌⠄⡪⢸⠘⢄⠎⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⡡⢸
⢪⡪⡃⠅⠡⢢⠃⡕⡅⠅⢱⡘⠠⠨⡨⠂⠀⢀⠇⡈⡞⢩⣿⣿⡏⡂⢜⠎⣻⡿⢋⣺⠡⢂⠪⢸⢨⡊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠐⢼
⢱⣹⠠⠡⢁⠎⡌⡸⠠⢁⢵⠡⠡⠡⠁⠀⢠⢃⢌⠎⠩⠘⢿⡟⣠⠂⡳⠁⣎⢗⣸⢺⠨⠠⢑⢸⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⢸
⡪⣺⠠⠑⢌⢢⠁⡎⠌⢰⠱⢈⠐⢕⡀⠀⠹⣠⠎⠀⠀⡸⠉⠩⣿⣷⡃⠐⣜⢨⠃⠌⡎⠄⢅⠃⠁⠀⢀⠀⠄⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢘⢸
⢮⣓⠨⢈⢎⢂⠂⡕⡈⣎⠊⢄⠡⡑⢇⠀⢈⡎⠀⠀⢠⠁⠀⢀⠏⢙⢿⣾⣮⡐⢣⢁⠧⠊⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⢯
⢷⡑⡨⡘⡔⠠⡁⡇⡸⡐⠨⢐⢸⠨⠘⡄⡐⠀⠀⢀⠂⠀⠀⡞⠀⠀⡧⣿⣷⢱⡐⠅⠁⠠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠁⠄⡣
⣟⠆⢢⢣⢁⢂⠢⡅⡇⠂⠅⡢⢣⠡⢁⢣⠀⠀⠀⡂⠀⠀⠐⠅⠀⠀⣇⣿⣿⡇⠇⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠠⠁⡇
⣯⢃⠇⡎⠠⢂⢪⠪⠂⠅⢅⠎⡎⠐⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢟⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠠⠡⡃
⣿⣘⢸⠠⢁⠂⣇⠃⠅⡁⢎⢼⠀⠅⠅⡱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠅⠡⢱⠀

⠀⠀⠀⠀⢀⡠⠤⠔⢲⢶⡖⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡚⠁⢀⠀⠀⢄⢻⣿⠀⠀⠀⡙⣷⢤⡀⠀⠀⠀⠀⠀⠀
⠀⡜⢱⣇⠀⣧⢣⡀⠀⡀⢻⡇⠀⡄⢰⣿⣷⡌⣢⡀⠀⠀⠀⠀
⠸⡇⡎⡿⣆⠹⣷⡹⣄⠙⣽⣿⢸⣧⣼⣿⣿⣿⣶⣼⣆⠀⠀⠀
⣷⡇⣷⡇⢹⢳⡽⣿⡽⣷⡜⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⣿⡇⡿⣿⠀⠣⠹⣾⣿⣮⠿⣞⣿⢸⣿⣛⢿⣿⡟⠯⠉⠙⠛⠓
⣿⣇⣷⠙⡇⠀⠁⠀⠉⣽⣷⣾⢿⢸⣿⠀⢸⣿⢿⠀⠀⠀⠀⠀
⡟⢿⣿⣷⣾⣆⠀⠀⠘⠘⠿⠛⢸⣼⣿⢖⣼⣿⠘⡆⠀⠀⠀⠀
⠃⢸⣿⣿⡘⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠇⠀⠀⠀⠀
⠀⢸⡿⣿⣇⠀⠈⠀⠤⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⢸⠀⠀⠀⠀
⠀⠈⡇⣿⣿⣷⣤⣀⠀⣀⠔⠋⣿⣿⣿⣿⣿⡟⣿⡞⡄⠀⠀⠀
⠀⠀⢿⢸⣿⣿⣿⣿⣿⡇⠀⢠⣿⡏⢿⣿⣿⡇⢸⣇⠇⠀⠀⠀
⠀⠀⢸⡏⣿⣿⣿⠟⠋⣀⠠⣾⣿⠡⠀⢉⢟⠷⢼⣿⣿⠀⠀⠀
⠀⠀⠈⣷⡏⡱⠁⠀⠊⠀⠀⣿⣏⣀⡠⢣⠃⠀⠀⢹⣿⡄⠀⠀
⠀⠀⠘⢼⣿⠀⢠⣤⣀⠉⣹⡿⠀⠁⠀⡸⠀⠀⠀⠈⣿⡇⠀