Literacy Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠙⠋⠉⠙⠉⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⢀⠆⠐⠉⠁⠂⠉⠈⠉⠉⠢⠄⠀⢤⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣄⢀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢄⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢣⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⣖⣂⣀⣀⠤⣀⣀⣐⣢⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⠉⢉⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠚⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠈⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⣀⡆⠀⠀⠀⠀⠀⠀⣇⣀⣘⡃⠀⠀⠀⠀⠀⠔⢘⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠋⠉⠉⠉⠙⠙⠛⠛⠛⠛⠛⠛⡇⠀⠀⠀⠀⢀⣉⡩⠂⠀⠀⠀⠀⠀⡇⠀⠀⡂⠀⠀⠀⠀⠀⡎⣉⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠖⠖⠒⠒⠒⠂⠀⡤⠤⠀⠀⠀⠠⠵⠦⢄⡀⠀⠰⡤⠝⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠐⠭⢴⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡯⠂⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⣽⠑⠐⠁⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠒⢹⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⡟⠓⡗⠒⠒⠒⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠒⣫⡿⠒⠲⠂⠀⠤⠄⠤⠀⣀⡇⠀⠰⣇⡀⠠⠄⠤⠀⠀⠒⠂⢸⢿⢿⣿⣿⠟⠋⠉⠛⠊⠉⠛⢿
⣇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠋⢰⢆⠳⡆⠀⠀⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠂⣿⠁
⡟⠋⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⢺⠀⠈⡌⢧⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢞⠃⠀⠀⣿⡆
⣇⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠆⠀⠰⠘⡄⡇⠀⠈⡄⠀⣀⢀⣀⣠⣤⡤⠒⡎⠉⠀⣇⢻⡈⠀⢠⢡⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠢⣀⠛⠈⣣⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣾⣤⣀⣠⣅⣈⣁⢔⣡⣿⣿⣿⣧⣤⣤⣤⣤⣤⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠐⠒⢢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠒⠀⠀⠀⢀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠠⠀⠀⠈⠀⠀⠈⠁⢀⠀⠁⡐⠄⠀⠁⠀⠀⠀⠀⠁⡠⠌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠴⣱⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⠀⠈⠀⠈⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡴⢋⢖⡵⣱
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠄⠐⠀⢄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⢊⠔⡡⣪⡞⠁
⠀⠀⠀⢂⠤⠠⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⡠⡫⢊⡼⠋
⠀⠀⠀⣉⡋⣓⣒⣒⣒⠤⠭⠓⡢⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣌⠜⣡⠊⣚⡴⠋
⠀⠀⠀⠺⣆⠻⠿⠿⠿⠟⡻⠿⡶⣷⣧⣬⣥⣶⣄⡀⠀⢄⠄⣀⡠⠔⣒⣋⣉⣡⣤⣤⣤⣤⣤⡤⠤⣭⣉⣉⣐⡼⢃⢜⠕⡵⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠙⠛⠻⠿⢿⠲⢖⢚⣷⡾⠿⠿⠿⠾⠽⠧⠼⠭⣋⣒⠋⠩⡵⢖⣂⣈⠔⡡⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠴⢩⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠙⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠻⠯⠭⠁⠀⠀⠄⠬⠍⠛⣿⣿⣇⡀⠀⠠⠄⠀⠀⠀⠠⠤⠐⠒⠃⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⢿
⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴

⠀⠀⠀⠀⢠⠄⠀⢄⣴⢲⡀⢀⡰⠒⢦⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠚⠄⠠⠀⠀⠒⠄⠤⠄⠀⢠⡄⠀⠀⢀⡀⡀⠀⢀⢀⣠⢤⡄
⠀⠀⢠⡄⢸⠀⠀⢸⢸⢸⡇⠀⢣⠀⢸⢸⡖⠙⣆⠀⠉⠀⢠⣠⠃⠀⠁⠀⠀⠀⠀⠀⡈⠀⠀⢀⠠⢂⡀⠀⠈⠀⠀⡠⠔⠊⠉⠀⠀⠀⠁⡈⢉⣠⣫⡄
⠀⠀⡌⠀⢸⠀⠀⢸⢸⢸⡇⠀⢸⠀⢸⢸⡷⡀⠘⣆⠀⢰⠸⠘⢀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡐⠀⠐⠈⠀⠀⠾⡀⠀⠀⠀⠀⠀⠀⠢⠐⠈⢉⡴⠁
⠀⠀⠴⠇⢸⠀⠀⢸⢸⢸⡇⠀⢸⠀⢸⢸⡇⠱⡄⠘⢆⠈⠁⠀⠂⠀⠀⢀⣤⠤⢶⡀⠀⠀⠀⠐⠀⠀⠀⠘⠀⢰⠀⠱⡀⠁⠀⠀⠀⠀⠀⠀⠐⡈⠉⠹⠂
⠀⠀⠀⢀⣸⡀⠀⠼⠼⠬⠤⠤⠼⠤⠼⠼⠷⠶⠚⠒⠚⠒⠲⠀⠀⠀⠀⠀⣠⠀⠈⢏⠂⠄⡀⠀⠀⡔⠈⠉⠲⠀⠣⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠸⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠂⢀⡀⠀⡄⡬⠀⡐⠀⠀⠑⣄⠀⠁⣀⠀⠠⠀⠄⠂⠁
⠀⠀⢀⡀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⡀⣛⡋⠉⠀⠀⠀⠀⠧⠃⡜⡠⠂⠏⠀⠀⠟⠘⠁⠀⠈⠁⠀⠈⠓⢄⣄⢀⠠⡀⠠
⠀⠀⠀⠀⠈⠀⡀⠀⠈⡺⠃⠑⢄⠀⠀⠀⠀⣀⠀⠀⣀⡤⠤⠤⠤⣀⠀⠀⠀⠀⠈⢁⠔⠂⠐⠒⠈⠐⢄⣀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠈⠁⠀⢠⠖⠒⣄
⠀⠀⠈⢄⠀⡠⠀⠀⠀⠀⠢⣀⠀⠉⠢⡀⠈⢁⠄⠈⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠁⢀⠄⠁⢀⠤⢀⡆⢀⡀⠘⢦⠆⢸
⠀⠀⠀⠀⢉⡠⠂⠉⠉⠒⠤⡈⠑⢄⡠⠊⢠⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡆⢀⡟⠀⠒⠊⠑⠒⠲⡄⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡸
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⡇⠀⠀⠀⢰⣀⠠⠄⠐⠈⠀⠀⡇⢠⠀⢀⠀⠀⠀⠀⠀⠈⢒⠀⡜⠀⠀⠄⠀⠠⠈⠆⠀⠀⠐⠆⠠
⠀⠀⠀⢣⠕⠠⢀⠀⠀⠀⠀⠀⠀⢀⠘⡂⢃⠀⢀⡔⠀⠀⡀⠀⠀⠀⠴⠀⡇⠈⡀⠀⠀⠀⠀⠰⠀⠀⠎⡜⠁⠀⢀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠀⠄⡈⠂⢌⡐⠤⠀⠀⠔⡡⣎⠀⠈⡄⠣⢤⣀⣀⣀⡀⠤⠀⡀⠀⠐⠄⠈⠢⣄⣀⡀⣀⣠⣐⠐⠀⠈⠢⠊⠀⢘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢀⠀⡀⠓⠢⠁⠠⡄⠓⠾⠒⠡⠂⠡⠀⠀⡐⠘⠉⠀⠀⠀⠀⠈⠑⠩⡢⠤⡪⠒⠉⠀⠀⠀⠀⠀⠈⡗⢄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢰⠀⠀⠁⠒⠤⢉⢁⠀⠂⢀⠀⠂⠀⠈⡠⠛⢒⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⣠⢀⢇⠀⠑⡄⠀⠀⠀⠀⠀⠀⠈⠀⠂⡄⠀⠐⡀⡀
⠀⠀⠣⣀⣤⠀⠀⠄⣀⠄⠂⠀⠀⡀⠀⢞⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠞⠳⠀⠓⠠⠤⠠⠀⢀⠀⠀⠈⠀⠠⠀⠁
⠀⠀⠔⠀⠙⠦⠄⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⣀⠐⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡠⠀⠀⠀⠠⠀⠀⠁⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠁⠐⠀⠈⢉⣤⠀⢇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠠⠀⠀⠀⠀⡀⠄⠂⠉⠀⠈⡂
⠀⠀⢠⠀⠠⠀⠀⠰⠀⠈⠂⠀⠀⠀⠀⠄⣠⣋⠄⠀⢀⠀⢀⠀⠉⠐⠢⢥⣀⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠀⠀⠀⢀⠰⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀⠀⣄⡀⠀⠀⠀⡀⠄⠀⣀⣀⠠⠤⠤⣄⠀⠀⠀⠠⢀⡀⠀⠀⠘⠀⠐⠄⠂⠃⠐⠃⠀⠂⣥⣂⡄
⠀⠀⠀⠀⡀⠢⠀⠀⠉⠀⠁⠂⠀⠐⠀⣀⠀⠀⠈⠀⠈⠀⢁⠀⠀⠋⢠⢞⠉⡁⠀⠀⠀⠐⠈⢣⡀⠀⠀⠡⠜⠂⠀⠀⢀⠀⠐⠀⠔⠀⠀⠈⠢⡘⣻⡗
⠀⠀⠀⠀⠀⠒⠀⢀⠄⠂⠉⠑⠢⡀⢸⣀⡄⢀⠄⠀⠈⠈⠢⡉⠁⠀⠸⠘⡀⠡⣀⠠⠤⠐⠈⠀⠑⡄⠀⠀⠀⠒⡀⠀⠤⠄⠔⠀⠀⠀⠀⠀⠀⠐⠌
⠀⠀⡒⠂⡄⢀⠺⠄⠤⣀⠀⠀⠀⠙⠄⢀⠔⠁⠀⠀⠀⠀⠀⠈⣂⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣄⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠉⠈⢀⣈⠉⠁⠐⠀⠙⠢⣀⠀⠈⡇⠀⠀⠀⡀⠤⠒⠈⠁⠉⢢⠀⠈⡆⠡⠀⢀⡀⠀⠠⠤⠄⠒⡇⠀⠈⢆⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢀⣀⠄⠠⡆
⠀⠀⠀⢠⠔⠉⠀⠀⠀⠈⠐⠠⠈⢣⠀⠇⣠⠶⣛⣉⡀⠀⠀⠀⠀⠠⡂⠀⠘⣤⠁⠀⠀⠀⠀⣀⣀⡀⠇⠀⠈⠌⢆⠀⠀⠀⠀⠀⠀⠂⡠⠒⢁⡠⠄⠐⠁
⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⡈⢻⡏⠙⣏⣉⣁⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠁⠈⠉⠉⠉⠀⠀⢔⢡⠈⡆⠈⠈⢆⢀⡠⠒⢂⡉⠈⣣⢔⠥⡄⣶⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠐⠒⠊⠀⠀⠈⢄⠥⠊⠁⠀⠀⠠⠤⠞⠾⠗⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢧⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠰⡈
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠈⢀⢤⠞⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⠘⣇⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠃⡰⣢⠞
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⣦⣄⡀⠀⢀⡀⠀⣵⠀⠀⠀⣼⠃⠀⠸⣦⠀⠀⠈⣀⠀⠀⠀⣠⠄⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⡒⠶⠤⣤⣤⡼⠆⠙⠻⢥⡈⠂⣈⢣⣀⡼⠃⠀⠀⠀⠈⠛⠒⠋⠹⠤⠖⠋⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⡄⠁⠀⠀⢾⢛⣷⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣶⠀⠀⣠⠄⠉⣿⠁⠀⠀⠀⢸⣿⡅⠀⣤⢠⡟⠁⠀⢰⡄⢠⠀⠀⠀⠉⣽⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣶⠚⠁⠀⠀⠀⣿⠀⠀⣽⠀⠀⣿⠀⢿⣛⠁⠈⠁⠋⢰⣿⡘⣧⣤⠀⠈⢿⠟⠀⠀⠀⠀⠀⠉⠉⣉⡭⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⡷⠀⠀⠀⠀⠿⠶⠀⣿⠀⠀⠀⠀⢻⣋⡀⠀⠀⠀⣿⠛⡇⠈⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠺⣍⡀
⠀⠀⠀⠀⠀⠀⠒⠛⠯⢥⡀⠀⠀⠀⠀⠀⠀⠺⢷⣦⣀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠂⠀⠀⠀⠀⣤⡤⠴⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢀⣴⣶⣤⣄⡀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⢀⣀⣤⣶⣶⣄⢙⣳⣤⣄
⠀⠀⠀⠀⣀⣤⠶⣯⠥⠤⠤⠰⠿⢿⣿⣿⣿⣿⣿⣶⣤⣀⡙⢿⣦⡀⠀⠀⠀⠀⠀⣰⡿⠋⣀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣽⣟⣻⢿⣿⣿⣿⣷⣽⣿⣄⠀⠀⢀⣾⣯⣶⣿⣿⣿⡿⢿⣛⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣯⣟⠿⣿⣿⣿⡄⢀⣾⣿⣿⡿⣟⣯⣷⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣽⣛⡾⢿⣿⣷⣸⣿⣿⠿⣛⣯⣽⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣙⣛⣛⣻⣿⡏⠛⣿⣿⣛⣛⣛⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠘⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠉⠉⠉⠉⠉⠉⠙⠓⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠔⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠀⡴⢃⠀⠈⠒⠊⠁⢠⠀⠀⠑⠂⠺⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠌⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠈⠉⠢⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⠉⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠰⠀⢙⠊⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡘⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⡀⠀⣀⠤⢄⡀⠀⠀⢀⣀⠄⣀⠀⠀⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡠⠞⠙⠁⠒⠒⠒⠂⠤⠋⠀⠀⠉⠉⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠙⠢⢄⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡇⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠬⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⣠⣄⣀⣀⣀⡀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⣀⣀⣀⣤⡄
⠀⠀⠀⠐⠓⠚⠛⠛⠶⠿⠿⠿⢿⣷⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⠿⠿⠿⠶⠭⠉⠐⠚⠆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⡟⠻⠉⠈⠹⠻⡟⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡀⢼⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡧⢀
⡰⠋⠀⠚⠉⢀⣠⠏⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠹⣄⡀⠉⠓⠀⠙
⡇⠀⠀⠀⠀⠈⢀⣠⣤⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣀⡀
⠸⡄⠀⠀⠀⠀⠈⣠⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡄⠁⠀⠀⠀⠀⢠
⠀⠈⠢⢤⠤⠤⠤⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠤⠤⡤⠔⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠀⠀⠄⠤⠤⠀⢀⣀⡀⠀⠀⠀⠀⡧⠠⠤⠤⠠⠴⠀⠀⠀⠀⢀⣀⣀⠀⠤⠄⠠⠄⠒⠀⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢆⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠈⢣⡈⢇⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣿⣿⡿⠀⠀⢳⡘⡏⠉⠒⢲⣶⣶⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⡾⠛⠉⢉⣓⣦⡀⠀⢧⢱⠀⠀⠘⠛⠻⣿⣦⠶⠖⠛⠛⠛⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠉⠲⣼⣼⡄⣀⡤⠒⠛⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠘⣎⡱⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⣠⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⠀⠀⠀⠀⢹⡁⢀⡀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢰⠇⠀⢀⣀⠈⠉⢹⠉⠀⠀⠀⢸⡀⠀⠀⣞⢻⣇⠀⠀⠀⢸⣧⣛⣿⠀⠀⠀⣀⣀⣸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⣿⣸⡦⣸⡏⠙⠲⠾⣴⣾⡿⠛⠙⣏⠉⠉⢻⣿⡟⠛⢶⣶⣾⣿⣿⡿⠛⠉⠉⠉⢉⡟⠉⠉⠙⠻⣿⡦⠀⣀⣠⡄⣀⠘⣧
⠀⠀⠀⣿⡉⠑⠒⠪⢍⣒⠒⠤⠤⣉⠓⠢⢜⣆⠀⠀⠉⠀⠀⢈⡿⠉⠉⣿⠀⠀⠀⠀⣠⠞⠀⠀⢀⣀⠤⠟⠛⣉⣡⠴⠛⣿⢴⣿⡀
⠀⠀⣟⠛⠧⣄⣀⠀⠀⠀⠉⠓⠢⢄⡉⠓⠤⡉⠳⣦⣄⣀⠤⣾⠇⠀⠀⠹⣗⠒⠒⠋⠁⣠⠴⢚⡩⠔⠒⢋⣩⠤⠒⢚⣩⠵⠚⢹⡇
⠀⢀⣿⠤⠶⠦⣌⠙⠲⠦⣄⡀⠀⠀⠉⠓⠄⡈⠢⡈⠳⣄⠴⠋⠀⠀⠀⠀⠘⠢⡠⠖⢉⠴⠊⣡⡴⠖⠋⢁⣠⠴⠚⠉⣠⠴⠶⠼⢧⡀
⢰⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠑⠲⢤⣀⠀⠈⠑⢼⣦⠈⢣⡀⠀⠀⠀⠀⣠⢞⡥⠊⣀⠔⠋⣁⣤⠶⠚⠉⠀⠀⠀⠸⡇⠀⠀⠀⠀⠉⡇
⣼⠓⠒⠒⠒⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣉⠣⡀⠹⡄⠀⢀⡼⠗⣁⠔⣪⡈⠳⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⡷⠒⠒⠒⠊⢳
⣹⢦⣀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⢷⣛⣒⣛⣰⣾⠶⠛⠁⠹⣤⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡠⢾
⢧⠀⠈⠉⠙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡉⡿⠋⠉⠀⢠
⠈⠳⢄⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠒⠒⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄⠀⢸⣿⠿⠛⢧⣀⣀⡠⠋
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠒⠒⠒⢻⠀⠀⠀⠀⣿⣄⠀⠀⠸⣿⡿⣷⡀⠸⣿⣴⣶⠄⠈⢹⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣷⡄⠀⢿⡿⠿⠁⠀⠈⠉⠁⠀⠀⢸⡇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠚⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠇
⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠒⠚⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣀⣀⡇⠀⠀⠀⠀⠈⡇⠀⢀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⣠⠴⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢰⡖⢯⢍⣉⣉⡁⠀⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢀⣀⠨⣧⠀⠑⢌⠓⠤⡈⠉⠑⠂⠄⡀⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠔⢊⣀⠀⠤⠵⠣⡀⠀⠑⢄⠈⠑⢄⡀⠀⠈⠑⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡠⢚⠥⠊⠁⠀⠀⠀⢀⠵⡑⢄⠀⠀⠑⢄⠀⠉⠢⢄⡀⠀⠑⢄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡠⠊⡠⠊⠀⠀⠀⠀⠀⡠⠊⠀⠘⢌⠣⡀⠀⠀⠉⠢⢄⡀⠈⠑⠒⠤⢵⣄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠞⡡⠊⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠳⣌⠲⢄⠀⠀⠀⠈⠉⠐⠂⠤⠄⢀⡈⣉⣂
⠀⠀⠀⠀⠀⠀⠀⢸⣶⣃⠜⠁⠀⢀⣀⡤⠖⠁⠀⠀⠀⠀⢀⡤⠀⠠⡀⠑⠦⣉⠒⠤⠤⣀⣀⡀⠀⠀⣀⣀⡤⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠉⠈⠘⠉⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠶⠀⠰⠀⠀⠀⠀⠉⠐⠒⠂⢠⠤⠄⠀⠐⡎⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⢁⠀⢰
⠀⠀⠀⣠⣾⣶⣷⣷⣦⣶⣥⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣦⣤⣼⣶⠾⠶⣷⣄
⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⣦⣤⡤⠤⢤⣴⡶⠶⠶⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠀⠉⠉⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡉⠈⢁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣀
⡠⠊⠀⠓⠉⣀⣔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⣀⠉⠚⠀⠑
⡇⠀⠀⠀⠀⢁⣠⡤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣄⠈
⠐⡄⠀⠀⠀⠀⠠⠴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⠄⠀⠀⠀⠀⢠
⠀⠈⠒⠦⠀⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠠⠤⠤⠄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠤⠤⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠐⠒⠒⠠⠤⠄⣀⣀⡀⠀⠀⠻⠂⠀⠀⠐⢺⠀⠀⢀⣀⣀⠠⠤⠄⠐⠒⠒⠐⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠄⠰⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⡠⠄⠀⠀⠀⠄⠀⠀⡔⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠒⠐⠀⡀⠈⠰⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡈⠀⠀⠀⠀⠈⠀⠈⠀⠀⠡⠂⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠄⢀⠀⢇⣴⠟⠉⢄⢀⣈⣉⠉⠉⠛⠓⠶⢤⣀⣀⣤⠶⠖⠛⠛⠉⠉⠉⠉⢉⣉⡉⠛⠳⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠟⠁⢀⡀⠀⠂⠈⠉⣉⡛⠒⠶⢤⠀⢹⠁⢠⡤⠀⠂⠈⠉⠉⠉⠀⠀⠉⠁⠀⠀⢹⡀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⢀⠠⠀⠨⡄⠀⠀⢀⡞⠁⠀⠀⠨⠉⢙⡒⠀⠀⣀⡁⠙⠂⠀⠀⣿⠀⠀⣀⡀⢤⠄⠰⠖⠀⠘⠛⠋⠀⠀⠀⠀⢣⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠏⠀⠀⠀⠙⠒⠀⠀⠀⠀⠐⠀⠉⡀⠠⠄⠀⡟⠀⢀⣈⣀⠀⠠⠤⠀⢀⡐⡖⢒⠋⠉⠠⡀⠈⣇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡼⠃⠀⠀⢄⣉⠑⠒⠦⢤⣈⠙⠂⠀⢀⣈⠁⠀⠀⡇⠀⠀⠤⠤⠆⠀⠐⠀⠈⣷⠁⠞⡼⢠⠀⢳⠀⠸⡆⠀⠀⣠⡀
⠀⠀⠀⠀⡉⠀⠀⠀⢀⡾⠁⠀⠀⠀⡀⠀⠀⠀⠲⠄⠀⠉⠀⠠⢄⠀⠀⠁⢀⡇⠀⠀⠴⠀⠀⠒⠒⠒⠀⢻⠀⠀⠁⠈⠀⠸⠀⠀⢻⡀⠞⠁⠀⠠
⠀⢠⠁⠘⠀⠠⠀⣠⠟⠀⠀⠐⠦⢤⣀⣈⠁⠀⢤⣀⡀⠀⠐⠦⠀⠀⠈⠀⢸⡇⠀⠀⠀⠒⠒⠂⠀⠉⠀⠈⢀⣈⣉⡁⠀⠀⠄⠀⠈⣿⠀⠀⠀⠀⠀⡀⢂
⠀⠈⢀⠀⠀⠀⠈⠙⣶⠶⠤⣤⣀⣀⠀⠉⠁⠀⠠⣤⡉⠛⠂⠀⣀⠀⠁⠀⢸⡇⠀⠀⠒⠃⢀⡬⠉⠀⣀⣉⠉⠉⠀⠀⠖⠀⠀⠀⠀⣸⡆⠀⠀⡠
⠀⠀⡠⠂⠀⠀⠀⣼⣃⣀⣀⡀⠀⠉⠙⠓⠶⢤⣄⡀⠁⠀⠀⢤⡉⠓⠀⠀⢸⡇⠀⠀⢠⡤⠴⠀⠀⠀⠉⢁⣀⣤⠤⠶⢖⣒⣛⣋⣉⣽⠁⠀⠈⠀⠈
⠀⠀⢠⠀⠀⡀⠀⣿⠹⠭⢭⣭⣝⣛⣛⣓⠶⠶⢤⣭⣛⠲⣤⣀⠀⠀⠀⠄⢸⡇⠀⠀⠀⠀⢀⣠⣴⣶⣯⡭⠶⠖⠚⢛⣉⣉⣉⣩⣭⣭⣧⡀⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠐⣁⣴⣿⣽⣛⣓⡒⠶⠤⢬⣭⣭⣙⣶⠶⣬⣝⣓⣿⣿⣦⣄⡀⢸⡇⠀⣀⣤⡾⢟⣛⣩⡥⠴⠶⢒⣛⣋⣩⣭⣥⠤⠴⠶⠶⢾⡁⠀⠀⠈
⠀⠀⠀⠀⠀⢻⣍⣑⠲⠦⠬⣭⣙⣓⣲⡶⠤⢤⣿⢠⣿⠲⠮⠭⣽⣻⣿⣿⣾⣷⣾⠿⢛⣋⣭⠥⠶⠒⣛⣉⣭⠭⠤⠶⠒⣒⣒⣚⣉⣭⣿⠳⡄⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⠒⠦⠤⣌⣉⣉⣉⢛⣧⢸⣿⢽⣷⣶⣶⠤⣭⣍⣛⣯⠖⣛⣩⠥⠶⢒⣋⣩⡥⠴⠖⠒⠛⢉⣉⣉⣀⣤⣤⣤⠤⠶⠟
⠀⠀⠀⠀⠀⠆⠠⠀⠀⠈⠀⡄⠀⠀⠀⠉⠉⠉⠿⠟⠿⠦⢤⣄⣈⣉⡓⠒⠾⣿⠭⠵⠖⢚⣋⣉⣡⡤⠴⠶⠒⠛⠋⠉⠉⠉⠁⠀⠠⠁⠠⠒
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠔⡠⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠛⠓⠿⠖⠚⠛⠋⡉⠉⠁⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠂⠀⠀⡀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠊⠀⠀⠀⠰⠄⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⢠⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠈⠙⢻⣿⠟⠉⠀⠀⠀⡖⢰⠐⡇⣴⠰⢤⡆⢰⠐⡆⡀⢦⢸⠂⡆⡔⠐⡄⡖⢲⠀⢰⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢡⣿⠇⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠁⠘⠀⠓⠈⠒⠈⠁⠈⠀⠁⠑⠋⠈⠂⠁⠉⠚⠁⠃⠈⠈⠚⠁⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣾⡿⠀⢀⣴⡶⡄⠀⢠⣿⠏⠀⢀⣴⡶⡄⢠⣶⠂⡀⠀⠀⢀⣤⢦⣀⣤⡀⠀⣀⣤⣄⠀⣠⣄⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣰⣿⣯⠴⠁⢠⣿⡏⠀⣰⣿⣯⠼⠁⣠⠟⢋⣿⠆⣰⣿⠏⢠⣿⣿⢁⣼⡿⠁⠙⢠⣿⡏⢀⡼⣿⡇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⣿⡟⠀⢀⡴⣿⡟⠀⢠⣿⡿⠀⢀⡴⠃⢀⣾⡏⢠⣿⠏⣰⢻⣿⠃⣸⣿⠁⠀⢀⣾⡟⢠⡾⢱⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠹⢧⡴⠛⢠⣿⠃⣰⠏⠹⢷⡴⠋⠀⠀⢸⣿⢀⡾⠻⠾⠁⣿⡏⣠⠿⣯⣠⡴⠋⠻⠷⢟⡥⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣴⢶⣿⣿⣤⣀⠀⠀⠀⠀⠀⠘⢿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⠀⠈⠛⠁⠀⠈⠁⠀⠀⢀⡴⠋⢰⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣥⣾⠏⠀⠉⠛⠻⠶⠶⢦⡤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⡆⠠⣄⣀⢀⡀⠀⠀⣰⠟⠀⢠⣿⠏
⠀⢈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠴⠃⠮⠷⢘⡎⠀⢀⡾⠁⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⣤⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠂⠠⠄⡀⢀⣀⣀⢀⣀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⢀⠠⠔⢁⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⣖⣂⠐⠢⣄⣀⢀⠀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⢀⣠⠤⣸⠟⢀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠉⠉⠹⢦⣌⣉⡁⡛⡓⠺⠧⣄⢀⠀⠀⡠⠺⠗⢂⠛⣡⡴⠞⠃⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠦⣤⣀⠄⢉⠩⠟⠛⠻⠟⡛⢾⣇⣤⠴⡾⠟⠛⠛⠩⢛⠳⣤⣢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠐⢁⠔⠁⠀⠀⠀⠀⠀⠈⠢⠙⠃⠎⠀⠀⠀⠀⠀⠀⠑⠄⢫⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣏⠀⠂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⡽⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣃⠀⠁⢰⠀⠀⠀⢀⡶⠚⠑⢦⣠⡡⢷⡠⣰⠒⢤⣀⠀⠀⠀⠀⠀⢡⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠹⣄⠈⢆⠳⣄⠀⢿⠀⠐⠗⣰⡟⠉⢹⣯⡀⠶⠀⣹⠇⢀⡔⠡⢀⡟⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠊⠶⣄⠑⠨⢑⡺⠮⢤⠿⠟⣡⠀⡸⣿⢿⢦⡶⠚⠀⡉⠔⢡⡊⣨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣀⡤⢴⣶⣅⣜⣟⡀⠀⠁⠈⠷⢄⠀⡀⠉⠉⠉⠁⡀⠛⠳⣄⠉⣉⣈⠈⣁⡠⢶⡋⠎⣻⣜⣤⡄⡤⠒⠙⠓⠲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠌⠉⠛⠶⢭⣙⡻⢿⠻⠗⣠⡤⠤⣪⣟⣉⡙⡛⡘⠙⠑⠑⠀⢈⣛⡉⣡⣍⣉⡴⢦⣒⡾⠙⢋⠩⢀⣠⡴⠦⠛⠩⠄
⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠄⠂⣐⡆⠀⠉⠉⠓⠲⠦⣄⡠⢀⡀⠈⠉⠭⣻⣿⢧⡀⢚⠚⣭⠝⠛⠛⢉⣛⢿⣽⠶⠟⠚⠉⠉⡀⠀⠀⠀⠤⢀⣀
⠀⠀⠀⠀⠀⢠⠚⡁⠀⠴⠒⣩⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠓⢖⣝⡁⠀⡃⠈⠐⢄⠲⠎⠙⣊⡉⠀⠀⠀⠀⠀⠀⠀⠽⠳⠶⠦⠤⣀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⡅⠀⣠⠤⠖⣊⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡉⠉⠉⠉⠉⢙⢀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠤⢀⣀⣀⠉⠀⢀⡨
⠀⠀⠀⠀⠺⡄⢀⡠⠖⢋⡹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⢴⣀⢈⠁⢀⡠⠁
⠀⠀⠀⠀⠀⠢⠈⣠⡿⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⠀⠉⠁⡰
⠀⠀⠀⠀⠀⠀⠂⢼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡦⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠈⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠂⠔⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠤⢠⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⡐⢠⡀⠀⠀⠀⠈⠈⣀⣡⡤⠶⡖⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠧⣩⠑⠒⠀⠤⢀⣀⢁⢸⠀⠀⠀⢀⠀⠈⢐⡀⡤⠐⠘⠁⠁⢁⣴⠟⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⠌⣑⡦⡀⠀⠂⢄⠀⠈⠓⠤⠤⡴⠔⠟⠀⠀⠀⠀⠀⣠⠴⠫⠲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⢂⣉⣵⣈⠠⠦⣄⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡷⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⡠⠂⠀⠿⢣⣏⢑⡟⢫⠞⠋⡩⢈⠀⠁⠉⠋⠉⠉⠘⠛⠻⢿⣟⢿⡯⣿⠗⡁⠀⢈⠐⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠈⠋⠀⠀⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠂⠀⠐⠙⠛⠃⠂⠀⠐⠐⠁⠀⠀⠀⠐⠀⠁⠀⠁

⠀⠀⣀⠀⠀⠈⠤⠤⠤⠅⠀⠀⠀⠀⠀⠂⠄⣀⣀⣀⠀⠈⠉⠐⠂⠁⠄⠀⠀⠤⠤⠒⠢⠀⠁⠀⠤
⠀⠀⠀⣰⠐⣄⠀⠀⠀⠀⠀⡴⠛⢦⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠔⠀⣤⠀⠈⠉⠫⠉⠀⢀⣀⠀⢀⣀⢤⠀⢤⡀⣀
⢤⡀⠈⠁⠀⠙⣁⢤⡐⠒⠄⠥⠤⠈⠐⠂⠀⠐⠂⢀⠀⠀⠀⣀⠼⠤⣀⠿⠤⠀⠀⠀⠠⡀⠀⡄⠀⠀⠀⠀⠀⠈⠀⢈⣁
⠶⠀⠐⠉⠀⢰⡃⠀⣷⠀⠀⡀⠀⠸⠆⠈⠋⠉⠟⠁⠀⠀⠔⠡⠄⠠⠄⠀⠀⠈⠁⠀⢘⣙⣚⡓⠀⠀⠀⠁⠀⠀⢠⠤⠴
⠀⢀⣦⣀⣠⠈⠀⠀⠠⠄⠊⠀⠠⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠒⠀⣴⣦⡄⠀⠒⠒⠉⠁
⠀⠈⠶⠶⠄⠓⠂⠒⠀⠀⠀⠀⠒⠀⠈⣀⣀⣠⣀⡈⠁⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣀⡁⠀⢠⠈⢠⠐⠙⠃
⠀⠀⠤⠀⠤⠀⠀⠀⠂⠰⠒⠒⣚⡆⠀⠁⠀⠉⠙⠧⠀⠄⠀⠀⠀⠀⠀⠐⠂⠐⠂⠀⠀⣤⡀⠀⠀⠠⢼⠀⠚⠤⠠
⠀⠀⠀⠀⠀⠀⠤⠄⠴⠀⢉⠉⢩⠁⠉⠉⠁⠈⢩⡀⠀⢀⣀⣀⠀⠤⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠑
⠀⠈⠀⠀⠀⠀⠀⣴⠖⢳⣦⠀⢠⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⡈⠑
⠀⠀⢀⡠⣄⠐⠢⠽⠤⠤⠋⠠⠀⠁⠐⠈⠀⠄⠀⠀⠄⠰⣒⣒⣓⠀⠁⠐⠂⠉⠤⠀⠠⠀⠀⠁⠈⠙⠘⠀⠈⠀⠑⠀⣀
⠀⠄⣈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠨⠤⢤⣀⡀⠈⠈⠋⠁⠀⠀⠀⠀⠀⠄⡀⠀⠄⠀⠀⠀⠒⠂⠀⠐⠐⠈

⡎⣎⢏⢧⢣⡳⡹⡜⢎⢳⡙⣎⢳⡀⠀⠀⠀⠀⠙⣿⢽⢸⢸⢊⡇⣷⢹⡗⣐⣞⠿⣮⣙⣵⡫⣯⣮⢆
⢹⢸⡜⡎⣧⢣⢱⡜⣎⢧⠹⡌⢧⡙⢦⣄⣀⣀⣠⢮⠗⡏⡞⡼⣰⢃⡞⣰⠏⣼⠏⣮⢉⢡⡻⣿⣵⣻⣧
⣸⢸⡇⣇⢹⠸⡇⣧⢹⡌⣧⠹⣌⠻⠶⠬⢭⣭⣥⣼⢸⡸⣱⢱⢃⡞⣰⢋⡼⢃⡾⢁⡼⠋⣵⠸⠺⡚⡽⢧
⣿⢸⡇⣿⢸⡇⣷⢸⡆⢷⠘⣧⣙⣛⣒⣒⡒⠶⠶⠤⡾⡇⡧⢣⢎⡼⣡⠟⣴⢋⣴⠟⣡⠞⢋⣴⠇⢫⢪⡓⢥
⣿⢸⡇⢻⠈⣇⢸⡆⢿⡘⠷⠬⣭⣭⣭⣭⣍⣙⡛⠶⠶⠇⡇⢏⠞⡴⣣⠞⣡⠟⣡⠞⢁⡴⠛⣡⡶⠟⣁⣷⠜⣥
⣿⢸⡇⢸⡆⣿⠈⣧⣈⣛⣓⣒⣒⣒⣒⠲⢦⣭⣙⡛⠶⠶⠱⢸⢞⡴⣣⠞⣡⠞⣡⡾⢋⣴⠞⢋⣤⡾⠛⣁⣴⠗⣧
⣿⢸⡇⢸⣇⣘⠳⠶⠦⠬⠭⠭⠭⣭⣍⣛⠲⢦⣍⣙⠳⠶⢆⡎⢎⠜⣡⠞⣡⠞⣡⡶⢋⣡⡾⠛⣡⣴⠟⠋⣁⣴⠷⠣
⣿⣈⣛⡶⠮⠭⠭⣭⣭⣙⣛⣛⣒⠲⢦⣍⡛⠶⣬⣉⠛⠶⠞⡘⡜⣞⡵⢛⡥⠞⣡⡶⢛⣡⡴⠟⢉⣤⡶⠟⠋⣡⣤⡾⠇
⣒⣒⠮⠭⠭⣍⣛⣒⣒⠲⠶⢬⣍⠛⢦⣌⡛⠶⣤⣉⠛⠶⠶⡑⣜⢎⠴⣋⡴⢛⣡⠴⠛⣩⣴⠾⢋⣡⣴⡶⠟⠋⣁⣤⣶⠷
⣒⡪⠭⢭⣛⣒⡲⠮⠭⣍⡛⢶⣌⡛⢶⣌⡙⠳⣤⣉⠛⠶⡶⢌⢎⣯⢞⣡⠖⣋⣥⠶⢛⣩⣤⠾⠛⣉⣠⣴⠾⠟⠋⣉⣠⣤⣶⠄
⣲⠭⢭⣓⣒⠮⢭⣙⠳⣌⡙⢶⣌⠛⢶⣌⡙⠷⣤⣉⠻⢶⡼⡣⡫⡳⣫⠴⢚⣩⡴⠞⢛⣩⣤⠶⠟⢋⣉⣤⣴⠾⠟⠛⠉⠁
⠮⢭⣓⠲⣍⠻⣦⡙⢷⣌⠛⢦⣌⠻⢦⣈⠻⢶⣌⡙⠷⣦⡬⡪⣜⢝⡵⠞⣋⣥⠴⠞⢋⣩⣤⠶⠞⠛⠉⠁
⡙⢦⡙⢷⣌⠳⣌⠙⢦⡈⠳⣦⡙⠳⣤⡙⠳⣦⡉⠻⢶⣤⠯⢽⡫⣪⠞⣋⣩⡴⠶⠛⠋⠉
⠳⣌⠻⣦⡙⢦⡈⠳⣄⠙⢷⣌⠻⢦⣌⠻⢦⣌⠙⢷⣤⡽⠔⢟⢝⡵⠋⠉
⣦⡙⢷⡈⢳⣄⠹⣦⡈⠳⣦⡙⢷⣄⠙⢷⣄⡙⠷⣦⣈⣓⣾⡵⠋
⠈⢷⣄⠻⣦⡙⢷⣌⠻⣦⡈⠻⣦⡙⢷⣦⡙⠻⣦⡌⢷⡶⠋
⠀⠀⠙⣧⡈⢷⣄⠙⣧⡈⠻⣦⡈⠻⣦⡈⠻⣦⣈⡥⠊
⠀⠀⠀⠈⢿⣄⠙⣷⡈⠻⣦⡈⠻⣦⡈⠻⣦⡈⠁
⠀⠀⠀⠀⠀⠙⣷⡈⠻⣦⡈⢿⣆⠙⢿⡦⠈
⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⢿⣄⠙⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠁

⠀⠀⣿⠋⠉⠉⠉⠉⠙⠛⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⠛⠋⠉⠉⠉⠉⠙⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠛⢻⠋⠉⠉⠉⠉⠛⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠒⠛⠛⠉⠉⠉⠉⢙⡟⠋
⠀⠀⠀⠸⠶⢶⡶⠶⠶⠶⠶⠦⠤⣤⣄⣉⡙⠳⢦⣄⠀⠀⠀⣿⠀⠀⢀⣠⡴⠞⣋⣁⣤⣤⠤⠶⠶⠶⠶⠶⢶⡶⠶⠇
⠀⠀⠀⠀⠀⠘⠗⠒⠒⠚⠛⠒⠒⠒⠲⠿⠿⠿⢷⣾⣿⣶⣄⣿⣠⣶⣿⣷⡾⠿⠿⠿⠖⠒⠒⠒⠚⠓⠒⠒⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉





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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣷⢦⠄⣀⠀⠀⠉⠉⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⡈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡇⣿⠶⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠹⠉⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡰⠀⡄⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣿⡇⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡏⢠⠁⢰⡄⠀⣿⣿⣿⣿⣿⣿⠇⢹⣿⣿⣿
⣿⣿⣿⣿⠈⠹⠿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠼⠆⠸⠇⠀⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠛⠳⠀⠀⣠⣤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣄⣀⣳⣤⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⡤⠈⡉⠋⣿⣿⣿⣿⣿⣿⠋⢹⣿⣾⣿⣤⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠉⣄⣀⡀⢠⣿⣿⡟⢁⠀⣹⣿⠀⠀⠀⠈⠀⠈⠠⣾⣿⣿⣿⣿⣿⡟⢳⢸⣿⣿⣿⣿⡺⣿⣿⣿
⣿⣿⢿⠿⣿⣿⣖⡀⠈⢹⣿⣸⣿⣿⠁⠀⠀⣾⣇⠀⠀⠀⠀⠀⠞⣻⣿⣿⣿⢿⣿⣿⣿⣾⣼⣷⢛⣿⣿⠉⢹⣿⣿
⣿⡗⠀⠀⠉⣿⣿⣿⣦⠎⠙⠉⢻⠇⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠠⠈⢿⡇⢻⡶⢿⣿⣿⣟⣿⣿⣘⣿⣿⣷⣽⣿⣿
⣿⣷⡀⠀⠀⢈⣍⣿⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⢀⡀⠀⣾⣿⣿⣾⣿⣿⣿⣿⡿⠉⣿⣿⣿
⣿⣿⣷⡀⠀⠈⠙⠻⠯⠙⠁⠀⠄⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣶⡎⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿
⣿⣿⣿⣟⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣀⠀⠀⢀⠀⠠⡄⠀⣠⣾⣿⣾⣿⣦⡀⢀⣾⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⡗⢸⣿⣿⣿⣿⣿⣿⠇⢸⡝⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡱⢂⣨⡁⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢴⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⣋⣠⣭⣍⣀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠂⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠿⠿⠷⠶⠶⣯⣐⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠧⣟⢻⣿⣿⣿⣿⡿⢉⡿⠻⣆⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠷⡖⠤⠄⣤⣄⣦⣾⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠈⡈⣿⣿⣿⣿⣇⣼⢁⠀⠰⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡷⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠟⠋⠀⠀⠀⠀⡀⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⣤⡉⣁⣀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⢸⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⡇⣷⣤⢀
⠀⠀⠀⠀⠀⢀⣴⠏⡇⡟⣸⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣇⢻⢸⠹⣧⡀
⠀⠀⠀⢠⣤⣾⣿⠀⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠀⣿⣷⣤⡄
⠀⠀⠀⣸⣿⡟⢻⠀⡇⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⢸⠀⣿⢻⣿⡇
⠀⠀⠀⣿⡏⢷⢸⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⡇⡼⢹⣿
⠀⠀⠀⣿⠇⢸⠈⢸⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡌⡇⠃⠇⢸⣿
⠀⠀⢠⣿⠸⠀⡇⢸⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⡇⢀⠀⠃⣿⡄
⠀⠀⢸⣿⠀⠀⡇⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢸⠀⠀⣿⡇
⠀⠀⢸⡏⠀⠀⠃⡈⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⢁⠘⠀⠀⢹⡇
⠀⠀⣼⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧
⠀⠀⣿⡇⠀⠀⠀⠁⠀⠄⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣂⠥⠀⠘⠀⠀⠀⢸⣿
⠀⠀⣿⠃⠀⠀⠀⠂⠤⠤⣀⣉⠓⠪⢵⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣮⠗⠚⣉⣀⠠⠤⠀⠀⠀⠀⠸⣿
⠀⠀⣿⠀⠀⠄⠀⠀⠐⠐⠀⠤⠭⠕⣲⣭⣛⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣭⣖⠫⠭⠤⠀⠒⠂⠀⠀⠠⡀⠀⣿
⠀⢸⣿⠀⠀⢀⡀⠤⠄⣀⣒⠢⠬⣍⡒⠮⢭⣛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣛⡭⠵⢒⣩⠥⠔⣒⣀⠠⠤⢀⡀⠀⠀⣿⡇
⠀⢸⣿⣌⣒⡲⠤⢭⣑⡒⠤⢍⣓⠲⠬⣙⡒⠬⣙⠢⢍⠻⣷⡄⠀⠀⢀⣾⠟⡩⠔⣋⠥⠒⣋⠥⠖⣚⡩⠴⢒⣊⡭⠤⢒⣂⣩⣿⡇
⠀⠈⠉⠛⠻⠿⢿⣶⣦⣬⣉⣒⠂⠍⠁⠂⠈⠁⠀⠁⠀⠁⠀⠙⢆⡰⠋⠀⠈⠀⠈⠀⠈⠉⠐⠊⠩⠐⣒⣉⣭⣴⣶⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣤⣄⣀⡀⠀⠀⠀⣀⣴⣾⣷⣦⣀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⡿⠿⠿⠿⠿⢿⣶⠶⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣷⠀⠀⠀⡀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣀⠀⢻⣿⣿⣿⠀⠀⡈⠀⡘⠀⠀⡠⠊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠁⢀⡀⢀⠘⠿⠿⡟⠀⠀⡃⠰⠁⠀⢜⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⢹⡆⠀⠀⠸⠇⠀⡠⣞⠀⠀⢀⢷⠃⠀⠀⠀⢱⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣯⣑⠠⡀⠀⠀⠑⣄⠀⠲⠠⢓⣀⠜⠀⠀⠱⡀⡌⣘⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠔⠨⠝⠾⣆⣀⣼⣶⡾⣿⣿⣿⣿⣿⣷⡀⠀⢙⠛⠻⣿⣿⣶⣶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣐⠘⠂⠑⢹⣿⡄⡀⠒⠀⠀⠀⠀⠰⢸⠇⠀⠈⡄⠀⢸⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠉⣿⠜⣨⡸⣿⡇⡝⠇⠀⠀⢠⠆⣱⠞⠇⢢⢀⠧⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠶⢬⣁⣿⣿⢐⠇⠀⠀⠣⠂⣿⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠚⠛⠛⠛⠛⠋⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡂⠈⠁⠒⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠉⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢈⠊⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⣷⠀⠀⢠⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠈⠢⢀⡀⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⣿⡭⣽⡆⠀⢰⣾⢯⡻⡆⣶⠀⠀⠀⠀⣀⡴⣶⣄⠀⠀⢠⣾⣦⡐⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠏⣽⡋⣴⣷⡏⠓⢻⣿⣷⠈⣼⡟⠢⢀⠄⢶⡋⢉⣼⣿⠲⠲⣿⣷⡍⢚⡶⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠼⢀⡃⠙⠊⠋⠁⡀⡀⠉⠁⠊⠀⣃⠀⠡⡀⠸⠐⠢⠿⠛⠐⠂⠻⠟⠥⠆⠹⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠌⠀⠀⡄⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠌⠀⠔⢄⠄⡀⡀⠈⠂⠄⢀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⢠⠀⠀⠀⠁⠂⠖⠂⠀⠀⢒⠂⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠹⠁⠈⡹⠯⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠈⠀⠁⠀⠀⠁⠀⠀⠁⢆⠀⠀⠀⠀⠔⠃⠀⠀⠈⠉⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠈⠁⠂⠀⠠⠄⠀⠀⡀⠀⠀⠀⠂⠀⢀⠂⠀⠀⢀⠀⠀⠠⠀⠀⠒⠃⠀⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠈⠑⠠⡄⠀⢃⠀⠂⠉⠀⠀⠀⣀⠀⠀⠀⣀⡀⢀⡀⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠉⠀⣀⣀⠄⠀⠀⠀⠤⠶⣤⣀⠀⠤⠁⣀⣤⡖⠀⢀⡀⠀⠀⢀⡀⠀⠉⠀⠁⠹⢄
⠀⠀⠀⠀⠀⠀⡠⠊⠤⠄⠀⠐⠚⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⡡⠶⢌⡀⠀⠀⠀⠀⠀⠌⠁⠂⠈⠙⠒⠲⠤⠤⠀⠑⡄
⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠎⠀⠀⠀⠹⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡠⠄⠂⡉⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⣀⣠⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄⡀
⠀⠀⠀⡄⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣦
⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢐⣇⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⡇⠀⠀⠀⢠⠄⠀⠀⠀⠀⠲⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢸⠇
⠀⠀⠀⡇⠀⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠤⠄⠀⡀⡧⢀⣠⡤⠶⡒⠒⠒⠒⠀⠤⢄⣀⡀⠀⠀⢸
⠀⠀⠀⠓⠀⡭⠁⠀⠸⠭⢭⠽⠤⠤⠴⠶⠦⠤⢬⣕⡿⠳⠖⠒⠒⠒⠒⠒⠤⠤⠤⠤⠌⠀⣰⣬⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣀⠀⠠⠴⠒⠀⠐⢄⠀⠀⠀⠀⣀⠤⠐⢂⡉⢀⠄⠀⣇
⠀⠀⠀⠀⣤⠤⢥⠈⠩⠉⠁⠀⠀⠀⠀⠠⠀⠀⠖⠁⣠⡆⡁⣠⠰⠦⠙⠋⠘⠀⠀⣿⡀
⠀⠀⢀⣴⡋⢧⠀⢁⠀⢹⣿⣧⠀⠀⠠⠀⠀⠀⠀⢸⣿⣿⡮⠉⠀⠀⠀⠉⠀⠀⠀⣿⣅
⠀⠀⢸⡘⣟⣏⡄⠘⣆⠈⠟⢿⡂⠀⠀⠀⡀⢄⠀⢸⣿⡿⢻⡄⠁⠀⠈⠀⠀⠀⣀⢸⣧⢣
⠀⠀⠈⣇⠻⣿⡿⡄⢹⡆⠀⡠⠀⢀⡉⠀⠀⠀⠀⠀⢿⣧⠉⣇⠈⠀⠀⠀⠀⠀⠨⠀⢻⡆⡇
⠀⠀⠀⢹⡀⣿⡿⣷⠘⣿⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⠄⠤⠀⣀⣉⡁⠂⠀⠀⣟⢳
⠀⠀⠀⠀⣿⠹⣧⣿⡆⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣶⣿⣯⣭⣭⣛⣛⢾⣿⣿⡷⡀
⠀⠀⠀⠀⠘⣄⠹⡿⢱⠀⠛⠈⠀⣠⣶⣤⣤⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣛⣿⣿⣷⢿⠖⢄
⠀⠀⠀⠀⠀⢇⡀⣿⡌⡄⢀⣀⣤⣼⣿⣿⣿⣿⡿⠿⣷⠿⢿⣿⣿⠍⠉⠛⠛⠿⢭⣿⣻⡿⢿⣿⣭⣤⠄
⠀⠀⠀⠀⠀⠀⡇⠸⣳⣤⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢾⣽⣦
⠀⠀⠀⠀⠀⠀⠑⢄⣠⠬⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⣀⣀⡈⠉⠑⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠢⢄⠀⠉⠁⠒⠤⢄⡈⠉⠒⠤⣄⡀⠀⠀⠀⡠⠔⠈⣀⠀⠐⢂⣁⠁⠀⠐⠀⠀⠄⠀⠀⠀⢰⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡈⠀⠀⠀⠀⠙⠢⡀⠀⠀⢀⣈⣑⣢⣄⠀⠉⠓⠒⠉⠀⠔⠈⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⠄⠒⠂⠀⠀⠉⠉⠳⣄⠀⠀⠀⠀⡈⠀⠀⢀⠀⠀⢐⠀⠁⠀⠀⠦⠑⠀⠀⠀⠓⠃⠀⠀⠀⠀⣸⠠⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⡀⠭⡁⠒⠂⠤⣀⡀⠀⠈⠣⡀⠀⠰⠀⠀⠀⠆⠀⠀⢐⡈⠤⠒⢐⡨⠙⠇⠀⠈⠭⠝⠋⠀⠀⢀⠃⡼⢱⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢒⡀⠥⠀⠀⡔⣂⠤⠈⠑⠢⢄⡙⣄⠂⠀⠀⡀⠀⠀⠘⠓⢒⠰⠒⠃⠤⣘⠀⠀⣀⡙⠁⠀⠀⠀⡎⣸⣇⡞
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠘⠳⠶⠄⠀⠠⣨⠱⠊⠀⠀⢕⡢⡉⠉⠀⠀⠀⠁⠀⡐⡠⢀⡡⠤⠒⠈⠁⠀⠀⣀⣀⣀⡀⠀⠀⡸⢠⡿⣼⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠤⢄⡀⠀⠑⠒⠥⠀⠀⣚⠵⠢⠀⠀⠀⠀⡌⠀⠀⢟⡉⠄⢐⡂⠁⠈⠀⠀⢀⡥⠤⣁⠀⠀⢠⠃⣼⢱⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠒⣡⠄⣀⠍⣐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢅⠂⠈⡐⠀⠈⠀⠀⠠⢁⠱⡊⠍⠀⢀⠇⣼⠇⡞
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠔⣒⠠⢍⡀⠹⠒⠄⠀⠀⣙⠳⠒⠄⠀⠀⢀⠂⠀⢀⠠⠐⠀⠑⠀⠉⠉⠀⠀⠘⠃⠒⠚⠀⠀⡎⡰⡏⣸⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠐⠈⠑⠂⠀⠀⠀⠥⠚⠄⠀⠀⠀⡀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⡻⢰⠇
⠀⠀⠀⠀⢨⣈⣙⣑⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠂⠉⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠒⣒⣒⣒⡒⠲⠶⢡⣳⢣⡏
⠀⠀⠀⠀⠐⠦⠤⠥⠍⠽⠵⢦⢽⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣍⣕⣒⡪⡭⠭⠭⠭⠭⠭⢽⣍⡓⢣⠇⡺⠁
⠀⠀⠀⠀⠀⢸⡶⢶⠒⣒⣲⡶⠒⠶⠿⠿⠿⠿⠷⡦⣤⣀⡐⢰⣤⣾⠿⠿⠇⠉⠁⠒⠒⠶⠶⠖⠶⠤⢤⠤⢤⣄⣈⠉⣼⠃
⠀⠀⠀⠀⠀⠈⠑⠒⠐⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠈⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠃⠐⠒⠒⠲⠬⢥⣆⡐⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠐⠤⢒⠅⢒⠩⠀⢒⠩⠅⢒⠩⠄⢒⠩⠔⠊⠁⢒⠩⠄⢒⠉⠁⡂⠍⢀⠂⠍⢐⠨⠉⢐⠈⠄⢒⠨⠄⠒⠈⠄⠢⢤⠦

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⢻⡏⢹⠏⢉⣻⡍⣩⣭⣭⢿⣭⠍⢉⣿⡍⣭⣉⢉⣽⠯⢩⡍⢹⠉⡉⣽⣭⠉⣯⣽⣭⢉⣭⣭⣭⢭⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⡥⣿⣀⡘⣷⢿⣛⣁⡀⣾⡇⡀⠘⣷⢷⡾⠻⣿⠃⣷⡼⠃⠸⣷⣥⡏⣸⠿⡏⣿⠀⣾⡅⢰⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⣭⣤⣭⣭⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⡀⠉⠀⠀⠀⠉⠈⠀⠉⠀⠀⠈⠀⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢶⣾⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠉⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣇⠀⠀⠀⠀⢈⣿⣿⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⠿⡿⠸⢿⣿⣿⣾⠁⠀⠹⠂⠀⢠⠘⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⢶⣤⣀⢘⣿⣿⠹⠏⠄⠰⠀⠀⢈⢄⣴⠟⣣
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣄⡈⠟⠩⢽⣿⢿⢰⡀⠀⡶⠂⠀⢨⡿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣭⣍⣩⣤⣴⣿⠏⢈⡏⠁⠀⡀⠀⡀⠘⡧⢿⡅⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣦⣤⣼⣿⣿⣿⣿⠟⣁⣾⡇⢠⣠⣤⢰⡇⢸⠀⠻⡄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠿⠛⠉⢋⡡⠞⣽⣿⠁⡿⠛⠋⠉⡇⢸⡆⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⢆⣞⣀⣵⣾⣷⡿⣿⠋⢰⡇⠀⠀⠀⠁⠸⣿⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⡿⠿⠿⢏⣼⡟⣠⣿⠂⠀⠀⠀⠀⢨⣿⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠉⠀⠀⠀⣰⣿⣿⣿⣿⠇⠀⠀⠂⠀⡀⢸⣿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢀⣠⣶⢿⣿⣿⣿⡟⠱⡆⢀⠾⣿⠉⢻⣯⣐⣺⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⣾⣿⣿⣿⣿⠇⡄⣠⡏⠀⠙⠷⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡔⠀⠀⢀⣤⣤⣤⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⢠⣤⣿⡟⠛⠋⠋⠈⠉⠉⠉⠉⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣿⣿⣿⣿⡟⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣋⣴⣶⠃⠀⠀⠲⠦⢤⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢚⣿⣿⣿⣿⠁⠀⠀⢀⣤⣤⡀⠀⠀⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⡖⣿⡿⠟⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡆⣧⣾⣿⣿⣇⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠠
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠀⠈⠢⡀⠀⠀⠀⠀⠉⠙⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡇⠀⠀⠀⠉⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⠉⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠸⡄⠀⠀⠀⠀⠀⠀⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀
⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢿⣄⠀⠀⠀⠀⠐⠀⢻⠉⠢⡀⠀⠀⠀⠀⣠⠞⠁⠈⠛⢧⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠉⠂⠀⠀⠀⠀⠀⢀⡄⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡤⠞⠁⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡇⢀⠾⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢀⡞⢷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣠⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⣾⠁⠈⠁⢙⠳⣄⠀⠀⠀⠀⠀⠀⠠⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⢀⡏⠀⠈⠙⢦⡀⠀⠀⣸⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⠎⠀⠀⠀⠀⠀⠉⠳⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢒⣶⡖⠂⠀⠀⠀⠀⠀⣴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠀⠁⠀⢀⠀⢀⠠⢝⠦⣨⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠳⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⢂⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣀⠂⢰⡶⠀⠀⠀⠘⠀⠀⠠⠴⣊⡴⠋⠸⠻⢾⣦⡢⠠⠐⡀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢊⣭⡵⠋⠀⠀⠀⠀⠀⠀⡐⡒⢉⠥⠤⠀⠀⠀⠀⠈⠙⣙⡳⠌⢦⡀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣤⣧⡅⣠⢄⣀⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠡⠀⣄⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠋⡵⡣⠚⣘⡇⠀⢸⣿⠇⠀⠀⠀⠀⠸⣿⣯⠃⠀⢀⣸⠛⣸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣸⢱⠠⢀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⡇⡀⢇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⠸⣰⠘⡄⠀⠀⠀⠶⠄⠴⠀⠀⠀⠀⠀⠜⣸⠁⡄⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⣕⠜⢣⡘⡢⢄⡀⠀⠀⠀⠀⣀⡠⠔⢉⠔⡹⣄⠱⡝⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡝⢦⣅⡢⠕⠞⠋⠈⢍⠉⠉⠉⠈⠉⢰⠀⢔⣠⡟⠒⠬⠕⢭⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡠⠊⠀⢰⠀⠐⠄⠒⠻⠇⠂⢜⣠⠼⢄⣀⡙⢣⣄⣄⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣐⢀⢢⣦⡀⠀⠀⠀⢈⡷⣺⠭⠒⠊⠉⠀⠰⢀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⣀⠀⠈⠉⠛⠿⣦⣤⡤⡥⠋⠁⠀⠀⠀⠀⣀⣸⡢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠁⠓⢸⠄⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⠀⢗⠀⠀⡥⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣰⠎⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠤⢀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡄⢒⡈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡌⠀⠀⠀⠑⡄⡘⠶⠛⢃⠔⠠⠁⠀⠀⠈⢦⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣴⣈⣀⣤⣾⡇⠀⠀⠀⢠⣀⣬⣁⣀⣠⣴⣡⡅⠀⠀⠀⢸⣿⢶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⠀⠀⠀⠂⠈⣧⠤⠤⠄⠨⡅⢀⣀⠀⠦⠀⠠⠀⠀⠀⠀⠠⣇⠀⡀⠀⣯⠈⡉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠄⠀⡔⢐⡇⠀⠂⠂⠐⡋⠀⠀⠈⣛⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠉⣇⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣯⠌⠏⠉⢫⠉⠉⠁⢰⠛⠐⢢⡀⠉⣀⠀⠀⠁⠀⢉⠈⢀⡄⠐⠒⠅⠀⠈⠢⢤⣬⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⠂⠈⠁⠀⠈⠉⢀⣜⣀⡉⢠⠰⠀⠸⡀⠀⠈⢷⠈⠀⠀⢰⢦⢤⠄⢁⡾⠁⠀⢀⡟⣀⣀⠄⠀⠠⣔⡤⠀⠀⣥⡔⠦
⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⣘⠣⠇⠈⠈⠉⠉⠉⠉⠉⠉⠉⠢⡀⣸⠋⠉⠁⠙⠙⠙⠀⠸⣁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠈⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠶⠶⣖⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⡄⠀⠀⠀⠀⠀⣆⢀⡀⠀⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⠊⠀⡴⢻⠀⠀⠀⠀⠀⠀⢸⡎⢣⠀⠀⠀⢄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣧⠄⠀⡄⠀⠀⠀⡆⠁⢀⠳⡄⡇⠈⢆⠀⠀⢪⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⣼⡀⠀⠀⠀⢱⠀⠈⡆⠈⠧⠀⠈⣾⡆⠀⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⢠⠀⣤⠃⢧⠀⢸⠀⡏⢣⣠⣸⡄⠀⠀⡇⠸⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⠈⣶⢿⠦⠬⣿⣿⣆⣧⠀⡽⠿⠘⣄⢰⡇⠀⢰⢳⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣌⣇⢸⠀⠀⠀⠀⠀⠀⠉⠻⠄⠀⠀⠀⠈⠿⣇⣤⣼⢸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣾⠀⠀⢼⣯⠆⠀⠀⠀⠀⣾⣽⠄⠀⢠⢿⣿⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣍⣀⣄⣄⡀⠀⠀⣀⡀⠀⠀⣀⣠⣀⣈⣭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠛⢲⠖⢶⠚⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⡀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢘⢷⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢰⣟⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡿⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠸⣇⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠤⠤⠤⢄⣀⢸⠀⢸⢀⣀⠤⠤⠤⠤⣀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠉⠉⠉⠉⠉⠙⠛⢷⣶⣶⠟⠛⠉⠉⠉⠉⠉⠉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣀⣀⣀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣀⣀⣀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⠛⠛⠛⠛⠻⠇⠀⣿⡇⠀⠿⠛⠛⠛⠛⠛⠛⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠿⠿⠿⠿⠿⠷⠆⠀⣿⡇⠀⠶⠿⠿⠿⠿⠿⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⠿⠿⠿⠷⢶⣶⡆⠀⣿⡇⠀⣶⣶⠶⠿⠿⠿⠷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣀⣿⣇⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⢉⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡵⣾⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠾⠱⠿⠏⢺⣿⣏⣼⠋⢹⣯⡉⣯⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⢀⠴⠒⠿⠛⢁⣽⣯⠀⠀⠀⡛⠟⠚⢆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡼⣶⢁⠀⠄⡤⡸⠈⣻⣦⡀⢄⠹⠆⣀⣀⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠿⡀⢻⠀⢶⢋⣽⡿⠯⢭⣟⠿⠖⡺⢿⡝⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⣿⣿⣤⠾⣸⠏⠀⠐⡭⠛⠛⠋⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣔⡐⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⠐⠂⠀⠀⠈⠂⢤
⠀⠀⠀⠀⡴⠡⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀
⠀⠀⢀⠎⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢀⠔⠀⠀⠂
⠀⠀⡎⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠰⠃⠐⠀⠀⠀⠀⣠⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡄⠘⠀⠀⠀⠀⠐⠀⢀⠔⠁
⠀⡆⡠⠀⠀⠀⠀⠀⠀⠠⠼⠀⠈⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠢⠤⠄⠀⠀⠀⠈⢁⠂⠀⠀⠀⠴⢀⡔⠁
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠠⠁⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠘⠂⡀⠁⢦⣀⠴⠤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠨⠡⠀⠀⠀⠀⢀
⡄⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⡀⠕⡊⠁⠁⠀⠀⠀⢼⠀⠀⠁⠀⠀⠂⠀⠉⠁⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⢤
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠘⠒⠀⠀⠄⠀⠀⡀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⠤⠄⢀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⢤⣄⡠⠄⠀⡤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠐⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⠴⠛⢒⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣠⠊⢠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠀⠐⠬⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞⠁⣰⠋⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣤⣄⣠⡀⠀⠤⡤⣀⠑⠨⡲⣄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠔⠁⢀⣾⠏⢀⠏
⠀⠀⠀⠀⠀⠀⠠⢮⣾⢿⣿⣿⣿⠯⢙⣣⣭⣌⡓⠿⡳⢦⣄⢧⡀⠀⠀⢀⠔⠁⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣰⣿⡟⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣶⠿⣛⠿⠋⠉⠁⠀⠑⠻⣳⣿⣆⡰⣁⣤⡶⠟⠋⠁⠀⠀⠀⠀⠐⠂⠤⢀⣠⠊⠀⢀⣼⣿⡟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠊⢁⠴⠋⠉⠓⠶⢭⣒⠢⢤⣠⣙⣿⣿⣿⣿⣥⣤⣶⣄⣀⣀⠀⠀⠀⠄⠀⠤⣤⣀⡀⢠⣾⣿⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⡈⠻⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⠭⠭⢉⡑⠒⠂⠂⠨⠉⢻⣿⣿⢇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠿⠲⠛⠙⠛⠛⠿⠿⣷⣆⣀⡂⠀⠀⠀⠀⠀⠀⣿⣟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠄⡀⠀⠀⣹⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣥⣤⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⣓⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡔⣦⢄⣀⣀⣀⣤⡄⢀⣠⠔⠁⢠⡄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠛⠉⠁⠒⠉⠀⠀⠀⠘⡷⡀⠀⠀⢠⣴⡴⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠆⢸⠟⢡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠈⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠆⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠷⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠀⠀⠀⠀⠘⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣴⣾⣿⣿⡇⠀⠀⠀⠀⢠⡇⢸⣷⠦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠻⠿⠏⠀⠀⠀⠀⣴⠟⢀⣾⣿⣀⣀⠀⠈⠉⠉⠛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣇⠳⣄⠀⠀⠀⣀⡴⠋⢁⣤⣾⣿⣿⣿⣿⣰⣶⡄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⣌⣉⣛⡉⠁⠰⠞⠛⠛⠋⠉⠁⠈⢻⣿⣟⣴⣴⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⣀⣠⣤⣴⣶⡿⢿⡿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠽⠿⠛⠿⣿⡿⠟⠁⢀⣀⣤⣶⣾⡿⠯⠗⠋⠁⠀⠀⠔⠛⣹⣿⣿⣿⣿⣿⠏⣠⠆⠀⠻⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⢀⣈⣀⣠⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠩⠽⠯⢛⣉⡉⢉⠉⠉⠉⠉⠀⡹⢿⣋⠈⢻⣿⣿⣿⠳⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠉⠍⠛⠀⣀⣀⡀⠀⠀⠀⠀⢰⣿⣿⡅⠘⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠀⠀⢻⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣀⣤⠼⢆⠀⠀⠀⢸⠏⠹⠧⠀⠹⣿⡿⢋⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣀⣠⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⣀⣤⠮⠊⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠒⠒⠂⠉⠉⠉⠉⠛⠐⠒⠂⠤⠤⠤⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣒⣋⠄⡤⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⡠⠭⣭⣝⣲⠆
⠀⠀⠀⠀⠀⠀⢰⣱⠛⠉⠉⠉⠁⠓⠚⠛⠓⠶⠶⠤⠤⠭⣭⣁⣴⣒⣒⣶⡶⡶⡿⡯⡯⢗⢖⢟⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠰⢻⠀⠀⠀⠀⠀⠀⠤⠤⠀⣀⣤⣖⣀⣀⠀⠀⠀⢠⢟⢌⠈⠎⡪⡪⠂⢑⢅⣥⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠰⣟⠻⠳⠷⠶⡦⢤⣤⣤⣄⣀⣀⠀⠀⣀⣀⠀⠀⠸⣆⢕⣄⣨⣮⣶⣴⣗⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠒⠒⠒⠻⠲⣿⡿⣿⣿⣻⣉⣩⣿⣭⣍⣷⣄
⠀⠀⠀⠀⠀⠀⠠⠴⠁⠑⣵⣌⣀⣀⣠⡤⣤⣤⣤⣴⣶⡶⡦⡺⡻⢻⢻⡳⠫⢋⢏⢝⠝⡕⡝⡁⡝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠑⡕⡄⢹⡙⢻⡛⡋⡩⡫⡡⠪⢂⢊⢌⢜⠜⢔⢑⠝⡔⡡⡡⡢⢢⢊⢎⢌⢌⢌⣪⣿
⠀⠀⠀⠀⠀⠀⢀⡠⠼⣎⠄⠁⢰⢎⢈⢀⢔⢔⠕⡑⡡⡡⣢⡪⢪⣊⣊⣊⣌⣔⣔⣱⣡⣡⣵⣵⣿⣻⠟⣴⣿⠇
⠀⠀⠀⢀⡔⣪⠑⠀⠀⠈⠻⣤⣾⣗⣷⣷⡿⢾⣾⠿⠿⠿⠿⠿⠿⠟⣛⠛⠻⠛⣛⠛⠨⠙⣋⢉⣯⣿⡿⡟⠁
⠀⠀⣴⡿⠶⠒⠿⠿⢿⠥⣏⣐⣲⣈⠭⠭⣀⣀⣀⣈⠒⠂⠉⠉⠓⠊⠀⠀⠈⠀⠀⠀⠈⢀⣴⡿⢛⠡⡈⡵⡀
⠀⢈⣿⡆⠀⠀⡖⣰⠂⠀⠀⠀⠈⢉⡉⠛⠛⠛⠒⠦⠬⣭⣥⣒⣒⡠⣤⢀⣀⠀⢀⣠⣾⠻⠝⡀⠄⢒⣴⣷⡟⠲⠤⠄⡀
⠀⠀⠻⠷⢤⣬⣹⣯⣀⡐⠒⠂⠠⠄⠀⢒⣀⠤⠤⢀⢀⣀⠀⠈⠉⠉⠛⠓⢳⠾⡟⣹⠃⢁⡕⣠⢾⡷⢯⡅⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠫⠿⡲⢶⣦⣤⣄⣀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣎⢠⠁⡐⣈⣦⣿⠞⠙⢀⢀⣀⣤⡾⡛⣹⠃
⠀⠀⠀⠀⣎⡾⠝⠛⠓⠯⣥⣒⠠⠄⣀⠈⠉⠋⠛⠛⠟⠿⠲⠶⣤⣄⣠⢀⣹⣆⣦⣶⠛⠛⢒⣒⣶⡶⢿⡛⡱⡐⠙⣾⣀
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢈⡙⠺⠶⢬⣁⡂⠤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠫⠛⢛⣶⢶⣻⡽⠚⡣⠁⡑⡐⡔⠔⣨⣼⣶⡀⠠⠤⠄
⠀⠀⠀⠀⡹⣷⢄⠀⠀⠀⣀⠀⠀⠑⠦⢤⠈⠙⠛⠶⣨⣕⡒⠠⢀⡂⣔⣠⣴⡾⡿⢺⠩⡑⠠⠐⡱⡙⣕⣼⢼⡾⠟⠛⠀⣐⡒⠂
⠀⠀⠀⠂⠀⠉⠹⢗⣠⢄⡀⠀⠥⠢⣄⠀⠈⠐⠢⠀⠀⠀⠉⠛⣶⠾⡻⡹⡱⡱⡑⡁⡑⡐⣱⡱⣼⣻⠽⠎⠩⠁⠤⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠧⢔⡀⢄⡙⠒⠶⠦⡄⠀⠀⠀⠀⣇⠄⠌⠜⠔⡐⡐⣼⣔⣿⡽⠓⠫⠥⠤⠤⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢥⣒⡠⠌⣀⠀⠀⣧⢊⢌⣊⣼⣾⠽⠿⠍⠁⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠭⣑⠚⣿⣿⠾⠋⢁⣀⡈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⠤⠤

⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⢿⣿⣿⠿⠿⠿⠋⠉⠋⠉⠉⢉⠙⠛⠿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣀⣀⠠⢾⡅⡀⠀⠀⠀⠀⠈⠐⠠⣀⠈⠐⠠⡀⠁⠂⢀⣀⡀⠀⠀⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⣴⣿⡟⠁⠀⠄⠳⡀⠁⠂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠂⠄⡈⠻⣧⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⣿⠏⠀⠀⡀⠀⠀⡘⠲⡀⢀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠁⢀⣀⠠⠞⢻⡀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠏⠀⡠⠊⠀⡠⠊⠀⠀⠈⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠈⡉⠠⠶⠣⢴⡀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠚⢠⣤⡤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢴⣶⠁⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢻⣿⣿⣿
⣿⠿⠟⠋⠀⣠⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣧⡀⠀⠻⢿⣿
⣧⣤⣤⣤⣾⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠒⠶⢶⠶⠉⠰⢶⠶⠶⠚⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⢸⣤⣀⣀⣠
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⠟⠹⠐⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠺⠙⢿⣿⣿
⣿⣿⣷⠀⠀⠀⠡⠤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠄⠁⠀⠀⢸⣿⣿
⣿⣿⣿⣧⣀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⢸⠄⠀⠀⠬⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣤⣤⢤⢤⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠢⢄⡰⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⡠⢖⣉⢍⣯⣭⣄⡀⠀⠄⠠⣄⣄⣠⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣟⣀⣦⢀⣀⠤⠄⢀⣲⠾⠿⠓⠐⠦⠭⣝⣺⣦⣀⣸⡖⢉⣤⣶⣦⣥⣭⡉⣳⠶⢦⠤⣤⠤⠤⠤⠼⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⡇⠈⠈⠀⠒⣊⣉⣠⣴⣶⣼⣶⣶⣶⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣛⣮⣵⣒⣈⠒⣀⣀⣹⣿⣿
⠀⠀⠀⠀⠀⡟⢿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣅⣁⣿⣿⣿⡿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⠟⡇
⠀⠀⠀⠀⠸⠶⠾⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠄⠒⠐⠀⠉⠉⠀⠀⠒⠒⠂⠤⡤⠄⣀⣀⣀
⠀⠀⠀⡴⠒⠪⠭⢄⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⢒⣶⡤⠄
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠬⠭⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⢸⠃
⠀⠀⠀⠱⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⣶⠒⠊⠉⠀⠀⠀⠀⠀⣀⣨⡤⠄⣀⡀
⠀⠀⠈⣿⠯⢤⣀⠉⠉⠑⠒⠢⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠲⣦⣀⣀⣤⡶⠿⠯⠅⠒⠒⠈⠉⠱
⠀⠀⠀⣸⠀⠀⠀⠉⠓⠢⠤⣀⡀⠀⠀⠈⠉⣉⣛⣲⡦⠤⣤⣌⣧⣤⡶⠿⡿⠁
⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘
⢠⣶⣾⣉⣛⠷⣦⣄⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠴⣒⣒⣪⣭⠽⣿⠟
⣿⠁⠀⠈⠉⠛⠳⠿⢿⣷⣦⣄⡀⠀⡟⡀⠀⠀⣀⣀⣤⡤⠤⠶⣒⣚⣋⡭⠥⠴⠖⠒⠛⠉⠉⠁⠀⠀⠀⣾
⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣿⣯⣭⣽⠶⠶⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣄
⠀⠉⠛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣀⡀⠀⢠⡀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠶⠞⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠴⠫⣬⠏⠀⢠⠏⠀⡸⠁⠀⣩⠀⡇⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢻⠀⠁⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠈⠉⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⣴⠶⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣧⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠒⠒⠀⠀⡤⠷⠞⢋⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣧⣴⣾⣿⣿⣦⡶
⠀⠀⠀⢀⠀⠀⢀⣀⣀⡀⢀⢃⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠻⠿⠟⠛⣿⡟
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⢿⣷⣼⣵⣎⣉⣀⠀⡀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠀⠀⠈⠉⠉⠒⠂⠒⠒⠂⠘⠿⠋⣩⠖⠛⣩⡿⠏⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠒⠒⠒⠚⠒⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⣶⠿⠋⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠸⠾⠛⠱⠲⠶⠒⠒

⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡠⠴⠶⠛⠉⠉⠉⠀⢀⠐⠀⠄⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡠⠸⡧⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⠐⠠⡀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⢆⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠄⠀⠁⠂⠀⡁⢨⡀
⠀⠀⠀⠀⠠⠀⠀⠰⠀⠁⠀⡠⠀⠀⠀⠙⠄⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⣀⡡⠔⠚⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠠⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡉⠀⠘⠋⠒⢇
⠀⠀⠀⠀⠀⠀⠁⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠇
⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣀⠒
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠐⡀
⠄⠀⠀⠀⣠⠛⠓⠶⠶⠶⢦⣤⣤⣤⣀⣀⣀⣀⠀⠀⠐⢀⣀⣀⣀⣠⣤⣤⣤⠶⠷⠶⠞⠛⢣⡀⠈⠐
⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠀⠈⣙⠉⠉
⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠚⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡘⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠀⠀⠀⠄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠅⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣷⡟⣩⣥⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⠈⠉⠉⠙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡤⠀⣀⠒⠒⠲⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁⢠⡟⠊⠋⠃⢘⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠬⠿⠀⠀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢛⣒⡶⠀⢀⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠉⠂⣠⢾⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣿⡿⣹⣏⠳⣞⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠀⣰⣿⣻⣿⣿⣿⣿⣿⡄⠀⢹⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣾⢸⣿⣿⣿⣿⣿⣿⣿⣷⣠⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⡏⣷⠸⡷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢰⠂⠀⢿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⡟⠃⠀⠛⠦⡝⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢺⠃⠀⡄⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣄⠀⠀⠀⠀⠐⣝⢦⣀
⠀⠀⠀⠀⠀⢀⣞⠄⣸⠀⣸⠀⢹⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡆⠸⣦⠀⠳⡄⠀⠈⠡⠾⢷⣶⢦⡀
⠀⠀⠀⠀⠀⡸⡌⢀⡇⠀⡇⢠⣄⣿⣶⠲⢾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠈⠁⣀⠀⢀⣴⠟⠋⠉⠁⠈⢷⣀
⠀⠀⠀⠀⢰⢡⠁⣸⠀⣸⠀⠀⠉⣿⣿⣶⣤⣌⡑⠢⢍⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢦⣬⣼⣿⡟⠴⢋⣥⣶⠀⢀⣐⠳⣤⢤⣿
⠀⠀⠀⠀⡆⡘⣠⡏⢠⡇⠀⠀⠀⣧⣉⠉⠉⠉⠛⠳⢶⣤⣉⣳⣶⣤⣤⣉⣙⠛⠿⢿⣿⣿⠿⠤⢤⣄⣀⣉⣉⣽⣋⠵⠐⠊⠋⣿⣿⣷⣝⢻⣿
⠀⠀⠀⢸⠁⡗⣿⡁⣈⣠⣴⣒⡡⠞⠋⠀⠀⠀⠒⠒⠀⠼⠟⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣤⣄⡀⠀⠀⠀⠈⠙⢻⠒⠂⢙⣀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⣾⢰⣷⣫⡜⣫⡿⠋⠁⠀⠀⠀⢀⣒⣶⣶⣶⣶⣬⣥⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⢯⡍⠥⠩⣾⣿⣿⣿⠿⠁
⠀⠀⠀⡇⢸⣿⠏⢰⡏⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⠉⠙⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣴⣾⣿⣾⣾⣿⣿⣿⠃
⠀⠀⠀⡇⢸⠛⠀⣈⣧⡠⠴⠾⠿⠛⠛⠋⠭⠭⠬⠿⠛⠻⣀⣀⡹⠿⠿⢟⣛⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⡛⣿⡿⣽⣿⣿⣿⣿⡿⠿⠛
⠀⠀⢴⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠚⠛⠻⠿⠿⢿⣿⣇⡿⠧⠽⠛⠉⠈
⠀⠀⠀⠙⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣠⣀⣀
⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠖⠚⢿⠿⠇⣠⠙⠻⠿⢿⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠼⡸⠟⢩⣈⣨⣯⡽⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣛⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠉⠙⠛⠋⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡿⠃⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠐⠶⢤⠀⣠⠤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠛⠈⠀⡟⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⢘⢦⣄⠀⠈⠘⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡄⠑⠽⡷⣶⠶⠂⣿⣷⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⣿⠀⢰⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⢀⠀⠰⠂
⠀⠀⠀⠀⠀⠈⠙⠫⠳⠦⢤⢀⣀⣀⣀⣀⣉⣉⣩⣭⣝⣛⣦⣼⣿⣄⣾⡯⠭⠷⠒⠒⠂⠀⠀⠐⠈⠀⠀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢛⠁⢀⡀⠀⠠⠂⣶⠆⠀⠂⡇⠰⡏⡘⢹⡇
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⢉⡙⠐⠖⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠘⢷⣄⢸⠀⣿⠀⠘⠂⡗⠀⣷⣡⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣦⣤⣾⠀⠤⠀⠀⠀⠀⠉⠁⢸⠀⢠⡀⠙⠾⠀⠗⠀⠚⠀⠁⠀⣁⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠙⡋⠔⣫⣽⣿⣿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠄⢰⡒⠞⠛⠁⣸⡛⡯⢡⡆
⠀⠀⠀⠀⠀⠀⠈⠚⡀⠩⠭⢀⣶⡒⠀⠂⠆⠘⠿⠶⠶⠿⢿⠀⠀⠀⠒⠂⠐⠀⣸⢶⣶⣯⠁⣿⣾⠇⣾⡇
⠀⠀⠀⠀⠀⣴⠀⠂⠀⢀⣤⡿⠿⠀⠀⠀⡇⠐⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠀⣽⡿⠶⠤⠀⠊⢡⣸⣿⡇
⠀⠀⠀⠀⢀⣿⣄⡀⠟⠍⠀⠀⠀⠀⠀⠀⣳⠠⠠⠐⠂⠀⢡⡄⠀⠈⠀⠀⢰⠀⠿⢿⣦⡩⠽⢯⠤⢻⣿⡇
⠀⠀⠀⠀⠈⣿⣷⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠶⠒⠛⠘⠟⠓⢣⣾⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣿⠀⢀⣀⣀⣠⣤⣄⣈⣀⡀⠀⡀⠀⠀⠀⡆⢰⢠⣶⣶⣦⡤⣶⣶⣿⣼⣿⣿⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠃⢸⡄⠿⠿⠟⠃⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⡾⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠐⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⡒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣙⠲⠬⣝⡳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠒⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣒⠠⣍⡒⠦⣍⡐⠀⠉⠙⠳⣦⡀⢀⠠⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠬⣔⡢⢍⣒⠨⠅⡂⠈⠁⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣉⣳⣦⣍⡒⠠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣛⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⣤⣄⣀⣀⣠⣼⣋⣠⣤⡤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⣿⡻⣿⡛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣋⣻⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⢙⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠸⠈⢷⡈⣿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢻⣿⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⢀⣠⣤⠶⠖⠛⠋⣿⣥⠶⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⣷⡄
⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠩⣭⣿⣓⣒⣒⣒⣒⣒⣒⣂⣀⠈⠭⠍⠉⠉⠉⢩⣿⣉⠁
⣸⠋⠀⠀⠐⠢⢄⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠤⠤⠤⣀⣀⣀⣀⣒⣒⠒⠒⠲⠶⠦⠈⠀⠀⠀⠀⣾⠀⠈⠙⠲⢤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⣀⣀⣈⣉⣉⡉⠙⠛⠛⠒⠒⢒⣖⣶⣶⠶⠭⠭⠭⡉⠉⠉⠉⢀⣀⠀⠀⣿⠀⠀⠀⢀⣀⣉⣿⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⣬⣭⣭⣭⣽⣿⣁⢘⡀⡃⣐⢠⣀⣶⣶⣤⣤⡤⠉⠉⠹⢿⣛⣒⡀⠘⢷⡟⠛⠛⢉⡿⠉
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢄⣀⠉⠉⠉⠉⠉⠉⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠟⠃⠀⠀⢸⡇
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡾⠛⠉⠁⠠⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠤⠶⠒⠂⠀⠀⢼⠃
⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣩⣤⣤⠤⠶⠒⣂⣀⣠⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣘⠫⣓⠂⠀⠀⠀⠀⠐⠒⠚⣛⣛⣩⣭⣭⠴⠶⠶⠚⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣒⣶⣾⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⠷⢶⠶⠾⠓⠴⠚⠁⠀⢹⡄⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠠⣴⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠇⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⡀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡴⡄⠀⠀⠐⠲⠴⠚⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴⠇⠀⠀⠀⠀⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢴⣾⣿⣿⣿⠄⠀⠀⠀⢠⡟⢸⣿⠓⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠹⠛⠁⠀⠀⢀⡴⠋⢠⣾⣿⣤⣄⢀⠀⠀⠈⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣷⡘⠶⢄⣀⠤⠞⢉⣤⣾⣿⡿⠿⢿⣯⣾⡷⡀⡀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡦⠶⠀⠀⠉⠁⠀⢀⣀⣤⣤⣽⣿⣿⣿⣷⣀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣠⣤⣶⣾⣿⠟⠛⢛⣻⡯⣿⣿⣿⣿⣿⣧⠀⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠀⢨⠛⠫⢄⣶⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠐⠂⠹⣿⣿⣿⣿⣷⣾⡇⠀⠈⣆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠹⣶⣶⠖⢿⣶⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠐⢲⠾⠯⣉⣉⡉⠀⠀⠀⠈⣿⣿⡇⠸⣿⣿⣿⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⠉⢻⣿⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⢁⣨⡵⠆⠀⠀⠀⣿⠛⢿⠀⠽⣿⡿⢟⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣀⣤⠿⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠟⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠚⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠐⠒⠒⠒⠂⠰⠿⣍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⢀⡄⡠⠔⠋⣀⠴⠋⠀⠳⢄⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⠓⠤⠚⠛⠄⠀⠀⠀⠠⠌⠛⠺⠀⢛⠛⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡈⠀⠐⣈⣤⣄⠀⠀⠀⢰⣿⣅⠐⠀⠀⣄⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⢰⠃⠀⠀⣿⣿⡿⠀⠀⠀⠸⣿⣿⠇⠀⠀⢻⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠺⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠘⠆⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠉⠉⠁⠀⠇⠀⠀⠀⠈⢻⣪⠭⣭⣔⠏⠀⠀⠀⠀⠇⠀⠉⠉⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠙⠂⠒⠉⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣀⣀⠀⠤⣬⠍⡉⢉⢹⣥⠄⢀⣀⣀⢀⣀⣀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠖⠻⠀⠤⠤⠄⠀⢀⣀⣀⣄⣉⣋⣀⣀⡀⠀⠀⠠⠤⠤⠤⠛⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⣐⣂⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⣄⠀⠀⠀⠀⠀⠀⠀⠘⢭⡍⠭⢽⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡬⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⠋
⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀
⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠒⠒⠒⠚⠬⠡⠭⠼⠒⠒⠒⠒⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⡖⠙⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠓⠒⠒⠓⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠊⠙
⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠤⢤⡤⢤⡤⢠⣤⣤⡄⣤⣄⣀⣀⣤⡤⠤⠤⠤⠤⠄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠤⠤⠤⠤⠤⠤⣤⣀⣀⣠⡄⣤⢤⡤⠄⢤⢤⡤⠤⠆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀⠀⠀⠀⠀⠀⡏⠈⠀⠁⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠄⠀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⢀⡀⠠⡖⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣦⣰⣖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣌⠟⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠹⣡⠈⠳⡀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢘⠀⠀⡖⠲⠀⠀⠀⢀⡔⠃⢄⣘⠏⡘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢃⠻⣃⡠⠘⠲⡄⠀⠀⠼⠒⡄⠀⢸
⠀⠀⠀⠀⠀⣀⣨⠀⠀⡀⢀⠀⠀⠀⣶⠀⠀⠀⠉⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⠀⠀⠀⢰⠀⠀⣀⠀⡇⠀⢸⣀⡀
⠀⠀⠀⠀⠐⠁⠈⠄⠀⠀⠀⠀⠀⠀⠐⠆⣀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⣀⠔⠁⠀⠀⠀⠀⠀⠀⡎⠀⠳
⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣤⣄⣀⣀⣀⣀
⣿⣿⣿⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠛⠛⠛⠛⠲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠙⡷⠶⢶
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⣤⣀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣷⠀⢸
⠀⠀⠀⠀⢠⡴⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢻⠀⢸⡇
⠀⢠⡖⠛⢻⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡀⠀⡇
⣴⠛⡇⠀⠈⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣷
⣿⠀⣿⠀⠀⣷⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⢿
⢹⠀⢹⠀⠀⢻⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣷⠀⢸⡀
⢸⡄⢸⡄⠀⢸⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢻⠀⢸⡇
⠸⡇⠘⡇⠀⠸⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠈⡇
⠀⡇⠀⣇⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⣇
⠀⣿⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿
⠀⢸⠀⢸⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⢻
⠀⢸⡇⢸⡇⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠘⡇⠈⡇⠀⠘⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⢸
⠀⠀⣇⠀⣷⠀⠀⣧⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢸
⠀⠀⢿⠀⢻⠀⠀⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢸
⠀⠀⢸⠀⢸⡀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⣿⠀⢸
⠀⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⣠⡤⠶⠖⠛⣋⣉⣉⣉⣀⣀⣀⣀⣉⣉⠉⠉⠀⠀⣿⠀⢸
⠀⠀⠀⡇⠀⡇⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⣀⣀⣠⣤⡤⠤⠴⠶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣧⣶⣿⠿⠶⠒⠛⠋⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠛⠓⠶⣿⠀⢸
⠀⠀⠀⣷⠀⣿⠀⠀⣧⠀⠀⠸⣧⠴⠞⣋⣩⣥⠴⠶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠀⠀⠀⢀⣤⠤⠶⠶⠶⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⢹
⠀⠀⠀⢻⠀⢹⠀⠀⢻⣀⣠⡤⠶⠚⠋⢉⣀⣀⣠⣤⣤⠤⠶⠶⠖⠚⠛⠛⠛⠳⣄⡀⠀⠀⢀⣀⣤⠞⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠴⠶⠶⠶⠶⠞
⠀⠀⠀⢸⡀⢸⣦⣤⡼⠿⠶⠒⠚⠛⠉⠉⠉⠁⠀⢀⣀⣀⣠⣤⣤⠤⠶⠶⠲⠦⣬⣍⣉⣉⣉⣭⡴⠞⠁
⠀⠀⠀⠸⣧⠟⠀⣀⣀⣀⣠⣤⡤⠴⠶⠖⠚⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠉⠙⢲⡤⣤⣀⡀
⠀⠀⠀⠀⢠⠖⠚⠉⠉⠉⠉⠉⠙⠒⠲⠤⢄⣀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡇⢹
⠀⣀⣀⡖⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡀
⡠⢯⠀⢇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢳⠀⡇
⡇⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇
⢳⢸⡀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⢳
⢸⠀⡇⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⡇⢸
⠸⡄⡇⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸
⠀⡇⢱⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠘
⠀⡇⢸⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣇
⠀⢹⠸⡄⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹
⠀⢸⠀⡇⠀⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⠀⢸
⠀⠘⡆⡇⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢸⣀⣠⣤⣖⣪⠭⠭⠥⠤⠤⠤⠤⠬⢭⣀⣸
⠀⠀⡇⢸⠀⢹⠀⠸⣤⢴⣒⣫⠭⠽⠛⠛⠛⠛⠉⠉⠙⠛⠋⠉⠁⡠⠤⠤⠤⠶⠶⠒⠒⠒⠒⠒⠒⠛⠒
⠀⠀⢧⢸⠀⢸⣤⣒⣫⡭⠤⠴⠖⠒⠒⠛⢉⣉⣉⣙⠦⠤⠤⠴⣚⠵⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛
⠀⠀⢸⡜⣉⣉⣀⣠⠤⠤⠴⠒⠒⠚⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠂⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠁⠀⠀⠀⢀⠀⠀⠀⠀⠑⣼⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⡠⠊⠀⢀⡀⠀⠀⠘⠀⠀⠀⡀⠀⠂⠀⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠠⣿⡩⣭⡦⠀⠀⣦⡭⣽⣕⢸⠀⠀⠀⠀⢠⣠⠶⣤⠀⠀⠀⣤⣶⡔⠂⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡏⣻⡟⢰⣶⣯⠒⠊⣿⣶⠌⢫⡟⠀⡀⠄⢲⡞⠈⣭⣿⡗⠤⣺⣿⣍⠑⣳⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡰⢀⡃⠈⠊⠛⠁⠀⠀⠉⠉⠐⠁⣗⡠⠘⡀⠨⠃⠢⠙⠛⠁⠒⠈⠿⠋⠔⠙⠇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⡐⠁⡐⠀⠀⡁⠄⠀⠀⠀⠓⠛⠀⠀⠀⡐⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠰⠄⡀⠀⡁⠈⠂⠄⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠀⠀⠈⠀⠀⠴⠊⣀⠀⠓⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⡤⠭⡆⠀⢰⠯⠤⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⣀⠐⠀⠀⠀⠀⠈⠀⠀⠉⠲⠀⠀⠀⠀⠠⢃⠀⠀⠀⠀⠀⠀⢰⢸⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠘⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⠀⢀⠀⠀⠀⠀⠘⠘⠂⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⡔⠀⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⠀⠀⠈⠀⢤⣤⣀⠈⢢⠈⢀⣀⣄⠂⠈⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⢦
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠄⠒⠋⠉⠁⢂⠀⠀⠀⠀⠀⠀⠈⣁⡶⢄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠀⣈⢢
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⣜⠁⠀⠀⢙⡤⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣝⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠓⠤⣀⠀⠑⢄⠀⠀⠀⠀⡠⠊⠀⣀⠤⠚⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠀⠤⠤⢀⡀⠑⠢⡈⢆⠀⠀⡔⢁⠔⠊⢀⡀⠤⠤⠀⠒⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢌⢆⡆⣰⡰⡡⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠢⠤⣀⡀⠀⠀⢸⠀⠀⡇⠀⠀⢀⣀⠤⠄⠒⠒⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣸⠀⠀⣇⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠉⢻⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣤⠀⢠⡿⠁⠉⠳⡶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠎⠀⠀⠀⠐⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⢸⡀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠓⢄⡀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠓⢦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⢱⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡆⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⡀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⢻⠄⢄⣀⠀⠀⠀⠀⢠⡶⠾⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣽⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣼⡿⢿⣤⣤⣤⣤⣤⣤⣴⣶⣶⠚⠛⠓⠂⠀⠘⢰⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢁⣠⣶⣶⣶⣾⣿⣿⣫⡭⢉⣭⣴⣻⣭⣵⡆⠀⠀⠀⠀⠀⢀⣧⠁
⠀⠀⠀⠀⣠⡤⣂⢴⠦⣀⣄⢀⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠠⠀⣀⣴⣿⣀⣀⡀
⠀⠀⠀⠈⠁⠈⠈⠑⠾⠩⠾⠿⠿⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⠁⣶⣿⡟⠛⠋⠉⠀⠀⠀⠚⠛⠛⠶⠾⠿⠶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⡿⠿⠟⠛⠋⠁⠈⠉⠛⠶⠮⠛⠛⠉
⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⣥⣾⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠴⣶⣄⣀⣀⣀⣠⡄⢀⣠⠞⠁⢴⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠛⠛⠉⠁⠚⠉⠀⠀⠀⠺⣧⠀⠀⠀⢠⣤⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢆⣿⠟⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠨⠋⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠶⢄⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡴⡇⠀⠀⠀⠐⠲⠖⠋⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣧⡀⠀⠀⠀⠀⣰⠁⢐⠢⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠟⣿⣿⠋⠀⠀⠀⢀⡴⠃⢀⣾⣇⢀⡀⠉⠉⠉⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡎⢧⡀⠀⠀⠀⣀⡴⠋⢀⣴⣿⣿⣿⣿⣗⣴⣦⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⣉⠓⠒⠋⠁⠴⠾⠛⠛⠛⠋⠉⠙⣿⣿⣯⣌⡆⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⣀⣠⣤⣴⣶⣷⣾⢿⣿⣿⣿⣿⣶⣆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠻⡿⠿⢿⣿⡿⠟⠉⢀⣀⣤⣶⣶⣿⠿⠿⠛⠉⡉⠡⠿⢗⣿⣿⣿⣿⣿⡷⠃⣠⠀⠘⢆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⢎⡉⠑⣸⣿⣿⣿⠟⢋⠉⠀⠀⠀⠈⠁⠀⠀⠉⠁⠸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣛⠛⠛⠛⠛⠋⠙⠈⣿⣿⡟⠘⣿⣿⣯⡿⢷⣾⣯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠴⠭⠯⣛⣉⡁⠀⠀⠀⠈⢿⣿⣿⡁⢹⣿⣿⣿⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠙⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⣀⣠⡼⢖⠀⠀⠀⢸⠏⠻⣇⠠⢿⣿⡿⢛⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣀⣀⣀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢀⣠⡯⠗⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢴⠒⢮⢍⣉⣉⡁⠀⠒⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⣀⠸⣇⠀⠱⣌⠓⠄⡈⠁⠒⠂⠤⡀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣀⠔⠊⢁⣀⠀⢯⢢⠀⠈⠳⣀⠈⠒⢄⠀⠀⠀⠑⢄⡀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⢊⠄⠊⠉⠀⠀⠀⠀⣧⠳⡀⠀⠈⠓⢄⠀⠉⠢⣀⠀⠀⠙⢦⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡠⠊⡐⠁⠀⠀⠀⠀⠀⡠⠊⠀⠱⡌⠦⡀⠀⠀⠑⠢⣀⠀⠉⠐⠢⠄⡑⣄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡠⠊⡠⠊⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠢⡉⠦⡀⠀⠀⠀⠉⠑⠢⠤⢀⣀⣈⠉⠁⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⠔⣡⠎⠀⠀⠀⢀⣀⠔⠊⠀⠀⠀⠀⠀⣀⠀⢀⠈⠢⢌⡑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⢈⣩⢇
⠀⠀⠀⠀⠀⠀⠀⠰⢹⠙⠃⠔⠒⠒⠈⠘⠁⠀⠀⠀⠀⠀⠀⠈⣥⠀⢠⡁⠀⠀⠉⠑⠢⠤⠈⢉⣁⢀⣀⡈⢭⠋⠈⡌⠆
⠀⠀⠀⠀⠀⠀⢀⠃⠘⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠀⡇⠘⡀
⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⢸⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡇⠀⡇⠀⠃
⠀⠀⠀⠀⣠⢤⣆⣰⣀⣀⣚⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡃⣀⣥⣀⣺⡤⣄
⠀⠀⠀⡞⠙⠛⠚⠛⠛⠛⠿⠿⠿⠿⣷⣶⣶⣴⣤⣤⣤⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣷⡿⠿⠿⠿⠟⠛⠓⠒⠀⠒⢳
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡟⠛⠋⠙⠛⢻⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠂⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡠⠐⣇⠠⠔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⠀⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⠄⣸⠂⢄
⡎⠀⠀⠀⠀⠴⠚⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠓⠦
⢃⠀⠀⠀⠀⠀⠴⠚⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠦
⠈⠢⡀⠀⠀⠀⢐⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣓⡂⠀⠀⠀⢀⠔
⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⠒⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠒⠒⠂⠤⠤⠄⣀⣀⠀⠀⠀⡗⠒⠀⠀⠒⢺⠀⠀⢀⣀⣀⠀⠤⠤⠀⠒⠒⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡾⠋⠉⠙⠃⠀⡏⢹⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⣿⣿⣿⣿⣿⠉⠀⠀⣼⠀⢸⠁⢳⡸⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⡰⢶⣿⣿⣿⣿⢇⡞⠀⣰⠇⣰⠏⢀⢧⣧⣎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢠⠟⣰⣿⣿⣿⣿⣿⡿⢁⡴⢋⣴⢏⣤⣏⣮⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡏⣰⣿⡿⣿⣿⣿⣫⣴⣯⣴⠿⣷⠿⠧⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡿⢠⡿⣿⢣⣿⣿⣿⣿⡏⠁⠀⠀⣻⣶⠄⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠇⣼⢇⣿⢸⣿⣿⡿⠿⠇⠀⠀⠀⠉⠀⠀⠀⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠀⣿⢸⡇⢺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡿⢸⡇⢸⡇⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠀⡇⠘⡇⠈⢣⠙⣿⡟⠀⠀⠀⣤⣄⣀⣀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿⡀⢱⠀⢻⡄⠈⡆⠈⠻⢷⣤⡀⣿⣿⣿⡟⠉⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢗⠆⢆⠈⢿⡄⠐⡀⠀⣸⣿⠇⠘⢿⡿⠃⢀⡼⠃⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⠀⠘⢧⣈⣿⣶⣿⡿⠛⠁⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢻⡿⠋⠉⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠋⠋⣼⡋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠉⠳⣞⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠙⣇⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠠⣟⣷⡤⣤⠀⠀⠘⠂⠴⢱⡠⢤⣄⠀⠀⣼⢃⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠻⣧⡀⠀⠙⠲⢤⣀⡀⢀⣨⠏⢻⣦⣄⣀⡀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⣏⣹⣠⣄⠀⠈⠁⠿⠁⠀⣼⢃⣾⣿⠇
⠀⠀⠀⠀⢀⣤⣶⡟⠋⣤⣻⡝⣿⣶⣤⡀⠀⠈⠁⠉⠀⠀⣼⡇⢽⢿⣿⣶⡄⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠓⠀⠀⠀⠀⠀⣼⢃⣾⣿⠇
⠀⠀⢠⣾⠟⠉⢻⠻⢿⣾⣿⣿⣿⣿⠻⣏⠉⠐⠒⠒⠒⠛⠉⣷⣸⢿⣶⣿⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣾⣽⠏
⠀⠀⣿⠃⢠⡷⣈⠲⣈⣿⣿⣿⣿⡽⢣⠙⣧⠀⠀⠀⠀⠀⠀⢹⣇⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡟⣽⠏
⠀⢸⡏⢰⡏⢰⡟⣷⣽⣈⣿⣿⣿⣷⣌⣦⢹⣧⠀⠀⠀⠀⠀⠘⣿⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⢏⣾⠋
⠀⣿⡇⣾⠧⣾⣿⢿⡿⢁⣿⣿⣿⣿⣿⣷⠈⢻⡄⠀⠀⠀⠀⠀⢿⡆⢸⣷⠴⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⣴⡟⡜⣸⠏
⠀⣿⣇⣿⢄⣿⣷⣿⣷⣸⠻⣿⣿⣿⣿⣟⠁⠸⣇⠀⠀⠀⠀⠀⢸⡇⣠⣽⡤⠖⢻⡟⢶⣤⣀⠀⠀⠀⠀⢀⡴⠲⣾⠉⢾⡍⢳⣴⡟⡐⢰⠏
⠀⢸⣿⣽⡏⠉⣬⡍⡉⢹⠸⣿⣿⢻⣿⣿⢺⣧⣿⡀⠀⠀⠀⠀⢸⠟⠉⠀⢀⣴⣿⣏⣤⠶⢛⣿⣶⣤⣀⡏⢹⡀⠹⡄⠈⡇⠈⢿⡴⢡⠏
⠀⠀⣿⡿⣿⣦⣼⣯⠙⡟⢰⣿⣿⣸⣿⣿⣾⣿⢻⡇⠀⠀⠀⢠⡏⠀⠀⠀⠈⠉⠉⢀⣠⠴⢊⣿⣀⠹⢿⣿⡀⣧⠀⠣⠀⠀⠀⢸⣧⠊
⠀⢠⣿⢰⣿⣿⣿⡄⢈⣤⣾⣿⣿⣿⣿⢿⡼⢟⣈⣿⡤⠖⢶⡏⠀⠀⠀⠀⠀⠘⠋⠉⣁⠴⢋⣯⣽⡿⣦⣽⡇⠈⠀⠀⠀⠀⠀⠀⡟
⠀⢸⡏⢾⣿⣿⣹⡟⠀⣍⣱⣿⣿⣿⣷⣾⣶⠟⠛⠋⠻⣦⠀⢳⡀⠀⠀⠀⠀⠐⠊⣉⡠⢴⣯⣿⣿⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠸⣧⠸⡏⢋⠹⢟⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⢳⠀⠀⢀⣀⣈⣉⣥⣴⡿⠙⠾⡟⣁⠹⡟⠲⣤⣀⣀⣀⣤⠞⠁
⠀⠀⠹⣷⣷⣆⢱⣾⢿⣿⣿⡟⠡⠀⠀⠀⠀⠀⠀⣀⣀⠀⢹⡄⢸⡿⠛⠛⢉⢹⣿⣷⣿⣿⠠⢞⡓⣌⢦⠹⢦⣀⣌⡩⠏⠁
⠀⠀⠀⣿⣽⣿⣧⣴⣿⣿⣋⢀⣀⣀⣀⣤⢶⣷⣿⣿⣿⣿⢸⣷⣾⡇⠈⠀⢿⡌⣿⣿⣧⣝⣀⣀⣁⣬⣤⡶⠛⠉⠁
⠀⠀⠀⢻⡎⢻⢿⡾⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⡟⢋⣁⣾⡟⣹⡇⢀⠠⡄⠂⣿⡇⠈⠙⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠙⠄⠑⠹⢿⣿⣿⣿⣿⣀⣿⣿⣿⣿⠿⠿⠿⠻⣟⠀⣿⡇⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠘⠇


⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⠀⠀⢀⡠⢦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠴⠂⠀⠈⠁⠀⠈⠉⠁⠀⠘⠈⠁⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⣀⠠⣀⠠⡄⠀⣀⡀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢀⢇⡀⠔⠊⠛⠒⠈⠉⠓⠈⠀⠘⠒⠁⠀⡄⠀⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⠀⡆⢠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢇⢸⠛⠗⠀⡀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡁⠘⡀⢠⢧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⡻⠸⠢⢤⠀⠀⠀⠀⠠⣶⡦⠐⠂⢸⣶⡆⠀⠀⠀⠀⠰⡴⣷⠁⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠨⠀⠤⣀⣂⠀⠀⡀⠀⠀⠠⢄⡀⠆⢀⡀⡀⠀⢀⣀⣠⠤⠨⠗⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠒⠠⠨⢵⣅⣀⣠⣴⠭⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠄⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠊⠀⠀⠀⠰⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢷⡀⠀⠀⠀⠸⣤⣀⠀⠀⠀⠀⢸⠀⠀⢀⣠⡄⠀⠀⠀⢀⡮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡅⠀⠑⣄⠀⣠⠞⠁⠀⠉⠑⠒⠀⠘⠒⠉⠁⠈⠣⣄⣀⣠⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⠇⠔⠈⠀⠙⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢃⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠑⠀⠤⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠈⠁⠒⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⢀⠀⠀⢀⠄⢢⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡁⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢤⠈⠒⡁⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠈⡀⠀⡃⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠔⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣰⠃⠀⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠘⠃⡄⠉⠐⠀⠀⠀⠀⢤⣴⠒⠀⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠠⡔⠠⠤⠐⠀⠒⠒⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠂⠅⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠐⠉
⠀⠀⠀⠀⠨⢀⣀⣀⣀⣀⣀⡀⣀⡈⠀⠀⠀⠀⠀⢀⡴⠐⠈⠀⠀⠀⠀⢀⠄⠂⠀⠢⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢅⣀⡀⠀⣀⣀⣀⣀⠤⠂⠀⢀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠔⠁⠐⡁⠀⣀⠠⠐⠁⠀⠀⢀
⠀⠀⠀⠀⢀⣂⡀⠀⢀⡀⠀⠀⠀⠀⡰⠀⠀⠁⠀⠀⠀⢀⠀⠀⡀⠁⡠⣎⡁⠀⢀⣀⠐⠀⠢⡀⠀⠀⠁⠠⠄
⠀⠀⠀⢄⠀⠉⠉⣩⣍⣉⡉⠩⣭⣭⣥⠠⠀⠀⢠⠀⠀⠘⠀⠈⢀⠈⠐⠉⠀⢰⠀⠀⠉⠁⠂⠀⢑⠀⠃⠀⠀⠑
⠀⠀⠀⠲⠶⠦⠒⠒⠐⠂⠐⠒⠒⠒⠒⠀⠈⠒⠊⠀⠐⠡⠆⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠊⠀⠀⠀⠈⠐⠛

⠀⢀⠤⠤⠤⡀⠀⠀⢀⠤⠤⠤⡀⠀⠀⢀⠤⠤⠤⡀⠀⠀⢀⠤⠠⠤⡀⠀⠀⢀⠤⠤⠤⡀⠀⠀⢀⠤⠠⠤⡀
⠀⠇⠀⠀⠀⠈⡄⠀⠃⠰⣶⣆⠈⡄⠀⠃⠀⠀⠀⠘⠀⠀⠃⠀⠀⠂⠘⠀⢠⠁⠐⠀⠀⠘⠀⢠⢁⣴⣶⣆⠸
⠀⠣⡀⠛⢀⡴⠁⠀⠣⡙⠃⢉⡴⠁⠀⠣⡛⠀⢀⠜⠀⠀⠣⡐⠐⢂⠜⠀⠈⢢⡀⠀⢀⠜⠀⠀⢮⡁⠋⢋⠜
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉
⠀⡔⣉⡀⣉⠢⠀⠀⡔⢉⡀⣉⠢⠀⠀⡔⠉⠀⡉⢢⠀⠀⡔⣉⣀⣉⢢⠀⠀⠔⣩⣤⡉⢢⠀⠀⠔⠉⢀⢉⢢
⠀⡇⠿⣿⡿⢀⠃⠀⡄⠸⠿⠯⢀⠇⠀⡄⣬⠭⣥⢀⠀⠀⡄⠟⢻⠻⢠⠀⠘⡀⢿⣿⡧⢠⠀⠘⡀⣴⣬⡤⢠
⠀⠈⠂⠤⠔⠋⠀⠀⠈⠂⠤⠔⠁⠀⠀⠈⠂⠤⠐⠁⠀⠀⠈⠂⠤⠐⠁⠀⠀⠈⠢⠤⠐⠁⠀⠀⠉⠢⠤⠐⠁
⠀⢀⠤⠀⠤⡀⠀⠀⢀⠤⠀⠤⡀⠀⠀⢀⠤⠀⠤⡀⠀⠀⢀⠤⠀⠤⡀⠀⠀⢀⠤⠀⠤⡀⠀⠀⢀⠤⠀⠤⡀
⠀⠇⠀⠤⠄⠈⡄⠀⠋⣿⣆⢦⠈⡄⠀⠃⠀⠀⠀⠘⠀⠀⠃⢸⣿⡇⠘⠀⢠⠁⠲⣤⠂⠘⠀⢠⠁⠀⠀⠀⢸
⠀⠣⣀⠛⢀⠔⠀⠀⠣⣃⠙⣈⠔⠁⠀⠣⣀⠀⣀⠜⠀⠀⠣⣘⠛⣁⠜⠀⠀⠢⣈⠈⣃⠜⠀⠀⠢⣉⠉⣉⠜

⠀⡔⠉⠀⠈⠢⠀⠀⡔⢉⣀⡉⠢⠀⠀⡔⢩⣤⣍⢢⠀⠀⡔⢩⣤⡍⢢⠀⠀⠔⠉⠀⠉⢢⠀⠀⠔⠉⠀⠉⢢
⠀⡇⠤⠤⠤⢀⠃⠀⡄⢿⠿⡿⢀⠃⠀⡄⠈⠿⠁⢠⠀⠀⡄⢸⣿⠇⢠⠀⠘⡀⠸⣾⠇⢠⠀⠘⡀⠀⡤⠀⢠
⠀⠈⠒⠀⠒⠁⠀⠀⠈⠒⠀⠒⠁⠀⠀⠈⠒⠀⠒⠁⠀⠀⠈⠒⠀⠒⠁⠀⠀⠈⠒⠀⠒⠁⠀⠀⠈⠒⠀⠒⠁
⠀⢀⠄⠒⠢⣀⠀⠀⢀⠄⠒⠢⡀⠀⠀⢀⠄⠒⠠⡀⠀⠀⢀⠄⠒⠠⡀⠀⠀⢀⠔⠒⠠⡀⠀⠀⣀⠔⠒⠠⡀
⠀⡇⡞⠂⠰⠈⡆⠀⠃⢰⣷⡖⠈⡆⠀⠃⣴⢟⣤⠘⠀⠀⠃⢸⣿⡇⠘⠀⢠⠁⠈⠈⠁⠘⠀⢠⠁⣴⣿⣦⠸
⠀⠣⣀⠘⣃⠔⠀⠀⠣⣉⠉⣉⠔⠀⠀⠣⣀⠛⣁⠜⠀⠀⠣⣘⠛⣃⠜⠀⠀⠢⣐⠒⣀⠜⠀⠀⠢⣛⠋⣉⠜
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⡔⣁⣀⣈⠳⡀⠀⡔⣥⣤⣌⠳⡀⠀⡔⠁⠀⠈⢢⠀⠀⡔⢡⣤⡌⢢⠀⠀⠞⢡⣤⡌⢢⠀⢀⠞⣡⢀⣌⢢
⠀⡇⠙⠛⠉⢀⠃⠀⡄⠉⠉⠉⢀⠃⠀⡄⠀⠀⠀⢠⠀⠀⡄⢸⣿⠇⢠⠀⠘⡀⢹⣿⡇⢠⠀⠘⡀⠭⠈⡹⢸
⠀⠈⠒⠂⠒⠁⠀⠀⠈⠒⠂⠒⠁⠀⠀⠈⠒⠒⠒⠁⠀⠀⠈⠒⠒⠒⠁⠀⠀⠈⠒⠒⠒⠁⠀⠀⠈⠒⠀⠒⠁

⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⣠⠔
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢀⣿⢶⣤⣀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⢀⠴⠊⠀⢐⣇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠛⠦⢽⣷⣄⣠⣴⣉⣤⣀⣠⣀⡴⠊⠀⠀⠀⢀⡼⠋
⠀⠀⠀⣾⡷⠶⠤⠤⣄⣀⠀⠀⠁⠀⣀⣤⣴⡶⢊⣁⢹⡇⠀⠀⠀⠀⠀⠀⡨⠛⠛⠻⢭⣙⠒⠤⣄⠀⠀⠀⣠⠖⠁
⠀⠀⠠⠿⠯⠽⠯⠽⠶⠶⠿⠶⣶⡿⠿⠿⠿⠿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠈⠙⠲⢬⣦⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠈⠉⠐⢄⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢔⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠳⣦⡙⠢⣄⠀⠀⠀⠀⢀⡠⠴⢚⡁
⠀⠀⠀⢠⠿⣆⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣮⢄⠀⠈⠙⠷⣤⡙⣶⡕⢊⣡⠴⠒⠉⡠⠊⠉⠁⠐⠒⠒⠠⠀⡀
⠀⠀⠀⡈⠧⡀⠑⢄⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⣴⣗⡯⢶⣭⡄⠀⠀⠀⠈⠛⠷⠛⢯⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⣠⢾⡅
⠀⠀⠘⢿⡀⠉⢄⠀⠁⠀⠀⡀⠀⠈⠛⢦⡀⣼⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠊
⠀⠀⠀⠀⠙⢦⡀⠑⠄⣈⣠⣴⡶⢶⣾⣿⠿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣑⡒⠲⠤⠤⢀⣀⣀⡔⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠹⣄⢠⣤⡤⠷⠚⠉⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠑⠒⠦⠤⣀⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⣹⣿⣦⣤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⢿⣿⣿⠿⠋⣽⣿⣿⣿⣿⣿⣿⠟⠋⠀⢻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠈⣉⣀⠀⠾⠿⠛⠛⠛⠉⠁⠀⢀⣀⡀⠀⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣋⠀⠀⠸⣛⣿⡇⠀⠀⠠⠴⢦⠀⠀⠀⢟⣻⣿⠀⠀⠘⡋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⠀⠀⠀⠀⠀⢠⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠻⣿⣿⣷⣶⣶⣾⣿⣿⠃⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠻⢿⣶⣶⡿⠟⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⣀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠈⠑⠀⢡⠈⠀⠈⠁⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣶⣶⣶⣶⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣤⣤⣤⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣭⣭⣥⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣍⣛⠛⠛⣛⣫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⡀⠀⠀⢀⡀
⠁⠒⠀⠈⠃⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠢⠀⠄⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠒⠀⠴⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢡⡀⠀⣤⡠⠦⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠰⠄⠀⢈⡁
⠀⠀⡇⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠼⠀⠀⠀⠁
⠀⠙⠛⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⢉⠏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄
⠄⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⠆
⡀⠀⠀⠀⠂⠀⠁⠐⠂⠀⠀⠀⢶⣦⣀⣂⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⣿⣷⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠛⢶⣄⡀⠀⠀⢘⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣟⠻⢿⣿⣶⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢉⠛⢷⣦⣼⣷⠀⡅⠀⠀⠀⠀⠀⣀⡀
⣿⣶⣦⡜⠟⣷⣶⣆⣀⣱⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣩⣿⣿⣶⣅⡀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷
⠀⠈⠙⠻⣿⣿⣿⣟⣛⣛⣛⣛⣿⡟⣿⡆⠐⡀⠀⠀⠀⠀⠀⠈⠹⣿⢿⡏⠉⠻⣷⡤⠀⠀⠀⠀⠀⠈⠏⠉⣁⡀
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠛⠛⠛⠻⢿⣯⡻⢾⣷⣦⣀⠀⠀⠀⠀⠀⠘⠧⠉⠗⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣻⣦⡹⣿⣷⣶⣤⣀⠠⣄⠀⣠⡄⢀⡀⠀⠄⠰⠃⠀⢀⠃⠀⠀⣹⠀⠀⠘⢋⣀⣠⡄⠀⢀⣴⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⢿⣌⡻⣦⢿⣧⣿⣿⣿⣷⣏⢀⠀⠀⠀⠰⠄⣉⡀⠘⠃⠀⠀⠘⣟⣿⡿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣿⣾⣻⣿⣽⣿⣿⣿⣿⣏⡤⢳⡄⠐⣧⣶⡿⠃⠀⠀⠀⠀⠀⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣀⣿⣿⣿⣦⠄⠉⠀⠀⠀⠀⠘⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣟⡿⠋⠿⣿⣿⣿⣿⡷⠂⠀⣴⣀⠀⠀⠿⡟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣆⢶⣸⣿⡿⠛⠛⠷⢢⣽⡿⠋⠀⠀⠙⢆⡹⣄⢀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣿⣿⣿⣟⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⡷⠀⠀⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⡗⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⣷⣿⣿⡟⣿⣿⣿⡧⣿⣿⣷⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣄⡰⠂⣴⢶⠀⣀⣠⣿⣶⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⠻⣿⣿⡿⠀⢸⣿⣿⣛⠉⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡿⡯⢨⡷⠳⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣿⡿⠗⢰⣿⣿⣿⣿⡟⠐⠂⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢾⣷⣿⣁⣈⣠⠗⠴⠛⠿⠟⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⡏⠐⠛⢸⣿⣿⣿⣿⠛⠁⠀⠀⣤⢂
⠀⠀⠀⠀⠀⠀⠠⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⣿⢙⡅⣿⣇⢤⡀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠈⢆⠀⠀⠤
⠀⠀⠀⠀⢀⠀⣤⣤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣴⣿⣿⣽⣿⣟⣿⣿⡿⢻⣧⠤⣼⣿⣿⣿⣿⣇⢀⡀⠀⠈⡼⣄⠀⠀⠈
⠀⠀⠀⣀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣯⣿⠿⠟⠛⠃⢹⣿⠘⠛⠋⣿⣿⢿⣟⢻⣷⡀⠀⠠⢛⡷⠄⠶⣄
⣀⣤⡴⠛⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠙⠁⠀⠀⣀⡀⣠⣤⣿⠏⠀⠀⠀⠘⢿⣾⣯⢠⣿⠃⡀⠀⠘⠷⠤⣤⡀
⣿⠿⡑⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⠀⠙⣿⣾⣿⣷⣾⡟⠀⠀⠀⢀⣀⣉⣥⡈⠁⠀⠹⣦⠀⠀⠀⠈⠛
⣿⠦⣄⠘⠆⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠘⠛⠉⠙⠻⣧⠀⣀⣠⣿⠿⠛⠉⠀⠀⠀⢰⡿⠷⣄⣄
⠳⡀⢹⡇⠀⠀⠸⢿⣿⣷⠄⠀⣀⣰⣶⣤⣶⣶⣶⣤⣤⣶⣿⣿⡟⢹⣧⡘⠀⠐⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠛⠻
⠚⠋⠀⢠⠀⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⠏⠀⣸⡟⠿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣄⣀⣀⣀
⣄⣀⠰⣶⠖⣤⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢠⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠛⢿⡿⠋⠁
⠉⠉⠀⠀⠘⠛⢶⠂⠀⢻⣿⣿⣯⡛⠿⢿⣡⣾⠛⠉⠁⠀⢠⡤⣺⣿⣿⣷⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠠⠤⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣒⣒⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠤⢭⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⠉⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠶⠦⣤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⣈⣇⡀
⠀⠀⠀⠐⣤⣊⠉⠉⠉⠒⠒⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠃⢠⣤⣄⡀⠀⢀⣀⣤⣶⣛⡋⠥⠀⠀⠀⠂⠆
⠀⠀⠀⠀⢹⠀⠀⠉⠒⠦⣤⣀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣄⣀⡀⠀⠈⢸⡄⢀⣀⣽⣷⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣤⡤⠤⠔⠒⠒⠉⠉⠉⠛⠒⠿⠛⠉⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⣲⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⣧⣄
⠀⣾⠟⠷⢶⣬⣉⠓⠦⣤⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠄⠒⢒⣈⣩⠤⠤⠶⠒⠛⡿⠁
⢸⡏⠀⠀⠀⠀⠉⠙⠓⠒⠿⢿⣶⣤⣀⠀⡸⢡⠀⣀⣀⣠⣤⡤⠶⠶⢖⣚⣉⣩⡥⠤⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢿⣿⣭⣭⣵⠶⠶⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣠
⠀⠈⠙⠛⠷⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠞⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣦⣟⣀⣤⣤⠤⠶⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠀⠂

⠀⡈⠐⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣄⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠠⠚
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡠⠔⠈⠀⠀⠀⠠⠾⠃⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⢠⡁⠀⢠⠀⠀⠀⠀⠀⠀⠐⠊⠒⠀⠐⠂⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈
⠀⠀⠀⠀⠀⣠⢀⠀⠀⡀⣀⣤⡂⡀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠀⠀⢠⡀⢀⠀⠈⠃
⠀⠀⠀⢠⢞⣾⡿⠃⠀⠀⠀⠸⢁⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⣤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢠⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⢠
⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⡙⠂⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⣀⣀⣀⡀
⠀⠀⠀⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁
⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠐⠲⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⢀⡉⠀⢉⡀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠄⠈⠀⠀⠀⠠⠿
⠀⢀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⢀⠴
⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⡀⢀⣀⠂⠐⠀⠀⠀⠀⠀⠈⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣼⡽⠀⠀⠀⠈⠿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠈⠙⠂⠉⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠟⠋⠀⠀⠘⠛⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⢀⡀⠀⠀⢦⡔⠀⢉⣼⠏⠀⠀⠀⠀⠹⣧⡁⠀⢢⡵⠀⠀⢀⡀⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⠷⠀⣀⡄⠁⣠⣾⣿⡀⠀⠀⠀⠀⠀⠈⣓⣄⠈⠀⡀⠀⠾⠊⡰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⡤⠀⠐⠚⠁⠈⣿⠧⡀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠀⢤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⣉⡳⣄⠀⠀⠟⠀⠀⠀⠀⣀⢀⡈⠀⢁⠀⠀⡘⠀⢀⡀⣀⠀⠀⠀⠀⠡⠀⠀⣠⢞⣩⣻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠉⢻⠾⣷⣎⣤⣂⠨⠭⠒⡞⡿⠓⢀⢘⠀⠀⡁⡤⠚⢽⢓⢶⡭⣄⣀⣤⣁⣼⠿⠛⢻⣡⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⣇⠞⡕⢿⣿⠙⠓⠲⠒⠶⡓⢧⣀⣜⡸⠀⠀⠇⣢⣀⡼⠘⠉⠀⠚⢴⡋⣿⡿⡰⠒⢸⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡻⠸⠸⣿⡆⢀⠀⠀⢀⠶⠁⡇⠀⢠⠀⠀⡄⠀⢸⠸⢁⡀⡀⢀⣈⢱⣿⡇⡘⠌⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷⣶⣿⣷⣂⣤⣵⣶⣾⣿⣿⣶⠌⠀⠀⠡⣶⣿⣿⣶⣶⣦⣭⣌⣸⣿⣴⣾⣉⠁
⠀⠀⠀⠀⠀⠀⠍⠢⣀⡀⡤⠐⠊⠹⣿⣿⠿⠿⠿⠛⠿⣿⡿⠿⣿⠇⠀⠀⠀⠀⠘⣿⠿⠿⣿⠿⠛⠿⠿⠿⣿⣿⡏⠁⠂⢤⢄⣀⠔⠹
⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⠴⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡉⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠦⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣉⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠈⠉⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⢤⡤⠄⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣉⣉⣙⣛⣃⠀⠈⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢻⠟⢉⡟⢻⠉⠙⡟⣸⠁⠀⠀⠀⠀⠉⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⢿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣿⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠽⣿⣯⣦⣤⠤⠴⠶⠶⢒⣀⣰⠄⠐⠒⠚⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠀⠀⠀⠀⠀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠋⠰⠂⠀⠀⠀⠀⣀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠠⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠂⠀⠠⠤⢄⡠⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡾⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠛⢋⣉⣤⡶⠾⢛⣩⣿⣷⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠋⣉⣠⣤⡶⠟⠛⣉⣤⣴⡾⠿⠛⠛⣉⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠉⢁⣀⣤⣴⠾⠟⠋⣉⣤⣴⠾⠛⠋⣉⣠⣤⣶⣾⡿⠿⠛⠋⠉⠁⢸
⠀⠀⣀⣤⡶⠟⠛⠉⠁⢀⣠⣤⣶⠾⠛⢋⣉⣤⡶⠞⠛⣉⣡⣤⣶⡾⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢰⣿⣇⣀⣤⣴⣶⠿⠛⣋⣩⣴⠶⠛⣛⣩⣤⣶⠾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠙⠛⠿⣿⣶⣾⣿⣿⠿⢿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢀⣿⣿⣦⣀⡀⠀⠀⣀⣀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠉⠛⠿⠿⠿⠿⠿⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣦⣀⣀⠀⠀⠀⠀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⣿⣿⠛⠻⠿⢿⣿⣿⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠋
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠛⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠟⠋⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠟⠋⠉
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⣶⣿⠿⠟⠋⠉
⠈⠻⣷⣄⣀⣀⣀⣀⣤⣤⣾⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⠊⠉⠐⠀⠀⠐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⢠⠠⠔⠂⠀⠂⠀⠒⠂⠢⠀⣀⠀⡀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡈⢱⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⣤⣠⣤⣄⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣌⣤⣤⣤⢤
⠀⠀⢨⠁⠀⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⠦⢤⣤⠄⠠⣤⣤⠶⠶⠶⠶⠿⠟⠛⠛⠛⠋⠉⠉⠉⠁⠀⡅
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣉⣉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡀⢼⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡧⢄
⡎⠀⠀⠀⠴⠓⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠚⠦
⢁⠀⠀⠀⠀⢊⣩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⡑
⠀⠑⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠠⠠⠄⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠀⠀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠀⠠⠄⠀⣀⢘⠂⠀⠀⠒⡇⣀⡀⠠⠄⠀⠀⠐⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⡀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠿⠁⠀⠈⠉⠟⠦⣄
⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠦⠤⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣧⡤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⣸⠥⠖⠒⠉⠉⠉⠉⠉⠉⠓⠒⠦⢝⣢⡀⠀⣀⠤⠒⢋⡉⢥⠤⣄⣠⠒⡖⣈⣐⣢⠀⠉⡇
⠀⠐⢏⠀⢤⠒⠤⣬⠉⣐⣂⠀⠈⠉⠀⠂⢄⡈⠛⡞⢁⠴⢺⡏⡆⢾⢇⠈⠉⢀⡧⢍⠒⢄⠀⠀⣇
⠀⠀⠈⢧⠈⠄⢹⡶⠶⠶⠾⠆⠀⡎⠈⠱⠀⢱⠀⢣⢸⠰⣦⡁⣇⣛⡞⠦⠳⠼⠭⠭⠤⠋⠀⠀⣿
⠀⠀⠀⠈⣆⠘⡄⠀⠀⠖⠀⢲⠀⢠⠀⠀⡀⠀⠃⠸⠀⡤⠇⠉⢉⡀⢠⡖⣒⣈⡉⠉⢹⡆⠀⠀⣏⠙⣆
⠀⠀⠀⣠⠻⡄⢰⣀⡀⠐⠀⠈⡆⠀⡄⠀⠠⠀⠠⠀⡇⠠⢖⣫⠥⡂⠸⡥⠐⠘⢄⠗⠀⣧⠴⠒⠉⠀⢸
⠀⠀⠀⡇⠀⠉⠉⠉⠉⣳⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⢇⢘⠽⣒⠭⣗⠀⡇⠀⠠⡴⠀⢸⣁⣠⠄⠂⠀⢈⠇
⠀⠀⠀⡏⠀⠀⠐⠒⠺⢅⢀⣀⣀⣀⣀⠒⠐⠀⠤⠄⢸⠐⠭⣒⠭⣖⠀⣇⣀⣀⣤⠤⠤⢧⠃⢀⡔⢠⡯⠤⠤⠤⣄
⠀⠀⠀⢧⡀⠀⠐⠦⣴⠊⠀⡷⣶⡶⠖⠶⢋⣩⢷⡆⢸⠀⡯⣖⡯⢕⣀⣤⠤⡄⠀⠤⠤⠌⠙⡏⢀⡞⠀⠀⠀⠠⡀⠑⣄
⠀⠀⠀⠀⠉⠓⢢⣄⣈⡦⠀⡭⠤⢠⠀⠈⣉⣉⠙⠓⢸⠀⣫⠕⢊⠥⢄⡊⠉⡇⢈⡉⠩⠅⠀⡏⡁⠀⠀⠀⠀⠀⡀⠀⡿
⠀⠀⠀⢀⣀⣀⣀⡇⠉⠁⢰⣁⡒⠒⠃⠀⠶⣒⡯⣕⠈⠀⡇⣠⢃⡀⠤⠔⠓⠃⠐⠒⠒⠁⢸⠁⠙⢦⣀⡠⠴⠊⢀⡼⠁
⠀⡠⠚⠉⠀⠀⠀⠙⠚⠉⠉⠉⠉⣉⡟⠓⠲⠦⣌⡉⠀⡄⠟⣋⣡⠤⠖⠒⠛⠛⣻⢛⠗⠒⠚⢈⡦⣀⣀⡤⠴⠚⠉
⢸⡇⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠋⠉⠀⠀⠀⠀⠀⠉⠳⠖⠋⠁⠀⠀⠀⠀⠀⠀⠸⣄⡓⠒⣚⣡⠞⠁
⠀⠙⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⠢⢭⣙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠒⠦⣌⡉⠒⠦⣍⡛⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠤⢍⣒⠦⢌⣙⠲⠤⣀⡀⠀⠈⠙⠻⣦⣄⠠⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠒⢬⣝⡲⠬⣉⡒⠤⢌⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣙⣳⣦⣍⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣛⢻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⠉⠉⠉⠉⠛⠷⢶⣤⣄⣀⠀⠀⢀⣀⣼⠇⢀⣀⣠⣤⣶⠶⠞⠛⠉⠉⠉⠉⠉⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⢶⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡟⢧⡛⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠸⠀⠈⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⢀⣀⡈⣻⣿⣤⣴⣶⣶⣶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣀⣠⣴⠶⠞⠛⠋⢹⣿⣴⠾⠟⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣆
⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⣛⣒⣒⣒⣒⣒⡒⠲⠶⠶⠤⠤⠤⠭⠭⠭⠭⠉⠉⠉⠉⢉⣿⡉⠉
⢠⡿⠁⠀⠀⠤⣄⡀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣂⣀⣀⡀⠀⠀⠀⠀⠈⠭⠭⠭⣭⣭⣭⣭⣅⣒⠒⠀⠀⠀⠀⣾⠀⠉⠓⠦⣄⡀
⣿⠁⠀⠀⠀⠀⠀⠈⠉⠂⠀⠘⣷⡀⠀⠀⠀⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⣉⣉⣒⡒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠙⠳⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣐⡒⠲⠶⠶⠶⠶⣤⣤⣤⣤⣄⣀⣀⣀⣒⡒⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢷⣀⣀⣤⣤⡴⠶⣶⠟⠛
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠻⠷⠶⠶⠶⠾⠿⠿⠿⠿⣿⣿⣽⣿⣭⣭⣤⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣙⣏⠁⠀⠀⢰⠇
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣼
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠠⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠐⠂⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠶⠚⣛⣋⣉⣥⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣌⣛⣬⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡴⠶⠶⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠒⠲⠤⣄⡀⠀⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣊⠏⠁⠀⠙⢄⠉⠉⠑⠒⠤⣀
⠀⠀⠀⠀⣀⡴⠷⢞⡉⠁⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡴⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠸⠀⡜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢃⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⡇⡸⠀⠈⠢⢄⠀⠀⠀⠀⠐⢤⠄⣀⣀⣀⣀⣀⠠⡄⠀⠈⠀⠀⠀⠀⣠⠼⠁⠀⠀⠀⡰⠀⠀⢠⡆⠀⣿⠀⠀⠀⠀⠀⠀⢠⡆⠀⠘⢿
⠀⠀⠀⣇⠃⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠘⡀⢰⠀⠀⢀⠎⠱⣼⠀⠀⡴⠸⠇⣀⣀⢾⠀⠀⣿⡀⠀⠀⠀⣀⣀⡠⠧⢤⠀⢾⣼⠉⠑⢄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⢀⠇⡐⠀⣃⠀⢰⠁⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⢸⠀⢸⡈⠎⠀⠈⡆
⠀⠀⡎⠉⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⡀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠉⠑⡌⢰⠇⡜⠉⡶⠁⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠈⣀⡏⠈⣾⠀⠀⢸
⠀⠀⠑⠂⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠚⠁⠸⠀⠘⡆⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠊⠇⢠⠀⢸
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡀⣀⠂⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡀⠀⠀⠀⡇⠀⠈⠢⣀⠀⠀⠀⠀⠀⠐⠲⠒⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡼⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⠀⠀⣀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠠⠤⠀⠀⠤⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠉⠀⠀⠀⠐⠓⠐⠿⠤⠌
⠀⠀⠀⠀⠤⢤⣀⡀⢀⡤⢺⠹⡈⠀⠉⠉⠍⣱⣤⠀⠀⢀⣀⡵⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⠉⠉⠉⠓⠦⣄⢀⠀⠀⡀
⠀⠀⠀⠀⡇⠀⠀⠉⠙⠓⠦⢷⣦⡭⠭⣴⣾⡋⠤⠉⠊⠉⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢨⠉⠛⠒⠤⢮⣀⡀⠀⠀⠀⢀⣠⡛⣨⠤⠖⠚⠉⡁
⠀⠀⠀⠨⠁⡆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢰⠌⡇⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠀⠉⠛⠶⠾⠛⠉⠁⠀⠀⠀⠀⢠⠳
⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡌
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡐⠈⠂⠀⠀⠀⢠⠈⠡⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠓⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢠⣴⠃⠀⠀⡄⠀⠀⡄⠀⠀⢷⠖⠂⠁
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠌⠑⢶⠤⣦⡖⠉⢰⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⡗⠖⠈⡇⠀⠀⢸⡜
⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⡅⠀⢸⠉⠣⡜⣄⠀⠂⢀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⡀⡀⠀⣃⣄⣤⡇⠀⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠥⠠⠮⠤⠄⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠒⠀⠐⠢⠤⠒⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠶⠶⠶⠶⠒⠚⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⢤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢻⡏⠛⠛⠛⠒⠒⠶⠶⠤⢤⣤⣤⣤⠤⠤⠤⠤⠴⠶⠖⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⡄⠉⣿
⠀⠀⠀⢀⣠⣼⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⣐⣸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⠧⣼⠏
⠀⠀⠀⠀⣿⠉⠉⠒⠛⠶⣿⡿⠿⠛⠛⠛⠲⠿⠷⠶⠾⠖⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⢤⣞⣸⡇
⠀⠀⠀⠈⠉⠛⣶⠤⢤⣄⣐⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠤⠶⠶⠒⠒⠒⠚⠛⠉⠉⠉⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⡋⢩⠭⠑⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢳⡄
⢀⣤⣤⣶⠚⠛⣽⣁⡀⠀⠀⠀⠀⠀⠀⠈⢑⢺⡇⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠶⠃⢠⡇
⠀⠙⣯⠉⠉⠉⠉⠛⠛⠛⠓⠶⠦⣤⣤⣀⣀⢨⣇⣀⣀⣠⣤⡼⢷⡶⠶⠛⠋⠉⠉⠁⠀⠀⣀⡠⠴⢚⣉⣿⠷⣦
⢠⣴⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠛⣧⠀⠀⠀⠀⢀⣀⣤⣶⠿⠗⠒⣋⠉⠁⠀⠀⢹⡇
⠀⠹⣟⠉⠉⠉⠛⠛⠿⠿⠷⣶⣖⣒⣶⡦⠤⠤⠤⣌⣉⣲⣮⣍⣿⣀⣤⠴⠚⢋⣉⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⢸⡿
⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠷⣶⣶⣾⡛⠉⠉⠉⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠭⢖⣒⣚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⢿⡅
⠀⢶⣿⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡨⠭⠝⣒⣒⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⡾⠛⠉⠀⠀⠀⣼⠇
⠀⠀⠀⠘⢿⣽⣿⣿⣶⣶⣤⣤⣤⣀⣀⡀⢂⡀⠈⠭⠐⣒⣿⠃⠀⠀⣀⣤⠴⠚⢋⣡⠞⠉⠀⠀⠀⠀⢀⡴⠛⠻⠶⠶⣤⣤⡀
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣿⣷⣶⣿⣴⣾⣯⣭⣀⣠⡴⠛⠁⢀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣤⠶⠋⠉⢻
⠀⠀⢀⣠⡤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠉⠹⠛⣷⡀⢁⠸⠀⢀⡴⠋⠀⣠⡴⠚⠉⠀⠀⠀⠀⢸
⢶⣿⣭⣁⣠⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡒⣁⡤⠤⢽⡇⢸⢀⡷⣋⣤⠖⠋⠁⠀⠀⠀⠀⠀⣀⣴⣾
⠀⣿⠀⠈⠉⠙⠛⠿⠿⣿⣓⡲⠶⠦⢤⣤⣄⣀⣀⣀⠀⢀⢀⠞⠩⠬⠶⣒⣾⣿⣇⣼⠿⠛⠉⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠁
⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⣤⣈⣉⠉⠉⠛⠛⠒⠿⠿⢿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⢴⣿⡿⠛⠁
⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣦⣤⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⢔⣫⡷⠛⠁
⠀⠉⠛⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠥⣞⣭⢽⣿⡄⠀⠀⠀⠀⠀⠀⣠⢔⣫⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠠⠒⠊⠤⢒⣫⠼⣧⠀⠀⠀⡠⢔⣫⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⣄⣀⠀⡀⠡⢒⡭⣿⠀⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣶⣾⣿⡶⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣤⠄⠀⠀⡡⠒⡤⠐⠀⠀⠀⠀⠈⠀⠐⢄⠤⢔⠀⠀⠘⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢥⠤⢀⡠⢴⢀⠎⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠡⡀⠦⢄⠈⠉⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠔⠁⠀⠀⠃⠀⠀⡀⠤⠂⠁⠑⠤⣀⠀⠀⠀⢡⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠔⠚⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢹⠐⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⡀⠀⠀⠀⠙⠀⠀⠀⠉⠀⠀⠀⠀⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⠆⡀⠀⢀⠠⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⡀⠴⡁⠀⠀⠀⠀⠀⢀⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡦⠀⠀⠀⠀⢀⠔⡧⣀⠀⢀⠟⡀⠀⠀⠠⡧⣀⢀⣀⠄⣊⢅⡊⠅⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠢⠟⡁⠒⠀⠤⢀⡀⠀⢀⠀⣠⠔⢷⡉⠍⠀⠉⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⢌⢶⢁⡅⠊⠣⠀⢡⠀⠀⠀⠀⠀⢀⡠⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⢸⠰⢸⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⢀⡀⠀⠀⠀⠀⢰⠒⢺⠀⠀⠀⠀⠀⣀⠠⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠈⠢⠀⡠⠈⠁⠀⠐⠀⠤⢀⡸⠤⠐⠂⠀⠉⠠⡀⢠⠊⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠂⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⢀⣄⠠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣷⣾⣥⣲⣶⣦⣶⣿⢿⣿⢷⣿⣿⣿⣽⣿⣿⣷⠀⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⣯⣿⣟⣽⣿⣸⣯⣿⣿⣿⣻⣿⣿⣿⣿⡷⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠻⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡝⣋⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠈⠛⠓⠤⠒
⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠂
⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⣉⠁⠀⠀⠀⠀⡂⠀⣀⣀⡰⠄
⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠹⣆⡄⢙⠦⣄⣠⠴⠚⡀⢸⢀⣰⡀
⠀⠀⠀⢸⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⠀⠀⠀⠀⠤⠄⠀⠀⠀⠿⠄⣸⠙⢧⣄⢘⣀⡠⠤⠷⣋⡤⠴⠺
⠀⠀⠀⢸⠀⡄⠀⠀⣀⣀⣀⡀⠀⣀⢀⣀⣀⡀⠀⡶⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠰⠌⢲⣬⡀⠙⠉⣷⡞⠉⢀⣠⣤⣿
⠀⠀⠀⢸⣎⣭⡭⠬⢥⣤⡤⠽⠿⠿⠤⠴⠶⠤⠬⠇⢹⣆⠀⠀⠀⠇⣀⠄⠀⠀⠈⠀⠀⠀⣈⠁⠻⣿⠠⣿⡤⠖⠋⠁⣠⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠢⡛⠈⢻⡶⠖⠚⠋⠁⣈⣩⠧
⠀⠀⠀⠀⢀⣤⢲⠶⠀⠀⠀⠀⠀⢀⡖⠰⣶⡖⢢⠀⠀⠈⠃⢘⣦⡀⠀⠀⠀⣀⡠⠄⠖⠒⠃⠀⠀⠐⢼⣧⠴⠖⠚⠉⠁
⠀⠀⠀⠖⠧⡴⠋⢀⣀⠀⣠⠄⢰⣮⡟⠓⠛⡟⠛⠃⠀⠀⠀⠰⡄⣿⡶⠚⠉⠀⠀⢀⣀⡬⠆
⠀⠀⠀⡀⡀⣰⣴⣃⣉⣴⣧⣤⣼⠏⣏⠀⠈⣧⣤⡄⠀⠀⠀⠀⠈⢻⣧⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠅⡋⡏⠁⢈⠉⢫⣀⣀⣀⠀⢋⣉⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⡄⠀⢤⠀⠙⠀⢈⠀⢀⣈⣀⡤⠔⠀⠀⠒⠋⠉⠉⠉⠃⠀⠀⣀⡄⠑⠄⠀⠃⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠂⠒⠂⠟⠀⠀⠈⢿⡇⠀⠀⣠⣄⣀⡀⠈⣀⣀⠀⠄⠀⠀⠑⠂⣀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡀
⠀⠀⠀⠃⠀⢺⠀⣶⠄⠰⠐⡒⢲⣾⡏⠉⠉⠉⠉⠉⠀⠀⠈⠹⠃⠀⠈⠘⠓⠶⢾⣿⣿⡶⠤⠄⠠⠤⣤⠄⠀⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠀⡀⣀⣸⡀⠀⠀⣀⠘⢛⣬⡿⠷⠖⠲⠶⠤⠤⠛⠲⠶⠶⠦⣤⠀⠀⠀⠀⠀⠉⠉⠛⠷⢄⣀⠀⠁⢀⣠⠤⠒⠋
⠀⠀⠀⠁⠈⠁⠀⠁⠀⠈⠈⠈⠛⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⢠⣿⡿⠿⠿⠟⠻⠟⠿⠻⡿⢿⣿
⠀⠀⠀⠀⠈⠟⠀⠀⡀⠀⠀⢀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⡀⢴⣿⣿⣶⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠙⠛⠉⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⢀⠋⠉⣔⢲⠀⡠⢤⠀⢀⢼⠀⡀⢤⠊⢢⠀⠃⠘⡀⠀⢠⠋⢨⠃⠀⠀⣆⢄⠀⢀⣀⠀⡠⢤⠱⡜⠤⢀
⠈⠀⠈⠤⡀⠸⣀⣸⠀⡇⢈⡄⢡⠈⠆⠀⠃⠑⠊⢣⠀⠈⠓⠙⠀⠀⢠⠁⢀⠃⡎⠈⡆⢇⢀⡇⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠀⠙⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⣠⣿⣿⡷⠒⠒⠂⠀⠒⠒⠒⠀⢺⣿⣿⣿⣯⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠙⠛⠛⠀⠀⠘⠛⠛⢺⣿⣿⣿⣿⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣿⣿⣿⣿⣿⡇⠀⠒⠂⠀⠀⠈⠒⠂⢸⣿⣿⣿⣿⣷⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠛⠺⠗⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠆⠤⠀⠴⢺⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠙⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⡘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⢀⠉⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠒⠂⠂⠉⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠸⣅⡀⠢⣀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⣠⠕⢉⢄⡎⠁⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠻⠶⣷⣦⣄⠀⠀⠈⠀⠄⠀⠈⠀⠀⣴⠟⣊⡤⠞⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⣸⠀⠀⠙⠻⣷⣦⡀⡘⠀⢀⣴⣿⡿⠟⠋⢁⣀⣤⢶⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠄⠀⠠⠊⢋⠀⠀⣰⠿⠗⠀⠙⣷⢺⠟⢛⣁⣠⠴⠞⢛⡉⠓⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⠂⠔⠁⠀⠀⢶⡦⣿⡷⠟⢛⠛⣷⠆⠀⠈⣷⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠈⢰⡀⠀⡀⡈⠀⠀⠀⣤⣤⣋⣀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠈⠉⡍⢩⠁⠀⢾⡶⠀⢀⠋⠉⠉⠉⡁⠀⠀⠀⠈⠩⠋⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠰⠃⣀⢀⠀⠀⡆⢰⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⣶⠆⠀⢠⣦⡜⠀⠀⠀⠀⠀⠀⠹⠏⠀⢀⡿⠀⢇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⢸⠀⠃⠀⠀⠀⡛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡘⢠⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⡈⢠⢠⣄⡀⢰⠁⠀⠀⠀⠀⠀⢨⡀⠀⠸⣾⡇⢸⠀⠘⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠇⠀⡇⡸⠈⠛⢡⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠘⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⣿⣶⣶⢶⣄⠀⠀⠀⠀⠀⠀⢸⠀⢶⡶⡇⢡⠀⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⢹⣿⣿⣿⣿⣽⢷⡀⠀⠀⠀⠀⣾⣶⣤⣴⠀⠸⡀⡦⠀⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⣭⣿⣿⠀⠀⠉⠁⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁