Bio letters Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠰⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⣿⡆⠀⠀⠀⠀⠀⠀⣼⡟⢿⣷⠄⠀⠀⠀⠀⠀⢀⣠⠦⣽⡇⠀⠀⠀⠀⠀⠀⢸⡗⠟⠛⠛
⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠉⢋⣸⡷⠀⠀⠀⠀⢀⣀⣿⡟⣤⣾⡆⠀⠀⠀⠀⠀⠀⣿⠷⣶⣾⣶⡄
⠀⠀⠀⠀⠀⠉⣿⣿⡆⠀⠀⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⠛⢻⡇⠀⠀⠀⠈⠋⠤⠶⢈⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠾⠿⠿⠆⠀⠀⠀⠀⠀⠸⢧⠽⠿⠆⠀⠀⠀⠀⠀⠀⠛⠛⠿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠠⣶⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⡏⠀⠀⠀⠀⠀⣾⣿⣁⣹⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣾⠛⢷⣆⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⡄⠀⠀⠀⠀⠀⢸⣿⡀⢀⣿⡷⠀⠀⠀⠀⠐⣿⣿⡏⠨⣿⣿⠇
⠀⠀⠀⠀⠸⣿⡀⢀⣼⡿⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢿⣇⠀⢀⣼⡧⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣫⣭⠉⢻⣦⠀⠀⠀⠀⠤⣼⡷⣶⣿⠆⠀⠀⠀⣰⣾⣷⣦⠀⠀⠀⠀⢿⠿⣱⡟⠀⠀⠀⠀⠀⠸⣯⡾⢃⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⣿⠿⠾⢷⣼⠟⠀⠀⠀⠀⣴⣿⣤⣿⣧⠀⠀⠀⠀⠻⢿⡷⣦⠀⠀⠀⠀⠀⣰⠟⣠⣤⠀⠀⠀⢀⣾⠟⣷⣿⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠙⠳⠶⠶⠆⠀⠀⠀⠀⠀⠿⠃⠸⠟⠀⠀⠀⠀⠀⣤⣼⡷⠟⠁⠀⠀⠀⠐⠏⠘⠿⠟⠀⠀⠀⠈⠻⠶⠟⠻⠦⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠀⠘⢻⣦⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢻⡇⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠻⠛⢻⡇⠀⠀⠀⠹⣇⡀⠀⠀⠀⢤⣿⣦⡄⠀⠀⠀⣤⣶⣤⡄⠀⠀⠀⠀⢾⡧
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠐⢻⣇⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠹⠟⠿⠁⠀⠀⠀⣾⠿
⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠾⠇⠀⠀⠐⠶⠶⠶⠶⠶⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠈⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣶⠇⠀⠀⠀⣠⡄⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠰⡶
⠀⠀⠀⠀⠀⠾⠛⠷⠾⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡤⠤⠀⠀⠈⠁⠀⠀⠀⠀⠺⣿⡄⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠂⠔⠀⡀⠀⠀⠐⣄⣀
⠀⠀⠀⠀⠀⢀⡀⠠⣠⣥⡀⠀⠞⠒⠫⡀⣰⡎⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠂⠲⢗⡬⣼⠋⠀⠀⠀⠠⢁⣀⣀⡀⠒⠘⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠠⠉⠉⠡⠑⠤⠀⠘⠓⠂⠉⢈⡉⠀⠀⠉⠙⠇⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢹⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⣄⣤⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠢⠟⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠍⠲⡈⠑⠆⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠈⠐⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢐⡧⠀⠈⠁⡈⠄⠀⠀⠈⢻⣿⣿⢿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⡤⠖⠃⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠜⠢⣤⣀⠀⠀⠀⠀⢸⣯⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠉⡢⠝⣷⠭⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⡤⠤⡤⠤⠀⠓⠄⠀⠀⣼⢻⣿⢹⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠯⡄⡘⠁⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡦⠖⠃⠀⠀⠀⢿⣿⣖⣿⡁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⡆⠊⠀⢀⠂⠄⠀⠀⠀⣠⣿⡿⣿⠛⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⢀⢠⡈⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡃⣠⠔⢃⡄⠀⠀⠀⠀⣿⣷⣿⣻⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠁⠻⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡣⠗⠀⠀⠉⠃⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⣀⠀⠀⣁⠉⠉⡑⠀⠐⠀⠙⢀⡀⠔⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣤⣶⣶⣶⣦⣼⣿⣿⣷⡿⠃
⠀⠀⠀⠀⠠⠂⠑⣀⣚⠆⣷⠠⠀⠀⠈⠩⠐⠚⠲⢓⣀⢐⠉⠉⠲⠀⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠧
⠀⠀⠀⠀⠈⠂⠄⠉⠣⢼⠊⠉⣀⢀⡠⠔⠳⠤⠤⠀⠀⠌⠁⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⢽⠟⢿⣹⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⢀⡀⡀⡀⠢⠀⠀⠉⠿⠓⠀⠄⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⡄
⠀⠀⠀⠀⠀⡴⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠉⠉⠉⣧⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣀⣠⣤⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠁⠄⠐⠛⢻⡆⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⡇⠉⡅⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⣢⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⠀⢀⠙⠲⡖⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠠⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣬⠿⢂⡈⠻⠀⡰⠄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠄⠀⠐⠀⡄⠀⣷⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⡠⣧⣬⣶⣈⣙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠐⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⢀⠀⢻⣏⠃⢅⠐⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡂⠀⠀⠘⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠁⠀⢀⡏
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠘⣧⣀⣀⣤⣤⣴⡶⠆⠀⢿⠀⢀⣀⣀⣈⣀⣤⣤⣤⣤⣿⣤⡀⠀⠀⠀⠀⢸⡷⠀⠂⢀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⢀⡀⠀⠀⠀⠈⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⢸⡇⠐⠠⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⢀⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣶⣶⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂⠀⠀⠀⢈⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡀⠀⠀⠀⢠⡏
⠀⠀⠀⢰⠖⠀⠀⠀⠀⢀⡀⡀⠀⡵⠂⠁⠘⠀⠸⣿⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡰⠊⠀⠀⠀⠀⠀⠀⣿⠀⠠⠀⠀⠀⠀⣿⠰⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠀⢀⡀⠀⣿⠀⠀⣰⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⠀⡀⢀⠃⢀⣀⣀⣀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠘⠄⠈⠈⠉⠙⠛⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠠⠀⠀⠀⡇⠀⣿⠻⠒⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⣿⠀⠀⠹⠀⠀⠀⠸⠷⠶⠶⠶⠖⠀⠀⣿⠀⠀⠀⠀⣟⠀⠀⣀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠄⠀⠀⡇⠀⣿⠀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣟⠀⠀⠉⠁⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠈⠀⡆⠰⠀⠀⠀⠀⣿⣣⣤⣀⣤⣀⣀⣤⣤⣤⣤⡀⠀⠀⠀⢴⣆⠀⠀⠀⣯⣀⣀⣀⣀⣀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠀⢀⡀⠀⠀⠁⣆⠀⣉⣉⣉⠉⣈⠀⠀⠀⠀⠠⠼⠃⠀⠈⠁⠀⠐⡀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠁⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠁⢹⠀⠁⠨⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⠀⢀⠠⠈

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⢶⣶⡶⠶⡶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣷⣄
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢟⠁⠀⠀⣠⣾⣿⣿⣿⣿⣦
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣤⣤⣼⡿⠿⢿⣿⣿⣿⣿⣇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣤⣄⠈⢻⣿⠀⢸⣿⠏⢀⣤⣤⣄⠈⢻⣿⣿⣿
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠋⠠⣾⣿⠀⢸⣿⠀⣼⣿⣿⣿⡇⠀⣿⣿⣿
⠀⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⠀⢸⣿⠀⢸⣿⡀⠸⣿⣿⡿⠃⢠⣿⣿⣿
⠀⢻⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣠⣾⣿⣀⣸⣿⣷⣤⣀⣀⣠⣴⣿⣿⣿⡟
⠀⠘⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣭⣍⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣬⣙⠻⢿⣿⣿⣿⣿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣍⡙⠛⠳⠶⢯⣭⣭⣭⣤⣍⠙⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠿⢛⣡⣾⣿⣿⣶⣶⣦⣬⣭⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⣭⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠐⣀⠀⠀⡆⡀⠀⡤
⠀⠀⠀⢀⡈⠀⠈⠄⠈⠁⡰⠤⢖⡀⠪⡐⡀⠠⡀
⠀⠀⠀⠀⠈⠁⠄⠃⢀⠈⠀⣅⡀⡤⣁⡀⢌⠀⡀⡀
⠀⠀⠀⠀⠀⠅⢜⠁⠉⠀⠀⠀⠀⠀⢠⠁⠄⡁⠩⠀⠐
⠀⠀⠀⠐⠂⠃⡚⢒⡐⠀⠀⠀⠀⠀⠀⢠⡰⠀⠋⠀⠀⠀⠀⠀⠀⠰⣼⣷⣶⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⢤⠃⢅⠠⢤⠂⠠⠀⠀⠤⣀⢈⠈⠠⠀⠐⠄⠀⠀⠀⠀⢘⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⡤⠂⣀⠂⢈⠉⠀⠀⢠⠁⣠⠢⠐⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣿⡏
⠀⠀⠀⠁⢤⠉⠂⡁⠘⠉⠂⡉⠈⡌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⣀⣀⣀⣴⣿⣿⣿⠇
⠀⠀⠀⠀⢀⠠⠆⢠⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠈⠑⡀⡐⢃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠛⠉⠉⠉⠉
⠀⠀⠀⠰⠂⠈⢰⡈⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣤⠀⠃⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⡆
⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠹⡏⠁

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠄⢠⡐⢀⠔⡀⠀⢸⡀⣀⡒⣀⣠⠀⠴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠐⠂⠈⠸⢎⠁⠄⠁⣁⠀⡀⠑⢦⡚⢀⠁⡰⢁
⠀⠀⠀⠀⠀⠀⠀⢠⠰⠘⡰⠀⣴⠀⠀⠋⠁⠈⡖⠂⠑⠀⠦⢄
⠀⠀⠀⠀⠀⠀⠂⢐⠃⠇⢘⠐⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠀⠢⢁⡴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣄⢀⣀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⠜⠀⠉⠀⠀⠀⠀⢀⡀⠀⢠⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀⣁⡤⠀⢀⢘⡀⠑⠀⠰⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠙⠿⠏⠛⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠘⢵⣾⠒⠠⠄⠐⡒⠍⠨⡀⢤⠐⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⢷⠂⠀⠀⠀⠀⠀⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣄⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⡎⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡇⠐⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣽⣿⡏⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠨⠀⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠌⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠠⠜⠁⡀⠘⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠤⢦⣀⠄⡀⡩⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠠⠀⠀⢫⠔⡠⠄⠀⠒⠀⠢⠄⠲
⠀⠀⠀⠀⠈⠁⢠⡟⢴⡋⠀⠁⠀⠀⠀⠀⠂⠈⠀⠑⢆
⠀⠀⠀⠀⠑⢎⠈⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠐⠀⡌⠀⠂⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣶⣶⣤⡀
⠀⠀⠀⠄⣀⠂⢂⠀⠈⠉⠀⠀⠠⠀⠀⠀⠀⠀⠠⢀⢀⠠⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠛⠛⠻⣿⣿⣦
⠀⠀⠀⠄⠀⠂⠊⠀⠉⠀⠀⠀⠀⠄⣀⠀⠰⠂⠃⢀⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠈⠉⠛⠧
⠀⠀⠀⠀⡀⢠⢱⠀⠤⠀⠀⠀⡀⠠⠀⢀⠀⡍⠀⠀⣀⠜⠁⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠃⢠⠀⢁⡀⠀⠀⠀⠀⠁⠂⠀⡀⡀⠔⠈⡀⡀⠀⠀⠀⠛⣿⣿⣿⡇⠀⢈⣿⣷⣶⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠈⠂⠑⠈⠁⠀⠀⠀⠀⠀⠀⠘⠁⡄⢀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠈⠉⠙⢻⣿⣿⡗
⠀⠀⠀⠀⠈⠁⠀⡀⡘⠄⠐⢚⡀⠀⠀⠇⣀⠐⣨⡠⠈⠈⠀⠀⠀⠀⠀⠸⢿⣿⣿⣧⣀⢀⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠁⠛⠀⣀⠀⡈⠤⠤⢊⠀⠞⠃⠀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⣿⣿⠿⢿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠉

⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⢀⣤⡶⣦⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⠀⠀⠀⢠⢲⡂⠀⠀⠀⠀⣰⣤⠴⠆
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢁⣤⡿⠁⠀⠀⠀⠀⠛⣸⡧⠀⠀⠀⣀⣾⢧⣾⡄⠀⠀⠀⠀⣿⢶⣶⣦
⠀⠀⠀⢀⣽⣿⠂⠀⠀⠀⢰⣿⣥⡀⠀⠀⠀⠀⣴⣦⣉⡽⠀⠀⠀⠈⠐⠂⣿⡄⠀⠀⠀⠀⡀⢀⣰⣿⠃
⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⢠⣴⣤⣄⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢰⣏⣤⣄⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⢻⣧⣼⣟⠀⠀⠀⠀⢰⡟⠛⣿⡀⠀⠀⠀⣼⣿⠻⣿⡆
⠀⠀⠀⢸⡍⢀⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢾⡇⠀⣿⠄⠀⠀⠀⠈⠻⣾⣿⠀⠀⠀⠀⢿⣿⣾⣿⠇
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⡏⠀⠀⣾⣫⣍⢳⡄⠀⠀⠠⣴⠷⣾⠆⠀⠀⣴⣿⣦⠀⠀⠐⠿⣳⠇⠀⠀⠀⠐⣯⢗⡀⠀⠠⠆
⠀⠀⠀⠀⡇⠀⠀⢻⣟⣛⡚⠁⠀⠀⢰⡟⢺⡗⠀⠀⠀⠉⣿⣷⠀⠀⠀⣰⢏⣶⡆⠀⠀⢾⣉⣿⡀⠀⠰⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⢠⡄⢀⣀
⠀⠀⠀⠀⣰⠏⠀⠀⠹⣇⠀⠀⠰⠻⠆⠀⠀⢠⡴⣦⠀⠀⠰⡄⠀⠀⠀⣠⣄⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⣿⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢿⣀⠀⠀⠙⠋⠁⠀⠈⠻⠿⠁⠀⠀⡶⠇
⠀⠀⠀⠀⠈⠓⠀⠀⠛⠀⠀⠘⠛⠛⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⣠⠄⠀⠀⠠⣄⠀⠀⠀⠀⢠⠆⠀⠀⠰⠆
⠀⠀⠀⠈⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠐⠋⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣴⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⠃⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⠎⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢻⣧⠀⣀⣤⡀⣀⡁⠀⡐⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢟⠆⠀⠈⢿⣴⠁⡼⣿⢹⡇⣠⣇⣈⡿⠁⠀⠀⢠⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⠀⠀⠀⠈⠻⡌⠳⠟⠈⠙⠁⠈⠉⠀⠀⠀⢰⡿⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡇⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⡀⣠⠶⣄⠀⡤⠀⡖⠲⠀⣾⠋⠈⣿⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡤⣼⠇⠙⠦⣿⠼⣧⡀⠈⡾⠛⣿⣀⠀⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⣿⡇⠈⠳⠤⠞⠁⠀⠙⠛⠋⠀⠀⠈⠉⠉⠉⠻⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣼⡟⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠟⠁⠀⠀⠀⠀⠐⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠛⢄⣂⠄⠀⠀⠀⠀⠀⢸⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠃⠘⠆⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠨⢋⠉⠀⠀⠀⠀⠀⠠⢏⠮⠀⠀⠀⠀⠀⠀⠀⡠⠁⠘⡃⠐⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠠⡄⠁⠀⠀⠀⠀⠘⠓⡴⡐⠶⠀⠀⠀⠀⠀⢀⠣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⡀⠈⠱⠄
⠀⠀⠀⠀⡀⠐⠖⢀⠀⠀⣀⠀⢠⠄⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠛⠀⠄
⠀⠀⠀⠀⠰⡠⠀⠘⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠟⠐⠀⠄
⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠐⠾⡳⠎⠀⠀⠀⠀⠀⠀⠀⣆⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠊⢡⣈⡀⠁⠀⠀⠀⠀⠀⠀⢧⠀⠁⠜⠃⠀⠀⠀⠀⣤⣁⣄⠀⠀⠀⠀⠀⠀⢀⣚⣠⣆
⠀⠀⠀⠀⣂⣤⠀⠀⡄⠀⠀⠀⠀⠸⠀⠀⠀⡄⠀⠀⠀⠀⠰⡀⠀⠀⠘⠀⠀⠀⠀⠉⣉⣹⡆⠀⠀⠀⠀⢠⣞⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠣⣀⠀⠀⠀⠀⠀⡀⠡⡀⠀⠂⠀⠀⠀⠀⢀⠽⡩⡁⠀⠀⠀⠀⡼⡏⢈⣿⡇
⠀⠀⠀⠀⠸⠀⠙⠈⠁⠀⠀⠀⢀⡀⠀⢠⡄⡁⠀⠀⠀⠀⠀⠴⠛⠈⠄⠀⠀⠀⠀⠀⢠⡄⠹⠆⠰⠀⠰⠖⠐⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣀⢁⡀⠀⠈⠀⠀⠀⠀⠀⢀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⠒
⠀⠀⠀⠀⠛⠀⠈⠀⠘⠁⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠂⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠋⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣻⣷⣿⣿⣿⡄⠀⣸⡇⠀⠀⠀⣸⣿⡟⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇⠀⢀⣼⣿⣿⠀⠀⢖⣤⣤⠀⠀⣴⣿⠃⠀⠀⠀⢔⣠⣤⡀⣰⣿⣿⡿⢻⣿⡧⢀⣿⣧⠀⠀⠀⣿⣿⠇⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣴⣿⣿⡿⠃⢠⣾⣿⣿⣿⡆⢸⣿⡿⠀⠀⢀⣴⣿⣿⣿⣧⣿⣿⠏⠀⢻⣿⡇⣼⣿⣿⡀⠀⢸⣿⣿⢀⣾⡟⣻⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⣀⣿⡟⠀⢸⣿⣿⣾⣿⡇⠀⠀⣾⣿⠁⠈⣿⣿⣿⡟⠀⠀⠸⠀⢀⣿⣿⣿⡇⠀⣼⣿⡇⣸⣿⠃⣿⡇⠀⠀⢀
⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠋⠁⣹⣿⣿⣿⠁⠀⢸⣿⣿⣼⣿⠀⠀⣰⣿⠃⠀⢰⣿⣿⣿⠀⠀⠀⢀⣠⣼⣿⣿⣿⣇⢀⣿⡟⠀⣿⣿⣤⣿⣷⣦⣤⠖
⠀⠀⠀⠘⠋⢹⣿⣿⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⣼⣿⣇⣿⡟⠀⢀⣿⣿⠀⠀⢸⣿⣿⡇⣠⣶⣾⣿⣿⣿⣿⡏⣿⣿⣸⣿⣧⣾⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⣰⣿⣿⣿⡇⠀⢠⣿⣿⢹⣿⠃⠀⢸⣿⡇⠀⢀⣿⣿⣿⡷⠀⠛⢛⣿⡿⣿⣿⠀⢿⣿⣿⡿⢹⣿⠟⠋⢹⣿⡇
⠀⠀⠀⠀⢠⣿⣿⣃⣀⣤⣾⣿⠿⢻⡿⡇⢀⣿⣿⠇⣿⡿⠀⣀⢸⣿⡇⠀⣾⣿⢿⣿⣗⠀⢀⣾⡟⢠⣿⡟⠀⠸⣿⣿⡇⣿⡟⠀⠀⢸⣿⡇
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠋⠀⠸⣷⣷⣾⡿⠃⢰⣿⣷⣪⣵⣾⣿⣿⣾⡿⠋⠈⢿⣙⣲⣿⡿⠁⢸⣿⠁⠀⠀⣿⣿⣷⣿⡇⠀⠀⢸⣿⡇
⠀⣀⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠙⢿⣷⢟⣤⣾⣿⣿⣿⣿⠿⠿⠿⣷⠞⠁⠀⠀⠈⠻⡿⠋⠃⠀⣾⠁⠀⠀⠀⣿⠿⣿⣿⠀⠀⠀⢸⣿⡇
⠰⢚⠉⠟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⠸⠋⡟⠀⠀⠀⠸⣿
⠀⠈⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⣀⣴⣄⠀⢸⡟⠛⢿⡆⠀⠀⢀⣠⣤⡄⠀⣠⣤⣄⡀⠀⠀⣰⡶⠶⠤⠀⢠⣤⠴⢦⡄⠀⠀⣀⣄⡀
⠀⠀⠀⠀⢺⣿⡟⣿⡀⢠⣿⢶⣿⣇⠀⣰⣾⠋⠀⠀⠀⣿⣏⠈⣻⡄⠰⣿⣤⡄⠀⠀⢸⣧⠤⠄⠀⠀⣼⣋⣩⣅
⠀⠀⠀⢠⣿⠟⢹⡿⠃⠈⣿⣤⣴⠟⠀⠻⣿⣴⡶⠆⠀⣿⣿⣾⣿⠃⠀⣿⣦⣀⡀⠀⢸⡇⠀⠀⠀⠀⠿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣺⡇⠀⠀⣿⠀⠀⢰⣶⡟⠀⠀⠰⢶⡶⠆⠀⣸⡇⣀⠆⠀⢀⣶⠀⠀⠀⠀⢰⣆⠀⣶⡀⠀⠀⣶⣄⠀⢰⡆
⠀⠀⠀⣿⣤⡴⠖⡇⠀⠀⢸⣿⡷⠀⢀⡀⢸⣿⠀⠈⣿⣿⠛⠀⠀⢸⡿⠀⠀⠀⠀⣿⣿⣼⣿⣇⠀⢸⣏⠙⣷⣼⡇
⠀⠀⠀⠿⠇⠀⠀⠇⠀⠀⠈⣿⣇⠀⠸⠷⣾⠇⠀⠀⢻⠋⠳⢴⠆⠸⠿⠿⠷⠀⠸⠟⠻⠿⠋⠿⠀⠘⠯⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣀⡀⠀⠀⣀⠀⠀⠀⠀⠰⡶
⠀⠀⢀⣴⠛⠛⢷⡄⠀⣿⡋⢹⣧⠀⣴⡞⠛⠛⢿⡀⠀⣾⡟⠻⣷⠀⠀⢾⣯⡍⢧⠀⠈⠹⣿⡟⠛⠁⣴⠇⠀⠀⢸⠇
⠀⠀⠈⣿⡀⢀⣼⠇⠀⣿⡿⠛⠁⠀⢿⡀⢰⢶⣼⡇⠀⣿⡷⣾⣏⠀⠀⠀⠘⠷⣤⠀⠀⢰⣿⡏⠀⠀⢹⡆⠀⠀⣿
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠛⠃⠀⠀⠀⠈⠛⠛⠛⠿⠀⠀⠙⠃⠈⠙⠁⠀⠿⠿⣶⠏⠀⠀⠀⠙⠃⠀⠀⠈⠻⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣠⡀⠀⡿⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⣀⣤⠀⠀⠀⢠⣄⠀⠀⠠⣤⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣰⡿⠀⠀⢳⡄⣾⣷⢠⡟⠀⠀⠘⢷⣼⠟⠁⠀⢻⣧⣼⣿⠀⠀⠀⢀⣴⠟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠨⣿⠏⢿⣾⠃⠀⢀⣴⠿⠻⣤⡄⠀⢀⣽⡿⠋⠘⠀⡰⣏⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠈⠁⠀⠀⠉⠀⠀⠘⠋⠁⠀⠀⠀⠋⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠑⢄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢢
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⢣
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⡄
⢀⣤⣤⣄⣀⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡇
⢸⣿⠿⠛⠁⠙⠛⠛⠉⠀⠠⣂⡠⠙⢿⣿⣿⣿⣿⡿⠿⠛⠛⠟⠹⠿⠃
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠘⠿⠟⠁⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠
⠰⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣀⡀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⣶⣖⣶⣾⡿⠛⡀
⢀⣤⣈⠓⢦⣀⠀⠀⣀⣀⡘⠉⢦⠙⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢄⠐⣴⠢⡀⣿⣿⣿⣿⣥⣄⣇⣻⢿⣧⣶⣿⡿⠓⡀
⠠⣙⢿⣁⡀⠙⠑⢆⣼⣯⡇⠀⠘⣿⣄⠀⢰⠄⠠⠄⢀⡤⠀⠆⠂⠀⠀⠀⠁⠀⠀⠀⣹⣯⣽⣿⠀⠉⣿⣿⣾⣿⣟⢿⠀⠐⡟
⠀⣘⣷⣯⣽⣿⣾⣍⠉⠛⠿⣦⣄⠘⣿⣆⣿⡖⠁⢀⠞⣤⣴⣦⢀⣠⠀⠀⠀⠀⠀⠀⠘⡏⠛⠙⢦⣀⣿⡿⢛⣿⣿⡢⠶⠖
⠀⠀⠀⠙⠛⠛⠿⢿⣄⠉⠻⣶⠙⠷⠸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠤⠂⠀⠀⢀⠜⠋⢹⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡈⠙⠻⣦⣉⣠⣷⣤⣛⢿⡉⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢂⠂
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣆⣻⣇⣴⣶⣦⡀
⠀⠀⣾⠛⢿⣟⠛⣿⠛⣿⠛⣿⠛⡿⢛⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⣷
⠀⠀⡟⢷⡄⠻⣆⠘⣇⢸⡆⡏⢸⠃⡞⠁⠀⠀⠀⠀⠀⠀⣴⠶⢸⠱⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⣄⠙⢦⠘⢆⠘⠄⠃⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢺⠓⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⣌⡑⠦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡷⠤⢍⡑⠀⠀⠀⢀⠴⣚⣉⣉⡓⠦⣄⠀⠀⠀⠀⠀⠀⢻⣽⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡗⠒⠒⠂⠀⠀⢠⠃⣾⣿⣿⣿⣿⣷⣾⣷⡀⣀⡴⠀⠀⠸⣻⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠚⠉⢡⣶⣀⠞⣸⣿⡏⢹⣿⠿⣿⣿⣧⡝⣿⣷⠶⠂⠀⢸⠉⠀⠰⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠈⢻⣷⣾⣿⣿⠃⠀⠀⠠⣤⣉⡝⣡⣿⣟⠒⠂⠀⠀⠀⠀⠀⠘⣿⣿⢷⣄⣀⡀⠀⠀⠀⣿
⠀⠀⡇⠀⢀⡾⣏⠀⠉⠉⢡⡀⠀⠀⣀⣰⣿⣿⣿⣿⡛⠛⠂⠀⠀⠀⠀⠀⠀⠘⡷⠋⠁⢙⣿⠀⠀⠀⣿
⠀⠀⣷⠞⠉⠀⠈⠓⠦⢴⡟⠙⠒⢿⣿⡿⣿⡟⢿⡀⠉⠂⠀⠀⠀⠀⠀⠀⡤⡪⠕⠒⢺⡿⡇⠀⠀⠀⣿
⠀⡞⠁⠀⠀⠀⠐⢦⡀⢸⠁⠀⠀⠈⣿⠃⠘⠇⠀⠁⠀⠀⠀⠀⠀⠀⢀⢎⡾⢠⣴⣒⣙⣃⣁⣩⠗⠀⣿⢀
⣸⢁⠀⠀⠀⠀⠀⠀⢷⡈⣄⠀⠸⡀⢸⡀⠀⠀⠀⣠⣴⣶⣿⡶⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣆⡀⢀⡤⠛⣉⢽
⡿⢸⢸⡀⠀⠀⠀⠀⠘⣧⠘⣆⠀⢷⠀⢧⠀⠀⡰⠱⠈⢻⣿⠗⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⡿⠟⢉⡴⠊⢑⣿
⣇⠘⡏⣷⣄⠀⠀⠀⠀⢹⡆⢹⠀⢘⣷⣌⣽⣞⠁⢀⠴⠃⣿⣠⠤⠼⠿⠿⠟⠛⠛⣿⠟⢉⡤⠚⠁⠀⠀⢨⡻
⢻⡀⢻⡼⣿⣿⡆⠀⠀⠈⠻⣯⡤⠞⠋⠁⠈⣯⢗⡁⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢐⡏⢻⠉⠀⢠⣶⡋⠙⣎
⠘⣇⠈⣷⣿⣿⣿⣄⡀⣠⢀⡄⠀⠀⣀⣤⣾⣿⠎⣹⠗⢊⣉⠓⢤⣀⠀⠀⠀⠀⠀⡇⢸⣶⢀⣠⠙⣷⠀⢸
⠀⢹⡀⠘⣷⣻⣿⣿⣿⣿⣿⣶⣾⣿⡿⣿⣿⡿⠒⢬⡳⣤⡤⠶⣻⠟⠁⠀⠀⠀⢀⡇⢸⣿⣷⣝⠀⣿⠀⢸⡤
⠀⠘⡇⠀⣺⣷⣝⠿⠿⢿⣛⣭⣷⠞⢋⡁⠀⢀⡀⠀⠈⠉⠉⠉⠀⠀⢀⡤⣤⣤⣴⡇⢸⣿⣿⣷⡄⣿⠀⢸
⠀⠀⡇⠀⢐⠽⣿⣿⣿⣿⠿⡏⣹⠛⡏⣹⠘⡏⣿⠀⠀⠀⠀⢀⡠⢞⡅⣂⣽⣿⣿⡇⢸⢿⣿⠝⠋⣿⠀⢸
⠀⠀⡇⠀⠐⡫⢞⡽⠋⠁⠀⡇⣿⠀⡇⣿⠀⡇⣿⠀⠀⣠⢔⡫⣊⢕⡩⣺⣿⣿⢟⡷⠺⠊⠁⠀⠀⣿⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢀⢤⠀⠀⠈⡳⣞⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣈⣏⣀⡀⠀⢀⣄
⠀⠀⠀⠓⢾⠲⠚⠉⠁⠈⠉⠓⠖⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⢊⣭⠀⠶⠀⣭⠲⡞⠉
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣴⡄⣡⡰⠷⠀⣭⠰⡿⡄
⠀⢞⣱⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣏⡇⠀⠀⢿⡦⠖⢹⣏⠀⠉⠉⠲⢴⡿⠀⠀⠐⠿⠒⣇⣤⣀⣍⠰⠷⢠⡍⢴⡆⡗⠺⠗
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠀⠀⠀⡜⢁⣀⣈⠀⠀⠀⠔⡟⠈⢣⠀⠀⠀⠀⠀⠹⡉⣬⡏⢀⠿⢊⠱⠶⣰⠃
⠀⠀⠀⡤⢼⠤⢄⡀⠀⠀⢀⡠⢬⡧⢤⠀⠀⣤⣴⠃⢈⡛⠆⠀⡤⣄⠀⠀⠀⠈⣦⣤⠀⠀⠀⣤⠟⠪⢄⣛⣃⣸⠷⠚⢣⣤
⠀⠀⠀⠙⠚⠀⠀⠈⡵⢏⠁⠀⠀⠓⠁⠀⠀⠀⠈⣷⡯⠄⠀⠀⠑⠋⢠⣙⣶⣴⠁⠁⠀⠀⠀⠉⠀⠀⠀⢠⣧⠀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣹⡴⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⢠⠖⡆⠀⠉⠈⡧⡞
⠀⠀⠀⠀⠀⣤⠀⠀⠀⢈⡁⠀⠀⠀⣤⠀⠀⠀⠀⠛⠋⠙⠒⠿⣧⠤⠒⠋⠙⠛⠀⠀⠀⠀⠀⠀⠈⢙⡝⠚⡽⢻⡄⠙⠢⣄⣰⣙⡆
⠀⠀⠀⠀⠀⠀⣳⢔⡒⢩⣭⠒⡢⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⠏⠀⠀⠉⠏⠆⠀⠀⠀⢺⠉⠁
⠀⠀⠰⢤⣀⡜⣁⠘⠋⣨⣍⠘⠚⣨⣧⣀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠘⠧⠟⡅⠀⠀⠀⠀⠀⠀⠀⠠⣀⣘⡇⣀⡀
⠀⠀⠀⠀⢸⠉⡛⠘⠟⣨⣅⢘⠝⣩⡉⡇⠀⠀⠀⠀⠀⣀⡀⠀⣀⡠⠴⠃⠧⢤⣀⠀⢀⣀⠀⠀⢸⡀⢀⣠⣣⠄⠀⠈⠙⣧⢾⠚⢧⠍
⠀⠀⢀⣀⠼⣟⠛⣺⠗⢨⣦⠛⣣⡍⢱⠧⣄⡀⠀⠀⠀⠙⡎⠋⠁⠀⠀⠀⠀⠀⠀⠙⢫⡞⠀⡖⢾⠥⣌⠲⠼⠀⠀⠀⠀⣴⠃
⠀⠀⠈⠀⠀⠘⢦⡛⠠⣶⠀⣶⣌⡵⠃⠀⠀⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠙⠊⠀⠀⠉⣦⡔⠒⠊⠉⡞⣲
⠀⠀⠀⠀⠀⣤⠋⠈⠉⠒⡖⠉⠁⠙⣤⠀⠀⠀⢀⡤⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡀⠀⠀⠘⠥⠕⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢀⡤⢅⠀⠀⠀⠀⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡒⣆⠀⢀⣀⡧⣞⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣠⠄⢰⠄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢉⠏⠉⣝⣛⠆⠈⠑⠦⢴⣉⡧⠀⣴⡣⢤⣀⠀⠀⠀⠀⠀⢀⡤⢌⣦⠀⠀⡀⠚⡧⢜⠓⢉⣙⠚⠦⣜⠂⡀
⠀⠀⠀⠀⠀⡤⣄⣠⠋⠀⠀⠈⠏⠓⠀⠀⠀⢸⡀⠀⠀⠈⠁⠀⠈⠉⠓⣤⡒⠉⠁⠀⠀⠁⠀⡌⢹⠋⠀⠻⠃⣨⡋⠸⠽⢈⣳⡉⡀
⠀⠀⠀⠀⠀⠳⠚⢦⠀⠀⠀⠀⠀⠀⢀⡰⣤⣄⢇⣠⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢈⣉⡇⠻⠇⢖⡦⣙⡁⠰⡲⠙⠋⣏⢉
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡤⣧⠂⠀⠀⠈⠧⣺⠚⠢⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢉⡧⣶⠆⣴⡄⢛⡃⣖⠆⠫⠇⡏⢙
⠀⠀⠀⠀⠀⠀⣖⢺⠖⢤⡑⠚⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣹⣄⢰⡮⢀⣘⠊⣀⡺⠟⣼⠉⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⡷⡔⠛⠉⠉⣇⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣨⠗⢤⣘⣚⣀⣳⠷⢎⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠼⠄⠘⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣷⣠⣿⡇⣾⣟⣛⢰⣿⠛⢷⡄⣿⢠⡾⠛⠳⠀⣰⡿⣆⠀⣿⠀⠀⠀⠘⢻⡟⠃⣿⣟⣛⢰⣟⣛⠂⠛⣿⠛⢸⡇⢸⣷⡄⣿⢠⡾⠛⣳
⣿⠹⡿⢹⡇⣿⣯⣭⢸⣿⣤⡾⠃⣿⠘⢷⣤⣴⢠⣿⠶⢿⡄⣿⣤⡄⠀⠀⢸⡇⠀⣿⣯⣭⢠⣭⣽⡗⠀⣿⠀⢸⡇⢸⡇⠻⣿⠘⢷⣬⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣄⠀⢀⣤⣤⣤⡀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣼⡷⠸⣯⣤⣤⣿⠀⣿⣥⣤⣼⡇⢸⣯⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠀⣿⣧⣤⣿⠇⢸⣷⣤⣼⡏⠀⣿⣤⣤⣿⠀⢸⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⠀⣿⣧⣤⣿⡃⢸⣯⣤⣼⡇⠀⣿⣥⣤⣿⠀⢸⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣟⠀⣻⡇⠀⣿⠀⢸⡏⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢸⣿⠛⢿⡇⠀⣿⠀⢸⡇⠀⢸⣿⠶⣿⠀⠀⣿⣀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣿⠶⠨⣿⢸⣿⠀⢻⠃⠀⣿⣦⣼⡇⠀⢸⡇⠀⣿⠀⠀⣿⠉⢹⡇⢸⡇⠰⢾⣧⣠⣄
⠀⠀⠀⠀⠀⠀⣸⡷⠟⠉⠁⠀⠀⢀⣿⢸⣿⠀⣿⡇⠀⣿⠅⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⠀⠀⠀⠉⠛⠷⣧⡀
⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⢈⣿⠸⣯⠀⣻⠇⠀⢿⡄⢸⡇⠀⢸⣇⠀⣿⠀⠀⣿⡀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠙⠛⠋⠀⠀⠈⠛⠋⠁⠀⠀⠙⠛⠋⠀⠀⠈⠛⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠂
⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠃⠀⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣸⣯
⠀⠀⢀⣤⣤⣬⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣉⣀⣀⣀
⠀⠀⣿⡃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⠉⣉⣉⣻⣇⣀⣀⣀⣀⣀⣀⣸⣿⣉⣉⠉⣿⡇
⠀⠀⢹⡿⠛⢻⡿⠛⢻⡟⠀⠀⠀⠀⠀⠀⠸⣇⠈⠻⡾⠋⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠉⠉⠉⠉⢉⣉⣉⡉⠉⡉⠉⣿⠄⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠶⠶⠶⠀⢈⣉⣉⣁⣀⡁⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢈⡉⢉⣉⣉⡁⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⢀⣾⠋⠀⠀⣨⣤⣤⣤⣤⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠶⠶⠶⠀⢈⣁⣈⣉⡉⠁⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠛⠁⠀⠀⠀⣨⠉⣩⣭⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢈⣉⣉⣉⣁⡀⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣤⣬⣥⣍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠶⠶⠶⠀⢈⣉⣉⣉⠉⠁⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⢸⡇⠀⢀⡁⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢈⣉⣉⣉⣀⡀⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠀⣼⢿⡄⢀⡅⠀⣿⣉⣿⣉⣉⣉⣿⣉⣉⣉⣿⣉⣉⣉⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠶⠶⠶⠀⢈⣉⣉⣉⠉⠁⠀⣿⠀⣿⡇
⠀⠀⢸⡇⠸⣯⣸⡇⢸⡇⠀⣿⠉⣿⠉⠉⠉⣿⠉⠉⠉⣿⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣿⡀⠛⠁
⠀⠀⠘⣷⡀⠈⠉⠀⣸⡇⠀⣿⡀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠙
⣤⣤⣤⣬⣿⣿⣿⣿⣯⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠄⠘⠿⠿⢿⣿⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠸⣿⣿⣦⣤⣤⣤⣄⡻⣿⣷⡄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠱⡄⠀⠀⠁⠀⢀⣀⣤⡴⣶⣦⡀⣿⣿⣟⣁⡀⠀⠀⠈⠉⠉⠉⠙⣿⣿⣧⠘⠻⠋⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢢⡘⢆⠀⠀⢾⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⣿⠃⣀⣀⠀⠀⣠⣤⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠱⡙⣌⠳⡀⠈⠛⠟⠻⣿⣿⣧⠀⠀⠘⢿⣿⣿⣽⡿⠂⠈⠻⠿⠿⠛⠁⠀⠀⠀⠠⠖⣀⠀⢠⡾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⣝⢎⢣⡙⢆⠀⠀⠀⠘⣿⣿⣧⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠵⠚⢁⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢎⠣⡙⣌⠳⡀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⣀⡠⢐⣫⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢧⡙⢌⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⡠⠴⣒⡫⠵⣚⠩⠒⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡈⢣⡙⣌⠳⣄⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⣋⡡⣤⣶⠶⠷⢚⣩⠵⠒⠋⣠⢴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠹⡄⠱⣌⠃⠘⢦⣤⡤⠖⠚⣉⡥⢔⣒⡭⠖⠚⣉⠤⠒⠋⠁⣀⡠⠴⠚⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠘⢆⠈⠢⣀⡞⠀⠀⣈⡩⠔⠊⢉⡀⠤⠒⠁⠀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢹⠃⠀⠘⣁⠤⠐⠊⠁⠀⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⡾⠀⠀⠩⠁⣀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢷⣤⠴⠖⠋⠁

⠀⠀⠀⡆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⡖⠂⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲
⠀⠀⠈⡏⠉⡍⢁⠀⠀⢤⠀⠀⠀⠀⠀⣶⠾⠰⠆⡇⠶⠰⠰⢲⡆⠀⠀⠀⠀⠀⠈⡏⢉⠍⢅⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⡠⠀⠸⣀
⠀⠀⠀⡇⠸⣶⡶⠂⠀⠀⡀⠀⠀⠀⠀⣿⠘⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡇⠸⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣀⣀⣀⡇
⠀⠀⢠⣧⣤⣤⣤⡄⢾⡿⡧⠀⠀⠀⠀⠿⠚⠛⠒⠛⠓⠚⠛⠺⠇⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢰⠏⠁⠉⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡇⡉⠈⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⡄⠉⢢⡀
⠀⠀⠀⠀⠀⣸⣦⣄⣤⠟⠀⠀⠀⠀⠀⣏⠀⠀⢠⠦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⣶⡇⣆⣀⡇⠀⠀⠀⠀⠀⠀⢼⠐⠳⠌⠁⠻⠇⡇
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠈⠀⠒⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣄⠺⠆⠸⠗⣠⠃
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣠⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣦⣤⢛⠁
⠀⠀⠀⢠⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⡋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠐⠢⠬⢿⣿⠧⠄⠆
⠀⠀⠠⡜⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣽⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⢡⡉



⠀⠀⠀⢀⣔⠉⠟⠟⣑⡄⠀⠀⠀⠀⠀⠀⡀⠀⡭⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠉⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⠀⠁⠉⣄⠀⠈⠦⣐⣂⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣁⣀⣀⡀⢠⣤⣴⡀⠀⠀⠀⠀⠀⠀⠚⠀⠈⣄⢀⠨⠄⡀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠂
⠀⠀⠈⠻⠿⠛⠀⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠖⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡇⢸⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡴⠋⠀⢸⢸⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⡇⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣸⠁⠀⠀⢸⠘⢚⡥⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢸⠀⡇⡇⢸⠀⠀⠀⢀⢇⡀⠀⠀⣿⡀⢠⡀⠀⢣⠀⠀⠀⢹⠀⠀⢹⢀⣀⠀⠸⠚⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⡇⢸⢸⠀⡇⡇⢸⠀⠀⠀⢸⢸⠁⠀⢠⡧⡵⣌⡏⢶⢬⣇⠀⢸⠈⡇⠀⠀⡏⠉⡇⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⣀⣧⣸⣇⣇⣸⣸⣀⣇⣇⣸⣀⠀⠀⢸⢸⠀⠀⡾⠰⠀⠈⠉⠀⠆⢹⠀⢸⠀⡇⠀⣠⠕⠸⢵⡒⠒⠚⠉⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡆⢸⡇⠀⠀⠠⠄⠀⠀⢸⡆⢸⢀⡇⠀⠛⠚⠒⠚⠃⠀⢀⣀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠳⡙⣾⠙⢤⡀⠻⠟⢀⡴⢋⡹⣼⡞⠀⠀⠀⠀⠀⠀⠀⢀⡷⠾⢤⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⠸⠬⢷⠀⠀⠀⠀⠀⠈⠳⠞⢦⡏⠑⠊⢹⡤⠚⠓⠙⠀⠀⠀⠀⠀⠀⢠⢴⡏⠀⠀⠀⠹⡽
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡇⢐⣒⣒⡂⢸⠀⠀⠀⠀⠀⣀⣠⡴⢻⠁⠀⠀⣈⣟⠦⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠈⠙⡇⠈⠭⠭⠅⢸⠀⠀⡰⠋⠉⠁⢼⠀⡏⠀⠀⠈⠀⢸⠀⣹⠈⠉⠓⣄⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⣤⡤⢤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠷⠶⢶⠶⠖⠚⠀⠀⡇⠀⠀⢀⡜⠁⡗⠒⠒⠒⠒⢻⠈⢣⡀⠀⠀⢸⠀⠀⠀⡷⠒⠒⠒⠒⠒⠒⠛⠓⠲⡇
⠀⠀⠀⠀⢠⠜⠃⠀⣄⢸⢀⡄⠀⠸⢤⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡏⠀⡘⠀⠀⠀⠘⡃⠀⠀⡇⠀⠀⠠⡏⠉⡆⠀⠀⠀⡇
⠀⠀⠀⠀⢏⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡇⠀⠀⡼⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⢠⠃⣰⠃⠀⡆⠀⠀⡇⠀⠀⡇⠀⣀⣀⣉⣉⣓⣀⡀⠀⡇
⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⢧⠈⡇⠀⠀⡼⢠⠏⠀⠀⡗⠀⠀⢻⠀⠀⡇⠀⠭⠭⠭⠭⠭⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠘⡆⢻⠀⢰⠇⡞⠀⠀⢰⡇⠀⠀⢸⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡀⣸⡀⣀⣀⣸⣸⣆⣜⣼⢀⣀⣀⣸⡀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡇⠉⠈⠁⠉⠉⠈⠁⠉⠁⠁⠉⠁⠉⠉⠉⠉⢹⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠯⠥⢜⣦⣠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣿⡹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣶⠟⠁⠀⠀⢀⡧⣙⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠤⠤⠤⠴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢈⠆⠀⠀⠀⢣⡼⠃⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢪⢧⠀⠀⢀⠽⡇⠰⡁⢀⡸⠀⠀⢀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⠀⠀⢀⠤⣄⡠⠇⢷⠒⠊⠚⠓⠒⢾⣾⢄⣀⠀⣺⣠⡸⢈⣁⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠸⡀⠀⢀⠼⠊⠁⠀⠀⣘⠣⡀⠀⠀⠀⡈⣹⠀⠀⠉⠓⢧⡔⡽⠃⡎⢀⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠑⡌⠓⢡⠒⠉⣹⠀⠀⠀⠁⠐⢀⣀⠈⠠⠾⡥⡂⠀⠀⠀⠈⡳⢶⡕⠓⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠤⡄⠘⠧⢼⣦⠖⠀⠀⠀⠉⠙⢿⣇⠀⠀⠀⡜⠁⢀⠈⠦⠀⠀⠂⠀⠠⠔⣫⡞⠉⠙⣷⠀⠀⣠⠒⢆
⠀⠀⠀⠀⠀⠀⠸⡀⢢⣌⣲⢄⣰⠁⠀⠀⠀⠀⠀⠀⠈⣏⠓⡀⠀⠈⢢⣩⡽⠃⠀⠀⠀⢠⠒⠢⢍⠐⠃⢈⠃⠉⡭⠓⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⢓⠮⣕⠒⠀⠀⠀⠀⠀⠀⠒⢬⠖⠒⠒⢤⡻⢌⣊⠀⠀⢀⡆⠰⡤⡸⠀⡠⢣⢎⠆⣡⠀⠔⢒⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣤⡨⠯⣝⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠿⡀⠶⠆⣢⠇⠀⠈⠀⠀⠙⣚⠳⠞⠁⠀⠔⡱⠏⠙⢾⠋⠛⠛⢁⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡇⠀⠀⠀⡇⠠⣬⠼⢻⠦⠀⠀⠈⠙⠳⢗⠀⡔⠒⠒⣄⠀⠀⠀⠐⣂⣶⠟⡗⡦⠥⣾⠿⠭⠽⠟⢶⣦⠆
⠀⠀⠀⠀⠀⢀⡤⣀⠀⢀⣈⣇⡠⠄⠀⠈⠒⠁⠀⢐⠀⠀⠀⠀⠀⠀⠂⠘⢄⣒⣑⡼⠀⢀⡠⣊⠔⡑⣊⡬⠴⠒⠉⠑
⠀⠀⠀⠀⠀⢸⠀⢨⠥⠐⠶⡴⠒⠒⠀⠀⠀⠀⢀⡔⣠⣤⠀⠀⠀⠀⡆⢠⠈⢕⡩⠊⢀⣥⠾⠓⢦⣔⠍⡹⢉⣙⠿⠎
⠀⠀⠀⠀⠀⠀⠉⠁⠀⡠⣄⡸⠀⠀⢀⣠⣀⠔⡥⠊⡭⡪⠄⠀⡠⠒⠁⢿⡀⢔⡨⠀⢛⠝⣆⠴⢀⡡⢊⣴⡕⡉⣲⣤⡖⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡴⠊⢢⠠⣏⢀⠀⡞⠀⠀⢒⢂⡤⠀⢣⡈⣲⠜⠂⠀⢔⡳⢤⠊⢝⡋⢁⠔⠉⢫⢎⢰⢁⣀⠙⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣼⠷⡈⠛⠊⢀⡀⠤⣳⡫⠤⢒⡩⠜⡡⢔⡪⢐⢕⠝⣣⣑⠒⡔⠁⣂⣘⠦⣡⠛⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣴⠇⠀⡘⣡⠆⣸⣄⢐⡸⠐⡪⠕⣂⠭⢂⠁⡰⣁⠅⡊⢼⡉⠓⠓⠂⠺⣟⣿⢾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡪⠞⠁⠑⢆⡁⠔⣊⠁⠐⡩⢒⠩⢈⣧⡇⠐⣊⠔⣫⣔⣉⢄⣿⡽⠋⠁⠀⠙⡏⡉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⡏⠀⠀⠀⣠⡿⠋⠑⡞⣰⣋⠭⠐⡨⢒⣞⡝⢦⠔⣪⣖⢩⣵⠏⢣⢧⠀⠀⠀⠀⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣁⡼⠃⠀⡰⣱⠃⠈⠁⢶⡶⠘⠦⠥⠊⠙⣯⡀⠀⠀⠀⠀⢫⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢱⠃⠀⠀⢠⠾⡳⡄⠀⠀⠀⢠⣭⣎⡃⠀⠀⠀⢸⣐⢄⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡸⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠈⠙⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⢀⡀⠀⡠⠀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣂⠤⢒⡠⠔⢊⡠⠔⢊⡠⠔⣊⠄⢊⡡⠔⣉⠤⢊⡡⠔⣉⠡⢒⡡⠔⡩⠔⣉⠔⣊⠔⡪⢊⠵⠫⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⠀⠊⠁⠔⠊⠡⠒⠉⠤⠊⠁⠒⠉⠠⠒⠁⠔⠊⠀⠒⠁⠐⠉⠐⠊⠁⠊⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⠀⣿⣿⣳⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣿⣿⣆⠀⠘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣥⣄⣿⣿⠛⠃⠈⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⠅⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣶⣟⣿⣝⣿⣿⠀⠀⠀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣿⣿⣿⠟⠛⣻⣾⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠁⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠟⠀⠙⠿⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⣈⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣻⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣾⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡯⣫⣟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣹⣿⢿⣿⣿⣷⣝⣯⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣥⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠟⠛⠛⠉⠀⠙⠿⠂

⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠘⠤⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⢀⡀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⡀⢠⡜⠻⡅⠀⠀⠀⠠⣄⡀⠦⠀⣴⠀⡀⠀⠀⢴⡤⠾⠚⠠⢼⡆⠀⠀⢈⢞⡋⡁⠙⢲⡆⠀⢠⣆⠢⣼⢗⠚⠲⣏⣀
⠀⠀⢠⠏⣆⠀⠐⠀⡀⠀⢰⢳⠀⠀⢰⠉⠉⠇⠀⣂⡜⢰⠐⠶⠓⠎⣷⠂⠙⡯⡁⠆⠈⡆⠠⡋⠁⢨⡅⣞⣉⣭⣭⠀⠈⠦⠄
⠀⠀⣽⠀⠂⠐⠒⢉⣁⠀⢈⠿⢴⠖⠖⠙⢋⠖⠀⠀⣨⣀⡁⠈⢁⣰⡏⠀⠘⢹⣵⣚⡂⣀⣰⣉⠀⠐⣿⡝⠛⠋⠁⣀⡼⠳
⠀⠀⠘⢢⣀⣀⠠⡌⠀⠀⠀⠟⠐⢶⠒⠐⠛⠀⠀⠀⠉⠁⠸⠽⠀⠉⠀⠀⠀⠈⠀⠘⠁⣙⠀⠀⠀⠀⠀⠉⠹⠏⠹⠃⠉
⠀⠀⠀⣀⡀⢀⢀⠀⠀⠀⠀⣄⠀⢰⣀⢀⡄⠀⠀⠀⠀⡰⠛⣑⡒⢤⡀⠀⠀⠀⣀⡷⠫⣭⣿⢶⠀⠀⠀⣄⡤⠖⢺⣄⡀
⠀⣠⢂⠿⢁⡔⡑⡜⠃⠀⠀⢉⠏⡔⠮⠉⠑⡶⠀⠀⡸⢁⣨⣵⣱⣇⣹⢆⠀⠀⢩⣦⢀⡬⠶⠋⡀⠀⠀⣷⡴⢩⡉⣾⠁
⠘⠿⢠⣘⡼⠝⣿⠷⢷⡆⠈⠉⢢⠈⠄⠅⢀⠛⠂⢸⣃⠐⠸⣿⣿⡟⠛⡿⠀⠀⠈⡿⠀⠉⠙⢻⡁⠀⠀⠘⡜⣦⣾⣿⠃
⠐⣾⡛⠒⠒⠉⠀⠀⣱⡄⠀⠸⠚⡐⠂⡒⠟⠁⠀⠀⠉⠒⢤⣀⣥⠔⠊⠀⠀⠀⠘⠻⣤⣄⣀⣤⠋⠀⠀⠀⠙⡿⠿⠃
⠀⠀⢸⠢⠤⠒⠐⠒⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢦⡆⠀⣎⠄⠀⠀⠀⣀⣄⣠⣁⣤⡅⡄⠀⠀⠀⠀⠀⢸⡄⣤⠆
⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⣠⣂⡹⣅⣭⣿⣓⡄⠀⠠⣀⣴⣓⣞⣣⡄⠀⠀⣘⡻⢺⡴⢆⠟⠣⣞⡀⢀⠀⢘⢦⣿⣿⢿⣗⣆⢀⡀
⠀⠀⢠⠊⠁⠀⢀⠁⢆⠀⢬⠜⢦⣌⣉⣉⣭⡄⠀⣠⢇⣻⠿⠿⢿⢫⡁⠠⢼⠀⢀⡈⠀⢀⡄⣸⠆⣈⡛⠁⠈⠁⠉⠀⠉⠀⢹⠤
⠀⠀⢸⠀⢂⣚⣗⠃⠾⠀⠻⣀⠂⠈⡉⢆⢴⠃⠀⠐⣇⡀⠀⠀⠐⣾⠂⠀⢛⡀⠉⠀⠀⠀⢠⡏⠀⠀⣩⠆⠀⠀⠀⠀⣠⠤⡞⠆
⠀⠀⠈⠬⣈⣁⣀⡰⠚⠀⠀⠁⠛⠒⠲⠈⠀⠀⠀⠈⠀⢉⠋⡈⠃⠀⠀⠀⠈⠙⠋⠓⠲⠲⠉⠀⠀⠀⠀⠰⠋⢲⠒⠺⠈⠀⠁
⠀⠀⠀⠀⢀⡀⣄⢀⢀⡀⠀⠀⢠⠞⣔⠒⠆⠀⠀⠀⣀⣜⣾⡥⡆⢤⠀⠀⠀⠀⢀⡶⠢⡀⢠⢀⠀⠀⠀⢠⡀⠈⠀⣠
⠀⠀⠉⡞⢐⠛⠓⣾⠄⣣⠂⠀⡜⠤⢛⠄⢳⡀⠀⡌⠀⠈⠈⢂⣀⠀⠀⡄⠀⢰⡒⠂⣢⡎⢡⢘⠇⠀⠰⣾⠽⡇⢛⠶⣿⠃
⠀⠀⠘⣇⣘⣍⣾⢩⡶⠏⠀⢎⡁⡄⠀⠼⢧⡆⠀⡅⠀⠀⠂⠀⠈⠀⢀⡇⠀⠈⠳⠂⡥⠝⠻⠈⠶⠀⠀⢩⡵⡬⢧⡰⣬
⠀⠀⠈⠀⠙⠉⠋⠈⠃⠀⠀⠻⠴⢃⣬⠤⠚⠀⠀⠘⠒⠤⠄⠠⠄⠤⠈⠀⠀⠀⠛⡄⡤⠎⠲⠥⠚⠀⠐⡎⠈⠚⠟⠃⢈⡇
⠀⠀⠀⢠⣀⡐⣢⢤⣀⡀⠀⠀⢀⡀⠀⡃⡀⡤⢀⠀⠀⣀⢀⠷⠴⢧⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠩⠦⣤⢀⡤⠺
⠀⠀⠀⣈⢸⠜⠢⠣⢬⣡⡄⢠⢄⡱⣬⣧⣀⠷⡋⠀⢤⢜⣍⡂⣐⣠⡹⡆⠀⢾⢁⡾⢦⢷⡓⡂⠀⠀⠀⡠⢤⣼⠢⠶⣤
⠀⠀⢀⢀⠁⠀⢀⠀⠀⣉⠄⢀⣠⡍⢶⣂⡡⢃⠇⠐⠚⠀⣡⡀⣀⣤⠌⡅⠠⠊⠇⠈⣉⡁⢸⠙⠄⢠⡤⠹⠅⢧⡺⠗⠊⣢⡄
⠀⠀⠈⠩⣠⢜⠀⢩⣁⢯⡁⠀⠁⡼⠒⠤⡄⠈⠒⠂⠀⠷⡀⠀⠈⠀⢀⡁⠈⠒⡎⠲⠠⠔⠚⡞⠁⢀⣧⠂⢘⣿⣗⣠⢀⢸
⠀⠀⠀⠈⠀⠋⠉⠓⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⡴⠐⢲⠍⠀⠀⠀⠉⠈⠉⠑⠊⠀⠀⠈⠀⠉⠟⠈⠘⠞⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠑⠠⠑⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠠⠀⢐⠀⠂⠀⡠⠀⠁⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠰⢁⠠⠀⠀⠂⠀⢀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠂⠈⠁⠀⡇⠨⠭⠍⠀⠀⠂⠀⠀⠀⠂⠈⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠊⢁⠁⡀⠀⢀⡈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠤⠤⠄⢘⠃⠀⠘⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠈⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠤⠠⠤⠀⠠⠄⠤⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠊⠀⠒⠀⠘⠀⠒⠂⠀⠀⠀⡆⠙⠑⢄⠀⠀⠀⠀⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⢀⡀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⡀⡠⠠⡀⠀⢈⡁⡀⣉⡄⡄⡄⠀⠀⠀⠄⠃⠣⠜⡠⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⡀⠁⡀⠀⠀⠀⠁⠀⠁⠄⠀⢠⡀⠄⠀⠀⠑⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠅⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠒⠒⠁⣇⠈⠀⠀⠀⠀⠀⡀⠀⠑⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⢄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣦⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⡅⠈⠩⠉⠉⠁⠀⠈⠉⠉⠉⠠⡀⠀⣴⣾⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⡀⢀⠌⣈⣤⡐⢠
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠔⠇⠀⣀⣀⡀⢀⠀⡀⠀⠀⡖⠉⠉⠹⣿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⡀⢨⠂⢿⣿⡿⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣠⣠⣤⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⡇⠀⠈⠢⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⠀⠀⠉⢉⣉⣉⣉⡉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠃⠀⠈⠚⠀⠀⠀⠀⠀⠀⡠⡄⢶⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⡇⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢐⠈⠀⡀⠀⠀⠀⠘⢰⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⣀⣀⣀⣀⣀⣀⡀⢾⣿⣿⣿⣿⡿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠒⠈⠀⠐⠈⠀⡀⠀⣰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣽⣿⠀⠈⠭⠭⠭⠭⠉⠁⣾⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠂⠀⠙⠃⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡟⠛⠛⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⡀⣤⠐⣆⠀⢀⣀⠀⡄⢰⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⣦⠒⠀⠉⠙⠀⠀⣐⠽⠀⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⠀⠛⢛⣛⣛⣛⠛⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡠⠋⠉⡅⠀⢀⣀⡠⠤⠔⠊⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠙⠉⠛⢋⣵⡾⠿⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠤⠒⠊⠁⠀⠀⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⠤⠤⢀⣀⣀⣀⢀⣿⠃⠀⠀⠀⡆⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠸⣿⡉⠉⠀⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⣿⡏⣹⣿⡏⢻⣿⡋⢻⣷⠀⠀⠀⠙⢷⣤⣀⣠⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠙⠃⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣇⠂⠀⢀⠤⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⣿⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⢉⠀⠀⣀⠄⠀⢄⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⡄⠁⣤⠃⠀⠀⠀⠀⡔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⡇⠉⠙⠏⡀⠀⠀⠀⠀⠀⠉⠀⠈⠓⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡌⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠘⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣘⣛⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢩⣭⢹⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣬⣭⣼⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⠸⠿⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢩⣭⢹⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣈⣉⣸⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢸⣿⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠶⠶⠆⠶⠰⠄⠔⠶⠐⠲⠤⠆⠒⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠏⠉⢀⣀⡤⢤⠶⠤⢤⣄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠖⣋⠥⠚⠈⠁⠁⠈⠘⠛⠶⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠞⡥⠋⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⣇⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠁⠀⢲⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠃⠀⢄⠿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⣂⣠⠔⠋⠀⡠⣪⠛⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠁⠀⠀⢄⡮⠞⠉⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣠⠞⣳⠲⠤⣤⣀⣀⣀⣀⣤⠤⠔⢚⠉⢁⡸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠂⠀⢀⡠⢺⢀⠖⠉⠑⠲⠤⢦⣼⣄⣥⣰⡤⠦⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠊⠀⢀⡴⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⢋⣠⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⡔⢃⡤⠊⠁
⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⢁⡴⠋
⠀⢀⡴⣉⠀⠀⣠⠞⢁⡴⠋
⠀⢸⠀⠀⠙⡎⣡⠞⠁
⠀⠀⠓⢧⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢀⣀⡀⠀⠀⢹⣶⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣈⣏⣀⠀⠀⢀⣀
⠀⠀⠀⠺⢴⡣⠔⠊⠉⠀⠉⠓⠦⢼⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡦⢚⣭⠡⣶⠌⣩⡢⡜⠋
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣤⡈⣉⠰⣶⠀⣉⢡⣺⡆
⠀⣰⢳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡚⡆⠀⠀⢶⢦⡤⢒⣮⠉⠉⠓⠢⣤⢶⠆⠀⠀⢴⡶⢴⢁⣉⠈⡛⢱⡦⢀⡛⢡⣄⢸⠴⣶⠄
⠀⠈⠋⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠙⠁⠀⠀⡸⠃⠀⠀⠋⠃⠀⢠⢶⠎⢳⡀⠀⠀⠀⠀⠀⢏⠛⣘⡛⠀⣶⠟⢫⣮⢁⠎
⠀⠀⠀⢀⣨⣆⡀⠀⠀⠀⠀⠀⣀⣸⣁⡀⠀⠀⣀⣰⠃⠐⠿⡟⠁⢀⡀⠀⠉⠀⠀⢧⣀⡀⠀⠀⢀⣈⠷⣝⡁⢾⠆⢶⣦⡥⢏⣀
⠀⠀⠀⠹⠬⠇⠈⠙⠲⣰⠒⠋⠁⠹⠥⠃⠀⠀⠛⠺⣤⣔⡃⠀⠀⠫⠼⠀⠐⢤⡄⡿⠛⠃⠀⠀⠘⠋⠀⠀⠉⠙⣟⠉⠁⠀⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⢲⢀⡄⠈⠉⠛⡻⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⠛⠰⣏⣱⠄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣶⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⠝⠢⣄⣺⡿⣀⣀⡤⠺⣵⠄⠀⠀⠀⠀⠀⠀⠺⢴⢧⡤⢤⣴⡋⠧⣄⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠉⢧⣀⣀⠤⠿⠤⣀⣀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠧⡴⡃⠀⠀⠙⢚⠗⠚
⠀⠀⢀⡀⠀⢀⡴⠫⣶⠄⠯⠇⣴⡍⢢⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⣦⠞⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⡆
⠀⠀⠘⠙⠒⡞⢶⡆⣤⡔⠿⠂⡤⡔⠿⢷⠒⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⠀⠀⠀⠀⠀⠈⠉⠈⡇⠀⠀⠀⡀⠀⠀⠠⢌⡶⢲⣓⣤⢲
⠀⠀⠀⠀⠀⣇⣤⣀⣍⠑⠿⢢⣬⠱⡶⢸⠀⠀⠀⠀⠀⠀⢴⠦⣠⠴⠚⠉⠁⠈⠉⠒⠦⣀⡴⡦⠀⠀⣹⠀⢰⡚⢶⠁⠀⠀⠀⠓⡻⠁⠉⠊
⠀⠀⢰⠖⠊⠳⡈⣨⡍⠀⠻⠃⡁⢶⢆⠞⠑⠲⠆⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠘⣍⡷⠙⠢⣍⡉⠀⠀⣀⣤⣸⣁
⠀⠀⠀⠀⠀⠀⢙⠮⣅⣻⢇⣘⣿⠴⡋⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠵⣏⠉⠀⠀⢯⠴⠃
⠀⠀⠀⠀⠀⠲⠏⠀⠀⠀⣽⠀⠀⠀⠹⠖⠀⠀⠀⠠⣖⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣲⠄⠀⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⠒⢦⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣎⡹⣀⣀⣀⡼⠳⣅⠀⠀⢀⣀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⠀⢴⠂⢰⡂⢰⡦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠈⠰⣏⣽⠂⠀⠙⠢⢞⠤⠗⠀⢴⡡⠲⢄⣀⠀⠀⠀⠀⣀⡤⠶⣝⡦⠀⢀⡄⢉⠶⣊⡉⢩⢭⠉⣒⢾⡉⢠
⠀⠀⠀⠀⠀⡴⠦⣠⠎⠀⠀⠀⠘⠈⠃⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⡇⣞⠉⠁⠀⠀⠀⠀⢠⣌⡸⢃⠀⠓⠃⡬⡅⠘⠿⢀⣽⡅⣡
⠀⠀⠀⠀⠀⠑⠚⢳⡀⠀⠀⢀⠀⠀⠀⢀⣲⡤⣄⢧⡠⢤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣌⣨⡇⠳⠃⢾⠆⣉⡁⠰⣷⠈⡊⢹⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⢼⡴⠂⠀⠀⠘⠴⡿⠋⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢸⡷⣿⠢⣶⡄⢛⡃⢞⠆⠸⠟⣸⠉⡃
⠀⠀⠀⠀⠀⠀⢰⠛⡵⠢⣌⠒⠋⠀⠀⠀⡀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣱⡄⣴⡮⢀⣘⠚⣀⡘⠝⣠⡋⠙
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢙⢦⡖⠛⠉⠉⣎⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣨⠦⢄⣘⣚⣀⣳⠧⢾⣁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠾⠀⠽⠅⠸⠆⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡈⠙⠲⢤⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠋⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢿⠀⠢⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠉⡒⠤⣄⣀⣰⠙⢟⠢⡀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠈⢀⡼⠃⠀⠈⢧⠙⢆⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⢤⣀⡴⠋⠀⠀⠀⠀⠈⡆⠈⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡒⠒⠒⠒⠒⠒⡄⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣲⣒⣶⣒⣖⣲⠇⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣀⣀⣀⣠⠎⠀⠀⠀⠀⣠⠃⢀⠇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⢺⠁⠀⠀⠀⠀⡗⠒⢒⡲⠖⠁⡠⠋⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢉⣁⣠⠴⠊⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠭⠟⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠷⠶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠽⠛⠛⠛⠉

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣍⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣠⡶⠀⢹⡆⠀⠀⠀⠀⠀⣿⣤⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠛⠶⣦⠀⣿⡀⣤⡀⣠⡾⠋⠀⠀⢀⡟⠀⠀⠀⠀⠀⣿⠁⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢸⡇⠘⣧⡀⠙⠋⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣿⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠄⠀⢀⡿⠀⠀⠈⠛⠶⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢰⡏⠀⠀⠀⣠⠞⠋⠉⠀⠉⠉⠀⣀⠀⠀⠀⢠⡾⠋⠉⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠻⣇⠀⠀⣸⠏⠀⠀⠀⠀⣠⡶⠀⢹⡇⠀⠀⢸⣇⠀⢀⣀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⡀⢤⣄⣠⡾⠋⠀⠀⢠⡟⠀⠀⢀⣽⠟⠛⠉⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⣧⡀⠙⠋⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠶⣦⣤⡴⠶⠛⠁⠀⠀⠀⠈⣻⡶⠞⠛⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠷⣤⣴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠠⣶⣦⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠶⠶⠖⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠜⡇⢀⣼⠁⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⣄⠰⠀⡧⠃⣇⠔⢈⣔⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡒⠤⠠⠄⠈⠁⠀⠁⠀⠀⠀⠈⠀⢐⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⠄⠀⠀⠀⢀⠤⣤⣀⣠⠴⠚⠙⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠰⠂⡠⠤⣤⡅⠀⠈⣿⠀⠀⠀⠀⠐⣯⣤⣤⡤⡄⠀⠀⠀⠀⢸⢈⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⡀⠀⢘⡟⠂⠒⠁⠀⠀⠀⠀⠀⢹⣿⠋⡐⠀⠀⠠⢤⢀⠊⠉⢣⡇⠐⠈⢹⠠⢄⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠡⠀⣀⠤⠀⠀⠀⠀⠀⢸⡏⢠⠃⠀⢠⢺⢴⠘⣦⣀⣜⣧⠔⣦⢆⡴⢿⣁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⠻⠧⣀⠀⠀⠀⠀⠀⢸⣇⣘⣻⣿⠝⣿⣾⣵⢯⣹⣿⣟⣶⡏⠀⠑⢬⣭⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡄⠀⠀⠀⠁⢀⡄⢄⠈⣺⡙⠏⠻⣷⣋⣵⠌⠙⣿⣿⠻⡿⠀⣀⡤⠘⡀
⠀⣠⠖⠉⡁⠀⢀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡤⢦⡉⠉⠓⢴⡈⠀⢻⣕⠁⠀⢘⣻⣾⡿⢿⣿⠁⠉⡗⡇
⠀⠑⢡⡈⣿⡆⢀⠟⠒⢾⣧⣤⣤⣤⡤⠤⠤⢤⡄⠀⠈⢻⡀⠀⠳⠒⠒⡒⢵⡀⣸⢿⡟⣿⠿⣿⡿⡍⢹⣿⠀⠀⡇⡇
⠀⠀⠘⢣⣼⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢷⠀⠀⠀⠀⢈⢄⡇⠀⠀⢻⣷⣶⣧⡊⠀⠀⢹⠀⠀⠣⠇
⠀⠀⠀⠈⡆⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣇⣀⣀⣀⣀⣡⣇⣀⠀⠀⣻⣿⣿⣾⣦⣤⣿⠀⣀
⠀⠀⠀⠀⢃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠒⠒⡆⠸⣯⢀⡰⠈⠓⠒⠁⠀⠀⠙⣯⣯⢹⣾⡭⣿⡟⠓⠓⡀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⡇⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣺⣭⣿⡗⠤⠚
⠀⠀⠀⠀⠣⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠑⠒⠒⠚⢡⣤⣤⡿⢠⡤⠤⢤⡆⠀⠀⢸⡏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠘⠧⠄⡀
⠀⠀⣐⣿⣷⢶⣶⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣈⣁⣀⣀⣀⡀⠼⠇⠀⠀⠻⠤⠤⠤⠤⠤⠤⠵⠦
⠀⠀⠈⠁⠀⠀⠀⠉
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⣋⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡿⢧⣀⠀⠀⠀⢿⠹⡇⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣠⡖⠏⡑⢯⣀⡞⢉⣷⡄⢀⠞⢿⣾⡀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⢀⣼⠯⡂⠁⠀⠀⠙⢦⡞⠀⠿⠈⢢⢻⡇⢱⠀⠀⠠⡞⠒⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣛⢿⣦⣄
⠀⠀⠀⢠⠟⡂⠅⠀⠀⠀⠀⠀⠈⢛⡀⠁⣠⣚⣚⡏⠉⠀⠀⠀⢇⠀⣠⣇⣶⣴⣷⣿⠁⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣦⡀
⠀⠀⢀⡿⢑⠂⠀⠀⠀⠀⠀⣄⢲⢹⠃⡔⠋⠀⠀⡇⠀⠀⠀⠀⣀⣧⠉⣻⢿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⣿⣻⡽⣿⣦
⠀⠀⢸⠯⠐⠀⠀⠀⠀⡞⡧⠛⠄⠁⠀⡇⠀⠀⠀⠃⠀⣠⣴⠟⣽⣼⢊⡴⣩⠛⠢⣀⠀⠀⠀⠀⠀⣠⡾⢿⣛⠽⠗⠋⠉⠁⠨⡲⢕
⠀⠀⢸⠭⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠀⠰⠖⣩⣿⣿⢠⡿⠀⣫⢖⡁⠜⢴⣚⣦⣠⢴⣲⠿⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠨⡑
⠀⠀⢸⡅⠀⠀⠀⢸⠦⠽⢧⠀⠀⠀⠀⢣⢀⣠⣴⣿⣿⣿⡇⢸⡵⠊⣀⡼⠀⠀⠚⢿⣿⡏⠉⠀⠀⠀⠀⠀⢀⣴⣿⢿⣶⣄
⠀⠀⢈⡧⠖⣒⣶⣬⣯⣉⣚⣷⠀⠀⠀⠘⢿⣿⠿⠟⣿⣿⣧⢊⡤⠊⠁⠀⠀⠀⠀⠀⢻⣷⠒⠒⢶⠒⠒⡞⡿⡈⠁⡀⠙⢮⠇
⠀⠀⡞⢸⣿⣿⡿⣿⢿⣿⣄⣽⣇⣀⣀⣀⠀⠀⠀⠀⣸⣿⠱⠋⠀⠀⠀⠀⢠⣆⠀⠀⣸⣸⠀⠀⠀⠀⠀⣇⣱⠣⡀⢉⣰⠞⢦⡀
⠀⠀⢣⡼⠟⢁⡀⠉⣸⡇⢣⠀⠀⠠⠞⠛⠳⣤⠞⣶⣿⡇⠀⠀⠀⠀⠀⢰⠁⣸⠀⡠⣿⣿⠀⠀⠀⠀⣷⠀⠈⣳⠋⢋⣡⣰⣴⣽⣄
⠀⣴⣿⣟⢳⣌⢀⣠⣿⢃⢸⠀⠀⠀⠀⠀⡾⠓⠚⠉⠉⣇⣀⣀⣤⠔⠒⠉⠉⢀⣠⡿⣟⣽⢶⣒⠒⠒⢿⠀⡴⠃⣠⡎⠳⣄⣀⣀⣀
⣼⣿⣿⡟⠛⢻⣿⣿⣻⠏⠛⠇⠐⡄⠀⠀⢹⠀⠀⢦⣤⡟⠀⣢⢰⠀⣠⣾⢿⡻⠕⠊⣿⣟⣩⡖⠒⢲⣾⠟⢀⣼⣻⠁⠀⣾⣿⡛⠛
⣿⣿⠏⠉⣿⠾⣿⣿⣿⠀⠀⠀⠀⢳⡀⠀⠈⡆⠀⠀⠛⠛⣿⣿⣿⣦⣷⣾⡇⠀⠀⠀⢿⣿⡝⡇⠀⢸⠁⣠⣾⣏⡇⠀⣸⣿⡦⡝⢦
⠸⣿⠀⢸⣿⣷⡼⣿⣿⡆⠀⠀⢀⣿⣿⣋⣥⣷⠖⣶⣶⣿⣿⣿⡿⠿⠛⠓⢻⠀⠀⣠⣿⣿⣷⡁⠀⣸⠾⠛⠋⡽⠀⢠⣿⣗⠭⠂
⠀⢿⠀⠘⣿⣿⣧⣦⣿⣧⣀⡤⠾⠛⠋⠉⠀⡟⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣀⣰⡿⠿⠛⠋⣇⠀⠙⢦⣄⠰⣇⠀⣼⣿⡪⠕⠀⢸
⠀⠘⣷⡶⠿⠿⢷⡿⣿⣉⣹⣀⣠⣤⣴⣶⣿⢟⣶⣷⠤⣄⣀⣀⣀⣀⣀⣀⡸⠏⠀⠑⢄⡀⠀⠈⠙⠛⢿⡿⠀⢳⣝⣿⡳⢮⣀⠀⣿
⠀⢠⣿⣁⣀⣀⣸⣄⣀⣀⣈⣉⣿⣿⣯⣽⣾⣿⣸⣿⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣙⣦⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣷⣭⣻⣿
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠠⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⣤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠂⡙⠩⠊
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠉⣉⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡁⠀⠀⠀⠀⠐⠂⢲⠀⠀⠀⠀⠀⢈⣉⣉⠁⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⡇⠛⣿⣿⡟⠃⢸⣿⣿⣿⣴⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠘⠪⡇⠐⠖⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⠶⠶⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠰⠀⡂⢀⡀⠀⠤⠐⠀⠀⠀⠀⠙⠛⠛⠁⠀⠛⠛⢳⡴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠤⢠⣿⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣴⡖⢶⡶⢶⡶⢶⡄⠀⠀⢷⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠴⠿⢿⣿⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠉⠉⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠀⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⡇⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⡍⠙⠛⡀⠀⠀⠀⠘⠋⠙⠤⠀⠀⠀⠀⠀⠀⠈⠀⡝⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣠⠄⠀⠀⠀⠀⠀⣀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⢤⠉⠀⠀⠀⠀⢠⡾⠋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠃⠈⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⡾⠁
⠀⣠⣤⠴⢤⣄⠀⠀⠀⠠⠦⠶⠶⠶⠛⠉⠀⠀⠀⠀⢀⣤⠾⣿⠁⣤⠶⠋
⣸⠋⣠⣤⣄⠈⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠋⠁⢰⡇
⣿⠀⠿⠀⢸⡇⢸⡟⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠘⣇
⢹⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⢸⡇⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠙⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠉⠁⠀⠀⠀⣤⣀⠀⣀⣀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠰⣄⠀⠙⣿⠋⠉⠛⠋⠁⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢷⡄⠈⠓⠀⠤⠀⠀⠀⠀⠀⠀⠀⣀⣘⠋⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⣤⣄⣠⣴⠟⠀⠀⠀⠀⠀⠀⠻⣆⣠⠶⠛⠀⠀⠀⠀⠀⠀⠈⠉⠉⢳⡄⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⡼⠁⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠁⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⣤⣤⣤⠞⠋⠈⠛⠐⠂⠘⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⡖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⣶⣶⣶⣶⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣮⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⣿⣿⣷⡒⠀⠀⢰⡇⠀⠀⢠⣼⣆⡀⠀⠀⢀⣰⠀⠸⣿⣿⣿⣿⣿⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿⢻⠸⠁⠀⠃⠸⡇⢸⣷⠋⢂⣽⢩⣁⣠⣷⣾⠀⠀⠉⢸⣿⣿⡟⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣸⠂⣘⠀⠀⠂⣼⡇⣼⡇⠀⠀⠹⠂⠙⠉⠉⢹⠀⠀⡀⠁⠀⠈⢇⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢸⡇⣀⣠⣴⣷⣄⠛⠀⡦⠦⠸⣧⡟⠛⢀⠀⢸⠀⠀⠀⠀⠀⠉⢉⠇⠒⠂⠉⠉⠑⢄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢩⣤⡀⠀⠀⣿⣿⡷⢾⡆⠉⢃⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠡⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢻⣿⣿⣆⠀⣾⣶⠀⠸⡇⠀⠀⢣⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣸⣿⣿⣿⠀⣯⣭⣄⣂⣡⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡛⠉⢿⣿⣿⣆⡷⣤⠄⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠹⣿⣿⣿⣟⢰⣶⣶⠈⢆⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣘⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣿⣿⡇⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⣶⣤⡀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠁⠀⠀⠈⠙⠻⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢤⣍⣙⠛⠿⠛⣋⣩⣤⡶⠶⠿⣿⣿⡧
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢠⣶⣦⣬⣉⢋⣩⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⣀⣀⣠⣴⣾⡿⠏⣰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⢠⣴⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢹⡟⠀⠀⠀⢀⣀⣤⣤⢤⡄⠀⠈⠛⢿⣶⠖⠋⠁⠀⠀⠀⢠⡖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣰⣟⠀⠀⠀⢸⣿⠿⠋⣀⣤⢏⣀⣀⣀⡞⡎⠀⠀⠀⠀⠀⠀⠈⣿⣷⣞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠚⠧⣌⢦⡀⢀⣀⣽⠿⠟⠛⣻⠟⠉⠉⠙⢣⡇⠻⠶⢤⣴⠶⢤⣴⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡍⠋⠙⠷⣦⡤⠞⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⡀⠀⠹⣧⠀⠀⢀⣾⠳⣄
⠀⠀⠀⠀⠀⣠⡾⡆⠀⠀⠀⣠⣿⣥⡄⠀⠀⠀⠀⢳⡇⠀⢀⣤⠶⠶⠶⣶⡄⠀⠀⡼⣷⠦⠶⠟⠳⣤⣸⣿⡄⠸⣇
⠀⠀⠀⠀⢰⡟⢰⣧⣀⣀⣼⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⢰⣻⣅⣀⣀⣴⠟⠁⠀⠘⠱⠁⠀⠀⠀⡠⢊⠄⠻⢷⣤⠏
⠀⠀⠀⠀⢻⣧⠟⠓⠀⣿⡇⠀⣠⠿⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡽⠇⠀⠀⣠⠶⢤⡀⠀⠀⠀⠰⠃⡀⠻⣆⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠋⠉⠳⠬⠁⠀⢀⣴⠾⢿⠄⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⣦⠀⠀⠀⣼⠛⢷⠈⠤⠴⠚⢻⣷⣼⡿
⠀⠀⠀⠀⠀⢀⡶⢆⠠⡇⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠶⠾⠛⠀⠀⣠⣿⡀⢸⡇⠸⣿⠁⠈⠛⠛⠁
⠀⠀⠀⠀⠀⣾⠀⢸⣗⣒⠒⠒⠂⠀⠀⠀⠸⢿⡶⠛⠛⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠿⠁⠀⣿⠀⢀⣀
⠀⠀⠀⠀⠀⣿⣀⡞⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠈⢻⡦⠀⠀⠀⢀⡴⠒⣦⠀⠀⠀⢀⠀⢀⣿⣠⡿⠏⣷
⠀⠀⠀⠀⠀⠈⠉⠀⢾⡇⢰⡟⢿⣦⠤⠖⠋⠀⠀⠀⠀⠀⠀⢸⡻⣦⣤⡾⠁⠀⠀⣸⣿⠁⠀⣸⠀⠀⠀⠨⠭⠭⣭⣿⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⡿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠀⠀⠀⠀⠈⢿⣀⣰⠃⠀⣀⣄⡀⠀⢀⡏⠘⢷⠟⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠘⣇⠸⣦⣼⠃⠀⠀⣠⢲⡶⢶⣿⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⢿⡿⠁⢨⠇⠀⣼⠇
⠀⠀⠀⠀⠀⣿⡉⢳⣤⡿⢂⠀⠀⠀⠀⠀⢻⣌⢳⡀⢹⣿⠀⠀⠀⠀⣠⡿⠛⠛⢻⣷⠀⠀⠀⢸⣃⣠⠏⠀⣴⡟
⠀⠀⠀⠀⠀⣿⡀⠀⣿⠟⢯⡀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠋⠀⠀⠀⢰⣇⣀⣠⡴⠟⠁⣬⢷⡀⠀⠉⠠⣄⡘⠋⣠⠴⣦
⠀⠀⠀⠀⠀⠘⢷⣴⠏⠀⠀⢙⣦⡀⣠⢏⡀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠈⠁⠀⠀⠀⢀⣽⠞⢛⡿⢈⡷⢦⣙⣿⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠛⢷⣎⠀⠀⠀⠀⣴⠏⠉⠉⠙⢲⣤⠀⡀⡀⠀⢾⣧⣤⣮⠴⠋⠀⠀⢹⡇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⢻⡛⠳⢦⣄⡙⠶⢤⣤⣶⠾⠛⠀⣿⣷⠶⠶⠚⠉⠀⠀⠀⠀⠀⠸⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠃⠀⢀⣨⣿⣿⠛⠛⠛⠉⠉⢉⡿⠿⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣈⣱⡄⠀⠀⢰⣇⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⡏⡴⠋⠉
⠀⠀⠀⢻⡸⡄
⠀⠀⠀⠀⢣⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠹⡅⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⠹⡄
⠀⠀⠀⠀⠀⡟⢿⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡞⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢱⡘⣧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣆⢰⣆
⠀⠀⠀⠀⠀⠀⢧⢉⣁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠉⠛⣿⣿⣿⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⣀⣾⣿⢸⣿⣤
⠀⠀⠀⢀⣤⣶⣾⣿⣟⡁⢷⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠟⠛⣫⠛⠷⠶⠚⢻⣿⣿⡿⠀⠀⠈⢳⣦⠰⠖⠛⢡⣿⣟⣸⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣬⣇⠀⠀⠀⠀⠀⠀⢸⣀⡘⠛⡸⠁⣇⠸⠗⠀⣼⡙⡿⠁⠀⠀⠀⠸⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠿⣿⣿⣿⣿⣿⠛⠡⠼⡀⠀⠀⠀⠀⠀⠀⠉⢩⠉⢥⡄⠉⠉⠉⠛⣯⠜⠁⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡆⠤⣶⠴⠂⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣉⣁⣤⠞⠁⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⠀⠀⠀⢹⡍⠂⢄⡀⠀⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡤⠦⠤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠁⡼⠀⠀⠁⠀⠙⢦⠀⠙⣄⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠓⠒⠚⠀⠀⢳⣄⣀⡀⠶⣒⣨⡇⢀⣜⠀⡟⠺⢄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇⠀⠀⠘⠂⢰⡄⣿⣿⣿⣿⣿⡟⡔⠁⠀⢹⠃⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⢀⠎⠀⢀⡀⠀⣠⠏⠀⣿⣿⣿⣿⡟⠀⢹⡀⠀⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⡞⠀⠀⢸⡇⡰⠁⠀⠀⣿⣿⣿⡟⠀⠀⣠⠃⣸⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡼⠁⠀⠀⣸⠃⠸⡀⠀⠀⣿⣿⡿⠀⢀⡜⠁⢠⡏⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⠀⠱⡀⠀⣿⣿⠁⣰⠋⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⢀⡞⠀⠀⠀⠀⠱⣘⣿⢇⡼⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⢹⣿⠞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢰⠇⠀⣠⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢀⡼⠃⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣼⣤⡀⠀⠀⣀⣠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⡿⠿⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠦⠠⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠛⠒⠲⠶⠦⠤⢤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⣠⠜⠋⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣤⠀⠀⠀⣾⠁⠀⠀⣠⣤⣄⠀⠁⠘⢷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢸⡇⠀⠀⠉⠀⠀⠉⠱⠄⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠀⠀⠀⠀⢠⠀⠀⢰⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣠⣶⡾⠻⣄⠀⠀⣼⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⣿⠋⠉⠀⠀⠈⠛⠦⢤⣤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠷⠶⠶⠶⣦⣴⠶⠛⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⡀
⠀⠀⠀⣼⡿⣿⡿⢿⣿⣷⡀⠀⠀⠀⠀⣾⣿⡿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⡿⣿⡄
⠀⠀⠀⠙⣀⠀⡀⠸⠿⣿⠁⠀⠀⠀⠀⢻⢏⣭⠀⢤⠸⡏⠀⠀⠀⠀⠀⠀⠫⡌⠉⡀⢸⢿⡿⠀⠀⠀⠀⠀⠘⡇⢠⠈⢨⠀⡿
⠀⠀⠀⠀⠈⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠘⠀⠴⠀⠀⠁
⠀⠠⠄⢀⣀⠚⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠓
⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣿⡀
⠀⠀⠀⣿⠛⠋⠿⠛⢻⠇⠀⠀⠀⠀⠀⠸⡇⢠⠈⢩⠀⡿⠀⠀⠀⠀⠀⠀⢿⠁⡀⠉⣁⢸⠏⠀⠀⠀⠀⠀⠸⡏⢠⠈⢩⠀⡿⠁
⠀⠀⠀⠘⡀⠁⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠗
⠀⠀⠀⠀⣃⠤⡤⢜⠀⠀⠀⠀⠀⠀⠀⠀⡈⡂⣄⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⣈⣭⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣬⣤⣀⡁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀
⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠘⡏⠈⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⠸⡟⢉⠙⠛⠉⡿⠁⠀⠀⠀⠀⠀⢿⠁⡄⠉⡅⢸⠇⠀⠀⠀⠀⠀⠸⣏⢠⠈⢩⠀⡿⠁
⠀⠀⠀⠉⢁⠈⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠑⡈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡌⠀⠈⡈⠁
⠀⠀⠀⠀⠐⠒⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐
⠀⠀⠀⠀⡠⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠠

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣒⠚⠂⠀⠂⠤⠀⠀⠉⠈⠁⠐⣢⡀⠀⢀⣀⢀⡔⢒⠞⠑⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡼⠄⠀⠀⠀⠀⡜⠁⠠⠀⢀⡀⠀⠀⠸⠓⡨⠀⠭⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡠⢞⠓⠊⠀⠀⠀⠀⠀⣸⡵⠟⠁⢑⠢⠄⠑⠂⠜⣁⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⣠⡔⠴⠛⠁⠀⠀⠀⠀⢀⣀⢀⢨⠀⠠⠴⠀⠂⢡⡯⠖⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠥⠤⠚⠪⡢⣀⣄⡄⠀⠚⠔⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⣴⡂⠖⠓⠒⠁⠀⠀⠀⠀⠈⠀⠀⢐⡂⠀⢀⠀⠀⠀⠄⠀⠀⠃⠀⣀⠒⠀⠀⠀⠀⠲⠦⠤⣤⣤⠤⢀⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠒⠏⠀⠀⣆⣆⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠜⠃⠀⠀⢀⠀⠀⠀⠸⠀⠡⠄⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡤⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠂⠛⠉⣣⢤⠨⢀⠀⠀⢠⡆⠂⠀⠀⠐⡄⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠊⠉⠐⠀⠀⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢹⡀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠈⠵⠦⡀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠀⢀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⡅⠀⠀⠀⠀⠒⠁⠀⠀⠘⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠈⠁⠙⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠬⠀⠀⠀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⠀⣀⠤⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⡀⠸⠴⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠻⡄⠀⣠⠴⠂⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠴⣾⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡴⡿⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⢃⡴⠚⠙⠲⣤⡀⣾⡟⠀⠀⠀⠀⠀⠹⣆⠀⠚⠉⡉⠈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠙⢯⡿⢦⡀⠀⠀⠀⠀⠙⢧⡀⡿⠙⡟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣿⡄⠀⠀⠀⢀⣀⣭⡇⢀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠦⢤⣽⣷⣿⠤⠖⠚⠉⠉⠀⠙⠛⠓⠞⠷⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠴⠶⠶⠶⢦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⢦⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⠶⢾⣷⣤⣬⣵⣤⣤⣵⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⣙⢦⡀⠀⣠⡟⠀⠀⠶⠖⣻⣿⠟⠓⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠁⣿⠂⢙⡾⠋⠀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡶⠟⠁⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠀⠀⠸⣧⠶⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣄⣤⠶⡿⢲⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣽⣷⣭⡙⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⣈⡝⢿⡀⠙⢿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣇⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣠⣶⣶⠾⠷⠿⠿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡯⠀⣿⠷⢼⡇⢰⠜⠃⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⢹⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠠⣾⣥⣤⣤⣤⡴⠛⣻⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢳⠀⠸⡇⠈⡇⢸⠀⢸⡿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢷⣜⣧⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⢷⠀⣿⢸⠇⢸⣇⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⣄⡈⠻⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠸⡇⢸⡿⠀⠈⣿⢹⣆⣿⣤⢴⣶⡤⠶⣶⣆⢹⣷⠤⢀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠛⠋⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡀⠀⠸⡇⠀⣿⣸⣧⣤⠶⠛⠉⠉⠀⠀⢰⣿⠀⠀⣿⡽⠦⠿⠄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠛⠶⠖⠲⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠃⠀⠀⢿⡤⠼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣀⢹⡗⣶⠶⢆⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣒⣚⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣧⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣉⡚⣣⡇⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠙⠓⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠸⣿⡃⠀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡟⠉⠉⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⡏⠙⣿⠉⢻⣏⣉⣠⡤⠶⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⢿⣆⣠⣿⠀⠘⣏⠉⠀⠀⠀⠀⣿⣤⠤⠤⠴⠶⠶⠶⠖⠚⠛⠛⠛
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⡇⠁⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠂⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣧⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⠤⣤⠼⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠛⢛⣻⣿⣿⣿⠿⠧⠤⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠒⠒⠂⣉⡿⠋⠀⣮⠈⠛⠓⠶⠶⢠⡿
⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⢀⣀⣀⣤⣤⣤⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣀⣤⠴⠶⢿⡷⠻⠛⠒⠒⢠⡄
⠻⣤⣀⣀⣈⠹⣦⣹⣯⣭⡿⠿⠛⠛⠋⠉⠁⠀⠀⠉⠉⠐⠶⠾⠶⠧⠶⠶⠾⠋⠁

⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢄⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⢻⣟⣆⠀⠀⠀⠀⠀⠀⠠⠆⠌⠀⠊⠰⠀⠀⠀⠀⠀⠻⣿⢮⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣦
⠀⠀⠀⠀⠀⠙⠻⠗⠀⠀⠀⠀⠀⠶⠁⡀⡠⠈⠠⠀⠀⠀⠀⠀⠈⠊⣿⡇⠀⠀⠀⠀⠀⢾⣷⣾⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠐⠑⠈⠄⠠⠑⠀⠀⠀⠦⣄⠸⡇⠰⠛⠁⠀⠀⠀⠀⠈⠑⠀⠈⠀⠀⠀⠀⠀⠀⣺⣿⣿⣷⡄
⠀⠀⠀⠐⡐⢀⠂⠄⡡⠀⠀⠀⢀⣠⠆⢰⡆⠘⢷⠄⠀⠀⠈⡳⠀⢀⢀⠈⠀⠀⠀⠀⠀⠈⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠄

⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠇⡀⠀⠀⠀⠀⠀⠀⡀⢤⡀
⠀⠀⠀⠸⣻⡏⠙⣦⠀⠀⠀⠀⠐⠄⡀⠃⠘⠃⢀⠀⠀⠀⣠⢾⣟⠁⣸⠇⣠⠆⠀⠀⢀⡎⢁⣂⠂⠓⡀
⠀⠀⠀⠀⠙⠿⣿⣟⠦⠀⠀⠠⣂⢀⡀⠀⠀⠰⡄⡂⠀⠘⠁⠀⠁⣠⡾⠿⠃⠀⠀⠀⠀⢦⠈⠉⢁⡘
⠀⠀⠀⠀⠀⠐⠻⠋⠀⠀⠀⠀⠀⢀⠀⣘⡆⡀⠀⠀⠀⠀⠀⠀⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⣀⠄⠀⠀⠀⠀⢢⣶⣿⣶⣴⠀⠀⠀⠀⠀⠔⠀⢀⠀⠀⠀⠀⠀⠀⢠⢖⡄⢀⠀⠀⡀
⠀⠀⠀⢨⣿⡿⠻⣷⡆⠀⠀⠐⣿⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⢨⢢⣒⣀⡀
⠀⠀⠀⠈⢹⣷⣾⠛⠁⠀⠀⠀⠸⠻⢯⠟⠻⠦⡀⠀⠀⠀⠀⠀⠁⠒⢷⠀⡀⠀⠀⠀⠀⠀⡀⠁⠚⠥⡃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠝

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

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

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣠⠖⠩⠝⠿⠟⠻⠟⠛⣷⣄⣹⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠃⠀⢠⡄⣠⠀⡦⠀⠀⠘⠉⢻⣟⢦⣉⡓⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠘⠇⠀⠀⠀⠀⢀⣴⣿⣿⣆⠙⠯⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠦⠔⠀⠀⣠⣞⠛⠻⠛⠋⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠑⢶⠠⠤⢒⡏⠁⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠒⠒⠋⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠔⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣋⠉⡇⠀⣢⣼⣷⠷⠾⠿⠿⢿⣶⠶⠾⠵⣦⣄⠀⢀⡴⠿⠴⠦⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡞⢳⡞⠀⠈⢲⡽⢮⡇⡀⠀⠀⠀⢿⢫⢢⢀⠄⢈⡿⠚⠉⠀⠀⠀⢀⡴⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⠁⠀⠀⣠⠋⠤⠄⠀⠒⠂⠐⠀⠈⡻⠚⠳⠊⠁⠀⠀⠀⠀⢀⡴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣒⠒⠒⠒⠒⠒⠶⠤⠭⠭⠭⣭⣍⣙⣛⣒⣒⣚⣁⣀⡀⠀⠀⠀⠀⠀⡰⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠉⠛⠒⠒⠒⠒⠒⠶⠶⠤⠤⠤⠤⠭⢭⣭⣍⣩⣹⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡗⠀⠀⢠⣶⡆⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣷⡀⠀⠀⢹⡆⠀⠀⣾⡏⠀⠀⢸⣿⡆⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⣿⣤⣤⣾⣿⣿⣿⣿⣷⣤⣠⡟⠁⠀⠀⢀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⠟⠋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠞⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣶⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠘⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣴⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠻⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⢀⣼⠛⠛⢿⣿⣿⣿⣿⡿⠛⠛⣿⣄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠸⣿⡇⠀⠀⣸⡿⠀⠀⠸⣇⠀⠀⠈⢿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠸⠿⠃⠀⠀⢼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡴⠶⠶⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠛⠈⠛⠛⠛⠛⠀⠛⠒⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡏⠀⠀⠀⣬⢻⡄⠠⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⠻⣦⡾⠁⣸⠇⠠⡤⠤⠤⠤⠤⠤⣤⠄⢀⣿⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠶⢤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠐⠒⠶⢦⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠞⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣀⣀⣀⣀⢸⡇⠐⠶⠶⠶⠶⠶⠶⠶⠞⢧⣀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀⠀⠀⢀⡼⠁⠐⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⠁⠒⠒⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⠀⠀⠈⢳⡄⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠛⠛⠛⠛⢸⠇⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠧⣶⡄⣶⣠⣶⢄⣶⢰⠆⡖⠂⡗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠉⠀⠉⠈⠉⠈⠀⠉⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⢠⠒⣄⡠⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡠⠄⢘⠃⠀⠀⡖
⠀⠀⠈⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠘⠃⡼⠀⠃⣠⠁
⠠⡞⣒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠔⣦⡉⠁⠀⡀⣾⠀⠀⠠⡠⢾⡨⢈⡃⢖⢀⠇⣬⠀⠤⠒
⠀⠉⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢀⡈⠁⠀⠘⠇⠀⠀⠀⠀⠀⠘⣍⣜⢂⡸⢈⠱
⠀⠀⢰⢊⡔⠤⣀⠀⠀⠀⠀⠀⠀⠠⣴⡇⢈⡙⠀⢰⠂⠀⢀⣀⠰⠞⠀⠀⢀⡯⠑⠨⢧⠌⠂⠈⠒⠆
⠀⠀⠀⠉⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠹⡚⠁⠀⡄⡀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣀⡀⠈⠗⡀⠢
⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⡿⠢⠄⢽⣃⠀⠀⠚⠗⠀⠀⠀⠀⠘⢤⠳⢰⠶⠅
⠀⠀⠀⠀⢀⡷⡒⢂⠅⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢠⢤⣠⠏⠀⠀⠖⠆
⠀⠀⠒⢦⣮⠀⡁⢰⠁⣙⢠⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⢦⠀⠀⠀⠀⠀⠀⡰⠀⡀
⠀⠀⠀⢸⣤⢀⡅⠸⣠⡝⢰⠀⠀⠀⠀⠀⠀⣔⠢⠔⠒⠈⠀⠁⠀⠀⠀⠀⢀⣸⠄⢠⠈⠒⠀⠀⠐⠚⠁
⠀⠀⠊⠉⢣⣰⠁⡜⢂⡄⠃⠀⠉⠓⠂⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠋⠓⢭
⠀⠀⠀⠀⡰⠋⠒⢡⡄⠁⠘⢆⠀⠀⠀⡠⠴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡈⠇⠀⢠⠀⡀⠀⠀⠙⠹⡄
⠀⠀⠀⠀⠀⠀⢯⡘⠤⣤⣜⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⣲⠀⠇⢰⠂⢀
⠀⠀⠀⠀⣀⡀⡰⠁⠀⢡⠤⠀⠀⠀⠀⠀⠀⠣⠎⠑⠤⢤⠀⠀⠀⠀⠀⠀⠀⢒⡔⢩⡂⠰⠄⢤⠀⠁⠴
⠀⠀⠀⠐⢧⠭⡁⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⡿⠶⢠⡄⢛⠀⢤⠐⠇⠐⠚
⠀⠀⠀⠀⠀⠀⡇⠀⡀⠣⠀⠀⠈⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⠆⢠⡂⢙⠠⠎⡘⠅⢀⢉⠁
⠀⠀⠀⠀⠐⢍⡵⠒⢍⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢦⡮⠀⡌⢁⡄⠓⠠⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡖⢢⡀⢶⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⣿⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⡶⠛⠋⣿⠙⠛⠶⣄⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡾⠃⣠⠖⠛⠻⠙⠳⣦⠈⢳⡄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⡃⣸⡃⠀⠀⣠⡀⠀⠈⣧⠀⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣴⢟⣓⣛⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠉⢻⡉⢹⡉⠀⠈⠻⠉⠀⠈⣿⠉⣿⠉⣽⠁
⠀⠀⠀⠀⠀⢀⣴⢇⡶⠋⠉⠉⠛⣦⠻⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⣿⢀⣠⡾⠁⣰⠇⢠⡏
⠀⠀⠀⠀⠀⠈⣷⢸⡁⠀⠀⠀⠀⢸⡧⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⣿⢉⣁⣤⠞⠁⣰⠟
⠀⠀⠀⠀⠀⠈⠳⡎⢷⣄⡀⢀⣠⠞⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⣉⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠛⣶⣏⣭⣍⣵⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢈⣿⣯⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⣿⢹⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⢰⣷⣶⡿⣿⢸⡟⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣱⣿⠓⣛⣌⣓⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡿⠟⣾⠁⠀⠙⣧⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣸⣄⣀⣀⣙⣷⠹⢦⣤⡴⠣⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠉⠉⠉⠉⠉⠉⠉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠙⢿⡿⠋⣿⠉⠳⠛⣷⣰⡞⠳⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡟⠛⣵⠟⠉⠉⠻⣎⠛⢻⣆⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠘⢯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⢰⡇⠀⠀⠀⠀⢸⠆⣯⣭⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣄⠳⣤⣀⣀⣤⠟⣠⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣷⢀⣭⣭⡀⣾⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠛⠉


⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⡆⠀⡄⢰⠖⠀⠀⠐⣴⣿⣦⠂⠀⠀⢸⣿⣿⣿⣿⣿⣏⢹⣟⢻⡏⣹⣿⣿⣿⠋⠈⢹⣿⣿⣿
⠀⠀⢀⣀⠐⢦⣹⣶⣷⣿⡠⠂⢀⡌⠹⠛⠅⠁⠀⠀⢸⣿⣿⡿⢿⣯⡹⠂⠉⠉⠰⢟⣽⡿⢿⣶⣤⣾⣿⣿⣿
⠀⠀⠈⢉⣙⣿⣿⣿⣿⣿⣿⣟⣉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠶⡦⠀⠀⠀⠀⠀⠀⢴⠶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣈⡤⢿⣿⣿⣿⣿⡿⢧⣉⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⢛⡀⠀⠀⠀⠀⢀⡛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠁⠰⠎⣹⠛⡟⢿⠙⠆⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣏⣥⢁⣤⣠⡸⣮⣻⣷⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠇⠈⠃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣸⣷⣾⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠑⠢⢍⣛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠑⠦⣌⣉⠒⠤⡉⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣑⠢⢭⣑⠢⢍⡙⠒⠤⣀⠀⠀⠈⠙⢷⣄⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠓⠮⣍⣒⠦⢍⣓⠢⠄⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣭⣷⣦⣌⣁⠐⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣯⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣄⣠⣤⣴⣟⣁⣤⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢻⣿⢿⣿⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢛⣛⣛⣻⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡜⠘⣯⠉⣿⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠁⠀⠘⢧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⢶⡟⣀⣠⣤⣴⣦⣬⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⢤⣭⣉⣉⣉⣉⣉⣉⣛⣛⣛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⢶⡾⠿
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠒⠒⠤⠬⠭⠭⠭⠭⠭⠍⠉⠁⠀⠀⠀⢠⡟⠳⢤⣀
⣼⠃⠀⠀⠀⠉⠑⠢⠄⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣒⡒⠒⠒⠢⠤⠤⠤⠤⢬⣭⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠄⢀⣀⣀⣀⣀⣈⣉⣉⣉⠉⠉⠉⠉⠉⠉⣛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⣤⣽⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣭⣭⣭⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⡦⠄⠤⠄⠀⠀⠀⠉⠁⣀⣀⠀⠀⠙⣟⠛⠋⠉⠉⡟
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣉⣩⣭⡿⠿⠟⠛⠛⠛⠛⠛⠒⠶⠶⠾⠿⠛⠀⠀⠀⢸⠃
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠛⠉⠁⢀⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠶⠒⣛⣉⣉⣤⡤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣈⡳⣭⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⠟⢻⣿⢻⣿⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⣿⣿⣻⣿⣛⣛⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣟⡛⠛⢻⣿⣻⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⣛⠛⠀⠀⠀⠀⣿⣿⢟⣭⣶⠶⢶⣮⣝⠛⣛⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢛⣩⣴⣿⣿⣿⡏⠀⠀⠀⠀⣿⢣⣾⣿⣏⣾⣷⢹⣿⣧⠙⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⢸⣿⣿⣿⢋⣵⣿⣿⣿⢈⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⡌⣿⣿⣿⣿⣿⠀⠀⠀⠀⣽⣎⢻⣿⣿⣺⣿⣿⣿⢟⣼⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣃⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣷⣭⣛⡛⢛⣋⣥⣘⣉⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣙⡛⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣠⣴⡘⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣮⡛⢿⣿⣿⣷⣄⣠⣴⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⣿⡿⠟⠋⠁⠀⣴⣶⣶⣶⢂⣴⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠁⠀⠀⠀⠀⠀⠿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⢠⣶⣶⣶⡖⣴⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⢿⠁⠀⠀⠀⠀⠹⠿⠿⠿⡇⠻⠿⠿⠿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐




⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⣶⠶⢶⣶⣶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠦⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠦⡀⠀⠀⠀⠀⠀⣠⠔⢲⢰⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⡆⡇⠀⠀⠀⠀⠀⣼⠕⠂⢀⠀⢠⠂⠀⠈⢆⠀⠀⠀⡜⠁⠀⢸⢸⠴⣚⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢸⠀⡇⡇⠀⠀⠀⠀⡸⠁⠀⢠⢇⡴⠃⠲⡀⠀⠘⡄⠀⠀⡇⠀⠀⢸⠔⠊⠁⢀⡇
⠀⠀⠀⠀⠀⠀⡞⢳⢸⠀⢸⠀⡇⡇⠀⠀⠀⢀⠇⢀⡴⣷⢍⠀⠀⡠⣈⢦⠀⠱⡄⠀⢹⠉⡣⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⢀⣧⣸⣼⣠⣼⣄⣧⣇⣤⡀⠀⢺⠊⣏⠀⠐⠆⠀⠀⠰⠀⠀⣳⢄⣹⢀⡼⠃⠯⡖⠒⠊⠁⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣷⡀⠀⣐⣂⠀⢀⠟⡏⢀⡞⠈⠉⠉⠉⠁⠀⡤⡄⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢹⢦⡀⠀⠀⠀⠹⣄⣇⠙⡦⢍⡡⡴⠋⢠⢃⡟⠀⠀⠀⠀⠀⢀⡴⠋⠙⢢⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠭⠬⠉⡇⠀⠀⠀⠀⠈⢁⣹⡇⠀⠀⣸⣾⡓⠋⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡴⠚⠉⠓⡇⠀⣛⣛⠀⡇⠀⢀⠔⢺⠉⠉⢣⡈⢲⡞⢁⠇⠈⠙⡶⠦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠰⡁⠀⠀⡀⠳⠤⢤⠤⠄⠇⠀⠆⠀⣸⠀⠀⢘⠑⢻⡟⠋⠃⠀⠀⡇⠀⢹⠀⠀⢸⠖⠖⠖⠒⠲⠚⠳⠲⡇
⠀⠀⠀⢀⠔⠁⠀⢄⣇⡠⠀⠘⢦⠀⠀⢰⠀⠀⢻⠀⠀⠘⠖⠑⣞⠒⠂⠀⠀⡷⠀⠈⡄⠀⢸⠀⠀⠰⣉⣱⠀⠀⠀⡇
⠀⠀⠀⠸⣄⠀⠀⠀⠉⠀⠀⠀⢠⠇⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣧⠀⠀⡇⠀⢸⠀⠤⠤⠤⠬⠤⠄⠀⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣇⣀⡀⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⢳⠀⢸⣀⣉⣉⣉⣉⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠒⠬⣷⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣟⡩⠭⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡞⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣇⠀⣠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢼⣄
⠀⠀⠀⠀⠀⠀⠤⢤⡴⣫⡿⠓⠒⢾⢶⡥⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣳⣯⣻⣦⡤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠺⠛⡏⠀⠀⣀⠜⠓⠚⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⣀⡀⣄⡀⠀⠀⠀⣠⣤⣤⢤⣄⠀⠀⢠⣤⡀⠀⠀⣠⡀⠀⠀⣴⣤⣄⣤⠀⠰⠶⢶⣶⣶⣶⡦⠀⠀⡴⠀⠀⢀⣤⣶⣢⣄
⠀⠀⠀⣠⣾⠟⠋⠙⠃⠀⠀⢠⣿⠉⠉⠉⠉⠀⠀⣿⢿⣷⠀⠀⣧⡇⠀⢸⣿⠀⠈⠁⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⣿⠀⢠⣿⠏⠀⠈⠉
⠀⠀⢰⣿⠁⣀⣀⡀⠀⠀⠀⢸⣿⣤⣤⣤⠀⠀⢰⣿⠀⢻⣧⢰⣿⠀⠀⣼⣷⣶⡶⠆⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⡏⠀⢸⡟
⠀⠀⢸⣧⠀⠙⠛⠛⣿⡆⠀⣿⡏⠉⠉⠀⠀⠀⢸⣿⠀⠀⢿⣿⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢀⣿⠃⠀⢸⣇⠀⠀⢀⣤⡄
⠀⠀⠈⠻⠷⠶⠾⠿⠛⠁⠀⠿⠿⠿⠿⠟⠀⠀⠾⠇⠀⠀⠈⠻⠏⠀⠘⠿⠿⠷⠿⠂⠀⠀⠀⠿⠃⠀⠀⠀⠘⠟⠀⠀⠈⠻⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⣖⣤⠄⠀⣴⣶⣶⣦⠀⠀⣰⡾⠽⠗⠀⠾⠿⢿⡿⠿⠿⠀⠀⣴⡆⠀⢀⣶⣶⡀⠀⢰⡦⠀⠀⣴⣶⠿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢰⣿⣠⣄⠀⠀⠀⠿⣷⣤⠀⠀⠀⠀⣾⡇⠀⠀⠀⢀⣿⠃⠀⢸⡿⠙⣿⡄⣷⡇⠀⣾⠟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⢀⣿⠏⠉⠉⠀⠀⣀⡀⠀⣻⡇⠀⠀⢰⣿⠀⠀⠀⠀⣸⡿⠀⠀⣿⡇⠀⠸⣿⣿⠀⠸⣿⡀⠉⠛⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠸⠿⠿⠿⠿⠃⠀⠙⠿⣶⠿⠃⠀⠀⠸⠟⠀⠀⠀⠀⢿⠇⠀⠀⠿⠁⠀⠀⠛⠋⠀⠀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⢠⣤⣶⠾⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠷⢶⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⡇⢀⣤⣄⠀⢠⣤⣄⠀⢠⣀⡄⣴⣧⡄⠀⢸⣿⠉⠙⣷⡀⣭⡁⣠⣤⡄⢀⣠⣤⡀⢀⣤⣤⡀⢀⣤⣤⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⣿⡃⣿⡷⠾⠇⣴⠖⣿⡇⢸⡏⠀⢸⣏⠀⠀⢸⣿⠀⢀⣿⠃⣿⡇⠻⢷⣄⢸⡷⠾⠿⢠⡶⢺⡇⠘⠿⣦⡰⣿⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠁⠈⠛⠛⠁⠙⠛⠛⠃⠘⠃⠀⠈⠛⠃⠀⠈⠛⠛⢋⠁⠀⠛⠁⠛⠛⠃⠈⠛⠛⠃⠈⠛⠛⠃⠘⠛⠋⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⠀⠀⢠⣊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⢤⠷⠻⣿⡄⢠⣼⠿⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢺⡀⢦⡄⡔⠀⠀⠀⠀⠀⠀⠐⣎⢤⠆⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣼⣿⡿⢛⣛⡤⠀⠀⠀⠀⠀⠀⠀⡳⣜⡠⠙⠲⣴⣿⣿⢀⡤⠷⠣⣀⡴⠋
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣿⣿⣦⣴⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠄⣾⣿⣿⣿⣷⣼⣿⠀⠄⠀⠀⠀⠀⠀⠶⣞⣿⠗⠛⠻⢿⣟⣿⣿⡞⠛⠳⢿⣟⡵
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⡿⣾⣿⡉⠁⠀⠀⠀⠈⠀⣸⢷⡀⠀⢀⣾⣿⣿⣿⠇⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠜⡷⢻⡄⣸⣿⣿⣿⡿⠀⠀⣰⢿⠟⠌
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣾⣿⣿⣿⣷⣀⢾⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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