Kawaii cat Emojis & Symbols

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀
⠀⠀⢲⠖⢉⣹⠆⠀⠀⠘⡝⠃⠑⢎⡏⠀⢐⠉⠍⠛⠋⠍⣢⠀⠀⠀⠠⡀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠙⡄⠈⠀⠀⠀⠀⠉⢈⡱⠆⠀⠀⠀⡶⠤⠤⠴⡆
⠀⠀⡇⢠⠃⠀⠠⡄⢟⣤⠁⠎⠱⠸⡄⠀⢀⠤⠈⡗⢪⠀⠁⠀⠀⢀⠖⠑⠀⠛⠃⠐⠃⢧⠀⠀⠀⠀⠁⠀⠛⢀⡀⠛⠀⠈⡆⠀⠀⠀⠀⣆⠀⠀⠂⡠
⠀⠀⠡⡈⠂⠠⢛⡄⠘⡇⠰⠃⠒⡄⢃⠀⠀⠑⢿⡇⢨⠀⠀⠀⠀⡀⠀⠰⠄⠀⠀⠆⠀⠀⡆⠀⠀⠀⠑⣄⠀⠀⠁⠀⢀⡜⠀⠀⠀⠀⠀⠸⠓⠒⠙⣀⠖⣡⣆
⠀⠀⠀⠈⠁⠈⠁⠀⠀⠃⠂⠀⠀⠘⠋⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠒⠒⢀⡦⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠚⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠇
⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⣠⠴⣤⡀⣬⣽⡀⠀⠀⠀⡶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⢀⡠⣤⠆
⠀⠀⠀⠀⡏⠁⢙⡄⠀⠀⠘⠁⠘⡀⠀⠚⠃⠒⠒⠆⠁⠈⠀⠀⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢀⡔⠁⠀⢀⣴⠂⠀⠀⠀⢀⣄⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠠⠛⢀⠸⠇⠀⠀⠀⠀⠀⣧⣴⠂⠀⠑⠿⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠱⣀⡰⠏⠉⠁⠐⢻⠁⠀⠀⠀⠀⡘⠀⠉⠈⠁⠈⢹⠁
⠀⠀⣀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣗⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⢲⡖⢲⣼⠀⠀⠀⠀⠀⠃⠒⠒⠀⠤⡤⡜
⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠠⠤⠤⠿⠀⠀⠀⠀⠀⠺⠄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⢺⡆⠀⠘⡇⠀⠀⣇
⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠐⠂⠓⠠⠐⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠋⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠶⣀⡀⠀⠠⢾⠀⠀⠀⠀⡜⠉⠀⠑⡄⠀⠀⠀⣀⠄⡀⠀⠀⠀⠀⢠⡀⠀⣠
⠀⢀⡐⠃⠈⠙⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣦⠠⠠⣦⠸⡀⠀⠀⢸⠀⠟⠀⠀⡤⠀⠀⠠⣵⠊⠁⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡋⣠⡀⠀⠀⠀⢀⡔⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠰⠒⢺⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣺⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⣠⢄⠀⠀⢀⣀⡈⠻⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠀⠀⢀⠀⠀⠁⠒⢄⣠⡞⠀⠀⠀⠀⠀⠀⠀⣙⢱⡋
⠀⠀⠀⠀⢀⣠⣤⣠⣄⣀⡀⠀⠀⠀⢇⠀⠻⠿⠃⠀⠻⡿⠃⢀⠃⠀⠀⠀⠈⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⡀⠀⠀⠋⠀⠀⠀⠀⠀⢤⡀⢀⠋⠈⢰
⠀⠀⠀⠀⠧⢤⣤⣭⣤⣤⠼⠃⠀⠀⠀⠑⠄⣀⣈⣁⣀⢀⠤⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠛⠃⠠⠔⠃⠀⠀⠀⠀⠀⠈⢗⣼⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡧⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡁⢙⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⢸
⠀⠀⠀⠀⡠⠸⡇⠀⣙⡧⣀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⣶⠄⠀⠲⣰⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠂⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡸
⠀⠀⠀⠰⡄⣈⠛⠒⠚⣁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⣠⡘⡄⠀⠀⠀⠀⠈⠃⣀⠀⢀⠄⠊⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠉⠑⠂⠀⠐⠒⠁⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⡊⠈⠁⠀⠈⠀⢹⠆⠀⠀⠀⠀⠀⠈⣴⠁⠀⠀⠀⢀⠜⠀⢀⠼⠲⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠁⠁⠀⠀⡀⡇
⠀⠀⢰⠓⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠘⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠛⠀⠀⠀⣭⠃
⠀⠀⠘⠂⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⣠⠔⠒⢱⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡽⢄⣠⡄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣼⣁⣠⠴⠋⣀⡀⢤⣿⠄⠀⠀⠀⠀⠀⠀⣄⢀⡄⠀⠀⠀⠀⠀⠀⢠⡆⡞⣡⢀⢀⣌⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⢲⡄⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠰⢻⠣⡝⢸⠇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⠣⠤⠤⠤⠤⠤⢼⠄
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠘⢍⠉⣹⠃⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⣧⡿⣄⣠⠾⣄⣀⠀⠀⠀⠀⠀⠁⠐⠀⠊⠀⠀⠀⠀⠀⠀⠸⣸⠀⠶⠀⠀⠀⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠀⠁

⠀⠀⠀⢠⡟⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢲⡄
⠀⠀⠀⢸⡇⠈⠢⡈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⡠⠊⠠⣿
⠀⠀⠀⣾⡇⠀⠈⠭⢦⡀⠉⠳⣦⡀⢀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⠀⣠⡴⠋⠁⣠⢚⣒⡀⠀⣿
⠀⠀⠀⣿⡇⠀⠀⠙⣉⣛⣄⠀⠀⠙⠋⠉⢹⣿⠀⠀⣿⡿⢉⡟⠉⠛⠉⠀⢀⣞⣯⡭⠄⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠴⠶⠈⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠁⡼⠁⠀⠀⠀⠀⠉⠈⠡⠶⠂⠀⠀⣿
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢰⡏⠀⠀⠀⣠⣶⣶⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠓⣶⡦⣄⠀⠀⠀⢿⡀
⠀⠀⠀⣿⠀⣀⠀⡼⢱⣿⣿⣷⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣴⣿⣷⠘⡆⠀⡀⠘⣧
⠀⠀⢰⣿⡿⠋⠀⣇⠸⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠙⣿⣿
⠀⠀⠸⣿⣤⣀⡀⠘⢦⡙⠿⢿⡿⠟⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠿⢿⠿⠟⣁⡜⠁⢀⣠⣬⣿
⠀⠀⠀⢿⡟⠛⠁⠀⠀⠉⠓⠒⠒⠋⠁⠀⠀⠀⢤⣶⣦⠄⠀⠀⠀⠉⠛⠒⠒⠋⠁⠀⠀⠈⠛⢻⡟
⠀⢀⢀⣈⣷⣤⠔⠒⠲⠶⠶⠒⠤⠄⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠒⠒⣴⡿⣀⡀⢀
⠁⠈⠁⠀⢀⡹⣷⣶⡂⠈⠉⢁⠠⠀⠀⠀⠘⠦⠖⠋⠓⠶⠖⠀⠀⠀⠈⢍⠉⠁⠀⣒⣴⡾⢏⡀⠀⠀⠉
⠀⠀⠀⠊⠁⠀⢀⡽⠛⣷⣶⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⡞⠻⣁⠀⠀⠈⠑⠀⣠⡶⠶⣤
⠀⠀⠀⠀⢀⠔⠁⠀⣼⠃⠀⠈⠙⠛⠻⠶⠶⣶⣤⣤⣤⣤⡶⠶⠶⠟⠛⠉⠁⠈⢻⡄⠈⠑⠄⠀⠀⠀⢿⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⢀⡿⣶⣤⣼
⠀⠀⠀⠀⠀⠀⣸⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠸⣇⠀⠀⠀⢀⣾⡁⠀⢩⡟
⠀⠀⠀⠀⠀⠀⡿⠀⠘⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡿⠀⠀⢿⠀⢀⣴⠟⠹⣷⣤⠟
⠀⠀⠀⠀⠀⠠⡇⠀⠀⢿⠀⠀⠀⠐⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⠀⠀⢸⡇⠀⠀⢸⡟⢻⣿⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣾⠀⠀⠀⣸⣁⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡏⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣻⡆⡆⢠⡄⠈⣇⣀⣀⣀⣀⣀⣀⡏⠀⢠⠀⡆⣼⢓⣦⠾⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠶⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢄⢀⣀⡤⠖⠚⠉⠁⠈⠁⠀⠀⠀⠀⠀⣀⣠⠤⡄⠀⣼
⠀⠀⠀⠀⠀⡴⠒⠋⠉⠉⠉⠙⠓⠲⢤⠖⠉⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣤⠃⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢨⠇⡜
⠀⠀⠀⠀⠀⢇⠀⠀⠤⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠸⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡀⢀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⣿⡿⠁⠀⡞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣀⠀⠀⠀⠀⠀⠀⢀⡶⠒⢦⡀⠀⠀⠀⠀⠰⣶⠆⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠶⣾⡇⠀⠀⠳⠀⠀⠀⠰⠤⠞⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⢠⠖⠋⠙⠢⡀⠀⠀⠀⠀⠈⠉⡶⠲⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⣤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢢⡀⡀⠀⢰⠊⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠋⠉⠳⡼⠆⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⢀⠘⡇
⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢸⠀⠸⡇⠳⡄
⠀⠀⠀⠀⠀⠈⠳⢤⡤⠀⠀⠀⣀⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⡆⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠋⠁⠈⠉⠉⠓⢤⣤⡄⠀⠀⠐⠣⡘⡄⠀⡇⢠⡇⠀⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠲⠖⠋⠉⠒⠛⠊⠉⠙⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠒⠒⠒⠲⠶⠤⣤⣀⢀⡴⠚⠉⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⢤⠀⡼⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⣰⠃
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠰⠶⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣷⣄⣠⡄⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣿⡟⠁⠀⠀⠟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢦⡄⠀⠀⠀⠀⠀⠀⢠⣖⡦⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠙⠃⠀⠀⠀⠀⠀⠠⣤⣠⣿⠁⠀⠀⢻⡄⠀⠀⠀⠀⣄⠀⣹⠧⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠉⠉⠒⣒⡲⠤⠀⠀⠀⠀⠀⠀⠀⠐⣾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⠟⠉⠳⣄⣿⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠉⠙⢶⡀⠀⠀⠀⢢⠀⠀⢸⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡆⠀⢸⡆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣦⠄⠀⠀⠀⢀⣠⡆⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠀⣇⠀⢸⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠶⠚⠉⠀⠈⠉⠉⠉⠳⢤⣀⣀⡀⠀⠀⠀⠰⠯⣌⢧⠀⠀⢻⠀⢸⠃⠀⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣤⣤⣀⣀⣠⣼⠾⠳⣤⠾⣤⠞⠲⠶⠶⠴⠾⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡟⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⢻⡄
⠀⠀⠀⠀⠀⣸⠃⢀⣤⣄⣀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⣀⣤⣤⡀⠘⣇
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠉⠛⠦⣄⠈⠙⢦⣤⠶⠚⠻⣿⣏⠀⠀⠸⣿⣿⠇⠀⠀⣹⣿⠟⠛⠶⣤⡴⠋⠁⣠⠴⠛⠉⠀⠸⡇⠀⣿
⠀⠀⠀⠀⠀⡟⠀⣼⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⢿⡿⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣷⠀⢹⡀
⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣸
⠀⠀⠀⠀⠀⣿⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿
⠀⠀⠀⠀⠀⢸⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢀⣀⣸⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⡀⠈⢻⡟⠁⢀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣘⣇⣀
⠀⠉⠉⠉⠉⢹⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢸⡇⢀⣠⡤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⣄⡀⢸⡇
⠀⠀⠀⠀⠀⡠⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⢄
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠛⠛⠲⠶⠶⠦⣤⣤⣤⣤⣤⡤⠴⠶⠶⠖⠛⠛⠉⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠸⡆⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣷⠀⠀⣾⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢸⡄⢠⡇⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⣷⣾⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣇⣀
⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠈⠉⠀⠀⠀⣠⡶⠶⠲⠾⠷⣄⠀⠀⠀⢻⡟⠀⠀⠀⣠⠾⠷⠖⠶⢶⣄⠀⠀⠀⠉⠁⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆
⣀⣀⣀⣀⣀⣙⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣋⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣡⣬⣙⠻⣷⣦⣤⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣱⣿⣿⣿⣿⣶⣝⠋⡙⣥⠻⠿⠿⠿⠿⢷⣶⣶⣶⣤⣤⣤⣀⣀⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢡⣿⣏⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣭⣝⣛⠻⠏⠿⢛⣿⠿⠿⠿⠟⣛⣛⣛⣛⡻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⡝⢟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⡇⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣩⢉⣭⣭⣿⣿⡇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡸⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⡟⣼⣿⣿⣿⡿⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⣼⣿⣿⣿⠟⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⡏⣾⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡅⣶⣤⣿⣿⠃⣾⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⣤⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠸⣿⡔⣮⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⢛⣟⢿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣭⣤⣭⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⠰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣥⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣮⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣭⡙⠿⢟⣫⣵⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⣶⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⢇⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣭⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⣾⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣟⣛⣛⣭⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⢿⣿⣿⣿⣿⠿⢟⣫⣥⣶⠿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣎⠻⣿⣷⡔⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⣭⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⣠⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠉⠉⠁⠀⠉⠉⠙⠛⠿⠿⠛⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠐⠿⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣶⣤⡄⠀⢀⣤⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣦⣤⣾⡏⠀⠀⠈⠉⠙⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣤⣤⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⡙⢛⣿⣿⠋⠀⢾⣿⣦⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠸⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣤⣍⣁⣀⣀⣀⣀⣈⣩⣽⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⠃⠀⠀⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣰⣿⣿⣼⣿⠀⠀⠀⣿⣷⣿⣿⣦⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡻⢿⡿⣿⡏⠀⠀⠀⢹⣿⢿⡿⢟⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠋⠀⠀⠀⠀⠈⠰⡏⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⣿⣿⣿⣿⠿⠃⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣐⡠⠀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⡰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠁⠑⠠⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡠⠊⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠑⡄⠀⠀⠑⠒⠒⠂⢲⣶⠂⠒⠊⠀⠀⢀⠜⠀⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠟⠀⠛⠀⠀⠀⠀⢠⣦⠘⣿⠀⣴⠄⠀⠀⠈⠉⠸⣧⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠛⠠⠏⠀⠀⠀⠀⠀⠀⠈⠚⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⡠⣞⢿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⢻⣿⣿⠠⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣍⡀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢀⠀⢀⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠬⠙⠻⠟⠀⠀⠐⢄⡰⠀⠀⠙⠋⠉⠐⠁⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⡠⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠤⠊⠀⠂
⠀⠀⠀⠀⢨⢐⡀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢺⡀
⠀⠀⠀⠀⠃⡌⣋⠐⡁⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠈⠓⢬⣀⡈⠉⠉⢁⣀⡡⠔⠉⠀⠀⢘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⢢⠀⡀
⠀⠀⠀⢀⡀⣈⢁⢋⠐⠹⠀⠀⠀⠀⠀⠀⡐⠀⢢⠀⠀⠀⢲⠀⠈⡏⡏⠀⠀⡇⠀⠀⠀⡠⠚⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡑⣐⢻⡐⡅
⠀⠀⠀⠀⡑⠀⠘⠆⡧⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠑⠢⢀⠀⠑⠊⠉⠉⠀⠚⣁⠤⠒⠈⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠱⢈⣯⠅⣤
⠀⠀⠀⠀⠑⢄⠑⢬⠆⠀⠀⢀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⢉⠥⠐⡢
⠀⠀⠀⠀⠀⠀⠑⠤⡔⢀⠎⠸⠀⠀⠌⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣡⡐⠀⠒⠤⢀⠀⠀⡃⢀⢠⢸⠁⠄⠊
⠀⠀⠀⠀⠀⠀⢠⠀⢀⢻⢀⠃⠀⡼⠋⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⢟⠢⡀⠰⠛⢳⡄⢣⠀⡇⣆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠡⡈⠘⡁⠀⢠⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡀⢱⠀⠀⠀⠸⠀⠲⠀⡡⠔⠁
⠀⠀⠀⠀⠈⠓⠨⢁⠻⢆⡱⢰⡌⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡇⡸⠀⠀⠀⠀⣤⠧⢮⡀⠐⢂⡨⠒
⠀⠀⠀⠠⠀⠀⡀⡠⠏⠈⠕⠃⣸⣄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣴⠔⠁⠀⠀⠀⢸⢀⠄⠊⠙⡉
⠀⠀⠀⠈⠂⣤⠜⡇⠀⡂⠀⠁⠈⢆⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⣀⠊⠀⠀⠀⠀⣰⡏⠒⠀⠄⠒⡆⠂⠉⡩
⠀⠀⠀⠀⠀⠃⠒⢣⣠⣁⠁⢀⣠⠞⠉⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠀⠀⠈⠑⢄⠀⡠⠾⠔⠓⠣⠤⠦⢎⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⢱⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⢸⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⣠⡀⠤⠧⣀⠀⡀⢀⡰⠁⠀⠙⣤⠀⡀⢠⡸⠂⠤⢀⣇⠀⠧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⢀⣀⣀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢾⡎⣿⣿⣿⠣⣿⠆⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠛⠛⠛⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⠀⠀⠀⠈⢦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡿⡄⠀⣠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⢀⣠⢤⡤⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠗⢣⠎⠀⢀⡴⠋⠀⠀⠀⡞⠀⠀⠀⠀⣰⠂⠀⠀⠀⢠⡴⠋⠁⠀⣸⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠿⡤⠴⣞⠀⠀⠀⣀⣼⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢦⡀⣰⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠘⢤⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣠⠞
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⢸⡄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡖⠚⠁⠀⠉⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠓⠀⠀⠀⠀⠀⣀⡠⠤⣄⡟
⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢞⣇⡇
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⡸
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⡴⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠏⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⡀⠀⠀⢀⡤⠴⠦⠤⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⣠⠴⠋⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⢰⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣈⠉⠉⠉⠉⣀⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠈⠧⣼⣇⡜⡨⠗⠄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠓⠲⠖⠒⠒⠒⠒⠚⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⠙⠲⣄⢠⣀⢶
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⡄⠀⠀⠀⠀⠙⠉⠈⠉⠉⠉⠙⠛⠒⠒⠲⠤⠤⣄⣀⡀⣠⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢘⣦⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠉⠉⠉⠉⠀⠀⠀⠀⢹⠆
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢴⠖⠶⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⠏⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢧⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣠⣀⡏⠀⠀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⢀⣧⡈⠁⠀⢸⠇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⢻⣦⠀⠀⠀⠀⠀⠀⢀⣻⣀
⠀⠀⠀⠀⠀⢳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡵⠀⡀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⢨⠃
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠼⠣⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠝
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⡠⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⡽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠶⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⢶⣶⣶⣤
⠀⠀⠀⠀⠀⢠⣿⠁⠱⣄⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⢀⡴⠋⢻⣧
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠈⢧⡀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢈⣻⣤⡴⠶⠶⠶⠟⠛⠛⠛⠻⠶⠶⠶⢶⣥⣄⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣄⢠⡞⠁⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠉⢳⡄⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⢠⡾⠛⠉⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠙
⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⢀
⠀⠈⠉⠉⠛⠛⠶⣿⣄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⣀⣀⡼⠻⣄⡀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣠⣼⡷⠶⠚⠛⣿⠋⠉⠉⠉⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⢹⣯⠉⠓⠀⠠⠒⠀⠀⠀⠂⢀⠀⠀⠀⡏⠉⠁⠀⠀⠀⠉⠉⡯⠀⠀⢀⠀⠒⠐⠂⠠⢀⠀⠀⠀⠁⠀⣿⠃⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣇⣠⠔⠊⠉⠉⠑⢲⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⠋⠀⠁⠐⠒⠀⠈⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠐⠀⠤⠄⠐⠉⠲⢦⣼⣏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠙⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠙⠻⣦⣄⠀⣿⠀⠀⠀⠀⡿
⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠞⠛⠁⠀⠀⠀⠀⠀⠙⠳⣿⡆⠀⠀⢸⡇
⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⢦⡎⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡴⠞⠉⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⡀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢀⣀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡎⠀⡜⠀⠀⠀⣿⠀⡠⠀⢠⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠷⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠷⠖⠒⠊⠙⢶⣧⣀⣇⣀⣤⡶⠿⢥⣄⣀⣀⣀⣀⣉⣉⣉⣩⣴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⡠⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠒⠀⠈⣿⣶⣿⡏⠉⠉⠉⣿⣿⣿⣄⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣑⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⢙⣿⣿⣿⣷⣄⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣃⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣆⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡻⣷⣼⣿⡄⠀⠀⠀⣾⣷⣼⡿⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠒⠣⣄⢠⡄⠓⠛⠛⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⠀⠀⠀⡴⠚⠉⠉⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⠓⠒⠂⠀⠀⠀⣀⣤⣶⣾⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠐⠲⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠙⠲⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡀⢀⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⠆⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⣿⡿⠋⢪⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠁⠀⢹⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠚⠉⠉⠀⠀⠈⠙⠛⠒⠒⠶⠶⠶⠶⠒⠒⠒⠶⠶⠖⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡄⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠙⢿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣿⣿⣿⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⠋⢰⠿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⣴⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠶⢷⣶⣶⢾⠿⠿⠾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣉⡯⠀⢀⣿⣿⣿⣿⠟⠁⠙⡿⢩⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠛⠙⢿⠿⠇⠰⢾⠿⠿⠟⠁⠀⢀⣀⠁⠀⢙⣻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣶⣿⣄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣴⣏
⠀⠀⠀⠀⠘⢿⣶⣭⣀⣁⣀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠉⠙⠛⠋⠙⣿⣿⣿⠟⠛⠇⠹⠿⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⣉⣉⣹⣭⣿⣿⣯⠀⠀⢀⡀⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣟⣛⣿⣿⠋⣹⣿⣿⣿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠟⣩⣿⣿⣷⡄⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⣹⣿⡟⠙⠋⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⣤⣶⣶⣶⣾⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣤⣴⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠖

⠀⠀⠀⠀⠀⠀⣼⠟⠳⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠾⠛⣧
⠀⠀⠀⠀⠀⢠⡟⠀⣠⣤⣀⠈⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣠⣄⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⣀⣤⡄⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠉⠛⠲⣤⡀⠈⠻⣦⣀⣤⠴⠶⣿⣿⡏⠉⠁⢹⣿⣿⡏⠈⠉⢹⣿⣿⠶⠦⣤⣀⣴⠟⠁⢀⣤⠖⠛⠉⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣾⠁⢰⡿⠀⠀⠀⠀⠀⠙⠦⡀⠈⠉⠀⠀⠀⠈⢿⡇⠀⠀⠈⣿⣿⠁⠀⠀⢸⡿⠁⠀⠀⠀⠉⠁⢀⠴⠉⠀⠀⠀⠀⠀⢿⡆⠈⣷
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢹⡏⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⢹⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⡏
⠀⠀⠀⠀⠀⠸⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣠⣯⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣀⠈⣻⣟⠁⣀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣽⣄⣀⣀⡀
⠀⠀⠈⠉⠉⠹⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣦⣄⡀⠀⣿
⠀⠀⠀⠀⠀⢀⠼⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡧⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠳⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠶⠞⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠲⠶⢤⡀⠀⠀⠀⠀⣀⣀⣘⣷⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣃⣀⣀⠀⠀⠀⠀⢀⡤⠶⠖⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠉⠛⠂⠀⠀⠀⢻⡟⠀⠀⠀⠐⠛⠉⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡿⣼⣿⣿⣷⣴⣶⣦⣤⣤⣄⣀⡀⣸⡿⡙⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⣿⣿⣿⣿⣷⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣴⡌⣿⡟⠀⠀⢘⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠻⠷⠭⠓⠋⠠⠤⡄⢇⢾⠆⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠁⢀⠈⠙⠻⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣈⡀⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠈⣩⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⠗⠀⠉⠉⠛⠋⠉⠁⠀⡴⢿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣠⠤⢤⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⡇⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣀⣠⢀⡀⣀⡥⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠠⣸⡅⠀⡸⠀⠀⠠⠤⠤⠤⠤⠤⠄⠒⠚⠉⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⣠⣤⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠙⠟⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⣿⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⡿
⠀⠀⠀⠀⠀⠸⡆⠈⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠙⢷⣤⣠⣤⣴⣶⣶⣶⣶⣶⠾⠛⠁⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣤⡀⠀⠀⠙⠟⠋⠀⠀⣴⣻⣿⡆⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠛⢛⡛⠳⢦⡀
⠀⠀⠀⠀⢀⣸⣇⣤⡤⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⢻⣿⡆⠀⠀⠀⠀⠉⠉⠙⠛⢻⡟⠒⠂⠀⢸⡇⢸⡏⠙⢷⡀⣿
⠀⠀⠘⠛⠋⠉⢧⠀⣀⣤⡤⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠶⠤⣤⣤⣾⣀⠀⠀⠀⠀⠻⠶⠃⢀⣼⠁⣿
⠀⠀⠀⠀⠀⣀⣼⢿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⢿⣀⢉⡥⠶⠦⣤⣤⣤⡴⣟⡁⣰⡟
⠀⠀⠀⠀⠾⠋⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⢶⣤⣤⣴⠟⠀⠀⢀⣠⡴⠚⠁⣼⣿⣿⣄⣠⣤⣤⣀⣀⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⣤⣄⣀⣀⣠⣤⡤⠶⠚⠋⠁⠀⠀⠀⢻⣿⣿⣿⣯⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡤⠶⠶⢤⣤⣤⣄⡀⠀⠀⠀⢀⣴⠞⠳⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢠⡞⠁⠀⠀⠀⠀⢸⡅⠈⣷⡀⠀⣠⡟⠁⠀⠀⣷⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠻⠾⠋⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣦⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⣿⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⢻⣿⢋⡀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠿⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⢉⡩⠐⡀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⡀⠬⣉⠃⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⠔⠋⠀⠀⠀⠀⠀⠠⣀⣤⠾⠦⣤⡤⠀⠀⠀⠀⠀⠈⠲⣄⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄





⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣻⣿⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠛⠋⠀⠀⠀⠀⣤⣤⣀⡀⠀⠀⠀⣤⡖⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣹⣿⣶⣶⣾⣧⣄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣆⠀⠀⠀⠀⣿⣿⡹⢗⡇⠀⣋⠷⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⣹⣿⣿⠟⢃⣀⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡦⠀⠀⠠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢿⣿⣯⡁⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠀⠀⢸⣿⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⢼⡿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣾⠁⡐⠁⠀⠀⠠⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠻⣦⠀⣀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⢀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢦⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠈⢳⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⡤⠤⢄⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡏⠀⢠⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣀⡄⠙⡄⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠈⠀⢀⣴⣄⠒⠢⡀⠀⠀⠀⠀⠀⠀⠸⡙⠿⠿⠃⣠⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠚⣿⣿⣴⡆⢸⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠊⠁⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠰⣌⠛⠋⢁⠜⠀⠀⣠⣆⣽⡿⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⢹⡀⠀⢀⠆⠀⠀⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠔⠀⠀⠳⠄⠠⠊⠀⠉⠁⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠳⢶⡖⠖⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⢷⡀⠀⠀⠀⠸⣧⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢻⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⡇⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⣧⠀⠀⢀⡾⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⣠⡾⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢧⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡿⠞⠋⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠷⠶⠦⣾⣀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⣃⣀⣤⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡀⠀⢀⡞⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠶⠶⠶⣧⣄⣀⣀⣀⣀⣼⣤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⡷⣆⠀⠀⠀⡀⠀⠀⠀⠀⣀⣦⠍⠉⠀⢀⣰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣯⣭⠿⣿⡗⢻⢠⡶⢹⣿⢀⣧⠱⢸⣿⣟⡉⠁⠸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⣟⢙⢁⠈⢠⣯⠣⡀⠸⠷⡶⢼⣿⣿⠇⢿⡴⡟⢩⣽⣿⡟⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⢿⡙⠈⠀⣅⢀⡈⢁⢰⣿⣾⣍⡟⠂⢈⣆⡿⠆⢈⣻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠢⠄⡇⠸⣼⣾⡿⣼⠇⣇⢈⠟⠠⡼⡾⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠿⠋⢹⡅⠿⠲⣅⠀⠋⢹⠇⣽⠂⢋⣈⣬⣥⣬⣥⡔⢚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠻⠅⠀⠘⠻⢶⣿⣶⠖⢿⡀⠀⠘⣸⡇⣾⣇⣛⡴⣋⣽⣉⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠀⠀⠀⠠⠼⣿⣷⣾⡇⠀⠘⣻⣿⣿⣶⣿⣿⣿⣯⣁⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀⠀⠀⠠⠽⠛⠾⡥⢀⣀⣿⣿⣿⣿⡍⢻⠿⣃⣭⣼⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣥⡄⠀⠀⠀⠀⠀⠈⢩⡿⠋⠉⠉⣿⡷⢦⣄⣭⣽⣿⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠂⠀⠀⠀⠀⠀⠶⢦⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣹⣦⣤⡀⠀⠀⠀⠀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⡙⣿⣿⣶⣶⡾⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣿⣿⣿⣿⣿⣞⡯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡾⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡿⢻⡿⢻⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠋⠀⢸⣿⣿⣿⣿⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣤⣼⣿⣁⣿⣿⡿⠿⡿⣿⣦⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠙⠛⠛⢻⡤⠾⠿⠛⠋⠃⠉

⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⡟⠀⠈⢻⣦⠀⠀⠀⣀⣀⣀⣠⡶⠛⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣷⣦⣤
⠀⠀⠀⣼⣇⣴⣾⣿⣿⠀⠀⢠⣿⣿⣿⣿⣷⣤⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿
⠀⠀⢠⣿⡟⢉⡙⣿⠇⠀⠀⢸⡿⢋⣙⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟
⠀⠀⣸⣿⡀⢿⣿⠉⠀⠀⠀⠸⡇⢾⣿⡆⣿⣿⣿⣿⣿⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠉⠁⠀⠀⠠⠴⠀⠀⠀⠀⠑⠈⠉⠀⠉⠉⠙⠛⠿⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⢠⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠉⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⣿⣿⣿⣦⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢠⣾⣿⣿⣶⡀⠀⠀⣿⣿⣿⡏⠀⠀⣠⣾⣿⣿⣦⡀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠶⣤⡀⠀⣾⣿⣿⡇⠀⠀⢺⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡾⠁⣠⠴⠶⢤⡀⠀⠻⡄⢿⣿⣿⣷⡀⠀⠈⠛⠿⠟⠋⠀⠀⢠⡟⠋⠛⢧⡀⠀⠈⠛⠿⠟⠋⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⠁⡾⠁⣴⢶⡄⢻⠀⠀⣿⠘⢿⣿⣿⣿⣦⣀⠀⠀⠀⢀⣀⣴⣿⣷⣶⣶⣿⣷⣤⣀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⠀⣧⠀⠳⢬⠵⠏⠀⢠⠏⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠸⣆⠈⠳⣤⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⢹⡏⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⡏⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠒⠚⠓⠒⠀⠀⠀⠀⠀⠀⠚⠛⠒⠚⠓⠓


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠘⢿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⣠⣤⠤⠤⠤⢤⣀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠈⣷⠜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣟⡛⠂⢼⣿⡏⠀⠀⠀⠀⣀⡈⠙⠛⠁
⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⢠⡆⠦⣾⠿⡄⠀⠀⠀⣾⡽⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣩⡌⠀⢉⣉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢋⠀⠀⠁⠀⣁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⢈⡃⠉⠘⠋⢁⡠⠂⠀⠀⠀⠀⠀⠀⠈⢌⣀⣁⡈⠀⣽⠀⠈⠲⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠐⡟⠀⠀⡜⠠⠁
⠀⠀⠀⣀⣾⣽⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⡟⠻⢟⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⡀⠤⣷⠦⠒⣶⣆⠀⠀⠀⠀⠀⠀⠑⠊⠀⠂⠂
⠀⠀⠀⠈⠓⣶⣼⣿⣧⣤⣤⣤⣤⣤⣤⡜⡴⣷⣍⢱⠖⣿⣿⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⡤⣤⣀⣀
⠀⠀⠀⠀⠈⠈⠙⡷⡋⢃⡿⡿⢿⣿⣿⣿⣿⡜⡁⠀⢀⡜⣛⣿⠀⠀⣠⣴⠚⠛⠀⠛⠁⢀⣄⢀⡠⢘⠻⠿⠒⠘⡄
⠀⠀⠀⠀⢲⡄⠀⠁⠈⠁⡜⠉⠸⠛⠿⡿⣿⠿⣾⢷⠟⠛⠉⠁⢀⣞⠁⠁⠀⠀⠀⠀⠀⠀⠈⡏⠩⣹⡟⠀⠀⠀⣙⣢
⠀⠀⠀⠀⠈⣃⠀⠀⠀⣆⠈⠀⠒⠒⢋⡑⠃⢠⡔⠉⠀⠀⠀⠀⠈⠻⣶⣴⣶⡀⠀⣀⡀⢀⡐⠃⢠⡌⠂⠀⠦⣠⢸⣿⣧⡀
⠀⠀⠀⠀⠀⢃⡀⠠⠞⠰⡀⠀⠀⠀⠘⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠫⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⠈⠉
⠀⠀⠀⠀⠀⠈⠧⠀⠝⠀⠁⠀⠀⠀⠀⠀⠄⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⡽⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠿⢶⣔⣒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡦⣽⣿⣿⣦⠂⠀⠀⣠⢘⠋⠿⣢⠀⠈⠀⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣿⣿⠗⣉⠥⣓⢀⠁⠘⣇⠀⠁⠀⠀⡘⠋⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠟⣂⣻⠄⢉⠀⠀⠈⣩⣾⣿⣶⠒⠶⠇⣄⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⡿⢿⣧⠀⡄⠀⠀⣻⣧⡭⠋⠘⠂⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⠸⠂⠁⣒⣿⠗⠀⠀⡘⠁⠀⠀⠤⠀⠀⢶⣞⣟⡉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣶⣾⡩⢋⣠⠇⢸⣤⣤⡏⠀⠀⠀⡀⣠⣾⠞⡻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⢿⣿⣿⣶⠀⠀⠙⣧⠀⠀⢀⣨⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣷⣾⣿⣿⣿⣿⣶⠛⠉⠀⠈⣹⣿⣿⣯⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⣴⡿⡿⢳⣯⣉⣩⣿⡿⣿⢷⣿⣿⢿⣟⢛⠋⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣔⣿⡿⢻⢦⣬⠘⠁⠺⣧⡀⠢⠰⠛⠁⠈⠉⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠒⣒⠋⠈⠀⠀⠀⠈⠰⠣⣦⡿⠃⠀⠀⠀⠀⠀⡀⠀⠁⠔⠃⠀⠠⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⠆⠀⠀⠠⠠⣤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠄⠖⠤
⠀⠀⠀⠀⠀⠀⠠⣾⡿⠟⠁⠀⠀⠀⢠⣌⠉⠦⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢩⡟⠀⠀⢀⣠⣄⣀⣀⠀⡀⡔⠆⠈⠲⣆⠀⢼⠀⠀⠀⠈⡅⢀⡄⢹⡀
⠀⠀⠀⠀⠀⠀⣺⠓⠛⠙⠋⠙⠉⠉⠙⢷⣾⣤⣀⡄⢠⠙⣧⡀⠂⡀⠀⠀⣿⣰⣀⣾⣹
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⣾⣇⡀⣦⢸⡏⡃⠀⢻⡀⡀⣾⡿⠟⠉⠉⠁⠂
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠴⡈⠙⠻⢿⣿⣿⣿⠁⣿⢀⢸⣡⣿⠋⢅⡀
⠀⠀⠀⠀⠀⠀⠉⠡⠂⠀⠀⠀⠁⠀⠈⡠⠂⠀⠀⠀⠉⠁⠀⠁⠛⠛⠹⢧⣼⣾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠙⢟⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡟⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣠⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢠⠀⠀⠀⠀⢠⡀⠀⠀⠈⠙⢿⣶⣆⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣸⡀⢀⣬⢀⣸⠃⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠰⡛⣛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⢀⣶⣶⡈⣿⣿⣿⣿⣿⣿⡟⠁⢀⣤⣌⠻⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣤⣀⣛⣛⣴⣿⣿⣿⣿⣿⣿⣇⠀⠘⢿⡿⢀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⢈⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠘⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢻⡦⣄⠀⠀⠀⠀⠀⡴⠛⠛⠢⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠑⢆⢻⡈⠳⣄⠀⢀⡜⠀⠀⠀⠀⢉⠀⠀⢀⡠⠴⠒⠒⢢⡀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠢⡈⢻⡇⠀⠈⢧⣜⠀⠀⠀⢀⠖⠉⠀⡒⠉⠀⠀⠀⠀⢸⠖⠋
⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠹⢀⣁⣀⠀⠠⡝⢦⣄⠀⢸⣄⠀⠞⠉⠉⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠸⢀⣀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠰⢷⡀⠀⠀⣠⠖⠋⠉⠀⠀⣀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠎⠁⠀⠀⣠⠖⠉⠀⠀⠀⠀⢸
⣤⠀⠀⡀⢀⣀⠴⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⠴⠚⠀⠀⠀⠀⣼⠁
⡏⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⡏⣠⠖⠈⠁⠀⠀⢀⣿
⠰⡄⠀⠀⠀⠀⠾⡿⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢀⡼⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠐⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⣱⠁
⠀⢂⠀⠀⢀⡀⠀⢣⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣽⣷⣦⢆⣀⠀⠀⠀⠀⠈⢦⡄⠄⠚⠁⡰⠃
⠀⠈⢷⠒⠢⢬⣑⠢⣌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠜⠁⢰⡆⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠀⠄
⠀⠀⠀⢷⡤⠶⠬⠵⣫⡗⠀⢠⠤⡀⠀⠀⠀⠀⠀⣀⣨⣥⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⡀
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠣⣀⠀⡋⠁⠀⠀⠀⢰⡖⡐⠒⠲⠶⢤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠉⠓⠶⠤⠤⠔⠛⠣⢌⡉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⠛⠦⢄⡀⠀⠀⠀⠀⠀⢀⡤⠆⠸⠦⣀⠀⣀⡠⠤⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣻⠋⠀⠑⢤⣀⣈⠉⠀⠒⢢⡞⠁⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠉⠉⠛⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⡼⠟⠋⠉⠁⠀⠈⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢮
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⢄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣟⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡤⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠰⠋⠀⠀⠀⠑⣆⠀⠀⠀⠀⢀⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⣐⠃⠀⢀⡠⠈⡇⠀⠀⠀⠀⠀⣼⠁⢠⠄⠀⠈⡆⠀⣀⠴⠋⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢀⠘⡆⠚⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣹⣀⣸⠇

⠀⠀⠀⠀⣰⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⣾⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡇
⠀⠀⢀⣿⣃⠀⢻⣿⣿⣦⣺⣾⣿⣿⣶⣶⣶⣿⣿⡿⣿⡟
⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⣻⢿⣿⣿⣿⣿⡿⢿⢻⣿⡇
⠀⠀⠀⣹⣿⣿⣿⣿⣿⣦⣥⣾⣿⣿⣿⣿⣧⣬⣼⣿⣧⡀
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡈⢁⠈⠉⠉⢽⠿⢏⡫⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣥⠉⠀⢀⠀⠈⠰⢀⠀⠀⢁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣌⡪⢠⣄⠀⠁⠀⠀⢀⠀⠣⡈⢻⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣏⣿⣀⢀⡘⣆⣶⣦⣀⢙⣲⠤⣠⡘⢷⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⠿⠉⠉⠠⢁⢹⣺⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠃⠚⠋⠀⠀⠀⠀⠈⠓⠋⣻⡿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡳⣪⠀⠀⢀⠀⠆⠀⢤⠐⠄⢌⣷⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠧⢖⡀⠀⠀⢀⠀⠀⠉⠀⢀⢨⣿⣿⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠤⠌⠁⠀⠀⠀⠀⠀⠀⡆⠎⢂⡹⢿⡇⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣂⣀⢐⠀⠀⠀⠀⠑⠀⡀⠐⣠⣁⠀⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣧⠸⠀⠀⠀⠦⡀⠀⠀⠀⠘⠋⠁⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣂⢀⠀⠘⠀⠀⠈⢺⣀⡠⣘⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣭⠟⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡘⣸⢀⠤⠀⠀⠰⢿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⣿⣿⣭⣉⣻⢟⣻⣿⣿⠿⠿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣦⣭⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣀⡼⠀⠙⠀⠀⢀⣀⣀⣀⣤⡤⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠂⠁⠀⠀⢰⡟⠑⠉⠉⢠⠖⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢥⡴⣲⣦⡀⠀⠀⠈⠀⠀⠀⠛⡜⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠢⡘⡰⠿⢟⠇⠀⠀⠀⠀⠀⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⠈⡉⠁⠀⠀⠀⠀⠀⠰⣾⡿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠁⠀⠀⠈⠙⠉⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⢀⡶⠋⠉⠢⡀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⣻⠀⠀⣀⠀⠀⠀⠈⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⢤⠕⠂⠀⠈⣀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠐⠠⠤⢄⡿⠁⠀⣠⠆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⠀⠀⠈⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣄⣀⡀⠀⠀⢀⡄⢀⡀⢀⠀⠀⠀⢀⡰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠳⡄
⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢻
⠀⠀⠀⠀⢰⠃⠀⠀⠙⢦⡀⠀⢀⣀⡤⠤⠶⠶⠒⠺⠤⢀⡀⠀⠀⢸
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡹⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⡀⣼
⠀⠀⠀⠀⠈⣇⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠱⡇
⠀⠀⠀⠀⠀⠹⡄⡜⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⢈⠢⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠁⢀⣤⠀⠄⠀⠀⠀⠀⠀⢝⠿⠛⡠⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢿⡿⠃⠀⠀⣀⢠⣄⠀⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠐⠐⠈⠀⠀⠙⢛⠁⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠀⢀⣠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⢤⣤⡀⠀⠤⠤⠄⠒⠊⠁⠀⠈⢳⡀⠀⠀⠀⠀⣠⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣧⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠸⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡇⠀⣰⠇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠸⡀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣧⠖⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⠶⢠⣇⠀⠀⡅⠀⠀⠀⡘⠀⠀⠀⢸⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣤⣇⣀⣀⣰⠁⠀⠀⠀⣇⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⢹⣇⠀⠀⢻⢿⣿⣿⣿⣿⡆⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⡀⠀⣸⢘⣿⣿⣿⣿⣷⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠋⠀⠛⠙⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠠⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡰⠃⢀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠓⠋⠉⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠐⢛⠶⠦⣀⣀⡤⠤⣄⠀⢀⣀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠞⢧
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠐⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣸⡀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⢆
⠀⠀⠀⠀⠀⠀⠀⡇⠙⢦⣀⣀⣠⠔⠋⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⣸⠃⠀⠀⠀⡞⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠦⠤⣀⠜⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠉⠲⣤⣀⣀⣀⣀⠀⠀⠀⣀⠴⠒⠒⠲⡾⠁⠀⠀⠀⠈⠣⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⡤⠖⠋⠀⠙⠲⢤⣤⠞⠀⠀⠈⠉⠉⠉⠉⢇⡀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⢤⣀⡀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠄⠀⠀⠀⠂⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠆⠆⠆⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠘⣇
⢠⡶⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠀⠀⢻
⣿⠀⠀⠄⢄⠙⢷⡀⠀⠀⢀⣀⣤⠴⠶⠒⠛⠛⠛⠛⠲⠦⣄⠀⠀⠀⠀⢸⠁
⣿⠀⠈⠀⠀⠐⠄⠹⣦⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣾
⢻⠀⠈⠀⠀⢀⡴⠋⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠶⠶⠄⠀⠹⣴⡏
⠘⣇⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠙⣆
⠀⢹⡆⣸⠁⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣶⣷⡀⡈⠳⠀⠀⠀⢹⡆
⠀⠀⢻⡟⠀⠈⠁⢀⣠⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⡻⢿⡿⠃⢠⠀⠀⠀⠀⢿
⠀⠀⠀⣏⠀⠀⠀⠺⣿⣷⣴⡆⢡⠀⠀⠀⠀⠀⠀⠈⠒⠐⠒⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⠀⠀⠀⠐⣌⠛⠋⣀⠎⠀⠀⣴⣪⣿⠆⠐⢀⠀⠀⠀⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠉⠉⠀⡠⠂⠀⠈⠉⣇⠀⠀⠌⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⠊⠀⠈⠢⠤⠞⠁⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡠⠤⠲⡋⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢸⠃⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢷⡀⠀⠀⠀⢹⡄⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⣠⠟⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠈⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣥⠾⠋⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣄⣀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⢠⠖⠉⠁⠀⢠⠇⠀⠀⠀⠀⣞⠀⠀⠀⠀⣰⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⢦⣤⣤⣤⣼⣀⢀⠀⣀⣀⣿⣤⣤⠴⠞⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠉⠉⠳⣄⠀⠀⢀⣤⣄⠀⣀⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡆⠀⡀⠀⠀⢀⠀⢰⠘⡇⠀⢸⡇⠈⠋⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡇⠘⠋⠀⠀⠛⠀⣿⣠⠇⠀⢸⡇⢠⣤⠀⠀⣤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠻⠗⠀⣠⡏⠀⠀⠀⠀⢷⡀⠀⠘⠃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠙⠓⠶⠖⠚⠉⣷⠀⠀⠀⠀⢠⠟⠲⠶⠶⠖⠋⠙⢳⡄
⠀⠀⠀⠀⠀⣼⣇⢠⡏⠀⠀⡄⠀⣀⣀⣀⡀⠀⣿⠀⠀⠀⠀⢸⠀⠀⣀⣀⠀⠀⡀⠀⠹⡄⠀⣰⠶⡄
⠀⠀⠀⠀⠀⣿⠘⣾⠀⠀⠀⡇⠀⠀⢹⠉⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⢻⠀⡿⠀⡇
⠀⠀⠀⠀⠀⠸⣆⠋⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⡇⠀⠀⢸⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠙⠒⠒⠋⠓⠒⠚⠁⠀⠀⠀⠀⠈⠓⠒⠛⠙⠒⠚⠛⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠛⢷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⣏⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣇⠀⠈⢿⣿⣶⣶⣶⣶⣶⣯⣿⠉⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠐⠀⢂⣻⣿⣿⣿⣿⣿⣿⣿⣥⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⣾⠿⠛⠓⠈⠋⠛⠙⢿⠿⠿⣿⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⢀⣤⣦⣄⠀⠀⠀⢠⣶⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠁⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⢹⡟⣋⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠟⠀⢀⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠠⡀⠀⠈⠙⠲⣖⣉⣉⣽⢟⣉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣯⣏⣽⣟⣿⣟⢯⡩⢿⣿⣯⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣏⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣷⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⢿⠛
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡿⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠓⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣰
⠀⣼⣿⣿⣧⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠿⠻⡄⠀⠀⠀⠹⣆⢠
⠀⢹⣿⣿⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⠀⠀⠙⠀⡄
⢰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣤⡀⠀⠀⠀⢀⣠⣦⣤⠄
⠈⠛⠻⠿⠿⠿⠟⢻⠿⠿⠶⠤⢀⣀⣀⣀⣀⠀⢠⠤⠶⠶⠛⠛⠉⠙⠓⠒⠒⠛⠛⠋⠉⠛⠙⠋⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠶⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣛⠀⢴⠂⠀⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠀⢤⡄⠈⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣼⢃⡋⠀⠀⣄⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⠙⠂⠀⠉⢢⠁⣷⠀⢴⠆⣤⠐⢲⡎⢻⣇⠉⠉⠈⠳⢀⠐⢺⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡖⠲⣴⠇⠀⠀⠀⢸⡆⢠⠀⠈⠇⢸⡇⠀⠀⠀⠀⠈⠹⠿⣿⣿⠿⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣟⣡⣾⠛⠁⠀⠀⠀⠀⠈⣇⠸⡇⠀⡆⠘⣧⡁⠀⠀⠀⠄⠀⠀⠀⠙⣤⣤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣙⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⢻⡀⢳⡘⡇⢀⣏⠱⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠃⡀⠇⠄⢀⠉⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⣡⣾⣧⣤⠁⠀⠟⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⣤⣦⣶⣦⣌⠀⠀⠹⠇⢹⠟⠀⠀⣰⠟⣿⣏⡉⢻⣿⠷⠦⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⡏⢈⣹⣿⡝⢦⠀⠀⠈⠀⠀⠀⠀⣇⠘⢿⣿⠇⢸⡟⠀⠀⠀⠀⠈⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⢻⣇⠘⠿⠿⢃⣼⡃⠀⠀⠀⠀⠀⠀⣿⠷⢦⡴⠶⠛⢀⣠⡜⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠤⣄⠀⠙⠛⠶⠚⢋⣩⡏⠀⠀⠀⠀⠀⠀⠘⠓⠲⠲⣶⣿⠿⠿⠺⠿⠿⠶⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⣤⣴⣎⠿⢷⣾⣷⡟⠉⠀⠀⢠⣄⣀⣀⣤⣶⠀⠀⠀⠀⠘⠻⢻⣎⣁⠰⠂⢱⣯⠽⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠄⢙⠉⢋⣉⣉⣶⣶⠿⡷⣀⠀⠀⠀⠈⠉⢯⣭⡽⠁⠀⠀⠀⠀⠁⠤⠀⣹⢇⡀⠐⠀⠀⠀⣼⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠉⢀⣄⣠⠤⢰⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢀⣰⣟⢰⣾⡿⢋⠲⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡖⠂⢉⣥⣤⠊⣉⣶⣔⠂⠐⢀⣀⡀⢤⠞⠛⠛⠛⠖⠐⢶⣶⣶⡿⢻⣿⣿⠁⣤⢾⡛⠫⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠶⠞⠃⠀⠉⠿⣿⣿⣟⢛⡿⣿⣅⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢭⣿⣿⣭⡾⠿⠏⠀⠀⢀⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⠀⠈⠁⠀⠀⠀⡼⠉⢹⣿⣷⣊⡛⠛⣶⣦⣤⠤⣴⣶⣿⣧⣿⡿⠟⠉⠇⠀⠀⣌⡲⣷⠌⠁⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⣤⠀⠀⠀⠊⠁⢰⢏⡀⠈⠛⠙⠾⣿⢏⣼⣿⡿⠟⠟⠛⠁⠀⡤⢀⣾⣶⣿⠾⠇⠀⠀⠀⢠⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣋⡉⠉⠘⠓⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠄⢠⠀⠁⠀⠐⠂⠀⠲⠞⠃⠈⠈⠀⠉⠀⠀⠀⠀⠀⠼⠛⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⠋⠉⠛⢢⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣨⠉⠉⠛⠳⠶⢤⣬⣹⠿⣦⣀⠁⠀⡀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠸⢳⣦⠴⠂⠂⠀⠠⣤⠠⡌⠉⢙⣿⣿⣷⡄⠸⣦⢀⣄⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⣠⣿⡷⠄⠁
⠀⠀⠀⠀⠀⠠⣾⠏⠁⠐⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣿⡻⣿⣿⣿⣤⣾⣿⣶⣀⣼⣷⣶⣶⢶⣵⣶⣦⠘⠻⠗⠦⠶⡶⠟⠿⣧⣦⡀⠦
⠀⠀⠀⠀⠀⠀⣿⠆⢀⠶⠶⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠏⠁⠉⠁⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠳⣄⠀⣀⠈⠙⣿⠂
⠀⠀⠀⠀⠀⠀⢹⣶⣋⣴⡂⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣘⣙⣁⣘⠳⣾⠇
⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡂⠈⣿⣿⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣜⡀⢠⠄⠀⠀⡀⠀⠀⢸⠁⠀⣠⠀⢐⣾⣿⣤⠞⠁⣠⠆⠀⠀⠀⡤⠀⠀⠶⠀⢀⡀⢀⢀⣿⣿⡷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢤⡀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⢈⣿⣿⣿⣧⣼⡏⠀⢀⣠⠟⠁⠀⠀⣸⣷⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⢹⣤⣠⣿⣦⡿⠾⠛⠋⠁⠈⠙⠛⠛⠻⠿⠿⠷⠶⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠚⠛⠋⠉⠉⠉⠉⠉⠙⠛⠲⠦⠀⠠⠴⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠦⡄⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠸⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠊⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⣾⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡙⡇⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡹
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠹⡿⢏⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⡾⠃
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣆⠘
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⠸⠃
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠹⠏
⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠑⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢠⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠛⢦⡀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⣀⠹⣏⠐⠂⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⣠⠃⠀⠀⠀⢸⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⢣⡀⠀⠀⡎⠁⠙⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⡟
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢳⡀⠀⢣⠀⠀⠘⠀⠈⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⡼⠁
⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢧⠀⠀⡇⠀⠀⣤⠖⠋⠉⠀⠈⠙⠛⠒⠒⠒⠛⠋⠁⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠘⡀
⢠⠏⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠸⡇⠀⠀⠘⡀⠀⠇⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢀⣤⣠⢰⡖⢈⣭⠙⠆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⠀⢳⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣥⣍⣿⡄
⢸⢀⡄⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⡆⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠛⠿⠿⠂⡆
⠸⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢹⡄⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢀⡜
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢠⠞
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠛⢄⡙⢦⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⢁⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠙⢦⣄⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠞⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢼⣮⠙⢦⣄⠀⠀⢷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣧⡉⠢⢀⠀⠹⡄⠀⠀⠸⡀⠐⠢⢄⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠒⠾⠆⠀⠑⠷⠀⠀⠀⠈⠢⣄⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷

⠀⠀⠂⠻⠃⠢⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⡁⠐⠂⠀⠂⡡⠤⡤⠐⠎⠉⠀⠀⠈⠱⠄⣀⠀⠀⠀⢎⠑⡀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠈⢢⢤⣤⠄
⠀⠓⢂⣀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⡂⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⣐⡄⠀⢠⠀⠀⠁⠀⠐
⠀⢉⠏⠀⡰⠧⢀⣀⣀⠀⠄⠒⠀⢄⠀⠀⠀⡁⢱⠀⠀⠀⠀⡈⠂⠠⠘⣄⠀⠀⠀⠀⠹⣀⠘⠀⢜⠀⢀⠡
⡠⠁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠒⠐⠠⢀⠕⠒⠰⣁⠥⠤⠂
⠈⠀⠁⠀⠀⠀⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠊⠀⠏⠀⠁⠈⠀⠀⠀⠈⠈⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠑⠄
⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢠⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠐⣤⡀⠠⠔⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠕⠠⡄⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⡠⠂⠹⠁⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠔⠈⢦⠀⠀⠀⡌⠀⠀⠐⠀⠀⢀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠁⠄⠀⣄⠜⢰⠀⠀⠀⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⢀⡅⠀⠥⠐⠁⠀⠀⠀⢆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠡⠤⠀⠀⠀⠀⠀⠀⠘⣄⠂⠐⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⠉
⠀⢀⡄⠀⠤⠠⠂⠈⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⡄
⢀⠊⠀⠀⠀⠀⠀⡀⠀⠰⠀⢢⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠈⠉⠀⠂⢄⠀⠀⠀⠀⠀⠁⢀⠈⠀⢀⠜
⡀⠀⠀⢁⠀⣅⣀⠁⠀⣀⠄⠀⠀⠀⠀⠐⢲⠒⠊⠀⠀⠀⢀⠀⠀⠀⠀⢦⢀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠢⠄
⠇⠀⠀⣄⠄⠂⠈⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⣟⡒⠀⠀⠀⠀⡀⢂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡃
⠈⠀⡀⡇⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢡⠥⢄⠄⢀⠌⡠⠄⠃⢀⠀⢀⣀⡴⠃⡐⠀⠀⠐⠄⢠⠀⠁⠀⠄⢀⠇
⠀⠀⠀⠃⠀⠄⠠⡀⡠⠀⠝⠀⠀⠀⠐⠂⠘⠢⠈⠉⠑⠄⠺⠉⡉⠉⠁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠔

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠓⠰⢂⠀⣠⠛⢪⠐⠠⢀⠀⠀⠀⠀⠄⠠⠀⡤⠀⣤⣀⠀⠀⢀⠀⠀⠀⠐⡄⢀⢍⡵⠖⠐⠀⠉⠀⠒⠶⢮⢅⠀⢰
⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠏⠀⢠⢑⠀⠀⠀⠀⡁⠀⠂⠀⠀⠀⠈⠁⠘⠡⡀⠀⡀⠀⡇⡐⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢆⡾
⠀⠀⠟⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠺⠀⠀⠸⣀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⢸⠁⠀⣄⡀⠀⠁⠀⠀⠀⣀⡠⠀⠘⠁
⠀⠀⠀⠰⢿⣯⣽⡆⠀⠀⢸⣯⣽⣿⠆⠀⠀⠀⠀⠙⢨⣷⡒⣦⠀⠀⢀⡔⢲⣦⡀⠃⠀⠀⢸⢰⢿⣿⣽⣆⠀⠀⠀⣾⣯⣽⢳
⠀⠀⠠⠀⠑⠙⠛⠃⠀⠀⠘⠛⠛⠈⠀⡀⠀⠀⢀⠄⠈⠻⣿⣿⠀⠀⠸⡿⢿⠟⠁⢀⠀⠀⢸⠀⠊⢾⣿⠏⠀⡀⠀⠳⡿⠋⠈⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⢀⠀⠈⠉⡋⠉⠀⠡⣠⡆⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⢐⠒⠲⠒⡖⠒⡉⡝⠁⠂
⠀⠀⠀⠀⠀⠒⠂⠀⠀⠁⠀⠀⠆⠁⠀⠀⠀⠀⠀⢔⠄⢀⠞⠀⠀⠠⠂⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⢀⢰⠃⢀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⢄⠲⠀⠀⠀⡀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢘⠀⢡⠀⢉⠀⠎⠀⡟⠁
⠀⠀⠀⠀⠀⠈⠀⠐⠂⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠓⠒⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣭⣫⣬⣭⣯⣭⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⣀⣤⠴⠶⠚⠛⠛⠒⠒⠶⠶⢤⣄⡀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣩⣭⡳⡄⠀⠀⠀⠀⠀⠀⢠⣞⣭⣍⢳⡄⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢳⡸⣿⣧⣾⠇⠀⠀⠀⠀⡀⠀⠸⣿⣧⣼⣣⠇⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠆⠖⠒⠻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⢰⡀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠉⠉⠉⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⠀⠀⠀⢉⣀⣀⣤⠴⠞⠋⣧
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠁⠀⠀⠀⠀⠸⡄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠘⠳⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡇⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⢤⣤⣤⣀⡀⠀⠀⠀⠀⣿
⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢦⣄⢠⡏⠢
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⢱⡀
⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣀⣠⣀⣤⣠⣄⣀⠀⠀⠀⠀⠀⠀⡀⠻⡄⢳
⣿⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⡀⢀⣀⣴⠶⠛⠉⠁⡏⠀⡀⠀⡉⠛⣦⠀⠈⢢⡀⠘⣆⡿⢸⡇
⢹⣆⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣀⣀⣈⣧⣼⣄⣼⣥⣤⣿⣄⣠⣼⣁⣴⠏⢀⣼⠃
⠀⠹⣧⣀⠀⠀⠀⠀⠈⠉⠙⠙⠛⠛⠛⠒⠶⠒⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠻⢶⣟⠁
⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⢠⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣛⣻⣶⣾⣛⣁⣀⣀
⣿⣿⡟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⢿⣿⣿⣷⣄⠀⢀⣀⣀⣀⣼⣿⣿⣿⠋⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠉⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣾⣿⣿⣿⣿⣦⠠⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⣴⢲⡄⠈⠻⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⢿⣌⠉⠉⠁⠀⠀⠀⠰⢄⡩⠯⣤⠔⠀⠀⠀⠉⠉⢉⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠄⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⠇⠀⠀⣤⠀⠀⠀⣠⡿⠁⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⣿⠀⢀⣴⠏⠀⠀⠀⠸⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢿⣴⠟⢁⣦⠀⠀⠀⠀⢹⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣾⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠘⣧⠀⣼⡇⠀⠀⠀⢸⡏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⡄⣿⠀⠀⠀⠀⣿⣱⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠆⠲⢤⣤⡄⠀⢘⣷⠀⠀⠀⣿⣧⣿⠀⠀⠀⠘⣿⢾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⡃⢀⡆⢠⡿⣻⣯⠄⡄⢠⡿⠀⠸⣧⣴⣄⣹⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠘⠻⠾⠷⠛⠁⠀⠀⠀⠉⠉⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⣶⣶⣶⣶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠘⠛⠃⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⣠⡴⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⣻⣷⣤⣤⣼⣍⡀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⢀⣿⣿⢻⡝⡇⠈⡿⣯⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠈⣿⣿⣶⡾⠃⠀⢿⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣶⣶⣿⣿⣿⣀⠙⠋⢀⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡍⠙⠉⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣶⣀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠈⣿⣿⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡷⠀⠀⢹⣿⡇⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠇⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

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