CAPYBARA Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⠄⠚⢛⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠒⣴⡢⢩⠀⠑⠘⠷⢤⣾⣦⣭⣽⣋⠐⢈⡛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣡⣶⠞⢈⠂⢈⡁⠘⠀⠄⠀⠀⠚⠙⢛⠿⣿⣿⠿⢿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣏⣩⠀⠐⡿⣆⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⠟⠱⢿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣭⠁⠀⠈⢟⣿⡓⠀⠤⠀⠀⠀⠠⠀⠈⠀⣼⣿⣴⣞⢶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠸⣿⣿⣿⣿⣿⣿⣿⣅⣤⠀⠚⠛⣿⣾⣄⣄⡀⠀⠀⠠⣀⠑⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⣷⣿⣮⣿⣿⣿⣿⣄⠀⣸⣵⣦⡄⣿⣿⣿⣿⣯⣵⣼⣷⣾⣿⣿⣿⣿⣿⣽⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣤⣶⣿⣿⢋⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠙⠻⠿⣿⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣫⡤⣤⣾⡿⠟⡿⠣⢤⣤⣼⢿⣿⣿⣿⢿⡟⠼⠿⠿⠛⠛⠛⠛⠉⣹⣿⡿⠟⠀⠀⠀⠀⢸⣿⡜
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⡿⡉⠀⠄⢀⣾⣿⡏⠀⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⣀⡤⣾⣿⡋⠁⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣎⠉⣹⣿⣿⣿⣿⣷⣀⣺⣾⣿⣿⣏⣄⢠⡿⢛⠋⡀⣀⡄⣠⣤⣤⣶⣿⣶⣿⢿⣿⣷⣶⡦⢢⠄⢴⡏⣹⣷⡶
⠀⠀⠀⠀⠀⢀⠀⢙⢿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡟⠹⠿⠛⣋⢱⠾⠿⠯⠀⠰⠀⠁⠈⠈⠉⠀⠀⠀⠁⠉⠉⠉⠀⠀⠈⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⠏⠉⠉⠀⠀⠀⠂

⣿⣿⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠌⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⡄⣰⡿⠤⠄⠰⣜⠙⠆⠀⢸⣥⠀⣼⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡇⠙⠂⠀⠀⠀⢠⠀⠀⠀⠀⠈⠙⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⢤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠢⣿⠻⠂⠀⠙⠓⠱⠿⠘⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠁⠀⠀⠀⠀⠀⠀⠆⣤⡆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⣀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠈⠀⠀⠀⡀⠲⠶⠀⠀⠀⠘⢃⠈⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⡀⠀⠀⠀⠘⠿⢤⣴⠿⠋⠂⠀⠈⡅⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢸⡁⠀⠀⠀⠀⠀⢀⠀⠠⠀⢄⠀⠀⠘⠂⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠈⠁⡤⢀⣼⡱⠶⢺⡓⢤⣄⡀⠀⢀⠀⣠⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠴⢾⠀⢇⠀⠀⠀⠠⡝⡷⠀⠈⠜⢆⢈⣷⠞⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠐⠋⠀⠊⠀⢰⡆⡀⠀⢀⣀⣠⣨⣆⠙⣶⠂⢀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠠⠂⠃⠈⠾⢻⡾⡿⢿⠻⣧⠐⠀⢙⠣⡍⢈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠁⠀⠀⠁⠀⠀⢀⡀⠀⢂⠀⠘⠱⠀⠊⡗⡄⠀⠀⠀⠈⠓⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡅⠀⠀⠀⠀⠀⠀⢈⠜⠀⠔⠀⠀⡰⠃⠁⢠⡉⠙⠢⠀⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡴⠂⠀⠀⠀⠀⠀⠐⠁⠈⡀⠔⡇⠀⢱⠀⣀⢸⡇⠀⠙⠒⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⠃⠀⢿⠀⠀⢐⠀⠀⠐⢦⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠘⠀⠀⣧⣈⡇⠀⠈⠆⠀⠘⠆⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⡄⠀⠀⠀⠀⣠⠆⢂⠀⠀⠀⠀⠀⡄⣿⠻⢀⡆⠀⣼⡗⠬⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⠒⠀⠀⠀⢀⠠⠟⢻⡎⢀⠀⠀⠀⠀⠸⠀⣀⣿⠇⠑⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡐⢇⠖⠀⠀⠀⢀⡠⠀⠙⠀⠁⠀⠆⢸⠀⢸⡟⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠐⠂⠙⠒⠚⠒⠀⠒⠋⠁⠈⠛⠋⠐⠂⠒⠒⠲⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣦⣄⠠⣾⠃
⠀⠀⠀⠀⣠⣤⣿⠻⣫⣭⡿⠇⠀⠼⠃
⠀⠀⠀⣶⣿⣿⣿⣿⣏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢶⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠜⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠸⣟⠙⡿⠿⠏⠏⠀⠀⠀⢠⠀⠀⣐⣠⣀⡀⠀⢦⢇⡃⢀⠀⠀⠰⢰⠀⠀⠀⠀⠀⠐⠆⠀⠀⠘⠀⠠⡐⠀⠀⠀⠀⠀⠆⣀⠠⠈⠀⠀⠠
⠀⠀⠹⣆⣀⢀⣶⣱⣶⣶⣾⣷⣦⡶⣈⠅⢾⣷⠀⠢⠏⠩⢉⠀⠠⠰⠐⡀⣀⣄⠀⠀⠀⠂⣦⡠⢀⡑⣶⠟⣈⠀⠠⣶⣦⣺⣿⣮⠄⠆⠀⡠⡄
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠛⢿⣿⣷⣬⣤⣼⠿⣦⡄⠀⡖⠈⠢⢀⡄⠀⢂⡩⣡⣷⣻⣶⢤⣸⣧⢰⡜⢪⢧⠛⢧⡠⣽⣿⣿⣿⡋⠀⠀⢰⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣿⣷⣤⡀⢼⡃⠀⠁⣙⣽⢏⣘⣵⣿⣻⣼⣿⣿⣿⣾⡏⣤⢹⠒⡞⣿⣿⠿⠇⠰⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⡍⣷⣾⣦⠗⡖⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣿⠿⣿⣿⣆⠀⣹⣊⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣿⡿⠿⡷⠱⠀⡀⢻⣮⣿⣿⣿⣉⣛⣮⣿⣽⣿⣿⣶⣷⣾⣌⠂⠈⠃⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠋⠃⠀⠠⢄⡸⡥⠋⠉⠛⠛⠻⠿⠛⠛⢿⣿⣿⣿⣟⠛⠻⣤⣄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠍⢀⣡⣤⣆⡠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣫⠂⠀⠙⣿⣧⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣼⣶⡾⠛⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⠟⠁⠀⠀⠀⣼⠃⠀⣸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡈⣿⠇⠀⠀⠀⣿⣽⡧⠀⠀⠀⠀⠀⠀⠀⠴⠿⢿⡿⠿⠟⠁⠀⠀⠀⢀⣼⣷⣾⣆⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣷⣧⡿⠂⠀⣀⣰⣷⣿⠇⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⠟⠉⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⡻⣿⣻⣾⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⡤⣄⣤⣄⣀⣀
⠀⠀⠀⠀⢰⣿⡟⠁⠈⠻⣿⣯⡙⠉⠀⠈⠉⠲⣦⣸⣏⣟⡛⢛⣻⡛⠀⠋⡻⣿⠻⠉⠿⠆⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣶⣦⡀
⠀⠀⠀⠀⠘⣿⡇⠀⣀⠘⢯⡉⠛⠷⠷⡶⢤⣿⣿⣿⣦⣿⣤⠀⠀⠉⠐⢠⣦⣿⢐⡧⢤⠔⢤⠉⠴⠀⠀⠈⠁⠴⢠⡄⠀⠁⠘⢿⢿⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⡅⣄⡀⡀⢠⢀⡈⢿⣟⢌⣿⣷⣄⡀⠀⢈⣸⣿⣿⡟⠉⠄⠀⠀⠀⠀⠀⠀⠁⡸⣶⠶⡁⢀⡀⠀⠀⠂⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣬⣿⣿⠟⣧⣿⣿⢻⣿⣿⣿⠧⡟⣿⣿⣿⣧⣀⠀⣎⠁⠀⡀⣾⣾⣾⡏⡔⠌⠘⠃⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡹⢫⠈⡟⢻⢦⣼⣿⣿⣿⣿⣿⣉⢿⣦⣰⣶⣿⣿⣿⣍⢃⠀⠉⠀⠀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣯⢨⣠⢠⣿⡗⣌⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠋⣀⠀⠀⠀⠀⢀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣾⢟⠄⠺⢹⣿⣃⠈⢻⣿⣿⣿⣿⣿⣿⣶⣷⣦⣿⣿⣧⣁⠄⠖⠦⠃⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣿⣿⣿⡄⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡾⡋⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡿⣿⠛⠿⣷⣦⣠⣿⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠟⡾⠁⠀⠀⠀⠈⠉⠛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠠⠿⣿⣿⠯⣿⡖⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠟⠻⠿⠿⠈⠀⠀⠀⠀⠀⠀⠀⣀⣿⠏⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠑⠈⠀⠀⠀⠀⠀⠀⠀⢰⢿⡿⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠵⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠒⠈⠀⠰⢦⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠤⠤⢤⡤⠄⠀⠀⠴⠤⠤⠄⠀⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠁⢀⡀⠀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠴⠈⠁⠀⣀⠀⠉⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠁⠈⠀⠀⢐⠫⠭⣅⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠒⠒⠶⠦⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢿⣽⡷⢺⠀⠀⠀⠀⡀⠙⣄
⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠢⠤⣄⣀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⣸
⠀⠀⣠⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠀⠈⠉⠀⠀⢹
⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠏
⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠓⢄⣀⣀⣠⣆⠀⡼
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠉⠐⠈⠉
⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠘⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠠⠃
⠀⠀⠀⢘⣠⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⡆⠘⠘⠒⡄⠀⠀⠀⠀⠀⠀⡰⠣⠀⠠⡤⢀⣀⣀⣀⣀⠠⠤⠐⠲⠊⠱⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⣶⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠱⠀⠀⠀⢠⠃
⠀⠀⠀⠀⡘⠀⢠⠀⠀⠌⡁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⢀⠇
⠀⠀⠀⠀⢡⠀⠘⠀⢸⢰⠀⠀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠀⠸⡀
⠀⠀⠀⠀⠀⢢⠀⠀⠘⠀⠙⢦⡀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣇⠀⠀⠉⠂⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⠒⠲⠽⣆⠀⠀⠠⠤⣒⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⡦⠤⢬⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⢻⣿⣿⡿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⠤⠤⢤⣤⣤⣄⣀
⠀⠀⠀⠀⢸⣿⡏⠁⠈⢻⣿⣎⡛⠁⠀⠉⠐⢲⣦⣿⣽⣋⠉⣩⣟⠉⠉⣹⢿⠛⠉⠹⠂⠈⠁⠀⠀⠀⢀⡀⠀⠙⠋⢻⣿⣶⣦⡀
⠀⠀⠀⠀⠘⣿⡄⢀⡀⡹⣧⠉⠛⠿⠷⠷⢼⣿⣿⣷⣾⣦⠄⠀⠀⢉⢠⣶⣾⢆⣷⠶⠞⠲⠈⠰⠀⠀⠀⢁⠰⢤⡄⠀⠀⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣠⣄⣀⡀⣄⣰⠹⣿⢵⣹⣟⣶⣀⣀⡠⢤⣿⣿⣟⠃⠢⠀⠀⣀⠀⠀⠀⢀⢼⣞⠳⠁⢤⡄⠀⠀⢂⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠻⢿⣿⣷⣾⣿⣟⣻⣾⣿⣟⡿⣽⣿⡇⢾⣻⣿⣿⣷⢤⡀⣦⠀⠀⠄⣾⣶⣿⣇⡜⠊⣈⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡧⡋⡆⢹⣉⠿⣾⣿⣿⣿⣿⣿⣧⣻⣷⣼⣿⣿⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⣦⡆⢾⣯⣳⡸⡼⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⢻⣿⡃⡄⠀⠀⠀⡀⠄⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⡕⠘⣉⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⠀⣋⣛⠁⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⢿⣿⣿⣷⣾⣝⣀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢛⡟⠉⠛⠿⠷⣽⣿⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⡟⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⢫⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡑⠶⠀⠀⠀⠀⠘⠛⠟⣛⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡶⢿⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠐⠋⠟⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⣳⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠀⠀⠈⠋⠁⠒⠂⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢰⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣦⠚⠛⠚⠢⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢿⠆⢨⣀⣼⠀⠀⠈⢹⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣭⣽⣯⣥
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡌⠉⡏⢹⠒
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⣇⡸⠍
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣶⣶⠿⠋
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠁
⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣠⠟⢀⡰⠃
⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢀⣄⣤⣤⣿⣡⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣀⢀⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⠃⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠟⣠⣶⣾⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢹⣿⣿⣧⢘⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠛⠛⠛⠛⠾⠿⠿⠞⠃⠀⠀⠀⠉⠙⠳⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠶⣿⣿⣿⣿⡿⢷⡶⣶⣤⣄⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣯⣿⣿⣿⣿⡿⠿⣿⣿⣿⣶⣶⣦⣶⣶⣶⣶⣤⣤⣾⣿⣧⣥⣿⣿⣿⣉⡙⠛⠉⠀⠀⣌⠏⣵
⠀⠀⢀⣴⣿⣿⣿⣯⣿⡻⣷⢿⠟⠛⠛⠀⠀⠠⠁⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣶⣦⣤⣶⣼⣧⡟
⠀⢠⣿⣿⣿⡿⠋⠛⠛⢳⢇⡄⠀⡠⠀⠀⠀⠙⠃⢐⡾⣻⣿⣿⣿⣿⠛⣿⠿⣶⣿⣿⣿⣿⣻⣷⣿⡟⠛⠭⢿⡿⠿⠟
⠀⣾⣿⣽⣿⣿⡯⣯⡆⠀⠀⠀⠀⠀⠠⠚⠀⠀⢀⣼⣴⣿⣿⣿⣿⢹⣿⢿⡄⣱⡟⢻⣿⣯⣿⣿⣿⣿⣿⠟⠋
⠀⢹⣿⣿⣟⣿⣦⣻⠀⠀⠐⠐⠀⠋⠀⣠⡀⠀⡀⠀⣩⠏⠹⠿⠻⣄⠋⠛⠑⣟⠛⣀⣿⣿⣿⡿⠋⠋
⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⣀⣠⣀⡃⠂⡰⡿⠂⠁⣀⣾⣶⣶⣾⣆⡭⢱⢰⣦⣄⣥⣾⣿⡟⠋
⠀⠀⠈⠻⢿⣿⣧⣿⣿⡼⣿⣿⣿⣷⣶⡟⣧⡔⡷⣿⡏⢻⣿⣿⣿⣶⣤⣁⣅⡙⢹⣿⠏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣽⠿⠿⠿⠛⠷⠾⠇⠚⠙⠿⠟⠺⢽⣏⣿⢿⣿⣷⣼⠈⠉
⠀⠀⠀⠀⠀⠻⣿⣟⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣈⣣⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀⣀⣨⣿⣿⡦⣄⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⣈⠀⠀⠀⠹⠆⠁⠀⠀⠀⠀⠉⠫⠭⠿⠩⠅⣭⣿⣿⣦⣒⡖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠃⠀⡤⠋⠈⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠘⠆⠀⠆⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠶⠶⠦⢤⣤⣀⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠤⣀⣀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡆⣠⠀⠠⣦⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢦⠀⠀⠘⢇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⠀⢸⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠦⠴⡀⠀⠀⠀⡤⠦⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡆⡝⢦⠤⡦⠾⠂⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢼⢠⡇⠀⠀⡀⠀⢤⡀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠠⠃⠀⡆⢸⠀⠀⡼⠀⠀⠀⠑⢤⣀⣀⢠⣈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠶⠧⢒⡁⠉⠀⠀⠃⠀⠀⠀⠀⠄⠐⠚⠉⠉⠀⠈⠀⠀⢠⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⡷⠺⠷⠁⠀⠀⠘⡷⣥⣄⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⡀⢢⡄⠦⢭⠽⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠜⠌⠳⡀⠄⠀⠈⠉⠿⠿⣿⣿⣦⣤⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⡇⠠⡶⣎⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠾⠻⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣅⠀⠀⢻⣿⡂⠠⠀⠀⠀⠂⠀⣀⣾⣷⣶⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣸⣻⣿⣿⣿⣿⡷⠴⢀⢀⠙⢿⣷⣦⣄⣀⢀⣤⣨⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⡟⣿⣿⢿⣿⣿⣿⣿⣦⣼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣭⣴⡿⢿⠿⢌⣩⣽⣿⣿⣿⣿⠯⠾⠿⠿⠛⠛⠛⢻⣿⡿⠃⠀⠀⠈⣿⡼
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⡿⡉⠀⢀⣼⣿⠇⢘⣿⣿⠎⠀⠀⠀⠀⢀⣤⣲⣿⣋⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠰⣄⣹⣿⣿⣿⣿⣴⣽⣿⣿⣯⣦⣼⢫⣅⡤⠤⠠⡶⠶⠿⡿⠿⠻⠿⡿⠷⠱⠂⠾⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⠿⠿⠛⠉⠹⠀⠉⠁⠂⠋⠉⠁⠀⠁

⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⡀⡉⣤⡿⠂
⠀⠀⠀⠀⠀⣀⣴⢿⡿⣛⣻⣿⠁⢈⡿
⠀⠀⠀⣤⣿⣿⣿⣷⣞⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣤⣶⣿⣿⣿⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⡰⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⢸⣿⠿⣿⣿⡿⢿⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⢠⠈⠌⠀⠀⠀⢀⢄⠀⠀⠠⠀⡀⠀⡄⠀⠀⠐⠀⠀⠀⠄⠀⠀⠈⠀⠀⡀⠀⠀⠈⡀⠀⢀
⠀⠀⢿⡀⠉⠈⢁⠄⣤⣄⣤⣾⣡⣤⡔⢶⢻⣷⡆⠠⢩⠜⠖⠂⠀⢀⢠⠈⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠠⣁⣹⡄⠀⠀⢂⣄⡀⣴⣧⣀⠀⡀⠀⠀⠆
⠀⠀⠀⠛⠶⠶⠛⠛⠛⠛⢿⣿⣿⣷⡜⡊⡂⢻⣇⡀⠁⢀⡈⠂⡀⠈⡈⢀⡃⠾⠟⣤⢶⣄⣐⠘⣯⢀⡓⣜⢧⢴⣦⠀⡑⣿⣿⣾⣿⡟⠀⠁⣀⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣹⣿⣇⢨⠁⢠⠉⠰⠃⢤⢴⡾⠸⣟⣾⢿⢽⣷⣿⣮⣟⣬⠎⠳⣌⣑⣾⣿⣿⣿⠙⢀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⣿⢿⣎⣷⡠⣆⣀⠾⣿⣽⣶⣿⣿⣶⣿⣿⣿⣿⣯⣿⡾⣧⢣⡼⣼⣿⣿⠉⠠⣭⠠⣰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣏⣿⣿⣅⢇⡀⠐⣿⡿⣿⣿⣿⡿⣿⡟⢿⢿⣿⣿⣏⢻⣋⡝⢟⠛⢶⡠⣿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡋⠙⠫⠈⢀⠄⣼⢷⣾⣿⣿⣷⣵⣿⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣭⢃⠄⠀⠀⠀⢑⡈⠋⠀⠀⠀⠉⠉⠉⠉⠉⠘⢿⣿⣿⣿⢇⠀⠻⣿⣦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⡐⣀⣴⣶⣺⣥⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡧⠊⠀⠀⠙⣿⡇⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢶⣿⠟⠋⠁⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⠟⠁⠀⠀⠀⣰⡟⡁⢀⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⢸⣿⠀⠀⠀⢀⣟⣾⡇⢀⡀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⡼⠁⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⡾⠋⢀⣠⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠴⠿⣿⡯⠟⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣴⡿⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠀⣤⣀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣏⠀⠘⠿⠋⠃⣀⠀⢀⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠹⣿⣿⣧⣀⠀⢀⠀⠀⠀⢀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣾⡾⠃⠛⠛⠀⢀
⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣴⣧⡎⠀⡀⠀⠀⠀⢀⠛⠿⠿⢿⢿⡇⠀⠀⠀⠐⠉⠡⣄⢀
⠀⠀⠀⠀⢠⡇⠀⢠⣾⣿⣿⣿⠃⢸⡇⠀⠀⠀⣾⡀⠀⠀⠈⢸⡇⠀⠀⠀⠐⣘⣀⢱⡞
⠀⠀⠀⠀⣾⠀⠀⣸⣿⣿⣿⣯⠀⢸⡇⠀⠀⢰⣿⡇⠀⠀⣰⣾⡇⠀⠀⠀⠂⢘⣁⡉⠽⠁
⠀⠀⠀⠀⣟⠀⠀⠸⣿⣿⣿⣿⡀⠸⣿⠀⠀⢼⣿⠇⠀⠀⣿⣿⠃⠀⠀⠀⠁⠉⣿⢧⠐⡇
⠀⠀⠀⠀⢿⠀⠀⠀⠻⣿⣿⣿⣿⠀⢹⡎⠀⠸⣿⣇⢀⣸⣿⠟⠀⠀⠀⡀⠀⠉⠡⠀⠀⣄
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢻⣿⣿⣾⣿⡀⢀⡇⣋⣾⡿⠋⠀⠀⠐⠦⣄⣼⠆⢀⠀⢀⠟⠛⠚⠁
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣌⡷⣿⣿⠅⠀⠀⠀⠐⠀⠀⠈⠀⢈⣤⠛⠀⠰⢷⣄
⠀⠀⠀⠀⠀⠀⡀⢹⣷⣾⣦⣄⣼⠿⠟⢋⣿⣿⡇⣹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⡌⢁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠀⠀⠘⢻⠿⠷⠅⠈⠉⠋⠀⠀⠈⠃⠀⠀⠐⠓⠛⠁⠀⠐⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣠⣴⡿⢷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣁⣀⠉⠉⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏⠀⠀⣼⣿⠶⡄⠂⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠉⠉⠀⠉⠦⣀⣄⣦⣦⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣿⡿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⠙⠓⣻⣻⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠠⠀⠀⠀⠀⠙⣿⣿⣿⣦⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣷⣼⣦⣶⣼⡶⠠⠿⠷⠈
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡤⠷
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢀⣔⣾⣿⣿⡟⠀⣤⠁⠀⠀⠀⠀⣶⠀⠙⠉⠉⢻⢻⡇⠀⠀⠀⠀⠀⠀⣀⠘⡶⢁⠄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⣾⣿⣿⣿⣿⠁⢀⣿⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠈⣁⣡⣤⣨⡟⡁
⠀⠀⠀⠀⠀⣾⠁⠀⠀⣼⣿⣿⣿⣿⣏⠀⠀⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⣷⣾⡇⠀⠀⠀⠀⠒⠀⠋⢁⠑⡩⠇⠤
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⣿⡆⡀⠀⢠⣿⣿⠃⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠂⠼⢛⣿⣗⡠⢶⠄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⡄⠸⣿⠠⠀⠘⣿⣿⡄⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⢠⠽⠛⠈⠁⠘
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠛⢿⣿⣿⣿⣇⣄⢻⣇⠀⠀⢻⠿⣷⢀⣶⣿⡿⠃⠀⠀⠀⠀⢆⠘⡄⠀⠉⠀⠀⢺⣤⣀⢀⡠
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣾⣿⡄⠀⣸⠈⣡⣾⣿⠏⠀⠀⠀⠀⠙⠳⢦⣶⡟⠀⢠⠁⢀⡞⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣧⣹⠿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⣈⣤⠻⠁⠀⠾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣧⣦⣦⣀⡀⣸⣿⣿⣿⠟⣿⣿⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡞⠃⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠻⢿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣄⠛⠛⠿⢿⠇⠀⠠⠀⢤⠇⠄⠀⠀⣹⣇⣾⠦⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠇⠁⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠴⢒⠀⠈
⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠰⣷⣶⠇⠀⠀⠀⠱⡀
⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠘
⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⢈
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠈⠐⠂⠑⠘⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⢀⠞
⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁
⠀⠀⠈⠔⢢⢀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⡜
⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠀⠐⠄
⠀⠀⠀⠀⢡⡀⠐⠂⡼⣆⡀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⡢⠄⠑⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠶⣿⣿⣿⣿⡿⢷⡶⣶⣤⣄⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣯⣿⣿⣿⣿⡿⠿⣿⣿⣿⣶⣶⣦⣶⣶⣶⣶⣤⣤⣾⣿⣧⣥⣿⣿⣿⣉⡙⠛⠉⠀⠀⣌⠏⣵
⠀⠀⢀⣴⣿⣿⣿⣯⣿⡻⣷⢿⠟⠛⠛⠀⠀⠠⠁⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣶⣦⣤⣶⣼⣧⡟
⠀⢠⣿⣿⣿⡿⠋⠛⠛⢳⢇⡄⠀⡠⠀⠀⠀⠙⠃⢐⡾⣻⣿⣿⣿⣿⠛⣿⠿⣶⣿⣿⣿⣿⣻⣷⣿⡟⠛⠭⢿⡿⠿⠟
⠀⣾⣿⣽⣿⣿⡯⣯⡆⠀⠀⠀⠀⠀⠠⠚⠀⠀⢀⣼⣴⣿⣿⣿⣿⢹⣿⢿⡄⣱⡟⢻⣿⣯⣿⣿⣿⣿⣿⠟⠋
⠀⢹⣿⣿⣟⣿⣦⣻⠀⠀⠐⠐⠀⠋⠀⣠⡀⠀⡀⠀⣩⠏⠹⠿⠻⣄⠋⠛⠑⣟⠛⣀⣿⣿⣿⡿⠋⠋
⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⣀⣠⣀⡃⠂⡰⡿⠂⠁⣀⣾⣶⣶⣾⣆⡭⢱⢰⣦⣄⣥⣾⣿⡟⠋
⠀⠀⠈⠻⢿⣿⣧⣿⣿⡼⣿⣿⣿⣷⣶⡟⣧⡔⡷⣿⡏⢻⣿⣿⣿⣶⣤⣁⣅⡙⢹⣿⠏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣽⠿⠿⠿⠛⠷⠾⠇⠚⠙⠿⠟⠺⢽⣏⣿⢿⣿⣷⣼⠈⠉
⠀⠀⠀⠀⠀⠻⣿⣟⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣈⣣⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀⣀⣨⣿⣿⡦⣄⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⣈⠀⠀⠀⠹⠆⠁⠀⠀⠀⠀⠉⠫⠭⠿⠩⠅⣭⣿⣿⣦⣒⡖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣳⡀⠀⢀⣀⣀⠀⢀⠔⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡄⠟⠉⠁⠈⠂⠈⠀⠘⠳⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⣴⠿⠂⠐⠲⠂⠶⠺⠆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠄⠀⠀⠀⠀⠀⠀⢶⠆⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣤⠉⣡⡤⠄⠀⠧⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢺⠀⠀⠀⠀⠈⠉⠉⠀⡀⠀⠈⠦⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣀⠘⢁⠄⣰⡣⠤⣿⠦⣄⡀⠀⢀⠀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠐⡟⠘⡀⠀⠀⠰⠹⠆⠈⢘⠢⣸⠞⠁⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠐⣁⢰⣇⣄⣀⣤⣴⡶⢇⠹⣇⠠⠤⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠥⠀⠀⠀⠀⠀⠀⠀⢀⠈⢽⡟⢛⣧⡛⠀⠀⠀⢷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡋⠀⠀⠀⠀⠀⠚⠄⡀⠀⠀⡠⠂⠀⡒⠢⢄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠃⠀⠀⠀⠀⠐⠁⢀⠠⡆⠀⡆⢀⠠⡇⠀⠒⠄⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⢁⠸⡇⠀⢀⠀⠀⠲⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢈⣧⡟⠀⠀⢀⡀⡁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢢⡀⠀⠀⠘⢁⡶⣄⠄⠀⠀⠈⢋⡅⠇⣤⡝⠍⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠰⢂⠄⠀⠈⠉⠀⠙⠄⠂⠀⠀⡄⠀⡾⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠂⠀⠙⠒⠂⠀⠐⠚⠀⠙⠚⠁⠀⠲⠒⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⣶⢰⠀⠀⢸⣱⠁⠀⣼⡌⠁⡠⠁⠀⢀⣖⠀⠀⢀⡀⠀⢔⣨⣽⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡕⢸⢃⠀⠀⠀⢹⣼⡀⠀⣿⡿⠀⣸⡟⠀⣷⠇⠀⠀⣾⠏⢀⡴⣫⠔⠊⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡌⠀⢸⡘⣆⠀⠀⠀⢻⡇⠀⢹⣇⠀⣿⠃⠀⣿⠀⠀⢰⡟⢠⣯⠞⠁⠀⣀⣀⣤⣄⣀⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⢸⡇⠈⢣⡀⠀⠀⢻⡀⠘⣿⠀⣿⠀⠀⣿⡆⠀⢸⣷⡟⢁⣤⣾⣟⣻⣯⣭⢀⠉⡏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠸⣿⡀⠘⡟⡆⠀⠙⣦⣀⠀⢷⠀⢿⠀⣿⡇⠀⠸⣷⡀⢺⣟⣴⡿⠛⠋⠁⠀⠀⠀⠀⠙⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⣌⠉⣇⠀⠀⠙⢿⣄⣻⡁⠀⠀⠈⠻⣕⡜⡇⢸⡇⢻⣷⠀⠀⢻⣧⣼⡿⢋⣀⠤⣤⣤⣶⣶⢦⡤⡜⠘⠇⠡⡀
⠀⠀⠀⠀⠀⠀⢄⡙⠚⣟⠪⢷⣶⣤⣤⣹⣿⣇⠀⣤⣤⣤⢬⣿⣿⣸⡇⠈⣿⡆⠀⠀⡙⢽⠷⠋⣠⠝⠒⠚⠂⠒⠒⡺⢀⡀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠠⠿⠿⣿⠻⢶⣄⡀⠈⠉⠉⠻⠋⢺⡗⠛⠛⠛⢺⣦⣤⠀⠀⠀⠉⠀⠀⠀⠀⠣⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⠂⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⣅⣠⣤⣧⣤⣤⣙⠻⣦⡀⠀⠀⠀⢰⣤⣤⣀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢔⠒⠨⠅⠘⠅⠀⠠⢄⡀⠀⠀⠀⠘⠌⠑⢄
⠀⠀⠀⠀⢸⡿⠛⠉⠀⣾⠀⠉⡓⠶⡃⠀⠀⠀⠞⠈⠉⠟⠀⠀⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠈⢲⡕⠀⠀⠀⠀⠀⠀⢂⠀⠀⠆
⠀⠀⡀⠐⠈⠀⠀⢀⠄⢻⠀⠀⣿⠀⠁⠀⠀⢸⢀⣤⡖⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⢿⡷⠁⠈⠀⠰⠀⠀⠀⠀⠀⠡⠀⠀⢂
⠀⠀⠀⠀⢀⣰⢿⠇⢠⠘⠇⢠⡿⠘⠀⠀⠀⠘⠟⠋⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠘⠀⠀⠀⠘⢦⠀⣼⢃⠎⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⡼⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡏⠈⠀⠀⠀⠀⠀⠀⠘⡁⠑⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⡄⠀⠜⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠔⠀⠀⠀⢀⣁⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠈

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

⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠾⠟⠂⠀⠀⠀⠀⢶⣴
⠀⠀⢀⣁⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⢠⠠⠀⡀⠀⠀⠀⢸⣟⣿⣷⣄⡀⠀⢀⣀⡤⣶⣤⡀
⠀⠀⠀⢱⡌⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣿⣋⣿⡿⣟⣿⡿⣟⡵⣾⣿
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⢀⣴⣿⡟⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣼⣟⣉⡵⢿⣾⡃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣼⢳⠀⠀⠀⢹⣶⣿⡿⠛⠀⠀⠂⠙⠉⠀⠀⠀⠒⠳⢬⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠉⠉⠁⠀⠉⠘⣷
⠀⠀⠀⠀⠀⢹⡏⠈⠉⠁⠀⠸⣿⡇⠘⣧⠀⠀⠀⠉⠉⠀⠀⠀⣶⠀⠠⣄⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠉⠓⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠘⣦⠀⠀⠀⠀⠉⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠴⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⣀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶
⠀⠀⢀⡤⠞⠉⠀⠉⠈⠉⠀⠀⢸⡉⠣⠀⠀⣾⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣼⢻⡟⣿⣿⣇⡿⠿⡿⣿⣿⣿⡿⡟⣿⣿
⠀⢠⡿⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⢦⣤⣴⣿⣇⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣭⣛
⠀⠙⣿⠄⠀⢀⡀⢀⣤⣿⣿⣿⡃⠀⠀⣿⣿⡿⠿⣅⡈⢃⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⣿⣯⣿⠿
⠀⠀⢻⣇⢠⣾⣷⣽⣿⣿⣿⡿⢷⠀⠀⣿⠀⠀⠀⠀⠹⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠐⢸⣿⢛⡿⠿⠿⠛⠋⠁⠀⠘⣆⡀⠀⠀⠀⠀⣼⣂⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⣟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠋⢻⠀⠈⢆⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉
⠀⠀⡀⢿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⣼⠀⠀⠀⠀⢹⡀⢀⣤⡀⢀⣤⡄⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠓⠺⠟⠃⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠘⠛⠃⠀⠀⠀⠈⠘⠁⠀⠀⠀⠉⠱⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠀⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢮⡜⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢳
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣎⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⣿⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠣⣀⣶⣤⣴⠀⣠⣼⠄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⣿⣿⣿⣿⡇⠀⠀⠀⠠⣤⠀⠀⠀⠀⠉⡇⠀⠉⠑⢆
⠀⠀⠀⠀⠈⠃⢠⡈⡿⠿⠁⠀⠀⠀⠀⠀⠁⠘⠁⠈⠿⣷⡄⠀⠀⠀⠀⠘⣿⣿⣿⣟⣽⣿⠿⢿⠃⠀⠀⠀⡆⠙⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢠⡀⣀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⠃⠀⠀⢀⡄⠀⠝⠻⠋⠁⠀⠀⢊⠀⠀⠀⠀⠀⣧⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⡄
⠀⠀⠀⠀⠀⠈⠛⠻⣿⣷⡀⠀⡿⠿⣶⣴⣶⣾⣧⣀⠀⠁⠀⠀⠀⠘⠀⢰⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠓⠶⠂⢴⣿⣷⣤⣀⣠⣴⢿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⡎⠀⠀⠀⠙⠋⠁⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠉⠉⠉⠀⠈⡇⢻⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠷⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠀⠀⠀⠀⠀⠀⠄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠼⠒⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⢀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣶⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⠋⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⣿⠀⠀⠀⢘⣿⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣹⠆⠀⣠⠾⢁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣴⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⣦
⠀⢰⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣶⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣶⣿⣿⣿⣷⣤⡀
⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠋⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠋⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⣿⠀⠀⠀⢘⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⣿⠀⠀⠀⢘⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣽⠆⠀⣤⠾⢁⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣿⠆⠀⣤⠾⢁⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠙⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠘⠙⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡾⠒⠠⢤⣀⠀⢰⠆⢀⣀⠀⠀⢻⣷⠀⢀⡔⣱⠋⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡧⠀⠀⠀⠀⣀⠉⠀⠴⠀⠀⣠⣿⡿⠒⣾⠀⣿⠀⠀⠀⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣇⠀⠀⠀⠀⢸⠀⡤⢀⠄⠀⠈⠉⢹⠀⢻⡀⢿⡀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡀⠀⠀⠀⠸⡄⠉⠁⠀⠀⠠⠂⠀⠀⢸⡇⢸⡇⠀⢸⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠧⠤⠄⠒⣏⣈⣆⠀⠀⡠⢦⣀⠀⠀⠀⣧⠸⡇⠀⣿⣿⣿
⠀⠀⠀⠰⢸⡆⣤⣀⠀⠀⠀⠀⠀⡀⣀⣀⡀⢰⡀⠀⣀⠀⠀⠀⢀⠀⠀⢀⣼⠋⠒⠋⡀⠀⠈⠙⠓⢦⣿⠀⡏⢸⣿⣿⡇
⠀⠀⠀⣧⣿⡇⡇⢻⡆⠀⠀⠀⠸⡇⠈⢷⠀⠀⢀⠇⠈⠣⠀⢠⠎⢀⣴⠏⠁⠐⡀⠀⢹⣀⡀⠀⠀⠀⢸⢰⡇⣿⣿⣿
⠀⠀⠀⢹⣿⡟⢳⣸⣇⢶⣖⠲⠦⠥⠤⢈⣃⣀⣈⣃⣀⣁⣀⣈⠐⠛⠁⠀⢀⡞⠀⠀⢀⡟⠉⠛⠒⣠⡾⠛⢸⣿⣿⡏
⠀⠀⠀⠻⠽⠇⢰⣺⣿⡦⠙⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⡀⠈⢁⣠⣄⣤⣴⡶⠿⠟⠛⠁⠀⣼⣿⣿⠃
⡰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⣉⣛⣂⠉⠙⣒⠒⠼⠷⠦⣄⣀⡀⣿⢠⡇⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠉⠀⠀⠀⠀⠀⢸⡄⢀⣀⣀⣀⡀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠈⠀⡄⢠⠀⢀⠀⡀⠀⠇⣀⣀⡀⡤⠤⠤⠀⠙⠀⠀⠀⠀⠀⠀⠀⢿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⡇⡞⠀⠘⠀⠁⡄⢰⠀⠀⠀⠀⢧⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣇⣀⣀⣀⣀
⠀⠐⠄⠃⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠸⡄⠇⠐⠶⠤⠤⣤⣀⣀⠀⠸⠀⣿⠀⠀⢀⣀⣤⡤⠤⠶⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠠⢼⡟⢰⣄⣲⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠉⢻⣿⣿⡟⠻⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⡄⠀⢻⣿⣇⠀⠙
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠧⡀⠀⠀⠀⢰⣦⡸⣏⠉⠋⠀⠀⢹⣿⣤⣴⡄
⠀⠀⠀⠀⠀⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣴⣇⣀⠀⢸⣿⣶⣿⣷⣶⣄⣰⣾⣿⣾⣿⠁
⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀⠀⠀⠛⣿⣿⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀⠀⠀⠛⠘⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣴⣄⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣦⠀⠀⣰⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣋⠀⠀⢻⣿⡀
⠀⠀⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⣾⣿⣿⣿⣿⡿⢄⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣷⣻⡔⡙⠻⠿⠛⠛⠛⠚⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⣠⠒⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣇⠀⢄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠳⠤⢵⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠐⢤⣄⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠤⢞⣁⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢸⡀⠀⠀⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⡛⠭⢬⣉⠱⠶⣒⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⠒⠒⠒⠷⣇⠀⠀⠀⠤⣤⣤⣤⠤⠖⠉⠫⠽⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠂⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡄
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠙⠲⣄⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠒⠺⢦⠀⠀⠀⠀⠀⠀⠹⡄⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠹⡈⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠙⢄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠈⠉⠛⠦⡄
⠀⠀⠀⢀⣤⣴⣖⣒⣒⡚⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⡼⠁
⠀⢀⢶⡟⠉⠀⠀⠀⠀⠈⠉⠓⠤⣈⠁⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡹⢦⠄⠀⠀⠀⠀⠙⠒⠋⠉⠛⢐⡆
⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠓⠦⠤⢄⡀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢭⣹⡄⠀⠀⠀⣠⣤⣤⡀⠀⢀⡴⠉⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⡀⣾⡿⠛⠛⠃⠈⢳⡟⠸⠃⢕⠸⠷⣶⣁⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⠈⠙⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠈⠙⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⢀⣀⠠⢀⠐⡇⠀⠀⣠⠄⠀⠀⠀⠘⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⢸⣆⣲⣽⣷⣆⠀⠶⢾⣶⢧⣾⡶⢷⡎⢐⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠀⢠⣄⠹⠛⠉⠁⠀⠀⠀⠉⠔⢡⠇⣀⡈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢷⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢾⡇⣀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⣌⠁⢘⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠤⣤⡤⠄⠀⡀⠀⠛⡇⠈⠆⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⠀⠀⡠⠦⠀⠀⣀⠃⢸⣷⡄⣀⣠⣾⡖⣦⡀⠀⢛⠆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡅⠀⠨⣾⠇⠀⠀⠀⠀⠀⠉⠉⠟⠋⠁⢀⠐⠁⠀⠀⢳⡄⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠐⣧⠀⠀⣿⠆⠀⠔⠹⣧⢄⠀⢂⣆⠈⠻⠙⠚⠆⠀⠀⠀⡉⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠠⠀⠉⣠⣾⠉⣀⣼⠀⣴⣿⠿⠿⢚⣟⠓⢶⣤⣄⠠⠀⢦⡐⢀⣾⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠐⢡⣾⣿⠈⡟⠘⠁⠀⠒⠤⣏⢿⡶⠀⠉⣙⢷⣀⢸⣷⣾⠃⢈⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⠀⠀⠀⠀⣼⠗⠈⡼⢃⠄⣰⠀⠀⠏⠈⢱⠀⢀⡉⣶⠙⣿⣯⡧⠀⠒⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⣀⠠⠀⢘⣡⣡⡀⣿⣴⣾⣠⣴⣿⣾⣾⣿⡿⣇⠸⣿⡇⠶⠶⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⠀⠀⠀⣠⠤⡠⠂⠎⠁⢉⣡⠄⠿⣻⣿⢻⠿⢻⡎⠻⠎⡥⡀⠠⢌⣷⣖⡦⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠤⠊⠀⠠⣐⣬⢀⢚⡧⠀⢽⢸⡇⢰⠻⣿⢧⠀⠈⢮⢀⡀⠉⠣⣄⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠋⡱⠃⣠⠜⠀⠨⢱⣿⡋⡃⢨⡛⠏⠻⠦⡑⠟⠂⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣉⡏⠀⠀⠀⠀⠀⠀⠀⡴⠛⠐⠋⡠⣴⣎⢦⢻⡌⢃⢁⢨⣟⠢⡔⢶⣬⣦⡀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠿⢱⡏⢸⣼⠛⠸⣾⢨⢻⡄⣄⠀⠀⢠⣄⢀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡄⠒⢃⠀⠀⠀⢠⡴⠂⠠⠀⠀⠈⠃⠈⣾⠋⡏⣄⠀⢿⣇⠡⠁⢼⠀⠀⢀⡙⢷⡀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠊⠁⠀⠀⠀⠘⠁⠚⠀⠄⠀⠀⠀⠀⠞⠌⡃⢸⣧⣼⣿⢠⡄⠸⠆⡄⢀⠻⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣅⣠⠄⠀⠀⠀⠠⢃⣴⠴⢇⡄⡀⢠⠀⠀⠀⡇⢿⣿⣿⠀⣿⠃⢠⣾⣿⣤⣷⠈⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡥⢳⣶⡄⠀⠀⠀⠈⠁⢠⡿⢿⣧⣦⢀⠀⡆⠁⢸⡏⣿⠆⡏⣰⣿⣏⠻⠈⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣼⠐⢂⠀⠀⠔⠚⠉⠀⡞⢻⡝⢿⣤⠇⣢⠀⣧⠋⠈⣿⣿⢏⠀⠀⢀⠀⠀⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⣋⣞⡏⢀⠄⠀⢠⣤⠟⢠⡀⢡⢠⠁⣀⣟⠀⣿⣴⣰⡿⠀⠀⡠⢀⠀⠐⣌⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠈⠋⠀⠉⠛⠛⠃⠁⠈⠉⠉⠉⠀⠉⠙⠋⠀⠙⠀⠛⠛⠛⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠⠄⠀⠀⠈⠀⠛⠐⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣶⣶⣶⣦⣤⠀⠀⠈⠙⠲⠤⠰⠘⢀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⣾⠇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠛⠁⠀⢿⡖⣦⢀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⣀⣶⣦⡄⠀⠀⠀⠀⠈⢿⣿⣷⣦⡄
⢠⣤⠄⠀⠀⠀⠀⠀⠻⠟⢀⡀⠀⠀⣤⣄⡀⠀⢈⣾⣿⣯⣵⣶⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣴⡀⠀⠈⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠓⠙⠛⠛⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠻⠟⠓⢲⣦⣤⣤⣤⣄⠈⠙⠛⠁⠈⠉⠉⠉⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠷⠶⠿⣿⣿⣿⣧⣄⢀⡀⠁⠀⠀⠀⠀⢀⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⢿⣿⣯⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢫⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣏⢿⡸⣻⡇⡇⢸⠃⣶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡼⢚⡿⠙⡃⢓⠛⢼⢃⣾⠋⡠
⠀⠀⠀⠀⠀⠰⣾⣿⢆⡞⡅⣰⢡⠏⣴⠆⡘⠃⣼⠖⠋⢀
⠀⠀⠀⠀⣐⣺⣿⠆⣿⣾⡁⣿⢸⣤⠏⣼⠏⣤⠁⢠⣾⠟⢁⡀
⠀⠀⢀⡈⣩⡭⡍⣰⣧⢿⢳⢿⢌⡏⣼⢋⡼⢃⡴⠈⢡⡶⠛⣡⡀
⠀⣰⣿⡇⠲⣿⣽⡻⠸⠞⠋⢿⢸⢱⢣⢞⡴⠋⣠⠾⣀⠰⠾⢛⣷
⠀⠻⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⢋⡎⣰⠟⣠⠞⣡⡾⣿⢇⠸⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⣠⣴⣶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⢫⣞⡵⢛⡽⢛⡽⣻⣳⢻⠟⣤⢤⣤⡤⡄⣤⡄⣠⠄⣠⣶⠟⠋⣡⣶⣿⢟⣩⡶⠟⣋⣭⣤⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣁⣴⢟⡴⢋⡾⢱⡏⣾⢠⡟⢸⣿⣼⢁⣿⡿⠋⣼⡿⠁⣠⣾⣿⢟⡵⠟⣡⣴⠟⢛⣩⣥⣶⣶⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢡⡟⣵⠟⡀⣿⢰⡇⣼⠇⣼⣿⠇⣸⣿⠇⣼⠏⢀⣾⡿⢟⡵⢋⣴⡾⠋⣠⣶⠿⢛⣩⣥⣶⣆⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⣴⢏⣼⢏⡞⢰⡇⣼⠁⣿⠀⣿⡿⠀⣿⣿⡾⠁⢠⣿⠏⣠⠋⣠⡿⠋⣠⡾⢋⣥⣾⠿⢟⣛⣭⡥⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣡⣾⢋⡾⢡⣿⢡⣿⠀⣿⡆⣿⡇⠀⣿⣿⠀⢀⣿⡏⠀⢁⣼⠋⢠⠞⣡⡴⠟⠉⣐⣚⣉⣭⣴⣾⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣵⠟⣱⡿⢣⠟⢹⡇⢻⣧⠸⣿⠀⠘⣿⡀⢸⣿⠀⢀⡾⠁⠀⢁⠞⢋⡴⠞⢛⣋⣩⣭⠽⢿⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣉⡴⠋⡴⢋⣴⡄⢿⡈⣿⠀⢻⡇⠀⢹⡇⢸⡏⠀⡼⠁⠀⠐⢁⡀⠉⠠⠚⣉⠥⠶⠶⣞⣿⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣞⡵⣛⣅⡹⡌⠇⢸⠀⢸⡇⠀⢸⠃⠸⠁⠀⠀⠀⠠⢴⣿⡿⠷⢤⣀⣠⠴⠶⢛⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢯⣭⣅⠹⠄⠀⠀⠈⠀⠠⠤⠤⠐⠒⠈⠀⠀⠀⠀⢴⠶⠶⠖⡟⠑⠖⣛⣭⡵⣿⡝⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣩⠁⠀⠀⠉⢺⣫⣭⣽⣎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⡆⠀⠀⠀⠀⠙⣿⣯⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢭⡽⠃⠀⠀⠀⠀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣽⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠃⣸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠿⠏⣰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⢠⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠤⠠⠀⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣦⡄
⣶⣶⣶⠶⣶⠒⣶⣶⣶⠖⢿⣿⣿⣿⣿⣿⡡⣀⣠⣄
⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣠⠖⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⠄⠀⠀⠐⠻⠿⢤⠄
⠀⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠐⠆⠀⠀⣸⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⣁⣦⣬⣄⢠⣄⣀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⡈⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⡀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠛⢿⣿⣿⣿⣼⣷⣴⣿⣿⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⣠⣴⣾⣧⣀⣤⣴⣶⣄⣴⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢟⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣶⣿⣿⠿⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣿⣡⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⣶⠤⠤⠤⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠒⠒⠒⠒⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⠂⠋⠀⠀⠰⠶⠀⠀⠀⠀⠈⠑⢢
⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠤⠄⣀⡀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠖⠁
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠙⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⣇⠈⠒⢄⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⢤⠂⠀⠀⠀⢰⠁
⠀⠀⠀⠀⡏⠀⠀⠀⢙⡄⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢣⠀⠀⢠⠃
⠀⠀⠀⠘⠀⠀⠀⡠⠃⡇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡎
⠀⠀⠀⠸⡀⠀⠀⡇⠸⡀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠰⡃
⠀⠀⠀⠀⠱⡀⠀⠱⣄⠑⢤⡀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠺⣄⡀⢑⣦⣄
⠀⠀⠀⠀⠀⠱⣄⣀⠀⠭⠽⠯⠲⠄⠀⣙⣳⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⠴⠒⠛⠛⠛⠛⠛⠒⠢⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠈⠉⠑⢦⣤⣀⣤⠖⣻⠽⠛⠋⠉⠀⠀⢀⣈⠁⠀⢀⣠⡟⠻⠆⠨⠻⣗⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⡠⠊⠀⠀⠀⠀⠀⡄⢠⡾⠇⠀⠀⠈⠋⠑⠀⠰⣦⠀⠙⣷
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⢤⡁⢨⡇⠀⠀⠀⠀⠀⠛⣆⠀⠁⠠⠀⢉⢦
⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡝⡞⠃⠀⣠⠞⠁⠀⠀⠸⠀⠓⠀⠀⠴⣱
⠀⠀⠀⠀⠀⢠⢛⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀⣤⢸⡷⠀⢀⠔⠂⢀⠀⢴⢿
⠀⠀⠀⠀⠀⠈⢸⡥⠀⠀⠀⠀⠀⠀⠀⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠁⠀⠀⠀⠠⠔⠂⢀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⣀⣞⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⠀⠀⠀⠀⠀⠀⠀⠉⢀⢶⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢻⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⡈⡇⠀⠀⠀⠀⠀⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⢡⠸⣆⠀⠀⠀⠀⠀⠀⠘⠈⡀⡏⠙⠶⣤⣀⡀⠀⢀⣀⡀⠀⠀⠀⠂⠀⠂⢹⡿⣿⣷⣐⣄⠠⡀⠀⠀⠉⠄⠼⣄
⠀⠀⠀⠀⠀⠀⠈⡄⢻⡆⠀⠀⠀⠀⠀⠀⣰⠃⢀⢀⡀⠀⠉⡛⠛⠛⠟⣿⣷⣶⣶⡤⠶⠶⠋⠁⢸⠀⢻⠉⠳⣿⡀⠀⠀⠈⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⡄⠀⠀⠀⠀⠀⢾⠆⠀⠈⣧⠰⡷⢻⢀⣀⢀⡀⠀⢉⡰⠀⠤⠀⠀⠀⢸⠀⠈⢧⠀⠻⣧⠀⠀⠈⣆⡜⠳⣝⢄
⠀⠀⠀⠀⠀⠀⢸⠃⢇⠀⢻⡄⠀⠀⠀⠀⢘⣾⣆⠀⠀⠀⠉⠈⣷⣇⡟⡁⢼⣟⣡⣴⠇⠀⠀⠀⣸⠀⠀⠈⠳⣄⠙⢦⡀⣀⡐⣛⠀⠈⠉⠳
⠀⠀⠀⠀⠀⢀⡇⠀⠈⠆⠀⠻⣄⠀⠀⢲⣾⣿⣿⡆⠀⠀⠀⠀⠈⠁⣾⣧⠤⢴⣾⣿⠃⠀⠀⠀⡏⠀⠀⢠⢎⢈⡿⣦⣽⣿⣅⡎
⠀⠀⠀⠀⠀⢼⠇⠀⠀⠘⣆⠀⠀⣵⣆⢸⡷⠿⠿⣷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⣧⠉⠯⠀⠀⠀⡇⠀⠀⢼⠀⠸⠴⠃⠸⠇⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣸⣇⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⡇⠀⠀⠸⣦⡀⠀⠀⣠⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⣿⠘⡇⠀⠀⢸⠀⢠⡸⣶⢣⡇⠀⠀⠀⠀⠀⢧⠀⠐⠂⠀⡇⠀⠀⠀⠈⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⢈⡀⢧⠀⠀⢸⠀⢸⠇⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⢾⣿⠘⡆⠀⢸⠀⠀⣿⣧⣸⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠸⣿⣷⢷⠀⢸⠀⠐⢹⣿⣿⠀⠀⠀⠀⠀⢠⣿⡀⠐⠄⢀⠏⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠯⣽⠀⢰⣿⢸⡆⢸⠀⠄⠡⢄⣹⠀⠀⠀⠀⡠⠎⠀⠀⢈⣀⡈⠀⢠⣾⣶⢫⡾⣶⣿⣶⣿⣶⣶⢶⡶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢘⣛⠀⢳⣸⠀⠀⠌⠛⢹⡀⠀⠀⠐⣄⣀⠀⠀⠙⢻⠁⠀⠈⠉⠉⠈⠉⠿⠉⠈⠙⠃⠉⠈⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠻⡏⠀⠀⢁⡤⢀⣷⡀⠀⠀⠀⠉⠓⠪⠵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠤⠵⠞⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⣀⡄⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣿⣯⣄⣠⣾⣷⣏⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣻⠽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⣋⣠⠃⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣷⣞⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠸⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠼⣿⣿⠟⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠛⢻⠟⠻⠿⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠋⠉⠉⠋⠀⠘⢿⠟⡅⠀⠙⠙⠋⠉⠏⠙⠻⠿⠿⠁⠈⠣⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⢁⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠘⠃⠈⠁⠙⢦⡀
⠀⠀⠀⠀⠀⢸⣏⢁⣀⣀⣀⣀⣠⣼⠃⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⢻⡄⠀⠀⢰⡏⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⢦⡀⠙⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⠁⣠⣤⡄⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢿⣤⠟⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣰⠷⣦⡀⠈⢹⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢿⣄⣴⠟⠀⠘⠳⠾⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⢡⡴⣦⠀⠀⣀⠀⠀⢸⡟⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠸⠶⠾⠁⣼⠋⠻⣦⠈⠙⠋⠀⢉⣙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠃⣀⡀⠀⠀⠛⠶⠾⠋⢀⠀⠀⢸⠋⢹⡇⠀⣤⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣾⣉⣿⠀⢀⣤⣄⠀⠀⣿⣻⡆⠘⠛⠛⠁⠀⠷⣾⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⠉⠁⠀⢼⣅⣨⠗⢀⡈⠉⠃⣀⠀⢰⠞⠻⡆⠀⠀⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⠘⢧⡀⠉⠁⣀⣿⠁⠀⠀⠘⣧⠘⠳⠞⠃⠀⢰⠶⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡋⠀⢀⢹⡆⢸⡏⣿⠙⠛⠛⠃⠘⢷⣤⣤⣄⠀⠙⢶⡏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣾⠀⣷⠀⠉⣿⠀⠀⠀⠀⠀⣦⠙⢦⡟⠀⠀⢸⡇⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢹⡆⠀⣿⠀⠀⠀⠀⠀⠸⡇⠀⠻⣦⣤⡈⢳⣄⢿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣶⠟⠀⣿⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⠀⠈⣷⠀⢸⠀⠀⠀⠀⠀⠀⢽⠀⢀⡆⢹⡆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⣿⠀⡾⠁⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠈⡇⢸⡇⠀⠀⠀⠀⢀⡟⠀⣧⠀⠈⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⠀⣿⠈⣧⠀⠀⠀⠀⢸⡇⢀⡿⠀⠀⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⣿⠀⠀⢀⡿⠀⡟⠀⠀⠀⢀⡾⠁⣾⠁⠀⣠⡟⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠀⢰⣿⣥⣤⡿⠀⠀⠐⠿⠤⠤⠾⠂⠺⠧⠤⠤⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠒⠈⠓⠀⠒⠻⠷⣶⣤⣤⣤⣴⡾⠿⠂⠀⠘⠋⠈⠻⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢤⡀⠀⠀⠀⢈⡉⠿⠿⢹⡗⠀⠀⠀⣠⡄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⣸⠀⠀⠀⠸⣆⠀⠈⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⢀⣠⠴⠃⡄⠀⠀⠁⠘⢦⣀⣀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⣿⣿⣿⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠉⢭⣿⣿⣿⡷⠄⡀⠀⠀⢰⣦⠀⣀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⢃⣿⣣⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣿⣦⠖⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣇⠀⠀⠈⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡈⠀⠀⢤⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢩⣋⠀⠀⠀⢠⣹⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡟⣾⢟⡦⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠁⠚⡰⢀⡎⢈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⢀⡙⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠜⣡⣾⣾⣿⣏⣸⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⢲⡀⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠐⠁⣨⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⣀
⠄⡠⢀⠀⢀⣟⣁⠀⠀⠐⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠂
⢾⣷⠞⠻⣡⣿⣟⠀⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣾⣿⣧⡾⢡⣾⣿⣧⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣽⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠑⠊⠉⠉⠙⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠷⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠴⠞⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣦⡀⠀⢸⠀⢸⠀⠀⢀⡜⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢧⣟⣲⢾⠀⢸⣤⣴⢿⢶⡤⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⢸⠀⠀⠀⢸⡄⠸⡄⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠀⠀⠀⣸⢧⣠⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣉⡠⢼⣖⢤⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣐⠄⢻⣀⣒⣘⠢⢔⠘⡁
⠀⠀⠀⠀⠀⢀⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠛⠀⠠⢭⢿⠅⠀⠘⢃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢰
⠀⠀⠀⠀⠀⠀⠋⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣄⡀⠈⠻⠃⠀⠰⣿⣷⣴⣿⣿⠀⠀⠻⠋⠀⢀⣴⣷⢄
⠀⠀⠀⠀⠀⢸⣷⡦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠻⠿⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⠸⠿⠛⠁⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⢾⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠷⠀⠀⠀⠀⠀⢰⣤⡀
⠀⠀⠀⠀⠀⠘⠀⢰⣿⠀⠀⠀⠀⢀⠀⠀⠙⠛⠃⠰⣶⠶⣄⠀⣶⠖⠂⣶⠀⠀⠀⣼⡇⠀⣷⠀⣾⠈⠛⠉⠀⢀⣅⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢿⣷⣤⣀⠀⠀⢠⣿⢀⣿⠀⣿⠀⠀⣿⠀⠀⠀⣿⣇⠀⢸⣦⡏⠀⠀⣠⣶⣿⠟⠀⠀⠀⠀⢀⣤⣄⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⢂⣀⡄⠀⠉⠛⠛⠀⠀⠀⣿⣟⠁⠀⣿⠓⠀⣿⠀⠀⢰⡏⣿⠀⠀⣿⡇⠀⠀⠉⠉⠀⠀⠀⣄⣠⠀⠈⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⡿⠀⠀⠰⣷⣦⠄⠀⣿⢹⡆⠀⣿⠀⠀⣿⠀⠀⣸⣧⣿⡀⢀⡿⣷⠀⣄⣤⣶⠆⠀⠀⢿⠟⠀⣤⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⠃⠀⢀⣤⡀⠀⠀⠉⠀⠀⣿⠀⣿⠀⣿⣀⡀⣿⣀⡀⣿⠀⢸⡇⢸⡇⠘⣧⠈⢟⠁⠀⠀⢀⣀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸⣿⡇⠐⠁⣶⡤⢀⠁⠀⠈⠀⠉⠉⠁⠉⠉⠁⠁⠀⠀⠁⠀⠀⠀⠀⢶⣦⠓⠀⣠⣿⡟⠀⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣉⡀⠀⠀⠸⠿⠁⠀⠈⢐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⠀⠀⠸⠿⠀⠀⠀⠉⣵⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠃⠀⣠⣄⠀⠀⠀⢀⣼⡟⠀⠀⠀⣾⡇⠀⠀⠠⣶⡀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⢰⣿⠏⠀⠀⠀⠀⠉⠁⣰⣦⠄⠙⠁⠀⠀⠀⡿⠧⠀⠀⠐⣿⣧⠀⠀⠀⠀⠀⠘⢿⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠁⠀⠀⢠⣶⠄⠀⠀⠻⠋⠀⠀⠀⠀⢸⣦⡤⢀⡀⠀⠀⠈⠛⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠿⢿⠀⣀⠀⠀⠀⣰⣶⠄⠀⠈⠉⠀⠀⡀⠁⠂⠤⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠁⠉⠛⠲⠆⠀⠠⢠⣾⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣠⣄⠀⠀⣀⣀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣦⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⢿⢿⠟⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣹⣯⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠻⣿⠛⢿⡻⣿⡿⠇
⠀⠀⠀⠀⣀⣶⠶⠶⠶⢶⡼⣤⣦⣄⣝⣈⣭⣴⣤⡹⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⠟⠛⠉⠙⠯⣻⣿⣾⣿⡿⣿⣟⠛⠟⠛⢛⠂
⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣉⣉⣉⣍⣉⣿⣿⣴⣤⣤⣸⣿⣿⣿⣿⣿⣇⢀⣀⣠⣀⣄⣄⣠⣤⣤⡷⢻⡄⣉⢻⣭⠎⠀⠀⣤⣀⡀
⠀⠀⠀⢀⣀⣴⣾⣷⣾⣟⣛⡛⠿⠿⠿⣿⣿⣿⣿⣿⣟⡛⠋⢽⣿⣷⣿⣿⣿⣿⣿⣿⣟⡿⣏⣈⣴⣟⠛⠛⠻⠡⠛⠲⠫⣗⠿⣱⢦
⠀⠀⠠⡿⣿⣿⣟⣟⣹⢛⠛⣿⣿⣶⣶⣦⣿⣿⢿⣯⣿⣯⡧⠊⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠁⢶⠠⠂⠁⠀⢀⣀⢀⡀⡭⢤⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠙⠛⠛⠋⠙⠛⠿⠿⠿⢷⣶⠲⠶⠛⠛⠒⠒⠒⠒⠛⠛⠓⠊⠓⠒⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⡀⡀⠀⢀⠀⠀⡀⣀⢀⡀⣀⠀⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠈⠂⠇⠀⠘⠀⠀⠃⠘⠀⠃⠋⠂⠁⠘⠑⠀⠃

⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⣀⡀⢤⣀⣤⣶⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣀⣿⢷⣤⣹⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠙⣿⣿⣿⣿⡿⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣀⠀⠈⢿⣿⣿⡇⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠇⡔⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⣿⣿⣿⣧⡀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢸⠃⡀⠀⠀⠀⠀⠀⢻⣷⣆⡘⣿⠀⠈⠁⠀⠀⠀⠈⢻⣿⣤⣤⣾⡦
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢠⠀⠀⠀⢻⣿⣿⣴⣿⣿⣶⣤⣤⠀⢀⣶⣾⣿⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠠⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠇⣰⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⠀⠀⠁⠿⢿⣿⠰⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠙⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⢀⡀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣦⡀⢀⣀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡿⠋⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡗⢤⣀⣄⣀⣹⣿⣷⡀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠸⣷⣾⣿⣿⣿⣿⣿⣿⡿⢄⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠽⣷⠰⡘⢿⣿⣿⣿⡿⠿⠿⠿⠶⠿⠶⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠿⠦⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⣤⣶⡾⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠋⢭⣾⢇⣿⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⢀⣤⣶⣶⠀⠈⠀⠈⠛⠒⠀⠙⢿⣦⡀
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠠⠄⠰⣿⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠐⠈⠀⠙⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠛⢿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠈⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠈⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢳⡄⠀⣄⢰⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⣆⣹⣾⠏⠀⠀⠀⠀⠀⠀⢀⣰⣴⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⡘⣿⣿⣿⣀⢠⣠⣤⣦⣤⠧⡿⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⣿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠉⢈⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢛⠛⠁⠙⣷⣤⣶⣾⡿⢿⡿⠷⠶⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣥⣀
⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠷⠟⠛⣿⣿⣿⣷⣿⣽⣶⣧⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠾⠿⠿⠿⠿⠿⠷
⣿⡿⠿⠿⠻⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠙⠛⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⣿⡆⠀⠀⠀⠀⠐⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⡿⠋⠀⣠⣴⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠉⠛⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣷⣄⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣿⣯⡀⠀⠙⢿⣿⣿⡆⠀⠈⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦
⣾⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢀⣴⣿⣿⣿⣧
⠙⣿⣦⠀⠐⢶⣾⠂⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⣤⣴⡾⠟⠀⠀⠘⠛⠉⣀⣼⣿⡆
⠀⠈⠻⣷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⣤⣤⣀⡀
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⡷⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⠿⣿⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣶⣤⣤⣶⠟⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠋⠀⠀⠸⠟⠁⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⣿⣷
⠀⠀⠀⠀⠀⠹⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠋⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣏⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠁⠀⠀⠀⠀⠉⠉⠁⡀⠀⣿⣿⠃⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣷⣤⣶⣿⣤⣾⣷⣴⣿⣿⣷⣾⣿⣿⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⡟⠋⠀⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⣶⣄⣠⣄⡀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠻⠿⠛⠛⠉⠛⠉⠛⠛⠿⠟⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡀⠀⠀⠀⣀⣴⣶⣶⣶⣤⣄⠀⣴⣿⠋⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠉⠻⠂⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⢰⠟⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⣾⢃⣼⡿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠁⠀⠀⠀⠀⠀⠀⣿⡈⠛⢣⣿⣿⣿⣿⣧⠙⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠿⣿⣿⡿⠟⠀⠀⠙⠋⢸⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣧⡀⠈⠙⠛⠛⠉⠉⠛⠶⠶⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠉⠀⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣦⣤⣴⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡏⣿⠁⠀⠀⠀⠰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠙⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡇⠙⠇⠀⠁⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⣿⢿⣿⣿⣿⢿⡿⠿⠀⠁⠀⠀⠀⠀⠀⠀⣄⢰⣦⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⣴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⢶⡀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣇
⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡇⠙⠀⢻⣿⠂
⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡄
⠀⠀⢹⣿⠃⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠙⣿⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠏⠁⠀⠀⠀⢠⣿⡟
⠀⠀⠀⢻⣿⣶⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠐⣴⣿⣿⣿⣿⣿⣿⣿⡿⠉⠟⠀⠏⠀⠀⠀⠀⢀⣤⣾⣿⠃
⠀⠀⠀⠸⢿⣿⣆⠀⠀⠀⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⣿⠀⢀⢀⣤⡄⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣆⣼⣿⣿⠇
⠀⠀⠀⠀⠸⢿⣿⣦⡀⠀⠀⢹⣿⣴⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡠⢀⣤⣰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢻⣷⣤⣶⣿⣿⣿⣟⣠⣆⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⢠⣣⣾⣧⣿⣿⣿⣿⣿⡿⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⣽⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⠟⢿⡿⣿⡿⡏⠟⠻⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠻⠿⠉⢿⡆⠀⠀⠀⢹⣿⡆⠀⠁⠈⠁⠀⠀⢸⡏⠀⢠⣿⣿⣿⣿⣿⠟⣿⣿⡿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⡀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⣿⣿⣿⡟⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⢸⣿⣄⣿⣷⠀⠀⠀⠀⠀⣼⠏⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣰⣧⢸⣿⣿⣿⣿⣆⠀⠀⣠⠟⣡⣶⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠻⢿⣿⡇⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠘⢿⡿⠃⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠂⣀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⢠⠆⠉⠀⢀⡀⠈⠑⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠁⠁⠀⠀⢐⠫⢍⡀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢰⣟⣶⡶⡧⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠤⣄⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠓⠻⠖⠁⠀⠀⠀⠀⠁⠀⠘⣆
⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢒⣶⠚⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣸
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠐⠊⠀⠀⢹
⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⢀⡞
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠃⠀⠀⢀⡔⠀⣼
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠚⠋⠍⠓⠒⠁
⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠹⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⠀⡴⠁
⠀⠀⠀⠀⠒⡏⢡⣆⡄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠑⠄⡀⠀⠀⠠⠀⢰⠉⠁⠐⠚⠒⠒⠒⠒⠒⠒⠒⠊⠁⠈⢀⠨⢄⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢀⠆⠀⠀⠀⢀⣼⠃⠄⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⠀⢀⡇⠀⡎⡈⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠐⡀⠈⠀⠸⡀⢧⡀⠡⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠘⣄⠀⠀⢡⡀⠉⢦⡀⠀⠓⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⢧⡀⠀⢀⠈⠀⠢⡤⡀
⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣉⣉⣓⣻⢄⡀⠀⠒⠢⠍⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⡹⠒⠒⠠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡀⠉⠀⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⢰⣇⣠⠀⠀⠀⠔⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠈⠈⡫⠴⢺⠟⠋⠀⠀⠈⡀⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⢀⠀⠀⠀⠀⠀⠜⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⢀⠀⠀⡎
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠈⠁⡧⢀⣀⠢⠈⠂⡅⠀⡠⣄⡀⢀⠄⠀⠀⠀⠀⠀⠂⠀⡸
⠀⠀⢧⡤⠒⠄⣀⡀⠀⠀⠀⠀⣀⣀⣠⣄⡆⠉⠉⠉⣁⠀⠀⠣⠀⠀⠙⠀⠔⠒⠀⠜⠳⢶⣌⠀⡠⠂⡀⠴⠁⠐⠂⠈⠈⢣⠃
⠀⠔⢦⣉⣄⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠌⣃⠀⠀⢀⣀⠀⠤⠀⠉⠁⠀⠀⠠⠀⠀⠒⠀⢠⠃
⠀⠘⡂⠷⣄⠀⢀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⣂⢣⡀⠀⠤⠀⠀⠢⠀⠀⠀⠀⠈⠀⠀⠍⠀⠰⠖⠈⠀⠀⠀⠀⠂⠀⢠⠏
⠀⠀⠈⠪⡉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⢄⣀⠀⠀⠀⠀⠳⠀⠀⡞⠀⠀⠀⠐⡁⠊⠀⢠⠏
⠀⠀⠀⠀⠈⠢⣀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠨⣐⠒⠐⠒⠃⠀⠃⠀⠀⠀⠔⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠓⢬⡀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⡀⠀⢀⠀⠂⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⢀⣴⠣⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⡀⠤⠚⠓⠦⣀⠀⠀⠀⠀⠀⠉⠁⣀⡤⢒⣁⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠐⠉⠀⠀⠀⠀⡀⠤⠛⠛⠒⢒⣒⠬⠝⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠔⠊
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢨⠀⠀⠉⡅⠀⠀⠁⢤⠤⠤⠤⠤⠤⣤⠠⠀⠀⠀⠀⠀⢀⡀⠅⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠰⠸
⠀⠀⠀⠸⠀⠀⢈⠀⠀⠤⡀⠆⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⡂
⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⣀⡀⠀⠀⠀⡀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠆⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠠⠖⢠⠜⠉⠣⠀⠀⠉⠓⢤⠤⠥⢆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡠⠊⢉⣰⠎⡀⠔⠉⠀⠀⠀⡀⠀⠈⠉⠐⢱⡆⡈⠉⠷⠒⠒⠛⠘⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⣧⠔⠁⠀⡌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡼⠁⢉⠁⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡌⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠃⠀⠀⣰⠠⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢄⡀⢀⣀⣀⣀⠀⠀⠠⠊⠀⠀⠀⠀⠸⣇⠘⣖⣲⠆⠁⠈⢂
⠀⢀⠀⠀⠀⠀⣿⠄⠀⠤⠂⢁⡁⡀⢀⢀⡀⠀⢉⠐⠖⡀⠒⠐⣃⣤⡈⠉⠉⠀⠊⠉⠉⣨⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠀⠀⠀⠀⡏⠤⡎⠀⣀⠿⢣⠄⠀⠀⠄⣉⠞⠵⡀⢘⠀⠀⠉⠘⠁⠉⠉⠉⠋⠉⢻⣿⣉⣉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠰⠄⠲⠚⠚⢁⠄⠊⠐⠄⠂⢀⠀⠁⠀⠉⣛⡛⢛⠂⠻⣃⠀⠂⠂⠀⣶⣼⢇⡀⡈⣧⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠃⠀⠄⠀⢀⠥⢠⠀⠈⠁⠉⠂⠁⢤⠤⢄⠁⠈⠡⠃⠀⠩⡉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⡞⠄⠡⠔⠂⠇⢀⠌⠈⠓⠒⠐⠒⠂⠈⢄⢀⠃⠐⠀⠀⠄⠈⠡⠀⠐⠠⢤⠔⠈⠀⠀⠀⢠
⠀⠀⢠⠘⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠃⠀⠀⠈⠉⠀⠉⠉⠉⠁⠀⠀⠓⠀⠃⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠤⠤⠬⠥⠍⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⠀⢀⠀⣀⣀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣷⣾⢽⣷⡞⠏⠛⠛⡛⠛⠛⠫⠙⠛⢿⠛⠻⣖⣛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠻⣿⣶⡝⠊⠀⠐⠀⠀⠀⢀⣂⣀⣂⣀⣀⡀⠈⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡊⣭⣥⣴⣶⣾⣿⣿⣿⣿⠏⢉⣿⣉⣉⣹⣿⣿⣿⡟⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠻⠿⠿⢿⣿⣿⣿⣿⡟⢀⣾⡿⠃⠀⠛⠻⣿⡿⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⢸⣿⣿⣿⣿⢣⣿⡿⠁⠀⠀⠀⠀⠈⢣⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠂⠄⠈⠉⡉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠠⠂⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣴⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠂⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠔⠀⠐⠡⡂⠵⢒⢬⣆⡂⣁⡀⠀⠀⠐⠦⠴⠞⠶⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⢀⠀⠀⠀⠀⠀⠀⠀⠟⠝⠛⠿⣿⣶⣶⣦⣤⣤⣤⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣀⠈⠀⠀⠀⢄⠀⢀⠀⢤⡀⠀⠉⠙⠿⠿⡿⣟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡠⣠⣝⢦⢑⣕⢱⡣⣻⣇⠀⢀⠒⣠⣵⣾⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⡀⡻⢦⢣⠹⢿⠆⣽⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⣆⠈⣪⠀⣴⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣌⣦⣿⣷⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡆⠀⢰⣿⣆⠀⠀⠀⠀⠀⢸⡇⣡⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⡄⢀⠀⠀⠀⠀⠠⠊⡤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣄⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⠛⠻⢿⣿⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠘⠛⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠈⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢀⣼⣿⠟⠋⠙⢮⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⢉⠛⠻⡅⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⣴⣿⣿⣷⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⡐⢸⣿⣿⣿⡿⠿⢶⡿⠏⠉⠉⢛⠿⠖⣄
⠀⠀⠀⠀⣠⣴⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⠉⠉⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣄⡀⠀⠀⢠⠛⣮⢉⡟
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣛⡿⠛⠋⠉⠁⢀⠀⠀⣈⣅⠀⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⢠⣿⣿⣿⣿⣟⣁⣈⡉⠉⠿⠰⠆⠀⡀⠂⠀⣀⢌⠄⠉⠀⣸⢫⣿⣿⣿⣿⣿⣟⣹⣿⠛⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡕⣉⣂⣻⡿⠛⠛⠁
⠀⢸⣿⣿⣿⣿⣿⡿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⢀⣦⣷⣾⣿⣿⣿⣟⡍⣿⡿⣿⡄⢵⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠸⣿⣿⣿⢿⣿⣇⡛⡇⠀⠁⠚⠴⠀⠘⢀⠀⡔⡀⠁⢰⠀⢈⡹⠋⢹⠿⠟⢆⠘⣹⠟⠳⡏⡟⠀⢸⣏⡿⣿⣿⠿⠛⠉
⠀⠀⢿⣿⣿⣿⣾⣿⣿⣷⡀⠀⠀⢀⡀⡴⠠⠀⣥⣿⠄⠒⠀⢬⣧⣤⣴⣼⣄⣘⠏⣠⣠⣄⡈⢃⣠⣿⣿⡷⠟⠁
⠀⠀⠈⠿⣿⣿⣿⣿⢻⣵⣇⡼⣷⣿⣿⣿⣄⣼⣾⡆⢠⣤⣶⣿⢿⣿⣿⣿⣿⣟⡔⡁⠊⠝⢻⠿⣿⣿⡟⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣻⡇⣿⣿⣿⣿⣿⣿⢸⢻⡗⣉⣹⣿⣸⡝⣿⣿⣿⣿⣿⣷⣶⠗⢂⡀⠿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣾⠟⠋⠉⠛⠋⠙⠛⠉⠁⠉⠀⠉⠛⠁⠉⢹⣷⣴⡟⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⢿⡉⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠈⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣦⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⣀⣠⣿⣿⣿⠶⣬⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣷⣀⣘⠁⠀⠀⡈⠿⠄⠀⠀⠀⠀⠈⠁⠛⠯⡍⢿⡏⣉⣁⣉⣿⣿⣣⣔⢲⠶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠟⠛⠏⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠄⠀⠠⠀⠄⡀⠀⠀⠀⢀⡀⠠⠤⠤⠀⢀
⠀⠀⠀⠀⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⣀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠌⠁⠐⢄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠁⠃⠀⢐⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠁⠀⠀⠀⠀⠠⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠁⣀⠠⢄⡀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢐⠀⢰⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠾⣇⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⡛⠻⢯⣿⠻⠎⣹⢿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣓⣒⠀⠀⠄⠁⠀⡫⣽⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢟⡻⣿⣿⣿⢟⡻⣿⡿⢶⣤⣄
⠀⠀⢰⣿⣿⡿⠋⠐⠺⠖⠄⠐⠐⠲⣾⠋⡀⠁⡈⠪⢯⣉⢻⣿⣿⠟⠅⠀⠀⠐⡿⠿⠉⠙⠓⠘⠛⠀⠘⣫⣼⡇
⠀⠀⠀⢹⣿⣿⣿⣮⡤⠩⠬⢀⠀⠀⠀⡸⡠⠀⠐⠀⠀⠉⠋⠛⠳⡂⠀⠀⠀⢀⡀⣀⢺⣶⣀⣤⣴⡖⣤⣹⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣞⠂⠀⠠⡤⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠘⠛⠃⡀⢀⣲⣵⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁
⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⡤⢴⣣⣦⡟⠀⠀⢀⣀⡀⠀⡀⢠⡀⠅⠀⣶⣾⣿⡿⢛⣿⣿⡿⠟⠁
⠀⠀⠀⠀⣾⣿⡿⠛⢿⣿⣦⢿⣿⣿⣿⣾⣶⣾⣦⣼⡆⠄⣈⣅⣾⣿⣿⣿⢛⣡⣾⠟⠁
⠀⠀⠀⢰⣷⣿⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠉⠛⠻⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠄⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⢸⡿⣿⣿⣆⣀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠋⠉⠻⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⢨⠋⠉⢸⣿⣷⣄⠀⠀⠀⠀⠀⢀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠐⠀⠸⣤⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠻⣿⠟⠀⠀⠀⠀⢼⣿⣷⣀⠀⠀⠐⠀⠠⠤⢀⣙⡿⣦⣄⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⢧⣀⡤⠒⠂⠉⠒⢦
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠄⠤⠃⠈⠁⠀⠀⠀⠀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠖⠋⣿⠉⠳⣄⠀⠲⡄
⠀⠀⠀⠀⠀⣠⢊⡤⠛⠂⠀⠀⠀⠖⠫⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠆⠀⡏
⠀⠀⠀⢀⡞⠁⠎⠴⠒⠢⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠖⠋⡠⠀⢠⠏⢀⠜
⠀⠀⢀⠎⠀⠀⠆⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⡴⠃⠠⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢸⠀⠀⠀⠀⠑⠒⠒⠚⠉⠉⠑⠢⢄⣀⣀⣀⡤⠴⠚⠁⣤⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠑⡄
⠀⠀⠀⠑⠠⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠉⠓⠦⢄⣀⡀⠀⠀⢀⡴⠋⢁⠄⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣳⣤⣤⣀⠀⠀⠀⠀⣈⣩⠟⠋⢀⡴⠁⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⢢⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠈⠉⠓⠛⠋⠉⠀⠀⡠⠋⢀⣀⡤⠤⠴⠾⠷⠤⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⣇⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⢲⠖⠛⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢦⣤⣤⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈⠉⠲⡟⠛⠉⠉⢹⡇⠀⠀⠀⠀⢸⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢸⡇⠀⠀⠀⠀⠸⡧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣀⣤⣷⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⢤⣤⣤⣄⣀⣤⡤⠴⠖⠛⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠻⣯⢰⣿⡎⡇⢸⠇⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠿⡞⠸⠃⠇⠾⢠⡏⣰⡟⠀⡀
⠀⠀⠀⠀⠀⠀⣴⣾⢏⢄⡞⡁⣠⢡⡞⢠⡌⠐⠟⢀⣮⠴⠂
⠀⠀⠀⠀⠀⣤⣾⣋⣣⡏⣼⠁⡇⢸⢀⡿⢡⡷⢀⠛⠁⢀⣴⡷
⠀⠀⠀⠠⠖⣒⡲⠧⣸⢿⣿⢠⢿⢸⡿⢡⡿⢁⡾⢁⡀⠟⢉⣤⡾
⠀⠀⣴⡆⢚⡻⡽⡰⡏⣏⣯⠾⣼⢸⢃⡟⣰⢟⣴⠟⣠⡄⠛⣁⣴⡿⡄
⠀⣼⣿⣧⣤⠽⠟⠓⠁⠉⠀⠀⠋⡜⣸⠐⣡⠟⢡⡾⢋⣥⡦⠙⣁⣪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣱⢣⡾⢃⡴⣋⣴⢟⡯⣾⣷⡹⣯⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⢒⣡⣴⣿⠟⣛⣭⡵⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣱⡯⠞⢉⡴⣫⡾⣫⢏⡟⣽⢙⣷⢲⣶⡆⡖⢰⣶⣰⠞⣠⣾⠟⠉⣠⣴⣿⠿⣫⣴⠟⢋⣥⣴⡶⠿⠷⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣋⣤⡶⢋⡼⢋⡼⠃⣾⢡⡏⢸⡇⢸⣿⣼⠁⣿⣿⠋⣰⣿⠋⢠⣾⣿⠟⣡⡾⢋⣤⡾⠟⢉⣤⣶⣶⡿⠷⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠟⢠⡟⣱⡿⡡⢸⡇⣼⠁⣿⠁⣾⣿⡇⢸⣿⡇⣰⠟⠁⣰⣿⠟⣡⠞⢁⣴⠟⠉⣠⣾⠿⢛⣩⣴⣶⣾⡆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣴⠏⣼⡟⣰⢃⣾⢀⡿⢰⣿⠀⣿⡿⠀⣾⣿⡿⠃⠀⣼⡿⠁⡴⠋⣴⡟⠁⣠⡾⢋⣡⣾⡿⠟⣛⣭⣵⠆⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣼⠟⣼⠃⣼⡟⣼⣧⢸⣿⡄⣿⡇⠀⢿⣿⡇⠀⣸⣿⠁⠈⢀⡾⠋⣠⠞⢁⣴⠟⠋⠁⣚⣉⣩⣥⣶⡿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣡⡾⢃⣾⠟⣰⠃⢿⡄⣿⣇⠸⣿⠀⠘⣿⡇⠀⣿⡏⠀⢠⡟⠁⠀⢁⡴⠋⣠⠶⠟⢛⣛⣉⣭⠭⢿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⣠⡾⢃⡾⣡⣦⠘⣷⠘⣿⠀⢿⡇⠀⠸⣧⠀⣿⠁⠀⡞⠀⠀⡰⢋⡀⠚⠁⠴⠚⣉⣭⣴⠶⢾⡿⣰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⣴⢋⡴⢟⡉⢧⢹⡄⢿⠀⢸⡇⠀⢀⡏⠀⠟⠀⠈⠀⠀⠀⣠⢾⣛⣦⣄⠀⢈⣀⣤⡶⠾⢻⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣾⣛⣛⠂⣆⠀⠈⠀⠘⠃⠀⠘⢀⣀⠠⠄⠒⠀⠀⠀⠘⣉⣩⣥⡭⣹⠋⣥⠤⠶⣛⣹⣧⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⢻⣿⣓⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠤⠤⡇⠀⠀⠘⢫⡭⠷⢛⣣⡙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣚⣛⡇⠀⠀⠀⠀⠙⣟⡽⠿⡇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⢧⡗⠀⠀⠀⠀⠀⠘⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣭⣛⠟⠁⠀⠀⠀⠀⠀⠀⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠹⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠀⢸⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⢁⣼⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡛⣽⣻⣉⣝⣛⣛⣋⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡖⠉⠉⢲⣉⡙⡖⢦
⠀⠀⠀⠀⠀⢀⣠⠤⠔⠋⠁⠀⠀⠈⠉⠙⠉⠙⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠗⠀⢧⡀⢀⡼⠁⠉⠉⠛⠲⠤⣀⡀
⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣄⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠛⠓⢦⣄
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⣀⠀⢀⣠⣿⣧
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⢸
⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢿⣿⣿⠟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣠⡼⠃
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠛⢁⡴⠉⠉⠑⠲⢤⣠⣤⠤⠤⠴⠢⠚⠙⠁
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⡰⠃⠀⠀⠀⠀⢀⡠⢶⣁⣀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⢀⡴⢓⡻⠋
⡴⠀⠀⠀⣠⡴⠊⠁⠀⣴⠊⠉⠉⠉⠉⠉⠉⠉⢉⠏⠀⠀⠀⡠⠞⠁⠀⣎
⣇⠀⠀⠀⠑⣷⣀⣀⣀⣈⡗⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢳⣀⣀⣀⣈⠇
⣾⣿⠿⢿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠾⠛⠻⡿⠛⠻⡿⢿⠻⡿⠛⠻⡿⠛⠻⠀⠀⠀⢸⣿⣿⣿⣿⣡⣤⣄⣠⣤⣄⣠⣀⣄⣠⣤⣄⣠⣤⣌⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣄⡿⢣⣤⣀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠿⣀⠽⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⡿⢶⣽⣻⢿⣶⡶⢟⣻⣟⡷⢦⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢀⣀⠲⢤⡀⠙⣉⡥⠶⠤⣍⡛⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣾⣥⣤⣬⣽⣿⣶⣾⣿⣭⣭⣽⣿⣶⡀⠀⠀⠀⢸⣿⣿⣿⠿⠁⠿⠿⠿⠦⠈⠉⠁⠴⠾⠷⠦⠈⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠍⠉⢉⣭⣭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠍⠈⠀⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⡀⢠⠈⠀⢀⠀⠂⠄⠁
⠀⠀⠀⠀⡠⢺⠔⠀⠀⡀⠐⠐⠁
⠀⠀⡀⠀⠄⠘⠂⠠⢀⠐⠁⡠⠀⣀
⡄⠠⠀⠀⢀⣠⣴⣶⣿⣴⣷⠀⠺⣏
⡇⠁⢀⣤⣾⣿⣿⣫⣵⡾⠛⠀⠀⠋
⣇⣶⣿⣿⣿⣿⣿⣿⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡏⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠋⠉⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠂
⠁⠈⣧⠙⠛⠛⢉⢁⣀⣀⣤⣂⣀⡰⣴⣶⣤⠄⡀⢇⢦⠤⠀⠀⠀⠐⠀⠀⠈⠀⠀⠈⠀⡀⠀⠁⡈⣰⡀⠀⠄⢀⡀⢈⣲⡐⠁⠈⠌
⠀⠀⠘⠷⢤⡴⠷⠿⠿⢿⣿⣿⣯⠱⠆⠜⣿⡃⠐⠉⢀⠢⠀⠀⠈⢠⡀⢴⠶⣀⣆⡀⠄⢷⡕⡦⣙⢿⢫⣆⠀⢼⣿⣶⣿⣿⠇⠐⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣾⣿⣶⣋⢿⣾⠀⡏⠀⡘⠐⠇⣠⣱⣮⢾⣟⣿⣿⣻⣾⣧⢿⢮⠮⠫⣝⠺⣾⣿⣿⣟⠋⠀⢀⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣿⣿⣿⣟⡿⣧⣸⡃⢄⠀⠼⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣾⣼⢇⢧⣵⣽⣿⡟⠃⡈⡥⢄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣿⣿⣿⣅⣧⡀⠘⣿⡻⣿⣿⣿⢿⣿⠻⣿⣿⣿⣏⣻⣫⣻⣟⠟⡦⢺⣧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⡏⠉⠛⠈⢠⠂⡾⠿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⣿⣟⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠺⠎⠀⢀⡀⠀⣈⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢣⠀⠹⣿⣦⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣯⣥⡴⠾⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡗⠁⠀⠀⢸⣿⠃⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢿⡟⠉⠀⠀⣸⢿⣿⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⠟⠋⠀⠀⠀⢀⣾⣥⡄⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣬⣼⡇⠀⠀⢀⣿⣿⡿⠀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠿⠉⠀⠐⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠉⠉⠛⠋⠁⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡀⠠⣀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡄
⠀⠀⠀⠀⣠⠆⡀⠀⢰⣣⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢐⠏⠦⠃⠀⣏⣿⣾⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⢠⢿⡵⠀⠐⠈⠉⠩⠕⠒⠐⠒⠀⠂⠀⠀⠀⠀⠀⠠⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⢀⠄⠄⠒⡉⢍⠁⠈⠉⠛⠢⢄⠃⠀⠙⠁⠉⠁⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠰⠀⠀⠀⠀⡇⠀⠄⠀⢀⡠⢀⠔⠁⠀⠀⠔⢀⣴⠶⢉⣭⣥⣭⣹⣿⣆⡴⢠⣄⠀⡩⠤⠶⠊⠙⠃⠀⠤⡔⣖⠲⠦⣉⡱⠦⣤⠛⠉⠁⠈⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡰⠋⠀⠀⠀⣠⠂⡟⠃⡀⠈⢢⡴⠀⠲⢷⣍⣝⣵⠋⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⣷⠀⠈⠸⠇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡜⠀⡀⢙⣦⠅⠀⠀⠄⠀⡀⠀⠉⠀⠁⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⢼⡆⠀⠀⢀⢠⡀
⢀⠀⢸⠀⠀⠀⢸⡄⠀⠀⠀⢸⡆⠀⠀⣴⠁⠀⣃⠈⢤⡀⠀⠘⡀⠠⠃⠀⠀⠀⠀⠀⣧⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⢿⠀⡀⢸⢧⣿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡌⣇⠁⠂⠻⢰⣬⣿⣷⡟⠁⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⢸⠒⢨⠤⠙⣦⢚⡛⠁⠀⠀⠀⠀⢲⡟⣨⣎⣟⠀⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠙⣄⠀⢳⠌⣻⠿⡧⠁⠀⡄⠈⡀⠀⠚⠀⡿⠘⠀⠀⣾⠘⠀⠀⡸⠟⠉⠉⠂⠀⠀⠀⠀⢸⡇⡟⣿⣿⣿⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠃⣬⡟⠻⣶⠿⠦⣌⡀⠶⠀⠀⠀⠀⢀⡄⠠⠾⠿⠥⠞⠉⠀⠀⠀⠀⠀⠀⢲⡄⢀⣼⡿⠣⣿⢸⠃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⠐⣀⠴⠀⠀⠀⠀⠉⠓⠒⠲⠴⢶⣥⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⢃⡌⠀⠋⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠀⠒⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣀⣠⣤⡤⠤⠤⣲⣾⢻⠏⠀⠁⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠈⠉⠛⣼⠟⢡⣾⠇⠎⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢨⠎⠉⠀⠙⠒⠦⢤⣤⡤⠴⠛⠁⠀⠀⠀⡼⠋⠀⠸⠏⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠄⡲⠀⠀⢄⣟⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⣼⡃⠀⢀⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠁⠀⠀⠀⠃⠀⠀⡾⠊

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣀
⠀⠀⠀⠀⣾⣄⣀⣠⣴⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣗
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⢻⡁⠙⣆
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⣿⠏⠉⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠏⠀⡿⠛⠋⠉⠛⠛⠛⠛⠛⠃⠸⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⠟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠀⠈⠁

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣄⡀
⠀⠀⠀⠋⢿⣷⣶⣦⣶⣶⣦⡀⠀⠀⠀⣠⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠘⣿⡿⠿⠿⣿⣏⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⣿⠁⠀⠀⠀⠹⠋⠉⠉⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⢠⣤⡿⠿⢻⣿⠿⠿⠛⡱⠂
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠛⠀⠀⠀⠀⠘⠚⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁

⠀⠀⠀⢠⣶⣶⣾⣷⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢠⠾⢿⣶⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣄⣤⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⠿⣿⠁
⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠉⠀⠟⠆⠀⠼⠃⠿⠀⠀⠀⠀⠀⠀⢸⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⡂
⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣹⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠘⣟⡀⢿⡀⠀⠀⠀⠈⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡟⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⣤⣤⣤⡀⠒⠂⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⢨⣾⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⢸⡏⠛⠫⠙⠻⠟⣻⣿⣿⣄⡠⠄⠀⠈⠢⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠂⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣅⣒⣠⣤⣹⣿⡏⠀⠀⠀⠙⠢⡀⣀⣈⣂⣀⠀⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⢠⣄⣤⠀⠀⠂⢻⣿⣿⣿⠹⣿⠀⠀⠀⢀⠗⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⣿⠋⠉⠑⡄⡀⠀⠙⠻⣯⠆⢨⢀⠠⠒⠁⠀⠀⠀⢀⡀⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠢⡊⠀⠀⠈⠁⠂⣼⠷⠊⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢈⡢⠄⠀⠈⠁⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⠊⠁⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠂⠈⠉⠃⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣊⠻⠟⠁⣄⣲⡀⢠⠌⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠬⠟⠋⠁⠀⢻⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠚⢳⡿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⣤⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠶⣬⣋⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣄⣀⣀⣀⣻⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⣿⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⢸⡾⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⢈⣽⣾⣇⠋
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⣦⠀⠀⠀⠀⢀⣤⣻⣗⡆⠀⠀⠀⠀⠘⣾⣿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣦⣿⢠⣾⣿⣿⣿⣁⠀⠀⠀⣠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡈⠠⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢼⣇⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠈⠙⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠰⣶⡆⢀⡔⣤⠢⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢈⣿⡻⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣽⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠀⣀⢤
⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠀⢲⣁⠀⠀⠐⠒⠤⢀⡀
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠛⠀⠏⠀⠀⠀⠀⠙⢦⣀
⠀⠀⢀⠔⠁⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⢀
⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠓⠤⣤⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠉⠒⠒⠀⠀⠈⢉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠀⢀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣇⠀⠉⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⠀⢸⡀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⢆⣨⡁⠀⠀⠀⣘⡄⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⡛⢄⣀⣄⡵⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣰⢃⡇⠀⠀⡀⠠⣄⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠎⠀⡈⢸⠃⠀⡼⠀⠀⠈⠣⣄⣀⡀⢀⡙⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⡴⠦⢔⡃⠊⠀⠀⠃⠀⠀⠀⢀⠄⠘⠛⠉⠁⠈⠙⠀⢀⣠⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⡿⠺⡷⠁⠀⠀⠘⡷⣥⣠⠔⠒

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣸⠋⠉⠁⠀⢸⣿⠋⠉⠉⠉⢿⠋⢿⡅⠀⠀⠀⠀⠀⠐⢿⣿⣧⣤⣤⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠙⢧⣄⡀⠰⠋⠀⠈⢷⣤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢸⣿⡿⠉⠻⠿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠹⠹⠀⠉⠛⠁⠀⠀⠀⠈⠛⠋⠉⠉⠉⠁

⢀⠀⡀⡀⠀⠀⣀⢀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡀⠀⠀⡀
⣿⣿⢛⠿⢛⠛⢿⢟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠄
⠀⠠⢠⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡃⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢰⡀
⢀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀
⠈⡇⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⣱⠀⠀⠂⠀⢡⠀⠀⡐⠂⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⢈
⠀⠛⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⣤⠃⠀⠀⠐⠀⠀⠀⠠⡉⠀⢠
⠀⢻⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠊⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⣰⠀⠃⠀⠀⢀
⠀⢸⡤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡆
⠀⢰⡄⠀⠀⠀⠀⠀⡆⠀⢀⢁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⡇⠂⠀⠀⠀⠀⢧⠀⠈⠀⠀⠂⠀⢠⠖⠀⠐⠂⠀⠀⠀⠀⠀⠂⠀⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠰⠀⠈⡀⠀⢥⠀⠀⠀⢩⠀⠀⠀⠊⡀⠀⠂⡀⠀⠀⠀⠄⠀⠘⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⠄⢸⠀⠢⠠⠀⠀⠢⡄⠀⡀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⢠⢀⠀⡀⠂⣈⠠⡀⣂⡀⢠⣀⢐⠀⣠⠊⡂⠀⢀⡄⠀⢀⠆⠀⢀⠀⠀⢁⣆⢀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢀
⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⣿⡟⠛⠿⠿⠿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠟⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣀⣀⢰⡆⣀⣀⣀⢀⣀⡀⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⢹⢼⡇⡇⣿⢹⢨⢿⡇⡇⡻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⡉⣈⢈⣁⢁⠉⢈⣈⠉⢁⡉⣉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠐⠟⠻⠻⠛⠙⠃⠐⠓⠛⠛⠛⠋⠙⠃⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠖⠒⠋⠙⠉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠠⣤⣀⣀⣀⣀⢀⣀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⡧⠙⠉⠛⢶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⣈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⢻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⣠⣤⡴⣶⣶⣤⣄⣀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢻⡿⠀⠀⠀⠀⠀⣠⡀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠈⣿⣾⣷⠀⠀⠰⣿⣿⣧⣷⣶⣂⣤⣤⠤⣾⠀⠀⠀⠀⢶⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣀⣴⠟⢻⣿⠀⢄⣴⠋⠀⠀⠀⠀⠁⠀⠀⢀⠷⠂⢀⣠⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡖⠛⠉⠀⠀⢼⣯⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣴⠞⠁⠘⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣻⣄⣀⠀⠀⠈⠻⣄⠣⠀⠀⠀⠀⠀⠀⢀⣤⢂⡵⠾⠋⠀⠀⠀⢸⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠘⢦⣀⡢⣤⡀⠀⠀⠛⠁⠁⠀⠀⠀⠀⠀⠀⠘⠙⠳⠖⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣽⣇⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠉⠀⠉
⠀⠀⠠
⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⢸⣷⣤⣤⠀⠀⢠⣾⣿⣿⣿⣶
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠿⠟⠟⠹⠇

⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢿⡿⢿⡇⠀⠀⠀⠀⢹⣶⡄⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠘⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠹⠄⠱

⠀⠀⣀⣤⣤⣤⣄⠀⠀⢠⣶⠄⠀⠀⠀⠀⠠⢶⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠄⢀
⠀⠰⠿⠿⠿⠿⠿⠀⠀⠙⢿⣷⡶⠤⠀⠀⠀⠀⢛⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⣠⡀
⠀⠀⣠⣴⣶⣶⣶⠀⠀⠈⢻⣿⣿⠋⠀⠀⠀⣰⣿⣿⣿⠋
⠀⠀⠉⠁⠃⠈⠉⠀⠀⠀⠈⣿⡏⠀⠀⠀⠰⢷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠁
⣿⣟⣻⠿⢿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿