Pot roast Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⠉⠉⠁⠀⠐⠒⠀⠄⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡤⠬⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣤⡤⠤⣀
⠀⠀⠀⡀⢀⠾⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠂⠀⣀⡰⣏⣀⣀⣁⡱⣦⢷⡄⣀
⠀⢰⣘⠄⢁⡠⠿⣥⢉⡀⠄⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠘⠓⠊⠁⠀⣀⣀⠀⠬⢝⣠⠞⠀⠀⠁⠳⢄
⠀⠰⣁⠀⠀⠄⣄⠙⠏⣹⠏⢣⡀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠋⠁⠀⣀⠤⠐⠀⠉⠉⠀⠀⢀⠀⠠⠴⠛⠀⢴⡈⣶⢋⡉⠓⢢⡄
⢀⡴⠻⣆⣨⣀⣧⡑⢄⣌⠟⠛⠳⢎⢡⠤⢴⠂⠁⢀⣀⣤⢔⢂⠩⠤⠠⠀⠐⠀⠀⠈⡁⣀⢀⡠⠀⠤⢤⣴⠋⠁⣂⣕⠀⠀⢢
⡏⠙⠒⢩⡇⠀⡽⠃⠀⢀⣲⠂⢈⠕⠢⢴⠈⡉⣻⣿⠯⠭⠤⠤⠤⣴⢔⣂⡉⡀⡩⠭⡤⠤⠤⠶⠒⠛⠋⠋⣲⣶⡀⣤⠃⢀⣀
⠑⢀⠀⠀⢹⠋⠁⢹⠉⠁⢻⠹⠋⡲⠒⣶⠀⠴⡛⠉⠉⠁⠈⠐⠒⠒⠀⠀⠐⠐⠀⠐⠒⠒⠒⠐⠒⡶⠚⣚⡅⠀⠩⣍⣻⡏
⠀⠀⡟⠁⠉⣦⣀⡾⠈⢀⣠⣟⣀⣀⣊⣉⣀⢀⣀⣀⣀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣠⡇⠀⠀⠹⡀⠀⠀⢨⣇
⠀⠀⠧⠤⠤⠤⠀⠭⠅⠤⠄⠀⠀⠀⠀⠀⠠⠄⠀⠤⠠⠠⠤⠤⠤⠄⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⢠⡧⠦⠼⠁⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣼⣿⣶⡿⢻⣷⣶⣶⠦⠤⠤⠀⢀⡄⠈⠁⠀⠈⠉⠑⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣻⣿⣿⡉⢉⣁⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣌⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⢟⣉⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠨⣣⡏⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠿⠿⢧⡿⣿⡧⠴⠾⠟⠛⠛⠛⠛⠀⠠⠀⠀⠀⣀⣀⣠⣠⢦⣶⡏⢁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠉⠉⠁⠀⠐⣾⣯⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣏⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡔⣶⣶⡶⠿⠛⠛⠛⠛⠛⠛⠻⠖⣲⠂⣠⠾⢤⡄⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠂⢠⠔⠋⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢆⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣴⣯⠀⠀⠀⠀⢰⢸⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡝⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠐⠀⠀⠀⠀⠀⠀⣰⣯⡻⣧⣄⢀⣠⡵⠛⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⢀⣀⣀⠠⠞⠡⠼⠛⠛⣉⡿⣅⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢤⡤⠤⠤⢤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠂⠀⠀⠀⠈⡿⠻⢿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠙⠄⠀⠈⠉⠛⠿⣿⣿⣿⢷⣄
⠀⠀⠀⠀⠶⠆⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣷⡻⢰⠶⢶⡆
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⡿⡵⠛⡠⠛⠁
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⠠⠤⠤⠴⠒⣏⣽⡗⢠⠆
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡅⡞
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⠿⠋⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠤⠄⠀⠀⠐⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡆⢀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⣷⣴⣿⣷⣿⡆⡀⢀⠀⣅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⡿⣯⣽⣷⡟⢿⠿⣿⣿⣾⣧⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⡞⣏⣹⣚⠋⠟⣧⣜⡙⠻⠎⣽⣘⣛⣿⣮⠻⣿⣿⣿⣿⣿⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣬⣿⣿⣵⣌⠉⠙⢳⣰⣠⠛⢛⣀⢘⣠⣾⣿⠊⠉⣶⣿⣿⢻⠙⠁⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⣄⣿⠻⣿⣟⢺⣿⠻⠫⢍⣫⡟⣿⣿⣿⣿⣿⣿⣶⡤⠧⣽⠏⣀⣀⣠⣤⣶⡾⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠉⠛⠻⣷⣾⣧⣻⣉⠙⠈⣽⣿⣤⣿⠿⠛⠉⣀⣠⣤⣶⡾⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠰⠞⠓⣃⣠⠉⠉⠛⠛⢒⣛⣭⣭⡶⠦⠶⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠉⣀⣠⣤⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠉

⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠠⠮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡟⣻⣭⠄⠩⠀⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⢆⣠⠀⠀⠀⠀⡑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠟⡽⠀⠠⠄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠐⠀⠀⠀⠀⠀⡀⠋⠉⠀⣀⠀⠀⠀⠀⠀⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠒⠒⠐⠀⠀⠀⠴⠂⠈⣤⣾⣷⠄⠛⠁⡠⠀⠀⠀⠀⠰⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠃⠠⣄⡀⣀⢀⣀⣀⣀⣀⣀⣠⣟⣻⣁⣤⣴⣦⣤⣆⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠛⠉⠉⠤⠤⠤⠉⠉⢤⠄⠈⠀⠀⠀⠉⠉⠉⠉⠛⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠤⠜⠛⠛⢷⣤⡀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠚⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⡿⠀⣰⢤⠀⠀⠀⠀⠀⢀⡟⠿⠃⠀⠀⡀
⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠀⠀⠛⠛⠀⠀⠀⠉⠉⠉⠙⠁⠀⡀
⠀⠀⠀⠀⢿⡧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣬⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⣹⢃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣉⡙⠓⡆⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣶⣶⣶⠶⣒⣴⣾⣿⣿⣶⣶⣶⣤⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢻⢟⣿⣿⣿⣿⡿⣫⣴⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠞⡰⣱⠟⠋⠟⢡⢞⣼⡿⠋⢡⠾⠛⠉⣡⣴⡿⠛⣻⣿⠿⠛⠙⣻⢟⣿⣿⠟⢻⣿⣿⣛⣟⣉⣩⣭⣛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠔⣱⠋⣠⣤⡀⢡⣿⣯⣀⣀⠀⠀⢁⣼⣿⠋⠀⠈⠁⠀⠀⡠⢞⡵⠋⠉⢀⣴⢿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣞⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⣰⠟⠛⠽⢿⣤⣿⢿⣿⣟⡽⣽⣿⣿⣾⣿⣿⣿⣶⣦⣮⡴⣵⣋⣀⠀⠉⣼⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷
⠀⠀⠀⠀⠀⣰⠏⠀⠀⡔⣿⡆⠀⠀⣼⣿⣥⣄⡀⠈⣈⠉⣿⣽⢿⡉⠈⠈⠙⢻⣟⡞⠙⠿⠿⣻⠞⣡⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣟⣿⣇
⠀⠀⠀⠀⢀⡿⢀⠀⢠⢸⡏⠁⠀⣸⢳⣿⣿⣿⢿⠀⠀⢰⢷⡇⠀⣠⣾⡄⢠⣿⡟⠀⢀⣤⣾⢣⣴⣿⣿⡿⢱⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣸⡇⠈⠿⡿⢸⣿⢿⡿⠇⣼⣿⣿⣾⣶⣦⣄⡾⣾⣤⣬⣙⣛⣁⣾⣿⠀⠠⠿⣿⢣⣿⣿⣿⣿⣇⢺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢴⣆⡀
⢀⠶⢾⣿⣿⡀⠂⠀⡀⢸⡇⠀⠀⠀⣿⠛⠛⠿⠻⢿⣼⣧⣿⠿⠻⠻⠿⣿⣿⣿⣖⣶⣶⣿⣸⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠴⠾⠶⢦
⠈⠛⣲⠏⣻⣷⣄⢠⣥⡈⣇⠀⠃⢹⢸⠀⠀⠠⣶⣶⣌⣻⡇⠀⠀⠀⠀⣹⣿⠀⠈⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡒⣠⣭⠷
⠀⢠⣟⠛⠻⠿⢿⣿⣿⣷⡘⠀⣴⣾⣿⣇⣆⡀⠛⠻⠟⣿⡇⠠⠽⠃⠀⠿⡿⠀⣤⢣⡿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉
⠀⡴⢛⠛⠛⢐⠚⣻⡿⢻⡿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⠀⠀⢢⣼⡇⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⣴⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠙⠻⠶⠚⣯⣤⣾⣥⠀⣨⡍⡩⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⣟⣻⣾⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣙⡛⢛⣿⣠⣤⣾⣇⣼⢁⡤⠾⠛⣿⣿⣿⣶⣶⣭⣻⣿⣿⣿⣿⣿⡆⢻⣿⣿⠿⠿⢛⣛⡛⠋⠉⠁⠈⠉⢋⣉⣅⡠⠀⠀⠀⠀⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠠⠮⠅⠀⣿⣉⡠⢴⣄⡴⢋⣿⠗⡠⠚⠿⣿⣿⣿⣿⢿⣿⣃⠈⠉⠒⣛⡉⠉⠛⠛⠿⣿⣻⢶⡄⠀⠉⠁⠤⠶⠶⠾⠿⠿⢛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠠⣋⣠⣄⡜⣷⣴⡿⠛⠛⠐⣛⠉⣿⢀⡙⣶⠰⠭⣙⡲⠦⣄⡀⠉⠛⠦⠀⡂⠀⣛⣧⠤⠟⢸⠀⣟⠀⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠥⠤⠉⢩⣾⣴⣢⣾⠟⠁⠁⢸⠛⠻⠀⣦⠈⠙⠓⢦⣝⣶⣄⡀⠀⠧⢤⣭⠶⠶⠶⠟⣀⣬⣤⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⢷⡟⣦⠾⠀⣴⠀⠃⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠿⢷⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡊⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⠼⠿⠛⠉⠨⣧⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠁⠀⠀⠀⠀⠐⡀⠙⣆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣇⣠⡄⠀⠀⠘⠉⠀⡻⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢿⣄⠁⠀⠀⢀⡀⠀⢻⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⠰⣼⣶⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⡤⠊⣸⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⣠⣤⡄⠉⣠⣾⠟⢤⢮⣰⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠃⣠⣿⣏⡴⠞⡁⣸⣶⣿⢿⣯⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⠿⠏⠐⢲⣷⣿⣿⡿⣿⣿⣿⡓
⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⢟⣩⡿⢿⣥⣾⠃
⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣼⣿⢟⡯⣶⣮⣽⣿⠃
⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣶⣆⠀⠀⠀⠀⠀⢠⡾⣿⣷⢶⣛⣿⣟⣿⡿
⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠟⠋⠛⢟⣩⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣷⣵⣯⣛⡿⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠩⠯⠥⠶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢾⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⠟⠉⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠸⣷⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡾⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⢲⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⡐⠅⠀⠀⢐⠈⠋⠙⢛⣯⣟⠳⢶⠖⢤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠓⠷⠩⠟⡹⠒⠀⠀⠀⠉⠒⠂⠈⠑⠂⠑⠀⠀⠀⠀⠉⠉⢉⣉⣉⣳⣦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣴⠯⠗⡡⠨⠄⠀⠨⠐⠂⠀⠁⠀⠁⠀⠠⠄⢀⢀⡀⠀⠀⠀⣀⠄⣀⣷⣾⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠔⠛⣋⣤⣾⣿⣯⣜⣎⣖⡠⠤⠀⠈⠐⠀⠀⠀⠀⠈⠀⠀⠀⠉⢀⡤⢐⣼⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⡌⠀⠀⣾⣿⠻⣟⠿⢷⣾⣿⣺⣯⡔⡰⠂⠐⠀⠀⢁⠀⠀⠀⠀⡠⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣍⢫⠖⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠙⣿⣶⣿⣿⣿⣿⣷⣿⣿⣲⡂⠰⢀⡀⠀⠀⢈⣴⣿⣿⣿⣿⡿⢟⣛⣭⣽⣿⣦⣀⢙⡶⣤⡀
⠀⠀⠀⢀⣤⡀⠀⠀⠈⠂⢾⣿⡿⠿⢿⠿⣿⣿⣯⣟⣿⣿⣿⣾⣿⣷⠃⠾⣿⣿⢝⣋⣵⣿⣿⣿⣿⣿⡿⣿⣴⣿⣯⡙⢿⡄⠀⠀⠂
⠀⠀⠀⢼⣿⣿⣶⣄⠀⠀⠀⠉⠛⠷⣶⣴⣦⣯⣿⣿⣿⣷⣮⣽⣿⣿⡀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣷⣿⣿⡾⠁
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣤⡀⠀⡀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⡀⠆⠘⠻⠿⠿⠿⢟⣛⣛⣩⣬⣿⣿⡿⠿⠛⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠛⠛⠚⠓⠓⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⢀⣠⡤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⡀⣀⣀⣀⣀⣠⣠⡦⠼⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣤⡏⠘⠁⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠧⠃⠀⠀⢀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠮⡄⠆⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣧⣿⣿⣿⡿⢿⣿⣿⡁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡤⡥⠓⠈⠀⢀⣤⣶⣿⣿⠿⣿⣿⣿⣶⣿⣿⡿⣿⠻⠅⠀⠙⣿⣿⠛⠏⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠖⠁⠀⠀⠀⢀⣾⣷⠘⡃⠡⡄⠈⠎⠻⢿⣿⣿⣿⡿⢦⡀⠃⡄⢻⣯⡄⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣤⣤⣤⣸⣿⣧⣾⡿⠂⢤⠄⠀⠦⡀⠙⢿⣿⣦⡈⠱⠀⠀⠀⢿⠃⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠧⠼⠿⠟⠿⠿⣿⣿⣿⡤⠅⠀⠁⠀⢤⠚⠻⣿⡏⠑⠑⠈⠃⢰⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣿⣿⣿⠁⠀⠬⠓⠀⠒⠚⠌⠹⡛⢿⣄⡈⢁⠈⠀⠀⠙⣧⡀⠀⠀⢠⢸⣄⡔⣼⠏
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⡗⠒⠍⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠄⠀⠐⠤⠴⣿⡀⠂⢀⠁⣸⠷⠋⠁
⠀⠀⠀⠀⢀⡴⢿⣿⠍⠿⣿⣆⠀⠀⠈⢹⢿⣿⣦⡀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣠⣼⠞⠁
⠀⠀⢀⣴⠟⠟⠹⡇⠀⡠⠸⣿⣄⣻⡀⠀⡄⠙⠿⣿⣶⣄⡀⠀⠀⠀⡀⠀⠀⢀⣠⣘⣿⣾⠟⠋
⠀⢰⣟⣀⠴⠀⢈⣿⣄⡀⠀⠈⢻⣿⣿⣶⣶⣤⣤⣬⣙⢿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠸⣿⣷⣶⣤⣍⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⡿⠋⠉⠉⠁
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣠⠤⠐⠲⠿⠿⠦⢴⣾⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣴⣶⠟⣡⣤⣤⣤⣤⣄⣠⣤⣤⣭⣟⣿⡛⠻⢿⣿⡿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⠟⠓⠀⠹⣷⡄⠉⠻⠿⣦⣀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠋⣥⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣽⣀⠀⠰⠀⠀⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿
⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡞⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⡼⣷⠈⣿⣿⣿⣿
⠸⣿⣿⡿⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⡄⢀⡀⠠⢀⣈⣹⢿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣷⣿⣿⢀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⢿⣿⡷⢻⣿⣶⡾⣿⢋⣶⣼⣿⣿⣿⣷⡆⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣿⣿⣿⣿⠁⣾⣿⡗⢛⣿⣿⣿⡿⣾⡿⣩⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿
⣿⣯⡀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⠷⣿⢛⣿⢿⡄⠛⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣷
⣿⣿⣿⣿⣿⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠆⣰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠟⢿⣿⠓⠶⢿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠸⣿⣶⣦⠀⣀⣀⣿⣿⣿⣿⣿⣿⣥⢼⣿⣿⠿⢷⠄⠀⠀⠀⢼⣿⣿⠃⠉⠀⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿
⣿⠟⠃⣀⢰⣿⡿⠉⣶⡿⣿⣿⣿⣿⣿⣿⣿⡩⠈⢻⣇⣰⠄⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⢸⡁⠀⠀⠀⢠⣿⣿⣿⣿
⠀⣠⣀⢹⡿⢿⠀⠀⠀⠧⠻⣿⣿⣿⣿⣿⣿⣧⠀⡀⠹⢻⣦⣠⣤⠀⠀⠀⠀⢀⡀⠀⠀⠋⠀⠀⠀⢀⣾⣿⣿⣿⣿
⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⠇⠀⢀⣴⣤⠐⠁⠀⠀⠀⠀⠈⠀⣠⣿⣿⣿⣿⣿⠛
⢿⡿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠋⢿⣏⠀⢰⣾⣻⣿⠇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠈⠋⠀⠀⠀⣀⣤⣤⣄⣉⡁⠘⠛⠋⠈⠀⠀⠀⢸⣿⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠋
⠜⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠟⠓⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠔⣿⣿
⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣋⣸⣿⣿⣿⣿⣿⣿⠟⠁⠀⢣⣾⣿⣿
⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⡇⠐⣿⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣏⢉⡿⢿⣧⣼⠿⠋⢡⠴⠏⠹⠿⡉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣄⣀⢷⣼⣿⣿
⣿⣿⣿⣿⣿⣿⢻⡟⣿⣾⣷⣿⣤⣤⣁⣤⣼⣷⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⠎⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣯⣘⣿⣿⣿⣷⠋⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣮⣿⣿⣿⣿⣿⣄⣘⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⣹⣤⠈⣿⠏⣽⣿⣿⣿⢷⡼⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⠟⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠚⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠈⢷⣀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⡛⠛
⠀⠀⠘⠠⠷⠶⠚⠃⠀⠀⠈⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠉⠐⠚⢼⡿⠉⠀⠀⠈⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠂
⠄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠡⠀⠀⠀⠀⠰⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⡐
⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡴⠀⠈⠀⠀⠀⠀⠀⠀⡌⠑⠧⣲⣀⣂⣀⠀⠀⠀⠀⡮⠛⠁⡈⠀⢀⠜
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⢀⠀⢀⠀⡴⠃⠨⠀⠀⠐⢰⡄⠀⠀⠀⠀⠙⠒⠦⠀⠉⠭⠤⠄⠐⠀⠁⠀⠀⠰⠀⠀⠁
⠀⠀⠀⠀⠘⣳⡂⢠⡄⠀⠀⠀⠶⠚⠁⠀⠀⠀⣀⠔⠉⠓⠋⠀⢠⣤⣀⡰⠶⠓⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠂⠠⣤⣄⡀
⠀⠐⠶⠒⠉⠉⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠤⠀⠛⠒⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢘⡡⠜⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣀⠔⠀⣀⠤⠤⡄
⠀⠀⠀⠾⣄⣤⣤⣤⢼⡶⢦⣄⣀⣀⣴⡎⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡤⢦⣀⠀⠀⠀⠀⠄⠁⠀⢀⠌⠁⡠⢊⡠⠒⢘⣇
⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⡇⠀⠀⠀⠀⠀⠀⢤⣼⣿⣟⡛⠁⢀⠙⢷⡼⠫⣼⣁⢀⣠⠂⡠⢊⠔⠉⠀⠀⠉⠴⢆⡄⠰
⠀⠙⢦⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠉⣦⣬⣲⣄⣀⡩⠷⠿⡆⣀⣷⡤⠇⢽⡞⢻⠾⠷⠣⣴⡶⠶⠶⠊⠀⣌⣙⡂
⠀⠀⠀⠉⠛⠛⢿⣄⣀⣀⣀⣀⡼⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⠤⠄⠀⠀⠘⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣂⣤⠶⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⣪⠇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠀⠠⠂⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡷⠂⠉⠈⠉⠄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⢁⡰
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡉⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠃⠀⠀⠑⠀⢠⢆⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡰⣪⡀
⠀⠀⠘⢿⣦⣄⣀⣀⣤⠔⠻⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣤⡀⠀⠀⠁⠀⢠⠂⠁⠀⢘⠀⠀⠀⣠⣿⠁⣀
⠀⠀⠀⠀⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣠⡋⠙⣦⣄⡠⣠⠀⣉⠊⠁⣁⠰⢆⡹⠾⣉⡉⢣⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⣀⠀⠉⡀⣀⢀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠈⠉⠋⠄⠘⠠⠗⠛⠛⠃⠛⠉⠘⠁⠀⠈⠀⠜
⠀⠀⠀⠀⠀⡀⠄⠠⣦⣐⢇⠀⠀⠀⠀⠀⠀⠀⢤⣦⣤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣦⣀⡀⠀⠉⠁⠀⠀⠠⠄⠀⠀⠁⠉⠙⠁⡿⣸⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠐⠢⠄⠀⠀⠀⠂⠀⠀⠈⠓⢄⡀⠐⠠⣠⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⢲⠤⢀⡀⠠⠄⠀⠀⠤⠤⠄⢚⣴⡏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠃⠀⠀⠶⠄⠀⠀⠰⠂⠀⠀⠙⠂⡠⠀⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠤⠤⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣿⣲⡦⢄⣠⣴⠯⠔⠛⠈⠁⠀⠐⠈⢉⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢙⣆⡀⡸⣶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⡀⢸⠏⢛⠏⠟⢻⠏⣼⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡇⠐⣿⠀⠀⠀⠀⠀⠀⣀⣨⣧⣴⢶⡟⣛⣟⣭⣿⣷⠿⢿⡛⢶⣦⣄
⠀⠀⠀⠀⢀⣘⠯⡃⢠⣇⡀⢸⡝⡽⠞⠋⠀⠀⢠⣤⣴⣿⣿⣿⡵⠿⣟⣻⣯⠾⢷⣞⣻⣟⠻⣷⠾⣷⣿⣷⡄
⠀⠀⠀⠀⠐⢟⢦⣀⡈⠃⠙⠄⢃⠁⠀⠀⠀⣴⣏⠀⠀⠀⠁⠌⠉⠙⠻⠧⢿⡶⠿⣿⢋⣿⠟⣿⢿⡏⠘⠁
⠀⠀⠀⠀⢰⡚⠣⣁⠉⢀⣀⣤⡀⣶⣾⢀⣰⣿⣾⣥⣀⡤⠀⠀⠀⠁⠀⠀⠀⠟⠿⣿⡟⡿⣴⠇⠀⠁⠀⢀⡆
⠀⠀⠀⠀⡴⠊⠉⢟⣻⡿⠟⠻⣿⣿⣿⠟⠛⠙⣉⠹⠻⡿⣷⣶⣄⠀⠀⠀⡀⠀⣠⡿⠀⠀⠀⠀⠀⣀⣎⣭⠇
⠀⠀⠀⠀⠛⠁⠰⢻⠃⠌⠠⠀⣿⣿⡅⠀⠀⠄⠀⠚⠀⠀⠀⠙⠛⠿⣷⣶⣷⣴⣤⣯⣀⢀⣠⣶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⣿⣿⣵⣢⣄⠠⠀⠉⡀⠀⠠⠀⠀⠀⢰⠉⠹⣿⣿⣿⢿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣾⣿⣿⣮⢿⣿⣮⣈⡓⣦⣤⡀⢀⡀⠀⣀⣀⡹⢾⣿⣏⣛⢰⠛⣧⠀⢀⣠⣔⡄⣟⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣼⣿⣆⢠⣌⠉⠙⠿⡿⣿⣶⣶⣷⣿⡿⡿⠶⠛⠟⢬⣀⣈⣦⠟⢀⣎⣀⣸⣧⡏⢀⠖⠋⣷
⠀⣀⣤⠀⢀⣠⣤⣤⣀⠰⠷⠈⠉⠛⠿⣿⡓⠢⠤⣤⡠⠥⣽⡟⣿⡷⣬⡟⠾⢺⠈⠉⠉⠁⠀⢸⡆⠀⢨⣿⣼⡇⠤⣄⡾
⠀⠉⠉⢰⣿⠭⢭⣀⠉⠛⢦⠀⢠⣠⡀⠈⠙⠲⠶⣿⣧⣠⡬⠟⠋⠀⠀⠙⢦⡟⠀⠀⠀⠀⠀⠀⢴⣤⣋⠀⢹⡄⣀⡈⡱
⠀⠀⠀⠿⢦⣀⠀⠀⠉⢑⢺⡇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣯⣭⣥⣵⡞
⠺⠿⠃⠀⣴⣨⠙⠛⠋⠉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠆
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⣠⠴⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⠞⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⢀⡜⠁⠀⠀⢀⡞⠁⣀
⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⡼⠁⠀⠀⢠⠏⠀⠀⠀⡴⢋⡤⠞⠉
⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠚⠁⠀⠀⣰⠋⠀⠀⣠⠞⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡘⣀⣤⣄⣰⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⣀⣠⡤⠤⠶⠒⠒⠛⠛⢩⡉⠉⠉⡉⠠⠀⠀⢈⠟⣡⣄⠀⠁⠠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣋⣁⣀⠀⠤⠀⠘⠦⡜⠳⣄⠉⢣⡀⠙⠆⠀⣴⣫⠞⢁⡼⣡⠖⣆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠉⠉⠉⠁⠀⠈⠛⢦⡀⠲⡈⠳⡄⠙⠀⠀⠸⡏⣿⣠⢏⡞⠡⣠⢏⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⡤⠶⠒⠒⠲⠦⣄⠉⠀⠀⠙⢦⠙⠀⠘⣆⠘⠂⠀⣇⠹⡟⢻⢀⣴⣳⢋⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠈⢧⠀⠀⠘⣇⠀⠀⠘⡆⠀⠈⠿⠻⡇⢀⠳⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣸⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⡄⠀⠀⠈⢧⠀⠀⠘⣆⠀⠀⣷⠀⠀⠀⠀⡇⠘⣆⢠⠀⢻
⠀⠀⠀⠀⠀⢠⡇⢠⡏⡀⠀⢀⡴⠛⠉⠙⠲⣄⠀⠘⣧⢹⡄⠀⠀⠘⣇⠀⠀⠘⠀⠀⠈⢳⡀⢀⣀⡇⠀⢸⡄⠀⠈⡇
⠀⠀⠀⠀⠀⣼⠀⣼⠘⠃⠀⡟⢀⡔⠚⢶⡀⠸⡆⠀⠘⠂⢷⠀⠀⡄⢸⡀⠀⠀⣆⢠⠀⠈⡇⢸⠉⠀⠀⠀⣧⠀⠀⡇
⠀⠀⠀⠀⠀⡟⠀⡇⣤⠀⠘⡇⢸⡇⠀⢸⡇⠀⡇⠀⠀⠠⢸⡆⠀⢀⠸⡇⠠⠀⣿⠀⠀⠀⣧⢸⠀⠸⡆⠀⢹⢸⠃⡇
⠀⠀⢀⣀⣠⡇⢸⡇⣿⠀⠀⢳⡀⠙⠒⠋⢀⡼⠁⠀⠀⠠⡄⣇⠀⢸⢀⡇⢀⠀⠿⠀⡇⠀⠙⠞⠀⠀⠀⢀⡀⠸⢰⡧⣤⣀⣀
⣠⠞⠋⣡⠖⣧⠘⣇⡉⠀⠀⠀⠉⠓⠶⠖⠋⠀⠀⠀⠀⠀⠁⣿⠀⢸⠀⠀⣼⠀⢀⠀⣿⠀⠀⣶⠀⠀⠃⢈⣠⣴⣋⡉⠙⠲⣍⠛⢦
⠳⣄⡀⠘⠀⢌⠳⣤⣉⡓⠲⠦⢤⣤⣄⣀⣀⣀⣀⣀⣤⡤⠴⠞⠀⣈⣀⣀⣋⣀⣀⣀⣁⣠⣤⠤⠶⠚⠛⠋⠉⠉⣁⠀⠀⠛⠁⣀⡴
⠀⠈⠉⠓⠲⢦⣤⣄⣈⣉⣛⠓⠒⠲⠶⠶⠤⠤⠤⠴⠶⠖⠒⠛⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⢤⡶⠒⠋⠉
⠀⠀⠀⠀⠀⠈⠓⠒⠶⠭⢭⣭⣍⣛⣛⣓⣒⣒⡒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⣒⣒⣒⣒⣛⣛⣩⣭⡭⠭⠴⠖⠒⠋
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣀⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⠁⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⠀⠀⠀⢀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠘⡇
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢱⡀⠀⢻⠀⠀⠀⠀⠉⠉⢁⣸⣿⣿⡉⠁⣹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⣧⣤⣼⡆⠀⠀⢰⣾⣿⡿⠿⠛⠿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣾⣿⣿⣿⣟⣶⠲⣶⢶⣦⣼⣭⣻⣿⣿⣿⠀⠀⢰⣿⣿⣿⣧⠀⠀⠈⠁⣀⣤⣤⣤⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣵⢾⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⣠⣾⣿⠟⠛⠉⠉⠛⠿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⣹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣯⣭⣟⣺⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣶⣶⣶⣶⣿⡿⠋
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⢿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡄⠀⠀⢹⣿⣿⡟⠀⠀⢰⣦⣤⣌⣉⠉⠉⠉
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣟⣿⣿⣿⣿⣯⢷⣾⣯⣿⣿⣿⡟⣻⢝⣭⣯⡞⣻⣷⣿⣿⡆⠀⠀⠉⠉⠀⠀⠀⠈⠉⢻⣿⡿⢿⣿⣶⣦⣤⣀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⣽⣟⣿⡿⣟⣷⣿⣿⣿⣿⣿⣻⡿⢷⠛⣷⣻⡟⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣤⣤⣼⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⣷⣯⣿⣿⣾⣿⣿⣿⣿⣛⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡀⠀⠀⠀⠀⢰⣿⣿⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⢀⣴⣶⠀⠀⢀⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⡇⠀⣰⣿⣿⠟⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠘⠿⣿⣿⣿⠿⠋⠀⠠⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠒⠒⠚⠛⠉⠉⠉⠉⢉⣉⡉⠉⠙⠛⠒⠒⠲⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⡤⣾⠟⠉⠀⢀⣴⣿⠟⠉⠳⢄⣠⣤⡀⢀⣀⠀⠀⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠀⠀⠀⣀⣤⣿⡞⠁⠀⣠⣶⡿⠋⠀⠀⣠⣴⡿⠛⣡⣿⡿⠋⠙⠦⣄⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣴⣾⠽⠛⠉⢁⣠⣾⣿⠋⠀⢀⣤⣾⠟⢋⣴⣾⠟⠉⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⢄
⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⡠⠚⢹⡇⠀⠀⠀⠀⠀⣿⣿⠀⢠⣶⡿⠟⠉⠉⣀⣤⣾⣿⣁⣤⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠈⢳⡀
⢰⠃⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⣤⣷⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⠀⠀⢠⣾⡿⠋⣵⣾⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳
⡟⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣿⡄⢉⠳⢶⣦⣀⡀⢻⢻⠀⢸⢹⠀⠀⢸⣿⡇⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠀⠘⡇
⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣐⠡⡏⠀⠈⠉⠛⠾⣆⣸⠾⠦⣤⣈⣻⡇⠀⡋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢷⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠉⢿⣟⣋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠈⢆⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠚⠋⠉⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⢀⡤⠞⠁⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⣶⣿⣟⣥⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣦⣞⡭⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⡀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠲⠶⠶⠤⠤⠴⠶⠶⠒⠒⠒⠛⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⣀⣀⠔⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢧⡀⠀⣠⡀⠌⡅⢀⣀⠓⠤⠒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣦⣤⣶⣾⣿⣧⠀⠀⢼⣧⣷⣿⢱⣴⣸⠀⠀⢉⠙⠐⠒⠐⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣾⡿⣿⣧⠈⡠⢶⣧⡆⣸⣤⡆⢸⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄⠻⣿⣧⣽⠿⢛⣿⣿⣿⣶⣄⠻⡿⠿⡁⣇⡍⢹⠼⠇⠈⠙⠚⠡⠿⠗⠘⣽⣍⠀⢤⠀⠙⠂
⠀⠀⠀⠀⠀⢀⣟⣛⡏⢿⠻⣿⣿⣿⣦⣙⠿⣷⣶⣿⣿⣿⣿⣿⢢⡀⠀⣧⠛⣂⢸⡠⠤⠄⠀⢀⠀⢤⣾⣷⣄⣙⣷⣾⡆⠀⠀⣃
⠀⠀⠀⠀⠀⠀⢄⡀⠁⢀⡉⠉⠛⠻⣿⣿⣷⣦⣌⠙⠻⢿⡿⠋⣴⣅⢦⡉⢤⣤⣴⡀⠲⣦⡉⢻⣷⣤⠝⣛⣫⣿⣿⡿⠀⠀⣠⠇
⠀⠀⠀⠀⠐⠀⣀⠛⣆⡀⠀⠢⣀⠀⠉⠙⠿⢿⣿⣿⣦⣤⣀⡀⠈⠛⠶⠙⠲⠩⠻⣿⠚⠙⢟⣡⣽⣿⣾⣿⣿⠟⠋⠀⣠⠞⠁
⠀⠀⠐⡢⢀⡄⣤⣶⣿⣿⣶⣤⣀⡈⠁⠒⠤⠄⣘⣻⣿⣿⣿⣿⣧⣀⠀⠀⢴⣶⣶⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⣀⣤⣾⣅⣀⡀
⠀⠀⠀⠀⠴⢧⣤⡄⢤⣠⣄⣨⣿⣿⣿⣷⣶⣦⣤⣬⣥⣭⣭⣍⣙⣛⣛⣒⣘⣋⣉⣩⣭⣤⣤⣤⣴⣶⣶⣿⣿⠭⢍⠉⣻⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠁⠀⠁⠛⠛⠿⠟⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠟⠛⠉⠉⠙⠻⠖⠒⠶⠿⠿⠿⠯⠉⠁
⣿⣿⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣁⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⢻⡆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⢀⡾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣌⣑⠒⢦⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣄⢀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⣿⣿⣿⣟⣵⣾⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠵⡱⣵⠟⠻⢋⢟⣽⠿⠋⡴⠛⠛⣡⣶⠟⣻⡿⠟⠛⣻⣟⣿⡿⢛⣿⣿⣿⣛⣉⣽⣳⣦⡀
⠀⠀⠀⠀⠀⢀⠏⠠⡄⣽⣧⣤⡄⢠⣿⣯⣤⣀⡀⣡⢾⣟⣀⡀⠀⠀⢠⢾⡟⠉⡀⣠⢟⣿⣿⣿⣿⣿⣿⣟⣿⣟⢦
⠀⠀⠀⠀⢀⡜⠀⠀⣸⡋⠉⠉⣷⡟⠛⠻⠿⠿⢿⣿⣿⠿⠟⢿⣷⡶⡱⣯⣤⣄⣠⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⠁⠀⠈⡿⠃⠀⣸⣿⣿⣷⣆⠐⠀⣾⡟⠑⢀⡄⠀⣼⡿⠁⠈⣩⡞⣡⣿⣿⡟⣿⣿⣿⣿⣏⣿⣿⣿⣿⡄
⠀⠀⠀⢠⡇⠐⣶⠦⣷⣴⡶⢁⣿⣿⣭⣤⡄⣰⣿⣃⣐⡛⠋⢸⣿⠁⢠⢿⣏⣼⣿⣿⣿⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣤⣀
⢀⠶⣾⣿⡇⠂⠀⠁⣧⠀⠀⠘⡟⠛⠻⠻⠧⣿⣿⠟⠛⠻⢿⣿⣿⢦⣦⣾⣿⣿⣿⣿⣿⡞⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⠠⠾⠶⡄
⠈⢹⣖⣹⣿⣦⣴⣄⢻⠈⠁⢧⡇⠀⠀⣾⣶⣼⣿⠀⣀⠀⢸⣿⠁⢀⣉⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣯⣁⣤⠽⠂
⠀⢐⣬⣭⣙⣻⣿⣿⣦⣀⣿⣿⣷⣴⣦⣈⣉⣹⣿⠈⠙⢀⠈⣿⣠⣎⣼⣽⣿⣿⣿⣿⠟⣴⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⢳⣦⡤⣴⣀⣿⠁⠫⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣾⣿⢿⣿⡟⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠉⠙⡻⠷⣿⣁⣁⣶⣠⠟⣩⡽⢿⣿⣿⣯⣽⣻⣿⣿⣿⣿⣷⠹⣿⣿⡿⠿⠿⠛⠛⠛⠙⠛⠚⢋⣉⡉⠉⠀⠀⢁⣽⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠋⠡⠬⠁⠨⢏⡩⢴⣀⠜⣻⠗⠠⠛⢿⣿⣿⠿⢿⣿⡁⡉⠐⣚⣉⠛⠛⠿⢿⣶⢦⣄⣉⠥⢔⡲⢶⣾⣟⣻⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣥⡦⠎⣧⡾⡋⠉⢈⣭⠘⠇⣌⣷⠐⠪⢝⡒⠦⣄⠉⠓⠮⢭⣿⠿⢿⣿⣿⣿⡿⢛⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠂⠀⠘⠿⠗⢻⣅⣄⢀⡇⠉⠠⠇⠀⠈⠙⠾⣵⣦⣬⣙⣿⣿⣛⣋⣭⣵⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣙⣋⣀⣚⣀⣀⣀⣀⣀⣀⣈⣙⣛⣛⣛⣉⣉⣉⣉⣀⣀⣀⣀
⣿⣿⠉⡉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠔⣥⣾⣷⣮⢢⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣖⢄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⣋⠅⠊⠉⠉⠚⠀⠐⡧
⠀⠀⠀⠀⢀⠬⣤⣻⣤⡝⣧⢇⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣏⡿⢿⣿⣿⣧⣭⣽⣷⣿⣽⣿⣸⠀⠀⠀⢀⠖⢋⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠁
⠀⠀⠀⢠⢢⣶⣮⣻⣻⢋⣥⡌⢳⣄⢀⠢⡷⣤⠒⠉⡃⠀⠀⠀⡏⠙⠳⣆⠙⣻⡿⣿⣿⣿⣿⠟⢹⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⡄⠀⠊⠀⠀⠀⢀⡅⣦
⠀⠀⠀⡃⣿⣿⣿⣿⣿⣿⠿⣴⣇⣿⣾⠿⠛⠛⠓⠤⠇⠀⠀⠀⠈⠲⣄⠈⠍⣙⣿⡾⠟⠃⣁⠔⠁⠀⠀⠀⢻⡀⠀⠀⠀⡰⢃⡇⢰⠁⠀⠀⠀⢈⡿⠋
⠀⠀⠀⠈⠊⠉⢉⣻⣋⣿⣿⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠹⣦⣴⠙⣁⠾⠗⠛⠳⠖⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠥⠤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣦⣔⡢⡀⠀⠀⠀⠀⠘⠢⣄⠈⠂⢄⣀
⠀⠀⠀⠀⢀⣠⣤⣠⣤⣪⣵⣿⣾⢿⣿⣷⣝⡀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣈⣁⢀⣀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠦⠤⣀
⠀⠀⠀⣼⣿⣿⣿⣿⣯⣿⡯⢍⣶⣿⣿⣿⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡿⢁⣿⢛⣡⣟⡠⢷⡀⠀⠀⠀⠀⣠⣯⣉⠙⡆⠀⠀⠀⠑⠤⡀⠀⢀⡀⡀
⠀⠀⠀⡟⢿⣿⢶⣅⢻⣾⡿⢻⣿⡿⢟⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣈⡿⣫⣽⣿⡭⣼⡇⠀⠀⠀⠀⠯⣶⣷⠙⠛⢦⡀⠀⠀⢀⣀⣀⣀⠤⡇
⠀⠀⠀⣟⣦⣍⣛⣭⣖⡂⣴⣿⣭⢾⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡈⢻⣿⣼⡿⠷⡿⠀⠀⠀⠀⠀⠠⣝⠟⠔⣡⣿⣃⡤⠞⠉
⠀⠀⠀⠉⠻⢿⣷⣼⣌⣦⡧⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⠿⣧⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢫⡭⠍⣹⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⠠
⠀⠀⠀⠀⠀⠀⣠⡞⠛⣷⢦⣄⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⢠⠁⣠⡾⠋⠀⣀⣀⣼⣿⣝⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢺⠿⠿⢿⠻⣯⡑⢮⢳⡀⡇
⠀⠀⠀⢀⡴⠊⠉⠳⣲⣶⣶⣽⣷⡀⠀⠨⠛⢦⠀⠀⠀⡰⣃⣞⡝⢁⣴⣾⣿⣿⣟⡛⠻⢿⣶⣽⡄⠀⠀⠀⢀⡔⠋⠉⠙⢉⡻⡍⢢⢀⡇⣿⢃⣾⡿⠔⠁
⠀⠀⠀⠸⣄⠀⢠⣾⡵⠛⠁⠈⠙⠿⣷⣲⣤⡎⠀⠀⠀⣷⣟⣩⡴⠞⣵⠟⠻⢿⣿⣿⣶⣦⣬⣽⠇⠀⠀⠀⢮⣀⠘⢉⣴⣦⡤⢣⣾⡞⡜⠛⠉
⠀⠀⠀⠀⠈⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠻⠿⠶⠛⠁⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠓⠚⠓⠉⠉⠉

⠀⠀⠀⠀⠀⣀⠤⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣤⢤⡴⡄⣬⣤⢭⣧⢤⢤⣤⣤⡤⣤
⠀⠀⠢⠖⠡⠀⠀⢠⠀⠀⠐⠈⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⠉⠩⠉⠉⠨⠍⠛⠛⠋⠙⠉⠛⠙⠋⠙⠙⡟
⠀⡁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⣄⡀⠀⠀⠀⠀⡇⡇⠘⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠂⠀⠘⠀⠀⡧
⡟⢀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⡇⢀⣈⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⣿
⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠀⡏⠀⠀⠀⣿⢓⣶⣦⣐⣖⣀⣶⣆⣶⣶⣾⣆⣶⣶⣳⣶⣶⣷
⠰⡔⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠉⠈⠉⠈⠀⠀⠁
⠀⠙⢌⠢⠈⠀⠀⠀⠀⠀⠄⡀⢌⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠉⠒⠤⢭⣠⣤⠬⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡍⠉⢡⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⢔⡢⠖⠊⢹⡄⠉⠛⠷⣠
⠀⠀⠀⠀⠀⠀⢀⡆⠈⠈⢰⠄⠈⠉⣏⣉⠁⠀⢰⡂⠁⠠⡀⠀⠀⠠⡞⠛⠓⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⢺⠋⠀⠀⠀⢾⡗⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠘⢲⡀⠖⣠⠔⠉⠀⠠⠀⠀⢉⠂⡝⢶⢀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢈⠀⠀⣀⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡼⠁⢠⣄⠀⠀⠀⢀⡀⠑⠘⡀⠁⠀⠀⠀⠀⣷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡈⠁⠀⠀⠀⠘⠁⠉⠋⠁⠀⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠀⠉⠳⣦⡞⠋⠀⠠⠀⠁⠀⠀⠀⠀⠀⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠫⢄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣐⡅⣀⡀⣀⡠⢦⣔⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠠⠀⠀⠄⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠿⡟⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠒⠒⠂⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠙⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⣻⠞⠁⠀⠀⠀⠀⢀⠀⠤⠀⠁⠼⠤⠥⢈⣀⣤⣀⡀
⠸⠧⠥⠴⠦⠤⠄⠄⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠀⠀⠀⠀⠙⢦⣀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠰⠾⠿⠾⠿⠿⠿⠷⠶⠶⠶⠶⠶⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⡄⠀⠀⠀⠀⠀⢻⡇⢀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠘⣇⣾⡿⠁⠀⠀⠀⠀⠀⠈⠉⠏⢈⠁⠁⠀⡀⢀⠀⠀⠀⠙⢏⠁
⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣶⠄⠀⠀⢠⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡅⠀⠈⠂⠀⢀⢸
⠀⠀⠈⠐⠄⠂⠂⠈⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡧⠐⠾⢿⡗⢦⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡀⠀⠀⢀⡀⠀⣀⠀⠠⢸⠈
⠀⠀⠀⡀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⣰⠀⠠⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⢸⠸
⠀⠠⢁⠄⠀⠀⠀⠐⠀⠑⡄⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⣔⠁⠀⠼⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠠⠄⢀⠠⡀⠀⠀⡀
⠀⢃⠇⠀⠀⠀⠀⠀⠀⠱⢡⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⡏⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠂⠀⡞⢹⡏⠙⠂⠈⠀⠀⡀⡆
⠀⡀⠃⠀⠀⠀⠀⠀⠀⢈⢨⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠇⠉⣠⢂⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠇⡈⠡⠀⠀⠀⠀⠀⠀⠇
⢠⣗⣐⣒⣆⣓⡒⠚⠒⠒⠚⠆⠀⠀⠀⠀⠈⠠⣈⣀⣠⣤⣼⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠛⠋⠙⠛⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⠀⠀⠰⠆⠀⠀⢀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠈⠁⠀⢸⡇⠀⠀⠋⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⢀⣴⠟⠁⠀⠀⠀⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣠⠈⠁⠀⠀⠀⠀⣀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠁⠀⠀⢰⡆⠀⠀⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⡴⠞⠋





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

⠀⠀⣴⠶⠄⣤⢀⣄⠀⣠⡀⣶⢀⡀
⠀⠀⢬⣹⡆⣇⢸⣺⠡⣗⣇⣼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠲⣀⡀
⠀⠀⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⣆⠐⠂⠚⠻⣿⠓⠶⠤⠻⢧⣄⣀⣤⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠼⣿⣆⣸⡀⠀⠐⠄⠘⢷⡀⠀⠀⠈⢷⣄⠉⠉⣻⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠿⠲⢾⣇⡐⠀⠩⡈⢿⡟⠒⠲⠶⠮⣷⣄⣀⡁⣀⣙⣦⣴⣿⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⢿⡟⠛⢶⣤⣼⣧⠀⠀⠀⠀⠈⢳⡌⠉⠉⢹⠛⠻⠔⣹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⡎⠛⠓⠶⢤⣄⣸⡇⠀⠀⠉⠑⢿⣷⣤⣀⠀⡀⢀⢿⣦⡄⣴⢠⡀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⡀⠀⠀⣇⠀⠀⠀⠀⠈⠉⣿⣦⣄⣀⠀⠀⢹⡆⠉⠛⠛⠻⠯⣛⣲⡿⢰⡿⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⣾⣧⣀⠀⠀⣤⠀⢸⣿⠉⠉⠛⠲⠾⣷⣄⣀⠀⠀⠀⢸⡿⢀⣿⣦⠀⠀⠀⠀⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠀⡐⠲⡀⠀⠙⢿⡻⠶⢦⣤⡈⣿⣀⠀⠀⢠⠀⠈⢿⡙⠛⠃⢠⣿⣴⣿⣿⠃⠀⠀⠀⠀⣿⣻⠧⣲⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⣻⣤⣭⣄⣀⠀⠣⠀⠳⡀⠀⠈⠉⢻⣿⢦⣀⠈⠀⡄⠘⣧⢀⣴⣿⡿⠜⣿⡇⠀⠀⠀⠀⢀⡘⠁⣰⣿⣷⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⣤⣀⣧⣀⠀⠀⠀⢿⠀⠈⠛⣷⣤⣴⣾⣿⡿⠿⠃⣰⣿⠀⠀⠀⠀⠸⣿⣦⡞⠉⠛⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢿⣮⣻⣿⠛⣿⣿⣷⣷⣤⣼⣧⣴⣿⣿⡿⣿⣿⣿⡧⢀⣿⢻⠃⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⣱⣌⢿⣿⣻⠿⣿⠟⣻⣟⣿⡟⠉⢑⢢⣴⣿⣥⠾⠛⠁⠀⠀⠀⠀⣀⠀⡈⠉⠘⠷⠞⠀⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠻⠾⠿⢿⣶⣿⣿⣿⣿⣿⣧⣴⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⣀⡀⠈⢈⡛⠊⠀⠆⠈⠁⠘⢡⠆
⠀⠀⠀⠀⠴⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⠀⠈⠀⠀⣯⠁⠾⠌
⠀⠀⠀⠀⠈⣁⣈⣙⣒⢄⣤⠄⡀⢂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣴⡉⠳⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⠿⠿⣟⣛⣻⣿⡿⣿⣶⣶⣤⣶⣶⣤⣄⠄⢤⡀⠀⠀⠀⠀⠀⠀⢤⣿⡿⠛⠿⣷⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠨⠽⠻⠖⠛⠋⢻⠗⠉⠛⢻⣿⣿⣿⣗⣲⣶⣤⣄⣀⠀⠉⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠛⠒⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠀⠀⠀⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣷⡄⠀⢤⣤⣠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠛⣁⣀⣸⣀⡙⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⣩⣷⡾⠟⠛⠛⠛⠛⠛⠿⢶⣿⣙⠛⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡄⠀⠀⠈⠙⢢⣦⡄⠀⠤⠤⠄⢤⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠉⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⠷⣶⣶⣶⣶⡶⠿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡠⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣶⣶⣾⣥⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣴⣾⣿⡿⡗⠛⢉⠉⠻⢿⣿⣿⣭⣟⣿⣿⣿⣷⣖⢯⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣷⣾⣿⠿⣟⣿⣿⣿⠐⣹⣿⣿⣷⡖⢈⣿⠛⣯⢻⣿⣿⣿⣿⠿⢿⣿⣯⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠙⢟⣏⢻⣾⣿⣿⣿⣿⣷⡃⢚⢛⣢⣵⣾⠁⣰⢿⡏⢿⣿⣿⣿⣷⣾⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠈⢁⣿⣿⣯⣶⣟⠛⠻⠿⣿⠿⢟⣵⣿⣾⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣧⡀
⠀⠀⠀⢀⣤⣤⣶⣾⠀⠀⠀⠀⢠⣿⣛⣽⠟⣿⣩⢰⣶⣞⣩⣴⡿⣹⣿⡿⢫⣾⣿⠿⠋⠉⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⣿⡟⠉⢩⣷⡆⠀⠀⣠⡿⠏⠉⠀⠠⣻⣿⣿⢿⣿⡿⠋⣼⣳⡟⠁⣿⡿⠃⠀⠀⢠⣿⣿⣴⡿⣹⠿⢿⣿⣦⡀
⠀⠀⠀⢿⣿⣧⡿⣿⣷⣦⣾⣿⣶⡁⠀⠀⠀⣹⣿⣿⣾⣿⣿⡲⣾⣿⣆⣤⠠⡆⠀⠀⢀⣾⣿⣿⣿⣷⣿⡄⡜⠛⢻⣿⣦
⠀⠀⠀⠘⢿⣿⣷⣽⡿⣷⣸⠿⣿⣿⣷⣤⣼⣿⣿⣿⢿⣿⠟⠀⠈⡹⢿⣿⣤⣇⠄⢠⣮⣼⣿⣿⠿⠋⠉⡴⠀⠀⣸⣿⣿
⠀⠀⢠⣶⡟⠻⣿⣿⣧⡹⠿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣏⠙⠧⢀⠀⠐⢋⡽⣿⣿⣿⣿⣿⠟⠛⠉⠀⣰⣾⣤⣶⣾⣿⣿⠏
⠀⠀⠀⠹⣷⣄⠈⢿⣿⣿⣆⠀⢻⣿⡻⠿⠿⡿⠇⢻⡿⣿⣶⣦⣤⣤⣤⡴⣿⠋⠉⣁⣠⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠘⢿⣷⡾⠿⣿⣿⣷⡄⠈⠙⠳⠦⣤⣴⣿⠟⠓⢿⣄⣀⣀⣤⣾⣿⣾⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠈⣳⣤⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿
⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠀⠀⠀⣾⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏
⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣿⠀⠀⠀⢾⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢺⡇⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⠀⢸⣿
⣿⠀⠀⠀⢺⡇⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣹⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡿
⣿⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢺⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡿⠛⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠀⠐⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡻⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⠀⠀⠀⠀⠀⠈⡀⡀⠄⠀⠀⠃⠠⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⢠⢇⡓⢤⡄⠐⠒⠐⡞⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⠁⠀⠀⡘⠈⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠐⠁⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⠀⠀⠀⠀⠀⠆⠀⠘⠀⠀⠀⠀⡐⠹⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠐⠦⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠙⠉⠉⢣⠰⢎⣠⠀⠀⠀⠀⠄⠀⠘⡀⠀⠀⠀⠈⠂
⠀⠀⢰⠁⢅⠀⠀⠀⠀⠉⠉⠉⠛⠓⠂⠠⠶⡈⠀⠀⠀⡀⠀⣷⠀⠈⠢⣀⣠⡤⣤⠤⠤⢷⡶⠒⠃⠇⠴⢠⡠⢀
⠀⠀⠠⠀⠀⠑⠢⢤⡤⠤⠤⠤⠔⠀⠄⠠⠤⡁⠀⡀⠚⡐⠚⠸⡍⠢⡀⢁⠘⠀⢤⢠⡄⠼⠀⢐⡀⠯⠷⠠⣄⠱⠍⡄
⠀⠀⠀⠗⠢⢄⡀⠀⠀⠉⠑⠂⠲⠤⠤⣀⡀⠱⡄⣈⣠⠔⠒⠀⠁⠀⣄⣈⣦⠂⣠⣊⠠⠌⠄⠂⠚⠉⠈⠁⠀⢀⣠⠃
⠀⠀⠀⠘⡀⠀⠀⠉⠐⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⣀⣀⡀⠤⠄⠐⠂⠉⠀⠆
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠂⠀⠀⠀⠐⠒⠀⠒⠒⠂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⡠⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠉⢳⠣⢀⠀⠑⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠠⠄⠒⠨⠋⠉⡱⠈⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢁⠤⠊⠐⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠱⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠚⠓⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⣀⣠⠤⠤⠶⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢿⢟⣛⣟⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡄⣀⣸⣠⠄⡧⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢹⣿⡟⣿⣿⣿⣿⡿⡃
⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⠀⠈⠉⠀⣸⣀⠀⠁⠀⡠⠒⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⣶⣿⣿⢾⣿⣿⣿⣿⣟⣭⣾⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠒⠐⠘⠉⠉⠉⠀⠀⡠⠋⠀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣽⣿⣶⣶⣷⣿⣿⣿⣫⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢿⠑⠦⢀⣀⣀⣀⣀⣀⠤⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣝⡿⣿⣿⣿⣿⣿⠿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉


⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠋⠉⠉⠉⠉⠉⠉⠑⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣀⡤⠴⠒⢚⣉⣉⣉⣉⣉⣉⣉⡙⠒⠲⠤⣄⡈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⡠⠖⢋⡡⠔⠚⠉⠉⠀⠀⡄⠀⠤⣄⠀⠈⠉⠙⠒⠤⣉⠓⠦⣀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⣀⠔⢉⡴⠊⡅⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⢠⡄⠉⠢⣌⠑⢤⡈⠳⣄
⠀⠀⠀⠀⣠⠋⢀⠜⢁⠔⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢄⠙⢆⠈⠣⡀
⠀⠀⠀⡼⠁⡰⠃⡴⠁⠀⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠱⣄⠳⡀⠙⡄
⠀⠀⡜⠀⡼⢁⠞⢠⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⢆⠹⡄⠘⡄
⠀⡼⠀⡼⢁⠎⠀⢸⠀⣯⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠹⡄⠸⡄
⢠⠃⢠⠃⡞⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⡆⢳⠀⢳
⡼⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢳⠘⡆⠸
⡇⠀⡇⢸⠀⢀⠄⢦⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⣀⣀⣤⠤⠤⠶⠒⠒⠻⠖⠉⠀⠐⠦⠀⢸⠀⡇
⡇⠀⡇⢸⠀⠈⢃⠟⠛⠧⠼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢄⡼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢘⠀⡇
⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⡇
⢫⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇⢰
⠘⡄⠘⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃⡼⠀⡜
⠀⢳⠀⢱⡈⢇⠀⠀⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠗⢀⠏⣰⠃⢰⠃
⠀⠀⢣⠀⠳⡈⢦⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⠃⢠⠃
⠀⠀⠀⢳⡀⠱⣄⠳⡄⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⡴⢃⡴⠁⣰⠃
⠀⠀⠀⠀⠙⣄⠈⠢⡈⠢⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢀⡠⠊⡠⠊⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠈⠢⣌⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡤⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠑⠢⣌⡑⠲⠤⣄⣀⡀⠀⠀⠣⠘⠀⠀⣀⣀⡤⠴⠒⣉⡤⠖⠉⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡉⠑⠒⠤⠤⣍⣉⣉⣉⣉⣉⣉⡥⠤⠔⠒⠉⢁⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢤⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀⠠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⣰⠀⠀⢀⡌⠀⠀⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠤⠔⠒⠘⢧
⠀⠐⠀⡄⠈⠀⠀⠀⢀⡀⣠⠴⣾⠏⠀⠀⢼⡄⢀⡀⠎⠀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣾⣌⡿⠀⠀⢠⠋⠀⠀⡀⣄⠀⡀⠀⠀⡤⠤⠀⠒⠒⢻
⠀⠀⢇⡻⠇⢶⠂⠀⠁⠀⠄⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⢠⢾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠠⠠⠐⠒⠒⢛
⠀⠀⠀⠀⠀⠚⠀⠈⠁⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠆⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⠤⠴⠁⠄⠀⠀⠀⠀⠀⠐⠒⠒⠉⣹
⠀⢶⢆⠀⠀⠀⠀⠀⠐⠀⠀⢢⠀⠀⠀⠀⠀⠀⠂⠰⢁⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⠰⡌⠀⠁⠀⠰⠀⠀⠂⠀⠀⠒⢀⣉⡽⠃
⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠘⡿⣦⣄⣠⣄⣀⡀⠀⠀⠀⠀⠐⠀⣠⠀⢾⠤⢼⠤⢴⡀⠀⠀⠙⠷⢤⡴⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⢀⡀⠀⠉⠉⠉⠚⠛⢿⡿⡇⠀⠀⡤⠤⠠⠀⢦⠀⢼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⠖⢀⠔⢀⠜⢁⠴⠉⣄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⡷⠤⢴⠤⢰⠄⣸⡟⠺⠃⠀⠄⣁⣄⢀⡀⠀⠸⣶⣃⡰⠁⡀⠊⣠⠎⢀⠄
⠀⠀⠀⣿⣦⣤⡀⣤⣴⢤⠤⡴⡏⠀⠀⠀⠐⢤⣀⠀⠀⠀⢤⣐⡄⢸⡄⣬⡶⠧⠟⠁⠀⠀⠀⠀⠉⣳⠿⣄⡀⠁⠉⠭⡞⣤⢴⣁⣠⠃⣀⣃
⠀⠀⠀⠘⠿⢵⠀⣿⣄⠦⠀⠓⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠻⠿⢿⠿⠾⠗⠂⠀⢴⠶⠄⠀⠐⠈⠁⠀⠈⠁⠀⠀⠀⠀⠈⠙⠉⠿⠿⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠂⠀⠍⠀⠂⠀⠈⠀⡀⠀⠄⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠥⢈⡑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠿⠷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢠⢦⣀⠀⣀⠤⠔⠒⠉⠀⢀⣠⣴⡶⡆⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠻⠶⣶⣤⣀⠠⠜⠋⠉⠀⣀⣤⠀⢰⠟⠛⠉⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡇⢀⣤⡴⠞⠛⠉⢩⠀⢸⡇⠀⠀⠀⠀⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠅⡂⠀⠠⢀⣾⠀⢸⣅⠀⢀⡐⠁⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢢⡇⠀⡤⠂⠸⠀⢼⡗⠀⠝⠔⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢸⠌⠇⠀⠁⠀⠀⠀⣸⠁⠁⠎⠀⠸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠁⣧⠀⠎⠀⠀⠀⣾⡆⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⡇⢸⣧⡷⠤⠦⠠⠆⠀⠛⠂⠒⠂⢈⠥⢤⡄⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⡂⢘⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡄⢠⣤⣤⣤⣤⣄⡄⠀⡴⠴⠶⠶⠾⣐⡾⠇⢸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠁⢀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢸⠀⢸⠁⣦⡀⠀⠀⢀⠀⣷⠀⠠⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⢈⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢸⠀⢸⢸⡆⠀⠀⠆⢸⠀⣿⠀⠀⠀⡐⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠈⡂⢸⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⢸⠇⠰⠃⠄⠘⠀⣿⣈⠀⢬⠂⡀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠨⡀⢸⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⢸⣤⠈⠀⢄⠀⠀⠀⣿⠴⠺⠣⠈⠁⠀⠀⢼⡗⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⢸⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢾⣿⡲⢀⣠⣴⡇⠀⣿⠁⡐⠀⠂⡆⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⢈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠓⣂⡇⠀⣿⠀⠀⢀⡀⡇⠀⠀⣋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢰⢨⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⠼⠾⠦⣬⣀⠀⠀⡀⠀⠁⠀⠛⠳⠖⣀⠤⡇⠀⠀⢵⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠕⠄⠰⢸⠀⠀⡀⢸⠀⠀⠀⠀⡀⠤⡐⠪⢉⢁⣈⠀⠂⠀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢿
⠀⠀⠀⠀⠀⠀⡀⠁⠰⢸⠀⠀⠂⢸⣀⣠⠴⠊⠀⠁⠀⠀⠀⠀⠈⣁⢀⡀⠀⠒⠐⠀⠀⠈⠉⠉⠒⣢⣄⣀⠀⠀⠠⢸⣽⠀⢀⠐⠊⠉
⠀⠀⠀⠀⠀⢀⠈⡀⢸⣸⠀⢐⣩⡼⠿⠟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠤⠄⠈⠉⠛⠲⢍⣸⣿⠠⣀⣀⠠⢤⣆
⠀⠀⠀⠀⠀⢈⣡⡤⠚⠛⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠈⠄⢐⡀
⠀⠀⠀⠴⠚⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⢠⣷⣶⣤⣤⠀⠀⠀⣀⣀⣠⡀⠀⠀⢠⣾⡿⠿⠿⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⡿⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠼⠇⠀⠀⠀⠤⣀⠀⠠⠄⠂⠁⠀⣁⣀⣈⠐⠠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠸⢿⣷⣦⡀⠀⠀⠀⠀⠀⣰⡀⠀⢉⠄⠿⠋⡭⢙⣷⠒⠛⣏⢤⣿⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡄⡀⠀⠀⠀⠻⣿⣤⣏⢠⣧⠴⠿⠿⡬⢹⣿⠩⡿⠤⠐⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣾⡏⣹⡷⢦⡜⢿⣮⣷⠀⡙⡿⡟⠛⠛⠛⠙⠛⣯⣵⣫⣾⡯⠭⣐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣿⣿⣿⣿⢷⣦⣿⡟⢿⣿⣿⣶⡇⠀⠀⠂⢰⡀⢀⣿⢯⣿⠏⠉⠀⢸⡀⢤⡈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠛⠲⣿⠏⠛⢷⣙⣷⣹⣿⠋⠀⡆⣠⣼⠞⣿⣷⠿⣅⠔⢌⣠⠏⠀⠀⢉
⠀⠀⠀⠠⣄⡐⠂⢀⠀⠀⠈⠙⠿⣿⣦⣝⡷⣤⣤⣽⣿⢛⣿⡟⠚⢻⣿⣩⣶⡿⢛⡄⠀⡸⠛⡅⠀⣸⢰⠙
⠀⠀⠀⠀⠙⠳⠤⣀⠀⠂⢀⣀⡀⠈⠙⠻⢿⣾⣽⣍⠛⠳⢿⠛⢒⡒⠛⠟⡯⢭⣁⠟⠆⠠⡀⠀⡔⡻⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢧⣮⣁⠀⠀⠀⠀⠈⠛⠿⣷⣦⣙⢦⣼⠇⠀⠂⠙⠶⣿⣉⢦⣤⣾⡿⠋⠀⢔⠍
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣾⣝⡊⠀⠀⠀⠀⠉⠛⠋⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠘⠛⠦⠤⢤⣀⣁⡒⠠⠶⠄⠀⠀⠀⠲⢤⣀⠠⣦⣄⡉⠻⢿⣷⣤⣄⣀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠂⠀⠀⣀⡀⠂⠀⠈⠙⠷⢮⡓⢄⡉⠛⠿⠥⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠦⠀⠙⢦⡙⠂

⣿⣿⢛⠿⣛⠛⣟⢛⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠲⡄⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠄⡔⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⡖⠲⠒⠒⠂⠐⠂⠒⠀⠐⢺⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡀⠀⢰⠀⠃⠀⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⡇⠀⠀⢰⠀⠃⠀⠀⠀⢰⠀⡄⠀⠀⡈⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡇⠀⠈⡀⢰⠀⠀⠀⠀⠀⢁⠀⠀⠀⡇⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡇⠀⠀⡇⢸⠀⠀⠀⠀⡇⠸⠀⠀⠀⠁⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠧⠤⠔⠃⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠒⠒⠚⠒⠒⠚⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠐⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠒⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⠎⣀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⢤⡈⢇
⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡒⠒⠒⠒⢲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠚

⠀⢰⡶⠶⠶⠶⠶⢦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢸⠃⠀⠀⢰⠶⠶⠶⠶⠖⠒⠒⠒⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠀⠀⠀⣿
⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡆
⠀⢸⡀⠀⠀⢸⠀⠀⠀⠀⣟⡽⠯⠭⠿⠿⠛⠳⠙⡇⠀⢸⣏⡭⠭⠭⠭⠽⠭⢍⣶⠀⠀⢸⡇⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⡇⡇⠀⢰⣧⡄⠀⠀⠀⠀⠀⢸⣽⠀⠀⢸⠇⠀⠀⢸⡇
⠀⢸⡅⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⡏⡇⠀⠸⣿⡇⠀⠀⠀⠀⠀⢸⣼⠀⠀⢸⡀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣻⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⠇⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⡇⡧⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⣿⠂⠀⠀⠀⠀⠀⢸⣾⠀⠀⠘⡇⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⡆⠀⠐⣿⡁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⠀⡇
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⡇⢼⠀⠀⠀⠀⠀⠀⣿⡁⠀⢰⣿⡇⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⡇⠀⠀⢀⡇
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢷⢸⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣧⠆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⡇⠀⠀⠘⡇
⠀⢸⡇⠀⠀⠘⡇⢀⢤⡀⢸⣜⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⣻⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠘⡇⠀⠀⠀⡇⢼⠀⠇⠸⠯⠭⠿⠿⠷⠿⠟⠿⠆⠀⠀⠫⠿⠶⠶⠾⠶⠿⠿⠿⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⡇⡜⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⡇⠳⠤⠞⢀⣄⣀⢀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⢤⣄⣤⣄⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⡇⢀⠁⡆⢸⢹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠋⠛⠉⢻⢸⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⡇⠈⠒⠁⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⡇⠀⠀⠀⣧
⠀⠈⡇⠀⠀⠸⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠎⡄⠀⠀⡇⠀⠀⠀⡿
⠀⢸⡇⠀⠀⢐⡇⠀⠀⠀⠸⢾⠭⠭⠿⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⠭⠭⠭⠭⢶⠇⠀⠀⣗⠀⠀⠀⣟
⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣟
⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⢰⣖⣒⣒⣶⣶⣶⢶⣶⣶⣶⣾⣷⡾⣶⠶⠶⠶⠶⢶⣶⠀⠀⠀⡗⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⡇⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⡇⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠘⡇⠀⠀⢀⡇⠀⠀⠀⠀⡿⣿⠾⣿⣿⣿⣿⡿⠿⠾⠶⠿⠷⢾⣓⠺⠶⣖⠚⠛⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⣠⣧⣤⣤⡤⣷⠶⠦⡶⢦⣴⠴⠦⣤⣶⠶⣦⣶⣶⣶⣶⡶⢶⣶⡦⠶⠶⢶⠿⢿⠿⠗⠒⠧⠀⢤⡤⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠒⣶⠒⠦⣤⣀⠀⠀⢰⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⣀⡔⠾⣀⠀⠉⠀⠀⠀⠙⢷⣄⣈⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⣀⣬⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠹⣿⠂⠀⠀⡱⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⣸⣿⣿⣿⣿⡌⠉⠀⠀⠀⠀⠀⠀⠀⢡⢴⣿⣶⠐⠃⠱⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⣠⣠⣶⣿⢏⣿⣿⣿⡆⢀⡀⠀⢀⠠⠤⠾⣞⠁⠀⠀⢿⡅⠆⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡤⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣾⡓⠀⠀⠀⠀⠀⢫⠀⠀⠉⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣀⣠⣿⣖⣻⣿⣾⣿⣟⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠘⠄⠀⢢⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠸⣶⠀⢸⣦⡾⣿⣤⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠛⠛⠋⠀⠈⠉⠉⠉⣉⣉⣭⣽⣿⣬⣽⠙⠓⠒⠒⠛⠛⠁⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⡾⠀⠀⠀⣀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⣠⣽⣿⣄⠀⠀⠀⢿⣦⣠⢈⣽⠻⣿⣿⣿⣿⡄⠀⠀⠀⣐⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠛⠛⠻⠿⢿⣿⡿⠿⠿⠀⠀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠾⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣃⠉⣉⡁⣠⡄⡄⡄⠀⢠⣤⣀⣤⡈⣉⡙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡭⠘⣿⡃⡷⠀⣑⡆⡗⣇⠀⢸⡞⢻⣃⡇⣿⡟⣸⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⡆⠀⠀⠀⠃⠀⠁⠁⠉⠁⠈⠀⠁⠀⠀⠈⠀⠀⠉⠀⠁⠁⠃⠛⠀⠀⠀⡆⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠓⠲⢤⣀⠀⠀⢀⣀⣀⣠⣤⣤⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣠⡇⠀⠀⣠⠬⠛⠋⠉⠁⠀⠀⠀⠀⠈⠉⠓⠒⠮⢭⣓⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⠙⠲⣄
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣙⣦⣀⣀⣀⡀
⣰⠋⠀⠈⠓⣄⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠈⠉⠉⠓⠦⣄
⣇⠀⠀⠀⡴⠋⠙⠲⢤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠈⠙⠢⠤⡇⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢀⡤⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⠴⠚⠉⠀⠀⢸⣄⡠⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢰⠃⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⡄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣤⣀⡀⠀⠀⠀⢸
⠀⠳⢄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⠤⠖⠒⠒⠒⠒⠶⠤⣄⣀⣉⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡰
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠀⠀⠀⠀⢰⣣⠔⠋
⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠖⠛⠺⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣄⠀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⠟⠛⣫⡉⢙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠰⠬⡁⠀⠲⠈⠷⣄⣠⡶⠺⠚⠉⠙⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⡻⠿⠀⠈⠉⠉⢶⣤⠀⠀⠀⠀⠐⠳⣝⠀⣉⣣⣽⠟⠿⠿⠶⠶⠂⠚⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢺⣗⣄⡀⠀⠀⠀⠰⢧⣀⠀⠀⠀⣄⡀⢠⣄⣀⡞⠈⠁⠒⠢⠀⠀⠈⠛⠾⣿⠶⠶⠶⠖⠶⠂⠀⠠⠞⠁
⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⣨⣷⠟⢷⣢⣄⠀⠀⠙⣧⣐⢤⡼⢿⣿⠮⣍⣀⣉⣤⣼⢦⣤⡄⠢⠀⠘⠂
⠀⠀⠀⠰⠁⠆⠀⠀⠀⡁⠈⠻⣿⣴⣆⢱⣌⣆⠀⠀⠈⠉⠛⢧⣬⠿⠓⠛⠉⠉⠁⠈⠉⠉⠛⠛⠋⣀
⠀⠀⢀⠀⢰⡯⠃⠀⠀⠇⠀⠀⢹⣷⣿⣷⣼⣿⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠈
⠀⠀⠀⠱⢚⠋⠁⠀⠘⠦⠀⠀⠈⢿⣿⣿⣭⣥⡾⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠂⢘⢃⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢢⡄⠐⠀⠀⠀⠐⠢⢄⡀⠙⠛⣻⠟⠁⠀⠀⠀⣀⢤⠒⠀⠀⠀⠠⡂⣊⠟⠂⢽⡃⡆⠀⠀⠀⠀⢀⣀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢤⠁⠀⠀⠀⢖⣀⣄⣠⣾⣶⣴⣾⣿⡿⠀⠀⠀⠀⠀⠉⠐⠎
⠀⠀⠀⠀⢀⡀⢀⣤⡒⣦⣤⠀⠠⡀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡦⠄
⠀⢀⠀⢀⣼⠿⢋⡿⣤⣽⣾⢛⣳⡛⡆⠀⠀⠀⠘⠱⡂⠟⠁⡠⣿⣯⣷⣿⣿⣿⠉⠋⠹⠍⠙⢢⡁⣾⠁⠀⠀⠀⠀⡠⠂
⠀⠘⢶⣿⠿⠴⢻⡅⢿⣿⡟⠫⡿⣷⣤⡀⠀⠀⠀⠴⠶⠴⠷⠾⠿⠟⠁⠈⠙⠻⣿⠒⣶⢒⣦⣶⣯⣿⣖⡒⠾⠀⠊⠀⠶⠆
⠀⠀⢨⣸⣦⠈⡷⢳⣌⡙⢻⡄⢡⡹⣦⣈⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠿⠮⣭⣹⣿⠿⠋⠀⠀⠀⠀⠂
⠀⠀⠘⠿⢻⣛⣿⣯⣤⢴⡀⠀⠘⣷⣹⡿⢿⡿⢧⠀⠀⠀⠀⡀⣠⢨⣱⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠶⠀⠀⡀
⠀⠀⠀⠘⠻⡿⠿⣦⡿⠀⡛⣶⡶⢷⣟⣳⢿⣿⣿⡇⠀⠀⠘⢿⣿⠄⠛⡇⠀⠲⠂⠆⢰⣀⡠⢀⣡⣴⣤⣤⣀⠀⠒⠐⠋⠁
⠀⠀⠀⠀⠁⠀⠒⠂⠒⠂⠛⠻⠿⠿⠿⠽⠻⠛⠉⠀⠀⢀⠀⠀⠹⠢⣈⠤⠆⡀⠀⠀⠀⢹⣿⣿⣟⣿⣯⣻⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⢠⡀⠀⠀⠘⢻⡜⠃⠰⠀⠀⠀⠁⠹⣿⣿⣿⢩⣿⠏⡀⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠤⠄⠀⠀⠀⠀⠘⣷⣈⠌⠄⠀⠀⠀⠉⠿⠀⠀⠀⠀⠒⢃⡔⣿⣿⡿⣾⣟⣇⣀⠀⠀⡀⢣
⠀⠀⣦⣄⢠⡶⠛⡛⣉⣁⡤⢮⡀⡠⠂⠀⠀⠀⠀⠀⠘⡿⣿⣽⡟⠺⠖⣡⠤⣬⣋⠄⠀⠀⠨⣴⠋⣿⣿⢿⣿⣿⣿⢁⠰⢀⡄
⠀⠀⣿⣼⣧⣴⢙⡓⣛⣻⣿⡇⡰⠁⠀⠀⠀⡀⠀⠀⠀⣀⠀⠈⠀⣚⣁⣀⡶⢻⣿⠄⠀⠀⠀⠐⠞⢁⣿⣿⣿⣿⣿⣿⠷⢾⠃
⠀⠀⢹⣿⢶⢿⣿⣿⣿⣿⡌⠘⠀⠀⠀⡠⠞⠀⠀⠀⠐⠉⠑⠠⠜⣷⡾⠿⠛⠋⠁⠀⡄⠀⠀⠀⠐⢛⣩⣉⠛⠻⠯⡝⠛⠁⠂
⠀⠀⠀⢿⣾⡿⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠘⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠂⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢷⠀⠀⠀⠀⠼⠷⣼⣦⡾⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠐⠊⢉⣡⢤⡞⠀⠀⣠⢤⣀⠰⢠⣀⠈⠐⣿⠿⣿⡟⠻⣿⣦⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⡋⣽⠉⠐⠚⠀⠀⣴⠶⢬⣿⣿⣦⡈⢹⡷⠿⢦⣄⠀⠀⠀⠙⠻⢦⣄
⠀⠀⠀⠀⢨⡉⠂⠀⣀⠊⠀⣀⣤⣞⣯⣶⣾⠟⠁⠀⠀⠀⡀⠠⠀⠀⠁⠀⠉⠁⠉⠹⣿⣶⢦⣄⠈⠛⣆⠀⠀⠁⢠⡈⠻⣶⣖⣦⡄
⠀⠀⠀⠀⠀⣙⠣⡀⠀⢠⡾⢻⣴⣻⠟⠋⠀⠀⠀⠀⠁⠂⢤⣤⣴⣾⣧⣀⠀⠀⠀⠀⠈⠉⠛⠿⠷⣄⠸⣦⠀⠀⠀⠈⠰⠈⡉⠿
⠀⠀⠀⠀⠀⠈⠁⠤⣸⣿⣳⡿⠛⠁⠀⡠⡤⠀⢰⣃⠲⢤⡾⣿⣿⠿⡇⢡⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⡄⠀⢾⣇⣹⠦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⡥⢄⢀⡾⣿⣿⣾⣿⣿⣾⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣤⣀⣀⣀⣀⣭⢿⣛⣻⣿⢁⡩⠀⠂⠀⠀⣄⢰⠠⠊⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣽⠿⠛⠛⠻⣭⣿⣿⣿⣿⢋⣹⠀⠀⠀⠀⠲⠞⠛⠂⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡞⠉⠉⠉⡟⠉⠉⠙⡆⠀⠀⡇⠀⢰⠖⠒⠒⢲⠒⠒⠒⢲⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡟⠉⠉⠉⡏⠉⠉⠉⡇⠀⠀⡇⠀⢸⠒⠒⠒⢺⠒⠒⠒⢺⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⣀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠛⢻⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣧⣤⣤⣤⣧⣤⣤⣤⡇⠀⠀⡇⣶⣼⣀⣀⣀⣸⣀⣀⣀⣸⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠁⠀⠀⢸⠁⠀⠀⢹⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡗⠒⠒⠒⡗⠒⠒⠒⡇⠀⠀⡇⠀⢸⠦⠤⠤⢼⠤⠤⠤⢼⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠧⠤⠤⠤⠧⠤⠤⠤⠇⠀⠀⡇⠀⢸⣄⣀⣀⣸⣀⣀⣀⣸⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢶⣶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠹⣷⣶⣭⡻⣿⣶⡤⠖⠚⠋⠉⠛⠻⣿⡷⡶⠾⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠠⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠒⠒⠒⠒⠒⠢⠤⠤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣧⠀⣀⣶⣿⣿⣿⡿⠋⠀⠀⠈⠙⠲⣤⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣀⢔⣪⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⢛⣶⣦⣼⣷⣽⠉⠛⢿⣿⠟⠲⣾⣏⣿⣷⣄⠈⠃⠀⠀⠀⣠⡘
⠀⠀⠀⠀⠀⢀⢞⣵⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠏⣿⣿⣿⣿⣦⣤⣼⣿⣤⠀⠠⠛⠛⢿⣿⣷⣄⠀⠀⠀⠉⠁⡀
⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣸⣿⣿⢃⢂⢀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣶⡛⣿⣿⣦⡇⢾⠀⠀⠀⠘
⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣾⣰⡀⡆⢀⠀⠀⠀⠀⠀⠀⠀⣤⣷⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣷⣤⣀⣤⡦⠊
⠀⠀⢀⡾⠃⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣼⣆⣆⣇⣧⢀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣹⠟⠋
⠀⢀⠞⠁⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⢿⣿⣿⣿⣿⣿⣷⡮⠭⠍⠉⠉⠉
⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡌⠈⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣼⣿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⡃⠀⠀⢠⣿⣿⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣼⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢹⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣧⣀⡆⠀⠀⠘⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡀⠀⠀⠙⢻⣿⣿⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠞⠀⠉⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⡿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠘⠟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡈
⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡷⠆⠀⠤⠀⠠⠂⠀⠀⠀⠀⡰⠒⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡇⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠠⠃⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠰⢻⠃⠀⠘
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠈⠙⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⠀⠀⢀⠄
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠃
⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⢠⠑⠤⢀⠌
⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠁⠂⠀⠀⠄⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠁
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡟
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣿⣿⡄⠀⠀⠀⠆⠀⠈⡀⠀⠀⢼⣷⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣠⠿⠃⠿⠿⠿⠿⣆⠀⠀⠰⡀⠀⠁⠀⠀⣾⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠈⠀⢀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣧⡀⠀⠱⡀⠠⠂⢀⣭⣭⣏⣉⣉⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠄⠁⠀⣰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣦⡤⠊⠀⣴⣿⡉⠀⠙⢿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⢀⣠⠚⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⡟⠠⠂⢸⡿⠃⢤⡄⠀⠀⠹⢿⣷⡄⠀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢰⣏⣉⠀⣩⣭⣭⣭⣭⡁⣩⣭⣭⣭⣭⣭⡸⠀⠀⡈⠀⠀⠠⠄⠀⠀⢰⡀⡘⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⡆⠀⣀⣀⣀⣀⣿⣿⡇⣿⣿⠿⠿⠿⠃⠛⣻⠿⠿⣿⣿⡇⠀⢀⠀⠀⠤⠀⠀⠀⠐⠀⢐⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠃⠉⠁⠀⠀⠀⠉⠉⠙⠓⠢⢄⡀⠀⠀⠀⠉⢬⠀⠘⢁⡿⠙⠁⢆⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠉⠳⡄⠀⠀⠀⠚⠀⠘⢇⣠⣤⣈⣦⣤⠀⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢻⠵⠶⠷⣖⣛⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⢃⠀⣀⣉⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠉⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⠄⠀⠀⠀⠀⠀⠑⡅⠐⠴⠀⠀⠉⠙⠝⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠛⢥⢀⣀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⢀⣀⡀⠠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡰⢻⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢸⠳⡀
⠀⠀⠀⠀⢰⠁⠘⡄⠀⠀⠈⠙⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠉⠀⠀⠀⡜⠀⢳
⠀⠀⠀⠀⣸⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⢀⣀⠤⠄⠒⠒⠒⠒⠤⢄⣀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢹⠀⠀⠀⠀⠐⠆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠆⠀⠀⠀⠀⢸⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡸⠀⠀⠀⢰⣿⣆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣾⣷⠀⠀⠀⠸⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⠀⠀⠀⠌⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠋⠄⠀⠀⠀⢱⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⢉⣉⣉⡁⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢁⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢸⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡂⠈⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡈⠀⡺⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⢠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢦⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠴⠶⠄⠀⠀⠴⡶⠄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠣⣳⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢠⡡⠋⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠠⠤⠤⢀⣀⡠⠔⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠤⢄⡀⠀⠀⢀⡀⠤⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⠴⠲⠖⠶⠆⣰⡔⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡰⠞⠋⠀⠀⠈⠙⠋⠐⠂⠐⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠹⣿⡾⠀⢀⣀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣿⣥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣶⣦⡈⠋⠀⣠⣴⣦⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣯⡰⡌⣿⡿⣿⣷⣿⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⠿⠾⠿⠿⠛⠛⠋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣧⡜⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠘⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣏⠄⢴⣠⣴⣿⣿⣿⣿⣴⣶⡒⣤⣾⣿⣎⣷⢪⣆⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡏⠀⢀⣠⣴⣷⣷⣿⡿⠟⠝⠛⠩⡿⠿⣿⠟⠟⠻⠟⠛⢻⣿⠀⠁⣄⠈⢫⣷⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⡉⠁⣠⣴⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠉⠐⠺⠿⣦⣀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⣚⣿⢏⣽⣻⡿⠛⠛⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⢀⡈⣴⡴⢿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⠟⢿⣷⣦
⠀⠀⠀⠀⢸⠏⠻⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⣶⣠⣼⣿⣿⣷⡟⠀⠍⢀⡚⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⠃⢻⣿⠁⠀⠀⢸⣿⣿⢡⣧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠻⠄⠀⢼⡿⠄⢠⠀⢻⡿⡧⡿⠉⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣭⢻⣛⣿⡟⡟⣟⠿⢻⡻⠏⡟⣿⢻⢸⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣟⠉⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⠿⠛⠋⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠰⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⢘⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠀⠆⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂
⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⣟⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢊⡈⠁⢨⡉⠉⠉⢠⡈⠁⢁⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠈⡇⠀⣸⡀⠀⠀⣸⡀⠀⣸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠠⠏⠉⢻⠋⠉⠉⢻⠋⠉⢻⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢠⡆⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢀⡗⠒⢻⠗⠒⠒⢻⠗⠒⢻⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢘⡇⠦⢾⡆⠶⠤⢾⠦⠤⢾⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠸⣇⣀⣸⣀⣀⣀⣸⣀⣀⣸⣷⣶⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠉⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⠀⠈⠉⠙⠛⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⡀⠄⠒⠀⠀⠀⠀⠠⣤⠀⠠⠄⢦⡄⠀⠈⠀⠃⠠⠀⠀⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⠄⠈⠀⠀⢻⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⠀⢀⣀⣋⣀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⢤⠀⠙⢿⣷⡀
⠀⠀⠀⠀⢀⣼⡿⠋⠀⠄⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣦
⠀⠀⠀⢠⣾⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⢿⣷⡀
⠀⠀⢠⣿⠏⠀⠦⠀⢠⣤⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠆⠀⢻⣷⡀
⠀⢀⣿⡏⠀⡠⠀⠀⢸⡏⠀⣸⡃⠀⢸⡇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠤⠀⢻⣷
⠀⣼⡟⠀⢠⠀⠀⠀⢸⣇⠀⢹⡇⠀⢸⠇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡀⠈⣿⣇
⢰⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠛⠀⠀⠀⢀⠀⢸⣿
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⣿⡇⠀⠀⠀⣠⠂⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠃⠀⢿
⣿⡇⠀⠆⠀⠙⠶⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣬⡀⠀⠀⠶⠀⢹
⣿⡇⠀⢀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣕⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⡄⠀⣿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠐⣿⣿⣿⡟⠁⢀⠀⠀⣿
⠸⣿⡄⠀⠀⠀⠀⠀⢀⡀⢀⡐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣤⣴⣶⣾⣿⣿⣿⣦⣈⠀⢸⣿
⠀⢻⣷⠀⠙⡀⠀⠀⠸⣆⣠⠃⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⡏
⠀⠈⢿⣇⠀⠐⠀⠀⣴⠉⠙⣷⣰⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠘⣿⣦⠀⠖⠀⠈⠓⠚⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠈⢿⣧⡀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠲⠀⠀⠀⠈⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⣿⡧
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠃⢀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⠠⣿⣿⣿⣿⣿⣿⣿⢠⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠁⢾⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⡇⠈⢻⡆⠀⠀⠀⠀⠀⠘⠂⠈⠁⢠⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠓⠀⠚⠁⠀⠀⠀⢀⠀⠤⠐⠈⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣧⠁⠉⠀⠘⠂⠀⠉⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋⠁⣼⣿⣿⣿⢿⣿⣿⡏⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⡿⣷⣶⣶⣶⣶⣾⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣏⣻⣿⣦⣈⣏⣙⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣑⣾⣿⣛⣿⣁⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⣿⣿⣿⣷⣶⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⣿⣇⣐⠃⣼⣿⣾⣿⣿⣿⡿⣿⣮⡻⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠅⠊⣟⠃⠛⠀⢿⣿⣿⣟⣾⣿⠇⣨⣽⣿⣾⣯⠹⣿⣿⣿⢿⣿⣿⣶⣦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⢠⣼⣿⠂⠐⠤⠰⣿⣟⢿⣿⣇⠀⢿⣷⣿⠋⠀⠀⣿⠛⣌⢛⡿⠓⢹⣿⡏⣛⣿⣶⣾⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⠄⢸⣿⣍⠁⠀⠀⠁⣀⡶⢿⣿⣿⣆⣴⢻⡧⢀⠀⠀⢈⠉⠀⠀⠈⠂⠸⣿⢃⠤⢺⣾⡉⢿⣿⣿⢷⣶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠘⢿⣿⣿⣧⣤⣿⣏⣫⡀⠈⠀⣀⢹⣿⣿⢿⣟⡁⣙⠂⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⡿⣡⣿⡇⡘⠻⠿⣮⣿⠛⣶⣿⣅⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⠉⠉⣸⣿⣿⡿⣷⣀⠀⢀⢀⣀⠀⠛⠀⠉⢀⠄⠐⠂⠀⡀⠀⠰⢶⣄⣀⣺⡟⢰⣿⢛⣅⣈⠀⣠⣠⢤⣴⣿⡿⢏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⢿⣿⣿⣶⣾⡿⠗⢤⣤⣽⣿⣷⣶⣾⠀⢠⣶⣿⢣⣤⣤⣶⣶⣾⣿⡿⠁⣿⣿⣿⡿⠿⠶⠦⠙⡚⣉⡥⣎⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣷⡤⢄⡙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣾⣿⣷⠺⠿⠿⠿⠛⠛⡉⡀⠂⠨⠭⠄⡒⠈⠉⠀⣁⡠⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠈⠁⠒⠠⠄⣉⣉⡉⠉⠉⣉⣁⣀⣀⣀⠀⠠⠤⠤⠤⠒⠒⠉⣾⠁⠀⠀⢀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣄⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⣀⣀⣤⠴⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠤⢤⣄⣠⣴⠤⠴⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣄⡀⣀⡀⣠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢸⠷⣿⢸⣟⣠⡿⣧⢸⡇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠒⠒⠂⠒⠒⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣀⣈⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠙⠻⢷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⡟⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡘⠀⠀⠀⡰⢻⣆⣌⢛⣦⠀⠘⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢰⣧⣶⣠⣦⣷⣿⣼⣿⣿⣿⠀⢈⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣦⠀⢸⡏⠸⡏⠀⢹⣿⣿⡇⠐⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡇⠀⡇⠀⢸⣿⣿⣷⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣅⣤⣡⣤⣬⣭⣭⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠋⠻⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠾⠷⠒⠒⠛⠛⠛⠛⠿⠦⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠒⠂⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠴⠊⠀⠀⠀⠀⣠⠔⠚⡛⠥⠐⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⢐⠵⠁⠀⠀⠀⡀⠐⢉⠤⠂⠁⠐⠂⠀⠀⠀⠀⡶⠀⡷⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣀⡀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⣠⡖⠡⠀⠐⣄⢳⡀⠀⠀⠀⠀⢠⡄⣿⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠙⢷⣝⢦⡀⠀⠀⠈⢿⣆
⠀⠀⠀⡰⠁⠀⠀⠀⣴⢃⡴⠃⠈⠀⠀⠀⠈⠳⣳⡀⠀⠀⠀⠘⠓⠛⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡙⢶⣿⣦⡀⠄⠈⢿⣆
⠀⠀⡴⠀⠀⠀⢀⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⠈⠀⠈⢻⣿⣿⣶⣆⠀⢿⣆
⠀⢠⠃⠀⠀⠀⠞⠠⠀⠀⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⣴⠿⠛⠀⠀⢻⣿⣿⣿⣶⠘⣿⡄
⠀⡄⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⣠⠖⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⢻⣧
⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠸⣿
⠃⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⣿⡇⢿⡇⠐⣿
⠀⠀⠀⠐⣼⡇⠰⠀⠬⠍⠉⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠿⢀⡀⣿⣟⢸⣷⡀⣿
⠀⠀⠀⠘⡎⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡿⣌⠧⠀⣿
⢠⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣸⣿⡇⢟⠁⢀⣿
⠈⡤⠀⠀⢹⡿⢣⠀⠀⢀⣄⢖⣫⢱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⣄⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⣦⡀⠀⢠⣿⡻⠼⠞⠀⣸⡏
⠀⠐⢀⠀⠘⣷⡉⣧⡀⡈⠻⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉⠛⠶⠙⠀⢠⡿⡷⢡⠚⠀⣸⡟
⠀⠀⠀⢂⠀⢻⣷⡹⢿⡇⠀⠋⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⠀⢘⣧⡀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣏⡟⣡⠎⠀⣰⡟⠁
⠀⠀⠀⠀⡣⡈⣿⣿⣌⠢⣾⣦⠀⠀⠀⢀⣤⠏⠗⠀⠀⠘⠃⠈⠛⠉⠀⠀⠀⠈⠀⠻⣄⠀⠀⠠⠄⣠⣾⣯⢏⣴⠁⠀⣰⠟
⠀⠀⠀⠀⠘⢷⠈⢿⣿⣷⣝⠿⣷⣄⠀⠈⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠂⢀⣤⣾⣯⠟⣡⠟⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢂⠉⢿⣿⣿⣮⡝⢷⣦⢄⡀⡀⠀⠀⠀⠘⠂⠰⡆⡀⠀⠠⠀⡀⣠⡴⣞⠿⠟⢋⣴⡟⠉⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⢻⣿⣿⣿⣷⣮⣘⣤⠉⡀⠐⠒⠂⠤⣤⣤⣶⣶⣶⣿⣿⠿⢞⣋⣴⣶⡿⠗⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣍⣉⣁⣀⣠⣤⣤⣶⣶⣿⢿⢛⣉⢤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣥⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢰⡒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠶⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣠⠖⡄⢸
⠀⠀⠀⠀⠀⢀⠤⢤⡰⠊⠁⠀⠈⠙⠁⠀⠀⠀⠀⢡⡔⠊⠉⠉⠐⠖⠒⢢⣀⠤⠤⣄⢀⠠⢤⡀⠀⡠⣇⠸⠧⢤⣄
⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠙⢫⢣⠜⢰⢀⣦⢼
⣠⠊⢉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⣈⣀⢏⠈
⡇⠀⠣⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠒⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡤⠖⠁
⠀⢸⡉⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⢸⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⣆⡀
⠀⠀⢀⡽⠀⠈⢉⠗⠒⠲⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠊⠉⣳⠀⠀⢀⣹
⠀⠀⠘⠤⣀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⠟⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠏⠀⠀⢠⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠸⠋⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠛⠀⠀⠛⠀⢀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠒⠶⣾⣧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣷⣾⣿⣿⣾⣭⣍⠛⣦⠰⣧⣤⣼⠇⢾⣁⣀⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⡄⢀⡞⣽⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣀⣿⣄⣀⣀⣈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡟⣧⠀⢿⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡿⠀⡾⠀⣿⣿⣿⣿⣿⡟⣉⣤⠶⣛⣫⣭⣭⣿⣿⣿⣿⣿⣷⣶⣿⡟⠻⣿⣿⣿⡇⢸⠄⢸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⠀⢿⣿⡿⢋⡽⠛⣩⣶⣿⠿⠛⠛⢉⣉⠉⠉⠛⠻⠿⣿⣿⣿⣷⣄⠉⠛⠧⡿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠻⣤⠞⠁⣰⠋⣠⣾⡿⢋⡅⠀⠀⠀⢸⣿⠀⠀⠀⠀⠖⠈⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣾⡿⢡⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⠶⠀⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢿⣸⣿⡄⠛⠃⠀⠀⠀⠀⠀⠀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⡀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⢸⣿⠁⢠⡏⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⣇⠀⠹⣿⣿⣧⠀⡤⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢡⣿⠏⢀⡾⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣦⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⠞⣱⣿⠋⢠⠞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢳⡀⠈⢻⣿⣿⣷⣤⣘⠃⠀⠀⠀⣿⠄⠀⠀⣀⣤⠞⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢻⣿⣿⣿⣿⣶⣶⣶⣶⠶⣖⣛⣭⣴⡿⢿⣯⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠋⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠉⠀⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋

⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⢿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⡿⢟⣟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⣿⣿⣿⣿⣿⣿⣿⢋⡾⣿⣿⣿⠀⣻⣿⣿⣿⣿⣿⣿⡏⡄⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣿⣿⣿⣿⣿⣿⡇⣾⡇⣼⣿⠟⣠⡿⡿⢿⡿⠿⠿⣿⠀⢡⠿⣿⣿⣿⣿⣿⣿⣿⠿⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⣿⣿⣿⣿⣿⣿⠀⣿⡅⣨⣷⣾⡟⢠⢰⡄⢿⢰⠆⣿⠀⣴⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢻⣿⣿⣿⣿⣿⣆⢿⠇⣿⣿⣿⣷⡘⠷⢀⣴⣿⠐⣫⠀⣤⡙⢟⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⣭⠙⠛⠛⠻⠟⠛⠛⠛⠛⠛⠋⠉⠉⣶⣍⢿⣿⣿⡟⠛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠛⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠛⠉⢋⠛⠛⠲⠶⠶⠟⠛⠋⠉⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢢⡖⠉⠀⠀⠀⠀⠠⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢇⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠁⢠⠃⠉⡆⠘⠉⠄⢸⠇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠸⣆⠀⠀⠀⠀⠘⠀⣸⠀⠀⠀⠘⢄⠐⠏⠀⢸⡀⢺⠛⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣤⣿⠿⠿⠷⢦⣤⡤⠤⠶⠶⠾⠛⠛⢻⣿⣦⠀⠀⠐⠟⠗⠒⠒⠒⠂⠐⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢳⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠙⣄⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⠻⠿

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢨⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠤⠤⠤⠤⣤⠤⠤⠤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⡤⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠄⠀⠠⠀⣠⠕⠒⠘⠒⠤⡁⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢠⠒⠉⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠦⠔⠒⠬⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠠⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣬⠉⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠸⡀⢸⠛⠈⠺⡇⠀⠀⠀⠀⢠⠦⠄⠤⠔⠉⠓⠒⢲⢸⠗⠁⠋⣧⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⢀⠞⢁⠆⠀⡠⠊⠀⢰⠢⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢄⠀⠹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡸⡀⡜⠀⡰⣳⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⢸⠀⠸⡆⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠁⢸⠀⠀⡿⣹⠀⠀⠀⠈⢦⣤⠴⠃⠀⠘⣲⠀⠙⠲⠒⠃⠀⢰⢱⠀⠈⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⢇⢈⢆⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠀⠀⡀⠀⢀⢀⠎⡟⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠄⢀⠈⠘⡆⠀⠈⢢⡈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⢋⡔⠁⠀⢰⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠈⠒⠱⠦⢄⣀⣀⡀⢀⣀⣀⣀⠤⠶⠏⠒⠁⠀⠀⣠⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠰⠀⠂⠘⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠘⠀⠈⠀⠐⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠁⠠⠀⠁⠀⠀⠃⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢸⡇⠀⠀⢀⠘⠀⠀⠀⢈⠀⡀⢀⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠂⢀⠀⠀⠀⢀⡀⠈⠀⠈⠀⡀⠀⢀⢘⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡤⠤⠄⠀⢤⣤⡤⠀⠤⢤⡶⠚⠉⣁⣴⣶⣿⠟⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣠⣶⣯⣴⠶⠞⣿⠟⠁⠀⠀⣰⣿⣡⣴⡾⠿⣽⡿⠁⠊⠀⣀⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠶⣶⠟⠛⠉⠁⠀⣠⡾⠁⠀⣀⣤⣶⠿⠟⠋⠁⠀⣰⠋⢀⣠⣶⣿⡿⠋⢀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡾⠃⠀⠀⠀⣠⣾⣿⡴⠾⠛⢻⡟⢁⡤⠀⠈⣠⣾⣧⡶⠿⠛⣡⡟⠁⠈⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡋⣀⣠⠤⣶⠾⠋⡁⠀⠀⢠⣼⠏⢐⣁⣴⣶⠟⠛⠛⠁⠀⠀⣼⣿⣥⡶⠶⠶⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⣠⠞⠁⠀⠀⠀⣠⣞⣩⣴⠞⠉⣼⠟⠁⠈⠀⢀⣨⣤⠞⠉⠡⠀⠀⢀⡾⠃⣀⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠻⣄⠀⠀⣀⣠⠞⠛⢩⠄⠂⣠⡜⢁⡠⠔⠒⠋⢉⡼⠃⠠⠄⠂⠈⣠⠎⢀⣠⣾⣿⠀⠈⠲⠦⠞⠀⠴⠺⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣪⡟⠁⠀⠀⠀⣠⣾⣿⣾⣿⣗⣶⣶⣶⣿⣤⣤⣄⣐⣦⣾⣧⣶⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⣿⣧⣠⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣑⣟⣹⠟⣿⣷⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⣿⣧⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⠆⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣸⣻⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣐⣚⣍⠴⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠚⠋⠉⠉⠀⠈⠉⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁





⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠈⠁⠀⣹⠀⣠⠴⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣄⡀⠀⢀⣠⠔⠛⠳⣍⢀⣠⠴⠒⠚⢁⡼⠁⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠻⣍⡀⠀⠀⠀⢸⣏⡤⠖⠒⢾⡉⠀⢀⣠⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠽⠦⠴⠖⠋⠁⠀⠀⠀⠀⡿⠾⠿⠶⠶⠶⠶⠶⠤⣤⣀
⠀⣠⠴⠖⠒⠚⠛⠛⠋⠉⠉⣩⠟⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⠭⣍⠓⣆
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠥⠤⠶⠶⠖⠒⠒⠲⠦⢤⣀⠀⠀⢀⣿⣀⣈⡇⠈⣧
⠈⡟⠲⣄⡀⣀⣀⣀⣀⣼⠀⠀⣰⡏⠀⠀⢣⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⠞⢹⠉⣁⣠⡴⠟
⠀⢿⠀⠀⠙⠧⣄⠀⠀⠘⣇⠀⠁⣹⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠋⠁⠀⡟⠉⠉
⠀⠈⢧⠀⠀⠀⠈⠑⢦⣀⠈⠳⣄⡱⢄⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣥⠤⠴⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠓⢦⡀⠙⢆⠀⠈⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠶⠖⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠙⡟⠚⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢀⣤⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠘⢳⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡱⠀⠀⢀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⣀⠤⠤⠤⣀⡀⠀⠀⣠⡔⣃⠙⠃⢀⢤⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⡇⢀⣤⣀⡀⠀⢱
⢀⠔⠋⠙⠲⢤⡀⢀⡐⠉⠙⠞⠀⠀⠈⠖⠉⠀⠀⠀⠀⠀⠙⢆⠀⠀⠿⠛⠁⠀⠈⢛⡀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠑⠊⠀⠀⢹⡀⢸
⡌⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⢿⠀⠀⠀⢸⡇⢸
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠰⠆⠉⠉⠳⡁⠀⠀⠀⠀⠀⠀⠀⡷⠒⠒⢄⠀⠀⠀⡀⣔⢀⢸
⠈⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⢱⠯⣷⣊⣨⣧⣤⣀⡀
⠀⠀⠈⢇⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢸⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⠐⠈⠂⠒⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠂⠩⢥⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⡀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠠⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠁⠀⢀⡸⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⡜⠀⠀⢀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡜⠀⣄⣸⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢡⠀⢹⣤⠃
⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣴⣼⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣽⣾⣧⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣥⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠋⠙⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣠⣤⣤⣄⡀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⣀⠀⠄⠐⠀⠀⠀⡀⠀⠀⢀⠛⠁⢂⠀⠀⠀⠤⠜⠉⠀⠀⠀⠈⠀⠀⠂⠀⠉⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠞
⡔⠈⠁⢱⠀⠀⢲⠂⠀⠀⠁⡄⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣌⡀⠀⠀⣄⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠐⠄⣀⣀⣠⢴⠢⢄⠀⠀⠃⠀⠀⠀⠀⠀⢨⠁⠈⠉⠃⠀⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠘⠁⠐⠀⠀⠈⠛⠁⠠⠖⠀⢀⠀⠀⠠⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠃⠈⠀⠆⠀⠀⠀⠀⠀⠁⠀⠒⠢⡀⠀⢄⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⠈⠁
⠀⠀⠀⡤⠯⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡓⠀⠂⠀⠂⠀⠀⠆⠀⠀⠃⠐⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠰⠀⠀⢀⡀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣤⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠄⣀⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⣋⣉⣉⣩⣭⣥⣤⣥⣤⣤⣤⡶⣤⣶⣶⡤⠶⠶⣶⣾⣿⣿⠿⠿⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣀⡀
⠀⠀⠀⠀⠓⠒⠀⠂⠀⠀⠒⠢⠀⠀⠀⠒⠂⠠⠤⢀⣀⠠⠤⠤⠄⠠⠤⠐⠒⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⠁
⠀⢀⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣄⠀⠆⠀⠀⠀⠀⣄⣘⡛⠓⠦⣤⣈⣉⣉⣓⣀⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠠⠀⣐⠋⠙⢶⢤⣀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠻⠿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠢⣿⣿⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠻⢢⡄⠀⠀⠀⠀⠠⣄⠀⠈⠀⠀⠀⠀⢿⣿⣶⢶⡶⣶⣦⣤⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠃⠐⠀⡀⠀⠀⠀⠀⠘⠿⢶⣤⣬⣝⣛⠳⠶⢶⣯⣭⣋⣛⢁⢀⠀⢀⣠⣶⠖⠒⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠘⣦⠀⠀⠄⠀⠈⠁⠀⠃⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⣿⢶⡶⠋⠉⠉⠁⢠⠟⠁⠐⠒⠐⠲⠒⣦⣀⣤⠈⠻⡷⡀
⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠳⠶⠶⡶⣶⣶⢶⠤⠶⠶⠖⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⣏⣺⡄
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⢀⣰⣽⡥⠀⠰⡖⠀⠀⠀⠀⠿⠷⣦⣤⣤⣦⣤⣤⣤⡶⠖⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡀⠀⠀⠉⠒⠛⠛⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣼⣿⣷⣦⣶⡴⠃⣾⡁⠀⠙⠳⠶⠦⢤⣭⣉⣩⡭⠵⠛⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢹⣅⡀⠀⣠⣴⣷⠀⣾
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠻⠿⠿⠿⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠿⠀⠛⠟⢫⣿⢰⡟
⠀⠀⠀⠀⠀⠘⣧⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠖⢮⠷⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠣⠀⠁⢠⡋⠰⣢⠚
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠷⣤⣤⣤⣤⣤⣴⠏⠀⠀⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠁
⠀⠀⠰⡶⠒⠒⢶⡄⠀⠀⠀⠀⣤⣶⣤⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠆⠠
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⠋⣈⠉⡉⣄⡉⠀⠀⠀⠀⠀⡠⢃⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⢇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡞⠁⠈⠀⠀⠀⠀⠀⠀⣼⠟⣻⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣧⣴⣤⡇⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⢠⡥⠠⠀⢿⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠁⠀⠀⡠⢤⣀⠀⠀⡀⠀⠀⠉⠙⢿⣿⠎⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⣤⢴⣿⣶⣦⣭⣅⣀⠀⠒⠒⢚⡟⣡⠏⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⢀⣹⡾⠋⠋⠉⠻⣯⠚⠟⣦⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⠇⠀⡄
⠀⠀⠼⠟⡜⠀⠀⣀⣐⠇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣄⡈⢣⡀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠠⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠶⣿⣿⠄⡀⠀⠀⠀⠀⠀⠋⠀⠀⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠀⠀⣤⡴⠶⠔⠿⠃⡀⢠⢠⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⡀⠀⢠⡄⠀⢦⣠⣆⠀⠀⠰⠁⠀⠀⠶⠋⢁⡀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠸⠟⡃⠄⢰⣶⠿⢈⣉⣭⣤⣤⣦⣴⣤⣿⣧⣀⡺⠻⣦⣤⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡈⠁⢀⣠⣴⣾⠛⠛⣻⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⣦⣄⡀⢠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠶⠀⠈⣁⣿⣿⣿⣿⣧⣄⡨⣽⣿⣿⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⣠⡦⢀⣶⣿⣿⣿⣿⣿⣹⣿⡇⠋⠈⠛⠛⠋⠙⠛⠻⣿⣿⣼⣿⣿⣿⣿⣿⣷⣠⣬⠁⠀⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⢀⣾⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⡄⢘⡁⠀⠀⢾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠺⢦⣾⣿⣿⣿⣿⣿⣿⣿⢸⣟⠠⣠⣤⣤⣤⣤⣤⣤⣤⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣞⣁⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠙⢿⣿⣿⣿⣿⡿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡻⠇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⡄⠀⠙⢿⠿⠉⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡎⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣙⣿⣿⠀⠀⠈⠀⠀⢠⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢠⠆⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣷⠀⠀⠀⠠⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣟⣈⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣞⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⡈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⢶⠄⠘⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⢀⣴⣦⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⢋⡄⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠐⢤⡄⠈⢻⣿⣿⣿⣿⣿⢿⣿⣧⣀⣴⣿⣿⡿⢿⣦⣠⣿⣿⢿⣿⣿⣿⣿⣿⡿⠋⢘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡄⠙⠿⣿⣿⣿⣾⠟⠿⢧⣶⣿⣿⣷⠒⠿⠿⢿⣿⣾⣿⣿⣿⡿⠋⣄⡀⢊⡙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠟⢴⣌⣻⢿⣿⣤⣈⣿⣿⣿⣿⣿⣭⣥⣤⣿⣿⣿⡿⠟⠉⠠⣶⡈⡁⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢨⡿⠻⢂⣤⠉⡙⢻⢻⠿⠿⡿⡿⠟⠛⣛⠉⢡⡄⢀⠛⠀⠂⢀⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⢰⣶⡄⠻⠆⠛⢃⣈⡁⠀⠀⣿⣿⠶⣿⠁⠈⠁⣿⠁⠛⠀⠙⠋
⠀⠀⠀⠀⠀⠐⠀⢱⡜⢂⣀⣀⣠⣄⠱⣆⠀⣄⠀⣰⠃⠀⡙⠁⠾⠂⠠⠚⠛⠋⢰⣿⠀⠁⢴⡷⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⢀⣡⣼⣿⣿⣿⡏⣩⣦⣦⣶⣿⣿⡟⠀⠢⠉⠀⠀⠀⠀⠀⡀⠀⠀⠁⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠩⠭⢩⡛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⡟⡳⡄⠀⠀⠀⠁⡍⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠓⠾⣗⢦⠀⠀⠨⠁⢢⡙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠈⢻⡷⣄⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠒⠒⠲⠶⢤⣤⣤⣀⡀⠈⠻⣦⡀⡀⠀⠀⠹⣎⢗⡦⡄⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠔⠒⠈⠀⠂⠀⠀⠀⠀⠀⠠⠙⢦⡀⠈⠻⢦⣤⣀⠀⠈⢳⡳⢷⣀⣼⠇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡆⣿⠀⠀⠀⢈⣹⡿⠗⠒⠿⠟⢻⣇
⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣀⡤⠶⠒⢒⣒⣶⣶⣾⣿⡫⢟⢁⡟⢀⣠⠖⠉⠀⠀⠀⠀⠀⣨⢽⣻⢦⣄
⠀⠀⠀⠀⠀⠀⣿⠤⠶⣛⣥⠴⡾⠾⠟⠛⠋⠉⠀⠀⠀⢁⡾⣴⠋⠀⠀⠀⠀⠀⠀⢠⡞⢡⠟⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢷⡮⠥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠇⠀⠀⠀⠀⠀⢀⣴⢏⣴⠏⠀⡀⡨⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⣀⣠⠶⠋⢸⡟⠂⠀⠀⢠⠶⡛⠋⢡⠋⠁⠀⠀⢈⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠚⠛⠋⠉⠀⠀⠀⢸⣇⠀⣠⡴⠇⢂⡔⠋⠁⠀⢀⠀⠴⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡩⣢⠴⠃⠀⠀⠠⣴⢕⣬⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣴⣔⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⡄
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⡴⠒⠚⠒⠲⡄
⠀⠀⢸⡇⠀⠀⠀⠼⠥⠤⠤⠤⠤⠼⠄
⠀⠀⢸⡇
⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⠀⠀⡀⠉⠉⠉⠒⠒⢦⠞⠉⠉⠙⢦⣀⣀⠀⣀⣀
⠀⠀⢸⡇⠀⠀⠀⣠⠖⠒⠲⠴⣒⠃⠀⢠⡦⢀⡈⠋⠀⠘⠃⠀⠀⠶⠆⠀⠰⠆⠀⡀⠈⠋⠁⠈⠙⢦
⠀⠀⢸⡇⢀⡤⠚⠁⠰⠇⠀⢀⣍⠀⠀⢀⡀⠈⢁⡀⠠⡦⠀⠀⢠⡄⠀⢀⣄⠀⠈⠛⣀⠀⢤⡄⠀⢉⡉⠓⣄
⠀⠀⢸⡇⡏⠀⠀⠀⠀⠠⡦⠀⠁⢤⠄⠘⠁⣤⠈⠉⠀⠀⠴⠆⠈⠀⠶⠀⠁⠠⡦⠀⠛⠀⠀⠰⠆⠈⠁⠀⠚⠒⠲⣄
⠀⣠⠚⠓⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⢢
⠀⠙⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠜⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⡖⠒⢲⠶⡶⠶⠶⢶⠶⡶⠶⢶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⢶⣶⣶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⣀⠀⠀⠀⠉⠉⠓⠒⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠮⠅⠈⠻⠏⠁⣿⠒⠂⢰⣄⠀⣤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⢛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠶⠶⠶⣶⠄⣀⡀⠐⢐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠓⠀⠉⠃⠁
⠀⠀⠀⠀⠀⡤⢾⢸⣏⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣠⡖⢟⣹⡥⠧⢠⣿⣿⣿⣿⣿⣿⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⡄⢶⣶⣾⠿⠶⠒⣀
⠀⠀⣘⣯⣽⣬⠧⢦⢻⣾⣿⣿⣿⣿⣿⣿⣿⣟⡿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⠁⠀⠙⣊⣉⣭⣭⣤⣤⡤⣄⣛⠙⢿⣿⠇⣀⡀⠒
⠀⠀⠸⣿⣿⣒⣇⣫⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠒⠀⠙⠋
⠀⠀⠀⠘⠿⢿⣿⣿⣿⠟⡹⠿⠿⠿⠛⡛⠿⠎⠋⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠟⠿⠿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣉⡷⣾⣿⣿⣿⡿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠞⣿⣷⣶⣿⣿⣿⡶⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣛⣿⣿⣿⣽⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠓

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣄⢀⡀⣀⠀⣀⣀⢀⡀⣠⡄⢀⣀⢠⢀⡀⡄⣀⢀
⠀⠸⠻⠸⠟⠾⠯⠿⠺⠻⠟⠿⠇⢸⡿⠸⢻⡇⠗⠿⠹
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⣀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠋⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⣶⠀⠀⠀⠀⠀⢼⣧⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⣤⣠⣦⣶⣷⣴⣿⡿⠋⠀⠀⠀⣤⠶⠛⠡⣨⣖⣀
⠀⠀⠀⠀⠀⠀⣿⢁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⢰⣿⡟⡋⠻⣿⡿⢋⠀⣀⣀⣠⠾⠁⡀⢀⣤⣾⢋⡹
⠀⠀⠀⠀⡀⢲⡷⣦⡏⠀⢶⣦⠀⢀⣀⣀⡤⠾⣿⠋⠀⠀⠀⢀⣠⣴⣿⣷⡀⢠⣿⣧⠀⠀⣾⣿⡏⢰⣿⣷⣟⠋⠃⠊
⠀⠀⠀⡁⠀⠀⣶⣿⣷⣤⣚⣡⣶⣿⣿⣿⠄⠀⣸⣧⣤⣤⣼⣿⡿⢿⢿⣦⠉⢩⡋⡙⠒⠚⠙⠷⡑⠚⢉⡣⠜⠅⠂
⠀⠀⢠⢷⡾⠟⠛⠛⠻⢻⠛⢻⣟⡛⡻⠿⡷⠒⠻⣏⢙⢈⡿⣌⠑⢽⣈⠫⠃⢀⣤⣶⠦⠠⣼⡧⠱⠀⢄
⠀⠀⠀⠀⠳⠀⢀⣴⠀⢨⣄⡾⠛⠛⠡⢄⣀⠰⠶⠛⠛⠉⠉⠓⠺⠿⠸⠄⠋⣉⡡⠤⠒⠈⠁
⠀⠀⠀⠀⠈⠓⠚⠉⠒⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡖⠅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢭⡭⢭⣛⠀⠲⡀⠘⡄
⠀⠀⠀⠀⠀⢀⡠⠖⢚⣅⠴⢄⠲⣾⠂⠒⠠⡿⣶⣌⢀⠘⢆
⠀⠀⠀⢀⡔⢩⡆⠀⠙⠀⠀⠀⠀⠉⠳⠪⠀⠀⠈⢻⣦⡀⡈⢳⡀
⠀⠀⠀⡿⢐⠈⠉⠀⠀⠀⠀⠀⠀⣠⣀⡰⣶⡒⠆⢉⠈⢻⣌⢄⠙⣆
⠀⠀⠀⢳⢹⡆⠀⠀⡀⠰⠂⠀⠀⣙⣿⣥⢉⡁⠀⡨⠃⠈⡹⣧⡁⠈⠳⣄
⠀⠀⠀⠀⠞⣷⢀⠀⠉⠀⠀⣤⡌⠋⠲⣄⠠⡔⠂⠀⠀⢰⡘⠜⢿⣄⢢⠈⠢⡀
⠀⠀⠀⠀⢺⢻⣚⠄⠀⠀⠈⠻⠄⠂⠠⡙⢗⠀⢀⡐⠞⠃⠀⣠⠀⢙⣦⣘⢄⠈⠢⣄
⠀⠀⠀⠀⠈⢯⢿⣄⠀⠀⠀⢰⣄⠀⣤⠃⠀⠀⡘⠃⠀⠀⠠⣿⡎⠀⠘⠻⠶⣕⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠈⢻⡿⡶⢗⣈⠐⠉⠵⢂⠀⠀⠴⡿⡄⠀⣴⢂⡹⠁⠀⠀⠂⠀⢻⡓⢄⠠⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⢿⣦⣤⣒⡈⠀⢠⡤⠤⣀⣘⣗⠁⠀⠰⠊⠀⠀⠀⠈⠙⠚⢷⣤⡑⢄⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⢈⢉⣀⠈⢩⡍⠻⠯⡅⣄⡐⠐⠀⠀⠀⠀⠀⠈⠛⢆⣉⡠⠬⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠿⠿⢿⣿⣄⣀⠊⠉⣠⣰⠡⠄⠀⣔⠦⠄⣀⣀⠉⠛⢶⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢖⡉⢰⣾⡆⠒⠉⠀⠀⠉⠉⣛⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣯⣬⣥⣀⡀⠀⡀⠀⠀⣠⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠺⣿⡷⣲⣠⣴⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⠭⠭⠿⠿⠿⠿⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⠗⠛⠛⠛⠛⠒⠒⠒⠒⠒⣒⣶⣶⠶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠤⠄⠒⠒⠈⠉⠉⣀⠀⢸⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢠⠒⠒⠂⠉⠉⠉⢸⠀⢸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠘⠒⠒⠒⠒⠒⠒⠉⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢠⠖⠒⡆⠠⠖⠒⢲⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠈⠀⠀⢸⠀⢸⡇⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡛⢻⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⠈⠒⠒⠃⠠⢄⣀⣸⠀⢸⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠉⠁⠒⠒⠤⠄⣀⣀⠀⢸⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡘⣿⣧⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⢀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠝
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣿⢻⣿⣿⣻⣇
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣿⣼⣧⣿⣇⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠛⠛⠛⠿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⠏⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠘⢿⡟⠹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⣀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁

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

⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⡹⢁⡾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠡⡃⠐⠁⣀⣐⠄⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠀⠐⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠱⣔⠸⠆⢼⣦⡀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠑⠀⠐⢊⡀⣀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠁⠈⠋⠉⠀⠀⠀⠀⠀⠘⠀⠢⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡐⠁⡐⠀⠀⠀⠀⠀⠀⢰⠟⠁⢀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⣊⡄⠀⠀⠀⠀⠀⠀⢀⣆⠀⡘⢠⠀⢀⠀⠀⠄⠀⠀⠀⣿⠆⠀⠀⠄⠀⠂⢈⠀⢐⢴⠀⠠⠤⠤⢤⣅⡐⠢⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢸⠋⡄⠀⠀⠀⠀⠀⠀⡆⢻⠎⣠⢬⠼⣦⣰⡄⣀⡀⠀⢠⡇⠀⠂⡀⠄⠁⠀⢸⡄⢀⡿⠀⠀⠀⠀⠀⠀⠋⠻⣇⠀⠳⣄⡄
⠀⠀⠀⠀⠀⠀⢸⣾⡧⡀⠀⠀⠀⣄⢄⣤⣸⣯⡔⠁⠂⠈⠋⠺⡿⢸⣤⣾⣇⠀⣞⠄⠈⠀⠀⠠⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⡄⠈⠂⠀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠑⠿⣧⠀⠀⠀⡿⠐⣼⢿⡗⡹⠃⠴⠡⠠⠀⠀⡄⢹⣯⡻⣶⣿⣇⠸⡆⠀⠀⢸⣿⣯⡘⠄⠄⠀⠀⠀⡐⠳⣤⣭⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠃⠀⠄⣀⣴⡁⣁⠋⠘⠓⡁⠀⣴⣮⣾⠕⢅⣠⡷⠁⠁⢁⠂⠀⠑⣴⠟⠁⠉⠀⠁⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣄⣼⠟⡟⠉⠀⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⠰⣆⠀⠢⣾⡿⡇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⣵⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣀⠀⡀⠋⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠻⡟⠆⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠃⠑⠀⢰⣤⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⣄⡘⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠶⣤⠎⠍⣩⣥⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⢤⡖⠰⡤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣨⡧⠀⠀⠠⠔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⢐⠴⢋⡽⢃⡬⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠒⠀⠀⠀⠒⠒⠢⠤⣀⣠⠴⠒⠺⣍⣤⣷⣥⡴⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⣤⣍⠳⡶⠞⠋⠁⠀⠈⠙⠊⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣨⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠀⠚⢸⠁
⠀⠀⠀⠀⢀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⠃
⠀⠀⢠⠾⡧⢈⠓⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠁⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⡾⢋⡴⠃
⠀⠀⢿⣘⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣡⠔⠋⠀⠀⢀⣀⣄⡀⠀⠀⠹⡄⠀⠀⠈⠐⠂⠳⠋⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣴⠋⠁⠀⠈⠀⢠⠀⡟⠀⠀⠀⠀⠀⢀⣀⡼⣿⣇⠤⠒⣒⡆
⠀⠀⠀⠀⣠⠐⠒⢴⡋⠿⣦⡃⠁⠠⠀⠀⠀⠀⠀⠀⠻⡘⠆⠀⣤⠤⢃⡴⠃⠀⠀⢀⣀⣤⡾⢞⣿⣿⣤⣦⡼⠗⠠⣄
⠀⠀⠀⠀⣇⠁⠴⢒⡛⡚⠛⠻⠦⣄⡐⠲⢤⡀⣠⠚⠁⠻⡙⠒⠒⠚⠉⢀⠀⢠⢷⡞⠓⣉⣾⣟⠁⠈⠉⠉⠑⣶⣀⣼
⢴⣲⠌⠁⠝⠓⠲⢿⣊⣉⠀⠉⠩⠭⠿⣓⡶⠚⠛⠲⡤⠚⢳⣀⣀⣐⣋⣉⣥⣤⢴⡶⡿⢧⣄⣨⣶⠚⢓⡖⠲⢿⣉⡹⠛⣆
⠀⠈⠑⠒⠤⢀⣀⠀⠀⠈⠉⠉⠙⠭⣉⡉⠢⣥⡤⠜⠧⢤⠴⠿⠭⠭⠽⠭⠥⠶⠚⠙⠒⠋⠀⠉⢉⣉⡉⠀⠀⠀⠉⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠢⠤⠤⠬⠭⠭⣖⣒⣶⣶⣶⣖⣀⣐⣐⣒⣒⣒⣒⣀⣉⣉⣉⡭⠥⠤⠴⠒⠒⠋⠉

⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡤⠀⠀⢀⣌⣩⣉⡁⢴⠀⠀⠀⠀⡔⠀⠀⠈⠙⠀⠀⠀⣀⢶⠀⡹⠆⠀⠀⠀⠀⠀⢾⡉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠀⠀⢾⠖
⠀⠀⠈⣄⡁⠘⣟⠀⢹⠀⣉⢀⣿⠀⠀⠀⠰⠆⠀⠀⡠⠋⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣦⣀⣹⣦⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⢀⠄⠀⢀⡤⠋
⠀⠀⠀⠈⠉⠈⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣌⣱⡶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠈⠒⠚⠾⢞⣫⠔⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂⠀⠀⠋⠀⠀⠀⠀⠀⣆⠀⣧⠀⡆⠀⠀⠈⢟⡉⡄⠀⠐⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤
⠀⠀⠀⠀⠐⠒⠛⠉⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣐⣂⡀⣇⠨⡅
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⠀⠀⠄⠐⠶⣈⠳⢄⠀⠀⠀⠀⠀⠩⠰⢖⡀⣶⠆⢴⡿⠀⠀⠀⠀⠀⠀⡠⣔⡨⠀⠐⠄⠀⠀⠀⠀⠂⠡⠉⣨⡩⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠳⠄⠀⠀⠀⠀⠀⠈⠑⠊⠉⠛⠁⠀⢀⡀⢀⣤⢴⣩⣐⢃⣘⣡⣴⡇⠀⠀⠀⠠⣀
⠀⠀⠀⠠⠒⠒⠛⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣶⣾⣿⣭⣿⣈⣴⠿⠟⠁⠀⠀⠈⠓⠛⢵⣶⣷⡆⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⡀⠀⠀⣡⠀⠀⠀⠀⣠⡄⠤⠴⡂⠐⢻⣯⣢⣤⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⢰⣖⣿⣷⣶⣿⣿⠟⠀⠀⠀⠘⣏⢲⣦⣄⣀⠀⠀⠀⠀⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⡀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣯⠽⠛⠋⠀⠀⠀⠀⠀⠙⠳⣕⣦⢙⠲⢶⣤⡀⠀⠈⠻⣆⣌⠀⣄⡀
⠀⠀⠀⢠⣄⣀⢖⠢⢠⡜⣀⣀⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⣌⡑⠂⣤⣑⡂⠀⠀⠈⠻⠀⠙⠋⠱⠶⣄⡀
⠀⠀⠀⠈⠓⠻⠭⠱⠈⠽⠃⠚⠋⠁⠀⠀⠀⠀⠀⣀⡀⢂⠠⠀⠀⠀⠀⠰⢦⣄⣤⣤⣠⡴⣤⠤⠶⠀⠀⠀⠀⠀⠉⠖⢦⣄⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠀⠀⡏⣧⡇⣿⢰⢇⣇⢷⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡄⢻⠎⠧⠀⠓⠙⢃⣙⣈⣀⣈⣈⣥⣭⡤⣤⡤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠾⠓⣙⣤⢖⡚⣿⣿⠉⣿⣿⢩⡆⢹⢸⢁⠹⢡⣿⣁⣧⣣⡾⣿⢳⠦⣄
⠀⠀⠀⠀⠀⠀⠹⠂⣴⢛⠏⠌⡆⣧⢹⣿⠀⢻⣿⠸⡇⡇⢸⢸⠀⣾⣯⣳⣃⣁⡾⡟⣨⣤⣿⡿⣾⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣄⣾⡞⠘⠀⢱⣸⣼⣿⣀⣨⣽⣷⡾⠿⠿⣿⣾⣿⡟⢿⡏⢻⠟⠛⣿⠙⣿⠁⢹⠇⠁
⠀⠀⠀⠀⠀⣰⠓⡍⣿⣧⣣⣷⡿⠛⠟⠛⣿⣻⠛⠻⡶⣶⠶⠶⠶⣿⡇⢸⡇⢸⡄⡇⢻⠀⠸⠀⣼
⠀⠀⢀⣀⠔⢏⣴⡾⠛⣿⣿⢡⠀⣰⡆⠀⡇⣥⡦⣦⠶⢿⡖⠶⠒⡹⣷⡀⣄⠈⡇⠃⢸⢀⠀⡇⡏
⠀⢺⡏⣧⣸⣼⣿⡣⣠⢻⣿⡎⣀⠸⠇⠀⡇⢻⣗⣂⡀⣸⣇⣴⣤⣤⡾⠗⣜⡀⠃⢰⢸⢸⢀⠜
⠀⠀⠋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⣇⣾⢻⡟⢻⡟⣿⡏⢹⠘⣷⣀⣿⣿⢿⣾⣾⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⣿⠉⠉⠉⠈⠓⠛⠓⠚⠂⠉⠀⠈⠄⢨⡀⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣸⡧⠄⡇⢰⡟⣦⡼⢳⢀⡗⡄⢸⢠⡏⢀⠇⢽⢿⢭⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡥⢻⡏⢛⡇⢸⣁⡟⡇⢸⢰⣇⡇⣼⡟⠰⢯⠿⣻⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠋⠁⣾⠉⠀⡇⢸⢸⠟⡇⣿⣧⠀⠀⠚⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠳⠾⠸⠄⠓⠋⠈



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣬⣷⣦⡝⠿⢳⣀⣠⡤⠖⠲⢶⣦⣤⣀⣰⠟⣟⣵⣶⣯⣭⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠛⠿⣿⣿⣿⣶⠀⠋⠁⠀⠀⠀⢀⡄⠈⠛⠋⢀⣿⣿⣿⡿⢛⣿⣿⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⠛⢿⣿⣿⠏⣀⡀⠒⡀⠀⠀⠈⡴⠀⢀⣀⡈⢿⣿⣿⣿⡟⠹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⣿⣿⠟⢼⣿⣆⠀⠀⠀⠀⠀⠀⠁⡛⣼⣿⡞⠻⣿⣿⡅⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢉⣤⣾⢘⡛⢻⡄⠀⠀⣀⣉⠓⠀⢰⡛⢛⡺⣷⣶⣉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠰⠋⢀⢀⡯⠩⠭⣅⣀⡀⠳⢌⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠆⠀⢀⣵⢋⣴⡀⣠⣌⠻⣦⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⡀⣇⠚⠛⠁⠙⠛⠃⣿⢠⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣝⠿⣷⣦⣤⣤⣶⣿⢟⣁⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⣷⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⣶⣶⣶⡶⠶⠶⠶⠿⠶⠾⠿⢿⠿⠿⠿⠿⠿⠟⠿⠿⠻⠛⠛⠛⠻⢿⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⡀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠘⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠻⡇⠀⢸⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣯⢿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣧⠀⠠⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣆⢺⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢹⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣻⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣛⢽⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢾⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⠀⠀⢻⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠤⢢⡄⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⢀⠀⣿⣸⣧⠀⣀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠐⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠑⢿⣆⡬⢤⣤⣥⣭⠂⢀⠀⢰⠀⠀⢸⡇⠀⠀⠰⠂⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣽⠀⢰⣿⣠⡸⣷⣀⣀⣀⣩⣠⣾⠀⠀⢸⣗⣒⣒⣒⣒⡷⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢻⠰⠞⠛⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣻⠀⠓⠤⠛⢠⣦⣶⣶⣶⡶⣶⣶⠀⠀⢶⣶⠶⠶⠶⠶⡿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⢠⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢨⠀⠀⢸⡗⠀⠀⠀⠀⡃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠂⠄⠀⠀⠸⣿⠀⠀⠀⢀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣵⡂⣀⠀⠀⠀⣿⠀⠀⠀⢀⠀⢸⠀⠀⢸⡇⠀⠀⠀⡄⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠘⣿⡇⠀⠀⠀⠀⣿⣄⣀⣀⣉⣀⣸⠀⠀⢸⣷⣀⡀⠀⠀⣤⡇⠀⠀⠀⡄⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡃⠤⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⡀⢿⣇⣀⢀⠀⡀⡀⢀⠀⠀⡀⣀⣀⡀⢀⠀⠀⡀⣀⣀⢀⠀⠀⠴⠖⢠⡇⠀⠀⣀⣘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣭⡭⠱⠛⠛⠛⠛⠛⠻⠛⠿⠛⠿⠿⠽⠧⠽⠬⡧⢤⠶⠶⠶⠾⠶⠶⠶⠿⠾⠷⠶⠤⠭⠬⠴⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠉⡍⠉⠁⠛⢛⠙⢋⠜⢋⠗⠠⠖⠠⠖⡰⠆⡰⠆⠶⠲⠆⠴⢢⠦⢠⠄⡤⢀⢄⠀⢠⠤⠴⢠⠄⠶⠰⠖⠰⠂⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡔⣠⢂⠐⡀⠐⡡⢊⠥⢊⠠⢊⠄⢊⠤⢊⠔⡢⠀⡠⢚⠔⡡⠒⡡⢊⠔⡨⠊⢔⠤⠂⠀⡡⢊⠔⡡⠂⠀⡠⣚
⠀⠀⠀⠀⠀⡀⠤⠔⠊⠁⠁⠈⠉⠉⠙⠃⠚⠒⠛⠒⠓⠶⠃⠶⠃⠶⠅⠾⠤⡾⠶⠷⠞⡴⠿⠶⠷⠶⠶⠳⠗⠶⠒⠷⠲⠧⠾⠖⠺⠚⠛⠙⠢⣄
⠀⠀⠀⠀⠛⠩⠂⠦⢤⠄⣤⣠⡄⣠⣄⣠⣀⣀⣀⣀⣀⡀⢀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄
⠀⠀⠀⠀⢸⠑⠡⠒⠤⠢⠔⡡⢒⠤⢂⠤⠊⠄⠈⠠⢊⠡⢋⠝⣉⠝⡩⢋⠉⠉⠝⡉⢝⠉⠋⠝⡋⠋⠙⠋⠜⠁⠟⡡⢋⠉⡩⢉⠍⡩⢋⠍⡩⠉⢋⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠁⠐⠁⠊⠀⠀⠔⠁⠈⠀⠊⠐⠁⠐⠀⠂⠐⠀⠊⠁⠂⠠⠊⠐⠀⠂⠀⠀⠈⠀⠁⠈⠀⠁⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡏⠚⠀⠀⠀⠙⣿⣿⣿⣿⣆⠀⠀⡻⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⢀⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠂⠑⠛⠘⠀⠃⠀⠃⠂⠃⠋⠞⠁⠐⠃⠀⠋⠘⠁⠐⠑⠃⠀⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⡴⣾⠋⠑⠒⠾⣿⣿⣟⠿⠿⠷⣿⣿⣿⣶⣶⣴⡦⠤⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣋⣄⡔⣏⠀⠀⠀⠈⡟⠀⠉⢻⣟⢦⣼⣯⣀⠀⠀⠹⣿⡗⠶⠮⢽⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠉⠈⡇⠈⠉⠉⣀⡟⠂⢠⣤⣼⡇⠀⠀⠘⣿⢷⣍⡻⣷⠴⠤⠤⢼⣿⡄⠀⠀⢹⣿⠉⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⠉⠙⠙⠻⡧⢤⣀⣀⣸⡇⠀⠀⠀⢸⡏⢓⢤⣼⡟⠈⢻⠆⠹⣦⡀⠀⠀⠈⢿⡟⠓⠚⠿⠥⣤⣀⣹⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢿⣷⣤⣄⡀⠀⠅⠀⠈⠙⠻⣷⣤⣀⣀⣸⡁⠀⠀⢹⡿⣷⠛⠧⠸⣿⣿⣦⣤⣤⣼⣿⡀⠀⠀⠻⣯⠉⠉⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⢀⡯⠀⠉⠉⠉⠀⠤⠄⣀⠀⡇⠀⠉⠉⣿⡧⠤⣠⣴⠏⢹⢠⠊⣤⡿⣿⡃⠈⠉⠘⢻⣟⣶⡶⣶⣿⣇⠀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⡟⠛⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣀⠀⠼⠅⢹⣿⠘⠀⣶⢛⣾⣿⣷⣿⣿⣤⣀⣀⣠⣿⡿⠀⠈⠉⣿⣿⣿⣿⣭⡿
⠀⠀⠀⠀⠀⠀⢿⣿⣾⡀⢸⣿⠚⠉⠙⠾⣷⣀⡀⠀⢀⡆⠀⠈⠉⢸⡀⣼⡏⠰⠶⢿⣿⣿⣿⣷⣾⣿⣏⣉⣙⣻⣿⣿⣤⣴⣾⢿⣿⡽⢈⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⡀⠀⠀⠀⣞⠋⠙⠳⢾⣧⣀⠀⣰⣷⡿⡏⠙⣷⡺⣿⣿⣿⣿⢿⣿⣿⣿⣯⣟⠟⠿⢯⢭⣿⢫⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣶⣇⢠⣿⠀⠀⠀⠀⣻⣝⣿⣯⢾⡅⢘⣶⡿⠿⠋⠙⣿⣿⣶⣷⡿⢿⣆⣷⡙⣷⣶⣿⣥⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⡿⡽⠙⢿⢳⣾⡟⠀⠀⣠⢎⣴⣶⣺⣽⢧⣶⣯⣿⢟⡋⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⢿⣿⣿⡿⢻⣿⣷⣧⣦⣿⠟⠉⠀⠀⡼⢩⢸⣽⣿⠋⢻⡞⣿⣿⣆⡀⠈⢽⣖⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠶⣤⣀⡙⠛⠻⠿⣿⠿⠿⠟⠛⠉⠀⠀⢀⠀⢸⡇⢸⡜⣿⣿⡀⢀⡿⡜⢿⣿⣿⣷⣿⣿⡷⡏⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⡾⢷⣝⢿⡶⣤⣄⡀⣠⣖⢄⢉⢢⠀⠋⣀⠘⢧⡀⢳⡘⣿⣿⣿⠀⠘⠦⣝⠻⠿⠿⣟⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠾⠿⣿⣒⢾⣿⣬⣙⠳⢿⣦⣧⣀⣉⣀⣀⠙⠻⠿⠶⠤⠟⣀⡼⢷⣮⡉⠙⠛⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⡭⠭⠭⠟⠟⠛⠋⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠛⠀⠠⠦⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣶⣿⠆⣿⣿⣿⣿⡏⠉⠁⠉⠁⠈⠀⠉⠉⠉⠁⠉⠁⠉⢹⣷⣶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⢿⢧⣿⣟⣛⡿⣧⣤⡤⠤⠤⠤⠤⠤⠴⠤⣤⣄⣠⣤⣼⣿⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡇⢸⠷⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠿⠙⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⡈⠋⠀⠀⠀⠀⠀⢶⣾⠡⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢄⠀⠀⠀⠀⢀⡾⠁⠁⠀⢀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣾⣿⠀⠀⠀⠀⠀⢄⠀⢀⡮⠊⠀⠀⠀⠈⠷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⢿⣷⠀⠀⠀⠀⡀⠈⢸⠀⠑⠀⠀⠀⠀⠀⡾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠈⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⡀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠣⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠈⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⡃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠑⢾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡇⣸⣦⢤⣤⡤⠀⠀⠀⠀⠀⠠⠧⣴⣃⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣾⣾⡞⣿⣯⣽⣷⡟⠛⠳⠒⠒⠒⠒⠲⠖⠒⠛⠋⠑⠛⢻⣷⣶⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⣿⢆⣿⣿⣿⣿⣇⡀⠀⠀⡀⢀⠀⠀⢀⡀⣀⣀⣀⣀⣸⣿⠿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⡤⣞⣡⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠖⠊⠉⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⠙⠲⠤⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⢀⠄⠐⠂⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠐⠀⠀⠂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠐⠂⠉⠀⠀⠀⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠠⣤⠤⣤⣤⣤⣰⣀⣀⣂⣀⣀⣀⣀⡀⢀⠀⠀⡉⠀⠀⠀⣀⡀⠀⣀⡀⣀⣀⣀⣁⣀⣀⣀⣐⣠⣄⣀⣠⣥⣤⠤⣤⣤⠤
⠀⠀⠀⠀⠈⠉⠒⠦⠤⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣭⣭⣯⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣭⣽⣿⣽⣿⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠠⠤⠄⢀⠀⣀⡀⠀⠀⠀⠀⠔⠒⠔⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠒⠖⠶⠶⠤⠤⢤⣀⣉⣀⣁⠀⠐⠒⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣠⠆⠠⠀⣂⠀⠀⠀⢀⣈⡉⠉⠙⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢻⠀⠀⠀⠀⠸⣿⠈⠉⠀⢻⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢸⠀⠠⠂⠀⠀⣿⠀⠀⠀⢸⠀⠀⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⢸⡇⠀⠔⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣄⢄⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⢻⢸⡇⠀⠀⠀⡄⣿⠀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠷⢮⠞⠿⢳⣶⣦⠇⣿⣤⢄⣀⣨⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇⠁⠁⣄⣀⡀⠀⠀⠉⠈⠉⠛⠚⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⡇⠀⠀⡏⢈⣐⡉⠓⠶⠤⢤⣤⣀⡄⠀⠀⡇⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢰⡂⢸⡇⠄⠉⠡⠒⠂⢤⠈⠃⠀⠀⠃⠘⠀⢤
⠠⣄⣀⠀⠀⠀⠄⠀⢸⠀⣹⡇⠀⢸⣇⠸⠷⢦⣤⣀⣀⠀⢸⠀⠀⠀⠠⠀⠸⠀⠹⠂
⠀⠀⠈⠙⠓⠢⢤⣄⣸⠀⣿⡇⠀⠈⠉⠛⠻⠶⢶⣤⣭⣉⣛⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠑⠲⡢⠤⢄⣀⠀⠀⠀⠀⠈⠉⠙⠃⠀⣸⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠕⠃⠒⠦⠤⣄⣀⣘⣻⢀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠂⠜⠖⡲⢄⣀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠉⠫⠲⣶⢤⢄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⠿⠿⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠿⠛⠉⠀⠀⠀⠀⣿⢸⡀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⢦⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⡴⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡞⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠤⠴⠄⠀⠀⢀⣀⣤⣤⣤⣤⣴⡛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡼⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⡜⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠋⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠁⣀⡴⣫⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⣀⠀⠀⠘⠃⠀⢀⣀⣠⣴⣾⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠒⠚⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠀⠲⢄⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠓⣐⡃⠀⢸⢵⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠯⠠⠜⠁⠀⠁⠸⡤⢤⠏⠓⢤⡀
⠀⠀⠀⠀⡰⠋⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⣄⡀⠀⠉⠲⣄
⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⠀⠀⠀⡔⠂⠒⠐⠁⠈⡇⠀⡦⣈⠓⢄⡀⠀⠑⠦⣀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠑⢴⠉⠉⠀⠀⠀⠀⠀⠐⠃⠀⠣⠌⢃⠀⠉⠢⣄⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡀⠉⠢⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠢⡀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⠈⠑⢄⡀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⠆⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣸⠆⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠁⠀⣰⣄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠉⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠁⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⡀⠀⠀⠀⠀⠀⣀⠠⠔⠊⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡄⡔⢂⣤⠀⠀⠀⢀⣀⣠⠴⢶⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠰⡋⠉⠉⠉⠁⠀⠀⠙⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠚⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⢤⡀
⠀⠀⠀⠀⠠⢴⣒⣤⢀⡀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠻⢆⡀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠠⠔⢄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠑⠀⢥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⠀⠈⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⡈⠑⢀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⠄⢸⠿⡄⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⣃⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⣒⢀⠀⠀⠠⣤⣶⡿⠟⢋⣀⣤⣔⠂⠽⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡐⠚⠒⠈⠉⠋⠁⠁⠀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⠀⠈⠀⠀⠀⡀⢀⠐⠀⠀⠀⠀⢀⣤⢀⡀⠀⠀⠉⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⣥⠀⠀⠀⠀⠉⠀⠀⠀⠠⠤⠐⠈⣁⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⡿⣿⢛⡻⣿⡟⣿⣿⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⢳⣄⣠⣀⣀⣤⣶⣿⣿⠏⣾⢿⢮⣿⣿⣿⣿⣷⡻⣜⣳⣾⣶⣱⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⣴⢄
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣟⢿⣿⣿⣿⣿⡿⣿⢸⡇⠟⢻⣿⡈⠋
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⡧⢼⣿⣿⣿⣿⣶⡏⡁⣷⢀⣾⣿⡇
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣗⣽⡎⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⡿
⠀⢿⣿⣿⣿⣿⣿⣟⣿⣭⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢥⢟⣾⣿⢷⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⢹⣿⣿⣿⠇⠀⠉⠉⠛⠛⠓⠻⠞⠚⠛⠛⠋⠉⠁⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠐⣩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣍⠂⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠐⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠆⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠘⣽⠛⠛⠛⢯⠁⠈⡽⠛⠛⠚⣮⠃⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⣿⢀⣀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠠⠝⠒⠒⠒⠊⠄⠠⠑⠒⠲⠒⠣⠯⠬⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠐⣭⠉⠉⠉⢭⠃⠘⡭⠩⠈⠍⣍⠂⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠰⣝⣀⣀⣀⣚⡄⢠⣓⣀⣀⣀⣫⠄⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⢤⣀⣀⣀⠀⠀⠀⣠⠔⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠃⠀⠀⣀⣀⣀⡀⠀⠉⠙⠛⠋⠁⠀⢀⡼⠓⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡥⠴⠒⠛⠉⠉⠉⠉⡭⠉⠉⠉⠓⠒⠦⠤⣤⣾⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⠴⠋⠱⠖⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⡽⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢰⣠⠟⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡾⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠠⢻⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢹⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⡇
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡼⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⠀⠐⠧⠴⠒⠒⠒⠺⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⢸⡀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣷⣤⣀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣈⡳⢤⣄⣀⣀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁