Washing clothes Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡶⠀⢠⣀⣷⡴⠒⢱⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀
⠀⠀⠀⢠⣄⢴⣷⣀⣶⣴⣶⠀⠀⠰⣆⠀⠀⠀⠀⣠⣶⣄⣙⣾⣟⣷⡾⡿⣿⣍⣽⣯⣿⣤⡂⠀⠀⠀⢀⣀⡀⠀⠀⡀⣿⠷⠀⣠⣶⣦
⠐⠛⠛⠛⠙⠚⠛⣿⡟⢻⣿⣦⣿⠀⢾⡆⠀⠀⠛⠋⠉⠉⠉⠁⠀⠀⣸⡄⠈⠿⠁⢠⣿⣟⠛⢠⣾⣿⣿⠿⣿⣿⣦⡏⢀⢉⠚⡧⢄⡩
⠀⠀⠀⠀⠀⠀⠐⠿⠀⢸⣿⣿⣿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠉⠓⠀⠀⢠⠀⣿⡿⠓⠀⣭⠀⠘⢿⣿⣿⣿⡷⢾⡋⠐⢻⣮⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⡟⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⠈⢱⡀⠀⠀⢸⡀⠀⠙⣿⣶⠋⠀⡀⠘⠁⢻⣿⣿⣿⠇⠤⠓⣤⣤⠀⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⢠⣤⠀⠀⠀⣷⡟⠱⣄⠀⢷⡀⠀⠘⣷⡀⠀⠘⣿⡄⠐⢀⣀⠀⠋⢻⡟⢡⡆⣰⠦⠀⢴⠄⢀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⣿⠀⠀⠀⢸⣱⡄⢰⡎⠀⠧⠀⠈⠓⠀⠈⠂⢄⣟⠡⡀⠀⠀⠁⡼⠩⠻⠄⣀⡬⢵⠿⢽⣏⠀⠠⣧⠴⡇⠊
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢿⣿⢀⡀⠄⠊⣿⠀⢰⣇⠀⠀⠀⠀⠀⠈⢢⠀⠀⠙⠦⣈⣶⢲⡄⠃⡈⢠⠀⠀⠀⠐⢻⠇⠗⠸⠆⠟⠀⠁⠂⠐
⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠻⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠁⠀⣤⠐⣉⠈⡄⠀⠀⠀⠘⡙⣿⢿⣿⣿⠿⡿⣿⢷
⠀⠀⠀⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⡀⠀⠀⠀⠀⠀⠀⠙⠂⣤⣤⣤⡾⣆⣸⣇⣈⠲⡿⠀⢸⡇⠛⢼⠧⣿⠐⡇⣿⢸
⠀⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡷⠿⣿⡉⠉⠀⠀⠀⣿⡆⣿⢸⡇⢸⠀⡇⣽⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⣸⠻⡗⠀⠈⠁⠀⠀⠀⢀⡿⠀⣙⠘⠃⠠⠄⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠬⠀⠀⠀⢂⠀⠀⠀⠀⠀⡀⠀⢹⠀⠉⣴⣶⣶⡶⠾⠿⣿⣯⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⢀⠆⠀⠀⠀⠀⠡⠀⠘⣶⢉⣉⡁⢀⣄⣀⠀⠀⠙⠻⣿⡉⠋⠹⢍⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢰⣄⣸⣿⣤⣼⣯⣙⣿⣦⣄⠀⠈⠡⠀⠀⠀⠛⠒⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠓⣤⠁⠀⠀⠀⠀⠀⠀⣠⡄⢼⢋⣿⣋⢉⡿⠃⢹⣿⡶⣉⣷⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢁⣉⣀⠠⠄⡄⠤⢾⠀⢀⠞⣿⠟⠛⣿⡷⢻⣿⣧⡕⣹⣿⡌⠁⠛⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⣀⡀⠄⢎⠀⠲⢸⠀⡾⣿⡟⠻⣿⣿⠿⢷⣯⡿⣿⣿⡀⣹⣦⣺⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡍⠈⠰⠠⠀⠄⢸⢠⣿⣿⢛⣿⠿⢷⣶⣿⡉⢹⣿⣄⣹⣿⠹⣿⡆⠀⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠴⠂⡞⢰⠀⣿⢿⣿⠳⣶⣿⣯⡙⣷⣦⠀⠹⣿⠟⢿⡟⢷⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡑⠂⢈⠀⠈⠁⢰⠀⠁⠈⢻⣿⣯⣌⣩⣿⣿⣿⣿⣧⠙⣷⡎⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠘⢀⠀⠀⠀⠀⠀⠘⢸⠀⠀⡏⠀⠀⠙⢿⣄⣿⣿⣿⢻⣷⡟⢻⣶⠛⣷⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⣼⡏⠙⠛⠿⣼⣿⣏⣩⣿⣿⠀⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣶⢖⡶⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢸⣿⡿⢿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⣀⡀⠘⣯⡶⠲⡖⠲⣟⡠⣤⢤⣄⠀⠀⠀⠁⠐⠃⠀⠤⡀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢰⣿⣷⣾⠟⢻⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣯⣿⡿⠛⠛⠿⠿⠿⠿⠛⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⣿⡇⠀⢠⠀⡟⢸⣥⣿⣷⣾⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⢱⡄⢨⣿⠀⠀⠀⠀⠇⠀⢿⣿⣧⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣼⣵⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⡇⠀⠀⠀⠀⠀⠀⢢⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠔⠊⠀⠀⠀⠘⣿⡞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢦⠄⣨⣤⣷⠁⠀⠀⠐⠦⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⠲⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣮⠓⠉⣨⡴⠞⡟⠀⠀⠀⠀⠀⢃⠀⢠⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣮⣩⡔⢒⡒⠤⣤⠤⢀⡄⠀⢈⡠⠦⡤⣴⠎⣇⢡⣬⣷⣠⣏⣀⠀⠀⠀⢀⣾⠋⠉⢉⡉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⢷⣦⡾⢧⣦⣤⣼⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣟⣷⠻⠋⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⣽⣿⣉⣳⣟⡻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢻⣾⣿⣿⣿⣿⣿⣿⣿⣧⡾⠿⣤⢯⣵⣯⣿⠮⣿⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠶⣶⣦⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡿⣿⣿⣷⣿⣿⣾⣻⣾⣿⠶⣧⡞⣻⣄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⠿⢿⣿⣷⡾⣯⣘⠿⣤⡿⣢⣿⣿⣿⣿⣿⣿⣿⠿⠙⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣰⢀⣴⠟⠛⠛⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠛⠛⠷⣦⡀⢦
⠀⠀⠀⠀⠐⠃⣾⠃⠀⢰⡟⠛⣛⣋⠉⠉⣉⣭⣍⠁⢠⣴⠶⠶⠶⠶⠶⠶⢶⣶⠶⣶⡀⢀⡤⠤⣄⠀⣠⣤⣍⠉⠹⣇⠀⠀⠘⣷⠈⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣼⣟⢻⣷⠰⣿⣋⣿⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠓⠒⠋⠀⠻⠶⠞⠀⢰⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⠈⢻⣿⠋⠀⠙⢻⣟⠁⠀⢿⣤⣤⣤⣄⣀⣀⣀⣀⣠⣾⠃⠸⣏⣹⡇⠀⣿⣉⡿⠀⣼⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠷⠶⠶⠶⣶⣶⣦⣤⣦⣤⣴⣶⣶⣤⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠛⠛⠷⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⢶⣴⡾⠛⢉⣩⡤⠖⠛⠉⠉⠉⠉⠉⠉⠛⠒⠦⣍⡙⠻⢶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀⣴⠟⢁⠴⠚⠉⢀⣀⣤⣤⠶⠶⠶⠶⠶⠶⠶⣤⣀⠀⠉⠓⢦⡙⣷⡄⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠃⣴⠋⠀⣠⠾⢛⣭⠴⠒⠛⠉⠉⠉⠉⠉⠓⠦⣍⠻⣦⠀⠀⠹⡌⢻⣎⠃⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⣸⠃⠀⣼⠏⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡘⣷⠀⠀⢻⡀⢿⡄⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠘⣷⠀⢠⣤⣿⠀⡏⠀⠀⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⡇⠀⠘⡇⢸⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⢻⡄⡇⠀⠀⣿⠸⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢻⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡇⠘⣧⢻⡀⠀⢸⣇⢳⡸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⢸⠀⣿⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷⠀⢹⣎⢷⡀⠀⢻⣆⠱⣌⠛⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢹⡇⠀⠀⣼⢰⡟⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢲⠘⣷⠀⠙⠛⠛⠻⣇⢳⡀⠀⠙⢷⣌⠙⠲⢤⣄⣀⣀⣀⣀⣀⡤⠴⢋⣴⠟⠀⠀⡼⢃⣾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠃⣿⠀⠀⠀⠀⠀⠹⣧⡙⢦⣀⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠛⠁⢀⣠⠞⣡⡾⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣌⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⣠⣴⠏⠀⠀⠀⠀⢸⡇⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢤⣉⠻⠶⣤⣬⣉⣉⣛⣒⣒⣒⣋⣉⣤⣤⠶⠟⠋⠀⠀⠀⠀⠀⠀⣾⠃⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡚⠛⠛⠛⠛⠛⠛⠚⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠓⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠙⠛⢿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠀⠂⠀⢈⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⡀
⠀⠀⠀⢰⣶⡆⣶⣆⣐⣶⣶⣰⡖⣖⡾⠀⠀⠀⠀⠀⢠⠖⠒⣆⠀⠀⠀⠀⢀⣮⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢦⡀⢼⡥⠨⡟⠀⠩⡟
⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⡄⢸⣗⡲⠓⠞⡋⠼⡀⠈
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣧⢼⡿⢧⡤⢲⡿⢩⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣠⠀⣾⠇⠀⠀⠀⠀⠙⠺⠷⠾⠷⠾⠷⠚⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠙⢿⣦⣤⣭⣵⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⠉⠁
⠀⠀⠀⠐⡖⠒⠒⠒⠒⠒⠒⠒⠒⢲⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠰⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣄⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣿⣿⣿⣿⣿⢦⡢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⠊⢽⣿⣿⣧⢱⡹⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⡇⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⡄⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⣿⣿⣿⣿⣿⣿⣿⡿⣰⠃⠉⠀⠂⠀⠄⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠿⣿⣿⣿⣿⢻⣏⡁⣀⠄⠤⢀⡀⠀⢠⡀⠂⠀⡀⠀⢘⣦⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠤⠤⠁⠀⠀⠀⠐⠒⠒⠚⠛⠉⠉⠐⡯⠿⠤
⠀⠲⢶⣶⣶⣶⣶⣶⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⢀⠉⠉⠀⠈⠉⠀⠂⠀⣀⡀⠁
⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣤⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⢄⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦⣘⡀⠀⠀⠁⠀⠠⠀⠀⠀⣀⣀⣴⣿⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⢸⠙⠉⠉⠉⠉⢩⡟⠻⣭⡟⢻⣽⣟⣛⣛⣛⣛⣛⡏⠉⡇
⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠮⠷⠾⠥⠷⠾⠽⠷⠷⠶⠶⠷⠷⠧⠤⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠠⠄⠠⠄⣤⠠⠤⠀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⠖⠚⠉⠉⠉⠉⠓⠲⣄⠀⠀⠀⡔⠉⢁⣀⣀⡴⠮⠅⠴⠭⣶⠂⣵⣸⣓⣤
⠀⠀⠀⠀⢸⠀⠀⠀⣠⠋⠀⡠⠒⣉⣉⣉⣉⠒⢄⠀⠙⣄⠐⡅⠀⠀⠀⣴⣭⣭⣭⣭⣭⣥⣴⡀⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠀⣰⠃⢠⠊⡴⠋⠁⠀⠀⠈⠙⢦⠑⡀⠘⣆⠃⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⡇⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⡇⠀⡆⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⢰⠀⢹⠇⠀⢀⠷⠶⠶⠶⠶⠶⠶⠶⠶⠷⠀⠀⢠⠁
⠀⠀⠀⠀⢸⠀⠀⣇⠀⢃⢸⡀⠀⠀⠀⠀⠀⠀⢠⠇⡸⠀⣸⢸⠄⠜⠒⠒⠲⠒⠲⠒⠒⠖⠒⠒⠳⢄⣈
⠀⠀⠀⠀⢸⠀⠀⠹⡄⠈⢆⠙⢤⣀⠀⠀⣀⡤⠋⡰⠁⢠⠇⠈⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢰
⠀⠀⠀⠀⢸⠀⠀⠀⠙⢦⡀⠑⠢⠌⢉⡉⠡⠔⠊⢀⡴⠋⠀⠀⠇⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠲⠤⣤⣀⣀⣤⠤⠖⠋⠀⠀⠀⠀⡄⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢀⡃⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢡
⠀⠀⠀⠀⠈⠲⡖⣒⢲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣖⠒⢲⠾⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠙⠁⠀⠀⠀⠀⠈⠋⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣷⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⠔⠖⠁
⠀⠀⠀⠀⠀⡏⠁⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⣿⣤⣦⣀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠸⠸
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠃⠀⠀⠀⠀⠂⠀⠘⠶⣋⢿⠆⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⣀⣄⣀⠀⠀⠈⠹⠁⣰⠀⡃⢀⣴⣶⠀⠒⣿⡿⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢜⠫⠀⠀⠀⠐⠄⠀⢀⡉⠉⠋⠉⠁⠀⠈⠈⠳⣎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠤⣄⣀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢲⡺⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠙⠶⢰⠺⠂⠀⠀⠀⠀⢈⡾⠀⠀⠀⢂⣿⣿⣿⡂⣤⣀⣀⣠⠶⠒⠶⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⡅⠈⣣⠤⠴⢶⠤⣄⡀⡗⠀⠀⠀⣨⡽⠋⠉⣧⠘⠶⠦⠤⠒⠀⠀⠀⡝⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢠⡟⠀⠀⠀⠀⢠⠟⠁⠀⢀⣜⡿⠃⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣰⠃⠀⠀⠀⢠⣏⡀⠀⣤⡞⠁⠀⢀⠀⠠⠀⠀⢰⠆⠀⠈⠉⠛⠛⠙⣛⡃⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡰⠋⠀⠀⠀⠀⠈⠹⡿⠘⠛⠀⠀⠀⠐⠊⠀⠈⠐⡞⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢰⠃⠀⠀⠀⠀⠜⠀⣤⠖⠇⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠁⠀⠀⠀⠀⠀⠀⣼⡀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⡎⠀⠀⠀⢀⠔⠀⠙⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢷⣦⡄⢠⠴⣦⣄⡀⠀⣜⢹⣰⡏
⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠃⠀⠀⠒⠉⠉⠡⠀⠀⡰⠃⣠⡆⠀⠀⡇⠀⢀⣴⡖⠒⠂⠉⠀⠀⠀⠨⣯⠛⡀⢠⡍⢻⡿⣧⣬⣿⡿
⠀⠀⠀⠀⠀⠸⡛⢿⠿⣅⣑⣀⣈⣀⣡⣀⣀⣀⣀⡠⠮⠴⡞⢻⠁⠀⠀⢆⡀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡈⣄⣷⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣧⣘⡄⠀⢰⡆⠀⠀⠄⠀⠀⡆⡄⢠⡇⣠⣿⡏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⡎⢿⣿⡿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢠⠀⢙⠀⢘⠇⠀⠒⡗⠐⠲⡷⠶⢾⠛⣿⣿⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠈⢬⣿⣧⡻⣿⡀
⠀⠀⠀⠀⠀⠠⠀⣧⢈⣄⠈⣷⠀⠰⠁⠀⠘⠃⠀⣈⣀⢩⣾⣿⠃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠹⠌⣿⣧⣿⡿⠇
⠀⠀⠀⠀⠀⠘⠃⠘⠦⣉⠀⠙⠀⠈⠗⠂⠹⠛⢛⣛⣿⣿⣿⡟⠗⠀⠀⠀⠀⠈⠓⠐⡶⠒⠒⠒⠒⢒⣶⣶⣤⣈⣁⣠⡿⠛⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠈⠁⠐⠚⠓⠒⠛⡛⢋⡛⠛⢁⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⢸⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢨⠉⣽⠉⣟⠉⠙⠛⠛⠛⠛⠛⢛⠛⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠⠆⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠛⢸⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡏⠀⢾
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠀⠀⠀⠀⠀⣈⡉⢐⡂⢠⢸⡏⠑⠊⠉⠁⠀⠀⠀⠀⢀⡴⠂⠀⠉⠈⡁⣠⣾⣠⣤⡤
⠀⠀⠀⠀⠀⠀⢀⠈⣄⡇⣀⠂⠠⠤⢤⠤⣈⠄⠐⠂⣼⢇⣀⡀⠀⠀⠀⠀⠀⢴⣿⣷⡤⠔⠒⢊⠽⠿⠦⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠄⠠⠠⠀⠠⠀⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠆⠀⠀⠆

⠀⠀⠀⢠⢤⣤⣤⣤⣤⣤⣤⣤⡄⠄⣠⣄⠠⠤⣠⣄⠠⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠠⠤⡄
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⣇⣾⠉⠙⣧⣼⠋⠉⣷⢸⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀⠀⡇
⠀⠀⠀⢸⣸⣤⣤⣤⣤⣤⣤⣤⣇⣹⣶⣾⣋⣘⣷⣶⣏⣸⣷⣾⣴⣧⣾⣴⣷⣼⣶⣿⣀⣀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⠉⠉⠉⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⢀⡠⠤⠤⠤⠤⢄⣀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⢀⡼⠋⠀⢀⡴⠊⢁⣠⣤⠤⠤⣤⣄⡈⠙⠢⡀⠀⠈⢷⡀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⢀⡾⠁⠀⣠⠋⢀⡴⠋⠁⠀⠀⠀⠀⠈⠙⢶⡄⠘⢆⠀⠀⢳⡀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⣸⠃⠀⢰⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⡆⠀⠈⣧⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⣼⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢱⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⢹⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡜⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀⠈⢆⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⠁⠀⢰⡏⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⢻⣄⠀⠈⠣⡀⠙⠶⣤⣀⣀⣀⣀⣤⠶⠋⢀⡴⠁⢀⡤⠿⠠⠤⠤⠤⠧⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⠲⢤⣀⠈⠉⢉⡩⠤⠤⠴⠩⠤⠤⠼⠶⠶⠶⠶⢶⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠈⠉⢩⣗⡒⡒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣺⠉⠉⠉⠉⠉⠉⠉⠉⢙⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⢶⠴⠧⢴⠒⠒⠂⠤⠤⠤⠤⠴⢦⠤⠼⠭⠭⠭⠭⠭⠭⠭⠭⠭⠧⠤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠶⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠶⣶⠶⣶⠶⡶⠶⡶⠶⡶⠶⡞⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⣯⢸⣿⢸⡏⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢿⠀⡷⠸⣿⢸⡷⢀⡇
⠀⠀⠀⠈⠣⣤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡆⣻⡏⣿⠋⣿⠋⣿⠋⣿⠉⣿⠀⣿⠀⣿⠀⣟⢸⣿⢸⡇⢨⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠙⠃⠛⠃⠛⠀⠛⠀⠛⠀⠛⠀⠛⠀⠛⠀⠛⠈⠛⠘⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠒⠂⠒⠂⠒⠀⠒⠒⠐⠂⠒⠐⠒⠒⠂⠒⠒⠒⠒⠋

⣾⠛⠛⠛⣛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⣋⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣙⠛⠛⠛⠛⠛⠛⣟⠛⠛⠛⠛
⣿⣀⡀⠀⣽⠀⠀⣬⡁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⡀⣀⣀⣀⣠⣵⡤⠤⠒⠂
⣾⠀⢈⠉⠿⡏⢉⡿⠟⠉⠁⠐⠒⠛⠛⢸⣿⡿⠟⠛⠻⠿⣿⠿⣿⠟⠉⠉⠉⠉⠉⠉⠀⢀⠄⠢⢉⠠⠀⠠⠀⠀⡋⠑⡄
⣿⠀⠈⠮⠀⡀⠀⠱⢨⠀⠀⠀⠀⠀⠀⠘⠿⢷⣦⡄⠠⠆⠀⠰⢋⠋⠱⢦⣄⠀⠀⠀⠀⢸⣤⡜⢢⠀⠀⠀⠀⢴⠉⠢⠟
⣿⠀⠀⠰⠀⡃⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠻⢔⣂⠤⠀⣄⡀⡔⢱⠁⠀⠙⣄⠀⠀⠀⠉⠀⢉⠀⠀⠀⠀⢸⡄
⣿⠀⠀⢰⠀⡨⠀⠨⠀⡀⠀⠀⠀⠀⢀⡤⠞⠰⣾⢸⠋⠲⣋⠀⡴⠁⡇⣰⠀⠀⠙⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣃
⣸⠀⠀⣦⠎⠀⠠⡴⠁⠀⠀⠀⠀⠠⡯⡶⠒⢦⣸⡌⢤⣀⣘⣛⡅⠀⣇⣿⠤⠄⠀⣘⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡄
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⢸⠿⠳⠤⢤⡀⢀⣀⡀⣸⠗⠦⣄⡀⠀⠙⡤⡯⣷⡄⠀⠀⠀⠀⠀⢳⢀
⢸⠀⠀⠀⢀⣤⠤⠶⢤⠀⠀⠀⠀⠀⠀⠑⡀⡈⣦⡾⡉⠁⠐⠒⣲⠞⠁⠀⢀⡌⠋⢘⡟⢻⣟⡟⠋⠀⢀⠀⠀⠀⢨⣄⡆
⢻⠀⠀⠀⢿⠀⣐⣦⢸⣤⣤⣤⣤⣤⠆⣶⠉⠈⢭⡷⠛⠒⠐⠈⢀⣠⣤⡶⡉⡴⡟⠙⡇⠈⣿⣷⠐⠒⠃⠀⠒⠒⠈
⢸⠀⡠⡶⠟⡀⠉⠀⠀⠀⠀⠀⠀⡆⠀⢸⣵⡶⠉⣼⣀⠀⣤⣖⡿⠋⣼⡆⢠⡀⠁⢠⠁⠀⣸⣿⡆
⢸⠀⢧⠳⢄⣇⠀⣀⣠⣤⣤⣤⣴⣷⣺⢋⠏⠀⠀⢱⠟⣻⢯⣩⡟⠨⠛⡇⠸⠇⠀⢸⠀⠀⡆⣿⣷
⢸⠀⢸⣄⠹⠒⠨⠯⡟⠿⠿⠻⡿⠷⠽⢧⡤⠤⠲⠿⠂⠃⠉⢠⢀⣠⣾⡇⠀⠀⠀⠘⠀⠀⠃⢹⣿
⢸⠀⠀⣟⠻⣶⣤⣄⣄⣀⣀⣀⣇⠀⣀⣀⣀⣀⣀⣄⣤⣤⡶⠾⠛⠋⣾⣇⠀⡆⠀⠀⠀⠀⢨⢸⣿⡀
⢸⠀⠀⠸⡀⠀⠀⠀⢩⠉⠉⠉⡛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⡄⠀⢀⡇⠈⠀⡇⠀⠀⠀⠀⣿⢸⣿⡇
⢸⣖⣒⠛⣧⠀⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠁⢀⢸⠇⢠⠀⡇⠀⠀⠀⠀⣿⠈⣿⣷
⢸⠑⢲⢭⣽⣦⣆⣀⠀⠃⠀⠀⢸⠀⠀⠀⠇⠀⠀⢠⠀⠀⣀⣤⡾⠯⣤⣼⣀⡗⠀⠀⠀⠀⡏⠀⣿⣿
⢸⠀⢸⠈⠉⠀⠉⠛⠿⠿⣶⣶⣾⣤⣤⣤⣶⣶⣶⡾⠾⠟⠋⠉⠀⠀⠀⠀⠉⢉⣓⡶⡄⠀⡇⠀⣿⣿⡆
⢸⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠓⠲⠭⢝⣒⠲⠤⣄⣀⣀⣀⡤⠴⢒⣋⣭⡴⠒⠁⠀⡇⠀⣿⣿⡇
⢸⠀⢸⠇⠀⠀⢀⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⡶⣦⣽⣴⠶⠿⠛⠋⠉⣷⠀⠀⠀⡇⠀⣿⣿⡇
⢸⠀⢸⡆⠀⠀⡼⣿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡇⡏⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⣿⣿⣷
⢸⠀⣸⡇⠀⣸⠃⠘⣽⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⡇⠀⠀⠀⣠⡄⠀⠀⢻⠀⠀⠈⠁⠀⣿⣿⣿⡀
⢸⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡇⠀⠀⢠⣿⡜⡄⠀⢸⣀⠀⣆⡇⠀⣿⣿⠿⠃
⣼⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣷⣶⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣾⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⣿⢿⡟⠟⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻⡆⠄⠀⠦⢀⣻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠭⡀⠀⠐⡄⠀⠀⠀⠀⠠⠘⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣴⡀⣄⠈⠒⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢹⣄⠘⢦⣀⠄⠁⢰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡇⠀⠀⠈⢳⡟⠐⠀⠸⠀⠀⡘⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢧⠀⠀⠀⠀⢻⠸⠀⠀⠀⠀⡇⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠈⢢⠀⠀⠀⢸⡐⠀⠁⠀⠜⢄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠁⢀⡴⣧⠀⡠⠺⣗⠀⠠⠁⠀⠀⢤⠂⠉⢃⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠌⠉⠙⠀⠈⢻⠀⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠑⠀⠀⠀⠁⠁⠀⠀⠁⡀⠀⠈⠀⠀⠀⠐⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠀⣾⠰⠀⣀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠘⢄⠀⢢⡀⣠⠖⠈⠑⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⡇⠌⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⡖⠀⢙⠆⠀⠀⠁⠀⠀⠀⡀⠄⠀⠈⠉⠀⠰⢄⠀⠐⠀⠇
⠀⠀⠀⠀⠀⠀⢠⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠰⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠐⠢⣄
⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢾⠘⠇⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣂⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⢀⠰⡀⠀⡄⠉⠀⠐⠂⠀⠂⠀⠀⠀⠴⠤⠠⠐⠦⠐⠂⠀⠒⠂⠀⠀⠠⡄⣄⡀⢀⣠⠆⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠂⢰⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣈⣿⠊⠉⠚⠛⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠐⡂⠀⠀⠨⠇⠛⠂⠶⠶⠶⢶⣶⣤⣤⣤⣤⣤⣤⡶⠶⠶⠶⠶⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠈⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠋⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠐⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢠⠀⣄⡰⣃⠠⠤⠶⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⡄⠀⠀⠀⠐⠒⠄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠉⠀⢀⠖⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠙⠁
⠀⠀⠀⠀⠀⢀⠐⠘⠐⠈⠃⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠔⠈⠀⠀⠀⠀⢈⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⡀⠀⠀⣀⡄⠄⠂⠁⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠐⠉⠐⠒⠈⠉⠀⠀⠀⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠌⠁⠀⠀⠈⠁⢸⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⡀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠒⠀⠌⠁⠀⠀⠀⠍⠀⠀⠔⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡇
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⢁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠂⠠⠉⣀⠒⠒⠒⠀⠀⠀⠀⠂⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠐⠒⠁
⠀⠀⠀⠀⠑⠂⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⢨⠐⠓⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠈⠳⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠔⠀⠉⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠔⠓⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠁⠀⠉⠀⠀⠀⢀⡀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠊⠄⠂⠀⠐⢄⠱⡀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⡄⢑⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠠⠈⠢⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠠⠀⠣⡐⠀⠀⠀⢀⠌⣠⣡⢤⡎⠀⠀⠄⢱⠤⢄⡀⠁⠀⠀⠀⠀⠀⠀⠰⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠀⠙⠒⠠⠄⠀⠊⠈⠢⠀⢀⣀⣀⣀⠀⠀⠒⡅⠀⠀⣠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠒⠂⠀⠀⠀⡉⠁⠀⠤⠤⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠀⠈⠀⠀⣠⠤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠤⠀⢀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⣶⠋⣷⣞⠙⣦⡿⡭⡭⡭⡭⡽⡇⠀⡇
⠀⠀⠀⠀⠐⠓⠒⠒⠒⠚⠚⠛⠓⠚⠛⠓⠛⠛⠛⠛⠛⠛⠓⠒⡇
⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣤⣀⡀⠀⠀⠀⠀⢀⡠⠧⠔⠂⢉⠐⢒⠦⣐⠒⣢⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⠀⠄⢀⣀⠉⠳⢄⠀⢀⠧⠀⠀⠒⢲⢭⠁⠐⠓⣺⢃⠚⠃⠃⠽⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠔⣡⠴⠒⠒⠲⢤⡑⢄⠈⢳⡈⠆⠀⠀⢰⠛⠛⠛⠛⢛⡛⠛⣃
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠆⡼⠁⠀⠀⠀⠀⠀⠙⡄⢃⠀⢷⡀⠀⠀⣏⣉⣉⣉⣉⣉⣉⣉⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⢡⠀⣸⣉⣉⣉⣉⣉⣉⣉⣉⣉⣣⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⣇⠀⢆⠹⣄⠀⠀⠀⠀⢀⡴⢃⠎⠀⡟⠸⢩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢸⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠑⢌⡑⠒⠖⠒⣋⠤⠊⢀⡞⠁⢠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣈⠉⠉⢁⣀⡠⠖⠋⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⡀⠀⢀⠀⡇⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⡄
⠀⠀⠀⠀⠐⢤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⢭⡭⠭⢥⣤⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢰⢲⡶⠶⠶⠶⠶⠶⢶⠒⣒⣶⣒⠒⢒⣶⣖⠒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⠒⢲
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢴⡏⠀⢹⡦⣟⠀⢘⡇⣿⠧⡤⢤⠤⡤⣤⠤⡤⢷⡇⠀⢸
⠀⠀⠀⠀⠀⢸⠼⠶⠶⠶⠶⠶⠶⠶⠤⠽⠿⠯⠤⠽⠿⠿⠥⠿⠶⠷⠾⠾⠷⠿⠶⠷⠾⠧⠤⢼
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣀⠤⠒⠒⠀⠒⠒⠢⢄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠏⠀⢀⡴⠋⢀⣤⠶⠚⠛⠓⠶⢦⣀⠉⠢⡀⠀⠘⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠇⠀⢀⠎⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠘⡄⠀⠈⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⡜⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⠀⠀⢸⡄⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠆⠀⢸⡇⠀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢷⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣸⠀⠀⣸⠃⠸⣅⣀⣀⣼
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⣆⠀⠈⢦⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠃⠀⢠⡿⠒⢲⠯⠭⠥⠿⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⣆⠀⠀⠑⢄⡈⠙⠲⠶⠤⠴⠶⠛⠁⣠⠖⠁⠀⣠⣿⢠⢒⠇⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠓⠢⠤⠤⠤⠤⠒⠉⠁⠀⣀⡴⠋⢸⡼⠋⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⣀⣀⣤⡴⠞⠉⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⡗⠒⠒⠀⣤⡔⠒⠒⢺⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠲⣷⠒⠊⠁⠀⠈⠉⠉⢺⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⢚⠯⢵⣶⣖⣒⣒⣶⡭⠽⡇
⠀⠀⠀⠀⠀⠀⠈⠫⠤⠤⠤⠼⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠀⠀⠈⠁⠈⠯⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢠⠀⢀⡀⢆⠀⠠⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠂⠠
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠋⠉⠀⠈⡰⠂⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠂⠀⠚⠛⠃
⠀⠀⠀⠀⢠⠁⠠⠐⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡤⠐⠁⠀⠀⠀⠀⠂⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⡌⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠠⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⡀⠄⠂⠀⠀⠀⠔⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠂⠐⠂⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠀⠀⠄⠀⠀⡉⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⣰⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠠⠄⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠃⠀⠀⠀⢀⠂⠀⠀⠄⠚⢤
⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠘⠠⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘
⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠑⠠⠀⠒⠠⠀⠀⣀⣀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⢰⣀⣉⢈
⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⢀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠒⠠⣄⠸⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡀⠀⠀⠀⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢀⠄⠈⠉⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠄⠒⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡀⢀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠐⡠⠀⠔⡈⠈⠉⠰⠈⢄⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⢈⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠉⢢⠀⠀⠀⠀⢀⠄⠤⠤⠤⠤⠐⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠓⡄⠀⠀⠀⢀⠔⢠⡥⠴⠶⣁⠀⠀⠀⠷⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⢁⠈⠀⠘⠐⠀⠀⠐⠊⠀⣁⠠⠀⠀⢀⠀⠀⠠⠐⠂⠅⠀⢀⣠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠒⠀⠀⠀⠀⠀⠉⠁⠈⠆⠤⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠄⠀⢸
⠀⠀⠀⠀⠀⠒⠒⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠐⠈⠐⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣰⠔
⢀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⢤⣀⣄⣀⣀⣀⣀⣠⡠⠤⠤⣤⠤⠤⠤⢤⡠⠤⠤⣤⣀⣠⣀⣀⣄⣀⣠⣠⣠⡠⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⢰⡟⠛⢻⡄⣴⠛⠙⣷⠀⣟⣉⣉⣉⣉⣉⣉⣉⣉⣹⢹
⠀⠀⠀⠀⠀⠀⢀⢸⣀⣀⣀⣀⣀⣀⣀⣸⠘⢧⣤⡼⠃⠻⣦⣤⠟⠀⣿⣩⣏⣽⣩⣯⣽⣏⣽⣩⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃

⠀⠀⠀⠀⠀⠀⢰⣴⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⡠⠤⠒⠒⠒⠒⠤⢄⣀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⡠⠊⠁⣀⣤⠴⠶⠶⠦⣤⣀⠈⠑⢄⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⠞⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠳⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡎⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢱⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢧⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡼⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢣⡀⠙⢦⣄⡀⠀⠀⠀⠀⢀⣠⡴⠋⢀⡜⠁⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠙⠦⣀⠈⠙⠓⠒⠒⠛⠋⠁⣀⠴⠋⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠉⠒⠒⠂⠐⠒⠒⠉⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠤⠤⠤⠤⠤⠤⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⣶⠒⠒⠒⠒⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠒⠒⠒⠒⣶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢿⡿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡁⠀⠀⠈⠁⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠀⠀⠈⠙⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠴⠋⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⡞⠀⠀⠀⢀⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⠾⣍⡉⢝⡲⠤⣀⡀⠀⠀⢀⡇⢠⠏⠀⠀⠀⢠⠎⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠋⠀⡇⠀⢸⠀⠀⠈⠑⠢⠭⣙⠒⢾⣥⡏⠀⠀⠀⡴⠃⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡟⠀⢰⡇⠀⢸⡎⠉⠲⢄⡀⠀⠀⠉⠚⠋⠉⠓⢦⠞⠁⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠃⠀⢸⠁⠀⢸⡇⠀⠀⠀⠉⠓⢤⣀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⣼⠀⠀⣾⠀⠀⢸⢱⠀⠀⠀⠀⠀⠀⠈⠙⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⢠⣏⢀⡇⠀⠀⡇⠀⠀⢸⠘⡆⠀⠀⠀⠀⠀⢀⣴⡏⠉⠛⠓⠒⠒⠒⠒⠚⠚⠉⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢸⠃⠀⢰⠃⠀⠀⢸⠀⠇⠀⠀⠀⢀⡴⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠛⢻⠀⠀⠀⠈⡗⠛⠀⠀⣠⠎⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠶⠶⠦⠴⠇⠀⠀⢠⠇⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠆⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿
⠀⢠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⢀⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸
⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠑⠀⢀⠇⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸
⠀⠀⢋⠉⠙⠓⠒⠒⠤⠤⠤⠤⠤⠤⠴⠚⡛⠀⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠑⠲⠦⠤⠤⠤⣤⣤⡤⠤⠤⠤⠖⠁⠀⣿⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⢸⡂
⠀⣠⣖⠊⠉⠉⣑⣢⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠉⠒⠒⠒⢾⠀⡇⠀⠀⠀⠀⠀⡇
⠐⣇⢹⡉⠉⠉⠉⡏⣀⣀⣀⣀⣀⣘⣥⣤⣀⣀⣀⣀⣀⣤⠴⢃⡤⠗⠢⠤⠤⠤⠴⡇
⠀⠈⠉⠙⠛⠛⠛⠉⡧⡘⠻⣉⣉⣉⣳⡑⢄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣲⡤⠤⠤⠤⠐⢺⠀⠀⠀⠀⠈⠓⠒⠒⠒⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⠀⣠⡶⠶⠶⠶⠶⠶⠒⠒⠒⠚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⠒⠒⠶⠶⠶⣤⡀⢀⡀
⠀⠀⠀⠀⠎⣼⠃⠀⣴⠶⠒⠛⠛⠛⣛⣛⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⢉⣩⣍⠉⣉⣉⡙⠛⣷⠀⠀⢹⡆⠓
⠀⠀⠀⠀⠀⣿⠀⠀⣿⢰⣟⣻⡇⢼⣏⣻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠒⠚⠀⠻⠶⠇⠀⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠹⠟⠁⠈⠙⠿⠁⠘⠷⠶⢤⣤⣤⣤⣤⣤⠾⠃⠸⠭⠝⠀⠯⠭⠇⢰⡏⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣓⣚⣒⡒⠲⠶⠶⠶⠶⠶⠶⠶⠛⠛⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣤⠶⠞⣛⣩⠭⠭⠭⠭⠭⠭⢭⣛⠳⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠾⢋⠴⠒⠋⢁⣀⣠⣤⣤⣤⣤⣤⣄⡈⠙⠲⢬⡙⣿⡉⠉⠛⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃⡴⠁⢠⡴⢛⣩⠭⠒⠚⠛⠛⠛⠒⠮⣝⢷⣄⠀⠙⣎⢻⡝⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⡼⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡹⣆⠀⠸⡀⢿⡀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠘⡇⢀⡶⢾⡇⡇⠀⢸⡅⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⡀⠀⣇⢸⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣷⠘⣇⠸⡇⣇⠀⠸⣇⢧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⢸⠸⡇⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⢻⡸⡄⠀⢻⡌⢮⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠁⠀⢸⢰⡇⠀⢠⡏
⠀⠀⠀⠀⠀⢠⢸⡇⠘⠳⠾⢿⡜⣆⠀⠙⣦⡙⠦⢌⣀⣀⣀⣀⣀⣀⡤⢞⣱⠟⠀⢠⢏⡾⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠘⠈⣇⠀⠀⠀⠀⢻⣌⠳⣄⡈⠙⠳⠶⣤⣭⣭⣭⣭⣤⠶⠛⠁⣀⠔⢁⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠳⣦⣙⠲⠤⣀⣀⣀⠀⠀⢀⣀⡤⠖⢊⣡⡴⠋⠀⠀⠀⢀⡟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠐⠦⠉⠛⠶⠶⠤⣬⣭⣭⣥⠴⠶⠞⠋⠉⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠒⠶⠶⠶⠶⠧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟
⠀⡀
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⣤⣤⣠⡟⠁⡴⠃⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡾⠋⠁
⠀⠀⢀⣀⠀⠀⠓⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢶⣤⣀
⠀⠀⣏⠀⠴⢤⠦⣾⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⠿⠆⠀⢰⣿⢐⡇⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣸⠀⠀⢀⣤⣤⠞⠋
⠀⠀⣀⣌⣤⠆⣼⠃⢸⣷⠀⢸⡇⠀⢰⡀⠀⠀⠀⠀⣠⠄⠀⢠⣿⠀⠀⣀⡈⠁⢀⣴⠟⠉
⠀⢰⡏⠀⠁⠀⢹⡄⢹⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⣼⡿⠀⠀⢸⡏⢀⡀⣨⠟⠀⣼⡟
⠀⠀⣿⠂⣀⣀⡀⢻⡌⢻⡀⢸⡇⠀⢸⡟⠀⠀⣰⡏⣴⠀⠀⣸⡟⠈⣹⠁⠀⣼⣿⡁
⠀⠀⠈⢻⡋⠀⠁⢀⣽⠶⢿⠈⣧⠀⣿⡁⠀⠀⣿⠃⢿⠀⠀⣿⣁⡿⠋⢀⣾⠟⢉⣷
⠀⠀⠀⣾⣧⡾⠀⣾⠃⠀⡘⣧⣹⡄⢸⣇⠀⠀⢿⡀⠘⢧⣀⡟⠈⣠⡴⠛⠁⠀⠈⢿⡀
⠀⠀⠀⢿⠀⠀⠀⣿⢀⡾⢁⠀⠉⢳⣜⣿⡀⠀⢸⡇⠀⠀⢉⣴⠾⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡷⠂⠀⢻⡾⣱⠏⠀⣴⡿⠉⠛⢻⡄⠈⣿⢀⣴⡾⠋⠀⠀⠀⠀⠀⢀⣷⠏
⠀⠀⠀⣼⠋⠀⠀⠸⢷⡟⢀⣸⡟⠁⢀⡖⠀⢻⣦⠟⠋⠁⠀⠀⡄⠀⠀⢀⣷⠾⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠘⠛⠛⠋⠀⠀⠻⠶⠶⠛⡉⠀⠀⠐⢦⡖⠃⠀⣀⡾⠁
⠀⠀⠀⠸⣧⡀⠀⡀⠀⠀⠀⢧⣠⠀⠀⢀⣀⣠⠷⣄⣀⣠⡾⠃⠀⠉⣿
⠀⠀⠀⠀⠸⣧⣴⠏⠀⠀⠀⠀⢙⣻⣷⡚⠉⠁⠀⠸⣏⠉⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠛⠋⣩⢙⠻⢷⣤⣀⠀⠈⠛⠒⠚⠋
⠀⠀⠀⢰⣞⣷⢸⣿⣄⡀⠀⠘⠶⠟⣠⠤⢤⡈⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠁⢸⡇⠈⠛⢶⣄⡀⠀⠙⠚⣯⣤⣶⣶⠀⠙⠻⢶⣦⣄⠀⠀⠀⠀⣏⣹⠆
⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠋⡵⢶⣻⠆⠀⠈⠙⢻⣶⡄⠀⠈⠉
⠀⠀⠀⠀⣴⣋⠙⢷⣄⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⣀⣤⣤⡶⠞⠋⠉⡇⢀⡠⢤⡀⠀⠀⠀⡶⠛⡆
⠀⠀⣀⣸⣇⠙⢷⣾⣉⠳⣤⡀⠀⠀⠀⠀⠀⠈⠙⣿⠟⠋⠉⠀⠀⠀⠀⠀⣇⠈⣀⣨⡿⠀⠀⠀⠀⠉⠁
⠀⠈⢯⡽⠙⠛⣿⠀⢈⣷⠈⠙⢶⣄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁⣰⠛⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⢺⠀⠀⠀⢀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠻⠤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠒⢂⠀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⠒⠒⢲⡔⠊⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢀⢀⡤⠖⠂⠀⢈⣉⠩⠅⠀⠀⠰⡄⠀⠀⢀⠤⠒⠀⠀⠀⢖⠉⠓⢤⡎⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢜⡄
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠹⡀⡴⠁⣀⡠⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⢀⠆⠀⠀⠀⢠⡎⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣠⡾⠟⠁⠀⠀⠀⠀⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠑⢦⡀⠀⣿⡟⡠⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠖⠒⠂⠤⢄⣀⣀⣀⡀⠀⠠⠤⣀⡀⠀⣠⠔⠂⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠈⠳⡶⠲⢾⣶⠦⢄⡀⠀⠉⢉⣩⣥⣤⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣈⠱⠦⣤⣀⣈⣩⡤⠤⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⠷⣄⣈⠀⢉⠼⣇⠀⠀⢹⠁⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⠀⠀⢀⣹⣯⠄⠀⠀⣸⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠉⣹⠇⡀⠈⠁⠀⠀⣷⣶⣴⣿⣷⣦⣄⣀⡈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠛⠋⠉⠀⠀⠀⣰⡇⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠙⠓⠀⡷⢄⠀⠀⠀⠀⢠⠃⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⢤⣄⡀⠀⠀⠀⠀⢸⠀⢀⣀⣠⡤⠶⣻⣿⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡔⢺⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⢸⠋⠉⡡⠤⡄⠀⢻⣇⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢃⠐⡄⠐⠒⠶⠀⠀⢸⠓⢦⠀⠀⠀⠀⠀⠤⠶⢄⠀⠀⠀⠀⠀⠼⡆⠀⠀⠀⣸⠀⢰⠁⠀⠆⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⢫⠁⠂⠀⠀⠀⠈⣇⠘⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠀⡆⠀⠸⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡆⠘⣏⠑⠒⠒⠀⠀⡿⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⢠⠃⢰⠁⠀⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠄⢘⡦⡀⠀⣀⢴⠁⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡦⠔⠁⠀⣈⠀⠜⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠀⠀⠸⣀⡀⣠⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⣆⢀⡠⠅⠀⠀⠀⠁⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢺⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠇⠀⠀⠀⡖⠒⠢⠀⠀⠀⢠⠤⠤⢤⠀⠀⠀⠀⠖⠂⢲⠀⠀⢠⠁⠀⡆⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠇⠀⢸⠀⠀⠀⠃⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠈⠀⢰⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⠀⠀⡆⠀⠀⢠⠀⠀⡅⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠀⢀⠃⠀⡌⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠑⠐⠁⠀⠀⠸⡀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢆⠀⢠⠃⠀⠀⠑⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠉⠊⠁⠀⠀⠈⠦⠤⠴⠀⠀⠀⠈⠉⠁⠀⢀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠔⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⢀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠤⠤⠤⠤⠤⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠽⠟⠻⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⢞⠀⠀⠀⠀⠀⡠⠐⠒⠒⢲⠓⠂⠤⠤⠄⠒⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⢀⠤⣀⡜⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡠⠄⠒⠒⠒⢢⠀⠀⡴⠲⡄⠀⢽⠀⣃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢰⠀⢸⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢨⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⡇⢸⡋⠁⠒⠒⠒⠰⠦⠤⠴⠖⠐⠒⠒⠂⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠣⠤⠜⠀⢸⠂⣀⣀⣀⡠⠔⠒⠒⠒⠒⠢⠤⠄⠠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⡀⠀⢸⣿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠐⠚⠀⠀⢸⡀⣙⣒⣢⣤⣤⡤⠤⠤⠤⠤⠐⠒⠊⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⢶⣶⣶⠿⠿⠿⠟⠛⠛⠛⠻⣿⣿⣏⣛⠶⢶⠒⠒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠒⠻⢶⠶⠶⠶⠛⢛⣛⣋⣉⣡⣭⣤⣤⣤⣼⣄⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⢸⢀⠚⠻⠭⢿⣿⣛⣉⣭⣭⣥⠭⠿⠿⠓⠚⢹⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣄⣸⣨⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠼⠷⠖⠚⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⠦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠖⠦⣄⡤⠴⠖⠁⠀⠀⠀⠂⡨⠏⠙⠟⠢⢤⣀
⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⠀⢀⣠⠴⠒⠛⠁⠐⠀⠸⠁⠀⠂⢁⡀⠀⠀⠰⡉⠀⡠⠴⠲⠒⠊⠨⢦⡀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⢿⢱⣎⢳⡄⡴⠋⠀⠀⠈⠉⢀⠟⠉⠀⠠⠀⠙⠉⠋⠀⠀⠀⠈⠁⠀⠘⡀⠀⠀⠀⠀⢳⣠⡟⣇⢹⠂
⠀⠀⠀⠀⠀⢸⡞⣯⣧⣿⢰⣦⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⠐⡀⢰⣦⡄⠉⢿⣽⢸⡇
⠀⠀⠀⠀⠀⢸⡟⢮⣿⣇⠀⠉⠀⠀⠀⠀⠠⠄⢀⠂⠀⢀⠄⠀⠀⠀⠤⠀⠀⠀⢀⠀⡄⢀⠀⠈⠀⠀⠂⣸⠼⣾⡇
⠀⠀⠀⠀⠀⠀⢷⣤⣽⣍⡙⣮⠥⠄⣀⣰⣀⣀⣁⠄⠖⠺⠐⠄⠀⠀⠀⢤⡂⠀⢸⠀⣠⣘⣋⣠⣦⠶⠾⣡⣬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣟⠛⣿⡟⠛⢻⣶⣾⣮⣀⣀⡩⠀⠀⠀⠐⠀⠀⠀⣸⡛⣳⣂⣉⣙⣫⣭⣭⠷⠿⠖⣛⣉⡼
⠀⠀⠀⠀⠀⠀⠀⢻⡍⢫⡙⠻⠿⠯⢏⡉⠛⠛⡇⠀⠀⠀⢀⠀⢴⣿⣿⠉⠭⠭⠭⠽⠿⠷⣴⣶⡶⠟⡿⠋⡗
⠀⠀⠀⠀⠀⠀⠀⢸⡗⢾⡛⠷⢶⣆⡚⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠉⡗⣒⣲⣂⣴⣶⣶⣬⡥⣤⣶⢿⣶⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⣶⢶⡖⠿⢤⣤⣶⡇⠀⠀⠀⠀⠃⠀⠀⣯⠤⢭⣭⣤⣤⣴⣚⣉⣠⣥⢾⡗⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡳⣽⣦⣌⣹⡷⣦⣤⣽⠆⠀⠀⠀⠀⠀⠀⢠⣗⣒⣚⣛⣙⣩⣤⣟⠉⣭⣐⣿⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢯⣦⣉⣙⡲⢀⣉⡟⢀⣴⣦⡄⠀⠀⠀⢸⡷⠈⠛⠛⣏⢋⣩⣷⣛⣉⣽⠿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⢧⣙⡛⠯⡬⢛⡃⠘⠻⡿⠀⠀⠂⠀⢸⡕⡬⠵⠾⠟⠋⠡⠕⣛⣫⢾⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⢦⣍⡙⢻⡍⢛⡇⠀⠀⠀⠀⠀⡀⠀⣏⣩⠷⠿⠾⠝⢛⡫⠗⢋⣴⠷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢮⣙⡻⠿⣻⠇⠀⠈⠀⠀⢀⣿⣦⢋⡴⠖⠲⠾⢛⣫⡷⢛⣩⣶⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡷⣮⣛⠭⣝⠢⠦⠤⢥⣤⣖⡦⠍⣛⣛⠾⠴⠛⣛⣫⣛⣩⣵⡿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⡦⣍⣛⣍⡛⠻⣶⣳⢄⣛⣛⣛⣻⡯⡽⠛⢛⣻⣽⣯⡥⢾⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⡙⠨⣛⣦⣉⣛⡿⢿⣍⣩⣉⣩⣍⣭⡔⣛⣉⣭⣾⡯⠖⣉⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⠳⢿⠿⢮⣙⣛⣛⣂⣤⣭⣥⣤⣍⣉⣹⡭⠶⣗⡴⠊⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣁⠢⠬⢭⢉⢵⣦⡤⣥⡴⡽⠍⠤⠒⠉⣁⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣤⣤⣤⣤⣤⠤⠶⠒⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⠲⣄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡧⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡤⣤⣤⣤⣤⣤⣤⡤⡤⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠤⣄⠀⠀⠀⠀⡼⠋⠈⢹⡆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠃⠀⠀⢸⡇⠀⢸⣧⣤⣤⣤⣤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⣠⠟⠈⢳⡄⠀⠀⢿⠀⠀⢻⠀⠀⠀⢸⡇⠀⢸⡷⠶⠶⠖⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣰⠋⠀⠀⠀⠹⡄⠀⠘⣆⠀⠘⣇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣏⠀⠀⠀⠀⠀⡷⠀⠀⠘⣦⠀⠈⢧⣀⢸⡇⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⠦⣄⣀⣤⠞⠁⠀⠀⠀⢸⠀⠀⠀⠉⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣪⢍⠕⢼⡁⠀⠀⠐⢮⡓⢄⠀⠀⣀⠤⠔⢒⣦⢤⣤⣤⡀
⠀⠀⠀⠀⠀⣀⣀⠀⣠⠎⢸⡁⡀⠼⠤⠤⡻⢶⡛⣷⣒⠬⣻⢔⠋⠀⠀⣴⣿⣿⣿⠿⠛⣇⡀
⠀⠀⠀⡎⠉⠀⠀⣈⣭⣟⡛⠛⠛⠓⠒⠒⠯⣉⠁⠀⣀⣙⣎⠁⢳⣠⣾⣿⣿⡯⣒⠒⠒⠁⠈⠉⠩⡇
⠀⠀⠀⡟⠀⣠⢮⣽⣒⣂⡀⠭⠭⢝⣲⠀⠀⣀⣻⣖⡤⡀⠉⢈⡿⡿⢛⡻⣿⣵⣛⢮⠷⣮⣤⠛⡷⣮⣦⡤⣀
⠀⢠⣾⣇⣰⢈⠟⢹⣟⣓⠻⠦⣴⡿⣣⣼⣿⣿⣿⣧⣦⣬⣽⣧⣄⢃⠀⠤⢈⡽⠛⠋⠁⢀⠶⠧⣟⣱⠿⠃⡸
⢰⠋⡇⣨⢣⠊⠀⢸⠀⠀⠉⠑⠒⠬⠭⣙⣛⠻⠿⠿⢿⣿⣿⣿⣿⣬⣶⣿⣀⠠⠷⣦⠔⠁⠀⢀⡼⠖⠒⡏
⠀⠑⠷⠤⡅⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⢆⢀⠴⠋⠀⠀⢀⡇
⠀⢀⠀⠀⠈⢑⠖⣃⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⡀⡤⣀⣤⣀⢤⠀⠀⢠⢤⢠⣤⢠⢲⢠⣷⢰⣷⠀⠀⢸
⠀⢸⠀⠀⡠⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⡇⡟⣤⣿⢸⡄⠀⢸⣾⢸⢻⢸⢸⢸⢹⢸⢻⠀⠀⣸
⠀⢸⣠⠊⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡃⢻⡃⣳⡃⣳⠋⣲⠁⠀⢘⣟⢘⣎⢨⣏⢨⢏⡰⢧⠀⠀⡇
⠀⣿⠃⠀⠀⢿⡃⠈⡆⠀⠀⠀⠀⠀⠀⡿⡇⡇⡇⡇⡇⡇⡇⣧⡇⠀⢸⣸⢸⢸⣸⢿⣷⡞⣿⡇⠀⠀⡇
⠀⠸⡄⠀⠀⣸⣧⡤⣻⡄⠀⠀⠀⠀⠀⢧⠇⢧⠇⠷⠇⠧⠇⠧⠇⠀⠸⠼⠸⠜⠙⠊⠙⠃⠙⠁⠀⢸
⠀⠀⠈⢶⡫⠗⠚⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣦⣤⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠿⡏⠙⠋⠙⠋⣿⡿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠖⠂⠀⠀⠀⠀⠋⠁⠠⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣦⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⡀
⠀⠀⠀⠀⠀⣴⠚⠉⠉⠉⠉⠉⠉⣹⠆⠀⠀⠀⠀⠀⠀⠸⣧⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⢟⠛⠳⣄
⠀⠀⠀⠀⣀⣹⡶⠤⠴⠖⣶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣧⣆⣤⡴⠚⢷⣠⢞⠕⠁⠀⠀⠈⢷⡄
⠀⠀⠀⢰⢱⠛⠓⠒⠒⠒⠛⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⢁⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⢸⡘⢦⡤⠤⠤⢤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⣴⠏⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣷⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⡅⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⣠⡾⢁⣴⠋⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⢠⢎⣠⠼⠁⠀⠀⢀⣴⠟⠛⣦⡞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢻⡀
⡔⠒⢤⡀⠀⢀⣀⡀⠀⠀⢸⠀⠀⣇⣀⣉⠉⠀⠀⠀⣀⣀⣿⣀⣰⠟⠻⣦⡀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠒⠤⢵⡄⠸⣄⡙⡄⠀⣼⠀⢀⣯⣍⠉⠙⠛⠋⠉⠉⠉⠈⣿⠁⠀⠀⠀⠙⢦⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣶⡏⠀⠻⣍⣉⠛⠳⠶⠶⠶⠶⠒⠛⠋⢳⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠶⠖⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⡀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠠⣏⣉⡩⠶⠀⢻⣿⠿⣛⣋⠀⠀⠀⠀⣠⡾⠛⠛⠛⠉⠉⠉⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣀⣠⠀⠀⠀⠀⠀⡈⣿⣟⣭⣵⠞⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡔⠋⣠⠏⠀⠀⠀⡴⢚⡇⠀⠉⠈⠛⠋⠁⠀⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠾
⠈⠋⠁⠀⠀⠀⠸⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠁⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠉⠀⠀⠠⠖⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡞⣠⠖⠉⠀⢠⡞⠁⢀⡾⠁⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣠⠗⠁⠀⢀⡠⣾⠁⠀⣾⠀⠀⡼⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣩⣤⡤⠴⠒⠉⠀⣿⠀⣸⠇⢀⡾⠁⢠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⣰⣯⡶⣋⠤⠚⠛⠳⠆⠹⣄⠀⡆⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠾⠋⠀⠀⠉⠉⠉⠀⠀⡠⠀⠐⢤⠀⠘⣶⡇⢪⡖⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠂⣤⠠⠙⠒⠀⢠⢩⡆⠀⣠⣬⣌⠑⡄⠀⠀⠀⢰⣿⣿⣶⡀⠁⠀⠛⠁⠈⡛⠠⠞
⣀⡀⠤⠄⣠⠂⠀⠀⠀⠁⠀⠀⠙⢄⡀⠄⠐⠈⠀⠀⠑⠻⠀⠹⢿⣿⡇⠄⡠⠖⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⡜⢀⠀⠄
⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠚⢄⠀⠀⠀⠀⠙⠒⣀⢰⡄⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠉⠀⠀⠀⠀⣀⡤⢲⠙⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡀⠸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢲⠶⡲⠖⠒⡉⠍⠀⠃⠀⠀⠀⢡⡀
⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⡀
⠀⡇⠀⡇⠀⠀⠧⠆⠀⠀⡇⠀⣿⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⣀⣠⡤
⠀⣷⠀⣧⠀⠀⠀⠐⠀⠐⠓⠂⠉⠀⠀⠀⠀⡀⠀⠠⠤⢤⣀⣀⡠⠔⠁⠀⢑⣄⡄⠀⠀⠀⠀⣀⠜⠐⠂⠠⡤⠀⠀⠀⠈⢄⣤⠴⠒⠋⠙⠢⢄
⠀⢹⠀⢸⡀⠤⠄⠀⠀⣀⠠⠄⠂⢀⡀⢀⣀⠀⠤⠀⠠⠗⣴⠂⠀⢀⠠⠖⠋⠡⢑⠦⠂⠐⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⣦⡀
⠠⠘⠉⠀⠀⠀⡠⠂⠁⡀⠀⠀⠐⠃⠀⠀⠀⢙⠁⠀⠹⢤⡙⡢⠈⠉⠒⠀⢴⡒⠈⡀⠀⢀⡀⠄⠐⠉⠀⠀⠀⠀⢀⠠⢖⠉⠄⣈⡱⠶⢖⡊⠉
⠀⠀⠀⠀⠀⠀⣄⠀⠣⡀⠀⠀⡈⠀⢠⠉⠑⠥⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠆⣠⠊⠑⠠⣀⢀⡀⠄⠒⠈⠀⠀⠀⠂⠌⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡈⠑⣤⠀⠀⠆⠀⠀⣠⠼⠆⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠏⠲⣄⣀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢌⣂⢐⠦⡀⠁⠀⢀⡰⠶⢃⡀⠁⠒⠠⣀⠀⠀⠀⠀⢀⠠⠀⠊⢀⡤⢺⠐⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠈⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡈⠑⠤⣀⠻⣀⡉⡼⠀⠀⠀⢀⣀⠦⠐⠈⣀⡠⠔⠊⠁⠀⠸⣠⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠉⠂⠤⠤⠄⠒⠈⢁⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢠⠌⠙⠤⠄⠀⠐⢒⣉⡠⠤⠛⠻⢅⡀
⣀⣤⠴⠖⠋⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡄⠀⠀⢨⣅⠀⠀⠀⠀⠀⠈⠙
⠧⣄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡐⠳⡀⠀⠈⡄⠉⣒⣤⣤⠖⠊⠉
⠀⠀⢉⣲⠤⣔⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠗⠂⠔⠒⠈⣱⠀⣈⠢⠀⠙⠲⢄

⠀⠀⠀⠀⠀⠀⣠⡾⠳⡀⠀⠀⠀⢀⡠⣚⢦⡤⡀
⠀⠀⠀⠀⠀⣾⣧⠏⢑⢾⣄⣠⠔⠉⠀⣸⠄⢠⣿⢳⡶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⠟⡠⢚⢁⠂⠙⠧⣀⣀⡀⠁⠀⢧⡏⣸⠅⣿⣃⠄⣩⠖⠉⢙⡦⠴⣒⠉⠳⣤⣄⣀⡀
⠀⠀⠀⠸⡗⠒⠚⠋⣉⡭⣷⣺⡥⢠⣿⠢⣠⣠⠇⡯⢾⠉⡠⠊⣠⠴⢚⡩⠔⠚⣩⣄⠀⠙⢶⡉⠍⠻⡄
⢀⣀⠀⠀⡌⠙⠒⣊⣁⣨⠄⢀⢀⡞⢂⢢⢹⡿⠖⠉⡠⠊⡠⠚⠶⠚⠁⠀⡔⠉⠀⠈⠙⠓⠲⠥⢬⡀⡇⡰⠲
⣾⢉⠱⠀⡄⢠⢠⢃⢠⡄⠆⠋⢰⠡⣸⠜⠋⣀⡀⣎⣴⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠁⠳⡅⣽⢡
⠸⡜⣇⠀⢳⠃⢃⡎⢁⠀⢠⡄⠛⡙⠁⠘⢉⢠⡖⠉⢀⡇⢰⠻⣦⣀⣀⣀⡀⢃⣠⠵⠒⠒⠒⠓⠢⡄⠈⢋⣮
⠀⢡⠙⢦⡈⠁⠘⠀⠁⢴⣾⡇⠰⢁⣤⡶⣿⣾⡘⠀⠀⣠⠊⢠⠄⠀⣀⣠⡜⢋⣠⠒⠁⣀⠀⠀⣸⢒⣀⡼⠛
⠀⠀⢹⢤⡀⠀⠀⢀⡠⠿⠷⠧⠶⠥⠞⣛⡛⠃⣾⣆⠀⠁⠀⠉⠀⡟⣏⣧⢁⡻⣮⢣⠀⠉⠀⠀⡏⢉⢀⠆
⠀⠀⠘⣧⠙⠄⠐⠐⣟⠉⢩⣭⠉⠉⢙⣛⡀⠀⣿⢸⡆⠀⡔⠀⡰⠋⢹⣬⠏⠱⣜⢮⣝⣓⣓⡀⠠⡂⡜
⠀⠀⠀⠘⣦⠁⠀⠀⠤⠆⠀⠴⠆⠀⠐⠒⠂⠀⢿⢸⡇⠀⢀⡼⠁⠀⢨⣭⠁⠀⠀⣛⡒⠫⣭⠇⢝⡲
⠀⠀⠀⠀⠹⣆⢐⠀⠩⠥⠀⠩⠭⠄⠀⠭⠄⠀⠬⢿⣇⡴⠯⠭⠀⠀⢘⣒⠀⠀⢀⣒⠀⢠⠄⢠⣱⠁
⠀⠀⠀⠀⠀⢹⡄⠂⠀⠩⠄⠀⠭⠥⠀⠩⠭⠀⠨⠭⠛⠀⠭⠭⠀⠀⢀⣀⠀⠀⠒⠃⠀⠝⢐⣪⡇
⠀⠀⠀⠀⠀⠀⢻⡌⠀⠀⠯⠀⠈⠭⠄⠈⠭⠀⠨⠭⠁⠀⠭⠭⠀⠀⠭⠀⠀⢀⣚⠀⣸⠃⢪⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡔⡂⠈⣧⡀⠩⡭⠀⠭⠥⠈⠭⠅⠀⠭⠭⠀⠀⢭⠂⠀⠸⠁⢀⡞⢨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠄⠈⢥⠀⢈⡂⠐⣒⠀⢐⠀⠀⣉⣉⠀⢘⣛⠀⠀⡿⠀⣜⢁⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠈⠥⠀⣒⡀⢒⡂⢒⣂⠀⢐⣒⠀⠐⠃⠀⠨⠅⠠⠃⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠴⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢆⠀⠀⠀⠀⣠⢖⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⠋⣳⣧⣀⡴⠊⠁⢸⡅⢠⣿⢲⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢴⣫⣐⡈⠻⢤⣀⣀⠉⠀⠷⡏⣼⢠⣿⡤⣀⠽⠊⢉⡷⠶⣚⠉⠳⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⡒⠋⢁⡴⡺⠿⠵⢦⡾⠷⣤⣴⠁⡗⠯⣡⠞⣡⠴⣊⡥⠖⢋⠩⢤⣀⠙⢮⠄⡉⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠆⠍⢋⡥⠤⠶⢀⡄⡾⢙⠆⣻⠟⠋⢁⠞⣡⠞⠑⠋⠁⠀⠼⠁⠀⠀⠩⠉⠓⠒⢦⣸⢰⡋⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡡⡌⠀⣆⡐⡜⣤⠶⠚⠉⢠⣇⡴⢋⣡⠤⢀⡷⢾⡄⢀⡀⠀⠀⠀⠀⡀⠀⡀⢐⣀⣀⡀⠀⠻⣼⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠧⢿⡀⠹⠐⢸⠁⠆⢀⣶⠀⡐⠀⢀⣤⣲⢯⠀⠸⢁⡿⠙⠲⠶⠶⠤⣤⠖⢋⠍⠉⠉⠉⣵⢀⠨⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⠂⠀⠀⠀⢈⣿⣿⢀⣤⣺⣯⣿⡿⣦⡀⠠⠊⠀⠎⢠⣴⢶⠫⣤⡺⡅⠀⠆⠀⠀⡯⠖⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⢦⡀⡠⢾⡦⠤⢼⡥⠴⢶⣶⡂⠀⣿⢷⠀⠀⡀⠀⣼⠼⡼⣦⢦⣻⣜⠤⠤⠤⠘⢀⢂⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢀⠀⠘⣣⠀⢸⣧⠀⠐⡶⠆⠀⣿⢸⡆⠈⢀⡼⠁⠀⢻⡇⠀⠙⣿⣿⣛⣓⡦⡴⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠤⠀⢒⡀⠐⣛⡀⠀⠘⡀⠀⣹⣾⡇⣰⣿⡄⠀⠀⠿⠆⠀⠀⠭⠀⢈⠁⢐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠄⠀⠦⠀⠘⢓⠀⢐⣒⠀⠐⠛⠟⢐⣒⠁⠀⠨⠭⠁⠀⢰⠃⠀⠿⠠⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡈⠀⠨⠤⠀⠶⠄⠀⠒⠀⠀⠤⠀⠀⠭⠅⠀⠭⠭⠀⠀⣒⠀⣼⠃⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡠⠀⢹⡄⠘⣟⡀⠸⠧⠀⡭⠀⠈⠩⠅⠀⢨⡃⠀⢸⠁⢀⡖⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡡⠀⠭⠄⠘⠇⠀⣓⠀⣿⠀⠈⣛⡁⠀⣻⡃⠀⡿⠀⣼⢡⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠩⠄⠩⠄⠐⠀⠠⠄⠀⠤⠤⠀⠉⠀⠀⠇⠐⠂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠶⠶⠤⠤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠒⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣗⣈⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⢫
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⡜⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢱⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣎
⠀⠀⠀⠀⠀⣇⡀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⢤⣀⡀⠀⢀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢰⡉⠀⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢉⡆
⠀⠀⠀⠹⣏⣉⣉⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠏
⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣦⠀⠀⡴⠢⡀⠀⡠⠲⡄⠀⢠⠖⢄⠀⢠⠔⢦⠀⠀⡴⢢⡀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⡟⠚⡇⠀⡟⠒⡇⠀⢸⠒⣻⠀⢸⠓⢻⠀⠀⠓⠚⡀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠠⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⢹⠀⠀⡧⢤⡇⠀⣧⠤⡇⠀⢸⠤⣾⠀⢸⡤⢼⠀⠀⡧⢴⠁⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸⠀⢺⠀⢸⠀⢸⠀⠀⠆⠀⡇⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣸⠀⠀⡟⠚⡇⠀⡟⠛⡇⠀⢸⠛⢻⠀⢸⠋⢻⠀⠀⡟⠛⡄⠀⢸
⠀⠀⠀⠀⠀⣇⠀⢠⠁⠨⠉⠉⡗⠒⡖⠊⡟⠉⡟⠑⢲⠒⢶⠒⢶⠶⢲⠒⠁⡇⢸⠀⠀⣇⣠⡇⠀⣧⣀⡇⠀⢸⣀⣼⠀⢸⣀⣸⠀⠀⣅⣠⠆⠀⣼
⠀⠀⠀⠀⠀⣸⠀⢰⠓⢚⠀⠀⡟⠚⡇⠀⣟⠒⡇⠀⢸⠒⢻⠀⢸⠓⢻⠀⠀⡗⢺⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸⠀⢸⠀⢸⠀⢸⠀⠀⡇⠈⠀⠀⡇
⠀⠀⠀⠀⠀⢹⠀⢀⡦⢼⠀⠀⡧⠤⡇⠀⣿⠤⡇⠀⢸⠤⣾⠀⢸⠤⢼⠀⠀⡧⢼⠀⠀⡗⠒⡇⠀⡷⠒⡇⠀⢸⠒⢿⠀⢸⠒⢺⠀⠀⠗⠺⡁⠀⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠳⠞⠀⠀⠓⠔⠁⠀⠙⠶⠃⠀⠘⠢⠋⠀⠈⠢⠚⠀⠀⠳⠞⠀⠀⠓⠖⠁⠀⠙⠖⠃⠀⠘⠶⠋⠀⠈⠢⠚⠀⠀⠳⠞⠀⢠⠇
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⠿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⠀⠀⠀⠀⣼⡿⠿⠿⠿⠿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠈⢻⣧⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⠛⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠿⠿⠿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⣾⡏⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣴⡾⢷⣦⠈⣿⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠛⣷⡄⠀⣼⡟⠀⠀⣿⠀⢸⣇⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⢀⣤⠀⠀⠀⣿⡇⠀⣿⠁⠀⠀⣿⠀⢸⡟⠛⠛⠛⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣰⡿⠻⣷⡄⠀⢿⡇⠀⣿⡀⠀⠀⣿⠀⢸⣷⠶⠶⠦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⣰⡟⠁⠀⠘⣿⡄⠸⣿⡀⠹⣧⡀⠀⣿⠀⢸⣇⣀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⢿⣇⠀⠀⠀⣼⡇⠀⠘⣿⡄⠙⢷⣤⣿⠀⢸⡏⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠈⠛⠷⠶⠿⠋⠀⠀⠀⣿⡇⠀⠀⠉⠛⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⣷⣤⣤⣤⣤⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣿⠘⢯⣤⣤⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠁⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠛⠳⠶⣤⣀⣀⣤⠤⢿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⠋⡴⠄⠀⠀⠴⠂⠈⡏⠀⠀⠀⢸⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⣀⣀⣀⣿⠀⠀⢻⡝⢣⡟⠀⠀⣿⡀⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡰⢋⡴⠖⠒⠻⢦⣐⣒⠈⠭⢐⣒⡿⠟⠛⠲⠶⠾⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⠀⢸⡆⠀⡇⢸⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⡃⣞⠛⣋⣉⣉⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡹⢋⡞⢡⠄⠀⣄⢲⡹⣝⡆⠀⠀⠀⠀⠀⠀⠀⢠⡿⢛⡻⣿⠟⣛⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡈⠀⠈⠀⠸⢘⡣⠘⠄⠙⠀⠀⠀⢰⣲⠀⠀⠀⠀⣿⠿⣯⡀⣇⠸⣿⢇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠞⠁⡠⠀⢠⠀⠀⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⡠⣄⠀⣹⣧⢭⣥⠿⢷⡶⠻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣀⡀⠀⠰⠁⢀⡾⠛⠛⠳⣄⣸⣤⣄⢱⡞⢙⡇⠈⠂⠊⠀⣿⢅⡲⣿⢘⣻⡘⠟⣻⡽⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣉⣹⢆⡴⠚⠛⣷⠶⣤⡟⠻⣄⣠⢼⡇⠙⠋⠁⠀⠀⠀⠀⠻⣮⣥⣾⣶⣾⠿⠛⠉⣾⣿⡞⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡁⢾⠀⣰⠶⣿⡀⠘⣷⠀⠙⣷⠀⠻⡟⠓⣦⠀⠀⠀⠀⠀⠈⠉⠋⣉⠀⠀⠀⠀⠉⠉⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠴⢿⡾⢧⣽⡄⠈⢧⠀⠈⢧⠀⠘⣇⠀⠹⣆⠘⡇⠀⢰⣷⠀⢀⡀⠀⣿⠀⠀⠀⠀⢀⣴⣶⠸⣷⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⠀⢀⡿⣞⠁⢻⡄⠈⢧⠀⠈⢷⠀⠈⠀⠀⠘⣶⠇⠀⢸⣿⠀⣼⣧⠀⣿⣀⣶⣶⣦⠘⠿⣦⡄⢿⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠙⣩⠖⠛⣰⠶⣿⡄⠈⠧⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⣿⣀⣿⠿⣷⣿⢿⣇⣾⣿⣄⣴⡾⠏⠘⠃⠰⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⠀⢻⡄⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⠿⠟⣠⡉⢁⣈⠛⣋⣈⠛⣡⠀⣶⣾⣆⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢿⣇⣼⣿⣼⡟⢻⣿⣿⣀⣿⠻⣿⠏⠙⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠈⠳⢤⣤⣤⣶⣋⣷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠙⢛⣿⠙⠿⠿⢃⣙⠛⣿⣠⣿⡶⣶⡜⢿⣦⣍
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢸⡁⢈⡇⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠙⣆⠀⢸⣆⠀⢿⣿⠋⣴⣶⡀⢸⣿⣧⣿⡇⣿⡆⢸⣿⠀⠈⢻⣧
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⣧⠸⣿⠀⢘⣿⡀⣿⣛⣿⡌⣿⡝⣿⣿⢸⣷⣾⢿⣦⣤⣼⡟
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣠⠏⠀⢿⡿⠛⢿⣇⣿⠟⠙⠿⢿⡇⠈⠛⠀⠛⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠤⠴⠚⠁⠀⠀⢸⣷⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⡧⠐⢿⠂⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⡉⠑⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢡⠃⠆⠠⣷⡄⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡹⠁⠀⣸⠷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⠘⠿⣲⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⣐⣂⣁⣤⢤⠛⢷⡀⠀⠀⠀⠀⣀⣤⣶⣦⡴⢁⣎⠉⠁⠀⠀⠀⢀⣴⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⢸⠃⠈⠁⠀⠘⠊⠉⠪⡑⠦⢐⡨⠿⣿⡯⣿⣷⣼⣯⣷⡄⠀⠀⣠⠏⠈⢯⣦⣿⠋⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⣿⣿⣞⣯⣿⡼⢏⠳⢔⣫⡟⣴⠀⣸⢹⡀⢸⡾⡇
⠀⠀⠀⣛⡭⠭⠝⠒⠒⠉⠉⠉⠛⠓⠒⠲⠤⠤⠤⠀⣀⣀⣀⠀⠯⠽⣿⣛⣿⣿⡥⠄⠀⠉⢩⢎⡾⢹⠀⢸⡄⢳⢈⣧⡙⢦⡀
⠀⠀⢰⠋⡿⠿⢿⣶⣶⣶⣦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡾⠯⠝⢻⣷⠁⠀⠀⠀⣇⣾⢁⡾⠀⢈⡇⢸⠸⢸⡎⣇⣷
⠀⠀⢸⠀⡇⠀⠀⠀⣀⣈⠉⠉⠉⠙⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡟⣿⣶⣿⣇⠀⠀⠀⠈⠉⠻⢧⣀⣼⣤⡷⠤⠼⠃⠈⠁
⠀⠀⢸⠐⡇⢀⡔⣫⠭⠭⡙⢷⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣽⣻⠿⢿⣿⡆
⠀⠀⢸⠐⡿⣿⢸⠃⠀⠀⠘⡌⣿⣤⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣥⣹⣷⣶⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣀⣀
⠀⠀⢸⢸⡏⠹⡜⢧⣀⣀⡴⢠⡿⢭⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⣿⠉⠀⠀⠀⠀⠀⠀⢀⣜⣹⡭⢷⣿⠋⠁
⠀⠀⢸⢸⡇⠀⠈⠒⠭⠭⠔⠋⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡤⣤⠤⠿⠀⠀⣀⣀⣀⣀⣀⢎⣾⡿⢣⡿⠁
⠀⠀⢸⢸⡇⠤⠤⢀⣀⣀⣀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣠⠔⠒⢉⣩⠭⠤⠒⠲⠏⢾⡷⢳⡿⠳⢤⡀
⠀⠀⢸⢸⡧⢤⣀⣀⣀⠀⠀⠉⠉⢹⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⡀⠔⠋⠁⢀⡀⠈⢀⡀⠤⠀⡉⠙⢂⣠⡏
⠀⠀⢸⢸⡗⠂⠤⠤⠄⣉⣉⠉⠓⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢛⣏⠙⢛⣟⡲⠲⠶⠾⠗⠶⠚⠻⠿⣿⣏⠗
⠀⠀⢸⣸⡋⠙⠒⠂⠄⠤⠤⢈⣉⣹⡇⢸⠀⠀⠀⠀⢀⣤⣶⠋⠀⠀⠀⠟⠘⡆⠈⠻⢀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠛⠻⠿⢷⣶⣶⣤⣤⣄⣀⣸⡇⢸⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠢⣀⣀⠀⠀⠀⠀⠀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠤⠤⠤⠤⠤⠤⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠉⠉⠉⠉⠉⠉⠉⠉⢧⡀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⢸⠋⠭⠭⠭⠭⠙⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠈⠳⡾⠠⠤⠤⠤⠤⠤⠔⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡀⠀⡜⠀⠀⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡠⠖⠊⠉⠀⠀⠀⠀⠙⣄⠃⠀⡎⠀⢙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠤⠄⠤⠔⠊⠉⠀⠀⠀⠀⠉⠙⠒⠒⠒⢢⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⠈⠦⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠛⠛⠿⠶⠶⠶⣦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣉⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣉⣉⡉⠛⠛⠛⠷⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣤⡶⠟⠛⣩⣴⠟⠿⣿⡟⠛⠩⣉⠉⠉⠛⠛⠻⠟⠛⢻⣧⣭⣭⣿⡿⣿⣿⡿⣷⣶⣶⣤⣤⣄⣩⣭⣟⢿⡄
⠀⠀⠀⠀⣼⠏⠀⢴⣿⣏⣀⣙⣂⡈⠻⣶⣶⣧⡶⠶⠾⠛⠛⠷⢶⣌⣿⡄⢰⠈⢢⣀⠹⡻⣿⣍⣽⣿⡛⠋⠉⢤⡙⢿⣇
⠀⠀⠀⠀⠹⣧⣀⣀⡀⠉⠉⠉⠛⠛⠻⠶⠿⣿⣶⣶⣔⣀⣒⣒⣈⣉⣻⣿⣼⠶⣦⣄⣤⡶⠿⠿⢭⡉⠙⢦⡀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠈⠹⣿⠛⠛⠻⠶⠶⢶⣤⣤⣤⣀⣀⣀⠈⠉⠙⠛⠛⠿⠿⢿⣶⣦⣤⣽⡿⢿⡷⣦⡀⠉⠀⠀⠀⢀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⠶⠶⣦⣤⣤⣄⣀⣀⣀⣠⣼⣷⠘⣷⠀⠹⠄⠀⢸⡇⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⢻⡆⠀⢰⠦⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⣿⠀⢿⡄⠀⠀⡆⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣧⣨⡇⠀⢸⡀⡇⠀⢸⠉⣿⠀⢸⠛⡶⠀⣠⣤⡄⠀⠀⠀⢰⣿⡇⢸⡇⠀⠀⠃⠀⠀⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢰⡶⣦⠀⢨⣭⡁⠀⠘⠶⠿⠀⢸⣤⣇⠀⣿⠀⡇⠀⠀⠀⠸⢾⡇⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣇⣹⠀⢸⡇⣿⠀⢸⡏⢻⠀⢰⠶⣤⠀⢙⡛⠃⠀⠀⠀⢀⣸⣧⢻⣿⠀⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣬⢭⡄⠈⣛⡛⠀⠸⠧⣾⠀⢸⡀⣿⠀⣿⠉⡇⠀⠀⠀⢸⣯⣿⢸⡏⠀⣧⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡀⡇⠀⡏⢹⠀⢰⡶⣦⠀⢀⣉⣉⠀⠻⠶⠇⠀⠀⠀⠘⢻⡇⣸⡇⠀⢸⡆⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⠓⠇⠀⢿⣼⠀⢸⣇⣻⠀⢸⡇⢹⠀⢰⠶⣦⠀⠀⠀⢰⡟⣿⣿⣄⣤⣬⣇⣠⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠷⠼⠂⢸⣀⡏⠀⠀⠀⠸⠷⢋⣼⠟⠋⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⢶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣤⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠸⠇⠿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⡿⠿⠿⠿⢿⣷⣄⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣡⣶⣿⣿⣿⣶⣍⠻⣷⡄⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣾⣿⣿⣿⠩⣿⣿⣿⣷⡹⣿⡄⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣾⣿⣿⡻⣿⣿⣿⣿⣿⡏⢷⢹⣿⣤⣤⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⢡⣿⣿⣿⣷⣿⡿⣫⡛⣿⣿⢻⡜⣛⡻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡸⣿⡿⢛⡛⠿⠿⣮⣴⣿⣿⢸⢃⣿⣿⣷⣮⣭⣵⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢿⣇⠿⣿⣾⠇⣽⣿⣷⠝⡿⣸⣿⣿⣿⣿⣿⣿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡜⢿⣇⠻⠿⣸⣿⣿⣷⡾⢣⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡻⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣮⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣲⡶⠶⠶⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣤⡇⠀⠀⠀⠀⠀⢠⡒⠒⠒⢲⠀⠀⠀⠀⠀⢀⡔⠒⠒⣎⠀⠙⠢⢄⣀⣠⠤⠚⠁⠘⡖⠒⠲⡄
⠀⠀⠀⠀⠀⡴⠒⠒⡟⠒⠒⠒⢳⡀⠀⠀⠀⠀⢸⠉⠉⠉⠉⡆⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⠲⢤⢴⠋⡦⠤⠤⠒⠋⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⡇⡎⡜⠀⠀⠀⠀⠀⢳⠀⠀⠀⣠⠞⠒⠒⠀⠚⢧⣀⣀⣠⣋⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣧⠟⠀⠀⠀⠀⠀⠀⠀⢣⢠⠎⠁⠀⣀⣀⣀⠀⢀⡈⢳⠖⠤⠤⠬⠭⠭⣉⣉⠭⠶⣆⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⠋⠁⠀⠈⡆⣿⢱⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣤⡿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⡇
⠀⠀⠀⠀⠀⠳⠦⠤⠤⠤⠤⠤⠤⠴⢲⡏⠀⡇⠀⠀⠀⠀⡇⣿⢸⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠯⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡇
⠀⠀⠀⠀⠀⢰⠤⠔⠊⠉⠉⠉⠒⠒⣾⡇⠀⡇⠀⠀⠀⠀⡇⢿⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣶⡟⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⠉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠀⠀⠀⠙⠒⢄⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠷⡿⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠛⡆
⠀⠀⠀⠀⠀⣘⡒⠤⠤⠤⠤⠤⠤⠐⣻⡇⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠤⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡅
⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠉⠁⠀⣇⠀⠈⠉⠐⠒⠒⠂⠉⠁⠀⡟⠒⠒⠲⠦⠤⠤⣧⠤⠲⣟⡿⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠇
⠀⠀⠀⠀⠀⠳⠤⠤⢀⣀⣀⣀⠤⠤⠔⠻⠤⣀⣀⣀⣀⣀⣀⣀⣀⠴⠋⠙⠛⠓⠒⠲⠶⠾⠖⠚⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠁⠀⠀⡇⠀⠈⠙⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠀⠀⣀⣠⣤⠴⠞⠛⡟⠓⠦⣤⣀⠀⠈⠉⠛⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⣀⣠⣤⠶⠞⠛⠉⠉⠀⠀⠀⢰⡇⠀⠀⠀⠉⠛⠲⢤⣄⡀⠀⠈⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠛⠛⠉⠉⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⣴⠦⣤⣤⣄⣀⠈⠉⠛⠶⢤⣀⡀⠀⠉⠛⠶⣤⣀⡀
⠀⢀⣀⣤⠴⠚⠉⠁⠀⠀⣀⣀⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣦⣿⡾⠋⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠈⠉⢛⡳⢦
⠀⢿⠓⢤⣀⣀⡤⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠤⢤⣄⣀⣬⠿⠶⠚⠉⢁⣼
⠀⢸⣆⡀⠈⠙⠲⢦⣄⡀⡠⠴⠖⢶⣤⡶⠟⠋⠙⢢⡀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⢶⣤⠒⠋⠁⠀⠀⣀⡤⠞⠋⣿
⠀⠀⣿⠉⠓⠲⢦⣄⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⣀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠙⠶⣤⣄⣀⣠⠴⠖⠛⢿⡁⠀⠀⠀⢻⣀⣤⠴⠖⠋⠁⠀⠀⢠⡇
⠀⠀⢸⡆⠀⠀⠀⠈⢙⠶⣤⣀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠙⠯⣍⣉⣉⣉⠉⠉⠉⠙⠛⢷⣤⠤⠖⠋⠉⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣷⠀⠀⠀⠀⢸⣠⡇⠈⠛⠦⣄⡈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣦⠸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢹⡆⠀⠀⠀⠈⣟⣇⠀⠀⠀⠀⠙⠲⣄⣀⠈⠉⠛⠷⣦⣄⡀⣀⡤⠖⠋⠉⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⠀⣿⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⢮⣗⣦⣄⡀⠀⠀⠀⠉⣻⠶⢦⣄⡀⠉⣿⠁⣀⡤⠖⠚⠉⢉⡇⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⣿⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣤⡴⠋⠀⠀⠀⠉⠓⣿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⡄⠀⠀⠀⣿⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠃⣸⠁⠀⠀⠀⣿⠀⢀⣀⣀⣼⡇⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⣿⠾⠛⠋⠉⠉⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠃⠀⠁⠀⠀⢀⣀⡛⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣤⡶⠶⠟⠛⠉⠀⢀⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⣠⡴⠞⠉⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⣿⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠶⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠶⠶⠼⢿⣍⡙⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⠿⠿⠷⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣻⠟⠉⠀⠀⢀⡤⢶⠒⠒⠲⠦⠤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡞⢁⡀⠀⢀⡞⠉⠀⡞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠳⣄⢀⡾
⠀⠀⠀⠀⣠⡿⣿⠋⠁⢀⡟⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⢉⡾⠁⠀⠀⠸⡇⠀⠀⠀⣤⡶⠿⠿⠶⠜⡆⠀⠀⠀⣠⣴⣦⣄⠈⣇
⠀⠀⠀⢠⣟⣴⡖⠀⠀⠀⣷⠀⠀⠘⠋⢀⡤⠤⢤⣀⠀⠀⠀⠀⢉⣀⡀⠙⠆⡷
⠀⠀⠀⠿⢫⡟⠀⠀⠀⢸⠁⠀⠀⠀⡴⠁⠀⠀⠀⠈⢦⠀⢠⠞⠉⠀⠈⢳⣰⡇
⠀⠀⠀⣠⠞⠋⡑⠒⣆⠸⡆⠀⠀⢸⠃⠠⠄⠀⠀⠀⢸⠀⡟⠀⠀⠀⡄⠀⣿⣇⡀
⠀⠀⣸⢣⡞⣉⢉⣠⣿⡂⣷⠀⠀⠘⢦⣀⣤⡴⠒⠲⠞⢀⡧⠴⠒⠲⣄⡰⠛⠉⠉⠛⠲⠴⠖⠛⠓⢦⡀
⠀⠀⣿⠘⣾⠁⢿⡀⠈⠉⠉⠀⠀⠀⠀⠐⠋⠉⠉⠉⠀⠈⢧⠀⠀⢓⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢦⡀
⠀⠀⠘⣆⣀⣈⣛⠀⠀⠰⢚⡥⠖⠒⠤⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⣾⣠⣄⣀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣀⡀
⠀⠀⠀⣼⢉⠉⢉⡧⠀⠀⠛⣠⣞⣉⠙⢢⡀⠀⣾⠁⠀⠀⣸⢀⡾⠯⣤⣀⠈⢳⠀⢰⠇⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣀⠀⠀⠀⢹⡆
⠀⠀⠀⢿⢿⡀⢸⠃⠀⠀⢸⠏⠀⣸⡷⠤⣝⣄⠙⠚⠳⠴⠇⠸⡄⠀⠀⠈⠙⠞⣰⠏⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡼⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠘⡇⣿⠀⠀⠀⢻⠶⠞⢻⠀⠀⢸⡷⠿⢶⣒⣶⣶⣛⣩⣷⠦⣤⠤⢺⠏⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣰⠃⠀⠀⢠⠀⢸⠇
⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠸⡀⠀⠈⠑⠶⠻⣄⡀⢀⣿⠀⠀⢈⣷⠃⠀⠀⠀⡾⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⠏⠀⠀⢠⣏⣀⡾
⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⢳⣠⠶⢤⡀⢀⣈⡉⠛⠉⠛⠒⠛⡏⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠇⠀⠀⠀⢀⡞⠀⠀⣠⠟⠋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠙⢦⣀⣿⠋⠀⢙⡶⠛⢲⠶⣤⢧⠀⠀⠀⠀⠙⢷⡒⠒⠚⠳⢤⣤⣤⡴⠋⠀⠀⡴⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠒⠛⠿⠯⠽⠶⠿⠋⠀⢈⣷⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠓⠶⠋⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠙⣆⠀⠀⠀⠀⢀⡟⠳⢤⣄⣀⣀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠞⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⢤⣴⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠰⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣠⣤⣧⣤⣾⡀⢀⣧⣤⣤⣤⣄⡀⠀⠈⠙⢷⣌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠚⢯⣁⢀⣀⣀⡀⠉⠉⠀⢀⣀⣠⠬⣝⠳⣦⡀⠀⠛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡖⠁⠀⢀⡸⠋⠉⠉⠉⠉⢉⣻⠟⠉⠉⠁⠀⠈⣇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⣰⡶⠚⠛⠛⠛⢣⣀⣠⢿⣤⣀⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⢹⠄⠈⢷⣄⣀⣀⣀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣻⣿⡶⠶⠤⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠆⠘⢧⣀⣀⣤⠀⠀⠀⣠⣼⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠴⢧⣀⡀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠲⠤⠖⠁⠈⠷⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⡇⠀⠀⠹⡛⢻⡁⢀⡿⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠆⢨⠿⡟⢿⠄⠀⢀⣧⣄⣉⣉⣀⣀⣀⣀⡤⠤⠔⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠃⢪⡀⠀⢸⠋⢻⠛⡏⠉⡿⠛⠃⠀⠀⠀⠀⠠⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡍⠛⢿⡶⠾⠿⣶⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⣀⣤⡶⠛⠛⠛⠓⠒⠶⠶⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣁⠀⠈⢳⡒⣦⣀⣀⣀⠳⠤⠴⢶⡀⠀⢀⣖⣋⣀⣤⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠉⠁⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⢣⡱⡞⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡙⠄⠀⡠⠔⠉⢉⣀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⢀⡀⠀⠀⠀⢀⡠⠊⠁⠀⣈⣆⣯⠀⣠⣶⠗⠉⠱⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠁⢠⢃⢾⠱⣀⠠⣚⢣⠀⢀⠴⠊⠀⠑⠤⡙⠓⠤⠤⠀⠠⠬⠆⠒⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⠰⢁⠎⠀⠳⡈⠢⣀⠡⠻⡁⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠒⠂⠉⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⢠⠁⠎⠀⠀⠀⠈⠲⢄⡐⠤⡘⣄⠀⠀⣀⠀⠀⠠⠠⢄⠀⠀⡠⠒⠢⢄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⠊⠀⣂⡸⠄⠒⠉⢃⠀⣀⡀⠬⠷⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠢⣀⠷⡀
⠀⠀⠀⣠⠄⠠⠤⢒⡡⢊⠥⠔⠊⠁⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠢⡀
⠀⠀⠀⠏⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⣘⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠃⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡘⠒⠄⣀⠂⣀⠠⠤⠐⠀⠲⠀⢂⠀⠀⠀⢀⡠⠤⠦⡄⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠤⢤⡀⡀⠀⢸⠀⡠⠤⠀⠀⠒⠂⠀⠀⠠⠄⣀
⠐⡤⠄⠤⠦⢼⠀⠀⠀⠀⠀⠆⠀⢨⡄⠄⠤⠼⠵⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡴⠡⠤⠠⠤⢯⠀⠒⢄⠀⠀⠀⠀⠀⠀⠈⠱⢲⣄⡀
⡠⠇⠀⠀⠠⡌⠀⠀⠀⠀⠀⠰⡀⡰⠀⠀⠀⠀⠀⠈⢆⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠀⠀⠀⠀⠀⠀⢂⠀⠀⢣⠀⠀⠀⠀⠀⡰⣱⣗⣝⢝⢓
⠓⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠨⠀⠆⠀⠀⠀⠀⠀⠀⠀⠓⠢⣸⠀⠀⠀⠀⡔⢰⢏⢾⣢⢃⠊
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡌⢀⣀⠀⣀⣀⠀⣀⡀⢀⣈⣄⠀⠈⢢⠀⠀⠀⠀⠀⠀⣀⣤⣧⣀⢀⣀⡀⢀⣀⠀⣀⣀⠀⠉⠢⢄⡌⣰⢣⡿⣱⢃⠂
⠀⠀⠀⡶⠒⠀⠒⠀⢀⠀⠀⡐⠁⠀⠀⡇⡇⠅⢸⠀⣀⠸⠀⠈⢦⡀⠀⠱⣄⣠⠔⡖⣋⢠⠀⡳⢾⢸⡰⡇⡇⠀⡅⡇⠘⠀⠀⠀⠀⠉⢳⢿⣼⢣⠂
⠀⠀⠀⠐⣄⠀⠀⠀⠀⠑⣴⠁⠀⠀⠀⡅⡇⢹⢸⠀⣧⢰⠀⠀⠂⠐⠤⠆⣉⢘⡩⡇⠖⠸⠀⠽⢸⢸⠀⡇⡅⠀⡃⡇⢘⠀⠀⠀⠀⠀⠘⠀⠈⠁
⠀⠀⠀⠀⠈⡗⠂⠀⠒⠉⠀⣒⡁⢈⢒⠁⢑⣋⠀⣓⡋⢈⢒⠁⢙⣊⠀⣑⡋⢈⣓⡁⢘⣊⠀⣑⡋⠈⣒⡁⢉⣚⠀⣑⡊⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠈⠀⡇⡇⠈⢸⠁⢉⢸⠐⠆⡥⢬⠀⣇⡿⠀⠀⡇⠀⠈⠀⠃⢸⢸⠀⡇⠁⠀⠁⠃⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⢸⠀⠈⢸⠀⠀⠆⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸⢸⠀⡇⡄⠀⡀⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠂⡁⢈⠂⠁⠑⡊⠈⠁⡃⢈⠐⠁⢙⢘⠀⡃⡃⠈⡀⡁⢘⢈⠀⠑⠈⠈⡂⡁⢉⢈⠁⡑⡊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠁⠈⠀⠇⡇⠈⢸⠁⢐⠸⠀⠀⠁⠈⠀⠁⠈⠈⠀⡇⠀⢨⠀⡇⢸⢸⠀⡇⡇⠀⠁⡇⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⢸⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⢾⢸⠀⠇⡇⠀⠁⡇⢰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣀⡃⢈⣐⠁⢑⣊⠈⣃⡀⢈⣐⠁⢙⣈⠀⣃⡋⢈⡂⡁⢘⣈⠀⣃⡈⠈⣐⠁⢙⣈⠁⣁⡊⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠁⠈⠀⠇⡇⠈⢸⠁⠀⢸⠀⠀⠅⠈⠀⠁⠀⠈⠀⡇⠂⠨⠀⠁⢸⠸⢆⡃⠏⠀⠀⡇⠸⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⡆⡇⠀⢸⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⢸⢸⠈⡇⠃⠀⡆⡇⢠⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠂⠃⠈⠒⠁⠑⠊⠈⠓⠂⠘⠒⠁⠑⠘⠀⠃⠊⠈⠂⠁⠑⠘⠀⠑⠊⠈⠒⠃⠑⠒⠁⠓⠊⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠁
⣿⣿⡿⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠋⡈⠉⠉⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢒⠖⠡⡀⠀⠀⢀⡐⢆⡀⢀⡠⠀⠉⠶⡢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠀⠀⠈⢉⠜⠋⠀⠀⠒⠄⠀⠀⠀⠀⠙⣏⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⡠⠎⠀⠀⠀⢀⠀⠀⢱⠀⠀⠀⢀⡇⠀⠧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣶⣄⣀⠀⠈⠁⠐⠀⠉⠀⠀⣀⣤⡎⠀⠀⠀⠀⡆⠀⠰⡉⠁⠎⢀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⢀⣧⠀⠀⠹⠀⢀⡠⠊
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠁⣘⢦⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣿⡿⠁⠀⠀⢀⠼⠁⠁⠀⠀⣠⠂
⡠⠂⠉⠉⠀⢰⠀⠁⡆⡠⠊⠀⠉⠒⠤⢀⣈⠙⠛⠃⠀⠀⠀⠀⠛⠛⢉⣀⠠⠄⠂⠁⠀⠣⡀⠖⠈
⠑⢆⠝⠃⠀⡊⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠈⠂⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⣀⡀⠤⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⣀⠠⠤⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢴⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠵⠖⠢⣤⢤⣤⠄⡀⠀⠀⣠⠐⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡋⠁⠀⠀⠀⠀⠀⠀⢀⣣⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⢀⡀⠤⠒⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣥⣤⣬⣵⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣉⣉⣁⡀⠀⠉⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣷⣛⣋⣉⣉⣉⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠉⢉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠤⣄⠀⠀⣠⠤⣄⠀⠀⣠⠤⣄⠀⠀⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡇⠀⣿⠀⠀⡇⠀⢹⠀⠀⡏⠀⢹⠀⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣇⠀⣿⠀⠀⣇⠀⣼⠀⠀⣇⠀⣸⠀⠀⣇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢛⣁⠀⠀⠙⢛⣃⠀⠀⠙⣛⡋⠀⠀⢙⣛⠛⢧⠞⣛⡓⢦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣾⠉⣷⠀⢰⡏⠹⡇⠀⣼⠉⢹⠀⠀⡏⠉⣧⠀⢰⠋⢹⡆⢻⡀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⢸⠀⠀⡇⠀⣿⠀⢸⡀⢸⡇⠘⡇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠶⠋⠀⠈⠳⠞⠁⠀⠘⠲⠛⠀⠀⠛⠾⠃⠀⠈⠳⠞⠁⠀⡇⠀⠀⢰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡴⠲⣆⠀⣰⠚⣦⠀⢠⡖⢶⡀⢀⡶⢳⡄⠀⣴⠒⣆⠀⣰⣿⠀⠀⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⠘⢶⠴⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠴⠃⠀⠹⠦⠟⠀⠘⠧⠞⠁⠈⠳⠼⠃⠀⠻⠴⠏⠀⠘⠦⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⡀⢀⡴⢦⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠷⠼⠃⠈⠧⠼⠃⠈⠧⠼⠁⠈⠧⠼⠁⠘⠧⠾⠁⠘⠧⠾⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣤⡄⠀⣠⣤⡀⠀⣠⣤⠀⢀⣤⣄⠀⢀⣤⣄⠀⢠⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⣿⠀⣿⠀⡇⠀⡇⢸⡇⢸⡇⢸⠀⢸⠀⣿⠀⣿⠀⡷⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠹⣤⠟⠀⠻⡴⠇⠀⠷⡼⠃⠘⢧⡾⠀⠸⢦⠟⠀⠻⣤⠏⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣉⣉⡉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠶⠶⠶⠤⠤⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠙⠛⠛⠒⠒⠶⠶⠶⠤⣤⣤⣤⣀⣤⠶⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⢀⠀⡀⢀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠷⠻⠾⢻⣽⡅⣻⣄⡿⣄⣨⢠⣤⢀⣀⠀⠀⡇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣄⣠⣀⠀⡀⢉⡌⠁⠉⠉⠋⠘⠘⣿⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠏⠁⠙⠉⠛⠛⠿⠻⡇⡷⠆⠀⢠⣴⡿⠁⠀⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣤⣀⣀⡀⠀⠀⠀⠚⠡⠚⡴⢂⠀⠀⣿⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⠤⣤⣄⣀⡀⣸⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⢤⡤⣔⢲⣆⣲⠰⠯⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸⢹
⠀⠀⠀⢀⠆⡃⡞⠙⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠡⠤⠠⠤⠐⠒⠒⠒⠢⠤⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⡸⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⢀⠠⠤⠐⠒⠂⠀⠀⠒⠒⠤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠐⠒⢲
⠀⠀⠀⠀⢰⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⢇⡀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢸⠀⠠⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⡖⠉⠉⠀⠘⠀⠁⣢⠀⠀⠀⠀⠀⠀⠀⠠⢀⠒⠠⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡁⢘⠀⠀⠀⠀⢈⠀⠈⠉⠁⠈⠉⠉⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⣤⠀⠀⡀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠤⠀⡇⢰⠀⠀⠀⠀⠸⡀⢰⠁⠐⠒⠈⠂⢸⠀⠀⢀⠀⠀⠀⠈⠄⠈⡁⢀⠀⠠⠀⣊⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣧⠜⠀⠀⠀⢀⡔⠃⠈⠢⠨⠬⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⢌⠀⠠⠀⠀⠀⠊⠀⡀⠈
⠀⠀⠀⠀⠈⡗⠢⣤⠦⠒⠙⠀⠀⠀⢠⢊⡔⠊⠈⠉⠉⠁⠐⠒⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡐⠉⠁⠀⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⡄⠀⠀⠀⣀⣀⡀⠀⢘⢓⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢬⢠⡈⡰⠂⠤⠀⡤⠠⠔⡨⡤⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⡜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠌⠡⠁⠀⢀⢂⣤⠀⠀⠀⠀⠀⠈⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⠀⠐⠒⠀⠉⠀⠀⣀⠠⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠤⠤⠔⠒⠋⢉⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠉⠉⠉⠉⠉⠉⠉⠁⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠠⠄⡀⠀⠀⢀⡀⢠⠈⠀⠀⡀⠠⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⡄⠤⠁⠈⠆⡤⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠊⠁⠀⠀⢢⡜⠀⠀⠈⠐⠠⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠊⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠑⢤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠒⠈⠉⠀⠒⢄⠀⡀⠄⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠁⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠟⢢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡶⠋⢤⠀⠀⠀⠀⠀⡰⢆⡀⠀⠀⣀⠇⠀⠱⣶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠒⣾⠎⠁⠀⠀⠑⠒⢒⡶⠎⠁⠀⠩⠄⠈⠁⠀⠀⠀⠈⠳⡖⠒⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡾⠁⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠙⢶⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢠⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢠⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠉⠂⡀⠀⠀⠀⠈⠉⠐⠒⠒⠈⠉⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠤⠤⠤⠤⠤⠄⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢀⡜⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⢆⡠⠤⠤⠤⢄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⣡⠀⠀⠀⠀⠀⠀⠙⢄
⣀⠶⠈⠉⠉⠀⢠⡖⠉⠁⡶⠀⡰⠉⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠉⠆⠀⠆⠉⠉⢲⡀⠀⠉⠉⠑⠢
⠧⣤⠐⣶⠆⠀⣰⠃⠀⢀⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢻⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⡀⠀⠘⣄⠀⠰⣶⠢⣤
⠀⠈⠊⠀⠰⢀⡿⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢿⣠⠖⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠐⢦⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠶⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⣀⠀⣤⠄⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⣀⠤⠄⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣘⠧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠴⠞⠛⣠⣤⣤⣤⠶⢤⡀⠀⠀⠀⣤⠂⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡉⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠱⢮⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠋⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣢⣴⠀⠀⢰⣖⠛⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣤⣴⣶⣤⣾⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⢩⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠋⢉⣀⡤⠴⠖⠋⣻⠙⠲⢤⣀⠉⠛⠲⢤⣄⡀
⠀⠀⠀⠀⢀⣠⠤⠴⠒⠚⠉⢁⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⢀⡇⣠⣤⣄⣈⡉⠓⠢⢤⣀⠉⠓⠦⣄⡀
⠀⣤⠒⠊⢁⣀⡤⠤⠖⠚⠉⠉⠀⠀⠀⠀⢀⣠⠴⠒⠚⠓⢺⠟⠁⠀⠀⠀⠙⢦⣀⣀⡈⠙⠢⣄⣈⡩⠗
⠀⣇⡉⠚⠯⣄⣀⠤⠴⣤⡴⠖⠲⣄⣠⠖⠋⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣀⣠⢬⡭⠟⠋⠉⣀⠤⢺
⠀⢹⡈⠉⠲⢤⡙⠲⢤⣄⡀⠀⠀⠈⠣⣤⠤⠤⠤⠤⠤⣤⣈⠑⣲⠤⠖⠊⠙⡇⠀⠀⢷⠔⠚⠉⠀⠀⢸
⠀⠈⣇⠀⠀⢰⣿⠑⠢⢌⡙⠶⣤⣀⡀⠈⠉⠉⠁⠀⣀⢴⡛⠉⠀⠀⠀⠀⠀⢱⠀⢠⢸⠀⠀⠀⠀⠀⡟
⠀⠀⢹⠀⠀⠀⢿⣄⡀⠀⠉⠲⢤⣈⡙⠳⢦⡤⠒⢉⣠⠴⡇⠀⠀⠀⡀⠀⠀⢸⠀⣸⢸⡆⠀⠀⠀⢠⡇
⠀⠀⠸⡆⠀⠀⠀⠙⠛⠷⣤⣀⡴⠁⠉⠓⠲⡗⠋⠁⠀⢰⡇⠀⠀⡸⢀⠀⠀⢸⠀⠋⠀⡇⠀⠀⠀⡼
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⠇⡌⠀⠀⢸⣀⡤⠴⠇⠀⠀⢠⠇
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⠀⠀⠘⠀⠀⠀⢀⡼⠁⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⣠⠴⠒⠒⠋⢉⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠋⠁⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⡇⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠧⠖⠚⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣤⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⡠⠤⠤⠤⠧⠄⠀⠀⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⡠⠀⡜⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⢰⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠤⠒⠉⠉⠉⠑⡀⢰⠉⢣⠀⠀⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⢀⠁⢸⠀⠀⡇⢸⠒⠒⠀⠠⠤⠤⠤⠤⠤⠀⠐⠒⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠤⠔⠁⢸⢀⢀⣀⠤⠐⠂⠀⠐⠂⠤⠄⠠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⣀⣀⣀⣀⣀⣀⣀⠠⠆⠀⢸⠘⠤⢀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣴⣶⣾⠶⠿⠿⠿⢿⣿⣶⠒⣦⣤⠠⠐⠒⠣
⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⢺⠀⠈⠐⠛⢳⠶⠖⠒⢚⣛⣛⣩⣭⣥⣥⣤⣼⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠣⠀⠀⠀⠀⢸⠀⠋⠋⠝⠿⣭⡭⠭⠴⠶⠛⠛⠃⠉⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠒⠤⢄⡀⣇⣀⡤⠤⠴⠒⠒⠋⠉


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

⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⠶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣸⠦⠤⢾⠀⠀⠀⠀⢰⠁⠀⢱⡀⠀⠀⠀⡠⠊⠁⠧⡀⠑⠢⣤⠐⠊⠁⡸⠈⠑⢄
⠀⠀⠀⠀⠊⣤⡏⠈⠉⠈⢆⠀⠀⠀⣠⠀⠀⠠⡇⠀⠀⡰⠁⠀⠀⠀⠀⠁⠚⡄⡃⠉⠁⠀⠀⠀⠈⢢
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠆⠠⠊⠀⠀⣀⠀⠈⠲⡭⠅⠀⢐⣒⣒⣒⡤⡄⠇⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⢠⠊⠁⠀⡇⣿⡇⢠⠀⠀⠀⠀⠀⡇⠀⢿⣤⠧⠤⠤⠤⠤⠤⠤⠄⠀⡃
⠀⠀⠀⠀⡗⠐⢒⠒⢒⣒⣒⢺⠁⠘⠀⠀⠀⡇⣿⠀⢸⠀⠀⠀⠀⠀⡇⠀⣿⣛⣗⣒⣒⣒⣒⣒⣂⣂⡐⡇
⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠣⢙⡃⢸⠀⠀⠀⠀⠀⡇⠀⣿⣿⡧⠤⠤⠤⠤⣤⣤⣤⣤⡆
⠀⠀⠀⠀⣟⠤⠀⠀⠀⠠⠤⣻⡀⢠⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⣿⡤⡥⠤⠤⠤⠤⠤⠤⠤⢤⡇
⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠁⢸⡇⠈⠉⠀⠀⠀⠉⠀⢸⣁⡒⠒⠀⠠⠧⠐⣯⣿⣏⣉⣉⣉⣉⣉⣉⣉⣀⠇
⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⠈⠑⠒⠀⠠⠤⠄⠐⠒⠁⠀⠉⠉⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠀⠀⢀⢄
⢠⣄⡰⠂⣈⡥⠂⠀⠶⣟⣀⢄⡾⠛⣁⣀⣤⡀
⡀⠀⠀⡩⠟⠿⠿⠷⠶⠾⠷⠾⠟⠋⠉⠙⣋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠏
⠈⠉⠐⠠⠤⢄⢀⣀⡀⠀⠀⠀⣀⡀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠠⠤⠀⠠⣠⠤⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢿⡏⠀⠀⠀⡠⠔⠶⠁⠐⠐⠈⠀⠀⠒⠻⣷⣬⡁⢀⣀⡉⢈⣺⡷⢂⢤⡀
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢿⢢⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠘⠂⠌⠉⠄⠄⠀⠀⠀⠈⠙⡎⠡⠆
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡋⠀⠀⠀⠀⠀⠲⠆⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣐⡀⣬⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣽⡆⠀⠀⠀⠀⠀⢙⡂⠲⠤⠀⠀⠀⠀⢈⣉⣉⢨⣭⠍⠬⠤⠄⣒⣚
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⡇⠀⠀⠀⠀⠀⠀⠭⢘⡒⠀⠀⠀⠀⠠⠥⠤⠐⢒⡂⣒⣛⢉⣭⠥
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣯⡅⠀⠀⠀⠀⠀⠀⢑⡠⢭⠀⠀⠀⠀⢘⣛⣃⢨⠭⠄⠤⠶⠐⣒⡂
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠰⠶⠆⠐⠒⠀⠛⠁⠈⠉
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣭⣿⣯
⠀⠀⠈⠀⠠⠀⠒⠀⢤⠴⠶⢾⣟⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⢤⣄⣈⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣤
⠀⠀⠀⠘⠋⣤⡶⠚⠋⢉⣠⡤⠶⠒⠚⠓⠛⠒⢖⣶⣦⣤⣌⠉⠛⢷⠀⠀⠀⠀⠀⢠⣾⡿⠯⠉⣉⠩⣥⠴⠶⠶⠀⠶⣤⣀⡀⠀⢐⢶⣈⡀
⠀⠀⠀⠀⡜⠉⢂⣴⣾⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠈⠀⠀⠀⠀⡰⢫⣿⠃⠀⠾⢋⠠⢴⣚⣩⣽⣶⣶⣶⣭⡋⠀⠀⠻⣿⡇
⠀⠀⠀⠈⠁⣠⣿⠟⠋⠀⣀⣤⣶⣾⠿⠿⠿⣿⣷⣶⣄⡀⠈⠙⣿⣷⠀⠀⠀⠀⣇⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠊⢾⡝⣆⡀⠀⠘⡇
⠀⠀⠀⠀⢠⠇⠁⢀⣴⡾⣟⣉⣥⣤⣶⣾⣿⡟⣀⠉⠻⣿⣄⠀⠈⠿⠀⠀⠀⠀⣿⡟⡙⢠⢻⣿⠿⢻⣿⣿⣿⡷⣦⣄⠀⢰⣿⡿⣿⠀⠀⡇
⠀⠀⠀⢠⡏⠀⣠⣿⣿⣿⣿⣿⣿⣿⢛⣋⡉⠈⠛⣷⣴⡞⣿⡆⠀⠀⠀⠀⠀⠀⣿⠟⣿⡻⠍⠀⠀⣾⣿⣿⣀⣀⠈⢹⣇⣼⣿⠋⠐⣁⠀⡅
⠀⠀⠀⠸⠃⢠⣿⠃⠛⣭⢵⣿⣿⡏⠛⠙⠻⣶⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇⡃⠀⢰⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣾⢙⣿⡷⡇
⠀⠀⠀⢸⠀⢸⡇⠀⢸⡇⣼⣿⣿⢡⣾⣷⡆⢹⣷⣿⢿⣷⣾⣿⡄⠀⠀⠀⠀⠀⣻⠀⣿⡇⡂⠀⣾⣿⣿⣷⣾⣿⣿⡿⣿⣿⠹⣿⣬⣷⠂⠁
⠀⠀⠀⢰⠀⢸⣧⠀⢸⣷⣿⣿⢇⣈⣿⣿⣿⢿⣿⡟⣿⣿⣻⡿⠁⠀⠀⠀⠀⠀⣿⠀⣿⠘⣗⢰⣿⣿⠧⣿⣿⠹⣿⣿⡿⢿⡄⢬⠋⠁⠀⣦
⠀⠀⠀⠈⡆⠸⣿⡄⠀⣿⣿⡿⢸⣿⢿⣿⣷⣾⡿⠓⠛⣻⡏⠀⣠⡇⠀⠀⠀⠀⢻⡀⣿⠀⠈⣾⣿⣿⢰⣿⡟⠀⣈⣁⣠⣄⡤⠃⠀⠀⠀⣿
⠀⠀⠀⠘⢳⠀⠙⢿⣾⣿⣿⠳⡿⠟⠼⠿⠽⠃⢀⣴⡾⠋⢀⣴⡿⠇⠀⠀⠀⠀⢸⠃⣿⡇⢰⣿⣿⠣⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⢀⡈⡡⢛
⠀⠀⠀⢀⡈⣦⡄⢀⣿⣿⡏⣶⣤⣤⣤⣤⣶⠾⠟⠉⣀⣶⡿⠋⢀⠀⠀⠀⠀⠀⢸⡆⢸⡛⣾⣿⡿⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⣚⡷⠋⣀⠘
⠀⠀⠀⠀⡇⠸⣷⣾⣿⡿⢁⠀⠉⠩⠍⠉⡀⣀⣤⣶⠿⠋⠀⣤⣾⠀⠀⠀⠀⠀⢸⡏⢸⢇⣌⡙⠲⢤⣿⣿⣛⣺⣲⣜⢭⠖⠒⠉⠠⠊⠁⢸
⠀⠀⠀⢰⠱⠀⠉⠋⠱⠶⣿⣿⣿⣷⣿⣿⡿⠟⠋⠁⣀⣴⣾⠿⢋⠀⠀⠀⠀⠀⢸⡧⣼⣧⣉⠛⠲⠦⣤⣨⣍⣅⠀⣤⡤⠶⠘⠋⠀⠀⠀⣸
⠀⠀⠀⠘⠆⢲⣧⣆⣀⣀⡀⡀⠀⠀⢀⣀⣀⣤⣶⣾⠿⢋⣁⣠⣼⠀⠀⠀⠀⠀⢸⡗⡿⠻⢾⡿⣶⣶⣶⣶⣶⣶⣶⠤⠶⠶⠛⠟⠛⣫⠟⠉
⠀⠀⠀⠀⠀⢈⠛⠻⠿⠿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠖⠓⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠠⠜⠉⢆⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠚⠒⠈⡐⡆⢄⡀⠀⡐⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⡤⠔⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡠⠔⢀⡀⠀⠀⠛⢶⢇⠀⠀⠀⠀⠈⠄⠀⠈⠂⠔⠉⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣀⡠⠤⠤⠤⠇⠚⠁⠀⢠⡞⠉⠉⠁⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⣄⡐⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠩⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⡰⢨⠀⠀⠀⠀⠀⠀⢠⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠚⠋⠴⠒⠲⠦⠤⣄⣀⣀⣐⣹⠄⣀⠀⠀⠀⡀⠎⠂⠉⡄⠀⠀⠀⠀⠀⣬⣹⣀⣀⡀⠤⠤⠤⠀⠒⠂⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈⠉⠙⠛⠋⠋⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⢑⠒⠢⠤⠤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠒⠈⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠬⠀⠀⡃⠀⠆⠀⢸⠈⠉⠉⠉⠷⢒⡒⠀⠀⣀⠐⠪⡏⠀⢘⠁⠈⠇⠀⢰⠊⠀⠀⠀⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠈⠉⠁⠀⠘⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⠑⠤⠆⠀⠘⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⠀⠀⣏⣰⡆⠀⢠⠤⠤⠀⠀⣀⣀⣀⠀⠀⣀⣀⢀⡀⠀⢠⠤⠀⡄⠀⢰⣉⠽⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠸⠀⠀⠇⠈⠗⠀⢨⠀⠀⠀⠀⡀⠀⠘⠀⠀⡁⠀⠀⠀⠀⢀⠀⠀⠁⠀⢰⠀⠘⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢⠀⠀⠃⠀⠈⠀⠀⠁⠁⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢠⠤⢤⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⢠⠤⠤⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⡁⠀⢸⠀⠘⠀⠀⠗⠀⢠⠀⠀⡅⠤⠤⡄⠀⠸⠒⠒⠃⠀⢠⠤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠉⠃⠀⠈⠀⠀⠀⠀⠃⠀⠠⠀⠀⠇⠀⠠⠆⠀⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠂⠀⢠⠤⣄⠀⠀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⢠⠤⠤⠄⠀⢰⠈⢹⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⡇⠀⢨⠀⠈⠀⠀⡁⠀⠈⠀⠀⠗⠀⠠⡄⠀⠘⠀⠀⠀⠀⢸⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠐⠃⠀⠈⠀⠀⠀⠀⠓⠠⠨⠀⠀⢤⡤⡤⠄⠀⠘⠀⠀⠁⠀⠈⠉⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢰⡒⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡝⠆⠀⠸⠀⠘⠀⠀⠆⠀⢴⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠃⠀⢨⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠴⠀⠀⢤⣀⣰⠀⠀⡍⠀⠰⠇⠀⠰⠤⠤⠃⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠠⣄⠀⠀⠀⢀⡀⢀⠀⠀⣀⣀⣀⡀⠀⠀⠤⠤⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠈⠉⠀⠀⠈⠀⣻⠀⠀⡏⠀⠈⡁⠀⠠⠄⠀⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠽⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⡀⡨⠀⠀⠀⠊⠀⡖⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠀⠊⠁⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⢀⠙⠐⢁⠤⢊⠂⠀⠀⣈⠂⠤⠊⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣉⡉⠙⠀⡇⠀⠀⠀⠀⠀⠀⠈⡠⠊⠀⠒⠓⠊⠀⠀⠒⣄⠀⡂⡂
⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠉⣉⢀⡐⡲⠛⣈⠝⢀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣞⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢄⣀⡠⠴⠮⠤⠤⠜⠀⡇⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⠤⢤⠐⠊⠥⣂⡈⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠃


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠙⠀⠉⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡁⠀⠀⠙⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠄⠀⠈⠀⠈⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⣉⣀⡀⠀⠀⠀⠀⠀⠂⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠒⠠⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠚⠉⡉⡉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢲⢙⠠⢙⠃⠄⢡⡐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠰⠀⠐⣤⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⠀⢳⡨⡀⠌⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠢⣁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⢠⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣴⣶⣶⣶⣦⡄⣰⣄⠈⠁⠼⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⢠⡀⢿⡳⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⡅⣀⠀⠀⢀⣀⡀⢀⢸⣧⠀⠀⠀⠀⢘⣈⡗⢽⣦⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⡿⠿⣧⣀⠈⠷⠀⠀⠀⠙⢦⠀⠀⠀⠀⠘⠆⠙⢻⠓⢿⣦⠀⢸⢳⠀⠁
⠀⠀⠀⠀⠀⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⠔⠂⣠⣩⣴⣿⡿⣛⣿⣶⣦⠀⠀⠀⡀⠀⠀⠰⢚⣅⢾⣿⣼⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢴⠲⡶⠚⣮⢥⣑⠂⠛⠛⠉⠀⠀⢀⠋⣠⡭⣛⡀⠀⠀⠀⠀⠀⠀⡿⣾⣾⣿⣧⣟⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⣠⣴⣦⣶⡶⣿⣷⣿⣿⣿⣶⣬⣙⣧⣺⣻⡿⢿⢳⣹⣇⠀⠀⠀⠀⠊⢶⣿⣿⣿⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡿⠛⠉⠉⠀⠀⠀⠀⠉⠙⠻⠿⢿⠿⣦⣿⣿⣷⣷⣾⣿⣿⡀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣢⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⣦⡻⣷⣿⣿⣿⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣏⡀⠘⢿⣶⣄⠀⠀⠀⠀⠀⡀⠙⣿⣿⣿⣿⣿⠛⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡙⢿⣿⡇⠀⠈⠙⢿⣿⣶⣦⡄⠈⠀⣼⣿⣥⡥⠀⠀⢠⣬⣯⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢤⣀⠙⠳⢦⡭⠋⠁⠀⢀⢐⣿⣿⣗⡀⠀⠊⣽⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠌⠻⣿⡦⠀⠀⠀⢠⣀⣰⣾⣿⡷⠌⠁⢰⣿⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠆⠙⠿⢶⣤⣴⣾⣻⣟⣿⠟⠉⣀⣦⣸⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠰⡿⠀⣠⣿⠿⠿⣷⣿⣟⡶⠶⣿⣿⠿⣋⣵⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⠉⠙⠻⢿⣧⣦⠾⣋⣵⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠅⠚⠛⠉⠉⠉

⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⡆⠐⢘⠀⡁⣁⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⠇⠹⡹⠁⠳⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠴⠣⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⢀⣠⣄⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⠻⢿⣿⣿⠿⠛⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡋⠙⣿⡏⠀⠀⠹⡏⠀⠀⠈⢿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠃⠀⠀⠈⣿⠁⠀⠈⣿⠋⠉⣿⣿⣿⣿⣿
⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣤⣤⣤⣾⣧⣤⣤⣤⣿⣧⣤⣤⣤⣿⣦⣤⣤⣴⣿⣶⣶⣶⣿⣿⣿⣿⡿⡟⠋⠁
⠀⠀⠀⠀⠈⠉⢿⠁⠈⠹⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⡟⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠘⣆⠀⣰⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣇⠀⣠⠇
⠀⠀⠀⠀⠀⠀⣤⣿⡿⠻⣿⡿⠉⠉⢻⡏⣿⡇⢹⣿⠀⠀⠘⣿⡇⠀⠀⢸⡟⢹⣿⠉⣿⠋⠉⢻⣿⠿⢿⣿⣤⠆
⠀⠀⠀⠀⠀⠀⠋⢹⡇⠀⠸⣿⠀⠀⢸⡇⢸⡇⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⡇⢸⣿⢠⡿⠀⠀⣼⡇⠀⢸⣏⡹
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣶⣿⣧⣀⢈⣿⣾⣷⣤⣿⣀⠀⣸⣿⣇⠀⢀⣸⣧⣼⣿⣼⡇⣀⣴⣿⣷⣴⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⣿⣿⡛⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠛⣿⣿⠁⠀⡝
⠀⠀⠀⠀⠀⠀⠀⢠⣈⣷⡾⣿⣿⠛⠻⣿⠻⣿⠏⣿⠁⠀⠈⣿⠃⠀⠀⣿⠟⣿⡟⢻⡿⠛⢻⣿⠷⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⠀⢻⠀⠀⢿⠀⣿⡄⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⣿⠀⢸⠇⠀⠸⠁⠀⢹⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠀⢸⠀⠀⢸⡄⣿⡇⣸⡇⠀⠀⣿⡀⠀⠀⣿⠀⣿⠀⣼⠀⠀⡄⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠖⣾⣧⣀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣄⣴⡿⠒⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠙⣆⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⠆⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⢠⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠋⠉⠛⠉⠙⠛⡇⠀⠀⠀⠀⠈⠁⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠄⠀⠀⠀⠀⢀⡞⠀⢀⡼⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠢⠀⠀⠀⠀⢀⡾⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠋⠉⣉⡇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⡼⠁⠀⢸⠀⠀⠀⠀⠀⣠⠞⠋⢀⣠⠴⠖⠛⠋⠉⢹⡀⠀⢀⣀⡾⠁⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡸⠁⠀⠀⢸⠀⠀⠀⢠⠞⠁⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⢳⣀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣼⠃⠀⠀⠀⢸⠀⠀⢀⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠃⠀⠀⠀⠀⡏⠀⠀⡿⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠚⠁⠀⠀⠀⠀⣼⠃⠀⢰⠋⠀⠀⠀⠀⣰⠁⠀⠘⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⢧⡀⠀⠀⠀⣰⠁⠀⢠⠏⠀⠀⠀⠀⢰⠇⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⠇⠀⢀⡞⠀⠀⠀⠀⢠⡟⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⢀⡞⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⣆⠀⢀⡞⠀⠀⠀⠀⢸⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⢷⠟⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣄⣤⣤⣠⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣠⣄⣠⣤⣀⣠⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠛⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⢀⣠⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣀
⢀⣿⣿⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠙⢿⣷⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣷⣦
⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣦⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢿⣷⡄⠀⠀⣀⣤⣴⣿⡿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠈⢿⣿⡀⠀⠛⠿⢿⣿⣦⣼⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠹⣿⣆⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠘⣿⣷⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⠀⠀⠀⢀⣴⣿⣿⣧⣀⠀⠀⠀⠹⣿⣧⡀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⢹⣿⡆⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⣿⣿⠀⠸⣿⣿⣿⣏⢈⣿⣿⣿⡷⠀⠀⠈⢿⣿⣦⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠉⠻⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠉⠛⠿⣿⣶⣶⣾⡿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⢠⣤⣶⣿⡟⠻⣿⣶⣦⣄⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣾⣿⠟⠛⠉⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡄
⣿⡟⠀⠀⠀⠀⠀⠸⢿⣿⣿⣇⣨⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡟⢙⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣧
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣠⣾⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⢿⣿⣿⣅⣼⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿
⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠈⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠻⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠃
⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⣿⣿⡟⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣛⣭⣭⣭⣭⣭⣝⣛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢿⣿⣿⣿⣿⢋⣭⡛⢿⣿⣿⣿⡎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣍⢻⣿⡟⣾⠀⣿⢸⣿⣿⣿⢇⡟⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣡⣿⣿⢸⣥⡟⣼⣿⣿⡟⣼⣷⢟⣭⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡼⣸⡇⠈⣿⢱⣿⣸⣿⡿⢋⡼⠉⣏⢾⠿⢿⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣫⡭⠶⠒⠓⠚⠲⠿⣀⣰⡏⢾⡇⣿⣿⣅⠻⢤⣀⣹⡦⢡⣾⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣝⠘⠷⣝⣿⣶⣶⣶⣾⣿⣿⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡱⣮⣛⠿⣿⣿⠿⢟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡉⠛⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣃⣴⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⣝⢳⡀⠀⣀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠻⢶⣦⠀⠀⠀⠀⣠⠲⢸⣇⠛⣋⣥⠶⠶⠓⠒⠒⠶⠶⣭⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠉⠉⠁⠀⢀⡆⠀⠀⠀⠀⠀⠠⠤⠀⠉⠀⠀⠀⢀⠄⠲⠠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣿⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣤⣤⠾⣄⣀⠀⠤⠠⠌⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⡀⣿⡏⠀⠈⠉⠁⠰⠦⠶⠆⠈⠀⠀⠀⢀⣿⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡰⠁⠀⠀⣾⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠹⣎⢻⣿⢿⣄⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⣠⣾⣿⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣼⠁⠀⠀⣼⢇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣭⡙⣦⠀⠀⢹⡎⣿⣧⡙⣷⣦⣾⣿⣿⣧⣀⣠⣴⣾⣫⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠒⠒⢺⢇⡾
⠀⠀⠀⠀⠀⠀⠀⢸⡃⡟⠰⡇⣿⠀⠀⢸⡇⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⣌⠳⢦⡀
⠀⠀⠀⢀⣤⡤⠶⠾⢃⣿⠀⠹⣼⣇⠀⡿⣸⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠀⠘⠛⡇⣿
⠀⠀⣴⢫⡴⠒⠛⠛⠉⠁⠀⢰⠏⣟⢸⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⠖⣚⣰⠇
⠀⠀⢷⣙⣛⣛⢻⣄⠀⢤⡀⢸⠷⣝⡛⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠋⠉⠁
⠀⠀⠀⠈⠁⠙⣦⡻⣿⣻⡟⠁⠀⠈⡛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⢸⡁⠀⠀⢀⡠⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡟⠒⠒⠋⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣾⢱⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠻⣤⡀⠀⠀⠀⠀⠀⢀⣠⡴⢋⡴⠷⣬⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣛⡳⠶⠶⣖⣚⣋⡭⠖⠋⠀⠀⠈⠛⢮⣝⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⣛⣛⣯⣭⣭⣭⣭⣭⣛⣛⣛⣫⣥⣾⣿⣦⣄⣀⠀⠀⠀⠀⠀⢀⡴⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠃⠀⠀⢀⣤⠶⣶⣶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠉⠛⠛⢛⣿⡿⢛⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⡞⣴⠋⠉⠉⠉⠙⠒⠶⢭⣭⣵⣒⣒⣒⣒⣚⣛⣭⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣆⠀⠀⣷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠳⣄⠹⣯⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣛⠾⣷⣮⡙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠽⠶⠋

⠀⠀⠀⠀⠀⢹⠛⠛⠛⠛⢻⣩⠿⣏⣩⠿⣏⣽⠿⠿⠿⠿⠿⢿⡏⠙⡆
⠀⠀⠀⠀⢠⣼⣤⣤⣤⣤⡼⠹⣦⠞⠹⣦⠟⢿⡽⣽⣽⣽⣽⣽⠇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠐⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠲⠶⠶⠶⠶⠶⠶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠲⠦⢤⣀⠀⠀⠀⠀⡠⠔⠓⠈⠁⣀⡄⠈⠍⠢⢄⠩⢥⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⠤⠄⠀⠠⠤⣀⠈⠳⣄⠀⢰⠓⠒⠀⠀⣻⠷⠤⠬⠭⠭⠟⢈⠉⠓⠓⠚⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠊⣠⠖⠚⠛⠓⠲⣄⠑⡄⠈⢷⠈⠀⠀⠀⢠⣋⣋⣉⣉⣉⣉⣉⣛⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⠁⡞⠁⠀⠀⠀⠀⠀⠈⢳⠈⡄⠈⣿⠀⠀⠀⣎⣉⣉⣉⣉⣉⣉⣉⣉⣡⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿⢃⠀⣰⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⡄⢳⡀⠀⠀⠀⠀⠀⢀⡞⢠⠃⢀⡏⢸⢀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⢑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⢆⡙⠲⠤⣤⠤⠖⢋⡠⠃⢀⡞⠀⠸⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠈⠐⠒⠀⠒⠊⠁⣀⡴⠋⠀⠀⠀⠀⣉⣉⣁⣉⣉⣁⣉⣉⣁⣉⣈⡁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠈⠁⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢠⡆⣈⣉⣁⣉⣉⣈⣈⣁⣉⣀⣀⡁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠸⡃⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⡀⡄
⠀⠀⠀⠀⠀⠑⠖⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠲⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠐⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠉⢳
⠀⠀⠀⠀⣠⠤⠤⢤⠧⢤⣤⣤⡤⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⠒⠒⠛⡆
⠀⠀⠀⡎⠀⣀⣀⡼⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⡇⢸⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣀⣀⡀
⠀⠀⠀⡇⢸⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡤⠄⢀⣈⣉⣉⣉⠉⠁⠐⠒⠒⠒⣒⡶⡄
⠀⠀⠀⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠀⠀⣠⠤⠒⠒⠐⢦⠀⢠⡖⢆⠀⢡⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠉⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⡎⠀⠀⠀⠀⠀⠈⡆⢸⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢣⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⡎⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⡇⢸⡇⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⢀⡠⠤⠤⠤⢄⣀⣀⢀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⡎⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠸⣇⡰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⣸⣈⣉⠒⠒⠒⠒⠒⠒⠒⠒⠊⣉⣀⣇⡇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇⠀⠀⠈⠉⠙⠛⠀⠐⠛⠋⠉⠉⠀⠀⢸⠓⠒⠒⠂⠤⠤⠤⢄⣀⣀⣸⣀⡤⠤⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠤⢤⣤⣀⣀⣀⡀⠀⢸⠀⣀⣠⠇
⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠀⠈⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢙⠵⠤⠴⠒⠐⢾⢦⡒⠒⢈⠡⣄
⠀⠀⠀⠀⠀⠀⠐⠈⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠤⠤⠁⢄⠀⠛⠳⡉⣸⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣁⠀⡈⣉⢤⡄⠀⡀⠳⠴⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠤⠐⠁⣠⡈⠢⡈⠢⡠⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢐⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢱⠦⡤⠀⣀⣀⣀⣀⡀⢠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠀⠒⢥⣊⣀⡀⢀⠜⠀⡠⠒⠐⡵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠒⠓⠃⠉⠈⠀⢘⣯⣀⠔⠁⠀⠀⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⡄⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢄⡐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠉⠢⣄⠀⢀⣠⠴⠊⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⡀⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣀⠠⠄⠂⠈⠀⠀⠈⠑⢆⠀⠀⠀⡆⠀⢃⢀⠠⠔⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⢄⠀⠀⢃⠀⠀⠑⠀⣀⠃⠀⠀⠀⠠
⠀⠀⡄⠠⠀⠠⠀⠀⠀⠀⠀⢰⠀⠠⠊⠐⠄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠑⠀⢸⠀⠀⠀⠀⡈
⠀⢨⠀⠀⠀⠲⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⠠⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡌⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠑⠂⠀⠊⢃⠀⠀⠀⠀⢸⠄⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠮⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡤⠚⢙⢠⣀⠀⠀⠀⠀⠀⠣⠇⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠖⢁⡄⠨⡑⠞⠉⠀⠀⠀⠀⠀⢸⠀⡠⠒⡩⠙⠃⠀⡀⠀⠂⠈⠉⠉⠁⠂⠂
⠀⠀⠀⠀⠀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠓⠈⠜⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠈⢀⣊⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠘⠒⠀⠉⠀⠀⠀⠀⠀⠈⠓⢄⡀⡀⢀⣠⡄⠒⠁⠀⠀⠀⠀⠀⠉⠀⠂⠠⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⣀⢀⣀⡀⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡔⠈⠑⢆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢱⣄⡀⣘⠀⠀⠀⡇⡠⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠄⠤⠀⢊⠉⢻⠉⠀⠀⢰⠉⢩⠋⠛⡏⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⡎⢀⢀⠀⢈⡆⠊⠉⠒⠀⠒⠁⠙⠢⠐⠃⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡋⠊⠴⣾⠿⣀⣀⣀⠀⠀⠀⠀⡠⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢞⠆⠒⠉⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣢⠤⠤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⢀⡠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠤⠔⠊⠁⢀⡰⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⣀⠠⠐⠊⠁⣀⠴⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠠⠤⢲⠋⢀⣀⡤⠖⣛⠢⠬⣁⠒⢤⣀⠤⠊⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⠢⢔⠛⠥⡜⣀⠀⠉⠈⠉⠁⠀⡀⡡⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⠪⢕⠢⠬⠭⢿⡤⡁⠒⠀⢐⠬⠡⠔⠁⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠉⠀⠀⠁⡠⠭⠙⠁⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠀⢎⠀⠀⣀⡀⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠂⠒⠠⠤⣄⠒⠂⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠉⠀⠀⠀⠀⡠⠒⠒⠒⠠⠁⠂⢤⣀⠤⠀⠌⠉⠗⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠠⠠⠤⠤⠀⠤⠶⡩⢍⡉⠉⠁⠀⠐⠒⡩⠐⠒⠒⠲⠤⠦⠤⠬⣇
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⢠⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠒⠒⠀⠀⠀⠀⠂⠚⠃⠀⠀⠐⠺⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡧⠤⣤⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠁⠉⠁⠉⠙⠉⠉⠉⠋⠈⠉⠉⠛⠉⠉⠉⠉⠈⠓⢄⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⢤⡤⠤⠤⡤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠊⠉⠙⠉⠉⠙⠉⠙⠁⠁⠛⠈⠉⠉⠙⠋⠉⠛⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⣄⠄⠠⠀⠤⠤⠠⣠⠤⠤⠤⠀⠤⠤⠠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠉⠉⠛⠉⠉⠉⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⡤⠤⢤⡤⠤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠥⠤⠤⠼⠫⠤⠤⠤⠤⠤⠤⠤⠯⠯⠤⠤⠼⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠀⠠⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣉⣉⣉⣙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣛⣛⣿⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠋⣿⡏⣿⡟⢻⣿
⠀⠀⠀⣤⣤⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣿⣇⣼⣇⣸⣿
⠀⠀⠀⣿⣧⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠛⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠈⠉⠙⠛⣿⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⣿⣷⣴⣦⣶⣾⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⢀⣿⣼⡟⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣥⣿⣷⣶⣶⣶⣶⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠻⠟⠋⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⢀⠀⡀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡁⠀⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠠⠤⠀⠀⠂⠀⠀⠀⠀⠤⠤⠤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⡀⠀⠀⠀⢸⢕⡇⠀⢯⡽⠀⢮⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠈⠀⠁⠀⠀⠀⠐⠂⠒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⠳⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠁⠀⠈⠛⠆⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⣰⠁⠀⠀⠀⠀⠀⡑⡈⢇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⡤⠠⠄⢘⣃⠀⢀⡴⣟⠩⠥⡀⢁⣐⠚⢠⡀⠀⡠⠤⠊⠀⣣⠀⠀⣾
⠀⠀⠀⠀⠂⣈⣉⠑⠲⢿⣯⣋⠩⠽⣩⡃⠐⡂⢬⣰⣊⠸⣥⢉⣘⣷⠷⠶⡶⠧⣇⣴⣾⢶⢰⢰⡄
⠀⠀⠀⠀⢊⣀⣀⣀⣀⡀⠀⠀⠄⣸⠿⠷⠀⠶⠶⠀⢿⡇⠈⠃⣤⣷⠴⠖⠴⠻⠆⠶⠶⠿⠘⠚⡇
⠀⠀⠀⠀⠀⣸⠌⢛⠛⢛⠙⠛⣚⠛⢘⣛⠃⢛⠚⠀⢛⣳⡄⢸⣅⣩⡛⣧⡽⠟⠋⠉⠉⠉⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠉⡛⡈⣓⣃⢙⢛⢈⡁⣁⢈⣉⡁⣉⣉⠁⡞⠀⢈⣉⣁⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠭⠥⠭⠭⠬⣭⠭⠭⠭⠬⠭⠤⠭⠥⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⠛⠃⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡔⡤⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠅⢢⡐⠀⠀⠀⠀⠀⠰⠤⠀⣠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠈⠁⢀⠀⣀⣄⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣁⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠼⠡⠀⡉⠁⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡰⠼⢴⠋⠒⠀⡀⠿⣄⣈⢀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠁⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⢠⠔⠋⠉⠓⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠁⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⣀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠰⡀⣶⡀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⠄⠂⠻⠁⠀⠀⠀⠀⠀⢀⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠀⠀⠀⣠⠀⠀⠆⠐⠛⠀⠀⠐⠀⠁⠀⠀⠀⡀⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠰⠂⠐⠀⠈⠀⠠⠂⢠⠖⠚⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠤⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡅
⠀⠀⣀⡠⠦⣤⣀⢀⠀⠀⠀⠀⢠⠔⠒⠤⠤⠤⠠⠄⡀
⡄⢾⡏⠀⠀⠀⠹⡆⡄⠀⣴⠶⠷⢾⡷⠾⠷⠷⠿⠟⠟⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠
⠐⠀⠻⢄⡀⠀⠀⢷⣰⠾⠅⠀⠉⠀⠀⠉⠀⠀⠀⠘⠋⠡⠒⠒⠀⠀⠉⠁⡀⡐⠔
⠀⠀⠀⠀⡉⣀⠠⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢤⣄⣴⠛⠷⠾⠂⠊⣄⠕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠣⠲⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⣙⣒⣺⡿⠶⢄
⠀⠀⠀⠄⠤⢀⠄⠀⠀⠀⣴⣾⣖⣒⣒⣒⣒⣒⣢⣠⣱⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠚⠑⠐⠚⠋⠉⠉⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠠⠤⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢃⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠎⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠒⠠⠤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠎⠀⠐⠋⠁⠈⠑⠒⠤⡤⢀⣀⣀⡀⠀⠈⣂⠀⠀⠈⠙⠀⠀⠀⠀⠹⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠀⠀⠀⠀⠀⠀⢡⠀⠸
⠀⠀⠀⠀⠀⠀⢀⡤⢦⣀⠃⠀⠀⠀⠈⠄⡄⣱⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⡀⢦⡄⠁⠀⠀⠀⠀⠀⠈⣄⠧⠤⡀
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠙⠀⠀⠀⠀⠻⡜⢧⠟⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢷⣟⡵⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠉⠉⠉⠉⠉⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡛⠛⠛⠛⠛⣏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠥⣀⣀⣀⠠⠜⠙⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠑⡄
⠀⠀⠀⠀⠀⠀⢠⠖⣉⢉⡑⢄⠀⠀⢠⠏⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡆⢸⠁⠀⠱⠞⠀⠀⡞⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣀⣀⠀⢸⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⣅⣠⠤⠤⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣈⣉⣉⣉⣧⠀⠀⠀⠀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠸⠥⣴⠒⠊⠉⢳⡀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣰⠃⠀⠀⡸⠁⠀⠀⠀⠀⢀⡠⠦⠼⣀
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠙⠢⣄⣀⠀⢠⣄⢀⣈⣀⡴⠁⠀⠀⡰⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⢶⠀⠀⠀⠀⠀⡝⠲⢤⡀⢀⡀⠈⠈⢠⣍⠀⠉⠁⠐⣀⡴⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣧⣸⣄⠀⠘⠖⠀⠀⠀⠀⠀⡇⠀⠄⠀⠉⠉⠉⠉⠰⠓⠄⠒⠂⠉⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡠⠤⠶⠤⠤⠼⠇⠤⠤⠤⠤⠤⠤⠤⠧⠄⠤⠤⠤⠬⠶⠶⠦⠤⠶⠠⠾⠁⠤⠄⠼⠤⠤⠤⠤⠤⠤⠼⠄⠤⠤⠤⠤⠴⠦⢤⡀
⠀⠀⠀⠑⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠲⠀⠠⢤⣤⣤⡤⠤⠄⠒⠒⠈⠉