Text wings Emojis & Symbols

⠀⠀⢫⣍⣉⣩⠴⠶⣤⠳⣠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡖⢦⡶⠶⢬⣉⣉⡽⠃
⠀⠀⠀⠉⠳⣖⡒⠒⣊⡤⢕⣻⡷⢂⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣀⢺⣷⡺⠥⣉⡒⢒⣒⠖⠉
⠀⠀⠀⠀⠀⠈⠋⠭⣤⡴⠋⡹⣷⢸⠀⠀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⠀⣿⣼⣿⠉⠳⣄⡭⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⠃⡉⠻⡷⣔⣒⣥⠶⡞⠀⠳⡶⣮⣔⣲⡴⠿⢻⠀⣷⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣇⡴⡘⢾⠚⢎⣮⠁⠀⠈⢷⣻⢺⢳⢫⢰⣸⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠞⠞⠁⠀⠀⠀⠈⠱⠛⠞⠚⠛⠋⠁
⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⢀⣴⣞⡭⠍⠒⠂⠒⢦⡀⠀⠀⠀⣤⠖⠐⠒⠫⢭⣳⣦⣄
⠘⣄⢱⣦⡤⣀⠀⠀⠀⠀⠀⢀⡠⣤⣶⢡⠞⠀⠀⠀⠀⠙⢤⡚⠉⢹⣔⣟⠀⠀⠀⠀⢺⣃⡎⠉⠑⣦⠋⠁
⠀⠀⢈⣻⣷⣿⣄⣀⡀⣀⣀⣼⣷⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⠣⠌⣉⡛⢽⡆⠀⠀⢀⡯⠟⣩⠡⠴⠁
⠀⠀⠀⠉⠉⠚⠉⠉⠀⠈⠙⠙⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⡤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠖⣒⡢⢝⠿⣛⡆⠀⠀⠀⠀⠀⠀⠀⢠⣛⠿⡫⢔⣒⠲⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠁⢪⢷⢽⠄⠀⢠⠀⣄⠀⠠⣯⡾⡕⠈⠲⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⠃⠀⠈⢻⠟⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢹⣆
⠀⠀⠀⠀⠀⠀⢾⡿⣭⣭⣵⣶⣾⠟⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⣴⠂⠀⠀⣀⣀⣠⠴⠋⠀⢰⢿⠇⠀⠀⢀⣀⣀⡤⠞⠁⠀⡾⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣯⣭⣭⠅⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣟⣃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠠⢾⠆⠀⠀⠀⠙⢦⡀⡤⠄⠀⠴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⣿⣄⠀⠀⠀⠀⠀⣀⡤⠞⠁⢸⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⢟⣋⣄⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⢲⡉⠉⠀⠀⠀⠀⢀⡟⠀⠀⠐⣎⠉⠁⠀⠀⠀⠈⣸⠃
⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⠟⠀⠀⠀⠈⠳⣴⠒⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣶⣤⠄⠀⠀⣴⠋⠉⠉⠉⠀⢀⣨⡿⠁⠀⢠⡞⠉⠉⠉⠁⠀⣀⣽⠏
⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡛⠉⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⡭⠀⠀⠀⢰⠃⠀⠀⠐⠛⢋⣩⠟⠀⠀⠀⡟⠀⠀⠀⠚⠋⣉⡽⠃
⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢸⡀⠀⠀⠀⢉⣩⠃⠀⠀⠀⠀⣇⠀⠶⡂⠈⢉⡟
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡾⢶⣾⣿⣿⣍⢻⣿⡄⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⢠⣿⡿⣉⣿⣯⣷⡿⢶⡦
⠀⠀⠀⠀⠀⠀⠀⢻⡿⣶⡟⢛⣿⡿⣷⣿⢿⣄⣀⡀⠀⠀⡏⣿⠀⠀⠀⣀⣀⣾⣻⣿⢿⣿⡿⢛⣷⡿⡟
⠀⠀⠀⠀⠀⠀⢰⣟⢰⠿⣿⣿⣿⣧⣻⣿⣿⣿⣽⢳⡀⠀⠀⠙⠀⠀⡺⣯⣿⣿⣿⣿⣼⣿⣿⣿⡿⣇⢻⡆
⠀⠀⠀⠀⠀⠀⣹⣿⣫⡄⠟⣿⣿⣻⣿⣷⣟⣽⣿⣷⡀⠀⣤⢰⠂⠀⣼⣿⣿⣻⣭⣿⡟⣿⣿⠿⣡⣙⣿⣏
⠀⠀⠀⠀⠀⠀⢈⣵⣟⡼⣿⣿⢻⣿⣻⣿⣿⢺⣿⠏⠃⢠⣿⣾⠀⠘⠻⢿⠷⣿⢿⣿⣻⡟⢿⣧⢧⣻⣮⡅
⠀⠀⠀⠀⠀⠀⢸⢟⡿⣼⣿⣽⢿⣧⣿⣟⣾⡟⠿⡆⠀⠈⠁⠏⠀⠀⢠⢿⢳⣿⣿⣿⣸⡿⣿⣿⣧⢻⡻⡆
⠀⠀⠀⠀⠀⠀⢀⣼⢻⡿⢻⢿⣿⠻⣿⣿⣿⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⢋⣿⣿⣿⡟⣿⡼⣟⢿⡏⣷⡀
⠀⠀⠀⠀⠀⠀⠋⣧⣿⢳⣿⣾⡞⣷⣟⡏⢺⣟⠹⡆⠀⠀⡞⠉⠀⠀⢠⡟⢻⡗⢺⣿⣶⢧⣿⣿⡞⣿⣘⠙
⠀⠀⠀⠀⠀⠀⠀⠘⠏⣾⠻⢿⢷⠜⣿⢿⡶⣝⠦⠘⠀⠸⣇⡾⠀⠀⠋⡰⢋⢴⣿⣿⠏⡞⣿⠟⣷⠸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡇⣿⣸⣼⡽⡦⣿⣌⡂⠀⠀⠀⠈⠀⠀⠀⠀⠐⣫⣾⢵⣏⣦⡇⢿⣸⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⣿⣿⣷⣿⣜⡏⠉⠀⠀⠀⡤⠤⠀⠀⠀⠊⢹⣧⣾⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢸⠏⣿⣿⢿⢛⣻⣥⠀⠀⠀⢰⡗⠂⠀⠀⠀⠀⢬⡿⡛⣽⣻⣿⠃⡇⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣟⢿⣬⢿⣳⡝⢦⠀⠀⠘⠶⠚⠁⠀⠀⡠⢟⣞⡽⣧⡿⢻⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡏⣷⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣼⢿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢝⢷⣝⢧⣙⠂⠀⣼⠀⠀⠐⢋⡸⢟⣾⣿⢸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢳⡝⢷⣌⠓⠀⡏⣀⡀⠐⣋⣴⢟⡵⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⢷⣜⠋⠁⢠⡾⠋⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠿⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⢀⣤⠖⠁⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢶⣄⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠹⣧
⠀⠀⠀⠀⣠⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣷⡀
⠀⠀⠀⣰⡟⠀⠀⠀⣾⣧⠀⡼⠁⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠹⣄⢠⣿⣆⠀⠀⠈⢷⡀
⠀⠀⢰⡟⠀⠀⢠⣼⣳⣿⣿⠁⣠⠄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢠⡀⢹⡿⣷⣻⣦⠀⠀⠘⣷
⠀⢀⡿⠁⠀⢠⣸⠃⠻⡽⣿⢠⡏⢀⡄⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⣄⠈⣧⢸⡻⣽⠃⢻⣤⠀⠀⠸⣧
⠀⣾⠃⠀⢀⢸⡏⠀⠘⡵⢻⣿⠁⡾⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠹⡆⢹⣿⡹⡜⠀⠈⣿⢀⠀⠀⢻⡆
⢰⡏⠀⠀⢸⣿⠁⠀⣸⠃⣏⡿⣿⣧⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⡿⣏⡇⢹⡄⠀⢸⣿⠀⠀⠈⣷
⣾⠇⠀⠀⢸⡏⠀⢰⡏⠀⢠⠀⠱⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⠁⢠⡀⠈⣷⠀⠀⣿⠀⠀⠀⢿
⣿⠀⠀⠀⣿⣧⣠⣾⡇⢀⡿⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠸⣇⠀⣿⣧⣠⠿⡇⠀⠀⢸
⣿⠀⠀⢠⡇⠈⠏⣿⣇⣸⡇⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⣠⣿⡏⠇⠀⣷⠀⠀⢸
⣿⠀⠀⢸⣷⣿⢸⡇⣾⣿⡷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⣿⣿⡇⣿⠸⢷⣿⠀⠀⢸
⣿⠀⠀⣾⠏⠀⣾⠸⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡿⢸⡆⠈⢻⡇⠀⢸
⣿⡆⠀⣿⠀⠀⡿⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠘⡇⠀⢸⡇⠀⣿
⠸⣧⠀⢻⠀⠀⡇⢀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⡀⣇⠀⢸⠃⢠⡿
⠀⣿⡄⢸⢠⣾⣇⣩⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣁⣿⣶⢸⠀⣼⡇
⠀⠸⣇⢸⣾⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⢀⡿
⠀⠀⢿⡸⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡿⣸⠃
⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏

⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠀⠀⠀⠀⠰⣦⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠋
⠀⠀⠀⢀⡔⠉⠀⠀⣀⡤⠊⠀⠀⠀⠀⢀⡾⣟⣛⣿⡭⠉⠀⠀⠀⠀⠀⠀⣿⣿⣷⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣽⠇
⠀⠀⠀⢸⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⢀⢞⣚⣻⠏⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃
⠀⠀⠀⠸⠤⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⢣⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⡱⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⣀⠤⠔⠒⢉⡼
⠀⠀⠀⠀⠀⣠⢿⣷⢿⡀⠀⠀⠀⠀⡰⠁⠀⠰⠶⢾⠁⠀⠀⠀⠀⢻⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⢿⠆
⠀⠀⠀⢴⣿⣿⣯⣷⣿⡅⠀⠀⠀⠀⡇⠀⠴⣦⠔⠃⠀⠀⠀⠀⠀⢸⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢎⡀⠀⠐⣾⠍
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠤⠒⠉⡹⠀⠀⠀⠀⢀⣴⣶⡶⠶⠶⠶⠖⠀⠀⠀⠀⣀⡤⠖⣚⡭⠄⠀⠀⠀⠀⠀⣀⡤⠶⠚⣻⠟
⠀⠀⠀⡰⠊⠀⠔⢊⠝⠀⠀⠀⠀⢠⣿⣿⣟⣛⣛⡛⠉⠀⠀⠀⠀⠈⢷⢐⡫⠥⠶⠀⠀⠀⠀⣠⠎⠁⠀⢀⣬⠇
⠀⠀⢸⢠⣤⠀⠩⠃⠀⠀⠀⠀⠀⢸⣿⣿⣭⠏⠉⠀⠀⠀⠀⠀⠀⢀⡞⣨⠶⠒⠀⠀⠀⠀⠀⠛⠀⢀⡴⠏
⠀⠀⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⣟⣿⣿⣿⣿⠉⠁⠀⠀⢀⡴⣖⣛⣛⣛⣛⡉⠀⠀⠀⢀⠴⠚⢉⣀⡠⢤⠞⠁⠀⠀⠀⠀⣠⣴⣶⣿⠛⠁
⠀⠀⠀⣼⢡⣿⡿⠉⠀⠀⠀⠀⠀⡞⠈⣵⢬⠿⠶⠆⠀⠀⠀⠀⠉⢢⠀⠤⠄⡶⠉⠀⠀⠀⠀⢠⣾⣿⡿⠋⠁
⠀⠀⠀⠳⠖⠃⠀⠀⠀⠀⠀⠀⠀⠘⠦⠭⠜⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠨⠋⠀⠀⠀⠀⠀⠠⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠖⠒⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⠏⠀⠀⢀⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠙⠃⠀⠀⢹⡄⠀⢀⡤⡀⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢠⡏⠀⠀⠘⠋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠳⠦⠀⠀⠀⠈⣧⠀⢸⡇⠃⡇⣸⠀⣄⢰⡆⡴⢳⡄⣴⠂⠀⣿⠀⠀⠀⣾⠁⠀⠀⠀⠴⠞⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⠀⠹⡄⠈⢧⣸⠁⠸⡆⡇⣼⡌⠳⢺⡇⠻⠄⠀⠿⠄⠀⢰⠇⠀⠀⠀⡀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠐⢸⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠓⠲⠤⠤⠤⠤⠞⠃⠀⣸⢻⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠄⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡴⠀⣠⠀⡀⠀⠀⠙⠂⠀⠀⠀⠀⡆⢸⡇⣄⡠⡄⢠⠤⡄⢠⠴⠄⢸⡏⠀⠀⠐⠋⠀⠀⢀⠀⣄⠀⢦⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠼⠁⣰⠏⠀⢧⠸⠢⠖⠀⢀⠀⠀⣸⠉⢹⡇⢿⠀⡇⢾⣰⡇⣾⠊⠀⢸⡇⠀⠀⠀⠲⠔⠃⡼⠀⠸⣄⠈⢧⡀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠔⠋⣀⡴⠁⣀⡜⠀⠋⠀⠀⠀⠘⠦⠶⠃⠀⠈⠇⠘⠀⠃⠈⠁⡇⠈⠋⠀⠀⠉⠀⠀⠀⠀⠀⠑⠀⢣⣀⠈⢦⣀⠙⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠁⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⢤⣤⠤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠈⠉⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣀⣀⣀⣈⣉⠰⠀⠀⠀⠀⣠⡴⠒⠉⠁⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⡏⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠓⠚⠋⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠀⠀⠘⡄⠀⠀⠀⠀⠈⠙⠃⠚⠫
⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⢤⠤⠖⠚⢀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣴⣡⢃⣀⣤⢀⠤⡄⣠⠤⠀⢰⠟⠁⠀⠀⢀⡇⠀⠀⠀⡀⠓⠲⠤⡤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠞⠋⠀⡀⠀⠀⠉⢀⠀⠀⡼⠁⡟⢸⢁⡇⣮⣸⡇⡗⠀⠀⡿⠀⠀⠀⡀⠉⠀⠀⢀⡀⠙⠳⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠫⠥⠤⠒⠉⠡⠤⠚⠁⠀⠃⠀⠘⠀⠀⢸⡇⠉⠁⠀⠳⠔⠁⠀⠈⠉⠒⠤⠤⠝⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡼⠁

⠀⢀⣠⡴⠖⠒⠒⠒⠒⠒⠶⠤⢤⣀⣀
⠀⣾⣿⠅⢠⠀⢶⣦⣤⣆⡀⠠⢤⣀⡈⣉⠓⠢⠄⣀
⠸⣿⣿⡅⠀⠐⠇⠀⢒⣨⣉⣁⣀⣀⢭⣽⣶⡷⢂⠀⠉⢓⠲⠦⠤⣄⣀⡀
⠀⣿⣿⣯⠀⢀⡠⠃⢹⡆⠀⠤⠘⠥⠤⣤⣀⣀⣀⢈⣀⣩⣛⡠⠲⠶⠄⣨⣍⣓⠲⠤⢤⣀⣀
⠀⢸⣿⣿⡀⢀⠀⢡⠈⢻⡟⠛⠶⢶⣖⣒⣚⡃⠈⠉⠘⠚⠒⠿⠧⢭⣍⣉⠒⠚⠉⠍⠐⡒⠬⠭⣽⣒⡶⠤⣀⡀
⠀⠀⢻⣿⡄⠁⠔⠀⢰⠞⠁⠘⠃⣖⣂⠈⢙⣿⡿⠿⣿⣗⡶⠤⠴⣦⣛⣙⣓⡛⠳⢶⡖⢦⣬⣥⣔⣛⣻⣷⡶⠬⣵⣦⣄
⠀⠀⠀⠻⣿⣦⡂⠐⠈⠀⠀⢩⡭⣝⣯⣉⣙⣓⣶⡶⠤⢤⣌⣽⣛⣿⣓⡒⠻⠿⠯⠽⠿⠿⠿⠛⠛⠶⠍⠉⠛⠳⠆⠀⠈
⠀⠀⠀⠀⠘⣿⣷⡓⠀⢀⣈⡙⢧⢀⠉⣻⣟⣏⡙⠛⠃⠀⠀⠀⠈⠉⠉⠉
⠀⠀⣀⣀⣤⣿⡟⣧⠀⢢⣌⠙⣿⠦⢤⣭⡳⣌⠁
⣰⣿⣿⡟⠁⢠⠺⠫⣀⡄⠈⣻⠡⡉⠛⢖⠹⣿⡷⣄
⠈⠻⣿⣀⣰⠤⠂⠑⠄⡈⠰⣯⣝⡢⠀⢠⡑⣄⠑
⠀⠀⠈⢿⠻⣆⢢⢄⣲⣬⡶⠸⠂⠈⠂⢢⣆⠈⢢
⠀⠀⠀⠘⡆⠈⡟⢷⢤⣱⡀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠘⡆⣹⣌⡇⠈
⠀⠀⠀⠀⠀⠘⠟

⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿
⠛⠛⠻⢂⣤⣤⡞⠻⠛⢧⣤⣤⣜⠻⠛⠛⣠⣤⣤⡿⠿⠿⢧⣤⣤⡼⠿⠻⢿⣤⣤⣴⠟⠛⠻⣤⣤⣤⡸⠛⠛⢓⣤⣤⣤⠿⠛
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯⠀⠀⠀⣿⣿⣿⡁⠀⠀⢺⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷
⣶⣶⣾⠏⠉⠉⣹⣶⣶⡎⠉⠉⠁⣶⣶⣶⠈⠉⠉⣷⣾⣶⡏⠉⠉⢹⣾⣶⣾⠉⠉⠉⣾⣾⣶⠏⠉⠉⢹⣶⣶⡏⠛⠉⠙⣶⣶
⠿⠿⠿⣆⣀⣀⡼⠿⠿⢇⣀⣀⣸⠿⠿⠿⣄⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⣰⠿⠿⠿⣃⣀⣀⡸⠿⠿⢧⣀⣀⣐⡿⠿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⣿⣿⡇⠀⠀⢨⣿⣿⣿⠀⠀⠀⣽⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡙⠋⠛⢳⣤⣶⡜⠋⠛⢻⣶⣶⡶⠟⠛⠛⠦⣤⠤⣜⠛⠛⢡⣦⣶⣼⢛⠙⠛⣶⣶⣶⠟⠛⠛⢳⣦⣴⡎⠛⠛⢻⣶⣶
⣿⣿⣿⠄⠀⣀⢸⣿⣿⡇⠀⠀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⡏⠉⠀⠈⠈⠁⠉⠉⠻⠥⠄⡀⢸⣿⣿⡇⠀⠀⠘⣿⣿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠄⠀⢰⣿⣿⣯⠁
⣤⣤⣤⠿⠟⠟⢧⣤⢄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⣼⠛⠛⠷⣤⣤
⣿⣿⣿⠆⠀⠀⠨⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢀⣿⣿
⠉⠉⠉⣿⣶⣾⡉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢵⣲⣾⡯⢀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣶⣷⣾⠈⠉
⣀⣀⣀⡿⠿⠿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⣈⣁⣼⠿⡿⢧⣀⣀⣘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣄⣀
⣿⣿⣿⡂⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢘⣿⣿
⠛⠛⠛⣷⣤⣦⡾⣻⠟⣽⣯⣿⣿⠁⡛⠓⣴⣤⣤⡟⠛⠛⢷⣦⣤⡞⠛⠛⢻⣦⣦⣦⠐⠐⠀⣀⠀⡀⠀⠀⠈⠢⣵⣤⣴⠛⠛
⠀⠀⠀⢿⣿⣿⡚⠫⠀⣹⣿⣿⣧⠀⠀⢀⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⡀⢀⣿⣷⣷⡄⠠⠀⢄⣹⢿⣿⠂
⣿⣿⣿⡆⠁⠀⣼⣿⣿⡇⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⠀⠀⠨⣿⣿⣿⡅⠀⠈⢸⣷⣷⡇⠀⠀⢘⣿⣿
⠿⠿⠟⣣⣄⣠⡞⠻⠿⢣⣄⣤⣸⠿⠿⠿⣆⣀⣠⠻⠟⠻⢃⣄⣀⡼⠿⠻⠿⣤⣠⣴⠿⠟⠻⣤⣤⣤⡼⠿⠿⢳⣀⣄⣌⠻⠿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡍⠉⠉⢱⣶⣶⡎⠉⠉⠙⣶⣶⣶⠉⠉⠉⣷⣶⣶⡏⠉⠉⢱⣶⣶⣾⠉⠉⠉⣶⣶⣶⡉⠉⠉⢱⣶⣶⡎⠉⠉⠩⣶⣶
⠿⠿⠿⢅⣀⡀⠼⠿⠿⣇⣀⣀⡰⠿⠿⠿⢀⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⡀⠿⠿⢿⣀⣀⣀⡸⠿⠿⢧⣀⣀⣈⡿⠿
⠀⠀⠀⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⡿⣿⡏⠀⠀⢸⣿⣿⣿⠂⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯
⣶⣶⣦⠟⠙⠛⢳⣤⣴⡾⠛⠛⢫⣤⣴⣤⠟⠛⠛⣷⣤⣴⣫⣛⣛⣱⣦⣶⣤⠛⠛⠛⣶⣴⣦⡙⠛⠛⢣⣴⣦⡾⠋⠛⢱⣦⣤
⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠉⠉⢹⣿⣿⣿⠀⠈⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⢐⠩⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠠⠠⠀⠀⠀⠁⠀⠀⡴⠀⠀⠀⠀⡔⠀⠀⠀⠀⠄⠤⠀⠀⠀⢨⠁⠀⠀⡀⠀⠀⡈⠀⠀⠈⢀⠀⢀⠂⠀⠀⠍
⠀⠀⠀⠀⠠⠕⢀⠀⠀⢀⠞⠲⠠⣤⠆⠰⠁⠀⠀⢀⠠⠅⠀⠀⠀⠀⠀⠠⠀⠀⢰⠀⡀⡧⠠⣤⡄⡜⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠈⠢⠄⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⡀⠀⠆⠀⠀⠴⡫⠀⠀⠀⠀⠀⠈⠆⠀⠀⢰⠀⠀⠀⠐⠀⡜⠀⢀⠃⠀⠀⡀
⠀⠀⠀⠀⠢⠥⠀⠀⠅⠀⡄⡇⣀⡀⣀⢸⠀⠀⠇⠀⠠⡄⠂⠀⠀⠀⡰⠠⠠⠀⠀⠀⠤⢠⠠⢰⣰⠀⡇⠀⠁⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⠉⠀⠨⠏⠘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠈⠇⠀⠀⠀⠃⠀⠀⠀⠠⠃⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣴⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀
⢠⡤⣄⣀⣀⣀⡀⠀⣤⡤⠤⠤⠬⢿⣭⠤⠤⠀⠀⠉⠻⢿⣿⣧⠀⠀⠀⠀⢰⣿⣿⠿⠉⠁⠀⠤⠤⣼⡿⠥⠤⠤⣶⣶⠠⠤⠤⠤⠖⢚⡽
⠀⠉⢲⣤⣀⣉⡉⠉⠙⠻⣶⣶⠆⠀⠉⠛⢷⣒⣋⣀⡀⠀⢙⡟⠀⠀⠀⠀⢻⡟⠁⣀⡀⠒⣒⣶⠟⠉⠀⢒⣲⡿⠏⠁⠀⠠⠤⠶⡾⠇
⠀⠀⠀⠉⠢⣭⣅⣀⣀⡀⠀⠉⠻⢿⣯⣁⣀⡀⠉⠛⢒⣻⠏⠀⠀⠀⠀⠀⠀⠳⣶⠶⠟⠋⢉⣀⣈⣩⠿⠏⠁⠀⠠⠤⠤⢶⡶⠏
⠀⠀⠀⠀⠀⠈⠑⠲⣦⡤⠤⠤⠤⠀⠈⠙⠛⣒⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣖⠛⠛⠁⠀⠀⠀⠔⣲⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣤⣶⡶⠂⠀⣠⣾⣿⠟⠀⢀⣴⣾⠏⠀⠀⢠⣶⡿⠁⠀⣴⡿⠟⠃⠀⠀⣶⡿⠃⠀⢀⣴⣿⡿⠋⢠⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⣴⡾⠁⠀⣤⣶⠞⠋⠀⣀⣴⡶⠖⠀⢀⣠⣶⡶⠋⠀⣠⣶⡶⠂⠀⡴⣶⡶⠖⠀⢀⣴⣿⡿⠁⢀⣴⣶⠖⠁
⠀⠀⠈⠉⠁⠀⠀⠛⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠁
⠀⠀⣴⣶⣶⠖⠀⢀⣠⣶⠏⠀⢠⣶⣶⠖⠀⠀⣀⣠⣴⠂⠀⢠⣶⡶⠂⠀⠀⣠⣾⠀⠀⣠⣶⣶⠖⠀⠀⣰⣶⡿⠁
⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⠀⠁⠉⠁⠀⠀⠀⠛⠉
⠀⠀⠀⣤⣶⠇⠀⢀⣀⣤⡖⠀⠀⣼⣿⡿⠁⠀⣶⣶⡞⠀⠀⠀⣠⣴⡞⠀⣴⣶⡶⠖⠀⢀⣤⣶⡶⠂⠀⣰⣶⠖
⠀⠀⠚⠋⠁⠀⠀⠀⠉⠋⠀⠀⠈⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠒⠛⠋⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠁
⠀⠀⢀⣠⣤⠆⠀⢀⣴⡶⠚⠀⠀⢀⣴⡿⠀⢀⣤⣴⠖⠁⠀⣠⣤⡤⠄⠀⣠⣶⣶⠖⠀⠀⣰⣶⡶⠀⢠⣶⣶⡤⠄
⠀⠀⠉⠛⠁⠀⠀⠙⠋⠀⠀⠀⠀⠚⠛⠁⠀⠈⠛⠁⠀⠀⠀⠙⠉⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⡄
⠀⠀⢀⣾⣿⡇⠀⠀⠀⣼⣿⡄⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⣰⣿⡟⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⣀⣶⣀⠎
⠀⢀⣾⣿⣿⠃⠀⠀⣠⣿⣿⠁⠀⠀⣠⣿⣿⡿⠃⠀⢠⣾⣿⣿⠇⠀⠀⣰⣿⣿⠏⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⠃
⠀⠀⠛⠛⠋⠀⠀⠀⠻⠛⠁⠀⠀⠀⠁⠛⠛⠁⠀⠀⠘⠛⠋⠁⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁
⠀⠀⠀⣤⣄⠀⠀⠀⠀⣤⣦⡀⠀⠀⣴⣶⣦⡀⠀⠀⣰⣷⣆⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠀⢰⣤⣤⣴⣶⣶⣤⣀
⠀⢀⣶⣿⣿⠀⠀⠀⢠⣿⣿⣿⡄⠀⢿⣿⣿⡧⠀⠀⠙⢿⣿⣧⡀⠀⠘⣿⣿⢿⣿⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⣿⡏⠀⠀⢼⣿⣿⠟⢿⣧⠀⠘⢿⠉⠋⠀⠀⠀⠀⠙⠻⠷⠀⠀⠉⠁⠀⠈⠉⠓⠂⠀⠈⠙⠋⠁⠀⠈⠉⠉
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⡇⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠰⣦⣤⣀
⠀⠀⠀⣴⣾⣿⡇⠀⠀⠀⣰⣿⠀⠀⠀⣰⣿⡇⠀⠀⠀⣰⣿⣿⡇⠀⠀⢀⣤⣼⣿⣿⡇⠀⣀⣠⣿⣿⢿⣷⣤⡀
⠀⠀⣰⣿⣿⣿⠀⠀⠀⣰⣿⡟⠀⠀⢠⣼⣿⡇⠀⠀⠀⣿⣿⠏⠀⠀⠻⣿⣿⣿⣿⡟⠁⠀⠻⠿⡿⠋
⠀⠀⠿⣿⣿⠃⢀⠀⢾⣿⠟⠁⣴⠀⠺⠟⠋⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠘⠛⠛⠁
⠀⠀⠀⠀⠀⣠⡌⠀⠀⠀⠀⢰⣿⠀⠀⣤⣀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤
⠀⠀⢀⣠⣾⡿⠀⠀⠀⢀⣴⡿⠁⢤⣴⣿⣿⣷⠀⠀⠀⢼⣿⣿⡏⠀⢠⣶⣿⣿⡟⠁⠀⠀⣤⣀⣼⣿⣿⣿⠟⠋
⠀⠀⣸⣿⡿⠁⠀⠀⣀⣾⡿⠁⠀⠀⢿⣿⣿⣿⡇⠀⣠⣾⣿⡿⠁⠀⠈⣿⣿⠋⠀⠀⠀⠀⠹⣿⣿⣿⠍
⠀⠺⠟⠋⠀⠀⠀⠐⠟⠋⠀⠀⠀⠀⠈⠛⠛⠻⠇⠀⠿⠟⠋⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⣾⣿⡆⢠⣿⣿⡄⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⣴⠃⠐⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⣿⣿⣆
⠰⣿⣿⣷⠈⢻⣿⣧⠀⠹⣿⣧⠀⠀⠀⢀⣤⣴⣾⡿⠀⣴⣾⣿⠏⠀⠀⣸⣿⣿⠛⠛⠛⠛⠃⣀⣴⣿⣿⣿⡄
⠀⠹⣿⡟⠀⠀⠹⣿⣄⠀⠙⢿⡄⢠⣤⣼⣿⡿⠏⠀⣴⣿⠟⠃⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠿⠿⠿⠋⠘⠻⢷
⠀⠀⠸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠙⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⣨⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠈⠀⠀⠈⠃⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⡆⠀⠀⢀⡀⠀⠿⠆⠀⠀⣰⣿⣇⠀⠀⢠⣿⠀⠀⠀⠀⢀⣠⣴⠃⠀⠀⣠⠀⠀⠀⢀⣴⡃⠀⠀⢰⡇
⠀⠐⣿⡇⠀⣸⣿⡇⠀⠺⢶⡆⠀⠙⡏⢿⡇⠀⢻⣃⠀⠀⠀⢠⣿⣿⡟⠀⢀⣼⣻⣎⠀⠀⠻⣿⠀⠀⢀⣠⣿
⠀⣶⡿⠀⠀⢹⡏⠀⢰⣇⡤⠀⠀⠀⠀⠉⠂⠀⠈⠻⣦⠀⠀⠠⡟⠿⠁⠀⣠⣾⠟⠋⠀⠀⢰⣿⠀⣠⣾⠟⠛
⠀⠙⠀⠀⠀⠞⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠉⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠀⠀⢀⠀⢀⣀⣤⡤⠀⠀⠀⢀⣀⣤⠄⠀⠀⣀⣀⣴⡾⠁⠘⢿⣿⣶⣄⡀
⠀⠀⠀⠀⣠⣿⣿⣿⡿⠃⠀⣰⣾⣿⣿⡿⠛⠀⢴⣿⣿⣿⠿⠏⠀⠺⣼⣟⣭⠟⠁⠀⣠⣿⠿⣿⣿⣿⣦⣄
⠀⠶⣶⣾⣿⣿⠿⠏⠁⢠⣌⣿⢿⡿⠛⠁⠀⠀⢸⣿⣏⠀⠀⠀⠠⢬⠿⠋⠁⠀⠀⠀⣿⠿⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣄⣀
⠀⢀⢀⣀⠔⠓⠈⠀⠀⠀⠀⠀⠱⠀⢰⣶⡆⠀⠀⡴⠟⠿⣷⡆⢀⣽⣿⣆⠀⠀⢀⣴⡇⢀⡤⣿⡿⢿⣷⠖
⠰⣿⡿⠉⠚⠁⢠⡀⠀⢰⡦⣄⡀⠀⠾⠛⠀⠀⠀⡡⢤⣴⠏⠀⠘⢻⠛⣃⠀⢰⣿⣿⠁⠘⠀⠀⢠⣤⣤⣤⣔⡦
⠀⠈⣵⠀⠀⠀⠀⢛⣻⣿⡵⠿⠛⢠⣀⣐⣀⣀⠀⢠⠌⠁⠀⠀⠀⠛⠾⣿⠀⢘⠛⠁⠀⠀⠀⠀⣨⡿⢃⣿⣭⠁
⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠐⠻⠟⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠀⠈⠀⠀⠀⠀⠀⠀⠱⠗⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⣾⠀⠀⣀⡀⠀⠀⠀⠐⣤⣤⣾⡆⠀⠀⢀⡠⠄
⢠⣶⣾⣧⡀⡆⣠⣿⣿⣿⣿⠋⠀⢀⣴⣿⣿⠟⣠⣾⣿⣧⣾⡀⠀⠀⢀⣼⡿⠀⠀⠀⣼⣷⡚
⠀⢹⣿⣟⡽⠀⣿⣏⣿⣿⠟⠁⠀⠻⣿⠟⠀⠀⣿⣿⣿⣿⠟⠀⠀⢠⠞⠋⠀⠀⣾⣿⣿⣿⠃
⠀⠾⠟⠋⠀⠀⠻⣿⠛⠁⠀⠀⠀⠘⠋⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢋⣉⠉⠁⣒⡄⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀⡐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣰⠋⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠳⠄⠀⠘⣆⠀⠀⣀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⠃⠀⠠⠞⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠳⣤⠀⠀⠠⢻⡀⢸⡇⢇⡀⡏⣠⡠⡆⡴⢦⢀⡔⠀⣼⠀⠀⢀⡟⠄⠀⠀⣤⠖⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠈⣇⠀⢧⡼⠁⢷⠸⢸⡗⠳⣻⠚⠧⠀⠻⠜⠀⣼⠁⠀⠀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⡀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⣈⣼⠀⠀⠀⠀⠠⠞⠁⠀⢀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠰⡄⠀⠺⠬⢭⣍⣡⡼⠶⠀⣰⢳⠀⠀⠀⣰⠃⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠄⠀⠀⣠⠏⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠃⣠⠀⡄⠀⠈⠓⠀⠀⠀⢰⡀⣿⢠⡠⣦⢠⢦⡀⡴⡆⢠⡏⠀⠀⠚⠁⠀⢠⠀⡄⠘⡄⠘⡆
⠀⠀⠀⠀⠀⠀⢠⢃⡴⠋⣠⠻⢀⠇⡘⠘⠁⢠⡄⢀⡽⠉⢿⢸⡇⡏⢻⢼⠰⣏⡀⠸⣇⠀⠀⠈⠃⢃⡸⡀⠟⣄⠙⢦⡘⡄
⠀⠀⠀⠀⠀⠀⠘⠋⠰⠔⠁⠠⠊⠀⠁⠀⠀⠀⠙⠋⠀⣀⠬⠤⠤⠁⣀⢸⡧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠔⠈⠢⠆⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⣉⡉⠉⠉⠓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠰⢥⣍⣉⣁⣉⠰⠀⠀⠀⠀⡤⠖⠚⠉⠉⢉⣉⣡⠜⠁
⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⣈⣉⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡞⠂⠸⡁⠀⠀⠀⠉⣉⣁⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⣔⠒⠉⠉⢉⣀⡀⠀⠀⠀⡎⠀⠀⠀⠀⢠⢯⠏⠀⠀⠀⠀⠀⠀⠀⣼⡘⠀⠀⢱⠀⠀⠀⢀⣀⡉⠉⠉⠒⣢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⣁⡴⠀⠀⠀⠳⠄⠀⠀⢲⠧⡏⡶⡺⣰⢺⢠⣞⠇⣴⠋⠀⠀⠠⠞⠀⠀⠀⢦⣈⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠉⠥⠤⠔⢃⣀⠤⠔⣂⡴⠃⠸⠀⠣⠇⠙⣻⠞⠧⠀⢺⣀⠄⠐⠢⠤⣀⡘⠢⠤⠬⠉⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡂⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣒⣪⣽⣿⡯⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⣾⣿⡿⠽⣋⣩⣬⣿⣭⣴⢾⠝⣃⠈⢧⡀⠀⠀⠀⠀⠀⠀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⢋⣡⣾⣿⠋⢽⣿⣿⣿⣿⣽⡶⠋⣽⡿⢋⣴⡶⠀⠉⠛⠒⠒⠚⠋⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢋⣣⣶⠿⢯⣥⣴⣶⣛⣿⣛⣽⢿⡯⢝⣽⣟⢷⣿⡿⣡⣾⣿⢦⣴⠤⠀⣴⡆⠀⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣥⣾⠟⠋⣁⣤⢿⣿⣿⡿⢛⣽⣿⢍⣤⣶⡛⣂⣴⡿⣫⣾⣏⣿⠁⣼⣇⢠⣴⡗⣶⣾⢃⣴⣰⣾⡏⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⢁⣵⠾⣫⣁⣿⠟⣩⣾⡿⠛⢁⣼⠟⠉⣹⣟⣻⣶⣿⣬⣿⠗⢔⣿⠏⢠⡟⠀⣿⡇⣸⡇⣿⢇⡇⡟
⠀⠀⠀⠀⠀⣠⣴⠟⠋⣨⣴⠾⡟⢕⣥⡾⢋⣤⣾⢿⠛⢁⣴⠿⢛⣴⡾⣫⣾⣿⡟⣩⡾⠃⠀⣼⠋⢠⡿⡀⣸⡿⢰⡟⢰⠏⢸⡇⡇
⠀⠀⠀⠴⠚⠭⠔⣢⣿⡿⢿⣻⣶⡿⠋⡰⠛⡹⢟⡠⠂⠁⠈⠉⠙⠿⠕⢻⠁⠋⣠⣿⠁⣠⢾⠏⢠⡿⠁⣠⡟⢡⠟⠁⠈⠀⡿⠀⠁
⠀⠀⠀⠀⠀⢀⡞⣋⠵⠚⢁⣞⠫⠔⠉⠀⠆⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠈⠁⠀⠐⣿⡃⢴⠟⡔⢣⢁⠈⠀⡠⠁
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⣶⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡿⠉⡠⠚⠿⢫⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡷⠋⡰⠂⡴⢃⣾⣿⢿⡛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⣻⠧⢾⠡⠞⣡⣾⡿⠯⠅⠦⢺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡰⠁⠀⠁⠀⣰⣿⡟⠿⠁⠀⢀⡈⢿⣿⣦⣀⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⢠⣿⡆⢧⡀⢉⠛⠛⠛⠉⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣭⣇⣒⠲⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⢀⣠⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣽⣿⣮⣿⣯⣿⣿⣿⣿⢿⣿⣿⡛⠷⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣏⢻⣿⡙⢻⣿⡟⣹⡏⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⡿⠛⢻⣶⡟⠛⣷⣾⣏⢻⣷⠟⢛⣛⣛⢿⡟⠋⣛⣛⡟⠛⣿⣾⡿⣿⣻⣿⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣻⣿⡟⣴⠂⣸⣿⠁⡀⠸⣿⢧⣿⠁⢰⣇⣙⢛⣼⠀⢰⣿⣻⡇⠀⣿⣿⣷⣹⡷⣿⣿⣿⣿⣹⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⠉⣛⣡⣍⠀⠿⣿⠀⣧⠀⠉⣼⣿⠀⢻⣿⠍⢹⣿⠀⢘⣽⣿⠗⠀⣿⣿⡿⣿⣷⡿⣿⣿⣿⠇⠻⣧⡀
⠀⠀⠀⠀⠀⣀⠴⠋⢹⣿⣿⡜⣯⣹⣿⣥⣿⣿⣦⣤⣯⣼⣿⣧⣼⣿⡝⢷⣦⣤⣤⡿⣿⣤⣬⣯⣽⣴⣶⣤⣌⣧⣿⡿⣰⣿⣏⣿⡀⠀⠈⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣻⣯⣿⣿⢻⣿⢯⣿⣹⣜⣹⢿⢿⡇⠀⣾⣿⣿⣷⣿⣸⣿⣙⣿⣿⠿⣫⣿⣿⢟⣼⡿⣹⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣻⣿⣿⣯⣿⣿⣿⣾⣗⣜⣳⣟⣿⠓⣬⣾⣿⣷⠈⠉⢡⣿⢻⣿⣬⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢻⡿⢿⣯⡻⣿⣿⣿⡿⢿⣿⣯⡿⢳⣿⣿⡌⠀⠀⢀⡾⠃⣼⣿⢛⣽⢿⣿⣵⢿⣯⣷⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣿⣾⣿⣻⣮⣿⣿⣿⣷⣿⣿⡿⠿⣿⣎⠙⢦⡀⠼⠁⣰⠟⣿⣿⢟⣿⣿⣴⣿⡟⣼⣿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣮⣽⣿⣿⡺⢿⣿⠿⣿⣏⠳⠀⠁⠀⠀⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⢷⡄⠀⠀⠀⢸⠏⣴⣿⣿⣿⣾⣿⣟⣿⣿⣿⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣿⣿⣿⣷⣿⣿⣿⡳⣌⠀⠀⠀⠃⡼⢫⣿⣿⣿⣿⣣⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣷⣽⣿⣿⣿⣿⣦⠀⠀⠀⠀⢡⣿⣿⣿⣹⣿⣏⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⡁⠀⠀⠀⠞⣿⣿⣯⣿⡿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠳⣿⣿⣷⣦⡀⠀⢸⣿⣿⣯⡞⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢫⣿⣎⠻⣶⣿⣩⣿⡟⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⠻⣷⠟⢸⣿⣼⠁⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢿⠀⣾⠻⣿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⣿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺
⠀⠀⠀⠀⠀⠀⠀⣸⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡼
⠀⠀⠀⠀⠀⠀⠀⢣⠙⢄⡀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⣠⠞⣰
⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠉⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⠉⣀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⡙⠒⠂⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠒⢋⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡒⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡻⠉⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠐⠙⣷⠀⠀⠀⠀⠉⠓⠲⠶⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠁⠄⠀⠀⠀⢐⠒⠒⠚⠉⠀⠀⠀⡀⠀⢠⡿⠁
⠀⠀⠀⢸⡄⠀⠀⢸⡇⠀⠀⢀⠀⠀⣠⠞⡁⠀⢰⠏⢀⠀⣄⠀⣷⠀⢰⠆⠀⣼⠀⣰⠂⢀⡾⠋⠀⢠⡖⠀⢀⠀⠀⣿⢀⡿⠁
⠀⠀⠀⠈⢷⠀⠀⠈⣧⠀⠀⢸⠇⠀⠏⢰⠇⠀⠸⠄⢸⡇⠛⠀⡇⠀⠸⣄⠀⢸⡀⠻⠀⢸⡇⠀⠀⢾⠁⠀⠙⠀⢰⠃⢸⠇
⠀⠀⠀⠀⠈⢳⡄⠀⠹⠂⠀⡿⠀⠀⠀⢸⡀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣽⣽⣭⣮⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣽⣽⣿⣯⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣦⠀⣼⡿⠉⢠⣛⡿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣋⣤⣾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠠⠄⠸⣯⣿⡁⢀⡿⡻⠀⢈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣾⡿⠿⣿⣿⣿⡆⣤⣴⣆⣴⣶⡴⠖⠂⠀⠀⠀⠀⢀⣠⣄⣤⡴⢖⠂⠀⢀⣀⣬⣤⡈⠁⡠⣀⠈⠉⢁⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣤⠶⠾⢿⣿⣿⣿⣟⣿⣊⣁⠀⠀⠀⠀⠀⢀⠴⠯⠟⠻⢋⡅⠀⠀⡲⢋⡟⠁⢘⣷⠘⠣⡈⠁⠈⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⣡⣰⡿⣿⣿⣿⣿⣿⡿⣷⣄⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⡀⠀⢰⠃⠀⢸⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣟⣴⠟⢹⣿⠛⡟⠛⣿⡆⠉⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⡀⠀⠺⠀⠘⡆⠀⠀⢀⡀⠀⠀⢼⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠁⠀⣸⣯⣸⠇⠀⠙⡥⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠺⡆⠀⠀⠁⢸⡃⠀⠀⠸⠄⠀⠈⠠⠂⠀⡿⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠿⠿⠃⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⣷⠀⠠⠁⡆⢸⠇⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢸⠄⠀⡞⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢀⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢸
⠀⠀⠀⠀⢧⢀⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣲⣄⠀⠀⢀⣹⣇⠀⣿⠀⠀⠈
⠀⠀⠀⣀⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⣎⡨⢡⣏⡜⢛⡩⠯⢳⣿⠀⣿
⠀⠠⢽⡿⣿⡟⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣬⢎⠥⡄⠤⢉⣵⠔⡫⠐⢖⣾⣿⣧⣿⣶
⠠⠤⢼⣿⣿⣿⣿⣶⣗⠢⣄⣂⣤⣦⣄⡀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠸⣉⣀⡬⠽⠥⠐⣈⣉⣴⣬⣱⣾⣽⣿⣿⣿⣿⣓⣞⡂
⠀⢰⣿⣿⣿⠿⠾⠿⣭⠭⢿⣿⣿⣿⣿⣿⡶⠂⢸⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣷⣾⣷⣶⣶⣶⣾⣿⣿⣿⡿⢿⣿⣿⠿⣟⠋⠉
⠀⠸⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⠟⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠿⢯⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣭⣿⣇⠙⠻
⠀⡤⢿⠋⠐⠞⠻⠿⣿⡿⢛⠆⠐⠛⠏⠀⢀⠀⠘⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠋⢤⣾⣿⡿⣿⠿⠻⠿⣏⣱⣿⠿⠟⠺⠛⠛⠛⠈⢻⣆⠀⠙
⣤⡼⠁⠀⠀⠀⠀⠉⠉⠀⠾⠅⢃⡀⠐⠇⠀⠀⢼⢸⡇⡗⠀⠀⣀⣀⣠⣤⠤⣤⣴⣲⠟⣉⣉⣭⣽⡛⣿⡿⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⠉⠒⠛⠒⠒⠀⢻⢻⠃⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠛⠛⠒⠋⠁⠊⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣏⣭⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡦⠌⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠨⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠉⢤⠀⠀⠀⠀⠀⠀⠈⠁⢠⠄⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠊
⠀⣄⢰⢾⣇⡄⣶⣰⣠⣦⡄⣴⣼⣆⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠐⠂⠀⠀⠀⠀⣀⠈⢻⣋⡀
⠘⠛⠛⠻⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣉⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠂⣠⡓⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠘⠒⣫⣽⣷⡬
⠀⢠⣷⣄⣤⣏⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢾⣃⡘⠻⣭⣹⣯⠖
⠈⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠐⢜⣻⡭⠄⠀⢤⣸⡧⠞
⠀⣿⣿⣿⣿⣿⡿⠿⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⣷⣁⠈⣒⣿⣯⣉⢀⣰⣿⣿⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠄⠀⠀⠀⠀⠀⠀⠀⢰⠓⣦⠀⣀⠀⠀⠀⠑⠚⠒⠒⠒⠓⢒⠒⠂⠀⢂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠴⠄⠀⠁⠀⠀⠀⠁⠀⣿⡄⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡷⠀⠠⣦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠚⢁⡿⠀⡰⠁⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠿⠢⠄⣀⠀⢀⠈⠀⠀⠀⠀⠀⠈⠀⣀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠁⠀⠀⠐⢧⠀⠄⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⡀⢈⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⢂⣀⠀⠐⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣷⠘⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⡀⠈⠀⠀⢠⠞⠚⠁⠉⠁⠀⠀⠀⠀⠈⠷⣶⡁⠀⠀⠀⠻⢷⠠⠴⠠⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⣤⣀⡰⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠹⢆⡀⠀⠀⠀⠀⠀⠀⠸⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠁⣀⣀⣀⠰⠋⠀⡀⠀⠀⠀⠀⠀⣼⠦⠀⠀⠀⠀⣀⣌⣯⠤⠤⠴⠿⣶⣷⡥⣀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡬⠥⠄⠒⣩⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡂⣡⣴⡖⠋⠉⠀⠀⠀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠉⠁⠀⠀⠤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢀⠀⠀⣀⣀⣀⣀⢀⣾⣿⣯⣴⣶⣾⣷⣶⣦⣤⣀⡀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⣿⠇⠈⠉⠉⠉⢉⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣯⡙⠳⢭⣗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠇⢰⡿⠀⢀⡀⢊⡴⠃⣀⠀⠀⡀⠀⠀⠁⠀⠈⠙⠻⢿⡻⣦⡍⠻⣷⣌⡓⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⢀⡜⣡⡴⠋⢠⠿⠁⠰⢿⡷⢠⠀⠁⠀⠀⠀⠈⠁⠀⠀⠙⠺⡟⢦⡄⠙⢷⣦⣄⠈⠉⠁⠻⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⡾⠔⣩⠤⢀⣵⠾⠚⢁⠔⡀⠁⠈⠳⡄⠀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠙⢧⣄⠀⠉⠛⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣬⣷⠊⡡⠺⢋⡔⣫⣦⣵⣊⣀⡠⠒⠀⣤⣴⣄⠀⠢⠈⠀⠀⠀⠀⠀⠰⡈⠙⢿⣦⡀⠀⠈⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⠙⠉⠀⠂⠂⠉⠙⠚⠉⠉⠀⠎⠐⠒⠒⠂⠀⠀⠀⠀⠘⠂⠀⠙⠛⢶⣤⣀

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀
⠀⠀⠀⠀⠀⢹⡄⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢠⡏
⠀⠀⠀⠀⠀⠈⣿⣌⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣡⡿⠁
⠀⠀⠀⠀⠀⢧⡘⢿⣮⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣵⡿⢃⡼
⠀⠀⠀⠀⠀⠘⢿⣌⢻⣷⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣾⡟⣡⡿⠃
⠀⠀⠀⠀⠰⣄⠈⢻⣷⣿⣿⣟⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣻⣿⣿⣾⡟⠁⣠⠆
⠀⠀⠀⠀⠀⠹⣷⣦⣙⢿⣿⣿⣷⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣋⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣿⣫⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠲⢦⣤⣬⣉⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣥⣤⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⡇⢸⣿⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠿⠟⠋⣹⣿⡿⠀⠀⢿⣿⣏⠙⠻⠿⠿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠛⠂

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⡤⣀⣴⡾⣃⠀⠀⠀⠀⠀⠀⠠⡆⠠⡆⠀⡴⠀⠀⠀⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠔⣴⣢⠭⢝⣛⣫⠵⠚⣋⠜⠃⠀⠀⢀⣄⣂⣥⣾⠤⣊⡥⠖⠉⣁⡴⠞⠁
⠀⠀⠀⠀⠀⢀⣤⣶⡽⠱⠃⣀⠬⠿⠭⠭⠥⠶⣒⣚⣋⡴⠛⠀⠠⣤⢠⢟⡿⢫⠞⠉⠠⠐⠒⠋⠱⠊
⠀⠀⠠⢀⣼⡟⡹⢋⣴⣶⣾⢛⣓⠿⠭⠭⣭⣭⣭⡭⠷⠛⠀⠀⠀⢋⢷⡞⣿⢥⠤⠀⠒⣢⠶
⠀⠀⠀⣾⣟⡴⣉⣿⣷⣭⡒⢭⣓⠶⣤⣖⣲⣶⣶⠚⠁⠀⠀⠀⠈⢄⠸⣧⡗⣤⢭⡟⠃
⠀⠀⣠⢇⡩⠆⠛⠛⠛⠛⠻⠷⠻⠿⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢊⠐⣿⣚⣛⡟
⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⢀⢸⡀
⠀⠀⠀⠀⠀⠰⣤⣤⣄⣼⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠐⣿⣼⣷⠂
⠀⠀⠀⠀⣀⠀⣀⠉⠛⢿⣷⣾⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣿⣿⣿⣿⣼⣦⡀
⠀⠀⠀⠹⢿⣷⣛⣿⣟⣻⣁⣉⠙⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣤⣴⣏⠈⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⣻⣿⣼⣧⠄
⠀⠀⠀⠀⠀⠉⠛⠋⠉⣿⢿⣿⣿⣿⣇⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠛⠲⣧⣀⠀⠀⠀⢤⣧⢆⣠⣿⣏⡛⣿⣿⣿⡷⠦⠤
⠀⠀⠀⢸⣿⣄⣔⣦⣰⡟⣶⣿⣿⡿⠃⢀⡠⠎⠁⠀⠀⢀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠤⣴⣷⡿⠆⣾⣿⣼⣿⣷⣿⣆
⠀⠀⠀⣠⡉⠉⠛⠛⣣⣾⣿⣯⣽⣦⡶⠄⢀⡰⠀⠤⠚⠈⢀⠀⠀⠀⠠⡄⠀⠀⣀⠀⢀⣀⣒⣾⣿⣄⣺⣻⣿⣛⣳⣯⣿⣙⡛⠂
⠀⠰⣿⣿⣍⣤⡀⢁⣸⡇⡭⣯⣵⣾⣷⣿⣧⠄⠀⠠⠁⠀⠀⠀⠒⠒⠖⠛⠚⠛⠻⠿⠿⢯⣯⣽⣿⣌⡵⢻⣽⣝⣛⣿⣿⣿⣅⡀
⠀⠀⠀⣄⣸⢾⡿⢆⣹⡇⠿⠿⠿⣿⡯⠾⢯⣤⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣴⣶⠟⠛⠙⠙⠛⠉⣿⠹⠿⠟⡟⠛⠛⡇⠶⠠⠈⠈⠁
⠀⠀⠀⠀⢀⣀⣘⠛⠛⡟⢢⣄⡀⠐⠀⣀⡀⠀⠉⠙⠋⠋⠙⠊⢈⣉⡉⠈⠉⠁⠀⠀⡀⡄⣤⡐⠿⠶⠦⠤⠠⠔⠶⠷⢿⣶⠦⠂
⠀⠀⠀⣀⠙⣛⣝⠛⠚⣇⠨⡀⠙⣻⣏⣹⡛⠂⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠒⠈⠁
⠀⠀⠛⠻⢿⣾⠟⠀⠈⣿⠀⠆⠀⠿⢿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⠤⠶⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢛⣃⣀⣀⡀⡀⢠⣠⣴⣶⣶⣶⠀⠈⣧⣴⣤⣱⣤⣤⡀
⠀⠀⠀⠀⢀⣀⣴⣾⣾⡿⠀⣄⡀⢀⣀⣰⡄⢰⣄⢀⢀⢠⠀⢀⠀⠀⠀⠘⢿⡿⠿⠟⠋⢉⣉⣁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⣾⣿⣿⢸⠿⠆⠿⠶⢶⣧⠄⠀⠀⠈⠉⠉⠁⠀⣀⣀⣀⣀⣀⣤⢤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⠤⣈⡀⠲⢦⣄⠀⠀⠈⠉⠘⠓⠦⠀⢤⠤⠤⠤⠄⠈⠉⠉⠋⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠋⠋⠙⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠃

⢀⠀⣤⣶⢰⡤⢈⠎⡆⠀⠓⣴⠶⢆⣰⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠏⠙⢻⣿⢹⣧⡾⠛⣿⡟⠉⣄⡗⣿⡷⣂⡔⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⢀⠄
⣼⠀⢻⡏⣷⡟⣿⡴⣿⡟⣧⢿⣿⣿⡷⣾⣷⣮⠄⣟⠡⠒⣒⡒⣠⣶⡤⠤⠤⠴⠤⠬⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⢠⠀⢰⠿⠀⣼⠋
⣿⣧⢸⡗⡏⢳⣻⣷⣏⣷⣻⡏⣼⣿⠞⣱⠞⣩⢞⣡⠤⡤⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⣠⠎⠘⠃
⣿⣬⡼⣿⣷⠎⣿⣿⢟⡴⢿⡟⣱⢛⣼⡻⢾⡟⠁⠀⢠⣴⣿⣿⣿⣿⣽⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠂⠈⢷⣌⣇⠀⠀⠀⠀⠀⠠⠄
⢿⡎⣧⣿⣿⣀⣿⣿⠟⡵⣿⢿⣿⡿⣫⣾⣫⢠⢀⣼⣿⣿⣿⣯⣿⣿⣿⣟⣿⣿⣶⠀⠀⠾⠷⣂⡄⣠⣤⣄⠀⠀⠀⠀⠙⣦⡀⢀⠀⠀⠡⣾⣺
⢷⣿⣯⡷⣿⣿⣿⢃⣾⡼⣡⣿⣿⡚⠽⠟⣻⣿⣿⣾⣿⣿⢹⢻⣿⣿⡿⣿⣿⣿⣿⣷⣄⢠⣽⣿⣿⣿⣿⣿⣶⣆⠉⠀⠀⠘⣿⣎⠾⣭⣿⣿⣷
⣼⠹⣜⢧⣹⣿⣯⣾⣽⡿⣻⣟⣵⣠⢾⢟⣷⣢⣿⣿⡟⡇⣏⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣥⣄⣼⢙⣿⣷⣜⣿⣿⣿
⡙⠶⣼⣆⣿⣿⣿⢋⣿⣾⢟⡭⠿⣵⣷⣿⣿⣿⣿⠟⠷⣷⡇⣿⣿⣿⣿⣿⣿⢸⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⢳⣄⡈⣿⣿⣻⣧⡞⣴⣿⠿⠃⠩⠴⠿⣿⠋⠀⢹⠀⢰⣷⠇⣧⣿⡞⣿⣿⡿⣿⢻⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⢿⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⣤⣼⢹⣸⣽⢻⠁⣿⢹⡇⣽⢸⢷⣿⢻⣾⡏⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⢃⠠⡔⢄⣠⣶⣶⣠⣼⣷⡾⠟⠛⠿⠿⠿⠟⠿⠷⠿⠿⢿⣿⣾⣿⣿⣼⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⡂⣿⣿⣿⣿⡎⢁⣿⢦⣿⡟⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⠟⣿⣿⡇
⢴⢖⣿⣿⣿⣿⣿⣍⣉⢀⠀⠾⠷⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡯⢕⣋⣿⣿⡇
⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⠀⠀⠀⣀⣀⣴⣚⣱⣞⡩⢔⡵⠒⣿⣿⡇
⠚⠖⢛⣽⠋⠉⠹⡏⠻⠟⠋⠑⠂⠀⠀⠀⣴⣿⡧⠀⠀⣶⡿⠆⠀⠀⠀⠀⢀⠀⠀⣄⣚⡥⣿⣿⣟⣷⣼⠿⠿⠿⠿⠿⠗⠚⢹⣾⣷⣿⣿⣷⣴
⠙⡿⠉⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⣦⠀⠀⠰⣾⣿⣿⣿⡿⠒⣿⣿⡏⠀⠠⡴⣶⢶⠒⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠉⢀⠠⠊⢀⣿⣿⣷⣦⠀⠙⠋⠈⠁⠀⠠⠶⠶⠷⢿⡿⡿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿
⠀⠀⠀⠀⠀⠀⢴⣿⣿⣯⣭⣭⣴⣶⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣏⣤⠂⠀⠀⠀⠀⢀⣠⠞⠁⠀⡿⡿⠀⠀⠀⠀⠀⣀⣠⠞⠁⢀⡿⡏
⠀⠀⠀⠀⠀⠀⠈⠻⣾⣽⣛⣛⣋⠁⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢯⡉⠀⠀⠀⢈⡴⡧⠀⠀⠀⠙⢯⡁⢀⣀⠀⢈⡴⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠚⠁⠀⠀⠀⠀⠀⠉⠚⠥⠁⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣤⠀⠀⠀⣤⠤⠒⠋⠁⠀⠀⠚⢻⠂⠀⠀⣤⠤⠒⠋⠁⠀⠀⠛⣻
⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣷⣶⣿⠂⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢦⡀⣀⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣟⣛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠉⠲⠤⠄⡤⠔⠋⠀⠀⠀⠀⠀⠙⠳⠊⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠶⠖⠒⠶⢦⡄⠀⠀⢀⣤⠤⠶⠶⠖⠒⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣶⠆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠟⠀⠀⢀⡞⠁⠀⢀⣀⣤⡤⢶⡟⠁⠀⢀⡟⠀⠀⢀⣀⣤⡤⢶⠟
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢸⠁⠀⠀⠀⢀⡤⣴⠋⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠘⠤⣤⣤⣤⡤⠔⠃⠀⠀⠀⠀⠸⠤⣬⡭⠂⠠⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣽⣿⣿⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣿⣭⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣯⣽⣿⣿⣿⣾⣿⣿⣿⡶⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢶⣿⣿⣿⣷⣿⣿⣿⣯⣽⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠟⣿⣿⣿⣍⡿⡿⡾⢻⣿⣿⣿⣿⡟⢷⢿⢻⣩⣿⣿⣿⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⢿⣿⣿⠟⣶⣿⣿⣿⣿⣿⣷⣾⠻⣿⣿⡟⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣀⡀⠀⠀⠀⠀⡠⣢⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠉⢰⡄⠀⡠⡪⢊⣀⣙⠲⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠈⠀⡌⡡⣪⠊⢗⡾⣭⠻⣓⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⢫⠞⠀⠀⠘⠙⠚⠛⠋⠀⠀⠈⠙⢦⡀⣄⣀⣾⣍⣇⡀⠀⠀⠀⠐⠃⠀⢠⣴⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢴⠗⠒⠂⠀⠀⠒⠒⠒⠒⢒⣐⡒⠒⠒⣿⡶⣿⣭⣭⣭⣥⣥⣤⣤⣤⣿⠤⣍⣜⣟⠉⠃⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠇⠀⢀⣈⣰⠂⠀⠀⠀⢚⣙⡇⠂⠀⣿⠃⠁⠀⠀⠀⠈⠀⠀⠉⠉⢳⠝⠣⣏⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡠⢰⡇⢀⠫⡂⠀⢠⣹⡥⠤⠀⠀⠠⠌⠃⡧⠀⠀⣿⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠠⠤⡭⣤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠂⡐⣾⡶⣞⣥⣃⢘⡃⢾⢦⡧⠀⣠⣶⣴⡤⣤⣥⣤⣤⣤⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣰⣤⢐⡗⠇
⠀⠀⠀⠐⣶⡾⠶⠿⡟⣩⢫⡄⠀⢈⡀⠚⠔⠀⠏⠋⠉⠀⠀⠉⠉⠁⠀⠍⠁⠀⠁⠀⠀⠒⠶⠶⡶⠶⣶⣟⢿⡛⠮
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠠⠀⠄⠀⠐⠈⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁


⣿⣟⢻⡿⢿⣿⠿⢿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣸⡇⠀⠀⢸⣆⠀⣴⣰⣿⠇
⠦⠖⠋⠁⠀⢠⡀⢸⣿⣀⡏⣿⡿⣄⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⣧⣸⣿⠟⣼⣿⠃⠠⠑⠠⠀⠀⠀⡀⡆⣀⠄⡤⢂⠆⠀⢤
⠅⠀⠀⠀⡀⠀⠈⢻⣿⣦⣿⡏⢀⣤⢠⣨⡧⠚⠻⢿⡻⢧⡀⡆⠊⢀⢃⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣶⣿⣿⠟⠛⠳⠞⠛⢾⡛⠢⡾⣿⣋⣉⠟⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⢿⠋⠠⡀⠀⠀⠀⠀⠙⢾⣁⠙⣲⠉⠓⠤⡀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠁⢠⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⡼⠀⠀⠀⠀⠈⠂
⠿⠆⠀⠆⢰⢲⣿⣿⡿⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⡀⠀⡀⠀⡀⣾⣿⣿⡇⠀⢀⠈⠀⠀⠐⠘⠂
⠹⣶⠛⣄⡧⡼⠋⠉⢃⣥⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⣶⣶⣶⡶⣶⣾⣷⣶⡶⣀⠀⠰⠲⣐⢂⠀⣀⣠⡎⠕⠆
⡟⢹⣿⢙⣿⢷⢂⡎⡘⣠⠗⠁⠀⢤⡦⣄⠀⠀⠀⠀⠀⠠⠄⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢀⠌⠀⠀⠈⠀⠙⠏⠉
⠶⢻⡿⣾⣿⣿⡅⣷⣿⠥⢀⠄⠀⢁⡷⠈⠓⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠒⠒⠲⠶⠖⠆⠀⠶⢶⡶⢶⣤⣶⣶⣤⡴
⠀⣼⡇⡇⣻⠝⣿⠟⣏⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠐⠒⠄⠀⠁
⠀⢸⠀⢷⠛⠐⣧⠸⠡⠺
⢲⣦⣷⣸⣀⣾⣿⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡠⠔
⠛⠛⠙⡿⠿⣿⣿⡟⢦⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⢄
⠀⠀⢠⠔⠈⣹⣮⣷⣠⣴⣟⡚⡻⣿⣷⡄⠀⣠⣀⡔⠁⠀⠀⠀⠀⠀⠀⡐⡰⠋⠀⣯⡁⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣄⡀
⡁⠄⠀⠀⠈⣙⣉⣉⣿⣯⣉⣵⣷⣾⣿⣷⣾⣿⣿⣿⡄⠀⢀⡀⣄⣀⣠⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⢃⠈
⣄⣅⣰⣮⣥⡈⣙⣿⣯⣽⣯⣠⣾⣾⠋⢻⠿⠟⣻⣿⣿⡿⣿⣿⣿⡏⣽⡟⠁⢀⣀⢀⠀⠀⠀⢠⣀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⢙⣿⣿⣿⣻⡿⣲⠞⠯⠷⠿⣿⣿⣿⢿⣂⠊⠿⣶⠎⠁⠉⠙⠀⠀⠀⠶⢦⠀⠀⠀⠀⠀⠠⣀
⣿⣿⣿⣻⠟⠁⠒⣤⣤⡶⠾⢿⣷⣾⣥⣴⣏⣼⣿⣯⣿⣯⣿⡟⠀⠀⠀⠀⠙⣀⣀⣿⣿⣥⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣴⣦
⢿⣿⡿⣯⣤⣆⡐⠘⠛⢶⣶⣶⣿⣿⣿⣿⣿⣧⣄⡠⠈⠿⢿⣿⣿⣿⣿⣶⣾⣿⣿⠿⠋⠁⣀⣀⠀⣀⣠⡤⠖⠛⠀⣀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠆⠀⠀⠀⠉⠛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠄⠀⢀⡀⢀⠀⢀⠐⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣙⣿⣧⣼⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⣤⡴⠂⣠⡾⠟⠁⠴⢾⣯⡴⠓⠂⠀⣰⠾⣿⣿⣿⣿⣿⡷⠲⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⣿⣏⣉⡀⠀⠀⠀⠰⣾⡋⠀⠀⠀⠀⠀⠠⢾⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠠⣬⣽⠿⠶⠖⠂⠤⣤⣼⡧⠀⢀⠀⠀⣀⠤⣾⣿⣿⡗⠊⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣐⣏⣙⢓⣶⠀⠒⠾⣿⣥⡤⣤⡟⠁⠀⠀⠀⠀⠋⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠁⠀⣉⣵⡶⠤⠜⣇⠈⠻⣾⠁⢀⡀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠨⠟⢿⣯⣁⠀⢀⣴⡿⣦⡀⢹⣴⡏⢀⣠⠷⣀⠀⠀⠀⠠⠄⠀⠀⡤⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣒⢆⠀⠈⢷⠀⠀⢼⡀⠈⠻⣾⠯⠀⢸⣧⣀⣈⡄⠤⠀⠐⠂⡴⠞⠁⠀⠖⠀⠗⠀⠂⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⣿⢶⣾⡅⠀⢸⣷⡶⠤⠘⣣⡤⢻⠋⠙⠃⠀⠀⠀⢹⣿⣿⣿⣟⣐⡁⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠉⠣⣴⠟⠉⠀⣀⣼⠏⠀⣼⣄⣨⠄⠂⠘⠛⣿⣿⣿⣿⣿⣿⡥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢤⣽⠅⠾⣛⣉⡩⠧⠀⣿⣝⡇⠀⠀⠀⠈⠉⠀⣾⠿⠛⠛⠿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠾⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⢀⣤⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⠀⣤⡀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠘⢌⡀⠈⠑⣊⡥⠔⠚⢡⡶⠉⣹⠒⡶⠼⠁⠈⠧⢶⠒⣏⠉⢢⣌⠓⠢⢄⣑⠊⠀⠈⡰⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠁⠋⠀⠂⡟⠡⢼⣋⠷⣸⡷⠃⠀⠀⠘⢾⣇⠾⣙⡇⠌⢻⠐⠀⠙⠈⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠠⡈⡒⠤⣀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⣀⠤⢒⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⡦⢀⡉⠲⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠖⢉⡀⢴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣤⣉⣳⡠⢈⡐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⡁⢄⣞⣉⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠬⠥⠼⡿⠿⢦⠙⠀⠀⠀⠀⠀⠀⠏⡴⠿⢿⠧⠬⠥⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣫⠥⢻⣭⡺⣦⡣⣀⠀⠀⣀⢜⣴⢃⣭⡟⠬⣝⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠵⣫⢾⣜⣫⣹⠀⠀⣏⣽⣣⡷⣝⠮⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠈⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠦⢀⢀⢀⣀⣀⣀⣙⣣⠬⢭⣭⣭⢩⠃⠀⠀⠀⠀⠘⡭⣭⣭⡤⠤⢝⣃⣀⣀⣀⡀⠀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣟⣉⠥⢛⣯⣘⠿⣿⡞⡀⠀⠀⠀⠀⢀⣳⣿⡿⣁⣼⡛⠬⣙⣻⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡾⣥⢚⡽⣳⢾⣿⣾⡵⡆⢰⢮⣷⣿⡿⣟⢯⡓⣬⢷⡚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠤⣀⠀⠀⠉⠙⠊⠷⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠾⠑⠋⠉⠀⠀⣀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣄⣉⢲⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡗⣉⣠⢴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣈⣹⣙⠲⠬⣑⠢⡄⠀⠀⠀⠀⠀⠀⢠⠔⣊⠥⠖⣋⣏⣁⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣤⣬⣯⣭⣑⣺⣇⠱⣀⠀⠀⠀⠀⣀⠎⣸⣓⣊⣭⣽⣥⣤⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣠⡬⢶⣖⣢⢝⠷⣤⡇⠀⠀⢸⣤⠾⡫⣕⣲⡶⢥⣄⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢤⡶⠛⣰⣫⣞⡼⠃⠀⠀⠘⢧⣳⡝⣖⠛⢶⡤⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢺⣃⠾⠽⠁⠀⠀⠀⠀⠈⠯⠷⣘⡗⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

⢰⣶⣶⣶⣶⣶⣶⡖⠒⠒⠒⠒⠒⠲⠒⠖⠒⠶⠶⠶⢶⡆⢰⡖⠲⠖⠲⠶⠶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡟⣿
⢸⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣰⣿⣿⡿⣿⡟⣿⣿⣿⢛⢿⢸⠡⠘⣽
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⣾⣿⠳⣟⣿⡛⠆⣽⣿⢿⣬⡸⣾⠀⢠⣿
⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⣿⡧⣿⣿⣼⣽⣦⡸⢿⠈⣿⠇⡿⠀⡟
⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⡿⣾⣇⣙⡶⣜⢾⡀⡇⢀⡇⣸
⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠘⠿⣿⣟⡛⠙⢿⣿⣷⣿⣿⣷⣳⢸⢰⡉
⢸⣿⣿⣿⣿⣿⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠓⢮⠀⢸⣿⣿⣿⡇⣿⢸⣼⠃⢱
⢸⣿⣿⣿⣿⣿⣾⡈⢳⡴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⣾⣿⣷⣿⣾⣿⠴⠞
⢸⣿⣿⢻⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡿⣿⣿⠛⠙⡱⢀
⢸⣿⣿⣿⣿⣿⡟⣾⢙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣄⢘⡶⢫
⢸⣿⣿⣿⣹⣿⡟⣿⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣏⣸⣧⣿
⢸⣿⣿⣿⣹⣟⣷⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⣿⣿⠛⠟⠩
⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣋⣾⣿⠏⡀⢠⢂
⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠈⡴⠁⠀⡼
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠂⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠶⠷⠷⠶⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢹⠓⢄⠀⠀⠀⠀⠀⠀⢀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢹⠉⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠸⡀⠄⠁⠢⠀⠀⡠⠒⠡⠁⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⡠⠔⠁⠘⣆⡈⠁⠀⠀⠀⠀⠉⠙⠠⡀⠀⠀⠀⠱⡘⢔⣌⠴⠋⠀⡠⠃⢠⠀⢠⠀⠀⠈⠑⠢⢤⠤⣤
⠀⢀⣠⠔⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠚⠉⠀⠀⠀⢀⠀⠀⢸⠀⠈⢢⡀⠀⠀⠀⠀⠀⠈
⠚⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠃⠀⠀⠉⠰⠂⠄
⠀⠀⠀⠀⣆⠰⠀⠀⣠⡀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙
⠀⠀⠀⡐⣸⠇⠱⠀⠯⢯⠁⠀⠀⠀⠀⡌⠲⠀⡀⠂⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠉⠀⠠⠀⠁⠤
⠉⠉⠶⣣⡿⡄⠁⣛⡁⡇⠈⣂⠀⠐⠺⠀⠠⠆⠰⣼⣁⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈
⠶⠶⠖⠛⠒⠛⠚⠛⠃⠒⠒⠒⠒⠚⠛⠛⠛⠛⠓⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠓⠚⠛⠚⠒⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⢀

⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄
⠀⠀⢀⣄⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢠⡀
⠀⠀⣼⣿⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣿⣷
⠀⣴⢹⣿⣧⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣼⣿⡏⣴
⠰⣿⣧⢻⣿⣷⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣾⣿⡿⣸⣿
⣀⢿⣿⣷⡹⣿⣿⣜⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⣿⣿⢟⣾⣿⡿
⣿⣮⠻⣿⣿⣮⣻⣿⣷⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣟⣵⣿⣿⡟⣱
⠸⣿⣷⣝⡻⣿⣿⣷⣽⣿⣷⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿
⢷⣝⢿⣿⣿⣮⣝⡿⣿⣿⣿⣿⣿⢟⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡛⣿⣿⣽⣿⣿⢿⣻⣵⣿⣿⡿⣫
⠘⢿⣷⣭⣻⢿⣿⣿⣷⣿⣿⣿⡇⣿⣿⣿⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⢟⣫⣾⣿
⠀⠈⡻⢿⣿⣿⣾⣿⣿⣿⣿⠟⣴⣜⡻⣿⣿⣿⣿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⣽⣿⣿⠟⣫⣦⠹⣿⣿⣿⣯⣷⣿⣿⣿⢟⠁
⠀⠀⠹⣶⣽⣛⣿⠿⣿⣿⣿⠆⡻⢿⣿⣾⣭⣛⢿⣷⣿⡻⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⢟⣯⣾⡿⣛⣯⣶⣿⣿⢟⠰⣿⣿⣿⡿⣿⣛⣭⣶⠟
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⡸⣿⣷⣮⣽⣿⣻⣿⣿⣿⣿⣦⡻⣿⡄⠀⠀⢠⣿⢟⣵⣿⣿⣿⣿⣟⣿⣯⣵⣾⣿⠇⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠘⢷⣶⣿⣿⡟⢡⣾⣭⣿⣽⣿⣿⣿⡟⣛⣭⣥⣤⣽⣷⠀⠀⣾⣯⣤⣤⣭⣙⢻⣿⣿⣿⣯⣽⣭⣷⡄⢹⣿⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣼⣇⣛⣻⣿⣿⣿⡿⢣⣾⠟⠛⠉⠉⠙⠻⠄⠀⠟⠋⠉⠉⠙⠻⣷⣜⢿⣿⣿⣿⣟⣛⢰⣧⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢇⡹⢿⣿⣿⣿⣏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⣿⣿⣿⢿⢟⡸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣾⡇⢿⣿⢿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⡿⢸⣷⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⢸⣿⣿⣿⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⣿⡇⣾⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⣶⡝⠿⣿⢷⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣾⣿⡿⢫⣶⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟⣦⢉⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣉⣵⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠻⣆⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⢴⠿⠉⠁⠉

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠀⠀⠀⠀⠀⠀⠲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣶⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⠿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⢷⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠋⣰⢟⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣈⡿⡄⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣷⣾⠁⡀⠀⠚⠻⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠛⠇⠀⣀⢘⣷⡯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣾⡿⣟⢙⣵⣷⣢⣶⢰⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠆⣶⣴⣾⣮⠉⣿⣿⣟⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡟⣹⢻⡇⠾⢻⡟⢿⠋⣴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣄⠹⡟⣿⡟⠇⢹⡼⡎⣿⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⡕⢈⡆⣼⡾⣧⣆⡆⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢠⣰⡽⢳⡆⢮⠀⢍⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣾⡇⣾⡁⠻⠇⠘⢹⣧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣜⠁⡸⠏⢸⣧⢸⡆⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠙⢹⡆⡇⣸⡏⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⣿⡆⣧⢰⡝⠛⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⢰⡸⢿⡇⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣿⣺⠸⢟⡆⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇⠀⠇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠝⡀⢸⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸⡄⢻⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⢰⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡌⣿⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡼⡿⢰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⣦⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣾⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣄
⠀⠐⠐⠋⠉⠉⠱⠤⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠉⠀⠀⣀⣀⣀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⣤⡀⢀⠀⣴⣿⣦⣤⣶⣂⣀⣀⣨⣍⠁⠀⠁⠙⠒
⠀⠀⠀⠀⢀⣤⠠⠷⠞⠁⠀⠀⠀⢀⣠⡴⠿⠛⠛⠋⠁⠀⠀⠀⠘⠋⠉⠉⠁⢀⡤⣶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡤⢴⣶⢾⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣰⣮⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠉⠙⠩⢘⡑⢆
⠀⠀⠀⠀⠀⠀⢀⠀⠒⣉⣠⣬⣇⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣦⣤⠀⣴⢻⠷⣿⣿⡷⠇
⠀⠀⠀⠀⠀⣀⣸⣇⣀⡿⣿⣿⢭⡗⠚⠁⠀⠀⣠⣦⣤⣴⡿⠿⢿⣿⣿⡿⠛⠛⣳⣦⣤⣥⣸⣷⡶⠆
⠀⠠⠙⠛⠛⠛⠋⣭⣍⡉⠉⢻⠎⡡⠿⡿⠶⠓⠛⠉⠉⠀⢀⠀⠈⠉⠛⡀⠀⠘⠋⣙⢹⡁⠀⠈⠉
⠀⠉⠁⠀⠀⠀⠀⠙⠋⠉⠉⠒⠉⠈⠛⣈⣀⣠⣤⣤⠀⠀⢉⠀⠁⠀⠀⠀⠀⠐⠚⠛⠛⠓⠒
⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⣤⣶⣟⣯⡿⠛⠛⠛⠉⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⣀⣀⣴⣦⣶⣿⡯⠿⠛⠋⠉⠁⠀⢠⡀⠠⠀⠀⢀⣤⠄⢀⣠⣤⣤⡤⠖⠂⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠰⠿⠇⠎⠉⠙⠄⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠋⠁⠓⠚⠛⠋⠁⠀⠀⠀⠀⣀⠀⠁⠄⡀⢐⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠈

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠁⠀⠀⢀⣀⣹⠀⠜⠀⠀⠀⠀⠠
⠀⠠⠀⠐⠦⢤⡀⠀⠃⣼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠆
⠀⠀⠀⠐⠓⠒⢿⣦⢰⡇⠀⠀⠀⠀⡀⠀⢐⣀⣤⠀⣠⡑
⠀⠀⠀⠀⠀⠀⠀⠈⡌⠃⠀⠀⠀⣀⣁⣀⣀⣀⣀⣀⠀⡌⠷⢶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠯⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣠⠞⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣀⣀⣄⣠⣤⣠⣤⣤⡌⠁⣠⠟⠁⠈⠐⠀⠀⣈⣁⣀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⠿⠗⠋⢩⠻⠀⠇⠸⠁⠿⠿⣿⠿⣿⡀⢀⣀⣀⡀⠐⠧⠀⣠⡀
⠀⠀⠀⠀⠀⠒⠚⠒⠀⠀⠐⠋⠛⠁⠀⠀⠀⠐⠃⠀⠘⠀⠘⠀⠰⠀⠐⠂⠐⠀⠊⠃⠠⠄⠉⠃⠘⠅⠀⠀⠀⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⢴⢀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡰⢺⣷⡆⠀⠸⢄⡀⠈⢤⣄⠀⠀⡄⠀⣤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣰⡆⠀⣀⠀⣴⠾⠃⠀⠻⠲⠿⠛⠓⠓⠒⣾⣟⠋⠠⡘⠃⠇⠃⠀⠛⠀⠚
⠀⠀⠀⠀⠒⠊⠉⠉⠉⠋⠀⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠚⠉⡀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢩⠇⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠠⠂⠈⢼⠀⠠⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢄⡀⠀⣸⡰⠁⠀⠙⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠈⠑⢿⠣⣠⡹⢑⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡂⠂⠁⡿⢀⠤⣌⡡⢻⢦⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠒⡒⣒⠊⡉⠐⠒⢉⠢⡀⠀⠀⠀⠀⠀⡃⠄⢀⡠⠀⢾⢚⢰⠙⡡⣳⠁⠀⠀⠀⣸⠟⠢⢂⠄⢐⣒⠰⢒⠋⠁
⠀⠀⠀⠀⠀⣌⡷⡦⣄⠀⠈⢆⠈⠉⠧⡐⣌⠠⠇⠄⡎⠀⠀⣯⠚⡡⠆⡴⣩⣀⡔⣃⠂⡃⠘⢀⠜⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⠒⠀⠀⣀⠈⠉⢷⠀⢠⢬⣨⡦⡾⡟⠔⣡⠈⠉⠓⢷⢀⡇⣀⡂⠷⠀⠒⠒⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⣗⠦⠠⠀⠄⠠⠐⠉⠓⢢⣈⣇⠸⠃⡎⢼⠁⣟⠴⠁⡆⠀⠀⣸⠝⠁⣭⡄⠉⠀⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⠀⠐⢤⠀⠀⠔⢀⡀⠀⣻⡬⡽⠳⢄⠱⣘⣆⢳⠂⠀⠀⢠⢚⢧⡂⢀⠐⠂⢀⠖⡾⢢⡤⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣈⠁⡌⠀⠘⢷⢒⠆⠳⢤⣈⠟⠀⣠⡞⠉⠁⠈⢿⡸⠆⠯⠷⠞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣱⣞⡠⣤⠄⡿⠷⡖⠷⡲⢿⡶⠶⡍⠂⡤⠆⢀⣄⠻⢆⣀⣤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡡⠖⢺⡟⢸⠀⠆⠀⠈⢈⢠⢆⣡⠞⠀⠀⠈⠲⣀⣠⠊⣉⣀⢨⡟⢭⣱⡚⠵⠦⠄
⠀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠢⠬⠤⢌⣑⠚⠂⠀⣝⡠⠛⠁⠀⢀⠀⠀⠀⠈⢂⣩⠵⠎⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⢀⠀⢀⣀⠀⠠⠀⣀⢀
⠀⠀⠀⢚⣶⡓⠀⠀⢀⡀⠒⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠤⠄⠄⠀⠄
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢠⣌⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡀⢀⠠⠤⠄⠒⠂⠀⠀⢰⣿
⠀⢀⣾⣷⠀⠀⠐⠰⠀⠀⠈⠛⠛⠿⠃⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡐⡱⠐⢶⣶⣶⡀
⠀⠈⠹⠋⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠐⠃⠀⠀⢀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠿⡿⠟⠙⠁⠀⠀⠠⡄⢀
⠀⢀⠀⢀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠠⢄⡀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⣀⣤⣀⣴⣶⣶⠿⠿⢶⣦⣤⣽⡷⠖⣿⣭⣥⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠀⠀⠀⠀⠉⠃⠀⠀⠐⠚⠛⠛⠉⠁⠀⠀⠀⠘⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⠀⢀⠠⠀⠀⠐
⠀⠀⠀⠠⡿⠄⠀⠀⠄⠂⣿⡇⢀⣤⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠿⣿⣿⠇
⠀⢀⣼⣆⠀⠚⠛⠿⠷⠎⡏⡗⢿⣿⣿⡗⠢⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠦⠌⡤⠥⣼⣰⣾⣦⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠈⣙⣋⣀⣀⣀⣀⣀⣠⣤⣥⣀⣸⠀⠼⠧⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠲⡚⠳⣶⣿⣿⣿⣿⣾⣿⣉⣉⣉⣠⡼⠶⠶⠶⢶⠶⠦⠄
⠀⠀⣿⣿⣿⣿⣿⡿⡿⣿⢿⠿⡻⡻⣟⢟⠷⡲⡶⣶⢦⣤⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⡿⣻⢏⠝⡽⣫⢫⢞⡝⡹⣫⢏⠟⡽⣻⢶⢿⣔⡃
⠀⠀⠋⠙⠉⠁⠁⠉⠈⠈⠁⠁⠉⠈⠈⠁⠁⠉⠈⠈⠁⠁⠉⠉⠛⠀⠀⠀⠈⠉⠉⠉⠈⠈⠁⠁⠉⠈⠀⠁⠁⠈⠈⠁⠁⠉⠈⠀⠁⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀
⠀⣰⣦⡀⣀⢀⠀⠀⢤⠄⠁⠈⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⠀⠀⠀⠒⠢⣀
⢠⣿⣿⠧⠀⠀⠐⡒⠒⠀⠀⠠⣿⣿⣧⠒⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢉⣶⣿⣿⣿⣦⣀⣀⣈⣫⣦⣤⣤
⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠈⠈⠀⠀⠠⠀⠨⠁⠉⡏⢹⣿⣿⣯⣿⣿⣿⣿⣽
⠀⠿⠿⠿⠿⠿⢿⣿⣯⠉⠉⠉⠉⠁⣿⣿⠖⠠⠤⣤⣤⡤⡤⡶⡶⡶⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠂⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠉⠚⠌⠌⠌⠂⠀⠀⠐⠋⠋⠉⠙⠁⠈⠈⠂⠀⠑⠈⠈⠊⠀⠑⠉⠉⠋⠋⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠂⠐⠀⢸⣿⡆⠀⠀⡀⠀⠀⠀⢠⡄⣿
⠀⢀⣸⣿⣿⣿⣷⣶⣾⣿⣿⣤⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⣿⣾⣷⣾⣮⡄⠈⠑⣿
⠀⠸⣿⣿⣿⣿⡟⣿⢻⣿⠛⣿⡛⢻⡄⢀⣠⣄⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⣤⡶⠶⠶⠶⠶⠶⠤⢦⣤⣴⣤⣄⣈⣋⣡⣿⣿⣿⣿⣿⣿⠉⢹⣏
⢀⣀⣀⣈⣿⣀⣿⣿⣿⣿⣿⣿⣿⢿⣰⣿⣿⣿⣷⠈⠉⢻⠙⠁⠀⠀⠀⠀⣤⠀⠑⣒⣒⣒⣒⣀⣥⣤⣁⣤⣾⣿⣿⣛⣟⣛⡿⣿⣿⣿⣿⣿⣿
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⣡⣼⣿⣿⣿⣿⣷⣶⣿⣶⣶⣖⡀⠀⠀⢚⣳⡶⣖⢯⠻⡙⣍⢮⠳⡙⣌⢮⡳⡝⣎⢫⡻⡝⢟⢶⡿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠁⠁⠈⠀⠁⠉⠈⠀⠁⠈⠈⠀⠁⠈⠈⠀⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠⠖
⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠖⠁⠀⠰⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⠀⢱⡀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠙⢦⡑⠀⠀⢠⣮⡏⠓⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠙⢧⣤⣼⣿⠁⠀⠆⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡂⠀⢀⣠⠀⠸⠿⣆⠀⢀⡀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢊⡄⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠁⠀⠙⣿⡆⠀⠀⠈⠓⠀⡡⠀⠀⠀⠛⠙⠂
⠀⠀⠀⠀⠀⢸⣿⡟⣡⠞⠁⠀⠀⠟⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⣸⣿⠏
⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⣤⣤⣀⡀
⠀⠀⣠⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⣄⡉⠉⠛⠲⠶⣤⣄⣤⣄⣀⣀
⠀⣰⣿⣿⣟⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠈
⣴⣿⣿⣿⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣷⣦⣀⡀
⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣤⣤⣀
⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲⣀⣀⣤⣤⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡻⣭⠩⠁⠁⠄⠤⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⣱⡟⣌⢧⡛⣀⣀⢀⣀⠁⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢻⣛⠛⠁⠛⠃⠻⠎⠻⣦⣀⣠⣴⣤⣤⣤⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⠏⢻⣿⣥⢿⣄⢦⡸⣟⣼⢿⣏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢹⡋⠈⠉⠂⡅⣿⠃⠀⠻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⠀⠀⠀⠘⡧⠶⣶⣦⠀⡇⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⣀⡀⢿⣠⢤⠀⢠⡏⠀⣽⡟⠀⣷⣀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢉⡕⠛⠶⣾⣿⣿⣿⠐⣻⣿⣇⣿⠿⠿⢛⣻⣧⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣦⠚⣻⣤⣶⡖⣫⣿⣷⣶⣐⣶⣾⣭⣿⣿⣿⣿⣏⡉⢈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢩⣿⣧⠀⠄⣧⠀⠀⠈⠉⣙⣇⢉⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣉⠀⠉⠻⠂⠀⠛⠀⠰⡶⠶⠛⢟⣻⣿⣿⣿⡟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠠
⠀⠀⣠⣔⣄⣨⣴⣿⡧⠈⠩⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⣯⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⢀⣾⡆⢻⠀⠩⣿⣯⡖⠃⠂⠈⢿⡀⠀⠀⠀⠀⠀⠤⣗⢤⣀⣌⣳⣼⣛⣒⣋⢦⡀
⠚⠛⠓⠾⠿⣷⣿⣿⢷⣤⣜⡀⠢⣤⣤⣤⣤⠲⣿⣚⣛⣳⣿⣏⠉⣹⣍⣓⣦⣸⣿⣶⡀⢀⣤⣄⣀⡀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⠀⡀
⠀⠐⠀⠀⣸⡯⣿⡃⠀⢰⠀⠀⠀⠉⠉⠂⠀⠼⢿⣿⣿⣾⢿⢷⣶⣾⣿⣯⣷⣿⣿⣿⣿⡙⣯⢽⡿⣏⡆⠰⡿⢩⡍⠳⠛⢦⣤⠭⠽⠧⠀⠒⠂
⢨⡅⠤⡀⠻⠺⡋⢧⠀⡚⠡⠀⠀⠀⠠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠈⠀⠉⠉⠉⠙⠛⠛⠿⠿⠿⢯⣴⣶⣏⣘⡉⠈⠁⠀⠤⠒⠉⠀⠀⠀⡀
⣸⣿⠶⢦⡄⢻⡿⣦⠈⠀⠀⠀⠀⢁⠀⠐⠀⠀⡅⢻⢂⠓⠀⠀⡀⠙⣇⣰⣁⣶⣤⡤⡦⠶⠶⠶⠶⠛⠛⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉
⢾⣿⠛⠹⠿⠿⠤⡷⠆⢀⡄⠀⠀⠂⠀⣀⢀⣰⠟⣹⣊⣠⠌⠷⠼⠶⡿⠭⣭⡤⣀⠀⡀
⢠⢿⡿⠀⠀⠈⢀⣷⠆⠀⠀⠀⠈⠀⠀⠠⢭⣥⣤⠤⠀⠂⠰⠦⠶⠂⠇⢸⣶⣤⣄⣘⣋⢹⠓⠲⠦⡄⣀⡀⡄
⠀⠈⠛⠛⠛⠁⠋⠋⠐⠀⠀⣀⠀⠀⠀⠉⠁⠂⠀⠀⠠⣄⡀⠀⠀⠒⠓⠀⣈⠉⠩⠙⣛⣿⡶⡶⣤⣄⡀⢀⡟⠳⠦⢄⣲⠦⠤⢴⡆⣀⣀⡀
⠀⠀⠀⠀⠘⠒⠒⠀⠒⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢢⣅⡀⠀⠀⠀⠀⠀⠉⠁⠐⠐⠀⣭⣟⣩⣭⣇⣉⣄⣒⣰⣦⣤⣰⢤⡀⠈⠉⠉
⠀⢔⡟⠻⠉⢉⡀⠀⠀⠀⠐⠀⠤⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⠈⡖⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⢿⣿⣿⣿⣿⣿⣤⡒⣤
⠀⣞⠛⢀⡀⠀⠀⠀⠀⠠⣤⠀⠄⢈⠐⠆⢂⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠡⢂⣀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠋⢹⠿⠿⢿
⠈⠏⠀⠀⠁⠀⠀⢤⣉⠠⠈⠁⢣⡀⢀⠀⠉⠀⠀⠀⠈⠛⠢⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠐⠉⣁⣤⠐⠛⠙⠃⠤⠄
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠠⢉⠀⠑⠀⠀⠀⢀⠘⡁⠀⠀⣀⡈⠓⠶⣤⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⡄⠀⢀⡄⠀⢠⡆⠀⠀⡆⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⣰⣿⣆⠀⠀⠀⣏⠀⠀⠀⠀⠀⣾⠇⠀⢸⣿⠀⠀⡇⠀⠀⠀⠠⠀⡊⢑⠄⠄⠀⠀⠹⣦⣄⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠘⠻⣿⠟⠂⠀⠀⠛⠀⠀⠀⠀⠀⠈⠃⠀⠈⠋⠀⠀⠣⠀⠀⠀⢐⠂⠈⡁⠐⡇⠀⠀⠀⠰⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣐⠀⠀⢸⡇⠀⠀⠀⠀⠘⠙⢷
⠀⠀⠀⠂⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠀⡆⠂⢀⠂⢐⠂⠀⣰⠀⡄⡆⠂⠀⠀⠀⡇⢉⣿⣷⠈⢧⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠁⠀⡆⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠹⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣦
⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠻⠏⠉⠟⠇
⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠸⠀⠀⠀⣠⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⣀⠀⠀⠀⢸⠁
⠀⢰⠋⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⣾⣟⡝⢾⡗⡀⠀⠀⠂⠀⣄⠀⠀⠀⠀⣀⠠⠂⠀⠀⠐⢿⡿⣜⣿⣦⠀⠀⠐⠄⠀⣰⣾⣿⣿⣿⣿⣆
⠀⢠⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣽⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⣼⣿⡅⠀⠀⢈⣤⠀⠀⢨⠟⡏⢙⡟⣯
⠀⠘⢄⡀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠂⠀⠀⠀⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⣸⡿⠋⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠒⡀⣠⠒⠀⠀⠀⣆⠀⠀⠀⠀⣠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣦⠀⠀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣽⡄⠀⠀⢀⣿⡄⠀⣿⠀⠀⠀⣤⡤⠈
⠀⠠⠴⠶⠶⠶⠿⠶⠤⠤⠀⠀⠀⠻⠃⠸⠿⠀⠀⠿⠁⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⠻⠀⠀⠘⠻⠀⠀⠁⠀⠀⠀⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢢⠄
⠀⠀⠀⠁⠥⠀⠀⠀⢀⣜⡁⠀⡀⡰⠀⠀⠀⠠⠁⠁⠀⠀⠐⠀⠀⢰⠀⠀⡆⠀⠀⢀⠆⢠⠁⠀⡐
⠀⠀⠀⠀⠁⠒⠀⠀⠂⠀⠀⡛⠁⠁⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠂⠀⠀⠐⠉⡈⡛⠘⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠳⠄⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⡄⠀⠀⠴⠁⠀⠀⠀⠀⠱⡀⠀⠰⠀⠀⠀⠂⢰⠀⢠⠃
⠀⠀⠀⠐⠌⣀⠀⠀⢠⢸⡠⣤⡤⡊⠀⠀⢀⡨⠔⠀⠀⠀⠐⠀⢄⠀⢀⠔⢲⠰⡦⠆⠊⠀⠀⠄⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⣓⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣚⠋
⠀⠀⠀⠀⠭⠽⠿⣿⣿⣿⣯⣿⣿⣶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣶⣿⣿⣽⣿⣿⣿⡿⠭⠭⠄
⠀⠀⠀⠀⠀⠂⠀⠐⠚⢛⣷⡹⠷⣍⡿⣶⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣶⠟⣩⠾⢇⣾⡛⠓⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠘⢒⠂⣉⢽⣿⣕⠬⡿⣶⣿⣿⣿⣷⣶⣶⠇⠸⣶⣶⣾⣿⣿⣿⣶⢿⠥⣪⣿⡯⣉⠙⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢚⣿⢿⣶⣢⣫⣻⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣟⣝⣔⣶⣿⣿⡓⠦
⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠪⠿⢿⣿⣿⣿⣟⣷⣶⣶⢶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣶⣶⣾⣻⣿⣿⣿⣿⠿⠕
⠀⠀⠀⠈⢍⣉⡯⠽⢿⣮⢿⢿⣍⡛⢿⣿⣿⣦⣤⣀⣴⣶⡆⢰⣶⣤⣄⣤⣴⣿⣿⡿⣛⣩⡾⣯⣱⡿⠯⢽⣉⡩⠁
⠀⠀⠀⠀⠀⠂⠒⡒⠭⣿⣷⡢⠚⠟⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⠻⠓⢔⣾⣿⠍⢒⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠿⢿⣿⣿⣴⡔⡕⣯⣾⣿⣿⡟⠁⠀⠀⠈⢿⣿⣿⣷⣭⢪⠮⠠⠋⠛⠻⠿⠁

⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠤⠄⠄⠀⠀⡀⠀⠀⠀⠴⠖⠿⠙⠻⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠩⠄⠀⠀⠀⠀⠺⠋⠀⠀⠈⠀⠀⠀⠀⠽
⢠⣀⣀⠀⠀⢀⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠤⡀⠀⠛⠃
⢨⡙⠉⠫⠽⣾⢋⣿⣯⡀⠀⠀⠀⠰⠛⠵⠂⠐⠿⢇⣠⢴⣶⠀⠀⠀⠐⢄⡀⢀⡀⠀⠀⠀⠀⣘⣿⠀⠛⠀⠀⠈⠀⠀⠀⠂
⠈⠁⠓⠂⠀⡿⠟⠋⠁⠁⠀⠀⣀⢠⠀⠀⡆⡰⠀⠀⠁⠀⠀⠀⢠⠆⠀⠀⠋⠉⠉⣠⣄⠀⠀⠀⠁⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠓⠀⠈⢹⡦⠄⡏⢣⠀⡆⠰⡄⠐⡄⠈⠤⡀⠴⠀⠀⠾⠿⠃⠸⠃⠀⠒⠚⠋⠀⢀⣿⣧⠀⣼⣧⡀
⠀⢰⣍⣿⣿⡾⢂⡄⠀⣀⣀⣀⣀⡄⠀⡀⠀⠀⠀⢠⠆⠀⠀⡀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠄⠀⠀⢸⣿⣿⢸⣿⣿⡇
⠀⠀⠙⠉⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⢶⠘⠄⠀⠃⠙⠀⠳⠀⠃⠈⠂⠓⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠈⠀⢸⣿⣿⣧
⠀⠠⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⡿⠻
⠀⠀⠀⠀⠀⠀⠈⠃⠀⡏⠀⠀⠀⢀⠴⠤⡀⠀⠀⠀⠀⢀⣠⠀⢀⣄⠀⠀⠀⠦⣄⠀⡀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡰⠀⠁⠀⠀⠀⠿⠏⣸⠳⠀⢠⠁⡀⠻⠃⢀⣄⣄
⢠⠀⠀⣀⠀⠀⠀⣼⠇⢀⣷⣿⣿⠀⠀⣢⣀⡀⣤⠀⠠⠀⠖⠀⠀⠦⠀⠄⠀⠀⠀⠀⠀⠀⠰⣤⣾⣦⣤⢀⢸⣿⣧⣿⡄
⠀⢀⠔⠁⠀⢰⡐⠋⠀⠀⣱⢛⡄⠘⡾⠉⠛⠛⠁⠀⠀⢢⠀⠀⠀⢀⠞⠀⠀⠐⠂⠛⠃⠀⠀⣼⣿⠻⠟⣾⠏⣿⣿⠀⠙⢷⡄
⠀⠸⡄⠀⠀⣸⠃⠀⢠⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠰⣰⡟⠀⠾⠟⠀⠀⠀⠃
⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠁⠀⠀⠀⠀⠈⠀⢠⡤⠄⠀⠀⠀⠂⠀⠀⠀⠉⠠⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⣡⣤⣤⣤⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⣤⣤⣌⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠞⣡⣼⣿⣭⣭⣻⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣟⣭⣭⣿⣥⣈⢳⡄
⠀⠀⠀⠀⠀⣰⠏⣰⣩⣴⣊⣭⣋⠹⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⡿⠏⣙⣭⣙⣦⣍⣄⠹⡄
⠀⠀⠀⠀⢠⠏⣼⣿⡿⠿⡿⡿⡿⠾⣻⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡟⠶⣿⠿⣛⢿⢿⣿⣧⠹⡄
⠀⠀⠀⢀⡞⢈⣡⣾⣤⣾⣧⣾⣷⣿⡹⣇⠙⠷⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠿⠃⣸⢏⣷⣾⣷⣼⣷⣼⣷⣌⡀⢳
⠀⠀⠀⢸⣷⣿⡿⡿⠓⠻⢣⠛⢻⠟⡟⢻⢧⡀⠉⠷⠤⠤⠟⠈⣻⡄⠀⠀⣰⣏⠁⠿⠤⠴⠞⠁⣀⡼⡟⢻⠻⡛⢹⡝⠗⠘⢿⣿⣿⣾⡇
⠀⠀⠀⣿⢿⢻⠀⢀⣷⣠⣿⣷⣿⣾⣻⡿⣧⣿⣳⣶⣤⣴⣿⣿⠛⠁⠀⠀⠈⠛⣿⣿⣦⣤⣶⣞⣿⣾⢿⣟⣷⣿⣾⣿⣄⣶⡀⢈⡙⡇⣧
⠀⠀⠀⣿⣆⣾⣦⣾⣿⣿⡿⠟⠻⠃⣿⣿⣧⣿⣭⣥⠄⢛⣹⡇⠀⠀⠀⠀⠀⠀⢻⣇⡃⢰⣬⣭⣧⣿⣿⣯⠘⠟⠿⢿⣿⣿⣷⡼⣧⣠⣿
⠀⠀⠀⡧⣿⣿⣿⡿⢻⠉⢠⣇⣾⣡⣴⣩⣦⣾⡴⡷⠿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⣾⢦⣧⣼⣍⣦⣼⣷⣸⡄⠉⡟⣿⢯⣿⣿⣿
⠀⠀⠀⢿⠸⠇⡇⠀⣾⣴⣿⣿⡿⢿⠟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢻⡿⢿⣿⣿⣦⣧⠈⢸⠹⠇⡟
⠀⠀⠀⢸⡞⣀⣿⣾⣿⣿⢻⢃⣆⡾⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢧⣸⡙⡿⣿⣿⣶⣿⣠⢻⡇
⠀⠀⠀⠀⢧⢻⣿⣯⠿⠛⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠻⠏⣿⣿⡟⡾
⠀⠀⠀⠀⠘⣏⠻⢸⠀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡄⢠⡏⠟⣹⠃
⠀⠀⠀⠀⠀⠹⡄⢸⣧⣿⣿⣿⢿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡿⣿⣿⣿⣼⡇⣰⠃
⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣦⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⡼⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⣿⡞⣏⠙⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡵⠋⣹⢱⢫⢿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⡄⠘⣆⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣰⠃⢡⠇⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⡄⠘⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣰⠃⣠⠋⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠹⡆⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣰⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡿⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⢿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀

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

⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⣷⢤⡀
⠀⠀⢺⣿⣿⣿⠃⠀⢀⣾⡄⠀⠀⠀⣠⣾⠟⡏⠀⢻⣧⠙⠲⣄⠀⠀⠀⢀⣴⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢄⠀⠀⠀⢠⣦
⠀⢠⣿⣿⣿⣿⣷⠀⢼⣿⣿⠀⠀⣰⡟⠋⠀⠙⢆⠀⢿⡄⠀⠈⠑⢶⣾⣿⣿⣿⠂⠱⢄⠀⠀⢀⠖⣷⣤⢴⣿⠋⠀⠈⢳⣿⣆⣽⣿⣇
⠀⣸⣿⣿⣿⣿⣿⣦⣿⣿⣿⣦⣾⣿⣿⣷⣦⡀⠀⠁⠈⠳⡀⠀⠀⣸⣿⠟⠋⢹⡀⠀⠀⠹⣝⠣⣄⠘⣿⠳⡕⠀⠀⠀⣼⣿⣿⣿⣿⣯⡀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠉⣠⣾⠟⠁⠀⠀⠈⣇⠀⠀⠀⠘⠂⠀⠑⠺⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿
⠘⠉⠛⠚⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⡀⢀⣤⣤⣤⣤⣄⣀⣰⣦⣄⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⠾⠿⢷⠶⠤⠤⠄⠀⠀⠻⠿⠻⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠠⣤⣤⠄⠀⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡰⠂⠉⠁⠐⢄⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠐⡀

⠀⠀⠀⢴⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⢀⠀⠀⠀⠀⠣⠒⠉⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣠⡴⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⡠⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠃⠀⠀⠀⠀⣿⣰⣠⢸⡆⡏⢠⠂⠀⠀⠀⠈⠄⠀⠀⠐⠂⠐⠂
⠀⠀⢔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣾⡇⠘⠈⢛⠀⠉⠓⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⡇⡄⣠⣼⣡⢠⣰⢰⢀⡤⡀⠀⠀⢹⠃⠀⠀⠄⠙⠃⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠸⠜⠀⠉⠓⠙⠿⠘⠈⠀⠀⠁⠁⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁
⠀⠀⢠⣆⠀⠈⠑⠀⢀⣂⣀⡀⠀⠀⠀⠠⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⢐⣀⠀⠀⠁⠀⠀⡄
⠀⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡀⡥
⠀⠀⣀⣄⡘⠃⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠐⠒⠘⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠁⠀⠀⠠⠠⠀⠀⠃⠀⠀⠀⠀⡆⠨⠥
⠀⠀⠉⢁⡠⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠂⡠⠒⢠⠄⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠐⠶
⠀⠀⠀⠈⠀⠒⠂⠀⠀⠓⠘⢂⡀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠫⡀⠰⠄⠈⠓
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⡓⠩⡬⡱⠂
⠀⠀⠀⠐⠰⠉⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠱⣦⣄⡀⠀⢠⣄⣿⣿⣏⣠⠄⠀⢀⣠⣶⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣴⡄⢻⣿⣿⣿⠏⣦⣰⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣽⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠻⠛⠉⠈⠙⠟⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠟⠋

⠀⠀⢰⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣆⢹⣀⡇⠀⣄⢺⡥⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣿⢼⣷⣟⠀⣧⣽⣯⠀⣗⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠙⠿⢿⣿⡀⣿⣾⣯⢠⣿⣿⡄⢿⠀⣸⠄⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⣗⣯⣼⠠⢀⡀
⠀⠀⠀⠀⠰⠏⠙⠚⠿⢼⢿⣿⢖⣿⣀⣽⣅⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠓⢿⣞⡗⢰
⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⠄⠰⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠮⠂⠀⠀⠘⡄⠀⢠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠑⠁⠁⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠷⡀⠀⢄⣵⠀⠘⠀⣀
⠀⡀⣤⠀⢀⡔⠐⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢣⣤⢆⠀⠸⠈⠆⣙⣒⣌⠂
⠀⣀⠍⣠⣵⢢⠑⠁⢁⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢸⠂⡄⠶⠄⠈⢲⣹⡹⠘⢟⡉⢥⠘
⢀⠟⠘⣷⣦⣤⣦⣿⢣⣦⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⢀⠀⠨⡎⣄⣟⣁⣶⣄⡷⡏⢿⣷⣍⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣶⡶⢖⣒⡶⢶⣶⣀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣴⡶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣲⣿⠃⠌⠁⢁⠙⣿⣖⡒⠀⠀⠀⠰⣶⣶⡆⢺⣿⣿⣿⡷⢰⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣶⣀⡀⣠⣶⠭⠍⠀⠀⠀⠀⠀⠛⣿⣷⡲⣝⣛⣫⣄⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠛⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣄⣀⡀⣀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣽⣻⡞⠹⠯⠏⢶⣻⣯⡭⠁⠀⠀⠉⢿⣿⣷⡛⣿⣿⣿⢟⣾⣿⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣺⣄⠀⠀⠐⣸⣓⡛⠁⠀⠀⠀⠀⠈⢿⣿⣿⣬⣿⣇⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠩⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⢢⡴⠶⢦⡔⣶⣶⣶⡖⠀⠀⣠⣠⣠⣠⣶⢶⣒⡶⣶⢄⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣚⣒⢾⣿⣿⣿⡷⣒⣒⡒⠀⠀⠀⠈⢿⣿⣧⢏⠀⠀⠀⡹⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠙⠛⠋⠐⠒⠂⠀⠀⠀⠀⠀⠈⠽⠿⠯⠳⠶⠞⠽⠿⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠁
⠀⢀⠈⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⢀
⠀⠈⠻⣶⣤⣙⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣟⣡⣴⡾⠋
⠀⠀⢤⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣠⠄
⠀⠀⠀⠙⠿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣭⣛⣛⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⣛⣛⣫⣽⣿⣿⣿⣿⣿⣿⣯⣴⡾⠟⠁
⠀⠀⠀⠀⠀⢬⣙⣛⣿⣿⣿⣿⣿⣿⠿⠭⠭⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠬⠭⠿⢿⣿⣿⣿⣿⣿⣟⣛⣩⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣛⣛⣋⣁⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⡠⠟⠁⠠⣄⣉⣛⣛⣻⣿⣿⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣟⣋⣥⣤⠖⠂⣀⠈⠁⠀⠀⠀⠀⠉⢀⡀⠒⢦⣤⣭⣛⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⣿⣶⡾⣋⣥⠖⠀⠀⠀⠀⠀⠐⢦⣍⡻⣶⣾⣿⣿⣿⣟⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠯⠉⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⡀⢀⣀⣀⢀⣀⠀⢀⡀⠀⣀⡀⡀⢀⣀⡀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠘⣧⡸⣧⡸⠀⣿⠀⡟⢷⣌⠁⣾⠁⢈⣃⠸⣦⣅⠀⠀⠀⢸⡇⢸⣷⢸⣯⠤⠁⠿⣬⡁⢸⡇⣼⡇⢀⣁⠈⡻⣦⣸
⠀⠀⠀⠀⠀⠀⠙⠁⠹⠃⠐⠻⠀⠧⠀⠙⠀⠙⠦⠜⠃⠘⠤⠋⠀⠀⠀⠞⠧⠚⠃⠸⠳⠴⠃⠓⠼⠃⠞⠇⠘⠳⠼⠛⠸⠇⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣃⡀⠀⠀⠀⢀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠈⠛⠻⠿⠇⠀⠀⣠⣿⣿⡿⠟⠀⠀⠀⡖⠀⠀⢀⠀⠀⠀⠀⠈⡇⡂
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠁⢠⡀⠀⠀⠀⠂
⠾⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡁⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣄⣀⠀⠀⠀⠀⢠⠆⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣽⣿⣽⣷⣄⠀⣀⣤⣀
⠀⠀⠂⠀⠀⠀⠁⠈⢀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⢠⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠖⠾⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠛⠷⣴⣤⣿⣿⣿⣿⣷⣶⣒⠛⠠⠈⠉⠹⣛⣩⣽⣽⣿⣿⣧⣯⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠠⠀⠙⠚⠀⡠⢸⣿⣿⣿⣟⡶⠾⣿⣟⡁⠈⠰⠀⠀⠈⠁⠈⠛⢷⣿⣿⣕⣄⡀⠀⣀⣿⣿⣷⣤⣶⣦⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡠⠀⠀⡀⠀⠈⠀⠀⠙⠛⣻⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦
⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠿⢿⣿⣿⣿⣿
⠀⠀⠰⠀⠒⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⣿⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿