Girl fixing hair Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣯⣠⣜⠂⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣽⣿⣶⢀⡀⠀⡀⢀⣴⡈⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣾⡿⡄⠂⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡞⠁⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣛⣩⣴⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⡉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⡛⠛⢁⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⣿⣿⣿⣿⣟⢕⢴⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣮⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣿⡿⠻⢾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⢻⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⣿⣿⣿⡇⠀⠀⠀⠉⠉⠙⣻⠟⣿⠀⠀⠀⠀⠀⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⣻⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⠁⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣠⣿⣀⣀⣀⣀⣠⢸⡀⢸⡇
⠀⠀⠀⠀⠀⢠⣄⣠⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢤⢸⣿⣤⣤⣤⣤⢤⣵⡤⢭⡇
⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⢡⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠀⠀⠀⠀⠀⢸⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠄⢸⡇⠀⠀⠀⠀⠀⢸⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠙⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠲⢶⠦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢇⣽⣿⠙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⢶⣤⣤⣀⣀⣀⢀⡞⠛⠛⠁⢀⠆⠀⠀⠀⠀⢀⠀⢰⡀⠀⢰⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⠃⣞⣿⣿⣷⣿⣿⣿⣿⠟⢺⠋⠀⠀⠀⠀⠀⠈⡇⠀⢳⡀⢸⠘⠏⠀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⡎⠀⣸⠇⠈⠀⢹⡏⠉⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⢸⠀⣴⡆⠿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⠇⡸⠀⢸⠁⠀⠀⠀⠘⢿⣿⡆⣶⣾⡄⠀⠀⡇⠀⠀⠀⣷⣀⡀⣽⠀⢠⣿⡇⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣻⠁⢠⠃⠀⢸⠀⠀⠀⠀⠀⠈⠛⠌⠁⠀⠀⠀⠠⠄⠀⣀⣾⣥⡀⠈⢿⠀⠘⣿⢧⡈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⡇⠀⠀⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⢸⡇⢰⡟⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⣧⠀⢠⠋⠀⠝⠒⢲⠖⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⢀⣄⡼⠀⡸⠁⢸⢁⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠈⠳⢮⠀⠀⠀⠀⢿⡗⠀⠀⠀⠀⠀⠀⣴⣦⠀⠘⢻⠟⠓⠒⠊⠁⠀⢠⠆⣸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠂⠀⠚⠳⠄⠁⠀⠀⢀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⣦⠄⠨⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡠⠶⢺⢀⣀⣻⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⣉⣴⣴⣿⣿⣯⡴⢹⡟⣿⡀⠀⣼⠈⡆⠀⡄⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⢰⠃⠘⣄⠃⠀⠇⠀⣿⢹⣿⠀⠀⠀⠀⠠⣬⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠐⠀⠀⢈⠀⠀⠀⠀⢹⠈⠿⠢⢭⣴⣒⠀⠰⠈⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡿⢿⣿⣿⣿⡿⣿⠃⠀⠀⠀⢿⠀⠀⠀⠀⠸⠀⢠⢤⣄⡀⠉⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡗⣷⣿⣿⡎⣿⣿⣥⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⡟⢒⣶⣦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢻⣿⣿⢇⣿⣿⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⣿⣿⣿⡺⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⣦⣹⣯⣵⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣉⣹⣿⣷⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⢿⡟⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠏⠉⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⡟⠈⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠒⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⠀⠀⠰⠆
⠀⠀⠀⡛⣟⣻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣯⡽⠂⠀⢺⠀⠀⠠⣟⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⠀⠀⢸⡟⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠏⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡟
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠄⠀⠀⠀⠀⠀⠀⡇⠀⠠⡿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢙⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣀⣄⣀⣀⣤⣠⣾⣿⣿⣷⡆⠀⠸⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡿⠿⠛⠁⠀⠀⠀⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠨⢿⣿⣿⣿⣿⠿⠛⠛⠛⠀⠐⠛⠓
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⠀⠤⠀⠀⠀⠀⠉⣿⣿⣶⣶⣶⣶⣶⣤⣶⣶⣶⣤⣴⣴⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⡋⠛⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣠
⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣿⠃⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠉⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠿⠿⠿⢿⣿⣷⣿⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠖⠂⠀⠵⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢰⠀⢠⣤⠀⠀⡿⣿⡿⢻⠛⢏⡁
⠀⠀⠀⡌⣠⡼⠃⠀⠀⠀⠙⠋⠉⠀⠀⠈
⠀⠀⢸⣧⠏
⠀⠀⢸⣿⡀⠀⣀⡔⠂⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢸⣿⣧⢰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢸⣿⠇⡆⠀⠀⠀⠀⠀⠀⠀⣤⠾⠁⠀⠀⠄⠀⠀⠀⠀⢰⡄⡀
⠀⠀⢸⣿⣼⣿⠀⠀⠀⣠⠀⣠⡾⡃⢶⡀⢰⣄⠀⠀⠀⠀⠀⢸⣿⡟⠀⡆
⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⡃⠀⠀⠀⠀⣸⣿⡇⠀⡇⠀⠀⠀⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠠⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠉⠇⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡇⠡⠀⠀⡘⠀⢀⠠⠒⡀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠰⠀⡰⠁⠀⡧⠄⠀⠱⢖⡓⣤⡀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡇⢀⡷⠆⠂⠀⠖⠀⠀⢇⠏⢱⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⣉⣻⡖⠁⡇⠁⢃⠀⠃⠀⠀⠀⠀⠉⢐⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢛⢂⣿⡌⡇⠀⡇⠀⡈⢄⠈⠉⠀⠀⣠⠊⠘⡄⢇⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢉⠚⠁⢸⢡⠀⠃⠀⠱⣄⠑⠠⠖⠈⠀⠀⠀⠱⡀⠑⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⢼⡄⠀⡇⠀⢀⣇⣦⠔⠃⠀⠀⠀⠀⠀⠈⠑⢣⠤⢄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⠎⢸⡇⠀⡰⠒⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠃⠌⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢸⠀⠀⡜⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠠⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢰⠁⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⠀⡌⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣾⣿⣶⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⢰⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⠄⠈⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⠙⠛⠀⠀⠸⣿⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇
⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠦⣤⣤⣤⡤⠖⠋⠀⢀⡴⠖⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠈⠀⠀⠒⠊⠉⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⣶⠀⡠⢤⣄⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠙⠲⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⢸⡿⡇
⠀⠀⠀⠀⠘⡟⠀⠀⠀⠘⠀⠀⠀⠀⠘⢆⠈⠻⢿⣿⡿⠗⠒⠀⠀⠀⠙⡀⣿⣷⣦⣀⡈⢡⠇⠀⠀⠀⣦⣤⣤⠁⢸⠀⠀⢸⡇⡇
⠀⠀⠄⢀⠤⠤⠤⠤⠀⠼⠤⠤⠤⠄⢠⠀⡀⠰⣄⣀⡀⠀⠀⢠⣤⠀⠀⡇⣿⣿⣿⡿⠁⠈⠀⠀⠀⠠⢏⣿⠁⠀⢸⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣈⠻⣿⣦⣤⠘⣿⣆⠀⣧⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣬⠅⠀⢼⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣦⠀⠊⣿⣆⠸⣿⣿⣧⠹⣿⣷⠯⢸⡏⢠⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠍⠀⠀⠸⡟⠀⣿⣿⣿⣧⣿⣿⡇⣸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠠⢾⣿⡇
⠀⠀⢀⠀⠀⠀⣀⣀⣀⠉⡉⠀⢀⣀⠀⠀⠀⠿⣄⢿⣾⣿⣿⣿⣿⣿⣿⣿⣽⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠁⠀⠀⠘⠛⠛⠛⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠈⠉⠈⠉⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠀⠀⠀⠀⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠛⠋⣰⣌⠀⠀⣤⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠶⠁⠀⠀⠛⠉⠆⠀⠐⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⡾⣳⠓⣇⢉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⡾⠳⠂⣿⠀⠟⠁⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡧⣤⡶⠊⢀⡴⠃⠀⠀⠀⠀⠘⠇⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢁⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠌⠁⠒⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢆
⠀⠀⠀⠀⠀⢠⠶⠶⠚⠛⠻⣆⠀⠀⢛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⠂⠈⣁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠃⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡜⠀⠂⡀⠀⡟
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠰⢣⡾⠁⡈⢀⠁⢠⠇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠙⣦⣐⢀⠤⠀⠀⠁⠒⠶⣤⡀⠀⣠⠟⠉⠙⣳⡶⠦⡄⢠⠜⠀⠀⠀⠆⢠⠏
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣀⣈⡿⠷⠖⠒⠂⠀⢀⡤⠖⠻⠖⠀⠀⢠⠞⢁⣤⠞⣠⠂⡠⠀⢀⠄⢠⠊
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠀⠈⠉⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⢀⣅⠀⠉⠁⠚⢁⡜⠁⣰⠏⡠⠹⢠⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠱⠀⠀⠀⠈⡄⠰⠏⠰⠃⢶⠈⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡄⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠁⠛⠰⠀⠀⠀⠀⠀⠀⢛⣹⣿⡄⠂⠀⠀⠀⠘⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢠⠔⠂⢀⡴⠛⠉⢸⡇⢀⣠⠄⠐⠀⣿⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣤⠀⢀⡟⠀⠀⠀⠘⣿⣿⣻⡄⠀⠀⣾⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠨⠂⠀⣼⠁⠀⠀⠀⠀⠈⠁⢙⠀⠀⠀⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⢀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⠀⠀⠀⢀⡀⢸⣧⡀⢀⡴⠋⠀⠀⠀⡀⠔⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡠⢿⡷⠋⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣧⠀⢀⡠⠔⠋⡠⠊⠀⢀⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢿⡾⠋⠀⠀⠊⠀⢀⡔⠉⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠄⠤⠜⣣⠆⣠⠀⠀⠀⠰⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠡⠀⠀⠀⠗⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣉⣌⣹⣅⣼⣉⣩⣏⣁⣷⣟⣽⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡼⠁⢀⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢻⡆⢸⣇⢰⡏⢼⣿⣄⣀⣀⣀⣤⣤⣤⣤⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡀⠤⡹⣸⣅⣘⣧⠈⠻⠟⠛⣿⣿⣿⣿⡀⠀⠈⠙⠻⣿⣯⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠙⣷⣶⣾⣿⠏⢈⠃⠀⠀⠸⣟⡿⠋⣩⣵⡤⠤⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢽⡒⣻⣿⣿⣿⠠⠃⣠⠀⠀⠀⣿⡳⣿⢟⠁⠀⠠⠤⣤⡀⠀⠀⢀⣀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⣳⣮⣿⡿⠃⠀⠳⣧⢧⡀⠀⠈⠁⣸⢁⣤⣶⣿⣷⣆⠈⠘⣦⣤⣠⣮⡂⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⡙⠀⢈⣠⡋⠀⠀⠀⠀⢿⣮⣙⠢⠄⢀⣼⠺⡟⠛⠉⠉⠻⡄⣼⣏⣿⣿⣷⡿⣵⣄⣦⣹⡄
⠀⠀⠀⠀⠀⠀⠐⠙⠟⡶⠛⢿⣷⠀⠀⠀⠀⠀⠁⢤⣀⠀⢚⣳⣶⠁⠀⠀⠀⠀⠀⢻⣿⣖⣹⣿⣿⣞⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠯⠻⠹⣿⣧⡀⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡾⢿⠿⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠋⠙⠒⠊⠙⠇
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢰⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣦⣶⣦⣄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⢁⡜⠀⠀⠀⠀⠀⠉⠻⠷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠑⢮⣻⣿⣿⣿⡆⢄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⢀⣂⣐⡠⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠹⣿⢿⣿⣿⠈⢧
⠀⠀⠀⣼⠇⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⡹⢻⣿⣂⠀⠀⠈⢷⠀⠀⠀⠀⠀⢰⡆⡇⠀⢠⢠⡀⠀⠀⣟⢿⣿⣿⣻⣷⣴⣄⠀⠀⠀⠀⣀⠤⠤⡄
⠀⠀⠀⡿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣼⢿⡄⠀⠀⠀⠀⠀⠀⡄⠀⢸⣧⢣⠀⠸⡎⢿⣾⡄⠈⢪⣳⡍⠻⠷⣮⣏⣀⣠⠖⠉⣠⡤⢶⢾⡄
⠀⠀⢠⠃⠠⣖⢄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⣸⣿⡿⢧⡀⠙⠢⢍⡛⠁⠀⠈⠛⠀⠀⣠⠜⠉⣠⣴⢻⡅⣧⡰⣻⠟
⠀⠀⢸⠀⢠⡟⢦⡓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣷⣝⠗⠀⠙⠢⡀⠐⢻⡿⠿⣶⢦⡤⠊⢀⣤⣾⣿⣽⣆⢿⠔⠋⠁
⠀⠀⡇⠀⡿⠿⣄⡈⠓⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡘⢌⢿⣟⠃⠀⠀⠀⠘⠀⠊⠙⢃⡜⠁⣠⡶⣿⣿⣿⣿⣼⣷⡌⠀⡀
⠀⢠⠇⠘⣧⠐⠬⣿⣶⣦⣭⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠙⠀⣘⡷⠦⠀⣀⣠⠤⠴⠒⢞⠛⢩⡽⢠⠷⠛⢿⣿⣿⡟⣏⣿⣷⣬⡇
⠀⣼⠀⠀⠈⠳⠦⣤⣀⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⣀⣀⣤⣴⣟⢀⣴⠌⠀⠛⢻⣿⣿⣧⣾⣿⣿⠇
⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠀⠀⢀⣠⠖⣺⠟⣩⠞⢿⣥⣿⣟⠿⠆⠀⠙⣷⣿⡟⣉⠵⠞⠫
⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠀⠀⠀⣠⠞⢉⡴⢋⣴⢟⣵⡗⣬⡸⠛⣿⣳⡶⠞⢠⢿⣿⠆⠀⠈
⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⢒⣵⠟⠁⠀⠀⠀⠀⠀⠀⠑⠚⠓⠒⠛⠴⠿⣏⠑⢯⣿⠄⠁⠀⠈⠩⢄⣾⠇⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠺⠛⠁⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠋⢱⡈⠹⠿⣶⣾⣿⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠴⣶⡶⡶⣦⠀⡧⠀⠀⠙⠐⢢⣬⣅⣤⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠻⠿⠿⠟⠓⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⡀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⣼⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣟⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠓⢾⣁⣰⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣦⡀⠈⠙⠲⣤⣀⠙⠷⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣀⠀⠒⠦⣷⣂⣀⡉⣿⠢⣤⡞⠛⡿⠶⣿⣛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⢦⣄⣉⣉⣉⣙⣷⣌⣓⢾⡓⠦⣤⠻⣧⣀⣠⡤⠤⠤⣤⣄⣀⣤⡶⠞⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⢀⣴⣶⣶⠚⠳⠻⢿⣭⠽⢛⡝⣹⣏⡿⢦⣏⠶⣌⣽⡛⠉⠁⢀⣀⣤⣤⣾⣷⡭⢍⣹⠿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠟⣿⣾⣿⣿⣿⠷⠶⠶⣿⣿⣿⣷⣟⡣⠟⣿⡇⠀⠙⢶⣏⣙⣡⡴⠛⠉⣠⣾⡭⢛⡭⢶⠋⠁
⠀⠀⠀⠀⢀⣴⡾⢦⣅⣭⣴⡿⠵⣀⡀⣦⣔⡺⣿⣿⣿⣿⣿⣿⣹⣧⡀⠀⢰⡏⢹⣯⣿⡶⢫⣿⠿⠋⠉⡙⠛⣧
⠀⠀⠀⠀⠸⣿⣤⣿⣿⢿⣭⣤⣳⣮⡻⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⢻⣦⡀⠙⣦⠈⢉⣿⠋⢁⣀⣤⣤⣥⠶⠾⢧⡀
⠀⠀⠀⠀⣾⣿⢻⣿⣇⣾⣏⠘⡛⠛⠁⠛⠛⠋⠛⠛⠋⠛⣿⡟⢻⡷⣤⡸⣿⠀⠘⡇⠿⢾⠞⢻⣁⡼⡅⣠⣤⣤⡾⠁
⠀⠀⠀⠀⢿⣿⣦⢿⣿⠟⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢊⣯⠀⠻⣿⣿⠀⠀⢻⡄⢸⡇⠀⠙⠿⠛⠃⣴⡟⠁
⠀⠀⠀⢠⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠷⠏⢾⣿⣇⠀⠀⠀⠙⣦⡀⠀⠀⠀⢀⡼⠋⠻⣦⡀
⠀⠀⠀⢸⣿⣼⣿⠦⣤⡀⠀⠀⠀⠀⣠⠴⠚⠛⠦⠀⠀⠀⠘⣿⣿⣴⣾⣿⣿⠀⠀⠀⠀⠈⢷⣄⣠⡄
⠀⠀⠀⠀⠙⢻⢿⣤⣶⣶⢠⡄⠀⠀⠠⣶⣶⣶⡄⠀⠀⠀⠀⢟⠹⢸⣷⣼⡿⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄
⠀⠀⠀⠀⠀⠸⣾⣷⠿⠋⠀⣻⠀⠈⠀⠈⠋⠀⠀⠀⠀⠀⠀⣤⠇⣼⣫⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢠⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⣇⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠓⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠰⣶⠚⠛⣛⣶⠖⠀⠀⠀⠀⣼⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⠳⠷⠚⠁⠀⠀⠀⣠⡾⠁⢸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⣀⣤⠾⠋⠀⢀⡴⠛⢹⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣉⡿⢾⡿⣯⣥⣀⡤⢶⡟⢀⡴⢻⡇⠈⣷⣤⣀
⠀⠀⠀⠀⠀⣰⡿⠿⣿⠛⣿⢻⣟⠓⠾⠿⣅⣿⡦⠤⠿⠛⣡⢶⣯⣦⡴⠋⣤⠙⢷⣤
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠀⠀⠙⢷⣄⠳⣤⣀⣐⠶⠶⠛⠁⠀⠀⠁⠀⠐⠋⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⢦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠿⣯⢤⡉⠺⠓⠶⠼⢥⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢛⣥⣾⡿⠀⣀⠾⠀⢤⠀⢠⠀⠱⡀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣾⣩⠝⣢⣽⣴⡖⣦⣴⣯⣤⣤⣴⣿⡏⠀⠀⡄⠀⠀⢃⠀⢳⡀⠀⡀⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⡏⠀⢧⡟⠿⠿⢿⣿⡿⠿⠿⣿⡏⠀⠀⠀⠇⠀⠀⢸⠀⠀⢳⡀⡇⡇⡇⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢻⡏⢰⠃⢠⠞⠁⠀⠀⢹⣧⣀⣀⢀⣠⣷⠀⠀⢸⠀⠀⠀⢸⡀⠀⠸⣇⠇⣇⣿⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠟⢀⠇⠀⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⡟⠀⠀⢸⠀⠀⠀⣸⠧⠤⣄⣿⠀⣿⣿⠀⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⠏⠀⡌⠀⠀⡟⠀⠀⠀⠀⠀⠀⠙⢫⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⡦⠀⠈⣷⠀⣿⣿⢾⠀⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⢸⡇⠀⠀⡧⢄⡀⠀⠀⠀⢀⣀⣠⠀⠀⠑⠒⠀⠉⠉⢁⠀⠀⠀⡀⠀⢸⠀⣿⠧⡞⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠘⣇⠀⡼⠁⠀⠛⠉⣻⡏⢏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⡤⠃⣠⠟⠀⡿⡸⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⣇⠀⠀⠀⠀⣻⣷⡺⣤⣀⠀⢀⠀⠼⢿⡦⠴⢛⠟⠛⠛⠉⠁⠀⠀⣳⠃⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢚⡛⠻⣦⣉⠉⠁⢀⣴⠆⠀⣰⠏⠀⠀⠀⠀⠀⢀⡴⢁⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢔⣝⣻⣷⡌⠻⢷⡄⠀⢿⡃⠀⠈⡇⠀⠀⠀⠀⠠⠊⠠⠊⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣶⣽⣻⣾⣻⠿⢿⢇⣀⣙⡧⢀⠒⡁⠹⢒⠠⡀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣯⡴⢛⡟⣧⣅⠀⢸⠅⢳⠀⢠⣀⣹⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⠃⡟⠈⢆⡸⠀⠸⠀⠘⡇⣿⡇⠀⠀⠀⠀⢠⣍⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⠰⠀⠀⠈⠁⠀⠀⠀⠀⡇⢸⡿⢬⣕⣂⠀⠀⢤⠈⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⣇⣀⡀⠈⠙⠛⠒⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢿⣿⡿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡯⠛⠁⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠆⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣷⣶⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠣⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⡄⠀⠛⢿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠈⠛⠷⠆⠀⠀⢿⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢳⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠐⣟⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⠃
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⡀⣀⣠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣆⠀⠀⢩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠀⠀⢀⠞⠉⠁⠀⠙⠦⡄⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡆⠀⠐⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⠳⢦⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢸⣿⢹
⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⢧⠀⠀⠈⠛⠲⠻⠖⠒⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠉⡼⠀⠀⠀⠀⣦⣤⣤⡜⠀⢸⠀⠀⢸⣿⢸
⠀⠀⢀⠀⢀⣀⣁⣀⣀⣀⣀⣭⣀⣀⣀⣀⠀⡄⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⢰⣲⡄⠀⠀⠀⠐⠁⠀⠀⠀⠀⣟⠻⠟⠁⠀⢸⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠉⠉⠇⠈⢦⡀⠁⠀⠀⠀⠀⠀⠈⣾⡄⠀⢸⠸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠹⢦⣄⡀⢸⠀⠀⢸⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠹⣶⡄⠀⠀⠀⠀⠀⢸⣷⠀⢸⠄⡇⠀⠀⡐⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⠑⠋⡀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣤⡤⠀⠀⠀⢸⠀⠀⠀⢹⡞⡀⢀⣀⡀⠀⠀⢹⡄⢸⠀⢃⣆⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠁⠀⠀⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠀⠀⠀⠀⠐⠀⢀⡀⠀⣇⠁⣸⣿⣿⣆⡀⢸⣿⡎⣠⢻⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠀⠁⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⣠⣠⣄⡀⠀⠀⠀⢀⣤⡀⠀⠀⠈⠻⡕⠼⣢⣿⣿⣿⣿⣿⣮⣿⣿⠇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠈⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⣶⠒⠒⣶⢶⡶⡶⠶⢶⣶⠶⢶⠶⠶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⡶⢶⣶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠀⣶⣿⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣨⣿⡟⣭⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠋⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⡋⡟⢯⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣱⣇⣀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠙⢄⣼⣸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢻⡟⠛⢻⠛⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⢸⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣠⠴⠚⠛⠋⠙⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠙⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡠⠴⢤⡄⠀⠀⡔⠛⠓⣆⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠼⠀⠀⠀⠙⠀⠘⠀⠀⠀⠘⠀⠀⢸⢷⡀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢇⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠳⠄⠀⠀⠀⠀⠀⠀⠙⠳⢤
⠙⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⢣⡀⠀⠀⠠⣀⡠⠀⠀⠀⢀⣴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠈⠛⠶⢤⣄⣀⣀⠀⠀⠀⢀⣀⣠⡾⠋⠳⠦⣤⣤⣤⣤⠴⠖⠋⠀⠀⠉⠛⠒⠶⠶⠶⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠓⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡼⠃⠙⠤⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠮⠤⠤⢤⣄⣀⣀⣀⣀⣀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠂⠀⢐⡄⠀⠀⠰⢂⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠹⣿⣟⣿⢻⣋⣿⣯⣽⣅⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡯⠁⠁⠉⠈⠉⠙⠋⠉⠻⢿⣿⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⢶⣿⣿⣶⣤⣤⣤⣾⣿⣿⣤⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣩⣿⣿⣿⠇⣃⡀⣿⣿⣿⣿⣿⣿⡇⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡟⠿⠃⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢘⠉⢉⡙⠃⠀⠀⠀⠀⠀⠉⠉⠉⢠⣿⣉⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣆⠀⠀⠀⠀⠸⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣷⣄⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⣾⣷⣶⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣿⣿⡿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣽⣽⢿⣿⣿⣶⣾⣿⡶⣾⣩⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⠁⠀⠉⠻⠿⣿⣿⣿⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣜⣿⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⣠⡤⠄⠀⠀⠈⢻⣿⣿⣷⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⡁⠀⠀⠀⠠⠤⠆⠀⠀⢸⣿⣿⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠻⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣿⣻⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡿⣿⣿⠿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣿⣻⡌⠙⣿⡿⠿⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⢠⣶⣶⠆⠀⠃⠀⠀⠀⠀⢰⣨⣿⣆⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⢿⡄⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⡄⠸⣿⡆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢣⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠛⣻⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢞⣻⣿⡙⠳⣦⡀⠀⠀⠀⠀⠀⠈⠉⠋⢁⣼⠏⠻⣟⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⢻⣟⠁⣸⣧⣤⣬⣉⣙⠛⢦⡀⠀⠀⢀⣴⡿⠿⣶⣾⣿⣷⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠛⠞⠋⣹⡷⠟⠀⠀⠀⠈⠉⠳⣦⠹⣆⣴⡿⠁⠀⠀⣠⡈⠉⠉⠉⠉⣿⣿⠛⠛⣻⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣤⡀⠀⠈⢻⣿⡟⠀⠀⠀⠀⠙⠁⠀⣤⡄⠀⣿⣿⣷⢴⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠏⠀⠀⢿⠆⠀⠉⠁⠀⠀⠀⣿⡇⠀⣼⠃⠀⠀⠀⠀⠉⠁⠀⣿⣿⣅⣤⣿⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⠀⠀⠀⢀⡀⠀⠀⠀⢸⡆⠀⣸⣧⡀⠘⣦⣄⣀⣠⡾⠃⠀⠀⠘⣿⣿⠏⠀⣴⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠘⢷⣄⡀⠀⠘⢷⣤⣤⣤⠞⠁⣠⣿⠉⠻⣦⣀⡉⠉⠉⠀⠀⠀⠀⣠⡾⠋⠀⠀⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠉⢻⣦⣀⠀⠀⣀⣀⣤⡾⠋⣿⠀⠀⠀⠉⢻⠛⢷⡶⢶⡾⠿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡟⠋⠛⠻⢿⣯⣍⣀⠀⢠⡿⠶⠶⠶⠶⢾⣇⣼⣷⣫⢆⡄⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣦⣤⣤⣶⠿⠛⠉⠀⠑⠳⠾⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⡾⠏⠀⠀⢘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣤⣄⣀⣀⣠⣤⡄⠊⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣶⠞⠻⢭⠽⢿⣦⡀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠈⠉⠉⢀⣀⣀⣤⡀⠀⢤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠠⠭⠏⠀⠙⢿⣄⡀⠀⠀⢀⣼⡿⠛⢿⡛⠛⠛⢋⣿⠟⠁⠈⢹⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⢧⠀⢀⣀⣤⣽⠿⢶⣴⡿⠟⠀⣀⣤⡿⢦⡶⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡀⠀⠀⠈⠉⠉⣀⣀⣀⣤⣤⣴⡶⠛⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠦⠴⠚⠛⠛⠛⠋⠉⠉⠉⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⢀⣤⡶⠛⠉⠉⣷⠀⠀⠀⠀⢀⣠⣤⠶⠛⠁⠀⠀⠈⠙⠻⢶⣦⣤⣀⣀⠀⠀⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⢠⡶⠛⠁⣀⣀⣀⣠⠾⣧⣤⣤⣾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣾⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⢰⣏⣀⣀⣠⣿⣿⣤⠿⠲⢤⣀⠀⠉⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣄⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣴⡿⠛⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠛⠷⣦⣤⣀⡀⠀⠀⢸⡇⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⠉⠙⠛⠛⠿⠿⠇⠀⠀⠘⠛⠿⠿⢿⡿⠿⢿⣿⡿⠛⢻⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⣿⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣀⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⣠⣷⣿⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠹⠧⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣉⣭⣼⣿⣦⣴⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⢤⣄⡉⠉⠙⢦⡀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠀⠈⣉⣥⡶⢿⣤⣴⠾⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣠⣿⠀⠀⠀⠀⠘⢷⣄⣀⣠⡾⠛⠉⠁⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢦⣤⣤⣤⠶⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⢒⣩⣶⣿⣿⣿⣿⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢑⣡⡶⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡧⢖⣒⣂⡀⠀⠀⠋⠉⠛⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠚⣹⣿⣿⣷⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⢁⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢀⡴⠞⣲⣦⠀⠀⢸⣿⣿⣿⣿⣿⣎⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠘⠿⠟⡿⠅⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠂⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢸⡄⠀⠛⣛⣛⠛⣛⠿⢟⣥⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠹⣾⠟⠙⢿⣿⣿⣿⣮⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣎⢿⣿⣿⣿⣿⣿⣧⣀⣽⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣽⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⣩⠟⠉⠀⠈⠁⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⠟⠁⠀⠔⠈⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⡉⠉⠁⠀⠐⠂⠀⠀⠐⠒⠀⠀⠀⠄⢀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⠤⠂⠁⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠐⠠⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠔⠁⠀⢀⠄⠂⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⠔⠁⠀⡠⠀⠁⠀⠀⠀⠀⠉⠒⠢⠤⢀⣀⣀⠀⠀⠀⠑⢄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠂⢀⠴⠊⢀⠀⡴⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡰⢃⡜⠁⠈⠳⣄⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢊⠴⠋⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣄⣀⣀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠒⠚⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠀⡇⠀⠀⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢀⡇⠀⣠⡶⠖⠒⠒⠦⡄⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠲⠶⣦⢸⠀⢠⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣿⣥⣼⠋⠀⠀⠔⣠⣅⠘⡄⠀⠀⠀⠀⢀⠆⣨⣀⠢⠀⠀⠘⣏⣇⢸⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡿⠈⠙⠀⠀⠀⢄⠻⠟⢀⠃⠀⠀⠀⠀⠈⠄⠻⠟⡠⠀⠀⠀⠛⠋⡻⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⡆⡀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣇⠀⡠⠳⡀
⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢄⡀
⠀⠀⠈⢏⠁⠠⠤⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠤⠀⠈⡹⠃
⠀⠀⠀⠀⠳⢄⠀⠄⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠠⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠄⠠⠤⠤⠓⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⠤⠤⠄⠠⠤⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠠⡀⠀⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣩⠕⠓⠙⠒⠒⢀⠀⠀⠀⠹⡄⠀⢀⠴⢪⠽⢉⡁
⠀⠀⠠⠔⠒⠒⠲⠤⣄⠀⠀⢀⡞⠀⠀⢀⡤⠴⡇⢀⢠⠁⠀⡂⠀⠱⠀⠀⠀⢹⣴⣡⠂⠀⠀⠀⠘⡆
⠀⠈⠉⡩⠋⠁⠀⠀⢀⡕⡘⡿⠀⢀⡔⠁⢀⣀⠣⣼⠒⠦⠀⡇⡐⢠⢇⠀⠀⠀⡇⠑⡄⠀⠀⠀⠀⡇
⠀⠀⢰⠁⠀⠀⠀⡀⡰⣇⣤⠇⠀⡎⠀⠚⠉⠉⠀⠈⠁⠀⠼⠖⢶⣥⡀⢱⠀⠀⢷⠰⠷⡀⠀⠀⢠⠇
⠀⠀⢸⠀⠀⠀⣼⠀⡇⠈⢹⠀⢠⠁⣠⠖⢒⣦⠀⠀⠀⠀⠀⠀⣤⠶⢬⠙⢆⠀⢸⠀⠀⢹⣠⣾⠏
⠀⠀⠀⢣⡀⢠⠁⠙⠃⢀⣈⡄⢠⠗⡇⣤⣼⣿⠇⠀⠀⠀⠀⢨⣀⣿⠌⡧⢸⠀⣟⣀⠀⠛⠑⠁
⠀⠀⠀⠀⠙⠺⠀⠀⢸⠁⠤⣧⡎⠀⠀⠘⠛⠋⠀⠀⠀⠒⡆⠈⠻⠛⠀⠀⠀⠱⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠏⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠳⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠂⠀⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡶
⠀⠰⠿⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⡶⠲⠶⠶⠶⠶⠶⠶⠶⢾⢿⡿⠿⠂
⠀⠀⠀⠿⠆⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠠⣿⣿⡟⠛⠛⠛⠛⣻⣯⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠐⣿⠃⢿⠀⠀⣠⡿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣀⣨⣀⣀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡍⠻⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⣀⢸⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⢩⢨⡇⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣶⡘⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⢈⡃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⣆⣶⣤⣤⣦⣹⣿⣿⣷⡿⠁⠀⠀⠀⣾⣷⣾⣾⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢘⢉⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⠟⣻⠛⠁
⠀⠁⠀⠀⠀⠘⣿⣿⣿⠃⠙⠀⡁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⢠⠛⡄⠄
⠀⠄⠀⠀⠀⠀⠛⠛⠛⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣴⣾⣿⣙⡋⠀⠀⠉⠀⠀⢈⣋⣹⣷⣶⣾⣾⣍⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠘⠮⠄⣀⡙⢋⣽⣶⣦⣶⣿⣍⣛⢁⡠⠬⠥⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⢀⠄⠎⠀⠈⠁⡆
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠉⠢⢣⠀⠀⠀⠀⠐⠉⡄⠀⠀⠀⠀⠀⠀⢸⣦⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠤⣀⣀⣀⣀⠅⡜⠀⡀⠀⡄⠐⢹⠀⠀⠀⠀⠀⠀⢠⠿⣿⡏⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢂⠀⡀⠀⢀⡔⠀⠓⢤⣼⣯⣄⠤⠊⠀⠀⠀⠀⠀⡠⡃⠰⠉⢧⣴⣶⣦⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠃⢀⡞⠀⠀⣀⢀⠄⠀⠀⠰⣿⣿⡟⠀⢀⣤⡀⠀⠀⢰⠁⠀⠘⢶⡜⣿⣿⣿⡿⠹
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡶⣶⣿⡄⠀⠀⡀⣿⡿⠀⠀⢈⣿⡇⠀⠀⠀⢄⠀⠐⠁⡇⠘⢿⠟⡡⠁
⠀⠀⠀⠀⠀⠀⢠⠓⢢⠉⠉⠀⠅⠁⠳⠠⠎⠀⢽⠇⠀⠀⣼⣿⣇⠀⠀⠀⠀⠈⣤⣴⣷⠒⠈⠉
⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⠈⡀⠀⡠⠃⠀⠀⢸⠛⠿⢛⠄⠀⠀⣠⡟⠋⠁⠸
⠀⠀⠀⠀⠀⠆⠀⠀⠎⠀⠀⢀⡄⠀⠀⢓⠈⠀⠀⠀⠀⢸⣄⣀⡸⠤⣠⠊⠀⠈⡆⠀⠀⡇
⠀⠀⠀⠀⡜⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠘⡀⠀⠀⠀⠀⠀⠙⢻⡁⠀⠉⠀⠀⢀⠇⠀⠀⢰
⠀⠀⠀⣤⠉⠀⠴⠁⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠤⠊⠀⠀⠀⠀⢆
⠀⠀⠀⠛⠶⠎⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⠶⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠘⠤⠤⢀⣀⣀⣀⡀⣸⣀⠠⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣠⣤⣤⡤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⢉⡁⢠⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡜⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣽⡿⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡉⠀⠀⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢿⡷⠂⠀⠀⠀⠀⠀⠈⡆⠀⣀⠼⠿⠛⠐⠒⠋⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⢰⢁⠞⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⣤⡦⠀⠀⠠⣶⡀⡇⠉⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠘⠿⠃⠀⠀⠀⠙⠃⡇⢰⡆⠛⠋⣀⣀⣠⡼⠛⠻⠦⠴⠤⠄⠒⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣦⠀⠀⢠⣤⡤⠀⢀⡇⢸⠃⠀⠀⣤⣴⡄⠈⠋⡤⠦⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠈⠛⠦⠀⠉⢁⡴⠋⢿⡀⠁⠀⢢⡄⠀⠀⣤⠞⠐⢁⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⣳⣼⣆⣀⡀⠀⠀⢋⡠⣰⣈⠳⡄⠀⠀⡇⠀⠀⢀⡤⠊⠉⠀⠀⠀⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠘⠁⠀⠀⢸⠃⠀⠈⡀⠘⠆⢀⡷⠀⠀⢘⡇⠀⠀⠀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡀⣾⠑⠘⠋⠈⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠓⣬⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢋⠀⠀⠀⠀⡀⠀⠀⠀⠆⣠⣾⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⠀⠀⠀⢀⠁⠀⠐⠀⢀⡼⠹⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⠂⠀⠐⠀⢸⡇⠀⠀⠀⠀⢇⠘⠀⣠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡾⠈⠀⠀⠰⠇⠉⠀⢀⠀⢸⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⣶⢸⠗⠀⠀⠀⢻⣘⡀⢰⠖⠖⡒⠓⠛⢩⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠋⠟⠙⠋⠛⠛⠛⢯⣻⠀⢨⠀⠸⠀⠀⡀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠘⣧⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡠⠤⡇⠀⠀⠀⠀⣀⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠙⠉⠀⠀⠈⠀⠛⠉⠉⠉⠁⠛⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠏⠁⠀⠀⠉⠦⠒⠒⠢⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⠂⠋⠀⠀⠀⠀⢀⠔⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣥⣤⣤⣤⣤⣮⣭⣭⣤⣤⣤⣀⡀⣤⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣀⣀⣠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣷⣾⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠬⠇





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⢠⠾⠛⠃⠐⠀⠀⠀⠛⠢⢤⡑⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠗⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠦⠸⢶⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢣⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⡖⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠀⢀⠀⠈⠉⠛⠿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠀⠡⡾⠀⠀⠀⠐⠀⠀⠀⠀⢠⣌⣠⣤⣬⣦⣤⣀⠀⠀⠀⠈⠛⠃⠀⠀⢀⣠⣤⣤⣤⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡣⠀⡇⠀⠀⠀⠀⠀⠐⠆⢀⡀⠙⠛⠻⢿⣿⠾⠬⣓⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢻⣴⡇⠀⡴⠂⠀⢀⠀⠀⠈⠐⠲⣶⣤⡟⠁⠁⠀⠈⠾⠚⠓⢆⠀⢀⣠⣴⠶⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰⠇⣰⢡⠃⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⢉⠟⠋⠑⣼⣿⡛⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡼⢀⡏⡎⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡰⠋⠉⠙⡟⠀⠀⠀⠉⣄⡹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠰⡀⠀⠀⠀⠀⠀⢣⠁⠇⠀⠀⠐⠀⠀⠀⠀⠀⢻⡀⠀⠀⣀⡴⠪⢄⠀⠀⠀⡈⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠈⢢⣑⠀⠀⠘⢦⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⡔⠉⢀⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠉⠉⠛⠳⣾⡟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠉⠀⠀⠸
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⢆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣬⠏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣿⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⢀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠊⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠲⡼⡇⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣶⠞⠁⠈⠆⠀⠁⠀⠀⠀⠀⠀⡉⠁⠠⣧⠁⡠⠄⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠛⠻⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢰⣤⣀⠈⢿⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⢖⡀⠈⣹⠟⠃⢀⡔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠾⡏⡄⠀⢳⠇⠀⠀⠀⠀⠀⠀⣗⣾⠇⢠⣴⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⢸⣿⡃⢠⣾⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠛⠿⠞⠋⡆⠀⠀⠀⠀⠀⠀⠋⢰⠂⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⠀⢴⠀⠀⢢⡀⠀⠀⣀⢀⠀⢎⠀⣴⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠐⠁⠀⠀⠹⡄⠀⣿⠇⣼⡇⠀⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠃⠀⠿⢰⡏⠀⣰⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⢰⠀⠀⢀⠀⠐⠈⡆⢰⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢌⣻⡆⠀⢸⠀⠀⠻⡇⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠁⢄⣸⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡴⠛⠉⠳⣄⠳⠟⠀⡤⢤⢰⡇⠀⠀⠘⡶⠦⡄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠰⣇⣈⡇⣇⠀⠀⠀⡽⣠⠴⠚⢧⡼⠋⠳⣤⣤⠾⣅⣠⠏⠀⢿⣀⣸⢂⣀
⠀⠀⠀⠀⣰⠶⢶⣶⣶⡧⠤⣬⣥⣤⡾⣗⣒⣋⣁⣏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠋⣳⣀⣩⣥⣽⠼⢷⣶⣶⡶⠶⣆
⠀⠀⠀⠀⠙⠲⢦⣄⠉⠉⠛⠓⠶⠶⠿⣭⣭⣍⣉⣙⣶⣤⣞⣛⣛⣛⣛⣛⣉⣉⣩⣽⣭⠥⠶⠶⠚⠛⠉⠉⣠⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠞⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠳⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢀⣽⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⣯⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡤⠤⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⡆⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠃⠀⠀⠈⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡤⠞⠀⠀⠀⡏⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⡀⡇⠀⡇⠀⣀⡀⠸⣥⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠒⢦⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣀⣸⣇⣠⣇⣇⣀⣇⢸⠁⢸⠀⠀⢰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢳⠀⢀⡖⠛⢲⣤⠤⣄⠀⠀⢠⠏⠉⢹⡄
⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠶⠤⠬⣯⣅⣀⣀⣀⣀⣀⣀⣀⣀⣧⣠⣤⣤⠤⠤⠾⠶⠾⢦⣀⡼⠁⠀⠈⡿⠉⠉⠳⠤⠾⡄
⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠴⠃⣀⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠉⢳⠲⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⢼⣉⣹⢲⠏⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣇⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⠙⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⢹⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠳⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠂⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⠞⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣠⡴⠞⠛⠋⠉⠙⠛⠻⠶⣤⣀
⠀⠀⠀⠀⢀⡾⠁⠀⢀⡟⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⠗⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⣾⠁⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⢷⡀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡤⢤⡟⢁⣠⠤⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⢸⣧⣤⣤⣤⣼⣧⣼⣧⣤⣄⣀⣀⣀⢀⡀⠀⠀⢈⣷⣠⣴⣿⡷⣄⠀⠀⠉⠛⠲⠶⣤⣤⣤⣿⣄⡈⣿⠿⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⣿⣿⣬⣿⡿⠹⡏⠉⠛⢻⣿⣿⣯⣯⣨⣿⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡈⠛⢛⣩⡾⠁⠐⣳⡄⠀⠈⢿⣿⣿⣿⡿⣣⡎⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠟⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠋⠙⠋⢀⣁⠀⠀⠀⠙⢷⣤⣀⣀⣉⣡⡖⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⢧⡀⠀⠀⠀⠁⠀⠈⠿⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡀⠀⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⡀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⣶⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣸⠀⢀⡇⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡏⠀⣸⠁⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣴⡶⣶⡿⠛⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠁⢰⠇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡓⠒⠊⠁⠈⠦⠏⠀⠀⠉⠉⣛⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠇⢀⠏⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠳⡤⠤⡀⢠⠔⢄⣠⠖⢲⠜⢧⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⠀⠘⠀⢠⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣸⠀⠀⠉⠁⠀⠀⠀⠀⢸⡆⠀⠉⢓⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⡆⣰⠀⠈⣆⠘⣇
⠀⠀⠀⣰⠁⢀⠀⠀⢀⠠⢔⣪⠝⠳⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⠶⢟⠣⣀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣦⠀⠈⠳⠬⣷⣦⣤
⠔⢂⡍⠉⠂⠀⣑⠤⠔⠚⠉⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠳⢬⣓⠦⣄⣀⢀⡤⠊⡰⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠛⠛⠉
⠰⢢⢂⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠉⠛⠲⠭⣭⠀⠀⠃⠙⣥⠒
⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠤⣘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⣤⣤⢶⡶⣶⠳⠶⠦⢤⣤⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣸⠇⡿⠀⠔⠊⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⢠⠛⠆⠐⡌⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡌⠀⠀⢀⡇⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠐⠣⠤⢤⡿⠭⣤⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣤⣤⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣍⣉⣻⣿⣿⣿
⣿⣿⣉⣩⣄⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶⣶⣤⣄⣠⣴⣦⣦⣭⣿⣿⣯⣭⣿⣿⣤⣦⣤⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘⢇⠛⣿
⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠀⢻
⣽⣦⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⢻⣿⣿⣿⣥⠙⢿⣿⣷⣌⠻⣿⣿⣿⣿⣿⠇
⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆
⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣛⣿⣿⠉⠙⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣿⡟⢻⡿⠀⠀⣿⣿⣿⣿⣧
⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢸⣿⢿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠒⠲⠾⠿⣯⣴⣖⣚⢩⣅⣤⣀⣤⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠙⠚⣫⣵⣿⣿⣽⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⠉⠛⠻⢶⣬⣙⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣿⣿⠛⠉⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠈⡛⢷⣮⡿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣵⡿⣛⡁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣦⡙⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⣷⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠙⢿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠋⡈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣤⣭⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁
⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⡁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢾⡿⠿⠿⠿⠷⠆⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⠶⠴⠞⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏
⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠁⣸⠃
⣿⣧⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠙⡿⢿⣿⣿⣿⠿⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣽⣧⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠙⠓⢦⣀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡄⠀⠄⣀⣠⡴⠶⠶⠦⣴⠾⠛⠉⠻⣿⣿⣿⢿⣿⣷⣍⣻⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⣴⣿⣿
⣿⣿⣿⣿⣿⣣⡤⠟⠁⠀⣠⣶⠂⠀⠀⠀⠀⠀⠈⠿⣾⡀⠈⠙⠛⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣴⠇⣠⣿⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⠀⠀⠀⠀⡀⢀⡈⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣦⣼⣧⣴⣧⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠄⠢⠠⠀⣠⣿⡇⠀⠀⠀⠠⠀⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠐⡄⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⢀⠀⢀⣾⣿⣿⠁⠀⠀⠀⢰⠁⡀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠃⠀⠀⠀⠘⠛⢿⣿⣷⠃⠀⠀⠀⠁⠀⢤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠠⠐⠀⠀⢀⠂⠀⠘⣆⠀⠀⠀⢠⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠠⠤⠔⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠹⠿⠛⠛⠋⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠛⢻⡻⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡐⠀⠀⠀⠀⣿⣿⠏⠠⠤⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡇⠀⠀⠠⣜⡏⢦⣶⠂⠀⠀⠀⢀⣄⠚⠻⣿⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠀⠀⠠⡀⢃⠘⠿⠇⠀⠀⠀⠘⠿⠇⠀⢨⠎⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⠀⠀⣿⣧⡀⠀⠀⠛⠟⠋⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠶⠂⢿⣿⡿⠶⣤⠀⡀⢠⡴⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈⡐⠐⠈⠀⠠⠐⠐⠒⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡔⢀⠂⠀⠀⠀⠀⠀⠘⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠆⠀⠀⠀⠀⠀⠀⠠⡄⠀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠀⠤⠀⠀⠀⠀⠠⠄⠐⢸⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠉⣛⠛⠛⠛⠛⠛⡋⠉⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡆⠀⠀⠀⠀⠀⢰⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⠀⠐⠒⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⣀⡄⠀⠀⠀⠀⠀⢤⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓

⣿⣿⡿⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠆⢀⠃⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠄⢀⣿⠁⢏⡠⠀⠀⠀⠀⠀⣼⠃⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠁⣸⡇⠀⠈⠀⠀⠀⠀⣀⠀⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠤⣄⢀⡴⠆⠀⣿⠀⣿⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣻⡇⠀⡿⢺⠃⣰⠀⢸⡆⣿⢀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⠘⢣⡸⠃⠈⠁⠉⠀⠈⠀⠘⠂⠀⢸⡇⠀⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⠀⢡⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⡿⠀⢾⡇⠀⠀⠄⢀⣄⠀⣀⡐⣷⠀⢠⡖⣾⡇⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠁⢸⡇⢀⠘⢳⡆⣼⠃⣿⠀⡀⣿⠀⣿⠀⣿⠀⣿⠀⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡗⠄⠀⢸⡇⠻⡌⠳⠐⠀⠋⠀⣿⠀⠉⠈⠘⠇⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡥⡀⠀⣰⠒⡄⠀⠀⠿⠌⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⢀⠁⠀⣿⢀⠃⣀⠄⠀⠀⠰⠖⢒⠊⡵⠂⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣀⠈⠓⢸⡇⠂⠀⢀⢻⢆⡀⢁⡤⠀⣤⠀⣼⠁⠀⠻⡶⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⡄⠀⠀⢸⡇⢄⣾⠐⠇⢸⡇⢸⠇⠀⢿⡄⢯⠀⠈⠸⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠐⠀⢸⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⢠⠄⠀⢤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠄⢀⠄⠁⠀⠀⠀⠀⢀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠄⠃⠀⠠⠀⢀⠀⠀⠀⠀⠀⠐⡰⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⠀⠀⠀⠀⠀⡄⣄⠘⠀⠀⠉⠁⠠⠀⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣸⠀⠀⢰⠳⡈⠢⣤⠀⠒⠊⠁⢗⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⢁⡉⠠⠉⠁⡙⠀⠇⠀⠀⠀⠀⠀⠀⠀⢿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠏⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⢸⡄⡸⠀⠀⡠⠂⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⡰⡇⠀⠀⠊⠀⠀⠀⢀⡤⠆⠀⡄⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⣀⠀⠀⠀⠀⠁⡀⢀⠄⠀⠀⠀⢀⠔⠁⠃⠀⠂⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⠀⠊⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠈⠀⣀⡀⠄⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠰
⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⠉⠁⠙⡖⠲⢇⣠⠀⠀⠀⠀⠀⠄⠀⠀⣇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡎⠸⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠶⠀⠤⣔⠉⠀⠀⠀⠀⠀⢀⡷⠀⠈⠳⣀⣀⣠⣤⣀⣤⣄⣼⣦⠴⠶⠃⠿⢸⢒⡤⢄⡀
⠀⠀⠀⡁⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⡠⠀⣀⠠⣀⣸⠁⠀⠀⠰⠃⠤⠾⢸⡒⢦⡀⠘⠉⠝⢀⢁⠀⡀⢀⡏⠐⠴⠒⢞⢦⠄⣀⠑⢪⡑⡄
⠀⠀⠀⢱⢄⡀⠀⠀⠈⠁⠒⠶⠤⣈⣤⡀⠁⠀⠄⠈⢆⠈⠐⠒⢈⡠⡔⠒⠃⠀⢱⠘⢢⢀⠅⢉⡩⠋⠨⠂⢀⣘⡱⠦⠄⠒⠈⠉⠁⠀⡇
⠀⠀⠀⠈⡄⠈⠑⠂⠤⢀⡀⠀⠀⠀⠀⠉⠉⠑⠒⠂⠈⠇⠰⠾⠯⠤⠄⠤⠤⠤⠷⠶⠾⠗⠐⠚⠒⠈⠉⠁⠀⠀⠀⠀⠀⣀⡠⠤⠒⡋
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠐⠒⠒⠉⠁⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠑⣆⢇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠄⣲⠎⠛⢢⠀⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠄⠤⠘⠀⡸⠀⣔⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠋⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠤⠤⠄⠚

⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢸⡇⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣥⡜⠀⠀⡴⠞⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⣸⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠠⠾⠟⠛⣸⠀⠀⣿⡗⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⢀⣴⡷⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠻⠀⠀⠈⠉⠉⠀⠀⠐⠑⠛⠀⠀⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣼⡇⠘⢹⣿
⠀⠀⠀⠀⠀⠀⢀⣿⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⡇⡅⢸⣿⠄
⠀⠀⠀⠀⠀⠀⡸⡏⢸⣧⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠈⠀⠀⣿⡇⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠱⠇⢀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⢰⠀⠀⢠⣿⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⢸⣾⣇⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⠈⠀⠀⢸⡸⠆⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠁⠀⢰⢸⢸⢻⣿⣆⠀⠃⠀⠀⠀⠀⠀⠐⠀⠘⠋⠀⠀⠄⠀⠀⢠⠀⠈⡇⠛⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢸⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠈⠀⢰⠁⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢸⠀⣠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣾⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣸⠀⡏⢸⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠟⠀⡇⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⢠⠀⠀⢻⢸⣆
⠀⠀⠀⠀⠀⠀⢁⠀⠀⣸⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣸⠀⢄⡿⢸⠌⡆
⠀⠀⠀⠀⠀⠀⡘⡆⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⣰⠀⠀⠀⡇⠀⢸⡇⠎⢦⣙⣶⣦⣤⣤⣀⡀
⣀⣠⣤⣤⣤⣤⣴⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢙⠇⠀⢰⠁⠆⠀⣿⣷⣮⣭⣭⣿⣿⣿⣿⣿⣷⣤⣀⡀
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⠀⠀⢸⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠘⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⣴⣿⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢸⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣼⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⣿⡿⣿⡟⣿⣽⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⠀⠀⡟⠀⠀⢿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠈⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢾⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⡇⠀⠀⠀⣰⠟⠀⠀⠀⠀⢰⡗⡆⠶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠠⣠⡚⠁⠀⠀⣴⡿⢻⠈⠻⣦⣤⠂⣿⡆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⢷⣄⢸⣿⡥⠋⠀⠀⡜⢹⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣸⢀⠀⠀⠀⣸⡟⠀⠛⠒⢃⡤⡐⢤⡾⠏⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠱⢀⣀⣠⠏⠈⠓⠒⠛⠉⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢣⡄⠉⠠⡄⠀⣀⡀⢠⡄⢀⣤⣀⡴⠾⣷⠡⣟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡸⠧⣤⠠⣶⢠⣿⠹⢸⣧⠏⢿⡟⣇⣀⢿⣀⠘⠻⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀⢿⡀⣿⡈⠿⠤⠊⠛⠀⠸⠇⠈⠁⠀⠁⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠈⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣒⣒⣦⣤⣀⣠⡤⢄⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠑⠒⠮⠥⣌⢻⡗⢦⢡⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⠀⠀⠀⢰⣖⡒⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠡⠇⡸⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⡢⢄⡀⠀⠀⡀⢴⡩⢉⢹⢎⠢⡀⠀⠀⠈⠢⣀⠀⠀⠀⢀⡰⠂⠈⣩⡶⠾⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡙⠒⠤⣄⡧⠞⠋⠀⠑⢌⡑⠸⠤⠤⠜⠁⢸⡉⢁⣀⣴⠞⡡⢊⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠈⠑⠒⠤⣈⠑⠢⣠⠀⠀⠈⢑⡶⠀⠐⠀⢠⣌⣙⠛⣓⣫⠴⢃⡀
⠀⠀⠀⠀⠀⠐⠤⣀⣤⣤⢴⣴⡒⣢⣀⣠⣄⣎⣩⣉⣳⣄⣈⣒⣂⡰⢙⣱⣋⣣⣳⣿⣏⣀⣉⣄⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠭⠵⣆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠽⠈⠉⠀⠀⣠⠐⠀⠀⠀⢀⢴⣙⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣠⡺⠋⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠙⢴⡀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣤⠂⠒⡆⠲⡀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⡇⢀⢪⡢⠜⢗⣦⡵⢀⣨⡙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠎⠀⡯⠇⡈⡀⠀⠸⣿⣷⣬⣭⣀⣘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⣫⡷⠞⠛⠈⠀⠀⠈⠻⠮⡏⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⢀⡀⠀⠀⠀⠀⠀⢀⢈⠀⠘⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠓⠤⢀⣀⠈⠀⣀⡤⠄⢺⣸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⡀⢀⠼⢧⡀⢀⡞⡧⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢤⢰⠃⠀⠐⠌⠁⠂⠀⠘⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡿⠈⢀⠀⡆⠀⠀⠀⠀⢠⠀⡈⡙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡃⠀⡈⢘⡇⠀⠀⠀⠀⢸⡇⠁⡟⣿⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣰⠁⡉⠀⢠⠀⠀⢀⠀⠉⠈⢶⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠘⠚⠀⠐⠀⠀⠀⠈⠄⠀⠀⠸⣧⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⠸⢀⠀⠀⡀⠀⢀⡀⡠⠦⠤⠤⠠⠤⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⡠⠖⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠈⠃⠀⠀⠀⠃⢀⣙⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠁⠀⡨⠇⡠⠠⠔⠐⠲⠤⣄⠘⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣤⣀⣀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠼⠋⠀⠀⠀⠈⠷⢀⡀⠀⠀⠀⠀⠀⠈⠉⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢠⠞⡕⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⡆⠀⠉⠉⣱⠟⠂⠀⠀⠀⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢢⠑⠀⠀⠀⠀⢰⠏⠀⠣⣀⠀⠀⠻⠲⣀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢠⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠜⠀⡀⢀⠀⠀⡏⠀⢠⠄⠬⡙⠒⠒⠈⠋⠁⢀⣀⣜⠀⠀⠀⠀⣯⠀⣀⡀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡩⠭⣉⠙⡦⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡠⠖⠢⣀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⢈⣉⡼⠁
⠀⢀⠠⠤⠀⠀⠠⠠⠀⠀⠀⡀⣠⣲⠉⠙⣏⠉⠑⠔⠒⠒⠉⠙⠒⠀⠤⠤⠀⠀⠠⠤⠤⠴⠒⢾⠭⡀⢏⣉⢉⠉⠁⢸⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⣀⡀
⠰⡁⢰⣖⠆⠐⠀⠀⠑⠢⠠⡙⢁⡠⢤⣠⠬⡄⠢⣠⠔⠲⠄⠀⡄⠀⠒⠀⠀⠰⠖⠆⠀⢂⠙⡋⠙⢆⣠⠷⠈⠙⠒⠙⠲⠀⠀⠀⠀⠀⠀⠠⠄⢤⣲⠝
⠀⠙⢦⣍⣙⡒⠀⠤⠀⣀⣀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠉⣠
⠀⠀⠀⢻⡈⠉⠙⠒⠒⠀⠤⠄⢈⣉⡀⠐⠒⠂⠀⠤⠤⠤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠠⠤⠄⠐⠒⠀⢁⣀⡤⠤⠖⠒⣽⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠀⠤⠤⢤⣬⣉⣉⣉⣉⣉⠛⣉⣉⣉⣉⣉⠀⠠⠄⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⣤⠘⠙⠁⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⠋⠷⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣇⡔⠂⢀⢀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⢦⣘⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠈⠉⠛⠀⠲⠶⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⠴⠶⠒⠚⡇⠀⣨
⠀⠀⠀⠀⠀⠀⢠⠖⠊⠁⠀⠛⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠃⠀⠙⠒⢦⡀
⠀⠀⠀⠀⠴⢶⣿⣶⣧⣀⣀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣀⣠⣷⣶⣷⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢖⢀⣀⣤⣄⣀⣀⣤⣔⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣻⣿⣿⣿⠿⣿⢿⣿⠤⣀⢀⡄⠀⠀⠀⠀⠈⢧⡀⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣷⢦⡽⢼⡿⠖⢋⡉⠁⠀⠀⠀⠀⠀⠀⠙⢾⣿⣦⡖⣲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⢽⡿⣹⣿⣿⣦⢹⣿⣿⣦⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣿⣫⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠞⠁⠈⠹⠿⣿⢻⡁⠁⠉⠛⠙⠒⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣟⠋⢉⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⡧⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⠁⢠⣾⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣤⣤⣶⢿⣿⣂⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣳⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠢⣤⣴⣤⣄⢀⣀⣠⣴⣫⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠹⠃⠱⠀⠙⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⡀⠀⠀⠲⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣦⢠⡆⢠⣶⡆⢶⡶⠆⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⢻⡇⢸⣟⣷⢸⡇⠀⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠸⠇⠾⠋⠿⠸⠇⠀⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣤⢠⡆⢰⡶⠀⣿⢻⡆⢻⣴⡇⣼⢻⡇⢰⣆⡦⢰⣤⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⢿⠆⢸⣿⡇⢸⡟⠀⣿⢾⡇⠈⣿⠁⣿⢸⡇⣸⣿⡇⡿⠃⠀⠸⠂⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡷⠀⠸⠧⠀⠿⠇⠸⠷⠆⠛⠘⠃⠀⠻⠀⠙⠛⠃⠻⠛⠙⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠊⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠑⠂⠦⠀⣀⣀⣀⣤⢀⢀⡀⠤⠐⠂⠁⠀⠀⠀⠀⣀⠌⠉⣇

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣠⠖⠉⠉⠀⠉⠙⠲⡄
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠻⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠼⠆
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⣀⣠⣀⠀⠀⠀⠀⢀⣠⡤⣄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠀⠀⠀⣀⡀⠀⢀⡈⠛⠋⠛⠶⠋⠀⠀⠀⠉⢦⣤⣄⡀⣀⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠖⠒⠲⠤⠖⣒⠃⠀⠀⣴⡄⢀⡀⠙⠁⠀⠘⠋⠀⠀⠰⣶⠀⠀⠠⣶⠄⠀⠀⠀⠛⠁⠀⠈⠙⢦
⠀⠀⠀⢸⠀⠀⣀⡤⠞⠀⢰⡦⠀⠀⢈⡛⠀⠀⠀⠈⠀⠘⠋⠀⠀⣠⣄⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠘⠟⠀⠀⢀⣀⠀⠀⠚⠓⠒⢦⡀
⠀⠀⠀⢸⠀⡼⠁⠀⠀⠀⠀⠀⣀⠀⠙⠋⢀⠀⠐⠿⠀⡀⠐⠿⠂⠈⠁⣠⡀⠈⠛⢀⣀⠈⠛⠁⣀⡀⠀⢶⠆⠈⠉⢀⣄⠐⠿⠂⠀⢽⣤⣀⡀
⠀⠀⠀⣸⣀⣇⣀⣀⣀⣀⣀⣀⣛⣁⣀⣀⣛⣃⣀⣀⣘⣟⣀⣀⣀⣀⣀⣉⣁⣀⣀⣈⣋⣀⣀⣀⣙⣃⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣙⣆⣀
⠀⢰⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆
⠀⠈⠳⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠞⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠛⠙⢻⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠋⡿⠛⠛⢏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⣶⠒⠒⣶⠶⡶⠶⡶⠶⡶⠶⡶⠶⠶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⢶⡶⣶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠛⠉⠁⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣤⣴⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣟⢛⡛⣿⡷⢦⡀⠀⢠⣿⣿⣿⣿⡟⠓⢤⣀
⠀⠀⠀⠀⠀⣠⣤⣤⣶⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⠛⠁⠂⠚⠀⢀⠱⣾⣿⣯⣻⢿⡟⢀⣯⣙⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡳⣦⡀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⡐⠀⢻⠉⠙⠿⠁⠁⣸⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣷⣸⡿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣸⣿⠉⠛⠂⢀⣀⣀⡙⠀⠈⠀⠆⢴⡀⠀⢀⡈⠉⣿⠟
⠀⠀⠀⢸⣗⣿⣿⣿⣿⣿⣷⣿⡏⢿⣇⠻⣿⠀⠀⠀⣰⣏⡏⢰⣶⣶⣶⡶⠎⠀⠀⠀⠀⠀⢈⡁⠰⠋⠷⣠⠏
⠀⠀⠀⠀⠻⣿⡿⠿⠛⠛⢻⣿⣿⣸⡏⣿⠊⠀⠀⢀⠟⢸⡇⢸⠿⣷⣿⡇⠀⢰⣏⡆⠀⠀⠈⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢿⣿⣿⣇⠸⣧⠀⠀⠈⠠⢨⣀⡸⣶⣦⣌⠁⠀⠸⢋⠄⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⡟⣧⠀⠀⠀⠀⠀⢸⠀⢰⣶⣤⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠉⠀⢠⣄⠀⠀⠀⠃⠀⢰⣦⣤⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡷⠀⣿⡇⠀⠀⠀⠀⢸⣷⣤⣄⣨⣀⣤⣴⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⣉⠛⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣶⣦⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠊⠁⠀⠑⠤⠒⠢⣄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠋⠀⠀⣀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⠚⠒⠒⠒⠚⠒⠒⠒⠒⠒⠤⠴⢄⠀⢀⠤⠤⠴⢄⣀⡠⠤⠔⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢀⠞⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠙⢆⠘⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⢀⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⢸⣿⣿⣿⣿⡇⢰⣿⣿⣷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠘⠟⠛⠛⠻⣷⣿⣿⣿⣿⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠟⠟⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⢈⣿⠇⠀⢲⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠺⣿⠀⢀⡀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣼⣿⠀⢠⣄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⠀⢀⣄⡀⠀⢀⣀⣤⡁⠀⠀⠈⢹⣿⡧⢤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢈⣿⡄⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⠇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⡀⠉⣀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⠿⣿⠉⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠂⠻⠀⠀⠈⠃⠀⠘⠃⠀⠀⠘⠀⠀⠀⠆⠈⠙⠿⠏⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⣿⡇⠀⠀⠄⠀⢀⣄⣦⢀⢀⣿⡄⢀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣹⢼⡀⠀⢿⡇⠀⢰⣿⡟⢢⣄⠲⣾⣟⡟⣶⡷⢼⠷⠶⠼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡦⠠⢥⠴⠏⠛⠀⢚⠠⠟⠿⠷⠾⠟⠟⠀⠘⠀⠀⠀⠈

⠛⠿⠿⠟⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠠⡈⠻⣿⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠋⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠙⠫⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣫⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⠀⠀⠀⠀⠀⠻⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠋⠉⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⣤⣤⣼⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣾⣿⡿⠿⣻⣿⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣷⡀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢛⣴⠏⠀⢰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣵⣿⠏⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣼⣿⠋⠀⣠⣾⣿⣿⣥⣤⣴⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⡽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣯⣵⣾⣿⣿⠟⠉⣁⣀⣀⣀⣉⠙⡛⠛⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⣰⣾⣿⣿⣿⣿⠁⢾⣿⣿⠿⢻⣿⣿⣿⣦⠐⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⣿⣿⣿⣿⣟⠻⠿⠀⠀⠉⠻⢦⣼⣿⣿⣿⡿⠇⠀⠀⠀⠀⣿⣁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣟⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠙⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠛⢿⣿⠻⢿⡷⠂⠀⣠⣾⣿⣿⣿⣿⠿⠋⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⣿⣷⣦⣀⠀⠀⠀⠉⠛⠉⠀⣠⣾⣿⣿⣿⣿⣯⡄⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣤⣤⣤⣴⣾⣿⣿⣿⣿⠿⠛⠛⠻⠷⣶⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢿⣿⣿⠋⣽⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣩⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣦⣄⠀⣤⠄⠠⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠱⠄⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⣿⣿⣿⣿⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿