Diving Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⣴⡾⠿⣶⣀⣀⣤⡾⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠞⠉⠀⠀⠀⠀⡍⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⣠⡾⠁⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⠶⠀⣠⠶⠆⣸⠟⠁⠀⣰⠟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠞⢁⣠⠞⠁⠀⠀⡴⠃⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡜⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠋⢠⣴⣞⡉⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢠⡴⢿⣥⣀⠀⠈⠉⠙⠳⠶⣤⣾⣿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠰⣮⣥⣤⡀⠈⠙⢷⣶⣶⡶⠶⠾⢿⡋⠀⠀⣠⣼⠷⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠉⠙⠛⣶⣿⣿⠋⠀⠀⢀⣾⣿⠟⠛⢉⣤⣶⣿⠿⠿⠛⠻⣷⡄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⢰⣿⣿⠁⠀⠀⣠⣿⣿⠋⢀⣾⠿⠟⠋⠁⠀⠀⢀⣠⣼⣿⡄⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⡏⠀⠀⢠⣿⣿⣧⠞⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⠟⢻⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⣤⣤⣾⡿⠉⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋⠁⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣾⣿⣿⠿⠿⠛⠉⠁⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣦⣤⣤⣤⣶⣶⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⠛⠿⠛⠉⠁⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣶⣤⣤⢀⣠⡤⠀⠀⠀⠀⢀⣴⠟⠋⣉⣤⣀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠛⠛⠋⠑⠋⠁⠀⠀⠀⠀⣴⠟⠁⣠⠞⢛⡝⠋⠀⣈⣤⣄
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣤⣀⣀⣀⣤⣤⣤⣶⡇⠀⠀⠀⣼⠇⠀⠘⠁⠐⠊⠀⣰⣾⠋⠉⠹⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠰⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣶⣠⡟⠁⠀⠀⠀⢀⣀⣀⠀⢀⡀⣸⣇
⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣀⣀⣀⡠⠤⠠⢶⣾⣿⣿⣿⡟⠀⠁⠔⠀⠰⠏⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⢻⠋⡩⠽⣇⠀⠀⠀⠀⠀⠀⢤⣤⠂⠀⠐⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⠉⠉⠙⣄⡀⠀⠀⠱⣾⢀⡐⠀⡌⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⢙⣦
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣴⣿⡇⠀⠀⠀⢹⣿⣷⣄⠁⠀⠀⠀⣰⠿⠋⠉⠀⠀⠰⠟⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠿⢿⡇⠀⠀⠀⠀⠛⠀⣿⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡜⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣾⣇⠀⠀⠀⠀⣷⣶⣿⣇⠀⠀⠀⠀⠈⠳⢄⣀⣀⠴⠛⣠⡟
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⠀⠙⢷⣄⡀⠀⠀⠀⠛⠉⠉⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣅⠀⠀⠀⠀⠙⣿⠛⢷⡖⠒⠒⠉
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣆⠀⠀⠀⢸⣿⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣧⠀⠀⢰⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⡀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⡤⠤⠒⠛⢋⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⡇⠀⠀⢻⣇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠌⠀⠒⢛⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢠⠀⠀⠈⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣈⣁⣤⡤⠒⠒⠉⠉⠀⡉⠈⠉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⢙⡇⠀⣇⣰⠶⡆
⠀⣤⡤⠶⠖⠋⠉⠁⠀⢀⣀⣤⣴⣶⣾⣿⣶⣦⣄⣀⠀⠉⠻⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣤⡴⠲⠻⢧⣤⠿⠋⢸⣧⡴⠛⣿
⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⠀⠀⣀⣠⣤⠶⢋⣁⠴⠞⠁
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⢇⠀⠀⢰⠋
⠈⠛⠛⠋⠈⠛⠿⣿⣿⠿⠟⠛⠛⠉⠁⠀⣀⡀⠀⠤⠤⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⠘⣇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠖⠛⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⡀⢰⠉⡄⢻⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⢸⠀⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢾⣀⣧⣤⣽⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⣦⣴⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⣴⣶⣶⣶⣶⣶⣶⣶⡆⠄⣤⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣹⣿⣧⡀
⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣿⣿⣿⣥⣄
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠻⠿⣷⣿⣷
⢀⣶⣤⡻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣿⣼⣿⣿⣶⠄
⠀⠀⢹⣧⡛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⣿⣿⠇
⠘⢷⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠠⣴⢮⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣷⣬⣠⣤⢀⣀⣻⣿⣿⣷⡄⠀⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⡇
⠀⠁⠉⠀⢈⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣤⣸⡿⢿⢿⣽⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣵⠾⣼⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠛⠛⠛⠓⠲⢦⣄⢰⠋⢳⠀⠀⣀⡀⠀⠀⠀⠀⠳⣀⡀⣀⡰⠃
⠀⠀⠀⠀⢀⡞⠉⠈⠙⡄⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢻⡉⠁⢠⡏⠁⠈⡇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠈⢷⣀⣀⡴⠃⠀⠀⠀⣿⣡⣴⠃⢀⣀⠤⠊⠀⠈⠢⡀⠀⠀⣷⡖⢢⠓⠦⠖⠃⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡴⠒⢤⠁⠀⠀⠀⠀⢀⣿⡤⣤⡾⠶⠾⣚⣛⣛⢷⣤⠗⠚⠉⢻⠉⠉⠀⠀⠀⠀⠀⠀⢰⠋⠉⣳
⠀⠀⠀⠘⢧⣀⡼⠀⠀⠀⠀⠀⣿⣾⡟⢉⠭⠁⠀⠁⡔⢌⣾⢿⣆⡠⠔⣿⡿⠿⢿⣦⠀⠀⠀⠀⠈⠓⠚⠁⠀⣠⡀
⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡘⠜⢲⣿⣶⣈⣁⣿⡿⠁⠀⢠⣿⣤⣤⣼⢿⣦⣄⡀⠀⠀⢾⣩⠆⠀⠓⠁
⠀⠀⠧⡤⠇⢰⠋⢳⠀⠀⠀⠀⠀⠙⠿⣿⠿⠛⣀⣘⡛⠛⠋⠀⣀⣴⣯⠿⣭⢭⣉⠉⠁⠀⠙⢦⠀⠀⠀⡴⠚⠓⣄
⠀⠀⠀⢀⣀⠈⢉⣁⠀⠀⠀⠀⠀⠀⠀⢈⣷⣾⣿⣿⣿⣠⡴⠚⠁⠀⠀⠀⠇⠀⠈⢳⡀⠀⠀⠈⣇⠀⠀⠳⣀⣀⠞
⠀⠀⠀⠸⠼⠃⠘⠛⠀⠀⢀⡀⠀⢀⣼⣻⣿⣿⣯⣥⣂⣀⣧⣀⣄⠀⠀⢰⠀⠀⠀⠀⢷⣀⣀⣀⣿⠀⠀⠀⠀⢀⡠⣀
⠀⠀⢀⣤⢶⣻⣿⣿⣽⡷⠮⣍⡓⢾⣿⣿⣿⢹⠉⠉⠉⠉⠉⠉⠉⣷⠀⢸⠀⠀⠀⠀⢸⡀⢀⣂⣿⠀⠀⠀⠀⣇⠀⢈⡇
⠀⣠⣞⣿⣫⡁⠀⠀⣿⣟⠓⠦⣍⠃⠈⠻⣏⠘⠶⠶⠶⠶⠶⠶⠶⠃⠀⢸⠀⠀⠀⠀⢸⣯⢿⣿⣿⠀⠀⠀⠀⠈⠙⠉
⡒⣶⣾⡛⢸⡇⠀⠀⠙⠮⣍⣛⡒⠀⠀⠀⠈⡇⠉⢢⠤⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠗⠶⠶⣿⠀⠀⠯⠇
⣨⠤⠴⣙⠈⢧⣤⣤⣤⠴⠇⠀⠀⠉⢰⣶⣤⢣⠀⠰⠀⠀⠀⠀⠉⠐⠒⠒⠀⠀⠀⠀⣼⠉⠳⠀⢻
⠒⢤⣶⣞⠁⠀⢘⡶⠈⢷⠀⠀⠀⣠⢿⣯⣿⡉⠘⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢀⡴⠁⢸⠀⠀⢏⡽
⠀⠈⠻⣿⣿⣶⣌⠁⣀⣞⣀⣠⠴⠃⢸⣯⣷⣇⠀⠀⠀⠀⠈⠉⠐⠂⢤⣄⣀⣀⣠⣴⣿⡋⠀⠀⢸
⠀⠀⠀⠀⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⢻⣽⣿⣬⣀⣀⣀⣰⡶⠿⣽⠋⠡⠉⢿⡾⡿⣿⡥⠤⠄⢼⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⢤
⠀⠀⠀⠀⠀⣞⠁⢉⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⣿⣿⣵⡒⠓⢫⣄⠀⢀⡼⢋⠕⠉⡇⠀⠀⢸⡆⠀⠀⠀⢀⡤⠾⡉⠉⠑⡌⣧
⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠒⠤⣀⠉⠉⠀⠉⠉⢉⠔⠁⠀⠀⢿⠀⠀⢸⡇⠀⢀⡴⠋⠢⢀⣨⠀⠀⣠⡿⡆
⠀⠀⠀⠀⠀⠀⠿⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣆⠀⠀⠉⠒⠠⢀⢀⠆⠀⠀⠀⠀⢸⡆⠀⢸⣇⡴⠋⠀⠀⢀⣴⡿⣶⣾⡿⡇⢹⡄
⠀⠀⠀⠀⢀⣀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⣢⡾⠋⠀⠀⢀⡴⠋⢸⡇⣨⢰⠇⢠⠀⢷
⠀⠀⠀⠀⢯⣨⠇⠀⣈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠸⡋⠀⠀⠀⡴⠋⠀⠀⢸⠀⠛⢸⣶⠘⡀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⡶⠄⠀⠀⠀⠀⣠⢀⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣸⠀⡆⠀⣾⠀⢃
⠀⠀⠀⠀⠀⠶⠆⢈⢿⡟⢉⣀⠀⠀⣄⡠⢼⣯⡶⠂⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣿⠀⠁⠀⢺⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣽⡶⣷⣾⠅⠀⠐⣷⣮⠞⠛⡉⠀⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠲⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⢸⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠉⢳⣮⣿⠀⢀⣿⣿⢏⠀⢀⣿⣾⣽⡂⠀⠀⠀⠀⠈⠳⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣀⡀⢸⠀⣀⢃
⠀⠀⠀⠀⠀⢤⢴⡄⠈⠻⢿⣦⣸⡻⣞⡖⣲⢟⠷⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠉⠹⣼⠞⠉⠻

⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣀⡄
⠀⠀⠀⠉⠻⢿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⣶⣿⣿⣿⣦⡄⢀⣤⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⣀⣴⣯⣙⠻⢷⣤⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⢀⣠⠤⠔⠚⠉⠉⠉⠛⢿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠐⠉⠁⠀⠀⢸⣿⠛⠻⣿⣿⣿⣿⣿⣷⣤⡀⠀⣾⡿⠘⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢹⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣦⡾⠟⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠻⢿⣦⣄⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣶⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⠃⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢀⣀⣴⣾⡿⠿⠿⠛⠉⠀⠘⣿⣿⡇⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⢠⣿⠟⠉⠁⠀⠀⠀⣀⣤⣀⣤⣾⣿⣧⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⢾⣿⡿⠂
⠀⣠⣿⡟⠀⠀⠀⢀⣠⣾⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⡄
⢰⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⠉⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠿
⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢻⣿⣿⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⢶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠸⣿⣿
⢦⣵⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣆⣈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⣿⣿
⠀⠈⠉⠻⣿⠇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠛⠿⣿⣷⣤⣀⣀⣀⣴⠾⠋⠉⠉⠉⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⢀⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠉⠉⠁⠢
⠀⠀⠀⠀⡠⠄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠭⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠤⠀⠂⣀⣡⠌⠹⠑⡀
⠀⠀⢀⠎⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠒⠉⠉⢈⠠⠁⠐⣤⠈⢀⡤⢧⡂
⠀⠀⡀⠀⠀⠈⠐⠠⠄⠀⠀⠁⠁⠒⠠⠤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠚⠋⡏⠩⠐⡀⠀⠤⠀⣼⠁⠀⠈⡆
⠀⠀⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢹⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⡇⠀⠀⡇⠀⠑⠨⠢⠴⠚⣥⠀⠠⠊
⠀⠀⠠⠀⠤⠀⠒⠀⠀⠀⠂⠤⠀⡜⠀⠀⢸⠠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⢁⢀⠀⠠⠠⠔⠛⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠘⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠻⠀⠑⣐⣎⣀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠂⠀⠈⠩⠁⠘⠁⠀⠀⠀⠠⠊⡩⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠕⠀⠀⠐⠀⠤⠀⢠⠄⠀⠀⠀⠀⠀⠐⠈⠀⠀⠘⠀⠀⠀⡇⠰⠀⠀⠀⢀⠃⠊⠐⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡡⡈⠂⠤⠚⢁⠔⠀⣀⠔⠁⠀⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢐⡖⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠖⠀⠑⠀⠁⠙⠆⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⡜⠃⠒⢣⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⡁⠀⠀⠀⠀⡨⠷⠦⣤⣀⣈⣻⡉⠙⢄⠀⠀⠀⠀⠀⠀⠀⠉⣓⡶⠶⢖⠒⠀⠁⠀⢠⠊⠔⠈⢑
⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠐⠀⠈⠑⠂⠀⠒⠁⠀⠀⠀⠀⠈⢙⠟⠉⠂⠀⠓⠀⠠⠤⠤⠀⢶⡟⠁⠀⠀⠀⠈⠁⠒⢰⠂⢀⠒⠫⠭
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⡲⠄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀⣀⡀⠤⠚⡆⠈⠒⢠
⢀⠠⠒⠉⠀⢀⠄⠀⠀⡠⠊⠀⠀⠈⠉⠒⠲⠤⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠐
⠃⠀⠀⠠⠊⠀⠀⠄⡔⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄
⠘⢄⠀⠀⠀⠀⠐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠐⢄⡀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⡀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠠⣯⡄⢀⠜⢕⠻⠛⠐⠂⠀⠀⠴⢖⣶⠋⠀⠀⠀⠀⠠⠄⠀⢀⠀⠤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠁⠀⠀⠀⡀⠂⠤⠀⠠⠸⡅⢈⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠈⠳⠦⠤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠂⠀⠀⠐⠷⠾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⡿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⣀⣴⡞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡼⢁⠀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣇⠈⠄⠀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⣇⠌⢦⡈⠂⢌⠢⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠈⠳⢶⣭⣓⠶⣌⡢⡑⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣤⢺⠇⠈⠡⠐⠀⠀⠀⠀⠀⠉⠛⢦⣳⠐⡄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣳⠝⠁⡞⠀⠀⠡⠀⠔⣀⡀⠀⠀⠀⠀⢀⠿⠶⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠦⣞⠁⢀⣠⣤⣄⡀⠒⠁⠀⣠⢤⣶⣯⡓⠛⠫⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⠇⢠⠏⡔⠛⠲⣝⣦⣀⣠⢾⠍⠂⠑⢝⢷⣘⡚⠒⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⢸⢸⡁⣀⣤⣸⣇⢣⣹⣅⠀⣾⡷⠀⢢⢻⡁⠉⢸⠈⢧
⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣠⠴⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠓⠚⠛⢛⣧⡄⢹⢸⢋⠕⠋⢷⡄⠀⠀⠀⢣⠃⡀⢸⠀⣸
⠀⠀⢻⠀⠀⡉⣉⣉⣉⠥⠴⢒⡿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠲⣤⣤⡤⠖⠋⠉⡀⢸⠟⡜⣖⠤⠤⢊⡷⠸⠿⠇⠈⢰⠀⠀⣤⠏
⠀⠀⡸⠁⡰⠀⠀⣼⠀⠀⢀⣿⡀⠀⠀⠱⣄⠀⠀⠀⢀⣀⣴⠛⢿⠉⠁⠀⠀⠀⢀⡠⠛⠻⢤⣘⣦⡉⠛⣉⢣⡡⣀⠠⣸⣞⣠⠶⠃
⠀⠀⢧⣀⣉⠒⢆⠘⣦⠖⠉⠀⢳⡀⠀⠀⠈⠳⠴⠚⠉⠀⠘⡄⠘⣄⠠⠔⠒⠉⠁⠀⠖⢄⠀⣹⢆⡿⠲⠤⠤⠛⠋⠛⠚⠙
⠀⠀⠀⠀⠈⢳⢸⣾⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣄⠀⠀⠀⠀⠈⢁⣨⣴⠃⠀⠑⢤⣀⣀⣀⣀⡴⣳⡤⣤
⠀⠀⠀⠀⠀⣏⡴⠁⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣠⣤⡀⠀⠘⣆⠘⢦⣀⣠⠤⣞⡽⠛⠉⠳⣄⠀⠀⠈⠉⠁⠀⢧⠀⣯⢽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡶⡶⠒⠲⠦⠤⠤⠤⠖⠋⠀⠀⠀⢈⡷⠲⠯⠔⠋⠁⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠒⠚⠒⠭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⣠⠴⣋⠜⡽⠁⠀⡗⠲⠶⠤⠤⠤⣤⡤⠴⠊⠁
⠀⠀⠀⠀⢰⡊⢡⣊⣁⢰⠃⠀⡼
⠀⠀⠀⠀⠀⠙⡄⠀⡰⢉⠳⣾⠁
⠀⠀⠀⠀⠀⠀⢇⠸⣔⠉⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠏⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡴⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢠⠞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⠏⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠚⢠⠏⢀⡶⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⠋⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣤⣤⣤⡀⡞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢡⠞⠁⠀⠙⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠋⠁⠀⠋⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⠛⠛⠻⢶⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀
⠀⠀⠀⠀⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⢸⣿⣿⣿⡷
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠒⢶⠀⢸⣿⣿⡿⠁
⠀⠀⠸⠀⠀⠀⠀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⢷⠀⣿⡀⠸⡟⠉
⠀⠀⠀⠀⣠⠖⠉⢧⣀⣀⡴⠒⠋⠙⠶⣄⠀⢸⡇⠀⣹⠂⣿
⠀⠀⣧⠘⠁⠀⠀⠀⠉⠉⠀⣀⣠⠀⠀⠘⢆⠸⣇⠼⠃⠀⣿
⠀⠀⠸⣇⠀⢀⣀⡀⠀⠀⠙⠁⣀⠀⠀⠀⠘⣠⠃⠀⠀⠀⣿
⠀⠀⣀⠙⠷⡈⢉⡉⢣⠀⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿
⠀⠀⠉⠛⢤⢅⠈⠉⠀⠀⠀⢀⣀⣤⠀⠀⠀⡿⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⣌⠁⠤⣀⣐⠛⠿⠿⠋⠀⢀⡼⠃⠀⠀⢠⡟
⠀⠀⠀⠀⢀⡏⠀⠀⢸⡏⠈⠁⠒⠒⠚⢁⠃⠀⠀⢀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⡞⠀⠀⢀⡾⠁
⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⠀⠀⢀⡞⠀⠀⢠⡟
⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⠀⠀⢀⠎⠀⠀⡠⠋
⠀⠀⠀⠀⠀⣷⠀⠀⡏⠀⠀⣠⠋⠀⢀⡞⠁
⠀⠀⠀⠀⠀⢻⡀⠀⣇⣴⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠸⣧⣦⡅⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠹⣎⣠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⠟⠀⠐⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠟⠛⢦⣀⡤⠾⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠶⠶⠤⠶⠈⠀⠀⠀⠀⡠⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠙⠂⠉⠀⠀⠀⠀⠀⢀⠄⠀⣴⠞⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠥⠀⠀⢀⣀⢀⣠⡖⠁⢀⡾⠃⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢁⡠⠞⣩⡼⠋⠀⣠⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣡⠞⠁⠀⠀⣰⠏⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡾⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣏⠀⠈⠙⠓⠲⢤⣄⣤⣶⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢤⣆⣈⡀⠉⠛⢷⣶⣶⣶⠤⣾⡟⠉⠀⢀⣨⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⡀⠀⠀⠈⠉⠙⠓⢶⣾⣿⠋⠀⠀⣼⣿⡷⠞⢋⣡⣴⣿⣿⡿⠿⢶⣄⠀⠀⠀⢸⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⢠⣿⣿⠃⠀⢀⣾⣿⠏⢀⣴⡿⠟⠉⠁⠀⠀⢀⣼⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡏⠀⠀⣼⣿⡧⠒⠋⠁⠀⠀⣀⣠⣴⣾⣿⠟⢻⡿⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠧⠤⢴⡿⠋⠀⣀⣠⣤⣶⣿⣿⣿⠿⠛⠁⠀⣸⠇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣿⠿⠿⠟⠋⠉⠁⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠈⠉⠉⠀⠀⠉⠁⠀⠀⢀⣠⡴⠤⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⠿⣧⠶⠛⠀⠀⠀⢀⣾⠟⢁⣤⣶⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡿⠁⠰⠋⢠⠊⠀⣠⡴⠶⠦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣧⣀⡼⠋⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⠀⢤⣶⣾⣿⣿⡿⠁⢋⡄⠀⡴⠋⠈⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠛⠉⠿⢇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠈⠹⢀⡀⠀⠀⢢⢀⡀⠐⡬⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠘⢻⡄
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣤⣴⣿⡆⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠜⠏⠀⠀⠀⠀⠟⠛⠘⡏
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⢻⡇⠀⠀⠀⡇⠀⣯⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⠄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡇⠀⠀⠀⣿⠿⠿⣆⠀⠀⠀⠀⠈⣓⠀⠀⠐⠉⣠⠏
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⡁⠀⠀⠈⠳⣤⣄⣀⣀⣉⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢧⡀⠀⠀⠀⢸⣏⠉⢻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢳⡄⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⣀⣤⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢸⡇⠀⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⢀⣀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠒⠉⠉⡏⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿⠀⠀⠘⣿⠀⣿⢠⣤⡄
⠀⠠⠤⠔⠒⠋⠉⠁⢀⣀⣠⣤⣴⣶⣿⣶⣤⣀⡀⠉⠛⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣤⡤⠶⢿⣤⣿⠞⢺⣃⣠⠖⣶
⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠉⠀⠀⢀⠀⡀⠴⢛⣩⡤⠞⠋
⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡀⠀⢰⠋
⠀⠈⠉⠀⠀⠉⠻⠿⠟⠛⠉⠁⠀⢀⣀⣠⠄⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⡄⡦⢰⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡇⢸⢀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢷⡾⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⡀⠀⠀⠀⢀⡀
⠠⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣷⢻⡟⢿⣿⣿⣿⣿⣿⡿⠷⠄
⠀⠘⠓⠦⣤⣀⠀⠀⠐⡶⣿⣿⣿⣿⣾⡁⠋⢙⡛⠋⠁
⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⣷⣤⡾⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣯⣷⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣙⣿⣿⣿⠿⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠉⠻⢿⣿⣿⣿⣦⣤⣴⣶⣶⠶⠟⠛⠋⠉⠛⠛⠻⠿⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢦⡙⢢

⠈⠛⠷⢦⣤⡀
⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⢿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣇⣀⣀
⠀⠀⠀⢀⣠⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠰⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⡿⠿⣿⣷⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠸⠂⠦⡤⠀⢉⠀⠡⠄
⠁⠀⠀⠀⠀⠘⠠⠀⣀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠃⠀⠑⠀⠐⣂⡍⠀⣠⣔⣿⣀⢀⡀⠀⠴⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⡀⠄⣀⠁⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⠀⠀⠀⠀⠀⠈⠀⡠⠠⠞⠻⡤⠀⢣⠀⡏⠀⠉⠳⡺⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠄⠀⠀⠀⠰⢆⠁⠀⠀⠀⠀⠀⠀⢀⢀⠠⠐⠁⠐⠀⠈⠄⠈⠲⣼⣄⣌⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢄⠀⠀⠈⡀⠀⠀⠀⣀⠤⠒⠚⠺⠅⠀⠀⠀⡇⢀⡆⠀⠀⣈⠌⠈⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⢀⠚⠀⠈⠕⠀⠀⠀⠐⢤⠂⠀⠀⠀⠠⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢀⠌⠀⠀⠀⠀⠀⡊⢁⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠐⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠉
⠀⠀⣀⠠⠀⢂⡡⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠖⠒⠲⢜⡆
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⣤⣄⡀⠀⠹⡄
⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⢠⠊⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣶⣶⣾⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠈⠉⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣶⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣾⣤⡝⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣏⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠙⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢨⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⢁⣀⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⢀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣤⣆⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣖⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⢉⡙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡹⣦⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢹⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⣠⠔⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⡇⠀⠀⠀⠀⢰⣦⠀⣹⠀⠀⠀⠻⠷⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⠀⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠼⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣠⠔⠀⠋⠀⠈⠱⣶⠊⢀⡀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠛⠓⠒⠊⠉⢈⠇⠀⠀⠀⠐⣦⡀⠈⠒⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⣀⣄⣀⣀⣀⠀⠀⣀⡼⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⡤⡄⠀⣾⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⠉⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⢺
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡔⠁⠀⠀⣠⠶⠒⠲⣶⠒⠴⠶⠚⠉⠢⡤⣤⡄⡤⠔⠻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⡰⠊⠉⠈⠳⡄⠈⠙⠓⠶⠶⣄⠀⠀⠀⠀⣠⡄⠀⠘⢆⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠱⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠙⣆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⢠⠶⡄⠀⠐⢀⡴⠋⠀⠀⠀⠙⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣡⣤⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⢀⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⢀⣴⡿⠡⠆⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⡄⠀⠀⣸⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⢠⣾⡟⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⠏⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⣼⠻⡴⢋⣰⣿⠟⠀⠀⠙⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡼⠃⠀⠀⠀⠀⠛⠀⠈⠻⢦⣀⠀⣸⡿⠀⠙⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⡏⠀⠀⠀⡰⠚⠛⢦⠀⠀⠀⠀⠙⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣦⡀⠀⠀⠀⣰⢶⣶⣶⡄⠀⠀⣾⣷⣿⣿⣿⣿⡿⠇⠀⢀⣀⣀⣠⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣈⣻⣶⣾⣿⣿⠿⠿⣏⠀⠀⠀⠉⠙⢿⣿⣿⡿⡿⢿⠿⠿⠟⠛⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠤⠶⠛⠛⠃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⣿⣷⡄⠀⢀⣿⣿⣿⠁⠀⠀⢀⣠⡤⡖⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⢧⠀⠠⢾⣿⣿⢻⣿⡀⠸⣿⣿⡿⠀⠀⠈⠉⠉⠀⠀⣀⡀⠀⠀⢰⣧⡴⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠀⠈⢀⣠⣾⣿⠿⠋⠿⠃⠀⢻⣿⣇⠀⠀⠀⠀⠰⠾⠿⠋⢀⣠⣴⡾⠃⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣷⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⢠⣀⠀⢀⣠⣿⡟⠋⠀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣦⠀⠀⠀⢀⡞⠀⠀⣿⡀⠀⣸⢿⣿⣿⠿⢻⡀⠀⠚⠉⠩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⢀⣿⡄⠀⠀⠸⡇⠀⠀⣿⠃⠀⠘⢾⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠳⣄⡈⢷⡀⠀⠙⠛⠛⠁⠀⣢⠆⠀⠀⢸⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣷⣽⣤⠀⠀⠀⠀⠀⠀⠈⢧⡀⣷⣄⠀⠀⠀⠤⠴⣿⣶⡶⠆⠘⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⡌⠙⠳⠶⠦⣤⣤⣀⠀⠀⠈⠛⢻⣿⣿⣷⣦⡀⠀⠈⠉⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⣦⣄⡀⠈⠛⠿⡿⠀⠀⠀⠉⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣷⣤⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠋⠉⠛⠿⠛⠛⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⡟⠁⠀⢀⣀⠀⠀⠀⠀⢀⣕⣦⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠙⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⢠⡈⢹⠀⠀⢰⣬⠇⢸⡇
⠀⠀⠀⠀⠀⢀⠴⢄⠀⠉⠀⢻⡄⠀⠀⠀⠁⠈⠀⠀⢀⠀⠀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠛⠦⣄⣀⠠⠤⡖⠁⠀⢀⠈⠻⡠⠄⠀⠀⠈⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⣰⠀⠀⠀⢈⡧⠀⠀⠀⠀⢀⡀⢀⣆⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠊⠁⠀⢀⠀⠀⠀⢀⣄⠀⠀⠉⠁⣠⣦⠀⠀⠀⠀⠀⠙⠿⣶⣾
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⠴⠫⣅⠙⠯⢍⣁⡀⠑⠒⠂⠈⠉⢫⠀⢀⡀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠖⠣⡀⠀⠈⢧⠀⠀⠀⠉⠒⠖⠒⠙⢆⠀⠳⠀⠁⠀⠀⠀⠀⢀⠤⡁
⠀⠀⠀⠘⠃⠀⢀⡞⠁⠀⠀⠡⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢀⡀
⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠸⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⣠⡿⠰⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢠⠟⠓⢦⣄⠀⠀⠀⠀⢀⣦⣠⠆⣼⡟⠀⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡠⠋⠀⠀⠐⠊⠙⢦⣀⢀⣾⠉⠳⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠁⠀⠠⠋⠙⠄⠀⠀⠈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣀⣀⠄⠂⣔⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠿⠟⢆⠀⠀⢀⠟⠛⡇⢠⡄⣿⣟⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⣀⢙⢦⣄⢀⡀⠈⠁⠊⣻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⣤⡀⠀⠀⠀⢀⠚⠋⠀⠀⢀⠌⠛⠛⠲⣄⠚⠻⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⢶⣄⠔⠁⠀⠀⢠⠞⠁⠀⠈⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠂⠀⡀⠴⡀
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⡤⠊⢀⠔⠊⠁⡀⠈⠒⠤⣀⡀
⠐⠀⠀⠀⢀⡉⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⢲⠁⠀⠀⠀⠀⠑⠀⠀⠀⠈⠁⠢⣤⡤⠄
⡄⠀⠀⠀⠀⠈⠉⠒⠤⢈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠄
⠀⠀⠀⠀⠀⠀⠉⠀⠒⠠⠤⢀⣠⣯⣤⣠⡆⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠐⠌⠂⢄⡀⠄⠀⠀⡠⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠈⠀⢀⠎⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠐⠀⠒⠂⠀⠀⢲⠁⣀⣿⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠄⠊⢀⠠⠄⠒⠈⠁⠀⠁⠀⠀⣀⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢂⠀⡠⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠫⣠⠊
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡛⣽⢳⣴⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣗⡹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡿⠟⢯⣿⣿⣿⣿⣿⣿⣿⣧⠇⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣤⡴⣚⢻⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⢍⣜⢿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠇⣵⠀⢀⣿⠃⠈⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⠋⢀⣼⣿⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⡀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⢀⣴⡿⠋⠀⣰⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣴⠿⠋⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠈⠁⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣎⣀⣀⡸⡄
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠹⣆⠀⠿⠯⡉⠉⢣⣧
⠀⠀⠀⠀⠀⢠⠊⠀⠉⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢠⠊⢻⣄⠀⠤⠛⠀⠀⢀⠛⡍⠉⠉⡆
⠀⠀⠀⠀⠀⠮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⣀⣀⣀⣀⡀⠀⠐⢊⣥⣔⣃⠞⠒⠂⠉⠄⠀⠠⠐⢀⠜⠀⠈⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠐⠂⠒⠠⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⣄⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠖⠀⠀⠂⡠⢎⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⠠⠤⠤⠒⠀⠉⠁⢀⡠⠒⣆⢠⡘
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠒⠁⠀⣀⠠⠖⠂⠒⠂⠉⠉⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡠⠄⠊




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆
⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆
⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡀
⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⢀⣤⣾⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⣰⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣄⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣠⣴⣿⡿⠟⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣶⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⢿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢄⠀⠈⠓⢿⡦⢔⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠠⠤⠤⠀⠐⠒⠐⠒⠒⠒⠒⠛⠚⠢⢄⡀⣂⠌⠀⠀⠘⢣⢋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢗⡀⡠⠀⠀⠀⠀⠀⠀⠀⠐⡤⠄⣀⠀⠀⠀⠀⠀⡰⠙⡁⠀⠀⠀⠰⡀⢉⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⡔⠉⠀⠀⡠⠊⠉⠒⠒⠉⠀⠀⠰⣠⠐⠉⠒⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⣄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⡩⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁
⠀⢀⣀⠠⠤⠤⠤⠤⠤⠀⠀⠠⠤⠀⠀⠠⡄⠠⠤⠀⠒⠂⠀⠉⠐⠒⠂⠩⠁⠀⠀⠀⡰⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠂
⡎⠁⡠⠤⠄⠐⠒⠒⠒⠂⠀⠐⠄⠀⠀⣈⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢠⠀⠀⡠⠊⠀⠀⠀⠀⠀⣱⠄⠒⠈⢁⠔⢁⡠⠊
⠱⡀⠢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⡠⠚⢡⡄⠀⠐⡁⠔⠁
⠀⠸⠀⠇⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⣀⠔⠉⠀⠀⣞⣷⡠⠜
⠀⠘⣀⣑⡠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⡁⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠔⠉⠉⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⡠⠊⠀⠀⠀⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠔⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠤⢀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⠡⣀⢌⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣦⣤⣶⣿⣶⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣃⡈⠁⠛⠿⣿⡀⣥⠀⠠⡀⠀⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣠⣴⣼⠾⠁⠈⢿⣿⠗⣲⠲⢾⡇⢩⠂⠐⡃⠀⠀⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⣠⣤⣬⡾⠿⠏⡀⢀⢄⠀⣣⣼⡿⠓⠃⠈⢂⡀⢀⣽⠊⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠛⠉⠉⠠⢁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⡌⠳⢫⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠀⠀⣠⣿⣻⣿⣶⣤⡤⢀⣀⣤⣤⣶⢍⣐⣠⣿⡏⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢸⣠⣾⣿⣿⣿⡿⠟⠋⠀⠀⢉⡁⠀⠁⠛⠛⠛⠋⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠁⠀⠀⡴⢾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⣀⣀⣀⣠⡤⡤⠤⠊⠀⠀⢙⡿⠟⠁⠀⠀⠀⣀⣀⣤⡄⠀⠀⠘
⠀⠀⠲⠀⠀⠀⠀⠉⠀⠀⣤⣤⡖⠊⠀⠈⠉⠉⠁⠉⠀⠀⢀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠘⠂
⠀⠀⠀⠈⢆⢹⣦⣄⣀⣴⢿⣥⠖⠃⠙⠒⠒⠒⠒⠂⠐⠈
⠀⠀⠀⠀⢠⡯⣿⣿⢋⣴⠟⠁
⠀⠀⠀⢀⣎⣀⡿⠟⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣧⣤
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡋⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣿⣟⠿⠇
⠀⠀⠀⠀⢰⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣿⣿⣧
⠀⠀⠀⠀⢸⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠿⣯⡉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠻⣷⡶⠖⠚⠛⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠸⣧⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⣄⣾⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⠉⠉⠻⠿⠟⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣤
⠀⠀⢀⡿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⣾⣿⣿⣿⣿⣿⡻⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣏⠹⡀
⠀⠉⠛⠛⠀⠹⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⣿⠻⣿⠈⠃
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⣿⡿⠿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⣣⠀⠀⠀⠀⠀⠀⣀⡴⠇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⢴⡿⠋⠀⠀⠀⠀⢻⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢤⠀⠓⠲⠤⠀⢈⡀⠠⠄
⠁⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠐⠀⠙⣴⡀⠀⢶⠼⣇⣀⣀⡀⠰⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⡀⠄⠞⡩⢷⡂⠘⡆⢨⣀⡀⠙⠟⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⠂⠠⠐⠀⠈⡲⡷⣴⠼⡉⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢂⢀⠀⢀⡤⠒⠉⠉⠝⠢⠀⠀⠀⠀⠸⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠉⠂⠀⠊⠀⠀⠀⠀⡶⡀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠆⠴⠀⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠠⠊⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠋
⠀⠀⠀⢀⠀⠄⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠂⢄⠀⢀⣶⠋⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣬⣦⣄⣙⣿⣿⣿⣇⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⣠⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⢀⣀⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⢰⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢀⣠⣶⣶⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀
⠀⠀⣀⣤⣤⣄⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⢀⣾⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣴⣾⣿⡿⠋⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⣶⣶⣄
⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠠⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⠿⠋⠁⠀⠀⠙⠛⠛⠿⢿⡿⠿⠿⠟
⠀⠀⠈⠛⠛⠁⠉⢪⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠋⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣤⣤⣄⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⣤⣭⣭⣿⣿⣧⣶⠾⠶⢷⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣾⡟⠁⠀⢀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⢻⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣾⠋⢀⣾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣏⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣹⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠟⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⠋
⠀⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣀⡈⠙⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⡆⣠⣤⣀
⠈⠻⢦⣄⣀⣀⣀⠹⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠋⠀⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢀⡠⠤⣄⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⢠⠴⠒⠒⠂⠀⠀⢀⠌⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⣶⡈⠀⠀⠀⢀⡤⠀⡴⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⢚⡽⠋⢀⡞⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠋⠀⣠⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣴⡁⠘⠓⠤⢄⣠⣶⠶⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠲⠤⢄⢉⣿⡷⠒⢺⣯⣀⠤⠾⣦⣤⣤⡀⠀⠀⠀⡇⠀⠈
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⢀⣾⡿⠀⢠⣾⠟⣡⡶⠟⠋⠉⢉⣽⣆⠀⢸⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⢀⣿⠟⠈⠁⢀⣠⣴⣾⡿⠋⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣹⣧⣤⣶⠿⠿⠛⠋⠁⢀⣴⠃⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣉⣀⣀⣀⣀⣀⣤⣴⠶⠋⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠛⠛⠛⠛⠛⠉⢀⣀⡀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⡿⠶⠶⠒⠀⠀⣠⠞⢋⡴⡦
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣤⣤⣤⣤⣴⡇⠀⢠⠏⠀⠁⠀⠀⠔⠋⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠉⠙⠙⠋⠉⠀⣠⣀⠞⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣤⣤⠖⠐⢺⣿⢿⡏⠈⠆⠐⠁⠀⠀⠀⠘⡀⠀⠀⠀⢨
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠙⠇⡀⠀⢀⢀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⢧
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣾⡇⠀⠈⠟⢦⠀⠀⠀⠘⠀⠀⠀⠋⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⡇⠀⠀⣦⢾⡄⠀⠀⠀⠂⠀⠠⠂⡸
⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡁⠀⠈⢲⣤⣤⣨⣤⠴⠊
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠱⡀⠀⢸⣷⠀⡆
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⠀⠘⡇⠀⢻
⠀⠀⠀⠀⠃⠀⠀⡒⠚⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡇⠀⢷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣈⠥⠤⠐⢚⡛⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡇⠀⠸⡇⣸⢠⡄
⠀⠐⠊⢉⣁⣤⣤⣶⣶⣿⣿⣶⣤⣄⡉⠳⠆⠀⠀⠀⠀⠀⠀⠈⢷⠐⠖⠛⠳⠞⣉⠦⢒⡿
⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢆⠈⡵⠋⠉
⠀⠉⠀⠈⠙⠛⠉⠉⠀⠤⠀⠀⣒⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⠀⡇⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⢤⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠐⠁⠀⠀⢀⠄⣨⠁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡧⢁⠁⠀⠀⠀⠀⣈⠴⣶⠎⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠠⠁⠀⣠⣤⡾⠿⠕⠊⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⡤⠴⡂⠈⠀⠀⠀⠠⠐⠈⠄⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⢀⣤⡶⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⢭⡃⠀⠀⠉⠙⠒⠂⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠠⣸⢉⠋⠓⢂⢀⡀⠀⠀⠀⠀⠘⠛⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⢠⠁⠀⠐⣀⣠⣤⣀⠀⠀⢹⠉⢉⣩⢌⡤⠀⠀⠀⠀⠀⠀⠀⠈⡥⠱⡄⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠉⠥⠠⠀⠀⡀⢲⣶⠡⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠇⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠄⠀⢄⣲⣤⣄⡼⠗⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠛
⠀⠀⠔⠉⠀⡏⠀⠀⠀⠁⢶⣹⠆⠘⠁⠀⠀⠀⠀⠀⡁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⡄⠀⠄
⠀⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠋
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠁⠴⠀⠁
⠀⠀⠀⡤⣀
⠀⢀⣜⣿⡟⠁
⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢀⢠⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⣀
⠀⠀⠀⠀⣀⡀⠰⠖⠈⠘⠁⠀⠀⠀⠀⠀⠓⣰⡦⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⣀
⠀⢠⢖⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠊⠁⠀⠀⠀⠉⠢⠤⣤⡀⡎⠑⢄⠀⠀⠀⠀⠀⠀⠉⠐
⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡀⠈⠒⡄
⣎⡀⠀⢀⣀⣀⢀⣠⠔⠚⠈⠀⠈⠧⡄⠀⣠⠤⢤⡀⠸⡓⠒⠤⣀⠀⠀⠀⠀⢀⠧⠇⠰⡀⠘⠤⡀
⠀⠀⠀⠀⠈⢩⡀⢈⣆⡎⠉⠑⣄⠀⠣⡼⠱⠛⢀⠇⢰⠀⠀⠀⠀⠑⣄⢰⢀⢼⡒⠒⡴⢣⢠⡹⠁
⠀⠀⠀⠀⠀⠀⢹⠁⠀⢣⡀⠀⡸⠀⠠⡄⠀⢴⠭⡖⠁⠀⠀⠀⢀⡴⠛⣯⠁⠀⠱⡀⠑⠉⠉
⠀⠀⠀⠀⢀⠔⠚⠓⠒⠉⠈⠩⠁⠀⢀⡿⡀⠀⠉⢁⠔⠲⡈⢲⠉⠑⠊⠀⠑⠄⠀⠑⢦
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣀⠄⠀⠀⢀⡼⢾⣧⠀⠰⠁⠀⠀⠈⢦⠱⡀⠀⠀⠘⠷⠧⠗⠚
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠏⠠⠤⠒⠉⠀⢀⡟⢠⠃⠀⠀⠀⠀⠀⠱⡘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⡷⣲⠁⠀⠀⠀⠀⠐⢏⣋⣁⠀⠉⢊⣉⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡍⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢦⢤⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⡱⢂⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠏⠴⠇⠜⠠⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠄⢀⡠⠒⠠⠤⠠⠔⠒⠤⣀⣀⡶⠢⠤⣀⣀⠀⠀⣀⡖⠢⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⢀⣤⣸⠃⠐⠂⢻⠤⠀⠈⣴⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣹⣿⢿⡧⣷⣄⣰⣿⣤⣤⢤⣾⣄⠀⠀⠀⡄⠀⠀⠀⢀⣴⡄⢠⣤⣈
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠱⣿⢯⡾⣶⣿⣿⣿⣿⣿⣛⣟⡓⣿⣿⣏⠋⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠉⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠸⣦⣨⣿⣤⣦⣾⣶⣿⣿⣿⣿⣿⣿⣿⢿⣧⠶⣿⣿⣿⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣠⣤⣤⣤⣴⣦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠓⠋⠉⠙⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁⠉⠙⠻⣿⣿⣟⠛⠛⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈