Stick figure ascii Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⢠⣤⡄⠀⠀⢀⣠⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⢺⣷⣮⡛⠁
⠀⠀⠀⠀⠈⢛⣥⣶⡿⣋⣁⣿⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⢋⣄
⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠿⢿⡜⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣾⣭⣀⣀⣀
⠀⠀⢀⣾⣿⣿⣿⣅⣠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠈⣿⣿⣿⡋⠁
⠀⠀⡼⠃⢸⠏⠹⣯⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠿⢿⡿⠿⠶⠶⠤⠄
⠀⠀⠁⠀⠈⠀⠀⠘⠆



⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⣶⡄⠀⠀⠀⣈⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢀⣘⣋⣠⠔⠂
⠀⠀⠈⣩⣶⣶⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⠁
⠀⣠⠞⠛⠻⢿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⡟⣿⠸⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠘⠁⠇⠀⠙



⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣾⡧
⠀⠀⢠⠑⣄⣈⣻⣅⠀⣰⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣤⣴⣾⣶⣤⣄⡤
⠀⠀⠺⠛⣿⣿⣿⣿⣶⣿⡮⠕⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢘⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠘⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇
⠀⠀⠀⠀⣼⠏⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣿
⠀⠀⠀⣰⠋⠀⢸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠏⠀⣿⠆
⠀⠀⠀⠁⠀⠀⠈
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠉⠉⠉⠉⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⣿⣿⠿⠿⠿⠿⣆⡀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠿⠇⠀⠀⢸⣿⣥⣤⣤⣤⣤⠿⠃⠀⣿⡇⠀⠀⠀⠀⣽⣿⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠛⠛⠛⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣶⡆⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠿⠇⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⡤⣠⢤⡀⠀⠀⣄⣀⠀⠀⠀⠀⣤⣀⣀⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⢠⡀⠀⠀⣤⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠈⠢⣴⣷⡴⠋⠀⠀⣀⣴⣷⣤⡀⠀⠀⢹⣿⡟⠀⠀⠀⢹⣯⣄⡀⠀⠀⠘⣯⣿⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⢹⣦⡾⠁⠀⠀⢀⣤⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠙⢻⣿⡟⠁⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⣿⣿⠀⠀⠀⠉⢸⣿⡇⠉⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⢿⣿⡇
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⢸⡇⡇⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⡼⠿⠿⡄⠀⠀⠀⢸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠁


⠀⠀⠀⠀⠸⣦⣦⡞⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⢀⣀⡰⡷⣀⣀⠀⠀⠀⢀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢰⡖
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢴⣿⣿⣷⠄⠀⠀⠀⠀⠈⠉⢹⣿⡋⠉⠁⠀⠀⠈⠉⢹⣿⡏⠉⠀⠀⠀⠀⠀⣠⣼⣥⡀⠀⠀⠀⠀⢴⣿⣿⣳⠄
⠀⠀⠀⠀⢀⡿⠻⣄⠀⠀⠀⢠⣾⠚⠛⠛⠛⢻⣦⡄⠀⠀⠀⢀⡾⠻⣆⠀⠀⠀⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⢠⣬⣿⣿⣿⣯⣄⠀⠀⠀⢀⡟⠻⣇
⠀⠀⠀⠀⠚⠁⠀⠙⠂⠀⠀⠘⠛⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃


⠀⠀⠀⠀⢦⢀⣄⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣠⡄⣠⠀⠀⢠⡀⣀⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⣀⡀⡤⠀⠀⠀⣠⢠
⠀⠀⠀⠀⠈⣷⣥⣄⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⢠⣼⣴⠃⠀⠀⠀⢳⣽⣄⠀⠀⠀⠘⣯⣿⠁⠀⠀⣠⣭⡟⠁⠀⠀⠀⣽⣸⡀
⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠐⢋⣿⣿⡏⠃⠀⠀⢻⣿⣿⡟⠀⠀⠰⢻⣿⣿⠀⠀⠀⠀⢸⣿⣿⠳⠀⠀⢰⣿⣿⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⢹⠁⠀⠀⠀⠀⣿⢹⠁⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠈⡏⣿⠀⠀⠀⠀⢨⡏⡏⠀⠀⠀⠈⡏⣿⠀⠀⠀⢸⡏⡏⠀⠀⠀⢠⢟⡛⣆
⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠋⠙⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠈⠃⠃⠀⠀⠀⠀⠃⠉⠀⠀⠀⠈⠃⠃⠀⠀⠀⠋⠈⠉⠈⠃


⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⢀⡤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣄⢠⠄
⠀⠀⠀⠒⠒⣶⣶⡒⠒⠂⠀⠀⠀⠘⢧⡰⢆⡼⠃⠀⠀⠀⠀⠈⢷⣭⡞⠁⠀⠀⠀⠳⣤⣶⣶⣤⠃⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠈⣷⣷⠋
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠠⠤⠴⠿⠿⠦⠤⠄⠀⠀⠀⣰⠋⠉⠻⣄⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠒⠒⠛⠛⠳⠒⠒⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠿⠻⠿⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⡃⠀⠀⠀⠘⠛⢣⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢾⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢿⣿⠇⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠸⡿⠿⢿⠇⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠿⠗⣀⡀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠇⠀⠸⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢀⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⣿⣿⢀⡀⣀⡀⣀⣀⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⠿⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢀⣀⡀⠀⢀⣀⣀⣀⡸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢡⣤⡘⠛⢣⣤⡘⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣣⣤⡘⠛⠃⠀⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡅⠀⠀⠀⢸⣿⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠘⠛⢹⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⡇⠀⠀⠀⠀⠀⠈⠉⢹⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣿

⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⣠⡇⠀⠀⠈⣿⣁⠀⠀⠀⠘⣿⢤⡀⠀⢳⣧⠀⠀⠀⠀⢀⣸⠀⠀⠀⢰⣿⡆⠀⠀⢀⣼⣧⡀⠀⠀⣾⡷⣄⠀⠀⢠⣿⡞⠀⠀⠀⣬⡥⡄
⠀⠀⠀⣠⠃⠀⠀⠀⣿⡄⠀⠀⠰⢋⡟⠀⠁⠀⠈⣿⠀⠀⠀⠀⣠⠟⠀⠀⠀⠘⣿⡇⠀⠀⠀⢻⡏⠀⠀⠀⣹⠇⠀⠀⠀⠘⣿⡇⠀⠀⠀⢻⢳
⠀⠀⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⣀⡀⠀⠀⢄⣠⢀⡤⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠤⠀⠀⠀⠀⣆⣰⠀⠀⠠⡀⡤⣠⠄⠀⢠⢤⢠⡀⠀⠠⣄⣀⡀
⠀⢀⣠⡶⢷⡖⠀⠀⣿⡇⠀⠀⠈⣿⡟⠒⠂⠀⢸⡧⡂⠀⠀⠀⣾⠖⠁⠀⠈⠉⣿⡋⠁⠀⠀⣿⣿⠀⠀⠀⢘⣿⠁⠀⠀⠈⣿⡏⠀⠀⠰⢻⣷⠃
⠀⠉⠱⠃⠀⠙⠀⡜⠁⠙⠒⠀⠠⠃⠹⠀⠀⠀⠘⠋⠙⠀⠀⠀⠹⠃⠀⠀⠀⠰⠃⠇⠀⠀⠀⣿⣿⠀⠀⠀⠸⠉⠇⠀⠀⠀⠀⡇⠀⠀⠀⡞⠈⠇

⠀⠀⠺⣜⣀⠀⠀⢠⢶⣮⡁⠀⠤⣼⣧⠤⡀⠀⢠⣼⣄⠀⠀⠸⣤⣧⡀⠀⠀⢠⣯⡼⠀⠀⢀⣸⣧⡀⠀⣀⢤⣿⣠⠄⠀⠀⣼⡀⠀⠀⠀⢷⣆
⠀⠀⠀⡿⡿⠀⠀⢀⡟⢿⠁⠀⠀⠀⣿⠇⠀⠀⠘⡟⣎⠀⠀⠀⢸⣯⠀⠀⠀⢢⣿⠀⠀⠀⠈⡾⢿⠃⠀⠀⢸⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠃⠃⠀⠀⠘⠀⠘⠂⠀⠀⠀⠋⠀⠀⠀⠀⠃⠁⠀⠀⠀⠘⠛⠀⠀⠀⠘⠛⠀⠀⠀⠀⠉⠘⠀⠀⠀⠘⠋⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠛
⠀⠀⣤⠀⡀⠀⠀⠀⢠⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣠⠀⠀⠀⢀⡀⣀⢀⡄⠀⠀⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⠀⠀⠀⠀⡀⢀⡄
⠀⠀⢻⣯⣥⠀⠀⠰⢾⣏⠀⠀⠴⣼⣀⡤⠄⠀⠀⣹⡷⡀⠀⠐⠚⣯⠁⠀⠀⠙⣿⡏⠀⠀⢰⣿⠒⠄⠀⠀⠚⣿⡿⠀⠀⠉⣿⡏⠁⠀⠀⣭⣿⠇
⠀⠀⣸⠁⠈⠀⠀⠀⢸⠈⠇⠀⠸⡍⠛⠓⠆⠀⠜⠹⠀⠀⠀⠀⠏⠹⣄⠀⢠⠴⠋⠳⡄⠀⠸⣿⠀⠀⠀⠀⠔⢻⠁⠀⠀⠀⣿⡇⠀⠀⠈⠁⢸⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⡼⠀⠀⠐⣣⡖⠀⠀⠀⢀⣆⠀⠀⠀⣀⣰⣀⡀⠀⠠⣐⣂⣀⠀⠀⢰⣠⡄⠀⠀⠠⢒⡞⠂⠀⠀⡤⣴⣂⠀⠀⢠⣯⠗⠀⠀⢀⣀⣶⡼
⠀⠐⠒⢛⣷⠀⠀⠐⢉⡿⠀⠀⠀⢻⣿⡃⠀⠀⠀⣹⣇⠀⠀⠀⣸⣯⠀⠀⠀⣾⡟⠓⠃⠀⠀⣿⡉⠂⠀⠀⢠⡯⡄⠀⠀⠏⣿⢦⡀⠀⠀⠀⣿⡆
⠀⠀⠀⠏⠘⠆⠀⠀⠃⠳⠀⠀⠀⠋⠀⠃⠀⠀⠘⠁⠘⠀⠀⠀⠃⠈⠃⠀⠠⠃⠹⠀⠀⠀⠀⠇⠓⠀⠀⠰⠋⠀⠁⠀⠀⠀⠿⠀⠃⠀⠀⠀⢹⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠐⢀⡐⢄⠀⠀⠀⢀⣄⡀⣀⠄⠀⠀⠀⠀⠀⠠⠐⠢⡄⠀⠀⠀⠀⢀⠀⠀⠐⡄⠀⠀⢠⡠⠂⠈⠁⠀⠀⠀⠀⠀⣔⡀⢉⡐
⠘⠒⠙⠂⢠⠀⠀⠀⠈⠑⠉⠓⢰⠀⠀⠀⠀⠘⢤⠠⠵⢐⠀⠀⠀⠀⡇⣃⠘⠔⡀⠀⠀⠀⠁⠂⠤⠀⡴⠁⠀⠀⠀⠁⠁⠑⢁
⠀⠀⠀⠐⠉⠀⠀⠀⠈⢲⠀⠂⢉⡠⠀⠀⠀⠐⣠⠀⠀⢺⠀⠀⠀⠀⠁⢠⠀⠂⣗⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⡑⠒
⠀⠠⡀⠀⡔⠀⠀⠀⠀⠸⡀⠀⡈⠁⠀⠀⠀⠈⢠⠀⠀⡀⠀⠀⠀⠀⠀⢈⠀⢀⡉⠀⠀⠀⠀⠠⡀⢀⡄⠀⠀⠀⠀⠀⠄⣀⣠
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠔⠠⡀⠐⣀⠀⠀⠀⠀⠀⢠⠠⠀⠐⠀⠀⠀⠀⢀⠀⢴⡢⠀⠐⡀⠀⠀⠀⣠⠦⡀⠐⠄⠀⠀⠀⠠⠂⣤⡀⡀⠀⠄
⠀⠰⠀⢄⠐⢃⡄⠄⠀⠀⠀⠀⠀⠁⠘⠜⠄⠀⠀⠀⠀⠉⠀⠀⠏⣀⠃⠀⠀⠀⡀⡁⠁⠕⡄⠀⠀⠀⠒⠜⠁⠀⠜⢄
⠀⢀⠌⠈⢀⠋⠀⠀⠀⠀⠀⠓⡉⠀⢀⡙⠄⠀⠀⠀⠀⠀⠍⠀⢈⠁⠀⠀⠀⠀⡘⠁⠀⡸⡀⠀⠀⠀⢈⠦⠀⠂⠀⠀⢣⢀
⠂⠑⠄⣀⠂⠀⠀⠀⠀⠀⠘⠙⠠⣀⡜⡀⠀⠀⠀⠀⠊⠒⠄⣀⢂⠀⠀⠀⠈⠘⠀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠁⠁
⠀⠀⠀⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠁⠄⢀⠐⢢⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠡⡀⣌⢂⠀⠀⠀⠀⠀⠀⠡⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢅⠀⠀⠚⡠⠀⠀⢀⠋⠠⡠⠡⡀
⠀⠀⠀⢦⣀⠀⠀⡘⠀⠀⠀⠀⠄⢠⡤⣀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠑⡄⠀⠀⢀⠜⠁⠀⠸⠀⠀⠀⠘⠑⠂⠀⠰⠉⠢
⠀⠀⠘⠈⠁⠈⠉⠁⠉⠀⠀⠀⡀⡠⠀⠀⡈⠀⠀⠀⠀⠤⡀⠀⠀⠀⣀⣈⠔⠀⠀⠒⠉⠀⣀⠊⠉⠀⠀⠀⠀⠀⠀⢸⠲⡀⣠
⠀⢀⠗⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠥⠦⠔⠀⠀⠀⠀⠠⠤⠤⠄⠢⠘⠉⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠀⡅⠀⠀⠀⠀⠀⠀⠖⠂⠐⡂⠁⠀⠀⠀⢲⣀⠹⠢⠠⠄⢀⠠⠂⠀⠀⠠⡅⡆⢄⠄⠀⠀⠀⠀⠀⡎⠆⢖⡂⡂
⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠐⠀⠄⠀⠀⠀⠉⠐⠁⠀⠰⠋⠀⠀⠀⡠⠒⠀⠀⠀⠰⠃⠂⠀⠀⡀⢄⣀⠀⠰⠃
⠀⠀⠀⠀⢆⢀⠈⠈⢡⠀⠀⠀⠀⠀⢓⢀⡘⢠⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠄⡃⠰⢠⠔
⠀⠀⠀⠀⢠⢠⡄⠲⡸⠀⠀⠀⠀⠀⠘⠦⢈⢤⠊⠀⠀⠀⠀⠀⡆⢠⠚⠀⠀⠀⠀⠀⠀⠀⡓⠀⠞⠀⠀⠀⠀⠀⠀⡑⠀⠸
⠀⠀⠀⠀⠀⢑⠒⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠄⠐⠠⠀⠀⠀⠀⠀⠁⠠⢀
⡐⢡⢤⠱⡄⠀⠀⠀⠀⢀⠂⠀⠠⢀⠀⠀⠀⢊⢤⠀⠚⡄⠀⠀⠀⠀⣤⢄⢠⠌⠂⠀⠀⠀⠻⠠⠒⠂⠱⡀⠀⠀⠎⡂⠰⠆⠁
⢓⠒⠁⣢⠊⠢⠀⠀⠀⠸⠈⠋⠈⣡⠀⠀⠀⠀⠁⢀⠠⢆⠀⠀⠀⢄⠄⠀⠀⠁⣦⠀⠀⠲⢄⡤⠀⠐⡓⠇⠀⠀⠂⣀⠀⢠⡇
⠀⠑⠂⡧⡀⠀⣰⠀⠀⠀⠀⠷⡀⠁⠀⠀⠀⠠⠃⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠰⠔⠊
⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⢢⠠⠤⠀⠀⠀⠀⠐⠀⠔⠀⠀⠀⠀⠀⠀⢱⠀⡴⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⠙⠂⡔
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣶⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⣾⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⣶⡟⠛⠀⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶
⠀⠀⠀⣿⡇⠀⠀⠀⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠿⣧⣤⣤⠀⠐⣿⡏⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣶⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣶⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣼⣿⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠈⠻⠿
⠀⠀⠀⠀⠀⠀⣤⣤⠿⠿⠀⢸⣿⡿⠿⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣸⡷
⠀⠀⢀⣀⣶⣶⠛⠋⠀⠀⠀⢸⣿⡇⠀⠘⠛⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣤⡞⠃
⠀⠀⢸⣿⠉⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠸⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⣿⡷⠿⠁
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⣷⣦⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⡏
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⠋⠉⠀⠘⠛⢳⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠶⠖⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⢸⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣒⣚⠚⢒⣪⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿⣿⡇⡔⠉⠉⠉⠉⠉⠉⠉⠉⠉⡭⠛⠉⠛⠭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠤⢀⣀⣀⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢓⠁⠀⠀⠀⠉⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡀⠀⢀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠘⠒⣶⠒⡒⢲⠒⡖⢲⠒⣖⢲⡇⡇⠀⠀⠀⠀⠀⠀⢀⠜⠁⢣⢨⣛⡁⡆⠈⠢⠀⠀⠀⠀⠀⣔⣖⡤⡾⣸
⠀⠀⠀⢱⠆⠲⠐⠆⠰⠀⠆⠰⡀⠇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢩⠉⡏⠀⠀⠀⡇⠀⣴⡎⠉⠹⠞⠉⠫⠏⠉⢳
⠀⠀⠀⠀⢯⡌⢥⠩⡌⢥⠨⡄⢡⡄⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣘⠀⡃⠀⠀⠀⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠘⡖⠐⠂⠒⠐⠂⠒⠐⡇⠣⣀⣀⣀⣀⣀⣀⣸⣤⣤⣤⣬⣶⣥⣤⣤⣤⣇⣠⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⢤⢤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⡤⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⡔⡲⡢⡤⠤⠤⠤⠤⠤⡤⣚⡸⡀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡇⠀⠀⣜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠮⣒⡣⠋⠉⠉⠉⠉⠉⢇⣣⣋⠇⠀⠀⠀⠰⣍⣉⣉⣉⣉⣉⣉⣉⠇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢿⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣄⠀⣤⣀⠀⠀⠀⢰⣿⣿⣿⣿⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣇⢿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⠋⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣦⣴⣤⡼⠿⠟⠛⠛⠀⠈⠛⠀⠀⠀⠀⠀⠐⠐⠀⠠⠄⢠⠀⠀⡠⠀⢀
⠀⠀⠀⠀⣾⣿⣸⣿⣉⠘⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠈⠛⣹⣿⣿⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⢀⣰⣦⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠙⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣷⣤⣀⠀⠀⠀⡙⠉⠉⠛⠻⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠒⢦⠀⣀⣠⣿⣀⣀⣀⡀⠀⢀⠤⠤⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢡⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠻⢿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⢼⣏⡀⠀⠀⠸⠻⠿⠿⢿⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣷⠺⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⣤⣀⡀
⣿⣿⣿⣿⣶⣶⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠋⠉⠀⠀⠈⠻⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⡏⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⡧⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣆⠈⠁⣀⣠⣤⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⠂⢰⣶⡄⠰⡄⠀⠀⠀⠀⣾⣿⠆
⢀⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⣻⣏⠀⠀⠀⠀⣀⣜⠛⠃⠀⠀⠀⣀⣼⣿⣧⡀⠀⠀⠛⠦⣬⣿⡤⠶⠃⠀⠀⠀⣶⡦⠁
⡾⣿⣿⡟⣇⠀⢀⡀⠀⠀⡞⣿⣿⢳⠀⠐⢿⣿⣿⠀⠀⠀⠀⢰⠇⣿⣿⡇⢹⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠰⣿⡇
⡇⣿⣿⡇⣿⠀⣸⣇⠀⢸⢀⣿⣿⠸⡇⠀⠈⢿⣿⣳⠆⠀⠀⠸⣦⣿⣿⣧⣼⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⠆
⠀⣿⣿⡇⠀⢸⣿⣯⠇⠀⣼⣿⣿⣧⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⣿⢸⣷⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⢀⣿
⠀⠿⠻⠇⠀⠀⠿⠿⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠿⠻⠇⠀⠀⠀⠀⠸⠇⠀⠿⠀⠀⠀⠀⠤⠬⠥⠤⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⡀⢀⣸⠛⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢸⡿⠿⠿⣶⣶⣴⣿⣿⣿⣤⡀
⠀⠀⣧⢸⣿⠳⠶⢶⣤⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠙⣷⡀⢸⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣿⢸⣿⣤⣭⣍⠉⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣾⣝⠿⠃⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⠒⠛⡏⣽⡏⠀⡇⠀⠀⠀⠀⠀⠀⣰⡿⣶⣤⣶⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠸⡿
⠀⠀⠋⠉⠉⠓⠛⠀⠀⠃⠀⠀⠀⠐⠿⠿⠿⠿⠿⠟⠛⠿⠶⠟⠀⠀⠀⠀⠀⣠⠖⢚⣻⠻⢦⡀⠀⠀⠀⣾⣿⡟⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠺⡿⠀⠀⡧⠀⠀⢰⣿⣿⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠸⣿⠗
⠀⠀⣴⣶⣤⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⣠⣽⣯⡴⣿⣿⣥⠞⠃⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣬⣛⠃⠀⠀⠀⠀⠰⣿⣷
⢠⡿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⢦⡀⢠⡴⣶⣿⡀⣀⡄⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⢠⡄
⢸⡇⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠙⠏⢀⣿⡏⠉⠉⠀⠀⠀⠀⢸⠏⠉⠉⢿⣽⣿⣿⣯⡿⠉⠉⢹⡇
⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣼⡏⠀⠀⠀⠀⠀⢾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⣀
⠀⠐⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢰⡟⠀⠀⠀⠀⠀⢀⣼⠟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠛⢻⡟
⣀⣈⣿⣿⣃⣚⣛⣛⣂⣀⣂⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣛⣋⣀⣀⣻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣀⣀⣿⣁⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠈⠀⠠⠔⠊⠁
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢵⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⡄⠀⠀⡆⠰⠀⢀⣀⠄⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢁⡀⠀⠧⣈⡀⠬⠃⠀⠂⠓⠘⠂⠑⠐⠠⣙⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠘⣄⡠⠀⠀⠀⠀⠀⡀⢆⠐⠀⠀⠀⡀⠀⡄⠀⢠⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠸⡀⠀⢸⠠⡄⢼⡀⠰⠤⣇⠀⡸⢠⠉⠁⠤⠀⠀⡄⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⡀⠀⢧⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⢦⣀⠀⠀⢸
⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠐⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠣⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡿⢿⣻⣛⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⠿⢿⣿⡿⠿⠿⢟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠠⠶⢤⡀⠀⢀⣀⣀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠓⠂⢻⠀⠤⠤⠀⢁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⠀⢀⠰⠆⠠⠀⠀⠀⡌⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⡂⠤⠈⡠⢊⠵⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠻⣷⡄⠀⠉⠀⢰⣡⢋⠊⣄⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⣿⢻⠀⢩⡛⠓⠒⢂⡿⢿⠾⢻⠟⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⡿⠟⠻⠿⠛⠋⢉⡆⢸⡏⢸⡀⠀⠑⣄⡠⠼⣷⡀⢠⠂⠀⣰⢿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠀⢧⠀⠀⠀⠀⠀⡼⠀⠈⠁⠀⡇⢀⡴⣿⣿⡄⢻⣿⡀⠀⠀⠈⢆⠀⠈⠉⠙⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣦⠀⢸⡀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢳⠈⣴⣿⣷⡀⢸⣿⣷⠀⠤⢂⡌⠱⡀⠀⠀⡔⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠧⡐⠦⣄⠀⡇⠀⣌⠉⠉⠉⠛⠃⠀⠀⢸⣴⣿⣿⣿⣇⣿⣿⣟⡃⢀⣾⠀⠀⠑⣄⠘⢀⣴⡇
⠀⠀⠀⠀⠀⠀⣴⠛⠧⣀⡀⠀⠈⢳⣷⡀⢿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠘⡆⠀⠀⠈⢲⡟⣹⣇
⠀⠀⠀⠀⠀⢰⡟⢆⠀⠀⠻⢯⡛⣯⣽⠇⠈⢻⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠘⢿⣿⣷⠀⠀⠑⠀⠄⠀⠀⢻⡁⠈
⠀⠀⠀⠀⢀⣿⠇⠈⠑⠢⠤⠤⣙⣰⣿⠀⠀⣸⡿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠘⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⡳⢬⡳⡀
⠀⠀⠀⡠⣫⠵⣚⣛⡛⠛⠟⠞⣿⣿⣿⠀⠀⣿⠁⠹⡄⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠈⢿⣿⣿⢧⡀⠀⠀⠀⠀⢱⠈⠇⣷
⠀⠀⢸⣿⡿⠏⠁⠘⠙⠳⣄⣴⣿⣷⡛⡀⢰⡏⠀⠀⠱⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢈⣿⣘⣧⡙⠂⠀⠀⠀⠀⢇⢀⡏⣠
⠀⠀⢸⠉⡜⠀⢀⡤⠆⠀⠈⡙⢿⡿⠛⢥⢾⢧⡀⠀⠀⠹⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣾⣿⣟⠉⢿⣤⡀⠀⠀⠀⠈⠚⣴⠃
⠿⠿⠿⣦⣀⣴⠋⠀⡠⠔⣫⣾⡏⠐⠦⡀⠓⢟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⢾⣯⣛⣷⣄⢀⣠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠙⠿⠷⣶⣦⣼⣄⣏⣻⡅⡙⠶⢁⠐⠠⠜⣿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣈⡹⠿⠆⠉⠳⣝⣃⡀⠈⠗⠒⠙⠇⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⡀⣀⡤⣤⣀⠠⠴⠶⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠶⠖⠁⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⢀⢀⣀⠤⠴⠞⠓⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡷⠀⣀⣀⠀⠛⡤⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣩⣿⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣒⣊⡡⠞⠋⢩⣰⠞⠁⣠⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡦⠀⠀⠐⣤⡷⠀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢧⣀⣀⣀⣀⡀⠀⢠⠀⢸⡕
⠀⠀⠀⠀⠀⠐⠺⢄⡗⠀⠀⠀⠐⢿⣤⣠⢤⡔⠋⢩⣭⡿⣄⡐⡀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣀⡀⠙⣻⠃⠀⡜⡇⠀⢹⡄
⠀⠀⠀⠀⠀⡇⠠⡞⠷⢶⡀⡆⢱⣤⠼⠟⣼⣁⠀⠉⢁⠥⣍⠀⢰⠀⠀⠀⠀⠀⠀⢠⡟⠉⢰⠃⠀⡞⡀⢠⡁⢁⡀⠘⣣
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣯⡀⠀⠈⠉⠉⣀⣀⣼⠖⠟⠀⠈⡆⠀⠀⠀⠀⢀⡼⠀⢀⣟⠓⢒⣆⡄⠘⢺⠘⢂⣄⣇⠄
⠀⠀⠀⠀⠀⠥⠤⠤⠤⠤⠜⠉⠋⠉⠀⠀⠚⠋⢿⠁⠀⠀⠀⠤⠤⠄⠀⠀⠀⢶⣯⡀⠀⠐⣗⠐⠐⣗⡇⠂⢢⠐⠀⣼⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢄
⠀⠀⠀⠀⠀⠀⡴⠊⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⢯⡀⠀⣸⠃⣀⣤⠤⠄⠀⠀⠀⠠⠚⠹⡀⠀⠀⢠⠖⠲⣄
⠀⠀⠠⠤⡄⠀⠻⣄⣠⠜⢁⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠲⠭⠿⠓⠉⡁⠀⠀⠀⠀⠀⠀⠀⢤⣀⠱⠀⠀⣾⠁⢀⡼
⠀⠀⠀⠀⠿⠳⣄⣼⠷⣴⡅⠀⡙⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠈⠉⠙⠒⢲⠿⡍⠉
⠀⠀⠀⠀⠀⠀⠛⠹⣇⣤⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢡
⠀⠀⠀⠀⠀⠀⢠⡀⢭⣯⡽⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠂⢤⣀⣤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠸⡇⠘⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⣹⡄
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⣆⠀⠈⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣧⣀⡤⠏⠀⢦⠀⠀⠀⠀⠀⠀⢀⡀⢻⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣙⣤⡴⠃⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⢂⣤⢀⣬⠀⠀⠀⠀⠀⢀⡒⠭⣀⡿⠋⠁⠀⠀⠀⠀⣴⣾⣯⣉⡏⠑⢄⣠⣠⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣼⠈⠷⠋⠁⠈⠁⠀⠀⠀⠀⠀⣘⡦⢅⣾⠇⠀⠀⠀⠀⠀⠀⣹⡃⠈⢙⣳⡶⠌⠁⠀⠓⠦⣶⣧⡀
⠀⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣤⣼⢻⡀⠀⠀⠀⠀⠀⠛⠋⠁⠸⣿⠁⠀⠀⣀⣠⠔⢫⣽⣏⣛⣶⣄
⠀⠀⠀⠀⠀⡼⠁⠉⠓⠦⣤⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠘⠛⠁⠀⢠⡽⠻⣭⣿⣟⣁
⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠐⠠⠐⠛⠟⠚⠛⠉⠩⠿⠃
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢰⡏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⢹⡆
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢰⣱⠀⠀⢀⠤⠒⠉⢹⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢸⣹⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢸⣹⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠸⠼⢿⠀⠀⠀⢀⡰⡞⠀⠀⠀⠀⠀⢸⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠘⣄⡠⠖⠁⡰⠁⠀⠀⠀⠀⢀⡜⠀⡔⠒⠚⡦⡀⠀⠀⣀⠴⠦⡀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠈⠢⣀⢠⠃⠀⠀⠀⢀⡠⠊⠀⠀⣧⠀⠠⡇⣈⣖⣉⡖⠒⠒⡎⠲⣄⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋⠁⠀⠀⠀⠀⣧⠤⢤⡇⡄⠀⢼⡗⠒⠒⡇⠤⠬⢤⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⡇⠖⠒⢺⣟⠉⠉⡇⣗⣒⣺⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡇⡋⣉⣹⣏⢉⢉⡇⡒⡒⣺⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠁⠈⠉⠉⠀⠉⠉⠁⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠸⣇⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣸⠇

⠀⠀⠀⠀⠀⠀⢀⣀⠐⣦⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⡿⣣⡿⠀⢿⡰⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⢿⡿⣷
⠀⠀⠀⣀⢀⣴⣿⣿⡏⠀⠀⠀⢹⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣤⡤⣤⣄⡴⣿⣿⣿⠂
⠀⠀⠈⠉⠙⠁⣿⣿⡇⠀⠀⠀⢠⣿⣧⠈⠉⠉⠀⠀⠀⠀⠠⠶⠛⢹⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡈⠳⠦
⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣆⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠺⠿⠛⣿⡇⠀⠀⠀⠸⣿⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢨⣿⠀⠀⠀⠀⢸⣏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⠃⠀⠀⠀⠀⠀⠻⠸⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⠟⢷⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠶⣿⡆⢸⣿⡀⠸⣿⠇⢀⣹⠆
⠀⠀⠀⠀⠀⣠⢶⣿⣿⠳⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⣿⡿⠋⠉⠙⣿⣿⣿⠋⠁
⠀⠀⠀⠀⢠⡏⢠⣿⣿⠀⠀⠀⢹⣿⣿⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠈⣴⣿⣿⣿⡆⠀⠀⢸⣏⠙⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⣿⠏⠻⣦⡀
⠀⠀⠀⠀⠀⠈⠻⢾⡇⠀⠀⠀⢸⣿⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣿⠀⠀⠀⣿⡀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠀⠀⠀⠻⠇⠉⠁

⣿⡫⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






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

⠀⠀⠀⠀⠘⣿⡄⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣴⡟
⠀⠀⠀⠀⠀⠈⢿⣎⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢃⣼⠟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣽⡷⠀⠀⢀⣴⡿⢹⣿⣿⣿⣿⠻⣷⡄⠀⠀⠘⣿⣼⣿⣿⣿⣧⣿⠃⠀⠀⢀⣴⠟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠀⣾⣿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠙⣿⡟⢻⡟⠃⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⠍⠀⠀⠀⠀⠀⠀⠈⢹⣿⠙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⡀⠀⢀⣤
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣛⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢸⣿⡿⢀⣾⠏
⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⣿⣿⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⣿⡄⢸⣿⡿⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠿⠿⠿⠿⠿⠷⠶⠶⠶⠆⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠻⠇




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠰⣖⣤⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⣾⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡵⢎⢾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠷⣿⡿⣯⣙⠗⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠙⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡿⢻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣣⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⣀⣤⣤⣾⠿⠛⠉⢀⣤⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠂⠀⠀⠀⠀⠀⢀⣠⣶⣶⣸⣰⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠻⣿⣿⡉⢹⣿⣇⣀⡀
⠀⠀⠀⠀⣠⣴⡄⡆⣰⣦⡀⠀⠀⠀⠀⣀⣤⣶⢨⡍⣁⠀⠀⠀⠀⠀⢸⣿⠟⢻⣿⣿⣿⣀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣌⣻⠿⠿⠿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⡿⢻⣿⣾⣾⣿⣷⣀⠀⠀⠀⣼⡿⠀⢸⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣼⣿⣦⣴⣿⠂
⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⠀⠀⣸⣿⠁⣾⣿⣿⡿⠈⠛⠿⠿⠗⠀⠈⠁⠀⢸⣿⣿⠁⠀⢸⣿⢠⣤⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⣾⡟⣼⣿⣿⣿⡇⣿⡇⠀⠈⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣷⣶⣿⣿⣷⣶⣿⢂⣀⣿⣿⣿⣿⠛⠉⠻⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠈⠀⣿⣿⢿⣿⡇⠈⠀⠀⠀⠀⢸⣿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⣀⣰⣿⣿⠋⠉⠻⣿⣿⣼⡿⣿⣿⣿⣷⣀⠀⣠⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⣸⣿⡏⠈⢿⣿⡄⠀⠀⠀⠀⠀⠰⣿⠟⠁⠀⠉⠻⣿⣷⣤⠀⢴⡿⡿⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣷⠀⠀⠀⠀⢠⣿⡟⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⡿⠿⣷⠆⠀⠀⢹⣿⡿⣿⣿⣿⢿⣿⡁⠈⠁
⣶⣶⣶⣶⣶⣿⣷⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣾⣿⣶⣶⣿⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣄⠀⠀⠀⠀⠙⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⣴⣦⠀⠀⢼⣿⢶⡆⠀⠀⠀⠀⠀⠀⠀⢻⣄⢾⣿⢆⣼⠿⣆⢰⣿⡦⣼⠇
⠀⠀⠀⠀⣠⣴⣿⣿⣿⠛⠛⠃⠘⠓⠶⣶⣷⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⠈⢷⣿⣾⠧
⠀⠀⠀⠀⢿⣄⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⡆⠀⠀⠀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⣠⣿⠋⣿⠀⠀⠀⠀⠀⠈⣿⢻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣷⠀⠀⠀⢹⡟⢿⡏
⠀⠀⠀⠀⠸⠟⠁⢸⡿⠀⠀⠀⠀⠀⠀⢿⡆⠙⠿⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠸⣿⠀⠀⠀⢸⡇⠘⣷



⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣠⣤⣤⡄⠀⠀⢠⣄⠀⠀⠀⣴⣦⠀⠀⣼⠇
⠀⠀⠀⠀⢀⣧⣿⣏⣀⢰⣶⣀⣠⣽⣯⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣼⣿⣥⣤⠴⠋⠙⠷⠶⣤⣽⣯⡴⠞⠋
⠀⠀⢀⣠⡾⠋⣿⣿⠉⠛⠙⠛⢹⣿⣿⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠈⠁⠀⣰⣿⣿⡀⠀⠀⠀⢸⣿⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢻⡿⣿⡇⠀⠀⢠⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠂⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⠄
⠀⠀⠀⠀⠀⢸⡏⣾⠃⠀⠀⠸⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉
⠀⠀⠀⠀⠀⠘⠉⠋⠀⠀⠀⠀⠙⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣗⣾⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡠⠄⠢⡄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠠⢀⠀⠀⢠⣰⠄⠠⠤⣄⠀⠀⠈⠀⠀⢴⡄⣤⠀⣀⠀⠀⠀⠐⠂⠚⠀⠀⢙⣄⡆⣀⠀⠀⠃⡰⢊⠍⠓⠛⠳⣼⣄⠈⢷
⠀⠀⡀⠀⠀⠄⢀⠀⠈⢳⠇⠀⠀⠀⠘⡆⠀⠀⠀⢢⡜⠉⠈⠙⢿⡄⠀⠀⠈⠐⠀⣠⠊⠀⠈⠹⡇⠀⡞⠉⡼⡏⠐⠀⠀⠀⢸⡿⣀⣸⠄⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠈⠀⠀⠸⣆⠀⠀⠀⢠⡇⠀⠀⠀⢸⡀⠁⠀⠁⢸⠃⠀⠈⠀⠀⠀⢿⠀⠀⡅⢀⡇⠀⠓⡇⠀⡹⢤⡀⠀⢀⡜⠀⠀⢧⡀⠀⠀⠉⠀⢀
⠀⠀⠀⡴⠊⣒⢦⣀⣀⣠⠏⠓⠀⢐⡉⠳⡄⠀⠀⡴⠓⠦⠀⠔⢻⠀⢀⣀⣀⣀⣊⡉⠙⠂⠐⠻⡄⠀⠈⢁⡞⠀⠀⠈⠀⠀⢻⢀⡤⠀⠀⣀⡀⠀⠀⠉
⠀⣤⣰⠇⣸⢈⡟⣹⣩⠏⠳⡄⠈⠉⣀⣦⣵⣾⣿⣲⣄⠀⠀⢀⠔⡵⠫⠏⠟⠙⣿⣌⢦⡀⡐⣦⠞⠉⠉⠳⣤⠄⣠⠀⡀⠀⡅⠻⣄⣤⠀⠳⣿⡀
⠀⠙⠦⠠⠏⢸⠉⠀⢀⡀⠀⡿⠀⠄⢰⣿⠇⠉⠁⠠⠘⡇⠀⠾⠸⡇⠀⠀⠀⠀⣽⢸⠈⠇⢈⡇⠀⠀⠠⠄⢹⠁⠻⠼⠿⢸⠀⠀⠀⠈⠙⣾⠁⠙⢦
⠀⠀⠀⠀⠀⠈⠳⣄⡁⢠⣼⡁⠀⠀⠘⣟⠀⠀⠀⠄⢀⡇⠀⠆⠀⠙⣢⠭⠤⢶⡁⠈⠀⠀⠀⢳⡀⠈⠂⢀⡞⠀⠀⣧⠀⠈⣳⣄⣠⣃⢰⡃⣤⠀⣸
⠀⠀⠀⠀⠀⢀⠔⡿⠀⠀⣧⠹⣄⠀⠀⠈⢳⣦⠤⣔⢻⣄⠀⠀⠀⡼⣽⠀⠀⢸⠻⡄⠀⠂⡴⡿⠩⡍⢪⠙⣯⠳⡀⢿⡠⠞⡟⠀⠀⣿⢧⡙⠉⠉⠁
⠀⠀⠀⠀⢠⠋⢠⡇⡀⠀⢹⡄⠸⡆⠀⢠⠎⢹⠈⠉⠘⡏⢧⠀⢰⢃⡇⠀⠀⢸⡇⢻⡀⢸⢡⡇⠀⠙⠊⠀⠸⡆⢙⡆⠀⣸⠁⠀⠀⢹⠀⠹⣄
⠀⠀⠀⠀⠘⠦⣼⠀⠉⠉⠒⣧⠐⠃⠀⡏⠀⢸⠀⠀⠀⢿⢸⡇⡟⢸⠁⠀⠀⠀⡇⠈⣇⠘⢾⣄⣠⣤⣀⠤⣀⡷⠊⠀⢠⠇⠀⠀⠀⠸⡏⠓⠘⠂
⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣼⣦⣤⣤⣿⣤⣼⣦⣤⣤⣾⣾⣴⣧⣿⣤⣤⣤⣤⣿⣤⣿⣤⣾⣤⣬⣤⣤⣤⣤⣿⣤⣤⣾⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣶⣾⣿⣾⣷⣿⣾⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⡰⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠡⡐⢌⠳⡀⣷⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢶⣿⡵⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠂⢌⣿⣠⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⠖⠋⠑⢦⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⢿⠘⠛⢻⢇⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⣸⣿⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⣀⣟⡟⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⡬⢧⣿⠾⠓⠁⠀⡠⠤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⣲⠆⠘⠁⠈⣭⣭⡇
⠀⠀⠀⠀⠀⠀⠀⢾⡰⢧⠐⢛⣦⠀⠀⠀⡇⢰⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⢹⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣻⠀⠀⠀⣷⢸⡄⠀⠀⠀⠀⠀⠰⠰⠀⠀⠚⠸⠂⠀⠀⠀⠀⠀⠀⠀⡟⠐⡏⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⣧⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢠⠀⡀⠀⢀⡀⡄⠀⠀⠀⠀⠈⠀⢰⠇⢸⠇⠀⠀⠀⣠⢞⡵⠒⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⣴⡇⠀⠀⠘⡇⢷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⡟⠀⣽⠀⠀⡴⢛⡵⠋⠀⠀⠀⠱⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢧⢸⡀⠀⠀⠀⠀⠒⠒⠀⠚⠀⠰⠀⠀⠀⠀⠀⠀⢸⡇⢨⡇⠀⠈⠓⣯⠰⡋⢶⠟⣱⠀⣸⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢄⠀⠀⠀⠀⢸⠈⣇⢀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠀⣼⠀⠀⠀⠀⠸⡄⠈⠠⠞⠁⢀⡏
⠀⠀⠀⠀⢀⡤⡶⠋⠀⠀⠀⢀⣤⣓⠂⠄⡀⠘⢦⢈⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⢀⣤⣤⣤⣤⣤⡤⠶⠃⠀⠀⠀⠀⠀⠙⠚⠉⠉⠉⠉⠁
⠀⠀⠀⠠⡏⠈⠂⠤⢤⣴⡶⢍⠫⠤⠴⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢻⡴⡿⠐⣲⡄
⠀⠀⠀⠀⠙⠶⣤⠤⠤⠴⠶⠾⣐⣶⡾⠟⠁⢀⣀⣀⣀⣀⣀⣀⣈⣷⣶⣖⣒⣒⣒⣿⣁⣀⣀⡠⢤⣤⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢠⠇⣦⠗⣆⠖⢠⢄⡴⡄⣠⠀⠀⠀⠀⠀⠀⠀⠊⠇⠫⠊⢆⠀⢀⡄⡐⡋⠀⠀⠉⠐⠠⣠⣄⡀
⠀⠀⠀⠀⠀⢠⡀⠠⠂⠀⠀⠀⠀⠀⠀⢠⡏⡜⠒⢋⢛⢖⢼⢸⣷⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠘⠂⠫⠘⣉⣡⣿⣣⣤⣴⣴⡿⠀⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣃⣀⣁⣴⣋⠁⠀⠀⢀⡞⠴⡳⠰⣋⠇⠈⢢⠀⠀⠘⢖⣾⣊⣀⡀⠀⠀⠩⠆⠠⠟⢋⣉⣃⠀⠉⠉⠉⠉⠉⠀⠀⠘⢣⡀⠐⠃
⠀⠀⠀⠀⢺⡭⣤⣤⣤⡤⠤⣿⠀⠀⠈⠓⠒⠲⠶⠶⠒⠒⢺⡄⠀⣴⡟⠤⠔⠒⠒⠒⠒⠒⠚⠻⠛⠋⠉⠃⠀⣀⣤⡤⠞⠏⠃⠀⠀⠀⠈⠻⣉
⠀⠀⠀⠀⠀⣣⡀⠀⠀⠐⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢭⠓⠈⡤⠀⣀⡜⣀⠀⠀⠀⠀⠀⠙⠫⡉
⠀⠀⠀⢰⠏⠁⠭⠖⣛⠻⠭⠆⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢃⣚⣨⢴⣺⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣷⣶⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣶⣶⡆⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣖⠀⢻⣿⠀⢰⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣆⠘⡇⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⣧⣰⣿⣿⣿⣿⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠈⢿⣿⣿⣟⣹⣿⣿⣿⠃⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⡇⠀⠀⠀⣀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢈⣽⣶⣀⣴⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣻⠿⣻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⠀⠀⣴⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠻⣿⡿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⣠⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠉⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣤⣿





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡃⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⡁⠛⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠒⠚⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣟⣻⣿⣿⣯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣝⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⣴⠋⠹⠇⠈⠛⢮⠽

⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠨⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣠⣀⣤
⠀⠀⠀⠲⠀⠁⠀⠀⠀⠈⡔⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⣤⡄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢣⠐⠠⠤⠄⠠⠰⡿⡿⢿⠿⡿⠿⠿⢿⡟⠀⠀⠀⠸⠳⣿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡂⠀⠀⠀⠁⠁⠉⡉⢉⢉⠩⠉⠉⢹⣇⠀⠀⠀⠀⠁⠁⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠠⠄⠤⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠀⠀⠀⠘⡧⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢖⠑⠛⣿⠀⠀⠀⣸⠀⠀⠀⣀⠀⢰⡏
⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣐⣾⠀⠀⠀⢸⡆⠀⠚⠺⢯⡿
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠠⠐⠃⠀⠉⠀⠀⠀⠀⠀⠉⠈⠉⠁⠁⠀⠀⠀⠀⠀⢚⡇
⠀⠀⠀⠀⠀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⡆⠈⠛⢿⠟⠡⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣇⠀⢹⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢺⣿⡆⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣷⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡆⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⣿⣿⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⣀⣀⣀⣀⣀⣀⣙⣛⣁⣀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠿⠿⠿⠿⠿⢷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣴⡿⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣷⣄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣴⡿⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⢀⣴⣿⠏⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⣴⣿⠛⠀⠀⠀⠀⣴⣾⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠙⢿⣦
⢿⣿⡁⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⣠⣿
⠀⠙⢿⣦⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣴⣾⠟⠁
⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣦⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⣿⡆⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢸⣿⠈⣿⡆⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⣿⡇⠀⢹⣿⡀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢸⣿⠁⠀⠀⣿⣇⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣤⣤⣤⣼⣿⡄

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⣴⣿⡿⡟⠃⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠍⠿⠿
⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⠛⢻⡇⠀⠀⠀⠀⠀⣀⣀⡀⣠⣤⣀
⠀⠀⠀⢠⣾⣿⣿⣿⣦⠤⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⢺⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠶⠿⠗⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣀⣀⣴⣶⣾⣿⡆
⠀⠀⠀⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠟⠈⠿⠿⠿⠋

⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠻⣄⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡤⢭⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⡏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⢳⣤⣾⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢹⣬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣽⣦⣴⣫⢤
⠀⠀⠀⠀⠀⣠⡾⠋⠻⣌⡲⠶⠊⠀⠀⠀⠀⠀⠀⠀⠠⣤⡘⠲⠖⣋⡾⠛⢿⣦⠀⠀⠀⠀⠀⠀⠐⢦⣄⡀⠀⠉⠻⣏⠀⠳⠂
⠀⠀⠀⠀⢠⣿⣧⣀⣀⣀⣉⡉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⠁⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⢶⣿⣦⡀
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠲⠚⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣍
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦
⠀⠀⠀⠀⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⡆⣠⡤⠀⠀⠀⠀⠀⢀⣄⠀⠀⣯⠀⢰⠋⠉⠙⡄⠀⠀⠀⠀⠀⠀⢠⡏⠁⠈⢳⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣴⣣⠏⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠙⣦⠸⣄⣀⡴⢃⣤⡀⠀⠀⠀⠀⠈⠳⣤⣤⣏⡴⠃⣤⣄⠀⣀
⠀⠠⣄⣀⠀⠀⣠⠴⠶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠈⣿⠷⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠥⠶⠊⣁⣤⡾⠉
⠀⠀⠈⠻⡟⠻⠃⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣴⠞⠉
⠀⠀⠀⠀⠙⠖⠛⠛⣛⣳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁
⠀⠀⠀⠀⠀⣦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⢿⠀⢰⠏⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⡀
⠀⠀⠀⠀⠀⠈⢧⣘⣦⣄⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⢀⣠⠇⠀⠀⠀⠀⠘⢷⢸⡁⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⣽⠷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⣼⣿⡿⠥⣄⠀⠀⠀⠀⠀⠈⠳⣿⣶⣞⣥⠴⠶⢤⡶
⠀⠀⠀⠀⠀⠀⢰⣟⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢦⣀⢸⡇⠀⠹⡄⠈⢷⠄⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠠⣧⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣶⣄⣀⣠⡴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠶⠶⠾⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣈⣇⠀⠀⣹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁

⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⡀⣀⣠⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣿⣟⣿⣷⣿⡇⠘⠓⠛⠛⠚⠐⢠⣺⣷⡄⡀⠀⠀⠀⠰⢆⣂⣂⠈⠀⢀⣀⣠⡶⠋⠀⠀⠠⣀⠀⠀⠀⠀⠳⢎⡸⠀⠀⠀⠀⠄
⠀⠀⠈⠛⠿⠟⢿⠋⠀⠀⠀⣠⠶⢄⠀⠀⠉⠉⠀⠀⠀⠲⢣⣞⠁⠈⢻⣛⣆⠛⠋⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠸⠟⠻⠇⠀⣠⡄
⠀⠀⠀⣠⣴⣤⣌⡀⠀⣀⡤⣷⣤⡾⠃⠀⡀⠀⢠⠀⠀⠀⢾⣿⡄⠀⠈⣿⡏⡇⣰⠆⣠⡦⠀⡴⡄⠀⠀⢠⡶⣦⢠⣶⣦⡸⣧⣸⣿⡀
⠀⠀⢰⠻⣿⣿⡿⠟⠋⠑⠀⡼⠁⡀⠐⡤⡾⣿⡯⠑⢏⠀⠘⢏⡁⣠⣤⣍⡠⠃⠋⠊⠁⠀⠐⣃⡀⢠⣦⠘⢷⡿⢻⣧⣴⣷⠘⠋⠹⣧
⠀⠀⡏⠀⠘⣯⣠⣄⣀⣀⣾⣇⠀⣧⠈⠳⢤⣮⣦⠴⠋⠀⠀⠀⠉⠙⠛⡉⣠⡄⢠⣠⣦⢠⣿⠛⣿⡌⣿⣤⣴⡆⠀⠻⢿⠿⠀⣀⡀⢀⡄
⠀⠀⢿⠀⢤⠁⠉⠻⢮⣿⣿⣿⡇⠈⠷⣶⣆⠀⠀⠀⢤⣰⠚⢣⣤⣄⣺⣧⣸⣷⢻⣿⣿⣎⣿⣦⣿⠇⠻⠿⠛⠋⠀⠀⢰⣾⣿⢿⡇⠈⠇
⠀⠀⠈⢷⣤⡀⠀⠀⠀⣈⡽⠟⠁⠀⠀⠉⠀⣀⣤⣴⡄⠈⣀⣿⡏⠙⠛⣿⡏⢿⡞⡿⠙⠟⠈⡉⠁⠀⠀⠀⣧⠀⠀⠀⣸⣷⣤⣄⣧⣀⡀
⠀⣤⣶⣾⣍⣛⣻⣿⡛⠉⢀⢤⡒⠄⣇⡀⠹⠛⣿⡏⢺⣿⣽⡜⢿⣶⣿⠻⠗⠈⠀⠀⠀⡀⠛⠁⠲⠄⠀⠤⠞⠀⠀⠘⣿⣷⣾⣿⣿⣿⠃
⠀⣿⣟⠛⠛⠛⠛⠛⢻⠃⡜⠀⠀⠀⠀⠂⢀⠀⢹⣿⡘⣿⣷⠶⠀⠉⢁⠀⠀⠀⢹⡀⠀⠸⡄⢠⠤⠒⠀⣀⣠⣤⣤⣀⠀⠙⢿⣿⣿⠃
⠀⣿⠿⡀⠀⠀⠀⢀⡏⠀⢷⠀⠀⠀⠀⢈⡆⠀⠀⠉⠀⣀⡀⠀⠀⢰⣬⣟⣲⠤⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣟⣿⣿⡟⠀⢠⡀⠙⠁
⠀⠻⣧⣇⣀⣀⣀⡼⠁⡀⠀⠑⠂⠔⠐⠀⢀⣠⠤⠒⠉⠙⣁⣀⣤⣼⣿⣿⡿⢿⣿⣶⡆⠀⡁⠀⠀⠈⠙⢿⣿⣿⣿⠀⠰⡏⠘⠳⠆⣀⡀
⠀⠀⠀⠉⠉⠉⠁⠀⢄⠀⠠⣀⡀⠰⠞⠛⢉⣀⣤⣶⣺⣿⣿⣿⣻⣿⣿⣾⣿⣿⡿⠃⠈⡥⠁⠀⠀⠀⢀⡀⠈⣵⡆⠀⣼⣿⣦⣦⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⡔⠀⠸⣃⣤⣶⣾⣿⣽⣿⠿⠿⠟⠛⠛⠛⠉⠹⣿⡿⠋⠀⠂⡠⠔⠉⡁⠀⢤⣿⣷⡄⢸⡆⠀⠻⠿⠛⠁⠐⣿⠂
⠀⠀⠀⠃⠁⡔⠀⠀⠉⠉⠀⠈⠛⣛⠋⠉⠉⠀⠀⠀⠀⠀⢈⣶⠃⠀⠀⠉⠈⠆⡆⠀⠀⣀⣀⢿⡿⠄⢉⣩⠥⠔⠧⢄⡀⠀⠀⠀⠬⡁
⠀⠀⠀⠂⠀⠀⠀⠀⠂⣤⡞⢉⣻⣅⣈⠑⣤⠢⠐⠀⠻⢷⣾⠋⠀⠀⠑⠈⠢⣠⠖⣆⠀⡇⠈⡎⠁⣰⠋⣠⣶⣶⣶⣦⣙⡄⠀⠠⣤⣄
⠀⠀⠀⠀⡀⠰⡆⠀⣾⣤⣾⣿⣽⠶⠶⠟⠾⠷⣉⡴⠠⠐⠀⠀⠀⣤⣦⣤⣤⡘⣦⣈⠛⣷⣤⠇⢰⡇⣬⣿⣿⣿⣿⣿⣿⣇⠀⢨⣷⣾
⠀⠀⣠⣾⣷⡀⠉⠘⡿⢋⠉⠀⢻⡀⠀⠀⢤⣤⢸⣷⡀⠐⡅⢰⣟⣛⣿⠻⡟⣿⣎⠙⢻⣿⣿⣆⠈⣧⠸⣿⣿⣿⣿⣿⠏⢹⡀⠘⠿⠟⠂
⠀⠀⠛⣿⡟⠓⠀⢸⣿⡾⠆⢠⣾⣿⣷⣦⣄⣀⠞⠙⣿⡀⢇⢸⣿⣛⣿⣠⣇⣿⣿⠀⠘⣏⡕⡻⣷⣿⡦⠄⣉⣉⣉⡤⠒⠉⢿⡵⣦⡀
⠀⠀⠀⣿⡇⠀⢠⣿⠉⠓⢦⣾⣿⣿⢿⣿⠟⢅⠀⠀⢸⣧⢪⢸⣿⢙⠏⡿⡏⣿⣿⠀⠀⠙⣾⣱⣹⣿⢴⢒⣍⣩⣭⡍⡭⣽⠸⣿⣒⣳
⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠘⢯⣛⣛⠛⣋⡠⠆⠀⠀⣴⣛⢦⡀⣿⡞⡿⣷⣗⢿⣿⡆⢰⠄⠈⠛⠿⣿⡸⣙⠞⠙⢿⠇⢉⡼⠀⣿⣿⣾⡆
⠀⠀⢀⣿⡇⣴⠋⢿⣳⡄⠀⠀⢨⠏⠛⠂⢲⠀⠀⢸⣿⡦⡌⢷⢹⣷⣤⢿⡼⠼⣿⣧⠘⡄⠀⠀⠀⢸⣦⣄⣉⣘⣛⣋⣥⣴⣾⣿⡿⠙
⠀⠀⢸⣿⡇⢹⡀⡏⢿⡷⠀⠀⣸⣀⠀⠀⡇⠀⠀⠈⠛⠓⠘⠉⣿⣿⡆⣾⡿⠾⣿⣿⡙⡄⠀⠀⠀⠈⣿⠿⠿⢿⣿⣿⡿⢟⣹⡞⢷⣰
⠀⠀⣾⣹⣷⠀⠉⢡⣴⣶⠆⠀⠀⢸⠁⠀⢉⠇⢀⣀⣾⣀⡀⠀⣾⡿⣻⢻⡟⢿⢻⣿⡧⡇⠀⠀⠀⢀⣿⣭⣭⣭⣧⢸⣿⣿⣶⡷⣶⣄
⠀⢰⣿⣹⣿⣧⡀⢀⡏⠀⣾⠆⠠⠚⠚⣧⠎⠀⠀⢹⢿⡏⠁⠀⢻⣷⠹⢿⡇⣆⢘⣿⠇⡸⠀⠀⢰⣯⣛⣿⣿⣿⣿⠸⣿⣿⡿⠿⠿⢿⡆
⠀⠈⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠁⠀⠀⠈⠛⠿⠿⠿⠿⠿⠋⠀⠁⠀⠀⠘⠋⠋⠛⠛⠛⠉⠀⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠠⣶⠆⠀⠀⠀⠀⠀⢴⡶⠀⠀⠠⣄⡀⠀⢴⣶⠀⠀⠀⢻⣄⠀⣶⡦⠀⣰⠇⠀⠀⠀⣶⡦
⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⣴⣾⣿⣦⡀⠀⠈⠙⠛⣿⣿⣦⡀⠀⠀⠉⠙⣿⣿⠋⠁⠀⠀⣀⣴⣿⣿⣆
⠀⠀⣿⢸⣿⡇⣿⠀⠀⢸⡇⣿⣿⠈⠙⠓⠀⠀⠀⣿⣿⠘⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠀⣿⣿⢸⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢰⡏⢿⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⣿⡿

⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡴⣀⡀⢦⡀⠀⢠⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢀⣈⣿⣃⡀⠀⠀⠛⢦⣿⣯⡴⠋⠀⠈⠷⢤⣽⣿⣀⠀⠀⠀⠀⣈⣿⣃⠀⠀⠀⠀⠀⣹⣟⡀
⠀⠰⣏⣹⣿⣏⣹⠆⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣉⡷⠀⠀⢰⣿⣿⣿⡆⠀⠀⣠⡼⣿⣿⣷⣄⡀
⠀⠀⠈⣹⡿⣯⠁⠀⠀⠀⢠⡿⣿⡀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠁⠀⣿⣿⠁⠀⠁
⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢀⣿⢻⡄⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠋⠀⠙⠁⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠘⠛⠃

⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⢴⣶
⠀⠀⢀⣶⣿⣶⡄⢀⣀⣠⢶⣾⣷⢦⣀⣠⠀⠀⢰⣾⣿⣦⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⣴⣾⣷⣦⡀
⠀⠀⠙⢻⣿⡟⠋⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠰⠚⢹⣿⣿⠀⠀⠀⠞⠁⣿⣿⡆⠻⠆
⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⢸⡇⢿⠄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢠⡿⠹⣧⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢰⡟⢸⡇

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⠒⡖⣢⠨⣡⣶⡔⠦⠃⢀⠀⠂⠀⡤⠀⠒⠒⣂⣀⡐⠒⠒⠂
⠀⠀⠀⠀⣀⠤⣺⠁⢠⣤⣤⣤⣶⣶⣶⣾⠀⠀⣾⣦⣴⣿⣿⡧⠀⠨⢎⠌⠜⡼⠠⣖⡻⠷⣔⠃⡎⠀⠀⡀⢰⣷⠀⠁⢻⣿⡇⠀⠿⠿⠿⠿⠗⠐
⠀⠀⠀⠸⢐⠥⠚⡁⢸⣿⣿⣛⣟⣻⣿⣿⠀⠀⠙⢿⣿⣿⡟⠁⠀⣐⣠⣂⣊⣾⡀⠢⠄⠉⣹⡶⣄⠀⢀⠁⠸⠿⠀⢠⠘⠛⣁⣤⣤⣦⣤⣄⠀⠀⡀
⠀⠀⠀⡋⠤⢂⠥⡇⠈⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠄⠙⠉⠀⠀⣸⡿⠿⠿⠿⢿⣧⣀⠀⢀⡟⠃⠙⠆⠘⠀⢠⣶⣦⠸⠀⣼⣿⢟⣩⣍⡝⠻⣿⣄⠁
⠀⠀⠀⡇⠊⡡⠔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⣼⡟⠁⠀⢀⡀⠀⡉⢻⣧⠈⠁⠆⠀⠀⠀⠀⠈⠻⠋⠀⢸⣿⡇⣾⣿⣿⣿⣇⢹⣿
⠀⠀⠀⡇⣈⠔⣊⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠹⣿⣇⠀⠀⢘⡁⠉⠁⣸⡟⠀⠀⡃⠀⠀⠀⠀⠀⠀⢠⠀⠘⣿⣧⡹⠿⣿⠿⣣⣿⡟⡀
⠀⠀⠀⣋⡠⢊⠅⠘⠼⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⠀⠀⠙⢿⣷⣤⣨⣁⣠⣴⠟⠁⠀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠀⠀⠈⠻⢿⣷⣶⣿⠿⠋⠀⠂
⠀⠀⠀⠧⢈⣤⢊⣠⡀⠀⠀⠀⠀⠀⢀⢼⠀⠀⡒⠄⡁⠠⠐⠀⠀⠈⢻⡻⠻⠟⣿⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⣀⣀⣠⡄⣠⡠⠠⠤⠤⠤⠤⢠⠲
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠐⠊⠀⠀⠈⠢⣿⠤⠚⠀⠀⠀⠘⠒⠀⠒⠞⢀⡴⣤⠀⠘⠀⠠⡶⣦⠈⠓⠓⠚⠓⠒⠒⠂⠋⠂⠈⠈⠁
⠀⠀⠀⠋⠀⠀⠀⣀⠄⣆⣂⣖⡠⡀⠀⠀⠀⡌⠁⡀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠿⠂
⠀⠀⠀⠀⠀⠠⡎⢰⠊⠉⠙⢿⣿⣮⣢⠀⠈⠀⠁⠠⣿⡴⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣥⣥⣤⣤⡀⢱⡀⠀⡊⠁⠰⠈⠀⣧⢀
⠀⠀⠀⠀⣐⢃⡡⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⣠⣤⣿⢀⡀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⡉⠉⠙⠛⢻⣿⡇⢸⡇⠀⠀⡀⠀⠀⣰⠏
⠀⠀⠀⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢷⣆⠀⢸⣿⡇⢸⡇⠀⢀⠀⢠⡴⠃
⠀⠀⠀⢠⡁⣈⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠈⠛⠛⠁⠀⠀⢀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢀⠀⠀⣸⣿⠀⠻⠃
⠀⠀⠀⠀⡁⢌⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⢠⣄⣰⡆⢀⠀⣿⣿⠀⠀⠀⠀⠐⠘⢿⣷⣿⣽⣿⡛⠋⠀⠀⣿⡇⢨⡇⢸⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢅⠈⣭⣉⠛⢶⣄⠠⠐⠂⢩⣙⢻⣿⡄⠀⠈⢿⡿⠃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⡇⢠⡇⠸⠂⠀⣿⣼⠇
⠀⠀⠀⠘⠂⠁⠈⢿⣷⣄⠻⣧⠔⢠⣿⣿⡆⣿⣷⠀⠀⠀⠀⠀⠀⢄⠻⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣾⠿⠿⠿⢃⣸⠇⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣆⠻⣿⡄⢻⣇⣿⣿⣿⡇⣿⣿⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⠉⠁⠁⠈⠻⢿⣿⣿⣷⣾⣟⣃⣉⣀⣀⣉⣑⣒⡄⠀⠀⠸⠀⠰⠁
⠀⠀⠀⠀⣿⣿⣿⣿⡆⢹⣷⢸⣿⣿⡿⠏⣰⣿⡟⠀⠀⠠⠀⠀⢷⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠠⠀⠐⠀⠈
⠀⠀⠀⠀⠻⣿⣿⣿⡏⢨⣟⣿⣧⣤⣴⣾⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⣲⠄⣀⡲⠄⢠⠰⠤⠀⣀⣀⡀⠀⠀⠀⢀⠠⠐⣒⣒⣒⡀⠄⠁
⠀⠀⠀⠀⠄⠈⠛⠛⠴⠛⠋⠀⢀⠉⠁⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠘⠛⠀⠀⢹⣿⣷⠀⠁⠀⠓⣿⣿⠿⣿⣿⠿⢷⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢠⠂⠚⠀⠠⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠀⠀⠀⣿⡇⠀⣿⡏⠀⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠡⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⢹⣷⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠒⣴⣶⣶⢽⣿⢿⡍⠃⣉⣶⣶⣿⡙⠻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠀⢀⣿⠀⣸⣿⠀⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣼⣿⣽⡧⠧⣿⣿⣿⣿⡷⠀⠀⢐⢂⠀⠀⠀⠀⠀⠉⠉⠈⣈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣴⣾⣧⣀⣿⣧⣸⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⠙⠛⠛⡉⢩⣉⣠⡂⠙⠻⠿⠛⠁⢠⠀⠈⠀⠀⠀⡦⠠⠤⠀⠤⠤⠤⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠂⠂⠒⠒⠒⠓⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠄⠀⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒
⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡝⠀⠀⠀⢀⣤⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣿⡿⠿⢻⠿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠠⠄⠀⠁⠀⠠⠀⠀⣾⣿⡿⠿⠿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠙⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⢠⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠰⠃⠀⠀⠀⢀⠄⠀⠀⠀⠜
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠵⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⡂⠀⠀⠭⢖⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠅⠀⠀⡭⢵⡂⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣅⠀⠀⣈⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⣒⡫⠅⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣖⣚⠁⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠍⠀⠀⠭⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣁⠀⠀⠉⠑⠂⠀⠄
⠀⠀⠀⠂⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⣭⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⣘⢐⡂⡂⠐
⡀⠐⠀⡁⠐⠀⠐⠀⡁⠀⠀⠀⢰⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡒⠡⠀⠄⢈⣉⡁⡀⣂⢀⣀⢀⣀⣠⠨⠅⠄⠆⣐⢀⡀⡆⢀⣀⡀⣀⣄⢀⣀⣀
⠀⢀⠀⠀⠈⡁⢀⠀⠄⠄⡂⠭⠨⠐⠀⠠⠀⠀⠀⠀⠀⠀⠨⠀⠄⣒⢀⠀⡃⢒⠈⠈⠁⠛⠙⠁⠈⢤⣺⡥⡬⠅⠦⢽⠸⠇⠯⢿⣙⡆⣿⢿⣧⣼⣭
⠀⠠⠀⠂⠀⡀⢀⠀⠀⡀⠂⠅⠨⠀⢀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠅⠀⢐⠀⡂⠸⠨⠀⠃⠒⠀⠀⠀⠀⠙⠚⠃⠀⠉⠉⠠⠄⡭⣸⢻⡇⣿⣧⣌⣹⡿
⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠅⠁⠈⠨⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠅⠁⠨⠀⠅⠠⠘⠈⡇⠤⠂⠀⠐⠀⠐⠂⠀⡄⠛⢽⠠⡄⠛⠚⠻⠃⠛⠓⠞⠛⠓
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠄⣀⢘⠈⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠁⢠⠀⠁⠈⢀⠀⡀⠄⠀⠀⠀⠀⠀⠐⠂⡀⠂⣀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠁⡁⠂⣀⠐⢀⠈⠠⠀⠀⠀⠀⠀⠀⠐⠂⡀⠂⠀⠀⡀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⢀⠐⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡯⠈⠀⣾⣧⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠇⣨⡝⠂⣸⣿⡏⠀⠀⠀⢋⠁⢤⠤⠒⢂⣷
⠀⠀⠀⢀⡀⠀⠀⠐⠀⢠⠥⠄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠒⣞⠀⠈⡀⢠⣿⣿⠁⠤⢤⣄⡐⢠⢯⢐⣦⣍⡿
⠀⠀⠘⡄⠀⠀⠀⢀⣂⣀⣭⣵⣀⣿⡿⠟⠋⠁⣀⣀⣀⣀⠈⠉⠒⠋⠚⠛⠁⠀⠀⠀⠀⠫⠉⠭⠜⠛⠉
⠀⠀⠀⠙⠛⡛⢛⡻⠛⠉⠀⣹⠛⠛⢋⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⢠⠉⣐⢎⠐⠁⠀⠀⠀⠀⡇⢠⣿⣿⣷⣶⣶⣶⣶⣦⣤⣬⣤⣤⡀⠀⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⢰
⠀⡼⠣⢍⡁⢱⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠟⠻⣧⣐⣲⣆⡼⣸
⡘⢠⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠛⣙⣤⣶⣿⣿⣿⢟⡠⠋⠔⠁
⠇⢸⡀⠀⠀⠀⠀⢀⣀⡀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢾⣟⠁⣿⣿⣿⣿⡟⠉
⠈⠀⢱⢤⡒⣈⣭⣤⠄⠀⢀⠗⠘⠛⢛⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿⢤⣤
⠀⡔⠁⠀⠚⠛⠋⣁⡤⠖⠉⠛⢶⣤⣤⣀⣈⣉⠉⠙⢌⠻⣿⣿⣿⣥⠖⣺⣿⣿⣿⢿⣫⣷⣿⣿⠀⣀⡀
⠀⠈⠒⠒⠒⠛⠛⠳⠤⠄⠀⣶⠻⠿⣒⣚⠛⠛⠛⠓⣚⣓⣍⠻⣿⣿⣷⠞⠛⣫⣵⣿⣿⣿⣿⣿⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣐⡒⠫⠉⠩⠉⣙⣓⠒⠓⠾⠛⠿⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠠⠬⠥⢉⣑⣒⠒⠂⠨⠥⠄⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠠⢍⣉⠑⠒⠒⠤⠬⣭⣉⣉⣉⠀⢻⣿⣿⣿⠟⠁⣀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣈⣉⠛⠓⠶⠤⣤⣄⣀⣀⠀⠀⠉⠁⠀⢸⣿⡿⢃⡴⠊⠑⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⡂⠭⢉⡓⠒⠦⠤⢤⣉⣉⡙⠛⠻⠶⠶⠾⠋⠠⡏⠑⢢⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣚⠁⠀⠀⠈⢉⠚⠂⠀⠨⠉⠐⠂⠀⠀⠉⣍⣩⢿⠒⠒⢂⡄⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣀⣀⡉⠒⠒⠀⠀⠀⣠⢮⢟⣰⢃⢞⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣤⣽⣷⣶⡖⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣶⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠀⣤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⡀⠀⠀⠀⠴⣇⣹⣆⡿⣥⠿⠶⠁⠃⢲⠀⠀⠀⠀⠀⠀⣀⢀⡄⠈⠤⣶⠀⠄⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇
⠀⠀⠀⢠⠁⠀⠀⠀⠈⠙⢉⣥⠈⠒⠀⠀⠀⠸⡆⠀⠀⠀⢈⠀⠀⠀⠀⠀⢠⠇⠄⢐⠀⠈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⢠⣴
⠀⠀⠀⠀⠂⠀⠀⠀⣀⠦⠈⢿⡃⠀⠀⠀⢈⠁⠌⠀⠀⠄⠙⠀⢁⠁⠀⠀⡾⠀⠀⠀⠌⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⠘⠁
⠀⠀⠀⢠⠐⠀⢉⡀⢻⡄⠩⠄⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢈⣀⣀⠀⠀⣼⠁⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠐⠁⠏⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠊⠀⢀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⠀⠠⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⠆
⠀⠀⢀⠀⠀⠠⡄⠀⡄⣄⠀⣤⡴⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⢔⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠀⠀⠀⠀⠀⢀⠐⠤⢠⠈⠀⣠⠋
⠀⠀⢸⠀⠀⠀⢳⠀⠄⣸⠀⠾⢀⡀⡿⢻⡆⠀⠀⠀⠀⠀⠬⠬⠿⠧⠳⠚⠒⠈⠉⠑⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⢄⡘⠆⠠⠀⢀⡴⠁
⠀⠀⠘⣧⠀⠀⠉⠀⠈⠁⠀⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠮⡤⠄⣠⠎
⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡴⠃
⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⢤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣠⢄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠈⠁⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠵⠄⠠⡾⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣄⠘⢂⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠠⡷⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡔⠂⣈⡊⢷⡀⠹⠦⠀⢈⡅⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡷⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠈⠂⠠
⠀⠀⠀⠀⠀⠀⢠⡀⠸⡏⠁⠰⡷⠶⠠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠱⠦⢀⣤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣤⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀⠈⠙⠿⠟⠀⢼⠘⣄⢸⣧
⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣤⣀⣀⣼⣿⣴⣿⡆⢀⡀⡇⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠂
⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠊⠁⠀⣀⡉⠛⢿⣷⠘⢿⣿⠈⠀⠊⠀⠀⡃⠀⢀⡀⣀⠀⠀⠀⠀⠀⠐
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢋⣴⠋⠀⠀⣼⣿⡯⢡⠀⠀⢹⣦⣸⣿⡄⠀⠀⠀⠰⠛⠛⣿⣿⣿⣁⠀⡀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖⡒⢀⣴⠞⠁⢰⠘⠀⡀⠻⠿⠛⠁⠀⠀⠘⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣷⡀⠄⠀⠀⠀⢀⣸⢆⡀
⠐⠠⠿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⠉⠀⠀⠀⢸⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣾⣿⣠⣀⣀⠀⠀⠀⠗⠙⣿⣿⣿⣿⣿⣏⣀⣤⣾⣿⣿⣿⣦⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡯⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡇⠈⠉⠁⠹⣆⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠣⣂⡀⢸⠳⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣸⡇⠀⠀⠀⠀⠘⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠿⠷⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⢮⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣼⠋⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣀⡀⠙
⠀⠀⠀⠀⠀⠒⠶⣶⣤⠤⢤⣤⣤⣶⣿⠆⣀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⣰⡇⣸⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣭⣭⣭⣤⣨⣛⣳⢦⣄⣤⣴⡍⢀⠤⠞⠋⠰⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⣩⠟⢠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠙⠛⠛⣋⡈⣩⣌⣁⢀⣀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣵⡆⠘⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣌⣛⠛⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⣦⡀⠀⠀⢸⣿⣿⣿⡿⠿⠛⢛⣉⣀⣨⣭⣭⣴⣶⣶⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⠈⠂⠀⠀⠀⠀⠀⠀⠠⠐⠁⣭⠟⠀⢀⠀⠀⠀⠀⠐⢻⣷⠀⣾⡿⣿⣿⣿⣤⣤⣤⣾⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠈⣷⠾⠄⠀⠀⠀⠀⠇⢀⡀⠐⠀⠀⠀⠀⠰⠂⠉⠀⠚⠓⠸⢫⣤⡛⡉⠁⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠁⠋⠀⠀⢀⠁⠀⠀⢀⡒⠮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢡⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⢾⣿⣿⡟⢭⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠂⢀⠀⠀⠀⠟⠲⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠞⠃⠿⢿⢦⠹⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢦⣴⣿⣷⣤⣬⠋⠐⢦⣶⠶⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢽⣷⡄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣀⡀⠼⠅⠀⠉⣦⠟⠓⠤⣺⣟⣻⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠐⡀⠸⣿⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠃⠈⠀⠀⠀⠀⠈⠉⣽⠿⠭⢤⣀⠀⠀⠀⠀⠤⣄⡰⠁⠀⠈⠀⣐⣤⣤⣴⣶⠷⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠵⣈⣁⣀⣈⠽⠋⠀⠁⠀⠠⠀⡀

⠀⠀⠀⣄⡀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⢹⣟⠁⠀⠀⠀⣠⣿⣄⠀⠀⢄⠀⠀⠀⠀⢨⣧⡀⠀⡠⣧⠴⠀⠀⣰⣦⠀⣨⡿⠀⢨⡧⠊
⠀⠀⠀⠀⡟⠙⠋⠁⠀⠉⣿⡈⠀⠀⢘⣷⡀⠀⠀⠘⣯⠁⠀⢠⣿⠀⠀⣼⠋⠆⠀⢻⡄⠀⠘⣇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⠉⠇⠀⠀⠟⠘⠉⠲⠀⠰⠿⠀⠀⠀⠟⠀⠀⠙⠆⠀⠀⠞⠻⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢤⡿⠖⠂⠀⠠⣼⣅⡀⠀⠀⢠⠄⠀⠀⢠⣾⣅⠀⠀⣺⣦⡒⠀⠐⠤⢴⣆⡀⠀⠀⣀⣠⡄
⠀⠀⠀⠸⡏⠓⠀⠀⠀⣿⡆⠀⠀⢈⣹⡷⠀⠀⠀⣿⠄⠀⠈⠁⢘⣧⠀⠀⣀⣼⣇⠀⠀⢸⢯⠉⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠋⠀⠀⠀⠘⠛⠖⠂⠀⠀⠛⠀⠀⠀⠀⠸⠁⠀⠀⠈⠁⠏⠀⠀⠏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⡀
⠀⠀⠀⣠⣴⡛⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠆⠀⠀⠀⣀⣠⡄⠀⠀⢸⡟⠁⠀⠀⠙⣿⣷
⠀⠀⠀⠀⣿⠈⠀⠀⢀⣿⠁⠀⠀⠿⣯⠙⠀⠀⢘⣧⠀⠀⠀⢸⢿⠇⠀⠀⠀⢸⣆⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠘⠙⠃⠀⠀⠘⠛⠀⠀⠀⠀⠛⠁⠀⠀⠚⠋⠀⠀⠀⠋⠘⠀⠀⠀⠀⠚⠛⠀⠀⠀⠚⠉

⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⢭⠋⠀⢀
⠀⡀⢄⠀⠠⠘⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠛⠀⠀⠐⠁⠀⠀⠀⡐⠉⠋⠁⠀⠀⠀⠀⠀⠠⠘⠢⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠱⢲
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠀⠰⠀⠄⠀⠀⠀⠀⠤⠠⠂⠀⠤⠠⠀⠀⠀⠀⠄⠠⠂⠀⠠⠀⠄⠀⠠⠀⠔⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠐⠀⠒⠀⠂⠂⠀⠀⠀⠀⢂⡁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠀⠒⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⡀⠠⠈
⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢈⠂⠆⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠠⠈⠂⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠐⠁⠃⠀⠈⠉⠂⠀⠀⠀⠀⠀⠋⠙⠃
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠸⠄
⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⢈⠀⠤⠐⡢⠄⠀⠐⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⡐⠀⠀⠐⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠠⠔⠁⣆⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⡨⢀⡀⠀⠀⢀⣀⢄⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡄⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠛⠉⣿⡏⠙⠻⢷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣠⡀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⣿⡇⠀⣴⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠀⡀⠀⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡗⠀⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⢸⣿⠀⠀⠘⠃⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⣿⡏⠛⠻⢿⣿⠀⣶⡆⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⣴⡿⠛⠿⠷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠁⠀⣀⣿⡇⠀⠀⢸⣿⠀⠻⠃⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠟⠀⢀⡀⠀⢀⣀⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣴⣶⠿⠛⣿⡃⠀⠀⢸⣿⠀⠀⢠⡄⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⢸⡇⠀⠸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⢀⣀⣿⡇⠀⠀⢸⣿⠀⠀⢸⡗⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡶⠿⠛⠛⣿⡇⠀⠀⢸⣿⠀⣀⡀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⢸⡇⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣠⣿⡇⠀⠀⠈⠁⠀⣿⡇⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠈⠁⠀⠈⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠛⠉⣿⣷⠿⠻⢷⣦⠀⠉⠀⠀⠀⣿⡇⠀⠈⠁⠀⢸⣿⠀⠀⢰⡆⠀⢰⣶⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣠⣴⣿⠃⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠿⠀⠀⠘⠃⠀⠘⠛⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠋⠉⢻⡇⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⠀⢠⡄⠀⢀⣾⠟⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣦⣀⣀⣠⣾⠏⠉⢉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⣿⠀⠸⠇⠀⠸⣿⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡏⢻⣿⠋⠁⠀⠀⢸⡟⠛⠛⠛⢻⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠙⠻⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣿⠇⢸⣿⠀⣤⣤⣤⣼⣷⣤⣤⣤⣼⣿⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢻⣦⣤⣀⠀⠀⠀⠀⢠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⠀⠈⠳⣄⠀⠀⢻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⢹⡷⢦⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠉⠉⠉⢷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣄⠀⠈⠙⠋⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⣧⣤⡟⠀⠀⠀⠀⢀⣸⣀⣀⣀⣸⣀⣀⣀⣸⣇⣀⣀⣸⣃⡀⠀⠀⠀⠀⠘⢷⣤⡿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⣻⠀⠀⠀⡇⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⡇⠀⠀⢼⡋⢙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠋⠀⠀⠀⠓⠒⠒⠒⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠃⠀⠀⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⣨⡷⠒⠒⠒⠒⠒⠒⠒⠲⣿⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡘⠃⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⣿⣀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣻⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⢿⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠸⠧⠤⢴⡏⢉⣷⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⣀⣀⣠⠞⠁⠀⠀⣾⠋⢹⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠟⠀⠀⠁⠀⠀⠀⠀⠘⠛⠛⠁⠀⠈⠳⣄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⣇⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⠶⠶⠶⣶⣶⠶⠶⣶⠶⠶⢶

⠀⠀⠀⠀⡧⡷⢗⢛⠡⡠⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠐⠂⠈⠁
⠀⠀⠀⠀⢱⠏⣛⣁⠬⠔⠒⠸⠀⢂⠠⠄⠀⠒⠈⠈
⠀⠀⠀⠀⢘⠉⠁⠤⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣻⡿⣿⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠠⣤⠠⠠⠀⠀⣿⣛⣷⡿⠫⣿⣿⣼⠀⠀⠀⠀⠐⠒⠓⠀⠐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⣰⡂⠀⠀⠀⣯⣭⣭⣤⣬⡍⢙⡙⠀⠀⠀⠀⢰⡂⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡤⡄⠀⡷⢶⡟⢻⣿⠖⣾⡿⠀⠀⠉⠁⠉⠉⠉⠉⠉⠁⠀⠀⢰⠆⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠉⠁⠀⠀⠀⠐⡆⠀⡀⠀⣿⣿⡟⠉⢹⣸⣿⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣃⠀⠁⠀⣿⣿⡇⠀⠸⣿⣿⣷⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⢅⡀⠀⠀⠋⠙⠛⠀⠀⠻⠿⠿⠲⠶⡤⠁⠍⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⡀⠀⠀⠀⠀⠀⠀⠏⠀⠙⠀⣐⣶⣸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠓⠆⠈⠰⠀⠀⠀⠨⠄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⢐⠀⠆⠀⠀⠀⠒⢌⢩⠉⠀⡇⡃⣀⣈⣈⣈⠀⠄⠀⠀⠀⢤⠀⠁⠀⠀⣀⠀⣱⢆⠀⠀⠀⠠⠀⠠
⠀⠀⠁⠐⡀⢨⢄⡅⠀⠈⠎⠉⠬⠵⠉⡇⡂⡀⢐⠨⡆⠀⠀⠀⠀⠘⠀⠀⠀⠘⠈⡈⠃⠨⠀⣀⣀⡰⠀⠀⠀⠀⠈⠁
⠐⠀⠐⠄⠌⠍⠠⠴⠶⠶⠖⠁⠀⠀⠀⡇⣀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠗⢋⠈⠂⢸⠉⠀⠀⡀⠈⠂
⠃⠀⠀⠐⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢒⢠⠉⠉⠘⣀⠀⠀⠁⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠠⡄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠏⠸⠀⠀⠀⠘⡄⣀⠀⠀⡒⠛⢳⠒
⠀⠀⠀⡇⠐⠒⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠴⠆⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⣴⣶⣶⡶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡶⢶⡄⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣾⠀⠙⠇⠀⣧⡴⣳⠄⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣤⣤⣤⣤⣿⠟⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⣉⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇⣠⠀⠀⠀⠀⠀⢰⡞⠋⠉⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣿⣟⣴⡞⠃⢀⡀⠸⣿⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⢟⣿⣿⣷⣞⢻⡿⣼⡟⣇⠀⠀⠀⠀⢹⡄⠀⠀⣀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠶⣤⡾⠛⠋⠉⢻⣿⣿⡟⠁⠈⠁⣿⠀⠀⠀⢀⣀⣷⠶⠛⠉⠙⣏⠻⢿⣿⣿⣶⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⡴⠿⠤⠤⠤⠶⢶⡟⠛⠛⠶⡶⣶⠿⠶⢶⡿⢻⡏⣿⠀⠀⠀⠀⢹⡆⠀⠁⠘⠏⢻⡿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢧⡻⣄⣠⠞⣁⡞⢡⡟⠀⠀⠀⣴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⠳⢼⣟⣛⣩⡴⠋⠀⠀⠀⣰⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢧⡀⠀⠀⠀⠀⠀⠀⠙⢯⣿⠀⠀⠀⣀⣰⡷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡟⠲⠶⠶⠦⠴⠶⢶⣿⡷⠛⣿⠉⢹⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠘⢦⣄⣙⠛⠛⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡇⠀⠀⠀⣻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠲⢦⣴⡶⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⡀⣀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⢠⣴⣄⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⠀⠀⠀⠀⣀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⣀⣤
⠀⠀⠀⣿⣧⣼⣿⣯⣶⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⢀⣼⣿⣷⠿⠃⠀⠀⠀⠹⣧⣤⣽⣯⣤⡀⠀⠀⠀⢠⣴⣿⣿⡿⠶⠿⠋⠁
⠀⠀⠀⠈⠀⣿⣿⠉⠉⠀⠀⠀⠀⣰⣿⣿⣷⣾⠃⠀⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣟⣀⡀
⠀⠀⠀⠀⠀⣿⣿⣷⣶⡄⠀⠀⠀⠙⣿⣿⠃⠁⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠇⠀⠀⠀⠀⢿⣿⠟⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣾⠟⠀⠀⠀⠀⠀⠙⢻⣷⣤⠀⠀⠀⠀⠀⢸⣿⠈⣿⡇⠀⠀⠀⠀⢼⣿⠋⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⢸⣿⠀⣿⠇⠀⠀⠀⠀⠘⣿⡆⣿⡇⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢁⠀⠀⠹⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⣠⡴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⢂⡀⢀⡅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠀⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡀⡉⢷⡄⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠡⢄⠘⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢀⠀⢀⠈⡀
⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⣤⡀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⡌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠆⠈⠀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈
⠀⠀⠀⠀⠀⠈⠂⡈⠀⣀⡑⠂⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⢇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠈⢄⠀⠀⢼⠁⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠈⠒⢀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢦⠤⠤⠤⠤⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡛⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠱⡈⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢽⠛⠒⠠⠄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠐⠚⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⡠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠒⠂⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⣁⡀
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠂⠀⠉⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⡣⢿⡄⣼⣿⡄⢸⡇⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⡀⢠⣾⣿⣿⠀⢸⣧⢸⣿⣿⢧⡄⣿⣷⣶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠀⣬⠉⣀⣻⣿⣿⣿⡿⣤⣷⣿⣯⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⣣⡄⠀⠈⢀⣸⣿⣿⣿⣿⠙⢻⣧⣿⣧⣿⢯
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠓⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠒⣀⣮⣿⣿⣿⣻⣿⣿⡘⣿⣯⡿⢿⣿⣿
⠀⠀⠀⠀⠈⣿⣤⡀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠤⡐⠻⠟⠉⠻⠆⢾⣿⣿⣿⣽⣿⡏⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣌⠉⠲⣶⣤⣤⣀⣀⡀⠹⣷⣤⠀⠀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠁⠀⠀⠘⠃⠀⢠⣤⡼⠃⠀⣨⣽⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⢿⡟⠳⣦⣤⣬⣤⣭⣬⣭⣽⣿⣿⠿⣶⣶⡦⠼⢦⣄⣀⣀⣀⣘⡃⠈⠁⠀⣠⣤⣀⡀⠈⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠘⢿⣶⣾⣾⣿⣿⣾⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢱⣿⣿⣿⡿⠿⣿⣿⣿⣀⣤⣤⣸⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⣿⣿⡁⡀⢠⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠆⠀⠞⠀⣤⣤⠀⢰⣿⣿⣧⡀⣁⠀⠙⠿⢀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣷⣿⣷⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠂⠀⠀⢠⡦⡀⣀⡀⠁⠀⠸⣿⣯⣷⣿⣯⡈⣹⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠺⠗⠀⠁⠇⠀⡰⠂⣶⠢⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⠿⣿⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠛⠋⠙⠉⠿⠷⠈⢿⡿⠿⠿⠆⣿⣵⣿⣿⣿⣟⣿⡟⣿⣙⣿
⣿⠿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠁⠈⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠁⠣⡈⠠⠤⠊⡰⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊⠀⠈⡆⢠⡀⠑⢄⠈⠀⠀⠉⡠⠊⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢎⠈⢄⠑⠀⠚⡠⠂⠸⠀⢸⠀⢀⡀⠀⡇⠀⡠⠀⡎⠀⠀⠁⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠁⠉⢀⠔⠁⠀⢸⠀⡀⢀⠀⡇⠸⡀⠣⣈⠒⠂⣁⠌⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⢸⠀⠀⠀⠸⣀⠇⠸⣀⡇⠀⠑⢂⠀⠉⠁⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠀⠠⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⢀⠤⠾⠿⠿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣄⣀
⠀⣠⣴⣾⠿⠋⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⣽⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷
⣿⠟⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠁⠀⡿⠟⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣋⣽⣿⣿⣿⡿⠟⢿⣷⣶⣤⣀
⣿⣿⣿⣿⣿⣾⠉⠉⠛⠻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢈⠍⢺⣿⡇⠀⢸⣿⠟⠉⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣠⣶
⣿⣿⣿⣿⣿⣿⣦⣤⣶⡾⠛⠃⣀⠖⢶⣄⠀⠀⠀⣤⠿⠟⠃⣰⣄⣀⣴⡾⠛⣁⠀⠛⠃⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣦⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣿⡿⠄⠀⢿⢿⡾⢛⣽⠟⢶⣴⠿⠀⠐⢋⣠⣍⣿⠏⢀⣼⠋⠑⠂⠀⢀⣬⣿⠶⢦⣤⣼⣿⠏⠁⢸⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡘⠁⡿⢣⣾⠿⠁⠰⠿⣶⠛⠋⢀⣄⣉⣿⠿⣿⣷⣾⣿⣿⡧⢠⣾⣿⣦⣄⣠⣿⣦⡾⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⣃⠀⠀⢠⣤⣉⣷⣶⣾⡿⣿⠷⣶⣤⣾⠋⠀⣉⡳⢾⠛⢍⣙⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣿⣷⣶⠎⣛⢉⣩⡿⠀⠀⠤⢱⡌⠛⠁⣧⣀⢨⣶⡿⣷⣶⣀⣻⣿⣷⣦⣤⣩⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣭⠤⣿⣦⣩⣶⣿⢤⠄⠀⣻⡀⠈⣥⣼⣿⣭⠟⠻⠟⢋⣿⣿⣿⣿⣿⣿⡿⢻⣷⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣽⠶⣿⣉⢛⣿⣿⡟⣯⣾⠿⣿⣿⣿⣽⣯⣀⣀⠀⠀⠀⢉⣿⣿⣦⣭⣿⣿⡟⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⡳⡝⠲⣶⣬⣽⠟⠁⣠⣵⣏⡃⠺⣦⠟⢈⣿⠉⣿⣿⣿⣴⣾⣿⣿⣿⣿⡿⢷⣼⣿⣷⣾
⣋⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡳⠏⣧⣉⣙⣷⣶⠿⠷⣶⣾⣿⣿⣤⣙⢛⣛⣶⣿⠟⣷⣿⣽⣿⣿⣿⠻⠖⣿⣿⣷⣿⡋⠘⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⢠⡶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠰⣦⣄⠀⢠⣴⣿⣿⣿⢶⡀⠴⠟⠁⠀⠠⣾⠇⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⢠⣿⣿⣿⣻⣿⠛⢿⡠⣤⣤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠘⣿⣿⣿⣿⣿⣛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠈⠻⢿⣿⡿⠟⠁⢶⣄⠀⠀⠀⣠⠞⠛⠻⣆⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠷⣄⠀⢠⡖⠀⠀⠀⠀⠀⠀⠉⢰⡆⠀⣿⡀⢀⣰⠏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣈⢉⣉⣡⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣙⣛⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠉⣩⠟⢷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢻⣴⠏⠀⠈⢷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⠀⠀⣼⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠚⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⣤⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿