Parisian Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠲⢶
⣄⡀⠀⠀⠀⠒⢿⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠈⠉⠠⡟
⣸⣧⠀⠀⠀⠀⢸⡇⠀⣿⢘⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢠⠀⠰⠟
⠛⠉⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣠⢄⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣶⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⣥⣌⠹⣿⣿⣿⣿⡇⡀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣾⣿⢿⠤⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⠆⠀⠱⡀⠰⡀⠴⠋⣠⣬⣥⡄⠘⢿⣿⣿⠀⣿⢆⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠤⠠⠤⠄⠀⠀⠀⠉⠙⠋⠙⠛⠓⠲⠦⢤⣥⣀⣁⠀⣼⣟⣧⣾⣛⡇⠀⠻⣯⣶⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⠀⠀⡀⣼
⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠉⠉⠉⢹⡿⢿⠯⠁⣾⣷⠈⢿⡟⣶⡖⣿⣿⠧⠾⠟⠀⠘⠓⠒⠟⠃⠀⠛⠚⠉⠉⠛
⠀⢺⡶⠆⠀⠀⢸⡗⠂⠀⢐⣿⣷⣷⣦⣤⣤⣌⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠐⠲⠶⣖⡐⠒⠒⠓⠀⣭⡉⠉⠉⠛⠉⣭
⣄⢀⡀⠄⢤⠄⢴⡦⡴⠶⡦⠉⠉⠉⠉⠉⠛⠻⠁⠀⠀⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⢹⡇⠀⠒⠂⠀⣿⡇⠀⠈⠛⠀⣿
⠀⠊⠁⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡄⠀⠀⠠⣿⡧⠄⠀⠀⠀⠿
⢠⣦⡀⠀⠀⢠⣾⣶⡄⠀⠀⠀⠀⢠⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀
⠈⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢰⣶⣶⣶⣶⡎⢻⣿⣿⣶⣶⣶⣶⡆⠀⠀⢻⡿⠂⠀⠀⠀⣿⡏⠀⠀⠀⠀⣿
⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡄⠀⠀⢰⣿⣿⣿⡿⣿⣶⣿⣯⡩⡇⠉⠙⠃⠀⢠⣼⣿⡆⠀⠀⢠⣿⣷⡄⠀⠀⠠⣿
⢀⣧⣤⠀⢠⣤⣴⣶⡄⠀⠀⠀⠀⢠⡄⠀⠀⢀⡁⠀⠀⢀⣿⣿⣿⣤⣿⣼⣿⣟⣿⣆⠀⢀⡀⠀⣀⡿⣛⢷⡀⠀⢘⠿⡟⢋⡀⠀⣈⣛
⠈⠉⠁⠀⠘⡉⠉⠁⠿⠀⠀⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⢸⡿⠿⠿⢛⣉⡉⠉⠋⠁⠀⠈⠉⠀⠀⠈⢱⣯⡈⠀⠀⠀⢲⣶⠀⠀⠀⠀⣶
⠀⣶⡄⠀⠀⠀⣶⡆⢀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠉⡀⠀⢸⡏⠁⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸
⢀⣿⣇⠀⠀⣀⣼⣷⡈⢀⠀⠀⠀⢸⡅⠀⠀⢀⡅⠀⠀⢘⣀⡀⠀⣸⣟⠛⠀⠀⠀⠐⠀⠀⠸⣿⣿⣾⠿⢷⣦⣇⡰⣿⠿⢧⡄⠾⣷⣿
⠛⠛⠋⠀⠀⠿⠏⠙⡇⠸⠃⠀⠀⠘⠃⠀⠀⠘⠟⠀⠀⢠⡀⠀⠀⢠⣤⣄⠀⠀⠀⠠⠀⠀⠀⠀⢷⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⠾⠖⠂
⢠⣤⡀⠀⠀⠸⣶⣾⠇⠀⠀⠀⠀⢠⡄⠀⠀⢠⡆⠀⠀⠀⡀⠀⠠⣼⣿⣿⡀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡿⠁⠘⠅⣴⣿⣿⠛⠁⢀⣀⣉
⣈⣿⣄⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣸⣃⣀⣀⣼⣇⣀⣀⣤⣧⣴⣶⣿⣿⣿⣿⣖⣒⣛⣃⣀⣀⣤⣀⣼⣿⣄⣀⣀⣿⣿⣿⣉⣉⣉⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠈⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠘⠻⠦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⠀⢠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⡄⠀⣀⠀⠀⣼⢁⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣽⡟⢻⣿⣿⣷⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⣾⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⢀⡀⣨⠻⣿⣾⣿⣿⣧⣤⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢰⡟⠠⢦⣽⣿⣿⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢘⣿⣭⣽⣿⣿⠇⠀⣿⣤⣤⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⡟⣿⣿⣿⣿⢀⣾⣷⣿⠀⠛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣾⣿⣿⡿⣿⣿⣿⣿⠟⣿⡆⣀⠉⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡞⠋⠉⡁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣯⠀⠀⠀⢱⣦⣤⢤⣶⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠏⠀⠀⠀⠀⠟⠛⢾⠇
⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡄⢀⡴⢸⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡿⣿⡀⠀⠀⢰⣿⢿⣽⣧⣾⣿⣠
⠀⠀⠀⠐⠊⠁⠉⠈⠉⠉⠛⠋⠛⠒⠒⠒⠒⠒⠀⠀⠀⠠⠤⠤⣤⠀⢀⠟⠀⠹⣇⠀⠀⠀⠹⢿⣿⣿⠿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⡦⠀⠀⠀⠀⠀⠀⠀⢐⣇⣈⣥⣁⣰⣿⠀⠀⠀⢰⣿⣿⢰⣆⣴
⠰⠷⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⣀⢀⠀⣠⣷⣄⠀⠀⠀⠀⢀⢀⢸⣿⣿⣿⣿⣿⣿⠀⣀⠀⢉⣿⣟⢶⣿⡧
⠀⠀⠀⠀⠀⣀⠀⠦⠀⠒⠀⣈⡿⢯⣿⣶⣿⣿⣿⣛⠀⠀⠀⠘⢛⡁⠙⠋⠉⠉⠛⢁⣀⠈⠓⡟⠁⠙⡘⣿⢿
⠀⠀⣠⠀⠄⠀⢆⠓⠲⣀⣉⣀⣤⣾⡿⣿⠿⣿⠿⡉⠀⠊⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⠃⢩⢷⡾⣿⠟⠛⢊
⠠⠀⠃⠒⠂⠐⠺⠿⣷⡿⢛⣻⡿⣦⢩⡁⢠⣭⡞⣛⠀⠄⠀⠐⢶⣦⠉⠟⣛⡋⠉⣴⣿⠦⣶⢶⣶⣶⢶⣛⣋
⠰⠤⠁⠸⠁⠀⢠⣤⣤⡴⠋⠍⠑⠂⠹⠀⠰⠿⢻⡦⠄⠀⠀⣀⠀⠀⢹⠻⣿⡿⡭⠀⠙⣶⡏⠀⡀⡆⠙⢹⠙
⢃⡘⠂⠙⢻⣿⡃⢈⡀⠀⠀⠀⠀⢲⣾⡗⠒⠒⠐⠂⠒⠀⢸⣿⣤⣤⣤⣶⠾⣿⣥⣤⣬⣿⣿⡿⠏⢷⣶⡟⠓
⠛⠛⠛⠛⠛⠛⣿⡯⠔⢊⣡⣴⣶⣿⣿⣷⣶⣶⣦⣶⣶⣶⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠁
⠀⢐⡻⣿⣿⣿⣿⣴⣿⡿⢿⣿⣿⣿⣿⣿⣻⣿⣛⣊⡙⣋⠉⠳⠂⠉⠉⠁⠀⠀⠉⠁⠲⠟⠃⠀⠀⢀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⠄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⢁⣼⡗⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠄⠑⠀⠀⠀⠀⠀⠀⢲⠿⠸⠇⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⢿⡿⠟⣑⠄⠀⠤⠀⠀⠀⠐⠦⢶⡴⠶⠶⠶⢶⠖⠒⠒⠤⢬⣅⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⢸⡄⡿⢶⣤⡄⠀⣀⣠⣀⠰⡿⣿⣿⣿⣿⣯⣤⣤⣤⣀⣀⣠⣬⣭⣛⣦⣀⢲⠀⠆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⣿⣿⠟⡛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣷⣾⣿⡇⠈⠛⠛⠃⠀⡆⣼⡇
⠀⠀⠀⠀⠀⠀⠖⡤⣤⣤⣴⣿⢧⠄⠀⣿⣿⣿⡟⢛⣿⣿⣷⣿⢿⣿⠀⢸⣿⣿⣽⣇⠀⠀⠀⠀⣠⠇⢿⡇
⠀⠀⠀⠀⠀⠀⣤⣶⣬⣿⣼⣿⢾⣶⠶⣿⣿⣷⣏⣘⣿⣿⣿⣿⣶⣄⣴⣿⣿⣿⣿⣿⣶⡄⣿⣦⣿⡆⠔⠃
⠀⠀⠀⠀⠀⠀⢿⡿⣿⠟⠛⠁⠀⣼⠀⣿⠿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡟⠻⣋⣫⠼⠴⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⣏⠃⠀⠀⠀⠀⠀⠘⠥⠤⣿⠘⠒⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠶⠶⠶⠶⠶⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⢀⣈⣄⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠨⠯⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⡜⠁⣦⣽⡄⠇⠀⡇⠀⠏⢰⣥⣦⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠁⠈⠁⠋⠉⠉⠉⠁⠉⠉⠁⠉⠈⠁
⠀⠀⠀⡇⠀⣿⣿⠀⠀⠀⡀⠀⠆⢸⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⢠⢁⠈⡌⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠬⠩⠅⠈
⠀⠀⠀⠇⠀⠿⢿⠇⠀⠠⠧⠀⠆⡸⠿⠿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠶⠲⣀⠖⠶⢦
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠡⠁⢍⣦
⠀⠀⢸⢹⠗⢠⠟⠃⠀⢀⡀⠀⠀⠚⢷⠀⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠦⠴⢾⠁⠀⠀⠀⠹⡷⠶⠴⠶⠶⠦⠄
⠀⠀⠀⢸⢸⣷⡾⡇⠀⠺⡿⠃⠀⡟⣷⣿⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⠶⠒⠺⠶⡇⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠤⢬⠭⠥⣥⣤⣄⠀⣤⣤⡤⠭⢭⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠉⠛⠃
⠀⠀⠀⠀⠀⠂⢶⡇⠀⠀⠀⠀⠀⣱⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠰⠀⡐⣀⠃⠂⢠⢀⡄⠀⢉⡐⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠉⠀⠁⠘⠈⠁⠀⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⣂⣀⡀⢀⢀⣒⣖⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠘⠧⠢⠮⠘⠛⠶⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⢲⠀⢰⠶⠖⠶⠶⠄⠘⡖⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡶⠈⠀⠀⠀⠀⠀⠀⠙⢆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣶⢤⠀⢀⠴⠊⠄⢉⠟⠠⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣰⣊⡄⠂⡴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⢠⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄⠟⠁⠀⠐⠒⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠄⠀⢀⠠⠌⠀⠀⠀⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡦⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⠄⠀⠀⢴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣇⡿⣟⡧⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀⠰⣤⠰⡦⣤⣠⡴
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠐⠦⣐⠀⢀⠀⣠⡀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠰⠷⠄⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠁⠐⠂⠤⡀⠀⠙⠲⢤⣠⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⡀⠁⠂⠠⠀⠀⠀⠐⠂
⠀⠀⠃⠠⠆⠄⠀⠀⡍⠁⠢⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠠⠶⠀⢸⠧
⠀⠀⠂⠀⡄⠀⠀⠀⠇⠀⠀⠀⠄⠀⡀⠈⠠⠆⠀⠀⠀⠀⠀⠀⠋⠙⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⠀⢐⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⢈⠭⡂⠀⠀⠀⠀⠐⢺⠲⠂⡠⠤⠤⠄⠀⢀⣴⣶⠀⢶⡉⠐⠛⠀⠚⠋⠑⠁⣗⠖⠀⠀⠀⠀⣀
⠀⠀⢰⡄⣶⣖⣶⣶⣓⣻⣤⣤⣤⣌⠉⠹⠏⠀⠀⠀⠀⠀⣀⠀⣷⣾⠀⡀⣩⠷⠄⠁⠀⠀⣄⡀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⢠⡀⡄⠀⠀⠀⢸⡀⠀⠀⡖⠠⢰⠒⠒⠀⠀⢠⠀⠀⠿⡀⢻⣿⠀⠈⠓⠂⠀⠀⠀⠀⠉⡿⠉⢙⣦⣤⠀⠈⠐
⠀⠀⠀⠀⠀⠠⣤⠤⡄⡁⡄⠐⠇⠍⠛⠠⠐⠒⠊⠦⠀⠀⠆⣠⠐⠂⠳⠶⡶⠆⠐⠆⠲⠶⢞⣥⡄
⠀⠀⠀⠀⠔⠒⠊⠀⢽⡇⠀⠀⠰⠤⠐⠁⠀⠀⠀⣓⡃⠀⠄⣬⠁⠀⣼⢀⣦⡠⣤⠀⠠⢰⣄⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡥⠀⠀⠀⠀⠀⠚⠀⠙⠆⣤⠈⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣲⠦⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⣽⠀⠀⠀⠀⠀⠈⠛⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠒⣃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠝⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣾⡿⣷⡀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⢀⠀⠀⠀⣤⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⢶⡿⣷⣿⣷⡀⠠⢐⠀⠀⠈⡆⠀⠦⡀
⠀⠀⠀⢀⣐⣀⠈⠴⢄⡛⢗⠄⢠⡂⣤⡀⣀⣠⡀⢀⣠⣶⠁⠿⠏⠋⠉⡋⠉⣻⣂⣄⣀⡀⣀⠁⠐⠀⡀
⠀⠀⠀⠜⠁⢀⠴⠄⡀⠀⣤⣴⣾⣿⠄⠀⣀⠀⠉⠟⡿⠷⠆⠀⠤⠀⠀⠀⠀⢨⣿⣿⢿⡦⠼⢉⠉⡙⠛
⠀⢀⠀⠅⠄⢀⣀⠉⠀⣆⣨⣿⡷⠫⠀⢘⡀⠀⠈⡀⠼⣟⡄⠀⠀⠄⠀⠀⢸⡙⠟⣿⠋⠁⠀⢸⠁⠲
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠂⠠⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢐⠀⠀⠄⠀⠀⠀⠀⠘⠋⠉⡃⠀⠀⠀⠀⠠⢠⠈⠀⠠⠀⠀⣷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠀⠈⠃⠐⢨⡂⠀⠀⠀⡌⡽⠇⢁⠀⠀⠀⠀⠸⢿⠀⠾⣿⠠⣿⢿⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢺⢸⡇⡇⢀⣰⣦⠀⣈⡐⠉⠑⠄⣰⣳⡇⣀⣀⣆⠀⠓⠀⠐⠄⡄⡒⠂⠒⠒⠲⡚⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡐⠛⠧⡀⠆⠐⣀⡐⢀⣒⣒⣚⣱⡀⠀⡖⠀⠘⠀⠀⣶⡆⠀⡴⡀⠈⡆⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠁⣠⡄⠀⠺⠦⡅⠐⠀⠀⠈⡀⠲⠄⠈⠅⠀⡒⠂⠀⠀⠟⠘⠈⠈⠻⠿⠇⢨⡯⠅⣰⠔⠋
⠀⠀⠈⠆⠀⠀⡀⢀⠀⠙⠃⠀⠀⡀⡀⠀⠀⠀⠀⣠⡃⠐⠂⠀⠀⠈⢷⠀⠀⣿⠀⠸⣷⠤⠠⣾⣼⡇⡠⠣⡀
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠠⢷⣆⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠛⠂⠀⠛⢻⡷⡃⠀⠀⡆
⠀⠀⠀⠀⠀⡇⠋⢀⠂⠀⠀⠀⢠⠀⠆⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡀⠀⠰⠀⠐⠂⢸⡇⠀⢠⡄⡀
⠀⠀⠀⠀⠀⣇⡠⠋⠈⠁⣀⣠⣀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣯⠀⣀⡿⣅⣷⡿⣟⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⡏⠁⠀⠀⠈⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠂
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⢀⡀⡀
⠀⠀⠀⠀⠀⡀⠄⠁⢈⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠄⠀⠀⠀⠄⡄⢠⡄⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠠⠀⠄⢠⠀⠀⠀⠀⠐⢀⠀⡀⠀⠀⠀⠈
⠀⠁⠀⠈⠉⡄⠄⠀⠀⠀⠈⠂⠒⠚⠐⠂⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄⠀⠀⠀⢠⠀⢠⣂⣂⠀⠈⢈⠀⠁⠄⠀⠀⠀⢠⠀⠁⠁⠈⠡⠤⠤⠠⠄⡄⢠⡔
⠀⠁⠀⠈⠀⣄⡀⠀⢈⣀⡝⠀⠃⠀⠀⠃⠤⠮⠥⠄⠀⠄⠠⠀⠀⠄⠀⠀⠀⢠⠀⣀⢀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢠⠀⠀⠁⠈⠀⠀⠀⠀⠄⡄⣀⠀⡀
⠀⠁⠈⢨⣤⣿⣿⣿⣿⣿⣟⡐⠂⠀⠀⠂⠠⠄⠤⠄⠀⠀⢠⣤⣶⣦⠤⠀⠀⠠⠀⡬⠤⠅⡀⠀⠈⠀⠁⠀⠠⠀⠀⢀⠀⠀⠁⠈⠀⠀⠄⠀⠄⡄⠁⣈⢀
⠀⠁⠀⠸⢿⣿⠋⠻⣿⠛⣿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠀⠀⠁⠈⠀⠀⠄⠀⠆⠆⠈⠉⠉
⠀⠀⠀⠂⢈⠠⠀⠀⠧⠀⠩⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣠⠞⢉⡞⢁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢿⡞⠡⠁⠘⠛⠉⢉⠉⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠲⣤⡀⠀⠀⢰⠏⠀⠆⠈⠀⠃⡠⠐⠈⠀⠀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⢦⡀⣿⠀⠀⡄⢀⠔⠉⠂⠀⠀⠀⠘⠛⢒⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣿⠍⠛⠳⢦⣄⠙⢦⡙⣿⠀⠀⡴⠡⠄⠀⠀⠀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢾⣯⠁⠀⠠⠀⡀⠀⠉⠂⠈⠳⣄⠹⡌⢧⣈⡤⠶⣤⡴⠶⣄⣈⣩⠿⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠂⢈⠀⠁⠀⠀⡨⠓⢢⡼⢧⡟⠉⠛⣆⠀⡏⠀⠀⢸⡏
⠀⠀⠀⠀⢠⣏⣤⡤⢤⡄⠀⠁⡀⠀⠀⠁⡴⠶⠿⣤⣸⡄⠀⠀⢸⣦⣷⣀⣀⣼⣁
⠀⠀⠀⠀⠈⠀⠀⢰⣯⠤⠶⣺⠏⣀⣠⡼⡇⠀⠀⠈⢻⣷⣦⣤⣿⠁⠀⠙⡿⠁⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⣽⢦⣄⣠⣾⠀⠈⢹⣿⣄⣀⣠⣧⡀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⣿⣿⣦⣤⣼⠋⠉⠹⣿⠟⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡶⠃⡴⠛⠛⢿⡀⠀⢀⣟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣇⠀⠀⠀⣿⣶⣾⡿⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡶⠖⠛⢻⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⣷⣄⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡟⠉⠩⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢵⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢠⣧⠤⣤⣦⡽⠃⠀⠀⢶⣀⠀⠀⠀⠐⢠⡐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠐⠒⠻⡾⠀⠀⠀⠀⠈⣋⠀⠐⢦⣾⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠇⠀⠀⠀⠀⣻⡀⠀⠀⠀⢠⠇⠀⠀⢠⡆⠀⠀⠱⡶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⢨⡖⠐⢢⡀⠀⠀⢀⠜⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠞⠋⢿⠁⠀⡌⠀⠀⠀⣹⣿⣿⣷⣄⣀⣀⣤⡾⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢆⡀⢀⡀⠀⠰⠒⣉⠛⠉⠈⠉⠛⠉⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠑⠶⠶⠾⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣿⠀⠀⠀⠀⠀⢀⠿⢶⡞⢃⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠢⣄⣀⣠⠄⠋⠃⠀⠹⡿⠋⠛⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡄⢸⣦⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆⠀⠀⠀⢀⡞⠟⠛⠶⡤⣤⡖⠛⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⣴⠛⠁⠀⠀⡀⢠⡌⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠛⠁⠙⢄⠠⢀⠰⠀⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣭⠴⣧⠀⠀⠑⢲⡶⡞⠀⠘⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢛⣧⣤⣠⣬⡌⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠋⠀⠘⠇⢹⣶⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠐⠫⠹⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⢀⣀⠀⠀⠀⠀⣿⣶⣄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⠓⢦⣀⠀⠀⢀⡀
⠛⠿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢭⡉⠛⠒⠚⠀⠀⣌⠓⠒⠋⠙⡆
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠉⠓⢤⣸⡄⠀⠀⡀⢿⠀⠀⠀⣠⣤⡀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣴⣿⣿⣮⡷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠤⠤⢤⣌⣳⡄⠀⡇⢸⢀⡤⠞⠙⢦⣹⠆
⠀⠀⠘⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣒⣦⡀⠀⠀⠈⠙⣦⠇⣸⠟⠀⢀⣴⣞⡁
⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡴⠋⠉⠉⢉⡷⠚⠛⠛⠻⣴⠃⢀⡴⢻⡶⣈⡉⢩⣝⢲
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⣤⣿⣏⣈⣿⡷⢹⣿⡇⠀⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡷⠻⢦⣾⢸⣅⣹⢸⠏⣧
⠀⣰⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠟⢁⣼⣿⠃⠀⢀⡞⢧⡀⠀⠀⢻⣄⡤⠤⣤⡀⣠⠇⠀⠀⠙⡷⠮⠶⠋⣠⢏
⠀⢿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣧⣷⣴⣿⠀⠀⠀⠘⠛⠁⠀⠀⠸⣇⣠⠭⠿⣶⡟⠁⠀⠀⠀⠙⣧⠀⠀⠀⢀⡇⠀⠀⠀⠛⠋
⠀⣼⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⣸⣤⣤⠴⢿⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢳⣤⣀⣀⣀⡴⣇⠀⠀⠀⠀⣿
⠀⠙⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣠⡟⠀⠈⠉⠀⠀⢸⡆⠀⠀⣠⠏
⠀⢰⣿⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠉⠀⢷⡀⠀⠀⠀⠀⣸⠓⠒⠛⠁
⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣹⠶⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⠀⠤⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡆⠀⠰⠃⢀⠠⠀⠀⠈⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢠⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣜⣰⠟⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣀⠄⡤⠤⣀⣀⢀⣇⡼⠋⠁⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠊⠙⢻⡷⣿⠛⣛⠿⡟⢿⣛⠛⠉⠉⠁⠀⠀⠀⠴⠶⣭⡀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀
⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠂⠀⠀⢘⣘⣇⢿⠟⠁⣰⡇⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⢰⠁⠀⢀⠄⠠⠂⠘⣋⠟⢹⡈⠀⣠⠾⡄⠀⠜⢸⡟⣿⣙⠃⠁⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠸
⠀⠀⠀⠀⢰⡇⠀⠈⢁⠀⠀⠒⠈⠉⠐⠈⡇⣾⡻⠀⢴⠀⠀⠐⣇⠸⡟⣷⣤⣀⣀⡀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠊⡘⠃⠐⠚⠦
⠀⠀⠀⠀⢠⢁⠀⠀⠀⢄⣱⠆⠀⠀⠀⢸⠇⠹⡎⢴⠘⢧⠀⠈⠏⢈⡾⣻⠍⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠂
⠀⠀⠀⢀⡤⠚⠲⣦⣀⣴⠿⠴⠮⣄⡡⢞⣴⢠⡳⣿⡀⡠⣡⠀⣀⠀⣐⣿⡧⣤⣽⣦⠤⣈⡚⠋⠃⠀⠀⠀⠀⠀⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠲⠶⠶⢼⣿⢟⠌⡟⢟⣶⠎⠀⠀⠀⠙⢋⡿⠁⠀⠀⠈⠑⡄⠀⠘⣦⡲⠒⠖⠀⠀⠀⠈⢀
⠀⠀⠀⢇⠀⠀⠀⢀⣜⠃⠀⠀⠀⢸⡏⠛⢶⡇⣎⠸⢂⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡄⠀⢠⣯⠙⢶⣤⡥⠀⠀⠀⠹⡀
⠠⠂⠉⠙⠳⣦⠎⠁⠀⠈⠳⡀⠠⠜⠀⠀⠀⣿⣁⡽⠗⠒⠠⣠⣾⠭⠦⣀⢀⡀⣠⠴⠶⢾⠉⠸⡇⠀⡛⡳⢤⣐⠀⠒⡟
⣧⠀⠀⠀⢰⣥⠀⠀⠀⠀⠀⡿⢑⣲⢄⣀⣀⣿⣽⣃⠀⠀⠀⠀⡀⠀⠀⠈⢯⢍⡵⠒⠐⠚⠢⡀⢹⡀⠸⣇⠈⠛⣦⢀⠘⢆
⢸⠷⠀⠐⣪⣵⣄⡀⣀⢀⡠⠃⠀⠈⠻⣷⠏⠀⠀⠈⠱⠀⣠⣘⣃⠀⠀⢀⣞⠾⠂⠀⠀⠀⠀⠙⣄⠀⡄⠌⢤⣀⣟⣑⠢⢄⠣
⢸⠀⢀⡞⠁⠀⠈⢻⣿⡛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡆⠁⠉⠀⠙⢶⠎⠉⠙⣧⡀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢳⡞⠁⠀⠀⠀⢸⡍⠣⢄⣤⣤⣶⣿⡿⣦⣴⣠⣴⣿⠀⠀⠀⣠⠤⠘⠦⡤⠤⣷⠓⠙⡋⠉
⠀⠀⠛⢄⠀⠀⡠⡎⠀⠐⡞⠁⠀⠀⠉⣿⣿⣿⡿⠿⣿⣷⣧⣼⠁⠀⠀⠀⢸⠀⠈⣆⠔⠁
⠀⠀⠀⠀⠙⣄⠀⣹⣦⣤⡇⠀⠀⠀⢀⣿⣿⣿⡗⠀⣀⠴⠛⠛⠦⡀⠀⢀⣼⠀⣠⡷⢄
⠀⠀⠀⠀⠀⠀⠉⡔⠀⠀⢑⠦⠠⠴⠋⠀⠀⠘⣇⡰⠉⠀⠀⠀⠀⠘⡷⠃⠀⠀⠀⠈⡆⡇
⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠑⠠⣆⠀⠀⠀⢀⣼⣧⠁⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⣤⠚⠉⣱⠖⠒⠉⠛⢿⣦⣄⣀⣀⣀⣾⣷⠖⠛⠛⢶⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⡀⢰⡃⠀⠀⠀⢠⠊⠀⠈⠉⢻⣿⣿⡏⠀⠀⠀⢈⠁⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠚⢷⣄⣀⣀⣼⡀⠀⠀⠀⣸⠟⠛⠻⢦⣤⡴⠎⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣈⣽⠉⠀⠉⠒⠲⣾⡇⠀⠀⠀⢈⣿⡷⠶⠶⠦⣤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣰⡿⠷⣄⣀⢀⣼⡿⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢻⠃⠀⠀⠈⢹⡟⠋⢹⣄⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⢀⡞⠀⠀⠀⠉⡛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⣀⣀⢀⠴⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠈⢷⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⣦⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⡁⢤⠀⡄⢠⠀⠀⠒⢠⣄⢠⠀⠂⠀⠀⠀⠀⣿⠀⢹⡆⠘⢧⡀⠀⠠⠛⠶⠀⠀⠀⠂⠀⠀⠀⣠⠶⣥⣛⠶⣮⠃⠀⠀⠀⠀⠀⠀⢀⣰⢶⣄
⠀⠀⠉⠙⠉⠁⠘⣄⠏⠸⠀⠀⠰⠶⠶⠶⠶⠛⠀⠀⠀⠀⠻⠇⠈⠁⠀⣰⠇⠀⠀⠤⠰⠶⠔⢠⠀⠀⠀⠰⢫⣾⢱⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⡗⣬⠟
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⢄⠶⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠢⡀
⠀⠀⠀⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠾⠂⢠⠀⠀⠀⠷⣿⣷⣿⠿⠃⠀⠀⠀⠴⠀⠉⠒⢄⢀⡀⠀⠀⠀⢰⣶⣶⣶⣾⣧
⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⣮⠙⠃⠀⠀⠀⠀⢷⡆⠉⠀⡠⠋⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣾⠃⣀⡀⠙⠷⠀⠀⠀⠈⠉⣙⠿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰⠈⠁⠈⢁⡀⠐⠀⠀⠀⢀⡀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⠀⠰⠏⠁⣀⣉⣁⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠉⠛⠉⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠁⠂⠀⠀⠀⢠⡀⠀⢛⠿⠀⣀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⢴⠁⠐⠀⠀⠀⠀⢸⡇⠀⠀⠙⠂⠀⠐⠀⠈⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠁
⠀⠀⠀⠀⠀⢨⣯⡹⡭⠀⠀⠀⠁⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠟⡷
⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢐⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣦⠀⠀⠀⠀⠀⢀⡀⠲⡀⠚⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠛⠃⠀⡘⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⢁⡇⠀⠀⠀⠄⠘⠃⢀⡵⠚⠃⠀⠤⠀⠀⠈⠂⠀⠃⠀⠀⠀⡟⠻⠿⠿⠛⢋⢳⡆
⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡄⠀⠀⣤⠀⠀⠀⠀⠀⢤⡄⠀⠠⢦⣤⠇⠀⠐⠲⠖⠲⠟⠁⠀⠀⠀⠀⠲⠐⠆⠀⢠⡤⠄⠀⠀⠀⠈⠢⠄⠀⠴⠋⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣮⠀⠀⠀⠀⠀⠈⢀⠀⠐⠀⠀⠀⠀⠀⢀⠄⠴⣿⡟⠀⠀⢀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠒⢠⡆⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠀⢀⡤⠈⠀⠀⠀⠈⠀⣄⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⣄
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⠀⠠⢾⣥⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠊⠀⠀⠀⠀⠀⠀⠉⠉⡆⠀⠀⠉⠀⠀⠀⠈⠀⠂⠰⣆⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠊
⠀⠀⠀⠀⠸⠷⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢟⡻⢿⣧⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠰⠾⠦⠀⠀⠀⢰⠆⢀⡛⡄⠀⡀⠀⠀⠀⣠⣶⣶⣴⡆⠐⠓
⠀⠘⢶⣶⣄⣤⣴⣶⡞⠀⠀⠈⠛⢧⣼⣿⡶⠟⠀⠀⠀⡀⠈⠁⠈⠀⡀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠂⠀⠰⠃⣠⢻⡿⠓⢾⠉⢓⡄⠘⠿⠶⣤⡞
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠞⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⢾⣤⠴⠛⠓⠋

⠀⠀⠀⢀⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠤⣴⡄⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖⢠⡀⠀⠀⠀⠀⠀⠂⠀⡈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠄⢀⡤⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢲⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓⠇⠀⠀⠄⠀⠀⠀⠙⠷⣶⣶⠶⠟⠁
⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠆⠈⠄⠀⠑⠄⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠀⠀⠀⣤⣙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣧⡄⠀⢀
⠀⠀⠀⠴⠆⠀⣤⣾⠃⠀⠀⠤⠤⠤⠌⠉⢫⠀⠀⠀⠀⣤⣹⣿⣧⣄⠉⠀⠀⠀⠀⠀⢠⡄⠐⢳⡄⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢠⡤⠲⡦⠴⠶⠀⠀⠂
⠀⠀⠀⠤⠄⠻⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠋⣻⡑⢫⣧⠀⠀⠀⠀⠤⠸⠃⠶⠊⠀⠀⠀⠀⠿⠟⠀⣀⢠⣦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠐⠛⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠉⠀⠀⠀⠈⠤⢀⣀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠉
⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡦⠄⠀⠀⠀⣀⠐⠂⠀⢠⡤⠀⠀⠀⠀⠠⠶⠶⠦⠀⢀⠀⠀⠀⠀⠛⠏⠀⠀⣤⢶⠒⣄
⠀⠀⠀⣤⣴⣶⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠀⠀⠀⠀⣴⠿⠛⠉⠀⠀⠀⠘⠀⠀⠁⠀⣄⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡌⠄⠀⠀⠀⠁⠂⠂⠀⠐⠫⠜⠋
⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠟⠃⠀⠀⠀⢈⣿⡷⠲⠶⠿⠓⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡿⢿⣿⡿⠛⢿⡿⣿⡿⣿⠿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣥⣤⣼⣷⣠⣾⣠⣴⣷⣬⣴⣿⣥⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠁⠀⢀⠤⠀⠀⢀⡠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠈⠀⠀⠀⠈⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠁⠐⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠯⡈⠑⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⣀
⠀⠀⠀⠀⠀⠀⠱⡀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠴⠋⠀⠀⠑⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠑⡄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠡⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡷⠚⠉⠙⠲⢤⡀⣠⡤⠴⢧⡈⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡴⠛⠉⠓⠦⣶⡁⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠙⡆⠀⠄⠀⠀⠀⠢⠀⠀⠀⠀⠀⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⡤⠒⠻⣄⠀⠀⠀⣀⣀⣈⠓⣤⠤⠤⣄⠀⠀⡼⠀⠀⢀⡿⠋⠁⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠠⠖⠊⠁⠀⠈
⠀⢸⡃⠀⠀⠈⠑⢲⠞⠁⠀⠀⡟⠀⠀⠀⠀⠙⢏⡔⠋⠉⠉⠓⢄⠀⠀⠀⠀⣷⠤⣄⠀⠀⠀⠠⠀⠄⠋⠁⠀⠁
⢀⡤⠛⠉⠉⠉⠉⢿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧⣀⣠⠔⠃⠀⠈⢳⠀⣀
⢸⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⠓⢤⣀⣀⡤⠞⣄⠀⣀⣀⠀⢀⣿⠤⠤⣄⣀⠀⢀⡼⠀⠀⠆
⠸⣄⠀⠀⢀⡴⠖⠋⠉⠉⠁⠀⣠⠊⠀⠀⠀⠀⠀⡼⠋⠉⠈⠙⢾⡁⠀⠀⠀⠈⠑⢯⡄⠠⠀⠄⠰
⢠⠞⠓⠒⣾⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⢻
⡟⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⡸
⢷⡀⠀⠀⠀⣨⠿⠒⠒⠒⠒⠀⠈⠓⠢⠄⠒⠀⠀⠀⠙⠢⠤⢶⡋⠀⠈⠙⠒⠲⡖⠋⠁
⠈⠳⠦⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⢸⠶⠤⠴⠚
⠀⠀⠀⠀⢹⣦⣀⣀⣠⡴⠋⠀⠻⣄⡀⢀⣠⠋⣨⠷⢦⣄⣀⣀⣠⡞
⠀⠀⠀⢰⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠇⠀⠀⠀⠈⠁⠀⠘⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⢷⣄⠀⠀⠀⢸⣄⠀⠀⠀⠀⡠⢆⠠⠊⠉⠁⠲⢤⣤⠴⠟
⠀⠀⠀⠀⠀⠈⢩⡟⠋⠉⠈⣱⠒⠊⠛⢦⢰⠃⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠘⠦⣄⡀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⣹⡀⠀⠀⠀⢀⣎⠀⠀⠀⠙⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠙⣦⠤⠖⠋⠀⠙⡄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣰⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣤⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⣰⠋⢳⡄
⠀⠀⠀⠀⢀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣩⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⣤⠐⠿⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⠛⣡⢼⡛⠷⢯⣷⡀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠒⠚⠉⠀⠀⢸⡆
⢀⡞⣹⠷⠒⠿⣄⠀⠀⠈⠓⠦⢤⣄⣀⡄⠀⠀⠀⣸⣴⣣⢾⠷⠶⢿⢻⡞⠁⢧⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠛⠛⠳⣄⠀⠳⣄
⠉⠉⢻⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⠿⣽⠀⠀⠀⢻⠙⠛⠻⠶⠶⢾⠏⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡼⠀⢸⠀⠀⠀⠀⣹⠀⠀⠈⢳⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠉⠛⠛⢦⣴⡆⠀⠀⠀⠈⢦⠀⠈⠁⣰⠋⠈⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠈⠳⢤⣤⠴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⠤⢿⣸⠇⠀⠀⠀⠀⠈⢧⡀⣰⠃⠀⠀⠘⠀⠠⠈⣇⠀⠀⠀⢿⡀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⠀⠀⠀⢸⡆⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⠀⠈⠀⠀⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠙⢦⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⣠⠤⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⡟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠙⣦⠟⠳⣦⡟⣏⠹⣞⣦
⠀⢠⠶⠶⠶⠶⠚⠓⠓⠒⠒⠒⢲⡄⠀⠀⠀⠀⠀⣞⣛⣛⣛⣛⡇⠀⠈⢇⢹⢀⣤⣄⣠⡿⠋⠀⠀⠀⣏⣛⠛⢦⣞⢹⢠⡿⣆⠘⢧
⠀⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏⠁⠀⠀⠀⠀⡴⠛⠉⠉⠉⠉⠑⢦⠀⠞⢀⢸⣄⠈⢹⡇⠀⠀⠀⠀⢀⣈⡟⣆⠈⢻⣸⠃⣼⣄⣨⣷
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣞⠉⠙⢿⡳⠞⠁⠀⠀⠀⠀⠀⢻⠉⠉⠙⠛⠛⠉⠉⠁⢠⡇
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠶⢿⡶⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣀⣷⣠⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⡏⠐⠈⠙⣏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠒⠒⠒⠶⠟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⡿⢦⣧⡴⠋
⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠲⠶⢤⣄⡀
⠀⠀⠀⣰⠿⢞⠳⠮⣍⡹⣯⣽⣇⣤⣀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠶⠒⠒⣖⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⣠⠀⠈⠉⠳⢤⡀
⠀⢀⡞⠁⠀⠈⠀⡄⠀⠙⢦⡸⢭⣳⣈⠱⡄⠀⠀⠀⠀⣴⢋⡀⠳⠀⠶⠀⠡⠆⢈⠳⡄⠀⠀⠀⠀⠀⢸⡷⣤⡈⠉⠓⠦⣤⡄⠀⠀⠙⢦
⠀⠸⡆⠠⠀⠀⠀⠀⠀⠂⠀⠹⡄⢿⣽⣇⢹⠀⠀⠀⠀⢷⣌⣁⣀⣀⣀⣖⣀⣈⣋⣁⣹⠀⠀⠀⠀⠀⢸⡷⢈⡇⢀⣩⡤⣤⣙⠶⣞⠀⣈
⠀⠀⠘⠦⣀⠈⠁⠀⢀⠀⠈⠃⠹⡄⣹⢾⣼⠀⠀⠀⠀⣸⣭⣭⠭⣍⣉⣩⠽⢯⣍⣩⠿⡄⠀⠀⠀⠀⢸⠟⠋⢠⣯⡴⡖⣟⣮⠷⠞⠋⠉
⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠠⠄⠀⢷⡷⢺⠃⠀⠀⠀⠀⠹⣦⠤⠶⠶⠿⢶⣶⠶⠶⠖⢺⠁⠀⠀⠀⠀⢸⠶⣄⢘⣦⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄⣸⡴⠃⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣈⣹⣦⡴⠋⠀⠀⠀⠀⠀⢾⠴⠛⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣼⠁⠀⡞⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠇⠀⡼⠁⠀⡼⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡏⠀⡿⠀⢰⠃⠀⣼⠁⠀⡼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣛⡉⠉⢸⡇⢸⡇⠀⣿⠀⢰⠇⠀⣸⠁⠉⠙⠳⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⣾⣯⡥⠖⢀⣸⣇⣸⡇⣀⣇⢀⣸⠀⣀⡟⠀⠀⢬⣙⠲⢬⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡌⠙⢃⣰⠇⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡙⠢⠄⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣀⣤⠶⣛⣵⠰⠿⠧⣍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⢛⣋⣩⣥⡶⠿⣛⡅⠘⠛⠛⢾⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠓⢸⣟⡳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢋⣉⣉⣭⣴⡶⢟⣫⠁⠀⢒⣤⣾⣧⢠⡟
⠀⠀⠀⠀⠀⣠⡴⢛⡭⢖⡢⠄⠀⠀⢻⣟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⣭⣥⡶⠾⣛⠍⣶⣛⣭⣾⢟⣵⠟⠶⣄
⠀⠀⠀⠀⡾⢋⡾⢋⡴⢋⡴⢊⡠⠀⠀⢻⣝⡒⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣩⣭⣥⡴⠶⠾⣛⠋⡼⣟⣛⣭⣶⠋⠁⢄⠲⡌⢷⡀
⠀⠀⠀⢸⡇⢸⣇⠸⣇⠸⣆⠸⢄⡀⠀⠀⠹⣯⣅⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠶⢶⣛⣿⣫⣾⣿⣿⡿⣿⡿⣧⢹⡌⣧⠛⢸⡇
⠀⠀⠀⠀⠻⣦⡻⣦⣌⠳⢮⣟⡲⠤⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣀⣒⣒⣚⣻⣿⣿⣿⣿⢟⣿⡇⣿⡇⣿⡇⡟⢸⠇⠇⣠⠟
⠀⠀⠀⠀⠀⠨⠿⠶⣭⣛⠶⢦⣍⣑⠂⠀⠀⠀⠀⠀⠉⠛⠳⠾⠭⠭⠭⠽⠶⣟⣛⣫⣭⡶⢿⣫⣼⠟⡵⠋⠈⣀⣡⣶⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣷⢶⣬⣭⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⠭⠵⠶⣚⣛⣉⣤⣤⣶⣾⣿⣿⣿⣿⣿⣏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣒⡒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣶⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⢜⠀⠀⠀⠠⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠳⠐⠊⠁⠀⢸⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣟⣿⣿⣿⣿⣿⣿⠻⢻⣾⣿⣟⣡⣤⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠻⠟⠉⠉⠉⠉⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⡀⣾⣿⣿⠈⣻⣿⣋⡙⠿⠟⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⡄⠋⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢛⣿⣿⣿⣉⣿⣷⣤⠹⣿⣿⡗
⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠙⢿⣿⣿⢆⢛⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⣷⡄⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄⢰⣿⣿⣦⢾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⣦⠀⠘⠿⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⣿⣶⣾⢿⣿⣟⢠⣭⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣻⣤⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠻⣿⠟⢠⣿⣿⣧⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠉⣿⡟⠀⠈⠙⡃⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⣾⣷⡆⣘⣿⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⣀⡀⠀⠀⠀⠀⠄⠀⠐⠛⠃⡀⠀⢠⡟⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣼⣿⣿⡄⣾⡧⣽⣧
⠀⠀⠀⠀⠀⠀⠘⢀⡞⣁⠠⠃⠀⠀⠈⠀⠠⠘⡇⠀⣠⡟⠀⠀⠸⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢟⣀⣿⢾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠈⢳⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠆⠀⠀⠀⠀⠀⠈⠄⠠⠋⠀⠀⢰⠁⢰⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡍⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠙⡃⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣶⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⡛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡏⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠋⢳⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣿⣿⣿⣿⣟⣿⣿⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⡠⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢀⠠⢐⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⣀⣢⢠⣈⣀⣥⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡿⠂⠀⠀⡐⢁⢲⡀⠀⠸⠀⠀⠀⠀⣠⠤⠶⠶⠿⠿⢶⡄
⠀⠘⠈⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠾⠀⠀⠀⠀⠀⠛⢾⡡⠀⢁⡆⠀⠀⠀⢹⠀⠀⠀⠄
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠠⠀⠀⠀⠀⣶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠀⠐⠀⠀⠀⠐⠒⠘


⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⠀⢀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢘⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠰⣆⠀⡀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⡄⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠠⠂⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠲⢎⠣⣄⠀⠀⠈⠀⡃⠈⠠⠈⠀⠠⠀⠑⠠⠀⠀⠀⢀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢙⡧⠄⠀⠀⠀⠀⠐⠨⠤⠒⠀⠡⠀⠀⠀⠀⡁⢈⠀⠠⠋
⠀⠀⠈⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠊⠀⣀⣤⣤⣀⡈⠀⠀⠀⠀⣿⢿⡄⢸⣟⠖⠁⠀⠀⠀⠀⢀⡨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠐⠀⠂⠀⡰⢛⡅⠈⠀⠁⠀⠀⠰⠀⠀⢨⠉⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢋⣀⣠⡠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠨⡀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠠⡬⠀⠀⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠀⠀⠀⠀⠀⢀⣠⠄⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢀⠂⠈⠂⠀⠀⠀⢠⡏⠃⠀⠀⠀⠙⡆⠀⠀⠀⡀⠔⠒⠂⠀⡀⢀⠠⠀⠀⢀⠔⠀⠀⠀⠑⠄
⠀⣀⠀⠀⠐⠚⠛⠛⢲⠇⠀⠀⢀⠈⠀⠂⠂⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⢈⠀⠀⠒⡄⠶⠀⠒⢄⡜⢂
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆⠤⠁⠔⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠘

⠀⣀⠀⠀⠀⠀⡀
⢀⠀⠀⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣰⣤⣤
⠀⠀⡀⠙⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠃
⠀⠀⡇⠀⢣⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⡜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠦⡀
⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠶⠒⠃
⠀⠀⢀⠀⠸⠀⠀⠠⠀⠘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠄⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢷⡄⠀⠀⠰⠛⠐
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠈⠓⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣷⣤⣿⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠐⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠂⠀⠀⠄⠀⢀⠀⡔⢲⠲⣶⢲⡖⣲⢰⡂⢸⠃⡶⡶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠰⠶⠖⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠚⠚⠃⠀⠀⠘⠚⠒⠘⠀⠉⠁⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡁
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⡄⠀⠀⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠁⠒⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣒⣾⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⢿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠆
⠀⠀⢀⠀⣀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠘⠛⠛⠃⠀⣀⠘⢂⡀
⠀⠀⠀⠀⠤⠤⠴⡆⠀⠀⠀⠀⢀⣄⣄⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⣀⣀⠀⣀⣀
⠀⠀⠀⢰⣶⣶⡆⠃⠀⠀⠀⠀⣀⣠⣤⣤⡀⠸⡄⠀⠀⠀⢰⣶⠀⠈⠛⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⢠⣀⣀⡄⠀⠀⠀⠛⠛⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠉⠀⠸⠿⠀⠀⠀⠀⠸⠿⢿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⣀⣬⣭⣿⣿⣿⣿⣧⣤⣄⣀⠈⠥⢜⢇⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⣼⣭⣻⣿⣿⣿⣿⠀⠐⣶⠮⠁⠈⠉⠒⠀⠀⠒⠈
⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⡟⣿⣿⠟⡟⢻⡓⢠⡄⠈⢠⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠙⢡⣾⣿⣿⢹⢟⢣⣶⠈⠈⠇⢸⣟⠳⣾⡆⠀⣿⡀⣰
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⠀⣀⣿⣆⠀⣀⣼⣿⢠⣾⠟⠛⢻⡞⠛⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢃⣤⣿⣯⣌⣾⣿⣿⣄⠀⢘⣄⣀⣄⣿⣆⣴
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⣿⣿⣛⣿⣿⣿⡿⢿⣿⡌⠁⢻⣿⡿⠛⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⢹⡏⠀⠀⢨⣿⣦⣎⠈⢿⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⠿⠾⢷⠋⠀⢸⣿⠷⣿⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣤⣼⠷⠒⠻⠃⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⢿⣷⣠⣼⡟⢻⣷⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣾⠋⠉⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⡿⣦⣠⠜⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢦⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⣄⣆⠀⠀⠀⠀⠀⠐⠀⢀⡖⢶⡟⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣈⠙⠒⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡏⢠⢇⠁⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣋⣤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠯⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣳⡀⣀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠀⠀⠀⠀⢀⡄⢸⣧⣽⣯⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠻⠿⠿⠿⠿⠟⠻⠿⢿⣿⣛⣛⣫⣵⣾⡿⠟⠒⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠇⠂⢀⣤⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠃⠀⠐⣤⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢁⢿⣾⣿⠿⢛⣭⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⢃⡴⢣⣤⣤⣬⣁⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣨⠿⣻⣠⣹⣷⣻⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢨⡇⠸⣿⣿⣿⣿⠿⠓⢲⣤⣴⣶⣿⣿⣿⢭⣾⣷⣿⣿⣿⣿⡿⠛⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢳⣂⠁⠄⠙⢿⣿⠯⠀⠀⠀⣿⣿⠿⠿⠷⠟⠛⠛⠛⠛⠛⣋⠉⠁⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡪⣤⡄⠀⠙⠿⠷⢾⣿⣏⣙⠛⠲⠶⣤⣄⣀⠀⠒⠉⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣄⣀⣀⠀⠀⠀⠉⠈⠃⠮⣍⡛⠛⠂⠠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣾⣧⣧⣷⣼⣿⣿⣿

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡏⢿⣿⡟⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⢀⣤⣾⣿⣿⣿⣿⣿⡿⠛⣣⣬⣿⣿⠟⠛⠛⠋
⣿⣿⣿⣈⣿⡷⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣧⣄⠀⠀⠉⠋⠁⠀⠘⠉⠙⠉
⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⡿⣿⣶⣌⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢹
⠈⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣆⣀⣶⣤⣦⣄⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⢿⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⣤⣄⡀⠀⠈⢻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣀⣀⣤⡶⣤⠄⢤⣴⡶⠀⠴⣦⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡆⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣇⠀⠀⢀⣾⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢫⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⢉⠟⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣷⠲⢄⡄⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣴⣦⡄⠙⠂⢸⣿⣿⣿⣿⣿⣯⠸⠉⠻⢿⣿⣿⣿⠛⠋⠉⡘⠉⠋⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣖⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠟⢛⢷⣤⣧⣸⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⣠⣷⣦⣤⣾⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢠⣤⠄⣿⣿⣿⣀⣿⣿⣿⣿⣿⡿⠿⢸⣿⣿⣿⣿⣿⣿⡿⠷⠀⠄⠉⣥⣀⣠⠖⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠚⠃⠀⠻⣿⡉⠿⣿⣿⣿⣿⢿⠿⢃⣽⣿⣿⣿⣿⣿⣿⠓⠒⠐⣦⡤⠞⠛⣨⣟⠛⣿⣖⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠷⠶⠿⠿⠟⠱⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⢀⢷⡞⣉⣥⣾⠿⠛⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⣤⣶⣶⣶⣤⣄⣀⣤⣠⣤⣤⣠⣄⠀⠀⣿⣿⣿⣿⣿⣿⠇⢁⣠⣶⢿⡟⠁⢙⠀⣁⣦⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠤⠛⠿⠏⠉⠈⠛⠋⠉⠉⠀⠀⠀⠀⣸⣿⣯⣿⣿⣟⠶⠟⠉⠛⠃⢠⣧⣤⣾⡞⠛⢿⡀⢀⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⡟⣿⡋⠀⣤⣀⣾⡶⠿⡿⡁⢙⡀⠀⡼⠇⠈⣡⣼⣿⣾⠟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣫⣽⣿⣿⣿⣿⡟⢿⠉⢙⡃⠠⡆⠀⢻⡅⠀⠰⡆⠀⢻⠛⣹⣯⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣻⣿⠿⠿⢿⠁⠰⡞⠀⢸⡅⠀⠃⠀⠈⠀⠀⢀⡇⠀⠛⠛⢻⣿⠟⠋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣛⡭⠀⠂⡿⢿⠀⠀⠟⠀⢀⡀⢀⣤⠀⢸⡇⠀⠈⣅⠀⠰⠆⠠⣿⠀⣤⣸⣧⣿⣿
⣿⣿⣿⣿⡷⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣀⠀⠠⠈⠋⢡⣴⣦⣼⣿⣿⡄⠀⡟⠀⢘⡅⠀⠿⠀⠈⠓⠀⠀⢩⠀⠀⣣⣀⣿⡀⢿⣿⣿⣿⣿
⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢲⣀⠠⣤⣴⣶⣾⣋⠀⠀⠀⣴⡴⢿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠉⠀⠀⢁⠀⣀⡀⠀⣤⠀⠀⠚⣀⣭⣷⣶⣿⣷⣿⣿⣿⣿⣿
⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠧⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⣀⣻⡀⣨⣧⢤⣼⣖⠲⣾⢇⠉⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢽⣿⣦⠈⠻⠇⠉⠛⠃⣀⠈⠁⢸⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠹⠏⢘⡟⠀⢿⠃⠀⢟⠂⠀⢹⣁⣀⠙⣿⣻⣾⣿⣧⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⡉⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠷⠈⣿⡆⠻⡇⠀⢘⡇⠀⠸⣿⣿⢰⣿⣿⣿⣿⡟⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣧⣴⣿⣿⣿⡿⠿⠏⣿⣿⣟⣻⣟⣻⣧⡀⢰⡤⣠⣿⣷⣶⠷⠀⠈⣿⣤⣤⣿⣿⣾⣿⣿⣿⣯⣽⣶⠻⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣶⣿⣦⣧⣼⣿⣿⣿⣆⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣷⡟⠟⠛⠛⠛⠋⠉⠉⢻⣿⣯⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣷⣶⣭⣭⣭⣭⣭⣍⣉⠛⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠿⠇⠈⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠉⠉⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣶⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢰⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⡀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⣿⣷⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠇⠸⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⣋⠀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠸⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠇⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⠀⢀⢈⣈⣀⡀⡀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⣾⣿⣿⡿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⡏⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣬⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⡀⠋⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⡿⠿⠿⠽⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠴⠤⠶⢷⣦⣤⡴⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠠⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇
⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣇
⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣆
⠀⠀⠀⠀⠀⡠⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⡀⠀⠀⠀⠀⡀⠀⠀⠈⢳⡘⣧
⠀⠀⠀⡀⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⡦⠶⠶⠦⣤⡀⠀⣠⡶⠛⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⢦⣀⡾⠋⠀⠀⠀⠀⠈⢻⣤⣿⣤⣀⠀⠀⠀⣨⣧⣀⡀
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠉⠻⣦⠟⠉⠀⠈⠙⠳⣄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣿⠀⠀⠀⣠⡶⠋⠉⠉⠛⢦⠀⣠⣤⠤⠼⣧⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠹
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⢧⣀⣠⡏⠀⠀⠀⠀⠀⠈⡟⠉⠀⠀⠀⠀⠙⢧⡀⠀⢀⡇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣧⠀⢀⡴⠋⠀⠘⣇⠀⠀⠀⣀⣠⣄⡁⠀⠀⠀⠀⠀⠀⠈⣧⠴⠾⠷⠦⣄⠀⠀⠀⢠
⠀⠀⠁⠀⢀⠀⠀⠠⠠⠄⠂⠂⠒⠂⠉⠀⣀⠀⠀⠀⠀⠙⢦⣼⠁⠀⠀⠀⠈⠳⣴⠛⠁⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣤⠶⠋
⠴⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠄⢻⡄⠀⠀⣠⡤⣼⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣄⣼⡃⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠂⠀⠀⠀⠀⠙⢳⠞⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠈⠙⢷⡄⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⡋⠙⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡴⠖⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⣀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⣴⠞⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢛⣡⣤⣤⣀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⢻⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⣀⠀⣀⡀⠀⠚⠉⠛⠦⠀⠀⠀⠀⣤⣾⣁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠞⠉⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣤⠴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣤⠶⠛⢉⡿⠒⠛⠁⠀⠀⠀⢤⠀⠰⠞⠳⢤⡀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣹⠷⣄⣀⣀⣀⣴⢿⡄⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⡟⠀⠀⠉⠉⠉⠀⠀⢹⡶⣴⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⣀⣀⣤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡠⠊⢸
⠀⠀⠀⠀⠀⠀⠀⣎⡁⣅⣀⡸⠛⠢⡤⠻⡇⠀⢢⠀⠠⠀⠀⠀⠀⠀⢀⠄⢘⠤⠠⢁⠀⠦⣮⠆⠑⢼⡄
⠀⠀⠀⠀⠀⠀⡆⠀⡌⠀⠀⢱⠀⢀⡿⠀⠁⢤⠐⢢⠀⠁⠀⠀⢀⠎⢘⠄⣎⠀⠀⡎⠀⠀⢘⡆⠀⢲⠋⠀⠀⢆
⠀⠀⠀⠀⠀⢄⢸⠁⠀⡤⠤⣞⠀⠈⠻⠄⣠⠞⠀⡜⢢⠀⠀⠀⠀⠁⠺⡀⢸⠁⠀⠈⢠⠤⠎⣇⠀⢀⡇⢀⢀⠎⠀⢱
⠀⠀⠀⠀⠀⡆⢠⠃⠺⣀⠀⣸⠆⠐⢄⣠⠿⣄⠠⣇⠰⠀⠀⠀⠀⠀⠀⠀⢈⠄⡀⠠⡆⠀⠀⢹⠁⢹⡄⢨⡇⠀⣱⠁
⠀⠀⠀⠀⠘⡀⡨⠒⠞⠁⠙⣧⡀⢀⣸⣁⣀⢼⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢣⢰⡁⠀⠑⡄⠄⠃⢠⠈⠀⠣⢱⠐⠁
⠀⠀⠀⠀⠀⠀⡱⢤⠊⠀⣾⠁⠈⡟⠁⠈⡧⠰⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡐⠁⠀⢢⠠⠎⣀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⢇⣀⡦⢴⠁⠀⣏⡩⠄⡈⢹⠖⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠒⢧⠀⠀⠜⠀⠀⡸⠘
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡓⠂⠑⣄⢀⡏⢹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣰⠋⠈⢹⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠱⠄⠰⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡢⠀⢻⠄⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠂⠺⣀⢠⡏⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⡁⠀⡸⢀⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⣸⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡸⠀⢤⠎⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⡟⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠂⠀⠁⠀⠀⠀⠀⠀⢀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⠉⠀⠀⠀⠀⢀⠀⡀⠠⠐⠀⠂⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⠀⠀⠀⠀⠀⢀⢀⠠⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠁⠀⠀⢀⡀⠤⠤⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢀⠀⠄⢀⡰⠮⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠠⠄⢀⢀⣊⠡⠀⣂⡤⠤⠒⠒⠉⠁⠀⠀⠀⠀⠉⠀⠐⠀⠤⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠀⣀
⠀⠀⠀⠀⡔⠂⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡄
⠀⠀⡀⢰⠇⠀⠀⠀⡠⠑⠄⠀⠀⠠⠤⠤⠤⠠⠀⠀⠤⠄⠠⠤⠤⠤⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡁
⠀⠀⠀⠳⠄⠄⠩⠤⣀⠠⠀⠀⠤⠤⠞⠱⠤⠄⠀⢠⠀⠤⠀⠤⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄
⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⡄
⠀⠀⠀⠒⠀⠀⠆⢀⡇⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠈⡆⠁⠀⢀
⠀⠀⡍⠁⠄⠀⡈⠀⠁⠀⠀⠀⠠⡇⠐⠀⠒⠄⠀⠈⠁⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⡠⠄⡅⠀⠀⠀⠢⠖⠡⡤⠔⡦⠀⠈⠀⠃⡏⠁⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠙⠂⠀⢠⢸⠆⠄⠀⠀⠀⠀⠐⠁⠀⣃⠀⡎⠀⠐⠂⠤⡂⠖⠀⠤⠀⢀⠀⠀⠁⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡊⠉⠉⠑
⠀⠀⠀⠀⠈⠀⢸⡆⠀⠀⠀⠀⠀⠀⣾⠂⠉⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠈⠀⠀⠀⠠⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠢⠀⢰⠂⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠆⠀⠀⠀⢀⠔⠈⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠆⠄⠀⡀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠘⠘⠀⠀⠀⠀⠤⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠀⠀⠀⠐⠂⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢠⡄⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀⢀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⡃⠀⠀⠁⠈⠀⠀⠹⡀⠀⢡⡄⢀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢠⡄⠀⠀⢣⠀⠀⣣⠊⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠄⠈⢂⠀⢼⣀⠀⠂⠘⣄⠠⡞⠀⠰⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠲⡆⠀⢩⠧⠀⠀⠙⣿⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦⠀⠀⠈⢣⡀⢧⡀⡄⢀⢸⠀⠀⣼⠂⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢱⣤⣽⣷⣆⢾⣦⣤⣿⣤⢤⣤⡴⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⢀⣼⠻⣟⠛⣟⢸⡟⣿⠋⣍⣿⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⡿⠸⠤⣽⣶⣿⣾⣧⣿⡠⠿⠿⠰⠶⠸⡄
⠀⠀⠀⠀⠀⠀⠐⢆⠀⠄⠀⠀⠀⠀⢀⣤⣀⣛⣃⣀⣀⢘⡟⠉⠉⠉⠉⢙⣿⣏⡟⠉⠉⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⢤⠀⠀⠘⣇⢵⣀⣄⢀⡿⢸⡇⠀⡠⡦⠀⢘⣿⣿⡏⠁⢰⣄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠑⣌⠃⠀⢀⠹⣿⣅⣠⠏⠀⠀⢁⠀⠈⣿⠀⣈⣿⣿⣅⣤⣸⣽⣧⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⣤⠀⠀⡀⠻⡤⢀⣸⡟⠉⠉⠱⣞⡄⠠⠀⢠⠉⠀⠹⣿⣿⣧⣿⣭⣿⣯⣿⣧⣷
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠂⣤⣠⣿⣧⡄⢀⣠⣿⣼⡧⠄⢀⣀⠀⠀⣿⣿⣧⡄⠁⠉⢨⣤⡤⠁
⠀⠀⠀⠀⠀⠀⣴⡄⣀⠀⡓⢠⡀⢺⣿⢛⣋⣠⣼⣗⣛⣻⡇⠄⢸⣿⠀⠀⢻⣿⣿⡆⠀⠀⢸⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠐⠿⠀⠀⣿⣿⣿⡇⠀⠀⢸⡿⡇
⠀⠀⠀⠀⠀⢰⡿⢶⣦⠌⠃⠗⠲⣾⣿⣿⡿⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠨⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠁⢰⢀⠀⣄⣠⣄⣼⡿⢣⣄⠄⠠⣬⡂⣻⡷⠶⠃⢰⣶⠀⢼⣿⣿⡇⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠈⠉⢹⡿⠿⠿⠧⠼⠿⠿⣿⡇⠀⠀⠘⣿⠀⢸⣿⣿⣧⠀⠀⠀⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠀⠀⣀⣀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠘⠿⠀⢼⣿⣿⠁⠀⠠⠄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠲⢀⠀⡀⠀⠀⠀⠀⠂⠀⠋⠉⠙⠳⠀⠐⠀⠀⢒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠲⠶⠟⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣟⣻⣿⣯⣬⣟⣿⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣽⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⣇⣀⣠⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢲⡄⠀⠀⠀⠀⠀⡎⠹⠇⣀⣀⠀⠀⠀⠀⣠⣞⣤⣼⣷⣶⣿⣿⣷⣼⡿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠡⡖⠛⠈⠀⣾⠟⠃⣸⠆⠝⠀⠀⠀⠀⢙⣻⣽⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠞⠀⠀⢄⠀⠉⠂⠀⠋⡤⠒⠀⠀⠠⣴⣼⣿⣾⣿⣿⣿⡻⣿⣯⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣿⢷⣽⣱⣿⢟⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠦⢷⣾⣿⣿⣿⣏⡿⠏⣻⣿⣻⣿⡇⢇
⠀⠀⠀⠀⠀⠀⠀⢠⢖⣡⣒⣲⣶⣥⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠾⠟⠁⠃⣿⡢⠐⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠿⠾⠗⠏⣀⢱⣕⣄⣤⣄⠠⠤⠄⠐⢒⠒⠂⠀⢐⣂⢴⣦⢤⣤⡀⠀⠀⠀⢸⡇⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡈⡀⠴⣶⣶⣯⣭⣭⠅⠀⢀⣀⠀⠄⠀⠠⠀⠀⣠⣾⣿⠉⠁⢀⠀⠘⠇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⢴⣶⣾⣍⡉⠻⠛⠿⢷⣾⣥⠀⣂⡄⣴⠿⣯⣯⣏⠀⢀⣾⣿⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠾⡝⡟⠃⠘⠐⠒⠂⠀⢽⡇⡿⡿⠁⠨⣼⣿⠿⠀⢸⣿⣿⠀⠀⢠⢶⣶⣾⣴⣦⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⣸⣼⠀⠠⢴⢻⠊⣥⡤⠭⠖⠀⠒⠏⣿⡗⠀⢀⣸⣿⡏⠀⠀⠘⡆⠄⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠲⣯⣹⣿⢩⣥⣼⠽⣮⡀⠀⠀⠀⠀⠀⡇⣾⣶⠆⠀⢙⣾⡇⠀⠀⠀⡁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠸⣿⠤⠄⠠⡇⠀⠙⢩⣶⣤⣀⠖⡆⣽⠿⣤⠄⠀⢤⡆⠀⠀⠀⣇⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⡿⠀⠀⠀⣥⠄⠠⠠⢝⡻⢷⣶⣶⠏⠉⠀⠀⠀⠀⢿⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣀⣠⣤⣴⣛⣔⠙⣻⡇⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⡟⠁⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠙⠛⠿⣿⣷⠀⠈⣷⣷⣶⡶⠶⠶⠶⠲⠟⠋⠁⠋⠙⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⡐⠁⠀⠀⠀⣀⠈
⠀⠀⠀⠈⢻⠒⠂⢿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⣀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣤⡄⠀⠀⢸⠏⠈⡓⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⣾⣿⣿⡟⠉⠀⠀⠀⠀⠀⣅⠠⠄⠀⣐⣀⣨⣥⠤⠶⠖⠚
⠀⠀⢶⣶⣾⡇⠀⣷⣤⣤⣤⠀⠀⢾⠃⢠⠄⠀⢧⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⡞⠛⠉⠉⠁
⠈⠄⠀⣿⣽⡇⠀⢫⣭⢹⠉⢀⡦⢾⢧⣮⡀⢀⡠⠿⠟⠃⠇⠀⠀⠀⠀⠀⠀⠀⡇
⡐⡀⠀⢻⢻⡇⠀⢸⣿⢸⠀⠄⣾⣬⠾⣽⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⢰⡇
⠲⠀⠀⠀⢸⡇⠀⢸⢼⢸⠀⠀⠸⡽⠀⠛⠀⠀⠀⠀⠀⠀⢀⢸⡄⠀⡇⠀⠀⡠⠧⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒
⠷⠄⠀⠠⢸⡇⠀⢸⠑⢸⠞⠀⠠⣸⣀⣴⣶⡄⠀⣰⣶⡆⠈⠉⠀⣤⣧⣤⣠⡤⠤⠤⠤⢤⣤⣤⣄⣠⣤⣤⣤
⣷⡗⠀⠀⢸⡇⠀⣸⠓⢸⠘⠛⢛⣻⡛⣿⡛⠗⢠⣿⣿⣿⣷⣿⣿⣿⡯⣷⣾⣷⣶⣶⣶⣿⣷⣶⣶⣶⣶⣿⣳
⣿⡇⠀⠀⢸⡇⠀⣸⠏⢸⢠⣾⣯⣭⣿⣿⡿⠿⢿⣿⡿⣿⢹⣿⣿⡟⠃⠞⠻⠸⠿⣿⣿⡏⠿⢿⢿⣿⣯⣿⣸
⣿⡇⠀⠀⠸⡇⠀⠀⠠⢤⣤⣭⣉⣭⣭⣴⣶⣶⢸⣿⣿⣟⣿⣿⣿⢳⡖⣶⡦⢰⣴⣾⣿⡇⣒⣐⣀⠛⠯⠅⠈
⣿⣧⠤⣴⣶⣟⠀⡀⢾⣿⣿⣮⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇
⣿⣋⢁⣛⣻⣏⡁⡅⢸⠿⠿⠿⠿⠛⠛⠛⣛⣛⢸⣟⣿⣿⣿⣿⣿⢸⠿⢿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇
⣙⣖⣴⣻⣿⡃⠀⡇⢠⡶⠶⢶⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡿⣿⣷⣶⡆⣷⣿⣿⣿⡇⠿⢿⣿⣿⣿⡇
⣯⣷⣭⣵⡾⡿⠛⡇⢙⣺⣿⣿⣯⣟⣻⣽⡿⠷⡀⡿⠝⠻⣿⠿⡿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣶⣶⣤⣭⡅

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠓⣦⠀⠀⢀⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡏⢀⠖⠉⢰⠁⠀⢀⣠⠖⠛⠉⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⡇⠀⢀⣷⠋⠀⠀⢸⢀⡴⠋⠀⠀⠀⣠⠏
⠀⠀⢀⡶⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢳⡀⠀⠀⠀⢰⠃⠀⢸⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⡰⠃
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⡜⠀⠀⠀⢧⠀⠀⠀⣼⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡠⠤⢄⣀⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢀⠇⠀⠀⠀⢸⠀⢀⡞⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⣤⠋⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠉⠉⠓⠦⣼⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢄⣀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠉⠓⢴⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⢀⣀⣀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢳⣄⣤⠤⢤⣄⣀⠀⠀⠀⢳⡄
⡴⠖⠒⠚⠛⠋⠉⣡⠖⠋⠉⠉⠉⠉⠙⡇⠀⠀⣠⡤⠴⠶⠦⢤⣀⠀⠀⠀⢸⣆⣀⣀⣀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⣷
⠘⢦⣀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢧⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⢦⡔⠋⠉⠉⠉⠉⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⣿
⠀⠀⠀⠉⠑⡞⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢷⠃
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣸⠓⠦⡀
⠀⠀⣠⠞⠉⢧⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⢦
⠀⡼⠁⠀⠀⠈⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣠⠎
⢰⠃⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠤⢤⡤⠖⠋⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠒⠊⠁⠀⠑⠦⣄⣀⣀⣀⣀⠴⠚⠁⠀⠀⠀⠈⡇
⠀⢧⠀⠀⠀⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠣⡀⠀⠀⠀⢀⡞⠀⠀⠙⠲⠤⣤⣀⣤⠤⠖⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡷⢤⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠈⠓⠢⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢀⣀⠴⠋⠲⠤⣄⣀⣀⣠⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⠉⢙⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⣤⠒⠊⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣄⣀⣀⣀⡠⠴⠊⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⠀⠀⣀⡤⠷⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠁⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠑⠦⣄⣀⣀⣀⣀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠖⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣀⠤⠖⠉

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢷⡄⠀⠀⢰⠖⢤⡀⠀⡾⢸⠃⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡒⠦⣄⠀⢧⠸⣷⠀⠀⢸⠀⢸⡏⠀⡇⢸⠀⡞⢠⠋⡝⢧⠀⠀⡠⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⠈⠳⡘⡄⢻⣇⠀⢸⠀⣿⡇⢸⠁⡇⢰⢃⡎⣰⠁⣸⡤⠊⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠑⣄⠙⢷⠈⢿⡆⢸⠀⣿⡇⡞⢸⠁⡞⡜⢠⠃⡴⠋⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡶⣍⠳⣷⣌⠣⡈⢇⠘⣿⣼⠀⣿⣷⠃⡏⢸⡟⢠⣯⠊⣠⣾⠟⠁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⣌⠻⣦⠙⣜⣆⠘⣾⡤⠿⠿⠾⠶⠿⣤⠟⢁⣴⢟⡡⠖⠉⣀⡤⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢢⡙⢷⡈⢿⣤⠞⠀⠀⠀⠀⠀⠀⠘⢤⣿⠟⢉⡠⠖⢋⡡⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡽⠦⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠯⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⡋⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⢱⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣤⣤⡤⠤⠞

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⡤⠤⣀
⠀⠀⠀⠀⠀⡀⢤⠒⠋⢹⡖⠂⠈⢳⡌⢂⠙⣿⠣⡀⠀⠀⠐⡟⠡⠔⣛⣫⣶⣦⠀⠀⢀⠎⠀⣀⠤⠜⠀⠧⣀⠀⠡⡀
⠀⠀⡠⠒⣭⢄⠸⡍⠳⡈⢳⡀⠀⠀⢻⡌⡄⠘⣄⡇⠀⢸⠀⠃⢠⠊⠉⠉⢉⣈⣁⠀⣸⡀⠚⠀⠀⡄⢠⠀⠀⠱⠀⡧
⠀⠰⠁⠀⢿⠀⠂⠹⣆⢱⡈⢷⡀⠀⠘⡇⣧⣶⠟⠀⠀⠘⢧⡀⠐⠔⠒⠉⠉⢉⡟⠀⢿⣧⡀⠀⠀⠸⠂⠀⠀⣀⣴⠇
⠀⢠⡀⠀⠈⠓⠄⣦⣘⢦⣧⣀⣷⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⠴⠚⠁⠀⠈⠻⣿⣷⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠉⠛⠓⠒⠛⠛⠛⠛⠛⠋⠉⠀⡠⠒⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⡩⠭⠟⠫⢤⣀⣀
⠀⠀⣠⠒⠫⣅⠉⠉⠱⣶⢤⠀⠀⡌⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠀⠀⠙⡿⠉⠱⡀⠀⠀⢀⣴⡙⠀⠀⠀⠀⢨⠀⢨⣉⠵
⢀⣞⠣⠄⢈⢮⡀⠀⣠⡇⢠⠳⡄⡇⠁⠀⠀⠀⠀⠀⣸⠀⣸⠶⢦⣄⡰⠁⠀⠀⣷⠀⣰⡋⠀⠘⢎⢂⠀⠀⣸⠀⠊⠁
⠠⠁⠀⠉⣷⣿⣿⡾⠛⠶⠾⢤⠁⠘⢄⣀⣀⣀⣠⠴⠃⠀⡇⠀⠀⠘⡇⠀⠤⠞⡿⠠⠀⠬⢷⣤⠼⠿⠶⠛⠁
⠘⠦⠒⠛⣉⣁⠀⠄⡠⠠⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠰⣄⠀⠚⠀⠀⠀⠀⠤⠶⠾⠥⣄⡀⠈⠙⠲⣄
⠀⠀⣴⠍⠁⠀⠀⠀⠀⠀⠛⣯⠀⠀⠀⠀⠀⠀⠀⠤⡤⢤⣤⣤⣭⣉⠉⠁⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠈⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⠈⠢⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡱⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠀⢹⠁⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣸
⠀⠀⠀⠙⠢⠤⠴⠄⠂⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠘⠓⠢⠤⠤⣄⣀⡀⠀⡼⠖⠉
⡶⠒⢶⢶⡶⠶⠶⣶⢶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⠶⠶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⢿⣿⡟⠀⠀⠀⠐⢋⣳⠄
⠀⠀⠀⠀⠀⠠⢀⢠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣠⢸⡡⠀⠠⠙⠀⠀⠀⠀⠀⠀⡾⠿⠿⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⣿⣿⢇⡲⠀⠰⠄⠀⠀⠐⠒⣶⠶⢷⣶⣶⠖⠒⠓⠲⣾⣥⣀⡀
⠀⠀⠀⠀⠀⠷⢽⢸⢛⣷⣶⣀⣤⣴⣤⣸⣿⣿⣿⣿⣿⣴⣶⣤⣤⡤⢶⣶⠯⣷⣦⣸⠀⠃⢸⡆
⠀⠀⠀⠀⠀⡁⠀⠀⠛⣿⣿⢛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⣿⠀⠉⠉⠉⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢛⣓⢶⣿⣿⣿⣇⣉⣿⣿⣟⡇⢼⣿⣿⣿⣟⡛⢀⣼⣿⣿⣿⣦⡀⣠⡀⣾⡉⣹⠃
⠀⠀⠀⠀⠐⣿⣿⣿⡿⠿⠛⢹⠏⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢽⢻⣏⣧⠵
⠀⠀⠀⠀⠀⠉⠉⡟⠁⠀⠀⠘⠊⠛⠛⠋⢛⡟⠋⠙⠛⠙⠉⢹⣏⣙⣇⠿⠴⠓⠊⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠿⠠

⣿⣿⡏⣾⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⢸⣿⣿
⣾⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢛⣿⢋⣴⡿⣯⣿⠈⣿⣿
⣿⣞⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⡋⢹⣏⢉⣿⣿⣿⡿⢿⠿⣤⣿⣟⣿⡏⣿⠀⣿⣿
⣾⢿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣋⣼⣿⣿⣿⣿⣿⣷⠟⣽⣿⣿⣿⣿⣧⣿⠀⣿⣿
⣿⣾⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⣾⢏⣿⣿⣯⣿⣅⣿⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⣹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠶⣶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣭⣬⣽⣿⣿⣿⣿⣯⣿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⠙⢿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣣⠭⠿⢟⣛⣻⣿⣻⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠙⠻⣮⡻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⣧⡌⢳⣾⣏⣩⣿⣿⣿⣥⡍⠋⠉⠀⠈⠉⠙⠋⢻⣿⢻⡟⠿⠿⢶⣿⣿⣿⣿⣿⡿⢿⣿⠀⣿⣿
⠀⠀⠀⠀⠈⠻⢯⣿⣿⣿⣿⣿⣿⣽⣿⣯⡿⣯⡽⠛⠛⢀⣉⣩⣽⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡟⠘⠟⠂⠀⠒⠁⠿⣿⣿⡿⠀⠈⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣤⣿⣿⡿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⢶⡑⠀⠒⠀⢰⠀⠀⠀⠁⠀⢠⡏⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠄⢀⣀⣤⡄⠀⠀⠀⠀⠀⠉⠉⢹⣏⣥⣤⣤⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⢸⣿⡷
⠀⠀⠀⠀⢴⣶⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠏⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⠸⣿⣿
⠀⠀⠀⠀⠀⣿⠠⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⢻⣷⢸⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⠈⢁⣈⣀⣸⣷⣶⣶⣶⣶⡄⣿⡛⣾⡇⠀⣿⣿
⠀⠀⠀⠀⢀⣶⠸⠃⢸⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣇⠀⠈⠀⠀⠀⠀⠀⠘⠒⡆⢸⣿⣿⣿⡷⠒⠀⠐⣿⡆⣿⣁⣾⡇⠀⣿⣟
⠀⠀⠀⠀⠈⠛⠀⠀⠀⣿⣿⢻⡇⣿⣧⠀⠀⢠⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠰⠈⠀⡇⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⣿⠟⢹⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢠⡦⢸⡆⠀⠃⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠻⠀⢀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⡧⢾⣿⠀⠀⠀⠀⠀⠂⠀⠀⡇⠘⣿⣿⣤⣤⣼⡟⣤⣼⡿⠀⠀⢸⣿⡟⣿⡧⠀⠀⠀⣿⡇⣼⣿⢾⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠸⠿⠤⠶⠤⠄⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣠⣄⣠⣸⣟⣿⣇⣀⣀⣀⣿⡏⣿⣏⣸⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⡶⣶⡶⡶⠒⢲⠶⡀⠶⠀⠰⠶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠻⢻⡿⣿⣿⡿⠿⡟⢻⠃⣿⣿⢻⡇⠘⣿⡇
⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⢠⡶⠦⢶⠀⠠⠶⠆⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣧⣾⣿⡏⠘⠛⢻⣷⣿⣿⢸⡇⢰⣿⡇
⠀⣿⢈⠀⠒⠀⠀⠀⠘⣿⣿⠀⣇⢸⡇⠀⠘⠀⢀⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠐⠾⡇⣿⡿⠀⠛⡀⢸⣿⣿⣿⣿⡇⢸⣿⡇
⠈⠛⠀⠀⠀⠀⠀⠀⠀⣝⣿⠀⣿⢸⡇⠀⢀⣀⡀⠀⡆⠀⣀⣤⡀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣶⡤⠀⢾⣿⣿⣿⣿⡁⢸⣿⡇
⠀⢰⡔⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡷⢰⣿⣿⣿⣾⡿⢸⣿⣿⡇⠀⠈⢹⣿⣦⠠⡦⠶⠶⠶⠶⠾⠛⠛⠛⠛⠋⠀⠺⣿⣿⣿⣿⣿⡇⢸⣿⡇
⡜⢾⠁⠀⠀⠀⠀⠀⠀⣿⣿⣀⣿⣿⡇⣾⣿⣿⣿⣿⢷⣿⣿⣿⣿⠆⠀⠘⠿⣿⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡇⢸⣿⡇
⠁⢸⡀⠀⠀⠀⠀⠀⠀⣾⣿⠏⢉⣁⡰⣾⣿⣟⣛⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠠⠀⣷⡄⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣼⠇⢸⣿⡇
⣷⣾⡇⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣤⣤⣤⣤⠴⢄⣤⣴⣶⠚⠻⣿⠀⡀⠀⢹⣿⠊⣿⡧⠀⢢⠀⣋⣉⣉⣀⣀⣠⣤⣤⣤⣤⣤⣤⣿⠄⢘⣿⣧
⢿⡿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣷⣯⣿⣷⡾⠿⡷⠾⣟⠿⠟⠛⢋⠓⠀⠀⠀⢉⣏⠁⣼⣿⠀⡀⢘⢹⣿⡟⠛⠛⠙⠋⠉⠉⠉⠉⠉⠉⠀⠈⣿⡟
⢻⣿⣿⠄⢀⠀⠀⢀⣀⣿⣏⡛⠦⣬⣉⠶⣦⣴⡶⢦⠐⠠⠂⠉⠶⡗⠀⠀⠀⣃⠀⠸⣿⡄⢳⣿⠈⣿⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⢠⣉⣿⣏⣉⠛⠻⣀⡀⠀⣤⣬⣑⠲⣮⣿⡧⠞⣯⡥⠶⣀⠐⠂⠤⢦⣤⠀⠀⢻⡄⢀⠈⡇⠈⠟⠀⣅⢹⣆⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⡟⣿⣿⣿⡿⠶⠊⠉⠋⠡⠔⠋⠟⢁⠉⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠁⠠⠀⠀⠀⢉⣩⡇⠀⠀⡇⠉⢸⣿⣷⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣏
⠀⣿⣿⣿⢿⣷⡀⠰⠶⣤⡂⠛⠦⣞⠉⠰⠶⣈⠙⠂⢤⣀⠈⠳⠄⢈⠀⠀⠀⢀⠘⢹⣿⣇⠀⡄⡇⠀⣸⣿⣿⣿⣦⡈⠧⣀⣀⣀⣀⡀⢰⣿⡇
⣟⣿⣿⠻⢦⣄⡙⠒⢤⣄⣉⠑⢂⣀⠈⠀⢂⡤⣈⠁⠴⢄⣀⣤⠦⣤⣬⠷⠀⣼⢿⣿⣿⣾⠀⠁⢇⠀⣿⣿⣿⣿⣿⡿⠄⢘⠋⢻⢹⡇⢸⣿⡇
⣿⠟⠛⡷⠞⠛⢉⠶⠛⠋⠁⠞⠉⣁⡬⠛⢁⡴⠛⢁⡀⠀⠀⣀⠴⠋⢡⠔⠀⢁⣼⠿⣿⣿⡀⠀⢸⠀⠉⢹⡅⢀⠀⡆⠀⠈⠀⣼⣾⡇⢸⣿⡇
⠄⠘⢁⡀⠄⠁⢀⠴⠚⢃⡠⠄⠉⣀⡤⠞⢁⣠⡄⢈⣁⢶⣞⠁⡠⠦⢀⡀⣻⠳⢦⣾⣿⣻⡇⠀⠸⠆⠠⠈⠀⣿⡀⢸⣶⢀⠀⢸⣿⡇⢸⣿⡇
⠤⣌⠁⣠⠰⢶⣄⡀⠈⠻⢦⡶⠛⠙⠣⢶⡍⢉⠉⠻⣋⣄⡈⠛⠒⢤⣀⡉⠙⠷⣦⣬⣿⡿⠀⠀⣶⠀⠀⠀⠀⢿⣇⠀⢿⢸⡀⣾⢿⡇⢸⣿⡇
⠀⠈⠉⠦⣄⡀⠈⠑⠢⢄⡀⠀⠁⠶⢤⣄⡀⠈⠻⢤⡀⠀⠝⠻⢶⣆⡹⠟⢷⣤⣄⣈⠙⣻⠁⣸⣿⡄⠘⣦⠀⠸⡟⠄⠀⢸⡅⣴⣼⡇⢸⣿⡇
⠛⠶⣀⠀⠈⠙⠲⣄⡀⠀⠙⣶⣦⣦⢀⣨⣷⠶⣤⣀⣼⠟⢲⣦⡴⢟⡹⣳⣶⠋⢀⣙⡿⠋⠀⣬⣿⡷⠀⢻⣥⡀⡏⠀⣀⠈⠃⣿⣿⡇⢸⣿⡇

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀
⣿⠀⠀⠀⠒⠀⠀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠓⠒⠶⠦⠤⠤⠤⣤⣀⡀
⣿⠀⠀⠀⠠⠐⢂⣀⠨⠕⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀⠀⠀⠀⠀⢀⣀⢀⣀⡀
⣿⠀⠀⠀⠀⣿⡖⠛⣊⡁⠀⠉⠉⠀⠘⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁
⣿⠀⠀⠀⠉⠉⡩⠅⢀⣒⣲⠶⣶⣶⣶⣤⣤⣤⣭⣬⣬⣤⣬⣤⣤⣤⣤⣿⣿⣿⡿⣇⠈⠁⣀⠈⠈⠙⠖⠲⠦⠤⠤⠠⠤⡄
⣿⠀⠀⠀⠴⠖⠞⠋⠉⠁⠻⣷⣿⣿⣿⣹⠉⠉⠛⢿⣿⡿⠟⣿⣿⣿⡟⠉⠻⣷⠷⠏⠹⠁⣿⠛⠻⠛⠇⢀⣀⡀⠀⠀⢀⠄
⣿⠀⠀⠀⠂⠀⠃⠀⣢⡀⡃⣿⣼⣿⡿⠝⠒⠒⠒⣿⣿⣿⠾⠺⠿⢼⡁⠀⠰⠿⡇⠀⠀⠖⡿⣄⡀⠀⢠⣼⣿⣥⡄⠀⣸
⣿⠀⠀⠀⠣⢼⣹⠀⢸⡏⠛⡿⣿⠀⠀⣰⠀⠀⠰⣶⡏⢸⠐⠀⠀⠈⠅⠀⢀⠀⡇⠀⠀⠀⠀⡿⠐⠀⠑⢶⡏⠅⠂⠀⣿
⣿⠀⠀⠀⢠⣾⣿⣿⡙⡄⠇⢱⠈⠆⠀⢹⣴⣦⣴⡇⠀⢸⣤⡴⢤⠽⠀⠠⠀⠀⡇⠀⣺⣦⠀⡷⣶⡄⢀⡀⠒⣀⡙⣈⢿
⣿⠀⠀⠀⠈⣿⠻⣿⣿⠻⡇⢸⠶⠞⣇⠈⣻⠏⣽⡯⠀⢀⢻⣟⡈⠅⠀⡌⠠⢄⣇⣙⠋⣹⣾⣿⢿⡇⠀⠈⢶⣿⣦⣹⣿
⣿⠀⠀⠀⠀⢹⣷⢾⠃⠀⠘⠈⣄⣠⣿⣽⣿⡟⡍⠀⠀⢰⣿⣿⣡⣇⡀⣉⣉⣟⡿⠯⠾⢧⣿⣿⣿⣷⢆⡐⢺⣿⣿⣁⡨⠁
⣿⠀⠀⠀⢠⡿⠹⣟⡀⠀⢐⠀⠏⢿⢹⣿⣿⣄⠀⢀⠰⠘⠿⠿⠟⠞⠛⣿⣿⣿⣦⣻⣿⣿⣿⣿⣿⠿⢂⣷⠾⣿⣷⣿⡇
⣿⠀⠀⠀⠙⠁⠀⠙⠃⠀⠐⠒⠐⠚⠚⠿⠽⠟⠓⠈⠀⠀⠀⠀⠀⠀⠃⠒⠻⠿⠻⠿⠻⠻⠿⢟⡵⠶⠛⠛⢤⠛⠛⠛⠓
⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡞⠀⠀⠀⠀⠌⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠈⢦⣈⢢⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠳⠾⡥⠄⢀⠀⠀⠀⠀⣀⠀⠴⠶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠛⠁⠀⠀⢀⡐⣶⣵⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⢷⡀⠠⢀⠀⠀⠀⠀⠛⠷⢮⣇⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡂⠀⠙⠄⠀⠈⠀⠀⠀⠛⠲⡂⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢦⡀⠉⡦⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠈⣷⣦⠀⠀⠀⢠⣿⠀⢰⠀⠀⠀⠈⣍⠀⠈⠃⢁⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣿⣿⣷⠀⠀⢘⣿⣦⠈⠀⠀⠐⠀⠈⣦⡦⢠⡀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣈⣿⡇⠘⣃⡤⠞⢹⣿⣧⣤⣀⠀⠀⠀⠀⠑⠥⣻⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⢤⣤⠤⢿⣷⡀⠉⠀⠀⠀⢚⣿⣟⣿⣧⡶⢦⣀⡀⠈⢀⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⠏⠀⠀⠀⣘⣷⣦⣄⣀⣀⣠⣿⣾⠩⣦⣀⣠⣩⣿⡷⣎⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠸⣤⣀⣴⠏⠉⠀⠈⠙⢿⣭⡿⠉⠀⠀⢀⢻⣿⣿⠛⢿⣷⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⣰⠟⣿⠉⠀⠀⠀⠀⠀⢢⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢻⠀⠀⠀⠀⠀⢰⠋⣿⡀⠀⠀⠀⣸⣤⣿⣽⡄⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠳⣄⠀⠀⢈⣰⢏⡡⢿⣦⣄⣠⣼⣿⢾⠿⡤⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣆⣐⣩⠿⠉⠉⢿⣿⡿⠁⠀⢨⣍⢿⣷⡄⠀⣀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠰⣾⡟⠀⠀⠀⠀⢸⣶⣿⡵⢧⣾⣯⠿⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⡀⢿⣷⠀⠀⠀⣀⡿⠋⠀⠀⠀⠀⠉⢶⡀⠀⠈⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣀⣘⣚⣵⠷⠦⢄⣿⠁⠀⠀⠀⠀⠀⠀⣼⣥⡀⣢⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠁⠀⢀⠈⢿⣇⠀⠀⢀⢀⣤⢸⣿⣿⣿⣿⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡶⣿⣶⣤⣤⣼⣤⣟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⣽⣿⠏⠈⠉⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣼⣿⣿⡇⠀⠀⠀⠀⢀⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⠉⠳⣄⣄⣀⣴⣿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣷⣾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣭⣥⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⢻⣟⣻⣙⣟⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣻⣿⣿⣿⣷⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣿⣿⣿⣿⣿⢿⡾⣷⣿⣻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣿⣿⣿⣿⣿⣽⣿⠿⠿⠷⠟⣛⡛⢛⣋⡋⣭⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣟⣛⡛⣹⣽⣽⡵⡶⠶⠲⠾⠟⠛⣙⣫⣫⣎⣍⠁⣤⣤⣤⣤⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⣉⣥⠶⣓⣲⣤⣴⣶⣶⣶⣶⣗⣒⣒⣲⣶⣤⣬⣀⡈⠙⠿⢿⣿⣆⣠⣍⣰⣤⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⢄⣨⣿⠟⣫⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⡻⢿⣦⣽⣿⣫⣄⣌⠱⠤⢄⡀⣼⣿
⠀⠀⠀⢀⠠⠴⣮⣴⢟⣭⣚⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠹⠿⣿⣿⡿⣟⣄⣲⣿⣿⣿
⣀⡤⠒⠡⣲⣷⡿⢛⣵⣿⣿⣟⡻⠟⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣷⣶⣿⡛⣷⣾⣼⣟⣻⣯⣝
⣿⢿⣴⣾⣿⣿⠾⣯⣿⣿⡵⠋⠀⠀⠀⠀⠀⠀⡟⢸⣿⡿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣷⣝⢶⣭⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣵⣿⣻⡿⠁⢀⣀⣠⡀⠀⠀⠀⢰⠥⣿⣿⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⣀⣹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿