Celebrate Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡢⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⢝⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠛⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⠨
⠀⠀⡂⠀⠀⠀⠀⢠⣤⡄⢴⠀⠀⢸⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⡀⠀⢸⣿⡇⠘⢧⣘⣿⣇⣰⠏⠀⣤⠀⠀⢠⠀⠀⣠⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⣶⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠀⠀⢼⣷⠀⣰⠇⠀⠀⠀⢹⣿⣿⠁⠀⠀⠸⣆⠰⣾⠆⣠⡟⠀⠀⢻⡀⢲⣶⠂⠀⠀⠀⠻⣄⠰⣷⠆⣰⠇⠀⠀⢾⣷⠀⢀⡶⠀⠲⣦⣀⠀⢿⡷⢀⡼⠃
⠀⠀⢠⡶⣶⣶⡞⠁⠀⠀⠀⠀⣸⡿⣿⡀⠀⠀⠀⠈⢻⣿⣿⠉⠀⠀⠀⠀⠙⣿⣿⡟⠛⠲⡄⠀⠈⠻⣿⣿⠁⠀⠀⣠⢶⣿⣿⠉⠁⠀⠀⠀⠉⣻⣿⣶⠋⠁
⠀⠀⠈⢷⣿⣿⡇⠀⠀⠀⠀⣴⠏⠀⠈⢷⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⣧⠈⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠰⠂
⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠾⠃⠀⠀⠀⠀⠻⠆⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠚⣿⢿⡟⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⠈⣷⠀⠀⠀⠀⠚⣿⢿⡿⠃
⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢀⡿⢀⣿⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠘⠠⠆
⠀⠀⠀⠀⠀⣼⢻⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣶⣄⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⢻⡟⢹⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⣿⣽⣟⢻⣿⠙⠛⠁⢠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠳⠀⠸⠀⢠⣚
⠀⠀⠀⠀⠀⠀⢸⣧⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡛⠿⣦⡀⠀⢠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⠀⡀⠀⣀⣄⡀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠛⢶⠀⠸⣿⣿⣷⣶⣶⣾⠇⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠿⠁⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢰⡟⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⣠⣻⣿⠀⠀⢈⡘⢶⣄⣬⢩⣿⣿⣿⠉⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⡄⠀⠻⣿⡿⠇⣀⢠⢷⡀⢹⣿⣧⢿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣿⣿⣷⣴⣶⣿⠟⣴⣶⣵⣼⣷⡟⣾⣇⠘⠻⢟⣁⣀⣤⡾⠟⠉
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣽⣛⣻⣿⣿⣿⣆⣙⣻⣛⣹⣿⣿⣿⡙⣿⣿⣿⣿⡏⠉
⠀⠀⠀⢸⣿⡷⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⢿⣾⡛⣿⣿⣿⣿⣿⢹⣿⠃⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣾⣆⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⣿⡷⣿⣷⣿⣿⣿⣿⣿⢸⣿⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⡟⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡇⣿⡇⣸⡷⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠛⣿⡿⣿⡇⣿⡇⣿⣷⣿⣿⢹⣿⠉⠈⠋⠈⠉⣿⡇⢸⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠛⠃⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢸⣿⠃⠀⠀⣿⡇⢿⡿⣿⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢸⣿⠀⠀⠀⠈⠀⠈⠁⣿⣿⢸⣿⠀⠀⠀⠀⠀⠻⠃⠸⠟
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠻⠟⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢠⡞⢭⣱⠀⠀⠀⠀⠀⠀⡍⠒⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⢃⡤⠦⠀⠀⠀⠀⢀⡴⢯⣅⡢⠁⠀⠀⠀⠀⠐⠚⠲⡀⠄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠞⠢⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⡈⠳⠃⠀⠀⢀⠤⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠏⠳⠎⠀⠀⠀⠀⢀⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠈⠀⠀⠀⢎⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣄⠀⠀⠀⠀⠀⣤⠠⠃⠑⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠱⡀⠀⠈⠢⣀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⣔⠲⠈⢃⡿⠘⠀⠀⠀⠀⠀⢘⣀⠤⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠓⢄⠀⠀⢈⠀⠀⢸⠀⠀⠀⢀⡤⢄⠀⠙⣠⠗⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⠁⠀⠈⠢⡀⠀⠑⠒⠙⢄⣀⠀⡈⠳⢨⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⡴⢸⠙⢬⡯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⠃⠀⠀⠀⡠⠛⢦⡀⠀⠀⠀⠙⡆⡹⠶⠋⠀⠀⠀⢀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠴⠟⠫⣚⡰⠀⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡠⠁⠀⠀⢀⠜⠁⠀⠀⠙⣢⡀⠰⢭⠟⠣⡀⠀⠀⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠘⠾⠖
⠀⠀⠀⠀⠀⠀⠀⢀⠂⡰⠁⠀⢀⡴⠁⠀⠀⢀⡠⠊⠁⠈⠢⢄⠀⠀⠘⢄⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⡎⡰⠁⠀⣠⠊⠀⠀⣀⠔⠉⠀⠀⠀⢀⠠⠒⠉⠢⢄⣨
⠀⠀⠀⠀⠀⠀⡘⡐⠁⢀⠞⠀⢀⡠⠊⠁⠀⢀⡠⠖⠉⠀⣀⠤⠐⠀⠁
⠀⠀⠀⠀⠀⢠⡑⠀⡔⠁⢀⠔⠉⠀⡠⠔⠊⢁⡠⠔⠂⠉
⠀⠀⠀⠀⢠⡟⡠⢊⡠⠊⣁⠤⣒⠩⠄⠒⠉
⠀⠀⠀⢀⣿⣌⣔⣩⡶⠝⠂⠉
⠀⠀⠀⣾⠿⠛⠉


⣿⣿⣶⣶⣷⡿⢾⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⡿⣾⠿⠶⠶⢶⣿⡶⠶⠶⠶⢾⠶⢶⡶⠶⠾⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣴⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢈⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣛⠂⠀⢀⣠⢶⣀⡀⢀⣄⠛⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠁⠀⡄⡇⡄⡀⠂⠶⣠⠸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠙⢿⡉⠉⠉⠩⠩⠩⠩⠩⠍⢹⠃⠀⠁⠸⠭⠄⠀⠀⠀⠡⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢧⠀⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢲⠖⡐⡒⠀⢓⣃⠱⢇⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠣⠻⣉⡦⣎⠙⠃⠀⠉⠁⠑⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠆⠈⢘⢭⠀⠠⠄⡀⠀⠰⠣⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠠⠀⡴⣎⢨⢦⠀⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠃⢨⠀⠈⣿⡗⢡⡏⠀⠀⢣⡀⠀⠀⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⡣⢬⠁⠄⡬⠋⠀⠠
⠀⠀⠀⠀⣤⠀⠁⣉⡀⠀⢘⡇⠀⢠⢿⣴⢬⠷⡀⠀⠈⡇⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠓⠀⠀⠀⢀⠰⣄
⠀⠀⠀⣠⡄⠈⡁⠈⣽⣄⡼⣇⡀⢂⠄⠈⠖⠠⢄⢀⣰⠿⡄⣴⡄⡄⠀⠀⠀⢠⠁⡀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘
⠀⠀⠀⠉⠁⠀⠀⢀⠸⢷⣆⠌⡝⢁⠀⠁⣀⡁⣠⡡⡐⠶⠀⠉⠀⠀⠀⠀⢀⠘⠌⠃⡫⠨⠈⠀⠃⠀⠀⠀⠀⠀⠸⠀⢀⡖⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠥⠘⢛⣛⣭⡤⢷⢶⢬⣭⣐⣀⠂⠀⠀⠁⠀⠀⢼⠀⢐⠀⠅⡠⡆⡀⠀⠀⠀⠀⠀⠀⠉⢐⠾⠀⡀⠂⠁⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⡍⠀⢑⠀⣖⡆⠐⢇⡄⠉⠙⣅⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣃⠀⢿⠀⣛⣇⠀⠠⠖⡀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣸⡄⠈⠄⢹⡽⡄⠸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⡶⣤⠀⠀⣆⣥⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢱⡄⠀⠀⠀⠠⡦⠤⠂⠀⠀⠀⠀⡀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠃⠿⠀⠀⣧⣿⠗⡄⠀⠀⠀⢠⣤⠀⠀⠸⠀⢸⠀⠈⡇⡀⢀⠄⢸⠂⡆⡆⡤⣃⢤⠘⠇⠆⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⠀⣮⣀⣿⣼⣠⠝⠀⡀⠀⠀⠉⠀⠀⠀⠀⢸⠀⣸⠓⠇⠘⠂⢸⠀⠁⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢁⡛⠀⠘⡮⣙⣿⣟⠰⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠏⠑⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢡⣦⠈⡿⠃⠈⠶⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠸⠏⠀⠀⠀⠛⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠐⣆⠀⠀⠸⣦⣄⣠⣾⠃⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣼⡆⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠰⢿⣾⠃⠀⠀⣀
⠀⠀⠀⠀⣼⣿⡆⠀⠀⠁⠀⠻⠷⠀⢀⣀⣀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣶⣦⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢠⣦⣅⡀
⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢿⣿⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣹⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡇
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡿⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⡇
⠀⠀⠀⠀⠀⠰⠄⠀⠠⠒⠀⠀⠠⠀⠹⠀⠸⠧⠀⠘⠉⠩⠅⠀⠀⠠⠄⠄⠀⠀⠠⠄⠀⠀⠠⠤⠀⠠⠄⠠⠄⠀⠛⠀⠀⠃

⣿⣿⠿⢿⡿⢿⢿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠆
⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⣰⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠀⢈⡿⣦
⠀⠀⢀⣹⣟⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠶⢶⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⠆⠀⡄⠀⠀⠀⠀⠀⠈⠟⠀⣾⠡⣼⡀
⠀⠀⠈⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠅⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠘⠋⡀
⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢠⡟
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣿⣆⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠏⢿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣁⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠈⣿⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⣀
⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻
⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠚⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠛⠛⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠘⣿⣿⡀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⢀⣼⠛⣿⣿⠁⠀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣀⡀⣹⣿⠷⢤⣀⡀⢀⣼⣿⣦⠀⠀⠀⢠⡟⠁⢀⡿⠿⣄⣀⣤⣶⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠉⠉⠛⣻⣧⣀⠀⠀⠙⠻⣿⡿⠉⢷⡀⢠⣿⣷⣴⠋⠀⠀⢸⠿⠛⠋⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣿⣿⣿⡿⠛⠲⢤⣄⣈⢧⡀⠈⢷⡞⢹⡟⣁⣠⣤⣶⣇⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⢤⣄⣉⠙⢻⡦⢸⡇⢿⣿⣅⣠⡴⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠿⣿⣿⠉⠋⠉⠉⠉⢻⠋⠉⠉⠉⠛⠛⠓⠒⠒⠲⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣀⣀⣠⣤⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⡇⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠦⢤⣤⣤⣤⡼⠷⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢠⡞⢭⣱⠂⠀⠀⠀⠀⠀⣿⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⢻⡿⠆⠀⠀⠀⠀⢀⡴⢯⣍⡢⠁⠀⠀⠀⠀⠐⠛⠻⣿⠟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠞⠣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡈⠳⠃⠀⠀⢀⠤⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠳⠎⠀⠀⠀⠀⢠⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡋⠁⠀⠀⢎⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠂⠀⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡄⠀⠀⠀⠀⠀⣤⠰⠃⠑⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠈⠢⣄⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣔⠲⠈⢃⠿⠟⠀⠀⠀⠀⠀⢙⣀⠤⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠓⢄⠀⠀⢈⠀⠀⢸⠀⠀⠀⢀⡤⢤⠀⠙⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠈⠢⡀⠀⠑⠚⠙⢄⣀⠤⡈⠻⢸⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⣴⣿⠙⠬⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠙⡆⡹⠶⠃⠀⠀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⣴⠛⠫⣸⡿⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣦⡀⠰⠿⠟⠣⡀⠀⠀⠀⠀⢂⠀⢀⡄⠀⠀⠀⠀⠘⠺⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣴⣿⣿⣿⣿⡿⠋⠁⠈⠲⢄⠀⠀⠘⢄⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣶⣿⣦⣤⣨
⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⣼⣿⣿⡿⠋⠁⠀⢀⣠⣴⣾⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢰⡟⠀⣴⣿⣿⠟⠁⠀⣠⣴⣾⣿⡿⠟⠋⠉
⠀⠀⠀⠀⢠⡟⣠⣾⡿⠋⣁⣤⣶⡿⠟⠛⠉
⠀⠀⠀⢀⣿⣼⢟⣩⡴⠟⠛⠉
⠀⠀⠀⣾⠿⠛⠉⠁


⣿⣿⣿⣶⣶⡿⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣶⡿⡶⠿⡶⠶⠾⣶⡶⠶⠾⠶⠶⠾⠿⡾⠷⠿⠶⠿⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠀⠀⠀⠛⠟⠃
⠀⠀⢠⣶⣦⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⣹⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠉⠈⠃⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⠘⢿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⢶⣤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠼⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣶⣶⣤⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠐⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⣄⠀⠀⠀⢸⡆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣧⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⠿⠿
⠀⠀⢠⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⣀⠀⠀⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⣠
⡀⠰⠀⠄⠈⡄⠀⠀⡄⠁⠀⠀⢀⠀⠀⠀⠀⠐⠀⠇⠀⢠⠀⢢⡀⠀⠿⠀⡀⠓⠀⠀⢠⠀⠀⠑⡀
⠛⠄⠀⠀⠀⢠⠀⠀⢣⡄⠷⠀⢨⡀⢠⠀⠸⠆⠘⠁⠀⠀⠀⠈⡹⠂⠀⠀⠛⠆⠀⠀⢸⡄⠀⠀⠀⡄
⣀⣃⣀⣀⣀⣈⣁⣀⣸⣻⣀⣳⣀⣀⣀⣀⣀⣘⣇⣀⣀⣆⣀⣰⣀⣄⣀⣀⣀⣀⣀⣃⣈⣃⣀⣀⣐⣃⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢦⠀⠈⠁⠀⠈⠁⠈⢢⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠈⠃
⠀⠀⠀⠀⢠⣿⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠐⠀⠀⢿⠇⠀⠂⠐⠲⡄⠐⠶
⠀⠀⠀⠀⠀⠩⢿⢫⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠐⠄⠀⠀⢀⡤⣀⣤⠀⠸⠋⠀⡀⢶⠶⠄⠀⠀⠀⠀⣤⡁⡄
⠀⠀⠀⢀⠀⣠⢎⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣶⠊⠀⠈⠁⠘⡀⠀⠀⣃⣒⣤⢤⡤⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠻⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⣠⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠠⠀⠀⠈⠠⠀⠀⠀⠀⢴⠏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠈⡀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠆⠁
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢀⠀⢰⡀⠀⠸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⢀⠈⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⡀⠸⠇⠀⠆⠁⠀⠚⠀⠒⠂⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⢀⠀⡶
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⣊⣀⢀⡂⠀⣀⣀⠀⢀⣠⡄⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡦⠀⢀⠃⠀⠠⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠒⣈⠀⠀⣤⣼⠟⠋⢻⣧⡀⠤⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠁⠀⢈⠀⠂⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠀⢇⠀⠐⣿⣿⠀⠀⢈⣿⠁⠠⠀⠀⠁⣀⣅⡃⠀⠀⠀⢣⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠈⠐⠃⠀⠀⠀⠉⢩⠟
⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⣿⠂⣠⠞⠁⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⢀⠈⠁⠀⠐⢂⣾⡟⠉⠒⣀⣀⣍⠀⠀⣀⠀⠄⠀⢤⡀⠀⠰⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠦⠤⠠⠞⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠁⠈⠀⠉⠀⡄⠀⠻⠟⠁⠀⠀⢸⡟⠋⠉⠻⠃⠀⠉⠀⠀⠁⠐⠀⢶⠀⠀⠀⠀⠀⠰⠈⠁
⠀⠀⠀⣠⣤⣼⠃⠀⡀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⡇⠠⠀⠂⠀⠀⠈⢂⠤⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠈⠉⠙⠂⠠
⠀⠀⠲⡿⠁⠉⠀⠀⠃⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠎⡇⠀⠀⠐⠀⢀⠀⢈⠆⠀⠀⠀⠀⠀⠑⠂⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠖⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠉⢁⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⠈⠐⠂⠀⠂⠠⠆⠀⠀⣤⣶⣾⡿⠖⠀⡀
⠀⠐⠃⠀⠀⡀⠀⠈⠀⠀⠀⠈⢁⡀⠀⠈⠀⠠⠀⠀⠀⠀⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⡙⠋⠽⠒⠂⠀⡄
⠀⡋⠁⠀⠀⠀⠄⠀⢂⠀⢠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠒⠈⡀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠃⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣋⢂⡀
⠀⠀⠀⠀⠒⠀⠠⡀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠂⠈⠠⠀⠙⠛⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠡⠄⠐⠀⢠⠀⠀⢪⣀⡤⠘⠂⠀⢠⠄⢀⠱⠠⠆⠲
⠀⢀⡀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠉⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠀⠀⠠
⠀⠀⣠⡄⠀⠀⡂⠀⠀⠀⢀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠃⠀⠲⡶⠦⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡘⠀⠀⠈⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⣀⠀⣀⡀⡀⠀⠀⠈⡀⠀⠀⢀⣰⠁⠀⠀⠀⠦⠀⣀⣤⢀⠀⠁⠒⢸⠁⠀⠂⠀⢀⡄⠀⠀⠀⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠂⢐⡀⠈⠁⠀⠀⠒⠖⠀⠀⡃⠀⠅⠨⠭⣅⠉⠙⠛⠋⠀⠀⠀⠚⠓⠒⠲⡇⠀⡆⠀⠀⠀⠓⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠄⠀⠁⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⢀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣁⣉⣋⣀⣍⣉⣯⣉⣭⣛⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⠀⠀⡄⠀⠀⠀⠀⢀⡠⠤⠴⣶⠖⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢶⣶⣦⠀⠀⠀⠈⣇⠀⠀⢰⡟⢛⡄⢰⠁⠀⠀⠐⠉⠁⠀⠀⣰⠇⢀⡤⣴⠾⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣟⡆⣴⢋⣉⣤⣼⡙⡅⠀⣰⣿⡀⠸⡄⠀⠸⡄⣠⣷⢸⠀⠀⠀⠀⠀⣠⣤⡀⠉⠀⠘⠋⠁⢀⣼⠗
⠀⠀⠀⠀⠀⣀⣠⣽⣾⣯⠥⢈⡟⠻⠿⠟⠛⣿⣃⠞⢁⠅⢧⠀⢡⠰⣶⣧⠙⠛⠀⠀⣠⣶⣿⣿⠿⠿⠟⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠛⠋⢹⡘⢇⣠⠞⠁⠀⠀⠀⠀⡧⠋⠀⢸⣀⣘⡆⠈⣆⠀⠁⠀⠀⣠⣤⠟⠉⠁⠀⠀⣰⠞⠂⠀⢀⡟⠋
⠀⠀⠀⠀⣀⠀⢀⠎⠉⠁⡽⠀⢠⡀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣷⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⡶⠛⡀⠹⣄⠖⠱⡄⠙⠛⠛⠲⣄
⠀⠀⠀⠀⠉⢁⣾⣶⣿⣿⠇⠀⠀⠙⠂⢀⢞⣭⠖⣀⠀⢀⡞⢉⡠⡀⠀⠀⠀⠀⠀⡹⢿⣇⠀⠉⠁⢠⡌⣣⠀⠘⡄⠀⠀⠀⡟
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡌⠁⠸⠫⠆⠀⠳⡀⠀⠙⣆⠀⠀⠀⠀⢳⡀⠉⠀⠀⡄⠈⠉⣹⡄⡀⣷⠀⠠⠞
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⢀⣀⠀⠀⢈⡿⣄⠀⠀⠀⠀⠒⡊⢐⡆⢹⡀⠀⠀⠀⠀⠉⠛⢧⡀⢣⡀⢿⡿⠂⣧⣯⣤⣤⣤⣤⣤
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠘⠒⠁⠀⠘⢦⡒⠀⠀⡇⠲⢯⣶⣿⡏⢸⡇⠀⢀⡀⠀⢀⣴⣶⣏⠒⠬⣤⠶⠾⠋⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣤⠀⠀⠀⠀⠀⠀⠈⠛⠳⣜⠦⣀⠉⢉⠀⣼⣃⣴⣿⣿⣶⣿⣿⣿⣿⣆⢠⣌⣢⣘⣴⣿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣦⡀⠀⠀⣹⡉⠓⠶⠶⠛⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⠛⠿⣯⣿⡿⠿⣟
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⡄⢳⣦⣼⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠿⠃⠀⠠⣎⠹⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡵⠶⠶⢦⡀⢹⣿⠿⣿⣿⣿⣿⣿⡄⢻⡟⠉⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣤⠈⠩⢭⣉⠓⡆
⠀⠀⠀⠀⢠⣦⠀⠀⣾⡡⠔⠀⠀⠀⣡⡿⠋⠉⠲⣍⢻⣿⣿⣿⡄⠁⢰⣢⠀⠻⠉⣩⡍⠉⠻⠿⢿⣿⠟⠻⠂⠀⠁⠀⠀⠀⠀⣱⠇
⠀⠀⠀⠀⠀⠁⢠⡞⠉⠀⠀⠀⠀⠘⠁⢀⡀⢠⠖⠚⣦⡻⣿⣿⣿⣆⠀⠀⠀⣀⣀⣉⣁⣐⣟⣀⣀⣀⣀⣀⠀⢠⡤⠀⣀⡴⢋⠏
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⣾⡫⠀⠀⠀⣾⠟⠤⣈⠹⣿⣿⡆⠀⠀⠙⠣⣟⠒⣦⠐⠒⢒⣶⠟⠉⠀⠀⣠⠞⣉⠔⢁⡀
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣰⠯⢟⣀⡀⠀⠀⠉⠀⠀⠚⠁⠙⠛⠛⠀⠀⠀⠀⠈⠑⢯⡠⠶⣯⠀⠀⠀⠀⣾⡣⠊⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠀⡏⠙⠻⠀⠀⠀⠀⢠⣞⣃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣗⡴⡼⠀⠀⠀⣸⣏⠀⠀⠲⢤⣄⡀
⠀⠀⠀⠀⢠⡀⠀⠻⣿⣄⠀⠀⠀⠀⠙⢦⣤⡴⠀⠀⠀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⢀⠎⣠⠿⠿⠀⠀⢀⠀⢿⡘⠳⣤⡀⠀⠀⠉
⠀⠀⠀⠀⠈⢿⣶⣄⠹⣿⣦⠀⠀⠀⠀⠀⠀⠲⣤⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⢀⠎⡼⠁⠁⢘⡀⠀⠛⠁⠀⠙⠢⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠈⢧⠙⠇⠙⣿⣷⡀⠀⠀⡄⠀⠀⢸⣷⢸⠁⠀⠀⢀⣠⠴⠒⠂⠀⡎⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡑⠄⣿
⠀⠀⠀⠀⠠⣶⣾⣧⠀⢀⣘⣿⣷⡄⠀⣧⣄⣠⣼⣿⠀⠆⠀⡴⠋⠀⠀⠀⠀⠀⢷⠀⠀⡟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⢻⣿⡀
⠀⠀⠀⠀⠀⠈⠛⠋⣴⡿⠃⠈⢿⣿⣆⢷⡈⠉⢉⣿⠀⠈⣾⠁⢀⡤⠚⠉⠙⢷⣌⣇⠀⢣⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣠⡿⡋⠙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⣠⣤⠀⠻⢿⠦⠙⠾⠿⠋⠀⠀⢹⣾⠋⠀⠀⠀⠀⠀⠙⣿⡀⠀⠂⠀⠀⠠⣶⠀⠀⠙⣤⣾⠏⡰⠁
⠀⠀⠀⠀⠀⣠⡄⠘⣿⣧⣿⢸⡆⣰⣶⣆⣀⣿⡆⠀⠀⢀⣿⠷⣄⠀⠀⢄⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣀⣤⠶⢋⢳⡎
⠀⠀⠀⠀⠀⠉⠁⠀⠈⠛⠻⣿⣿⣿⠋⠉⠛⠉⠀⠀⠀⢸⣿⠀⠈⠛⠶⢤⣵⣄⣀⣀⣀⣁⣤⡤⠴⠖⢛⡉⠄⠊⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠐⢎⠂
⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠁⠀⡁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⠢
⠈⠐⡆⠀⠀⠀⠁⠀⠀⠀⠦⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⢠⡄⠀⢅⡂⠀⠀⠀⠐⢠⠀⢀⡀⠐⠠⠀⠚⠲⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⣼⢢⡄⢀⠀⠀⠀⠂⠜⢦⠀⣤⠤⠇⠰⠃⣅⠀⢠⠀⠀⡦⠍⠈⢀⡖⠀⠀⠀⠀⢹
⠀⠀⡎⠀⠀⠀⡀⠄⢁⠰⠉⠉⠀⠨⠂⠂⠀⠘⠋⠐⠃⠀⠀⠀⠈⠄⠐⠖⠊⠑⠀⡇⠀⠂⢀⣿⠧⢄⠀⠀⠘
⠀⠌⠀⠀⠀⠀⠡⢄⢀⠀⠀⠀⠀⡦⣂⠍⠂⢀⠀⢀⠀⠀⠀⠀⢀⠔⠀⠁⡔⠁⡎⠑⢄⠀⠋⢛⠟⠛⠉⠦⡀
⠀⢐⠀⠀⠀⠀⡄⠈⢢⠑⠀⢀⠈⡠⠊⠀⢉⡟⢀⠿⠀⠠⠒⠀⠀⣠⡆⠀⢀⠌⠁⠀⠈⡀⠀⠀⠀⠀⡀⠀⢃
⠁⠈⠉⢲⠀⠀⠎⠢⠀⠂⠔⠡⠊⠅⠀⡐⠀⠀⠀⠀⢆⡀⠈⠐⠂⠁⠩⡀⣀⣀⣀⠀⢰⣾⠀⡀⣀⠀⡀⠀⢸
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠂⠐⡁⠀⢀⠎⠀⠐⠤⠤⠔⠃⠀⠤⠀⠀⠀⠀⠑⠒⠳⠤⠤⠤⠋⠙⠃⢀⠀⠓
⠀⠀⠘⠀⠀⠀⠂⠐⠂⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠊⠉⡇⠁⢐⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡴⠋⠘⡆⠀⢉⢶⠲⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣧⠔⠁⠈⣇⢀⠔⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠋⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡰⠁⢀⣀⣰⢇⠞⠉⠳⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠋⡜
⠀⠀⠀⠀⢸⠁⠀⡸⠉⣀⡜⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠘⠤⠤⡄⠈⠙⢦⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⡼
⠀⠀⠀⠀⡌⠀⠀⡇⠸⣅⡀⡗⢤⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠳⡀⠀⠀⠈⣧⣀⣠⠴⡆⠘⢣
⠀⠀⠀⠀⣇⠀⠀⢳⠀⢸⡇⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⢆⠀⢠⣄⡀⣀⡔⢰⠚⠁
⠀⠀⠀⠀⠘⢦⡀⠀⠉⠚⠀⠀⠀⠉⠀⠧⢄⠀⠀⠀⠀⢰⢢⠀⠀⠀⠀⠈⠢⡀⠀⠉⠋⠀⠉⠁⠀⠳⠦⡄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡞⠘⡄⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠃⠀⠸⠀⠀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⡜⢆⠀⢳
⠀⠀⠀⢀⣀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠠⠤⣄⣀⡰⠃⠀⢇⠀⡸⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⣀⠇
⠀⠀⠀⢸⠀⠀⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⢤⠒⠋⠁
⠶⠶⠖⠚⠂⠀⠻⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠈⠒⠒⠂⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠶⠶⠶⠶





⣿⣿⠟⢿⢛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⣤⡏⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡞⠁⠌⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⠦⣄⡀
⠀⠀⣠⣴⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠠⣿⠀⠀⠀⣠⡶⠶⢦⡀⠀⠀⠀⠀⠹⣏⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⠘⢧⡈⣷
⠀⠠⣟⢠⡟⠰⢈⡷⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⢸⡏⡛⠲⢮⣷⠀⠀⠀⠀⢠⡟⠉⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠻⣤⣀⣀⣹⡿⠶
⠀⢀⣽⢿⣤⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣁⣀⣴⣿⣤⣤⡤⢤⣼⣇⡶⢶⢹⡆⠀⠀⣀⣤⣴⣿⡆⢹⡯⣭⡿⠂⠀⢀⡾⠋⣉⣻⡄
⠐⠛⠁⣾⡁⠙⢦⡀⠀⣠⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣼⠇⣠⡗⢀⡼⢿⣿⡇⢸⡀⣿⠀⠀⠙⣿⣺⣟⠁⠿⣿⡿⣄⠀⠀⣿⢡⡾⠋⣿⡇
⠀⠀⢰⡟⢷⡀⢀⣹⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢃⡶⢮⣴⢏⣴⠿⣅⢸⡍⣧⠸⣧⣼⣦⠴⠞⠋⣿⠟⠃⢀⡏⠙⢮⡳⠦⠿⠛⠀⣸⠟⡇
⠀⠀⢸⣇⣠⣵⣿⡷⠛⢷⡄⠀⠀⣀⡀⠀⠀⢾⣟⣉⣭⡭⠴⠟⣱⣿⡵⢿⡅⠀⢹⣿⡇⠙⢦⣄⣠⣤⣤⣤⠴⣿⠀⠀⠙⠃⠀⠀⠙⢲⡦⠤⠾⠋⢠⡇
⠀⠀⠈⠛⠛⠛⢷⠀⠀⠀⢻⡶⠛⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢀⡿⠀⢀⣿⡇⠀⠀⠀⢰⠀⠀⠀⢠⣿⠄⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣸⠷⢦⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣁⠀⣼⣿⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣽⠂⢠⡟⠀⣾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣰⠟⣿⢹⡏⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡟⢠⡟⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⣏⣸⣧⡿⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡞⠀⢰⠀⡇⢸⡇
⠀⠀⠀⠀⠀⢀⣾⢡⡟⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣉⣿⣿⠁⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⢁⡀⢸⠀⡇⢸⠁
⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢷⡄⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡏⢸⠀⣸⢠⡇⣿
⠀⠀⠀⠀⣰⠏⣼⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⡇⢻⡄⢹⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⣀⣸⣀⣿⣸⣇⣿
⠀⠀⠀⢠⡟⣼⠃⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⢿⡏⢸⣷⠟⠁⠸⢦⣤⣤⣬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⣽⣟⣋⣉⣿
⠀⠀⠀⣾⣱⠇⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢸⣿⣿⡾⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⣙
⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢧⣤⠆⠀⠀⠀⠀⠀⠀⠀⠲⠀⠋⠱⠂⣤⣤⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡰⠋⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠔⠀⠒⠀⠀⢀⠀⠂⠈⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠩⠭⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⣄
⠀⢀⣀⠀⠀⠀⠀⠰⠪⣺⠀⠀⠀⠀⠀⠀⠈⠒⠒⢸⣧⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠰⠂
⠀⢈⣷⡀⠀⢀⣊⡐⠥⢀⢱⠁⡨⠀⠀⠀⠀⠀⠀⢸⡟⡀⠈⠢⡄⠠⠔⢁⡀
⠀⠀⢨⡇⠀⠀⠀⠈⠐⢧⡶⠋⠦⡀⠀⠀⠀⠀⠂⣸⡇⠈⠢⠀⠀⠀⠎⠉⠪⣕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠘⠢⡆⠀⠀⠀⠀⠀⣿⡁⡀⠀⠀⠀⠀⢱⣉⣄⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢄⣑⣠⠫⡤⡀⠀⠀⠀⣁⠋⠆⠀⠀⠀⢘⠀⣈⠤⢳⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠲⠇
⠀⣜⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠑⠃⠀⠀⠀⠀⡐⠀⠀⢀⠄⡾⢄⢘⡖⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠉⠉⠀⠀⢀⡄⡸⠳⡆⠀⠀⠀⠸⡧⡀⡶⡼⠀⠀⢀⠤⡶⠑⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⢔⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⡌⢀⡨⣿⡿⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠙⠒⠉⡁⡿⢶⡈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠖⠤⣤⠚⣴⠏⢉⣿⡆⣡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡩⣚⠓⠀⠀⠀⠀⠈⡳⠏⠀⠈⢩
⠀⠀⠀⠀⠀⢀⠤⣎⠕⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠐⠁
⠀⠀⠀⢀⠔⠁⡠⠇⠢⢀⠀⠀⠀⢀⣠⠜⠉⠚⠀⢀⠂
⠀⠀⠀⠘⠐⠊⠀⠀⠀⠀⠐⠂⠉⢀⠊⠀⠀⠀⠀⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠉⠐⠫⠥⠀⠀⠀⠨⠇

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⣀⡉⠙⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠷⠆⠀⠀⢀⠀⠀⣤⣶⡧⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠿⠋⠀⠀⠀⢠⣄⣄⣀⡏
⠉⠀⠃⠀⠀⠀⠀⠀⠀⣼⣟⡀⠀⠰⡄⠁⠀⣿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠛⠻⣿⡅⠀⠘⠀⣄⡀⠀⣤⠄⠛⠁⠀⠀⠀⠀⠀⠀⣿⠟⠋⣉⣀
⠀⣀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠃⠀⠀⠀⠀⢰⠁⠸⠀⠀⠀⠀⠃⠀⠀⠀⢸⣧⠀⠀⠀⠸⣿⠀⠀⠀⠀⠉⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣠⣾⠿⠿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡄⢸⣶⣶⣄⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣀⡀⣠⣮⠀⠀⠀⠀⠀⠸⠇⢠⣴⠶⠀⠀⠀⠀⢠⣿⢻⡿⠁⠈
⠐⠋⠀⠀⠀⠀⠀⢀⣰⣾⣿⠿⠟⠋⠉⢓⣟⣋⣉⣽⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⢻⣷⣿⠁⠀⠀⠀⠀⠀⠀⢿⠼⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠇⠀⠀⠀⠀⠘⠿⠛⣿⡿⠋⠉⠀⠀⠹⡆⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⡄⠀⢀⣀⣀⣀⣀⣀⠀⠀⣤⠀⠀⠰
⠀⠀⠀⠀⠀⠐⡶⢶⣀⣤⠀⠀⠀⠀⠀⢠⣤⣤⣿⡇⠀⠀⠀⠀⠀⣷⠀⠀⢀⣄⣠⣘⡀⠀⠀⠀⠀⠀⠀⠀⡎⠰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣽⡆
⠀⠷⠀⠀⠀⠠⠷⠾⠏⠉⠀⠀⠀⠀⠀⠸⠿⠿⠏⠇⠀⠀⠀⠀⠀⠷⠶⠶⠾⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠸⠘⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⣶⡄⠀⢀⣄⠀⠀⠀⠀⠠⣴⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡄⠈⠻⠟⠃⣀⡼⠋⠛⣿⠁⠀⠙⡿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠈⠙⣧⠶⠿⠆⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡄⠠⠟⠀⢨⡿⠀⠀⠀⠉⠀⠀⠀⠀⣿⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣏⠀⢸⡅⠀⠀⠀⢠⡿⠂⠀⠒⠀⢀⣤⣤⣄⣿⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠋⠀⠀⢠⡼⠇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡼⠋⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⠛⠃⠀⠀⢰⡟⠛⠒⠋⣠⣤⡄⠈⠹⣦⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡉⠳⣤⡀⠀⠀⠠⣄⣨⡇⠀⠀⠀⠻⡿⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣷⣄⠀⠙⢦⡀⠀⠀⠉⠀⠀⠀⢀⡀⣴⢦⣴⠶⣤⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠙⢷⣄⠀⠙⢦⡀⠀⠀⣠⣤⠟⠉⠁⠀⠀⠀⠀⠀⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣶⣿⣷⣄⠀⠹⣆⠀⠘⠂⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡈⣧⠀⠛⠉⠉⠉⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠿⠿⠿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠋⠉








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⢠⡄⠀⠚⡉⡦⠀⠀⠀⠀⠀⠠⠂⠠⠂⠄⡐⡃⠘⠀⠂⠀⣸⠀⢠⠀⡄⣀⠇⡄
⠀⠀⠀⠀⠀⠀⢾⠻⢶⣛⡒⢚⣛⠚⠛⠚⢻⠋⠐⠰⣖⠄⠀⠀⢠⠄⡄⠀⠄⠀⠀⠀⠀⠀⠛⡈⠘⠀⠀⢹⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣋⣟⠐⢛⣘⡟⣌⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⢿⣯⠗⠧⡟⠈⢀⡅⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀
⠀⠀⠀⠀⠀⣰⡳⠀⡌⠃⠀⣾⣦⣿⡴⠀⢌⠱⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠻⣮⠿⢿⣺⠿⣯⡿⠃⢀
⠀⠀⠀⢀⠀⢚⡃⠀⢸⠇⠀⣽⣧⣽⣏⠀⠘⡇⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠾⠹⠦⠈⠁⠀⢸⡀
⠀⠀⢠⡎⢨⡁⢩⣧⡼⣆⢘⠄⠘⢒⠨⣦⡰⢷⢼⣆⡄⠀⠀⠀⠆⠀⡀⡄⠠⡀⠀⠀⠀⠀⠀⠀⠪⠀⠁
⠀⠀⠀⠀⠀⠀⢌⠛⡷⣲⣯⣄⠤⠤⠤⣾⢊⠛⠀⠁⡀⠀⠀⡄⠉⠁⠃⢋⠀⠁⠀⠀⠀⠀⡄⢀⠞⢀⠀⠀⠄⠨
⠀⠀⠀⠀⠀⠀⠀⠁⠿⢥⠗⢺⠛⣻⠛⣳⡒⠦⠥⠀⠀⠀⠸⠇⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⢿⠀⣿⡀⠙⡧⠀⢸⡓
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣧⠈⠀⢯⣧⠐⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣶⠀⠸⣾⣄⠈⠀⠀⠀⠀⠀⠀⡀⢰⠀⢷⠀⠀⠀⢰⠐⢂⠀⡀⠀⡄⢨⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣏⡋⣠⠰⣿⠏⢃⠀⠀⠐⠷⠀⠀⠁⢸⠀⣸⣴⢰⠀⡏⠸⠋⠂⠓⠂⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⠁⠻⣿⣿⣿⢁⣠⠀⠀⠀⠀⠀⠀⠘⠀⠃⠈⠀⢀⠇⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⢹⣤⠘⠿⠉⠻⡆⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠰⡷⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⠛⠛⠁⠀⠙⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⡄⠀⠀⢰⡶⠀⠀⠀⠘⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠿⢿⣾⣿⣀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠻⣍⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣷⡀⠀⠀⠀⣸⡆⠀⠙⠻⣷⣄⠀⠀⠀⠀⠻⠷⠦⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠻⣷⡄⠀⠀⠉⠁⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢀⣀⡀⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⡀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⣿⠏⠉⠀⠠⠾⠿⠋⠉⠑⠠⢤⣤⣾⠟⠛⠓
⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠁⠀⠀⠀⠰⡷⢻⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠒
⠀⠀⠀⠀⢀⣾⡏⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣄⣀⣀⣼⡟
⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣩⣿⡿⠟⠋
⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣶⣾⠿⠋⠁
⠀⠀⢀⣿⠇⠈⠻⢷⣦⣄⣀⠀⠀⠀⢀⣤⣶⡿⠛⠉
⠀⠀⣾⡟⠀⠀⠀⠀⠉⠛⢛⣿⣿⡿⠟⠋⠁
⠀⣼⣿⣷⣤⣀⣀⣀⣤⣶⠿⠛⠉
⢠⣿⠃⢈⣩⣿⡿⠟⠋⠁
⣾⣿⣾⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⠿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠹⣿⣇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⣿⣿⠸⣿⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⣴⣦⣄⡀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⣿⣿⠀⢻⡷⠀⠀⠘⠻⠃⠀⠀⠀⢠⣿⠏⠉⠛⠿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠉⠙⠶⣤⡀⠀⣾⣿⠁⠀⠀⠀⠀⠰⣿⡷⠀⣀⣀⣀⠀⣹⣿⠀⠀⠀⠰⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣧⠀⠀⠀⠀⠈⠙⣾⣿⡏⠀⠀⠀⠀⠀⠀⠈⠀⣾⡿⠛⠻⠿⠟⠋⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⢧⡀⠀⠀⠀⣰⣿⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣾⠿⠟⠛⣿⡇⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⢳⣄⠀⣰⣿⡟⠀⠀⠈⠳⣄⠀⢀⣠⣴⣾⠿⠁⠀⠀⠀⠙⠛⢁⣄⡀⠀⢹⣿⣾⡿⠉⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠙⢶⣿⠟⠀⠀⣀⣤⣴⣾⣿⣿⠛⠋⠁⠀⢠⣶⣦⠀⠀⠀⠘⠟⠃⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠛⠉⠉⠀⠀⠙⢧⡀⠀⠀⠀⣉⣁⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀⣀⣿⣶⣾⣿⠿⠿⠟⠛⠛⠛⠛⠻⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⣾⣿⠿⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⠀⠀⠀⠀⠸⡆⠀⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣄⣠⡿⠀⠀⠘⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠙⣿⣿⣆⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⡴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⣀⣤⡴⠟⠛⠉
⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⢀⣉⣿⠿⠟⠋⠉
⠀⠀⠀⢀⡾⠀⠙⢿⣿⣦⣤⠴⠞⠋⠁
⠀⠀⠀⢸⣅⣤⠶⠚⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠖⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠀⠀⠀⠠⣶⠠⡀⠀⠀⠀⠈⠀⠹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⠀⡀⠀⠀⠠⠋⠓⠷⠂⠉⠐⠀⢠⠀⠀⢈⠆⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⠀⠀⠊⢆⠀⠑⠀⠀⡤⢈⡀⠠⠀⠀⠠⠀⠀⠘⠂⠀⠀⠀⠀⠼⠆⢀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠀⠀⠁⠀⡠⠀⠀⢠⠀⠀⠀⠈⡀⠒⠀⠀⠸⢲⠀⠎⠐⠚⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣀⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠠⢺⠀⠀⠒⠚⠀⠁⠁⠀⠀⠀⠀⠊⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢌⡀⠐⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠈⠁⠂⠉⠲⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⠘⠀⠀⢀⠀⠀⠀⠉⡀⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡀⠀⠈⠆⠀⠀⠀⠈⣤⣤⠀⠀⣀⣠⠀⠀⠆⠀⠀⠀⠀⠠⡁⠀⠈⣀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⢣⠀⠀⠂⠀⠆⠀⢠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠠⡤⠶⠂⠄⠁⠀⠄⠁⠡⠇
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣿⣶⣿⣿⣶⣶⣶⣶⣿⣶⣶⣷⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣦⣾⣵⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠈⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠊⠁⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠒⠢⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠢⣀⠀⠀⡁⠁⠀⠀⠀⢄⠀⠀⠀⠀⠋⠛
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢏⠀⠁⠁⠸⠝⠀⠀⠀⠈⠁⠀⢠⠂⠀⠒⢄⠀⠠
⠀⠀⠀⠀⠉⠒⢤⡤⠆⠁⠀⡠⠊⠀⠀⠀⠑⡤⡀⠀⠀⠀⠀⣚⠐⠀⡠⠏⢠⠄⡸⣝⢷⡀⠑⠄⣀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠑⢄⠀⠀⠀⢈⠦⣼⠤⢤⣤⡐⠽⢀⠜⠁⢸⡸⡐⠌⣧⢫⣷⡰⣹⠘⠙⠉
⠀⡠⠂⠉⠉⠉⠢⣄⠑⠣⣤⡄⢠⠓⢄⡔⢁⣜⠤⠂⢉⣏⡧⠔⠁⠀⠀⠀⠳⡱⣌⡮⠱⠟⡇⠬⠆⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠄⠆⠀⡎⠀⡆⡄⠋⠀⠗⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣁⠀⡰⢃⡤⢄⣆⡤⢣⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠠⠚⡝⠀⠀⠀⠠⡔⠦⢄⣀⣀⣀⣀⣀⠠⠤⢠⠆⠙⠽⢾⡉⠑⢣⠀⢤⣜⡀
⠡⠀⠀⠀⠀⠀⠀⠀⠰⠽⠀⣀⠀⠀⠑⠄⠀⠀⠀⠈⢦⡔⠤⡼⣀⠀⠀⠀⠀⠾⡔⠒⠊⢁⠔⠊⠀⠀⠀⠈⠉
⠀⠑⠢⢄⣀⡠⠐⢀⡄⡀⠑⠊⢰⠑⠄⠀⠐⠃⠀⠀⠀⠉⠂⠤⠌⠂⠒⠀⠀⠀⠈⠲⡊⠁
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢬⡅⢀⠆⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠏⡽⠢⣀⣀⠀⠀⠀⡀⣀⠠⣤⡶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠃⢀⡔⠁⠀⡐⠁⠐⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠄⠏⠀⠀⠀⠁⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠛⠒⠦⣄⠀⢀⠜⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠀⠒⠂⠠⡀⢀⡞⠁⠠⣶⣶⣿⣿⡆⠀⠈⢳⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢷⣾⣶⠶⠄⢠⣄⣄⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⣀⣠⣌⠭⠖⢋⡁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣓⠭⢟⣋⣭⣴⠶⠿⠟⠛⢆⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⣒⣫⣭⠭⡄⠰⠖⠒⠒⢚⠉⠀⠀⠀⣈⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠋⠳⡀⢀⠀⠀⠀⠠⠞⠘⢇⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⣀⣀⠌⠀⠀⠙⡏⠀⠄⠀⠀⠰⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢀⠔⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠀⢹⠏⠀⠀⠀⣸⣤⣤⠋⠀⣀⣤⣷⡀⠀⠀⠉⠒⠤⢄⠀⠀⠀⠀⢐⠫⠔⣊⡤⠖⠛⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⡀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢣⡅⡜⢁⡴⠊⠁⠄⢐⣶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠀⠀⣧⣿⣿⣗⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠆⠀⠂⠀⠀⢀⠟⣿⡗⠀⠙⠦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⢃⡆⠎⠙⣼⡄⠀⠙⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣾⣶⣶⣾⣾⡇⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡇⣼⡇⢸⣿⣿⣿⡄⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⡴⢧⢹⡇⢸⠿⠿⠿⠿⠿⠿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠾⠶⠶⠶⠾⠶⢶⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠿⠓⠛⢛⠇⠘⢆⠒⢂⡛⢻⣛⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢠⣀⠀⠁⠀⠀⢸⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⡔⠋⠀⣀⣈⣓⠦⠄⣴⠁⠈⢆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⡇⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⠒⠂⠂⠛⠒⠐⠓⡰⠒⠋⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⢷⣶⣷⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠙⠃⠉⠉⠉⠁⠀⠍⠉⠉⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⠀⣀⣀⠀⠀⠄⠊

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛
⠀⠀⠸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⡀⠀⠀⠀⠀⠀⠀⢰⡄⢠⡟⢳
⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢈⡹⠀⠀⠀⠀⠀⠀⠀⠸⠇⠙⠁⠈⠀⠀⠀⠀⠀⠀⠠⠾⠣⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⢀⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⡀⠀⠀⠀⠀⠀⢿⠇⠀⠘⠁
⠀⠀⠀⠀⢸⣶⣶⣶⡇⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⡄
⠀⠀⠀⠀⢸⣿⠉⣿⡇⠀⠀⠀⠀⠘⠿⣿⣷⣦⠸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠁⢈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⢸⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠸⡏⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠘⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⠒⡄⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢰⠀⠀⠉⠀⠀⠀⠀⣀⠤⠃⠀⣠⠤⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⣀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⢇⠀⠀⠀⠙⠒⠁⠀⠀⠘⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⡘⠀⢠⠢⡄⠀⢀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢠⢃⠀⠈⠒⠁⠀⣇⠀⠀⠀⠆⠀⢰⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡀⠃⠀⠙⠢⢠⠄⠐⠋⠀⡠⡀⠀⠀⠀⢀⣀⡀⢀⡜⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠱⡀⠀⠇⠀⢨⠐⢄⠀⠀⠑⠁⣀⣀⢀⠎⠀⠈⠉⠀⠀⠀⠀⢰⣒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠀⠙⢆⠀⠀⢀⣀⠀⠑⠄⠀⢸⠁⠀⠀⠀⠀⠑⠀⢀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠘⡀⠀⠀⠀⠀⠓⣄⠘⠶⠁⠐⠒⠒⡁⠀⡖⢳⠀⠀⠀⠀⠘⠚⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢱⡀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠄⠀⠘⠆⠈⣁⣠⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠠⠔⡋⠁⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢣⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢙⡲⠶⠂⠀⠘⠚⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⠤⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⠀⠀⠀⠈⠢⢄⡀⠀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⢦⡀⠀⠀⢀⡠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⡩⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⣹⠘⡇⢊⡆⣦⢋⣿⢐⡉⣶⠃⣊⠑⣊⢰⡗⢪⣿⠉⣶⡅⡎⠉⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣶⣴⣷⣧⣿⣼⣿⣼⣷⣭⣧⣿⣾⣿⣬⣽⣶⣿⣶⣭⣦⣵⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠉⠹⣦⣤⠁⠀⠘⡟⠙⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣄⣴⣿⡏
⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⣁⠀⠀⠀⠀⠀⠀⢀⠏⠘⠀⠀⠀⠀⣻⣦⡄⠀⠀⠀⠉⢻⠟⠋
⣰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣼⡁⠀⠤⠄⠀⠸⠛⠇
⠿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣿⣦⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶
⠀⠀⣰⣷⡀⠀⠀⠀⠀⢀⡀⠉⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⣦⠀⠀⠷⠀⠀⠀⠀⠹⣿⣿⡇⠀⣠⣤⣴⣶⣦⣤⣼⣿⣿⣿
⠀⠀⣿⣿⣿⡄⠀⠀⠀⡚⠉⣷⡆⠀⠀⠀⠀⠄⠀⢠⡤⡀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿
⢀⣴⣿⣿⣿⡇⠀⠀⢠⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣼⣿⣿⣿⣿⠏⠁⠀⠈⠙⣇
⣿⣿⣿⣿⡿⠁⠀⠀⠀⡀⢸⣏⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⣠⣄⡀⣰⠒⢲⣾⣆⠀⠀⠀⣀⣿⣿⣇⡈⠃⠀⠀⠐⠀⠘⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣓⣹⠦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⣡⠔⠳⠖⠋⠀⠀⠀⠠⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⣰⢳⠀⠀⠀⠀⠀⠀⠀⠉⡦⡨⠇⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠏⠆⠀⣠⠆⠑⢄
⠀⠀⠀⠀⠀⢠⣄⠈⢋⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠡
⠀⠀⠀⠀⠀⠈⠁⠰⣌⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠉⠒⠺⣗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣦⠤⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣆⡰⠃⠀⠮⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡇⠀⠀⠀⠀⠀⠀⢴⣠⠜⠁⠀⠀⢀⡀⠤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⡄⠠⠔⠁⠀⡀⠔⠊⠁⠀⠀⢔⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⢦⡀⠀⠊⠠⠤⠒⠒⠀⠀⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣅⡇⠀⡌⠱⣦⡀⠀⠀⠀⠀⠏⠕⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣇⢁⠣⢠⠟⣠⡯⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⣮⡬⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠄⠀⠠⠠⠀⡀⠀⠀⢀⡀⢀⣠⣤⡟⠀⠀⠀⢀⣀⣤⢀⠀⠀⠀⠀⠀⠀⢠⡤⡄⠀⠀⡀⡐⢀⠤⢤
⢠⢀⠀⠂⠃⠀⢃⠀⢀⣐⠁⠈⠁⠀⠛⢹⠖⠚⠃⠀⠀⠀⠀⠉⣀⠀⠁⠀⣤⠶⠓⠂⠈⠀⢠⠀⠀⠀⠠⢈⠀⠐⠂⠀⠀⠁⠆⠁⠀⠉⠀⠀⢀⣐
⠘⠀⠀⠀⠁⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⡈⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣤⡄⠀⡀⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠿⠟⠁
⢠⠀⠀⠀⠀⠀⠒⠒⠃⠀⠉⠀⠀⠀⠈⠑⣿⠊⢠⣦⣼⠃⠀⠀⢺⠟⡀⢿⢋⠁⠘⣕⡏⣱⣶⡦⠀⠀⠀⠁⠀⢰⡿⠃⠀⠀⠀⠀⣤
⢚⣶⣦⠀⠀⠀⠰⣦⠘⣧⠀⠀⠀⠄⠀⠀⣀⡀⠿⠃⠋⠀⠀⠀⠀⠀⢱⡏⠀⠀⢸⣟⠀⠸⠟⠁⠸⠇⢀⣀⢀⡜⠁⠀⠀⢤⠔⣆⣿
⢀⣽⣿⣆⠀⢀⡋⠁⠷⠈⠀⠀⠀⠀⠀⣿⣿⣿⠆⡘⠃⠀⠀⠀⢸⣶⠀⠈⠡⠄⢀⠈⠀⠶⠀⢠⣖⠀⠀⠹⡿⠷⠾⠀⠀⠉⠠⢿⡶
⠛⠛⠋⠁⠀⠈⣇⣤⣶⣷⠀⠀⠀⣀⣀⠻⠿⠛⢸⡃⠀⠀⠀⠀⠘⡥⢂⡀⠀⣰⠀⠀⢠⣾⣷⡌⢿⡦⠀⠐⠀⠀⣴⣦⡀⠀⠀⢀⡀
⠀⠀⠀⣴⠃⠀⣿⣿⣿⡿⣀⣶⣾⣿⣿⣿⣶⣶⡿⠋⠀⠀⠀⢀⡀⣴⠛⠛⢠⠟⠲⣶⣾⠟⠋⠀⠀⠀⠀⢰⡶⠿⠚⢿⣿⠉⠻⣭⡀
⠀⠀⠀⠻⢿⣴⠟⠻⣿⣄⣿⣿⠟⠿⠿⠿⠟⣻⠁⠀⠀⠀⠀⠀⠀⠛⠶⡖⠻⠂⠀⠀⠁⠃⠀⠀⠀⠀⠀⠸⡶⢰⣄⠈⠁
⣀⣀⣀⣀⣠⣗⣀⣀⣹⣿⣿⣃⣀⣠⣿⣶⣾⣃⣀⣀⣀⣀⣀⣴⣗⣈⣀⣀⣀⣠⣆⣀⣀⣿⣦⣀⣀⣀⣀⣢⣀⣀⣀⣿⣀⣀⣀⣀⣾
⣿⣿⢛⠻⠟⡛⢻⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠠⣤⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡆⠀⠀⠀⠀⠀⢀⠾⢕⠶⠆⠀⠀⠀⠀⣠⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠙⠏⠉⠀⠀⠀⠀⣴⡋⠙⠶⠁⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⣃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠰⣭⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡾⠃⠀⠀⠀⠀⠀⠀⠀⣴⡇⣌⡳⠀⠀⠀⠀⡊⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠛⠁⠀⢰⠂⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣢⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷⠆⠀⠀⠀⠀⢠⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠈⠁⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⣀⡀⠀⠀⠀⢠⡄⠂⠙⣲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠈⠒⣤⠄⠤⡀⠀⠀⠀⠀⠀⠀⣶⠱⡈⣇⠛⠃⠀⠀⠀⠀⠈⣧⠔⠼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⢦⠀⠀⢇⠀⢀⡇⠀⠀⠀⣴⠲⡀⢈⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠑⣄⠀⠈⠁⠑⢤⡖⢢⣙⣢⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣶⠿⣗⣾⡏⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢀⣼⣿⣷⣄⠀⠀⢀⣙⣘⠛⠁⠀⠀⠀⠔⠈⠒⡄⠀⠀⠀⠀⢀⣶⠋⠙⠿⠟⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⣴⣿⣿⣿⣿⡿⠓⢄⠙⠋⠈⠢⡀⠀⠀⠀⠓⠤⠔⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⢉⣦⣄⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣾⣿⣿⡿⠋⠁⠀⢀⣠⣴⣾⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⣰⡟⢀⣴⣿⣿⠟⠉⠀⣀⣴⣶⣿⡿⠿⠛⠉
⠀⠀⠀⠀⢰⡟⣠⣾⡿⠋⣁⣤⣶⡿⠿⠛⠉⠁
⠀⠀⠀⢠⣏⣾⢟⣡⡴⠾⠛⠋⠁
⠀⠀⢀⣿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠐⡍⠀⠀⠋⠃⠀⠀⠀⡤⠠⠀⠀⠀⠀⠨⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠦⢤⡄⠀⠀⠀⡀⠀⠀⠄⠉⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠐⡀⠀⠀⢀⠔⠁⠐⠀⠀⠀⠀⢀⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢄⠁⢂⡤⠐⠀⡆⠀⠘⠉⡐⠂⠤⡰⢶⣀⠈⠒⠃⠀⠂⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠚⡌⠀⠀⠀⠐⢡⠀⠀⠀⠁⠀⠐⠚⠀⠐⠐⠃⠀⠊⣀⠀⠀⠘⠁⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⣀⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢁⣀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⡀⠀⢠⠀⠀⠀⠑⣀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠉⠀⡀⠈⠈⠀⠀⠀⢀⡤⠤⠀⠉⠀⡀⠙⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⣀⠑⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣞⣿⠟⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠠⣾⠂⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠁⠺⠁⠀⠀⠀⠈⠄⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⢀⣤⣀⠋⠉⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠀⣠⠀⠀⠀⠨⠀⠀⢠⣶⠀⠀⠀⠀⠄⠠⠄
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⣥⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠀⠀⠀⠂⠀⢀⠁⡁⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠤⠊⠕⠀⠀⠀⢠⠂⠀⣀⠠⡀⠀⠀⢀⣤⠀⡠⠀⠒⣾⠇⠀⠀⠀⠀⠀⠁⠰⠂⠀⠁⣀⠀⠀⠀⠀⠀⠀⠒⠀⢭⡓⠶⣄
⠀⠀⠠⠂⠀⠀⠀⠀⡠⠢⠄⠜⠀⣨⠀⠀⠀⡇⠀⡘⠃⠀⡀⠀⠀⠀⠀⠀⠑⡄⠀⠘⠄⠠⣤⡢⠀⣠⣵⠤⡂⢀⡢⢄⠙⢦⡀⠀⠀⠀⠻⠃⠀⣿⠄⠘⡆
⠀⠀⠀⠂⠀⠀⠀⠀⠙⠃⡀⠀⢀⠠⠂⠀⠀⡇⢰⡁⠙⠬⠁⡆⠀⠀⠀⠀⠀⠘⢄⠀⣠⡀⠻⠐⠀⢹⠚⢀⡁⡠⠀⡘⠀⢆⢣⠀⠠⢇⠄⠀⠀⢀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠘⠦⠘⠀⠂⢤⠀⢣⡐⠎⠑⠢⠞⠀⢠⡐⢢⠀⠀⠀⠈⢆⠀⠀⢀⠀⠂⣁⠎⠀⠭⣤⠜⠀⢀⡸⠙⠀⠀⠂⣠⠤⣊⠎⣡⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠖⠁⠀⠀⠈⢇⠀⠈⢰⣒⠀⢰⠀⡎⠀⠈⡄⠀⠀⠃⠀⢮⠀⠀⠗⠤⣀⠀⠀⠀⠊⡰⠋⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡇
⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡀⠉⠨⡄⠈⠑⢤⡁⠀⠀⠀⡐⠀⢹⠺⡀⠀⠀⠉⠁⠠⠭⠤⠤⠐⠉⠀⠀⠀⢀⣠⠴⠂
⠀⠀⡘⠀⡘⢃⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣄⠘⢇⠀⡇⠀⠀⠁⠀⠀⠀⡹⠀⠀⠠⠀⣤⠀⠣⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠃
⠀⢀⠃⢀⠃⠸⡀⠀⠀⠀⠀⠤⣭⡭⠰⡍⠙⠂⠀⠁⠷⢀⣀⣀⠔⠉⠉⡄⠀⠀⠐⠊⠉⠀⠀⠱⡄⠀⠪⡙⠒⠤⣤⠔⠚⠉⠀⠀⠀⠀⠀⡠⠁
⠀⠘⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠙⠛⠒⠀⢄⠀⠒⢂⠐⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡁⠘⢆⣴⡡⢄⢀⠎⠀⠀⠀⠀⠀⠀⢀⠴⢤⡤
⠀⠘⡄⠐⠓⠤⠵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡀⢃⠀⠀⠀⠀⠀⡤⡠⠙⣄⠀⠀⠀⠀⢧⡄⠀⣼⡦⠀⠏⠀⠀⠀⠀⠀⠀⡴⠓⠊⠁
⠀⠀⠈⠢⡀⢠⠾⠕⢰⠆⠀⠀⠀⠀⠀⠀⡴⠾⠃⠀⠘⠄⢆⡴⣿⡟⠚⠹⠟⠂⠈⢦⠀⠀⠀⡇⠀⠀⠈⠉⢙⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⠢⡀
⣀⣀⣀⣀⣀⣁⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣎⣴⣋⣀⣀⣀⣒⣃⣀⣘⣆⣀⣀⣇⣀⣀⣀⣀⣸⣀⣤⣄⣀⣄⣀⣀⣀⣀⣀⣀⣘⣦⣀⣀⣀⣀⣀
⣿⣿⡟⡛⠿⠛⡻⠻⣟⢟⣿⢟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠂⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⢀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠈⠀⠊
⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⠿⢿⢸⠿⠿⠿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠻⢿⡿⠃⠘⠿⣿⠿⠛⠛⠛⠛⣻⠋
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡼⠸⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣠⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⢷⠀⠀⣠⠞⠀⠀⠙⢆⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠘⣧⡴⠁⠀⠀⠀⠀⠈⠳⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠐⠺⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠷⠦⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤
⢀⣠⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣶⡦⢶⣶⣾⣿⣿⣿⣿⣿⣿
⣼⡏⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⣤⢢⡄⠀⠀⠀⠀⠀⠀⠸⣏⠉⠉⣿⡄⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⣿⠁⠘⣯⠉⠉⠉⠉⠉⠉⢹⡆
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣸⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⡇
⢿⣆⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⣷
⠀⠙⢻⡿⠀⠀⠀⠄⠀⠀⠀⣾⠁⠀⢹⡄⠀⠀⠠⠁⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣧⣄⣀⣀⡀⠀⠀⢀⡿⠀⠀⢸⣇⠀⠀⠀⣀⣀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⣽
⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣾⡟⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⡇⠀⠀⣾⡟⠀⠈⠹⠛⠂⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⣰⡟⠀⠀⡀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣧⠀⠀⢠⡟⠀⠠⣏⣹⣢⣾⠟⢁⠀⠀⠀⠀⢠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⠀⠸⠋⠀⠀⢠⡟⣀⡀⠀⣨⡾⠋⠁⠀⢾⣿⡇⠀⠀⣀⣥⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣄⠀⠀⠀⠈⠘⠿⣧⡾⠋⠀⠀⠀⠀⠀⣁⣤⣶⡿⠟⠋⠉⣶⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⣠⡴⠾⠛⢉⣤⡄⠀⠀⠛⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣤⣄⡀⠀⢠⣶⠀⢴⣞⣉⠁⠀⠀⠀⠈⠛⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣶⣤⣀⡀⠀⠈⠙⠛⠿⣷⣄⠀⠀⠾⣿⠷⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⠿⣿⣿⣶⣤⣄⡀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣤⣄⡀⠀⠈⠉⠛⠿⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠉⠛⠻⠿⣿⣶⣤⣄⡀⠀⠈⠉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣷⣦⣤⣀⠀⠀⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⡼⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⣎⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠛⡗⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠬⠭⠍⣵⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⣀⣠⣋⡛⠒⠒⠖⠴⡇⠀⠀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⠀⠉⠲⠤⠼⠾⣀⣀⡄⠀⠀⠀⠀⢠⠞⠉⠀⠉⠙⠢⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡉⠉⡉⠐⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⠒⠒⠹⡄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠡⢀⡤⠤⢷
⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢾⡏⠉⠙⠲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠤⠞⠛⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣸⠀⠀⢠⣶⡄⠀⠀⢸⣧⠀⠀⣀⡗⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⣰⠃
⠀⠀⠀⠀⡤⠠⢤⣠⠔⠒⢢⠀⠀⠀⠀⣾⡷⠤⠤⠤⡏⠀⠀⣾⠇⢷⠀⠀⠘⣿⠒⠋⠁⢠⡶⠒⠢⣄⠀⠀⢿⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢙⠾⡅
⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⣸⠀⠀⠀⢐⣿⠇⠀⠀⢰⡇⠀⣼⣯⣤⣼⡇⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠈⡇⠀⠈⣿⡞⠁⠀⠀⠀⣠⢄⣠⢤⠀⠀⠀⠳⣏
⠀⠀⠀⠀⠈⠳⣀⠀⠀⡰⠃⠀⠀⠀⠸⣿⠀⠀⠀⢸⠀⢰⣿⠀⠀⠀⢹⠀⠀⢿⡆⠀⠀⢸⣇⣀⣠⡴⠃⠀⠀⣾⡇⠀⠀⠀⠀⠙⢄⣡⠞⠀⠀⠀⠀⢸⡄
⠀⠀⢠⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠻⠃⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠉⠓⢦⠀⠀⠀⢸⣧⠀⠀⣰⡞⠛⠲⡄⠀⠉⠉⣿⡏⠉⠀⣀⠀⠀⠀⠀⢸⡇⠀⠙⢦⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⣠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣸⠀⠀⠀⣼⡇⠀⠀⣿⡇⢀⣠⠇⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⢸⠇⢸⣷⠀⠀⠘⡇⠀⠀⠀⠀⠈⣿⡄⠀⢠⠇⠀⠀⢸
⠀⠀⢀⡀⠀⠀⠀⢸⣷⠶⠚⠧⣄⠀⠀⣿⠇⠀⠀⣿⡿⣍⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣀⣀⣼⠀⠈⣿⠀⠀⢠⡇⠀⣰⣿⡀⠀⠘⣿⣀⡞⠀⠀⠀⢸
⠀⠀⠁⠑⠙⠆⠀⠈⣿⠀⠀⠀⢸⠀⠠⠿⠄⠀⠀⣿⡇⠈⠳⠀⠀⠀⠀⠿⠀⠀⣿⡇⠀⠀⡿⠀⠀⣿⣀⡠⠏⠀⣰⡟⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⡇⠀⠀⠙⠉⠀⠀⣰⡟⠉⠙⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡶⡄⠀⠀⠰⠟⠀⠀⠀⠾⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡆
⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠄⠀⠀⠀⠀⠀⠀⣞⠑⠞⢱
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⠉⢳⠦⣄⡀⠀⠞⠀⠀⠠⠖⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⠤⠴⢆⠀⠀⠘⢦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⡏⠑⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣋⣉⣩⣤⡤⠖⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠸⡆⠁⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣁⡨⠤⠔⠒⠋⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⢸⡀⢀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠉⠀⠀⠀⣀⣠⢤⡤⢴⣛⡦
⠀⢀⡤⢤⡀⠀⠀⠀⠀⢠⠗⠋⠀⠀⠀⠀⠀⠖⢦⣀⣀⡀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢸⣓⣮⣽⠯⠽⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤
⠚⠉⠀⠀⠙⠢⠤⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢰⡇⣿⡿⠟⢸⣿⢸⣿⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⣿⡇⠀⠈⣿⣾⡿
⠿⠿⠟⠟⢀⡦⠀⢀⡄⠒⠶⠶⣴⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣾⣦⣸⡇⣾⣥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠛⠀⢠⠏⣀⠀⣀⡀⠈⢣⡈⢃⠀⠀⠀⠀⠀⢹⠀⠀⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣷⡿⢻⣿⠋⠒⠶⠱⡌⠀⠀⠀⠀⠀⠈⠀⢰⣿⠛⣿⣇⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⡏⣿⣿⡯⡿⣿⣿⢿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠁⣀⠀⠀⠀⠀⣴⢷⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⣉⣉⣉⣀⣉⣁⣈⡠⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠿⠛⠃⠚⣿⣿⣴⣿⢿⣷⡿⡏
⠀⠀⠀⠪⡀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠐⢶⡤⠉⠁⠤⠤⠤⠄⠀⠀⠀⠀⠒⠲⠟⠁⠀⠀⠀⠀⠀⢐⠀⠉⣀⣠⣤⣄⣙⡿⠛⠛⠓⠚⠗⠺
⠀⠀⠀⠤⠇⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⣴⣋⣽⠽⠷⠾⣿⣿⡧⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠠⡏⠬⠉⡁⠀⠀⠀⠀⠀⡼⢀⡏⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠉⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢂⠠⠀⡐⠑⢦⣤⠄⣆⢟⠀⠐⠌⢀⡦⠝⣢⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⢠⡤⠋⠀⠀⠌⠠⠤⠤⠠⠬⡄⠃⠋⢀⠈⢁⡄⣁⠀⠀⠀⠀⠀⢠⡴⣿⠯⠽⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⣀
⠀⠀⠐⣯⠴⠲⠜⠀⣇⠀⠀⠀⠀⠀⡄⢂⠠⠀⣠⣾⣿⣧⠀⠀⠀⢰⣿⣿⣷⣿⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢉⠥⢘⡶⠉⣿⣿⣿⠀⠀⠀⠀⠙⠻⢿⣿⡶⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⣠⠀⢆⠀⠀⠀⡀⠀⠠⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠄⠀⣑⠀⠀⠠⠤⠤⣮⣦⣼⣶⣶⣾⣿⣿⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⢹⡋⠿⠈⣶⠈⠳⣴⣆⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠘⠉⠂⠀⠀⢀⠠⣤⣤⣦⡄⠦⠠⢿⣶⣴⣧⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣀⣴⠋⣁⠀⠆⢀⡀⠃⠘⣿⠛⣧⢠⢤⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠄⠀⢀⡀⣠⠤⢤⡀⣁⠀⠒⠩⠀⣰⢬⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠟⠉⠉⡄⠉⢀⣀⠈⡅⠀⠁⣼⡟⡇⠀⠀⠁⠄⠤⠁
⠀⠀⠀⠀⠀⢸⣄⠁⢀⣢⣄⡓⠙⣘⣀⠀⠄⠀⠀⣘⠬⠻⣈⡁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⢰⠄⠀⢤⠀⠂⠈⠉⣀⠀⠀⠓⠈⣿⡇⠀⠀⡀⠀⡀⠴
⠠⠀⡶⠆⠠⠦⠾⠀⠠⠥⣼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶⠀⠀⣀⠀⠄⠰⣷⠀⢀⡀⠃⢘⠁⢻⡇⠀⠀⠈⠀⠁
⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⢀⣤⣤⣍⣀⠴⠀⢀⣄⠠⠁⠄⠉⠀⠈⠁
⠀⠀⠀⠑⠀⠐⠀⠀⠀⠐⠆⠀⠀⠀⠶⠀⠀⠀⠦⠀⠠⡆⠀⠐⣤⠀⠀⠀⠀⠀⠀⠈⣷⠟⠻⣿⣿⣿⣿⣦⢀⡄⠴⠛⢆⠀⠄⢰⠴⠆
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⡀⢀⡁⠀⠀⠀⠶⠂⠀⠀⠀⢀⣘⢁⡀⠀⠀⠙⢿⣿⣿⠈⢀⡂⠀⢈⡀⠀⢀⠀⢴⠀⠀⠀⠀⢠
⠤⠄⠂⠈⠁⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣦⣤⡔⠀⠀⢬⡁⠀⠀⠀⠈⠁⢸⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⡀⡼⠀⠀⠀⢀⣾⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⠿⠃⠀⠀⠐⣿⡟⠁⠀⠀⠘⡧⢀⡀⠀⠀⢀⣤⠄⠀⣻⡟⠛⠉⠉⠛⠀⣿⠀⠠⠤⠤⠤⢤⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠟⡄⢰⣿⣧⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢠⠤⠞⠛⢢⣤⡾⣧⣿⠁⠀⠀⠀⠹⣿⣿⣀⠀⠀⠀⡜⣸⣿⣇
⡄⠀⠀⢀⣴⣶⣶⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⣴⣶⣶⡂⠀⠉⠀⢸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢻⣿⣿⣀⠀⣀⣀⣴⣿⠋⠛⠳⢄⠠⣷⣿⣿⣿
⠉⣀⡀⢈⣉⣉⠉⣁⣀⣀⣉⣉⡉⠉⡁⢀⡘⡛⢉⡉⠃⢀⣾⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠻⣿⣏⠉⠉⠉⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠘⠅⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡿⠀⠀⠀⢨⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⡄⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⠀⢠⠦⠀⣴⢖⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠆⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠿⠷⣨⢻⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡟⡸⡘⡼⡏⣯⣦⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢲⣾⣯⣶⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠛⠛⠁⠉⠀⠀⠀⠀⢠⠱⢠⢣⢡⢳⢰⣿⠸⠸⣷⠢⠄⠀⠀⠀⠀⠀⠀⢰⣶⠚⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣀⡀⣀⣀⣀⣒⡀⠒⠂⠂⠘⢘⠀⡀⠂⠐⠰⠀⠀⠐⠒⢀⣀⣨⡇⡆⡜⡄⡈⡆⣼⢸⡇⠟⠘⡀⠀⠀⠀⠀⠀⠀⠀⢫⣥⣸⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠃⠀⠸⣿⣿⣿⠋⠈⢿⢡⡇⣿⣿⠋⣿⢸⣇⢿⣿⡿⠃⠙⣿⣿⢰⢀⢣⠀⢷⢀⡇⣇⢷⡸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠹⡿⠁⠀⠀⠀⣼⢀⡿⠃⠀⠘⡼⣿⡸⡿⠁⠀⠀⠸⣿⢘⢸⡜⢸⡈⢸⢰⣹⣸⣇⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣅⠛⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⡈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠒⠈⠳⡀
⠀⢰⠀⠀⠀⠀⠈⠁⠐⠒⠒⠤⠤⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠒⠒⠒⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠪⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠈⢫⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⣀⣤⠔⠈⢡⠃
⠀⠀⠀⠀⡆⠀⠀⢩⠙⠒⠠⠄⢀⡠⠀⣀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⢁⣀⠠⡀⠦⠐⠈⠁⠸⠀⠀⢸
⠀⠀⠀⠀⡇⢰⡄⢸⠀⠀⠀⠀⠀⠀⠈⠁⠐⠊⠠⡄⠀⠀⠰⢄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠛⠀⡁⠀⠀⠁⠀⠀⠰⣤⡄⢸
⠀⠀⠀⢰⡵⠃⠸⡰⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⢠⠀⠀⠀⠀⠈⢡⡀⠀⠹⡄⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⡄
⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠠⠡⣀⠀⠀⠀⢠⠀⠀⠀⣀⠀⣀⠙⣄⠀⠜⢢⡤⠖⠋⠀⠀⢀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠑⢄⠀⢉⢠⠴⠁⣉⡀⠉⣀⠛⠳⡄⠙⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢂⠾⢀⠔⠋⠉⠀⠀⠉⠙⠢⡉⣤⢀⠔⠘⠀⠘⠓⢦⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⢱⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠓⠄⡀⠀⠀⠀⢀⡄⡼⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠓⠄⠘⣶⡶⠶⠶⠶⢾⠇⢠⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠸⠀⣤⣀⠊⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠲⢄⡀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠴⠛⣫⠟⠣⢖⡀
⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠫⡀⠀⠚⠃⠶⠭⠬⡍⠉⢁⡱⠤⡀⠀⠀⠁⠈⠀⠀⢡
⠀⠈⠁⠀⠀⠉⠢⣄⠐⠀⠀⠀⠀⠱⠇⠀⠀⠀⠀⢀⡤⠐⠉⠁⠀⠀⠀⠈⠓⠢⢄⠹⠒⠛⠊⠐⠋⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸
⠀⠄⠐⠀⠀⠀⠀⠀⡆⠀⡰⠒⠖⠒⠶⢧⡱⡖⣶⠀⠄⠀⢀⠘⠃⡄⠀⢤⠃⠄⠀⡳⠃⠀⠀⠠⡦⠄⡴⢈⡀⠀⡠⠐⠒⡄⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠃⠀⡄⠀⠀⠀⠀⠐⡋⣴⠂⠀⠁⢌⠀⠀⠀⣤⠀⠀⡄⠀⠛⠙⠺⣥⠓⢦⠶⡮⢷⡬⢶⣦⣄⠛⠌⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡀⠬⡖⠀⠂⠡⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠹⠒⢶⠙⠚⣆⠀⢈⠇⢀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣄⠁⠀⠀⠀⠀⠀⣠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠠⠀⠀⣸⠀⠀⠹⣦⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⢈⣁⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⢄⠉⠘⢄⡄
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⡎⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⡓⠀⠀⠈⠐⠂⠄⢄⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠀⡀⠣⡀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⠔⠉⠓⠦⣄⡀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠂⠤⡤⣉⣐⠂⠀⠠⠤⠤⠔⠚⠋⠁⣠⡤⠔⠁⠀⠀⠀⠀⠀⠉⠳⠀⠂⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⡼⠀⠀⠀⠀⠀⠩⠈⠉⠛⠛⠛⠙⠒⠋⠈⠭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠖⠓⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠄⠐⠒⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⢠⡄⠀⠀⢀⡆⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠐⢤⠴⠃
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠈⠢⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⠜⠀⠈⠳⣄⠀⠀⢀⡗⠀⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀
⣿⢻⡟⢿⢛⣟⣛⡛⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣛⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠠⣾⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠰⣶⣶⡄⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠄⣀
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠀⠆⠀⠀⠀⠀⠀⠀⠻⠀⢸⡀⠀⢰⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⢴⣿⣿⣿⣿⡗⠀⢀⣠⣶⣀⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⠖⠘⠓⣂⡀⠰⠐⡶⢴⠶⠀⣿⣿⣹⣶⣦⣿⣿⣿
⠀⢸⣿⣿⣿⣿⠁⣾⣿⢿⣿⣇⢻⡿⠀⠙⠁⠀⠀⢀⣤⣦⣄⠀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⢻⣿⣿⡿⠛⣿⠿⣧⣶⣦⡄⠀⠛
⢀⣾⣿⡿⣿⠃⢀⣬⣵⣿⣿⣿⠈⠀⡀⠀⠀⠀⠀⡾⣿⣿⡏⣴⣴⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣈⡇⠾⠇⢰⡆⠀⠙⠛⠁⠀⣷⣦⠛⣿⣿⣧⡀⢀⡀
⢾⣧⣾⣷⣿⣦⣾⣿⣿⣼⣿⠋⠀⣠⣿⠄⠀⠀⠀⠀⠿⠏⠁⣿⣿⡁⠀⢻⣷⠄⢼⠛⠟⠻⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠃⠈⢿⣿⣿⠈⣿⢿⣷⣦
⠀⣿⠉⠈⢿⣿⣿⣿⠏⠁⠀⠀⠀⠙⠋⠀⣀⡾⠁⠐⠛⠀⠀⠈⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⡟⠁⢸⡧⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⣠⠀⠀⠸⡇
⢸⣿⠀⣿⡄⠛⠉⠉⠀⠀⠀⠗⠀⠀⠀⠀⡿⢰⣶⠀⢀⡀⠀⢶⣿⣷⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣶⡀⠹⣯⠀⠀⣀⣀⣤
⠘⠁⠰⠿⠇⠀⠀⠀⣤⣶⣿⣾⡂⣠⡆⣸⠃⠨⣧⠀⢘⣷⡆⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠉⣀⣴⣿⣿⣿
⠀⠀⠀⠀⣰⣦⣄⣸⣟⣿⣿⡟⠉⡋⠠⡿⠀⠀⠀⢠⣾⡟⠀⣿⡇⣀⠃⠀⠀⢀⠦⠄⠀⠖⠀⠀⣹⢿⠿⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠙⠁⢴⡅⠀⠉⢸⣿⣿⣿
⢰⣶⣤⡄⠲⣿⣿⣿⠏⠁⠀⠀⠈⠁⠒⠁⠛⠀⠀⢠⣉⡀⠀⠉⣠⣵⣄⡀⠀⣠⣶⣶⣤⡀⠄⠀⠹⠴⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⢀⣀⣈⢃⢀⣀⣾⠛⢿⣿
⠈⠙⠛⠀⠈⠿⢿⣿⠀⠀⠀⠀⣀⣠⣄⣠⡄⠀⠀⠈⢿⣧⠀⣾⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡄⠀⠀⠀⠀⠙⠿⣯⣙⢿⣿⡄⠈⠻
⢰⣾⠟⠃⠀⠐⣃⣀⣀⡀⠀⠈⠙⠿⣿⣿⠓⠀⠀⠀⠘⣷⣄⠛⢻⣿⣿⣿⣼⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⢿⣆⠀⣾⣿⠒⠀⠀⠉⠹⢿⣿
⠈⠁⠀⠀⠀⠐⣿⣿⣿⣇⠀⠀⠀⠀⠈⠛⠃⠰⠦⣠⣾⠻⢿⣦⠀⣿⠿⠿⠿⣿⣯⡤⠀⣴⣷⣧⠀⢴⠟⢻⠿⣃⣀⣀⣀⣼⡿⠷⠍⢀⠀⣀⣀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⢸⣿⢺⡿⠀⠀⠀⠙⠋⢁⡄⣩⠕⠤⠀⢠⣶⡟⠠⣿⣿⠟⠈⣁⠀⠀⠀⠀⠙⠿⠛⢀⡀⠀⠀⠀⢰
⠀⣀⣤⣴⠀⠀⠀⢀⣻⡷⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⣀⠹⠃⣀⡀⠀⠀⠀⠀⠀⠀⠸⢏⡀⠀⠀⢸⣟⡁⠀⠻⠃⠀⠀⠛⠀⢠⣄⡀⠀⠀⢀⣾⣿⢐⡖⢸⡤
⢀⣨⣿⣿⣄⠀⠀⣘⠁⠀⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⡀⠛⣁⠀⠀⠀⠀⣿⣾⠀⠈⠁⠤⠐⣀⠀⠀⠸⠧⠀⢠⣾⠃⠀⠀⠹⡏⠀⠀⠿⠉⠁⠈⠁⠬⣿
⠸⠿⠟⠛⠉⠀⠀⢻⢀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠠⡟⠘⣿⠁⠀⠀⠀⢛⡁⠄⠀⠀⠀⡐⠁⠀⠀⣴⣶⢦⡘⣿⣷⡄⣀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⣠⡆⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠘⠻⣷⣦⣀⣀⣤⠙⠂⠿⠀⠀⠀⠀⠻⣿⠇⠀⢀⢸⡇⢀⣤⣸⣿⠿⠇⠈⠀⠉⠁⠛⠃⠀⠀⠀⠀⢹⣷⠂⠀⠀⠚
⠀⠀⠀⠀⡿⠤⠀⣸⡟⠁⢀⡄⠀⡀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⢈⠃⠤⠒⠀⣿⠀⠀⠀⠉⠀⠈⠙⠿⢻⣤⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀
⠀⢀⣠⣶⣶⣤⡘⠋⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⢁⡟⠀⠀⠀⠀⠀⠀⠀⢠⣬⠈⣹⡀⠃⠀⠀⠀⠀⠀⢀⡽⢀⣸⣄⠀⠸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⢻⣿⣿⣿⣿⡏⠀⢠⣶⣿⣤⣶⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠘⢿⣥⣈⣉⣩⣤⣄⠀⣿⠟⠓⠀⠀⢾⡟⣹⣿⣷⣿⣿⡿
⠀⢸⣿⣿⣿⡟⠀⠀⠘⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣶⣷⣦⡀⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⣉⣀⣠⣤⠀⠈⠛⠛⠋⠉⠉⠙⣷⣿⣷⡆
⢠⣿⣿⣿⡿⠁⠀⠀⠀⣽⣿⣿⣿⠟⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣾⡇⠀⢸⣆⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⢰⣶⠀⠀⠀⠀⠀⠉⢻⣿⣷⣴⣤⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⢲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠭⠀⡀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢄⠀⠀⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠺⣬⠂⡀⠪⡩⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⡈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠒⣤⡄⠀⠐⠁⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⢠⢃⠀⡄⠑⣄⠀⠀⠀⠐⠕⠀⠀⠀⠀⠀⠀⠀⡘⡃⢨⠈⢢⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢚⠀⡇⠑⣤⠀⠠⣲⠀⠀⠁
⠀⠀⠀⠀⢠⠇⠘⡀⢡⠀⢇⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠀⠆⠘⡈⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⡄⠰⠀⢣⠑⡎⠉⠉
⠀⠀⠀⢀⡆⢰⠀⢣⡠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⡃⠈⣆⠸⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠸⠀⠰⣀⠧⠚⠁
⠀⠀⠀⠌⡰⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣢⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢐⡤⠗⠈⠁
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡠⠂⠀⢠⠊⢀⠀⠀⢀⣀⡠⠄⠀⠀⠀⠀⣀⠂⡀⠀⣀⣀⠀⠄⠀⣤⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠁⢠⢢⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠀⠄⠀⠀⠀⠀⠀⠊⠀⢏⠇⠀⠀⠀⠀⠀⠳⠊⠀⠈⠋⠇⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠂⡸⠀⠀⠀⡠⠋⠁⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠒⠇⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⠀⠀⠄⣀⡀⠀⠐⠀⠀⠀⠀⠀⣠⡎⠀⠒⠀⢈⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡎⠈⠓⢄⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢘⠲⣁⠰⠆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡏⠢⡀⠀⢀⠄⠐⠊⠁
⠀⠀⠀⠀⠀⡌⢠⠀⡂⠘⡣⡔⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⡀⢘⠣⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣸⠐⠀⢠⠀⠟⢢⠁
⠀⠀⠀⠀⡘⡇⠈⡄⠰⣀⠥⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⡀⢡⡀⠦⠚⠀⠀⠀⠀⠀⠀⠀⠀⣐⢹⠀⢃⠀⣆⠨⠄⠃
⠀⠀⠀⠰⠇⢰⡤⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡄⢠⠤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠈⡆⠜⠃⠁
⠀⠀⠠⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠉

⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⣄
⢸⣿⡿⠟⠛⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠳⣷⠆⠀⠹⠃⠀⢀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠙⠁⠀⠀⠀⠀⠀⣴⣴⣿⠇⠀⠀⠀⠀⠘⠊⢷⡀⠀⠀⠀⠃⠀⠀⠀⠸⠷⣿⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠀⠄⠠⣤⠀⠀⢸⣌⣷⠀⠀⠀⠀⠀⠀⡀⢴⡄⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⣂⡀
⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⣴⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⠀⠀⠀⢁⣄⠆⠀⠀⠀⠀⠀⠌⢍
⢸⣿⡆⠀⠀⢰⣶⣶⣦⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀
⠈⢉⡁⡀⠀⠀⠠⣿⣯⣀⠀⢀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠘⠛⠿⡿⠀⠀⠀⠈⠉⠛⠛⢿⡀⠀⠀⠈⠀⠀⠀⠰⣷⣦⡀⢀⡀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⡀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡀
⠸⣷⣤⡀⢰⡀⠀⠀⠀⠀⠀⠈⠀⢹⡇⠴⠴⠒⠈⠀⢀⣼⠟⠛⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣤⠀⠳⠈⠁⠀⣿⡇⠀⠀⠀⠀⠀⠘⢛
⠀⠀⠻⡟⢻⣇⠀⠀⠀⠀⢀⣤⡀⠀⠁⠀⠉⣠⣤⡀⢸⡟⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢛⡤⠀⠋⠀⢀⠾⠧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢛⣛⣢⣤⠴⣦⣤⡈⠹⠃⠀⡆⠈⡇⢀⣈⢶⢻⡎⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠠⣶⡅⠀⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⢴
⢠⣤⣀⡀⠀⠉⠛⠁⠀⠀⠹⣿⡶⠄⠈⠀⠀⠛⠛⠻⣶⠀⢠⡆⠀⠀⠀⠴⣷⣶⡛⢿⠁⠈⠃⠀⣽⣷⡂⠈⠛⠿⠛⢿⡆⠀⠀⠀⠀⠀⠈
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⢀⠀⠀⠀⠀⠀⠟⠀⠀⢙⡀⠀⠀⠀⠀⠹⣷⣸⣷⣶⠀⠀⠉⠀⣼⡗⣧⡀⠀⢠⠅
⢸⣿⣿⡇⠀⠠⢦⠀⠀⠀⢴⣿⣷⣔⣿⣶⣷⣀⣀⣠⠀⠀⠀⠈⣷⠀⠀⢸⣾⣻⣽⣿⣿⣧⣤⡶⠀⣠⠘⠀⠿⢱⡆⠰⢴⡀
⢸⣿⣿⡇⠀⠀⣰⣷⣶⠾⠿⣝⠻⢿⣿⣿⠿⢿⣷⡏⠀⠀⠀⣾⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠠⣿⣧⣀⡸⡣⠀⠀⢀⣴⡿
⢸⡿⡿⠇⠀⠀⠈⠸⠇⠀⠀⠀⣶⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⢰⣿⣿⣿⠟⠉⠉⠛⢿⣿⣿⡇⠀⠀⠀⠐⢶⣎⠁⠀⠀⠀⢸⣿⡆
⢀⣀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣥⣤⠄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠈⢻⠋⠀⠀⠠⣄⠀⠀⠀⠘⡿⢠⣷⡀⠀⠀⢸⡷⠀⢰⡆⠘⣿⣷
⢸⣿⣿⣿⣿⣿⣦⣀⠘⢷⣶⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⢀⡴⠶⣧⡀⠀⠀⠂⠀⠁⣾⣿⣿⣆⡀⠸⣿⠀⠘⠁⠀⠉⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⣤⣀⡀⠀⠀⠛⠑⠿⠟⣿⡆⠀⣀⠀⣸⣿⣿⠿⠿⢿⣦⣹⠀⠀⠀⠀⠀⠈
⠈⠻⢿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⠿⠿⠿⢿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠴⢋⣀⣤⣤⣤⠈⠙⠁⠾⠆⣴⣿⣿⣷⡿⢢⠀⠀⣤
⠀⠀⠀⠉⠀⢙⣿⣿⡟⠀⠀⠈⠟⠻⠗⠖⠀⣾⣿⣿⣿⣿⢃⡿⠟⠃⠘⠃⠀⠀⠀⠀⠈⠙⠋⠀⠉⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇⠀⠀⠀⣀
⠀⢠⢠⣤⡄⠈⠙⠋⠁⠀⠀⣀⡀⠀⡀⠀⢨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⢀⣠⣀⠙⢻⣿⣿⣿⣿⣿⡀
⢠⣷⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⣿⣶⣤⣿⠿⠿⠤⠆⠀⠀⠁⠀⣠⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⠟⢠⣿⡀⢀⣀⣀⣨⣿⣶⣶⣦
⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⡇⠀⠀⠀⣰⠖⢶⣿⡾⢉⣷⡟⠛⢦⡆⠀⠀⣀⠀⠀⠁⠀⠀⣿⠿⣷⠀⢻⣿⣿⣿⡏⠁
⠀⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⢹⡆⠀⠀⠀⣿⡀⠀⠿⠀⠛⠛⠷⠀⠈⣀⣰⣾⣿⠉⢿⠀⠀⣠⣿⣷⣷⠀⢘⣡⣼⣿⣷⣾⣿
⠐⢃⣀⣨⣿⠀⠀⠀⠀⠀⠀⠀⢩⣿⡇⠀⠉⠁⢀⣀⣠⣄⡀⠀⠀⣀⠀⣶⣤⣶⣾⠟⣿⣿⣏⣠⣾⠤⠛⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣧⣀⣤⣤⣄⣀⣀⣸⣿⣥⣀⣴⣶⣾⣏⡉⠛⢿⣶⣿⣿⡀⢹⣿⠛⠁⣴⣿⣿⣿⡿⠿⠀⠰⣟⠛⠛⢣⠛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⡔⡂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣡⡀⠀⠀⠀⠈⠠⠿⠂⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠤⢄⡀
⠀⠀⠀⠀⠊⠀⡏⡇⠀⡇⢇⠀⠀⠀⠀⢠⢤⣤⡤⡐⡓⡌⢀⢎⢟⠤⠇⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢀⡦⠒⠤⣀⠀⠒⠤
⠀⠀⠀⡀⠀⠀⢠⢧⠠⣃⢹⢀⢪⠛⡌⡇⡇⢇⢘⡸⢣⠡⠡⠃⠀⠁⣍⠇⠀⠀⠈⠏⠠⣲⠀⢸⠹⡀⠄⠀⠀⠀⠀⣁⣀⣀⡠⣤⣀⣄⠀⠈
⠀⠀⠀⠀⠀⠀⢸⢰⠉⠈⡌⡎⠪⠖⠃⠃⡇⡏⠀⠀⠸⠀⠀⠈⠉⠃⠉⠀⠀⠃⠀⠀⠀⠫⣑⣪⡆⣧⢊⡿⢱⢄⢏⡆⡆⡟⢸⢸⠁⠀⠀⠀⡂
⠀⠀⠀⠀⢀⡀⠚⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢰⠒⡄⢸⡏⡠⡀⢔⡒⡔⢲⢹⠀⡤⣀⡀⣠⢣⠋⢾⣤⣲⢆⠓⠭⠲⠟⠘⠚⠀⠀⠀⠀⠐
⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠠⠚⠱⠂⢸⢰⣞⠆⡿⡔⣉⣬⢹⣡⠣⣸⠄⠀⠈⠂⢒⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠈⠰
⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠼⠼⠘⠦⠃⠈⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠛⣏⠀⠀⠺⠦⠒⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠄⠀⠀⠀⠀⠠⠀⣅⠀⠐⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠁⠉⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠌⡐⣁⡠⠤⡄⢀⣾⣧⡆⡗⠚⢻⣧⡀⠑⠄⣀⠀⠫⡀⡸⠀⠀⠀⢅⠄⢀⠀⣔⠙⣄⠀⠀⠦⠀⠶⠈⢫⡉⡍⢠⠴⠒⠒⠲⣤⠀⡋⠉⡇
⠀⠀⢸⣴⠋⣀⣤⣶⣷⣲⢣⠀⣧⠧⡰⢱⢋⠙⣆⠀⠀⠀⢰⣾⣷⠀⠀⠄⠀⠀⠀⣮⣤⣠⣈⣧⡀⠀⢠⣀⣀⠀⢩⣡⣼⣶⣶⣶⣶⣧⠠⠟⠒
⠀⠀⢠⣨⢿⠿⠏⢘⠀⣧⢀⠳⢁⡰⢡⣯⠖⣾⠾⣇⡀⠀⡼⢠⠏⢾⠛⢷⣀⠀⣟⣿⢺⠓⠋⣹⣟⠴⣞⠉⠃⠀⡿⣁⣿⠙⢆⠛⢈⡿⢞⠀⢰
⠀⠀⠰⠘⠛⢦⣀⢚⣠⠟⠉⣢⡔⠱⡘⡇⠀⠈⢉⣼⢃⣴⣗⠜⣴⣦⠠⣸⠋⠓⢿⣟⡶⢥⣴⠛⡧⠒⣧⣀⣀⣴⡣⢏⣹⣦⣭⣴⣞⣵⣽⢬⣻⣤
⠀⠀⠀⠣⠀⠈⠉⠭⠉⠀⣼⣁⣃⠀⠑⠷⣄⣀⣠⣾⠿⡁⣼⠶⣏⢨⡀⣻⣀⡤⠖⡟⠿⢾⠁⡈⠀⣉⢈⡙⢹⢿⠹⣄⢩⣵⣶⣿⡍⣛⣿⠿⣍⢹
⠀⠀⠀⠀⢇⢀⣀⡴⠊⠉⢀⡠⣤⣷⡄⠀⠈⢉⠟⢱⢫⠖⠁⠀⠘⢆⢣⠻⡇⠠⡇⠀⠀⣿⠀⠀⠀⣼⣩⣥⣤⡤⠀⡬⢤⡍⠭⡁⣤⣿⣿⠀⡏⡽
⠀⠀⠀⠀⠀⡟⠻⠪⢿⣿⠛⡿⣉⡟⣧⠐⢂⡏⠀⣇⡼⠻⠶⢲⠶⣶⡗⡄⠻⣄⣂⣠⣔⠛⣶⡀⣠⣷⢿⡿⣿⡷⢺⠁⣾⠀⣼⠀⠉⣸⢗⡜⠀⡇
⠀⠀⠀⠀⡾⠛⡃⠀⠈⢧⡉⠙⢃⣠⠏⠀⡠⡇⠀⢟⣷⠄⢀⡼⠁⣸⢣⠁⠀⣸⠏⢳⣬⣟⠄⠈⣼⢿⣯⣠⣈⣷⠈⣀⠜⣶⣤⣤⡾⠓⠊⠀⢰
⠀⠀⠀⢀⣀⣶⠿⠒⠴⢯⣟⡟⡻⠋⠁⣉⢴⣯⣶⣌⢳⣄⣈⣠⡞⢉⠎⣴⣻⠋⠀⠀⠈⢯⢇⣰⣇⠸⠆⠐⢉⣏⡼⠡⠤⠠⠍⠉⠤⢀⣀⠴⠃
⠀⠀⢀⠈⠉⠑⡄⢀⡴⢿⠝⢓⡦⠀⠘⣲⣿⠫⢝⣷⣹⢏⠛⢁⣄⡘⠀⠻⣿⡻⠋⠙⠛⢻⡄⢨⣝⠷⠶⣶⠯⠌⠤⠤⠤⠤⡆⢻⡆⣀⡇
⠀⠀⣼⠷⢾⠀⠱⣼⠃⠀⠀⢺⡇⢀⠐⣷⠀⠀⠀⣽⠀⢸⢨⡏⣉⡿⠀⠀⠹⣆⣀⣀⣀⡿⠀⢞⢈⠗⠈⠀⠀⠀⠀⢀⣀⠞⠁⠙⠁⠀⢰
⠀⠀⠙⠢⡌⠣⠀⡼⠳⢤⠶⢟⠙⣯⣀⠜⠛⠾⠛⠋⠢⣠⠎⣽⠁⠡⠀⠀⠀⡎⠉⠉⠉⠑⠂⠼⠈⡀⠀⠀⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠸⢷⣄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⠛⢶⠹⡊⡴⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⣶⢏⢹⣿⡐⠢⣜⠐⠀⣣⠔⢒⣿⡏⡹⣖⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠁
⠀⠀⠀⠀⠘⣿⣏⣾⣺⠁⠙⢽⠻⡟⠑⡼⠂⣰⢿⡟⣧⠙⢿⣦⡑⠂⠘⢊⣴⡾⠋⣾⢛⡿⣆⠐⢤⠊⢹⠿⡯⠋⠉⣗⣷⣻⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣡⣿⣭⣒⡬⢄⡁⠠⣕⣻⠃⢾⠧⠟⣤⣦⡍⠛⢦⡴⠛⢩⣴⣤⠷⢾⣷⠘⢟⡫⠄⢈⡠⣥⣖⣽⣿⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣉⡽⣿⡿⣷⣌⠄⠩⢙⡲⠛⠉⢰⣿⣿⡏⠀⠘⠋⠀⢹⣿⣿⡆⠹⠛⠖⢏⠌⠐⣡⣾⢿⣿⢧⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⢟⡄⢙⣿⡌⢠⡆⢀⡀⠰⠄⢸⣿⡇⣤⣠⣆⣤⢸⣿⡃⠰⠄⢀⡀⢰⠄⢁⣿⡋⢠⡻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢰⣷⡇⠀⠁⡿⡏⢠⢒⡟⢢⢹⣾⠳⢞⣷⡏⡔⢳⡒⡆⢹⣿⠈⠀⢸⢿⡄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣗⡇⠀⠀⡇⢠⠌⠉⢸⡟⣸⠛⠃⠘⠛⣇⢿⡇⠉⠡⡄⠺⠀⠀⢸⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⢿⣳⣶⣾⣧⣿⡀⠀⠀⢀⣿⣼⣷⣦⣞⡿⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣽⣆⣸⢿⢧⡀⢀⡼⡿⣅⢰⣯⣾⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠀⠈⠙⢦⡀⠀⠀⣀⠀⠀⠀⢰⠃⠀⠘⠃⠀⡀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠛⠀⠀⡰⠃⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⠧⠀⠀⠀⠀⣼⠀⠀⠀⠀⡴⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⡠⠤⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠀⠀⠀⠀⢠⡏⠀⠀⢀⠞⠀⠀⠀⡠⠋⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⣀⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣠⠋⠀⠀⢠⠞⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⣰⠏⠀⠀⡴⠁⠀⢀⡴⠁⠀⠀⣠⠖⠁⠀⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⡞⠁⠀⣠⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣠⠏⠀⢠⠞⠁⠀⣠⠞⠁⠀⠀⣠⡴⠞⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣾⠃⠀⡴⠃⢀⡴⠋⠀⣠⠞⠁⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⡘⠃⠀⠚⠁⠠⠟⠀⣠⠞⠁⠀⣀⡴⠟⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⣄⠀⠀⠀⢠⡾⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⢂⠐⢿⠿⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣴⠾⠋⠀⠰⠿⠀⠀⠀⠀⠀⠑⠢⠤⠔⠊⠁
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠁
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠉
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠠⠛⠻⣿⣿⠏