Family Tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠠⠒⠀⢢⠊⠀⠁⠠⠀⠀⠀⠲⠀⡐⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢠⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡄⠁⠀⠃⠀⠈⠀⡀⠐⠀⠈⡄⠂⠀⠀⢠⡖⠂⡀⠤⠠⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⢤⣸⡅⠀⠀⠈⢦⠀⣁⠀⠀⢁⡄⠀⡄⠀⠈⣧⠊⠀⣀⣀⠄⠂⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠈⠙⢦⡄⠀⠈⠑⢻⡄⢠⣋⡤⠴⠓⠃⠀⣸⠖⠋⠉⠉⠙⢋⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⡛⠛⠓⠾⢷⣤⣀⡀⢀⣿⢻⡅⠀⠐⠀⠀⣾⢃⣀⠤⠄⠀⠀⠀⢀⠄⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⢄⠀⠀⠢⠤⠴⢒⠋⠉⠉⢻⣾⠃⠈⢷⡀⡈⢁⣼⡟⠉⡀⠀⣇⠤⠶⣐⠋⠀⠀⢀⠀⠀⠀⠑
⠀⠀⠀⠀⠄⠀⠠⢐⠀⠈⢇⠈⠙⠶⣦⣀⣀⣀⣀⣀⠀⢸⡿⠀⣈⡬⢿⣾⡏⠁⠀⣴⢁⡼⠃⠀⠶⢀⡀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠄⠀⠄⡈⢑⡦⢬⣻⣷⣤⣶⠿⢿⠛⣿⡿⢿⣾⣿⣾⠃⠀⠀⣿⡇⢀⣼⠷⠿⠟⠛⠛⠓⠂⠄⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠉⢀⡀⠠⢄⡜⠃⠀⠀⠙⢿⣿⣄⣀⣸⣿⣷⣿⠷⢲⠳⢬⠀⠁⢀⠀⠁⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⣀⠀⠀⠀⡀⠀⠀⠃⠐
⠀⠀⠀⣀⣠⣴⣦⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⡀⠀⠀⠠⠄⢀
⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠒⠒⠈⠁⠻⢶⡾⠓⡶⣶⡿⢿⣟⠉⠙⠛⠛⠟⢶⠦⠄⠀⠀⠒
⠀⠀⠀⠘⠛⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠎⠈⠀⠀⠀⠀⠔⣾⠉⠐⠀⢀⡠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠐⠀⠈⠀⠈⠂⠔⠀⠈⠀⠀⠁⠁⠀⠀⠂⠐⠀⠂⠘⠀⠀⠁⠀⠰⠒⠒⠐⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠶⢀⠐⠦⠸⡧⢾⠈⠦⠀⠀⠀⠰⠂⡄⠄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠐⠯⠇⠀⠅
⠀⠀⠀⠀⠀⡀⡢⠀⠀⠀⠏⡑⠏⠀⠀⠀⠂⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠆⠲⠀⠀⠀⠀⠠⣁⠀⠠⠀⠁⠀⠀⢨⡀
⠀⠀⠀⠄⠀⠀⠀⠸⠚⠀⠘⠗⠂⠀⠘⠶⠦⠃⢰⠒⠐⠀⠀⠀⣆⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⣀⠀⠠
⠀⠀⢠⠄⢩⡖⠀⠀⠔⢤⣀⠀⠀⠂⠠⠀⣀⠀⠀⠧⠀⠀⠀⠀⠀⠠⠒⣴⡀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢸⡅⢠⢰⠀⠀⠀⠀⠺⠂⠀⣀⠀⢀⠠⡈⠇
⠀⠀⠡⠂⠀⠀⠀⠀⠀⣤⡨⠲⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠄⠘⠁⠀⠀⠀⠀⠀⢀⢀⣀⠂⢀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⡠⢈⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠱⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠉⠀⠠⠁⠀⠀⠀⠐⠠⠃⠉⠒⠠
⠀⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⠀⠀⠰⡄⠀⠀⠀⠀⠤⠀⠀⠤⠔⠒⠁⠀⠀⠈⠁⠀⠀⠀⢀⡀⠈
⠀⠀⠊⣁⣄⠀⢀⡩⠂⠀⠀⠐⡗⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠠⠤⣖
⠀⠀⠀⠈⣹⠂⠀⢴⡐⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⣴⣀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠈⢲⡴⠀⠐⠈⡱⠀⢀⢀⠀⠀⠁⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠁⡵⠄⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⡦⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠂⠐⢠⠸⡝⠇⠆⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡦⣠⣤⣤⣴⢶⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⡔⠗⢎⢹⣷⡿⢾⣭⡉⠹⣾⠟⢯⠻⣿⡷⣿⣠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣿⣣⣿⢷⡷⣮⣀⣾⣿⠸⣟⣳⣾⣦⣞⣿⣜⣿⠏⣿⣵⡋⣭⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡜⣻⡶⢿⠫⠿⣿⣿⣿⣙⢢⣜⣛⣻⣿⢿⣿⣽⠟⣋⣁⠿⣿⣼⠟⠯⣼⣿⣦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢁⣆⣜⢿⣶⡀⣇⣙⣿⡟⢻⡿⣿⡟⠻⡆⣬⣿⣶⣽⠟⣶⣏⠿⠾⢷⣨⢿⡱⣯⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢨⣟⣻⣿⣟⣻⣭⣿⢿⡟⣹⠯⡿⢿⣷⡶⣿⡿⠶⣇⣼⣿⣯⡽⠋⠷⢿⣰⣿⡷⢿⣫⣷⢮⣙⣯⡀
⠀⠀⠀⠀⠀⠀⣀⣤⡿⣾⡛⠡⣙⡵⠿⣒⣾⣇⣾⡟⣇⡽⠿⣿⡇⢰⣿⠛⣿⣿⣆⣴⣶⡿⠏⣡⣭⣾⡧⢴⣎⣭⣟⣿
⠀⠀⠀⠀⠀⣤⢸⡿⣦⡿⣿⢳⣿⣿⣧⣽⣿⢿⣿⣯⣿⣽⡅⢿⣿⣾⣿⣿⣿⣷⠟⣷⠰⢿⣿⡉⡛⠛⢹⡯⣯⡿⣿⢉⣿⡀
⠀⠀⠀⠀⠘⢋⡹⣷⣌⣿⣿⢿⣟⡹⢿⣟⢐⣿⣿⡿⠧⠍⣿⣿⣿⣿⣿⣾⣿⣿⠶⣿⡿⢿⢿⣿⠷⣿⣾⣿⣿⣴⣼⡿⠏
⠀⠀⠀⠀⠈⡷⠛⠋⠛⠋⠁⠻⠉⠻⠟⠉⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠋⠉⠛⠃⠈⠹⢾⠫⡄⠀⠛⠀⠙⠹⠿⠿⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠠⠤⠒⠋⢉⣹⡿⠟⢻⣿⣿⣿⡟⠛⠛⠛⠛⠿⣶⠶⠶⠶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⢤⣀⣤⠶⠛⠋⢀⠜⢩⣿⣏⣿⣷⣶⣦⣀⠀⠀⠙⢷⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⢈⣴⢿⣿⠛⢻⣿⠀⠙⣷⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢒⣲⣶⣦⠶⠛⠁⣸⡇⠀⣸⡿⠂⠀⠘⢷⣤⣀⣀⣠⡤⠶⠒⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⢀⣀⣠⡾⠋⠀⢰⡟⠻⣷⡀⠀⠀⣯⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣾⡀⠀⠻⣇⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⢸⠈⡇⠀⠀⠈⠛⠛⠲⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠁⣠⣤⠶⢤⣠⣄⠐⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⠄⣼⠋⠀⠀⠀⠙⣎⠓⡾⢾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢉⠈⠃⢾⣛⣷⢰⡇⠀⠀⠀⠀⠀⠸⠀⢀⠀⠈⢺⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⣸⡀⠴⠋⠈⠁⣿⠸⡇⠀⠀⠀⠀⠀⢠⠔⠃⠀⠤⠞⠉⠅⠀⠀⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠙⠉⠀⢠⡰⡋⠀⡇⠀⢣⡀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡴⠚⠛⠳⣆⢻⠈⣠⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢮⡀⠀⠐⣄⠘⢷⣌⡀⢳⠀⢀⠁⠀⠀⠀⠀⣠⠀⠀⢀⡟⠀⠀⠀⠀⠈⢧⠛⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⣤⡤⢬⣄⠠⠄⠀⠀⠙⠿⣶⡆⠀⠀⠀⢀⣤⠞⡁⢀⡀⢸⠃⠀⠀⠀⠀⠀⠈⣰⡟⠀⠀⠀⣠⡞⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⢠⡞⠁⠀⠀⠈⢳⡀⠠⠀⣠⠴⠮⣁⡴⠞⠛⠺⣤⠈⠀⠀⢰⠘⡆⠀⠀⠀⠀⠀⠰⠋⡠⠀⠀⢠⡏⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣶⣿⠀⠀⠀⠀⠀⠀⣧⡀⠀⢿⣀⣴⡟⠁⠀⠀⠀⠈⣧⠀⣀⣈⠀⢱⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⣼⠁⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠜⢿⠀⠀⠀⠀⠀⠀⠘⡟⠂⡀⠀⢸⠃⠀⠀⠀⠀⠀⠸⠋⡄⠙⡇⠀⠄⢰⡀⠀⢀⡀⠀⠀⠀⡼⠁⣐⣭⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⠀⠘⡄⠀⠀⠀⠀⠀⠀⡈⢀⣘⣒⠸⡆⠀⠀⠀⠀⠀⠈⠀⠙⠛⣱⠀⠁⠸⠙⣆⣠⣾⣤⣀⠾⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠐⢰⠂⠈⡂⠄⠀⠀⠀⠀⣸⣠⣼⡿⠗⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢐⠅⠀⢠⠟⠁⠀⠀⠙⢦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡶⠉⠀⣀⠙⠳⢶⣶⣶⣾⣿⠛⠁⠀⠀⠐⣀⣀⡀⠀⣿⢶⣞⠁⣀⣀⠈⢂⠀⡟⠀⠀⠀⠀⠀⠈⡦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⡀⠈⣷⡀⠀⢀⣴⠛⠉⠙⠳⡄⢠⠞⢩⠀⠙⠆⢼⣷⣝⡳⢦⣭⠥⣤⣴⡇⠀⠀⠀⠀⠀⠀⡅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠈⠁⢻⣿⣦⣾⠁⠀⠀⠀⠀⠹⡎⣰⠀⠀⠀⠀⢸⣿⣿⡇⠀⠠⠜⠋⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠓⠂⣌⢉⡇⠀⠀⠀⠀⠀⠀⡷⠏⣀⠕⢐⠀⢸⣿⣿⡇⠀⠀⠀⣴⣦⡤⣁⠀⠀⢠⡔⠑⠋⡀⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣥⠎⠙⡿⢣⠀⠀⠀⠀⠀⢀⣧⣌⣛⡷⠆⠉⠘⣿⣿⣿⠀⠀⠘⠁⠁⡇⠈⠓⠀⠟⠁⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣵⠎⠣⡀⠀⠀⠀⣾⠻⡷⢮⡙⠓⠦⣤⣿⣿⣿⣦⠀⠀⠐⠀⠳⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠤⠀⠀⠁⠀⠀⠁⡀⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⢀⣠⠟⠀⠂⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠟⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠄⠰⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⣠⢀⠒⠈⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡚⠛⠛⡤⢠⡾⠛⠛⣠⢀⡀⠀⠀⠀⠀⠀⠀⠰⢤⡷⣜⡷⣃⠀⡘⢯⡺⢵⢆⡀
⠀⠀⢀⢀⠀⠉⠀⠀⠈⠴⢀⡅⠈⢥⠉⠠⠄⠀⠀⠀⠀⠀⠤⠏⠀⢡⡇⣀⠤⠠⣀⢀⣤⡋⠀⢢⠄⠀⠀⠀⢀⠶⠛⣛⠀⢈⠿⣯⠿⢻⣿⡀⢀⡽⠶⢦⡄
⠀⠀⣈⠁⠠⣀⢋⠐⢻⡂⣈⠘⠊⣸⡔⠂⢆⠀⠀⠀⠀⢀⡾⠒⢰⠎⠉⣬⠜⠊⢬⡈⠁⡦⠐⠳⣆⠀⠀⠀⣉⢷⣤⢯⡔⠩⡌⡓⠚⠻⡯⣏⠾⡽⢄⡟⣿
⠀⠘⠃⠀⢈⡝⢦⡀⣠⠆⣱⡇⣀⡤⣚⠁⠰⠆⠀⠀⠀⠠⡅⠀⠻⡄⠄⢩⣢⣄⣨⢁⠀⡬⢁⠀⠄⠀⠀⠀⠼⣛⠉⢻⣿⡀⣼⡯⣀⢠⣿⣄⠀⢿⡏⠈⢾⣄
⠀⠀⠒⠄⡁⠀⣸⣟⢯⣿⣿⣵⣮⠀⠸⣡⡈⠀⠀⠀⠀⠀⢻⡎⠻⡄⠀⣬⣭⢮⣧⡄⠀⣸⠛⣎⠁⠀⠀⠀⢛⣷⢠⠌⣈⠟⠉⣹⣯⣿⣽⡽⠛⠉⣡⡄⣶
⠀⠀⠘⡱⠀⡐⠋⠄⢻⣿⡏⠈⠈⠊⢁⠡⡑⠀⠀⠀⠀⠀⠈⠁⠰⠆⢼⠀⢰⣾⠀⢸⠀⠾⠂⠁⠀⠀⠀⠀⠀⠹⠧⡆⠘⣧⡀⣈⣿⣯⡽⣦⣀⡜⠏⠈⠃
⠀⠀⠀⠀⠈⠀⠈⠁⢀⣿⡆⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠛⠉⢸⣷⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉
⠀⠀⠀⠀⠀⡄⡤⠜⣢⠎⢗⣴⠦⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠒⢀⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠤⢸⠑⠪⣋⡷⡀⣼⢾⠛⠑⣸⡤⠄⠀⠀⠀⠀⠀⠀⠀⠨⠀⠂⠀⠂⠂⠐⠔⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦
⠀⠀⣐⠲⢺⢆⣠⡇⠛⠉⢹⠟⢦⢰⢬⡵⡖⣂⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⠒⠀⠐⠈⠀⠂⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⢸⡀⣠⠀⠂⠀⠠
⠀⠀⣢⣀⣈⡾⠁⠰⣟⠶⡬⡻⡂⠘⢎⣁⣀⡄⠀⠀⠀⠀⠀⠀⢀⠈⡐⣙⡓⢀⣀⣏⠊⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⣿⠀⡄⠀⠀⡂⡀
⠀⠀⠶⣫⠈⢶⢄⣞⡍⣎⡼⡭⣧⢠⡾⠁⡟⠤⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⢷⣇⣼⢋⠁⠎⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⠡⠟⢦⡀⣿⣠⠐⠒⠐
⠀⠠⢏⣳⢠⣌⡧⠈⠳⣿⣷⠋⠁⢍⣡⢠⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⣿⠇⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏
⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿⣏⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⢠⡤⢾⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⡃⠀⠀⣤⡍⣥⣄⠀⠀⠀⠀⠈⢳⣾⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⠿⣤⡾⢻⣇⣿⠻⣦⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡍⢀⣿⣿⡄⠉⠁⢸⣿⣿⠀⣽⣦⡄⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠘⠛⠾⣿⢿⡷⠀⠀⢸⡇⣿⠀⠛⠛⠃⠀⠀⠀⣿⢹⡏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢸⡇⠀⠀⣼⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢀⡴⠁⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⢠⣼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣁⣀⡤⠾⠛⠛⠳⣆⠀⠀⠀⠀⠀⢉⣨⠟⠋⠀⠀⢀⣼⣿⣷⡀⠀⠀⡀⠀⣰⢻⣿⠷⡄⢀⠀⠀⡀⣰⠿⣿⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣴⠞⠋⠁⠀⠀⢰⣦⠟⢰⣿⡇⠑⠀⣰⠁⡀⠀⣼⣿⣇⠈⣿⣇⣴⣿⠁⢸⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡾⠋⠀⠀⠀⠀⠀⠀⣻⡇⠀⢾⣿⡿⠀⣴⢃⡞⠀⠀⣹⢻⡏⠀⣿⡇⢹⣿⠀⢸⣟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⢸⣈⣷⡾⠃⣼⠁⠀⠀⠙⠈⠃⠀⠉⠀⠈⠉⣀⣨⡧⠿⠃
⠀⠀⠀⠀⠀⠀⣴⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠟⠋⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢻⣭⠁⣀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣀⠀⠈⠢⡀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠀⠀⢠⣴⣤⣦⣿⡀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣸⣿⣽⣿⡇
⠀⠀⠀⠀⣴⢿⡇⠀⠀⢨⡿⣆⠀⠀⠙⡀⠀⠀⠈⠻⣿⣶⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⣻⠿⠛⠀⢷⡄⠀⠀⠀⢀⡿⠀⢠⣾⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣇⠀⠀⠀⢀⡇⠀⠀⠀⢰⣦⠙⠛⠿⢿⣿⣷⣤⣀⠀⠀⠀⢸⣿⣿⣷⠄⠀⢻⡄⠀⠀⣸⡇⠀⠙⠁⣿⣿⣿⢻⡇⠛
⠀⠀⠀⠀⠀⢸⣿⢸⣿⢿⡟⠀⠀⠀⣸⠇⠀⠀⢠⣼⣧⡄⠀⠀⠀⠀⠉⠙⠻⣷⡄⣰⣿⣿⣿⣿⣶⡄⠀⢹⣆⠀⣿⠀⠀⠀⠀⣡⣿⣿⢩⣿
⠀⠀⠀⠀⠀⢸⡿⢸⣿⠈⣇⣀⣤⣾⣿⠀⠀⣰⠿⣿⣿⡿⣆⢀⠀⠀⠀⠀⠀⢸⣿⠋⣿⣿⣿⣿⣏⠻⠄⠀⣿⣦⣿⠀⠀⠀⠀⣿⣿⣿⠸⣇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠙⣿⠀⠀⠀⢸⣿⢿⡇⠈⢿⣧⡀⠀⠀⠀⣼⡿⠀⣿⢻⣿⣿⣿⡀⠀⠀⣿⣿⡏⠀⠀⠀⢀⣡⠾⠟⠊⠁
⠀⠀⠀⠀⠀⣰⣶⡆⠀⠀⠐⣿⡇⠀⠹⣆⡀⠀⢸⡿⢿⡇⠀⢻⡏⠁⠀⠀⣼⣿⠃⠀⣿⢸⣿⡏⣿⠁⢀⣴⣿⠟⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⢸⣿⣿⣇⠀⢀⣶⣿⣷⠶⣤⡈⠛⠳⠾⠿⠿⣷⣶⣿⣿⣶⣄⣰⣿⠁⠀⠀⠛⠘⠛⠃⣹⣶⣿⠟⠁⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠚⢻⣿⡟⢶⡿⣻⣿⣿⠀⠀⠁⠀⢀⡤⠖⠛⠉⠁⠀⠀⠉⠻⣿⣿⣄⠀⠀⢀⣀⣴⣾⡿⠛⠁⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⣾⣿⣧⠀⠸⣿⡿⣿⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⢻⠿⡟⠀⢠⣿⡏⣿⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⣿⠀⠗⠀⢘⣿⣥⣿⠶⠛⠋⠉⠉⠉⢛⣿⣶⣤⣤⣤⣤⣶⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⡿⣦⡾⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⢰⠏⣿⣿⠹⣆⢀⡀⡾⢻⣿⣿⡟⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⠋⢰⣿⣧⠈⠀⣿⢿⡇⠈⢱⣿⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⢰⣿⣿⡆⠈⣿⡟⠀⢸⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⢻⡿⡿⠀⠀⣿⢸⡇⠀⢰⣿⠁⢀⣼⣿⣿⣿⠀⠀⠀⠀⠙⡟⢻⠃⠀⣿⡇⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠸⠃⠿⠀⣀⣿⣼⣧⣤⣼⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠇⠸⠃⣀⣿⣧⣀⣼⣯⣼⣧⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⡿⠿⠛⠋⠉⠉⠉⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠱⠄⠀⣠⠄⠂⠰⠀⠀⠀⠀⠀⣠⠀⠀⢀⢀⠀⠠⠖⠑⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡤⠀⢘⠂⡠⠄⡀⠲⠀⠠⠶⢂⡉⠃⡀⠠⠆⢀⠊⠲⠒⢈⣔⠠⢦⡔⡄⠈⣰⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡈⠈⢡⠀⠀⠈⠒⠃⠀⠀⠠⡀⠂⣀⡄⢀⠈⡡⠀⠀⠀⠃⠀⠀⠀⢠⠴⢈⣀⣀⡘⢃⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⢰⠚⠁⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢸⡇⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⠓⠈⠀⢀⠴⠂⢦
⠀⠀⠀⠀⠠⠁⠘⠆⡀⠈⢱⡄⠀⠀⠠⠠⠂⠀⣀⡀⠀⣀⡀⠀⠀⠀⠃⢰⢸⡇⠀⠀⠃⢀⡀⠀⢀⢀⠀⢀⠐⠀⢈⠘⠃⠉⠙⢾⡆⠀⠈⠉
⠀⠀⠀⠀⠀⢠⠃⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠄⠀⣀⢘⠀⠀⠐⠖⠂⠀⣼⡇⢠⡖⠐⠀⠀⠀⣤⢀⡄⠂⠃⠀⠀⠰⠉⠀⠀⠀⠀⠉⠀⠁⠂
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⡀⠂⠈⠋⡠⡄⢀⠖⠈⡁⢻⣧⠈⠜⠵⠂⡐⠠⣸⠀⢀⠠⣄⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠁⠄⠐⢁⠙⠁⢀⣇⠀⠀⠀⡼⡁⠀⢸⡇⠐⠂⢀⣈⡘⠁⢺⠆⠀⠀⠀⠨⠄⢀⡀⠀⠀⠀⠄⠀⣠⡄⣁
⠀⠀⠀⠀⢀⠀⡋⠙⠁⠀⠃⠐⠷⡜⠁⠁⠀⠀⠔⠀⠀⠀⠀⠀⠈⠀⠀⡄⣸⡇⢰⠈⠀⠀⠀⠀⠈⠉⠀⠆⠀⠐⢀⠀⠀⠴⠀⠠⠂⡀⠉⠀⠀⠄
⠀⠀⠀⠀⣀⠀⢀⠔⡰⠀⠀⠒⠀⠁⢀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⢠⠄⠁⠀⠈⣁⠄⠀⡰
⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠲⡀⠙⢤⣤⡀⠀⠀⠀⠀⠤⠠⠤⠤⣄⠀⠀⣿⣿⠈⠀⢤⠤⠀⠀⠤⠤⠄⠀⢀⠀⢀⣠⠎⢀⠐⠀⠀⠀⠁⠀⠈⠐
⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡑⡀⠀⢀⢤⠲⢆⡀⠰⡆⠀⡼⡛⠲⣿⡿⢛⠉⠀⣈⠀⢀⠴⠒⠠⠓⠠⢄⠀⠘⡳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡄
⠠⠇⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠇⣀⣀⣀⠀⠀⣈⠀⢙⣦⣦⡁⠀⣿⡇⠐⢖⣠⡶⠿⠇⠦⢀⡴⠀⢀⠐⠃⠀⠐⠀⠠⠀⠀⡀⠀⠀⠀⣀⠄⠀⠼
⠀⠀⠀⠰⠃⠂⠀⠀⠀⠀⠂⢀⡰⠄⠴⢲⠑⠃⠀⠔⠺⠙⠲⠁⠈⠁⠝⣦⣿⣯⣰⠟⠥⠀⡀⠴⠒⠀⠶⠂⣀⠀⠀⢦⣄⠠⣔⠲⠂⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠁⢰⠘⠀⠀⠀⠀⠀⡴⠀⠈⡐⠒⠘⠓⠀⠂⠒⠐⢐⢴⡖⠘⣿⣿⠃⠈⡶⠔⠂⠀⠒⠐⠂⠀⠀⠢⠰⠙⡇⠐⢞⣁⠠⠀⠈⢠⠈⢀⢀
⠀⠀⠀⠠⠤⡄⣈⢁⠀⠠⠀⠰⠊⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⠀⢃⠀⣿⣿⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⠄⠀⢀⠒⠶⢌⣃⠔⠃⠂
⠀⠀⠈⠁⠂⠀⠘⠂⠀⠀⠀⠀⡀⠈⠁⢠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢆⣿⣿⡸⢠⠂⠤⠀⠀⠀⠀⠀⠀⠀⠠⢀⢉⠃⠀⠀⠀⠀⠀⠀⠓⠀⠀⠄
⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠈⣀⡀⠠⣄⠀⢸⣿⣿⡇⠈⠚⠓⡀⠀⣤⢀⠀⡀⡄⠀⠀⠠⠂
⠀⡆⠄⠃⠀⠀⠀⠀⠀⠀⠀⣀⠂⠘⠎⠀⠀⢀⡀⠑⠦⠀⠈⠷⠀⠤⠐⢸⣿⣿⠀⠈⣂⠀⠀⠆⠀⠀⠸⠤⠀⠀⠀⠢⠃⠀⢀
⠀⠀⠀⠀⠀⢜⠁⠀⠀⠀⢠⡜⠒⠒⠀⠐⠲⡶⠒⠛⠲⠛⠓⠶⢦⣙⠀⢸⣿⣿⠀⠀⣩⡠⠖⠀⠀⠙⣂⠀⠲⡶⠂⠀⠶⣄⠈⠁⣄⠀⠀⠈⢫
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠠⠠⢄⣀⠄⠀⠰⡄⠠⠀⡐⠐⠂⠀⠉⢳⣼⣿⣿⣠⡾⠋⠴⠁⠐⠄⢀⠸⠀⠀⣎⢢⠀⠀⡂⠐⠈⢌⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⡟⠀⠄⠀⠀⠀⠀⠀⠀⠘⠂⠁⣰⡇⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡐⠋⣀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⡈⠐⠦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣿⣿⡇⠘⡀⠀⠀⠀⠀⠀⠀⢀⠄⡐⠘⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⣰⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣽⣬⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣿⣷⣶⣶⣿⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⢀⣀⠀⡀⠠⢀⠀⠠⡄⢀⡀⡠⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠉⠈⠀⠃⠀⠉⠀⠀⠂⠐⠀⠓⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠄⠀⡀⢰⠁⠀⠨⣤⡀⠠⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⣠⠁⠀⠉⠀⠀⠉⠈⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⠁⠤⠀⠉⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠤⣠⠀⠀⠀⠉⠉⠓⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠲⠀⠀⠀⠀⣀⣀⣙⣃⢀⠐⠢⡀⠀⠀⠀⠀⠀⢀⡤⠤⠽⠀⠄⠐⠄⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⣠⠔⠲⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠗⠢⠔⠉⠢
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡀
⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⣴⠀⠀⡀⠀⠐⠀⢤⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠌⠁⠀⠀⠠⠃⠀⠑⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⢦⡀⠀⠐⠀⠐⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢃⠀⠾⠁⠄
⠀⠀⠐⠁⠀⠀⠀⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⠊⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡀⣀⠀⠀⢦⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⢀⡀⠀⠀⢄⠀⣀⣀⠂⠀⠀⡀⠀⠀⠰⢀⢠⡄⠀⢀⠀⠀⠀⠀⡤⠄⠈⢙⠈⠲⠊⣸⣋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⡀⠀⡘⠲⢞⠂⣀⠇⠱⣦⡚⠛⠧⡠⠶⠇⠀⢀⠎⠀⡀⠊⠀⠀⠈⡆⠀⣄⠀⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠢⠄⠙⠆⠔⠉⠈⠀⠀⠀⠒⠠⢤⣀⠀⠙⠚⠀⠀⠀⣄⡤⠂⠀⡰⠁⠀⠀⠀⠀⠈⠃⠙⠂⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠐⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠁⠈⣄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠉⠀⠀⠀⢄⣀⠏⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠈⠉⠀⠀⠀⢣⣀⣘⠎⣁⣉⢋⡉⠿⠷⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡖⢬⠁⣀⠔⠂⠉⠀⢀⣿⡀⠀⠀⠀⠀⡠⣀⢀⠈⢀⣤⣀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⣤⣤⠀⠠⠴⠾⠶⣧⣤⡴⠧⠤⠴⠶⠙⠞⠟⠚⠂⠀⠈⠘⠀⠁⠈⠙⠙⠈⠘⠛⠑⠒⠒⢾⠆⢤⡤⠤⠤⠴⠶⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣟⡀⠀⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⢤⣬⡅⢀⣲⡟⢢⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢥⡆⠀⠀⠂⠀⠀⠀⠀⠀⢸⡷⢂⠠⣿⠄⢶⡆⠀⠀⠀⠀⠀⢬⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⣴⠆⡀⢁⡀⠀⠀⠀⠀⠞⢻⣏⣰⣿⠃⣀⣞⠃⠀⠀⢀⣐⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣧⣜⣾⡃⡘⣷⣂⠂⢰⣷⣆⠩⣽⣿⠛⠀⠀⠈⠐⣤⣷⣾⣭⡽⠚⠓⠂⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠟⢳⣮⣿⣂⣠⣩⠰⡅⠺⡇⠀⠀⠀⠀⠀⠀⢴⡅⠀⠀⠀⠀⠀⠀⠙⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠇⣴⠀⡾⣀⠀⠀⠀⠀⠀⠀⠈⡄⣛⠹⡟⢻⠿⣿⣷⣿⣄⡀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣸⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢫⡶⢒⣯⣀⠀⠀⠀⠀⡈⠀⠁⠸⠛⠿⠲⣧⣍⡻⣿⣿⠁⠠⣶⠄⠀⠙⠋⠀⠀⢠⡤⢰⡾⠷⢂⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠈⠩⣽⣾⠆⠀⢐⣿⡆⠀⠻⠏⠀⡀⠍⠝⠷⣿⡟⢁⠶⢠⣆⣠⣟⣀⢸⣧⣴⣟⣙⣋⣠⣝⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡌⢛⣧⡲⢿⣾⠃⣌⠻⠃⢙⣖⡀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⡏⠉⠋⠀⠀⠀⠘⠃⠙⠃⣦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠁⠉⠙⠛⢷⣿⣄⣿⣠⡜⠷⡀⠀⠀⠀⠀⢀⣾⣟⢱⣤⣶⡃⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠨⠹⠟⠹⠛⡿⢻⡿⣦⣤⣤⣤⣾⣟⠻⠉⣳⣄⠀⠀⡀⠀⣀⠄⠁⢠⡀⢰⣆⣜⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⢀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠂⢠⠷⡞⣶⢷⣿⣿⣿⣿⢫⣄⢦⠬⣻⣆⣼⣇⣀⣿⣀⣤⣼⡗⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡟⢀⠸⠶⠆⣠⠈⠀⠸⣿⠇⠀⠠⠀⠀⠘⠡⣿⣿⣿⣎⣵⣾⢿⣟⠻⠏⠉⠿⠉⣿⠖⠺⢷⡘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡀⣤⠛⠛⢶⡟⣀⠀⠶⡞⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣵⠋⠀⠀⠀⠈⢀⣴⠈⢠⡆⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⣹⡿⢦⣿⣬⣿⣿⣶⣧⣴⡀⠀⠀⠀⠀⣼⣿⣟⠻⢆⣠⠀⠀⠀⠀⠀⠨⠉⠲⢯⠀⠀⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠉⣀⠰⠛⠀⠚⠃⣈⣛⣻⣿⣶⣶⣶⣿⣿⡥⢩⣼⣏⣥⠶⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⡄⠀⠀⠀⠀⠙⣛⠛⠉⠽⣿⣿⣿⣿⣾⣫⣿⣿⡍⠃⠀⠀⢰⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⢿⠇⠀⠛⣿⣿⣿⣿⠉⠛⠓⢼⡆⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠿⢿⣭⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠾⠛⠛⠛⠉⠉⠉⠉⠉⠙⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⢀⡀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣧⡞⡀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎⠀⠀⠀⢠⡿⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣀⡀⠀⠀⢸⣿⠀⠀⠀⣠⠟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣶⣾⣿⣤⣴⣾⡥⠶⠚⠛⠒⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⠀⠀⠙⣿⣿⣿⠋⠀⠀⡀⠀⠀⡠⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢿⣦⣤⣼⣦⣀⣀⣿⣿⣧⣀⣠⣎⣠⣴⣾⢤⣴⣛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⣧⡐⣦⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠶⣶⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠔⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⠶⢶⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣶⣿⣷⣶⣾⡿⠶⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠉⠛⠦⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠛⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢆⣄⠀⢠⣅⠠⢾⠇⢉⣥⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⢀⣠⡘⠷⠸⣦⠹⠷⠈⢛⡄⣬⣁⡇⡠⣤⡌⠁⢀⡰⣦⡈⠁⠾⢇⣀
⠀⠀⠀⠀⠀⠀⠉⣡⡤⢀⡔⠢⣄⡀⡝⢣⣬⡉⣿⢰⡿⠆⢠⣘⠗⢉⡧⢲⣦⡜⣫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡾⠇⣨⠛⠦⣍⡁⢻⡀⠼⠇⠈⠋⣧⠋⠀⠀⣷⡄⠙⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠾⠟⢡⣾⡄⠉⠙⠻⢦⣀⠿⠆⣟⢀⠸⠷⢀⠎⢈⡋⢀⡺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⣠⡀⢠⣬⡉⣄⢶⡄⣤⡀⢙⢷⡄⢿⠸⢗⡴⢟⣏⡹⠶⠜⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠙⠁⠀⠉⠀⣛⣀⣀⠻⣅⠿⠎⣿⢸⣠⠟⠀⣬⠙⠃
⠀⠀⠀⠻⠇⠀⣤⡀⢀⠻⠇⣧⠲⠿⠀⠛⠃⣴⡏⣭⡛⣷⡀⣿⢸⠏⣶⡈⢩⣤⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢤⣦⠀⠫⢅⣺⠇⠀⣿⠺⠟⠀⠀⠀⠀⠘⠛⠁⢸⣿⣏⠞⠀⣠⠃⠈⣵⡖⠰⡟⠐⠟⢠⣶⠆
⠀⠀⠀⠀⠀⠾⣟⠀⢬⣝⠲⣼⡠⣿⠃⣀⠀⠀⠀⢀⣴⣿⠋⢀⣠⣾⣥⡤⢶⠾⢶⡖⢒⣤⡰⠶⠄
⠀⠀⠀⠀⠀⢘⡛⠃⡈⠓⠒⠬⣿⣆⠸⠟⠀⠀⣴⣿⢏⣵⡾⠛⠉⠁⠀⠀⠿⣷⠙⠻⠀⠉⠁
⠀⠀⠀⠀⠀⠛⠛⠸⠟⠠⠟⣰⡷⠙⣷⡀⢠⢠⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢿⣼⡆⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡜⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣮⡻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⡻⣿⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣯⡛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣠⡶⠿⠛⣩⣴⡿⠉⠛⠻⣿⡄⠙⢿⣷⣄⠲⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠜⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠉⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⡀⠇⡉⠤⠴⠘⣐⣉⠸⢀⡂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⡃⢨⡌⠡⢜⠁⠐⠡⢏⠢⢈⡣⠌⢡⡅⢘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⡘⢃⡲⡐⣖⢢⡒⢃⢒⣸⠋⠀⡔⣲⢂⢖⡘⢃⡖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢡⠠⠙⢀⣹⣒⠈⣷⣷⠀⣷⡯⠀⣺⣿⠁⣚⣏⡀⠊⠅⡌⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠢⣐⠜⢠⠻⣴⣀⢰⡇⠂⡘⣧⠀⢸⡆⣀⣦⠞⡄⠳⣂⠔⡈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⣈⡆⢿⡀⠁⢂⠀⠉⠛⢷⣄⠙⢻⣷⡾⠛⠉⠀⡐⠈⢀⡿⢰⣁⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⢛⠛⡹⠟⠳⠶⣦⣌⣿⣧⣼⣿⣡⣴⠶⠞⠻⢏⠙⡛⠱⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡲⠴⢒⣶⣦⣤⣀⣀⣴⣿⣿⣿⣿⣦⣀⣀⣤⣴⣶⡒⠦⠖⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⠖⠛⣛⣛⣿⢿⣿⣿⡿⣿⣛⣛⠛⠲⡄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣽⠀⠈⠏⣠⣴⠞⠃⠸⣿⢦⣄⢹⠁⠀⣯⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⢻⡆⢀⣧⡈⠀⠀⠤⢞⠀⡸⠀⢰⡟⠅⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠆⢈⠉⠳⠀⢠⠏⠰⡁⠰⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡇⠀⢀⡀⠶⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠷⡉⢀⠀⠈⣧⡄⠙⠛⠦⢰⣦⡈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⠛⠀⢀⠈⡁⢰⣿⠅⠊⠉⠀⠀⠀⠻⠆⢽⠁⢀⣶⣂⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠙⢇⠀⣄⠉⠀⠛⢼⠃⢠⡀⠀⠀⢤⣿⠀⣠⡄⣦⠀⢻⠏⠁⢀⣄⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⢶⣦⣈⠀⠺⣗⣾⢰⠟⠀⠀⣦⠸⠇⠀⢙⣵⣿⣦⣸⠀⢀⣄⠙⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣅⠀⣤⡀⠀⣴⠆⠉⢛⢿⡀⠾⠀⠀⡌⣦⣴⠆⣸⣇⠀⢀⣩⡳⣬⣿⣴⣁⡴⠷⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠌⠛⢧⠈⠁⠀⠐⣿⠂⠹⣄⣶⣀⠞⠉⠉⠀⢹⠃⣠⠈⠋⠉⠉⢻⣯⠀⣀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣤⠀⠀⠀⠙⠂⢢⣟⡇⠀⣡⣆⡀⢸⡿⠵⠆⠀⢠⣄⢸⠈⡿⠁⠀⠸⣷⠀⣿⣷⣟⡁⠠⠴⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣌⣁⠀⠰⠷⣴⢸⠏⠒⠛⠛⠏⠁⢈⠃⣀⠀⠀⠬⠵⣿⣦⠀⠀⣠⣄⠙⢀⡾⠋⠁⠀⢠⣶⡀⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢺⣍⢩⡍⠉⠛⢿⣇⢰⠄⣀⠀⢠⠀⣼⣿⢏⠀⠀⠐⠛⠊⠉⠳⣄⣻⣟⣠⠏⢠⣠⣦⠀⠠⠏⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠻⡏⠀⣤⡄⣆⠈⢣⣘⠿⢇⡸⠚⢡⣤⢠⡄⢀⣶⡀⠀⢷⣴⡌⢻⣿⡏⢀⣾⠿⠖⠀⠺⠾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣵⠤⠬⠿⢿⣦⡀⢹⣿⡿⠁⠀⠠⠽⢿⣷⡈⠏⠀⢀⡈⠉⠙⠢⣿⡴⠋⣠⡄⠈⠻⠓⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢚⡭⠀⠀⣤⡴⠊⣠⣉⠲⣿⣡⠿⢋⣀⠚⠂⠉⠻⣄⠰⣿⡿⠀⣠⠀⢸⡄⠚⣋⡀⠀⣶⢠⢨⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⡘⠛⠁⠀⣉⡁⠀⣿⠀⢄⣺⠿⣀⡔⠀⠀⠘⢷⣶⣶⡟⠁⣦⣼⣇⢸⣿⣿⠆⢠⣾⡿⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠸⣿⡿⣠⣿⠀⠈⢻⣿⡟⣀⡀⠀⢷⡌⣿⡿⣀⡀⢸⣿⣿⣦⣍⣉⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣷⠷⠦⠤⠴⣾⣿⣿⣆⠹⠦⣿⣰⢟⣤⣤⡀⠉⣿⡷⠋⣰⣿⣿⠿⠛⠛⠉⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣤⣈⣙⣻⣷⡀⣿⠁⣿⣿⣿⣿⠀⣿⣠⡾⠟⠉⠀⢀⣠⠤⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠋⠉⠀⠀⠀⠙⢿⣤⣈⣛⣛⣁⣴⡿⠋⠙⠛⠛⠿⣿⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣄⢻⣿⣿⣿⣿⣟⣴⠿⠟⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⠿⠿⠿⠷⠶⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠳⠏⠉⠀⡞⠐⠉⠁⠙⠉⠉⠒⠓⠋⠀⠀⠀⠠⠓⠊⠁⠈⠂⠒⠀⠑⣄⣀⠙⠛⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⠀⡺⠅⠲⢰⠐⡆⠀⠸⠀⠶⠐⠄⠆⡆⡀⢰⠀⠀⢸⠠⢖⢸⠀⡆⠀⢵⠀⠀⢉⣹⠂
⠀⠀⠀⣠⠶⠯⠁⠈⠀⠀⠀⠀⠸⡄⣀⢤⢀⢀⣠⢴⡂⠀⠀⠀⡀⠀⠀⡀⣀⣀⡤⣄⠀⠀⠀⢀⡀⠀⣸⠀⠀⠀⢿⣤⣤⣤⡀
⠀⠀⠀⢻⣦⢀⡴⠠⣄⣀⣀⠤⠠⣄⣀⠀⢁⣤⣀⣀⣉⡉⠉⠉⠙⠦⠏⠁⠀⣀⣀⣈⠉⠓⠒⣋⠈⣉⠥⡀⢀⡤⣀⠀⠀⢈⣿⡀
⠀⠀⠀⢸⠇⣸⠀⠀⠈⠀⠀⠀⠀⠈⠨⢳⡇⠀⠈⠀⠀⠙⠞⠉⡷⠀⡞⠙⠚⠁⠀⠈⠱⠖⢲⠇⢙⣀⢀⡉⣉⢂⡉⢣⠀⠈⣩⠇
⠀⠀⠀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠁⠀⠀⠳⢸⡀⠀⠁⠀⠀⠁⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⣿
⠀⠀⣼⠧⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠧⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠐⢻⣄
⠀⣸⠏⠀⠀⢧⠤⠔⠛⢦⡀⣰⠇⡓⠒⠍⣲⠖⢶⣀⡴⣅⠀⠀⢻⠧⣄⢀⣶⡄⠀⣀⣰⢖⣻⣄⡤⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⣹⡇
⠀⢿⣄⣀⠀⠀⠀⠀⠀⢀⣉⣅⡠⠨⣦⡀⢀⣴⢧⠀⡀⠉⠑⠒⠋⠀⠈⠈⢀⣛⡯⣝⠱⠀⡀⢠⡮⣙⡉⠓⠚⠲⠜⠀⠀⢀⣀⡿
⠀⠀⢹⡇⣀⠀⠀⠀⠀⢏⠀⠀⢀⠀⠀⠛⠉⠀⠈⠋⠉⢣⡀⠀⠀⠀⠀⣐⣧⠀⠀⠈⠉⠳⠴⠋⠀⠈⣩⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡞⠉⠀⠀⠀⠀⣴⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡽⠀⠀⠀⠰⣇⠀⠀⠀⠀⠐⠀⠁⠂⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⢴⡏
⠀⠀⠻⣤⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢴⠃⠀⠀⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣿⠀⠀⠀⠀⠉⠛⢅⡠⠖⠦⣄⣰⠀⠀⠀⢠⣼⡈⠙⠢⢄⡀⣠⠚⢶⠂⠀⣠⣀⡀⠀⠀⠀⠘⣲⠔⠃⠀⠀⠀⠀⠈⢹⡅
⠀⠀⠀⣷⠄⣀⣼⠙⠞⠉⠓⠴⠋⠳⣄⠈⠒⠋⠙⠋⠀⢑⡒⢄⡀⠉⢀⠔⠊⠑⠚⠀⠀⠙⠦⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⣸⠇⢯⠀⠀⠀⠈⠊⠘⠀⠀⠀⠸⣆⠀⢠⠔⠒⠲⠏⠈⠲⠷⡄⣠⢤⡴⠓⣤⡤⠦⢤⡀⢀⣀⡴⠤⢄⠀⠀⠀⠀⠈⠙⠷⡄
⠀⢸⡇⢰⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠶⢾⡦⠀⡄⡄⠀⢀⢀⠉⢁⠀⠀⡀⠀⠀⠀⠔⠓⠋⠀⠀⠀⠈⠳⢤⠀⠀⠀⢀⡀⣿
⠀⢸⣇⣀⣹⠔⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⣈⠾⠃⠀⠀⠈⠀⠈⠀⠀⠀⠈⠀⠁⠈⠁⠉⠀⠈⠁⠉⠉⠉⠀⢠⠏⠀⠀⢀⣼⠏⠁
⠀⠀⠉⠙⣯⣠⡤⣄⣠⡀⡠⣀⡰⠊⠁⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠀⠀⠐⣿⠁
⠀⠀⠀⠀⠈⣯⣀⣤⡄⠈⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢀⡀⢀⣄⢠⣤⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠉⠈⠛⠶⣶⠈⠀⠀⠀⠀⠹⡀⠀⡴⠚⢽⠁⠘⡏⠸⠤⠤⠶⠯⠛⢦⡀⠀⣠⠤⡤⠤⣞⡀⠀⠀⣤⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣶⡀⠀⠀⣨⣉⣡⣬⡀⠀⠀⠀⠀⠃⠐⠀⢀⠴⢋⣉⣭⣥⠀⢀⣼⠋⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⣻⠀⡤⠤⡤⠒⠲⣠⡷⡴⠋⠁⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡀⠀⠀⠀⠠⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⣄⢀⠴⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠏⢀⠀⠘⠷⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠐⠀⠀⠀⠀⠀⢠⠖⠒⠒⠋⠓⠒⠒⢶⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⢤⣀⣀⣀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⢀⣠⠤⡅
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢈⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⠋⠙⠚⠉⠳⠶⠧⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⠓⠛⠓⠦⠚⠛⠚⠁⣠⠟⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⡀⠔⠈
⠀⠀⠀⠀⣱⠊⢧⣠⣤⣀⢀⣤⣄⡴⠃⠀⠉⠦⡀⢸⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢸⠉⠉
⠀⠀⠀⠀⣇⠀⠈⠉⡂⠈⠁⠀⠀⠀⠀⠀⠀⠁⠙⢿⠀⠀⢀⣉⠖⠋⠉⠉⠙⠶⠚⠒⠒⠋⠀⠀⠀⠀⢀⣤⣀⡤⠦⣄⣠⣄
⠀⠀⠀⠀⠈⠷⠤⠴⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⡀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠆⠉⠁⠀⢫⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠋⠉⠉⠀⠉⠉⠙⡖⣧⡾⠁⠀⢀⠀⢠⡞⠙⠛⠁⠉⠛⠋⢳⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢧⠘⣧⠀⣰⠤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⡽⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡎⠀⠹⣿⡁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠙⠦⠒⠦⡤⠖⠲⠾⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣄⣀⣠⣄⣠⠇⢀⡠⠼⣷⡄⠀⠰⡃⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⢩⠟⠋⠓⢾⣹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠠⠄⢿⣷⡀⠀⠀⠀⠀⠀⢹⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⡠⠂⠢⠀⠈⣿⣧⠀⡠⠀⢄⠀⣿⡴⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⢹⡄⠀⠂⠄⠀⠀⠀⠀⢻⣿⡏⠀⠀⠈⢠⡇
⠀⠀⠀⠀⠀⠈⠂⠀⠊⡇⠀⠀⠀⠀⠀⠀⢾⡴⠶⠾⠛⠛⠋⠛⠓⠶⣿⣿⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠦⣄⣤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠉⡀⠘⠁⠀⠀⠂⠀⠀⠀⠀⠀⠐⣄⠤⠀⠘⢰⠒⢊⣲⡄⠐⠀⠐⢄⡀⡀
⠀⠀⠀⠐⠚⠀⠀⠈⠀⠎⠄⠁⠀⠀⠰⠠⠴⡎⠀⠌⠈⠁⠀⡉⠠⠀⡀⠄⠀⠋⠂⣔⠂⠀⡀⠠
⠀⠀⢈⠰⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡜⠋⢡⠁⢀⣀⡀⠐⠿⠄⠈⠁⠉⣄⢂⣾⡈⠙⠻⣐⠀⠀⢤⡀
⠀⠰⣩⠑⢛⡧⠀⠀⠈⠢⡀⠁⠀⢿⠿⠳⢁⡀⠀⠦⠜⣠⣾⣠⠀⠀⠀⠁⠈⠈⠛⠛⠲⠝⠐⠐⠀⠁
⠀⢠⠃⡄⠍⠄⠀⠀⠀⣠⠰⢄⠀⠀⠂⠁⠈⠁⡁⢀⠈⢉⡙⠀⢐⠀⢀⡔⠾⡀⠀⡌⡀⠀⠠⡀
⠀⠀⠸⠁⠀⠠⠀⠘⠀⢀⢄⠈⠂⠀⠀⠐⠴⠂⡄⠀⠀⢀⣠⠔⡠⠐⠈⠀⠠⠀⠨⠋⠐⡀⠀⢄
⠀⠀⠔⢀⠀⢈⡐⠢⣀⠀⠀⠀⠘⢂⠀⠀⠓⢦⡤⠒⠋⠁⢀⠜⠅⠀⡀⣁⡀⠀⠀⠀⠚⠒⠀⠀⠀⠰⡀
⠀⠀⠈⠚⢧⠀⠋⠁⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠃⠀⠀⠈⠀⠀⠀⠠⠘⢐⡄
⠀⠀⠀⠈⠁⠀⠁⠈⠀⠐⠂⠀⠀⠀⠃⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣴⠀⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢆⡄⣏⢲⠤⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⡄⣀⡠⠀⠑⣼⡗⢾⢠⡼⢻⣏⡞⣸⠁⠀⠀⣾⣄
⠀⠀⠿⠚⠀⠀⠀⠀⠀⠀⠀⠂⠐⢂⢀⣀⡀⠀⡁⠀⠀⠀⣇⡀⠀⠸⣷⣸⣟⣰⠋⠀⠀⠀⣦⠖⡿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠉⣁⠠⠜⠛⣅⢀⡀⣀⡿⡽⡶⢶⣿⣿⣿⣿⡆⠀⢀⡠⢃⣜⣤⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠔⠈⠁⠀⠀⣀⠀⢀⡀⠓⠾⡑⢿⠎⠀⠀⢹⠛⢧⣼⣿⡿⠏⠉⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⡍⠉⠁⠀⠀⠀⢁⠀⠀⠈⠘⡀⠀⠀⢸⠀⣼⣿⠏⡴⠶⠋⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢀⣀⣀⣀⡌⠀⠀⣠⠀⠑⣤⣤⢃⣼⣿⡿⠋⠈⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⢰⣿⣿⣿⣿⠏⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⠉⠉⡀⠀⢀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⠀⠒⠀⠀⠀⠒⢀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠊⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠤⠤⠤⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡉⠁⠀⠉⠉⡏⠉⠉⠉⠉⠉⠉⢁⠀⠀⠀⡂⠀⠀⠂⠀⠀⠐⠐⠂⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠉⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠠⠤⠀⡀⠀⠈⠀⡀⠀⠀⢀⡀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⡀⣀⠂
⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⡀⠤⠤⠴⠦⠤⠄

⣿⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠄⠀⣀⠀⢰⡄⠀⠀⠀⢀⠀⠀⠑⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠁⣄⠀⠰⣿⠀⠹⠁⠀⣿⡄⢸⡇⢠⡄⠀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠈⠙⠀⠸⡿⠀⣄⠈⠀⢰⡄⠀⠛⢁⠀⠀⣿⠇⠀⡉⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢀⡄⠀⣦⣄⠀⣿⡷⠀⣿⠷⠀⣼⣿⠀⠀⣀⡀⢸⠇⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣾⣿⠀⠻⣿⢂⠈⠁⣠⠀⣠⠀⠙⠃⠀⣾⣿⠁⢀⣤⡶⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣀⠉⠋⣠⣦⠀⢾⠆⣀⠙⠃⠛⣠⣄⣾⠀⠉⣴⡆⠸⠿⠁⠾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢿⣿⠀⣿⠿⠀⠀⠈⠛⠀⠀⠀⠈⠁⠀⠀⠰⣿⠇⢰⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢃⣴⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣭⡐⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⢠⣶⣦⠀⢀⠀⠀⠀⠀⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠉⢁⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⣇⢸⣿⣿⣿⣿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⠘⣿⣿⣿⣿⢠⠁⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢷⣿⣿⣿⣿⢸⣷⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣸⣿⣿⣿⣿⢸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠈⠁



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

⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⣼⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⡀⡠⡼⠁⢀⠀⠂⢀
⠀⠀⠀⢠⢹⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⠛⠄⠀⢆⣰⡂⣠⣷⡇⢠⣏⣭⡤⠼⠶⣥⣄
⠀⠀⠀⣾⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣷⣮⣿⡟⣠⡟⣁⡈⠛⢷⣴⡄
⠀⠀⢠⣿⣿⡷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡈⠛⢋⡛⢿⠿⣼⡀⣥⠴⠄⢨⣶⣿⠄
⠀⠀⣸⣿⣿⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⣿⣿⣧⠀⠑⣄⠀⠘⣣⠀⣾⡿⠶⢸⣟⠑
⠀⠀⣭⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⣴⣤⣧⢠⣤⣤⣿⣍⣻⣿⣷⣀⠈⠳⡀⠛⢸⡗⠂⠰⢌⣏⠀⡌
⠀⠀⣿⣿⣧⢴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⠁⠀⠀⠁⠀⠈⠈⢹⣿⣿⣿⣿⣿⣦⠀⡇⠀⠈⢀⠔⠒⢾⣿⠄
⠀⠀⢛⣿⣿⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣿⣿⣿⣿⣤⣦⣤⣷⣶⣧⣄⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡠⠀⢙⡟⢴
⠀⠀⣿⣿⣿⣶⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢿⣿⣿⣿⠰⠿⢂⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠁⠅⠁⠀⣸
⠀⠀⢹⣿⣷⣌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠿⠿⡂⠻⢿⣿⣷⣶⢿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⣿⠗
⠀⠀⠸⡿⣿⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⠀⠀⠈⠰⣷⣤⡉⠛⠥⣈⣿⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣷⣿⣟⣏⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠤⣍⡭⠛⢿⣿⣿⣶⠂⠀⠀⠁⠀⠀⠀⢠⣷⢇⠸⢿⠇
⠀⠀⠀⢻⣿⣿⣿⣟⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢉⣡⣾⡏⠙⢧⢀⣫⡿⣮⡷⠖⠶⣆⠀⠀⢀⣼⣟⠊⠀⠀⠀⠐⡶⣀
⠀⠀⠀⠈⣿⣿⣿⠯⡤⠉⢇⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⡇⢠⣾⢯⣿⣇⠉⢻⣤⠄⠈⠻⣿⢯⣏⠛⢪⣷⣄⣴⠾⢷⠛⠇
⠀⠀⠀⠀⠘⢿⣟⠿⣷⡆⠘⣄⡠⠀⠀⠀⣴⣿⣿⣿⣿⠟⣿⣿⠇⢸⣯⢸⣿⣷⡀⠀⠙⢦⣤⣴⣬⡳⡗⠀⠀⠀⠀⠙⢾⣾⣹⣷⡀⢢
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣧⣡⣿⣄⡀⣠⣴⠟⠛⠛⣻⣷⡎⣿⣿⠀⢸⣇⣼⣿⢯⣀⠀⠀⠘⢿⣿⣁⣀⣿⡇⠀⠀⠀⠀⠈⣿⠋⠈⣷⡌⠢⡀
⠀⠀⠀⠀⠀⠀⠈⢙⠤⣾⣿⣭⣙⡏⡨⠈⠲⣴⣀⠉⣻⣿⠋⠀⣠⣾⢿⣿⣿⡷⠈⠘⠀⠀⢸⢿⣿⣿⢟⠛⢦⡄⠀⠀⣀⣟⡀⠀⢟⠛⢷⣤⣄
⠀⠀⠀⠀⠀⠀⢀⢿⣿⡎⣿⣿⣷⢛⢷⡄⠸⣏⡉⠈⢿⣧⣵⣾⣟⣩⣾⣿⣿⢧⣌⠒⠀⠀⠈⠀⠀⠻⣌⡀⣈⠿⡆⠀⣿⣟⣁⡰⠛⢙⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣳⣾⢗⠸⣿⣿⣿⠮⢀⢹⣿⣷⡄⣿⣿⣉⣱⣿⣿⣿⣿⣧⣿⡟⠀⠀⠀⡀⠀⠀⠐⢿⣯⡧⠂⢻⣿⣽⣿⣼⠀⠀⠀⠉⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢲⣿⡄⢸⣽⣿⣴⣿⣾⣿⣿⣦⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣇⣴⣁⠀⠀⠀⣻⡿⣷⣴⣾⢿⣼⠿⠃⠴⠖⢾⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⠛⢿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠾⠿⢷⣿⢷⢿⣷⡧⠀⢐⣂⣀⣠⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⡆⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣟⣒⠀⠀⠀⢀⣿⣦⢱⡙⠃⣤⣄⠀⠹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣖⣒⣀⣀⣙⣿⣎⣷⣸⣿⠋⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣨⡅⠀⢻⠀⠀⠀⠀⠈⠉⠉⣿⠉⠹⣿⣽⣿⣿⣦⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢯⠃⠀⠸⡆⠀⠀⠀⠀⠀⠀⢹⠂⠀⠹⣿⢹⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣎⠃⢀⡄⠳⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠹⣧⢻⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⢸⣿⠀⠃⠀⠀⠀⠀⠀⢸⡇⠈⠂⠀⢹⡟⣿⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣦⣠⣾⣿⣿⣿⣿⣦⣴⣾⣿⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡻⣿⣿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠄⠆⢿⣷⣤⣤⣀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣀⠀⠀⠈⣛⡛⠛⠿⠿⠿⠿⠿⠿⠿⣿⡏⡇⠤⠐⠛⠇⠸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⠧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣠⣶⣶⣦⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⡿⢿⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡤⠙⠻⣿⣄⠀⠀⠠
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⢻⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⢃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢹⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⠐⠘⠛⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣦⠠⢿⣿⣯⣶⣤⡀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣸⣿⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣮⣝⣤⠾⠛⠻⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⠘⠇⢶
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢨⣿⡟⣿⣿⣿⣿⣿⡟⠁⣠⣶⣶⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⠀⠀⢸⣷⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠟⠁⠿⠟⠿⠛⠏⢀⣾⣿⣿⣿⣿⣦⠈⣉⠁⠀⠂⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠀⠁⠀⠻⢏⠀⠐
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣾⣿⣿⣿⣿⣿⣿⣆⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉
⠀⢺⣿⣿⣿⡇⠀⠀⠀⣀⣸⣿⣷⣿⠁⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣾⣿⣿
⠀⠙⠛⠛⣿⣇⠀⠀⢀⣿⣿⣿⣿⠃⢀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⢸⣧⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠻⠿
⠀⠀⠀⠀⠿⠟⠀⠀⠘⠿⠿⠿⠟⠀⠸⠟⠀⠿⠿⠿⠟⠿⠿⠿⠟⠀⠗⠀⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠶⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠘⠣⠄⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠚⠀⢀⡠⡤⣀⠴⡽⠤⠄⠀⠠⠤⢀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠤⣀⡔⠁⠀⠀⠈⡎⠃⠀⠀⠀⠀⠀⠈⠇⠐⠀⠀⠀⡇⡀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡂⠀⠀⣹⡇⠀⠀⡀⢼⡛⢦⢄⠀⠀⠀⠀⠀⢳⠦⠀⠄⢠⡏⠀⢆⣤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⡀⠙⠒⠈⠀⡏⠀⠀⠀⠀⡀⡏⠰⠂⠀⠙⠒⢦⡔⠂⠀⠀⠈⠇⠀⠀⠁⠀⠐⠋⠈⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠳⢄⠀⠀⣠⠆⠐⠀⠀⠠⡄⠓⠒⠊⠳⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠎⠓⠲⠀⠀⠾⡟⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠻⢀⡀⢠⠀⠀⠀⠀⡈⠂⠒⠒⠲⠚⠋⠀⢠⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠤⠤⢀⣀⣘⠋⠉⠀⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠀⠀⠀⣠⠊⠃⠀⠀⠀⠳⠀⠀⠀⣠⡄⠀⠀⠘⠆⡀⢀⡀⠀⠀⢘⠃⠀⠀⠀⠀⠀⡀⢹⠀⠀⠆⠀⠐⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠙⠶⠀⠀⡀⢀⣤⠀⡰⠶⠒⠁⠀⠰⠶⠀⠀⠁⠀⢀⠀⠈⢀⣀⠀⠀⠀⠀⠉⣶⠀⠀⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⣀⣠⡜⠀⠀⠀⠀⠈⠏⠀⠁⡄⠀⠀⠀⠀⢀⠲⡇⠘⠀⠀⠀⠀⣀⠀⠀⠀⢀⡈⠁⠀⢨⡀⠀⠀⠀⠠⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡟⠂⠀⠀⠈⡆⠀⠀⣷⢀⠀⠀⠀⣀⣤⠉⠦⣀⢠⠖⠉⠁⠀⠀⡆⢈⠞⠒⠋⡩⠟⠛⠓⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠨⢣⡀⠃⠀⠀⠀⠀⣇⠀⠀⡅⠘⠀⠀⠀⠈⠀⠈⠀⠀⡆⠀⠀⢠⠀⠀⠐⠃⠀⠀⢰⠁⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠙⡥⠀⠀⠈⠀⠀⠀⡶⠤⢤⣠⡄⠀⠀⠀⣠⠴⢇⣀⣇⠀⠀⡆⠀⠀⠐⠀⠀⠀⠘⡧⢀⡀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠔⢰⠁⠋⠀⠀⠈⠻⡆⠀⡎⠀⠀⠈⠃⠈⡆⠀⠳⠄⠀⠐⠁⠀⠀⠀⣾⢠⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⠸⣤⡀⠀⠀⠀⢠⠇⠀⢦⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢀⡀⠀⠀⢀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠤⠀⡀⠀⣈⠛⠲⠶⠖⠋⠀⠀⠀⠑⠒⠀⠀⠈⠀⢀⠠⣤⠤⠮⡅⠠⡄⠈⣆⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠙⠶⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠈⠁⠀⠰⠀⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢀⢀⠀⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠤⠄⠀⠀⠉⠀⠀⢠⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⠤⠀⠀⢀⡳⠦⠄⠤⠤⠀⠈⠳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡇⠘⠀⠙⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⡗⠀⠀⠀⠂⠀⠀⠀⠀⡅⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⣿⣿⡿⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⣀⣀⣀
⠚⠃⠶⠿⠤⣾⣿⣿⣿⣶⣶⣾⣿⡷⢠⣾⣾⣞⢻⣾⣶⣾⣷⣾⢻⡾⢌⣧⣤⣴⣄⣹⡽⠇
⣶⠆⣶⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⣿⠋⢾⣯⣿⣿⣿⣿⣿⣶⡴⠟⣉⠛⠀⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀
⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣷⣴⣿⣿⡿⢻⣿⣿⣿⣿⣅⠀⡤⣤⣲⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠠⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣯⣿⣿⡿⠻⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠉⢙⡿⢿⠃⠀⠀⠇⣿⣿⣿⡏⠷⠃
⣿⣿⣿⣿⣿⡿⣿⣿⠻⢿⠉⠀⠀⠀⠀⠘⡧⢸⠀⠀⠀⠐⢿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⠄⢸⣿⣿⣧⣬⣥⣶⣾⣷⣿⡿⠿⠀⠀⠁⢀⠀⠀⠀⠀⢘⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡟⠻⣿⡿⣿⣿⠇⢠⣇⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⢀⠀⢀⡄⠀⠀⢠⠀⠀⠀⣄⠀⠀⢠⡄⠀⠀⠀⡀
⣿⠘⣿⠀⠁⠈⠀⠀⠁⠀⠀⣿⠄⢠⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⣇⠀⠀⣸⡀⠀⠀⣍⠀⠀⡈⡄⠀⠠⠀⠀⠀⢀⠀⠀⠀⠈
⠿⢻⡟⠺⠀⠀⠀⡀⠀⠀⠀⣿⠀⠁⠊⠀⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠸⠿⣶⣶⣆⢀⠰⠆
⣾⢸⡇⠻⠀⢠⠴⢿⡇⠀⠀⢻⠀⡰⠆⠐⠂⣠⡀⠀⠉⠁⠉⠁⠀⠀⠀⢀⣟⣦⢀⠻⣶⠛⠀⠀⡀⠀⣡⠀⠀⢄⣀⣿⡏⡭⢉⠛⣳⡖⠠
⣧⣼⡅⣰⠄⢤⣤⣻⡇⠀⠀⣿⣾⣿⠁⠀⠀⢻⠀⠈⠁⢀⡄⣜⣠⣀⡀⠀⡿⣻⣏⠀⡘⣴⡟⣼⡷⢦⡠⠴⢀⣼⡍⣯⣌⠓⡀⣌⣼⣤⣽
⣿⣾⡇⠀⢠⣾⣿⣿⣿⡄⠀⣿⣋⠁⠀⠀⠀⡇⠀⠀⠆⠈⠁⠋⠹⠟⠁⢸⣇⣽⣯⠀⣿⡿⡏⢻⣿⣿⡇⠀⠀⠛⣃⠈⠯⢀⣱⠿⣻⣿⣿
⣿⣾⠁⣿⣿⣿⣿⣿⢿⣧⣀⣿⣿⣷⣤⣀⣠⣶⣦⠀⠀⠲⠾⠀⢴⣤⡇⠀⠸⠉⠁⠀⡬⢻⣿⣿⡏⠿⠃⠀⠀⣆⢻⡀⠀⠸⡄⠀⢻⠛⣿
⣿⣿⢺⡟⣿⣿⡿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠋⠓⠀⠀⠀⠀⠀⠁⠀⠉⠋⠉⠉⠀⠁⠀⠉⠙⣁⠐⡶⠛⣶⣾⣻⣒
⡿⠋⢀⣼⣿⣿⣿⣼⣿⣿⣿⣸⣿⢿⣿⣿⣿⣿⣿⣠⣤⠀⡐⠂⠀⠀⢀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠶⠛⠋⠿⠵
⡏⠀⠀⠙⣿⣿⣿⡤⢿⣿⣿⡇⣩⡍⢿⣿⣿⣿⣿⣻⣾⢟⣻⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⡇
⡟⠁⠀⣱⣾⡿⢯⣷⣿⣿⣿⣷⠸⢇⣸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣶⣶⣤⠄⠀⠀⠀⠀⣼⡇
⣷⠀⠀⠘⣿⣧⣾⡟⢻⣿⣟⠋⣠⣤⣷⣿⣿⣿⣿⣿⡿⣿⣿⣥⠄⠀⢀⣠⣀⣀⠰⣾⣿
⣿⣦⠀⠀⢀⢸⣿⣇⣀⣸⣿⣦⣴⣿⣿⣿⡿⠿⣭⣁⣀⠈⠿⢿⣷⢸⣿⣿⣘⣿⣷⠋⠉
⣿⣿⣤⣤⡀⠈⠛⠿⠿⠋⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣸⣯⢿⣿⣟⣻⣿⠉
⣿⣯⣩⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⢻⣾⣼⣿⣟⢩⣧⣄⡄⢀⡀
⡏⠻⠿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠁⠈⠻⠾⠿⢸⣹⣿⣿⢿⣿⠿⠟⠻⠋⢛
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⢀⠻⣃⣽⠀⠀⠀⠀⡈⣶⢀⠀⠀⠀⣼⣼⣷⣿⠆⠀⠀⠀⣥⡄⠀⠀⠀⠀⠀⢶⣶⡀⠀⠀⠀⣘⢿⡞⠓
⠀⠿⠿⠿⠿⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⠛⠘⠃⠛⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠘⠛⠛⠛⠚⠃

⠀⢠⠾⢦⢤⠀⠀⠀⢠⠚⡗⢦⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⢠⡖⠰⣆⠀⠀⠀⡴⢆⠠⠶⠄
⠀⣴⣄⣰⣿⠀⠀⠀⠘⢾⡿⠏⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢛⠠⣧⠈
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⡠⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⡠⢤⡀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⡎⠸⡗⠘⡄⠀⠀⠠⢁⡌⢠⠀⠀⠀⡄⢐⣇⢰⠄⠀⠀⠀⢺⣿⠀⠀⠀⠀⠌⡉⠅⣯⠀⠀⠀⡇⣲⡴⠀⡇
⠀⠙⠿⠿⠟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠏⠩⠆⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠐⠿⠧⠟⠀⠀⠀⠛⠛⠛⠛⠃

⠀⡠⢢⣔⢢⠀⠀⠀⠀⠀⣀⡦⠀⠀⠀⢤⡰⡇⣠⠀⠀⠀⠀⠒⠀⡄⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⢀⣠⡄⢀
⠀⢧⣭⣨⣤⠁⠀⠀⣠⡾⠟⢁⠀⠀⠀⡼⢤⡧⠧⠀⠀⠀⠘⠃⠀⡄⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣃⣈⢁⣘⡀
⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⡎⣤⢠⠘⠀⠀⠀⠀⣴⣾⠋⠁⠀⠀⢠⡀⠀⠛⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⢠⡀⠀⠋⠀⠀⠀⠸⠟⠰⠲
⠀⠙⠿⠷⠞⠀⠀⠀⠲⠋⠁⠀⠀⠀⠀⠈⠀⠀⠧⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠀⠀⠧⠀⠀⠐⠟⠿⠛⠞⠃

⠀⡠⠒⠐⢢⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⠀⡄⢠
⠀⢿⣥⣯⣿⠂⠀⠀⠒⠀⠀⠐⠀⠀⠀⠈⢋⣸⣈⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠸⠇⠀⠓⠀⠀⠀⠚⢘⣗⠘
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂
⠀⠀⠀⠀⣸⣿⣅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦
⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⢸⢠⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢾⢸⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠸⢺⣿⣿⣿⠺⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⢀⡄⠪⢿⠛⠹⠌⠲⣤⢴⢖⡊⡽⣿⣿⣿⣿⢻⡯⡛⢒⣤⠖⢚⡟⣹⢿⣿⣿⣝⠒⠢⠤⣄⡀⠀⠏⡿⠝⠍⠁⠢⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠔⢉⡠⠚⣡⠏⡹⢧⡇⠁⠑⡐⠘⠀⢈⡴⠃⣮⣹⠙⢌⠃⠀⠀⠀⠑⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡜⠋⠘⠁⠘⠇⠀⠀⠀⠀⠀⠌⠀⠠⠀⠁⠀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⣾⣷⡆
⠀⠀⠀⠀⠀⡼⣽⣿⠛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠟⠻⠿⡟⠂
⠀⠀⠀⠀⠀⠗⣻⠗⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠀⢈⣱⣤⣀⣀⣀
⠀⠀⠀⢀⡔⠛⣋⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣿⢲⡿⣿⣿⣿⣿⡆
⠀⠀⠌⢩⠑⠶⢏⠿⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢀⢹⣿⠠⢁⡄⣿⣿⣿
⠀⠀⢀⣾⠀⠀⠀⠈⡇⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠂⣷⠇⠀⠀⣿⣿⣿⡄
⠀⠀⡼⡻⡄⣠⠖⠀⣀⢀⡇⠀⠀⠀⠀⣠⠂⠉⣒⡰⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⠀⠀⠋⠀⠀⠀⣿⢻⣿⣧
⠀⢠⣾⠁⡱⠀⠠⠤⠃⢾⢷⣤⡀⡤⢞⣲⡾⠍⠹⡃⠀⠀⠀⠀⣀⠀⠀⠸⣾⣿⠈⠀⢸⠀⢚⣻⣿⣿⣿⡿
⢰⠀⣿⢠⠃⠀⠀⢀⣄⠘⡟⠛⢳⣷⣿⣿⠳⣴⣶⡋⠀⢀⣶⡏⢉⠃⠀⠛⢸⡏⠀⠀⢀⡷⣴⣶⣾⣿⡏
⡜⢠⡇⠘⠉⠉⠉⠀⠀⠈⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣇⠀⡈⠀⢠⢸⡇⠀⠀⢸⡇⠀⢹⣿⣿⡇
⢘⠉⡀⢀⡄⠀⠀⠀⠀⠀⡇⠀⠘⠋⢙⣿⣿⣿⣿⣿⠀⢠⠔⠞⢿⡗⠂⢈⣥⡃⠀⢀⡿⠃⠀⡾⢫⣿⠁
⠈⣾⣷⡀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⡶⢃⠁⠀⢸⠀⢀⣧⣴⣧⠀⠉⠀⣸⡀⠀⣾⡇
⠀⢿⣿⡇⢁⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡿⣿⣿⡇⣿⣟⢹⡿⡅⠘⠀⢸⠙⠛⢠⠀⠄⢠⣿⡇⠀⣿⠇
⠀⠀⠀⠀⢈⠀⠀⠀⣀⠀⡇⠀⣸⣿⠟⢁⣿⣿⡇⣿⣿⠿⢄⠀⣸⠀⢸⠀⠀⢼⠂⠀⠸⣿⣿⣸⣿
⠀⠀⠀⠀⠎⠀⠀⠀⡏⠀⡇⠀⠻⠿⣤⣼⣿⣿⣧⢿⣟⣀⣿⣛⣲⠑⡿⠀⠀⣾⣦⣤⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠠⣤⢰⠊⢹⠂⠁⠀⠀⠀⠜⢠⢾⠀⠇⠀⠀⢈⠇⢀⣿⠶⠃⠀⠀⢹⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠇⠘⠀⡏⠀⠀⠀⠀⢸⢀⠃⡈⢸⠀⠀⠀⡾⠖⠁⡏⠀⠀⠀⠀⠘⣿⠇⠀⣿⣿⡏
⠀⠀⠀⣠⢀⠀⠘⠐⠀⠀⠀⠀⠀⡈⡁⠀⡁⡼⠀⠀⢜⡿⠀⠀⡷⡆⠀⠀⠀⢰⣿⠀⢰⣿⣿⠁
⠀⠀⠀⠘⠋⠀⡆⠄⠀⠀⠀⠀⢰⠞⠀⠀⢁⠁⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠻⠏⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠛⣤⡤⠤⠶⠶⠶⠞⠃⠐⠣⣵⠐⠒⠀⠀⠀⠀⠧⠕⠒⠒⠊⠁⠀⠀⢸⣿⣧⡤⠴⠶⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣏⡀
⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⢹⣿⣿⣿⠸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⢸⣿⣿⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⣠⠔⠭⡟⠻⠹⠍⠲⢤⡠⡴⢒⣚⡽⣿⣿⣿⣿⡿⢿⢍⡛⢓⣤⡴⠒⢻⠟⣹⢻⣿⢿⣍⠳⠶⠤⣤⣀⠀⠐⢻⢹⢻⠹⠈⠑⢢⡀
⠀⠀⠁⠀⠀⠘⠐⠀⠈⠀⠘⢀⠔⠋⢠⠴⢉⣼⢙⢿⣸⠈⠂⠣⠠⠉⠇⠀⢁⡴⠃⣜⢹⠺⢎⠳⡂⠀⠀⠌⠛⡀⢈⠊⠘⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⣰⠞⠩⠞⠈⢝⡄⠀⠀⠂⠀⠀⢀⠎⠀⢀⠉⠟⠁⢌⠳⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢧⠆⠀⢀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡷⠂⠠⣼⠧⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠞⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣡⠐⣾⣋⠀⠀⡄⠀⠀⠀⠀⠐⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢉⢳⡟⣀⠀⣀⠀⠀⠀⠀⠀⠉⣹⣧⣼⡿⠉⣠⡿⠍⠀⢀⠀⣤⣽⣃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣶⣹⣯⣠⠽⣖⣠⠀⠀⠀⢀⡐⠾⣿⠅⠠⣿⣅⣸⣦⡾⢿⡿⢶⠻⠙⠎⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠛⣳⢾⣿⣥⣴⣤⣚⣅⡒⣿⡟⣱⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠴⠾⢏⣸⠄⡾⢃⡀⠀⠀⠀⠀⠀⠀⢠⡀⣉⠸⡋⠽⠻⣿⣷⣿⣿⣿⡺⠏⠓⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⡻⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⡶⢞⣿⣰⡆⠀⠀⠀⠀⠀⠈⠁⠙⠋⠿⠺⣧⣇⡹⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣹⡞⠟⣂⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣼⣦⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡩⠽⣷⣿⣿⠁⢰⠆⣴⣀⣼⣃⣀⣿⣤⣼⣟⣙⣋⣠⡽⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡰⠾⣧⡟⢀⡀⠀⠈⣳⢆⠀⠀⠙⠓⠳⣭⣿⣿⣮⣿⣾⣟⠉⠹⠏⠉⠻⠀⠙⠃⠙⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⣿⠷⣾⣇⣸⡇⣨⠹⢶⣇⠀⠀⠀⣽⣿⣿⣿⠋⣄⣤⡚⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⡿⠛⣿⢛⡷⢾⣿⣦⣗⣤⣼⣿⡟⢿⡟⠻⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡆⡹⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⢦⡾⣴⣯⣿⣿⣿⣿⡟⡄⣤⣠⢠⡆⢀⣾⠀⢰⡟⢀⣀⣿⠤⣾⡝⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⡾⠀⢠⣤⡷⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠚⣹⣿⣿⣿⡴⣋⣴⣷⣾⠿⣟⠛⢻⡟⠻⣿⣭⣹⣧⠰⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢷⣼⠆⣀⠷⠼⣇⣰⡆⠀⢠⣠⡄⢀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣋⣥⣙⣠⡍⣤⡄⢀⣀⠛⢀⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⣿⣀⣰⡔⣿⣶⣇⣰⡘⣓⢺⣅⣄⣸⣿⣿⣿⣿⢿⣟⠙⢿⠍⠹⣿⠛⣶⡾⠧⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⢉⣿⠟⢛⣿⠛⢻⡿⣿⣮⣽⣷⣿⣿⣿⠟⠷⠀⡴⢖⣠⣆⣠⢶⣠⠌⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠒⣾⠿⣿⣿⣿⣿⣿⣻⡴⢿⣽⠿⣯⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣍⣿⣿⣿⣿⣿⣿⣟⠻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣤⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣷⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣛⣿⣿⣿⣿⣿⡿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⡐⠀⠀⠀⠐⡃⠄⠀⠀⠀⠠⢰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠘⠀⠀⠀⢀⠘⠐⠀⠀⠀⠀⠀⠠⡑⠀⠒⡐⢊⠄⠀⠀⠀⠀⠈⠉⠌⠈⠁⡁⢁
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠩⠐⠁⠀⠀⠀⠀⠀⠀⠀⡈⠑
⠀⠀⠀⠀⢀⡈⠁⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠴⠠⠤⠔⠆⠂⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⡈⢂⠁⠀⠀⠈⡂⠀⠀⠀⠀⠀⢘⣐⣐⣒⣒⣒⡃⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⢁⠄⡀⠀⠀⢀⠥⠀⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠅⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⢀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠂⡱⠒⠒⠲⢎⠄⠀⠀⠀⠀⠀⠈⠐⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠄⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⣩⠰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁
⠀⠀⠀⠀⢠⠂⠄⠀⠈⢠⠂⠀⠀⠀⠀⠀⠔⠴⠤⠤⠤⠌⠂⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡖⠠⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⠘⠒⠒⠒⠒⠚⠂⠀⠀⠀⠀⣐⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠙⢦⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠳⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢦⡈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⣾⠿⠿⣿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⣄⠘⢦⡈⠳⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣄⠙⢦⡈⠱⣄⠙⢦⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠢⡈⠳⣄⠉⢦⡈⠱⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠑⢄⠉⠢⡈⠳⣄⠙⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⡀⠑⣄⠈⣦⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣾⣷⠶⠿⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢟⠉⠣⡀⠑⢄⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⠉⠢⡀⠑⢄⠈⠢⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠣⡀⠑⢄⠈⠢⡀⠑⢄⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑⢄⠈⠢⡀⠑⢄⠈⢢⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠢⡀⠑⢄⠈⠢⣀⣱⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢄⠈⢢⣀⣵⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣶⠶⢾⡿⠾⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⣅⠙⢦⡈⠣⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣄⠙⢦⡈⠳⣄⠙⢦⣼⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠛⢦⡈⠳⣄⠙⢦⡈⠳⣤⡿
⠀⠀⠀⠀⠀⠀⢸⡏⠳⣄⠙⢦⡈⠳⣄⠙⣦⡿⠁
⠀⠀⠀⠀⠀⠀⣿⡟⢦⡈⠳⣄⠙⣦⣼⡿⠋
⢀⣀⣠⣤⣤⣤⣿⣧⣶⣿⡶⠾⠟⠛⠉
⣟⠙⢯⡈⠳⣄⣿
⡈⠳⣄⠙⢦⣨⣿
⠙⢦⡈⠳⣄⣽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢄⣣⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠷⢶⣤⣄⣀⠀⠀⠀⢤⣍⣙⠛⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠉⠙⠻⠶⣦⣼⣿⣿⣿⡆⠀⠈⠉⠛⠛⠿⠛⠿⠿⠻⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠛⠻⠶⠦⢄⣀⡀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠛⠶⠦⠄⢀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣀⣀⣀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠐⣦⣾⠇
⠀⠠⠒⠉⠐⠀⠁⠐⠠⢜⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⡛⠃⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠉⠉⠉⣙⣋⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢠⠄⢂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⡄⠀⡐⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⠋⠀⠀⠀⢹⣤⠖⠉⠈⠀⠀⠀⠀⠄⠀⠀⠀⠚⠁⠀⠀⠙⢇⠔⠉⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠑⣶⠇⡀⠁⡰⣁⠀⠑⠀⠀⡀⡂⠀⢠⠀⠀⠉⢳⡄⣐⠁⢀⢢⡄⠐⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠁⠙⠇⡀⣠⡀⢨⡟⢀⢄⠠⡠⡀⠀⠀⠀⠀⠈⠉⠏⠓⠀⢉⢀⡿⠁⣀⠀⣀⣄⠄
⠀⠀⠀⠀⠀⠀⠤⠀⡀⢠⣈⣿⣿⠁⣀⠀⡸⠀⠄⠀⠀⠀⠐⡡⠄⠐⢈⣅⣻⣿⡇⠀⠀⢙⠇⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠳⠰⠀⠀⠈⢤⡤⠂⡤⠠⠀⠀⠀⠀⠀⠀⠀⡑⠀⠆⠀⠀⢥⡄⢚⠀⠱⠄
⠀⠀⠀⠀⠀⠈⠀⣌⡐⡄⡠⠄⠀⢀⣼⢆⡀⠁⠀⡀⠀⠀⠈⠁⢬⡐⡦⠤⠆⠀⠀⠀⢑⡉⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⣿⡅⠂⠄⠊⠀⢡⠀⡀⠀⠐⠄⠀⠐⠂⠐⠀⢹⣇⠰⠀⠐⣼⠇⠀⠀⠀⠔⠠
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠠⢠⣦⣼⠇⠀⡾⠀⠀⠢⠀⠀⠀⢀⠀⠀⠁⢈⠀⣠⣰⡟⠀⠐⢢⡇
⠀⠀⠀⠀⠀⠀⠈⠠⠂⠀⠰⢿⣿⣤⡾⠃⠈⠁⠁⠀⠀⠀⠀⠊⠀⠀⠘⠓⠎⠀⣡⣴⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣟⣁⠀⠀⠀⠀⢈⣛⣿⣟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣛⣱⣿⢿⣿⣿⣿⣿⢿⣷⣸⣿⢿⣿⣿⣿⣿⢻⣷⣙⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⠘⣿⣿⡟⢸⣿⣿⣿⣿⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⢿⣿⣴⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣶⣶⠚⢚⣿⣿⣿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⢹⣿⡟⣿⣿⠉⠀⠀⠀⢸⣿⡟⣿⣿⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡇⣿⣿⠀⠀⠀⠀⢸⣿⡇⣿⣿⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠃⠀⠸⠿⠇⠿⠿⠀⠀⠀⠀⠸⠿⠇⠿⠿⠀⠀⠿⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡀⢸⠀⠀⠉⠉⠁⠀⠀⠻⣿⣿⠟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⢸⣧⠀⠀⣴⣿⣷⣦⠀⢀⣠⣶⠟⣡⣶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⡀⠘⣿⣷⡀⢿⣿⣿⡿⣠⣿⠟⠁⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⡄⠀⠙⢿⣷⣽⣿⣿⣄⠉⠁⣼⣿⠏⠀⠀⠀⢀⡍⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠙⢿⣿⣿⣿⣷⣼⣿⣿⠀⠀⠀⣠⣾⠁⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢤⣤⣤⣄⡀⠹⣿⣿⣿⣿⣿⣿⣀⣤⣾⠟⠁⠀⡘⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠈⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⡾⣃⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⢁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⣤⣤⡉⢿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠦⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢻⣿⣿⣿⡟⢁⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠘⣿⣿⣿⡇⠈⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢀⣀⣿⣿⢀⣴⣄⠀⠀⠀⠀⣼⣧⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⣿⣿⣾⣿⣷⣠⣿⣿⣿⣾⡇⢸⣿⣿⣀⠀⠀⢠⣿⣿⡇⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⣸⣧⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣸⣿⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⡿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠛⠉⠉⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⡠⠤⠴⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⣖⣨⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⢀⣠⣤⣤⣤⣤⣤⡀
⠀⠀⠀⣿⣿⠿⡏⣝⣿⣿⡇⠀⢸⣿⣿⠿⣿⣿⣿⣿⠀⠀⣿⣿⠉⠉⠉⢹⣿⡇⠀⢸⣿⣿⡿⠿⣿⣿⣿
⠀⠀⠀⣿⡟⣶⣯⣟⣙⣿⡇⠀⢸⣿⣿⠿⠿⢯⣼⣿⠀⠀⣿⣿⠀⡜⣣⢸⣿⡇⠀⢸⣿⣿⣿⣾⣟⣿⣿
⠀⠀⠀⣿⣿⣦⣼⣧⣾⣿⡇⠀⢸⣿⣯⣤⣬⣿⣿⣿⠀⠀⣿⣿⣤⣀⣄⣼⣿⡇⠀⢸⣟⣉⣿⣿⣋⣹⡿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⡀⠀⢀⣴⣶⣶⣶⣶⣶⣄⠀⠀⣠⣶⣶⣶⣶⣶⣦⡀⠀⢠⣴⣶⣶⣶⣶⣶⣄
⠀⠀⠀⣿⣿⠉⢻⡟⠻⣿⡇⠀⢸⣿⣿⣾⣿⢻⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠛⠓⠡⠺⡗⢻⡇⠀⢸⣿⣿⣿⣿⢸⣿⣿⠀⠀⣿⣿⡿⣻⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣶⣶⣶⣶⣶⣾⠇⠀⠸⣿⣿⣿⣿⣾⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⣴⣿⡿⠛⣿⣿⣷⡄⠀⢠⣾⣿⠟⠻⣿⣿⣦⠀⠀⣴⣿⣿⡿⣿⣿⣷⡄⠀⢰⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣿⣿⣇⢀⣼⣾⣿⡇⠀⢸⣿⣇⣴⣆⣻⣿⣿⠀⠀⣿⣿⣿⣀⣸⣿⣿⡇⠀⢸⣿⣫⡿⡿⣿⣿⣿
⠀⠀⠀⣿⡏⠉⠛⠉⣻⣿⡇⠀⢸⣿⠉⠻⠏⢘⣿⣿⠀⠀⣿⣿⡉⠉⠉⣹⣿⡇⠀⢸⣿⣿⣷⢴⣿⣿⣿
⠀⠀⠀⠹⠷⠶⠶⠶⠿⠿⠃⠀⠘⠿⠶⠶⠶⠾⠿⠟⠀⠀⠻⠿⠿⠿⠿⠿⠿⠃⠀⠘⠿⠿⠿⠾⠿⠿⠏
⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⠟⡛⢻⣿⣷⠀⠀⣾⣿⠛⠿⣿⢻⣿⡆⠀⢸⡿⠻⠿⠿⠟⠻⣷
⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⡇⠀⢸⣿⣏⢀⠀⠐⣿⣿⠀⠀⣿⣯⣤⡾⢿⡏⣿⡇⠀⢸⡇⢿⡈⢛⣽⢰⣿
⠀⠀⠀⣿⣿⣿⣶⣮⣻⣿⡇⠀⢸⣿⣿⣤⣉⣼⣿⣿⠀⠀⣿⣿⣿⡄⣸⣿⣿⡇⠀⢸⣇⣀⣀⣀⣁⣨⣿
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠈⠛⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡤⠆⠀⠀⢰⡶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⡇⠀⠀⢀⠈⠀⣾⡅⠈⠑⠄⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠀⠀⠀⠃⠿⣥⣀⢿⣝⠒⠀⠀⠹⠶⣶⢀⣈⣽⣷⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠈⠹⠀⠙⠓⠂⠀⠀⠀⣽⢿⠏⠁⣿⠀⢀⠀⠀⠀⠀⢤⣀⠀⡠⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠠⢄⣾⣁⡤⣠⠀⠿⡿⠟⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⣿⠈⠃⠀⠏⠒⡿⣤⡀⢠⠞⠛⠀⠀⠀⠠⠖⢿⣧⠀⣄
⠀⠀⠀⠀⠀⠀⠸⠇⠉⠛⠁⢀⣤⣶⣾⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⢠⡤⠀⠈⠀⠀⠀⠀⠀⠁⠀⠃⠈⠀⣰⠄⠀⠀⣀⣀⣀⣿⣶⡿
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⣼⣿⡿⠋⠙⣿⣿⣄⠀⠀⠀⠀⣀⠄⠀⢰⠃⠀⠀⠀⠀⠀⢰⣿⡿⠷⠄⠀⠈⢹⡋⠂⠀⠀⠈⠉⠁⢰⡆
⠀⠀⠀⠀⢀⡇⠀⢰⢀⡿⠙⠿⣇⠀⠀⢿⣿⣿⡿⣶⠶⠛⠁⠀⠀⢀⡤⠀⠀⣴⣶⡄⢻⣿⣥⣀⣤⣤⣤⣜⣧⠀⠀⠀⠠⡀
⠀⠀⠀⣀⢸⣧⡶⠿⠟⠁⢦⡆⠀⠀⠀⠘⢿⣿⣷⣶⣦⣤⣶⣶⠞⠋⠠⣶⠀⠉⠛⠁⠘⣿⡟⠛⠛⠿⣿⡻⢿⣷⡱⠴⠶⢻⠍
⠀⠀⠈⠛⠘⢷⠶⢠⣤⠀⠀⠙⡆⣀⣀⢠⡦⠈⢙⠛⠛⠉⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠹⡇⠀⢻⣷⠀⣠⡴⠶⣦⣄⠀⣀
⠀⠀⠀⠀⠀⠀⣶⢶⣥⣄⠀⠀⠀⠋⣹⣷⡀⠀⣬⢶⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⢀⣀⠀⠀⠙⣆⠀⠀⠘⠁⠀⠀⣿⠀⠁⠀⠚⠛⠻⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠁⣸⡇⠈⠑⢄⢀⣾⡏⠀⠹⡀⠀⠈⠻⠥⠄⠀⠀⠀⠉⣀⣽⣷⠘⠛⠁⠀⠀⠈⢣⡀⠒⠓⠗⠀⠁⠀⣀⠠⠤⠒⠚⠋⠱⠷
⠀⠀⠀⠀⠀⠀⠀⢻⣟⠒⠀⠀⠘⣧⠙⠂⠀⢁⡠⠀⠀⠀⠀⠀⣴⣾⣿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢻⣷⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠈⠓⠀⢠⡞⠀⠒⢤⡀⢠⣼⡟⠸⡇⠀⠀⡿⠀⠀⠀⢠⡄⠀⠀⠠⡷⠀⠀⢀⣴⣿⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢤⣠⡿⣎⠘⣇⠀⠈⠀⠀⠇⠀⠀⠾⢻⡶⢤⡀⠐⠃⠀⠀⢸⡇⠳⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡙⠾⠋⠐⠋⠀⠈⣠⣤⣤⡀⠀⠀⠀⠀⢺⡧⠄⠀⠀⢀⡜⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⢉⣃⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣄⣉⣛⣋⣡⣤⣤⣶⣶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣀⣙⠁⣼⡟⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣈⠁⢰⣿⡀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⣾⠏⠙⠶⣄⡀⠀⠀⠙⠳⢦⡀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠙⠳⣤⡀⠀⣠⡿⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠈⠙⢶⡟⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⠲⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣤⣸⠇⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣧⡀⠀⠉⠛⠳⢤⣀⠀⠀⠀⣠⡾⠋⣄⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⣿⠙⠳⢤⣀⠀⠀⠉⠓⢶⡿⠋⠀⠃⠈⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢿⡄⠀⠀⢉⣻⣦⣤⣀⣀⣹⠄⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣧⠀⠀⢸⣷⠶⠟⠛⠉⠁⠀⠈⢉⣡⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠟⠛⠉⠉⠘⣿⠀⠀⠘⣿⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠟⠛⠉⠁⠀⠀⠀⣀⣠⣤⣾⣿⠀⠀⠀⣿⡶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⢀⣤⣤⣴⣶⠟⠛⠋⠉⠁⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣿⡃⠀⢀⣼⠷⣄⡀⠉⠛⠳⢦⣄⠀⢸⡟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠰⠆⠀⣴⠟⠁⠀⠀⠙⠳⢦⣄⡀⠈⠙⣿⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣤⣼⣏⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⡟⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣅⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡟⠶⣤⣀⠀⠉⠛⠦⣄⣀⣴⠟⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣧⠀⠀⠉⠛⠶⣄⣀⣬⡿⠋⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢿⡄⠀⢀⣀⣤⡾⢟⡉⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣀⣠⣼⣿⠾⠛⠋⣁⢲⡘⢧⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠈⠁⢀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢀⣠⣴⠶⠿⢿⣟⠉⠉⠀⠹⣷⡀
⠀⠀⠀⠀⢠⡾⢋⡲⡝⢀⣴⣾⣟⣉⠀⠀⠀⠀⠻⣧⡀⠀⠀⠘⢿⡄
⠀⠀⠀⣰⡟⠁⠈⢁⣴⣿⣁⠀⠀⠉⠛⠲⢦⣄⡀⠹⣷⡀⠀⠀⠘⣿⡀
⠀⠀⣼⠟⠀⠀⣠⡾⠋⠀⠉⠙⠲⢤⣄⡀⠀⠈⠙⠳⠿⣇⡀⠀⠀⢹⡇
⠀⣾⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣀⡀⠈⠙⣦⠀⠸⣿
⣼⠏⠀⠀⣰⡟⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠒⠋⠀⠰⣿
⢿⣦⣠⣼⠟⠙⠳⢦⣤⣀⠈⠉⠛⠲⠦⣤⣀⠀⠀⠀⢀⣿⠀⠀⠀⢸⣿
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⠀⠈⠙⠓⠦⣼⡏⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣄⣀⠈⢹⡆⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠋⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠻⠿⠿⠿⠿⠟⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠶⠶⠶⠶⠶⠶⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡉⠉⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠷⠶⠶⠾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣹⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⢛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣽⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⣉⣉⣉⣉⣉⣹⣿⣿⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢉⣉⣉⣉⣉⢉⢹⣿⣿⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⡀⠀⠀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⣿⣻⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⡟⣹⠀⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⡀⣼⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⢸⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⣈⠁⣿⣿⡏⢹⣿⣿⣿⡇⢹⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⡇⠀⢹⣿⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣅⠀⠀⠀⠀⣸⣿⣀⠀⠀⠀⠀⠀⢀⣽⣿⣅⠀⣨⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀⢀⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⡇⠃⠀⠘⢱⣿⣿⣿⠉⠀⠀⠀⠀⠛⣿⣿⡇⠛⣿⣿⣿⡌⠃⠀⠀⠀⠀⠀⠛⣾⣿⣧⠛⣸⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠈⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠛⠛

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢠⣤⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⢀⣤⡀⠀⠀⠀⠀⢦⣄⠀⣴⣦⠀⣠⣤⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⣤⡄
⠀⢀⣨⣯⣀⢀⣬⣿⣤⡀⠀⠀⠀⠀⢠⣼⣿⣤⠀⣨⣿⣅⠀⠀⠀⠀⠀⠉⢳⣼⣷⢞⣹⣯⡀⠀⠀⠀⠀⢀⣤⣿⣤⡀⠀⠀⠀⢀⣤⣿⣧⡄⣀⣽⣅⡀
⠀⣎⣿⣿⡟⣿⣿⣿⡿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⣾⣿⣿⡟⡇⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⢳
⠀⢸⣿⣿⣿⠙⣿⣿⡏⠃⠀⠀⠀⠀⠋⣿⣿⡟⢳⣿⣿⣿⠍⠀⠀⠀⠀⠀⢰⣿⣿⣼⣿⣿⣿⠉⠀⠀⠀⠙⣻⣿⡇⠁⠀⠀⠀⠘⢹⣿⣿⠉⣿⣿⣿⡏⠁
⠀⠀⢿⣿⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⣿⡏
⠀⠀⠙⠛⠀⠀⠙⠙⠃⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠛⠛⠀⠀⠀⠀⠀⠀⠙⠋⠃⠀⠀⠀⠀⠀⠘⠋⠋⠀⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⣿⡆⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⢾⡗⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⣦
⣴⣿⣷⡄⠀⠀⠀⣴⣿⣦⡀⠀⠀⣴⣿⣷⡆⠀⠀⠀⣴⣿⣶⡀⠀⠀⣰⣿⣷⣦⠀⠀⠀⣰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⢠⣾⣷⣄
⠛⣿⡟⠃⠀⠀⠘⢻⣿⡿⠃⠀⠀⠛⣿⣿⠃⠀⠀⠐⢻⣿⣿⠃⠀⠀⠛⣿⣿⠛⠀⠀⠀⢻⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠘⣿⣿⡟
⠀⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢸⣿

⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡏⠀⠀⣷⢠⠎⠀⢈⡇⢠⡞⠉⠁⢰⠋⠉⠓⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⠋⠉⠙⢷⡀⣰⠇⠘⣧⢀⡼⠗⠚⠛⢳⡄⠸⣆⠀⠀⠀⠈⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠹⠀⠀⠀⠀⣷⡟⠀⢀⣿⠋⠀⠐⢲⡄⠘⠁⣀⣸⡆⣀⣤⠴⢯⣄⡤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣇⠀⡠⠲⠀⠀⣦⣤⣤⣸⡇⠀⣼⠃⠀⢀⣠⠞⠀⠀⠈⠀⢻⣿⠿⢤⣀⡄⠈⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡙⠶⣇⡀⠀⠸⠁⠀⠀⠈⠻⣶⣿⣴⣾⠟⠁⢴⡄⠀⠀⣠⡿⠁⠀⠀⢀⣀⣀⠀⠀⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠷⢤⣇⠀⣀⡽⠟⠛⢟⠛⠛⠲⢦⣹⣿⣿⠃⣀⣤⣾⠴⠶⠾⠯⣤⣀⠀⠀⠉⠀⢈⣇⠀⠀⠀⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣠⠀⠈⢙⡟⠀⠀⠀⠚⢀⡤⡄⠈⢻⣿⣿⣿⣿⣄⣀⡄⠀⠀⠀⠀⠉⡛⠶⠤⠴⠞⠋⣻⢄⣼⡟⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⣈⣒⠚⠋⠙⠦⠔⢀⣀⣾⠀⠀⢀⠀⣿⣿⡇⠀⠀⢈⣠⣶⣶⣿⡛⠻⢧⣄⣀⠀⢀⣀⡴⠟⠋⠙⢷
⠀⠀⠀⠀⠀⣀⠀⠉⠉⢻⡀⠈⣧⠀⠀⣀⠰⡃⠈⣿⠀⠀⣸⠆⢻⣿⣧⣠⣴⡿⠋⠁⠀⣸⠷⡤⠆⠘⣿⠉⠙⠧⡀⢀⠠⠴⠛⠦
⠀⠀⠀⠀⠀⠹⣄⡀⠀⢰⡀⠀⢸⡀⢰⡉⠀⠁⢠⣏⡠⢾⡋⠀⢸⣿⣿⣿⠏⢀⡀⠀⠉⠁⣠⡴⢦⡀⢹⡄⠀⠀⠹⠉⣀⡀⠐⣦
⠀⠀⠀⠀⠀⠐⠏⠹⡆⠀⠙⠓⠾⠷⢌⣷⡀⠀⣼⡟⠀⠀⠁⠀⢸⣿⣿⣏⡴⠋⢺⣤⣤⡾⠁⠀⣐⠃⠈⢧⣀⡖⠀⠘⠉⠙⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⣀⣤⠶⠟⠻⢷⣿⣇⡀⠀⠀⣱⢸⣿⣿⣿⠁⠀⠉⠀⢹⣁⣀⡤⠞⠀⢀⣀⣠⡴⠒⠆⠀⢠⣧⠴⠦⡀
⠀⠀⠀⠀⠀⣾⠀⠀⠈⣻⣶⠾⣿⠁⠀⠀⠀⠈⣻⣿⠉⠙⠋⠁⣾⣿⣿⣿⡀⠀⠀⢀⣾⢛⣛⣓⣊⣁⣀⣨⣿⡀⠀⢀⣠⣾⠁⠀⠀⠁
⠀⠀⠀⠀⠀⡽⠛⠛⠛⠉⢀⡼⢿⡓⠶⠃⢰⠛⠛⢿⣷⡀⠀⢀⣿⣿⣿⣿⣧⣠⣴⣿⣿⠿⠿⣿⡏⠉⠉⠛⠿⣟⠛⠉⠀⠘⡇
⠀⠀⠀⠀⠸⠀⣠⠴⠖⠛⠉⠀⠈⣧⠀⢀⡘⠀⠀⠈⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠁⡏⠀⠀⠈⣧⣀⢀⠄⠀⠘⣇⠀⠠⠴⠃
⠀⠀⠀⠀⠀⠰⣇⣀⡠⠀⠠⣄⢀⣼⠀⢸⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃⠐⠖⠁⠈⠁⠠⣄⣴⠿⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣽⡇⠀⡀⠀⡟⠁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣷⠶⠶⢤⣄⣼⠶⠋⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠁⠀⠙⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠶⠒⠒⠛⠋⠁⠀⠀⠀⣀⣀⣀⡠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠤⠤⠒⠒⠒⠛⠋⠉⠉⠉⢁⣀⣀⣀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠦⠤⠶⠒⠒⠒⠛⠉⠉⠉⠉⠉⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠒⠲⠖⠒⠒⠒⠋⠉⠉⢉⡽⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡒⠓⠒⠚⠛⠊⠟⠉⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠲⠋⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⡠⠂⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⢀⡤⠞⠓⠒⠓⠶⠒⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡠⠾⠿⠶⠶⠶⠶⠶⠶⠶⠲⠶⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠶⠓⠲⠒⠒⠲⠦⠦⠦⠤⠤⠤⠤⠦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠦⢤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠤⠊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠤⠴⠤⡤⠤⠤⣄⡤⠖⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣤⠦⠐⠉⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡀⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⣤⣆⣉⣄⣀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣀⣴⢮⣅⣀⣀⣀⣀⠉⣌⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠾⠥⢄⣀⣀⣀⣀⣀⠀⠈⠉⠙⠉⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⣤⣀⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠄⢀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣶⠛⣶⡄⢸⣟⢛⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣩⡿⠀⠻⠶⠟⠁⠀⠙⠋⠁⢰⣟⠛⣿⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢶⡆⠀⠹⡄⠀⠀⣠⠀⠀⣀⣀⠣⠀⠀⠙⠛⠋⠀⣾⡋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠓⠤⣄⡃⠀⠀⡇⠀⣾⡟⣻⡿⣤⠇⠀⠀⢠⠂⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣄⡇⠀⠈⠙⠋⢁⡟⠀⢀⡴⠁⠀⣴⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⣿⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢠⠇⣠⠾⠡⠤⠀⠙⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠈⠉⠉⠽⠓⠚⢿⡄⠀⣰⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣠⡾⡟⠿⡿⢆⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣂⠀⢣⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠴⠘⡘⢃⡄⣀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣻⣿⣬⠿⡿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡏⠀⢠⣆⠀⢈⣍⠈⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⡿⣿⣿⠋⢿⣿⠶⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠊⠁⠈⠁⠉⣿⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣾⣷⡄⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠛⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣦⡌⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⣗⠁⠀⠀⠀⡸⠗⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡏⢿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⡠⠑⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠠⡛⠿⣦⣜⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡘⠛⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣡⠓⠀⠀⠈⠹⣇⡔⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣯⣿⣿⣿⣦⡈⢟⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⢀⢀⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢁⠙⠿⣶⣤⡘⠒⠀⠆⣠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠈⠛⠻⣭⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⡠⢀⡔⠟⠙⠻⣷⣔⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣧⣶⣤⡈⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣇⠃⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣀⠀⢠⡾⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡈⠙⠿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠋⠊⡟⢻⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢷⣿⡦⣤⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠤⠙⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣟⣶⡌⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠤⡀⣼⠁⠀⠀⠀⢻⡠⠆⠔⠂⠀⠀⠀⣿⣿⣿⣿⣿⣝⣿⡏⣿⣿⣿⣿⣧⢼⣽⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡅⢿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⢠⣀⠀⠀⠀⢤⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣼⣃⡀⠀⢤⣨⣍⡿⠷⡆⠠⠦⣼⠁⠀⣾⠶⠦⠀⢻⡼⠃
⠀⠀⠀⠀⠀⢴⡀⠰⢼⣷⠁⠈⠁⠀⠀⢹⡟⠀⠀⡠⢀⣰⣾⡀⢀⣾⠷⠤⠀⠀⢳⣷⠔⠀⣴⠄
⠀⠀⠀⠀⢶⠞⢓⣤⣀⣿⣄⠀⣠⣤⡀⣸⠿⠶⢿⡗⢀⡄⠈⠛⣿⡁⣠⣤⡀⢀⣾⣁⣠⣞⠛⠶
⠀⠀⠀⠀⠀⠀⣨⠟⠉⠁⠙⢷⣿⣿⣿⠃⠀⠀⠀⠈⣯⡁⠀⠀⠈⢻⣿⣿⡷⠋⠁⠉⠙⢯⡶
⠀⠀⠀⠀⠘⠟⢱⡀⢻⠖⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣿⣿⠁⠀⠐⣷⠁⣄⠹⠃
⠀⠀⠀⠀⢀⡀⢋⣹⠿⣤⣀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⢀⣠⠾⣯⣙⠂
⠀⠀⠀⠀⠐⠋⠙⡏⠸⢿⣿⠿⠛⢿⣿⣆⠀⠀⣴⣾⣿⣶⡄⠀⣠⣾⡿⠟⠻⢿⣿⠷⢸⠟
⠀⠀⠀⠀⠀⠴⢠⣤⣴⡏⠀⠀⠀⠀⠙⢿⣷⡜⢿⣿⣿⣿⢇⣼⡿⠋⠀⠀⠀⠀⠙⡦⣤⣤⢮⠄
⠀⠀⠀⠀⠀⠀⠈⠃⡸⠷⢤⠤⠀⠀⠀⠀⠹⣿⣦⣿⣿⣷⣿⡟⠁⠀⠀⠀⠀⢀⠼⠧⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⢀⣶⡆⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⣿⡟⣇⠀⠀⣀⣿⣇⡀⢀⡿⣹⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⣿⣧⢹⡀⣼⢿⣿⣿⢻⣸⡃⣿⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⢿⡿⣷⠋⠁⣼⣿⣿⠀⠉⣻⢿⣿⢿⣿⡚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣿⢸⣷⠜⣧⠸⡟⣹⠟⢧⠀⣿⡾⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠳⣄⢸⣷⢿⡿⡀⠾⣿⣯⣴⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⢠⠿⣾⣿⣿⣿⣻⣾⣿⣿⣿⣇⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⡴⢤⣿⢿⣿⣿⣿⣿⣿⣟⡿⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠹⣿⣭⡶⠛⢓⠺⢻⣿⣿⣿⣿⣿⠟⢿⡻⣦⣠
⠀⠀⠀⠀⠀⠀⠼⣶⠔⠋⠀⠀⠙⡉⠃⠠⣷⣾⣟⣿⣿⣿⣿⣿⢷⠈⠀⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⣿⠃⠀⢹⣿⣿⡹⠛⠛⠀⠀⠀⠈⠙⠳⣄⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠒⠢⠤⠀⠀⠀⢠⠀⠀⢄⣀⠹⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡿⠃⠀⠠⠀⠀⣀⡀⠀⠀⠉⠒⠈⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡽⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣀⡄⠐⠚⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠐⠊⠉⠉⠁⠛⠰⡄⠀⠤⠭⠱⠲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡜⠄⠀⠀⠀⠀⠤⠈⠐⠒⠒⠒⠲⠶⣶⡁⠀⠈⠃⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠂⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠓⠂⠒⢆⡈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⣎⠉⡁⠀⠀⢀⠀⠀⠐⡀⠀⠀⠀⣀⡠⠔⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⡀⠁⡁⠚⠛⠲⠄⢀⡠⠄⠈⢁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⣗⠶⠒⠉⠁⠀⠀⢀⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠒⠛⠁⠈⠛⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣀⠀⠀⠉⠉⠈⠉⠙⢣⣄⣁⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠑⠐⠒⠂⠀⠀⠀⠃⠀⠀⠀⠢⡤⣤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠀⠀⠀⠀⠠⠤⠄⠠⠤⠀⠀⠀⠠⠀⠀⢠⠟⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⢲⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⡉⠛⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡴⠎⡃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠈⢛⣍⣉⣉⣉⡁⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣲⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⣀⣀⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠀⠿⠦⠾⠉⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡀⠈⠁⠁⠉⠉⠎⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣃⡀⠀⠀⠀⠀⠀⠀⠉⠒⣤⠀⡀⠈⡓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⢌⡚⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢾⠚⣲⠆⠂⠒⠂⠃⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀⠀⠀⣿⣷⡄⠘⢿⠟⠀⣠⣴⡦⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⡙⠿⠇⠀⠈⠀⠐⣿⠿⠃⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡀⠀⣧⠀⠀⣰⣷⡄⠀⢀⣠⠴⠀⠀⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢤⣀⡀⢿⣧⡀⢻⣿⠇⣴⡿⣣⣴⡄⠈⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠙⠻⣾⣿⣷⣄⢁⣾⡟⢸⣿⢟⡄⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⠉⠀⣀⡀⠘⢿⣿⣿⣿⣿⡇⢀⣠⡾⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠈⠙⠻⣿⣦⣿⣿⣿⣿⣿⣿⣋⣀⣤⠂⣤⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⢀⡴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠚⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣤⠙⣿⣿⣿⡿⢋⣩⣽⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇⢸⣿⣿⡇⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢶⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⣸⣿⠟⢿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⠿⠃⠀⠀⠈⠻⣿⡌⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠠⡶⣦⡄⣶⡦⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣄⡀⣀⣀⠀⣠⡀
⠀⠀⠀⣒⣮⡳⠀⠾⢾⣽⠧⣖⠻⠛⢀⡉⠀⠀⠀⠀⡤⣄⠀⠤⡄⠀⢉⠌⠃⠘⢾⣏⠙⢉⣘⡿⠳⢂⡄
⠀⢠⡤⣅⠑⠀⠐⡆⠈⠹⠽⠻⠴⠀⠀⣿⣿⠽⠃⢰⠂⠈⠁⣠⠦⢴⣁⢶⣿⢠⢈⡦⡥⡳⣽⠵⠃⠘⠁
⠀⣨⣾⢿⡶⠦⠀⠩⣄⡠⡰⠶⣖⣤⠞⠘⠻⠗⠀⠀⠦⣄⢫⢻⠞⠀⡀⠂⢳⠈⡾⡷⣬⣼⢝⣬⠊⣳⠒⣦
⠀⡣⠮⠀⠀⡀⢰⣫⡧⠑⢎⠣⣬⠠⠀⠀⠀⢤⠀⠀⢳⣊⣶⣿⠴⠞⠇⠀⠀⠀⣠⡢⠓⠀⠙⠛⠉⠈⠃⠁
⠐⠗⣶⠙⠶⠈⠮⣛⠁⣼⠞⢠⡀⠀⠑⠀⢀⡄⡠⣠⣀⠀⢩⣉⠀⢈⡁⠀⡰⠹⢎⣀⣀
⠐⠽⠃⠩⠷⣶⣧⣯⠉⠀⠂⠠⣗⠀⠀⠈⠡⠞⢡⠇⢈⠂⣂⣤⡖⡡⠀⠀⢀⠀⠾⠠⠽⢋⠹⡀⠄⢤
⠀⢼⢻⣦⠘⣿⢟⣣⣀⣀⣀⠀⣘⢓⡀⠀⠈⠀⢬⡖⠺⠫⠁⢈⡜⠀⠀⣀⠂⠀⢀⢠⠀⠀⠊⠓⠢⠆⡀⠁⢦
⠀⠈⣻⢻⡤⠺⡿⢗⠁⣀⠀⠀⠀⠉⢓⠀⠀⠀⠀⢀⡠⠔⠓⠚⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡌⠁⢢
⠀⠀⠀⠛⠁⠈⠛⠛⠪⠿⠇⠀⠀⠀⠈⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄⢀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⢤⠌⣬⠁⠻⢏⣄⡉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠛⢘⡢⠉⠉⠂⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣴⡯⠉⠙⢻⣷⣆⡀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣰⣿⡇⠀⠄⢀⣼⣿⠟⢻⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣅⣀⡠⢿⣿⣿⠀⣿⣿⡆⠀⠀⠀⠃
⠀⠀⠠⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠄⠠⠬⠻⠀⠀⠐⠈⢻⡟⡠⣿⣿⠧⣖⠀⠆⠇
⠀⠀⢀⡀⠠⢤⣀⢄⣀⣠⣤⢤⡄⠀⠘⡄⠄⠤⣤⣌⣦⣀⣤⠤⠞⠀⢷⡀⠈⢘⣿⣆⣤⡇
⠀⠀⠈⡄⠀⠀⠐⡆⠉⠤⣄⠞⠃⠀⣤⣿⠎⣦⣴⣼⣷⢞⡉⠀⠀⠀⣿⠙⣆⠈⠿⢻⣿⣿⢏⡉⠉⠉⠭⠉
⠀⠀⢰⠃⣀⣁⢀⠈⣠⠖⠉⠀⠀⠀⣾⣭⣟⣻⣿⡿⠛⠂⠀⠀⡀⠈⠁⠀⣥⡄⠈⣼⣿⣿⠖⠈⠁⠀⠀⠁
⠀⠀⠘⠉⠉⠉⠉⠩⠏⠀⠀⠀⠀⢸⠛⠻⢟⡻⠛⠁⠀⠀⠀⢈⣻⡆⠀⠀⠉⠁⠀⢈⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢨⡔⠂⣷⠀⠀⠀⠀⣠⣴⣿⣿⡻⢅⡀⠀⠀⠀⠈⢹⣿⣬⡡
⠀⠀⢠⣤⣤⣴⣦⣠⣄⣀⣠⣬⣯⣿⣾⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣹⣦⣄⣐⣤⣤⣤⣾⣿⡟⠷⠤⢀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⢿⣿⣿⣿⣶⢦⣄⠙⣂
⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⠻⣿⠛⢆⠴⠃⠀⠀⠃⠀⡍⣿⣿⣷⣾⣿⣽⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢁⣠⠤⣞⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣽⡹⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣭⠿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⡇⣽⣿⣿⣿⣧
⠀⠀⢸⣿⣯⣤⣴⣿⣿⡿⠋⠀⠋⠀⢀⣽⡆⠀⠀⠀⠀⠀⠆⠤⠀⠀⠀⠀⠀⡀⠀⠀⢀⣸⢓⣿⢿⣿⣿⣿
⠀⠀⢨⣭⠿⣿⣿⣷⡟⠣⡔⠊⠀⠀⣸⡏⠃⠀⠀⠈⠀⠀⠀⠀⠏⢵⡶⠛⠢⠐⠂⣰⣿⣇⣠⣯⣿⣿⣿⣿
⠀⠀⢸⣿⣿⠷⣾⠛⠻⣶⣙⣲⣶⠧⣽⣟⣠⡄⠀⣀⢀⣀⠀⢀⡴⠻⠇⡅⠰⣰⣿⡿⣾⣿⣿⣋⢻⣿⠡
⠀⠀⢸⡿⡿⠀⠈⠳⠀⠘⢿⣿⣿⣷⣿⣶⣿⣭⠟⣺⣿⣥⣤⣥⣷⣶⣾⣶⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢸⡟⠃⡀⢀⣼⣀⡤⢤⣏⣶⠗⠛⠛⠋⠙⠛⠋⠛⠈⠉⠉⠻⠛⠛⠛⠛⠛⠋⠛⠛⠻⠿⠻⡇⣸⣷⡆
⠀⠀⠹⣀⣀⣵⣿⣿⣁⣀⣄⣻⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠃
⠀⠀⢼⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⣴⣿⣿⠀⠸⣿⣷⣴⣶⣶⢲⣿⣿⡇⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣶⣮⡙⠋⠁⠛⠟⢁⣶⣄⠈⠡⠛⢛⣁⡜⠻⠟⢡⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⢛⡿⠣⠤⠦⣥⣄⣘⡻⠋⢠⠶⣿⡿⠦⣤⣀⠀⠌⢉⣽⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⢿⣿⡟⠀⣿⣿⡦⠀⠀⠀⠀⠌⠙⣶⡏⠸⠿⣃⣀⣀⣉⡲⠤⣌⠛⠛⠛⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⡀⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠁⢸⠀⢀⠂⠀⠀⠀⠀⠈⠠⢿⡇⠀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠘⡀⠀⠀⠀⠀⢀⢄⣿⠀⠸⠀⠀⠀⠀⠀⠀⡀⠈⣠⠄⢈⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⢈⡲⢮⣄⠰⠆⠐⣡⡾⢁⣀⡀⣑⣄⢀⣀⠀⠔⢁⡼⠁⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⡁⠒⡀⢀⣀⡀⡀⠈⢳⣄⣴⡿⠋⠀⠀⠀⠀⠀⠰⢴⣶⣾⣉⣸⣿⠏⠀⠈⢉⣥⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡧⠊⠀⠀⠀⠀⠀⢡⠈⣿⣿⣴⡀⠀⠀⠀⠀⠀⢀⣾⣿⣇⣈⣉⣉⡈⠈⣤⣼⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⢘⣄⢸⣿⣿⠑⠄⢀⣀⡀⢄⣡⣤⠀⠀⠀⠀⠀⠈⠊⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠠⢀⣀⠀⠔⠘⣿⡈⢿⣿⣄⠀⢀⣠⡤⣼⡛⠰⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡿⡿⠀⠀⣠⠔⠋⠙⠉⠉⠻⣿⣿⣿⠋⢡⣾⣿⠏⠓⢕⠄⢀⣀⠀⣐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠟⠁⠐⠴⠞⡑⠉⠉⠉⠉⠉⠂⢹⣿⣿⣇⠈⡉⠁⠀⠀⠀⠱⠆⢤⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡔⡀⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠐⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⢸⣿⡗⢄⠀⠀⠀⡠⠊⣸⣿⣿⣿⡟⢄⠀⠀⠀⠀⢀⠄⠈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠉⠀⠀⢀⣿⣿⣿⣿⣿⠀⠑⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠈⠡⠞⠉⡼⠋⠙⠏⠻⠏⠙⠛⠉⠉⠙⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⢀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣵⢲⡆⡶⡶⣶⣸⢼⢡⡆⡴⠀⠈⣸⠹⡶⣰⠶⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠌⠙⠙⠙⠃⠃⠛⠛⢙⡾⣿⠷⠋⠀⠛⠁⠋⠛⠊⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⢤⡀⠀⠀⠀⠀⢠⣦⣽⣥⣦
⠀⠀⠀⠀⠀⠀⡠⢄⡠⣀⠀⠀⠀⠀⢀⣾⣶⠛⠛⣷⣿⡄⠀⠀⠀⢿⣯⠉⢩⣿⠇⠀⠀⠀⡀⠄⢀⡀
⠀⠀⠀⠀⠀⢸⣿⠛⠿⣿⡇⠀⠀⠀⠘⣿⣷⣉⢌⣼⣿⡇⠀⠀⠀⠈⠛⠟⠛⠋⠀⠀⣰⣤⣰⢿⣄⣽⣦
⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠁⠀⠀⠀⠀⠘⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢿⣿⡁⠀⢙⣿⣿
⠀⢀⠀⠤⠀⡀⠀⠀⠀⠘⢆⢀⠀⠀⣀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⢻⣿⣶⣿⠿⠃⠀⠀⠀⢀⣤⣲⣠⣄
⣴⣷⣶⣿⣶⣿⣦⠀⠀⠀⢨⣿⡟⠛⢿⣷⠀⠀⣧⠎⠀⠀⠀⣀⠤⠤⣀⠈⣇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⣿
⣿⣿⣅⠀⣩⣿⣿⠀⠀⠀⠀⢿⣧⣤⣾⠟⠰⣸⠏⠀⠀⢠⣿⣶⣿⣿⣮⣷⣸⡄⠀⣶⠁⠀⠀⠀⠀⠀⠀⣄⠔⠀⠙⠿⠶⠿⠋
⠈⠻⢿⣿⡿⠟⠉⠛⠲⢶⣄⣐⡏⠉⠀⠀⠀⣿⠀⠀⠀⢸⣿⣯⠉⠀⣽⣿⠇⣧⢰⠏⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣤⡀⠀⠀⣿⠀⠀⠀⠀⠛⢿⣷⣾⠿⢏⠀⣿⡟⠀⠀⠀⠀⡀⢀⡞⠁⠀⠀⣰⣯⡶⠿⢶⣽
⠀⣀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠻⢦⡀⣿⡄⣠⣦⣶⣵⣆⠀⠀⠀⠀⢳⣹⡇⠀⠀⠀⢰⣠⡿⠀⠀⠀⠀⣻⣿⡁⠀⢈⣿
⢸⣿⠿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⣿⣇⠉⣸⣿⠀⠀⠀⠀⠀⣿⠆⠀⠀⢀⣾⠏⠀⠀⠀⠀⣀⠸⠿⣷⣤⣾⡿
⠈⠿⣷⣾⠿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⢻⠿⠛⠁⠀⠀⠀⠀⣸⡏⠀⢀⣴⠿⠷⠤⠶⠶⠾⠉⣀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠲⠶⣶⣦⣤⣜⣷⣼⡇⠀⠀⠀⠀⢀⣼⣟⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠲⠋⠁⠀⠀⠉⠙⢿⣷⡀⠀⠀⣰⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⠀⠀⠠⢄⠀⠖⠠⠠⣄⠀⡀⠐⢲⣰⢀⡆⠀⠀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠄⢇⠀⢀⣀⣀⣀⣈⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠅⠀⠀⠀⢀⡠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠨⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣀⡄⠀⠀⠚⠛⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⠉⠀⠀⡀⠀⠀⠀⠀⡀⠀⠈⠛⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⠀⣐⠀⠀⠀⠃⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠠⠐⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠸⠀⠀⠀⠀⠨⠂⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢉⡀⠀⢀⠀⡀⠀⠀⡉⢀⠀⢰⡀⠁⠀⠀⢐⢐⠀⠀⠈⠁⢐⢨
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠚⠁⠀⠀⠄⠄⠀⠀⠂⠀⠀⢠⠀⠃⠀⠀⠠⠠⠀⠀⠐⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠷⢺⠀⠀⠈⠀⠁⠀⠀⠀⠈⠀⠈⣁⣠⡤⠞⠾⣌⡀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⡰⢇⡴⢋⡎⠀⠀⢀⠖⠲⠤⠖⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠒⠒⠒⠛⡥⠶⢶⡋⠁⠀⢠⣯⢝⠿⠊⠁⣤⣀⣀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⣀⡴⠓⠲⠶⠻⠀⠀⢈⡔⠛⠒⠒⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡀⢀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠯⠇⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡔⠁⠀⠀⠀⠀⠀⠙⣖⠲⠶⢦⡤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠁⣠⠊⣀⣠⢤⡆⢀⡤⠶⠦⣬⡑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⢡⠴⠿⠒⠋⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢃⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠈⠹⠃⠀⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⢀⡈⠛⠉⡄⣠⣶⡆⠘⠽⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡈⠻⠙⢰⣿⡄⠀⠘⣿⣷⡀⡇⠻⠟⠀⠠⣶⣶⠆⠀⠀⠀⠀⠀⣾⣿⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣀⠹⣿⣷⠀⣿⣦⡘⢿⡷⠄⠘⠛⢃⡀⣤⣈⠁⢰⡇⢀⣄⣤⣄⡋⠁⠀⠀⠀⢴⣤⡀⠉⠋⠠⢿⡿
⠀⠀⠀⠀⠘⠻⣿⡟⠀⠀⠀⣙⡋⠁⠀⠀⠀⢡⢰⣿⡇⠹⢿⠛⣾⢡⠋⢸⣿⡋⠁⠀⠀⢸⣷⡘⠿⢳⠀⢀⡀⠈⠠⣶⣶⠦
⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢀⣤⣌⠙⠒⢦⣄⡈⢧⠉⢠⣤⣤⡄⣿⣾⠀⢽⠿⠟⠁⢰⣦⣘⠛⠃⢀⡾⠋⢩⣿⣷⣦⠉⣡⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠟⠛⠃⣰⣿⣧⠈⠙⠾⣷⣄⠙⠛⠂⢸⣿⠀⠀⣼⣿⠀⠈⠻⠟⣷⣠⠟⠀⠀⠀⢉⣧⡀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⢁⣴⣟⡄⠀⢉⡛⠶⣦⣤⣹⣧⡀⠉⠛⢀⣤⡀⠀⣿⡏⠀⠀⢠⡀⠘⠿⡇⡰⠀⣴⣿⠇⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠾⠿⠛⠁⣴⣿⣵⠆⠀⠈⠙⠛⢿⣶⣄⠀⢿⡿⠆⣿⡁⢀⡀⢿⣿⠄⢀⡾⠁⠀⢘⡁⠀⠀⠹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⡀⠀⠀⠀⠸⠿⠛⠁⠀⣤⡀⠀⢀⡀⠈⠻⣷⣦⡀⠀⢻⡇⣾⣷⡄⠀⣴⣯⡴⠶⠛⣭⣁⠰⣿⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣼⣿⡀⠀⢻⣿⣦⠀⣿⣆⢻⣿⠆⣼⣷⠀⢀⣬⠻⣷⡄⢸⣧⠘⠛⣡⡾⠋⢁⣲⣦⡘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣳⠀⠈⠙⠁⠀⠀⠉⠁⠀⣛⠛⠀⠀⠐⠮⣝⠀⣾⢿⡇⢹⣿⠀⣿⢀⣾⠋⠀⠀⣬⠙⠛⠛
⢤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢇⠀⡄⣠⣤⠄⣠⣤⣴⠍⠛⡒⠶⠶⣬⣿⣮⠉⠀⢸⣿⡇⣿⣿⢃⡀⠀⣾⣿
⠈⠿⡟⠀⠀⣾⣦⠀⠀⣀⠙⠿⠉⢸⡾⠘⠿⠏⠀⠈⠙⠋⢁⣾⣿⠆⣴⣖⡌⠻⣷⡀⢸⣿⠃⣿⠃⢾⣿⡄⠀⣥⣶⡖⠀⠀⠀⠀⠀⠀⢀⣠
⢀⣀⣤⡀⠠⣝⡛⠃⢰⣿⣧⠀⠀⢸⡇⣴⣶⡗⠀⠀⠀⠀⠈⠉⠀⢸⡿⠟⠁⠀⣿⣧⣿⡟⣸⠏⠀⠈⢈⡞⠀⠘⢋⣠⣤⠀⣴⣾⠆⠠⢿⡿⢀⣠⣤
⠙⠻⠿⠀⢀⣨⡙⠓⠦⣥⣁⡀⠀⢸⡇⠘⠉⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⡴⠃⠀⢀⣰⠟⠀⠀⠀⢟⣿⠇⠀⠙⠋⠀⣀⠈⠀⠈⠿⠟
⠀⠀⠀⠠⠿⠿⠃⠀⢠⣤⣍⠛⢷⣦⣷⠀⡿⣿⠇⠀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⠀⣀⣴⣿⣯⣤⣶⣶⣶⠶⠶⠶⣶⠞⠛⣩⣥⡀⢼⣿⡶⠄
⠀⠀⠀⠀⣴⣾⣿⡄⠀⠛⣿⣃⣀⠈⠻⣷⣌⠁⢠⣾⣿⠀⠀⠀⠀⢠⣾⣿⣿⠟⢁⣤⣶⣿⠿⠟⠛⠉⠉⠀⣤⣲⣦⡀⢶⣿⣷⡀⠛⠛⠗
⠀⠀⠀⠀⣀⣤⠀⠀⣀⡄⠀⢀⣉⠉⠓⠿⣿⣦⡈⠿⠃⠀⠀⠀⢰⣿⣿⠟⣡⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠇⠀⠀⠉⠁
⠀⠀⠀⠰⠿⠿⠋⢰⣿⠟⠀⣾⡿⢃⣾⣧⡌⠻⣿⣄⠀⠀⣰⠀⣿⣿⣏⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠿⠋⠀⠀⠙⣿⣦⠀⣿⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⡆⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣌⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣙⠻⢿⣿⣿⣮⣝⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⣬⣙⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠟⣿⣿⡻⣿⣿⣿⣿⣷⡄⠙⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠄⣠⣶⡿⠿⠛⠉⢁⣤⣾⣿⡿⠁⠀⠉⠛⢿⣿⣿⠀⠀⠙⢿⣿⣷⣦⡘⠷⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠉⢁⡾⠋⠀⠀⠀⠀⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠈⠙⠛⠿⠶⠆⠀⠀⠉⠉⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣿⠿⠻⢷⡀⠀⠀⣠⣴⣶⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⢀⡀⠀⠀⢀⡀⠈⠳⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠘⣁⣄⣄⣈⠁⢀⠜⢸⣿⣿⠿⠿⠿⢿⣿⠟⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡁⢲⡖⢸⣿⡿⠀⠘⣿⠁⢀⡀⠀⠀⢀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠟⠀⠀⠀⢹⣆⠀⠁⣀⣀⠀⠁⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣤⣤⣤⣤⣿⣶⣦⣤⣼⡿⠿⣶⠤⠤⢴⠾⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⣻⢭⣿⣟⢿⣿⣷⡊⠁⠀⠀⠀⠉⣒⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡻⠯⣽⣾⣿⣿⣷⣼⣿⣿⣧⢿⣿⣻⣽⣿⣽⡻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣵⣿⣴⣿⡿⠿⠻⠋⠀⢻⣙⣻⢣⡿⠿⣿⣿⣿⠿⣮⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣿⡟⡏⠀⡄⠀⠈⠁⡸⣿⣧⠋⠀⣀⠀⠀⢀⠀⠘⢎⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣫⣾⣾⣢⢄⣈⡡⣺⣽⣿⣷⡷⡀⠉⢀⣀⠈⢁⣴⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣖⣢⣤⣒⡽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⣀⣤⡾⠛⠉⠉⠉⠉⠉⠉⠉⣉⢉⣟⡷⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡎⡏⣾⣁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠸⣿⡀⢻⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢦⡓⣄⣀⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠀⠀⢀⣠⡶⠂⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠶⡟⠥⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⣠⡶⠛⠙⢦⣄⠁⢾⠿⣿⣿⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢀⣤⣶⠟⠉⠀⠀⠀⠀⠘⠉⠉⠛⠉⠉⢙⠛⢿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣔⡝⣽⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⡀⢡⡈⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⣾⠠⡛⠒⠒⠀⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⢒⣶⢀⢧⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣵⠇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⣠⣄⣤⠠⣄⠀⣤⡀⠀⠀⣠⡶⠿⠋⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⡷⠈⠁⢯⣭⡷⠟⠉⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⢀⡠⠴⠻⢿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠠⡄⠐⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⢀⣠⡴⠿⠩⠅⠀⠀⠀⠀⠀⠐⣿⠀⢁⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣤⣶⠟⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣮⠜⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⣺⣿⠯⠥⠤⠬⠤⠤⠌⠒⠒⠒⠒⣲⣶⠿⠛⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡘⡀⠹⣄⠀⠀⠀⣀⣤⠾⠛⢉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡤⠈⡷⠖⠊⠉⠀⠠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠻⣯⠾⣷⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣤⡶⠟⠉⠈⠙⠶⠄⠳⠌⠛⠾⠟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣠⣾⡿⠉⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⡌⢻⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢮⢫⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⢤⡤⠴⠄⡷⡇⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢸⢿⠘⠛⠛⠛⠛⠛⠛⠛⠛⠐⠒⠒⠒⠒⠒⠒⣾⡰⡵⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⡦⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠬⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡰⠸⠃⠈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢔⠭⠁⠀⠂⢁⠀⢠⠑⠂⡀⠀⣴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠡⠤⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢐⠀⠇⠀⢉⣀⡀⠀⠀⠹⠃⠑⣤⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠆⠀⠀⠀⠼⠆⠁⠀⠀⠀⠙⢄⠌⣰⠀⠀⢡⠰⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⠀⠀⢀⡀⠁⢠⣐⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠁⡀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢢⡄⠀⠆⠀⠆⠀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⠠⠆⠢⢈⠀⠀⠀⠀⠈⠀⢂⣁
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⠉⠀⠋⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠔⠀⠐⡄⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡤⢤⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠇
⠀⠀⠀⠀⠀⡀⢀⡏⢀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠉⠉⡆⢸⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⠀⠂⠒⠐⠂⠐⣀⡀⢀⠀⡀
⠀⠀⠀⠸⡤⠀⠀⡡⡸⠂⠀⡀⠀⠤⠀⠤⠠⠀⠤⠀⠀⠀⠘⠂⠆⠐⠒⠃⠀⠀⠉⠈⠈⠈⠀⠠⠐⠸⠀⠙⠂⡇⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁