Trick or treating Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⣠⡄⠀⣀⣴⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣠⣤⣤⣤⣤⣀⣤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⡿⢲⡟⠉⢻⣆⢀⣀⣀⡀⢀⣤⣄⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣶⡇⠀⢸⣿⡏⠉⣉⠉⠻⣿⠷⢾⣿⠋⢉⡉⠛⣿⡏⠀⣿⠟⠉⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢉⣿⠃⠀⢸⣿⡇⠀⠛⢁⣠⣿⠀⢸⣿⠀⢸⣿⣶⣾⡇⠀⠉⠀⣼⣿⠃⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⠀⠸⣿⡇⠀⣧⡄⠹⣿⡀⢸⡿⡀⢘⣷⣈⢹⡇⠀⢠⡀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣿⣷⣶⣿⣷⣾⣿⠿⠃⣰⢲⡄⣰⢦⡄⠐⣦⣾⣿⣦⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⠉⠙⠛⠛⠛⠋⢉⣷⣦⠘⠀⠸⠴⠃⠻⠹⠄⠀⠀⠀⢹⡏⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣶⠄⠀⣶⣶⠛⠛⠛⠯⣴⡞⠒⠂⠐⢦⣶⠒⠛⣿⠉⠉⠁⠀⠉⠋⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⠀⠸⠇⠀⣿⡇⠀⠻⠿⣿⡇⢠⡄⢸⣿⣿⡇⠀⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⢰⡄⠙⣿⡇⠀⣶⣶⣿⠀⣈⣁⠀⢿⣿⡇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣸⣿⣶⢾⣷⣤⣬⣷⣶⣦⣴⣷⣶⣿⣿⣶⣾⣿⣦⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠙⠋⠉⠃⠀⠉⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠘⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠛⠻⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⡀⢀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⡀⠀⠆⢘⡛⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢢⠉⠀⠀⠀⣴⣯⠽⠶⣶⣷⠄⠀⡇⠀⠰⠐⠲⠦⠐⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⠀⠹⡷⠇⠀⠀⣠⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⢀⡺⠁⠀⠀⠘⠇⠀⠀⠀⡀⠀⠀⠂⠀⣰⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⣷⣦⣄⣀⣀⡼⣧⣠⣄⢀⣣⠀⠀⠀⠈⠛⠬⠁⢰⢻⡝⣌⢆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⣼⠄⡀⠘⣿⣿⣿⣿⣱⣿⣷⠀⢸⣿⣄⠀⠀⠐⠀⠀⢀⢮⠉⠙⠛⠧⠤⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠁⠀⠘⣿⣿⣿⣼⡁⡈⢑⣿⣿⣿⢷⣦⣰⡶⣶⣿⣦⠀⠀⠀⢀⣀⠀⠠⠀⢷
⠀⠀⠀⠀⠀⠐⠀⠛⣿⠀⠀⠀⠀⠀⢽⣿⣿⣿⡀⠉⠀⣿⣿⣧⠀⠸⣿⠆⠀⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡐⣀⠀⣿⠀⠀⠀⢀⡴⡬⣿⣿⣿⣤⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⣻⡿⡕⠦⠀⠠⠠
⠀⠀⠀⠀⠀⣿⡿⣦⣿⡹⠁⠁⠘⠓⢻⣿⣿⣿⡄⠀⠀⣿⣿⣿⠀⢀⣀⣀⠀⠠⢘⣏⡈⠀⠀⠈⠉⢁⡟⠳⠤⠄⡠⠺⠆⠉⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣾⣾⣧⣤⣼⣿⣿⣿⣷⡶⣶⡟⠁⠸⣿⣿⣿⣿⣿⣿⠀⢿⠭⠽⢯⡤⠾⠛⣷⡀⠀⢸⠁⠀⠈⣁⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠁⠀⠀⠀⠈⢀⢀⠀⢀⠈⢧⠀⠀⠙⣿⣿⣿⣛⡛⣷⣾⢀⢀⣠⣿⣳⣥⣾⣷⡀⠜⣉⡉⠉⣉⡉⢸⠇
⠀⠀⠀⠀⣠⠀⠀⠀⢤⣹⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠡⠀⠀⡛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣷⣻⡿⡀⡋⢱⡆⠉⠁⡀⠀⠰
⠀⠀⠀⣾⣀⠑⠰⢤⡬⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣷⣸⣿⣿⣿⣿⡇⠀⠀⠀⠘⢸⣽⣿⣽⡇⠀⠻⢒⡖⠚⢋⡁⠐⠃
⠀⠀⡜⠛⠿⠿⠶⢤⣤⡤⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣤⢶⡟⠛⠛⣫⠀⠀⠀⠀⠀⠈⠁
⠀⠀⡇⢀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣼⢁⣸⣶⠃
⠀⠀⡐⠿⣷⣦⣴⡆⠀⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⡄⠀⢀⡊⠁
⠀⠀⠁⠀⠀⠉⠹⠃⠀⠀⠀⣠⣧⣐⣢⣤⠇⠀⠀⣀⣀⣁⣘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡤⠤⢷⣤⡤⢄⠲⡄
⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡍⢿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡸⠨⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣄⡼⠃⠀⠀⠀⢀⡠⠶⣄⠀⠀⠀⠀⠀⠀⢠⠞⢁⠀⠈⠙⣆
⠀⢀⣀⡬⠿⢉⣼⡀⠀⠀⣠⣏⣀⡀⠘⡆⠀⠀⠀⠀⠀⢼⠀⢸⡈⠄⠀⡟⠀⠀⠀⠀⠀⣠⡀⣀⣤⠆⠀⣀⣀
⠀⠀⠉⠉⢹⠟⢡⠟⢓⣴⠵⠒⠛⢿⡓⣷⣠⠚⠉⢙⣲⣜⢦⡀⢀⣠⣼⠥⠒⡖⠒⡦⣤⠁⠉⠐⢧⣠⠞⠁⠈⢳
⠀⠀⠀⠀⢸⡴⠁⣠⠋⢀⠔⠚⠳⡄⠙⣿⣣⠴⠚⠉⠀⣨⢿⡹⣩⢾⠁⠀⢸⠁⠀⡇⠈⣷⠲⢤⡿⠍⠙⠲⢦⣼⡇
⠀⠀⠀⠀⢸⣦⣤⣧⣤⣾⣤⠶⠦⠽⠤⠾⠤⠤⠤⠴⠿⠶⠾⠿⠷⠿⠶⠖⠚⠒⠒⠒⠒⠛⠒⠛⠓⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⣀⡀⢀⣤⣤⠀⣴⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⠃⢹⠛⢷⡄⢸⡇⢸⡇⠈⠀⢹⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⣷⡞⠁⠀⡇⠈⠳⣄⠀⠸⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⢂⣀⣀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢻⡇⢹⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣸⠇⢸⠷⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠀⢈⡁⠀⢀⣀⣤⡄⢰⡆⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠶⢿⠛⠖⢿⢷⣤⠀⣿⡙⠃⠀⣹⢻⡆⠈⢹⡇⠁⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣤⠿⠃⢻⣀⡀⢀⠟⠉⣻⠀⠀⡇⠀⠰⠆⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠈⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠉⠈⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⡇⠀⣿⢷⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡧⠀⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣷⠀⢸⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡤
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣟⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⢛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⡿⠟⠋⠛⠛⠛⠛⠻⠿⢿⣿⠿⠛⠁⠀⠀⠀⠈⠙⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣀⣀⣤⣄⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠿⣿⣤⣤⡄⢙⣋⠁⣼⢿⣷⢠⣶⡆⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⡄⣿⣧⣾⠇⢸⣿⢠⡟⠈⠁⣼⣿⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢸⣿⢻⣧⢸⣿⢸⣇⣶⢦⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣈⡛⢈⣭⡘⢻⣬⣟⠋⠸⠿⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠧⣿⣽⡗⢸⣿⣏⠀⢿⣷⣶⣾⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⣿⣏⠀⣤⣬⡍⢁⣬⣥⣭⢠⣦⠀⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢹⣿⣇⠘⣿⠶⠀⣿⣿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠸⡷⠙⡷⠿⠾⠾⠇⠸⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠉⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣸⡿⢶⣤⣥⣤⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠉⠀⠚⠉⠫⠉⠳⣶⠤⣀⠀⠀⠙⠻⣦⣠⡿⠀⠀⠀⠉⠉⠁⣀⣴⢿⡄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡻⠁⠀⠀⠀⠀⠒⠚⠂⠀⠀⠓⠈⠓⣆⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣿
⠀⠀⠐⠛⣯⡀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⠀⠀⠀⢀⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠶⠶⢶⡿
⠀⠀⠀⠰⣿⠀⠀⠀⠀⣀⠀⠀⠙⣆⠀⢠⡇⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⣀⠀⠀⣾⣿⣿⣦⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⣀⣿⣧⠀⠀⢰⣿⡆⠀⠀⢘⠀⢸⡏⠀⠀⠀⢻⣿⣿⡟⠀⠀⠉⠹⠀⠀⠙⠿⠿⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⣤⡀⢸⣿⠉⠉⠀⠀⠀⠀⢀⣶⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣏⠉⠙⣧⣤⣤⣴⣤⣶⣾⠇⢀⡊⠀⢸⡀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⣠⣠⡄⣼
⠀⠘⠧⣄⠈⠛⠙⠋⠉⠁⠀⡠⠊⠀⠀⠈⢧⠈⠱⠾⠛⢦⠿⣤⠗⣤⠟⢿⡟⢦⠏⠻⠁⡉⣰⠃⠀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤
⠀⠀⠀⠈⠉⠒⠒⢶⡖⠂⠁⠀⠀⠀⠀⠀⠈⢳⡀⢦⡀⠀⡀⠀⠀⠀⠤⢬⠀⠀⢠⠀⣼⡱⠃⠀⠀⣿⠟⢷⣄⠀⣴⣿⣛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢷⣄⠱⣄⣄⠀⣀⡠⠀⣠⣯⢾⡉⠀⠀⠀⢼⡏⠀⠀⢹⣿⡏⢠⡏⢻⣿⣴⠶
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢉⣳⣿⣿⣷⡷⣷⠾⢿⡗⠈⠙⠢⣄⠀⠈⣿⠀⣠⣾⢿⡇⠸⠃⡿⢧⣿⡓
⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣠⢞⣴⠟⢁⡞⠁⢠⡿⣧⠀⠙⢦⡀⠀⠈⢣⡘⠿⠟⠋⠀⠈⢻⣦⡀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡠⠶⢅⡀⠀⠁⣸⡇⣰⠏⠀⠀⢈⡇⢹⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣤
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣥⡕⠲⣤⡏⢰⡀⠀⠘⠶⠀⣿⠁⠉⠀⠀⠀⠈⠁⢸⡇⠀⠀⠀⣇⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡷⠤⣿⠀⠈⣿⠢⡱⡄⠀⣰⡞⠃⡞⠛⠛⢻⠂⡷⠀⠘⣷⠀⠀⠀⡏⠙⠓⠒⠾⢦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⡷⠶⣿⠀⠀⢸⡆⢹⣿⣦⠈⠀⠀⠙⠛⠛⠋⠀⡇⠀⠀⠹⡷⠀⠀⢷⠀⠀⣀⣠⡄⢉
⠀⠀⠀⠀⠀⠀⠘⠿⣷⢴⡿⠀⠀⣸⠇⢸⣸⠎⢣⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡴⢿⡄⢸⠟⠋⠉⠁⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣀⣴⣿⡦⠊⣿⠀⠀⡆⠀⠀⠀⠀⠀⠘⡄⢠⡴⠋⠀⢠⣿⣏⡤⠖⠋⠈⠀⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠉⠀⠀⠀⠀⠀⡏⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠘⢷⣠⠾⠋⢼⠉⠀⣄⣠⣤⣶⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠨⠧⣀⡈⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⢀⣀⣉⣒⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠉⠔⠚⣩⡽⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿⢺⡏⠀⠑⠋⣽⡿⢟⠿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡆⠀⠀⠀⠀⠀⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⢠⡞⡇⣠⠔⠊⠉⡁⠀⢷⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢷⠀⠀⠀⠀⠀⡠⢿⠀⢹⣆⠀⠀⠀⠀⠀⣸⢇⡟⠁⡠⠀⠀⠃⠀⢸⡇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡄⠀⠀⢠⠞⢡⠎⠀⡇⠈⠣⠀⠀⠀⡰⢁⡞⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠋⠀⣿⠀⠀⢇⠀⠀⠀⠀⠀⡀⣚⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⣀⠀⠀⢀⡴⠃⠀⠀⠈⣆⣀⣧⢤⣾⣡⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⢉⠜⠉⠙⡇⠹⡇⠀⠀⢀⠞⡩⠋⠀⠀⢹⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⡋⠠⠄⣀⠘⠀⡽⠀⠀⡎⠀⡡⠂⠀⠰⡞⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⢄⣎⠀⠀⠀⢸⣤⠞⠁⠀⠀⠘⠶⣅⠀⢀⣸⠁⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠦⢄⣀⣀⣑⣄⡀⠀⠀⣀⡀⠠⠤⠄⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣦⣄⠀⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⢦⣰⢃⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡿⠾⠿⠟⠻⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⠿⠿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠀⣼⣿⠃⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢰⣿⠇⠰⣿⣆⣤⡄⢠⣶⠆⢀⣴⠾⢷⠀⣼⡿⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⠀⠀⣿⣿⠀⣠⠏⣽⡟⠀⣿⡏⢠⣾⡏⠀⢈⣴⣿⠑⢻⣷⠀⡀⠀⢀⣤⣤⣤⡀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣿⣛⣷⡄⣿⣿⡀⠀⠀⢿⡷⠞⠿⠟⠋⠿⣷⡶⠟⠹⣿⠄⠘⠿⠛⠁⣰⣿⣿⣿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⣛⣛⣫⡿⠃⠈⠻⢿⣷⣶⡶⠶⠆⠀⠀⢀⣤⢤⡀⢤⣀⡀⠀⢤⣤⣤⣄⠛⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣀⣀⣀⣀⠀⣾⠁⢺⡦⠞⣿⢁⡆⠀⠈⠛⢿⣿⣶⣤⣦⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠉⠀⠀⣸⣿⠏⠉⠙⠛⠛⠻⠟⠛⠉⠀⠘⠛⠛⠁⠀⠛⠋⠀⢀⣀⡀⠀⣿⣿⡏⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣿⡿⠀⢰⣷⡆⣀⡀⠀⢀⣤⣶⠶⣦⠀⠀⣴⣿⠟⠻⣿⣿⠁⠀⣿⣿⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢈⡿⢷⣿⠏⢀⣾⣿⠁⣀⡾⠁⣸⣿⠃⠀⢠⣿⡟⠀⣼⣿⣿⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠠⠞⠀⣾⡟⠀⣸⣿⣟⠋⠉⣀⣴⢿⣿⣦⣤⡿⣿⣷⣾⠛⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠿⣿⠟⠉⠻⣿⣿⡿⠋⠁⠀⠉⠉⠉⠀⠈⠉⠀⠀⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⠿⠟⣛⠛⠩⠍⣉⠛⠻⢿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⡜⠉⣯⡀⠀⠀⠀⠀⠈⠐⢤⣀⠉⠂⢄⢈⡏⠙⣄⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣴⣿⡿⠉⠛⠛⣎⠑⠢⢄⡀⠀⠀⠀⠈⠓⠄⡀⠉⠺⢇⡈⠛⢷⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡟⠀⠀⡰⠀⠈⡷⣄⠀⠈⠁⠒⠤⡀⡀⠀⠈⠉⠐⠆⢀⣥⠶⢇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡟⠀⢀⠔⠁⢀⠎⠀⠈⠓⠅⡒⠀⠤⠀⠀⠈⠩⠤⠲⠟⣁⣤⣂⡻⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠟⠋⠉⠛⠛⠿⢿⡇⠴⣊⡠⠒⣁⠤⠊⠁⠀⠀⠀⠀⠂⠀⠙⠒⠒⠒⠂⠒⠒⠲⠍⣈⣁⣈⣽⠂⠀⠿⠟⠛⠉⠉⠛⠿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠇⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⢰
⡇⠀⠀⠀⠀⠀⠀⡠⠁⠀⡜⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠱⠀⠀⢆
⣿⠀⠀⠀⢰⠐⠊⠀⢀⡜⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠣⡀⠀⠑⠴⡄⠀⠀⢸
⣿⣧⠀⠀⠀⠑⠀⠊⠁⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⠂⠐⠐⠁⠀⢠⣿
⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠠⣭⣉⠀⠒⠒⠒⠂⢈⣉⡧⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠀⠀⢠⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠐⣄⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣡⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠀⠈⠑⠦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢠⠴⠚⠈⠱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢲⠆⡀⠀⠀⠀⢸⣈⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠈⠺⣁⡖⣰⣆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠡⡇⠀⠀⠀⢠⠐⡶⣍⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠈⠁⢹⣯⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⢶⡃⡐⢂⣰⣈⡗⠉⠐⣝⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⣧⡜⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢑⣾⣣⢊⣽⣁⡝⠃⣺⠟⢻⡟⠟⢡⣿⣿⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠉⠀⠀⠈⡨⢳⠀⠀⠀⠀⠀⢰⠒⡟⠛⠋⠉⠛⠉⠉⠑⠉⠉⠁⠋⠉⠛⠋⠙⠛⠻⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠁⠀⡀⠘⠁⠸⡆⠀⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣷⣄⣀⢀⣀⣠⣤⣶⣿⣿⣿⣾⣷⣿⠙⠲⠖⠁⠈⣦⣤⣤⠊⠀⢰⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⢀⠛⡄⠀⢠⠛⡀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠁⠀⢀⡀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠘⡦⣀⠀⠀⠀⠀⠀⢀⠔⡏⠁⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠤⠄⠤⢸⣿⣿⣿⣇⣴⠀⢠⠀⠀⠀⠀⠘⢮⣧⠆⠀⢤⣼⡡⠊⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣀⣀⠀⠹⣿⡿⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣧⠴⠶⠶⠶⡃⣹⠐⡷⢾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⡀⠀⠀⠀⢈⡡⣟⠄⡉⠻⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠠⢤⡜⠉⠁⠀⠀⠀⠀⠀⠀⠤⡠⠊⠁⠀⢀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⣀⣀⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢥⣈⠖⣄⠀⢀
⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⡈⠑⢶⠉
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡼⠁⠀⠀⠀⠀⢀⠠⠐⡺⠹⣆⠀⠳⡀
⢰⡇⢀⣠⡴⣶⣶⣶⣶⣶⣶⣤⣄⡀⢸⣠⢏⣤⠶⠶⠒⠶⠛⠛⠒⠂⠐⣦⣜⣼⠁⠀⡀⢤⠒⠈⠀⠀⠀⠀⠀⠙⠆⠀⢧
⡜⣴⣿⠿⣵⣦⠙⠃⠉⠁⣽⣿⢿⣿⣮⣿⢿⡇⠀⣶⡆⠀⠀⠀⢠⣶⡄⠸⡿⣿⠀⢨⠁⢰⣶⠀⠀⠀⠀⣰⣦⠀⠀⠀⣸
⡟⢿⡿⠀⠙⠋⠀⠀⠀⠀⠙⠋⠈⢿⠿⣻⢆⡇⠀⠛⠃⠀⠀⡀⠈⠛⠁⢀⣠⢿⡀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠋⠀⢠⢀⡏
⢻⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⢀⡏⠀⠹⣦⣀⣀⡀⠀⠀⣀⣀⡤⠞⠀⠈⠃⠿⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢏⠘⡀
⠀⠳⡀⣸⠭⠽⣟⣛⣛⠋⠩⠩⣇⢀⠞⠀⠀⠀⡸⠑⢨⠉⠉⠉⠉⠐⠙⡄⠐⡴⠀⢀⠀⣾⡉⠉⠉⠉⠉⢉⣹⠀⠠⣠⠇
⠀⠀⢙⡟⢠⠀⠀⠀⠀⠀⠀⡄⠙⡏⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⡀⢱⠀⠁⢀⢾⡞⠀⡈⠉⢰⡖⠈⢁⠈⢆⠘⡹
⠀⠀⡼⢠⡾⠀⠀⠀⠀⠀⠔⡿⡤⢻⡀⠀⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⢃⢨⡇⠀⠀⣜⠁⣾⡅⠀⢨⡇⠀⢸⣆⠘⣾⠃⠰
⠀⠀⠙⠚⡇⠀⠀⠀⢠⢋⡉⠉⢉⢺⢁⠁⠀⠘⢾⠁⠀⠀⠀⠀⠀⠀⠸⠾⠃⠀⠐⣽⠛⢹⠣⢤⠥⠥⠠⢿⣭⣿⣿⣦⡀
⠀⠀⠀⢠⠇⡀⠀⠀⢼⢨⣁⢆⣉⣸⠈⢀⡂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠉⠢⣼⠀⠀⡿⡇⠀⢸⠁⡆⠀⢰⠸
⠀⠀⠀⠸⢅⣀⣀⣀⣈⣓⣿⡿⠟⠋⠀⠈⠉⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠉⠀⠀⠀⢸⡀⢀⡇⣇⠀⣸⣔⠦⠭⠴⣺
⠀⠀⠀⠀⢰⣃⣉⡿⢹⣉⣘⡇⠀⠀⠀⠀⠀⠀⠉⣟⣛⣑⠖⢶⣘⣛⡯⠁⠀⠀⠀⠀⠀⣞⣈⣀⠇⢟⣈⣘⡏⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠩⡋⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠙⠋⠄⣤⠤⠀⠀⠀⣀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢀⣤⡀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣈⡛⠛⠣⠀⠀⠀⣻⠀⢠⡤⠤⢭⢠⡖⠆⢸⡰⠂⠀⠀⢰⣿⣿⠁⠸⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⢿⣿⣷⠀⠀⠀⠀⠛⠀⠘⠃⠀⠚⠈⠓⢆⠈⠘⠋⠀⠐⠈⠛⠃⠆⠆⠙⠋⠀⠄
⠀⠀⠀⠀⢀⠀⠻⠿⢁⠤⡜⠿⠟⠀⠀⠀⠀⠀⠀⠰⢀⡤⣄⢀⣤⡄⠀⠀⠀⠀⠀⠁⠄⣀⣀⣀⡀⠄
⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠋⠀⠘⠦⠟⠈⠇⠀⠀⠀⠀⠀⢰⣶⣦⣤⣬⣤⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠚⠋⠁⠀⠀⠈⢹⠉⠁⣀⡀⠀⣀⠀⠠⣤⡀⣴⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡆⠀⡏⠉⠸⣏⡅⠶⠨⠇⠸⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠙⣿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣇⣀⣀⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⣿⣿⡇
⠀⠀⣀⣤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠃⠀⠀⠙⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠋⠙⠛⠛⠛⠛⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⢤⣀⠀⠀⢀⡠⠖⠋⠉⠙⠲⢤⣀⡀⠀⣀⣠⠴⠚⠛⠛⠲⢄⡀⠀⠀⣀⡤⠤⣄⣤⣄
⠀⠀⢀⡴⠛⠓⠒⠚⠁⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣁⣠⠞⠹⣄⠔
⢶⢖⠋⠀⠀⢀⠔⠓⠢⣀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⢤⡀⠀⠀⠀⡠⠛⢦⡴⠻
⠘⡆⠉⠢⠔⠁⠀⠀⠀⠀⠑⠀⡀⠀⢀⡔⠉⠀⠀⠀⠀⠑⠤⣀⣠⠔⠁⠀⠀⠀⠙⢦⣀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⣀⡀⢀⣀⣠⠤⠤⠤⡀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢻⠀⠀⠀⠀⠀⢸⣉⠁⢀⣸⠡⡄⡹⢲⢐⠐⠃⢎⡥⠼⠃⠀⣇⡴⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⡄⡏⠹⢀⡘⠧⡼⠸⠤⡀⡘⠂⢤⡄⢠⡀⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣃⡇⠢⠼⠙⠶⠃⠒⠒⠂⠑⠦⠼⣇⡇⠘⢄⡸⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣸⠀⣧⣝⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠴⠂⠀⠀⠒⠲⡤⠤⢄⢀⣀⣀⠀⢀⡀⢀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⠔⢲⢀⡀⣀⠇⠆⢀⡽⢰⠒⢃⠁⡘⣾⣀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢈⠀⠀⢠⡄⠛⢾⢠⠕⡸⢀⡅⢰⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠤⠸⠀⠱⠞⠈⠖⠻⢄⣉⡵⠞⠐⠴⠀⣄⠇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠄⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⣰⡆⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢉⡛⢦
⠀⠀⠀⠀⢲⣼⠻⢱⠁⠀⠀⠀⢀⠞⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡏⠀⣾⠐⠄⠘⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠲⠿⠭⣭⣴⠟⢢⣄⡀⡠⢛⣛⣶⣦⣤⣸⡄⠀⣠⠤⢤⣄⠈⣇⠠⡘⠒⠁⢀⡼⢀⣀⣀⣀⡀⠀⡸⠻⠴⢚⡟⠁⢀⠴⠒⢦⡀
⠀⠀⠀⠀⠀⣼⢁⡴⠋⢀⡽⠛⠉⣉⡉⠙⢶⣼⣧⠞⠀⣀⣠⠼⠛⣎⣳⣤⡤⢴⡿⠛⠉⢹⠃⠈⡟⠻⣇⡀⠀⠈⣳⣶⣅⣀⠀⠀⢻
⠀⠀⠀⠀⠀⣿⠎⠀⣰⠋⠀⡴⠋⠉⠙⢧⠀⢹⣿⠴⠚⠉⠀⢀⣠⠜⢧⣞⡴⢻⠁⠀⠀⡿⠀⠀⡇⠀⢹⡏⠛⣲⡟⠃⠀⠉⠛⢶⣾⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣦⣤⣿⡤⠴⠧⠴⠿⠷⠾⠶⠶⠷⠶⠶⠶⠶⠿⠶⠒⠚⠛⠓⠛⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⣠⡄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣶⠶⠔⢿⣷⣤⡀⠈⣿⡃⣾⠏⠹⠇⢸⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣀⣹⡿⠀⢹⡇⠹⣇⠀⠀⠀⡟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⠛⢧⡀⠀⠸⠀⠀⠙⠓⠂⠀⠃⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢁⣤⣤⣄⠀⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢻⡇⢸⡏⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣼⠃⢸⡷⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠓⠀⠀⢀⣀⣀⡀⠠⣤⡄⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣦⡰⣶⣦⣄⠀⢰⡿⠿⠧⠀⢰⣿⣦⠀⠛⢻⡏⠛⠀⢹⠇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⢹⠉⢻⣷⠸⡟⠁⠀⠀⣸⠷⠻⡇⠀⠘⡇⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠿⣏⠁⠀⠻⠶⠂⠀⠋⠀⠰⠇⠀⠀⠇⠀⠀⠉⠁⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⡟
⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉⣛⣛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⢀⣾⠛⠉⢀⡀⠉⠛⢷⣄
⠀⠀⠀⠀⣾⠃⢀⣾⠟⠛⢷⡄⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣿⡄⠈⠿⡿⠇⢨⣿⠀⢸⠇⠀⠀⢀⡴⠶⠛⠛⠛⠶⢦⣄⠀⠀⠀⠀⡀⠈⠀⠀⢠⣴⣦
⠀⠀⠀⠀⠘⣿⣦⣤⣤⣴⣿⠏⠠⠏⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣿⣾⣿⡅
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠄⠀⠀⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡀⠀⣀⣠⣴⣦⠀⠀⠀⢀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣄⣴⣿⡿⡫⢻⣿⣿⡋⠉⢹⣉⢀⣸⣯⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢰⣿⡍⢩⣏⣟⢹⡟⣫⣹⡇⠾⢯⣽⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⢸⡿⡇⢸⣿⡯⢸⣇⠻⢿⡇⢰⡌⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣿⣷⣶⡿⣻⢿⢿⢻⣿⣷⣾⣿⣬⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠙⢿⣿⣿⣷⣭⣿⢸⣿⣿⣿⡟⢘⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢰⣿⣷⠈⣷⣸⢟⢻⣧⣷⠸⣿⢸⡿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣜⠏⣿⠀⣿⡇⢸⣾⡏⢷⠀⣿⣬⣷⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣛⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⡿⠗⠂⠀⠀⠀⠀⢲⣶⣦⡄⠀⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠈⣿⡇⠀⣤⣤⣤⣤⣄⢠⣄⣀⡄⢀⣴⣶⣷⣦⡈⣿⣿⡇⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠉⢹⣿⡎⣿⣿⠁⣾⡿⠋⢹⣿⣿⢸⣿⣧⣿⡿⠁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⢰⣿⡇⠀⣿⣿⣶⣿⡿⠀⢹⣿⠀⣿⡇⠀⣚⠉⠁⠈⣿⣿⣿⡅⠀⠛⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⢸⣿⡇⠀⣿⣿⢹⣷⡀⠀⢸⣿⡀⣿⣇⠀⠘⣿⣿⢁⣿⣇⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⢠⣿⣿⠌⣿⣿⣄⠸⣿⣧⠘⢿⣷⣾⡿⠏⣸⣿⣿⡀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠈⠁⠀⠀⠀⢀⠠⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣶⣿⣷⡀⠀⠘⠤⠔⠙⠺⠀⠀⠀⣼⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⣿⡏⠉⣩⣭⣁⡀⠀⢠⣤⣤⣶⣶⡇⠀⣿⣿⣿⡆⠿⠛⠉⣿⡏⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇⠀⣿⡟⠛⣿⡆⢸⣿⠉⠉⠉⠃⢀⣿⡿⣿⣧⠀⠀⠀⢻⡇⠀⣤⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⣿⡇⠀⣿⣧⣠⣿⠇⢸⣿⣤⣶⡏⠀⢸⣿⣇⣿⣿⡀⠀⠀⣿⣧⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢰⣿⡇⠀⣿⣿⣿⣏⠀⠘⣿⡏⠉⠁⠀⣼⣿⡿⢿⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⣿⣿⡸⡿⣷⡄⣿⣧⣴⣶⡆⣿⣿⡇⢸⣿⣿⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠁⠀⠈⠀⠀⠀⠀⠈⠉⠙⠛⠃⠀⠙⠇⠀⠀⠉⠁⠈⠋⠉⠁

⣿⣿⠿⣟⠛⠛⠛⣟⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣻⠛⠛⠛⣻⠿⣿
⣿⣧⡴⣦⠀⠠⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠄⢀⣀⣀⡀⠀⠀⠀⠈⢤⠄⠀⣴⢦⣼
⣿⣿⣬⡵⠶⣄⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡴⠾⠻⠯⡭⠭⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢮⣥⣿
⣿⠛⠇⠀⠤⠞⠀⢸⡿⠿⠿⣿⣿⣿⠟⠛⠉⠁⠀⠄⠀⠀⠀⢠⠒⠶⣤⣤⠌⠁⠀⠀⠀⠀⠀⠀⠳⠤⠆⠨⠛
⣿⣰⣋⣁⠀⠀⠀⠈⠀⠀⠀⢸⢿⡏⠈⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣆
⣿⠟⢉⣸⠇⠀⠀⠀⠀⠀⠀⢸⣟⡇⠂⡘⠀⠀⣴⣶⠀⢀⣰⣶⣶⡀⡟⣹⠀⣸⣦⣀⠀⠀⠀⠀⠀⠸⣇⡉⠻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇⠀⠀⠀⠀⢬⣤⡴⣿⡟⠀⡟⠁⡇⣣⣼⡿⠋⠁⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇⠀⣿⡿⢿⣶⡿⡇⢿⣇⠀⠀⡤⣧⣽⣧⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡟⡇⠠⠟⣧⡇⠈⠿⣷⠿⢣⣿⡏⠙⠻⣿⣦⡀⠈⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠖⣷⡇⠀⣠⣿⣧⣤⠆⠀⠰⠊⠙⠷⢤⣀⣀⠉⠙⠛⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⡴⠛⠓⠒⠅⠀⢀⣠⢔⡂⢄⣀⣠⣶⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣤⣴⣶⣶⣾⡁⠹⣶⣶⢛⠁⣟⡟⣖⡎⣁⢺⣿⣿⣿⠇
⣿⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⣿⣿⠛⠉⠙⡇⢠⣿⣿⣷⡦⠼⠷⣋⢦⣊⠞⠻⠿⠟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢤⣄⣠⠉⠉⠉⣁⣀⠐⠒⠤⢤⣀⣀⣰⣤⣤⡤⢤⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⢻⠿⣷⢰⣿⠟⣿⡇⠠⠖⢷⣆⠉⢻⠋⠉⠀⠀⠁
⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⢸⢸⠀⠁⡟⢹⠞⠋⡀⢈⡤⢻⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⠹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⢧⣸⣀⣀⡟⢸⣅⣸⣇⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏
⣿⣄⡻⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣀⡉⠉⠉⠁⠀⠉⠛⠉⠀⠀⠉⠁⠁⠐⠛⠻⠦⠆⠀⠀⠀⠀⠀⠀⠠⢟⣠
⣿⢉⢻⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀⣀⢀⢀⢀⠀⣀⢀⠀⠀⠀⢀⡀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡉
⣿⢏⠙⣧⣀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣄⣸⠏⡹
⣿⣶⣭⣦⣭⣭⣥⣶⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣴⣶⣬⣭⣭⣵⣯⣶

⠀⠀⠀⠀⠀⠀⢀⠔⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠔⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⡰⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣾⠆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠜⠀⢁⠜⠀⠀⠀⢠⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣷⣶⣶⣤⣄⢸⠆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢨⣿⠀⠁⠀⠰⠆⠀⠀⠀⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⡏⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⢸⣿⠠⣶⡶⢰⡆⣠⡶⠀⣿⠾⠂⠀⢰⠏⣸⠇⢸⡿⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡀⢀⠀⠀⠀⠘⣿⠀⣿⠀⢸⡇⣿⣀⡀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⣀⡀⠁⠈⠉⠁⠁⠈⠁⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠑⠄⠀⠀⠀⠀⠀⣰⡟⠛⠻⣧⣤⣤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⠀⠀⠀⢀⣤⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠆⠀⠀⠀⠀⠀⠀⠻⣧⣀⣤⡿⢿⡏⠀⠀⠀⠀⠀⢀⢶⡴⠿⠯⣵⡄⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠉⠙⠉⠀⠈⠀⠀⢠⣦⠀⠀⠐⠋⢀⣂⡶⡏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠘⢻⣿⠛⠀⠀⢀⢢⠄⠼⡁
⠀⠀⠀⣤⠀⠀⠀⢠⡔⡺⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⣤⢀⣤⣤⡀⣠⣤⣴⢸⣿⠀⠀⠀⡸⣭⠀⠘⣣
⠀⠀⠀⠉⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠁⣏⠾⣋⡀⣯⣠⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣼⣿⣴⣾⡆⠀⠙⠁⠉⠀⠈⠉⠉⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⢿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⣠
⠀⠀⢠⣦⢰⣻⡆⣴⡄⢸⢿⡄⠀⠀⠀⢰⣿⠀⠀⠲⣾⣷⠂
⠀⠀⢸⣿⣼⣿⣠⣷⣧⣼⣿⠇⠀⠀⠀⠘⣿⣄⠀⠘⠉⠙⠂
⠀⠀⠀⠀⠹⠹⠿⠉⠿⠿⠹⠃⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠄

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠆⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠙⠁⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠀⠁⠂
⠀⠀⠀⠀⣀⣀⣀⠀⣀⣴⣷⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠈⠁⠀⠀⠐
⠀⠀⠐⢻⣍⣁⣀⣀⣀⣀⣈⣉⣭⠟⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣜⡛⠻⣟⣂⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⡿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠁⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠘⠃⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⢼⣟⣿⣻⡆
⠀⠀⠀⠸⠋⠉⠉⠉⠉⠉⠉⠉⠹⠂⠀⠀⢀⣤⣤⣤⣤⣿⣤⣤⣤⣀⡀⠀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠁⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣷⡀⠀⢰⣧⣾⣇⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣶⣾⢿⣷⣶⣿⣿⣿⡇⠀⠘⣿⣾⣿⡿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⠞
⠀⠀⠀⢶⣾⣿⡶⢷⣾⣿⣷⡶⠀⠀⠀⢿⣿⣿⣯⡉⠛⠉⠛⢉⣽⣿⣿⡇⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠺⠆⠀⢀⠤⢤⣀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣿⣾⣿⣿⠿⠟⠁⠀⠀⢀⡤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⢻⣿⡟
⠀⠀⠐⠀⠀⠻⣿⣿⡏⠀⠀⢀⠀⠀⢠⡀⠀⠀⠉⠛⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢰⡟⠉⣿⠀⠸⢻⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠁⠘⠁⠀⠀⠈
⠀⠀⢀⣀⡀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠼⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠰⠿⣿⡛⠃⠀⢿⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢹⣿⣿⣿⡟⠁⠀⠀⠙⠿⠟⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿
⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠀⣴⣿⣿⣿⡆⠸⣿⣿⠟⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⢠⣾⠟⣹⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⢻⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⣆⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣦⣉⣼⠃
⠀⠀⢠⣧⡄⠀⠀⠀⠀⠀⣽⣿⣆⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠐⢻⠷⠂⠀⠀⠈⠉⢉⠉⠉⠻⠅⠀⢀⣀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⢠⣭⡄⠀⢀⣀⣠⣤⣭⣭⣥⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠛⠦⣤⣤⠀⠀⠀⠁
⠀⠀⢸⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣠⣤⣶⡤⠄⠀⠀⠀⢠⣾⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠁⠀⢀⣼⣿⡿⠀⠀⣎⠺⠟⣹⣿⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠹⢿⣿⣿⠟⠀⠀⠉⠈⠛⠙⠻⠻⠿⠉⠀⠀⠀⠀⣤⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠿⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠟⠋⣁⣤⣴⣶⣾⣿⣿⣿⣶⣶⣤⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠗⠉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠊⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿
⣿⣿⠿⠿⢿⠿⠿⡿⠿⠥⠾⠋⠉⠙⠻⠿⠛⠉⠀⠈⠙⠻⠿⠛⠉⠀⠈⠉⠛⠿⠿⠟⠋⠉⠉⠛⠿⣿⠿⠛⠋⠻⢿⣧⣹⠿⠿⣿⣿
⣿⣿⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⢀⢿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠶⠒⠃⠀⢠⡀⠀⠘⠳⠤⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⣸⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠃⠀⠀⠀⠀⠀⢸⣿
⣿⡟⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⡴⠁⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⢀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⢸⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡱⠀⣠⠤⢀⣀⣀⡠⣄⠀⠐⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣗⠦⠇⠀⠀⠀⠀⠀⠘⠦⠖⢃⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⢸⠀⠀⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠁⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠀⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣷⣼⣄⡀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣷⣾⣤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⡤⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣼⠀⠗⢀⢐⡦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⣛⡤⢄⣠⠂⡄⠀⠸⣨⠞⠃⠉⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡔⠉⠀⠀⠀⠀⢰⡅⠘⠋⠉⠀⠢⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢁⡀⡀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠁⠀⣀⡤⠖⢉⠱⣄⡇⠀⠀⠀⠀⣠⢟⠀⠀⢁⣢⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠘⠛⠒⠶⠾⠤⣬⣑⣄⠀⢀⣴⡧⠾⠶⠛⠉⠉⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡄⠀⠀⠀⠻⣌⠱⡆⠺⠆⠀⠀⠀⢀⣈⠉⣡⠞⠁⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠸⡀⠀⠀⠀⠈⠳⣅⡉⠀⠀⢀⡟⠋⣿⢿⠃⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣑⡀⠀⠀⠀⠀⢨⠋⠉⠉⠉⠁⠀⢠⠎⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣭⣶⣤⣤⣤⣾⣤⣄⣀⣠⣤⣶⣷⣶⣶⣾⣥⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠿⠛⠛⠂⠀⠀⠀⠀⠀⢿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢩⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⡀⢸⣮⣧⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢻⣇⢀⡀⠀⣠⠀⢰⡎⠀⡘⣩⠻⠀⣿⣠⠃⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⠷⡴⠋⠀⢸⡃⠀⣷⠈⠁⣠⣿⣧⡤⠖⠋⠁
⠀⠀⠀⠀⢠⣦⣤⠶⠋⠙⢦⣸⠀⠀⣧⠀⢀⠻⣧⠄⠹⠶⠞⠁⠉⠀⠀⠀⠀⠀⣰⠚⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⠀⠀⠘⠛⠁⠀⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠚⠛⢉⢀⡄⠀⠀⡴⠀⠀⠀⠀⠙⠛⠃⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⡄⠀⠓⠀⠈⠉⠀⠀⢸⠃⠀⠀⢀⡀⣠⠖⠒⠉
⠀⠀⠀⠀⠀⢀⠴⠛⠉⣡⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⠶⢦⣾⣠⠴⠚⠉⠀⢿⣦⡄
⠀⠀⠀⠀⠐⠁⠀⠀⠀⣿⡄⣤⣀⣰⠆⠀⣠⡀⢀⠖⠻⣿⠛⠛⡏⠻⡆⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡐⠀⠀⣀⣀⠀⢸⡇⡏⣹⠁⢀⡎⢹⠇⡏⠀⢀⣿⠀⣀⣷⣀⠇⠀⠀⠀⠘⠋
⠀⠀⠀⠻⠟⠋⠁⠈⠣⢸⠋⠀⣿⡀⢸⣧⣋⣨⢿⡶⠊⠉⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠈⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣷⣶⣶⣾⣷⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠛⠋⠉⠉⠛⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡉⠉⠉⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⢀⣴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣮⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⢤⣤⣽⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠞⠿⠛⠛⠻⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡾⠟⠋⣁⡤⠴⠒⠚⠉⠉⠉⠒⠲⠦⣄⡉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣺⠗⠉⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⡞⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⣌⢣⡀
⠀⢀⠤⠤⣤⠤⠤⡶⠿⠥⠾⠋⠉⠓⠦⠴⠚⠉⠀⠈⠙⠢⠤⠚⠉⠀⠈⠙⠒⠤⠤⠖⠚⠉⠉⠓⠦⣤⠤⠒⠛⠲⢬⣣⣱⠤⠤⡄
⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⢸⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢀⢿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠶⠒⠃⠀⢠⡀⠀⠘⠳⠤⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠃⠀⠀⠀⠀⠀⢸
⠀⡜⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⡴⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡱⠀⣠⠤⢀⣀⣀⡠⣄⠀⠐⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣗⠦⠇⠀⠀⠀⠀⠀⠘⠦⠖⢃⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡇⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠇⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢸⠀⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠳⠼⣄⡀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠉⠓⠺⢤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣆⡀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣦⠀⠀⣶⣾⢻⣿⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⢉⣹⣏⢁⣍⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣽⣻⣷⡿⠀⠈⢻⣿⣾⣟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣷⢻⣽⣿⣷⡿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡈⣉⣓⠀⠀⢘⣩⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣮⣿⣿⣿⣟⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣶⣯⣻⡆⠀⠾⣵⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠚⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠿⠟⠚⠁⠀⢻⣽⠿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣿⣿⣿⣿⡞⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠿⠿⠇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢘⣟⣼⠟⠳⢦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⠛⠋⠀⠀⣨⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣻⣷⡄⠀⠀⠀⢈⣽⣿⣟
⠀⠀⠀⠀⠀⠀⠀⣿⢦⣠⠾⡇⣿⣿⣿⣿⣟⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⢿⣳⠃⠀⠀⠀⠈⣿⣭⣟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢁⡤⢅⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣯⡄⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠘⢧⣼⠉⢽⣿⣯⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠀⠀⠀⠐⠻⣿⣯⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣸⠀⠀⠉⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠛⠀⠀⠀⠈⠋⠉⠈⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢀⠀⠠⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⡀⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠘⠀⢀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⣀
⠀⠀⠀⠡⠠⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⢨⠀⠀⣠⢀⡀⠂⡀⡀⠀⠀⠀⠀⠚⢀⠔⠆⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠈⢀⠠⠙⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠂⠀⠀⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⡎⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠄⢐⠄⠁⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⠸⠀⠀⠀⠀⢀⠔⢦⡀⠀⣀⠄⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⣠⠆⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡈⠃⠀⣹⠆⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠤⠤⠠⠤⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠦⠐⠀⠀⠀⠀⠀⢐⠏⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠔⠂⠘⢣⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠑⠍⠢⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠤⣀⠢⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠁⠀⠀⠀⠀⠀⠸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡀⢀
⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠄⠴⠀⠀⠀⠌⠤⢴⠄⠀⠈⠰⠁⠌⠀⠐⡀⢀⠀⢠⡀⢰⢨⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠛⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠐⠀⠀⠀⢀⠁⠂⠄⠀⠁⠀⡎⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠂⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠴⣨⠀⠀⠀⠀⠀⠀⠀⠀⠉⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢘⡃⡀
⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠠⡄⠀⠀⠀⠀⠈⠈⠙⠂⠀⠀⠀⠔⠀⠀⠀⢄⡀⠀⢠⡀⠀⠀⠀⣴⠄⢑⣄⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠍⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠉⠉⠀⠉⡠⠁⠀⠀⠈⠢⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡀⣀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠊⠉⠉⢁⣀⡀⣀⣀⣀⣀⣀⡀⠀⣀⠉⠉⠐⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⣸⠀⠠⠄⠀⢈⠁⠀⠀⠀⠀⢀⡰⠖⠛⠉⠉⠉⠉⠙⣦⣀⣐⡸
⠀⠄⠀⠀⠀⠀⠀⠀⡄⠸⠌⠃⠀⠀⠆⠊⢇⠰⠉⠑⠒⢤⡑⢢⡤⠔⠊⠁⣐⠢⠀⠔⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢀⣀⡠⠜⠋⣁⠶⣶⠖⢠⣬⡄⣨⣀⣀⠀⠀⠀⠈⠦⣀⣀
⠀⠀⠀⠀⠀⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢻⣧⣤⣶⣶⣚⣶⠁⠌⠲⠂⠻⣄⣀⣐⠜⠙⢯⡁⣶⡀⠀⠀⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⣠⠊⢻⣿⣿⣿⣿⡿⢄⡀⠁⠀⠀⣀⣀⡠⠤⠚⡀⠫⢍⠧⣉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⢀⣔⠵⠊⠁⠉⠀⠙⠛⢺⣟⢉⠑⡒⠒⠒⢲⣶⠟⠫⡄⠬⡉⢶⠰⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢸⣡⡄⠀⠺⡽⠁⢀⠔⠲⠟⠑⣎⢀⠟⠒⡆⠈⠀⠀⠴⢄⡈⠢⡷⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢺⠀⢰⡟⠉⠹⡆⠈⡇⢌⣠⡀⠀⠐⠛⠂⣶⢷⡴⣼⣿⣦⣰⣷⣽⡄⠀⠘⠊⠁⣠⡇⠀⡾⠉⠱⣶⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣇⠀⠀⢱⠀⢳⡀⠘⠒⠖⠉⣦⣤⣾⣅⣳⢉⡿⣿⣁⡿⠐⣦⢠⠒⠉⠛⣸⠁⢰⠃⠀⢀⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹⡀⠀⢰⡀⠈⣏⠲⠎⢱⡤⠜⢲⠈⠉⠉⠉⠉⠀⠀⠀⢨⢩⠥⢄⢸⠉⡏⠀⢸⠀⠀⣼⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠛⠛⣡⢤⠈⠉⠓⠒⠀⠴⢿⣦⣤⣤⣤⣤⣤⣄⣄⠊⠛⠀⠚⠒⠈⠀⣀⢽⠓⠳⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⠤⠤⢴⠃⢠⠧⠤⠤⠤⠤⠤⢼⣄⣠⡆⠂⢠⣀⣠⢸⠦⠤⠤⠤⠤⠤⠼⡅⢸⣇⣀⠼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⣀⣠⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠠⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⠉⠧⣈⠿⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠙⠃⠐⢲⣠⠏⡏⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣿⣛⣷⢼⣟⡃⣾⠛⢳⡄⣿⢀⡿⣧⠘⢻⡟⢸⣟⣻⡆⣿⣰⠟⠛⠂⣿⢀⡿⣧⠀⣿⣆⣿
⠀⠀⠀⠀⠿⠉⠀⠺⠷⠆⠻⠶⠞⠁⠟⠼⠛⠻⠇⠸⠇⠸⠏⠻⠄⠿⠘⠷⠶⠂⠿⠾⠛⠻⠇⠟⠘⠿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣠⡿⣆⡀⠈⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠈⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣟⡛⠛⠛⢛⣻⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠋⠈⢿⣍⣀⣀⣨⡿⠃⠙⠷⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⡴⠿⠖⠛⠁⣀⣀⣤⣴⠿⣬⣤⠿⢶⣤⣀⣀⠈⠛⠻⠷⢦⣶⣀⣠
⠀⠀⠀⠀⢠⡴⠞⠋⠉⠀⠀⠀⠀⣴⠞⠋⠁⠈⠻⢦⡾⢻⡴⠟⠁⠈⠉⠻⣦⠀⠀⠀⠀⠉⠙⠳⢾⡀
⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢳⡾⠁⣤⣤⣤⣄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣶⠀⠀⠀⠀⢸⡇⢠⣇⣀⣀⣿⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⠀⠀⠀⠀⢸⡇⠀⠈⠁⠉⣥⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠙⣧⡀⠀⠀⢀⣀⣀⡀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⢀⣀⣁⣀⠀⢀⣀⣀⣀⠀⣴⠷
⠀⠀⠀⠀⣩⡵⠞⠛⠋⠙⢿⡉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠉⠳⠟⠁⠀⠉⢳⡄
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⣀⣀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠐⣯⠹⣆⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⣼⢋
⢀⣼⡇⠀⠀⢀⣤⣄⠀⠀⠀⠀⣠⣤⡄⠀⠀⢸⣧⣀⠀⠀⢹⡆⠙⣷⢦⡀⠘⢷⣄⠀⠀⣰⠟⠁⣠⡶⣾⠁⣼
⣿⠈⠁⠀⠀⠘⠷⠟⠀⠀⠀⠀⠹⠶⠋⠀⠀⠈⠁⣹⠆⠀⠀⢿⡀⢻⡄⠹⣦⡀⠙⢷⠞⠁⣀⡾⠋⣰⠏⢰⡏
⠙⢧⡄⠀⠀⠀⢀⣤⠶⠦⠴⠶⣤⡀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠈⢷⡀⠛⠀⠈⠙⣦⠀⢀⡾⠋⠀⠐⠋⢠⡟
⠀⠀⢿⡄⠀⠀⢸⡃⢠⡶⠶⣄⠈⣷⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢸⡇⢼⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠻⣦⡀⠈⢻⡾⢧⠴⢿⡞⠁⢀⣤⠞⣀⠀⠀⠀⠀⠀⠀⣠⡄⣸⠇⠀⠀⣸⠇⢸⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠙⠳⠾⢷⣤⣤⡾⠷⠞⠋⠁⠀⠹⠟⢶⡶⢶⡶⠛⠏⠀⠛⠀⠀⠀⠛⠀⠈⠃⠀⠀⠈⠃
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣱⠂⠠⣌⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⡇⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡞⡇⠀⠀⢀⢱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣇⡇⡅⠀⡹⠼⣮⡀⡄⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⢠⣏⡷⠊⠚⠉⣁⡉⢻⡿⠀⠀⠀⠀⠀⢰⠰⡀⠀⠀⠀⠠⠂⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢨⠭⣇⣀⣀⡀⣦⡄⠀⠁⢢⠀⠀⠀⠀⣦⡊⢱⣄⢀⡠⠀⢀⡼⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⣗⠀⠸⢠⡍⠄⡇⠀⣰⡀⠈⣧⠀⠀⡰⠃⠘⣾⣷⣉⠤⠴⠛⠓⢦⡼
⠀⠀⠀⠀⠀⠀⠀⡾⠉⢉⡿⠌⡧⠀⠘⡇⠀⠐⠀⠈⠇⢁⣹⠇⡰⠁⠀⠀⢚⡇⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⠀⢠⡞⠒⠂⡀⠀⠉⢪⣡⣄⢀⢿⣰⠃⠀⣰⠞⠙⠢⡀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⠲⠓⡴⠊⠉⠹⡓⠚⢻⢿⠁⢼⠇⠀⣀⡞⠦⠴⠊⠁⢀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡘⢀⡠⠄⠂⢷⠠⢼⡀⠀⠘⠀⡴⣫⠄⠀⠠⣌⣀⠘⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡟⠁⠀⠀⠀⢘⣀⠞⠁⠀⢰⣸⡿⠵⠧⢀⠠⠶⠀⠉⢦⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⡖⠴⣖⠊⠉⠘⢃⠀⠀⢸⡏⡇⢻⣄⣙⣀⠴⠂⠀⡘⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡌⢉⣀⣿⣷⣿⠄⠀⡿⠀⠙⣄⠓⣒⡓⠁⠀⣠⠃⢰⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠈⠒⠓⠚⠉⠁⠀⠀⡇⠀⠀⠀⡏⠙⢻⠛⠋⢸⠄⢸⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⠀⠀⡇⠀⠸⠀⠀⠰⠀⠘⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣤⢸⡆⣦⠀⠀⡀⠀⡸⠀⢠⠀⠀⡇⠀⠈⡇⠀⢿⣤⣈⠁⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⠀⣿⢸⡇⣿⢸⡆⣧⣼⠃⠀⢸⠀⢰⠇⠀⠀⣇⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠸⡇⣿⠞⡇⣿⣸⣿⣿⣿⠒⣄⣈⠀⢸⠀⠀⠀⢻⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢰⣇⣽⠀⠛⣽⠙⢿⡟⣿⠀⠀⡇⠉⡟⠀⠀⠀⠘⡆⠸⣤⡀⠀⠀⠀⠀⠀⠀⠸⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠻⢸⠀⠀⢿⡀⠀⠀⠓⣄⢀⡇⢸⡇⠀⠀⠀⠀⢣⠀⠀⢹⡀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⢽⡂⠀⠀⠘⢺⣃⢸⠁⠀⠀⠀⠀⢸⠀⠀⠈⢧⣀⠴⠋⠉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠤⠘⠀⠀⠀⠀⠈⠙⠉⠲⠤⠒⠛⢺⡀⣀⣀⣨⣍⣠⠔⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⢀⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠈⢄⠀⠹⠀⠄⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠰⠖⠸⠂⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⡠⢛⠆⠀⠀⠀⠀⠣⣀⠀⢀⣀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢡⠁⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠼⠦⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠀⢦⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⠘⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⠧⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠃⠂⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⣤⣤⣤⣤⣤⣤⣦⣵⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣼⣤⣤⣴⣬⣵⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠁⢠⢿⠒⠒⠒⠒⢴⣾⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠹⡟⢁⣴⣦⡙⣆⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠠⠤⠤⢀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠳⡈⠻⠿⠃⣼⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠊⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠓⠲⣿⣿⣿⣷⣤⢇⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠒⠀⠒⠠⡈⠢⡀⠀⠀⠀⠀⠙⢿⣿⣿⠃⠀⠀⡅
⠀⠀⠀⠀⠀⠤⠀⠘⡄⠂⠀⠀⠀⠀⢰⣿⣿⠀⡞⠀⠀⠀⠀⠀⠀⠈⢢⠈⠳⢄⡀⠀⠀⠀⠘⡇⠀⢀⠎
⠀⠀⠀⢀⣄⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠉⣠⢺⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠲⢄⡀⠀⢇⠀⡈
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠙⢄⠈⠓⠀⠐⠉⠀⠘⠄⠀⠀⠀⠀⠸⣿⡿⡠⠀⠀⠀⠀⠀⠀⢈⠗⠾⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠁⠂⠉⠦⡀⡀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⣠⠎⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠤⠀⠚⠄⢄⡀⠀⠀⠀⠀⠀⠀⠄⠰⠋⠁⠀⡀⡀⢀⠆⠀⠰⠀⠀⣉⠉⠁
⠀⠀⠀⠈⡀⠀⡀⠐⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠘⠂⡀⠄⠦⠃⠨⠇⠀⡰⠁⡘⢳⣘⠃⣴⠁
⠀⠀⠀⠂⡄⢀⠈⠎⠀⠀⣰⣶⣦⠀⠀⠀⠀⣰⣿⣷⡀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠙⠁⡀⢏⣉
⠀⠀⠀⠊⠀⠀⠙⠇⠀⠀⠹⢿⡿⢀⠀⣘⢀⡘⠻⠟⠀⠀⠰⠖⠁⠀⠀⠘⠃⠀⡀⠀⢴⠆⠀⠀⠀⠠⢴⣈⢳⠆⠉
⠀⠀⡁⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠁⠔⠂⠀⠀⠀⠈⠲⠶⠂⠀⠀⠀⠀⢀⣰⡦⠏⠁
⠀⠀⠱⢄⡀⠀⣀⠔⠁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠽⠁⠈
⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣉⣁⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⢠⠀⢰⡀⠀⣘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣤⣶⣶⣾⣶⣶⣤⣄⣀
⠀⠀⠀⣲⣆⢺⣆⣿⡇⢸⡇⢠⣿⡆⠀⢰⣷⡀⠀⣠⣿⡏⠀⠶⣿⣷⢀⣹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠂⠛⠉⡏⠀⡇⠀⠁⠀⢻⣿⠀⠘⣿⠇⠈⣿⣿⡇⠀⢹⣿⣿⠁⠸⣿⠀⠸⣿⠀⣿⡿⣿⢿⡟⣿⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠇⠀⠀⠀⠘⡿⠀⠀⠼⠀⠀⠘⣭⠀⠀⠈⡿⡅⠀⠀⣿⠀⠠⣿⠀⣿⠁⣿⢻⡇⣿
⠀⠀⠀⠶⠶⢶⣶⣶⡑⠒⠓⠤⠔⠣⢤⡤⢤⣀⣀⣀⡡⣀⣀⣀⡥⠧⠤⠴⠛⠙⠊⠉⠉⢉⠚⢿⡾⠗⣿
⠀⠀⠀⠀⠀⠀⠹⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠎⢀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠀⡳⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⣀⣼⣿⡿⣻⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⡅⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⣆⠀⠀⢰⣦⠀⠀⢸⡀⠀⠀⣾⠀⠀⣿⡇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢄⠀⡟⠀⣷⠀⢀⠀⠘⣷⠀⠀⢸⣆⠀⠀⠀⣧⡀⠀⠀⣧⠀⠀⣿⠀⠀⣿⣥⡿⣿⣿⣯⡿⠋
⠀⠀⠀⠀⠈⠓⢤⡀⠁⠀⣾⠉⠂⢻⣧⠀⠰⣿⣆⠀⠠⣿⣧⠀⢸⣿⣦⠌⢻⣶⡄⢨⣿⡷⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⡀⠀⠚⠻⠀⠀⠙⣋⠴⠒⠚⠯⠄⣀⡘⠿⠇⠀⠸⣓⣀⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣤⣸⣿⣯⣴⣿⣧⣶⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄⢒⡀⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡿⠿⠿⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡟⠂⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⡇⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣛⡃⠀⠀⠤⠄⣹⣿⣏⣹⣿⣷⣦⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⣷⠀⠀⠰⢾⡗⠿⠛⢶⣶⢂⣄⡀⠀⠀⢠⠈⡄⠀⢻⣿⠀⠀⠀⠙⠛⠻⣿⠧⠜⠿⠃⠘⢻⣽⣯⠈⡶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⣿⡀⠀⠀⠀⠀⠀⣀⡀⠉⠑⠈⠁⠀⠀⢨⠈⡁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠠⠂⠈⠻⠓⠿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣆⢸⣷⣶⣆⠒⠀⢈⣭⣿⡁⠀⠀⠀⠀⠀⠸⡔⢰⡀⠐⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣅⣶⣶⡄⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⣾⣿⣿⣷⣷⡿⢯⣉⠁⠒⠀⠀⠀⠀⠀⢘⡚⠾⣇⠀⣿⣿⣿⣿⢶⡚⢼⠗⠀⠀⣀⣠⣾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠹⣿⣿⣿⣿⣷⣤⣿⡁⠀⠀⠀⠀⠀⠀⠰⣂⠏⢻⣶⣾⣿⣿⣿⣿⣇⣯⣤⣶⣾⠿⠿⠿⠄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣜⢿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠠⢾⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣷⣶⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⣄⠀⠘⣿⣆⢻⣿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢾⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣆⣨⣽⡟⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠉⠻⣧⢿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⠹⣿⣿⣌⢻⣿⣿⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣧⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⡿⣿⣷⡆⢻⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣇⠀⢀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠈⠽⢿⣿⡄⢻⣿⠀⠀⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠶⢦⣄⡀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠳⠦⣄⠀⠀⠀⠀⠀⢀⣀⣤⣄⢀⣀⣀
⠀⠀⠀⠀⣠⡤⢤⣤⣄⣠⠶⠋⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠞⠋⠁⣠⠿⡏⠉⢉⢿
⣀⣀⣀⡴⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣠⡖⠒⠞⠁⠀⠘⠚⠁⢸
⢻⡿⣍⠀⠀⠀⢀⡴⠋⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⢦⡀⠀⠀⠀⠀⡰⠋⠈⢦⡼⢱⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣇⠀⠙⠢⡴⠋⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⠢⣄⡀⢀⡤⠊⠀⠀⠀⠀⠀⠙⢦⡀⢀⡜⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠈⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⡤⠤⠤⠤⢤⠀⠀⢀⣀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠈⡟⢉⣍⠉⡷⡆⢠⠖⠾⢀⡜⢉⣉⡇⡇⠀⢸⠀⣤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠛⢲⡀⢰⠚⡟⠀⢁⣔⠁⣰⢸⡀⠀⢸⢰⣃⠀⠁⡇⠀⠘⢋⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡇⢰⣦⡈⢹⠏⠈⠋⠓⡜⣆⠉⠉⣹⠇⢰⠦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠈⠶⠼⠆⠙⠛⠒⠒⠒⠚⠁⠈⠓⠒⠻⣄⣼⠀⠙⢄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠅⠈⡇⠀⡇⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⠃⠀⠛⠛⣬⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡶⠦⠤⠀⠀⠒⠒⣦⠤⠦⢄⠀⢀⢀⣀⡀⠀⢀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⣀⣤⡄⠀⠀⠀⢿⢠⡄⠀⢣⡏⣩⠭⠷⡸⠉⠹⣸⠁⠀⠈⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⢹⠋⠈⠡⣴⠋⡇⠻⢤⠀⡇⠰⠆⢹⠛⢳⠀⡞⠃⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⠀⢸⠀⡟⢆⠀⢙⡇⢾⣋⣸⠁⡴⡆⠘⡆⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⣤⡼⠀⠘⠖⠃⠈⠶⠋⠧⣄⣀⣸⠶⠃⠘⠶⠇⢸⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⡀⠠⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⡷⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠈⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀⣀⠤⣴⣶⣦⣤⢤⣤⠤⣤⣤⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢠⢶⣿⣽⣷⣾⠿⠻⢿⣿⣿⠿⢿⣿⣿⣭⣻⢶⣤⡀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢚⣶⠾⣿⠏⠀⢹⠏⠀⠀⠀⢿⠁⠀⠀⢹⠟⠛⣿⣿⣮⡻⣦⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡾⠛⠃⠀⣿⠀⠀⢸⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢸⠟⠙⣿⣮⣧⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⣾⣾⡿⠁⢀⠀⠀⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣸⡀⠀⡛⠛⣿⣿⠄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡇⠀⡝⢹⣷⡄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠁⠨⣿⣷⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠉⠛⣷⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡇⣿⣇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡇⠐⠞⢻⣴⣿⣿⣿⣍⣿⣽⣿⣤⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⡯⣿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⢾⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⠃⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣦⣿⡇⠀⣇
⠀⠀⠀⠀⠀⢰⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣼⣷⠀⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣒⡂⢀⡭⠙⢿⣿⣷⣿⡿⢏⡴⠖⠊⢙⠋⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡇⢀⡄⣄⣨⣿⣿⣾⣿⡟⢃⠈⠀⠀⠀⠘⠿⠹⢿⣆⠈⠓⠊⠀⠀⠀⢀⣄⣲⣿⡏⢻⣿⠻⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣧⠈⠠⠉⠜⢿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠂⠀⠀⠀⠀⠀⠀⠡⠼⣿⣿⣧⣈⣡⣰⡟⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡐⠘⠛⡉⣿⣿⡷⣀⠀⠀⠀⠀⠀⠈⠛⠥⠀⠀⠀⠀⠀⠀⣀⣤⣴⡟⢿⡏⠘⣛⢛⣿⠃⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠄⢠⣿⣿⣷⡭⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⣶⣿⠹⡿⠙⣿⠏⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⡼⠻⣿⣿⣜⡲⠄⠀⠠⠄⠨⠐⠀⠀⠀⠀⠀⠀⢠⣴⣶⡟⠙⠒⢢⢠⠏⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡇⠀⡟⠉⢻⡷⢄⣉⣈⣡⣴⢢⣄⠀⢀⣠⣴⣶⠶⣿⠁⢸⠄⢠⡾⠂⢠⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣧⠀⠰⡀⠀⢸⠉⠉⠹⡏⠉⠉⡏⠉⢉⡏⠀⡏⠀⢸⡷⠋⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠙⠻⣦⣴⣧⡀⣸⡆⠀⢠⡇⠀⢸⡇⠀⣸⠀⣀⣿⡶⠋⠁⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣦⣾⣷⣶⣿⣷⣶⣿⠿⠟⠉⠀⠀⠀⣰⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣦⡠⢀⣀⣀⣀⡀⠀⠀⢀⡀⣀⣠⣤⣶⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢾⣿⣭⣯⣿⣿⣽⡿⠿⠟⠋⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣶⣚⡟⠃⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠙⣦
⠀⠀⠀⠀⠀⢐⡉⣿⠛⠗⠀⠀⠀⡷⣾⠓⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣠⠋⠀⠀⣀⣀
⢀⣴⣿⣅⣾⣿⣿⡟⠛⠀⠀⠀⠀⠘⢻⣿⡷⣼⢷⡄⠀⠸⢠⡀⠀⠀⢸⣦⠀⠳⡄⠀⡠⠃⠀⠀⡤⠊⠀⠀⠀⣴⣦
⠸⠿⠼⣷⠈⠙⠛⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠈⡀⠻⠷⠀⢛⠋⠀⠀⠛⠉⠀⠀⢀⣀⡱⠀⠀⠀⠈⣈⣡
⠀⠀⠀⠀⠀⠀⢤⣄⣠⡞⢶⣛⡄⠀⢄⠀⠀⠀⡤⠀⠤⠼⠃⠀⠀⠲⠞⠀⠀⠀⠀⢰⠯⣤⠏⠀⠀⠀⠀⠀⠀⡏⢻
⠀⠀⠀⡔⠀⡔⠁⠀⠉⠀⠀⠀⠀⠐⠀⠱⡀⠸⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠄⢈⠙⠀⠀⠀⠀⠀⢸⠄
⠀⠀⢰⠁⢸⠁⠻⣦⡀⠀⠀⣠⣾⠀⢳⠀⡇⠀⠀⠦⠷⣀⣿⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⢀⠌⢹⡀
⠀⠀⠸⣆⣄⠀⢀⠉⠠⠻⠀⠙⡁⠀⢸⢀⡇⠀⠀⠀⠀⠈⠁⠀⠳⠀⠀⠀⠀⠀⠀⠰⠛⠓⠊⠀⠠⣤⡀⠀⠙⠒⠒⠈⠁
⠀⠀⠀⠈⠛⢦⣤⡛⠳⠞⠾⢛⠁⣠⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠒⠤⠤⠔⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠉⠉⠁⠀⠀⠀⣠⠖⠄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢀⣄⣠⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢠⡴⠅⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣶⡆⠘⠛⣿⣿⣿⣿⣿⣶⡆
⠀⢠⠀⠀⠀⢀⡀⢠⣀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠰⣄⠀⠀⠀⠀⢰⣶⣿⣟⣿⣿⠀⠀⠀⣿⠟⠉⣿⡏
⠀⡟⠀⠀⡄⣾⡇⠸⣿⠀⠇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠰⢹⡇⠀⠀⠀⠀⢠⣻⣗⣹⣿⣧⣤⣼⣿⣤⣤⣿⣿⡤
⠀⢳⡀⠜⡀⠉⠑⠓⣀⠠⠀⠀⠀⢰⡜⠁⠀⠀⠀⠀⠀⢼⣣⡀⠀⠀⢹⣿⣝⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣦
⠀⠀⠉⠉⠁⡲⢶⡒⡂⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⢠⣸⣿⣷⣸⣿⣿⣿⣿⣿⣧⣿⣿⣿⡿⣿⠛⠯⢛⡩
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣀⠀⠀⠀⢀⣺⡏⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⡿⢿⣿⡏⣿⡿⠁⣹⠂⢰⠀⡠
⠀⠀⠀⢀⣀⠀⢀⠊⠉⠉⠀⠄⠀⠀⠀⠀⠈⠁⠀⠐⠚⠛⠁⠀⠀⠀⠀⠀⠀⢿⣗⣿⢓⡂⠆⢻⣧⣿⣿⢷⣹⠒⢊⣜
⠀⠀⠀⣏⡄⢑⣣⣄⡀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠘⣿⣿⠀⠀⠀⠀⣿⣿⣿⡌⠛⠳⡋
⠠⠟⠞⠁⠙⠛⢁⣼⠿⠶⢖⠠⠤⡄⣀⣠⣀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠘⣹⣾⣿⣿⣷⣿⣿⣯⡙⠻⣿⣿⡄
⠀⣄⣀⣤⠦⠰⠟⠻⠶⠤⠾⠒⠓⠀⢉⠀⣲⠾⠆⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⠛⠉⠐⠿⠿⣿⣷⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣸⣿⡇⣾⡟⣛⠃⣿⡟⠻⣶⡀⣿⠀⣶⠟⠻⠶⠀⣰⣿⣇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿⡟⣻⡇⣿⣟⣛⡁⣿⣇⣀⣾⠇⣿⠈⣿⣄⣀⣤⢠⣿⣦⣿⡆⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠁⠈⠉⠉⠁⠉⠉⠉⠁⠀⠉⠀⠈⠉⠉⠁⠈⠁⠀⠈⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢴⣤⣤⡄⢰⣴⣦⣤⠀⣤⣤⣦⠀⢀⣴⣄⠠⣦⣴⣤⠄⣴⣤⠀⣴⣦⠀⣴⡤⣤⢀⣦⡄⠀⣤⠠⢤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣷⣶⡿⢀⣿⠶⠶⠀⣾⣋⣿⡆⠀⣿⠀⠀⣿⢿⣶⡟⣿⠀⣿⠶⠶⢠⣿⢻⣶⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠇⠘⠷⠀⠿⠿⠿⠺⠟⠉⠙⠿⠀⠿⠀⠀⠿⠂⠿⠀⠿⠀⠿⠿⠿⠈⠿⠀⠙⠿⠀⠘⠿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⣿⡆⠀⠀⠀⠀⠀⣠⣀⣀⣤⡀⠀⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢉⠉⢻⡆⢀⣼⡷⠾⠛⠛⠛⠛⠛⠻⢿⣦⡀⢠⣾⠛⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠀⣸⡇⠙⠁⠀⢀⣀⡀⠀⣀⣤⣤⣤⣬⣁⣸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠀⠛⠀⣿⡇⠀⠀⢠⣿⠙⣿⡿⠋⠁⠀⣀⣼⠟⢿⣇⠀⠀⠀⠀⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣤⡾⠿⠟⠛⢀⣿⠀⠺⠀⢿⡇⠀⠀⣰⡿⠀⢿⡄⠀⢀⣴⠟⢁⣴⠟⢻⡿⠿⠿⠿⣿⠘⠛⠿⢶⣤⣶⡀
⠀⠀⠀⠀⢰⣷⠟⠋⠁⠀⠀⠀⠀⠀⣿⠶⣶⡶⣿⡇⠀⠀⣿⡇⠀⢸⣇⣴⠋⢁⣴⠟⠁⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠻⢶⣶
⠀⠀⠀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣶⣾⡷⠀⠀⣿⡇⠀⢸⣟⣁⣴⠟⠁⠀⠀⣠⣿⠁⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣦⣤⡄⠀⠀⠻⣧⣤⣾⠟⠿⠷⠀⣤⠄⠘⠋⠻⢷⣤⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠆
⠀⠀⠺⣿⡀⠀⠀⣴⡾⠛⢻⣿⠛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⣿⣷⡀⣼⡏⠀⢀⣼⣿⣄⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠛⢷⣤⣴⠟⠋⠉⠉⠙⠻⣦⡀⠀⠀⣼⠟⠋
⠀⠀⠀⠀⠈⠁⢻⡿⠿⠛⠋⠀⠙⠛⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⡀⠾⠛
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠀⠀⢠⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣶⣶⣶⣴⡿⠉⣿⠀⣴⣶⡾⠻⣶⣶⣶⣶⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣭⣀⣀⣀⣨⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣉⣉⣉⣹⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠀⠘⠟⠀⠀⠀⣴⡿⠋
⠀⠀⣠⣴⡶⠿⠛⢿⣯⡉⢹⣿⣏⠉⣩⣿⠟⠻⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢀⣠⡾⠋
⠀⣼⠟⠁⠀⠀⠀⠀⠉⠻⣿⠃⢻⡿⠋⠁⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡾⠋⠀⢀⣀⣀⣀⡀⠀⠀⣠⣤⣤⣤⣤
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡿⠁⣠⣤⣤⣤⣤⡀⠀⠸⣿⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠛⠛⠛⠛⠛⢻⡇
⢸⡇⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠉⠉⠉⢹⡇⠀⠀⣤⠀⠀⠀⠠⣿⠉⠙⣷⣄⣴⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣾⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠛⠛⠛⠛⠛⠃⠀⠀⣀⡀⠀⠀⠀⠙⢷⣄⠈⠻⣷⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢰⡆⠀⠀⢻⡇⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⡶⣶⣶⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠘⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣶⣦⣤⢀⣛⣘⣛⣃⣙⣃⢠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠰⠛⣉⣠⣼⡏⢁⣼⠟⠉⠉⠛⣿⠛⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣦⣶⣦⡀
⠀⠀⠀⠀⠀⣴⠋⢠⠞⠉⠀⠈⣿⠋⢀⡟⠀⢀⣀⠀⢸⠀⠀⣿⠀⢈⣿⣿⠿⠿⣿⡿⠿⢿⣿⣿⣦
⠀⠀⠀⢀⣾⡟⢠⡟⠀⣀⠀⣰⡟⠀⢸⡇⠀⢸⣿⠀⣸⡇⠀⣿⠀⣼⣿⣷⠀⣀⣀⣳⠀⣀⢙⣿⣿⣧
⠀⠀⠀⣼⣿⠁⣼⠃⠸⠃⣴⣿⡇⠀⣸⣧⠀⢸⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣇⢻⣿⢜⣇⠙⠸⣿⣿⣿⣇
⠀⠀⢀⣿⡏⠀⣿⠀⢀⠀⠘⣿⠃⠀⣿⣿⡄⠘⠟⠉⣿⣷⠀⢰⡄⠈⢿⣿⣿⣧⠀⠀⣿⡀⢠⠈⠻⣿⣿
⠀⠀⢸⣿⡇⢰⣿⣀⣼⣆⣀⣼⣄⣠⣿⣿⣷⣤⣤⣾⣿⣿⣄⣠⣷⡀⢈⣿⣿⣿⣶⣶⣿⣷⣾⣷⣶⣿⣿⡇
⠀⠀⠀⣿⣯⣭⣽⣯⣿⣿⣿⣿⣿⣿⠛⠛⠋⠉⠛⠛⠛⢻⣿⡿⠛⠛⠛⢻⣿⣿⠟⠛⢿⡟⠉⠉⢁⣠⣴⡇
⠀⠀⠀⠹⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣶⠀⢰⡾⠛⠛⠛⠻⣿⡇⠀⠀⠀⣸⣿⡇⠀⠀⢸⣿⣷⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⣹⡇⠀⣾⣿⣿⣿⠃⠀⠀⢸⣿⡏⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣭⣿⣿⣿⣿⠀⢸⡇⠀⡾⠁⣰⣿⠃⠀⣀⣀⣿⡟⠀⣾⠀⢸⣿⠃⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠘⣷⠀⢀⠀⠹⣿⠀⢰⣿⣿⡿⠁⣠⣴⡄⢸⡿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⢿⣿⣷⣤⡝⢤⣼⣧⣀⣸⣆⠀⣀⡼⠁⢰⠿⠋⠀⠈⠁



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

⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠖⠋⠓⠢⢤⣀⣀⣠⠖⠋⠉⠉⠓⠦⣄⣀⣀⡤⠖⠋⠉⠙⠲⢄⣀⣀⣠⠴⢶⡤⠤⣤⡀
⠀⠀⠀⣀⣀⠜⠉⠉⠉⣉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣡⠄⠔⠁⠱⠖⢹
⠀⠀⠈⣟⠣⣀⢀⡴⠉⠀⠑⠄⠀⠀⠀⠀⢀⠴⠊⠉⠐⠄⠀⠀⠀⡠⠐⠉⠑⢄⠀⠀⠠⠋⠈⠒⠡⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢹⠀⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⣀⡀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢆⡉⠁⣘⠁⠄⡱⠆⡖⠊⠐⡡⠼⠈⠀⣡⢦⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⢸⢨⢀⡜⢢⠆⠂⢤⢁⠓⢢⡄⣤⡐⢏⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠜⠘⠚⠈⠛⠀⠀⠊⠈⠑⠚⠧⠇⠐⠤⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠄⠰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠘⠛⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠤⠤⡄⣀⣀⠁⡄⢡⠌⡭⠇⠎⠱⣌⠉⠉⣈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠈⢠⡘⠣⡆⡵⢰⢀⡁⠁⢹⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠨⠤⠀⠐⠚⠘⠊⠧⠄⠽⠂⠐⠘⠨⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⢤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⡷⠊

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠉⣻⡟⠛⠛⣃⣠⣤⣤⣤⡀⠀⢀⡁⠀⠀⢀⣠⣤⡄⠀⣿⡆⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⢰⡿⠛⠛⠛⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠛⠉⠉⠉⣻⣿⡆⣼⣯⠀⣴⣿⡿⠛⠇⠀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠙⢿⣷⡀⣸⣇⣀⣤⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⣿⣤⣶⣶⣿⠿⠋⠀⣿⡇⢸⣿⣿⠁⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢰⣿⡟⢿⣿⣤⡀⠀⠀⣿⡇⠸⣿⣿⣀⣠⡄⢸⣿⠛⢿⣿⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⡿⠀⣿⣿⠉⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠘⣿⡇⠀⠙⢿⣷⠆⠀⢸⡿⠀⢿⣿⣿⣿⠇⢸⣿⠀⠀⠙⠿⠇⠀⠀⠀⠀⠙⣿⣶⣤⣶⣿⠟⠁⠀⢹⣿⠀⠀⠹⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⡿⠿⠿⠇⠀⢀⡀⠀⠀⠀⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⡿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⡾⠿⠿⠿⢿⣦⡀⣿⡇⠀⢀⡀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⢸⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⢀⣀⣤⣴⣾⠿⠁⣿⣿⣿⣿⣿⠀⠀⠀⣼⡟⢿⣿⣿⡄⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⡋⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⣰⣿⣤⣼⣿⣿⣿⡀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡆⠙⢿⣿⣦⡀⠀⣿⣇⣀⣤⣤⡀⢠⡟⠉⠉⠀⠘⣿⣿⡇⢸⣿⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠛⠁⠀⠀⠙⠋⠀⠀⠛⠛⠛⠛⠛⠃⠚⠀⠀⠀⠀⠀⠙⠛⠃⠘⠛⠀⠀⠀⠘⠃








⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠒⠦⣄⡀⠀⠀⠀⣀⡴⠚⠋⠉⠓⠲⢤⣀⡀⠀⠀⢀⣠⡴⠖⠛⠛⠲⢤⣀⠀⠀⠀⢀⣠⡤⣤⣀⣀⣀
⠀⠀⠀⢠⠖⠒⠶⠤⠴⠋⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⣉⠁⡠⠛⢏⢀⠼
⣤⡤⠴⠃⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣠⠦⡀⢠⢾⠁⠉⠀⠀⠈⠁
⠸⡍⠲⢄⢀⡠⠊⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⠓⢄⠀⠀⠀⢀⠴⠋⠀⠀⠉⠢⡀⠀⠀⡜⠁⠀⠘⠃⡎⠀⠀⠀⠀⠀⠀⢰
⠀⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠀⠀⠀⠀⠈⠲⠞⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⡇⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢻⠀⠀⠀⠀⠃⠀⠀⢀⣀⣀⣤⣀⣀⣀⣤⠖⠒⠶⢦⠀⢀⣀⣀⢠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⣁⠀⠀⣀⣏⢰⠆⣸⢳⠰⠋⠛⢰⢫⠤⠼⠙⠀⢸⡠⠖⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⡇⢸⠉⡇⢀⠚⠥⣼⠀⣧⣀⢠⠻⠤⢤⡌⢀⡈⠰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢡⢸⠐⣄⣸⠱⡴⠧⠤⠤⠼⠈⠢⣤⣼⡇⢸⠈⢆⠈⡳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠀⠀⠀⠀⢠⡇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⡆⢸⡇⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠃⠈⠛⠣⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠉⠀⠀⠈⠉⠉⡖⠛⠒⠄⡤⠤⠤⠀⡠⢤⢠⠴⠶⠤⠤⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠓⠚⡇⢠⠤⡤⠇⠟⢀⡴⡇⣞⠉⢱⢀⣄⢿⢤⡄⢀⠤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢰⣄⠙⠲⡇⡤⠇⡌⢠⡍⠸⡀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠠⣅⡼⠀⠳⠼⠈⠦⠚⢇⣈⣉⡧⠞⠸⠤⠇⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⡄⠀⠀⣸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠞⠁

⠀⠀⠀⠀⠀⠤⣷⡧⠄⠀⠞⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠗⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⣤⣠⡄⢰⣾⡆
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢹⣿⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢦⣵⠀⠀⣀⠀⠀⠀⠀⠀⢰⣾⡇⠘⠋⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⢸⣿⡇⢸⡿⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⢸⣿⡇⠾⠿⠇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣤⣥⣄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⣮⣽⣆
⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⡰⠚⠉⠰⣶⣾⣿⣷⣶⡦⠈⠙⢢⡀⠀⠀⠀⠀⠀⢸⠟⢿⣿⣹⣌⣿⣿⡆⢀⣤⣶⣤
⠀⠀⠀⠀⠀⣘⠋⠀⠀⠀⢧⠀⠀⠀⠹⣿⣿⣿⡟⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠸⣷⣾⠻⣿⣽⠛⠿⣃⡄⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠙⣅⡦⠀⠀⠀⠯⣬⡷⠀⠸⠿⠟⠀⠸⣯⡬⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⠃⠀⠀⠀⠀⠁⠀⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⠘⠀⠀⢀⣴⠃⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢩⡀⠀⠀⠈⠛⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⡄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓