Frust Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣉⣉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⢩⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢠⡿⠀⠘⣿⠀⠀⠀⠀⣠⣶⠾⠛⠛⠉⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⢿⡆⠙⠻⠶⣤⣄⣀⠀⠀⠀⣀⣤⠶⠛⠛⠛⠛⠷⣦⣼⠙⠳⢦⣤⣾⣁⠀⠀⢹⣇⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⣷⡄
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠉⠙⠛⣳⠾⠋⠀⠀⠀⠠⠶⢤⣄⠀⡏⠀⠀⠀⠈⠉⠙⠛⠻⠶⣿⣾⠟⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⠛⠉
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢸⠿⠶⠶⣦⣄⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠑⢤⡀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣀⡴⠋⠀⠀⣠⡾⠋⠙⢶⣤⣀⣀⣀⣀⣀⣠⣤⡶
⠀⣀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣠⠤⠤⠤⠹⢿⣦⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⢷⣄⠀⠀⠀⠙⢷⡶⠞⠋⠀⠀⣠⣾⠋⠙⠳⠦⠤⠌⠉⠉⠉⢉⣩⡿⠋
⠈⢿⣟⡛⠛⠛⠛⠛⠛⠋⠉⠁⠀⣠⣤⡴⠶⠛⠛⢛⣿⣷⣶⣤⣤⣤⣤⣿⡆⠀⠀⠀⢻⣆⠀⠀⠀⢈⣧⣤⣤⠶⠛⠙⠛⠛⠛⠻⠿⠶⢶⣶⡿⠟⠛⠁
⠀⠀⠉⠛⠷⣦⣤⣄⣀⣀⣈⣈⣁⣀⣀⣀⣤⡴⠞⠛⠁⠀⠀⠉⠉⠉⠉⠉⢿⣤⣀⣀⣈⣿⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⢀⣤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⢻⣆
⠀⠀⣰⡟⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣆⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⢿⣆
⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠊⠐⠀⠀⠀⠀⢀⠀⠀⠘⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠂⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡀⠀⢻
⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠠⠴⠋⠀⠀⠀⡀⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢸
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⢸
⣿⠀⠀⢀⠀⠀⠀⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⣼
⢿⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠑⠞⠀⠀⠀⠀⠀⠀⠀⠠⠒⡆⠀⠉⠆⢠⣿
⢸⣧⠀⠀⠸⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠓⣦⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠘⠀⠀⢀⠐⠂⠀⢸⠀⠗⠀⣾⡟
⠀⢿⡆⠠⠀⠀⠀⠀⠰⡆⠀⠀⡄⡄⠀⠀⠀⠠⡇⣹⠀⠀⠀⠀⠀⠸⣦⠟⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⠀⠀⠡⠀⠀⡺⠤⠂⠀⣀⠀⠀⣸⡿
⠀⠈⢿⡄⠑⠀⠀⠄⠀⠁⠀⠀⠶⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⣠⠞⠁⠀⣰⡿⠁
⠀⠀⠈⢿⣆⠀⠀⢙⠆⠀⠀⢡⢄⠀⠀⠀⠒⢀⠀⠀⠀⠀⠘⢀⡄⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣀⠀⠀⠰⠀⡠⠀⢠⣿⠃
⠀⠀⠀⠀⢻⣦⠀⠙⠀⠀⠀⠘⢬⠆⠀⠀⠐⣍⠳⡀⠀⠀⠀⠘⣇⣸⠇⠀⠀⠀⣀⣀⠀⠀⠈⢠⡈⢦⠀⠀⠀⠀⣿⡠⠁⠀⢼⠍⠀⠀⢰⠊⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠓⠁⠀⠠⡤⣀⠈⠁⠀⠀⠀⠀⠈⡨⢠⡄⠀⠈⠷⠾⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠄⠀⠐⡖⢡⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠐⢨⡆⠀⠀⠊⡤⣀⠀⠀⠀⠀⠇⣸⠆⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠴⣁⠄⠀⠀⠉⡁⠀⠄⠘⢀⠀⠐⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⡳⣌⠀⠀⠀⣀⡀⠉⠀⠀⠀⠉⣉⢳⡄⠀⠀⣴⠛⣠⠀⠀⢀⣄⠀⠀⠀⢀⣀⠀⠀⠜⠋⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢂⠀⠀⠈⠀⠀⠀⠀⠸⡈⣦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠃⠴⠀⠀⠰⡆⠄⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠀⠀⠀⠢⡄⠀⠒⢠⠈⠁⠀⠀⠈⢁⢱⡄⠀⠒⢉⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡒⠂⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠠⡀⠈⠀⠀⠈⠀⠀⠀⠆⢤⠀⠀⠁⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠙⠀⠀⠀⡀⠁⠀⠀⠀⠘⠁⠀⠀⠐⠂⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠂⠀⠉⠐⠆⠀⢠⠤⢄⠀⠀⠀⠀⠔⡚⠂⢠⡴⠂⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠰⠁⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠈⡧⠀⠀⠀⠰⠒⠀⠀⠀⠀⠚⠙⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⢀⣀⠀⠀⠠⣦⠤⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣦⣤⣀⣉⣁⣀⣠⣴⣾⠿⠋

⠀⠀⠀⣼⡀⡶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠠⠀⠀⠀⠀⣀⠠⠔⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠈⠈⢻⠄⢀⣴⠀⠀⠙⡦⡀⠀⢀⠀⠀⠀⠑⠤⣤⣠⠤⠀⠉⠁⠀⠀⠘⣿⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠃⢿⠛⠁
⠀⠀⢠⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠊⢲⣎⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠠⣤⣴⡿⢀⢨⣿⣦⡀⠀⢀⠜⠉⠁⣰⣿⢿⣷⣀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⡀⠀⠀⠀⡠⠀⠁⢀⠀⠀⠀⣸⣿⠁⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢹⣿⣷⠉⠐⠆⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢰⡃⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠠⠃⠀⠀⠸⠀⠙⢿⣿⣿⠀⠀⠀⢸⣿⠿⠁⠀⠀⢀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⢷⣄
⠀⠀⠀⠙⠀⠁⠀⠀⠀⠠⣿⣶⣶⣤⣿⣿⠋⠀⠀⡴⠁⠀⡀⡀⠀⠀⡀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠀⣀⠀⠑⡄⠀⠉⠏⠉⠀⠀⠀⢠⢴⠄⠀⠙⣦⠀⠀⢲⡀
⠀⠀⠀⣄⠀⢀⡀⠀⠀⠀⠋⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠇⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢠⣄⠀⠁
⠀⠀⠘⢣⡼⢿⣤⣤⢄⣴⡆⠀⠀⠀⠀⠒⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣶⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠉⣀⣾⠁⠙⠀⡽⣋⠱⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢠⣿⠯⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢀⣶⡄⠀⢀⣀
⠀⠀⠀⠦⠛⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠐⣶⢀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢲⡄⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠋⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠒⣶⠀⠀⢰⡄⢠⡄⣘⣾⣿⣿⡳⣆⠀⠀⠀⠀⠀⢀⢀⣿⣆⡀⠀⠀⠀⠀⠀⠉⠚⠂⠀⠘⠇
⠀⠀⠀⠀⣶⠆⠀⠀⠀⠸⢿⡇⠉⠀⠀⠈⠉⠘⡾⠛⠟⠉⠙⢿⡌⣧⠀⠀⠀⠠⠈⠈⢻⣿⣷⡄⠀⠀⢀⢺⣿⡖⣶⣶⡄⠀⢀⠀⠀⠲⣶⣄⠢⣠⣦⢴⡞⠁
⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀⠈⣀⠰⠂⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠸⣷⣿⣇⢻⣿⡇⠀⠀⠀⠀⠀⠈⠉⣁⠟⢁⣀⣠⣄⡀
⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠒⡏⠀⠈⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⢰⣷⠀⠈⠙⠋⠈⠛⡡⢴⡒⢶⡄⠀⠠⣾⣈⠀⢻⡇⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⣧⠸⡑⣌⣿⠀⣌⢿⣿⣿⣺⢷⢼⣿⠇
⠀⠀⠀⠀⠀⠀⣀⠠⠂⠀⠀⢤⣤⣤⣤⡀⠀⠀⠀⠙⠛⠂⠀⠈⠀⠳⡾⠿⠋⠀⠀⠀⢴⣦⣒⠶⢻⣀⣤⣴⠋⠀⠀⠀⠘⠷⠬⠟⠃⠀⠹⣿⣿⡿⠁
⠀⠀⠀⠠⠾⠟⠉⠰⢀⡀⠀⠀⠙⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⢀⡀⠀⢸⢓⣯⠉⡄⠴⠶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢲⠂
⠀⠀⠀⠀⠀⠀⣶⣶⣿⠁⣹⣾⠉⠁⠀⠀⠀⠀⠀⠀⣆⡀⠀⠘⠿⡇⠀⠀⣠⡾⢿⠀⠀⠀⠈⣇⠁⠀⠀⠸⠇⣥⠆⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠐⠿⠛⠻⠇⠁⠀⠀⠀⠀⡶⠤⠀⠀⠀⠴⠇⠀⠀⠀⠀⠰⢾⡯⠟⠁⠀⠀⠀⠴⠋⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠘⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣉⡡⣤⣤⣶⣦⣦⣾⡍⣙⣓⡲⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡼⢁⣴⣬⣿⣻⡟⣻⣿⣽⡷⣿⣿⣾⣿⡿⣣⣤⣍⡓⠦⣀
⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⠻⠛⠿⣿⣯⢷⣿⣿⣷⣬⡑⢦⡀
⠀⠀⠀⠀⢸⣿⣷⡈⠛⣛⣿⣿⣟⣿⣿⣿⣿⣗⣤⡀⣼⣾⣷⣻⣟⣻⠿⣿⣕⣠⠹⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣦⡙⢿⣿⣿⣿⡽⣿⣿⣿⣿⣷⣿⠟⣫⡍⠙⢙⠛⠷⣾⣯⠀⣷
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣌⡉⠉⢾⣿⣿⣿⣿⡲⠀⣂⣻⣿⣧⡄⠄⠉⠀⠛⢦⡏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⠿⠀⠐⢀⠀⠀⢀⣣⣤⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣥⢤⠆⢈⠛⣷⣴⡆
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⠦⠄⡒⠂⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⢯⣈⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢮⠻⠾⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠦⠀⢴⣶⠇⠢⠈⢿⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠷⠀⠀⠀⠀⡆⡄⠀⠏⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣦⣄⣠⣠⣾⡇⣉⠀⠀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠞⠦⠀⠙⠻⢿⣿⣷⣿⡞⢉⡄⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠙⢿⣯⣴⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠋⢉⠉⠉⠛⠻⠋⢻⣿⣿⣖⠀⠀⠀⠀⠘⢿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⢂⠀⠀⠀⠀⠐⠀⣀⠙⣿⣿⣿⣿⡟⠛⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣡⢁⣀⣠⣿⡟⠃⣬⣻⣿⣿⣷⣿⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣼⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀⠀⠈⢀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠴⠀⠀⣀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠠⠊⠀⠀⠈⠀⡂⠥⠤⠤⠤⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠒⠖⠠⣄⠠⡴⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴⠠⠀⢄⠀⠄⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⢰⠋⠀⠈⢢⣀⠈⠒⠄⠀⠀⠀⠀⢀⣠⣶⣌⠢⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠋⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⢿⣿⡿⠋⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠐⢠⣤⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠂⠀⠀⢠⠔⠏⠀⠠⣀⡀⠀⠀⢀⡠⠄⣤⣤⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⢿⠋⠙⢉⡄⠱⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠠⠃⠀⢤⠀⠀⠀⠀⠀⠀⠈⠳⠂⠐⠈⠂⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟
⠀⠀⠀⠀⠘⢰⠀⠀⠀⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠘
⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣤⣀⠖⠃⠈⢉⣉⣁⣠⣽⣦⠀⠀⠀⠀⡀⠐⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣸⣿⣿⣿⣯⡀⠀⠀⢈⣿⣿⣿⣿⣿⣆⠄⠀⢰⣧⠀⠀⠙⠓⢢
⠀⠀⠀⠀⠀⢀⣀⣄⣉⣹⡿⢿⣿⣟⣻⡗⠛⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣯⠴⣥⡆
⠀⠀⠀⠀⢀⠁⣹⣿⣿⣿⡄⠉⠀⣀⣠⣤⣾⣅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠏⠛⣿⢷⣴⣿⣶⣶⡄
⠀⠀⠀⠀⠀⢻⡫⢟⣽⡿⣿⢦⣾⢯⣴⣿⣿⣿⣯⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠂⡐⢛⣿⣿⣧⣴⣦⡀
⠀⠀⠀⢀⣧⣶⣿⣾⣿⡿⢻⣿⣿⣿⣿⣿⡏⢁⣬⣽⠳⣿⣯⣀⣀⣠⡄⠈⣀⣠⣤⣴⣿⣿⣿⣿⠏⠉⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠻⠿⠿⠛⠛⠙⠛⠿⠿⠿⠿⠿⠛⠛⠉⠉⠛⠛⠛⠿⠟⠛⠛⠛⠋⠁

⠀⠀⠀⢀⡠⠔⠂⠀⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣒⡒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣉⡑⢒⣤
⠀⢀⡔⠉⠀⠀⠀⠀⢀⣜⣴⠀⢣⠀⠀⠀⠀⢠⡶⢤⡀⠀⠀⠀⠀⠀⠀⡠⢿⣽⣹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⠤⡀⢸⡏⠉⠉
⠀⠎⠐⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⢣⠀⠀⠀⠈⢧⡐⠌⡑⢂⣀⣒⡮⠝⣠⠎⢨⡯⡇⠀⠀⠀⠀⠀⠀⠀⣰⣡⠚⠓⢲⣉⣱⣏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣮⠋⡒⠤⠤⠤⠤⢒⠫⣀⠔⡱⠁⠇⠀⠀⠀⠀⣀⡤⠲⣁⡜⠁⠈⢳⢈⠀⢀⡏⢳
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠈⣶⢚⠽⠿⠿⠍⠒⢋⡡⠊⠀⡘⠀⠀⠀⠀⢎⣠⠓⠴⡁⠙⡖⢒⠛⠒⢏⣁⣟⢹
⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠑⢄⠉⠁⠒⠀⠉⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⠓⠚⠬⡹⢍⡹⠤⠤⠾⠴⠋⠉
⠀⠀⠀⠈⠉⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠈⠢⣀
⠀⠀⠀⠀⠀⠀⡀⢰⢆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⠶⠲⡖⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⢀⣱⡘⠈⣎⠟⡄⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠈⠓⣄⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⢀⠎⠀⠖⢠⡝⢦⡉⠠⣇⡤⠒⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡸⢀⡴⡫⠤⣤⢄⡀⠀⠀⠀⢠⡇⡆⠀⠀⠀⠀⠀⠈⢦⠀⠀⢸⡀
⠀⣰⢡⠀⠛⠀⢠⡄⢈⠙⢦⢠⡬⠆⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠈⣠⡿⣟⠃⠄⡨⢃⡙⡦⡀⠀⠘⡇⠳⢆⠀⠀⠀⠀⠀⣸⠀⠀⢸⠇
⢰⠃⢀⠀⠐⠆⢀⠀⠈⠁⠘⡆⢻⡀⠀⠀⠀⠀⠈⠑⠢⠤⡤⠤⠚⢱⡏⣹⣏⡹⢌⣁⡌⡇⢳⡀⠀⠈⠲⠬⣙⣁⣀⡠⠴⠧⠤⠖⠋
⣦⠁⣈⠀⢠⠀⠀⣤⠈⢋⡸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡞⢙⠉⠒⡌⡰⠁⡠⠟
⢧⣀⡄⠰⠆⣀⣤⡤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⣭⣮⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣿⣦⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣄⠀⣀⠤⠒⣒⡶⣤⠄⠀⠀⠀⠀⠀⠐⠲⢶⠶⢼⠹⡿⣿⠟⢻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡌⢶⠅⠂⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠚⠆⡧⠚⢈⣩⠽⠒
⠀⠀⠀⠀⢀⣤⠤⢤⣀⠦⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠹⣼⠓⠢⠤⠔⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⣭⡽⠯⢷⡛⠛⢿⢶⠈⠶
⠀⠀⡠⢚⡥⢂⡛⠰⠮⠗⢘⣛⢲⡄⠙⢦⠀⠀⠀⠀⣾⠸⣅⠀⠈⠚⠛⠁⠀⠀⠀⢂⡇⠀⠀⠀⠀⣠⡖⠩⠥⠄⠩⠬⢽⣻⡕⢸⠙
⠀⡸⠁⠚⠉⠰⠗⠛⣼⠉⠺⠧⠀⠀⠀⠈⡇⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⡴⠁⢠⣀⡀⣄⣀⣆⣀⡄⡇⠈
⠀⢧⢆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠼⣸⠁⠀⠀⢸⠛⠉⠈⡀⠀⠃⠀⠀⠀⣿⠃
⠀⠈⠯⣓⠉⠒⠒⠦⠆⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠘⡂⠒⡗⠂⡏⠈⣏⡴⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠉⠑⠒⠚⠁⠀⠀⠀⠀⠀⠙⢯⣀⡃⣸⣃⠼⠋

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣴⣿⣿⣿⣶⣄⠀⠀⠀⠀⣠⣴⣤⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⡀⠀⠀⠀⠀⡀⣀⠀⣄⣲⣄
⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣶⣼⣿⣿⣿⣿⣿⣤⠀⠀⣾⣷⣿⣶⣿⣿⣿⡆⠀⠀⠀⠀⢷⣶⣀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⠦⠖
⠀⠸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠙⠛⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⢀⣰⣾⣿⣷⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⢠⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠄⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⢾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⡀
⠀⠀⠀⠈⢻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠘⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⣿⣆⠀⣀⠀⠀⠀⢠⣾⣿⣿⣶⣦⠀⠀⢀⡮⣿⣿⣿⣿⠆⠀⠀⠴⢶⣶⣷⣿⡿⢦
⠀⠀⣴⢊⣹⡿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣇⠀⢸⣷⡀⠛⣻⣿⣏⠀⠀⠴⠟⢻⡟⠙⠛⠂
⠀⠀⣿⣧⣻⣿⣺⣿⣿⣿⣿⣿⠇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠻⣿⣾⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢶⣶⣶⣶⠆⠀⠀⠀⠈⠿⡿⠟
⠀⠀⠀⠀⠀⡀⢠⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠠⢀⣀⡀⣀
⠀⠀⠀⢶⣺⣟⣟⣿⣿⣓⠖⠀⠀⠀⠀⣤⣴⣶⣿⣶⣦⡄⠀⠀⠀⢀⣀⡀⢈⣠⣤⠀⠀⠀⠀⣦⡿⡛⣯⡻⣿⣷⡄⠀⠀⠀⠀⠀⠠⠀⠀⠠
⠀⠀⢰⣟⣿⣿⣯⣿⣿⣿⣷⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣇⢻⣼⣧⢘⣻⡇⠀⠀⠀⠀⠀⠀⠀⠒⠁⠄⠂
⠀⠀⠈⠉⠉⠉⠈⠁⠉⠈⠉⠁⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣦⡻⢿⣸⣿⡇
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣄⡄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⠻⣿⣿⣶⣿⣿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣷⠟⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⡀⠂⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⢀⡤⠌⠀⠀⠀⠀⠀⠢⠂⠠⠀⠀⠀⠀⠀⠀⠀⠈⠸⠅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⠄⠀⠀⠀⠁⠈⠀⠀⣰⠶⡀⠀⠀⣉⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠀⠀⠀⠀⢸⣿⣾⣇⣾⣿⣾⣿
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣽⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣿⣿⠿⠻⠿⠛⡿⢿⠿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⢺⠒⢄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⣑⣤⣵⢂⡀⠀⠀⠀⠀⠀⡹⠺⣄⠀⠀⠀⠀⠀⡱⠤⠵⣋⡜⠀⠀⠀⠀⠀⠀⠀⢸⠆⠑⡄
⠀⠀⠀⠀⠀⢎⠆⠀⠉⠁⠈⢣⠀⠀⠀⡸⠀⠀⠘⡄⠀⠀⠀⢸⠰⠀⠂⠂⢸⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⡜⡁⠀⠀⠀⠙⡄⠀⠀⠈⢎⢘⢀⢁⠆⠀⠀⣀⠠⠴⠚⢁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣠⠃⠀⠀⢇⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠒⠊⠀⠀⠘⢥⣉⣉⣉⣁⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠉⠉⠁⠀⠀⠀⠀⠑⠒⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢢⠀⠀⠀⠀⠀⢀⡤⠤⠼⡤⢮⡀
⠀⠀⠀⠀⠀⢀⣴⠍⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡤⢴⡺⠯⢷⡼⠤⠤⡀⠀⠀⡏⡎⠀⠀⠘⡄⠈⡆
⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢰⠚⢄⡠⢇⠀⣰⡿⠶⡖⠁⠀⠀⡗⠂⠀⠀⠐⠁⢀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣟⡩⠻⢄⠀⡏⠉⣧⠠⠏⠀⠀⠀⠘⠦⣀⣀⣀⠴⠊
⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⠤⠖⠁⠀⠀⠀⠸⠤⠷⠤⠚⠐⠉⠉⠁⠀⢠⢤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⡌⠁⡈⠀⠄⢀⠀⢁⠀⠂⡈⡸⢰
⠀⠀⠀⠀⠀⠀⢸⠦⡸⠙⣤⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣦⡀⠂⠠⢈⠀⡄⠐⠀⡰⣡⠃
⠀⠀⠀⠀⠀⠀⢸⠳⢽⢊⡤⢻⠀⠀⠀⠀⡴⠊⠁⣶⣀⠤⢄⣀⠀⠀⠀⠀⠀⠙⠪⢕⡲⠤⠤⠤⣒⡭⠚⠁
⠀⠀⠀⠀⠀⠀⣠⠓⠻⣟⠙⣧⡀⠀⠀⠈⠓⠒⢩⣋⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣎⠈⣦⡊⠈⡱⠧⣵⠀⠀⠀⠀⠀⡇⡃⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⠴⢒⠩⠭⣑⠒⠤⢄
⠀⠀⠀⠀⠀⡟⠻⣄⣩⠾⢄⣰⢹⠀⠀⠀⠀⠀⠳⣁⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⢳⠶⣊⠑⢢⠼⣉⠏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠁⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠑⠶⣋⡱⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠐⡖⠲⣄⠀⢀⠴⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠶⡁⣰⣁⣀⡀
⠀⠀⠀⠀⠶⣉⠉⠉⢙⢃⣶⢧⣦⢋⡤⠖⠛⡩⠍⣀⠤⠀⠉⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⢀⣄
⠀⠀⠀⠀⢀⠔⠓⠈⣺⠾⠾⠾⣿⣿⣧⡀⠀⣒⠭⠒⣈⣀⣀⠀⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣤⠋⠈⡆⠀⠀⢀⣀
⠀⠀⠀⢀⠗⠊⠉⠈⢳⡀⢀⣾⣿⠏⠀⠑⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢿⢀⢀⠷⠊⠉⢀⡇⣀
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠱⠎⠡⠉⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣀⣀⣤⡴⠶⠶⠶⢤⣤⣤⣀⣀⡜⠀⢋⡬⢈⡨⣇⠐⢋⣠⠞
⠀⠌⠀⠀⠀⠀⡠⢒⠤⡲⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⠛⢉⣠⠔⢲⠖⠒⢄⠀⠉⠉⠀⠀⠸⠜⠛⠞⠀⢀⣼⠟⠁
⡸⠀⠀⠀⠀⠈⠀⠁⠈⠀⠊⠁⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢆⠀⢀⢖⠕⢀⠤⡌⣁⠹⠤⡾⠦⢴⡋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇
⡇⠀⠀⠀⠀⠀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢰⠝⠡⢈⣴⠟⢡⠊⢣⡠⠋⣥⣤⣤⠷⠤⠖⠉⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣐⣆⣲⠸⠄⠀⢠⢿⠃⡠⠾⣄⡠⢧⡀⣸⡁⢘⣤⡖⠙⡶⠉⠀⠀⠀⡠⡖⠒⢲⢉⣦⡀⠈⣷⡄
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⣻⣒⠹⠇⠀⠀⣟⠇⠈⠀⠀⠸⠤⣔⣉⡜⠙⢧⣦⡷⠾⡀⠀⢀⡮⣉⠀⣸⢤⠿⣏⢀⡽⢆⢻⡝⡄
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣘⢓⢳⠹⠏⠂⠀⣎⠏⢀⡰⠉⣏⣀⡠⠋⣨⠧⣀⡞⠉⣧⣶⡃⠀⡏⠀⠀⡏⢣⣬⣀⡜⠻⡀⡜⢸⡏⢽
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⢦⢙⣒⡛⠎⠯⠧⠄⢸⡏⠀⡏⠑⠺⣁⣀⢹⣽⣁⣠⣨⠛⠒⡏⠀⣹⠀⢸⢦⡾⠤⢞⡔⠛⠧⣤⡽⠁⣼⠀⢛
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠰⠈⡄⠀⠘⡝⣖⠲⠈⠹⠌⠏⠀⣾⠀⡠⠓⠒⣴⠉⠹⡏⢠⣹⢽⡝⠂⠲⣏⣉⢱⡇⢸⠸⣴⣲⣘⣤⠯⢷⠁⡸⡰⡏⠀⣼
⠀⠀⠈⢆⠀⠀⠀⠀⠄⠁⠡⡀⠀⠐⠑⠐⠀⠩⠀⠑⠀⠀⣿⡄⢣⡦⠷⣸⠊⠚⣿⢿⡁⠞⣧⠴⠾⠟⠙⡿⠓⢣⠔⠚⣇⡈⢧⡤⢬⠟⢁⡷⠁⢐⣿
⠀⠀⠀⠈⠣⡀⠀⠀⠀⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣼⣇⠘⣷⣀⣜⣠⢴⣅⠀⣼⠉⣹⢴⣦⠗⠸⣆⣠⡧⠶⡾⠛⠳⡏⣀⠎⡠⡺⠁⠀⢴⡿
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⢜⠫⠪⣿⡀⠀⠳⡀⡧⠤⣜⠉⢙⠛⠁⢴⢛⠦⡇⢀⣇⣀⣄⣧⡞⠉⣹⠁⣰⡱⠁⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⢀⣠⠠⡢⢐⢅⣊⡵⠬⠞⠉⠳⣤⡀⠳⢧⡔⣋⣉⡁⠀⡠⠼⢇⢀⡸⡏⠀⠉⣏⠀⢸⠞⢁⣴⠟⠁⠔⢘⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠙⢮⣦⠀⠈⠁⠀⢹⣠⠧⢤⡼⣍⡞⠛⡟⠉⣉⠖⢁⣠⡿⠃⠀⠀⢈⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⣀⠀⠀⠉⠛⣆⣈⣦⣠⠟⢉⣁⣴⣿⠟⢁⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⢷⣶⣶⣶⠦⣴⡦⣭⠿⠟⣋⢥⣰⣵⠞⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣶⣶⣿⣷⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⠒⠀⡠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠆
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠤⠀⠐⠠⠞⠛⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⢀⡆⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖
⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠈⠈⠻⠶⠶⠶⠊

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠠⠆⠉⠀⢳⣧⡴⣊⢁⠙⢧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⠗
⠀⠀⠀⠀⠀⠆⠘⠁⢀⠗⠁⢤⣭⢉⠙⠉⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡀⠐⠤⠄⠄
⠀⠀⠀⠀⠤⠀⡙⠋⠛⠤⣈⠂⠉⠉⠠⠠⠤⠈⠓⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠴⠛⠣⠞⠀⠀⠃
⠀⠀⠀⠀⠀⠸⠃⠄⠀⠘⠋⡄⠀⠀⠀⠀⡄⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣏⠁⠀⢀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠐⠊⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡔⠒⠛⠹⣷⣤⠘⣁⣨⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠾⡆⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⢯⣽⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠐⣀⣐⡤⣠⠋⠀⠛⣄⠘⠂⠀⠀⠀⠀⠀⠀⣊⠁⠀⢠⠄⢀⠋⣱⠊⠿⠂
⠀⠀⠀⠀⢀⠀⠚⠁⠀⢨⠀⠱⣦⠉⠀⣷⠂⠀⠀⠀⠀⠀⠀⢁⠈⠲⠢⡔⠋⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠊⠀⠁⠀⠀⠀⠀⢆⠀⠁⠀⠀⠀⠀⠀⠀⠈⠈⠷⠜⠻⠦⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠂
⠀⣀⡀⡀⠀⡀⡀⡀⡀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠔⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⢀⠠⣀⠀⠀⠀⠀⠀⠀⣖⠥⢂⣠⠶⡄⠐⠂⠀⣠⠀⠀⠠⠈⠁⢶⡦⠿⣀
⠀⠈⢄⠈⡀⠸⡃⠀⠀⠀⠀⡄⠀⠀⢰⠁⠀⡀⠀⡀⠑⠮⠉⠂⠀⠀⠀⠀⠈⠉⠏⠈⠁⠈⠁⠀⠊⠁⠀⠀⠀⠠⣦⣷⠺⡴⣯⢧⡀
⠀⠀⠀⠉⠉⠀⠙⠀⠀⠤⠞⠁⠀⠀⠈⢇⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠘⠑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂


⠀⠀⠀⠤⢀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢈⣛⣦⣀
⠀⠀⠀⠀⠈⠈⠀⠂⠒⠉⠀⠀⠀⠀⢰⠀⠀⠀⡀⢀⠄⣀⡤⠀⡀⠀⠀⠀⣠⠰⠆⢘⣤⡆⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠁⠜⡙
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠤⠄⠊⡄⠑⡀⢀⠙⠀⠀⠀⠹⣄⡬⠝⠀⠳⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⡆⢀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⣉⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄⢀⠔⠎⠛
⠀⠙⠛⠀⠀⠈⠉⡒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⢁⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠖⠛⠛⢓⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⠉⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⡠⣄⡀⠀⣀⠀⢀⡆⠔⠀⠀⠀⠀⠀⢀⠠
⠀⢁⠀⠆⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⡑⠀⠀⠁⣿⢳⠆⠀⠀⢀⡤⠊⠁⣀⠀⠀⠀⠐⠃
⠀⠀⠀⠄⠢⠀⠄⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠋⠋⠀⠀⠀⡈⠀⠀⠀⠈⢀⡰⠈⠄⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠂⠱⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⡀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⣦⡀⠀⢿⣿⣧⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣴⣿⣿⣿⣷⡀⠸⡯⠙⡇⠀⠀⣴⣿⢿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠻⣿⢻⣿⣿⣦⣙⡆⡇⠰⣇⣴⡿⠟⢡⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢷⣶⣤⣤⣭⣷⣝⣿⣛⣿⣛⣓⢶⢿⣿⡶⠶⣀⣠⣟⣁⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⣤⢶⡚⠟⣫⣀⣭⢹⡟⠻⢞⣱⣿⡟⢩⣾⢉⣙⣓⢿⡛⠒⠶⢿⡿⠿⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡀⣶⢸⣝⡿⢦⣴⢰⣿⡙⣿⣷⣿⣛⣿⣽⣿⡿⣦⢺⣷⣴⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡇⢸⣥⣏⢻⣿⢃⣬⣿⣏⣿⡿⢿⣧⣻⣿⣿⣿⢿⣷⣿⡶⣦⢿⣿⣷⣬⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⠈⣴⡀⣅⢻⣯⣁⣼⡛⢿⣛⣻⣷⣽⣿⣿⣿⣻⣿⣼⣿⣿⢧⡅⣦⣿⣽⡜⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⣴⠈⠑⣏⣷⣼⣷⣭⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏⢻⣾⣿⡿⢻⣾⣷⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠻⣂⠚⣮⠁⣿⣙⡦⣻⣤⣽⣿⣯⣻⣿⣿⡿⣻⣿⣸⣿⣾⣿⣿⢧⡻⣿⡶⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿⣦⠻⣷⠛⣶⢳⠘⣛⠻⣿⣟⡻⣿⣿⠟⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⢉⣿⣦⢰⡬⣉⠸⣿⠇⠻⣿⣿⡟⢿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⢻⣍⠘⢯⣼⡅⠋⣿⣳⣬⣿⣿⣿⣿⣏⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⠻⠰⣶⡌⠁⢰⣮⢻⣿⡴⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠱⣇⢙⣇⡸⠿⣿⣼⣿⡿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢹⣿⢿⣿⠀⣾⣿⣻⠱⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠟⣿⠛⣦⡝⠻⣃⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⣿⠏⢴⣦⡍⣿⣿⣻⢿⣿⣾⣿⣏⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⣦⠺⡆⢶⣏⣹⣿⣾⣿⣿⣛⣿⣟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣤⡰⡷⣿⣷⣏⣰⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⢿⣿⣟⡛⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠗⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡟⡌⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢼⣿⣼⣿⣿⣿⣫⣶⠄
⠀⠀⠀⠀⠀⣰⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣻⣸⣿⣿⣿⣿⣿⣿⣿⣢⡼⠃
⠀⠀⠀⠀⢸⣭⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣲⠿⢻⣉⣿⣿⣿⣿⡿⣛⣯⣖⣿⡂⡆
⠀⠀⠀⠀⢾⣿⣯⣶⣶⣂⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⢢⣋⡻⣿⢿⣿⠿⠷⠳⣱⣿⠃⠁
⠀⠀⠀⠀⠸⣿⣷⣽⣾⣿⣄⠠⠶⣶⣨⡀⣀⣠⠆⠀⠀⠀⠀⠙⢯⣇⢠⡔⣹⣆⡖⣶⣞⢠⠟⠁⠈
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡛⠉⠉⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⢀⣿⣇⣤⣴⣶⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⢀⣙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠛⠛⠉⠁⢀⣀⣤⣤⣶⣾⡿⠿⠟⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⣴⣦⣴⣦⣴⣴⣶⣾⠿⠿⠛⠛⠉⠁⢀⣀⣤⣤⣶⣶⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⢹⣿⠟⠉⠁⢀⣀⣤⣤⣶⣾⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⠄⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⣶⣶⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⣴⣿⢿⣦⠉⠹⣿⡆⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡍⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠰⣿⡌⣿⣿⣩⡀⢻⣿⠈⣥⡄⠀⢻⣿⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣧⠀⣤⣴⣦⣄⢸⣿⣟⡋⠀⠀⠀⢿⣷⢸⣿⣟⣡⣌⢿⣿⡿⠃⠀⠈⠉⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⡆⢿⣿⣽⣿⠈⣿⣿⠛⣀⢰⣷⣾⣿⠂⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀⡀⢻⣷⠘⣿⡿⣿⣦⠹⣿⠿⠟⠃⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠛⠛⠛⠛⠃⠘⣿⣇⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⡿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⣀⣠⣤⣴⣶⣿⠿⠿⠛⠋⠉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⢀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀
⠐⠀⠀⠀⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⢁⠀⠀⠀⠀⠰⠀⠀⢀⠴⠃⠉⠀⠀⠀⠀⠀⠰⠋⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠁
⠃⠀⠀⠀⠀⠠⢀⡄⣀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⡀⠀⠀⣾⣷⠋⠀⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣆
⠀⠀⡀⠑⠦⢠⠘⠊⠐⢀⠠⠀⠀⢸⡅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠎⠙⠓⠓⠖⠰
⠀⠀⠈⠉⠓⠢⢄⠀⣰⣿⣀⡀⠀⠚⠦⠤⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠛⠻⢧⠀⠀⠑⢑
⠀⠀⠡⠀⠀⢤⠊⠙⠉⠏⠏⠉⠀⠀⠀⢠⡀⠉⠑⢄⠀⠀⠀⠀⢠⣄⢀⠴⠚⢲⠋⠀⠀⠀⡇⠀⠀⠐⣇
⠀⠀⠀⠀⠀⡀⠀⠦⠄⢀⠀⢀⢀⠀⡀⠀⠈⠁⠀⠀⠑⡀⢀⡴⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠘⣄⠀⠀⠈⠂
⠀⠀⠀⠀⠁⠆⢀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠸⠢⠄⡸⢦⣷⠊⠀⠀⢰⠃⠀⠈⠀⠀⠀⠺⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢽⣆⠟
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠉⠓⠠⡄
⠀⠀⠀⠀⠀⠄⠀⠐⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈⠰⠂⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠑⠀⠄⠐⠁⠀⠀⠀⠀⠀⠠⠀⢀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠩⣉⠑⠂⠀⠈⠇⠐⠈⠁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⡄⠐⠒⠒⠀⠉⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠠⠀⠒⡠⠖⠁⢀⠁⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠂⠁⠀⠈⠢⡀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠔⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⢀⣀⣀⡠⠤⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⢠⣶⣆⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠃
⠀⠀⠀⠀⣀⣤⡏⠀⠀⠀⠀⠀⣀⡀⡀⠀⡠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⢀⠠⠀⠂⠠⢾⠁⠀⠐⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⢤⠲⢦⠴⠀⡠⢤⠤⠀⠀⠀⢀⠢⡀⠀⣠⡆⣸⣇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠘⣀⡀⣱⣯⣤⣶⠂⠀⠀⠈⢳⣸⡿⠛⠉⠀⠀⠙⣆⣀⡄
⠀⠀⠀⠀⠀⣰⣟⠙⣿⣿⣿⡆⣤⣠⣯⣉⠀⠀⠄⠁⠀⠀⠀⢀⠇⠀⠀⠌⠠⠤⡞⠛⢈⣙⡁
⠀⠀⠀⠀⢸⣟⠻⣥⣜⣿⣿⣿⣿⣟⡟⠃⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠂⠀⠀⢹⣧⣥⠈⠇
⠀⠀⠀⠀⠐⣿⣭⠐⠀⢥⣝⢿⣿⣿⣿⣋⣉⠁⠀⠠⡏⠀⣼⣅⡀⠀⠀⠀⠀⠀⠈⠛⠳⠒
⠀⠀⠀⠀⣀⣨⣿⣧⡲⢾⣿⣦⡋⣹⣿⡿⠀⠈⠛⠧⡝⢼⠧⠋⠈⠀⠀⠀⢰⣶⣶⣶⣤⣄⣀
⠀⠀⢀⣼⣿⠋⠛⣛⠟⣻⢹⣿⡿⢿⣿⣤⣄⠀⠀⢀⠟⠀⠀⠀⠀⣀⠀⣠⣾⣿⣿⡫⢟⠿⠛⠤⢀
⠀⠀⣼⡯⠔⠀⠘⢉⡼⡟⠘⠀⢠⣾⣿⣿⣿⣦⠀⡞⠀⡆⣠⠄⢺⣷⣾⣿⣿⣿⣭⣀⣁⣀⣀⠀⠘⠂
⠀⠀⠸⣧⣴⠅⣶⡟⣇⣻⣴⣶⢿⣾⡟⠓⠨⡉⠘⠇⠀⢷⣽⣴⡍⣿⣿⣿⣏⡙⠋⠛⠳⢤⡈⠻⢿⠏
⠀⠀⠀⠙⠓⠘⠛⠿⣿⣿⠟⠿⠶⠾⢿⣤⣴⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⢿⣾⣯⣤⣤⡈⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣓⣶⣶⣚⣶⣶⣬⠟⣻⣿⣷⣤⡀⠀⠀⠀⠀⠀⣸⡋⠉⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠟⠁⠆⢻⣿⣿⢿⢻⠆⠀⠀⠀⣾⣿⣿⣶⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⣋⠩⠋⠀⠀⣀⣴⣾⣿⡿⢧⡘⣷⡀⠀⣠⡇⣿⣿⡂⠑
⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣀⣤⣴⣷⠿⠟⠛⣩⡏⠀⣿⠿⣿⣷⣿⣏⢝⢹⣟⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⢸⡇⢰⡏⠀⠹⠿⣿⣿⣏⣩⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡃⡟⠀⠀⠀⠀⠈⠉⠛⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢻⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣾⣷⣄⠀⢹⣿⣦⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣿⣿⣿⣦⠀⡿⠘⡆⠀⣠⣾⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⣀⣀⡀⠀⠈⢿⡿⢿⣿⣦⣧⡄⢘⣥⣾⠛⠁⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⣿⣿⠟⢲⢿⡾⣿⡾⣷⣾⢝⣻⠿⣟⣰⣾⣃⣲⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠀⡔⣷⣟⣍⣁⢩⡖⢿⣿⣼⢷⣶⣲⣾⣇⣴⣍⣽⠬⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⡆⢸⣡⡓⣿⡟⣘⣿⢚⣿⢾⣏⣻⣿⣿⡿⣧⣽⣸⣽⣷⣲⣝⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠛⠄⢱⣄⣕⢿⣍⣤⡛⣿⣛⣿⣾⣿⣿⡟⣿⣿⣿⣿⢧⣡⣼⣯⡆⡿⡇
⠀⠀⠀⠀⠀⠀⠀⡺⠀⣴⠆⢘⢧⢇⡿⡶⣿⠾⣿⣿⣿⣿⣬⣿⣿⡿⣿⣹⣿⣷⢏⣿⠿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⡆⢠⡌⢱⣜⣧⣘⡢⣿⣼⣿⣿⣷⣾⣿⣿⣯⣿⣷⣿⣿⣿⣟⣷⣽⣟⣣⡎
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠻⢨⡛⢀⡳⠇⣶⡌⢿⣶⣽⣿⣷⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢻⡋⠺⣌⣇⠛⣴⢮⣹⣿⣶⣿⣟⢿⣽⣿⣿⣿⣿⣿⣿⣿⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣬⠙⢰⣦⠉⣰⣮⢻⣿⣮⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠢⣦⣭⣜⠛⢿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢺⣏⣿⡅⢿⣻⢭⣼⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣘⣧⡟⣃⣈⢾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⣮⢼⡉⣼⡛⣿⣾⣿⣟⢿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣤⡰⢾⣿⣿⣱⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢟⣯⣿⣝⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡤⣴⠶⢍⡇⢠⡎⠉⠃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡌⠠⡶⡤⣟⠄⠁⢠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠀⢘⡄⠀⠀⠀⠀⠀⠀⠆⠀⠡⣀⣙⠁⠎⢈⣒⠮⠐⢐⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⠀⣼⠀⠀⠀⠀⠀⠀⠀⠰⡀⠤⠀⠂⠀⣁⣡⡤⠖⢛⣩⡥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠈⠈⡱⠂⠀⠀⠀⠀⠀⠰⠶⠒⠛⠉⠉⠰⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠒⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⢉⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠚⢉⣁⠤⠴⠒⠚⠉⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠒⠊⢉⣁⠤⠴⠖⠒⠉⠁⣀⣠⠤⠴⠒⠋⠁⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡠⠤⠶⠒⠚⠉⠁⣀⡠⠤⠶⠒⠋⠉⢀⣀⡤⠤⠖⠚⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡤⠤⠖⠒⠊⠉⢀⣀⡤⠤⠖⠒⠉⠁⠀⣀⣠⠤⠴⠒⠉⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⠤⠴⠒⠒⠉⠁⠀⣀⡠⠤⠖⠒⠋⠉⠀⢀⣀⠤⡤⢖⠿⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡤⠤⠖⠒⠊⠉⠀⢀⣀⣤⠴⠒⢊⣉⣥⠴⠊⠉⠀⣀⣀⠀⢹⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡠⠤⠴⠒⠚⠉⠁⢀⣠⡄⠀⠀⠁⢀⣀⣤⡴⠺⣿⣹⣇⠀⢻⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⢀⣠⡤⠔⠚⠉⠁⠀⣤⣦⡞⠻⣏⠙⣿⣫⡹⠿⠟⠀⠀⢻⡆⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁⠀⠀⣤⢰⣟⣁⢹⡄⢤⡄⠻⠆⠙⠉⠀⣀⣄⠶⠚⠉⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠉⠀⣀⣄⠰⣾⣃⠀⢹⣆⢻⣥⠆⠛⠋⠀⢀⡀⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⣿⣽⣅⢻⣯⡼⠛⠛⠀⠀⣀⣤⡴⠜⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠘⠷⠙⠃⠁⠀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠄⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣄⠴⠚⠈⠉⠀⡀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠉⠀⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⠉⠛⠳⢦⣠⡟⠁⠘⣧⠀⠀⣠⡶⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠘⢷⡀⠀⠀⠀⢈⢣⡀⠀⢸⡤⣚⡥⠶⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⢠⠀⠙⠦⣄⣀⣀⣙⣷⣴⣼⠿⠿⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠀⠀⠛⠋⠀⣀⣴⠿⠋⠁⠒⢺⡿⢿⠳⢌⠀⠀⠈⠛⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⣡⠇⠀⠀⠲⢾⣯⣅⣀⣀⣤⡾⠟⣷⡀⠀⠀⠹⣶⡶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡴⢲⠀⠈⠉⠉⠉⠁⠀⠀⠈⠿⣶⣄⣀⣹⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⢤⠀⠀⠀⠀⠓⠋⠀⠀⣴⢉⡆⠀⠀⢠⠚⡆⠀⠉⠉⢉⠍⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠞⠀⠀⠀⢠⡖⣢⠀⠀⠘⠛⠁⠀⠀⠘⠛⠃⠀⠀⠀⢸⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡠⣄⠀⠘⠷⠃⠀⠀⠀⢀⡴⢤⠀⠀⠀⢠⠎⡢⠀⠈⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣧⡟⠀⠀⠀⠀⠀⠀⠀⠾⠶⠋⠀⠀⠀⠘⠛⠁⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣏⡹⠀⠀⢀⣀⡀⠀⢀⠄⢢⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠰⠉⡧⠀⠀⠀⠈⠉⠁⠀⠐⣯⡤⠃⠀⠙⢚⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠙⠁⢀⡔⡆⠀⠀⡠⢶⡀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⠶⠃⠀⠀⢓⣋⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠋⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣭⣬⣭⣯⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⡄
⠀⠀⠀⠀⢀⠀⣶⣄⡠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⢾⣿⣧⣽⡿⣾⡇⣄
⠀⠀⠀⣀⣸⡆⣿⣿⣿⣿⠿⣛⣙⣦⡸⢍⠄⡀⠀⠀⠀⠀⠀⢠⣾⠿⢉⠘⣻⢷⣯⠿⣷⣿⣿⣧⡴
⠀⠀⡀⠈⠻⣿⣿⣿⡟⣽⣿⣾⣿⣿⣿⣾⡇⡒⠤⠀⠀⠀⢠⣟⡓⠆⠖⣰⣶⣿⣿⣛⡿⣿⣿⣿⣆⣀
⠀⠀⢹⣿⣿⣿⣿⣯⢩⣿⣿⣿⣿⣿⣽⡇⠲⠨⢁⣀⠀⠀⡓⠠⢀⢸⡏⣻⣿⣿⣿⣿⣻⣿⣿⣿⣇
⠀⠀⠀⣹⣿⣿⡿⠥⡜⣿⣿⣿⣿⣿⣿⣷⣻⢒⣐⠠⠄⠀⠳⣇⣖⣰⣠⣷⣿⣬⣿⣥⣾⢹⣟⠃
⠀⠀⠚⢩⡿⠿⢻⡠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣋⠀⠀⠈⠛⠿⢿⣿⣿⣿⣯⣿⣷⠿⠋
⠀⠀⠀⠉⠁⡜⢀⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠑⡈⣯⠛⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠈⠈⠷⣾⣷⣾⣯⣯⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡕⠋⠰⣤⣿⣷⠛⡉⠙⠫⣖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⣠⡤⠔⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣠⡆⠘⣿⣿⡋⢄⠀⠄⠐⠛⣭⣓⡢⠤⠤⠀⡀⠔⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠤⠄⢠⠤⠄⠀⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⠃⠀⡄⡥⢂⢭⠖⠀⠀⠀⠀⠈⣸⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠆⠐⠀⠀⠀⢀⠔⢁⠘⢦⡀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠄⡜⠡⡀⢩⣄⠋⠈⠀⠀⡀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠆⠀⠚⠒⠀⠀⠈⠉⢐⡀⠠⠊⣷⠀⡀⠀⠀⠀⠀⠀⠀⠰⣄⣖⢀⠴⠊⠁⠀⢀⠀⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠚⠐⠃⣠⠀⡁⠀⢰⠃⣷⠤⠰⠄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠰⢄⣀⣀⡜⡀⠂⡴⠐⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⣠⠀⠀⢀⡤⠀⠀⠀⠀⡙⢠⢣⣀⠀⠀⠀⠀⣀⢀⠀⠀⠰⢤⠄⣠⡤⢰⠎⠉⡉⠉⢟⠙⢒⠷⡀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠁⡴⠀⠀⠀⠀⠤⠂⠈⣠⠈⠗⠈⠀⠀⣠⠀⠉⢛⠯⣿⣋⡥⠊⢁⠀⠀⣀⠀⠃⠀⢠⠀⠈⡅⢘⠦⡀
⠀⠀⠀⠀⠈⠀⡄⠀⠀⣠⠀⠀⠐⠋⠀⢀⠄⠀⠀⠔⠀⠀⠀⠀⠀⣩⠴⢃⡇⠀⡄⡌⠀⠀⠘⠀⠀⠘⠀⠀⠄⠈⠀⠀⠃⠈⡆⠐
⠀⠀⠀⠀⢀⠈⣠⠄⠈⢁⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠔⣈⢡⠠⡼⡇⠹⠀⠠⠀⢨⠁⠀⠀⠂⠀⠀⡌⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠁⠐⠀⠀⠉⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠉⡀⠴⢤⠓⠀⠀⠈⠀⢀⠄⠀⡤⠀⢠⠄⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⢁⡄⠀⠀⠀⠀⠇⠀⠘⠀⢀⠀⠀⡈⠀⠈⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠊⠀⠀⠀⠀⠀⠀⠻⠀⠐⠁⠘⠃⠀⡄⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢠⡂⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠐⡾⠡⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⣀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣁⠀⠀⠄⠀⢀⣘⡁⠨⠍⠉⠁⠲⢝⢧⠀⠀⠀⠠⢄⣀⣀⡀
⠀⠀⠀⠀⠃⠀⠀⠐⠒⠒⠐⠛⠓⠙⠛⠩⡳⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠤⢢⣆⣦⣒⡂⠀⠀⠀⠉⠙⠓⠶⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⠀⢠⣄⠔⠊⢈⡝⢏⠠⠙⠐⡐⠆⠀⠀⠀⠀⠈⠋⠙⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠼⣧⢳⣏⠀⠀⠄⠀⣉⡀⠀⠘⠀⠈⢁⡄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠢⠀⠐⢕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠊⡛⠻⡉⠝⢦⣁⣟⠰⠄⠋⠤⢀⡈⠁⣄⠸⠇⠀⠀⠀⢀⠀⢀⠃⠀⠀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠉⠀⠁⣤⠃⠀⢿⠎⡈⢃⠻⠐⢆⠘⠀⠀⡁⢀⡉⠟⠀⣤⠔⡿⡻⢽⣿⣦⡀⠄⢠⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣤⠲⡡⡘⠂⠀⠐⡆⠹⢉⠰⠇⠀⠀⢝⠀⢁⡈⠈⠀⣀⢘⡂⡀⠂⠁⣻⠆⡏⠀⠋⢸⠙⣮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡆⢰⠀⢁⠈⠁⠄⠀⣀⠉⣄⠀⠀⠀⠀⠑⠚⠁⠀⢀⡉⢠⠀⡁⡤⢈⡍⣴⡿⣁⠰⡆⡀⢉⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣄⠈⠂⢀⡉⢀⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⢠⠆⠰⠂⠶⠋⡦⠹⠀⡄⣁⢨⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠓⠀⣁⠘⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡰⢂⠴⠓⠁⠀⠀⠲⡄⠦⠀⡈⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⠇⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⠛⠶⣦⡘⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠻⣿⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠲⠶⠶⣶⣶⠿⠿⠿⠿⠿⠿⠿⣷⣦⣄⠀⠋⠀⠀⣿⣇⣀⣤⣶⠶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠛⠒⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⣿⣆⠀⢠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⢙⣷⡦⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡉⠁⠀⠀⠤⠤⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠛⠳⢦⣄⢘⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣛⣿⣃⣀⣀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⡿⠋⣍⣿⣤⣴⡶⠾⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠉⠉⢉⣩⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⡐⠼⠶⠶⠛⣋⣡⡴⠶⠛⢋⣩⡿⠟⣿⠗⣨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⢟⣋⣥⣶⣶⣿⠟⠁⢀⣾⠃⣰⣿⣿⣯⢠⣤⠤⣂⡤⠄⠀⠀⢀⣠⣤⣤⣤⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⣻⡿⠛⠁⣠⣶⣿⡏⢰⣿⠉⠻⣿⣦⣝⡛⠛⠛⢉⣀⣀⣠⣤⣤⣭⣝⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢀⣼⠟⠀⣠⣾⠟⠉⣾⠃⢸⡇⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣾⣏⡀⠀⠀⢠⡾⠁⢀⣼⠟⠁⠀⠀⣿⠀⢸⠁
⠀⠀⠀⠀⣠⣾⡿⠟⠋⡉⠉⢩⡿⠟⠛⠿⠿⣶⡿⠁⣠⡟⠁⠀⠀⠀⠀⣿⠀⢸
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠻⣦⣈⣤⠆⠀⠀⠀⡿⠁⣰⣿⡀⠀⠀⠀⠀⠀⣹⡄⢸⣄⣀⣀⣀⡀
⠀⢠⣿⠏⠀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣸⠃⣰⡏⢿⣷⠀⠀⣠⣶⣿⣿⣧⠈⣿⠿⠿⠿⣿⣿⣷⣤⡀
⠀⢸⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⢸⣿⣧⣾⣿⠟⠉⠀⠘⣦⠘⣦⡴⠀⠀⠀⠉⠙⢿⣷⡄
⠀⢸⣿⡀⠸⣿⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⡇⣼⣥⣤⣾⣿⣿⡿⠁⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⢿⣷⣄⠈⠃⢀⣴⣾⡿⠟⠋⠉⠉⢹⡃⡏⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠈⠻⣿⣦⣴⣿⠟⠉⠀⠀⠀⠈⢷⣼⣅⣧⣤⠞⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⣸⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⢀⣴⣿⠏
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢠⣿⡿⠻⢿⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠠⢤⣤⣤⣤⣤⣶⣿⠟⠁⢀⣴⣿⡿⠁⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣬⣍⣉⣉⣉⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠄⠀⠀⠀⢤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠓⠢⠀⠐⡄⠲⠀⢄⣃⠱⢆⡈⠀⢀⡠⠂⠀⠀⠀⢦⡾⠕
⠀⠀⠀⠀⠀⡟⢉⢴⠂⠡⠀⠃⡰⠀⠀⠈⠑⠋⠭⠽⠁⠀⠀⠀⠉⠁⠙⢋⠉⠀⠀⠀⠀⠀⠰⠋⣀⡶⢂⠋⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠆⢐⠔⠉⡱⢎⠑⠚⢩⡡⡱⠀⠀⠀⠀⠈⡐⠀⠀⠀⠀⠀⠀⡀⢠⣾⡃⠀⢂⠚⠠⠄⡄⠆
⠀⠀⠀⠀⠀⢀⢠⣬⢐⡆⣀⡀⠀⠀⠠⠀⢸⡔⠧⣔⠀⠀⠀⠀⠀⠁⠠⠀⠈⠀⠀⠺⡀⡩⢈⠓⡀⠈⠃⠍⢀⡁
⠀⠀⠀⠀⠀⡁⠄⠑⠺⠛⡟⢃⢄⡤⣿⡷⠗⡚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠊⠊⠠⠇⢁⡐⠋
⠀⠀⠀⠀⡄⠁⢂⠁⠀⠀⠉⢋⠋⠅⢠⢀⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⡄⠄⣠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠠⢀⠐⠀⠀⠄⠌⡀⠄⠀⠀⠀⠀⠀⠀⠀⢂⠄⢀⣄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⡂⠆⠀⠠⠠⠀⠄⠂⠀⠀⠂⠕⠆⠀⠀⠀⠀⠀⢄⠂⠀⢘⠛⠯
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠈⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠠⠴⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⠿⢿⡀
⠀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣕⣦⠾⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⡀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢤⠀⡀⠀⠔⠉⠩⠐⠀⡁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⣎⣰⢔⣶⡶⠑
⠀⠀⠀⠀⠀⠠⣠⣰⣤⣍⣤⣄⠀⠀⢀⠁⡈⠀⡂⠅⢀⠆⠂⠀⠀⠀⠀⢀⠀⠀⠀⠠⠈⠉⠙⠉⠉
⠀⠀⠀⠀⠀⢀⠀⠂⠆⠘⡈⠩⠁⠀⠀⣄⠁⠄⢁⠐⠀⢄⠁⠀⠀⠀⠀⠈⠚⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠃⠀⡄⡁⠀⠀⠁⠐⠂⠢⠈⡀⠃⠀⠀⠀⠀⠀⠑⠀⡉⠉⠀⠀⠖⠘⠲⣶⣦
⠀⠀⠀⠀⠀⠀⡈⢀⠁⡈⢀⢀⠁⠀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠂⠀⠞⠹⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢂⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⡘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡄⠨⡙⣶⠃⡀⠱⡄⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠛⠒⠾⢾⡄⣇⠀⢹⣀⡴⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣄⠀⠀⢰⡆⠀⠀⠈⠛⢄⠸⠯⠶⢧⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠁⠀⣀⠀⠀⠀⣀⠀⠀⠈⠳⡄⠀⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⣰⡄⠀⠘⠛⠀⠀⠈⠑⠁⠠⢆⠀⢹⡋⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁⠀⠈⠀⠀⠀⣀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣧⡈⠢⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⠃⠐⠃⠀⠐⠣⠂⠈⠁⠂⠀⠀⠑⠊⠀⣰⡀⠂⣿⠹⡗⠂⠀⠑⠀⠀⠀⠀⠀⠀⠀⣸⢰⢀⡤
⠀⠀⠀⠀⠀⢠⣯⠀⢀⣄⠀⢀⡄⠀⠀⢠⣶⠀⠀⣠⡄⠀⠀⠀⢠⠏⠂⠁⠀⠀⢀⣠⠖⠚⠉⠉⠛⠲⣿⠘⡟⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠈⠂⣠⡄⠀⠀⠀⠀⠀⣊⡤⣂⡴⠋⠀⠀⠀⠀⡴⠋⠀⠀⠀⢄⡀⠀⠀⠈⢧⡸⣸
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠚⠄⠀⠀⠐⡊⢤⣒⣲⡯⠽⠖⠛⠉⠀⠀⠀⠀⣠⠞⠀⠀⢀⣡⠶⠚⠉⠀⠀⠀⠈⠻⣭⢍⡑⠒⠂⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⠶⠋⣀⡠⢀⣠⠖⠁⡀⠀⠀⠘⡆⠉⠲⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠀⠜⣡⠴⣊⣥⠖⢋⡡⢴⠊⠳⠀⠠⣰⡟⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡀⠀⠾⠷⠻⠭⡖⠋⠹⠀⠈⠀⠀⣀⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠐⣀⣊⣀⣀⣡⣤⣤⣶⣖⠻⠍⠁⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣭⣭⣉⣀⣀⣀⣀⣀⣀⣀⡤⠽⠛⠁


⣤⣤⣴⣶⣶⣤⣴⣶⣦⣴⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⣉⣉⣉⣩⠿⠋⣠⣾⣋⣉⣉⣉⣉⣉⠉⢻⡆⠀⣿⣉⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡇⢸⣿⣿⣿⣿⣶⣄⠙⠿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣦⠈⠛⣿⣿⣿⣿⡇⢸⡇⠀⣿⣿⣿⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣉⣈⣀⣀⣀⡈⠁⣿⢀⡼⢋⣀⣁⣈⡀⢸⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣉⣉⣉⣉⣉⡁⢰⣿⠟⣀⣈⣉⣉⠉⠁⢸⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣉⣉⣉⣉⣉⣁⣈⣁⣀⡉⠉⠉⠉⣀⣀⢸⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣉⣉⣉⣉⣉⡉⣉⠉⠉⠉⢀⣤⣾⣿⣿⣿⣧⡀⠹⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠉⠉⠉⠉⠉⠉⠉⠁⣠⣶⣿⣿⠟⣫⣝⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠛⠛⠛⠛⠛⠋⠀⢸⣿⡿⠛⠁⠸⣿⣿⠇⠈⠛⢿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠛⠛⠛⠛⠛⠛⠛⠀⢹⡇⠀⢀⣴⣶⣶⣶⡄⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⡾⠛⠷⣴⣶⡀⠀⢸⡇⠀⢸⣿⣿⣷⣶⠆⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣀⣀⣀⣀⣀⣈⣀⣀⣸⣇⣀⣸⣿⣿⣿⣿⣇⣀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠠⠦⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣠⡇⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⢀⠀⡀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣢⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠀⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠒⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠁⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠊⠀⠁⠀⠀⠀⠀⠰⠤⠀⠔⠃⠀⠐⢄⠀⣀⡀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠏⠀⠀⢀⣠⣤⠶⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⠀⣠⠞⠋⣰⠏⣠⡴⠞⠋⠁⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⢀⡞⠁⠀⢰⣿⠞⠉⠀⠀⠀⢀⣠⡶⠟⠳⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡇⣿⠀⠀⡞⠀⠀⣠⠞⣡⠔⠂⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⣹⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⣾⣿⡸⣆⡼⠁⠀⡼⠃⡴⠃⣠⣾⠿⠶⠛⠛⠛⠛⠛⠛⠒⠒⢒⣻⠟⣦⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⣧⠹⣇⠀⣸⠁⣼⠁⢀⣤⠶⠒⠒⠀⠀⠀⣀⣀⣤⣤⡶⠟⠉⠀⠈⠃⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠛⠋⠹⣧⠙⢧⡁⣼⣧⡾⠋⢁⣠⣤⠶⠾⠛⠛⠋⣉⠉⠀⠀⣠⡀⠀⠀⠀⣀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⣴⠟⠉⢀⡤⠶⠖⠛⠛⡛⢷⣼⡿⣸⠋⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠘⠟⠀⠀⠀⢿⡇⠀⠸⣷
⠀⠀⠀⢀⡾⠁⠀⠘⢁⣀⣤⣴⡶⠛⣵⠟⠁⡄⠀⠀⠀⠀⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡆
⠀⠀⠀⡼⢁⣠⡶⢿⡟⠁⣴⠏⢀⠞⠁⠀⣼⡇⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡇
⠀⠀⣼⣵⠟⠉⢀⡿⠀⣼⠏⠀⡏⠀⢠⠞⢸⣇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⢴⣄⠀⠀⠹⠇⠀⣿⡇
⢀⡾⠛⠁⠀⠀⣼⠃⢰⡿⠀⠀⠀⣰⠏⠀⠀⢻⣦⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⡇
⠉⠀⠀⠀⠀⢠⡟⠀⠸⣇⠀⠀⣼⠏⠀⠀⣤⡀⠈⠻⣦⡀⠸⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⢰⡟⠀⠀⠀⠙⠷⠀⠀⠈⠻⣦⣧⠀⠀⠘⠿⠃⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⣿⣆⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢸⡇⢀⡀⠈⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠘⠋⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⣿⠘⣷⠀⢹⡟⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢿⣧⠈⠀⠈⡇⠀⠠⣤⡀⠀⠀⠈⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⢀⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠸⣿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢀⣀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠁⢸
⡉⠏⠁⠉⠁⠁⠁⠁⠁⠉⠛⠿⢷⣀⢈⠛⠛⠈⡢⢘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⢸
⡐⠠⠀⠠⠀⠤⠤⠤⠖⠀⠀⠠⠈⠛⠿⢷⣶⣶⣬⣤⡂⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢀⣾
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⣙⠛⠿⠿⢿⣶⣤⣤⣀⠀⠀⠉⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠻⢷⡄⠀⠀⠻⣷⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡿⠁⠀⣀⣠⡴⠖⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠻⡶⠀⠀⠀⣴⠞⠁⣼⣃⡴⠞⠉⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⢀⡞⠁⠀⣸⠟⢋⡀⠀⢀⣠⡴⠞⠋⠉⠛⠛⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠢⣤⣤⣀⣸⣇⢷⠀⡼⠁⢀⡼⢋⡴⠉⣠⣞⣋⣥⣤⣤⣤⣄⣀⣀⣀⣤⡞⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⠛⢿⡘⣾⠁⠀⡞⢠⡞⠀⠚⣋⣉⠁⠀⠀⠀⠀⠀⢀⣠⡴⠟⠘⢷⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⡴⠞⢷⡘⢧⡸⢡⣟⣠⠶⠋⢁⣀⣠⣤⠶⠶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢀⣴⠞⠋⣁⣤⡤⠶⠾⢷⣌⣷⢘⡟⠁⠠⡞⠋⠉⠀⠀⠀⠀⣿⡄⠀⠀⢿⡆⠀⠀⢸⣦⠀⢸⣇
⠀⠀⠀⢠⡞⠁⠀⠊⢁⣀⣤⡴⢞⡵⠟⢁⠈⠀⠀⠀⡟⠀⢰⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⣿
⠀⠀⢀⡟⢀⣤⠶⡿⠋⣱⠟⢠⠞⠁⢠⡟⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⡆
⠀⢀⣾⡾⠛⠁⣼⠁⣼⠏⠀⠏⠀⣰⠋⣿⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⣦⡀⠀⠸⠇⠀⣿⡇
⢠⠞⠋⠀⠀⢰⡇⠀⣿⠀⠀⢀⡼⠁⠀⠘⢷⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⢀⣾⠁⠀⢰⣦⠀⠙⢷⣄⢸⡆⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⣇
⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⣸⠇⠀⠀⠀⠙⠀⠀⠀⠙⣿⡇⠀⠀⠙⠃⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢻⣷⠀⠘⣿⡀
⠀⠀⠀⠀⠀⣿⠠⣆⠀⢷⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⢻⣇⠹⠇⢸⡇⠀⢀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠃⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⢰⣆⠸⣷
⠀⠀⠀⠀⠀⠀⠈⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠸⢶⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⣾⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢷⣶⣤⣄⡀⠀⠈⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣦⣄⠀⠀⠀⠀⠈⠻⠦⠀⠀⠘⢷⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁

⠀⠀⣠⣤⣤⣤⣀⣸⣷⣦⣴⣾⣿⣦
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣀
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠘⠿⠿⢟⠋⡙⢛⡉⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠸⠙⠁⠼⠇⢸⣿⡿⠛⣿⣿⣿⠛⠉
⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠈⠇⡀⠀⢀⣀⣤⣼⣿⣍⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⣰⠟⠛⠉⠉⠁⣨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠟⠻⠿⢿⣿
⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⢹
⠀⠐⣠⡗⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣿⣿⣿⠀⠂⣹⡇⠀⠒⣀⠀⠄⠸
⠈⣼⠋⠀⢀⣴⡀⠀⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣤⣹⡏⠛⢛⠇⢠⣿⡇⠀⠁⠿⠋⠀⡄
⠰⠛⠄⣠⠏⢹⡷⠀⠀⢺⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⠉⠛⠿⠛⣷⡐⠃⠀⠀⠉⠁⠀⠀⠀⠀⢰⠁
⡆⠀⠀⠁⢀⢼⣇⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⢠⡟⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜
⠧⠠⠐⠊⠀⣸⠏⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣿⠃⠀⣸⣿⠟⠀⢀⣀⣠⣀⠔⠁⢂⡀⠃
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⢠⡿⠀⣴⣿⠁⡘⠂⠚
⠀⠀⠀⢀⣾⠁⡶⢠⣄⣀⣀⡠⣤⢶⢾⡆⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢀⡼⠁⠐⣿⡷⢠⣿
⠀⠀⠀⢸⡏⢰⡇⣾⢹⡇⢻⡇⠹⡎⣇⢻⡀⠀⠀⠀⢀⣿⠁⠀⠀⢀⣾⠁⠀⣠⣤⡄⠠⢿⡀
⠀⠀⠀⢸⡄⣾⠀⣿⢸⣿⠘⣷⠀⣿⢹⢸⡇⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⠀⠀⣀⣀⡀⣷⢸⣷
⠀⠀⠀⢸⡇⣿⠀⣿⠈⣿⡄⢻⡀⣿⢸⢸⡇⠀⠀⠀⣿⠁⠀⠀⠀⢼⣿⠀⠈⢉⡉⣱⠋⢸⣿⡄
⠀⠀⠀⢸⡇⣿⠀⣿⡆⢻⡇⢸⡇⣿⠸⢸⡁⠀⠀⢸⡏⠀⠀⠀⠀⠈⣿⡀⠀⢸⡇⢿⠀⣸⣿⣿⡄
⠀⠀⠀⢸⠁⣿⠀⢸⡇⠘⡇⢸⡇⢸⡄⢞⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⢸⡆⢿⣿⣿⠇
⠀⠀⠀⠧⢠⣿⡠⠾⡁⢰⡇⢸⡇⢸⡇⢸⠅⠀⢸⡏⠀⠀⠀⠀⠀⢘⣿⠀⠀⢸⣿⠊⣧⠈⢿⡏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠸⣿⣇⣀⣼⡿⢧⡿⠄⠈
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠸⣅⣀⡀⠀⠀⠀⠀⠀⢹⣿⣷⡖⠒⠒⠠⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡄⠀⠀⠆⠀⠀⠀⠸⠳⡀⠉⠒⠢⠤⠄⣀⣈⣙⡃⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⣀⡹⢆⣀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠶⣌⣠⠐⠢
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⠂⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠲⣎⣸⡒⢠
⠀⠀⠀⠀⠀⠀⠀⠸⢀⣶⣶⣴⡆⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠡⠘⠬⠋⠤⣀⠀⡄
⠀⠀⠀⠀⠀⠀⢠⣤⡿⢻⣿⣿⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⢰⠈⠦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢲⠚⣛⠠
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠋⠉⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡏⠛⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡄
⠀⢀⠀⢀⣉⠄⡠⠊⠀⠀⠀⠈⠀⢉⡝⠶⢄⡀⠀⠀⡜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠸⣍⡵⢃⠀⠀⠀⠀⠐⠠⠁⠀⠀⡀⠈⠐⠶⠁⠀⠀⠀⠀⠀⠇⠀⠀⢀⣀⡤⠐⠸⠉⡁⠀⠢
⠀⠀⠐⠀⠤⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡀⠀⠣⠀⠀⠀⠀⠀⢛⠉⠱⠒⠒⠂⠒⠒⠊⠉

⠀⢀⡤⠀⢠⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡟⢛⠀⢸⠳⠃⡟⠓⠻⠜⠒⠃⠀⠀⠀⠀⠀⡠⣄⠀⠀⢠⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢈⠀⠀⠀⠀⠀⡇⠀⠀⡠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠈⠀⠀⡐⠀⠛⣇⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢃⠀⢸⠀⠙⣥⣾⡇⠀⢀⣿⣷⡏⠀⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣤⣼⣤⣾⣿⣿⠆⠀⢸⣿⣿⣿⣦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠠⢿⣿⣿⣿⣿⣟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⠀⢀⡿⠿⠿⠟⠉⠁⠀⠈⠙⣿⣿⣿⣿⣿⣶⣭⣽⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⢀⣀⣔⣚⠲⣄⠀⠀⢹⠋⠉⠉⠙⢿⣿⠿⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠀⣿⢋⣾⣿⣿⣿⡄⢳⡀⠸⠀⠀⢀⣴⡊⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⣸⣿⣿⣿⣿⡏⢸⡀⠀⢷⠚⠁⠀⠁⣠⠾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣴⠋⠀⠀⠀⠀⠀⡠⠊⠀⠀⣿⣿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠻⢿⣿⣿⣶⣟⡻⣿⣿⣦⡀⠀⠀⢀⠞⠀⠀⠀⢀⣿⣿⢱⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠉⠛⢿⣿⣿⣦⣉⠛⣿⣦⠔⠁⠀⠀⢀⣴⣿⡟⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⠂⠀⡌⠙⣻⣿⣿⣿⣿⠀⠀⣠⣾⣿⡿⣯⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠀⠀⠀⢰⡇⠀⠈⣿⣿⣿⠏⠀⣾⣿⣿⣿⣵⣿⡿⠋
⣷⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⠀⠀⠀⢸⠁⠀⠀⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣶⣀⣀⡀⠀⠀⠀⣿⣿⣿⣗⢆⠀⠀⠸⠀⠀⠀⢇⠀⠀⠀⠀⠹⣿⣿⣿⣟⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢻⣿⣿⣿⣿⡀⠀⠈⠆⠀⠀⢼⡄⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣷⣄⣀⣤⣤⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⣴⡤⠠⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠈⠀⠈⠀⠈⠂⠀⠀⣠⡄⠴⠄⠀⠀⠀⠀⠀⠀⢠⡴⡛⠂⠀⠘⠚⠈⢏⠄⠀⠙⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠤⠀⣠⢀⠀⠀⠉⠀⠀⠡⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢄⣄⡠⠤⠘⠉⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⢨⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠁⠀⠀⡵⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⡀⠈⠡⣶⠀⡰⣫⡄⠠⠀⠀⠀⠀⠀⢠⡤⠀⠀⢿⣶⠤⠀⠀⠀⠀⠀⠤⠐⡟⠫⡠⡀
⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠈⠰⠀⡀⠆⠘⠆⡷⠀⠀⠀⠀⠀⠀⠃⠀⠁⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠐⡀⠌⠘⠄⠠⠈⠀⠀⠀⠀⠀⠀⡀⠀⠨⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠾⠄⠀⡁⠀⠀⠀⠀⠀⠀⠐⠆⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢁⢐⠂⠐⠁⠀⢔⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⡄⠐⢀⠀⠐⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⢔⣇⡄⠈⠀⠂⠀⠀⠀⠀⠘⠁⠂⠀⠠⢈⠐⡈⠁⠀⠀⠠⠓⣿⠒⠀⠀⠃⡄
⠀⠀⠀⠀⠀⠀⠈⡑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠠⠈⡀⠁⠀⠀⢠⠀⠀⠀⠀⡀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠄
⠀⠐⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠟⠛⠛⠛⠻⠶⢶⣤⣤⡶⠛⠉⠉⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠠⣤⡀⢀⣤⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⢈⣿⣿⡁⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠛⠁⠈⠛⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⢶⣦⠀⠀⠙⠷⣦⣄⣀⣀⣠⣴⡾⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣉⠉⠉⠉⠀⢿⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣿⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠀⠙⠻⣿⢻⣿⠻⠛⠛⠛⠟⢿⡟⣿⠟⠋⠀⣿⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣿⠀⠀⠀⣿⣸⣿⠀⠀⠀⠀⠀⢼⣇⣿⠀⠀⠀⣿⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣿⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣄⣀⣀⣀⣀⣀⣠⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠶⠞⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠁⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠹⣷⣶⣶⣦⡀⣠⣴⣿⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢹⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠈⢧⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠃⠀⠠⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠐⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⣀⣤⠂
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣽⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⡀⢹⡿⠃
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⢿⡿⠿⣿⣿⡖⢻⣿⣿⣿⣿⠿⠖⠒⠒⢲⠄⠀⠀⠐⠛⢿⣿⠁⠀⠱⡄
⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠹⡄⠹⣿⡄⠀⠈⣿⣿⡇⠀⢠⣶⣷⣋⠀⠀⢠⠀⠀⣸⣿⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠸⣷⣦⣤⣤⣴⣿⣦⣸⣷⡀⠀⣿⣿⣿⡄⢸⣿⠏⠉⠻⣶⣾⠀⠀⠻⢿⣿⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⣿⣿⣿⣿⡷⠀⡿⠟⠏⠀⠸⡉⠁⠐⠠⢈⠛⠃⠀⠀⠈⠙⢧⣤⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠈⢿⡿⠟⠃⣂⣆⠀⠘⠦⢤⣯⡑⢦⣤⣴⣿⣦⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⢀⣀⣤⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⢠⣿⠀⠀⢠⠙⠉⠑⠢⣤⠤⠤⢴⣿⣮⣤⢘⣿⠟⢦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠉⠠⢀⠀⠑⠀⠀⠠⠻⠒⠛⣲⣤⣀⠀⢸⡟⠀⠀⠳⡀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣄⠀⠙⢦⡀⠀⢀⠠⢶⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠈⠀⣀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⣰⠟⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⢉⣉⣉⣹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣉⣉⣉⢹⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡟⠛⠻⠿⠿⠾⠿⠿⠷⠿⠿⠿⠾⠿⠿⠛⠛⣿⣾⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠰⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠐⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢠⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣿⣾⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⢟⣭⣶⣶⣾⣭⡻⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢱⡿⣉⣿⣾⣿⠿⠛⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣇⠻⠟⠛⢉⣁⣤⣴⣾⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⡄⢶⣿⣿⣻⣿⣠⡿⣣⡿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡿⣶⣽⣛⣛⣛⣭⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣻⣿⠉
⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣿⢻⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣼⣇⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣁⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⢀⣦⣴⡶⢀⣄
⠀⠀⠀⠀⢐⣤⡶⠋⡉⢰⡌⠱⣋⣠⢤
⠀⠀⠀⠀⢨⣝⡃⠀⢿⣿⣿⡄⠨⣦⣼
⠀⠀⠀⠀⠈⣭⡶⣆⠈⢿⣿⣿⡀⣷⠆
⠀⠀⠀⠀⠀⠈⢴⣯⣿⣤⠉⠿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡜⠂⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠖⠃⠈⡰⠀⠈⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢦⡠⡈⣧⣰⡎⠀⠀⠀⠀⠌⢀⠀⠠⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠄⠅⡤⢻⠿⡟⢿⡅⠀⡀⣀⣄⣤⡑⡌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⠼⠾⡯⢸⡇⠦⠹⡶⠂⠄⠀⠀⠀⠙⠲⡴⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⡈⣸⡃⠀⡿⠀⠀⠀⠀⠀⠀⠊⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠘⠠⢀⠃⡁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡄⠰⠀⡄⢰⡮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠐⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠿⠶⣦⣄⡀⢀⣴⠏⠁⠸⣷⡀⠀⠀⠀⢀⣤⣾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠈⠙⢾⣿⠀⠀⠀⠹⣧⠀⣠⣴⠟⠋⣁⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠈⢿⣦⠀⠀⠀⠀⠐⢄⡙⣆⠀⠀⠀⣿⠜⣩⣴⠾⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠤⣄⠀⠙⠳⣦⣀⡀⠀⠀⠉⠺⣧⣴⣠⣷⡿⠿⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢷⣴⠏⠀⠀⠀⣠⣽⣿⠟⠛⣉⣩⣿⣿⣿⣷⡖⠒⠢⠀⠈⠙⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡠⣄⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠀⠀⠀⠀⣀⣾⣏⠙⠢⣉⠳⣄⡀⠀⠀⠀⣈⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠠⣯⣠⠞⠀⠀⠀⠈⠻⢿⣿⣤⣄⣀⣀⣤⣴⣾⠿⠉⣿⣆⠀⠈⠢⠈⢻⡿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⠁⠀⠀⠀⢀⡴⢦⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠘⢿⣷⣄⡀⠀⠀⢿⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣯⣠⠎⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⣠⡀⠙⠻⠿⢷⣶⣾⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠚⣶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣟⢀⣼⠀⠀⠀⠀⣾⡁⣼⠀⠀⠀⠀⠀⢰⡖⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣾⠏⠀⠀⠀⠀⢀⡖⠻⡄⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠹⠿⠛⠀⠀⠀⠀⠀⣸⣇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⠃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡴⢤⠀⠀⠙⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠋⣷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡿⠉⣹⠀⠀⠀⠀⠀⣿⣀⡾⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡴⢦⡀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⢀⣴⠛⢙⡆⠀⠀⣾⣡⡴⢁⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠚⠀⠀⠀⠉⣡⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡈⠉⠀⠀⣠⠖⡄⠀⠀⠀⣠⠖⢦⠀⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠰⣇⣴⠃⠀⠀⠸⣧⡴⠋⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣭⣀⣀⣀⣀⣤⣤⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⡉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠉⢩⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⣦⡀⠀⠀⢠⡿⠀⠈⣿⡀⠀⠀⢀⣠⣶⠿⠛⠋⠉⠉⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⢻⡄⠉⠛⠷⣤⣤⣀⡀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠻⢦⣼⠉⠻⢦⣤⣾⣁⣀⠀⠹⣧⠀⣴⡿⠋⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢙⣷⡄
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠉⠙⣷⠟⠉⠀⠀⠐⠒⠒⠤⣄⣀⣿⠀⠀⢀⠀⠈⠉⠙⠛⠶⣿⣾⠏⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⣾⠋⠁
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⠿⠛⠳⢶⣄⡀⠀⠀⠀⠈⠙⢻⣄⠀⠀⠐⠦⣀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣠⡴⠋⠀⢀⣴⡿⠋⠙⠷⣤⣀⣀⣀⣀⣀⣤⣤⡾
⢀⣀⡀⠀⠀⠀⠈⠻⣷⣦⣄⣀⣀⠤⠤⠤⠤⠘⢿⣦⣀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠙⢳⣄⠀⠀⠀⠈⢷⡶⠟⠉⠀⢀⣴⣿⣋⡙⠓⠶⠦⠀⠉⠉⠉⣉⣥⠾⠋
⠈⠻⣿⡛⠛⠛⠛⠛⠋⠉⠉⠀⣀⣤⡤⠶⠞⠛⠛⣋⣿⡿⣶⣦⣤⣤⣤⣿⣆⠀⠀⠀⢹⣦⠀⠀⠀⢈⣷⣤⠶⠾⠛⠉⠙⠛⠛⠛⠛⠿⠿⣿⡟⠛⠋⠁
⠀⠀⠈⠙⠻⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠟⠋⠁⠀⠀⠀⠉⠉⠉⠈⠻⣦⣤⣄⣠⣿⣤⣤⡶⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⢀⣴⠏⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠹⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠂⠀⢻⣧
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠈⣿
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢹
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⡀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⢸
⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠲⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠀⠀⣼
⢻⡇⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⣆⠀⢠⣿
⠸⣷⠀⠀⠘⠇⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢰⡉⢾⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⢀⠄⠒⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠂⠀⠀⠀⠋⢀⣾⡏
⠀⢻⣇⠐⠄⠀⠀⠀⠰⡇⠀⢀⠚⡄⠀⠀⠀⠀⣇⡹⠀⠀⠀⠀⠀⠘⠷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠠⠆⠀⠞⠀⠃⢀⡠⠀⠀⣼⡟
⠀⠀⢻⣆⠰⠀⠀⢀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠏⠀⠀⣰⡿
⠀⠀⠀⢻⣦⠀⠀⣈⠀⠀⠀⠰⠆⡀⠀⠀⠉⢠⠀⠀⠀⠀⠀⢠⠖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⣤⠀⠀⠰⠀⠔⠀⢠⡿⠁
⠀⠀⠀⠀⠹⣷⡀⠈⠀⠀⠀⠈⠲⠃⠀⠀⠀⣤⢹⠄⠀⠀⠀⠈⢧⣼⠃⠀⠀⠀⡄⢠⠀⠀⠀⢠⡆⢲⡀⠀⠀⠀⡿⠐⠁⠀⠘⠃⠀⠀⢠⠁⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠖⢄⠀⠀⠀⠀⠀⠀⠐⠆⠘⠀⠀⠈⠓⠞⠁⣠⣤⠀⠀⠀⠀⠀⢠⠶⠂⠀⠐⠞⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠢⠀⠀⠀⠈⡵⢄⠀⠀⠀⠀⠠⠼⠃⠀⠀⢤⢄⡀⠀⠀⠀⠀⣠⠤⠒⠠⠈⠠⠀⠀⠀⠀⠀⠀⠃⠀⣀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢐⡶⠃⠀⠀⡤⢀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⢶⠉⠠⠂⠀⡠⠤⠀⠀⠀⠀⡤⠀⠀⠊⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⢀⡄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠃⠄⠀⠀⠀⠧⠂⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠐⠆⠀⠁⢠⠀⠀⠀⠀⠀⠡⣘⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠊⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠑⣄⠀⠀⠀⠀⡀⠀⠈⠃⠰⡀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠂⠀⠀⣠⠶⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠂⠀⠀⢀⠀⠀⣀⠀⠈⠀⠀⠀⠉⠉⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠁⠀⠁⠘⠃⠀⠰⠖⠦⠀⠀⠀⠐⠊⠙⠁⢠⠞⠁⡀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠂⠐⠠⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⢀⡀⠀⠀⠘⢁⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠳⠀⠀⠀⠊⠉⠀⠀⠀⠀⠈⠉⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠠⢤⡀⠀⠐⠛⢃⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣤⣤⣶⡾⠿⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀
⢀⣤⣽⣷⣄
⡋⣉⡵⠻⠿⣿⣦⣄
⣿⣯⣀⡀⠀⠛⣿⢟⣳⣄
⡟⡻⠫⡊⠀⣠⣶⣿⣿⣿⣿⣦⣄⡀
⣾⣿⢒⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⡿⡅⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀
⢞⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠲⢤⣀⡹⣶⣤⣀⠐⣦⣄⡀
⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠛⠿⣿⡙⠻⢾⣿⡟⠿⢶⣤⣀
⠿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣆⠙⠿⣿⣿⣿⣿⣄⠀⠢⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣿⣦⡀⠈⠻⡟⢦⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡟⣿⣿⣿⡿⢿⣿⣿⠇⠀⣄⠀⠻⣿⣿⣿⣷⡄⠀⠀⠀⠙⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠀⠀⢿⣶⠀⠈⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⢠⣧⠀⠀⠸⢻⣤⡄⠀⠹⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇⠀⠀⢹⣯⠀⠀⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⡄

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠖⠒⠲⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⢳⡀
⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣧
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠰⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⡌⠀⠀⣀⡀⡀⠀⠀⠀⠈⡇
⠀⠀⠈⠙⠒⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡇⢀⡜⠀⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⡸⠓⠲⢤⣤⣴⠆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⠃⡼⠀⠀⡇⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⣠⣌⡉⠓⠚⠹⣅⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⠺⠶⣇⠀⠀⢹⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣄
⠀⠀⠀⠀⡌⠀⢀⡤⠖⠋⠀⠀⠈⠳⣄⢀⡷⣌⠉⠙⠒⠀⠀⠄⠀⣀⣀⠀⠀⠀⠈⠳⡄⠈⢧⡀⢰⣄⠀⠀⠀⠣⠤⠄⠉
⠀⠀⠀⠰⠀⠈⢃⠀⠀⠀⠀⠀⠀⢀⣨⡏⠀⠈⠳⣄⠀⠀⠀⠀⠀⡿⠂⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⠈⠳⢄⡀⠀⢀⡠⠔
⠀⠀⠀⡆⠀⠀⠀⠳⣤⣀⠀⠀⠀⠈⢹⡆⠀⠀⣾⣾⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠓⠒⠋⠉⣇⠀⠀⡠⠊⠀⠀⠀⠀⡄⢀⣀⣀⣀⣠⠞⠁
⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠀⠀⠀⠀⠀⠀⠉⠠⠀⢄⠈⡁
⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣄⣀⣐⣀⣀⣤⡤⠤⠶⠒⠋⠉⠀⢳⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣤⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⣀⡀⣀⣀⣀⣀⣀⣀⡠⠤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⣈⣒⡫⠭⠛⠳⠶⢖⣒⣚⣿⣋⣈⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⠉⠉⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠄⠘⠋⠉⠑⠻⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⣳⣤⣄⠀⢀⣴⣎⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢻⡿⠇⠀⠸⠿⠟⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄⠀⠀⠀⢠⠁⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠑⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠆⢤⣤⣤⠀⠶⠆⢸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⡀⠀⢠⣥⠀⠀⠒⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠎⠁⠀⠀⠈⠑⢂⡀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣿⠟⢣⡀⠂⢀⣤⠰⠂⠠⣀⠈⢢⡀⠀⠀⠀⢀⠘⣹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢪⡑⠦⡀⠀⠀⠉⠑⢦⡄⠀⠀⢠⠌⠀⢠⣿⠀⠀⢹⢠⡉⠀⠀⠀⠀⠈⠳⣀⠻⡀⢠⠶⠉⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡰⠁⠀⠀⠈⠱⢮⡑⢂⠀⠀⠀⠈⠑⢦⡁⠀⢀⣾⣿⠀⠀⠘⣾⡁⠀⠀⠀⠀⠀⣠⣷⠀⢃⣤⠷⠊⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡄⠒⠢⡀⠀⠀⠈⠓⢬⡑⢠⡀⠀⠀⠘⠳⣬⡿⣿⡇⣠⠈⠀⠀⠀⠀⠀⢀⣄⠸⠄⠀⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠰⢡⡟⢀⡔⢀⠔⡀⠈⡆⢀⡀⠀⠀⠈⠑⢮⡔⢠⠀⠀⠀⠙⠷⣦⡈⠁⠀⠀⠀⣀⡘⠓⠒⠒⠈⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⡌⢠⠋⢠⠂⠀⠑⠂⠂⢠⡑⠀⠀⠁⠢⡀⠀⠀⠈⠑⢪⡕⣠⠀⠀⠀⠉⠓⢢⣄⢸⡟⠘⢷⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⢀⠘⡰⠃⡰⠂⡄⢻⠀⠴⠊⡑⠁⢴⠉⠒⠠⠂⠀⢀⣄⠀⠀⠈⠑⢮⡑⠂⠀⠀⠀⠈⠙⢦⡀⠀⠙⣦⡀⢀⠆
⠀⢀⠂⠉⢫⡴⠁⠀⠓⠒⠀⠈⠀⡀⠀⢀⢤⡄⢉⡄⠀⠀⡰⠂⣈⠳⠆⣄⠀⠀⠈⠑⢮⡕⠢⡀⠀⠘⠈⠑⢠⣈⠻⠎
⠀⢼⡀⠀⡜⠓⢤⡀⠀⠀⠀⠒⢰⡏⠀⠂⡄⠈⣁⡀⠀⡰⠁⣰⠆⠀⠀⠀⠁⠀⠀⠀⠀⠈⠑⢮⡑⠢⡀⠀⠀⠈⠑⠂⡀
⠧⡀⠉⠁⠀⠀⠀⠈⠐⢦⣄⠀⠀⠈⠒⢤⢀⡿⠁⢸⠆⢀⠲⠉⠀⠐⠀⠀⢀⠄⠂⠀⠰⠀⠀⠀⠈⠑⢮⡑⠢⠄⠀⠀⠀⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠀⠘⢤⡄⠐⠠⠃⡐⠁⠂⣄⠾⠁⡰⠈⢱⠀⣤⠂⠐⢄⠀⠀⠈⠑⢦⡉⠲⣄⠀⠀⠉⠁⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠘⠣⡀⠈⠒⠀⡘⠁⠞⠁⠀⠈⠈⠁⡤⢀⡀⢉⡶⢠⠀⠀⠈⠑⢦⡉⠲⣄⡀⠀⠀⠙⢢⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠙⠲⣤⡀⠀⠈⠑⠒⠀⡁⠘⠄⠐⢂⠀⢀⠜⠀⠎⢀⡛⢠⡄⠈⠒⡄⠀⠀⠈⠑⢦⡉⠂⢄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀⠀⠀⠑⠂⠀⠒⠁⢠⠂⠠⠁⢀⠎⠀⠣⡈⠑⢺⠂⠉⠒⢀⠀⠀⠈⠑⡌⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠐⢦⠔⠀⡀⠀⡀⠒⢤⠀⡐⠀⡄⠁⠄⢸⠀⠀⢠⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠗⢤⡀⠀⠀⠀⠐⢅⠀⠑⠂⣀⠐⢠⠌⠀⠘⢠⠄⠀⡰⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠑⠦⣀⠀⠀⠉⠒⠰⠏⠀⠃⠄⠂⡠⠁⠀⠞⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠈⠒⠀⠐⠊⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠢⣄⡀⠀⠀⠀⣴⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠲⣤⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠬⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⠤⠤⠤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⠀⠀⠀⠀⣀⣠⣤⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣼⠏⠀⢀⣠⣴⠶⠟⠋⠁⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠛⣿⠇⠀⠀⠀⢀⣴⠟⠁⠀⣼⢏⣠⡶⠟⠉⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⢠⡾⠁⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⣀⣴⡾⠛⠛⠛⠳⠶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⡄⠀⢀⡿⠀⠀⠀⣰⠟⢁⣤⠖⠀⢀⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣶⣦⣤⣸⣿⠸⣇⠀⣼⠁⠀⢀⡾⠃⣠⠟⠁⢀⣴⣋⣭⣴⣶⣶⣶⠶⢶⣶⣤⣤⣤⣤⡴⣶⡿⣀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠉⠛⢿⣇⢻⣾⠃⠀⢀⡾⠁⣰⠏⠀⠰⠛⢋⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠀⢻⣧⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣀⣼⣿⡄⢻⣦⠀⣸⠃⣼⡏⢀⣠⡶⠟⠋⠉⠀⠀⣀⣀⣠⣤⣤⣶⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠟⠋⠁⠘⣿⡄⠙⣷⡀⢰⣿⣴⠿⠋⢀⣠⣤⡴⠾⠿⠛⠋⠉⠉⣉⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⡀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⣠⣤⡶⠶⠾⠿⠟⠻⣦⣼⣿⢀⡿⠁⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠘⢿⠇⠀⠀⠀⢸⣿⡆⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣰⠟⠁⠀⡰⠛⠉⠀⢀⣠⣤⡴⠞⣠⡿⠋⠁⠈⠀⠀⠀⠀⣿⡇⠀⢰⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿⣧
⠀⠀⠀⠀⣰⠏⠀⠀⢀⣠⣴⠾⠟⣻⡿⠋⢠⡾⠋⠀⢠⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢠⠏⣠⣴⡾⠛⣽⠏⠀⣴⡟⠁⣰⠏⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⠀⢸⣿
⠀⠀⢠⣯⣾⠟⠁⠀⣰⡟⠀⣼⡟⠀⠀⠏⠀⠀⣴⠋⢸⣧⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⢻⠇⠀⢸⣿
⠀⣰⡿⠛⠁⠀⠀⢠⣿⠀⢰⣿⠃⠀⠀⠀⢀⡾⠁⠀⠀⢿⣷⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⢸⣿
⠜⠉⠀⠀⠀⠀⠀⣸⡏⠀⢸⣿⠀⠀⠀⢠⡿⠁⠀⢀⡀⠀⠙⢿⣦⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⣿⡀⠀⢠⣿⠃⠀⠀⠈⣿⣧⠀⠀⠙⢻⣶⡀⢻⡀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠹⣇⠀⣾⡏⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠙⢿⣾⡇⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠨⣿⡄⣀⠀⠀⢿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣷⡀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠹⠇⠀⢻⡇⠀⠀⣀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠸⠇⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⠄⠀⠀⠀⠀⣴⡄⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠙⢿⡦⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠰⣿⣦⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⢻⣷⡄⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣦⣤⣄⣀⣤⣤⡶⠿⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣠⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠗⡀⠈⠀⠀⠀⠀⠀⠠⣠⣤⣤⢦⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢐⠓⠊⠨⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⢎⠰⠈⡟⠉⡵⡄⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠢⣤⠤⠔⠉⠀⡀⠀⠀⠀⠂⠟⢳⡋⠛⣲⣾⠁⠀⠀⠀⢠⠊⠵⠇⢪⠓⠂⢑
⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠊⠀⠀⠀⠀⠀⠲⠦⠉⠙⠀⠁⠀⠀⠀⠀⠈⠂⠤⠠⠛⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢀⠀⠀⠀⠀⠀⠀⠀⣁⢓⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠈⠤⠀⢀⡦
⠀⠀⠀⠀⠀⠈⡸⠶⡇⠀⠀⠀⠀⠀⠀⠢⠜⠫⠙⣉⣃⠖⠀⠀⠀⠀⠀⠀⠘⢃⡀⣄⣀⠀⠀⠀⠀⠦⠊⠀⠉⡉⢢⣀⡠⠀⠀⠀⠰⠃⠀⠀⠈⣄⡀
⠀⠀⠀⠀⠓⢺⠀⠀⠐⠂⠀⠀⠀⠀⠈⢈⠃⡉⢰⡈⡐⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠂⣸⠉⠀⠀⠀⠀⢠⡀⠀⣠⡟⡠⢤⡱
⠀⠀⠀⠀⠀⠀⠁⠐⢀⡠⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠬⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠿⠃⠀⠀⠀⠈⠓⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⡊⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢀⡜⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠶⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⣀
⠀⠀⠀⠐⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⡡⠀⠀⠀⠀⢺⠮⣿⢿⠆⠀⠀⠀⠀⠀⠀⣢⣄⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢛⣬⣇⣐⣨⣻
⠀⠀⠀⠠⡀⠀⣠⠶⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢜⢎⣷⡦⠀⠠⠀⠀⠀⠀⢰⣿⣿⣳⣦⣀⠴⠋⠀⠀⠀⡈⣿⢫⠞⢁⠏⡠⡅
⠀⠀⠀⠀⠈⠉⠛⢄⡑⠖⠊⠀⠀⠀⠀⠀⢀⣦⣄⡀⡠⠃⠀⠀⠀⠀⠀⠣⣳⢟⡅⠨⠀⡀⠀⠀⠀⠀⠑⢿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠈⠻⠴⠚⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠜⢂⠍⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠾⣷⣶⣤⠀⠀⠀⠈⢢⡀⠀⠀⠀⣤
⠀⠀⠀⠀⢆⣤⣶⣶⣆⡘⠂⠀⠀⠀⢠⡄⢠⣀⣀⣠⣿⣀⡀⠀⠀⠀⠀⢘⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡻⣿⣇⠀⠀⢀⡀⠃⠐⢓⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⣠⡬⣿⠿⣿⡾⠏⠀⠀⠘⡀⠀⠁⣴⠋⠉⠲
⠀⠀⠀⠻⣿⡿⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠠⣠⣀⣠⣀⠇⠀⠀⠀⠀⠈⠈⢷⣼⣀⣼⡷⠃⠀⠀⠀⠀⠀⠀⠒⠚⠻⣄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢠⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡄⠀⠀⢀⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠋
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⢹⣷⠘⠁⠀⠀⠀⠀⠀⠄⠀⣾⣿⣿
⠀⠀⠀⠀⠘⠎⠁⠀⠀⠀⠛⣶⣶⣶⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠙⣉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡄
⠀⠀⠀⠀⠀⣀⡥⠀⠀⠀⠈⠻⠿⠿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠍⠡⠋

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠖⡒⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡈⡆⠍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠄⠐⡀⠀⠀⠀⠀⢀⡊⠐⠁⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠸⠀⠀⠀⠠⠈⡉⠰⠃⠰⠆⠘⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠘⠁⢰⠂⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⣀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠂⠀⠀⣁⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣯⡀⢋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⢱⡖⠂⢀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠙⣄⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠰⠙⢘⡠⢇⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠅⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠷⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠠⢀⠹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠝⠀⠒⠂⢈⡉⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⡀⢒⣾⠀⢤⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠠⠐⠂⠌⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠸⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡉⠤⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⢀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠓⠠⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢼⡤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠉⠄⠡⣄⡗⠋⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠛⠛⠈⠀⠐⡽⠦⣀⣀⡀⠀⡀⠈⣃⢀⠊⢉⢧⡀⢁⠨⠧⡀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⣾⠛⠂⢤⡠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⣈⠀⠀⠿⠀⠀⠐⠲⠀⢀⠀⠐⢌⠂⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⡂⢀⡍⠀⠠⠋⠈⢠⠠⡂⠌⠐⠀⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢐⠡⠀⠐⠁⠄⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡜⠀⠀⠀⠀⠂⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠒⢒⡄⠈⡄⠀⠀⠀⠀⠀⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠓⠒⠉⢀⠄⢰⠀⠀⠀⠀⠀⠠⠀⠀⠅⡀⠀⡀⠀⠀⠀⡀⠀⢊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠀⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⣀⣀⡀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠃⡰⠀⡄⡐⣀⠠⠀⢰⠁⠤⡂⢀⠂⠰⠂⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣬⣁⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣶⣿⢚⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⣼⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡃⠚⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠄⠀⣀⠔⠀⠀⠀⠀⠀⠀⠈⠀⢈⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⣠⡔⠉⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⡺⣦⣾⠇⠉⠉⠒⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢠⠐⠁⠀⠀⠈⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠅
⠀⠀⠀⠀⠀⡂⠐⠉⠀⠙⡏⠀⠀⢸⠏⠀⠀⠠⠀⠀⡺⢀⠃⢀⣆⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣷⠀⢰⠟⠀⢀⡠⠞⠉⣽⣱⡬⠶⡋⠉⠾⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡼⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠐⡀⠀⠀⠀⢉⡛⠂⠾⠶⣂⣾⣡⣴⣾⣿⠃⠀⠀⠈⠈⡇⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⢾⡧⢂⣽⣷⠂⠛⠛⣿⠀⠀⠀⠀⠜⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠞⠀⠀⠀⠀⠀⠀⠸⠋⠀⠁
⠀⠀⠀⡀⠀⠀⣦⢠⡒⠄⠡⠀⠐⠚⢻⠷⢎⡄⠀⠘⢧⣀⠀⠄⠀⠈⠄⠰⣿
⠀⠀⠐⠀⠀⠄⠻⣷⣿⡎⠉⠒⢦⣶⢼⡄⠘⢛⢸⠓⠒⠉⠐⠢⣄⡀⠂⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠇⠀⠓⠾⠮⡳⣽⠁⣀⣴⠲⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠀⠠⢄⡀
⠀⠀⠦⡀⣀⣀⡀⠀⠂⠀⠀⢀⠀⠔⠀⠸⡟⣱⠃⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⢠⡀⠀⠂⠘⠆⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠿⠄⠀⢡⣦⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⢱⡄⠀⢀⠀⣰⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠘⣷⡰⣨⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣠⣄⣺⣽⣇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⠛⠟⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠠⠤⠐⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢉⡍⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡈⠀⠀⠀⠀⠀⠀⠀⣀⣈⣛⣛⣁⡀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣥⣀⠀⠀⠀⣿⣿⢹⣿⣿⣿⢟⣛⣻⣯⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⡿⡷⠀⠀⣿⣿⢸⣿⣿⠧⣿⢿⣿⣿⣿⡿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⢝⣛⣛⣻⣅⢿⡄⠀⣿⣿⢸⡿⠿⣸⡷⣼⣿⣿⣿⣧⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣟⣛⡛⠯⠾⠃⠀⠙⠟⢸⣿⡟⣿⣇⣿⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣧⣛⢹⣿⣿⣿⣿⣿⡏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣟⢻⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣷⣭⢛⣿⣛⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠯⠨⠿⠄⠀⠀⠀⠀⠀⠰⠶⠮⠸⠶⠰⠯⠉⠽⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⡟⢿⡀⠀⢀⣠⡶⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣷⠀⠀⠀⠀⢠⡟⠻⣆⣰⠏⠀⠸⣇⣰⠟⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⣾⠁⠀⠹⡟⠀⠀⠀⢻⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠹⣆⠀⢰⡏⠀⠀⠀⠹⡄⢠⠀⢸⢀⣴⠤⠴⠟⠶⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⣴⣤⣤⣤⣄⣈⣳⣄⠙⣦⣸⠃⠀⠀⠀⠀⢹⠘⣀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠉⠛⠳⢌⣻⡀⠀⠀⠘⡀⠈⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⣇⠀⠀⠀⡇⢀⡏⠀⠀⠀⠀⠰⠟⠁⣀⡀⠀⠀⠀⢆⠑⡀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠐⢄⠀⠀⠘⢆⠀⠀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠸⣭⣿⠆⠀⠀⠀⠁⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢀⣀⣤⡤⠿⠦⣄⡀⠀⠑⢤⣀⣈⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⢠⣾⠋⠉⠀⠀⠀⠀⠀⣉⣙⣻⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀
⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣤⣤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠄⠀⠀⠀⠐⠨⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣰⠁⠀⠀⠀⠀⢰⠇⢀⣠⣀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠘⢼⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣧⣤⠶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢐⠢⠀⠀⠀⠈⢠⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠁⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⡒⠄⠀⠀⠀⠀⠍⡂⠀⠀⠀⠈⠥⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⠿⠿⠿⠿⠿⠷⠴⠶⣷⣶⣤⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠋⢉⣄⠀⣴⡆⠀⢠⣶⠀⢠⣦⣤⣀⠉⠙⠛⠿⣿⣶⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢋⣀⠀⠺⣇⠀⢿⠳⣼⡇⢀⡿⢾⣇⠀⢸⡇⠉⠀⣿⠂⢀⣀⠙⠛⠻⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣁⠀⢸⡿⣆⡀⣹⡦⠘⠃⠈⣋⣈⣉⣈⣉⣀⠛⠃⠠⣼⡇⣴⠋⠙⣷⠀⠀⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠘⢻⡟⢶⣷⠘⠋⣠⣴⣶⡿⠿⠿⠛⠛⠛⠻⠿⠿⢽⣿⣦⣄⡙⠶⠶⠋⢀⣼⡆⠀⠙⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢁⡴⢳⣆⣀⡻⠃⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⣿⣦⡀⠺⠏⣼⣥⠿⠂⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡘⣙⡟⠀⠘⠛⢾⣭⠙⢀⣾⡿⠋⠀⠀⠀⠀⠀⢴⣷⠂⠀⠀⠀⢀⣤⡀⠀⠀⠀⠈⠙⣿⣦⡀⠛⠁⠀⠀⣀⣀⣿⣷⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣵⡟⢀⣟⢣⠰⣦⠉⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋⠃⠀⠀⠀⠀⢀⣀⣻⣽⣶⣶⣿⠿⠿⠛⠋⠉⠉⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⠁⣘⠉⠛⢶⠃⣰⣿⠃⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣾⡿⠿⠟⠛⠉⠉⣀⡀⠀⢠⢠⡀⢻⡇⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⣿⡏⢸⣯⣄⣀⡄⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⠿⠿⠛⠋⠉⢁⣀⣠⣤⡰⣶⠂⣾⠋⠉⣷⠀⣧⡙⢶⣧⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⢠⣿⠃⠸⠇⠈⠙⠃⢸⣿⠀⣀⣀⣤⣤⣶⣶⣿⠿⠟⠛⠋⠉⡁⢀⣤⡄⠀⣾⣆⠘⠋⣿⡈⠀⢸⣇⠹⢦⣴⠟⠀⠛⠃⠀⢁⣀⣤⣴⣿⠏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣠⣤⣴⣿⠦⠬⠛⠛⠛⠉⠉⠀⢠⣤⠄⢶⡗⠹⣿⣦⣹⡆⢸⡷⠛⣧⡄⠼⠷⠀⠘⠋⠁⣀⣀⣤⣴⣶⣾⡿⢿⣿⡟⠉⠁
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠛⠋⠉⡁⣀⣤⣤⣄⠘⣿⣧⡀⣿⢻⡆⠈⣷⡀⣿⡌⠹⠿⠘⠛⠀⢉⣀⣠⣤⣶⣶⣿⢿⡿⠟⢻⣍⣁⡀⠀⢰⣿⠃
⠀⠀⢼⣯⠃⠉⣀⣠⣤⣴⠰⣾⣛⠿⠈⣿⡴⣿⡀⢹⣏⠻⡿⠸⠟⠈⠋⠉⣀⣀⣤⣤⣶⣾⣿⠿⠟⠛⠋⠉⠀⠀⣸⡇⠀⣈⣭⠿⠛⠁⢸⡷
⠀⠀⠸⣿⡄⠀⠙⠁⣿⠀⠀⢸⣏⣰⡆⠼⠷⠘⠋⠈⢉⣀⣠⣤⣴⣶⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⠇⠀⠉⠙⠛⠟⢀⣿⣷
⠀⠀⠀⢿⣷⠀⠀⠀⠾⠷⠀⠈⠉⣀⣀⣤⣤⣶⣶⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡗⠀⠀⣰⣿⠏⢰⡟⠙⢻⡄⠀⣼⡿⠂
⠀⠀⠀⠸⣿⣆⣀⣠⣤⣴⣶⣾⡿⠿⢿⣟⠻⣿⣧⡀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⣀⣾⡿⠋⣤⡈⠳⠶⠾⠁⣰⣿⠏
⠀⠀⠀⠀⠙⠻⠿⠛⠻⣿⣧⠀⢠⣤⠞⠻⠷⡈⠛⢿⣶⣄⡀⠀⠈⠉⠀⠀⠀⠀⠀⠻⠏⠀⠀⢀⣠⣾⡿⠋⣠⣬⠉⠻⣦⡄⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠋⠀⠀⣰⡟⢷⡄⡙⠻⠿⣷⣶⣤⣤⣀⣀⣀⣄⢤⡠⡴⢿⠿⠛⡉⠀⡾⠻⣦⣀⠀⠉⣠⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠦⢀⠻⢯⣥⠈⢠⣟⢳⡄⢀⣉⠉⠛⠛⠛⠛⠋⠁⣉⠀⢠⠄⠈⣟⣷⣄⠀⠘⠋⣠⣼⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⣄⡁⠰⢾⢙⡟⠁⢸⣿⡆⣰⣿⠇⠘⣟⠈⢿⡶⣄⠀⠀⣿⡄⠛⢁⣤⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣷⣄⡈⠉⠀⠿⠆⠿⢋⣿⠀⢠⣿⠀⠸⠷⠈⠃⢀⣠⡴⠾⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢻⠿⣶⣦⡄⡀⣤⣤⣤⣤⣤⣴⣶⠶⠛⣋⠻⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠛⠉⠉⠉⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⣶⠶⢶⣶

⠀⠀⠀⠀⠀⣤⣶⠷⠖⢲⣢⡀⠀⢰⠁⠀⠀⠀⠈⡂⠀⠀⠀⠠⡶⠤⠀⠀⠁⠀⠀⠀⠀⢀⡔⠁⠈⠢⠀⠀⠀⠀⡷⢺⣄⠀⠚⢺⡆
⠀⠀⠀⠀⢈⣻⠕⡶⡒⡦⡽⣓⠀⢸⠀⠀⠀⢀⡔⣓⡢⡀⠀⢀⣠⣤⣤⣄⢤⣤⡀⠀⠀⠘⢆⣂⣴⣶⠷⡀⠀⠀⡿⣀⣤⣤⣄⣸⣇
⠀⠀⠀⠀⢈⣭⠘⡙⣉⠀⢥⣭⠀⢸⢀⣴⣿⣏⢃⡥⢠⡇⠀⠈⠻⠉⡒⢈⣠⡠⢃⠀⠀⠀⠀⢹⠷⠦⠟⠁⠀⠀⡿⢈⣿⣿⣟⣻⣭⡇
⠀⠀⠀⠀⠈⠻⢗⡤⣤⣶⠗⠁⠀⢸⠀⠀⠀⠈⠛⡟⠋⠀⠀⡀⠘⣛⣃⠉⡥⠐⠊⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣷⣈⠉⠉⢉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣈⣀⣁⣈⡀⠀⠀⠀⣀⣈⣉⣉⣀⣁⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠈
⠀⠀⠀⠀⠀⢠⠔⣂⢄⠀⠀⠀⠀⠀⡏⢉⣀⣀⠀⣡⡀⠀⠀⠶⠒⣚⡒⠒⠒⠒⠲⠀⠀⠐⠷⠆⠉⠛⠒⡆⠀⠀⠀⠀⣾⠒⠙⡆
⠀⠀⠀⠀⠀⠘⠀⡀⡏⢀⢀⣀⠀⠀⡗⣾⡷⢺⣟⣌⠼⠀⠀⠀⠐⠛⢃⣭⡙⠁⠀⠀⠀⡀⣰⡞⢋⠛⣿⠃⠀⠀⠀⠀⣫⡦⣶⣅
⠀⠀⠀⠀⢀⠀⠾⢿⢛⣷⣛⠛⠇⠀⡟⢿⠿⠞⣋⡃⠀⠀⠀⠀⢯⣸⣟⣽⣭⡿⠀⠀⠀⡇⠚⠷⠤⡶⡣⡀⠀⠀⠀⡮⡽⢖⡠⡇⠇
⠀⠀⠀⠀⠥⠤⠨⠿⠟⠁⠬⠷⠄⠀⠇⠀⠀⠘⠧⠇⠀⠀⠀⠤⠯⠠⠯⠽⠯⠽⠤⠀⠀⠣⠠⠀⠸⠼⠏⠚⠀⠀⠀⠢⠤⠨⠱⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀⠀⢀⡀⣀⣀⣀⠀⣀⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⡏⢸⡷⠶⠀⡀⢸⡇⣿⡷⠶⢸⣏⠈⣉⠈⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠛⠘⠛⠛⠃⠙⠛⠁⠙⠛⠛⠀⠙⠛⠉⠀⠘⠁

⠀⠀⠀⠀⣒⣒⣲⣒⣒⣒⣒⣒⡄⢀⠤⡠⠤⠤⠤⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⢒⠒⠀⠀⠀⠀⢀⣀⣔⣢⣀⣀⣀
⠀⠀⠀⠀⢡⣋⣉⣉⣉⣉⣉⣦⡁⢸⠊⠁⠂⣀⣀⠂⠑⡆⠀⢄⡀⢀⠀⠀⠀⢀⣠⠀⠀⢸⠸⠾⠌⢀⡀⠀⠀⠀⠸⡕⢾⣻⣏⠢⢸
⠀⠀⠀⠀⢸⠩⠛⠍⣩⣩⣉⢹⡀⢸⠀⢴⣾⢿⣛⣥⡀⡇⠀⢁⠄⢄⠀⠤⠤⠤⠈⠀⠀⢸⢩⢭⡿⣟⣫⠄⠀⠀⠀⡀⠢⠉⠫⢁⡍
⠀⠀⠀⠀⢨⠐⠒⠂⣈⣉⣉⢸⡃⠘⠈⠋⠉⠙⠻⣿⡗⠂⠀⠘⠌⠔⠀⠉⢡⠤⡄⠀⠀⢸⢸⣖⣿⢿⠋⠀⠀⠀⠀⢁⠐⠉⠊⢁
⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠉⠈⠁⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⡀⠀⠀⣀⢀⣀⠀⢀⠀⢠⣶⡶⡄⠀⢀⢴⣶⡄⠀⢀⡴⠼⠟⡛⣧⡦⡀⠀⠀⡴⢑⡶⣴⡂⠒⣶⡀⢠⠀⠼⢄⠔⢢
⠀⠀⠀⠀⠂⡤⡉⣭⠍⠉⠠⠐⡇⠀⢿⠀⡈⣤⠁⠀⡸⠀⠀⢲⠁⣼⢀⠮⠻⠗⡔⠀⠘⢫⣣⡏⢩⡶⡴⡎⠀⠸⣀⠉⠩⠉⠩⢈⡍⠉
⠀⠀⠀⠀⠀⠤⠤⣠⣴⣾⣭⠕⡁⢸⠰⠌⠋⠀⡿⠣⠔⠃⠀⠜⢴⡯⠓⠫⠀⢀⡣⠀⠀⢸⣿⡠⠿⠄⡛⠄⠀⠀⠀⢄⣼⣶⣌⡁⣀
⠀⠀⠀⠀⠈⠉⠁⠛⣽⣰⠟⠉⠀⠸⡀⡀⠔⠈⠢⢄⢀⠄⠀⠈⠢⢺⣧⣤⡿⠕⠁⠀⠠⢿⠟⠀⠀⠈⢣⠖⠀⠀⠀⠘⢵⣲⠇⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡿⠟⠛⠛⠛⠛⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣠⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣰⣿⠏⠀⠈⠛⠿⣿⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⢿⣷⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣶⣶⣶⣶⣿⠿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠿⣿⣿⡿⠿⠿⢿⣿⡇⠀⠀⠈⠉⠉⠁⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⢿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣾⡿⠁⠀⠀⠀⠈⢉⣻⣿⣷⣤⣤⣤⣄⡀
⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡷⠀⠀⢻⣿⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠀⠀⢾⣿⣅⠀⠀⢀⣤⣾⡿⠟⠛⠉⠉⠉⠛⠻⢿⣷⣄
⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠀⠀⠀⠸⣿⡏⠛⠛⠛⠛⠛⠉⢹⣿⡇⠀⠀⠀⣹⣿⡇⢠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣴⣿⠏⢠⣿⡟⠀⠀⠸⣿⣦⡀⠀⢀⣴⣿⠇⠀⠀⢻⣿⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⢹⣿⡀⠀⠀⠀⠀⢀⣿⡏⠀⢀⣾⡿⠃⠀⢸⣿⠁⠀⠀⠀⠈⠻⣿⣶⣿⠟⠁⠀⠀⠀⠘⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠘⣿⡇⠀⠀⠀⠀⢸⣿⠇⣠⣿⡟⠁⠀⠀⢸⣿⡀⠀⠀⠀⢀⣴⣿⠿⣿⣦⡀⠀⠀⠀⢰⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣿⣿⠀⠀⠀⠀⣾⣿⣴⣿⠏⠀⠀⠀⠀⠈⣿⣧⡀⠀⠰⣿⠟⠁⠀⠈⠻⣿⠆⠀⢀⣾⡿⠁
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣧⣤⣤⣼⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣹⣿⣿⣶⣤⣤⣤⣤⣤⣶⣿⠿⠋
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠿⣫⣷⣶⣶⣯⣽⣛⣛⣟⣛⡋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⢨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⢸⣿⣿⣿⣷⣶⣶⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣾⣿⣴⡎⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣱⣿⣿⣿⡇⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣧⣿⣿⣿⡿⣱⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠝⠛⠛⠛⠽⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀



⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣟⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡡⠚⠉⠉⠉⠉⠒⢤⡀⢰⡕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠁⠆⠀⢀⠖⠚⠓⠢⢵⠀⠐⠫⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠸⡀⢠⠎⠐⠃⠀⢉⠀⡇⠠⡄⢒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⠀⡟⢳⠇⣤⠘⠀⠀⠀⠀⡇⢈⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠦⠄⠈⣆⡼⢲⢄⣰⢣⣠⠒⢲⡦⡃⡏⢿⢸⢾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⣤⣧⠙⢘⠜⡻⢹⠉⢯⠙⢦⠈⢘⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠦⠀⠸⠀⡧⠊⠀⢸⢦⣘⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⠤⢾⠁⠀⠀⡜⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⠀⠀⠀⣇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠫⣑⡒⠃⠀⠀⠀⢀⣼⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣒⠯⠤⢭⡭⠭⣗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⡞⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣇⠀⠀⡇⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣠⣾⡿⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⡇⠀⠐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣿⣿⣿⣆⠀⠘⣴⠃⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠼⣿⣷⣷⢀⢢⣸⣿⣿⣼⡆⠘⠡⢀⡔⣚⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⠛⣉⣀⣀⣈⠛⢿⡗⠒⠛⠛⢡⣿⣿⢴⣮⡉⠻⢿⣛⠛⠶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠂⢸⣿⡿⠾⠿⣿⣆⠀⢹⠇⠹⠉⠉⠉⠲⣤⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣄⢸⠘⠗⠀⢀⣌⠉⢧⡼⣇⠀⠈⠛⠦⠀⢰⣿⣦
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠈⣁⢄⡀⠀⣿⠝⠀⠀⣿⣺⠆⢀⣀⠀⣶⡘⠛⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣻⣷⠰⣯⡞⠁⠀⠁⠠⣴⣄⠘⠃⠀⢸⡞⠆⠈⢣⣤⡌⣾⣇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⡿⢁⣤⡄⠀⣠⡄⠘⣯⠘⠀⠐⠟⡊⠛⠀⠀⢬⡻⠳⣾⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠸⠓⠁⠰⣟⠏⠀⠈⠁⠀⢾⣉⡠⠀⠀⢤⡈⠁⠘⣫⣼
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⢀⣾⣿⡄⠉⣠⣤⡀⣠⢶⡀⠉⠀⠀⠀⣿⡟⠀⠀⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠑⠹⠞⠇⠀⣽⡻⠁⠙⠧⠁⠀⣴⣶⠀⢁⣤⠀⠀⢙⡇
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣶⣦⠀⢀⣀⠈⠉⣀⠀⢀⣤⠈⠿⠋⠀⢼⡿⢀⣿⡿⠃
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⠃⠠⣮⣽⣢⣞⣻⠂⢸⣾⠃⠀⢀⣦⡀⢀⡈⢁⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⢫⡵⣦⡀⢽⠏⠀⠈⠁⠀⠀⠉⠀⠀⠸⠋⠀⣾⣿⡾⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣻⡿⠀⠀⢀⢞⣍⡀⢠⣞⣷⡄⢀⣴⡄⢉⣼⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣯⣁⣰⣶⣏⠸⠞⠉⠋⣻⠂⠀⠘⠿⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⡾⣿⡿⢷⠉⠓⢀⣤⣤⠁⣴⣿⣄⣤⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡋⠁⠀⣴⣶⠘⠷⠉⣀⣉⣹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢕⣧⡄⠐⣿⣿⠀⠀⣽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣟⣄⠩⣽⢸⣶⢆⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡾⡧⣸⣽⣾⣿⣿⡟⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣷⣿⣿⣽⣿⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣀⣠⣿⣇⣺⣆⣽⣽⣷⣶⣿⣿⣭⠭⠭⠅⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠛⠙⢻⣿⣿⣿⡋⠉⠛⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠠⢦⣄⣰⠀⠀⡀⠀⠀⠀⢻⡏⢹⠃⣄⣀⣠⡀⢀⡤⡧⢹⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⢠⠘⣇⢸⣾⣿⣛⣛⡞⢸⠇⣦⣼⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⢰⡆⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣂⣤⣼⣶⣿⣾⣿⣿⠇⢁⣠⡽⠗⣾⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡿⡇⠀⠀⢠⡴⠾⠻⣟⠛⣿⠿⢯⠙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣇⣿⣿⢴⣿⣿⣇⣠⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡼⡷⣗⠤⠄⠀⢀⣠⣽⣿⣾⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠉⢸⣿⠁⣠⣿⠃⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣳⣆⠀⢀⣸⡛⠉⠤⢿⣿⣭⣍⣀⣴⣋⡛⠛⠛⠉⠉⠉⣉⣩⡿⡟⢿⠃⠀⣼⣁⣴⠿⢿⠛⢟⣻⣷⢿⡅
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡧⠋⢁⣤⣴⣿⣭⣽⣿⣿⣿⣿⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣭⣥⣤⣼⣶⡿⠿⠉⣃⠸⡇
⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⡯⠉⣙⢑⡺⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠉⠀⠹⠆⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣠⣏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⣀⢈⠙⡿⣿⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡦⠏⢉⣛⣿⣿⡏⠀⢀⣠⡤⠾⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣟⣉⠛⠛⠿⢿⣿⣿⣷⣷⣮⣿⣷⣞⠛⠉
⠀⠀⠀⠒⠛⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣭⣉⣀⡐⠛⠻⠿⠿⣿⣿⣯⣟
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⠙⠿⠗
⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠈⠛⢻⣿⠿⠟⠛⠻⣿⡭⠿⠋⠉⠉⠛⠛⠛⠟⠋⡉⠋⠀⠉⠉⠉⠉⠉⠉⠋⠛⠛⠛⠛⠛⠶⣿⠿⠿⠿⠟⠻⠷⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠿⠆

⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣤⢠⡀
⠀⠀⠀⠀⢠⣄⣸⣇⣠⣼⠇⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⡀⢸⣸⣿⣧⠀⠀⠀⢼⣿⣿⠃⠀⠀⠀⣤⣶⣾⣿⣿⣿⡀
⠀⠀⢠⠾⢩⠏⠛⡿⣿⣿⢧⣤⠄⠠⠮⣴⣧⡇⡇⡄⡀⠀⢰⢃⡇⣿⡯⠴⣻⠄⠀⠸⡽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣽⣦⣤⡀
⠀⠀⡿⠛⢘⡌⣖⣻⣿⣿⣧⠀⠀⠀⡑⠚⢻⣿⣧⣸⠁⢸⡟⣸⡿⠧⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠂⠀⠩⣻⣿⣯⣿⡀
⠀⢸⠖⢈⠀⠟⣿⣿⣿⣿⣿⠀⠀⠀⠙⢭⠬⠵⠿⢿⡆⢸⡿⠿⠏⠉⠁⠀⠀⠀⢠⡀⣤⡄⠀⢠⠀⠐⠈⠀⠀⠀⠀⠀⢞⡽⣿⡷⡉⠁
⠀⠈⡒⡤⣇⣿⣿⢿⡟⠷⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢢⣤⣤⣄⣂⢀⡀⠀⠀⣯⣿⣷⡿⠙⠻⣿⣦⠴⣀⣤⠆⠀⠀⠎⢸⡿⠳
⠀⠀⠙⣿⣿⠿⠛⠋⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⢿⣿⣖⣒⣶⠀⠀⠉⢩⡟⠓⣺⢫⣿⢿⣿⣿⣷⢷⣦⡀⠀⠘⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⢸⡻⣿⡓⢮⡀⠀⠀⢘⡠⢱⣸⣿⠩⢿⣟⣷⣤⣿⣿⣷
⠀⠀⠀⢄⣀⣀⢺⣷⣏⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠃⠁⠀⣣⠀⠀⠀⠀⠸⣥⣯⣿⣷⣘⢀⠋⢁⣸⣿⣿⡇⠀⠀⣰⣆⡈⠙
⠀⠀⣠⠴⠚⢿⡻⢿⣿⣟⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠠⠂⠼⣿⣿⡟⠀⠀⠸⣿⣤⠋⣠
⠀⢰⡿⢂⠛⡀⠟⣰⣿⣿⣧⠀⢦⢑⣌⡀⠀⠀⠀⠀⠀⢠⣄⣄⣴⡧⠖⠀⠀⠀⠀⠀⠀⢰⣯⠤⢤⣄⠀⠘⠛⠋⠀⠀⠀⠀⠈⠀⠀⠁
⠀⢸⣧⡈⣀⣹⣬⣿⣿⣿⣿⠀⢻⡂⢿⣷⣠⢸⡀⠀⠒⣺⠿⣿⣿⠛⠿⢷⣄⠀⣰⡷⡶⠿⠃⡘⠠⠌⢱⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⢿⡰⠁⢿⣿⣿⣿⡿⠃⠀⠀⠁⠭⢿⣿⡎⠀⠀⡾⠉⡅⠉⣈⡀⠐⠚⢹⡆⢠⠀⠐⠂⠈⠛⠂⠈⡀⢣⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠹⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣀⡹⠇⠀⠀⢧⠀⠠⡄⠹⠇⠐⠀⢠⠇⠘⢧⣄⣈⠁⠈⠀⠁⠀⢀⠀⠀⣠⣄⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡰⠛⠋⠏⠀⠀⠀⠀⠈⢣⡀⠀⠂⠀⠈⢀⡞⠀⠀⠘⠥⣙⣿⣿⣿⠿⠛⠁⠀⢿⣭⣯⣻⡾⢉⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢹⡿⠋⠘⢯⣽⡿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠤⢤⣀⠈⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠓⠦⢄⡘⡆⢸⡤⠖⢛⡓⠶⣤⡴⠛⣦⠀⠀⠀⢀⣠⠖⠋⠉⠉⠙⠒⣢⣄⣈⠑⢶⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⢶⡶⠶⠄⢀⠀⠉⠃⠈⠀⠈⠀⣤⣤⣹⣦⠀⠘⣇⠀⣰⠟⠁⠀⠀⠀⣠⡶⣋⣉⣁⣀⣀⠀⠀⠀⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⢋⣠⣴⡞⠁⣰⠀⠰⣌⠑⠶⣤⣀⡀⠈⠻⣧⠀⢸⣴⠏⠀⠀⠀⠠⡞⠛⠛⠋⠉⢉⡽⢋⣴⠀⠠⠀⠂⢄⡈⠉⠓⢄⡀
⠀⠀⠀⠀⠀⢀⡞⠀⣤⡄⠛⠋⠁⣼⠀⡴⢹⡄⠀⡙⢷⣤⠼⠿⠿⢿⣶⠾⡇⢸⣏⡤⠶⠶⣤⣀⠁⠀⠀⠀⣠⣾⡴⠋⠀⡇⢀⠳⣄⠀⠙⣎⠲⣦⠭⣦
⠀⠀⠀⠀⠀⣼⠁⠀⠻⠟⠀⠀⠀⣿⡼⠁⠈⣧⠀⣿⣾⣥⣤⣤⠄⠀⠈⠙⠇⠸⠁⠀⢈⣁⣀⣀⣉⣑⣦⡀⠉⠁⡔⠠⠀⢧⢰⡇⠈⠳⣄⠘⣧⠹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⣾⢲⣸⠞⠁⢠⠞⠁⣠⡴⠚⢁⠆⠠⣄⠲⢤⣄⡀⠈⠉⠫⡉⠙⢧⡀⠀⠳⠊⠀⠸⣼⡇⠀⠀⠘⢧⣿⠀⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⡶⡄⠀⠀⠀⠘⣽⠃⢠⡀⠻⠚⠋⢱⠃⢠⠟⡄⠀⠛⢧⣀⠘⢏⠛⠶⠦⣽⣄⡈⢷⡀⠀⢀⡀⠀⠻⠀⠀⠀⠀⡟⠏⠀⢸⡆
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠷⠁⠀⠀⠀⢰⡇⠀⢹⡽⠀⠀⠀⢸⣰⠏⠀⣧⠀⢸⠀⠙⢷⣌⢧⠀⠀⠀⠣⡼⠈⣷⠀⢀⡸⠀⠀⠀⠀⠀⠀⠙⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣤⣼⡀⠀⠀⠀⠀⠀⠀⠸⠋⣴⠦⡘⣧⣸⠀⠀⠀⠙⢿⡆⢀⣀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠖⣄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠳⢿⡇⠀⠀⢀⣤⡄⠀⠀⠀⠘⠊⠀⠈⠛⠀⡤⢤⡀⠀⠀⠹⢄⠆⠀⠀⣾⠀⠀⠀⠀⠘⠶⠃⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⡴⡄⠀⠀⠀⣿⡀⠀⠈⢧⠏⠀⢀⣄⠀⠀⠀⠀⠀⠀⠙⠖⠁⠀⠀⠀⠀⠀⠀⢠⡟⠠⢄⠀⠀⠀⠀⠀⣀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠑⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡀⠀⠀⣾⠁⠰⠎⠀⠀⠀⠀⠀⢭⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠠⠦⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⣼⠇⠀⠀⠀⣠⡀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠛⠀⠀⠀⢿⣆⠀⢠⡀⠀⠀⠀⠀⠀⠀⢯⡗⠀⠀⠀⣀⠀⠀⠀⣼⣏⡀⠀⠀⠀⠳⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣬⡶⣤⣀⢻⣆⠸⠎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣏⠇⠀⣼⠏⢫⠟⠀⠀⠀⢀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣆⠀⠀⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠀⣼⠯⣤⣤⣴⢞⣁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠱⠀⠀⠀⢿⡹⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣐⣦⣀⠀⠀⢀⡴⠛⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢶⣤⠀⠀⠀⠀⣠⡾⠋⢩⣿⠁⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣉⣡⣴⠿⣿⠀⠀⢠⣾⠏⠀⠀⢸⣿⣤⣶⠿⠟⢋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠉⠀⠀⢿⡆⢠⡿⠁⠀⢀⣴⠿⠛⠉⠀⠀⢀⣾⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢸⣷⡿⠁⠀⣰⡿⠃⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡙⢷⣌⣿⣇⣠⣾⣋⣀⣀⣤⣴⡾⠟⠉⠀⠀⠀⢈⣿⡏⠀⠀⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠟⠛⠛⠛⠛⠛⢿⣾⡿⠛⠛⠻⢿⣿⣯⡀⠀⠀⠀⠀⣀⣤⣾⠟⠀⢠⠶⢦⡄⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠈⠻⣿⣦⣶⣶⡿⠟⠋⠁⠀⠀⢾⡀⢸⡇⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣤⣤⣤⣤⣶⡾⠋⢠⣿⠻⣧⡀⠀⠀⠀⠀⠘⣿⣏⠁⢠⠞⠲⣦⠀⠀⠀⠙⠋⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠉⠁⠀⠀⣰⡿⠃⠀⣽⣷⣄⠀⠀⠀⠀⠹⣿⡄⠸⣄⣀⣽⠃⠀⠀⠀⢀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢸⣿⡟⢷⣦⡀⠀⠀⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⣿⠉⣧⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣀⣴⡾⣿⠇⠀⠀⠀⠀⠀⣿⡇⠀⠙⠻⣶⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠟⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣶⣾⠿⠛⠉⠀⣿⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⡟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⣾⠻⣦⠀⠀⠀⠀⠀⢸⡏⠹⣆⠀⠀⢀⡀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⠋⣼⠛⢳⡄⠀⢻⣤⣿⠀⠀⠀⠀⠀⠸⣧⡼⠃⠀⢀⡟⠙⣦⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣴⠞⢶⡄⠀⣿⣀⣴⡿⠋⠁⠀⠻⠷⠾⠃⠀⠀⠀⠀⠀⣾⠛⢳⡄⠀⠀⠀⠀⠀⠸⣇⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣯⠀⢨⡇⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⠀⠀⠀⢀⣤⣄⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⣴⠛⢷⡀⠀⠀⠀⠀⣰⠞⠛⣦⠀⠀⢠⠟⢳⡄⠀⠀⠠⣧⠀⣿⠀⠀⠀⠀⢸⡇⢹⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠹⣦⣸⡇⠀⠀⠀⠀⠙⠶⠶⠟⠀⠀⠙⠶⠾⠃⠀⠀⠀⠙⠛⠃⢠⣤⠀⠀⠈⠙⠛⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡇⠀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡟⢻⡄⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣦⣤⣀⠀⠀⠀⠛⠶⠶⠟⠀⢀⡴⢦⡄⠀⠀⠀⠀⠀⠈⠻⠾⠃⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣶⣤⣤⣄⣀⡀⢸⣇⣀⡿⠀⠀⠀⠀⣀⡀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣶⣶⣶⣶⣿⣭⣽⣦⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣯⣽⠻⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠻⢿⣿⣿⠆⠎⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡃⠘⠛⠃⠀⠰⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡀⠀⠀⠀⠄⡐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⣠⣃⣼⣿⣿⣤⠤⠼⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑⢠⡄⢠⠖⢼⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠒⠀⠀⢀⣠⣾⣧⣡⣴⠚⣴⣿⣿⣟⣿⠠⠃⠀⠀⣠⠤⠛⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡎⠔⠚⠉⢁⡸⠶⣾⡞⣻⣫⣾⣿⣿⠃⠈⣶⣾⣿⡋⢀⣴⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⣦⠊⠉⢡⣿⣿⣻⣿⢳⣿⣈⣽⣿⣷⣿⢿⠿⣿⣤⠯⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠈⣳⣤⡺⣯⣿⡿⠛⠧⣿⣛⣁⠋⠏⠐⡇⢀⠹⢿⡟⢵⣆⡀⣀⣤⣦
⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠶⠾⠟⠋⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⣯⣰⣾⣿⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡚⣟⣿⣯⣤⣼⣿⠿⠋⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠉⡻⡻⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠉⠙⠛⠋⠁
⠀⠀⠀⠄⡀⠀⣠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠾⢭⡅⣼⠃⢃⠎⠐⡄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔
⠀⠠⣈⠂⠀⣰⣿⡿⢋⠉⠀⣀⡤⢠⠀⡄⢲⡁⡠⣐⣳⣈⢩⠄⡎⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠤
⣈⠒⢄⠁⣰⠟⠉⠁⠛⠸⠇⠘⠟⠛⠋⡁⠙⣆⠑⢛⣿⢋⢂⠎⠀⠀⠀⠀⠀⠀⠀⠄⣀⠥⠀⣖⠄
⠤⢅⣠⡾⢛⡟⢡⣆⣴⠢⣔⢰⣌⣧⠈⠇⠀⣉⣤⣿⡱⡳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠅
⠀⣴⡿⠓⠪⢄⠉⠈⠈⠀⠉⠀⠀⠀⣠⡻⠿⣿⣭⡾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁
⠈⠋⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⣀⣴⣽⠳⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡇
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⡀⣨⡿⢫⠆⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⠙⣻⣴⣿⣶⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢿⡿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⢀⠄⠀⣀⢀⡤⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠋⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠛⠭⠀⡀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣤⡀⣠⠞⠃⠀⠉⣉⣉⣉⣀⣤⣿⣦⠀⠀⠀⠀⠠⠀⠀⠙⠿⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⢠⣿⠀⠀⠀⠙⠷⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣿⣦⣤⣾⣿⣿⣿⣟⣻⣟⠂⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣷⠤⢀⠆⢀⠀⠸
⠀⠀⠀⠀⠀⠀⢠⠴⣶⣿⣤⣤⣾⠛⣻⠿⠿⠧⠞⠛⠈⣥⡤⠾⠷⠶⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣾⣿⣿⣿⡶⠛⣶⡟⠀⡀
⠀⠀⠀⠀⠀⠸⡄⢀⣾⣿⣿⣿⣿⡄⠀⠀⣀⣀⣴⣶⣾⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠛⣿⠟⣷⣸⣷⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢻⡟⢫⣷⢩⣿⣿⡿⣦⣸⢿⣍⣭⣽⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠗⠒⠒⠿⣿⣿⣿⣤⣠⣶⣄
⠀⠀⠀⠀⠀⡄⣠⣽⣧⣼⣿⣯⡥⣿⣾⣿⣧⣿⣿⣿⣿⠟⠛⠟⢷⣶⣤⣶⣶⠂⠀⠀⢀⠀⠀⠲⠀⠠⠙⢀⣸⣶⣶⣿⣿⣿⡛⠛⠛⠛
⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣧⣸⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠈⠙⠿⣶⣤⡴⠂⠀⠙⠻⣿⣄⠀⠀⠀⢈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡈⣿⣿⣁⣀⣀⣀⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠿⡿⠿⠿⠿⠿⠟⠛⠛⠃

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⢀⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠉⠛⠻⠿⣿⣿⣿⣿⣽⣿⣭⠯⠀⠤
⠀⠀⠀⠀⣠⣾⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣶⣦⣵⣆⡀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⣄
⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⢿⢿⣷⣶⣾⣷⣶⣶⣭⣄⣒⣺⣾⣧⢀⣠⠾⢀⡀
⠀⢠⣾⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣛⣁⣷⣖⣤⣆⡠⠶⠤⡀
⠀⠘⠃⠀⠀⠈⠀⠀⠀⠀⠀⣰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⢿⣿⣿⣿⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢸⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡻⣿⣿⣿⣷⣌⠙⠁⠒⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣿⡇⢠⣄⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⣻⣮⠛⣿⣿⣿⣧
⠀⠀⠀⠀⢠⣬⣷⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡌⢻⡛⢿⠟⠛⠟⡛⠀⠀⠀⣸⣿⠏⢣⣸⠟⢿⣿⣷⡀
⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⣐⢂⣺⡆⡐⠀⢹⣿⣿⣌⠷⠸⢿⣌⠂⠶⠄⡟⠀⢠⣾⣿⡟⢢⡟⢷⣴⡍⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡏⠀⠀⠀⠈⠉⠀⡼⢚⣂⣢⣻⣗⠉⠄⣀⣼⣿⣧⣦⠀⠀⢀⣾⣿⢯⡞⢓⣿⠖⢻⡁⠈⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠊⠀⠈⢩⢿⣿⣾⠃⣠⠄⠠⣿⣿⣿⣿⣿⣷⣠⡾⠛⣿⣿⡿⠈⠁⠀⣼⣿⡄⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⡀⠀⢀⣀⣀⣀⣭⣿⣶⣿⣃⣴⣶⡿⣿⣿⠏⠁⢀⠄⠀⠉⠁⠀⠀⣠⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣦⣽⣿⣿⣷⠞⠛⠛⠿⠶⠂⣼⣿⠃⢴⣾⣂⣠⡴⠾⡛⠛⠛⠛⠛⣋⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⣬⣉⡟⠟⣻⠲⢲⢒⣶⣶⡶⠲⡶⠛⣿⣉⣱⣶⣷⠀⠀⠀⠀⠀⣼⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⠀⢉⠩⠽⠿⠿⠿⣿⣿⣾⣿⡿⠿⠿⢿⠿⠷⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣷⡄⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⣀⣤⣠⣄⠀⡀⣶⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡰⢿⠈⣻⣿⢿⣿⣿⣿⣯⣬⢻⣃⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⡶⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣏⡿⢿⣾⣋⢿⣻⠏⠉⠚⠛⠿⠿⠿⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⣿⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⣋⣭⠉⢡⡦⣤⠈⢭⣭⡙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢟⠉⠀⢿⡄⢻⡶⠂⢸⡇⣤⠀⣸⡇⢀⣿⡛⠆⢙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠰⣏⣥⠀⣬⣿⢘⣛⣯⣬⣿⣯⣤⣿⣀⡾⣯⠉⣴⠟⣿⠌⠹⣷⣄
⠀⠀⠀⠀⠀⠀⣴⡟⣱⢶⣆⣙⢷⢞⣴⡾⠛⠉⠀⢀⠀⠀⠀⠉⠉⠛⢶⣮⡓⠾⠃⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⣼⡟⠀⠙⠻⣯⢙⣴⠟⠁⠀⢠⣤⠀⣾⢿⠀⠾⠇⠀⠀⠀⠈⠻⣦⣀⣀⣀⣠⣤⣿⣧⣴⣶⠆
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢠⡿⠃⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⣶⠶⠶⠿⠿⠛⠛⢛⣛⣉⡉⣩⣥⣤⣄
⠀⢀⣀⣠⣿⣧⣤⣴⣶⠶⠿⠿⠟⠛⠛⠋⢋⣉⣉⣉⠀⣠⣶⣶⣄⠰⢶⣾⠿⠃⣿⡟⠛⠁⢸⣿⠉⣿⡇
⠀⠈⠉⣉⣭⣤⣄⠀⣴⣶⡶⠆⠀⠀⣿⡇⢸⣿⡋⣉⠀⣿⡇⠘⠛⠀⠈⣿⡇⠀⢿⣿⠿⠃⢸⣿⡀⣻⡇
⠀⠀⠀⢹⣿⢙⣿⠇⢻⣷⣤⡆⠀⠀⢹⣯⠈⣿⡟⠛⠀⢻⣧⠀⣶⡆⠀⣿⣇⠀⢸⣿⣶⣶⠀⠿⠿⠟⠃
⠀⠀⠀⢸⣿⠛⣿⡆⢸⣿⣀⣀⠰⣶⣸⣿⠀⣿⣷⠶⠆⠘⠻⠿⠛⢀⣀⣈⣉⣀⣤⣤⣤⣤⣶⠶⢶⣾⠟⠛⠃
⠀⠀⠀⠈⠿⠇⠻⠿⠀⠛⣛⣛⣁⣉⣩⣥⣤⣤⣶⡶⠶⠶⠟⠻⠛⠛⠛⠋⠉⢉⣿⠏⠀⠀⠀⠀⣸⡏
⠀⠀⢀⣶⡶⣶⣾⠿⠟⠛⠛⠛⢿⣍⠉⠉⠀⠀⢠⣤⠀⣦⣖⠀⠾⠂⠀⠀⣠⡾⢣⣤⣄⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣠⡙⢷⣤⣀⠀⠈⠁⠈⠙⠋⠀⢀⣀⣴⡾⢋⡤⠻⣦⣙⡷⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⢀⣴⢯⣽⢆⣬⣝⠛⠷⠶⠶⠶⠶⠿⠛⢫⣥⡖⠻⣶⣃⡀⣉⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣅⡿⢁⣾⠷⠌⠀⣸⠇⣾⣛⠀⣿⠙⠂⠈⣷⡀⢘⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣭⣓⡐⣧⡟⠀⣿⣭⠀⠻⣶⣟⣀⣬⡷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠶⠶⠶⠾⠿⠛⠛⠁⠁

⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⣠⣀
⠀⡗⡇⠀⠀⠀⠀⠀⠁⠉⣿⣿⣿⣟⣻⣤⣴⣾⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣷⣶⡦⡄
⠀⠖⡇⠀⠀⠀⠀⠀⠀⠀⠿⠟⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⠟⠀⠁⠁
⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⢄⡀⢤⠄⡀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠠⠄⢀⠀⠀⠀⠀⡠⠀⠤⢄⠀⠀⠠⡴⠒⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⢠⠋⠀⠀⠀⠈⢂⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠑⠀⠒⠁⠀⠈⠀⠇⠀⠀⠰⠀⠈⢃⠘⠁⠉⠠⡘⠀⠀⠀⡔⠉⠀⠙⠆
⢠⠀⠀⠘⡀⠀⠀⠀⠀⠈⢄⠀⢏⠑⠀⠒⠒⠒⠂⠈⠁⢀⠆⠀⠀⠀⠀⢀⠄⠀⠀⠢⡀⠈⢢⣄⠜⠀⠀⠈⠀⠀⠥⠈⢁⣀⠀⠀⡇⠀⠀⠀⡅
⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⡃⠈⠢⠄⡀⠀⠀⣀⣀⠠⠊⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⡠⡉⠡⡀⠦⡀⠙⠢⠤⠚
⠀⢄⠄⠒⠒⠂⠌⡁⠒⠀⠂⠁⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠨⡀⠽⠂⠠⠀⠀⠀⠠⠀⠀⠘⠂⠁⠀⣠⠤⠠⠄
⠀⠸⡀⠀⠀⠀⠀⠤⠁⠢⡀⠀⠀⠉⠀⠁⠀⢀⣴⣤⣄⣀⢀⠀⢰⠃⡀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡱⠌⠐⠀⠀⡎⠡⣀⢀⡌
⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠁⠀⠘⢿⣿⢿⣿⣿⠇⠀⠑⠂⠁⠬⠀⠃⢀⠶⠀⠀⠢⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠑⠤⠄⠋
⠀⠀⠀⠀⣀⠨⠤⠬⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡂
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠃⢠⠤⡀⠀⢔⠒⠂⠤⠤⠐⠈⠀⠀⠀⡔⠀⢐⠀⢱⠀⠀⡤⠀⡃⠀⠀⠰⠉⠀⠀⠀⠂⠹⣌⠉
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠰⠀⠈⢆⠀⠀⠤⢀⡀⢀⣀⠀⠄⠊⠀⠀⠈⠀⠁⠀⠈⠀⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡆
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠁⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠑⠠⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⠀⠰⠇⠣⡀⠀⠀⠀⢠⠂⠆⢄⠀⠀⠀⠀⠀⠀⠐⠊⢀⣀⣀⡀⠀⠑⠲⠄⠠⠄⠊
⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠐⠎⢦⠀⢸⡆⠐⠀⠀⠀⠘⠄⢀⡌⠈⢁⠄⠀⠀⠄⠀⡔⠋⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⡠⠀⠲⠆⠁⠐⢄⠀⠀⢀⠈⠀⢀⢣⠀⡇⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠐⠀⢀⣀⢄⠄⠀⠁⠂
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠄⠀⠤⠅⡔⠊⣃
⠀⠀⠀⠀⠀⠠⣀⡀⢀⠈⠄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠦⠼⠦⢀
⠀⠀⠀⠀⠑⠠⠄⢃⠜⠀⠈⠂⠤⠔⠒⠒⠁⣠⠄⠒⢦⣼⣁⠀⠀⠀⣠⣾⣿⡳⣷⣶⣶⣶⣶⣾⣶⡄⠀⠀⢠⠀⢄⠀⠀⠀⡎⠀⠀⠀⠀⠈⠆
⠀⠀⠰⢢⣀⡀⠐⠀⠀⢞⠉⠑⠄⠀⠀⠀⣸⠁⠀⠀⠈⠀⠈⣣⢠⣾⣿⣿⣿⡗⠟⠿⠋⠿⠹⠿⠿⠇⠀⠀⠀⠓⠤⠀⠀⠀⠅⠀⠀⠀⠀⠀⠸
⠀⠀⣺⣉⣱⣿⣷⣦⡀⠀⠍⠀⠙⠈⠁⠀⠹⣄⣀⠀⠀⣀⠔⡋⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘
⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠍⠉⠠⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢀⣀⡀⡠⠊
⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠲⡄
⠀⠀⠙⠛⠿⠿⠟⠟⠀⠀⢠⠊⠁⠱⣄⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢂⠱⠀⠀⣐⡀⠎⠀⠈⠂⠒⠁⠀⠀⠲⠒⠁⠀⠀⠀⠈⠁⠀⠀⠀⠠⠒⠑⢄⠀⠀⠀⢀⠀⠂⠢⠦⢄
⠀⠀⣴⠂⠉⠁⠀⠀⠀⠘⠀⠁⠀⠀⠈⡄⢃⠀⡇⠀⠀⠐⠀⠀⠀⠀⢀⠄⠒⠂⠈⠑⢄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⢠⠁⠀⠀⠀⠀⠀⠱
⠀⢸⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⠄⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠠⠀⠈⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⡄⠀⠘
⠀⠈⢿⣿⣦⣂⣀⠕⠀⠐⢄⠀⢀⡠⢊⠐⠀⠀⠣⡀⠀⠀⠀⠸⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠑⢄⡀⠀⠀⡀⠈
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠠⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠖⠒⠒⠒⠒⠶⠤⢤⣄⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢯⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠐⠺⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠡⠖⣀⡴⠛⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣠⠴⢏⣉⠓⠒⠢⠤⠄⣈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡤⠖⠋⠀⠀⠀⠈⠳⡀⠀⠠⡀⠀⠈⠉⠉⠛⢒⡶⠂⠀⠀⠀⠸⠧⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢧⠀⠀⠀⠀⠀⢠⣀⠌⠀⠀⠈⠳⡀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠹⡓⢄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⢰⣶⣼⠂⠀⢸⠃⢀⡤⠤⢤⣄⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠒⠮⡙⠒⠒⠂⠘⣄⠀⠀⠈⣡⠏⠀⠀⢉⣉⠉⠐⢦⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⠤⠤⠄⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⢀⡀⠻⠽⠆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠚⠉⠒⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠠⢄⠀⠀⠀⠀⢀⣠⢤⡎⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⣤⠤⠴⠚⠉⠀⡾⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢾⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠤⢤⡤⣀⣤⣤⠤⠤⠤⡃⢸⠤⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⠀⣬⠀⠀⠀⠀⠈⠉⠋⡀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡗⠛⠂⠀⠀⠀⠀⠐⠋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⣧⣄⣠⠼⣇⣀⣀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣯⠈⣾⡀⣰⠛⡏⢫⢹⡙⠓⣒⣒⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠩⠭⠭⠭⠭⠷⠖⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⠔⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠥⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠠⢧⣀⠀⠀⠈⢷⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠧⠤⢴⠄⠀⠈⠳⡄⠀⠀⢧⠀⠀⢀⣋⣀⣀⣤⣄⣼⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣧⢀⡤⣍⡦⡀⠀⠳⣞⠉⠀⠀⠀⠀⠀⡀⣹⢀⣀⣰⣃⣀⣀⣠⡤⠤⠶⠖⠚⠋⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡟⡾⠀⠈⠳⣿⢆⠀⠈⠓⠒⠦⠤⠴⠚⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠴⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠙⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⠀⠤⠀⢀⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣠⠜⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠉⠉⠙⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⡴⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⡓⠠⠧⢤⣀⣀⣀⣀⣀⡀⠀⠊⢀⢀⣀⣀⣀⣸⣓⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢬⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣼⡙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣇⣀⡉⠉⠐⠒⠠⠤⢤⣀⡀⠀⠀⡜⠉⢧⣿⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣥⣄⣀⡀⠀⣀⡉⠉⠉⠉⠉⠓⠐⠒⠒⠘⠳⠶⠤⠤⢸⣇⣣⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⡿⢸⣿⠀⣿⡿⠙⠇⠀⢰⣶⠆⢰⣶⠠⣤⠀⣠⠄⣀⢀⡀⣀⠈⠉⠉⠉⠐⠒⠒⠒⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⡏⣿⣦⢀⣿⡗⠟⠀⠀⢸⣿⠀⣾⣿⣰⠁⣼⣿⠀⠹⠺⢹⣿⠋⠇⣿⡿⠸⡆⢲⣶⢠⣄⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⠛⠃⠻⠟⠸⠿⠇⣼⠺⡟⣿⡿⢀⣿⡇⢈⡄⣿⡇⠀⠀⠀⢸⣿⠀⠀⣿⡇⡎⠀⣿⡿⢸⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠘⠓⠒⠁⠀⠿⠿⠀⢸⣿⣇⣴⢀⣿⡇⣾⡟⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⠉⠁⢛⢲⠒⠒⡶⢤⠤⠤⠤⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⡌⢧⡼⢁⡼⠃⠀⣀⣀⣀⣀⡍⢸⣍⣩⡭⠭⢶⡶⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡉⠉⠉⠁⠀⡼⠛⠃⠉⠉⠉⠁⡏⢰⣷⡌⢱⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣀⡀⠀⣀⠔⠁⠀⠀⠀⠀⠀⡼⢁⣏⠙⢇⡼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡟⠉⠉⠁⠀⠀⠀⠀⠒⠛⠛⣛⢋⣉⣑⣂⣾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⠽⠿⠿⠷⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠓⠛⠛⠒⠚⠃