Exasperation Emojis & Symbols

⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠑⢄⢀⠤⠤⡀
⠀⠀⠀⠀⢤⣌⠳⠤⠴⠋⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠘⠁⠀⠀⡜⠀⠀⢀⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⢹⠆⠀⠀⣾⠁⠀⠀⣀⠳⣤⣀⣠⠞⣤⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠾⡀⠀⢀⣸⠀⠀⠁⠀⡸
⠀⠀⠀⠀⠴⢋⣤⠶⢦⡈⠳⠄⠀⠈⢳⠀⠉⢠⡞⠁⠀⠀⠀⠀⠀⠀⠘⢲⠄⠀⢀⡀⢠⠤⠔⠁⠀⢏⡀⠀⠀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠀⠀⠀⣴⢏⣤⢤⣄⠳⣤⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠱⣸⠀⠀⠀⠀⠀⢨⡧⢲⡀⣰⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⢀⠤⠤⠤⢄⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢄⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⡔⠁⠀⡠⣄⠀⠈⢆⠀⠀⠸⣯⠽⠿⠯⠟⢦⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡤⡀⠀⠑⡄⠀⠀⠾⡭⠿⠿⠯⠓⡄
⠀⠀⢰⢁⡤⢊⡁⢈⠓⢤⠘⡀⠀⡠⡇⢠⡆⠐⡆⠈⣦⠀⠀⠀⠀⠀⡜⣠⠔⢊⠀⣈⠢⣄⢱⠀⠀⢼⠁⢰⠀⢰⠀⢸⠄
⠀⠀⠘⡮⣇⠘⠀⠈⠃⣼⢽⠀⠀⠈⢧⠀⡈⠀⡀⣰⠋⠀⠀⠀⠀⠀⢸⢽⡄⠛⠀⠘⢀⡯⡿⠀⠀⠙⡆⠀⠐⡀⠀⡜⠁
⠀⠀⠀⠱⣌⢳⡷⢼⠚⣡⠊⠀⠀⠀⠀⢳⢦⠤⣖⠁⠀⠀⠀⠀⠀⠀⠈⠣⡘⣢⠥⣴⠋⡴⠁⠀⠀⠀⠈⣲⠤⡤⡊
⠀⠀⠀⠀⢨⠯⠰⠄⢿⡁⠀⠀⠀⠀⢀⠏⠒⠑⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠰⠨⢏⠀⠀⠀⠀⠀⣰⠃⠊⠒⠹⡄
⠀⠀⠀⢀⡎⠠⠀⢀⠊⢣⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠋⢂⠀⠠⠈⡄⠀⠀⠀⢠⠇⠀⠀⠀⠀⢹
⠀⠀⠀⢸⠀⠀⠱⠀⠀⠘⡄⠀⠀⢰⠃⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡎⡄⠀⠲⠁⠀⢹⠀⠀⠀⢸⠀⠀⠀⠀⠀⡎⡇
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⡇
⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣈⣀⣀⣈⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣁⣀⣀⣀⣀⣀⣁⣁⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡶⠾⠿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⣠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣄
⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠙⢷⡄
⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢻⣆
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⡄⠀⠈⣿⡄
⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠉⠀⠀⠀⠻⣆⠀⢸⡇
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠸⣿⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣤⣤⣤⣤⣴⠶⠶⠶⠾⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⣿⡀⠀⠀⠀⠀⢿⡍⠉⠉⠉⠉⢀⣤⡴⠶⢦⣤⣀⡀⠀⠀⢤⣴⣶⠶⣦⠀⠀⠀⢰⣟⣩⡿⠋⠀⣀⣠⠶⣶⠾⠛⠛⣶⠘⣷⡀
⠀⠀⠀⢹⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⡀⠀⠀⢸⣏⢹⡷⢦⣄⡉⠛⠶⠏⠀⠀⠀⠀⠉⠉⣠⡶⠛⠉⠛⢶⣾⣤⣴⠞⠋⠀⠈⢻⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠛⠻⢶⣦⣿⣟⣀⣀⣈⠙⢳⣄⠀⠀⠀⠀⠀⠀⢴⣯⣤⣤⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⢹⣇⣀⣀⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣠⣤⣀⣀⣤⣤⣀⣠⣴⣦⣤⡶⢶⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠸⣷⡀⠺⠿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠈⠙⠛⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⡄⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⢀⣴⠶⣦
⠀⢾⣏⣿⣶⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⣴⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠁⣠⡶⢷⣄⣴⠶⢿⣷⣄⣀⡀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠷⢶⣤⣄⣀⠀⣸⡟⠀⠈⠙⠻⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡶⠞⠛⠉⠁⠘⣷⢀⣾⠋⠠⠿⠋⠁⠾⢛⣙⣿⠿⠛
⠀⠀⠀⠀⠰⣿⡛⠛⠛⢦⡀⠀⠉⠛⢷⣿⠃⠀⠠⣄⠀⠀⠈⢳⣄⣀⣀⣀⣀⣀⣀⣠⡿⠁⠀⠀⣰⠆⠀⢀⣹⣿⣅⣠⣤⣤⣤⣴⠾⠛⠉
⠀⠀⠀⠀⣴⡟⠛⠻⠆⠀⣁⣀⣠⣤⣴⣿⡄⠀⠀⢨⡇⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⡇⠀⠀⣿⠋⠉⠉⠉⠁⠀⣿⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠛⢻⡟⠉⠉⠉⠀⠈⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠙⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠋⠉⠙⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢼⠇⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣦⣤⣄⣼⣇⣀⣀⣀⣼⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣤⣤⣤⣤⣭⣉⣿⢯⣭⣭⣭⣭⣭⣭⣿⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣶⣾⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠾⠛⠋⠙⢿⡁⠀⠀⠉⠉⠻⣿⡛⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⣷⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠈⠻⡦⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣠⡴⠶⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠉⠙⠷⣄⠀⢻⣆
⠀⠀⠀⠀⢀⣾⠇⠀⣴⠟⢁⣤⡶⠶⠆⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⡀⠀⠀⠀⢀⡶⠀⠙⣷⡀⢻⡆
⠀⠀⠀⠀⣼⡟⠀⣾⠃⣰⠟⠁⣠⣤⣀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢠⡟⠀⠈⠻⢶⣄⣰⠟⠁⠀⠀⢸⡇⠀⣿⡀
⠀⠀⠀⢠⣿⠃⢸⡇⠀⣿⠀⢾⣋⣤⠉⢻⡄⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠻⢦⣄⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⢸⣿⠀⠸⣇⠀⠻⣆⡈⠉⠁⣀⣼⠃⠀⣸⠇⠀⠀⠀⠀⠀⠸⣧⠀⠀⣰⠟⠁⠀⠀⠉⠃⢀⡾⠁⠀⠘⣷
⠀⠀⠀⢺⣿⠀⠀⠻⣦⡀⠈⠛⠛⠛⠋⠁⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡉⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢠⣿
⠀⠀⠀⢸⣿⡀⠀⠀⠈⠛⠶⢦⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠛⠋⢿⡉⠉⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⠛⢶⣄⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢀⡾⠋⠁⠀⢸⣇⣀⣠⣼⡇⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⢹⡇⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠈⢿⣄⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣼⠇⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠙⠷⣤⣀⡀⠀⠀⢀⣴⠞⠋⠉⠉⠉⠉⠛⢶⣄⣀⣤⡶⠛⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠉⠛⠛⠳⠿⠷⠶⢶⣶⡶⠶⠶⠶⠟⠛⠉⢁⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉

⠒⢄⡀⠈⠢⡀⠈⠢⡀⠈⢄⠀⠣⡀⠑⠀⠐⠀⠡⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠊⠠⠁⠠⠊⢀⠈
⢄⡀⠉⠢⢄⠈⠒⢄⠈⠢⢀⠑⢄⠈⠂⠀⠂⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠠⠁⡀⠁⠄⠀⠔⠁⡠⠊
⠀⠉⠂⢄⠀⠑⠢⡀⠑⠠⡈⠓⡄⠑⠄⠐⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠁⠈⠠⠂⡠⠈⡠⠊
⠉⠒⠤⢀⠈⠂⢄⡈⠓⠄⡈⠢⠀⠂⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠠⠈⡠⠊
⠑⠢⢄⠀⠁⠢⢄⡈⠀⠄⠀⠀⢀⠐⠀⠀⠀⠀⢠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠐⡀⠀⠀⠀⠈⠠⠀⡀⠐
⠂⠤⣀⠈⠑⠂⠀⡈⠀⠀⠈⠀⠀⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣴⠁⡀
⠂⠤⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⢿⣿⠟⡻⠻⢙⣭⠧⣕⡗⠶⡆⣀⠅⠀⠉⠉⠻⣿⣿⣿⣿⣷⡇
⠠⠄⢀⠀⠉⠒⠠⠄⡈⠀⠂⠄⠀⠀⠀⠀⠀⣿⣿⡟⠓⠁⠈⠀⡴⢪⡄⡗⠮⠙⠋⠃⠀⠂⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄
⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠀⠀⠀⠀⠂⢏⡾⢃⠔⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣿⣿⣿⡇
⠀⠠⠤⠀⠀⣀⡉⠁⠀⠂⠀⠄⠀⠀⠀⠀⢸⣿⠁⠀⠀⢀⣤⣈⣈⠁⣢⠮⡳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣿⣿⠇
⠀⠤⠤⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⣠⠋⢙⠻⣿⣿⣷⣵⡌⠐⠅⠀⠀⠀⠀⠀⢀⣀⣁⡈⠀⣿⣿
⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⠃⠀⠀⠀⢀⣤⣼⣿⣿⣿⣻⢇⠈⣂⠀⢠⣿⣿⠿⡿⠟⠛⢳⡀⣿⡇
⠒⠒⠒⠒⠂⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣼⣟⢹⣿⡿⢿⣿⣷⣢⠄⠀⠈⣧⣶⣾⣷⣷⣤⠜⠀⣿⡃
⠂⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡇⠀⠀⠀⠀⠉⢻⣿⣷⣿⣿⠯⢰⠀⢀⠘⣿⣿⣿⣇⣽⡿⠀⢠⠏⡤
⠀⠉⠉⢀⡀⠠⠄⠒⠀⢉⠀⠄⠀⠀⠀⠀⠘⣱⠀⠀⠀⠀⠠⣍⣿⣿⡟⠉⠀⢐⠀⠐⠀⠉⠋⠋⠙⠁⠀⠀⢨⠰⠃
⠒⠈⢁⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠷⣼⣝⣷⡁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠂
⠂⠉⢀⡀⠄⠒⠈⣀⠀⠀⢀⠠⠐⠀⠀⠀⠀⢘⠀⠀⠀⠀⢜⢿⢿⣿⡏⣀⠀⣾⡀⠀⠀⠄⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠒⠈⠀⡀⠄⠒⠁⡀⠄⠊⠀⠄⠈⠀⠀⠀⠀⠘⡆⠀⠀⠀⢈⢕⡟⠉⠴⢟⣯⠭⠵⠺⠚⣷⠦⠐⠄⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠔⠂⠀⡀⠄⠂⠁⡠⠐⠉⡠⠀⠁⠄⠀⠀⠀⢰⣧⠀⠀⢂⢠⠎⠀⠀⣀⣉⣐⣒⠒⠒⠂⠋⠃⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠄
⠤⠒⠉⢀⡠⠒⠁⡠⠔⠁⡠⠊⠀⠔⠀⠀⠀⠘⠾⠀⠀⡱⢫⢠⣴⣿⣿⣿⣿⣿⣿⣿⣎⠐⡐⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠄⠑⢄⠀⠄⡀
⣀⡤⠚⠁⣀⠔⠈⢀⠄⠊⡠⠀⢁⠔⠀⠀⠀⠀⠀⢠⡄⣱⡇⢿⡿⣿⣿⣿⣿⡿⣿⢿⣿⡆⠇⢠⠂⠙⠋⠀⠀⠀⠀⠀⠐⠄⠁⠄⠑⢄⠈
⠀⢀⠤⠊⠀⡠⠂⠁⡠⠊⢀⠔⠁⡰⠀⠀⠀⠀⢀⣿⣝⣽⣿⣿⣿⣬⠻⠿⠿⢷⢋⣿⡿⢻⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⡀⠁
⠊⠁⢀⠤⠊⢀⡠⠊⢀⠤⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣜⢩⠟⡿⣿⣼⣿⣯⡿⣟⢹⣨⣿⣿⣷⠠⡄⣀
⡠⠖⠁⢀⡔⠋⠀⠰⠂⠀⠀⠀⠀⠀⡀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣼⣃⡏⡼⢰⠃⣣⣴⣿⣿⣿⣿⣿⣧⢱⡈⣇⠹⡄⢲⡀⢢⡄⢤⣀
⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⢀⡞⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⠘⣆⠹⡄⠹⡄⠹⣆⠙⢧⡀
⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡴⠃⣠⠏⢠⡆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⡆⠹⡄⠙⣆⠘⢧⡈⠻
⡀⠄⠀⣠⠎⠁⢠⠞⠁⣠⠞⠀⣴⠃⣠⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⡄⠘⡆⠈⢦⠀⠳⡄
⠀⣠⠞⠁⢀⡴⠋⢀⡴⠋⢀⡾⠁⣰⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⡀⠘⣄⠀⢣⡀⠘
⠴⠁⠀⣰⠟⠀⣠⠞⠁⣠⠞⠀⣰⠋⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢱⡀⠘⢆⠀⠳⡄
⠀⣠⡾⠁⢀⡴⠋⠀⣴⠋⠀⣼⠃⢀⡞⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢣⡀⠈⢆⠀⠹
⡾⠋⠀⣠⡟⠁⢀⡾⠁⢀⡾⠁⢀⡾⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢣⠀⠈⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⢀⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⣄
⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢧⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢦⠀⠈⣧
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠈⢳⡀⢿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⢹⣾
⠀⢸⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢿
⠀⠈⣷⠀⠀⠀⢸⡉⠁⠀⠀⢠⠶⠶⠶⣤⣄⡀⠰⢶⣶⣶⠄⠀⠀⢿⡽⠋⣀⣤⡴⢶⠒⢛⣷⠘⣧
⠀⠀⢻⡄⠀⠀⢸⡇⠀⠀⠀⠘⠷⣤⣀⣻⡼⠛⠓⢦⣍⠉⠀⠀⠀⠀⣠⠞⢉⣀⣹⠿⠞⠋⠁⠀⠘⣧
⠀⠀⠘⣇⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠚⠃⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣄⣠⠴⣤⡴⠶⡴⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠙⢦⣉⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠟⠛⣆⠀⠀⠀⠀⠐⣺⡟⠛⠷⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠈⠙⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠉⠉⢻⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⡿⢦⣀⠀⣠⣤⡀
⠀⠀⣤⢤⣀⡴⠞⠉⢧⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⢁⣿⣀⠀⠈⠛⠋⠸⠗⠓
⣞⣛⠛⠀⠉⠀⣠⡴⠛⢷⡈⢧⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢷⡾⠃⠈⠙⠲⢤⣄⠀⣌⣛
⢾⣉⡤⢠⠴⠛⠁⠀⠀⠀⠙⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠏
⠀⠸⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠉⣉⣉⣉⣉⣉⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠉⠉⠉⠉⠉⠉⠉⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣏⣀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣈⣉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣀⣀⣽⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣼⠄⠀⢀⠔⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡤⠀⠀⢀⡴⠀⡦⠀⠀⠁⠀⢠⠄⡇⠀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣄⠡⠀⢀⠂⠀⠁⠉⠄⠀⠀⠀⠀⠀⠁⠀⠀⢤⡀⠉⢊⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠈⠁⠌⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢠⡆⣠⠀⣸⠃⢾⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠊⠁⠐⠉⠹⣟⣡⡜⠛⠛⣣⡤⢫⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣀⢴⣖⠂⣲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠶⠟⢁⣩⣏⢠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣤⡞⠋⠉⠉⣳⡆⠀⠀⠀⣀⠀⠀⠀⠔⠠⠀⠒⣀⣠⣬⠷⠲⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⢶⢷⣶⣛⣛⣿⠶⠿⣥⣀⣴⢦⣼⠉⠳⣼⢦⡀⢠⣄⣨⣿⣤⣀⣴⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠋⠉⠉⠀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⡀⠳⠟⠉⠃⠉⠛⠛⣿⠇⠀⣵⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡋⠸⡟⠉⠀⠀⠀⢀⡠⠞⠁⠀⠀⢀⣀⠀⠀⢸⣟⣀⡼⢋⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⢰⣿⠀⠀⡖⠛⠉⠳⣄⠀⠀⣰⠋⠉⠙⠋⠻⣦⠠⠴⠋⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡞⠀⠀⠀⢠⢾⣁⠀⣿⠀⡘⠀⢠⡆⠀⢘⡆⠀⢿⠀⠀⢠⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠉⢦⠱⡄⢀⡴⠃⠀⢸⠿⡿⠂⣧⣀⠀⠀⣠⡞⠀⠀⠘⣦⡀⠀⢀⣠⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢣⠹⡞⠁⠀⠀⠸⣿⡆⠀⠘⠧⣭⡼⠍⠀⠀⠀⠀⠈⢿⣟⡻⠃⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢷⠆⠀⠀⠀⠀⠈⣅⠀⠀⠀⠀⠀⠰⠧⠤⢤⣤⣄⣸⡟⢡⡀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⣤⣤⣀⣀⣐⣦⣀⣀⣨⣷⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣯⣙⠛⠿⣭⣭⣭⡽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣦⣶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢠⣿⣿⣿⡟⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡾⣿⠛⠛⠛⠷⠾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡧⠟⠿⠿⠿⣭⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠦⣀⠀⠀⣸⠈⠒⠀⠀⠀⠀⠀⣤⠤⠟⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠝⠁⠽⠀⠀⠀⠀⠀⠀⢰⡁⢀⡀⢀⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⡟⢃⠀⠀⠉⠓⠖⠢⢤⡴⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠳⣄⠀⠀⠀⠀⣠⠇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢱⡶⣶⣿⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡾⣿⣿⣿⣧⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠙⢶⠃⢿⣿⣿⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣬⣥⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣻⣛⣛⣛⣛⣙⣛⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣏⣽⣿⣏⣋⣻⣿⣏⣹⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣄⡀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠛⠉⠀⠀⠀⢸⡏⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠛⢦⡀
⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠉⠙⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣼⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⣠⡶⠞⠛⠋⠉⠉⠉⠉⠉⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠈⠛⠒⣲⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⣀⡴⠞⠉⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠐⠿⠶⠶⣻⡿⠋⣠⣾⠏⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡆⠀⠀⣼⣋⡴⠞⢡⡏⣰⠏⠈⠛⠆⢀⣀⣠⡤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⡇⠀⠀⠉⠉⠀⠀⠸⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠁⠀⠘⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⣤⣤⠴⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⠶⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠛⠛⠛⠛⠛⠛⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⢉⣀⣤⣤⣴⣶⣶⣶⣤⣄⢀⣀⣤⣤⣍⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡿⢿⣿⣷⣿⣿⣻⣯⣿⢿⣿⣻⣿⣟⢿⣿⣮⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣟⣿⣿⡿⠟⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⢿⣿⡃⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣫⣿⣿⠷⢶⣤⠀⡆⢠⣴⣶⠶⣿⡷⣼⣿⣿⣿⣟⣷⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣽⣦⣤⡄⢨⡁⠀⡘⢋⣤⣤⣼⣟⡍⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⣼⣿⣿⡷⣿⣯⡓⠛⢻⡧⢠⣶⠞⠙⠋⣩⣿⣗⣷⣿⣿⣷⣿⣯⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢒⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷⣿⠇⢘⡿⢻⣶⣾⢿⡟⣻⣿⣿⣿⣿⣷⣼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣥⡄⣤⣿⣼⠄⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⣿⣟⡿⣿⣽⣿⣿⣿⣿⠀⠀⡿⣿⣿⠟⠉⠀⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠾⢿⣿⣷⣟⣿⣿⣿⣿⡟⠀⢠⡴⠾⡽⣦⣄⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣋⠹⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣟⣿⣿⣿⣿⣧⣀⣈⡻⢿⡞⠛⠁⢀⣀⣾⣿⣿⣿⣿⣿⠛⢿⣿⠿⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠾⠿⠭⠭⠷⠾⢿⣿⢿⣿⣿⣿⣿⣷⣾⣦⣿⣶⣿⣿⣿⣿⣿⡟⠙⢿⣿⣶⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⣦⣀⠙⠿⣕⠈⠙⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣉⠠⠴⢺⡿⢓⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢷⣜⠶⡖⠛⠓⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣩⠟⢁⡤⠞⠁⠀⣸⠋⢠⣿⡿⠁⣿⢷⣽⣌⠻⣧⠈⠻⡀⠀⠈⠳⢍⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣡⠞⠉⠀⠀⠀⠴⢓⡶⣠⠞⠁⠀⠐⠈⠳⡍⢤⣹⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⢀⢎⡴⠁⠀⠀⠀⠀⠀⠀⠈⠪⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⣯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡤⢖⡉⠉⢉⠲⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⣐⡤⠒⠉⢉⠩⠒⠂⢀⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠫⠠⠐⠈⢀⣠⠆⠉⠹⠷⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠃⠀⠀⠀⠀⠀⠀⣀⠠⠐⠒⠀⡺⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⣉⠹⣶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⢆⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⢀⢀⡠⠴⠷⠶⢷⡤⠄⠺⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⡠⢚⠓⠊⢠⠖⠚⢲⡄⠑⠒⠇⢸
⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢏⠲⡀⣦⡇⡀⠤⢀⢸⣼⢀⠖⡙⢨⠐⠤⢄⡀
⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠢⠟⢅⢉⡹⢴⢏⡉⡐⠻⠄⠀⢀⠀⠸⠀⠹⠁⠢⡄⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠑⠤⣜⡶⣀⢲⣧⠥⠊⠀⠀⡘⢀⠂⠀⠘⠀⠀⢡⠀⠑⢄
⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠔⢀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠑⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠁⠀⠀⠘⠀⠀⠀⠠⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⢀⠌⠀⠠⠃⠠⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠃
⠡⠀⠀⠀⠀⠀⠀⢀⣠⡊⠄⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢀⠔⠁⠀⡐⠁⠠⠁⠀⢀⠂⡐⠀⠀⠀⠇⠀⠀⠘
⠀⠑⠄⠀⠀⠤⠒⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠊⢁⡠⠂⠁⠀⣠⠊⠀⡰⠁⠀⢀⠂⢀⠃⠀⠀⢠
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠻⠀⢠⣄⠀⠀⠀⣠⠀⠀⠞⢁⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡝⠶⣄⣀⡟⠙⣶⣀⣼⠛⣇⢀⣰⠏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣤⣀⡀⢷⡀⠈⠛⠁⠀⠘⢿⠃⠀⢹⠞⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼⣎⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⣻⠞⢀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡐⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⢉⡿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠙⣯⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣼⡥⠾⢻⡇⠀⣴⢿⡀⣸⣆⠀⣿⠉⠳⢬⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠉⠀⠀⢸⣧⠞⠁⠌⢷⡏⢈⠷⣽⠀⠀⠀⠈⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⠀⠈⣦⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⣀⠠⠔⠀⠊⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⣠⢄⠄⠀⣀⠤⠺⣿⠟⠋⠉⠉⠉⠉⠀⠈
⠀⠀⢰⠊⠖⠉⠀⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣬⣥⡅⣲⠚⠁⠀⠀⠁
⠀⠀⠌⠀⠀⡂⠀⢀⣂⣬⠴⢋⡽⠊⢉⣥⡍⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢠⣄⠀⠘⣀⡀⠄⢀⡠⠋⠰⣄⡀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⢂⠀⠉⠁⣀⡴⠋⠀⠀⠀⢭⡀⠄⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢨⠄⣾⠋⠢⠀⠀⣰⠿⠚⠃⣠⠖⡹⣊⡀⢠⣀⠀⢐⢼⣶⡟⢁⢝⠆
⠀⢠⠀⠄⠀⠈⠄⠠⠿⠋⠀⠀⣿⠀⠀⠐⠁⠀⠈⡈⡀⠀⠀⢀⣠⡄⠀⠀⡇⠇⣿⠀⠔⠀⠀⠁⠀⢨⡀⡁⢰⢡⡏⠁⠐⠂⢬⠿⡦⡈⠀⣵⠋⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠠⢄⡨⠴⠀⠀⢠⡿⠿⠃⠀⠀⠈⡄⣠⡁⠔⠁⠀⠀⠀⠀⠐⣥⠞⡞⠀⠀⠀⢐⡑⣴⣿⠁⠌⠅⠀⠀⠀⠂
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⡿⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠀⠀⠀⠀⠀⠆⠀⠀⠀⢈⣳⢖⣒⣀⠄⠃⠩⠽⠿⠃⠀⠀⠀⠠
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠃⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠖⡀⢀⠀⠀⠀⠀⣬⢂⠀⠀⠀⠀⠀⠀⣰⣦⢡⠏⠀⡟⠀⠀⠀⠀⡀⠀⠀⢀⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⣩⣄⠀⠀⠀⠀⠀⠀⠈⣡⠀⠈⢨⣇⠀⠀⠘⠀⠀⢉⠉⠐⢄⠀⠀⠙⣿⡿⠀⠀⡇⠀⠀⠠⠊⣀⠌⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣸⡁⠀⠿⠟⠀⠀⠀⣸⠆⠀⢠⠃⢰⠸⣿⣈⡦⠀⠀⠀⡠⠋⠀⠀⣰⠆⢀⡀⠻⡧⠡⡡⠔⠰⣷⣘⣮⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠈⠀⠀⠀⠀⠀⠀⠊⠀⢀⡀⡟⠀⠈⢁⣿⠃⣱⠁⠀⠔⠁⠀⠀⠜⠁⡴⢟⠙⠷⢀⠊⠀⠀⠀⠻⡟⡑⠁⠂⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠚⠁⢀⡰⠘⠈⠀⠹⠀⠀⠀⠀⠀⢀⣀⣼⠷⣒⠤⡌⠄⠀⠀⢀⡴⠀⠀⠁⠀⢀⡠⠀⠀⠀⠁
⠀⠀⣤⡰⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡀⠀⠀⠀⡄⢢⠀⠀⠀⣩⣶⢸⠨⠄⠐⠕⠀⠀⠀⠌⠀⢀⣤⡀
⠀⠀⣾⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠘⠐⠁⠈⠁⠐⠂⠐⠒⣈⡕⠆⠈⠄⡀⠀⠀⡸⠀⠀⠈⢹⣿⢰⠙⠻⠇⠀⡀⠀⢀⢰⠻⡜⢟⡧⠅⠀⢀⣀⡀⠀⡀
⠀⠀⣧⠀⠀⠐⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠈⠁⠀⠀⢀⣠⡼⠟⠠⠋⢀⠀⠠⠊⠀⢅⣭⠜⠀⠙⠚⠢⡤⠀⢚⢕⡒
⠀⠀⠁⠈⠀⠀⠀⠣⡘⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⠀⠳⠀⠀⠀⠨⡄⡛⢅⠀⣠⠤⠒⠁⢀⠄⠀⠀⠁⠈⠀⠀⠀⠀⠀⢀⠈⠠⠩⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⣀⠀⠀⠊⠀⠀⠀⣀⢀⣀⡀⠀⠐⠀⠈⢉⠀⠀⠀⠀⠀⠀⢌⠳⣍⡁⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠨⠀⠡⠁
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⠌⠂⠀⡒⠥⠢⠀⠀⠀⠈⠡⠂⠀⠀⠀⢀⣀⡀⠠⠉⢻⡄⡀⠀⠀⠀⠀⠀⡀⠀⠤⠐⢈⢶⣬⡴⡒⢆⣠⡆
⠀⠀⢀⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢦⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⢓⠢⣙⠁⠀⠀⠀⠀⢂⣐⣾⡎⠀⠀⠀⠉⠛⠊⠀⡼⣸⡇
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠴⢰⠠⠀⠂⠐⢠⣄⠀⠠⠄⠀⡐⠀⠀⠐⡂⣻⡍⠉⢷⠀⠀⠀⢨⣾⡿⠿⠀⠀⠀⠿⠟⠀⢅⠀⡇⠙⠃
⠀⠀⠀⠀⣀⠤⠒⡆⠀⠀⠀⠀⠀⠆⢐⣈⠅⣉⣖⠀⠈⠁⠘⡀⠀⠔⠁⣠⣋⠄⢀⣠⡴⢠⣟⠀⢀⡾⣀⡁⠀⡀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠂⠁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠁⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢥⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢰⣄⠀⢀⠧⣀⡤⠛⠂⠚⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠶⠀⠊⠀⠓⠃⠈⠉⠉⠂⠀⠀⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⠀⠁⠀⠠⠀⠀⠈⣧⡴⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⡀⠂⣀⡀⠀⠀⠀⠀⠀⠀⡿⡇⠏⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡤⠀⠔⠀⠀⠀⠀⢀⠔⢂⡉⠉⠀⠀⠀⠉⢢⠀⠀⢀⡼⢳⣀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣑⣄⡀⠀⠀⡴⠉⠁⠀⠀⠉⠓⢤⠀⢀⡜⢀⡤⢊⡴⠋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⠷⠤⣑⣤⣀⣀⣀⣀⡀⢠⣓⠭⠶⠿⠚⠉⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠸⣅⣤⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣜⠀⠈⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣤⣤⣤⡤⠤⠤⠤⠤⠖⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣰⠒⠛⠉⠉⠉⠉⠉⠹⡅⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠙⢧⣼⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣠⣿⡀⠀⠈⢻⡄⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⠋⠁⠈⠙⠳⢤⣼⠁⠈⢳⡄⠀⠀⢳⡀⠀⠈⣧⣠⠴⠶⢦⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡄⠀⠈⢷⠀⠀⠸⡇⢀⡴⢾⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⢰⠇⠀⠀⠀⠀⠀⠀⣰⠶⢿⡀⠀⠀⢳⡀⠀⠘⣇⠀⠀⢷⣸⠁⠘⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠻⣇⡿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢳⡀⠀⠈⣧⠀⠀⢹⡄⠀⢸⣿⠀⠀⣷⢀⡟⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢳⡀⠀⢸⡆⠀⠈⠇⠀⠀⣿⠀⠀⢸⣼⣁⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠉⣿⠀⠀⠀⠀⠀⢠⣤⣤⣈⣧⠀⠀⠈⣧⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠀⢸⡿⠉⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⡇⠀⠀⠀⢀⣀⠀⠀⠈⠙⣇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣇⠀⠀⠀⠈⠉⠐⠶⠤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⠰⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡄⠙⣦⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠈⠙⠦⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⣤⣄⣈⣷⣄⡀⠻⣤⣀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⡇⠈⠳⣄⠀⠀⠀⢤⣄⣠⣬⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠶⢤⣀⡀
⠀⠀⠀⢀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠈⠉⠛⠓⠲⠦⣤⣀
⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡄⣠⠞⠋⠉⠁⠀⠀⠀⠉⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡛⠻⠄⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣠⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⢀⡞⠀⠀⣸⠀⠀⢰⠀⠀⢸⠇⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⡖⠻⢄⠀⠀⢠⠇⠀⠀⢀⡞⠀⠀⢠⠇⠀⠀⡞⠀⠀⢸⠀⢸⡟⡄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣟⠉⠁⣠⣿⠀⠀⢀⡾⠀⠀⢀⡞⠀⠀⣰⠃⠀⠀⡎⠀⣸⠁⢳⢀⡿⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠸⠴⠞⠁⢯⣀⡴⠋⢿⣀⡠⡎⠀⠀⣰⡇⠀⠀⡼⠙⠚⠁⠀⢘⣈⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⠶⠶⣄⢸⡄⠀⡀⢀⠔⣾⣎⠓⣄⠀⠀⠈⠒⠋⠁⠓⠖⡺⢒⡭⣍⢲⡀⠈⣸⡇⠘⠭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠦⣐⡎⠉⠁⠀⠀⠙⢞⠉⢉⠗⠋⠀⢠⠴⠒⠲⢄⠀⠀⠑⢪⠉⢹⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⡦⡶⠀⠀⠀⡎⠀⢸⠆⠀⢠⠧⠖⠒⣦⠈⣧⠀⠀⡎⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⠀⠀⠓⠓⢦⡀⠀⢜⠀⢸⠆⠀⡜⢀⡐⠻⡅⢀⣸⠀⢀⠟⠀⢰⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡴⣧⣀⣰⣇⣀⣠⡈⡓⠾⢄⣸⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠈⣇⣠⠴⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠛⠛⠲⠶⣮⣽⠓⠦⣄⡀⠒⣶⢶⡶⠒⣊⣭⣤⣶⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠳⣄⠀⣹⠿⢥⣠⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⠀⢈⣫⠥⢤⡀⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⢸⡉⠀⠀⠀⡇⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢳⠀⠀⠀⢳⠃⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢱⣀⠙⠒⣦⡀⢀⣤⣄⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡠⠔⠒⠛⠳⢤⣥⡬⠿⣍⣉⣉⡿⢡⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣴⣭⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⣾⠉⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠉
⣿⠀⠀⠀⠀⠈⠉⣻⣶⣤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠉
⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⢦⣄⣠⣴⠃⠀⠀⠀⠀⠀⠐⢦⣀⣀⣠⡴⠾⣿⣿⣿⣿⣿⠆
⠸⣇⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⢁⣼⣍⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣷⡀⠹⢿⣿⡿⠏⠀⠀⠀⠀⠀⣸
⠀⠙⢦⡤⠶⠶⠶⠶⠒⠛⠛⠛⠛⠁⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠒⠛⠉⠈⠛⠛⠛⠛⠓⠶⠶⠶⠶⢤⡴⠋
⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣀⣀⣠⡤⠄⠀⠀⠀⠀⢀⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣤⡶⠿⠛⠛⠛⠋⠙⠛⠛⠛⠻⠶⠦⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠐⠶⠷⣀⠀⠀⠈⠉⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣄⣠⣿⢿⣦⣀⡠⠀⠙⠃⠤⠤⢤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠶⠋⠉⠁⠀⠈⠉⠳⢾⣥⡔⠂⠀⠐⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⠶⣤⣄⣠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⢣⡄⠀⠰⠶⠶⠤⠄⠀⢀⣴⣿⣤⣈⠷⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⣿⣄⠙⢦⠀⠠⠤⠤⠄⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠙⢷⣄⠑⡄⠀⠀⣰⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⣀⡀⠉⢛⣿⣦⣾⣿⣟⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠻⣟⠛⠛⠛⢻⣿⣟⢛⣿⠟⣟⠛⠛⠛⢻⣿⣿⠛⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠳⣤⣤⣤⣬⣽⡟⠁⠀⠘⠳⣤⣤⣀⣩⣭⠟⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣠⠋⠉⣿⡇⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠛⣦⡀
⠀⠀⠀⠀⢻⣄⣀⣿⠇⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣸⡄
⠀⠀⠀⠀⠀⠉⠉⣿⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⡀⠤⠴⠶⠦⠴⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠲⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠟⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣷⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⠶⠶⠛⠛⠛⣿⣷⡀
⠀⠀⠀⠀⠀⢠⡜⢫⠀⠀⠀⣸⠉⠀⠀⠈⢻⠉⠀⣻⡇⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⡎⠀⡸⠀⠀⢠⡏⠀⠀⠀⠀⢸⠀⢠⡟⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀
⠀⠀⠀⠀⣶⠁⢰⡅⠀⠀⢸⣧⣴⠖⠀⠀⠈⠁⣸⠇⠀⠀⠐⣶⣤⣿⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⢠⠁⢀⣘⠁⠀⠀⠘⠉⢿⡀⠀⠀⠀⣸⡇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⢸⡇
⠀⣀⠐⣾⠶⠊⣩⣤⣦⠀⠀⠀⠈⢻⡄⠀⢰⣿⠃⠀⠀⣰⠇⠀⠀⠀⠀⠀⠉⣉⣨⣿⠂⠀⠘⣇
⠀⢳⡶⠃⢀⣴⠋⢁⣼⣇⠀⠀⠀⠀⣹⣆⣀⣿⣀⣠⣴⣷⣤⣤⣤⣤⣤⣜⠛⣉⠉⣿⡆⠀⠀⣿⡇⢐⢀⡀
⣠⠏⠀⣠⠞⠁⢠⠟⠉⢹⡦⠴⠶⠞⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣤⠶⠟⠋⠉⠉⠉⢿⠇⠀⠀⢻⡏⣉⠉⠳⠆
⠻⣤⣴⡏⠀⣰⠃⠀⣴⠟⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⡟⣋⣉⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡧⠈⠛⢺⣆
⠀⢸⡇⠀⣶⠋⢀⣴⠿⠶⠶⠶⠶⠶⠛⠛⠛⣿⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⢿⣧⠈⢶⣄⣼
⠀⠘⢷⣤⣽⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠶⠉⠁
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠢⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣿⠃
⠀⠀⠀⠀⠻⠶⢶⣶⣶⣤⣤⣤⣤⣤⣄⣠⣠⣿⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⢶⣿⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠤⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⡿⠖⠊⠙⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠋⠀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣀⠀⠀⠙⠛⢷⣦⣄⣀⡀
⠀⠀⠀⠀⣠⠴⠖⠋⠁⠀⣠⣤⠾⢿⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣤⣝⠙⠶⢦⣤⣄⡀⠀⠈⠉⠙⢶⣶
⣀⣘⣿⣦⣤⣤⣤⣴⣛⣛⣉⣁⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣉⣉⣙⣛⣛⣉⣀⣉
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠞⠛⠙⡳⢦⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠅⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡠⠀⠀⠀⠀⠀⢀⣤⠀⣠⠎⣠⠞⣧⠀⡆⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⣠⢔⣡⡴⠋⣯⣶⠷⠋⠁⠀⠘⣧⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣤⡴⠿⠛⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀⠘⣷⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡆⠀⠘⠛⠲⣤⣀⠀⡀⠀⢀⣠⠴⠋⠉⠀⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⢸⣷⣶⠀⢸⠁⠀⠈⢡⣶⣶⠀⠀⣿⢰⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠬⣉⠥⢀⡟⠀⠀⠀⠈⣛⣫⠄⠀⢿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠓⠶⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⠈⠉⠉⠩⠍⠉⠁⠈⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⠒⡶⠒⠒⠒⠻⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⢺⡏⠙⡇⠀⠑⠀⠀⠀⠀⡷⠈⣿⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⠀⠀⠀⠀⢸⠀⠀⠹⡄⠀⠀⠀⠀⣰⠇⠀⢸⠀⠀⠀⢀⠈⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢢⠀⠀⠀⢸⠀⢀⣀⠘⢦⡀⢀⡼⠃⣀⡀⡾⠀⠀⠀⡎⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠃⠀⠀⠈⠛⠉⢻⣀⠀⢹⠋⠀⣠⡏⠉⠁⠀⠀⠐⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢱⡖⠛⠛⠛⠛⢦⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠸⣏⡙⠲⠤⣄⣀⡄⠘⡇⠀⠀⠀⢀⡏⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡤⠶⠋⣁⡿
⠀⠀⠀⠀⠀⠀⠀⣸⠛⠳⠶⢤⣭⣷⠀⠈⠓⠲⠚⠉⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⠴⠶⠛⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢀⣀⣸⣧⡤⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠙⠛⠛⠶⢦⣤⣤⣶⠶⠶⢤⣤⣼⣧⣇⣤⣤⣴⡶⠛⢋⡉⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀
⠒⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢲⣶⣟⠛⠋⠉⠉⠉⠙⠛⠿⣿⠆⠀⠀⠀⠀⢀⡼⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣟⠀⠀⠀⠀⠀⠀⢤⣓⢮⣷⣤⣤⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠳⠶⣤⣤⣒⣮⣳⣵⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣤⣀⣀⡴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠦⢤⣤⠼⠁⢀⣀⣀⣠⣴⣿⣶⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⢀⣤⣶⣶⣤⡤⠀⣀⡬⠙⠛⠛⠛⣋⣡⣾⣿⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡾⢋⠉⠙⠛⠉⣴⠟⣁⣴⣦⡀⠀⣀⡈⠉⠙⠉⠱⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢰⢏⡾⠁⠀⢀⡀⢸⡟⢰⣿⣿⣿⣿⣿⣿⣿⠂⣄⠐⢶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⢿⡸⣧⢸⣿⣿⣇⠸⡇⣿⣿⣿⡿⠿⠿⣿⣷⣄⠈⠙⠒⠚⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⠶⠦⣄⠀⠘⠷⠙⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢠⣀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⣳⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢹⡄⠀⢹⣷⡄⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡄⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⣇⠀⠈⡛⢿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡄⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢸⡆⠀⠙⣦⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⣤⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠈⣿⡿⣿⣿⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⡇⢀⣼⣇⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣁⣶⡶⣷⣶⠖⠀⠹⣿⣭⣛⢷⣌⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⣿⣿⣿⡄⠠⠞⠉⠁⢀⣈⣉⣉⠛⠳⢶⣄⠀⠾⣤⡟⠠⠞⠻⠿⣧⡴⠀⠀⠀⠀⣿⣧⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣄⢿⣿⣿⣿⠀⠀⠀⣤⣬⢿⣿⡿⠓⠶⠀⠙⠆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣿⣿⠆⠙⠁⠀⠀⠀⠀⠙⠉⠐⠝⠛⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⢳⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣦⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⣀⡀⢰⡶⠏⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣽⣿⢃⣉⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⣿⢙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⢿⣇⣿⣿⣿⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⣤⣶⣿⣶⣤⡄⠀⠀⠀⢸⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣯⣿⣿⣿⣿⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⣛⣋⣉⣭⣿⡿⠀⠀⠀⠀⢠⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣷⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠛⠛⠳⠶⠞⠛⠛⠛⠉⠁⠀⠀⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⢩⣟⣃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧⣠⠞⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠙⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⣀⣤⣤⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣸⠄⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⣠⠞⠁⠀⠙⢮⡁⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢱⠐⣆⡑⠒⠤⠄⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢧⠀⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣚⣷⠿⠋⠙⠲⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠈⡏⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠀⡾⠋⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⣄⢸⠀⠀⠀⢸⣇⠀⣀⠀⠀⠀⣄⡀⣰⡟⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⠀⠙⠾⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⢸⢁⡼⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢨⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠹⠆⠀⠀⠀⠀⠀⠀⠘⠏⣠⠴⠄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢯⣈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠶⠦⣤⡀⠀⠀⠀⠀⡸⢹⠆⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣭⣤⡇⠀⠀⠀⢀⣴⣿⣭⣤⣤⣤⣴⣶⣾⡇⠀⠀⠀⣀⠁⠜⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⣿⣟⣉⣭⠽⠿⠿⠛⢻⡇⠀⠀⠀⣿⠴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢈⠧⠖⠒⠛⠋⠉⠉⠉⠛⢧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⣤⣤⡤⠤⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠲⠶⠛⠴⢆
⠀⠀⠀⠀⠀⠀⠀⣰⢾⠁⠀⠀⠀⠀⠀⠀⠐⠎⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣾⠁⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⢛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⢀⡴⢻⠇
⠀⠀⠀⠀⠀⣼⠃⠀⡀⠉⠀⠀⠀⢀⠊⢠⡌⠀⠈⠀⠺⠶⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣧⠀⣀⡴⠋⣠⡿⠞⣻
⠀⠀⠀⠀⠀⡟⠀⠀⠇⠐⠀⠀⠀⠀⠂⠤⠔⠀⠀⠀⠀⠀⢀⣠⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⠟⠉⠀⠈⢉⣠⣾⠷
⠀⠀⠀⠀⠀⣇⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢲⡏⠀⠀⠀⠀⠀⠀⣈⣡⣴⣞
⠀⠀⠀⠀⠀⠸⣄⡠⠰⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢢⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠁⠀⠀⠀⠀⢀⣀⣩⡥⠴⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣄⣁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⣀⣤⡤⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⢢⣀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⣀⣀⣠⣼⡉⠉⠁⠚⠉⠙⠆⠀⢤⣤⣤⠠⠄⠠⣖⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⢀⡴⠟⠉⠁⠀⠀⠈⠐⠤⣆⠀⠀⡇⠀⠀⠠⠛⣀⣀⠀⠭⡀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠠⠀⣿⠀⠀⡇⠀⡔⠁⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⢠⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠐⠲⠒⠋⠻⣆⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⡀⢇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⣟⣀⡀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠈⠉⠉⠓⠲⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣇⠀⠀⠀⠠⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢰⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣬⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⣥⠤⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠙⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠀⠀⠀⠹⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣶⣶⣶⣶⣶⣶⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣓⣒⣒⣒⣛⣒⣚⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡟⠉⠉⢻⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢁⢀⠁⣷⣿⠈⡀⡈⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣦⣼⢯⣽⣧⣴⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠆⠰⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢻⡀⠀⠀⢀⡟⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⣰⣦⠀⠀⠀⠠⣤⠰⠛⠶⠶⠛⠂⣤⠀⠀⠀⠀⣴⣆⠀⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⠟⠻⠆⠀⣾⣯⣀⢰⣤⣶⣶⣤⡆⣀⣽⣷⠀⠰⠟⠻⣿⡿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢾⠋⠃⠈⠉⣀⠀⠀⠀⣠⡿⠛⠈⠁⠈⠁⠈⠁⠛⢿⣄⠀⠀⠀⣀⠉⠁⠘⠙⡷
⠀⠀⠀⠀⢠⣶⣦⣬⣤⣄⠀⠺⠿⡷⣞⢿⠁⠀⣰⣿⣠⣄⣠⣄⣿⣆⠀⠈⡿⣲⣾⡿⠇⠀⢤⣤⣥⣴⣶⡄
⠀⠀⠀⠀⠀⠹⠿⣿⡿⣡⡀⡠⠺⣟⠿⣛⡵⣿⡿⠛⣿⣿⣿⣿⠻⢿⣿⢾⣛⠿⣻⠗⢄⢀⣌⢿⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢾⣿⡁⠸⣧⣄⣿⣿⣀⠉⠉⠉⠉⣀⣿⣿⣠⣼⠇⢈⣿⡷⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠈⢷⠿⠒⢀⣼⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⣧⡀⠒⠿⡞⠁⠐⠚⠁
⠀⠀⠀⠀⠀⠐⣿⠄⠀⢰⣷⠀⢀⣀⣾⡟⢁⣽⠿⢿⡆⠉⠉⢰⡿⠿⣯⡈⢻⣷⣀⡀⠀⣶⡆⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢻⣷⣾⣿⠃⢁⡌⢿⣿⣤⡿⣶⣶⢿⣤⣿⡿⢡⡈⠈⣿⣷⣾⡟⠿⡦
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠋⠀⠛⠋⠁⠀⠙⠿⣷⣯⣽⣿⠿⠋⠀⠈⠙⠛⠀⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣦⣄⣀⣄⠀⠀⠀⣤⣀⣀⡠⢫⡿⢿⡝⢄⣀⣀⣤⠀⠀⠀⣠⣀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⡉⠻⠻⣄⢻⣿⣶⣬⣉⣁⡤⣄⣠⢤⣀⣉⣥⣶⣿⡟⣰⠟⠟⢉⣳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠘⣿⣎⠉⠉⠋⠙⠾⠃⠘⠳⠋⠙⠉⠉⣱⣿⠃⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠆⠀⠀⠰⠶⣤⣤⠶⠆⠀⠀⠐⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⣿⢧⣤⣤⣤⣀⡼⢧⣀⣤⣤⣤⠼⢿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠁⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⢋⣭⣾⣿⣿⠟⠙⣿⣿⣿⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣷⠀⠀⠻⣿⣿⡿⠀⠙⢿⣿⣿⠏
⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠸⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⡿⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⠄⠀⠀⠘⣿⣆
⠀⠀⠀⢀⣿⡏⠀⠀⢀⣠⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⢀⣸⣿⠀⠀⢠⣿⠟⠉⠉⠉⠙⠿⣷⡄⠀⠀⠀⠀⣠⣾⠟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⣴⣿⠿⣿⣿⠀⠀⠀⠁⠀⢠⣾⣿⣦⠀⠈⠁⠀⠀⠀⠀⠙⠋⠀⠀⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶
⢿⣧⣀⣿⣿⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣹
⠈⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛
⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣤⣀⣀⣀⣀⣠⣤⣴⣶⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣤⣾⣿⣿⣿⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡧⠀⠀⡿⠶⢶⡶⠶⣶⡶⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⣧⣤⣼⣧⣤⣿⣧⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠛⠃⠙⠛⠁⠀⠀⠀⡏⠉⢹⡏⠉⣿⡏⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣤⣄⠀⠀⣀⣤⣀⠀⠀⡿⠛⢻⡟⠛⣿⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠳⠤⠼⠧⠤⠿⠧⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠻⢿⣿⣿⠿⢿⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣟⣿⠀⠀⣻⣹⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣽⠇⠐⣯⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠛⣛⣛⡻⠶⠿⢛⠛⠏⢩⡙⠻⣦⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠛⠋⣉⣩⣤⣽⣿⣿⣿⣷⣼⣿⣶⣌⣿⣷⣌⢻⠟⠛⣙⡛⠻⢶⣤⣄
⠀⠀⠀⠀⠀⠀⣠⡶⠾⠛⣛⣭⣵⡾⠿⢿⣛⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣶⣶⢗⣠⣿
⠀⠀⠀⠀⠀⠀⠹⣷⣬⠛⢛⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠟⢡⣾⣿⣿⣿⣿⣿⡿⠿⠯⠙⢳⣶⣶⣿⣿⣿⣿⣋⣘⣿⣿⣿⣿⣿⡛⠛⠿⣿⣿⣿⣮⣛⠛⢷⣦⡀
⠀⠀⠀⠀⠀⣼⠇⣴⣿⣿⣿⣿⣿⣿⣍⣀⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⢸⡇
⠀⠀⠀⠀⢰⡟⠼⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣠⠔⣠⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢠⣿⡃
⠀⠀⠀⠀⠸⣧⡀⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⣿⣿⣿⣿⣿⡿⠿⠆⣸⡇
⠀⠀⠀⠀⠀⢿⡄⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⠷⠦⠘⣿
⠀⠀⠀⠀⠀⠸⣧⠛⠁⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡆⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠙⢻⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠛⢿⢡⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⠋⠉⠻⣿⠇⢿⡿⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠿⢿⣧⠀⠉⠃⠀⢹⡏⠰⠀⡜⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⡀⠀⠀⠹⠀⣈⣃⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠀⠀⣠⡔⠉⠀⠀⡃⣠⢎⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡱⡄⠀⠠⠀⠀⠉⢛⣶⣶⣤⣤⡤⠀⠀⠀⠠⣤⣤⣶⡿⢯⡄⠀⠀⠀⠣⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⠈⢻⠀⠀⠀⠈⠑⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣜⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢂⣀⠀⠀⠀⠀⠀⠀⠀⢰⢱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⢣⠀⠀⠀⠀⠀⠀⢰⣦⣄⣀⣉⣠⣴⣿⡄⠀⠀⠀⠀⣠⠣⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⠔⠉⢣⠀⠀⠀⠀⠀⣾⣿⡿⢿⡿⠛⢿⣿⡇⠀⠀⢀⠔⠀⠉⠢⡙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡱⠃⠀⠀⠀⠁⢀⠀⠀⠀⡿⢹⣧⣀⣀⣠⣾⡆⠀⢀⠴⠁⠀⠀⠀⠀⠘⡜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⠁⠀⠀⠀⠀⠀⠀⢙⠲⠤⠔⠈⠙⢛⣛⣛⠩⡰⠿⠉⠀⡄⠀⠀⠀⠀⠀⠘⡸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠠⡈⠑⠂⠤⠄⠊⢁⠃⠂⠀⠁⠀⡀⠀⠀⠀⠀⠁⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢎⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠒⠀⠤⠀⠂⠅⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⣰⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⠓⢤⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠤⢶⢫⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠸⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⢸⠉⠢⠭⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠈⠑⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠁⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡷⠀⠀⠔⠣⠉⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠈⠦⠆⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠀⠸⢟⣛⠚⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⡄
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠
⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠁⠀⠀⠀⢠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠶⠶⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣿⣿⣆⡀⠀⠐⠀⠐⠀⠀⠀⠀⠐⠀⠂⠂⠀⠐⠀⣀⣸⣿⡇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣏⠙⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⣿⣿⣿⡏⣹⣿⣦⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⣿⡏⣻⣿⣿⡷⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⣿⢿⣿⣿⣛⣩⣷⣄⣠⠃⠀⢱⣄⣤⣿⣍⣻⣵⣿⠿⣿⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠑⠒⡲⠛⠉⣠⠂⠉⠉⠉⠉⠁⢰⣄⠉⠛⢖⠒⠊⢻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⡞⠁⣠⣾⠻⢶⣤⡀⠀⢀⣴⠾⠟⣷⣄⠈⢷⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣴⢋⡏⠀⠀⢹⠿⢿⠿⠁⠀⠀⢸⡝⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠃⢸⠃⠀⠀⠸⣷⣤⡀⠀⠀⠀⠀⣷⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣾⠀⠀⠀⠀⢉⣩⣴⠶⠶⠶⣼⣿⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⣻⣦⣤⣴⣾⣿⣥⣶⣴⣷⣾⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣤⣀⡀⠀⠀⣀⣀⣤⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠛⠉⠉⠉⠉⠛⢻⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠐⡇⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⠀⠀⢠⣖⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠶⠶⠤⠀⠀⠀⢀⣿⣿⣷⢖⡠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠈⠒⠢⠄⢁⣑⣈⣿⣿⡿⣫⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠒⠀⠉⠉⠉⠉⠛⠟⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡭⠂⠀⠀⠀⢀⡀⠀⠐⠂⠀⢀⡲⠈⣋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡴⡿⢋⣀⡀⢀⠔⠊⠁⠀⠀⠂⠀⠀⠠⢜⡆⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢀⣾⠛⠋⠁⠀⠀⠀⡀⣀⣀⣥⣤⠴⡤⠃⢰⣄⡀⠀⠀⠀⠀⠀⠡⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣠⠂⠀⢀⡴⢛⡿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⠃⠀⣠⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠘⡀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⢰⣿⠃⠀⡴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠂⠀⠀⠀⢨⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢺⠏⡆⣼⣞⡢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡇⠀⠀⠀⠠⣄⣄⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡣⠊⠌⣼⠁⠝⠁⠙⠋⠳⢼⠐⠰⣴⣲⠟⢷⡖⢶⡤⠄⠀⢠⡀⠀⠀⠀⢈⠋⠀⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⠋⣢⢤⣄⣙⡛⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⣿⠻⣡⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡿⢘⠉⣿⠟⡆⠀⡆
⠀⠀⠀⠀⠀⡠⠚⠋⠀⠀⢀⣠⠞⠹⢹⣿⣇⠀⠀⠈⠁⠀⠀⣀⠠⠁⠀⠀⠀⠀⠀⢀⣾⣿⢟⡵⠹⢸⠇⢀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣶⡶⢋⣏⡇⢰⠀⠈⢹⠛⡆⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⠛⠉⡠⠁⠀⠀⡜⢣⡀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠻⣡⢋⠇⠀⡈⠀⠸⡄⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⡰⢻⠀⢤⡦⠉⠀⠀⣠⣾⣇⢨⠓⠫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠐⢩⡇⠀⠁⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠘⠀⠁⠀⠤⡴⢊⡿⡟⡜⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠨⠊⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⠶⠶⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡔⣲⠀⠀⠀⠀⠀⠀⠀⠀⣔⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣀⣤⡴⠾⠋⢁⠀⠀⠀⢀⠀⠤⠄⢀⡀⠀⠀⠀⢀⡤⠔⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⡾⠋⠀⠀⠀⠀⡞⢀⠔⠁⠀⠀⠀⠀⠀⠈⠱⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣾⠃⠀⠀⠀⠀⢸⠇⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⣿⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⠻⠂⠀⠀⠸⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⢹⣇⠀⠀⠀⠀⢸⡇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢀⡿⠻⣷⠞⢧⠀⠈⠁⠀⠈⠢⢀⠀⠀⠀⣀⠴⠊⠀⠑⢄⡀⠀⠀⠀⠀⢀⡠⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠘⣷⠀⠉⠀⠈⠛⠳⠶⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⣀⣴⠞⠋⠀⠀⠉⠛⠳⠶⣤⣤⣤⣄⣀⣀⣀⣤⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡴⠶⠺⢿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠈⠳⣤⡀⢀⣼⠋⠉⠀⠹⣷⢦⣀⡴⠋⠀⠉⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠙⣇⠀⠀⠀⠀⣤⠀⠈⠙⠛⣧⠀⠀⠀⢀⡿⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠰⢿⣤⣤⡴⠿⠶⠶⠶⢾⡏⠀⠀⠀⠀⠈⢷⡄⢰⣟⠀⠀⠀⠀⠀⢻⠶⠶⠀⣀⡞⠀⠈⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣰⠟⠀⠀⠹⣆⠀⠀⠀⠀⢻⡇⠀⠀⠉⠛⠛⠶⢶⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠸⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣴⠏⠀⠀⠀⠘⣧⠀⠀⢀⣀⣤⣤⣤⣾⠛⠉⠙⠷⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣤⡞⠁⠀⠀⠀⠀⠀⣿⣤⡶⢟⣩⡶⠟⣿⡁⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣀⣀⣀⠀⠀⠀⢀⣉⡀⠀⠀⠀⠀⠀⠀⢹⣋⡴⠟⠁⠀⠀⠘⠻⠶⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣉⣉⣉⣛⣛⣏⣥⣽⣿⣟⣛⣛⠛⠉⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢨⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡁⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠤⡄⠀⠀⠀⠠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠃⠈⠀⠀⠍⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢰⣶⣀⣠⣤⣤⣠⣿⡆⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠘⢄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢈⣉⣹⠟⢿⠛⣧⣠⣄⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠳⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠘⠿⠉⠛⠿⠟⠃⠛⠁⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠈⢦⠀⠑⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠔⢄⠜⠆⠀⠀⡤⠐⠊⠁⠀⠀⠀⢀⣀⡀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⡀⠀⠀⠀⠈⠉⠹⡆⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⢳⠁⠀⢰⠈⢇⠀⠀⠀⠐⠺⡿⠖⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠤⢀⡤⠀⠀⠙⠟⠂⠀⠀⢀⡴⠃⠀⠐⠪⣚⠀⢠⠂⢀
⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⢹⠇⠀⠑⠢⢤⣀⠀⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⢀⣁⡠⠔⠊⠁⠀⠀⠀⢰⡀⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠣⡀⠀⠀⠀⠀⠀⠉⠙⡔⠀⠀⠀⠀⣀⣀⣤⣄⣠⠖⣊⣡⡴⢶⠆⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡔⡟⣦⠔
⠀⠀⠀⠀⠀⠀⡔⠁⠀⡇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⣿⣿⣿⣿⣿⠟⠋⠙⠋⠀⡸⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢠⠎⢜⠑⡇
⠀⠀⠀⠀⠀⠀⠢⠀⠴⠹⣆⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⡤⠘⠿⠿⠿⠟⠋⠀⠀⠁⠂⠈⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠱⡄⠀⠀⠀⠀⠀⠈⠄⠀⠀⢀⡄⠀⡀⠈⠁⣠⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡰⠃⠀⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠀⠀⠈⣑⠤⣀⣀⠀⣀⣀⡄⠀⡏⠁⠡⠀⠀⠀⠐⠀⠀⢦⢀⣀⣀⣀⣀⠠⢶⠁⠀⠀⠐⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠑⡠⠔⠀⠀⠘⠋⠁⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⠈⠋⠀⠀⠀⠄⡀⠐⠁⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠀⠀⠀⢂⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠁⠀⡀⠴⠁⠀⠀⠀⡀⣠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠵⢀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡤⠒⠀⠀⠈⠙⠲⢄⠀⠀⠀⠀⠈⢠⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠄⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠄⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⠶⢶⢶⣶⡶⡶⢶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣀⣠⣴⣶⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠠⠶⠚⠛⠛⢻⡿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠋⢻⡇⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣤⣶⣾⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣏⠀⣹⣿⠟⠙⠛⠻⠿⢿⣿⢻⡿⠿⠛⣿⠋⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣼⠇⠘⢷⡀⠀⠈⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⣀⠀⠀⠀⠀⢀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⢹⡏⠁⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠉⠙⠓⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⣯⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣀⣀⣿⣤⣤⣤⣤⣤⣤⣤⣼⣧⡤⠤⠤⠶⢶⣶⠶⠿⠗⠒⠚⠛⠛⢻⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⢠⠀⠀⢸⡇⠈⠻⣄⠀⠀⠀⢀⣀⣠⣤⣿⡶⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⢶⣴⣿⣄⣀⡀
⠀⠀⠀⠀⢸⡆⠀⠘⣷⣄⣀⣹⡷⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠈⢳⣄⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠒⠒⠒⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡐⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⢳⠈⠳⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣘⡳⠛⠸⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣠⠀⠀⡰⠀⢀⠏⠀⢀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⣹⠂⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣄⠔⠁⢀⠜⠁⣠⠎⠀⣠⠋⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⡠⠖⠙⣤⠔⠁⢠⠞⠁⠠⠞⠁⠀⠀⠸⡄⢀⣠⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠉⡇⠀⠀⠈⠳⢤⣀⡀⣠⣀⡀⠀⣀⣠⠤⠻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢸⠀⠠⠤⠤⣄⣀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠛⠂⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡾⠀⠀⡴⠃⠀⠀⠿⠯⠍⢡⠤⠂⠀⠀⠤⣤⣄⣀⡀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠈⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢤⠉⠙⠛⠀⠀⠀⠘⡆⠀⢸⠀⠀⢇⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢷⠀⠸⡄⠀⠀⠀⠀⠀⢰⣓⣖⣻⡉⠯⢷⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⠀⢸⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠱⠀⠘⡄⠀⠙⣄⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⠀⡇⠀⢸⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠈⠙⣆⠀⠓⠀⠈⡎⠳⢄⡀⠀⠺⠤⠿⢽⣍⣆⣺⠀⠀⠀⠀⣀⠴⠊⡅⢸⠀⢰⠇⠀⡸⠀⠸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣀⠈⡴⠊⠉⢱⡄⠀⠀⠀⠀⠈⠈⠙⢲⣦⣤⣤⠀⠀⠤⡤⠶⠶⠭⣀⡀⠠⠃⢸⠀⠘⠀⠀⠃⠀⠀⡠⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢘⣷⠚⠁⡼⠁⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⡟⠀⠀⡴⠃⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⢀⡤⣾⠀⢀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢶⡁⢈⣠⠀⠙⢦⣀⠀⣠⠔⠋⠀⢀⠜⠀⠀⠙⠒⠋⠀⠀⠀⠀⢠⠀⠀⠀⠙⣄⠀⠀⠀⠀⡏⢀⠈⡇⠉⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠳⣄⡼⠉⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠓⢦⠤⠶⠛⣌⠛⡅⠀⠚⠂⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⣀⣤⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⠀⠀⠀⠯⠀⢀⣀⣼⣄⠱⣤⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠛⠛⠉⠉⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣴⠞⠳⣦⠀⣀⣤⣄
⠀⠀⠀⠀⠀⣰⡟⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡿⠋⠀⣾⣤⠶⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠼⢋⣠⠞⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣠⡶⠋⢹⠙⠒⢒⣤⣤⡤⠤⠤⠤⠤⠖⠒⢒⠾⠯⢭⣀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢠⡾⠋⠀⠀⡘⢀⡾⢅⡀⠀⠙⢆⠀⠀⠀⠀⡼⠣⣄⠀⠀⠈⢣⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⢦
⠀⠀⣴⠏⠀⠀⠀⠀⡇⢸⡀⠀⢹⡄⠀⣸⠀⠀⠀⠀⣇⠀⠈⣇⠀⠀⢸⠀⠈⠧⠶⠰⢤⠀⠀⠀⠀⠀⠀⠀⢈
⢀⡾⠃⠀⠀⠀⠀⢸⠁⠀⠳⢤⣰⣧⠴⠃⠀⠀⠀⠀⠈⠢⣄⣼⣠⠴⠃⠀⠀⠀⠠⠀⡴⠃⠀⠀⠀⠀⠲⢤⣾
⣼⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢿⡀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠙⠛⠚⠛⠛⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠋⠛⠙⢱⣶⠋⢹⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠶⠶⠤⢤⡞⠀⠈⢷⡀⠀⠀⠀⠀⣿⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣶⢶⠆⠀⠀⠀⣼⠀⠀⠀⠀⢰⡇⠀⠀⠈⠛⢦⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠏⠀⠀⣠⠞⡇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢦⣀⠴⠁⠠⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠛⠉⠙⠛⠛⢻⡄⠀⠀⣰⢇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣄⣀⣀⣀⣤⠀⠀⠀⠘⠃⠀⣰⣿⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠖⠒⣻⠟⠛⠉⠉⠉⠉⢹⡄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢻⡄⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣩⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⡿⣿⣿⣿⡿⠟⠛⠉⢛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⡀⠀⠀⠘⠋⠀⠀⠀⢀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣄⠀⡈⠀⢀⣧⣯⡍⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⡟⡧⠀⠺⠟⠻⣶⢳⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡎⠙⣿⣸⠇⡀⠀⠀⢀⣼⢃⠀⠈⢑⡄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⢿⣀⠀⠹⣿⣦⣿⣿⣾⣿⣏⣼⣶⣶⠟⠁
⠀⠀⣮⠠⠀⠀⠀⠀⠀⠀⠙⠿⢆⣙⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠠⡘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⣀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⠈
⠀⠉⠀⠈⢁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡁⠀⠀⠀⡀
⠀⠀⠁⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠻⣿⡟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣽⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠐⠂⠈⠉⠀⠀⠀⠈⠉⠐⠂⢴⣿⣿⣿⣿⣶⣦⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⠤⠴⠒⠀⠈⢁⡈⠀⠐⠒⠸⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠐⠂⠒⠠⠄⣀⠀⠉⠐⠢⢄⡀⠀⠈⠉⠛⢿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠑⠢⢄⠀⠀⠈⠑⠤⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠊⢯⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⣀⠉⠢⢄⠀⠀⠈⠑⠠⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⠀⠈⢧⡀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢌⡒⠤⣀⠀⠈⠑⢄⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡰⠀⠀⠀⠙⣦⡀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠫⠶⠤⣄⣁⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡰⠁⠀⠀⠀⡜⠀⠙⠲⣤⣀⠀⠀⠀⠈⠐⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣊⠁⣠⡁⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠀⠀⠀⢀⠜⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠁⠂⠅⣒⠀⠠⠄⣀⣀⠀⠈⠉⠐⣒⡒⠲⠖⠒⠊⢉⠠⠴⠞⠑⠈⣀⠎⠀⠙⠿⣿⠿⠿
⣿⣿⠟⠁⠀⠀⡠⠐⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠀⠤⠤⠤⠤⠤⠄⠒⠲⢌⣉⠁⠐⠒⠀⠈⠈⢈⠸
⣿⣥⣤⡄⠒⠉⣀⡀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⢫⠉⡄⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⡏⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣶⣤⣤⣴⣾⣿⣿
⣿⣿⡟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣒⣀⣀⣒⣁⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠰⣿⣇⣡⡄⢠⣼⡂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⡀
⠀⣾⣿⡈⢻⣧⣿⣯⡁⢠⣤⢀⠤⡦⠠⣜⣇⣠⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⢺⡿⣧⡀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⣿⣿⣧⠀⣿⣿⡹⣧⣿⣿⣿⣤⣿⣶⣿⣯⠉⢻⣿⣤⣳⡿⡀⢸⣧⣠⡶⠀⠀⠈⣠⡀⡼⢡⣿⣿⣷⡄⠀⠀⠁
⠀⠹⣿⣿⣃⠉⢹⣿⣿⢛⡿⠋⠀⡟⠛⣿⣷⡿⠄⣽⢟⢻⠀⢐⣿⣿⠗⢒⡀⠀⠀⢻⣿⡇⢸⣿⣿⣿⣿⣆⠀⠀⠀⠒⡆
⠀⣼⣿⣿⡟⢀⢠⣿⠂⣠⣏⠠⢀⠓⠠⠿⠉⠀⠀⠘⠀⠚⠛⠙⣮⡿⠀⣿⡀⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣏⠀⠀⠀⢤⡇
⠀⣿⣿⣿⣿⣾⣿⣄⠀⠈⣿⣿⣶⣿⣶⡄⠀⠀⠸⢢⣤⣴⡞⠶⢾⡿⠆⣹⡋⣀⠀⠀⠀⠈⠋⣿⣿⣿⣿⣿⡆⠀⠀⠀⡇
⢀⣿⣿⣿⣿⣿⣏⠸⠿⠿⠋⣿⣿⡯⣽⣧⠀⠷⢀⣴⡯⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣴⣳⣿⣿⣿⣿⢻⣷⣠⣶⣞⠇
⠸⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⣿⣷⣮⣁⠀⠂⣸⣿⣀⡀⠀⠀⠂⠄⠀⠀⠀⢐⣄⡄⢀⣏⣿⣿⣿⣿⠇⢀⣴⣭⣧⡄⡦
⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢐⣤⣽⣏⢥⣾⡆⠠⠉⠀⠀⠀⠀⢌⢲⣾⣼⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢄⣩⡿⠑⠀⠀⠀⡢⠀⢢⣸⣧⣹⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣾⣷⣖⢎⠀⠀⠀⠀⡐⠷⢤⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⣛⠏⠀⠒⠠⠶⠿⠿⢿⣿⠟⠛⠻⠶⠶⠦⢤⣼⣿⣿⣿⡟⠒⠛⠛⠋⠃
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠋⠉⠉⠉⠉⠉⠀⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⢀⣀⣀⡀
⠀⠀⠀⣠⠤⠶⠶⠚⠉⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠛⢦⡀
⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟
⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⡴⠦⣤⣀⣀⣀⣀⣀⡼⠖⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡓⣶⡄⠈⠉⠉⠁⠀⠀⢀⣰⣤⣤⣤⣀⣠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢛⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢀⣿⣿⣿⡿⠟⠛⠙⠻⣿⣿⣿⡿⠃⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠀⢀⣀⠀⠀⠈⠉⠁⠀⣀⣀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣻⣿⣷⣦⡀⢀⣴⣿⣿⣿⡂⠀⢸⣧⠀⠀⡒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡸⠿⡇⠀⠘⢠⢊⣝⡟⠁⠀⠛⠻⣭⡆⢹⠀⠈⡼⢿⠁⢤⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣁⠸⠲⠱⡀⠀⠈⠮⠾⠭⠄⠀⣀⠘⠦⡠⠄⠋⠀⠀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⡤⠟⠀⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠠⠤⠤⠤⠤⠔⠒⠚⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣡⢖⣫⣷⣿⣿⣿⣷⣶⣶⣶⣶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣣⣾⣵⣿⣿⣿⣿⣿⣿⣿⠿⠶⠶⠮⢭⣳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⣵⣷⣿⣿⢿⣿⣿⣿⣿⣿⠿⣚⣿⣿⣿⣶⣤⡀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣾⣸⣿⣿⢏⣴⣿⣾⣿⣿⢫⣴⣿⣿⣿⡿⠿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣷⡿⠟⡛⠛⠿⠿⣿⣿⣿⣿⣭⣉⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣏⣴⣶⢿⣿⣿⣿⢻⣿⣿⣿⢷⣍⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⣷⡿⣿⢿⣿⣿⣷⢿⣿⣿⣿⢿⣿⣿⣷⣌⠳
⠀⠀⠀⠀⠀⠀⠀⢘⣼⡯⠖⠒⠛⢿⣿⣿⢿⣿⣿⣿⡯⠑⣾⣿⣯⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠘⣿⣿⣿⣿⢿⣿⣦⣽⣿⣿⢷⡻⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠸⣧⣿⣽⣿⣿⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⣶⣧⣿⣿⣿⢹⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢿⢿⣫⣾⣿⡟⣿⣿⢿⣿⠙⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣩⣿⣿⣿⣿⣿⠇⢸⠏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠋⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⣠⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣷⣆⣰⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣠⣶⣿⣷⣦⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⣴⣾⣿⣿⣷⣶⣤⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⡄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣄⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣯⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣻⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣌⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡾⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢂⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠃⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠈⢳⡦⣄⠀⠀⠑⢤⡀⠺⠛⠀⢠⠈⠲⣤⠄⠳⣀⢠⣉⠢⡄⠀⣄
⠀⠀⠀⠀⠁⠐⠐⢿⣄⡙⠒⠖⡲⠟⢻⣿⠉⡷⢶⣤⠈⠳⢄⣍⡓⣮⡓⢝⠓⢦⡙⠂
⣤⣀⠀⠀⠀⠀⠀⡀⢳⡌⠁⠀⠀⠙⠺⣟⣟⣾⣮⣍⣳⣦⣄⣿⣷⣦⣝⣦⠽⠋⡹⢦⣮⠀⣀
⠛⠛⠿⠣⣠⣅⡐⠀⠈⠳⣄⣀⡉⠙⢳⣄⠉⠹⠾⡻⣮⣿⠽⠿⣿⣛⡿⣦⡾⢟⡻⣿⡧⣴⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠉⠙⠻⣷⣦⣤⣤⠽⣟⠲⢾⣿⡒⣤⡬⠺⠋⢺⡏⠉⠻⢿⠁⢀⡉⠁⣿⠈⢍⡈⠙⠙⣿⡆
⠀⢄⠀⠀⠀⠀⠀⠀⢀⠭⠏⢉⣛⣿⣷⣦⣽⡿⢋⠀⢰⡄⢸⡇⢸⡆⢸⠀⣨⡿⣤⣿⠀⠸⠟⢳⣬⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⢀⣬⡿⠿⣅⣈⣻⢰⣟⠀⢨⡄⢻⡅⢨⡄⠈⠀⢠⣅⠀⢿⠀⢰⣿⣼⡿⣿⣿⣿⣿⡁
⢶⣤⣄⠀⣀⠀⠀⣀⣠⠖⠋⠁⣀⣀⠤⣌⣹⣓⡾⡆⠘⣿⠀⣷⠘⣿⠀⠃⠈⠟⢀⣼⠃⠈⠛⠛⠁⢻⣿⣿⣿⣛⠃⣀
⠀⠀⠙⠳⢿⡿⠛⠋⠐⣀⣀⠤⠤⠛⠋⠝⠛⠿⢿⠇⢀⣿⣷⣬⣴⣽⣷⣷⣴⣶⣶⣿⣿⣶⣶⣽⣷⣬⣿⣿⣿⡿⠻⢿⡳⠄
⠁⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠤⣿⡿⠟⠉⣁⣿⣿⠛⠉⢉⣛⣿⣿⣿⣿⣟⠉⠉⠻⢿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⣇⠀⠀⠀⠙⣿⣧⡀⠈⠉⢿⣿⡏⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠙⠟⠃⠀⠀⠸⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣢⠀⠀⠀⠀⠀⠘⠺⠇⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣀⣀⡀⠀⠀⢀⠤⠀⠒⠀⠤⡐⣮⠙⠛⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠑⢴⠃⠀⠀⠀⠀⠀⠘⢾⡇⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣿⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢃⠀⠀⠀⠈⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠇⣿⡀⣴⣤⣿⣦
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠢⣀⠀⠀⠀⠀⣠⠞⠈⠓⠒⠄⠐⠊⢅⣰⣽⡷⢟⡽⡏⣿
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡇⠀⠀⠀⠉⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢂⡄⣴⡽⣽⠏
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢹⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣽⡻⣫⡾⠋
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠄⢀⢀⣄⠖⣫⣴⠟⠋
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡀⠘⢧⡀⠀⠀⠀⡀⠸⡯⠀⠀⠀⢀⣀⣀⣤⣵⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠈⢧⡀⠀⠉⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⣛⡉⠑⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣢⢍⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⢶⡄⠀⠀⣀⣠⣤⠾⡃⠀⠀⠀⣀⣀⣀⣀⣀⣒⣺⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣠⡿⠿⠿⠿⠷⠞⠛⣷⠀⢠⡾⠉⠉⠉⠉⠉⠉⠛⠛⠻⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠈⠉⠉⠁⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠠⠄⠀⠀⠀⠄⢀⡀⡀⠀⠀⠤⢀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⣀⣀⡀⠀⠀⠠⠄⠀⠈⣂⠀⠀⠀⠀⠑⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠉⠁⠀⠤⠀⡀⠁⠒⠀⠄⡀⠀⠁⠂⠄⡀⢁⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠁⠢⢀⠀⠀⠙⠢⢀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⢫⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡈⠂⢄⠀⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠆⠀⠳⡀⠀⠁⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠐⠠⣀⠀⠑⠌
⠀⠀⠀⠀⠠⠁⠀⠀⠀⡈⠀⠀⠀⡘⠲⣄⡀⠀⠈⠐⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠒⠔⡀
⠀⠀⠀⠀⠃⠀⠀⢀⠌⠀⠀⢀⠔⠀⠀⠀⠙⠢⠀⠠⠀⠀⠀⠀⠁⠂⠀⠀⠤⠀⢀⠤⠤⠀⢒⣫⠖⠆⠚⡀⠐⢄
⠀⢀⠔⠁⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠌⠡⠄⠀⠀⠨⠀⠠⠔⡂⠛⠀⠀⠐⠂⠈⡰
⠐⠁⣤⡐⣈⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡉⢃⠀⠀⠀⠀⢀⠔
⠀⠀⠠⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡁⠐⠂⠈
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡉⠀⠀⠀⠀⠀⠀⠠⢝⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠩⠐⠊⠁⠁⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⠃⠀⠀⠀⠀⠀⠀⠀⡐⠦⡙⢎⠣⡀
⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⠎⠤⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⠱⡙⡄⢣⠱⡄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⣠⡀⢠⠏⠌⠁⠀⠀⠀⠀⠀⠀⢀⠐⠁⠐⡄⢢⠡⠘⡀⡆⢧
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠳⣌⠋⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠁⠀⠱⠰⠀⡆⠃⢁⢰⢸
⠀⠀⠀⡆⡡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣳⠃⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢌⢂⠱⠀⢠⠘⡀⠃⡆⢡⢰⠈⢸⢨
⠀⠀⠀⡇⠔⡡⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠱⡢⣄⠀⠄⡐⠘⠈⡌⠀⠈⡴⠀⡇⠀⠁⢸⢸⠀⠼⡀
⠀⠀⠀⠀⠐⡡⢂⠀⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡆⠀⠑⠈⠀⣹⡆⢀⠀⠃⡀⢀⠁⡇⠀⠇⠀⠀⢸⠘⢠⢀⠃
⠀⠀⠀⠰⠐⡱⢁⠔⡀⠈⠀⠊⡔⢁⠔⣠⢂⠔⡠⢀⠆⡄⠀⠀⢞⡟⠁⠀⠐⢣⡾⠋⠀⠀⠀⣄⠣⣽⠀⠟⠀⠆⡄⡆⡈⠀⡈⡌
⠀⠀⠀⠀⠡⠀⢁⠎⢠⠂⡠⠀⡀⠀⠀⠀⢀⠄⢀⠀⡀⢠⢀⢂⠌⣱⡄⠀⠀⠀⢱⣄⠱⡱⠰⠘⢠⠇⡘⡏⠰⢠⢀⠁⠁⡄⠷
⠀⠀⠀⠀⠀⢣⠀⠔⢁⠎⠠⠊⡠⠊⡰⢣⠊⠔⢁⠌⡐⡡⢣⠊⡴⣿⢃⡄⠀⣰⡟⠁⡰⢡⢃⢆⣾⢀⠿⢀⠃⡆⠘⠰⡰⢠⠃
⠀⠀⠀⠀⠀⠀⠡⡀⠈⠰⢁⠜⢀⠌⡐⢁⠊⠠⢃⠌⡐⠠⣡⢞⠞⠁⠈⠁⣴⡟⠀⡴⢡⢊⠎⣼⢃⠎⠇⡜⢠⢠⢃⢃⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠎⢠⠊⡜⠠⠃⡐⢡⠂⠌⠠⢁⠻⣏⠲⠀⠶⠀⢻⡄⠊⣠⢃⠎⡐⡌⡘⡜⢰⢁⠇⡆⡜⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠁⡌⠰⠁⡔⠠⢁⠎⠠⢡⠃⣮⡿⠀⠀⠀⠠⡟⠁⡔⢁⠎⡰⡱⡑⢰⢀⠇⡜⡰⡰⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡔⠠⢁⠊⢠⢃⠂⡄⡈⠑⣦⡀⠙⠀⠉⣢⡀⠃⠴⠵⠳⢡⠇⠞⡴⣰⢣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢁⠃⡌⠀⠂⡌⠠⢠⢁⠮⡻⠡⠰⠀⣼⠟⢁⠞⡴⠱⢃⠏⠞⠰⠑⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠑⠤⡈⢰⢠⠁⠃⢸⣾⠁⠀⠀⠀⢹⠰⢃⠞⡰⢁⠏⡜⢸⡡⠋⠔⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣐⠰⢀⢿⡆⣠⡀⠀⠀⢇⠉⡴⡡⠊⢎⠔⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠼⠇⠀⠀⠀⠀⠘⣌⣐⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⢜⠆⠀⣬⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢀⣀⠀⠰⡦⠈
⠀⠀⠀⠀⢀⠄⡠⠀⡠⢀⠄⡠⢀⠄⢀⠄⡀⣀⠀⡀⠀⡠⢀⠀⡀⠈⡉⠀⠀⡀⢀⠀⢠⠀⡀⢀⠀⡀⢀⢀⠀⢀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠉⠐⠉⠒⠑⠊⠐⠁⠒⠁⠊⠐⠡⠊⠴⠋⠔⠡⠊⠠⠊⠔⠠⠊⠔⠡⠊⠠⠊⠔⠁⠊⠐⠑⠃⠂⠁⠊⠐⠁⠊⠐⠁⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⣿⡿⠋⠀⠀⠉⠛⠋⠁⠀⡀⠀⠀⠙⠛⠋⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠋⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠈⠛⠉⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠆⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠃⠀⡀⣀⠀⠀⠘⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⣀⠔⠒⠒⠀⠠⠀⠤⠄⠀⠔⠁⠀⠈⠑⠂⠁⠀⠀⠈⠑⠠⠐⠊⠁⠀⠀⠉⠐⠠⣀⠀⠀⠀⢿⣿⣿⣿
⣿⣿⣿⣿⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠸⣿⣿⣿
⣿⣿⠋⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⣆⠙⣿
⣿⡟⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈
⡇⠀⡇
⣿⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣑⣂⢀⣒⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠿⠟⠑⠿⢻⣟⣿⠿⠿⠻⣿⣿⣷⢹⠻⠗⣏⣻⣦⣍⠂⣆⣹⢽⣯⣯⣽⣷⣾⣿⠂⣿⣺⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣿⣿⣾⣿⣷⣯⠻⠿⠿⡃⣂⠙⣁⢙⠿⢷⣻⢰⣿⢿⡍⢾⣿⣿
⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣏⣽⣵⣷⣿⣷⣧⣋⠛⣽⣧⣛⣥⡘⠻⢆⣿⣿⣷⣬⢻⡟
⠃⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢹⡹⣿⣽⣿⣿⢿⡄⢙⠤⣽⣿⣽⣷⣄⡂⠼⣿⣺⣆⠸
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣼⢻⣿⣯⣿⠿⢞⣧⣿⣿⣾⣿⣿⣷⡄⡑⢶⣌⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣾⣿⣿⢛⣷⣾⣯⢻⠿⣿⣿⣿⣿⡁⢿⣿⣯⣻⡏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⣿⣟⣿⣣⣾⣿⣯⣟⡺⢿⣷⣿⣿⣿⣿⢸⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣏⣿⠀⢠⣾⣿⢍⣹⣿⣿⣿⣯⡛⣿⣷⣿⣽⡏⣿⣿⣾⣿⣟⢿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⢟⢸⣯⣿⣴⣽⣝⡿⣶⠉⣿⣿⢹⣿⡏⢹⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠟⠂⠀⠀⠈⢉⣿⣴⣿⣿⣿⣿⣿⣿⣿⠂⣾⣉⡷⠿⡅⣼⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⣿⣿⣿⣿⣼⣯⣿⠷⣟⠿⣧⠘⠁⢼⣷⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠟⢿⡁⣷⣿⣂⠐⣣⡿⣿⡷⣰⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣻⣶⣿⣾⣧⡍⣿⠃⣴⣿⣷⢌⡹⣿⣿⣧⣙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣣⣾⣿⣿⣛⣦⣹⣷⢻⢸⣿⣿⡟⢼⣷⢼⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢟⣩⣿⣿⣿⣁⠉⣬⣼⣿⢑⡿⣿⠘⠉⣿⣽⣽⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣟⣿⣼⡿⢿⠟⡀⡉⠀⡶⢛⣯⣴⢸⣿⣛⡷⠸⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠂⣸⠾⠷⠛⠋⠁⢹⠘⠇⠀⠅⠨⣤⠠⡎⣿⣻⠈⣛⣉⡇⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢟⡓⠀⡴⣾⢿⢋⣤⣤⣤⣽⠹⠇⠐⣒⢠⢄⡀⢻⣿⡇⢿⢟⣽⢢⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠛⣽⡤⠾⡟⣶⢿⣿⣿⣿⣬⠿⣷⡈⠋⣿⣫⣿⣿⣸⡷⠀⢰⣾⣿⢨⣭⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡅⣌⠳⡜⠺⢟⣝⡛⣿⣿⣏⣶⣻⣵⢳⣿⢽⠟⣿⣯⢰⡇⣼⣷⡷⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣣⣹⣦⠘⠙⣿⣿⣿⣏⠙⠣⣿⣿⡹⣅⣿⣿⠗⠘⢱⡿⠁⣧⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠆⠈⢉⣥⣾⡧⣔⢿⣿⣗⡈⡅⣶⣶⣧⡌⣴⣤⣿⣽⡏⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣠⣤⣤⣜⠶⣿⢫⡟⢋⣵⣦⣿⣿⣿⢋⡆⣿⣿⣿⢧⢻⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⡌⣡⡄⠐⠨⠰⢾⣿⣟⢷⣻⣽⣿⡏⣳⠘⢟⣭⡦⣾⡷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣶⣼⣷⣀⡙⠿⠟⠿⣳⡧⠗⠛⣃⠙⠠⠹⣿⡃⣻⣽⣿
⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣞⠿⡿⠿⣿⡻⠟⠇⠄⠈⣉⠀⣙⢘⣭⣋⡄⢰⣷⣹⣧⣾⣾⣿
⣯⣿⣿⣇⣿⣷⣦⣀⠀⠀⣀⣄⣶⣿⣮⣭⡽⢶⣦⢦⣀⡀⠄⠒⢻⣿⣷⣦⣿⣿⣿⢯⣾⢷⣾⣿⣿⡷⢿⣿⣿
⢉⢩⡉⠁⣩⢥⣿⣿⣿⣿⡿⣛⣿⣿⣿⠿⠟⣋⣵⣮⣿⣿⣿⣟⣶⣸⣽⢻⣿⣿⣍⣿⣿⡄⢹⢿⠟⡗⣸⣿⣿
⠰⢱⠃⣶⡿⣸⣻⣿⣿⣿⠻⠿⣛⣭⣶⢾⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣯⣹⣿⣿⣽⣷⣿⡷⣹⣿⣦⢉⣿⣿⣿
⢢⣾⢴⡦⠀⢿⠛⠛⠙⢑⢪⣿⣿⣽⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣮⡹⣋⡇⣿⣿⣿
⣶⣒⣸⣷⡘⣯⡇⣿⣽⣿⣿⣿⣿⣷⢺⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡻⣿⠿⡿⣿⡿⢿⣿⣿⡿⣷⣾⡟⣳⢿⣻
⣿⣶⣶⣿⣷⢿⣿⢸⣿⣿⣿⣿⣿⣿⣇⣛⠻⣿⣿⣿⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⠷⡞⠿⢶⣿⣿⠭⣷⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠿⠿⣿⣦⠀⢀⠴⠛⠉⠉⠉⠁⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠹⡤⠴⠒⠋⠱⣄
⠀⠀⠀⠀⠀⠀⢸⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⡿⠟⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⠟⠃⠈⠛⠿⣿⣿⣿⣷⣶⣤⡷⣄⠀⠀⠀⠀⠙⠲⣤
⠀⠀⠀⠀⠀⡤⠖⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠛⠛⠉⠁⠀⢠⣿⣿⡿⠋⢀⣾⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠗⢤⡉⠓⠒⠒⠒⠋
⠀⠀⠀⠀⡞⠀⠀⣿⣿⣯⠉⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠠⠿⠛⠁⠀⠀⠸⠛⠋⠉⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠹⡄
⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢈⣩⣭⣿⣿⣷⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⣶⣿⣿⣭⣍⣉⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⡇
⠀⠀⠀⠈⣇⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠉⠻⠾⠏⠀⠈⠃⠀⠀⠀⣸⠃⠀⠀⠀⠘⠉⠀⠙⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⢠⠇
⠀⠀⠀⠀⠈⠢⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠦⠤⣤⣤⣤⣤⣤⣤⠤⠴⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⣀⣀⠀⠈⢧⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣾⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢱⠾⢯⢭⡭⣝⢷⠀⠀⠀⠀⠀⠀⢀⣔⣋⣙⣒⣦⠀⢸⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡇⠉⠉⠉⠉⠁⠀⡜⠀⠀⡇⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣯⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⡜⠁⠀⠀⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⡀⠄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠟⠇⠀⠀⢸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠃⠀⢃⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣿⡿⠀⠀⢀⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⡞⢰⡏⠀⠀⠀⠀⠚⠓⠤⠤⠤⠤⠖⠻⠂⠀⠀⡸⠉⠜⠀⠀⡎⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠑⠼⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡜⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢿⠀⠀⠀⠲⠾⠛⠛⠛⠛⣭⠿⠛⠒⠒⠋⠀⠀⠀⢀⠃⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠈⣆⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠉⠉⠙⡗⠛⠛⠛⠛⠛⠉⢉⡍⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⡴⠋⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⣶⣶⣶⣶⣶⣶⣾⣅⣀⣤⣤⣤⣀⡀⠀⠘⡄⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⡞⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢡⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⠤⠄⠀⠩⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠝⠁⠂⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠲⡘⠀⠦⠀⠄⠂⠉⠉⠣⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠐⠁⠂⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠀⠈⠁⠢⡀⠀⢠⠠⡀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠂⠁⠀⠀⠩⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠃⡀⠸⣀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠠⣐⠀⠀⠂⠀⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⠀⢀⠄⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠠⢄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠓⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠁⠉⠆⠀⠁⠀⠀⠀⠨⠀⡸
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠔⠁⠠⠀⠀⠀⠀⠁⠐⠁
⠀⠀⢀⠀⠐⠀⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠉⠂⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠠⠐⠈
⠀⠀⠀⠀⠀⡄⠀⠀⡘⠐⠀⠀⠀⢀⣀⠀⠀⠀⠈⢯⡀⢣⡀⠀⠀⠀⡀⠀⠐⠃⠓⠀⠀⠀⠀⠀⠀⢀⠈⡀⠐⠈⠀⠀⠄⢈⠄⠐⠈
⡆⢰⠀⠈⠆⠀⠀⢠⠀⠈⠒⠂⠈⠀⠀⠙⡄⠀⠀⡄⠙⠒⠟⢀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠀⠀⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠢
⠈⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠐⠀⠀⠀⠀⠘⠘⠀⠈⠂⠀⢀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠈⢣⠀⡇
⠀⠀⠀⠀⠀⢏⠄⠀⠄⠒⠐⠢⡀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⡉⠀⠀⠀⠐⠠⠤⡀⠀⠀⠀⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⢱⠀⡐⠀⠀⠁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠀⠁
⠀⠀⠀⠀⠀⢨⠀⠀⡰⠐⠄⢸⠀⠌⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⢀⠁⠨⡁⠀⠂⠀⢀⡀⠐
⠀⠀⠀⢀⡀⠈⠑⠊⠀⠀⠀⠀⠌⠀⠀⠂⠀⠀⠀⠀⠀⠐⢢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢌⢂⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡆⠀⠉⠀⠀⡈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⡀⠤⢄⡀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⢡⠀⡄⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⢀⠀⡆⠀⠀⠀⠀⡐⠀⠀⠀⠀⢡⠀⠀⠁⠈⡂⡠⠐
⠀⠀⠀⠀⠀⢄⠀⢀⠱⠀⠀⠸⡄⠀⡆⠀⠀⠀⠣⠄⠀⡆⡄⠀⠀⡠⠁⠀⠐⢸⠀⡀⠀⠀⠀⠀⠀⠀⡴⠀⠀⡀⠈⠀⠀⠀⠓⠂⠀⡑⠀⠆⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢙⠢⠀⠀⠀⠀⠀⣠⠀⢇⠇⠀⣐⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢐⠄⠀⢰⣀⡸⠀⠀⠀⠀⠀⠄⠈⠀⠊⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠘⠎⠀⠢⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠀⠀⠁⠠⡒⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠼⠄⠀⠀⡘⠃⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠌⠅⠀⠀⠀⠀⠀⠀⠀⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁
⣿⣿⡟⠻⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣤⣶⣶⣶⣦⣤⣀⣠⣿⣿⣿⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⢻⣿⣿⢛⣿⣿⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠹⡀⠀⣠⣴⣾⣿⣿⣿⣧⣺⣿⣮⣷⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⣀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢽⣍⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⣿⣿⣿⣿⡃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣿⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣏⠈⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣦⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢻⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⡟⠈⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣹⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⢰⣿⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠂⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠰⠋⢉⣩⡭⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⢏⠀⣠⠴⠶⠶⠶⢬⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡴⠚⠉⠉⠉⠁⠓⠶⣤⠶⢤⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠁⢀⣀⡀⠀⠀⠀⠀⠀⠙⠲⡌⢇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡏⠀⠈⠉⠀⠀⠀⠀⠤⢤⡀⠀⢻⠈⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠁⠀⠀⠛⠀⠀⠀⠀⠶⠀⠀⠀⢿⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠈⠠⣄⠀⠀⠀⢀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠒⠒⠦⠸⡄⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠯⣌⣉⣀⣀⣻⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⢧⣀⣠⠞⠉⢧⡀⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠙⢧⡀⠀⣠⠟⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⣾⣿⠷⢦⡀⢙⣾⠥⢶⡦⣄⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠳⣅⣠⠴⠛⠉⠀⠀⠀⣹⣈⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠁⠀⠀⠀⠀⢀⡴⠚⠁⠉⠁⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⣤⡤⠤⠖⠚⠳⠤⣄⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⡀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣾⣿⣿⣷⣿⣾⣦⣾⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠙⢿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠈⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⠀⠀⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠐⣿⣿⣿⣦⣀⠀⠀⠀⣠⣶⣿⣿⣿⡧⠀⠀⠈⣿⡇⠀⠀⣠⠴⠲⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡰⠛⣛⣿⣿⣿⡷⠀⠸⣿⣿⣿⢟⡋⠳⡄⠀⠠⠟⡳⣄⡠⠗⠀⠀⠀⠚
⠀⣀⣠⠴⠦⡀⠀⢀⠜⣛⠻⡀⠀⠀⡇⢾⢠⣴⣮⢏⠀⠀⠀⢻⠀⢷⣾⠇⠀⣿⠀⠀⠸⠟⣹⠊⠉⠯⣤⣴⠟
⢾⣁⠀⠀⠀⠉⣀⢽⠲⡋⡇⠀⠀⠀⠙⢬⣿⣯⣥⠎⠀⠀⠀⠈⢷⣄⣠⠤⠺⠃⠀⠀⢰⠚⠁
⠀⢧⣀⡀⠀⣹⠆⠈⠓⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣤⣤⣀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠁⠒⠒⠂⠮⠿⠟⠢⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢟⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡪⠇⠀⠀⠀⠀⠀⠀⢺⣱⡀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠓⠲⠶⣄⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠉⠒⢄⠀⠔⠂⠉⠉⠁⠒⢄⠈⢆⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢡⢸⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠀⠀⠀⠀⠺⠂⠀⠀⠀⠘⠀⠀⠐⠟⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠎⠀⠃⠀⡼⠳⡟⢹
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⡀⠤⠒⠁⠀⠙⠢⠤⠄⠀⠂⠁⠀⠀⠒⠋⠀⠀⠀⢸
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⠤⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁
⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠁⠀⠈⣻⠆⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠴⢶⡞⠛⠉
⠀⠀⠈⠙⠛⠲⠶⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢰⠋⡧⠴⢤⡀⠀⡤⠦⢤⡏⢆⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣧⡀⠀⠀⢰⡇⠀⠈⠁⠀⠀⢀⡼⠃⠀⢷⣀⠀⠀⠈⠉⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣷⠀⠀⠘⣧⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⡦⣄⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⠶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠐⣲⠞⠛⠛⠛⠛⠛⠛⠛⢿⠂⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠶⠦⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢀⡄⢀⡄⣤⡄⣠⣶⡆⢀⡀⣀⠉⠙⠓⠶⡄
⠀⠀⠀⠀⠀⢀⡴⠊⢀⣠⠰⢆⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣰⣆⡄⠈⠐⠢⣀
⠀⠀⠀⠀⠀⠈⢰⣤⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀⢈⠳⣄
⠀⠀⠀⠀⢠⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣀⡈⠙⢦⡀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠈⠙⠦⣄⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢀⣀⡀⢈⣩⣭⣆⠔⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⢣⡟⣷⢹⣿⣿⣿⡿⠿⢫⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⣿⣿⣿⡏⢋⢿⣾⣿⣿⠋⠀⠀⢈⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣿⣷⣿⣿⣿⠇⠸⣿⢁⣿⣇⡀⠀⠐⢻⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⡿⠑⡋⢀⣾⣿⣿⠟⡻⠛⣀⠀⢀⣼⣿⣿⠉⠀⠀⠀⠈⠀⠀⠿⡿⠏⠀⢿⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠃⢰⠇⠘⢻⣿⣿⢠⡀⠘⠿⢣⣿⣿⣿⣿⣧⣦⡀⠀⠀⠀⠀⠀⠀⢶⠀⠈⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⣿⡁⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣤⣶⡴⠷⢮⡀
⠀⠀⠀⠀⠀⠀⢀⡄⣿⠀⠀⣿⠹⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⢀⡄
⠀⠀⠀⠀⠀⠀⠈⢷⡷⠀⠀⡯⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣙⠛⠿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡼⠃⢀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠘⠁⡰⠊⠀⠀⠸⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⡿⠀⠀⢀⣀⣠⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣀⣼⣿⣣⣴⣾⣿⣿⣿⣟⡁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠛⠿⠟⢛⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠛⠋⠙⠛⠉⠀⠀⠈⠁⠀⠀⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄⢰⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡃⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⢻⣿⠀⠘⣿⣿⣿⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢸⣿⣿⣿⠇⣾⣿⠿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠃⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⣿⡏⠀⠋⠀⣀⣌⣹⣿⣤⡼⠀⠀⠀⢠⣼⣿⣯⠤⠤⢤⣀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⠋⣀⣄⠈⠋⠉⠁⠠⠤⠄⠀⠉⠉⠐⢦⡴⠀⢻⡇⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠁⢀⠉⡉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠴⠋⠀⠀⢀⣿⣿⠛⠲⢦⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠺⣿⣿⣇⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣀⣀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡠⠤⢌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢙⣴⣋⠉⠉⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⢀⣤⣷⣛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⢸⡇⠘⠁⠈⢳⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠈⠁⠀⠀⠘⠁⠉⠀⠀⣀⠀⠀⠀⣼⡇⠦⣀⡤⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠳⠶⠛⡇⠀⠀⠀⠀⠀⢀⣤⢤⠴⠦⢤⠤⢤⣤⣥⣀⡀⠀⠀⠀⣸⣦⣤⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⣷⡀⠀⠆⠀⢀⣿⣀⣼⡤⠶⢾⠶⠶⠷⢤⣯⡇⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣇⠀⠀⠀⠐⣇⣣⣤⠷⠶⢚⣛⣛⠛⠛⠛⠃⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢈⠁⠀⠀⠈⡕⢊⠉⠀⡀⠐⠈⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣄⠀⠀⠁⠀⣴⣷⣾⣷⡀⢀⣠⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠳⠶⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠋⠙⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡁⠀⢄⣠⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣯⣵⣶⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣽⣿⣿⢹⣿⣥⠿⣟⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⣿⣿⣿⠘⣿⠁⠀⠘⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠙⣷⣄⡀⠘⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠛⢻⠟⠋⠀⠈⠻⣿⣿⣿⠿⠛⠏⠻⠿⢿⠿⢶⣤⢶⣶⣶⣌⣻⣿⣿⣿⣿⠛⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣠⡾⠁⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠓⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⠀⠀⠀⠀⣸⠃⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣄⠀⠀⠀⡾⠀⠀⠈⢧⡀⠀⠀⣿⡤⠞⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⡗⠤⠾⠃⠀⠀⠀⠀⢻⡄⠀⠁⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣰⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⢷⡄⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢾⡋⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠈⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⡞⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠠⠟⠒⠛⠉⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠳⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣤⣤⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡄⢸⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⢃⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⣴⡿⠛⢯⡉⠻⠏⢸⡇⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢰⠃⠀⢡⡇⠀⣿⣻⣦⡤⢷⣤⣾⣟⣷⠀⠈⡧⠀⠀⢸⡇⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡟⠀⠀⠈⠓⠦⢤⡥⠟⠀⠀⠈⠷⠬⣅⣤⠞⠃⠀⠀⢸⡇⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠇⠀⠀⠀⠀⢀⡤⠶⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⠶⠾⢷⠀⠀⠀⠀⢀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠚⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⣤⡴⠖⠛⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣛⣁⣀⠉⠀⠀⠀⠀⣀⣠⣀⢻⣇⢹⣿⣿⣆⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠙⠛⠁⠀⠀⠀⠈⠙⠛⠁⠘⣿⣾⣿⣿⣿⣧⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣤⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠛⠿⠟⠋⠀⠀⣺⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⠋⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⠁⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠰⢿⡿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠶⠃⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⢿⣿
⠀⠰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠤⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⠑⢤⡀⠠⠤⣠⠿⠚⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢢⠀⠁⠰⠶⡔⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⠀⠀⠀⠀⢸⠀⠈⢙⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠘⡄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⣀⠀⢳⢾⢀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⣀⠀⢸⠖⠁⠀⢱⠸⣽⠇⣴⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠑⠆⠀⠀⢀⠆⠀⠻⠀⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⣀⠔⠛⠦⢄⠁⠀⠀⠀⠀⠢⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⠀⠀⠀⣀⣀⠀⠀⠈⠢⡀⠀⠀⡈⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢸⠀⠀⡴⠓⢄⣱⡄⠀⠀⠈⢦⠀⠁⠠⡘⣄
⠀⠀⠀⠀⠀⡠⣤⣄⠀⠀⢀⠊⠀⠀⠀⠀⠀⢸⠀⢰⠋⠢⣀⡟⢈⣄⠀⠀⠀⠻⣀⡀⢣⠐⢠⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⣸⠁⡆⠈⠑⢀⠂⠀⠀⠀⠀⠀⠀⢸⠀⡘⠒⣤⠎⢡⢸⣿⣆⠀⠀⠀⠀⠈⠺⡆⠀⡦⡴⠠⠔⠁⠀⠱⡄⢒⡉⠥⠄⠀⡄⠆
⠀⠀⠀⠀⡟⢆⠐⣄⠀⠌⠀⠀⠀⠀⠀⠀⢠⠏⣄⡟⠲⠁⢀⠖⠶⠛⠛⡆⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⢰⠈⢆
⠀⠀⠀⠀⡇⠀⣁⡜⢷⡆⠀⠀⠀⠀⠀⡠⠋⠀⠈⠀⠀⡔⠢⠤⠤⣄⣀⣸⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣀⣀⣀⡆⠀⠀⠀⠀⠀⡇⠈⠦⠂⠑⡄
⠀⠀⠀⠀⡨⠄⠸⡆⠀⣧⢝⠒⠰⠖⠋⠀⣀⠄⠀⠠⠛⠓⠢⠦⠤⡧⠬⠜⠀⠀⠀⠀⢀⠃⠀⡇⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢳⡄⠤⢇⣀⣼⣤⠃⠀⠀⠀⠀⠀⠐⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢣⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠢⢀⣠⡀⠀⠀⠀⢀⠰
⠀⠀⠀⠀⠘⢄⢀⡔⠉⣩⡭⣵⢠⡊⠉⠗⢄⠀⠀⠀⠀⢑⡤⣀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠐⠂⢼⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⡰⠤⠂
⠀⠀⠀⠀⠀⠀⠸⣄⠐⡇⠐⢤⡏⠘⡀⠀⠡⢣⠀⡿⢿⠉⠁⣈⣩⠴⠦⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⢦⣀⢇⣆⣦⣾⣧⠀⠈⢀⢴⡄⠀⡒⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣼⣷⣶⠟⣛⠥⠚⠣⡀⠃⡠⠶⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡠⠿⣫⣰⠀⠀⠀⢨⠞⠉⠉⠁⢀⠶⡒⠶⠶⠶⠤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⣠⠤⠒⠉⠀⠀⠀⡰⢡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⢀⣀⠼⠛⠛⠉⠙⠛⠻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀⠀⢀⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⠒⠐⢿⡓⢛⣲⣤⣀⣀⣀⣀⡀⠀⠀⠀⣀⣈⣑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠈⠹⠦⠉⠉⠋⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⡾⢮⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣮⣿⡅⣮⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⢿⣟⣼⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣫⣵⣾⣿⣿⣿⡏⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣟⣾⣿⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣮⣻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡸⣿⣿⣿⣿⣿⣷⣶⡶⣶⣷⣶⣶⣶⣾⣿⣿⣿⣯⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣎⣽⣭⣷⣭⣭⣽⣶⣮⣭⣭⣵⣮⣭⣥⣭⣻⢛⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⣝⡻⠿⠿⣿⠿⠿⣟⣵⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠖⣩⣯⣿⣿⣿⣯⣿⣿⣿⣿⣾⣝⡻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢣⣾⣿⣟⣭⣿⣿⣯⡯⣽⣿⣽⣿⢿⣿⡜⣿⣿⡿⣙⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡻⣿⣿⣮⡻⣿⣿⠿⡧⢿⢿⢟⣵⣿⡿⣣⣿⠟⢱⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣝⢛⣣⣷⣿⣣⣏⣽⣿⣯⣛⢡⣾⣿⢱⢯⣶⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡟⣿⣸⣿⠿⠟⠇⠿⠿⣿⣹⣼⣿⡿⣸⢸⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣁⣚⣯⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⢟⣴⣶⣶⣶⣶⣶⣶⣦⡻⡧⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠳⡶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣷⠿⠋⠀⢠⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠴⠶⠟⢛⣩⠟⠙⢦⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠺⠛⠀⠉⠉⠉⠛⠛⠛⠻⠶⠖⠲⠶⠾⠿⠛⠛⠛⠉⠀⠀⠉⠉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣄⠀⣀⣴⢶⣤⣀⣀⣀⣴⠿⣦⣀⣀⣀⣤⡶⢶⣤⣤⣤⠾⠛⠛⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠚⠃⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⢀⠀⠀⠀⠀⣀⠀⠤⠀⣀⠀⠀⠀⠙⠳⣦⣀⣀
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢣⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣼⠀⡆⠀⠀⠀⠀⢸
⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⡠⠁⠰⠁⠀⠀⠀⠀⣼
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣀⠀⣀⣀⠠⠂⠀⠀⠓⠤⠀⢀⠀⠄⠈⠀⠀⠀⠀⠀⡜⢳⣾⠿
⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠁⢠
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣟⣷⣄⠀⠀⠀⠀⠀⣀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠈⠙⠛⠶⠶⠴⠦⠶⠶⠶⠶⠾⢛⣿⠿⠛⠉⠉⠙⠻⢦⡄⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⣀⣀⡀⠀⠀⠀⢻⡄⠀⠀⠐⠶⠶⠦⣤⠴⠶⠶⢶⡶⠞⣿⠛⠉⠁
⠀⠀⠀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⢿⣤⡶⠛⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠞⠋⠀⢠⡿
⠀⠀⠀⣿⠀⠈⠙⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⢷⣤⣠⡴⠿⢿⣿⣿⡶⣤⣀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠀⣀⣀⣈⡉⠛⠿⣍⡛⠷⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢼⣏⠉⠉⢻⣤⣠⣬⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠙⠛⠶⣤⣀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣴⠞⠁
⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣦⣄⣀⣠⣤⣶⣶⣶⣾⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⠛⣋⣉⣥⣤⣴⣶⣶⣶⣶⣾⣷⣶⣶⣤⣉⠙⠟⠛⣉⣉⣀⣠⣤⣤⣤⣤⣌⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⣉⣤⣴⣾⣿⣿⣿⣿⣿⠟⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀⠀⢠⣄⢸⣿⡁⠙⢿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⡟
⢀⣤⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⣠⣾⡿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣧⡸⠟⢠⠌⠉⣾⢟⣴⣾⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⡿⠋⣠⣾⣿⡟
⣿⡟⠉⣉⣭⣭⣙⣛⠻⠿⣷⣶⣾⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣭⣛⣛⠶⠤⣴⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠛⣁⣴⣾⣿⣿⠏
⢿⣧⠀⢿⣿⣿⣿⣿⣿⣷⣦⣿⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣤⣶⣦⣭⡍⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⣿⣧⠈⢻⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣱⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣭⣽⣿⡿⠃
⠀⠸⣿⣷⣄⠙⠿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠁
⠀⠀⠹⣿⣿⣷⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⠉⠉⣠⠴⠞⠛⢉⣡⣤⣶⠾⢿⣏⡉⠉⠉⠛⠻⢿⣦⣍⢙⡿⠋
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⡾⠟⠋⠀⠀⣀⣤⣶⡿⢟⣿⣿⠿⣷⣶⣽⣿⣷⣦⣄⡀⢀⣼⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣯⡥⠖⣋⡵⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣀⣤⣴⣾⠿⠛⠋⠁⠀⠛⠋⠀⠒⠲⢾⣿⠿⠃⠉⠛⢿⣿⣟⣹⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣯⣵⡾⢛⣿⣿⣿⣿⡟⢁⣬⡙⢿⣿⣿⣿⣿⣦⣾⠀⠠⠽⢷⣄⣶⣿⣿⣿⣻⣷⡄⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣾⣿⣿⣿⡇⢾⡉⢻⡦⢹⣿⣿⣿⠋⠁⠀⠀⠈⠉⠀⠀⠉⠙⢋⣩⠟⠁⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⡿⣻⣿⣧⠸⣇⣾⠀⠈⠿⣿⣿⠀⣦⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁⢀⣴⠞⠳⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣫⠾⡟⣼⣿⣷⣝⣿⣇⠀⠘⠻⠋⠀⠘⣷⡀⠀⠀⠀⠀⢠⣤⡀⠀⠟⢿⣤⣤⠤⣤⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠉⠼⣱⣿⣿⢿⣿⡏⢹⣷⡆⠀⠀⠀⠀⠘⣷⠀⠀⣤⠀⣀⠙⢿⣶⣶⣶⣿⣿⠇⢿⣷⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⠀⠀⣰⣿⠟⣵⢏⡽⢃⣿⣿⣿⡀⠀⠀⠀⠀⠸⠃⢠⡏⢸⡟⠐⠷⣟⡛⠛⠓⠒⣶⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣴⣿⣿⡜⠿⠟⣡⣾⠟⢿⣿⣧⡀⠀⠀⠀⠀⠀⠈⣧⢸⡇⠀⠰⣬⡙⠻⠶⠿⠛⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠘⠻⢿⣿⠿⠋⠀⠀⠻⣿⣷⣄⡀⠀⠀⣄⠀⠘⠀⠁⠀⠀⠀⠉⠓⠶⣶⠾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣌⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣤⣀⡀⠀⠀⢀⣶⣠⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠙⠐⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⣤⢠⡄⠀⠀⠀⢳⠘⣿⠉⢰⣶⣄⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⡾⢿⣿⢼⡇⠀⠀⠀⠸⠀⣿⣤⣾⣿⠋⠙⣦⣁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⣿⣇⠀⢻⣦⠳⣄⣀⣀⢃⣼⣿⣿⣿⠿⣦⣾⡟⠉⣷⣄⣀⠂⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣵⠛⢿⣿⣿⣿⣿⣷⣦⣥⣤⣾⣿⣿⣿⣿⠀⠀⠈⠓⠚⠋⠘⠀⠳⢟⢖⠢⢢⡤⢍⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⡠⢖⣹⣾⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠉⠊⠙⠵⢷⡌⠧
⠀⠀⠀⠀⣠⣼⣧⣾⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣼⣆⣴⣟⡾⢋⠔⢁⠔⢀⣄⡀⠀⠀⡀⠀⠘
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣧⠞⣁⣴⣿⣿⣷⣷⡞
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣉⣠⠤⠒⠒⠀⠈⠀⠉⠉⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣭⣀⠀⠀⠀⡀⣀⣠⣤⣤⠈⢿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⢟⠛⣛⣿⡟⠁⣿⣿⠛⠉⠃⠀⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡇⠀⠀⢉⣽⡇⠀⠉⠈⠓⠀⠀⢀⣾⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣶⣿⣿⣿⣿⣤⣴⡟⢹⡆⠀⢀⣀⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣻⠁⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣉⣄⡀
⠀⠀⠀⢀⡴⢶⡀⣴⣧⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣛⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣬⣄⡀⠁
⠀⠀⠀⠀⠀⠈⠛⠋⢸⣿⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣋⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢠⡴⠾⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣯⡉⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠞⠀⣴⡿⠚⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠃⠀⠘⢷⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠰⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡝⣿⠟⢻⠋⠀⠀⠙⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⠿⡏⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡶⠃⠀⠀⠀⠀⠻⣌⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⡝⠁⠀⠀⠀⠀⠀⠀⠈⣭⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⡿⠟⠃⠾⠟⣿⣻⣿⡿⠿⢿⣿⣿⣧⢹⠻⠷⣏⣛⣦⣍⠐⢰⣨⡯⣯⣽⣏⣿⣷⣿⠗⠸⣗⣞⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣷⣾⣿⣷⣏⠻⢿⡿⠇⠘⠙⢃⠈⠻⠿⢞⡧⣾⣿⣶⡉⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡋⣯⣭⣿⣾⣶⣦⣿⠹⢳⣾⡸⢋⣄⠻⣷⢸⣷⣿⣶⡈⣿⡿
⠃⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣍⢻⢻⣿⣻⣿⣿⣿⣁⢘⢫⣝⣻⣍⣻⣦⠀⠀⣽⣏⣿⡌⢹
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣹⢿⣿⣟⣿⡿⣵⣿⣸⡇⣮⣿⣿⣿⣭⠘⢶⣌⡛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⠿⣶⣤⣿⠹⣿⣿⣿⣿⣾⡟⢸⣷⣾⣟⢮⡛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⢟⣰⣷⣿⣿⢿⣷⣿⣽⣿⣿⣿⡖⣽⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⣶⠶⡶⠀⢀⣼⣿⡳⢻⣿⣿⣻⡟⢿⣿⣬⣽⡿⣿⢻⣿⣥⣿⣿⣷⣽⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢸⣿⡿⢰⣾⡿⣋⣻⡿⣷⣘⠻⢿⣿⡿⣼⣿⠛⢿⣿⣇⣴⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣧⠀⠀⠀⠸⠏⣴⢺⣿⣿⣿⣿⣿⣷⣼⣃⢘⡿⢧⣻⣿⠁⣿⣾⣏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢿⣿⣿⢿⣿⡛⣿⢿⣧⣸⣷⣾⠀⡽⠒⢻⣿⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡟⣿⣻⣏⠙⣨⢹⣧⣦⡈⢻⣿⣷⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣉⣣⣹⣷⠿⢾⡵⠂⣰⣿⡙⢿⣧⣾⣿⡛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢀⡀⢀⣼⣿⣿⡟⢫⣶⣾⡇⣼⢿⣿⡟⣦⠙⣿⣿⣿⣦⣉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣾⣿⡿⢿⣷⣿⡎⣿⠈⡆⣿⣿⢾⣅⡿⣿⢿⣿⣿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣫⣴⢿⣽⣿⣧⡀⢾⠰⠿⢃⣽⡽⠇⣀⡰⣿⣾⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣊⡿⣿⣷⠷⣾⠿⡛⠋⢠⠠⠀⠸⠋⣥⣾⣏⢻⣿⣽⠏⠙⣛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠁⠼⢛⣚⣉⠁⠀⠸⣀⣟⡀⠀⠀⠶⠆⠾⢨⣯⣏⢨⣭⣼⡄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣻⣋⠃⢠⣞⠿⢻⣩⣤⣴⣶⣯⠘⠇⣀⣹⡁⡆⣀⡘⣻⡿⠘⠿⣧⡶⢡⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢈⠹⢷⠔⢻⠟⣾⢻⣽⣿⣾⣦⠟⣿⡆⠉⠸⣣⣼⣿⣦⣷⠆⠀⣾⡿⡇⢨⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠁⡜⢻⠟⢼⣟⣭⡙⣿⡾⣇⣾⣿⣷⡏⣿⣮⣛⢹⣷⡆⢞⢠⣷⣿⠇⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣦⣿⡆⠉⠩⣿⣿⣿⣯⡙⠣⢾⣿⡏⢇⣿⣿⠟⠀⠉⣾⠉⢸⣧⣿⣷⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡿⣿⠰⠆⠉⣋⣥⣾⡧⣔⢻⣿⡇⡀⢄⢰⣶⣾⣤⢰⣤⣼⣯⣿⡇⣿⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣙⣠⣭⣤⡝⠶⢿⢿⡽⠛⣡⣦⣼⣿⣿⡟⣡⢸⣿⣿⣿⡧⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠉⣣⡀⠐⠨⠈⣵⡿⣿⠿⣛⣿⣿⣿⠙⡄⠻⣛⣥⡄⣾⡷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣭⣝⣷⡀⠚⢷⡟⠿⢗⣭⠹⠿⠟⡀⠃⡀⢿⣿⠃⣿⣱⣾
⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣽⡲⣿⣿⣿⣿⠿⠿⡗⣈⠂⠛⠀⠉⠐⣒⡛⢃⠀⣼⣌⣿⣅⣿⣾⣿
⣞⣿⣿⡏⣿⢷⣄⡀⠀⠀⠀⢀⢠⣴⣯⣛⣛⣫⣭⡤⣄⠀⠈⡁⠤⠶⣶⣷⣬⣰⣿⣷⣽⣛⣿⣤⣿⣿⣾⣹⣿⣿⣿
⠛⢛⠛⠓⢙⣛⣹⣿⣶⣶⣾⡿⢿⣿⣿⣻⣿⠶⠛⢩⣔⣿⣷⣶⣶⢦⣙⣛⠿⣿⣿⣟⢰⣿⣧⠙⣿⣿⢿⠏⢻⣿⣿
⢠⢈⡆⣠⣻⢸⡿⣿⣿⣿⣿⣼⣿⠿⣛⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢳⣿⣿⣛⣿⣽⣿⡄⣷⣾⡘⢻⣿⣿⣿
⣄⣨⣀⣋⠉⣾⡾⣿⠿⠟⡁⢭⣶⣞⣿⢟⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⣿⢳⡾⣿⣿⣿
⣈⣉⢁⣿⠀⣼⡆⣴⡶⣴⣶⣿⣿⣿⣝⣽⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣆⣾⣦⣟⣿⣿
⣿⣒⣞⣿⣧⣿⣷⣜⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡆⣽⣿⣭⣭⣽⣭⣩⣭⣿⣹⣿⣷⠰⣎⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⢤⣀⣤⣤⠴⢦⡴⠖⠋⢝⣷⣒⣒⣂⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⢒⠉⣩⡻⢷⡦⠶⠶⠟⠃⠙⣦⠈⠁⣐⣾⡿⣸⢿⣿⣿⣛⣛⣛⠛⠓⠒
⠀⠀⠀⢀⠖⠐⠹⢳⢶⠞⠷⠺⠄⠀⡼⠁⢰⣶⠞⠀⣴⡇⠀⢠⣼⢋⡴⠳⠿⠟⠿⣿⣉⣀⣀⣤⣤⠤
⡴⠒⣿⡅⠀⠄⣲⣦⡑⢀⣀⣴⠻⣄⠀⠞⢸⡏⠀⠀⢸⡷⠄⢈⠛⠛⠁⣠⣤⣶⣶⠶⠛⠉⠁
⠙⣾⠁⠒⣛⣛⣿⣿⣷⡈⠛⠇⠀⠈⢲⣶⣿⡀⠀⠀⣾⡇⠀⢸⣧⠀⠀⠈⢿⣿⠀⠀⢀⣀⣀
⠀⢻⣶⣶⣾⣿⣿⣿⣿⣷⣄⠀⠰⠂⡏⠀⣽⠋⠀⣿⠿⠁⢰⣾⠛⣧⠀⡀⠀⠉⠛⠦⣈⢻⡆
⠀⠀⠈⢸⡇⠀⠉⠈⠉⠈⠻⣷⡀⠀⠧⢸⡇⠀⣼⡟⠀⠀⣼⠁⢀⠘⠻⢾⣦⣄⣀⠀⠙⠿⣇
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢈⢿⣦⠀⠋⢡⣾⡿⠁⡀⢰⡟⠀⠘⢧⡀⠀⠙⣯⠙⠓⠂⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣿⣧⠀⢾⠀⣀⡴⠃⢸⡇⢠⠀⠀⠹⣆⠀⠸⣧⠀⠈⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⡄⠸⣷⣿⢃⣾⣾⢻⣾⡆⠀⠀⢿⣄⠀⢻⣆⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢹⣿⣿⣿⣄⣐⣤⣷⣷⣶⣾⣿⣶⣬⣿⣶⣤⣄⣙⡛⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⠈⠁⢰⡿⠛⠛⠋⠙⠛⠋⠉⠉⠉⠀⠀⠈⠛⠿⠭⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣇⣀⢠⣼⣧⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠓⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⠚⠀⠀⠀⠀⠀⠈⠂⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢀⡤⠖⠛⠁⡄⠀⡠⠄⠀⠠⠀⠀⢀⠠⠐⠒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⡞⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠸⡇⠀⠀⠀⢐⠖⠀⠀⠀⠖⠀⠀⠆⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⢠⣿⣄⣤⠀⠘⠈⠆⠀⠀⠀⠀⢀⠐⢄⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢸⡆⠉⠈⠓⠢⠀⠀⠈⠀⠒⠀⠁⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠦⢄⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠈⠙⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠆⢀⣀⣤⠞⠁⠀⠙⢿⡶⠦⠤⢤⣤⡤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⣰⠲⣆⠉⠛⠛⠒⣶⠖⠒⠒⠒⠚⠋⠉⠀⠸⣄⣀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢻⠀⠘⠦⠤⠴⡞⢡⡆⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠻⣦⠀⢸⡇⠀⠀⣀⡴⠿⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠹⣧⡼⠃⢀⡞⠁⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⠼⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⣴⡷⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡤⣞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⡀⠀⠀⢀⣀⣠⡤⠖⢫⡞⠁⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠙⠛⠋⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣴⠏⠀⢀⣠⣤⠴⠶⠶⠚⠛⢷⣄⠀⠀⠀⠀⠀⢀⣠⡴⠛⢦⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⣁⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢤⡤⣐⣌⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠉⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠁⠀⡈⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡔⢻⡛⠦⠀⢄⠀⢀⣀⣀⠀⠤⠤⠤⠤⣿⣿⣖⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢛⡁⠃⠠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡉⠁⢅⡀⠀⠁⠀⣀⣀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⢡⠌⢛⠄⡁⠀⠂⠁⠈⠑⡀⠀⡀⠀⠀⠀⠑⠄⠀⠀⠈⢢⡀⠈⠈⠉⠀⠁⠀⢀⡈⢩⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠟⣀⠛⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢰⠀⠀⠀⠀⠢⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠈⢀⠀⠣⢈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢶⡅⢀⢀⢁⡀⠀⠀⡀⠀⠉⠀⢑⠀⠀⠀⠀⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀⡀⠙⣉⠱⠂⠀⠠⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠠⠀⣈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠠⠃⠀⠀⠀⠁⠐⣄⡀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⠠⠀⢀⡇⠀⣀⠀⠀⠠⠀⠘⣤⣀⡀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣇⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠠⢍⠉⠑⠚⠃⠀⠀⠈⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣀⠀⢀⠀⠀⠘⠣⣍⠀⠄⡈⠠⣀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠦⣈⠐⠀⡁⠢⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠈⠒⠀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠈⠉⠉⠀⠋⠉⠉⠉⠛⠉⠉⠉⠉⠛⠀⠉⠁⠸⠛⠉⠀⠉⠉⠃⠈⠉⠉⠉⠉⠁⠉⠉⠀⠋⠋⠉
⠀⠀⠀⠀⠚⠓⠛⠓⠐⠓⠒⠚⠂⠀⠀⠃⠓⠓⠚⠀⠓⠒⠚⠒⠓⠓⠀⠒⠚⠒⠒⠒⠒⠒⠒⠂⠰⠖⠒⠛⠓⠀⠒⠙⠒⠒⠓⠛
⠀⠀⠀⠀⠀⠰⠶⠦⠆⠰⠖⠦⠶⠶⠶⠶⠀⠒⠶⠤⠶⠢⠶⠦⡤⠀⠶⠦⠴⠶⠴⠆⠀⠶⠴⠶⠀⠤⠤⠤⠄⡴⠴⢦⠴⠶⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣤⡤⠠⣤⢠⣤⠀⢤⡄⢠⣤⡤⢠⡴⠀⠀⡤⠀⢠⣤⣤⡀⡤⢀⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣤⣀⣀⠀⠤⣴⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⢰⠆⣠⠾⠁⠉⠀⠈⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⢶⣄⡀⠀⠰⣦⡀⠀⠀⠀⠀⢀
⠙⠚⢿⡀⡀⠀⡀⠀⡄⠀⢀⡆⢀⣆⡀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠳⣿⣿⡿⣷⣄⢉⣿⣽⡲⠀⣀⠉⢀⣤⣤
⠀⠀⠘⠓⠙⢾⡿⢶⠿⣿⣿⣯⣭⣿⣿⣒⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⠙⢿⣟⣿⣿⣶⡟⣵⠋⢸⡇
⠀⠀⠀⠀⠀⠈⣿⡄⣿⣫⣵⣾⣿⣿⣿⣯⣥⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣤⣤⣀⣀⣤⣾⣿⣿⣏⣹⣿⡟⣠⡾⠇
⠀⠀⠀⠀⠀⠀⣿⣧⢻⣿⡿⠿⠛⣶⡿⠛⠉⠛⢪⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠀⠈⠛⠉⢉⡷⢟⣿⣭⣿⣿⡿⢿⡋
⠀⠀⠀⠀⠀⠀⠙⣿⣸⣿⣏⠀⠚⠁⠀⠀⢀⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⢀⣠⡤⠶⠶⣤⣾⣶⠽⠷⠵⣯⡹⠀⠁⠰
⠀⠀⠀⠀⠀⠀⢰⣿⢱⣿⣟⡳⣶⣶⠶⠖⠉⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠈⠉⠻⠿⠷⢶⣿⣭⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠈⡟⣾⡽⢯⢁⣿⠃⠀⠀⠀⣀⢠⡔⢿⡀⠀⠀⠀⠀⠀⠀⡰⠏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⢏⡔
⠀⠀⠀⠀⢠⡤⣼⠿⢷⣿⡯⢿⡉⠤⣤⠔⠃⣌⠑⠇⡿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⠀⠴⠀⠐⠂⠐⠆⢰⡏⣾
⠀⠀⠀⠀⢹⡇⠈⠀⠀⠻⠀⠸⠀⠀⢸⠀⠀⠈⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣰⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠋⠰
⠀⠀⢠⣾⠛⠓⠚⠒⠠⠤⣄⣀⣀⠀⠈⣄⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⠉⢸⣿⠀⢀⣤⣠⡦⠶⠶⠾⢶⠾⠷⠾⠷⠶⣤
⠀⠀⠀⠛⠶⣤⡀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠟⠛⠋⠁⠀⠀⠀⠀⠒⠶⣾⠷⠷⠒
⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⢀⣴⣋⣷⡀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⢣⡀⠀⢠⡆⠀⠀⠀⡴⠋⠀⢀⡴⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖
⠀⠀⠸⢿⣆⠹⣦⡀⠁⠀⠀⣀⠀⢀⠴⠋⠀⠀⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣧⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⣠⠋⠂
⠀⠀⠀⠀⣉⡷⣾⣿⡗⠚⠺⣷⡖⠁⠀⠀⢀⣠⣞⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡙⢦⣀⣹⣿⣦⡷⠀⠀⣼⣷⣾⣿⠁⠀⣀⠀⠔⠁
⠀⠀⠀⢀⡈⠁⠠⠏⠀⠀⠀⠻⣿⢗⣲⠒⠛⠁⣋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠿⠛⠃⠀⠀⠈⡿⡝⠛⠒⠒⠂⠀⠢⠂
⠀⠀⠀⢈⣦⡀⠀⠀⠀⠀⠀⠀⠉⠂⠀⣠⡀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠘⣿⠳⠶⠦⡤⠤⡦⠖⠞⠉⠙⢻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢡⣿⡁⠹⠛⢦⣄⡀⣀⣀⣠⣤⢶⡶⠛⠛⣷⠸⠆
⠀⠀⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⢷⡄⠀⠀⠀⠉⠉⠁⠉⠀⠀⠁⢀⡾⠀⠰
⠀⠀⠀⠀⣼⡟⠀⠀⠉⠁⠛⠂⠒⠠⠶⠀⠀⠼⣿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢻⠄⠤⠀⢀⠀⢀⡀⠀⠀⣠⡎⢸
⠀⠀⢀⣄⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢷⡈⢆
⠀⠀⠺⢯⡉⠉⠙⠓⠶⢤⡄⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣠⣆⣠⣦⣤⣴⣦⣦⣀⣄⣀⠈⢣
⠀⠀⠀⢨⡟⠀⣰⣦⠄⡀⠈⠐⠛⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠉⡁⣀⡀⣠⣠⡀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⢀⣆⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⡆
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⣠⣾⠟⠀⠀⠀⢀⡀⠀⠀⠁⠢⡄⠀⠀⠀⠀⠀⣀⠤⠐⠚⠻⣇⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠁⣀⡤⠤⢶⠟⠃⠘⣷⠠⠀⢸⡇⠀⠉⠁⠚⠛⣱⣄⠤⠒⠉⠀⠀⠀⢀⡤⠛⠀⠀⣴⡾⠛⠛⠋⠂
⠀⠀⠀⠀⡐⢀⣸⡇⠀⡀⢘⡀⠀⠀⣹⡇⠀⠈⠁⠀⠀⠀⣠⡾⠋⠀⠠⣄⡀⢀⣤⠔⠉⠀⣤⠤⠤⢿⠇⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠘⡻⠋⣿⠡⣾⢀⣠⣴⢾⣿⡿⠁⠀⠀⠀⠀⢠⡾⠋⠀⠀⣐⡀⠀⠉⠉⠀⠀⢀⣄⣸⣧⠀⠀⠀⢠⣆⠀⢻⠶⣴
⠀⠀⠀⢰⠁⠈⠁⠐⢻⡿⠋⠀⣾⡿⠁⠀⠀⢠⣾⣴⡟⠀⠀⠀⢀⡠⠘⠀⠀⢠⢀⡴⠋⠉⣿⠇⠀⣀⣠⣾⣿⣶⠟⢀⠞
⠀⠀⠀⢸⡲⠁⠀⡴⠋⢀⣀⠠⠿⢟⣿⣿⣿⠏⠀⢻⠀⠀⣠⡖⠁⠀⠀⠀⠀⠘⠉⠀⡀⣸⣿⣶⣿⠿⠟⠛⠁⠉⢠⠎
⠀⠀⠀⢸⡀⠀⠚⢶⣴⡏⠀⠀⠀⣿⣿⡏⠀⠀⠀⠈⠇⠊⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⡍⠉⠀⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠳⡄⠀⠀⣿⣏⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣀⣴⡿⠉⠷⣄⡀⠀⠀⢀⣸⣿⣿⡉⠀⠀⠀⠑⠒⣤⠞⠁
⠀⠀⠀⠀⠀⠹⣆⢲⣿⡏⠀⢠⣴⠿⠋⠀⡠⠒⠶⠞⢱⣿⣇⠀⠀⠈⠻⠿⠿⠟⠋⠉⠻⢿⣦⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢾⡿⡅⡀⠘⣿⡄⢀⡜⠁⠀⠀⠀⣴⠋⠘⣷⣄⠀⠀⠀⠀⠀⠀⢀⣰⠞⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠈⢻⣾⠀⠀⠀⢠⡤⠽⠆⠀⣼⡿⠀⠀⣦⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⢸⡀⠀⣾⠁⢀⣀⣠⠟⠀⠀⠀⢰⣿⡇⢀⣠⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠷⡾⠛⠀⣿⠈⠉⠀⢿⣇⢀⣸⠿⠿⠛⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣆⣀⡤⠞⠉⠛⠁⠀⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠾⠋⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡯⣲⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠘⠏⠚⠒⢼⣓⠒
⠀⠀⠒⣻⡽⠯⠭⣍⣓⣂⡀⠒⢦⠀⠀⠀⢠⠊⣀⠀⠀⠠⠀⠀⣀⡀⢳⡀
⡠⠂⠩⠀⠐⢤⠀⠀⠀⢀⡠⠖⠉⣠⢶⣲⡇⠀⢀⡑⣄⢧⢠⠊⣁⠀⠀⣧⠤⡄
⠉⠉⠁⠈⠓⣄⣳⡀⠰⡿⢄⠀⠀⡧⢋⠟⠀⢰⢡⢙⠘⠺⠃⡎⣉⡣⠀⢳⠗⢼⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⡀
⠀⠀⠀⠀⡼⠤⠤⣉⠊⣠⠌⢣⠀⡇⢠⠂⠀⠈⠑⠋⢀⠤⣄⠈⠋⠁⠈⢢⠀⡸⠀⠀⠀⠀⠀⡅⡅⠀⡰⢩⠇⠀⣀
⠀⠀⠀⢈⠗⠒⠒⠦⣍⡟⠁⢸⠀⢙⠇⠀⠀⢀⠤⠂⠉⠃⠛⠠⣀⠀⠀⠀⢳⠁⢘⠑⢄⠀⢸⠁⡇⣰⢁⠎⢠⠎⡸
⠀⠀⠀⠈⡗⠚⠒⠒⢾⡃⠀⣸⠀⢸⠀⠀⡔⠁⣴⣿⣭⣭⣵⣢⣄⠳⡀⠀⠈⡇⠈⢆⢸⠀⡸⠀⠳⠃⣞⡰⢃⠜⢁
⠀⠀⠀⠀⠳⣽⠛⢻⢶⡃⠲⡇⠀⠸⡄⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆⠱⠀⠀⡷⠀⢸⠈⠛⡡⡌⠀⠀⠈⢡⡋⢔⡽
⠀⠀⠀⠀⢠⠏⠀⠘⠄⠙⡄⠈⠀⠀⢱⡀⠀⠀⠈⠛⠿⣟⣛⣛⣫⠝⠀⠀⣰⠓⠂⢸⠀⠀⢸⠙⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⢸⠐⣖⢲⣤⡀⠈⡄⠀⠐⠋⠙⢦⣀⠀⣀⣀⠐⠒⠒⠒⠀⢀⡴⠃⠀⠀⠘⣆⠀⠇⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠘⠒⠚⢸⣃⣈⠐⠁⠀⠀⠀⠀⠸⡏⢙⣶⡧⠤⠤⣶⣒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠛⣿⣿⡿⠿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⣽⣿⠃⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣷⠞⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣾⣿⣿⣷⣿⣾⣦⣾⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠙⢿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠈⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⠀⠀⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠐⣿⣿⣿⣦⣀⠀⠀⠀⣠⣶⣿⣿⣿⡇⠀⠀⠈⣿⡇⠀⠀⣠⠴⠢⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡰⠛⣛⣿⣿⣿⡷⠀⠸⣿⣿⣿⣟⡋⠳⡄⠀⠠⠟⡳⣄⡠⠕⠀⠀⠀⠚
⠀⣀⣠⠴⠤⡀⠀⢀⠜⣛⠻⡀⠀⠀⡇⢾⢠⣴⣮⢏⠀⠀⠀⢫⠀⢷⣾⠇⠀⣿⠀⠀⠸⠏⣹⠊⠉⠯⣤⣴⠟
⢾⣁⠀⠀⠀⠉⣀⢽⠲⡋⡇⠀⠀⠀⠙⢬⣿⣯⣥⠎⠀⠀⠀⠘⢷⣄⡀⠤⠺⠃⠀⠀⢰⠚⠁
⠀⢧⣀⡀⠀⣹⠆⠈⠓⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣤⣤⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠁⠐⠒⠂⠬⠿⠟⠢⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠚⠛⣉⡛⠛⠦⠀⠚⣡⡴⠶⠶⣄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⡶⠋⠉⠉⠳⣆⠀⢠⡏⢰⣶⡆⠘⡇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⠀⠀⢸⣛⡇⢹⡆⠀⢷⣌⣉⣁⡼⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠹⣦⡀⠀⠉⣠⡾⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⣀⣠⣤⣤⠤⣤⡀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣾⣯⣭⣵⠶⣤⣀⢈⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠰⠾⠿⠓⠚⠛⠳⢦⡈⠻⣆⠉⠻⡄⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠀⢀⡿⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡛⢿⣿⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⢟⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⢿⠭⠥⣄⡀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠚⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠏
⠀⠀⠘⠛⠛⣛⡃⠀⠀⢀⣠⣤⡴⣄⠄⢀⠀⠀⢨⡕⠚⠛⠷⣦⣄⠀⡉⢉⠹⣿⡿⡷⠖⠀⠀⠀⠀⠀⠀⢦⣈
⠀⠀⠀⠀⢀⣿⠿⠶⠋⠀⠀⠉⠛⠻⣷⣦⣄⠀⣀⢷⣄⠀⠀⠀⠘⣏⢱⡞⠃⠹⢷⣷⣶⣩⣤⣴⣦⣠⡜⠑⠈
⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣷⣹⡏⡛⠷⢦⣾⣿⣸⣶⣤⡀⢻⣿⠿⠿⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾
⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠑⠊⠻⣛⠁⣿⣇⡁⠈⠁⢶⠴⣋⢆⠀⠀⠀⠠⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣫⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⢦⣙⣿⡙⢦⠤⣴⣯⠆⠈⠳⣄⠀⠶⣮⣿⣦⣄⠀⣀⣠⠤⣤⣶⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠳⣄⠁⠀⡙⠛⠣⠶⢾⣿⢿⣦⠀⠀⢸⡀⠀⣿⣿⣶⡙⣿⠃⣴⣿⣿⣿⣿⡇⢹⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠨⣿⣦⣤⣤⡉⡴⠁⠀⠀⠀⠀⣠⣼⡛⠷⣶⣌⠁⠀⢿⣟⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠂⠀⠀⠀⢠⣤⣾⣿⠄⣈⡽⠛⠋⢉⢷⣤⡀⠀⣠⣩⣿⣿⣿⣦⡀⠙⠻⢦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠘⣿⣿⣿⠳⣧⣀⣀⡆⠀⠐⢄⢉⣀⣴⣞⢩⡀⠻⣿⠟⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⡀⠀⣰⠀⠀⣽⢾⣿⣧⣬⣭⣭⡙⠳⠦⢤⠀⣽⣿⣿⢀⣽⠞⠀⢀⡠⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠄⠑⠀⠈⠁⢶⣌⢏⠻⣭⣼⣿⣿⡳⢶⣶⣾⣷⣿⣿⡷⠛⠁⠀⢐⣩⣶⠾⠟⠚⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠴⠂⠀⡢⠀⢀⣿⣟⢷⠻⣭⡽⣿⣿⣙⣻⣿⡋⠜⠉⠀⠀⣼⣶⣿⡓⠒⠶⠦⣄⡀⠀⠀⠉⠛⠛⠉⠛⠛⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠀⠈⠕⠀⢸⣿⡿⣶⣬⡇⣩⣿⣿⢿⣫⡍⣠⢖⣄⣠⣾⣿⣿⣿⣿⣿⣿⣷⣾⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⢷⣿⣿⣿⣷⣿⣾⢟⣽⢿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⡌⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⣿⣿⣿⣿⡿⠟⠋⠉⢹⣿⣿⣿⣿⣷⣿⣻⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⢠⣿⡿⣿⣿⣿⡟⠀⠀⠀⣰⡿⠟⠋⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣛⣉⣭⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡼⢿⣧⣀⣰⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠶⠾⢿⣿⣻⣿⣿⣯⡤⠄⠀⠀⠉⣉⠶⠂⠀⢠⠄⠁⠀⠀⠂⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣛⠿⢟⣹⣥⣶⠿⠛⢉⡀⠀⡜⢶⡄⠀⠀⠀⠀⡇⢀⠏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢏⣽⣴⡏⠁⠾⠁⢀⠁⣠⠅⠀⠂⠀⠈⠄⠀⠀⣠⡶⠋⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠊⠉⠂⢄⡀⠀⠀⠀⣿⠧⢁⣾⡿⣠⠔⠁⠔⠃⠀⠁⣤⡀⠤⡀⠰⠑⢠⡾⣫⡴⠊⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢡⣤⣤⣀⠀⢀⣷⡄⠀⣴⢉⠂⡈⠳⡘⣥⣆⡤⢞⠡⠂⠀⠁⠀⠀⠀⠀⠸⣿⡿⠓⢠⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠙⢷⣽⣿⡇⠀⣉⡎⢠⠀⠀⢛⡿⠃⠐⠀⢀⠀⡀⢂⣤⠧⠆⠀⠀⣈⠁⢪⡒⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣤⣤⠀⠈⢿⣿⣿⡀⢹⣇⡿⢀⠀⣼⠁⣴⠁⣴⣣⣴⣟⣯⠅⠒⣨⢅⡨⢿⡛⡟⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢷⣄⣀⣈⡛⢿⣿⣡⠀⣼⠃⡎⠀⡿⠄⢉⣼⢟⣡⢞⡡⠀⢠⣾⣥⣿⣾⠏⣽⢿⡟⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠤⢨⣭⣭⣤⣶⣿⣷⡦⣿⡠⢃⣼⣅⣠⣾⠅⠙⠛⠋⣠⠔⣡⠺⢋⣡⣿⠈⢹⡀⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠈⠛⠛⠋⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣏⠰⠒⠒⢉⣱⠞⢁⣴⣿⣽⣿⣶⢰⣿⠄⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠿⣑⠶⠶⠶⠶⠶⣶⣶⣿⡿⢻⣯⣿⣿⣿⣷⣬⢍⣉⣤⣴⢡⠿⢻⣿⣿⣿⣟⣽⣿⢸⡆⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠾⣷⠱⣄⠉⠀⠉⢙⣭⣿⣿⣿⡇⢸⡏⣿⠖⢿⠋⠻⠀⠉⠀⠇⠈⢰⡈⢟⣿⣿⡟⠁⠻⣷⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠢⣄⠛⢷⣬⣏⣌⡴⢫⣷⠛⢋⠹⡇⢠⣤⣿⣤⡴⠃⢐⠀⠀⠀⠀⢀⡘⣷⢟⣼⣿⡇⠀⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⣄⠘⠛⠛⠣⠛⢿⣻⣿⣆⣀⣠⡿⢋⠔⠀⢀⠀⠈⠛⠛⠛⠁⠨⣯⡿⢻⣿⣇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣿⣇⡴⠿⠶⠤⣾⣿⠟⠏⢉⣹⡟⠀⠂⣀⣾⡷⠋⠀⢦⠀⠀⠀⠈⣧⠈⢷⠹⣦
⠀⠀⠀⠀⠀⠀⣷⠙⠍⡿⠘⣿⣧⠈⠀⠐⢼⣧⣤⣤⣿⡿⠖⠾⠋⠉⠉⠁⠀⠀⣈⠀⣶⠀⠀⠹⡆⠈⠃⣮⢷⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⡧⢸⡿⣟⠀⠀⠀⡘⠁⠀⠈⠃⠀⠀⠀⣀⣀⣠⣶⣶⣾⣿⠂⣿⠀⡀⢰⡇⠀⣼⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣡⣧⣼⡷⡟⠀⠀⠀⢹⣦⣶⣶⣶⣶⣶⠾⢿⡟⢻⣍⡽⢿⠃⣸⡇⠀⣴⠏⢀⣼⡏⢸
⠀⠀⠀⠀⠀⠀⡐⢉⠀⣿⡏⠀⠇⠀⠀⠀⡘⠋⠉⣋⣠⠶⠛⠒⠉⣉⣤⣈⣿⠟⣰⣿⠷⠿⣋⡴⠟⢹⣿⣘⣧⡀
⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⣧⣶⣤⡀⡀⠈⠛⣶⠾⡟⠁⠀⢀⡴⠚⡿⠟⢋⣡⣶⣿⣿⠀⣼⣣⢢⠆⠘⠁⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣽⣷⣌⠁⢿⡑⠶⣼⡟⢿⣿⣷⢖⡀⠀⣠⣾⡟⣹⣿⠉⢿⠀⢹⣴⡇⢸⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠸⢏⡙⣌⠉⠻⣷⡌⢿⣴⣿⠷⠌⠛⠅⠉⢀⣾⣿⣿⣿⣿⣷⣦⣬⡤⢾⡸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣿⠿⣶⢢⠻⠀⠘⣿⡄⠀⡿⠀⡴⠻⢷⣿⣿⡿⣿⣿⠟⡡⠀⢹⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠉⠁⠑⢀⡌⢹⣧⣰⡀⡠⠁⣴⢸⡿⡿⣷⠋⣀⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣶⡍⠀⠙⣿⣿⠃⢰⣧⣾⠓⣽⢃⣾⣉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡻⣿⣦⢠⢸⣿⡄⠰⣿⣯⣶⡭⢘⣋⣉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⡿⣇⢻⣄⣹⣿⣧⡀⣠⠜⣫⠟⠁⠀⠈⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢹⡟⠈⠛⠛⢻⣿⣾⣧⠀⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⡀⣰⢰⣇⡸⢻⡏⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡝⣿⣿⣼⡗⢻⣆⢳⣾⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠞⠉⠀⠀⠹⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠂⣉⠉⠉⠉⠉⠉⠐⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⣤⠚⠀⢧⡀⠀⢀⠜⠸⡆⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠈⠂⠒⣤⠵⠛⣁⠤⠠⠞⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣴⠉⠋⣠⠐⠾⡈⠓⠶⢤⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⡜⠀⠀⠀⠈⣆⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⣀⣤⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠻⢊⣠⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠋⠳⡴⢾⣭⣀⣀⠀⠀⠀⠀⣀⠀⢀⣀⣤⠴⠐⠲⠖⠈⠲⡄⠀⠀⠀⠀⠙⠷⣄⠀⢀⠾
⠀⠀⠀⠀⠀⡸⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⡿⠒⠒⠒⠒⠒⠊⠉⠙⢇⠀⢧
⠀⠀⠀⠀⣼⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠣⣀⠀⠀⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢃
⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠊
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣽⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠈⠇⠀⠀⠙⠶⣖⠒⠒⠀⠀⠀⠐⢒⡶⠒⠉⠉⠉⣿⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠑⠦⣀⠀⣀⠔⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⣋⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣤⠟⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⡸⠄⠤⣄⡀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⡀⢠⣼⡄
⠠⠞⠁⠀⠀⠀⠉⠐⠂⣤⠈⡆⠀⠀⣀⣀⣀⠀⠀⠀⠀⠘⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠤⠤⠒⠉⠁⠀⠀⠈⢢
⠳⢀⡴⠀⣀⠀⠀⠀⠀⠀⢳⠖⠚⠀⠀⠀⠀⠈⠓⠄⣀⠀⠀⠀⣀⠤⠚⠛⠛⠛⠓⠠⢼⡇⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠣⡼⠏⠀⣿⠀⡎⠉⠺⢤⣀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣤⠋⠀⠀⠀⠀⠀⣀⣀⣤⡞⠀⡤⠲⡀⢰⡄⠸⣧⢈⠅
⠀⠀⠀⠀⠈⠚⠈⠉⠁⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠙⠚⠳⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡤⠐⠒⠢⠤⠔⠒⠤⣀⡸⢆⣀⠤⠒⠤⠤⠔⠒⠤⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠒⠉⠉⠉⠉⠲⣄⡃⠀⠀⢿⡠⠖⠉⠉⠉⠑⠢⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠈⢓⡀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⠶⢶⣤⣤⣤⣄⠒⠳⠀⢱⡇⠰⡒⢛⣋⣁⣀⣙⠛⠲⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠛⠒⠒⠀⠀⠐⠛⠻⠀⡸⡇⠠⠏⠉⠉⠀⠀⠉⠛⠻⠂⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣒⠤⢀⡀⠀⠀⣀⠀⠤⢚⡵⢍⠢⢄⡀⠀⠀⠀⢀⡀⠄⣚⠏