Witty Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠠⢟⡂⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⠁⠀⠀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠀⠠⠖⠃⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠚⠀⡄⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⡄⠚⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠶⡀⠀⠀⠠
⠀⠐⢫⡀⠁⠀⠐⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⢀⡁⠀⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢉⠠⠄⢀⠀⢀⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠤⠐⠈
⠀⠀⠀⠀⠣⡤⠐⠄⠐⠤⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠃⢀
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠉⠉⠉⠈

⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠉⡓⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠉⠃
⠀⠀⡤⠀⠈⠉⠁⠀⠀⠀⠘⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡑⣢⣤⣤
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢆⠀⠀⢀⠄⠀⠀⠀⠠⠄⠀⢀⠙⠿⠟⠡⠍⠛⠋⡀⠀⠐⠂
⠀⠀⠀⠈⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠘⠦
⠀⠀⠈⠙⠛⠻⣶⢦⣴⣤⣶⡞⠛⠉⡏⠀⠀⠀⠀⢖⠉⢁⡄⠈⠇⣀⡉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂
⠀⠀⠀⠈⠆⠀⢀⠠⠂⠐⠄⣀⠀⠔⠀⠀⠀⠀⠀⠐⠀⡀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⠛⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠁⠒⠒⠁
⠀⠀⠀⠀⡤⠪⢀⡠⠄⢠⠤⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣀⡀
⠀⠀⠀⠸⣡⠀⠴⠂⠀⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣰⣦⣻⣷⣾⣷⣶⣦⣠⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣼⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣵⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡟⠀⠀⣀⣀⣀⠀⠀⠀⢀⡤⠴⠒⠒⠲⣤⣀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡏⢠⣶⣿⠟⠉⠉⠉⠑⠋⠁⠀⣀⣀⣀⠀⠈⣿⣧⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡟⢠⣿⡟⠁⣠⡴⠞⠛⠓⢦⣴⠋⠁⠀⠈⠻⣄⠈⠋⠀⠀⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠃⠀⠉⠀⣼⠋⠀⢠⣦⠀⠈⣧⠀⠀⠿⠆⠀⣿⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡿⣦⣀⠀⠀⢀⣿⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠘⢷⣤⣤⣤⣾⠏⠀⠈⢻⣿⣿⣛⣁⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣺⠟⢱⠀⠀⠀⠀⢻⣏⡓⠂⠀⠀⠀⠀⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⣴⢺⡇⠀⠀⠀⢸⣿⠹⡆⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⣬⣷⣀⣀⣠⣾⢿⡾⠟⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠈⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠐⡀⠀⠀⠀⠀⠀⠂⠙⠻⠿⣇⠀⠀⠀⡀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣥⣀⣀⣀⣀⠀⠀⠀⠀⠲⠈⣷⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁


⠀⣁⡈

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣤⣤⡤⠄
⠀⠀⠀⠀⠀⢰⡆⣿⡏⣿⣇⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡴⠋⠁⣀⣀⣀
⠀⠀⠀⠀⠀⢹⣿⠻⢟⣙⣫⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣿⣵⣾⠿⠛⠛⠻⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣸⣿⡿⢁⠔⠛⠛⠛⠦⣌⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣤⣀⠘⣿⣿⣧⡇⡴⣊⣉⣑⢦⠈⠳⡈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⣶⣅⣀⡉⢢⠳⡄⠙⢦⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⢠⣾⠋⠉⠀⠉⠉⠻⣿⡉⠛⠛⠿⣿⣷⣬⣢⡀⠳⣄⠙⢿⣷⡀
⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣟⡳⢸⣧⠀⠀⠀⠀⠉⠻⣿⣯⢦⡈⢳⡈⣿⣷
⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠀⠀⠉⣁⣼⠇⠀⠀⠀⠀⠀⠀⠈⢻⣷⡝⡀⡇⣿⣿
⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡇⣿⡿⣇⣀⡄
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⢻⣧⠈⠉
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣽⣷⣤⢀
⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣏⠙⠂⠀⠀⢀⣴⡾⠿⣿⣿⣿⣿⡵⠃
⠀⠀⠀⠈⠻⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⢀⣾⠋⠀⢿⡄⠀⠀⠀⠈⠉⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠉⠉⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⢸⡇⠀⠀⠀⢀⣄⡀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢤⣤⣤⣴⠶⠞⠋⠁⠀⠀⢀⣴⣿⡇⠀⠀⠀⠈⠿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿⡄⠀⠀⢀⣀⣴⣿⠿⣿⠃⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠋⠀⣴⡟⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢀⣤⣶⣤⣠⣼⣿⣤⡾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠈⠛⢿⣤⣤⣤⡾⠋⠀⣰⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣤⡾⠟⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠿⠟⠁⠙⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⣀⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢧⣤⣤⣬⣉⣉⣉⣛⣻⣦⣀⣴⠟⠛⠓⠛⠛⠛⠛⠋⢹⣿⣇⣠⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⢾⣿⠛⠋⠉
⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⢀⣾⠋⠈⣿⠄⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⣸⡏⠐⠀⣿⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⢿⡇⠀⢰⡏⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⣴⠾⠗⢠⣟⣀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⡴⠶⠛⠛⠻⠿⢿⣶⣦⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠷⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠶⢦⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⡆⠈⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⡾⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⡛⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⣈⣀⣈⣀⣈⡉⠳⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⠦⣀⠀⠀⠀⠀⠀⠀⣀⣤⢾⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣄⠈⠉⠛⠛⠛⠛⠉⠉⢀⣼⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⣷⣦⣤⣤⣤⣤⣴⣾⣿⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⡾⠥⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣁⡀⠀⠀⠈⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⠙⠛⠳⠶⠶⠞⢛⡿⠋⠙⠓⢦⡀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⣠⠤⠶⠒⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠁⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠈⢻⣄
⢀⡀⢀⠔⠉⡀⠀⠐⣆⠀⠀⢢⡀⠈⠙⠛⠓⠒⠛⠛⠋⠉⢸⠃⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢀⡠⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢨⠿⣆
⡟⠉⠿⠴⢾⣇⣀⣠⡟⢷⠶⢿⣥⣀⡀⢸⡟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣀⡤⠖⠋⠀⠀⠀⠀⠈⣷⠀⠀⠀⠒⠒⠁⠀⢻⡄
⠷⠤⠤⢤⣤⣭⣭⣉⣀⣀⣀⡀⠀⠈⠉⠛⢿⣄⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢳⠀⠢⡤⣙⠳⣤⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣧⠀⠉⠓⠧⣈⠳⣤⣤⣤⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⢻⡄⢹⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⠀⠀⠀⠀⠈⣹⠦⣀⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆⢀⣀⡤⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⠀⠀⢿⠀⠈⠛⠞⠁⠀⠀⣀⣀⣠⣀⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣿⠃⢸⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡿⠀⡿⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⢀⣾⠁⣸⠇⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠷⣦⣀⠀⠈⠙⠛⠒⠒⠒⠒⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⠾⠛⢶⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠁⠀⠀⠀⠈⠉⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠟⠛⠛⠛⠛⠛⠛⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡇⢸⠁⢀⣠⣤⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⣄⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢻⡈⠉⠉⠉⠉⡷⠋⠁⠀⠈⢻⣇⣀⡀⣤⠀⠀⠀⢰⡀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⡦⢷⣄⠀⠀⡼⠁⢀⡴⢶⡄⠈⣯⠉⠙⠛⠓⠶⠶⠾⠟⠛⠛⠉⠛⠻⠶⠶⣦⣤⣤⣤⠖⠛⠛⠲⣤
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⢻⠳⢶⡇⠀⢸⡀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣠⠶⣄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣠⡴⠏⠀⠘⡇⠀⠈⠛⠁⠀⢰⡟⠛⠓⠒⠶⠶⠶⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣸⡇⠀⣧⣠⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠉⠹⣇⠀⠈⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠿⠳⣦⣤⣴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀⢶⠋⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⣀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠁⢼⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⢸⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠈⠀⠀⠀⠀⢸⣿⠙⢿⣿⣦⣄⠀⢸⠀⠈⠀⣠⣾⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠻⢿⣿⣿⣶⣶⡿⠿⢿⣷⣦⣤⣶⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⢠⣿⡏⠀⠀⣶⠚⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠾⠿⠷⣄⣀⣸⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⢳⣠⡞⠁⠀⣀⣀⡀⠀⠀⣹⠟⣧⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠀⢀⣼⣿⣀⣀⣀⠀⣶⠞⢧⡀⠀⠀⠀⡟⠀⠀⢿⣮⢠⡾⢟⣛⣿⠿⠾⠟⢲⣿⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢶⣶⣶⡾⠛⠉⠀⠀⠀⠉⠓⢿⣿⡧⠹⣦⠀⢰⡇⠀⠀⠈⣿⣿⡁⠘⣧⠀⠀⠀⠀⢸⣿⣇⣀⣸⣏⠒
⠀⠀⠰⡦⠞⡆⠀⠀⠀⠀⠀⠀⢹⣿⡠⠀⣠⣤⣦⣤⡀⠀⠀⢻⡏⢄⠈⠳⣼⠁⠀⠀⠀⠘⣿⠳⣤⣿⡾⠟⠀⠀⣼⠙⣏⠁⠀⢿⣤⣤⣀⣀
⠀⠀⠰⠧⢄⡶⠀⠀⠀⠀⠀⠀⣿⣿⣟⣾⠏⠁⠀⠉⢻⡆⠀⠀⢿⣡⡄⠀⠉⠀⠀⣿⡀⠀⠸⣇⠀⠀⠀⢀⣠⡾⣫⡴⣿⣶⠶⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣯⣿⠀⠀⠀⠀⠀⡿⠀⠀⣸⡟⣿⣦⡀⠀⢸⡟⣷⣀⣀⣽⡿⠿⠿⠟⠋⢰⡟
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣠⠞⠁⠀⢀⣿⣿⣿⠙⢿⣤⣾⠀⠘⠛⠛⠉⠁⠀⢄⡀⠀⠀⢳⡀⠀⠀⠀⠀⣨⠁⠸⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⠊⢻⣿⣿⣷⠀⠀⠀⠀⠀⣠⣾⡿⠿⠟⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠵⣎⠹⣍⠉⠉⠉⠁⠀⠀⠀⠀⠱⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠈⠛⣿⣷⣶⣶⡶⠟⠛⠻⣷⡄⠀⠀⠀⠀⢀⣠⣤⢤⣄⡀⢸⠀⠈⢧⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠟⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢀⡴⠋⠁⠀⣀⡀⠈⠲⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠘⡇⢀⡞⠁⢠⡞⠋⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠋⠀⢲⠅⠀⠀⠀⠀⠀⣿⡞⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⢤⣰⠇⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢶⣤⣀⠀⠀⢀⣤⣤⣤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠈⠙⠷⣴⡟⠁⠀⠀⠙⢿⣮⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⠶⠶⠶⠶⠶⣾⣷⣀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢞⠋⠁⠀⠀⠻⢷⣦⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢰⠟⢉⡙⢷⣴⠞⠛⠳⣌⠁⠀⠀⠀⠀⠀⠹⣧
⠀⣀⣤⣀⠀⢀⡞⢉⡗⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢹⣄⠘⢋⣼⣧⠀⠻⢇⡿⠀⠀⡄⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠲⣆
⠀⠻⣄⣈⡙⠾⡄⠾⢦⣄⣠⣤⣤⣤⣄⣸⡿⠀⠀⠀⠀⠀⠀⠙⠋⠉⣹⠏⠻⠟⠛⠁⠀⣸⣧⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣿
⡴⠒⠒⣺⡇⠀⣇⠀⠀⢉⣀⣠⡤⠤⠤⢼⡇⠀⠀⠀⠀⣴⠟⠛⠛⠛⠁⠀⡀⠀⠀⠀⣴⠋⣿⠀⠀⠀⠀⠀⣿⣟⣛⣛⣛⠛⠒⠶⡞⠋⠛⣰⣇⣀⣀⡀
⠉⢛⡩⠽⢃⣤⣀⣀⡴⠋⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣠⡿⠀⣠⡾⠁⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⠓⣦⠀⠀⠀⣿⠀⢦⣈⠉⠳
⠀⠘⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⣥⡴⣾⠋⠀⣠⡞⢹⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠘⣦⡀⠐⠋⠀⣼⠙⠻⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠉⠀⣼⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⡄⢧⠙⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠋⢠⣇⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣀⡆⢠⠄⠀⢀⠀⢀⠀⢀⣐⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⣿⠻⠶⢿⡄⠸⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢿⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠾⠦⠸⣇⠀⢸⡇⠸⠿⠶⠶⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣛⣋⣉⣁⣀⣀⣀⣀⣀⣤⠟⠀⠸⢧⣤⣤⣄⣀⣀⣀⣀⣉⣹⣷⡄
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠊⠀⢀⡀⣣⠴⠂⠉⠁⠺⠎⢅⠀⠀⠈⠢⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠚⠉⠆⣥⡄⣤⡀⠀⠀⠀⢎⠲⠤⠤⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠃⠦⡟⠁⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣤⠀⠀⠀⠀⢰⠆⠀⣠⠞⠁⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠳⢼⣄⣀⣀⣠⣦⠴⠚⠁⠀⠀⠀⠀⠀⠱⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠉⠐⢤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠀⠀⠉⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡀⠀⠹⣄⠀⠀⠀⠀⠀⠸⣄⠀⢀⠀⠀⠀⠀⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⡀⠀⠈⢧⡀⠀⠀⠀⣰⠋⠁⠀⠁⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⢳⠀⠀⠀⠹⣄⣠⠞⠁⠀⣠⠟⠢⢄⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠑⣤⠞⢀⡿⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠖⠋⠀⠀⠉⠀⠀⠈⢀⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⣤⠎⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠒⠒⠉⠓⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⠞⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢠⠚⠒⠒⠦⠤⢄⣀⣀⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⢦⣀⡀⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡴⠓⠦⠤⠤⠴⠒⠚⠉⠀⠀⠀⡼
⢌⣀⠀⢀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢠⠖⠉⠀⠀⠀⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⢸⣉⣉⣉⣰⠒⠒⠒⠒⠒⠒⠛⠓⠇⠀⡆⠀⠀⠀⡆⠀⡿⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠤⢾⠀⡆⠀⠀⢀⠀⠀⡀⡋⠛⠒⠒⠶⠶⠶⠒⠛⠉
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⢇⣀⣀⣤⠗⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢧⣄⣀⣴⠤⠤⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠔⠲⠏⠉⠉⠍⠐⢢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠁⡀⠀⠀⠗⠀⠀⠂⠀⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣀⣠⣀⣰⣆⣀⣰⣆⣨⡀⡇⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡊⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠑⡆⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠈⠳⣄⠀⠉⠀⠀⠀⠀⠀⠈⠉⢀⣠⠞⠑⢆⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠈⠳⣤⣀⠀⢀⣀⣤⠴⠚⠋⠀⠀⠀⠸⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⠉⢙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢀⠀⠀⠀⣠⠞⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠀⠀⢸⠀⢀⠞⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⡘⢠⣿⣿⣿⣿⣿⣿⣿⣆⠰⡄⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠀⠀⡇⢸⣿⡿⠛⠛⠋⠙⢿⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⠀⢻⠸⡿⠶⠶⠶⠶⠶⠾⡿⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⠀⠘⡄⠻⣄⠀⠀⠀⠀⡴⠃⡀⠀⠀⠘⡆⠀⠀⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠗⠋⠀⠀⠀⢀⠇⠀⢠⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣤⡴⠃⠀⠀⠚⠀⠀⡾⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡼⠉⠉⠈⠳⣄⠀⠀⠀⢀⡼⠃⠀⠀⠀⡇⠀⠀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡼⢆⡀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠙⠶⠤⠶⢻⠀⠀⠀⠀⠀⡇⠀⠀⠈⢆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠈⠙⠲⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡄⠀⢀⡞⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠸⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧⠔⠉⠀⢀⡞
⠀⡠⠒⠂⠒⠒⠒⠀⠀⢼⠁⠀⠀⠀⠀⣇⢸⠀⠀⢰⡄⠀⠀⠠⠶⠂⠀⠀⠘⡄⠀⠀⣧⠀⠀⠀⠀⠀⠸⡦⠤⠖⠛⠉⣉⠱⡄
⡜⢀⠎⠀⡰⠒⠁⠀⢠⡏⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⣧⠀⠀⠀⠀⡇⠀⠀⠀⠹⡄⠀⡟⠀⠀⠀⠀⠀⠀⠘⢦⣀⠐⡄⠈⢧⡱
⠙⠺⢤⣤⣇⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢹⠀⠀⠀⠀⣧⠀⠀⠀⠀⠹⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢾⡀
⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⢀⣠⠤⠤⠏⠀⠀⠀⠀⢸⣦⣤⣤⣤⣷⠤⠀⠀⠀⠀⠈⠛⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⡴⠋⡀⠀⠀⢀⠀⠀⠀⢀⠈⠳⡄⠀⡞⠁⠀⢰⠂⠀⠀⠀⡀⠀⠀⡄⠘⣆⠀⠀⠀⠀⠀⣀⣠⡴⠟
⠀⠀⠀⠈⠛⠛⠚⠛⠛⠙⠦⢼⣃⠀⠀⢸⡀⠀⠀⢸⣄⣀⣿⠀⠳⠤⠴⢿⣄⣀⣀⣀⣇⣀⣀⡽⠒⠋⠙⠛⠛⠛⠛⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠪⠭⠩⠍⠉⠉⢉⣒⣒⣒⣒⠒⠒⠤⠤⠤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⣷⡾⠯⠍⢉⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣁⣐⡒⢒⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠲⠦⠤⠤⠤⠤⣤⣉⣉⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠐⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠷⠟⢿⡀⢠⠞⠉⣉⡻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇
⠀⠀⢔⢢⡀⢀⠖⠆⠀⠀⠀⠀⢸⠀⢾⣿⠇⢸⠀⢸⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⡇
⢯⡙⠺⠆⠱⣼⠐⢦⠀⠀⠀⠀⢀⡟⠚⠉⠀⠀⠑⠲⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡇
⠪⠭⣭⠄⠀⠧⠀⣘⠤⠤⠔⣂⠭⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠀⠀⡇
⠀⠰⠥⠊⠑⠒⠚⠁⠉⠉⠉⠀⠀⡇⠀⢢⡀⠀⠀⠀⣈⢷⢦⠀⠀⠀⠀⠀⠀⢣⠘⢄⠀⣿⠀⠀⡇⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢏⠂⠉⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⡑⠿⣤⣠⠗⢁⡜⣀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠼⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⢦⠀⠀⠀⡇⠀⠒⠚⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⢳⣄⣀⣄⠠⣍⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣎⡇⠀⠈⠦⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠉⡟⠙⠛⠓⠒⠒⢶⠲⡶⠶⠦⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡙⣄⠀⠀⠀⠀⢰⠃⡜⠀⠀⠀⠀⠀⠀⠀⢣⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠓⠤⣀⣠⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⠇⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣠⡶⠶⠀⠀⢀⣤⣄⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠞⢩⣿⣦⡔⢹⣿⣆⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠇⠀⠀⠘⣇⠘⢻⡿⢧⡈⣋⡝⠀⠀⠀⣀⣿⣤⣶⡶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢇⠀⠀⠀⠀⠉⠛⠉⠀⠀⢉⣡⣤⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠂⠀⠀⢤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣾⠀⠈⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⣀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠙⠛⣿⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⠀⠹⣦⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣷⠉⠳⢦⣄⣀⣄⣉⣉⡅⠀⠀⠀⣀⣠⣴⡾⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣠⠞⣿⠀⠀⠀⠈⠉⠛⠛⠻⠶⠾⠛⠛⠛⠉⠁⠀⠀⣿⡟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢁⣤⠞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡌⠻⣦⡀
⠀⠀⠘⢍⠓⢤⣠⠴⠶⠶⠋⢀⡴⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢦⡈⠛⢦⡀
⢰⣚⣛⣛⣛⠂⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢦⡀⠙⢦⣀⠀⠀⢀⠔⣶⣀⡀
⠯⣀⣀⠠⠤⠀⠀⣀⣤⡀⢀⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⡀⠋⠉⠙⠃⢚⣩⣔⣁
⠀⠯⠤⠤⠖⠚⠉⠀⠀⢹⡀⠳⣄⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠤⠔⠋⣠⣄⡀⠀⢀⣬⣥⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⠶⠞⠁⠀⠙⠶⣄⣈⠙⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠾⠇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠉⠛⠛⠛⢻⡟⢻⠉⠉⠀⠀⠀⠀⠀⣠⠞⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢿⠳⠶⠶⠶⠶⢶⣼⡇⢸⡀⠀⠀⠀⠀⢀⡇⢸⣀⣀⣀⣀⣀⣤⡞⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢷⡀⠀⠀⢰⡟⠁⠉⠉⠀⠀⠀⠀⠈⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⣶⣦⣤⣴⡾⠃⠀⠀⠘⠷⢶⡶⠶⠶⠶⠶⠶⠶⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣤⣀⡤⢾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣤⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣷⣄⣘⣿⣿⣿⣿⡟⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀⢿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣧⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠠⣆⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⢀⣀⣤⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟⢻⡄⠉⠛⠻⠿⠿⠿⠿⢟⣿⣿⡿⠋⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠁⣀⡜⠀⠀⠻⣿⣿⣿⡿⢁⣠⣤⣶⡿⠀⠈⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣿⣿⣿⠿⠋⢁⡶⢲⣿⣄⠀⠀⠀⠈⠻⢿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⠿⠇⠀⠀⠀⠀⠩⠋⢹⡯⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⡦⢄⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡀⠀⠀⠀⢀⠔⠈⠀⠠⠈⠀⢀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠸⠀⢆⠀⠄⠀⡀⠐⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⠻⠒⡽⠃⠈⠂
⠀⠀⠀⡠⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠤⠤⠤⢄⣀⠈⠁⠀⠀⠀⠄⠦⠤⠤⠤⠀⠀⡀
⠀⠀⢀⡁⠀⠀⠀⠂⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠐⠠⡀⠀⠈⠑⠢⣄
⠀⠀⢼⠀⠀⠀⠂⠐⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⢦
⠀⠀⠘⡀⠀⠀⠀⠈⢼⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⡈⠍⠛⠀⠀⠈⠀⠁⠈⠉⡉⠉⢉⠉⠉⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠂
⠀⠀⠀⠳⠀⠀⠀⣀⠙⠀⠀⠀⠀⠀⠀⠄⠈⠢⠠⠤⠂⠡⠔⠠⠀⠠⠀⠀⢄⡀⠐⠢⠤⠀⡀⡀⢤⣶⠀⠀⠀⣀⠤⠄⠒⠈⢀
⠀⠀⠀⠀⠉⠂⠀⢀⠀⠀⠀⠀⠀⡃⠀⢀⢬⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⠀⠈⠁⠈
⠄⠀⠤⠁⠀⠐⠂⣁⣀⡀⠀⠀⠀⠁⠊⠁⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⠄⠈⠍⠉⢀⡀⢀⣐⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⡠⠘⠣⣀⢀⣈⡍⠁⠈⠀⠀⠀⠀⠀⢰⠂⠐⠒⠒⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⡔⠋⡀⢀⠀⡬⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠔⠂⠈⠒⠑⠊⠀⠀⠣⠘⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡨⠄
⠀⠀⢀⠂⠤⠀⣀⡀⠀⠘⠀⡠⠔⣊⠤⠊⠀⠀⠀⠀⡀⠀⡀⠀⠐⠉⠉⠉⢨⡂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠈⠑⠒⠦⠬⣉⣹⣁⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠐⣐⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠜⠀⠰⠤⢀⣉⠐⠒⠠⠤⠤⣸⡄⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠢⠤⠆⠂

⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠘⡃⢠⣊⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⡸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠱⡀⢰⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⡰⡥⢤⡀⠉⢣⣄⣀⠀⠀⠀⠀⠐⠒⡲⠒⠈⠉⠉⠉⠲⢞⠀⠀⠀⠀⠀⢉⠱⠦⠷⠯⠤⠤⣼⡡⠤⠤
⠀⠀⠀⠀⢸⠁⠦⠶⢣⡏⣻⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣟⡃⣰⢀⣀⡀⡊⢟⢿⠉⠂
⠀⠀⠀⠀⠈⢇⠀⠴⠌⡩⠃⠀⠀⠀⠀⠀⠀⠀⢸⠠⣇⢆⠇⠀⣫⡱⠀⡴⠀⠀⠀⠀⠨⡉⠒⡄⠀⢤⠈⢑⠉
⠀⠀⠀⠀⣠⢴⠃⠀⠀⠁⢻⡒⢤⠀⠀⠀⠀⠀⠀⠙⢲⡄⠠⠦⠀⠀⡎⠁⠀⠀⠀⠀⠀⠉⡾⠀⠀⠸⡞⠉
⠀⠀⠀⠐⠃⢸⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡄⢀⡴⠀⡃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⣘⣁⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡤⠤⡞
⠀⠀⠀⠀⠀⠀⣹⠒⠐⠂⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠐⢄⠀⡀⠷⠼⠶⡁⠀⠀⠀⠀⠀⣀⠀⢄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣤⣏⣀⣀⢀⡀
⠀⠀⠀⠀⠤⠤⣱⠞⣡⡠⠄⣞⡷⢘⠆⠀⠀⠀⠀⢀⣽⡞⠓⢓⣠⡀⠀⠀⠀⠀⢠⢎⢥⡨⣏⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢸⡀⠃⠑⠣⠴⢠⡎⠀⠀⠀⠀⢸⠸⡧⠞⠰⣟⡼⢳⠀⠀⠀⠀⢸⡙⠓⣡⢢⢰⠶⣄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⡶⠑⡄⠀⠀⠀⠈⠲⡄⠐⠂⢀⠀⠘⣆⠀⠀⠀⢰⠋⡷⢺⠛⠉⢀⡌⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡜⠀⠈⠦⣄⠠⠃⠀⡟⠀⠀⠀⠀⠀⣇⠙⠂⠘⠀⠀⡸⠀⠀⠀⠀⡄⢆⠈⡀⠀⡞⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⡠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢖⠒⠒⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠚⡡⠔⣀⡀⠀⠀⠀⠀⠀⡤⠤⢄⣈⣵⡦⢤⡧⠴⣎⣈⣁⠀⠀⠀⠀⡤⢰⡡⢤⡀⢀⢈⢊⡃
⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠢⡤⠄⠀⠀⠀⠀⣀⢤⠞⠱⠼⠇⠫⡸⠂⡈⢳⠈⠁⠀⠀⠀⠜⢩⠳⣂⠇⢦⣂⢶⡍⢀
⠀⠀⠀⠀⠀⡜⠀⣀⣀⡀⠀⢀⢹⠀⠀⠀⠀⠀⠁⢸⠀⠙⠋⠉⠉⢉⣉⡥⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡀⠀⠘⡧⠞
⠀⠀⠀⠀⡴⡇⠘⢥⠣⠇⠀⢷⠟⡧⡀⠀⠀⠀⢀⡟⡆⠀⠀⠀⢰⠧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠁⠑⢤⣀⣀⣒⣒⣢⠔⠁⠃⠀⠀⠀⠀⠀⠈⢦⢀⣀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣠⣗⣦⣤⣦⣴⣤⣼⣾⣿⣷⣿⣷⣤⣴⢤⣤⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⠿⠿⠟⠛⠛⠻⠿⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⣿⣿⡿⢿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠺⠛⠯⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠚⣿⣿⣟⣀⣀⣴⣆⣄⣀⢀⣀⠀⠀⠀⠀⠀⠄⢄⣀⣠⡦⠦⠤⡿⠛⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠡⠄⠀⠀⠈⠀⠀⠸⣯⣿⣿⣿⣿⣿⡿⠛⢿⡟⠛⠛⠛⠿⠀⠀⠀⠀⠀⢾⢿⣿⣿⣿⣷⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⢸⣿⠿⠟⠙⠉⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢀⡄⢀⡀⠈⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣼⠀⣿⣿⣿⣷⡉⠻⠧⣤⣀⠻⣿⣿⡙⠛⠿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢻⡄⠹⣿⣿⣿⣶⡶⠠⠤⣤⣁⡈⠛⠻⠶⣶⣤⡤⢄⣀⡂⢤⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠻⣶⣄⣈⣩⣴⠟⢀⣀⣄⣈⡀⠈⠐⠂⠤⢀⡀⠀⠀⠛⠁⠀⠀⠀⢀⣴⣮⡶⠊⠀⠀⠀⢀⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣴⡾⠞⠛⠻⣿⣿⣅⠀⠀⠀⠀⠑⠀⠙⢊⠀⠀⠀⠀⣿⣷⡟⡇⠁⠀⠀⣰⣏⣿
⠀⠀⠀⠀⡠⠤⠀⣀⠀⠀⠀⢸⣿⣁⠀⣸⢀⡇⡠⠀⠀⠀⠀⢀⣾⣏⠀⠀⢀⣤⣄⠻⣿⣦⡀⠀⠀⠀⠈⠢⡘⢄⠀⠀⠈⠿⠟⡁⢃⠀⠀⠀⢿⡿⡣
⠀⠀⠀⣸⣿⣿⣷⣆⠱⡀⠀⠀⣿⣯⣠⢏⠼⠰⢡⣤⡀⠀⠀⢨⣿⣿⠀⠀⣼⣿⣿⣷⡙⢿⣷⣦⣀⣀⡀⠀⠰⣄⠙⠒⠒⠂⠀⠀⠀⠢⠄⠀⠠⠐⠁
⠀⠀⠀⣿⣼⡿⣱⣿⡇⠙⠂⠀⢛⣋⣁⣩⣤⣶⣶⠲⠀⠀⠀⢸⣿⣿⣧⣄⣻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣤⣠⣿
⠀⠀⠀⣿⡈⢰⣿⡋⠀⠀⢠⡴⢿⣿⣿⣿⡿⠙⠣⠁⠀⠀⠀⢸⣿⣿⣿⣿⣯⡿⠟⢛⣛⣛⡻⣿⣿⠹⡛⠉⠙⠁
⠀⠀⠀⢿⢿⣦⣻⣿⡆⢰⠃⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⡾⠋⢀⣤⠟⣻⡿⠓⣛⣉⣐⠂⢄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠘⢷⣍⣍⣉⣴⠏⠀⠀⠀⠈⣿⣞⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⠁⢀⡟⠁⡼⠃⣠⣿⣿⣿⣿⣿⣄⢢
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢹⢰⡈⠀⢸⡇⢸⡇⢰⣏⣙⠛⠻⠿⠟⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡆⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢧⠀⠀⡇⢹⡀⢸⣿⣿⣿⣿⣿⣿⡿⢿⠟⠛⠳⠄⣿⣿⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⢷⡀⠀⠸⣧⠀⠻⣿⣿⣿⣿⠟⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⠳⣤⡀⠙⢷⣄⣀⣈⣉⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠈⠙⠳⢦⣬⣽⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠶⠴⠶⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠄⠀⠔⣊⣥⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠰⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⢏⣥⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣵⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠉⠉⠉⠻⣿⣿⣿⣿⣿⢀⣤⣶⣶⣶⣿⣿⣎⢿⣿⡿⠛⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣴⣶⣾⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣴⣶⣶⣦⣄⣹⣿⣿⣿⡿⠛⠉⠙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣹⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣣⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣍⠛⠻⠿⠿⠿⠛⠋⠀⢰⣿⣿⣼⣿⣿⠟⠋⠁⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⣿⠃⢀⣀⣤⣀⡀⠀⠀⠀⢹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⡀⠀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⠿⠟⠋⠀⠀⠀⠙⠻⠿⣿⣿⠿⠟⠉




⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⣿⡟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢣⢸⢇⠎⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣿⣿⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣯⣽⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧⣟⡿⡾⢾⠶⣟⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡾⢽⣭⣟⣹⡏⢹⣅⡼⡆⠀⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣏⣹⠓⡿⢤⣯⡼⣯⡽⢧⡤⢷⢀⡴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢧⠀⠀⣸⠦⣯⣹⣿⣾⡟⠚⣟⠶⢻⠒⠛⡏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣄⣟⢺⠧⢼⡇⠙⣏⢛⣏⠓⣻⡓⢚⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⣍⣽⠓⢺⡇⠀⢹⣏⣿⣙⣹⣏⣉⣼⢰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢦⣻⡀⢼⠢⣿⣝⣽⠇⠀⠈⡯⢾⣍⣉⣿⣭⢼⣾⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠻⡇⣾⣉⡿⢤⡟⠀⠀⠀⡷⢺⡯⡭⢿⠦⠾⡿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡷⢭⣽⣾⠁⠀⠀⢰⣟⣹⡗⠶⣿⡓⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡖⢿⡏⠀⠀⠀⢸⣧⣤⣏⣋⣹⣿⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⢿⣹⠇⠀⠀⠀⢸⠶⠾⣧⣉⡽⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢿⠀⠀⠀⠀⢸⣓⢚⣷⠏⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠸⡇⠀⠀⠀⠸⣯⡟⠁⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢻⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢳⣄⠀⠀⠘⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣷⣤⣼⡧⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸

⣿⠋⠙⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⡿⡏⡌









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣩⣩⣭⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣶⣶⣾⣿⣷⡴⠛⠉⠁⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⠻⠿⣿⡀⣴⣶⣤⣤⣀⣠⣔⣃⡀
⠀⠀⣠⠖⠒⢂⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⣿⣯⣤⣾⣿⣿⣾⣿⣷⣿⡿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⢧⡀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⡞⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠦⢿⣿⣿⠟⠉⠉⠻⣿⣿⣿⣶⣶⣿⣿⣤⣬⣿⡤⠖⠒⢲
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠿⣤⣾⣿⣶⠏⢻⣿⡿⢿⣿⣿⣿⣿⣿⣇⡤⠖⠋
⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠙⠛⣫⣿⣤⣵⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣈⣻⣟⠋⠀⠀⢻⣧⡀⠀⢀⣴⡿⣻⠏
⠀⠀⠀⠈⣿⣿⣿⣿⡿⢟⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣄⠤⠤⡀⠈⠉⠉⢉⣉⣀⣼⠇⠀⠀⠀⢻⣿⣿⣿⠏⠀⠻⠤⠤
⠀⠀⠀⠀⢘⠛⠿⢋⡀⠘⣶⣉⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠳⢤⣿⡉⠑⣬⠁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣶⣿⣿⣷⣶⣤⣤⣄⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠤⣌⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠿⠿⠿⠿⠟⠋⠁⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣩⣽⣿⣯⣶⣾⣿⣟⣍⣻⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⡤⠤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠻⠿⠋⣿⣿⠟⠛⠻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⣠⠴⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣼⣿⣷⣿⣿⣦⠟⠁
⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠋⠁⠀⣾⣿⣶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠛⠁⠙⠻⠛⠁
⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⣻⣄⣴⠉⢸⣿⣿⣿⣿⣿⣿⣿⠛⠛⣦⠀⣤⣄⣀⣀⣤⣤⣶⣿⡇
⠀⣴⠞⠉⠉⢻⣛⣿⣿⣿⣿⣿⣯⣩⣿⣶⣽⣿⣿⠿⣿⣁⣤⠾⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣤⣤⣤⣄⣀
⠘⣧⣤⡤⠖⠒⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣠⠤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⡿⢿⡏⣠⣴⣾⣿⣷⠈⠛⠛⣻⡟⠁⠉⠉⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣞⣥⠖⢿⠿⣿⠿⠉⣿⣷⣶⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠔⠋⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⠗⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⡠⣠⣶⢰⣦⢂⠀⠀⢀⠠⣄⠐⣰⣦⡀⠀⠀⠀⠀⣠⢤⣠⠖⣲⡄⠀⠀⠀⠀⡔⣲⡆⣲⣦
⢧⣈⡥⠑⠤⠜⠀⠀⢌⠛⡃⠠⣙⢋⡇⠀⠀⠀⢰⣃⣺⣃⣈⣿⣸⠄⠀⠀⠀⡇⠛⢡⣌⣸⠇⠀⠀⠀⣠⡄⣰
⠀⠀⣔⣒⡀⠀⠀⠀⠀⠉⠀⠀⠈⢉⡀⣠⠀⢀⣩⣤⣤⣤⠶⠦⠤⠤⠄⠀⠀⠙⠶⢋⣈⣩⠔⠒⠀⠰⠍⠀⣙
⠀⠘⢿⣿⠇⠀⠀⠀⠐⠔⣂⡭⠥⠤⠀⠀⠀⠀⠨⠭⠕⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠀⠀⢠⠤⠤⠄

⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣔⣴⠄⣾⡷⠀⠀⠀⠀⠀⠀⠀⣤⡠⡀
⠐⢾⣬⠇⠀⢰⣐⡇⠀⠀⠀⠀⣾⠰⠟⡠⠿⢊⡆⠀⠀⠀⠀⠀⠸⣆⣡⠂⢘⣲⠁⠀⠀⠀⠀⠀⠶⣿⠇⢸⠄
⠀⡐⢂⣂⠶⠴⠀⠀⠀⠀⠀⠠⢙⣓⣚⡉⠒⣚⣁⡤⠖⠀⠀⠀⠀⢈⠔⢈⠤⠀⠀⠀⠀⠀⠀⠈⠢⠤⠴⠋⣠
⠀⠪⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠈⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄
⢀⣠⡄⣼⡗⡀⠀⠀⠀⠀⡜⢡⠔⣲⣝⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀⡾⢋⠆⠀⠀⠀⠀⠀⡜⣤⣀⢀⣠⡎
⢸⣙⡱⢤⣴⠃⠀⠀⠀⠀⡜⠟⡠⡙⢋⡆⠀⠀⠀⠀⠀⠀⠈⠉⠰⠤⠞⠀⠀⠀⠀⠀⠀⠳⠽⠋⠯⣫⠇
⠀⠉⣀⣀⣄⠀⠀⠀⠀⠀⠈⠉⢀⣈⣉⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⣀⣠⠄⠀⠀⠀⠀⠀⣰⣄⣆⡄
⠀⠀⢿⢛⢻⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠈⡻⢟⠁⠀⠀⠀⠀⠀⠀⠘⠹⠻⠻⠇
⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣮⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣷⣾⢡⡶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠶⡟⣻⣦⣿⣧⣙⣲⣯⠶⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠐⠦⣼⣸⢿⣵⠊⠁⠀⠈⣙⢯⣔⡃⠄⠀⠀⠀⠀⣷⢀⡟⠀⡀
⠀⠀⠀⢀⡀⠈⢷⣠⡟⠀⠀⢸⡛⣦⢼⡿⢋⡀⠀⠀⠀⢊⡥⢄⢻⡿⠗⠀⠀⠠⣀⣸⣾⡶⠋
⠀⠀⠀⠀⠉⢓⣬⡟⢻⡄⠀⠐⠒⣨⡿⠁⢾⣿⠀⠀⠀⡋⣶⠀⠘⣷⠀⠀⠀⠀⠈⣿⡼⠋⠛⠒
⠀⠀⠀⠀⠛⠛⢉⡿⠛⢷⢦⡀⠀⣿⡇⠀⠠⠤⠂⠒⠀⠘⠒⠁⠈⣿⡆⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠣⡱⣄⠹⡅⡄⠀⠀⣶⡟⠿⣷⡄⠀⣼⠿⠁⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠳⣝⢌⡲⣜⡛⠾⠟⢛⣠⡾⢋⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠘⠋⠹⣿⠮⠵⡶⢾⣁⣴⠏⢉⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠘⢧⣼⠁⠀⠙⠃⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⣩⢿⣖⠒⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⣴⠏⠸⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠢⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠸⠿⠶⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣏⡁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⠀⠀⡀⠀⢀⡿⡆⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠸⣷⣄⠀⢳⣰⡇⢠⣸⠁⣷⠇⢸⠁⣤⣴⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢦⡀⠢⡈⠲⣿⡙⢶⡀⢻⣇⠀⡏⠀⠙⠀⣿⠀⠁⣾⠞⣰⢁⣤⢔⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠢⣌⡃⠙⢦⡈⡦⠈⢅⡄⠀⢧⠉⢸⠀⠀⡤⠀⠀⢰⠆⠏⢀⠀⠚⠁⣽⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣥⣀⣬⠿⠶⠱⣦⠙⠆⠀⠉⠀⠠⠄⠈⠀⠇⠀⠸⠀⠈⡠⠀⠋⢠⠀⢘⡿⠋⣀⠄
⠀⠀⠀⠀⢤⣀⠀⠀⠒⠮⣿⡌⢍⠁⠠⡀⠈⠀⢢⡀⠁⠀⠀⠄⠀⢀⠀⠂⠀⡀⢀⠁⢠⠀⠁⠀⠠⠴⠯⠗⣶⠃
⠀⠀⠀⠀⠀⠈⠙⠳⠦⠍⠒⠦⣄⠁⠀⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣷⡀⠀⣾⡴⠀⠀⠀⠀⠀⠬⣭⣤⠄
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⠀⠠⡀⠀⠀⠙⠂⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣄⣿⠳⠀⠻⠁⠀⠀⠀⠀⠐⢻⠯
⠀⠀⠀⣤⣤⣽⠿⠧⣤⠀⠒⠚⠛⠂⠈⠁⣀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣬⣆⠈⠛⠀⠀⢀⣄⠀⠀⢠⣀⢸⡇
⠀⠀⠀⠀⢀⣀⣠⡤⠀⢉⠿⠒⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⠀⠀⠋⠥⡀⠀⠀⠪⢸⡇
⠀⠀⠀⠀⠀⠰⠶⣤⣤⡄⠐⣋⡀⠀⡴⠀⠠⠀⠀⠀⠒⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠰⠇⡇⠀⢞⢣⢺⠇
⠀⠀⠀⠀⠀⠐⠋⠉⠐⠚⠉⡉⠁⠊⠀⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⡞⠀⠀⢀⣀⣀⡀⠈⠒⠃⢀⠬⠛⠛⠛⠻⢶⡞⢻⣦
⠀⠀⠀⠀⠒⠚⣋⣴⡾⠀⠚⠇⠀⠚⠀⡄⠀⠆⠀⠀⠂⠀⠀⠀⠈⠃⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠤⠚⢩⣟⣥⡶⢀⣠⣀⣄⡀⡁⠰⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⣀⣀⠀⠀⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠠⠟⠋⢰⡷⠛⢛⠁⠀⠉⠀⠀⣄⣀⣀⣀⡀⣶⠀⠀⠀⠀⠀⠉⠉⠽⣦⣠⣶⣭⡽⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⣤⣤⡼⠶⠏⠈⠉⠉⠁⠙⠳⠶⠶⢶⣦⣀⣠⣤⣾⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⠰⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠠⢆⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⠀⠀⠀⠁⠀⠀⣅⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⣤⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⢠⠀⡠⠜⡿⢯⠂⡃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⣒⣺⠤⠗⢃⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠀⠢⠀⣳⢀⢐⣽⣿⣷⣾⣿⣿⣿⣿⠈⠀⠀⠀⠀⠑⢀⣐⣀⠀⢱⠄⠊⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡄⢻⣧⠀⣷⡀⢂⡄⢀⣍⣀⣾⣿⣿⣿⠟⠁⢚⠻⢇⠀⠀⠀⠀⠀⡈⠒⠒⣶⣟⠉⢳⠐⠻⢥⡂⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⡟⠁⠀⣶⣿⣿⣿⣿⠛⠛⠓⠺⠶⣼⣇⠈⠀⠀⠀⠀⡀⢠⠀⠀⡟⢁⠀⢀⠀⠀⠀⢻⠏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⢸⠓⠢⢄⡀⠉⠛⠦⣄⠀⠀⠀⠈⠀⠀⠃⢸⠀⠘⠀⣠⠄⠸⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⣿⣿⣧⣀⢠⡏⠀⠀⠀⡽⠑⠢⣄⡈⠂⠀⠀⠀⡄⠀⠀⠈⠀⢆⡴⠃⢠⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠩⡹⢟⠠⢈⣉⠀⠀⠀⢰⠇⠀⠀⡇⠉⡁⠀⢣⠀⡇⠀⠀⠀⢠⡟⠁⡰⠻⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⢠⠁⠀⠈⠒⠏⠲⢄⡠⣿⠀⠀⠀⡇⠀⠃⠀⠀⠳⢸⣀⠠⢦⠎⠀⡔⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠉⡇⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⡹⠛⠉⣲⠊⠈⢢⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠋⠀⠀⢰⢇⠀⠀⠀⡇⠀⠃⠄⡀⠀⢠⠃⠀⠐⠷⠆⢀⠀⠉⠐⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢁⠀⠂⣄⣄⢨⠶⠬⠆⠈⠓⠐⠒⠒⠒⠈⠈⠀⠀⠀⠁



⣷⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⣠⠶⠛⠉⠉⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⡀⠀⠀⣀⣀⣀⠀⠘⣷⠞⠁⣀⣀⠀⠀⣀⣀⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠟⢻⣿⣷⣾⣿⣿⣿⣧⠀⠸⣇⣾⢋⣿⣿⣾⣿⣿⣿⡆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠀⢀⣀⣀⡀⠀⠀⠀⢻⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⡇⠘⠻⣿⣿⣿⣿⡿⠋⠀⠀⢀⡿⠀⠀⠀⠴⠞⢻⠷⣦
⠀⠰⠟⣿⡉⠉⠁⠀⠀⠈⢧⡀⠀⠀⠈⠛⠿⣿⣿⠿⠛⠁⠀⢀⡾⣧⡀⠀⠀⠉⠉⠁⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣼⠀⠈
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠈⠙⠶⣤⣄⣀⣀⣠⣤⠞⠋⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡛⠛⠛⠛⢛⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⣴⠃⢀⡴⢖⣶
⠀⠀⠀⠀⠀⠀⣿⡀⢸⡅⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤
⠀⠀⠀⠀⢀⣠⣬⣿⣦⣝⣶⣦⣴⣶⣾⣿⣿⣶⣾⣿⣿⣿⣯⣤⣤⣤⣀⣀
⢀⠀⢀⡴⢋⣴⣶⣿⣿⣿⠿⠛⠉⠁⢠⡿⠋⠀⠀⠀⠈⠻⣧⠀⠈⠉⠉⠛⠛⠷⢶⣦⣤⣀⡀
⠙⠶⠋⣰⡿⣻⣿⣿⠟⠁⠀⠀⠀⠀⣿⡇⣾⡆⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⡀
⣀⣀⣴⠟⣱⢿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⣠⠼⠁⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣤⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢰⣿⠏⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠰⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠃
⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠉⠉⠉⢻⡿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠻⣿⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⠶⠾⠛⠋⠻⣦⣀⠀⠀⠀⣠⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⠉⠉⠛⢿⣦⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡄⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢈⣿⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠻⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡠⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⡐⡱⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⢴⣦⣈⠏⡴⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⢰⣿⠁⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠹⢿⣦⡀⠀⠀⠀⣠⣿⠋⠊
⠀⠀⠀⣸⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⣷⣶⣿⡿⣷⣷⣤⡄
⠀⠀⠀⣿⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣟⣾⣷⣯⣭⡶
⠀⠀⢠⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢠⢊⠟⠿⣾⠏⠉
⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠁
⠀⠀⢸⣿⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠿
⠀⣀⣨⡍⠉⠉⣿⠋⠉⠉⠉⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠁
⠀⠻⣿⣯⣤⣤⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⢉⣡⣤⣤⡤⠤⠤⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢰⡏⠁⠀⡄⠀⢀⣀⡄⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⣤⣀⠀⠀⢰⠀⠈⣻⡆
⣀⣀⣀⣈⣻⣶⣶⣷⣚⣋⣉⣷⣶⣛⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣏⣙⣛⣷⣾⣶⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠾⠀⠀⠀⣀⡀
⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠉⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠰⠀⠀⠀⠀⠆⡀⠀⠀⠄⠀⠠⢶⢶⣤⣀⣠⣀⣠⣤⡶⠟⢻⠉⠀⠃⠀⠀⣀⠙⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠘
⠰⠀⠸⠇⠀⡇⠛⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠩⡁⠈⠁⢀⠌⠀⠀⠇⠀⠀⠿⢠⠙⠁⠀⠌⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠈
⠀⠑⠀⠀⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠒⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⢒⠀⠀⠀⢠⠴⠒⠀⠀⠐⠢
⠀⢀⣠⠾⠛⢁⡐⠳⣄⡀⠀⠀⢀⣤⣤⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⠂⠀⠀⠐⠂
⠐⡏⠁⣤⠄⠨⠄⡤⠀⠈⡃⠀⠀⠀⠀⠉⢻⡆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠
⠀⢳⠀⠀⠀⢠⡄⠀⠀⢠⠁⠀⠀⠖⠒⠬⣆⠀⠣⠘⠃⠀⠄⠀⠀⠡⡀⠀⣠⡄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠈⠁
⠀⠀⠑⠄⠀⠃⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣀
⠀⠀⠀⠐⠶⠐⠁⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠴⠂⡘⠛⠦⣄⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠀⠀⠀⠠⢡⣶⢦⡄⠁⣴⣶⠆⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠱⠆⠀⠀⡉
⠀⠐⠀⠀⠠⠇⠀⠀⠐⠖⠀⠀⠀⢀⠤⣿⡷⠀⡄⠭⢿⠟⠀⠀⠀⠆⠀⠒⢀⡆⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⣀
⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠄⡀⠀⠙⢛⡢⠀⠀⠀⢘⠩⠅⢀⠀⠈⠍⢃⠀⠀⠀⠀⠨⠀⠠⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠟⠛⠷⠆⠀⠀⢄⣀⣒⡂⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⢀⣤⢶⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣀
⠃⠀⠐⠛⠀⠰⠀⠘⠛⠉⣀⠂⠀⢠⠀⢉⡀⠀⣣⣼⡁⣰⡇⠀⠘⡀⠀⠈⠛⠸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠈⠣⣙⣋⠼⠓⠉⠉⠚⠀⠀⠀⠻⢄⢀⡴⠋⠲⠤⠚⠁⠀⠀⠀⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢚⠉⢑⠰⠻⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠉⠁⠒⠒⠀⠤⠄⠠⣧⠬⠄⠚⡂⡤⢏⡗⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠄⠐⠂⠒⣿⢸⠀⠀⠠⠒⢧⡟⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣍⢠⠱⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢈⠉⠢⠀⠀⡊⠀⠀⢻⠀⠀⢀⠄⠀⠀⡌⠁⢱⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⣀⠙⣑⠀⣇⠄⢌⠁⡟⠀⠁⠉⢋⡠⠠⠀⢱⢐⡑⢁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠴⠀⠀⠯⢔⠖⠉⠀⠀⠀⠀⠎⢐⣓⠤⠎⠈⠐⡂⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠔⠹⢀⢀⢠⡎⠀⠀⠀⠀⠀⠀⡄⠑⢄⢑⠀⠀⠘⠈⠢⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠣⡀⠀⠀⠀⢀⠔⠁⡘⠀⢫⠃⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣉⣔⠉⢁⡀⢠⠃⡰⠃⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠊⠀⠀⠘⠓⠁⠈⡡⠊⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡑⡈⠢⠔⠁⢰⠀⠀⡔⠁⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⠓⢄⣀⡘⢀⡊⣀⠴⠶⣒⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⠣⠘⠁⠁⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡀⠀⠀⠀⡩⣀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠠⡤⢷
⠀⠀⠀⠀⠀⠀⠀⠪⡑⢄⣈⣦⡀⡸⠀⠀⠑⢤⣁⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⢘⠻⣅⠀⠀⠀⠈⠀⠉⠒⠦⡤⠌⠡⠤⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⡦⡀⠀⠦⢄⠀⢀⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢕⢝⣶⡙⠀⠉⡟⠛⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠛⠀⠀⠀⢱⣀⣀⣀⣀⣀⣐⣦⣤⣤⣤⠠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠙⠊⠉⠋⠉⠉⠉⠋⠛⠋⠉⠀⠈⠋⠉⠉⠭⠟⠓⠒⠓⠒⠘⠓⠢⠝⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣿
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡿
⠀⡡⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⠀⠇⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⢀⣀⠀⠠⡀⢄
⠀⠀⢀⠐⣏⠢⡀⣠⠒⡦⠀⠀⠀⠀⠀⣠⠴⠖⠳⠀⠀⠶⠿⢥⡀⠀⠀⠀⠀⢀⣀⣀⡿⠸⡴⢋⠜⠀⠀⢱
⠀⠀⠣⣉⠺⠖⣱⠇⣜⠁⠀⠀⠀⠀⣼⠳⣎⠀⠀⠀⠀⠀⠀⢦⡙⣦⠀⠀⠀⠾⠔⢢⠙⢦⡀⠛⣊⡵⠀⠀⠇
⠀⠀⣔⡂⡛⠰⠃⠀⣸⠀⠀⠀⠀⠀⡏⢀⡏⠢⣀⡀⠀⢀⣠⠞⡇⠘⡆⠀⠀⠀⠀⢸⡀⠀⠃⣈⣓⡄⠀⠸
⠀⠀⠀⣔⠡⠦⣤⠤⡉⢦⡀⠀⠀⡴⠧⠀⣧⠀⠈⠉⠉⠉⠀⠀⣷⠀⠿⢦⠀⠀⣠⠎⣰⠛⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⡀⠻⡖⠀⣿⣿⣦⣤⣤⣤⣤⣶⣿⠀⢶⠞⢀⡔⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢤⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡴⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡇⠀⠀⢿⠻⠿⣿⣿⣿⡿⠁⠀⢸⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠈⠣⣄⣀⣤⠞⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠳⢤⣀⣀⣀⡴⠂⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠑⠲⠤⢬⣭⣥⠤⠴⠒⠋⢹
⠀⠀⠀⠀⠀⠀⡠⢂⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⢠⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡈⠑⢦
⠀⠀⠀⠀⠀⠀⡎⠀⢸⢱⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣤⡄⠱⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⡞⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠳⣄⠀⠘⣳⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡶⡃⠀⣠⠞⠉⠈⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠳⠴⢃⠏⠀⠈⠉⠉⠉⠉⠁⠀⠀⠳⣝⠊⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣤⢤⠴⢶⠶⠤⣤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡚⠿⢧⡘⠈⠈⣷⣶⣇⠈⠙⠨⣇⣈⣿⠻⢦⣄⠀⢀⡴⠚⣉⣥⣤⠀⣤⣉⡙⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡼⣗⠀⠋⠸⠃⣿⠒⠚⠛⠛⡏⠹⢶⡶⠽⠽⠷⢤⠔⠋⣷⠏⣴⡏⠁⠀⣿⢭⡟⠈⢙⣦⡈⢷⡞⣀
⠀⠀⠀⠀⠀⠀⡎⠀⠉⠳⠦⠤⠞⠁⠀⠀⠀⠀⠃⡄⢈⠂⠀⠰⠂⠒⠒⢶⡇⡞⠻⢷⡀⠀⣿⢸⡇⢀⡄⡀⢳⠈⣷⣥⡀
⠀⠀⠀⠀⣰⣾⣷⣤⡀⠀⡠⠄⠀⠀⠒⠲⢄⡀⠀⠀⠀⠀⠀⢴⠀⠀⠀⢸⠙⣧⡀⣠⠀⠀⣿⢹⡇⢻⣄⣠⣾⡇⢸⢀⡀
⠀⠀⠀⢀⣻⣛⠛⣤⠁⠀⢠⣶⡏⣤⡌⣿⣷⡦⠀⠀⢠⠀⠒⢂⡛⠃⠀⠘⣇⢣⠈⠁⠀⣰⡿⠴⣧⡈⠙⠛⡻⠀⣾⡈
⠀⠀⠀⠈⣿⠬⠃⠀⠀⠀⠈⠛⠛⠈⠐⠛⠉⢀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠘⢆⠳⣤⣾⢋⣤⡀⣬⡙⢷⡔⢁⣼⠉⠁⡤
⠀⠀⠀⠀⠈⠳⢤⣄⣈⡇⠀⠀⠀⣠⠄⠀⠀⡁⠀⢄⡄⢤⡑⠀⠐⠲⣄⢀⡆⠈⠳⢤⣉⡉⠁⠀⠀⢉⣡⣴⡋⠙⢃⣼⠃
⠀⠀⣶⣶⣶⣶⣶⣿⡏⠀⠀⠀⣾⠁⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠐⡴⣏⢽⡻⣟⣛⣍⣴⢬⣥⠖⢫⠏
⠀⠀⣿⠀⠀⠉⠛⠻⢷⠀⠀⠀⢻⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠀⠶⢿⡟⠛⠀⢠⣌⠩⢰⣍⣽⡀⠁⡹⣀⣙⣴⠏
⠀⠀⣿⣤⣤⣤⣤⣤⣾⣧⡀⠀⠀⠁⠀⠀⣤⣶⡀⢹⣿⣠⣶⣤⢀⣴⣿⣷⣠⣤⣿⣋⠐⢋⡆⠐⢁⢔⡅⠋⢉⢖⣤⡀
⠀⠀⣿⠛⠛⠛⠛⠋⢟⣿⣿⣶⣤⣀⠀⠀⠿⣿⠛⢻⣿⢸⣿⢏⣼⢻⣿⣿⣻⣭⡏⣿⣏⢏⡁⡄⡩⢨⢰⢀⢎⡞⠿⣿⣦
⠀⠀⣿⠀⣀⣤⣴⣾⣿⠿⠋⠁⠀⢸⣿⢄⠀⢨⠶⡌⢿⣼⣿⣿⣿⣿⣽⣿⠋⠿⢶⣿⠋⣢⠁⢀⣥⠌⢰⣯⡟⠘⢀⣥⣼⣷⠄
⠀⠀⠿⠿⠿⠛⠛⠛⠚⠒⠒⠒⣒⣚⣛⣚⣓⣲⣤⣴⠔⣙⣿⣿⣿⣿⣯⣟⣶⣦⡜⣀⣠⡿⠀⢁⣀⢀⣀⡉⠀⢠⣿⠋⢀⣟⡠⠜⣷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣭⣭⢛⣯⡼⣿⣿⣿⡿⠆⠤⣿⠃⢸⠀⡏⠉⢀⠖⡉⠀⠀⠀⢹⠀⠘⣧⣤⣾⠁⠀⠀⣋⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢛⣺⢿⣙⡻⠋⠘⡹⡵⠋⡏⢣⣤⢴⣯⣀⠙⠀⡇⠀⣾⠸⢄⣀⣀⠴⠃⣠⠞⣹⣿⣃⠤⢂⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⡒⣶⡝⣆⠠⡄⢹⡆⣥⣾⣿⡏⣿⣯⢦⠀⡇⠀⠹⣄⠀⠀⢀⡤⠋⠁⢠⣿⢿⠁⠀⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⣿⣿⣼⠀⠁⠘⠃⢻⣿⣿⡧⢶⣾⡘⢸⡇⠐⢀⠈⠉⠉⠁⠀⣀⡴⢻⣿⠈⣧⡶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠻⢿⣿⣿⠷⠃⠀⠀⠀⠀⠈⠛⠯⣭⡽⠗⠁⢸⡇⠀⡀⠁⠂⠐⠒⠋⠁⠀⠈⣿⡊⠹⡄⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠁⠀⠈⠒⠤⠤⢤⠤⠤⠒⠉⠘⢷⣄⣰⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠈⣹⠋⠉

⠀⣠⣤⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣄
⢰⠟⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠀⠀⢽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠀⠀⠹⣿⣷
⣸⣀⣴⣶⣰⣶⣄⣼⡀⠀⢀⣤⣤⣦⣤⣄⡀⠀⢸⣇⣀⣀⡀⣰⣿⣿⣿⠀⠀⣠⣤⣶⣶⣦⣤⡀⠀⢾⣀⣀⣀⢀⣠⣧⣿
⢻⠀⠀⠈⠀⠀⠀⢸⠁⣰⠟⠁⠀⠀⠉⣻⣿⡀⠨⡏⠈⠉⠀⣿⠈⢹⣿⠃⢰⠋⠁⠀⠀⠸⣿⣷⠀⠐⠀⠈⠉⢸⡉⠹⢿
⠐⡄⢀⣙⣟⡀⠀⡇⠀⣿⣀⣤⡄⢀⣦⣾⣿⡇⠀⡟⡖⠀⠀⣾⣿⣿⡟⠀⣏⣀⣀⠀⢀⣰⣿⣿⠀⠀⠀⢀⣀⣹⣿⣆⡟
⢀⣿⣙⠻⠯⠋⣼⣧⠀⣿⠀⠙⠁⢸⠉⠛⣿⡇⠀⢸⠀⠉⠉⠽⣿⣿⣇⠀⢻⠉⠉⠉⢹⡉⠛⣿⡇⠀⣴⠀⠉⠀⢻⣿⣿
⠛⠻⢻⣿⣿⡿⢻⡟⡇⢨⠀⠀⠀⢾⣷⣸⣿⠇⡖⢻⠀⠠⢤⣴⠟⡿⡿⠂⢿⣱⣁⠀⢾⣿⡞⣿⠁⢰⣿⠀⠐⢾⣿⣿⣿
⠀⠀⢿⠛⠛⠀⠘⠀⠀⢈⣄⠐⠚⠹⣿⣿⣏⠀⠀⠈⠀⠀⠘⠃⢀⠀⠀⠀⡠⣧⡈⠙⠿⣿⣼⣧⡀⠚⣋⣄⠀⠈⢸⣯
⠀⠀⠈⠁⠀⠀⠀⠠⠤⢻⠆⠳⣤⣴⣿⣿⡿⢧⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠙⢶⣶⣿⣿⣿⡟⠀⠛⠛⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⢿⣿⢿⣷⣿⠧⠄⠁⠀⠀⠀⠀⠀⠀⠀⠄⠹⡆⠈⢙⣟⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠠⡢⠀⠠⠀⢠⡊⠑⡄⠠⡀⠀⠀⢀⡐⠢⡄⠀⠀⠀⡤⠤⠄⠀⠤⠀⢀⠀⠓⢒⠀⠒⠀⠀⠠⠀⢀⠾⠶⣭⡾⠉⣯⠓⢢⣄
⠀⠀⠀⠠⠊⡱⠊⠁⣀⣠⡑⢢⡔⢠⠀⠰⢈⠐⠁⠀⠀⠀⢗⢭⡉⠀⠛⠀⢅⣤⢀⡄⡁⠀⠈⡁⠀⠀⠿⢶⠦⡂⢩⢀⠁⡠⠋⠂⠂
⠀⠀⠀⡊⢙⠁⠀⠏⢼⡧⣿⠀⢡⠴⡀⠀⠀⠀⠠⠈⢢⠀⢸⢺⠣⠁⠆⠀⡙⠇⠹⠆⠅⠀⠀⠇⠀⣸⢶⠦⠀⠈⣤⠮⡼⠐⣂⡷⠁
⠀⠀⠀⡌⠉⡀⠀⢌⠉⠙⠡⠀⡬⢤⠃⠀⢄⡀⠈⠃⠁⠀⠀⣌⣂⣠⠀⠀⡅⠀⠈⢀⠀⠀⢀⠀⠀⠰⢰⣀⣀⡠⢧⠀⠈⠟⠉
⠀⠀⠀⠈⢊⠑⠦⣀⣈⣁⡠⠚⡤⠈⠀⢤⡘⠮⠂⠀⠀⠀⡀⡀⠀⠠⡢⠀⠀⠀⡄⢄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠃⠀⠨⠀⠀⣼⠃
⠀⠀⠀⠀⣤⣍⡃⠤⠧⠀⠕⡂⠁⡄⠀⠀⠀⠀⠀⢀⡀⠢⡔⠊⠀⠀⠀⣀⠀⠀⠁⠂⠀⠐⢀⠴⠃⠘⢤⠀⡂⠀⠀⠆⠀⠀⠀⠨⠜
⠀⠀⠀⣠⣬⡝⠓⠀⠒⢠⡖⣀⠔⢁⠄⢄⠀⠀⠀⠈⠷⠀⣍⠄⠀⠀⠀⠈⠁⠀⠀⠀⢀⠼⢁⡴⠆⠲⢦⠰⠦⡀⠀⢄⢀⡐
⠀⠀⠐⠛⠊⢦⠠⡄⠘⠁⠀⠀⠀⡬⠰⠠⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⠑⠢⠀⠩⢠⠄⠊⠀⠀⢀⣀⠓⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠈⢀⠇⠀⠀⠀⠘⠸⣰⢋⠆⢂⠀⠀⠀⣤⢤⣀⡄⠀⠠⢠⢤⡔⣌⠂⡀⢠⠑⠤⠬⠧⠴⠁⡇⠀⠀⠀⠃⠈⠒⠀⡘⠋
⠀⠀⠀⣀⠄⠀⠠⠊⠀⠐⠅⠀⠠⢀⣭⠄⢦⣬⠀⠀⠀⠷⠘⠧⠁⠀⠀⠀⠘⠃⠉⠀⠃⠀⠀⠀⠑⢊⠀⡀⡐⠈⠉⠐⡀⡀⠈⠂⠂⠃
⠀⠀⠈⠀⠂⠀⠀⢀⠠⠠⡀⠀⠀⠉⠻⠀⢸⠁⠀⢀⡊⠀⠄⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠋⠀⠀⠈⠄
⠀⠀⠀⠀⢀⡔⠪⢙⠀⠅⠨⠢⠀⠀⡆⠀⠰⠀⠀⠈⠉⠀⠀⠀⢀⠴⠘⠃⣛⠰⣀⠀⠀⠈⠀⠀⡡⣀⠀⠀⠈⠔⠐⢌⠀⠀⢀⠠⠁
⠀⠀⠀⠀⣥⠮⢙⣭⣒⡰⢅⣂⡥⠀⠀⠉⠀⠀⠔⠆⠀⠀⠀⠀⠬⠀⢩⣿⢸⣷⢰⠳⣆⠀⢠⠁⠀⠀⠀⢵⢰⡟⠀⡀⢱⠅⠀⠀⠀⢡
⠀⠀⠀⢄⠈⢻⠏⢁⠿⠷⠦⠣⠂⠀⠠⡄⠤⣊⣀⢰⠤⢠⠄⠀⢘⡀⠌⠩⠈⠅⠰⠔⠃⠀⠀⠀⢀⠀⠠⠘⠢⡁⠀⡀⠘⠠⠀⢀⠀⠈
⠀⠀⠀⠁⢀⠂⠀⠆⠀⠀⢀⢀⡀⠄⠀⠈⠂⠡⠿⡾⠗⠁⠀⠀⠠⠃⠃⠈⠀⠁⠣⠀⠀⣄⠀⠀⠊⠀⠀⠀⠀⠁⠉⠐⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠨⡀⡰⠀⠀⠀⠀⠂⠅⠁⠀⢠⡁⠄⠰⠄⣘⡀⠀⠀⠀⠇⠒⠒⠒⠒⠂⠀⠜⠒⠆⠀⠀⠄⠀⠠⡆⠀⠀⠀⠦⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠉⣶⢄⢀⠀⡿⡇⠐⠀⠀⠀⣸⡄⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡀⢃⣯⣆⢸⣒⡇⠐⡒⣶⣿⠟⢀⣠⡶⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡈⠙⢯⣿⣼⣶⠇⠀⣿⢋⣡⡞⡹⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣧⣅⠀⠹⣿⣦⡀⠜⠋⠉⠑⢦⣿⣿⡿⠋⠀⣴⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣿⣷⠦⠼⠞⡀⠀⢀⠀⠀⢀⣈⣿⢦⣀⠾⠛⠛⠛⣛⠍
⠀⠀⢀⣀⣀⠄⠀⠐⠀⠀⠀⠁⠀⠀⠀⠈⢀⡠⣤⡄⠀⠸⣋⣉⣀⠾⡇⠉⠉⠀⠛⠀⠀⠠⠄⠀⢀
⠀⠀⠀⠈⠉⠙⠛⠛⠻⠯⠭⣹⣟⣟⡏⢇⠀⠀⡉⠀⠀⡀⠀⠉⠠⣴⣿⣶⣶⣶⣶⣶⡶⠶⠶⠶⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣠⣴⣿⣿⣆⠀⠀⠀⢈⣉⠀⠀⢀⡝⠻⣍⣉⣉⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠿⠾⡿⣿⠞⠁⣡⣦⣄⣐⡁⠤⣶⣿⣧⣀⠘⠟⠛⠉⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡁⣴⣾⠇⢸⢁⢹⠀⢠⣧⡉⠻⢿⣷⣌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠈⠀⢸⣿⢀⠼⡾⢻⠀⠸⢿⣿⣦⠂⠉⠻⢷⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⡼⠃⠀⠀⢳⣻⠀⠀⠀⠀⢙⡇⠀⠀⠀⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢹⠀⠀⠀⠀⢠⣞⣙⡷⠤⠤⠶⠾⠾⠶⠦⠤⣤⣤⣒⠙⢦⠀⠀⠀⢀⡔⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡼⣧⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠿⣄⡀⢀⡜⣀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠀⠀⡴⠚⢶⠀⠀⢀⣠⣀⠀⠀⠀⠠⠊⠉⠇⠀⠀⠀⠈⠙⢿⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠞⠁⠀⠀⠀⠀⠉⠀⠀⠀⠸⣇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡠⠒⢳⡄⠀⡹⠃⠙⣦
⠀⠀⣀⡀⠀⠀⠀⠐⣧⠚⠁⣠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠞⠀⠚⠁⣠⠖⢷⡒⠋⢻⠆
⠀⣼⠁⢹⣀⠀⠀⡜⠁⠀⠸⣥⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠋
⠀⠘⠷⠶⢽⣷⡞⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢻⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⡌⢷⡀⠀⠀⣠⠶⠶⣄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡸⠀⠀⠀⠀⠀⠀⠒⢉⡀⢀⡿⠘⣧⢴⣊⣥⣤⣄⡏
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⣷⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⢹⡏⠁⠀⠀⠈
⠀⠀⠀⠠⣯⡇⠀⠰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⣿⣿⠇⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⠋⢹⠆
⢀⣀⣀⣀⣙⠁⠀⠀⢳⡈⠉⠛⢶⣶⣦⠤⣤⠄⠀⠈⠈⠙⠒⠦⠤⠤⠤⠤⠖⢉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣦⠀⠀⠉⣿⢉⣀
⣎⡀⢈⠥⢼⡆⠀⠀⠀⠳⣄⡀⢈⣛⠯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠀⠀⠐⢿⣀⢹⠆
⠈⠉⠀⢀⠔⡇⠀⠀⠘⠦⣌⣉⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠘⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠸⡆⢠⡏⠀⠀⠀⠀⠀⠀⠀⠰⣏⠈⢧⣀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠜⠀⠀⢠⡀⢹⡶⢤⡀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⡔⠹⡌⠙⠛⠀⠀⢠⡔⠹⣆⢀⡹⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢃⡟⠀⠀⢧⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠳⠤⠿⣆⠀⠀⠀⠀⢹⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⣦⠀⠈⠳⢤⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣦⠰⠽⢦⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⠛⣧⠰⠋⠀⠀⠀⢀⡟⠀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⢹⠀⣠⠜⣻⣦⡀⠀⠀⠀⠀⡟⠀⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠦⠴⠃⠀⠀⣠⡞⢥⡀⠸⡆⠀⠀⠀⠀⢸⠀⣤⡀⢰⡈⡇
⠀⠀⠀⠀⠀⣴⠊⠉⢀⡞⠁⠀⢙⡶⣄⡀⠀⠻⠖⠋⠀⠀⠀⠀⢸⣄⣸⠄⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁⢹⡄⠙⡆⢿⠀⠀⠀⠀⢸⡼⠁⠹⣄⡿⡗
⠀⠀⠀⠀⠀⠘⠳⠶⢞⠁⠀⠀⠸⡇⠀⠉⢳⠶⣦⣤⣤⣠⣀⣀⣀⣉⣡⣤⣤⣤⠴⠶⡖⡟⠧⠙⢦⡀⠀⠈⠛⠊⠁⢘⡀⠀⠀⠀⠈⠁⠀⠀⣿⠀⠁
⠀⠀⠀⠀⠀⠀⡞⢀⡎⠀⠀⠀⠀⣷⠀⡴⠋⣼⠁⠀⣰⠁⠜⠁⠹⢡⠀⠘⠒⠂⠀⠀⡇⠙⢶⡄⠀⠙⢦⡀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠇⠈⢶⠲⡄⠀⠀⢻⡘⠷⠤⠟⠀⣰⠃⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠙⠳⡶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⣆⢸⣇⡸⠀⠀⠘⣧⠀⠀⢀⡴⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣄⠹⠦⣬⣷⡼⠟⠀⠀⠀⣽⣂⠀⠈⠳⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠳⢦⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⡵⠞⠛⠶⠲⠦⠟⣠⠼⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠇⠀⠀⠤⠍⡁⠶⠂⠴⣤⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢼⡟⣥⠶⣄⣀⡴⠒⠦⣤⡤⠛⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠭⠔⠒⢦⣀⣠⠔⠒⢠⡀⠀⢀⡨⣷⣄⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠿⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢧⣽⠙
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶
⣿⣿⣇⣀⣀⣀⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢑⣰⠇
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠂⡀⢀⠀⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⡀⠈⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡞⠑⠠⣀
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⣰⡁⠀⡉⡆⠀⢘⠀⠁⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡀⣀⠀⣢⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣴⣶⣾⣶⣿⣾⣿⣾⣿⣷⢴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣳⣻⡿⠿⣿⣟⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⢽⢭⡻⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣭⣿⣞⣿⣷⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⡿⣟⡽⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⢿⣽⣻⢶⣿⣗⡐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣽⣿⣿⣷⢾⣁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣻⣯⣿⣷⡿⣹⣅⣿⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣗⣿⣿⣿⣟⣿⣿⣗⣯⣿⣼⡋⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⡿⣿⣿⣿⠭⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣽⣿⣿⣿⣯⠟⡟⠻⣿⣿⣿⠿⠟⠛⠿⣿⣾⣻⣿⢯⡳⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⢿⣻⣷⣿⣿⣿⡿⠛⠛⠻⠶⣤⣭⠡⢤⠞⠛⠞⠒⠛⠻⣯⣷⣟⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢉⡻⠍⣙⠢⣤⣤⠀⠀⡀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣟⣦⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⢰⠏⣡⣬⡌⢑⡀⡄⢹⣿⣷⣶⣾⣿⣿⠿⡿⠛⣿⠏⠿⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠈⠳⠬⠍⠵⠎⠀⠀⠸⠛⠛⠋⠋⠉⢀⡠⠔⣡⣯⡶⣃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣥⣤⣶⡘⠛⠓⠒⠶⢤⡄⠒⠈⠀⢀⣴⠃⠌⡋⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠿⣿⣦⣤⣶⢮⣻⣻⡿⡱⠎⣙⠲⣮⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡛⢿⠵⣶⣻⠓⠛⡹⡛⠅⢸⣦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⣷⢾⠙⡤⠎⢑⣵⢦⡷⣈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⡃⢠⡅⢀⣼⠳⣽⢎⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣴⠾⢷⡞⣾⠛⢄⣳⣾⡻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢾⣿⡓⡳⡿⡊⣼⠋⣏⣧⣾⡗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⢤⠳⣼⣿⠿⣧⡾⠿⠟⠁⠀⢀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣎⣟⢣⡙⢏⡵⢈⢶⡥⠈⠉⠀⠀⠀⠀⣠⣾⡗⣂⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⣿⡿⣾⢞⢾⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⣀⠌⠓⠻⠛⠂⠀⠀⠀⠘⠽⠒⢠⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⠿⣿⡛⣴⣷⣻⠟⢊⣾⠛⠁⠀⠀⠀⣠⣶⡶⠘⡽⣿⠋⢐⠀⠚⠛⠛⠓⠓⣳⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣶⣿⣽⣥⣻⡶⣭⣿⣿⡿⣯⡿⣭⡉⠀⠀⠀⢠⣾⡉⠁⠀⣬⠤⠏⠀⠈⠑⠚⠓⡄⠰⠾⠋⠍⠁⡄⢠⡀⠀⠰⠀⠂
⠀⠀⠀⢀⣿⣿⡿⣿⣾⣯⡿⣿⡿⢿⣷⡽⠗⠋⠀⠀⣠⡔⢃⡙⠀⠀⣿⠇⠂⡀⠀⣦⠀⠀⣠⡇⠀⠉⡀
⠀⠀⢀⣾⢟⣛⠆⣻⢹⡷⠧⣟⡷⠟⠉⠁⠀⣀⣴⠀⠙⣧⠋⠰⣶⢶⠿⢦⢢⡀⠚⠷⠂⣈⠁⢐⣀⡀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⢸⡿⣏⣿⠲⡵⠊⠘⠃⠉⠀⠀⠀⠀⢰⣿⠿⠇⠈⣀⠀⠀⠄⢠⡀⣷⣙⠃⠐⠀⢀⡤⠒⠊⠅⠀⠰⠿⡅⠀⠀⠀⠄
⠀⠀⢸⣦⡏⠹⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⣻⡋⠙⢾⣶⣃⡤⣔⣠⡯⣴⡟⠁⠒⢂⠀⢀⣠⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢒⠒⠒⡂⠠⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠔⢠⠄⠦⠘⠷⠀⠀⠀⠓⠉⣒⣄
⠀⠀⠀⠀⠀⠀⡠⠨⢄⠀⠀⠉⠀⠀⠀⠐⠀⠒⢣⡀⠠⠶⢠⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡰⠵⠄⠀⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢫⣅⠉⠹⡀⠀⠠⢀⡔⠉⠀⠂⡤⠐⡄⠂⢐⡠
⠀⠀⠀⠀⢀⢁⡌⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⣥⠄⠁⣘⡀⠀⠦⢀⣈⠁⠈⢁⠸⠠⠁⠀⠠⡀
⠀⠀⠀⠀⢸⢋⡀⡜⠁⠀⠀⠀⠈⠂⠀⠀⠀⢠⣤⣤⣤⣤⣀⠀⢻⠚⢗⡤⠐⠊⠀⠀⠀⠀⠀⠀⠐⠠⡤⠀⠑⣌⠄
⠀⠀⠀⠀⠀⠪⣥⠃⠈⢀⣠⣤⣴⢞⢠⠖⠒⣀⠉⣋⠭⠭⢽⠉⠘⡧⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠢⠌⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠴⠫⣋⠭⠽⢤⡙⡄⠀⠻⠘⣤⣔⣒⡿⠀⠘⡇⠈⠀⣀⣀⡠⢂⠄⠀⠀⠀⠀⣄⠀⠈⢯⠋⠳⡆
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⠥⣄⣒⠾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢿⣚⠛⣛⡿⠛⠡⠄⣀⠰⢦⣀⡀⠐⢇⢾⣑⢂⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢤⣶⡄⢰⣼⢇⠤⠄⣹⠂⡇⠀⣰⢄⣘⣛⡻⢶⣄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀⢀⣄⡜⠁⠶⣦⣤⡼⠋⠀⠀⡘⣇⣾⡗⠀⠉⠉⠁⠀⠀⠀⡄⠩⣦⠄⠈⢢⠉⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠱⡌⢿⠠⠀⠀⠀⠐⠛⠀⠀⠀⢄⣼⣿⣀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠚⢤⠢⡀⠀⠀⠀⠀⡠⠊⠈⢁⣷⠘⠀⠁⠈⠻⣤⣀⣴⠌⠳⢤⡀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠁⠀⠩⣉⣡⡤⠔⠁⠀⢠⡟⠀⠔⠀⠒⠀⠼⠧⢀⡀⠀⣌⡏⣠⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⣀⢀⢀⠜⡃⠀⢂⠠⠄⢀⡀⠀⠀⠈⣂⣸⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠴⠶⠾⠿⠛⠁⠀⢱⠀⠀⠀⠲⢶⠲⠭⠒⠜⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⡀⠀⣀⠀⠀⠀⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠷⠖⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⢤⣄⡀⠀⠀⠀⠈⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢸⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣣⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⡲⠞⣁⡴⠖⠛⠉⠉⠉⠉⠉⠛⠓⠦⣄⡀⠀⠀⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⣠⠖⠉⠀⠀⢀⣾⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡶⠒⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⣻⠁⣴⠷⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢿⡄⠀⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠋⠀⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠃⠀⠀⠀⢀⡿⢄⡀⠀⠀⠀⠀⢀⡠⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⢀⡀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠙⣦⠀⠀⠀⣾⠁⠈⢧⠀⠷
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠭⢍⡀⠀⠀⢿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠦⡀⢸⠀⠀⠀⠀⠈⠳⣄⠀⣼⠋⠉⢢⣏⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⢦⠀⢸⠀⡴⠋⠀⠀⠙⣆⢀⣤⢤⣄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⣠⣀⣤⣈⡄⣏⠀⢀⡏⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣷⡀⠀⠸⣇⠤⣇⢧⣠⣤⣤⣄⠀⢾⠀⠀⠘⠃⠀⠠⠴⠖⠛⠛⠛⠿⢿⡷⠀⠙⢦⡜⢡⡏⠀⠈⠁⢉⡒⠋⠀⠀⢀⡜
⠀⢰⡆⢀⡴⠞⠓⢶⠋⠀⢀⠙⠀⠀⣇⠀⢸⠛⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢸⠁⠈⢳⡖⠓⡆⠘⠃⠀⢠⡴⠋
⡄⠀⠀⢸⠀⠀⢀⣼⡀⠀⢹⡄⢠⠀⠉⠀⡇⠀⠀⢀⠔⠚⠉⠉⠉⣱⠶⠤⢄⣀⡀⢀⣀⡡⠏⠀⠉⠁⠀⠀⠀⣤⠤⠚⢀⡜⠀⠀⠀⠀⢸⠁
⢱⡀⠲⡀⠳⠖⠁⠀⠙⣶⠚⠀⠘⢦⠀⠀⣇⠀⠀⠻⡀⠀⠀⠰⠋⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠎⠀⠀⠀⠀⠀⡸
⠀⠹⢄⠙⠆⠀⠀⠀⠀⠈⠛⠒⡞⠀⠀⠀⠘⠦⣀⠀⠙⠲⠤⣀⣀⣀⠤⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⠉⠒⠶⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣰⠖⠒⠙⠋⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢀⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣐⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⠙⠲⠦⢤⣀⣠⠤⠤⠖⠛⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠲⣶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢤⣀⡀⠀⠀⠀⣘⢻⡀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡏⠉⠛⠶⣄⡟⠘⡇⣠⡴⠶⠖⠲⣞⣸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠳⣄⠀⠀⡟⠃⠀⠛⠒⣷⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⣤⣤⣬⠦⢤⣄⢸⡇⣸⡳⡄⠀⠀⠀⣷⠶⠚⠛⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⣭⡟⠁⠀⣎⠩⠷⠤⣒⡶⠾⠷⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠢⣤⡀⡀⠀⠀⠀⠀⣨⠇⣀⣠⠔⣫⠃⠀⠀⢸⣇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢌⣉⣑⣒⣒⣚⣉⣉⠭⠔⠊⠁⠀⠀⠀⠈⢯⡛⠧⣄⣀⠀⠀⠀⢀⣠⠼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⠉⠉⠉⠁⠀⣤⠖⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢳⠀⠀⠀⠀⠀⠀⡈⠒⠀⠀⠀⠀⠀⠀⠀⣿⠐⠂⠀⠀⠀⠀⠀⠀⠐⠏⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠆⠐⠐⠀⠐⠠⠀⠀⠁⠀⠁⠁⠀⠀⠡⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠁⠀⠆⠀⠄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⠀⠀⠀⠀⠀⣀⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠀⠀⠠⠘⠆⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⢢⠄⠤⠂⠲⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⡀⠨⠃
⠀⠀⠓⠀⠀⠀⠋⠀⠀⠀⠀⠃⡀⠀⣀⡀⠀⠀⠀⢠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠅⠀⠀⠀⠀⠁⠀⠀⠝⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠲⡀⠀⠀⠀⠀⠀⠀⡒⢲⡄⠀⠀⡀⣠⡔⠦⡄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠀⠠⢤⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠑⠀⣰⠀⠀⠀⠀⡀⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⡦
⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢠⠄⠀⠀⠀⠀⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀
⠀⠀⠀⡴⠢⠰⠀⠀⠀⠀⠀⠀⠐⠚⠲⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠀⠀⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠒⠂⠐⠒
⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢤⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠠⠀⠄⠀⠌⠁⠀⠀⠐⠀⠐⠀⠀⠂⠀⠚⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠀⠑⠖⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠢⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⣠⠶⠛⠉⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠀⢹⢀⠠⣤⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢗⣺⣿⠀⠀⠀⢸⠻⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⠶⢶⢦⡄
⠀⡴⠛⣏⠉⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠳⣤⣀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⣠⠄⠀⠀⠁
⠀⠀⠀⡀⣀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠍⣶⠐⠆⠀⠀⠘⡄
⡔⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡈⠁⠀⠀⠀⠀⡅
⠑⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⢿⠆⠂⠀⢴⠀⠃
⠀⠀⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⢈⠣⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠈⠤⡀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠄⠀⡀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠰⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡄⠀⠀⠀⠢⠤⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠑⠒⠒⠀⠋⠭⠀⡁⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⢀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⢀⠌⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢄⠁⠀⠠⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠐⠀⢀⠔⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠈⠀⠀⠀⠀⠉⠙⠀⠀⠀⠁⠀⠀⠂⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⠋⠀⡠⠊⠈⢐⡄⠀⢄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠰⡄⠀⠀⠀⠀⠀⠀⡀⠀⢸⠄⠈⠜⠀⠀⠀⠀⠀⠀⠉⠐⠠⠄⠀⠀⠠⠄⠀⠀⠀⠄⠿⢀⣆⢠⠎⠀⠀⠀⡜⠀⠀⠀⡅⡀
⠀⠐⠀⠀⢃⠀⠈⢆⠀⠀⢀⠀⠀⡟⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⡀⠀⢀⡌⠀⠀⢀⡜⠀⣸⠂⠐⠐⠒⠂
⠀⠀⠀⠀⠀⠐⠤⠸⠦⣀⠜⠁⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠉⠉⠁⠑⠤⠤⠋⠔⠚⢁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣾⣿⣼⣿⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠣⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠘⢦⡀⠀⣀⠾⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠐⠀⠈⠉⠀⡄⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣏⡀⠐⠂⠀⠀⠀⣀⠠⠀⠀⠀⠳⠤⠤⢶⡞⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣠⠋⢫⠀⠀⢀⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠈⢲⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣰⠏⢃⠀⢀⠜⠁⠀⠀⠉⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠡⠀⠀⠀⠀⢀⣃⣀⣀⠀⠀⠀⡰⠁⠀⠀⠑⠁⠀⢀⠁⠀⠈⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⡋⠀⠀⠀⠀⢀⣠⠤⢄⠀⡞⠁⠁⠀⠙⣆⡜⣁⣄⠀⠀⢀⠀⠂⠀⠁⠐⠠⢈⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⢤⣸⠀⠀⠀⡽⣇⠀⠀⠀⠀⡼⡏⠀⠀⢱⠊⠀⠀⠀⡠⠖⠊⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠙⠒⠊⠀⠈⠓⠤⠤⠚⠁⠑⠤⠤⠊⠑⢤⣀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⣀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⡠⠖⠁⠀⠀⠈⠳⣄⢀⡠⠞⠁⠀⠀⠈⢦⠀⠀⡠⠤⢄⡀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠉⠉⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠋⠁⠀⠀⠉⠒⠶⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⡄⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⢶⠆⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠾⠂⠀⠀⠀⠀⠶⠄⠀⠀⠰⠆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢀⡀⣀⡇⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠸⡁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠙⠓⡲
⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠚⠛⠋⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⣘⡅⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁⠀⠉⠀⠳⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣀⡴⠀⠀⠀⣠⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠾⢥⣀⠀⠀⠀⡹⠦⣄⡀⠹⡆⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳⡄⠤⠄⢀⡧⠚⠀⠀⠀⠙⡆⠀⡾⠁⠀⠀⠙⣦⢹⡖⠒⠲⠚⠁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⢻⡸⠃⠀⠀⠀⠀⢿⠈⣇⠀⠀⠀⢸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡄⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢾⣿⠀⠀⠠⢐⣀⣺⡇⣿⠀⠀⠀⣾⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⣯⡀⠀⠀⣰⣿⡛⣿⣿⠀⠀⣴⣿⣏⣿⡇⣿⡀⠀⠀⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⡇⠀⣰⣿⣿⣿⡿⢸⡆⢰⣿⣿⣿⣿⠃⡿⢣⠀⠀⠏⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⢀⡜⢣⢱⡄⢿⣿⣿⣿⣃⠀⢻⣿⣿⣿⣿⡟⢰⠇⠈⢦⡀⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢀⠔⠊⠀⠘⣄⠻⣿⡟⠟⢁⠈⠀⠀⠙⠛⠿⠟⢡⡟⠀⠀⠎⠩⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⣄⣠⣄⡀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⡇⠀⠀⠈⠳⣄⠀⠘⠀⠈⠉⢧⠀⠚⣧⠀⠀⡤⠚⢄⠀⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡆⠀⠀⠗⠈⠑⠆⠀⠈⠳⡇⠀⢀⠀⠀⡇⠀⣿⡤⠶⡀⠀⠐⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣷⠀⠀⢠⠀⠀⠐⠂⠀⡊⠳⢤⣶⣤⣿⡇⠀⣿⠀⠀⠄⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⢹⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠿⣿⣿⡇⢠⡏⠀⠀⠀⠀⠀⠀⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠋⢻⠀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢸⡀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢀⡴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⠿⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⠀⠀⠈⡄⢧⠀⠀⠀⠀⠀⠀⠀⠑⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡈⡠⢀⣈⠀⠳⣄⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢠⡿⠠⡇⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠈⠘⢁⠈⠙⢧⣄⠈⢧⡜⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⡘⠃⠈⠁⠀⠀⠀⢢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⡖⠉⠳⢶⣄⣉⠳⠄⠁⢀⠃⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠇⢀⠀⠦⠄⠀⠠⠖⠐⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠐⠒⠋⠀⢸⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡞⠀⢸⣀⣀⡀⠀⠀⠙⠉⠁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⠁⠀⠀⠀⠀⠈⠛⠒⠲⠶⠖⠁
⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⡿⠙⠒⢰⡖⡶⠒⠒⠒⠲⠶⠦⣾⠁⠀⠇
⠀⠀⣰⠚⠉⢻⡆⠰⡈⢳⡀⠀⠀⠀⢀⠞⣡⠬⡇⠀⠀⡛⠤⠠⠜⡰⠁⠀⠀⠀⠀⠀⢰⡏⠀⢸
⠀⠰⠃⠀⠀⢠⡇⠀⠩⡄⢳⣀⢀⡰⣡⠎⠀⠀⡶⠀⡼⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢾
⢀⠃⡄⢠⠀⠸⡀⠀⠀⠙⢄⣉⣩⠾⠁⠀⢠⣞⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠻⡀
⠘⠁⠁⣎⠘⣄⡙⠦⣀⡀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠒⠒⠲⣬
⠀⠀⠀⠉⠀⠈⠙⠓⠉⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡆⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠈⢳⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣘⣷⣤⣤⣴⣒⣚⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣳⣶⣶⣒⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠷⣄⠀⣠⠶⣄⠀⠀⣀
⠀⢀⡤⣾⢻⡏⣷⣀⠀⠀⢀⣀⠀⢸⠉⠳⢤⡏⠀⠈⠛⠁⠀⠹⠞⠋⢹⠀⠀⠀⠀⠀⠀⠀⣀⣴⠳⣄⣤⡀
⠀⠸⣄⡈⠀⠀⣉⣹⠆⠀⢸⡍⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠘⠛⢹⠇⠀⠀⠀⢸⣍⠛⠀⠋⠼⠷⡄
⠀⠀⠈⢧⣀⠀⠻⣅⠀⢶⠤⠇⠀⢠⢎⠏⣯⢱⠀⠀⠀⠀⡏⣼⢹⢹⠀⠀⠛⢲⠆⠀⠀⣀⡾⠁⢀⣠⠤⠞⠁
⠀⠀⠀⠀⠉⢧⡀⠀⠙⠾⠇⠀⠀⠘⢾⣦⡯⠞⠀⠀⠀⠀⠑⠿⠾⠋⠀⠀⠴⠯⠶⠶⠛⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⢠⠴⣞⡿⠉⠉⠉⠹⠽⠋⠳⡀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡇⠀⠀⣀⣀⡀⣀⣤⣀⠀⠀⡇⠀⠀⢙⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠳⣄⣞⡁⠀⠉⠁⢀⣈⡦⠞⠁⠀⢘⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⢶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⡀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡇⠀⢤⣀⡤⣄⣀⡴⢶⠀⠀⣿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⠀⠈⠉⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⢀⠟⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠤⠭⠥⠤⠾⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠾⠃

⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢸⣿⣇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⢷⣄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⣠⣤⡀⣰⣿⡟⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠞⠲⣄⠀⠀⠀⢴⠀⢀⣴⣿⣿⡿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠻⠿⠃⣿⣿⠀⢠⠀⠐⢄⣀⡤⠏⠀⣿⣇⠀⠀⠋⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠐⠂⠈⣻⣿⣿⣿⣷⣶⣶⣾⣿⣿⣦⣤⣄⡀⢀⣴⡄⠀⠀⢹⣿⣦⣤⣴⣶⣶⣶⣶⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠸⠷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣋⣭⣭⣿⣿⣿⡏⢸⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣶⣿⠿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⣬⣿⣿⣿⣿⣿⡿⢛⠛⠻⣿⡿⠀⠈⣿⣿⣿⠟⢛⣻⣿⣿⣿⣿⣿⣭⣤⣬⣽⣿⡿⠋⠀⠀⠀⠀⠀⢹⣧
⠀⣰⡟⠉⢳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠃⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟
⠀⢿⣧⡀⠀⣾⣿⣿⣿⣿⣿⣟⡿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⡿⠿⢿⡿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠲⠖⠋
⠀⠀⠛⠿⢿⢿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠸⣿⣿⣿⣿⣿⣿⣿⡷⠾⠿⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠉⠙⠛⠛⠛⠉⢩⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣀⠉⢉⡛⠿⣿⣿⣿⣿⡏⠀⠀⢀⣀⣀⣀⠀⢻⡿⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⣤⣤⣴⣿⣿⡟⠉⠛⢿⣷⡈⠁⣠⡤⠿⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⠁⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠰⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢹⣷⠀⣿⡀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠻⢿⣿⣿⣿⠟⠁⠀⡅⠀⠀⠀⢸⡟⠀⠻⣿⣶⣾⣿⣿⡿⢿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣀⠀⠀⠀⠀⠙⠦⠤⠶⠛⠀⠀⠀⠀⢹⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛


⣶⡶⢶⢶⢶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠘⠀⢩⠁⠀⠀⢩⠀⠘⠀⠀⠀⠀⠚⠀⠭⠀⠀⠀⠭⠀⠞⠀⠀⠀⠀⠳⠀⣬⠀⠀⠀⣥⠀⠓⠀⠀⠀⠀⠃⠈⡍⠀⠀⠈⡍⠀⠃
⠀⠀⠀⠀⢄⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠒⠐⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠂⠰⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂⠐⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⣀⡀⠁⠀⣀⠀⠀⠀⠀⠀⠀⢀⠈⣀⠐⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡈⠀⠰⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠙⠀⠴⠀⠀⠀⠴⠀⠋⠀⠀⠀⠀⠙⠀⠥⠀⡀⠀⠭⠀⠋⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠀⠂⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠒⠀⠒⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠒⠐⠂⠃⠀⠀⠀⠀⠀⠀⠂⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠂⠂⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⢠⠀⠠⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠄⠈⣠⠀⠀⠀⠀⣄⠀⣀⡀⠀⢀⣀⠀⡄⠀⠀⠀⠀⡄⠀⠤⠀⠀⠠⠤⠀⡄
⠀⠀⠀⢀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⢀⠀⠒⠀⠀⠀⠒⠀⡁⠀⠀⠀⠀⠈⠀⠛⠀⠀⠈⠛⠀⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠃⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⣀⠐⢺⣥⣀⣀⣾⣶⡴⡀⢰⡆⣠⣇⣀⢔⡴⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⠻⠤⣜⢿⣦⢿⡓⣟⣟⣾⣮⣧⣴⣬⣟⣞⣿⣷⡯⣖⡥⢊⡁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⢼⠛⠓⠛⠉⠉⠉⠉⠀⠀⠀⠁⠈⠉⠙⠛⠛⠛⠿⢿⣿⣿⣓⠨
⠀⠀⠀⠀⠠⠽⢶⣒⣾⣷⣶⣷⡷⢬⢦⣔⣄⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⡀⠀⠀⠙⣿⣿⠂
⠀⠀⠀⠀⠒⠈⡰⠋⣝⡵⢋⢁⡈⠀⠀⢐⠨⡑⢶⠶⠤⣤⣤⠠⠤⣤⣼⣵⣶⣦⠀⢹⣿
⠀⠀⠀⠀⠀⣸⠁⣸⠏⠠⢠⢟⣢⣤⣀⠰⠄⡌⠀⢡⠀⡇⠀⠀⢀⢱⢡⣖⠊⠿⠓⠲⠇
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠰⠹⣼⣟⡿⣸⠀⠀⠘⠀⠘⠃⢀⠀⠀⠈⠈⠲⠋⡢⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠛⢄⢣⢧⠀⠆⠈⡛⠉⠅⡀⡡⢀⢠⠞⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⣧⠏⡦⣍⠓⠶⠤⠤⠴⠚⣂⣴⢾⠡⠀⠀⢸⣤⣄⢀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⡗⠄⢌⢙⠒⡶⠒⡞⢉⠝⣸⢺⠸⠀⠄⠀⢃⣀⣀⣤⣤⠤⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠁⡞⠀⡏⡄⢣⠀⡇⢮⠀⡇⢸⡄⠀⠀⡠⠃⠀⢀⣄⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⡇⠳⠀⡇⠘⠀⠀⢰⡇⠔⠊⠀⠀⠀⠘⢸⠀⠀⠀⠘⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣀⡠⠥⠖⠒⠉⠁⠀⠀⠀⠀⠀⢀⠇⢸⢀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⢒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢘⠂⡞⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠤⠤⠤⠤⠀⠒⠒⠂⠠⠤⠤⠄⠒⠁⠀⠈⠛⠊⠉⠉⠛⠒⠒⠒⠒⠶⠶⠞⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠂⠤⣹⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠥⡤⢤⡄⠀⠀⠀⠘⠂⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⠀⠀⡠⠒⠒⢄⠘⢋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢤⠶⠂⠀⡠⠄⠀⠀⠀⠀⡱⡈⠉⠢⡀⠀⠀⠀⢀⠤⠢⢄⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡎⠀⡀⡌⠀⠀⠀⠀⠀⣀⠀⡘⡄⢐⠇⠀⠀⡰⢁⠔⠎⢂⢳⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠞⠀⠇⢠⠂⠉⠁⠒⠃⠀⠀⠎⢦⠀⢀⠜⡠⠉⢀⣰⠉⠁⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⡀⠑⠒⢄⠀⠀⠀⠀⢤⣄⠀⡠⠂⠘⠷⢊⠌⡡⠐⠉⠀⠓⢖⠒⠀⠀⢀⡀⠁
⠀⠀⠀⠀⢀⣀⠀⡆⠀⡔⠒⠤⢬⣐⡚⠧⠀⠀⢈⠁⠀⠀⠀⠂⣀⡀⠋⠀⠀⠀⠀⠀⠀⣈⠍⢁⠎⠉⢁⠀⢀
⠀⠀⠀⠀⡁⠀⠀⠛⠒⠓⢤⡄⢠⣀⣸⣑⡒⣤⡆⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⠀⠀⡏⠶⠊⠀⣀⠈⠆⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣴⡾⠟⠻⠯⡀⠀⠀⠀⠀⢀⠃⡤⠊⣁⡀⠱⠃⢀⠇
⠀⠀⠀⠀⠀⡆⠀⠀⠠⠮⢌⢆⠀⠀⠀⠀⠀⠙⡿⠋⠉⠉⠅⠀⠀⠀⠀⡰⠀⠀⠀⠀⡘⢀⠀⠀⠀⡠⢃⠔⠁
⠀⠀⠀⠀⠀⢰⠈⡏⠑⢄⠀⣧⠱⡀⠀⠀⠀⠀⡀⠀⠀⢀⠄⠂⠤⣤⡶⠡⠀⠲⣂⠞⢠⠃⡱⠒⠉⡰⠋
⠀⠀⠀⠀⠀⠀⡆⠸⡀⢈⠭⠤⠵⡌⠢⢄⠤⠄⠘⣓⠞⢁⠀⠀⠀⠀⠀⡭⣁⣈⣁⢴⡇⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠑⢧⠀⠧⠚⠀⠰⠤⣈⣙⣊⡡⠜⠑⠒⠀⡔⠚⣇⢀⣠⠊⠀⠀⠱⡊⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠅⣂⠀⠐⠣⠄⣀⠀⠀⡤⠂⠤⠠⠴⢲⣀⠸⠂⠀⠀⠀⠀⡠⠔⠀⠀⠠⠋⠑⢄⡀⣀⠄⠀⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠀⢠⠃⠀⠀⢸⣹⡅⡓⠠⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢓⠇⠀⠀⠀⢸⢸⠉⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⣼⡿⠀⢀⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⣠⠲⡁⠀⠀⠀⡠⠚⣆⢼⣿⠇⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠒⠈⠉⠉⠀⠘⡄⠱⡀⡠⠊⠀⠀⠘⣎⡟⡠⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠴⠖⢇⠀⠀⠀⠀⠀⠈⠻⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⢄⠀⠀⠀⠀⠀⢀⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⠿⣿⣶⠶⢶⣿⣷⣫⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⢸⡑⠊⠉⠉⠉⠙⠓⠾⠾⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠒⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠒⢄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠁⠀⠒⠀⠀⠀⠀⠀⠘⡄⠀⠀⠧⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠣⢾⡕⠐⠤⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⢀⡤⠀⠘⢦⠀⠀⠀⠀⠇⠀⠀⠀⠀⠔⠀⢠⠀⠀⠀⠀⠀⠀⡴⡁⠓⣺⢷⡹⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠙⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠈⠀⠈⠲⡄⢺⣷⣃⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠛⠀⠙⠃⠀⠀⠀⣐⣸⠃⠀⠤⠴⠊⠀⠀⠀⢠⣀⠜⢳⠄⠀⠀⠀⡜⠱⢿⠅⠦⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⢀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠋⠀⠀⠀⠐⣄⣀⠺⠼⣴⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⣤⡤⠎⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠴⣁⡜⠁⠀⠀⠀⠀⠀⠀⠈⢣⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡒⠒⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⡰⣡⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢃⠘⠦⠍⡡⠤⠞⠁⡄⡇⠀⠀⠀⠀⠀⠜⡴⣣⢏⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠢⡈⣇⠀⢀⡀⠀⢀⠔⠀⣇⡠⠖⢲⡀⢌⠈⠱⢣⢏⠜⠂⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⠎⠛⢉⣙⡋⠁⠀⡠⠋⠀⠀⠀⡇⠈⣷⢄⣀⠞⢴⠋⡓⢠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⡶⠁⠀⠈⢳⡪⠀⠀⠀⠀⢀⡇⢔⠝⢦⢄⡀⢇⣴⣡⣆⡀
⠀⠀⠀⠀⠀⠸⡆⠀⢀⣠⠖⠋⠻⣄⠀⣀⡼⡁⠀⠀⠀⠀⢨⡇⠀⣡⠛⣆⢧⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠋⠐⠀⠀⢀⠈⢉⠁⠀⠘⢦⠀⠀⠀⢸⡇⠀⣇⠀⡆⠘⢦⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠐⠈⠳⢤⣤⠞⠀⠀⢹⡄⢃⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⠀⠀⢠⡎⠀⠀⠠⠀⡀⠀⢠⠇⢸⡆
⠀⠀⠀⠀⠀⠰⡀⢀⠃⠀⠀⠀⢠⠀⢸⠀⠀⠀⡇⠄⠀⠀⢧⠑⠶⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⣷⠀⠀⠀⠸⡗⠤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⠒⠒⠒⠂⣿⠈⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢀⣎⣀⣀⣀⣀⡠⠹⠀⠀⠀⠀⠧⠤⠴⠤⠤⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣄⡀⠀⠀⠀⣀⣠⢶⡋
⡴⠒⠶⣄⠀⠀⠀⠀⠀⠀⢸⢃⠇⠈⠉⠉⠉⠁⢸⡄⣷⠀⠀⠀⢀⡤⠖⠋⠉⠓⣆
⣇⠀⠀⠈⢣⡀⠀⣀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⣸⠃⢻⠀⢀⣰⠋⠀⠀⠀⠀⠀⡿
⠘⣆⠀⠀⠀⠓⠉⠀⠀⠀⠒⠶⠒⢠⠀⠀⢰⠃⠈⠉⠉⠀⠀⠛⠀⠀⠀⠀⣠⠞⠁
⠀⠈⠳⢤⣄⡴⠒⠒⠦⠤⠴⣆⣀⣀⡆⠀⠸⣄⣀⠽⠉⠑⠒⠲⠶⠶⠚⠋⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠖⠃⠈⡴⡦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠀⠀⠤⢀⡀⠀⠀⠀⡲⢀⣂⣈⣆⣁⣨⢦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡛⡇⠀⠀⣐⢸⢀⠽⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⡇⠄⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠊⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢲⢤⠀⡆⠀⠐⠀⠀⠀⠂⠀⠤⠊⠀⠀⠀⡀⡠⠢⠂⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⢂⠓⠂⡇⢁⠁⠠⠈⠀⠀⠀⢰⠖⣡⡁⢀⠇⠐⢁⢒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢀⠭⠀⠀⠉⠡⠈⠀⠀⠀⠀⠀⠰⠄⡲⠪⡉⠀⠀⡄⢄⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢐⢠⠐⠇⠀⠀⠀⠀⠀⠀⡰⠀⡌⢢⠧⠀⣀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠀⠤⠒⠀⢀⠀⢠⠃⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠠⣄⡀⠂⠀⠂⠔⠁⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠑⠤⡼⠀⡮⠤⠔⣓⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠅⣀⠀⠀⠉⠉⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠐⢄⠀⠀⠀⠔⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠒⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠑⠀⡤⠲⣀⡀⠀⠀⠀⠰⠧⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡙⢆⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠐⠚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⡷⣄⠀⢱⠠⣀⣀⡆⠆⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⢎⠪⣣⡌⠀⠀⢙⠉⠑⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠑⠊⠀⠀⠀⢸⣤⣀⣀⣀⣀⣄⣾⣦⡴⠤⡖⠒⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠉⠉⠉⠙⠉⠉⠁⠈⠑⠋⠉⠩⠙⠁⠀⠀⠒⠒⠋⠉⠭⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠂⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣉⣭⣭⣭⣭⣿⣷⣶⣤⠤⠤⠤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢺⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⡾⠿⣿⣿⠛⠓⠶⢦⣬⣿⣛⠿⣷⣯⣁⡤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣭⣴⣾⣿⣿⣿⣿⣷⣶⣬⣍⢻⡷⣤⣙⡲⣄⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⡿⣝⠋⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡄⠀⠀⠀⠀⣰⣿⣿⡿⢋⣿⣿⣿⣿⠿⠛⠛⠿⢿⡟⣿⣿⣿⣿⣿⣧⡘⣏⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣚⣧⡀⠀⠀⢠⣿⣿⡟⠀⣼⣿⣿⡟⢁⣀⣤⣤⡀⠀⠘⢮⣿⣿⡏⠙⢿⣿⡛⢷⣤⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡻⣿⣿⣿⣿⠁⢸⣿⣿⣾⡇⡾⢁⣶⣦⡙⢷⡄⠈⣿⣿⣧⠀⠸⣧⠙⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠂⢾⣿⣿⡿⣷⣷⡀⠻⣿⠇⢈⣷⠀⢿⢹⣿⡄⠀⢿⣷⡚⠛⠛⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠘⣿⣿⣷⣉⡿⣿⣶⣶⣶⣿⡏⠀⣾⢿⣿⠻⡄⠈⢻⣟⣓⠶⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠘⢿⣿⣿⣳⣮⣿⣿⣿⡿⠂⣰⣿⣿⢇⣳⣽⡄⠀⠉⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣄⠀⠉⠛⠿⠿⠿⠛⣉⣴⣾⣿⣏⠁⠀⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⡙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡟⣭⡿⠿⠿⠿⠿⠿⠛⠉⢷⡀⢿⣧⠀⠀⠀⠀⢷⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⡿⡆⠀⠀⠀⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡛⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣽⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⡿⢿⣷⣿⣷⣦⣤⣀⣀⣠⠀⠀⠀⣿⣿⣿⡀⠀⢀⠀⢠⣀⢰⠁⠈⠙⠛⠿⠿⠿⢿⣿
⠀⠀⠀⢻⣷⣾⣿⣿⣿⢸⣿⣮⣿⣟⣛⣿⡏⠀⠀⠀⣿⣿⣿⣧⠀⠉⠀⠀⠀⢸⠀⠙⠂⠀⠤⠄⢀⣿⣿
⠀⠀⠀⠀⠻⣿⣭⣬⣽⢸⣿⠿⣿⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠴⠛⠓⣸⡀⢄⣀⣀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠻⣷⣶⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡷⢶⣶⢶⣿⣷⣈⣉⣉⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣠⠀⡀⢀⡠⣄⡀⠌⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡴⣋⡀⢈⢀⣤⡈⢳⡐⠀⠀⠀⠀⠀⠀⠀⡤⠖⢂⠀⠀⢀⡀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠿⠟⢹⠸⠿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠥⠵⠎⠥⠌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⣆⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⢣⡄⠷⠀⡸⠁
⠀⠀⠀⠠⢞⡉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⠚⠉⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠒⠋⠙⠒⠊⢁
⠀⠀⠀⠐⣡⠖⠒⢄⠀⠀⣀⣀⣀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣤⠤⠶⣲⠚⠂
⠀⠀⠀⠀⡇⠀⠀⠈⣷⠋⠀⠀⠈⢣⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⠤⠀⣠⣤⣀
⠀⠀⠀⠀⢧⢠⣶⡄⡇⠀⠠⣿⡆⠈⡇⠀⠈⠀⠀⠠⠖⣂⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⡀⣀⣤⡆⠀⠘⠿⡿⢋⡔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠔⠚⢆⠭⠀⠧⠠⠤⠤⠤⣤⡃⠀⠀⠀⠀⠀⡼⠉⣧⠀⡴⢳⠀⠀⠀⠀⠀⡌⣤⢹⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢃⣴⡿⠐⣧⣾⠀⠀⠀⠀⡀⠉⠧⠞⠑⠃⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢡⠔⠊⠉⠲⡀
⠉⠐⣦⣀⣀⠈⠁⠁⠀⠀⢀⣀⡀⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⣉⣀⠀⠀⠀⣸⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⢿⣆⣈⣸⡷⠀⠀⡇
⠀⠀⠹⡷⠶⠭⢭⣭⣉⣉⣩⠞⠁⠁⠀⠀⠀⠀⠀⣜⠉⢉⣿⣿⠏⠉⠁⠀⠀⠀⢿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⡃⠀⠈⣆⣠⠜
⠀⠀⠀⠈⠒⠤⣄⣠⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⣁⠔⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⣦⠀⠀⡔⠊⠉⠑⡄⠀⠀⠀⠀⠈⣉⠒⠒⣊⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⢂⠤⠬⣉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⡆⢀⢰⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢏⠀⠀⠈⢧⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠈⢊⠉⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠁⣀⠤⠤⢄⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠣⣀⣀⡜⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⠒⠭⠒⠉⠉⠉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⣀⣤⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢱⠦⡝⣲⠶⢶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⠛⣉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⣦⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⣃⡴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣏⢉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⡘⠉⠀⠀⠀⠀⠀⠠⠋⠀⠀⠈⠉⠉⠉⠉⠉⢉⡟⠉⠉⠉⠉⠉⢉⣽⢿
⣿⠀⠉⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠁⢼
⣿⣄⣀⡀⠀⠀⠰⠇⣠⢴⣤⡀⡠⠚⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⡄⠀⣀⣀⣥⡠⠔⠃⠀⠀⠀⠀⠀⢸
⣿⣄⠁⠉⠓⢶⡖⠛⢷⣮⡼⠿⣅⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡔⢀⡼⠋⠁⠀⠀⠀⡀⠀⠀⣀⠀⠀⣻
⣿⠻⣷⣄⣀⣸⠤⠾⠼⡿⠤⣴⣻⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠔⠀⠀⡆⠀⠠⢀⠊⢀⡞⠀⢀⠠⠀⠂⠁⠀⢀⣾⠋⠀⠀⣿
⣿⠀⠀⠉⣿⠀⠀⠀⠐⠲⠄⠀⠻⣄⠀⠀⠀⡇⠀⠀⠀⡄⣸⠃⠀⢠⣾⠑⢢⡤⠴⢶⣿⣀⡴⠀⠀⠀⠒⠆⡀⠘⣿⡄⠀⠀⢿
⣿⠀⠀⠀⣿⢄⠈⠉⠉⠀⠀⠒⠂⠈⢳⡀⢠⡄⠀⠀⢀⣧⡟⠢⠀⢘⣿⣿⠋⠀⠀⠀⠿⠁⠀⠀⠀⣠⣶⣶⣾⠿⠏⠀⢀⡴⠁
⣿⠀⠀⠀⣯⡓⠂⠀⠀⠀⠀⠀⡰⢂⣊⡏⠲⣧⣀⣤⣼⣿⣷⣶⣶⠿⠛⠛⠇⡀⠀⢠⠀⠀⠀⠀⠀⠻⣿⣿⠁⠀⠀⠀⢸
⣿⠀⠀⢾⠁⠉⠉⠀⠀⣠⣤⡴⠁⠈⠉⠀⢸⠉⣳⠟⠛⠋⠁⠀⠀⠀⢀⠀⠀⢈⠆⠘⠀⠀⠀⠀⠀⠀⢌⠙⣧⡀⠀⠀⢰⡇
⣿⠀⠀⠈⢇⠀⡀⠀⠀⠋⠼⠠⠔⠋⠀⠀⠈⠻⠃⠀⠀⡀⠀⠀⠲⢶⣄⠀⣌⠀⠀⠀⠀⡀⠀⠀⣤⠀⠠⠆⠻⠃⠀⠀⣸⠃
⣿⠀⠀⠀⠀⠙⠿⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠈⢀⣸⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⡏
⣿⠀⠀⠀⠀⡀⠀⠐⠄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠄⠀⢀⠈⠀⠀⠀⠰⠄⠀⠑⠆⠈⠀⠀⠀⠀⠀⠀⢡
⣿⠀⠀⢀⡼⠉⠛⠳⢾⡗⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣨⡤
⣿⠠⢞⡏⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⣧⠀⠀⢀⡆⠁⠀⠀⠁⠀⠀⠁⠆⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠄
⡿⠀⣾⠁⣤⣄⠀⠀⠀⣷⠀⡄⠀⣸⠀⠘⣧⠀⣠⣿⠀⠀⠀⠀⠀⢰⠃⠂⠀⢠⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⣴⠞⠳⢿⣤
⣷⢠⡇⠀⢁⠘⠃⠀⠀⢹⡀⠇⢤⡿⠀⠀⡇⢸⣿⡇⠀⠀⠰⡿⠆⠸⠀⢀⣤⡀⠃⠀⠀⠈⠻⠃⠀⠀⠀⠀⠹⣿⡂⠀⠀⠄
⣷⠞⠁⠀⠀⠀⠀⠀⢀⣼⠟⢃⣼⡇⠀⠘⢷⡌⢻⣿⣦⡤⠀⠀⠀⢘⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⢰⠊⠁
⣟⠀⠀⠀⠀⠀⠀⣠⡞⠻⠀⣸⡿⢇⡀⠀⣯⢠⣾⣻⣏⡙⠀⠀⠀⠄⠀⠀⠁⢠⡞⠁⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⠇⠘⠂
⣟⠻⣄⠀⡀⠀⠀⢩⣀⢶⢀⡟⠀⠀⠉⠛⠋⢸⣇⡼⢋⠱⠀⠄⠀⢀⣄⣀⣴⠊⠀⠀⠀⠀⠽⠀⠀⠄⠀⠀⠀⠀⡇
⡇⠀⠈⠳⣄⠠⣰⠈⠛⢾⠺⣷⡄⢤⡷⠀⠀⠈⠧⣦⣀⣆⡟⠶⠌⢋⡁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠢⣤⡄
⡇⠀⠀⠀⣨⣷⣮⣦⣤⣿⣰⣻⠅⢾⣅⡖⠀⡄⠀⠈⠉⠀⠀⠛⣳⣗⠤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠘⣇
⣷⣤⣤⣴⠏⠀⠀⠀⠁⠙⢻⠃⠀⠀⣹⠂⢸⣿⡆⠀⠐⠀⠀⠀⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⣸⠇⠀⠀⠀⠘⠂⠀⣶⠀⠀⡠⠁⣤⡿⣿⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠁⠀⠁⣿⢻⡆⠐⠂⠐⠉⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠀⠈⠲⣤⣀
⡷⡏⠀⠀⠀⠀⢀⣠⠀⠀⠈⡤⠀⠀⠀⠀⢸⡿⣻⡷⠀⠀⠀⠀⢀⡖⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠸⠻⣷⡄⢊
⡇⣷⠀⠀⠀⠀⠀⠈⠀⠀⢹⢱⡄⠀⠀⠀⢈⣧⣼⠟⢠⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢈⠀⢹⣧⣾
⣧⡇⠀⠀⠀⠀⠀⠐⠀⠀⠈⡶⡯⠀⠀⠀⠸⠿⢿⠆⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠈⠆⠈⢿⣿
⣿⣇⠀⠀⢀⠤⣄⡀⠀⢀⣴⡶⠓⠀⠁⠀⠀⠀⢸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠷⠀⠀⠐⡀⢸⣿
⠇⣿⠀⠀⠀⠀⠬⡉⠀⠘⠁⠁⠀⠀⢀⠀⠀⠀⢸⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⠀⠀⠂⠀⠀⠀⠀⠀⠈⢲⣿
⣴⠋⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢰⣿⣾⣤⡤⠴⠚⣏⠂⠌⡑⠢⠄⠀⠀⠀⠀⢀⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣷⣶⣶⣶⣶⣶⣶⣤⣤⣾⣿⣧⣿⣿⣿⣿⣧⣤⣤⣿⣤⣠⣬⣿⣄⣴⣤⣀⣀⣨⣿⣿⣿⣧⣀⣀⣄⣀⣀⣀⣖⣀⡀⠄⢘⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⠹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡌⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⣼⡿⠋⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣀⠀⠀⠻⣿⡄⢻⣿⣦
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⢰⡟⠁⠀⠀⢀⣴⣾⠿⠛⠛⠉⠙⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠙⠳⣆⠀⠹⣷⠀⢻⣿⣧
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠘⠁⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠘⠀⠀⠻⣿⣧
⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠐⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠀⠀⠀⠀⠀⠐⣿⣿⢦⣤⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⣀⡴⠋⡄⠀⠀⠀⠀⠀⠀⠈⢻⣦⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣠⠖⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣼⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡿⢷⣦⣤⣤⣤⣶⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠉⠉⠉⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣈⣷⣀⣼⣧⣄⣀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠉⠉⢉⣩⣭⣍⡉⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣤⣤⣶⣶⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠒⠢⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣒⡧⠀⠈
⠀⣹⠄⠒⠚⠉⠛⠋⢣⡀⠀⠀⠀⠠⠊⠀⠀⠂⠀⠀⡀⠘⣆⠀⠀⠀⠀⢀⠚⠩⠄⠄⠐⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂
⠈⡁⠀⠈⠁⠈⠀⠀⠀⢀⠀⠀⠀⠇⠀⠀⠁⠀⠁⠀⠈⢀⣸⠀⠀⠀⠀⡜⠀⠀⠀⠂⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢫⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⢃
⠀⠐⠤⣀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠌⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣀⠀⠠⠀⠀⠀⠀⠠⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠉⠀⠉⠑⠢⣄⢀⠀⠀⠀⠀⡠⠐⠒⠓⠃⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠈⠑⠃⠀⢄
⢄⡐⢄⡦⠴⠦⠴⠆⠰⡁⠁⠀⠀⠨⠀⠂⠋⠙⠈⠦⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠔⠁⠀⠀⠰⠀⠤⡀⠀⠈
⢬⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⠀⠹⡟⡄⠀⠉⢀⠠⠀⠀⠀⠀⠀⠀⡂⡀
⠀⠀⠈⠀⠀⠁⠀⢨⠄⠀⠄⠀⠀⠂⠀⠀⠁⠀⠠⠀⡔⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⣆⡄⡇⡇⠀⠀⢀⡆⠀⠁⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⠀⠀⠀⢢⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠘⠶⣄⠀⠀⠀⠀⠠⠟⠃⠁⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⡠⠊
⣤⣤⣤⣤⣤⣤⣤⣽⣧⣥⣤⣤⣤⣤⣤⣭⣴⣦⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣴⣦⣶⣭⣤⣤⣤
⣿⣿⣥⣤⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠘⢧
⠀⢀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠚⠉⠀⠀⠀⠀⠀⠀⣹⡆
⠀⠉⠉⠀⠀⠟⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⣀⠀⠀⠀⠀⢿⡉⠀⠈⠉
⠀⠀⠀⠀⣆⠀⢀⢤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⢢⡄
⠀⠀⠀⠀⠙⠋⠀⢠⣿⣿⣿⣿⣿⣿⣟⣫⣽⣿⣧⠀⣠⣴⣶⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣿⣿⣿⣿⣋⣭⣿⣿⣦⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⢤⣀⣠⣶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⡿⢷⣽⣿⡿⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠛⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⣿⣿⣿⣶⣄⣻⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡤⠶⠾⠿⣿⢗⠲⡒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢮⣍⠁⠀⠀⠀⠛⠷⣶⡀⠀⠑⠹⣶⠈⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣬⣉⣀⣙⣉⡙⠳⡌⢻⡆⣰⠀⣿⡇⠘⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠹⢿⣬⣝⡻⠟⠭⠟⡻⢾⠈⣴⠏⣠⠟⣰⢂⣼⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣷⣿⡶⠿⠛⣿⣿⡿⢷⣾⣾⣷⣟⣵⣞⣥⣿⣱⡟⢁⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⣀⣴⡿⠛⠳⣤⡀⠙⣿⡛⠛⢿⠿⠻⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠄⣠⣿⠟⠛⠶⣄⡈⠻⣄⠈⢷⡀⠸⣆⠈⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢀⣿⣋⠛⠳⢦⣌⠻⣦⡙⢷⡈⢷⡀⢻⡄⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠅⣽⣏⣉⣙⡓⠦⣍⡓⢦⡹⣆⣿⣄⣷⣀⣷⠀⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡈⢉⠀⣿⡥⠤⠭⣍⣓⣲⣽⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⠉⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢶⡟⠀⣿⠖⣚⡳⠤⣴⣿⠟⠑⠀⠑⠰⢰⢸⠉⡟⣿⣿⡷⠆⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⣿⠀⠹⣯⢖⣮⡱⣿⣯⣷⣿⣟⠿⣶⣄⠈⢠⠀⡏⣼⣃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠻⣇⡀⠙⣧⣪⣾⣿⣿⣿⣿⣿⢧⡈⢻⣦⠀⠘⣰⡟⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣿⣱⢆⡌⡙⠻⠿⠿⢟⣿⠏⢼⡇⠑⣻⣇⠀⢙⣤⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠿⢾⣷⣧⣿⠾⠟⠁⢐⡾⠁⠨⢽⣟⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢠⡀⢀⠠⣄⠢⣝⠾⠁⠐⢒⣿⣏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣽⣌⢳⡌⠷⠈⢁⣠⣭⣽⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠡⣿⠀⠈⠻⣤⣀⠀⠒⠶⢦⣼⠟⠛⢀⣆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠀⠙⣄⠀⠀⠈⠻⣿⣷⣾⠟⠁⠀⠀⣸⠏⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⠀⠘⢦⡀⠀⠀⠀⠉⠁⠄⠐⠀⠔⠉⢠⠀⠀⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⢿⡄⠀⠀⠀⠀⠡⠀⠈⠳⢄⠀⠀⠀⠈⡐⢀⡄⠀⠀⠁⠀⠀⠀⠀⣿⠳⢤⣀
⠀⠀⠀⣀⣤⠶⠚⠋⠉⣁⠀⠴⢤⠉⢻⡄⠀⠀⠀⠀⠀⠁⠀⠀⠙⣲⡆⡼⢏⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠬⠍⣉⣉⣑⠒⠦⣄
⠀⠀⠺⢁⣀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣴⣾⣶⣷⣻⣶⣧⡀⠀⠀⠀⠀⡐⣴⠯⠃⠀⠀⠀⠀⠀⠀⠀⠈⢁⣈⡷
⠀⠀⠀⠀⠰⣒⠚⠡⠶⣄⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣠⣾⠿⡙⣿⣿⣿⢿⣿⣷⡀⠀⠀⠈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⡫
⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⠙⠢⠀⠀⠀⠀⠀⢹⡆⢀⣴⠟⠁⠀⢹⣿⡹⣿⣾⠃⠈⠿⣄⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⡠⠀⣨⢵⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠈⠷⠛⠁⠀⠀⠀⠈⣹⣻⠛⠁⠀⠀⠀⠈⠓⠞⠀⠀⠀⠀⠀⠀⣞⡡⠔⡠⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣷⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣤⡐⢒⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⣸⣿⣟⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⢈⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢟⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡁⠀⣀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠊⠀⠀⠈⠀⠀⠀⠉⠀⠀⠈⣧⠠⠤⠔⠒⢒⠶⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠠⣉⣡⣀⣁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠠⠋⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠠⠤⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⡰⠃
⠀⠀⢀⠀⠐⠈⠑⢀⣴⡁⠀⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠂⠀⠀⠀⠀⠀⡜⠁
⠀⢀⠔⠒⠶⢄⠀⡜⠠⢸⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡼
⠀⡌⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⡤⠆⠀⠠⠋⠀⠐⠊⠈⠉⠉⠑⢤⡀⠀⠀⢰⠁
⢠⠁⠀⠀⠀⡆⠀⢘⠂⡀⠀⡀⠀⠃⠀⠀⠀⢠⠃⠈⠁⠀⠀⡇⠀⠉⠉⠉⠉⠉⠀⢹⠀⢀⠇
⡌⠀⠀⠀⢠⠃⠀⢨⣀⡡⠂⠄⠀⣂⡀⠀⠀⣸⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠊⠁⠈⠉⠉⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇
⠣⢄⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇
⠀⠀⠀⠉⠀⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⣃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⣇⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡤⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⡘⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣤⣀⡀⠀⠀⠀⠀⣀⣤⣙⢿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣼⡿⢿⣿⢅⣤⣌⠛⠀⠀⠀⠘⣉⣤⣤⠀⣿⣿⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠈⠁⠀⠀⠀⠐⠁⠈⠀⠀⣿⣿⣿⣿⣿⣋⣁
⠀⣠⣤⣤⣶⣶⣶⣿⡿⣿⣟⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡼⣯⣟⣿⣿⣾⣿⣿⣿⣿⡿⠷⠶
⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣖⣖⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦
⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠛⠟⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿