Rabbit ears Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠳⣄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣠⠞⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⠳⣄⠀⠀⠈⢷⠀⠀⠀⠀⡼⠁⠀⠀⢠⡞⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠻⣷⣄⣀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠙⢦⠀⠀⠘⣧⠀⠀⣼⠃⠀⠀⣴⠋⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⣆⣰⡏⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠛⠛⠛⠛⠿⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠛⣥⣄⣀⣬⠛⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢸⡟⢻⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⠏⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣼⣿⣿⣿⠂⠀⠀⠀⠀⢼⠁⠀⢻⡄⠀⠀⠀⢀⣴⣿⣿⣶⡄
⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠹⡆⠀⠀⢰⠏⠀⢀⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣇⠀⠈⣇⠀⠀⢠⡞⠉⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⠟⠻⣄⠀⢿⠀⠀⡿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠐⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⢠⡟⠀⣠⡾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⢸⣆⣰⡇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣟⣀⡼⢠⠾⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠳⢤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠳⢤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⢠⡾⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⢧⠀⠀⠀⠀⣿⠁⠘⣷⠀⠀⠀⢠⡟⠁⢹⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠋⠹⣆⠀⠀⠀⡾⠉⢻⣿⣿⡇⠀⠀⣾⠀⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣟⢘⡇⠀⠀⠀⢹⡄⠀⠸⣇⠀⠀⡿⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢿⣿⢿⣄⠀⢻⡀⠀⣸⠃⠀⣴⢿⣿⠇⠀⠀⠻⠛⠉⢿⣿⣿⣇⠀⣿⣿⣿⡟⠉⠻⠃⠀⠀⠀⠀⢻⡄⠀⢿⠀⢸⡇⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠙⢦⠘⡇⠀⡟⢠⡞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⠀⢸⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠿⠷⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠶⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠾⠷⠾⢾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠶⣄
⠀⠀⠀⠀⣰⠟⠀⠀⡀⠀⠀⠈⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢰⠏⠀⠀⠀⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢳⡀
⠀⠀⠀⢷⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⢸⡄⠀⠀⢸⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⣤⡾⠋⡇⠀⠀⠀⡟
⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢹⡀⠀⠈⡀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⡇⠀⠀⡼
⠀⠀⠀⠀⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢰⡇⠀⢠⠇
⠀⠀⠀⠀⠀⢸⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣠⣼⣿⣶⣶⣶⣶⣶⣶⣾⣇⡀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼
⠀⠀⠀⠀⠀⠀⣧⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠸⡄⢸⡄⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢳⠀⡇⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢰⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡧⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢸⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣤⣰⣀⣀⣤⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣷⣽⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣷⣿⣷⣮⣿⣷⣿⣿⣿⣶⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⣿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⣿⣿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣴⣾⣿⣿⡏⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣠⣾⣿⣿⣿⣿⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣴⣿⣿⣿⣿⣿⠃⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢉⡍⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣾⣿⣿⣿⣿⡿⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⣧⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣾⣿⣿⣿⣿⠏⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⣿⣿⣦⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣿⣿⣿⡟⠁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⣿⣿⣿⠏⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠟⠿⣿⣿⣿⣧⠀⠈⣇⠀⠀⠀⠀⠀⠀⡿⠀⣾⣿⣿⠋⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡼⠳⣄⠈⠛⢿⣿⣧⠀⢸⡄⠀⠀⠀⠀⢀⡇⢀⣿⣿⠃⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢰⠃⠀⠈⠳⣄⠀⠻⣿⠆⠀⣷⠀⠀⠀⠀⢸⡇⠘⠿⠃⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢠⡏⠀⠀⠀⠀⠈⢧⡀⠀⢀⣀⣼⣦⣴⣶⣶⣾⣧⣄⣀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣷⣾⠿⠛⠉⠉⠁⠀⠀⠈⠉⠙⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡞⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣾⣷⣆
⠀⠀⠀⣠⣿⡿⠙⢿⣷⣄
⠀⠀⢰⣿⡟⠀⠀⠀⠹⣿⣷⡄
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠈⢻⣿⣦
⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄
⢰⣿⡟⠀⠀⠀⢀⣷⣄⠀⠀⠀⠈⢻⣿⣆
⣸⣿⠇⠀⠀⠀⣸⣿⣿⣦⠀⠀⠀⠀⠹⣿⣧⡀
⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⣀
⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠿⠟⠛⠛⠛⠻⠿⠿⣿⣷⣶⣄⡀
⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣦⡀
⢿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠘⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⢹⣿⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠈⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠘⣿⣧⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠹⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣼⣿⠿⢿⣷⣤⡀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⢀⣾⣿⠋⠀⠀⠙⠻⣿⣷⣤⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠘⣿⣿⣿⣿⣿⡇⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⢸⣿⣿⣿⣿⣿⠋⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠈⢿⣿⣿⣿⠇⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠈⣿⣿⣿⡿⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠻⠿⠟⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠻⠿⠟⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠰⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠰⡕⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⠈⢰⠇
⠀⠀⠀⠀⢺⣦⡙⠲⣄⠀⠀⠀⠀⡜⢡⡾⠀⢀⡟
⠀⠀⠀⠀⠀⢳⡱⡀⠀⠓⣀⠀⠘⠀⢸⡷⢂⠜
⠀⠀⠀⠀⠀⠀⠳⣼⢀⠀⠈⠁⠀⠀⠈⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠶⡀⠀⠀⠀⢘⠀⢻⣿⠷⠶⠶⠛⠛⠛⠓⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠘⠀⡠⣸⠁⠀⠀⠀⠈⢷⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⠇⢸⡇⠇⠀⠘⠣⠘⠀⠈⣀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢸⠄⠸⢧⠄⣀⣠⠤⣄⣀⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢾⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⡷⡄⢧⣀⠀⠀⢀⣴⠎⠀⠀⠀⡀⠀⠛⠉⠀⠀⢀⡀⠀⠀⠀⠀⢑⣾⡏
⠀⠀⠀⠀⢀⣠⠾⠀⠀⣠⡟⠀⢁⡜⠁⠀⠀⣠⡾⠁⠀⠀⢀⣤⠴⠯⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⣾⣄⣠⣤⣾⠏⠀⢠⠞⠓⠀⣠⣾⡿⠿⠷⢶⣾⡋⠀⠀⠀⠀⣀⣀⡀⠀⣀⣤⣿⣿⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠚⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠡⡄⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⢀⡗
⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠱⣦⡀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣠⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠙⠀⠘⣦⠈⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⣼⡇⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠁⠀⣹⡇⢺⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⠃⠀⣼⣿⠇⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢹⡇⠀⢻⣿⣿⣆⠀⠀⠀⣾⣿⣿⠄⠀⣿⡟⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢸⣧⠀⢀⣿⣿⣿⡆⠀⢸⣼⣿⠿⠀⠀⢸⠃⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢻⠀⣸⡿⠋⠉⠙⠀⠛⠛⠉⠑⢀⡀⠘⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠹⣀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⣀⣀⣀⣠⣄⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⡀⠀⠈⠀⠀⠀⠉⠳⠀⢰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢁⡾⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⡟⡀⠈⠋⠠⣀⡀⠀⠀⠀⠀⠀⢱⡄⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣸⣁⣡⣀⠀⠑⠺⡷⠊⠀⠀⠀⠀⣈⠁⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠶⢿⣿⡀⠿⠲⣴⢶⡿⠢⠴⡇⢠⣼⣿⢷⠄⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢻⣿⡷⠀⠠⠔⠚⠛⠒⠠⠄⠀⢻⣽⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣞⡒⠀⣄⣠⣤⣤⣀⣀⣰⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢠⠟⠀⠁⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⢁⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠠⡋⣠⣄⣘⢛⠲⡟⢹⠷⣿⣿⣿⣿⣿⣿⠉⡅⢀⡄⠀⠉⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠋⠀⠀⢹⡟⠛⠚⠀⣿⠠⡏⠛⢙⣷⡟⠛⠀⢰⠦⣁⢲⣦⠀⠉⠰⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠉⠙⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠛⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⣿⣿⡄⠀⠀⠀⣼⣿⡟⠀⠀⠀⢀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⢀⣿⣿⣇⣀⣀⣀⣿⣿⠁⠀⠀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⢋⣝⡁⠛⣆⢛⠙⢿⣄⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⣴⢛⣿⠀⠀⣿⠿⣦⠀⠹⣝⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣾⣿⣤⣴⣿⣦⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⡿⠋⠉⢻⡟⢻⣿⣿⡟⠉⠙⢿⣙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⡾⠟⠻⢿⣿⡄⠀⠀⠀⣿⠋⠈⠻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⡟⠀⠀⠀⠀⢻⣿⣦⣤⣴⡏⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠈⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⣿⡏⠀⣸⣿⡇⠀⠀⠀⠀⣼⣿⠃⠀⢻⣿⣦⠀⠀⢠⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣶⣿⣿⣿⣦⣀⣠⣾⣿⣿⣧⣠⣾⣿⣿⣷⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠉⠙⢿⣿⠟⢿⣿⣿⣿⣿⡿⠛⠛⠛⢿⣟⢉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⡇⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⢿⣄⠀⠀⢀⣿⠿⠛⠿⣿⣿⣇⠀⠀⠀⠀⣰⠋⠁⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣿⣶⣿⠁⠀⠀⠀⠀⢻⣿⣷⣶⣶⣾⠁⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣷⣌⣿⣷⣀⠀⠀⢀⣼⣿⠉⣩⣿⣷⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢍⡙⠻⣟⣿⣿⣿⠟⠛⢙⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠁

⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡔⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡀
⠀⠀⠇⠈⢷⠀⠀⠀⠀⣠⠞⢸⠄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠶⢍⡁⠢⠀⠀⠀⠀⢀⡤⠠⣄⠀⠀⡎⠀⠹⢤⣹
⠀⠀⢀⠀⢸⡇⠀⠀⣰⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⡼⠉⠂⠀⠀⠀⣠⠊⠜⠀⢸⠀⢠⠃⢀⠃
⠀⠀⠀⠳⡸⣿⠀⠀⣟⣡⠞⠁⠀⠀⠀⠀⠀⠀⢀⢻⡀⢈⡼⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠐⣊⠄⠂
⠀⠀⠀⠀⠠⠛⠋⠉⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈


⠀⠀⠀⢀⡶⡀⠀⠀⠀⠀⠀⠀⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⡘⠀⠡⠀⠀⠀⠀⠀⡘⠀⢣⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⡎⠀⠈⠳⡀⠀⠀⡇⠈⣧⠀⠀⠀⠀⡞⢹
⠀⠀⢠⠁⠀⠀⢇⠀⠀⠀⢠⠀⠀⢸⡄⠀⠀⣰⠋⠀⡠⡿⠀⢸⠀⢱⠶⠄⠃⠀⠀⡇⠀⡟⡆⠀⠀⢸⠃⣸
⠀⠀⢸⡄⠀⠀⢸⡀⠀⠀⣾⠀⠀⢸⠇⠀⠰⣇⡠⠾⡁⢯⢀⠃⡰⠃⠀⠀⠀⠀⠀⢹⠀⢇⢷⠀⠀⡏⢀⡏
⠀⠀⠈⠟⠄⠀⡿⠁⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠱⡸⡄⠐⠁⠀⠀⠀⠀⠀⠀⠈⢧⡈⠸⡆⢰⡷⠞
⠀⠀⠀⠈⢊⢢⣡⠀⠀⠀⢰⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠁⠛⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡶⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢲⠶⡄⠀⠀⠀⢀⣴⠿⡧⠀⠐⠋⠀⣸⠀⣿⠀⠀⢠⢞⡝⢡⠏
⠀⠀⠭⢭⣅⠀⢶⡆⠀⠤⠤⠤⠄⠀⠀⢼⡰⠳⠀⣿⠀⠀⠀⡾⠁⢸⠇⠀⠀⠀⠀⢻⠀⣿⠀⢠⣯⠎⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡿⣆⠀⠸⠃⣀⠟⠀⠀⠀⠀⠀⠘⢧⢻⡄⣾⢣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠂⠣⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠓⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠸⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢰⣇⡠⡪⢳⡄⠀⠀⣿⠀⠀⣿⠀⠀⢀⡴⣻⣿⣦⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡯⢊⠔⠁⢹⡄⠀⢿⡄⠀⣿⠀⠀⣾⣳⠟⠝⢹⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣷⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⣯⣷⢷⣺⣿⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠸⣧⠔⠠⠂⢹⡆⢸⡇⠀⣿⠀⣿⣻⣵⣯⣿⠇⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡙⣷⡀⠀⠸⣇⢸⣧⠀⣿⢰⣿⣿⣿⣽⢏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡸⣿⣄⣼⣿⣼⣿⣤⣿⣾⣿⣿⣿⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⢰⠁⣀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠀⢳⠀⠀⠀⠀⡎⠀⡀⠑⢄
⠀⠀⠀⡟⠀⣿⣷⡄⠙⣄⠀⠀⠀⠀⠀⠀⢀⡞⠁⣴⣿⡆⢸⡀⠀⠀⢰⠃⢸⣿⣦⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣀
⠀⠀⠀⡇⠀⣿⣿⣿⡄⠘⡆⠀⠀⠀⠀⢀⡎⢀⣾⣿⣿⡇⢀⡇⠀⠀⢸⠀⢸⣿⣿⣷⡀⢱⡀⠀⠀⠀⠀⢠⠎⣴⣿⡿⠦⠑⢦
⠀⠀⠀⢷⠀⣿⣿⣿⣿⡄⠸⡀⠀⠀⠀⡜⠀⣼⣿⣿⣿⠇⢸⠀⠀⠀⠘⡆⠸⣿⣿⣿⣧⠀⢧⠀⠀⠀⢀⡏⢶⡙⠉⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠸⡀⠸⣿⣿⣿⣧⠀⣇⠀⠀⢰⠇⢰⣿⣿⣿⡿⠀⡞⠀⠀⠀⠀⢣⠀⢿⣿⣿⣿⡆⠘⡄⠀⠀⣸⠀⣼⣿⣦⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢣⠀⢻⣿⣿⣿⠀⢸⠀⠀⢸⠀⣸⣿⣿⣿⠃⣰⠁⠀⠀⠀⠀⠘⡆⠘⣿⣿⣿⣇⠀⡇⠀⠀⡇⠀⣿⣿⣿⡿⣦⣄⠀⢀⣿
⠀⠀⠀⠀⠀⢣⠀⢻⣿⣿⣤⣼⣤⣦⣾⣤⣿⣿⡿⠃⣰⠃⠀⠀⠀⠀⠀⠀⠘⣄⢘⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣟⢀⡜⠈⠙⢿⡿
⠀⠀⠀⠀⠀⠀⣳⡾⠟⠋⠉⠉⠀⠀⠉⠉⠙⠛⢷⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠋⠉⠁⠀⠈⠉⠉⠛⢿⣿⣏
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⣸⣿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⡆⠀⠀⠀⠀⢰⣿⠿⣿⣦⡀
⠀⠀⠀⠀⣿⡏⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⣿⣷⠀⠀⠀⠀⣾⣿⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀
⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣷⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⣿⣿⠀⠀⠀⠀⢿⣿⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⣿⣇⠀⠀⠀⣾⡿⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⢻⣷⠀⠀⠀⢰⣿⠟⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⢹⣿⠀⠀⢠⣿⡇⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡆⠀⠀⣾⣿⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢸⣿⡇⠀⢸⣿⠁⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⣿⡇⠀⢀⣿⡇⠀⠀⢠⣾⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣦⣶⠾⠟⠛⠛⠛⠿⠷⣦⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣴⡾⠿⠛⠛⠛⠻⠿⣶⣴⣿⠟⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣷⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣠⠟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠿⠀⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣤⣶⡴⠞⠋⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⢀⣴⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡀
⠀⠀⠀⠀⠀⠙⢷⣶⣭⣽⣛⣛⣻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣛⣛⣯⣥⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠂⢊⠀⢫⣟⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⣿⣷⡔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣀⣲⡶⠒⠒⠒⠒⠀⠙⢻⠇⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠹⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣼⠀⡸⢠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠨⠛⣹⣿⡆⡄⠀⠁⠇⠀⣰⣿⠃⣀⣀⡀⠀⠇⢸⠇⠀⢰⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠘⣿⣆⠐⣯⡃⠀⢠⣤⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⡅⠤⠈⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⣷⣬⠀⢀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠬⠄⢀⡀⠀⠀⠀⠔⠀⢀⣿⣿⢰⠃⠏⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡀⠠⢤⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠃⡸⠀⠀⡀⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢋⠿⠇⠀⠀⠀⠀⠀⢀⣠⣴⠾⠿⠋⠠⠞⣁⠀⣰⠁⢀⠄⠁⠂⠀⠸⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡟⢻⡟⠫⠆⠀⢀⠉⠀⠀⠊⠁⠊⠑⠀⠈⠜⡸⢁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⣰⣶⠖⠂⠉⢀⡀⠀⠀⠀⢅⠋⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠋⠀⠀⠀⠀⢀⡠⠋⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠔⠋⠀⠀⠀⡀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠁⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



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

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⣠⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⢉⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡰⠿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠐⡀⣤⡆⠀⠠⣀⡛⠁⠀⠀⠀⠀⡀⠄⠠⠠⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠈⠛⠤⣄⣀⡀⢀⠀⢀⡉⠁⣤⢠⡄⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢠⡸⢷⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠴⢠⡀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡄⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⢤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⣈⣁⠈⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠘⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠷⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡾⠋⠉⠉⠉⠉⠻⣿⣿⣿⣇⠀⠀⠀⠀⣾⡟⠋⠉⠉⠉⠙⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⢿⡿⠛⢿⣿⠟⠛⠻⠿⣿⠀⠀⠀⠀⠀⠠⠴⠄⠠⠦⠤⠀⠸⣿⣿⣿⣧⠀⠀⠀⠻⣤⣤⠀⣤⣤⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠃⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣾⣿⣿⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣆⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠛⣿⣿⣷⠀⠀⠀⠀⢈⣿⡿⠟⠛⠛⠛⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣯⣤⡄⠀⣤⣄⠀⢻⣿⣿⠀⠀⠀⠀⠈⢃⣀⣀⠀⣀⣀⠀⢻⣿⣿⠀⠀⠀⠀⠸⣿⠤⠴⠄⠠⠤⡤⠀⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⣀⣀⡴⠶⢶⣄⣀⣀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⡤⠶⠶⠶⠤⠦⠶⠤⠶⠶⠦⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⠩⠅⠒⠛⢉⣀⣤⣒⣦⣂⣠⢀⣤⡴⠶⡶⢖⣠⣤⣀⣀⢀⣉⣛⠻⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣩⣴⠾⠋⠁⢀⣀⠔⣩⣴⠖⢈⡥⣌⣩⡿⢶⣻⣿⣷⣿⣾⡅⠉⠙⠏⡏⠙⣻⢷⢻⡲⣄⠈⢽⣦⣄
⠀⠀⠀⠀⠀⠀⣰⣟⠴⠛⠛⡇⣠⣴⢔⣺⣔⣺⣏⣵⣲⡿⠚⢥⣞⡫⠽⣧⣻⡤⢶⣝⢷⣤⣀⣀⣄⡀⢀⣴⢘⡣⠛⢿⠓⣌⢻⣕⣆
⠀⠀⠀⠀⠀⢰⣿⠏⠀⢠⣎⣹⠥⡙⢢⠌⢛⣗⣲⣿⣷⢶⡶⢤⡾⢻⣷⣞⣱⣯⣟⢋⣹⡏⠘⣿⢿⣿⣷⡿⠽⣗⢊⡽⢗⢹⠈⠊⣾⡀
⠀⠀⠀⠀⠀⢸⣿⣧⡘⢥⡼⢛⣿⣳⣿⣟⣯⣝⣂⣿⣭⡷⣊⢿⣿⢓⣶⡛⣿⡖⣴⣋⣁⡶⠶⠭⣿⣩⡵⣿⣟⣻⣛⣣⣹⡮⢷⡴⣿⡇
⠀⠀⠀⠀⠀⢸⡇⢻⣿⡲⢿⣻⡿⢿⡶⣤⣉⣂⣉⡥⢾⣛⣶⣥⣿⣿⣶⣬⣿⠽⣖⣿⠭⠄⣀⡤⢺⣗⣾⣭⣠⡾⢿⡿⢿⣭⣯⠞⣽⠁
⠀⠀⠀⠀⠀⠈⣿⠈⠀⠙⡛⣶⢭⣉⡘⠶⣞⣛⠆⣼⠻⣶⣷⡾⡾⠿⠏⣾⠿⣿⣷⡞⣏⣿⣉⣳⠮⣗⣒⣾⣫⠽⣟⣿⡷⡟⡏⢠⡿
⠀⠀⠀⠀⠀⠀⢹⡇⠀⡄⠁⢸⠐⢮⣍⣛⠒⠶⠭⢥⣶⣿⣽⣧⣬⣷⣤⣈⠇⣉⣾⣽⣼⣷⣶⣿⣿⡿⠿⠿⠛⠛⢹⠋⢀⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⠀⠀⠀⠐⠂⠬⠭⢑⠒⠂⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠐⠒⠊⠁⠀⠀⠀⠄⡼⠁⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⣉⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣈⣉⠑⠒⠒⠒⠒⠒⠛⢉⣉⣠⠤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠉⠀⠀⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠀⠀⠀⠉⠐⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠰⠁⠀⠀⢈⠂⠀⠀⠀⠀⠴⠒⠀⠀⠀⠒⠀⢳⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠰⠆⠠⠀⠂⠒⠉⢸⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡠⢊⡠⠊⠁⠒⠤⠤⠤⠤⠤⠤⠤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠆⠀⠀⠀⠀⠀⠐⠀⠠⠁⠀⡇⠀⠄⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠬⠙⡆⠀⠀⠀⠠⣤⣤⠤⠴⠋⡼⢄⡀⠀⡀⣀
⠀⠀⠀⠉⠉⠙⠁⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⠆⢀⠏⠀⠈⠓⠄
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠕⡦⢀⠀⢀⣠⠆⠀⠀⢸⠀⠀⠀⡰⠈
⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⡌⠀⣠⡈⠓⠢⢸⡀⠀⠰⠁⢱
⠀⠀⠌⠀⠀⠑⡄⠀⠀⠀⠜⠀⠀⠀⠀⠠⣀⠘⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⡸⠀⠀⠀⢦⡇⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠑⠢⢄⢰⡀⣀⠄⠀⣸
⠀⠁⠀⠀⠀⠤⣙⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢦⠀⠀⣀⣀⡴⠃⠀⢠⠃
⡄⠀⠀⠀⠀⢀⠘⠐⠂⠤⠀⠀⠀⠀⠀⠉⠁⢠⠀⠘⡀⠀⠀⠀⠀⢸⠀⢸
⢷⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⢀⡇⠀⢸
⠀⠳⡇⠀⠀⢸⡤⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⡾⠀⠀⢸
⠀⠀⠹⠄⠠⠒⠀⠐⡄⠀⠀⠈⠑⠢⠤⠤⠤⠜⠀⠦⡀⠀⠀⢠⠇⠤⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠁
⠀⣁⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡚⠉⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠐⠀⠥⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⢀⡤⠚⢁⠀⢈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⢠⠾⣅⣀⣀⠀⠀⠀⠀⠂⠀⠀⡀⠀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⢻⣀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠧⠤⢬⣄⣀⣆⠀⠀⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⢀⠎⠀⠉⠙⠒⠒⠲⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠲⠤⠤⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄
⠀⢸⠀⠀⠀⠀⢀⣠⡤⠤⣄⠀⠀⠀⢀⠉⠉⠙⠓⠒⠲⠶⠤⠤⣄⣀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠶⠶⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠞⢳⡄
⣰⠋⠙⠒⠒⠋⠉⠀⠱⡀⠈⠓⠒⠚⠉⢧⡀⣀⡴⢲⠶⡄⠀⠀⠀⠀⢀⣈⠉⠉⠉⠙⠒⠒⠒⠶⠶⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣜⠁
⢧⡤⠖⡲⠖⢲⠤⢤⣀⣉⣢⣄⣀⠀⠀⠀⢉⣡⠴⠋⠀⠑⢤⣤⠴⠊⠉⢻⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⢣
⠀⢠⠞⠲⢤⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣤⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠑⢤⡈⠙⠒⠲⠤⠤⠴⠒⠊⢉⡠⠋⠀⠙⢦⠀⠀⠀⠀⡴⠛⢦⡀⠀⢀
⠀⠘⠦⢤⣸⣄⣀⣀⣀⣤⠤⠤⠖⠒⠚⠛⠻⠤⠤⣤⣀⣘⣟⢦⣀⣀⣠⠤⠖⠒⠛⠓⠢⠤⠤⠤⠤⠤⣶⣉⣀⣀⠀⠀⠈⠳⢄⣠⠴⠁⠀⠀⠉⠙⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠲⠦⠤⠄⣀⣀⣀⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠀⠲⢋⡉⠉⠉⠉⠛⠒⠒⠒⠦⢤⣀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠚⠦⠤⠤⠤⣶⣖⣒⣋⣉⠉⠀⠀⠉⠉⠉⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⢀⡜⠋⠙⡶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠒⠒⠒⠒⠶⠶⠤⠬⠷⠦⣄⣠⠮⠤⠤⠚⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣽⣿⣿⣷⣿⣶⣶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⢀⣀⠀⢀⡀⠀⢀⣀
⠀⠠⠁⠀⠲⡄⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠈⠉⠀⢫⡀⠀⢀⡈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫
⢀⠀⠀⠀⢀⠀⠉⠀⠂⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙
⡎⡀⠀⢀⠂⡀⠀⠀⠀⡌⠀⢸⡀⢠⠤⡴⡂⠉⠀⠀⠂⠀⠒⠀⢒⣀⣾⣷⡶⢠⣐⡀⠀⠀⠀⠀⠀⠂⠐⢻⡂⠀⠀⠀⠀⢧⠙⡄
⢠⠁⠠⠃⢠⠁⠀⠀⢀⠆⠀⠈⠀⣼⢀⠀⢉⠄⣀⠀⠀⣀⡀⣺⡟⡉⢡⢔⠀⠀⠈⡕⠒⢤⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠐
⠇⡰⠃⢠⡇⠀⠊⡁⠀⠀⠀⠀⠀⡄⠘⢀⢸⠂⣿⠴⢋⢹⢭⠉⠉⣡⠱⠛⠓⢤⣤⣄⠠⣠⣶⠀⠃⠀⠀⣴⡈⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢡⢀
⠐⠋⣥⡄⠀⠰⠍⠠⢄⠠⠄⠠⢈⣧⠟⣬⡇⠨⠄⠠⢘⣼⠖⣏⠚⣧⡟⢿⡉⢸⡆⡿⠒⢘⣿⣄⠀⡴⠀⠄⡡⠶⠀⠔⠀⡐⠀⠀⠀⠀⠀⡀
⠢⢄⠈⠑⠢⣄⠀⠑⠠⡐⠀⠑⢼⠉⡖⢦⢄⡑⠦⣀⢸⣛⠲⠦⣌⣧⠥⡤⠦⢤⠭⡿⠆⠹⣿⣧⣾⡢⠄⢠⠀⠀⢂⢀⣌⠄⠊⡀⠄⠂⡀
⢸⠀⠹⢢⣄⡀⠙⠢⣀⠈⠐⠄⡆⠀⡇⠸⠨⠘⡑⠠⢙⣎⣂⣁⣚⣛⡛⣶⣯⡴⣊⢀⡤⠤⣭⠿⡏⠀⠰⠈⡄⡈⠌⢋⡠⠐⢀⠠⠂⠁⣀⠴⠞
⠇⢀⠇⡸⢘⡏⢰⠤⠀⠙⠢⢀⠃⢀⠇⡆⠈⠦⠥⠀⠀⠉⠁⠦⠄⣀⠀⠀⠀⠞⣁⣩⠜⠋⠀⠀⠀⠀⠀⠀⠉⢡⠈⢌⡄⠊⢀⣠⠔⠊⢅⠘⡄
⠀⡼⢠⠇⢸⠁⢸⡂⠀⠁⠂⣼⣄⠈⠠⠄⠀⠀⠔⠀⠀⢄⠀⠠⠀⠈⠙⠒⠶⣶⠿⠀⢀⣤⣄⣠⡄⢀⣠⡄⢂⡔⠀⣪⡼⡖⠉⠀⠀⠀⠈⢢⠐
⠀⣇⣞⠀⠛⠀⠈⠁⠐⠂⠈⠉⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣴⡿⢶⠐⢂⡁⠲⠀⠀⠀⠀⠀⣠⡴⠚⠉⠒⠒⠶⠶⠶⠶⠶⠶⠷
⣸⣿⣟⣉⣙⣑⣀⡒⠒⠂⠒⠒⠖⠖⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠠⢀⠑⠦⠖⣊⠴⠊⠁⠀⠀⠀⢀⣠⡖⠛⠁
⣍⣁⣀⣀⣀⣉⣉⣉⣉⣙⣛⣛⠛⠒⠒⠒⠒⠖⠚⠻⠦⣄⡀⠁⠂⢀⠉⠒⠋⣀⡤⠊⠁⣀⣴⠾⠉⢁⣀⣀⣀⣀⣀⣀⡀⠀⠈⠁
⣿⣽⣯⣭⣭⣭⣭⣭⣭⣭⣙⣛⣛⣛⣛⡛⠛⠛⠓⠶⠶⠾⠿⢶⣄⡀⠑⠲⠟⠁⢀⣴⠾⠯⠤⠤⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠤⠤⠄⠤
⣿⣭⣽⣯⣭⣯⣭⣭⣭⣩⣍⣩⣉⣉⣉⣛⣛⣛⣛⣛⣓⣶⣶⣶⣮⣿⣶⣤⣤⣾⡛⡒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄
⣿⣯⡛⣿⣯⣝⣯⣿⢿⣭⡋⠩⠻⣿⣍⠉⠙⠻⣯⣍⡉⠛⢿⣍⠉⠉⠉⠙⠛⠉⠉⠉⣉⡿⠛⠉⠙⣻⡿⠛⠛⠛⣓⡿⠛⠒⢒⡶⠛⠒⠒⣲⡶
⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣖⢹⣿⢷⣌⡠⠐⠉⠻⣶⣄⡙⢷⣄⠀⠀⠀⢀⣤⠾⠋⠀⣀⣴⠟⠉⠀⢀⣤⠞⠉⠀⣠⠶⠋⠀⣀⡴⠛⠁
⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣽⡯⣿⢷⣧⡶⣉⠻⣦⣔⠉⡈⠙⢿⣦⡙⢷⣶⡾⠛⠁⢀⣤⠞⠋⠀⢀⣤⠾⠋⠁⣀⣴⠟⠁⢀⣤⠞⠉⠀⠀⣠⠴
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⡻⣿⣿⣦⣗⡬⣻⢷⣤⡀⠀⠙⢻⣦⡉⠀⣀⣴⠟⠁⢀⣤⠾⠋⠁⣠⡴⠟⠉⢀⣠⡶⠋⠁⠀⣠⠴⠋⢁⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣮⣿⣷⣤⡷⣝⡿⣦⣄⠀⡈⢿⣿⡟⠁⢀⣴⠟⠁⣀⣴⠟⠉⠀⢀⣴⠟⠁⠀⢀⡴⠋⠁⣠⠔⠉

⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⠀⠀⠀⠀⢄⠀⣀
⠀⠀⠀⠀⠄⣁⠊⠈⠆⣀⠀⠀⠀⠀⠀⢀⣸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠠⡂⢀⠘⣸⠃⠆⠀⢀⠀⠁⠙⠉⠈⠙⠙⣿⣥⡀⠀⠒⠀⠄⠀⠀⢀⡀⠔⠛⠀⠀⠠⣀⣀⡀
⠀⠀⠀⠈⢀⡙⣤⡀⠜⠈⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣿⡇⠘⢦⡂⡒⢐⠒⠆⠲⡀⡶⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠈⠃⠁⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠉⠙⠚⠓⠛⠊⠉⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣻⣄⢀⣠⣿⣿⡟⠀⠀⠀⠒⡀⣀⠀⠀⠀⡇⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠁⠀⠀⠀⡆⠀⢠⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠌⠀⠘⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠙⠈⢀⣤⠃⠀⠀⢇⣀⠀⣀⣀⣦⠆
⠀⠀⠀⠀⡀⠀⠠⡏⠀⠀⠀⠀⢋⡀⠀⠀⠀⠹⣶⣶⣾⡟⣰⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⢁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠕⠚⠁⠀⠀⠐⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⡀⠀⣀⣶⠀⠀⡀⣀⢠⡄⢀⠀⠀⠀⠀⣼⠀⠀⣧⡀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠁⢸⠀⠀⠈⠳⠤⡧⡴⠟⠃⠠⠥⠼⡿⠟⠛⠻⣷⡄⠀⠀⣧⠀⠀⠈⠳⢦⣤⣤⡴⠷⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠇⠀⠀⠀⣀⠀⠐⢄⠀⠀⠀⣠⣠⣼⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⣤⡼⠋⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠀⣠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⣶⣤⣤⣤⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡞⠀⠀⠀⠀⡸⠿⠛⠏⣗⢀⡀
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠆⠀⠸⣤⣀⠀⠀⠀⠀⢀⣄⣀⣽⡿
⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠋⢠⣤⣤⣀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠃⠈⠉⠉⠁⠀⠀⠀⠀⣻⣯⣽⣿⠀⠈⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠁⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠛⠃⢀⣀⣠⣤⣤⠶⠶⠶⠛⠛⠛⠀⠰⢶⣤⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⣤⡶⠶⠞⠛⠋⠉⠁⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⢩⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀⠉⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣯⣽⡿⠀⢀⣠⣤⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⢛⣹⡷⠞⠋⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠶⠾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠟⠋⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠐⣾⣟⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⢦⣄⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣀⣠⣤⡾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣯⣴⣆⣠⡌⠉⣩⡉⠀⣠⠀⠀⣈⠉⢉⡁⠈⢉⠉⠉⣉⠀⠀⣀⠀⢀⣀⠀⢠⡀⢀⣬⠉⣭⣄⣶⣤⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⠉⣿⡾⠛⣧⡼⢻⣇⣾⢿⣄⡾⣿⣠⡿⣧⣸⠿⣆⣰⠿⣆⣼⠿⣦⡿⢻⣾⠟⣷⡏⢹⡏⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⢹⡆⠀⣿⡁⠀⣿⠁⠈⣿⠁⠘⣿⠁⢹⡟⠀⢹⡟⠀⢹⡏⠀⢻⡇⠀⣿⠀⣼⠇⣼⠇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⡇⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣼⠃⠀⣿⠀⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣷⠀⣿⠀⢸⡇⠀⢨⡀⠀⣿⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣿⠀⢰⣿⠀⣿⠀⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⢿⡀⠈⣿⠀⢸⡇⠀⣿⡀⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠰⠏⢸⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡇⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⢰⡆⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣧⠘⣧⠀⢹⡆⢸⣇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⣸⠇⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣥⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⡇⠘⣧⠀⢸⡇⠀⢸⡇⠀⣿⠀⣿⠁⣿⠀⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇⢻⡆⠸⣇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⣿⠀⣿⢸⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣧⢸⡇⠀⣿⠀⣿⠀⠈⣷⠀⢸⡇⠀⣿⠀⢸⡇⠀⠸⠃⢀⣿⠀⣿⢠⡟⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠈⣷⠀⣿⠀⢿⡆⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡆⢸⡏⠀⣿⢸⡇⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⣿⠀⢹⡇⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⢸⡇⢠⡏⢸⣇⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠾⠷⠾⠷⠶⠿⠶⠾⠷⠶⠿⠶⠾⠷⠶⠿⠷⠾⠷⠾⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠄⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠖⠉⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⢡⠖⠛⢛⢲⣞⠒⢇⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋⠉⠉⠓⢦⠤⠤⣤⠶⠤⣤⠤⠖⢉⣨⠽⠛⣿⣆⠀⠀⠇⢴⠊⢱⠛⠉⠁⠀⢓⠩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢀⣀⣈⣷⢖⣚⡷⢀⡔⠒⠛⠉⠀⢀⣴⡿⠋⠀⠀⠀⠘⠑⠎⡳⠖⢟⡠⠳⡄
⠀⠀⠀⠀⣠⣶⠿⠷⠈⠙⢷⣦⣀⡏⠉⠉⠁⠀⠀⠛⠉⠳⣄⣀⣤⡶⠛⢁⠀⣀⠤⠤⢤⡀⠀⠀⠁⢴⠈⢱⡆⣿⠐
⠀⠀⠀⠀⠛⣿⣄⠀⠀⠁⠀⡀⠉⠛⠷⠶⠶⢤⠶⠶⠶⠛⠋⢉⣀⣤⠖⠃⠰⢑⡄⠆⣤⢹⣄⡤⠦⠉⠙⠈⠡⠃
⠀⠀⠀⠀⠐⠈⠛⢷⣤⡀⣎⠉⠉⠀⠀⠀⠠⠀⠠⣄⢀⣠⣴⠿⠋⠁⠈⠀⠀⣈⠃⣄⠿⣸⠃⣠⠰⢤⡘⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣤⠴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⢿⢦⡀⠗⣤⡺⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣴⣻⡌⡇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠚⢉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⡀
⠀⠀⠀⠉⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⠄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠁⠀⠘⠐⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑
⠖⢺⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⢀⠆⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠐⡁
⠀⠐⠅⠀⡄⠐⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⡍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠐⠢⠐⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠐⠘⠀⠀⠛⠢⠀⠀⠈⠁⠀⠀⠀⠉⢀
⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠘⠘⠀⠈
⠀⠀⠀⠀⠄⠀⣀⣀⠀⠄⠂⠁⠀⠀⠀⠀⠐⠠⢀⡀⢀⠤⠂⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠠⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠂⠠⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠊⠠⡔⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠢⡄⠈⠀⠀⠀⠀⠀⠗⢀⠀⠀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠥⠄⠁⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⠁⡀⠀⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠰⢆⠠⠄⠠⠔⠀⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠲⠂⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠐⠒⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠦⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠄⠀⠀⠘
⡄⠒⠠⡀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠁
⠃⠀⠀⠈⠀⠉⠀⢀⠁⠀⠠⠂⠀⢀⠂⠉⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠠⠄⠀⠤⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡈⠣⡙⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠠⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠣⠄⠀⠀⠀⠀⠀⠐⠀⣀⣑⡎⠀⠀⠀⠀⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣄⣠⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⡴⠶⠞⠋⣠⣶⣶⣄⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⡗⠀⠀⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣈⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣈⣁⣤⣤⠶⠶⠞⠛⠛⠋⠉⠉⠉⠀⠘⠛⢶⣤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠷⠾⠛⠛⠉⠉⠀⠀⠀⠰⣷⠆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⣾⣾⣷⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠐⢿⡾⣿⣃⣤⠶⠞⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠷⠶⠶⢦⣤⣤⣄⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠿⣷⣿⠗⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣉⠈⢛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠶⠖⠀⠶⠶⠞⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⡛⢋⣉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡾⢻⣧⡾⣿⣀⣾⣧⢠⣾⡆⣰⣷⠀⣾⡆⢠⣷⡀⢠⣷⡀⣸⣷⣠⣿⣆⣾⢷⣼⠿⣾⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⠘⣿⠀⢸⡟⠁⢻⡟⠈⣿⡏⠸⣿⠏⢻⡿⠉⢷⡿⠈⣿⡏⠘⣿⠁⢹⡏⠈⣿⢀⣿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⠀⣿⠀⠘⣧⠀⢸⡇⠀⢻⡄⠀⣿⠀⢸⡇⠀⢸⡇⠀⣼⠀⠀⣿⠀⢸⡇⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢹⡆⢹⡆⠀⣿⠀⢘⡃⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⢸⡇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⢸⡇⠀⢿⡀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⣸⠇⢼⠇⣿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢠⣿⠀⣿⠀⣤⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄⢿⡄⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⢸⣧⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⣿⢰⡏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢨⡄⠀⣿⠀⣿⠀⠘⣧⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⢰⡏⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠘⣧⠀⣿⠀⢻⡄⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢠⡟⢸⡇⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄⣿⠀⢹⡆⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⠛⠀⢸⡇⢸⡇⣸⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡇⢻⡆⢸⡇⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⡇⣿⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣸⡇⠘⣧⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⡇⣿⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⠉⣁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠈⠁⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠀⢄⠔⠒⠢⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠈⠉⠂⢀⠀⠀⠈⠂⠀⣀⡀⣀⠤⠄⠊⠀⠀⠀⠀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄
⣤⡒⠁⠁⠀⠈⠈⠝⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠚⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡎
⠑⠈⠦⣄⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠠⠁⠀⠈⠀⠀⡤⠄⠚⢡
⠀⠀⠀⠈⠢⡀⠉⡀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠈⠁⠙⡄⠀⠀⠙⠄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠄⠠⠀⠰⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠈⠐⢲⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠁⠒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⢄⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠁⠺⠀⠀⠱⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠑⢄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣀⣄⠐⠂⠀⠠⢄⠀⢤⠃⠀⠀⠀⠀⠠⠄⠒⠂⠒⡠⠴⢤⡀⠀⠀⠂⠀⠀⠁⠢⡀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⢏⠙⢳⣻⠁⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠀⠀⠁⠀⠀⠀⡠⢡⡀⠤⢈⠀⠀⠀⠰⡀⠀⠀⠈⠑⠠⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡋⠀⠄⡀⢐⣠⢜⠤⠉⠀⠀⠀⢄⠀⢠⡄⠀⠀⠁⠀⣀⣀⠚⠁⠀⠀⠀⠈⠐⠢⢀⡀⠀⠀⠈⢛⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠍⢐⡀⠀⠀⢄⠀⠈⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠁⠁⠀⠄⢛⣒⣐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⢀⢀⡀⠀⠀⠘⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠈⠁⠀⠀⠤⠀⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠎⠀⠀⠀⠐⠛⠋⠀⠀⠀⠲⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠴⣦⣤⣤⣤⡀⠤⠒⠊⠁⢈⣽⠍⢻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠈⠉⠹⣝⠐⢯⠀⠔⢨⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⣶⠀⠇⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣻⣦⠀⠰⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⢀⣧⠳⣀⠀⠄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠂⠉⠉⠉⠉⠉⠛⠢⣌⠲⢌⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠐⠒⠲⣄⡊⠁⠉⠙⡆⠀⠑⢄⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠁⠀⠀⡁⠀⠀⠀⠄⠳⠣⠔⠂⡸⢡⠟⢆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⡰⠂⠙⡦⢤⡐⢄⠠⣦⠃⣰⢓⠛⠀⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢹⠀⠀⡇⠀⠀⠘⠂⣈⠀⣳⣷⣶⣋⠯⢔⣐⠫⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⠀⠀⠑⠶⠖⠒⢶⠞⡭⠗⢻⣍⡑⠶⡃⠈⠀⢰⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⢧⠀⢰⠁⠀⠔⠰⠀⢰⡜⠈⢻⢁⠁⡈⢦⠴⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣇⠀⠀⣣⡀⠳⣀⠀⠀⣠⢎⡄⠖⠈⡄⠀⡅⢠⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⢢⣤⣤⠍⠩⠿⠶⠷⠿⠿⠿⣷⣄⣰⠿⣦⣈⠉⠉⠱⢠⣀⣀⡣⠓⠦⠚⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠙⠻⠾⢏⡗⠢⣤⣤⢀⣀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠉⠁



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

⠀⠣⠀⠀⠀⠀⡠⠒⠉⠁⠀⠈⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠁⠀⠁⠀⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠙⢦⣀⠀⣀⣀⡴⠂⠀⠀⠀⠀⢁
⠐⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⢀⠀⠀⠉⠢⠤⢀⣀⠀⠀⠔⡣⠒⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⢀⡠⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠰⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠀⠐⠠⠄⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⡠⠂
⠀⠈⠀⠀⢀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⠁⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⢠⡴⠶⣦⡀⣠⡶⠶⣤⠀⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢿⡀⠀⢸⡇⣿⠀⠀⣸⠇⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣾⡄⢠⠞⠓⠀⣦⠆⢠⠞⣓⡂⣾⣳⢠⠞⠓⡆⢶⢰⠆⡷⣄⡆⣾⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⠉⠙⠈⠓⠚⠀⠋⠓⠈⠓⠚⠁⠉⠑⠈⠓⠚⠁⠙⠚⠀⠃⠘⠃⠛⠚⠁

⠀⢀⣀⣀⡀
⠑⡈⠶⠆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠖
⠄⢰⠸⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⢄
⠀⠀⡠⠀⠐⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠐⠢⠄⣀⠉⠂⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⣀
⠒⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⣀⠠⢔⡡⠒⠀⠀⠁⠒⠢⢄⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⡴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⡆⠐⠀⠀⠀⡅⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠘⡀⠈⠂⠄⣀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠙

⣤⣤⣤⣤⣤⡤⠄⡠⠤⣤⡠⣤⡤⠄⠤⡄⠠⡤⡤⢤⣤⠤⠀⢠
⣿⣿⣿⣿⣿⡧⠄⡇⠀⣿⠀⠀⠀⠀⡄⣿⡄⠀⣿⠜⣿⡄⣩⢸
⠉⠉⠉⠉⠉⠉⠁⠉⠈⠉⠉⠉⠁⠁⠁⠀⠀⠃⠀⠘⠋⠀⠉⠙⠁⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢩⡈⠾⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⡀⠠⠁⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠔⢀⠤⠞⠀⡛⠢⠜⠛⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠉⠻⠷⡨⠦⠄⠀⠀⣈⡀⠀⠀⠀⠀⡀⠄⠒⠈⡴⠃⠀⠀⠰⠆⠓⡀⠀⠰⡄⠀⠀⠈⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠣⠘⠄⠀⠀⠀⠀⠟⠀⠀⠀⠤⣀⠀⠈⠛⠀⠀⢀⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠂⠀⠀⢠⠀⠠⠀⡀⠀⢀⠀⠀⠈⠆⠀⠀⢀⠛⣼⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠢⠀⠀⠀⠀⠀⠀⢠⠀⢁
⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠈⠀⠀⠲⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠸⡆⠀⢠⣧⣄⠀⢀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⣀⣡⣤⡤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⠀⣀⡤⠂⡠⠐⠁⠀⠀⠀⠀⠀⠘⡄⠀⠃⠀⠈⢀⣀⡤⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠋⠉⠐⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠇⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠤⠠⢍⡒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⡠⣈⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠃⠀⡁⠈⢈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⣄⡀⡄⠀⢠⣤⠀⠀⠀⢀⠊⠀⠊⠁⠀⠀⠐⠈⢳⡄⠀⠀⠀⣀⠀⠀⢸⠇⠀⠀⡁⠒⠒⠀⠀⠀⠐⠢⠍⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠰⡀⠇⢆⡀⠐⠐⢻⡟⢃⣤⡞⠃⠀⠀⠀⡟⢀⡀⢸⠀⠀⠀⠀⠀⠘⣟⠄⠀⠀⡀⠸⠆⠀⠀⠰⢺⠁⠀⠀⣠⡖⠀⠀⣰⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣙⠓⠂⣈⠓⠄⢠⣁⠀⠀⠀⠀⢯⡀⠀⠘⠀⠐⠃⢀⠊⠀⢻⠈⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡥⠀⠁⢀⡱⠎⠀⠀⠀⠀⠀⠉⢙⣢⣦⡤⠴⠦⠀⠐⠁⠀⠀⠀⠀⠈⠢⣀⠰⠆⠤⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠢⡀⠀⠀⠀⠠⣄⢀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠄⠀⠀⠈⠁⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⡀⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠓⠒⠦⣤⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⠱⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠈⣀⠴⢻⡠⡀⠀⠀⠀⠀⠀⠀⠀⠔⣉⠽⠓⠀⢀⣩⢶⣤⡗⣦⠀⠀⠀⠀⠀⠀⢀⡶⠹⠀⢹⣌⢏⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣟⢋⢸⣦⣟⢀⡅⠀⠀⠀⠀⠀⢠⣶⣞⠁⠀⡠⠊⡸⠋⠁⠀⠀⣼⡆⠀⠀⠀⢀⠴⠋⢁⠁⠀⠸⠈⠢⠀⠂⠹⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠹⡉⠉⠉⢁⡀⠀⠢⡄⠀⠀⢸⡿⢁⣤⣬⠄⠊⠁⠀⠀⠀⠘⢹⠋⣧⠀⠀⢀⠘⢀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡔⣰⠚⢀⠆⠀⠀⢱⠀⠀⠀⢏⢦⠀⠜⡆⠀⡾⣻⡜⠟⠁⠀⠀⠀⢀⡤⠂⠔⠃⡸⡇⠀⠀⠂⠃⠸⠀⢸⠀⠀⡀
⠀⠀⠀⠀⠀⡇⢀⠔⠋⠀⠠⡴⠋⠀⠀⠀⠀⠈⠀⢰⡇⠀⠁⡉⣈⠃⠀⣀⣀⣤⣬⣤⠄⣠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢇⠀⠀⣴⣰⠠
⠀⠀⠀⠀⠀⢁⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⡀⠃⠀⠀⠁⠉⠑⠀⠉⠉⠉⡀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⢀⡀⠖⠀⠀⠈⠈⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠳⠉⠓⠂⠀⣀⠰⠖⠒⣀⠶⠐⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠤⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⠲⢤⡟⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣠⠟⡧⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⣠⠴⢾⣁⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀⣤⠖⠛⠛⣆
⠀⠀⠀⢀⣶⡈⠉⢻⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠁⣠⠖⠺⣅⣛⢳⡿⣆⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠉⣉⣀⡀⠀⠀⢿
⠀⠀⣤⣏⣤⠟⠉⠙⢷⣄⠀⠀⠀⠉⠓⠶⠤⣤⢶⠀⠀⠀⢠⣧⣯⡞⡿⠛⠙⢯⣹⠏⠀⢹⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⢠⠞⠉⠈⠉⢳⡄⠈⠳⢤⡀
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠳⢦⣤⣀⣀⣀⡤⠿⣼⠀⠀⠀⠘⡇⠉⠙⢛⠒⠒⣿⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⠞⠀⢺⡀⠀⠀⠀⢸⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠉⠙⠛⢦⠶⡆⠀⠀⠀⠀⠹⡄⠀⠉⠀⡼⠁⠈⠀⠀⠀⠸⡆⠀⠀⠀⠀⡞⠁⠀⠀⠀⠓⠦⠤⠶⠋⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⠴⢿⣸⠇⠀⠀⠀⠀⠀⠙⣆⢀⡾⠁⠀⠀⠘⠃⠀⠀⢻⡀⠀⠀⠘⣇⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⢀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡄⠀⠈⠁⠀⠘⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢳⣄⠀⠀⠄⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣩⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡇⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣄⣴⠓⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡄⠀⠀⠀⠀⣴⠂⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣄⣽⢾⣄⣽⣴⠻⣦⢶⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣼⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⡶⠧⠤⠽⢶⡄⠀⠸⡇⢺⠁⠀⠀⠀⣠⣾⠟⠀⠀⢠⡶⠤⣽⣃⣠⠟⡇⣸⣆⠈⢷⡃
⠀⠀⠀⠼⣧⡤⠤⠤⠤⠤⠴⠶⠶⠶⢶⡾⠇⠀⠀⠀⠀⠀⣸⠶⠶⠶⠶⠾⣇⡀⠀⣿⠘⢡⡟⠙⠻⣿⠁⠀⠀⠀⠘⠓⠒⣦⡉⠻⣼⡇⣿⠙⣆⠈⢳⣀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⢳⠀⣩⡤⢬⣷⣄⣈⡿⠀⠀⠀⠀⠀⠰⣶⠿⢷⣤⣬⣷⣧⡼⠿⠖⢛⡏
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⢯⡀⠀⢘⡏⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟⠛⡻⣿⠳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡴⠶⣴⣷⣴⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡀⠁⠀⠙⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⣲⣾⠷⠮⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⣰⡯⠶⠓⠶⢭⣉⢿⣩⣽⣇⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠶⠖⠒⣖⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⢠⡄⠀⠈⠙⠶⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠁⢀⠀⠈⠳⣄⢿⣍⢳⣈⠳⣄⠀⠀⠀⠀⢀⡾⢋⡐⠶⠀⣦⠀⠁⠶⠈⠻⣆⠀⠀⠀⠀⠀⠀⢸⡷⣄⡉⠙⠛⠦⣄⣤⠀⠀⠈⠳⣄
⠀⠀⠀⢸⡇⢀⡀⠀⠀⠈⠀⠠⠄⠈⢧⡈⣿⣩⡗⢹⠀⠀⠀⠀⠸⣇⠛⠀⠀⠀⠠⠴⠀⠀⠚⠃⠸⡇⠀⠀⠀⠀⠀⢸⣧⠉⡷⠀⢘⣂⣀⣙⠳⣴⠞⠀⠘⣧
⠀⠀⠀⠀⠙⢦⡀⠀⠃⠀⠀⠀⠀⠘⠂⢷⠀⣻⣿⢸⠃⠀⠀⠀⠀⣿⣉⣛⣛⡛⠛⢛⣻⣟⣛⢛⣿⣇⠀⠀⠀⠀⠀⢸⠷⠚⢁⡾⣫⣤⢲⢯⣳⣬⠷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠃⠀⢀⠀⠘⣧⣿⣼⡟⠀⠀⠀⠀⠘⣯⣉⣁⣨⣭⣿⣭⣥⣤⣭⣭⣥⡾⠀⠀⠀⠀⠀⢸⣤⡀⠘⣏⣳⡼⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣈⡀⠀⢻⢡⡞⠀⠀⠀⠀⠀⠀⠘⢯⣉⠀⠀⠀⠉⠛⢶⣄⢀⣴⠃⠀⠀⠀⠀⠀⣿⣠⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠖⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠈⠁⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘
⠀⠠⣀⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠖⠂⠀⠀⠀⠀⠀⠀⠠⢠⠄⠀⠠⠆
⠀⠀⠈⠀⠀⣠⠴⠉⠀⠀⠀⢀⡀⡈⠀⠠⠤⠒⢀⣰⡾⣍⣉⠜⠀⢂⣻⣄⠄⠀⢀⠀⠀⠀⡀⠘⠁⡠⠀⠀⠀⠀⢀⠀⡀⣣⠋
⠄⠀⠀⠀⠀⠈⢖⢒⣛⣥⡽⠁⠤⠖⠛⠓⠂⠀⣀⠀⠀⠀⠠⠀⠀⠀⠉⠁⠩⠭⠤⠔⠂⠉⠀⠀⠰⡁⠀⢀⡀⡄⠄⠈⣽⠏⠓⡲⠖⠚⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠈⠉⠉⠤⠤⠤⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⠀⠨⣟⠓⠂⠈⠀⠀⠀⠆⠀⠨
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⡼
⠓⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⣠⠞⠁⠠⠄⠀⠀⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⡇⠀⠀⠀⠀⠀⢈⠀⠀⠉
⠀⠀⠀⠀⠒⠛⠖⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠸
⠀⠘⡿⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠃
⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡊
⢀⣠⠌⢉⢻⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠄⠀⠀⠀⠀⠀⠘⠰⢒
⠀⠀⠀⠈⡟⢶⡤⠄⠒⠊⠁⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⢂⣤⠖⢃⠀⠀⠁⡨⢶⢀⡄
⠀⠁⠀⠀⠘⣟⠛⠁⠠⠀⠀⠀⠐⠊⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡈⠀⠂⠀⠂⠀⠂⢀⠠⣾⠃⠀⡇⠈⠃
⠀⠁⡆⢀⠀⠘⣟⣀⣐⣃⡀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠄⠤⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⡀⠒⠘⢭⣁⡀⢀⣊⠀⠁⠂⠤⣖⡁⠀⣿⡧⠘⠁
⠂⠐⠁⠀⠀⠀⠘⡝⠋⠀⠀⠀⠰⠀⠀⢀⠇⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣶⡟⠠⢤⠤⣞⡀⠀⢠⡬⠗⢻⠁⠀⣿⡧⠐⠁⠀⠀⢀⣀
⠤⢄⠀⠐⠂⠰⠀⠙⢄⣀⣀⣀⣈⠀⠀⠁⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⡀⢠⣤⡀⢸⣯⠉⣷⡀⢸⡻⠐⠁⡀
⠀⢸⠂⢀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠿⣶⢆⠄⢀⡀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠈⠉⠁⠒⠻⠧⠽⠗⠈⠀⡀⠀⠀⠀⡀⠀⢀⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⣄⠀⠀⠀⠀⠀⣠⡖⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠁⠉⠉⠉⠉⠉⠊⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣄⠀⠤⠄⠀⣤⡀⠀⠀⡼⠑⠒⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⣳⡄⢆⣰⣆⡠⠀⣒⡾⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡌⢢⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣠⠓⢤⣀⣀⣠⠴⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢱⡀
⠀⠀⠀⠫⡉⠈⠀⠀⠀⠀⢹⡀⠀⠈⠉⠀⠀⠀⠀⠀⡔⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠈⡇⠀⠀⠀⣞⠒⠒⠛⠒⠒⠲⠤⠤⠤⠈⢧⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠳⣄
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠻⠦⠴⠒⠒⠒⠒⠒⠒⠒⠒⠮⠷⣄⡀⠀⠉⠒⠦⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠐⠒⠒⠀⠠⠤⠤⠤⠤⠄⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠔⠒⠊⠉⠉⠉⠉⠒⠒⠲⠤⠤⠤⠖⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠞⠃⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢀⢤⠴⠇⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠈⠃⠒⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠃⠈⠲⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⢀⠀⠄⠂⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⢀⠀⢀⣀⡤⠀⠠⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠈⠈⠃⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠑⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⢩⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢸⠀⠀⢨⠁⠀⢀⠀⣄⡠⠄⡄⠤⠈⠡
⠀⠀⠣⣀⡁⠐⠒⠈⠅⠀⠀⠠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠁⢂⠘⠈⠀⠐⢸⠀⠀⠸⠀⠀⢈⣉⠀⠈⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠜⠀⠈⠁⠀⢰⠈⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠉⠁⢀⠀⢀⠀⠐⠀⠀⡆⠀⣥⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⡀⢤⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⡍⠍⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⣀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁
⠀⢀⠊⠈⠁⠢⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠐⡂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠇⠊⠀⠀⠀⠠⠀⠄⠀⠒
⠀⠀⠀⣀⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄
⠀⢰⡄⠀⡶⢢⠀⡄⡄⠀⢸⠀⠀⠀⠀⠀⠀⠾⢁⣈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠐⡀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠘⠠⠀⠀⠠⠜⠀⠀⠈⠀⠀⠀⡄⠉⡁⠘⠒⣒⡓⣊⠉⠹⡄⠀⠀⠀⠀⠀⠀⢐⠠⠤⣃⡀⠀⠀⠂⠀⠀⠀⠁⡠⠒⠉⠀⠤⠠⠈⠉⠒⣄
⠀⠀⠀⠐⢤⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⡜⠥⠲⠷⠈⠇⠭⠆⢠⠇⠀⠀⠀⠀⠀⠁⢃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡴⠡⠠⠤⠤⠀⠤⠰⠔⠆⢸
⠀⢠⠀⠀⣈⠑⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣄⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠘⢀⠀⠀⠀⠀⠈⠰⡀⠂⠀⠀⠀⠀⠀⠀⢄⡀⠀⡀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⢠⡀⣠⣄⢀⣤⡀⣠⣄⢠⡀⠀⣠⡀⣤⣤⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣿⣼⢿⡇⣿⣾⠈⠃⡇⣿⢸⡇⠀⡿⣇⢸⡇⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠇⡿⢸⠟⣧⡿⢺⣴⠇⣧⡿⢸⣥⣴⠗⢿⢸⡇⢸⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⠤⠤⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠄⠈⠀⡽⢇⡠⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡂⠀⠀⠀⠈⠉⠉⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠤⠀⠀⠀⠀⠄⠀⠀⡰⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⡞⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢩⠔⠒⠞⡰⠁⢠⣟⠁⠀⠠⠤⠤⣄⢀⣰⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡴⠁⢠⠇⠀⠉⠁⠒⠐⠊⠀⠠⢙⠥⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡖⠀⠀⠓⠂⠤⠼⠁⠀⡿⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡀⠀⠀⠀⠁⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠒⠦⢤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠠⠤⠤⣄⣀⣀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⣠⣤⣼⣿⣿⣿⠶⠀⠀⠀⠐⠁⠐⡄⠀⠀⠀⡠⠤⠶⢶⣦⣀⡀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠠⠞⠀⠠⠞⠁⠀⠴⠋⠀⠄
⠀⠀⠀⠉⠉⠋⡁⠰⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠄⠀⢾⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⢰⣦⣤⣴⣦⣀⣰⣤⣀⣠⣤⣄⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⠀⠰⠀⡿⠀⠀⠘⠛⠈⠡⠜⠆⠛⠰⠼⠧⠴⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⢀⡀⠀⣠⡆⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠈⠁⠀⠀⢀⣴⡿⠛⠛⠻⠛⠢⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣶⣿⣿⠻⠿⠇⠀⠉⠉⠀⠁
⠀⠀⢀⠐⠄⠀⠀⠀⠀⠂⢈⠄⠀⠀⠀⢀⣽⠏⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⡄⠀⡀⠀⠘
⠀⠀⣄⠀⠁⠒⠠⠁⠀⠖⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⠀⠀⠀⠀⠇⠀⠀⢰⠘⡆
⠀⠀⠓⠺⢿⣈⡢⠞⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⣠⠁⢀⠘⠞⢣⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡷⠈⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⡅⠀⢠⡇⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣿⣿⣟⣩⠁⠀⠀⠈⢂⠀⠀⠸⣿⣏⠰⡇⠀⠀⠀⠀⠀⢁⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠓⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠿⠉⠉⠉⢙⠉⠹⠀⠀⠠⠀⠀⢻⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⡁⣹
⠀⠀⠀⠀⠈⢡⡆⢈⠜⢧⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣄⣠⣄⠀⢀⠀⠀⣦⠀⠀⢆⠃⣿
⠀⠀⠀⠀⠀⠉⡤⠋⠀⠈⡆⠒⡀⠀⠀⠀⠀⢀⣠⠄⡐⢻⠷⠢⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⠛⠋⠉⠻⠀⠈⠙⠂⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣮⣿⣷⣽⣭⣦⣴⣿⡤⠀⠆⠀⣠⠋⠀⠀⠷⠂⠀⠀⠀⠀⢀⡀⠀⠀⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣐⠶⢿⣯⣝⡳⣆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠃⠀⠚⠀⠀⠘⠆⠀⠀⠀⠄⠀⣹⠀⢀⡳⢶⣶⡼⢷
⠀⠀⠀⠀⣀⠀⠀⠛⢷⣦⠋⠟⠁⠛⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⣴⠏⠀⠀⠉⠀⠋⠑⠚
⠀⠀⡆⠀⢹⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⢴⡶⠀⠀⠀⠀⠜⠀⣼⠇⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠈⡱⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠜⠋⠀⠀⠀⠀⠀⠤⣴⠏⠀⠀⠀⠠⢸⢃⠐
⠀⢀⡇⠀⠀⡷⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⡴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⡀⠀⠀⠀⡘⠘⠀⣇⡁⡐
⠀⠸⡇⠀⢀⡘⠂⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁⠁⠈⢹⡷⠁
⠀⠀⡇⠀⢠⠟⠀⠀⠀⠀⣄⡀⣔⡾⢤⠗⣤⢠⣆⠤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⡄⠄⠆⢂⢐⡐⡀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡾⠂⠀⠀⢃⣀⠐⣛⣂⢛⡚⣘⣋⢳⠞⠋⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⡟⠒⠐⠂⠂⠃⠐⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠋⠀⠈⠃⠀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠘⡄⠀⠀⠀⣀⣀⣀⠀⠂⠀⡰⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠉⣭⡉⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡟⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⢤⡀⢀⠀⢨⡄⠀⠀⢂⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡇⠀⠆⢸⠁⠀⠀⠰⣿⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠐⠒⠤⣐⢕⠠⡀
⠀⠀⢠⠠⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠒⠒⠒⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⡀⠈⠑⢕⡌⢂
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠈⢫⠀⠃
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢁⠀⠀⢀⣀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠈⠐⠢⠤⣀⡀
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⠜⠀⠀⣖⡄⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠠⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢀⣀⡀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢎⠆⠀⠀⠀⠉⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢣⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⣾⠓⠒⠓⠂⠂⣴⠲⠤⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⢉⡅⠀⠀⠈⠀⠀⠾⠀⠀⠉⠀⠀⠀⠈⠁⠛⠡⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠂⠀⠀⣀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠉⣀⣀⣀⣀⣀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠐⠃⣀⣀⣀⣠⣠⡴⠒⠖⠲⢶⢿⡛⡟⢛⠛⣯⡉⠛⠛⠛⠛⠁⢉⣉⠉⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡶⣛⠹⠿⠟⠷⠀⠤⠀⣏⣀⣀⠀⢀⠃⠘⠻⠄⢡⡜⠀⠃⡚⢺⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠐⠒⠳⠒⠐⠒⠒⠚⡆⠉⠈⢉⠀⡤⢄⣀⡄⠀⠈⠉⠉⠉⠉⡏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠲⠆⣴⣤⣤⣄⣠⣤⠷⠔⠓⠋⠉⠀⠀⠉⠉⠓⠛⠒⠶⠶⠖⠓⠛⣈⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠚⠹⡍⠀⠀⠀⠈⠉⢙⣳⣋⣭⣉⡲⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠋⠁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢻⡄⠀⠀⣀⣾⡿⠗⠉⠉⠉⠉⠲⣤⣢⡀⠀⠀⠀⠀⣠⠿⠁⠀⠊⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⣄⠃⠀⢹⣄⣰⣷⠉⠀⠐⠢⠄⠀⠄⠀⠀⠉⢦⡠⠀⢀⡼⠁⢀⡀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠳⠦⡀⠈⠁⠀⠣⠀⠂⠀⠀⠀⠄⠀⠄⠀⠘⢒⣠⢟⠁⠤⠄⠀⠀⣈⠀⣶⣗⣀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢷⣦⣄⢉⠁⠉⠃⠦⠤⠤⢤⣀⣀⣤⣀⣠⣀⠠⠤⡤⢦⢤⡔⣆⡴⠻⠛⠛⢁⡹⠬⢣⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣄⠈⠁⠀⣍⠸⠿⠷⠶⣤⣤⣀⣀⣀⠀⠁⠈⠉⠉⠀⠀⠈⠁⣀⢀⣤⠴⠶⠲⢟⡁⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⠀⠠⠖⠁⢀⡦⠀⣀⢁⠀⠉⢉⣉⡉⠙⠃⡳⠋⠉⡉⠙⠛⠉⣉⡠⠤⠀⠀⣀⢴⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⠁⠀⢄⠀⠀⠂⣠⠉⢀⡠⠂⠏⠀⠀⢤⡁⠀⠀⠉⠀⢦⠄⠀⠐⠒⣀⠦⠤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣔⠂⠘⠶⠤⣦⣤⡀⢚⡄⢀⠀⡴⠒⠂⢰⢀⡀⢦⣀⣤⠲⠴⠶⠄⠈⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠛⠉⠉⠿⡆⠀⠀⢀⡀⡼⠁⠁⠈⠀⠀⠀⠀⠀⡀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠀⠀⠀⠀⠀⠈⠓⢮⡴⠛⠁⠀⠀⠀⠀⠀⢀⡀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠲⠦⠀⠤⠤⠀⠄⠀⠒⠚⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡒⡳⠓⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠅⠚⠙⠣⠴⣶⠪⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢗⠉⠑⠿⠤⣄⢈⢀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠸⠛⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠂⢀⡔⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⡠⠞⠉⡅⠀⣠⠞⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⠀⠀⠀⠈⠙⠒⠤⣀⣀⡾⠀⠀⠀⠈⠙⠁⠀⠀⡠⠕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⣠⣶⡟⠓⢄⡀⠀⠀⠀⠀⠀⠀⡍⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢄
⠀⠀⠀⠀⣀⣤⠶⠋⠁⢀⢤⠂⠀⠙⠋⠐⠠⡎⠈⠉⠉⠁⠀⠀⠾⢁⠃⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈⢦
⢀⣠⠴⠚⠉⠀⠀⠀⠀⠈⢈⠢⡀⠀⠀⠀⠀⠈⢣⡒⠤⣀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠑⢌
⠻⣧⡀⠀⠀⠀⠀⠀⠀⠠⡊⠑⢌⠢⡀⠀⠀⡀⢸⡁⠀⠈⣡⠾⢻⢀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇
⠀⣿⠙⠷⣄⠀⠀⢠⠀⠀⠘⣄⠈⠢⠟⣖⠭⠒⢉⣠⣶⣋⡥⠴⡇⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⡸⠁
⠀⣿⠀⠀⠈⠻⢦⡈⠘⡄⠀⠈⠢⠖⠉⣀⡤⠞⠋⠁⠀⠀⢀⡄⠈⠒⠤⣀⠀⠀⠀⠀⢀⠀⠀⢀⠞⠁⠐⢀⠞
⠀⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠀⣰⠟⢴⢡⠄⠈⠧⠚⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠶⠋⢹⡆⠀⠀⠐⢼⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠁⢀⡸⣃⡠⠎
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣸⠀⠀⠀⢀⣤⡤⠖⣾⠛⠒⠒⠒⢶⠚⢻⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⢹⡀⠀⠀⠀⠙⡆⠀⣿⠀⠀⠀⠀⢸⡇⠸⣿
⠀⢹⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⡇⠀⠀⠀⡏⢳⡀⠀⠀⠀⠹⡀⣿⠀⠀⠀⠀⢸⡆⠀⣿
⠀⠘⢧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⢳⡀⠀⠀⠀⢳⡟⠀⠀⠀⠀⢸⠁⠀⣿
⠀⠀⠀⠻⣄⠀⠀⠀⠀⢸⠀⣀⣠⡷⠤⠴⡖⠃⠀⠀⢳⡀⠀⠀⠈⡇⠀⠀⠀⠀⠚⠂⠀⢹⡄
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⠋⠉⠀⣀⣀⣀⡗⠀⠀⠀⠀⢳⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠸⠷
⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣶⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠃⢀⣀⡀⡀⠀⠀⠀⠀⠈⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⣄⠀⠀⠈⠁⠸⠄⠀⠀⠀⠀⠀⡈⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣤⠀⠀⣠⣤⣤⣤⡉⠢⢀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣼⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠍⢠⡄⠀⢈⣤⠀⠀⠉⠂⠀⢷⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠁⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠉⠂⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠐⠢⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠁⠈⠄⠁⠤⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⢀⣠⣤⣴⣆⣀⡀⠀⠀⠀⠀⢸⣤⠀⣈⠆⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠠⠄⠀⡀⠂⠀⠈⠙⠻⠯⣭⠍⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠴⠋⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠦⠤⠶⠒⠁⠀⠀⡰⠋⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢲⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠓⠦⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠒⠁⢠⠋⠀⠈⠸⣖⣤⣤⣤⠠⠄⡐⡅⠀⢀⣠⠂⣠⡊⠀⠀⠈⡉⣲⠶⢄⠀⢰⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠞⡵⠃⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⢉⠀⠐⡎⠃⢰⡟⠀⣦⠀⡾⢰⠃⠀⠀⠑⢬⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠔⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠀⣤⣼⠁⠀⠁⢸⠃⢀⡔⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⡏⡜⠀⡠⡿⢸⣿⡧⠊⠀⣀⣈⢢⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⢹⢹⡇⣼⢡⠇⡾⡏⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⠚⠀⠀⢸⣿⠃⠸⠈⢱⡇⠀⠁⡀⠀⡂⠀⠰⡀⠀⠀⡰⠀⠦
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⢰⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡏⠀⠆⠀⠀⢧⡀⠋⣀⣾⡗⠄⠀⢈⠉⠉⠀⢀⢰⠂
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⡀⣿⢣⠐⣄⠀⠻⣆⠀⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠇⠹⡈⡄⠈⢗⠀⠙⠂⠀⠀⡐
⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⢮⠀⢈⡇⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡇⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠛⠒⠠⠀⠀⠀⠐⠈
⠀⡧⠘⠀⠀⠀⠀⢀⡔⠁⠰⠰⠊⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽
⠀⠸⡀⠃⠀⠀⡠⠋⠀⠠⠃⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠃
⠀⠀⠑⣦⠤⠐⠁⢀⡴⠕⠊⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠒⠶⠒⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠳⠞⠙⢿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠛⡅⠀⠘⣅⣸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠹⣦⣬⠲⣶⡵⠉⠙⠯⢟⣛⡒⠒⠶⠶⢤⣀⠀⠸⡏⠉⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠃⠐⠀⠑⠀⠀⠀⠀⠀⠀⠁⠀⠲⠄⠉⠳⣄⢳⠀⠘⡆⠸⡄⣀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⣯⢧⠠⢱⣠⢋⢡⠴⠖⠲⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠳⣾⣿⣮⡅⠀⠴⠚⠋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡞⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠾⢋⣵⢚⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠼⠶⣞⡩⣁⢀⡽⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⣉⡀⠀⠀⢠⠃⠀⢓⣠⢇⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⣀⢔⠑⠖⠇⠀⡔⠀⢸⠆⠀⡙⢈⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠛⠁⢀⢼⠀⠤⣀⡀⢼⡉⠁⡶⠓⣆⠽⣘⢊⡹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠳⢄⣘⢢⡄⣀⣬⣀⠄⠨⠂⢳⡔⢻⡤⢇⡠⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣏⡳⠀⢸⠁⠀⠈⠗⠒⠾⠒⢦⡀⠜⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⣴⣭⣤⣶⣾⠿⠿⠗⠙⠳⣤⡀⠀⠂⠃⠢⠒⠃⢀⣊⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⢀⣄⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⣀⡰⢦
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠗⠲⠔⠂⠳⠀⠀⠀⠀⠀⠀⠀⠀⡐⣇⢠⠉⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠖⠀⣔⠉⢂⣸⡭⡤⠖⢈⠅⣠⠋
⠀⢠⣆⣀⣀⡀⢀⣀⣠⣀⡖⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠬⠕⠶⠀⠀⠀⠀⠀⠀⠜⢭⡀⢆⣐⠶⠶⠒⠉⠅⡀⢀⣠⠕⢋⣼⠑
⢤⠃⠊⣿⣓⣀⣐⣛⣓⡿⣅⣀⣄⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠃⠐⠒⠀⠘⠀⠀⠀⠀⠀⠘⣆⠘⢷⣺⡔⣺⠃⣠⢒⣓⡩⢿⠓⢚⡭⠊⢠
⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡉⠙⠶⠓⠯⠥⠖⠉⠉⣁⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⡿⢦⣠⡞⠁⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⢀⡜⢩⡀
⠀⠀⠀⠈⣾⠛⠀⡀⢉⠀⠘⠈⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠤⣞⣉⡉⣱⠞⢫⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡟⠝⠓⠈⠋⠢
⠀⠀⠀⢰⣟⡲⠦⠤⠬⠴⠾⠤⣺⣶⠀⠀⠀⠸⡁⠩⣍⡖⣲⠋⠀⠀⢈⢷⣓⡾⠧⣮⠏⡀⠀⠀⠀⠀⠀⢸⣤⣤⣅⣠⣤⣾⡇
⠀⠀⠀⠀⡏⠈⠉⠉⢹⠉⠉⠉⢹⠁⠀⠀⠀⢠⢹⣫⠍⡾⣻⠦⣤⣐⣫⡾⠤⠓⢔⣩⠿⡇⠀⠀⠀⠀⠀⠀⢛⠛⠛⠛⠛⡋
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⡷⣝⠚⠚⠤⢞⡚⠋⠉⠗⣲⡶⠊⣩⣾⠃⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠄⡇
⠀⠀⠀⠀⠘⣦⣀⠀⢘⠀⢀⣠⠞⠀⠀⠀⠀⠀⠑⣌⠉⠓⠒⠶⢷⡀⢀⡼⠷⠚⢋⡡⠋⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠈⠫⠭⠭⠭⠭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⢦⣽⣯⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⣸
⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⣠⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⣠⠚⢱⠀⠑⣀⣹⣫⣏⣠⣮⢞⣥⡷⠀⠀⠀⠀⠀⠀⠀⣙⡦⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢰⠃⢁⣌⣵⣷⠛⠁⣤⢸⡍⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠉⠙⠒⢄
⠀⣿⡤⢛⡻⣭⡇⠐⢾⣀⣀⡆⠀⣸⣷⠀⠀⠀⠀⠀⠀⢰⢻⠟⠲⠖⠒⠲⡗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⢈⡀
⠀⣿⢮⣷⣾⣧⣵⣦⣤⣬⣥⣶⣿⡿⣿⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⢀⣰⠂⠀⠀⠲⠁⠉⠉⠉⠈⠡⠃⠀⠐⣆⡀
⠀⠹⣷⣌⡉⠉⠛⠛⠛⠛⠉⠉⠁⣠⠇⠀⠀⠀⠀⠀⠀⠘⢦⣙⠲⣤⠖⣋⡠⠃⠀⠀⠀⠘⠃⢭⢀⣷⣆⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⡬
⠀⠀⠈⠳⣍⣙⠒⠂⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣉⣯⡁⠀⠀⠀⠀⠀⠀⠀⠸⣌⣛⣙⣛⣁⣀⣀⣀⣀⣈⣋⣀⡠⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠠⢌⡑⠂⢄⠀⠀⠀⣀⣤⣤⣶⣿⣿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣂⡐⠲⠿⣓⡀⢄⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣾⡿⣻⣡⣿⣾⣿⣿⣿⣿⣟⠿⣏⠟⠻⠛⠛
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⢺⢷⡶⠿⠻⢛⠟⣹⣟⢿⡻⣌⢣⠙⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠅⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢠⣾⣿⣿⢦⠳⡈⢀⢡⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠠⠀⠀⠀⠰⣟⡻⠯⡹⠽⠖⢱⡀⠀⠃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣐⠀⢀⡀⠄⠀⠀⠀⠂⢀⠀⠀⠀⠀⠒⠉⠉⠁⠂⠀⠀⠀⠀⠀⠚⢸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣨⣷⣄⡀⢤⡁⠀⠁⠀⠀⢈⢲⣴⣋⠀⣀⠀⢀⠀⣀⠀⣀⣀⣀⣀⡀⡉⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠠⠾⠻⠙⠋⠦⠈⠑⠈⠙⠭⡙⠽⡿⣿⢯⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⠑⠀⠀⠀⠀⢸⢦⡀⠀⠑⠤⠑⢌⠛⡾⠁⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⢀⡀⠠⠄⡒⠈⠁⠀⠀⡀⠀⠀⠀⠀⠏⡙⢦⣀⠠⠈⠢⠈⠃⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠌⠷⣶⡾⠁⠀⠀⠀⠔⠀⢞⠀⠀⠀⠀⠁⠈⢻⣷⣄⠐⠄⠐⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠋⠀⠀⠀⢀⠄⡠⢁⣾⠀⠀⠀⢸⠀⠀⣛⣷⡍⠳⠄⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢁⡴⠠⣿⣿⠁⠀⠀⠈⠀⠛⡡⢋⠔⢁⠄⠉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠄⠀⠒⠀⠈⠒⠀⠉⠑⠀⠀⠀⠀⠘⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠃⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡀⣠⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⣤⣶⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣻⣾⠿⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠋⠁⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡛⠿⣦⣌⣉⣉⣉⡉⣻⠉⠉⠉⠉⠉⠁⠀⠀⠀⣉⣈⣀⣀⣠⡤⠤⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡍⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⡀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣿⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣶⠿⠶⢷⢶⣶⠶⠾⣿⠿⠋⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣅⣀⠀⠈⠉⠀⠀⠁⠠⠴⠀⠈⠀⠰⠒⠀⠀⠳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⢻⡛⠭⠽⠋⠿⠿⣷⣦⣀⢀⡀⠀⣀⠀⢀⣀⣠⣤⡶⠖⠛⠛⠛⠉⠉⠁⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⣦⠄⣀⡀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣾⡿⠛⠛⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⡟⠅⠁⠀⠀⠀⠀⠀⠀⣠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣭⣟⠉⠉⠙⠙⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⣁⣤⣄⣤⣤⠶⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡳⠦⢙⠻⢿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣦⣶⣶⣶⣾⣷⣾⣿⣿⠿⠛⠋⠡⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣈⡙⠛⠲⠶⠍⢉⡛⠛⠛⠛⠉⠉⠋⠙⠛⠛⠛⠛⠛⠋⠀⠐⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠁⠀⠀⠀⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠱⡄⠀⠀⠆⡇⠀⠀⡀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡀⡙⠄⠄⠀⠀⠐⡈⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠸⡀⠹⠀⠀⢀⠇⠀⠀⡑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠾⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠀⠀⢣⠰⠀⡀⠠⠀⠐
⠀⠀⠀⠀⠳⡀⠀⡄⠈⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠠⠀⠀⠓⠚⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠻⢿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⢀⣸⠰⠀⠀⠀⠀⠀⠀⠈⠂⠨⠤⠀⠀⠀⠀⠀⠀⠀⢦⠞⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⢰⢂⡄⠀⢁⠉⢉⠁⢀⡀⠀⢰⡖⠂⠀⣀⢸⠋⠀⡄⠀⠀⠀⠀⠀⠈⠓⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠹⡖⠋⢸⠟⡿⠋⢨⠃⠀⢸⡗⠰⠧⠱⣼⡺⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠹⠀⠘⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢄⠠⠀⢀⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠰⡼⣶⠂⠀⠀⠀⠀⡀⢲⢠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠫⠍⠈
⠀⠀⠀⢀⠲⡀⠀⠘⠒⠚⠀⢀⠀⠀⠀⠈⣏⠉⠀⠀⠠⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢸⠀⠘⡄⠀⠀⠀⠔⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠃⠸⡄⠀⡀⠀⡄⠀⠀⠀⢀⠓⢦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢆⠀⠃⢀⡀⠌⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠢⠀⠀⠀⠀⠀⠀⢨⠀⠀⠃⠀⠀⡔⠀⡄
⠀⠀⠀⠀⠈⠃⠘⠋⠛⠀⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠢⠀⠘⠋⠻⠂⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣾⣷⣿⣾⣥⣾⣿⣷⣞⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣾⣿⣷⣾⣿⣿⡿⠿⠟⠛⠛⠛⠻⠿⣿⣯⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢟⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠻⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣥⡾⣻⣿⠟⠁⠀⠀⡀⠀⠀⠀⡀⠐⠋⠉⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡿⠃⠀⠀⠐⠋⡉⢁⡀⠋⠉⠀⢠⠟⠁⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠁⠀⠀⠀⠀⠠⠛⠾⠿⠤⠴⠞⠉⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠉⠀⠀⠀⠀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣄⡀⠰⠋⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⡄⠫⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣴⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠒⠚⠋⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠀⠀⠀⠦⣝⣳⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⠶⠶⣬⣓⣶⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⢌⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠙⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠿⠆⠀⠀⣶⡇⠀⢿⣧⡤⠴⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⠀⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⢀⣀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠙⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠛⣯⣏⡂⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣩⠤⣤⢤⢦⣤⣬⣬⣈⣁⣈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠥⠦⣤⣴⡃⣈⠘⣋⢈⢉⣙⣋⣛⡿⠗⠢⢤⡤⢤⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠍⠛⢛⠛⠻⠯⠭⠤⠤⢄⣤⠞⠋⣠⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡚⠉⠀⢂⠉⠀⠀⠀⠀⠉⠙⠁⠀⢀⠀⠙⡆⣼⢛⣿⡈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠁⠨⢣⣿⣼⢹⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠕⡹⣿⢧⡀⠻⣾⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠎⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣦⣡⣹⡌⠻⣄⡹⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⠀⠀⢀⣀⣉⠓⠦⣈⠳⢾⣚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡠⠒⠒⠒⢤⡌⠅⠀⠈⢳⠀⠈⠓⣄⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠀⠸⠀⠀⠀⠀⠄⠱⠜⡠⠒⢀⠏⣠⠓⠌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⠀⠀⡴⠂⠳⡤⣠⡀⢄⠀⣧⠐⡀⡾⠞⠃⠀⢹⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡆⠀⢸⠁⠀⠀⠴⠠⠍⢂⠲⣿⣠⡞⣳⣗⠂⠵⢇⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠘⢤⣤⡤⢠⣤⡽⢒⣿⢼⡟⠻⢥⡴⠍⡑⠀⢥⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⡇⠀⢷⡀⠀⢰⠂⢀⡠⢈⠐⢠⣠⠁⢿⡻⠐⠈⢢⡄⣄⠌⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣣⠀⠈⢱⡀⠸⡄⠈⠀⠀⠁⡨⢋⣠⠀⢇⠁⡰⠀⢉⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠊⠄⣀⠃⠄⠨⠤⠤⠘⣧⡀⠈⣻⣄⠈⠒⠤⠤⢞⠁⠃⠘⠤⢸⣀⣘⡦⠃⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠆⠨⠭⠭⠭⠵⠖⠺⠛⠶⢾⣭⣿⡶⣄⡀⠀⠙⠒⠒⠚⠁⠈⠁⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠁⠬⠷⢶⡴⠴⠶⠶⠚⠉




⡟⠉⢹⡟⠻⠿⠿⠟⠿⡛⠿⠻⠿⠿⠟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡠⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠀⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡜⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠐⣄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡎
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠑⡄⠀⢣⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡰⠁⠀⠀⡆⠀⠀⢠⠇
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸⡀⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇⠀⠀⢀⠇⠀⠀⡜
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⢱⠀⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⢸⠀⠀⢰⠁
⠀⠀⢸⠀⠀⠀⠀⠀⡴⢣⠀⢇⠀⠀⠈⡆⢱⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⢠⠇
⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⢣⠈⢆⠀⠀⢱⠸⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠘⠀⠀⡎
⠀⠀⠘⡄⠀⢀⠜⠀⠀⠀⠀⢣⡈⢦⠀⠸⠀⡇⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠱⠔⠁⠀⠀⠀⠀⠀⠀⠱⡀⠣⡀⡇⢣⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠃⠸⠀⠀⠀⠀⠈⠁⠀⠇⠀⢀⠎

⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢪⢧⡀⡇⠀⠀⠆⠡⠀⠁⢀⠀⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⠰⣬⠶⣂⡀⠀⠀⠀⠉⠁⡒⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀
⠀⠠⠂⡠⢁⠆⢵⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠅⢀⢀⠀⠀⠀⠐⠀⠀⠀⠨⠑⢆⡃⣩⠶⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡀⢊⠔⠀⢠⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠃⠘⡣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡤⠁⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠊⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣿⢻⡟⠄⠀⠀⠀⠀⠀⠀⠀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⢰⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠷⠇⠆⠀⠀⠀⢀⠅⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⠀⠆⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠄⠀⠀⠀⠀⠴⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠺⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⢀⠒⠑⢄
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡁⠀⠀⠀⠀⠀⢦⠆⠀⠀⠀⠐⠛⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢀⠠⠀⠈⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⢤
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠈
⠀⠀⠀⠀⡄⠀⠰⢄⠀⠀⠀⠀⠀⠥⠀⠁⠀⠀⠀⢀⡀⠸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠒⠂⠀⠀⠀⣀⠄⣬⠇
⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠿⣿⣻⣶⡝⢪⢁⢄⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠘⠛⣋⣽⢤⣾⣩⣌⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⡣
⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠙⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⠀⠀⠀⠀⢀⣤⣔⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡀⡀⠛⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠦
⠀⠀⠀⢠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠐⠋⠀⠀⠀⠘⠋⠉⠀⡀⢀⠄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠁⠀⢀⣤⢀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠀⠀⢀⠀⠀⠘⡻⠋⠀⠀⡔⠁⠀⣾⠖⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⢸⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣀⠴⠂⠀⠀⠀⠀⡛⠁⠀⣤⣄⣀⠤⠚⠁⠀⠀⢰⡗⠃⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⡀⣠⣆⢒⣈⣀⣤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠰⡿
⠀⠀⠘⠻⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⠀⠀⠞⠀⠘⠟⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⣤⣀⡀⢀⣾⢃⣼⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠘⠲⣿⠆⠀⠀⠈⡁⠀⠐⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣠⣿⠃⠘⠟⠛⠙⠛⠛⠛⣿⡟⣛⡁⣘⠁⣤⢤⢿⣼⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⣿⠇⢀⣶⠲⡄⣼⡏⢹⢠⣿⣏⣼⢣⡿⢸⡧⢊⣔⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠛⢂⣾⣯⣠⣧⣿⠣⡼⢻⡟⢿⣄⠘⢓⣉⣙⡉⢸⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣠⠞⠻⣧⠟⠁⠙⠚⢁⣀⣥⣼⠿⢿⣍⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠈⠿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠞⠃⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⣴⠆⠀⠀⣤⠀⠀⠀⠈⠙⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠒⠓⠚⠃⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⡾⠖⠋⠉⠁⠙⠒⠀⠀⠀⠰⠒
⠀⠀⠀⢠⠀⠘⠷⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠉⠉⠀⠄⠀⠀⠀⡠⠂⠛⠁⠀⠐⠟⢃⡀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⠘⢿⠁⣠⣤⠀⣀⣘⣀⣀⠠⣤⠀⠀⢤
⠀⠀⠀⣿⣧⠀⠀⣠⣄⢠⣴⣦⠀⠀⢠⣶⣤⠀⠔⢠⠆⠀⠀⣼⠃⠀⢛⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⢦⡤⠒⠉⠉⣉⠉⠉⠉⠓⢄⢀⡀⠁
⠀⠀⢰⣿⣿⣿⣧⣤⣤⣄⡀⢤⣄⣀⣀⣀⣀⣀⣴⡏⠀⠀⢀⡴⠀⠀⠙⠁⠀⠀⠀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⠀⠀⠋⠀⠀⢀⡀⠀⠈⠡
⠀⠀⠘⢿⣽⣋⡉⣉⡉⠹⠿⠟⠛⠉⠉⢉⣽⡷⣀⣶⠀⠀⠈⠳⠀⠀⠦⢀⠐⠀⠈⠀⠁⠚⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⣏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⢰⣿⣿⣿⣭⢤⣦⣦⣤⣤⣴⡷⠾⠿⠛⠙⠋⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠉⠀⣀⠀⠀⠤⠀⠀⣀⡀⠀⠀⢸⡇⣴⠄⠀⠀⠀⠀⢴⣆⠀⠀⠀⡀
⠀⠀⠀⢨⣥⣌⣉⠀⠀⣀⣀⣀⢠⠾⠆⠀⣀⣠⣤⣴⡛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⢉⠾⠋⠉⢭⡉⠉⠋⢹⠟⢻⡏⠉⠉⠉⢈⣉⣤⠀⠀⠀⠀⠀⣀⣀⠀⠰⠖⠒⠒⠀⠉⠈⠁⠀⢠⡀⠀⠀⠀⠀⠘⣇⠀⠈⠁⠀⠶⠂
⠀⠀⢠⣿⡟⢛⡶⠶⣤⣤⣤⣤⡶⠶⠶⠞⠛⢋⡉⠡⢄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣦⡄⠀⠀⠀⠙⠁⢠⡆⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⢶⠆⣀⠤⠔⠁
⠀⠀⠀⠨⣷⣿⣿⣄⣀⠺⠷⠀⠀⠀⣀⡀⠀⣛⣣⠴⠊⠀⠀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠉⠁⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣀⠴⣲⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢼⠀⠈⢆⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠢⣈⣦⣤⣜⠝⠻⣖⡠⢤⡤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠓⠄⠙⠄⠀⠈⡻⢭⣅⠂⠐⢤⡈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡳⠃⠀⠀⠀⠀⠀⠀⠈⠢⠘⢷⣗⣄⢧⡈⢀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⡀⠹⣯⣎⢿⣯⣧⢷
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡠⡹⣇⣜⣿⣿⣾⡇⠀⠀⢀⡴⡒⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⠣⢏⢹⣻⣿⡿⣧⠴⣊⡏⣥⡼⣌⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢱⣀⡼⠞⣫⣥⣤⢷⡶⢾⣶⣚⣒⣾⣼⣡
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⣨⣼⠟⢃⠴⠯⢳⢈⣉⣘⣋⣹⡿⣽⣿⣯⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠀⠀⢀⠀⠈⢰⢟⡋⠁⣴⡻⠚⠳⣼⠿⢯⣤⣼⣭⣭⣤⣤⢭⡼⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠁⠈⠀⠈⠂⠈⢦⡉⠢⣿⡷⠜⢿⠧⠶⣾⢫⣬⡿⣭⠿⢻⡾⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⡀⢠⡀⠀⢰⣿⣿⣾⣥⡝⠻⠿⣾⣶⣾⣇⢙⣯⣉⡾⠋⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠛⠛⠋⠉⠁⠀⠈⠓⠤⣀⣀⣀⣉⣁⡠⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠛⣁⣴⠿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⢀⠀⠀⡠⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⡫⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣒⡀⠀⠐⠛⠠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣦⣶⣦⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠏⠉⠾⠉⠻⠝⡏⣩⣗⣜⢩⠗⠀⠀⠀⠀⠀⠀⠀⠙⡛⠉⠸⠛⠈⠙⠏
⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⠁⠊⠀⠀⠀⠀⠀⢀⡶⠞⠃⣠⣾⠿⠋⣰⡾⠓⠐
⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠐⠒⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠨⣤⡶⠟⠋⣀⣴⠾⠋⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠠⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠟⠋⣠⠴⠿⠫⠔⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣪⣭⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠠⠞⣁⠀⡉⠉⣀⠬⠉⠃⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⠀⠀⠀⠐⢄⠀⠀⠙⢷⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢁⣀⠀⡆⠀⠀⠀⠀⠀⠀⢘⠠⠩⡀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⢐⡏⠃⢀⠀⠈⠠⣿⡇⠀⠀⠀⠀⠀⠈⠎⣓⠊⠒⣤⢄⡀⡀⢤⣊⡔⠁⣧⢤⡀⣀⡀⣀⡆
⠀⠀⠀⠀⠀⠀⢸⣬⡋⠅⣸⡿⠗⣀⢴⠈⠂⠤⠄⠒⠀⠀⡁⠌⠓⢒⠉⠁⠄⣀⡤⢋⣁⠀⠀⠉⣁⣙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢬⡓⣶⢒⠭⠒⠋⠀⡄⠀⠀⢁⠀⠐⢘⠀⡀⠀⠠⠶⠘⠷⠢⠤⠊⠀⠀⠊⡀⢀⡑⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠁⠀⠁⠀⠐⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠀⡀⠀⡠⠀⠀⠀⠄⡀⠄⠒⠀⠉⠀⠉⠉⠀⠂⠀⠢⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⡀⠒⠰⠉⠘⢀⠉⣂⠈⠄⠀⠀⡈⠑⡄⠀⠀⠀⠰⠀⢠⠄⠀⠀⠐⠀⠀⡜⠛⡂⢎
⠀⠀⠀⠀⠀⠀⢀⡈⠣⠄⠸⢡⣾⡆⠈⠡⠢⠀⡄⠸⠀⠀⠠⠀⠅⣀⡀⠤⠖⡀⠘⠀⠀⠀⠔⠀⠄⢰⠀⡠⠈
⠀⠀⠀⠀⠀⠦⠤⠥⣤⣤⣤⠴⠶⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠁⠄⠘⠃⠂⠀⠈⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⡾⠉⠙⣆⠀⠀⠀⠀⠀⢀⡴⠋⠙⣆⠀⠀⠀⠀⠀⠀⢠⡟⠉⠳⣄⠀⠀⠀⠀⠀⢠⡾⠉⠹⣆
⠀⠀⠀⠀⣼⠁⠀⠀⠘⣧⠀⠀⠀⢀⣾⠁⠀⠀⠸⡆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠹⣆⠀⠀⠀⢠⡿⠁⠀⠀⢹⡆
⠀⠀⠀⠀⡏⠀⠀⢠⡀⠸⡆⠀⠀⣾⠇⢠⡀⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⣤⠀⢹⡄⠀⢀⣿⠃⣠⠀⠀⠀⡇
⠀⠀⠀⠀⣷⠀⠀⣿⣷⠀⣿⠀⢸⣿⢠⣿⡇⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⣿⣇⠈⣷⠀⣼⡿⢰⣿⡆⠀⢠⡇
⠀⠀⠀⠀⢻⡄⠀⣿⣿⡆⢹⡇⣿⡏⢸⣿⡇⠀⣼⡇⠀⠀⠀⠀⠈⣿⡀⠀⣿⣿⠀⣿⡄⣿⡇⣾⣿⠇⠀⣼⠃
⠀⠀⠀⠀⠘⣿⡄⢸⣿⡇⣼⡇⣿⡇⣿⣿⠃⣰⡿⠀⠀⠀⠀⠀⠀⢸⣷⡀⢿⣿⠀⣿⡇⣿⡇⣿⣿⠀⣼⡟
⠀⠀⠀⠀⣀⣹⣿⣼⣿⢃⣿⡇⢿⣧⠸⡛⣰⣿⡁⠀⠀⠀⠀⠀⠠⣄⣻⣷⣾⣿⢰⣿⠃⣿⡇⢿⡋⣼⣿⡁
⠀⠀⠀⠀⡌⠛⠿⠟⠉⡈⠛⠀⠚⠻⢶⠇⣻⠏⣷⠀⠀⠀⠀⠀⢰⡝⠻⠿⢿⣷⣾⡟⣴⣿⣿⣾⣷⡿⢻⣷
⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠁⠀⣆⠀⠀⠀⢨⣽⡾⣧⣞⠛⣟⡩⣿⣿⣿⡇⣤⡷⢿⣷⣠⣆⡀
⠀⠀⢀⡀⠀⠘⠂⠀⠐⠃⠈⠀⠀⣠⠄⠀⠐⠃⠀⠀⠄⠀⠀⢐⣿⣿⣘⣸⣷⠚⠁⠉⠙⢙⣽⢫⣿⣜⣣⣿⢧⠌⠁
⠀⠀⠀⠤⠄⡀⠀⠀⣀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⡌⠂⠀⠀⠨⠤⢏⡛⠙⠈⡀⠀⠀⠀⠈⠀⣈⠋⠹⢹⣭⣜⠆
⠀⠀⠀⠀⢀⠃⠀⣼⣿⣅⠀⠀⠀⢠⣿⣿⠀⠀⢃⠈⠀⠀⠀⠀⠀⠸⠁⠀⣿⣿⡄⠀⠀⠀⣠⣿⣧⠀⠈⠃⠙
⠀⠀⠀⠀⡾⠀⠀⠘⠟⠃⠀⠀⠀⠘⠻⠋⠀⠀⠘⣆⠀⠀⠀⠀⢠⡇⠀⠀⠙⠛⠁⠀⠀⠀⠘⠛⠃⠀⠀⠘⡆
⠀⠀⠀⣸⠇⠀⠀⠀⠄⠀⠢⣄⡤⠂⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢦⣀⡤⠂⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠐⠛⠒⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠶⠞⠻⠷⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠻⠶⠟⠻⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠈⠀⢀⡀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠈⠀⠀⢀⠴⠶⠄⠀⠤⢢⣄⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠦⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⢉⣉⡼⠓⠢⢤⡤⢶⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠿⠿⠟⠻⠿⠭⠥⣤⣤⣀⣴⠟⠉⡸⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡒⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⣹⡄⡌⠀⢃⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⣿⡄⢰⠐⠈⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⢻⣷⣄⠀⠳⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⢤⣬⣼⣆⣸⡈⠢⡈⠐⡄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢁⡠⠤⠤⣄⠀⠀⠀⠉⠛⢦⣀⠈⠢⣄⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⡤⡖⢢⡞⢀⠀⢀⠌⡤⠖⠒⠒⠤⡀⠉⠳⡀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡏⠀⢹⣌⡇⠀⢹⢈⠞⠰⠀⡀⠀⠀⢱⠀⠀⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⠀⢀⣥⢹⡤⢰⡾⠐⡠⠎⣄⣀⠴⠧⣄⠀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⠉⠰⠬⣝⠺⣦⣷⣾⣷⣂⡒⣉⣥⣎⡀⢀⡨⡆⠀⣸⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⢀⡐⡀⠍⣛⣉⣩⠿⢸⣗⠈⡉⠒⠋⠈⣐⣽⠇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⡞⢀⠀⡡⢫⠟⠂⣍⣏⣀⣉⣉⠉⢍⣉⠉⠀⢈⣃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠐⣀⡼⠀⣠⠏⢰⠤⠙⡍⠉⡙⠈⠃⠀⡏⠀⣠⠿⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣄⠀⢀⣀⣀⣀⣀⣀⣄⣀⣄⣢⣵⣄⠈⠣⠦⠶⡰⠀⠀⠁⣘⢦⣀⣠⠤⠋⢀⡴⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠵⢖⣚⣒⣀⣚⣛⣛⣛⣛⣛⣻⡭⠗⢤⡀⠀⠁⠒⠐⠛⠁⠀⠀⣀⣤⠶⣿⣓⢀⡥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠷⢴⣶⣖⣚⣋⡯⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⣾⣦⠀⠀⣰⣿⡄⠀⠀⠀⣴⢦⡀
⠀⠀⠀⠀⣾⣿⡿⡄⠀⠀⣰⠋⢸⡇⠀⠀⠀⣿⣿⣇⢠⣿⣿⡇⠀⠀⠀⡏⠈⢧⠀⠀⢀⣶⣶⣦
⠀⠀⠀⠀⣿⢿⡀⢹⡀⢠⠇⢠⠞⠀⠀⠀⠀⢻⣿⣿⢸⣿⡿⠁⠀⠀⠀⠹⡄⢸⠀⢠⠏⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢄⣇⣸⡰⠋⠀⠀⠀⠀⠀⠀⢻⣿⣸⡿⠁⠀⠀⠀⠀⠀⠹⣸⣀⣎⡴⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠙⠂⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠂⠀⠀⠀⠀⠀⠚⠉⠉⠉⠓

⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣤⣤⣄⠀⠀⢀⣤⣤⡀⠀⠀⢰⡿⢦⠀⠀⠀⡴⢿⡄
⠀⠀⠀⢸⣿⡿⢻⡀⠀⢠⠟⢿⣿⡇⠀⣼⢹⣿⣿⡆⠀⣿⣿⣿⢹⡀⠀⠸⡇⠈⣇⠀⣸⠁⢸⠃
⠀⠀⠀⠸⠟⢳⡀⢧⠀⡞⢀⠞⠿⠃⠀⠙⠉⢻⣿⣧⢸⣿⡿⠉⠛⠀⠀⠀⠹⡄⢹⠀⡇⣠⠏
⠀⠀⠀⠀⠀⠀⢙⣼⢤⣧⡋⠀⠀⠀⠀⠀⠀⠀⣹⣿⢼⣿⡁⠀⠀⠀⠀⠀⠀⢘⣼⢤⣷⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠚⠓⡓⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡓⣨⠰⠏⠟⢥⠄⣴⠎⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠔⠛⠶⢧⣄⡠⢈⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠹⠶⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⢠⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⢤⠐⠁⠀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠛⠲⢤⣀⠀⠀⠀⢀⡔⠉⠀⠈⠢⢠⠎⠁⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⣀⣤⠆⠀⠀⠀⠀⠀⠈⠙⠲⢶⠎⠇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠋⠀⢀⠴⣮⠟⠁⠑⣄⣠⣀⣀⠀⠀⠀⠀⡌⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⣤⢒⠊⠀⠐⠉⠈⠑⠺⣁⠀⠀⠀⠀⠀⠀⠛⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠈⢨⡑⠄⠀⠀⠀⠀⠀⠈⢮⠑⠢⣄⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⠳⣄⠂⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⢄⠠⡀⠀⠀⢀⠀⢺⠀⠀⢀⣡⡾⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠷⣄⡀⠀⠀⡄⠀⠀⠑⡄⠈⠳⠼⠦⣚⠥⠒⢁⣠⣶⣛⣁⠴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⢀⡏⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⢦⡀⠰⢰⡀⠀⠘⢦⠴⠂⠁⣀⣤⠾⠋⠉⠁⠀⠀⡠⠈⠳⢤⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠋⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢷⣄⠁⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠒⠒⠀⢠⡾⣠⠒⣈⠁⢲⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠶⠛⡇⠀⠀⠀⢀⣦⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠀⢸⠗⠁⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣉⣁⣀⣠⡤⢴⡏⠙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠒⢿⡋⠁⣸⡇⠀⠀⠀⠀⣿⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢷⠀⣿⡇⠀⠀⠀⠀⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠀⢳⡀⠀⠀⠀⠈⡇⣿⠁⠀⠀⠀⠀⣿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣿⠀⣀⣴⠿⠒⠒⢶⠛⠀⠀⠀⢳⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣿⠋⠁⠀⣀⣀⣀⣼⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣠⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⠴⠛

⣶⣶⣶⣶⣶⡾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠶⢶⡶⠶⠶⢶⣶⡶⠶⠶⠶⢶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠈⠁⠁⠀⠀⠘⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠄⣀⠤⠶⠒⠀⠤⡀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠀⠀⠀⠢⢀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⠻⣿⣿⢦⡀⠀⠀⠀⠀⠀⠂⢠⠚⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⣿⠿⢿⠳⢄⠀⠀⣸⣿⣷⡄⠀⣠⠟⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠚⠁⣀⣠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⢃⡄⣷⠚⢄⣀⣀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠔⠉⠀⢈⠀⠀⢲⣦⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠛⠔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠃⠀⠀⢀⠂⠀⠉⠁⠙⠿⠷⣤⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⣬⡗⠠⠤⠤⠄⠒⠉⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢰⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⢀⣡⣄⢠⡤⠎⠁⠀⢣⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⠀⠀⠀⠀⢠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⣸⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⠢⠄⠀⢠⣿⠁⡆⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⢩⡍⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⡐⠀⠸⠀⠀⠀⠀⠀⠈⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠑⣄⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠀⠀⠀⡸⠀⠀⡄
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠉⠀⠈⠒⠂⣴⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣴⡾⠃⠀⠀⡇
⠀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠃⠀⢸⣿⠁⠀⠀⠀⢹
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠁⠀⢀⡽⢰⠇⠀⠀⠀⠀⢸⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡇
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⢈⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⡇
⠀⠀⣆⠀⠀⠀⠀⠠⠔⠊⣡⢀⡄⣸⠔⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠙⠢⠤⠴⠶⣶⠾⠷⠛⠉⠀⠀⠀⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠁⢁⠀⠀⠀⠀⠀⢠⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠑
⡿⢿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣻⣿⣛⣿⣿⣟⣿⣿