Archaeology Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠳⢄⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠚⠋⠀⠀⠀⠀⡐⠄⠁⠀⠀⣀⣀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠀⠀⠀⠀⢀⠔⠁⢀⠀⢠⠠⠐⠩⠀⠄⠀⠀⠀⡀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠚⠂⡄⠀⠀⠉⡁⠁⠈⡁⠈⠀⡠⠃⠠⡂⣼⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢤⠀⠫⣇⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠔⠀⠏⠀⢀⠀⣀⠀⠂⠀⠐⠱⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀
⠀⠀⠀⠀⠠⠇⠛⠀⠚⠑⢇⠀⠀⠀⢀⠔⠁⠀⠀⠀⡘⠀⠀⠀⠀⠑⢄⡐⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠃⠀⢠⡄⠀⠀⣤⠂⠀⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠉⠚⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⡄⣠⠀⠀⠆⠈⠀⠠⠄⡄
⠀⠀⠀⠀⡇⠀⢀⡙⡆⠀⠱⣸⠀⠀⠀⠀⠐⠁⠆⠈⠂⠀⠀⣾⠔⠁⠀⠀⠀⠐⠘⠁⠀⠀⠀⣰⣂⢉⡉⢀⣁⣦⠀⠀⠀⠀⠃⠨⡴⠂⢈⠀⠀⡀
⠀⠀⠀⠀⡁⠀⢸⡇⠀⠀⠀⢂⠃⠀⠀⠀⠈⣄⠄⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠱⡀⠀⠸⠃⢀⠌⠀⠀⠀⠀⠆⠐⠆⠀⠈⠠⠔⠚
⠀⠀⠀⠀⠁⠤⠴⠧⠤⠠⠐⠚⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠀⠀⠀⠀⠸⠀⠀⠐⠁⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠾⢷⠂⠰⣦⠂⢠⡶⠿⠆⢹⠟⢻⠀⣴⣿⣷⠆⣰⠆⢀⠀⠈⠀⣴⠆⢄⠀⣼⠟⢿⠰⣦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠇⠠⡇⠀⠸⣅⡀⠀⢸⠀⠀⠀⠙⢤⡀⠀⠹⠦⠼⠁⠀⠀⠻⠦⠞⠁⠻⠤⢾⠀⠻⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⡌⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠤⠖⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠐⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡊⣠⠔⠊⠉⠐⢄⠀⠀⡤⠂⠀⣠⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⢀⠆⠙⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⡆⠀⠀⢸⠠⠁⠀⠀⡏⠈⠰⠀⠀⠠⠂⠊⠁⢀⠀⠠⠀⠀⠀⠀⠢⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⣀⠀⢀⠐⠴⠀⠰⠀⠀⠀⠀⠀⢀⡄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡀⠈⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠠⠐⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠃⠀⡤⠤⠔⠀⠀⡘⡀⠀⠀⠈⡞⠹⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⢸⣸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠂⡀⠠⠂⠀⠀⠈⠀⠀⠁⠀⠀⠀⢀⡌⠀⠀⠀⢀⠁⠀⠃⠀⠀⣶⣤⡂⠀⠀⠀⠀⠀⡀⠀⠉⠀⡠⠾⡏⠈⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠈⠀⡁⠀⠀⠀⠀⣖⠸⢆⠀⠐⢀⣀⢈⠦⠼⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⡀⠀⢞⠀⠀⠀⠀⠠⠊⠀⠀⠈⠋⠀⠀⠠⠀⠁⠀⠀⠀⠠⣤⡀⡄⠀⠀⠀⠀⠙⠀⠈⠁⠀⠀⠏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⢰⠘⡏⣑⣭⠛⢻⣄⠀⠀⢸⠆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⡌⠝⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠙⠸⠂⠦⠤⡤⠀⠛⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⡀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡜⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠱⣵⢊⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠙⠛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣩⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠐⠀⠂⢉⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠺⣿⠶⢶⡴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢢⡀⠀⠾⠁⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠄⠀⢻⣀⡀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠲⡄⠀⠀⠀⠈⢻⣀⣠⠾⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⡠⠛⠻⠷⠶⢿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡀⠀⠀⠈⠉⠉⠓⠲⢟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⠈⠓⡈⠀⠀⠀⢀⣴⠿⠿⣧
⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠈⠒⠢⠀⡀⠀⠀⢀⣀⠸⢱⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠛⣄⠀⠀⠀⢰⠋⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠇⢸⡉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⢦⡀⠀⠐⠊⠑⠀⣀⡈⡀⠀⣀⣠⡶⠟⣁
⠀⠀⠀⡤⣀⡀⠀⠘⠠⠤⢤⡀⠀⠀⠀⠘⣡⣷⣄⣀⢰⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⡤⠀⠉⠀⢀⣠⠈⣀⣰⠖⠚⡋
⠀⠀⠀⠀⠀⢁⡀⠀⡄⠒⠒⠆⠈⠀⠀⡴⡃⠰⠞⠛⢢⣥⣅⣉⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⡠⠀⠀⠀⠀⠀⣀⣀⡈⠛⠀⠉⠙⠛⠿⣶⡀
⠀⠈⠷⣦⢂⠁⡇⠀⠀⠀⠀⡸⢻⠗⠀⠶⠀⠀⠀⢢⡴⢤⡼⣣⡼⣆⠀⠀⢀⡁⠤⢊⠉⣘⠑⠀⠀⢠⣶⠂⡞⠁⡜⠉⠒⠦⠀⣽⠁⢤⣌⣃
⠀⠋⠋⠀⠐⠀⠀⠀⠀⠀⠀⠹⠟⠰⢶⡆⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠐⠃⠐⠁⠀⠀⠀⠀⠙⠐⣽⠋⠁⠀⠀⠀⢼⠏⠀⠾⠻⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⢻⠟

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡆
⠀⠀⠀⣰⣶⣿⣿⠿⠟⢻⣝⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣶⣾⣳⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢅⣿
⠀⠀⠀⣿⡇⢿⣿⣲⠀⠀⠙⣛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⢯⡧⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠣⡸⣸⠇
⠀⠀⠀⢹⣷⠀⠉⠃⣤⠘⠃⠈⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡸⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡌⠖⢡⡟
⠀⠀⠀⠀⣿⡆⠀⠀⢀⠀⣠⠀⠆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠷⣦⣤⣤⢞⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡟⠓⠛
⠀⠀⠀⠀⢸⣿⢀⣛⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠾⠳⣎⠊⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡦
⠀⠀⠀⠀⠀⣿⣇⠛⣃⣠⣤⣤⣶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⢍⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣵⣿⠋⠁
⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⣛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣳⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⣿⣵⣶⡆
⠀⠀⠀⠀⠀⠀⢠⣟⣉⡁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣡⡇⠀⣠⣤⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⣯⠉⡶⠒⠒⠾⠃
⠀⠀⠀⠀⠀⠀⢸⡷⢯⣭⣉⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢠⡟⡼⠁
⠀⠀⠀⠀⠀⠀⣿⢁⡝⣪⡍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢟⡿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣾⡇
⠀⠀⠀⠀⠀⠀⠻⢦⣴⢿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢴⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣶⡀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣶⠿⡩⣙⠿⣿⢿⣧
⠀⠀⠀⠀⠨⣇⠀⣘⡒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡞⢅⡳⠛⠆⣿⠘⣿⡿
⠀⠀⠀⠀⠀⠙⣏⣯⣉⣿⣕⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣯⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠠⡅⠀⠀⢹⣶⡏
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣉⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡞⣀⢇⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⣾⣹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⣅⢾⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⡿⢧⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣠⣱⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠒⢀⣀⠀⠀⠀⠀⠀⠀⠤⠄⠠⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠛⠻⠤⠄⠀⠀⠀⠀⠀⠀⠙⡿⢱⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠛⠻⣿⡟⠀⠀⠀⠀⠀⢀⡄⢠⠀⠀⠀⠀⢀⡴⠲⣜⣦⣤⠇⠀⢠⡾⣧⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⣧⠀⣽⡏⠀⠡⠄⠀⠁⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⢀⣠⠀⠃⠀⠀⠀⠠⠤⠀⠹⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠀⠀⠀⠀⠀⢸⠿⣿⢿⣾⣿⠇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡀⠀⠀⠀⠢⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⢿⠀⠀⠀⠀⠀⣴⡏⣴⣶⢸⢿⣿⣇⠘⠻⠷⠤⠤⢀⣾⠄⠀⢈⣽⣿⣿⣿⡟⠤⠤⠤⣤⣄⠀⠀⢈⢸⣷⡀
⠀⠀⠀⠀⠶⠖⠀⢀⠀⢀⡟⠀⢹⣷⠀⠀⠀⠠⠽⠇⢻⣿⢈⣿⠟⠡⠀⠀⢀⣙⣿⣿⣿⣷⣄⠀⡈⢹⣿⠟⠀⠀⠀⠀⠻⣿⡄⠀⠸⠠⠉⢻⡄⠀⢦
⠀⠀⣤⣤⣀⣠⣤⣤⢰⢸⣧⣀⡼⠟⠛⠓⠒⠶⢯⣧⢸⡟⢀⠏⠀⢀⠀⠀⠨⣟⣿⣾⣥⣰⣿⡆⠁⣿⣿⠀⠀⠀⡀⠀⣄⣿⣿⠓⠛⠀⠀⢸⣿⣧⣼⣇
⠀⠀⠸⠀⠀⣃⢀⣹⡈⢸⣏⣭⠀⠀⠀⢀⣠⣠⣼⠿⠸⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣧⡄⣿⣿⣦⣤⣄⣹⡼⢿⣿⣿⣿⡀⠀⠀⣼⣿⣿⠿⠇
⠀⠀⠀⠀⠂⠛⣺⣿⣯⣭⣟⣛⣛⣟⣛⣛⣿⣿⠏⠁⠀⠀⠀⠄⠈⠆⠐⣂⠐⣞⣼⣏⣿⣿⣟⣬⣿⡄⠉⠉⠉⡽⠛⠓⢿⣯⣍⣭⣵⣄⣀⣿⣿⣧⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠇⢀⣀⣰⣆⣀⣀⠺⣾⣷⣶⡟⡶⠈⠋⠉⡉⠉⢉⡃⡄⠐⠛⠛⠛⠋⠹⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠉⠁⠉⠲⢶⣶⣼⣶⣿⣿⠷⠾⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠠⢀⡤⠀⠀⠠
⠀⠂⠀⠰⠤⠄⠀⠈⠀⡀⠀⠀⠐⠐⠀⠀⢨⠀⠀⠀⠀⠀⠘⢮⠧⠁⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⡀⠲⠤
⠀⠀⠀⠀⠊⠀⠀⠀⢰⠀⠀⠁⠀⠔⠀⠀⠋⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠘⠋⢀⡗⠀⠣⠉⡐⠁
⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠠⠒⠈⠀⠀⢀⠀⠀⠀⠀⡔⣀⡰⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠠⠤⠂⠀⠀⠆⠀⠈⠠⠂⠀⢀⡄⠀⠀⠁⠀⠀⠀⠛⠈⠁⠀⡀⠀⠔⠁⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠠⡆⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⢀⠀⠀⠀⠸⣡⠀⠁
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠈⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣠⡾⠀⠈⠁⢁⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡀⠀⠀⠀⠀⠅⠉⠤
⡀⠐⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠆⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠁⠀⠀⠀⠰⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡁⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⣀⠴⠊⣡⡄⠀⠀⠀⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⡴⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣐⣀⣃⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⡏⠀⠀⡇⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⢰⠋⠀⠀⠀⢚⠀⠀⠀⣶⠀⢘⡇⠀⠀⠀⠀⠤⢠⡀⠦⠀⠀⠸⣿⠏⢀
⠀⠈⠑⠊⠳⠄⠀⠀⠀⠸⠿⠿⠀⠀⠀⠐⠥⠤⠤⠤⠜⠀⠀⢠⣿⠀⢰⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠂⠀⠀⠀⢀⡀⢠⣶⡆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⡶⣦⡀
⠀⠀⡠⠊⠀⠀⠀⠀⢀⣼⣁⢠⠀⠀⠀⠀⠀⣱⢖⠉⠁⠀⠀⠀⣸⣿⡿⠃⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⢸⣿⣄⣽⡿
⠀⠊⠀⠀⠀⠀⠀⠀⠈⠛⠋⠛⠀⠀⠀⠀⠘⠁⠀⠑⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠙⠛⠛⠁

⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⣨⠗⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⢠⡀⠀⡀⠀⣤⠀⠀⢠⣾⣿⢷⣆
⠀⠉⠙⢻⡇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⣓⡶⠧⢤⡄⠀⠀⠀⠆⠁⠀⠀⠀⠀⠈⠛⣿⣿⠟⠁⠀⠀⠸⣿⣵⣿⡏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⣶⣌⡀⠀⠀⠀⠀⠀⠀⡚⠿⠃⠀⠀⠀⠀⢃⠀⠃⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠐⠤⣶⠤⠂⠀⠀⠀⢸⣿⣿⡿
⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣎⠁⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠘⢾⣷⠋

⠀⠀⣀⣀⣠⠀⠀⠀⠀⢀⡀⣦⡄⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⡤
⠀⠀⣿⣿⡇⠀⠀⠀⠐⣿⠃⣽⠇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢀⡤⢊⠔⠁
⠀⠈⠉⠋⠀⠀⠀⠀⠀⠙⠃⠉⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠛⠉⠛⠋⠀⠀⠀⠙⠛⠻⠟⠁⠀⠀⠈⠑⠋

⠀⠀⠀⠾⡄⠀⠀⠀⠀⡂⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠙⢦⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣴⣿⣿⣦
⠀⢀⡴⠃⠀⠀⠀⠀⠀⠹⣿⡯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡁⠶⣶⠠⠀⠀⠀⣀⡤⠴⠛⠁⠀⠀⠀⣿⡾⢷⣿
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⣤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣠⣤⠀⠳⠀⠀⠀⠀⠀⠀⣠⣾⠷⢆⠀⠈⠁⡅⠀⢀⣀⡀⢀⣐⣲⣀⠠
⠀⠀⠀⠈⠁⠀⠋⠊⠑⠀⠀⠀⣴⠛⠒⠀⠀⠴⠞⠁⠀⠀⠀⠈⢣⣾⣿⣿⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠠⠴⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀⡸⠂⣠⣧⠀⠐⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠀⠀⠀⠀⢠⡟⠃⢡⣿⣶⣶⣶⣶⡂⢸⡿⢁⠐
⠀⠀⡄⠀⠰⠀⠀⠂⠀⠀⠐⢰⣖⣤⡒⣾⠀⡦⠈⣿⡷⣯⣏⣿⣿⠟⠣⠆⠀⠀⠠⠄
⠀⠀⠄⠀⣈⣀⣀⣀⣀⡀⣶⣸⣍⡃⣿⢻⠆⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠄
⠀⠀⠀⢀⠈⡅⡑⢸⣾⠅⣿⣻⣧⣼⣿⣼⣦⡧⠤⠂⠀⠉⠉⢈⣉⣹⣤⣤⣿
⠀⠀⠀⢘⣴⣀⣃⠶⠗⢊⣙⣛⣙⣛⣋⣉⠀⡀⠀⣀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣶⣶⣜⡀
⠀⠀⠀⣠⣚⣭⣉⡋⠣⠻⢿⣿⡿⠻⣽⠾⣧⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠉⠉⠉⠉⠲⠀⢸⣇⢀⣠⣀⣀⣀⣙⣹⠿⢟⠛⠟⠁⣩⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣄⣀
⠀⠀⠴⠚⠉⠁⠀⠀⢠⠄⢾⣿⣛⣿⣿⣿⣿⣿⣿⣆⠂⠁⢀⣿⣿⡧⣴⢶⣴⣿⣷⣴⣶⣯⣿⣿⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠟⠋⠟⣯⡝⠿⣭⠛⠻⣿⣶⣿⠾⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⢀⡀
⠀⠀⠀⠀⠚⠂⠘⠁⠀⠀⢠⡶⣀⠀⠴⠵⠤⣄⡤⡄⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠽⠇⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⠤⣤⠀⠀⠀⠀⠀⠤⠁⣈⣠⠀⠀⠀⣤⣤⣤⣤⣤⡄⢀⠀⠀⢠⡀⠀⠀⠀⢠⣤⣴⣦⣴⣦⣶⢄⣄⠀⠀⠀⠀⠀⡀⠀⣤⡴⢄⡀
⠀⠀⠀⠘⢺⣉⡷⠀⠀⠀⢸⡞⣞⢛⣤⠀⠀⠀⣹⠟⠿⠿⠿⡿⠙⢿⠔⢻⡇⠀⠀⢰⡏⠙⣍⡿⠎⠀⢸⡾⠋⠃⠀⠀⢠⢺⠷⣾⣯⡀⣴⠏
⠀⠀⠀⠀⠐⠶⠒⠰⣱⣾⣎⣯⠁⠊⠁⠀⠀⡸⠋⠀⠀⠀⠙⠀⠚⠀⠄⠀⢹⠀⠀⢸⡇⠀⠸⡗⠀⠀⠘⠁⠀⢰⠀⠀⠀⠙⠲⢿⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠘⠬⣉⡍⠋⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⢷⠤⠐⠀⠀⠀⠀⠠⣤⠎⠀⠀⠀⠀⠀⠀⠘⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⢤⣄⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣾⢀⠀⠀⠀⠉⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⡠⣲⠝⠑⠂⢩⢉⡽⠾⠃⠀⠀⠀⠀⠳⣆⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⡟⠀⠉⠹⠁⠁⠀⠰⠉⠀⠈⢷⠀⠀⠀⠀⠀⠀⢰⡀⢦
⠀⠀⠀⢠⡎⢊⢜⣠⣤⣡⣈⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⣬⠾⠟⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄
⠀⠀⠀⣾⣣⣿⠿⠏⠄⠀⠈⠙⢿⡄⠀⠀⠀⢠⠋⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠰⠸⣇
⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠛⠂⠀⠘⡄⠀⠀⡀⠀⠀⠈⠓⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿
⠀⠀⢸⣿⡧⠀⠀⠀⣤⣶⣴⡆⠲⠒⠊⣫⣆⠀⠈⢅⡾⠀⠀⣼⣉⡇⢀⠀⠄⢘⢦⡀⠘⠆⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢸
⠀⠀⠘⣿⣹⠃⢀⣼⣿⣷⣶⠷⠶⠞⠛⠂⠘⠓⠀⠀⠀⠀⠀⠘⣯⢂⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡸⠁⠀⠀⣀⣤⣶⣦⣤⡄⠀⠀⠈⠛
⠀⠀⣸⣿⢃⣰⠋⢸⡿⠓⠃⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⣀⡤⠴⠂⠀⠀⠘⢷⣶⣤⡾⠁⠀⣠⣾⣿⣿⣅⣨⣿⣿⣷⡆
⠀⠸⡿⡫⠞⠁⠀⠸⣉⠀⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⢀⡟⠙⠛⠉⠛⠛⠛⠛⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠠⢄⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣁⣉⣙⣋⣉⣋⣙⣒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣤⡔⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠛⢛⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⢀⣄⠰⢬⣷⡄⠂⠁⣠⡙⠦⣇⡠⠀⠈⠳⣄⢶⣈⡧⣿⡠⠴⣚⡋⠀⣩⣴⠀⠆⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠻⠛
⠀⠀⠀⠀⡀⠲⣘⡛⢄⠈⣁⠸⣦⡀⠙⠿⠆⡊⣟⠛⠛⠛⢚⣀⡋⡟⠟⠷⣆⡛⠋⠈⠉⣿⠀⡗⠠⡲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⣄
⠀⠀⠀⠘⠒⠲⠆⠄⢘⡋⢻⠁⠓⠘⣶⡐⠺⠧⣌⠲⡀⣴⢷⡛⠁⣹⠀⣀⣙⣃⠀⠀⠐⠉⠘⢧⣄⡸⣀⡀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⡏⢑⠈⡄
⠀⠀⠀⠀⢸⣳⠀⣾⠈⣗⢸⣷⠈⢶⡌⢧⣄⠀⠀⠹⠋⣑⣤⡈⠂⠀⠀⠉⣽⣯⠍⢍⡐⠒⠒⠤⣈⠀⠙⠉⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⢧⡇
⠀⠀⠀⠀⠀⠹⣆⠙⣧⡈⢿⣿⢷⡀⠉⣦⡙⢧⣀⠈⠉⢹⢻⣷⡄⠀⠀⠈⠛⠦⡘⢶⣦⣉⠒⠠⣀⣍⡰⣖⣶⡶⢾⡏⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳⣄⠙⢯⣻⣄⠀⠘⢷⣈⡟⠂⢸⢰⠇⡿⠀⠀⠀⠀⠀⠈⠑⠿⣿⣯⠦⣀⠉⠛⢋⣉⡡⠆⠀⠀⠀⠀⠀⠀⠀⣻⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⣳⠀⠉⠹⠷⠄⠀⠀⠁⠀⠘⠀⡄⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢬⣂⠠⣌⠃⠀⣏⡆⠀⠀⠘⠦⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠥⠖⠒⣂⣈⣉⣩⡆⠀⠀⢅⡰⣬⡻⠦⣄⣀⠀⣀⣠⠀⡀⠀⠀⠦⣄⣸⣿⡿⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠂⢀⠩⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠴⣢⡉⠀⠭⠴⠆⣙⠀⠀⠀⠀⠉⠛⠷⠶⠛⠳⢦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠠⠀⠆⠀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠐⠒⡄⠌⡀⠠⠐⠘⡀⠈⢀⠐⠂⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠄⢨⠁⠘⠤⠦⡆⠀⢤⠀⠀⠐⠁⠁⠀⢀⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠠⠀⠄⠑⠀⠀⠁⠀⢆⡀⠀⠀⠀⡀⠠⠛⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠯⠈⢳⠀⠀⢀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⡧⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢲⢲⠁⠉⠀⠀⠸⠠⠄⠀⠘⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠠⠖⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠠⡠⠤⡠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⣴⠀⡆⠄⢠⡌⠀⠀⣀⠀⠀⠀⠀⠔⠁⠀⠀⢀⠄⠱⢠⠀⠀⠀⠀⡁⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠄⡅⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⢠⣅⠀⠀⡀⠁⠀⠀⡞⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⣤⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⡀⢘⠂
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢤⢄⠀⠀⠀⠩⠀⠀⠤⠄⠑⡀⠀⠉⠀⣐⢺⠹⠟⣲⠀⠁⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠍⠀⠀⠀⠀⡇⢄⡸⠀⠀⠀⠀⠀⠀⠃⣤⠐⠀⢀⡀⠀⠀⠉⠉⠉⠀⠀⠀⠑⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡈⠁⡀⠨⣡⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠀⡀⠀⡀⣀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠰⠀⡀⢀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠐⠚⠀⠁⠀⢨⠀⠐⠀⢠⣠⠀⠘⠑⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠣⡄⠸⢒⠆⠀⠜⠙⠀⠐⠀⠉⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⠁⠀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡀⠁⠅⠀⡐⠁⠀⠀⠒⡎⢉⠉⠉⢉⣀⡏⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠷⠀⠂⣰⠆⠀⠷⠉⠉⡕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠂⠖


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⢀

⠀⠀⡤⠤⢤⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠁⠀⠙⡆⠀⠀⠀⢸⠁⠀⢹⠀⠀⠀⠀⠀⠠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣯⡀
⠀⠀⢠⠀⠀⠀⡇⠀⠀⠀⣼⡗⠒⠋⠀⠀⠀⠀⠠⡺⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠈⠉⣹⠃
⠀⠀⠁⠀⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡠⣶⡄⠀⠀⠀⠀⣾⣽⣯⣷⠀⠀⠀⠀⠰⣾⣿⡄⠀⠀⠀⠀⠺⣿⣿⣆⠀⠀⠀⠀⢀⣣⣜⡀
⠀⠴⠿⠿⠜⠿⠦⠀⠀⠀⢻⡿⢿⡟⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⣰⡆⠀⠀⠀⠘⣿⢻⡟⣿⠃⠀⠀⠘⢻⣿⣿⡟⠃⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⡅⢨
⠀⠰⠿⠻⠿⠧⠄⠀⠀⠀⣿⢸⡇⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠸⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠂⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡟⠋⡀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠀⢻⠉⠉⡟⠀⠀⠀⠀⠸⣿⣏⠇⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠈⣀⡾⠂⠀⠀⠀⠀⢴⠟⠋⠀⠀⠀⠀⠀⣼⣀⣀⣧⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⢐⠾
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣤⠤⠶⠚⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⢻⡀⠰⠆⠀⠀⠈⡉⢻⠀⠀⠀⠀⠀⠀⠀⢰⡿⢩⠀⠈⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠈⣇⠀⠈⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢸⣇⠓⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿
⠀⠀⠀⢸⡄⢀⠐⠀⠂⠈⠀⢹⡄⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⣇
⠀⠀⠀⠀⢧⠰⠧⠀⢀⣀⣤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⡴⢡⡞⠉
⠀⠀⠀⠀⠘⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⡟

⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡦
⠀⠀⠀⠀⠀⠀⣀⡼⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣼⣯⣴⡆
⠀⠀⠀⠀⠀⢸⡀⠀⢀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⢠⣾⡽⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠛⠛⣿⡟⠉⠉⠉
⠀⠀⠀⠀⢀⣿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟
⠀⠀⠀⠀⠘⠻⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣤⣤⣤⣤⠤⣤⠀⠀⠀⠀⠀⠀⢠⠴⣤⣶⣶⣦⡴⢦
⠀⠀⠀⠈⡄⢉⣓⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢟⣿⣿⣿⣿⣟⠾⠿⠁⠀⠀⠀⠀⠀⠘⣴⣿⣿⣿⣏⣿⡜
⠀⠀⠀⠀⠘⢾⢤⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⢻⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠈⠓⠛⢼⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⢸⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏
⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠹⠒⠚⠋⠀⢀⠀⡀⠀⠀⠀⠀⠓⢀⡀⠀⠈⠉⠀⢠⠖⠢⠀⠀⠀⠀⠀⠠⡀⢠⡄⣭⠳⠄⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠒⠶⠛⠀⡄⠀⡘⠳⡄
⠀⠀⡙⠀⠀⠶⠶⡶⠀⠈⠉⠁⠀⡠⠀⠀⠀⠘⠃⠞⠀⠐⠂⢨⡇⠀⠀⠀⠀⠈⠀⠀⠱⣾⠿⠈⠀⠀⠀⠀⢀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⠇⢶⠀⠃
⠀⠀⠅⠀⠀⠈⡴⠃⠀⠀⠀⠀⢸⠃⠀⠀⠖⠀⠀⣠⠀⠀⢠⡟⠀⠀⠠⠀⢀⣠⠴⠊⠀⠈⠀⠀⠀⠀⠀⠘⠦⠉⠀⠀⠀⠐⡿⠓⠒⣶⠦⠀⢿⠙⠊⠢⠎
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⠀⠸⡄⠀⠀⠀⣠⠞⠁⠀⠀⠈⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠒⠀⠀⠙⠀⠴⠟⠀⠀⠈⠑⠐⠃
⠀⠠⠌⠀⡀⠀⢀⡀⠀⠰⠀⠀⠀⢈⠐⢒⠋⠁⠀⠀⠀⠀⠠⠶⠋⠁⠀⠀⡔⠃⣰⠀⠀⠀⠀⠀⠰⠎⣀⣤⠻⠀⠀⠀⣀⣤⣶⠀⠀⠀⢀⣀⡠⢤⡤⠀⠀⠰⠋
⠀⠀⠀⠀⠇⠀⢨⡇⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣡⠆⠀⠀⠀⡶⠀⠠⠚⢁⡴⠃⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠀⠹⠗⠘⠛⠁⠀⠀⠀⠀⢴⠃
⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠁⠀⠈⡷⠢
⠀⠀⠘⠆⠈⡀⠀⡇⠀⠀⢀⡁⠀⠆⢀⡄⠰⠂⠀⠀⠀⠈⠀⢠⠠⠀⡋⠁⠈⠀⡐⠀⠀⠀⠂⠀⠀⢠⣆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢃⠀⢼⠀⠀⡨⢁⠀⠶⠨⠀⠀⠀⠀⠑⠂⠀⠀⠀⢄⠀⠛⠀⠀⠀⢷⠀⣀⠀⠀⠀⡀⢼⣗⡇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠨⡰⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠘⣀⠈⠀⠀⠁⠀⠀⠂⠀⠀⠁⠒⠀⠀⠀⠘⠀⠀⠈⠀⠛⠀⠀⠀⠐⠒⠃⠀⠤⠠⠀⠀⠙⠃⠀⠂
⠀⠀⠀⣨⠀⠀⢿⠀⠀⠀⠀⠀⠀⣈⡙⠁⠀⠀⠀⠀⠀⠀⣠⠪⢉⡷⠀⠀⣦⠠⠶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣹⣅
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⠃⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠀⠋⠁⠀⠀⠢⡈⢢⡄⢀⠀⠀⠀⠀⠰⠮⠶⠶⠟
⢀⣀⠠⠐⠄⠀⠀⠂⠀⠀⠀⠑⠨⠁⠀⠀⠀⠀⠀⠀⠁⣀⠤⠈⠁⠠⠀⠀⢀⣴⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡀⡀⠈⠀⠀⢀
⠈⠃⡔⠀⠀⠀⠘⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠐⠀⠀⠀⠀⠀⠀⠦⠄⠀⠰⣷⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⣹⠁⠀⠀⠀⠀⠈⠤⠃
⠀⠀⠀⠀⢀⠀⠀⣠⠉⠛⠲⢦⣤⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠃⡁⠀⣇⠀⠈⢠⠄⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠶⠀⠀⠀⠀⠀⠠⠀⣀⠀⠚⠀⠰⠶⠒⠀⠀⠀⠉⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⣠⣦⠖⠋⢀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠠⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠀⣠⡾⠋⢁⣠⣶⠿⠀⠀⠠⠜⠀⠘⠛⠓⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠈⠁⠁⠀⠀⠠⠀⠉⠀⠀⠀⡠⠒⠂⠈⠰⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠉⣠⣶⠟⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠤⠦⠘⠃⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣸⠏⠘⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠸⣦⣀⣠⣾⡇⠀⢠⣤⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡴⠶⠶⠶⠶⠶⠛⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠛⠛⠛⠛⠛⠋⠀⣼⠟⢁⣠⣤⠶⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠶⠶⠶⠶⠶⠄⠀⣼⢃⡶⠋⣁⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⠀⠀⠀⣿⣟⣠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠀⠀⢠⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠀⠀⠘⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣆
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠛⠈⠁⠀⠀⠀⠙⠋⠙⢿⣌⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠱⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠟⢿⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠈⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡆⢠⣶⠟⠁⠀⠀⠀⠀⠀⠠⡄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⣥⠀⠀⠀⠀⠀⢠⡀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣤⣟⣤⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢤⠄⢠⡄⠠⡄⠀⠈⠉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡗⢺⡇⢰⡇⢰⣭⡆⣿⠃⣴⠋⣶⠐⣷⠒⠰⣆⡐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠃⠚⠓⠘⠛⠘⠒⠃⠙⠛⠙⠓⠋⠘⠛⠀⢤⠝⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⣿⠡⢿⣷⠟⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣿⣿⣥⣾⠃⠸⢦⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣿⣤⠟⠁⠀⢀⣼⡿⠋⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠻⣿⢷⡆⢉⣶⠟⠁⠀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣿⠀⣿⣿⡾⠋⠀⠀⠀⣀⣈⡤⡾⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡔⠁⢸⡶⣿⣡⠄⣠⣦⠤⠚⠉⠁⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠅⠀⣀⠄⣸⡇⠘⣷⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⡁⠔⠋⠀⠀⠀⣧⠀⢹⡗⢀⣄⣀⠹⠶⠒⠒⠚⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊⡁⠀⠀⠈⠀⣀⣀⡄⠀⢠⢿⣦⣼⣯⡉⠐⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⡯⣐⣉⣥⣤⣶⣤⣭⣥⣤⣤⣠⣄⣶⣶⣿⣇⠈⢧⡶⠶⠤⠄⠴⠶⠤⠀⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣀⣸⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣦⣈⣧⠠⣄⠠⡁⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⣼⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡍⢳⡀⠈⠙⠲⢦⣀⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⣤⡆⠠⣾⠧⠽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⡿⢦⣀⠀⠀⢈⡳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣧⡷⠶⣯⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣯⣴⣙⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠏⠀⠀⠘⣧⣞⣁⠀⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠉⡙⠋⣤⢼⡡⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⡀⠀⠀⠀⠀⠀⣐⣾⣤⣾⣷⠄⢸⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢷⠴⣿⣄⣎⠉⠉⠉⠙⠛⠿⣷⠛⠗⠛⠛⠋⠉⠉⠁⢀⡦⠤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣼⢷⠿⠛⣿⠿⠿⠿⣷⣶⣶⣶⣦⣤⢴⣶⣶⣶⡷⠿⣋⠤⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⡿⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⡇⡷⣛⣛⣛⣲⣙⣑⡛⣟⣥⣄⢷⣾⢻⠏⡯⠧⣴⣿⣷⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣧⣠⣧⠷⣮⣯⣿⣿⣽⠛⢛⣻⣯⣧⣾⣿⣸⡀⣿⡿⣿⣯⣿⣏⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣿⣯⣷⣦⣤⣤⣤⣬⣽⣿⣿⣽⣍⣉⣩⣼⡻⣥⠖⣸⡟⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠶⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠶⠒⠒⠊⠉⠉⠉⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢸⠀⠋⢻⣏⠙⠂
⠀⠀⠀⠀⢀⡴⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣄⠀⠀⠀⣠⡄⠀⢸⣸⠀⡀⠻⢸⣿⠀⡇
⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⢄⣴⠷⣄⢸⣟⠫⣇⠸⡆⠀⠀⣿⠀⠀⢸⣿⠀⡇⣾⢸⣿⠀⡇
⠀⠀⠀⣿⢼⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣴⡶⣆⣲⠠⢭⠵⠒⠊⣿⠃⠀⢹⢸⣇⠀⣿⠀⢻⡄⢸⡇⠀⠀⢸⡏⢨⡇⠻⠘⢻⠀⡇
⠀⠀⠀⣿⣾⡇⠀⠠⣶⠀⠘⢋⠀⣿⡇⡿⢋⣀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⢾⣷⣾⠁⠀⠀⢻⡟⠀⠀⠀⢸⡇⠸⠇⠀⠠⢸⠀⡇
⠀⠀⠀⣿⢰⠇⠀⠀⢾⡀⢀⢰⠀⣿⡇⠁⠈⠡⠖⢳⣄⠀⠸⢠⠀⠀⣿⠀⠀⣸⠸⡇⠈⢷⡀⠀⢸⡇⠀⠀⠀⢸⡇⡇⣦⠀⠃⢸⠀⡇
⠀⠀⠀⣿⣾⠀⠀⠀⢸⡇⠌⠸⠀⢻⡇⠀⠀⠀⠀⢀⠼⡁⠀⢸⠀⠀⢻⣄⣰⠟⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⡇⠇⣿⠀⢀⣼⠀⡇
⠀⠀⠀⣿⣿⠀⠀⢸⢱⡎⠉⣷⠀⢸⡇⠀⢤⣄⣰⣮⠞⠁⠐⠾⠀⠀⠀⠉⠁⠀⠐⠇⠀⠨⣟⠀⢸⣇⠀⠀⠀⢸⡇⡄⠿⠰⢸⣿⠀⡇
⠀⠀⠀⣻⡟⠀⠀⢸⢸⡇⠀⣿⠀⢸⠇⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡿⠀⠀⠀⠀⡇⡇⠀⠀⢸⢹⠀⡇
⠀⠀⠀⣻⡿⠀⠀⢸⠀⠅⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡙⡦⢸⠀⢸⠀⡇
⠀⠀⠀⢻⣿⠀⠀⠸⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠀⠀⠀⣤⣤⡄⠀⠀⠉⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⣿⠁⣇⠘⠀⢸⠀⡇
⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠀⠀⡄⠀⠀⠠⠟⣦⡀⠀⣇⣸⣟⠄⠀⢰⡂⡀⠀⠑⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⡇⣾⠀⡁
⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢰⠈⣅⡀⡶⢻⠀⠀⠟⠉⠈⣶⠐⠺⡯⣿⡁⠇⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⡇⣿⠀⡇
⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣐⠂⣶⠟⣥⠨⣶⣯⣽⠀⠀⣀⡿⠳⢾⡀⠰⠂⠈⠁⢠⠃⠀⠀⠀⠀⠀⡟⠀⣼⠀⡇⣿⠀⡇
⠀⠀⠀⣧⣾⠀⠀⠀⠀⠀⠀⠀⡿⢀⡌⣩⣸⡇⠘⠁⢀⡏⢁⠈⠻⣦⣿⣷⢦⠄⠛⢶⡖⢠⡴⠃⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠁⣿⠀⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢣⡖⠁⠠⢴⡏⠙⢿⡶⢦⣜⡛⠋⠻⣍⠉⠁⠈⢺⡧⣀⣸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢀⠀⣿⠀⣇
⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠑⠠⢀⠰⣦⠶⣎⢡⠈⠋⠋⠉⠀⡝⢧⣀⣀⠼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⢀⡇⢸⠀⣿
⠀⠀⠀⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠻⠷⠄⠰⠒⠒⠚⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣧⠸⡇⣿⠀⢻
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⡇⡏⡆⢸
⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⠀⡇⡇⡇⢸
⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡏⠀⠀⡇⡇⢸
⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠃⢱⢸⡆
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠄⠀⡇⡇⢸⢸⡇
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⡇⢸⢸⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠁⡇⢸⢸⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⡇⢸⠘⡇
⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢱⡆⡇⢸⠈⡇
⠀⠀⠀⠈⡷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣽⡷⠗⠛⠚⠁
⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⡤⠄⠀⠀⣸⠿⠛⠉
⠀⠀⠀⠀⣯⣿⠂⠐⢲⣶⣤⠤⠤⠾⠿⠶⠀⠀⠀⠈⠁⢀⣀⣀⣀⣈⣉⣉⡩⠭⠭⠥⠤⠤⠴⠴⠄⠒⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⠉⠀⠙⡆⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠰⠟⠈⠉⠁⠨⡇⠀⠀⠀⢠⡄⠀⢰⣿⠀⠀⠀⠀⠀⢀⠀⡀⠠⣄⠀⠀⠀⢸⣿⡶
⠀⠘⢤⣀⡴⣇⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢘⣿⠀⠀⠀⠀⠀⠈⠀⠹⡦⠉⠀⠀⠀⠘⣿⠉⠀⠃
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠛⠛⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣸⢇⠀⠈⠀⠀⠀⠀⠀⠉⠳⣴⠛⠛⠀⠀⠀⠀⠀⢾⣟⣿⠟⠀⠀⠀⠀⢀⣴⣿⣷⣀⠀⠀⠀⠀⢾⣿⡃⣸⣿⡇
⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⢷⡧⠀⠀⠀⠀⠀⢴⠊⠈⠳⡄⠀⠀⠀⠀⡴⠋⠉⠁⠀⠀⠀⠀⠐⠚⠛⠛⠓⠛⠒⠀⠀⠀⠘⢿⣷⣿⡿⠃

⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⢰⡀⠀⢀⠀⠀⣤⠀⠀⠀⣰⣿⣿⢿⣷⡄
⠀⠘⠉⠿⢿⡇⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠛⠶⡴⠯⣄⣠⠀⠀⠀⠀⢲⠘⠉⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⠟⠃⠀⠀⠀⢿⣿⣡⣿⣿⠇
⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡆⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣠⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠹⠟⠀⠀⠀⠀⠀⠀⢉⠀⡘⠀⠀⠀⠀⠀⠀⢠⡿⣷⠀⠀⠀⠀⠀⠈⠒⢶⣗⠖⠁⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⡻⠡⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⢶⣿⡶⠃
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣶⣶⠾⠁⠀⠀⠀⠀⣴⣶⢸⣿⡆⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣤⣠⣤⣄⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠜⢁⠄
⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⢿⡏⢠⣿⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⡶⣁⡔⠁
⠀⠐⠁⠉⠉⠀⠀⠀⠀⠀⠀⠘⠟⠈⠁⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠛⠋⠀⠀⠀⠀⠙⠛⠛⠿⠛⠁⠀⠀⠀⠈⠘⠋

⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⢈⡝⠛⠀⠀⠀⠀⠀⠧⣤⣦⡴⠃⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣿⡃⣀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⣿⠻⡿⢻⡇
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠒⢿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠛⢿⡠⠃⠀⠀⠀⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⣿⣿⠛⣿⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠐⢤⣐⠶⡀⢹⣯⠑⢾⣈⡙⢿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⡐⠀⣀⢈⢩⠻⠾⢿⣄⠀⢂⡘⡇⠹⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠙⠋⠁⠸⠠⠀⠑⢄⡀⠈⣧⣈⣯⠳⢤⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠈⢉⠀⢘⠏⣯⠻⡼⣿⡀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⣤⣤⠤⣄⠀⠀⠀⢩⡾⠛⣟⣷⣤⣀⣳⡀⣸⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠿⠓⠋⠀⠀⠘⢰⣏⣭⣿⠿⠿⡯⣷⣿⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⣼⠟⣼⣷⣏⠀⢱⣀⢻⡄⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⡽⢢⣾⣿⣯⣷⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣨⣿⣿⣿⣿⣿⣿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠙⣿⣿⣿⣿⣟⣯⣷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠂⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣿⣿⣿⣿⡏⣯⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⣤⣤⣤⣤⣤⣶⠞⠁⠀⠀⠀⠀⠈⠻⢿⡋⢴⠟⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡈⠓⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⢀⣀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠑⠀⡂
⠀⠀⠤⢤⡄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠐⠀⠀⡤⠰⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠂⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⠉⠀⠀⠈⠀⠀⠀⡀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠆⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛
⠀⠀⠀⡼⣆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠁⠂⠆⢀
⠀⠀⢠⣧⣽⡄⢠⣀⠀⣠⣄⢸⡤⡄⣠⣤⡀⢠⠀⠀⠏⢀⡄⠀⢠⣤⡄⡀⠀⡀⠀⠀⠀⡮⠂⠀⠀⠀⠻⠂
⠀⠀⣸⠃⠀⠡⠸⠇⠘⠅⠀⢸⠀⠁⠹⠍⠁⠻⠤⠃⠀⠘⠦⠇⠹⠤⡇⠻⠴⡇⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠆⠀⡄⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠘⠀⠠⠄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠂⠀⠀⠂⠂⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⠄⠰⡀⠀⣠⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠄⠀⠀⠘⠃⠀⠀⠀⠸⠈⡀⠀⠀⠀⠀⣇⠀⢀⠄⠀⠈⠻⠋⠀⠀⠆⢐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠤⣶⡦⢄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢓⠲
⠀⠀⠀⠀⠀⠀⢸⠟⢿⣿⣿⡿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⡇
⠀⠀⠀⠀⠀⢀⡀⣀⣀⣈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⠧⣉⣁⡀
⠀⠀⢀⣤⠠⠿⢿⣿⣿⣿⣷⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣴⣶⣿⣿⣿⣿⣿⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⢃⣀⢤⡀
⠀⠀⠀⣽⠀⣀⣀⠀⠈⠉⠛⠿⣶⠟⠋⠀⠀⠀⠀⣠⠤⠔⠒⠉⠁⣀⡴⠾⠛⢛⠩⢸⣿⣿⣿⠀⠀⠄⠀⠀⢠⡄⠀⣴⣶⣿⠟⠻⣷⡤⠆⠄
⠀⠀⢴⣿⡿⣿⠟⠒⠒⢂⡀⠀⠛⢧⣤⢠⠀⣤⠄⠀⢀⣀⣀⣶⣿⣥⣶⣶⣾⠁⠀⠘⣿⣿⡿⠂⠈⠁⢀⡀⠀⠨⣭⣿⣿⣦⣄⢻⣏⣉⠀⠀⣠⣀
⠀⠀⠀⠀⢠⣿⣶⣤⠤⢒⣶⠀⣤⠀⢡⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⣿⣿⣼⠀⢸⡇⠈⠉⠉⠛⡛⣧⣀⢸⣿⠤⠾⠋⣩⣶⣺⣯
⠀⠀⠘⣻⣿⣿⣿⣿⣶⣿⣿⠋⠉⢩⡍⣾⣿⣿⣿⠃⣿⣿⡇⣿⣇⣤⣿⣿⡇⠀⠀⡄⣿⣿⣿⠀⢸⡇⠀⢸⠀⢠⣿⡅⠘⣿⣇⣀⣀⠪⢴⣟⣻⣯⠀⠂
⠀⢀⠸⢍⣭⣷⣿⣿⣿⣯⣿⠀⣤⣾⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣦⣞⣿⡿⡇⠀⠸⠇⢿⣿⣬⣄⢸⡇⣀⠸⠀⢸⣿⣿⣧⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣅
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣟⢹⣸⣿⣿⣿⠿⢛⣩⣼⡿⠿⠟⣻⣿⣻⣿⣿⣿⡷⠀⣤⣶⣿⣿⣿⢽⡉⠱⠛⠂⠺⠶⣼⣻⣟⣿⣭⣯⣽⣿⣿⣿⣿⣿⣿⡧
⠀⢀⣤⣥⣤⣤⣤⣿⣿⣿⣿⣿⠩⠉⠉⠉⠉⠉⠉⠙⠒⠛⠋⠉⠙⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠩⠍⠉⠉⠉⠁
⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣸⣿⣿⣿⡀⠀⢀⣾⠏⠀⠀⠀⠈⠙⠻⣷⣦⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣀⠙⠻⣿⣿⡇⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣉⣉⣉⣉⣁⣀⣀⣉⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣿⣉⣹⣿⣉⣿⣏⣹⣿⣉⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⣠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⣿⣉⣽⣿⣆⠀⢿⣷⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣻⣿⣿⣿⣁⣹⣿⣿⣿⣿⠿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠃⢈⣿⣿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⡟⢀⣴⣾⣿⣶⡄⠰⣶⣶⣶⣦⣤⣤⣴⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡅⢸⣿⣿⣿⣿⡷⠀⣿⣿⣿⣿⠛⣻⣿⣿⣿⠛⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠿⠿⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠉⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠉⢿⠿⠿⠿⠿⠿⠇

⠀⠀⠠⣤⡄⠀⢨⠁⠀⠀⠀⠀⢀⣤⣀⣾⣿⣶⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣾⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⣿⢀⠀⡈⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⢿⣄⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣷⣾⣷⣶⣤
⠀⠀⢿⣿⡿⢲⡇⠀⠀⠀⠀⠀⠀⠉⠁⠘⣿⣤⡿⠀⠀⠀⠀⢸⣿⡄⠀⣸⣿⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁

⠀⠀⢀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⣾⡟⣿⣿⣏⠀⠀⠀⠀⠀⣤⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢿⢿⣟⠆⠀⢀⡀⠀⠀⠀⠀⣿⣿⡿⣫⣿⣷
⠀⠀⠁⠀⠛⢻⣯⠀⠀⠀⠀⠀⠙⣙⡿⠳⠶⢴⡶⠀⠀⠀⠀⠈⠙⢉⡀⠴⠛⠏⠀⠀⠀⠀⢿⣿⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣺⢾⠁⠀⠀⠀⠀⠀⣶⣤⣴⣶⣬⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⣾⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⣹⣿⣽⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣅
⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠚⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠛

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣰⣾⠃⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠
⠀⠀⢿⡟⠗⠀⡌⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡿⠅⣠⣤⣀⠀⡇⠀⠀⠀⠀⣀⡴⠋⣠⠞⠁
⠀⠀⣸⡇⠀⠂⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠘⢤⣈⣛⡯⠜⠀⠀⠀⠀⠀⠙⠱⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⡠⠚⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠋⠀⠀⢀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢎⡂⢀⡈⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⢰⠃⢣⠃⠀⢃⢐⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠐⠀⠀⠈⠀⠁⠚⠀⢠⠜⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⡩⠔⠃⠀⠀⠒⠣⡄⠁⠀⢠⡎⢀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⢀⠀⠈⠄⠀⡀⠀⠀⠀⠈⡟⠀⢢⠙⢀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⠀⡔⠀⠀⠀⠀⡀⠀⠀⠰⠀⠁⠀⠀⢄⢆⠀⠀⠀⡄⠈⠀⠠
⠀⠀⠀⠐⢄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠈⠀⠀⠀⢹⠢⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠙⠢⡄⠀⠀⠀⢀⠀⣀⢀⠄⣂⡀⢸⣠⣄⣄⠀⠀⡷⢇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠉⠀⠀⠀⠴⢀⡀⠐⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢄⣀⣀
⠀⠀⠀⠀⢀⡤⠒⠉⣀⣶⠀⡇⠈⠉⠉⠑⠒⠒⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠈⠑⢲⣾⣿⠿⣿⠀⡇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠦⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⣿⡉⠶⣃⡇⢰⠁⡘⠀⡰⣆⠄⠶⡀⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠲⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⣗⣂⣬⡾⢀⠟⣰⠁⠀⠀⠁⠀⠚⠀⠙⠀⠦⠄⢀⣹⠀⢠⡄⢠⣀⡀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠉⢹⠑⡒⠢⡀
⠀⠀⠀⠀⣰⠿⠞⠋⠉⠙⠒⠓⠶⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⣱⠀⠸⠀⠘⣹⢐⣢⠀⣄⡀⢸⠁⡇⠀⡇
⠀⠀⠘⠛⠒⠒⠲⠦⠤⠤⢄⣀⣀⡀⠀⠀⠀⠉⠉⠉⠒⠒⠶⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠀⠏⠀⡼⢠⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠲⠤⠤⢤⣀⣀⣀⠀⠀⠀⠉⠉⠉⠒⠒⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⣰⠋⡜⠀⡸⢄⠆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠦⠤⣄⣀⣀⡀⠀⠀⠉⠉⠓⠒⠖⣷⣾⣄⠔⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⢉⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠉⠋⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣄⣀⡉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣫⣟⣯⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠤⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣉⣶⡶⠤⣄⡀⠀⠀⠀⠀⠀⡴⢃⣼⠟⠉⣿⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠤⠾⡿⠻⠛⠒⠒⢿⡩⠭⠟⠛⠉⠀⠀⠀⠀⡞⢡⣿⠃⠀⠀⣿⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣤⣤⣶⠶⠴⠶⣖⠛⠉⠉⠉⠁⠀⣀⣐⣂⣀⠠⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⡿⠃⠀⠀⢠⡿⢾⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⡖⢈⠉⠀⠀⠀⠀⠐⣟⠀⠀⠀⢠⠞⠉⠀⠀⠀⠉⠉⠣⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⡇⠀⠀⠀⣼⢇⡾⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⢾⠃⠀⠀⣀⣀⡀⠸⡆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢄⡧⠤⠴⠞⠉⠒⠦⢄⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⢰⢳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡶⠋⢉⣉⣉⠳⢧⠀⠀⠀⠹⠦⠀⠤⠤⢤⣴⠋⠀⠀⠀⠀⠀⠉⠉⢙⡏⠳⡄⠀⠀⠀⣌⠀⠀⣠⠏⢠⢯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢹⡀⠀⠉⠉⠉⢃⣀⡀⠀⠰⠳⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⣠⠇⠀⠰⡀⠉⢆⡰⢃⡴⣻⠋
⠀⠀⢰⡏⠙⡆⠀⢀⣠⠤⠛⡇⠀⠀⠉⠛⠛⠛⠋⠉⣿⠈⠙⣲⣦⣄⣀⣀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠁⠀⠀⠀⠈⢺⠲⡭⠵⠚⠁
⣏⠙⠲⠗⠀⠱⠚⣉⡤⠔⢲⣇⣠⣤⡴⠶⠒⠀⠀⠀⠻⠚⠉⠁⠀⢳⡠⠞⠋⠉⠛⣿⣿⠋⠉⠛⠳⣤⡄⠀⠀⠀⢀⠴⠒⠲⡦⠼⢄
⠈⣓⡶⠀⠀⣠⣌⠓⠒⡄⠀⢁⠴⠋⣀⠼⣧⣨⡟⠒⠒⡶⠀⢠⢴⡷⢠⣋⠉⣷⣖⣙⡇⠀⠀⣴⡋⠛⠦⠤⠤⠴⠃⢰⣀⡠⠇⣀⡜
⠀⠷⣤⠤⠊⠀⠈⠓⠚⠁⡔⠁⠀⠈⠣⢴⣉⠝⠉⢉⡏⠀⠀⡼⠂⠀⠀⠀⠈⠋⡏⢿⢤⣀⣞⠜⠉⠓⠒⠤⠤⠤⡄⠀⠙⣄⣀⡤⡧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠢⣄⡀⠀⠀⠉⠓⠲⠞⠀⢀⡜⠁⠀⠀⠓⠒⠒⠓⠓⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠶⠀⡼⢤⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣉⠓⠦⢤⣀⣀⠀⣠⡟⠀⠀⠀⠀⠀⠀⢀⣀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⢾⡟⠒⢦⣤⣈⡉⣥⡛⠒⣒⣒⣛⣉⣩⠭⠀⠚
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡒⢍⠙⢧⡉⠛⣿⠿⠃⠉⠉⠩⡟⣏⣉⣡⣿⡦
⠀⠀⠀⠀⠀⣠⠞⠋⠙⣲⣌⣦⣹⠳⠧⠞⡧⠀⠀⠀⠀⣾⣟⢠⡴⠒⠚⢧⡀
⠀⠀⠀⠀⢠⣧⡀⠀⠘⡇⠀⠉⠀⠀⢀⣈⣹⡆⠀⢀⣏⠀⠈⠛⠛⠩⣟⣩⠝⣛⣳⣄
⠀⠀⠀⠀⠈⠳⠮⢭⣿⣟⣋⣩⠭⠭⠽⠷⠖⠃⠀⠈⠫⢝⡲⢤⣀⡀⠀⠈⠙⣯⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠯⢿⣓⡒⠷⠤⠤⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠄

⠀⠀⠘⠃⠀⠀⠛⢂⠀⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠛⠀⠀⠘⠃
⠐⣶⠂⢰⡮⢳⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⢠⡄⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⡞⢵⡆⠐⣶
⢳⣦⡂⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⣠⠛⠷⣀⡉⠓⠿⠿⠛⢉⣠⠾⠛⣀⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⢐⣴
⠃⠾⠛⣀⠛⠁⠀⠀⠀⠀⠀⠂⣠⠀⠈⠰⢝⣛⠛⠫⠤⠄⣴⣦⠠⠤⠙⠛⣛⡋⠆⠁⠀⣄⠒⠀⠀⠀⠀⠀⠈⠛⢈⠻⠷
⡆⠰⠞⠀⠀⠀⠀⣠⡄⠀⠀⡜⠹⢦⣄⠀⠀⠀⣀⣠⣄⡀⣾⣷⢀⣠⣀⣀⠀⠀⢀⣠⡴⠏⢢⠀⡀⢠⣄⠀⠀⠀⠀⠳⠆
⠀⠀⠀⠀⠈⢀⣼⡟⠀⢄⠶⣰⠶⣦⣌⣉⣩⡁⠤⠶⠆⠉⠛⠛⠉⠰⠶⠦⢈⣍⣉⣡⣶⠶⣆⠶⡠⠀⢻⣧⡄⠁
⠀⠀⠀⠀⣰⣿⡿⠀⠀⣈⣾⠓⢚⣡⡉⡿⠷⠶⠄⠀⠾⠷⠖⠲⠾⠷⠆⠠⠶⠾⢻⢉⣌⠓⡚⣷⣡⠂⠀⢿⣿⣆
⠀⠀⠀⠘⣿⣿⠃⠀⠀⠘⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⠣⠀⠀⠘⣿⣿⠃
⡀⠀⢄⠀⢻⡟⠀⠀⣀⡔⠉⠀⠀⠀⠀⢀⣀⠠⣤⣤⣤⣤⠉⠉⣤⣤⣤⣤⠄⣀⡀⠀⠀⠀⠀⠉⢠⣀⠀⠀⢻⡟⠀⡀
⠀⠀⠈⠀⢸⠃⠀⢀⠛⠀⠀⠀⣠⠴⠒⢛⡡⠖⠋⠁⠀⠀⠺⠗⠀⠀⠈⠙⠲⢌⡛⠓⠦⣄⠀⠀⠀⠻⡀⠀⠘⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⢋⣀⣼⡟⠀⠀⠀⠀⢠⣤⡉⢉⣤⡄⠀⠀⠀⠀⢻⣧⣀⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⠛⠉⠛⠃⠀⠀⠿⠀⢾⣧⣨⣅⣼⡏⠰⠿⠀⠀⠘⠛⠉⠛⢿⣟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⠛⠿⣿⡿⠂⣀⠀⠀⢀⠀⠈⠁⠤⠤⠈⠁⠀⡀⠀⠀⣀⠐⢿⣿⠿⠋⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⠀⢀⠘⣿⣤⣼⠟⠀⣴⡿⢷⣆⣀⣤⣤⣤⣾⣷⣤⣤⣤⣄⣰⡶⢿⣦⠀⠻⣧⣤⣿⠃⡀⠀⠇
⠀⠀⠀⠀⢀⠀⢠⢿⠀⣿⣴⡟⠀⣔⣩⠶⠛⠉⠁⢀⣀⣀⠘⠃⣀⣀⡀⠈⠙⠛⠶⣍⣡⠀⢻⣶⣿⠀⡿⡄
⠀⠀⠀⠀⣸⠀⠈⠀⢀⣙⠋⠁⠘⠋⣀⠤⣚⠦⠈⠛⠉⠉⢱⡎⠉⠉⠛⠁⠼⣓⠤⣀⠙⠃⠈⠙⣉⡀⠀⠁⠀⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⠀⠀⣠⢞⡷⠾⠏⠀⠀⢤⠠⣾⣡⣌⣷⠄⡤⠀⠀⠹⠷⢾⣳⣄⠀⠀⣿⠁⠀⠀⠀⣿
⠀⠀⠀⠀⡟⠀⠀⠀⢸⠁⠀⠘⢻⡏⢠⠆⣠⡀⠀⠀⠀⠁⢬⡥⠈⠀⠀⠀⢀⣤⠰⡤⢝⡟⠃⠀⠈⡇⠀⠀⠀⢻
⠄⠀⠀⠀⢃⡀⠀⠀⠈⠀⠀⠠⢟⡵⠁⠰⠟⠚⠉⠉⠀⠀⠐⠂⠀⠀⠉⠉⠓⠻⠆⠈⢮⡻⠆⠀⠀⠀⠀⠀⢀⡜
⠀⠒⠻⢿⣿⠇⠀⠀⢠⡄⠀⢰⡿⠀⡶⠁⠀⣀⡴⠀⠋⢉⣉⣉⡉⠉⠀⢶⣀⠀⠈⢶⠀⣿⡆⠀⢁⡄⠀⠀⠸⣿⡿⠟
⠀⠒⠒⢾⡇⠀⠀⠀⠈⠁⠀⠘⠁⠀⢰⣾⠋⠉⡀⠀⠁⠘⢻⡟⠃⠈⠀⢀⠉⠘⣷⡆⠀⠈⠃⠀⠘⠁⠀⠀⠀⢸⡷⠒⠒
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢁⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠣⡈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠰⠆⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠄⠶⠆⠰⠶⠐⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠰⠆⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠐⠚⣿⠃⠀⢀⠀⠀⠀⣰⠞⠁⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠈⠻⣤⠀⠀⠀⡄⠀⠘⣿⠓⠂⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠠⣿⠀⠀⣸⠀⠀⠘⠁⢀⠴⣛⣁⣉⣙⣛⣛⣋⣉⣉⣙⠦⡀⠈⠃⠀⠀⣇⠀⠀⣿⠇⠀⠀⢸⡇
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠘⡏⠀⠘⠀⢀⢏⣾⣿⡿⣯⢻⡿⢿⡟⣽⢿⣿⣷⡙⡀⠀⠇⠀⢹⠇⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⢀⡏⢸⡏⠀⣿⢸⡿⠟⢿⠁⠈⠁⠈⠁⠈⡿⠻⢿⡇⣿⠀⢹⡇⢹⡀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣿⢿⣛⣛⣛⣛⡿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣿⣿⡛⣛⠛⠛⣿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣿⣿⡏⢉⡁⢸⣿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣿⣿⠃⢀⡀⢸⣿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣼⣿
⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣾⢻⡃⣾⡇⢸⣿⣿⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠀⠀⠀⣿⣿
⠀⠸⠂⣿⣿⠀⠀⠀⣿⠀⢸⣇⢸⡇⠀⣿⠀⠀⠀⣼⣟⣩⡦⣠⣼⣿⣿⠀⠀⠀⣿⠀⢸⡇⢿⡇⠀⣿⠀⠀⠀⣿⣿
⠀⠸⠆⣿⣿⠀⠀⠀⣿⡄⣸⣿⡼⣿⠀⣿⣀⣀⣀⣿⣿⣿⡾⣿⣿⣿⣿⣀⣀⣀⣿⠀⣿⢧⣿⣇⢠⣿⠀⠀⠀⣿⣿
⠀⣿⣶⣿⣿⠀⣀⣴⣿⣇⣠⠙⣷⡄⠀⠛⠋⠙⢉⣽⠋⠛⢿⣿⠛⠉⣯⡉⠉⠙⠛⠀⢠⣾⠋⣄⣸⣿⣦⣀⠀⣿⣿⣦⣶
⠀⣽⣿⣿⣿⣦⣉⠈⠉⢹⣿⡀⠉⠁⠀⡰⠁⠠⣾⡿⠀⠀⣿⣿⠀⠀⢿⣿⠄⠀⠆⠀⠈⠉⢀⣿⡏⠉⠉⢈⣴⣿⣿⣿⢋
⠄⠽⠯⠙⠛⣿⣿⠀⠀⢹⠀⠀⠀⢀⣤⠁⢀⣴⣿⡇⠀⢠⣿⣿⡄⠀⢼⣿⣦⡀⠀⣦⡀⠀⠀⠀⡇⠀⠀⣿⣿⠛⠏⠁
⠀⣰⣾⠓⠈⣿⡏⠀⠀⠘⠁⠀⠠⠶⠀⠀⢴⣿⠿⠄⠀⠴⣿⣿⠦⠀⠠⢿⣿⡦⠀⠀⠶⠄⠀⠈⠃⠀⠀⠹⣿⠀⠚⣷⣄
⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀⠀⣠⡛⠃⢀⣙⣿⣿⣛⠁⠀⣛⣿⣿⣛⠀⠈⣛⣿⣿⣋⡀⠘⢛⣄⠀⠀⠀⠀⠸⣿⠀⢸⣿⣿
⢠⣿⣿⣯⡀⣿⠆⠀⠀⢀⣤⣭⡀⢀⣬⣽⣿⣭⣅⠀⣠⣭⣿⣿⣭⣄⠀⣨⣭⣿⣯⣤⡀⠈⣭⣤⡀⠀⠀⠰⣿⢀⣽⣿⣿
⢙⣿⣿⠿⠛⠁⠀⠀⢀⣬⣅⠀⢀⣠⣬⣿⣯⣥⡀⠀⣠⣬⣽⣯⣥⣄⠀⢀⣬⣽⣿⣥⣄⡀⠀⣨⣥⡀⠀⠀⠈⠛⠿⣿⣮
⠛⠉⠁⠀⠀⠀⠀⢀⣉⡉⠁⠀⣈⣉⣽⣿⣉⡉⠀⠀⣈⣉⣿⣿⣉⣁⠀⠀⢉⣉⣿⣯⣉⣀⠀⠈⢉⣉⣀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣤⣤
⠀⠀⠙⠶⣄⡠⠖⠉⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠆⠈⠀⠰⠶⠦⠄⠀⠀⠀⠀⣴⡌⢉⢰⣄⠀⠀⠀⠀⠀⠀⠐⢈⡿⠉⠩⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣁⣀⣂⣀⣂⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠒⠒⠒⠒⠒⠒⠒⠳⣄
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣀⣀⣉⣉⣁⣁⣈⣉⣉⣈⣈⣳⡀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⢺⣟⣱⡶⣪⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠰⠆⠀⠀⠀⠀⠀⠡⠀⠠⠄⠤⠀⠄⠀⠀⠀⠀⠠⠄⠠⠠⠙⢦⡀
⠀⠀⠀⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣷⣻⣿⣧⠀⠀⠀⠀⡠⢰⣿⣏⣽⠿⡂⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⣰⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠘⠿⠿⠛⠋⠉⠀⠀⠀⠀⠑⢄⠉⢉⡩⠐⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣴⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣦⣤⡀⠀⠀⠀⠀⠀⢀⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢐⣶⡆⠀⡀
⠀⠀⠀⣠⣾⣭⣁⣩⣽⣶⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣽⡉⠃⠀⠀⠀⠀⣼⣿⣦⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀
⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡷⠒⠒⠒⠢⣄⠀⠀⠀⠀⢀⣿⣿⣛⣾⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣻⣟
⠀⠀⠀⠀⠉⢿⣿⣿⠏⠁⠙⠻⠿⠋⠛⠷⢶⠶⠟⠃⠀⠀⠀⠀⠘⠟⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣜⣷⣿⣿⣿⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠦⢤⣤⡤⠴⠄
⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠦⡄⠀⠀⠀⠀⠐⠷⠶⠾⣿⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠋
⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣛⣛⣛⣚⣛⡟⠛⣟⣛⣒⣚⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⡀⠀⠀⠀⠀⣀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⢭⣭⣭⣭⣽⠀⠀⢫⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠲⠒⠒⢲⡏⠀⠀⢸⡖⠒⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣝⠿⠻⠿⠛⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⠈⠛⠿⠿⠶⠶⠿⠛⠉⠀⣦⠇⠀⠀⠀⠀⠀⡼⠁

⣷⣤⣄
⣿⣿⡿
⣿⣷⣶⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣠⣠⡤⣤⣶⣶⣶⣦⣶⣶⡶⢆⣤⣄⠀⠐⠂⠒⢠⣴⣤⣶⣴⣾
⣿⣿⣿⣿⣷⡤⢠⣄⣤⣤⣤⣠⣤⣄⣌⣵⣴⣷⣻⣿⣿⣿⣾⣿⣄⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣦⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿
⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣈⡙⠙⠛⢩⡦⢛⣛⣉⣉⣥⣶⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⢷⣧⣽
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⣸⣙⠋⠁⠀⠈⢿⣿⣿⣿⣻⣿⠿⣿⣿⣿⣋⣽⣿
⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⢠⠞⠀⠀⠀⠀⠈⠈⢽⣎⣸⣿⣿⣿⣿⣿
⣤⢤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣾⡏⢸⣿⣿⣿
⣧⣈⣡⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⡟⠀⢘⣿⣿⣿
⣿⣯⣨⡁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⣠⣄⣤⣤⣤⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡨⠿⢿⣿
⣿⣿⣿⣷⣼⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⢈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣋⣉⣀⣤⣶⣶⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣾⣿⣿⣶⣤⣤⣴⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣠⠄⢀⠀⢀⢮⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢁⠔⢠⠑⠬⢎⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠀⠀⢆⠀⠉⠩⣫⠸⡅⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⢉⡖⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⠓⠀⠀⠀⠀⢐⠈⠀⠀⠀⠉⠀⡄⡎⢇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠘⠠⠀⠀⡤⢴⠈⡀⠀⠀⠀⢀⠀⢰⢸⠈⡎⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡄⠀⠌⠈⢀⠅⠀⠀⠀⠀⠀⠈⢇⠘⠇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢰⠬⠂⠀⠌⠈⠀⠤⠤⠤⠤⠤⠤⠌⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠤⣄⠢⡀⡆⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠓⠉⠈⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠀⠀⠠⠄⠤⠤⠴⠤⣀⣀⡠⠤⠤⠄⠤⠸⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⣾⣿⡿⠟⣿⣿⣿⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣴⣿⣿⡿⠋⠀⠀⢿⣿⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⣾⣿⣿⠟⠋⠀⠀⠀⠀⠘⣿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣗⣷⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠷⠿⠷⠿⠾⠿⠿⠷⠿⠷⠿⠾⠷⠿⠿⠿⠛⠁

⠀⠉⡁

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⢀⣤⣤⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁
⠀⠀⣴⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢊⡄
⠀⠀⠀⠈⠻⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠄⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠈⠻⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣢⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣍⡉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠝⠃⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⡕⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠻⡿⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣩⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠶⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢠⠂⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣧⣠⣼⣧⣤⣠⡤⢤⣶⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡵⢲⠞⠯⣽⠾⢮⣣⡞⢻⠀⢨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣯⡄⠀⠆⠀⠀⠙⢿⣾⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠹⡌⠀⣠⠄⠀⠀⣼⡽⠛⢤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡏⠈⣷⣈⣶⣶⡶⢶⡞⡽⠁⠀⠀⠉⠳⢤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠴⠶⠶⠴⠦⠶⠶⠶⠶⠶⢤⠞⣿⣇⡿⠶⢦⡞⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⣠⠖⣉⠀⡇⠀⠀⣞⣉⣉⣉⡇⠀⢀⡤⣄⢸⡀⠾⣿⠛⣲⠋⠀⣠⣼⠃⠀⠀⣰⣃⠀⠀⠀⠀⠀⢳⡀⢰⣛⣷⢸⠈⠙⢦⣀
⣀⣀⣠⠴⠋⠀⠰⣇⠃⡇⠀⢰⢲⠀⠀⠀⠀⠀⠘⠶⠋⢀⣙⣛⣥⣀⠀⠀⢰⣷⠃⠀⠀⡼⠁⠈⠳⣦⣄⠀⠀⠀⢳⡀⠈⠀⢸⢀⡴⢦⡈⠳⢤⡀
⠉⠉⡇⠀⡔⠒⠢⠈⢘⣇⣀⣈⣁⣀⣀⣀⣀⣀⡤⠖⣛⡉⠉⠉⠿⣿⣙⣒⣻⠇⠀⠀⣼⠁⠀⠀⠀⢌⠻⣝⠶⣤⣄⣷⣀⣀⣸⡘⣇⠀⠉⢳⡀⢹⡏
⠀⠀⡇⠀⣇⡠⢇⡴⠋⠀⣈⣤⣉⡈⢀⡴⠿⠓⠚⠉⠁⠀⠈⣳⡤⠟⡏⢹⠋⠀⠀⣸⠉⢧⠀⠀⠀⠈⢧⠈⠙⠳⠦⡟⠀⠀⠀⠙⢮⡙⠲⠚⠁⢸⡇
⠀⠀⡇⠀⠀⣠⠎⠀⠀⠈⠉⠉⠉⠁⠀⢙⣶⠤⣄⣠⣶⣚⣭⠥⠶⠚⢃⣿⣄⣀⣰⠻⡄⠈⢧⠀⠀⠀⠈⢧⣀⣠⡾⢁⡴⠶⠒⠒⠦⡝⢦⠀⠀⢸⡇
⠀⠀⡇⣠⠞⠡⠖⠛⡷⠦⠄⠀⠀⠀⠒⠛⠓⠒⠒⠾⠿⠤⠀⣠⣴⣞⣉⠙⢻⠟⣵⠋⠉⢻⠛⠉⠙⠛⠛⠙⡏⠀⠀⠀⠙⠒⠒⠛⠋⠁⠀⠱⣄⢸⡇
⠀⠀⠿⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠽⠿⠿⠿⠿⠭⠤⠬⠭⠭⠭⠿⠿⠿⠿⠿⠯⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠿⠃

⠀⠀⡤⣤⡠⠀⠀⠀⡰⢌⣨⣄⠀⠀⢠⣤⣴⣶⣤⣤⣀⠀⢠⡄⠀⠀⢀⣤⣤⣦⣶⣦⡶⣤⣀⠀⠀⠀⢀⠀⣤⡴⠦⡀
⠀⠘⠻⠭⢗⢀⣀⡀⣿⣿⢿⡾⠀⠀⣸⠟⡟⢛⡿⠟⡻⠟⠻⣇⠀⢀⣾⠉⢫⣿⡏⠀⢻⠏⠙⠀⠀⢰⣻⢷⣿⣥⣴⠇
⠀⠀⠀⠈⠁⣾⢾⣿⣿⠀⠀⠀⠀⠐⡃⠀⠀⠀⠉⠀⠁⠀⠀⢸⠀⠀⢻⠀⠀⠟⠀⠀⠄⠀⢀⡆⠀⠀⠈⠙⠻⣿⢿
⠀⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠀⢳⡈⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡞⠛⠉⠀⠠⠀⠀⠑⠯⠀⠀⠀⠀⠀⠀⢹⢼
⠀⠀⠀⢀⣠⣶⡦⢿⡯⢿⣷⠄⠀⠀⠈⢳⡄⠀⠀⠀⠀⣀⡜⠁⠀⢠⡗⢲⢠⡄⢤⠀⣤⠄⠐⣷⠀⠀⠀⠀⠀⠠⡀⡅
⠀⠀⣴⢟⣿⣴⣶⣊⢻⡏⠀⠀⠀⠀⠀⠀⠙⢷⣌⣲⡾⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢇⢸
⠀⢰⣷⣿⣿⠿⠉⠉⠛⢿⣄⠀⠀⠀⡴⡐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠂⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢘⢘⡇
⠀⣿⣿⡡⠀⠀⠀⠀⠀⠈⠙⣦⡀⠘⠃⡀⢈⡆⠀⢀⢠⠀⠀⠓⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡟⢿
⠀⣿⣷⡇⠀⢠⡶⠒⠖⠒⣋⣩⠿⣆⠀⠩⠿⠀⠀⣮⣿⠠⠔⠂⣹⠦⠀⠹⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣺
⠀⣿⡿⢃⡼⣾⣿⣿⢟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠸⡟⡆⠀⠀⠀⢨⠀⠀⠳⣄⣀⣀⣶⠃⠀⢀⣤⣶⠶⢶⣦⣄⠀⠀⠁
⣴⣿⢵⠟⠀⢿⠏⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⠒⠊⠉⠀⠀⠀⠙⣿⡿⠃⠀⣠⢿⣿⢿⣶⡾⣿⣿⣦
⠉⠁⠁⠀⠀⠘⠿⡀⠀⠈⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣿⠆⠲⠶⠶⢲⠂⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣾⠿⢺⣾⣶⠟
⠀⠀⠀⠀⢀⡀⢤⣳⣄⠀⠈⣉⡢⣴⣉⠉⠉⠢⡄⣆⣻⢽⢃⠤⣶⡛⢈⣭⡄⠦⠀⠀⠀⠀⠀⠈⠙⠻⠲⠿⠛⠉
⠀⠀⡀⠰⢬⡿⣄⢉⡈⣦⣄⠹⢿⣴⣽⡛⠛⠛⣛⣈⣻⡻⠳⢆⡛⠃⠊⢹⠇⡟⠪⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣄
⠀⠈⠁⡛⢢⠀⣹⠻⣇⢋⡈⢯⠉⠛⠦⢙⣄⡾⠿⡉⠠⠇⢠⣭⣥⣀⣀⠋⠀⠳⠶⠌⣤⡀⠀⢰⣄⠀⠀⠀⠀⠀⡏⠉⣘
⠀⠀⠈⢿⠈⣧⠘⣥⣿⣆⠹⣎⠻⣄⠀⠨⠵⢾⣶⣨⠀⠀⠀⣾⠗⣒⣆⢭⣉⠑⠢⠄⣀⣀⣀⣘⣿⠀⠀⠀⠀⠀⡍⠀⠿
⠀⠀⠀⠘⢧⠈⠷⡈⠻⡟⣦⠈⠳⢮⡳⢤⡄⠸⢹⢿⡄⠀⠀⠈⠙⠪⣻⣷⣬⣄⠒⠷⠿⡾⠟⡙⠃⠀⠀⠀⠀⠀⣦⣀⡄
⠀⠀⠀⠀⠈⢷⣄⠘⣦⠘⠟⢷⣄⠀⠙⠛⠀⠆⢘⢨⣇⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠶⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠻⡉⡡
⠀⠀⠀⠀⠀⠀⠙⠳⣌⡃⢀⡘⠂⢰⠂⠀⠀⠸⣬⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠧⠄⢀⣚⣛⣀⡦⠀⠰⣠⣦⣿⡦⣄⡀⠀⣀⡄⠀⠀⠠⢿⣿⣽⣿⢷⣦⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠖⢂⡩⠅⠐⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⠈⠙⠺⢦⡉⠠⠭⠶⢩⠀⠀⠀⠈⠉⠛⠶⠛⠳⢶⣤⣀
⣤⣤⣤⣤⣼⣷⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠭⠢⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⡆⠡⢑⡀⣖⣙⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠒⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢙⠁⠀⢄⡄⢀⠈⢄
⠀⠀⠀⠀⠀⠠⠊⠀⠀⡈⣖⠉⣀⡿⠛⢀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⡄⠀⠀⢀⠀⠀⠀⢐⣠⠙⡀⠐⢄⠧⢘⠛⠛⠁⣼⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠵⢛⣧⡝⣖⡩⠒⠀⠀⠀⢀⠤⠚⠉⠀⣀⣀⣀⣀⠀⠀⠈⠐⢄⠀⠀⢀⠵⣂⠀⠀⠀⠉⢛⠊
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠀⠈⠀⠀⠀⠀⡀⢀⡴⠁⢠⠴⠊⢉⣀⣀⣀⠈⠉⠳⣤⡀⠀⠧⠄⠐⠒⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢀⡀⠄⠐⠀⠀⡞⠀⢰⠃⠠⠊⣡⠤⣄⠈⠓⢦⠀⠈⢢⠀⠀⢀⡤⡔⢺⡇⠀⠀⠀⢠⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠴⣀⣀⢀⣀⠀⠌⠡⠠⡀⠀⠀⡀⢗⠀⢻⡀⠳⡈⠠⠖⠈⣹⠄⠈⡇⠀⠐⠂⠀⠓⠋⢠⣯⡏⠀⠀⠀⣴⣟⣛⡫⢄⢀
⠀⠀⠀⠀⠀⠤⠨⣽⢳⡤⣤⡑⠲⠃⠘⡤⢼⠚⣆⠀⠙⠦⣌⣉⡉⡉⣀⣀⠜⠀⠀⢠⠁⢈⠘⠢⣹⠫⡇⠀⣠⠐⠲⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠰⢄⡒⠃⠈⠓⢄⣤⠀⠈⠉⠉⠉⠀⠀⠀⠔⠁⡴⠁⠀⠈⣷⠋⡆⠀⠏⠈⣡⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣐⡄⡐⠀⡀⠀⠉⠓⡎⢫⠫⠑⠒⠂⠂⠐⠀⠀⠀⣸⡤⣄⡤⠋⠁⢦⡞⠂⢀⠤⠌⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠺⠃⠀⡄⠀⠡⡆⠀⡐⠂⠶⠒⠈⠉⠉⠀⢘⡩⣟⠁⠀⠀⠈⠧⠺⡖⡒⠀⠱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⡆⠀⠀⢽⠀⠈⡇⠰⢠⢀⠀⠀⠀⠀⠀⠄⣹⠱⡃⠐⠆⠀⠀⠈⢄⠈⠁⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⡞⡄⠀⢷⠁⢀⠏⠀⠀⣇⡼⠀⠄⢸⡞⠁⠂⠀⠀⠀⠀⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣤⡀⣀⠀⠈⠀⢀⠀⠠⢀⣈⣀⠠⠇⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⡤⠥⠔⠚⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡽⠲⠤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠉

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⡀⠀⠀⡀
⠀⠠⠀⠈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⢐⠀⠀⠀⠀⠀⠠⣴⣧⠓⠁⠀⠀⠀⡠⠀⠀⠀⠀⠈⠉⠀⢠⣄⡀⠄
⠀⠀⠀⠀⠠⠆⠀⠀⠀⡘⠀⠠⠄⠀⡠⠀⢀⠎⠀⠀⠀⣀⠤⠒⠈⠁⠀⠀⠀⠰⠝⠁⠀⠀⡶⠂⣤⠄⢸⠐⠐⠔
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠱⠀⣀⡠⠚⠀⠀⠀⢀⡠⠐⠊⢁⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈
⠀⠈⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠀⢁⡀⠀⠐⢀⠜⠀⠀⠀⠀⠁⠒⠃⠀⠀⢶⠸⠷⠀⠀⠐⢂⠕⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⢐⠆
⠀⠀⠁⠈⠀⢁⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈⠀⠀⡄⠀⠀⠀⠀⢰⣆⠀⠔⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠰⠂⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠸⠀⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⡠⠊⣱⠀⠰⠄⠔⠀⠀⠀⠀⠀⢠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠹⢄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠉⠉⠈⠁
⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⠋⢣⣤⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠚
⠀⠀⠀⡀⠀⠠⠉⠓⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠐⠀⠰⠀⢐⠂⠀⠀⠀⠀⠀⠀⠄⢀⡀⡀⠀⠀⠐⠀⠀⠠⠊⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⢀⡴⠛⣡⡴⠆⠀⠠⠂⠐⠺⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⢶⣶⣶⣤⡀⠀⠀⠔⡠⠬⡀⠀⠀⠀⠀⢈⣴⣦⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⢹⣿⣿⡛⠆⠀⠀⠀⠀⣀⣀⠀⠂⠠⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⢀⠇⠀⠀⠀⡀⠐⠀⠀⠀⠀⠙⠈⠁⠀⠀⠀⠀⠀⠈⣿⠛⠋⠀⡀⣀⣤⣤⣤⣤⣈⣑⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡤⠋⠀⠀⠀⠀⠚⠁⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠹⢿⣿⣧⠻⢿⣿⣿⣿⠆
⠀⢦⡀⠀⠀⠞⠀⢀⣠⡴⠋⠁⠀⠐⢃⡠⠀⠀⢠⠀⠀⠀⢸⡿⠃⢡⡀⠀⠠⡀⠀⠀⣴⡿⠟⠁⠁⠀⢀⡿⠿⠋⠐⣿⣿⡿⢀⠀⠀⢤
⠀⠈⠳⣦⣠⡤⠞⠉⠀⣴⣳⣆⣀⣀⡀⠁⠐⢦⣀⡸⠇⢀⠀⠀⠀⠛⠄⠀⠀⠈⠉⠐⠃⠠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⣀⠀⡀⣀⡼⢀
⠀⠀⠀⣀⣀⠀⠀⢰⠚⣿⡿⠁⠀⣼⠁⠀⠀⡀⠟⡫⠔⠁⠀⠈⠲⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⡀⠀⠀⠘⠁⠈⠉⠉⡏⠉
⠀⡀⠉⣤⠈⠣⡄⠀⠘⠻⠧⠀⣴⡏⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠀⣐⡅⠀⠀⠀⠀⡀⢀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⠀⠀⠀⢀⡆⠘⠀⠈⠁⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠐⠈⠁⠀⠐⠀⠀⠘⠃⡚⠠⣿⣶⠞⠀⢀⠀⢠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠉⠳⠀⢸⠀⢘⡇⠐⠀⢀⡀⠼⡧⠄⣀⠀⣀⠀⢀⠀⡀⠀⢈⣀⠐⡄⠀⡀⢀⡄⠀⠀⠀⠉⠡
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣰⠟⠙⠲⣄⠀⢸⠋⠉⡇⢸⡀⠻⣄⠀⡇⢸⠉⣳⣿⠋⠘⣦⡇⠀⠐⠤⣀⣨⠷⠛⠉⢙⠻⠆
⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢸⡆⠸⠇⠀⠷⠘⠃⠛⠋⠀⠁⠈⠛⠁⠘⠀⠀⣸⢃⣶⣷⠀⠀⠀⢂⠀⠈⢅⡄⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠳⣤⣤⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠒⠃⣾⣯⡏⠀⠀⠂⠐⠆⠀⠈⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠄⠂⢀⠀⣤⠄⢠⠌⠀⠀⠀⠀⠀⣼⡏⡿⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣋⣤⡄⠐⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⢰⡟⣸⠃⢀⠀⠀⠐⠀⠀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⡞⠋⠁⡜⣇⠀⠀⠀⠲⠤⠐⠂⢤⠀⡃⠀⠿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢨⠀⠀⠀⠀⠀⠀⡇⠈⠟⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⢀⠂⠀⠀⠀⠚⠳⠀⠀⠀⠒⠂⠀⠀⢸⣷
⠀⢀⠀⠀⠀⠈⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⢻⠀⠀⣀⢘⣇⠀⠐⣄⠀⠀⡔⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⣿⡟⠀⠐
⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠴⠀⢠⡄⢸⡦⠶⠛⠛⠉⠀⠀⠈⠀⠀⢀⠆⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⠏⠀⠀⠐
⠀⠀⢂⠀⠀⢠⢄⠀⠀⠰⠀⠀⠤⠀⠀⣠⠀⠀⢠⡄⠀⠀⠀⠀⠠⠤⠤⠤⠼⠀⠀⢁⡄⠁⠀⠀⠀⠘⢡⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠐⡉⠙⠓⢻⠃⢀⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⢰⡖⠀⠀⠀⠀⠀⠒⠂⠸⣇⠀⠀⠀⠘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆
⠀⠀⠃⠀⠀⠂⠀⡏⠀⠙⢿⠉⠉⢹⠋⠁⠈⡿⠉⠉⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠹⣦⣤⣤⣴⡿⠿⠻⢿⣿⣿⣿⠿⣿⡏⠀⣤⣠⠄
⠀⢰⣿⣶⣶⡀⠸⣧⠀⠀⢸⡀⠀⢸⣆⡀⠀⣹⣤⠄⠘⠖⠐⠒⠀⠀⣹⣭⡍⡍⠀⠀⠠⠄⠌⠄⠀⠀⠀⠀⠀⣿⣿⡇⢰⣿⣷⠀⣿⠀⠇
⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣈⣁⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣘⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣁⣀⣉⣉⣈⣓⣀⣀
⣿⣿⣿⣛⣟⣝⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣤⡐⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠚⠉⠀⠀⠀⣿⣿⣿
⣗⠀⠀⠀⠀⠀⠠⡀⠀⢀⣀⣴⣇⣀⡀⢰⣦⣀⣈⡉⠁⣀⠀⠀⣀⠀⢀⠀⠀⠀⢡⢁⡀⣄⢀⣀⡀⢀⣶⡶⣾⡠⠇⣶⢠⣼⣇⣼⡤⢧⠀⠀⠀⢠⣿⣿⣿
⣿⣶⣦⣄⣄⠒⠀⠀⠐⠛⠛⠙⠛⠻⢳⣾⣿⢛⠵⢾⣐⣯⢿⣿⣿⣿⣻⣿⠛⣷⣿⢸⡷⡿⠸⠛⠸⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠤⡤⣸⢿⣿⣿
⣿⣿⣿⣟⣛⣉⣡⢀⡀⣤⣤⣄⣄⣁⣨⡙⡀⣟⣿⠛⡿⠋⠿⠙⡇⣺⢸⡟⢣⣋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢧⢺⣿⣿
⠘⠻⣿⡿⠿⢛⠋⡉⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠏⣷⣶⣶⣶⣶⢦⣭⣿⢙⠟⡷⠊⠀⡄⠐⠰⣿⢠⡆⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣿
⣶⣷⣹⢿⡿⠿⠿⠿⢿⣛⠛⢛⡿⣿⣽⣯⣷⣤⣤⣿⡿⡿⣿⡇⠈⠃⠈⠀⠉⠉⠙⠻⣯⡀⢑⠛⣍⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⢘⡚
⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇⣿⣯⣽⣿⠀⣿⡷⢸⡇⢒⣲⣷⣆⠀⠀⠀⠰⣾⠁⣰⣎⣶⣴⣷⣿⣿⣿⣿⣿⠎⣭⡽⢅⠈⠠⢼⣝⣿⣤⣬⣿⣿
⣿⣿⣿⣧⡀⢻⣿⡿⠿⠿⣿⣿⡇⣼⡇⢸⠟⣿⠟⠀⣹⢋⣼⣇⢹⡏⢩⣷⡀⡷⢹⡟⠉⣅⣿⣟⣻⣿⣿⡿⣿⣿⠥⢀⠠⠖⣠⡛⠳⣴⠋⠙⠛⠛⠛⠋⣉
⣿⣿⣿⣿⡵⠞⣏⣤⣤⣼⣿⣥⡿⣿⡇⠘⣿⣦⡠⠀⣿⡏⢹⡿⣾⠀⠈⢠⣼⡇⠀⢺⣷⣿⣿⣻⣿⣿⣭⡼⣟⠁⢀⣠⣴⣿⣿⠟⢉⣀⠠⢶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣷⢂⣩⣸⣿⣿⣿⣿⣷⡟⢧⣧⣿⣸⣧⡀⣿⡇⢸⣷⢨⠄⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣾⡷⠿⠛⠛⢛⣿⣽⣡⣾⣤⣦⣽⣿⡿⢛⣿
⣿⣿⣿⣿⣵⣾⣛⣿⣿⣿⣿⣟⣟⢛⡀⣉⣭⣴⡆⠽⢿⠣⣿⣿⣿⣤⡄⣀⣀⣶⣾⣾⣿⣿⣿⣿⣾⣿⣷⣿⣿⣗⡀⠀⢠⣼⣿⡿⢁⡿⠋⢋⠁⣤⡶⠏⢉
⣿⣿⣡⣤⣼⣿⣿⣿⣿⣿⣿⣿⣆⢁⣈⣉⡏⠙⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⠻⢿⣿⣿⣿⣯⡅⠀⣠⡄⣾⡿⢿⡵⠛⠁⠀⠈⠿⠏⢀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠟⠀⢀⠛⣰⣯⣿⣿⣏⣼⣿⣿⡿⢿⡿⠿⣿⣫⣞⣯⣴⠖⢉⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⢿⡷⠒⠀⢁⣠⠶⠉⠿⠿⠛⠛⠿⠇⢿⠿⠿⠗⠀⠀⣺⢏⣿⡿⠋⠀⣀⣹⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢟⣟⣉⣍⡭⢝⣯⣅⣹⣭⣽⡿⡟⣀⣤⡄⠴⣶⣿⢻⣷⣤⣆⡀⠒⣶⣶⣴⣶⣶⣾⣿⣿⣿⡿⠛⢱⣶⣦⣼⣯⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣴⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣴⣤⣿⣵⣿⣿⣿⣿⣿
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠆⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢂⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⣠⠞⠉⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠄⢀⠘⠁⠀⠀⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣤⡘⠤⠐⠀⠒⡄⠀⡄⠀⠀⠀⠈⢦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⡀⠀⣺⠁⠟⣇⠈⢣⠘⡄⡀⠀⠀⠀⠀⠀⠀⢧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠛⠀⠏⠀⠸⠀⠢⣀⡦⠓⠀⢠⠀⠀⠀⠀⠀⠈⢧⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠡⠀⠀⡴⠀⡠⠂⠉⠀⢁⠀⠀⡀⠉⠀⠀⢸⡙⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠉⠴⠒⠁⠀⠀⠸⠉⠂⢤⠀⠀⠀⣤⡁⢡⠠⠑⢄⠀⠀⠀⠀⠀⠱⣤⣀⠄
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠱⡀⠀⢀⠀⠀⠀⠀⠈⡷⠒⠱⣼⠐⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠐⠁⠀⡠⡆⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⡏⠀⠀⢀⡀⡄⠈⠀⠀⢩⠀⠉⢁⢀⡀
⠀⠀⠀⠉⣄⠀⠀⡁⠇⠀⢀⠀⠀⠂⠀⠀⠀⠸⠄⡀⠀⠀⠀⡇⠱⠀⠀⠀⠘⣆⡂⡈⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠙⢦⡠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠱⡙⣆⠀⠀⠄⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢀⡀⢀⣰⠆⠤⠤⠤⠂⠤⠤⠠⠼⠶⡦⠶⠔⠒⠒⠛⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠚⠣⡤⠀⠙⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡝⠟⣿⣷⣾⣷⣶⣶⣤⣤⣶⣾⣧⣼⣧⣤⣄⣴⣾⡟⣹⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡱⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠛⣷⣾⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣷⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣄⣸⡿⣻⣿⣖⣘⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠈⠹⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠃⠐⠿⠿⠛⠛⠃⠛⠙⠠⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡏⢻⣿⣿⣿⢻⣟⣇⠀⡞⣿⣿⣻⣿⣿⣿⣿⣿⣧⠀⠀⠐⣷⣷⠀⠀⠀⢰⣶⡆⠀⠀⠸⣿⣿⣿⣿⣗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡀⣿⣿⣿⡀⣿⠀⠘⠒⠛⠛⠻⠿⠿⠿⠿⠿⠶⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢐⣿⣿⣿⣿⢿⢦⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⣜⣹⠀⣍⣡⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⡀⠀⣀⣀⠀⠀⠰⢀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡀⠤⠀⢤⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⢹⡿⠿⠿⣿⣄⣿⣿⠀⠀⢠⣿⣿⣿⡇⠀⠀⠈⢁⣄⡉⠙⠋
⠀⠀⡀⠶⠶⠂⠈⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⢸⣯⣤⠀⣰⠁⠀⣿⣿⠀⠀⠘⠹⣿⣿⣇⠀⠀⠀⠘⣿⣷
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠄⣠⠂⠄⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⡇⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⢶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿
⠀⠋⡉⠧⠀⢀⠠⠄⢘⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠁⠀⢀⣴⠶⢦⣀⢈⣀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡇⣋⣱
⠀⠀⠟⡞⢢⡇⡴⣦⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⡀⢦⡀⠀⠀⢀⣤⣄⣤⣷⠤⣦⡉⠚⣏⣛⢐⣍⣧⣀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣀⢸⡄⠀⠀⢠⢸⣇⠙⢿⡦
⠀⠃⣠⣿⡾⣧⣹⣿⡄⡆⢰⣶⣤⣷⣤⣷⣾⣷⡋⠲⣱⡄⣐⢿⠙⠛⢼⡿⣷⣙⣋⡠⠀⣿⣠⣿⠙⠎⢁⡀⠀⣀⣠⣧⣥⣠⣦⠭⠾⠷⠷⢶⣿⠺⢿⣶⣶⠿⢄
⠀⠈⠀⠈⠙⠊⠙⠛⠐⠯⠛⠛⠛⠉⠙⠃⠛⠛⢿⣙⡛⠻⡯⠙⠳⠛⠿⠿⠛⠛⢿⣿⡿⠿⠿⠿⠶⠟⠛⠋⠉⠩⠍⠀⠙⠛⠀⠘⠻⠤⢤⡀⠀⠒⣀⠙⠫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⠈⠂⠋⠀⠀⠀⠁⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣬⡈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣿⡿⠈⠙⠻⢿⣷⡄⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⣴⣄⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇⠀⠀⠀⠀⠙⣿⣀⠀⠀⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⢸⢀⣼⣿⡇⠀⠀⠀⢀⡌⣼⣿⠀⠀⣶⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣻⣿⣿⣿⣿⣷⣶⣶⣶⣿⣆
⠀⠀⠀⠀⠀⠀⣤⣄⣿⣿⡇⢀⣴⣶⡯⣾⣿⣿⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠋⣡⣬⣭⣭⣼⣻⣿⣆
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣴⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣻⢻⡛⢻⠛⢹⢏⣩⢟⠻⡟⢻⡟⢻⣟⠂
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣻⣟⣶⣽⣯⣿⣻⡽⠍⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠘⠞⠘⠓⡘⠒⡘⣚⢙⠚⢘⠓⠺⠧⠼⠯
⠀⠀⠀⠀⠀⠀⣴⠂⣶⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠛⠛⠛⠘⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⣿⣻⣿⠿⣏⠁⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠧⠁


⠀⠀⠀⠀⢠⣄⢤⣀⢠⣤⡀⣤⣤⡀⢤⣤⣤⡀⣤⣠⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⢐⢠⡠⣀
⠀⠀⠀⠀⢸⣿⢸⣻⠅⡇⡀⣧⡀⣯⠗⢯⠇⢽⡃⣿⡃⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣷⣾⣤⡀⠀⠈⠉⠉⠿⠖⣀
⠀⠀⠀⠀⡸⠯⠐⠓⠈⠉⠉⠁⠀⠀⢉⠈⠉⠈⠁⠚⠃⠡⢅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠉⠀⣿⣿⠀⠉⠛⠿⣷⡀⠀⠀⠀⠀⠁⢂⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⡋⠉⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⣧⡔⠀⠘⠀⠀⠙⢚⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢠⣾⣧⣤⣿⣿⣇⣀⣀⣰⣀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢶⣿⡇⠀⠀⠀⠀⣠⣿⣇⠀⣸⣷⣄⠀⢈⣑
⠀⠀⠀⠀⠈⡄⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠇⠀⠀⠀⠀⠀⠀⠒⠂⠀⢾⣶⣾⣿⡇⠀⠀⡀⣘⣿⣿⣿⣿⣿⣿⣟⠀⠘⠃
⠀⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣟⣃⣀⡀⠀⠀⠀⠀⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣯⣿⣿⡻⣿⢿⣿⡿⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⠿⣤⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⣷⣮⣭⣛⠻⢿⣿⣿⣿⠿⠟⠋⢈⣉⡛⠛⣉⣉⣽⡀⠀⠀⠀⠀⢸⡿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣏⢿⣤⣤⣶⡿⠿⢛⡛⠉⠉⠀⠀⠀⠀⠀⠀⠘⠓⠐⠛⠋⠛⣯⣯⣿⣿⣿⣿⣿⣿⡛⠛⠚⠘⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠻⡿⠛⠙⠃⠁


⣿⢿⡿⠿⡿⢿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡋⠀⠀⠀⡝⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠽⣶⡀⠴⠦⢿⣆⠐⠤⠻⣷⡀⠶⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣠⡿⠟⠂⣴⡾⠛⠒⠒⠒⣿⣿⣶⡖⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡶⣶⣶⣿⣷⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠚⢻⡿⠛⠟⢻⣿⠛⠛⠛⠛⠻⣿⣿⠟⠟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡾⠃⠀⢀⣼⠗⠀⠀⠀⠀⢀⣙⣿⣧⠀⠸⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣤⣤⣼⣤⣴⣦⣤⡄⠰⠶⠟⠻⠿⠟⠛⠿⡇⠰⣠⣤⣦⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢄⡉⣿⣧⡦⣌⡉⠀⡀⠀⠼⢷⡆⣰⡾⢶⣷⡀⣯⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠻⠎⠁⢈⡙⠓⠋⣟⣾⠇⠈⠛⠋⠃⢻⠟⠛⢿⣿⣿⣿⢩⡽⣿⣄
⠀⠀⠀⠀⠠⠊⠀⠀⢀⠀⢹⡄⠀⠀⠀⠀⢻⣤⣀⣠⣿⣿⣤⣾⠈⢩⡅⠀⣠⣶⣤⣾⣦⣴⡟⢙⠛⢿⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢆
⠀⠀⠀⠀⡃⠀⣠⣤⣿⣾⠃⠀⠀⠀⠀⠀⠀⠸⢿⣾⣿⣿⡿⣁⠀⠄⠐⢰⣿⣿⣿⣿⣿⣿⠀⠇⡜⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣼⣶⣴⣆
⠀⠀⠀⠀⠓⠶⣿⣿⣿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢻⠳⣤⠶⣿⣇⡀⠉⣩⣴⣶⡿⢤⣴⣿⢻⣿⡟⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢉⡜⢣⣼⠀⠀⠀⠀⠀⠀⠀⣤⡞⢸⣿⣿⣇⡈⠙⠃⠀⣿⣾⠹⣉⠷⣿⠟⠃⢸⡟⣿⠀⢹⡇⣹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⣤⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⣿⣿⡃⣼⣿⣿⣿⠉⡀⢈⣠⣾⢻⣄⡀⠀⣠⡴⠁⣼⢿⣿⢴⣿⣯⢹⣿⣿⣿⣷⡆⠀⠀⠀⠀⠠⣾⣿⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣿⣦⡀⠀⠄⢀⠀⠙⠃⢿⣿⣿⣿⠀⠰⣨⣿⣿⣿⣿⡟⠙⢿⡁⠠⡿⠛⠻⣾⣿⠇⣸⣿⣿⣿⣿⣧⢠⡄⠀⠀⣴⣟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣉⢛⣿⠇⠘⠒⠊⠀⠀⢉⣿⣿⣿⡍⢤⢸⡟⢿⢿⣽⠅⢀⠀⡇⢸⣧⣦⣰⣿⣿⡇⢾⣿⣿⣿⣿⣿⡈⠀⠀⠲⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠄⠀⠀⢀⣠⣴⠿⠓⠚⣿⡛⠿⣷⡀⠨⣟⣀⠔⠉⠀⠀⠁⠀⢸⣧⣿⣾⠿⣿⣤⣾⠿⠿⠉⣍⡙⠁⠀⠄⢠⣿⡏⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣼⣴⣶⣿⣿⣁⠀⠀⠀⠀⢁⣴⣿⣷⣤⣽⣿⢿⣦⠶⠂⣤⠆⢈⡁⠴⢿⣿⠿⠛⠿⢷⣶⣦⣌⢻⣷⣀⣰⡿⠋⠀⢀⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⡿⣿⡇⢸⡿⢷⡞⢡⣶⠿⣿⣄⣿⣦⣤⣤⣤⣮⣿⣿⣿⣶⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⢣⣿⣿⣤⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣇⣿⠇⢸⠟⠀⣹⣿⣉⣾⣿⣿⣿⣿⣹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⢀⡾⣿⣿⣿⡟⣠⣿⣿⣿⣿⣿⣿⡟⢻⣿⣧⡆⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⠏⢈⢇⠹⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⢀⡄⠘⠁⣰⠏⢠⡿⢠⣿⣿⡟⣴⣿⢿⣿⣿⣿⣿⣿⣧⠑⢊⣩⡵⠏⢁⣉⣉⣴⣿⣿⣿⠟⠁⡀⠈⣹⣇⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢃⠀⠞⠁⣠⡿⢡⠟⠉⢀⣴⣿⣿⣉⣿⣿⣿⣿⢛⣉⠶⠃⠈⠈⠒⠂⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⢿⣤⠻⣿⣏⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠀⣴⠟⣠⠃⠀⢀⣼⣿⡿⢣⣿⣿⣿⠋⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠻⣿⠙⠷⠀⠀⠻⣿⣿⣿⣿⣿⠁⠈⡙
⠀⠀⠀⠀⠀⠐⡦⠈⣴⣿⡆⢀⣿⣿⡟⢡⣿⣿⡟⠁⠀⠀⠀⠙⣿⣿⢷⣦⣤⣤⡞⠁⣀⡠⠀⠈⠂⠀⠀⠀⠀⠀⠘⣿⡆⠘⣆⠀⠀⠀⠀⣿⡟⡿⠻⡇⠀⠸⠃
⠀⠀⠀⠀⠀⠂⣤⣾⡟⢁⣤⣿⣿⣿⣵⡿⠟⠉⣆⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡃⢰⣿⣵⣾⣏⣀⣀⢀⡀⠀⠀⠀⠘⢻⡌⠿⣷⣀⣴⣾⣿⣟⣀⠾⠀⠀⣾⣰
⣀⣀⣀⣀⣀⣤⣿⡟⠀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠈⠷⣄⠀⠀⠂⠀⠀⣸⣿⣿⣿⣷⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣆⣻⣿⣿⣿⣿⣿⡿⠂⠀⣨⢁⣿
⣿⡿⢿⣿⣿⣿⠟⢡⣾⣿⡿⢻⣿⡁⠀⠀⠀⠐⠁⣴⣿⣷⣦⣀⠀⢠⣿⣿⡿⠿⠋⠀⠤⠤⠀⠂⠀⣀⣤⣾⡿⠋⠈⡉⠉⠻⣿⡔⢿⣯⠉⢛⣿⣧⣤⣾⣱⣼⣿
⠿⣿⠂⣺⠿⠏⣰⣿⣿⡿⠁⠈⢿⣿⠀⡀⠂⢠⣾⢿⣿⡇⣸⠛⠗⠛⠯⠤⣤⣄⣀⣤⡤⢤⣤⣶⠾⠿⠋⠉⠀⠀⠀⠀⠀⣄⣿⣿⡉⣹⣧⣩⣿⣿⣯⣽⡿⢹⣿
⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣤⣤⣄⣻⣷⠀⣴⡋⠀⠿⠿⠇⠉⠀⠀⠀⠀⠀⠀⣠⣠⣥⣶⠾⠋⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⣟⣿⣷⡤⠿⣿⣿⣿⣿⣿⣿⣿⣿
⡛⠉⠋⠛⣹⣟⡛⠛⡛⢻⡅⠀⣹⠆⠈⠷⡿⣿⣶⠖⠀⢀⡀⠀⠶⠶⠾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⢸⡟⢹⣿⣿⣙⣿⣿⣿⣻⣿⣿⣿⣿
⡀⢠⣇⠺⢿⣿⡿⠿⠿⠿⠿⠿⠷⠀⠀⡀⠀⢀⣀⣀⣴⣿⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢸⣿⣷⣦⠀⠠⡿⠃⢼⣿⠟⠿⠿⠿⠻⣿⣷⣾⣿⣿
⡇⢸⡿⢿⣾⣿⡇⠀⠀⠀⠀⠀⠰⢶⣶⣤⣴⡾⠟⣿⣿⣋⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⢀⡿⣿⣶⣆⣀⣠⣿⡟⢸⡏⠀⠠⣶⣶⣿⡉⠀⠀⠀⠀⠀⣿⣯⣿⢼⣿
⠀⠀⢉⣠⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣧⡈⣿⣇⠙⠶⠶⠟⣫⡿⠸⢧⣤⣤⣶⠟⢡⡿⠛⢈⣙⠛⠋⢠⡟⠀⠀⢀⣿⡏⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠁⠈⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢯⣿⣷⣶⡾⠿⣏⣀⣴⣦⣉⡉⣠⣴⣾⣥⣠⣾⠿⣿⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠙⢻⣿⣿
⠀⠀⠉⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠿⠀⠀⠀⠙⠛⠉⠈⠙⠿⠟⠁⠀⠉⠛⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠟⠉⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣠⡴⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠦⠤⠤⣤⣤⣤⣤⣄⣀⣀⣀
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⣄
⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⢠⡄⢠⣤⣤⣤⡀⠀⣀⠀⢀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠀⠀⠐⠀⠀⠀⠘⠀⢧⡼⢱⠘⠒⡄⡴⠛⢼⠁⠠⣞⡸⠤⣄⢀⣀⣵⠖⣉⡙⢶⢊⣕⣶⠲⣀⢶⡄⠀⠸⡆
⢸⡆⠀⠀⠀⠀⠀⠀⠀⡆⣠⢤⢸⠀⠀⡇⢣⠀⠈⠙⢳⠄⢹⠀⢸⠸⡀⢸⢸⠁⢹⢸⢎⡙⢇⢳⣠⠚⠀⠀⠀⣷
⢸⡇⠀⠀⢀⠀⠀⠀⠀⢧⡇⢸⣈⡦⣖⣃⣈⣹⠶⣋⣉⣠⠞⠀⢸⠀⡇⠸⣌⣉⣡⠞⠿⠙⣬⢾⢸⠀⠀⠀⠀⢻⡀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠘⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠸⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⡇
⢸⡇⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠲⠶⠶⠦⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⢸⡇⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠤⠤⠤⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢨⡟
⠀⣧⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠒⠂⠀⠀⢸⠃
⠀⠸⣦⡀⠳⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠭⠍⠩⠭⠭⠭⠭⣭⣭⣀⣀⣀⣀⣀⣀⣀⣻⠄
⠀⠀⠈⠙⠲⠶⠤⣬⣭⣭⣉⣉⣙⣛⣒⣒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠤⠽⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠏⠁⠠⠴⡇⠀⢫⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠙⣀⣀⣀⣀⢀⣵⠀⠀⢎⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠔⣽⠋⣀⠀⠀⠀⠈⢇⠀⠘⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⠃⠀⠈⢣⠀⠀⠀⠈⡄⠐⢿⠉⣃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡖⠀⠀⢲⠀⢠⡀⢰⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠘⠉⠣⡀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠘⣆⣀⣀⣘⣤⣤⣇⣀⣏⣀⣤⣤⠶⠃⠀⠀⠀⠸⣥⣤⡀⠀⡇⠀⠀⠀⠀⠘⡇
⠀⠀⠀⣀⠠⠤⠀⠈⠉⠉⠙⠦⠤⠤⠏⠤⠤⢤⣤⠤⣤⡀⠀⠀⠀⢸⡇⢀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣨⠿⠀⠀⠀⢸⠇⣜⣀⢀⣀⡀⣀⢠⠇
⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠚⠉⠀⠀⠀⠀⠀⠀⣼⠞⡿⢻⠟⣿⢹⢿⡿

⠀⠠

⠀⠀⠀⠀⠀⠠⡐⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠄
⠀⠀⠀⠐⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣶⠀⠀⠀⡟⠑⣓⢫⣦⣆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡒⠀⠀⡐⠂⠡⠄⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⠉⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠁⡌⢉⢉⠁⠎⢁⡞
⠀⠀⠈⠁⠀⠺⠷⢠⡔⠿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⣡⡁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠈⠐⠒
⠀⠀⠁⠀⢀⠀⠀⢛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠳⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠄⠀⠀⠠⠂⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⠃
⠀⠀⠀⠀⠂⠐⠠⢄⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠠⠀⠀⠑⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⠀⠁⠀⠀⢀⡠⠄⠀⠀⠀⠈
⠀⠐⠢⢽⣍⠶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠠⠂
⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⠇⠀⠉⠀⠀⠐⠀⡄
⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⢠⠀⠁⢠⠀⢀⡴⠶⠄⠀⠰⠶⠶⡶⠶⠖⠀⣠⠶⠶⣄⠀⣠⠶⢦⠀⠰⡄⠀⠀⢀⡤⠀⠀⢠⠀⠠⡄⢰⠇
⠀⠀⠀⠨⠁⣖⢲⡖⠤⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⠃⠀⠀⢹⠀⢼⠀⢸⠇⠀⠘⣆⢠⠞⠀⠀⠀⢀⣀⢔
⠀⠀⠀⢠⠎⡄⢠⠩⠄⠀⠀⡿⠒⠒⢺⠀⠀⢸⠀⠀⠈⠑⢢⡀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⢸⠀⢸⠶⣍⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⡇⢼⡆⡰⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⢠⡀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⡾⠀⢸⠀⠈⢳⡀⠀⢀⡇⠀⠀⠀⠀⠸⠂⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠘⠁⠀⠙⠒⠋⠀⠀⠀⠈⠁⡀⠀⠀⠉⠒⠚⠁⠀⠙⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢹⣀⡴⠀⠀⠀⠀⠀⡀⠀⣀⠀⣀⠀⢀⠄⢀⣀⠂⠀⢐⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠙⠀⠀⢈⣿⠇⠀⠀⠀⠀⠀⠛⣋⠉⠉⣌⣉⠉⡉⠀⠘⠿⠇⠀⠚⠃⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠙⠀⠂⠀⣉⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⠦⠀⠀⢀
⠀⠀⠀⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣄⣁⣀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⠀⠀⠀⣋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠀⠀⠀⠠⠄⠐⠒⠗⠒⠐⠒⢆⠀⠰⠶⠦⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠁⢠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠠⡤⢀⣠⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢿⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠐⠈⠀⠈⠀⠁⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡼⡟⠀⠠⠀⠈⠲⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢢⠀⢀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⡴⠒⠰⠈
⠀⠀⠀⠀⠀⠀⢰⣻⠁⠀⠂⠀⠀⠀⠑⡍⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠚⠂⠀⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈