Calcium carbonate Emojis & Symbols

⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⡏⠁⠀⠀⠀⠙⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⣤⡴⠂⠀⠀⠀⠀⠀⢀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿
⡀⠸⠉⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠀⠀⠉⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠐⠶⠚
⢿⣿⣄⠐⢢⣤⡐⠉⠀⠀⠀⢠⡈⢛⣸⣧⠀⠀⣿⠿⠙⠆⠀⠀⢀⣤⡀⠀⠀⠌
⣾⣿⣿⣿⠛⠛⠁⠀⣠⡄⠀⠘⡷⠉⠛⠛⠷⠌⠁⠀⠳⣦⣀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡇⠀⠀⡀⠀⣿⣿⣤⣦⣤⣤⣀⠀⠀⢤⡀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⣀⣁⣀⠀⠀⠀⠀⢀⠨⣭
⣿⣿⣿⠋⠰⣦⣴⣾⣿⣾⡟⢡⣼⣄⡉⠀⠀⠀⢃⡀⠀⠀⠀⡾⣧⡀⠀⢀⣄⠀⠉⣡⣦⠀⠀⠀⢈⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠻⣶⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠁⠀⠀⠈⢳⣌⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠚⡦⠺⠆⠀⠀⠘⢷⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠳⣄⠀⠀⠀⢾⠀⠀⠀⠀⢀⣠⡤⠻⡷⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⢰⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠘⢧⡴⠞⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣷
⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢳⠞⠷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡆
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠘⡧⠘⠃⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢹⡆
⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⣷
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⣷
⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⢹⣆
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⢳⡄⠀⠀⢻⡀
⠀⢠⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢱⡄⠀⠸⡇
⠀⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢳⡀⠀⢸⡄
⠀⢸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣨⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢻⡀⠈⣧
⠀⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⢀⡿⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢣⡀⠙⣄
⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣴⢋⡀⢻⡆⣸⡇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢿
⠈⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣾⡁⠈⠁⠈⠀⠉⠁⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⠇
⣷⠀⠀⠀⠈⣇⠀⠀⠀⢀⡴⠏⠁⠈⠉⠉⠛⠋⠉⠓⠂⠠⠾⢦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄
⣿⠀⠀⠀⠀⢹⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⠀⠀⠀⠀⢸⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡏⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢺⡆⢸⠆⢱⡆
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⣾⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠾⠁⠿⠀⠿⠖
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠛⠉⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣿⡇⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣿⠃⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⢀⣿⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇⠀⠀⠀⠸⢏⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢿⡇⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⣷⡈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⢴⣿⠀⣶⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⢁⣸⠃⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⡿⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣆⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣼⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠀⠹⣧⡀⠀⠀⠸⣿⡀
⠀⠀⠀⢰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠹⣧⡀⠀⠀⠸⣿⡀
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠸⣷⡀
⠀⠀⢠⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⣿⡇
⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢸⣇
⠀⢀⣾⠃⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠈⣿⡆
⠀⢸⣿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢻⡇
⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣜⣿
⢠⣿⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⢸⣿⠀⠀⠀⠀⣿⡆⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⢸⣿⠀⠀⠀⠀⢻⣇⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢸⣿⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⡟⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣄⢀⣄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡿⠁⣿⠃⣸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⠃⣹⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠰⠏⠀⠻⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠰⠿⠀⠿⠀⠹⠷⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠛⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣴⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡯⠀⠀⠍⠁⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄⣠⠀⠀⠀⠀⠀⠀⣠⣤⡀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢿⡽⢻⡆⠀⠀⠀⠀⢀⡀⠀⠀⣏⣹⣗⣶⢢⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣰⠛⠐⠋⢙⣦⢻⣍⣿⣄
⠀⠀⠀⢠⣼⣿⣷⣄⣀⣾⢋⣧⠈⠑⢦⣤⠟⠀⠀⠀⣰⣟⣯⣸⣇⠸⡏⣽⢻⡏⡻⢷⡄⠀⠀⠀⠀⢠⠞⢻⠿⢜⡷⠀⠛⣤⣭⣦⠶⣧⢾⠇
⠀⠀⠀⠰⣿⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢰⡾⣯⣍⠸⣡⡿⣃⠛⠿⢈⣥⣟⠋⠀⠀⢀⣀⡀⠈⣿⠛⠧⣞⣣⠄⣤⣮⡟⠷⠶⣿⣤⡄
⠀⠀⠀⢈⣽⣿⣿⣉⣿⣤⣾⣠⢤⣀⣠⣄⠀⠀⠺⣤⣤⡤⣶⣯⣿⣙⢶⣠⡔⢢⣼⠂⠰⣏⣹⢤⣟⠀⢈⡗⢲⠾⣧⡞⣿⡶⣯⡦⢾⣇⣿⠃⠆
⠀⠀⠀⢨⠛⢿⡏⣙⠿⣯⡠⠟⢀⣿⣥⣿⠂⠀⠀⠙⠛⠁⠘⣿⣤⡽⢀⣉⠰⡀⣸⠀⠀⠈⠑⠶⠏⣶⣏⣹⠿⢰⠷⢛⣽⡛⡷⢿⢾⡏
⠀⠀⠀⠈⣻⠈⠓⣿⡁⣾⣀⡶⠯⣹⣧⠾⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⠌⠛⢯⠁⠀⠀⠀⠀⠀⠰⣟⠛⠄⢳⣾⠶⣿⢤⡽⣿⡮⠿⢛⣷⣦⡄
⠀⠀⠀⠘⠋⠀⠀⠙⢤⣥⢀⡿⣮⡅⢀⠚⢳⡄⠀⠀⠀⠀⢀⡰⠦⣤⡼⢃⣤⠺⣦⠀⠀⠀⢀⡖⣻⢿⣛⡷⢷⡹⣶⠿⣄⣽⢎⣶⠶⡿⢧⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣁⣿⠷⠛⣩⡿⢓⡆⠀⠀⠀⡟⢛⡒⢣⣤⠆⠀⢺⡏⠀⠀⠀⣾⠟⣡⡜⣿⡱⢏⣁⣧⠀⠈⠛⢿⣤⣤⡙⣧⣼⡇
⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⣿⡋⠀⣿⣩⣿⠋⠁⠀⠀⠀⢾⡟⣙⠄⠲⠴⠟⠉⠀⠀⠀⠀⠉⣙⣧⡼⠻⣷⣿⣍⡸⠃⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠘⣫⡿⢶⡆⠀⠀⠀⠹⣿⠛⡷⢾⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣿⣽⠇⠀⠀⠀⠀⣀⠀⣤⡤⣄
⠀⠀⠀⢸⣏⠻⠟⢳⡄⠀⠀⠀⠙⠧⠶⠂⢀⡤⣄⣤⣤⣤⢤⡄⠀⠀⠀⠀⢀⣴⣶⣆⣠⡀⠀⠁⠀⣀⡤⢀⣼⠓⢷⡶⠛⣿⠛⠀⣾⠏⢢
⠀⠀⠀⠸⠿⣗⣾⠟⣳⠄⣠⡀⠀⢀⣦⡈⡛⠢⠘⣡⡜⢣⡴⢧⡀⠀⠀⢰⣶⠱⣦⡈⢿⣋⣳⡴⠛⣎⢳⣊⣼⣓⡛⠰⣟⣉⣥⣤⣽⠛⠋
⠀⠀⠀⢠⣴⣏⠿⢛⠛⣦⠿⠁⣴⡉⢋⡸⣿⠀⠶⣞⡙⢧⣴⡾⠃⠀⠀⢺⡏⢹⣿⣍⣤⠉⢼⢷⡾⠃⢻⣉⣿⣋⣴⡶⡎⢋⠴⣄⢉⡑⠞⢢⡀
⠀⠀⠀⠘⠛⠁⣀⡈⣿⠃⡆⠠⣭⣧⣘⡗⠀⠀⢾⠳⣳⣾⢻⣦⠀⠀⢰⠿⣿⠈⣾⠛⠣⣴⣶⡎⢻⣷⣞⣯⣷⣿⣯⢥⡽⠛⣶⢚⣣⣭⡾⢻⡇
⠀⠀⠀⠀⠀⠘⠷⠇⠙⠋⠀⠀⠻⣴⠟⠻⠀⢷⣤⠀⠙⠶⠞⠁⠀⠀⢀⠲⢟⢐⣿⠛⠳⢊⣹⡿⢿⣿⣿⣯⣠⡏⡿⢉⣿⣾⣏⡿⢡⣤⣷⢦⡆
⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠙⠶⠦⠲⣄⣽⢿⣟⡞⢳⣄⠀⠀⠘⠴⢏⠙⢋⡻⢸⣿⠁⣝⠛⣟⣁⣿⠁⠃⢳⣼⡻⢿⣉⣁⡹⣄⠛⢿⡇
⠀⠀⠀⢠⣿⡏⢸⣷⣀⡴⢦⠀⠀⠀⠀⠀⠀⢯⣨⡙⢿⡴⣌⣹⡇⠀⠀⠰⣼⡧⢼⡖⢠⠟⠲⠆⠜⠋⠐⠉⠀⠈⢋⣡⣍⠙⣯⠉⠉⢻⡾⢿⠃
⠀⠀⠀⠘⢮⣶⣾⢸⣟⡻⡞⠀⠠⡞⢀⡀⠀⣸⠛⢰⣦⣤⠈⢳⠀⠀⠀⢶⣬⡷⢶⣿⠾⡶⠊⢠⡘⢓⣀⠞⣹⣿⠇⢀⡈⢾⠛⣦⡀⠈⠳⠊
⠀⠀⠀⠀⠀⠻⣤⠘⢯⡏⡀⠀⠀⠉⠉⠀⠀⡹⠦⣿⣣⡼⠓⠛⠀⠀⠀⠀⠀⠓⠊⠙⠲⠏⠀⠀⡿⣿⣿⢻⡟⠀⢲⡈⣡⠞⣭⣿⡿
⠀⠀⠀⠀⢀⣸⣶⢿⣴⣿⣙⣓⠀⠀⠀⠀⠀⠓⢤⠿⠉⠀⠀⣀⠀⠀⠀⠀⢠⣤⣴⠀⠂⠀⠀⠀⠙⠋⠀⠈⠀⠀⠠⣅⣹⣤⡿⠟⠀⢀⡘⣶⡀
⠀⠀⠀⠰⣯⠉⠱⣦⣬⡏⣬⢉⣦⠀⠀⠀⠀⠀⠀⣠⣤⢲⡾⠟⣙⠛⣦⠀⠀⠀⣼⡗⡿⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣼⣀⠉⠁
⠀⠀⠀⠐⣎⣉⠒⢿⣉⠡⢾⡟⠃⠀⠀⠀⠀⣠⠾⣄⡾⡀⡀⠲⡝⠫⠉⠀⠀⠀⠀⠀⢠⡄⠈⣁⠈⠓⣶⣴⠀⠠⢒⡆⠀⠀⠀⢴⣰⠍⡀⠟
⠀⠀⠀⢀⣟⣽⣶⡿⠛⣿⡾⠋⠀⠀⠀⣠⢤⣦⣰⡟⠀⢈⣙⠳⡟⠖⣱⠄⠀⠀⣠⣤⡈⠉⠀⣡⢶⣮⣉⡍⠛⡦⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⢈⣁⣿⣬⣧⣼⡧⡶⠀⠀⢠⠞⢧⣴⣿⣉⠓⢒⢧⡼⠿⢿⢊⣹⠀⠀⠀⠥⠀⠀⢴⠳⢾⣶⣾⣋⣁⣟⠣⣘⠁⠀⢀⠴⢆⢠⡤⠀⠿
⠀⠀⠀⢸⣗⣾⣧⠘⣧⡿⠀⠀⠀⠀⣤⣾⣅⡀⢁⡛⠓⢾⡿⣶⣮⣉⠁⠀⠀⠀⠀⠀⠀⡘⢶⣬⣽⣿⣏⡣⠸⣿⣏⠁⠠⣬⣶⠆⠙⡀⢚⣤⡇
⠀⠀⠀⠀⡽⢉⠿⣶⠏⠀⠀⠀⠀⠼⠷⡎⢉⠁⠈⠁⠞⠛⣠⣯⠉⠉⠀⠀⠀⠀⠀⠀⠀⢉⣀⣽⣿⣿⣿⡈⢠⣤⢸⡇⠀⣠⡟⢀⣭⡟⢫⣉⠁
⠀⠀⠀⠀⠀⣤⣈⡀⢠⣄⠀⠀⠀⠠⢴⡷⣤⠂⠤⠿⣳⣶⣉⡃⣦⠀⠀⠀⠀⠀⠀⠘⠓⠀⠉⢟⣿⣤⣼⣿⡤⣇⠈⡗⠀⠈⢶⡀⣴⠾⣳⡼⡅
⠀⠀⠀⠀⠸⠟⣋⣹⣿⡟⢳⡄⠀⠀⠀⠀⢠⣤⣦⣹⣏⡿⣏⣡⢙⠟⣻⡤⣄⠀⠀⠀⠘⠃⣴⣞⢹⡃⣴⠈⠗⢛⣉⠁⠀⢀⣴⣈⣹⢾⣿⣷⡏
⠀⠀⠀⠀⠰⡋⠛⡿⠘⠛⠋⠀⠀⠀⠀⠀⣸⣻⡄⢽⠙⢣⡼⣯⠏⠸⡭⠓⣼⡁⠀⠀⠀⠈⠣⣏⠸⡣⠞⢀⣴⠟⠁⢠⡷⢠⠉⣿⡇⣼⢻⣽⡇
⠀⠀⠀⢸⡇⠈⠉⠀⢀⣀⡀⢀⠀⠀⠀⠘⢅⣘⣧⠘⣷⡏⢸⡅⣸⡶⣆⣘⠈⢣⣄⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⢰⡶⠺⢾⣬⣭⣿⣄⢸⠇
⠀⠀⠀⠈⡿⠀⠀⠀⣿⣩⣿⠛⣄⠀⠀⠀⠈⠷⠲⢦⠁⠋⠀⣹⣿⡀⣽⠿⣤⠰⣶⣤⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠛⣷⡔⠺⠛⠯⢨⣯⡼⠓
⠀⠀⠀⠀⠀⠀⢤⡤⠈⢹⡏⣉⣧⡤⡀⠀⠀⠀⠲⠛⠀⠀⡊⢁⣿⠀⠈⣶⠛⠻⣆⣠⢷⡄⠀⠀⠀⡴⠒⠒⠀⢎⣉⣿⡏⣹⡟⢳⣾⣋⠘⢻⣇
⠀⠀⠀⠀⣤⣤⣀⣠⣿⣾⣿⡉⠹⣤⣬⡀⠀⠀⠀⠀⠀⠠⡛⢹⡏⠙⡙⠁⠉⣉⣧⡥⣘⣿⠆⠀⠈⢷⡀⣀⡤⠀⠉⠀⠙⠉⠙⠛⠉⠉⠀⠈⠋
⠀⠀⠀⠀⡁⣤⣈⢁⣿⣆⢁⢘⡤⢾⡯⠇⠀⠀⠠⣶⠀⠀⠹⡋⣺⠿⢻⠆⠚⠋⠼⣷⡇⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⢴⣃⣀⣤
⠀⠀⠀⠈⠻⣧⣼⣏⣻⣍⣉⣙⣧⠾⠁⠀⠀⠀⠀⠈⠃⠀⠀⠉⠉⠑⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣦⣶⣶⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⡕⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠗⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣻⣼⣸⣟⣿⢷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⠄⠈⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣧⣶⣾⡿⠿⠿⣽⣷⣷⣾⢿⣻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⣴⣾⣿⣿⣿⣿⣿⣿⠯⠭⠭⠒⠀⠚⠛⣛⣶⠿⣷⣿⣼⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣽⣟⣛⠛⡋⣶⡆⠨⣭⣥⠀⠩⣴⣤⠚⣿⣿⠿⣿⣶⠿⣿⠿⣿⢿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣆⢰⣿⣿⠆⣿⣿⣆⣽⣿⣐⣿⣧⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠷⢾⣿⣛⣂⣻⣿⣈⢸⣿⠀⣸⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⢿⣟⣛⣓⣶⣿⣇⣄⢀⣡⣌⠥⡙⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣿⣯⣿⣧⣾⣧⣾⣦⣿⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⢿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⠋⠸⣿⠈⣉⣀⡈⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣶⠻⣶⢲⣾⢦⡤⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣭⣤⣤⣬⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡠⡄
⠀⠀⢀⠴⠊⠀⠀⣤⡀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠑⠀⡉⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⢿⠀⣤⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⢀⢈⠐⢄
⠀⢠⠋⠐⠄⠀⠐⠃⠃⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡆⠀⣅⠀⠘⡆⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⢸⠉⢃⠀⠀⠀⠀⠀⡠⠻⡄⠀⢲⠠⣆⡀⠱⡄
⢰⠁⠀⢸⣷⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠁⢄⢀⠀⠀⠘⠀⢣⠀⠀⠀⠀⠀⡰⡁⠀⠄⢂⠀⠀⠀⡔⠀⠀⢸⠁⢰⠂⢠⠈⢃⠘⡀
⠀⠙⠢⣀⠀⠀⢀⠌⣸⠻⠁⠀⠀⠀⠀⠀⠘⢅⠀⠀⠀⠀⢀⠠⠛⠀⠀⡈⠀⠸⡀⠀⠀⠀⢠⢃⠃⠀⠀⠈⠆⠀⠀⢆⠀⠀⡄⢸⠈⠀⣠⣆⠀⠂⢡
⠀⠀⠀⠈⠑⠤⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠂⠁⠀⠀⠀⠀⠁⠀⠀⢇⠀⠀⢀⠇⡌⠀⡠⠀⠀⠘⠄⠀⠈⠆⢀⠀⢘⠇⠊⢰⠀⠈⠢⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡀⠀⡌⢠⣇⠀⠇⠀⡆⠀⢨⠀⠀⠈⣦⠀⠁⠀⠀⠠⠀⠀⠀⢨
⠀⡼⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠒⠚⠀⡇⢸⠂⠀⡆⠉⠂⢄⣠⠐⡍⠀⠀⠀⠀⢀⠀⠀⠰⡁⠢⣀⡔⠁
⢀⡄⠀⠈⢀⡈⢁⠁⠂⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⠈⣆⠀⠀⠀⠀⠀⡌⠸⠀⠀⠀⠀⠀⠀⠀⠠⢴⡆⠀⠉
⠀⠱⣀⠠⠀⠁⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠚⠀⠀⠀⠱⡀⠀⠀⠀⢰⠰⠀⠀⠀⢠⠇⠀⠈⣆⠘⡀⠀⠠⠠⠁
⠀⠀⠈⠑⠢⠤⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⠀⠀⠀⠀⠀⠂⠀⠀⡆⡄⠀⠀⠘⣆⠃⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡆⠀⢂⠀⠀⠀⠀⢸⠀⢀⠃⡇⠀⠀⠀⠘⣤⢠⡇⠀⠀⠀⠀⠀⠀⡀⡀⢀⣤⠄⢦⣃⡀
⠀⠀⣖⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡆⠀⢰⠀⠀⡄⠸⠰⡇⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠐⠓⡣⠁⢀⡖⠀⠀⢳
⠀⠀⢀⠔⠁⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢰⡇⠰⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠉⠀⠀⠀⡇
⢀⡄⠁⢤⠄⢰⠀⢣⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⠌⡈⠀⠀⢈⠀⠀⢸⠁⠀⠀⠀⠘⠀⣠⠠⠤⠀⣄⠀⠀⠀⠀⠀⡌⢣⠀⠀⠀⠀⠀⡼⡇
⢘⠀⠀⠉⠀⡸⡀⠀⢃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢄⠜⠀⡅⠀⠀⠸⠀⠀⢸⠀⢸⠀⢠⠋⠁⢹⣀⠤⠀⠛⠐⡀⠀⠀⠀⡇⠀⢳⠀⠀⠀⡰⠁⠃
⠀⠀⠀⡠⠈⠀⠘⣄⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠇⠀⢸⠀⡆⠀⠈⠉⠁⠋⠀⡀⠀⠐⠀⢡⠀⠀⠀⠃⠀⠀⢧⠀⠰⠁⢰
⠀⣧⠊⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠆⠀⡜⠀⠀⠀⠀⢈⠀⢸⢰⠁⠀⡄⠘⠀⡂⠀⠃⠀⠀⠼⠀⠀⠀⢸⠀⠀⣀⠀⢢⢁⡆⢸
⠀⠘⡄⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⠂⡘⠀⠀⠀⠀⠀⠀⠆⠀⡌⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠓⠀⠀⠈⢡⠃
⠀⠀⠈⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⡰⠁⠀⠀⠀⠀⠀⠀⠐⣰⠁⠀⠀⠣⣀⢀⠗⠀⠄⠠⢄⠀⡇⠀⠀⠀⠱⡀⠀⠀⡇⢀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠓⢤⡀⣝⡠⠤⠛⠀⠀⠀⠀⠀⠁⠒⠲⠒⠋
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢈⢀⣀⠀⠼⣿⠿⢷⣾⡏⢻⠙⣶⣤⣴⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡟⠈⠘⣇⠀⠀⠠⢀⣖⠊⡁⢸⣦⡹⣻⣅⣂⢢⣬⡍⠍⢀⣧⡀
⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⣿⣿⡙⢆⠀⠀⠦⣀⢀⡤⣄⢀⡇⠀⣿⣽⡟⠑⢜⠦⠍⠀⢠⣿⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠸⡽⣶⣿⣿⡿⢿⡁⠈⠄⠀⢰⣷⠤⠜⡳⣴⠃⢠⣿⣇⢠⣀⣁⣀⠀⢠⣟⡃⠳⣝⣿⣿⡆
⠀⠀⠀⠀⢠⣾⡧⠼⣧⡿⢰⣿⢆⠀⠀⠤⣄⣶⣶⣿⠋⢁⠄⢸⠓⣄⠤⠤⡤⠅⢰⣼⣙⣿⣷⣌⣻⣿⣿⣦⡀
⠀⠀⠀⢀⣾⣿⣍⠢⡈⠳⣍⣻⣫⢆⠈⠳⡄⢁⣀⣀⣴⠞⠀⢸⣷⣛⣙⣯⡖⠀⢨⣸⡙⢿⣬⡟⠷⡵⣿⣿⣇
⠀⠀⠀⢸⣿⣿⡹⣆⠘⣇⠀⢙⣿⡿⢀⠀⢉⠛⣻⣿⡴⠆⠈⣱⡿⠧⠽⣉⠁⣠⣴⡜⠳⠚⠷⣄⢱⣦⣻⣾⣿⡆
⠀⠀⢠⡟⢩⣿⣥⣿⡗⠾⣖⡩⠑⣛⣏⠭⣭⣥⠶⠲⢴⠠⠰⠛⠾⢶⣶⣄⣀⣿⡿⠯⠹⠏⢶⣟⣣⣿⣿⡿⢛⢿⡀
⠀⢠⣿⣸⣿⣿⣿⢿⡣⠤⠈⠱⢟⡥⢴⣒⡒⡒⣻⣅⣉⣛⠐⠳⣴⢶⡶⠶⢾⣯⣙⣻⣛⣙⢺⣝⡿⠷⣏⣴⣾⣿⣿
⠀⠀⣿⣈⠨⢽⣰⡿⢴⣦⠀⢐⣻⣶⠿⣛⣉⣉⠉⣥⣴⣉⡛⠿⠶⢶⡾⠒⣻⣧⠬⠟⠂⢤⣅⣭⣳⣽⣿⢼⣷⣾⣿
⠀⠀⣿⣉⣀⣀⣈⣉⣿⡿⢆⠿⢿⣸⣟⣯⣽⣯⣅⣴⣭⣬⣉⣛⣋⣋⣉⣹⣿⡶⣚⡉⢳⣲⡙⢄⢨⣿⡽⣞⣿⣿⣿
⠀⢰⣿⢿⣿⠿⢿⣿⣛⣷⣾⣿⣿⡶⣩⡿⠷⣶⡦⢤⣀⣩⠈⠉⣉⠽⠁⣬⣩⣩⡉⣈⠧⡙⠳⣼⢧⣻⢺⣿⠻⣿⣿
⠀⢈⣿⡛⣡⣾⠅⠀⠙⢹⡿⢿⣿⣿⡄⢛⣿⣯⣿⠈⢷⢽⡯⣁⣒⡾⢺⣷⢦⣯⣘⠿⣷⣭⡁⢏⣧⢹⡾⣀⣿⣿⣻
⣀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠹⡏⣦⡝⣉⣭⣵⡮⢩⣭⡀⣼⣿⡄⠜⠛⣂⠀⣉⡻⠓⠄⠫⠀⠇⣿⣿⣼⣿⣽⣿
⠹⣾⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣴⢗⠛⣟⣱⣿⣿⣯⠈⢯⡄⣬⠸⠭⡑⠧⠄⠈⣌⡧⠾⣟⢿⡆⡧⣿⣿⣷⡿⣿⣿
⠀⢻⣿⡿⢧⠀⠀⠀⠀⡀⠀⣴⣷⣻⣺⢟⢷⣉⣽⣷⢀⣿⡇⣰⣧⢔⣿⣵⡐⢯⡁⠻⣇⡮⢱⢻⡇⣿⡙⣝⣃⣼⡇
⠀⢸⣿⣶⡾⣷⣶⣄⣺⡿⣛⣏⣦⣝⣓⣲⡿⠦⢼⣿⠻⣞⠀⡛⠽⠀⣻⢋⡿⢾⡇⠂⠈⠏⠛⠊⣿⣈⣿⣿⢹⣾
⠀⠸⢿⣿⣿⣿⣏⣻⡿⠿⣿⣿⣿⣯⠤⢟⡴⣾⣹⡿⢷⣶⢶⣿⣮⣀⠓⠢⣘⡛⣸⡖⣢⡇⢿⡈⣾⣾⣧⣇⣿⡏
⠀⠀⠀⠙⠿⣿⣿⣟⣿⣿⣿⡿⠟⠘⠋⡈⠟⡷⢿⠾⠩⠝⠿⣿⡁⢈⠿⣽⠢⡷⣾⣧⡟⠰⣲⣿⡟⠝⠈⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣟⣇⠀⠀⠀⠀⠈⠑⠀⠀⠈⢳⡜⠺⢿⣮⣿⣽⣦⣿⣿⣿⢹⡼⣇⣻⣴⣿⣽⠯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠃⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⣿⣿⣿⣿⣿⢿⣿⣼⡝⢿⡿⣿⣿⣩⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠊⡠⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠈⠉⢻⣿⣽⣿⡏⣾⣿⣿⣧⡴⠛⠋
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠰⠀⣤⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠶⠚⠋
⠀⠀⠀⠀⠀⠘⠟⣟⠀⣀⡤⠆⢀⣰⣾⣿⣶⣶⣤⣼⣷⡶⠶⠦⠤⠒⠒⠚⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣿⣭⣭⣬⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣥⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠈⢦⠇⠀⠀⣰⠂
⠀⠀⠀⢀⠀⢺⣀⣼⠤⡶⠋⠁⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⡀⣀⡀⢀⢀⡀⣀⡄
⠀⠐⠦⠤⢤⣖⠋⢢⢬⡷⡞⠃⠀⠀⣄⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠃⠑⠉⠚⠉⠈⠑⠃
⠀⠀⠀⠀⠀⠉⢤⠟⢸⠍⠃⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠤⣤⣤⢠⡀⡆⣤⣤⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⣾⠷⡤⣤⣤⠄⡄⡤⣤⢴⢠⡤⣦⡤⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣀
⠀⢀⡀⠀⠈⣀⠁⣀⡁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡀⣆⠀⠀⠀⠈⠠⢿⠿⠟⠀⠘⠻⠂
⠀⠫⠤⠼⠞⠧⠜⠥⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡾⠾⣿⣷⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠁⠀⣤⣆⠀⠀⠰⣴⣒⣴⡴⣷⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠛⠛⠀⠀⠈⠛⠟⠋⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⢰⣉⢰⢢⣰⡄⢰⡄⠀⠀⠀⠀⣠⠂⢸⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠤⠤⣴
⠀⠀⠀⣀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠃⠀⠸⡇⡄⠐⡄⠀⢸⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⣈
⠀⠀⠘⠤⠰⠿⠣⠄⠣⠜⢠⠀⠀⠀⠀⠀⢸⠇⣷⠀⣻⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠞⠀⡟⠀⡾⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠞⠃⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣄⡠⠤⢤⣤⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢈⣡⣼⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣟⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⣿⣧⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣷⣿⣶⡦⣤⡠⣼⣦⣄⣠⣤⣰⣶⣾⣿⣿⠟⠋⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠠⡤⡤⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢩⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⣨⠥⠔⠒⠀⠀⠀⠈⠀⠀⠀⠺⢿⣿⣷⣶⣦⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣞⣏⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠰⣦⣤⡤⢄⠀⠠⡄⣀⣤⣶⣀⡈⠙⠛⠿⠿⢿⣶⣦⡀⠛⢿⣿⣿⣯⣭⣿⣿⣿⢙⣟⣻⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠛⡛⣄⣠⣚⡀⢺⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣶⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⣋⡛⣿⣿⠏⠉⠀⣿⣭⡍⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢢⣤⣀⠀⡄⠀⠀⣦⠶⠒⡿⡿⠆⠈⠟⢻⣶⣶⡀⠀⢈⣉⠉⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠟⠛⠈⠃⠄⠀⠀⠀⠀⠉⠀⠁⠀⠈⠉⠉⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠤⠀⠒⠀⠀⠀⠄
⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣤⣤⣶⣦⣦⣶⣶⢦⣶⣶⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠿⢿⠛⠛⢿⠛⠛⠛⢋⠉⡑⠇⠕⠉⠉⠨⠑⠂⠉⣉⢛⣛⠿⢶⠶⢴⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣹⣩⢀⣄⣠⢨⣤⣠⣈⢆⢵⣦⣦⣤⣄⣤⣠⣀⣀⣲⣾⣦⣶⣄⣶⣌⣠⣤⣶⣄⣾⣙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠋⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⡀

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠇⠀⡰⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⡘⠀⠀⠀⡇⠀⠀⢠⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⣾⠀⠀⠐⡇⠀⠀⠀⠀⡞⠁⠀⠀⢀⡄⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠎
⠀⠀⠀⠀⠐⠢⣄⢱⠀⠀⢋⠀⠀⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠸⠁⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠐⠀⠀⠎⠀⠀⠀⢠⠁⢈
⠀⠀⠀⠀⠀⠀⢈⡋⠀⠀⢸⡄⠀⠀⣇⠀⠀⠀⢰⠃⠀⠀⡘⠀⠀⠀⠆⠀⠀⠱⢄⠀⠹⡄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠃⠀⠀⠘⡂⠀⠀⢢⡀⠀⠀⠑⠀⠀⢠⠀⠀⠀⠀⠀⠃⡴⠁⠀⢠⠃⠀⠀⠀⠀⠀⠐⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢦⠀⠀⠀⠁⢀⠀⢰⠁⠀⠀⢰⠆⠀⠈⠂⠀⠀⠀⠀⠀⠂⠀⠀⠰⣄⠀⠀⠀⠀⠀⠠⠇⠀⡈
⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠸⠆⠀⠀⠀⠀⢦⢘⠃⠀⠀⢄⡀⠀⠀⣼⠀⠀⠀⠀⢀⡉⠀⠀⠀⠙⠀⠀⠀⠀⢠⡇⠀⠀⢩⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡴⠀⠀⠀⠀⠸⡏⠀⠀⡰⠊⠁⡀⠀⡁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢁⡀⠀⠀⠐⡆⠀⠀⠀⢰
⠀⠀⠀⠀⢃⠀⠀⢡⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⠓⠀⠃⢀⡀⠀⣸⡋⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⡇⠀⠀⠀⣎
⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⠀⠀⠸⣦⢀⡀⠀⢠⡇⠀⡼⠀⠀⣠⠡⣴⢒⣞⣙⡶⠟⢱⣦⠀⢠⡖⢺⡜⠷⣶⣤⢄⣥⢀⠀⣤⣟⢳⢦⡖
⠀⠀⠀⠀⢣⠀⠀⢇⠀⠀⢀⣴⣶⣡⣯⣽⣿⣣⣧⣈⡷⠀⣼⣧⣠⣾⣿⣼⣿⣿⢿⣿⣻⣦⣿⡗⣿⣣⣶⡜⣳⣿⣷⣯⠵⣨⡷⢈⡶⠆
⠀⠀⠀⠀⣾⣀⣀⡾⣀⣴⣟⣥⣿⣿⠝⢋⡿⢿⣿⡽⠥⠄⠐⠚⡛⠛⠛⠛⠐⠈⢉⣀⣨⣀⠙⠛⠚⠋⠛⠛⠿⠟⠛⠋⠀⠙⠟⠛⠐⠂
⠀⠀⠀⠀⢹⣤⣽⣿⣿⡾⠋⠀⠀⠛⠻⡿⢿⣿⠿⠃⢠⣤⢶⣶⢿⣶⡦⠀⠺⢿⡟⠃⠙⠋⣁⠀⠀⢀⠀⠀⠀⣠⣶⣶⣶⣿⢶⣎⣴⠄
⠀⠀⠀⠀⣼⢯⠿⠋⢉⣴⣾⣶⣷⣶⣦⣾⣤⣄⠀⠀⠛⠛⠿⠋⠚⠉⠀⠀⠀⠀⣤⣤⣶⢿⡾⣷⣾⡗⠀⠠⠀⠉⠉⠙⠛⠛⠚⠛⠉
⠀⠀⠀⠀⢀⣀⠀⠀⠛⠿⢿⠿⠻⠯⠙⠏⠉⢁⣄⣷⣶⣷⣿⣿⣿⣿⣾⣷⡶⠀⠈⠙⠛⠋⠛⠛⢋⡁⣤⣠⣤⣴⣶⣴⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣻⣿⡿⠟⣀⣠⣤⣦⣤⣴⣶⣶⡄⠻⠟⠛⠿⠛⠛⠉⠉⢉⠀⡀⢀⣀⣴⣶⣷⣶⠇⠀⠛⠿⠿⠿⠛⠛⠉⠁⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠛⠉⠱⠾⠿⠿⠿⠟⠿⠒⠛⠉⠀⠀⣀⣄⣤⣤⣠⣄⣀⣾⣄⣍⣻⣿⣿⠟⠉⠀⠀⠀⡀⣠⣆⠀⣠⣴⣴⣤⣶⣶⣶⣖⣄
⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣾⣿⣿⣿⣿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠲⠖⠷⠷⠿⠋⠋⠛⠋⠈⠉⠈⠉⠉⠉⠛⠃
⠀⠀⠀⠀⢿⣿⡟⠟⠀⠀⠛⠛⠛⠛⠛⠉⠁⠉⢻⣿⣏⠁⠀⠀⠀⠀⠀⠈⡀⣀⣀⣀⣀⣀⣠⣤⣄⣤⢀⣴⣔⣦⣤⣤⣤⣴⣴⣶⣖⡀
⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⣀⠠⣄⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣽⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠋⠀⢀⣄⡀⢀⣈⠉⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠄⣰⠖⠒⠻⣟⣀⣿⡙⢃⠻⣶⣾⣧⣿⡇
⠀⠀⠀⠀⣽⣿⣟⣿⣯⣿⣿⣶⣧⣶⣴⣼⣶⡷⠶⢶⡶⠶⣶⡶⠀⢀⠂⢀⣀⣤⢾⣿⣧⣏⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣿⡿⠿⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠛⠛⠛⠻⢯⣿⣽⢯⣻⡿⢿⣦⣶⣦⣤⡙⣻⠃⠶⠔⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⢿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠛⠛⠶⠇⠈⣛⣳
⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠐⠂⢤⡀⣀⠘⢢⡐⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠴⠺⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⢳⣄⠡⡎⡠⣦⠶⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀⣀⣀⣠⣀⣤⣤⣤⣤⣶⣶⣶⣿⣶⣤⡄⠀⠐⣦⣤⣔⡰⣠⣴⣦⣤⣤⣤⣤⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠙⠋⠉⠙⠋⠋⠉⠛⠋⠛⠁⠀⠈⠉⠋⠉⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠋⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣳⣤⣀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⣄⠀⠀⢠⣷⠀⠀⣠⣶⡀⠀⠀⠈⠻⣿⣿⣷⣤⠞
⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⠞⠁⠀⠀⠀⠀⢰⠀⢸⠈⠓⢦⡆⢸⣧⡼⠃⢸⣧⣤⣤⣤⣤⡈⠻⣿⣿⡆
⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠘⢿⣟⠀⠀⢸⣿⣿⣿⠛⡿⠀⠀⢻⣿⣷
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⣀⣨⡀⠂⠀⠀⠀⠀⠀⠙⠂⠀⢸⣿⣿⣧⡘⠁⠀⠀⠈⣿⣿⡀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⣶⣿⣿⣿⣿⣿⡟⢟⠲⠤⣀⣤⣴⣾⣇⠀⠀⣿⡬⠟⠳⣄⡀⠀⠀⢹⣿⡇
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢎⠙⠿⣿⣿⣧⠈⢧⡀⠏⠛⢿⡁⣻⠀⠀⠉⠁⠒⠒⢚⣿⡦⠀⠈⣿⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢣⠀⠀⢙⡿⠶⠲⣿⡶⠤⠀⣤⡄⠀⠀⣠⠰⣶⡛⠉⠁⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠷⡴⢋⣠⠠⠦⠘⡗⠦⣠⣍⡆⠀⠀⢿⣶⡏⠉⠓⢶⣄⠀⠀⠘⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢯⣀⡜⠀⢻⣧⡿⢐⠶⠘⠒⠋⠀⠀⠀⠀⠘⣿⣇⡤⠒⠉⠁⠀⢠⢦⡿⠛⠛⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡁⠀⠀⠀⡽⠁⠀⠀⣻⠞⢃⣄⠀⠀⠀⠀⢰⠶⣄⡀⢻⡏⠳⡄⠀⠀⢀⣦⠟⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠙⣄⠀⠀⠙⠂⢤⣀⣿⣰⣾⣿⣇⠀⠀⠀⣿⠀⠀⢰⣾⡁⠀⠠⠆⠀⣼⠏
⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⣿⣿⠿⠋⠙⢧⠀⢠⡇⠀⠀⣿⣿⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⣤⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠉⠀⠀⠀⠀⠘⢧⡘⠢⣄⠀⣿⠇⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠙⠿⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠴⠶⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⠀⢀⡴⠄⣠⡴⢦⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⢴⠛⠿⢋⣷⠀⠀⠀⠀⣀⣀⠀⠀⣯⡹⣟⣿⣢⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡞⠃⠈⡉⣷⠜⠇⢹⣆⡀
⠀⠀⠀⢠⣾⠻⣷⣤⣰⣟⣹⡇⠈⠛⠶⠾⠁⠀⠀⣰⣿⡹⣬⣧⡸⡿⢔⢻⡍⣛⣳⠀⠀⠀⠀⠀⢜⡋⡻⠗⣙⠆⠈⢱⣌⣷⠖⢷⠾⠇
⠀⠀⠀⢐⣿⣿⣿⣿⡿⢽⣏⠀⠀⠀⠀⠀⠀⠀⠿⠻⢦⠜⢡⣞⣧⠉⡛⠠⠶⣯⠁⠀⣀⣠⢤⡄⠸⣟⡛⠲⣭⠆⣰⡾⣿⠻⢟⣿⢶⡆
⠀⠀⠀⢠⣾⣿⣯⣼⣿⣶⢷⡖⢦⣤⢶⣄⠀⠘⢶⣶⡦⠻⣷⠿⣭⠿⣴⠎⠳⣶⠁⠸⢤⡷⢾⡇⣀⣸⣉⠿⢻⣚⣹⣿⣿⣆⠺⣿⡼⠃⠃
⠀⠀⠀⣸⣉⢿⡥⣽⠛⠦⠚⠁⣶⡷⢾⣏⠀⠀⠀⠉⠁⠀⠻⠶⠞⠠⢤⣘⣀⠞⠀⠀⠀⠈⠛⢁⣿⣤⠝⠛⣟⢋⡷⢯⣱⣻⢛⣧⡀
⠀⠀⠀⣠⡽⠀⠉⣿⠰⠟⢨⡝⠦⠿⠛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⠉⢣⠀⠀⠀⠀⠀⣀⣸⣍⣩⣉⢿⣟⣻⡗⢶⡛⣟⠙⢀⡿⠿⡆
⠀⠀⠀⠈⠁⠀⠀⠘⢳⣇⣼⣻⣿⣠⡄⣬⣷⡀⠀⠀⠀⢠⣼⡉⣶⠛⠁⢲⣙⡷⠀⠀⠀⣰⣯⠟⣷⣼⣛⠧⣍⠛⠳⢾⣿⡜⠃⢻⡙⠷⡄
⠀⠀⠀⢠⣤⠀⠀⠀⠀⠉⢡⣾⡟⢃⡤⣾⣥⡼⠀⠀⠀⢲⣬⣤⠈⣚⠃⣥⣼⠇⠀⠀⠐⣿⣥⡞⣬⣷⣛⡶⠼⡇⠀⠀⠉⠛⢿⣦⡼⠚⠃
⠀⠀⠀⣠⠿⣇⣀⠀⠀⠀⠸⣧⣄⣼⡖⣾⠃⠀⠀⠀⠀⠙⠧⠴⠃⠈⠛⠁⠀⠀⠀⠀⠀⢠⡾⢿⠃⠙⠛⠿⠂⠁
⠀⠀⠀⢸⡶⣯⣽⣇⠀⠀⠀⠹⣧⠘⣉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠒⠛⠛⠀⠀⠀⣠⣰⣂⣸⣟⣷⡄⢀⡤⣄
⠀⠀⠀⣼⣶⡬⣥⣿⣄⡀⠀⠀⠀⢉⡁⢤⣞⡛⠞⠛⣿⢉⣗⠀⠀⠀⢀⣺⢻⡋⠳⣿⠶⣀⣠⣤⢺⡇⠾⣧⣬⡟⣡⠾⢧⢀⢸⣯⡾⠃
⠀⠀⠀⠈⣩⢷⣿⡴⢮⢩⣷⠀⡤⠻⠷⣶⡄⢡⣘⠷⣌⢋⣉⡧⠀⠀⣸⠿⢦⣿⠦⠙⠖⣻⣅⣜⠣⡟⢿⣷⢖⣀⣛⠶⣚⡛⠻⠆⣠⣄
⠀⠀⠀⢸⡿⠛⠁⠰⣾⢋⠀⢘⣻⡠⣷⠘⠁⣠⣽⣦⣼⢿⡇⠀⠀⠀⣼⣧⢘⣿⢿⣏⣠⣭⡽⣷⣤⣷⣞⣹⣿⡟⢹⡶⣆⡽⢆⣛⣠⢾⡆
⠀⠀⠀⠀⠀⠰⣞⠐⠷⠞⠀⠸⣋⣹⣾⡄⢠⡉⠂⠸⢏⡨⠟⠀⠀⠀⣣⡟⢠⣿⠶⣈⠋⢿⣤⣾⣿⣿⡛⣹⢳⡇⢻⣦⣜⣷⠟⢹⣿⡌⡇
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⡄⢹⣤⡶⣤⠤⡄⠀⠀⠐⣀⡇⢺⠟⢦⢸⣤⠘⡷⠿⠟⢻⣟⠻⠼⣔⣾⣿⠟⠃⢰⣉⠻⣦⡇
⠀⠀⠀⢈⣿⠏⣻⡇⠀⣤⡀⠀⠀⠀⠀⠀⢈⣛⡐⢿⣩⣘⢛⡦⠀⠀⢠⣸⡆⣸⡅⢘⠷⣤⠀⠴⠓⠾⠃⠀⠲⠛⣳⠸⢿⡛⠓⠿⣴⣾⡇
⠀⠀⠀⠸⣹⣤⣟⢹⡿⣶⠏⠀⢠⠀⠀⠀⢀⠿⠭⣄⣁⡜⢫⡁⠀⠀⢤⣉⡥⣬⣷⣼⡤⠆⢀⠑⠀⢠⡞⣲⡶⠉⠉⢡⡟⣧⠀⠀⠷⠼
⠀⠀⠀⠀⠈⢯⣥⠚⣿⠉⠀⠀⠈⠒⠃⠀⠘⣦⣼⢏⣹⠷⠾⠀⠀⠀⠀⠉⠳⠘⠳⢤⠇⠀⠘⢶⣿⡺⣾⠏⠱⡄⠉⡴⢋⣹⡿
⠀⠀⠀⠀⠀⣴⣴⣦⣼⣎⡓⠂⠀⠀⠀⠀⠘⠄⡸⠏⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⠂⠂⠀⠀⠀⠛⠋⠀⠉⠀⠀⣌⣹⣧⣽⠿⠃⠀⠀⣦⡀
⠀⠀⠀⢰⣏⠉⢡⣄⣽⢫⡝⣳⡄⠀⠀⠀⠀⠀⣀⣤⡐⣶⡿⢓⠖⣦⠀⠀⢠⣼⡕⡇⠀⣀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣨⡃⠈⠁
⠀⠀⠀⠐⣏⠁⠀⣯⡉⠠⣿⠛⠁⠀⠀⠀⢀⡴⢇⣸⠇⡉⠲⡞⠛⠉⠀⠀⠀⠀⠀⢠⡄⠙⡉⠛⠞⣦⡖⢠⠀⢢⠀⠀⠀⢰⣤⡌⢀⠾
⠀⠀⠀⢀⡝⣷⣾⡟⢹⠷⠟⠃⠀⠀⢀⡤⣾⣀⡾⠀⢈⢉⠳⡏⠶⣲⠄⠀⠀⣀⣤⠉⠁⠀⠠⣦⣆⣹⠋⢻⠄⡉
⠀⠀⠀⢈⡠⣿⣼⣧⢾⡶⠇⠀⠀⡴⠻⣦⢿⣬⣉⣚⠳⡴⠿⢿⣋⣹⠀⠀⠀⠁⠀⠀⡿⠳⢾⣶⣿⣉⣸⣟⣆⡃⠀⠀⡴⢢⢀⡴⢀⠿⠂
⠀⠀⠀⢸⣒⣿⣆⢘⣾⠇⠀⠀⠀⢰⢶⣧⣤⠀⡘⠛⢲⡿⢷⣿⣍⡀⠀⠁⠀⠀⠀⢀⡙⠳⣭⣿⣿⣉⡖⢿⣿⡍⠀⠤⣷⡆⢈⡁⢘⣤⡗
⠀⠀⠀⠠⠏⠡⢷⠾⠃⠀⠀⠀⠰⠛⢳⠀⠄⠀⢁⡛⠋⢠⣾⠉⠉⠀⠀⠀⠀⠀⢀⠀⢥⣤⣿⣿⢿⣇⡀⢴⣤⣕⠀⢠⡼⠁⢨⡿⣫⣭⡁
⠀⠀⠀⠀⢠⣤⣤⣄⣲⣄⠀⠀⠀⠠⠿⠷⠂⠰⢚⣯⣿⣤⣍⣰⡀⣀⠀⠀⠀⠀⠘⢃⠀⠨⣽⣿⡶⠿⣿⠺⣄⣸⠀⠀⠸⡆⣰⡟⣹⡞⡇
⠀⠀⠀⠀⢘⣹⣥⡽⢿⣉⡷⠀⠀⠀⠀⠀⣴⡶⢬⣷⡜⠻⣰⣌⠋⣽⡖⢦⡀⠀⠀⠙⢠⣿⡏⢹⡀⡖⠚⠉⣧⠌⣀⠀⣴⣧⣬⠻⣿⣟⡗
⠀⠀⠀⢀⠘⢈⡹⠗⠉⠉⠁⠀⠀⠀⠀⣠⢏⡶⢸⡇⣩⠞⡿⢋⡘⠗⢁⢾⡄⠀⠀⠀⠀⢸⣇⠩⠝⠁⠴⠟⠁⠀⠿⠣⡄⡻⣏⣸⠛⢾⣇
⠀⠀⠀⢸⡇⠀⠀⢀⣤⣤⣔⡄⠀⠀⠀⠑⣤⢛⢂⠿⣯⠘⢧⣤⠟⢧⣬⠀⢶⠆⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⣠⣿⠋⢛⣷⣲⠾⣷⢌⡅
⠀⠀⠀⠀⠃⠀⠀⠘⢷⣾⡯⣱⠆⠀⠀⠀⠘⠋⣹⡄⠀⢀⠼⣿⠄⠾⡉⣧⣘⠛⠳⡀⠀⠀⠀⠀⢀⡀⠀⠀⡼⣧⣸⣿⣩⣍⢙⣢⠿⣼⡇
⠀⠀⠀⠀⠀⠀⠺⠃⣀⣿⡵⢴⡗⠒⠀⠀⠀⠈⠉⠀⠀⢢⢴⡾⣠⣤⡟⢧⢼⠗⠞⢻⣆⠀⠀⢰⠉⠈⠁⠀⠠⠾⠷⡤⢿⣤⡿⠤⠄⠨⣷
⠀⠀⠀⠐⠟⠛⠶⠾⣟⠿⠗⡀⢹⣿⢦⠀⠀⠀⣀⠀⠀⢢⣼⢇⣤⣤⡀⢠⡴⢿⣿⡞⠋⠀⠀⠈⢧⡴⠞⠃⠀⠀⠀⣠⠀⠉
⠀⠀⠀⢠⣾⡛⣦⣴⡿⠦⠦⣼⠊⡟⠋⠀⠀⠀⠻⡤⠀⠀⠣⠼⢏⣉⠇⠁⠄⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠾⠂
⠀⠀⠀⠀⠈⠛⠛⠶⠿⠒⠶⠞⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣯⣭⣭⣤⣭⣽⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣧⣷⣷⣿⣾⣥⣥⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠂⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣹⣖⣠⢀⠀⡀⠀⠀⠀⠀⠀⡰⣌⠀⠁⠘⠀⠀⠠⠀⠁⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠱⢞⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⡷⣶⠿⠀⠀⠀⠀⠀⠠⠶⠀⠀⢶⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⣿⣿⣿⣿⣽⣭⣿⣿⣿⣷⣞⣶⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠐⠢⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡽⣿⣿⣿⣿⣿⣟⣮⣺⣾⣷⣾⣯⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣯⣿⣿⣿⣿⣶⣿⣦⣼⣿⣽⣿⡏⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢻⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣟⣛⣿⣷⣽⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣷⣿⣿⣯⣽⣿⣭⣿⣽⣯⣿⣿⠀⠀⠀⠀⢂⠠⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣟⣷⣴⣿⣿⣟⣦⣿⣿⣿⣿⡋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠀⠂⠨⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⣶⣿⣿⣿⣿⣿⣿⢏⡯⢩⣭⣝⡻⠃⠀⠀⠠⠝⠀⢂⡆⡀⠄⠈⠡⠠⠡⠤⣽⣯⣽⣿⣿⣽⣿⣯⣛⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣟⡛⡟⠀⠈⠀⠀⠀⠀⠀⡀⢁⠀⠂⠀⠀⠂⠈⠯⣭⣿⣿⡿⣿⣿⡿⣭⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⡿⢾⡿⣷⣾⡷⣿⣿⠂⠀⠀⠀⢀⡀⠂⡄⠀⡀⠀⣤⢾⠾⢄⠘⠍⡹⣟⡿⣿⡟⢻⣿⣙⣿⣿⣿⣿⠝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣯⣽⠷⣷⣿⣿⣿⡏⠀⠀⠀⠑⡄⠒⠀⠃⠀⣱⠴⣶⠀⠲⠾⠁⡶⠿⡟⢿⣿⣿⣾⣞⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣯⣿⣭⣿⣯⣿⢧⠀⡁⠠⣈⡵⠘⢀⡸⢟⡁⣀⣹⠓⢻⠤⢀⠰⠈⣿⢼⠿⠿⢿⠶⠿⢿⣿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣿⣿⣿⣗⣾⣿⣟⣟⣾⣿⠉⢀⠘⢤⡄⢀⡞⢻⠁⠈⠀⠉⠨⠛⣧⠀⠀⠠⢼⣿⣨⣽⣬⣬⣽⣟⡿⣿⣾⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣍⣯⣽⣿⣽⣿⠆⠴⠂⢯⣄⠈⠃⣀⣷⣶⣶⣶⣾⣰⣃⠀⠉⡡⢤⣭⣉⣷⣶⣦⣿⣍⣵⣿⢯⡝⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⢟⣋⣿⣟⡻⠫⢿⡖⠒⡴⠋⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡜⢀⣸⣧⣵⣬⣹⣻⣞⢁⢻⣿⣷⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣶⣿⣿⣿⡟⢋⡙⡿⡕⢣⡟⠐⠉⠢⣴⣿⣿⣿⣿⣿⠹⡏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡿⣿⠿⣛⣻⢿⣣⡿⠀⢀⣶⣿⠏⣿⡇⠙⠧⠀⠇⠸⠉⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣽⠧⢿⣿⣿⣿⢿⣿⡿⢷⣾⣿⣿⠄⡛⠃⠀⠀⠀⠀⠸⢁⡿⣿⣿⣿⢹⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣼⡷⣯⣿⣿⣾⣯⡼⣿⣯⣿⣿⠹⠀⠃⠀⠂⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠁⠀⠹⠈⠛⣫⢿⢿⣆⡾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣿⣻⣿⣽⣿⣻⣶⣾⣹⣾⣿⡟⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣗⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣫⢽⣾⣿⣿⣳⢻⣧⢿⠞⣮⣾⣿⣿⣷⡌⠠⢄⠀⠀⠀⢀⣮⣭⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡾⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⡙⣿⣬⣥⡞⣂⢻⣿⡭⣿⣿⣿⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠭⠻⡹⢿⠿⢟⣻⢿⣿⠟⠿⡿⠛⠛⠋⠉⠊⠝⠋⠗⠉⠛⠁⠀⠉⠑⠀⠀⠉⠈⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣶⠛⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣴⣿⣷⣿⣿⣍⣿⣾⡛⣻⣿⣉⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣸⠀⠐⢿⡿⠛⠛⠛⠋⠉⠉⠻⣿⣥⣿⣉⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠻⠇⠀⠗⠋⠀⠀⠀⠋⠀⠀⠀⣀⣤⡤⠀⠙⣿⣾⣏⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣆⠘⢋⠕⣶⡤⠀⢿⠿⠻⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡹⠀⠀⠀⠀⠀⠀⠁⠖⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⠠⠦⠀⠀⠀⠀⠀⢰⣏⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣒⠒⠂⠀⠀⠀⣠⣾⣿⠟⣿⣴⡀
⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⣤⣴⠞⠋⠸⡏⣴⣩⡷⣿
⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⣤⣄⣀⠀⢀⣀⢀⣠⣤⣤⣀⠀⠀⣽⡿⠛⠁⠀⠀⠀⢳⣾⣭⣷⠏
⠀⠀⠀⢸⡆⠀⠀⠀⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠙⠻⢍⣻⡁⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⡿⣷
⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣷⠀⠀⠘⠿⣻⡋⠛⠻⣄⠀⠀⠀⢠⡾⠁⣸⠷⣄
⠀⠀⠀⠀⠉⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢠⡟⠀⠀⠀⠀⣀⣀⣴⣶⣸⣆⡴⠞⠋⠀⢰⠏⠀⠈⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣹⣻⣿⡃⣘⠀⣶⠀⠀⠀⠉⠉⠀⢸⢧⣿⠞⠉⢻⡄⢾⠀⠀⡠⠀⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣟⣴⡟⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠑⠿⣠⠞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⠄⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠄⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠙⠀⡀⢸⣿⣀⣠⡤⠶⠶⣄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⠹⡿⠓⠚⣛⣓⠢⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠈⢢⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣷⣤⠶⠿⠿⣿⣯⡒⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢲⡀⠘⡇⣿⠀⠀⠀⠀⠀⠈⠀⣻⡧⠞⠋⠀⠀⠀⠀⠀⠈⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢄⠘⢦⠘⢾⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠛⠄⠀⠀⣃⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⡠⠤⠖⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢶⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢂⠈⡀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣼⠁⣶⣶⣆⡄⠀⠂⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣶⣿⡿⢿⣿⣖⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠠⠙⠄
⠀⠀⢀⣠⣴⠶⠆⠀⠉⠑⠲⢤⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠀⠀⠀⢠⡇⠀⠀⠀⠀⣂⠈⡄
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⠖⠚⠉⠀⠀⠀⠀⠀⠐⢦⡀⠀⢸⡇⠀⠀⠀⠀⣿⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣶⡾⣷⡀⠀⠀⣴⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⢻⣦⡀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⢿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⡿⣿⡿⠃⡄
⠀⠀⠀⠀⢀⣠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠚⠛⠹⠛⠉⢁⣄⠸⣿⣿⣿⣿⣷⡼⠁
⠀⠀⠀⢠⣿⣿⣿⠟⠁⠐⢻⣿⠋⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀⣀⣠⣶⣿⣿⡿⠿⠾⠿⠟⠋
⠀⠀⠀⠉⠁⠛⠋⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠓⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⡽⠋⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠚⠛⠉⠀⠛⣆⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠉⠒⠄⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠤⢄⣀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠑⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢲⡟⠓⠲⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡏⡵⠠⣤⡋⠀⠀⣴⠃⠈⠈⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠉⠃⢀⣴⠷⢤⣀⡀⠈⢦⣀⡠⠀⠛⠁⢰⡿⡆
⠀⠀⠀⠀⠀⠀⢀⣤⠞⣁⡠⢴⠖⠊⠉⠀⡸⠀⠀⠈⠉⠒⠦⢤⣁⠀⠀⠀⢸⡇⠹⡄
⠀⠀⠀⠀⠀⡴⠟⠓⠉⠀⠀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠉⠒⠦⢼⡇⠀⢳
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠰⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢷⠀⠀⢧
⠀⠀⠀⡼⠁⢀⠀⡀⠀⠀⡆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠈⡇⠀⠈⣆
⠀⠀⣼⠃⠀⠨⡇⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠁⠀⠀⠀⠸⡀⠀⠸⣆
⠀⠀⣿⠀⠀⠀⠉⠀⢀⡃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠉⠀⠀⠀⣧⠀⠀⢻⡄
⠀⢸⢹⡄⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠈⢇⠀⠀⢿
⠀⢸⢸⡇⠀⠀⠀⠎⠀⢠⠀⠀⠀⠀⢀⡇⠀⠀⠀⡀⠀⢰⠆⠆⠀⠀⠀⠀⠀⣸⠃⠀⠈⢆⠀⠸⣇
⠀⡇⠀⡇⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⡜⢃⠀⠀⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢠⠇⠀⠄⠀⠘⣄⠀⢻⡄
⠀⡇⠀⣷⠀⠎⠀⠁⠀⠀⠁⠀⢀⡞⠀⠘⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠄⠀⠘⣆⠀⣷
⢸⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢄⠀⠸⡆⢨⡆
⡸⢀⠆⢸⠀⠀⠀⠀⠀⠀⢀⡼⢡⣦⣴⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢀⡀⠹⡄⢇
⡷⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠇⠀⠙⢦⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣼
⡇⠀⠀⠸⡇⢀⡴⠊⠁⠰⣦⠀⣾⠁⠀⡆⠀⠀⠀⠙⢦⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠹
⡇⠀⠀⠀⠶⠋⠀⠀⠀⠀⢻⠄⣿⠀⠀⡄⠀⠀⠀⠀⠀⠙⢦⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇⠀⠀⠀⡇⠀⠀⠀⠈⠋⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢤⠀⡄⢶⠀⠀⠀⠀⠂
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠇⡟⢰⠁⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠾⠰⠇⠸⠂⠀⠀⠀⡄
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠯⠥⢤⣱⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣀⡀⣀⠀⡀⠀⣶⠀⠲⠀⠐⢁⡠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⢲⠀⢷⠀⢸⠀⠀⡆⠀⠀⢨⢸⡁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠒⠈⠚⠈⠊⠈⠊⠀⠉⠀⠈⠋⠑⠁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⢤⣖⣒⣛⣛⣛⣛⣛⣛⣛⣒⣶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⢸⣤⣒⣒⠉⠛⠛⠛⠉⠑⣒⣒⣦⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠠⠭⠍⠀⡇⠀⣠⠖⠉⠉⠲⢤⣤⡤⠖⠋⠁⠀⠀⡇⠀⠀⢸⡀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠥⠖⠀⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣒⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠧⠤⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣾⠂⠀⠃⣼⣧
⠀⠀⠀⠀⢀⠞⢻⡇⠀⢹⣿⣇
⠀⠀⠀⠀⣿⣷⣾⡇⠀⠸⣿⣿
⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣁⡌⠙⣦⠀⠀⠀⠀⢀⣴⠿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠘⣧⠀⠀⠀⡼⢋⣀⠀⠀⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠸⠲⢄⠀⠂⠀⠉⠀⠚⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⣶⣬⠀⠀⠈⢧⣀⠘⠟⠻⢆⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⣿⠀⠀⠀⠈⢻⣧⣤⣴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠉⡿⠿⠟⠒⠙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⣿⣇⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⢿⣿⣦⣀⣀⡴⠁⠀⠀⠀⠀⠀⢂⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠈⣽⡯⠰⣿⣦⣄⣀⣀⣭⣿⣦⡐⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠀⢀⣀⣀⡈⠙⠿⣿⣿⣿⣿⠃⠻⣦⣀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠀⠉⠻⢶⣦⣶⡿⣿⠃⠀⠀⠈⠙⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣩⣿⣿⡾⠃⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⢶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠲⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡎⢦⣤⣤⣤⣤⡰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣿⣟⢥⡹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠉⣻⣿⣿⠃⠀⠀⠀⠀⠀⠻⢿⠈⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⣃⣻⣤⣭⣭⣭⣬⣥⣭⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⢶⣶⡶⠶⠾⠿⠿⢿⢿⡿⠿⠿⠿⣷⢶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⣿⢸⡀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣀⣧⣷⣀⣀⣀⣀⣸⣠⣇⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣿⣸⣀⣀⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣤⣀⡀⣀⣀⣀⡤⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⡉⠉⠉⠉⣁⣠⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠹⣄⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⣦⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⢧⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠈⢳⣽⡇
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⡤⠖⠛⠓⢦⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢠⣿⡀⠀⢀⡞⠁⠀⠀⠀⣸⠃⠀⠀⠀⡟⠀⠀⠀⠹⣄⠀⠀⠀⣴⠖⠒⢦⡀⠀⠀⠀⣿⠷⠦⣄⠀⠀⢠⠶⠒⢦⡀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⡟⠙⠛⠉⠀⠀⠀⠀⠀⠻⣄⠀⠀⣠⠇⠀⠀⠀⠀⠙⠲⠤⠞⠃⠀⠀⠀⣇⠀⠀⢸⡏⠀⢀⡟⠀⠀⢸⠀⠀⠀⡇⢀⣼⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⡇⠀⢸⣇⠀⣀⡼⠀⠀⠀⠉⠉⣿⠃
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⣿⢿⣆⣴⣾⡆⠀⣀⠀⠀⣿⠇⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⠈⠛⠁⢸⣇⠀⣩⡀⠀⣿⠀⠀⣿⣴⣿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠹⠇⠀⠀⠸⣿⠀⢿⠇⠠⡿⠀⠀⣿⠉⠻⣦⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣀⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⣀⡀⣠⠀⠀⠀⢤⣤⣤⡆⠀⠀⠀⠀⠁⢀⣤⢴⣦⡰⠀⢀⣠⣷⣾⣶⠀⠀⠀⠌⠀⢘⡀⣤⠄⠀⣰⡄⠂⣀⢬⢠⣔⣄⣼
⢀⣀⣈⣽⣿⡿⠛⠀⠐⣶⣾⣿⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⠛⠁⠀⠈⢹⣟⡏⠀⠀⠀⠀⠰⢿⣾⣵⣿⣿⠟⠛⠀⠈⠻⢿⣿⣻⡏⠉
⠀⢰⣿⠟⣿⡁⠀⠀⠀⢹⠏⣿⠀⠀⠀⠀⠀⠀⠀⠸⡏⡿⠀⠀⠀⠀⠸⢸⠇⠀⠀⠀⠀⠀⠀⠙⡯⣿⡿⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠙⢰⣿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⢩⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣤⣆
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠋⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣆⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⣳⣇⣿⡀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⢤⡼⣇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⢭⡿⣧⡀⠀⠀⠀⠀⠀⢦⣷
⠀⣌⢁⣽⢭⣿⠀⠀⠀⠰⢿⡾⣆⠀⠀⠀⠀⣀⣸⣿⣇⣀⣷⠀⠀⢰⣿⡏⠳⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⠀⠀⠀⠀⠈⢹⣿⣇
⠀⠙⠛⠉⠛⠃⠀⠀⠀⠷⠞⠿⠏⠀⠀⠀⠀⠈⠉⠀⠙⠛⠉⠀⠘⠛⠉⠻⠟⠃⠀⠀⠀⠀⠘⠛⠋⠀⠛⠁⠀⠀⠀⠰⠶⠋⠙⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣧⠀⠀⠙⠛⠛⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣇⣽⣟⠀⠀⠀⠀⠀⠀⠋⠓⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢟⣿⣥⣧⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⡀⢀⣀⠄⣀⣸⣿⣿⣿⣷⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⢁⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⠛⠛⠁⢺⣸⣿⣿⣧⣿⣿⣿⣿⣿⡿⣿⣶⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⠋⠀⠀⣶⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠸⢰⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠆⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠃⣿⣿⡇⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣼⡇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡝⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣣⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠷⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠶⣤⣤⣄⣀⠀⢀⣀⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠞⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢸⡆⠀⡇⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣾⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⢸⣀⣀⣧⣤⣧⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⣀⣠⣽⣤⠶⠷⠛⠛⠉⠉⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢷⡖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣄⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢀⡼⠃⢀⣀⣤⡤⠴⠶⠚⠛⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢠⡿⠷⢿⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠿⣦
⣿⠁⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠋⠉⠁⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣀⣘⠆⣀⣀⣤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢸⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⡄⠰⡟⣷⠞⣹⠆⠸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢸⠀⠀⢰⠲⡆⠀⣾⣆⠈⣏⢿⢻⡘⡇⠀⣷⠀⢠⣏⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠙⢶⠇⠹⡆⢻⢸⣼⡇⣿⣀⣽⠀⣶⣝⢦⡀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⠀⢀⡀⢹⣼⡎⣿⣧⣈⣠⣿⣧⡽⠘⠾⠁⢸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⡟⣧⢘⣿⣦⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠚⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⣿⠀⠀⣒⠦⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⢠⣭⣟⡒⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠈⡇⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢹⡀⠀⢇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⣧⡀⠈⠳⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞
⠀⠀⠀⠀⠀⠉⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⣸⣤⡶⠞⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠘⣦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡋
⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣇⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠈⠳⢤⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⡴⠋⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣷⣿
⠀⢸⡿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢟⣭⣴⢿⣿⢿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⠿⣻⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢽⣶⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣏⣽⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣄⣀⠀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢀⣾⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠻⣷⡀⣼⡟⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣷⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡄⢻⣶⣿⠁⣿⣿⠀⠀⢿⣿⡇⠀⢸⣿⣇⠀⠀⠀⠀⢸⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠇⠈⠻⠃⠀⣿⣿⠀⠀⢼⣿⡇⠀⢸⣿⣿⣶⣶⣶⡆⢸⣿⣇⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣧⣿⣿⣿⣿⣿⣿
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⠉⢉⣭⣍⡙⠿⢶⣶⣶⣶⠶⠋⠉⠻⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠯⡭⠤⠤⣤⣀⡘⠻⣿⣇⠀⠈⠛⠛⠋⠠⣿⣆⢠⡀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢡⣿⠇⢠⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣄⠀⣿⣀⠀⠀⣀⣠⣤⣤⣀⡀⠈⢆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⣿⠀⠀⠉⠁⠈⠛⠛⠛⠙⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⢻⣻⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⠟⡀⠀⠀⠀⠀⠀⠀⡧⠞⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣾⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⣤⣤⣿⣧⣼⣿⣥⣤⣤⣤⣤⣤⣼⣿⣥⣤⣷⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣵⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣶⣤⣤⣤⣶⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⡿⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠀⢰⠀⡠⢀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⣀⠀⡆⠀⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⢄⣉⣡⣍⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠷⠂⠐⠾⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣌⣉⡠⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⡀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⠢⠧⠴⠜⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠛⢦⣼⣧⡶⠛⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⣿⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠿⣿⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿
⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣷⣶⣶⣆⣀⠀⠀⠀⠀⠀⢀⣠⠀⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⣄⡀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠤⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣧⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡀⡟⠀⠼⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡄⢈⠁⠀⠠⡘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠴⠁⣿⠀⠀⠀⡁⠸⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢠⡀⠀⡿⠀⠀⠀⢁⠀⢿⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠈⠀⢸⡇⠀⠀⠀⠘⠃⠸⣇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠸⠇⠀⢸⡇⠀⠀⠀⠀⠤⠀⢹⡄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡆⠀⠀⣸⠁⠀⠀⠀⠀⢠⠀⠀⢷⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣈⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠂⠀⠘⣇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠠⠍⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠶⠀⠀⢸⡆⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⡀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣷⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡆⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢹⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⣷⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢈⡷⠸⠂⠀⠀⢠⡏⠀⠀⠀⠀⠀⢰⣆⣤⡄⠀⠀⠃⠀⠀⠀⠀⢱⡄⢠⡌⣷
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⠷⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡏⠀⠀⠘⠀⠘⠃⠀⠀⠀⠈⠁⢸⡇⠨⣇
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠧⠀⠀⠀⠈⣄⠉⠀⠸⣇
⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⢿⡀⠀⠀⠙⣄
⠀⠀⠀⠀⣼⠉⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⢳⡀⠀⠀⢹⡆
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢷⡀⠀⠀⢱
⠀⠀⠀⢰⡏⠀⢹⡀⠀⠀⣰⠆⠈⠀⣤⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠄⠀⠀⢣⡀⠀⠘⣇
⠀⠀⠀⢸⡇⠀⢸⡇⢠⡶⠀⠀⠀⠀⠀⠰⠆⠀⠀⣿⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠠⠄⠀⠈⢷⠀⠂⣿
⠀⠀⢠⣿⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⡀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣤⠀⠈⣷⠀⢹⡆
⠀⠀⢸⡏⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠀⠈⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⢧⠀⣇
⠀⠀⣾⡀⠊⠀⠈⣇⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⢠⡆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⢶⣹
⠀⠀⣿⠁⠀⠀⠀⣿⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠹⢦⡀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿
⠀⠀⣿⠀⠀⠀⠀⣿⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣰⡆⠛⣄⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⢠⡄⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢶⡄⢦⡀⣦⠀⢀
⢰⡇⣰⠇⣴⡁⠀⣿⠀⠀⠀⠀⠀⠀⢈⡿⢀⡿⢹⡇⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⡾⢁⡾⠀⣿⠀⠻
⠀⠀⣿⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠈⠛⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃
⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣐⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠈⠠⠀⠂⣀⣀⡀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠁⠀⠀⠀⠀⡀⠀⢴⣤⣠⣴
⠀⠠⠀⠀⠀⠀⡴⣻⣿⣿⣿⣶⣶⣤⡧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣧⠀⠈⠀⠉⢠
⠀⠀⠆⢸⣄⣼⢷⣿⣾⣿⣿⡿⡿⣿⣿⣿⡀⠀⠐⠀⠀⠀⣠⠀⠀⠀⢸⢸⡇⠀⠀⣰⣤⣾⠿⣧⡄⠈⠐
⠀⠀⠼⣆⣿⣷⣾⣿⣷⣤⣿⠟⠛⣿⣿⣿⣷⠀⠀⠠⠁⢀⣸⠀⣠⠀⣇⣾⠀⠀⣺⣟⡅⢇⣠⢈⢙⠀⠻⢈
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣂⠠⣴⣿⣿⣷⣦⣤⣀⣸⣮⣡⣸⣼⣷⣿⣛⣻⠋⠙⡿⣿⣾⣿⡆⠂
⠀⠀⠀⣿⣿⡟⢿⣿⡿⣴⣿⡿⣻⣿⣀⣹⣿⣿⡿⣿⣿⢿⣿⢿⣿⠿⣿⣻⣿⡿⣿⣧⣾⣟⡿⢟⣿⣿⣾
⢀⠀⠙⢿⡿⣿⣿⣿⣘⣧⣤⣿⣿⣦⡶⡛⢛⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣯⢹⣛⣾⡏⠽⢿⡿⣿⣿⣿⣿⢀⣀
⠙⠀⡀⢀⡿⡿⢂⣿⡻⡿⡛⠋⣩⢎⣙⣛⣇⡻⣿⡇⣘⣿⣿⣿⣿⣿⣿⣿⡳⣿⢻⣇⠀⣸⣿⣟⣻⣯⣿⠀⠁
⠀⠙⡅⠃⢀⣤⣿⡞⢝⣯⣼⠻⣴⣠⠟⡸⣶⢃⣿⣿⣿⣻⣿⣿⡿⡿⣿⣿⣧⣿⡿⡽⣿⣿⡟⣯⣟⡻⢟⡇
⠀⠀⠰⡛⣏⣹⣷⣃⣅⣯⠿⣹⣾⣭⣴⣿⣸⡿⠿⢿⣿⣿⣿⣿⣷⣿⣿⡏⣈⡙⣽⣿⣿⣷⢻⡟⣿⣷⣿⡇⠂
⠀⣀⣀⢰⣿⢿⣯⣭⣙⣿⣿⣿⣿⣿⣿⣿⡏⣠⣷⣗⣿⠿⡇⢉⡉⢘⠛⣓⠾⣷⡏⣿⣿⣟⡟⣋⢿⣾⣉⠁⢁
⠰⠐⠢⢼⡗⢼⣿⣿⣿⣿⣙⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣷⣥⣮⣤⠒⣷⣿⣴⣾⣿⣿⡟⠛⠢⡐⠖⣿⣼⡋⠁
⠀⠀⠀⠈⣿⣻⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⡟⢿⣧⢴⡿⠟⡛⣿⣃⣸⣇⣴⣾⣷⢴⡏⣹⠋
⠀⠀⠀⠀⢿⡿⣽⡵⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣰⣤⣾⣿⣿⣿⣀⣋⣥⣀⣽⣿⠏
⠀⠀⠀⠀⠘⠀⠻⠐⠁⠀⠀⠁⠙⠋⠁⠈⠙⠁⠀⠉⠉⠙⠛⠙⠛⠛⠛⠛⠙⠋⠉⠙⠋⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠡⡐⠆⡄⡰⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣊⣲⣿⡇⠀⣉
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠍⠹⡑⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⢸⣑⣿⠄⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠁⢰⣶⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠒⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠰⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠙⠃⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠉⢀⠀⠀⠀⠀⣤⣟⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠐⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⠀⠛⠃⠀⠀⠀⠋⠿⠀⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠱⡆⣾⠀⡠⠀⠺
⠀⠀⠀⠀⠀⠰⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠹⣿⣠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣤⣄⣀⠀⢸⣿⣦⣖⢦⡀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠿⢿⣶⠿⠿⣿⣿⣦⣿⣿⣿⣿⣿⣷⣺⣶⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣷⣶⣶⣶⣿⣦⣭⠿⢿⣿⣿⣿⣿⣿⣷⣬⡉⠳⢆
⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣟⢻⣿⣿⣿⣿⣿⠟⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡥⡀
⠀⠀⠀⠀⢠⣿⣿⣿⠏⣾⣷⣲⣾⣿⣿⣿⣿⢟⣿⣮⢉⣿⣿⣿⡿⣚⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣻⣆
⠀⠀⠀⠀⡼⢿⣿⣿⣠⣹⣿⢿⣛⣿⣧⡋⠁⣈⣹⡿⣷⡝⠻⡜⡿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣯⠹⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣣⣸⣿⣿⣿⣾⣷⣦⣿⢿⣿⣿⣷⣿⣿⣿⣷⣿⣷⣾⣤⢹⣿⣟⡵⠛⠛⠿⢿⣿⣿⣿⣷⣄⢻⡿⣿⣭⡇
⠀⠀⠀⢸⣿⡟⣿⣿⠟⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⢿⠿⣄⠀⣸⠑⠲⣿⢻⣿⣿⣿⡿⡷⣴⣿⣿⣿⣿⣦⡀⡟⢸⣧⡀
⠀⣀⣤⣿⣿⣿⣿⡏⢱⣿⣿⣿⣿⡿⣿⣯⡟⠉⠊⣤⣄⣿⡈⢃⢇⠀⠹⣯⣿⣿⢿⢧⣟⣿⣿⣿⣌⠈⣿⣿⢛⡿⢿⣧
⠘⣷⢿⣯⣿⣿⣻⣷⣼⣿⣿⡿⢛⣿⡿⠀⡀⠰⢻⣷⣿⣿⣧⠰⣾⣄⠀⢻⣿⣿⣷⣿⣿⣟⣿⣿⣿⡂⣿⣿⣏⣳⡰⠃
⠘⣷⣾⣿⣿⣿⣿⣷⣿⣿⣿⠿⢋⠝⠗⠉⣉⣷⣿⣿⣿⣿⣿⡄⠸⢻⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠘⢿⣻⣿⣿⣿⣿⣽⣿⣿⢟⠕⢧⣥⣾⣿⡏⠉⠛⢿⣿⡿⣿⡀⢡⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠇
⠀⠀⠀⠛⢿⣿⣿⣿⣿⡿⠇⣀⣴⣿⠛⡋⢘⠎⠳⣤⣶⣿⣷⣿⣷⡀⠻⣿⣀⣾⣿⠿⣿⡿⠛⠋
⠀⠀⠀⠀⠈⢿⣿⣿⠿⡿⠍⢿⡿⢷⣶⣶⣤⣶⣿⠾⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠛⠺⠟⠿⠿⠁⠀⠉⢿⣿⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠐⠒⠲⠤⠖⠒⠲⢤⠴⠒⠒⠒⠊⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⠀⠀⠐⠲⠶⠶⠶⠶⠒⠒⠒⠒⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⣤⠒⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠉⢧⡀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢶⣄⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠳⢦⣀⡰⠎⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠹⣆
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⡙⢇⠀⢠⠻⡆⠀⠀⢸⠋⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡉⡇⠀⣀⡤⢶⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠸⠃⠈⢷⡎⠀⠻⡀⠀⠘⠀⠇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡆⠰⠞⠁⣠⠏
⡇⠀⠀⠀⠀⠀⠀⠇⣠⢦⡀⢀⣤⡀⢣⡀⠀⡆⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⣞⠁
⡇⠀⠀⠀⠀⠀⢰⢀⡉⠀⠳⠎⠀⢳⠈⢧⠀⣇⢸⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⡇⢸⣧⠘⠦
⣿⠀⠀⠀⠀⢀⡇⡜⠁⠀⠀⠀⠀⠀⢧⡈⡇⣿⢈⠀⠀⣇⠀⠛⠛⠛⠂⠒⡄⠃⠸⠈⢧⠘⢣
⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⠇⠈⠛⠀⠀⠘⠓⠒⠲⠖⠒⠋⠀⠙⠃⠀⠈⠳⠞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠐⠒⠒⠲⠶⠶⠶⠶⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠁
⡇
⢣
⢸
⢸⡆
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟
⠀⠀⠻⣷⣶⣤⣤⢤⢤⣤⢤⣤⣤⢤⣤⣤⣤⣤⣤⡤⣤⡤⠤⣤⡤⠤⠤⢤⡤⠲⠲⠖⢶⠖⠒⣩⡟⣻⠟⠁
⠀⠀⠀⠈⢿⣀⣳⣀⠀⠳⠀⠈⠃⠀⠘⠃⠀⠉⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣞⣡⡞⠁

⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⢀⠐⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠒⢄
⠀⣀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠿⠟⡃⠀⢀⡀⣸⣤⣤⣀⣰⡇⠀⠀⠀⠀⣦⣠⣤⣠⡆⠀⣀⡀⡁⠀⠀⠀⠀⡀
⠘⢿⣿⣿⣿⣿⠟⠋⠀⠺⠿⠛⠇⠀⢠⠶⠁⠀⠢⣤⣤⣾⣿⣿⠝⠁⠀⠀⠤⣤⣴⣿⣿⠋⠁⠀⠄⠀⠀⠀⣠⡤⠒⠀⠀⠀⠀⢀⣠⠔
⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⢾⡀⣠⠀⠎⠀⠀⠀⠀⠱⢿⠟⣿⣇⠀⠀⠀⠀⠀⢿⡟⢻⡇⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠹⣿⣿⡏⠀⠀⠀⠀⠘⣧⣿⠀⠃⠀⠀⠀⠀⠘⡞⢠⣿⠇⠀⠀⠀⠀⠀⠐⠁⣿⡇⠀⠀⠀⠀⢱⡀⠀⢡⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢰⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⠀⠀⠀⠀⢸⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠇⠀⢠
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⢸
⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢸⢿⠀⡆⠀⠀⠀⠀⠀⠰⡄⣿⠀⠀⠀⠀⠀⠀⠀⢰⣼⡆⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⢨⣿⣿⣿⡀⠀⠀⠀⠀⢸⠰⡆⠇⠀⠀⠀⠀⠀⣿⣿⣻⣆⠀⠀⠀⠀⠀⢈⣿⣸⣇⠀⠀⠀⠀⢈⠃⠀⠀⣄
⠀⢰⣿⣿⣿⣿⡗⠀⠀⠀⡰⣾⠆⢐⠂⠄⠀⠀⠀⣎⠀⣽⠧⣿⠀⠀⠀⠀⢠⡁⣸⡿⣼⡇⠀⠀⢀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠛⠋⠉⠛⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠙⠛⠉⠛⠋⠀⠀⠀⠀⠈⠛⠋⠉⠛⠀⠀⠀⠀⠃⠐⠙⠂⠈⠀⠀⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⣖⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⣁⣴⣿⣿⣿⣿⠛⠛⢻⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠟⣵⣧⣤⣶⣿⣿⣛⠋⠙⠺⣧⠀⣿⡟⠃⢸⣦⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄⣤⠀⣠⡶⡿⠀⣼⣿⣿⣿⠟⣁⣽⣿⣶⣤⠀⠀⠙⣿⡇⠀⢸⣿⢲⣲⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠛⠛⠉⠈⠐⣿⣿⠟⠛⠀⣰⣿⣿⣿⣿⡟⢷⠀⠀⢯⣷⠀⠀⠻⢶⣿⣿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣦⡀⢀⠉⠁⢀⣴⣦⣿⡿⠃⠀⠀⣠⣿⣿⢏⣵⡎⡟⣻⡆⠀⢸⡿⣷⣤⡀⠀⠁⠀⣀⣬⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣻⠕⠀⠀⣰⣿⣿⣏⣾⣿⡇⣿⢿⣇⠀⠈⡇⠐⠛⠿⠿⠿⠿⣿⡧⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⢄⠐⡯⠍⠀⠟⠈⠀⣀⣤⣴⣟⣉⣑⣫⡽⢯⡰⡼⣞⣿⣦⡀⠈⠒⠒⠐⠒⢖⣺⣭⣠⢀⡇⣠⡆
⠀⠀⠀⢀⣦⣴⣶⡄⢀⠀⠙⠂⡀⠤⣴⡇⢀⣀⣰⣴⣾⣿⣿⣽⣯⣾⣿⣿⠁⠈⢿⣿⣼⣟⣿⣿⣷⣦⣀⣀⣰⣿⣿⣶⣿⣿⣿⣿⣿⡄
⠀⠀⢀⡾⠿⢿⡿⣿⣿⣦⣼⣧⣤⣴⣾⣿⣿⡿⣿⣟⣛⣿⣿⣿⣿⣿⠟⣿⣇⣀⠘⢿⣿⣟⣿⣟⠿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣷⣤⣾⣥⡾⠽⣿⣿⣿⣿⣿⣿⣿⣶⣭⣏⣭⣶⡶⠿⢋⣿⣿⠾⢟⠿⠻⣷⣀⠻⣿⣿⣿⣷⣽⣿⣛⣻⣟⡽⢿⣿⣾⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⣿⣿⠿⢿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣥⣤⣾⣿⠿⠖⠒⠿⠳⣶⣝⠿⣷⣍⢻⠿⠯⠽⠋⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣍⣿⣿⣿⢿⣿⣿⣿⠿⠿⠟⢛⣉⣤⣦⣤⣤⣤⣀⣤⣤⣭⣾⢿⣿⣦⡂⠀⠐⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⢸⣷⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣾⣿⣿⠿⡷⠞⠉⠈⠉⠉⠉⠉⠙⠛⠛⠛⠿⣿⣿⣥⣽⣻⣿⡶⢖⠻⠷⢋⣭⣫⣿⣿⡿⠋⠁
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣤⣤⣴⡾⠟⠛⠉⠉

⣷⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠚⢻⠛⠉⢹⠉⠉⠏⠉⢹⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⠼⠦⠶⠾⠖⠒⠛⣛⣋⣉⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⠽⢦⡀⠀⠀⠀⠀⠀⣾⡏⠀⠙⡆⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠚⠁⠀⠈⠳⣄⠀⠀⠀⠀⠻⣿⣦⠾⠁⠀⠀⢀⣈⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠿⣶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠤⠶⠶⠖⠒⢹⡇
⠀⠀⠀⢠⣟⣛⠓⠒⢶⣄⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠖⠒⠒⠢⠤⣀⣀⣇⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⢧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡜⣷⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⢀⡇⠀⣄⣀⣀⠠⠄⣶⢸⣿⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⢾⡇⠀⠀⠀⢸⡇⢸⡏⠉⢹⡜⠇⠙⠈⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠙⠒⠒⠒⠊⠉⠉⠉⡏⣿⠀⠀⠀⠀⢸⡇⠀⠀⢠⠖⠳⣄⡰⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠉⢆⠀⡴⢺⡏⢦⣀⠜⠀⠀⠈⠀⣀⠀⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡟⠉⠓⠶⢤⣄⣸⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣭⣒⣒⣒⣤⡤⢤⣔⣚⣥⠞⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠾⢛⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⢀⠀⣤⣦⡀⠀⢀⡞⠀⣼⠇⠢⣽⣿⡟⠛⢷⣦⣤⠀⠀⠀⡶⠀⠀⠀⠰⢄⡀⠀⠀⠀⢀⠀⠴
⠀⠀⠀⠀⢰⠀⠈⢀⣿⣿⣿⣯⣉⡠⠂⠸⡁⠀⠈⠻⣧⠀⠈⢻⣿⣶⣶⣿⣧⣤⣄⣀⣀⣾⡿⣿⣷⠀⡸⠠⠖
⠀⠀⠀⠀⠀⠀⣿⣬⣿⢿⣿⠋⠻⣿⡀⠀⢈⣦⣤⣤⣼⠃⠱⣄⣿⡟⠳⢿⠿⣿⠋⢉⡽⠟⠛⠿⢿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⡛⢿⣤⣹⣿⣶⣿⣿⢿⣿⣿⡃⠀⠈⢻⣷⠀⠀⠀⠈⠙⠛⠀⠀⠠⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠈⣡⠀⠙⢷⣤⣌⡹⢿⣿⣿⣿⡛⢿⢿⣿⣦⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⡶⠘⣿⣄⠀⣹⠿⣇⠀⢈⣾⢿⣿⣿⣆⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠃⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣬⣽⣿⠋⠀⢿⣷⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣷⣤⣴⣾⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⠟⠻⠿⠻⣧⣄⠀⠻⣿⣿⠙⠿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⢸⡁⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠿⡟⠉⠀⠀⠀⠻⠿⣿⣧⣄⢹⣿⡀⠀⢉⠏⣹⣿⠀⢀⣀⣀⣀⠀⠼⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣷⣶⣿⣆⠈⣿⣴⠟⠉⣬⣁⡿⠶⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣄⣰⣿⣷⡶⠂⠈⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⢶⣶⣄⠀⠀⠀⠀⠀⠀⠙⡶⠼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣤⣤⡶⠋
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠌⠀⢠⣴⣿⣿⠿⣷⣿⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⢁⣼⠟⠋⠁⠐⠛⢻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠙⠻⣿⣿⣤⡀⠐⠿⠋⠀⠀⠀⠀⠀⣼⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠤⠤⣉⡐⠁⠀⠀⣀⣀⣤⣤⣠⣴⠟⠉⠀⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣜⣛⠁⠀⣀⣀⣀⡀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣷⠀⢻⠿⣿⠅⠀⠀⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣿⣧⣶⣶⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠦⠤⠛⠟⠀⢀⣾⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠉⠉⠁⠀⣰⣷⣿⠏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣶⣤⣾⡿⣯⡝⠀⠀⠈⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⣿⣿⣿⡟⣹⣿⠁⠀⠀⢀⣠⣶⠊⣡⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠇⣿⣋⣩⣽⣿⣿⣇⣿⣿⡶⠤⠴⠟⢻⠃⢰⠇⠀⠀⠀⠙⠓⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠀⠉⠩⠀⢸⠀⠀⠈⠉⠻⣿⣿⠁⠀⠀⠀⢀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠑⡯⠀⠀⠀⠀⠀⡸⠀⢰⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡆⠸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠃⠀⢼⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣾⡷⠀⠀⠁⠘⢿⣷⣀⡅⠀⠀⢣⡀⠀⠀⢠⣷⡀⠀⠀⠀⡜⠀⠀⣿⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠩⣿⣿⣿⡄⠀⠀⠀⠱⢤⣀⣼⣿⡃⠀⣠⠞⠀⠀⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⣀⣀⣤⣿⠟⠉⠛⠋⠁⣀⣀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠛⠉⠙⠛⢧⣄⡀⠀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣿⡏⠀⠀⣠⣾⣿⣿⣿⣿⣵⣦⣤⣤⣤⣄⡤⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣍⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⠀⢀⠠⠃⡸⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡅⡼⠁
⠀⠀⠀⢿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡾⠋⡾
⠀⠀⠀⢸⣇⢰⣶⣶⣄⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣉⣱⣒⣛⣳⣾⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠚⠉⠉⠉⠀⣿⣿⡿⠟⠛⠉⠁⢠⠉⠻⠟⠻⢿⣿⣿⣿⣿⣿⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠶⠓⠒⠛⠚⠚⠓⠒⠒⠒⠒⠢⠤⠅⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠻⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢣⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⣶⣦⣤⣤⣄⡠⢄⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⡀⠀⠀⢇
⠀⢠⣦⢶⠒⣀⣤⡀⢐⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡯⣶⡵⣂⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣬⣓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⢀⣤⣀⡀⠄
⠀⠀⠀⠀⠀⡐⡰⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⠿⣻⠂
⠀⠀⠀⢀⢠⣷⣻⣿⡿⢿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⢷⣶⡔
⠀⠀⠀⠶⠿⠿⠛⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠻⣿⣿⣿⣿⣯⣟⣿⡿⠻⠛⠛⢉⣥⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡹⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠙⢻⣿⣿⡅⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⡿⣿⠏⠀⠀⠀⠀⣽⣿⡷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⡯⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⣽⣿⣿⣿⣿⣟⠭⠊⠁⠀⠀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⣞⡽⣻⠽⡫⠅⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠩⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⣶⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣻⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡝⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡷⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⠫⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⢹⡏⠉⠁⠀⢈⡽⡅⠀⠀⢿⣯⠉⠉⠉⢉⡟⡏⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣿⠀⠀⠀⠀⡇⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⣤⣤⣤⣴⣷⣧⣤⣤⣼⣷⣤⣤⣤⣼⣷⣧⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣿⢦⣄⣀⣀⣤⠴⡎⣿⠀⠀⠀⠀⠀⠀⠀⣼⢳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣤⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠱⡄⠀⣷
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⣆⢹⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢮⣷
⠀⠀⠀⠀⢠⡏⠀⠀⣠⠖⠋⠙⣆⠀⠀⠀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⢸⡧⢤⠴⠁⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠹⣄⣀⣠⠋⠉⠑⡄⠀⢀⡟⠉⢳⠀⠀⡞⠉⢱⡄⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠓⠤⢼⡇⠀⣏⠀⢀⡇⠀⠈⠓⢺⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠉⠉⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣴⣦⠀⣠⡄⠀⠀⠀⣶⠀⢠⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠘⠟⢹⡇⠐⣃⠀⣿⠀⢸⣤⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠃⠀⠀⠿⠀⠟⠀⠟⠀⢸⠏⠻⣆⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⠶⠟⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠾⠛⠋⠉
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⠴⠞⣛⣉⡙⣦⡀
⠀⠀⠀⠀⠀⣾⡟⠛⠉⣉⣉⣻⣾⠹⡆
⠀⠀⠀⠀⢀⡟⠴⠂⠀⣀⣀⣈⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠄⠀⠀⣀
⠀⠀⠀⠀⢸⡇⠐⠋⠡⣤⣀⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠀⠠⣤⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⣯⣴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢸⠀⣰⠀⠀⠀⣸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠸⣇⠘⠓⢶⣚⣫⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠞⣳⣒⡫⠍⠂
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠽⣄⠻⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠺⠿⢶⣤⣾⣤⣄
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠘⢦⠙⣦⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣌⢳⡄⠙⢶⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠀⠀⠀⠈⢷⣄⠀⣸⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⣄⠀⠻⣦⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠻⣿⢠⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⢦⣈⠻⢶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⠀⢀⠈⢷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠰⣄⠈⣿⡷⣄⢀⣀⠀⠀⠀⠀⠸⣇⠹⡆⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠈⡇⣸⠀⠘
⠀⠀⠀⠀⠀⠀⠸⣇⠚⠀⣿⠈⠚⠛⠒⠂⠀⠀⠀⠀⣿⡿⡅⠦⣤⣤⣤⣴⠾⠋⢀⣴⡣⠀⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠸⣦⡀⠀⠀⠀⠀⠤⠤⠞⠁⣧⠀⠀⠀⠀⠀⣀⢄⣀⢯⠏⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⡛⠛⠶⠶⠶⠖⠂⠀⠀⠏⢀⡆⠀⠀⠀⠈⠳⠥⠬⡇⠀⠀⣾⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢦⡀⠀⠀⠀⠀⢠⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠈⠻⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣙⠓⠒⠒⠀⢀⣠⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⣠⣄⣀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⢠⣾⢰⣿⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣯⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⠟⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⣀⣠⣄⠀⢀⡀⠀⢀⠀⠀⣄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠻⠟⣿⢈⠌⠁⡁⠉⠘⢶⣿⠻⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄⠀⠿⠎⠂⠀⠉⠀⠈⢿⠏⠀⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⣀⣀⣀⢀⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢩⣍⠉⢉⡥⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢡⡌⠉⢉⡤⠵⠆
⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⣠⠔⠛⠲⠣⣈⠀⠀⠀⠶⠜⠓⠦⣀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠤⠤⠤⠄⣀⡀
⠀⢰⠂⠀⠝⠓⠲⠖⠲⢚⡂⠀⢙⡶⢤⣄⣠⠎⣡⠄⠛⠶⠖⢸⠉⠉⢻⠶⠶⠛⠢⣄⠰⣄⣀⣤⢶⡛⠁⢒⣓⠒⠒⠶⠞⠫⠄⠀⡄
⠀⠀⢢⣠⣤⡀⢀⡤⠖⢦⡈⠝⠋⡩⠖⣤⣍⠘⠓⠒⠒⠉⣻⣼⣛⣛⣺⣟⠙⠛⠒⠚⢋⣉⣥⡶⢍⠛⠋⢁⡴⠦⢤⣀⢀⣤⣄⡔
⢠⠚⠀⠀⠀⠙⣇⡀⠀⡠⠀⢀⣼⢁⠊⠀⣉⣱⣤⣀⠘⠋⠀⠀⠈⠉⠀⠈⠙⠂⣀⣠⣎⠉⠀⠑⡀⣧⡀⠀⢄⠀⠀⣸⠋⠀⠀⠀⠓
⠸⡀⠀⠀⠀⣠⡇⠀⠀⠁⡰⠉⢿⡌⢶⣉⡀⠀⠀⠉⠻⣤⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢈⣁⡶⢡⡿⠙⢦⠈⠁⠀⢈⣄
⠀⢱⠀⠀⣰⠋⢃⡀⠀⠸⣣⠟⣩⠻⢦⣙⠣⠬⢍⡥⢤⠄⢧⠀⢀⡀⠀⣼⠣⡤⢈⠭⡭⠔⣋⡴⠛⣍⡻⣌⣅⠀⠀⡨⠙⣆⠀⠀⡞
⠀⢸⠀⠀⠈⠀⠀⠙⡄⢿⡸⣏⡡⠒⣹⡥⠝⠒⠲⣥⠀⠀⣬⠉⠉⠉⠉⣯⠀⠀⣼⡄⠒⠫⢩⡇⠒⠌⣹⠏⡽⢀⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠙⠷⣌⡳⢦⡤⠒⠀⠀⠀⠀⠀⠶⠟⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠢⢤⡴⠞⣡⠾⢋⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⢀⠛⡇⢃⡼⠛⣶⣄⡀⠒⠶⠭⠙⠉⣤⣛⠀⠀⠀⠀⣗⣤⡉⠛⠭⠷⠖⠀⣠⣴⠛⢣⡘⢸⠟⡇⠀⠀⡄
⠀⠀⠀⠀⠘⠀⠀⠘⡀⣻⣌⠳⣭⠔⠊⠉⣠⡤⠶⢛⡓⣨⢟⡀⠀⠀⢀⡻⣅⣚⡛⠦⢤⣔⠉⠑⠦⣩⠞⣡⣿⠄⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⡉⢓⣌⠙⠒⠠⣤⣀⡉⡄⢚⣡⡎⠁⠀⠀⠈⢳⣌⡛⠁⣀⣀⣤⡄⠲⠚⣡⡶⢉⠟⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠹⣄⠙⣉⠠⠛⣠⢄⣈⣉⠡⠐⣽⠏⢼⡇⠀⠀⠹⡧⠟⢬⠲⠌⣉⣁⣠⡄⠛⠅⠉⠊⢠⠏⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠈⡴⢋⠳⣌⠒⢎⣠⠘⠉⢀⡠⢞⡝⡳⠎⠀⢀⡀⠀⠱⢞⢪⡳⢄⡀⠉⠳⣄⡱⠖⣠⠖⠙⢦⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠰⣌⠃⣀⠟⠂⣀⣈⣀⡠⠐⣩⠜⣡⠚⡴⠉⠉⢦⠓⢌⠳⣍⠂⢄⣈⢁⣀⠴⠛⢁⡸⢣⠎⠀⠀⠀⡇
⠀⠀⠀⠀⣸⠀⠀⠀⢀⠘⡶⢉⠰⢎⣩⡌⢉⡠⢞⡡⢚⠏⡼⠓⠒⠒⠲⢦⠙⡓⢌⡳⢄⡉⢩⣍⡠⠄⣉⢴⠋⡀⠀⠀⠀⡗
⠀⠀⠀⠀⢸⠀⠀⠀⢸⣇⠱⡎⡱⢤⣇⣀⡡⠔⠋⡡⠋⣼⢣⣀⣠⣄⣀⡌⣧⠙⢌⠙⠢⢈⣁⣹⡤⢎⢁⠎⣸⡃⠀⠀⠀⠃
⠀⢠⠀⠀⡼⠀⠀⠀⢸⠏⢡⡌⢦⣈⡡⠉⠀⣠⠞⠁⣸⠏⣿⠁⠀⠀⠀⡿⠸⣇⠈⠳⣄⠀⠉⠌⢁⡤⢋⣜⠹⡇⠀⠀⠀⢣⠀⠀⡆
⠀⠘⠀⢠⡇⠀⠀⠀⣦⢷⡘⡜⢠⡌⠓⠛⣉⠀⠀⣰⠇⠀⣹⡤⠒⠒⠦⣇⢀⠈⣆⠀⠀⢉⠛⠚⢩⡄⢣⢎⡾⣡⠀⠀⠀⢸⡄⠀⠃
⠀⡆⠀⠸⡇⠀⠀⠀⠸⢾⡷⠘⣆⠈⡉⣋⡴⢃⡰⠃⠀⠈⠙⠂⠀⠀⠀⠿⠈⠀⠘⢆⠘⢦⡙⢈⠁⣰⠂⢾⡷⠉⠀⠀⠀⢸⠇⠀⢸
⢠⠀⠀⠀⠙⡀⠀⠀⠀⠻⣔⢏⠄⢙⣉⣡⡴⠚⠃⠀⠔⠀⡾⠀⠤⠶⠒⢛⠖⢂⠀⠘⠓⢦⣌⣉⡋⠡⡺⣆⡟⠀⠀⠀⢀⠊
⡎⠀⠀⠀⠀⡘⡄⠀⠀⠀⠜⢧⡛⠾⠣⠉⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⡀⠉⠈⠧⢞⣴⠋⠀⠀⠀⢠⢂
⢹⣆⣀⣄⠀⣻⠁⠀⠀⠀⠸⣌⠻⣹⡽⣢⠎⠀⠀⠀⠀⠀⠘⠚⠋⠭⠒⠋⠀⠀⠀⠀⠀⠑⣔⢮⣋⠿⣠⠇⠀⠀⠀⠀⣟⠀⣠⡀⣠
⣤⣬⣭⣬⣽⣭⣤⣤⣤⣤⣤⣽⣧⣴⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣵⣶⣼⣯⣤⣤⣤⣤⣤⣭⣯⣥⣭⣭
⣿⣿⣿⠋⠙⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠼⠤⢠⣄⣠⣰⡀⡇⣰⣶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠐⠔⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠋⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⣄⣀⠠⠤⠖⠒⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⡠⠤⠔⠒⠈⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⠀⠈⠉⠉⢉⡍⢹⠀⢀⡀⠀⡄⠀⡟⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣀⡀⢀⠀⢀⠀⢸⠀⢸⡇⣼⠁⠀⠇⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠸⠁⠃⢸⠀⣿⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠈⠀⠛⠀⢸⠋⢷⡄⢀⡀⠀⣠⡠⠴⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠄⠒⠒⠒⠒⠒⠒⠒⠀⠁⠀⠀⠬⠭⢼⠗⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠼⠛⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡤⡄
⠀⠀⠀⡠⠖⠁⠀⢀⣀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠇⠐⢌⠘⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⢷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⢀⠉⠐⢄
⠀⢀⠎⠁⢄⠀⠀⠜⠸⠀⠀⠈⣢⠀⠀⠀⠀⠀⠀⠀⢨⠀⢘⡀⠀⠱⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢰⠛⢆⠀⠀⠀⠀⠀⠀⡔⢇⠀⠀⢦⢈⣄⡀⠱⣄
⢠⠎⠀⢀⣦⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠐⠉⠁⠠⡀⠃⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⡰⡉⠀⡄⢆⠀⠀⠀⢀⠌⠀⠀⢱⠈⢠⠀⠸⠉⢆⠈⡄
⠈⠲⢄⠈⠉⠁⠀⢀⠋⣴⣶⠀⠀⠀⠀⠀⠀⠐⢆⠁⠀⠀⠀⠀⠀⢈⠾⠀⠀⠘⠀⠈⡇⠀⠀⠀⠀⢰⢁⠇⠀⢀⠈⢆⠀⠀⢩⠀⠀⠀⡆⢰⠘⠀⠀⡀⠀⠂⠸
⠀⠀⠀⠙⠢⣄⢀⡪⠚⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠆⡜⠀⢀⠀⠀⠘⡄⠀⠀⢃⠀⠸⠁⢰⢄⠔⠊⠍⠑⢄⠠
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡆⠀⠀⡞⢠⠃⠀⡎⠁⡀⠀⠘⡀⠀⠀⢆⣀⠠⠀⠀⠀⢐⠀⠀⠀⠙
⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⢰⡆⢳⠀⣜⡠⢺⠐⠤⣀⠀⢣⠀⠰⠃⠀⠀⠈⠇⠀⠀⠀⢀⠜⡀⠀⠀⡴
⠀⠛⠁⠀⠠⠐⠦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢏⠀⠈⡀⠀⠀⠑⢺⠂⡌⠀⠀⠀⠀⠈⠲⠀⠀⠈⠂⠈⠱⠎
⠐⡎⠀⠀⠀⠶⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⢰⡖⠂⠌⠱⡀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⢸⠀⠈⢇⠀⢡⠀⠀⠀⠆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠃
⠀⠘⠦⣒⠀⠁⠀⠀⠀⣀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠟⠀⠀⠈⢆⠈⡄⠀⢠⠠⠁
⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢡⠀⠀⠸⢠⠀⠀⠀⠈⢆⠂⠀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢼⠀⠀⢢⠀⠀⠀⠀⠈⡄⠀⡇⢸⠀⠀⠀⠀⠈⢶⢰⠇⠀⠀⠀⠀⠀⠀⢠⢄⠀⡤⠶⠤⠷⠧⡄
⠀⠀⢾⠁⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡄⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢡⢨⠃⣿⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠘⠊⠌⠀⠠⣿⠀⠀⠘⡄
⠀⠀⢀⠔⠁⢸⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⢱⠀⠀⢸⠀⠀⠸⡾⠀⠿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠁⠀⠀⠀⣸
⢀⡤⠁⠰⡄⠀⡆⠘⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⡀⠀⢀⠂⡆⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠛⠀⣤⠤⠤⠀⣤⠀⠀⠀⠀⠀⠀⡏⢧⠀⠀⠀⠀⠀⣰⢻
⢸⠀⠀⠘⠀⢀⢇⠀⠈⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢡⢀⠂⠀⠃⠀⠀⠸⠀⠀⢰⠃⠀⡇⠀⡔⠉⠀⣿⢀⠥⡀⢹⠀⢆⠀⠀⠀⢠⠁⠈⢇⠀⠀⠀⢠⠃
⠘⠀⠀⢀⠔⠁⠈⢢⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠇⠀⢸⠀⢸⠀⠀⡏⠈⠐⠊⠀⠀⠀⢱⠈⠉⠀⠀⠀⢸⠀⠀⠈⠆⠀⢠⠃⠀⠇
⠀⣆⠔⠁⠀⠀⠀⠀⠣⣉⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⠀⠀⠞⠀⠀⠀⠀⠘⠀⢸⠀⡇⠀⠀⠃⠴⠀⠀⠀⠇⠀⠘⢰⠀⠀⠀⠀⡜⠀⠀⡀⠈⢄⠂⡄⢠
⠀⠙⡀⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰⠀⡌⠀⠀⠀⠀⠀⠀⠁⢨⢠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢯⠀⠀⠧⠀⠬⠘⠃⡜
⠀⠀⠘⠄⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀⡸⠀⠀⠀⠀⠀⠀⠀⢠⢐⡜⠀⠀⠸⡄⠀⢀⡄⣀⣀⣀⣀⠀⢐⠀⠀⠀⠈⡆⠀⠀⠀⡆⠀⡜
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⠳⢎⡀⠀⣥⠀⢈⣢⠎⠀⠀⠀⠀⠘⠤⢄⣠⣁⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⣀⠀⠀⢀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣿⣿⣷⣦⡀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⠿⣿⡇⢰⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⠟⠋⠁⠀⠀⢀⣤⡀⠀⠘⡇⢸⠁⠒⠀⠤⠤⠤⠤⠤⠀⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡦⠀⠈⠁⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣆⠀⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⣤⣄⡈⠛⠿⠻⠿⣿⡿⠃⠀⡆⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⢀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠸⢿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢛⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⢀⠜⠀⠀⢸⣰⢀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠢⠤⠤⠼⠿⠿⠟⠛⠒⠁⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠖⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠛⠛⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⢁⣀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠀⠈⠉⠉⠈⠉⠄⡰⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⢀⣷⡀⠀⠀⡀⣴⢶⣴⣿⣶⣄⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢸⣿⡿⠂⣤⣄⢀⣼⣿⣿⣿⣿⣷⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢈⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⣿⣿⣿⣿⣿⣯⠀⠈⠉⠛⠉⣿⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡼⣾⣿⣿⣏⣿⣿⣿⠟⠀⠀⠀⢠⣇⠘⠇⠑⠁⠂⠠
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣽⣿⢣⣾⣿⣿⣿⠏⠉⠁⠀⠀⠀⢀⠜⣿⣦⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠸⢃⣿⣿⣿⢹⡧⢀⣠⡤⣶⣶⡾⠃⠀⠈⠻⣿⡀⠀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠠⠂⠀⠀⠈⢘⡟⣻⣿⡿⠟⠋⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⡀⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⠀⠀⠀⠀⠠⠞⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⢠⡖⠀⣀⣴⡟⢠⡾⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠐⠿⠛⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣾⣷⣶⣶⣴⣴⣶⣾⣷⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⣿⣿⣛⣿⣿⣿⣿⣿⣋⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢋⣙⠉⢿⠿⠹⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⣀⢾⣿⣧⣇⢰⣷⣿⣿⣿⣯⢿⡗⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⢿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠛⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠛⢷⣝⣿⣿⣿⡿⠻⠿⠎⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣬⠉⠉⣷⣦⢶⣄⢊⡀⢳⡀⠀⠘⢿⣷⢀⣴⣿⣿⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⣀⣰⣧⠛⠃⠀⠹⠛⠻⠛⢁⡶⠆⠹⡷⡞⠋⢁⠿⢁⣨⡄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠒⠛⠛⠁⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠘⢰⣤⣤⣷⣿⣿⡇⠀⣺⣤⣤⡀⠀⡄⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠄⠀⢀⠢⠷⣦⣀⠀⠉⠙⢶⣤⣿⢃⡁⣩⣏⣿⣿⢿⣿⣅⣈⣿⢉⣐⢾⢟⡄⡀⣀⠁⠠⣄⠀⠈⢀
⠀⠀⠀⢄⠠⠴⠎⠃⠀⣽⣈⣄⣀⠀⠀⢍⡉⣲⣿⣿⡿⣷⣿⣿⣿⣿⣷⣿⠁⢸⡃⣤⣹⣿⣿⡴⣶⢋⢀⣀⡆
⠀⠀⠀⢸⠇⡄⠙⠃⠀⢹⡟⢻⣿⣷⠰⢾⣴⣿⣿⢻⣷⣿⣿⣿⣿⢿⣿⣿⣧⢘⣿⢙⣩⣿⣿⣿⣿⣷⣔⠸⠓
⠀⢰⠀⠰⠀⡇⠀⠀⠀⣾⡆⢸⡟⢙⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣍⣸⡿⠀⢀⣿⣿⣇⣼⣶⣛⡑⠓
⠀⢸⠀⣂⢸⣇⣀⣴⣴⣿⡇⢹⣴⣿⣟⣻⣖⣿⣿⣿⣿⢯⣽⣿⣿⣷⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘
⠀⢸⣁⠈⢘⡏⠛⠡⣭⢹⣏⢹⣯⣿⣿⣍⣫⢿⣿⣿⣿⢿⣿⠏⠉⠹⣿⣿⣿⣿⣿⣇⣿⣿⢋⣏⡴⠠⠆
⠀⠺⣿⢇⡐⡇⠀⠀⠠⣼⣟⣸⡏⣉⣽⠛⠉⠛⣻⣿⣿⣛⣿⣷⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠄
⠘⠲⡽⠊⠈⠃⠀⠐⠂⠙⣿⣿⡇⠀⢹⠀⠤⠶⠀⠰⠼⠿⣷⣤⡤⠄⢻⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣠⣽⠏⠀⠀⠀⠀⠤⣿⣟⠋⠀⠀⢹⡀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠠
⢀⠽⡯⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⢀⣈⡄⠀⠀⠀⠶⠿⠉⠉⠛⠛⠛⠟⠛⠻⠿⡋⠙⠻⠿⣧⠠⠀⠀⠀⠒⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣒⠀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⢟⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠳⠞⢿⡟⠫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣦⢺⣿⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣏⡡⠄⢺⣿⣿⣿⣿⣷⠹⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⡀⣀⡀⠀⢀⡾⠿⣿⣷⠀⡆
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⠉⠐⢴⣦⣿⣿⣿⢟⣋⠑⠢⠒⠋⠉⢐⣢⣤⡤⠶⠒⠒⠶⣖⣉⡀⠀⠀⣤⣶⣾⣷⣿⠿⢶⣶⠮⣵⣿⣯⡼⠁
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⣿⢇⣼⣿⣶⡦⠀⢰⣶⣎⠉⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢸⣿⡃⠀⠀⣠⣾⣧⡀⠀⠀⠀⣠⠟⡿⢿⣿⡿⣰⠓⣸⣿⣿⡷⠦⢴⣶⡿⠟⠋⠀⠉⠉⠁
⠀⠀⠀⠀⠈⣿⡇⠀⠰⠟⠀⠘⣿⣶⣄⣼⣵⣷⣿⡿⠿⢷⣡⣾⠟⠉
⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⠀⠀⣿⠿⠋⠀⣨⡝⠉⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠰⠋⠀⠀⠀⣸⡿⢳⣶⣦⠴⠋⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⡔⠀⠀⣼⡿⠁⠈⣿⠃⡜
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣤⣤⣀⣴⠿⠚⠂⢀⣿⡜
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⢉⡴⠶⠒⠀⣾⠁
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣯⠀⠀⡰⠶⠦⢤⣏⡟
⠀⠀⠀⠀⢀⣾⣭⣽⣛⣛⣿⠿⢗⠒⣒⣻⡋
⠀⠀⠀⠀⠋⠀⠀⠈⠈⠃⠛⠙⠛⠙⠙⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⡧⡷⢿⢿⡇⠀⡇⣿⠄⠀⠀⠀⠐⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣷⡀⢰⡇⠀⢰⣴⢿⣧⢰⡶⣦⠀⢶⡆⣴⣶⡄⢠⡾⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠛⢻⡿⠛⢿⡿⢸⡿⣿⡄⢹⡇⢸⣿⡏⢸⡇⣿⠃⢻⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠁⠀⢸⡇⠀⣸⡇⣼⠇⢹⡇⢸⡇⢸⣿⠁⢸⡇⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⡆⠀⢸⡇⠀⣿⡿⠋⠀⢿⡿⣾⡇⢸⡟⠀⣾⡇⣿⡐⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣾⡟⠀⠘⣧⡀⢹⡟⠲⠀⠘⢧⡿⠉⢸⡇⠀⠿⠇⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢱⣿⣿⣿⡏⢘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡼⢿⣿⣿⡟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡦⠀⠀⠀⠀⢀⣿⣿⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⡟
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣴⡆⠀⠀⢻⡿⢻⣦⠀⠘⠃⡄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⢠⡀⠀⠀⠀⠀⢨⠢⠀⠀⠀⠀⠀⢄⠑⠶⠀⣰⣦⡀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣼⣿⣿⣧⠀⡇⠀⠀⠿
⠀⠔⡀⣿⣿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢧⢹⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡖⡋⠿⣿⠏⠀⡇
⠀⠀⠀⢿⣿⡟⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠈⣎⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠁⠀⢸⠀⠀⡇
⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢹⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⢰⣿⡄
⠀⢰⠀⢸⡄⢠⣤⠀⠀⠘⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣤⡌⣧⠀⠀⣮⠛⢀⠀⡀⠀⠀⠉⠀⠀⢹⡌⢆⢠⡄⠈⡗⢤⡀⠀⠀⠀⠈⠀⠾⠛⠏
⠀⢸⡇⢸⣷⣿⣿⠀⠀⠄⠀⣶⠈⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⣄⢹⡄⠔⠉⠀⡏⠀⠛⠀⢀⣀⡤⠀⢸⡇⠘⡎⡇⢈⡇⡀⠳⡄⠀⠀⠀⠀⠂
⠀⠀⢻⣿⠊⢻⣿⣶⣿⢟⣿⠃⠀⠀⢀⠀⠈⠙⢿⡉⠉⠟⣇⠀⢹⡎⣿⡆⠀⣸⡇⠀⠀⠀⠐⠻⠆⠀⠀⣷⠀⢻⣷⢰⡇⢡⠀⢹⡄⠀⠀⠀⠀⠀⢀⡔
⠀⠀⢸⠸⡁⢹⡟⠉⣙⣯⣿⣀⡀⢀⣸⠀⠀⠀⠀⡿⣄⠀⣿⠀⠀⣷⢹⡁⠀⡿⠀⠀⢠⠀⠀⢀⠄⠀⢀⣿⣀⢈⣿⣾⡇⢸⣤⠀⢻⡀⠀⠀⠀⣠⡾
⠀⠀⣼⠀⣇⣹⣿⣿⢿⣿⣿⣯⠛⢉⣿⣶⣾⣷⡄⢹⣿⣷⣼⡆⠀⢸⣾⡇⢰⡇⠀⠀⣴⠀⠀⣼⠀⠀⠈⢻⡙⠛⢿⣿⡇⢸⡿⠀⠈⣧⠀⠀⠾⣿⠃
⠀⠀⣿⡄⠹⡇⢸⢹⡀⢟⠛⢿⣿⠾⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⣷⣿⢸⡇⠀⣀⠃⢀⣼⣃⣴⠏⠀⣿⡿⡄⣸⣿⡇⢸⡇⢡⠀⢹⡇⠀⢠⡟
⠀⢠⣇⡇⣦⣇⢸⡇⣷⠈⢳⡀⣷⠀⢸⣿⣿⣿⡿⠀⣿⣿⣿⡇⢠⠀⢹⣹⣼⠀⠀⢹⢰⣠⡿⠻⣇⠀⡜⢹⡇⢳⡏⢹⡷⣾⣇⠈⡆⠘⡇⣧⣾⠇⢰
⠀⢸⠉⡟⣿⣿⢻⣷⢸⣵⣾⣷⢸⣆⣼⣷⣽⢻⡇⠀⣟⡏⠈⣇⢸⠀⢸⣿⣿⣶⣿⡿⣿⣿⠿⣷⠿⣸⠁⢸⡇⢸⣇⢸⡇⣿⢹⠓⢷⠀⡇⣿⣹⡀⠀⡇
⠀⣿⠀⣿⡇⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢸⡇⠀⣿⡇⠀⣿⢘⡇⢘⣿⣿⣿⠙⣇⢻⡏⣰⠋⢀⡏⠀⢸⣁⣸⣿⢸⣇⣏⢸⠀⢸⠷⣟⡿⡿⠃⠀⢱
⠀⣿⠀⣽⣧⣼⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⡇⠀⣿⣧⠀⣿⠸⡇⢸⡿⣿⣯⣠⡏⣼⣡⠏⠀⢸⠃⡤⢾⠏⢸⣿⣿⣿⣿⣸⠀⠈⡇⣿⣇⡿⣼⠀⢸⡀
⠀⣿⢠⣿⣏⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⢠⣿⣿⡀⢿⣐⣇⢸⡇⣿⣿⣿⢻⣿⣾⣦⣦⣿⠟⠀⢸⠇⢸⣿⣿⣿⣿⣿⣢⠖⡏⣿⣿⡇⢹⡀⠀⡇
⠀⣿⣤⣿⣿⢸⡇⣿⡏⣿⣿⣿⠛⣿⣿⣿⣼⣿⣿⣾⣿⣿⣧⣿⣿⣿⢸⡆⣿⢻⣿⢸⣿⣿⣿⣹⣿⣄⠀⡾⠀⠘⢿⣿⣿⣿⣿⡅⠀⡇⣿⣿⣇⠸⡇⠀⡇
⠀⣿⡟⣻⣿⣸⡇⣿⣷⣽⣿⣿⣠⣿⣸⡟⠈⡿⡿⡟⢻⠃⣟⢻⠛⡋⣾⡄⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⢀⡇⠀⡇⢸⣿⣿⣿⠘⣧⠀⡇⢹⣿⣿⠀⣧⠀⣷
⠀⣿⠁⢹⣿⣿⣷⣿⣿⠿⣿⢻⠿⣿⢹⡇⠀⡇⣿⡇⢸⢰⢸⣸⠀⡃⣿⡇⡇⠀⣿⣿⣿⢏⡟⣼⠁⡀⢸⡇⢠⣧⠿⣿⣿⣿⠀⠀⠀⣧⢸⣿⣿⠀⣿⠀⣿
⠀⣿⠀⢸⣿⡿⡃⢹⡿⣆⣿⢸⠀⢿⢸⡇⠀⡇⣿⠃⢸⠸⢸⣿⠀⠁⢸⡇⡇⠀⢻⠃⡇⣾⣷⣿⣟⡉⢹⡇⢸⣿⠀⣿⣿⠉⠀⠀⠀⣿⡿⣿⢻⠀⣿⠀⣿
⠀⣿⠀⢸⢹⡇⠀⣿⡇⠀⣿⢸⠀⢸⢸⡇⠀⡇⣿⠀⢸⡇⢸⣿⠀⠀⣿⣷⡇⠀⢸⠀⡇⡿⠋⣼⠈⠃⢸⡇⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⠇⣿⢸⠀⢻⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢠⣦⡴⣦⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠈⣧⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠸⡇⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣇
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢹⡆
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣹⠈⠃⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢿⡄
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠔⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣷⡀
⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣧
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠹⣇
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢻⡄
⠈⢿⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡿⣄⠀⠀⠈⢿⡀
⠀⠘⣧⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠉⠀⣸⠁⠘⢷⡀⠀⠘⣷
⠀⠀⠸⣆⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠙⣦⡀⠸⣇
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠳⣄⢹⣆
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡄
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⡟⠀⢀⣠⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠙⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣧⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⣦⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠀⠀⠈⠳⣄⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⠶⣄⠀⠀⣧⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠈⠛⢦⣽⣄⠴⠞⠋⠁⠀⠀⢻⡆⠛⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠈⢧⡀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣠⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠳⡄⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠳⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠉⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢹⠄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠿⠴⣟⠀⠀⠀⠀⠀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⡿⠿⢿⣿⣦⣀⣀⣠⣤⠶⠶⠾⠂⠀⠀⠀⠀⢸⠋⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⠕⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠞⠁⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣉⣉⡋⠀⠀⠀⠀⠀⣼⠆⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⢏⡴⠋⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠛⠉⠀⠀⠀⠀⠀⠀⠘⢡⠞⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢠⡾⢁⡞⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠀⠀⠙⠛⠋
⠀⠀⠀⠀⢠⡟⢀⡿⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⠙⠆
⠀⠀⠀⢠⡟⠀⠸⠁⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠙⣀⡀⠀⠀⠀⣠⣴⡾⠃
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⣠⠞⠋⠉⠉⠉⠉⠙⢦⣤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠛⠲⣄⡀⢹⣤⠤⠶⠚⠋⠁
⠀⠀⢸⡇⠀⠀⠀⢰⡆⠀⠀⠀⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡲⠞⠋⠉
⠀⠀⢸⠀⠀⠀⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠸⣇⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠙⠳⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣧⣄⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠟⠀⠀⠀⠙⠛⠷⢶⣶⣶⣶⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣄⣀⣀⣀⡀⣀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠟⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠈⢳⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⠶⠦⣄⣼⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠟⠉⠉⠙⢳⡀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠙⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⠟⠉⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢧⡀⠀⢀⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⢀⡤⠴⠾⠿⣯⡙⢦⡀⠀⠀⠀⠀⠈⠳⣄⡀⣰⠟⠂⠀⠀⢀⠀⠉⠙⠲⣤⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠻⢦⣽⣆⣀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⢀⠀⠀⠀⠀⢀⡤⠋⠁⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠚⠻⠿⠿⢭⣿⣶⣦⡴⠋⠀⠀⠀⠀⠀⠀⢀⠤⠾⠻⢷⡦⣤⣀⡀⠀⣀⣀⣀⣀
⠀⠀⠀⢠⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣀⣠⠊⠁⠀⠀⠀⠀⠱⠀⠉⠙⠻⠋⠀⠀⠉⠻⣆
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡟⠛⠛⠓⠶⠶⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣀⠀⠀⠀⠀⠻⣷⠛⠁
⠀⠀⠀⠈⠷⣤⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠉⣹⠟⠒⠶⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠉⠻⣆⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠛⠁⠀⠀⠀⢀⠜⠉⠙⠻⣍⠙⠛⣷⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠛⠛⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠙⠋⠀⠀⠀⠀⢀⣴⠋⠀⢀⠀⠀⠈⠳⣄⣘⣦⣄⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣏⣳
⠀⠀⠀⠀⠀⢠⡞⢳⡄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠳⣄⠀⠀⠀⠀⠀⠈⠉⠙⢯⠉⠉⠉⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠙⢦⣤⡤⢾⠀⠀⠀⠀⠀⣸⠃⠀⣟⠁⠀⠀⢠⣄⣀⣀⣠⡞⠀⠀⠀⠀⣼⡁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣠⡤⠞⠃⠀⠀⠻⣄⠀⢀⡼⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⡴⠊⠀⠀⠀⠀⠀⢠⡦⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠊⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢡⣤⣄⣀⣀⠀⠀⠀⣴⡞⠲⠤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠁⠀⣈⡶⠉⠁⠀⠀⣸⣿⡿⠛⠶⣤⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⣹⣷⣶⣶⠖⠀⣠⡄⢀⠀⠀⠀⠀⢀⣄⡉⠁⠀⠀⠐⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠀⠀⣾⣽⡷⠋⢀⣶⣶⣤⣤⣿⣷⡤⠠⣤⣄⠀⡿⠀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⡄⠀⠀⠀⠊⢻⠁⠀⠸⡿⠃⠀⠘⠛⠋⠀⠀⣼⣿⣿⡇⣰⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⢠⣿⣿⣿⣿⣿⡟⠉⠉⠀⠰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⢠⡦⠶⠆⠰⣿⡿
⠀⠀⠀⠀⠀⠰⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⣀⣼⢿⡴⠃⠀⡤⣄⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⢀⣤⣿⣿⡏⣠⡾⠋⠁⣼⣧⣤⣤⣦⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⡀⠀⠀⣠⡴⠀⠀⠀⠀⠀⣈⠉⠀⠐⢿⣿⡟⣿⠃⠀⠀⠀⠈⠯⣽⣽⡿⣽⣋⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠈⠉⣿⣧⠀⠀⠀⢀⣼⠌⠀⠀⠀⠘⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⡵
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠀⡄⠀⠀⢹⠻⡦⠀⠐⣾⣿⠀⡀⠀⠀⠀⣿⢹⠇⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣻⢸⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣤⣠⣤⣿⢸⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⢰⡀⠀⠀⣸⡄⠀⢻⣾⣿⣿⡘⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⠏⠀⠀⠀⢹⣷⠀⠐⢨⣬⡽⠃⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠉⠀⢦⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠂⢧⣀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠶⠁⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⢀⣠⣤⣤⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣗⣞⣦⡆⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠠⣅⢠⣔⣁⣠⣿⠀⠀⠀⠀⠈⠀⠐⠀⢀⡀⠀⠀⠛⣿⠋
⠀⠠⢤⣶⣿⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⠙⣿⡿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣲⣿⢿⡟⠋⠉⠀⠀⠐⠀⡀⠀⡌⢰⠋⠁⠀⠀⠀⣿
⠀⠀⠻⡟⢻⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⢱⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡧⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠆
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠁⣽⠁⠀⠀⠀⠀⠀⠀⣸⠳⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⠃⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠐⣾⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢴⡧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿
⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢨⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠿
⠀⠀⢀⣽⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⢦⠿⣇⠀⠀⠀⠀⠀⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⠶⢾⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣦
⠀⠀⣌⢠⣿⢴⡇⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢠⣤⣿⢿⣄⣤⣷⠀⠀⠀⢀⡤⡄⠀⠀⠆⠀⠀⠀⠀⣀⣀⡼⣿⣿⡤⠀⠀⠀⠀⠀⢀⡴⢤⡀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠙⠋⠉⠛⠁⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁
⠀⡟⠉⠓
⠀⠙⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣂⢁⣩⠁⠐⠒⠄⢀⠀⠀⢆⠆⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣅⠁⢨⠃
⠀⠀⠀⠀⠀⢀⠄⢦⠤⢠⣀⠄⠀⣠⠄⡬⠉⠐⠈⡇⠀⠠⢃⠶⡄⠀⡸⠀⠈⠒⠁⠠⠂⠉⠀⠀⠑⠠⡀
⠀⠀⣀⣄⠌⣤⠀⠀⠲⠚⣁⢍⠀⠀⠈⠀⠐⠀⠀⡀⠰⠧⠌⠚⠃⠴⠠⠴⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⣅⠈⠂⢁⠅⠀⠐⠒⠣⢸⠀⠀⠀⠀⠀⠀⢈⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠑⡌
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⢊⠰⠴⠛⠒⢈⢀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠰⣤⡀⠠⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠡⡀⢀⠌⢐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡠⠤⣀⣐⠀⠀⠀⠀⠀⢂⡀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⡇⠀⢰⣲⠚⢠⣤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢁⠈⡉⢁⠉⡀⡀⠂
⠀⠀⠀⠀⡇⠀⠀⠉⠒⠙⠋⡀⠀⠀⠀⠀⢸⡠⠓⢄⠨⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠘⠛⠛⠻⠄⠛⠆
⠀⠀⠀⢀⠃⠐⠂⠀⢤⠄⠄⠬⠦⡀⠒⠀⡚⠀⠀⠊⠰⡀⣀⣀⣀⣄⣀⣀⠀⠑⠌⣃⣀⣀⣀⣀⣀⣀⠁⠌
⠀⠀⠀⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⠢⢸⣥⣡⠊⠀⠀⠀⢠⡤⠤⢤⠀⠀⢠⡤⠤⣤⠀⠀⢠⡤⠤⣤
⠀⠀⡌⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠫⠃⠀⠖⠒⠺⠀⠀⠀⠖⠒⠺⠀⠀⠰⠖⠒⠇
⠀⠀⠉⠂⠄⠀⣌⣀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠐⠈⠀⠀⠀⠨⠉⠉⠉⡀⠀⡘⠉⠉⠉⠀⠀⡈⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠀⢠⢤⠀⠀⠀⠀⠡⢤⠀⠀⠀⠀⢣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠐⠂⠀⠀⠀⠤⠴⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠠⠘
⠀⠀⠁⠂⠄⠠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠐⠈⠀⢰⠚⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⢒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡊⠁⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠙⢦⡀⠀⣀⡤⠶⠚⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢹⠋⠁⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠢⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⣄⠀⠀⠀⠺⠀⠀⠀⠀⠀⣠⠀⠀⢉⠀⠀⡝⠉⢳⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢀⡀⠐⠚⠋⠀⠀⠀⠀⠀⠀⠛⣶⢺⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣄⠀⠀⠀⠀⠀⠰⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⣤⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢈⠳⣄⡀⠀⠀⠠⡇⠀⠀⠀⠠⠀⣈⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠻⢦⡀⢀⡇⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠙⢶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣀⣸⡇⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠿⣷⣶⡾⠟⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠶⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠐⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⠄⠀⠀⠀⠀⡀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠡⠊⠁⠀⠀⠀⡠⢊⣼⠏
⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠿⠷⠶⠟⠋⠀⠀⠀⠀⠀⠀⠠⢊⣴⡿⠁
⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠘⠷⣦⣤⣀⣀⡀⠻⣦⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⠀⠀⠀⠀⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠁⣠⠟⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠒⠋⢁⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢠⣿⣿⡛⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⢟⣿⣿⡄
⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄
⠀⠀⣾⣿⣿⣿⣷⠀⠀⣀⣀⣀⡠⣶⣾⣿⣷⣶⣤⣴⣤⣼⣿⣿⣿⣿⣧⣤⣦⣤⣶⣾⣿⣷⣶⢄⣀⣀⣀⠀⠀⣾⣿⣿⣿⣷
⠀⢸⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⡇
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠉⠉⠙⠿⢿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣿⡿⠿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠛⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢸⠁⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⢀⠏⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣿
⢀⡇⠀⠀⠀⠀⠀⡼⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢹⡄⠀⠀⠀⠀⢸
⢸⠇⠀⠀⠀⠀⢸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣷⠀⠀⠀⠀⠸
⡜⠀⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠸⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⡟
⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠛⠿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠸⣇
⢹⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⢸⡆⢠⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢰
⠀⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠈⢻⡳⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⢖⡿⠁
⠀⠀⠀⠹⡄⠈⢿⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⡞
⠀⠀⠀⠀⢹⠀⠘⡆⢻⣿⣿⠈⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⢱⡏⠀⡟
⠀⠀⠀⠀⣸⠀⠀⢹⠀⠙⠛⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠘⠛⠁⡞⠀⠀⣧
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⠇⠀⠀⣼
⠀⠀⠀⠀⢹⡄⠀⠀⢧⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣄⣀⣤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠦⣄⣸⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣤⡴⣶⢲⡞⠹⡟⠈⢻⠀⠈⣿⠀⠈⣿⠁⢻⠋⢷⠚⡶⢦⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⡏⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣇⣿⣸⣇⣠⣧⣠⣾⣤⣤⣿⣤⡤⣿⣀⣼⣄⣼⣀⣇⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣏⣿⣹⣇⣿⣨⣇⣸⣀⣯⢈⣇⢸⣀⣼⣀⣯⣨⣇⣿⣨⣏⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠈⠈⠉⠉⠉⠉⠉⠋⠉⠋⠉⠉⠉⠈⠉⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⣀⣠⠤⠴⠦⠤⢄⣀⣀⡠⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠃⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣙⠖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠠⠀⠈⢢⠀⣀⠔⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠙⡀⠚⠀⠀⠈⠽⠍⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠀⠀⠀⠀⠀⠀⠛⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢀⣤⡶⢈⡦⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠄⠀⠀⢀⠀⠀⠈⠀⠰⢆⢭⣦⢤⣄⣨⣑⣄
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠘⠻⠷⠚⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⢀⡓⠲⡤⠤⠼⢥⣴⣾⣀⣆
⠀⠀⣾⣿⡟⠀⠀⠀⢀⣤⠂⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠠⠄⠀⠀⠄⠀⠀⢀⠀⡉⠹⢯⡽⠒⠒⠏⠀⠀⢁⡠⠷⡀
⠀⠀⢿⣿⡇⠀⢀⣴⣿⡿⠋⠀⠀⠛⠄⠀⠂⡀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠐⠀⠀⠂⠀⠐⠐⠠⣀⠈⠂⠌⠀⠛⣋⠛⢀⠀⢃⣀⡤⢞
⠀⠀⠈⠿⣿⡄⠉⠛⠻⠷⠀⠒⠋⠑⠊⠂⠀⠲⠆⡤⠀⠀⠀⠀⠀⠁⠀⠔⠄⠀⠀⠘⡇⠀⠆⠀⠹⡔⠀⣀⡀⠂⣠⠖⠀⠀⠰⣯⣭⣭⣴⣾⡿⠀⢀
⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠔⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠅⠀⠀⣆⠀⠇⠠⠀⢀⠞⣁⠀⠀⣴⣾⣿⣿⣿⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠒⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠖⠁⠁⢉⣥⠾⢴⣥⣩⠖⠡⢦⣾⣿⣿⣿⣿⣿⠀⡀⣀
⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠿⣯⣖⠤⠋⠀⠉⠂⢄⠉⠉⠉⠉⠉⠀⠀⠐⠅⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣽⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣷⣿⣷⣶⣿⣷⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠐⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⠇
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣬⢷⡦⠀⠀⠠⠰⣾⢭⠅⠀⣿⡖⡏
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⣽⢣⣷⣄
⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠻⠀⢻⣿⣧⡀
⠀⠀⠀⣼⣿⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠴⠤⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣄
⠀⠀⢰⣿⣿⠆⠰⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠾⠋⠀⢀⣴⠃⠀⠀⠀⠸⣿⣿⣿⣿⣧⡀
⠀⠀⣼⣿⣿⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣇⡀⠀⡔⠓⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣿⣿⣿⣇⠀⠀⠀⢀⠀⡀⠀⠀⠀⡤⠀⠘⠀⠀⢂⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠲⢄⠀⠀⠙⢿⣿⣿⣿⣿⣧
⠀⠀⣿⡿⣿⣿⡄⠀⠀⠀⡰⠇⣠⠖⠁⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣿⣿⣿⣿⣿⡆
⠀⠀⣿⣇⠘⢿⣷⠀⠀⠈⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿⣇
⠀⠀⢻⣿⣦⡐⣷⣤⣤⠆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠖⠋⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⣦⣝⣛⡛⠛⠃⠋⠀⠀⢀⣀⣀⣍⡙⢿⣦⣤⣤⣤⣤⠐⠀⢹⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⠯⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢰⡧⠀⠀⠀⠐⠶⠤⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⠛⠉⠀⠀⠉⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⣶⣶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠈⢿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠈⠃⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⡀⠀⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⠳⡄⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣼⡇⠀⠀⠀⠻⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠀⠀⠀⠐⠛⠉

⢀⣤⣦⣄⠀⣠⣶⣦⠀⣠⣤⣄⠀⠀⣠⣤⠄⠠⠀⠢⡀⠀⡀⠒⡆⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠄⠀⢄⠀⠀⠔⠢
⠸⣿⣿⣿⣿⣿⣿⡿⠂⠿⠛⠯⠗⠘⠛⢋⡄⢈⣤⣜⣮⣿⣶⣶⡿⠀⢁⣦⣲⣨⣯⣶⡾⠇⠘⡀⠀⠀⠈⠁⣠⣄⠆⠀⠀⠀⠀⠀⢠⠤
⠀⠘⠛⣿⣿⣿⠁⠀⠀⠀⠃⠰⠄⠓⡜⠀⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠙⠻⣿⣿⡇⠀⠀⠀⠈⠒⠆⠐⣴⡏⠀⠀⠀⠁⠐⠀⢦⡍
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣷⡆⠃⠀⠀⠀⠀⠀⡏⣻⡇⠀⠀⠀⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⣿⠁⡀⠀⠀⠀⠀⠀⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⠁⠃⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢰⡄⠀⠀⠀⠀⠀⡇⢺⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢰⣹⠨⡇⠀⠀⠀⠀⢠⠷⣼⣖⠀⠀⠀⠀⠀⠀⢦⣷⠂⠀⠀⠀⠀⠀⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⣽⡶⠂⠸⣷⠀⠀⠀⠜⢉⣿⣿⡉⠀⠀⠀⠀⠈⢹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠿⠿⠉⠻⠋⠀⠀⠀⠘⢋⠅⠠⠠⠂⠀⠀⠰⠶⠟⠹⠿⠋⠀⠀⠀⠰⠶⠋⠹⠟⠁⠀⠀⠀⠄⠴⠟⠧⠄⠀⠀⠀⠀⠀⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣺⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠠⠹⢹⡀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⣠⠃⣸⠀⢳⡀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠀⠈⣧⠀⠀⠀⠀⠈⠐⢤⡀
⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⣿⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⠀⣠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠠⠄⢠⡏⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣄
⠀⡰⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⠀⠀⠀⡇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣀⠄⠊⠁⠸⡣⡀
⡐⠁⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⢿⡀⢀⡠⠐⠉⠀⠀⠀⠀⠀⢣⠙⢄
⠱⠢⣀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⣼⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣠⠼⣿⠁⠀⠀⠀⠀⠀⣀⠤⠒⡍⠱⡈⠣⡀
⠀⠡⠀⠑⠢⡀⠀⠀⠀⠀⠀⠈⠒⢄⠘⡝⠂⡀⠀⠀⢈⡇⣀⡤⠖⣋⠤⠂⡟⢧⠀⠀⡠⠔⠊⠀⠀⢀⠃⠀⠈⢆⢡
⠀⠀⠑⠦⢀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠐⣤⠼⣟⣁⠴⠊⠁⠀⢸⣀⠤⠇⠁⠀⠀⢀⠤⠒⠉⢢⠀⠀⠀⠱
⠀⠀⠀⠈⠢⡑⠢⡀⠈⠒⢄⡀⠀⠀⠀⠀⢣⢹⡏⠀⠹⡏⠀⠀⢀⡤⢴⠏⢁⠂⠀⡠⠔⠊⠁⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠘⢄⠈⠑⢤⡀⠈⠢⢄⠀⠀⠀⢿⠁⠀⠀⣇⡤⠞⠉⠀⡾⣀⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣠
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠒⢄⠀⠁⠢⣀⡘⣤⠶⠋⢇⠀⢀⣠⢴⠋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠈⠢⢄⠀⠇⠘⠄⣀⣿⠒⠉⠀⡞⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠑⠺⡔⠻⡅⢸⣄⡀⣼⡽⠁⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠘⢄⠹⡀⡟⢰⣿⠁⠀⠀⠀⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠣⡹⣧⣿⠃⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⡧⠖⠉