Happy rabbit ascii Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⢠⠞⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡟⣿⢻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣈⢉⡙⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠛⠛⡞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣐⣳⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⠶⠖⢳⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠔⡿⣅⠴⣦⠤⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⣛⠲⣶⠚⣋⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⠹⠖⠟⠟⠷⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣧⣰⢻⣆⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢅⡠⠉⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⢸⡇⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠦⠤⠾⡽⢤⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⢠⣇⠁⢈⢳⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⠰⠷⢿⡶⣷⢾⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠈⠳⠼⣶⠟⣳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠸⡆⣤⣤⣄⣠⣤⣤⣰⠇⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⢠⡄⠀⠀⡄⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢐⣶⣖⠈⠁⠀⠀⠁⢰⣶⡖⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⠉⠉⠀⠀⠴⠀⠀⠈⠉⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣀⠠⣄⠀⠀⠀⠀⠀⣠⠄⣀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠙⠀⢹⡄⠀⠀⠀⢠⡏⠀⠋⠃⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣼⠃⠀⠀⠀⠈⣧⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠃⠀⠙⠛⠋⠀⠘⠁⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⢢⡖⣞⡧⠀⠄⠀⣿⣰⡿⢒⣿⠀⠠⠀⣾⠗⡷⣶⢾⣷
⠀⠀⠀⠀⠀⠀⢠⢠⣤⠠⡄⢤⢀⣄⣠⣤⢠⠀⢠⢤⣠⣤⣤⣤⣤⣤⡄⢠⢤⣠⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠈⠈⠀⠁⠈⠀⠈⠁⠈⠁⠁⠁⠀⠁⠉⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⣼⠟⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠘⣿⡄⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⠀⣀⡀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣴⡟⠀⠀⢿⡇⠸⢿⠀⠀⠘⣷⡄⠀⠀⠀⠀⢠⡿⠁⠀⠻⣿⠀⢿⡇⠀⠈⢻⣆
⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣼⡿⠀⠀⠀⠾⠁⠰⠟⠀⠀⠀⠘⣿⡄⠀⠀⢠⣿⠃⠀⠀⠴⠋⠀⠞⠁⠀⠀⠈⢿⣆
⠀⠀⠀⣾⡿⠉⠀⠈⠙⣿⣆⠀⢀⣿⡇⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⢸⣿⠁⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠸⣿⡆⠀⠀⠀⠀⣼⡿⠀⠸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠙⢿⣦⣤⣤⣾⠟⠁⠀⠀⢿⣧⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠘⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡄⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣠⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠓⡄⠀⠀⢠⠚⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⢀⠆⠀⠀⢣⡀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⣀⠀⠀⠉⠉⠉⢆⠀⠀⡰⠉⠉⠉⠀⠀⣀⠤⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣀⣀⣀⡀⠀⠉⠢⡀⠀⠀⠘⡄⢠⠃⠀⠀⢀⠔⠉⠀⣀⣀⣀⡀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⡰⠁⠀⠀⡠⠒⠉⠀⠀⠀⠀⠉⠒⢄⠈⢢⠀⠀⢡⡂⠀⠀⡔⠁⡠⠒⠉⠀⠀⠀⠀⠉⠒⢄⠀⠀⠈⢆
⠀⠀⢰⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠗⠊⠉⠉⠑⢾⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⡆
⠀⠀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⡀⢀⡀⢀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠈⢆⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⣀⣀⣀⣀⠠⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⡰⠁
⠀⠀⠀⠈⠢⡀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⡠⠔⠋⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠑⡲⠂⢀⠜⠁⠀⠀⠀⠀⠀⠸⠉⠐⠒⠒⠒⠒⠂⢉⠃⠀⠀⠀⠀⠀⠈⠳⡀⠐⢖⠊⠁
⠀⠀⠀⠀⠀⠀⡔⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⣀⣀⣀⠠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⢣
⠀⠀⠀⠀⠀⢰⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠀⠀⠀⠀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡆
⠀⠀⠀⠀⠀⠘⡄⠀⠈⢆⠀⠀⠀⠀⠀⣀⠔⠁⡰⢗⠒⠒⠒⠒⡺⢆⠈⠢⣀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠑⠒⠒⠒⠉⠀⡠⠎⠀⠘⣄⣀⣀⣠⠃⠀⠳⢄⠀⠉⠒⠒⠒⠊⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⠀⠀⠉⠒⠤⢀⣀⣀⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣯⣿⠇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⠿⠿⡿⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋⠁⠠⣤⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⢹⣦⣜⣛⣛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⢀⣀⣻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠙⢋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣦⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠺⠿⠃⠀⠄⠀⠀⠀⢠⣿⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢾⣿⡟⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣾⣿⣿⣿⡄⠀⠀⡀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⢀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣿⣿⡏⠉⠉⢻⣿⠀⠀⠃⢀⣿⡿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⣿⣿⣶⣤⣦⣿⣆⠀⠀⢸⣿⣧⣄⣠⣴⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠻⠟⠛⠛⠛⠛⠉⠁

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠒⠛⡹⢉⠽⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠋⣉⠤⠔⠊⠉⢣⠚⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⢡⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣫⣽⠿⡆⢹⡟⣻⣶⣭⣓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣵⠾⢻⣿⣿⣿⣿⣉⣻⣿⣿⣿⣯⡻⣮⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⣾⣿⣵⣶⣾⣿⠿⢛⠂⢹⡙⠯⣙⠻⢿⣿⣾⣿⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⡿⠟⠋⠉⠀⠀⠁⠀⠀⠂⠀⠈⠣⡀⠉⠻⢿⣿⡎⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⢟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢢⡙⢿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⡄⠁⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠈⣿⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣌⡙⠒⠤⠴⣁⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡇⢀⣀⣸⠧⠟⠃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⠬⢭⣒⠲⠦⠤⢤⣬⣍⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣥⠤⠤⠶⠒⠋⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢍⣀⠀⠡⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢊⡩⢄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡾⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⣿⣿⡿⠁⣶⢻⣿⣿⣿⣿⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣹⡇⠀⣿⣿⠟⣻⣿⠇⢾⣿⠃⣾⣿⢿⣿⣿⣿⣟⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣧⠀⢿⡿⠀⣿⣟⠀⣿⡇⠰⡟⢀⣿⠋⣾⣿⣿⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣷⣾⣿⣶⣾⣿⠐⣿⡇⢿⣿⣶⣿⣶⣿⣿⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣿⡏⢹⣻⡟⢿⣿⡷⢼⣿⡶⠿⡿⢿⢫⣿⣿⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⣿⣇⢸⣿⣧⠸⣷⡇⢘⣿⡇⢠⣿⡮⢸⣿⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣶⣾⣿⣦⣿⣧⣼⣿⣧⣷⣾⣶⣿⡿⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⣿⣿⡄⢹⢿⣿⠍⢸⣇⠰⣿⢰⣿⣿⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣿⣿⡇⢸⡏⣿⠀⢼⣿⡀⠋⣾⣏⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⣿⣷⠘⢧⣿⢰⣾⣿⣷⢤⣿⣹⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣯⣿⣴⣿⣧⣸⣇⣿⣬⣾⢧⡟⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣍⣛⡛⠿⠿⣿⣿⡿⠿⠟⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠛⠉

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣳⣶⣾⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡄⠀⠀⠀⢠⡾⣻⠏⣿⢻⣇
⠀⠀⠀⠀⢀⣸⢃⣿⠀⣿⠦⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⢏⠹⡇⡹⡆⠋⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠋⠸⠟⠀⣴⣿⣿⠛⢿⣿⣦⡀⠀⠀⠀⠀⡄⡆⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡟⠀⠈⢻⣿⣿⣦⡀⠀⢀⡡⠐⠊⠁⠀⠀⢀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣷⠀⠀⣀⣹⣿⣿⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⠀⣠⣄⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⡄⠀⠀⣀⠀⠀⢸⣿⣿⠿⢐⣇⣈⡄⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⢿⣿⣿⠦⣀⠀⢀⣠⠞⣿⡿⠀⠘⠉⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠛⠉⠁⠀⠀⠀⠃⠀⡀⠠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⣿⠀⠠⠄⠀⠄⠄⠤⠂⠈⠀⠀⠀⠑⣄⢚⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣇⡀
⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠋⠘
⣿⣶⠀⡀⢀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⣠⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣥⠤⠞⠓⠒⠒⠚⠓⠢⢄⣙⢢⠀⠀⠀⠀⡠⠐⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢃⢀⡴⠋⠀⢀⡠⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡈⠋⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⡄⣤⠠⠤⠒⠊⠁⠀⡼⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠋⠀⠀⡀⠠⠄⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⠻⢷⣄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡀⠐⠄⣴⠋⣰⠊⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠃⠀⠀⢹⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠇⠀⢇⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠘⢦⡀⢀⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠬⠷⣖⠊⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠠⠄⠐⠂⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠑⠄
⢀⡤⠤⠀⠶⣀⠠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⣀⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠑⠠⡰⠆⠠⠤⣄
⣏⠀⠀⠀⠀⢸⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢸⠀⠀⠀⠀⢈
⠈⠁⠀⠀⠐⠊⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⠒⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠢⢍⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡰⢲⠶⢿⢷⡠⢌⠁⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠴⣒⡁⠒⠈⠙⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰⠃⠀⠇⡎⠎⠞⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢞⣠⡿⢻⠛⢷⠚⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠒⠚⠀⠗⠁⣀⡠⠤⠐⢒⡈⠀⠀⠀⠘⠢⢀⡀⠀⠀⠈⢸⣰⠸⡀⠀⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠤⠒⢊⠩⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠍⣐⠢⠄⣉⠀⠉⠊⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠨⠙⠒⠤⠴⠋
⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣭⣬⣭⣬⣭⣭⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣶⣾⣿⣶⣶⣶⣾⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠉⠓⢄⠀⠀⠀⠀⡰⠚⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢸⡃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣤⡎⠀⠀⠀⠀⢳⣄⣀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢳⠀⢀⡏⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣀⠴⠒⠉⠉⠉⠉⠉⠑⠲⢄⡀⠈⠳⡀⠀⠀⠈⡆⢸⠀⠀⠀⢀⠜⠁⠀⣠⠖⠊⠉⠉⠉⠉⠙⠒⠦⣀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⢀⡎⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⡄⢀⣠⠧⠤⣄⡀⢠⠏⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢱⡀
⠀⠀⠀⡼⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⠟⠁⠀⠀⠀⠀⠉⠻⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢧
⠀⠀⠀⡇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠀⠀⠀⠀⣀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢯⡽⠀⠉⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣸
⠀⠀⠀⢹⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡇
⠀⠀⠀⠀⢣⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠒⠲⠤⠤⠤⠤⠤⠤⠖⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠑⠦⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠊⠁⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣤⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠲⠦⠤⠤⠤⠤⠴⠖⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⠤⠤⠤⠤⠤⠤⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⢨⣷⠲⠤⠤⠤⠤⠖⣾⡅⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⠦⣀⣀⣀⣀⡠⠴⠚⠁⢀⡴⠃⠸⡄⠀⠀⠀⠀⢀⠇⠈⢦⡀⠈⠓⠦⣄⣀⡀⣀⣀⠴⠋⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠱⡦⠤⠤⢴⠎⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣤⣀⣀⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⣄⡤⠋⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣤⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⡿⠿⣿

⠀⠀⢀⡀⢀⠀⡔⠀⠢⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⢰⠄⢰⠂⢀⠆⠀⢲⠀⣀⠀⠀⠔⠒⠒⡄⠀⣀⠀⠀⡠⠄⠤⡀
⠘⠁⠃⠀⠀⠁⠀⠀⠀⠄⠘⠀⠀⠑⠂⣤⡈⢿⣵⣮⠣⡈⣄⠾⠲⣤⣘⡠⢃⣀⠀⠀⠀⠀⠘⠨⠁⠀⠈⠀⠀⠀⠸⠀⠀⠀⠉
⠀⠤⢄⠀⠆⠉⠁⠀⠀⠀⢀⠀⠰⠃⠀⢻⣝⣶⣇⣉⢦⢋⣤⣶⣶⣄⣈⡶⣋⠏⣄⠀⠴⠤⠀⠔⠀⠀⠈⢢⠠⠄⠀⠂⠈⠁⠂
⠀⠤⠄⠀⠀⢂⠀⠘⠁⠀⠀⠀⠠⡔⢂⢦⣽⣿⣿⣄⣶⠸⣿⣟⠛⠛⣇⡶⠧⠾⣥⣄⣀⠀⠀⡀⢐⠈⠉⠀⠀⠀⠀⠉⡀⠀⠁
⠀⠀⣠⠴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠙⠣⠿⢿⠛⠛⣏⣉⠭⣿⣶⣾⠟⠃⣸⠒⢾⣿⣿⣿⣷⠄⠀⠀⠱⣠⣶⣶⣾⣿⣳⣶⣤⡀
⢠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣛⣀⡤⠞⣹⠉⡸⣧⢴⣇⣴⡦⠻⣎⢙⠉⠙⠈⠛⢯⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡽
⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠐⠃⠚⠅⡾⢳⡈⠁⠈⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣄⠀⠀⠀⠀⢠⠞⠀⠀⠙⣄⠀⠀⠀⠀⢠⣴⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⢦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠸⡻⠟⠋⠹⡄⡴⠁⠀⠀⠀⠀⠀⠀⠈⢧⢀⠟⠉⠛⠛⡏⠉⠛⠛⠛⠛⠛⠋⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⣳⡀⠀⡇⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⡀⠀⠲⣭⣯
⠠⣶⣦⢠⣤⣄⢀⣄⡀⠙⠿⠋⢀⡀⣧⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⡏
⠀⢹⠇⠂⠻⠃⠘⠿⠃⠒⠚⠒⢻⠟⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⣇⣀⣀⣠⣤⣤⠴⢻⠲⠤⠒⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠀⠐⠀⠐⠒
⢠⣀⣀⣄⡄⣀⢠⣀⣀⣀⣤⣤⠤⠖⣺⡆⠀⢨⡴⣖⣋⠉⠉⠉⠉⠉⠉⣓⣲⢤⢰⠀⠀⣼⠆⣄⡀⡀⣀⣀⣀⠸⠴⡇⠀⠤⠤
⣼⣿⣿⠿⠿⠟⠛⣋⡉⠀⠢⠃⠫⣯⢽⢳⠀⡿⢸⣏⡛⠻⠿⠿⠿⠿⠛⣋⣿⡜⣿⠀⢠⣿⠈⣐⡪⣳⠐⢚⡀⢀⠐⠀⢀⠊⢰
⢀⢢⢤⠤⣷⡉⠉⢤⠐⣾⢫⡶⡂⢠⢸⡘⣷⠇⢸⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⡇⢻⡄⡼⢸⢰⢢⠢⠄⠡⠠⣤⠳⣞⣀⡸⠱⣅
⠐⢽⡉⢡⣈⡟⣉⣉⣇⣼⠐⠀⠅⣀⠘⣷⡇⠀⠘⠿⢿⣧⣶⣤⣦⣼⣿⣿⡿⠁⠀⢻⡇⣾⢀⠝⢁⡂⣸⡀⠨⠤⠏⠋⣠⣀⣤
⠰⣄⡈⠣⡜⡷⣨⠃⡦⢤⠼⠲⠠⠁⠄⣟⠧⣴⣶⣾⡿⠿⠿⠿⠿⠿⠿⣿⣷⣶⡦⠞⢡⡇⡜⠋⢯⢔⡹⠈⠞⠆⢒⠫⣥⡽⠥
⠀⡁⢈⠀⢿⢻⡁⡈⢤⡾⣤⢺⡜⡼⠀⡜⢦⡀⠉⢪⡻⠭⠭⠭⠭⠭⠭⢋⡞⠁⠀⣠⠏⠄⢧⠆⣸⣁⡄⠁⡘⠧⣾⠤⢃⠰⢰
⠀⡧⢸⠎⠉⢸⡈⢣⡘⠿⠛⡯⡠⠃⡂⠹⣄⠳⢄⡀⠳⣄⣀⣀⣀⣀⣠⠞⠀⡠⢚⡁⠐⣞⡎⢉⠓⢴⠘⣒⢡⣥⡌⣢⢌⠄⢛
⠀⠎⡆⢼⠫⣳⠙⡼⣗⠓⢊⡅⡀⠼⣡⠀⡏⠳⣄⠉⠓⠦⣍⠉⣉⠭⠖⠒⠚⠱⡱⠀⠆⢻⠘⢤⡾⠀⡣⣠⠸⣍⡆⠣⡜⢢⠐
⠈⡄⡱⠼⣥⡥⡜⢫⣘⢾⠄⣹⠁⡄⠀⡴⡁⠸⡈⣉⠙⢲⢬⡛⢁⡴⡞⠛⡩⢠⠁⣶⠀⣟⢉⡌⠩⢹⢴⠈⢏⢸⠰⣃⡨⢶⢸
⠀⠻⠆⠲⠑⠃⠣⠇⠋⠖⠈⠻⠄⠫⠁⠠⠅⠸⠰⠇⠎⠀⠰⠟⠻⠴⠁⠘⠓⠚⠷⠠⠆⠨⠉⠃⠰⠚⠖⠖⠉⠾⠰⠡⠰⠟⠂

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢩⠇⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠠⠂⠈⢼⠀⠠⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢄⡀⠀⣸⡰⠁⠀⠙⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠈⠑⢿⠣⣠⡹⢑⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡂⠂⠁⡿⢀⠤⣌⡡⢻⢦⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠒⡒⣒⠊⡉⠐⠒⢉⠢⡀⠀⠀⠀⠀⠀⡃⠄⢀⡠⠀⢾⢚⢰⠙⡡⣳⠁⠀⠀⠀⣸⠟⠢⢂⠄⢐⣒⠰⢒⠋⠁
⠀⠀⠀⠀⠀⣌⡷⡦⣄⠀⠈⢆⠈⠉⠧⡐⣌⠠⠇⠄⡎⠀⠀⣯⠚⡡⠆⡴⣩⣀⡔⣃⠂⡃⠘⢀⠜⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⠒⠀⠀⣀⠈⠉⢷⠀⢠⢬⣨⡦⡾⡟⠔⣡⠈⠉⠓⢷⢀⡇⣀⡂⠷⠀⠒⠒⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⣗⠦⠠⠀⠄⠠⠐⠉⠓⢢⣈⣇⠸⠃⡎⢼⠁⣟⠴⠁⡆⠀⠀⣸⠝⠁⣭⡄⠉⠀⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⠀⠐⢤⠀⠀⠔⢀⡀⠀⣻⡬⡽⠳⢄⠱⣘⣆⢳⠂⠀⠀⢠⢚⢧⡂⢀⠐⠂⢀⠖⡾⢢⡤⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣈⠁⡌⠀⠘⢷⢒⠆⠳⢤⣈⠟⠀⣠⡞⠉⠁⠈⢿⡸⠆⠯⠷⠞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣱⣞⡠⣤⠄⡿⠷⡖⠷⡲⢿⡶⠶⡍⠂⡤⠆⢀⣄⠻⢆⣀⣤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡡⠖⢺⡟⢸⠀⠆⠀⠈⢈⢠⢆⣡⠞⠀⠀⠈⠲⣀⣠⠊⣉⣀⢨⡟⢭⣱⡚⠵⠦⠄
⠀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠢⠬⠤⢌⣑⠚⠂⠀⣝⡠⠛⠁⠀⢀⠀⠀⠀⠈⢂⣩⠵⠎⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢲⠁⠐⠋⠀⣀⡀⠉⢷⠉⡴⢟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⣎⣀⢠⠔⠀⠀⠀⠀⡀⠀⠀⢁⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠉⠎⡉⠣⠀⡀⣤⠔⠒⠉⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠘⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠚⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠰⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠅⠀⠀⠀⠀⠠⣿⣾⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⠀⡿⠋⠻⣷⣄⣠⠤⢼⣿⡦⠤⣄⣠⣾⠟⠋⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣌⣓⠂⢉⡻⠀⠘⣿⠀⠀⢟⡉⠐⣒⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠞⠛⠁⠀⠀⠉⠀⠀⠉⠛⠳⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠛⠀⠀⡞⠿⠄⠀⠀⠀⢠⠿⢱⠀⠀⠛⠛⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠷⣦⡤⠤⠄⠀⠑⢐⠀⠀⠀⠀⠀⠒⠂⠀⠠⠤⢤⣶⡾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡀⢀⡤⠂⠀⠁⠐⠢⣎⡀⠀⠀⠀⢀⣣⠔⠂⠈⠁⠒⢄⠀⢀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠈⠀⠀⠠⡄⠈⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⡠⠄⠀⠀⡇⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⡄⠀⠀⠘⡄⠀⠀⠀⠀⣿⡀⠀⠀⠀⡰⠁⠀⠀⣠⠃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⢦⡀⠀⠈⢲⠀⠐⠊⠀⠉⠀⠀⡍⠀⠀⢀⡴⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢼⡀⠀⠀⠀⠀⠀⢠⠧⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣒⠒⠒⠒⣂⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⠉⠻⠿⠏

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⣀⣤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣇⢸⣻⣿⡇⠙⢶⡀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠈⣏⠟⠓⠲⣾⣿⣷⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⡀⢐⡶⢿⡗⢠⡄⠀⠙⢻⡟⣉⣉⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣨⣃⡈⠙⠊⢱⠀⢠⡄⢀⡬⡟⢿⡟⠷⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠬⢭⣀⠀⠀⢢⠀⠀⣈⣿⡟⡮⢁⣄⠐⣜⣳⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⢽⣛⡟⠡⠴⠷⣾⣿⣿⣎⠝⠋⠀⢀⡜⠿⢽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣾⣧⣞⠉⠀⢤⢞⠀⠀⠈⢉⣀⡤⡄⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠈⠋⠤⠴⠿⠿⢟⢵⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣽⣿⣷⣦⠀⢀⡀⠀⣀⠜⠫⠄⠂⢈⣷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⡯⢾⡟⠉⠀⠀⡐⢈⢂⣾⣿⣮⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠙⢳⣸⠃⣍⣷⣤⣤⠾⠛⠁⠈⣻⠟⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠟⠛⠋⠉⠀⠀⠀⠀⠼⠣⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠰⠄⠀⠀⠀⠀⠈⠻⣿⠿⠀⠐⠾⣻⢓⣧⠀⠀⠀⢠⠤⢀⠀⠀⠀⠀⣀⠒⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⡀⠰⠦⠐⠓⠸⠃⠶⢰⠦⠒⠘⠛⢶⣶⣿⡄⡀⡍⡉⡁⠰⠃⠀⠀⠀⣴⣦⡤⠀⠀⠙⣉⣿⣿⠏⠁
⠠⢊⣠⠀⠀⠀⠤⠀⠆⠐⠂⠛⡀⠛⢠⣮⣤⠆⠀⠀⠀⠈⢹⠇⠆⠻⠃⠓⠀⠀⠀⠀⠀⣿⡟⠁⠀⠠⠾⠟⠛⠁
⠀⠈⠀⠀⠰⢠⡄⠰⢂⠐⠃⣈⠁⠶⠂⣈⠙⠀⠀⠀⠀⠀⣾⠀⠀⣀⣀⠀⣵⣦⡤⣴⢶⣿⠈⠠⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡄⠗⠈⢁⣄⠋⡀⠒⠀⠉⣀⠉⠁⢠⡤⠚⠽⣏⣻⠟⣡⣼⣿⣿⣿⡇⣓⠿⡻⠆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠋⡀⠛⣀⠁⠘⠋⣠⣏⣭⣽⢛⣛⠭⠥⢲⣿⠿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠛⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢠⠞⢉⢤⡈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢠⡏⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⢀⠉⠀⠀⠀⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣠⡄⢰⣅⢀⡀⠀⢀⠙⠀⠀⠀⣠⠀⠀⠀⠀⠂⢹⠃⢀⡾⠁⠀⠛⠍⠀⠀⣀⣷
⠀⠀⠀⠠⢀⡸⠀⡠⠆⡠⠼⠿⠨⠦⣤⣄⡙⠲⣼⡄⠀⠂⣤⣤⣿⠶⠯⠴⠿⣿⠶⢤⣤⣤⣭⠟
⠀⠀⠀⠀⠙⠀⠀⠇⣀⠃⢀⣨⣤⡶⠶⣿⣿⣷⡘⣿⣆⣼⡿⠛⠉⠐⠀⠈⡀⢈⣳⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡸⠋⠀⠁⡀⣀⡀⠈⢿⣿⣾⣿⢏⣴⠶⠛⠛⠓⢒⡀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠻⠆⡮⠚⢿⡰⣶⠀⠙⣿⣿⡟⢀⣠⠘⡄⠁⢈⣉⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠋⡀⠉⠁⠂⠀⢘⣿⠇⠐⠂⠁⠀⠀⠉⠘⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡿⣹⡆⠀⠉⠀⠈⠀⢨⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠄⣸⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠟⡁⠀⣼⠞⣧⡤⢸⣦⠀⣳⡶⠶⠀⣬⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⡸⡝⠀⣈⣵⡄⠈⢬⠃⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠘⣤⠀⠀⠁⠁

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠀⠐⡀⢀⠀⠀⢠⠀⡈⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠈⠀⢰⣧⣷⠀⠀⢰⣮⣷⠀⠘⠀⠀⠀⠀⢼⣥⡧⠀⠀⣠⢠⡐⠄⠀⠀⠀⠀⠈⠀⢰⣧⣶⠀⠀⢠⣴⣦⠁⠰
⠀⠀⠀⠠⠶⠉⠉⠘⠛⠈⠉⠱⠦⠀⠀⠀⠀⠶⠂⠉⠁⠶⠆⠻⠿⡃⠀⠀⠀⠀⠀⠀⠠⠦⠙⠉⠰⠖⠘⠛⢫⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡄⡆⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢒⣫⡀⠀⣜⡒⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢁⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⣰⢣⠃⠀⠀⢀⣸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⡇⡇⠀⡌⠀⠀⣛⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠃⢰⠀⠀⠀⠸⣿⣿⡗⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣽⡄
⠄⠀⠀⠀⠀⢻⡀⢰⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⣿⣦⡀⡀⡀⣾⡟⠀⠀⣠⣼⣿⣿⣧
⣧⠀⠀⠀⠀⠀⢳⡀⢆⠀⢀⣶⣿⣿⣿⣿⣤⣤⣤⣻⣿⡿⣷⣿⣿⣅⣶⣿⣿⡟⣿⣿⢯⢃⡀
⣿⣧⡀⠀⠀⠀⠀⠙⢌⢲⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⡿⡌⠛⢸⣿⡿⠉⠙⠜⢋⣵⣿⣿⣷
⣿⣿⣷⣶⣦⣄⣀⢀⣼⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣾⣤⣼⠿⢤⣤⡴⣚⠛⢛⣛⡿⠟
⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠛⠀⠀⠈⣿⣿⣯⣿⠿⣿⣿⠁⠀⠀⠉⢅
⠀⠀⠀⠀⠅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⣠⣿⣿⣟⢃⣶⣤⣭⣔⢦⣄⠀⠀⠱⡀
⠀⠀⢠⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢫⣿⣿⣿⢿⣿⣷⡄⠀⠐⡀
⠀⠀⢼⢷⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠙⣿⣿⣿⣿⣿⣟⣿⣿⣿⣦⣾⣿⣿⢹⣿⣿⣿⠛⠀⠀⠱⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⠉⠻⢧⣅⣈⣿⣿⣤⣿⣿⠃⠀⢀⣴⣶⣿⠇
⠀⢠⠷⣿⣿⣻⣿⣿⠟⡃⠀⠀⠀⠀⠀⡿⠛⠃⣥⣿⣧⡄⠀⠀⡀⢰⣼⣿⣿⣿⣹⣾⣟⠞⣻⡿⡏
⠀⠀⢠⠟⢿⣿⣿⣧⣦⢉⠁⢀⠆⢸⣾⣃⠀⠀⠉⠿⠏⠁⠀⣼⠇⣸⣿⣿⣿⣿⣶⠁⠈⠉⠁⠀⡁
⠀⢰⣧⣦⣶⣿⣿⣻⠇⠘⠐⣿⠀⠀⢻⣿⢷⢦⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠋⣠⡖⠀⠀⠀⠀⠀⠃
⠀⢰⣿⣿⣿⣿⣿⡁⠀⣆⢤⠉⠀⠠⣾⣿⣅⣁⢡⠀⠀⢀⣤⣆⢀⣙⠋⠉⠀⠁⠀⠀⠀⠀⠀⠰
⠀⠈⠇⣿⣹⣿⣿⣿⣦⡘⣤⡀⠀⣼⣊⣿⣝⠈⠳⠀⠀⣿⡻⣿⠇⠀⠀⠀⠠⣀⢠⣀⠀⠀⢠⠁
⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⢛⣿⠛⠿⣿⣿⣿⣆⠀⠀⠐⣿⡿⠯⠀⠢⠀⠀⠀⢽⣿⣿⣷⣶⣧⣤⣀⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠆⢤⡤⢘⠻⣷⣄⡀⠀⠀⠙⣷⢂⠀⠈⠢⡀⠀⠀⢋⠟⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⢿⢿⠿⣿⣫⣿⣿⣿⣿⣆⣿⣿⣾⣿⣿⣦⣈⢿⣿⣿⣆⡀⠀⠀⡡⠖⡁⠀⠀⠈⠈⠙⢿⣿
⠀⠀⠀⠀⢸⣆⡴⣷⡿⣿⣿⣿⣟⢿⣿⣿⡿⣿⡝⡿⣿⣿⣿⣿⣿⣿⣶⡶⠉⠀⠈⢊⠲⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠟⢰⢻⢹⢻⢉⣎⡾⢿⣿⣿⠻⢿⡿⡸⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢃⠙⣆
⠀⢤⠄⠀⠀⠀⠘⡆⡸⣼⠞⠋⠀⢠⢏⡿⠀⠀⠙⣧⡼⠏⠉⠀⠈⠹⣿⣿⡇⠀⠀⠀⠘⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢼⠃⠀⠀⠀⢸⠞⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢰⠀⢠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣿⣿⣯⡅⠀⠀⠂⠀⡌⡞

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⣴⠛⠛⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⢾⠆⠀⣿⠤⠄⠀⠀⢸⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠁⠀⢷⣤⣤⡄⠀⠸⣤⣤⡤⠀⠀⢧⣤⣤⠀⠀⠘⢦⣤⠜⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣤⢤⣄⡈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠊⣉⢤⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣞⠀⠀⠀⠙⠳⣄⠈⠳⣄⠀⢀⣀⣀⣀⣀⡀⢀⡤⠚⢉⡤⠖⠋⠁⠀⠈⡣⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⠀⠀⠀⠀⠀⣠⠗⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠰⣉⠀⠀⠀⠀⠀⢀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠰⡆⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡼⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠲⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⣸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡤⠝⠦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠊⠉⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣽⣯⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠒⠮⣉⡽⢁⠜⣰⠋⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⢞⠀⡞⠀⠉⣆⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠤⠒⠀⠉⢙⠗⢖⠋⠁⠀⠀⠀⠀⠢⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⡰⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡖⠁⠀⠀⠉⡰⠖⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⠻⣕⣲⠔⠓⠒⠉⠉⠉⠉⠉⠘⠁⠀⠀⠒⠂⠤⠤⠤⠄⠀⣀⣠⡀⠀⠀⠁⠀⡄⠀⠳⡶⠶⡏⠈⣶⠓⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢲⣼⡦⢬⣷⣀⢰⠀⢤⣀⣀⡀⠀⣀⣠⣤⣤⣤⠤⠴⣖⠈⠉⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⢠⠛⡋⠙⣏⠁⡿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢲⠤⡀⠀⠀⠉⠙⢦⡈⠁⠉⠉⠡⠉⠐⠀⠉⠉⠒⢤⣈⠁⠐⠂⠀⠀⣀⡀⠸⠊⣸⠦⣾⠓⡋⢻⡉⢹⣦⣼⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡈⠲⣄⠀⠀⠀⠈⠳⢤⡀⠠⠀⠀⠀⢀⠀⠄⠀⠈⠛⢿⡃⠀⠀⠀⣠⠖⠛⠛⠒⣿⡂⠙⠳⢾⣉⣤⣼⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠐⣄⠀⡙⢲⠤⣄⠀⠀⠑⣦⣄⣀⠀⠀⠈⡀⠀⠄⠀⠂⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⣯⠉⡤⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂⢾⡖⠓⠒⠒⢾⡀⢈⠂⠐⢈⠉⠒⢤⡈⠳⡉⠓⠦⣤⢀⡤⢤⣬⣠⣐⡠⣳⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠦⢿⠄⡟⢢⡆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⡗⠤⢄⣄⠨⠻⣷⠶⠶⠶⣛⡯⠭⠤⣼⣾⡇⠤⠤⣀⠀⠀⢀⡞⠁⠀⠈⠓⣏⣹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡊⠀⢀⠂⡁⠀⠈⢳⣄⣉⠁⠀⠈⢧⠀⡜⠁⠀⠀⠀⠀⠿⠄⠀⠀⠀⢱⣴⠟
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢧⡙⢦⣄⡀⠀⠀⠀⢀⠻⣟⠛⠳⠶⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠓⠤⣌⠳⣌⠛⢶⣀⣠⠂⢁⠈⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠤⣤⠴⠛⠁⠀⠀⠀⠙⠲⠼⣆⠀⠉⠙⠛⠶⠖⠞⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⣄⠀⠀⠀⠀⠀⡉⢠⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢻⣦⠀⠀⠀⡰⠁⣾⠃⠀⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⢀⡠⠀⠈⢿⡄⠀⢻⣧⠀⢰⠇⣸⡏⠀⢸⣿⠀⠀⠀⢂⠄⠉
⠀⠀⠀⠀⠻⣿⣛⠛⠻⠷⢶⣤⣄⡒⠉⠲⣄⠘⣿⡀⡄⢻⣆⠈⢰⡿⢀⠆⣼⡇⠀⣠⠔⠁⠀⣀⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠈⠉⠻⢷⣤⡈⠳⣼⣧⠰⠈⣿⣧⣿⢁⡞⣠⡿⢀⠜⣁⣤⡶⠟⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠠⣀⠉⠻⣦⡙⣿⡆⠃⢸⣿⡇⠎⢠⣿⣷⡷⠟⢋⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡙⢦⡈⠻⣿⣷⣿⣿⣿⣿⣶⣿⠟⢋⡠⠖⣁⣴⠿⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⢲⣿⣿⠏⣁⠉⠻⣿⣿⡎⣁⣤⣾⠿⠥⠖⠚⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠒⢂⣴⣿⣿⣿⡏⢀⣭⠖⢀⣿⣿⣿⠿⠿⠿⠶⠶⠶⠶⢶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠁⠀⢀⣤⣾⠟⠋⡩⣿⣿⣷⣤⣥⣤⣾⣿⡿⠉⠈⠛⠒⠀⠀⠂⠀⠀⠀⠀⣉⣉⣛⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⠿⠋⠔⣪⣵⠞⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣤⡶⠛⠉⢀⣴⣿⢃⠏⣸⣿⣿⢰⠀⢿⣿⣌⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠞⠋⠁⠀⠀⡠⠊⣼⡏⡎⢰⡟⢸⣿⡀⠆⠸⣿⢻⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⢀⠜⠁⢰⡿⡘⢠⡿⠀⡟⢻⣧⠘⡀⢿⡄⢿⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠑⠀⠀⣾⠃⢡⡿⠁⢠⠇⠈⣿⣆⠀⢸⡇⠸⣷⠀⠀⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡿⢠⡿⠁⠀⡞⠀⠀⠘⣿⡄⢸⡇⠀⣿⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣾⠁⠀⠰⠃⠀⠀⠀⠹⣿⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⡇⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢷⢀⣿⣡⠞⠫⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢸⣿⡿⠋⠆⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣸⣿⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣧⡾⠋
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀
⠀⢈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠱⣦⣄⡀⠀⢠⣄⣿⣿⣏⣠⠄⠀⢀⣠⣶⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣴⡄⢻⣿⣿⣿⠏⣦⣰⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣽⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠻⠛⠉⠈⠙⠟⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⣄⠀⠀⠀⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⢿⢰⠋⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⡇⠀⠘⡆⠀⣸⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠼⢸⠀⡤⣤⠤⠚⠀⠀⠀⠀⠀⠰⢶⣿⣟⠃⢹⡀⡀⢹⠀⡇⡀⢠⠇⠀⢀⣶⡧
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠁⢀⠤⠀⠀⠠⢄⠀⠀⠀⠠⣄⠀⠀⠀⠀⣻⠉⠚⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⡁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣴⣶⠀⠀⣴⣶⡄⠀⠀⠀⠘⣇⠀⠀⣸⠁⠀⠀⠀⠀⢠⣶⡄⠀⣴⣶⡀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠁⢀⣀⠈⢉⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⡁⠀⢈⠉⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⠄⡀⠀⠀⢺⣸⠇⠘⠄⠀⠄⠀⣰⠃⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢹⣩⠋⠀⠀⠑⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡤⠀⡀⠀⠀⠄⠤⠁⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠈⢹⠑⠀⠐⡌⠁⠙⠀⢐⠁⠈⠅⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣆⠀⠀⢠⠏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⡆⢀⡏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠳⡄⠀⡴⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⠀⠇⠸⠇⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⠀⠷⠸⠁⣤⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⢦⠀⠀⠀⠀⠀⢠⢃⡀⣇⠀⣀⠞⠀⠀⠀⠀⠸⣄⠀⢈⡇⡀⢇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠒⡶⠀⠀⢶⡖⠂⠀⠀⠈⣇⠀⠀⠀⢀⠃⡞⠀⠈⠉⠁⣀⠀⠀⠀⠀⢀⡀⠉⠉⠀⠘⡄⢃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠊⢁⣀⣄⣠⣿⣦⡄⠀⠀⢹⠀⠀⠀⠈⢰⡇⠀⠀⠀⠀⡨⠽⠂⠀⠻⢭⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⠃⠀⠀⡟⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡴⢳⢰⢲⡀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠰⠃⢸⢸⠀⠳⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡐⠀⡆⠤⡆⠀⢐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⡀⡐⠸⠀⣀⡀⡄⠸⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠀⠀⠓⠃⠄⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠉⠀⠉⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⡠⢄
⠀⠀⠰⠒⢄⠀⢠⢬⢰⠀⡠⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠆
⠀⠀⢠⠀⠀⠱⡈⠀⠀⠔⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⢄⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⠂⢄⡀⠀⠀⠀⢸
⠀⠀⠈⡀⠀⠀⢐⣀⡌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠺⡂⠀⠐⠢⢄⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⣠⠄⣀⣰
⠀⠀⠀⢱⠔⠈⠁⠀⠀⠉⠂⠜⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠁⠖⠁⠀⠀⠀⠈⠢⡀
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⡀⢎⠀⠀⠆⠀⠈⠀⠀⢈⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠸⠀⣀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⡔⠑⢤⡉⢉⠈⠒⣤⢀⣀⢀⠠⠔⠁⣠⠂⠀⡠⠜⠁⠀⠀⢰⠈⢰⡆⠀⠂⠀⣤⠀⠐⠂⢸
⠀⠀⠇⠀⠉⠀⠀⠴⠄⠀⠉⠀⢀⠀⠀⠁⠊⠀⠈⠈⠀⠀⠈⠀⠀⠈⠂⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣱⠇⡀⢢⡄⠀⠉⠀⠀⠴⡁
⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⣠⡄⠀⢀⡴⣀⠀⣰⠂⡀⠐⠠⠀⡀⡄⠀⠘⡄⠀⣮⣨⠀⠀⠀⠰⠀⠀⢁
⠀⠈⢀⠤⠂⠀⠀⠀⠀⠀⠀⠢⣄⠱⠀⠀⠀⠀⠀⠔⠀⠀⠔⠀⠘⠖⠉⠤⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⡄⠀⢰⠀⠀⠀⠀⠑⠁⠸⢂
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⢡⡄⠀⡇⠀⠐⠐⠐⡀⡔⠄⠆⠀⠀⠀⠀⠀⠀⠀⠐⠁⠓⠓⠢⣮⡀⠤⠐⠓⠊
⠀⠐⠧⠀⠤⠠⠄⠀⠀⠤⠤⠄⠤⠇⠀⠀⠀⠀⠀⠐⠀⠑⠃⠀⠀⠐⠀⠀⠆⠑⠊⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡄
⠀⠰⠈⠑⣤⠂⠐⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡀⠈⡄⠀⠀⠀⢀⠀⠀⠠⢄⢀⡀⢠⡄⠐⠀⠀⡇
⠀⠀⠁⠈⠈⠂⠀⠒⠒⠁⠀⠐⠒⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢂⠀⠌⠀⠀⠁⠀⠀⠀⠀⠡⢉⢛⠲⠲⣪⠋⡀⠦⠤⠠⣃⡠⠐⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠑⣄⠀⠀⠀⠀⠀⠀⢣⠀⠀⢉⠀⠀⡌⠀⠀⠀⠀⢀⡄⢂⠀⠉⠉⣠⠊⠀⠀⠀⠀⠉⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠔⢊⠥⠐⠈⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠀⡥⠄⡔⢊⠀⠁⡀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⡌⠰⠁⣀⡀⢠⠤⠂⠀⠀⠀⠀⠀⢰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⣋⠊⠀⢀⠘⢋⣤⣘⠃⠀⠐⠀⠀⡐
⠀⠀⣀⠧⠇⠀⠀⠀⠀⢆⠀⠀⠀⠀⢠⡀⠐⢐⠀⠀⠀⡆⠀⠀⡠⠄⡄⠀⠀⢘⠀⠀⠢⣀⠇⠀⠣⠄⠊⠀⠇⠐⠀⣀⣀⠤⠁
⠀⠀⠃⠀⠀⠐⠠⠤⠄⠬⢆⠠⣄⠀⠀⠤⠴⠉⠃⠀⠘⠢⠄⠀⠣⢄⣊⡀⠠⠐⠁⠀⠀⠀⠁⠠⠀⢀⣀⠀⠀⠠⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣃⠀⠀⠀⠀⠀⠙⠋⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠘⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠙⠀⢀⠈⠁⠀⠺⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢛⢫⡀
⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢀⡀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠉⠁⠛⠑⢯
⣶⣼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⡶⠖⠒⠀⠀⠀⠸⠆⢀⡀⠤⠀⠒⠐⠒⠂⠠⢸⠁
⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⠇⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣍⣩⡆⠀⠀⠀⠀⠀⠴⡀⠣⡀⢠⡄⠀⠀⠀⢴⡄⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠠⣀⣤⡀⠀⠀⠀⠸
⠉⠀⠀⠀⢀⠀⢀⡀⠈⠅⠀⠀⢀⠀⢠⠼⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠋⠁⠀⠀⠀⢀⡀⢐
⠀⠀⠐⠇⢀⡠⠀⠀⠀⠀⢀⡀⠛⠛⠛⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⢒⣶⠶⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡀⡠⠀⠠⢰⡀⣴⠶⠶⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠪⠟⠷⢆⣤⠦⣀⣤⠂⠀⢦
⠀⢀⣤⠀⠀⠀⠓⠀⢤⠀⣌⡁⠀⠀⢊⣡⡍⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣴⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⣄⠀⠀⡀
⠀⠈⠙⣄⢀⠀⠈⠁⠀⠀⡏⠉⠀⠀⠨⠉⠹⠶⣤⣿⣤⣴⠆⠠⠲⢲⠚⠧⠤⠤⢀⣀⠀⣿⢀⢀⡄⣀⡀⠢⣠⡏
⠀⠀⠀⠍⣧⢀⠀⡈⠁⣁⣁⠀⠀⠀⠀⠀⠁⠀⠈⡈⠁⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⢈⡧⠒⠻⠙⣷⠉⠻⣏⠑⠂
⠀⠀⢠⠆⠁⠘⠉⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠡⡀⠀⢈⠁⡈⠐⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡟⢿⡄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⢾⠋⠩
⠀⠀⠀⠈⠉⠀⠀⢉⠖⠤⠀⢃⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⠋⠀⠀⠹⡄⠀⠀⢀⠶⠦⠐⡀
⠀⠀⠀⠀⠀⠙⠀⠀⢟⣿⠶⣾⡄⠀⠰⡖⠋⢹⠀⢀⣴⠁⣠⡄⢀⡀⢰⡀⢠⠿⠀⠂⡐⠉⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⠒⠒⠉⣿⣾⡟⢼⡧⠤⠧⠀⠺⣤⠟⠁⠚⠛⣣⠾⠿⠈⠛⠋⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣴⣤⠈
⡀⣀⣠⠀⠀⣤⡄⠀⠀⠙⠛⠻⠦⠄⠰⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠛⠷⠚⠀⠀⠀⠀⠀⠸⠋⠠⠤⠀⠂
⠅⠈⠀⠂⠀⠼⠤⠊⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠖⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠂
⠀⣶⠄⠁⠀⣀⣥⠰⠃⠀⠈⢡⠀⠌⠀⠀⠀⠀⢀⣀⢀⢀⣠⣴⠶⢶⡀⢀⡀⠀⠀⠀⠀⠀⠰⠀⠶⠂⠀⠀⠀⠀⡀⠀⠀⠓
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⣀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⣾⣿⣷⣤⣿⣿⡋⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠃⠀⠀⠛⠃⠀⢰⣦⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⣿⣀⣿⣿⡟⢻⣿⣉⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣤⠀⠾⠇⠀⢠⣤⠀⢶⠆⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣷⣾⣿⡿⠻⣿⣷⣿⣿⣿⣏⣈⣿⡿⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠉⠀⠀⣤⡀⠀⠁⠀⠀⠀⠿⠂⢀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣹⣇⣸⣷⣶⡿⣿⣿⣀⣿⡿⠿⣿⡄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⠗⠘⠿⠀⠉⢁⡀⠀⠾⠇⠀⣠⡀⢛⣯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⣶⡶⠾⠏⢻⡿⠿⣿⣤⣾⣿⡿⠿⣷⠶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠉⠉⢉⣉⣠⣧⠀⣠⡀⠛⠃⠀⠀⣀⡀⢉⣅⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠻⣿⣿⠀⠀⠀⠀⠑⠖⡻⢿⢹⣏⠷⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⢰⠀⠀⣸⣿⣿⣿⣷⣋⡥⣀⠆⠀⢂⡙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢱⣿⣿⡄⠀⠀⢀⠀⡀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠹⣿⠀⢠⣬⣥⣥⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢰⠀⢹⣿⠛⠚⠛⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠈⣿⣿⣿⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡆⢸⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠥⠤⠠⠠⠤⠦⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣽⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⣾⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣏⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣴⣿⡅⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄
⢤⣾⣷⠆⠀⠀⠀⠀⢠⣿⠏⠀⠙⠿⣿⣷⣄⣠⡤⠶⠖⠺⣿⣿⡿⠒⠶⠤⣤⣀⣴⣾⣿⠟⠁⠈⢻⣿
⠀⠟⠛⠃⠀⠀⠀⠀⠨⣿⡄⠰⢦⣤⣤⠉⠛⢿⣿⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⠟⠋⢩⣤⣤⠴⠂⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣦⣤⠄⢀⣠⣤⡙⠀⠀⠀⢹⣿⠀⠀⠀⠙⣡⣤⣀⠀⢤⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⡼⠟⠛⠛⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠛⠛⠷⡄⠈⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣤⣄⡀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣀⣤⣤⣷⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠉⠁⠀⠀⢸⡇⠿⠏⣇⠀⠀⠀⠀⠀⠀⢀⡏⠿⠃⣿⠀⠀⠀⠉⠉⠉⠉⠙⢆
⠀⠀⠀⠀⢀⣴⣯⣄⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡤⠏⠀⠀⠠⠤⠄⠀⠈⠧⣄⡴⠃⠀⠀⠀⠀⠀⠀⣀⣀⣬⣷⡄
⠀⠀⠀⢠⠞⠛⠛⠿⠿⠿⠟⠛⠛⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠟⠛⠛⢦
⠀⠀⢀⡏⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠓⠲⢄⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠴⠚⠋⠉⠉⠙⠓⠦⣀⠀⠀⠀⠈
⠀⠀⢸⣷⣶⠆⣰⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⣿⣶⣦⣤⣤⣤⣤⣴⣶⣾⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢴⣶
⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠒⢦⡀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠈⠁⠀⠦⣠⠖⠂⠀⠀⠀⢸⡇
⠀⠀⠀⢧⠀⠀⢹⡀⠀⠀⠀⠀⠀⢻⡀⠆⠀⠀⠉⠀⠀⠉⠙⡏⠉⠁⢠⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡼⠁⠀⣠
⠀⠀⠀⠈⠳⣄⠀⠹⣄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠠⠀⠀⠀⣸⠛⣄⠀⠀⠀⠀⢀⣡⠞⠁⠀⠀⠀⠀⢀⡼⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠛⠦⣌⣢⣀⠀⠀⠀⠀⠙⢲⠶⠤⠴⠶⠚⠁⠀⠀⠉⠛⠛⠋⣏⠀⠀⠀⠀⠀⢀⣴⣋⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⣀⡤⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣀⣀⣤⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⡀⠀⠀⢀⣠⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠉⠻⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣟⣛⣁⣀⣀⣀⣀⣀⣙⣻⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠐⡆⠀⠀⠀⠀⢀⣰⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⠎⠀⠀⠀⠀⠀⣾⡏⢸⠁⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠗⠁⠀⠀⠀⠀⠀⢸⣿⢀⠇⢠⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠀⣠⣤⡄⠀⠀⠀⣾⣿⡞⠀⣾⢇⠎⠀⠀⢀⣀⠀⡠⠚⠉⢀⡤⠖⠂⣩⠟⡿
⢀⣤⣄⡠⡀⠀⠀⠁⢹⣿⠞⣴⣿⠁⣀⡀⠀⢻⣿⠀⢸⣿⠏⠀⠀⡆⠙⣿⡿⠀⠀⡴⠃⠀⣠⠞⠁⢠⡇
⢠⠿⠣⣅⠓⢰⣀⣀⠈⠉⢰⣿⠇⣼⡏⡼⢀⡞⠻⡤⢾⣿⠀⠀⡼⢧⣠⡿⠃⠀⠀⣳⢶⠊⠀⠀⢀⡜
⠈⢹⠓⠈⠳⢌⡁⢠⡇⠀⢸⣿⠀⣿⣏⣠⠊⠀⠀⠀⢸⣿⣠⠞⠁⠀⠀⠀⠀⠠⠊⠁⠀⠑⠒⠛⣉
⠀⠀⢡⡏⠀⣨⣹⠲⢍⡀⠀⠉⠉⠈⠉⠁⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⡏⠁⠀⠳⣤⡀
⠀⠀⠀⠉⠛⠁⠁⠀⠀⢉⣀⣀⣀⣀⣀⣀⣿⡏⠀⠀⣀⣀⡤⠤⠈⠁⢠⣤⠊⢹⣿⠁⣿⡇⠀⠈⠒⠒⠋⠺⠃
⠀⢠⣶⠛⢢⡀⠀⠀⠐⠉⠀⠀⠈⠉⠉⣻⣿⠛⠋⠉⠉⠁⠀⠀⠀⠀⣾⡏⠀⣼⡇⢰⣿⠃⠀⣀⡀
⢠⣿⢁⣴⣿⠁⠀⣰⣦⠀⠀⣴⡆⠀⠀⣿⡏⠀⢀⣾⠂⠀⣠⡀⠀⠀⡿⠃⠀⠈⠀⢸⣿⠀⠀⣿⡟⠉⢉⣷
⠘⠟⠋⣽⡟⠀⣰⣿⠇⢀⣼⣿⠇⠀⡰⢻⣷⣠⢾⣿⠀⢰⣿⡇⠀⡼⠁⠀⠀⠀⠀⢸⣿⠀⢸⣿⠇⠀⣰⣿
⠀⠀⠀⢿⣇⡼⠉⢿⠴⠋⣼⣿⠀⡼⠁⠀⠉⠀⠘⢿⡴⠚⣿⠀⡼⠃⠀⠀⠀⠀⠀⠐⢿⣀⠼⠟⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⣢⣭⡭⣭⣭⣫⢭⢭⣭⣅⡓⢄⡀
⠀⠀⠀⢀⣤⣶⣶⣿⣶⣦⣀⠀⠀⠀⠀⣀⡴⣿⣷⣿⣿⡙⠋⢟⣱⡮⡽⠟⡕⣿⣾⣾⣿⢦⣄⡀⠀⠀⠀⢀⣤⣶⣾⣶⣶⣤⣀
⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⣫⣷⣿⣿⠟⠛⣿⣷⢀⡄⠚⡛⠠⢀⣷⣿⠋⠛⣿⣷⣾⣭⣋⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⠏⢘⠽⣦⣫⣽⣿⣿⣟⣩⣿⢶⠂⠀⡻⠿⣶⣦⣾⣾⠿⣟⠀⠐⣶⣿⣭⣿⣿⣿⣯⣭⣅⡟⠓⣈⣻⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣷⣼⣷⣛⣽⣻⣴⠿⢯⡁⠀⠙⠏⢿⡀⠁⡀⠘⢻⡿⠡⢐⠉⢀⡿⠝⠉⠀⢈⡽⠿⢶⣟⣯⡟⣿⣯⣷⣿⣿⣿⣿⣿
⠀⠀⠛⢿⣿⣿⣿⣿⣯⣵⣮⣾⣷⣖⣢⡈⢂⠀⠈⡇⠹⣟⡛⢷⡃⢨⡞⡋⢟⡋⣬⠀⠀⠐⢁⣔⣲⣾⣷⣽⣧⣭⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⡿⣿⠻⣿⣿⣿⡄⡇⠀⣷⠀⢀⣟⣼⣁⣈⣧⣯⡜⠀⣾⠀⢸⢠⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⣿⡿⢿⡿⣧⡀⠟⡠⡾⠁⠀⠀⠀⠀⠉⢳⢄⠁⢀⣾⢻⡿⢿⣿⠀⠀⠀⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠸⣷⡘⣇⠠⢀⠤⣒⠋⠙⠛⠑⣒⢌⡀⠀⡾⢡⡾⣇⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⠀⢣⣸⢳⢹⡶⣭⠀⠉⠀⣆⣡⠄⠉⠑⣝⢦⡇⡾⣷⡼⠀⢸⢄
⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⠏⣩⠗⣻⡄⠈⣿⣼⣼⢱⡀⢰⡖⠈⠀⠀⠉⠰⡄⢀⡟⣷⡇⣿⠁⢀⣟⢹⣉⡝⣷⡦⢄
⠀⠀⠀⠀⠀⠀⣸⡴⠟⠛⠋⢿⢸⠁⠻⣄⣿⣿⢻⠁⣈⠃⠱⠤⠄⠤⠤⠌⢸⡁⣁⡇⣿⣿⣠⠞⠀⣇⡿⠙⠛⠳⢦⣡
⠀⠀⠀⢀⠋⠀⡟⢀⠀⠀⠀⢸⡾⡄⠀⠈⣿⢹⣼⣫⠥⠖⠓⠋⠉⠉⠙⠛⠺⠮⣟⣣⣿⣿⠁⠀⢠⣿⠇⠀⠀⠀⡈⢷⡀⠑⡆
⠀⠀⠀⠁⠀⠘⢷⡀⣸⡆⢀⡼⠃⢽⠂⠒⣾⣿⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⠒⢐⡏⠼⠦⣀⠠⠾⣀⡾⠃⠈⠉⡄
⠀⠀⠀⣆⠀⠀⢨⠈⠀⠀⢈⣧⡟⠷⠃⣼⣹⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣧⠘⠾⢻⡼⣇⠀⠀⠀⢕⠀⠀⣀⠁
⠀⠀⠀⡏⠑⠓⡻⠂⠶⣀⠉⠀⢨⠎⠉⢹⡿⠀⣸⣿⣿⣿⣷⡙⣿⣿⢫⣿⣿⣿⣾⣧⠀⢻⠋⠉⢻⡁⠀⠉⢩⠖⠂⢞⠓⠪⢹⠂
⠀⠀⠀⢹⣤⢰⡀⠀⢀⠘⡶⠖⠻⢇⠠⣼⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠀⢸⡇⠄⡸⠗⠲⢶⠁⡀⠀⢀⣅⣠⡄
⠀⠀⠀⡇⠀⢀⡵⢤⡏⠩⠰⠐⠀⣄⡷⣽⢻⡀⠀⠙⡻⢿⡿⠿⠿⠿⠿⠿⡿⢟⠋⠀⢀⡞⣿⢿⡤⠀⠀⠈⡉⠰⡤⣮⡁⠀⢸
⠀⠀⠀⢳⠀⢸⠀⢈⣷⠀⠀⡀⠀⠐⠛⢸⡷⠿⠿⣿⣿⣦⣄⡀⠀⠀⠀⣀⣤⣿⣿⠿⠿⢾⠃⠿⠀⣀⣈⠁⢀⣿⡀⠀⡇⠀⡚
⠀⠀⠀⡴⠓⠛⠻⢹⠀⠱⡶⠀⠀⡓⠐⣸⠃⠀⣴⠳⢼⣾⡍⠉⠉⠉⠉⢉⣷⠋⠲⡆⠀⠘⡆⠀⢎⠀⠠⢷⠀⢀⡟⡟⠓⠛⢳
⠀⠀⠀⣧⡀⣰⠞⢸⡗⠀⠀⠠⢎⠄⡰⠙⣄⢀⡿⠀⠚⢇⠙⠶⣤⣤⠔⠋⡸⠃⠁⢦⣀⣰⠹⣄⠨⠓⠠⠈⠠⣶⠗⠚⡄⠀⣸
⠀⠀⠞⠉⠉⡻⣄⣠⣝⣚⣓⡠⠄⠈⣇⣀⡟⠈⠀⠀⠀⠀⠉⢲⡇⢸⡗⠉⠀⠀⠀⠀⠉⢻⣄⣸⢁⠬⡀⣐⣛⢫⣄⡴⡟⠉⠁⢁
⠀⠀⡇⠀⠀⣐⠀⠀⠈⡸⠛⠙⠷⣋⡽⢅⣸⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⣧⣠⢿⣈⠻⠛⠙⣇⠀⠀⠁⣃⠀⠀⢈
⠀⠀⠈⠀⠈⠿⡦⡀⢾⠁⢀⠀⣸⡝⠈⠀⣀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⠀⡀⠩⣇⠀⠀⠘⡷⠀⣴⣿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠑⠀⣛⣒⠪⠊⠈⠁⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠁⠀⠀⠃⠙⠗⡒⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠜⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢡⠀⡌⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠘⣮⡖⠁⠀⣀⡤⠤⠤⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡃⡠⠊⠁⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠉⠉⠉⠉⠉⠉⠀⠚⠀⠀⠀⠀⠙⠀⠀⠀⠠⠎⠀⢠⣤⠤⠖⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⢖⡁⠀⠀⠀⠀⠀⠀⠀⡤⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣄⣀⣀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠐⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⡀⠀⠀⠀⠀⠀⠁⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⡠⠒⠈⠐⠀⠠⠤⠐⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠑⠢⠄⠂⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢒⠢⠋⣀⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⡂⠅⠐⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢁⡨⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢈⣁⣀⣤⣭⣤⣌⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⢉⠑⠠⡀⠀⠀⡀⠀⢉⢑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠑⠤⢈⣀⠡⠔⠐⢤⠃⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⠁⠀⠁⠢⣀⠀⠀⠀⣀⠤⠀⢄⡏⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠒⠒⠂⠀⠤⢀⡀⠉⠈⡁⠤⠐⠒⢸⠁⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢰⣋⠉⡋⠍⣋⠉⣉⠉⠙⣒⠢⠤⣼⠁⣀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣼⠀⠀⢀⠤⣄⠀⠀⠘⣆⠔⣲
⠀⠀⠈⠲⢖⡢⠁⠒⠒⣀⠐⠢⠀⠈⠀⣿⡊⠄⠒⠂⠠⠄⣁⠒⠠⠀⠠⠐⡩⠐⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠓⡄
⠀⠀⠀⠀⠀⠈⠉⢓⡲⠖⠈⠀⠀⢀⠍⢿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⢀⡠⠤⢼⠀⠀⠀⠀⠀⠀⠀⢰⠉⠒⠒⠃
⠀⠀⠀⠀⠀⢀⡴⡫⢂⠀⠀⠡⠐⡡⢂⡩⢦⡠⠂⠈⠁⠐⠠⢄⡀⢀⡠⠔⢁⠔⠀⠘⣆⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⣞⢁⠄⡡⣒⠒⣂⠼⠚⠉⠀⠀⠳⣎⠀⠀⠀⠑⠀⠠⠤⠄⠂⠁⠀⠀⠀⢘⣆⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠘⠳⠮⠾⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⡀⠤⠤⠄⢀⣀⠠⠔⡡⠊⠳⢄⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠮⣤⣂⠈⠀⠒⠒⠒⠈⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⡃⠘⣉⠉⠩⠋⠉⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠤⠤⠖⠋

⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡚⠄⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠂⠀⠀⡀⢉⠉⡡⠆⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠃⣀⠈⠢⡄
⠀⠀⠀⠀⣄⠢⢀⢸⣏⢛⠂⠤⠀⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠉⠀⠀⠀⠠⠀⠀⠀⠄⠀⠤⠆⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠈⡀⠀⠁
⠀⠀⠀⠀⣈⠁⠈⠁⠀⠀⠓⡄⠀⠀⡀⠀⢀⠀⠀⠘⠃⠀⠀⢀⠀⠄⠁⠁⠠⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⠀⠀⠀⠑⠢⠀⠀⢀⠀⠀⢁⠀⢰
⠀⠀⠄⠀⠀⠘⠀⠠⢀⠓⠀⠀⠁⡄⡄⠀⢀⡀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠁⠀⢠⡄⠃
⡲⠍⢇⢲⡀⠈⢢⠄⠊⠀⠈⠁⠉⠙⠃⠀⠀⣀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠁⠀⠐⠉⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠁⠁⠘⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠒⠀⠀⠀⠉⠀⠀⠠⠖⢰⠀⠀⠙⢄⣀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠰⠂⠁⠀⠀⠀⠀⠀⠦⠀⡰⠀⠀⠄⡈⠀⠀⠀⠈⢉⠀⠀⠁
⠈⠁⠀⠀⡄⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠆⠀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠆⠃⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁⠠⠀⠺⠁⣀⠀⠤
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⠄⠀⢦⡀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠂⠀⠀⠈⠁⠈⠉⠀⡀⠀⠔⠀⠀⢉
⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡄⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⠀⠐⠈⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⡀⠀⠑⠂⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠠⠄⠀⡄
⠠⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠀⠄⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠴⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠂⠐⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⢀⠆
⠀⢠⠀⠀⣀⠀⠀⠈⠀⠀⠺⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠩⠿
⠀⠀⠺⡄⠁⠑⢤⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⡀⠀⠀⠀⠁⠒⠠⢅⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⢀⠀⠠⠀⠄⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⣤⣀⠀⡠⠄⠀⡀⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠆⠀⢠⢲⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢁⠏⢹⠍⠀⠁⠀⠒⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠈⠑⠂
⠀⠀⠀⣀⣀⡘⢦⢾⡙⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠩⠀⠁⠀⡌⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠉⠈⠁⠀⠀⠀⠀⠓
⠀⠀⠘⠳⠜⣷⢸⣪⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠔⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄
⡀⢀⣀⢀⣀⣉⣀⣉⣀⣀⢀⢀⣀⣀⢀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⡀⣀⣌⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡸
⠀⠀⠀⠀⠀⢀⣀⠉⠉⠓⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡴⠁⠒⠒⢂⣠⠶⠀⠀⠀⠀⢀⣠⠴⠖⠚⠋⠉⢁⣀
⠀⢸⡀⠀⢀⠤⠮⠷⣄⠀⠀⠀⠀⠉⠛⢦⣀⠀⢀⡴⠊⠀⠀⠀⠈⠀⠀⠐⠚⠫⠤⣀⠀⢀⣤⠞⠉⠀⠀⠀⠀⢀⡾⠧⠦⢄⠀⠀⡇
⠀⠈⣇⠀⠁⠀⠀⢀⣈⣆⠀⠀⠀⠀⠀⠀⠿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠶⡶⠦⢤⣄⣈⠳⡿⠁⠀⠀⠀⠀⠀⢠⢋⡀⠀⠀⠀⠀⢰⠇
⠀⠀⠹⡄⠀⠀⡴⠉⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠈⢆⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⠏⠉⠉⠳⠀⠀⢀⡟
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⣈⣧⡀⠀⠀⠀⠐⠛⠓⠆⠀⠀⠀⠀⠀⠀⠈⠑⠬⠂⠀⠞⠛⠒⠀⠀⠀⠀⣰⣃⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠵⠢⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠥⠾⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⣶⣄⠀⠀⠀⠀⠀⢠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢼⣥⡄⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⣼⣯⠀⠀⠀⢀⣿⣿⡆⠀⢠⠀⠠⡤⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠣⢾⠀⢸⣿⣿⣿⣷⣶⣾⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣿⣿⣿⣿⠀⣸⠼⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣏⣿⡟⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⠟⠛⠛⣿⢯⡏⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠹⣎⡣⣄⣀⣨⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣇⣀⣀⠴⣣⡞⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠈⠙⠒⠛⠛⠉⠀⢀⢀⡠⢤⣀⣀⠀⠈⠛⠛⠒⠋⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⣠⣤⣖⡚⠋⠉⠉⠙⠲⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠑⠔⠉⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠔⠛⠉⠉⠉⠓⣲⣦⣄⡀
⠀⠀⠔⠋⠉⠉⠉⠉⠙⠒⢦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠃⠒⠒⠒⠒⠂⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠉⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡁⡀⠀⠀⡠⠖⠚⠉⠉⠙⠒⢤⡀⠀⠀⡈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠛⠛⠻⣿⢶⣤⣀⣤⠶⠶⠟⠛⠛⠷⠶⢦⣤⣀⣴⢾⣿⠟⠋⠛⠛⢛⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠈⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠈⠁⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠃⠀⣠⣶⣿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣶⣄⠀⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⣴⣾⣿⣿⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣟⣿⣿⣦⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡄⠀⢻⣿⣷⡇⠀⠀⢠⣤⣄⠀⠀⣠⣤⣄⠀⠀⢀⣤⣄⠀⠀⠀⢻⣾⣿⡟⠀⢠⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣄⠙⢿⡇⠀⠀⢶⣿⡿⠃⡞⢹⣿⣿⣧⠀⢦⣿⣿⠇⠀⠀⢸⡿⠋⣠⣦⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⡇⠀⠀⠀⠀⠀⠀⣇⢸⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⡷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⠶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠉⠉⠉⠀⠠⢤⣄⣀⡀⢡⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⣄⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠑⣌⠛⠶⣤⣄⣀⣠⣤⡿⢉⡇⢀⣴⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠈⢣⠀⠀⠈⠉⠉⠁⠀⣸⡿⠋⠀⠈⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⣰⣿⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣶⣿⣿⣦⣀⣀⣏⠀⠊⠀⣿⣶⣶⣿⣿⣿⣷⣤⣾⣷⣶⣦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠤⢤⣦⣶⣴⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠀⠀⠈⢀⣠⠶⠶⣦⠈⠙⠻⠏⡟⣾⡆⠀⠀⠀⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡲⠋⠽⠁⠀⠀⠈⠀⠀⣀⡄⣀⣀⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣁⣴⣷⣾⣿⣵⣶⣦⠀⢠⣤⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠘⣿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⣿⣷⣽⣿⣿⣿⠛⠛⠁⠀⠀⠉⠉⠀⠈⠀⠀⢀⣤⣼⣤⡘⢿⠇⣴⣿⣿⣦
⠀⠀⠀⠀⣰⣧⣼⣷⣤⣀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠃⣄⠀⠻⢿⣿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⡀⣀⠀⠀⢀⢀⢀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢰⠿⠀⠀⢰⣇
⠀⠀⠀⠀⠙⢿⣿⠇⠀⣩⠀⠀⠀⠀⠀⠇⠿⠀⠳⠸⠺⠈⠇⠨⠇⠈⠳⠀⠇⠀⢠⢯⠇⣀⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⣸⠟⢰⣾⣿⣿⡆⣠⡀⠀⠀⠀⠀⢠⡄⣤⢠⡀⡄⣤⠀⠀⠀⠀⠀⢈⠁⢸⣿⡿⠛⣿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡋⠱⠟⠃⠀⠀⠀⠀⠘⠁⠛⠀⠁⠃⠛⠀⠀⠀⠀⠀⠌⢀⣼⣥⣠⣦⢈
⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢎⣤⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⠿⠛⠘⣿⣿⣿⢿⣿⢿⣿⣿⣤
⠀⠀⠀⠀⠀⠛⠿⣧⡻⣿⣿⣿⣟⣫⡿⠋⢀⣤⣶⠆⠀⠀⠀⠀⠙⠛⠉⠀⣰⡁⠈⠙⠻⡀⠉⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠋⠉⣩⣴⣾⣿⡿⠋⠀⠀⣄⠀⣆⠀⠀⠀⢠⣿⣷⠀⣿⠀⠡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠁⠀⠈⠀⠀⠀⢉⡧⢀⣤⣿⣿⣿⠀⢯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠛⠁⠀⠉⣓⠀⣀⠠⣶⠁⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡄⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠖⡉⠑⠀⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠢⣰⠂⠈⠁⠋⢶⠀⠚⢰⡀⣊⣀⡬⠤⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠢⡄⠈⡆⠀⣏⠠⠂⠀⠀⠸⠀⠀⢀⡟⠉⠀⠀⡄⠀⠀⠀⢨⠏⠈⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀⡸⠀⣇⠀⠀⠀⠀⠀⣇⡴⢋⡶⢈⠁⢤⠀⠀⠀⣸⠃⢂⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⡴⢠⠀⠱⢇⠀⢹⠀⠀⠀⡦⢠⣏⡤⢋⠆⠸⠀⠀⠀⠀⠀⣅⠤⠚⠉⠩⠀⠑⠂⠀⠀⠊⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡆⠀⡀⠁⠀⢆⠀⠈⢧⠀⡇⣄⠐⣁⣾⡏⠀⠴⠀⠀⢇⠈⡀⣀⡴⠃⠀⠋⠀⠀⠆⠀⠆⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡹⠣⡀⢸⠀⢰⠈⢻⡇⠀⣠⠏⠈⣷⠀⠀⠀⠀⠈⡤⠴⠚⣤⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠀⠙⢾⠀⠀⡀⠀⣿⡞⠁⠀⠀⢸⡆⠀⠀⣠⠚⠀⠁⠂⠠⠀⣰⡄⠀⢠⡄⠊⠀⠀⠀⠀⢀⠀⠀⠀⡅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠒⠒⢾⡀⠀⠈⢧⠀⢡⠀⠸⣧⠀⠀⠀⠀⢻⣦⠚⠁⠉⠀⠀⠈⣀⠠⠢⣄⠀⢈⠁⠀⠀⠀⢀⠄⠛⠀⢦⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠳⡀⠀⠈⠓⣎⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣰⠁⠠⠀⠀⣀⡜⠒⠒⠖⠒⠣⢄⣴⠡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠃⣠⠙⠲⣤⡀⠸⡄⠀⠙⢷⠀⠀⠘⡛⠀⠁⠀⠀⠀⣸⢁⣠⡾⠛⠋⠉⠀⠀⠀⠀⠀⣤⠄⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⠞⠚⠶⣿⣦⡀⡀⢀⠀⢰⣷⠀⠀⣀⣤⣦⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠓⠁⠀⠀⠀⠀⠈⠙⠻⣿⢷⡸⣿⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠞⣹⣿⣿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⣿⣽⣿⣟⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇
⠀⠀⣠⠀⡀⣄⣠⣀⡀⢀⣀⣀⡀⢀⣠⣠⣾⡿⣿⢿⣿⣿⡿⣿⣿⣾⣾⣿⣿⣷⣶⣄⠉⣁⡀⠀⣀⢀⣀⣀⣀⣠⡀⠀⢠⣀⣀⣀⣀⠀⠃
⠀⠀⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣟⣽⣟⢸⣯⣽⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡎⣿⣿⣿⣞⣿⣷⣽⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠈⠀⠀⠈⠈⠀⠀⠁⠀⠁⠈⠁⠀⠁⠈⠀⠈⠀⠀⠀⠉⠁⠀⠀⠉⠀⠉⠀⠀⠁⠉⠈⠁⠀⠀⠁⠀⠈⠀⠀⠈⠁⠀⠈⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢳⠀⣸⠁⢱⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⣿⠻⣇⣿⡶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣆⡇⠀⢸⡏⠈⡉⠂⠐⠂⠀⠀⠀⠀⠤⣷⡝⢿⣩⣿⣼⡿⢽⣿⣣⡀
⠀⠀⠀⠀⠀⣀⣤⣔⠉⢀⡈⠉⢁⡀⠈⢪⠗⠗⢺⠴⠀⠀⠀⠀⢰⣷⣾⣓⢝⣯⣽⣿⣏⢿⣿⣵⠇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⡌⠁⠈⠈⠁⠠⢸⠏⠒⠁⠀⠀⠀⠀⠀⢸⣷⣶⡆⣼⣿⣿⣿⣿⡎⣿⠟⡿
⠀⠀⠀⠀⠹⢿⣿⣿⢿⡷⠄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⣋⣉⠉⢙⡃⢉⣛⡃
⠀⠀⠀⠀⠀⠀⣿⣶⠿⣥⣄⣀⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣭⣭⣭⡴⠲⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡻⣧⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⢰⠀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠹⠸⠀⠇⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡗⠪⠝⠫⠑⢾⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⠀⠠⠚⡄⠀⠀⠀⠀⠀⠀⠀⠈⣛⠀⠁⠀⠀⠀⠀⠈⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠰⢹⠀⢸⣀⡀⢀⣠⡅⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠑⠀⠀⠀⠀⠀⠀⠣⢼⣀⠘⣿⣇⣼⣽⠀⣀⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠉⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠀⠈⠛⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠁⠀⠀⠀⠀⠀⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⡀⢀⢠⣠⠜⣦⠀⠀⠀⠀⠀⠀⢀⡗⠒⠲⣿⡷⠚⣃⣤⡁⠀⠀⠀⠀⣀⠀⠔⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠀⠘⠃⠋⠉⢠⣉⠁⠛⠷⢀⠠⠰⣆⠀⣞⣠⣤⡠⢬⠿⣟⠰⡏⢂⠀⠀⠀⠀⠈⣦⠛⠀⠀⠠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠁⠀⠀⠀⡀⠤⠞⠁⠀⠜⣳⡴⣀⢠⣜⣀⡈⢉⢻⣿⣆⢿⢹⡏⠉⣺⢀⠀⠀⠀⠀⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡐⠛⠉⣀⣠⣼⠿⢈⢴⣋⠞⠻⡇⠁⣨⢁⡾⢆⡛⡛⠚⠶⣧⣾⡇⠉⢀⠤⠞⢃⡠⠄⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢿⡽⣇⢀⡀⡾⠞⣇⡠⠆⣷⣾⣉⡉⠀⣻⠀⢽⠛⢀⣿⡾⢿⣠⠀⠈⢁⠤⠀⠀⢦⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠧⢽⢱⣷⣿⣾⣧⠀⠛⠙⢙⣿⠤⠅⠀⠀⠰⢿⣟⠤⠀⢘⣿⠢⠖⣢⠊⣀⠈⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠾⢼⡟⠛⣩⣭⡁⢲⢖⠙⠁⣠⣷⠤⡄⢀⠉⢁⡂⠴⢾⣬⠯⠿⠿⠤⠁⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⢀⣼⣿⡟⠀⠀⢻⠿⣇⡟⠀⠀⢸⣟⡟⢠⣇⣠⣀⡀⡶⠚⠁⠀⠒⠐⠒⠀⠀⠀⣠⠴⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡞⠀⠈⠿⣛⡆⢱⣣⣯⡀⡹⠇⡀⠔⠣⣴⢻⠀⠆⠊⠀⢐⡉⢳⡻⠀⠀⠀⣀⠘⠂⠰⣾⡗⡁⠂
⠀⠀⠀⢰⠉⠀⠀⠀⠀⠉⠋⠀⣁⠐⠶⠭⠭⡅⢸⠟⠁⠘⠛⢉⢉⠶⠔⢹⠃⡈⠀⢀⡀⠸⢁⡀⠃⢷⢀⠀⠉⠀⢠⠄⠘⢻⢼⣦⡀
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢻⠋⢘⣷⠦⠄⡀⠧⠀⠀⠀⠀⠀⠀⠉⣶⣶⠏⠀⠑⠚⠋⢹⡄⠘⠃⢀⠀⠈⠣⠀⠀⠀⠰⠋⠀⠑⣋⠙
⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠊⠁⠀⠻⣶⠄⢳⢴⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠔⠓⢀⡀⠈⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢵⣠⣴⡆⠀⠈⠀⠀⢠⢋⡠⠂⠀⢰⣭⡿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠟⢠⢊⣷⣀⠀⠀⠀⠰⡂
⠀⠀⠀⠀⠀⠀⢙⡤⢀⠆⢠⡄⣷⠕⣼⡇⠀⠓⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⢲⠸⠟⠉⠀⠀⠰⠀⠰⠂
⠀⠀⠀⠀⠀⠀⡧⠀⠈⢠⣄⢉⢤⣵⠃⠀⠀⠰⣤⡼⠛⠋⠴⠂⠒⡴⠤⠶⡴⠋⢿⠀⠀⠉⠀⡀⠀⠀⢀⣀⡀⠠⣀⣀⣀⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⣤⢞⠹⡏⠀⠀⠀⠀⠈⣿⣠⡧⢳⡄⢸⡄⠛⠀⢀⡠⠉⡀⠀⠀⠀⢩⡟⢤⡏⢸⠉⠾⠛⠚⠈⠁
⠀⠀⠀⠀⠀⠀⣟⠄⠆⠀⢀⢶⡾⠆⠀⠀⠀⠀⠠⡯⡼⠅⠉⠀⣟⢀⣠⢖⢉⡀⡠⠟⠀⠀⠀⠸⡆⠉⡠⠂⣠
⠀⠀⠀⠀⠀⠀⢠⡁⠥⠀⠘⢠⡴⠉⠂⠀⠀⠀⠈⠁⠁⠀⠀⠀⠙⢻⡍⢁⣨⡄⠀⠀⠀⡂⠀⣰⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠣⠀⡀⢀⠈⠇⠀⠀⠃⡄⠀⠀⠀⠀⠀⢁⡠⠘⠻⠀⠈⠀⠂⠀⠀⠀⢿⣯⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣃⠐⠘⠂⡆⠀⠀⠀⠉⠘⠆⢠⡀⢀⢀⡀⠀⠈⠓⠀⠀⠀⠀⠚⠃⠀⠀⠛⠃⠀⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡗⣢⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠄

⣿⡿⢿⣿⠿⣿⣿⠿⠿⠿⠛⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⢿⠿⠻⠿⢿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡏⠂⢙⠻⣿⠿⠶⠒⠊⡞⣿⠄⣉⣅⠀⠀⠿⠇⢀⠀⠈⡆⠀⢀⡄⠠⠃⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⢀⡁⡔⠂⠙⡴⢷⡈⠀⠀⠘⣿⣷⡤⢁⠀⠀⠘⠋⣀⡀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸
⣿⡇⣜⠋⠉⠑⠤⡄⠀⠘⠛⢦⠀⠀⠸⣿⠁⡏⠀⠢⠀⠀⠀⠉⢹⢶⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣿⣿⡉⡧⣀⠁⠴⠴⠛⠻⢧⠀⠲⡗⢠⠷⠀⠐⠢⠀⢠⠀⠀⠈⢿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡆⢻⣿⡗⡁⣸⣆⠠⠀⠀⢄⣿⣿⡴⠙⢏⠂⠀⢾⡄⡀⠀⢃⡀⣀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣬⡉⠁⠀⢹⣿⡇⠀⠐⢻⣿⡏⠀⡀⠈⠀⠀⠀⣀⠙⣦⣋⠈⠩⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠂⡀⠀⢸⣏⠈⠙⡥⠀⠄⠣⠀⠀⠀⠀⠀⠙⠁⠀⠀⣼⣿⢠⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡇⠀⠒⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠌⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⢰⡀⢀⣐⡿⢿⡞⠋⠛⣿⣷⣦⠀⠀⠀⡄
⣿⡄⠈⠀⠀⡄⡀⠀⠀⡀⠀⠈⢀⣾⠟⢿⣷⠀⢰⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⣿⠎⠀⠈⠛⣹⣆⣀⣈⡍⠀⣬⡿⠿⠖⠀⠀⠳⣦⡄⠀⠀⠀⠀⢰
⣿⣤⡴⠀⠈⠀⠘⢦⣤⠁⠀⢀⣼⣿⣶⣾⣿⡧⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡀⠀⠀⢀⣿⣿⠈⠀⠀⢀⣁⡐⡧⠀⠀⠀⣼⣿⡇⡀
⣿⡇⢱⣶⣝⣿⡤⠾⠠⠀⠆⠬⣿⡏⠙⠉⣿⣇⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡋⢴⠂⠤⠄⠤⢀⣀⣼⣿⣯⣀⣠⣴⣿⣿⠱⠷⠄⠀⠀⣝⡛⢪⠀⠀⠀⠀⢸
⣿⡇⠈⠁⢈⡏⠀⠀⠀⠀⠀⠘⠛⠃⠘⠀⠛⠃⠉⠉⠉⠛⠛⠳⠄⠄⢀⡀⠀⠀⠷⣮⣆⣀⡇⠀⠀⠀⠀⢸⠂⠀⠀⣾⠀⢠⣾⠂⢨⣿⢀⣸⣧⠄⠂⢀⣠⣤⣾
⣿⣇⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠉⠐⣆⣿⣿⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠁⠛⡟⣿⣿⣿⣿⡯⠇⢀⠈⠉⠉⡉⠈
⣿⣗⣤⠬⠥⣀⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⠲⢬⡒⢬⣑⠢⣕⡲⣅⣚⠙⢛⠁⢶⠀⠀⠄⠀⢠⡄⠀⠀⣤⠄⢴⣶⠟⢿⡟⠛⣿⠹⠉⠀⠀⠀⠀⢰
⣿⠗⣒⣉⡭⠥⠔⠒⣊⣉⠠⠤⠀⠂⢀⡀⠀⠀⠀⢀⣈⣳⣦⠽⠶⠞⠛⠋⠉⠩⠁⡀⡘⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⢸⣿⠀⣸⡇⢠⡏⠀⠁⠐⠀⠀⠀⠈
⣿⣏⣥⠤⠶⠒⣋⣩⡥⠴⠖⢒⣉⣩⣤⠴⠶⠚⠛⠉⢁⠠⠄⠀⠈⠉⠁⣠⠐⡶⠚⢣⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⣿⠇⢸⡇⠀⠀⢀⠀⠀⠀⠘
⣿⣧⠴⠖⠛⣋⣩⣤⠶⠖⠛⠋⠉⠀⢀⠀⠒⠁⠀⠀⢠⠴⠀⠘⠁⢀⡐⠃⠘⠃⠀⠸⢤⣅⠀⡀⠀⠀⠀⠀⡀⠀⠀⡇⠀⢸⡏⠀⣿⢀⣼⣠⠼⢠⣇⠄⠀⠀⢈
⣿⣧⠶⠞⠛⠉⠁⡀⠤⠀⠀⠀⠀⠀⠀⠛⢛⣿⣦⡀⠀⠀⠀⠀⢈⠀⢀⡀⡀⠀⠂⠠⣘⣿⠄⠀⠀⠁⠀⠀⠁⠀⠈⠉⠒⠋⣹⣿⠛⠉⠿⠇⠰⣿⠿⣄⡀⠀⢰
⣿⡇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢠⢤⡀⠀⠌⠛⠛⠁⠀⠀⠀⠄⠈⠿⠛⢂⠀⠀⠀⠀⡄⠀⠀⣤⣀⣦⣴⡇⠀⠀⠀⣸⣷⢨⠀⠀⡀⠐⠋
⣿⡇⠀⢀⡠⠀⠀⠀⠀⠀⠐⣦⣷⡤⠀⠀⠀⠀⣄⡀⡁⠀⠀⠀⠀⠀⢀⠔⢒⣁⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀⣉⠀⡰⠏⠀⢀⡼⢧⠀⠀⢠⣿⡿⣣⣆⡀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠀⠀⠰⠊⠉⠉⠓⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⣬⠒⠁⠂⠀⠉⠂⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⠀⠟⠀⠀⠁⠀⠚⢋⠁⠉⠉⠁⠀⣠⠘
⣿⡇⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⢰
⣿⣧⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⡿⠿⢿