⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠸⣿⠇⠄⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠁⠀⠀⣀⣴⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢸⣿⠀⣭⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠆⠁⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⢀⢠⣾⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⡿⡗⢂⠀⡀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠆⠀⠐⠂⣀⣀⣀⣀⣀⣂⣀⣀⣀⣁⣠⣤⣍⣀⣀⣀⣂⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠾⠿⠛⠛⠋⣉⣉⣉⣉⣥⣤⣤⣤⣭⣭⣭⣭⣭⣽⣛⣛⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠶⠾⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠷⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣏⣀⣤⣴⡶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣦⣄⡀⠀
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⠶⠶⠶⠶⢶⢶⣶⣶⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⣤⣤⣤⣶⣶⡶⠶⠾⠿⠿⠛⠛⠛⣻⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣤⣀⠉⠉⠙⠛⠛⠻⠿⢿⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠉⠙⠻⢶⣤⣀⠀⠀⠀⠀⠈⠻⢿⣦⡈⠉⠉⠉⠉⣛⠛⢻⣿⠛
⠀⠀⠀⠀⢸⣿⣿⠀⣠⣾⡄⠀⠀⠀⣼⣿⠶⠶⠶⣶⣿⡆⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣠⣴⠶⠶⠿⣿⣿⣶⣤⣀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠉⠀⢿⣿⠀
⠀⠀⠀⠀⠀⣿⡿⣼⣿⣿⡇⠀⠀⣸⡟⠁⠀⢀⣴⣄⠙⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⣴⡿⠋⢀⣀⣀⠀⠀⠉⠻⣿⣿⡆⠀⠀⠀⢻⣧⠀⠀⠀⢀⠀⢸⡿⠀
⣤⣶⣦⣤⣄⣹⣿⣿⠃⢿⣿⠀⠀⣿⡇⠀⣿⡛⣿⣿⡇⠘⣿⣦⡀⠀⠀⢸⣿⠟⣿⠏⢀⣴⢾⣿⣿⡆⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⢰⡄⣸⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣄⠸⣿⡆⠀⣿⡇⠀⠘⣿⣿⣿⣿⠀⢿⡟⢿⣤⡀⢸⣿⣸⡏⠀⠉⣷⣶⣿⣿⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣟⣀⣀
⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣇⠀⠀⢹⣿⣿⡿⠀⣾⡇⠀⠙⠛⠿⢿⣿⣇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢰⡌⠉⠉⠉
⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⢿⣿⡆⠿⣿⣷⣄⠘⣿⣿⠇⣰⡟⠁⠀⣶⡆⠀⠀⠈⢿⣄⠀⠀⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⠀⠀⠀⢸⣿⠀⢀⠀⣴⡾⠿⠶⢶
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣷⢸⣿⠀⠙⠻⠾⠷⠟⠋⠀⠀⠘⠿⠟⠀⠀⠀⠀⠙⢷⣤⣌⣛⣋⣀⣀⣤⡾⠛⢹⣿⠀⠀⠀⢸⣿⢀⣿⣴⣿⠿⠿⠷⠶
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⡆⢿⣇⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⡼⢿⣯⣟⡿⢶⣦⣄
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⣩⣴⣿⣿⡄⠻⣧⣄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣠⣿⣿⣿⣧⠀⠙⢿⣿⣦⡀⠉
⠀⠀⠀⠈⠉⠉⠉⠀⣠⣾⣿⣿⡿⢿⣷⢀⣿⠛⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣣⣾⣿⣿⡿⠁⠻⣷⡀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠘⣿⣿⡏⣠⡾⠛⠉⠙⠛⠷⣶⣶⣶⣤⣤⣤⣤⣶⢶⣶⣾⠿⠟⣋⣡⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠙⢿⣆⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠀⠀⠀⠘⣿⡾⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠈⠻⣷⣜⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⠈⢻⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣷⡷⠀⠀⠲⠶⠤⠀⠀⠀⠤⠤⠶⠶⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠻⣷⡄