Cute Animals Emojis & Symbols

⠀⠀⣀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⢀⣿⣿⡿⠿⣿⣿⡇⠀⠀⠀⢠⣶⡚⢓⣦⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⡤⡘⠠⠀⣤⠄
⠀⢸⢿⣿⠁⠃⢹⣿⠥⠀⠀⠀⡿⠿⠣⠻⠿⢿⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠋⢿⡆⠀⢸⠟⠃⠀⠀⠸⣷⣤⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠈⠙⠛⣛⡃⠀⠀⡀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣭⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠁⠀⠈⡀⠈⠉⡉⢉⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣍⠁
⠀⠀⠀⠀⢤⣦⣂⠀⠰⠦⠉⠀⠀⠈⠆⠇⠘⠇⠿⠇⠿⠸⠿⠿⠁⠿⠸⠀⠇⠸⠇⠿⠇⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠆⠄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠰⢆⡀⠀⣀⠶
⠀⠀⠰⡦⢠⣤⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣆⣶⡄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣸⡿⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣾⠇⠀⠀⣌⣻⠋⢁⠈⠻⣋⣄⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣿⡇⠉⢸⡇
⠀⠀⠀⠍⠉⠐⣚⡃⠀⠀⠘⡧⠀⠀⢰⡟⠀⠀⠈⣭⣟⠀⠀⠀⠀⣯⣭⠀⠀⠀⠀⠈⣽⣿⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇
⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⣽⡶⣶⣶⢾⡏⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣷⣤⡎
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢋⡛⠈⠀⠀⠀⢠⣶⠆⠀⣩⣭⡀⠀⠶⠶⠀⠀⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡀⠀⣀⠀⠀⠀⠀⠀⠀⢺⡒⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠐⠃⢢
⠀⠈⠘⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⡠⠀⠀⠈⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠺⠶⠐⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠚⠃⠀⠀⠀⠚⠖⠳⠂
⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢠⠅⠂⠑⠀⠀⠀⠀⡀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢀⡐⢀⡀⠄⠀⠀⠀⠀⠀⢠⢲⣷⡆
⠀⠀⢢⡴⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢈⡰⢾⡇⠀⠰⠀⠀⠀⠰⠃⠀⠁⠃⢠⡶⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢠⡝⠄⠀⠀⠀⠣⠤⠄⠂⠀⢂⠀⠀⠀⠀⣠⡆⠀⠈⠉⠂
⠀⠀⢠⣮⣤⣤⠀⠀⠀⠀⠠⠄⠀⠢⠈⠀⠀⠀⠈⠀⠜⠅⠃⠀⠀⠀⠠⠆⠀⠴⠈⠃⠀⠀⠀⠈⠋⠙⠚
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠤⠄⡀
⠀⠀⣊⣉⠑⠀⠀⠀⠀⠐⢀⣅⠀⠀⠀⠀⠀⠀⠀⣤⣧⢡⠀⠀⠀⠀⠐⠉⠀⣅⠀⠀⠀⠀⣀⠀⠒
⠀⠀⠙⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠂⠚⠐⢠⠀⠀⠀⠀⣄⡠⠈⠁
⠀⠀⠀⢀⠁⣀⠈⠀⠀⠀⠀⠀⡀⠀⢀⡀⠁⠀⠀⠀⠌⠬⠱⠸⠂⠀⠀⠀⢠⡌⢤⡌⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠋⠂⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠹⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠁⠀⠀⠀⠀⠴⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣦⣄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⠤⠤⠤⠐⠒⠒⠒⠒⠒⠒⠤⠤⠤⢤⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠏
⠀⠀⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣩⠶⣶⣦⡙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⠶⣶⣮⡹⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢸⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡷⣿⣶⣿⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⡷⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸
⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⡙⠿⠿⢟⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣝⠻⠿⠟⢡⣿⣿⣿⣿⣿⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⡤⣶⣶⣶⣦⡄⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠠⠴⠄⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣵⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣯⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠟⠛⠛⠻⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⠟⠛⠛⠻⠿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡀
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠛⢿⣦⣄⣀⠀⠀⠀⣀⣠⣴⣿⠟⠛⠻⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠛⠻⣷⣦⣀⡀⠀⠀⠀⣀⣠⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠉⠉⠙⠒⢦⡀⠀⠀⠀⣀⠤⣤⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙⢆⣠⡮⠥⠶⠶⠿⠤⣰⠁⠀⣀⣀⡀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⣀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠙⠾⣁⣀⠈⢢⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡔⠁⢠⠋⠣⠀⠀⠀⠀⡠⠴⠤⡀⠀⠀⡴⠉⠀⠙⡆⢣⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⡼⠀⢠⠇⠀⠀⠀⠀⠀⡼⠁⠀⣠⣜⡄⠀⡇⠀⠸⣹⣿⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠁⠀⢸⠀⠀⠀⠀⠀⠀⢧⠀⠀⠣⢾⡇⠀⠳⣄⢀⡠⢇⣀⣀⣙⠢⠤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⠤⠴⠊⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠦⣀⡠⠞⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠇
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠑⢤⡀⠀⠀⠀⠈⢣⡀⠉⢶⣤⣀⡀⠀⠀⣀⡠⠔⣋⡴⠋
⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠙⠦⡀⠀⠈⠓⠦⣀⠀⠀⠙⢄⡀⣹⠹⡙⡿⠛⠛⠛⠉⠁
⣰⠁⢹⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠙⠒⢤⣀⠉⣣⠀⠃⡿
⡇⠀⠀⠳⣄⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⡀⢹⣿⠷⠚⠓⠲⢄
⣇⠀⠀⠀⠀⠉⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠔⠋⠉⠉⠻⢧⠀⠀⠀⠀⠀⢣
⠸⡄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠯⠇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⣀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡠⠴⠚⡹⠀⠈⠑⢤⣀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠃⠀⠀⠀⢸⠀⠛⠒⠶⠓⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠉⠉⠀⠀⠀⠀⠠⠶⠭⢵⣒⠒⣾⠀⠀⠀⠀⠈⠑⠒⠶⣶⢬⠳⡙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠐⠦⡉⠓⢝⡜⢤⡀⠀⠀⠀⠉⢢⠀⠈⣧⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢤⣀⣀⣀⣹⡠⠜⠁⠀⠈⠑⠒⠤⠤⠼⠔⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⢿⠦⡀⠀⠀⠀⢀⠃⠀⠀⢀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣀⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡗⠀⠀⠰⣫⣄⠀⠀⢈⡀⠀⠰⡖⠀⡰⡇⠀⠀⠀⢀⡠⠀⠀⠲⣡⠴⢾⣿⣄⣀⠁⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠐⠊⢡⣘⠦⡄⢯⣔⢬⣀⠀⠠⠿⠟⠀⠀⠀⠐⣆⢠⡄⢰⠖⠀⠀⠀⠀⠘⠟⠀⠀⠀⠓⠀⠸⠦⠜⢙⣦
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠶⣭⡓⢦⡒⢮⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠓⠦⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡀⠀⠀⠠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⢀⢀⠀⠀⣀⡄⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠸⠀⠰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠛⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠳⠇⠀⠘⠋⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠒⠒⠈⠀⠀⠀⠀⠀⢠⡠⢦⡀⠀⠀⠀⠀⠀⠀⠈⠰⠆⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⡴⢘⠃⠀⠀⠀⠑⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡚⢋⡙⠃⡄⢠⠈⠁⠀⠀⠀⠀⢰⡀⣆⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠘⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡄⠀⠰⠎⢀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠘⢡⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⢀⡴⠂⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠛⣠⠀⢙⠃⠚⠀⠤⠘⠐⡆⡃⠀⠀⠀⠀⢀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠃⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡍⠀⢨⡤⠀⠀⠰⠇⠀⠰⠇⠀⠀⠀⠀⢸⡇⠀⠸⣿⠇⣠⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡀⠀⠘⠛⣠⠁⠈⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠸⠗⠀⠙⠀⠀⠀⠀⠀⡀⠀⠉⠠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⢠⠴⠲⢤⣀⣠⠖⢀⠀⠖⠀⠀⠀⠀⠀⠀⡀⢃⡀⠀⠀⣬⠱⠆⠀⠀⠀⠀⡀⠀⠀⠀⠁⠘⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠜⠁⠐⠢⠉⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠛⠷⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣤⡴⣶⢶⡶⣶⠲⣶⠞⠛⠒⠀⠀⠠⠄⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠈⠁⠀⠀⠁⣀⢀⠀⠄⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠠⣤⠀⠀⣤⠬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⣶⣤⡆⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡀⣶⣦⡾⢷⣤⣴⡄
⢴⣆⠈⠀⠈⢀⣶⠆⠀⠀⠀⠀⠀⢠⡟⠀⠘⠉⠘⣇⠀⠀⠀⠀⠀⠀⢉⣴⡆⢠⣶⡌⠀⠀⠀⠀⠀⣀⣿⠋⠀⠀⠀⠈⢛⣷⡦
⠸⣒⠀⠶⠆⢀⡺⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⡘⠋⢡⣤⠙⢛⠀⠀⠀⠀⠀⢙⣿⠀⠀⠴⠦⠀⢀⣿⡀
⢶⠉⡄⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⣦⣤⣤⣴⠁⠀⠀⠀⠀⠀⠈⢹⣷⣤⣄⣤⣴⣿⠉⠁
⢸⣰⠇⡀⣀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣻⣛⣧⠀⠀⠀⠀⠀⠀⠀⢠⠁⣭⢩⡄⢂⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠐
⠐⠿⢀⣇⣺⠠⠿⠀⠀⠀⠀⠀⠀⢠⣟⣓⡛⣛⠻⠦⠀⠀⠀⠀⠀⠀⠿⢿⣿⣾⡿⠿⠃⠀⠀⠀⠀⠀⠰⠾⠿⣿⣿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠚⠛⠈⠛⠲⣷⠆⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣤⣄⣀⠁⠀⠀⠀⠀⣰⢉⣿⡿⠿⢿⣦⡀
⠐⠁⢀⣀⣀⠀⠱⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⢰⣟⣿⠁⠀⠀⠀⠈⣟⣻⡆
⠐⡀⠘⠿⠟⠀⡀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠸⠹⠀⠀⠀⠀⠀⠀⠀⠹⣍⣢⣀⣀⣀⠀⢉⣽⣦
⠀⠈⠂⠀⠀⠊⠀⠀⠀⠀⠀⠈⠛⠛⠳⣆⠀⢀⡞⠛⠛⠋⠀⠀⠀⠀⠀⢀⢪⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡿⣜⡟⠶
⢀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣼⡿⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⢠⡨⡄⡛⠚⣤⠄⠀⠀⠀⠀⠀⢠⣿⣧⣀⣼⣿⣾⡀
⠑⠲⣔⣦⣖⡦⠒⠁⠀⠀⠀⠀⠀⠀⠿⠶⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠶⣦⢥⠍⠖⠀⠀⠀⠀⠀⠀⠈⠉⣿⠯⢿⠉⠙⠃

⠀⢀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣱⠀⣀⡡
⠀⠛⢛⣝⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣲⠥⠿⠌⢒⡂
⢠⠈⠈⠈⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠴⠉⠉⠙⠈⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⣀⠤
⠀⠐⠀⡄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠠⡀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠈⠂⠀⠐⢤⡄⠀⠀⠀⠀⠀⠘⡀⠀⡤⠀⢄
⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠈⠙⠀⠂⠀⠀⠀⠀⠀⠉⠐⢤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠓⠁⠂⠚⠛
⠀⠀⠀⠀⠉⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠣⣀⠁⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣⠀⠀⠀⠀⢰⢇⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠈⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⡠⠴⠁⠀⠱⡀⢸⠧⠃⠀⠀⠀⠀⡷⠆⠉⠑⡀⠀⠀⠀⠀⠀⠡⡄⠀⢠⠄⠤⠠⠠⠀⠤⠠⠔⠄
⠀⠀⠀⢀⣄⢀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⠀⠀⣰⠃⡄⠀⠀⠀⠀⠀⠀⡄⣠⢛⠀⠙⠊⠀⠀⠀⠀⢰⣦⣤⣴⠀⠀⠀⢼⣶⣦⣤⡄
⠀⠀⠀⠈⠛⠋⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⠉⠂⣂⠒⠲⣄⠀⠀⠀⠀⠀⠀⢤⠬⡹⢍⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣀⣒⠈⠁
⠀⠊⢠⠌⠑⠛⠐⡀⠀⠀⠀⠢⡀⠀⠀⠀⠀⡇⡂⠋⢉⣆⠉⡃⠀⡈⡇⠀⠀⠀⠀⣀⠼⠜⠛⠠⠴⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠷⠌⠧
⠒⡀⠀⣀⡤⣤⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⡇⠈⠻⣿⣿⠇⠀⠛⢀⠇⠀⠀⠀⠀⢇⠀⠀⢀⡀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠹⡄⠂⠄⠀⢀⠠⠀⠸⢄⡀⠀⠀⠀⠀⠈⠀⠀⠰⠠⠓⡾⠀⠇⢲⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⡆
⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣆⠀⠀⠀⠈⠑⠒⠰⡆⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠘⡆⠈⢡⢀⠀⠈⣅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠐⠂⠀⢀⠀⢀⠀⠀⠰⠈⠀⠀⠀⠀⠀⢀⡤⠃⠸⡒⣲⠆⠀⠽⠷⠀⠀⠀⠀⠀⠀⣸⣈⡀⢸⣀⡀⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠐⠁⠓⠆⠂⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠒⠁⠉⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠃⠘⠛⠃
⠀⠀⠀⢀⡀⢀⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⣠⡄
⠀⠀⠀⣁⠊⠚⢀⡀⠀⠗⢄⡀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠒⠶⠖⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠚⢃⣎⢛⢠⠂⠀⠀⠀⠀⠀⠀⢀⠸⡁⠼⠄⠙⠂⡀
⠀⠀⡠⠇⡠⠧⡈⠀⠀⠀⠀⠹⢤⠀⠀⠀⠀⠀⢸⠁⡤⡄⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⡀⠌
⠀⠀⣷⡈⣁⡤⠣⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠃⠀⠠⠀⠄⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⢺
⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⡀⡟⠀⠀⡖⢲⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⡀
⠀⠀⠀⠀⢠⠉⡀⠀⣤⠀⢤⠒⠀⠀⠇⠁⠀⠀⠀⢣⣷⠀⠀⡇⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠠⠐⠀⡀⠀⠀⠀⠀⠐⢄⢀⡀⠰⠃
⠀⠀⠀⠀⠀⠙⢿⡔⠁⠀⠸⠷⣶⠖⠀⠀⠀⠀⠀⠈⡿⡧⢀⡹⠸⣦⡄⠤⠄⣈⡱⠤⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⣼⣴⣄⠀⠀⠀⠀⢠⣾⣴⣤⣮⣤

⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡤⣄⠠⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⢋⠎⢁⣤⣰⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠇⢨⠀⠺⡿⠛⡄⠀⠀⠀⢀⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⣦⠀⠀⠀⡀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠈⠢⢀⣀⣀⠸⡖⠒⠂⠤⠬⠵⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻⠟⠀⡀⠸⣿⡿⠀⠀⡄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠁⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠢⣰⠤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡑⢁⣤⡈⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣀⣀⣤⣜⣁⠦⢖⣘⣿⠀⢡⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠘⠿⠃⠀⠀⠊⢉⡡⠁⠀⠀⠀⠧⢠⡀⢀⣄⠸
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠃⠈⠁⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠀⣀⠀⠄⠒⠂⠐⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⢀⢀⡀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⠀⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠢⡀⠀⠀⡜⠀⠀⠀⠑⡀⠂⠃
⠀⠀⠀⠀⠀⢰⠁⢑⡤⠒⡈⠁⠈⠉⠒⠤⡀⢀⠀⡀⠀⠀⡀⡁⠢⠂⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠁⠀⠉⠀⠀⠡⠄⠄
⠀⠀⠀⠀⠀⠀⡹⢋⡅⠀⠠⠀⡉⠀⠰⠀⠈⢇⣀⠄⠀⠀⠀⠈⠂⠄⡄⠀⠀⠊⠀⡠⠄⠀⠀⠀⠀⠐⠡⣓⣠⠔⠊⠀⠀⠀⠒⢤⣔⡘⠐⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠐⢈⠇⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⡰⠈⠀⡪⠀⠀⠀⠐⠁⠈⠸⠡⠀⠀⠀⠀⠀⠀⠠⠹⠈⠀⢇
⠀⠀⠀⠀⠀⢸⠀⠐⣿⣿⡗⠀⠀⣶⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⣴⣦⠀⠀⢠⣶⡄⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠈⢄⠀⠈⠉⢹⣶⡶⠘⠟⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢂⠀⠛⠛⣤⣤⠌⠛⠃⢀⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠑⠬⣀⣀⣀⣀⡀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠐⠤⢀⣀⣀⣀⠁⠔⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡠⢒⠃⢀⠀⠀⠀⠱⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡤⢄⢀⣀⠀⠀⠠⡀⠌⠉
⠀⠀⠀⠀⠀⣐⣪⠵⣾⢀⠨⡀⢠⠄⠀⣶⠮⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⢦⡄⠀⡂⠈⣁⠀⢧⠞⡢⡀
⠀⠀⠀⠀⠀⠙⠣⠄⠹⠄⣤⠼⢥⡄⠠⠇⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠧⣀⣠⢯⣠⠀⠏⠀⠜⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⠀⠀⠀⣴⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣿⣿⠃⠹⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠁⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠒
⠀⠀⠀⠀⣠⣾⣿⣿⡷⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠂
⠀⠀⠀⠀⠿⣿⣿⠏⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⣴⣤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠄⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢰⣦⣤⠀⠀⠀⠀⠀⠀⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠙⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠚⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⢀⠢⠄⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⣀⡀⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⡄⠃
⠀⠀⠀⠀⠀⠀⠀⣦⡾⠿⠛⠃⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⣾⣟⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⢀⣿⠀⠀⠀⠀⠠⠀⠀⠤⢠⡀⢴⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠾⠗⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⣷⡄⠀⠀⠀⠀⠀⣴⡶⢂⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠛⡀⠀⢀⠔⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⢀⣀⣀⣀⣀⠀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⡄⡀⠀⠈⠀⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⣶⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢠⣿⠆⠀⠀⡀⠈⢀⣄⠐⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⡀⠆⠀⠀⠈⠙⡀⠠⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡔⠀⠠⢠⠂⠀⠀⠀⠐⠪⠋⠀⠀⢀⣀⠀⢀⣀⠀⠀⢠⡄⠀⣰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⢻⠊⠀⠀⠀⠄⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⡜⠓⠀⠀⠀⠀⠈⣹⠁⠐⠀⠀⠄
⣀⠀⠀⠀⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠸⠀⠀⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⡋⠀⠠⠄⠉⠉⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⢀⡀⣠
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⣀⠀⠀⠐⠀⣀⡀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠈⠙⠀⠀⠈⢸⣷⡀⠀⠀⠈⠁⢀⡀⠄⣧⢀
⣀⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠠⠀⠀⠀⠘⠁⠀⣿⣿
⢈⠙⠂⠀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠋
⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠀⠀⠀⠀⣿⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⢱⡇⣀
⠆⠀⠀⠀⣀⡳⠀⢠⠄⠀⠀⠀⠀⠈⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣾⠁⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐⠄⠀⠀⠁⠀⠙⠋⠀⠀⠀⠹⠟⠃⠀⢀⠀⢀⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠐⠋
⡀⠀⠰⠆⠀⢠⡇⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡤⠃⠀⠀⠰⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⣤⡄⠉
⠁⢀⠀⠀⠀⢹⡇⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈
⠀⠀⠄⠀⠀⠘⠇⠉⠀⠄⠀⠀⠐⠐⠀⠓⠀⢀⡀⢰⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠈⠂⠀⠄⠐⠀⠀⠀⢀⡌⠀⣼⣿⣾⣇⢀⡀⠀⠠⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠈⠁⠉⠉⠙⠉⠀⠀⠂⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠂⡀

⠀⠀⠀⠀⠠⠦⡀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⡿⡿⢦⠤⣾⢱⣏
⠀⠀⠀⠀⠀⡦⠁⣤⠀⠉⠋⢹
⠀⠀⠀⠀⠈⠇⣄⢋⡿⠷⡀⢈⣆
⠀⠀⠀⠀⠸⣇⣿⣧⠀⠀⠄⢸⣧⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠈⠀⣽⣿⠶⠤⢶⠖⠒⠒⠀⠐⠒⠒⠦⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄⠀⠐⡀⠀⠀⠀⠂⠂⢄⠁⠾⣿⣿⣿⠿⠷⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢚⣿⣼⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⡷⢾⣿⣿⣗⣙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⣬⣹⣉⣧⡀⠀⠀⠀⣀⣀⢔⠀⠀⠀⠀⠘⠟⢿⣽⣿⠏⠾⢣⢴⣬⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣤⣵⣾⣌⣿⣿⣿⣿⠿⠿⣯⣿⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⢿⣝⠀⡰⣍⠂⠉⣭⠿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠈⣿⣿⡟⠀⠀⠀⠀⠀⠙⣧⣷⣦⢁⣀⡈⠀⠀⠀⠀⠀⠈⠳⣧⣀⠾⣿⢋⠒⣹⣿⣿⣻⡖⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⠻⣿⡳⡄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣈⠛⣿⡀⠉⣿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠶⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠾⠿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠛⠃






⣿⢿⠿⠿⣿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣤⣀⣤⣤⣤⣄⣀⣀
⠀⢀⣀⣤⣤⣤⣤⠶⠶⠶⠶⢶⣶⡶⠿⠛⠛⠋⠉⠛⢻⣿⣿⠿⣿⣿⣋⣉⣉⣹⣿⣭⡿⠟⢋⣩⠿⣷⣶⢾⣿⣿⣿⣷⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⣿⣿⣿⣟⠿⠿⢷⣤⣤⣤⣾⣯⣀⣀⣀⣀⣀⣤⡴⣾⣧⣤⣶⣿⣿⣿⣭⣭⠷⣾⣿⣶⠾⠉⠁⢀⣸⣷⠿⠛⠉⢸⣿⣶⠟⢻⡿⠁⠀⠀⠀⠉⢻⣷⣦⣄
⠀⣿⡟⣉⠛⠿⣾⣷⣌⣁⣽⣿⡏⠉⠉⠉⠉⠉⠀⠀⠈⣿⠁⠀⢀⣀⠉⠉⢀⣲⠄⣹⣿⣶⡶⠾⠛⠋⠁⠀⠀⠀⢸⣿⡁⠀⠘⣧⠘⠀⠀⠀⢠⡾⠃⠀⠈⠳⣄
⠀⣿⠠⠉⠀⠀⠀⠀⠉⠉⠙⠛⠻⠷⠶⣶⣶⣶⣤⣤⣼⣷⣤⣤⣬⣵⠶⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢵⢀⣠⣿⣷⣤⣄⣤⡟⠁⠀⠀⠀⠀⢹
⢰⣿⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣤⠔⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⠀⢸⣿⡷⠛⠉⠀⠀⠀⠈⢻⡁⣄
⢸⡏⠈⠀⣴⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠞⠁⠀⠀⠀⣤⣄⡀⠀⢄⠀⡈⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠛⠒⠚⠻
⢸⡇⠀⠀⠋⠈⠁⠀⠀⠐⣿⡅⠀⠀⠀⢀⠏⢁⣤⣾⣿⠀⣿⣿⠚⣦⠐⣿⣷⢤⣀⣤⠀⠈⠉⠛⢪⣿⣦⡂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⡐⠁⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⢷⡀⡜⠀⣿⢁⣸⣿⠀⢻⡏⠻⠟⠁⣿⡇⢸⡇⢸⠀⠀⠀⠀⢡⠉⢿⠉⠿⣧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀⡀⢀⣾
⢸⡇⠀⢀⣀⡀⠀⠀⠰⠆⠀⡿⠇⠈⠿⠇⠀⠉⠉⣹⣿⠀⠿⠿⠀⠀⠀⠿⠧⠘⠃⠘⠀⠀⠀⠠⢧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠗⠎⠉⠙⠻⣿⠇
⢸⡇⣰⡿⠋⢻⡄⠀⠀⡀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⡎⠉⢳⠄⣿⡇⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⠟
⢸⡇⠘⠳⠶⠟⠀⠘⣿⡇⠀⠀⢨⡋⠻⠛⠀⣴⣶⣀⠀⣼⣿⠧⠀⢀⣴⢦⠄⠀⣾⣧⠴⢶⡄⠀⠀⠘⠷⠖⠋⠀⣿⠁⠀⠀⠀⠀⠀⣰⠿⣦⡀⠀⠀⣰⠏
⢸⡇⣤⠀⠀⠀⠀⠀⢻⣧⢀⡄⢸⠀⣿⡟⠀⣾⡿⢹⠇⣿⣇⡴⡄⣾⡟⠉⢠⠀⣿⡏⣶⡤⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠏⠀⠀⠙⢷⣴⠏
⣸⡇⠀⠀⠀⠀⠀⠀⠈⣿⡏⠹⣾⡀⣿⡏⠀⣹⡟⢸⡀⢿⣇⣃⠇⠸⠿⠾⠃⠀⣿⡇⠀⠀⠀⠀⠐⣶⣧⠄⠀⠀⣿⠀⠀⠀⣠⣾⠡⠀⠀⠀⢀⣼⠏
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠀⠙⠉⠈⠃⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⢀⣠⣀⠀⠀⠀⠹⠄⠀⠀⣿⠀⢀⡼⠋⠙⠷⣤⣀⣠⠞⠁
⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⣠⠀⣶⠄⣴⠞⠙⢳⣴⡶⢀⣴⠻⡆⣼⡏⢠⣽⠇⠀⠀⠀⠀⠀⠀⣿⣴⡟⠀⠀⠀⠀⢨⡿⠃
⢻⡇⠀⠀⠠⣤⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⡏⢠⣤⡄⣿⣆⠓⠋⢹⡇⢸⣿⠞⡁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣌⠀⠀⢀⣴⠋
⢸⡇⠀⠀⠀⠈⣃⠀⠀⠀⠀⠈⣿⣀⢿⡅⢸⠀⠀⣿⠀⠈⢿⣧⠀⣿⣧⣄⠛⠛⣁⡀⢹⣿⠀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠉⣷⣤⠞⠁
⢸⡇⠀⠀⠀⢠⣴⣞⠀⠠⣤⣤⣿⡏⠀⢻⣧⠀⢀⣿⡌⢿⣤⡿⠀⣿⡇⠈⡇⠀⠹⠶⠾⠃⡀⠀⠀⠀⠀⠀⠀⢸⣯⠀⣠⡾⠋
⢸⡇⢤⢿⠒⠃⠉⢻⡧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠛⠋⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋
⢸⣷⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢀⡶⠛⠛⢆⠀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⣿⡄⠂⠀⠀⠀⠀⠟⢉⡀⠀⠀⠀⠸⣧⣤⣴⠏⠀⠀⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⢀⣼⣿⠁
⠀⠙⣿⣄⡋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠞⣁⣴⣾⣿⠃
⠀⠀⠈⠻⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠻⢿⡿
⠀⠀⠀⠀⠈⢻⣯⡟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣉⣉⣅⢀⣀⣀⣸⣵⣿⠇
⠀⠀⠀⠀⠀⠘⠻⠿⠿⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠾⠶⠿⠟⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣸⣿⣢⠀⢀⣄⠀⠀⢀⣴⡜⡉⣀⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⠿⠛⢉⣻⠘⣻⣇⣻⣾⣯⣼⣻⠷⣠⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⡟⠃⠈⡅⡀⢀⣼⣮⣹⠗⢈⣼⠦⢉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⣐⠠⠸⣿⡟⣾⢸⠠⠋⠚⠟⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠉⠵⣬⣷⣍⢿⠀⠀⢷⡏⣴⠶⣹⢻⠿⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⠈⠽⣿⣾⡇⠀⢻⣿⣯⣿⣿⣿⣁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⠀⠐⠋⠙⠣⣤⣾⢿⣿⣎⠛⠫⢶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠄⠀⠀⠀⠀⣭⡀⠀⠈⠉⣹⣿⣿⣯⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⡀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠊⠀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⢿⣽⣿⡿⢻⣿⣷⣿⡟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠉⠋⠁

⢀⡤⢤⡀⠀⠀⡀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄
⠈⠳⠞⠁⠀⠀⠀⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣿⡤⡆
⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠇⠀⣀⠀⢸⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠙⠃⠀⡿⡿⣿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡼⢿⣿⠀⣰⠂⢰⢶⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⣮⣆⣀⠤⡀⠐⠒⠂⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠃⠀⠈⠙⠉⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄⢰⢶⢤⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠒⠐⠐⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢘⣳⣷⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣶⡆⢀⠀⠀⠖
⠀⠀⠀⠀⢰⣿⠎⢹⡇⠀⠀⠀⠀⠀⠠⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢿⣯⡠⣿⡍⠉⢹⣿⣿⣷⣤⣾⣿⡀
⠀⠀⠀⠀⣾⣿⣷⣼⠀⠀⠀⠐⠽⠇⠀⠀⠉⠉⠹⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⡟⠀⠀⠀⠘⣿⡇⠛⠿⠿⠾⢿⣾⠟⠉⠋⠉⠃
⠀⠀⠀⢠⣿⣛⣟⠵⡶⠃⢀⡀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⠉⠉⢹⣿⣿⣿⣿⠃⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⢸⠃
⠀⠐⠘⠋⠈⠉⠁⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⢀⣸⡟⢙⡿⠀⠀⣸⡟⠀⢙⣿⠆⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡤⠃⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠞⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⢞⡜⠃⠀⠀⠀⠀⠀⣄⠀⠑⠄⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⡩
⠀⠀⠀⠀⣀⣤⣴⡿⣿⣷⢉⡆⠀⠀⠀⠀⠀⠀⣿⠀⠤⠈⢶⡄⠀⢰⣿⣿⠶⠂⠀⠀⠀⠀⣤⠏⠐⢤⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⣾⣿⢿⢻⡞⢛⣷⡌⣥⠀⠀⠀⣴⣦⣀⡏⠀⠀⠦⠈⠀⠀⢸⣿⣩⡴⠖⠀⠀⠀⠀⠳⠶⠶⠟⣫⠷⠉⠉⠁⠀⠉⠚
⠀⠀⠀⢻⡇⠀⠸⡇⢀⢹⠃⠀⠀⠀⢠⣅⣿⣿⣇⠀⠀⠀⠀⠀⠠⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦
⠀⠀⢀⣄⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡝⡛⢫⡭⠿⠀⠀⠀⠀⣠⣶⣾⣶⣶⣶⣶⣦⣶⡗⠀⠀⠀⠀⠀⣤⡀⣠⣾⣿⣿⠏
⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠁⠀⠈⣰⣿⣿⣿⣿⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠘⠹⡋⠁⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠱⠄⠀⠀⠀⠚⠀⠰⠄⠀⠀⠀⢀⣿⣿⣻⣿⣿⣿⣿⠇
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣿⣿⣿⠏
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠰⠟⠛⠉⢷⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣶⣆⠀⠀⠀⠀⠀⠋⠈⢿⡿⠟⠒⢶⠛⡿⠶⣦⣀⡐⠿⠻⠿⠟⠟⠁
⠀⠀⢿⣿⣿⣿⡟⢿⣿⣿⣿⣸⣿⣿⣿⣿⠿⢿⠿⢷⣄⠀⠀⠀⢠⣴⣿⣦⣀⡀⣠⣧⣀⠀⣾⠁⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢸⣿⣿⡿⠇⠠⠿⠿⠿⣿⢿⡟⠉⠉⠑⠘⠦⠼⠟⠀⠀⠀⢠⡟⠁⠉⠉⠉⠉⠀⠁⠹⡏⠀⠿⠀⠀⢠⣤⣾⣟⣿⣿⣿⣷⡀
⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢃⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠁⣿⠿⠿⠿⠿⢿⡋
⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠠⠂⠀⠉⠉⠉⠉⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡉⠁⠀⠀⠀⠓⠀⠀⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢰⠀⠘⠛⡁⠀⠀⠈⠻⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡆⠀⠀⠸⡀⢀⡀⠀⠀⠀⠀⢀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢷⡘⢄⠀⣈⢌⣀⣀⡤⠞⢀⣼⢦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣌⠾⠀⠀⠀⡥⢊⠔⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠈⡇⠀⠀⠀⠗⠁⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⢇⠀⠀⡠⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⠀⠈⢆⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡇⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⡾⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⢡⠀⠀⠀⣇⠀⠀⠀⠀⢀⠎⠱⡀⠀⠀⠸⡄
⠀⣠⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⣴⠁⠀⠀⠱⡀⠀⠀⢇
⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠇⠀⠀⠘⡄⠀⡜⢹⠀⠀⠀⠀⠙⡄⠀⠸
⡇⢰⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⢧⠈⠀⡼⠀⠀⠀⠀⠀⠘⡄⠀⢇
⠳⡀⠳⢄⡀⠀⠀⣀⡇⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⣖⣋⣄⡀⠀⠀⠀⠀⠀⠱⡀⠸⡄
⠀⠙⠢⣄⣈⠉⠉⠀⣘⡦⠀⡀⠐⠺⣄⣀⣀⣀⣀⣀⣀⣀⣧⠀⠀⠹⣄⡀⢨⡣⠀⠀⠀⠀⠀⠘⡄⠈⠒⠢⣄
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠑⠲⠷⠤⠦⠃⠀⠀⠀⠀⠀⠀⠀⠹⣀⣰⠀⢈⣹⠉⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣇⢈
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⣀⠀⠀⠀⠀⠤
⠀⠿⢿⡮⠀⠀⠀⠀⢰⡿⣿⡇⢤⣄⣀⠠⠀⠀⠤⠀⡀⣄⣤⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⠀⡀
⠀⠀⠘⡆⠀⠀⠐⠓⠌⣿⠏⡀⠀⠈⠉⠀⠀⠀⠀⠈⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠙⠋⠁⠈⠙⠛⠿⣦⣄
⠀⠀⡀⠄⠀⠀⠀⣀⣇⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣷
⠀⠀⢿⣿⣥⣤⣶⣿⣿⡽⣿⣿⣿⣷⡟⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⢄⠿⣧⡤⣾⠀⢿
⠀⠀⠀⠀⠀⠀⠙⠛⢿⡄⠙⢿⣿⣿⠅⣤⣾⠀⠙⢷⣿⣦⣀⣶⣆⣧⣄⣾⡆⣴⡀⣠⣾⣿⣿⡑⠀⠉⠋⠉⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠘⠻⢿⣻⣿⣿⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣤⣠⢈⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⢸⣿⣿⣿⣄⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣀⣈⣛⣿⣿⣿⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣢⣤⢿⣷⣽⣿⣿⡤⠮⣿⣿⣿⣿⣿⣿⣿⣟⡀⠠⠍⠉⢹⣿⣧⣿⠻⣿⠙⢻⣶⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣶⣿⣿⣿⡟⠎⠀⠀⠀⠀⠈⠉⠉⢻⠟⠉⠀⠀⠀⠀⠈⣿⣿⣿⠄⠈⢶⣿⡟⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣧⠾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⢻⣷⣄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠇⠀⠀⠀⠀⢿⡇⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠾⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠨⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠃⠀⠀⠀⠀⠀⠠⣖⠶⠂

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢟⡻⡿⢿⣿⢿⣻⣿⡿⠿⣻⠿⣟⢿⢟⡻⢿⣿⡿⣿⡿⡿⢛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣠⣙⣣⣿⣿⣿⣜⣻⣏⣇⣜⣛⣤⣛⣻⣜⣣⣞⣿⣩⣼⣇⣿⣘⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡯⣿⣟⡩⣟⡯⣫⣿⢻⣿⡟⢿⠛⡿⢻⣟⢻⢻⣛⣿⠛⢻⠟⣿⢻⡿⣿⣿⡟⣟⠛⣿⣿⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣵⣦⣧⣼⣧⣽⣼⣤⣶⣦⣵⣦⣧⣿⣽⣧⣭⣾⣤⣦⣿⣧⣿⣿⣿⣿⣧⣿⣿⣯⣿⣿⣿
⢸⣿⣿⣛⣩⣭⣶⠀⠀⠐⠒⠒⣶⡶⢭⣭⣛⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠛⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠈⠛⠛⠋⠉⠛⠛⠓⠚⠓⠒⠖⠛⠛⠛⠋⠉⡟⠛⡛⠛⠛⠃⠀⠀⠙⠛⠛⠛⢛⡛⠋⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⠠⠀⠀⠀⠀⢀⠇⠀⠯⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢿⠿⠛⠁
⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠲⠶⠚⠛⠛⡋
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠶⠂⢀⣶⡶⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⢀⠐⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⠤⠼⠿⠖⠘⠋⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠈
⠀⠀⠀⠀⣠⡄⢶⠀⠀⢁⣀⣸⠿⠛⠀⡄⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⣀⠌⠀⣤⠀⣀⡀
⠀⠀⠀⠀⠉⠙⠛⠁⠈⠉⠁⠀⠀⠀⠀⢻⠀⣀⣤⢔⣐⣶⣤⠉⠙⢯⣭⣭⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠛⠉⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠃⠀⠀⢠⣪⣵⣦⣀⣤⣀⣹⣿⣶⣶⣾⣿⣿⠿⠀⠀⠀⣀⠀⠀⠀⠀⢀⠸⣧⠁⠀⠈⠹⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠄⠀⠖⢀⣀⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣁⣀⣴⠀⠀⠈⠁⠀⠢⠀⠀⠘⠓⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀⠀⣾⣿⠟⢷⣤⣤⣤⣤⣴⣶⣶⣶⣿⠿⠟⠋⢉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣧⠀⠁⠉⠉⠉⠉⠉⣉⣁⣀⣠⣤⣴⡆⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠿⠿⠿⠿⠿⠿⠿⠛⠛⢉⡁⣴⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣤⣤⣶⣶⣶⣶⣿⣿⠿⠇⠛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⢋⣉⣉⣉⣉⣁⣤⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠈⠻⠿⣿⣦⡀⠀⠀⠀⠀⣀⠼⠅⢡⣄⣀⠀⢀⡀⠀⣼⡋⠉⢹⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠠⠆⠈⣿⣏⠁⢦⣀⠘⠅⠀⡄⠀⠀⠀⠀⠀⠀⠀⢻⣷⣥⣿⠃⠀⠀⠀⢠⡀⢀⡀
⠀⠀⠀⠀⠀⠘⠿⠶⠋⠀⠀⠀⠀⡈⠀⠐⣶⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠋⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢽⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⡤⠀⡠⡏⠀⢻⢄
⠀⠀⠔⠀⠀⠀⠲⠀⠤⠂⢸⡇⠀⠀⠀⠀⠠⠂⣠⡋⠀⣀⠀⠀⠀⠀⠐⠛⠉⢻⣿⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣇⡄⠀⢀⡇⠀⠘⣿⡏⠀⠀⠀⢀⢀⣾⠟⠁⠀⠀⠤⠀⠄
⠀⠐⠀⠀⢠⠀⠖⠒⠀⠀⠘⢽⢿⣷⡄⠈⠀⠀⠈⠓⠀⠀⠘⠃⠐⠀⠀⠈⠹⠁⢀⠠⠤⣀⡀⠠⡄
⠀⠸⣿⣤⣼⣷⢶⣧⠀⠀⠈⠃⠘⠏⠀⠄⠠⣤⣠⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠁
⠀⠀⠙⠋⠁⠙⠛⠁⠀⠀⠤⠠⠀⠂⠄⠀⠠⠔⠋⠉⢹⣿⣿⡿⢿⣿⠿⠷⢤⠀⠠⠈⠃⢲⠆⠉⠉⠁
⠀⠀⠀⠀⠀⡴⠀⠀⢰⢹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⢠⣏⡀⠀⠈⠈⢡⣤⠐⠠⡀⣀⠐⢛⣇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣶⣤⣤
⠀⠀⠀⣠⣾⡏⢧⠀⠀⢠⡀⠁⢰⢄⠀⠁⠐⡯⢙⢷⣦⠀⠂⠀⢤⣀⠀⢀⢀⡀⠀⠆⠀⠈⠻⣿⡟⠁
⠀⢀⣴⢿⣿⣿⡋⠀⠘⢈⠁⢠⠃⡎⠀⠀⠀⠇⠈⢏⠿⠀⠀⠀⠀⡟⠀⠈⣿⠁⣸
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡏⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣀⡼⡴⢃⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣛⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣠⠏⠀⣏⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡤⠤⢤⣤⡼⠛⢩⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣶⣶⣶⣶⣶⣖⣒⣒⣒⣖⣾⣵⣾⣿⣶⣶⣬⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠁⠈⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⣀⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⢳⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠦⣀⣿⣠⠔⠃⠀⠀⠀⠀⠀⡗⠋⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠶⠒⣺⣿⣗⠒⠶⠀⠀⠀⠀⠀⣇⣀⡤⠏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁⣿⠈⠧⠀⠀⠀⠀⠀⠀⣇⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡤⠖⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠦⣤⣈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠁⣴⠋⠀⠀⠀⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣠⠏⠀⠀⡈⠙⡆⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⢄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⣡⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠉⠓⠲⠦⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠊⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⡤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡞⢶⣣⠀⠀⠀⠀⠀⠠⣖⠤⠒⠒⠒⠒⠒⠒⢖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⢿⡀⠠⠌⠳⣄⠀⠀⠀⠀⠈⠃⠘⠀⣬⣥⠈⠃⠸⢤⡤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠈⢷⡀⠀⠀⢈⣷⡄⠀⠀⠀⢧⡀⠀⠜⠅⠀⠀⣀⡀⢠⡄⠉⠀⠰⠟⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣿⣿⡉⠳⣄⠙⣦⣤⣿⣷⡇⠀⠀⠀⠀⠉⢲⡖⠒⣈⠁⠙⠁⣈⠀⠘⠛⠀⣤⠘⠓⠀⣷⡀
⠀⠀⠀⠀⢀⣠⠖⠹⡏⠁⢿⡀⠹⣇⠈⠳⣄⠈⠳⣇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⡁⢀⠉⢠⣤⠀⠛⡀⠸⠇⢀⡀⠀⣶⠄⢴⢌⣑⡒⢠⣶⣶⠄
⠀⠀⠀⣰⡟⠹⣆⠀⢻⡀⠘⣧⠀⠙⣦⠀⠙⢦⡀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⢳⠀⠞⠉⠉⠉⠉⠑⠺⡏⢸⠉⡄⣇⠀⠈⠉⠉⠉
⠀⠀⢰⠅⣿⣄⡙⢦⡀⢳⡀⠈⣧⣀⠈⠷⣤⣤⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⢸⣴⠇⠀⠀⠀⠀⠀⠀⢹⣾⠀⣷⡇
⠀⠀⠀⠀⣇⢹⢹⡈⡟⠉⠉⠀⠀⠉⢻⡀⡏⢸⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⣀⢀⣀⣀⣀⣀⣠⣌⣡⣀⠈⣡⠴⢤⡀
⠀⠀⠀⠀⡟⣿⢸⣛⡇⠀⠀⠀⠀⠀⢨⣛⡇⠸⣦⡇⠀⠀⠀⠀⠀⣠⢤⣄⣶⢲⣮⠶⠭⠿⠾⠗⠚⠒⠛⠚⠓⠚⠓⠉⠉⠁⠈⠀⠉⠙⠓⠒⠒⠲⠦
⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠉⠁⠀⣠⠔⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣙⣎⣱⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠓⢦⡉⠒⠒⠒⠒⠲⠦⠤⢤⣄⡀⠀⣀⠀⠀⣠⣤⠤⠤⠤⠤⠤⣤⡀⢠⣄⠀⣤⠴⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣀⠀⢀⣀⣀⣀⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡏⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢧⠏⠸⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠳⠍⣤⠀⠄⡀⢠⠉⡿⠃⢸⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣞⠝⠶⠒⠒⠢⢤⣠⢤⡀
⠀⠀⠀⣠⠴⠒⠛⠋⠉⢹⡇⠀⠘⡄⠀⠘⢿⠃⠀⠀⡇⠀⢸⠀⠀⢀⡠⠟⠛⢧⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣣⣏⡀
⠀⣠⢾⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠑⠤⣈⣁⣁⡤⠞⠀⢠⠟⠀⣴⣋⣀⠀⠁⠘⡿⡆⠀⢀⡖⣋⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠉⠉⠓⠲⢄⠀⢀
⣰⡇⣪⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠙⣧⠶⠆⢻⣳⡄⢸⡄⠋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡼
⠉⠁⣵⠀⡴⡄⢀⣤⣤⣤⣤⣤⣤⣄⠀⡬⡍⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣾⡿⣆⠀⠳⣄⣀⠈⠁⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⢰⠁⡇⣿⠀⠀⠀⠀⠀⠀⢹⠀⠇⢇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢟⣻⡀⠀⠀⠈⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠸⠞⠀⠣⠇⠀⠀⠀⠀⠀⠀⠘⠾⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢸⣭⣇⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⡤⠦⠤⠤⣤⠀⠀⣀⠀⠀⡇
⠀⠀⠀⢀⣠⣤⣄⢀⣀⣀⣀⣀⠀⢀⡠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣄⡷⢼⡆⠀⠀⠀⣇⠀⣸⢻⠀⢀⠇⠀⠀⠀⢸⡀⣸⢿⠀⢀⠇
⠀⠀⢰⠋⠀⢀⡼⠉⠀⠀⠀⠈⢹⣏⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⠁⢻⡒⣇⠀⠀⠀⠉⠉⠁⠈⠓⠋⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉
⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡀⠀⢹⣿⡿⠋⣭⣭⡉⠉⠉⠉⠋⢿⣿⡗⠲⣦⡀
⠀⠀⠹⣄⠀⢿⠙⠂⠀⠀⠉⠛⠀⠼⢤⡀⠀⣀⡼⠛⠓⠶⢤⡀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⣤⡀⠀⠻⠟⠃⠀⣶⡆⠀⠀⢀⣶⣦⠀⢻⡀
⠀⠀⠀⣈⠉⠙⣆⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢿⠀⠀⠘⠿⠟⠀⠰⣾⡦⠀⠈⠀⢰⣶⡄⠉⠁⢀⠾⡇
⠀⠀⠸⣍⠳⠶⠋⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⢀⡶⡄⣾⠿⠤⠤⠬⠤⠶⠶⠖⠒⠻⡆⣴⡆⡜⠀⣧
⠀⠀⠀⠈⠑⠲⠤⠴⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠧⠀⠀⠀⣼⢸⠇⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⡇⡇⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡄⠀⠀⣀⣀⣀⣠⣀⣀⡀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣿⢸⠀⢻⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢳⠀⠀⡏⠀⠀⠀⠀⠀⢳⠀⢸⡇⠀⢸⠀⠀⠀⠀⢹⢸⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣷⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣸⠀⠀⠀⠀⢸⣾⠀⠀⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠗⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠈⠓⠚⠁⠀⠀⠀⠀⠀⠘⠒⠋⠘⠒⠃⠀⠀⠀⠀⠀⠁⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠘⠁⠀⠀⠀⠐⠀⠂⠒⠀⠃⠐⠀⠒⠐⠐⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢆
⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣿⡿⣄
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣀⣰⣿⢴⣦⣶⡿⢿⣿⠃⣏⠁⠘⢢⣀
⣿⣿⡿⠋⠀⣠⢤⣠⠄⡚⢻⡷⠾⠛⣩⣿⠱⠟⣼⠰⠸⠆⡀⠀⠉⠻⡒⠀⢄⡀⠀⡀
⠟⠋⠀⠀⣰⣿⣧⠚⢁⠴⠀⡠⢴⣿⣣⢀⣠⣾⢿⡆⠀⡀⠸⢆⠀⠹⠀⣀⠀⠉⡓⣧⡆
⠀⠀⠀⢸⣿⣿⡿⣻⠶⣛⣡⣼⡿⢣⢇⡞⡋⢡⠎⠹⡆⠀⠲⠎⠀⡄⣸⠀⣵⣇⣤⣧⣷⡀
⠀⠀⢠⣿⠟⠁⠀⣀⠛⣋⡙⠋⠀⣠⠎⢠⠉⢠⣆⠀⢀⠠⢠⡄⣀⣡⣬⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠙⠳⠚⠛⠛⠛⠛⠛⢿⡄⡄⠁⠁⣾⣇⣸⣻⣤⣸⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⡅⣃⣣⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣧
⠀⠀⠀⠀⢰⡄⠀⣧⣎⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⢡⣀⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣸⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⡷
⠀⠀⠀⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⠟⠀⢀⣤⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡶
⠀⠀⠀⠀⠀⡀⠂⣀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢁⢹⡀
⠀⠀⠀⠀⠸⢷⣤⠀⠉⠟⢡⣤⠻⡇⠀⠀⢠⣬⣆⠿⠒⠒⠂⢀⣰⢠⡄
⠀⠀⣠⠒⠐⡆⠀⠑⠻⠏⠙⠉⠘⠇⠀⠀⠘⡟⠙⠓⠂⠀⠐⠚⢣⠀⠀⠀⠀⠀⠀⣄⠀⠐⢄⠉⢀⡀
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠉⠉⠁
⠀⠀⠈⠓⠦⠴⣆⣀⣀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣯⣗⠶⠂⠀⠀⠀⣀⣀⢀⠈⠂⣉⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡛⠻⢄⣀⠟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠝⠈⠁⠀⠀⠀⠀⠉⠈⠀⠉⠁⡁⠈⠁⠀⠀⠀⠀⠀⢀⣀⠙⠣⠤⠶⠶⠬⠴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠀⠄⣤⡤⣾⠋⠘⡆⠀⠀⠀⠘⠁⢱⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⡀⠀⠄⡂⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠃⣿⠀⠀⡇⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⣿⡑⣦⡍⢉⡅⣠⣾⡇⠀⠀⠀⠀⢸⣇⠀⢀⢨⠀⣿⡤⠀⠀⠀⠀⠀⠈⢀⣘⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠋⣽⣩⠄⠀⠀⠀⠈⠻⣦⣬⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠤⠀⠀⠸⠾
⠀⠀⠀⠀⠀⠈⠓⠄⠠⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠸⡥⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣐⣺⡛
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠓⠚⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢶⡂⠐⠠⠀⡠⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⡀⠀⠀⠀⠐⠒⡶⣴⣶⠾⣿⣧⡀⠇⠀⢠⡆⢀⡐⠋⢉⣻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⣀⣀⣤⠴⠞⠉⢰⣿⣇⣾⣿⣿⣗⣀⣸⣿⠀⢘⣷⣶⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣾⣿⡟⠁⠀⠀⣼⡿⠛⠿⣿⣿⡟⠉⡉⠉⠩⡿⢿⣿⣿⣿⢷⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡏⠀⠀⠀⢸⣿⠁⠀⢠⣿⣭⣿⣶⣬⣶⣿⣷⡈⡿⢿⣿⣯⣿⠽⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢰⣿⠃⠀⠀⠀⣼⣿⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢸⣿⠀⠀⠀⣴⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣤⣶⣿⡿⣿⣿⠀⠀⠀⠉⠙⣿⠿⠿⣿⠿⠊⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠐⣿⣿⡀⣀⣤⣴⣶⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠉⢳⣤⣤⠄⢀⣈⡛⠳⢤⡀⠀⠀⠀⢠⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣉⠎⣱⠿⣿⣿⣇⠈⠋⠀⠹⠒⠋⠛⠛⣶⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠏⢀⠏⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣾⢢⡀⢸⣽⣿⣷⠀⠀⠀⠀⠀⠀⡘⢻⣿⡇⠀⠉⠻⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⣿⣿⡇⢘⠁⠟⢻⡄⠀⠀⠀⠀⢠⡷⠞⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣧⣸⠀⠀⠀⢷⠀⠀⠀⢠⠎⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡆⠸⣿⣿⣿⣧⡀⠀⠀⠠⡆⠀⠀⠃⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡙⢿⣿⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⡠⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣭⣙⢷⣄⠄⠀⠀⠉⠀⣆⣳⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣄⣄⣴⣾⡷⠈⢛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠃⠀⠒⠤⣙⢿⣿⣿⣿⣿⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢦
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢠⠀⠀⠐⠢⣄⠀⠉⠉⠓⠶⣤⡀⠀⠀⠀⢀⡴⠋⠀⠀⠞⠀⠁⣉⠤⠞⠁⠀⠀⣀⡴⠖⠋⠉⠁⢀⡤⠒⠀⠀⢀
⠀⢸⡀⠀⠊⠉⠉⢣⡀⠀⠀⠀⠀⠙⢦⡤⠔⠋⠀⠀⠀⠀⠀⣀⣈⡁⠉⠒⢤⣴⠞⠁⠀⠀⠀⠀⣠⠋⠉⠉⠂⠀⣸
⠀⠈⣧⠀⠀⢀⠔⠒⢷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠉⢫⡉⠙⠓⠶⠏⠀⠀⠀⠀⠀⣰⠗⠲⢄⠀⠀⢠⡏
⠀⠀⠘⢦⠀⠈⠀⠀⠀⠱⡀⠀⠀⠀⠠⠴⠦⠀⠀⠀⠀⠀⠀⠙⢦⡡⠀⠠⠶⠤⠀⠀⠀⠀⡰⠁⠀⠀⠈⠀⢠⠞
⠀⠀⠀⠈⠳⣄⠀⠀⠀⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⠇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⠀⠀⠀⣴⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⣶⡄⠀⠀⠀⠀⢠⠔⠋
⠀⠀⠀⠀⠀⠀⠸⠥⠆⡀⡀⠀⣼⣿⣇⠀⠀⢀⣿⣆⠀⠀⠀⠀⢀⣾⣇⠀⠀⢀⣿⣿⡄⠀⡄⡀⠦⠽⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠊⠑⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢀⡗⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡹⡏⠀⠉⢻⣿⡟⠀⠀⠀⠀⠘⣿⣿⠋⠁⠈⡿⣹⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠙⠮⣖⣶⡾⠟⠀⠀⠀⡀⠀⠀⠘⠿⣶⣖⡮⠞⠁⠀⠈⡇
⠀⠀⠀⠀⢀⣠⠤⠤⠶⠚⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠊⡉⠖⠂⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞⠒⠦⠤⢤⣀
⠀⠀⠴⠚⠛⠓⠒⠒⠤⣄⠀⠀⠀⠉⠉⠒⠒⠒⠶⠆⠀⠤⠤⠤⠐⠶⠖⠒⠒⠊⠉⠁⠀⠀⢀⡤⠔⠒⠒⠛⠛⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⣆⣀⠴⠋⠁⠀⠀⠀⠉⠳⢄⣀⣂⣨⠆

⠀⠀⠀⠀⠀⣀⣀⠀⢠⠀⠐⠀⠠⠀⢀⠀⠀⠀⠄⠀⣤⠀⠀⠄⠠⠀⠀⠀⠠⡄⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⢀⠈⠀⢨⠀⠀⡀⠀⠀⠘⠂⠀⠀⡂⢰⣠⡼⠃⠀⠄⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠶
⠀⠀⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⢈⡅⠀⠀⠀⠸⠅⠸⠎⠰⠿⠀⠀⠀⠈⠀⡀⠉⠀⠐⠂⠀⠀⠀⠀⡀⠀⢠⡀⠀⢀
⠀⠀⠀⣀⠐⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⠀⣤⠚⣿⠆⠀⠈⠁⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⠀⠠⠂⠠
⠀⠀⠀⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠽⠆⠋⢀⠀⠁⠚⠀⠀⠀⢀⣀⠀⡄⠚⠀⠀⠀⢀⡀⣀⠈⠂⠊
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢤⠄⠀⠀⠠⣶⣦⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄⠀⠈⠀⠀⠄⠀⠘⣿⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠠⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠐⠂
⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣼⣿⣿⣶⣷⣶⣶⣶⣿⣿⣆⠀⠀⠘⠳⠂
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⣀⠀⠀⢿⣿⠻⢿⠿⡟⢻⡿⣟⣿⡏⠀⠀⠀⠀⠀⠀⢀⠛⠠
⠀⠀⠀⠂⠀⠒⣠⡀⠀⠀⠀⠈⠀⠛⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⡀⠀⠤⡄⠀⠀⠀⠖⠒⠂
⠀⠀⠀⠤⡀⠀⠐⣿⣾⣋⠀⠀⠂⠀⠀⠒⡴⠂⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠗⠢⠄⠐⢒
⠀⠀⠀⠀⠀⠀⠄⠇⠀⠤⠅⠀⠀⠐⠚⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠠⠀⠀⠒⠀⡠⢆⠀⡀⠀⠀⡐
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠒⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢤⡂⠀⠣⠰⠂⠁⠀⠰⠉⠆
⠀⠀⠀⠀⠀⠰⡄⠀⠀⣠⣀⣸⡄⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⠙⠂⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢄⠉⠁⢠⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠈⠁⠀⠁⠁⠀⠉
⠀⠀⠀⠀⠠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⣀⠀⠀⠄⠀⠀⠀⠀⠠⡢⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠈⠑⠀⠆⠄⠀⣀⠀⣠⠀⠀⠀⠠⠀⣀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣤⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⢀⢀⣾⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠫⠷⠊⣴⡾⢣⡮⠟⣡⣿⡦⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⣶⣷⠊⠀⠁⢰⣼⢃⣤⠂⢈⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣸⢋⣿⣴⣶⡀⢺⡆⣸⠋⣄⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣱⡟⡁⠀⠈⣾⣿⣈⣡⣾⡿⡿⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣥⣶⣿⡾⣷⢀⣐⣁⠙⠿⣟⡙⠇⡀⣇⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣄⣀⣼⣣⡶⣛⣉⡙⢷⡜⣶⣝⠆⢹⣿⡆⣿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⣱⠋⣾⡿⠛⡿⣸⠇⣿⣿⡄⢚⣳⡄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠁⠀⣿⣷⡀⠠⠴⠾⣿⣿⠇⠞⠛⠢⡜⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⣀⣈⠻⢿⣶⣶⣾⣿⣿⣷⣦⡈⢻⡟⣸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⣾⣿⣿⠁⠀⢘⣿⠀⠃⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠶⠾⠏⣸⣧⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⡉⣷⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠉⠉⢿⣎⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢠⠀⠀⠀⣿⣿⣿⡇⠀⢲⡀⠈⢿⡜⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⢸⡄⠀⢀⣿⣿⣿⣿⣶⣾⣿⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠘⣿⣷⣿⡿⢻⣿⡿⠛⠛⢿⣿⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠹⣷⡀⠀⢸⣿⡇⠀⠀⠈⣿⠇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠙⣿⣦⡈⣿⣇⠀⠀⢀⡿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠈⠻⣷⣾⣿⡄⠀⠘⠁⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠉⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠰⠂⠑⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠂⠠⠤⡀⠀⢘⠀⢸⠀⡐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠃⠠⠇⠀⠀⢀⠀⠀⠈⠀⠈⠀⠈⢠⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⣄⡀⣀⠀⠈⠆⠀⣸⠏⣔⠀⢀⣸⠆⢠⠁⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣜⢋⠁⡀⠂⠁⠈⢲⡁⠄⠤⢍⠐⠍⡆⠈⠼⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⡉⠀⠀⠹⠦⠀⢤⠀⢨⡀⠀⠀⠁⠀⠱⠾⢦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠄⠐⠐⠆⢊⡀⡔⢁⡘⠀⠀⢨⠒⣄⡴⠂⠸⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⡄⢀⠀⠀⠠⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠠⠈⠀⠂⠠⢂⠄⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⠁⠱⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡊⠴⠂⡅⠀⠒⢌⡒⢀⠀⠁⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠆⠂⠀⠀⠀⠇⠍⠀⠀⠀⠂⠋⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠈⠙⠳⢆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣦⡤⣤⣼⡀⠉⠙⢿⣶⣤⡈⢷⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣍⣿⣿⣿⣷⣄⠀⠀⢹⣿⣇⠈⠐⠄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣩⠟⣱⣿⣥⣤⣨⣿⣿⠒⠀⢀⡈⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⠁⠿⢿⣿⣿⣿⠿⠏⠀⠀⠀⠁⣠⠈⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣾⣿⣿⡀⠀⠀⠀⠠⣾⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣿⣿⣿⣿⣿⡟⠻⠿⡮⠀⠒⠂⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⣴⣿⣦⣤⣙⣧⠀⠀⠻⠄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⣿⣿⣿⠿⣿⣿⣷⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⠁⢀⣾⣿⠛⢿⣴⣾⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⠿⠿⣿⣿⣷⣾⢿⠍⠀⠉⠉⠀⠀⢸⣿⠛⠳⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠅⠀⠀⠀⠠⠀⠀⠀⠀⠈⢫⡀⠀⠀⠻⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢁⡒⠁⠀⢀⢠⣤⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠎⠁⡀⠀⠀⠀⣤⣤⢟⠛⠋⠀⠀⣴⣿⣿⠯⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣠⡀⢠⠄⢪⣼⣿⣿⣯⣴⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣟⡛⠴⢾⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠰⣶⡌⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠾⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣰⣔⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡤⣴⣿⣿⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⣶⣿⣯⣷⣾⣿⢻⡟⣹⡇⡄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣤⡀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠛⣿⠿⡆⠀⢠⣶⠾⠓⠶⠄
⠀⠀⠀⠀⠀⠀⠉⣿⡿⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⢰⣄⡀⠁⠀⠃⣠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣼⣿⡟⡛⠿⣿⣿⣿⣿⡷⠀⠀⠀⢿⡟⠉⠙⠻⢿⣿⡿⠟⢫⣴⣶⣶⣾⠏⠁⠀⠴⠏⢹⣿⣿⡝⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠸⣿⣿⠇⡏⠀⣸⡏⠈⢻⡇⠂⣀⡀⠸⣇⠀⠀⢀⡄⢿⡀⠀⣿⣿⣿⠋⢹⠀⠀⠀⠀⢠⣼⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⣴⣀⣭⣆⠀⢸⠛⠁⣧⣀⣛⢁⣄⠘⣯⠄⠻⠀⠀⠀⠀⠀⢈⡷⢀⣀⣀⡟⠙⢿⣆⣀⡀⠀⢀⡐⠋⠘⠟⠉⠀⠛
⠀⠀⠀⠀⠀⠀⠉⠻⠋⢉⣥⡴⠁⠀⡟⢿⠇⠘⢿⣿⡷⠀⠈⠰⣦⣤⣶⠔⠊⠁⢠⣴⣶⣤⣤⣤⣤⡀⠀⠰⣿⣿⣿⣶⣄⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠰⠒⢺⡿⠋⠀⢀⣠⣴⡶⠀⢀⣨⣭⣁⣀⣀⣀⣼⣿⣧⠀⠀⠀⣿⡿⠿⠿⢿⡟⠛⠿⠀⣼⠟⠻⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣤⣴⣿⠿⠛⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠁⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣿⣿⡟⠁⠀⠀⢶⣶⣦⠀⢀⣴⣆⣀⣶⣄⠀⠀⠀⢸⠙⠂⠀⠀⢀⢷
⠀⠀⠀⠀⠀⠀⢠⡾⠿⠋⠀⠀⠀⢀⡀⠀⢸⢿⠋⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⢿⣿⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠞⠠⠃⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⣶⠶⢟⠂⠀⠸⠸⠄⠀⠀⠀⠀⠅⠀⠇⠀⣀⢠⣤⠈⠛⠛⢿⣿⣿⣿⣿⢿⣿⣷⠀⢀⣤⣤⣄⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣠⣴⣶⣶⣦⣤⣶⣾⣷⣦⣀⣄⠀⠀⠀⠈⢹⣿⢋⣀⠀⠀⣿⠀⠀⠀⢘⡏⣿⠀⠋⠟⠉⠉⠃⢈⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡠⠀⢲⡚⠛⠿⠃⠀⠀⣷⠆⠀⢠⠜⠁⡏⠀⣶⣶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢰⡿⠋⠉⢻⣯⡙⠛⣿⢟⣿⠁⠈⠛⠛⠀⠴⠂⠁⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⢠⡿⢋⡛⠋⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣘⠃⠀⠀⠀⠉⠁⠀⠛⠂⠉⢀⣴⣿⡆⠀⠀⢸⣀⡠⠚⠀⠀⠀⢿⣿⣿⣿⣷⣶⣄⢸⠀⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⣀⠀⠀⠀⢠⣴⣾⣿⣿⠿⣧⡀⠀⠈⢿⣷⣤⣦⣴⣤⠀⢿⣿⣿⣿⣿⣿⠀⠀⢤⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣆⠀⣻⡿⣿⣽⣿⠀⠹⢿⡄⠀⠈⠙⣿⠛⢿⣿⠀⠈⣿⣿⠉⢿⡟⠀⠋⠀⠉⠈⠻⠯⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⣿⠏⠰⠿⠁⠘⠛⠃⠀⠀⠀⠁⠀⠀⠀⠽⠀⠜⢈⠀⠀⠿⠇⠀⠾⢇⣀⣠⣤⡊⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠘⣿⣴⢀⣴⣶⣶⣶⣶⣾⣿⣶⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣄⡈⠉⠉⠙⠿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⡀⠀⠀⢿⠁⠘⠟⢻⣿⣿⣿⡿⢻⡿⣿⡦⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⠧⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⣸⢸⡄⠀⠀⣼⠋⢻⠀⠀⣸⠇⠀⠓⠀⠀⢸⡟⣿⠛⠻⠛⣻⣿⠋⠛⢿⣿⡄⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡉⠀⠃⠚⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠀⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢧⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠄⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣸⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠿⣿⡿⣿⠛⣷⠀⠀⣼⠃⠉⠛⡿⢿⠿⢿⡇⠀⢀⣈⢁⣠⣤⡀⠙⣿⠙⠛⠟⠛⠁⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠰⠃⠀⠸⠀⠀⠻⡆⠀⢠⠃⢸⠀⠈⣡⡾⠛⠿⠿⣃⣨⡁⠀⣿⠀⢶⣶⣶⡄⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠋⠀⠈⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢴⣄
⠀⠀⠀⠀⠀⣀⠠⣄⣲⣾⠓⢛⣿⣷⢤⠀⠀⠀⠀⢤⣴⣺⠟⠁⠀⠣⡀⠀⣍⠉⢁⣶⣾⣫⠽⠛⠁⠀⠘⠈⠻⣶⣄⡀
⠀⠘⢿⠀⠀⠀⠀⠩⡍⠉⠀⠙⢻⣟⠀⠈⠀⠄⢀⠛⠛⢧⣤⣀⣀⠀⠙⢄⡇⣠⡾⠝⠋⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⡷⡀
⠀⠀⠈⠳⣶⣤⣤⣄⣄⡀⠀⠀⠈⠉⠐⠤⣀⠀⡜⠑⠦⣀⠻⣏⣈⡩⠛⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣀⣠⡤⠟⢳⣽⣄
⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠀⣽⠷⠶⠤⣌⣑⠨⣿⣁⡼⠃⠀⠀⠀⠀⠀⡀⠄⠠⠀⣺⣋⠉⠀⡁⠄⠊⠁⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣾⡏⠀⠀⠀⠀⠀⠈⠉⠻⣇⡀⠉⠀⠀⠀⠀⠀⠀⠀⣰⢻⡅⠀⢀⠠⠐⠀⠀⠀⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠰⡎⠢⣄⠀⠀⠀⠀⠀⢠⠃⣟⡷⠈⠀⠀⠀⠀⠀⢀⠠⠐⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣦⡀⠀⠀⠀⠀⠀⢐⠀⢹⡤⢊⣱⢦⣀⠀⢠⡆⠀⣧⣿⡀⠄⢀⠠⠄⠈⠀⠀⢠⣇⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣵⣄⠀⠀⠀⠀⢴⠀⠀⢡⡄⠈⢉⠙⢳⡟⠓⠶⠿⡿⢶⠚⠁⠂⠀⠀⠀⢠⣿⣿⠿⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣀⠠⠄⠾⣟⣿⡟⠙⠻⢷⡟⢿⡇⠠⣠⠚⠁⠀⠑⣄⠀⠀⠀⢀⣿⠟⠉⢠⣟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⢿⢀⠎⢸⣷⣾⠇⠀⠀⠀⠈⠙⣿⠚⢀⠀⠀⠀⠀⠈⠠⡀⢀⡞⠁⠀⣰⡏⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢰⠎⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉⠀⠒⠀⠂⣨⠾⣷⣄⣴⣿⣿⣶⣾⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡆⠀⠐⢄⠀⢀⣠⣶⠟⠁⠀⠀⠙⢿⣧⢸⣿⠟⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡟⠉⠓⣿⡟⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣿⡿⠖⢩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⢀⣹⣀⣀⣼⡟⠀⠀⠀⢀⣀⣀⣤⣴⠿⣿⣦⣰⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣷⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠋⠉⠛⠛⠁⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠉⠲⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⡤⠼⡄⠀⠀⠀⢋⠀⠀⢀⣹⣴⡊⠉⠉⠙⣆⣀⣀⡀
⠀⢀⣤⠒⣉⣁⣠⣤⠤⡴⠳⣀⢀⣠⣎⣀⡔⠉⠀⠀⠹⡄⠀⠀⣵⡤⠤⣉⣉⡉⠉⠒⠒⢤⡀
⠀⢸⠈⠉⠓⠒⠾⠤⠤⠧⠤⠬⢧⣀⣀⣀⣱⣄⡀⠠⠤⠿⠭⠭⠤⠷⠴⠒⠒⠛⠛⠉⠉⠉⡇⠀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⠀⠀⠈⠙⠢⣄
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⠒⠦⡀⠀⠀⠀⠱⡀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡇⠀⠙⢦⣧⠎⠀⠀⢳⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⢧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⣼⠀⠀⠀⡇⠀⠀⠀⣵⠾⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠑⢄⠀⡇⢀⡴⠊⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⣤⣄⡬⢶⠤⠤⠤⠤⢵⣷⠯⠤⠤⠤⢄⣴⣊⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠸⠀⠀⠀⠀⠀⠀⠀⠉⢀⡔⠁⠀⠀⢀⠔⠁⡇⠑⢄⠀⠀⠀⠘⢦⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠞⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣴⠋⠀⠀⡇⠀⠈⠳⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠊⠉⠀⠀⠀⠀⣠⠃
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⢸⠀⠀⣰⣇⠀⠀⠀⡏⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡠⠞⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠠⠊⣸⡀⠳⡄⠀⠃⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠒⠒⠒⠊⠉
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⢳⡀⠀⠀⢠⠎⠁⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣰⠃⠀⠀⠸⡄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠓⠒⠚⢣⠀⠀⠀⠀⡜⠓⠒⠊⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⢣⠀⠀⡜⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⢀⡠⠤⠔⠒⠒⠤⢤⣀⠀⠈⢢⡀⠀⠀⠈⡆⢸⠁⠀⠀⢀⡔⠁⠀⣀⡤⠴⠒⠒⠢⠤⢄⡀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⢀⠎⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠱⡄⠀⠀⣇⣈⠀⠀⢠⠎⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠱⡀
⠀⠀⠀⡞⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡸⠊⠉⠀⠀⠉⠓⢏⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢣
⠀⠀⢀⠃⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠘⡀
⠀⠀⠈⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢏⡷⠈⠋⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⠁
⠀⠀⠀⢣⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡜
⠀⠀⠀⠈⢇⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠒⠢⠤⠤⠤⠤⠔⠒⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠈⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⠚⠁⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠒⡲⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠸⠉⠑⠒⠒⠒⠒⠒⠒⠊⢉⠃⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠙⠛⠛⠋⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣇⡀⠀⠀⠀⠀⣀⣰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡴⠻⡈⠉⠉⠉⠉⢁⠟⢦⠀⠙⠦⣀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⡠⠊⠀⠀⢳⣀⣀⣀⣀⡞⠀⠀⠑⢄⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠣⡀⢀⠜⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡒⠉⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠜⠀⢀⡻⠁⠀⠠⠤⠈⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⢷⡀⠄⠀⠈⠣⡄
⠀⠀⠀⠀⡐⠀⠀⠀⢹⡇⠀⠠⣾⣿⡆⠐⠀⠀⠀⠀⠂⣠⣾⣽⣦⠀⢸⣿⡆⠀⣀⠀⠱⡀
⠀⠀⠀⢀⡇⣀⠀⠀⣿⡇⠀⢀⠈⠉⠄⠀⠀⠀⠀⠀⠈⠃⠈⠉⠀⠠⠄⢻⣧⠀⡏⠀⠀⠀⢀
⠀⠀⠀⣸⡞⠋⠀⠀⢹⡇⠠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⢸⣿⡆⠀⠀⠀⠀⠠⠦⡀
⠀⠀⠀⣿⣿⣦⣀⢀⠘⣇⡖⡀⡀⠀⠀⣰⣶⣶⣶⣿⣦⡀⢀⠀⠀⣀⡉⣾⣻⣷⢿⣶⠀⣰⡦⣴⠆
⠀⠀⠀⢻⣿⣿⢫⣯⡇⣟⢇⠘⣧⠠⠀⠻⢿⣿⣿⣿⠿⠁⠀⠀⣴⠟⣡⣿⣿⣿⢸⣿⣟⠋⣴⠋
⠀⠀⠀⠈⠳⣿⣿⣟⢁⣿⠀⠁⠘⡀⠀⠀⠀⣈⠋⠁⠀⠀⠀⣸⠁⠀⢉⠃⣈⣿⡸⣿⣏⡸⡜
⠀⠀⠀⠀⠀⠛⣿⣏⣼⣥⠗⠀⡀⢿⣦⣴⣶⠿⢿⣶⣶⣤⢖⡹⠋⠀⠁⠁⠸⡻⣇⠿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠉⠀⠙⢿⡄⠀⠀⠀⣼⣿⠋⠀⠀⠀⠐⠀⢀⣨⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠀⠀⠈⠿⢶⣶⠾⠟⠁⠀⠀⢀⡀⠰⡄⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠻⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠿⠿⠟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢷⣀⠀⢀⠀⠀⠀⠀⠀⠄⢨⣅⠰⠄⠀⠀⢄⡀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠿⠦⣷⢲⣤⡶⠾⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡄⠐⡖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⢁⢀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⣨⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⡈⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠤⠤⠤⢴⣿⣿⣯⣾⠄⠘⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢦⡀⠀⠐⠄⢱⡾⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⣿⠏⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣿⠀⠀⢰⡾⠁⢰⣿⠀⠀⠀⢰⠀⠂⠀⠀⣀⣀⠀⠀⠀⠀⠈⠀⣿⣆⢀⠀⣀⡔⠃⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⣤⠂⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⡀⢰⡿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠟⠺⡕⠤⠄⠀⢤⡆⢹⣿⣿⣷⠏⠀⠀⠀⠀⠠⠀⠀⠸⠀⡘⠃⠒⢿
⠀⠀⠀⠀⢀⡀⢀⠛⣦⣄⢹⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠈⢇⡾⠀⣿⢿⡀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠼⠆⣰⠀⣸⣧⡠⠳⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠐⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠖⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⡃⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⣠⡤⠀⠀⠀⠀⢀⣤⢤⠶⡖⠔⢾⠟⠉⠋⡀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠊⠉⠈⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⢨⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢰⣿⣶⡎⢻⠁⠀⠀⠀⠀⠀⠠⢀⡄⠀⡀⢦⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⣼⠀⠠⣾⡄⠀⠀⢠⠆
⠀⠀⠀⢀⠄⠀⡞⠉⠇⠈⠉⠉⠁⠈⢇⠀⣇⡖⠀⠀⠀⣰⣣⡾⢹⠀⠀⠈⠀⠈⠉⠉⢀⠻⠁⠀⠀⠀⠀⠟⢀⡞⠁⠉⠀⠀⠀⠀⠠
⠀⠀⠀⡌⢀⠾⡇⠀⠀⠀⠀⠀⠀⠀⢹⡤⣿⠃⠀⠀⣴⡿⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣿⣿⠀⠷⠼⠶⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⡄⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⠁
⠀⠀⠀⠀⠀⠛⠀⡀⠒⠬⠀⠄⠢⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣶⡴⣽⣲⣤
⠀⠀⠀⠀⠀⠐⡛⠲⠶⠤⠦⠴⠶⠚⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠶⠶⠒⠛⢣⠀⢀⠀⠀⠀⠀⠀⡠⣼⠈⠀⠉⢹⠹⠅⢘
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡶⠣⢀⣀⡀⠀⠀⠀⣿⣰⣧⡀⠀⠀⠀⠐⠄⢸⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⣠⠎⠁⠀⠆⠀⠀⠀⠀⠀⢀⡿⠀⢰⡿⠀⠉⣿⠛⠛⣿⠁⠄⠀⠀⠀⠀⠑⠺⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠘⠶⣶⣾⣿⣿⠿⠿⠿⠖⠚⠁⠀⠀⣷⠐⠐⣶⠉⠳⢄⣸⣇⣀⣀⣿⣀⣤⡟⠔⠁⠀⠀⠀⠀⠒⠿⠷⠶⠤⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠿⠒⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠸⡗⠀⠀⢀⠀⠀⢈⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣥⠐⠂⠉⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢘⠛⠛⠛⠛⠛⠛⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡁⠀⠀⠂⠈⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⣶⣶⣾⠷⢶
⠀⠀⠀⠀⡌⠀⠟⠉⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠉⠉⠁⠀⢰⣄⠠⠀⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢻⣄⠀⠀⠀⣐⣴⡀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠂⠀⢈⡀⠠⠀⠄⠠⠡⡈⠀⡡⠀⠀⠀⠀⠀⠀⠀⡇⠱⣄⠀⠀⠀⠀⢸⡸⣦⠀⠤
⠀⠀⠀⠀⠀⠙⢣⡀⠀⠘⠉⠂⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⣆⠉⠀⠀⠈⢠⠿⠎⡀⠀⠀⠀⠀⠀⠀⠂⢹⠀⠀⠉⠐⠒⠒⠚⠛⡹⠄⠂⡤
⠀⠀⠀⠀⠀⠀⢈⣏⡓⠒⠒⠓⣻⠃⠀⠶⠀⠀⠀⠀⢠⣥⣀⡐⠨⠷⠦⠤⠶⠋⢀⣀⠬⠀⠀⠀⠀⠀⣈⣄⠈⠢⣀⡀⠀⠀⠀⣀⣠⣁⣀⡎
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣶⣶⣄
⠀⠀⠀⠀⢀⣠⣴⣶⣤⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡀
⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠻⠟⠀⣤⣤⣤⣀⣤⣶⣿⣿⠉⠇
⠀⠀⠀⠊⠙⠋⢛⣛⠉⢙⣿⣦⠀⠀⠒⠀⠃⠉⠉⠉⠁⠐⠚⠓⠃⠀⠀⠀⢶⣒⡿⢙⠛⠷⠿⠋⠁
⠀⠀⠀⠁⠈⠉⠉⠉⠉⠋⠉⠛⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠄⢈⣟⠟⠀⠉⠈⢿⠆
⠀⠀⠀⠀⠀⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣨⣀⢂⠀⢀⡀⣨⣇
⠀⠀⢠⣴⣶⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠿⣿⣟⠉⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⡀
⠀⠀⠸⠯⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠙⠂⢤⣷⣞⡿⠠
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠀⣠⣶⣿⣿⡿⣉⣾⣿⡿⣿⠁⣼⠁⡀⠀⠸⣁⡼⠁⢧⣠⠇⠀⣠⡀
⠀⠀⠀⢀⣠⠎⢝⢽⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣶⣿⣷⢻⣦⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣥
⠀⠀⠀⡿⢋⡴⢾⠖⠋⠁⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⡿⠈⠻⡇⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⣼⡿⣿⡟⠀⠀⠀⠀⠀⣿⢿⠃⠀⠀⠱⣄⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⢀⣤⣼⣿⠿⠷⠤⠤⢤⣤⣤⡿⠺⠆⠀⠀⠀⠉⠀⠀⠀⣠⡼⠋⠋⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉
⠀⠀⠀⣿⣥⣴⣾⡿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⡀
⠀⢀⣠⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢿⠛⢻⡿⣿⡆⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠰⠛⠉⠁⠘⠳⣿⣿⣿⣿⣿⠿⣿⣻⣿⠏⠀⠀⠀⠋⠘⠀⠼⠀⠈⠂⢸⠹⣿⠋⠙⠛⠛⢿⣏
⠀⠀⠀⠀⠀⠀⢠⣿⣹⣇⣀⣀⣀⣈⣿⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠆⡏⢀⣀⣀⣀⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣤⣶⣤⣤
⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⡩⠀⠀⢀⣀⣠⣤⣤⣤⢶⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠐
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠚⠛⠛⠛⠯⠙⠋⠉⠙⣇⠀⠀⠀⡄⠀⠀⢠⣤⠀⠀⢠⡄⠀⢀⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠶⠛⠁⠀⠀⠀⢹⠀⠸⡇
⠀⠀⠀⠀⠘⢿⡇⠘⠻⠆⠹⣿⡈⠿⡄⠀⠀⠐⡄⠴⣾⣷⠆⠀⠀⠀⠀⠀⠁⠀⣀⠐⠂⠀⠉⠒⠀⠀⠀⠀⠲⠦⠖⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠋⠀⠘⣿⠁⠀⢀⣴⠻⡿⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⢤⣤⡤
⠀⠀⠀⠀⠜⣿⣿⣿⣿⡿⠻⠟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠁⢀⠀⠀⢀⣠⠄⠀⣠⢦⠟⠉⠁⠛⠈⠁
⠀⠀⢠⡴⠃⠐⠇⠀⠹⠃⠀⠀⠀⠀⠀⠀⣤⣄⢰⡄⣀⢀⡀⡀⠁⠐⠀⠀⠠⠖⠩⠶⠃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠟⢿⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣰⢻⢠⠼⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢾⠅
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠷⠶⢦⠟⠀⠀⠀⠀⣠⡴⠀⡿⢛⡒⠛⠛⢷⣦
⠀⠀⠀⠀⢸⣾⣿⣶⣶⣶⣾⣿⣿⠀⠀⢲⣶⣶⣶⡆⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠼⠵⠷⣦⣴⣿⣿⣷⣶⡸⣿⡇
⠀⠀⠀⠀⠘⣿⣿⠿⠿⣿⡿⠟⠛⠀⠀⠞⠉⠉⢹⠟⠐⠧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⡻⠉⠽⠟⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣔
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⡷⠀⠀⡞⠉⠉⠙⠁⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣾⠃⠀⡾⢇
⠀⠀⠀⠀⠀⣶⣿⠷⡶⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⢺⡁⠉⢸⣿⣿⡏⠈⠙⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⡶⢿⠇⠸⠀⠀⠧⠀⠀⢹⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠉⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣤⣽⠃
⠀⠀⠀⠀⠀⣀⣀⣀⡀⣠⣤⣠⣶⣤⠀⠀⠀⠙⠀⠀⠀⠁⠀⠀⠠⠶⢾⠷⠶⠂⠀⠀⠀⠀⠰⣤⠖⠀⠀⠐⠛⠀⠀⢈⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⠿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣄⠠⢴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⠾⠃⠀⠀⢸⣿⡷⠿⠷⠿⣿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡴⡿⠛⠉⠛⣿⠀⠀⠀⠀⠁⠈⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠂⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⣭⡶⠾⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣼⠟⠁⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠀⠀⠀⠀⢸⣇⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣄⠈⠢⣤⣤⡴⠿⠋⠉⠀⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣷⡘⢷⣄⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⡙⢷⣄⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠻⣶⡿⣧⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠚⠉⠙⢿⣎⠻⣯⣿⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡟⠁⠀⠀⠀⠀⠀⢿⡄⠈⢻⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⣷⣄⡀⠀⠀⠀⠀⠘⣇⠘⣦⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣿⣿⣿⣷⠶⠖⢀⣈⠀⠸⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠶⣛⣛⣛⡻⣦⢹⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠻⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠾⣇⡀⠀⠀⠀⣿⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠁⠀⠀⢠⡿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣤⣄⡀⠀⣼⠃⠐⠀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠑⠒⠀⠛⠀⠀⠈⣠⡤⠶⣦⣬⣙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣤⣤⣤⣤⣀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⢷⡌⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠸⣷⡀⢿⠉⠀⠈⠉⠉⠓⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⣿⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣽⠟⠉⠁⠀⡛⢷⣦⣀⡀⠀⠸⣧⣄⣀⣀⡀⠀⠀⣹⡇⠀⠀⢠⣿⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⡇⠀⠀⠀⠀⣿⠘⢮⣍⣛⠻⠶⣤⣭⣉⡉⠶⠾⠛⠋⠀⠀⣠⠾⣫⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣤⡀⠀⠀⢹⡄⠀⠈⠙⠛⠷⢶⣮⣭⣝⣓⠦⠀⠀⠠⢊⣵⡾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⢶⣄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣦⡀⠰⠋⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣡⠔⠀⠀⠀⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣉⠙⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠉⠛⢦⡈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣷⡀⠀⠀⠀⠀⠀⢠⡀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⡟⠁⢢⠀⠀⠀⠘⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠻⢶⣤⣀⠀⠀⠀⠻⢦⣄⣈⠉⠛⠛⠿⠿⠟⠛⠋⠁⢀⣠⠟⠀⠀⠀⣰⡟⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣬⣙⡛⠷⣶⣦⣤⣌⣙⠛⠿⠶⢶⣶⣶⠶⠾⠟⠋⠁⠀⠀⢀⣴⠟⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⡷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠿⣿⣶⣄⠀⠀⠀⡼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠄⠀⢰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠇⠀⠀⠘⠀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢗⡐⣂⢁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣿⣿⣿⣿⡿⣿⣏⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⡴⡰⣶⣄⣄⡀⠀⠀⠀⠀⠀⢺⣾⣾⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠛⠁⠈⠉
⠀⠀⠀⠀⠀⠀⢀⢶⡽⡿⡗⠓⠺⢏⢿⣿⢇⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾
⠀⠀⠀⠀⠀⢀⣸⣿⠻⠀⠇⠀⢸⠀⠩⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⡀
⣿⡄⠀⠀⠀⢸⠭⠭⡆⠤⢈⠀⢸⠀⠀⡒⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣀⣀⢠
⣼⡆⠀⠀⠀⢩⡭⠭⡇⠀⠸⣶⣾⠀⠀⠳⢶⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⣀⡀⠀⢀
⣿⣷⠀⠀⠀⠐⣻⢭⣧⠀⠀⠈⠁⠀⠀⡸⣬⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢶⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡄⢾
⢿⡇⠀⠀⠀⠀⠠⡿⡷⣵⣶⣶⡖⣦⣥⣿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠀⠀⠈
⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢀⣀⣀⣀⠀⣠⣤⣀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⣿⣿⡟⠈⢿⣿⣿⠃
⠀⠀⢀⣀⡀⡀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢒⣦⡀⢼⠾⠗⣰⡨⠃
⠀⠀⠘⡉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⠉⠁⠈⢻⣱⣦⣄⡀
⠀⠀⠀⠀⠀⠄⣠⣄⠀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠾⡏⣯⣿⠂
⠀⠀⠀⠀⠀⢰⠉⠇⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣻⣇⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣒⣒⠂
⠀⠀⠀⢀⠀⢠⠀⠄⡀⠀⠠⠘⡇⠀⠀⠀⠀⠀⢀⡀⡀⠴⠒⠲⠲⠒⠤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠙⠋
⠀⠀⠀⠀⢂⢀⠃⠈⢁⡠⠁⠀⠀⠀⠀⠀⠀⠀⣏⠾⠃⠀⠀⠉⡍⠀⠀⠈⣷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣴⣶⡄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠿⠿⠟⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⣿⣿⣾⣿⡇
⠀⠀⠀⢀⣤⡀⢀⣀⣀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠻⠿⠿⠟⣿⣿⣷⣶⡦
⠀⠀⠀⠀⠁⠈⣿⣿⣽⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠀⢸⠀⠀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢻⠟⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⠀⠸⠐⠀⢻⣿⣿⡿⠃
⠀⠀⠀⢀⡛⠃⣶⣶⡾⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠑⠂⠀⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠸⣾⠂⢸⣿⣿⣿⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⠳⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⣯⡤⠤⣰⣾⣿⣿⣿⡏⢘⡟⠂⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣟⣭⡵⠞⢝⣽⡿⣡⡿⣻⠀⠌⢷⡀⠀⠀⠈⠻⣶⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⢛⣯⠔⢂⠰⠛⠉⣋⣴⡞⠻⠁⠉⣡⣿⡇⢁⠈⠈⠢⣄⠀⠰⣬⠣⠀⠈⠳⢦⣄⣰⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠌⡀⠴⢋⣠⠴⢚⣿⡿⣵⠀⣤⣶⠟⢻⣿⡀⠒⠆⠀⠻⡔⠀⠈⢀⠲⣄⡀⡖⡤⢹⢾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⣵⠟⣋⣡⣴⣿⡟⣠⠇⣼⢫⡁⢠⠞⠈⡿⡀⠀⠚⢶⠀⢠⡀⣸⡇⢠⣿⣇⣵⣾⣾⣧
⠀⠀⠀⠀⠀⢀⣼⣿⠟⠓⠀⠠⠴⠟⢋⡩⠟⠋⠀⣡⡎⠁⡈⠇⢨⡆⡀⠧⠀⢄⠀⡄⠀⡸⢁⣘⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢿⣥⣶⠶⠶⢿⣥⡶⢿⣷⡀⢀⠠⠋⠆⢠⣿⡀⣼⡧⡇⡀⣷⠀⣰⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢸⠀⡄⠀⢺⣿⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠀⢰⠀⣀⣿⢸⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⡦⣈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣽⣿⣿⣯⡶⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠉⠀⠀⣰⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠟⣆⢀⣀⣀⣼⣻⠏⠉⠉⠙⠷⣠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠞⠉⢻⣀⡤⣧⣬⠶⢛⠉⠛⢀⢀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣀⡁⠄⠚⠑⠀⠀⠀⢰⣼⢅⣀⠀⠸⣀⠘⣠⡷⠄⠠⠾⠉⣟⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⠐⡆⠀⠀⠐⡄⠱⣦⡀⠐⠁⠘⠶⢴⣦⣀⡈⠢⠚⠁⠀⣈⣳⣄⡋⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⡇⠀⠀⢀⠏⢢⠰⡁⢠⠐⠉⠉⠉⠀⠀⢷⠘⣀⠀⢦⠁⠉⠉⠠⡁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡾⠈⣀⣴⠎⠀⠀⠈⡇⡹⠸⡆⠂⠀⠀⠀⠐⠘⡇⠃⠈⠾⣇⠠⠀⠀⠈⠀⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠲⣴⠳⣄⠀⠀⠊⠰⡧⠀⢻⡀⠀⠀⠀⠀⠀⢷⢷⠀⢠⠏⠀⣁⣴⡿⠖⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⡶⠶⠤⣄⣸⠃⠀⠀⠘⣗⣨⢭⣁⡒⠶⠘⠆⣀⣳⡄⢠⠤⠶⣤⣀⡶⠶⣻⡼⣿⠉⠀⡎⢂⢰⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢞⡽⠛⢩⠽⠿⠯⢭⡓⠀⣽⠀⠀⠀⠀⠈⠁⠀⠀⢹⡶⣤⡤⢦⡁⠀⣡⠋⠛⠉⠁⠙⠞⠋⠀⢸⣷⣼⠁⠈⡏⢸⡇
⠀⠀⠀⠀⠀⠀⣰⠃⢀⡴⠖⠚⠛⠛⠓⠦⣅⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠈⣿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠀⠀⣧⣿⡇
⠀⠀⠀⠀⠀⢠⡏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠘⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡇
⠀⠀⠀⠀⠀⢸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠘⣇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠐⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢹⡄⠈⠳⣄⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠞⠓⠚⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠈⠉⠙⠛⠒⠒⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠂⠠⢀⣄⣁⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠶⠛⠓⠋⠉⠉⠄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⠤⠴⡶⢶⡴⠶⠦⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣖⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣿⣿⣿⣿⡿⣾⡟⣿⡏⢾⡿⣿⣿⣿⡏⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣉⠙⣹⠁⣿⢿⣫⢯⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡜⣿⢸⣿⡼⣿⡏⣿⠀⣿⠀⡟⡾⠀⡾⢀⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢿⡄⢿⡇⢻⡇⢿⠀⣿⢠⡇⡇⢸⠇⣰
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⡿⣏⢷⡈⢧⠘⣧⠘⡇⢸⡆⣿⢰⣵⠀⣾⡴⠃⡆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢧⡙⢌⠫⣷⠘⣇⢹⣆⢿⣸⣇⣿⣼⣾⣵⣿⡷⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢦⠑⠈⢳⡈⢧⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡅
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠷⠦⣀⠀⠁⣽⣾⣿⣿⣿⣿⣿⠿⢻⠿⢿⡿⣿⣿⣦⣀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⢬⡀⠀⠀⠑⣶⣿⣿⣿⡿⢏⡁⠉⡄⠀⡂⢀⡀⠈⢋⠝⣿⣷⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⡀⠀⠀⠀⢀⣿⣿⣿⣿⢧⣄⣑⣢⣼⣿⣿⣿⣿⣷⣯⠈⠉⢽⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠈⠭⠀⠀⣬⣽⣿⣿⣷⠦⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠐⠫⣿⣇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣭⣥⠤⠤⠀⠸⣿⠿⠿⠟⠚⠻⠻⣿⡿⠿⠿⣿⠿⣿⣿⣿⢧⣴⣾⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⠒⠂⠀⠀⢿⢂⣷⣷⣵⢄⣴⢋⣿⣿⣍⣽⣾⣿⣿⣿⠯⢷⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡊⠁⠀⠐⠀⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⠫⣛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣾⡅⢤⣀⡄⣊⡾⢻⣿⣿⣿⢿⢿⣿⣿⡏⠙⢄⠀⠸⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣫⣾⠘⠁⢠⠃⠃⡀⠀⠈⡅⠈⠁⡀⢀⡻⣮⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠆⡀⡾⢀⢀⡇⠀⡄⣸⡴⣤⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣽⣿⣿⣿⣿⣿⡧⣷⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠿⢯⣿⣟⣿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡍⢊⢘⡞⣸⢫⡾⣻⡷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠿⢠⠘⣾⡼⢡⠟⣵⢏⡿⢫⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣜⡅⢋⢍⠞⠀⢼⢠⡏⡼⢣⡟⣱⠟⣵⣿⡀
⠀⠀⠀⠀⠀⢀⣿⣌⣩⣾⡧⠷⠚⠻⡞⣰⢣⠟⣸⠇⡼⢃⣴⢟⡴⢠⢄⡄⣀⡀⣀⢀⢀⣀⣀⣤⣴⡶⣶⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠈⠧⠽⠿⠋⠀⠀⠀⠀⠘⢧⡶⢛⣉⣼⢣⣾⠃⣾⢣⡟⣸⢣⡇⣿⣿⢨⡟⣫⡴⣫⡵⢛⣵⣾⠿⠛⠛⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⣫⣵⡾⢁⣼⢣⢟⣴⢫⣿⢃⡿⣾⣾⢰⡟⣼⠋⣴⡿⢉⣤⣶⡿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⠴⢛⣵⡿⢛⡅⣾⡏⣸⢧⣧⣇⣿⡟⣡⡾⢋⣴⠟⢋⣥⣤⣶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⣾⣫⣄⣄⠿⣘⣿⠁⡿⢸⣿⢸⡏⢰⡟⢠⡿⣡⡾⠛⣋⣁⣤⣴⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⢉⡭⢬⣓⣜⣿⠀⣿⢸⡇⣿⠀⣿⢀⡟⣰⢋⠔⣋⣩⣭⣥⡎⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⡞⢛⣺⣽⣸⢀⡏⢸⡇⣿⠸⡇⢸⠀⡏⠿⣋⠵⠶⢶⢋⣿⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠿⢷⣒⠋⣩⠉⠙⠃⠛⠀⠛⠀⠓⠈⠁⠀⠀⠈⠭⢛⣭⠔⣲⡀⢹⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢤⠎⠩⠭⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡟⠶⣚⣷⠄⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣚⠻⠀⠘⣿⡭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠇⠀⠑⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⠂⠀⠀⢨⠽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡱⠆⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⠀⠀⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠁⠀⠀⠀⢠⣇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠄⠀⠀⠀⢀⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡼⠃⠀⠀⠀⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡄⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⣀⣀⠀⢀⠔⠉⠀⢁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠄⠰⠄⠀⢸⡠⢇⡀⡸⠷⢒⡠⠂⠁⠀⣀
⠀⠀⠀⠚⠀⠀⠀⠀⠀⢠⠂⠐⢢⣀⣀⠚⠐⠣⡀⠠⠃⢦⠀⣸⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠒⠚⠒⠒⠑⠀⠠⠦⠶⠀⠤⠤⢈⡐⣇⣈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠤⠀⠤⡀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⢐⡄⠀⠀⠀⠀⠀⠀⠀⢸⡔⠂⠲⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠐⠛⣥⣰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢲⢦⣁⠉⢀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠌⠀⠄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡰⠀⠁⠒⣛⠋⠄⠀⠀⠀⠀⡜⠁⠈⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠓⠒⢲⣲⠒⠀⠉⠀⠀⠀⡜⢁⣉⡀⡠⣐⠀⠀⠐⡦⢀⠠⠀⠄
⠀⠀⠀⢚⡚⣦⠀⢀⠠⠒⠠⡀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⢶⣀⢁⣀⠌⠁⠈⠍⠈⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠊⠉⠛⠉⠕⠛⠂⠄⣀⡘⠉⢽⣖⠋⠠⢬⣋⡀⠂⢈⠉⠉⠀⠈⠉⠋⠉⠙⠚⠉⠁⢀⠙
⠀⠀⠀⠠⠀⠀⠤⣀⡂⣤⡠⢅⡠⠍⠠⣅⣄⡀⣀⠁⢀⠀⠀⠠⠍⠍⠀⠐⢖⠂⢠⣠⣄⣐⣡⡄⠀⠁
⠀⠀⠀⠭⠨⠙⠁⠀⠊⠀⠀⠈⠃⠐⠀⠀⠀⠈⠉⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠑⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⠂
⣿
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⣤⣤⣄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⣸⣿⡿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⢳⠦⠊⠙⠿⣿⢿⡀
⢸⠀⠀⠀⠀⠀⢾⣿⣶⣶⣶⣦⣤⣄⠀⠀⠀⠘⢿⣿⣤⣾⣷⣶⣶⣿⣶⣦⡈⢃⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣴⡄
⢸⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠠⠈⢻⣿⣿⣿⣿⠋⡽⠋
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣇⡾⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⡤⢿⣟⡻⠏⠊
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣶⡟⠉⠙⣿⠏⠸⣿⣿⡯⢀⣹⣿⣿⣿⠗⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠉⠃⢹⠀⠐⣿⠁⠀⠀⠀⢿⡿⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⢀⠀⣴⣿⣷⡀⠆⠀⠀⠀⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢿⡌⠀⠈⢿⠀⠀⠀⡚⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⢀⣀⣀⣀⣄⣀⠐⢠⡆⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠹⠋⠋
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡜
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⠿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣿⣿⣿⣿⣧⣶
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠻⠾⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠓⠿⠿⠿⠿⠿⠟⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡌⢻⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣶⣿⣴⣤⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⢹⣿⠟⠿⠇⠀⠈⢻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠁⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣦⣀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡶⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠶⠖⠂⠀⠠⣈⠛⠓⠀⠀⠀⠉⠛⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠐⢦⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⣀⠀⣰⣄⠀⡀⠀⣼⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣯⣴⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠘⠋⠈⢋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣄⣤⣝⠈⠁⠀⠀⠀⠤⣴⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡄⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣪⣠⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⣄⢀⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⡇⢀⠀⢀⠸⠿⠿⠿⠦⠤⠄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠰⣶⣶⠆⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⣀⣤⣄⡀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡦⠀⠀⣀⣀⠀⠀⠀⣠⣄
⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠐⠻⣯⣭⣽⣿⣿⣿⣿⠄⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⣿⡿⠋⠉⠀⣤⣾⠟⠁⠀⠀⠀⠛⢿⣿⣶⣶⣶⣄⡀
⠀⠀⣼⣿⣿⡟⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⡀⠀⠀⠈⢻⡟⠛⠻⣿⣧⡀
⠀⢾⣿⣿⣿⡇⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣠⡿⠻⣿⣿⡆⠀⠀⡿⠦⠀⠀⠀⠹⠄⠀⠀⢀⣿⣿⠁⠀⠘⠁⠀⠀⠉⠘⠁
⠀⠈⠁⠙⠉⠛⠀⠀⠀⢿⠿⠧⠤⠀⢀⣴⣶⡦⠴⠖⠃⠀⠀⠀⠈⠑⠚⠛⠛⠁⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⢠⡷⠇⠀⢀⣴⣿⠗
⠀⠰⣿⣦⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠿⣶⣶⣾⣶⡶⣄⠀⠀⠘⠲⣾⣿⣧⠀⠀⣤⣿⣿⣿⡇⠀⠀⠀⢻⣦⣀⢼⢿⠏
⠀⠀⢸⣿⣷⣶⣶⣶⣿⠟⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⡀⠀⠀⡴⠋⠹⠀⠹⠟⠈⠁⠀⠐⠛⢫⣿⣧⠀⠀⠙⠛⠁⠋⠃⠀⠀⠀⠤⣼⣟⠀⣁
⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⡟⡹⠋⢿⠻⢟⠳⠄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢰⡕⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠹⠾
⠀⠀⠀⠀⠘⡿⠛⠟⠁⠀⠀⠀⡄⠀⠈⠐⠃⠀⠈⠀⠰⠃⠀⠀⠀⠀⣼⣏⠁⠀⠀⣀⠀⠙⠁⠛⠁⠀⠀⠀⠀⠀⠸⠟⢿⣷⣤⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠑⣯⡀⡀⠀⢀⣀⣀⠀⠀⣠⣀⣀⣾⣿⡇⠀⠀⠀⠹⣷⣦⣤⣠⣴⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣤⣤⣀⣐⣂⣄⣠⣤⠀⠀⠀⣠⣿⠟⠉⠀⠈⢻⣿⣧⡀⠈⠉⠉⠉⠉⠁⠀⡀⠀⠀⠙⢿⡿⡟⠋⠁⠘⠀⣤⢀⣶⠇⠀⠸⣯⠉⠀⠀⢻⣿⣿
⠀⠀⠛⣫⣛⣛⣿⠛⠁⠀⠀⠘⣿⠁⠀⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⠈⡐⠄⠀⠀⠐⠀⠘⠀⠀⠀⣴⣿⣿⡟⠀⠀⢠⠯⠆⠀⠀⠼⡼⠙⠃
⠀⠀⠀⠁⠛⡛⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⢀⠀⠀⠀⠘⢹⣊⠓⠄⠀⠀⠀⠀⠀⠀⠙⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣀
⠀⢀⣀⡀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⣿⣷⡀⠀⠀⠀⠈⠳⡄⠟⠀⠀⠀⠀⠀⠔⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣻⠉⠁
⠀⠀⠉⢿⣤⣤⣾⣿⣿⣿⣿⣷⡄⠀⠀⣠⣶⣶⣿⣿⣷⣾⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⣤⣤⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠆
⠀⠀⠀⠀⠉⠉⢹⣿⠛⠋⠁⢿⣇⠀⠺⠟⠛⠉⢻⡟⠛⠿⠿⠿⣧⡀⠀⠀⣤⣴⣦⡄⠀⠀⢀⢤⡘⣯⡀⣹⣷⡏⢿⣀⣀⡀⠀⠀⢰⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠏⠇⠀⠀⢸⠘⠆⠀⢀⠀⠀⠘⡗⠦⠀⠀⠖⠁⠇⠀⢠⠿⢛⣿⣿⠀⠀⠀⠀⢧⣸⠇⣿⢀⣿⠈⠉⠉⠁⠠⠤⢾⡿⣿⡯⣯
⠀⣺⣿⡄⠀⠀⠐⠀⠘⠀⠀⠂⠘⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢤⣾⣶⡀
⠀⠘⢇⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⡿⠁⠀⢀⣠⣤⣤⣶⣶⣄⠀⠀⠀⠈⢿⣿⡿⡇⠀⣾⡲⢄⠀⠀⢀⠴⣺⡆⠈⠉⣿⣿⣶⣶⣶⣶⣶⣤
⠀⠀⠈⠳⠄⠈⠒⠦⢤⠤⠖⠂⠁⡠⠋⠀⠀⠀⠉⠛⣿⢿⣿⣿⣿⠀⠀⢠⢦⠀⣿⠃⠀⠀⠙⣷⠤⠐⡶⠀⢤⡞⠁⠀⠀⠹⣿⡿⠿⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠚⣠⣤⣤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠴⠃⠀⠘⠶⠾⠟⠀⠀⠀⠀⠻⢷⠆⠁⢶⡿⠃⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣹⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡷⠁⡿⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢹⡴⠁⠀⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠀⠠⢷⠒⠒⠒⠶⢤⠀⠀⠀⡰⢻⣸⠁⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠉⣍⡷⠒⠚⢛⢢⠀⡠⠞⠓⠒⠒⢧⣸⠃
⠀⠀⠀⠀⠀⠀⢠⡶⠛⢋⠹⡄⠀⠀⠀⡇⠀⠀⠈⢸⣴⡇⠀⠀⠀⠐⢻⡟⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠘⢬⣓⠶⠤⣭⣙⣛⣩⣓⡒⠂⠤⠾⢋⣓⣒⣈⣚⡭⠭⠗⣚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠓⠒⠶⠦⠬⠭⠭⢭⠭⠭⠭⠭⠥⠶⠖⠒⠚⠉⠉⣇⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⠀⠪⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡇⠀⠀⠀⠱⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⣿⣹⠿⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢴⡶⢾⣿⣗⠚⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⣠⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢲⢏⣿⡈⠿⠂⠀⠀⠀⠀⠀⣀⢸⡏⠉⠉⠉⢀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠚⠛⠛⠉⠉⠉