Genoise Emojis & Symbols

⣿⠛⢁⡀⠋⠀⠀⢰⣾⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠻⠃⠒⠒⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣾⣿
⠠⣾⣿⡿⣿⠏⢰⠈⣿⢿⢀⡟⣠⣤⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⣿⡏⠀⢠⣿⣿⣿
⣴⣿⣿⢞⠍⠀⢀⣤⠘⠋⢙⠕⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⠟
⠛⠋⠀⢠⠄⠀⢀⣅⣠⣤⣭⠠⠤⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠄⠀⣀⣄⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠛⠛⠻⠶⠀⠀⠀⠀⠈⠈⡟⠁⢠⣾⡟⠉⣇⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠉⢀⡄⠀⠙⠂⠀⠈⠉⠛⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣾⣿⣧⠀⠈⠀⠀⠀⠈⣿⣿
⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡀⣠⡄⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣦⡀⠀⠉⠈⠁⠀⠀⢀⣴⣿⣿
⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣷⣾⣿⣿⣷⣶⣤⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⣶⠾⡿⣿⢛⠛⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⠿⣿⠛⠙⠛⠋⠻⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣤⠀⠀⢀⡀⠀⡀⠀⠄⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣎⣤⣜⠀⠀⠀⠀⠀⢀⣿⡆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⢤⣾⣦⣦⡀⠀⠀⠀⢀⠠⣔⣶⣴⡀⠀⠀⠀⢠⣠⣶⣶⣶⣦⡀⠀⠀⢠⡶⣴⣿⣶⣶⡄⠀⠀⣀⣠⣤⣶⣴⣄⡀
⠀⢀⡀⠀⠉⠀⢁⣠⠀⠀⠀⠀⠀⠈⠀⠀⣀⡄⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠉⠛⠻⠛⠛⠉⠀⠀⠀⠀⠉⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⡀⠀⠀⠀⢀⣠⣴⣦⣦⣄⠀⠀⠀⠀⣠⡀⣤⣤⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠈⠛⠻⠿⠿⠛⠂⠀⠀⠀⠘⠁⠘⠓⠈⠁⡀⠀⠀⠈⠛⠛⠟⠋⠛⠀⠀⠀⠀⠿⠻⠟⠻⠋⠀⠀⠀⣾⡿⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠒⣲⣤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⢯⣄⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠰⡦⢷⣄⣶⣀⡄⠀⠀⠰⠾⣿⣿⣿⢿⡿⠆⠀⠀⢘⡄⠛⣸⠅⠶⠀⠀⠀⢠⣤⢀⠤⣦⣴⠄⠀⠀⠀⠴⢶⣿⠶⠆
⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠤⠤⠔⠂⠀⠀⠑⠲⠤⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣀⣤⣠⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣠⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣤⣀⣤
⠀⠀⠛⠿⠿⠛⠟⠃⠀⠀⠚⠿⠿⡿⠿⠿⠟⠀⠀⠀⠻⠿⢿⢿⠿⠟⠀⠀⠀⠰⠖⠃⠖⠿⠟⠀⠀⠀⠘⠿⠿⠷⠿⠟⠁

⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⢸⣿⣿⣿⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿
⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢰⠉⣿⠉⡇⣠⣄⢀⣄⣰⣇⢀⣀⡀⢀⡀⠀⣰⠒⢦⣦⣀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣿⣿
⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠸⠀⢿⠀⣧⣖⣿⢙⣲⠼⣇⢿⡒⠇⡏⠀⠀⢿⠀⣀⣿⠉⣧⣾⣭⡷⣼⠉⠀⠀⠀⠀⢘⣿⣿
⠀⠀⢸⣿⣿⣿⡷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠁⠀⠀⠈⠉⠁⠁⠀⠋⠘⠓⠂⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⢸⣿⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣾⣷⣾⣶⣶⣦⣤⡤⢀⠠⠦⣤⣤⣤⣄⣀⡀⣀⣀⣠⡄⠀⣀⠀⡀⠀⢠⣤⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⢟⣛⣫⡿⣿⣫⣤⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣏⣽⡟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⢰⣾⣿⣿⣿⣟⣛⣿⢿⣛⣩⠗⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠘⣿⣿⣿⣿⣿⣿⣷⡮⢝⣋⠱⡦⣎⠉⣿⣿⣿⣿⣟⠁⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠻⣿⣿⣿⣿⣿⣿⣻⡿⠛⣦⢹⣆⣖⣿⣿⣿⣿⣿⣿⡇⠐⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡾⣿⠿⠿⢿⣿⡿⠛⣛⠁⠈⠀⢹⣿⣿⣿⣿⣿⣯⣁⠤⣀⡼⣿⣿⠸⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠩⠀⠀⠀⠘⠛⠿⠿⠿⠟⢻⡄⣰⡿⠃⢹⣿⡆⣿⣿⣿⣿⣿⡿⠖⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⠃⠛⠟⠹⠿⠟⣡⣄⢘⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣀⠀⠁⠉⠉⠛⠛⢻⣯
⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⣷
⠀⠀⠀⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠠⠀⠀⠀⠀⠠⠈⠉⠉⠩⠉⠩⠉⠭⠁⠀⠀⠠⠀⠀⠀⠀⠄⠉⠨⠠⠄⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠄⠈⠩⠀⠂
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠠⠠⠠⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠠⠤⠄⠀⠀⠠⠄⠠
⠀⠀⠀⠀⠤⠀⠤⠤⠀⠀⠤⠠⠠⠠⠤⠀⠀⠤⠀⠤⠤⠠⠀⠄⠄⠠⠄⠠⠠⠀⠀⠀⠠⠤⠀⠤⠀⠄⠀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠤⠀⠀⠤⠀⠤⠀⠄⠠⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠒⠶⢟⣿⣄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠈⠙⠁⠀⠀⠀⠄⠠⠀⠀⠈⢛⡗⠀⣧⠀⠀⠀⣿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⢀⣼⣧⣴⣧⣤⣪⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠚⠛⣿⣿⣿⠶⠶⠶⠶⠂⠀⠟⠛⠛⠻⢿⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣑⡤⠄⠘⠻⠿⠷⣀⡀⣀⡌⠀⠀⠀⠀⢀⣴⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠘⠿⣿⠉⢀⣀⡼⡥⡀⡀⠀⠀⠈⠛⠃⠀⠀⢀⣴⣿⣿⠿⠃⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⢌⡷⢻⠵⣺⣟⣹⣏⣾⣷⣦⠀⣀⣀⣰⣿⠟⠋⠀⢀⣀⠠⠤⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠒⠟⠒⢈⣡⠔⠉⢍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠂⡤⠀⢀⠄⠄⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⣀⡥⠟⠁⣠⡞⠑⡀⢀⡶⣰⠆⣠⠖⢚⠀⣴⠟⡀⢀⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠈⠀⠀⠀⠀⠓⠐⠈⠖⠁⠺⠁⠘⠧⠂⠀⠘⠃⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠠⠀⠠⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠠⠄⠠⠀⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⡜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣶⣷⣾⡏⠘⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠱⣯⠻⡇
⠀⠀⠀⠀⣿⣿⣿⣧⠀⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠗⣼⠿⡇
⠀⠀⢾⣿⣿⣿⣿⣷⣾⣷⣤⣉⣷⠀⠀⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣦⣤⣇
⠀⢀⣾⡿⢛⣽⣿⣿⣏⣉⣛⠻⢿⣷⣟⠛⠃⠙⠛⢪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⡞⡛⠇
⠀⠈⠉⠺⠟⠛⠳⠏⠻⠯⠭⠿⠷⠟⠯⠶⠄⠀⠄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⣿⠷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⢀⣴⢿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡤⠀⢹⣿⣿⡄⠤⢼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠘⢢⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠻⠟⠉⠀⠀⢸⡟⣶⣠⣿⡿⢾⣯
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⠆⠂⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠝⢛⣠⣀⣼⢁⣿⣿⣿⣿⣿⠿⣤
⠀⠀⠀⠀⢲⣼⣿⣿⣯⣭⣤⣵⣦⣿⣿⣾⣿⡶⢦⠀⠀⠀⠀⠀⠀⢠⣿⣟⣣⣾⣿⣿⣏⠿⠿⠃⠙⠻⣿⣟⣴⡿⡇
⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡛⣹⡏⠹⣇⠀⠀⠀⠀⠀⠀⢸⣥⣟⣻⣾⣿⣿⠣⠬⢤⠀⠀⠀⠉
⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⠿⢿⡭⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠟⠿⠿⠛⠾⠛
⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡶⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⣿⠇⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠤⠠⣤⣶⡆⢀⢀⡁⢀⢸⡯⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⣿⣷⣶⣶⣶⡄⣽⣿⣿
⠀⢀⣶⣴⠖⡙⣯⢉⡑⠿⠏⢙⣻⣿⣗⠈⣻⡶⢦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⣿⣿⡿⠿⠿⣿⣿⣿⣿
⠀⠈⠭⢉⣬⣍⠟⣾⣿⡶⠿⠿⣯⡉⢉⠖⢫⣿⢾⣟⢛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠰⠂⠀⠀⠀⠀⠀⠉
⠀⠀⠒⠀⠉⠱⠿⠟⢱⠏⠰⣤⣜⣷⣮⡉⠤⠟⠀⠻⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠛⠀⠀⠀⠉⠻⠂
⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⣠⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡏⢀⣌⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣸⣿⡀⣀⣀⡀⣶⣶⣶⣤⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠀⣬⢙⣦⡞⠿⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠶⣾⣿⣷⣿⣧⣶⣿⣿⡷⡛⠋⣵⡄
⠀⠀⠀⢠⠷⠶⢾⠀⠈⠉⣟⢙⡛⢶⣤⣤⣹⠳⡀⠀⠀⠀⠀⠀⢠⣚⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏
⠀⠀⢠⣿⡀⠠⠸⠀⣤⠀⠈⠉⠰⠛⠛⠏⢿⣷⡌⠀⠀⠀⠀⠀⠈⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡄
⠀⠀⠋⠉⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠚⠉⠋⠙⠂⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠿⠛⠛⠛⠛⠉⠀⠐⠻⠟⠛

⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢋⣻⣆
⠀⠀⠀⠠⠖⠛⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠚⠛⠛⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠛⠉⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⡅⠈⣷
⢻⡳⡶⠋⠉⢁⣾⡘⢿⠙⡆⠀⠀⠀⠀⠀⠀⣾⡉⠘⣇⠀⠀⡞⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢻⣀⣤⣤⣀⡤⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⠛⣻⠇
⠈⢷⡀⠀⠀⢸⣭⡷⠈⡿⠁⠀⠀⠀⠀⠀⢸⣏⣹⣦⡼⣤⡼⣥⣴⣋⣹⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⡄⡍⣠⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢠⠏
⠀⠈⠳⢤⣄⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⣴⢞⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣛⣓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢤⡀
⠀⣠⡤⢤⡀⠘⣷⣋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⡴⠶⣄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⣁⣀⣀⣹⡆
⠀⣏⠱⣦⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⣤⡤⡼⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠶⠀⣸⠆⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣉⣉⣉⡉⢹⡇
⠀⠈⠳⣬⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣥⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠚⠉⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠾⠃



⠀⠀⣀⣤⣄⡀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⠋⠀⣈⣋⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠭⠤⠭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠓⠒⠶⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣼⠃
⠀⠈⠷⢸⡏⠉⢹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⠛⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠛⠛⢛⣅⢨⣇⠀⠀⠀⠀⠀⠀⠀⣤⡄⣤⣤⣥⣤⣤⣄⣀
⠀⠀⠀⢸⡇⠴⠾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⠀⢀⣀⡀⠙⣧⠹⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⣽
⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣸⡦⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠁⠉⠉⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⣤⡴⠟⠁⠁
⠀⠀⠀⠘⠧⠤⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠛⠛⠒⠚⠂


⠀⠀⠀⠀⡀
⠀⠀⠀⠰⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠉⠉⢩⢭⡉⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⡤⠠⠬⠥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣀⣀⣙⣚⣁⣀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣤⣤⣤⣤⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣁⣙⣛⡆
⠀⠀⡇⠀⠀⠀⢸⡏⢹⡆⠀⠀⠀⠀⠀⠀⢰⡇⠈⣯⠉⠙⢿⠟⠙⡛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠩⣭⣭⠍⣿⢶⡄
⠀⠀⡇⠀⠀⠀⢸⡇⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡯⠤⠤⠤⠤⠤⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⣣⠞⠁
⠀⣨⣵⣦⣴⣤⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠖⠒⠒⠒⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣤⠼⠋

⣄⣄⣀⠀⠀⠀⠈⠈⠛⠉⠳⠚⠶⠃⠐⠋⠉⠀⠀⠀⠀⢀⣄⢠⣀⣠⡄⠀⠀⠀⠀⠀⠀⠁⠉⠱⠿⠉⠉⠛⠋⠉⠀⠀⠀⢀⣤
⣿⡿⣿⣶⣦⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⣀⣀⣶⣿⣿
⠟⠙⠛⠿⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⠛⠉⠻⠿⠋⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠟⠉
⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠖⠚⠁
⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤
⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠈⠁⠀⠀⠀⢀⡀⢠⣴⣦
⣀⢀⠀⠀⠀⢰⣧⡄⣀⢠⣤⣿⣿⣿⣿⣿⡇⣠⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣥⢸⣿⣿⣿⣿⣿⣧⣄⢀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠉⠑⠊⠘⠛⠿⠋⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠘⠛⠛⠛⠛⠿⠛⠋⠀⠚⠉⢀
⠀⠀⠀⠀⠀⡈⠓⠀⠀⠀⣀⠀⠀⢀⡠⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠢⠤⠄⡀⠀⠀⣀⠀⠠⠐⠊⢁
⠀⠀⠀⠀⠘⠿⠶⣦⣄⠀⠀⠀⣀⡀⣀⢠⣤⣴⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣄⢀⣀⣀⠀⠀⠀⣠⣴⠶⠟⠁
⣤⣄⡀⠀⠀⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⣀⣄⣠⣀⣤⡀⠀⡀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣆⢀⠁⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠉⢀⢀⣶⣿⣿
⠋⠛⠛⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠹⠟⠛⠉⠻⠿⠋⠙⠉⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡤⠀⢉⡀⠀⢀⡀⠀⠡⡀⠀⠁⠀⠀⠀⠂⠀⠀⠩⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒⠀⠀⠀⠀⢠⡌⠁⠀⠈⠁⠀⠈⠷⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢲⠞⠁⠀⠀⠉⠀⠀⢀⠀⠓⠖⠒⠚⠿⠛⠀⠀⠀⠀⠀⠀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⠀⠺⠂⠀⠀⠀⠐⠈⠀⠀⠟⠀⠠⠆⠀⠀⠊⣰⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⠔⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡄⠀⢀⣀⠀⠀⢴⠆⠀⠀⠀⠀⠔⠀⣠⣏⢃⠀⠀⠀⡌⢎⠀⠀⡠⠒⠊⡀⠔⡁⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠉⠀⠀⠀⠀⢀⡠⠒⠁⢀⠴⠯⢤⣈⣁⣉⣈⣁⣁⡈⠥⠄⠐⠈⠀⠀⣀⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⢒⠀⠀⣀⣀⠀⡀⠠⠔⠈⠁⢀⠠⢞⠃⠀⠒⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠁⠀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⠠⠤⠐⠂⠈⠀⠀⠀⠉⠒⠤⢀⡈⠀⠈⠉⠀⠉⠉⠒⠂⡀⠠⠄⠂⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣀⣠⡤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠒⠒⠂⠠⠤⠤⠀⠐⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣰⣶⣴⣦⣤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣴
⠀⠀⠀⠀⠀⠀⠀⢸⠳⡞⢳⡁⣙⣿⡮⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠙⣄⡰⠏⠄⠭⣥⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣥⣶⣀⡄
⠀⠀⢀⣤⣤⣤⣶⠊⠹⢜⡄⡠⠄⠐⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣶⣿⣿⣶⣭⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠛⠛⠐⠓⠲⢠⡗⣄⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⢻⣿⣿⣿⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠉⠀⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⢧⣾⣿⠟⢿⡟⢷⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢲⣰⣦⣀⡀
⠀⠀⠀⠀⣀⠀⠚⣶⣆⡨⢴⣺⣿⣿⣤⠸⠦⣸⡁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣅⣜⣻⣽⣿⡀
⠀⠀⠀⠀⢿⢓⣾⡿⢿⡇⠀⢸⣿⠃⠈⠀⠀⣿⡇⠀⠀⠀⠀⢀⠙⣿⣦⣤⢤⣤⣿⠀⠅⢬⡄⢬⡅
⠀⠀⢺⠷⠧⢸⣿⠃⢠⠇⠀⢻⣿⣿⣷⠀⣤⣿⣿⡇⠀⠀⠀⣤⣤⣾⣿⣟⣛⣉⣾⠀⠆⠸⠟⢘⣥⡀
⠀⠀⠘⠂⠒⠘⠛⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠀⠂⠘⠿⠟⠋⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢠⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣧⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣀⣿⡟⠙⠟⠟⠙⢿⠃⠀⣖⣠⠴⠶⠒⠶⢶⡇⠀⠀⠀⢠⡀⢰
⠀⠀⡀⠀⠀⠁⢹⣯⣅⣬⣛⡃⣠⣮⣥⣤⡿⠣⠐⠀⠀⠃⠘⠇⠀⠀⠀⢸⡇⠕⠐⢚
⠀⠘⣷⡶⠶⡲⠶⣤⡿⠐⠒⠂⣴⡤⠤⠤⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⢸⠖⢶⠶⣏
⠀⢀⣏⡃⠀⠀⡀⣿⠃⠀⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⡃
⠀⠈⠋⠉⠀⠀⠀⠙⠁⠀⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣧⣾⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢉⠉⢙⣿⣧⣴⢥⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⢿⣿⣝⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡽⠧⣾⣿⣤⣼⠈⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠢⠌⠳⢛⣩⢽⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣿⣷⣶⣯⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡛⣾⡿⠈⠻⣿⣿⣿⣿⡃⣤⡀
⠀⠀⠉⣥⠀⠀⠀⠀⠀⢉⢀⣀⣀⣤⣜⢉⡁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢿⠙⣿⠁⠀⠰⠻⡟⢯⠜⠓⠳⠄
⠀⠀⡺⣿⠀⠀⠀⠀⠀⠅⣶⣯⠁⣼⣿⣏⣀⣄⠲⠿⡿⡶⠦⠀⠀⠀⣸⡷⢫⡆⠀⠀⡀⠀⠁
⠀⠈⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉

⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⣿⡑⢌⣠⢡⣝⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣫⡌⣄⡡⢊⡿
⠀⠘⣦⢻⡪⢙⣋⣙⡻⢯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⡼⢋⣋⣙⡋⢕⡗⣴⠃
⠀⠀⠘⣎⢧⣏⢲⡆⠀⠭⠟⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⠫⠩⠀⢰⡔⣹⡼⣱⠃
⠀⠀⠀⠸⡌⣎⠒⠬⢒⠤⡀⡀⠙⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⠏⠊⢀⠀⢤⣒⠥⠒⣱⢡⠇
⠀⠀⠀⠀⣿⢸⡗⠦⠔⢆⡈⠑⡓⠦⣌⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⣡⠴⢚⠈⢅⡐⠢⠴⢺⡇⡿
⠀⠀⠀⠀⢸⠨⡿⣓⣈⣀⢈⡁⠐⠤⠀⠙⠺⣿⡻⣦⠀⢀⡀⠀⣴⢟⣷⠗⠋⠀⠴⠃⢈⡁⣀⢁⡚⢿⠡⡇
⠀⠀⠀⠀⠘⣯⢇⣧⣤⣦⣀⣬⣨⣆⣠⠈⡂⠨⠻⣽⣇⣾⣷⣸⣯⠟⠁⢖⠁⣄⣰⣁⣥⣀⣤⣤⣼⡼⡽⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠄⠀⠉⠛⠲⢤⡈⣿⣿⣿⣿⣁⡤⠖⠋⠉⠀⠠⠀⠀⢀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡻⢣⠟⡟⣞⠗⠶⣾⣟⣽⣿⣿⣏⣻⣷⠶⠻⣳⢿⠻⡝⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⢸⠀⡇⣜⠤⠈⠹⢿⡿⢹⡏⣿⡿⠏⠁⠄⣣⢸⠀⡇⠀⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠠⠃⠨⡇⠸⡀⢇⡐⠀⣀⠇⣿⡇⠸⢀⠀⢂⡼⢀⠇⢸⠅⠘⠄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠹⣄⠙⢦⣈⢦⡞⠀⢹⡇⠀⢳⡔⣁⠴⠃⡰⠏⠀⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡌⢀⣀⡉⠓⠤⣤⠏⠀⠀⠘⠃⠀⠀⠹⣤⠤⠚⢉⣀⡀⢡⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⢦⢊⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡑⡴⠒⠾

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

⣿⣿⠿⠿⡿⠛⠿⢿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⢡
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣛⡹⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠑⠀⠀⣠⣿⣼⣇
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⢠⠿⠿⠁⠀⠀⡀⠀⠀⠀⢀⡡⠤⠀⠀⠀⠀⠐⣤⠇⠸⢿⠀⠂⠔⣿⣟⡠⠞⣷
⠀⠀⠀⠀⠀⠀⢸⡰⡆⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⣳⡜⠀⠀⢘⡁⢠⡦⠀⡀⠀⠸⡆⡾⠀⠣⠈⠠⣼⣿⠟⠁⠀⣠⡇
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⡀⠀⠀⠚⡉⠀⠀⠤⡄⠀⡶⢰⡖⣠⡜⠃⠀⠁⠘⢇⣠⡴⠇⠽⢤⣀⠀⡇⠿⢃⣤⠶⠋⠁⣿⠀⢸⡀
⠀⠀⠠⠁⣿⣿⠟⢉⡁⢈⣯⡠⠰⡿⠇⠀⢀⣶⡇⢠⣧⣼⡅⠘⠀⣤⣼⡟⣴⣿⣁⣀⣀⣀⣤⡬⠷⠁⢴⠛⣵⠀⣀⠴⠀⢀⣎⢸⡄
⠀⠀⣇⢰⣏⡩⣶⢁⠀⡂⠀⡱⣤⠁⠸⠿⠤⠙⠁⡞⠁⠈⣧⠀⠀⠏⠙⠃⣾⣅⡀⣀⡀⣀⡄⡠⣾⣷⠈⢆⣿⠊⢉⠄⠀⢘⡁⢀⣙
⠀⠀⠸⡢⣿⣧⡜⢂⣉⠔⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠀⠀⢻⣯⣽⣯⣼⣧⠯⠻⢿⠇⠀⠀⠡⣔⠉⠀⠀⣫⡀⢀⣈⣇
⠀⠀⠀⠘⠻⢿⡿⠧⠁⠈⠔⠁⠀⠀⢀⣼⣤⣀⣀⠀⠀⠀⠀⡟⢃⠀⠀⢀⠀⠙⠶⣶⠶⠖⢒⡾⠋⠀⠀⠀⠀⠀⠀⣠⣾⣯⣥⣤⣤⣭⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣏⠉⢄⠀⠀⢰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠂⠘⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠌⡌⠐⠀⠆⠱⠈⠆⡆⠀⢘⠀⠠⠋⠰⠈⠀⠘⢠⠁⠚⠛⢠⢰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢽⡞⠛⢻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⠛⢑⡮⢭⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠏⣻⡍⠿⡽⠓⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⠚⢫⡾⢩⣟⠹⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢶⠯⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡽⡶⢺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡷⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠙⠶⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣗⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⡄⢰⡦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡒⣥⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡷⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⢿⣼⣷⡿⠂⠀⠀⠀⠠⠤⠤⣄⣀⡤⢾⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠋⣡⠃⠀⢀⠠⠀⠀⠀⢀⡜⣿⣿⠣⡀⠀⠀⠀⠄⡀⠀⠈⢌⠙⢭⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠂⠀⠀⠈⠁⡄⠀⢀⡠⠴⠁⠀⢻⡟⠀⠈⠢⢄⡀⠀⠀⡀⠉⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣥⠀⠀⠀⠀⠀⠐⠀⠋⠐⠀⠀⠀⠈⠃⠐⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⣤⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣇⣠⠀⠀⡀⠀⠠⠁⠀⠀⠀⠌⠀⢀⡆⠀⠡⠀⠀⠀⠈⢂⠀⠀⠀⠀⢄⣸⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣇⣠⠂⢀⡔⠀⣠⣀⣴⡟⠀⠀⠘⠃⠀⠀⠹⣦⣀⣄⠀⠢⡀⠑⣤⣈⣏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣾⣶⣞⣶⣪⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣕⣶⣟⣶⣿⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⣹⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣯⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠘⠛⠛⠛⣧⠀⢰⡆
⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢠⠄⣀⠀⡀⠀⡄⢠⠀⠲⠈⠁⢀⣿⡇⠀⢠⣤⣄⠈
⠀⠀⠈⣡⡤⢠⠄⠀⣴⡇⠀⠀⠀⠀⠀⢠⡄⠀⡤⡀⢄⠀⠁⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠹⠿⠟⠀⠀⢀⣄
⠀⠀⠀⠀⠰⠈⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠰⡿⣄⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠉⠁⠈⠉⠀⠁⠡⠶⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠐⡅⠀⢠⠃⠀⠀⠃⠈⢀⣴⣷⡀⠛⠛⢁⣀⣀⡀⠀⢀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠑⢸⠘⠀⠀⠐⠰⠾⣿⡿⠆⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⢛⡉⣉⢳⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣀⠀⠀⢠⣈⣠⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠖⢳⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠙⠀⠀⠘⠖⠃⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⢀⣠⣶⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡒⠀⠀⠸⠀⠀⠀⠚⠁⠀⠛
⠀⠀⠀⠛⠛⠿⠇⠀⠛⠋⣤⡶⠀⡀⠀⠀⠈⠥⠀⠘⠂⠀⠀⢄⡐⠀⠀⠀⠸⡀⠀⠀⠀⡀⠀⠀⠛⠀⢀⢀⣀
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠻⣿⣿⣿⣄⠀⠀⣶⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠸⠇⡌
⠀⠀⠀⠻⠿⢿⣿⡷⠾⠛⠀⠀⢨⣯⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⡎⠀⠀⠀⣌⠀⠤⠀⠀⢠⡄⣬⠀⠀⢠⡆⠅
⠀⠀⠀⠈⠁⠈⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠿⠿⣿⠿⠗⠀⠀⠀⠀⠉⠀⠀⢀⣴⣄⠀⠹⠇⢀⡀⠀⢰⣿⣿⣷
⣿⡀⠀⠀⣿⣿⣿⠄⠀⠆⠀⣴⡁⠀⠀⠀⣾⣿⣷⠄⠦⠀⣾⣿⣿⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠉
⣿⣷⡀⢴⣿⣿⣿⣧⠀⠀⣼⣿⣷⡀⠀⣠⣿⣿⣿⡄⠀⠰⣿⣿⣿⡷⠀⢀⣄⣀⠺⠿⢿⣿⠿⠟⠂
⠻⠋⠁⣼⡿⣿⣿⣷⠀⢀⣼⣿⣷⡀⠀⣹⣿⣿⣿⡏⠀⠼⠿⣿⠿⠿⠄⣹⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢈
⠀⠠⠄⠀⠀⠙⢠⡄⠀⢉⣿⣿⣿⡉⠀⠛⠛⣿⠛⠛⠂⣄⢠⠘⠀⠀⠰⣿⣿⣿⠧⠀⠉⣀⠀⠐⢻⣤⡞
⣤⣤⣤⠄⠀⠀⣾⣿⡀⠚⠛⣿⠛⠛⠂⠀⠀⠉⠀⣸⡄⣏⢹⠀⣼⡆⠼⠿⣿⠟⠷⢀⣾⣿⣷⡀⠿⠛⣿
⠿⢿⢿⠀⠀⣼⣿⣿⣧⠀⠀⠉⠀⢦⡼⣆⠀⠃⢠⣿⣧⠈⠉⣸⣿⣿⡀⠀⡉⠀⠀⣸⣿⣿⣿⡇⠀⠀⣿
⠀⠸⢸⠀⣰⣿⣿⣿⣿⣇⠀⠋⠀⣾⡿⠉⣀⠀⠛⢿⠿⠓⢰⣿⣿⣿⣷⠀⠉⠀⠰⢿⡿⣷⣿⡿⠆⠀⠏
⠀⠀⣰⡀⠛⠛⢻⡿⠛⠋⠀⠀⠀⠙⠶⠿⢫⣾⣿⣄⠀⢀⣿⣿⣿⣿⣿⣇⢰⡆⢰⣿⣿⣿⣿⣿⡆
⠀⣰⣿⣷⡀⠀⡀⡀⠀⠀⣴⣶⣶⡀⠀⠀⢿⣿⣿⣿⠆⠀⠀⠉⠻⠉⠁⠀⣾⣷⡀⠀⠀⠟⠀⠀⠀⠀⠈
⠀⣹⣿⣿⡉⢰⡍⣵⠀⢈⣿⣿⣿⡅⠀⣰⣿⣿⣿⣿⢧⠠⢶⣀⡴⠃⠀⠾⢿⡿⠷⠀⢀⡄⠀⣼⣶⣶⡀
⠴⣿⣿⣿⡿⠆⠉⠁⠀⢾⣿⣿⣿⡿⠄⣹⣿⣽⣿⣽⣯⠀⣾⢿⣷⣀⣁⠀⢀⡀⠀⢠⠀⠀⢠⣿⣿⣿⡄
⣰⣿⣿⣿⣷⣄⠀⠂⢀⣾⣿⣿⣿⣷⡄⠛⠛⢻⡟⠛⠛⠃⡄⠀⣿⣿⣿⣿⣿⠀⢠⣿⣧⡀⢻⣿⣿⣿⡟
⠀⠀⢻⠁⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⣄⠀⢄⠈⠁⢀⠀⢀⣿⡀⡟⡇⠀⢸⢸⠀⣠⣿⣿⡀⠟⠛⣿⠛⠛
⠀⣧⠀⠀⠂⣰⣶⣶⡀⠀⠃⠀⠀⠀⣸⣶⣏⠁⠀⣀⢀⣾⣿⣧⠀⠁⠀⠈⠈⠘⣻⣿⣿⡛⠀⠀⣉⠀⠤
⣼⣿⣆⠀⠀⣽⣿⣿⡏⠀⣶⣶⣶⣶⣿⠋⠙⠁⢠⣿⣎⠙⠟⠉⠁⢠⣾⣦⡀⠘⠛⢻⠛⠛⠂⣴⣿⣷⡀
⠻⡿⠟⠂⢾⣿⣿⣿⡿⠄⡟⡟⠛⢻⣿⠀⠀⠐⢻⣿⣟⠂⠀⠀⢰⣯⣿⣿⣷⡀⠀⡈⠀⠀⢠⣿⣿⣿⡅
⢠⡄⣀⠀⣼⣿⣿⣿⣿⣄⠧⠃⣤⠘⠟⠀⢀⣠⣿⣿⣿⣦⡀⠀⣴⢿⣷⢿⣿⣄⢰⡟⣳⠀⣹⣿⣿⣿⣏
⢾⣽⡅⠈⠁⠀⢹⠁⠀⠀⠀⣸⣿⡆⠀⠤⠀⣰⣿⣿⣿⣆⠀⠸⣿⡿⣿⣿⢿⡿⠀⠓⠃⡄⠉⠉⢿⠉⠉
⣤⣙⡟⠀⠐⠂⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠘⠋⠉⣿⠉⠉⠃⣰⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⣦⣤⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⣤⣴
⠀⠀⠸⣿⣶⣩⡟⠋⠻⢾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⠽⠛⠚⣯⣹⣽⡏
⠀⠀⠀⢫⡽⣤⢟⠋⢀⣙⡿⠄⣹⣫⣵⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣿⡁⢾⣏⣉⣉⢻⢧⡼⣿⠃
⠀⠀⠀⠈⢯⣏⣹⣟⠁⠉⡻⢶⣉⣁⣞⣷⣭⣳⣤⡀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⣠⣶⣫⣴⣿⣟⣉⣵⢻⡋⠉⢹⡿⢉⣿⠏
⠀⠀⠀⠀⠈⢻⣿⣽⡟⠻⣽⡏⠁⠈⠑⠀⠀⠈⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠈⠁⠀⢉⡿⡤⠛⣟⣶⣼⠋
⠀⠀⠀⠀⠀⠀⠹⣯⣧⢾⣽⣦⣦⡀⠀⠴⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⡄⠀⣠⣛⣿⣷⢴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣟⣽⡏⢿⡏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣧⠽⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⡾⣧⣄⠀⠤⠤⠴⠖⠛⠓⠀⠀⠀⠀⠈⠳⡄⢠⣤⠀⡴⠋⠀⠀⡀⠀⠐⠛⠒⠶⠤⠄⠄⢀⣴⠟⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⢤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⠀⢀⣴⣶⣶⣶⣶⣦⣤⣀⣤⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠅⠀⠉⠉⠉⠉⠓⠈⠀⠀⠂⠀⢀⠿⣿⣿⡿⣇⠁⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠈⢭⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡤⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⠔⠉⠀⢹⣿⠑⡈⠓⢤⡀⠀⠀⠀⠀⠆⠀⠀⠠⠤⣼⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣾⠁⠀⠀⠀⣠⠄⠀⣀⡤⠖⠋⠀⠀⡔⠀⢿⣿⠀⠐⡀⠀⠈⠳⣦⣄⣀⡀⣄⡀⠀⠀⠈⢻⣾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⠿⣶⠦⠀⠈⣉⠔⠉⠁⠀⠀⠀⠀⠈⢁⡄⢸⣿⠘⣆⠉⠀⠀⠀⢀⡀⠉⠀⢍⡉⠓⠶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣄⣠⡞⠁⠀⠀⠀⠀⠀⢠⠂⢰⡞⠀⠘⠟⠀⠘⣧⠀⢢⠀⠀⠠⠀⠀⠀⠹⣦⣀⣾⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⣛⣿⣦⣀⣀⣴⠃⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⡀⠀⢳⣄⣀⣠⣿⣋⡻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣿⣭⣿⣻⣶⢾⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣿⢶⣟⣹⣯⣿⣽⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣿⡇⠀⠀⠀⠀⠀⡇⠰⠖⠘⡸⢙⡤⢤⢐
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠋⠀⠀⠀⠀⠘⠐⠻⠈⠒⠀⠱⢎⣀⢒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⠀⠀⠀⠀⣰⣀⡀⢠⡴⡴⢤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣾⢿⣽⠀⠀⠀⠀⠩⠸⠿⣿⡖⣲⡀⠿⡗⠳⠗
⠀⠀⠀⠀⠀⠀⣴⣯⣿⠿⣷⠆⠀⠀⠀⢴⣶⢶⡂⣟⣸⣶⣶⡶⠲⠶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠐⣿⣯⣿⢿⣿⣾⠄⠀⠀⢸⡿⣢⣴⣷⣶⣶⣶⡔⠤⠖⠀⠀⠀⠀⡼⠀⠀⠀⠔⠀⡰
⠀⠀⠀⠀⠀⣼⣹⣹⣿⣿⢻⣿⣦⠀⠀⠐⣪⣼⣿⣿⠟⢻⣿⡇⠄⡀⠀⠤⠀⠈⠑⠀⢀⣴⠃⢀
⠀⠀⠀⠀⢠⣟⣻⣿⣿⢿⣿⢿⡾⢀⠀⠈⠁⠐⣿⠁⢀⡈⢻⣇⠈⡇⢀⡰⢄⣠⣦⣾⢟⠋⢀⠄
⠀⠀⠀⠀⡷⣿⣿⣿⡏⠈⣹⣗⣿⠟⠢⣤⡀⠈⡿⡬⠿⠧⣿⡇⠀⠃⠀⠀⠈⠀⠁⢸⠁⣆⠊⣀⡀
⠀⠀⠀⠀⢛⠻⠁⢘⠟⢱⡏⠛⠀⡟⢰⡄⢀⠠⡴⣦⣾⡧⠾⠭⣦⠀⠀⠀⠀⠀⠀⠈⡇⡃⠀⠈⣤⠰⡃
⠀⠀⠀⠀⢷⡤⠀⣰⠀⠈⠀⢀⣿⡟⣾⠁⣸⡇⠠⠾⠿⠷⠶⠶⠶⠶⠺⠁⠀⠂⡤⠈⠁⠀⣿⠀⢻⠞⣧
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠉⠉

⠀⢠⣤⣤⣤⣀⡀
⠀⣮⣾⣾⣿⣴⣦⡉⠛⢶⡤⠀⡀
⠀⠻⣷⣿⣾⣿⣿⣟⣷⣶⣾⣿⣷⣦⣄⢀
⠀⠀⢸⣯⣇⣻⣿⣟⢛⠛⣯⣽⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢹⣿⡻⡟⢿⣍⣉⣹⡏⠀⠀⣠⣿⣿⣟⣷⡀⢄⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠈⢻⣿⠟⢻⣷⠤⠬⢿⡀⠰⣿⣿⠛⠉⠛⣝⢦⡁
⠀⠀⠀⠀⠘⢿⣿⢿⣿⣦⠴⠐⠚⠳⢬⡁⠀⣤⣿⣿⣷⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⡿⠶⠾⢿⡷⠒⠒⠒⠒⢿⣷⣮⣙⠻⡟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠐⢦⢿⡿⠿⢻⠦⠀⠀⠠⠶⣿⣿⣿⡟⠲⢄⡈⢻⣿⡄⠀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢙⣿⠻⢻⣴⠂⠀⠒⠒⠚⠻⠿⠷⢤⣀⣹⣿⣿⣷⣤⣞⣻⣿⡿⠃⠀⠀⠀⣀⣀⣤⣴⣦⣦⣤⣆⣴⣶⣒⡲⠶⠤⣤⣤⣀
⠀⠀⠀⠀⠀⣠⣼⠿⣿⠋⣉⣩⡷⠒⠚⠉⠉⠉⠙⠃⠐⠢⢭⣝⣻⣿⣿⣿⣿⣿⣧⡶⠾⠟⠛⠛⠛⠛⢛⣻⣶⡾⠒⢶⣷⣭⡍⣙⡛⠶⢦⣌⣹⣶⣤⣀
⠀⠀⠀⠀⠀⣼⣹⣷⢿⡋⠁⣞⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢙⣿⣿⣛⣿⣟⠿⢿⣿⡟⠿⠻⠶⠀⢤⣰⣿⠿⠃⢀⡽⣷⠇⠀⠈⢿⡗⠲⢶⣿⣿⣞⣛⢷⡆⡀
⠀⠀⠀⠀⢀⣼⣿⣤⣿⡟⢁⡼⠶⣤⣤⣤⣤⣶⠛⠁⠀⢀⡴⢪⣟⠦⣽⣿⡿⠋⠐⠈⡙⠢⣄⣀⣰⣾⣿⣿⣿⣲⢬⣿⣇⣀⣠⡤⡞⠑⢦⣴⣿⣽⣿⡟⣯⣅⣿
⠀⠀⠀⠀⠀⣿⣿⣱⣼⣿⡏⢀⣴⠁⠉⣡⠝⠁⠀⢀⣴⠟⣰⣿⣮⣿⡟⡀⠀⢰⡀⠀⠈⠲⣄⠙⠿⣿⡽⢏⡀⠁⠀⠉⠀⡈⠹⣦⣉⣷⣿⡛⢣⣭⢻⣧⡾⠟⠛
⠀⠀⠀⠀⠰⣿⣛⣫⣼⣿⣿⣿⣿⣤⣤⣧⣄⠀⣠⣾⠋⣰⣿⣿⣿⠏⣰⠇⠀⢰⣧⠀⠀⠀⠘⣿⠢⣬⣿⣶⣽⣆⣀⣶⣴⣼⣿⡟⣻⣞⣽⡷⡮⠟⠉⠉
⠀⠀⠀⠀⠀⣼⣿⡟⢫⣙⣿⡿⣻⣿⣿⣛⣿⡖⣷⠃⢰⣿⣿⠟⢁⡼⠋⠀⠀⢸⠟⣧⡀⠀⢀⡿⣦⣘⣷⣿⡿⣿⣿⣯⣽⣷⣾⣿⠟⠛⠋
⠀⠀⠀⠀⣸⢋⡔⠂⠀⣟⠿⠛⢿⡟⠘⠛⡟⣭⠏⠀⠘⠋⠁⡀⣺⠶⣶⣄⠀⣾⠀⢸⠉⠛⠈⣇⣸⡿⣶⣿⠇⠀⠉⠀⠉⠁⠀⠈
⠀⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⣠⠌⢿⡿⣸⣿⣀⡏⠀⣾⡀⣰⣶⡟⠻⣦⣿⣇
⠀⠀⠸⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⣠⣴⣿⣿⣿⣷⣴⣿⣿⣿⡋⢻⣤⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢙⣿⢿⣿⢣⣿⣀⣿⣷⣾⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡿⢷⣤⣿⣿⣿⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠳⣿⣿⡿⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣇⠈⡇⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⠚⢻⣿⣿⣿⠿⠶⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⢻⡜⡄⠀⢠⠀⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠚⣡⡾⠉⠉⡡⠄⢀⣈⢩⣶⣾⢣⡀⠀⠀⠀⠀⠀⠀⠀⣦⡆⢧⠈⢿⣜⠀⢐⡄⢀⠈⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⠹⣦⠟⣿⣿⣷⠀⠀⠀⠀⢠⣶⣼⣿⣧⠈⢇⠈⢿⡂⠀⠀⣀⣠⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠚⣡⣿⣿⣿⣿⠀⠀⡀⠀⠈⠿⢿⣿⣿⣿⣎⠢⣀⠛⠲⣶⣝⣿⣦⣿⠇
⠀⠀⠀⠀⢀⣎⡀⠠⠃⠀⠀⠀⠀⠠⠐⢁⣴⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⣀⣿⣯⣿⣿⣷⣬⠑⢄⡙⠿⣿⣿⡿
⠀⠀⠀⠀⢠⠟⡄⠁⠀⠀⠀⠐⢀⣴⣀⣨⣿⡿⠛⠃⠀⠀⠀⠾⡿⣿⣟⣻⡿⠛⠙⣿⡿⢹⣿⣿⣦⣬⣑⡢⣝⡗
⠀⠀⠀⠀⠀⣆⠀⢀⣀⢤⣔⠠⢚⣽⣿⡿⠋⠀⣠⠎⠀⠀⠁⣰⠟⠉⠉⠙⢿⣤⣴⡿⢁⣾⡿⠿⠿⠛⠛⠛⠺⠃
⠀⠀⠀⠀⠀⠘⠢⢽⣞⠯⣖⣤⣿⣿⣿⣷⢴⡶⠋⣀⣀⣤⣾⠏⠀⠀⣀⣤⡾⠃⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⣸⡀⠊⠀⠉⢙⣥⣄⡠⠴⠋⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣍⣙⣒⣒⢒⣁⣀⣠⣤⠖⠋⠁⢓⣿⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣻⡟⠁⠀⠉⠀⣰⣯⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣷⣍⣀⣠⠀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⠄⠃⠔
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠭⢹⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⢰⠄⠀⢀⠀⠀⠠⢠⠀⠀⠀⢀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠀⠠⠉⠀⡀⠀⡄⠀⡀⠘⠀⠀⠘⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⡴⢶⡎⣀⠀⠠⠄⠀⠔⠁⠑⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⡚⠣⡀⠀⠀⠀⠀⠢⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠲⠀⣨⠡⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⣳⠡⠠⠤⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢀⠀⠀⣠⠐⠫⠁⠃⡄⠀⢠⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠠⢔⡀⠄⠀⠀⠤⠀⠌⢢⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠐⢨⢇⠜⡕⠂⠀⠀⣀⠀⠀⠈⠑⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⡱⠒⠀⢀

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⣀⣤⠶⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠤⠤⢀⢀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠄⡀⠂⠀⠄⠀⢀⠀⢘⡀⠀⠀⠀⡠⠀⠀⠨⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡀⡋⠁⠀⠈⠂⠀⠀⢠⠃⠀⠀⠉⠀⢤⠈⠀⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢄⠀⠀⠀⢐⢯⠀⠀⠀⠀⠖⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣾⣧⣜⢦⠀⠀⣞⠀⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⠀⠀⠀⠈⠙⢦⣠⠻⣧⣾⠇⠀⠀⠀⠀⡀⠀⠠⠂⢀⠀⠀⠀⠺
⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠇⠀⠀⠀⢰⣧⣼⡦⢿⣦⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠀⠀⠀⠀⠁
⠀⠹⢄⠀⠀⠀⡄⠀⢳⠀⠀⠀⠀⣠⡆⠀⣨⣍⣭⠖⣩⡿⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠶⠁⠀⠀⠐⠁
⠀⠀⠀⠛⠢⡈⢧⠀⠘⠀⠀⠀⠀⠉⢃⠀⠙⠛⢿⣶⣿⡇⠀⠀⠀⢀⠔⣙⣀⡚⣀⢠⠀⠀⢀⣠⡦⣉⣠⠊
⠠⡄⠀⢀⠻⣤⠿⠗⠀⠘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⢸⡷⠀⣠⡴⠟⠛⠛⠙⡁⠉⣠⣦⣴⣿⢿⠔⣠⠃
⠀⠀⠀⠀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄⣦⡀⠸⢿⠟⠢⢀⠀⠐⠗⠀⠻⠛⠋⣹⣿⡿⠀⢀⡿⠤⠄
⠀⠀⠀⠄⠈⠂⢒⣇⠀⠀⠀⠠⠀⣼⣷⠄⠘⠿⠟⢹⣶⣿⠂⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⡟⢐⠀⠈⠁
⠀⠀⠀⠀⠐⠌⣻⣿⣦⡀⣠⢤⡾⠋⠀⠀⠀⣶⣤⣷⡟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠹⣍⡻⠦⠈⠁⠐⠒⠀⠀⠈⠉⠉⣶⣤⣿⠀⠀⠀⣀⠀⠀⠠⠐⢀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⣶⡿⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠛⢠⣤⣀⠀⠀⠙⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠁⠀⢸⡟⡤⠄⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠣⣀⣀⡈⢒⠀⠐⠀⠀⠀⡀⠀⠊
⠠⠒⠂⠀⣰⠏⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⡾⠀⢀⣄⣶⣤⣀⣦⢀⡾⠁⡌⠸⠛⠉⠠⠘⠋⠀⠀⠄⠘
⠀⠀⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢈⣻⡿⠍⢻⣿⡊⠀⠀⠀⠊⠁⠠⢄⠀⡠⠒⠀⠉⠛
⠀⠀⠀⢇⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡁⣨⡴⠚⠍⠉⢐⠦⣄⠈⠑⢦⡀⠀⠤⠒⠉⠉⠑⠒
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠍⠀⢾⣦⡷⠻⣾⡿⠀⠀⠀⠁⠀⠢⣤⣞⡁
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠷⠲⢤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢬⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⢡⡀⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡩⠥⠎⠄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⠤⣌⠍⠲⣄⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⣝⣁⡼⢸⠀⢹⠀⠄⣢⢹⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠷⢄⠀⠐⠁⠀⠀⠆⢉⠁⡘⡇⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⣖⡒⢦⠢⠁⠀⠀⠀⠀⠐⡀⠒⠁⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠈⠫⠥⠞⡠⠁⠀⠀⠀⢄⠀⠀⠀⢚⠃⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠦⣄⠀⠀⢸⡧⣿⢀⠀⢄⢈⠀⠀⠀⠀⠀⠀⣑⣤⣷⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣛⣤⣼⣧⡀⠈⣷⢻⠘⡡⠜⠘⠀⠀⣀⠬⣴⣿⠟⠛⠛⠁⠀⠀⢀⣴⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡘⢿⠻⡻⣆⣷⡀⠘⢿⣧⣀⣠⠴⠒⠉⠀⠾⠛⠁⠀⠀⠀⠀⠀⢠⣿⡜⣅⠔⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⣋⣉⣾⣷⣽⡟⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠟⣳⡤⠚⣫⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣻⡄⢿⣟⠿⣧⠈⣇⣘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⡟⣩⢷⡂⢁⠷⣻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣽⠓⢢⣿⣗⠘⢧⣹⣿⣷⢹⠀⠹⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣓⢿⣿⡡⠞⣯⡠⠞⣹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⣿⡿⠯⠁⠀⠻⣿⠟⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⢴⠀⠀⠀⠸⠻⠳⠤⣧⣛⡤⠂⢉⣧⠔⠁⠾⡇
⠀⠀⠀⣀⣤⣤⣶⣤⣬⣝⣿⣇⠀⠀⠀⠈⠙⠆⢻⡇⢠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡷⠋⡷⣳⣯⡴⠚⠉⣹⡖⠁⠘⠓⢲⡀
⠀⢀⣞⣻⡟⢽⣿⡄⢟⣆⣹⣟⣿⢾⣵⢶⡄⢸⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡠⢠⠿⣿⡾⠛⠉⣉⠴⣮⡤⠀⠉⢙⣦
⠀⢸⡭⣝⠰⠶⠦⠼⣏⡁⠐⠬⠝⣺⣿⣓⣽⣶⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠇⢃⠂⠀⢠⣿⢾⠋⢁⡈⠩⢷⡶⠒⠚⠛⣦
⠀⠘⢗⣻⣇⡚⢃⣬⣉⡝⣻⣿⣯⣽⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣄⣠⠀⠀⠹⢾⣝⣇⣀⠀⢘⣷⣂⠀⠈⠙⢂⣤⣄⣀⡀
⠀⠀⠈⠓⠾⠧⠾⠷⠚⠋⠉⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⠶⠦⠤⣟⣼⣧⡤⠤⣼⣇⡀⢾⣙⣯⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⠉⠓⠶⣾⣁⢾⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⠿⠯⢠⣾⣧⡀⠐⠀⠀⣾⠁⢨⡷⠀⣴⢒⣦⠀⢉⡀⢰⢿⠂⣰⡿⣛⠻⣇⠀⡞⠀⠈⢳⠋⠀⠙⡆
⠀⠀⠀⣰⣿⡟⣿⣷⡀⠀⠀⠹⢤⣀⡀⠀⢻⣌⣉⢰⠫⣽⠂⠀⠀⠹⣷⣭⣾⡏⠀⠳⡀⠀⢺⠀⠀⡸⠃
⠀⠀⣴⣿⣷⡅⣥⣿⣿⣄⠀⣶⠆⢨⠟⣉⠉⠉⡉⠙⢳⡀⠀⠃⠀⠐⢶⠭⠶⠆⠀⠀⠙⢦⣸⣠⠞⠁
⠀⠈⢉⣽⡿⠇⡿⣿⣏⠉⠀⡀⠀⠘⠦⠿⠀⠀⣉⣀⣰⣧⣄⣀⣀⡘⠻⠖⠿⠃⢀⣤⡀⠀⠙⣡⡶⣤⡀
⠀⠠⠾⢿⣿⡆⣾⣿⡿⠧⠀⡁⢀⠀⠀⣀⣶⣀⠙⣿⣿⣿⣿⣿⡿⠟⠀⠄⠀⠀⠈⠛⠃⠀⠸⣕⡿⣫⡇
⠀⠀⣠⣿⣯⡃⢋⣿⣷⡀⢸⣎⣹⡁⠐⣺⣿⣗⠂⢸⣿⣿⡟⠁⠀⢠⡄⢶⢦⣤⠀⠸⣿⠟⠀⢉⣉⠉
⠀⠐⢛⠛⠛⣷⡟⠛⠛⠛⠈⠑⣋⡁⠀⠀⠛⠀⠀⢸⣿⣿⣧⠀⢸⡗⢠⣶⣦⠐⣷⠀⠀⠀⣰⢿⣿⡷
⠀⠀⣉⠠⡄⢉⠁⠀⣠⡀⠠⣾⣿⣿⣆⠀⠀⠙⠀⢸⡿⡟⡿⣧⠘⢫⡄⣩⣡⣬⠋⠀⢼⣿⣇⣠⡿⠃
⠀⢠⣭⡷⢳⣯⣄⠘⠿⠏⠀⠘⢿⣄⣸⣿⣯⠄⢀⣿⡁⠀⠀⣽⣧⠀⠀⠉⠁⠀⠀⠄⠀⠀⠉⣉⠀⢠
⠀⠀⠴⢋⡏⠳⠀⠀⢀⠀⠀⢀⣀⣉⣉⣉⣤⣶⣿⡿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣦
⠀⠀⠀⢠⣤⡄⠘⠁⠘⢷⣾⣿⣿⣿⠿⠻⣻⣿⡃⠀⢐⣻⣿⣿⡿⠛⠉⢀⣿⠏⣿⡆⢠⣾⣯⣩⣿⣷⡀
⠀⢰⣿⡟⣙⢻⣷⠄⠀⢸⣿⣿⣿⣧⣀⢀⢸⣿⣷⣦⣷⣿⡿⠋⠀⠘⠃⢸⡿⠀⣿⠇⢀⣼⣿⢙⣿⣧⡀
⠀⠀⢽⣧⣭⣾⡏⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣁⡤⢤⣀⠀⣰⡞⠁⣴⠟⠀⠀⣼⣟⠛⣿⣇
⠀⢰⣶⣭⢀⣭⣶⡆⠀⢰⣿⣿⣿⣿⠋⠉⠀⣠⣀⠀⡼⢃⢮⣷⡂⢧⠈⡀⠀⢡⡀⠀⠈⠉⠉⡿⠉⠉⠁
⠀⠈⠻⠿⠿⠿⠛⠀⢠⣿⢣⣿⡟⠁⠖⠀⠀⠛⠋⠀⠸⣆⡛⢟⣂⠏⠈⠁⣰⣿⣿⡄⢀⡄⠀⠠⡞⢳⠄
⠀⠀⠠⠀⠀⠒⣠⣴⡿⠃⣼⡟⠀⣰⠚⣶⣴⣾⣶⡀⠀⠀⣍⢉⠀⠀⠀⠐⣿⣧⣾⡟⠂⠀⢀⡀⢉⠉
⠀⢠⡶⣲⢶⣰⡿⠋⣠⣾⠟⢁⠀⠹⣾⣿⣿⣿⡿⠀⠐⢶⡿⢻⡷⠂⠀⠰⣿⣧⣾⡿⠂⠐⠶⢟⡻⠶⠂
⠀⠸⣞⣿⣳⠇⠀⠀⡿⠋⠐⣏⣱⠀⠘⢿⡿⠋⠀⠆⠐⠛⡿⢿⠛⠃⠀⠰⠛⢧⡾⠿⠂⠐⢋⡶⢾⠙
⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣘⠃
⠈⠀⠀⠘⠄⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠔
⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⡆⠀⣂⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠗⠀⠀⠈⠓
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⢃⠀⠁⠀⠻⣤⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠰⣄⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠉⠁⠀⠀⠀⠀⠉⠳⢄⣀⡀⠀⠀⠀⠒⠂⠀⠀⠈⠽⠠⠄
⢀⡔⠢⠄⢤⣀⠀⠀⠀⠙⠁⣀⡤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂
⠋⠀⠀⠀⢀⣿⠆⠀⡴⠚⠉⠀⠀⢠⠏⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠄⠀⠀⠈
⢷⣤⣤⣤⠾⠋⢀⡎⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⠀⠀⡐⠀⠄
⠀⠀⠀⢀⣤⠖⠛⠁⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⢠⠶⠛⠛⠒⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⢰⠋⠁⠀⠀⠀⠀⠐⠀⡸⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠸⣄⡠⠄⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⢼⠁⠀⠀⠀⠀⠄⣀⡀⠔⠁⠀⠀⠀⠂⠀⠀⠌⠁⠀⠈⠀⡀⠈⠂
⠤⠄⠀⠀⠀⢈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠀⠀⠀⠀⠀⠁⠀⢂⠄⠀⣢⡷⠀⠐⠏⠀⢀⣠⢄⠔⠀⠀⠀⠀⠀⠠⠔⠂⠀⠈⠀⠀⠀⠠⠄⠀⠀⢰⡇⠈⠙⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠖⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⣀⠔⠋⠈⢷⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠙⢦⡀⢀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡁
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠳⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⢁⡀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠂⠠⠍⠁⠀⠚⠛⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊
⠀⠈⣆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠻⢀⠘⡀⠃⠀⠶⠧⠊⠃⢡⡴⠀⠶
⠀⠡⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⠁⠀⠠⣤⢠⣆⣃⠦⢯⢡⠑⣄⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠉⠓⠁⠈⠀⠀⠘⠑⠀⡄⠉⠉⢠⠀⠊⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠩⠁⠀⠒⠐⠊
⠀⠀⢠⡀⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡀⠡⠀⠀⠀⠂⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣦⢤⡶⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⡨⠂⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡤⠔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄
⠀⠀⠀⣸⠋⣀⣉⣐⡒⠨⢕⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⣂⣈⣀⡈⢳
⠀⠀⠀⢸⡍⡡⠤⠤⠭⣍⣒⡟⠚⠓⢄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⣠⠔⠛⠺⣖⣫⡭⠥⠤⢄⡉⣿
⠀⠀⠀⠀⢷⡀⠂⠒⠒⢒⣲⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⢗⣒⠒⠒⠂⠀⣼⠃
⠀⠀⠀⠀⠈⢷⡈⣉⣉⠀⠈⠩⣍⣳⣦⣀⡀⠑⣄⠀⡀⢀⠞⠁⣀⣤⣖⣉⡭⠉⠀⢈⣉⡁⣰⠃
⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠄⠠⠤⠤⠤⠤⣭⠷⢮⡶⢺⣧⠶⢯⡥⠤⠤⠤⠀⠒⢤⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⠛⠉⢙⣛⣛⣉⡩⢽⣷⣼⡿⢭⣉⢛⣛⣋⠉⠛⠛⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⠒⣉⠡⢤⠞⠉⠀⣠⠃⡿⢸⡏⢦⠀⠉⠑⢤⠤⢉⡑⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠁⡀⠔⣧⣀⣤⠞⠙⢰⠃⠆⢧⢠⠙⣦⣀⣨⡇⠄⡈⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠋⡠⠊⢀⠃⠘⠀⢠⡞⠐⠆⠸⡜⠀⠸⠀⢇⠈⠢⡈⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠁⢀⠂⠀⠀⠀⣸⠁⠀⠀⠀⢳⡀⢀⠀⠈⢆⠀⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠾⣤⣤⡼⠖⠋

⠀⠀⢀⣾⣟⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣆
⠀⠀⠀⢻⣯⣿⣿⣿⠿⠿⢶⣼⣿⣿⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢀⣠⣶⣿⣿⣿⡶⠾⠯⣿⣿⣯⣿⠋
⠀⠀⠀⠈⣿⣷⣿⣿⣶⠛⣿⣿⡇⠀⢈⣽⣿⣶⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣶⣿⡋⠁⠈⣻⣿⡿⠿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠙⣿⣼⣿⣿⡟⠋⣙⣻⣦⣿⣿⠏⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢿⣿⣧⣴⡛⠙⠛⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⠉⣉⣡⡽⠿⣆⣀⣠⣾⣿⣿⣦⡐⠀⠀⠀⢀⣴⣿⣿⣄⠀⢀⣼⣿⣉⠉⠙⢛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣯⣹⣿⣿⣿⡉⣀⡤⠶⠚⠛⢿⣿⣿⣿⣿⣷⣾⣿⣦⣿⣿⣿⣿⣿⠿⠿⠷⣤⣀⠉⣳⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⣀⠀⢀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⠀⣨⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣻⣿⣿⣿⢃⠠⠔⠚⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣍⠛⠛⠲⢤⣈⣸⣿⣿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⢿⣿⡆⠀⠤⠐⡘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⡌⠒⠠⢀⣼⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⡠⠐⢸⡇⢸⣿⣿⡿⣿⣿⢿⣿⣿⡇⠀⣿⠐⢄⢠⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣿⣿⣧⣔⠀⠛⢹⡿⣿⡇⣿⣿⡇⣿⣿⡟⢚⠣⠑⢤⣿⣿⣿⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣟⢻⣿⣿⣿⣷⣦⣼⣧⣼⣇⠸⡿⠁⣿⣧⣇⣤⣴⣿⣿⣿⣿⠿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⣟⣿⣿⣿⣿⣿⡻⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣽⣿⣯⣽⣿⣽⣷⡴⠁⠀⠀⠀⠑⣴⣿⣽⣿⣛⣻⣿⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠠⢀⠀⠀⠀⠀⡀⠀⢀⠀⠐⢠⡄⠀⠀⠀⠠⣸⣀⠤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢄⣸⣠⠄⠀⠀⠀⢀⡄⢂⠀⡀⠀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠱⠘⠀⠀⠀⠠⠄⣻⠄⠑⠆⣲⢒⡐⠂⠀⠐⠛⡝⠒⠀⠈⠒⣀⢀⠰⢀⠄⡠⠎⠀⠐⠊⡍⠓⠀⠀⠀⢂⡚⢖⠀⠎⠡⣞⠠⠄⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⢈⡁⠆⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠐⠀⠀⠈⠁⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠀⠀⠀⠘⢘⡠⢣⢜⡳⠜⠀⠁⠁⠈⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠀⠀⠄⡹⠃⡭⠀⠀⠀⢀⠐⠑⠠⠍⠂⠑⢦⡀⠀⠀⠨⢐⠟⡠⠀⠀⠛⠀⢀⠀⠀⢠⠀⠀⠀⠀⡀⠠⠄
⠀⢀⠀⢿⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠂⣼⠆
⠀⠀⠂⠠⡄⠀⠀⡀⠀⠀⠠⡇⠀⠆⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠆⢨⠅⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠤⠢⠀⢠⠀⠀⠐⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⡠⠀⠔⠤⠤⠄⠀⡄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠒⠀⣷⠀⠀⠀⠑⣄⠀⣀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⣀⠌⠀⠀⠀⣴⠀⠔⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠒⣀⠋⠰⠀⠀⠙⠛⠀⢣⠆⠀⠀⠀⡄⠀⠀⠐⡞⠂⠛⠊⠀⠀⠒⠘⣀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⡄
⠀⠀⠀⠀⢤⠘⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⠘⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣠⠁
⠀⠀⠀⠀⠀⡀⠊⢠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠤⠑⢂⠄
⠀⠀⠀⠀⠀⢀⠐⠆⢀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠘⠢⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠔⠛
⠀⠀⢠⡄⠀⠀⠀⠉⡈⠂⡑⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠐⢃⡈⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤⠄
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠄⠄⠡⠄⠤⠀⠀⠠⠀⠀⠂⠀⠀⠀⡈⢀⣀⠀⠄⢂⠀⠀⠀⠀⣀⡰⠤⡀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠃⠀⠀⠀⠀⠂⠀⠄⠀⠀⠤⠠⠤⠀⠠
⠀⠀⠀⠐⠈⢀⠂⠀⠀⠀⠀⠘⢣⣽⡀⣁⢒⢡⡤⠭⠒⢠⠊⠉⠀⠀⠀⢉⣇⣀⠟⠀⠀⠀⠘⡙⡄⠐⠭⠤⡌⠐⣀⢀⣼⣔⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠐⠋⣕⠉⠉⠀⡃⠠⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠘⡉⢢⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⢲⢺⠀⡉⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡗⢒⠢⠔⠂⠀⠀⠀⠠⡄
⠀⠀⠀⢈⣰⠀⠀⠀⠀⠂⠒⢋⠁⡈⠐⠀⠀⠀⠀⠀⠀⠀⠗⠔⠃⠠⠄⠀⡀⠀⠀⠃⠘⠀⠃⠌⠀⠀⠀⠀⠀⠀⠈⠐⢉⠀⡉⠒⠀⠂⠀⠀⠁⣦⠀⠆
⠀⠀⠀⠈⡃⡄⠀⠀⠀⠈⠄⢨⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⡁⠠⠁⠀⠀⠀⢁⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠃⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠀⠐⠀⠀⠀⠄⢰⡈⠣⢀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠓⡄⠀⠀⠀⠀⠐⠂⢲⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⠀⠀⢀⠞⠁⠃⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡯⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣙⣳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡙⠿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣋⣤⣴⣿⣷⣆⠈⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠟⢻⣿⠿⣿⣿⣿⣿⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣠⠴⠛⠃⣤⣾⣿⣿⣿⣬⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣧⠄⢀⣴⣿⣅⢀⣿⣿⣍⡻⡟⣳⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢆⢀⡷⣼⣿⣿⡿⠟⢁⡰⠎⣩⣿⣿⠏⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢿⣿⢿⣿⣿⡟⠉⣃⢲⡛⠛⠛⠻⢆⣈⣤⣤⠴⠋⣹⠇⠀⠀⢀⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢀⢉⡼⠋⠁⢠⣾⣿⣯⠝⢶⡤⡴⠾⠿⠟⢽⢳⣾⣥⣤⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⠞⠛⣿⡀⢀⡀⣀⣾⣿⣿⣿⣶⣤⣤⣤⣷⣶⣶⡘⣟⣿⢿⣿⠿⢿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣁⢀⣤⠂⠀⢀⣨⣷⣨⣿⣿⣿⣽⣿⣿⣿⡇⠀⢹⣿⡟⠿⡿⢧⣿⣶⣤⣴⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣒⠉⠙⠓⠲⠧⢬⣁⠛⠉⣫⣼⣄⡠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠛⢹⢿⣻⣽⠟⠋⢱⣾⠿⢿⣦⡽⠟⠛⠿⣿⡷⣶⡄⢠⡼⢋⢀⡀⠀⣠⣶⢶⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡂⣀⠠⣦⠰⠟⠉⠀⣀⣠⣾⣿⣄⣼⣿⣖⠶⢤⣤⡬⢿⣶⠊⠁⠙⠿⣿⣿⣶⣟⣁⣾⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣉⢩⣅⠀⠀⠘⣧⡀⣠⣾⠟⠛⠋⣠⣦⠀⠛⢿⣦⣆⡀⠀⠀⠙⠿⣷⣠⣤⣀⠈⠉⣉⠉⣭⣁⣴⣶⣾⠇
⠀⠀⠀⠀⠀⡸⢸⣿⣿⣦⡆⠀⠙⠣⣾⠟⣿⡷⢀⣷⣷⡟⠾⠁⣀⣴⣿⠧⣿⣷⡀⠀⠙⣿⣿⠂⠀⠀⡖⠉⢻⡟⣿⣿⣶⣿⣶⡏⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠐⣷⣾⡿⢣⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⢻⣿⣥⣿⠒⢿⣿⡇⠀⠀⠈⢿⡿⣿⣇⠰⢲⠞⠀⠀⠙⢿⣇⡁⠀⠀⠀⠀⠀⣠⡄⢰⣞
⠀⠀⠀⠀⢀⡿⠙⢱⡟⠀⣴⣶⣶⣶⠀⣠⣴⠿⠋⢀⡰⣷⣾⣿⣿⠿⢿⠦⢾⣿⣷⣶⠀⢀⠈⠙⠻⢿⣿⣛⢿⡷⢦⣄⣠⣈⢉⠓⢦⣤⣤⣾⢣⢿⣼⣿⡇
⠀⠀⠀⠀⢸⠃⠀⡾⢸⣿⡘⣿⣿⣿⡟⢉⠀⠀⣰⣿⣷⡸⣿⣷⣿⣤⣴⣄⣴⣿⣟⣻⣾⣿⡆⢰⣶⣾⣯⠉⠳⣄⠸⠟⠛⠛⢾⣿⣤⣦⣤⣿⣿⡜⠛⡿⠤⠴⠂
⠀⠀⠀⠀⢸⡆⢸⡇⠀⣿⣧⠹⣿⣿⣿⡘⢷⣿⠟⢛⣉⢷⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⣿⠇⣾⣿⣿⡟⢀⡼⠋⣀⣀⠀⠀⠀⣽⢻⡽⠿⣿⡍⠀⢸⠷⠿⠂
⠀⠀⠀⠀⢸⣇⠈⢷⡖⠛⡿⠃⠉⣀⣀⣰⣞⢳⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⢀⣤⣤⣄⢸⠟⠀⠿⢿⣿⣧⣾⣵⣿⠟⠻⣿⡆⠀⣷⢰⣇⣴⡟⣠⢆⡇
⠀⠀⢀⡴⠾⣷⡀⠈⢿⡾⣧⣴⣿⣿⠋⠉⣿⣿⣿⣿⡇⠀⠀⠸⡏⢿⡇⣰⠿⠋⠉⢻⡟⠶⠦⠶⣦⣿⣿⣿⣿⠀⠀⠀⢹⣿⢠⡷⠖⢛⣫⣾⣡⣾⣀⡀
⠀⠀⠈⢰⣿⣿⠧⡀⢨⢷⣿⣿⠷⠛⠀⠀⣸⣿⣿⡏⠤⠀⠀⠀⣿⡘⣹⣿⠀⠀⠀⣼⠀⠁⠀⠀⣜⢹⣿⠟⣿⠄⠰⠆⣼⣾⣯⠶⢒⣻⣿⣟⣥⣤⢀⡉⠁⣀
⠀⠀⠀⠀⠉⠃⠀⢻⣿⣼⣟⢣⣀⠐⣠⢤⣿⣿⣿⣿⠔⣄⠶⢰⣿⠇⢻⣿⠣⡜⠃⠻⡇⠶⠀⠀⠉⣻⣟⢦⡀⠶⣤⠴⠂⣠⢿⣾⡟⠋⢠⡅⠈⡿⠏⠛⠃
⠀⠀⠀⠀⠀⣼⢻⡏⠙⢯⠙⠿⢿⣯⣤⡞⠁⣉⣿⡀⠀⠀⠑⠉⠉⠀⣸⡈⣳⣶⣶⡾⠿⢆⠰⡶⠚⢿⣿⣿⣿⣶⣦⣀⠶⠋⣀⠬⠛⢁⡾⠶
⠀⠀⠀⠀⢰⡇⡀⠃⣀⢈⣷⣀⣀⠈⢩⡙⠚⠻⠿⣷⣤⣀⣀⣀⣄⣰⣿⣿⣯⢿⣿⣇⢀⡜⠉⢱⣄⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣸⣧⣄⠀⠈⡄
⠀⠀⠀⠀⣸⢟⣡⠋⣹⣿⣿⣿⡿⢣⢸⡏⡷⣶⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⡧
⠀⠀⠀⢀⡾⢹⡇⠀⢿⢻⠝⡏⠀⠀⢸⡇⡇⣿⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠆⢶⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣠⡄⣲⠴⢷⠀⣸⡿⢥⣠⠔⠋
⠀⠀⠀⢘⣷⠟⢳⡀⢀⡟⣰⠀⠀⠀⠘⠃⠗⠿⢸⡏⢸⡇⢸⡇⢰⡆⡆⠀⣿⠀⠀⢼⠐⡆⣷⠁⣷⠛⣤⣿⢸⣿⣿⠷⠟⠃⠈⢠⡏⠀⢠⡗
⠀⠀⠀⢸⡏⠀⢸⣿⣼⠁⠈⠉⠛⠲⠦⠤⣤⣀⣀⡀⠈⠁⠈⠃⠈⠃⡇⠀⠙⠀⠀⠚⠚⠃⠛⠀⠉⠀⠉⠀⠀⠀⣀⣀⠤⠤⠒⠉⢷⣠⠟
⠀⠀⠀⠈⢿⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢴⡦⠶⠶⠖⠙⠃⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢻⣦⡀⠀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣄⡆⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢈⡏⢻⣿⠉⡇⠀⠀⠀⢃⣤⣵⣾⣥⣜⠃⠀⠈⠻⣾⢶⣶⢷⡞⠃⠀⠈⢿⡿⣦⣴⢿⣿⠃
⠀⠀⠀⢸⣮⠁⠁⢡⣟⠀⠀⠀⠺⠽⠋⠉⠯⠿⠀⠀⠀⠸⣿⠊⠁⢿⠟⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣦⣀⡸⠇⠀⢠⠀⠒⣢⣆⠒⠀⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠀⠈⠇⠀⠂⠀⠀⠀⢿⣰⡟⠻⣆⣽⠀⠀⠀⠙⢟⠻⢟⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠖⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣄⠂
⠀⠀⠀⠸⣲⠚⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠸⣯⣻⢟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⢛⣛⣛⡉⣉⠙⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢩⣖⣦⣶⣆⢸⣿⠃⢹⡇⠸⢷⣿⠀⣿⠉⠉⠉⠛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣿⢸⡟⠁⠟⢻⠈⠋⠳⠈⠁⠒⢚⣁⣀⣯⣀⣀⣀⣘⠛⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⡶⠀⠀⣻⣄⣡⣤⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠙⠋⠀⣀⡴⠃⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠠⠀⡇⢨⡄⠀⣼⣡⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⠀⠀⠀⣹⣶⢶⡖⢲⢶⡶⡾⢯⣹⡇⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⢸⡇⣇⢸⡀⠀⠉⠁⠀⢠⣤⡤⢤⠤⣤⢲⣶⢿⡁⢹⣌⣿⠀⠀⠀⠿⠋⠈⢷⠇⠈⠻⠃⠀⠙⠃⢸⡇⣿⡇⢠⣤⡄
⠀⠀⣴⢒⠊⠉⠙⠋⠛⠙⢓⠒⢦⡀⠀⢸⣿⡇⢸⣧⣽⠸⣿⠾⡇⠀⠋⠈⠀⠀⠀⠀⢸⡇⠀⢰⣢⠀⠀⣴⣦⠀⢸⣧⠻⠇⠈⠛⠉
⠀⠀⡧⢀⣀⢉⣭⡉⣩⣅⢠⣤⡀⢻⠀⠈⠈⠀⠈⠀⡁⠀⠁⠀⠐⣦⣀⢿⣠⢿⠀⢰⢟⣧⠀⣰⠿⡀⠀⢸⣻⣦⠈⠿⠀⢠⣦⣀⡀⠻⠃
⠀⠀⢷⡟⢻⣿⣸⣇⣟⣻⡿⢹⡇⡿⠀⠀⠀⠀⣶⣾⡿⣰⠀⠀⠀⠹⡉⣂⡡⠼⠀⣯⣵⡿⠀⣿⠃⢷⡀⣾⣭⣼⠇⠀⠺⣼⢿⣻⠅
⠀⠀⣸⣗⠀⣤⠙⠿⣃⠉⢠⣌⣻⠧⣄⢠⡖⠒⢻⣿⡏⢉⣳⡄⠀⡶⣄⢠⢺⠂⠀⢀⡀⣀⠀⢙⡓⠛⠁⠀⠀⠀⠀⢀⣀⡙⠋⠁⣀⢀
⠀⢸⠁⠈⠉⠓⠒⠚⣉⠉⠉⠉⠀⠀⠘⡇⢳⠚⠹⣿⡏⠉⣹⠁⣤⣷⣿⣿⣾⣧⠀⡸⠖⢶⣉⡳⣆⡵⠀⡶⠉⢲⣤⠟⠁⢸⡆⠀⠻⠟
⠀⢸⣴⢶⣄⡞⣷⣼⢻⡆⣾⢻⢠⡟⣦⣿⢸⡀⠀⣿⡇⠀⡟⠀⢸⣏⠋⠋⣭⡏⠀⠁⠈⠁⢀⣉⡉⠀⠀⣷⡀⠀⠉⠀⠀⣼⠃⣶⣤⡤
⠀⠀⣏⠈⠿⠃⠻⡿⠈⠷⣏⠈⢿⡃⣸⡅⠀⠣⢀⠛⠓⠚⠁⠀⠈⣿⣀⣴⣉⡇⠀⠀⠀⣰⠋⠀⠙⣦⠀⠈⠙⠲⢤⣠⡼⠃⠀⠻⠟⠁
⠀⠀⢿⠺⡧⢮⡥⣬⢤⡴⠶⢋⣛⣬⠾⠃⠀⣼⢁⢹⣠⡖⢒⡄⠀⠈⠉⠉⠉⠀⢀⡴⠒⣿⠀⠀⠀⣿⠞⠉⣶⠀⠀⣽⠁⠀⢀⡤⠖⠂⢤
⠀⣠⡀⠉⠓⠒⠒⠒⠒⠛⠉⠉⠀⢠⣤⡀⢠⡬⠽⡿⠻⣿⠏⣤⢰⣿⣤⣶⠀⣤⠞⠳⣄⢿⠀⠀⢀⣟⣠⠤⣿⡁⠀⠙⢦⠀⡞
⠲⡋⠹⡃⢤⢤⣶⣶⡾⣹⠀⡤⣄⢨⣿⡁⠸⡇⠀⣇⢠⡧⠀⢼⢻⣿⣿⡅⣸⠃⠀⠀⢹⣮⠧⣴⠻⡿⠁⠀⠈⣿⠀⠀⣼⠀⡇⠀⠀⠀⢠
⠘⠛⠉⠁⠘⠚⠉⢁⡀⠀⣠⢿⡅⠺⠾⠇⠀⣇⠀⣿⢸⠇⣀⣿⣸⣿⣸⠇⢻⡀⠀⢀⣾⡏⠀⢸⣿⡇⠀⠀⢀⡿⠀⠴⠃⠀⣸⠶⠴⠒⠋
⢸⠖⢦⠀⠀⣠⠚⣵⠿⠀⢑⣛⣁⡔⢰⠀⠀⠈⠉⠉⠉⠉⠁⣀⣀⠀⠀⠀⠀⠙⢶⠋⣿⡄⠀⣸⡿⠙⣦⡴⢛⣀⣀⡀⠀⢠⡇⠀⣸⣷⣶
⠉⠻⠁⠐⢊⣲⠗⠁⣴⠰⣿⣌⠿⠃⠘⢡⣾⠀⠀⠀⢀⡴⠺⣅⡽⢦⡀⠀⠀⠀⠀⠀⠈⢳⣤⠟⠠⠀⡄⡴⠋⠀⠀⠈⢢⠈⢇⠈⠛⡽⠋
⠘⠃⣠⡤⣤⣁⣀⣀⡈⠙⠋⠀⠀⢀⠴⢭⠭⠵⢦⠀⢯⢌⣓⣉⣫⣭⡽⠀⣔⠀⠀⠡⣠⠀⡅⢀⠃⠜⠐⡇⠀⠀⠀⠀⣸⠇⢸⡆⢠⣤
⠀⠀⣿⠀⠖⠀⢀⣠⡾⣷⣀⠀⠀⡾⢉⢚⣩⢉⡹⣄⢸⢸⣻⢹⢸⣿⠃⠀⣾⡆⠀⠀⠈⢳⡁⢀⠎⠀⠀⢻⣄⣀⣀⡴⠋⢀⡼⠀⠙⠛⠁
⠀⠀⢻⣆⣤⡾⠛⢋⣠⠾⣹⠃⠈⣶⣦⡭⡶⣤⡖⡟⠀⠉⠛⠛⠛⠁⡔⠀⠉⠙⠒⢄⡀⠀⣿⠀⠀⠀⢠⠞⠋⠁⠀⠀⣶⡄⠀⣶⣤⠄
⠀⠀⠀⠉⣷⣤⠴⢛⡵⠚⢡⣄⡄⠹⢾⣷⣷⣿⠼⠁⡠⣠⣶⣄⠀⢺⡄⠀⠀⠀⡀⣠⡗⠀⣿⡀⠀⠀⠸⡀⠠⣿⣖⠀⣀⣠⡆⠘⠁
⠀⠀⠀⠘⠧⠔⠚⠉⠀⠀⢮⢿⠗⠀⠀⠀⠀⠀⠀⠀⣱⢺⡟⡞⠁⠀⠘⡏⡏⣿⣏⣿⠃⠐⠁⠀⠀⠀⢀⡇⠀⠁⠀⣠⣯⡀⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣁⣀⣀⣀⣷⣿⣟⣛⣛⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣈⣀⣈⣃⣀⣀⣀⣀
⣿⣿⠛⡻⢛⡛⠛⣟⢛⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⢠⠆⠀⠀⠀⠀⠠⡄⠀⠀⠰⢢⡖⠀⠀⠀⠀⠀⠀⢶⡴⠆⢰⡇⠂⠀⡀⠀⠀⡀⠐⠲⡷
⠀⠀⠀⠈⢦⣀⠀⣰⠀⢀⡠⠏⠀⠀⠀⣿⣰⢩⢄⡰⡍⣆⣻⠀⠀⠀⠈⠇⠀⠀⢠⡄⠀⠀⢾⠀⠀⠀⢳⠀⠀⠨⣶⡌⠀⠀⣺⠁
⠀⠀⠀⠀⣴⠀⠀⢼⠀⠀⢰⠄⠀⠀⠀⢩⣾⠘⣾⣷⠃⣷⣍⠀⠀⠀⠀⣠⡀⠀⠸⠇⠀⢠⡄⠀⠀⠀⠈⣳⢂⣴⢻⢲⣔⢲⠋
⠀⠀⠀⠀⠘⣷⠶⠖⠶⢶⡟⠀⠀⠀⠀⠈⢿⣇⠈⠁⣸⡿⠁⠀⠀⠀⠀⠙⢷⣤⡄⢠⣴⠿⠃⠀⠀⠀⠀⠹⣜⣱⠀⢸⣋⡼
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠀⠘⠁⠀⠈⠙⠀⣀
⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡂⠖⣤⡀⠀⠀⣠⠰⠂⡆⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⣆⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⣇⠀⠀⠀⣴⠀⠀⠀⣠⠃⠀⠀⢻⠙⠚⡘⣶⢚⠙⠚⣼⠁⠀⠘⡇⠀⠀⠀⣤⠀⠀⠀⣾⠁⠀⠀⠸⠟⠂⢰⠀⠚⠿
⠀⠀⠀⠈⣷⡀⠀⠹⠀⠀⣸⠏⠀⠀⠀⠨⣗⢆⡙⠻⠊⣠⢆⡏⠀⠀⠀⠻⡄⠀⠀⡟⠀⠀⣰⠋⠀⠀⠀⣆⠀⠀⠘⠀⠀⢀⠆
⠀⠀⠀⠀⠙⠿⠶⠀⠶⠾⠛⠀⠀⠀⠀⠀⠈⠣⠭⠀⠨⠵⠋⠀⠀⠀⠀⠀⠱⠤⠄⠀⠠⠴⠋⠀⠀⠀⠀⠘⢶⡤⠀⠠⣴⠟
⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⠀⡤
⠀⠀⠈⢷⡈⠊⠀⣀⠀⠙⠈⡼⠃⠀⠀⡀⠀⠀⠰⣿⡆⠀⠀⢀⡀⠀⠀⠐⢰⡆⠂⢀⠀⠂⣶⠐⠀⠀⠀⠀⠀⠠⣿⡆
⠀⠀⠀⠀⣙⠀⠀⢿⠀⠀⢚⠁⠀⠀⠈⠓⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢨⠃⠀⢻⠃⠀⢫⠀⠀⠀⠀⢀⣌⡓⣛⠒⣋⡄
⠀⠀⠀⠀⠘⠦⠦⠈⠰⠴⠛⠀⢤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⢠⣶⠯⢍⣩⣏⠭⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⣶⠖⣠⡄⠀⠀⠀⢠⣤⠲⣶⠄⠀⣶⣶⣤⡀⠀⠀⢀⣤⢶⣶⠀⠀⣶⣶⢄⠀⠀⠀⢠⣶⣶⠀⠠⣤⣄⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠹⠀⢿⠀⠀⣤⠀⠀⣿⠀⠘⠀⠀⢹⡀⢁⣞⢳⡞⢻⡈⢀⡏⠀⠀⢻⠀⠀⠡⣀⠊⠀⢨⡇⠀⠀⠸⣧⠀⠀⣤⠀⠀⢰⡟
⠀⠀⠀⠀⠘⢧⣀⣿⣀⣴⠋⠀⠀⠀⠀⠈⢓⠘⠏⠈⠁⠹⠃⣚⠁⠀⠀⠘⠦⠀⠀⡿⠀⠠⢴⠁⠀⠀⠀⢙⡗⠀⢹⠀⢰⡏
⠀⠀⠀⠀⢷⣦⣉⠀⢉⣥⡾⠀⠀⠀⠀⠀⠘⣦⡤⠀⠀⢤⣴⠃⠀⠀⠀⠀⢧⣤⠂⠁⠰⣤⡼⠀⠀⠀⠀⠈⢷⣴⠏⣧⡴⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⠖⠟⠳⢲⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢰⣶⣶⡆⢱⣶⣶⡆⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠾⢽⢯⠷⢀⢀⠆
⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡷⠀⠀⢸⣿⣿⡇⢸⣿⣿⠁⠀⠀⢾⣦⡀⠀⠀⠀⠈⠀⢰⣿⢾⣿⣄
⠀⠹⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⣸⣿⣧⣤⣄⠀⠀⠐⢿⠿⠀⠿⠿⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠸⠿⠿⠇⠸⠿⠿⠀⠀⠿⠟⠛⠉⠛⠛⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡁
⠀⠀⠀⠀⣸⣇⠀⠀⠀⠈⣚⣷⡴⠀⠀⢦⣴⣗⠚⠀⠋⣤⠀⠀⠀⠀⠀⢈⡉⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢀⡻⢟⡀⠀⠀⠈⠁⢖⣿⣶⣶⣾⣳⠋⠁⠀⠈⢃⡄⠀⠀⠀⠀⣈⡠⠄⠀⠸⠿⠆⠀⣀⠂⠀⡀⠀⠺⠿⠂
⠀⢻⣿⣸⣿⣿⣇⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣤⠄⠀⢀⣈⣁⡤⠖⠀⠀⠀⠀⠀⠈⠉⠹⣷
⠀⠈⠿⠋⠀⠀⠙⠻⠋⠀⠀⠈⣿⠛⠛⢻⠏⠀⢠⣦⠀⠀⢡⡆⠀⠈⣡⣀⡠⠵⠚⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⣾⣶⣶⣧⣄⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠀⠎⠸⠂⠀⠈⠈⠁⠀⠂⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣠⣶⣿⠓⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣾⣿⣿⠟⠃⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠐⠻⠿⠿⠀⠀⣤⣄⣻⣿⣿⣟⣠⣠⠀⠀⠀⢀⣴⣄⡘⠇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠂⠀⠀⠙⢿⣿⣷⣆⣹⡿⠋⠀⠀⣴⣿⣤⣬⣿⡆
⠀⠰⠿⠿⠿⠿⢿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠋⠈⠿⢿⠷⠀⠀⠿⠿⠀⠸⠿⠇
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⢀⣬⠁⠱⠆⠀⠀⠀⠀⠀⠀⠀⣔⣰⣶⣠⣾⣧⢀⣤⠀⠀⣴⡟⠛⠉⠉⠙⢳⣆⠀⠀⢀⣴⣾⣦⡀
⠀⠀⠘⢆⡛⣡⡿⡿⠳⠇⢀⠀⠠⠀⠀⢀⣹⣷⣽⣿⣿⣿⣿⠃⠀⢘⣿⠀⠀⠀⠀⠀⠀⣯⠀⢠⣿⡿⠟⢻⣿⡆
⠀⠘⠛⣤⠢⣤⠷⢆⠈⣘⠋⠀⢇⠀⠀⠸⢿⣿⣿⠿⠿⠟⠃⠀⠀⠀⢿⣤⣀⡀⢀⡀⣰⡟⠀⢺⣿⣭⢀⠰⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠘⠁⠙⠁⠀⠀⠑⠂⠤⠤⠤⠤⠤⠄⠂⠀⠀⠀⠀⠀⠉⠙⡿⡿⠛⠉⠀⠀⠈⠻⢿⣿⣿⠟⠃

⡾⣿⣿⣓⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢺⣿⣿⡟
⠹⣟⣿⣿⣅⣼⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⣿⣇⣴⣿⣿⣿
⠀⠹⣽⣿⣯⣈⠿⠀⢼⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣧⡠⠙⠓⣿⣿⣽⠃
⠀⠀⠹⡽⣿⣍⣁⠀⠸⣿⠀⣾⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⣠⠾⣿⡏⠀⣻⠏⠀⠶⣿⣿⢷⡏
⠀⠀⠀⢳⠻⣿⣦⣠⣀⠛⠢⣿⡇⠀⢹⣷⣄⠀⠑⢄⠀⠀⠀⠌⡠⣠⣾⣇⠀⠘⣿⠄⠁⠀⢬⣶⣿⣟⡿
⠀⠀⠀⠈⢷⠻⣿⣧⣤⣠⠀⠾⠃⠀⣿⣿⠙⣷⣌⠄⣿⣿⣄⣪⡾⠛⣿⣿⠀⢀⡛⠀⠀⢠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢷⣛⣿⣦⣤⡄⠀⠀⢀⣿⠋⠈⢾⣿⣷⣾⣿⣿⣿⠃⣀⣸⣿⣆⠀⠀⠠⢤⣴⣿⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢦⠄⠙⠁⢰⣆⠀⢹⣿⣿⣿⣿⡇⠈⢿⡇⢈⠩⣯⣜⠒⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠚⠀⢹⡀⠀⠐⣽⣿⢿⠁⠀⢸⠀⠈⡑⢿⣽⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⠀⢦⡀⠀⡧⠀⢧⢿⣿⡼⣇⠀⡟⠀⢠⡏⣿⡟⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⣿⣷⣤⠀⠅⠀⣷⢠⢸⠘⡟⢰⣄⢠⠃⠰⠋⣤⣼⢷⡟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⣿⣿⣰⡆⠀⢻⠈⣐⠀⠀⣸⠁⣸⠀⠰⣀⣬⡏⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⡿⣿⣵⣦⣾⣦⠶⠀⠀⠰⢆⣿⣷⣤⣾⣹⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣾⣋⣾⣥⣿⠋⠀⠀⠉⣟⣹⣟⣙⣏⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣹⣯⡞⠀⠀⠀⠀⠻⣽⣏⡙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢡⢠
⠀⠀⠘⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠆⠰⠈
⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠛⡘⠛⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠰⡇⠀⠀⠠⠤⠖⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠠⠄⠀⠀⠠⠠⠄⡄⠀⠀⠀⠀⡂⠆⠅⠀⠀⠀⠰⠰⠀⠀⠀⠀⡀⠀⠀⣠⢭⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠰⠠⠀⣃⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⡀⠀⠀⡀⢀⢀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢸⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⡀⢇⣃⠸⡤⡀⣧⣅⠈⣆⠀⠀⠀⠁⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⡀
⠀⠀⣩⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⢀⡄⡄⠀⣄⠀⢠⠀⡀⡀⢠⡀⠀⡄⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⢀⣿⡇⠀⠈⠫⣶⡽⠃
⠀⠀⡡⢖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠣⡀⠐⠇⠧⠀⠷⠄⠸⠀⠬⠄⠀⠧⠀⠧⠉⠆⠮⠐⠦⠰⠥⠀⠀⠠⠻⠛⠃⠀⠀⠀⣿
⠀⠀⠖⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠈⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢄⠐⠀⣠⠆⠀⠀⠀⡆⠀⡆⠀⢀⢀⠀⠀⠀⢀⣀⡀⠀⠀⣄⠀⠀⠀⢰⡿⠁⠀⢈⠀⠄⠀⠀⠁⢈⠄
⠀⠀⠀⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢒⣿⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣗⣒⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⣤⡼⠿⢟⣬⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⠿⠿⢧⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⠤⠤⠬⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠤⠤⠤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠱⢤⡀⠉⢷⡄⠀⣀⠀⣰⠟⠁⣠⠴⠁⠤⠤⠤⢤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⠀⠀⠀⠀⠀⠈⠑⠠⠙⣾⣿⣞⠡⠐⠉⠀⠀⠀⠀⣀⣀⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⠿⠿⠶⠶⢲⣿⢸⣿⠖⠶⠿⠿⢿⠿⢻⣟⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⢰⠊⠁⢀⠔⠨⢿⣿⠿⠀⠀⠀⠈⠱⠀⠀⠀⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣈⣁⠠⠖⠁⡀⠀⢸⣿⡀⠀⠄⠈⠢⠄⣈⣀⠀⠠⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⢀⠌⢠⡞⠀⠌⠀⠠⢹⣿⠑⡀⠈⢆⠀⢦⠈⢂⠀⢢⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣎⣀⡌⢀⠌⢀⡔⠀⠀⠛⠀⠀⢆⠀⢂⠀⣅⣀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣦⠞⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠴⠞⠁⢀⣤⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⢀⣶⣴⣿⣿⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇
⠀⠀⠀⠀⢀⣤⡤⠴⢖⣲⠟⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⡉⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢠⣾⢟⠅⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡇
⠀⠀⠸⣿⣍⣰⠇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⠀⠀⠀⠙⠻⣿⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠋⠀⡿⢿⣿⣿⣏⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⣄⣨⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣦⠀⠀⠁⠀⠀⠀⠤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠀⢀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡆⠀⣰⠀⠀⢀⠀⠀⠀⠀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣿⣆⣠⣾⡂⢠⣄⣠⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢳⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡞⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠽⢿⣛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⡿⠯⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠒⠲⢿⡟⠁⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡉⠈⢻⡿⠒⠒⢲⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⡒⠒⣚⣧⣰⣿⡿⢉⣿⣄⠀⠰⠀⠀⠆⠀⣠⣾⡉⢿⣿⣆⣼⣛⡚⢒⣾⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢉⣉⣉⢻⣿⡀⢸⣿⡿⣦⠘⡀⣠⠃⣼⢿⣿⡇⢀⣿⡯⣍⣁⡉⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣇⣀⢠⠤⠿⠟⣿⡿⢥⣹⣇⣿⣿⣸⣏⡬⢿⣿⠻⠿⠤⠤⢀⣸⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡤⠔⠒⠒⠒⢿⡟⠒⠦⣽⡇⢸⣯⠖⠒⢻⡿⠐⠒⠒⠂⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⡟⠛⢋⣉⣉⣽⠿⠛⣿⣇⣸⣿⠛⠿⣯⣍⣉⡉⠛⢻⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⡟⠋⡹⠋⢠⡿⢀⡼⣹⣿⣿⣏⢧⡀⢿⡄⠘⢏⠉⢻⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡷⠚⡇⠀⢘⣷⡾⢠⡇⢻⡟⠸⡄⢷⣾⡃⠀⢸⠓⢺⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣷⠞⣹⠒⡟⢻⣷⡿⠀⠀⠀⠀⢿⢺⡟⢻⠒⣏⠳⣿⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣍⣧⣧⣰⣧⣼⣽⡇⠀⠀⠀⠀⢸⣯⣧⣼⣦⣼⣼⣭⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣶⣿⣷⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣾⣿⣶⣿⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣽⡿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣯⡾⢿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠐⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⡩⠄⠀⠀⢀⡴⢏⡨⠁⠀⠀⠀⠊⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠀⠀⠀⠀⢠⡮⣕⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠋⠀⠀⠀⠀⠀⢰⠗⠥⠀⠀⠀⢈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣀⠀⠀⠀⠀⠀⢀⠢⢀⠄⠀⠀⠀⠀⠀⠐⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⠀⡀⢀⠀⠀⠀⠀⠀⢠⠀⢃⠀⠂⠀⠀⠈⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⠄⠀⡀⠀⠀⣔⢂⣨⠜⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠦⡀⠀⠈⠲⠐⠤⠊⠁⠀⡀⢀⠀⠀⠀⠀⠀⠴⢆⣄⠉⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠌⠀⠀⠔⠁⠀⢈⠦⡀⠚⠋⢄⠀⠀⠀⠄⠠⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠄⠄⠀⡠⠀⠀⡀⠐⠁⠀⢀⠰⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠈⠀⠀⠐⠈⠀⠄⠀⠈⠁
⠀⠀⠀⢠⠂⠔⡡⠀⡀⠄⡂⠠
⠀⠀⢠⣏⣀⡨⠔
⠀⠀⠚⠋⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣤⣤⣀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⣀⡠⠀⢤⣤⣤
⠀⠀⢹⣿⠋⠀⠹⣿⡏⠀⠹⣿⡯⠉⢽⣿⡷⠀⠲⣿⡶⠂⠰⣾⡶⠂⠰⣟⡶⠃⠈⢻⡿⠏⠈⢻⡿⠇⠀⠛⣿⠇⠀⠐⢿⠏
⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠈⠛⠀⠀⠀⠻⠃⠀⠀⠸⠃⠀⠀⠸⠇⠀⠀⠈⠏⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⡴⠄
⠀⠀⠀⠀⢛⣼⡺⠀⠀⠀⠀⠀⣻⣿⣿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⢠⣆⣀⠀⢿⣿⡘
⠀⠀⠀⠀⠀⠉⠁⠐⣶⣾⣇⠀⠈⠀⠉⠀⣾⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⡃⠈⠁⠈⠁⠀⠀⣀⠀⠘⢻⣿⣿
⠀⠀⠰⠖⠀⠀⠀⠰⠿⢿⡏⠁⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⣷⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⡞⡹⠇⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠘⠿⠾⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠁⠁
⠀⠀⠀⢀⡾⠿⠞⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠖⠄⠉⠃
⠀⠀⠀⣿⣧⠀⠀⢈⣿⡇⠀⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⣀⡀⢘⢋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡀⢀⡀⣀
⠀⠀⠀⠻⣿⠀⠔⢺⡿⠃⠀⠨⢛⣧⣧⠀⠀⡟⠶⢻⠀⡧⠄⢸⢴⠃⣯⢼⠁⢱⠎⠀⠀⠈⠁⠁⠀⠀⢛⠋⣉⣡⣟⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠈⢀⠃⠃⠈⠀⡁⠁⠈⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠊⠀⠀⠀⠀⠙⠁⠘⠃⠑⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠈⣠⣤⡀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣂⠀⠈
⠀⠀⠀⠰⣾⣷⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡄⠀⠀⠐⠽⠿⠯⠛⠄
⠀⠀⠀⢀⣝⣛⡿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⡖⠀⠀⠠⣄⣀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠹⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠠⡾⠃⠀⠀⠀⡞⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠤⠄⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠿⠿⠶⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣀⡀⢮⣷⡄⠀⠀⠀⠀⢀⡴⣆⣠⣄⣤⣀⡄⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢮⠅⠘⠛⠀⠀⠀⠈⠀⠠⢤⣀⠀⢠⣀⣈⡀⠀⠁⠠⠄⢀⣠⡼⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⠀⠀⠁
⠀⠐⠀⠀⠄⠤⠀⠀⠀⢀⣠⡝⠁⡈⣿⠇⠀⠀⠀⠀⠀⠀⢠⣦⣴⣦⣴⣦⣤⠀⠀⠀⠀⢿⡏⠋⠁⠀⠀⠀⠀⠒⠒⠲⠆⠐
⠀⠀⠀⠀⡀⠀⠙⠿⠛⠛⣿⣇⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠒⠒⠘⠋⠙⠀⠀⠀⠀⠀⠐⠋⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢹⡿⣋⡟⢿⣤⢶⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⠟⣿⣻⡟
⠀⠀⠀⢻⢻⠗⢿⣤⡀⠨⢿⣿⠛⢷⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠟⢻⣿⠯⢤⣤⣼⠛⣿⣿⠃
⠀⠀⠀⠘⣿⣹⢯⣦⣤⠴⠞⣯⣁⡾⡞⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣻⣿⡿⣆⣩⣷⠶⢦⣤⣮⢽⣽⡟
⠀⠀⠀⠀⠙⣷⣴⣿⣦⣀⡠⣏⣹⠶⠶⣏⠛⠳⠾⢿⣦⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣠⣾⠷⠶⠿⢿⡷⠶⠾⣭⡧⣀⣠⣟⡃⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣳⣾⠉⢱⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⠈⢹⣾⣷⠏
⠀⠀⠀⠀⠀⠀⠈⣻⣾⡟⣳⣾⢾⡧⠄⠀⠞⠦⢄⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⡤⠿⠆⠀⠴⢭⣿⢿⡳⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⠝⢿⠁⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⠞⢯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣛⣧⣤⠤⠤⠤⠒⠒⠛⠙⠓⠀⠀⠀⠀⠈⠳⡄⢰⣶⠀⡴⠋⠀⠀⢀⠠⠐⠊⠉⠓⠒⠒⠠⠤⢤⣤⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢁⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⠤⣤⣤⣤⣤⣽⣿⣿⣿⣤⣤⣤⡀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣠⣾⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠍⠉⠉⠉⠉⠉⠻⠆⠁⠀⠤⠐⠀⢉⡿⣿⣿⣿⣏⠉⠐⠠⠤⠉⠛⠛⠉⠉⠉⠉⠀⠫⣍⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣀⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⠴⠋⠘⢹⣿⠹⡈⠳⢄⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⣸⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠊⠁⠀⠀⠀⡀⠀⠀⢀⣠⡴⠊⠁⠀⡰⠀⣾⣿⠆⠁⡀⠀⠉⠲⣤⣀⠀⠀⠠⡀⠀⠀⠀⠈⢻⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣷⣄⣀⠀⠐⠚⢁⠴⠛⠉⠁⠀⠀⠀⠸⠃⡀⢸⣿⠐⡄⠙⠄⠀⠀⠀⠉⠙⠳⢀⠛⠒⠤⢀⣀⣼⣿⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣬⣿⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⢠⡼⠁⢸⡿⠀⠹⣴⠀⢀⠀⠀⠀⡀⠀⠀⠑⢦⡀⠀⢹⣞⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣷⣾⡇⠀⠀⠀⡔⠀⠀⣠⠃⢀⡿⠁⠀⠀⠁⠀⠀⠹⡆⠀⢣⡀⠀⠐⡀⠀⠀⠀⣿⡶⣿⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣶⢿⣿⡶⣶⣾⣇⣀⣴⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⣄⣀⣿⣶⡶⣾⢿⢶⣮⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣿⣲⣻⣭⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣾⣯⣿⣷⣺⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣭⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠉⢱⣿⣿⣿⡿⣄⣴⣶⡖⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⠾⣿⢻⣟⢛⣿⣾⠟⢻⣷⣟⣩⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡀⣀⠑⠾⣍⠈⣶⣾⣿⣾⣿⡟⣵⣢⣶⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣢⡅⠐⣿⣣⣤⠞⣟⠷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣥⣾⣖⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⠀⠀⠘⣿⠁⢸⣿⡤⡴⡆⠈⡇⣿⣿⣿⣿⡿⣿⣶⢮⠙⠡⠷⠈
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣧⣿⡟⣀⣠⣯⣾⠿⣿⣿⣿⣿⣧⡜⠋⡀⣰⠆⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠐⢻⡿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠟⠁⠸⡦⠚⣋⢤⣿⢿⣿⣿⣿⣿⣟⡿⢛⣿⣿⣿⡛⣟⠒
⠀⠀⠀⢀⠀⠀⠀⠠⠇⢙⢿⣿⣿⣿⣿⡿⠋⢀⣰⠓⣲⢶⣶⣇⣈⢀⣾⣿⣿⣿⣯⡾⢛⡋⢒⡀⠀⠈⠛⠁
⠀⣤⣶⣿⣿⣆⡀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠴⠛⡷⣤⣌⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠁
⠀⢿⣿⣿⣿⣿⣷⠻⣧⠀⣤⡜⣿⣿⣿⣿⡤⢬⡛⠻⠟⣿⡟⣿⣿⣿⣿⣿⣿⣿⠉⡜⠉⢩⠓⠂⣠⣤⣤⣀⠀⢀⣀
⠀⠈⠻⢿⣿⣿⣷⣄⣿⣾⡏⣰⣿⣿⣿⣿⣗⠛⢨⡿⠷⣬⣥⣤⣿⣿⣿⣿⣿⣿⣶⣿⡶⣾⡂⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡇⡋⢀⣻⣿⣟⣻⣿⣿⡿⠛⣻⠿⠻⣿⣿⣯⡥⡀⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⠀⢿⣿⣿⣿⣿⣿⡾⠋⣟⣼⣟⣻⣿⣿⡇⠀⣿⠀⢀⣿⣿⣿⣫⠥⢈⠀⠀⡉⣉⣀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⣿⣷⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡶⠢⠁⢠⠚⠙⠛⢛⣿⣿⠁⠀⢨⣿⣿⣿⣿⣏
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣘⡇⠀⠠⠐⠴⠿⠾⠛⠛⠁⠀⠀⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢻⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡿⣷⢾⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣷⣤⡀⣷⣶⣂⣠⣾⣧⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢘⣿⡿⣿⣿⠁⠠⢼⣧⣿⣿⢟⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⡽⠿⠻⡅⣟⢀⠀⢸⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢰⣿⡏⣿⡟⠀⢸⣿⠁⠸⣿⣰⡶⠛⠙⠁⠀⣮⠀⠀⢸⠟⠇⠸⣀⠟⠛⢿⣛⣿⠀⠀⢰⡇⠁⠀⡇⢸⠀⠀⢸⣿⣇⢸⣿⣷
⠀⠀⠀⠀⠈⣿⣹⣿⠇⠀⢾⣿⡀⢴⣿⣏⠁⠀⠀⠀⠀⣿⠰⠄⣻⠶⠀⠄⣿⠀⠀⠀⠿⠀⠀⠀⢸⡇⠀⠀⡇⠈⠀⠀⠸⣿⡟⠸⠿⣿⠇
⠀⠀⠀⠀⠈⠛⠻⣿⣷⣄⠈⢿⠄⠀⠸⠿⠀⠀⠀⠀⠀⠿⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⠿⠃⢤⣾⡿⠇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⣤⠤⣤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠘⣿⣧⡈⠻⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠟⢁⣾⣿⠃
⠀⠀⠈⢻⣿⡤⢿⠀⢀⣑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⡀⠀⡾⢤⣿⡟⠁
⠀⠀⠀⠀⣿⡇⢸⣰⣿⣿⣷⢌⡢⡀⠀⠀⡴⠊⡑⠢⡀⠀⠀⠀⠀⢀⠔⢊⠑⢦⠀⠀⢀⢔⡡⣾⣿⣿⣆⡇⣸⣿
⠀⠀⠀⠀⣿⣿⠉⢣⠹⠋⣗⡦⠙⡌⠢⡀⠙⠒⠁⠀⠹⡄⠀⠀⢠⠏⠀⠈⠒⠋⢀⠔⢡⠋⢴⣺⠙⠏⡜⠉⣿⣿
⠀⠀⠀⠀⢸⣿⣀⡸⠘⠤⣈⣀⠜⠦⡀⠙⢆⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⡰⠋⢀⠴⠣⣀⣁⠴⠃⢇⣀⣿⡇
⠀⠀⠀⠀⣾⡟⠀⢇⠀⠀⢀⣤⣤⣤⣈⠳⣄⠳⡀⠀⠀⠈⡇⢸⠁⠀⠀⢀⠞⣠⠞⣁⣤⣤⣤⡀⠀⠀⡸⠀⢿⣷
⠀⠀⠀⠀⠻⣷⡤⠤⣵⠀⣿⣿⡋⢑⠄⠙⢮⣢⡙⡄⠀⠀⣇⣸⠀⠀⣠⢋⣔⡵⠋⠠⡏⢙⣿⣿⠀⣮⠤⢤⣼⠟
⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠙⠿⣉⣉⠀⠀⠀⠑⣕⣜⣆⠀⣿⣿⠀⡰⣣⣫⠊⠀⠀⠀⣈⣉⠿⠋⠀⢸⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣗⠉⠱⢄⡀⠀⠀⣴⣿⣿⣿⣶⣮⣿⣾⣎⣿⣿⣰⣷⣿⣵⣶⣿⣿⣿⣦⠀⠀⢀⡠⠎⠙⣺⣿
⠀⠀⠀⠀⠀⠈⠻⠷⢴⣮⣭⣓⣶⣽⣿⣿⠭⠭⠭⣶⣶⣿⣿⣿⣿⣶⣶⠭⠭⠭⣿⢿⣯⣶⣞⣭⣵⣦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢫⠟⠉⣩⢟⡩⠔⠚⣩⣋⡟⠀⣿⣿⠀⢻⣙⣍⠓⠢⢍⡻⣍⠉⠛⡝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠘⠢⠚⣵⣿⠀⠀⣰⡷⣿⡄⠀⣿⣿⠀⢠⣿⢾⣆⠀⠀⣿⣮⠓⠔⠃⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⢿⣿⣷⡴⢻⠁⠸⣿⠀⢻⡏⠀⣿⠇⠈⡟⢦⣾⣿⣿⣀⠀⠀⢴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡖⢰⡋⢱⠌⠁⠀⠘⠢⠖⢹⡇⠀⠀⢸⡏⠣⠔⠁⠀⠀⠁⢏⣈⡇⢲⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠉⠁⠀⠀⠀⢀⣄⠀⣸⡇⠀⠀⢸⣇⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣾⣷⣄⣼⣿⣶⣾⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣷⣶⣿⣧⣤⣾⣷⣾⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠙⢿⡿⠋⠙⠿⠋⠉⠛⠋⠀⠀⠀⠀⠙⠛⠉⠙⠿⠋⠙⢿⡿⠋⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢦⡴⣟⠢⣶⣤⣌⣤⠞⣠⣄⡰⢦⢀⠀⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣶⣿⠦⢤⡄⣀⣀⢅⣀⣰⣸⡀⡄
⠐⣻⡅⠋⠑⠿⡟⢫⠈⢨⢈⣟⢫⠉⣿⠓⣹⣩⢇⡀⡀⠀⣤⠀⠀⣀⣀⡼⢀⠮⠂⢪⡇⣿⣣⡉⣿⡿⢁⠺⡘⣯⠼⡦⢿
⠈⢇⢓⡦⡟⡾⢹⡼⢗⣙⢈⡷⣈⡻⠖⢢⠒⣶⡐⣿⡟⣿⡙⢿⣿⢽⡿⣺⣍⣌⣇⣰⣆⠺⠧⡑⠾⣷⠈⠠⡌⢓⢂⡟⡶
⠀⠀⠼⡆⢉⠗⢜⠓⠎⠴⢖⣄⡹⠟⢵⣡⠟⡀⢌⡙⢶⠉⣐⠈⠷⠠⠃⠄⡂⣹⣧⢧⢸⠌⣣⡘⢲⢦⠈⠇⢉⠘⠾⠑⢹
⠀⠀⢠⠀⡌⠁⠄⡐⠀⠀⠈⠀⠁⠚⠂⠛⠀⠸⠾⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⢄⠉⠠⡌⠳⠶⠌⠀⠁⠈⠈⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁⠀⠑⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡷⠀⢀⡿⠹⢷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⣿⠷⠒⢀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠿⠥⠧⠤⣴⠿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣧⣶⠿⢎⣹⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⢤⠀⠀⠀⠨⢧⡀⠉⠛⣦⡀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣠⡯⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣟⡄⠠⠄⠀⠠⠷⢄⡀⠈⠻⣦⢠⣀⣔⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⣼⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣴⣶⣶⣶⣿⣷⢦⣬⣿⣿⡟⣡⣴⡬⠤⢤⣤⣤⣤⣤⣴⣟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣉⡅⠞⠛⠃⢠⠄⠉⠲⢺⢿⣿⢏⡷⡯⢤⡄⠂⠉⠛⢿⣿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣅⡠⠀⢀⡚⠉⡠⠊⢀⠂⢸⣿⠙⡇⡀⢄⠈⠫⠁⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠔⠑⠒⠁⢀⠂⠐⢨⣿⠀⠰⡈⠄⠑⡆⢬⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡄⠀⠀⠀⠂⢀⠀⢀⠠⢻⣿⠀⠀⢡⠈⣄⠈⠄⠣⡈⣲⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣫⣶⣠⡴⢀⢴⣠⡆⠀⠘⠏⠀⠈⢢⣆⣈⣄⡸⣤⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢀⡀⠠⠓⡀⠀⠀⠄⠀⠦⠊⠛⢲⠤⠀⢀⣀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡴⠛⠉⠋⠀⠄⠀⣐⠐⢀
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠟⠁⠓⠘⠇⠘⠋⢲⠞⠒⠁⠾⠁⠠⠈⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣸⠟⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠅⠀⠉⠒⠂⠀⠰⠀⠀⢠⠤⠀⠦⠀⠀⠀⠴⠂⢤⠄⠀⠚⠁⠘⠉⠉⠁⠀⢀⠀⠀⠁⠀⢸⢥
⠀⠀⠀⠀⠀⠐⠀⠀⠚⠠⡬⠑⠀⠸⠗⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠥
⠀⢀⣀⣤⣄⡤⠀⠂⠀⠈⠀⠀⠀⢀⠀⠀⠀⠉⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠫⡄⠀⠐⠂⠀⠲⠌⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠌⠀⠀⢄⠘⢁⠀⠀⠘⠁
⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡐⣒⠀⠀⠂⢀⡀⠀⡄⢸⡆⡀⠀⢄⠈⠉⠀⠀⢀⡴⠀⠨⠀⠀⠀⠀⠇⠀⠀⠀⣠⡄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⡀⠄⠀⡔⡷⠀⠯⠼⣧⢼⢦⠼⠷⠄⠀⠀⡖⠀⠀⠀⠀⠐⠀⠀⠚⠂⢠⠀⠈⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠀⠃⠞⠚⠀⠀⠂⡇⠀⠀⠀⠀⠀⡄⠀⠀⢠⡀⢠⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢖⡦⢀⢻⠀⢾⡘⠺⠈⢿⡚⠊⠓⡆⠀⠋⠀⠈⠀⠀⠀⠀⠀⠠⠈⠘
⠀⠀⡀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡀⠛⢀⡓⠀⣉⠀⠋⠁⢂⡑⠷⠀⠀⠆⠀⠂⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢨⠅⠀⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⡀⣠⠀⠀⠀⢠⡄⠀⠙⣓⠃⣼⠃⠠⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡾⠀⠦⡀⠀⠠⠄⠀⠀⢀⣀⣀⡀⠀⠀⠐⠊⠛⠀⠀⠀⠈⠀⠠⢀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠚⠋⠀⠀⠀⠀⠈⠀⠝⠲⢤⣉⣀⡀⠀⠉⠀⡀⠀⠄⠐⢊⠠⠸⢀⡀⠀⠀⠀⣀
⠀⠀⠀⣮⢧⢆⣄⠀⠀⠀⠀⠀⠀⠈⠫⠉⠁⠀⠐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⠁⠁⠀⠁⢐⢄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣼⡃⠠⠠⠀⠀⠀⠀⠀⠘⢞⡛⣭⡴⣄⣶⠀⠀⠄⠀⠨⠀⠀⡆⢸⠀⡆⡆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠳⣧⣾⣗⣻⡇⡮⠀⠄⠠⠸⠀⠀⠛⠘⠀⠃⠃
⠀⠀⠀⠠⠄⠐⠆⠠⠤⠀⠀⠢⣀⠀⠆⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠷⠍⠗⠀⢦⡤⢲⡀⠠⣆⠀⠀⠄⠲
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠙⡇⠀⠀⢤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⠀⡀⠀⠀⠀⠛⠀⠀⠲⠄⠀⠀⢀⡤⠘⣷⠀⠀⠀⢀⠀⠀⠠⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠘⣧⡀⠀⠀⠀⢠⣤⢲⡴⣲⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠂
⠀⠀⠀⠢⢡⠐⢤⠀⠀⠘⣿⡾⠞⠁⠀⠀⢀⣀⣀⣀⣀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀⠀⠀⠈⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆
⠀⠀⠑⢄⠘⠆⠀⠀⢀⡔⢩⠀⠀⠀⠀⠐⠛⢢⡤⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠰⢃⠀⠀⠀⣴⣾⠀⣾⡿
⠀⠀⡀⠈⠁⠀⢀⡴⠣⡈⣿⠀⠀⠀⠀⠀⠚⠃⠒⠒⠀⠤⠅⢀⣤⠀⠉⠁⠀⠒⠠⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠒⢾⣏⣩⠟⠃⠀⠙⠁
⠀⠀⠀⠀⢀⡴⣋⠐⢄⠘⣿⠀⠀⢀⣀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠢⠀⠀⠈⠲⣄⠀⠀⠟⠁⠉⠛⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⡀
⠀⠀⢀⡴⠋⠠⣌⠱⣄⢳⡏⠀⠀⢙⣞⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⣤⠌⣢⡀⠀⠀⠀⠀⡀⠀⢤⣞⠓⠀⠈⡿⠇⠠⠅
⠀⢰⡟⠒⠚⠦⣌⣆⠘⣎⡇⠀⠀⢸⠹⣆⣰⠋⣿⠀⠀⠀⣞⡦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡄⠈⠓⠀⢀⡤⠀⢠⠜⠉⠻⣀⣀⣠⠇
⠀⠀⠙⠦⣄⣀⠀⠉⠳⣿⠇⠀⠀⢸⠀⠙⠃⠀⣿⠴⠚⣹⠋⠀⢴⣏⠩⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡤⠖⠉⠄⠀⠀⢀⣀⢀⣀⣬⠁⠐⢄⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⣿⠭⠭⢭⣛⠲⢤⣠⠏⠀⠀⠀⠾⠋⡜⠑⢩⡟⢛⢶⠲⡶⢶⡶⡖⡻⣏⢹⠙⣄⢰⠺⠆⠀⠈⠒⠚⠲⠀⠀⠀⢰⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⣖⣶⣬⡙⢶⠋⢀⡤⠤⣄⠀⠀⠙⠚⠁⣷⠃⢸⣠⣀⡌⢧⠀⡇⠈⠺⠀⠈⠛⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠸⢆⠄
⠀⠀⠀⢴⠶⠒⠒⠒⢒⡶⠖⢦⠀⠀⠉⠒⠾⠭⠿⠃⢠⠏⡴⠶⣌⢳⠀⠀⠀⣀⣤⣄⡈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠐⡧⠀⣤⣀
⠀⠀⠀⠈⠳⣄⠀⠀⣾⡩⠽⠾⠦⣄⠀⠀⠀⢀⣀⠀⠸⡜⡇⠀⠈⢧⡇⢀⣾⠟⠒⢆⢻⠀⠀⠀⢰⣆⠀⠀⠀⢸⠁⠟⠁⠀⢠⠖⢉⡠⢪⠞⢀⠉⠛
⠀⠀⠀⠀⠀⠈⠳⣄⡿⢤⡠⠔⠒⠚⠻⢦⡀⠈⠻⣍⠲⢵⡹⣄⠰⡘⣷⣾⡣⠂⢀⠌⡼⠀⠠⣠⠤⠙⠀⠀⣀⣠⡤⠤⠄⠀⠈⠀⠉⡜⢁⡤⠃
⠀⠀⡋⢋⠢⡀⠀⡈⠓⠴⠛⢦⣀⠤⠤⠤⢽⣖⠺⠿⣅⣀⡉⠻⣧⣧⣿⡟⠁⣀⣴⡾⠥⣤⠆⠀⠀⣴⡙⠒⠻⣄⠀⠀⢀⠀⠀⠀⠀⢈⡉⠤⠤⢀
⠀⢠⠛⢶⣌⠁⠀⣍⢦⠀⠀⠀⠻⡄⣀⡤⠶⢻⡄⠀⡤⠬⠭⠷⢾⠧⠀⣹⣿⣭⣤⢤⠬⠑⣦⠀⢸⡇⠈⠉⢉⠃⠀⠀⢸⠀⠀⠀⡴⠅⠐⠂⠂⠀⠑⡄
⠀⠀⠶⡒⢆⠀⠀⣈⣟⡀⠀⠀⠀⠻⣥⠴⡖⠋⠀⠀⢷⡀⠀⠀⡸⠀⠀⡀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⢠⠏⢧⣀⢀⡼⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠈⠁⠀⠀⡏⢨⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠉⠉⠉⡇⠀⢀⠋⠉⠉⡏⠁⠀⠀⠀⠀⠘⢦⠴⠃⠀⠀⠈⢩⡄⠀⠀⡇⠀⠀⠂⡀⠀⠀⠀⡘
⠀⠀⠀⢀⡤⠶⠶⡇⣼⠠⠤⣀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⡇⠀⡘⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠎⠀⢀⠠⠀⠀⡴⠁
⠀⠀⠀⢸⠓⠲⠤⠽⠥⠤⠴⢚⠃⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⢀⣠⣿⡤⠄⠀⣆⣠⣁⣤⠶⠊
⠀⠀⠀⢸⣤⠋⠢⠚⣆⡰⠓⡼⠀⠀⢀⡷⢼⣷⡆⠀⠸⠤⠤⠤⠧⢼⣄⣀⣀⡇⠀⠀⠀⠀⢀⣀⡈⠁⠀⣀⣀⡀⠈⠁⠀⠀⠐⢏⡇
⠀⠀⣠⠼⣇⠀⠀⠀⠈⠁⢠⠇⣀⠀⠈⠿⣤⡼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⢻⠋⠉⢉⣩⣭⣓⠊⠈⢩⣑⢂⠀⠠⠀⠀⠀⠀⢀⣄
⠀⠀⠳⢤⣈⣓⠶⠤⠤⢖⣋⣠⠼⠂⢀⡼⠉⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⡰⢹⢋⣭⣭⠳⡄⣿⣼⡛⢠⠁⠀⠀⠀⠀⣸⠀⠙⣻⠷
⠀⠀⠀⠀⠈⠳⣭⣭⡭⠟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⠀⢇⠘⢆⠠⠀⠢⡀⠀⠀⣇⢧⠀⠱⣼⡜⠿⠿⣣⠇⠀⢠⠁⡆⠀⠀⠀⣴⠉⠉⠳⡞⠁
⠀⠀⠀⠀⠀⣠⣴⣖⠲⣄⠀⠀⠀⠀⢀⡀⠀⢘⠱⡄⢄⠈⠢⡀⠑⣄⠑⠳⠀⣘⣶⡦⠙⢾⣦⣀⠈⠉⠓⠚⠁⠀⢠⠃⢀⠀⠀⢀⠾⡈⠑⠦⢤⡞
⠀⠀⠀⠀⡞⢁⠄⠈⣷⢸⣤⡄⠤⠒⢯⢹⡆⠈⠣⡈⠢⢡⡀⠐⣴⣄⠱⣄⠻⠿⠀⠐⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠁⠀⢸⠀⠀⢸⡓⢌⡑⣒⠞
⠀⠀⠀⠀⢧⠈⠳⠴⠛⠁⠀⠀⣀⡤⠞⠋⠀⠀⠀⠈⠢⡀⠶⣿⠋⠙⡀⠈⠑⠂⠄⠊⠀⠀⠀⠀⢠⡀⢸⠙⡆⠀⠀⠀⠸⠀⢴⠋⠝⡲⠚⠁
⠀⠀⠀⠀⠀⠙⠒⠒⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠔⠁⠀⠀⠀⢀⡀⣀⡀⣹⢆⣀⠷⣄⢑⡗⠐⠀⠀⠀⠀⠈⠳⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⡖⠀⠯⠛⠧⢽⡷⣀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣈⡉⠀⡀⠀⣠⣄⠀⠈⠐⠒⠓⣊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡌⢳⡤⣴⢜⡛⢋⡅⠻⣖⡖⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡁⠀⠛⠋⢉⣀⠀⠻⣿⣺⡏⠑⢪⣠⡯⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⡀⣠⠶⠉⠘⠀⠀⠀⠀⠉⠀⠄⢀⠀⠉⠈⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣏⣹⡿⠖⠉⠠⠤⠠⠠⢶⣈⡓⠢⡤⠀⠤⠑⢀⠁⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠉⠉⠀⠈⠁⠀⠀⠃⠂⠙⢟⢷⡀⢀⡠⠠⣈⠉⠀⠈⠛⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⢠⠤⠠⡈⠂⠈⠳⣶⣆⣒⢾⠃
⠀⠀⠀⠀⠀⠨⡀⢠⡼⠠⠄⣠⢦⠂⠀⠊⠀⠀⠀⠠⠀⠁⠀⠀⠘⡆⢃⡈⠀⠏⢦⠀⢇⠈⠉⠉⣉⠇
⠀⠀⠀⠀⢠⠒⣿⠋⠇⠀⠀⢱⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢼⡿⠆⠒⣾⡦⠈⠛⠉⠋⢹⠀⠆
⠀⠀⠀⢠⠤⠹⢿⡴⠺⠆⠀⠐⣧⡀⠠⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⢳⣆⡀⡠⠶⠝⠦⠄⠋⠌⣿⣸⣆⣿
⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⢡⠘⢆⠈⠦⠀⠀⠄⠀⠀⡇⠀⠀⠘⠟⠇⢠⠀⠠⠄⠆⠰⠈⢙⢻⡏⡟⠑⡖⣒
⠀⠀⠀⠀⢐⡄⢘⡆⢀⠰⡂⡈⠪⠁⠈⣷⠄⠀⢤⣄⣀⡤⠰⠀⠈⢀⢠⡄⣠⠀⣠⢂⣠⣰⣦⣰⣤⠇⣥⢾⣶⡇
⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠁⠈⠉⠉⠉⠉⠁⠈⠉⠈⠁⠀⠀⠉⠀⠉⠀⠉⠁⠉⠉⠘⠛⠙⠉⠉⠈⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤
⠀⠀⢸⣿⣷⣿⣿⣿⣿⠿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣲⠿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠈⢻⣿⣿⣟⢉⣿⣶⡿⢏⣻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣟⡹⢿⣶⣿⡉⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠙⣿⣿⣿⡉⠉⠙⠻⡋⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠉⢙⠟⠋⠉⢉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠉⠀⠓⢤⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡤⠚⠀⠉⠉⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠒⠒⠒⠒⠒⠚⠓⠢⣄⠈⠻⣄⢰⡆⣠⠟⠁⣠⠔⠚⠓⠒⠒⠒⠒⠒⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠒⢬⣿⣿⡥⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡿⠿⠿⠿⢿⣛⣻⡿⠿⢿⣿⣿⡿⠿⢿⣟⣛⡿⠿⠿⠿⢿⣿⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡯⠤⠒⢒⡲⠋⠀⠀⡠⠖⣡⣿⣿⣎⠲⢄⠀⠀⠙⢖⡒⠒⠤⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠤⠒⢉⡝⢀⣀⡤⠊⢀⠜⡱⣿⣿⢏⠣⡀⠑⢤⣀⡀⢻⡉⠒⠤⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡤⠚⢁⠏⠁⡔⠁⢠⠊⡰⠁⣿⡿⠈⢆⠑⡄⠈⢣⠈⠹⡈⠓⢤⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⠎⠀⡸⠁⡠⠁⢰⠃⠀⢸⡇⠀⠘⡆⠈⢆⠀⢆⠀⠑⣤⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣷⣾⣧⣴⡁⣠⠏⠀⠀⠘⠃⠀⠀⠹⣄⢈⣦⣼⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡽⢩⣟⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡟⠻⠛⠉⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣴⢁⠔⠋⣀⠽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡏⠀⡟⢁⡠⠚⠁⣀⣼⡿
⠀⠀⠀⣴⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿⠀⢠⠓⠉⠀⣠⣾⠟⠁⣀⣀
⠀⠀⠀⠻⣿⣟⢲⡟⠫⣿⣷⣶⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎⠀⣠⣾⣿⡿⠛⢉⡻⠿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣯⣽⠿⠅⣨⡟⠻⢿⣶⣥⣀⠀⠀⠀⠀⠀⢸⠀⣸⣠⣾⢟⣟⡡⠔⢊⠡⠄⠒⠊⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡤⠤⠝⠲⢤⣀⡉⠛⠻⢦⣄⣰⣶⣾⡶⠟⣫⠔⠉⠉⠁⠉⣳⢶⣒⠉⠉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡒⠂⠉⠁⠀⠉⢉⣉⣽⣿⢿⣿⣷⣿⣒⠒⠒⠒⠛⠣⠤⣀⠀⠉⡳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⣿⣿⣿⣛⡫⠔⢋⠻⣿⣿⡪⢍⠒⠢⠤⣀⡀⠀⢉⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⠜⢫⠀⢀⠆⠘⡘⡝⣿⡁⠛⠦⣄⡀⢈⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠋⣤⡼⡄⠀⢇⠸⣸⢿⣄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⡑⡘⢄⠘⠀⢹⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠷⣷⡾⠁

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⡶⡶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠄⠀⠗⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡈⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠒⠀⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⠌⠉⠁⠒⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠚⠉⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣁⠀⠠⡀⠀⠔⠀⠀⠀⠔⠁⣀⡼⠁⠀⠀⠀⠀⡀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣖⠀⠀⠀⠀⡀⠀⠀⣁⣠⠜⠉⠀⠀⠀⢀⠔⠺⠀⠛⠀⠉⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠲⠖⠒⠊⠉⠀⠀⠀⠀⠀⣰⠛⠀⠀⡔⢁⡀⠀⠴⢊⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠘⢀⠄⠀⠈⢰⣯⠴⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠑⠘⠅⠀⠀⠈⢀⠀⡀⠊⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡜⢠⡀⠀⠀⠀⠀⠀⠀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠒⢠⠐⠀⠰⠖⠂
⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠄⠤⠍⠉
⠀⠀⠀⠀⠘⠈⣧⣸⣇⡘⢰⢲⡄⣿⢰⡖⣦⢰⡄⡦⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠃⠛⠁⠻⠘⠃⠛⠘⠃⠏⠘⠓⠛⠘⠃


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡄⣀⠰⣏⣁⠈⡁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⡄⠈⢺⣗⡤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⣀⣸
⠀⠀⠀⠀⠀⡜⠻⠿⢤⣈⣉⠻⠿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠐⡀⠚⠉⢉⣹⡿⠃⠨⠂⣸⣼⡦⠀⠀⠀⢀⠀⠚⠀⠈⣡⡤⠞⣋⡥⠰⠢
⠀⠀⠀⠀⠀⢳⣦⣴⠚⠛⠛⠲⢦⣄⣙⠿⡁⠀⠀⠀⢀⣼⡟⠀⡄⠂⠈⠉⠑⠋⠉⠙⡉⢹⡿⡆⠀⠀⡴⠀⢀⣴⡋⠤⣤⣴⡃⠀⠀⣰⣷
⠀⠀⠀⠀⠀⠈⠇⠻⠀⡀⢤⣦⣄⠀⠙⢛⡁⠀⠀⠀⠸⣜⠧⢄⣤⡀⠀⢀⣴⣇⠠⠷⠻⣃⡼⠃⠀⠀⢁⡐⠁⢀⣠⣤⡞⠁⢀⣨⠋⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⢬⣿⠝⠛⠁⠀⠀⠀⠀⠀⠈⠿⣄⠠⡌⣉⣤⣤⣤⣶⣶⣿⠟⠁⠀⠀⠀⠈⠠⠶⠟⠻⠁⢠⣦⣼⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠘⣒⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠄⠈⠀⣀⣔⣺⣷⣤⡀⠀⠀⠀⠀⣠⠄⣠⢮⣉⠓⢠⣤⠢⠄⡀⠀⠀⠀⠀⣄⢹⣖⢠⣼⣀⡅
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣴⡶⠿⢉⡍⠠⡟⣿⣷⠀⠀⠀⡜⢿⣶⣧⡀⢻⣿⡅⠻⠤⡀⢺⡢⡀⠀⠀⠐⢄⠈⠀⠀⡅⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣈⢶⠶⠛⠁⠀⠀⠂⠀⡀⢐⣿⣿⣿⠀⠀⠘⢦⣯⡄⠉⡛⠈⠙⠊⡀⠀⠁⠀⣿⡎⠀⠀⠀⠀⠈⠐⠔⠃⠀⠠⠆⢹⣦
⠀⠀⠀⠀⠀⠀⢿⠛⠀⠀⠀⠀⠀⠀⡐⣑⣿⣿⣷⡏⠀⠀⠀⢤⣉⡓⠸⢷⣄⣄⢀⡀⢀⣀⡽⢛⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠈⢦⡀⡀⠀⢀⡐⣤⡝⣾⣷⣾⡿⠁⠀⠀⠀⠀⠹⣿⣷⡖⢲⡨⠩⣭⠭⠤⠔⡿⠁⠀⠀⠀⠀⠀⠀⠸⡆⢐⣄⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢼⣿⠵⠶⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡔⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣲⣿⡟⠉⠉⠉⠙⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠉⠉⠉⠙⣿⣷
⣿⠅⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⢼
⠸⣆⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⢀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡾
⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⣦⣠⣿⣧⣠⡞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉
⠀⠀⠀⠈⢢⡤⠄⠒⠂⠁⠀⠀⠀⢀⣠⠤⠿⠟⠿⢿⣿⣿⠿⠿⠿⠧⢤⣀⠀⠀⠀⠀⠁⠒⠂⠤⣤⠊
⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⣀⣤⠞⠉⠀⠀⠄⠀⠀⡼⣿⡿⡄⠀⠀⠄⠀⠈⠙⠶⣄⡀⠀⠀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⠀⠠⠀⠀⠀⠀⠀⣿⡄⢹⠁⣸⡇⠀⠀⠀⠀⠠⠀⠈⢳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡟⠀⠀⠀⠀⠀⡀⠐⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡔⠀⠠⠀⠀⠀⠀⠀⠀⢡⠀⢠⠃⠀⠀⠀⠀⠀⠰⠀⠐⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠃⢀⠀⢠⠀⠀⠀⣼⠀⢸⡄⡀⠀⢠⠀⢠⠀⢁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⡆⠀⢸⠀⢀⡟⠁⠀⠀⠙⣇⠀⢠⠀⠀⣆⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡶⣾⠶⠿⠃⠀⠀⠀⠀⠻⠷⢾⡶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠈⠉⠂⠠⠠⠀⠀⠀⠀⠀⠀⡄⠊⠀⠈⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠴⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⢀⠀⠐⣌⣧⠄⠀⠀⢀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠿⡦⢴⡋⡀⠀⢸⡀⠀⠀⠀⠀⠠⠾⠁⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠠⠀⠈⠑⠃⠀⠈⢱⢾⡀⣀⣸⣁⣤⣄⣀⡀⠻⣦⠐⢦⠀⢄⠀⠈⢢⡀⠀⠑⢚⢟⡽⢃⡞⡀⠀⠀⠀⠀⠀⠈⣋⡰⢀⣧⡄⠀⠀⡄
⠀⢀⡤⠴⠒⠚⠛⠋⣶⡟⢻⠋⣩⡟⠁⠀⢐⡜⣄⠈⠙⢿⠁⣺⠁⢻⢀⡦⠈⠁⠆⠀⠶⠾⠷⠉⣅⠀⠀⠀⠉⠁⠉⠉⣉⢀⣤⠃⠀⠂⠠⠄
⠀⠀⠀⠀⠢⠄⠖⠂⡨⠊⠁⢻⡟⠑⢀⣠⢯⠊⢇⡀⠀⠈⠓⠋⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⡈⣠⢀⢈⡝⠻⠿⠛⠧⣈
⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⣺⠿⠂⢠⠋⠀⠀⠀⡨⡑⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⡃⢹⠉⠀⠨⢡⡀⠐
⠀⠀⠀⠀⠄⢀⡼⠖⠓⣂⢬⢀⣀⡠⠄⠀⠀⠀⠀⠁⠘⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠺⣥⠇⠰⠐⢦⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠐⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠄⠒⠁⣹⣁⣰⠂⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠿⠩⠖⠻⡤⠿⠥⣴⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡈⠁⣰⠶⡤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠇⠀⠛⠀⠈⠂⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠰⡀⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢣⠱⣤⠟⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⡽⢿⣿⣴⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷⠛⣿⣵⢋⣭⣿⡾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣼⣹⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢾⣿⡶⢻⣿⣯⣀⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣯⣽⣻⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣾⣯⡶⠋⠁⠀⠈⣻⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣷⡇⠀⢹⡟⣷⡄⠀⠀⠀⠀⢰⡿⠛⠋⢻⠏⠀⠀⠀⣠⣶⣿⣿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠙⢇⠀⢸⠉⢹⣿⡄⠀⠀⢠⣿⠀⠀⠀⣿⠀⢀⡴⠞⠋⠁⠈⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣆⢸⠀⢸⠛⢿⣤⣤⣼⠇⠀⠀⢰⣿⠞⠉⠀⠀⠀⢀⣤⣾⣿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡜⣆⠀⢸⣿⠀⣸⠀⢸⠇⣸⡟⠀⠀⢀⣿⠁⠀⠀⢀⣤⡾⠋⠁⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡆⠀⣿⠀⡿⠀⡌⢀⣿⠁⠀⢀⣾⣃⣠⣴⠾⠛⠁⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠹⡄⢸⣦⡇⢰⡗⣿⠇⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⣀⣴⣿⣯⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣆⢿⡇⢸⣱⠏⠀⢠⠞⠁⠀⠀⠀⠀⣀⣴⡾⠟⠛⢉⣙⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣬⣧⡑⣸⡟⠀⠔⠁⠀⠀⣀⣤⣶⠿⠿⠭⠴⢖⡉⠉⠁⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣯⣀⣤⣤⡴⠶⠛⠋⢉⣀⣀⡀⠠⢤⣤⣟⡉⠉⠉⠙⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⠭⢍⣉⡀⠉⠙⠓⠶⣤⣀⠀⠀⠉⠉⠲⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣙⠒⠲⠤⣄⣀⣉⣷⣶⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢲⠛⢶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢟⠟⢡⠂⡰⢹⢻⠟⣦⡀⠀⣠⢞⠏⠍⠀⠀⠀⠈⠀⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠏⡌⡎⢀⠏⢰⠃⡎⣼⢀⢇⢻⣶⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⢉⡟⡏⡼⢸⢀⠞⠀⠀⡸⡐⡏⠸⡌⢠⢻⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠰⡄⣼⢡⡇⠇⣜⠂⠀⡆⢀⡟⢰⠃⣴⠁⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢨⡇⠘⢰⢠⢿⠀⡸⠃⡘⢀⠏⡸⢃⣴⢃⡿⡀⠂⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠁⠀⡆⠌⡞⢠⢡⡶⠁⡞⠀⢀⠏⡈⣼⡇⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠚⠋⣿⡸⠀⣤⠰⢡⠇⡞⠀⠸⢃⡴⢁⡜⣼⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡇
⠀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠤⢀⡀⣿⡇⠀⠇⠀⡏⢰⠇⠠⢟⡽⡠⢊⡼⠃⠠⠀⠹⣆⠠⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠙⠳⢦⣀⠀⠀⠀⠀⠈⠦⠀⢀⡀⠙⣿⠇⡄⠀⡼⣡⠞⠀⡠⠂⣶⣡⢾⡀⠀⠀⠈⠦⢌⢧⡈⢦⡠⠀⠀⠀⠀⠆⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠐⠉⠀⠀⣿⠀⠇⠘⡰⠁⡠⠚⢁⣴⠿⠓⠒⠛⠶⣤⠤⠤⠤⠷⠽⣦⣙⠢⡀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⢹⣄⠀⡰⢁⠜⢁⣤⠞⠁⠀⠀⣤⠔⠊⠁⠀⠀⠀⠐⠚⠃⠈⠳⢤⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⡵⢾⣞⣋⣀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠒⠋⠉⠛⠲⠶⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁