Computer animation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⢠⡶⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢸⡇
⠀⠀⠀⠀⢰⣿⡇⠀⢰⡖⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇
⠀⠀⠀⠀⢸⡜⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⢸⡇⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠈⡇⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⣿⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷
⠀⠀⠀⠀⠀⣿⠸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⢹⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⠤⠾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡈⣷⠀⠘⢧⠤⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣀⣀⣀⣠⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠡⠀⠀⠆⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣷⠿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⢤⡤⠤⢤⠤⠒⢶⠒⠒⣖⠒⠛⡞⠙⣏⠉⢏⠉⢳⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻⡄⠀⠀⣶⠒⠛⠻⡋⠉⢹⡍⠈⣧⣀⣸⣄⣀⣵⡤⠼⣦⠤⠼⡶⠶⠾⡖⠒⢻⠒⠛⡗⠙⣟⠉⢳⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢷⡀⠀⠘⣷⠔⠒⢻⡚⠉⢻⠉⠙⡇⠀⢻⣀⣀⣧⣠⣼⣦⠤⠼⡴⠦⠻⡖⠚⢗⠛⠻⡉⠹⡍⠉⢧⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢿⡀⠀⠘⣧⡤⠤⢷⠔⠒⢷⠊⠙⡏⠉⢯⠁⠈⢇⠀⠹⡄⠀⢹⣀⣀⣹⣄⣸⣦⠤⢵⡤⢷⠤⠚⢇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡄⠀⠸⣆⠀⠈⣧⣀⣈⣧⡤⢽⡤⠼⣶⠒⠚⡗⠛⢻⡉⠉⢹⠁⠀⢳⡀⢹⣄⣀⣧⣀⣧⣤⣼⠆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡄⠀⠹⡏⠉⠙⣇⢀⣈⣧⣀⣱⣄⣼⣤⣤⣼⣤⣤⠷⠶⠶⠷⠚⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢷⡀⠀⠙⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⢀⣤⣤⣤⣤⡤⠴⠶⠶⠒⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠶⠶⠶⠒⠒⣖⣒⣚⣉⣉⣹⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣉⣉⣈⣡⣤⣤⡤⠴⠶⢶⣒⣚⣻⣿⣿⠿⠶⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣷⣤⣤⣤⣤⠤⠶⠶⠶⠚⣛⣛⣛⣛⣉⣭⣭⣭⠭⠵⠶⠶⠚⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠖⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠁⠀⡠⠤⠤⠤⠤⠄⠀⢨⠞⠃⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠉⠩⠭⠭⠭⠽⠶⣤⡀
⠀⠀⠀⡇⠀⠣⠤⠤⠤⠤⠜⠀⢸⠀⠖⠒⠒⠀⠐⠒⠀⠀⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⣀⠀⢣
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠁
⠀⠀⠀⠀⡇⠀⠀⠀⡠⡀⠀⠀⠀⢸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡸
⠀⠀⠀⠀⢰⠀⠀⠀⠉⠀⠀⠀⠀⠀⢇⠀⠂⠄⠀⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⣀⣠⠤⠁⢀⠇
⠀⠀⠀⠀⢸⠀⠀⢰⠁⢱⠀⠀⠀⢰⠀⠉⢒⡤⠤⠤⠤⠤⡤⠤⠤⡤⠤⣤⣤⡤⠤⠤⠤⠊
⠀⠀⠀⠀⠀⡆⠀⠀⠉⠁⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⢀⡇⠀⠀⢇⠀⠈⠯⠷⠾⠯⣷⠖⣒⠶⠦⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠚⠁⠀⠀⢀⡠⠋⠉⠉⠀⠀⠀⠈⠉⠙⢶⢶⠦⡀⠈⠛⢄⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈⢉⣉⣉⣉⣉⣽⢛⣻⣿⣿⣿⣾⣵⣃⣀⣀⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⠘⠃⠐⠂⠒⠂⠐⠖⠠⠶⠀⠤⠄⠤⠄⠠⠤⠠⠄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠥⠀⠉⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠠⠤⠘⠃⠺⢓⡐⠒⠂⠧⠇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠛⠛⠛⠓⠒⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠅⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢠⠀⢌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠒⠠⠀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⢉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠂⠀⠀⠤⠀⠀⡄
⠀⣀⡠⣀⡀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃
⡔⠀⠀⠀⠑⡤⠤⠤⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⠁⠉⠣
⢁⠀⠀⠀⠀⠁⠀⠀⠘⢢⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⡀⠀⠀⠴⠁⠁⠀⠃
⡜⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⡀⠀⠀⠀⣀⠀⢓⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠘⠠⠤⠆⠀⠀⠀⠀⠀⢠
⠀⠈⠑⠀⠉⡋⢀⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠊⠀⠘⠗⠆⠠⠐⠂
⠀⠀⠀⠀⠀⠁⠈⠉⠂⢄⡑⢄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡠⠖⣁⠔⠒⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣅⠢⣇⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⢊⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⢀⠚⠀⡐⠀⠀⡈⠀⠀⡂⠀⠀⠀⠀⡀⠀⢃⠀⠘⣂⠀⠳⡀⠈⢢⡀⠱⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠴⠁⠀⠬⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⡂⠀⠐⠂⠀⠐⡀⠀⠐⡀⠀⢐⣄⠈⢠⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠚

⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣒⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⣼⠋⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡶⠒⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡏⣿
⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⡿
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢸⡇⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣊⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⢀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⢻⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⣙⣛⣛⣛⣃⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠶⣖⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣲⣒⣶⣒⣶⣒⣶⣒⣶⣒⣲⣒⣲⣒⣲⡀⢰⠛⣿⠛⣿⠿⡍⢷⠀⠀⠀⢸⣣⠖⠋⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⡼⠲⡿⠲⠗⠒⡷⠒⢿⠒⢾⠖⢺⠖⠺⡧⠸⡇⠈⣯⠽⣭⠽⣭⠽⡌⢷⡀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢠⣏⣀⣉⣉⣉⣉⣉⣉⣙⣛⣉⣛⣛⣛⣛⣛⣛⣙⣛⣋⣀⣸⣶⣿⣶⣟⣶⣟⣈⣷⠀⠀⠀⠹⣦⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⠧⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠈⠛⠶⠶⠋⠁

⠀⠀⠀⠀⠀⡖⣂⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡆
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠸⢀⠰⠆⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⡠⠒⠀⠂⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠆⠀⠀⠀⠀⠀⠀⢴⠀⠉⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⣇⣑⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⣁⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣓⣒⣒⣒⣒⣒⣒⣒⣒⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠒⠒⠒⠲⠖⠖⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣉⣉⡉⠉⠉⠛⣲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠞⠁⠀⢀⣀⣠⡀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠋⠀⠀⠊⠉⠀⠈⠁⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡴⠁⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⠃⠀⢀⣀⠔⣾⣯⠁⠀⢈⠛⣢⣄⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡸⠁⠀⠀⢀⠯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠃⠀⠀⠓⠒⠒⠤⡅⠀⠀⢰⠀⠙⠛⢣⠀⠀⠀⠀⠀⡜⠀⠀⡸⠁⠀⠀⢀⡎⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠇⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡸⠁⠀⡰⠁⠀⠀⠀⡼⢀⠆⡇⡇⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡼⢰⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⠀⠀⢰⠃⡜⡸⠰⢡⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠇⠀⠑⢤⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡠⠂⠀⡏⠀⢀⠇⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠉⠀⠀⣸⠀⠀⡸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⠓⠦⣄⡀⠀⠈⠑⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⢀⡇⠀⢠⠇⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⠀⠉⠙⠒⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠀⠀⠀⢸⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⣀⣀⢀⣀⣉⠵⠶⠤⣄⡀⠀⠀⠈⠉⠉⠉⠙⠓⠒⠋⠀⢀⡇⠀⠀⠀⣀⢞⠉⠁
⠀⡤⠊⠉⠀⠀⠀⠀⠄⢙⡿⣋⠔⠠⠭⢍⣒⠚⠯⠽⢤⣋⣟⠑⠒⠲⣤⣤⣤⣀⣀⣀⣀⣸⡥⡔⠊⡹⠁⠀⣳⢄
⢸⠀⠀⠀⠀⠀⠀⣠⢖⡡⠎⣀⡀⠁⠐⠁⠰⠪⢨⠝⣀⡰⠒⢨⠉⣑⣚⣒⠚⠭⠭⢭⣛⠑⠒⠚⢋⣁⠤⠚⡝⢢⢳
⠀⠑⠢⠤⠤⢴⡊⠀⠃⠤⢄⣀⠀⠉⠀⠒⠀⠤⢀⣀⠊⢀⠜⢡⠞⠁⠔⠁⣨⠟⠀⠀⠈⢏⣉⣉⣀⣀⠤⠚⡠⢊⠞
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠉⠐⠒⠤⢄⣀⠀⢀⡜⢁⠴⢁⡤⡀⣀⠞⠁⢀⠠⠤⠤⠮⠤⠤⠄⢒⣒⡭⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢄⣀⠀⠩⠁⣐⠣⠤⣀⣀⠜⡡⠊⠀⢈⡩⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢌⣁⠒⠠⠈⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡗⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⡞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄⠀⡇⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠉⠍⠉⠀⠀⢸⠇⠀⠀⠀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡩⢭⡭⢭⡭⠭⣭⠭⢭⣉⣉⣛⣛⣛⣛⣓⣒⡒⠒⠒⠒⠒⣲⠟⠛⠛⠉⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡼⢁⣞⣹⣟⣉⣟⣉⣹⣛⣒⣞⣓⣶⠓⢲⡞⠥⣤⠿⢭⣽⠇⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢠⡞⣠⠧⣤⠯⣤⠏⢀⡼⢁⣠⣏⣀⣜⣁⣨⣋⣉⣝⣉⡽⡷⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢠⠏⠰⣷⣶⣷⣶⣷⣶⣾⣤⣾⢣⣤⣯⣤⣾⣥⣴⡯⢴⣻⠊⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢀⡿⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣈⣉⣈⣉⣉⣁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠁
⠀⠀⠀⠈⠓⠒⠒⠲⠶⠶⠶⠦⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣇⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⣿⣿⣿⡏⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⠈⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⣶⠀⠀⠀⠀⠀⢰⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠤⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠙⠛⠛⠒⠚⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡇⠀⢸⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⡇⠀⣿⡟
⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠁⠀⣨⡇⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣧⡇
⠀⠀⠀⠀⢸⠛⠓⠒⠒⠒⢶⠛⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠏⡇⢸⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⢿⠃
⠀⠀⠀⠀⢸⡆⠀⢰⠀⡇⢸⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣼
⠀⠀⠀⠀⠸⡇⠀⢸⠀⡇⣿⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠦⠃⣿⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡏⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣈⠀⣿⠀⠀⣷⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠚⠀⢸⣷⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠙⠁⣿⢀⣠⠟⢲⠖⠒⠶⠶⠶⠶⠶⣶⠦⠤⠤⠤⠤⣤⣤⢤⡤⢭⢬⡥⠤⠼⠏
⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠛⠋⠀⠀⠻⢄⣀⠀⠀⢠⡴⢞⣉⣉⠉⠉⠉⢭⣫⠇⠀⠳⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⣶⣶⡶⠦⠷⠤⠼⠿⠯⢭⣭⣽⣛⣛⣛⣁⣀⣀⡀⠀⠀⠀⠈⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⢾⣾⣓⣞⣳⡟⢢⠿⢭⠿⢭⠯⣴⣖⣒⢆⣔⣾⣩⣭⡍⢩⢿⡀⢠⠴⢾⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠥⠬⠉⢘⣒⣚⣒⡫⠬⠯⠭⠯⠽⣋⣲⣛⣲⢮⢞⡼⣥⢯⠝⡰⣣⠏⠀⣿⠊⠙⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠲⠶⠦⠭⢭⣭⣍⣐⣒⣒⡒⠂⠬⠭⠭⠯⢭⢎⡴⠃⠀⠀⣿⣄⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠈⠛⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠯⠿⠯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⣾⡟⢛⠛⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠐⠀⡿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⠻⣄⣠⠄⠀⢠⠗⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣈⡟⠀⣄⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣆⠀⠟⢦⣳⠖⠏⢹⠆⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣷⣀⠀⠀⠀⠀⡿⠄⠐⢘⣈⠐⠀⡃⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⠿⠷⠟⠛⠛⠛⠻⠿⠿⠽⠯⠿⠿⠿⠭⠿⣽⠿⠽⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠩⠒⠻⠟⠿⠛⠿⠳⠦⠅⢘⣊⣐⣦⣭⣼⠿⠿⠿⠿⠿⠿⠿⠞⠳⠌⠢⣄
⠀⠀⠀⠀⠀⢠⣴⠩⠤⢤⣤⡤⡤⠤⣤⡤⣤⣤⣤⢤⣯⡽⡽⣿⠿⡾⢤⢤⡤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣵⣦
⠀⠀⠀⠀⠀⠈⠛⠚⠛⠛⠛⠓⠚⠚⠛⠛⠓⠛⠛⠛⠛⠚⠒⠛⠛⠓⠚⠛⠚⠓⠛⠚⠛⠛⠛⠓⠚⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡶⢶⢶⢶⠶⡶⡶⢶⢶⡶⠶⡶⡶⡶⢶⠶⡶⡶⢶⢶⠶⣇
⠀⠀⠀⠀⠀⠀⣠⢞⢑⠛⠗⡛⡻⣻⢚⠟⡱⠫⠞⠸⠇⠳⢻⡙⡊⢳⠓⡙⡚⡎⢛⢊⢧
⠀⠀⠀⠀⠀⢾⠓⠒⣶⡖⠒⠲⠶⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠖⠒⠚⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⠖⠚⠛⠋⠉⠉⠙⠓⠒⠲⠶⢤⣀⡀
⢀⣤⣤⠤⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠒⠊⠉⠉⠀⢹
⡇⠀⠀⠉⠐⠒⠤⢄⣀⣀⠠⠤⠖⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⡖⠒⠂⠤⠤⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀
⣷⠙⠢⠤⠤⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣴⠛⠛⠛⠓⠒⠛⠉⠩⠭⠭⠍⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠩⠭⢭⢍⡙⢦
⢸⠀⠐⠒⠂⠤⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠠⠒⠒⠀⠠⠤⠤⠄⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠈⢁⣀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢
⢸⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⠇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡆⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⡇⠀⠀⠀⠀⡅⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡇⠀⠀⠀⠀⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⢣⠀⠀⠠⠒⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⠀⠀⠘⠒⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⣿⡙⡇⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠸⣄⠀⠐⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠉⣀⠠⣴⡿⢁⢧⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠒⠠⠦⠤⠴⠃
⠀⠀⠈⠓⠶⢤⣀⠀⠀⠀⡇⠀⣀⣀⣠⡤⠤⠶⠒⠋⠉⣀⣀⣀⡤⢂⣭⡴⠞⣻⠞⠓⠋⣉⣉⡻⢿⣶⣶⠖⠒⠶⡶⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⡰⣋⠥⠶⣏⡀⠙⠓⣚⣛⣛⣭⠭⠽⠖⠒⠋⠉⢁⡤⠤⠤⠤⣟⡀⠀⣫⣀⣀⠈⠦⢬⣷⣒⡺⠭⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⠤⠴⣶⡶⠿⠛⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣔⣁⣀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⡷⠀⠀⠉⠓⡌⠱⡄
⠀⠀⠀⠀⠀⠀⣀⡤⠶⢯⡉⠉⡎⢳⠋⠉⠀⠀⠀⣠⢖⡒⡒⠂⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠒⠊⠀⠀⠀⢀⣠⠇⠀⡇
⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠉⣉⡤⠞⠀⠀⠀⢀⠜⠁⣜⡖⢁⢙⠘⢀⣂⠒⠐⠒⠆⠀⠦⠄⠠⢤⠄⣭⣉⢉⣉⠉⠙⣶⣒⠒⠲⠶⠶⠶⠒⠒⠋⠉⠀⣀⡴⠁
⠀⠀⠀⠀⠻⣄⣀⣀⣀⠴⠊⠁⠀⠀⠀⢀⠔⢁⣀⡛⠃⢀⣦⠆⠠⠯⠈⢠⣬⠙⢁⣐⠒⠂⠠⠶⠄⢀⠤⣄⠀⡠⢊⡼⠉⠉⠉⠉⠛⠛⠒⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⡧⢀⣈⡁⠁⠈⠋⠩⠭⠭⠍⠁⠲⠖⠒⠂⠀⠰⠐⣓⣐⡁⠉⠴⣡⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⠤⠬⠭⠭⣭⣉⣀⣒⣒⣒⠒⠒⠒⠒⠂⠠⠭⠭⠥⣀⣔⡵⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠚⠛⢻⡧⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠀⠀⠰⣛⡧⢨⡇⠀⠉⠓⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣀⣤⣤⡤⠴⠶⢦⡄⠀⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⠦⠤⠤⠴⠶⠶⠞⠃⢀⣷⣀⣀⣤⣤⠴⠶⠖⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠙⣯⠉⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣤⣤⠤⠶⠒⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠶⠶⢶⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣠⣤⠶⠶⠚⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠉⠉⢈⢵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⠀⠐⡃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠶⠶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⡷⠀⠀⠀⠀⢀⣠⠶⠞⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⣀⠀⠀⠀⠀⠉⠙⡿⠒⠶⠶⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⣤⠞⢻⡥⢤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠉⠙⠓⠲⠶⢤⣤⣳⣤⣤⣤⣤⣤⣄⣀⣈⡉⠙⠛⠳⠶⠶⣤⣤⠶⠚⠓⠋⠉⠀⣠⠞⠁⠀⠀⠀⠉⠳⣤
⠀⠀⣀⠴⠊⠉⠀⠀⢀⡤⢶⣙⣶⠶⣀⡀⠀⠀⠀⣠⠔⠀⠀⠉⠉⠙⠛⠒⠶⠤⢭⣭⣙⣛⠒⠒⠒⠲⠶⠶⠶⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⣼⠁⠀⠀⠀⠀⠚⠛⠶⠾⣉⠽⠛⠉⠀⢠⡴⣯⣷⢛⣧⠶⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠛⠓⠲⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠓⠲⠤⣤⣀⡀⠀⠀⠈⠁⠀⠀⠀⠙⠙⠺⣥⠼⠋⠁⠀⠀⠀⠀⣠⠶⣛⡷⣶⣤⣂⡀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠇⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣄⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠜⠛⠧⢮⣥⣛⣩⠞⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁⡾⠀⠀⠀⠀⠰⠿⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠶⠤⣤⣄⣀⣀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢀⣠⠴⢋⣀⡤⠾⠃⠀⠀⢀⣀⣤⡤⢤⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⣤⣄⡀⠀⡴⣚⣭⠶⠚⠉⠁⠀⠀⢀⡤⠞⠛⠳⢤⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣆⠠⠖⠀⠀⢹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠒⠦⠤⢤⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⠶⠯⣭⣤⣤⣄⣀⣀⣠⠴⣲⣿⣛⣋⣉⣀⣀⣀⣀⠉⠉⠉⠉⠉⠛⠒⠒⠲⣤⡄
⠀⠀⠀⠀⡇⡐⠒⠒⠒⠒⠒⠠⡀⡿⢸⡇⠀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⡉⠉⠛⠓⢲⡏⠀⡇
⠀⠀⠀⠀⡇⡨⠭⠭⠭⠭⠉⢉⠀⡇⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡷⠀⢸⠁⢸⠟⡆
⠀⠀⠀⠀⡇⠑⠒⠒⠒⠒⠒⠊⢠⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡾⠀⢸⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⡟⢰⠇
⠀⠀⠀⠀⣧⠀⠘⠋⠒⠒⠂⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⢀⡇⣸
⠀⠀⠀⠀⢻⠀⠀⠀⣀⠀⠀⠀⡿⠀⢸⡀⠘⠒⠒⠶⠶⠦⠤⠤⠤⠤⠤⣤⡼⠀⣸⠀⣸⠖⠃
⠀⠀⠀⠀⢸⡀⠀⠀⠒⠁⠀⠀⣇⡴⠋⠛⠓⢲⢖⡶⠒⣶⡶⠶⠤⢤⡤⢤⡤⣤⡿⠞⠁
⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⡛⠉⠀⠀⠀⡊⠁⠸⣧⣤⣀⣉⣉⣉⣉⣤⡾⠀⠈⠒⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡩⢭⢭⠭⡭⢭⢉⡉⣛⣓⡒⠛⠻⠿⠯⠭⣭⣁⣀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⡼⡰⢥⠯⡯⣹⣩⣏⣞⣱⡓⡞⢺⢡⢮⠏⣴⣰⠂⡰⣹⠀⠀⣠⠖⣻⠟⠙⣆
⠀⠀⠀⠀⠀⠀⢸⣥⣍⣉⣚⡒⣓⣒⡒⠀⠧⠼⠥⠃⠎⢞⣲⣲⢃⢜⡴⠁⠀⡼⠉⠉⠉⠒⢤⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠒⠾⠿⠭⠭⢤⣄⣒⣲⡾⠋⠀⠀⠀⢷⣄⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠛⢛⣛⣋⡛⠛⠛⠻⣆
⠀⣠⠖⠛⣛⣉⣉⣉⡉⠥⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠋⠙⠛⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠳⡄⠀⢹⡄
⣰⠿⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⣇
⣯⢸⡄⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢿
⢿⠈⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡆
⢸⡀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣇
⠸⡇⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿
⠀⣧⠸⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡆
⠀⢻⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣇
⠀⠸⡇⢻⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢻
⠀⠀⣷⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡆
⠀⠀⢹⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇
⠀⠀⢸⡇⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿
⠀⠀⠈⡇⢿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿
⠀⠀⠀⣿⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠃⢀⡟
⠀⠀⠀⢹⡘⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⠖⢚⣛⣉⣉⣀⣠⣤⠤⠶⣿⡁
⠀⠀⠀⠘⣇⡇⠀⠹⣄⣀⣀⣀⣀⣠⣤⡤⠶⠒⠛⠋⣉⣉⣉⣉⡤⠤⠤⠤⠴⠒⠒⠛⠋⠉⠉⠉⠉⠁⢀⣀⣀⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠙⢿⣦⣤⣀⣉⣤⡤⠤⠴⠶⠖⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⢴⡖⠛⠛⠻⡁⠈⢙⣦⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢸⠻⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⡤⠤⠶⠶⡖⠚⠋⠙⣏⠉⠀⣙⣦⡠⠤⠷⣄⠒⠚⠙⢯⡀⣀⣙⣦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢻⠀⠱⡄⠀⠐⣏⠉⠉⠉⢯⡁⠀⠀⢈⣦⣀⠤⠤⠼⢶⠒⠒⠙⢏⠉⠁⠀⣳⣄⣠⠼⢶⡒⠚⠉⠻⣌⢀⣀⣙⣦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠘⣧⠀⠹⡄⠀⠈⢦⡤⠴⠖⠻⡛⠉⠉⠁⢳⡀⠀⣀⣨⣧⠴⠶⠚⢷⠉⠉⠉⠙⣄⣀⡤⢷⡖⠒⠚⠙⢯⣁⣀⡠⠽⢦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠹⣄⠀⠀⢳⣀⣀⣠⣽⠶⠒⠊⠉⠻⡅⠀⣀⣸⣦⡤⠤⠘⠳⡒⠈⣉⣉⣧⣤⡤⠿⠶⣖⠋⠉⢁⣀⣀⣠⣤⡽⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⣆⠀⠀⠹⣅⣀⣨⣧⠤⠖⠒⠈⢻⡉⠁⣀⣈⣧⣤⠴⠶⠛⠛⠉⣉⣠⡤⠴⠖⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⢆⠀⠀⠘⢇⣀⣸⠧⠤⠶⠒⣚⣟⣋⣩⣥⣤⠤⠤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠘⢆⠀⠀⠈⠷⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠒⠚⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡤⠤⠶⠚⠛⠉⠉⠀⠀⢀⣀⣀⣤⠤⠴⠶⠖⠚⢛⣉⣉⣥⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⢒⣒⣂⣉⣩⣥⣤⡴⠶⠶⠒⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⢦⣀⣀⣀⣀⣀⣤⠤⠴⠶⠒⠒⠚⠉⣉⣉⣡⣤⠴⠖⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣬⣭⣥⣤⣤⣤⡤⠴⠶⠒⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⢀⣀⠀⢀⠀⣀⣀⡀⡀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠒⠒⠒⡄⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠘⠒⠐⠒⠒⠒⠒⠂⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⢸⢠⣀⣀⣀⣀⣀⣀⣀⣀⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⣀⣀⣀⣀⣀⢀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡸⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠠⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣀⣒⣒⣒⡒⣂⣀⣀⢀⠀⠀⠀⠀⠀⠒⠒⢒⡲⢁⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢨⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⠸⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠦⣤⣤⣤⣤⣤⣤⣤⣴⠴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠉⠉⠀⠀⠀⠈⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⡉⠉⡉⠉⠉⠉⠁
⠀⠀⠀⡔⢀⠀⠠⢀⠀⢀⡀⠀⣀⠀⢀⡀⠀⡀⠂⢀⠀⣀⡀⠀⣀⣀⢀⡀⡀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠀⡀⠠⠀⠀⣠⠈⢠⡤⣄⠀⠑⣄
⠀⠀⡼⠀⠦⠤⠤⠬⠤⠦⠡⠴⠌⠠⠄⠥⠴⠭⠥⠤⠥⠤⠬⠤⠬⠥⠬⠭⠴⠤⠤⠤⠅⠰⠨⠄⠀⠠⠀⠸⠄⠣⠀⠈⠓⠓⠲⠬⠦⠤⠊
⠀⠀⠳⠖⠲⠒⠒⠒⠶⠲⠖⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠖⠲⠒⠒⠒⠲⠒⠒⠶⠒⠒⠒⠖⠶⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠀⢄⡠⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠐⠒⠂⠴⠉⠀⢀⣀⢄⣄⢠⢠⡀⢁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠄⠀⡀⠀⠀⠀⠀⠀⡍⠒⠒⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠓⠈⡁⠀⠀⠀⣤⠄⡱⠀⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢀⠝⢀⠔⠊⠠⡞⠁⠈⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠐⠄⢆⣐⠂⡄⠘⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠒⠒⠂⠀⠀⠂⢀⣀⣒⡄⠀⠀⠀⣝⡱⠁⣴⣒⣒⣒⣂⣶⣶⣿⣟⣖⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⢀⠀⠉⠩⠉⠉⠉⠉⠉⠁⠀⠀⠀⢧⠀⠀⢸⡈⠀⡞⠁⠀⠀⠀⡰⠀⢠⠞⠠⡡⡱⢩⡵⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⠆⣠⠇⠀⠀⠀⡔⡔⣰⠋⣐⠞⡜⡠⣫⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⣰⠏⠀⠀⢀⢎⠜⣜⠃⣼⢋⠌⡐⡱⣹⣫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢾⠁⠀⠀⢠⡞⢡⠂⢢⢠⢌⠎⠜⣐⠝⣼⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⠖⢻⠀⠀⣰⠟⡰⡡⡡⢡⢂⢊⠎⢌⢎⢎⢾⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⢹⡄⢰⢏⠔⡔⡔⠠⠡⢣⢊⣪⢣⢪⠪⣻⢞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⢠⠃⢰⠀⢊⠊⠌⡠⡡⡣⠁⠂⡡⠢⡱⡡⣹⢣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢁⢖⠀⠢⢁⠎⡔⠔⠔⡰⡁⠰⠘⠔⡐⡐⣹⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⡠⡣⠠⡐⢠⢃⠌⢌⠎⡔⡰⠌⠰⢎⠜⠜⠔⣽⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠊⢳⠀⢀⠜⡐⡁⡑⡰⠡⢢⢊⢊⢌⢔⠔⠀⠁⢊⢌⢎⢘⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⡁⠤⠤⠤⠤⠤⠤⠤⠤⣀⣎⣌⣨⣈⣠⣠⣥⣁⣁⣈⡨⣬⣬⣤⣤⣤⣤⣤⣴⢞⣘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡦⢴⣒⣒⣲⠀⠀⠀⠀⠒⠒⢷⣷⣷⡳⣷⣖⡷⣾⣗⣾⣺⣾⣶⣷⣶⣻⣿⣶⣲⣿⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣞⣉⣉⣉⣏⣉⣏⣉⣏⣩⣍⣩⣉⣽⣭⣍⣿⣩⣍⣻⡉⣉⣍⣙⣭⣽⣽⣿⣽⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡚⠀⠀⠀⠀⠠⠀⠀⠽⢠⡭⣬⠅⡬⢭⠹⡏⢿⠅⡿⠸⠏⠙⠋⠉⠭⠙⠁⠀⠀⠀⠀⡂⢛⣙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⢀⣀⣀⣐⣒⡖⢲⢚⡖⢳⡒⣳⣚⣖⣳⣞⣳⣞⣲⣛⣛⣻⣙⠙⣯⠉⠁⠀⠘⡍⠉⠄⢿⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣄⣀⡀⠼⠤⠯⠼⠤⠼⠤⠤⠤⠤⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⣬⣧⣤⢤⡤⣄⠴⣖⠶⣲⣲⡲⢾⡳⢧
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢣⠀⠙⠶⣕⡮⣢⢕⠢⣑⠬⣙⠿⣷⣮⣙⡆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠛⢾⣶⣍⡢⢕⠢⣑⠢⣙⠿⣷
⠀⠀⠀⠀⠀⠀⠀⣅⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠧⠀⠀⠤⠠⠤⠄⠐⠒⠒⠒⠚⠀⡀⢀⣀⣀⣈⣻⣝⣶⣭⢦⣵⡦⡷⣾
⠀⠀⠀⠀⠀⠀⠀⠙⠿⢟⣝⣹⣳⣊⣿⣏⣟⣙⣩⣋⣟⣝⣙⣩⣋⣟⣝⣹⣻⣋⣟⣟⡯⢎⠌⠥⠽⠿⠏⠘⠓⠛⠓⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⣀⣀⠄⢀⠄⢀⠠⡀⠄⡀⠄⡢⢄⠀⡠⢂⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⡀⢔⡂⠄⣈⠄⣀⠀⢂⠉⢀⠈⢀⠲⢂⠩⠐⡨⢄⣨⡔⠎⡡⠔⡨⠔⡠⠀⠠⠀⠤⠒⠄⠈⠐⠁⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠉⠀⠈⠀⠈⠀⠀⠀⠈⠁⠈⠁⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢶⡦⠤⠤⠤⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡿⠻⠿⠿⠿⠿⠿⠿⠻⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢚⠃⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣙⡁⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣬⣥⣿⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠁⢙⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠴⠶⠶⢦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡿⠥⣽⠥⢼⠯⢬⡯⠬⡿⠭⣿⠥⢽⠥⢽⡯⠬⣯⠬⢿⠤⢽⡭⠽⣷⠀⠀⠀⢸⣀⣠⣄⣀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⠿⢿⡿⢿⣿⣿⠀⠀⠀⣾⠓⠒⠛⠒⣿⠒⣺⡓⢺⡟⠒⣿⠒⢺⡗⠚⡗⠒⠛⠒⢻⡗⠚⣷⠒⢻⣇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣤⣾⣦⣼⣧⣼⣿⣿⠀⠀⢰⣏⣉⣽⣉⣹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣄⣈⣿⣉⣹⣏⣉⣿⡄⠀⠘⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢦⠀⠀⠀⠀⡇⠂⠀⠀⠀⠒⠀⢲
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡧⠄⠠⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⠄⠀⠀⠀⠤⠤⢨
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠀⣷⡀⠀⢀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠁⠀⠆⠀⠐⠀⠀⠀⠀⠀⠊⠁⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡀⣀⣀⣀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠚⠓⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠤⠤⠤⠤⠊
⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⢀⠀⣀⢀⢀⡀⡀⠀⠀⢀⠀⠀⠀⡀⠀⡀⠀⠀⢠⠈⡥⣄⠀⢆
⠀⢰⠁⠒⠒⠂⠒⠂⠒⠀⡒⠒⠂⠁⡃⠁⠀⠐⠒⠐⠂⠒⠒⢒⣀⠒⠂⠀⠂⠐⠀⡀⠈⠉⠑⠚⠒⠊
⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠁⠉⠀⠁⠉⠁⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡟⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠤⠤⠤⢀⠄⠀⠀⠠⠀⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⡀⢀⠀⠉⢑⡄⠁⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠒⠒⠭⠈⠃⠀⢸⠀⠀⡇⠀⠀⠤⠤⠤⢤⣄⣤⠧⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⠇⠀⡆⠀⢒⣒⠒⠀⠄⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠛⠉⠁⠀⣸⠀⡎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⢲⡒⠒⣒⣒⣒⣒⣒⣒⣶⣒⡛⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢘⣋⣉⣉⣉⣉⣉⣉⣉⣟⣉⣉⣀⠀⣇⣀⣀⣀⡀⠠⠠⠤⠤⠤⢤⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠂⡈⢉⠉⡏⢹⢹⠛⡛⣛⢻⠋⠉⠁⠀⠀⠉⠝⢏⠩⠭⣿⠿⠿⠤⣀⡆
⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠠⠠⠤⠤⠤⠤⠤⠤⠤⠠⠄⠀⠀⣠⣄⣈⣀⠘⣆⠀⠯⠤⠤⢄⢀
⠀⠀⠀⠀⠀⠀⠣⣀⣒⣒⣒⣒⣂⣀⣀⣐⣂⣐⣀⣀⣀⣒⣒⣒⣒⣒⣒⣀⣀⣒⡘⠀⠀⡀⢀⣀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠒⠂⠀⠰⠀⠀⠀⠀⠀⠩⠭⠭⠭⠭⠤⠍⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡘⣹⡇
⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡰⠀⢻⡃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡰⢡⠁⠼⣳
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢠⢣⠃⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢠⢣⠂⠀⡔⢸⣿
⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⢃⠇⢀⠀⢀⠸⣯
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠤⠂⠀⠀⠀⠠⠆⡿
⠀⠀⠀⠀⠀⠀⠀⡣⠀⠦⠄⠀⠀⠀⠀⠠⠤⢼⣼⣧⡯⣽⣿⣯⣿⣿⣿⣿⣿⣽⠿⡿⠯⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⣀⡀⡐⣀⣂⣘⡁⢙⣉⣙⡉⠍⣊⡩⣉⡉⠉⡉⢉⠑⣌⢆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠠⢁⠠⢁⠠⠤⠤⠤⠄⠄⠄⠤⠀⢌⢶⠦⡡⢄⡀⠀⡀⠤⠊⢣⣃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡂⠈⠀⠈⠀⠐⠒⠂⠂⠀⠒⠐⠒⠒⠒⢒⡚⠓⢴⡢⠈⠒⠲⢒⢻⢆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠁⠨⠉⠉⠙⠨⢍⠉⠊⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠁⠢⢀⠀⠈⠀⠈
⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠒⠒⠒⠒⠒⠂⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⡄
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠋⠛⠉⠚⠛⠛⠙⠛⠋⠛⠛⠛⠃⠛⠛⠋⠛⠙⠋⠋⠛⠛⠃⠛⠛⠛⠛⠉
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⢿⣶⣶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠤⠤⣤⣀⣀⡉⠉⠙⠛⠿⠿⣷⣶⣶⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠀⡟⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣤⣀⣉⠉⠛⠚⠿⠿⢷⣶⣦⣤⣄⣀
⠀⠀⠀⣀⣠⠤⠖⠛⠉⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⣤⣀⣈⡉⠉⠛⢿⢷
⣴⣾⣋⣉⠀⠀⢀⣠⠴⠒⢻⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡇⠀⡟⣸
⡇⠀⣀⡉⠉⢻⠉⠀⠀⠀⡿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⢃⡇
⣇⠀⡏⢹⠀⢸⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡾⢸⠁
⣿⠀⣿⢸⠀⢸⠀⠀⠀⢸⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⡟
⢿⠀⣿⢸⠀⢸⡆⠀⠀⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⢸⠇
⢸⠀⢸⢸⡄⢸⡇⠀⢀⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡇⡾
⢸⡄⠘⠾⠇⠸⡇⠀⢸⠃⠈⠙⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣼⣸⠇
⠘⡇⠰⣿⡇⠀⡇⠀⠈⠙⣒⡶⢤⣀⡀⠀⠈⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⣏⡿
⠀⠙⠲⠦⢤⣤⣧⠴⠞⠋⠁⠀⠀⠀⢉⣽⠶⠦⣤⣀⡀⠀⠈⠉⠛⠲⠦⣤⣀⣀⠀⠀⢀⡏⠀⣼⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠯⣭⣙⡓⣶⣤⣄⣀⡀⠀⠉⠉⠛⠚⠁⢠⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⢹⡟⠓⠶⠤⣤⣀⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣍⠳⠦⣄⣀⡀⠀⠀⠀⠀⢀⣠⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠬⣭⣭⣛⣛⣛⣭⠴⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠒⠒⠒⠒⠀⢄
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⢡
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠢⠀⢀⣀⡀⠀⠠⠂⠄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠏⠉⠉⠉⠩⠽⠿⠿⠿⠿⣷⠀⠀⠂⠀⡠⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠦⠂⠀⠀⢀⢂⠄⢎⣡⠀⠀⠀⠀⠀⢰⡠⠤⠔⠀⠀⠀⣿⠀⠤⠄⠊
⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠑⠢⡀⠀⠄⠀⠀⠰⠾⡀⢸⠣⠃⠀⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⣿⠀⠀⡠⠀⠂⠈⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠉⠀⠀⠀⠈⠄⠀⠀⠀⠀⠢⣙⡓⠂⠄⠀⠀⠀⠀⠠⡳⣴⠣⠄⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⡁⠀⠀⠉⠉⡡⠀⢄⠀⠀⠁⠈⠉⠉⠁⠉⠉⠍⡉⠉⠁⢸⠀⠂
⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⢀⡀⢎⠀⠀⠀⠀⢐⠒⠐⠄⠀⠀⠀⠀⠀⠀⢈⠊⠀⠓⣤⠀⠀⢸⠀⠈⠂⠀⠀⢀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠆⠈⠀⠀⠀⣠⣄⣤⡀⠀⠀⢰⠀⠀⠈⡳⢄⠴⡓⠀⠀⢸⠀⣠⠊⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⣀⣀⣀⣒⣠⣬⣦⣤⣴⣤⣤⣤⣬⣦⣶⣤⣥⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠤⠠⠄⠀⠄⢠⠈⡗⡺⣾⣽⣧⣗⣛⣗⠒⠚⠛⠛⢭⡷⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⡤⠬⠤⡅⢭⠸⡅⢯⠿⣿⢹⡿⣤⠀⡤⠕⣀⠱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠤⠤⠤⠤⠤⠍⠉⠁⠨⢭⣁⣉⣉⣩⠭⠽⠬⢤⢬⠭⣬⣥⣭⣿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣁⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣁⣠⣠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢰⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⣿⠂⢀⠀⠀⢀⠀⠀⣺⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣟⢿⣻⣿⣿⣿⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⣿⣟⡛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⢰⣖⣖⣖⣾⣷⣶⣶⣲⣲⣲⣶⣖⣖⣖⣶⣶⣲⣶⣲⣲⣲⣲⡆⣾⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⡇⢹⣿⣿⣷
⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⡇⠀⠙⠛⠁
⠀⠀⠀⠸⠯⠿⠭⠯⠭⠽⠿⠿⠿⠿⠿⠭⠯⠯⠿⠿⠭⠭⠭⠽⠭⠽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⢀⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⡀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⣠⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⡠⠐⠉⠀⠇
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⣁⠄⠊⠁⠀⠀⠀⢀⠅
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⡠⠐⠉⠀⠀⠀⠀⢀⠤⠂⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⣁⠄⠂⠁⠀⠀⠀⠀⡀⠀⠈
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⢀⠠⠒⠁⠀⠀⠀⠀⢀⡄
⠀⠀⢸⡀⠀⠀⠀⢀⡠⠐⠉⡀⠔⠊⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⢄⡠
⠀⠀⢸⡇⠀⠤⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⣀⡤⠚⠉⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠔⡀⠀⢀
⠀⠀⠸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠈⣀⠄⢒⡠⠐⡀⠄⠈
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⣋⠄⢂⠡⠂⠁
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠄⠔⣠⠄⣀⠉⠒⡈⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠠⠀⠢⠄⢀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠧⠶⠶⠶⠒⠒⠶⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠈⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠒⠛⠉⠉⠉⠉⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠠⠄⢀⡄⠀⠤⠀⠤⠄⠀⠤⠄⠠⠤⠀⠤⠄⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣐⡒⠀⣒⡂⢐⡒⠀⣚⡃⠀⣛⡁⠀⣉⡁⠈⠭⠄⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣒⣒⣒⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠘⠷⣖⣒⣒⣒⣒⣒⣒⣒⣒⣒⣈⠉⠉⠭⠭⠭⠭⠭⠭⠭⠭⠿⠿⠿⠿⠯⠭⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢉⣉⣁⣀⣄⣒⣒⣒⣒⣂⣐⣂⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢀⡀⠀⡠⠐⠀⢀⣉⠁⠐⢄⠀⠀⣠⢘⠃⠀⠀⠀⠈⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⡄⢘⢈⣅⠊⢀⠔⠉⡀⠀⣉⡆⠠⠆⠀⣭⢰⡆⠀⠀⠈⠀⡅⣺
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢼⠀⠀⡆⠼⠀⡀⠀⠼⣀⣀⣀⣀⣤⣰⣀⣼⡆⢠⠠⠆⠀⢀⠀⠀⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⡃⣒⢘⠀⠀⠐⠀⠀⢠⠠⡄⠀⠀⠀⠁⠃⠀⠀⠄⠀⠶⠀⠄⠖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠁⣭⢘⠀⠀⠀⠀⠀⢸⣅⡎⠀⠀⠀⠀⠗⠀⠐⠇⣄⠺⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠄⡇⠀⠰⠄⡄⠀⠀⠀⣼⡥⣷⠀⠀⠀⠀⡄⠀⠀⠂⣉⠀⠈⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠰⠀⠀⢇⡄⠀⠀⠃⠛⠙⠡⠖⠛⢅⠀⠀⢀⡇⠉⠀⠀⠁⠁⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣁⣉⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠶⠤⠶⠶⠂⢀⡈⠛⣿⣛⣟⣯⡿⣿⣿⣿⡺⢻⣺⣖⣶⡷⡿⡿⢿⣭⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⠀⠀⠠⠴⠤⠴⠤⠴⠤⠾⠦⡮⢠⠰⢤⠠⢄⠠⢄⡀⣄⡰⡄⠀⣀⢸⣕⡀
⠀⠀⠀⠀⠀⠀⠐⡐⠀⢀⠀⣐⣀⣱⢀⡑⣈⣱⠀⣱⠈⡒⠉⣎⢓⣜⢲⡚⠒⠆⠲⢶⠒⢦⠐⠃⢘⣇⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠒⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣶⣤⣤⣤⢤⣤⣤⢤⣄⣷⡇
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⢀⡄⠈⠒⢤⡑⢌⡓⢤⡀⠈⢗⠤⢺⠠
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠀⠈⢡⠀⠀⠀⠉⠲⢌⠒⢌⡓⠄⣌⡳⠅⠆
⠀⠀⠀⠀⠙⠛⠿⠭⠽⠯⠟⠝⠝⠴⠵⠴⠶⠔⠶⠲⡶⡶⡖⡖⡔⡖⡖⠶⡶⡶⢶⢾⢿⡾⡶⡳⡶⠿⠗⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠤⠤⠤⠴⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠚⢛⣛⣉⣉⣉⣉⡉⠛⢳⡄
⢀⡶⢋⣩⠭⠥⠤⠄⠀⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⡄⠀⣧
⡾⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⢳⠀⢸⡀
⣧⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢀⣽⠆⠀⠀⠀⠀⠸⡄⠘⡇
⢹⠸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠀⣞⠀⠀⠀⣀⠀⠀⠀⢇⠀⣷
⢸⡄⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⠀⠀⠀⠙⠲⠶⠞⠙⡆⠀⠀⢸⠀⢸⡀
⠀⡇⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣴⠀⠀⠘⠀⠀⠀⠀⣠⠇⠀⠀⠈⡇⠘⡇
⠀⢿⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⢀⡴⢋⡠⢊⠝⠁⣀⠴⠛⠶⠤⠖⠋⠁⠀⠀⠀⠀⢱⠀⣷
⠀⢸⡄⡇⢣⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠋⠰⡫⠞⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡄
⠀⠈⡇⣇⢸⠀⠀⠀⠀⠀⣿⢀⡤⠤⢤⡀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡇
⠀⠀⣿⢸⠘⡇⠀⠀⠀⠀⠘⠋⠀⠀⢨⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧
⠀⠀⢸⢸⠀⢇⠀⠀⠀⠀⠀⠀⠰⣖⠋⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⢸⡎⡇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠞⢀⡟
⠀⠀⠀⣇⠇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠴⢒⣒⣋⣉⣉⣠⠤⠴⠖⢾⡁
⠀⠀⠀⢻⣴⠀⠹⠤⠤⠤⠤⠤⠶⠖⢚⣉⣉⣭⡤⠤⠤⠖⠒⠒⠒⠋⠉⠉⠉⠁⠀⣀⣀⣠⠤⢤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⢹⣷⠲⠶⠖⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠴⢶⠒⠚⢏⠉⣀⡱⣤⠤⠽⢦⡀⠀⠳⣄
⠀⠀⠀⠀⢸⠉⢦⠀⠀⢠⠤⠴⠲⡖⠒⠒⠒⢟⠉⠉⣙⣧⣀⡀⠵⡤⠔⠚⠳⡉⠉⠻⡀⣤⠬⢷⡴⠒⠛⢦⡀⠈⠳⣄
⠀⠀⠀⠀⠘⣆⠈⢧⠀⠈⢦⣀⣀⡼⣦⠄⠒⠚⢻⠉⠈⠀⣣⣀⣤⠼⡤⠐⠒⠛⣏⠁⡐⢆⠠⠤⠿⢖⠛⠋⠙⠦⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠘⣆⠈⢣⠀⠀⢣⡀⢀⣈⣧⠤⠖⠒⢳⡈⠉⠈⣧⣀⠤⠸⢶⠒⠒⢙⣏⣁⡨⠧⢴⠒⠛⠉⢉⣀⣀⣹⠆⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⢳⡀⠀⠹⣍⣀⣽⡤⠔⠒⠊⢻⠉⣁⣀⣷⡤⠴⠞⠛⠋⣉⣡⡤⠴⠒⠚⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠳⡀⠀⠘⢦⡤⠷⠐⢒⣂⣹⡯⠭⠤⠶⠶⠒⠒⠋⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠱⡀⠀⠈⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠚⠋⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⣀⣠⡤⠤⠟⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠴⢚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⣉⣀⣀⠠⠤⠤⠰⢒⣒⣊⣩⣭⡥⠤⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢣⣀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠔⠒⠒⣛⣉⣭⡥⠶⠖⠚⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣬⣭⣉⣉⣥⣤⡤⠤⠶⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⣳⡂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣴⠚⣫⣽⣿⣿⣿⣿⣿⣿⣿⣧⢹⡅⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠿⠍⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⡀⠉⣍⠁⠀⠀⣖⢲⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠁⠐⠒⠒⠲⠶⠶⠶⠶⠶⠒⠒⠳⠤⠭⠤⠮⠀⣿⣻⣿⣽⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣤⣤⣴⣶⡆⠀⠠⠤⠤⠬⠭⠭⠥⠤⢤⣤⣤⡄⠀⣋⣭⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠤⠥⠭⢥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣛⣛⣃⣸⣀⣩⡥⣰⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣴⣴⢠⠴⠟⡟⣟⣻⢛⢛⡛⡻⢛⠿⠿⠿⣿⣿⡿⠿⠿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣁⣄⣴⣶⣹⣯⣯⡍⡏⡌⢡⠋⡖⡸⢂⢒⣶⠟⠀⠎⠛⠛⠛⠋⠀⠀⢀⣔⠘⣯⢐⡦
⠀⠀⠀⠀⠀⢀⠀⠀⠛⠷⠶⠶⢶⣶⣤⣼⣳⣷⣦⣼⣤⣥⣳⡟⠁⠀⢀⠀⢀⣤⠀⠀⠀⣠⣿⡿⢇⣿⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠚⠋⠟⠁⠀⠀⣴⣿⣿⢗⡿⠋
⠀⠀⠀⠈⠛⠻⠿⠿⠶⠶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⣾⢟⠫⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠧⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠶⠶⠦⢤⣤⣤⠀⣄⣀⣀⡀⠀⠀⠀⢀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢏⡻⠉⠅⠀⠀⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣐⡛⡗⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⣆⡄⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠂⢸⠏⠈⠛⠛⠖⠶⢶⣤⣄⣀⡀⠀⠀⠀⢀⡌⠁⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠙⠛⠓⠒⠿⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠠⠊⡩⠃⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠊⠈⠘⠀⠀⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠈⠊⡀⡩⣂⣂⠂⠱⢐⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠐⠃⠂⠀⠉⠨⢘⢠⢀⣇⢀⢐⣀⣸⡅⡠⢰⣦⠀⠠⢾⡿⠃⡀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠒⠼⢫⠏⠑⢱⡽⢁⣾⣾⠏⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⡟⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠋⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡍⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠂⠀⠴⠶⠤⣤⣤⠠⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⡌⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡼⠀⣀⡤⠒⠋⠑⠒⠢⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠀⠠⠩⠐⠀⠀⠈⠉⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠘⠀⠀⡇⢸⠁⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣀⠀⠀⠑⠁⠀⠀⠀⢀⠶⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢀⢀⡇⡈⠀⠀⣸⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⣠⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢸⠃⡇⠀⠀⡟⠀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠒⠄⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡞⢰⠁⠀⢸⠀⠀⠀⠀⠀⡀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠁⠈⠀⢀⠰⠖⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⠀⠤⠍⠁⡠⠠⢠⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠔⠏⢤⣾⣀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠀⡏⠁⠀⠀⠀⠀⢰⠁⡟⠀⠀⡇⠀⠒⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣤⡇⠀⢠⣇⠀⠈⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⣠⡴⣞⡁⠀⠀⠈⣠⣖⣀⣀⣀⣀⣀⢠⡤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⢥⡎⢨⡀⠀⢸⠇⠈⠀⠀⠰⠀⢰⠃
⠀⠀⢀⡤⠔⠒⠋⠉⠉⠉⠉⠉⠓⠢⠄⣉⠛⠀⡁⠀⣀⣀⠀⠀⠀⠀⠀⠆⠤⠐⠀⠀⠀⠙⠳⠤⠄⠲⠒⠲⢤⣧⠀⢸⠀⠀⠀⠀⠀⠀⣸
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⢦⠉⠑⠉⠏⠉⠉⢉⠹⠃⠀⠀⠀⠀⠀⠠⠅⠀⠀⠐⡄⠀⠀⠀⡛⢆⢸⠀⠀⠀⠀⣩⠁⣯
⡎⠀⠀⠀⠀⠀⠠⠊⠀⠃⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠠⠁⢘⠃⠀⠀⠠⠀⠀⠠⡄⠁⡰⠂⠂⠀⠀⣀⠤⠖⠊⠀⠘⣾⣀⣀⣀⣀⣀⣠⡏⢧
⢇⠠⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠠⢠⠇⢀⠂⠀⠖⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣤⣠⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧
⠘⢦⡁⠀⠀⠀⣸⠁⢀⢈⢻⡀⠀⠀⠀⢐⡵⠋⠛⠛⣛⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣸⡊⠅⠀⠀⠠⠶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠙⠲⠤⣄⣼⠀⠀⠀⢸⡧⠄⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⢽⠉⠉⠁⠀⠉⠉⠻⠤⠬⠛⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠋
⠀⠀⡀⠂⠀⠀⠸⡇⠀⠀⠘⡧⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠙⡖⠒⠒⢒⣇⠀⠀⠀⣷⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸
⠀⢰⠞⠉⠉⠉⠉⢹⢀⣀⠀⣿⠀⠀⠀⠠⠈⠉⠙⣦⠒⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠈⠣⣄⣀⣀⣀⠊⠁⢀⣤⣟⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⢀⠈⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠉⢱⡆⠉⠉⡏⠉⠉⢨⡟⠛⠁⠀⠀⠀⣠⣁⣠⡇⠀⠀⠀⠀⣧⠀⣀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⡃⣉⠀⣇⠆⡀⢾⡁⠀⠀⠀⠀⠀⡹⠁⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠠⠀⡟⠢⠰⣏⡀⠃⠀⣄⠠⠔⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢈⡇⠠⠀⡇⠰⠀⠩⡈⡁⠀⠺⢿⠛⠻⠶⠶⠶⠶⠶⠿⠿⠿⠿⠏⠛⠃
⠀⡀⣀⣀⠀⡀⡀⢈⡇⠒⠀⣏⣀⣡⣄⣤⣡⠶⠴⠶⡀
⢾⣁⣀⣭⣭⠭⠭⠥⣤⡄⢤⣤⠔⠐⠒⠢⣤⡤⢠⣶⣾

⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⢄⠀⡀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣿⠖⠚⠛⠛⠛⠓⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡛⠛⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡧⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⣤⣤⣤⣤⣤⠴⠶⠶⠒⠒⠒⠋⠉⠉⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⣶⣶⣤⡏⠀⠀⠀⠀⠀⠀⠸⣥⣤⣭⠭⠴⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠋⠉⠉⠉⣉⣉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⣤⠤⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀
⠀⠀⠀⢈⠀⠀⠉⠑⠂⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⣤⣤⣤⣶⣶⣶⠶⠿⠿⠷⠶⠒⠒⠂⠀⠙⠒⠆
⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠂⠌⢉⠙⠛⡶⠶⠾⠿⠟⠛⠛⠋⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⡤⠔⠒⢢⠒⢒⠫⢍⠁⠐⠈⡑⠦⣀⠈⠑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢔⠀⠀⠀⠀⠐⢂⡒⠉⠩⠁⠀⠀⠒⣄⠑⢦⡁⢤⡙⣢⡑⢬⡉⢤⣐⠢⣐⠈⣑⠦⣄⠀⠁
⠀⠀⠨⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠪⢆⠀⠀⠀⠈⠓⢶⣈⠙⠤⠑⠆⠑⢢⡉⢣⡙⠶⠈⠢⠝⢓⡊⠠⠍⠑⠀⠒⠈⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠚⢦⣀⠀⠀⠈⠑⢦⣈⠂⠍⠁⠠⠀⠐⠒⣈⣉⣀⠀⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⢁⣀⣀⣤⠤⠴⠖⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⣀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠉⠀⠀⠤⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⠛⠋

⠀⠀⠀⣠⢤⠆⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠁⠀⠉⠉⣉⠉⠙⡆
⠀⠀⢀⡃⢸⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⡇⠀⡇
⠀⡴⢹⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⡟⢹⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⡇⢸⡅⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣻
⠈⡇⢸⡯⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠐⢇⡐⡇⢼⡇⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠑⢯⣈⡅⠀⠁⠑⠠⠤⠀⠀⠀⠤⠀⠤⠄⠀⠀⠀⠀⠃⠀⢹
⠀⠀⠀⠀⠙⠣⣤⣤⣤⡤⡠⣤⡤⣤⣠⠄⡤⡤⡤⣡⣬⣬⠀⠅⠊
⣴⢦⡀⠀⠀⠀⢀⣦⣍⡁⠙⠛⠪⠁⠈⠈⠙⠉⠉⣉⡯⠑⠒⠤⣀
⣿⠀⠙⠢⣄⠀⠀⠈⠉⠙⠛⠛⠒⠂⠐⠒⠒⠛⠋⠀⠀⠀⠀⣀⡀⡉⡒⠦⣄⡀
⡗⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⢲⢠⡇
⠳⣄⠑⠕⢸⠁⠉⠀⠘⠛⠛⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⢸⢺⢸⡇
⠀⠈⠢⡀⢸⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢨⢨⡅
⠀⠀⠀⠈⠺⢄⣄⡀⣀⣀⣀⣀⣀⢀⣀⣈⣉⣁⡁⢁⢀⣀⣀⢀⣀⣀⠈⣼⡀⠇
⠀⢀⣤⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⢀⣀⣤⣤⣤⣤⣄⣠⣠⣄⣀⣀⣀
⠀⠀⠓⢝⡪⣒⢝⡐⠾⠓⣀⣷⠀⣀⣟⠀⠺⡓⢀⢹⡒⢒⢟⡒⠒⢟⣒⡺⠷⠤⠭⡮⠽⠷⣤⡀
⠀⠀⠀⠀⠑⢮⣓⣭⡲⠀⠀⢿⡐⣈⢻⡂⢁⠲⣌⣃⣀⣈⣃⣀⣈⣃⡀⠻⠅⠲⠙⠉⢺⣛⣻⣛⣷⢤⣀
⡀⢀⣀⣀⡀⣀⣈⢳⣿⣥⣄⣤⣤⣸⣫⣠⣭⣠⢎⡽⠣⠷⠃⠘⠽⢏⠬⢭⣍⣨⣁⠃⠎⠞⠻⠡⠥⠪⠝
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢌⣱⠢⢄⣀⠀⠀⠀⠀⠁⠂⠀⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠓⠤⣍⡒⠯⣝⢒⠇⣝⠲⠄⣀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠎⠹⠘⠤⣋⡚⠤⣏⡒⠦⣙⠒⠯⣝⠒⡤⣀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠉⠑⠒⠤⣄⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⡉⠚⠤⣋⡺⠤⣅⠒⠪⠉⠓⠢⣉⠂⠠⢀⠀⠀⠀⠀⠀⠈⠐⠀⠄⡀⠉⠐⠂⢰⠁
⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠠⢀⠉⠒⢤⠜⠒⠦⣩⠐⠀⣉⠑⠤⣅⡒⠢⠄⠀⠀⠀⠀⠀⠀⠁⠂⢠⠇
⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠈⠋⠢⠈⣉⠂⠔⣈⠀⠤⡉⠁⠠⢁⡑⠢⠄⣀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠄⠑⡢⠀⠉⠒⢤⠁⠐⠄⣀⡑⠠⠌⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠀⠐⠢⠄⡍⠲⢠⣀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡃⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡤⡄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⡩⢛⣽⡿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡵⢋⣴⠿⣻⣿⣿⠿⢹⣿⣿⣿⡿⢷⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⢸⣿⣋⣴⠟⠁⣴⣿⡿⠁⣠⣿⣿⣿⡿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣯⣀⣴⣾⠟⠁⣠⣾⣿⣿⣿⡿⠁⣠⣟⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⢸⣿⣿⣿⢟⣠⣴⣾⣿⣿⣿⣿⢏⣤⣴⡋⡫⠇
⠀⠀⠀⠀⠀⠈⠪⠢⡄⠀⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣿⡿⠋⣰⡗⡄
⠀⠀⠀⠀⠀⠀⠀⠑⣼⢾⡞⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠿⠿⠋⠠⠚⠛⠁⠃
⠀⠀⠐⠀⠀⠀⠀⠈⠙⢿⡇⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠰⢶⣶⣶⡶⠛⠛⠛⠛⠛⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠲⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⠠⠀⠠⡠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⠙⡒⢤⢢⢐⢦⡳⡱⡕⠌⢀⠒⢯⠓⠋⠛⠿⣽⣿⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢚⠉⠡⡀⢢⠘⣌⢣⠐⡅⣇⢱⠸⡄⣇⢷⠹⡜⣜⢎⡪⠁⢠⡀⠽⠕⠘⠙⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠐⠇⢕⠨⡂⢧⠸⡈⢧⠹⠜⠂⠃⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡘⠂⠁⠘⡅⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣻⣩⣛⣿⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣾⣛⣭⣭⣭⣿⣿⣿⣿⣿⣯⣭⣭⣭⠯⠭⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣛⣛⣷⡄
⠀⠀⠀⠀⢸⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢹⡿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⢸⡇⡇
⠀⠀⠀⠀⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⡇
⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⡇
⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⢿⡇
⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢸⠇
⠀⠀⠀⠀⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢸
⠀⠀⠀⠀⠀⡇⠘⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢸⣾
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠋⠉⠉⡏⣿⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣉⣉⣉⣉⡡⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⣶⡶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣤⣄⠀⠀⠀⣠⠞⣻⡽⠷⠶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⢣⣛⣟⣺⣓⣻⣒⣿⣐⣿⣀⣿⣘⣧⠸⡆⢸⡭⢯⠽⡭⢷⡹⣆⠀⠀⢻⡎⠁⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⣼⠃⠯⠼⠥⠽⠤⠽⠤⠽⠤⠽⠤⠯⠤⠭⠬⠵⠀⢫⣹⣏⣹⣍⣣⠙⣆⠀⠀⠻⣄⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠸⣏⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⡽⠀⠀⠀⠘⠷⣤⣤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⠠⠀⠀⠀⠀⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⠀⠀⢈⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⠉⠈⠙⠉⠉⠉⠙⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠭⠿⠾⠭⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠢⡑⢀
⠀⠀⠀⠀⠀⡠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢄
⠀⠀⠀⢀⠞⠀⠀⠑⠒⠒⠒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠃⠈⠣⡀
⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠑⠒⠀⠀⠠⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠄⠀⠀⠀⣀⣀⣀⣀⡤⠤⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⠾⠯⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠭⠭⠭⠭⠭⢭⣽⣷
⠀⠀⠀⠀⣿⢠⡤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄⣹⣿
⠀⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⢹
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣾
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⣿
⠀⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡏
⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣇⡇
⠀⠀⠀⠀⢸⠀⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⢸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣒⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢨⣏⣀⣀⣀⡈⡍⡇⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣒⣒⣒⣒⣊⣴⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡾⣽⣿⣻⣟⣿⣛⣗⣲⣖⣲⣛⣿⣻⡍⢹⣻⣟⣿⢿⡹⣆⠀⠀⢼⡡⠚⠉⠁⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡞⢱⣓⣗⣺⣒⣛⣒⣗⣚⣗⣺⣒⣺⣒⣣⠈⡗⢻⠚⣷⠳⡙⣆⠀⠈⢷⡀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⢾⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⣛⣛⣛⣛⣓⣺⡆⠀⠀⠹⣦⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⢀⡆⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠸⠇⠐⠒⠈⠐⠪⠟⠛⠴⠄⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡆
⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⡇⣷⠀⠀⠀⠀⠀⡆⢰⡆⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇
⢰⣇⢉⠀⠀⠀⠀⠀⠇⠸⠇⢿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢈⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠚⡆
⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⠉⠸⠿⠟⠛⠛⠛⠋⠉⠉⠁
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢨⢻⣦⡌⠜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⢺⣽⡇⣐⠄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⢀⣠
⠀⠀⠉⢗⣆⢃⣀⡀⠀⠀⠘⢇⠀⠀⠀⠀⠀⣿⣶⣇⣀⣀⣠⣤⣤⢴⣿⣿⡟⠋⡉⠹⢀
⠀⠀⠀⠀⠙⠫⡷⣈⠀⠀⢘⣸⠀⢠⠶⠶⠚⣿⣿⡏⠉⡁⠀⠀⠀⠘⠟⠛⠃⠄⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠻⢖⣦⠀⢻⠀⠀⠀⠀⠀⠛⠋⠡⠄⠀⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠳⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠈⠳⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣔⠈⠈⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣈⣉⠉⠙⠛⠒⠒⠲⠤⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡇⠀⠈⠉⠑⠒⠒⠦⠤⢤⣀⣀⣀⠀⠉⠉⠑⠒⠒⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⣤⣀⣀⣀⠈⠉⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡇⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡰⡣⣠⠖⡠⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡸⢨⠟⡡⢞⡴⢋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡇⠠⢞⠵⢋⡴⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣁⠐⠁⡴⠋⡴⣫⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣉⠉⠉⠓⠒⠲⠤⠤⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣴⣲⡬⢭⡝⢓⣲⣦⠤⢤⣀⣀⡈⠉⠉⠉⠓⠒⠒⠤⠤⣀⣀⡀⠀⠀⢀⡇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⠤⣤⣈⣉⠙⠛⠲⠼⠯⢹⣛⣒⡶⠩⢭⠟⣒⡲⠦⠤⠤⢄⣀⣉⡉⠓⠚⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡴⣉⣟⡓⡶⠧⢬⣏⣙⡖⠲⡦⠤⣤⣉⣉⡛⠒⠛⠶⠿⠭⣵⣒⣶⠢⡬⢍⠙⠓⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣠⡟⢢⠮⢄⣼⣉⣱⡛⢲⠿⠬⣽⣏⣺⡓⠰⡯⢬⣟⣲⢲⡶⡄⠀⡤⠤⣉⣉⣙⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⡀⠓⠛⠫⠭⢾⣓⣶⡯⢬⣟⣑⣲⡗⠤⡿⠬⣹⣋⣒⡗⢺⠭⢿⣿⡀⢳⠒⢷⠤⢯⣩⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣟⣻⣋⣶⢶⣶⢤⣤⣌⣉⣁⠒⠛⠬⠽⢇⣒⣾⠠⢼⠍⣹⡇⢺⡖⢇⠈⣏⣉⣗⠚⡦⠼⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠵⢯⣾⣿⣝⣽⡟⡷⡲⣶⣦⣬⣍⣉⣑⠚⠃⠭⠯⢹⠀⢻⠂⠽⣯⢽⣋⣧⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠾⠵⣵⣯⣾⣻⡫⡻⢫⠟⣲⣶⡦⣬⣍⣁⣛⣚⠓⠺⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠚⠻⠮⠾⡵⣵⣿⣿⣫⣿⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⢰⠒⠒⠒⠒⠒⠒⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⢹
⠀⢸⠀⠀⠀⠀⠀⠀⡇⢘⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠸⠤⠤⣤⣤⠤⠤⠏⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⣤⡀⠀⠀⢀⣀⣠⠖⠒⠢⣤⣄⡀⠀⠀⠀⠀⣠⠄⠀⢸⣦⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠏⢀⠔⠒⠉⠑⠒⢤⡙⠲⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⠀⠀⠀⠀⢳⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠬⠭⠭⠭⠭⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⣀⣠⡤⣤
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠴⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⡷⠒⠚⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣮⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⣠⣤⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣏⡀
⠀⠀⠀⠀⠀⢀⡼⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡙⢦⡀
⠀⠀⠀⢀⡴⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢦⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⡃
⠀⢸⣿⣤⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣧⣼⣿⣾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠻⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡏⡏⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣛⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⢸⣿⣺⣿⣿⣿⣿⡷⠓⣿⣿⣿⣿⣿⣿⣿⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠇
⠀⢸⣿⣺⣿⣿⣿⣿⡷⡴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⠶⠶⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣇⣇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣿⣿⣦⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⡶⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠸⡫⠀⠁⢀⠈⡲⠀⠑⠀⠠⠔⠀⠀⣠⠠
⠀⠀⠀⠀⢐⡄⡀⠀⠀⠀⠀⠀⠀⠰⢤⣌⣣⠢⣀⠆⠘⠟⠐⠂⠈⡂⡤⠀⢀⡀⢀⢦
⠀⠀⠀⢀⠤⠄⠑⠄⡀⢀⣀⠂⠀⠈⠁⠘⠙⠙⠯⠞⣗⡷⢥⣶⢥⣜⣋⠤⢈⠐⠀⢃
⠀⠀⠀⠀⠀⠠⠂⠀⠨⡗⡊⠀⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠓⠻⠽⢇⣶⡎⡴
⠀⠀⠀⠀⠦⠠⠤⠄⠵⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣈⡆⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡄⡀⠀⠀⢘⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠰⢩⣿⠦⢄⠀⠀⡀⡠⠢
⠀⠀⠀⣴⢄⠷⠀⣚⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣠⡤⠀⢠⡾⣿⡿⢿⢆⠀⠀⠀⢌⡊
⠀⠈⠻⡡⡑⠐⢖⣟⡆⠀⢀⠄⠀⠄⠀⠒⠀⢁⡉⠉⢈⡵⡺⡿⠋⠁⢀⢐⢾⢉⣻⠿⠷⡀⠀⢐⠂
⠀⠀⣠⡌⠀⠠⣨⡵⠀⠀⠈⠀⠁⢀⡤⣠⠄⠩⢳⢴⣿⢫⠔⠡⠀⢀⣵⠗⡑⣾⣿⣿⢗⠀⠐⠢⠃⠃
⠀⠀⠉⠀⠀⠪⡯⠇⠄⠂⠀⣪⢴⡛⢀⠴⣋⠔⣥⠳⠜⠕⢀⠦⣲⠛⢂⣈⢲⣿⢷⡮⡐⠉⠠⠢⢀
⠐⠼⠅⠐⠐⢴⠽⠁⠰⡊⡐⠡⣨⠔⢟⣅⠰⠋⢀⠀⠀⢐⠋⢜⣅⠖⣫⣓⢟⣿⣷⡁⠁⠕⠑⢈⣼⠔
⠓⠣⠂⠂⠀⠬⢽⣬⣀⠔⠠⠊⠰⠒⢹⡣⢴⠂⢝⣁⠀⡂⠀⢹⠓⠚⠚⢺⣿⣷⣾⠼⢶⣶⡶⠷⠷
⠀⠀⠀⠀⠀⠀⠘⡿⣯⣿⣳⣶⣶⡤⣌⣀⢂⣐⡔⠁⡊⠒⢀⣽⣯⣭⢽⣿⣭⣤⡭⠥⠤⢴⠄
⠀⠀⠀⠀⠀⠀⠐⢲⡽⢸⡻⣹⡟⣿⢿⢿⢿⣽⣿⣵⣷⣶⣥⣽⣿⣿⢾⠿⣶⡎⠁⢐⠄⠂⠑⢖⣠
⠀⠀⠀⡄⢀⡀⠄⢀⢀⠊⢁⠙⡉⠛⡚⡞⣾⣇⣿⢻⣻⢻⡿⣿⣿⣇⡼⡗⠂⠈⠀⠔⣀⠮⠦⠉⠈
⠀⠀⠀⠀⠡⠠⠀⠀⠀⢾⠬⡠⠀⠲⠰⣝⠠⠘⠙⠍⠋⠛⠓⠿⢴⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠊⠀⠀⠶⠀⣦⣁⠀⢠⣄⡀⡂⠠⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠀⠀⠑⢀⠱⠪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣠⣤⣄⡑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⢰⣿⣿⣇⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⢸⡟⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣶⣦⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡼⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠴⠞⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⣶⣾⣿⡿⣋⣉⣙⠉⠛⠛⠉⠙⠛⢛⠛⢛⣻⣶⣦⣤⠆⣾⣧⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⣭⣭⣿⣾⣛⣛⣛⣺⣶⠦⠤⠤⢄⣐⣒⣒⣒⣚⣛⣫⣽⣷⣾⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣯⣭⣍⢛⠉⠀⠀⠀⡀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣨⠤⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣿⣷⣒⣢⡭⠭⢭⣛⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣭⣭⣿⣖⣒⣪⠭⠭⣝⣛⣛⣛⣃⡶⠚⠁⠀⢀⠠⠒⢻
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡍⡟⠀⡀⠀⠀⠀⣠⣶⣁⡀
⠀⠀⠀⠀⢀⣤⣾⡿⠋⠁⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣄⣠⣴⣿⣿⣿⣿⠇
⠀⠀⠀⣾⣿⣿⣯⣭⣛⡲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢈⡿⠿⠛⠉⠁
⠀⠀⠀⠁⠉⠉⠛⠻⠿⢿⣿⣷⣶⣮⣭⣙⣒⡶⠤⣤⣴⣿⠟⠉⠀⠀⡠⣹⡿⠛⠛⠿⣿⣿⣿⠋⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣷⣿⣿⣯⣽⣶⣶⣯⣾⣁⡀⢀⣠⣶⣾⠟⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣫⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢹⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡭⠭⠭⠭⠍⠉⢉⣉⣉⣉⣉⣉⣁⣐⣒⣓⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠛⠓⠲⠿⠁⠒⠒⠠⠤⠤⢠⣀⣀⣀⡀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢲⠖⠤⣄⣀⣀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠚⠭⠭⠽⢥⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣉⡟⠓⢲⠧⢤⣏⣉⢹⠓⠲⡤⢤⣄⣀⣀⠀⠀⠀⠛⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢤⣏⡈⢩⠟⠒⡾⠤⢄⣝⡙⣲⠷⠦⡮⣀⣸⡋⠉⠗⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠤⠼⣄⣉⡟⠒⡾⠤⣤⣼⣁⣩⠋⠙⡺⠓⢦⡮⣍⣽⡛⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠉⣉⣓⠒⠲⠤⠬⣏⣉⣻⠓⢲⠾⠤⣴⣅⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⢀⣀⣀⠀⠀⢸⢅⣀⡉⠉⢒⡆⠀⠀⠉⠉⠉⠓⠚⠳⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠼⠍⣉⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠤⢤⣄⡼⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠒⠒⠒⠒⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠛⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⡄⠀⠀⡇⠀⠀⠀⠀⣶⣾⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠴⠦⠤⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⢜⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠿⠶⠦⠶⠤⠒⠒⠒⠒⠂⠈⠉⠁⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⢠⠃⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣦⣥⣀⣀⠀⠀⠀⡀⠀⠀⠀⠠⠶⠦⠶⠶⠒⠒⠚⢉⣉⣉⣡⣤⣤⣴⣶⣖⠉⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣇⠈⠙⠛⠿⢿⣶⣷⣶⣤⣤⣴⣶⣶⣶⣿⣿⣿⡿⣿⠿⣟⢻⡏⠻⠉⠧⠘⡂⣫⠈⡌⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠉⠙⢛⠛⠛⣏⠹⠏⠹⡂⠚⡀⣫⠉⡧⠤⡛⢂⢻⣈⠧⡑⢤⡒⡗⠪⠁⠀⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠻⣦⠀⠃⢚⣄⠩⣌⠶⡘⢲⡌⠳⠉⠂⠓⠈⠀⠁⣀⣵⠤⠤⠛⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢻⣄⠀⠈⠲⡈⠀⣈⣆⡤⠤⠄⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⠀⠀⠀⠀⠙⠃⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠴⠖⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⡤⠤⠔⠒⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠛⠛⠛⠻⠷⠶⢶⠂⣶⣦⣤⣤⡔⠀⠀⠀⠀⣤⡶⠟⠃⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣹⣯⠩⠃⠀⠀⠀⠀⠁⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠃⠀⡤⢄⣀⣀⣀⣠⡄⢸⠛⠓⠒⠲⠂⠀⣤⠀⠀⠀⣨⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣦⠤⢤⣄⣀⣀⠀⠀⠈⠉⠁⠀⠀⠀⠘⠀⠀⠀⢿⣾⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠼⢃⣄⣉⣙⠙⠋⠟⠛⠿⣶⣮⣤⣀⣐⡀⠀⠀⣠⡞⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠂⠀⠉⠁⠈⠛⠛⠻⠶⠶⣠⣤⡌⠉⠉⠙⠛⢛⠛⠿⠁⣼⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠖⢉⡝⣁⡀⠀⠀⠈⠛⠛⠢⠂⠀⠀⠀⠉⠀⠀⠀⠴⠑⠃⠞⡰⠀⠀⠀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠰⠖⠁⡔⣧⠏⠧⣇⡇⡆⡦⡄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠄⡾⢼⢱⣻⢻⢴⣰⣯⣇⣗⣇⡀⡇⣞⢰⢰⠆⠀⡀⣄⠀⠀⠀⣠⣶⣿⠋⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠪⠯⣸⣻⠡⠇⣷⠾⣼⢇⡜⡱⣻⠋⣰⣿⣿⠟⠁⡴⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠓⠋⠾⠃⠈⢸⡽⠃⣼⣿⡿⠋⠀⠐⡀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣿⠟⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⢛⣳⣶⣀⣠⡤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢰⠾⠿⠭⠤⠤⣤⣤⣤⣤⣤⣤⣀⣠⡶⣾⣿⣿⣛⣉⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⢓⣶⣦
⠀⠀⠀⠀⠀⣾⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⣿⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⠒⠶⠶⣶⠛⠁⣿
⠀⠀⠀⠀⠀⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢰⡏⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⣿⠀⠀⣿⣤⡀
⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⠀⢸⡇⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡟⠀⢸⡏⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋⠀⣼⠇⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⡇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⣿⠁⣾
⠀⠀⠀⠀⠀⢸⡀⠀⢀⣤⣤⣄⣀⣀⡀⠀⠀⣿⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⢀⣿⠀⡿
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠛⠛⠁⠀⢠⡟⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢸⡇⢸⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣁⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⠇⠀⣾⠷⠛
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⡿⠇⠀⠀⠀⣾⠃⣠⡾⠷⠤⢤⣤⣤⣤⣤⣀⣀⣃⣀⣐⣂⣀⣀⠀⠀⠀⠀⠀⠀⣿⣠⠾⠃
⠀⠀⠀⠀⠀⠀⢿⣤⣤⣄⣀⣀⣀⣀⣀⣀⣿⠞⠋⠀⠀⠀⣀⡤⠇⣼⡋⠀⠘⠿⢿⣿⣿⣿⣿⠟⠙⢻⡟⠛⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⣉⣉⣁⣀⡀⠀⠀⢸⠁⠀⠀⠹⢿⣶⣤⣤⣤⣄⣬⣁⢀⣒⣺⠻⠃⠀⠈⠛⠛⠶⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣟⣋⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⣲⠗⣾⠷⣾⠧⡾⢥⣽⣭⣽⣉⣿⣛⣿⣿⠿⡿⢿⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣤⣶⣶⡾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣹⡋⣻⠛⣺⠓⡾⠓⡾⠧⡼⠧⣼⢧⣼⣿⡟⣻⠓⡾⠒⣾⣿⣿⣿⡿⠃⠀⢠⣾⣫⣠⣿⠋⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣶⣧⣴⣿⣿⣭⣏⣽⣛⣿⣿⣿⣿⠏⠀⠀⢰⡏⠀⠀⠀⠀⠉⠲⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣇⠀⠀⠀⢀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⠛⠁

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⢸⡟⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟
⣿⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⣿⠀⠀⢸⡇⣿⠐⠶⠶⠶⠶⠶⠖⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠛⠛⠛⠛⠛⠋⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠘⠛⠛⠛⠛⠀⢸⡇
⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⢠⡶⣦⠀⠀⢸⡇
⣿⠀⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⠈⢛⠋⠀⠀⢸⡇
⣿⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣿⠀⠀⢸⡇⣿⠀⠀⠀⠙⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠞⠛⠛⠛⠳⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛
⠀⢀⡞⠩⠭⣉⡉⠭⢉⡉⠭⢉⡉⠭⢉⡉⠭⢉⡉⠭⢉⣉⠭⠍⢷⡀
⣠⣿⣤⣤⣷⣤⣤⣷⣤⣤⣿⣤⣤⣿⣤⣄⣻⣤⣤⣾⣤⣤⣾⣤⣤⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣆
⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⢠⠶⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣿⣀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⣶⣷⠒⠲⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢙⡻⠛⣛⠻⢟⠛⠛⠛⠛⠛⠛⠛⠉⠛⣿⣿
⠀⠀⠀⢤⣤⣀⣐⡒⠒⢚⣛⣛⣛⣉⣭⣭⡵⠖⡒⣿⡿⠀⠀⠂⢄⠀⠈⠓⢤⡀⠀⠀⢀⠀⠀⠀⠉⠓⢮⣙⠢⣕⢦⡀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⣿⡏⠉⠉⠙⠛⠉⠉⢹⢁⠀⣸⡇⠀⣷⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠠⠀⠀⠀⠀⠉⠓⢦⡑⠿⣶⣄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠁⠺⠿⠿⠿⠿⠀⣼⠸⠀⠉⠇⢀⣿⣿⡇⠀⠀⠑⢦⡤⢀⠀⠀⠀⠀⠀⠙⠲⣄⠠⡑⠠⡀⠀⠀⠀⠙⠢⣌⠻⣷⡄⠀⠀⣼⣿
⠀⠀⠀⢀⣿⠀⣠⣤⣤⣤⣀⠀⢸⠀⠀⠀⠀⢸⢿⣿⢁⠀⠀⠀⠀⠈⠈⠑⠦⣀⠀⠀⠀⠀⠈⠙⠦⣑⠨⠀⠀⠀⠀⠀⠈⠳⣄⠙⢶⣄⣿⣿
⠀⠀⠀⢸⣿⠀⠉⠙⠉⠛⠛⠀⣼⠀⠀⠀⠀⠘⢸⣿⠀⢭⡢⢄⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠈⠓⢤⡀⠄⠀⠀⠀⠀⠈⠑⢦⠀⣿⣿
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⠀⠒⢌⡋⠛⠦⣄⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠙⠲⣄⠀⠀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢀⣶⠿⡄⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠢⠐⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠓⠀⠀⠀⣿⡇
⠀⠀⠀⢸⡁⠀⠘⢿⣴⡇⠀⠀⡿⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠑⠀⠢⠈⠳⣄⡀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⣿⡇
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⠤⠽⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣙⣂⣀⡀⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⡿⠀⢠⣤⣤⣀⣀⡀⢸⠇⠀⠀⠀⠀⠀⠐⠳⠶⠶⠟⣛⣿⡧⠀⠈⠉⠉⠉⠉⠛⣟⡟⠻⠿⠿⣿⠷⢶⣤⣤⣷⣦⣀⣀⣀⣀⣠⣿⠇
⠀⠀⢰⣗⣲⣭⣭⣭⣥⣄⣃⣘⣀⣤⡤⢴⣶⡶⢶⣛⣛⠩⠟⠉⠉⣠⣤⡤⠴⠶⠒⠛⢙⠋⠃⠀⠰⠇⡿⢠⣄⡀⠀⠀⠉⠙⠋⠙⠛⠛⠟⠆
⠠⠄⠀⠙⠿⠛⠛⠛⠳⠿⠽⠿⠁⠘⠛⠉⠉⠉⠉⠁⣀⣀⠀⠚⠿⡍⣀⣤⣤⣴⠾⠿⠿⠶⠛⠀⠼⣖⣁⠈⠙⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠠⡤⣤⣤⣤⡶⠶⢦⡤⠔⠒⠒⠚⠈⣩⡿⠋⠹⠿⠶⠶⠶⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢍⡛⠻⢿⣿⣒⡓⠦⣅
⠀⠀⠀⡠⠚⠉⠉⠀⣴⣿⠖⡲⠋⠁⠀⠀⣠⣾⠋⠀⠰⠰⠲⠶⠶⠴⠦⠤⠤⠯⣭⡝⠛⡓⠒⠶⠶⠤⣤⣄⣀⡀⠒⠛⠛⠉⠉⠀⠀⠀⠀⠉⠓⠤⣀
⠀⠀⠘⠢⣠⣤⣀⣤⣴⣾⡟⠥⠖⠉⠀⢐⣏⠁⠀⢠⣝⣁⢋⠚⡐⠂⠀⠀⠠⠀⠌⢀⡈⠁⠀⡤⠠⠄⣀⢀⡀⠉⢉⡁⠉⠛⡛⠛⠿⠷⠶⣤⡀⠀⠀⠙⠦
⠀⠀⠀⠀⠙⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠭⢶⣦⣜⣼⣧⣞⣞⠁⠀⠀⠀⠀⠖⢠⠎⢀⡤⣭⠛⢀⠖⠠⠌⢈⡐⠃⠠⢌⠌⠁⠈⠛⠄⣴⢋⣟⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠶⠶⢶⣦⣤⣭⣜⣁⡐⡣⠞⢉⡔⠊⢠⠜⠵⠂⠀⠤⡡⢋⣾⣱⣯⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⠒⠶⣴⣭⣉⣀⣴⣧⣤⣠⠾⣿⡿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣬⣭⣭⣭⣭⣽⣴⣯⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣤⣶⣤⣶⣧⣴⣦⣴⣦⣤⣶⣤⣶⣤⣵⣦⣴⣦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⢻⣿⣾⣿⣾⣿⣶⣿⣷⡟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠐⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⠀⢀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠖⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣀⠀⠀⠀⢀⡀⠀⣀⡀⠀⣀⡀⢀⣀⡀⠀⣀⡀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⣬⠉⢠⣭⠁⠤⠤⠀⠤⠄⠀⠤⠤⠀⠰⠦⠀⠒⠂⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠒⠂⠀⠐⠒⠀⠒⢀⣄⣚⣃⣀⣈⠉⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣶⣶⣶⣶⡾⠧⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠤⣤⣤⡷
⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⠤⠖⢀⡉⠁⠤⠤⠄⠀⠀⠒⠒⠀⠀⠠⠤⠤⢈⣉⠐⠆
⠀⠀⠀⡆⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡄⠸
⠀⠀⠀⡇⢸⠀⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠃⠀⠆
⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠸⣿⠗⠀⣠⣄⠀⢿⡿⠂⠀⡇⢸⠀⡄
⠀⠀⠀⡀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡛⢻⠄⠀⠀⣀⡄⢒⣚⢒⡁⠈⠩⠭⠭⠉⠀⡐⣒⡒⢠
⠀⠀⠀⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⢀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠀⡄
⠀⠀⠀⠃⠈⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡆⠀⠀⠠⣴⠀⠀⠀⠀⣢⠄⠀⡇⡄⡁
⠀⠀⠀⠰⠀⠃⠤⠌⢉⢉⣉⣀⣒⣒⣒⣒⣒⣀⣈⣹⢸⠀⡇⠞⢆⠀⠛⠁⠠⠆⠀⠛⠁⠀⠃⠇⡇
⠀⠀⠀⠀⠉⠁⠐⠂⠠⠄⠠⠤⢤⡖⠉⠉⠑⠦⠀⢺⠸⠀⡙⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠒⠺⢧⣀⣀⡤⠓⠒⠲⡀⡆⠣⠤⠄⢀⣀⣀⣀⣀⣀⠀⠠⠰⠜⢠⠁
⠀⠀⠀⠀⠀⠀⠸⡒⠠⠤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⠷⣨⣭⣍⣠⣦⣴⣶⢶⡶⣶⢶⡤⢭⡶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠀⠉⠹⡓⢄⠱⢟⣿⣽⢯⡿⣽⢯⡿⣽⢯⡽⣭⠿⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕⣌⣁⣉⣉⣉⣉⣉⣭⣉⣭⣭⡭⠭⠥⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⡁⣉⢁⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡇⠠⣪⢄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣴⣶⣾⠿⠿⣅⠀⠀⠀⠀⠀⡇⢈⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠸⠥⠒⠒⠉⠁⡖⠒⢒⢒⡒⡓⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⢔⡵⡠⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⡇⠩⠊⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⡏⡇
⠀⠀⠀⠀⠀⣀⣀⣠⣖⣚⣛⣲⣄⣵⠘⣄⣠⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣗⣚⣒⣒⣒⣒⣒⣇⣀⣧⣧⣀
⠀⠀⠀⠀⠀⠓⢲⠒⠒⡖⠒⠒⠒⢻⠀⢻⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⢲⠒⠚
⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠘⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇
⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⢇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⡼⠿⠿⠿⠦⠶⠦⠶⠶⠦⠶⠶⠶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡
⠀⠀⠀⠀⠀⠀⠇⡘⠀⠀⠀⠀⠀⠀⢹⢫⠏⠉⢻⢹⠉⢹⠙⡏⠉⠉⢻⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⡎⡞⠀⠀⠘⠸⠀⠀⡆⡇⠀⠀⠘⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢰⣹⠀⠀⠀⡇⡇⠀⠀⡇⡇⠀⠀⠀⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⡆
⠀⠀⠀⠀⠀⡌⡎⠀⠀⠀⠀⠀⠀⣮⠃⠀⠀⠀⡇⡇⠀⠀⣿⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠿⠀⠀⠀⠸⠇⠀⠀⠀⠀⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⠔⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣒⠖⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⢀⡀⠈⢀⠀⠀⡀⠀⠉⠀⠀⠉⡀⠈⠁⠀⠈⢁⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡠⠊⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠠⠄⠀⠠⠄⠀⠤⠀⠀⠤⠀⠀⠄⠁⠀⠈⢀⠀⠀⡀⠀⣡⠔⠁⠀⠀⡠⠚⠁
⠀⠀⠀⢀⠤⠊⠀⠀⢀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠂⠀⠐⠂⠀⠐⠀⠀⠀⠀⠠⠂⠀⠄⠂⠀⠐⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢀⠔⠋
⠀⠀⠀⠃⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠄⠠⠀⠀⠀⠁⠀⠈⢀⡀⢈⢀⢀⣁⣀⣀⣁⣀⣀⣁⣀⡈⠀⠀⠠⠔⠁⠀⠀⡠⠊⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠶⠶⢆⣤⣤⣤⣤⣄⣠⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠉⠁⠀⠐⠀⠒⠒⠒⠂⠀⠠⠭⠭⠍⠩⠭⠉⢙⣉⣛⣛⡛⠛⠒⠲⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⢀⠀⠀⠀⠀⡇⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠌⣐⡒⠂⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⡉⠐⢂⠀⠒⢀⠀⠉⡉⠐⠒⠂⠤⠭⠍⢐⡒⠂⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠤⠀⡠⠄⡁⠐⠂⠀⠐⢀⡄⠈⣠⠀⠁⠠⠀⠂⠤⠀⢉⠉⠐⣒⠂⠤⠭⠍⢐⣒⠂⠰⠂⡇⡆
⠀⠀⠀⠀⢀⡠⠔⠉⡀⠀⢁⠀⠘⠠⠄⡀⡡⠀⣈⡀⠂⠀⠐⠂⣄⠈⢡⠐⠊⠀⠠⠔⢂⠤⠀⢁⣀⠠⠆⠐⠠⠀⣈⢥⣟⣉⠇
⠀⠀⠀⠀⢨⡉⠉⠒⠒⠦⠤⠴⣁⣀⠒⠀⠄⠁⠀⠀⠀⠀⠀⠀⢂⠄⢀⡀⠀⣁⠀⠘⠀⠄⡀⢩⠀⠊⣁⡤⠒⣉⠷⠒⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠤⠤⠄⣈⣉⠉⠐⠒⠠⠤⠥⢀⣀⠠⠂⠀⠤⢀⠀⠘⡁⠀⠃⣀⡤⠖⢉⡡⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢄⣈⣉⠉⠐⠒⠀⠤⡤⠖⢋⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠂⠗⠊⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣿⣻⣟⣙⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠛⠛⠉⠉⠉⠉⠙⠛⠓⣶⣦⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣭⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⢖⣫⡵⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠒⠶⢶⣤⡄
⠀⠀⠀⠀⠀⢸⡇⢠⡤⠤⠤⢤⣀⣀⣈⣉⣉⠉⢹⡇⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠓⠒⠶⠶⠶⠶⠤⢤⣤⡶⠋⢹⡇
⠀⠀⠀⠀⠀⢸⡇⢸⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⢸⠃⢸⡇⠀⢠⡖⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⣤⣤⣤⣀⠀⠀⢸⡇⠀⢸⣧⡀
⠀⠀⠀⠀⠀⢸⡇⢠⠶⠦⠤⠤⠤⠤⠤⠤⡄⠀⣾⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⠀⠀⣼⠛⣿
⠀⠀⠀⠀⠀⢸⡇⠸⠦⠤⠤⠤⠤⠤⠤⠤⠇⠀⣿⠀⢸⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡿⠀⠀⡿⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⢠⡇⠀⡏
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⠁⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠭⠭⠭⠭⠷⠀⠀⢸⠇⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣾⠀⣼
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣾⠀⠀⢸⡄⠀⢿⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡏⠀⢀⣏⣤⠏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡔⢢⠀⠀⠀⠀⡿⠀⠀⣸⣇⣀⡀⠀⠀⠀⠁⠉⠉⠍⠉⠉⠍⠉⠉⠛⠛⠛⠛⠃⠀⢸⠇⢀⡼⠋
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣇⣴⠞⠁⠉⠉⠉⠙⡟⢻⠟⠛⠻⣖⡒⠒⠲⠶⢶⣶⠶⢤⡤⠤⣤⡾⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠒⠲⠶⠶⠶⠚⠋⠀⠀⠀⠀⢠⠒⠉⠀⢿⣦⣀⠀⠈⠉⠙⠛⠛⠋⠁⣀⣴⡇⠀⠘⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠦⠤⠤⣼⣤⣤⣤⣈⣙⣺⣿⣿⣿⢿⣿⣿⡭⠿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣖⣲⡒⣲⠒⣲⠒⡶⠒⡦⠤⣤⠤⣤⣈⡉⠉⠉⠛⠛⠒⠒⠶⠶⠤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡮⢤⡏⣠⣏⣩⣏⣹⡋⣹⠛⢳⠓⢲⠗⢲⠁⣼⣩⣏⣹⣛⢓⠆⠀⡴⢉⡇⠀⠀⢀⣤⠞⣻⣫⠏⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⠤⠦⠤⠯⣠⣏⣠⣏⣩⣋⣩⡏⢉⡟⢒⠏⢰⠧⡾⢤⣏⣀⠏⢀⠞⣠⠞⠀⠀⣠⠟⠓⠒⠻⠧⣀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣭⣴⣖⣒⣒⣒⣒⠤⠤⠬⠭⠍⣉⣉⣉⣀⣙⡚⠓⠾⠤⠎⡰⢣⡞⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠲⠶⠶⠦⢤⣬⣭⣉⣉⣺⡵⠋⠀⠀⠀⠀⠀⢿⣤⣀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⣶⣶⣿⣷⣶⠶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣷⣵⣶⣦⣶⣶⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠆⠀⢰⠖⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠄
⠀⠀⠀⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠨
⠀⠀⠀⡄⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠚⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠤⢄⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠦⠤⠤⠤⠄⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠄⠀⠈
⠀⠀⠀⠒⠂⠀⠘⠘⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋⠈⠀⠁

⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⡇⠀⣾⠛⠛⡛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⢚⡵⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡅⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⢸⡈⠋⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⢒⣒⣒⣲⡖⢲⣖⣒⣒⡒⠒⠒⠒⠒⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⣍⡭⠹⣧⣼⠏⠉⠉⠉⠛⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⠦⠬⠤⠤⠤⠤⠤⠤⠤⠴⣒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡽
⠀⠀⠀⠀⣀⡴⠋⣩⠭⣭⠭⣭⠭⢭⠭⣭⢭⣭⣭⡭⢭⠭⡭⠭⣭⠭⣭⠭⣍⠙⢦⣀⠀⠀⠀⠀⢰⣟⡉⠉⠉⠁
⠀⠀⣠⡾⠋⢀⡞⢛⡟⢛⡾⠛⣲⠛⡾⠓⡞⢺⡗⢳⠚⢷⠛⣖⠛⢷⡛⢻⡛⢳⡄⠙⢷⣄⠀⠀⠀⠉⠙⢳⣄⡀
⢀⡼⣋⣆⢴⣯⣭⣯⣭⣿⣍⣽⣭⣽⣍⣽⣩⣽⣯⣭⣯⣭⣯⣭⣯⣩⣽⣭⣽⣯⣭⡦⠀⠙⢷⡀⠀⢠⡾⠋⠉⠙⢳
⣿⠶⠶⠾⠶⠶⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⡤⢤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⣿⠀⣿⢤⣤⣤⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡍⠉⠩⠭⠉⠉⠙⢛⠛⢒⡒⠒⠒⠲⠶⠦⠤⠤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠐⠂⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⡀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡃⠀⡀⠌⠡⠂⡒⠀⠄⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡁⠐⡈⠐⠠⠀⠢⠀⡂⠄⡀⠌⢁⠀⢐⠂⠈⠡⠀⠐⣀⠀⠤⠀⠀⣀⢠
⠀⠀⠀⠀⡀⠔⢊⠁⢂⠀⠂⠀⠀⠁⠀⠂⠠⠀⠡⢈⠁⢂⠀⠃⠀⠄⠈⠄⠈⠀⠀⠄⠀⠍⢀⣠⡞⡺
⠀⠀⠀⠸⣉⣁⠒⠒⠠⠴⠄⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠄⠈⠀⠄⠈⠄⢈⡠⠔⣊⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠠⠤⠌⢉⣁⠒⠒⠀⠤⠆⢀⣂⠄⠀⠅⢀⡡⠔⢊⠥⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠤⠄⢉⣹⠡⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠐⠀⢀⣤⢇⡎⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣀⠬⢀
⠀⠀⠀⠀⠀⢰⠀⠈⣿⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡠⠔⢄⡇⠀⠀⠀⠀⠀⠠⢰⠣⠤⡤⡇⠐
⠀⠀⠀⠀⠀⠘⢀⣨⡿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⢱⣰⣿⠁
⠀⠀⠀⠀⠀⠐⢲⢑⣿⠉⠁⢠⠀⣀⣀⣩⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⡭⠭⣍⢹⠂⠀⠀⠓⠛
⠀⠀⠀⠀⠀⠈⢉⡇⠐⡇⠀⠈⡄⡆⠀⠀⠀⠀⠤⠀⠠⠠⠀⠀⠀⠀⠀⠀⡇⡼⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢘⠀⠀⢰⠀⠀⡇⡇⠀⠀⠀⠀⠀⠄⠀⠄⠄⠀⠀⠀⠀⢸⢀⡇⠀⢀⡠⣪⠖
⠀⠀⠀⠀⠀⠀⠈⠢⠴⠟⠀⠀⢸⢸⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡏⢸⠁⠰⣯⢞⠅⣠⢄⠐⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡜⡆⢀⣀⣀⣀⡀⠀⣀⣠⠄⠤⠀⠴⠁⡏⠀⠀⠘⡄⠀⠵⠋⢰⠃
⠀⠀⠀⡠⡶⠋⠀⡀⣠⡌⠐⠠⠀⠃⠠⠤⠄⠀⠀⣀⡤⣤⡤⠤⠤⠤⠤⠚⠁⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠈⢄⣀⠀⢙⣋⣤⣈⣩⡴⠃⠀⠀⠀⠀⠀⣎⣀⡙⠉⢠⡇
⠀⠀⠀⠀⠈⠁⠙⠒⠈⠉⠁⠀⡼⢬⠫⡍⠩⣉⡍⡉⠈⠉⠉⠉⠉⠀⠘⠋⡄⢀⡀⡐⠊⠀⠀⠀⣠⢀
⠀⠀⠀⠀⢆⠀⠀⣀⠀⠀⠀⡰⣑⠉⣩⠹⡲⠿⢃⣁⣀⡀⠀⠀⢀⠀⢀⡀⢠⠘⠂⠠⡞⠥⠒⢲⠇⠀⠉⠐⠢
⠀⠀⠀⢴⣒⣂⣀⣑⣤⠀⠐⢧⣉⢨⣬⡤⢴⠀⢀⡽⣃⡀⠤⠤⠬⠤⠤⠶⠶⠀⠀⣀⣠⠤⠀⠀⠙⠥
⠀⠀⠀⣘⣄⠀⠀⢲⠧⠀⠀⠀⠀⠀⠀⠀⢘⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⢀⢤⢶⢛⠡⢀⣠⣢⠀⠀⠀⠈⠓⢆
⠀⠀⠐⢅⣀⣋⣉⣓⡡⠼⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠐⠀⢬⠶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠄⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡤⠤⠴⠶⠒⠒⠒⠋⠉⠉⠡⣼⢴⣶⣶⣼⣿⣿⣾⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⣁⣀⣤⣤⡤⠴⠶⠶⣶⣶⣿⣿⣷⡆⢸⣿⠀⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⠸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⠈⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⠘⣛⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠿⠿⠶⠶⠒⠒⠶⠶⠤⢴⣾⣟⣿⡁⢿⣿⠸⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢷⣼⣿⣶⣤⣤⣠⣴⣦⣤⣤⢾⠿⣿⣿⣧⣾⣿⡄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡏⠛⠋⠉⠉⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣀⡀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣿⡇⢶⣦⣤⣬⣤⡁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⣿⠇⠀⠀⠸⢿⣿⡄⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠒⡒⠦⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠘⠛⠒⠒⠶⠶⠦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣠⠇⢀⣀⠀⡯⠀⠀⠀⠀⠀⢳⣿⡇⠀⠀⠀⠀⠀⠀⢰⠆⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣶⣤⣤⣠⢘⣛⠛⠿⠿⢷⣶⣶⣤⣤⣟⣟⣥⣄⣀⣀⣀⠀⠀⢸⢻⣿⡃⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⡄
⠀⠀⠀⠀⣠⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣤⣭⣉⡙⠛⠛⠋⠀⠉⠉⠉⠂⠘⢻⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⣯⣽⣛⡿⠿⢿⣿⣿⣿⣿⣻⣿⣽⡉⠉⣠⣺⣟⣷⣺⣴⢀⡤⢀⣴⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠠⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢷⡿⣿⣭⠈⠉⠉⠸⠿⣿⣿⡿⢋⡵⢋⣴⣿⣿⡿⠀⠀⠀⢼⡿⠿⠿⢛⣡⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠋⠠⢶⣶⠄⢀⠴⢋⣴⣿⣿⣿⡿⠛⠶⢦⣄⡀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣿⣿⣿⣿⣿⡁⠀⠀⢈⣿⣷⠉⠙⠛⠿⢿⣿⣿⣿⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⣷⣤⣴⣿⣿⣿⣷⡦⠀⠈⠀⠀⠉⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿