Puppies Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠟⠟⠃⠐⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠇⠀⣀⠀⠀⠀⠀⠀⠐⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠛⢨⣲⣿⡀⠠⠿⠃⠀⠤⢤⡀⢀⣙⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣭⣥⡆⠀⠜⠋⠀⣾⠶⠟⠃⠀⠀⣀⠀⢀⡐⠊⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣗⣻⣧⣦⠈⢹⣃⠽⠋⠀⢀⣛⣁⠀⠘⠀⠰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⠛⢿⡟⣻⡙⠛⡀⣤⣦⣾⣿⠿⠆⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣷⡻⣡⣿⡁⠄⢧⠀⠈⠉⠁⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⣡⣴⣿⣿⣿⣷⣦⡘⢧⠀⠀⠀⠀⠀⠀⣴⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⣿⣿⣿⣻⣿⡿⡜⣧⠠⡁⠀⠀⠀⠈⠻⣟⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣿⣿⢻⣶⣽⣿⣿⣿⡛⣿⣿⠏⣿⣦⣄⣀⠀⣀⣪⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠿⣷⡄⠘⣟⢁⠉⡻⢿⣽⢿⣏⣬⣻⣿⡄⣿⠉⠉⡅⠿⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣁⠀⠈⠐⠈⡷⡃⠀⠀⠀⠉⣙⣿⡿⠙⠩⠰⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣋⠀⠀⠊⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠁⠅⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠐⢊⣹⣦⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣴⣶⠄⠉⠋⠻⣿⣧⣄⡐⠀⣉⣤⡄⠀⠀⠈⠀⠀⢀⠱⠶⣦⢷⡟⠀⠘⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡅⡀⠘⢠⠐⠄⠉⢯⣛⢷⣤⣋⡤⠀⠃⠀⠀⡰⠟⠀⠀⠙⡏⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⠙⢀⠀⠁⠀⠐⠈⣿⣷⣭⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠙⣇⣀⠀⡀⠀⠀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⣈⠁⠀⢠⠀⠀⣘⣿⣿⡄⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣭⣠⠂⠀⠀⠀⠘⢿⡻⢶⡞⢀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢖⣄⠁⡀⠀⠀⠉⠙⠓⢆⡀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⡤⣀⠀⠀⠇⠐⠆⢻⣇⣀⣄⣊⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠠⠾⠶⠗⠂⠉⠀⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⢀⢤⠄⠊⠀⠁⠈⠐⠠⣀⡀⠤⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡀⠔⡡⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠠⠐⠊⢀⠔⠀⠀⠀⠀⢀⠔⠂⠐⢄⠀⠀⠈⡀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⣷⡄⠠⠀⡠⠁⢀⠀⠀⠀⠂⠀⡇⠱⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠿⠷⠀⢀⠁⢠⣿⣗⠈⡇⠈⠀⡇⠀⠈⠂⢄⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣶⡉⠒⠚⢤⡀⠙⠻⠃⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠣⠀⣀⠀⠄⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠉⠁⠀⠀⠉⠀⣀⠠⢔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢲⡂⠀⠀⢀⣈⠥⠐⣈⠔⠈⠁⠒⠤⣀⠀⠀⠀⠀⠀⠰⠀⠸⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡙⠀⠉⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⢁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣹⠀⠀⠘⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢾⠀⠀⠀⣆⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⢉⣀⠉⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠖⠉⠀⠀⠀⠸⡀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠂⠀⠀⠀⡇⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⢀⠔⠀⠀⠀⠰⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠴⣀⣰⡡⢀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠊⠀⠑⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠊

⠙⢿⡗⠶⣤⣄
⠀⠀⠻⣆⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠋⠉⠙⠛⠛⠶⣤⣄
⠀⠀⠀⠘⢧⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠈⢳⡄⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠹⣦⣀⡀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢀⣠⠠⠠⠀⠀⠀⠀⠀⠀⢠⢤⢀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠛⠿⠟⠀⠄⠀⠀⠀⠀⠀⠸⡾⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠈⣯⢻⣄
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢹⡄⠉
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃⠀⠘⢷⣄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣰⡷⠶⠴⠶⠞⠛⠉⢻⡄⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣾⠁
⠀⠀⣴⠟⠀⠀⠀⠀⠀⠁⠈⢷⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿
⠀⢸⡇⠀⡀⠀⠀⢠⠀⠀⠐⢀⡿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡠⠼⢧⣄⡀
⠀⠀⠙⠶⢦⣄⣀⣼⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠊⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⣧⣀⣀⣧⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡤⠾⣥⣀⣀⣴⢦⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠓⠐⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠔⠉⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⢄
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⡇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢸⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠈⣧⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣷⣿⡀⠀⠀⠀⠀⢀⡟
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡸⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠜⠈⢧⠀⠀⠀⠀⡞
⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⠇⠀⠚⠛⠛⠃⠀⢀⣴⣒⣛⣓⣦⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸
⠀⠀⠀⠀⠈⢣⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠏⠳⣄⡸
⠀⠀⠀⠀⠀⠀⡇⢀⡜⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠟⠒⠤⠄⣀⡀⠀⠀⠁⠀⢀⠠⠄⠒⠊⠉⢆⠀⠀⠀⠀⠀⡈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊⠁⠀⠀⠀⠀⢀⠈⢆⠀⠀⠀⢀⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⡜⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⠀⠀⠀⠀⠀⢨⠓⢴⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⠀⠀⡾⢀⡌⠀⠀⠀⠀⠀⢀⠃⢠⠂⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢆⡆⠀⠀⠀⠀⢠⠉⡏⠀⠀⠀⠀⠀⠀⣸⠤⠇⠀⢀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠃⠀⠂⠁⠀⠓⠄⢄⣀⣀⠄⠠⠃⠀⠈⠁⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠚⠉⠉⠑⠒⢤⣀⡠⠔⠒⠊⠉⠉⠉⡛⠙⠒⠶⠤⢄⡀
⠀⢀⡴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠔⠒⠛⠛⠲⣄
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣾⣿⠋⢹⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⢻⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⠿⡁⢈⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢣⡀⠀⠀⢀⡾⣿⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢳⣀⣴⠟⠀⢿⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠉⠓⠦⣕⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⣷⡀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⢀⣠⣴⠏⠀⣨⡖⠀⡀⠀⠀⢀⡾⠁⠀⠈⢷⡀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠋⠁⣀⡴⠋⡇⠀⠰⠀⣠⣿⠀⠀⠀⠀⠀⢻⡄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⠴⠚⠉⣠⡾⠀⠀⢀⡶⠋⡏⢳⡄⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠿⠟⢁⣀⡴⠋⠀⠀⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠇⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⡰⠀⠀⠀⠸⡆
⢰⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠠⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢹⡄
⡇⡆⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣧
⡇⠸⡀⠀⠀⠀⡰⠊⣿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢣⠀⠙⠦⢤⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠄⠒⠒⠂⡄⠀⠀⠀⠈⡇
⠈⠳⢤⣀⡼⠁⠀⠀⣿⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⣇
⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡴⠛⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡁⡠⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠡⠀⠀⢸
⠀⠀⠈⠳⠿⣤⣶⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⣷⠀⠀⠀⠀⠀⠑⢄⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⠐⠀⠀⢸⠀⠀⠈⠛⠲⠶⠤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠸⣧⣀⢠⡏⠀⠀⣠⠀⠀⠀⠀⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠈⠉⠛⠻⣤⣀⣿⣀⣀⣀⣠⣾⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣄⠀⠀⢸⠀⠀⠀⢀⣧⣤⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣳⣶⣶⣛⣁⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⣶
⠀⠀⠀⠀⠀⠠⢣⠛⠛⡀⠄⠀⠀⢀⣀⣀⣤⣄⣀⣀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢼⡿⢆⠺⡶⠀⠀⠈⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠟⠿⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸⠟⠉⠛⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠻⠭⣀⠁⠁⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣆⠀⠀⠈⠈⠙⠋
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢀⠀⠀⠀⣴⣅⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠿⢷⣦⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣀⢰⠦⡀⠀⠀⠀⠀⠀⠀⣼⣬⡖⣠⠈⠆⠀⠀⣽⣿⣿⡿⣾⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛
⠀⠀⣶⣾⣿⣷⣶⣶⣦⣤⣤⣴⣌⣣⣾⣿⣻⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠰⠆⠀⠀⠙⣿⡿⠃⠀⠦⡀⠀⠐⠀⠈⠀⡀⡀⠄
⠀⠀⣿⠻⢿⣿⣿⣿⣿⣿⣿⠟⠏⠇⠀⣠⣉⡀⠦⠀⢠⠊⠙⠉⠛⠛⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠁
⠀⠀⣠⡀⠐⠯⠽⠿⣿⣿⣧⡐⠀⡀⠐⠁⠀⠁⠀⠀⡆⠳⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠒
⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠁⠑⠊⠉⠀⠀⠀⠀⠀⠀⠑⣄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉
⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣶⣦⠀⠀⠀⠰⠤⠂
⠀⠀⢿⣷⡀⠀⣼⡿⣷⠀⣠⣴⣶⣿⣿⣆⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣦⢤⣴⣶⣶⣦⣤⣀⣀
⠀⠀⠈⣿⣿⣿⣿⣧⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣯⣼⢯⣔⣆⣀⣀⣀⣀⣸⣿⣫⠟⠁⠀⣿⣝⡻⣿⣼⣿⡿⢸⣿⣿⣿⣿⣶⡼⣟⠛⠛⠛⠲⠦
⠀⠀⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠀⢸⣟⣅⢀⣙⣿⣿⣿⡿⣿⢝⡻⡟⠉⠀⠀⠀⠈⠉⠻⡏⣿⣿⣷⠘⢻⡿⣿⣿⡿⣿⣿⡀
⠀⠀⠐⣿⣿⣿⡿⣿⣿⣿⣿⡿⢃⣼⠃⠀⠀⠀⠀⠉⠻⠛⠛⠿⢯⡅⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⣿⡟⠛⠻⣶⡎⠀⠘⢿⣧⠙⢿⣧⡀
⠀⠀⠀⠀⠉⠉⠴⠟⠈⠙⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠂⠀⠀⠈⠢⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡇⠀⢀⣴⠏⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠙⠐⠁⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠿⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠤⠊⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣠⠊⠁⠉⠐⢆⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠑⠢⠄⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠋⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⣀⣀⣀⡀⠀⠀⢠⠖⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠹⡅⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠉⠈⠁⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣠⠶⠀⠋⠀⣀⣘
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠃
⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⢛
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢠⠇⢈⠀⠀⣀⣤⡠⠀⠀⠶⠀⢀⣶⠄
⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠁⠀⡘⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⢀⣤⣶⣶⣶⣦⣄
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⣤⣽⣿⡇
⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠶⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠘⠻⣿⣿⣿⣷⣄⣀⡤⠤⣄⣀⣀⠀⠀⠀⣀⣠⡀⠀⠀⠄⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⡁
⠀⠀⠀⠀⠉⠙⡻⠛⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⠙⢷⡀⠀⠀⠢⡀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡜⠁⢀⣤⣤⣤⣄⠛⠿⢿⠿⠟⠁⠀⠀⠙⢆⠀⠀⠈⠀⠄⡀⠀⠀⠀⢩⠈⠀⠚⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢸⠁⠀⣿⣿⣿⣿⣿⡆⠀⠀⢠⣴⣶⣶⣤⡀⠀⠑⠠⠀⠀⠀⠀⠐⠀⠀⠿⣤⡀
⠀⠀⠀⠀⢸⡀⠀⠹⢿⣿⡿⠟⠁⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠂⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋
⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠏⠀⠀⠀⠙⠐
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⠦⠀⡀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢅⠂⡄⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⠀⠳⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠄⠐⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠁⢀⣀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠈⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⠀⠀⠞⡟⠁⠀⠀⣀⣀⠘⠖⠀⠂⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠘⣦⡀⢀⠀⠀⠀⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⣴⣼⠀⠀⠀⠂⣉⣁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣀⣀⡀⢠⠀⠈⣿⣄⠁⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠠⢻⡏⠀⠀⢠⣼⣿⣯⣷⠀⠂⠀⠀⠀⠀⠀⠘⠀⡀⣾⣿⣬⣿⡦⠠⠀⣿⣿⣷⠀⠀⢠⠀⠀⠹⣄
⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢸⣿⡇⠀⠆⠀⠈⠛⢋⡁⠈⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠛⠛⠅⠀⢀⡃⢹⣿⣿⠀⢀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡼⢣⣰⡇⠀⠀⠸⣿⡇⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠃⠀⢹⣿⡄⠀⠛⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⣿⡇⠀⢤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢾⣿⣿⠀⡀⠀⠀⠀⠀⠀⠲⠛⢆
⠀⠀⠀⠀⣾⣿⣿⣦⣠⠀⠀⠀⢸⣇⢰⡄⠀⡀⠀⠀⠈⠀⣴⣥⣤⣤⣵⣿⣿⣆⠀⢀⡀⠀⠀⢀⢀⠉⢡⣴⢻⣿⡆⣿⣶⣄⠀⢠⣶⣆⣰⣦⡁
⠀⠀⠀⠀⢸⣹⣿⣿⣿⣾⣼⣴⠸⣿⣸⠐⢩⣞⠀⠄⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⠇⠀⢑⠀⠀⣸⣶⡇⢸⣿⢸⣿⣇⢸⡗⣿⣴⣾⣟⢠⡿⠏⠁
⠀⠀⠀⠀⢘⣽⡿⢿⡏⣴⣷⣾⠀⣇⡝⢆⡀⢿⡇⠖⠀⠀⠙⠻⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⠟⠁⣠⣿⣿⢾⣿⣿⠸⣿⣿⣯⡀⣰⣿⠁
⠀⠀⠀⠀⠀⠉⢳⣿⣿⣿⣿⠉⢰⣿⠀⠈⠁⠀⢣⠀⠀⠀⠀⠀⠀⠙⢋⡀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠘⠁⡀⢿⣿⠀⣿⣿⢏⢈⠇⡜
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⣼⠋⣱⡀⠀⠀⢸⣷⣄⠀⣀⡀⣸⣷⣶⣄⣀⣀⠀⢀⣠⢟⣤⠎⠀⠚⠓⠀⢹⣿⣿⡇⢹⣿⣿⣋⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠿⣸⡧⠿⠟⠀⠀⣤⣌⠻⣟⣿⣿⠿⠉⠉⡿⠿⠛⢻⣿⣟⡥⠊⠁⠀⠀⢀⠀⠀⠈⠲⡝⣿⡘⠓⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠀⠀⡀⠀⠀⠈⠉⠀⠈⠻⣿⡆⠀⠀⠀⠀⢀⣴⣿⠞⠁⠀⠀⠀⠀⠀⠑⠀⠀⣀⣪⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣤⣤⣾⡿⢋⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⢿⣄⠀⡆⠀⠀⠀⠀⠈⠊⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⣾⠇⠀⠙⣤⣠⣼⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡟⠈⢟⢆⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠾⠿⢟⠟⠙⠈⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠉⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡑⠀⢠⡄⢀⠀⠀⢀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⢷⣶⣄⠀⡧⠆⣀⠀⠀⣀⣠⣄⡀⠰⠿⠆⠀⠀⠀⠀⠀⠈⠙⠂⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⡽⠷⠹⡷⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡴⠟⠛⠿⠛⠋⠙⠛⠛⠛⢷⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣬⡤⠖⠛⠂⠀⠀⠉⠳⠀⠀⠀⠀⠀⠴⠊⠉⠉⠩⠿⠶⢶⣄⡀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⢀⣿⣥⠀⠀⠀⢀⣤⠴⣶⣦⣤⡀⠀⠀⠀⣠⣴⠶⣶⣶⣤⡀⠀⠀⠹⣿⡆⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠘⣿⣁⡀⠀⡴⣿⣿⣶⣿⣿⣿⣆⣄⢠⣀⣿⣿⣾⣿⣿⣿⡟⣦⢠⣿⢿⡇⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⣿⡿⠟⠁⢘⣿⠿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⣫⡄⠙⠋⠉⣀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣭⠀⠀⢀⡔⠉⠀⠀⠀⢀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠉⠲⠀⠀⣼⠁⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣯⣀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣋⣉⣽⣿⣷⡄⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣷⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣠⣴⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠛⣧⠀⠰⣄⠀⢀⣴⡤⠚⠁⠀⠙⠶⢦⣤⡀⠀⠀⡔⠀⣸⠛⠷⢶⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠻⣅⣀⠀⠀⠀⠀⠀⠀⣀⣨⠟⠛⠛⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡄⠀⠀⠌⠀⢂
⠀⠀⠀⠀⠀⡀⠄⠐⠒⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⡀⠀⠈⠀⠉⠀⠀⡠⠁⠀⠀⢠⠁⡠⠁⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⢠⣀⡠⠀⠀⠀⠀⠀⠀⢀⣀⡐
⠀⠀⠰⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠰⠀⠀⠀⠰⠀⠠⠀⠀⠀⠤⠀⢁⠀⠀⠀⠀⠈⠁⠀⠄⢀⣇⠀⠔⠀⠁⠀⠀⠀⠈⢙⠁⠀⠉⢀⣀⠈⠀⠈⡏⠁
⠀⠀⠀⠁⢀⡆⠀⠀⠶⠀⠀⢀⣇⠔⠁⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⣈⣉⠀⠀⠀⠈⠀⠀⠀⠀⢨⠀⠀⠀⡈⢏⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠀⠀⠀⠌⠀⠀⠀⠀⠀⠤⠀⣀⠉⠉⢁⠀⣠⠄⠀⠀⠀⠀⠀⠃⡀⣀⠀⠠⣀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠠⠒⠄⠀⠀⠀⠀⢀⠀⠀⠤⠤⠤⠐
⠀⠀⢠⢡⡄⢀⠉⠀⠀⠀⠁⠀⣢⠑⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡄⠈⢂⠀⠀⠀⢠⠀⠀⠁⠀⠀⠁⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠁⠘⠁⡄⠀⠀⠀⣄⠘⠀⠁⠀⠀⠈⠄⢀⠃⠰⠄⠀⠀⠤⠀⢀⠀⠐⠀⠀⠀⠈⠀⠀⡀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠘⠀⠄⠹⠿⠁⠄⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠶⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣙⡀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠘⠀⡰⠷⡄⠘⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠈⠀⠄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⠀⠀⠠⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠂⠉⠈⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠦⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠠⠤⠂⠀⠀⠀⠀⠘⢧⡂⠀⠶⠊⢲⠆⡀⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠀⠀⠒⠋⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⡀⢀
⠀⠀⡀⠀⢠⢠⡄⠀⠀⢠⡄⠀⠈⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠔⠁⠄⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⠀⠠⠀⠠⠄⢀
⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⡁⠀⡀⠀⠀⠀⠀⠀⠐⢤⡄⠒⠂⣄⠔⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠒⠀⠀⠀⡂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠨⠁⡀⠸⡟⠀⠈⠁⠔⠀⠀⠀⠀⠁⠀⢀⡄⠉⢠⡈⠁⣄⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⢶⠆⠀⡀⠀⢀⠃⠀⠀⠈⣇⠀⠁⢀⡀⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠙⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠺⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠒⠁⠡⠀⠸⠕⠀⠂⠁⠀⠀⠀⠀⠨⣇⠀⠘⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠲⠄⣤⠰⠆⠁⠀⠀⠂⠀⠀⠀⠘⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⠆⣠⡄⠰⠆⠂⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠉⡈
⠀⠀⠙⠠⢀⣤⡀⠠⠦⠄⢠⡄⠀⠄⠃⠀⠀⠀⢀⠀⠀⠀⠰⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⢈⡁⠀⠀⡘⠀⠀⠀⠀⠀⢰⠁⠀⢺⠂⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡⠠⠁⠤⠊⠀⠀⠀⠀⠀⠀⠈⠑⠀⠥⠈⠄⠊⠀⠀⠀⠀⠀⠀⠘⠶⢄⡉⣉⡴⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣤⣤⣤⣴⣾⡿⠛⠋⠉⠉⠙⢲⣶⣶⣶⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⡴⢋⣽⣿⣿⢫⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡕⣦⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⣸⠃⣠⣿⠀⢸⣿⣿⡿⣿⣿⣿⣷⡂⠀⠀⠀⢀⣤⣽⣿⣿⣿⣷⢹⣷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢠⡇⠀⢻⣿⣆⢸⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡟⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠻⣿⣧⣿⣿⣧⣿⣿⣿⣿⡿⠃⠀⠀⠈⠻⣿⣿⢻⣿⣿⠟⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⢿⣿⡇⣿⣿⣿⣿⠃⠀⠀⢀⣀⠀⠹⡟⠈⣿⠏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢾⣿⣿⠿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⠀⠀⠀⠀⢙⡟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⣶⡶⠛⠋⠈⠀⢰⡄⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠻⢿⣧⡙⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢬⣙⣓⠂⠀⠀⠀⠀⠀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠛⠛⠀⠙⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⠹⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠀⣠⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠢⢤⣄⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉
⠈⢳⣤⣀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡿
⠀⠀⠉⠉⠡⣴⠶⠊⢹⡇⠀⠀⠀⠀⠀⠀⣰⡯⢶⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡤⣰⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣤⣾⠋⠀⠀⢠⠟⠀⠀⠙⠓⠆⠒⠷⠒⠋⠀⠀⠀⠀⣸⢱⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠉⠀⠾⢦⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⣭⠆⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠘⠦⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠱⣦⣄⣀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢰⣬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠲⣄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⢠⠀⢠⠀⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠐⢂⡰⢯⡁
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠀⡀⠹⣤⣶
⠀⠀⠀⠀⠀⠀⣾⠀⡇⢀⣤⠀⠀⣠⡄⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡏⠀⡇⠀⠛⡼
⠀⠀⠀⠀⠀⠀⠘⠶⣇⠀⠁⣀⣀⠈⠀⣸⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⠶⠞⠳⠶⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⣀⠉⠉⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠀⠀⠀⠙⣦⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣀⣀⠀⢸⡇⠀⠘⣇⡼⢻⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢈⡏⠀⠀⢸⡇⠀⠀⠹⠁⡾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣰⠠⠄⠠⠄⣆⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣸⣧⡀⠀⣸⣇⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢆⣘⣃⡰⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⡄⠙⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠈⡇⠀⡇⠀⠉⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣷⣶⣷⣶⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣭⣞⣿⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢸⠟⠉⠉⢩⣳⣲⢿⣟⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢦
⠀⠀⠀⠀⠀⠘⢄⠌⠀⢨⢋⣿⣵⣾⣿⣿⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠉⠯⢠⣼⣿⣿⣿⣿⣿⡿⠛⠃⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⣿⡏⠁⠀⠀⠀⠀⠀⠈⢳⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⠶⠦⣤⣤⣤⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠇⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⣿⣟⣿⣻⣯⣿⣟⣿⣿⣿⠿⣿⣶⣤⣤⡈⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⠿⣿⢿⣿⣿⣛⠉⠻⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣦⢄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣻⣾⣯⣿⣿⣿⣿⡅⢄⣻⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠘⣆⠀⠀⢰⣟⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡦⠋⠟⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠟⠟⢛⡉⣉⡁⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢣⠀⠀⢫⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣭⠴⠶⠛⠛⠛⢻⣿⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠇⠀⢸⠇⠈⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢳⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡳⣆⣀⠮⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡞⢻⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣋⠁⢠⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⠁⢰⠁⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡴⢛⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠁⢀⠠⠣⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠴⡤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡆⠀⠰⣄⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢀⡟⠁⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡸⣿⡃⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣷⠚⠁⠀⠀⣀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢤⣿⣿⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣤⡞⣣⣤⢬⣹⣶⣷⣴⣀⣤⣾⣠⣴⣦⣶⣴⣞⣁⣁⠰⡄⠀⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣾⣿⣾⣯⡛⣓⣿⣙⠿⠛⠛⠙⠙⠛⠛⢿⣿⢻⣿⠾⠟⣿⣾⣦⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢸⣿⢿⠟⠧⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡉⠙⠛⢁⣽⣿⣿⡏⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣖⢸⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣼⣼⢸⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢈⣿⠀⠀⠠⠀⢄⣾⣶⠁
⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣶⣿⢇⣼⣿⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⣀⠀⠈⣶⡆⠀⠀⠀⠀⠀⢸⣿⣷⡜⣿⣿⣿⢸⡴⣺⡾⠁
⠀⠀⠀⠀⠀⣴⠟⠳⢦⣄⣠⣤⣾⣿⣿⡅⣠⠃⠀⠀⠀⠀⠀⢂⣿⣿⢿⣿⣿⣾⡴⠀⠀⠀⠀⠀⠸⣄⣾⣿⣿⣿⣦⣌⣈⣠⡴⠫⠤⠄
⠀⠀⡀⣠⣼⡇⠀⢀⣦⣿⣿⣟⠙⢻⣿⡿⠉⠠⠊⠠⢄⡤⠀⠀⠧⣴⣾⣿⣮⠌⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⢻⣿⣿⣧⡄⠀⠙⢀⣄
⠀⠀⡴⠟⢻⣷⠓⠛⠿⣿⣿⠿⣷⣿⣿⠅⠀⠀⠀⠀⡀⠠⠀⠀⠀⠈⢻⡿⠃⠀⠀⠰⠄⠄⠀⠀⠀⠀⢸⣿⣿⣷⣿⢾⣿⣿⠟⠒⣦⡾⠻⢧⡀
⠀⠀⠘⢶⣾⣿⣶⣶⣦⣿⣯⢴⣿⣿⣿⣧⡀⠀⠀⠀⠀⢐⡓⣃⣤⣴⣿⣿⣦⣄⣀⠀⠂⠀⠀⠀⠀⣠⣼⣿⣿⣿⣶⣈⣿⣤⣴⣶⣾⣳⣶⠎
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠉⠙⠉⠛⠛⠛⠛⠉⠁⠉⠉⠉⠛⠛⠛⠋⠉⠉⠙⠙⠛⠋⠉⠀⠀⠀⠀⠙⠋⠙⠛⠛⠉⠛⠉⠛⠛⠋⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣍⣫⣭⣉⣽⣭⣿⣻⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡍⢻⣿⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠁⠙⠁⣼⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠳⡀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⣿⢹⣿⣿⣿⠋⠀⠀⠀⢀⡀⢀⠀⠈⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡏⠁⠀⠈⠁⠀⠀⠀⢀⣼⣿⣿⣷⠀⠸⢿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠆⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠟⠀⠀⠀⠀⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣄⠀⠀⠈⠐⠐⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⣍⣀⣠⡴⠇⠀⠀⠀⢠⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⡄⠀⠀⠉⠉⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⢶⣶⢶⢶⡶⠿⣯⣍⠻⢿⣦⠙⣿⣟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣦⡴⠾⠻⠉⠁⠠⠀⠈⡜⠉⠈⠁⠀⠠⠙⣷⣄⠻⣦⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣶⠟⠿⢻⣽⣿⠏⠀⠀⠀⠀⠀⣧⡀⠀⢠⣥⢀⣄⠀⢀⠀⠹⣿⣦⠀⢲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡋⢸⠁⠀⠀⣾⣿⠏⠀⠀⠀⠤⢴⣾⣾⣧⠀⢠⣿⣿⡿⣧⣾⣿⣤⣤⣿⣷⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣤⠾⠿⢿⣿⣆⢸⣿⠁⠀⠀⣿⡿⢬⠉⠻⣿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢠⣿⣿⠀⠀⠐⣼⣧⡀⠀⠀⣿⣿⠈⢿⣷⣦⣾⣿⣷⢶⣼⣿⣿⡆⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣸⣿⣿⠀⠀⠈⢡⢴⣾⡓⢸⡿⠛⡆⢀⡛⢯⣼⣧⣵⠞⣼⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⠏⢸⣷⣠⣶⡞⠻⢌⡙⠷⣾⡁⠠⠐⠀⠉⠘⠙⢷⣶⣾⣿⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢚⡟⠁⠀⢐⣦⣀⣀⣠⠏⠀⢰⣶⣦⠀⠀⠀⠀⠈⠉⠹⠇⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠛⠿⠛⠃⠀⠀⣈⡉⠀⠐⣲⣶⣤⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠁⣴⣾⣿⣿⠗⠀⠀⠀⣼⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡷⢿⣿⣶⣦⡀⠀⠀⠀⠀⠐⣼⣿⢻⠿⣖⣆⠀⠀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣴⣽⣿⣿⣷⡄⡀⠀⠀⢸⣵⣧⡼⠦⠀⢉⣴⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠼⢿⣿⣿⣿⣿⣿⣉⠐⠛⢀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢈⡋⠈⣩⣾⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣉⠽⣿⣿⣿⣿⢿⡇⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠋⠀⠘⠲⠿⠞⢻⣏⣾⣸⠃⠹⣿⢳⣿⡿⣏⠻⠿⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⡄⢀⣤⠀⠀⠀⠈⠙⠁⠀⠀⠀⠊⠋⠉⠀⠀⠀⢀⣀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠛⢿⣿⣷⣶⣖⣫⣴⣸⡀⠀⠀⠀⠀⠀⢀⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠄⠚⠛⠻⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠘⣿⠏⢙⡿⢿⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡿⠛⠿⠷⠿⠳⠖⠚⢿⡀⠛⠀⠀⠀⠀⠉⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢰⡆⠀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠆⠀⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⠀⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠃⠀⢸⠀⠁⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⡰⣿⢶⣄⣸⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⠀⣿⣄⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⡐⢄
⠀⠀⠀⠀⠀⣆⠀⠀⠇⠀⣠⠇⢀
⠀⠨⡅⠀⠀⢀⣀⡀⢦⠔⢫⡆⠀⠠⣤⣀
⠀⠀⠀⢘⣃⠙⠊⠁⠀⠀⣸⠅⠀⡴⠋⣸⣇⠹⣶⣶⣖⠲⠖⣛⣓⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢹⠀⠀⠀⠀⢻⡏⠀⢻⠋⠀⡿⠋⠏⠋⠉⠀⢀⡄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡎⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠎⠀⠀⠈⢁⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣬⡃⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣆⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣽⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠘⢷⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣿⣿⣄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡟⠈⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠒⢡⣒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠟⠀⣄⣒⠄

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡭⠂
⠀⠀⠀⠀⠀⠉⠁⠈⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠠⢈⠀⠀⠀⠚⢱⠀⠤⠀⠀⠀⠀⠀⠁⢽⠉⠈⡇⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠠⠤
⠀⡄⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠉⠀⠀⠀⠁⠀⢀⠀⢄⠀⠀⠴⡀⠍⠨⣁⠀⠀⡀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠁⠀⠈⠀⡄⠀⠀⠀⠀⠀⠄⠀⢀⡄⠈⠀⠀⢸⠅⠀⠀⡠⠚⠑⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠘
⠀⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⣀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠂⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠠⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠈⠀⡼⠃
⠀⠀⠀⠁⡁⠀⠀⠒⠤⠀⠀⠀⠀⠈⢀⠀⠢⠔⠀⠄⠀⠀⠀⠀⣸⣀⡼⢸⣩⡧⣞⣽⢘⣯⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⡁⢠⢀⡠⢠⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠋⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⢠⣰⣦⠀⠀⠀⢀⡀
⢀⠠⠀⠀⠐⠀⠀⠀⠠⡈⠀⠀⠀⢀⡐⠀⠀⠀⡀⢀⠃⠀⠀⠀⣡⠁⡀⠀⠀⠀⠀⠸⠀⠠⢠⠀⡄⠀⠈⡀
⠀⠙⠁⠀⠀⡀⠰⡀⠀⡁⠀⠀⠠⠈⠀⡀⠸⠀⠐⠀⠀⠀⠀⠐⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠚⠀⠃⠀⠀⠀⠰⠊⠀⠀⠀⠀⠅⠈
⠀⣀⠂⠨⠁⠀⠀⠈⠂⠀⠀⠀⠁⠀⠊⠈⠀⢀⠐⠀⠀⠀⠀⠀⢠⠀⠡⠘⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠰⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂⠒
⠀⡁⠀⠖⠒⢠⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠱⠈⠶⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⢀
⠀⠀⡁⠀⠁⠞⠀⠀⠀⠀⠀⡆⠘⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠥⢀⠉⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⡄⠀⣠⠂⠈⡏⠻⠄⠀⠀⠀⠀⢠⠇⠂⢀⢀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠡⠄⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡤⠶⠶⠶⠦⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡄⣀⠀⢀⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣇⠈⢤⠈⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠒⠒⠁⠙⢧⡀⣠
⠀⠀⠀⠀⠀⠀⢀⡟⢰⡄⠀⠀⠀⠀⠀⠀⢠⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⠄⠀⡇⠀⢷⢻⡇
⠀⠀⠀⠀⠀⠀⠘⣇⣸⡇⠘⠟⠀⠀⠻⠃⢸⣇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⣀⣀⣇⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⠀⠀⢶⡶⠀⠀⣸⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⢤⣤⣤⡤⠞⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣆⠀⣰⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⣤⣤⠤⠀⠀⡇⠀⠀⢹⣴⠏⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠋⢠⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⡇⠰⠀⠰⠂⣇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢀⣸⢧⣀⢀⣠⣇⡀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢄⣙⣁⠴⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢹⠁⠀⡇⠀⠘⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣷⣶⣷⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⡄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⡶⢖⡤⠀⢢⠒⢶⡒⢄⡲⠍⢪⡙⠙⢿⣦⡸⣿⡓⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⣰⣏⢋⡖⡡⡊⣀⢵⡇⣧⡸⠮⣔⠈⠢⣄⠈⣢⡹⣿⣿⣷⣦⡀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣿⣾⡿⣩⠋⠼⠈⠊⢐⠲⡄⢏⡖⡩⠀⠀⠀⠀⠀⠀⠛⣮⠻⠿⣿⠛⣎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⡏⣵⠋⠀⠁⣡⢶⡆⠁⣧⢸⠀⠸⣟⣳⡦⢄⠀⠀⠀⠈⢳⡽⠃⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⢀⣤⣺⣿⣿⣅⡴⢿⢹⣦⣤⣿⠋⣷⠿⢶⣾⣆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡿⣾⣿⣟⣹⡿⣋⠕⠚⣀⣒⡁⠒⢅⠃⠘⠂⢸⠛⠆⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⣌⣼⡴⣣⣶⡖⡋⠙⠲⣍⠢⠙⣆⠶⠿⠀⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡟⣿⣿⣰⣿⣯⣿⣧⠻⠖⠘⠷⣌⣌⢆⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣧⣿⣿⠧⢻⣮⣛⣯⣿⠎⠀⣑⠲⢼⡈⡌⣆⢻⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢞⡽⢿⡌⣸⣞⢧⡀⠪⠍⠡⢧⢿⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡼⣎⣿⡽⣏⠻⣧⡈⢅⢲⣂⠜⣿⣸⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣼⣹⣷⣾⣿⣷⣿⣿⣄⣉⡁⣼⣿⠟⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣛⣿⣿⣷⣞⣿⣯⣿⣿⣦⣤⡽⠃⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⢿⣿⠿⣿⣿⣿⣿⣿⡛⣿⡏⢹⠏⠀⠀⠀⢈⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡆⢻⣆⡰⠈⣿⡍⢱⡇⢹⠇⠘⠇⠀⠀⠀⡌⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠸⣿⡀⠙⣿⣶⠴⣧⣄⣠⣴⠷⠶⠀⠀⠀⡐⠁⢀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠱⡤⠘⣿⡄⠸⣧⠄⠉⡽⠇⠁⠀⣶⡅⠀⡼⢁⡀⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⠀⠙⢇⡨⢿⡦⠙⣿⠇⠀⢸⡀⠀⡟⠀⣴⠄⠈⢁⣴⠁⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠹⣧⣀⠈⠷⢦⣤⡞⠀⣶⠀⠀⢁⡼⢁⣈⠁⢀⣰⣿⠃⠐⢡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣧⠀⠉⠛⣣⣄⡈⠁⠀⡀⠙⣿⡴⠟⠀⠘⠁⢀⣼⠋⠀⠀⣴⣛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠘⣦⣄⠀⠙⠻⢿⣦⠀⠻⡄⠸⠁⠀⠀⠀⣠⣎⠉⠀⢀⡾⠾⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⠀⠈⠉⠳⠦⠀⠀⠹⢧⣄⠉⠂⠀⠀⠀⣴⠁⠀⠀⠀⠚⠳⠐⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⠐⠇⠀⠒⠒⠒⠒⠒⠀⠛⠚⠃⠂⠒⠛⠛⠒⠒⠒⠒⠒⠂⠀⠂⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⣄⢀⣀⣠⣤⡤⠤⢤⣤⠤⠤⠤⢤⣴⡿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⡴⠂⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢾⠀⠀⠀⡠⢤⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣮⣽⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⢸⣿⣷⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⣿⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣤⡀⠀⢰⡏⠀⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣶⣾⣿⣿⣿⡇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢶⡄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣄⡀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠻⢦⣀⣀⣠⠴⠚⠉⢁⣀⣀⣠⡽⢳⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠀⠀⠀⠀⠀⠀⠘⠹⣿⣷⣶⣿⣿⣿⠿⠋⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠢⡀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⢀⣠⣴⣶⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣰⣄⡀⣠⣤⢀⣀⣤⣠⣾⣿⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠛⠋⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠋⠙⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⠶⠤⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀
⠀⠀⠀⠀⠀⠄⠀⠀⢀⡴⠁⠀⠀⠀⠈⢂⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆
⠀⠀⠀⠀⢸⠀⠀⢀⡞⠁⠢⠀⣀⣀⣠⣬⡤⣼⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣷
⠀⠀⠀⠀⠈⢆⣠⠎⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣀⡤⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⢀⠇⢸⠃
⠀⠀⠀⠀⠀⠀⡏⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⠤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸
⠀⠀⠀⣰⡂⠀⠸⣥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⣵⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡼⢿⡄⠀⡜⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢰⠁⢰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠳⠛⠀⠀⠃⠀⢀⠤⠒⠛⠉⠉⠉⠙⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢸⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠁⠀⢻⠛⠋⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢀⣠⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⡠⠋⠛⠓⢲⠟⡫⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡒⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⡴⠉⣈⠀⢀⡞⠀⠀⢀⡴⠁⠀⢀⣠⠤⠤⢄⣀⡀⠀⢀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠃⡜⠁⠀⠘⣇⣀⣠⠞⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠣⡀⠀⡆⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠠⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⠀⢳⡀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠚⠉⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠎⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⣇⠀⠀⡄⠀⠀⢀⡴⠃

⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠔⠁⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠆⢉⠀⠤⠀⠀⢨⢢⠀⠀⠀⠀⠀⠄⢈⠁⠀⠀⠀⢠⠐⡀
⠀⠀⠀⢸⠀⠚⢁⣀⣀⠉⠀⡥⠈⡄⠀⠀⠄⠀⠀⡃⢤⡴⠁⠸⠂⠀⠁⠀⠀⢐⠉⡔⠀⣀⡀⠀⣀⡀⠀⠈⡀
⠀⠠⠀⠘⠀⠀⠈⠻⡋⠀⠀⠀⠀⠁⠀⠰⠀⠀⠸⡁⠴⠀⢠⣤⡄⠈⢾⠀⠀⡅⠀⢆⠐⠉⣀⣀⠈⠑⡀⠀⠈
⠀⠀⠀⠀⢶⠠⠴⣌⠋⠗⠐⠃⠚⠀⠀⠀⠰⣠⠀⣇⠀⠀⡀⠽⢅⣠⠞⠀⠀⠡⠀⢸⠀⠀⢙⡋⠀⠀⠤⠀⡠
⠀⠀⠀⠀⠀⠙⠠⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠇⠀⠄⠂⠁⠀⠀⠀⠀⠑⠢⠛⠅⢀⠀⠀⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⡈⠐⠂⡀⠃⢀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠂⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠁⡀⣀⠈⠋⠀⣄⠀⠀⠀⠀⠐⠀⠀⠀⠿⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠋⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠖⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢁⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠇
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠘⠀⠡⠀⠀⠀⠀⠁⠑⠄⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠀⠀⢼⠀⠀⢀⡴⠀⠠⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠁⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠈⠃⠀⠀⠀⠀⠀⡇⠀⠀⢽⠀⣠⠀⠀⢀
⠀⠄⠀⠀⠀⠛⠀⠀⠀⠛⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠈⡁⠀⢈⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⣲⣿⡛⠈⣽⣿⣧⡐⠻⡏⣝⢛⣝⣿⣇⢻⣶⡤⠄⣴⣆⣶⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⣿⣿⠿⠋⠀⢈⣹⠍⣰⣿⠟⠋⠀⠈⠂⠉⠋⠫⣠⢋⠇⢉⠖⠈⠿⣿⣷⡀⠾⣏⠙⢶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠃⢈⣩⠁⠀⠀⢐⠾⢣⣾⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠉⠻⣿⣎⠛⣦⡀⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢿⡅⣾⡏⢀⡴⣽⠋⣰⣿⣿⠉⠀⠀⠀⠀⠄⣦⠀⠀⠀⣀⠀⢀⠄⡀⠀⠀⠀⠠⠍⢿⣦⠘⢣⡀⠈⠫⡉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⡇⣾⠀⠁⣴⣿⡟⠁⠀⠀⠀⠉⠀⣶⠻⡇⡀⠀⡿⠇⠈⣜⠣⠂⠀⠀⠀⠀⠘⣿⣧⠈⠁⠀⡐⣅⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢣⣶⣿⣿⠟⠀⠀⠀⠀⠹⢶⡴⠾⠴⣿⣧⠀⡤⡄⣼⣷⠶⠻⡧⠤⠀⠀⠀⠸⣿⣷⡀⠀⣉⣿⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⡁⣀⠀⠀⠰⠶⠶⠦⠀⠀⠘⣿⣿⡷⣿⣿⠁⠀⢰⠟⠂⠀⠀⠀⢰⣿⣿⠿⣦⡸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣉⣀⡤⢀⣠⣴⢼⣆⢀⣼⡏⠛⢷⠿⣿⣤⡴⡿⡶⣤⠀⢡⡀⢰⣿⠋⠀⠘⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡿⠟⠛⢻⠉⠋⣙⣛⢋⣹⠋⠀⠀⠋⠀⠉⢿⣴⣙⣿⠌⠱⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠘⢷⣀⠀⠁⡼⠋⠀⠀⠀⠀⠀⠀⠈⠻⡈⣁⣠⠞⠀⠘⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣯⠀⠀⣴⠈⠉⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠉⠃⣤⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡦⢙⣦⡈⢿⡅⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢀⣿⢀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠯⣤⣬⣷⡜⢷⡰⠟⠀⠀⠀⠠⣾⡟⠉⠙⣷⡄⠀⠀⢻⣿⢃⣼⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⢨⣿⣶⣾⣶⠂⠀⡀⠀⠀⢻⣻⣿⣿⡛⠁⠀⠀⢰⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠷⠀⠀⠉⠙⣩⣷⣿⣦⡀⠀⠀⢀⣤⢙⠻⣏⡅⠀⠀⠀⣾⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⢈⡹⢿⣿⣿⣿⣶⣤⣀⡀⠁⠀⢀⣠⣤⣴⡿⡿⠙⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠠⠔⠀⠀⠀⠀⠀⠈⠁⣼⠃⣯⡈⢏⡿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡟⣩⣶⣦⣀⠀⠀⠀⠀⠈⠉⠀⠈⢇⠈⠠⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢟⡾⠷⣿⡶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠖⠛⠿⢿⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠀⠉⠉⢴⣷⣿⣿⣦⣀⡀⠀⠀⠀⠀⣠⡾⢻⣿⡿⠧⢀⠀⣠⣙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⡀⠐⠀⠏⠕⠙⠃⠙⢷⣀⢠⡆⣼⡿⠀⠀⠀⠈⠀⠈⠁⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡦⠀⠀⢀⡠⠀⡀⠀⠀⠀⢿⣾⣿⡟⠀⢀⠄⢰⣠⠂⠀⢀⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠈⠁⠀⠀⠁⠀⠀⠈⢻⣿⡇⠀⠈⠀⠀⢸⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⣾⠀⠀⢠⡞⠀⠀⡇⠘⠛⠦⣦⣇⡀⠀⣤⠀⡟⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠾⠷⠶⠾⠿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠁⠒⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠲⡄
⢠⠐⠒⠀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠇⠈⠁
⡇⠀⠀⠀⢀⡀⠀⠈⠁⢀⡈⠀⠠⠀⠿⠀⠱⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠀⠀⢦⠈⢆
⢱⡀⠀⠀⠁⠀⠀⠀⠎⢉⣿⣿⣦⠀⠀⠀⡀⠀⠀⠀⠈⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⢀⣀⡀⠀⡼
⠀⢱⡀⠀⠀⠀⠀⠀⠁⢈⣻⡿⠟⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⠀⠀⢰⠀⠈⠀⠀⠊⠀⡀⠠⣿⠏
⠀⢀⠃⠀⠀⠀⠠⣀⡠⠴⠢⡀⠀⢀⠀⠀⣸⠇⠀⠀⣀⡤⠖⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢋⠉⠘⠁
⠀⠸⡀⡄⠀⠀⠀⡀⠀⠀⠀⠈⠉⠁⠀⠀⢱⠁⢀⠎⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠢
⠀⠀⠈⠀⣸⠀⠀⠇⠀⠀⠀⣰⠀⠀⠀⠀⢏
⠀⠀⠀⢠⠇⠀⠀⠘⠦⣤⠴⠃⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠂⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠠⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⣶⡈⢦⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⣀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⣀⠄⠈⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢣⠀⠀⠑⢄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠠⠴⠶⣤⡀⢘⢀⠀⠀⠑⠄⠀⠀⠳⣄
⠀⠀⠀⠀⢠⠔⠐⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⣶⣾⣻⡇⠀⠲⡄⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠁⢠⡀⠀⠀⠀⠛⡟⠋⠀⠀⡠⠓⠀⠀⠤⠤⠤⠶⠶⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣫⡵⠄⢹⡇
⠀⠀⠀⠀⠀⠀⣰⡶⠶⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⢀⣠⣴⠾⠋⢁⡞⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⢻⡆⠛⠒⠦⣌⡉⠛⠻⠶⣦⣤⣾⡟⠉⠀⠀⠈⡟⠻⠯⠄⠀⢠⡟⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⠙⢦⡀⠐⠋⠁⣀⠙⣄⠀⠀⢰⡇⠠⣄⠀⠀⠛⡿⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠐⠛⢿⡍⠀⢀⡴⣣⢠⣸⡄⠀⢸⣧⣐⡿⠦⠀⠈⢡⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⡀⢀⡀⠀⠈⠁⠙⠛⣹⠃⠀⠀⠻⣍⠁⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠀⠀⠀⠀⢀⡜⠁⢾⣭⣵⡆⠈⠓⢄⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⠏⠀⡀⠈⢹⣏⠀⢠⠀⠀⢳⠀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣄⡘⢆⡀⠙⠒⠋⠈⠛⠉⠀⣠⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣯⣀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠃⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⡿⠀⠀⢸⡃⠀⠀⠀⠀⠀⣰⠀⠀⢷⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⠀⢠⡳⣄⠀⠀⠀⡴⣧⠀⠀⢸⠆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠸⣆⠀⠈⢷⡀⠀⠀⠀⢰⠇⠀⠀⡾⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠓⠙⢦⠀⠀⢛⢦⣠⠴⡋⠀⢀⡾⠁⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣼⣷⣄⣨⣧⣿⣼⣅⣠⣾⣧⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣛⠟⠋⠠⣄⠉⠉⡁⠋⠙⠛⣟⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣿⠏⢀⣵⡄⣿⣆⣾⣇⣰⣶⡞⠻⣿⡻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢈⡅⢠⣼⣿⣾⢳⠁⠁⠿⣿⣿⣮⡀⢀⠃⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡿⣹⣮⣥⠋⠉⣿⢁⣄⠀⠀⠰⢫⣝⡁⠙⣆⣧⠠⣤⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣱⠋⡧⣥⣶⡿⢀⣴⣶⡦⣤⡶⣄⢣⣻⢖⣿⢸⠀⠁⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⢸⠅⣽⣿⠁⣾⠿⣣⣄⣠⡽⣿⡇⢹⣷⣿⠘⡆⡐⢿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣀⡆⣿⡟⠀⠉⣠⠨⣿⣿⠐⠄⠹⡠⣿⣿⢰⢣⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣮⠷⢿⡿⠂⣼⣴⡷⢾⡅⢾⣾⣦⣧⣼⡿⠙⣼⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢠⠼⣷⠂⢿⣿⣷⣶⣤⣾⣿⣿⣿⣿⣦⢄⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡧⢿⡀⢠⡼⡿⣿⣿⣿⢋⠟⢋⠟⠹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢤⡘⢿⠺⢿⣼⣮⣿⣵⡧⢶⢛⣤⣧⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢀⡀⢻⣌⢠⡟⠀⣼⣅⠀⢁⢸⡾⡿⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡁⠀⠁⠋⠛⠡⢮⣭⣭⣾⢮⣍⠈⡢⡀⡀⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡤⢋⣴⣔⠰⢠⣧⡼⠑⡈⢮⠀⠉⠑⠈⢀⠳⡄⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⢀⢸⡛⣴⣺⠀⣁⡆⠳⢸⠈⣦⠈⣆⡏⢣⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠇⠸⣿⠈⠰⣻⠇⢏⠁⡉⠼⠷⢼⡆⠃⡗⡺⠓⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢥⣷⢾⡎⠰⠖⠉⡄⠘⠀⠀⠀⠂⠈⠇⣼⠿⠷⢠⢀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠘⠻⠰⠀⢰⡦⢠⡈⠸⡀⣦⡿⠀⣤⡞⣉⡶⢀⡏⠃⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⡖⠋⢳⡄⢧⠀⢳⡝⠃⢀⢳⣿⣧⠈⣿⠟⢛⡃⢸⡏⣶⡶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣯⢆⠼⣷⡀⣄⠘⣿⠀⠈⠘⣼⢋⣰⣿⡄⢀⣵⣬⠀⢌⣷⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠁⠀⠺⡿⡱⣝⢦⣿⣧⣧⡴⢹⠀⣿⡿⣻⡿⡽⡀⠄⢈⣯⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠀⣼⡗⢁⢸⣷⠻⣿⢇⡇⠀⣶⠼⣫⡟⠴⡇⠈⡄⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣀⣌⣄⣄⣸⣷⠾⢷⣷⡶⠻⢾⣿⣞⣴⣴⣦⣻⣬⣿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣉⣉⣉⣁⣈⣉⣁⣀⣀⣉⣁⣀⣈⣉⣉⣁⣉⣉⣉⣉⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⢀⡈⠆⠐⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠑⡆⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡠⠔⠁⡐⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠘⡒⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⣠⢎⡀⠀⠀⠀⢀⠔⠁⠀⠀⠑⡄⠀⠀⠰⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢱⣿⣟⡀⠃⢀⠊⠀⣠⣄⢤⡀⠐⠀⠀⠀⠡⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠛⠻⠃⠀⠀⠀⢸⣿⣯⡄⡏⠀⡇⠀⠀⠀⠀⠑⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢾⣍⣉⠉⠙⣦⠀⠉⠛⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠀⠤⠀⠤⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⡀⠔⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡶⠀⠂⠒⠂⠀⡈⠅⠂⡩⠂⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢛⡖⠂⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠻⢶⡒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢰⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡴⢇⠀⠀⠀⢣⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⢸⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠸⠀⠀⠀⠘⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⢀⠔⠁⠀⠀⠀⣘⠤⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠣⠰⣥⠂⡄⠀⢀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿

⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⡄
⠀⢶⣯⡑⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡟⡄⡀
⠀⠀⠀⠁⠀⠀⣡⡀⠀⠀⠀⠰⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠁⠀⠀⠁⢰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣶⣧⣤⣶⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠲⡆⠠⠤⠤⢆⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠛⠉⠉⠉⠻⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡙⠀⠀⠀⠀⠈⡻⠁⠁⠀⠀⠰⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠼⡀⠠⠧⠀⢀⠀⠄⠀⠀⠀⠠⠀⣀⣀⣀⣀⠄⠀⠀⣀⠙⢠⡀⠀⣀⠀⠀⢷⣔⠒⠀⠀⠄⠀⠀⠉⠼⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠉⢠⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠋⠛⠉⠀⠀⠀⠀⢀⡀⠈⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⡀⢤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠙⠂
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢋⣤⠀⡠⣔⢂
⠀⠀⠀⠓⠄⠀⠈⠀⢂⠀⠀⠀⠀⢿⠶⠛⠈⠈⡃⠀⠀⢸⡟⠉⠁⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠓⠂⠘⠂⡀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠀⠁⠀⠑⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢈⡁⠀⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠖⠚⠉⠉⠉⠉⠒⠲⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⢀⣶⢦⠀⠀⠀⠀⠀⠀⡴⣶⡀⠀⠀⠸⡄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣞⣀⡀⠀⠈⠿⠞⣠⠖⠉⠉⠳⢄⡳⠿⠁⢀⣀⡀⢧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢠⠏⠉⠉⠙⠛⠛⠉⢰⣾⣭⣭⣷⡆⠉⠉⠉⠉⠉⠉⠙⡄⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⢀⡀⢉⣹⢿⣉⣀⡀⠀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠉⢏⡁⢀⡟⠁⠀⠀⠀⠀⠀⠀⣰⡷⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠤⣀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣠⣤⠚⢹⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠉⠓⠒⠒⠒⠒⠚⠉⠉⠁⠀⢸⢀⡼⠦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⢸⢯⡀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢳⠀⠀⠘⠦⣄⡀⠀⠀⢀⣠⠔⠁⠀⠀⡼⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣇⠀⠀⠀⠀⠉⢳⠏⠉⠀⠀⠀⠀⢰⠃⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠓⠆⡸⢦⣀⣀⣀⠀⢸⠀⠀⢀⡀⢀⡠⢇⠰⠞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⡠⢸⣡⡄⠀⡀⠀⠀⢸⡀⠀⠀⢩⠉⠠⡌⡇⣀⠀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠓⠖⠛⠧⠤⠷⠴⠒⠋⠉⠓⠶⠼⠤⠴⠛⠓⠻⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠘⠟
⠀⠀⠀⠀⢠⡟⣿⠄⠀⣶⠆⠀⠀⠀⠀⢤⣤⡀⠀⠰⠀⠀⢀⠐⠀⠀⢀
⠀⠀⠀⠀⠐⠇⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢐⣶⠀⠁⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡆⠀⣲⢀⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡛⣀⠀⠀⣠⣼⣿⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠤⠀⣷⢴⡁⣾⡇⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⡿⣿⣯⠋⢤⡀⠐⠒⢦⠄⠀⣷⠄⣀⢢⠀⣾⣇⣿⡗⣤⡟⠠⡁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡃⠰⠀⠐⢀⣄⠠⠄⠀⠈⢰⣌⡿⠻⡟⠋⢭⣿⣿⢶⡶⣷⠶⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣶⣍⣙⠋⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣭⣶⡶⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⣦⣄⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠈⠙⢦⣠⡞⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⡛⠷⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠉⠛⠷⣄
⠀⠀⠀⠀⠀⡾⠛⠉⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣷⡀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠸⣷⠀⠀⣠⡴⢤⡀⠀⠀⠀⠀⠀⢰⠿⣍⠻⣆⢻⣷⡀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣿⠀⢰⡏⢹⡆⢳⠀⠀⠀⠀⠀⢸⣆⣸⠀⣿⠈⢻⡿⠶⠚
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣿⠀⢸⣿⣾⡇⢸⠀⠀⠀⠀⠀⠈⢿⡟⣠⡏⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣰⢿⣄⡀⠻⣿⡤⠃⠀⠀⠀⣀⣀⣀⣀⠉⠁⠘⢾⣠⠴⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠌⢻⣶⡴⠀⠀⠀⢰⣿⣿⠛⠛⢻⡇⠀⠀⢨⠇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢷⡀⠀⠀⠈⢿⡿⠷⠶⠞⠃⣀⣴⡟⠀⠀⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⡆⠀⠀⠀⠈⠛⠳⠶⠶⠶⠖⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠉⠉⢻⡷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡶⠶⠶⣦⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⣄⠀⢀⣠⣾⠿⠟⠛⠛⣟⠁⠀⠀⠀⠀⠀⠈⠛⠿⠖⠃
⠀⠀⠀⡜⡀⠀⠀⢸⣆⠀⠀⠀⠀⠈⠻⣿⣿⠟⡟⠀⠀⣿⠀⣿
⠀⠀⠀⢳⠘⢦⣀⠘⣿⣆⠀⠀⠀⢀⣼⣿⣧⣀⡇⠀⠀⣿⣄⠘⠳⣦
⠀⠀⠀⠀⠓⠦⣌⣉⣙⣋⣀⣀⣀⣘⣉⡀⣶⡘⣇⠀⢠⡀⣌⢧⣷⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠙⠛⠋⠛⠉⠛⠋⠛⠋⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠠⠤⠀⠀⠀⠀⠀⢰⠜⠋⠁⠀⠶⡶⢯⠀⠂⡀⢀⡄⠂⠠⢸⡟⠉
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠚⢓⣷⡀⣮⠛⠟⠉⣺⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠻⠀⡀⠶⠔⠀⠀⠀⠆⠀⠢⣤⠀⠂⠠⠤⠤⠔⢻⣙⡝⠙⠁⠀⢴⠻⣿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⢀⡀⠘⡄⣤⣀⣿⡷⠻⢦⣄⣰⣆⣸⠟⠀⠀⡀⡒⠂⠀⣘
⠀⠀⠀⠀⠀⠀⠰⠸⣿⠂⢸⣿⠧⡼⣧⢼⠿⠋⢁⠀⠀⠈⠉⠹⢧⠀⠀⠘⠁⢀⣯⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⠘⣿⡄⠂⠙⠀⢠⠆⣾⣶⡀⠀⠀⣀⠁⠐⣾⡏⠠⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣯⠀⠈⠁⠀⠀⠀⢸⡦⠈⠿⠇⣀⣤⠇⣠⣶⣿⣄
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢿⠃⣾⣿⡌⠻⠟⢳⡀⠉
⠀⠀⠀⠀⠀⡝⠿⠋⠀⠀⢠⠀⠀⠀⠀⡀⣶⣤⣄⣶⣶⠁⠀⠀⢀⠬⣼⣷⣸⡆⠈⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠶⠀⡇⢼⡗⣿⣿⣿⣿⣿⠃⠀⠇⠘⣶⠟⠀⠀⠃⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡏⠈⠣⠘⡿⣿⢿⡇⠀⠀⠀⡀⣀⡄⣦⣆⠰⡶⠁⠤⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⣩⣷⣦⣀⣀⠀⠀⠀⢀⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠾⡀⠸⠀⠀⠀⠀⠈⠉⠑⠒⠉⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠑⠋⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠐⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠢⠀⠀⠀⢸⠀⠀⢀⣤⠶⣤⠀⠘⠘⡄⠀⠀⠂⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠈⠀⠀⢿⣷⣤⣿⠃⠀⢃⢱⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣠⣊⠀⠀⠀⢀⡀⠀⠀⠈⡄⠀⢲⣿⠉⣹⡷⠑⠀⠀⠀⠀⠀⠀⠀⠙⠛⣩⠆⠀⠈⡄⢧⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⠀⠀⠈⠀⠀⠀⠀⣇⠀⠘⠿⠿⠿⢃⠀⠀⠄⢀⣒⣤⣭⣍⠀⠀⠀⠀⠀⠀⠰⠈⢧⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢆⢀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠓⠂⠁⠀⠀⠐⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⢄⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⡇⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠃⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡤⣤⣤⣄⣀⠀⠀⣀⣠⠴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠘⢦⡀⠁⠙⠛⠛⠉⢠⠎⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠑⠒⢄⠀⡔⠁⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢤⠀⣠⠞⠉⠑⠢⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡔⠊⢰⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⡄⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⠂⢺⠀⠀⠀⠀⠀⢀⢷⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡀⠀⠀⠒⠲⢅⢸⠀⠀⠀⠸⡄⠀⠠⠋⡇⠀⠀⠘⣄⠈⠁⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⠀⠈⢢⡀⡼⠀⠀⠀⠀⠈⣆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣄⣤⡠⠼⢧⣐⡀⡀⠀⣀⡠⠃⠧⣄⣀⣀⣀⣄⠾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⣤⣤⣤⢄⣀⣀⣀⣠⣄⣀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣦⢉⣽⣿⣿⣿⣿⣿⣿⣮⣻⣗⢦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣤⣭⣗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⢿⣿⣷⢹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⢇⡔⢪⡳⣤⣿⣿⣿⣿⣿⣇⣠⢚⠤⣀⢹⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡗⣿⣜⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣁⣿⣶⡿⢀⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣿⣿⢹⡏⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⡟⣿⣿⠿⠉⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⢿⣿⢸⣧⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠈⢧⡈⠁⠀⢠⣿⣿⣿⡏⠈⠀⠀⠙⠟⠁⠀⢡⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⠁⠀⠀⠀⠈⢧⡀⢰⣿⣿⣿⣿⣷⡄⠀⡆⠀⠀⡄⣰⣿⣿⡏⠀⠀⠘⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣯⣉⣉⣻⣿⠀⠀⢑⣴⣣⣴⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢿⣿⣿⡿⠋⠀⢀⣼⠟⠋⣼⡿⢹⣿⣇⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠛⢷⡴⣤⠀⠀⠀⣷⢦⡽⠭⣤⡴⠶⠛⠁⠀⠀⡿⠁⣿⣿⣿⠀⠀⠀⣠⠞⣿⠋⢈⡿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣹⣦⠾⣧⣸⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⡇⠀⠀⢹⡴⠟⠓⢿⣤⠞⣷
⠀⠀⠀⠀⣤⣤⣤⣤⣷⣼⣿⣤⣤⣤⣿⣷⣤⣤⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣷⣴⣴⣿⣧⣤⣤⣤⣷⣶⣧⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⣿⡔⣶⣰⠂⣼⢳⢀⣶⣰⡟⡆⣶⢰⢢⡖⡦⡔⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠃⠙⠙⠊⠃⠘⠉⠊⠙⠈⠋⠙⠙⠚⠈⠋⠃⠙



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡦⠀⣿⣦⣤⣤⡄⢠⣠⣴⣾⣿⣦⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡅⢰⠿⡿⣿⣿⡇⢸⣷⣾⠿⠃⠉⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠿⠉⠁⠄⠠⣘⠵⢿⣧⢸⡿⠿⠒⠀⠀⠀⠀⠲⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢡⡶⠀⠀⠠⠞⠛⠂⡄⠁⠈⠃⠀⣦⡘⠿⣦⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠇⠀⠀⠲⢾⣿⣿⡦⠀⠀⠐⢿⣿⣿⠷⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠿⠟⠁⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⡀⠀⠀⣄⠀⠀⠀⣤⣤⣤⡄⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⡀⠀⠀⠈⠀⠀⠀⠸⣆⠀⠘⣿⣿⣿⠇⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣤⣿⣿⣦⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠋⣻⣿⣿⣿⣿⣿⢻⡆⠹⣦⣄⠀⠀⠀⠀⠀⠀⢹⠉⢹⠍⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣿⣿⡟⣿⣿⠇⢸⣿⡀⠻⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢤⠀⣿⣿⡷⣼⣿⣶⠟⠙⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡸⣿⡿⠀⠀⠀⠀⠀⠀⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⣿⣿⣷⡄⠀⠲⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠀⠉⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠠⢆





⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠶⠀⠻⠉⢂⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⢮⣍⠀⣀⢈⠵⠊⢡⣑⠠⠈⠘⠋⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠱⢆⡁⠀⠑⠁⠀⣀⣔⡏⠠⠀⠡⠊⢹⡄⣄⡁
⠀⠀⠀⠀⠀⠀⢠⢊⡴⠒⠒⣲⢚⡛⢻⡝⡄⣤⠋⠉⠉⣠⣴⠄⠽⠛⠃⠔⢱⡙⢦
⠀⠀⠀⠀⠀⠀⢸⠈⡔⠀⣀⡠⠤⣈⠢⡇⡇⢸⠀⠂⠎⢰⠏⠠⠂⠴⣀⡀⠐⠈⠆⢧⣀
⠀⠀⠀⠀⠀⠀⠈⣽⠀⠈⢃⡤⠄⠀⢀⠁⠀⠀⢀⣄⣀⣀⣠⣀⡀⣀⠀⠫⠁⠂⠀⠪⣑
⠀⠀⠀⢀⡀⠔⢻⡥⠂⠐⣭⠴⠒⠿⣿⢖⡮⠟⡄⠋⠈⠁⢻⢟⡁⠀⢀⠀⠀⢘⠀⠐⢬⢣
⠀⠀⢩⠁⡀⠐⡀⠀⡀⠀⠁⡆⠀⣀⠀⢿⡈⠀⠀⠀⠀⠀⠀⠈⠉⠓⣌⡀⢢⣀⣎⠀⠸⢸
⠀⠀⠀⡜⣴⠀⠼⠈⢆⠀⢀⡘⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⡉⠈⠐⠀⠈⠑⢦⡀
⠀⠀⠀⠘⠊⢀⢠⡀⠈⠀⠊⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡆⠀⠀⠀⠐⠀⠀⠀⠃⠀⢠⠈⡅⠂⠀⠃
⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠳⠥⠄⢌⡲
⠀⠀⠀⠀⠀⠀⠩⢄⢄⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⢠⢄⠑⠒⠒⠀⠂⠈
⠀⠀⠀⠀⠀⡆⠀⠀⠁⠂⠑⢄⠀⠀⠀⠀⠀⡠⠒⠁⠀⠈⠓⠒⠀⠨⠲⠀⠃⡀⠣
⠀⠀⠀⠀⠀⠀⢈⡶⠊⠡⠀⠈⢦⣤⣠⠔⠛⠀⠀⠀⠀⡀⣀⡀⡠⠃⠉⠂⠠⠴⠚
⠀⠀⠀⠀⠐⠀⢸⠁⢠⡈⠈⠢⠀⢄⠀⡎⠓⠐⠂⠀⠊⠁⠀⢀⠀⠂⠤⠤⡀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠓⠀⠀⠈⠀⠃⠀⢃⠀⠀⠀⠀⠓⠄⠀⠁⠀⠀⠀⠃⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⣶⡴⠚⠉⠉⠉⠉⠉⠛⢶⣤⠤⠶⠶⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠄⠈⢐⡂⠀⠀⠀⣒⡒⠄⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠑⢢⣄⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡾⠛⠀⠀⠀⠀⠻⠟⠒⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣀⡴⠚⠉⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠁⠀⠀⠀⠀⡘⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠛⠒⠶⣤⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢿⣷⣤⣀⣀⡤⠄⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⠛⠉⠀⠀⢀⣠⠖⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣲⠶⠶⢖⣚⣭⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⢟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠙⣄⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣰⠇⠀⣠⣟⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⢶⡞⠀⠀⠀⠀⠀⣰⣿⣶⠟⠁⠈⠓⠦⣤⡴⠃⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠤⣾⡁⠀⠀⠀⠀⣴⣣⡴⠋⠀⠀⠀⠀⠀⠘⢆⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⡄⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠶⠋

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

⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⢀⣀⣀⣀
⠀⢀⣤⢸⠞⣥⡾⢣⣄⡉⠉⢂⠀⠀⠀⠀⣰⣾⣿⠏⡿⣿⡑⣄⠀⠀⠀⠀⠛⠋⢰⠤⡤⠤⡀⣠⠄⠂⠀⠉⠻⣿⣿⣿⡿⠀⣿⣿⣽⡿⢿⠃
⠰⣿⠘⠸⡘⣿⡀⢫⠏⠉⠛⣨⡄⠀⠀⠀⡿⣿⡿⣇⡘⢿⣇⡣⡀⠀⠀⠀⢣⣏⠉⣴⠂⠀⣾⠁⣠⡆⠀⣩⣽⣿⡭⠃⢀⡘⢻⣿⣿⣷⣼
⠀⠉⣀⠠⣷⣴⡘⠂⠠⢺⣤⣿⠁⠀⠀⠀⢠⣿⡆⢘⠿⠲⡿⠛⣿⡦⢀⣴⣎⣅⡾⡟⠀⠞⠟⠻⣿⡇⠀⣸⣿⣁⡀⠀⠘⠛⠛⣿⣿⣿⡟
⠀⢸⣿⠘⣿⣟⠃⠀⠀⠀⢛⡁⠁⠀⠀⣰⣾⡟⠀⠀⢹⡛⠀⠐⠋⠁⠘⠛⠟⠉⢀⠀⠀⠀⠘⢆⣿⠀⠀⣿⣧⣯⣅⣀⣀⣤⣄⢉⠸⣿⡟
⠀⠺⡟⢓⣈⢙⣷⣴⣶⠟⠏⠁⠀⠀⣾⣿⣿⠇⣠⣠⢾⣷⠀⠀⠀⠀⠀⠈⠀⠐⠘⠀⢀⣱⣤⣾⣻⠀⠀⢙⠻⠟⠙⢁⡇⠁⣠⠞⠹⣿⣿⠣⡀
⠀⠀⠀⠼⢿⣷⡾⣿⠀⠟⠀⠀⢠⣆⣿⣿⣿⣿⣯⢿⣆⣼⣧⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⡿⢛⣿⣆⠀⢋⡈⡄⢀⢼⡆⠀⣠⣦⠘⠛⢦
⠀⠀⠀⠐⠀⠈⠀⠐⠀⠀⠀⠀⠀⠙⠛⠻⠿⠴⠯⠾⠛⠋⠉⠀⠀⠀⠀⠿⠿⢿⣤⣿⣿⠿⠿⠿⠛⠉⠀⠠⣾⠙⠋⠲⢀⠀⠉⣱⡖⠠⡌⠓
⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆⠖⠳⠆⠠⡀⣹
⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠄⣿⠉⢿⠟⢹⣷⡄⣦⡀⠀⠀⡶⠀⣤⠀⢀⡄⢠⣀⣤⣤⡠⠀⠀⠀⠀⠀⢠⣶⠉⣽⣾⡆⣀
⠀⠀⠂⢰⠉⠀⠀⠾⠗⠀⠀⠘⢃⠀⠀⣸⢿⡿⣿⡦⠀⠀⣼⠝⣱⣿⠇⠀⡸⣷⡆⠀⢠⣾⣷⣴⣿⢻⣿⣿⣆⠀⠀⠀⢸⣸⣦⣾⡍⢶⣝⢿⡇
⠀⠐⠀⠈⡀⠀⠀⠐⠁⠀⠀⢺⣶⡇⠀⢻⡞⣻⣶⡖⠀⢰⡄⠀⢉⡅⠴⠀⢱⡎⠀⠀⢠⣜⠛⠁⣬⣸⠉⣿⠿⢄⡿⣻⣟⣹⣯⠀⠀⢾⠟⢻⡟
⠀⠀⡀⢴⣧⣀⠒⣶⣤⢠⣤⣿⡛⠁⠀⠀⢿⠟⠉⣴⣶⡄⣅⠂⢈⣃⠄⠀⠰⣷⣷⣀⠈⠑⣶⣬⣿⣏⣠⠀⠀⠈⣿⣿⢿⣿⠀⢠⠅⢬⣶⢃⡗
⠀⣼⠃⠀⠐⠌⠁⠙⠻⣚⠻⠿⣗⠀⠀⠀⠐⢶⡠⣾⠿⣤⡿⠀⢈⣿⠀⠀⠀⠉⢿⠟⣳⡾⢟⣾⡟⠋⠀⠀⠀⠀⠀⠙⣠⢜⣴⢳⣴⣾⡟⡰⠛
⠀⠹⣦⡀⠀⠀⠔⠀⣸⡿⠗⣠⣿⡇⠀⠀⠲⣜⣃⡀⠀⠀⠀⠀⣿⣣⣶⡆⠀⠀⠀⢚⣿⣴⡟⠀⠁⡄⠀⠀⠀⠀⠀⠐⠛⠪⠓⠾⠟⠇
⠀⠀⠈⠓⢄⡀⠀⠀⣉⣴⣿⠿⠧⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⡿⠋⠰⠃⠀⠀⠀⠈⠻⣿⣧⣴⠿⠛⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣨⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⣾⢛⣬⢉⣼⣷⣄⠀⠀⠀⠀⠀⠐⢰⣼⡿⣿⣿⡌⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⡄⠀⠀⠘⣿⡟⢻⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⡜⡈⣿⢿⣟⠘⣿⣿⠏⢷⠀⠀⠀⢠⠀⣼⡻⡏⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⢀⣤⣔⠋⠴⣹⣧⠀⠀⠀⢛⢿⣿⣿⣴⣾⣿⣿⣿⣿⣿⡄
⠀⣰⢟⣴⢿⡉⢁⣀⠉⡿⣠⠸⣄⠀⠀⣿⡔⣎⠻⣆⡄⠀⠀⠀⠀⣸⣿⠁⣀⣤⢠⣾⠻⠇⠀⠐⣭⣋⣤⠀⠀⢎⣼⡟⠉⠙⠛⠋⠘⣿⣿⣿⡇
⠀⣿⣉⣽⢻⠇⣿⣿⢸⣟⣟⣷⣻⠄⣰⡇⠡⣍⣄⣿⡷⢂⣐⣀⠈⠉⠀⠀⠘⠇⠀⢥⡀⣴⣦⣤⡴⠛⡫⢻⣤⠘⣿⡁⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠘⢿⣿⢳⣾⣲⠟⡣⢞⣯⣛⣻⣿⡅⠙⢻⡆⣹⣿⠿⠀⡾⢹⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠁⠘⠁⡇⠹⣆⠉⠁⠀⠀⢠⣿⣿⠟
⠀⠛⠿⢟⣻⣿⡶⢧⡝⢿⣿⣍⣽⠃⠀⠈⠁⠹⢶⣄⠀⣷⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠂⠀⠘⠋⠁⠀⠾
⣤⡄⡴⢂⣄⠀⠀⡀⢀⡀⠀⠉⠁⠀⠀⣤⣶⡖⠒⠺⢤⠈⠁⠀⠀⠀⠀⠀⠠⠞⠟⠉⠀⠈⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⠑⠂⠢⡄
⠛⣡⠆⢠⠟⡞⢋⣙⢮⣻⡆⠀⢀⠤⣚⣉⡿⣻⣷⣆⠀⠠⡄⠀⠀⠀⠀⠸⠀⠰⣗⠀⠀⠸⣿⡟⡧⢤⡀⠀⠀⠀⡠⠀⠩⡍⢰⣿⠗⠂⠠⡄
⠀⠙⢺⣷⢘⢁⣯⣽⢤⣟⠀⢀⡿⢸⢋⡿⠋⠈⠉⠙⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣀⡝⠃⠀⠈⠗⠀⠀⢠⣷⠚⢁⡃⠄⠡⢤⠱⣶⠜⢦
⠀⢆⣤⣑⠊⢺⣿⣿⠊⣿⡇⢸⣱⣧⢻⣷⠀⣠⡴⠆⡀⠀⣴⣿⡸⣏⠀⣤⡀⠀⣰⣾⣟⣁⡠⠄⡠⠂⢰⡀⠀⠹⢃⠁⣿⣭⠀⠀⠀⢠⠛⡀⢶
⠀⣾⣋⣿⣷⡿⠿⢿⢃⣼⠷⠀⢸⣿⣿⣿⣿⣿⡵⣞⣿⣿⡟⠟⠁⢀⣶⢶⡀⣚⣿⢛⣨⡁⠹⠞⣷⠀⠀⢷⣶⡇⠀⣠⣀⡛⠀⠋⠁⠊⠘⢛
⢠⣾⣿⣬⣿⣦⡀⣠⣏⣽⡀⠀⠈⠉⠛⠙⣿⡿⣿⣛⠃⣤⠀⠀⠀⠈⠛⠛⢹⠛⠛⣌⠉⠀⣀⣀⣶⠾⠀⠟⢻⣧⠀⢨⡉⢿⣆⠀⢠⠀⣰⡆
⠘⢿⣿⢦⡟⣿⡟⠻⠋⣹⠇⠀⠀⠀⠛⠻⣯⣾⠋⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠰⢧⡅⢠⣶⣾⠟⠉⠀⠀⠀⠀⠻⡄⣠⡘⠧⠉⠂⠀⢠⣬
⠀⠈⠛⠊⠃⠛⠃⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡿⠿⠿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣿⣭⣭⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⠛⣷⡄⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⠻⣷⣆
⠀⠀⠀⠀⣀⣴⣿⠟⠁⢀⣀⣤⣶⣶⡄⠀⠀⠀⢀⣴⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢶⡄⠀⠀⠀⣤⣦⣄⡀⠀⠈⠻⣿⣦⡀
⠀⢀⣤⣾⣿⣯⣥⣶⣾⠿⠟⠛⢹⣿⠁⠀⠀⠀⣾⠋⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⢿⡄⠀⠀⣿⣿⠻⠿⣷⣦⣤⣈⡻⣿⣶⣄
⣼⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⣾⣿⠀⠀⠀⢸⣿⣿⠷⣆⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠷⣆⢸⡇⠀⠀⣿⣿⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣦
⠙⠿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣿⡟⠀⠀⠀⠘⢿⣿⣿⣟⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣟⣼⠇⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⣿
⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⢀⣠⣤⣤⣤⣤⠦⢤⣄⠀⠈⠉⠛⠋⠁⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣷⣶⣤⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣾⠿⠿⣷⣤⣤⣤⣴⣶⣾⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⠇⠈⠉⠉⠛⠛⠛⠛⠛⢿⣶⣾⠟⠛⠉⠉⠉⠁⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠘⣿⣦⡀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠈⠻⣿⣶⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠉⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣶⣄⠀⣠⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣶⣶⣶⣿⡿⠿⠋⠀⠙⠿⢿⣿⣶⣶⣶⣿⣿⡿⠿⠿⠛⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣤⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠐
⠀⠸⣟⠟⣿⡿⣿⣷⡄⠀⠀⠀⠀⣀⠄⠠⣤⣤⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣧⣧
⠀⢀⣿⣯⣛⣧⣷⡟⠀⠀⠀⠀⢀⣶⣿⢖⠈⡻⠁⠀⢀⠀⡆⠀⠀⢯⡃⢠⠀⠀⠀⠀⣠⠏⣭⣌⡿⣷
⠀⢸⣿⣉⣉⣻⣿⣷⣦⣄⡀⠀⢮⣰⣿⡷⠴⢿⡲⠰⡸⠣⠃⠀⣸⡀⠣⡀⠀⠀⠀⠀⠉⠛⣋⣿⣿⣿⣧
⠀⣿⣭⣿⣿⡿⣧⣿⣿⣿⣧⡀⠀⠀⠁⠀⠀⠀⠍⢀⣘⡆⠆⡞⠋⠁⠀⠈⠐⡀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣧
⠈⣏⠈⣩⣯⣙⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠎⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣏⣿⣿⡿⣿
⠀⢹⣾⣿⣿⣿⣾⣿⠛⠻⠻⣿⠀⠀⠀⠀⠀⡤⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠤⢸⣿⡿⣿⣿⣿⣶⣿⣷⣿
⠀⠘⣿⡇⠀⣼⣿⡇⠀⠀⠀⠸⡇⢀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣾⣿⡏⠀⠀⣿⣿
⠀⠀⢸⠁⠀⠉⠻⠃⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⣰⡟⠟⠀⠀⠀⠀⣿⡀
⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⢐⣄⣀⣈⣄⠀⠀⠀⠀⠛⠀⠀⣀⡀⠀⠀⠌⠁
⠐⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⣴⣿⠀⠀⢸⣛⡻⠷⢾⣮⠉⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡇⣾⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⢀⡤⣶⠹⢗⣦⣄⣭⠀⠀⣨⡈⣡⠀⠠⢿⡇⠀⠈⠁⠀⠀⠀⠐⣶⣶⣦⡀
⠀⣏⢿⣶⡾⠛⢿⢻⣿⣿⣿⡟⢫⠟⠀⠘⡀⢢⣛⣿⣯⣦⠀⣸⠃⠉⣠⣶⣵⣿⣦⣀⣀⣀⣀⠀⢀⣀⣩⡿⢣
⠀⠈⠉⠉⡇⠀⣄⢸⣿⣿⡟⣰⠘⢤⡘⣧⡉⢿⣿⠿⡿⠋⠀⢿⠀⠀⠁⠿⠃⢞⣾⣿⣿⣯⣻⣝⣿⣿⠿⠅⠋
⠀⠀⠀⢀⢷⠀⠠⢃⡙⠻⣷⢾⡄⠀⣳⠘⠇⠼⠟⠀⠀⠀⠀⠰⡄⠖⠁⡄⠀⣹⣿⣿⣿⣿⠟⢸⣿⡟⡇
⠀⠀⠀⠘⠷⠄⣤⡾⠟⠓⢄⣸⠀⢛⠱⠤⠖⡼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⣈⣉⢉⣤⣤⡅⢹⣿⣿
⠀⠀⠀⠀⣀⠀⠊⠃⠀⠀⠀⠙⠶⠶⢶⡂⠰⢤⣀⢀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠐⢌⠛
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠒⠂⠀⠀⠀⠦⠄⠈⠉⠀⠀⠀⠀⠀⠀⠠⠤