⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤⣠⣄⣤⣤⣠⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣟⣯⣷⢿⣿⣿⣿⣿⣷⣯⣟⣯⣟⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⡷⣻⡷⣯⣿⣿⣿⣿⣿⣿⣳⣯⢷⣯⣿⣞⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣟⢯⣾⣿⣽⢿⣯⢿⣽⣿⣟⣿⡿⣿⣟⣾⣳⣯⠳⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣯⢿⣿⣟⣾⣻⣞⡿⣾⣿⢯⣿⡿⣽⣿⣷⡟⣡⣾⡕⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⠸⣿⡿⣞⣷⣻⣞⣿⣿⣿⣿⡷⣟⣟⣭⣶⣿⣿⡿⣿⡼⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣷⣶⣯⣭⣥⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢁⡀⠀⠀⠀⠀⠀⣹⣷⣿⣿⣿⣾⣳⣿⣿⣿⣿⣿⣿⣿⣫⠿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡷⣷⣯⣤⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠲⣥⣂⣤⣀⣠⣿⣿⣿⣿⣿⣷⣿⡿⠓⣿⣿⣿⢃⠏⣠⣆⣈⣽⣬⣟⣿⣿⣿⣿⣿⣽⣷⣍⣜⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⢌⠛⢿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣀⣺⣿⠏⡀⠈⣀⠫⠛⠜⠿⠍⢨⡿⣿⢯⣿⣿⣿⣾⣿⣾⣷⣿⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢺⣼⡿⣟⣿⣿⣿⣿⣧⠿⠍⣼⠿⠏⢀⠟⠋⢩⠑⠤⠆⠖⡜⢩⢣⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣵⣯⣜⣿⣿⣿⣿⣿⣬⣗⠒⠒⠒⠚⠁⡄⠇⠀⠄⠀⠨⡚⠸⠁⣸⣿⢿⣿⣻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣖⠤⠂⢁⠠⠀⠰⠄⠨⠈⠀⢁⠂⡩⡛⢑⢋⣵⣾⣿⣿⣿⣿⣿⣽⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⡷⣿⢿⣿⣿⣻⠿⣧⡀⠀⢀⠠⢤⣶⠓⡖⠘⡈⣴⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣛⠏⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣆⣄⣿⣷⠥⡁⠀⠑⡈⠀⢆⠷⣻⣷⣿⣿⣿⣿⣿⣿⣟⠿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠵⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⢑⠲⠆⢾⠸⠊⢹⡿⢿⣿⣿⣿⣿⣿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡻⡷⠛⠿⣿⡿⡿⠟⠻⡾⠰⡈⠒⠄⠢⠞⡄⠀⠟⠣⠏⠀⠌⠉⣉⠨⠉⠀⠁⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⡅⡒⠤⠄⣡⣀⣱⠀⠀⠀⢰⠄⡘⣀⠰⠤⠅⠚⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⠀⢼⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠂⠵⡄⠀⠠⠀⠀⠀⠀⢱⠀⠀⠀
⠀⠀⠀⠀⣰⠁⠀⠀⠀⢀⠔⢀⢎⠠⠐⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢀⠸⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠆⠀⠀⠀⠘⣇⠀⠀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠂⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢠⠘⣠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠹⡄⠀
⠀⠀⢀⠊⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣛⠾⣑⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠮⣝⡲⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⣐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡜⠡⡀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣲⣿⣔⠈⢆⠀⢀⠔⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⢄⠀⡠⠊⣠⣿⢳⡄⢈⠂⠀⠀
⠀⢀⡀⢀⢂⡼⠋⢻⠀⠙⠢⣕⡘⠠⣌⡑⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢂⢁⣢⠀⢧⡡⢺⠃⣸⠀⠙⣄⠂⢄⠠
⠀⠀⠈⠑⠛⠤⠠⢾⠀⠂⠓⢋⢧⠂⢗⣌⡎⠈⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠃⣰⢃⣾⢀⡟⠓⠒⠂⡟⠒⠀⠛⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⢚⡌⡌⢺⡕⠠⡇⠀⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⠀⠀⠀⠘⠠⢸⡿⢁⢺⣅⣤⢀⡴⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠘⡕⠤⠴⡺⢣⠘⠀⠐⠀⠀⠀⠀⠀⠀⢀⠔⢱⡌⠀⠀⠀⠀⠀⠀⠀⠀⠣⠔⠁⡖⢤⣄⢂⠱⡐⠂⠤⢀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣤⣤⡶⣾⡗⢋⠔⡁⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢢⡸⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢈⠰⢱⣦⣓⣤⡧⣴⣀⣂⠀⠀
⠒⠂⠉⠉⠀⠀⠑⢤⢋⠟⣧⠈⢆⠘⡠⠌⢂⠅⢢⠐⢂⠡⢂⠉⣴⠁⠀⡧⡂⢆⠰⠠⡐⢠⠂⡑⣈⠡⠌⢂⡽⠟⣍⢣⠞⠁⠀⠀⠉⠉
⠀⠀⠀⠀⢄⠀⠀⠀⠩⡚⢬⢣⡌⢂⠥⠘⡠⠊⡄⢊⠄⠃⡔⣋⡜⣀⠀⣃⢝⡢⠈⠥⡐⢡⠘⡐⢄⠊⣴⠝⣌⠳⡸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⢂⢇⠺⡲⢬⡕⣀⣃⣌⣢⠬⠛⠊⠁⠉⠀⠁⠉⠀⠉⠚⠴⡤⢧⢬⣴⢒⠫⢆⡹⢄⠟⠀⠀⠀⠀⠀⠀⠀⠀
⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⠵⣡⠗⠛⠓⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢒⠚⠛⠧⡚⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢪⢔⢢⠀⠀⠀⠀⠀⠀⠀⠀⡨⠊⠁⠀⠀⡜⢠⡠⠐⠂⠉⠉⠁⠒⢶⣒⠶⠊⠉⠁⠐⠀⢄⠀⠇⠀⠀⠈⢺⡀⠀⠀⠀⠀⠀⠀⢠⣐⢣
⢣⠎⡎⠵⣂⠄⠀⠀⠀⢀⢴⠀⠀⠀⠀⠜⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢋⠚⠄⠀⠀⠀⠑⣦⡀⠀⢠⡐⢎⡵⢨⠖
⠁⢞⠩⠞⣌⡚⢥⠢⢤⠏⠆⠀⢀⡴⠁⠀⡦⠔⠂⠈⠉⠁⠉⠁⠘⠣⡱⠟⠂⠈⠉⠁⠐⠂⠬⡆⠀⠀⠄⠀⢡⠚⣦⡙⢦⡙⠲⣌⡓⠊