⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠅⢄⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⢀⠤⠀⢰⠔⠘⡉⠉⠁⠀⠀⡉⠭⠉⠒⠒⠦⢂⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠡⠈⠉⢀⣦⠋⠉⠠⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⡀⢠⠃⠐⠀⢀⡴⡟⠑⠐⢰⢀⠔⠁⠐⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠑⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠔⠶⢗⣂⣀⣠⠃⠊⠀⢠⢯⡽⢀⠀⠀⡰⠑⠀⠀⢀⠀⢀⠄⢀⠔⠁⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠣⣖⢆⠆⡬⢍⣈⢀⡂⠾⠽⡁⠈⠀⠐⠁⠀⠀⠀⠀⠀⠂⡀⠁⠐⠄⢀⠔⠀⠀⡔⠐⠻⣄⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠸⡐⠃⠞⡍⢮⣱⢂⠤⡑⠂⣠⠀⠀⠀⠀⠀⠀⡀⢠⠁⠀⢄⠄⠊⣀⠄⠒⠁⠀⠀⠹⡀⠀⢀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡶⣄⠋⣖⡇⠮⣖⣝⡢⡔⠀⠀⠀⡐⠃⠐⢠⠿⣲⠯⠓⠚⠅⠀⢐⠀⠀⠀⠀⠀⢳⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠇⠊⢷⣄⠙⣧⠳⣎⡷⠀⠀⠀⠀⠀⠁⡎⡺⠥⠤⣤⣄⠀⠀⠛⠀⠀⠀⠀⠀⢐⠒⢆⢀⠁⡇⠀
⠀⠀⠀⠀⢠⠀⡄⠀⢫⢗⣦⡉⠉⡁⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠈⠝⠷⠀⠀⠀⠀⢠⣒⣂⢀⢳⠎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⢱⠀⠸⣎⣿⣿⣶⣅⡀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣻⣿⠋⣿⡿⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠈⡆⠁⢍⣿⣿⢯⣿⣰⠀⠀⠀⠀⣼⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠁⠀⢈⡏⢠⠀⣄⡰⠀⠀⠀⠀⠀⠀⠀⣝⡺⣔⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⠀⠈⢄⠀⠺⡽⣿⢿⣳⣇⠀⠀⠀⣻⠀⠁⠁⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠈⢡⣖⡏⡜⠁⠀⠀⠀⠀⠀⠀⠀⡀⠈⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⠈⠙⢿⡿⣽⢆⠀⠀⠋⠑⢄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠛⠉⡜⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠐⠀⠀⠈⠛⢿⣳⣤⡃⠀⠀⠑⢄⡀⠀⠀⠀⠀⠁⠀⢀⠄⠃⠀⠘⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢡⡼⢆⠀⡀⠀⠀⠀⠀⠐⠠⠀⠈⠛⢦⣀⠀⠀⢰⡉⠐⠢⢄⣠⣴⠋⡛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⢆⠀⣧⡘⠖⣄⡀⠀⠀⠀⠀⠙⠀⢄⢈⠓⢄⠈⢳⣄⠃⠊⣿⢯⡀⠀⠂⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢠⠃⣈⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢺⠈⠻⣗⠿⣄⠀⠈⠁⠒⠠⢀⡀⠀⠀⠀⠑⠐⢌⠺⣧⣠⡤⠈⠛⠓⢚⠉⠉⠉⣉⠲⠤⢀⠲⠤⠴⠊⠁⢄⣀⣀⠀⠀⠂⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡼⠢⠤⠤⠹⠷⢯⣖⣤⡀⠀⣀⠉⠱⢲⡦⣄⣀⠀⠀⠊⠙⢶⣢⠀⣇⠃⢀⠀⠐⠁⠀⠘⠤⠀⡀⠀⠀⠀⢀⣈⣋⣠⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣴⣿⠷⠛⠋⡉⠛⠶⣤⣀⠀⠓⢦⣼⡈⢂⠓⡒⢤⣀⡀⠈⠐⠌⢻⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⢠⣾⡿⢋⠁⡠⠀⠀⠀⠀⠄⠈⠙⢷⣦⡀⠱⡟⡧⢈⡕⠮⠴⢻⢓⣦⣄⠁⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠀⢰⣿⠏⠀⡠⠈⠀⠀⠀⠀⠀⢀⠀⠢⠌⢿⣿⡂⣷⢁⠢⡘⣌⢣⢃⠞⣋⠈⠛⠋⠀⠀⢀⣠⠴⢐⡪⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠠⠀⠀⣿⠏⠈⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠂⠊⠤⢻⣿⠈⠣⣆⠱⡐⢎⡜⡀⠰⡕⢄⠀⠀⣯⡩⠆⢘⠈⢠⢠⡄⠀⢢⣶⠀⠼⢾⠘⠅⠵⠂
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠁⠀⢸⣿⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢹⠀⠀⠈⠳⡕⢪⠔⣁⢀⠊⢦⠕⢄⠀⠀⠀⠍⠃⠙⠘⢁⠀⢄⣄⣠⡴⢰⠂⠀⠡⢀
⠀⠀⠀⠀⠀⢸⠠⠀⠀⡐⠀⠀⢸⣿⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠆⠀⠳⣎⠴⡙⢾⡀⠜⣆⢚⡄⠄⠀⠀⡀⢀⠀⠸⠶⠘⠋⠉⢁⣘⢤⡄⡆⣎
⠀⠀⠀⠀⠀⢸⠀⣀⠀⢀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢸⠀⡀⠘⠀⠀⠈⠳⣍⣺⣡⠀⠘⢶⣹⡄⠀⡄⡞⣦⢦⣤⣦⣴⠖⢎⣼⣯⢷⣹⡼⢭
⠀⡀⢤⡷⠂⠈⣀⣤⡤⣀⠈⠁⢺⡿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠀⠄⠀⢃⠀⠀⠀⠈⠛⠧⢃⠀⠀⠝⡄⣎⢿⣽⣞⡿⣿⣏⣯⣨⣾⣿⣯⣿⣿⣽⣿
⠀⢉⠪⠠⢠⠾⠅⢈⡹⢦⣦⠀⠀⣿⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠈⠠⠈⠀⠀⠀⠀⠀⠈⠀⠉⠆⡂⢺⠘⠏⠊⣱⣻⣿⣿⣟⡮⡝⡿⠛⣉⣋⠛⢿
⠀⠆⠀⠣⢸⡌⣏⠈⠕⣀⠇⠀⣰⣿⠀⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⢰⢸⡿⣅⡴⣂⠍⠷⡳⠰⣿⣿⡿⣷⠌
⠀⠈⠠⡀⠀⠙⣽⣶⡚⣁⣤⣮⣹⣿⡄⠅⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⣿⠀⣿⣷⣹⣯⣿⣽⠤⢸⣸⣥⡤⣌⢾⡇
⠀⠀⠀⢀⠃⠀⢯⠟⠓⠬⠉⣉⢛⠛⠁⢂⠀⢉⢂⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡇⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣞⢰⣿⡇⣼⡿⣿⣿⣿⣻⣿⠷⢷⡟⠒⢫⣵⣻⡇