⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣹⡘⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⣼⣾⣿⣿⣿⣳⣼⡱⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣿⣿⣿⣿⣿⣿⣷⣮⣽⢣⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡐⠀⢸⣿⣿⣿⣿⣿⣿⡭⠍⠞⠹⠮⢔⡀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠀⠀⠀⠀⠀⢠⠰⠈⢸⣿⣿⠟⠋⠛⠈⢀⠀⠠⢀⠒⡎⣖⠀⠀⣾⡝⠠⣡⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⢲⢸⠀⠘⠉⠀⠀⠂⠈⢀⠀⠀⠀⠀⢀⣸⡼⡀⢈⠗⢠⢃⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⡻⠀⡀⠀⡀⠡⣄⣏⣀⣶⣽⡆⢈⣿⣿⡗⡇⠈⠀⢀⢊⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⢀⡀⠀⠀⠀⠀⠀⢥⣿⢇⠁⢀⡐⠠⠿⠿⠞⠛⠚⣡⣠⣾⣿⣿⣯⠇⡘⢀⢆⠃⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠮⠥⠊⠀⠀⠀⠀⢈⣼⣿⣧⣎⠰⣺⣿⣷⣾⣼⣷⣿⣾⣿⣿⣥⣿⣏⡷⢈⡐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣸⣶⣤⣤⣰⠄⠀⠀⢀⠀⢂⣿⣿⣿⡹⣆⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢱⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣿⣿⣿⣿⣿⠂⠀⠠⠀⠠⢹⣿⣿⣿⣿⢿⣌⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⡁⠠⠐⠀⢡⢺⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣨⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠄⠀⠌⢠⣿⣿⣿⣿⣿⡿⢻⢻⣿⣿⣿⣿⣿⣿⣿⢏⠢⣅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡹⢿⣿⣿⡄⠂⠈⡐⢢⣍⣙⠿⠟⡋⢤⣡⣿⣿⣿⣿⣿⣿⣿⠏⡆⠱⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡱⢯⣿⣿⣲⠁⠀⠄⣹⣿⣿⣿⣶⣵⣿⠿⣿⣿⣿⣿⣿⣿⡻⢜⡠⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣯⢿⣽⡀⠀⠂⠜⠛⠉⢋⠙⢉⡀⠂⠄⣠⣹⣿⣟⡳⡑⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢯⡻⡔⠀⠡⢲⣤⢃⡤⣈⣄⡰⡜⣘⣼⣿⢳⣏⠱⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡕⡃⠄⠡⣙⢎⡧⣌⠑⡈⠔⠠⣜⣺⣼⠳⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣱⢹⠀⠰⢸⡹⣾⣾⣷⣾⣿⣿⣿⣿⠣⢉⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⢀⠸⣧⠃⠈⠤⡙⢻⢿⣿⣿⡿⣿⢏⠃⠐⠀⠀⠄⢂⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⠀⠀⠀⠀⢯⢷⠀⠣⡜⢠⢊⡘⠠⠙⠀⡀⠀⠀⠀⠌⡐⠂⠌⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠈⢟⡦⢑⢯⣃⠦⣜⢡⢂⠁⡀⠀⠀⢌⠰⢡⠉⡔⠢⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⣎⢮⡹⡖⣭⠞⣆⠣⣄⠱⣘⣌⠳⣌⠲⢌⡅⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣉⠷⣱⢹⣒⠿⣜⠳⣌⢷⣹⢬⠳⣌⠞⡴⠂⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⢣⡙⠶⣍⠶⣙⢎⠧⣓⢬⡳⣏⠾⡱⢎⡝⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠐⡌⢣⢍⠳⢌⢣⡙⢎⢒⡩⢖⡹⣜⢣⡝⢎⡼⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⢀⠘⠄⡊⠔⡈⢆⠉⢆⠢⢱⡉⠖⡬⢣⠜⡢⢜⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⢀⠀⢸⡘⠴⣈⢆⡡⢈⠒⢠⠉⢆⡙⡜⡰⢃⡎⡱⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠤⡈⢆⠠⣉⠒⡡⢎⠰⢃⠌⠤⣉⠒⡘⠰⢁⠃⠌⡑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠰⢁⠊⡔⢀⠣⡐⠌⢢⠁⠎⡰⢀⠃⡌⠡⠀⠌⡐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠢⠌⢂⠡⠐⠌⡐⠈⠜⠠⠘⠠⠁⠌⠒⠠⠁⠌⡐⠤⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀