⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡑⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡐⠄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠄⡂⠔⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⢑⠢⢅⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡈⢂⠐⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣡⢡⣈⠂⠨⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠌⠰⠌⠚⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣄⠂⠉⠄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢁⢈⡀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⣈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠨⡄⡉⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⣀⠡⡄⢩⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠈⠐⢂⠐⢀⠀⠀⠀⠀⠀⠀⢈⠣⡐⡀⠂⠈⠀⣠⠄⠜⠀⣸⢜⡃⠀⠘⠀⠐⠀⠨⠅⠀⣰⢆⠠⠁⢀⡀⠀⠐⠠⣀⠤⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⢕⡀⠁⠀⢀⣝⢷⠂⠀⠀⣏⡞⡨⠀⡐⢂⠀⠠⠄⠀⢌⡣⠞⡄⠀⠀⢹⡖⡄⠀⠰⠐⡄⠌⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⠜⠪⡹⣯⢥⠀⣀⠇⡄⠙⠄⠹⡀⠄⠄⣂⠡⢂⠰⡙⣀⠀⢠⡟⢜⡱⠄⡀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠊⠝⣮⣽⢂⠈⡡⣡⢘⠐⠤⠂⡐⡀⢜⡱⣇⢮⠸⠐⠁⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠈⠘⣿⣦⠡⠎⡀⠔⠈⢂⠂⡴⠀⣞⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡎⡁⠈⠀⠆⠈⢆⢰⣿⡎⠀⠀⠀⠀⠁⠀⠀⠀⠀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠿⢿⣆⠀⠆⠀⠀⠀⠀⡀⠀⠸⣏⠱⠎⡬⠁⡄⢀⡙⢦⠘⣿⠄⠈⠆⠀⠀⠀⠀⠀⠌⢀⣿⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠠⠙⠻⢶⣤⣤⣤⣤⢄⠀⠈⢀⠡⢙⡰⢏⡼⣢⢄⡂⠣⠘⠀⠀⢈⣀⠄⠀⣀⣀⣤⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠐⡀⢁⠂⠁⢐⠈⡛⠿⠋⠂⠀⠔⠀⠩⣸⠜⡭⡖⡭⣰⢂⠤⠀⠀⠀⠐⢯⣿⢟⠛⠉⠁⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢁⠢⠀⠁⠀⠌⠀⢂⠄⠱⠀⠀⡘⢀⠀⠘⠀⡉⠴⣉⠲⡁⠎⠄⠀⠰⡀⠀⠀⡀⢀⠄⡈⠂⢀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠈⠀⠀⠘⠒⠂⠂⠤⢋⢧⣱⠈⠀⠀⠀⠠⢀⠄⡀⠄⠀⠀⠈⢓⠬⣕⢤⡉⢁⡐⠀⠀⠀⡀⠊⠁⡐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢤⡀⣄⠀⠀⠀⠭⣀⠈⠁⠥⠋⣞⢶⣧⣀⠀⠀⠁⠈⡐⠈⠀⠀⢀⣠⣮⠷⡤⡄⢍⠀⡐⢄⠁⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢂⠛⣦⡛⢄⠂⠀⢀⣤⠦⢒⡔⣾⢯⣽⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⣾⣻⣄⠰⣀⣀⠈⢀⠀⡄⠹⢬⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⣀⠄⠠⠬⢔⡈⠥⣂⡥⣔⣤⡾⢿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣳⣄⡭⠁⣈⠓⢂⡘⡐⠋⠂⢁⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢓⣩⡼⢖⣈⡆⢌⡠⢄⠡⣀⢭⡙⣯⡝⣻⣺⡭⢇⠀⠀⡬⢽⣪⡝⣖⣫⡛⣍⡘⠉⢉⢐⠤⡘⠠⢈⡰⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠉⠣⠟⣛⡭⢖⠧⢘⡉⠅⠂⠤⠉⢭⠽⡹⠞⠑⠃⠀⠐⠈⠘⠵⡻⡔⡍⠛⠑⢉⠋⠓⠽⢦⣜⠑⣲⢮⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡑⠖⢉⠂⠋⡑⢞⠥⡀⠂⡐⠀⠈⡄⠂⣁⠠⣆⢶⡢⡔⢌⢰⡀⠄⢡⠈⠠⠁⢀⣠⣥⢴⣖⣚⡹⠪⢒⠌⠀⠀⠂⢄⠀⡀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⡀⡐⠌⢠⠹⢌⠔⠈⡤⢄⡤⢈⠔⡀⠡⠐⠀⠃⠄⠑⠠⢓⡊⣎⠗⡙⡎⠃⠧⠙⢢⠘⣠⢎⡽⡚⡜⢭⢊⡔⡩⠍⡡⠑⠂⠀⠀⠀⠈⠀⠀⠉⠀⠀⠈⠀⠀
⠀⠀⠀⡀⠁⠀⠀⠀⢆⡿⡆⠆⢹⡈⢷⠾⣱⠎⡰⢆⠰⢁⠁⠆⡈⠰⠀⢀⠀⠆⠀⢉⠈⠰⢁⠆⣎⢱⡎⣈⢷⢉⡎⢷⠸⡰⢏⡀⢁⠀⠁⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠂⢀⠀⠐⠀⣀⠣⣎⠽⡙⠢⠱⢊⣃⢍⡺⣑⠮⣩⢆⡱⢬⡐⣂⠡⠄⣂⠀⠀⣢⠀⣐⢭⢺⡜⣧⢫⢗⡮⣓⢞⣊⠗⡣⢣⠐⡀⠀⠀⠀⠐⠀⠂⡀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠐⠠⠑⢎⡳⡑⡀⠁⢠⢎⠧⢝⡺⢍⣦⣫⢞⡳⡵⢡⡞⡰⣧⣿⣆⠱⡰⡜⣕⡫⡳⣝⡳⡝⢮⡕⠮⡘⢭⡐⠁⠂⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⠀⡥⠐⢀⠢⢔⡢⢥⣈⠠⠎⠍⡾⣙⠬⣫⢏⣟⣕⠗⡽⠁⢾⣿⡿⠀⣱⢹⣎⢷⣎⢲⢹⡝⡢⢞⠙⡖⣁⠂⠁⠀⠠⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠄⠁⢠⠊⣴⠀⠄⠒⢃⡝⢃⠴⡠⠀⢉⠐⠴⡹⢡⢚⢎⡞⡼⠃⢠⡟⡇⣿⠀⢧⢇⡏⣇⠞⡆⣍⠭⢊⠳⠁⠄⠀⠀⠀⢀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣐⡠⡔⣮⠲⡝⠐⠆⡀⠈⠀⢒⡱⢛⠤⣊⡌⠀⠀⠀⠁⠒⡩⠢⠁⠠⢰⢣⢳⠹⠀⠊⡜⡘⡌⠎⠜⢀⠂⠀⠁⠀⠀⠀⢀⠠⠌⡐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⡁⢎⣱⣼⣯⠃⠀⠉⠄⠀⠀⠀⠀⠁⠘⡰⠘⢀⠂⡀⢀⠀⡁⢰⠀⡖⡈⠰⡣⢎⠐⠰⠀⠡⠀⠐⠀⠀⠀⠀⠀⠠⢄⡂⡅⠪⡁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀