⠀⠀⠀⠀⠀⣻⠅⠀⠀⠐⣀⠀⠄⣈⠂⠀⠀⠀⢀⢄⣠⢑⡀⠀⠀⡀⠄⠐⠀⠐⢀⠀⡀⢀⣒⣀⡀⠐⠀⠀⠄⢠⠺⢋⠩⡂⠠⡀⠀⠀⠀⠀⠀⠀⡆⢄⠀⠀⠀⠀
⠀⢠⢠⢄⢜⠃⢀⡐⠅⠁⡰⡆⠀⠌⢱⠀⠔⠀⢤⡒⠈⠀⠈⠐⠷⢰⡨⠈⠠⠀⠂⠈⠀⠀⠀⠀⠀⠀⢠⠖⠔⢃⡁⣀⣂⣀⣢⣒⠐⠐⢇⡁⠈⠀⠘⡀⠐⠄⠀⠀
⠀⢐⠄⡈⡏⠠⢒⠓⠀⠠⠂⣦⡀⡤⣓⢳⡡⣊⡉⠀⠀⢀⠀⠀⠀⠀⠐⠒⠡⠨⠠⠆⠀⠔⠠⠰⠐⠐⢉⣄⣞⣶⣯⠻⣫⡍⢙⠟⠻⢟⣦⣑⡂⢄⡄⠆⠀⠈⡏⢂
⢀⡉⢰⡇⡑⠺⢊⣸⣂⢰⠁⡃⠍⣊⢠⢟⢞⣩⡯⠾⠾⢦⣾⣚⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣾⣿⣾⣶⣼⠋⠄⠐⠀⠫⢸⠦⠌⣛⢷⣆⡈⠛⢀⠀⡐⠒⠰
⠔⣰⣾⠃⣈⠊⢢⢣⠟⠰⢠⡝⢠⡟⣽⠑⣸⠝⠈⠀⠀⠀⠈⠿⣷⣜⢂⠀⠀⠀⠀⠀⠀⠀⠀⣷⣟⢽⣿⣺⣿⡇⠀⠉⢃⡠⠈⡂⡂⠖⢅⡓⣿⣿⡄⠀⠱⢀⢈⠀
⢐⡉⡗⠀⢿⣩⣲⠕⠋⣆⢚⢰⢽⡏⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⢷⣀⠀⠀⠀⠀⠀⠀⡨⢻⣿⢟⡧⣯⣿⠧⠀⠀⠀⠀⡐⠰⢀⠎⡀⣊⡩⣿⣧⢥⠀⡱⡐⠀
⠸⣼⣡⡐⡒⠨⢤⢉⢡⣻⣹⣟⣸⣗⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣾⡀⠀⠀⠀⠀⢀⡏⡸⣞⡧⡧⣧⢴⣋⠀⠀⠀⠀⠀⠈⠀⠊⠀⠂⡌⡿⢻⣉⣖⡅⡂⠀
⢽⣽⡮⠔⠉⢴⠰⡤⢓⢔⣶⢿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢸⢃⠀⠀⠀⠀⢸⠀⣂⣿⡽⣟⢷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⢯⠍⣾⠠⠀
⠍⣒⣷⢿⣱⣳⢿⢟⢹⢔⣿⠁⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠩⡀⠀⠀⠀⢸⠀⡿⣿⣧⣿⡖⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⠸⢈⠇⢀⠈
⡨⣎⠿⢑⢨⡟⢍⠈⢘⢲⣿⠀⢸⣷⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠅⡂⠀⠀⠀⢸⠀⠁⡽⣾⡞⣗⣿⣾⡦⢀⡀⠀⠀⠀⠀⠀⢀⣜⠃⡟⣸⡂⠙⡀⡢⠃
⢱⢊⢭⣓⡈⢰⠁⠀⢸⠚⣿⡄⠀⣿⢿⣾⣿⣄⡀⠀⠀⠀⠀⢀⣴⣽⣿⣻⣶⡇⠀⠀⠀⢸⠀⠀⠈⢺⣻⣽⡻⡷⣟⢧⣨⣢⣀⣀⡀⣠⠎⠃⣠⡧⣾⠌⠀⣂⡽⠂
⠈⡌⢢⣷⣆⢑⠀⠀⠈⣆⣿⣷⠀⢩⣿⢿⣿⣿⣛⣟⣛⣿⣟⣹⢽⣾⣷⣻⣑⠅⠀⠀⠀⠘⡇⠀⠀⠀⠳⣿⣷⣷⣮⡟⣏⣙⣓⣲⠛⣃⡾⣻⣗⣷⡟⠀⠀⣕⢝⠀
⠀⠈⢘⣿⣿⢳⠀⠀⠀⢸⢹⣾⠀⠈⠻⣿⣯⣿⠿⣿⡿⠽⢾⣷⢿⣞⣩⡼⠂⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠈⠓⢍⡛⢯⣍⣿⣙⣒⢯⣷⡫⣻⡿⠻⠳⢀⠊⢫⣣⠁
⠀⠀⠈⢹⡎⢣⢱⡀⠀⠀⢣⢛⢷⣄⠀⠈⠙⠫⢿⣿⣖⣽⣓⡺⣭⢷⢏⠃⠀⠀⠀⠀⠀⠀⠀⠘⣵⢄⠀⠀⠀⠀⠉⠉⠙⠚⠛⠉⠉⠉⠉⣵⢜⡡⡚⠁⠋⣷⡷⠀
⠀⠀⠀⢨⣕⢩⡆⢥⠀⠀⠀⢂⠎⢛⣇⣀⠀⠀⠀⠀⢀⣀⢔⢟⠹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⡮⣊⡒⠁⠀⠀⢹⣺⡀
⠀⠀⠀⢰⠙⣮⡺⣇⢡⠀⠀⠀⠈⠢⠸⢻⢭⢲⣒⣲⡶⠓⢁⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠫⠗⠤⠤⠤⠤⠤⠴⠊⠁⢆⠄⠁⠀⠀⠀⠀⣨⣼⡑
⠀⠀⠀⠈⠆⠰⢙⠻⣄⡂⠀⠀⠀⠀⠈⠀⠈⠂⠲⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠂⠀⠀⠀⠀⠀⢀⣿⢒⠆
⠀⠀⠀⠀⠈⢂⣑⢅⠸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⠀⠀⠀⠀⠀⠀⢀⢽⠕⢀
⠀⠀⠀⠀⠀⠀⠈⢵⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡼⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡻⡄⡸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆⠀
⠀⠀⠀⠀⠀⠀⠀⡀⣩⣈⣜⠃⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⢀⠠⢐⠋⠀⠀⠀⠀⠀⣠⠰⠀⠐⠃⠀
⠀⠀⠀⠀⠀⡠⠈⠀⣺⣿⠀⢫⡃⠀⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠂⠀⠀⠀⠀⠀⠀⡐⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀
⠀⠀⠀⠠⢂⠌⠀⠀⢚⡹⡆⠘⡅⠀⠀⣮⠙⡲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⢰⠕⠁⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀
⠀⢠⣈⠀⠀⠀⠀⠀⠋⢈⢿⡸⡃⠀⠀⣇⠀⠀⠀⠑⠚⠛⠓⠲⠴⠶⠮⠥⠅⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⡾⠂⠀⠀⠀⠀⠀⠀⠀⢐⠘⣺⡂⠀⠀⣷⡄⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⢰⣀⠂⢹⢳⠀⠀⡀⠀⠀⠀⢖⠃⠀⠀⠀⢀⠐⠀⠂⠀⠀⢀⠀⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⠐⡖⠃⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣺⠾⠁⣠⡞⡇⠀⠸⠠⠐⠒⢡⠀⠀⠀⠠⠀⠈⠠⠈⠀⢀⠐⠀⠀⠀⠀⠀⠨⠄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢄⡛⠈⡠⠓⠀⠀⠀⠀⠠⠁⠀⠄⠈⠀⠀⣠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠂⠁⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀