⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⣄⠀⠀⠀⢠⠎⠉⠓⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠉⠙⠻⣿⣷⡀⢸⠃⠀⠀⠐⣿⣷⠀⢿⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠒⠒⠂⠀⠀⠀⠀⠀⠹⣷⡞⠀⠀⠐⠈⣿⠃⣴⣾⣿⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢤⡀⠀⠀⠨⠉⠐⡀⠀⠸⣇⣠⢐⡤⢠⢏⣾⡷⠟⠿⠛⠀⠀⢉⡉⠒⠤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡤⠀⠒⠠⢤⡀⠀⣯⣇⣿⢃⣾⣿⢟⣔⠁⠆⠀⣂⡀⠀⠀⠀⣀⡀⢢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⠖⠲⠀⢠⠋⠀⠀⠀⠀⠀⡙⣆⢹⣿⡇⣸⣫⡿⣿⣿⣿⠊⠍⠒⠂⠀⢀⠉⠀⠛⠹⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢣⠀⠀⢀⠔⠁⣠⡆⢰⠁⡆⠀⠀⠐⠀⠁⠀⠀⣽⠼⣿⣷⣿⡿⡿⢧⠿⠥⠶⠤⢥⣀⠀⠀⠀⢀⣀⢤⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⡬⡄⣠⠂⠀⠰⡜⠀⡏⠀⡇⢠⠀⡀⠘⠃⠀⠈⠋⡂⢿⣿⠋⡉⠒⢮⣑⡊⢄⠀⠀⠀⠙⢏⠁⠀⠀⠀⡻⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡄⠀⣱⣿⠁⠀⢠⠁⠀⢰⠀⠀⢃⠀⠀⠀⠀⠀⠀⠠⠆⠐⢀⢈⢦⠁⠀⠀⠈⠺⠦⢍⢆⠀⠀⠀⢡⡀⠀⠀⠁⠀
⠀⠀⠀⠀⢠⠦⢦⣼⠀⣶⣄⣰⣚⣳⠇⢀⠀⠌⠀⠀⣼⣀⣤⣤⣭⣉⠉⠉⢲⣦⣥⣄⣀⣠⣤⣾⣷⣌⠀⠄⠀⠀⠀⠑⠕⠀⠀⠀⠃⠀⠀⠀⠀
⠀⠀⢀⡠⠂⢀⣌⠻⣧⡙⢟⢣⢛⣾⠀⡉⣾⠃⠀⢠⠁⠀⠀⠈⠙⠻⣧⠀⢸⢸⣿⣿⣿⠿⠿⠿⠛⠛⠳⢄⡀⠀⠀⠀⠈⠔⡄⠀⢰⠀⠀⠀⠀
⠀⠀⢧⠀⠀⠘⣿⡶⢿⣿⣮⠞⡇⣿⢰⣿⡟⠀⠀⣾⠷⠞⠀⣒⡠⠀⠈⢳⠘⢾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠲⡀⠈⢰⠀⣸⠀⠀⠀⠀
⠀⠀⠀⠑⢄⣨⣺⣿⣮⣷⣮⣻⣷⣽⣼⣿⡁⢀⣼⡿⢀⡠⠤⠔⠴⣤⣄⢈⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠰⠁⠀⠀⠀⠀
⠀⠀⣠⠖⠋⠉⢉⣛⠿⢽⣷⣿⣿⣿⣿⣿⣶⡿⢟⠋⠀⠀⠀⠀⠀⠙⣿⣿⣷⡏⠀⢀⠄⠒⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡞⠁⡀⠔⡊⠵⠲⠽⠋⠋⢁⣠⣿⣿⣿⡇⠀⠈⢢⠴⡾⠉⠱⡀⠀⠘⣿⣿⡠⠊⠀⠀⢀⠄⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡀⠈⠀⠈⠀⠀⠀⢀⣤⣶⣿⡏⠻⠍⠘⠗⡄⠀⠀⢧⢱⠀⠀⠈⢦⠀⣼⠟⠀⠀⠀⢄⠈⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⣀⣠⡤⠤⢲⢿⠟⠍⣷⣿⣿⡄⠀⠀⠀⠃⠀⠀⠘⡌⠚⡄⠀⠀⠣⠏⠀⠀⠀⢎⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣷⣿⣿⣧⡀⢸⠈⠐⢖⣟⢿⡿⡳⡄⠀⠀⠀⠀⠀⠀⣷⠰⡡⢀⣤⡄⢦⡀⠀⠀⡜⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠙⠛⠉⠁⠀⡀⠀⠀⡎⢀⢟⡜⠀⠀⠀⠀⠀⠀⢂⢀⣿⡆⢠⣿⡟⠁⠀⢣⠀⢂⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⢐⠤⣰⣿⣿⣿⣦⡀⣷⣴⡄⠘⣇⡎⠀⢀⢃⡠⠤⠒⠒⠒⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠰⠁⠀⠀⠀⠀⠒⠀⣗⡻⣿⣿⣿⣿⣿⣿⣿⠇⢀⡿⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠋⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠙⢿⣿⣷⡿⢰⣸⢃⣴⠟⠀⢀⣤⠖⠁⠀⠀⠀⠈⠁⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⠤⠭⠥⠤⠭⠗⠢⢤⣘⠻⣿⣿⣿⣿⣿⣛⣴⡶⠏⠉⠀⠀⠀⠀⣀⠀⠤⠤⠤⣈⠨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠁⠈⠈⠑⠠⢙⣺⣿⣿⡿⠛⠛⠻⢝⠀⢀⣀⡤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠠⠤⠄⣀⣀⣀⣀⣤⣤⠼⠾⣿⣿⢛⣿⣗⠀⠀⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡔⡩⠀⠁⣴⡿⠟⡟⠀⠜⢻⣂⠀⡀⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠀⠄⠀⠜⠉⠀⢰⡇⢀⠄⠀⠊⠃⠠⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⡿⢇⠀⠀⠂⠀⠐⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⢀⠃⠀⠀⠀⠀⠀⡰⣿⡷⠛⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠸⠀⠀⡆⠀⠀⡰⣹⡿⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠐⣄⠅⠠⢁⡀⢠⣱⣿⣵⣾⣿⣷⣤⡈⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⡀⢠⢃⣿⣿⣿⣿⣿⣯⣉⠛⠦⡉⠦⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⡧⠃⣾⠛⠛⠛⢿⣿⣿⣿⣿⣦⡄⠂⠈⠓⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⢹⣿⠀⣼⠏⠀⠀⠀⠀⠉⠻⢷⣝⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀