⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢂⢀⡀⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠀⢀⡰⠁⡴⠀⣀⣀⡀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠄⣁⠢⠜⡠⠅⠈⠀⠣⢔⣡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢉⣀⡠⠔⠁⠀⠉⠻⢷⡀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡘⠠⠄⡙⠢⠁⣤⠃⠀⢡⣾⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⢄⠀⡒⡀⠀⠀⠈⠳⡄⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡐⡁⠬⢠⠡⡟⠡⠀⠐⣸⢥⠆⠀⠀⠀⠀⣺⠂⠀⡤⠀⠀⠀⠀⢳⠈⠄⠐⢧⢰⡀⠀⠀⠹⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡅⠌⢐⠀⣘⠀⢾⠁⠐⠀⠀⣧⡾⠀⠀⡀⠀⢀⠇⠀⢸⡃⠀⢸⣆⠀⢸⠀⡃⠀⠘⡾⡅⠀⢄⠀⢱⠀⠐⡀⢯⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠤⢌⠀⣥⠇⠂⠐⠀⢰⣾⠁⢀⡆⣧⠀⢸⠀⠀⣺⠀⠀⢸⣷⠀⢸⢠⡁⢸⡄⢿⣷⡂⠸⡄⠈⣄⠀⢑⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠇⡨⠒⡠⠃⣼⠀⠀⠀⣤⢸⡿⠀⢸⢠⣷⠀⢼⠀⠀⣿⡂⠀⢸⣯⡇⠰⢸⠀⠠⡆⠺⣟⣧⠀⣇⠀⣡⠇⢨⢎⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⠐⢡⡅⠄⡱⢏⠐⠂⠡⡞⢸⠇⢀⣇⣿⡏⠐⢻⠀⠀⣿⡇⠀⢸⣿⣥⢃⠎⠀⠀⣷⠘⢹⣾⠀⡏⠀⠰⢘⠀⡌⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣜⡞⢠⡏⣀⠖⣁⡯⠐⠄⢸⣇⢸⡆⢸⣿⡿⠇⢰⠙⡀⡄⣿⣇⠀⢼⣾⡍⡔⠀⠀⢸⣽⣆⠈⢿⢡⡇⠀⠆⢸⢀⣧⡀⠑⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠁⣧⡿⡑⡈⢒⢸⣝⠀⠂⢹⡇⢸⡦⢴⡿⢧⢖⠇⠒⢏⠛⣽⡟⡄⢸⣿⣴⡆⠀⠀⠇⣬⡇⠈⣝⢵⠁⢹⠀⡇⢸⣏⡛⠦⣈⢢⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡿⢋⠠⢅⢫⢌⣯⠀⡄⢺⣏⢸⣿⡔⠁⡞⠂⠀⠀⢈⢦⠸⣽⠰⣸⣾⣿⠄⠀⡰⠈⣏⣤⣴⣥⡌⠠⡇⢸⠁⣞⣆⢷⠀⠀⠈⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⣴⢃⡐⢮⡞⡟⡞⣻⣀⠠⢹⣿⠀⢏⣹⣷⠾⢿⣿⣿⣿⣶⣶⡘⢗⠙⣿⡟⠀⡰⠑⣿⢿⣿⣟⣫⣷⢣⢣⡏⣸⣿⣿⣮⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡞⣽⠂⢮⡯⣼⣿⠋⢱⣋⢆⠀⢿⣆⢸⠈⠿⠀⣯⠢⠿⠖⡆⠀⠁⠀⠱⡻⢀⠞⠁⠈⠁⠹⡚⢁⣗⢁⢴⡾⡘⣸⠟⢿⣿⣿⢷⡀⠀⠀⠀⠀
⠀⠀⠀⢠⢫⣼⠃⡜⣼⣧⣿⣿⠈⢹⣸⡸⢖⠘⣿⢦⢦⠀⠐⠈⠓⠒⠚⠁⠀⠀⠀⠜⠂⠁⢀⠀⠀⠀⠀⠉⠀⠠⢾⣿⠏⣷⠇⠀⠀⠙⠺⠿⠿⠦⠀⠀⠀
⠀⠀⢀⣞⢞⢇⡚⡼⣿⣿⣿⣿⣦⡳⡟⣧⡸⡳⡸⣧⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣇⢘⡢⣝⢒⣹⣿⣿⣿⣿⣿⡷⢿⣷⣽⡌⠺⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣼⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⡀⢧⠹⣇⡸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⡢⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⣦⣑⢿⣧⣻⣿⣿⣿⣿⣿⠈⣿⣿⣇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⡿⠿⢿⣿⠟⡇⣿⣾⣿⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⣴⣿⡇⠈⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⣿⡏⠀⠇⣼⣿⣯⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⠇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠛⣿⣿⡇⠀⢸⢣⢿⣿⣀⠈⢀⠀⠀⠀⠀⠉⠒⠤⣀⠀⣀⣀⣀⣠⣶⢿⣿⡿⠿⢻⡅⠆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⣾⢆⣿⣿⣿⣇⡠⢾⣧⢾⣿⡏⠂⢀⠀⠀⣀⣠⠤⠒⠋⠁⠉⠀⠀⠀⠀⠀⠈⠉⠀⠒⠢⠧⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠠⠀⠀⠀⢀⡾⣏⣞⣼⣿⠟⡏⠀⠈⣿⣘⣿⣿⣠⣴⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠄⠀⣠⣾⢻⣭⣻⢻⡄⠀⠘⣆⠀⢻⣳⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⢀⠠⡐⠠⢀⠠⠠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⣁⡠⠞⠻⣿⣯⡞⣽⣧⡛⢦⠀⠘⢆⣸⣽⡞⠁⠀⠀⠀⠀⠀⠀⢀⡴⢁⠆⡑⢐⡠⠂⠑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀
⣢⠞⢡⠑⠌⡐⡈⠻⣿⡶⡹⣯⣋⢧⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠡⠒⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠤⠨⠷⠄⠰⠤⡄⠀⠀
⢡⠘⡄⢊⠔⠠⠐⠀⡙⢿⡗⣭⣧⢾⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡎⠜⢂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠥⡤⢤⣶⣤⡠⢌⠢⢤
⢂⠓⢌⠰⡈⠄⡁⢒⠠⠈⢿⡷⣹⡾⣽⠚⠓⠒⠒⠮⢉⠆⠀⠀⡼⢌⢸⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢊⠉⣁⣀⣀⠀⠘⡆⡘
⡘⣌⠢⡑⠄⢣⠘⠠⢁⠆⠈⣷⣳⡿⠁⢀⠴⠊⠉⠘⠛⠬⣰⠛⠣⡌⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢚⡩⠕⠉⠛⢤⢱⡃