⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠡⡁⠤⠂⠉⠀⠡⠆⠀⣑⣂⣤⣀⣀⣀⣀⣀⡀⠀⠉⠀⠈⡪⠦⢤⡀⠁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⢀⡡⠂⣁⠀⢀⣠⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⢄⠀⠉⢧⣄⡀⠉⠪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡔⠁⠄⣠⣴⣾⡿⠿⠛⢋⡉⠁⠁⢀⠀⠄⠂⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣦⣀⠀⠈⢆⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡠⠌⠀⠀⣐⠍⠀⣹⣾⡿⠛⠉⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣄⢩⡘⠀⠀⢦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠂⠀⢀⠮⠘⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣖⠇⡡⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡞⠀⠀⢄⡶⢀⣼⡿⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⢿⣿⣿⣿⣿⣎⡐⣼⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣘⠀⠀⠀⢮⠀⣾⠏⠀⢀⠊⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡉⢿⠋⠹⡿⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⠀⠀⢸⡆⣼⠏⠀⡐⠁⡠⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢡⠀⠱⠈⡇⠀⢗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⢃⢸⡟⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢃⠀⢧⢿⠀⢸⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⣾⠀⠠⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠈⡄⠈⡾⡆⠸⡷⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⠲⣸⡏⠀⠁⠰⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠀⠀⠐⠘⣅⠀⠀⠀⠀⠀⠘⠀⣷⣧⠤⠿⢷⠚⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠏⣾⡇⠸⠀⡤⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠆⠀⡆⠐⠀⠀⠘⡘⡆⠀⠀⠀⠀⠀⡆⢸⠁⠀⢀⠇⢰⢧⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢊⠘⢷⡀⠸⡇⠆⠀⠇⠀⠀⠇⢰⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡙⡌⢻⠒⠷⠠⢦⢄⡀⠡⠹⡀⠀⠀⠀⠀⢡⢸⠀⠠⠃⣴⢉⣮⢷⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠸⣇⠀⢷⡀⠀⠄⠀⡄⠸⠈⡄⢂⣀⠴⡀⠀⠀⠀⠀⠀⡄⠀⡄⠁⢸⠀⡌⢳⡀⢀⠀⠈⠆⡇⠀⠀⠀⠀⠸⠰⠀⠀⠀⣿⠈⡅⣿⠉⠰⣹⠆⣠⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⢹⡄⠈⢇⠀⢆⠀⢘⠀⣇⢷⠎⢧⠀⢡⠀⠀⠀⠀⠀⣇⠀⡇⠀⠨⠁⠃⡀⠩⢂⠡⠀⠈⡸⠀⠀⠀⠀⠀⢘⠀⠀⢤⡛⢰⣧⣿⡔⢲⣹⢶⠙⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣈⡧⢤⣾⠀⢸⡄⡄⢖⢣⢌⠚⢄⠳⢄⠢⡈⢀⠀⢀⢸⡀⢠⢠⠟⣸⣿⣿⣿⣿⣷⣤⡄⠐⡇⠀⠀⠀⠀⣸⠀⠀⠘⡄⠌⢟⠯⣻⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠁⢀⠻⡆⠀⢣⠐⠘⣌⠆⣩⣤⣴⣑⡑⠲⣄⠁⠀⢄⠗⣌⢆⠞⠉⠸⠿⢿⣿⣿⣿⣿⣦⡈⠂⡀⠀⠀⡼⠀⠀⠀⠙⠾⠬⢴⡞⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⠀⣧⠌⠌⢆⠄⢯⢶⡿⢹⣿⣿⣿⣆⠈⠀⢤⡈⢎⢎⠪⢂⠀⡀⣀⣞⢛⡹⣻⠿⢹⡏⠓⠴⣢⡀⣢⠀⠀⠀⠀⠀⣐⣷⣻⣢⢀⠄⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡶⠀⠌⠀⢩⣧⠈⡚⣄⠨⣧⡇⠈⡈⢿⠿⣿⣇⠀⢈⠐⣸⠀⠢⡌⠐⠀⠐⠌⡓⠚⢋⢰⠊⠄⠆⠀⢸⠎⠛⠉⠁⠈⠑⣿⣿⡞⡷⣹⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠴⠀⠘⠈⠑⣃⠑⠌⢆⡸⡽⣄⠱⠺⢕⡸⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⣸⠂⠀⢸⡇⣾⣻⠿⠷⡀⠈⠹⣷⡸⣹⡹⣷⣄⠁⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⠤⢲⣅⡪⣂⠘⢇⠑⢄⢳⡸⣄⠁⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠏⠀⢀⡇⣳⡿⠁⠀⡀⠠⡐⠀⠙⢧⠹⣏⡘⢧⡑⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡢⡐⣠⢯⠁⡰⠑⣼⢆⠁⡢⠙⣷⡱⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⠆⠀⢨⡃⣿⡇⡧⠀⠛⠓⠂⠀⠀⠀⠑⠻⣏⠢⠳⡀⠑⣄⠂⢄⠀ ⠀⠀⠀⣠⠊⠀⣰⠌⠃⣔⡡⠟⠡⠀⠰⢃⡔⠨⡑⢌⡐⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⣠⣾⢿⠸⠀⣟⠢⣏⢧⣇⠠⠐⠒⠂⠀⠀⠀⠀⠀⠙⠈⢣⡂⠄⠈⠕⠀⠀ ⠀⠀⣨⠀⠠⢚⠏⢁⡜⠑⠒⠈⠀⠀⢠⠀⢸⢥⡈⢄⡙⡆⠠⢀⠀⠀⠀⠸⡋⢑⠻⠀⠀⢀⣠⣾⠝⣭⢾⠀⢰⢹⢠⢻⢸⢿⣀⢠⢮⣔⠄⠀⠀⠀⠀⠀⠀⠀⠜⢂⢄⠀⢀⠀ ⠀⢰⠁⠐⠁⠋⠀⡞⠀⠀⠀⠀⠀⠀⢸⠀⡎⡆⠀⠐⣷⡄⠀⠀⠈⠃⣦⣤⠀⠀⠀⢠⣴⣿⠋⠀⣤⡟⠘⣤⠀⠈⠘⡌⡆⠀⡇⠉⠉⠛⠃⢡⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀ ⠀⠁⣰⢑⢵⠃⡜⠌⠀⠀⠀⠀⠀⠀⠈⠃⠐⠃⠀⡐⠃⠩⡉⠀⣀⢔⣶⡿⢿⣷⠚⣿⣟⡀⠀⡴⢁⠇⠀⢇⠰⣨⠃⡇⠀⠀⡇⠀⠀⠀⠀⠀⠳⢀⡀⠀⠀⠀⢠⡀⢪⡈⠀⠀ ⠀⢐⠀⠀⡦⠌⡐⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠳⡀⠱⠀⠀⢈⣾⣯⠏⠁⢀⣿⠇⢨⣿⢹⣡⢈⠃⡌⠸⠀⡙⠀⡞⠚⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⣌⠳⣂⣎⠈⠀ ⠀⡘⠀⠐⡈⠐⡈⠀⠀⠀⠀⢀⠀⠀⣦⡄⠀⠀⠯⢇⣀⡠⠂⠙⢿⣶⣀⣰⣿⠀⢸⣿⠀⣷⡿⢠⠁⠀⠑⠅⣴⠃⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⡇⠃⠈⢋⡖⠀ ⠀⠁⠠⠐⡆⠆⠁⠀⠀⠀⠀⠈⡄⠀⡼⡀⠀⡈⠄⠀⠀⠀⠀⠀⠘⣿⣶⣿⡇⠀⢸⣿⠀⣽⡿⠿⠀⠂⠀⢠⡏⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢘⡇⠑⡀⢄⡞⠄ ⠀⢀⢁⠀⠘⠘⠀⠀⠀⠀⠀⠀⣱⠠⠀⠣⣀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠁⠈⣽⣿⡿⠋⠀⠀⠢⢀⡴⠋⠁⠇⢸⠄⠀⠰⡇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⢻⡀⠀⠂⡠⠀ ⠀⡘⡈⠐⡀⢒⡌⣀⢀⣠⠤⠂⠀⠀⠀⠰⡒⠤⡀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⣿⠉⠀⠀⠀⢀⠔⠃⠀⠀⡈⠀⠈⡆⠀⠀⢡⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢀⣇⠣⠀⠀⠃⠀ ⡀⣇⠉⠂⠄⣈⣱⣮⡭⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠈⠒⠀⠄⣢⡞⠃⠀⠀⠀⠀⠈⢷⡄⠀⠉⠀⠀⠀⠠⠈⠀⠀⠀⡇⠀⢠⢋⠆⠀⠀⠀⢠⠁⠀⠀⠀⠀⢸⠀⡧⢂⠰⠀⠀ ⠀⠏⠦⠄⢒⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣙⠀⠀⠀⠀⠀⠀⠀⠀⠻⡢⡀⠒⠂⠀⠀⠀⠀⠀⠀⡄⠀⣾⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢣⠁⠄⠀⠀