⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⢤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡊⠁⠠⠄⢐⠲⡄⢂⢒⠢⠠⠤⢁⡀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡑⠨⢄⠂⠥⡈⠆⢒⡈⠔⡨⢐⠡⢊⠐⡐⠢⡍⢓⡢⣄⠀⢄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠰⢉⠄⠣⠌⡘⠤⠑⡌⢂⠜⡠⢑⠢⡘⠤⡉⠔⠡⢁⠂⠙⢦⠛⠲⣭⠢⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⠐⡂⣁⠊⠌⢰⣥⡈⢂⠱⣀⡇⢂⡑⢂⠡⢂⠱⡈⢌⢁⠂⡡⢊⠈⢳⡆⠌⡙⠾⠦⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣤⠍⡡⣿⣤⣡⣀⣬⣶⡿⣿⣿⣶⣿⠋⡐⢂⠰⢈⠂⡁⠆⠐⡀⠂⠌⡐⠄⠊⠄⢹⡠⠐⠠⠑⣶⡦⠭⠽⠴⠒⠂⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠢⡐⠌⡐⡙⠿⠻⠟⡋⢅⠂⡄⣠⡾⣣⠔⡐⡈⠰⢀⠡⣐⣬⠦⠔⠡⣈⠐⡈⠡⠈⠄⠗⡈⡁⠆⡀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⢠⠘⡃⢠⠃⡄⢃⠄⡃⠧⣜⣠⡼⣿⣻⠟⠃⡄⠠⢀⣣⡼⠛⠃⢀⠠⠘⠠⠀⢠⠀⠃⢄⡘⠠⢀⠠⢃⢀⠃⠄⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠆⡑⢂⠥⠘⡠⢁⠒⡨⠐⠡⠒⢠⠉⠡⡁⠄⡘⠐⣠⡵⠛⠁⠠⠀⠁⠂⠀⠂⠁⢨⠀⣤⡷⣿⠁⠂⠄⠒⡈⠄⠣⠙⡖⠽⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢢⠃⡔⢡⠘⡄⢊⠡⡐⢡⠊⡔⢉⠰⠉⡄⠌⠡⠐⠠⢁⡾⠋⠀⠀⠀⠀⣀⣀⣠⡤⠶⠷⠛⠉⠁⠀⣿⠈⠐⢈⠠⣧⠈⠄⠡⣞⡄⠪⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⢁⠒⡬⢂⡕⣸⠏⠰⡁⢆⠱⡐⠨⠄⢃⡐⢈⡅⠌⢠⣟⣤⠶⠒⠋⠛⠉⠛⠉⠋⠒⠒⠄⠀⠀⠀⠀⢻⣥⠂⠀⠂⣿⠐⡈⠃⣿⠲⡄⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠜⣴⣼⠕⣸⡅⢾⣈⠡⡘⢄⠣⢌⡑⠌⠢⣄⡛⡄⢰⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡦⡄⠈⡐⣏⠂⢄⠁⣾⠀⣼⠀⠈⢧⠀⠀ ⠀⠀⠀⢀⡀⢀⢘⡡⣿⠀⣿⣷⣙⢷⣄⠱⢈⠒⠤⡘⢌⠡⢧⠓⡄⢸⠀⠠⠱⣦⠶⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡿⣂⡄⣼⡇⡈⠄⢂⡏⠀⢲⣇⠀⠈⠆⠀ ⠀⠀⠀⠈⠀⠢⢎⢄⢹⣎⣿⠄⡙⢓⠻⠷⠮⡜⠤⡑⢌⠢⠸⡧⣃⣿⠀⢀⠄⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⣴⠊⠀⠀⠀⠘⡜⣟⣰⣿⠁⡐⢨⠘⢷⡀⢸⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠋⢤⡙⢿⣦⢈⠂⡔⢢⠚⡌⡱⢌⠢⡙⢤⢳⠹⣸⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡾⢡⠤⠶⢶⣮⡠⣡⣿⡟⠁⡐⢠⠂⠱⣀⢳⡼⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣏⠰⢸⡄⠣⢌⠣⡑⢌⠆⡓⢌⠔⣊⠱⣘⠀⠆⡙⣌⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠉⣰⡿⠃⠤⠑⡈⡔⢈⠡⠄⡚⡣⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣠⠙⣧⡱⢈⠆⡱⢈⠆⣑⠪⠔⢢⠱⢀⠃⡜⡠⢸⡅⠂⠙⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣠⢴⡋⡐⢌⠢⡑⠰⣈⠂⡱⢈⠜⣡⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢹⢳⡥⠿⢓⠺⣀⠣⢈⠄⡃⢎⣁⠢⡁⢎⡷⡘⡜⣽⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⣤⡒⠀⠀⢀⢼⡿⢁⠰⢠⠑⣌⠱⡠⡜⢀⠮⡘⣽⡗⣦⠀⠀⠀ ⠀⠀⣀⠴⢂⣉⡩⠭⠿⢼⡴⣞⠣⠄⡃⢌⠊⡜⢠⠢⡑⡌⣾⢇⡱⡸⣷⠀⠀⢰⠃⡍⢲⠤⠤⠘⠛⠉⠀⢀⣤⡾⠟⣀⠣⡘⢄⣪⠏⣔⣿⠇⡌⣰⢻⣼⡇⠀⠁⠂⠄ ⢠⠜⢡⡶⠫⠀⠀⠀⠀⠀⠀⠈⠓⠾⢴⣬⣶⣞⣢⣑⣦⣿⠿⠓⠉⠀⣿⣟⡄⠒⠃⠊⠁⠀⡀⣀⣤⣴⠾⢛⠡⢂⠥⡱⣶⣵⡞⣋⣴⠞⡡⠒⣀⠒⡿⠛⠀⠀⠀⠀⠀ ⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠘⠿⣿⠛⠁⠀⠀⠀⠄⠸⣿⣿⣦⣀⣤⣶⣷⣿⣿⠏⡐⠄⡂⠱⡈⢆⠱⢄⠣⡍⣍⠢⡑⠤⢑⠠⡊⠥⢀⣠⠤⠀⠀⠀ ⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⡈⠃⠢⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⡐⢂⠡⡑⢌⣢⠱⣈⠱⠒⡌⠱⣈⣎⠄⣳⡾⠚⠋⠁⠀⠀⠀⠀ ⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⡇⠀⠀⠈⠑⠢⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣶⣮⠶⠾⠛⢹⢶⣀⣣⣑⣨⣱⣞⣁⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡗⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢸⠀⢸⡆⠀⠉⠉⠛⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣫⡇⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢺⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢧⠁⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠰⠖⠉⠀⡿⠀⢸⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⡘⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠀⢘⡤⢶⣹⠇⠀⢸⣴⣻⡇⣴⢒⣇⣀⢄⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⢀⢇⢀⡇⠀⡼⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢝⢔⣯⠹⣦⡞⠃⠀⠀⠈⠙⠺⠤⣰⡌⣿⣗⢤⣣⣀⣠⡞⠁⠀⠀⢐⠢⢴⣒⡜⠀⣞⢠⡼⠁⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⣘⡴⠱⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢮⣮⢌⣻⣻⠀⢀⡤⢻⣯⠻⠚⡉⠀⠨⢷⣺⡇⢠⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⢱⢰⣒⣻⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣽⡟⣞⣋⡽⠋⠀⠀⠀⠱⡀⠀⢉⢿⡕⣎⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣘⡏⣡⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡽⠋⠀⣀⠀⠀⠀⠀⠱⡀⠀⠈⢾⣝⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀