⠀⠀⠀⠀⠀⠀⠄⡏⠀⣿⡿⠀⠈⡣⠀⠀⡆⠀⡇⢆⣹⢻⡐⢡⠎⣼⢁⡜⢤⢡⢐⣄⠸⣝⡜⣤⢃⢼⣙⠚⡭⢳⡂⣀⢀⡨⢀⡀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⡟⡄ ⠀⠀⠀⠀⠀⠀⠀⠡⠀⣌⡲⠀⠀⡤⠀⠀⣃⠀⣋⠰⣰⢻⢄⣣⣾⠼⠷⠚⠛⠉⠉⠉⠉⠉⠉⠛⠛⠺⠮⣵⣠⠓⢢⣌⣲⣴⣔⡐⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡏⠀ ⠀⠀⠀⠀⠀⠀⠰⣣⢀⣿⢻⠀⠀⠄⢒⣤⠿⠒⠛⠶⣭⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠛⠉⠁⠉⠙⣷⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⣿⠠ ⠀⠀⠀⠀⠀⠀⢸⠄⢇⣽⣪⠈⠀⠒⡟⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⣿⠡ ⠀⠀⠀⠀⠀⠀⢸⢟⢡⣏⣚⠀⠀⠌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣿⠡ ⠀⠀⠀⠀⠀⠀⢘⠊⠒⣻⣻⠀⡀⣠⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣽⢃ ⠀⠀⠀⠀⠀⠀⠀⣯⠒⣻⡁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⢺⡃ ⠀⠀⠀⠀⠀⠀⠠⣽⡱⢿⢎⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⡣⠔⡅ ⠀⠀⠀⠀⠀⠀⠀⡝⠘⣿⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⢺⡆ ⠀⠀⠀⠀⠀⠀⠀⡇⠜⣱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠨⡭⢨⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸⣃⢒⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⣜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⠦⠁⠇ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡶⣲⠆⢢⠸⡣⢐⠋ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡂⡤⠘⠨⡔⡩⠂ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣀⡤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠆⣘⢸⡒⣴⡃ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡭⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢢⢀⣝⠐⣨⢔⡅ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢺⣰⠺⡀⡾⠔⡂ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣴⣿⢟⠹⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⢴⢨⠀⠟⡁⠆ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠙⠻⠿⠶⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡢⢓⠘⠀⠳⡐⢇ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⠐⠀⢠⣷⠸ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⠄⢘⡳⠙ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠂⢸⣐⠂ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⢀⣠⠤⠤⣤⡶⡖⡾⡄⠀⠀⠀⠀⢀⣠⡔⠒⠒⠒⠒⠲⠴⣖⡒⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠄⠰ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⡜⢸⡽⡝⡜⡸⣸⣫⠿⠽⠭⡽⠋⠀⠈⠑⠦⡀⠀⠀⠀⠀⠉⠲⢴⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄ ⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢸⠁⡇⡇⡇⡇⣇⣇⣇⣀⣠⠤⡼⠥⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠥ ⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣞⣶⡿⢿⡿⡟⡟⡛⢿⠉⠉⠁⣇⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢧⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡟⢠⢀⡇⡌⡇⠁⡇⢃⠘⡆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠇⡸⢠⠃⡇⢀⢹⠈⡄⢻⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣤⠤⠤⠴⠶⠖⠲⡇⢸⢀⡇⠘⢰⠃⠈⠈⡇⢰⠘⡗⠒⠒⠒⠶⠶⠦⠤⠤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠀⠀⠀⣀⣀⣀⣠⢤⣿⡈⠀⡇⡆⢸⠀⡇⠀⡇⢸⢸⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡀⣠⠤⠖⠚⠛⠛⠩⢁⠉⢀⠂⠬⡇⠀⢣⢡⠸⡀⡇⢠⡇⢈⢸⡖⡫⠝⣹⠆⠀⠀⠀⠀⠈⠉⠛⠲⠦⣄⣠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠐⠢⠄⠆⠲⠒⠖⢾⣿⣿⣿⣿⣶⣦⣄⣀⣀⣄⡂⠌⠂⠤⣀⡇⠆⢸⣸⡄⣇⢱⠘⡄⢹⠀⣷⢵⣋⠁⠀⠀⠀⢀⢀⣀⣠⣦⣼⣿⣿⣿⣿⡿⠠⠤⠤⠦⠶⠴⠒⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⣾⣾⣿⣿⣶⣶⣿⣿⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠠⠀⠈⡀⠄⠂⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠀⠀⢳⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠄⠂⠀⠄⠂⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠐⠈⢀⠡⠀⠄⠈⠠⠈⠠⠀⠠⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠄⠈⢀⠈⠄⠀⠈⠀⢈⠀⠡⠀⠂⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣧⣶⡀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠁⠀⠂⠈⠄⠐⡀⠘⠀⠀⠀⠀ ⠐⠠⠁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠁⠀⠁⠀⠠⠀⠐⠀⠀⠀⠀