⠠⠀⣀⠂⢀⡀⢄⠀⢰⠂⠠⢀⠒⠒⠂⡴⢀⠒⣐⢠⠒⡐⣰⢰⡆⢖⢰⢲⡴⡶⢶⢖⡒⠖⠲⠖⡒⢔⠖⣴⢲⠒⡂⠦⠢⠔⠤⠔⠲⡠⠐⠤⠒⠆⠆⠲⢀⠠⠂⢢⡐⢀⠒⡰⢀ ⢀⠃⢀⠀⠀⠀⡀⢠⠐⠂⠀⠄⠂⢀⠨⡐⡠⡄⠠⡀⠠⡄⠤⡀⠤⢁⣤⢠⡁⠦⢤⠤⣴⣬⠠⢋⣤⡀⠴⠂⠀⣠⠄⡀⢤⣌⡤⣀⠉⠄⡀⡄⢄⡄⣄⠡⣄⠀⢠⡀⠠⡀⠀⠐⠆ ⢀⡌⠀⠣⡍⠵⠩⠇⠏⠯⠏⠻⠭⠯⠿⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠈⠈⢗ ⢈⢂⡐⡣⡍⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠃⠈⠁⠁⠁⠈⠁⠉⠈⠈⠁⠉⠈⠁⠉⠘⠘⠁⠁⠘⠃⠁⠁⠀⠁⠈⢀⠀⡁⠀⠀⠈⢿⣿⠀⠐⡂ ⢠⠆⢠⡇⣆⠇⠀⠀⠀⠀⠄⠠⢀⠀⠄⡀⠠⠀⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⢀⠀⠠⠀⢀⠂⠐⠠⢈⠐⡈⡐⢁⠊⠄⣁⠊⠄⢃⡘⠠⡁⢢⠁⠀⢈⢿⣟⠂⡐⣡ ⢈⡝⢁⡇⡎⡂⠀⠀⠀⠀⠀⠀⠀⠈⠐⣀⠁⡂⢌⡐⠠⠐⠀⠈⠀⠌⢀⠐⠠⢀⠠⠁⢂⠀⠄⢀⠂⠈⢀⠠⠈⠐⢀⠂⡐⠠⢈⠐⡈⠄⠌⡘⢠⠠⠑⢠⠂⠥⠀⠈⢾⡿⠀⠄⠰ ⠠⡂⠔⡆⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⢄⢀⠐⡀⢀⡀⠀⠂⢀⠂⠄⡈⠄⠂⡀⠡⠀⡀⠐⠈⠀⠠⢀⠁⢂⠐⠠⢈⠐⡈⠄⢂⡉⠄⠌⣂⠀⢸⢹⣿⠆⠚⡉ ⠰⠁⢨⣖⠣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⡿⡟⠘⠦⠙⠾⣵⣦⠀⠀⠂⠐⠠⠐⠠⠐⠠⢁⠀⠂⠌⠀⠁⠀⡀⠂⢈⠐⡀⢂⠐⡈⠄⡐⠈⠔⠠⠀⢸⢸⣿⠄⠡⢁ ⠀⡁⢂⡧⣛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢁⠣⡁⡘⢄⠂⠌⡐⠀⠌⡐⢀⠀⠄⠂⠀⡀⠄⠂⠐⠠⢀⠉⠄⡁⠂⢸⢼⣿⡯⡘⢠ ⠰⠉⢈⢱⣋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠃⠙⠀⠀⠀⠀⠀⠀⠀⠱⣡⠒⣤⠉⡔⠠⡉⡔⡀⠢⢈⡐⡀⠁⢀⠀⠠⠁⠐⠀⡈⠄⠐⡀⢸⣹⣿⡤⡖⢼ ⢘⠒⠈⢧⣋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡞⢿⣷⣴⣾⡆⠀⠀⠀⠀⠀⠀⠐⠫⠖⡩⢒⡱⡘⢴⡡⢓⡌⣲⠱⡈⠄⢂⠐⠠⢈⠀⠄⠐⡀⠀⢸⣸⣿⡇⠐⡐ ⠠⠂⢘⣰⢣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠤⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡙⢦⡙⢎⡖⡡⠓⡌⠄⢃⠈⡐⠠⢈⠐⠠⠐⠀⢸⢸⣿⡇⠁⣭ ⠈⡁⠠⢝⡆⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣶⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡝⠲⣌⡱⢡⡘⠌⣀⠂⠄⡁⢂⠈⠄⠡⠀⢸⢸⣿⡅⠀⠧ ⠸⡀⠔⣻⠸⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠓⡤⢃⠧⡘⠰⡀⠌⡐⢀⠂⠌⠠⢁⠀⢸⢸⣿⡟⠘⣛ ⢐⡃⠸⢻⠜⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣦⣦⠄⡀⢀⣉⣠⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢮⠑⣎⠱⢣⠜⡰⠐⠂⠌⠠⢁⠂⠀⢰⢺⣿⡇⢁⠮ ⢨⣔⠡⢺⢞⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⢾⣿⣿⣿⣿⣿⣿⣆⢹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡙⢦⡙⠤⡉⠜⠠⡁⠂⠌⠀⢸⢸⣿⡏⠉⣿ ⢈⠆⣐⣻⢺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⢙⢻⡿⠇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠱⣀⢃⠒⠠⢁⠊⠀⢸⢼⣿⡏⠿⣷ ⢸⠉⣡⢺⣟⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠃⡁⠂⠌⠀⢸⣼⣿⣧⠡⣖ ⢈⡘⡘⢾⣾⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠀⢸⣿⣿⣿⠐⢬ ⢨⡕⢈⢼⡽⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⡇⡱⢋ ⠸⣮⠺⣼⣽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠳⢛ ⢘⠆⠄⣻⣽⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡏⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡗⡉⡷ ⢘⡂⠘⣸⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⣭⡁⢻⣿⣿⣿⣯⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣻⡌⢨⣽ ⠸⡃⠖⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⠿⠇⠀⠉⠋⠛⠫⠉⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⠆⠨⠝ ⢘⡏⡐⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡉⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⢸⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠴⠈⢫ ⢐⠧⠰⢿⣿⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣤⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⠙⠛⠓⠦⡄⠀⠀⠀⠸⢸⣿⡌⢁⠷ ⢸⠚⡬⣿⣿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡖⣧⠘⡧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⢘⢸⣽⠭⢊⣿ ⢠⠊⡤⣿⣻⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣾⢐⠐⣍ ⠈⠄⠸⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠥⠓⡤⣀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣻⢼⠰⢌ ⠘⡡⡈⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⡠⠔⣈⠢⠑⡌⠡⠐⠠⠈⠂⠑⢄⠀⠀⠀⠀⠀⠀⢀⢸⣽⡈⠖⣘ ⠸⠵⠁⣿⣯⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠁⠂⠄⠀⠀⠈⠁⠀⠤⢀⠁⠐⠀⠄⠀⠤⠀⠀⠀⠀⠀⠰⢸⢼⠂⡐⣲ ⠘⢆⠄⣿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⠈⠐⠠⠀⠁⠂⠀⡈⠑⢢⡀⠀⡀⠈⠀⠀⠀⠀⢘⢘⢺⠈⠄⠥ ⢈⡂⠠⢟⡷⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠁⠐⠀⡀⠁⠄⠈⡑⠰⣀⠠⠀⠀⠀⢘⢸⢸⡇⠐⠎ ⠠⠄⠨⢹⡗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⠨⢼⠁⠀⠎ ⢀⠂⠀⣹⣛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠨⡘⢮⠁⠀⠔ ⢈⡁⠠⢗⡧⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡧⠈⢀⡊ ⢀⠀⡀⣏⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⡆⠅⠒⠒ ⢨⠐⠁⡆⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠏⡄⠠⠌ ⠀⠀⠀⠧⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⡅⠀⠄ ⠀⠀⠈⠡⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⡃⠀⠎ ⠀⠐⠀⠡⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⡆⠃⢀⡃ ⠀⠀⠀⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠆⡅⠂⠤ ⠀⠀⠀⠂⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡃⠀⢤⠃ ⠀⠀⠀⠄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠄⠀⠀⢤⢄⠠⢀⢀⠀⡀⠀⠀⡀⠀⠀⡀⢀⠀⠀⢀⠀⠀⢀⡃⡅⠂⠀⡠ ⠀⠀⠀⠐⠀⠎⠀⠣⠌⠂⠇⠣⡙⠜⠥⠛⠽⢫⠟⢽⡻⠿⠿⠿⡿⠿⢿⠿⣿⡿⠻⠿⠿⠿⢻⠿⠿⠿⠿⡿⠯⠿⠿⠯⠏⠿⠱⠫⠗⠜⠣⠱⠐⠣⠘⠡⠊⠄⠃⠂⠄⠁⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠈⠀⡐⠈⠈⠠⡄⠀⢀⡀⢀⢁⠀⡀⢀⢠⠀⠁⠰⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄