⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠉⠢⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠀⠒⠄⠤⡀⠀⠀⠀⢠⠊⠀⠀⠉⢎⢢⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠻⣆⠀⠀ ⠀⠀⠀⡰⢡⠤⣶⣀⠀⠀⠈⢦⠀⢀⠆⠀⠀⠀⠀⠈⠃⢑⠶⠎⠱⠀⠤⠤⡀⠀⠀⠀⢀⠀⠀⠙⠋⡇⠀⠀ ⠀⠀⢰⠁⠸⠷⢴⡏⠀⠀⣀⠤⠵⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢼⠂⣀⣠⠞⢧⠤⡄⠀⡇⠀⠀ ⠀⠀⠸⡄⠀⠀⠈⠁⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⠀⠛⣭⡐⠌⣴⠃⢰⠁⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⢸⡀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⠞⣷⠀⠀⠀⢈⡜⠀⠀⠐⠗⠋⠛⠿⠀⠧⣀⡀⠀ ⠀⣀⠤⠃⠀⠀⠀⠀⠀⠙⢳⡀⠀⠀⢟⣹⢳⠀⡤⡄⠸⡩⠇⠀⠀⠀⠀⢣⣀⣀⠔⠢⡀⠀⠀⠀⠀⠀⠈⠃ ⡇⠀⠀⠀⠀⠀⢀⠤⠤⣀⠤⢻⠀⠀⠀⠉⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⢐⡜⡄⠀⠀⠀⠘⢄⡀⠀⠀⠀⡠⠂ ⠑⣤⣤⣤⣤⡔⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⢠⡇⡝⢳⡄⣴⠒⠁⠃⡍⠉⠁⠀⠀ ⠀⠀⠀⢠⡷⣆⠀⠀⠀⠀⠀⠸⡀⣀⡠⢄⡠⠒⠉⠀⠀⠀⠉⠁⠒⠢⠬⠔⠁⠀⠉⠹⠡⢄⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠑⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠉⠙⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠶⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠲⠦⣄⠀⠀⠀⠀⢀⡼⠋⠀⠀⢳⣯⢧⡀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣠⣽⡆⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⡀⣠⡄⠀⠀⠀⠘⢧⡀⠀⠀⡾⠁⠀⠀⠀⠀⠘⣦⡹⣄⣀⣠⠞⣁⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠻⡆⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠘⡯⠉⢙⡶⠀⠀⠀⠈⢧⡀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠉⠰⠛⠋⠉⠉⠉⠉⠙⢲⡀⠀⠀⢰⡿⢧⣠⣤⡀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⠘⠗⠓⠾⠃⠀⢀⣠⡤⠴⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠇⠰⣞⡋⠀⠀⠀⡟⠁⢸⡃⡀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡞⠀⠀⠀⡟⣠⠖⠦⣽⠀⣾⢉⣯⣀⠀ ⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⣷⠀⠀⠀⠀⢈⣼⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠋⠀⠈⢳ ⢀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠈⠷⡳⣀⠀⠀⠀⣾⢟⣶⡀⠀⣀⡀⠀⡯⠵⡾⠁⠀⠀⠀⠈⢧⠀⠀⠀⡴⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⣮⡀⠀⠀⠹⣖⣃⠇⠘⠯⠟⠀⠙⠛⠁⠀⠀⠀⠀⠀⠘⡟⠛⠋⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⡴⠏ ⠳⣄⡀⠀⠀⠀⢀⣤⠞⠉⠙⠲⠶⠞⢙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢹⡀⠀⠀⠀⢀⣠⠞⠹⢬⡍⠉⠁⠀⠀ ⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠤⢤⣀⣀⠀⠀⠀⢠⣽⢸⠿⠿⢶⡶⠾⡄⢀⡀⢮⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣤⣠⠖⣠⡴⠚⠉⠀⠀⠀⠀⠀⠉⠙⠒⠲⠴⠗⠋⠀⠀⠀⠀⠀⠓⠋⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠭⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠟⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠀⠈⠉⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡗⠤⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣴⠿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡀⢀⣄⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢕⣎⢢⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⡉⢉⠿⢤⡀⠀⠀⠀⠘⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⣦⠑⢄⠀⠀⡠⠋⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡿⢦⣠⡤⢄⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠐⠿⠶⣄⢻⠋⠀⠀⠀⠀⠀⢻⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠽⠛⠒⠉⠉⠉⠉⠈⠉⠳⡄⠀⢀⡰⠃⠀⠀⠸⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣀⣠⠽⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢀⡇⠀⠻⠶⣄⠀⣸⣴⣘⣦⠀⠑⠤⠔⠒⠤⡀⠀ ⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡜⠀⠀⠀⠀⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⢀⡤⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠌⣰⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠷⢮⣇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⡠⠞⠓⠢⣄⠀⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠳⣄⠀⠀⠀⠀⠀⢀⡀⠤⢄⡀⠀⠀⠈⠣⡙⣀⠀⠀⠀⢀⡿⢟⣳⡄⠀⢀⣀⡀⠀⡿⠟⣹⠃⠀⠀⠀⠀⠀⠘⣄⡀⠀⣀⡠⠊⠀⢠⣀⠀⡈⠑⠒⠶⠒⠒⠉⠁⠀⠀ ⠀⠀⠀⠉⠒⠒⠒⠚⠉⠀⠀⠀⠙⢄⠀⠀⠀⠙⣢⣀⠀⠀⠈⠳⣖⣃⠞⠀⠻⠦⠃⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠁⠀⠀⠀⡇⠈⠉⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠈⡆⠀⠀⠀⠀⣮⣀⠀⣠⠌⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣍⡄⣯⡒⡒⠢⠽⠋⠙⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡄⠀⢀⡤⠔⠋⠁⠀⠀⠈⠉⠓⠒⠤⢤⣀⣀⣋⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⡟⠀⠀⠀⠹⣄⠐⢛⣉⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⡰⠰⢆⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠁⡀⢂⠡⢐⠳⡄⠀⠀⠐⡁⢃⠎⣇⠀⠀⢀⠴⢑⠨⡐⢭⡓⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⢸⢿⠂⣆⠡⢞⠽⣢⠠⢃⠄⢣⡘⠼⣆⠀⡎⣤⢇⣲⢉⢦⡹⣘⡇⠀⠀ ⠀⠀⠀⠀⠰⠂⠄⣈⠂⣭⠀⢂⠐⠠⠈⢄⡘⠤⡘⣁⠣⢃⡜⢤⢫⣷⣚⣾⣧⣗⡇⠀⠀ ⠀⠀⠀⠀⡀⠉⡐⢢⠕⣾⣷⠄⡘⣠⢉⡲⡠⣘⠐⣤⣏⡾⣜⢯⣿⠮⡕⢿⢻⢿⠀⠀⠀ ⠀⠀⠐⡁⠤⣁⡘⢦⡛⣶⢿⡷⠠⠐⢿⣻⡱⣁⢻⣿⢟⡳⣭⢿⣿⣟⣜⢣⢋⠼⣙⢳⡀ ⠀⠀⠘⢴⠳⡜⣜⠟⠀⠉⠁⡈⠈⡔⣎⠶⡝⢯⠻⢴⣫⢔⡳⠵⡉⠈⠁⠣⣋⠶⣍⡞⠃ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⣺⢕⠮⠓⠈⡃⠙⠣⢏⠾⡱⢛⠃⠀⠀⠀⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠤⠜⠸⢄⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣏⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀