Cute Cartoon ASCII Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠀⠀⠀⠀⠀⢀⡠⠔⣪⠽⠛⠒⢄⠀ ⠉⠻⢍⠉⠑⠒⠒⠤⢄⣒⠒⠢⢤⣝⣷⣄⠀⢀⡴⢋⠔⠋⠀⠀⠀⠀⠈⢇ ⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀⠭⠶⠄⠈⠛⠛⣳⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢙⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣀⡰⠃⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⣯⣀⠀⠀⠀⠀⢀⡤⠒⠉⠙⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⣠⠋⠀ ⠀⠀⠀⠀⢹⡉⠂⢠⡆⠀⢀⣤⣖⠀⠀⠀⠀⠀⢀⠘⢤⣀⣀⡤⠊⠁⠀⠀ ⣀⣀⣀⣠⡼⠯⣱⣾⣿⣶⡁⢈⡝⠀⣀⣀⣀⠠⠤⡽⠭⠍⠐⠃⠀⠀⠀⠀ ⠇⠤⠤⠿⣿⣿⡛⡟⡟⠁⢾⠛⢻⢟⠒⡲⠖⠒⢶⡁⠠⠤⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⢀⡝⠋⠛⡟⢿⣿⠮⠶⣴⡿⠟⠳⠶⠭⢑⡛⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⣰⡧⠊⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⢺⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢛⠚⠋⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢰⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡨⠟⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠁⠘⠦⣀⣠⠞⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⡄⠀⢀⡆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⣱⡄⡄⠇⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠉⢳⣿⣟⣟⠉⠘⠁⠀⠀⠞⠋⠑⡄⠀⠀ ⠀⠀⠀⢀⣴⣶⣷⣶⣶⣦⣵⣤⣄⡀⠀⠑⠂⠋⣠⣄⡀ ⠀⠀⢠⣾⣿⣿⢯⣷⣷⣮⣿⣿⣿⣿⡄⠀⠀⠀⠙⠋⠀ ⠀⢀⣿⣿⣿⣿⣞⡯⠯⣏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⢥⣄⡀⠀⢀⣀⡛⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠚⠉⢣⠚⠁⠀⠈⠚⢁⣀⠀⠑⡤⠇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠊⠀⠄⡇⠀⣰⣯⣷⡄⣼⣿⣷⡄⠸⣄⠢⠀⠈⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠰⡟⢇⠀⢻⣿⣿⠇⠿⣿⡿⠁⢠⠋⡆⠁⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠀⢸⡈⠒⢤⠤⢒⡺⠿⣒⠤⢴⢃⡾⠀⢠⠖⠁⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⣄⠀⢾⠘⡄⠀⠈⠻⣶⣾⠋⠀⠀⡸⢠⢇⡇⠀⢠⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⡷⣌⠒⠤⢀⠤⠥⠤⢴⡪⠔⢇⠈⠁⢠⠃⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠉⠑⠦⢄⡀⠴⠋⠀⣠⣎⣀⠔⠁⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢊⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢌⠢⡀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡎⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠘⡦⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⡄⠀⠀⠀⢀⡬⣦⠘⡃⠀⠀⠀⠀⠀⠰⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⢱⢀⠀⠀⠀⣯⠙⠈⣇⠀⠀⠀⠀⢀⠇⡘⠀⠀⡇⠀⠀⠀⠀ ⠀⢀⠤⠒⠉⡠⢦⠊⠈⠀⠀⠀⢸⠄⠤⡞⠀⠀⠀⠀⣞⠀⠀⠀⠀⠧⢀⡀⠀⠀ ⡼⠋⠁⠀⠀⠀⡃⠆⠀⠠⠀⠀⢸⠀⢠⡁⢀⠀⠀⠠⡈⢇⠀⠀⠀⠉⠑⠪⡑⠄ ⠳⣀⠀⣀⡤⠖⠓⠦⠤⠴⠤⠤⠊⠀⠈⠣⣄⣇⣀⣠⡯⠞⠢⣄⡀⠀⠀⢀⣱⠜ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢤⣤⣤⣤⣤⠤⠤⠤⣀⣀⠀⠀⡠⣿⠕⡝⠁⠀⠀⠀⣀⡤⢤⡶⠖⡻⠟⠋⠁ ⠀⠀⠈⠑⠢⡀⠈⠉⠒⠤⣀⣭⣿⣿⠉⠉⣷⣷⣶⡯⡉⡠⠚⠁⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡀⠣⢄⡰⢣⠿⣫⡥⠀⠀⢀⣈⠻⡆⠘⡄⢠⠁⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣩⡦⠤⠃⠤⣎⣀⣱⡀⢀⣎⣀⣱⣈⡠⠭⠵⣮⣀⣀⠠⠤⠀⠀ ⠀⠀⠀⠀⢈⠝⠓⢤⡄⣀⡀⠈⠙⣍⣇⣀⡏⡩⢊⡡⢤⣒⡪⢭⣽⣦⡄⠂⠀⠀ ⠀⠀⠀⠀⡿⡶⡝⡰⠛⡶⠾⢉⡶⡾⠓⡟⠙⢟⠃⠩⠤⠲⠉⠱⢰⠱⢷⠀⠀⠀ ⠀⠀⠀⠀⠑⠓⢺⡳⠤⠼⣒⠀⠀⡇⢀⣃⠀⢇⠂⠤⢤⠔⠒⢺⠚⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⠀⢀⠏⢳⢢⠺⡌⣀⣰⠃⢣⢦⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⠀⠈⠀⠀⢹⠒⢹⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠈⢻⢦⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠒⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⡇⠀⠀⢀⠤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠄⠚⠂⠤⠤⠤⠤⠤⠒⠡⠐⠈⠀⠄⠀⠄

⠀⠀⠀⠀⠀⣤⣄⠶⠬⢦⣠⠄⠀⠀⠀ ⠀⠀⠀⠀⠸⡷⠂⠀⠈⠀⠘⣿⠀⠀⠀ ⠀⠀⡠⢄⠜⣖⣇⣀⣶⡆⢀⡐⡀⠀⠀ ⠀⠈⡄⢡⣧⣌⠻⠃⠹⡝⠁⠀⢸⠀⠀ ⠀⡠⠂⠘⠈⢸⢰⡦⢀⠃⠀⣦⣚⣄⠀ ⢘⠀⠀⠀⣼⣿⠓⠦⠳⠇⠀⠀⠀⠈⡄ ⠘⠤⠤⠾⠳⣡⣴⣦⣠⣼⣦⣀⣀⡰⠃ ⠀⠀⠀⠁⠁⢿⣿⢯⣻⣿⣿⠈⡀⢡⠀ ⠀⠀⠀⠁⡄⠈⣳⠊⠙⣆⠀⠀⠇⠸⠀ ⠀⠀⠀⠡⡘⢄⡀⠀⠀⢀⡠⠊⢠⠃⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⡴⠃⠈⠀⠀⠀⠤⢀⠀⠀⠀⢸⠦⢄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡠⠊⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠁⠢⡉⠢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⡠⠄⠒⠒⠒⠒⠀⠈⠘⡀⠀⠀⠀ ⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡤⠂⠁⠀⠀⠀⠔⢒⣀⡀⠐⠂⠈⢄⠀⠀ ⠀⠀⠀⠀⠀⠉⡛⠿⣿⣿⡇⠀⢠⠊⠣⣀⠔⠓⡀⠀⠀⣼⢶⣶⣦⠖⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⢸⠙⡄⠀⠙⣧⣀⠈⠒⠀⠑⢤⢶⣿⡦⡀⠀⠉⠉⠁⠀⠀⠀⡗⠀ ⠀⠀⠀⠀⠀⢘⠀⣇⠀⠀⣘⣹⣿⣿⠉⢂⠀⠏⠉⠉⡇⢀⡀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⢰⠞⠀⠋⠛⢿⣿⣿⣿⡏⠀⠀⠃⠐⡀⠀⠈⣈⡠⠔⡟⠀⠀⡘⠀⠀ ⡀⣠⣄⣰⡟⡆⡇⠀⠀⠳⣿⣿⣿⠃⠀⠀⡆⠀⠈⠢⢄⡉⠒⠚⠁⢀⠜⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠙⢉⠀⠐⠒⠂⠀⠀⠂⢄⠀⠁⢒⡖⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠐⠂⢄⡀⠤⢆⠀⠀⠀⠀⠔⡠⠐⠒⠈⠁⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠣⠀⠀⠸⠀⠀⠀⠐⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡐⡄⠀⠀⠡⠀⠀⠀⠑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠗⢄⡀⠀⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠭⠨⢕⠓⢃⠀⢀⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⡐⠣⠈⡢⢼⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⠆⢄⡔⠊⠙⡦⢦⠵⠒⠊⠉⠉⠉⠑⠢⢄⣁⠐⠤⡀⠀⠀⢃ ⠀⠀⠀⠀⣄⡞⠀⠀⡸⠎⠂⠀⠀⢸⠀⠀⢀⡀⠀⢤⣤⣀⠰⡀⠉⠢⣼⠀⠀⠀ ⠀⠀⠀⠀⡜⠈⠉⠁⢀⠕⠀⢠⡄⡎⠀⠀⢈⡁⡴⣽⡄⢸⡿⡄⠀⠀⢹⣄⣀⢤ ⠀⠀⠀⢸⡇⠀⠀⢠⠞⠢⣒⡩⠊⠀⠀⠀⠀⠈⢳⠉⢐⡺⠻⡁⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠐⠱⡤⠤⠊⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⣙⡦⠤⠗⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠠⠀⠒⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣀⢴⠁⠀⠀⠀⠐⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⣻⡟⠛ ⠀⠀⠀⡎⡹⠙⠘⢸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠀⢠⢱⠀⠀⣗⡩⠻⠭⣘ ⢀⡠⢼⡭⠄⢔⡄⢆⢣⡀⠀⠀⠀⠀⠠⣎⠀⠀⠘⡀⠀⣨⣼⣄⣠⢟⣂⡤⠤⠀ ⣎⠀⠀⠈⢱⢀⠵⠥⠭⠽⠦⢯⣀⡀⢀⡶⢽⣦⡶⣿⣫⡷⠿⠧⡾⠄⠀⠈⠉⠁ ⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡰⠡⢀⣟⡧⠿⠓⠛⠛⠥⢖⣤⣩⢳⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢔⠡⡤⠄⠀⠀⠀⠀⠀⠀⠀⡠⡀⠈⠻⣿⠀⠘⠄⠀⠀⠀⠀ ⠀⠀⠀⠘⢡⡊⢀⠐⣿⣛⣢⣀⠠⢰⠩⠒⢙⣦⣆⢡⢣⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⡘⠀⢰⣹⠇⠀⡎⠀⢠⢡⣿⡿⢸⢸⠀⠀⢡⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⠇⠀⠘⡟⠀⠐⡄⠀⠸⡘⡿⢀⢸⡎⠀⠀⠘⡀⠀⠀ ⠀⠀⠠⠦⡎⢰⢃⠎⢁⠩⢈⠃⠀⠈⠒⣒⣊⠀⠈⢛⠟⣵⠀⠀⠈⢢⠀ ⠀⠀⠀⠠⢁⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠀⡀⢒⠆⡹⠀⠀⠀⠀⠆ ⠀⢀⣴⣥⣾⡛⠫⡑⠤⢀⡀⠀⠀⠀⠀⢀⡠⠔⠉⠒⠈⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⠋⢙⣻⡆⠈⡆⢀⠔⣟⣫⠝⡹⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢆⠹⣧⣦⣬⣿⢃⠔⠉⣭⣿⠊⡆⡐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠪⢵⣾⣓⡨⠒⠈⠏⠗⠠⠳⡝⢔⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢡⠀⡌⡆⠀⠘⣀⣎⡔⠑⠂⡜⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠂⢠⠋⠕⣲⣆⡤⢀⣀⡀⠈⠀⡐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣐⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⡈⢑⠨⠓⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠌⢄⡬⠂⣉⢾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⢶⣏⣈⣤⠿⠝⠚⣁⣌⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⠖⣸⠏⠄⠀⢰⣺⣿⡍⠉⢻⡿⢦⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⢸⣿⠉⠀⠀⡾⠟⠉⢳⣸⣉⣠⣜⣰⣼⡿⣦⠀⠀⠀ ⠀⠀⠀⡜⣲⢛⣾⠠⡂⢐⠣⣀⣀⣼⠻⠖⠲⠿⡿⠛⢁⣿⠀⠀⠀ ⠀⠀⢰⠇⡀⠈⠘⡆⠀⠄⠀⠰⢢⠀⢀⣀⣀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⡼⠁⡇⠀⠀⠹⡅⠀⠀⠀⢠⢖⣭⣷⣾⣷⡄⢠⠏⠀⠀⠀⠀ ⠀⢠⡇⠀⠁⠈⠀⠀⠘⢧⡀⡀⠽⠥⠚⠁⠄⢀⣠⠿⡄⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠌⠑⠺⠾⠖⠶⣿⠍⠀⠀⢿⡄⠀⠀⠀ ⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠌⢿⡀⠀⠀ ⢰⢆⣟⠔⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠀⠀⠂⠀⠁⠰⠀⠸⣷⡀⠀ ⢸⢏⡇⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢧⠀ ⣸⡀⡇⠀⠀⠈⠀⠀⡇⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⢸⡀

⠀⠀⠀⠀⠀⣠⠤⢤⡀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠒⠦⢄⣠⢖⣒⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣴⣿⣷⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⡄⡀⠀⠀⣾⣷⠄⢀⠀⢸⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⡉⠉⠀⠀⢐⠏⡇⠀⠀⠈⠉⡐⠁⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠄⠀⢀⡠⢼⣰⠀⠀⠀⢠⠤⣇⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⣀⠤⠧⢿⡢⢴⣤⠐⠊⠀⠞⠁⠀⠈⢻⡤⢯⢹⣋⣧⣟⢹⠊⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⢀⡴⠋⣧⡼⠊⠁⠀⢠⠟⠢⡀⠀⠀⠀ ⠀⠀⢹⠉⠉⠩⡉⠉⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⢸⠀⠀⠀⢸⡀⣰⠃⠀⠀⠀ ⣀⣀⣸⠀⠀⠀⠁⢰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣼⣤⣤⣤⣴⣋⣀⣀⣀⣀⣀ ⠀⠀⠀⣇⣀⣀⣀⣸⠀⠀⠀⠀⠀⢀⣀⠤⠒⠒⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀ ⢀⡤⠔⠦⣄⠤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠓⠿⣿⡎⡆⠀⠀⠀⠀ ⡎⣼⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⠀ ⠙⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠃⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣀⣀⡀⠀⣾⣿⠴⠀⠀⠀⠀⠁ ⢧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠀⠀⠀⠀⢀⣬⡢⢀⣀⠀⠀ ⠘⣆⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠟⡷⠉⣦⠏⠀⠀ ⠀⠈⠲⣄⡀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⢀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⠀⠨⠿⠧⠀⠐⢧⠄⠠⣄⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡎⡢⢄⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠄⠀⣀⡀⠀⠸⠩⣍⠉⠒⠈⠉⠈⠁⠋⢪⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢠⠊⠁⠀⠀⠑⣄⢱⠚⠀⠀⠀⠇⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡎⢀⣦⣀⣤⠧⡜⠐⠲⢶⡞⠉⡁⠁⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⣇⡉⠪⠟⠋⠁⠀⢇⠀⠑⣝⣠⠏⠁⠀⠀⠀⡰⡇⠀⠘⣤⡽⣢⠀⠀ ⠀⠰⠈⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⣀⡠⣊⠜⡀⠀⠀⠛⠓⠃⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠛⠉⠉⠉⠐⠊⠁⠀⠅⠀⠀⠀⠀⢸⣿⡇ ⠀⢰⠀⠀⠀⣠⣀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⡀⠀⠎⠀⠘⠑⢠⢰⠀⠀⠀⠠⢃⣀⣠⡴⠊⢰⠀⣠⣤⣄⠀⠀⠀⠀ ⠰⡄⢁⡎⠀⠀⠀⠣⠼⠀⠃⠀⠀⠎⠉⠁⠀⢱⠀⢠⠀⠹⠿⠟⠀⠀⠀⠀ ⠀⠈⠈⠁⠘⠒⠒⠚⠀⠀⠸⡀⠈⡄⢠⠤⠤⠀⠑⠗⠃⠒⠒⠛⠛⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⢀⣠⣴⣶⡖⠲⡂⠀⠀⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡼⠙⢿⣿⠃⠀⠈⡀⠀⢸⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠘⡄⠀⡀⢀⣿⣦⣤⣾⡇⠀⣸⡞⠉⠉⠳⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⢣⠀⠻⣿⠋⡇⢸⠟⠁⠐⢇⠀⠀⠐⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠚⠚⠢⡄⢮⣘⣠⠧⠄⠂⠀⠘⡄⠀⠀⠀⠸⡀⠀⠀⠀ ⠐⠒⠒⠺⣀⠀⠀⢀⡸⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠓⠒⠒⠂ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⣀⡀⣠⠔⠒⠲⢤⡀⠀ ⢀⠖⠉⠉⠑⣄⠴⠚⠉⠀⠀⠀⠀⡠⠊⠒⠠⡤⠉⣓⣦⣀⠀⠀⠹⡄ ⠏⠀⠀⠀⠀⢹⡀⠀⠀⠀⣀⠔⠈⠢⠀⠀⢀⢁⣀⣀⣀⣈⣳⣀⣴⣷ ⠀⠀⠀⠀⠀⠀⣇⣠⣔⣬⣤⣶⠒⠒⢃⠀⠈⡅⠈⣿⣿⣧⣀⣻⠿⡿ ⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣿⣷⣶⡏⠀⠀⠘⢄⠈⢻⣿⣿⣿⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⢄⠀⠙⠿⠿⠿⡻⠁⠀⢂⣀⠔⠉⠀⠀⠠⠍⠺⡁ ⡄⠀⠀⠀⠀⠀⡧⠄⠁⠒⠠⠐⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⠀⢡ ⢣⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢣⠀⠀⠀⠀⠀⠁⠀⡜ ⠈⣆⠀⠀⠀⠀⡇⠈⠙⠒⣲⣤⢤⠤⢤⠤⠖⠒⠓⠤⡀⣀⠀⡤⠊⠀ ⠀⠸⡄⠀⠀⠀⡇⠀⠀⣸⠁⢀⡛⠂⠈⢏⢳⠀⠀⠀⡇⠀⠀⡇⠀⠀ ⠀⠀⢁⠀⠀⢸⠀⠀⠀⡇⠀⢢⠃⠸⣉⠇⣹⠀⠀⠀⢃⠀⠀⡇⠀⠀ ⡀⢀⡜⠀⢠⠇⠀⠀⠀⡇⠀⢺⠄⠀⠀⡞⡇⠀⠀⠀⠸⡀⠀⣇⠀⠀ ⠛⠂⠤⠐⠁⠀⠀⠀⠀⡇⠀⠈⡆⠀⢀⠇⡇⠀⠀⠀⠀⠙⠦⠈⠱⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢱⠀⠆⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣞⠉⢡⠐⠒⠈⠀⠒⠒⢎⠐⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠥⠃⠀⣟⠊⠀⠸⠀⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⡄⡆⠀⠀ ⠀⢰⠸⠀⠀⠀⠀⠠⠤⠤⢄⠀⠀⠀⠀⠀⢀⠃⠧⡀⠀ ⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠄⡀⢨⠁⠀⠀⠈⡄ ⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⢀⠇ ⠸⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡎⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠒⠂⠉⠀⠃⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⢸⢸⠀⠀⠀⠀⠀⢲⠤⠤⡔⠒⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⣰⢠⠀⡀⠀⠀⠀⡦⠀⠀⢇⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠈⠉⠉⠈⠈⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣨⡽⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠒⠦⣤⡀ ⠀⠀⠀⠀⠀⣠⣤⣼⣿⡆⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣠⡇ ⠀⠀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⢠⣿⡈⡠⠀⣳⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣠⣅⠀⠿⡟⠡⣴⣶⣂⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⣩⣿⠿⣷⣦⣀⡈⢭⣉⠈⠿⣈⡁⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢶⠒⠲⠤⢤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢷⣦⣆⣘⣋⠂⠀⠀⢀⣠⣾⣿⠏⠀⠀⠀ ⣴⣾⣆⠀⠀⠀⢸⡄⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢸⡟⠷⠦⢿⣿⡟⠛⠁⠀⠀⠀⠀ ⢿⡈⣟⡀⢀⣀⠬⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣶⡀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠘⠳⢌⣷⠋⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢨⡿⠃⠀⠹⢿⡀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠛⣿⠉⠁⠀⠀⠀⣀⣽⣦⡄⠀⠀ ⠀⣰⠇⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠻⠟⠾⠆⠘⠛⠉⠀⠀⠀⢸⣏⣀⣈⢦⢸⣯⢀⣴⠏⠀⠀ ⢺⣅⣀⣠⣟⠋⠙⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠙⠷⠬⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠒⠚⠋⠓⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣸⠞⠁⠐⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡾⠃⠀⡀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀⡀⠀⠀⢸⣁⡉⠙⠶⣄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠉⠲⣄⠈⠙⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠤⠄⠒⠒⠉⠉⡇⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡤⠶⠊⠉⠉⠉⠉⠉⠑⠒⠀⠘⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡴⢿⡀⠀⠀⢀⣶⢀⠀⠀⠀⠀⠀⠀⣏⢉⣉⣥⣤⣄⣀⡀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠻⠿⣿⣿⣿⡇⠀⠀⠀⣞⠀⠈⠳⣤⠔⠋⠉⠀⣀⠀⠀⠀⠀⢴⠾⢻⣿⣿⣿⡦⠋⠀⠀⠠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣷⡀⠀⠈⠙⢿⣇⠀⠀⠀⠙⠦⣄⣀⠙⢦⣀⣠⣶⣿⣦⡀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⣦⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⡇⠀⠀⠀⠈⠻⣷⣦⣄⣀⣀⣀⣀⠀⠀⠙⢯⣻⣿⣿⣍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⠀⠀⠀⠀⢂⣁⣿⣿⣿⣿⠀⠈⢳⡀⠀⢸⠈⠉⠉⠁⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇⢸⡿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⡄⠀⣇⠀⠀⠀⠘⠧⠴⠛⠃⠀⣀⣴⡆⠀⠀⠀⠀⡜⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⡇⢸⠀⡇⠈⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢳⠀⠘⣄⠀⠀⠀⠀⣀⣤⠶⠟⢉⣼⠀⠀⠀⠀⡼⠁⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⣴⡿⢧⠀⡇⢸⠀⡇⠀⢧⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡞⠀⠀⠈⠳⢄⡀⠀⠉⠳⠦⠶⠟⠃⠀⠀⢀⡜⠀⠀⠀⠀⠀ ⣦⣤⣾⣿⣦⣾⣿⣧⣸⠀⠃⠘⠀⠀⠀⠀⠉⠻⢿⣿⣿⣟⠀⠀⠀⠀⠰⠁⠀⠀⢀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⢄⡀⠀⠀⠈⠉⠒⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢙⣂⣀⠤⠖⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠉⠑⢢⡤⠔⠒⠛⠀⠂⠀⠀⠀⠀⠀⠀⡜⢀⠔⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠴⣋⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢰⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡰⢣⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠣⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⠁⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠙⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡞⠌⠲⢄⡀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠖⠛⠉⠉⠙⠳⣴⣿⣳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⣶⠛⠁⠀⠀⠈⠉⠀⠈⠳⣽⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⣁⣤⡀⠀⠀⣠⣀⡀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⣠⠖⠒⠦⡞⠀⢿⣾⣧⠤⣼⣷⣿⠀⢀⣀⣀⠳⡄⠀⠀⠀ ⠀⠀⢻⠀⡏⢳⢹⡄⣘⠸⣿⡿⠀⢹⣩⠟⠁⠀⠸⡄⢿⡄⠀⠀ ⠀⠀⠈⡆⢱⣸⠟⣿⢻⠆⠀⠀⠠⠀⡟⠀⠀⠀⢸⠀⡿⠁⠀⠀ ⢀⡤⠞⠃⠀⠀⠀⢹⠘⡇⢿⣿⠄⢠⡇⠀⠀⠀⣾⣼⣙⣦⡀⠀ ⡏⠀⠀⠀⠀⠀⢀⣾⣶⣿⡶⣤⣖⣷⣷⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⡇⠀⠀⠀⠀⢀⣼⠿⡿⠃⠀⠈⠁⠈⠙⣆⠀⠀⠀⠀⠀⠀⢸⡇ ⠻⠤⠄⠠⠴⣿⢋⡞⢀⣴⣾⣷⡄⣠⣤⣾⣦⣄⡀⠀⠀⣠⠟⠁ ⠀⠀⠀⠀⢠⠃⡸⠀⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⠏⡏⠉⢳⡀⠀ ⠀⠀⠀⠀⣸⠀⡇⠀⢻⣿⡟⠛⣦⡼⠿⠿⡿⠛⠀⢸⡀⠈⡇⠀ ⠀⠀⠀⠀⢻⠀⢇⠀⠈⠻⣷⠞⠁⠹⣦⠀⠀⠀⠀⢰⠁⠀⡇⠀ ⠀⠀⠀⠀⠘⡄⠘⣆⠀⠘⠋⠀⠀⠀⠘⠇⠀⠀⣠⠏⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠹⣄⣈⡢⣄⡀⠀⠀⠀⠀⣀⡤⢞⡁⢀⣰⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠤⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣒⣩⠔⢓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠴⠒⣉⠼⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⢦⠀⠉⠄⢂⡡⠞⢦⣠⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠱⡀⠳⡄⣞⠉⠀⣀⠴⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡏⠆⠙⠀⠘⣿⣛⣭⡴⠞⠉⢀⠈⠙⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣿⠙⠛⣿⣶⣶⠟⠟⠉⠁⠀⢀⣠⣷⣿⢶⣤⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⡟⠃⣸⣿⠀⡄⠀⠀⠀⢲⢚⣿⣿⣨⠞⠉⠉⢿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⢁⣾⣿⡷⠶⠈⠀⠀⢀⣽⣿⡿⠿⣯⡁⠀⣴⠿⠟⠀⢈⣿⠛⠉⣭⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡅⢸⣿⣿⡦⡀⠀⠀⠀⣿⠏⠋⠁⠀⠈⢻⣜⣷⠤⣤⡴⣿⣩⣼⣿⣿⣿⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠧⢲⣼⡿⣼⡇⡁⢄⠀⠠⢿⡄⠀⠀⠀⢀⣼⡿⣥⠤⠤⣤⣿⣿⣿⣿⠿⠟⢈⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠴⠸⢛⡆⢻⡇⠄⠰⠀⠀⠀⠉⠓⠶⠒⠛⠙⠡⠈⠁⠀⠉⠛⠻⠉⠁⠀⠀⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡁⠤⠀⠂⠀⠘⣿⠀⠀⠰⡀⠐⠀⠈⣓⢢⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠄⢸⠂⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠛⣿⣉⣿⣧⡀⠀⠀⢘⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠿⠀⣾⠀⠀⡀⠀⠀⠹⣆⠘⠀⠀⠀⠀⠀⢴⣟⣩⣷⣾⣿⣿⡿⢿⡿⡄⢀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⢠⠐⠀⠀⠃⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣿⡋⣁⡴⠟⠉⢀⠀⠀⠁⢁⣼⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠷⠀⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠉⠳⣦⣐⠀⠀⡍⢡⠀⠀⢠⢬⣌⣢⡶⠿⠙⠉⣷⡀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠾⠷⠾⠿⣿⣿⠁⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀ ⠀⢸⡿⡅⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠄⠙⠉⠀⢀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀ ⠀⣾⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣧⠀⠀⠀ ⠀⣷⠀⣾⣅⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠃⠀⠠⠀⠀⠸⣿⣧⠀⠀ ⢰⣧⣶⣿⠄⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⢿⡿⡆⠀ ⢸⣿⢀⡏⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢸⡇⣻⡀ ⣸⠃⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⠈⣇ ⣿⠣⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⡆⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠚⠉⠁⠀⠀⠀⠘⠿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⠶⠶⠀⠀⠀⠀⠀⠀⣀⡀⠛⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⣿⠁⣠⠴⠚⠉⠉⠙⢶⣤⠞⠉⠉⠉⠉⠳⣄⠀⢹⡏⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⡼⠃⠀⠀⢀⣀⣀⠀⠀⠀⣠⣤⣄⡀⠀⠈⢳⡈⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⢀⠀⢸⠃⠀⠀⣰⣿⣧⣿⣦⠀⢠⣿⣼⣿⣿⣆⠀⠀⣷⠀⠐⡄⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⢸⣠⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⢸⢶⣄⠀⠄⠀⠀⠄⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠋⣏⠹⡆⠀⠀⠻⣿⣿⣿⡿⠃⠘⠿⣿⣿⡿⠃⠀⠀⡾⠀⣼⠃⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⡄⠙⢦⣀⠀⠈⣉⣭⠴⠶⠶⠶⠦⣄⣀⠀⣠⠞⠁⣼⡇⠀⠀⢀⣤⠞⠉⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣸⡷⣤⡀⠈⠹⠋⢁⣤⡶⠚⠛⣛⣶⣦⠉⠙⠓⠀⡼⠋⣧⠀⣠⠟⠁⠀⠀⡞⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢰⢿⡄⠸⡆⠀⠀⠀⠈⠻⢿⣷⣿⣿⠟⠁⠀⠀⠀⣰⠇⢠⣿⣀⡏⠀⠀⠀⣰⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠦⢷⣄⠙⢦⣀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢀⣠⠶⢋⣠⡟⠀⠻⠇⠀⠀⣰⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠷⣤⣈⠉⠓⠲⠖⠚⠛⠓⠒⠚⣫⡥⠖⠋⠉⣷⠀⠀⠀⠀⣰⠋⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡀⠀⠉⠙⠳⣦⣄⠀⠀⠀⣠⡾⠋⠀⠀⠀⣰⡏⠀⠀⣠⠞⠁⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡿⢿⣄⠀⠀⠈⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠾⠟⢿⡷⢿⡁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡞⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠙⢦⡀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠓⠾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡠⢼⣶⡄⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠄⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⣷⡄⢿⠇⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⣾⡇⠉⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡜⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠖⠋⠀⣠⣤⣤⠟⡁⠃⠀⠀⠀⠀⠀⠘⣇⠀⢀⣀⣼⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣫⡅⠀⠀⠠⠚⠉⣼⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠉⠁⡏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠀⠀⠠⣌⣉⡓⠦⣤⡀⠀⠀ ⣼⠟⠉⠀⠀⠀⠀⠀⠀⢰⡇⢰⠃⠀⠀⢠⠆⠀⠀⠀⠀⣿⠀⠀⢸⡁⠀⢀⡀⠀⠀⠀⠰⣤⡈⢻⡀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦⡉⢳⡄ ⢿⡀⠀⠀⠀⠀⠀⠀⣀⣸⠷⣼⡀⠀⠀⠸⡄⠀⠀⢀⣼⠃⠀⠀⠘⣧⡀⠀⢻⡄⠀⠀⠀⣸⡇⣸⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢀⡗ ⠈⠻⢦⣤⣤⣤⡶⠟⠋⠀⠀⠈⠙⠓⠒⠒⠛⠓⠒⠋⠁⠀⠀⠀⠀⠈⠙⠦⣼⣧⣤⣤⡾⠿⠟⠁⠀⠙⠳⠦⣤⣤⣀⣀⣀⣠⣴⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢛⣩⡽⠿⠛⠛⠷⣄⠀⠀ ⠀⡷⢶⣶⡶⠶⠤⠤⢤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣤⠾⠋⠁⠀⠀⠀⠀⠀⠘⣷⠀ ⠀⠃⠀⠈⠻⢦⣄⠀⠀⠀⠀⠉⠉⠛⠲⠦⣤⣀⠀⠉⠙⠻⢶⣦⣍⣻⣿⣦⡀⠀⢀⣴⠏⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣤⣀⣀⣈⣻⣿⣿⠎⠻⣤⠟⠁⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣠⡴⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⢀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠻⠂⠀⠀⠀⠀⠀⠈⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣶⡄⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠑⠀⢰⡄⣶⠀⠀⠀⢀⣤⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⢿⣤⣀⣀⣀⣀⣤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢦⣄⡈⣷⣿⡀⣠⠶⠋⠻⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⠤⠽⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⣤⣄⣀⣀⣴⣟⠛⠻⢦⣹⢿⣿⣿⣿⣿⣄⠀⢀⣰⠇⠀⣀⣀⣀⣤⣤⠤⠴⠶⠶⢶⠟⠒⠒⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⡿⢿⡿⠛⢀⣬⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣴⣤⣴⣏⣀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠉⠉⠉⠉⠉⠙⢿⣿⣿⣷⣬⣷⡈⣧⣄⣀⠹⣧⠀⠀⡟⢹⣦⣄⣴⡟⠁⢀⣀⣀⠙⢦⡀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠉⠉⠛⣿⠿⣯⣿⣿⣗⣨⣷⣶⣟⣿⡿⠿⠾⠿⠿⠭⣍⣉⡙⠛⠻⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢠⡏⢀⡴⠋⠁⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣸⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣠⣾⣷⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡧⠤⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠒⠒⠒⠒⠒⠒⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠹⣷⡀⠀⠀⠀⢀⣾⠋⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠈⠛⠦⠤⠶⠟⠁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⢰⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⠘⣧⡄⠀⠀⢿⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⢷⣿⣇⢸⣧⣈⣣⣀⣀⣠⡾⢋⡿⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠈⠙⣿⢿⢻⠻⣿⡋⠁⠠⠞⠁⠀⠀⠀⢀⣾⠋⠉⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣑⣠⣞⣉⣉⣉⣉⡹⠙⢦⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⢠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠈⠉⠉⠀⣠⡶⠶⣦ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣫⣶⣾⣷⣮⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣾⠿⢿⣾⡆⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣝⠧⠾⠷⢟⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡏⢸⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠈⣿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⣿⣷⣴⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣷⡀⠀⠀ ⠀⠀⠀⠀⢸⡆⢹⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⡤⠶⠶⠶⢶⣶⣤⠀⠀⠾⠛⠉⠀⠀⠈⣿⡀⠀ ⠀⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⣷⠘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡇⢀⣀⣀⣠⣴⠟⣿⠁ ⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⠀⠤⠶⠦⠤⠤⠤⠴⠾⠋⠀⠀⡇⠉⡉⠉⠀⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⢸⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠇⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⣶⠤⣀⣀⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢦⣀⣈⣉⣉⣿⡿⠏⠁⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⣍⣛⣶⣤⣷⣤⠄⠀⢀⡶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡛⠒⠒⠶⠤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⣼⣿⣿⠟⠿⢿⣿⣿⣿⠓⠲⡶⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⣸⣿⣿⣿⠀⠀⠈⢯⣯⠙⢷⡄⣓⣻⡼⣷⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠏⢀⣼⣿⣿⣿⣿⠀⠀⠀⠘⣏⣆⠀⢧⣿⣿⡇⠘⢷⣄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⡼⡜⡆⠀⠉⠉⠀⠀⢀⣹⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⠗⠛⠛⠒⠒⠋⠉⠉⠉⠀⠀⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⣄⡙⢿⣿⣿⣿⣿⡇⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢶⡉⢿⣿⣿⡟⠑⠒⠺⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⣧⠿⠿⠿⠷⠀⠀⠠⡿⠿⠿⠿⡿⠦⠤⠄⠀⠀⠀⠀⣘⡧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣉⣓⣛⠻⠾⠷⠻⡇⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠟⢁⡀⠀⠹⡆⠀⠀⠱⢄⡠⠴⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⢤⣔⠛⠳⠄⠀⠙⠠⠤⡗⠀⠀⠀⠀⠀⠀⠐⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⠴⠶⢤⡀⠀⡀⠀⢀⣀⣠⠤⠴⠿⠧⠤⠤⠤⢤⣀⡀⠀⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⢤⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⢶⣾⡁⠀⠀⠀⢻⠉⢻⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣇⣀⠈⠓⢦⡀⠀⠀⠀⠀⢄ ⠀⠀⠀⠀⠀⠀⠀⡄⣠⠟⠁⠀⠀⠀⣼⡇⠹⡀⠀⠀⠸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⣾⡆⠀⠉⠓⢦⣀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠟⠦⣄⡠⠴⠚⠁⡆⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢰⣶⠄⠀⣨⣾⡟⠋⢻⣶⣤⡵⠀⠀⠀⠀⠹⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢰⡷⠁⠀⠀⣼⡦⢰⡏⠀⠀⠀⠀⢀⣀⠀⣰⠫⣾⣷⠀⠸⣿⡿⢷⡀⠀⠀⠀⠀⢹⣆⢀⣠⠤⢶ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢤⢀⡿⣄⣀⣠⠾⠛⣱⠏⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣛⣁⣠⣶⡿⢷⠛⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⣏⠀⠀⣹⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠠⠤⠶⠂⠈⢧⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⢻⣤⣀⣀⠴⠋⢻⡀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣸⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠷⠞⠛⠋⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠠⠴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠛⣿⠿⠛⠿ ⠀⠀⠀⠀⠀⢀⡤⢤⣤⣴⠒⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡏⣀⡴⣿⡿⣄⡀⡴ ⠠⠀⠀⠠⢀⡟⠀⣰⠃⠈⠀⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⡞⢸⠀⠀⠀⢰⡟⣡⠞⠉⠳⠦⣤⣉ ⠀⠀⠀⠀⢸⡓⠋⠁⠀⠠⡀⠀⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣇⠀⠀⠀⢰⠇⣸⡇⠀⠀⣸⡿⣅⣀⠀⠀⠀⠀⠀ ⢀⡶⠚⠛⠛⠯⣍⠀⠈⠓⢧⢀⣽⢦⣹⣆⠀⠀⠀⣠⠄⠀⠀⠀⠘⠳⢤⣀⠀⠀⠀⢸⣄⠀⣀⣼⣿⣿⣿⡒⠚⣿⠓⠶⠤⣭⣍⣉⡀⠀ ⣾⡁⠀⠀⠀⠀⠀⢳⠀⢀⣼⣯⣥⣬⣤⣬⣿⣶⣾⣀⡀⠀⠀⠀⢀⡾⢿⣽⣷⣦⣶⣾⣿⠛⣭⣿⣷⣾⣿⣧⣾⣿⡀⠀⠀⠀⠀⠀⠈⠁ ⠉⠻⠦⣤⣀⣀⣤⠾⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⠾⠷⠶⠾⠿⠿⠁⠈⠙⢷⣿⠏⠈⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⠤⠤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣴⠶⠚⠛⠶⢦⣄⠀⠀⠀⠀ ⠀⠀⣀⣤⠶⠶⠶⣦⡀⠀⠀⣀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⢠⠤⣀⡀⠈⠉⠙⠛⠾⣯⣀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⢀⡼⠋⠀⠀⠀⠀⠈⢿⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠉⠉⢒⠆⠤⠤⢈⣙⣷⣦⡀⠀⠀⠀⠈⢿⡄⠀ ⡾⠁⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠙⢆⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣼⣧⡀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠈⢣⠀⠀⠀⠠⣧⠴⠒⣶⣶⣶⣶⡶⠒⠺⢿⣴⣿⡾⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣠⣴⣖⣭⣤⣴⣶⣶⠂⠀⠀⠺⡇⠀⠀⠀⢣⠀⠀⢸⣿⣿⣿⣿⣄⠀⠈⣿⠿⠖⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⣿⣿⣿⣿⣿⣿⣦⣀⢀⣰⡏⠀⠀⠀⠈⢆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠣⣀⠀⣈⣿⡿⢿⣿⣿⣿⡇⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠲⡀⠀⡄⢀⠜⠋⠁⠀⠀⠀⠀⠈⠙⢦⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⢄⡀⠀⠀⠉⠉⠉⢉⡥⠋⠀⠀⠀⠀⢱⣴⡿⠁⠀⠀⠀⠀⠀⠀⢠⠉⡆⠀⠙⡄⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣄⣀⣉⣑⣒⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⢹⠀ ⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠛⠳⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠷⢄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡞⠛⠿⣍⡿⠉⠉⢹⣯⣅⡀⠀⠀⠀⠀⠈⣿⠒⠒⠒⠊⢹⡏⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡏⠀⠀⡀⢸⠙⠂⠤⠼⢷⡈⣷⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠁⠀⢀⡇⡞⠀⢠⡤⣤⢤⠳⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⠀⠀⠈⢧⣤⠟⢀⣼⠇⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠠⣿⠀⠀⠀⠀⠀⣰⠟⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⣦⣠⠤⠞⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡋⠑⠒⠒⠒⣿⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⣧⡀⠀⡀⠀ ⠙⠓⠲⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣇⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣩⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡀⠀⠀⠘⢧⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣧⠀⠛⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠑⠢⢤⣀⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠛⠳⣦⣤⣶⠾⠛⠛⠛⠛⠳⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠿⣿⣄⣠⠶⢶⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⠾⢿⣶⣤⣶⣄⠈⢻⣧⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣄⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢶⣄⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠻⣧ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⢻⣅⣨⡇⠀⢈⡉⠢⡀⠀⠀⠀⠀⠈⣿⡄⢹ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠖⠂⢢⠀⠘⣿⠀⠀⢹⡆⠀⠉⡹⠁⠀⠈⣿⠓⠁⣴⠶⣦⠀⠀⢹⣇⣼ ⣠⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⠏⠀⠀⢸⠀⠀⣿⠀⠀⣾⠃⠀⢰⠃⠀⠀⣰⠏⠀⢰⢿⣤⣾⠇⠀⢸⡿⠋ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠇⢰⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⡀⠠⠾⣿⠀⢀⡞⠀⠀⠀⠀⠀⢸⡇⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⣰⣇⠀⠸⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠳⣄⣀⣉⡴⠋⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⣧⡀⡄⠀⠀⠀⠀⠀⢀⣤⣶⠶⠦⠀⢠⣤⠿⠁⠸⡆⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀ ⠈⠻⣷⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⢸⣆⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢦⣤⠾⠁⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣀⣀⣀⣀⡤⠖⠃⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠛⠻⠿⣦⣴⣿⠋⠉⠉⠙⠻⣧⣤⣤⣴⣶⡶⠿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠙⢿⣧⣤⣀⣠⣴⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡿⠀⠀⣀⣤⣤⡴⠶⠾⢿⡟⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⣿⡀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢰⣟⠁⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠈⢿⣶⣦⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣄⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢿⣥⠀⠀⠉⣿⣿⣿⡀⠀⠀⠸⣇⣀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠉⠀⠀⠈⠿⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠡⡌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⠒⠒⠒⠢⠤⠴⠒⠒⠊⠉⠛⠀⠿⠢⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠴⠊⠉⢀⣀⠠⠤⢄⣀⠀⠀⢳⠉⠻⢲⠆⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⣠⠞⠁⠀⠀⠀⠀⠈⠷⣄⠀⢳⡴⠓⠂⠉⠂⠀⠐⣏⠀⠈⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢀⠎⠀⠀⠀⠀⠀⠈⣻⠆⢈⡇⠀⠀⠐⠁⢀⡀⣠⣤⠦⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⢠⡏⠀⢀⣴⣄⡀⠠⣤⣿⣄⣼⠀⠉⠉⠿⢿⡿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠃⣄⠸⢿⣿⣿⠟⠋⠀⠀⡇⠀⠀⠲⣤⢾⡟⠒⣶⠴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⡋⠉⢳⡀⠀⠀⠀⠀ ⠀⠀⣹⢄⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⢄⣀⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⠀⠀⠀⢸⡗⣿⡟⣉⣷⠀⠀⠀ ⠀⣼⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢁⡽⢩⠀⠀⠀⠘⠿⢿⣦⡿⠁⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠦⣄⣀⣀⣀⣀⣀⡤⠴⢛⢱⡶⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠒⠯⠭⠥⠤⠤⠤⠖⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉ ⠀⡇⠀⠀⠀⠀⠀⢳⣤⣀⠀⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⢀⡴⠁⠀⠘⡗⢄⡀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⣤⠞⠀⢠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⡼⠀⡄⠀⠀⡞⠀⠀⠀⠀⡇⠀⠈⡷⠺⡇⠀⠀⠀⠀⠀⡞⣡⣤⣤⠴⡾⣿⠁⠀⠀⡞⠀⢠⣾⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣄⣀⣧⠀⢹⡀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠹⡄⠀⠀⡇⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠙⢆⣘⣾⡦⠀⣀⢀⡀⠀⠀⡈⠉⠁⠀⠀⣇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠷⡀⢠⣙⣦⠀⠀⠀⢹⣧⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠃⠀⠀⠀⠀⢹⡈⠀⠀⢳⡀⢠⣤⣤⣤⡤⠄⠀⠈⠻⣟⠉⡀⠛⠉⠈⠛⠛⠉⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠿⠿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⢀⣤⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣄⣀⠀⢀⣠⣴⠶⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣿⣿⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢋⣩⣤⣬⡙⢷⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⣽⠆⠀⠀⠀⠀⠀⠀ ⣾⠁⣿⣿⣿⣿⣿⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣆⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀ ⠀⢹⡷⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⢀⠎⠀⠀⠀⠀⠀⠀⠂ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⠀⠀⢠⣀⣤⣠⡄⠀⠀⠸⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠸⡧⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⢿⣌⠑⠒⣶⠂⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢻⣿⡆⠙⣷⣴⠏⠀⠀⠀ ⠀⠀⠻⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡏⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠶⣤⣀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠟⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⢹⡦⠒⠚⠋⠉⠉⠉⠉⠓⠒⠾⣅⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⢀⡀⠀⠀⣠⡴⣀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢭⡉⠁⠀⢀⡛⠛⠉⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣷⣦⠀⢀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠘⡆⢸⡀⠀⠀⠀ ⠀⠀⠀⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⡁⠀⠀⠀ ⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠲⡄⠀⠀⠐⠈⠁⠀⢀⡠⠏⠀⠈⠙⢢⡀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠢⢤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⡜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠟⠀⠀⠀⠀⠀⠀⢘⡇ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⡸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⢀⡠⢶⡉⠀⠀⠀⠀⠀⣀⡤⠚⣇⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⢸⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⢠⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀ ⠀⠀⠈⠓⠾⠥⠤⠧⠤⠤⠤⠄⠔⠚⠁⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⢤⣦⠤⠴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠙⠳⡄⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡿⠃⠀⠈⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠤⢤⡿⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠛⠙⠳⢾⡁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠳⡄⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⣾⡤⢀⠀⢠⣤⡀⠀⠉⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢹⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠯⠉⠱⠟⠶⠌⠹⠭⠇⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠖⠒⠛⠓⠀⠀⠈⠉⠉⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣄⡼⣆⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀ ⣰⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⣰⠆⢀⡼⢦⠀⢀⡘⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀ ⢻⡄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢸⡆⢠⡄⠀⣤⠀⢠⠀⣠⡄⠀⠀⠀⠃⠘⡇ ⠀⠙⠒⠲⣄⣀⣀⣀⣹⣄⣀⣀⣀⣀⣹⣀⣀⣠⣴⣋⡼⠁⠀⠀⠀⢸⣅⣸⣇⣀⣿⣀⣸⢾⣍⣀⣀⣠⣄⣠⠾⠃ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠀⠀⠐⠒⠂⠐⠒⠂⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠀⣸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣠⠞⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢶⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣴⠋⠁⠸⣿⠀⢀⣀⣀⣀⣀⣀⣀⣸⣦⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢧⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⠙⠀⠀⣠⡿⠛⠻⣅⠀⠀⠀⠀⠘⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⠞⠁⢀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠞⣏⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣰⠇⢀⣾⡏⠉⣇⠀⡧⣀⣶⣤⣀⡀⠀⠀⠀⣠⠴⠛⢿⣆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⠛⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⡇⠀⣿⣿⣷⣶⡟⢸⣿⣿⣿⣿⣿⣿⣦⡀⡼⠃⣀⣀⠀⠻⡄⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣇⠀⠻⣿⣿⣿⠇⣽⣿⣿⣿⣿⣿⣿⣿⡿⢠⣾⡏⠉⢳⠀⡇⠀⣰⣿⣿⠄⠀⠀⠀⠀⠈⡟⠇ ⠀⠀⠀⣤⡴⠛⠛⠛⠲⣤⣿⢾⣦⣀⣀⣀⣀⣀⣈⣹⣿⣿⣿⣿⣿⠟⢡⣿⣿⣿⣾⡿⠀⣧⠞⢩⣿⢧⠀⠀⠀⣄⢀⣾⠅⠀ ⠀⢠⡞⠃⠀⠒⠄⠀⠀⠈⣿⡀⢳⣴⣤⣼⣄⠉⣽⣏⣩⡟⠻⣯⣄⢰⡀⠛⢿⣿⣿⡧⠴⠿⢦⣼⠅⢼⣧⣤⣴⢋⡞⠁⠀⠀ ⠀⢺⣶⣽⠶⠶⢶⣄⠀⠀⠹⡷⣄⠙⢏⣳⠿⡍⠉⢻⣿⡿⢾⢯⠈⢙⡿⣤⣀⡴⠁⠀⠀⠀⠁⠀⠀⢿⣾⣿⣷⣋⣰⠄⠀⠀ ⠀⣼⣿⡿⣶⠄⢀⣠⣷⣶⡼⠃⢀⣷⢄⣑⠤⣽⡶⣌⣠⣀⣀⣬⣛⣻⣧⣼⠟⠀⠀⠀⠀⠀⠀⣀⠀⠾⢿⡯⣿⠛⠋⠀⠀⠀ ⢰⣿⣿⠓⠒⠀⠈⣼⠿⠛⠛⠲⠋⠀⢀⢹⡷⠈⠉⠙⠛⠟⠋⠠⣽⣵⠿⠋⠀⠀⠀⠀⠀⠀⠀⣹⡟⢹⣬⣿⣤⡀⠀⠀⠀⠀ ⠀⢹⠧⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣠⣼⡏⠀⡀⠀⠀⠀⠀⠁⣹⠋⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠛⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀ ⠀⢸⠀⠀⢀⠎⠙⠷⣴⣤⣤⣴⠿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⣦⡴⠋⠀⠀⠀⠀⠉⠉⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠻⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠘⠿⣽⠈⠸⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⡀⠀⠀⣥⣿⡞⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠓⢦⣤⣤⣤⣤⣴⠿⠛⠋⠙⢿⡀⢿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⠀⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣧⣄⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠠⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠙⠲⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⠉⠒⠢⢄⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠳⠶⠤⠤⣀⡀⢸⠀⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⢀⠞⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣰⠇⠀⠀⠀⠀ ⠀⢀⠎⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⣴⠿⣿⣷⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠠⣶⣿⡟⠛⢳⡴⢧⡀⣿⣿⡇⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠘⢿⣿⣦⣸⡇⠀⠻⠿⠿⠡⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣄⡈⠻⢿⡿⠃⣸⡿⠆⢀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⠀⣠⣤⣴⣾⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠋⠉⠈⠙⣧⠴⠚⠙⣿⣿⣿⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⣷⣦⡄⠈⠀⠀⠀⢠⣿⣿⣿⣿⣟⠿⡟⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣼⣳⣿⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣻⣿⣇⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⣠⣶⡄⣿⣿⣿⣿⣿⡀⠈⣿⡇⢀⣴⣶⣀⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣶⣿⣮⣱⣿⣿⣿⣿⣿⣿⣦⣿⣇⠘⠁⣹⣇⣽⢛⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠾⠿⠿⠿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣀⡀⢀⠀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠞⠛⠿⠛⠛⠛⠟⠻⠛⠐⠛⠛⠛⠃⠀⠐⠈⠳⠟⠛⠛⠛⠛⠒⠉⠛⠛⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⢠⣟⣧⣤⣴⣶⣶⣿⣿⣿⠭⢍⣉⠙⠒⠲⢤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠼⠈⠳⠤⢾⣽⣿⣛⠛⠉⠉⠉⠉⠉⠛⠒⠦⣽⡷⣦⡼⠋⡏⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⡇⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⠔⢊⠝⠋⠁⠀⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣣⡤⠄⠀⠈⢿⢷⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⠁⡔⣁⠀⠀⢀⣱⣿⡟⠉⠳⣄⣀⣀⡤⠖⣋⣡⠖⠋⠉⢻⣶⣾⠄⠸⡆⢣⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡥⠒⠋⠁⡼⠉⠉⢉⡟⣿⡏⠁⠀⢠⠏⠀⠀⠀⡼⢹⣿⣿⢯⣤⣇⢸⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⡼⠀⠀⠀⡎⣸⣿⠃⠀⢀⡏⠀⠀⠀⣸⠁⣿⣿⣿⡞⠀⡿⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢇⢿⠏⠀⠀⢸⡀⠀⠀⠀⢹⠀⣿⣿⠏⡇⢠⡇⡾⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠖⠛⣄⡀⢀⡨⢫⣤⠀⠀⠀⢣⡀⠀⠀⠈⠳⣼⠏⠀⢣⣸⣷⣇⣀⠀⠀⠀⠀⠙⣄⠀⠀ ⠀⠀⠀⠀⠀⡿⣤⠟⠀⢠⠛⢀⡽⠂⠉⢁⣀⡈⠀⠁⠀⠀⠀⠈⠑⢒⠒⠋⠁⠀⠀⠈⠛⣻⠟⢯⢷⠀⠀⠀⠀⠈⠻⡄ ⠀⠀⠀⠀⠀⠑⠒⡇⠀⠸⡆⠉⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⠉⢩⡿⠀⠀⠀⣰⣇⡀⠸⣸⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⢀⡼⠁⡀⢀⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠁⠀⢀⡀⠀⡠⠃⣠⠏⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⣴⢊⣠⣤⣿⠯⣿⡛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠓⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⡿⢻⣿⡢⡀⠉⠳⣄⠉⠓⠲⠤⠤⣄⣀⣀⣀⣀⣤⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡟⠛⠃⠘⠟⠻⣿⡀⠀⠘⡆⠀⠀⡴⠒⡟⢛⡧⠴⠚⡹⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠑⢻⣿⣿⠀⡀⠀⣿⣷⢿⠇⢀⡠⠧⠤⠚⣧⣄⡻⢏⠙⠒⡚⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠻⣷⢼⣿⣶⣾⣿⠎⢀⠎⠀⠠⣶⢻⣾⠟⠢⢼⠃⣰⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⢲⡞⠛⢶⣶⣯⠥⠔⣋⡤⠴⠚⢻⡟⡿⣆⣀⣸⣶⣏⣗⣲⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⡠⠀⠈⠉⡿⢿⠟⠒⠲⡏⠀⠀⢀⠎⢀⡇⠀⠈⠀⢸⠇⠀⠙⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⡀⠀⢰⣋⡝⠀⠀⠀⢹⡀⢠⠎⣠⠎⠉⠒⠒⢤⠎⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⣸⠤⢥⣀⡀⣀⠀⠉⠉⠉⠙⠒⠒⠒⠒⠞⠀⠀⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⢰⡇⠀⠒⠠⣽⢻⣉⣳⠦⠤⣄⣀⣀⠀⠀⠀⢀⡴⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⢦⣤⣄⠀⠀⠀⣀⣠⣤⡴⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠷⣦⣤⣀⣴⡾⠛⠛⣙⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢁⣤⣤⣄⣈⠙⢿⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣾⣿⣿⣿⣷⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣰⣿⣿⣿⣿⣿⣷⡌⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣬⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣤⣼⡇⠀⠀⠀⠈⠘⢿⣿⣿⡿⠁⠀⡠⠞⠋⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢾⡏⠀⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⢿⠀⠀⠀⠀⠀⢀⢰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣠⣴⠶⠿⠿⣷⣄⣼⠀⠀⠀⡄⠀⠀⠀⢠⣿⠋⠻⣿⢠⡀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣹⣷⣄⡀⠀⣀⣀⠀⠀⠀⣀⡴⠋⠀⠀⢄⣴⡿⠋⠀⠀⠀⠀⠁⣻⣟⠀⠀⣾⠛⠛⢻⣾⡾⠿⣷⢠⣿⡿⠛⢿⣦⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠶⠿⣯⣝⡛⠷⣶⣮⣭⣿⠌⠉⠀⠀⠀⠀⠿⠫⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠷⠛⣷⠀⢸⣿⣀⣤⣿⣾⣿⣇⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣶⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⣿⡄⠀⢻⣄⣼⠿⠋⠁⠀⠀⠈⠙⢷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢸⣇⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣼⠟⠉⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣤⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠉⠀⠀⠀⢸⡟⠙⣶⡄⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢻⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡘⠃⠀⣀⣀⣠⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⠤⠤⠤⠤⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣽⣿⣿⣿⠿⣯⣿⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠶⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠿⠛⠋⠀⠀⠀⡄⠄⠀⠀⠈⠙⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⢤⣄⣀⣀⣀⣤⡴⠶⠶⠶⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠿⢧⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠉⠛⠲⣦ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⣴⡿ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣿⡉⠀⡄⠀⢷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢁⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣉⠁⠐⠈⠁⣿⣿⡷⠄⢠⡀⣀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣶⢦⣤⣭⣯⠀⠈⠛⢿⣿⣦⡀⢸⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣤⣼⣿⠿⣿⣯⣦⣤⡀⠐⢆⡀⠀⠼⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠦⢤⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣧⣦⣖⣀⣛⠋⠰⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀ ⠀⢀⣰⣆⠀⠀⠀⠀⠀⣿⡀⣷⣐⣶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⡉⢹⣿⣶⣄⣀⣶⣶⣟⣻⡿⠟⠁⠀⠀⠀⠀ ⢀⣿⠋⢿⣆⠀⠀⠀⠀⢿⣇⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⡇⢈⠉⠉⠽⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡇⠸⣟⠀⢀⣤⠤⢶⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣧⡀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠐⠻⣦⣙⣷⠟⠁⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⣾⣿⠃⠀⠈⠿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠋⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢿⡶⠚⠟⠀⠀⠀⡄⠀⠈⠻⣆⠀⠀⠀⠀ ⠀⠀⠀⣴⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠆⠀⣤⢠⣄⣤⡀⠰⣿⣿⡇⠀⠀⠀⠀⢻⣦⠀⠀⣠⣀⠃⣤⡶⠟⠛⢻⡇⠀⠀ ⠀⢀⣴⠟⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠉⠉⠙⠁⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⡸⠆⢻⣴⣠⣴⠟⠃⠀⠀ ⠀⢻⣟⣀⣀⣠⣿⠉⠉⠹⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠉⠉⠉⠻⠶⢾⠟⠋⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠛⠓⠶⠶⠾⠿⠲⠶⣦⣬⣤⣄⣀⣀⣐⣀⣂⣀⣀⣀⣐⣀⣐⣠⣤⣤⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡦⡄⠀⠀⠀⠤⣾⣧⣶⡆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠟⣿⣶⠀⠀⠀⠰⢿⣯⢿⣧⡄⠀⠀⠀⠸⣿⣠⣤⡄⠀⠀⣶⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠁⠀⠀⠀⠻⣿⠇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣼⣿⠈⡷⣄⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⣍⣉⠉⠉⠉⠉⠙⠒⠚⠉⠀⠀⠀⠀⠈⠁⠀⠛⠊⠳⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠞⠉⠀⠀⣀⣤⡤⠤⠤⣤⣀⠀⠀⠈⢳⡀⠙⠋⣹⠏⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠙⢶⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⢳⣄⡾⠥⠖⠒⠲⡆⠀⠀⢾⡉⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⢮⣷⡀⠀⢿⠁⠀⠀⣀⡴⠃⠀⠀⠈⠑⠄⣀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⣠⠏⠀⠀⢀⠀⠀⠀⠀⠀⢰⣽⠁⢀⡟⢀⣠⣤⣤⣄⣤⢤⣦⠒⠚⠛⠋⠙⠋⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡃⢰⡏⠀⠀⢰⣼⣷⣀⡀⡐⣶⣾⠾⠤⣼⠇⠀⠁⠀⠘⠿⢿⣿⠋⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣇⠀⠇⣤⠀⢹⣿⡿⣿⣷⠷⠋⠁⠀⠀⡿⠀⠀⠀⠳⣤⣴⣿⡏⠓⠶⣶⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣰⡋⠁⢸⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣯⡀⠀⠈⠻⠦⠾⠉⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⣇⠘⠁⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⠀⠀⠀⠀⢻⣧⣦⣵⡿⠋⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠙⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠣⣿⢻⠀⠀⠀⠀⢸⣧⣿⣛⠀⣶⠿⠃⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡾⠃⣾⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡳⢦⣀⣀⡀⢀⣀⣀⣀⣤⡴⠾⠛⠉⣶⡾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠳⢦⣭⣭⣉⣉⣉⣠⣠⣠⠴⠶⠋⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣿⣷⣿⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠿⠿⠂ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢙⡶⣦⣀⠀⠀⠘⠄⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠹⡷⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⣠⣠⡿⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠀⡐⠀⠀⢠⠏⠀⠀⠀⠀⠀⡇⠀⠉⠓⢦⣬⣷⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⣀⢀⣠⢼⣿⡛⠋⠀⠀⢰⠇⠀⢀⣴⠶⣴⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠀⢸⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⢧⠀⠀⢰⡏⠀⠸⡆⠀⢠⠀⠀⠀⠀⣾⠴⠿⠟⠟⠋⠙⠋⣿⡇⡄⠀⠀⣾⠀⠀⠸⣿⣧⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣧⠀⠈⣄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⣷⠀⠀⢻⠀⠘⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢿⡀⠀⠀⠘⢿⣿⣏⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⣀⣙⣾⣷⠄⢀⣀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢠⣈⣳⣦⠀⠀⠀⠀⢨⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠈⠉⠉⠁⠀⠀⠹⠟⠛⠛⠒⠒⠿⠀⠀⠀⠀⠀⠘⣿⠀⠃⠀⠀⢷⡀⠀⣀⣀⡀⣀⣀⣀⡀⠄⠈⠛⢶⡿⠟⠋⠀⠺⠗⠃⠘⠯⠿⠟⠛⠀⠂⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⣠⡤⣬⡇⠀⠙⠟⠃⠋⠙⠉⠀⠀⠀⠀⠀⠙⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢻⣤⠶⠶⠲⢦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⣾⠃⠀⠀⠀⠀⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⢀⣴⠖⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠁⠀⠋⠙⠛⠈⠀⠀⠀⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠉⠻⣥⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠫⣤⣿⡄⣀⠀⠀⢠⣤⣄⠀⠀⠉⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡖⢫⠻⢁⣸⣷⣄⡙⠿⣜⢳⡆⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣦⣄⠀⠀⠀⠸⣧⣤⡤⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠀⠀⠈⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣤⣀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⢀⣴⠞⢛⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡍⠉⠁⣰⣄⡉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀ ⢸⡁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠙⠉⠙⠃⠀⠙⠂⣽⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⣶ ⠘⢿⣄⠀⠀⠀⠀⠀⠀⢶⢦⣄⠀⠀⠀⠐⠶⠶⢤⡄⠀⠀⠀⠀⠀⣠⠿⣤⡀⠀⠀⠀⠀⣸⡧⠀⣾⠀⠀⢸⠀⠀⢸⠀⣠⣿⠆⠀⠀⠀⠀⠁⠄⣹ ⠀⠀⠉⠙⠳⢦⣄⣀⠀⠀⢀⣿⣀⣀⣀⣀⡀⠀⣀⣿⣀⣀⣀⣴⣞⣋⣴⠟⠀⠀⠀⠀⠀⢿⣅⣀⣽⣆⠀⣼⣆⠀⣸⠿⣧⡀⠀⠀⣀⣴⣄⣠⡼⠏ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠁⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⢤⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠚⠒⠘⠃⠀⠐⠐⠛⠚⠃⠀⠊⠛⠀⠀⠀⠐⡒⠐⠂⢂⠀⠈⠑⠃⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠃⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠘⡀⠀⣴⣠⣾⣿⣿⣿⣿⣿⡄⠉⠻⢯⡀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⡂⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣾⠁⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢸⡆⠀⠀⠋⠀⠀⠀⠈⠉⢻⣏⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⢸⡇⣠⣶⣦⣴⠾⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⣸⣧⡏⠀⣆⠀⠆⠐⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢻⡆⠀⠀⢰⣦⣤⣴⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⡏⠀⠀⠀⣾⠟⠽⠃⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⠀⠀⠈⢿⣿⣿⣿⡿⠁⣿⠁⠀⣾⣿⡿⠋⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⠀⢻⡀⠀⠀⠀⠙⠻⣿⠁⢀⡏⠀⢀⣿⠋⠀⠀⠀⠀⠀⠈⠘⣧⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠶⠶⠾⣧⣄⡀⠀⠀⢸⠃⢠⡾⠃⢀⣾⠃⠀⢀⣠⡴⠖⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⠈⠻⣷⡀⠸⢷⣤⣤⣴⠿⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣄⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣀⣀⣠⣠⣄⣄⣄⣀⣀⣀⣠⣀⣀⣀⣀⣀⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣠⣤⣤ ⠈⠉⠉⠉⠉⠉⠉⢿⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠶⠶⠶⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢠⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡟⠀⠀⠀⢀⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⣠⡿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠷⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢠⡾⠟⠄⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣰⣿⡄⠀⠀⠘⣿⣀⣀⣤⡴⠶⠶⠶⠶⠶⠶⢦⣬⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢻⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡏⠊⠀⠀⢀⣰⠿⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠛⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⣤⢿⡏⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⢠⡾⠃⢀⣴⡾⠖⢶⡄⠀⣿⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠿⠮⢭⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⣾⠁⢀⣾⣿⣧⠀⢀⣷⢀⢩⣥⣶⣿⣿⣿⣶⣤⡀⠀⠀⢀⡶⠋⠉⠀⠙⣿⡆⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⡏⠀⢸⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⠎⠁⣠⣤⣄⡀⠘⢷⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⣠⢺⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣯⣇⠀⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⡿⠉⠉⢳⠀⢸⡆⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⢩⡟⠟ ⠀⠀⠀⠀⢀⣠⡶⠶⠶⠶⣤⣌⢹⣿⣽⣦⡀⠈⠉⠉⠉⠁⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⣿⣿⣦⣴⣿⠀⢸⣇⣴⠟⣻⣿⣏⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀ ⠀⠀⢀⣼⡟⢉⣀⠀⠀⠀⠀⠙⣿⡏⠙⣿⠛⣒⠒⢲⡖⠒⠶⢶⣶⣿⣿⣿⣿⣿⠿⠛⠑⠀⢻⣿⣿⣿⣿⣿⡟⠀⣸⣿⡁⢸⡿⠋⢻⡄⠀⣀⢠⣷⢀⣾⠋⠀⠀ ⠀⢰⡿⠁⠀⠀⠈⠑⠀⠀⠀⠀⠈⣿⣄⠈⢷⣿⣶⣾⢷⣄⣀⣾⣿⣤⣴⣏⠉⣻⡷⣦⡀⣧⠀⠉⠻⠿⢿⣿⠗⠚⠛⠛⡻⠿⠗⠐⢿⣿⣿⣾⡿⣡⡞⠡⠀⠀⠀ ⠀⢻⣶⣮⡿⢶⠶⢶⣦⣀⠀⠀⠀⢿⡿⣦⡈⠻⣏⢻⣾⣯⡀⠈⠙⣿⣿⣿⣿⣿⡇⠀⠉⣻⣷⣤⣀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⠋⢀⣶⠀⠀⠀ ⠀⣸⣿⣿⣯⣤⣀⠀⠀⢈⣷⣤⡄⣼⠇⠈⠙⣦⡈⠻⢄⡈⣷⣤⣀⠉⠃⠀⠀⠀⣹⠶⢿⣿⣀⣩⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⡿⠟⠁⠀⠀⠀ ⢠⣿⣿⣿⣀⣛⠈⠀⠿⢻⣿⣿⣿⣧⣀⡴⠾⠋⠙⠷⣤⡈⠻⠯⢼⣿⣿⣷⣷⠟⠙⢿⠟⣿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣤⣭⠹⣿⡍⠋⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⠏⠉⠉⠁⠀⣠⣿⠛⠉⠈⠈⠉⠁⠀⠀⢠⣠⡿⠃⠀⠀⠀⠉⠉⠉⣉⢉⣙⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠸⠧⢿⣿⣶⣤⠀⠀⠀⠀⠀ ⠀⢸⡿⠤⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⡼⠋⠻⣧⣤⣄⣠⣤⣴⣶⡾⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⡶⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣇⠀⣠⠾⠁⠀⠀⠀⠙⠛⠛⠛⠛⠁⢰⡿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣧⠀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠨⣿⣶⣶⣶⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⢸⣿⣿⣿⢿⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠅⠘⠿⢷⡇⠀⠘⢛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠙⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢈⣴⣿⡞⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⢀⣀⣴⣿⣥⠶⠾⢶⣦⠀⢿⣿⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠈⣿⡟⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠻⣶⣬⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢧⣀⣀⠀⣠⣤⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣷⣄⣽⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠶⠶⠶⠶⠶⠿⠶⠶⠶⣤⣤⣤⣀⣀⠀⠀⢀⣠⡾⠟⠛⠛⠛⠛⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⠶⠶⢶⣤⡀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠈⠉⠙⠛⠿⢷⣿⣏⡀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠋⠀⠀⠀⠀⠙⢿⣦⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠙⠒⠢⢤⣤⣀⡀⠀⠈⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⠉⠉⠒⠒⠺⠻⢷⣦⡀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠙⢆⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⢀⣴⢿⣧⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣼⣠⠤⠴⢺⣿⣿⣿⣿⣿⡿⠓⠾⢿⣧⣴⣟⣥⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣀⣠⠴⠋⣁⣀⣀⣤⣤⠤⠤⠤⠤⢼⣇⠀⠀⠀⠀⢸⡁⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⢿⣿⣿⣭⣼⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢶⣾⣽⣷⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⠉⠉⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣴⣿⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣤⠀⠀⢀⡀⠀⢈⡷⠖⠋⠉⠀⠀⠀⠈⠙⠓⢿⡁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⡀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⠿⢛⡽⠁⠀⠀⠀⠈⢣⠀⢸⣥⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⣧⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⡆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⣀⡀⠈⠉⠓⢒⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠻⠿⢶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡾⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣍⡛⢻⡟⠛⠛⢻⣿⢋⠉⠉⠀⠀⠀⠀⠀⠈⠙⣶⡶⠶⠤⠴⠶⠒⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢻⣿⣁⡀⠀⠀⣿⡋⠛⣧⡀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⡄⢸⠇⠈⠉⠉⠉⠉⢷⡀⢹⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢸⠀⡼⠀⠀⢤⡶⣦⡴⡆⠻⣼⣇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣶⠃⠀⠀⠸⣷⢀⣰⡇⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠛⠋⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠘⣿⣀⣀⡀⠀⠀⠀⢀⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣤⣤⠶⠛⠁⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡍⠉⠉⠉⠉⠉⢹⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠻⣧⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠒⠦⣤⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣼⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠈⠉⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢹⣧⠀⠀⣤⠀⠈⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⢿⡄⠀⢛⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣠⣤⣤⠶⠛⠛⠙⠛⣻⣯⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢟⣿⠿⠋⠙⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⢉⣴⠟⠁⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⢏⡴⠛⠁⠀⠀⣠⣴⣾⡿⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⣤⣤⣬⡛⢶⣄⠀⠀⠀⠉⣨⣷⣄⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⡞⠁⠀⢀⣴⣿⣿⣿⡏⠀⠀⢻⠀⠀⣿⠀⠀⠀⠚⠋⢁⣀⣀⣀⡀⠉⠛⢧⡀⠀⠀⢠⡟⠀⢿⣧⡄⠙⠳⣤⡤⠠⠇⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡞⠁⠀⠀⣿⣿⣿⣿⣿⣷⣄⣠⣾⡄⠀⣿⠀⢀⣤⡶⣻⣿⣿⣿⣿⣿⣿⣶⣄⠙⠧⠀⣼⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟⢠⡿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠠⡿⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⣿⣧⡀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣰⠇⠀⣴⠿⣷⡀⢹⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢹⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣸⠇⢿⣿⣿⣦⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢿⣿⠀⣴⠁⠀⣽⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢳⡄⠀⠀⠈⠛⠿⠿⠿⠟⠋⠁⢀⣴⠋⠀⠸⠹⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⢀⣠⣼⡏⢰⣿⣶⣾⣿⣿⡆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⣧⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠘⠻⢿⣇⡀⠀⠀⠀⣠⣼⣿⡿⡿⠀⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⣿⠀⠀⠀⣀⣀⣬⣽⠷⠶⠾⣯⣭⣿⣥⣤⠤⠤⠤⠤⣤⣤⣄⣀⣉⢻⡶⠶⠾⠛⠋⠁⠀⡇⠀⣿⣿⣿⣿⣿⡿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠁⠀⠀⢠⣿⣄⠰⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣤⣀⡀⠀⠀⣷⡀⠘⢿⣿⣿⡿⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠁⠀⠀⠀⣾⠃⢹⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣀⠀⠀⠀⠀⠀⠉⠙⠶⣄⡹⣷⡄⠀⠈⠁⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⣸⡏⠀⠀⡹⣯⡛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠙⠿⣽⡷⢦⡤⢶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⢰⠟⠁⠀⠐⠀⠈⢳⡄⠹⡏⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⠉⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣵⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣾⡄⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠠⠴⠶⣤⢶⣶⡶⠖⠒⠛⢻⣏⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⢀⣿⣼⠇⠀⠀⡔⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣳⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⣠⡾⡟⠋⠀⠀⣼⣿⡏⠀⠀⠸⣺⢯⠄⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⢸⠇⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⡆⢿⣿⡇⠀⠀⠀⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣾⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠶⠿⢬⣿⡇⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠻⣦⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⣄⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⣸⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠻⣄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡃⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⢿⡌⣷⣄⡀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠃⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⣿⣿⣿⣻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠉⣻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠻⣖⣀⠀⠀⠀⠀⠀⠀⠰⣦⠾⡿⢿⣧⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠙⠛⠻⣷⣆⡀⣻⣄⡀⣤⣽⣾⠁⡼⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠛⠛⠛⠿⣦⣀⣠⣴⣶⡿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣟⠁⠀⣀⣤⣄⠀⠈⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣿⠟⠉⠀⢀⠈⠙⠻⣷⣶⠋⠁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡾⠿⠟⠛⠛⠛⠛⠛⠿⠿⢿⣿⣷⣄⡀⠙⣿⡷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠙⢿⣆ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣦⠀⠀⠘⣦⡀⠀⣾⡟⠉⢻⣇⢀⠠⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠈⣿ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⣿⡆⠀⠀⢹⣧⠀⠹⢷⣶⣿⠇⠀⠀⢶⣤⣈⠳⡀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸ ⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢀⣴⠋⠁⠈⣷⠀⠀⣿⣇⠀⠀⢸⣿⠀⠀⠀⢠⠏⠀⠀⠀⠀⣿⠉⠀⢠⡿⠛⢻⣦⠀⠀⢸⣿⣠⣿ ⣠⡶⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢀⡾⠁⠀⠀⠀⡿⠀⠀⢸⣿⠀⠀⣸⡿⠀⠀⠀⡟⠀⠀⠀⢀⣾⠇⠀⠀⡾⣿⣤⣴⡿⠀⠀⢸⣿⡟⠁ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢀⡾⠁⠀⠀⠀⠀⠁⠀⠀⣾⡿⠀⠀⠉⠁⠀⠀⠀⡇⠀⢀⣴⣿⡇⠀⠀⢰⠃⠈⠉⠁⠀⠀⠀⢸⣿⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⣾⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⠇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣷⣴⠿⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⣿⣄⣰⡆⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠗⠀⢰⣶⠾⠟⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠀⠀ ⠈⠛⢿⣧⠀⠀⠀⠀⠀⠀⠈⢋⠁⠀⠀⢀⠀⠀⠘⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀ ⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠙⢷⣄⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣤⣄⠀⢀⣴⣶⠾⠿⠿⣷⣶⣿⡉⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠁⠀⠀⠘⠛⢿⣿⣿⠟⠒⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣤⣀⣀⣀⣤⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠻⣿⣯⣤⣀⣀⣀⣤⣾⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢛⣿⠋⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣿⠿⠿⠛⠉⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⢰⣿⠟⠛⠛⠉⠉⠉⠁⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣿⣧⡄⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠘⣿⣷⣿⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣤⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠿⠷⠶⣶⣤⣤⣶⠟⢉⣩⣤⣉⡙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣶⣦⣄⣀⠀⢀⣠⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡆⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⠟⢉⣡⣤⣄⡉⠻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠃⣰⣿⣿⣿⣿⣿⣦⡙⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⣿⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢻⣆⠘⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣶⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠃⠀⢀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⢿⣦⣼⣶⣼⠗⠀⠀⠀⠘⢿⣿⡿⠟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢿⣿⡿⠏⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡇⡀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣆⠙⠲⠤⠤⣶⠤⠀⠀⠀ ⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡌⡛⢿⣦⠀⣰⡟⠀⠀⠀⠀ ⠀⠀⠹⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡿⠕⢨⣿⡿⠀⠈⣿⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣇⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣦⣀⡀⠀⠀⠳⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠩⠑⠄⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⡶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠙⠛⠻⠿⣷⣤⣄⣀⣀⣤⣤⣴⠶⠾⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢶⣦⣤⣄⣀⠀⣠⣴⡾⠟⠛⠉⠁⠙⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣧⣄⡀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣄⡀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⣠⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢴⠦⢠⡄⠘⠿⣿⡿⠟⣤⢀⡀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⡀⠙⠁⣤⠈⠁⢀⣼⣿⣇⠀⢸⡬⢁⣾⠆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠉⠙⠿⣶⣤⣤⣴⣶⠿⠛⠈⠻⠷⢶⡶⠿⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀ ⠀⠀⠀⣼⣟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠻⣧⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢿⣆⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢸⣿⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⣿⡆ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⠀⠀⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡧⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠈⣻⠇⠰⣿⡀⠀⠀⢹⡇ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⢙⠛⠓⠒⠒⠒⠛⠉⠀⠀⢶⣖⣢⣦⣤⣶⠆⠀⠈⠛⠛⠒⠒⠒⠚⠉⣠⠄⢿⡇⠀⠀⢸⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡁⠀⢸⣿⠀⠀⢸⡇ ⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣸⡏⠀⠀⣿⡇ ⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢠⣿⠃ ⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢀⣾⠏⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⢀⣠⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠟⠋⠁⠀⣀⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⢷⣄⠉⠛⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠈⣿⡀⠀⠀⠀⢨⣿⡿⠻⠿⠿⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠿⣶⣤⣤⣤⣤⣴⡶⠶⠿⠿⠿⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⢹⣇⠀⠀⣴⣿⡏⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠸⣿⡀⣴⣿⣟⠁⠀⣶⡆⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠻⣿⡟⢈⠄⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⣰⡿⠀⠀⠀⠀⠀⣹⣿⡄⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⡀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⡶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⢶⣶⣶⣦⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⣁⣴⡾⠟⠋⠉⠉⠉⠛⢷⣄⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣷⠶⠶⠶⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀ ⠀⠀⠀⠀⡇⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⣤⣤⣀⡀⠀⠉⠙⠛⠿⢶⣦⣤⣈⠛⢿⣿⣦⣀⠀⠀⠀⠀⣠⡾⠋⢀⣤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⣤⣀⠀⠀⠈⠙⠻⣿⣷⣿⣮⣻⣦⡀⢀⡾⠋⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣬⣽⠷⠶⠶⠶⠒⠚⠻⠿⠟⠃⠉⣻⡿⠁⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⠀⠀⣀⣤⡶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠛⠉⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠙⠻⢏⠀⠀⣀⠀⣠⠀⠀⠀⠈⠁⠀⢀⣠⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⢹⡇⣿⠀⠀⠀⠀⣠⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡀⠙⠻⠶⢦⣤⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⠾⣧⣄⡈⣿⣽⣆⣀⣴⠟⠋⠀⠛⠛⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⠖⠒⠛⠋⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⣤⣤⣤⣤⣀⡀⠀⢠⣴⣿⠙⠛⠿⣤⡸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⣯⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡴⠶⠶⠶⣾⡟⠒⠒⠒⠒⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠉⢿⣿⡿⣷⣶⢶⣼⣿⣷⣿⣿⣿⣿⠏⠉⣉⣿⣶⣿⣿⡶⠶⡟⠛⠋⠉⢉⡉⠀⢀⣀⣀⡀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⡤⠴⠶⠶⠶⠾⢿⣿⣿⣿⣿⡛⠛⢿⡄⠙⣏⠀⠀⠘⢿⣿⠛⠛⠋⣻⡿⣯⠉⠉⠉⢉⣿⠟⠋⠉⠉⠛⢿⣝⠛⠓⠒⠶⠶⠄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣼⣿⣿⣿⡾⢿⣄⣽⣷⢤⣄⡈⢻⣆⠀⠀⣿⢀⡟⣿⣶⡶⣿⣁⣀⣀⣀⣠⣄⣀⣙⢷⣄⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⠁⠈⠙⢻⡿⠻⢧⣝⣳⣾⣭⣥⣽⣿⣶⣿⣻⣿⠿⠿⠛⠻⠿⠿⠯⢤⣤⣀⣈⠙⠛⠛⣷⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⣼⡇⠀⣠⡿⠋⠉⠉⠀⠀⠈⠉⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣦⡚⣿⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠃⠀⠀⠀⠀⣰⣿⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⣼⣏⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⠷⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣁⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠏⣠⡾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀ ⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣫⡾⠋⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⠿⢿⣿⡿⠿⠛⠉⠉⠁ ⠀⠈⠉⠛⠻⢿⣛⡛⠻⠿⠿⠿⢭⣭⣉⣉⡉⠉⠛⠛⠛⠲⠦⣤⣄⣀⠀⠀⣴⠟⣽⣿⣋⣀⣼⡋⢀⡀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠛⠛⣩⣴⠿⠋⠉⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⡀⠀⠀⠀⠉⠉⠛⠲⢶⣤⣀⠀⠀⠀⣉⣹⣿⣾⣿⣿⣟⠛⠉⠉⢻⣿⣿⣿⣶⣶⣶⣾⡛⠉⠉⠀⠀⣠⣶⠟⠉⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⢀⡀⠀⠀⠀⠈⠙⠷⣦⣤⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡷⣿⠿⣶⡄⢠⡾⠋⠁⢀⡀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢷⣀⠀⠀⠀⠀⣰⡟⢁⣾⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣦⠀⠈⢻⣟⠁⠀⠀⢸⠃⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠙⠷⢤⣀⣾⠋⢠⣿⡿⠋⣠⣶⣟⠛⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠙⣿⡇⠀⠀⢻⡄⠀⢠⡾⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⣸⡏⠀⠸⠋⢠⡾⠋⠀⠹⣦⠀⠀⠀⠀⠀⣰⡿⠉⠙⢷⡄⠈⢿⠀⠀⠈⣷⡴⠋⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠟⠒⠒⠛⠁⠀⢤⣤⣿⣀⣀⣀⡀⢹⡄⠀⠀⠀⣀⡟⠀⠀⣀⣀⣻⡄⢀⣠⣤⣤⡿⠶⠾⢿⣧⣤⣤⣀⡀⣀⣠⣤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣛⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣝⣿⣿⡿⣿⠂⠀⠀⢿⡿⢿⡿⠟⢉⣽⡿⠛⠉⠁⠀⠀⢀⣀⣤⡽⠿⠿⣯⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠙⠳⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣿⠀⣀⣀⠸⣇⠀⢀⣴⠟⠁⠀⣀⣤⡴⠶⠛⢉⣉⣀⣠⣤⣤⣾⠿⣶⡶⠶⠶⠶⠖⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⣠⠤⡤⠞⢻⣏⠙⠛⠷⠦⣤⣄⣀⠀⠀⠹⣧⣿⣞⣛⣛⣛⡿⣆⣞⣡⡴⢞⣛⣭⡤⠶⠟⠛⠛⣉⣭⣴⠾⠷⡶⢶⡼⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣛⣻⡿⢋⡟⠁⣸⠟⠛⠻⣶⣶⡤⠤⢬⣍⣛⣳⣶⣿⡉⠻⣿⠟⠋⠉⢾⣯⠿⠛⠛⠉⠀⣀⣠⡤⠴⣿⠉⠀⠈⢧⠀⢧⠀⣷⣼⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣽⠁⢸⡀⢰⡏⠀⠀⣠⢯⠈⠉⠛⠒⠒⠛⠛⣻⠃⠀⠀⢸⠀⠀⠀⠀⢹⡗⠒⠒⠚⠋⠉⠁⠀⠀⠋⠳⡄⠀⢸⠀⢸⠀⡏⠈⠻⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠄⣿⣤⣤⣽⣾⣧⡀⠀⣁⣨⣷⠤⠶⠶⠄⠀⠀⣇⠀⠀⠀⠈⡆⠀⠀⠀⡞⠀⢦⣀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣋⣤⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠈⠉⠉⠉⠁⢻⠄⣄⠀⠀⠀⠀⢹⡆⠀⣠⠤⠷⢤⡀⢰⢃⣤⡀⠈⠉⠉⠉⣹⠋⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣆⠀⠀⠀⠀⢸⡾⠙⣇⣠⣤⡀⣠⣹⡀⠈⠳⠄⠀⠀⣸⡾⠉⢷⣀⣄⠀⢀⣿⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡀⠀⠀⠀⣾⡇⠀⠹⣿⠀⢹⡏⠛⣿⡦⣤⣤⣤⣴⣿⠃⠀⠘⡟⠙⣶⣿⡇⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢀⣿⠀⠀⠀⡿⠀⠘⠃⠀⠹⣷⣄⣠⣤⠾⣿⠀⠀⠀⠃⠀⡗⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢷⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⠇⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⣿⠀⠀⠀⠀⠀⣀⡤⠖⠈⠉⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⢿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠁⢀⣀⠤⠶⠋⠁⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⢀⡠⠚⠋⠀⠀⠀⣀⠀⡄⠈⠃⠀⠀⠉⠓⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡻⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⣿⣿⣿⣿⣿⠟⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⠟⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⠿⠿⠿⠟⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⢸⣿⡁⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡶⠶⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣶⠶⠶⢾⣿⣶⣶⡄⠀⠀⠰⠿⠟⠉⠀⠀⠀⠀⢹⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠠⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢻⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⢸⣀⣀⣤⣤⣤⡶⠿⠛⠉⡇⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠤⢼⡷⠶⠦⣤⣤⣶⣶⡶⠟⠋⠀⠀⢸⡆⠀⢀⠀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢛⡿⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣼⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⡉⠲⠶⢤⣤⣤⣴⣶⣶⣶⣶⠟⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢻⣦⣤⣤⠤⢤⣬⣭⡭⠿⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢯⡙⠛⠲⣤⣈⣿⣄⣀⡀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠁⠉⠉⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⡉⠉⠉⠙⠓⠲⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠁⠀⣼⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡻⡖⠶⡤⢤⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠃⠀⣰⣿⣿⣿⣿⠀⠀⠀⠹⡟⣟⠻⣧⣇⠀⡧⠤⣧⡹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⡼⡆⠀⠙⡇⢰⣿⣾⡇⠹⣧⡉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢷⢻⡄⠀⠳⣼⣿⣷⠇⠀⠙⢷⣄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡜⣧⢻⡄⠀⠈⠉⠁⠀⠀⠀⠀⢻⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡧⠼⠮⠿⠤⠤⠴⠒⠚⠛⠛⠉⠉⠉⠙⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢶⣌⠹⣿⣿⣿⣿⡟⠒⠶⠦⢼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⢟⡴⠿⠿⠿⠿⠿⠀⠀⠀⠸⡿⠿⠿⠿⠿⣿⠷⠤⠤⠄⠀⠀⠀⠀⠀⠀⣸⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⣤⠴⠊⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠱⠶⠖⠋⣀⡼⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⡄⠀⠒⠋⣁⡠⠔⢛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠙⣆⠀⠋⣁⠠⠔⣋⣤⠿⣦⡀⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⡄⠈⢧⡈⣡⡴⠚⠉⠀⠀⣈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠙⣆⠈⠳⡜⢧⣀⣠⡴⠞⣉⣴⠿⠻⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⡇⠙⠆⠈⠁⠀⣙⣮⣭⣴⣶⠻⠍⢀⠀⡀⠀⠨⣹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡝⢟⠛⣿⣿⣿⣿⠿⠿⠋⠉⢀⠀⠠⢂⡄⣿⣼⢿⣦⣠⣿⣿⣻⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡶⡆⢪⣿⡗⠉⣁⠠⠀⠀⠀⢠⣠⢸⣿⣿⡏⢋⡸⠛⠛⢻⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠉⣠⣿⣿⠃⠁⠻⠀⠀⠀⠂⢨⣥⣼⣿⣿⣷⣮⠁⠠⠄⣀⣽⣾⠛⠛⢿⣶⣶⡶⠶⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣴⣿⢹⣏⠛⠛⠁⠄⠀⠀⣃⣴⣿⣿⡟⠙⠻⣶⣄⠀⣴⡟⠿⠋⠀⠀⣸⣿⠉⣁⠰⡆⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⣿⢸⡇⡄⠀⠀⠀⠀⠠⣿⡟⠙⠋⠀⠀⠀⠈⢷⡘⢿⣦⣤⣤⣤⣾⢟⣁⣤⣾⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣏⢡⣀⣻⣿⣸⣿⠘⠃⡀⠀⢀⢁⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⢷⠉⣀⣈⡁⣨⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⢩⠈⣞⣝⠁⣿⣧⠀⠶⢹⠀⠀⠈⠌⣿⣤⣀⠀⠀⣠⣾⣿⠏⠿⠾⠍⠉⡿⣿⣿⣿⣿⠿⡛⠉⠀⢰⣾⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢇⠛⠑⠃⣸⠆⢙⣿⡀⠂⠘⠁⠀⠈⠀⠀⠈⣙⠛⠉⠉⠁⠀⠀⠃⠈⠀⢈⠀⠀⠈⠘⠈⠁⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⠀⠧⠀⠲⠀⢀⠀⢻⣷⠀⠀⠀⣦⠀⠀⠆⠀⢉⣛⡃⣤⠀⠀⠀⠀⠀⠂⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣝⠀⢰⡆⠀⠀⠐⠀⠈⢿⡄⢀⣀⠘⠀⠃⠀⠀⠀⠀⠁⠹⠄⢅⣠⡼⠿⡾⠛⢿⣿⣁⠐⠀⠂⠀⢸⣷⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⡉⠀⣸⡇⢀⠀⠀⠀⠀⠘⣿⡀⠀⡄⠘⠀⠀⠀⠀⢀⠀⣤⡴⢿⣏⣀⣼⣿⣶⣿⣿⣿⣦⡄⣀⢁⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠘⠃⠀⣿⠀⠀⠀⣤⠐⠀⠀⠘⣷⣄⠁⠀⠀⠀⠀⠀⠈⣼⣿⣥⣼⡿⣿⣿⣿⠿⠿⠛⢻⡟⡇⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠄⠀⣀⠘⠂⠠⠰⠁⠀⠐⢂⠀⠈⡻⣮⡠⠀⠠⠀⠀⠤⢹⡟⠁⣀⣴⠾⠋⠀⠀⠂⠀⠀⠀⢀⢤⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢫⡄⠀⠈⠁⡀⠉⠀⠶⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⣖⠀⠈⢙⠛⢉⠀⠀⠄⢀⢙⡀⠩⢩⣤⣾⡯⠝⢙⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠉⠀⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣼⣄⣿⣀⣀⣶⣶⣼⣿⡿⠛⠋⠀⡀⠀⢈⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡀⠀⠁⠀⠠⠄⣀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠉⠙⡛⠛⠛⠟⠙⠛⣿⢿⡕⢂⠀⠄⠀⠒⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⢭⡅⢀⠀⠄⠀⠁⠀⢠⠀⠀⠈⢀⠀⠀⠀⡀⠀⠒⠂⡈⠁⠐⠂⠐⠀⠀⠀⠂⠰⡄⠉⠈⠁⢉⢀⡀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀ ⠀⢸⡟⠀⠀⣿⠃⠀⠀⠁⣠⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠱⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⠀⢸⣿⣧⠀⠀⠀⠀ ⠀⢸⡇⠀⣸⡿⠀⠰⡀⠀⠀⠀⠀⠠⠩⠀⡈⠀⠂⠐⠁⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⢒⠄⠀⠀⠀⠀⠃⢤⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀ ⠀⣿⠧⠁⣿⠷⢦⡷⠀⠂⠀⡀⠀⠀⠀⠀⠀⢠⣄⠀⠋⠀⠀⠄⠚⠤⠃⠉⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠂⢙⢀⠀⠀⢸⣿⢽⣇⠀⠀ ⠀⡿⣸⢻⣿⠒⠈⢠⠁⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⠀⠐⠂⠀⡄⠀⠈⠐⠀⠀⠌⠀⠂⠄⠁⠀⠈⠁⠀⠀⠀⠠⠀⠸⠧⠀⠀⠐⢿⡿⢻⡀⠀ ⢠⡇⢟⠈⣿⠀⡤⠀⠔⠀⠀⠄⠀⠀⠀⠀⠀⢸⣿⠀⡀⠀⠀⠀⠄⠀⠐⠂⠀⠂⠆⠀⠒⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣷⠈⣷⠀ ⢸⣿⠊⣸⣿⠀⠀⠀⠀⠀⠆⠠⡀⠀⠀⠀⠀⣼⡇⠀⠁⠀⠀⠀⠐⠀⠠⠀⠀⠀⠃⠀⠈⠀⠀⠀⢀⠀⠄⠀⠄⠁⠀⠀⠀⡀⠉⠁⣿⡆⢻⡇ ⢸⣇⢀⢰⣿⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢀⠀⣿⡇⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠠⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⢹⡇⠄⣷ ⣸⡏⠎⠁⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢸⣿⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠶⠚⠋⠉⠁⠉⠛⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠛⠛⢛⣓⣀⡀⠀⠀⠀⠀⢀⣀⣀⣈⣉⠉⠉⠛⠶⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣿⠃⠀⣠⣴⠟⠋⠉⠉⠙⠳⣤⣠⡞⠋⠁⠀⠀⠉⠛⢶⣄⠀⠈⣿⡉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠛⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⣀⣀⠀⠀⠀⠀⠙⣧⡰⠟⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣠⣶⡶⣶⣄⠀⠀⠀⣼⠟⣿⣷⣦⡀⠀⠀⠘⢷⡀⠀⢢⠀⠀⠀⠈⠙⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⣴⠀⣼⠃⠀⠀⠀⣰⣿⣿⣧⣾⣿⣦⠀⢰⣿⣶⣿⣿⣿⣿⡄⠀⠀⢸⣧⠀⠈⢣⡀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣇⡄⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢾⣄⠀⠰⡀⠀⠀⢰⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⡸⢻⡇⢻⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⡟⠀⢹⡗⠀⠀⠀⠀⠂⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⣄⠀⠀⠈⠙⠿⠿⠿⠟⠁⢀⣀⣈⡙⠛⠛⠋⠀⠀⠀⢠⡿⠁⢠⡿⠁⠀⠀⠀⠀⢀⣴⠟⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠙⠳⣦⣄⣀⣠⣴⠾⠛⠛⣋⣛⣛⡛⠻⠷⣤⣄⣠⡴⠋⠀⢸⣿⣇⠀⠀⠀⣠⡶⠟⠁⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣼⠿⣤⡤⠀⠀⠸⠟⠁⣀⣴⣶⠟⠋⠉⢉⣻⣿⣶⠀⠈⠙⠓⠀⢰⡟⠀⣿⠀⠀⣴⠟⠀⠀⠀⠀⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⣼⢿⠀⠸⣧⠀⠀⠀⠀⠀⠛⠿⣿⣶⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣾⠃⢠⣿⡄⢸⡏⠀⠀⠀⠀⣰⠇⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⣧⠘⣧⠀⠹⣧⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠀⠀⠀⠀⠀⣀⡾⠃⢀⡾⠉⢷⣼⡇⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⣹⣷⣄⠈⠻⠶⣤⣀⠀⠀⠀⠀⢀⣈⡀⠀⠀⢀⣀⣴⠞⠉⣀⡴⣿⡁⠀⠀⠙⠃⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠷⣦⣀⠈⠉⠛⠲⠶⠚⠋⠉⠙⠛⠚⠛⣉⣴⠶⠟⠉⠀⠈⣿⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠉⠛⠻⢶⣄⡀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⣀⡾⠋⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢻⣿⣆⠀⠀⠀⠀⠲⠍⠛⠷⠦⠤⠶⠞⠋⠁⠀⠀⠀⠀⣠⣾⣿⣶⣤⣤⠾⠋⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡟⠙⠿⠳⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠈⢻⣍⠙⢶⣄⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡟⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠙⢷⡄⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⣀⣴⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⣿⣷⠦⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣸⢿⡇⠠⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡆⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣗⠀⠛⠀⠀⢬⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠆⠀⠀⠀⠀⢀⣼⡿⣿⠀⠀⠀⠀⠀⠀⠀⠏⣿⠀⠀⠀⠀⠀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠋⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⢀⣴⢷⣶⡾⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣤⠴⣿⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⢞⣫⣤⠀⠀⠀⡠⠔⠋⠀⣼⠏⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣉⠙⠳⢦⣤⡀⠀⠀⠀ ⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⠃⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣀⠀⠹⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠛⠳⣦⣄⠙⠷⣄⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢰⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣿⠀⠀⠀⢿⣄⠀⠀⠀⠀⠈⢻⣧⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠹⡆ ⢹⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠷⣷⣄⠀⠀⠀⠸⣦⡀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠙⣷⣄⠀⠈⣿⡆⠀⠀⠀⢀⣼⡟⢠⡿⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠇ ⠀⠙⢿⣦⣤⣤⣤⣴⡿⠟⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣿⣧⣤⣤⣶⣿⡿⠞⠋⠀⠀⠈⠙⠿⣶⣤⣤⣄⣀⣀⣀⣀⣤⣴⠿⠛⠁⠀ ⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣳⣄⣴⠿⠟⠛⠺⢿⣦⣀⡴⠷⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⣿⣁⠀⠀⠀⠀⢤⡄⠉⠻⣿⡻⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢽⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣀⣠⡄⠀⠀⠀⣀⣄⢀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⢤⣀⣴⠋⣰⡟⣴⣧⣀⣀⢸⣯⣹⡟⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⣠⣤⡙⢷⡀⠈⣿⢻⣿⣿⣏⠛⢿⣿⠧⣤⠴⠒⠒⢦⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⢻⠀⢿⠀⢹⠘⣧⣀⡇⠈⢿⡿⠃⠀⠈⣧⣼⠃⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀ ⠀⠀⠀⠈⣇⠈⣇⢸⡇⣿⡟⢻⠦⠄⠀⠀⠠⠀⢸⡇⠀⠀⠀⠀⣼⠀⣸⠏⠀⠀⠀ ⠀⠀⣠⡴⢿⠀⠉⠉⠀⠙⡇⢸⡄⣾⣿⣷⡀⠀⣸⠀⠀⠀⠀⢠⣇⣰⠟⢦⡀⠀⠀ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⢠⣇⡀⣧⣙⠛⠋⣁⡴⢻⡄⠀⠀⠀⠀⠋⠛⠒⠒⠻⣆⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣿⡿⠟⠿⣯⡽⠞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⢷⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⡟⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣦⣀⠀⢀⣠⣴⣻⠟⢠⠏⠀⣤⣤⣾⣦⡀⠀⣀⣠⣽⣦⡀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠈⠉⠉⠉⢀⡏⢠⡏⢠⣾⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣗⢲⡶⠶⢶⡏⠁⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⣼⠀⣸⣿⣿⣿⣿⡟⠁⢿⣿⣿⣿⣿⣿⡿⠀⢷⠀⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡏⠀⠈⢻⣻⡿⠋⠙⣷⣾⠛⠿⢿⣿⠟⠁⠀⢸⡆⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠘⡇⠀⣷⠀⠀⠘⢿⣿⣶⡿⠋⠻⣷⡀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠸⡆⠀⠀⢰⡿⠋⠀⠀⠀⢘⢿⣄⠀⠀⠀⢀⡼⠁⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠞⠁⠀⢰⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⣉⡲⣤⣀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣁⡀⢀⣠⡏⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠛⠊⣑⣂⠛⠯⠶⣽⡦⠾⡇⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⠉⠙⢷⣄⠀⠀⠀⢹⣄⠀⠀⢀⣠⠾⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⣾⠏⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠙⠓⠚⠛⠁⡴⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠤⠶⣞⡉⠉⠛⠂⠀⠀⡛⠒⠒⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠋⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠶⢦⣤⡀⠀⢨⡄⠰⠄⠀⢀⣠⣤⣤⡾⠿⠧⠤⠤⠤⣤⣤⣀⡀⠀⠀⠀⢷⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⠞⠛⠳⢦⣀⡾⠋⠀⠀⠀⠈⢿⠶⢾⣧⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⡀⠸⡇⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⢨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠈⣿⠻⣦⠀⠀⠀⠀⠸⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⠛⠳⠶⣤⣀⠀⠙⢷⡀⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⣾⠃⠀⠀⠀⠀⠀⣴⠿⠆⠘⠢⡄⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣶⣦⣄⡀⠀⠾⣿⠀⠀⠀⠈⠙⢷⣤⠜⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⠳⢦⣀⣀⣠⠴⠛⠁⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢰⣿⣷⠄⠀⢀⣵⣾⡏⠉⠉⢛⣷⣦⣰⠖⠀⠀⠀⠀⠀⠹⣷⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠃⠀⠀⠀⣰⣆⠀⣸⡟⠀⠀⠀⠀⢀⠈⠉⠁⠀⢠⣿⣣⣿⣶⠀⠀⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⢰⢰⡟⠀⠀⠀⠀⠀⢀⡀⠀⢰⡏⠁⠀⠀⢀⣴⣳⠟⣠⡟⠀⠀⠀⠀⠀⠈⠘⠒⠲⣤⣾⠀⢻⣿⡏⢀⠀⡘⣿⣏⣭⡿⠀⠀⠀⠀⠀⠀⠀⢿⣦⣶⡟⣋⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠈⣾⡇⠀⠀⠀⠀⠀⠈⣧⣠⡞⠻⢦⣤⠶⠛⠉⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣬⣤⣤⠴⠶⠷⠟⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⢟⣷⠀⠀⠀⠀⠀⠀⢹⣏⠀⠀⠀⣿⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠤⠴⠞⠁⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠰⠄⢻⣦⡀⠀⠀⣀⡴⠛⢿⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠉⠉⠁⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⠀⢀⣾⣣⣴⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠻⠛⠛⠛⠉⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⣤⣴⡟⠛⠉⠁⠀⠀⢀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣉⣿⠛⠉⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣦⣭⡶⠚⣿⠃⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢸⡇⢀⣴⢾⣿⢿⣦⣀⠀⡼ ⢀⡀⠀⠀⠀⡀⣴⠟⠁⠀⡼⠀⠛⠀⠿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⠈⡇⠀⠀⠀⠀⣼⡷⠋⣠⠾⠻⣧⣄⣉⠙⠓ ⠀⠀⠀⠀⠀⠀⣿⣠⣤⠞⠁⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⣧⠀⠀⠀⠀⣿⣴⠞⠋⠀⠀⠀⠉⠙⠛⠛ ⠀⠀⠀⢀⣀⣠⣿⣀⣀⠀⠀⣀⠙⡆⠀⢰⡀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣾⢁⣴⢿⠀⠀⠀⣠⣏⠻⠶⢦⣄⣀⣀⣀⠀⠀⠀ ⠀⣶⠟⠛⠛⠛⠲⢤⣍⠉⠁⠈⠻⢿⠀⢀⣿⣦⣜⣿⣄⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠛⠲⣤⣀⠀⠀⠀⠀⠀⣧⣀⠀⢀⣀⣿⢿⣿⣿⣿⠛⠟⢻⡟⠛⠶⠦⢤⣤⣤⣈⣉⠉⠀ ⣼⠃⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⢸⣿⣋⣁⣈⣉⣈⣛⣷⣤⣤⡟⠁⠀⠀⠀⠀⠀⠀⣠⡶⣿⣹⡻⣦⣤⣤⣴⣿⡟⠟⣻⣻⣿⣾⣼⣿⣿⣇⣶⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⠻⣷⣄⠀⠀⠀⠀⠀⠀⢠⣇⣠⡾⠟⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠗⠶⢦⣤⣤⣄⣠⣿⣁⣉⣛⣻⣿⣿⡟⠛⠛⢿⣦⣼⣿⠛⠛⠛⠛⠛⠛⢛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠓⠶⠶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠁⠀⠀⠠⠙⠿⠏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣇⠀⠀⠀⣼⠟⣧⣠⠴⢶⣺⣯⣭⣭⣿⡿⠥⢤⣌⣉⠉⠉⠙⠳⠦⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⠘⢦⣀⣠⣏⣙⣿⣾⠿⠿⠟⠛⠛⠛⠛⠛⠳⠶⠦⣍⣙⢳⣦⣄⢠⡾⠻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣿⣿⣄⣶⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠉⡻⣿⣿⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠖⠋⣡⠖⠋⠀⠀⡰⣴⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢁⣻⣤⠴⠂⢀⠀⠙⣿⠻⡄⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢀⠞⢁⠀⠀⠀⠀⢿⣳⣷⠞⠛⠳⣦⠀⠀⠀⣀⣤⢖⡋⢁⣤⠞⠋⠉⠹⣷⣦⣞⣠⠀⢹⡄⢻⡄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡺⢋⡤⠖⠚⠉⣹⠟⠛⠒⠒⣶⣾⣿⡟⠉⠁⠀⢠⡟⠉⠀⠀⠀⣠⡞⣿⣿⣿⡴⠂⢸⡇⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡟⠉⠀⠀⠀⢰⠋⠀⠀⠀⣴⢃⣾⣿⠃⠀⠀⢠⡏⠀⠀⠀⠀⢰⠏⢰⣿⣿⣿⢉⡟⢹⣷⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⣠⡏⠀⠀⠀⢰⠇⣼⣿⡏⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⡞⠀⢸⡟⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡇⠀⠀⠀⠘⣇⢻⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⠀⢸⣿⣿⠃⡇⠀⢸⡇⣾⠇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠞⢧⡀⠀⠀⠀⢈⢟⣁⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠘⢧⣈⣿⠏⠀⢳⡀⣼⣧⣿⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣴⠏⠀⢠⢾⠁⠢⣤⠙⠲⠖⠚⠁⠰⠋⠳⠀⠀⠀⠀⠙⠳⠤⣄⣀⣀⡤⠟⠁⠀⠀⠘⢷⣿⣿⣟⣖⢶⣆⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠚⣫⠀⠀⣾⠀⣤⠴⠋⠀⠀⣠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⣤⠤⡀⠀⠀⠀⠈⢁⡼⠋⠙⡇⢿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⣶⠇⠀⠀⠀⢀⣼⣥⣄⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⠀⠀⡝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡾⠃⠀⠀⠀⠀⠀⠀⣠⡟⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣀⣸⣷⡛⢿⡾⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⣄⣈⣁⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⣰⢟⣵⣾⣿⣿⡿⣏⡉⠙⠳⢦⡈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⣿⢿⣿⣟⠇⢰⣿⣷⣝⣆⠀⠀⠙⣦⡀⠀⠀⠉⠛⠓⠲⠦⢤⣤⠤⠤⢤⣶⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⣟⠛⠛⠀⠈⠛⠛⠻⣼⡆⠀⠀⠈⣧⠀⠀⠀⣴⠟⢹⠏⠙⣷⠴⠞⠋⣨⠏⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢍⡀⠒⠺⣿⣸⣿⡆⠀⠀⠀⢺⢿⣷⣇⡇⠀⠀⢀⣿⣀⠤⠾⢧⣤⠘⣲⣋⠉⠳⠶⠞⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⢹⡦⠀⠘⣯⣻⣑⣮⣶⣄⣈⣿⣟⡼⠃⢠⡞⠉⠉⣀⣠⣴⣫⣯⢞⡅⣈⡇⠀⣰⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠈⠳⢦⣀⠘⠳⣽⡛⠛⠛⣻⣿⠞⠁⣠⠏⠀⠀⢈⣩⡧⣼⣿⡏⠀⠙⠙⡇⣠⢧⣄⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⠋⠻⣯⣈⠙⢻⣿⣿⠖⠒⠋⠥⡴⠖⠚⠉⠉⣹⠋⡟⢳⣤⣄⡼⢿⣿⡼⢯⣽⠗⢲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠄⢀⡤⠀⠀⠉⢉⡿⢿⣿⠓⠲⠾⣍⠁⠀⠀⠀⣴⠃⢀⡇⠀⠀⠀⠀⠈⣿⠁⠀⠈⢳⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠀⠀⣸⠓⣲⠃⠀⠀⠀⠸⡆⠀⠀⡼⠁⣠⠞⠓⠶⠤⣄⣀⣰⠃⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⢈⡇⠀⠀⣟⠒⡳⠀⠀⠀⠀⠀⠻⠦⠼⠧⠼⣇⣀⣀⣀⣀⣀⣠⠇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⣰⡟⠓⠓⠦⢤⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⢀⡞⠀⠀⠀⡏⠀⠈⠒⠒⢦⣿⢹⣆⣩⣽⠒⠦⠤⢤⣀⣀⣀⠀⠀⠀⠀⣠⠏⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡁⠀⠀⠈⠀⠀⢀⣷⠏⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣄⣀⡀⠀⣦⡿⠉⠀⠀⢀⠠⠒⠊⠉⠉⠉⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠶⣦⣀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠁⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⣄⣀⡀⠙⠶⢦⣀⠀⠉⠻⣦⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠳⣄⠀⠀⠙⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡇⠀⠀⠀⠀⠀⠀⠈⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠄⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠒⠒⠒⠒⠒⠲⢤⡄⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠛⠉⠐⢀⣤⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣴⠟⠹⣇⠀⠀⠀⢠⣸⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣦⣴⣶⣶⠶⢤⣀⡄⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠁⠀⠀⠻⣦⣠⡶⠟⠉⠀⠀⡀⠀⠀⠀⠀⠀⢀⣶⡾⢿⣿⣿⣼⣿⣧⡴⠋⠀⠀⠀⢠⠁⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣷⡄⠀⠀⠈⠻⢿⣿⣇⠀⠀⠀⠀⠸⢧⣀⠀⠀⠘⢧⡀⠀⠀⣀⡤⠽⣦⡀⠀⠀⠀⠀⠀⠀⠳⣽⡿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⠉⠓⠒⠒⠀⠙⣶⣶⡿⣿⣿⣿⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣤⣤⣠⣤⣤⣀⠀⠀⠀⠙⣦⣽⣿⣿⣿⣤⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⡇⠐⠀⠀⠀⠀⠂⢋⠰⣿⣿⣿⣿⣿⠀⠀⠙⢧⠀⠀⠀⣇⠀⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣿⣿⣤⣤⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢳⡀⠀⢸⡄⠀⠀⠀⠀⠸⣧⡀⣸⡿⠇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⡇⠀⡞⠉⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠇⢷⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⣴⠾⢛⡇⠀⠀⠀⠀⠀⣰⠃⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⡇⠀⡇⠀⡇⠀⢠⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⡀⠀⠀⠀⠀⢠⣤⡾⠛⠋⠁⣠⣾⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⠟⡇⠀⡇⠀⡇⠀⡇⠀⠸⣆⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠙⢦⣀⠀⠀⠀⠙⠻⢶⣶⡾⠟⠉⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣄⣀⣠⣾⣿⣆⣠⣼⣿⣿⠀⣇⠀⣿⠀⠇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⢿⡛⠛⠦⠤⠤⠤⠤⠤⠬⠤⠤⠤⠤⠶⠦⢤⣀⠀⠀⠀⠈⠙⠓⠦⢤⣀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠈⣳⣀⣤⡤⠴⠚⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠙⠲⢦⣀⣀⣠⠤⠾⠷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠚⠢⣄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⢠⠟⢄⠙⠳⢤⡀⠀⠀⠀⠀⢠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠛⣦⡀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⠀⢀⣤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⢸⠀⠀⠀⣟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⣦⡀⠀⢻⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢶⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⡀⠀⢰⠀⠀⠀⠀⣠⡾⣇⡀⠀⠠⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⠙⠛⠀⠀⠀⠛⠛⠶⠟⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⣠⣽⣤⣄⣀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡿⠀⠀⢦⡀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣧⠠⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⣿⠁⠀⠀⠀ ⠀⠀⠀⣾⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⠛⠲⢦⣀⠀⠀⠀⠀⢠⠤⠤⢤⠀⠀⠀⢀⡾⠁⠀⠟⠦⣄⠀⠀ ⠀⠀⢠⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⢸⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠓⠲⣤⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⡼⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⢰⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⣼⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏ ⢀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⣀⣤⢾⣍⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⢻⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠈⠙⠛⠒⠒⠒⠚⠛⠉⠀⠀⠀⠸⡄⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠁⠀⠀⠀ ⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡧⠀⠀⠀⠀ ⠀⠀⠀⡾⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣦⣤⣤⣤⣤⡴⠖⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⡀⣸⠇⠀⢀⡆⠀⠀⠀⠀⠀⠀⣀⡼⠇⠃⠀⠀⠀⠀⠛⠦⣤⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠓⠚⠓⠚⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠉⠛⠲⠦⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⢤⣤⢿⣤⣄⣀⡀⠀⠀⠀⢸⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⣀⣤⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣼⣇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣦⡀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡁⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⣿⠋⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢿⣿⣿⣍⠉⠉⣿⡞⠻⣦⡀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠻⣿⣿⣷⣀⣸⡇⠀⠙⠿⣿⡿⠇⣀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠙⢿⣿⣿⣿⠇⢰⣿⣦⡤⠀⠀⠈⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠉⠉⠉⠀⠛⠋⠁⠀⣸⣶⠴⢶⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⣇⣀⣤⣿⣿⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠁⠀⠀⠀⠙⣷⡴⠞⠋⠉⣿⣿⣿⣿⣿⡇⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠈⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⢿⢿⡿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣸⣃⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣛⣛⣻⣿⣇⠈⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⢀⣠⣄⠸⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣷⠀⠀⣠⣤⡀⢀⣤⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⣿⣞⠃⣿⡉⣿⢣⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⠀⢸⠟⢿⣧⠸⢻⣿⣇⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣝⣘⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀⠀⢀⣸⣏⣴⣿⣃⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣄⣄⣀⣀⣀⣠⣀⣀⣀⣤⡀⠀⣀⣀⣀⣀⡀⢀⠀⢤⢠⡆⢤⣠⣤⡤⣤⡤⡴⠴⣤⡤⣤⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠃⠛⠛⠓⠓⠓⠛⠘⡛⠛⠚⠛⠛⠓⠘⠚⠓⠛⠃⠃⠀⠀⠚⠒⠛⠒⠛⠛⠓⠃⠓⠚⠚⠀⠘⠁⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣜⣷⣾⣛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠉⠛⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠸⣿⣦⠀⠀⠀⠀⠀⠀⣼⡿⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⢿⣦⡄⠀⢀⣠⣾⠟⠁⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣤⠿⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠠⣄⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢸⣷⡆⠀⢀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣦⣿⣧⠀⣿⣆⠈⢛⡀⠀⠀⢀⣠⣾⠋⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠉⠻⢿⣶⣿⣿⣶⣿⣿⣿⠷⠛⠋⢁⣼⠏⠀⠀⠀⠀⠀⢠⣾⡯⠿⠋⢹⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⡿⣿⣝⣸⣁⣙⣿⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣾⠓⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⣴⣏⣀⣀⣀⣀⣀⣀⠛⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⣀⠀⣶⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⢀⣴⢶⣦⣄ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢟⣭⣭⣭⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣾⣲⠟ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⣰⡟⢻⣿⣿⠟⢷⠼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠿⠿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣧⣾⣷⣬⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

🃜🃚🃖🃁🂭🂺