Rengoku Text Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠓⠀⠀⠀⠐⢈⠀⠒⠉⠉⠀⠀⠀⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⡀⠄⡆⠄⠒⠈⠀⠓⠲⢤⡤⠤⠄⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢁⠀⢀⡈⠀⠀⠀⠀⠀⢠⠀⠀⡨⡶⠒⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠀⠀⣀⡀⠘⣷⡀⠀⠀⠀⢀⣿⣤⣾⠃⠈⠛⠩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠈⠻⣷⣿⣷⣄⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⢸⠀⢀⣤⣄⣤⣀⠀⠀⠀⠐⠉⠀⠉⠙⠫⠀ ⢀⠔⠒⠀⠉⠁⠂⡃⠀⣀⣀⠠⡆⢠⡀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠂⠉⠉⠐⣇⠀⠀⠀⠀⢠⢴⡈⠑⠂⠤⠀⠀⠀⠀⣀⠠⠤⠐⠒⡶⠀⠀ ⠈⠀⠀⠀⠒⠂⠠⠈⣦⠀⠀⠀⠈⢞⡟⣦⠑⡄⢰⡂⠈⠁⣀⣠⣤⣤⣶⠃⠀⢠ ⠈⡄⠀⠀⠀⢠⠄⢠⡟⡆⠀⠀⠀⠀⠘⠙⣄⠀⠀⠻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠣⠀⠀⠐⠀⢀⠾⠕⢱⠀⠀⠀⠀⠒⠆⠨⠳⢄⡀⠈⠉⠁⠈⠀⠀⡀⠀⡠⠊ ⠀⠀⠐⢢⣄⡴⠫⡬⠨⠞⡀⠀⠀⠀⣠⢎⠃⠀⢸⠉⡗⠒⠠⣤⣖⠏⢀⡔⡁⠁

⠀⢻⣷⣦⣤⣄⡈⣿⣿⣿⣇⠘⢌⠲⢦⣤⡀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠄⠀⠀⠀⠀⢀⠾⠿⠿⠛⠃⠐⢊⣡⣾⣿⣿⠗⣤⠀⠀⠀⠀ ⡀⠀⠙⢿⣿⣿⣿⡛⢿⣿⣿⣄⠈⢂⠀⠀⠈⠓⢦⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣿⣿⣷⣞⣉⣦⣴⠞⠁ ⠘⣷⣶⣬⣿⣿⣿⣷⡄⠙⠂⠀⠙⠂⠑⣄⠀⠀⠀⠙⢄⣂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠿⠃⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⡿⠖⠒⠒⠂⠤⠀⣉⣛⣢⣤⣀⠈⢿⠃⠀⣠⣂⣠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣤⣤⡀⠀ ⠀⠀⠀⢬⣿⣯⡛⠋⠁⠀⠀⠀⣠⠖⢻⠁⠀⠀⠀⠀⠙⠛⠒⠉⠉⠀⠀⠀⠀⠀⠉⠉⡶⢶⠒⠒⠀⠀⣀⠀⠀⠠⢿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⠀⠘⢛⡿⠂⠀⡰⣶⠊⢁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠳⡄⠀⠀⠀⠉⠲⣿⣿⣿⣟⠛⠉⠠⡀ ⠀⠀⠀⠀⠀⢠⣢⡔⠋⢤⠃⠀⢸⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡼⠀⠀⢫⠀⠳⡀⠀⠀⡀⠙⠩⢭⠢⠄⠀⠀ ⠀⠀⠀⠀⠀⢉⡟⠀⠀⡜⠻⣶⣶⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣾⣡⣤⠔⠊⢣⠀⠑⣄⠀⠸⡿⣍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡟⠀⣀⢾⡇⠀⠈⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠟⠉⠀⠀⠀⠈⡇⠀⠘⢷⣄⡙⣌⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡵⠋⣀⠞⢻⢶⡶⠿⠷⠶⣭⣛⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣶⡶⢦⣤⣤⠔⢻⢻⠀⠀⠈⢷⢌⠙⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢀⣼⠇⢀⣼⡈⣧⠀⢀⣾⣭⡉⣿⡏⠇⠀⠀⠀⠀⠟⢻⢳⢿⢿⣀⡙⢄⠀⢠⣿⢀⡏⢸⠀⠀⠘⣜⡘⡄⠈⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠧⣴⠋⡟⣇⠻⣦⣀⠻⣟⣁⠍⣧⠀⠀⠀⠀⠀⠀⢠⡏⠘⢼⣙⡻⢇⣠⡿⠁⣾⠃⠸⡇⢰⡀⠹⡇⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠋⣩⠃⡼⡇⢸⠀⠈⠉⠉⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠉⠀⣾⠏⠀⣠⡇⠀⣇⡀⠹⣿⣇⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣁⡰⢡⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⠚⢡⣷⡀⠸⡟⠲⣛⠛⠷⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⢁⡴⡏⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⡏⠀⣾⡿⡗⢄⠘⣄⠀⠕⢄⠀⠙⢅ ⠀⠀⠀⠀⠀⣠⢊⣼⠁⢀⣼⡄⢣⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢼⠟⠀⡘⢸⡀⢷⡄⢏⠘⠓⠐⠨⣷⠀⠀ ⠀⠀⠀⠀⠈⢁⣼⠟⡆⢸⢛⡇⢸⣧⠀⠀⠀⠙⣷⢤⡀⠀⠀⠉⠀⠀⠠⡼⠋⠀⠀⠀⢀⡎⠀⢰⠁⢸⡇⠀⠈⡊⢦⡊⠣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⠃⣰⣟⢰⣾⣇⢸⠈⢷⡀⠀⠀⠈⠻⢄⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⣠⣾⠀⡄⢸⡄⢸⣿⡌⠢⠙⠢⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⣏⣴⣿⣿⣿⣿⣿⣧⡷⣸⣿⠦⣄⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⢀⣴⣿⠟⢹⠀⣧⠈⣷⣸⠉⠉⠑⢲⠤⣄⡉⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⡿⡆⠈⠳⢤⡀⠀⠀⠀⠀⢀⡤⠞⠋⠹⠃⣠⣾⣾⣿⣷⣼⣿⣧⣁⡔⠁⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⢀⡤⢿⣿⣿⣿⣿⣿⣿⣿⣇⢸⢁⣧⠀⠀⠈⢏⠓⠲⠖⠊⠉⠀⠀⣠⠔⣺⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠂⠁⠀⢸⡏⣹⣿⡿⣿⣿⢿⡟⡇⢘⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣼⣵⠞⢁⣿⣿⣿⣿⡿⠁⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠻⣿⠀⠹⣿⢈⣷⠁⢸⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⠀⣼⣿⣿⢋⡟⠁⠀⠀⢡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢊⡽⠀⣹⠆⠀⠘⢿⠋⠘⢸⠀⠀⡇⠀⠀⢀⣠⣾⠟⠁⠀⠀⡠⠊⠈⢿⠏⠉⠃⠀⢰⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡐⢿⠀⣰⡃⠀⠀⢰⠸⠀⠇⠀⡇⠀⢱⡠⠖⣩⠞⠁⠀⠀⠀⠈⠀⠀⢠⣿⠀⠀⠀⠀⡎⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣽⣿⣷⣈⠲⡠⢌⡦⠀⠀⠀⠀⠀⠀⠀⠀⠤⢈⡓⠠⢄⡀⠐⠶⢿⣿⣿⣥⣴ ⣶⣿⣛⡃⠀⣛⡥⠔⠂⠀⠀⠀⠀⠀⠀⠀⢐⠋⠁⠈⠲⡈⠒⠤⡈⠶⣾⡿⠟⠁ ⠙⢻⣿⡫⣸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠈⢄⢆⠻⢆⠰⣾⠄⡀ ⠚⠛⠛⠟⢑⠳⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣶⣶⠶⠋⠀⠀⠈⡞⠀⠀⢅⠈⠳⣄ ⠀⠀⠊⢡⢺⣄⣧⣤⡀⠀⠀⠀⢠⠟⢋⣡⠴⠶⠶⢶⠖⠁⠀⠇⢰⠀⢪⣙⠉⢍ ⠀⠄⠀⢸⠸⣌⡹⢯⣽⡄⠀⠀⢣⠎⡾⣹⣦⠑⠀⡘⠀⢀⠌⠀⣼⠀⢸⠀⠈⡆ ⠀⠀⠠⠊⡴⣯⡄⢶⡎⢿⠀⠀⠀⠘⠌⠊⠭⠤⠊⡀⠔⠁⢀⠜⡞⠄⢸⠀⠀⡇ ⠀⠀⠀⠀⠑⠯⡌⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡏⢠⢉⠀⢠⠄⢠⠁ ⠀⠀⠀⡤⢀⠆⡇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠠⠁⢸⠀⡎⡱⡁⠀ ⠘⠀⢨⣾⡷⠘⠹⡀⠀⢠⠐⣀⣀⣀⣀⡠⠂⠀⠀⠀⣼⣵⠃⣸⢸⣤⡇⠀⡇⠀ ⠀⠀⣰⣿⡞⣰⢠⢱⣄⠀⠹⣟⢛⡩⠟⠀⠀⠀⠀⢸⣿⢽⣸⣿⣼⣿⣦⡀⠘⠀ ⠀⢰⡿⣿⣱⣿⣤⣾⣎⠢⡀⠀⠀⠠⠀⠀⠀⣀⠔⠻⠀⢸⣿⠻⣿⠃⢻⠛⠀⠀ ⠒⠛⠂⣻⡟⢿⣿⠟⣿⡄⣯⡓⣤⣤⡤⠖⠋⠀⠄⠐⠀⠊⡸⢸⡟⢔⠀⢇⠀⠈ ⠀⠀⠐⣬⣀⣞⡝⡰⠏⡰⢙⣧⠀⠀⠀⡤⣤⣤⣴⣶⣶⣶⣇⡎⢀⢲⡇⢸⡀⠀ ⠀⠀⣰⣶⣿⣿⣼⡇⣦⠗⠁⣻⠀⠀⠀⣽⢻⡿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣧⠹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⠾⠿⡟⢧⡄⠀⠀⢘⣷⡀⠀⠀⢸⡃⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡇⠀⢷⣤⡀⠀⢻⣿⣶⣤⣼⣷⣼⡟⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠏⢱⡀⠀⢳⣄⠈⣿⣿⣷⣾⢿⣿⡝⢿⣿⡇⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠓⠤⢄⣠⠎⠀⢠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢮⡁⠀⠀⣉⠶⢾⣻⣷⣼⡟⠛⠛⠂⠉⠃⠄⠈⠓⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠈⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⡞⠁⠀⢀⠹⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⠓⠉⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢻⡉⠉⠁⠀⠀⠀⠀⣀⣣⣀⠀⠀⠱⡀⠀⢳⠀⠀⠀⢀⡀⠤⠤⠤⠄⣀⡀⣀⠠⢈⡧⠤⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡉⠒⢤⣀⣀⠴⠊⡉⠀⠀⠉⠁⠀⠈⠢⣼⣀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⣾⣶⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣡⢀⡴⠊⡼⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣺⡥⠋⣠⡞⠀⢳⣄⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⢤⣶⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢄⣠⣤⡏⣉⡡⠿⠛⠁⠀⣻⡅⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠀⠙⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠊⠀⠀⣭⠶⠤⠀⠀⢀⣠⠛⡿⢦⣄⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡝⠒⠀⠀⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠈⠉⡶⢤⡤⠊⡝⢰⠃⢀⣈⢿⣮⡻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠀⢣⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⡤⠤⠒⠋⢀⡜⢁⠞⡇⢿⠀⡏⠀⠀⠘⢷⣽⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣯⣤⣠⠤⠾⠇⠈⡿⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣌⣙⣓⣒⡩⠔⠁⢸⠀⠘⢦⣵⡀⠀⠀⢸⠋⠀⠀⠀⠀⠴⢟⣛⣛⣛⣋⡉⠉⠉⠀⠀⢀⠃⠀⠀⡟⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠃⠀⢀⡟⠀⠀⠀⠀⠈⠑⠦⠞⠀⠀⠀⠀⠀⢨⠟⡋⠉⠉⢫⡙⠓⢦⣤⣤⡾⠀⠀⠀⡇⠀⡇⠘⡄⠀⠀⠀ ⣆⠀⠀⣀⢬⣶⣿⣟⣭⡾⢀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⡀⢀⣠⠇⣠⠞⢁⢾⣧⠀⠀⡗⠼⣦⢷⡰⢃⠀⠀⠀ ⠈⢶⡽⠚⢉⣉⣹⣿⣿⣷⣾⣿⡇⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⠤⠤⠞⠉⢠⠋⢸⠁⠑⢢⣝⣄⣘⣦⣝⣾⠀⠀⠀ ⠀⠘⠆⠈⠀⢸⣿⢻⣿⣿⣿⡿⣇⢹⠀⠀⠀⠸⣇⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠘⠀⠀⢰⠻⡄⠀⠈⠑⣼⠀⠀⠀ ⡠⠀⠀⠀⠀⢸⣇⣾⡿⠛⠁⡇⢈⣿⣇⠀⠀⠀⡟⢏⠒⠤⢄⣀⣹⠃⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⣇⠀⠀⢣⣄⣙⣆⠀⣰⠃⠀⠀⠀ ⠀⠳⠴⠧⠔⠚⠋⠁⠀⠀⠀⢧⠼⡿⡏⢧⠀⠀⠘⢄⣉⢒⠊⠽⠃⠀⠀⠀⠀⢀⣠⣾⣳⠀⢠⡀⠐⠼⢦⠀⣤⡹⢤⣀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣰⠁⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠉⢠⣯⣿⠀⣾⣧⡈⠀⠀⢁⠹⡝⠢⢍⣉⠙⠒⠢⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠓⠲⠒⠒⠋⠉⣩⣿⣿⠋⠀⢀⣾⣿⣿⣦⣿⣧⠹⡗⠂⠀⡇⠈⣟⠉⠉⠉⠁⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡞⠁⠀⢀⣾⢿⣿⣿⣿⣿⡏⠁⠘⣄⢀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠀⠀⡠⠔⠁⡴⠋⠀⠀⠔⠁⣇⣾⡿⠟⠁⣿⠃⠀⠀⠈⠣⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣠⠔⠋⢀⡤⠊⠀⠀⢀⣀⣤⣾⡏⠁⠀⢀⠀⢫⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⢧⣿⣿⣯⣑⠓⠚⠂⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠐⠉⣩⣾⣿⣻ ⣿⢻⣧⣿⣶⠄⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠢⠀⠀⠉⢙⣛⣽⡿ ⢻⣣⢛⣋⡁⣀⢀⢠⠂⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⢄⠽⡿⠻⢿⣿ ⡳⠑⡣⢫⢆⠄⠁⡷⣄⣀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⡠⠂⢋⠉⠀⣀⣹ ⠈⠀⠀⡙⡙⠀⠠⡇⠈⠛⠿⣿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠟⠋⢀⠄⠈⠢⠷⠽⢿ ⠀⠀⢈⣡⡃⠀⠎⢋⢳⠒⠲⠤⣉⠻⣆⠀⠀⡰⢟⡩⠖⠒⠺⢹⢸⡓⠲⣔⣶⣿ ⠀⠀⢀⣴⠊⢇⠸⠘⠈⠣⢐⡄⡠⣑⡎⠀⠀⢢⣛⠄⣠⡄⠋⠘⠆⢃⠀⡙⠻⣿ ⠀⠀⠀⠀⠑⢜⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢶⣬⣻⣿ ⠀⠀⠀⠀⠀⠀⠡⢠⢨⡄⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⠀⡸⣼⡀⣷⣖⢈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⢇⣿⣴⢄⠀⠰⠓⢆⠀⠀⠲⢻⠀⠀⡰⡃⢍⣿⣿⣿⣷⡕⠷ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠄⡳⣄⠈⠐⠒⠒⠀⠁⡠⢊⠏⡇⠀⡝⣿⢿⣿⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣷⣌⡙⠻⠦⣤⣤⡴⠟⢐⣡⣴⠁⠀⢠⡿⠀⠛⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⣿⣿⣿⣿⣷⣶⡄⠃⣴⣾⣿⣿⣿⠀⢴⢋⠀⢠⠂⡇⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⡯⠃⠙⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡄⠸⡾⢠⠛⠀⠁⠀ ⠀⠀⠀⠀⡠⠊⠪⠂⠤⠀⠀⠈⢿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠐⢳⠛⡟⢆⠀⠸⣦⡀⢸⣀⣤⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠹⡀⢳⡈⢿⣶⡿⣯⠿⣏⠣⡀⠀⠀⠀⠀⠀⠚⠃⣤⠄⠀⡄⠀⠀ ⠀⠀⠀⠈⠢⡠⠊⠑⢿⡿⡌⠁⠀⠁⠈⢀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢑⠤⢳⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⢈⠫⣉⠀⢀⠠⠑⠤⠈⠢⣸⠀⡠⠄⠒⠒⠀⠄⠐⣔⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢂⢍⠔⠽⠁⢸⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠺⠿⠿⠀⠀ ⠀⠀⠀⣀⣀⣐⣺⠟⠁⣞⠀⢳⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢿⠃⠀⠀ ⠀⠀⠐⠁⠐⠷⣂⢀⢤⢹⠓⢬⡻⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀⢉⢀⡠⠂⠀⠀⠀ ⠀⠀⠀⠤⣄⠒⡡⡡⡊⠆⡎⠉⠹⡽⠀⠀⠀⣠⣴⣶⣶⡯⠤⢰⠎⠒⢄⠀⠀⠀ ⠀⠀⠀⠀⣚⣲⠎⢀⠇⠈⠛⠢⠤⠀⠀⠀⢈⠟⠒⢒⠦⢀⣀⠆⠀⡄⢸⢃⠀⠀ ⢂⣠⡰⠿⣯⣾⣰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡄⢔⡰⢁⢺⠆⡸⡚⢞⢌⡀⠀ ⠀⠇⠀⣽⢿⣿⣿⢇⡆⠀⢸⣅⠒⠠⢀⠀⠀⠀⠀⠀⡠⠁⠘⠀⡘⠍⠉⢫⠀⠀ ⠠⠠⠠⠽⠛⠁⠸⣰⠟⡄⠀⢌⠨⣔⠞⠀⠀⠀⣠⣮⢀⠀⢥⡀⣙⣖⡢⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢞⠀⠈⠦⣀⣀⠀⠤⣤⡶⠉⣼⣦⢸⡧⡄⠈⠙⠴⠭⠭⠐⢄ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⡀⢜⠏⠀⢰⣿⣿⢿⠑⠑⡀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠄⢊⠔⠁⠀⣁⡖⠋⢁⢸⠀⠀⠈⢲⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⠿⠒⠀⠄⠀⠶⣆⠀⠀⠀⠀⠀⠟⠁⠻⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠠⢄⣀⣠⠔⠊⠀⠀⠀⠀⠈⢤⣠⣤⡙⠓⠀⠀⠒⣀⣴⣾⠟⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⢢⣔⠠⠈⣕⠦⠤⠀⠀⠀⡀⠀⢻⠫⣍⣶⣍⣻⣿⣿⣷⡿⢀⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣠⡔⠈⢻⡓⠂⢺⡧⡀⣀⣀⡀⠁⢀⡌⠢⡀⠿⢿⣿⡿⠟⠉⠠⡴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⣠⣾⠋⠀⠀⠈⢷⠶⡄⢳⠊⣠⠀⠉⢢⡀⢏⠁⠀⠀⠈⠉⢀⠀⠀⠔⠀⠀⠀⠀ ⣆⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⢠⠄⠰⣧⢸⠙⣤⣏⣏⣧⠀⣷⠬⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣷⣄⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠁⠀⣠⣴⡶⣿⠀⠀⢘⠾⠀⣇⠸⠀⡸⠀⡟⠠⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠈⢿⣿⣿⣿⣷⣤⣀⠀⢀⠀⠀⠀⣇⠟⠉⠀⢔⡷⡟⣉⣨⣝⣿⠀⠀⣾⠀⠇⣿⡶⠚⠁⡜⠙⠢⢌⣏⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⡠⠌⠉⠉⠉⠉⡙⠓⢦⡣⠀⠐⠃⠀⠀⠂⡞⠀⢇⠛⢋⡼⠋⠀⢸⣸⢠⡀⢸⣷⣀⣼⡓⠒⠤⢄⣠⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⣿⡙⢾⡟⠛⠻⠛⠿⣵⣤⠈⠀⠀⠀⠀⠘⠀⣇⢀⣀⡽⠋⠁⠀⠀⢸⠃⡆⠑⣄⣏⡙⢺⣇⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣽⠻⣆⠳⣄⠠⡀⣿⡋⢹⣄⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠸⣸⡱⠐⡄⠙⢇⣸⣿⡀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣌⣻⢣⡐⠛⠻⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡁⠀⠈⠂⠀⣬⣙⣳⢄⠀⠀⣀⣀⠀⠈⢻⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⡷⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⣦⡳⣤⣀⣳⣿⣿⣾⣿⣿⣿⣿⣿⡓⠂⢣⠙⢦⡀⠀⠀ ⡿⠿⠋⡼⠀⠈⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⣠⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⡄⠀⢣⠀⠉⠀⠀ ⡴⣷⠀⣧⡆⢠⣇⡌⠑⢄⡀⠀⠀⠀⠒⠒⠒⠒⠉⠀⠀⠀⠀⠀⢀⡜⢁⠇⢀⠜⢻⣯⣿⣿⣿⣿⣮⣝⣻⣏⠣⠀⠈⣵⡀⠀⢣⠀⠀⠈ ⣠⣾⣠⣿⣷⣸⢹⢇⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡟⠀⡸⠞⠁⣠⣾⣿⣿⣿⣿⣿⡇⠈⢻⠉⣶⠀⠀⣸⡇⠀⠈⢇⠀⠀ ⣼⣿⣿⣗⣿⡟⠈⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⡤⣀⣀⡤⠖⢡⡬⠔⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣧⡟⣰⡿⠋⠀⠀⠀⠈⠀⠀ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣉⡛⢅⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⠋⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣿⣿⣿⡜⢿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠏⢉⠙⠿⠛⠻⠟⣿⡿⠿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠀⠠⣾⣿⣿⣉⠁⡀⠠⣄⣨⣻⣷⠁⠀⢀⢀⣾⡿⣿⣿⣿⠟⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣿⣿⣿⠀⢠⣼⣿⣿⣿⡷⢿⠐⢾⣿⣿⣿⣾⠕⠘⢻⣿⣷⣿⣿⣧⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣧⡈⢉⠙⢀⠀⢈⢿⣿⡿⢁⠄⠀⠋⠝⠋⢡⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷⠀⢿⣿⣿⣿⣿⣿⡿⠍⣈⣳⣦⣽⣾⣿⣿⣷⣿⣧⣶⣟⡀⠀⣻⣿⡿⢛⣻⣿⣿⣿⣿⡗⢾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣤⣾⣿⣿⠟⡻⠿⠉⢀⠟⠻⠙⠛⠿⣿⣿⣿⡿⠟⠛⠟⠓⣄⡉⢻⡗⢉⣿⣿⣿⣿⣿⠆⣼⣿⣿⣷⣤⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⠀⣀⣸⣿⣿⢿⣿⡏⠹⣿⣿⣿⡮⣥⢄⡯⣀⢠⡀⠀⠀⠀⠈⠀⠀⠀⢠⣆⣀⠼⣉⢵⣿⣆⣙⣛⡛⠛⣁⡤⢾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⠻⣿⣆⠉⠓⠀⢒⣶⣶⣮⡅⠛⠇⢌⣿⣿⣧⡀⠀⠀⠀⢀⣴⣿⣿⣧⠀⡙⣿⣿⣝⡿⣭⣥⠬⠀⠠⣤⣽⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⠀⢝⡛⠓⠈⣽⣿⣿⣿⣿⣷⣿⡦⠈⠣⢻⡟⣻⣆⠀⢀⣿⢿⣿⡡⠃⠀⠃⠹⣿⣿⣿⣶⣭⣉⠠⢤⣌⣻⣿⣿⡟⠋⠀⣀⣤⡀⠀ ⠀⠀⠀⣿⣿⣿⣆⠉⣙⣓⣀⣉⣉⣿⣿⣿⣿⣿⣿⣿⠇⠀⡆⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣴⣿⣿⣿⣛⣂⣀⣠⣭⠍⣀⣤⣾⣿⣿⣿⣿⣇⠀ ⠀⠀⠰⣿⣿⣿⣿⣷⠄⠙⢟⣛⣿⣿⣿⣿⣿⣿⡟⠁⢸⣤⣼⣄⠀⠀⠀⠘⠇⠀⠀⡀⠀⠀⣜⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣛⠛⠛⠿⣿⣿⣿⣿⡀ ⠀⣴⣾⣿⣿⣿⡿⠡⢴⣿⣿⣿⠿⠟⠛⣿⣿⠟⠂⠀⣾⣿⣿⣿⣦⡀⠀⠀⢐⡂⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠛⠿⣟⡻⣿⣿⣿⣿⣿⣿⡇ ⢠⣿⣿⣿⣿⣿⣷⣿⢆⠞⠋⠀⠀⢀⣴⣾⣥⣤⢀⣾⣿⣿⣿⣿⣧⣻⣷⣤⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢷⣄⠈⠻⡅⣉⣻⠿⠛⠉⠁ ⢸⣿⣿⣿⣿⣿⣷⣤⠂⠀⠀⢠⣾⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠉⠙⠿⠟⠛⠛⠉⠁⣀⠀⠉⠻⣿⣧⡀⠙⢦⠀⠈⢢⣄⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⣰⡟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣠⣶⣶⣶⡾⠁⠀⠀⣀⣠⡄⠘⠋⠀⣤⠀⠹⣿⣿⣄⠈⢣⠀⠀⢻⣷⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⠏⠀⠀⣼⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⢿⣿⣿⠥⠀⢀⣼⣿⣿⡇⠀⠀⠀⠁⢀⣀⢿⣿⣿⣦⠀⠡⡀⠀⢻⣧⠀⠀ ⠀⢿⣿⣿⣿⡿⠀⢀⣼⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠉⢁⠤⣴⠋⠀⠛⢁⠀⠀⣿⣄⣀⣠⡾⠿⣿⣟⡃⠀⠀⡀⠀⢸⢿⣿⣿⣿⣿⣇⠀⠱⣄⠈⣿⡀⠀ ⠀⠸⣿⣿⣿⠃⠀⣼⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣆⠀⠀⣸⢠⣴⡞⡍⠙⣿⣿⣿⣿⣏⡇⠀⠰⠀⠀⣀⣾⣿⣿⣿⣿⣿⣇⠀⠙⣦⠘⡇⠀ ⠀⠀⢻⣿⡟⠀⢠⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⡆⠁⠀⠀⠈⠀⢠⣿⡇⣿⣧⡇⠀⢸⣿⣿⣿⣿⡁⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⢷⠁⠀ ⠀⠀⠈⢿⠇⠀⡼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣦⣤⠀⠀⠀⠘⠛⠃⠛⠛⠛⠀⢉⣯⠉⠙⠛⣇⣀⣾⣧⣤⣿⠟⠉⠈⠙⠻⢿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⢠⠃⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⣀⡈⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⣤⣄⣀⣹⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣦⣐⡄⠀⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠻⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠅⢘⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⠀⠀⠀⢸⣿⣿⠿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⢿⣿⣿⣿⣷⣄⠈⠲⣤⣀⠀⠀⠀⠹⣷⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠱⣭⣄⡀⠀⠈⠉⠉⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⠟⠁⠀⢀⣠ ⠻⣶⣶⣾⣿⣿⣿⣿⣾⣅⡀⠈⠺⣍⠙⠲⣤⡱⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⠦⣤⣀⠀⠈⠙⠲⢦⣄⡀⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣈⣻⣿⣿⣿⣷⣤⠀⠈⠉⠳⠶⠶⢤⣀⢀⣉⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠷⠚⠉⠉⠳⢦⡀⠀⠐⢦⣉⠀⠀⠀⠀⢶⣤⣤⣄⣭⣽⣿⣿⣿⣿⡿⠋ ⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠉⣛⣒⣶⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠉⠛⠲⢤⡀⠐⠮⢿⣿⣿⣿⣿⠿⠛⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣟⣛⡅⠤⠴⣋⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠀⣀⣙⣦⡀⠀⠉⡛⠛⠲⠤⠀⡀⠀⠀ ⠈⠙⠛⢻⣿⣿⠟⣋⣤⠔⣮⣽⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠹⣄⠈⢧⠈⠙⠻⣿⣄⠀⠹⣷⡲⣦⡀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣫⣴⡾⢋⣽⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠙⢧⠈⡇⠀⠀⠀⠙⢧⡀⠹⣿⣦⡉⠙⠲⠄ ⠶⠿⠿⠿⠿⠿⢿⡿⠁⢠⢿⠇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⣦⡇⠀⠀⠀⢠⣀⠈⠀⠈⠻⣿⣆⡀⠀ ⠀⠀⠀⠀⠀⢀⣞⣁⠄⠀⡿⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢶⣤⣄⣀⣀⣈⣿⣦ ⠀⠀⠀⠀⠰⠛⠋⠁⣴⠇⣧⠀⠀⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠉⠁⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⠉⠀⠀⠀⡟⠀⠀⢠⠀⠀⠰⣌⠛⢷⡖⠒⠉⣍⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢶⣶⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⡀⢀⣴⣾⠟⠛⠋⠉⠉⠉⠉⠉⣹⡟⠀⠀⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⢻⣀⣶⣔⡒⠀⠘⢧ ⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠛⠛⢿⣿⡟⠿⣷⡄⠀⠀⠀⠀⠀⠀⣸⠃⣠⡼⢡⣾⣿⠊⣉⣉⡉⠳⢄⠀⠀⠀⣹⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣿⠀⠀⠀⢸⠃⠀⠈⠙⢦⡀⠀ ⠀⠀⠹⠀⠀⠀⠀⠀⣿⡀⢿⣧⣀⣴⠾⢛⣛⣷⣞⢿⣦⠀⠀⠀⠀⠀⠀⢸⡟⢁⣾⠏⠁⣾⡿⣻⣿⢘⡎⡆⠀⣠⠇⠀⠀⠀⢀⡰⠋⠀⠀⠀⣾⣿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⣿⢻⡅⠀⣀⣤⣌⠹⣿⢿⣦⠀⠀⠀⠀⠀⠘⠀⠐⡏⠀⢦⡻⣿⡿⣿⠘⠁⢃⡰⠋⠀⠀⢀⡠⠋⠀⠀⠀⠀⣼⢃⢹⢀⠀⠀⢸⠘⠓⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠠⠞⠁⢀⣼⡟⢹⣇⢧⠀⢹⣯⣿⡆⠙⣿⣿⠄⠀⠀⠀⠀⠀⠀⠘⠣⠄⠀⠑⠢⣤⣤⡦⠗⠋⠀⠀⣠⠴⠋⠀⠀⠀⠀⢀⡾⠋⣾⠘⣼⠀⠀⢸⡄⠀⢳⠀⠀⡇⠀ ⠀⠀⠀⠓⠀⠀⠀⠀⠚⣿⢀⣾⢿⠈⢧⡀⠙⠋⢁⠀⣼⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⣯⣁⣀⡀⠀⠀⣀⣠⠞⠀⢀⣿⢸⡇⠀⠀⡜⠇⠀⠸⠀⢠⡇⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⢻⢼⡇⠀⠉⠉⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡟⠀⠀⢸⠃⢸⡇⠀⠀⢧⣸⠀⠀⠀⡸⠁⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠠⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣼⡏⠀⢸⡇⠀⠀⣼⢧⡀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣾⠀⣿⠀⠀⠀⠀⠈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⠁⠀⡀⢸⡇⠀⢀⡇⠈⢳⡜⠁⠀⠀⠀ ⢀⣀⠀⠀⠀⢀⣠⠗⢉⣤⡾⠃⢠⣿⡆⠀⠀⠀⠀⠀⠹⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣴⠃⠀⢰⠁⢸⠃⠀⢸⡇⠴⠋⢹⣆⠀⠀⠀ ⠸⠿⠇⠀⠀⠈⢉⣴⣿⢋⡴⠋⡾⢹⣿⡀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⣾⡏⠀⠀⣿⠀⢸⠀⡇⣾⠁⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⢰⠁⡌⡏⢧⠀⠀⠀⠀⠘⣯⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣵⣿⣿⠀⠀⣼⣿⡀⢸⢸⣷⣿⠀⠀⠀⠀⠿⡀⠀⠀ ⠀⠀⠀⠀⠈⠀⣴⣿⢟⣴⠆⠀⣰⠇⠥⡜⣷⡀⠀⠀⠀⠈⢻⣿⡿⠿⠿⠿⠿⠿⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢻⡿⢰⣧⣿⣿⡇⣸⢻⣿⣍⡁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⣰⣿⡀⢰⠁⣏⢿⣄⠀⠀⠀⠀⠻⣦⡀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡶⢻⣧⣸⣿⣿⣿⣧⣽⣿⣿⣿⣾⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⠇⣰⣿⣿⡇⠘⣄⣿⣰⡝⢧⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡿⣿⣿⢀⣿⣿⣿⡇⢰⣿⣿⣷⣷⠀⠙⢦⡀⠀⠀⠀⠂⠈⠉⠴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⡿⠀⠀⠀⢸⣿⣿⡟⡁⢻⣿⣿⡟⡆⠀⢻⡄⠈⠉⠀⠀⠀⠀ ⠀⣀⣀⣿⣟⡁⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⢀⢱⡟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠉⠀⠀⠀⠇⡴⠁⠀⣸⡿⢻⡿⠀⣾⢿⣿⡇⢀⢸⠈⢷⠀⠀⠀⠀⠀⢄ ⠙⠛⠛⠛⠛⠙⠈⣿⣿⡿⣫⣿⣿⣿⣿⣿⠟⣻⣿⢠⡞⢸⣇⢴⠘⠳⢤⣀⣀⣀⣠⣤⣶⡿⠛⠉⠀⠀⠠⠤⠤⠤⠞⠓⠒⠲⠋⠀⢸⡇⠀⡏⣷⠹⣧⠈⡟⠀⠘⣧⠀⠀⠀⠀⠈ ⣄⡀⠀⠀⠀⡈⠀⢾⡿⠛⠉⢸⣿⣿⣿⡏⠀⡟⣿⡾⠀⣼⡏⣾⣦⠴⠖⠺⠿⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⡇⠘⠀⢨⠓⣧⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⣀⠃⠀⠀⣼⠟⢡⡟⠀⣰⢻⣿⠀⢠⠟⠁⢿⣇⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣠⣶⣶⣶⣶⣶⣶⣾⣿⣿⢠⣾⡇⠀⠀⡼⢰⣿⡆⠀⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠿⠷⣶⣼⣧⣶⣿⠀⣰⡏⠘⣽⢀⡞⠀⣠⡿⡷⣿⡀⠀⠀⠀⠀⠀⠸⣿⣀⣾⣿⣛⣻⣿⣿⣿⣳⣿⣿⣽⣿⣿⣿⣿⣿⠀⠀⣼⡇⣾⣿⣧⠀⡆⢿⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠃⣼⣿⠁⢠⡇⢸⣡⠞⠉⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣩⣿⢟⡿⣿⣩⡿⢿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣤⣷⢸⠀⡿⣄⠀ ⢀⠀⠀⠀⣠⣿⣿⡿⢻⣿⣿⣿⣇⣼⣿⣿⠀⣸⣿⠛⠁⠀⢀⣠⣶⣿⡇⠀⠀⠀⠀⠀⢘⣿⣀⣘⣿⣟⢛⣛⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠙⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠠⣤⣀⣀⡀⠀⠀⠈⠳⠆⠀⣀⣬⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠤⣀⠰⣄⠀⠀⠀⠳⣄⠀⠐⣄⠀⠀⢰⡀⠀⠀⠑⠄⠀⠀⢀⠙⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢙⣷⠀⠀⠀⠀⠈⠹⣷⣄⠀⠀⠀⠀⠚⠋⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣷⣄⡀⠀⠘⢶⡄⢻⣧⡀⠀⢷⠀⠀⠀⠀⢂⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⢀⡾⠟⠁⣰⠟⠁⠀⠀⢀⣠⠴⠚⠁⠉⣻⣶⣤⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠲⢦⣌⡳⣯⣑⢦⣈⠈⠳⢻⣷⡀⠸⣧⠀⠀⠀⠈⠀⠥⠄⠀⠀ ⢀⠀⠀⠀⠀⠈⠀⢀⡼⢁⣀⣤⡴⠚⢻⢤⡀⢀⡴⠛⠉⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣁⣤⣴⡾⠿⢗⠚⠛⠛⠋⠛⢿⣷⣽⣷⣄⠀⢿⡑⠀⠟⣧⠀⠀⠀⣄⣀⠠⠤⠀ ⡠⠂⠀⠀⠀⠀⣠⠟⠐⠋⢡⠞⠁⠀⠛⣄⠱⠫⠤⠤⠴⠚⠁⠀⠀⠀⣰⠂⠀⣸⠀⢰⡋⣂⣾⠿⠛⠁⠀⠀⠀⢷⡀⠀⠀⠀⢰⡏⢧⠉⠛⢿⣆⢧⠀⠸⢸⡆⠀⠀⠋⠁⠀⠀⠀ ⠠⠂⠀⣀⣤⡾⠋⠀⣠⣶⠏⠀⠀⠀⢠⡞⢧⠀⠀⠀⠀⠀⢀⣴⠁⣠⠇⠀⠀⣇⢀⣾⡿⠋⠁⠀⠠⡀⠀⠀⠀⠈⣿⣦⡀⠀⢸⡇⠈⠃⠀⠀⠉⠻⣦⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣟⣥⣶⣿⣿⡏⠀⠀⢀⡴⠋⠀⠀⠓⢤⠀⠀⡠⢾⠃⢠⠏⢠⠀⠀⢸⣾⠋⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢹⣿⣿⣶⣼⣿⡄⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢉⣾⣿⣿⣿⡿⠟⠁⠀⠀⣠⠞⠁⠀⡀⣀⡼⠋⡠⠎⠀⡼⣠⠟⠀⣸⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀ ⣠⠀⠉⠛⢷⠉⠠⠤⠤⠤⠞⠃⠀⡠⠾⠋⢁⡤⢊⣀⣀⡼⢡⠃⡜⠀⡏⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇⣿⠻⣿⠿⣦⣄⡻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⠷⡄⠀⠀⠀⠀⠀ ⠛⠦⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣹⣿⣿⠟⢁⣼⠀⠀⢰⡇⣽⡀⠀⠀⠈⢧⠀⠀⠀⠀⢷⡇⢀⣠⠬⣍⡛⢿⣮⡻⡝⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⠀⠀⠙⢦⣄⠀⠀⠀⠀⢀⣴⡞⢰⢾⡏⠋⡥⠒⢿⣿⠀⠀⣸⡇⠘⢧⡀⠀⠀⠈⢧⡀⠀⠀⠀⢳⢾⣾⣿⣿⣿⡆⠙⣧⠘⣄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⣳⠖⠂⢰⡾⠀⠃⣾⣀⠴⠀⣀⣾⣿⠀⠀⣿⣧⠀⠈⢳⣄⡀⠀⠀⠑⢦⡀⠀⠈⢿⣿⣭⣿⣿⡇⠀⢹⡇⣿⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣿⢇⠀⢡⣽⠃⠀⠀⢸⡁⢸⠀⠀⢹⣟⡇⠀⠀⣷⠉⠓⠶⠶⠦⠭⠷⠤⠈⠻⣟⡻⠝⠁⠀⢸⡇⡷⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠾⠤⠤⠴⠚⠉⠀⢸⡀⠀⠹⠧⠤⠤⠼⢷⡾⠀⠀⢸⠘⢧⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡞⠁⢻⡼⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣠⣴⠗⠀⠀⠘⡄⠈⢧⡀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⡾⢿⣿⣿⠀⢀⠀⠀ ⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢳⣄⠰⠊⠉⢠⠟⠀⣴⠀⠀⠁⠀⠀⣷⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣶⣍⠈⢀⡇⠀⠐⠑⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⣀⠈⠙⣲⡶⢋⣠⣾⣿⠀⢀⡇⠀⠀⠸⣦⡀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⢿⠋⣻⣷⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠛⣻⠟⠁⠀⠀⠀⠉⣿⣿⠿⢾⣿⠿⣿⣿⠀⣼⣇⠀⠀⠀⣿⣿⣆⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠋⣠⣿⠏⠀⠀⢹⠀⠀⠀ ⡩⠟⠁⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠻⢀⣿⡟⣰⣟⣿⣠⠀⢀⣿⢽⢿⣧⡀⣿⣿⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣵⠃⢀⠆⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⣸⠃⠀⠀⠀⠀⣣⡾⠃⠀⢩⣿⡿⣿⠀⣼⠻⣾⠀⢹⣷⣽⡿⠀⠀⠀⠙⠲⢤⣄⠀⠀⠀⠀⠀⠀⢀⣤⢖⣾⠋⢡⣿⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣶⣟⡉⠀⢨⣭⠿⠷⠿⢤⣄⡀⠀⢚⣻⡾⢿⣿⡋⠛⢷⣿⣿⠇⣸⡟⠲⣸⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣀⠀⠀⠼⠿⠟⠁⠀⣾⢻⠀⠘⢿⡄⠀⠀⠀⠈ ⠀⠀⠀⠚⠉⢁⣠⡽⠟⣡⡶⠶⠒⠒⠒⠀⠀⢉⣉⣉⠉⢉⣾⠟⠁⠀⠀⣿⣣⡾⠻⡇⠀⠿⠸⠃⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⡀⠈⠳⡄⠀⠀⠀⢀⣼⣧⠀⣷⠰⠖⠋⠀⠀⠀⠀ ⠀⡀⣠⣀⣾⠛⢉⣴⢟⣉⣤⡤⠤⢀⣠⡴⣾⡿⠋⠁⣠⠟⠁⠀⠀⠀⣼⠟⠋⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⠄⠀⠘⠀⠀⣠⠟⣿⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⢈⠀⠉⠉⢿⣆⢼⡿⠛⠙⣭⡴⠶⠛⢁⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣿⡄⠀⠸⡏⠳⠠⣤⠀⠀⠄ ⣿⣿⠆⠀⣸⣿⣼⠷⠚⠛⣿⡇⠀⢐⣿⠟⢀⣤⣠⣤⣶⣶⣶⣶⣿⣿⠿⠛⢦⣄⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠙⣿⡄⠀⢱⡀⠀⠙⢦⠀⠀ ⣽⣿⣷⣾⡿⠋⠀⢀⠀⠀⣻⡇⠀⣸⢏⡴⠯⣿⠟⠛⢿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠳⢦⡀⠙⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢩⢸⠀⠀⠀⠀⠀⠈⠳⣄⢸⣷⢦⣈⠂⠀⠀ ⣿⠿⠁⢽⠁⠀⠀⢹⣤⡾⢻⣇⠐⠏⠚⣡⡾⠁⠀⠀⠀⠙⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⢷⣌⠻⣿⠟⠙⠲⠦⣄⣀⣠⠾⠋⠀⢀⠸⠘⣧⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⢸⡄⠀ ⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠢⢻⣞⠄⣴⡟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠈⠛⢯⡀⠀⠀⠂⠀⠀⢸⠀⠀⠀⣾⠀⠀⠈⢧⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢹⢦⣄⠀⠀⠀⣸⠀⡀⢸⡿⡄⠀⠀⠈⡇⠀⠀⣴⡶⠛⠲⠶⠶⠶⠚⠁⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡞⠁⣿⠀⠀⠠⣿⠞⠀⠈⠁⠻⡄⠀⢠⠇⠀⣼⣯⣧⣤⣤⣤⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⢠⡾⢀⡾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡼⠀⣸⠟⠁⠀⠀⠀⠀⡇⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠘⢠⣾⡞⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡀⢀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠠⣙⠀⠹⠦⣜⠂⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⢀⠴⠋⢸

⠀⠀⠀⠀⠀⢄⣤⠟⠉⠁⠉⠳⣄⣤⣖⣒⠒⣒⣀⣀⣀⣀⣀⣀⣤⠤⢤⣶⠲⠤⢤⣤⣲⡀⠀⠀⠀⠐⢁⡤⠖⠒⠒⣀⡴⠂⠀⣾⣿⣿ ⠀⠀⣠⠖⠻⠋⢻⡛⠒⠒⠒⠊⢉⣀⡤⠜⠛⠁⢀⣩⢥⣤⠚⠉⠁⠀⠀⠙⢄⠀⠀⠈⠉⠻⢤⣄⢀⣠⠏⣠⠴⣾⠯⣍⠀⠀⠀⠀⠈⠉ ⠛⠊⠁⠀⠀⢰⡶⠳⣄⠀⠘⠯⣅⣀⠀⠀⠀⢒⣉⣴⠋⠁⢢⠀⠀⠀⠀⢰⠈⠇⠀⠀⠀⠀⠀⠉⠙⠛⠾⠧⢤⡈⠙⠢⣄⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⣰⠋⠀⠀⠈⣱⡶⢀⣨⠟⠃⠀⢒⡉⡽⠋⠀⠀⠀⢳⣦⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠶⡦⠄⠀⠀⠀⠚ ⠀⠀⠠⠚⠁⠉⠳⢶⣿⣷⠚⠋⠀⠀⣠⠞⢁⣾⠆⠀⠀⠀⠀⠀⠹⣿⣷⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡈⠂⠐⠢⣀⠚ ⠂⠀⠀⠀⠀⡠⠀⢀⡼⣟⠉⢉⣰⠟⠁⠀⣼⠃⠀⠀⢢⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡿⣤⣄⣀⣀⡭ ⠀⠀⢀⣤⠞⢠⠔⢫⠞⢁⣴⣿⡇⠀⠀⢰⡇⠀⠀⠀⠀⠙⡟⠛⣻⣷⣶⣽⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡗⡀⠙⣆⣀⠠ ⢀⣴⣿⠃⢐⡏⢰⠋⡹⠟⠛⢿⡷⢰⠸⠘⡇⠀⠀⠀⠀⢰⣧⣾⣿⣻⣿⡇⠙⣷⡳⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⢹⡁⠈⠻⣦ ⢋⡼⠃⣰⡿⠀⣮⡞⣵⠗⢢⣸⠃⢸⡆⡇⠘⢆⠀⠀⠀⠀⢹⣷⣙⣛⡻⠂⠀⠈⡷⢿⣇⠁⠀⠀⠀⢀⣴⣿⣿⡿⠛⢱⡑⣼⣿⡖⠛⠛ ⡛⠷⠚⠉⠤⠞⣿⠙⡅⢰⣯⣿⠀⠈⡧⠠⡀⠈⠑⠒⢤⣤⠄⠈⠓⠢⠤⠤⢀⣀⡇⠈⠛⠀⠀⠀⣠⣿⣿⣿⡟⠛⣶⣾⣿⣦⣼⣷⣄⠀ ⣿⣶⣤⡄⠀⣴⣧⠀⠀⡼⠀⡇⠀⠀⡇⠀⠈⢷⠒⣲⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠯⣛⡿⠁⡴⣻⣿⣽⣯⣿⣿⣄⣠ ⣿⣿⡟⠀⡼⢳⠉⢆⠈⠓⢾⠀⠀⠀⢹⡀⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢕⠒⠒⠊⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠉⢠⠞⠁⡼⣠⠊⢳⡤⠃⡠⣶⠀⠘⡿⣆⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⠀⣸⠹⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⠀⠀⢃⣇⣠⣾⠛⡷⣤⡇⡄⠀⡇⠈⠱⡄⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⢠⣿⣇⠙⠿⠛⢋⣽⣿⣿ ⣠⡆⠁⢀⣠⢼⡿⠋⢁⣼⣶⠛⣷⣇⢸⡄⠀⠸⣦⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⣀⣀⠀⠀⠀⢀⣾⡇⣀⣁⣀⣤⣾⣿⣿⣿ ⠀⠉⣉⣉⢤⣊⡤⠖⣻⣿⣧⠀⢿⡻⣾⡻⣆⠀⡏⢳⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⣠⣾⡏⠃⠸⣿⣿⣿⣿⣿⣿⣿ ⠶⠤⠉⠛⠋⠁⢀⣠⢟⡝⠹⣦⣾⣷⡙⣧⠈⢷⠇⣿⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⣾⣿⠃⠻⢄⠀⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢰⢋⡗⠋⢠⣶⠟⡿⣏⣻⣿⣧⡀⠀⣿⣿⣿⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢳⡏⠀⠀⢸⣷⣄⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⢸⢀⣴⣿⣥⣀⣿⢯⢿⣿⡟⣷⣶⡏⢿⠻⠤⠤⣀⣉⠻⢷⣦⣀⣀⣀⣴⢻⣿⣿⣿⢸⣷⣴⡀⢸⣿⣿⠛⢿⣿⣿⣿⣿ ⠓⠀⠉⠉⠉⢻⢸⣿⠏⠙⢿⡿⠃⠀⠸⣿⡇⣿⠋⠀⣸⣄⣀⡀⠀⠀⠈⠉⠉⠛⠛⠿⢧⠼⣿⣿⡏⢸⣿⡋⢷⣼⣿⣿⣧⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢯⢸⠀⣠⣾⠃⢀⠀⠀⠈⡇⠘⠀⢀⣿⣿⣿⣿⣿⣿⣷⣶⣦⡄⠀⠀⠀⢀⣾⢿⣷⣾⠸⡿⢮⡯⢿⠈⠛⠿⠛⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠓⢸⡇⢸⢀⣟⣰⠀⠀⠸⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⢀⣿⡇⡼⡿⢛⠳⣿⠀⠹⣾⣷⠄⠀⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣾⣿⣿⡄⢸⡆⢰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣧⠹⣄⠀⠙⢧⡀⢈⣓⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢐⢰⡘⣷⣌⣿⢿⣿⣷⡈⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣷⣼⣧⣠⡀⢹⣦⡛⣭⠷⠮⡙⢿⣿ ⠀⠀⠀⠀⠀⠀⠸⠀⢳⣽⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣇⣿⣶⣿⣿⣷⡘⣿⣿⣾⣿⣿⣶⣬⣿

⣿⣿⣷⣬⣿⣓⠰⢽⣎⣿⣿⣟⠛⠿⢤⣶⡥⣴⣶⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠋⣡⣴⣟⣛⣿⣭⢗ ⡿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣦⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⣥⣿ ⣿⠹⣿⣿⣿⡌⢿⣿⣷⣌⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠿⣫⠶⢿⣿⣿ ⣿⡧⠘⣿⡻⣿⠺⣿⢿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⢀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿ ⣿⣿⣆⠘⢷⠹⣇⢯⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡴⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⢦⠀⠀⠠⣤⣤⣤⣶⣿⣿⣿⠿⣟⣦⣶ ⢻⣷⡽⣧⠈⠷⠉⠉⠁⠀⠀⠀⠀⡀⢀⡀⢀⡟⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠣⣄⠀⠰⣌⢽⣯⠉⠻⢶⣿⣿⣿⣿ ⡀⠙⣷⡙⣧⠀⢯⢩⢱⠶⢤⠶⢋⡡⠏⢠⡟⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡈⠳⣄⣈⣑⣲⡤⠄⠀⠉⢿⣿⣿ ⠛⢦⡈⠳⡌⣦⠈⢧⢸⡴⢋⡴⠋⠀⠀⢹⢷⣀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢠⡷⠋⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿ ⢧⡀⠑⠀⠙⢮⠃⣠⢏⣠⡟⠀⠀⡀⠀⣿⠀⠻⣿⣶⣦⣤⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣠⣤⣤⣴⡾⠋⡇⠀⠀⢳⡀⠀⢀⠀⣼⣶⣖⣂⣺ ⠀⠈⠂⠀⠀⠀⠚⢛⡝⢹⠇⠀⠀⠁⢀⣿⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠀⢠⡇⠀⠀⠈⢣⡀⢸⣶⣅⣛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠞⣠⣼⠀⠀⠀⠀⠉⣿⣄⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⣸⠿⣄⠀⠀⠀⠉⠒⢛⡉⠛⠛⢻⣿ ⠀⠀⠀⠀⠀⠴⠗⠋⢸⡿⠀⠀⠀⢠⠇⢿⡟⢿⣶⣤⣤⣤⣀⡀⠀⠉⠙⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠁⣀⣠⣤⣤⣶⣶⠋⣽⠀⡟⢳⣶⡦⣤⠤⠴⣦⣽⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⣠⣞⣫⣴⠂⢀⡴⡿⡆⠀⣧⠈⢻⡄⠀⠀⢸⠛⠻⢶⣦⣄⡈⠛⢿⣷⡀⠀⠀⠀⠀⣰⡿⠛⢁⣤⡾⠟⠉⠁⠀⠀⣸⠇⠀⣧⠀⢹⣸⠀⠉⠘⢷⣄⣹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠁⠀⣼⣁⢴⡏⠀⠑⣇⠀⢹⠀⠱⣿⣄⠀⢸⡀⡀⠴⠈⠙⣿⣦⡀⠉⠧⠀⠀⠀⣰⣛⠂⣾⢿⠋⠀⠀⠀⠀⠀⢠⣿⠞⠀⡟⡄⠈⢿⠀⠀⠀⠈⢿⣷⣦⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠀⢷⠀⠀⣿⠀⡀⡇⠀⠙⠚⢦⣀⠳⣤⠒⡀⡤⠃⠘⢻⠃⠀⠀⠀⠀⠀⠁⡴⠃⠈⠷⣤⣀⢠⣲⡴⠋⠁⠀⢀⡇⢷⠀⠘⣆⠀⢀⣀⠀⠉⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⠀⠈⣧⢠⠏⠀⠀⢣⠀⠀⠀⠀⠘⠉⠑⠒⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⠒⠚⠛⠊⠁⠀⠀⠀⣼⠁⠸⠀⠀⠘⢆⠀⠙⠻⣤⣤⣤⣭⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡘⡞⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡀⠀⢨⣖⢦⣦⣀⣉⣭⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠈⣧⡀⠀⠙⠯⠛⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢧⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢹⠀⠀⢸⣿⣾⡲⠤⠀⠙⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣆⢸⡼⣇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠤⣤⣀⢀⣀⣤⠤⠖⢦⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣷⡼⣷⡀⢸⣸⣿⣿⣦⡀⢤⣈⠻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣿⣆⣧⢹⣦⠀⠀⠀⠀⠀⢰⣿⢶⣤⣤⣀⣀⣀⣀⣠⣤⢴⡿⣷⡀⠀⠀⠀⠀⢀⣾⣧⡀⠣⠁⣿⣿⣶⣿⣿⣿⣿⣿⣦⡙⢾⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⣿⣿⣿⡈⠳⣄⠀⠀⠀⠸⣇⠈⠓⢤⣀⠀⠀⠀⠀⠠⠊⢀⡼⠁⠀⠀⠀⢠⡾⢻⡀⠈⠓⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣧⠀⠘⢷⣄⠀⠀⠈⠓⠦⢄⣀⣀⣀⣀⡠⠤⠖⠋⠀⠀⠀⢀⡴⢿⡇⡆⣷⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣽⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠈⠳⢄⡈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣸⠞⠠⡿⠀⠀⠀⣼⠉⣿⣿⡏⢻⣿⣿⡇⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣷⣄⡀⠙⠲⣝⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⢁⡠⠞⠁⢀⣼⠁⠀⠀⠘⠁⠀⡏⢿⡏⠀⢧⣿⡟⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠏⢸⣿⣿⣿⣿⣦⣄⡀⠉⠛⠿⢿⣿⣶⣦⣤⣤⣴⣾⣿⡿⠅⠀⠁⣀⣠⣶⣿⣿⠀⠀⠀⠀⠀⣸⣿⢸⠇⠀⠈⣿⢁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠈⠉⠻⡟⠉⠉⠀⣀⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡿⠋⠀⠀⠜⢀⠋⠉⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⡀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢀⣠⣾⠋⢀⡖⠀⠀⣠⡾⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠈⡷⡜⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠈⠉⠁⡇⠀⣾⠁⠀⢠⣿⠇⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⣇⠙⠲⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⡇⣸⢸⠀⢀⡎⡇⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⠀⠀⢸⠈⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠀⠀⠹⡟⠸⡄⣸⠁⠃⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢄⠘⠦⣄⡀⢀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠑⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠹⣿⣷⣯⣿⣟⣻⣄⣀⣀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡑⡄⠀⠐⢆⡀⠈⠤⡒⠊⠁⠀⠀⠀⠐⠴⣀⠑⢄⢦⠀⡀⠀⠀⠀⠻ ⠀⠀⠐⢡⣊⡤⢰⢌⡠⠚⡹⠋⠀⠀⠀⡔⣢⡤⠖⠙⠚⢺⣦⣍⠇⠱⡀⢀⡁⠀ ⢁⣀⡔⣁⡔⠁⠠⠢⡉⠁⣠⢠⠇⢈⡼⠊⠁⡀⠀⢳⣄⢸⠁⠈⠛⢄⠑⠀⠀⠀ ⠉⠿⠿⠋⣁⠔⢁⠤⡊⢊⠤⡃⡇⠈⠄⠀⠀⣱⣤⣈⢻⣿⣧⡀⠀⠀⠣⡀⠀⠀ ⠑⠀⠣⡀⠀⠀⡠⣪⢿⠫⡆⠀⠻⡀⠈⢄⠀⢻⣤⣮⡗⡝⡻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⣰⡇⢸⠂⢐⠃⠸⡆⠘⠢⠬⠐⠄⠻⣾⠇⢸⡷⡿⠀⠀⠀⠀⡀⠀ ⠀⠀⠈⠉⠉⠀⠡⠈⢈⠩⠇⠀⠘⠄⢣⡀⠀⠀⠀⠀⠑⠂⠙⠁⠀⣀⢤⣶⠃⠀ ⠁⠀⠀⢀⣠⠔⠁⢑⣲⣪⣾⠀⡀⠸⣄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠺⡿⣳⠎⠀⠈ ⠐⠀⠀⠀⠁⠀⢀⠚⠁⢑⠟⢼⣷⢠⣿⢧⣿⠀⠄⣀⠀⠀⠀⢀⣀⢥⡏⡆⠀⠀ ⠀⠠⠔⣫⢀⡛⠛⠂⠤⠿⣿⠉⢻⣣⡏⠮⠏⠀⠀⠀⣉⠂⢄⠘⠁⡜⢇⠳⠀⠀ ⡀⠒⡏⡾⢓⡢⢔⡞⠉⠈⠀⠀⢊⠔⢅⠀⠀⠀⠀⠀⠁⠀⠀⡠⠊⡇⠸⠆⡀⠀ ⣿⣴⠟⠉⢹⡅⣜⢵⠖⢿⣯⡉⠉⠑⢌⡻⣦⣀⠀⠀⢀⡠⠺⡃⠀⠙⢄⡦⠨⠀ ⠋⠈⠀⠈⠁⢳⣠⠃⠀⠀⠙⢿⣷⣦⣀⠈⠺⣅⠈⠀⡇⢰⠀⠱⠀⠀⣸⣁⣀⠀ ⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⢿⣿⡿⠁⢀⢊⡇⠀⠏⠈⢡⢀⢀⠾⠤⢴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢠⠺⣡⠀⠀⠀⡸⠀⠈⠀⢀⡌⢀⠼

⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⡙⢛⢻⣿⢿⡆⡘⢻⣿⣿⡙⣿⣷⣿⣿⣿⡇⠐⡙⢿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣻⣟⡿⣇⠈⠛⢯⠟⡛⠊⠍⡌⣍⣛⣷⠾⣿⣞⣿⣿⣷⣾⣿⣧⠳⠔⢠⠈⠻⣆⠄⡻⣿⣿⣟⡇⠌⡰⢀⠜⢻⣿⣷⡏⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣥⣂⠤⢀⡉⠛⠛⡙⢦⠉⡁⣷⠲⢯⣴⣱⡼⢋⠄⢢⡹⣿⣷⣻⣞⣿⣻⣿⣷⣌⡤⠈⠅⡌⠒⡈⢮⠻⣝⢿⣤⢁⠢⠌⢂⠙⣿⠠⢡⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠖⡉⠅⠃⡌⢍⠛⡻⣧⢉⠓⠛⢋⣐⡌⣌⣣⣟⣿⢿⣷⣿⣾⢿⣷⣾⠶⠬⢌⠂⡔⢡⣘⣘⢧⡌⢃⠅⣷⡂⠜⣆⠡⢌⣃⠂⡉⢧⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣻⣴⣶⣾⠾⢛⣰⣬⣖⡷⣾⣷⣬⠸⢤⣖⣻⢿⣿⢿⣻⣿⠯⠳⢛⣉⠄⠢⠞⠶⢮⣶⣮⣳⣭⣟⡿⣽⣮⣘⠬⢿⣎⣻⣧⡂⠼⡔⡐⠠⠱⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⡋⣡⡼⢿⠷⣻⣿⣟⣷⠟⣡⣾⣛⣮⢽⡿⣾⣿⣿⣿⣿⠟⠩⡐⢌⠱⡘⠬⢖⣾⣳⣟⣾⣽⡿⣷⡿⣯⣿⣶⣽⢷⣿⡽⣆⣿⣔⠡⡁⢿⠾⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣛⣥⣾⣷⡿⢋⣼⣟⡷⡟⣡⣾⣿⢋⣹⡾⣻⣿⣻⣳⣯⠟⠁⠄⢃⡔⡨⣞⢥⣟⣿⣿⣷⡿⢛⡙⣏⠭⡙⡍⠻⣿⡿⣿⣾⣻⣽⢾⣻⡆⡡⢺⡶⠞⠛⠯⣛⣿⣿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣴⣿⣻⣾⣿⣟⣿⡿⢡⡾⢯⣷⡌⡉⠡⠉⠄⣐⡼⢡⣿⠠⣹⣧⣿⣿⠟⡫⢔⡌⢣⠜⣹⣧⡱⢨⢱⡧⢱⡌⡙⠿⣿⣯⣷⣻⡔⣹⠐⡌⠒⡀⠆⣁⣶⡿⣿⡿⣿⣿ ⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢣⣟⠿⡿⣃⣿⣄⠣⢘⣠⢟⢃⣿⣼⠠⠸⣿⣿⠛⡜⢣⡘⣇⠇⡸⢀⣿⣿⣧⣸⣿⠸⡇⣃⠟⡘⢿⣿⣧⡟⣧⢛⣀⢧⣘⣼⣿⣧⣿⣧⣿⣟⣿ ⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠟⣣⡾⣽⢛⠵⣫⣞⡿⢋⣶⡝⡏⣾⣳⣾⢀⠃⢿⡄⣋⠜⡰⢠⢻⣖⡳⢄⡚⢿⣿⣿⣿⣧⡑⠤⠚⡌⢢⠹⢿⣷⢷⡯⢛⠩⢉⠉⠛⠛⠿⣽⣯⣿⣿ ⣿⣟⡾⣯⣧⢌⣛⡻⠙⠤⢾⡝⠗⡋⣱⣞⣯⣩⣞⣿⣵⡟⡽⢱⢣⣟⡆⠉⡌⢷⡐⢊⠔⡡⢸⣿⢿⣿⣯⣍⢿⣿⣿⣿⣿⡆⠱⡈⢆⡑⠪⢿⣿⣽⢯⢏⣭⣩⣤⣷⣿⣿⠿⣯⣿ ⢻⣽⣻⢽⣻⡷⡽⢝⣏⠳⡦⣔⡞⣾⡹⣞⡞⣡⣿⣿⢛⣰⡇⢋⢼⡾⣳⡡⠄⠩⢷⡉⢆⡑⣼⣇⣴⣶⣫⣝⣷⣟⣽⣿⣿⡇⢂⠑⠢⢌⡑⢢⠹⣾⢿⣦⣒⠲⢯⣿⣿⣾⣫⣷⣻ ⠈⠳⢯⣿⣿⡿⢻⡽⢿⣳⡶⣥⣾⢵⣻⡏⡞⣿⢻⣞⡿⣿⡇⠌⢾⣷⠙⣷⡌⡁⠚⠿⡄⢂⠱⣿⣿⡿⣿⡿⡌⢿⣌⣿⣿⣧⠈⢂⡑⠢⠘⡄⢂⣿⣧⢩⡛⠧⢉⣙⣿⣻⡿⣛⡵ ⣧⠦⣆⣸⠘⢤⣣⣼⣻⢷⣻⣿⣳⣯⣿⡅⢿⣵⢿⡹⣿⣋⡷⠈⣽⣾⠃⠌⣿⢷⣧⢲⣌⡓⢦⡙⠻⣿⣻⠕⠀⢸⣧⣿⢾⡏⠐⡠⢀⠃⡱⢈⠆⢾⣟⢿⡹⣿⣿⣿⠻⣍⢶⡝⣾ ⣽⣿⢯⣿⡐⣌⠓⠛⠹⠯⠾⠵⣛⣭⢾⣅⠂⢻⡯⠷⠯⢷⣇⠡⢸⠻⣧⢂⢸⡓⠮⠷⠤⡐⠄⡰⢀⠈⠓⠦⣀⡼⠋⣮⠟⢁⠂⡐⠌⢂⣡⣢⣼⣿⢿⣆⠻⣶⣿⣿⢿⡿⣾⡽⣶ ⣤⣆⠷⣾⣧⠙⠽⣦⠵⣦⢞⣾⡻⣞⣯⢿⣎⠤⣐⣼⡼⣿⠉⡤⠙⡄⡘⢧⠀⢿⣧⣘⠰⢈⠔⡀⠂⠌⡐⠠⢈⠁⠂⠌⡐⢀⠂⡐⣬⣶⢿⣻⢿⣿⢼⣍⠳⣬⣻⣿⣿⣽⣷⣟⣷ ⠷⣺⠿⠗⠋⡁⢆⣥⢻⣜⢯⣶⣻⣽⣾⢿⡿⣿⣽⣾⡽⢃⣾⡇⢬⡐⠠⢘⣇⠄⡙⢿⣧⡌⠰⡀⠅⠂⠄⡁⠂⠌⡐⢂⠐⡀⢶⣿⣿⡟⢷⣥⣾⢯⣯⢿⡿⣿⢿⣿⣻⣿⣿⣿⣾ ⡞⠁⢄⣠⡗⡞⡭⣚⡷⣮⢿⣾⢿⣻⣞⣯⡿⣿⣿⣿⣾⣿⣿⡗⣸⣇⠁⠆⣿⣷⣐⠈⣿⣇⠱⡀⠜⡀⠂⠄⡁⢂⠐⡀⢂⠐⡀⠻⡯⢁⣿⣿⣏⢻⣞⡷⣾⡿⣿⣿⣿⣿⣿⣿⣿ ⣤⣿⡿⣿⡿⢯⣝⢯⡽⣭⡷⣯⣟⡷⣯⢷⣿⣿⣳⢯⣿⣿⣿⡷⣿⣿⣇⢂⣽⣿⣿⣦⣻⣿⠐⢾⣄⠰⢁⠂⡐⠀⠆⠰⠦⠐⡠⠡⣈⢿⣿⢿⣾⢹⣯⣟⣷⡿⣿⡿⣿⣿⣿⣿⣿ ⣿⡻⢉⡵⣪⠗⢩⡵⣞⣧⣿⣷⣯⣿⣽⣻⣷⢳⣭⣿⣽⣿⣞⣿⣿⣿⣿⣼⣿⣿⣞⠿⣿⡏⡘⢄⠊⡙⠲⢤⣄⡉⠠⢁⢂⣿⣟⡿⢠⣿⡿⣿⣷⣟⣮⣽⣾⣿⣿⣿⣟⣿⡿⣿⣿ ⠓⣀⣞⣩⠎⣠⢯⡷⢿⣻⣿⣿⣿⣽⣯⣍⣙⠛⠶⡽⠾⢿⣿⣟⡿⣿⣿⢯⣷⡷⢹⡏⡿⢡⠘⡄⠣⢄⣁⣂⣈⠙⠳⣄⠌⢋⠡⢄⣿⣟⣿⡽⣛⠾⠚⡉⣄⣤⣾⡿⣿⢿⣿⢿⡿ ⣿⡿⣿⡇⠄⣟⡮⣽⣿⣿⡿⢏⣱⣦⠴⣀⣮⣷⠿⡛⣭⠿⢋⢎⢳⣿⠿⣋⣶⡷⢙⠣⡑⠢⡑⢌⠡⢂⠄⠻⡭⢷⡅⠹⠖⡈⣦⣿⣿⢯⣿⣆⠡⠌⡉⢉⠛⠿⣿⣷⣯⣟⣾⢿⡽ ⠀⡙⢺⡟⣿⣋⢏⢻⣿⣿⣿⣿⣿⣷⣿⣿⣟⡉⢢⠘⠡⡘⢄⣊⣅⣃⣦⣿⢿⣷⣌⢢⢁⠣⢌⠢⡑⢌⡘⠤⢉⠍⡠⢃⣜⣼⡟⣿⣯⣿⡹⡿⣗⣦⣥⣾⣾⣿⣯⣿⣿⡾⣹⢯⣗ ⠀⢀⣰⣾⣿⣿⣼⣾⡿⣟⣿⡻⣿⣿⣿⣿⢋⣴⣷⣾⣿⣿⡿⣿⢿⣿⢿⡿⣾⣹⣿⣷⣮⣐⠊⡔⢡⠂⡜⢠⢃⡘⣰⣾⣟⡳⣞⡽⣻⣧⢣⢳⣄⢬⣻⣿⢿⣷⣿⣾⣟⣷⢯⣟⡾ ⢠⣾⣿⣿⣿⣿⣿⣿⠁⢹⣶⢻⣽⣿⣿⣧⣿⣿⡟⣯⡟⣿⣿⣿⣯⡞⣿⣽⡏⣿⣾⣽⣿⣿⣷⣼⡄⢣⠘⣤⣶⣿⣿⢹⣧⢳⡝⣾⢱⠛⣿⣿⡟⢻⣿⣿⣿⣿⡟⣾⣽⠙⡇⠛⣽ ⣿⣿⣿⣿⡟⠋⠘⡇⠱⠞⠓⢯⠺⣿⣿⣿⣿⢏⢷⡹⢞⡽⢿⣿⣿⣿⣶⣷⡹⢷⣭⠷⣯⣿⢿⣻⣿⢶⡷⣾⣛⡾⣼⠻⡜⣧⢻⡜⣯⢻⡼⣿⡙⢧⣻⣿⡿⢻⡔⣿⡱⠂⡔⢂⡟ ⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡗⢪⠧⣙⠞⣜⡣⢟⣿⣿⣿⣿⣿⣷⣮⢟⣧⡟⣿⣯⡽⣞⡽⣧⢏⢧⣿⣹⣹⡜⣧⠻⣴⣷⣾⣥⣯⣷⣼⢟⣥⠟⢡⢿⠠⠑⣰⠏⠐ ⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣯⠑⢪⡑⡚⣌⠳⣍⡚⢿⣿⣿⣿⣿⣿⣚⡾⣙⣾⣽⣳⣝⡾⣧⠏⣸⢌⢿⣆⠁⣧⢻⣿⣿⣿⣿⣿⣿⣿⢟⡡⢊⣵⢏⣴⣟⠣⢄⡡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠌⠁⠀⠐⡱⢨⠑⠦⣙⢺⣿⣿⣿⣿⢲⢟⡼⣏⣾⣿⣗⢾⢪⠕⠪⡁⢎⢸⡇⡼⠣⣿⣹⢒⡖⠦⣿⣿⣿⣯⣶⣿⣿⣿⣿⣌⢳⢢⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠈⠀⠀⠀⠀⠁⠎⡱⢄⠫⣿⣿⡿⣣⡟⣞⣞⣯⢻⣥⡻⣎⢧⠈⠐⠀⢂⣸⠍⢀⠐⠀⡈⠳⠘⣷⣿⣿⣽⡿⣿⣿⣿⡟⢿⡽⢮⢷⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠄⠀⠀⠀⠀⠀⠀⠰⢈⠒⣿⣿⣿⣶⣽⣸⣽⣿⡦⡙⢝⡺⢅⡓⠀⢈⠀⢁⠸⣄⢆⡐⠤⠶⠿⠿⠟⡛⣝⢲⣛⢿⣽⣿⢎⡽⣫⢞⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣿⣿⣿⣿⣿⠿⣿⣿⣷⠱⠘⢖⢄⠈⠳⣦⡀⢀⢣⢚⡮⡵⣀⠂⡄⠠⢀⠰⣩⠶⡭⣞⢭⡻⢿⡜⣧⢿⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⡘⣿⣿⣿⣄⡈⠈⠡⠀⠈⠻⣄⢎⡱⣓⢧⡳⢎⡴⡑⣌⠒⡤⢋⠶⡹⢮⡝⣧⣻⡜⣧⣟

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⠿⠿⡙⠻⠟⠋⡽⠓⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢮⣤⣀⠒⠴⣄⣨⠎⠒⣀⣤⠶⢞⡿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⠻⠛⠒⠲⠈⢓⠲⠜⠃⠒⣹⠡⠴⠒⠋⠿⠽⠿⣹⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣧⣭⢉⠓⣦⠴⠋⠉⠙⠓⠚⠛⠙⠉⠙⣶⣄⠒⠹⢾⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣽⠟⠂⠀⡾⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠊⣻⢆⠋⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣅⡀⠀⣼⠇⠓⢿⣷⣄⠀⠀⠀⠀⣠⣴⣾⠷⠋⢹⡇⠀⠰⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣥⠀⡀⣼⡆⠀⣀⣀⣉⡽⡆⠀⠘⣟⣀⣀⣀⠀⢸⡥⣄⢠⣬⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣜⢧⣿⠛⠜⡇⠜⠃⠀⠘⠃⢠⠀⠀⠀⠀⠀⠘⠧⣼⠀⠸⢻⣟⣻⢧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⣮⣿⠃⢃⡄⣷⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡏⢠⠠⠈⢿⣭⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠾⣯⡵⠐⣸⠁⠛⡄⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠀⣼⡅⠸⡇⢀⢀⣼⣯⢻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣽⣿⣯⡐⢻⡷⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠃⠀⣷⠶⠋⠉⣡⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⡏⢡⣇⠉⣿⣾⢴⣣⣿⠾⣷⡙⢦⣀⠀⠀⠀⢀⡴⠋⢰⣧⡂⢰⡾⡆⡑⠡⢈⠉⣔⣾⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣝⣯⢿⡇⠸⣿⣶⣿⣿⣿⣿⣿⠀⢿⣿⣦⠉⣭⣶⣯⣿⣷⣤⣿⣿⣧⣾⣿⣷⣾⣶⣶⣭⢯⣍⠳⣟⡾⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⣟⣺⣡⡤⠿⣦⠈⢿⡟⠁⣼⠈⢿⠀⣦⣤⣿⣿⣿⠀⢸⡇⢸⠏⢠⡏⠙⡇⠀⣿⠀⡇⠀⣦⡀⢻⡷⣜⡿⣱⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡳⣏⣾⡴⠋⠁⢰⡶⢾⣷⠀⡇⠀⣭⣠⣽⠀⣿⡿⢿⣿⣿⠀⢸⡇⢸⡃⢸⣷⠀⡇⠐⣿⠀⡇⠀⣿⠛⠛⠃⠀⠙⠻⣮⡝⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⣯⠟⣵⠞⠁⠀⠀⠀⠹⣧⣘⣋⣠⣿⣄⠙⣀⣾⣄⠙⢀⣼⣿⣿⣄⡘⣇⢸⣧⣈⢛⣴⣧⡀⢛⣀⣧⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣗⢯⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣻⢞⡽⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠈⢻⣿⢿⡻⣟⡿⣿⢟⣿⣿⠛⢻⡇⢸⡿⠻⠛⠛⠟⢿⢿⡻⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣟⡳⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⢾⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⡇⠀⣠⡿⣹⣎⡷⣏⡷⣽⣿⠛⢻⣦⣀⣙⣼⣷⣾⡟⢻⡷⣴⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣳⢿⣿⣿⣿⣿ ⣿⣿⣿⢯⡿⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣷⡾⣏⠷⣧⢻⡼⣝⡾⣽⣿⠀⢸⣿⣻⠿⣝⣳⣿⡇⢸⣿⣹⡇⠀⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣾⣻⣿⣿ ⣿⡿⠛⠋⠉⠁⠀⠀⣠⡶⠛⠳⢶⡴⠞⠳⢾⡇⢰⠛⠻⣿⠿⠛⠻⣿⡿⠛⠻⣿⠀⢸⣧⣿⡿⠛⠛⢿⡇⠸⠛⢻⡇⠀⣿⠟⠛⠷⣞⠛⠛⠛⣷⡾⠛⠻⣦⠀⠀⠀⠈⠛⠳⢿⣿ ⡟⠀⢀⣀⣤⣤⣤⣤⣿⡀⠲⢦⣼⡇⢰⣧⣬⡇⠀⣷⠀⣟⠀⣾⠀⢹⠀⢼⡆⢸⠀⢸⣿⣿⡤⠜⠧⠸⡇⢰⣇⠀⡇⠘⡯⠔⠳⠀⣿⣶⠋⢰⣿⠀⠼⡆⢸⣷⣶⣶⣶⣤⣄⠀⢻ ⢁⣾⣿⣿⣿⣿⣿⣿⣿⠿⢶⡄⢹⡄⢸⡿⠿⡇⠈⣿⠀⣧⠀⣿⠀⢸⠀⢻⡇⢸⠀⢸⣿⣿⠀⢸⡗⢘⡇⢸⡿⠀⡇⠀⡇⢸⣷⠀⣿⡏⢀⣿⣿⠀⢴⡦⢼⣿⣿⣿⣿⣿⣿⣷⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣷⣤⣤⣾⣧⣼⣿⣤⣿⣦⣤⣦⣿⣧⣤⣤⣾⣤⣼⣿⣿⣦⣤⣴⣬⣧⣤⣥⣴⣧⣤⣷⣤⣬⣦⣿⣤⣤⣤⣼⣦⣤⣤⣾⣿⡿⣟⣿⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣾⣽⢻⣿⣯⣿⢹⡞⣭⢻⣼⢹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⢫⣽⢹⡝⢻⣿⣿⣯⣷⢻⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣾⣳⡟⣾⢽⣯⡷⣸⠹⡖⣭⢓⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⢲⢭⢺⡕⣫⢵⣿⣟⣳⢾⣽⣿⣿⣿⣿⣿⣿⣯ ⣯⢻⡽⣿⣿⣿⣿⣷⣻⡽⢮⡗⣿⣇⢏⡗⡬⣋⠶⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣜⢣⢎⢳⢎⣵⡿⣞⡾⣭⣿⣿⣿⣿⣿⣿⣟⠿⣼ ⣏⠷⣱⢛⣿⣿⣿⣿⣷⣟⣯⢽⡞⣽⣮⠖⣥⢉⠞⡌⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠳⢌⡲⣉⢞⣼⡿⣹⢧⣟⣷⣿⣿⣿⣿⣿⠟⣎⢻⡼ ⢎⡳⢱⢪⠜⣿⣿⣿⣿⣿⣞⣧⡟⣧⢟⣿⡰⢉⡚⢼⣿⣿⣷⣿⣾⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣾⣿⣿⣿⣯⡱⢊⠔⣣⣾⢯⣗⢯⣿⣾⣿⣿⣿⣿⡿⢥⠛⣌⠳⣜ ⢣⡝⢢⢃⠚⠤⠻⣿⣿⣿⣿⣾⣝⡾⠟⠛⣿⠀⠌⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡥⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢘⠠⣿⠛⠷⢾⣿⣿⣿⣿⣿⣿⠟⡰⢃⠭⣈⠳⣌ ⠣⡜⠢⢌⡘⠤⡉⠜⣿⣿⣿⠟⠁⢀⡤⠚⠙⠧⣌⣀⠈⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⡁⢀⣬⡴⠗⠲⢤⡀⠈⢻⣿⣿⡿⠃⠜⡐⠌⠒⡄⠓⡤ ⡑⠌⣁⠢⢐⠀⠢⠁⡈⢻⡧⣤⠔⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠍⡦⢤⣿⡟⠁⠌⠂⠌⡈⠅⢌⠱⠐ ⠄⠃⠄⢂⠡⠈⠀⡁⠀⠀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣈⠲⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⡔⣀⣴⠾⠊⠀⠀⠀⠀⠀⠀⠀⣸⣉⢉⣁⣀⠀⠀⠁⠂⠀⠌⡀⢂⠉

⠀⠀⠀⣇⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣭⣉⠉⠩⠽⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠏⠉⠉⣩⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡏⠀⠀ ⠀⠀⠀⣽⠀⠀⠙⣶⣄⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣤⣄⠈⠙⢦⣤⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⣢⠶⠋⢁⣠⣴⣶⣾⣿⣷⣶⣶⣶⣤⣤⣄⣠⣴⡾⠋⠀⢰⠃⠀⠀ ⠀⠀⢸⡞⡆⠀⠀⠈⠻⣿⣿⠟⣛⣉⠉⠉⠀⠀⠀⠀⠉⠛⠿⣦⣀⠈⢳⣄⠸⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣴⡿⠃⣠⣶⠿⣛⠭⠀⠀⠀⠀⠀⠨⢍⣉⠛⢻⣿⠋⠀⠀⠀⡼⢸⠀⠀ ⡠⢤⠀⡇⣷⠀⠀⠀⠀⠹⣿⣼⠁⠀⠀⠀⢀⣴⣶⣶⣶⣦⣄⠘⢿⣷⡄⢻⡳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢫⡟⣰⣿⣫⠕⡩⢔⣶⣶⣶⣄⠀⠀⠀⠀⠀⢱⣾⣏⠀⠀⠀⢠⡇⡾⠐⠀ ⠘⣌⠀⢧⢸⡀⠀⠀⠀⢣⣻⣧⠀⠀⠀⠀⣿⣻⠋⣠⣌⠙⣾⡆⠈⢹⣿⣎⢳⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣱⡽⣰⣿⡟⠁⡸⣿⠃⡤⣄⠙⣿⡇⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⣼⠁⡇⠀⠈ ⠃⢹⠀⢸⠀⡇⠀⠀⠀⠀⠳⣻⣆⠀⠀⠀⣿⢧⡀⠓⠚⢀⣿⡏⠀⠀⢹⡎⢯⢻⡅⠹⡄⠀⠀⠀⠀⠀⠀⠀⣾⡿⠷⢹⠃⠀⠀⢿⣷⡀⠓⠋⢀⣿⡟⠀⠀⠀⣰⡿⠃⠀⠀⠀⢀⡇⣸⡿⠀⠀ ⠀⠘⡆⢸⠀⣿⠀⠀⠀⠀⠀⠁⣿⣦⡀⠀⠘⠾⣿⣶⣾⣻⠟⠁⠀⠀⠈⣷⠀⠛⢿⡄⠹⡀⠀⠀⠀⠀⠀⠀⠟⠀⠀⡞⠀⠀⠀⠘⠯⣟⣷⣾⣻⠟⠁⠀⣠⣾⠏⠀⠀⢀⡀⠀⢸⣹⢷⡇⡀⠀ ⠀⠀⣧⢸⣄⣿⡆⢸⣷⣄⠀⠀⠈⠫⠛⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡆⠀⠀⠁⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⣠⠜⠀⠀⣾⡆⢸⠁⡇⠀ ⡆⠀⣿⢸⣿⡿⣿⠀⢻⣿⡼⠆⢀⣀⠀⠈⠙⠋⠙⠛⠛⠉⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⣠⢠⣾⠇⠀⠉⠀⠀⢰⣿⡁⢰⡆⡇⠀ ⢻⣶⠇⣼⣸⡇⢹⣇⠀⠁⠀⠀⠈⠹⡿⠃⠀⠀⢀⡤⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠾⠁⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⣼⢿⣧⢸⡇⣿⠀ ⢠⡟⢠⠇⡿⢷⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡞⢹⡞⣧⢹⣶ ⠟⠀⠈⢰⠇⠈⣧⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣷⢶⣿⠹⡀⢿ ⠀⢀⡏⠈⠀⢀⠟⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢿⠀⠙⢧⣇⠘ ⡿⡏⠀⢀⣴⣿⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⣀⢸⡜⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⣯⠀⣄⢳⣝⡆ ⡿⢁⣴⡏⣸⣿⣀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢾⣝⣇⠀⠀⠛⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣼⣿⣷⣌⢷⣿⣿ ⣵⣿⣿⣿⣿⣷⢿⡀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣸⢸⣇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⢤⣤⣀⡀⠀⠀⢀⣀⣀⡠⠤⢾⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣠⣾⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠋⠁⠀⠀⠀⠈⡇⠀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠉⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⣿⣦⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⢄⡀⠀⠀⠀⠸⡀⠉⢹⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣠⡞⢋⢹⡟⣿⣦⣀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⡴⣿⠓⠶⣦⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣰⣤⡀⢀⣠⠀⣰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⣿⠟⠛⢻⣿⡿⠷⠟⠿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣿⣷⣌⣤⣀⢤⣧⣴⡠⢀⡄⢈⣽⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢿⣿⠋⠹⢿⣿⣿⠟⠋⠋⣹⣿⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⢾⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⢲⣼⣿⣶⣿⣿⣷⣿⣦⣤⡆⠠⣿⣿⢇⠀⠀⡀⢤⠀⠀⠀⠀⣿⡇⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣟⡭⠋⠉⠉⠙⠛⠛⠛⠋⠉⠙⢔⢿⣿⣦⠀⠀⢳⠁⢀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⣿⠧⣤⣦⡀⠀⠀⠀⠀⣠⣶⡤⢸⣽⣿⣷⣖⣩⣬⡔⣈⣅⣁⣠⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⠒⣲⣶⣾⣿⣿⣿⣞⡎⠿⢿⣿⣦⠀⢀⣶⣿⡿⠏⢸⣻⣿⣿⡿⢿⣿⡁⣿⣿⡉⢉⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⣮⣿⣷⣾⣿⣿⣿⣿⡏⢱⠀⠉⠁⠉⡁⠈⠉⠈⠉⢀⣧⣀⣹⣿⣿⡷⡴⣿⣿⠉⢳⣧⠀⣾⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠀⠙⠿⠿⢿⣿⣿⣿⢿⣿⣻⣧⠀⠀⡀⠛⠁⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣃⣿⣿⡂⢹⣿⠞⠛⡋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠰⣾⣧⣤⣀⠀⠐⢿⣿⣷⣤⣽⣿⢿⣷⣄⡀⠈⠃⢀⣠⣾⡿⣫⣿⣿⣿⣿⣿⣿⣿⡟⢻⠸⠟⠓⠻⠿⠂⡀⣰⣇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠷⢄⠀⢲⣿⣿⣿⣶⣄⣀⣿⢿⢿⣿⣿⣼⣧⠸⣿⡷⠒⢛⠟⢩⣿⣿⣿⠿⠿⣿⣿⣿⡧⢣⣿⣀⣴⣶⠦⠴⠶⠿⣿⡿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠛⣿⣿⣿⣿⣧⠉⠛⠀⢸⣿⡀⣿⡙⣿⣋⣡⣴⣷⣶⠏⠀⢀⣁⣄⠰⠃⢠⠉⢳⣿⣿⣿⡋⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⣀⠴⠀⢸⢿⠛⠛⣿⡻⢳⣶⣶⣿⣿⣷⣧⣭⣝⣿⡿⢿⣿⡿⠀⣠⣾⣿⡏⠀⢀⠀⢰⣼⢻⡿⠃⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣋⣁⠌⠒⠀⠀⠠⢀⣠⣶⣿⣿⣾⣿⠩⣿⣿⣿⣿⣿⡿⠿⠋⠈⠉⡄⢈⣿⣤⣶⣿⢿⣿⡇⠀⢸⠀⡸⡣⢺⣧⠀⠀⠀⠑⣄⣀⠀⠀⠀⠀⢀⣠⣤⣤⣤ ⣿⠿⠛⠉⠁⠀⡀⠄⢀⣤⣾⣿⣿⣿⣿⣿⣿⡧⠪⡄⠙⠿⣿⡿⡄⠀⠸⠀⢰⣿⣿⣿⣿⣿⣿⣷⣜⠃⠀⣆⣀⠏⢀⣿⣿⠀⠀⠀⠀⠹⣿⠿⠿⠓⢻⣿⣿⣿⣿⣿ ⣷⣄⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠚⢳⠌⢻⣬⡄⠀⠀⠚⠿⠿⠿⠟⠻⡟⠙⠛⣿⣸⣿⣷⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠛⠿⠿⠿⠿⠿⠛ ⣿⣿⣦⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣧⣄⣰⣿⣶⢟⣻⡿⢄⠘⡄⠀⠀⠀⡇⢸⣿⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠻⣷⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⣿⣷⣼⣆⣶⢐⣇⣿⣿⠟⢩⡿⠋⢠⡿⣿⣿⣿⣿⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠛⠁⠰⣿⠟⠉⠉⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠿⣿⣿⣿⣿⠋⠉⢿⡿⠋⠀⡰⠋⠀⢀⡾⠀⠻⣿⣿⣿⣿⣷⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣷⣄⠀⠙⢿⡿⠒⠒⢺⣁⡴⠊⠀⢀⣴⣿⣷⣶⡆⠉⠙⣿⣿⣿⣷⡄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⣄⣀⠀⠀⠊⠁⣼⡶⠿⣦⠀⠙⠁⢐⢶⢀⣴⠿⠋⠁⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠑⠌⠉⠓⠤⠀⠀⠀⣠⠊⢰⠀⣠⡞⢡⡾⠛⠁⠀⠀⠀⠀⣾⣇⣴⣶⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡁⢴⠤⣄⡀⠈⠓⠀⢀⡾⠃⠀⢻⠛⠋⠉⠉⠓⠀⠀⠀⠀⠀⢀⡿⠿⠞⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⡀⠀⠀⠀⠠⢲⣷⠾⣤⣤⣈⣆⠀⠉⠓⡄⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠉⠛⠒⠦⠴⠧⠬⠦⡀⠀⠋⠈⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣠⠀⠀⠁⠀⠀⢾⣻⠡⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⡀⠀⠈⠀⢀⣴⣖⠿⡿⠷⠶⠖⠛⠛⠿⠿⣿⣉⡀⠀⠀⠀⠉⠓⠦⢷⠤⢴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡦⠭⢶⣄⣰⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠥⣀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣮⠗⠤⠀⠀⠀⢀⣽⡿⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠤⡠⣇⠀⣰⡞⢟⡉⠹⣍⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠫⣉⠛⠉⠀⠀⠀⠀⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠹⣦⣿⣧⠀⠙⢳⣾⣿⣿⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⢑⣢⣄⣀⠀⢠⣿⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣥⣤⠖⠀⢸⡇⣿⣧⣄⠀⣳⢚⣉⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⣹⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢾⡟⠁⠀⢀⣼⠃⢻⣷⡘⡏⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠷⠾⠃⠀⢸⡟⠀⠠⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡿⣿⣿⣿⣿⣿⡛⠛⡿⢉⡿⠀⣾⡟⡇⢹⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⢀⣀⢸⣷⠠⣠⣬⣿⣿⣿⣿⣿⣻⠷⣤⡀⠀⠀⠀⠈⠀⠰⣿⡿⣿⢰⣉⣿⡇⡼⠃⢸⠇⠀⢸⣷⣻⡼⠀⠈⠑⠢⠤⠤⢤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣿⣇⠈⢉⣩⡿⢿⡿⢻⡿⢿⣿⢿⣶⡄⠀⠀⠀⠀⣿⣤⠸⠿⠞⠛⠋⠀⢠⠏⠀⠀⠈⣿⣽⣇⠘⣦⡀⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠼⠉⡽⣿⡏⠙⢿⣤⠀⠳⣜⠷⣷⣏⣻⠿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡞⢀⠄⠀⠀⢻⡿⡈⢆⠀⢫⢙⠳⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠔⡇⢷⠈⣷⡀⠀⠈⠋⠐⠛⠋⠉⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡎⠀⠀⠀⢀⣇⠁⠘⣆⠈⢫⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠂⢃⣾⠧⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢿⡇⠀⠀⠀⢀⡏⣿⢄⢸⡧⡀⢹⣬⣑⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⠀⢀⠎⡟⠀⠀⢠⣈⡳⢄⠀⠀⠀⠀⠀⠈⠙⠿⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢧⡏⢣⠀⣸⠀⢠⡇⢹⡄⠉⠀⠱⡄⢷⡀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⣁⠴⠁⣸⠃⣤⠀⠀⠛⣷⡒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢷⠈⣷⣟⠀⣴⣿⡞⣧⠀⠁⠀⠘⠾⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠥⢠⣴⣿⡫⢺⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠤⠞⠋⣉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣧⡇⢹⡟⡅⠀⠀⠀⠀⢂⠀⠀⠑⠦⢄⣄⣠⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡏⠀⠈⢷⡀⢀⡀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣿⠋⡙⢯⣚⡷⡤⠀⠀⠀⠀⠀⠹⡦⡤⠤⣤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣿⠁⠀⡀⠀⠳⣘⠤⣿⡏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡋⢠⣿⡄⡇⠀⠘⡇⠙⢄⠀⠀⠀⠀⠀⠙⣑⣦⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣿⢔⣰⠁⠀⠀⢸⠇⢸⠁⠀⢹⣿⡟⢷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⢰⠃⠰⣿⣧⡇⠀⠀⣇⡀⠈⢣⠈⠑⢄⡀⢀⣀⣩⣧⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⠿⢺⣣⠀⠀⢠⢻⠀⡟⠀⠀⠈⣿⣏⠀⠈⠛⠿⣶⣤⣤⣤⣶⠟⠋⠀⠀⠀⠞⠀⠀⣧⣿⠙⠀⠀⢼⡇⠀⠀⠱⣄⠀⠈⠻⠿⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⠤⠴⠚⠛⠉⠀⠀⡽⠁⠀⢀⡏⡘⢠⡇⠀⠀⢀⣿⡏⡆⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⣻⡏⠀⠀⢰⣾⣇⠀⠀⢠⡈⠲⡄⡀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣢⡤⠤⢄⡠⠊⠀⠀⢠⣞⣴⠃⣸⠀⠀⠀⠈⣿⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⢠⢿⠃⠀⠀⠀⣿⣹⣆⠀⠀⠱⡄⠵⣌⡑⠲⣤⠤⠤⠤⠤⠤⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠀⠀⠒⠉⠀⠀⢀⣴⠟⠛⠋⠀⣿⠀⢀⡄⣾⡿⣇⠀⢣⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⣿⠏⠀⠀⠀⠀⣿⣮⣿⣦⣄⠀⠙⢶⣄⣹⠦⢬⣷⣦⣀⡀⠀⠀⣈⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣠⣤⣤⡴⠶⠀⡠⠀⠄⡞⠘⣰⠀⠀⠈⣿⣶⣷⠾⠋⠘⢿⠀⠈⡆⠀⠀⢱⡀⠀⠀⠀⠀⠀⣞⢀⣴⡿⢃⡴⠀⡀⠀⠐⢿⠈⠛⢿⣿⣿⣶⢶⡛⠛⢶⣖⣀⣀⣉⠙⠉⠉⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠋⠁⠀⡼⠀⣠⡎⢀⠀⠠⡇⢰⡇⠀⠀⠀⠘⢯⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⡀⠀⠀⠀⠘⠛⠛⠗⢲⠏⠁⢰⠃⠀⠀⠘⣇⠀⠀⠀⠉⠛⠷⣿⡟⠾⡿⢷⣤⣤⣴⣶⣶⣿⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣿⣴⣿⣀⣎⣠⣴⡇⣾⣷⡀⠀⠀⠀⠢⡳⣄⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡞⠀⠀⢀⡞⠁⠀⠀⠀⠠⠐⠶⡽⣹⣓⡗⠚⠁⠀⠈⠉⠁⠀⠉⠉⠛⠿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠽⠿⠿⡟⢻⠉⠛⠻⠿⢿⡹⣷⣀⠀⠀⠀⢹⣸⠂⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡿⣤⡼⠁⢀⣰⠞⠓⠉⠉⠉⠁⠀⠀⠴⠋⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠱⣜⣆⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠨⣿⠉⠛⠓⠲⠶⢤⡀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠁⠀⣴⣿⡥⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⢻⠀⠀⠀⠀⠀⠀⠈⠳⠾⠁⠀⠀⠉⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣿⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠚⠀⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠛⠃⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⢧⣄⠀⠠⠤⠤⠴⠶⣶⡤⠔⠊⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠤⠈⠋⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡄⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠋⠁⡠⠄⢘⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡤⠊⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⢻⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠁⠀⠀⢀⡄⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠀⢸⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣶⣤⣲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⢹⡟⠂⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣅⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢸⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠄⠂⠀⠀⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⡿⠿⣿⠅⣇⣈⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡟⠀⠸⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠫⣥⡿⠛⠛⠻⡉⡇⠀⡜⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⣟⣯⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠙⣿⣷⣶⣤⣄⢰⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠀⠀⠹⣷⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⣠⣶⡿⠁⢀⣴⠋⠀⠀⠀⠀⣱⡇⢰⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠜⠁⠀⠀⠀⢽⠋⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣇⡞⢨⣿⣎⡻⢍⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢻⡄⠀⠀⢠⣶⡶⠟⣷⣶⠿⠷⢮⡴⠖⠋⣁⡀⠤⠤⠒⠒⢿⣿⠁⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣟⣰⡿⢁⠝⢭⡒⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣤⣌⣷⠀⢤⡾⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⢠⡟⢀⣿⣿⠏⡠⢃⡴⠂⠈⣾⣋⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⡞⣉⣯⢻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⢸⣿⣏⠜⡡⠊⠀⠀⣼⣿⠿⠁⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠁⢀⣴⣿⢾⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠸⠇⣾⣯⢋⠔⠁⡐⢀⣾⡿⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣎⣴⣿⢿⣿⢾⢋⣿⡿⠁⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠖⠛⠛⢷⣄⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠄⠀⠀⠀⠀⢠⡿⣡⠋⢠⣎⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢋⡝⣡⣾⣿⣣⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠉⠉⠉⠉⠉⠙⣻⣦⡄⠀⠹⣿⢶ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠴⢶⡀⠀⠈⣯⠀⢻⠀⠀⢀⣿⣷⠏⢠⢏⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣠⡿⢻⢟⣏⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣷⣄⠀⢻⣄ ⠀⠀⠀⠀⠀⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⢈⡇⠀⠀⢹⡂⢸⠃⢠⣾⣿⡏⡰⢣⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⣟⣠⠃⢮⣿⣿⣿⠇⠀⠐⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣼⣿ ⠀⠀⠀⠀⠀⣰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⠿⠁⠀⠀⢸⡇⠀⢠⣿⢿⣿⠏⢠⣿⣿⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠄⠀⠉⠈⠁⠘⣿⣾⣿⣟⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠈⠉⠚⠻⣿⡙⢿ ⠀⠀⠀⠀⢠⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡄⠟⡏⣰⠋⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣿⡟⢹⣿⠁⠀⠀⢠⡞⠣⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠑⠺ ⠀⠀⠀⢠⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⡼⢠⠇⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣷⣿⠇⠀⠀⠀⠈⣇⠂⠱⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠟⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠈⢆⢹⣧⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⢸⢹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠂⠀⣀⣠⡴⢶⠛⠋⠉⠀⠀⠲⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⡇⡆⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⡏⢸⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣴⣠⣴⠞⠋⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢀⠀⢰⠃⡜⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠉⠀⠀⠀⣀⠀⠀⠀⠱⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠁⠀⡜⠀⡇⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣽⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⠋⠁⠀⠀⠀⠀⢀⡌⠁⠀⢆⠀⠀⡇⠀⠀⢠⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣇⡨⢉⠛⠓⠶⠦⣤⣄⣀⣀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣋⠝⠋⠀⠀⠀⠀⠀⠀⡠⠴⠛⠀⠀⠀⠘⡄⠀⠃⠀⠀⡾⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢠⠊⡰⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠉⠛⣿⣷⣖⠠⣀⣠⠈⠉⠛⠛⠾⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢶⣿⡥⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⡐⠐⠀⢰⡇⠀⠀⠀⠃⠀⠀⠀⠀⣀⣴⣷⢾⠇⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣄⣠⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣤⣴⣟⠨⢁⠀⡀⠀⢀⠨⠕⣙⣤⣤⢤⠀⠀⠀ ⠰⡂⡴⠷⠱⠤⠀⠈⠁⠈⢄⣔⠁⠀⠀⠀⠤⠪⢳⢤⣶⠂ ⢀⣙⣷⠧⢀⠤⠒⠀⠈⠁⠺⠒⠉⠁⠘⠓⡦⡀⠴⣗⣁⡀ ⠈⠻⡶⢠⡋⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⠜⣾⡛⠀ ⠤⣋⠀⠈⠀⢷⣤⣇⠀⠀⠀⠀⠀⠀⣼⣴⡞⠀⣇⢈⣟⠄ ⠀⡳⠀⢸⣤⣬⣭⣟⣷⡀⠀⠀⢠⣾⣿⣭⣤⣤⣃⢸⡕⠀ ⠀⢧⡄⣰⠙⢐⡍⣕⡽⠁⠀⠀⠰⢋⡌⡅⡜⢋⢣⣺⡸⠀ ⠀⣪⠏⢞⡧⠐⠬⠑⠁⠀⠀⠀⠀⠐⠊⠙⠁⢮⠿⣻⡃⠀ ⠀⢸⣠⣿⢹⣢⢤⣀⣀⣀⡀⢀⣀⣀⣠⣤⣶⢣⣆⡋⠀⠀ ⠀⠈⠁⠻⠙⠙⢟⠁⠀⠀⢸⡁⠀⠀⢈⡿⠃⠪⠏⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠉⠙⠘⣗⣦⣀⠀⠰⣳⡍⠒⢄⣄⠙⣧⠀⡿⢡⢀⡴⢊⣡⣟⣤⡶⢋⣠⣤⠈⠀⠀⢠⣶⠁⣀⠠⠤⣶⠟⠀⢀⣰⠏⠀⠀⠀⢀⠠ ⠀⠀⠀⠀⠀⠙⢷⣄⠀⠐⠶⣒⠀⠤⠄⠀⠐⠓⠀⠐⢬⣿⢦⡑⢤⣹⡘⣆⠀⠛⠳⡜⣿⡰⠛⢋⡴⠛⣠⡥⠞⠋⠱⠮⣤⣤⠴⢒⡾⠁⠀⣀⡤⠚⠁⠀⠠⢿⣏⣀⣤⠴⠚⢁⡴ ⢗⠒⠶⠖⠒⠒⠊⠉⣤⡒⠒⠊⠉⠂⠙⢷⣒⠒⢶⣒⠲⠥⣀⡈⠳⣌⠁⠈⠳⣄⠀⠹⣠⠃⢀⡜⢁⡴⠋⠀⣀⡤⠾⠭⠥⠤⠐⢿⠆⠀⠙⠳⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⣠⠎⠀ ⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⠉⢒⣲⢦⣤⡖⠃⠀⢀⣻⢷⠒⠺⢿⠒⠨⢷⠦⣄⣈⣣⡀⠀⣠⣮⣞⣯⣄⡤⣾⡿⢴⡾⠤⠤⣠⠆⠀⠑⢄⠀⠐⠤⣄⡒⠚⠁⠀⠀⢀⣠⣾⠋⠀⠀ ⠀⠀⠈⠳⣦⣄⣀⠀⠠⠖⣦⣍⣀⡴⠋⠀⣰⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠞⠉⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣄⠶⣓⠦⠲⠾⢋⣀⣠⣴⣾⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⣛⣻⡶⠊⠁⢉⡵⠊⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⢀⣑⣢⣄⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣼⠟⠋⢀⣠⣞⣥⠀⠀⣠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⠑⠦⣙⢧⣄⣀⡀⢀⣈⣓⣦⣄⠀⠀ ⠀⠀⠈⠉⠛⠒⠒⢺⢟⡾⡵⠃⡄⢀⡿⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⣀⠀⠀⠀⢱⣜⠳⡌⠀⢻⠈⠻⣏⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣰⣿⢿⣽⠵⢺⠇⠀⡇⠀⣠⢔⣷⡾⠿⠛⠛⠛⠻⠿⠿⢿⣶⣶⡆⠀⠀⠀⠀⠶⣶⣾⣿⠿⠿⠿⠟⠛⠛⠿⢶⣽⡂⠀⢸⠿⡆⠼⠦⠈⣦⣄⣙⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡿⡟⢛⣉⣁⢤⣏⡆⣰⡇⠀⠁⠏⠁⠀⠀⢀⠒⠒⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠒⠒⠒⠒⠀⢀⣀⡀⠀⠀⠉⠛⠀⡾⢀⢱⠸⣆⠀⠈⠉⠛⠿⣯⡷⠆⠀⠀ ⠀⠀⠀⠈⠉⠉⢋⡽⢁⠀⣸⣟⣴⡏⣿⠀⠀⠀⠀⣠⠞⠋⣿⣿⣿⣿⠹⣯⠂⢻⠀⠀⠀⠀⠀⢸⡇⠈⣿⠋⣿⣿⣿⡯⠙⢲⣄⠀⠀⠀⣧⣿⢦⣷⡘⣗⢒⣖⣚⢻⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣺⣵⣿⠰⢟⣯⣿⡇⣿⡀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠓⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⢸⡼⣧⣿⢹⡟⠺⡧⣯⡉⠛⠷⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⢟⣽⡋⠀⠸⢏⢸⡗⠃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⡏⡟⢹⠇⠀⠙⣬⣙⠛⢚⡿⠃⠀⠀ ⠀⠠⣤⡤⠤⠴⢚⡽⠀⠀⢀⠘⣾⡇⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀ ⣻⠃⡿⢡⡏⠀⠀⢯⣉⣁⡴⠏⠁⠀⠀⠀ ⠀⠀⠈⠙⠲⢾⣿⣶⠄⠀⣿⠀⠙⡇⢠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠎ ⠏⢰⠀⠀⠘⡿⣏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⣏⡞⠀⠀⡇⠀⢰⠇⢸⢰⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠗ ⢠⡇⣷⡇⢹⡄⠘⡇⠀⠀⢳⣹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⡜⠀⠀⠀⠇⣠⠞⠀⣸⣿⠆⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀ ⠀⣾⣤⣿⣿⠀⠻⡄⡻⠀⠀⠀⢣⡻⣦⡀⠀⠀⠀ ⠀⠀⠀⣴⡟⡸⠁⠤⣤⡶⠾⠅⠐⢺⣿⢹⡗⢻⣧⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠴⠖⠛ ⠀⠀⠀⡼⣸⡿⢹⡟⣿⠰⣤⣙⣓⣒⣶⣿⡀⠑⢮⠻⣦⣀⠀ ⠀⣀⠼⢋⣴⡧⣾⠇⠀⠉⡽⢫⢷⣯⡷⢸⡇⠘⢿⣧⠀⠀⠀⠀⠿⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⣿⢇⠸⣅⢸⣄⡹⡆⢿⠉⠁⠘⣏⠳⢤⣙⣦⢍⣉ ⠡⠤⠖⣿⠏⣰⠃⠀⢀⡼⡵⠃⠘⢹⠁⡟⣧⡆⢸⡜⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⡇⣸⣆⡏⢦⣧⢙⡃⠈⣷⡀⠀⠸⣆⠈⠳⣌⣉⣁ ⣦⠴⠟⢁⡼⠃⢀⣴⡟⣸⢁⣠⢿⠸⡼⠀⢹⡙⢾⣧⠞⡟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠢⣄⡿⢃⠸⡃⠀⠉⢹⠳⡄⢸⠻⣄⡀⠈⠳⣄⠉⢻⣿ ⠀⠠⠖⢛⣞⣴⣿⠻⠀⣿⡼⠃⢸⠈⠁⢀⡀⢹⣮⣿⡈⢷⡈⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠁⡿⢂⣸⣣⡎⠀⣿⣄⠀⠘⡇⠘⣼⠀⢻⣿⡄⠀⠈⠒⠦⣄ ⠀⢀⡴⢋⡿⢻⡇⠀⠀⠸⣡⣤⡞⣀⢴⡟⡆⢸⠀⣹⣟⢦⡉⠻⢧⡉⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣿⡷⢚⡵⢿⣿⣿⢹⣄⡏⡎⠳⣤⣹⡄⠛⠀⠀⢹⡿⣦⡀⠀⠀⠀ ⠀⠈⢀⠞⠀⡸⠀⠀⣀⣶⡿⢿⡟⠁⢸⢠⣿⣾⣀⣿⡽⣷⣍⠲⢄⡉⠓⠬⣙⣿⣷⣶⣤⣤⣶⣾⣟⡩⠴⢚⣩⠔⢋⣤⣾⣿⣿⡀⠙⢿⣷⠀⠘⢿⣿⣤⡀⠀⠈⢇⠈⠷⣄⠀⠀ ⠀⠀⠏⠀⠀⡇⣠⡴⠛⠁⠀⡼⠁⠀⣿⠏⢸⡏⢻⣿⣿⣿⣿⣷⣦⣍⠓⠦⣄⣉⠛⠻⣿⠟⠛⣉⣡⠤⢒⣫⣥⣾⣿⣿⣿⣿⣿⡇⠀⠀⠹⣆⠀⠀⠻⡙⠻⣦⡀⠸⠄⠀⠙⢦⠀ ⠀⢀⣠⡤⠶⠋⠁⠀⣠⠴⠋⠁⠀⣸⠋⠀⣼⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⡀⢹⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠆⢠⠀⠹⣶⣄⡙⠳⡦⢴⣀⠀⠀ ⠋⠉⠀⠀⠈⣉⡽⠛⢁⣴⡇⠀⢀⠁⠀⢠⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣶⠀⠀⢸⣣⡀⣀⡉⢻⣶⣅⠀⠈⠁⠀ ⠀⠀⠀⡴⢚⣟⡤⠞⡅⡾⠀⠀⣼⢠⡀⠏⣾⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⢀⣼⠿⣿⡄⠘⡇⠻⣸⡝⠢⣷⠙⣷⠀⠀⠀ ⠀⠀⢰⠅⠈⠋⣠⣾⠀⣇⡇⢰⢿⣸⣷⣄⡧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣿⣿⢹⠰⡅⢱⡀⡇⠀⠿⢷⣄⡉⠀⠘⣷⠀⠀ ⠀⠀⣼⠀⡴⠚⡹⠃⠀⣟⣷⠸⠀⠉⣏⠙⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣇⢻⠀⢿⠃⠀⡀⠀⠏⠙⢦⠀⠙⡄⠀ ⠀⠀⡏⣾⡰⡞⣇⠀⠀⢹⡸⡦⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣼⠄⠀⠀⢠⠁⢀⡆⠀⠈⣧⠀⡇⠀ ⠀⠀⢷⡇⠃⠸⡜⣆⠀⠀⣧⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⠀⠀⠀⠾⢀⡼⠁⠀⢠⢹⣰⠃⠀ ⠀⠀⠈⢷⡀⠀⠘⢮⣧⡀⠘⣆⠀⠀⠸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡟⠀⠀⣠⡾⠋⣿⠀⠀⠀⢸⠏⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆⠀⠀⠠⣤⣄⡈⢷⡀⠀⠀⠱⣄⠀⣦⠀⠀⠳⡄⠀⠘⢦⣻⣿⢿⣿⣿⣿ ⣿⣿⣿⣿⡿⠿⠛⣋⣉⠀⠒⠒⠶⠦⣤⣐⠒⠂⠈⠙⠲⣽⡦⣀⠀⠻⣦⡙⢷⡀⠀⣧⠀⠀⠀⠹⡅⢸⣿⣿⣿ ⠉⢙⡻⠿⢿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢐⣬⠉⢉⣛⣲⣶⣦⣿⠮⣝⣦⡑⠙⢌⣿⡄⢻⣧⡀⠀⠀⣧⠿⠿⠿⣿ ⠊⠁⠀⣠⠏⠀⠀⢀⡀⢀⡖⠀⣠⣾⣿⣵⢞⣫⠭⠲⡏⠉⠉⠙⢺⣿⡛⢷⣄⣹⡟⠜⣿⢧⠀⠀⣏⡠⠔⠚⠿ ⠒⠒⠚⠁⠀⡠⢀⣾⠀⣸⠃⣼⣿⣷⡯⠛⠉⠀⠀⠀⣿⣄⠀⠀⢸⡏⢱⡀⠈⠻⣿⡀⢻⢸⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⢣⡟⣿⠀⢻⣸⣿⠟⠁⠀⠀⣧⠀⠀⠀⠸⣿⣷⣦⣸⣷⠈⡇⠀⠀⠈⢻⣿⡀⢸⢀⠇⠀⠀⠀⣀ ⠟⣠⠞⢡⢇⣿⣡⢼⠀⠀⢿⠁⠀⠀⠀⠀⠸⣧⡲⣦⡀⠹⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠉⢿⡼⡜⢐⡦⠖⠉⠀ ⠀⣀⣠⠟⡾⣷⢹⡘⡆⠀⠘⣆⠀⠀⠀⠀⢰⣿⠛⠷⣯⣗⡮⣻⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢷⣿⣭⠤⣤⣀⡀ ⠿⣯⠋⣰⠃⠃⣼⣧⣷⠀⠀⠘⣆⠀⠀⠀⢸⣿⢀⣠⣤⣉⠻⣮⡳⡙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⢯⠓⢦⡀⠉ ⣾⠖⠺⣿⠀⠀⣿⡆⠻⣆⠀⠀⠘⢄⠀⠀⠘⣷⣿⣿⣿⣿⣷⠘⣿⠙⡜⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠙⠦ ⠛⠳⡼⢻⠀⢰⣿⣇⠀⠘⡦⣄⡀⠀⠑⠦⣀⠘⢿⣿⣿⡿⣿⠀⢸⡇⣿⡸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡐⢦ ⠀⠀⢧⡘⡆⢸⣿⢿⣆⠀⢳⡀⠛⣏⡓⠒⠚⠛⠂⠙⠻⣞⠁⠀⢸⡇⠇⠃⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠈⢄ ⠉⠉⠙⢳⡇⠘⣿⠈⢿⡆⠘⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡇⠙⠀⠈ ⠀⠀⢰⠏⣰⠀⢿⠀⠀⢳⡀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣝⣢⡈⣹⢠⠱⡤⣀ ⣤⠖⣁⣴⣿⠀⢸⠀⠀⠈⣧⡀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠈⣿⡿⢇⣄⠁⠙⢄ ⠿⢿⡿⢻⣿⠀⣾⣇⠀⠀⢹⣿⣆⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣃⣼⡟⣁⢸⣹⠉⠉⠉ ⠀⢨⣷⣼⣿⣾⣿⣿⡄⢀⣸⣿⠻⣧⣸⣿⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⢀⣀⣼⡿⡅⡿⡇⣸⠀⠀⠀ ⢀⣼⣾⣿⣿⣿⠻⣿⣧⣾⣿⣿⡆⢽⣿⣿⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⣴⣾⠏⠀⢰⣇⠹⣷⣱⠃⠀⢀⣠ ⠤⣜⡋⢉⠏⠀⠀⢹⣿⣿⣿⡏⢳⣼⣿⠃⠀⠀⠀⠀⠀⢀⣀⠈⠙⠢⡀⠀⠀⠀⠀⢠⢏⢻⣀⣉⣛⡾⠟⠋⢀ ⠶⢂⡴⠋⠀⠀⠀⣼⡿⠋⢀⡿⢸⠏⠁⠀⠀⠀⠀⠀⠀⠘⢯⠙⠢⡄⠘⠆⠀⠀⣠⡿⣽⠸⣷⡄⠀⠈⠀⠘⠻ ⠀⠉⠀⠀⠀⠀⠀⠋⢀⡴⢿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣠⣾⣿⡇⣿⡇⣿⠻⣤⣬⣽⣲⣤ ⣴⣶⣶⣶⣶⣶⡶⠞⠻⣄⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣗⠹⡜⣀⠈⣘⢿⣿⣿ ⠉⠻⣿⣿⣿⣿⣿⣶⣄⠀⠙⠦⣈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⣀⡴⠋⣸⢿⣿⣿⣿⣿⣿⣷⣽⣿⣷⣿⣿⣿⣿ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣄⡈⠓⢌⣹⠏⠉⠙⣶⠤⠴⣾⠁⢰⡦⠸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢢⣠⠞⠁⠀⢰⡏⢀⡏⣷⠀⢳⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⢋⢳⠀⠀⡿⣧⠞⢸⣿⣧⠘⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃⢀⣿⢣⣿⣣⣾⢟⣁⣤⣾⣿⣿⡗⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣖⣴ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⢀⣾⢣⡿⠻⣄⠀⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⢀⣾⣯⠋⠹⡢⢌⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

)∩͈` ᐜ ͈´∩ ( etaiporpani ot ton sti epoH ✧₊⁺⋆☾⋆.˚₊✩⁺₊✧˙⋆✮��☆ yyyysgemS ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠇⢾⣷⣴⣀⠀⠀⠀⠀⠃⠀⠀⠀⡇⢰⠀⠐⡐⠸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⡥⣿⢶⡴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣿⠾⠛⠛⠉⠈⣠⣀⠠⣖⣷⣿⠛⠉⡿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠀⠀⠀⡰⠊⢠⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡾⠀⠀⠃⠀⡄⠘⠀⠀⠀⠛⠴⡠⠀⠀⠀⠀⠀⠀⠋⠝⣋⠚⠶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⣀⣀⣄⣤⠦⠶⠓⠛⢉⡨⣇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠁⠀⠇⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⢠⠀⠀⡇⠀⠀⢆⠀⠁⡌⢀⠀⠀⠀⠀⠁⠋⠾⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣽⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⡇⠀⡜⠀⠁⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡀⠱⠀⠀⠀⣀⠀⠀⠀⠉⠛⠿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣴⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⡜⠃⢰⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠋⡴⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡏⢀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠋⠞⣴⣠⣴⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣸⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⢸⡏⠀⠀⠃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⡆⡇⢺⠈⠀⠀⠀⠀⠀⠀⠀⠁⣻⡿⠲⠀⠀⠉⠋⠛⢶⡴⣠⣀⠀⠂⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠏⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣤⢀⠀⠀⠀⠀⣧⢹⢆⠈⠀⠀⠀⠀⠀⡟⡿⣿⣿⠿⠶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠃⣿⣿⣼⠀⠟⣧⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠏⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⡇⠱⠂⣇⠈⠀⠀⠀⠇⣿⣷⣿⣀⢀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣾⠀⠇⢠⡼⣇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠀⠀⠀ ⠺⠑⠉⠀⠀⠀⠀⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠣⡞⢠⠀⠀⠁⣿⢹⡟⣿⠸⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢀⠋⣰⡏⠟⡄⣿⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⢠⠀⠀⠀⠀ ⢿⡙⣿⠻⠚⠉⠈⠊⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡟⣿⣟⣿⣾⣿⠘⠁⠈⠉⠀⠄⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⣿⣿⢠⠏⣿⢿⣿⢠⠀⡇⢸⠀⠀⠁⠿⣠⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⡽⣰⠀⠀⠀⠀⠀ ⣿⣼⣧⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠐⠀⠇⣿⣿⣿⢮⠃⣠⣟⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢣⡰⡏⣿⣾⢠⠃⢸⡂⢹⠀⠀⡇⢈⠀⣏⢠⠀⠀⠀⠀⠀⠀⠀⠇⣁⠀⠀⠀⠀⠀⠀ ⣄⢻⠀⣄⣷⠻⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⡠⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣏⢟⢻⡿⣠⣟⣿⢰⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡿⣾⢏⢠⠏⣷⣿⢀⠀⠀⢻⠀⣯⠈⠀⡀⢶⠴⢠⠀⠀⠀⠀⠀⠀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀ ⢶⣿⠹⠀⡄⣦⣻⠙⠉⠉⠉⠉⠉⠀⠁⠉⠋⠖⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣣⣿⣾⣡⡝⢋⡟⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠁⠟⣾⣠⣎⢠⠋⣡⡿⢠⠀⠀⠀⠀⠄⣤⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⣿⠘⠀⠀⠀⣄⢷⠛⠛⠖⠶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠁⡿⣿⢋⢾⣿⢿⣿⣴⣎⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⡿⣾⢀⡐⠁⠔⢋⣯⣾⠇⠸⠀⠀⠀⠀⠀⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⠈⠀⠀⠀⠀⠀⠀⣀⠤⠒⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⢾⣿⣴⢀⠁⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠀⠀⠁⠿⣿⣼⠀⠀⠊⡡⠜⣏⣿⢸⡇⢸⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣷⢻⣯⣉⡞⢀⠀⠀⡏⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⣋⣾⠈⠂⡴⢃⡠⠏⣿⣿⢀⡟⢠⠀⠀⠀⠀⠀⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠋⡾⢤⠀⣷⣌⣤⠀⠀⠀⠃⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢾⡒⢭⠝⢁⡿⣰⣟⣾⠀⣾⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠃⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⣿⢿⠒⠒⠤⠤⡀⣁⠋⠖⡴⢮⠷⠿⣶⣷⠟⡶⣶⢠⠀⠀⡄⢻⠀⠀⠀⠀⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⢍⡻⣎⣿⢨⡞⣇⢰⠇⢠⠀⠀⠀⠀⠀⠀⠀⠋⢽⠀⠀⠀⠁⠜⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⢰⡇⣱⠀⠀⠀⠀⠋⣴⢀⠁⡿⣶⣠⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⣷⠹⠀⠀⠏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣷⢰⣄⣤⣶⣷⣿⠙⣼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⠀⠀⠀⡀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⡜⠀⡇⡉⠻⠛⠛⡿⣥⠫⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠈⠏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠸⠀⡟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⣈⣇⠅⣿⠿⡿⣿⣿⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⠀⠀⠀⠂⠀⠀⠂⠄⠑⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡟⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⢸⠏⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣅⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠂⡟⢹⠀⠀⠀⠗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣲⣤⣶⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⢸⠀⠀⠀⠋⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠘⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢸⠀⠋⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣹⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡄⢀⠀⠀⠁⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡦⢻⣧⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠁⠊⡤⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⢘⠄⡠⠁⠋⠟⠴⣠⢀⠀⠀⠀⠀⠀⠀⠤⠤⠦⠲⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠈⡄⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢷⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠋⠟⣿⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⠀⠀⠋⠈⠤⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠊⠔⡤⣶⠶⠴⠤⠤⠠⠀⣄⢧⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡆⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠀⠃⠛⠀⠁⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀seiboob⠀⠀⠀⠀⠀⠀⠀seiboob⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣷⠀⠚⠈⠀⠀⠀⠀⠀⠀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⣿⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡴⣮⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⡴⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣸⠀⠀⠀⠀⠉⠀⠀⠁⠾⠳⠈⠀⠀⠀⠀⠀⠀⢻⣌⣷⠘⠀⠀⠀⠀⠀⠀⠀⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡥⣿⣴⠀⠁⠉⠟⡾⣠⠀⠀⠀⠀⠀⡀⢤⠶⠲⠓⠛⠉⣿⠨⡀⣄⠳⠙⠈⠀⠀⠀⠀⠀⣆⣜⠱⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠴⠀⠀⠁⠉⠉⠉⠓⠞⣰⢀⠁⡼⣤⡿⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠂⣸⢹⠀⠀⠀⣀⣷⡹⢿⠿⠻⠛⠉⢻⡟⠿⠿⠽⠾⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣷⠿⠛⠉⠉⠀⠁⠉⠈⠀⠁⠚⡗⣓⣹⡽⠶⠐⠠⠀⠀⠀⠁⡞⢀⠀⠀⡞⢀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⣄⡳⠢⠀⠀⠀⡀⣷⣾⡇⣴⣠⣎⣀⣿⣴⣿⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣿⣶⣶⣴⣤⣤⢷⡿⠾⡟⣿⠷⠛⠉⠀⠀⠀⣇⠘⠀⠀⠃⢰⠁⠏⢲⠗⠛⠛⠘⠀⠀⠀⡀⢻⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⡀⢯⠘⠀⠀⠀⡇⢰⡇⠠⠀⢀⡎⣠⠀⡼⠀⠁⠋⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢁⠉⠉⠙⣉⣀⣀⣖⢶⠛⡛⢶⣶⣿⣿⢿⠛⠈⢿⠐⠀⡀⠀⡴⢃⡿⣴⢀⣞⠀⠀⠀⠀⠀⡀⢱⠀⠀⡆⠈⠀⢿⠘⠋⠾⣷⣶⣿⠈⠀⠀⣰⠘⡞⠄⠀⡠⠀⠶⡴⣤⣤⣠⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⣈⠀⠀⡀⣀⣦⣷⢬⠦⣹⣄⢶⠙⠀⣄⣦⣿⣮⣿⠀⠀⠀⠀⠏⣿⢠⠀⠇⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢣⠀⣇⡿⣾⡄⢀⠀⣿⠀⠋⠛⠟⣴⢀⠀⠀⠉⠒⠀⠀⠉⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠽⠤⠤⠤⠤⠤⣤⠲⡑⣌⠵⡄⠱⠀⠀⣆⣹⣿⠀⠀⠀⠃⢿⢠⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡇⣿⠈⠀⠀⠀⣸⠃⣴⣞⢠⠀⠀⠊⡠⢄⠤⡤⣢⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠉⠀⠀⠀⠀⠀⠀⡀⡄⠲⡈⢠⠀⠀⣇⣾⢰⠀⠀⡏⣻⠀⠀⡆⠀⠀⠀⠀⠀⠀⠃⠚⠙⠀⠀⠀⠀⡆⡏⣿⢀⠀⠀⡇⢠⡘⡏⢀⠀⠁⡽⠀⠀⠉⠛⠚⠴⠤⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢦⠿⠻⠈⠀⣄⠱⠀⠀⡇⢼⠀⠀⠙⣿⣧⠀⠀⠞⠀⠀⠀⠋⠟⣶⣤⣤⣤⣶⠿⠛⠈⠀⣏⣿⠈⠀⠀⡟⠀⢻⢠⠀⠀⣣⢺⠿⣪⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠔⣧⣩⣀⢀⡀⢄⠑⠈⢣⠈⡀⣇⠀⠀⡇⣧⣿⠰⠃⢰⠉⠟⣾⣴⢀⠀⠀⠀⠀⠀⠀⣄⣦⢷⡟⣿⢹⠀⠁⢸⠇⢸⠀⠀⠁⣰⢔⣿⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠄⣦⣑⠙⠀⠀⠀⠀⠀⢄⠙⡇⠘⠀⡇⡄⣿⢠⡋⡿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⠻⡏⣿⠤⣘⠳⠀⡀⠀⠁⣿⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⠤⣤⠤⡤⡦⠹⠀⠀⠀⠀⠀⡤⡷⣚⢯⡙⠋⣿⢻⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⡀⢀⡀⢷⠈⠀⡏⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡶⣤⣠⣄⢄⠦⠑⠀⠀⢂⠀⠀⠀⠀⡅⡟⢹⡇⣧⣿⣿⣷⠘⠀⠀⠀⠀⠀⠀⠁⠉⠈⣉⠋⠞⠤⠀⠀⠀⠀⠀⠀⡀⣿⢻⠀⠀⠀⢺⡫⣿⣴⢠⠥⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠯⠾⠘⠀⠁⠀⣧⡞⣿⣴⠀⣟⣷⠈⢷⠈⠀⠀⠀⠀⠀⡀⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡒⣷⠛⠀⠀⣤⠃⣸⠁⠴⣁⠋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡀⢷⡄⠱⠀⠉⡄⢹⡇⢠⠀⣸⠀⢣⡏⢧⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠿⠙⠈⠀⠀⠀⠀⠀⢄⡳⣈⢠⠀⠀⡟⠎⢀⠀⢉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⣑⣬⢹⡀⡧⢸⢄⣿⡏⢀⠀⠀⠀⡇⢿⣡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⡄⢷⠘⠧⣾⢃⠂⡵⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠈⡀⢫⠈⣆⠘⠁⣇⢀⠀⠀⠀⡎⢀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣅⠀⠀⠀⠉⠋⠛⠐⠋⠈⠀⡀⣷⠈⢷⡇⠔⣧⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠳⢙⢫⠀⢆⡈⡿⢻⠀⠀⠄⢀⡞⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠿⣻⣏⣷⠷⣜⠳⠀⣤⢿⠙⡏⣿⡽⠉⠼⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠴⣀⣀⡀⣦⠘⣇⣽⣿⠈⠀⠀⠏⢠⠀⠋⠛⠞⠿⠸⣤⣿⠀⠀⠀⠀⡄⣶⢿⣿⢿⡿⢻⡿⢿⡿⣩⢉⠈⣇⣿⠙⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠤⠤⠢⠑⠈⠀⡼⣻⣷⢸⠀⠇⢸⠃⡼⡇⣿⣉⢰⣿⡿⣿⠰⠀⠈⠀⠀⠀⡀⣤⠷⣻⣿⣿⣿⣿⣿⣬⣠⠠⣷⢸⣀⢀⠤⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣽⠀⢹⡇⡟⣾⠀⡿⢉⡿⠛⡛⣿⣿⣿⣿⣿⡿⠿⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⠠⠀⡟⢸⠀⠃⠾⠷⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠙⡏⡘⣷⢻⠃⣼⢀⠀⠁⡟⢾⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠛⣹⠏⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣉⢚⣳⠀⣄⣧⣿⡇⢸⠀⠖⣤⣥⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⣿⢠⠀⣀⣄⣢⢑⠬⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠉⣿⣿⣾⢳⠙⠀⣧⣿⣦⠹⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣶⣴⠀⠀⠀⠀⠉⠛⣉⠫⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⡑⣍⠹⡉⢟⡞⣰⠀⣇⡠⠤⠀⠀⠀⠇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠖⡿⣽⢀⠀⠀⠀⠤⠗⣮⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡴⣀⠀⠀⠀⠀⠀⣀⠥⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⡿⠟⣰⣄⢶⠭⡦⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡶⢴⠤⢷⠦⠓⠉⠀⠀⠀⡀⣉⣿⠿⠿⠛⠛⠖⠶⠷⡿⠿⣖⣴⢀⠀⠈⠀⡀⠀⠀⠀⠀⠃⠟⠀⠀⠀⠀⠀⠀⠀⣄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢴⠡⣻⢾⠀⠀⠁⠀⠀⣠⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢺⠈⠀⠀⠀⠈⠋⠀⡀⠦⠬⠧⠴⠦⠒⠛⠉⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣿⣴⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠀⡄⠓⠉⠀⣆⣈⣤⣤⠾⣷⢲⠠⠀⠀⠀⡀⣀⣄⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠉⠞⠿⡿⢀⠀⠀⠀⠀⠀⠓⠉⠉⠋⠛⢻⠀⠃⡾⢀⠀⠓⠈⡀⣄⠤⢴⡁⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣴⣇⣾⠀⠀⠀⠀⠁⠛⡾⢡⡞⣠⠀⢰⠊⣠⠀⠀⠀⠤⠓⠉⠌⠑⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⢰⠀⠁⠋⠿⣴⢀⢶⢐⠁⠙⠀⣦⠿⡶⣼⠁⠊⠀⠀⣀⣄⠤⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀