⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣶⣽⣿⣿⣶⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠿⠟⢛⣛⣛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣾⣿⣿⣿⢿⠿⠛⠻⣿⣿⣌⠙⠛⠿⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠉⠁⡰⠁⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡀⠀⡰⠃⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠙⠷⣥⣸⣤⠶⠶⠛⢟⠛⠓⢲⠁⢀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣤⠤⠬⠤⠤⠤⠤⠤⠤⠦⠤ ⠀⠀⠀⠀⠀⠀⠠⠀⡐⠊⡌⠀⣄⡄⠀⠸⠁⢀⢀⠀⠀⠀⢣⠀⠸⠊⢅⠀⠉⡄⠀⠀⠀⡀⠀⠀⠀⣠⣞⢭⡒⢖⡒⢖⡒⢖⡒⢖⡒⡲ ⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠣⡀⠙⠁⢀⡡⠀⠻⠞⠀⠀⢀⡆⠀⠀⠩⠁⡁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠷⣎⡆⢉⠂⡉⢂⠉⢂⠉⢂⠉⠄ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣱⡾⠇⠁⠱⠆⠀⠀⣶⠿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠰⠀⠁⡀⠈⠀⠆⡈⠀⠈⡀ ⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⢀⠀⠀⢸⠀⠀⠁⢰⠀⠀⠀⠐⠈⠀⠀⠀⣾⢍⡳⢍⡳⣩⢍⡛⡼⣰⢋⡵⣒ ⠀⠀⠀⠀⠀⢠⠋⠀⣀⡀⠤⡄⠒⠀⠉⠀⠀⠀⢀⠠⠂⠁⠀⠀⠸⣀⠀⣴⣾⣿⣦⣸⠀⠀⠀⠀⢀⣾⠖⠰⢀⡡⢂⠢⣈⠔⡀⠦⢐⠠ ⠀⠀⠀⠀⠀⡳⠬⠟⠉⠹⡚⠀⠀⠀⠐⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⠀⠙⢩⡒⠂⡾⣭⠈⢓⡉⢂⠂⢰⠘⢒⢉⣦⠂⡄ ⠀⡄⠀⠐⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢰⢶⢻⣿⣿⣿⣇⠀⠀⠨⡘⢝⠄⣹⠖⣩⠩⢼⠳⡱⣹⢣⢞⡡⠌ ⠀⠈⠍⠇⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠋⠐⠄⠀⣼⠂⢸⣿⣿⣿⣿⡀⠀⠀⠈⠄⠙⢝⢺⠃⠈⢎⡇⣇⢎⡷⣸⡆⠉ ⠀⢀⡀⠆⠀⠀⢀⣉⠀⡇⠀⠀⠀⠀⢀⡠⢰⠉⠁⠤⡠⠇⠀⠠⠀⡮⡀⠸⣿⣿⣿⣿⣧⠀⡀⠀⠁⠀⠀⠻⡭⠭⢝⡂⡏⡩⢲⢹⡄⠳ ⠐⠈⠀⠃⠀⠀⠈⠈⠀⠈⠒⠒⠂⠈⠁⠀⢸⠀⠀⢸⡀⠂⠀⣀⡠⠇⠀⠉⣿⣿⣿⣿⣿⠊⠀⠄⠀⠀⠀⠀⠐⡄⢡⡇⠖⠐⣸⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⡔⠀⣤⠀⢸⠀⣬⠘⠒⠈⠉⠀⢣⠀⠀⠉⠉⠉⠛⣿⡟⠁⠈⠀⠀⡎⠀⠀⠀⠈⣧⡏⡇⡜⢸⢹⢡⡄ ⠄⠀⠤⠄⠠⠤⠤⠬⠤⠤⠥⢄⠇⠀⠈⠀⣸⢀⢆⠀⡠⠄⣲⠞⠉⠙⡆⠂⣤⣤⡀⠈⠑⢄⡇⠀⢠⠀⠀⠀⠀⠀⠘⡣⡎⡰⠘⢟⡀⠆ ⡀⣀⢀⡀⣀⢀⣀⣀⢤⠮⢒⣁⣀⠀⡖⣄⡧⠋⠁⢀⠀⠉⠑⡍⠉⠉⠉⠁⠀⠉⠙⠢⢀⠀⠁⠀⡄⢀⠀⠀⠀⠐⡀⠡⡔⢄⠲⡀⠲⡐ ⠖⡴⢂⡲⡖⢮⡱⢎⡥⢊⠒⡤⠀⢀⡈⣐⠀⠀⣈⡀⣏⡑⠖⠀⣑⠀⠈⡹⠿⠶⢤⣀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠐⡄⠗⠊⠐⠐⠁⠂ ⠫⣜⢣⢳⡙⢦⡝⢮⠔⢣⢉⠴⠓⠒⠒⢺⠄⠊⠀⣀⣀⢀⡉⡡⠄⢀⡀⢀⣠⣀⡀⠀⠈⠀⠐⡂⠀⠀⠘⡀⠀⠀⠀⠐⠘⡉⠉⠈⠉⠁