⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣟⣻⣿⣿⣿⣿⣭⣭⡩⣿⡿⠟⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡽⣯⠯⡝⠋⠋⠉⢻⠏⠁⠉⠉⣿⠁⠀⠈ ⣿⡟⣉⠭⠔⠒⠒⠠⠭⢼⣛⡿⢿⣿⣿⣿⣿⣿⠇⣾⣿⣿⠿⠟⠉⡿⡿⡯⠛⠁⠀⠀⠀⠈⢻⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⡶⡗⡀⣁⠀⣿⡇⠐⠀⠀⣿⠀⠀⠀ ⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠽⣿⣿⡟⠸⡿⣿⣯⣇⣶⣦⣯⣋⣀⣀⣀⣀⣀⡀⠀⠀⢷⠀⠀⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣟⣓⢴⡇⠀⣽⣗⠀⠀⠀⣿⠀⠀⠀ ⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡽⠿⠒⠛⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠙⠛⠙⠫⠶⠿⢲⣤⡄⣀⣸⣿⣿⣿⣺⣿⣿⣿⣦⣽⢳⠖⠀⢻⣷⠀⠀⠀⣿⠀⠀⠀ ⣿⣷⢇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣯⣻⠈⣺⣿⠀⠀⠀⣿⣀⡤⡴ ⣿⣿⣟⡆⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠽⣯⣟⠿⣿⣿⡠⠘⠀⢀⣠⢶⡫⠗⠉⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢷⣌⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣀⠀⠀⠀⠁⠫⢾⣝⠳⣥⡴⡫⠗⠉⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣤⠞⠉⠉⠻⢦⣀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢶⣤⣄⠀⠀⠙⠻⡣⣋⠒⠶⣀⣀⡤⠚⠉ ⡉⠉⠀⠀⡰⠃⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠉⠓⢦⣄⡈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣶⣦⣬⣻⢿⢦⡄⠀⠈⠻⢷⣦⠞⢁⡴⠊⠀ ⠍⠉⠉⡱⠁⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡶⠬⣝⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣷⣶⣙⣷⣄⠀⠀⠙⢷⣍⠀⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠈⠈⠉⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⢯⣷⣄⢰⣮⣿⢣⡀⠀ ⡀⠀⡎⠀⠀⠀⢸⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⣿⣣⠙⢿⣷⣿⣆ ⠀⠀⠇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡇⠀⠀⠀⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡉⠘⢷⣦⣑⡧ ⠃⠀⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡿⠥⠤⠴⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⢻⠛⠻⣦⣴⠊⠙⢦⣀⢀⡔⠁⢨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡆⠀⢻⣏⠉ ⠀⠀⢱⡀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣀⣀⣤⣤⣦⠶⡶⠶⠶⣶⡾⠛⡻⠛⠒⢺⠒⠒⠘⡿⣷⣄⠀⠹⠫⣂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠺⡄ ⣀⣀⣀⣿⣶⣯⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⣿⣿⣿⡍⠀⠀⠀⠀⠈⠒⠂⠤⠐⠊⠀⠀⢀⣿⡄⠀⠀⢻⠈⢻⠟⠀⠁⠊⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠁ ⣀⣀⣀⣀⣾⡏⠀⠀⠀⠀⠀⠀⢁⣼⠫⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⣹⠀⠀⠀⢸⡴⠁⠀⣴⣍⠢⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡀⠀⠰⡟⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⢀⡿⠃⠀⠹⣯⣉⣻⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣾⡟⣋⠿⠃⠀⠀⠀⢸⠙⠢⢞⣁⠙⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠘⢿⣦⡀⢡⠀⠀⠀⠀ ⠀⠀⠀⢨⣷⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢻⣏⠉⠛⠛⠛⠛⠛⣿⠋⠹⠏⠀⠈⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠉⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡌⢯⣷⣼⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡝⣎⣿⡳⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡟⠀⠀⢀⡀⠀⠀⠀⠀⣴⡏⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⢿⣷⠀⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠂⠀⢀⣼⡟⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⠃⠀⠀⠀ ⠉⠉⢹⣧⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠁⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀ ⣿⣷⣿⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⣿⣿⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡶⣤⣄⣀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀ ⣿⣿⣿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⡏⠙⠛⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢰⣿⡃⠀⠀⠀⠀⠀ ⣿⣿⡿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣾⣿⣇⠀⠀⠀⠀⠀ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⣿⡀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠙⡟⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣷⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢹⠈⠿⣄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀