⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⡟⡛⢛⣛⣻⣻⣿⢛⡛⠛⠛⠛⢿⡾⠟⠛⠛⠛⢛⢿⣟⣛⣻⡿⠛⠛⢻⡾⠛⠛⠛⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⡀⣤⡯⠉⠛⡇⠀⠀⢠⠄⠀⠈⣇⣀⡀⣤⠄⠀⠀⡇⠀⠀⢥⠀⠀⠀⡇⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠁⢿⡃⠀⠀⡇⠀⠀⠈⠀⠀⠸⡟⠁⠉⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢸⠇⠀⠀⡇⠀⠀⢰⠂⠀⢀⡇⠀⠀⠰⠀⠀⠀⡇⠀⠀⢼⠀⠀⠀⡇⠀⠀⠸⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣇⠀⠀⠈⠐⠄⠀⡇⠀⠀⢺⡀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣺⢀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠓⠛⠛⠁⠀⢠⣧⣠⣤⣾⡅⠀⠀⠛⠛⠓⢻⡿⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣾⠿⠿⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣤⣤⣤⣤⣤⣿⠏⠁⠀⢹⠦⠤⣤⡄⠀⠀⠘⠛⠻⢷⣶⠟⠛⠛⠛⠟⢷⣶⠟⠛⠛⠛⠛⢻⣿⠟⠛⠻⢿⢶⢶⣴⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⡇⠀⠀⢀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢻⡟⠀⠀⢸⡉⠉⠙⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠉⠉⢻⡇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠄⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢰⠤⠤⠴⡇⠀⠀⢸⡶⠿⠿⣿⠀⠀⢈⡗⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⡇⠀⠀⣸⠀⠀⠀⣇⠀⠀⠀⠀⠀⢐⣟⠀⠀⣺⣇⠀⠀⣿⡀⠀⠀⠀⠀⣀⣾⠇⠀⠀⠀⠀⢀ ⣠⡾⡟⠛⠛⢿⣿⣿⡟⠛⠻⣿⠻⠛⢿⡟⠛⠛⠻⠿⡿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⠀⢀⣤⡾⡭⢾⡃⠀⠀⡧⠀⠀⢸⠀⠀⠀⠀⠀⠀⢐⡟⠀⠀⢀⠘⠻⢿⡻⣌⠉⢁⡉⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣛⣭⣽⣿ ⣿⡟⠋⡉⡉⣳⠁⢸⡅⠀⠀⣗⠀⠀⢸⡇⠀⠀⢸⡍⠉⠉⣟⠀⠀⢸⡃⠀⠀⣷⣽⣷⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⣿⡇⠀⠀⣷⡇⠀⢸⠆⠀⠀⢯⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⡧⠀⠀⢸⡅⠀⢠⠿⠛⠻⣿⣿⡿⢿⣿⠁⢻⣯⡽⢻⣿⣿⡿⠛⡷⣄⠀⠀ ⢿⣇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⣰⣿⡀⠀⢠⣿⣿⣃⣚⣋⣧⣀⣍⣁⣜⣻⣿⡇⠀⠀⣿⣧⢠ ⠘⠻⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠟⠛⠷⠶⠶⠶⠶⠾⠻⠷⠶⠶⠶⣿⣿⡇⣠⣾⣿⣿⣿⡟⣿⣛⡿⡝⢹⣿⣿⣿⣷⣄⣰⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣾⣿⣿⣿⡲⣝⡺⣽⣿⣿⣿⣿⢾⣿⣿⣿⡜⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠟⠁⠀⠙⢿⣿⣿⡜⣳⣵⣿⡿⠋⠀⠈⠻⠿⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⣿⣵⣛⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⡀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⢀⡀⡤⠄ ⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠀ ⢸⣿⣿⠀⠶⣶⣶⡶⢶⠶⡲⡲⣶⢶⣲⡶⣶⣶⢶⣶⣶⣶⣶⡶⠶⠠⣿⣿⣿⠀⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠀⣿⣿⠀ ⢸⣿⣿⣶⣦⣤⣉⠻⣷⣩⢊⣛⣴⡳⡹⢳⡽⢯⣿⢯⣿⠏⢁⣤⣶⣶⣿⣿⣿⣶⣶⣤⣈⠹⣿⣿⣟⣯⢿⡽⠋⣠⣤⣶⣶⣿⣿⠀ ⠈⠉⠂⠊⠩⠙⠿⣦⡈⢿⣯⠋⡵⢡⠇⣏⢻⢯⣳⡿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣹⣿⣻⣿⠏⣠⣾⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠝⣷⡈⢿⣿⣠⡞⣰⢿⣞⡳⠿⡿⠿⠂⠘⠛⠛⠛⠛⠻⠿⣿⠿⢿⣿⣀⣿⣿⣿⠃⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠜⣷⣈⡿⠗⠫⢉⣂⣀⣤⡤⣴⣶⣶⡶⠶⣶⣶⣶⠖⠄⢤⣤⠤⣀⣈⠉⠝⠣⢴⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣐⠔⢋⣥⢴⣶⣿⣿⣈⣏⠛⠇⢸⣿⣿⡇⠀⠹⣿⣿⡆⢀⡾⠁⠀⣿⣿⣿⠕⢶⣤⣌⠑⠧⡠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢞⠁⠀⠀⠀⠈⣿⣿⣿⣟⠙⠀⠀⣸⣿⣿⡧⢀⠀⡹⣿⣿⠟⠀⠀⢰⣿⣿⡿⣿⠋⠛⠁⠀⠀⢨⣻⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⢰⣿⣏⠀⠀⠀⠀⠀⣸⡿⠿⠛⠛⠋⠈⠉⣀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠉⠙⠙⠻⡳⢾⣿⠋⠀⠀⠀⢘⣿⣿⡤⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠈⣀⡴⢤⢺⣷⣶⣿⣿⣿⡿⣿⣿⣿⣿⣏⠹⠏⣹⣿⣶⡞⢲⣤⢌⣈⢀⠀⠀⠈⢿⣾⣿⠗⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⡷⢃⡤⣒⣉⠓⢾⣿⣇⠹⣿⣯⠿⣵⠿⣿⣽⣻⡾⣿⣆⢰⣿⣿⡟⢠⣿⣿⠷⠊⣙⡚⣄⡠⣜⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡷⡿⣻⠭⣤⣀⡀⣹⣿⣆⠹⣿⣿⣻⣛⡿⣼⣻⣽⣷⠾⣿⣿⡟⢀⣾⣿⡏⢀⣠⣤⢭⡚⣟⢿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢼⣿⢸⣱⣮⣄⣟⠋⠙⠷⣽⣿⣆⠹⣿⣯⣛⡿⣽⣳⣯⣿⣷⣟⡟⢀⣾⣿⣯⠞⠋⠉⣿⢷⣶⢸⠀⣽⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣯⣀⣠⣽⠾⠃⠀⠀⠀⠉⠘⣿⣦⠘⣿⣿⢿⣳⢿⣽⡻⢽⡞⢀⣾⡟⠍⠁⠀⠀⠀⠈⠳⢼⣄⣀⣽⠕⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠘⣿⣟⣯⣻⣏⠷⡾⠁⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠘⣿⣷⣽⣞⡿⠁⣼⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠘⣿⣟⣶⠃⣼⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⣤⣄⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀