⣀⣉⣉⣩⣿⣯⣽⣉⣭⣀⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣍⣯⣿⣟⣔⣄⣤⣀⣠⣠⣤⣄⣀⣅⣠⣤⣆⣡⣴⣠⣠⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣠⣄⣠⣐⣌⣠⣀⣀ ⠀⣳⣿⣮⢺⣷⣧⣿⣼⢾⠛⠓⠶⠓⠉⠉⠉⠉⠉⠋⠉⠋⠙⡉⣝⣿⣿⠻⠙⠟⠋⠡⣔⡿⠽⢫⢾⢩⡶⢔⢀⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⣫⠹⡏⢫⠘⢸⢹⣽⡟⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⣿⣯⣿⠿⢿⡿⡿⢟⠻⠛⠙⠟⢩⠉⠩⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠔⠀⢠⠀⠀ ⠀⠀⠀⣧⣾⣷⣾⣶⣶⣶⣷⣶⣵⣬⣵⣬⣶⣤⣶⣶⣿⣿⣾⣳⣿⣿⣿⡋⣿⢿⠿⣾⣦⣋⣗⣥⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣦⠿⣿⣾⣿⣿⣿⣾⣤⡤⠀⡄⡤⢠⠀⢏⣿⣼⡴⣠⣄⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⢻⠘⠀⠀⠉⠋⠒⠒⠒⡶⣤⣦⣶⣶⢾⠒⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠖⠤⠤⠤⠄⠀⠂⣗⣷⣿⣿⣿⣿⠾⣀⣀⢀⠀⠀⠲⠛⠉⠀⠦⠛⣘⣤⠻⣀⢦⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣵⢋⠵⠚⠏⠀⠀⠀⠟⠿⡿⣿⣾⣴⢀⢨⠀⠄⠀⠀⠀⠈⠀⡀⣦⢶⠛⡈⣤⠲⣊⢽⠓⡙⣧⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠿⣠⢋⠴⣢⠥⣟⡴⢀⠀⠧⠛⣿⣿⣿⣿⠠⠀⠀⢀⠃⠛⠋⠀⠀⠋⠈⠀⠀⠀⣆⠹⠈⠲⡃⣮⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡟⣽⠿⡶⣀⠁⡞⣾⢾⠂⠄⢟⡎⣿⣿⣿⣸⢞⢀⠉⠀⠈⣿⣿⣿⠻⠘⣷⣿⣿⠨⠀⠀⡄⢻⠀⣄⣷⢿⣿⣿⣿⣿⣿⣷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀ ⠀⠀⠀⠃⣿⡟⣶⣰⠀⠘⡀⡼⢘⢃⣀⠠⡀⢇⣿⣿⣼⢸⢀⡇⣻⡾⢻⣝⣽⣿⣿⣿⣧⣿⢳⢈⠘⠀⠀⡀⢀⠀⠀⣄⣿⣿⣿⣿⣿⡹⣷⢹⠀⠀⠀⠀⠀⠀⠇⣦⣈⣀⢦⠙⠃ ⠟⡞⠋⣷⣾⢩⠟⠛⠀⠄⠀⠣⠃⣠⠀⠀⠄⡟⣿⣼⢻⢣⠀⠀⣧⣿⣿⣿⣿⢿⣼⡤⠀⣆⣸⢳⣻⠉⠈⠀⡀⠂⠀⠀⡿⣾⣿⢿⣎⣿⡌⣸⢿⠻⠈⠀⠡⠈⣿⠾⣿⠟⠛⣧⠹ ⣗⣷⢷⡄⣟⣷⢼⣿⠀⡇⠀⡏⠁⠉⠋⠉⠏⣿⣿⢧⣇⡝⠾⠿⡈⢰⡀⣆⡘⣷⢸⠀⠀⠀⢣⣿⣿⣿⢿⠀⠀⠀⡀⡆⣿⣿⣾⣿⢸⣧⢻⡇⡆⢟⣇⢿⡟⢹⡽⢿⣎⣾⢻⡟⣠ ⠀⡇⣿⠿⣾⡏⠀⣸⠹⠟⡿⣿⣹⠛⡿⣿⣼⣗⣿⡀⣧⣿⢹⣦⢿⠀⠈⠀⣆⠶⢛⠀⠉⠁⡈⣦⣷⣾⣾⠀⠿⡿⣿⣿⣿⣻⢸⣿⢿⡘⣼⡿⠀⣿⣛⡞⠉⣈⣇⣻⣷⢿⡿⢲⠵ ⠀⣇⣟⢰⢇⢀⠛⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡈⣧⣿⠠⣧⡟⣿⢿⠘⠀⣃⠿⣿⠻⢿⣿⠿⢛⢿⠐⣼⣷⣿⣿⣿⣾⢈⣿⣿⣖⢸⠃⠿⣿⣈⣤⢀⣅⠐⡾⡝⣞⠀⠀⡀ ⠀⠀⠁⠀⡅⠇⡧⢮⣧⣾⡠⣈⣧⣟⣟⣿⣿⣿⣿⡸⣶⠹⣌⠻⠷⣿⣿⣿⣿⠻⡟⣠⣾⣾⣿⣿⣾⣆⣧⣹⠋⠿⣿⣷⣷⣿⢀⣷⢨⠀⠑⣿⣾⢹⡤⠘⠀⡀⠁⣭⣞⢠⠀⠀⠀ ⠀⠆⣆⠛⡛⣨⠇⢻⠛⢊⠄⠀⠄⣾⡅⣿⣿⣿⣷⣿⠙⣄⢷⡜⠰⣆⣿⣿⣧⣿⣿⠘⠉⣌⣤⢀⠀⠉⠉⣿⣿⣿⣿⣽⣿⣿⠋⡗⣷⠀⡿⣾⡇⡟⣠⣧⠈⠀⠀⡄⢀⠀⠀⠀⠀ ⠀⠀⠹⣆⣘⣴⡻⠰⣷⣼⠿⠟⠟⣿⣧⣴⣿⣻⣿⣿⣌⢿⡘⢲⠉⠀⡀⣰⡄⣠⣠⢀⣄⣦⢷⠋⡿⣿⣿⣿⣿⣗⣿⣿⣤⣧⣿⡆⠀⡟⣻⠰⡿⣾⠀⠺⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠻⠑⠀⡄⢦⠘⠀⣠⣦⢼⠌⡀⡄⢄⡉⣿⣿⢿⠘⣆⠀⣀⢠⠀⠀⠂⠙⠋⠿⠾⠛⡈⣠⣀⡀⣾⣿⣿⣿⣾⢠⠁⡞⢰⠃⡿⣴⢀⡏⣧⢈⡏⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠉⣏⢛⣌⠱⠀⣦⠻⠛⠈⢂⠀⠀⠀⠀⣷⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⡀⣦⡀⢀⡀⣄⠶⠶⠿⣿⣿⣹⣿⣿⢠⡀⠁⠟⣿⢠⠀⠟⢻⣴⠁⢰⠁⢸⠏⠸⠀⠀⠀⠀⠀⠀ ⠉⠞⣴⣭⣙⢾⡙⠳⠈⡀⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠄⢞⣸⢠⠁⠛⠿⣿⣿⢠⠀⠏⢡⡼⠎⣤⠊⡷⣻⠓⣒⢻⠀⠁⠈⠀⠀ ⣂⠽⡖⢤⣀⠀⡀⢤⠑⠈⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣽⣯⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠂⣤⢀⡽⢉⠛⠿⣭⣿⣶⣠⢀⠃⡼⣛⣵⣖⢚⡤⣁⢠⡀⢄⡠⢀⠀⣤⠰⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠳⠛⠛⠛⡿⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠻⠛⠛⠛⠛⠛⠛⠶⣿⣿⣟⡶⣤⣏⢠⠀⠁⠞⣠⠟⢞⢋⡠⠋⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣭⣾⣷⣿⠛⣾⣦⣤⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣻⡿⣭⣚⡴⣠⣟⢠⠁⠞⣱⠚⡥⣿⡮⢵⢖⢃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣻⣷⠻⡿⣿⢻⠟⡿⣿⣿⣿⣿⣿⣾⣴⣥⣐⠊⠷⣾⣶⣞⣸⠀⡟⣤⣋⡩⠟⣽⢾⣷⣻⠥⢎⢞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠾⡠⣀⢀⠀⠀⠀⠀⠟⣿⣿⣾⢠⠀⡀⣀⣀⣆⣲⣯⣿⣿⣿⣴⣡⣚⡷⡶⢁⠟⣴⣫⠉⡿⣰⢁⡿⢛⡾⣭⣛⡟⣿⠤⣄⣢⣯⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣼⠀⠀⠀⠀⠀⠋⠑⡿⣿⣴⣡⠓⡜⣏⢋⢻⠗⡿⣉⡹⣟⣿⢻⡞⣷⣽⣁⠛⡞⣴⣠⢀⠉⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈ ⠀⠀⠀⠀⠀⠉⠈⠀⠀⠋⣿⣿⣰⠀⠁⠀⠀⠀⠟⢣⣿⣰⠠⡰⣹⡖⠤⣶⣴⠤⢀⡀⢄⡒⣵⣠⠤⡤⣤⡤⣤⣉⠋⠛⠿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⢠ ⠀⠀⠀⠀⡖⣤⠠⠋⡿⣿⣿⢫⠛⠟⢩⠉⠋⡿⣿⣽⢞⠖⣠⢀⠀⠀⠀⠀⠀⠀⣄⠦⠿⠿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢷⠻⠛⠙ ⠀⠀⠀⠉⢯⠠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢚⠀⠀ ⠀⠀⠀⡄⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀ ⠀⠀⠀⠉⠐⡀⣤⣶⣿⣿⣶⣴⣤⣨⠀⠁⠈⠀⠉⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣾⣿⣿⣿⣿⣿⣾⣶⣧⢛⣟⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠂⠀⣿⢳⠟⠛⣀⠀⠀⠀⠉⡏⣶⠟⣳⢸⡠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠀⠀⣀⣐⠛⠟⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀ ⠈⠀⠄⣾⣬⣱⢡⠀⠁⢇⠮⣾⠓⢆⡞⣺⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠉⠀⠀⡀⣭⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠐⠹⠏⢹⣏⡠⢰⠲⡉⣳⢡⡘⠀⣧⠦⠴⢡⠉⠀⠀⠀⠁⠙⡟⢿⠏⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⣮⣵⢿⣯⡻⠻⠙⠈⣁⠋⡹⣇⢉⣹⠿⠙⣿⣻⠉⠲⠛⡿⣿⣿⢿⠘⠈⣬⠻⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠀⠇⣮⣿⣿⣯⣴⢇⡿⣬⡰⢥⣾⣥⢯⣿⢣⣦⡉⢟⣜⡹⣿⣦⠿⠈⢳⣍⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⣿⠻⡿⢛⠛⠛⠛⢿⢿⣻⡛⣿⠿⣟⠻⠛⣟⣿⠿⠛⡿⢟⡻⣿⠿⡟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛