⠀⢀⣾⣿⣿⣟⡿⠛⣩⠟⣉⠽⠛⡂⣀⠀⠀⠀⡀⠬⣍⣓⠦⣈⢢⡻⣯⠳⣄⢺⡦⠙⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢋⣵⠏⢠⠀⣠⣯⠞⠁⢠⣾⠿⡿⡄⣾⣯⡙⣷⡌⠻⣷⡜⢳⣵⡈⢷⡈⢦⠙⣿⣦⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣵⣻⠇⡰⣁⡼⢉⠏⠀⢠⢣⡟⠀⠸⢀⡿⣿⡿⣯⠙⣖⡜⢿⣶⡟⢿⡄⢳⡘⣧⠈⢟⢷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⡳⢰⢁⣽⠁⡎⠀⢠⠇⣸⠀⠀⡿⠘⠀⢻⠁⢹⡆⢻⡾⡌⢻⣿⣌⢧⠀⢳⢸⣧⠈⢧⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣇⢇⣿⡇⢰⠀⠀⣸⠀⡏⠀⠀⠀⢠⠀⠸⡀⠀⣷⠀⢿⣿⣄⠛⢿⣇⣧⠀⢧⣿⡳⣎⣧⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡾⡼⣿⠀⣼⠀⢸⡇⢠⡇⠀⠀⠀⢸⠀⡆⡷⡆⠹⡆⢸⣿⣿⡆⠈⢿⣷⠀⠘⣿⣇⢸⣿⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢷⣷⡇⠀⡿⠀⣿⡇⢸⡇⢰⠀⠀⢺⠀⡀⡗⡁⢸⡗⠀⣿⡈⣿⡄⠈⣿⡇⠀⠉⣿⣮⣿⣷⣈⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⣾⣿⡇⢰⠁⠀⣻⡇⢸⡇⢸⡇⠀⣿⠀⡇⣿⡇⠸⢯⠀⣿⡇⠸⡇⠀⣿⣿⡀⠀⢹⣷⡟⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣾⣿⣿⡅⡈⠀⢸⣿⠃⢸⡇⣾⡇⢀⣿⡀⢿⣿⡇⠀⡄⠀⣿⡇⠀⢿⡆⣸⣿⣿⣼⠈⣿⡇⣿⣋⠹⡇⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠃⡇⢠⢸⣿⠇⢸⡇⣿⣿⣸⣿⣷⣶⣿⣿⠀⠇⣽⢿⠃⢀⣰⣿⣿⣿⢻⡿⡄⢿⣷⣍⣉⢋⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⡇⡇⢸⡜⢿⢰⣾⣷⣿⠻⣿⣿⣿⣿⠉⣟⠀⣆⣿⣾⡾⢟⣯⣴⣿⣿⣾⣿⡇⢸⡇⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣽⡇⡇⢸⡇⢸⣿⣿⠻⣿⣠⣿⣿⣿⣿⠀⢿⣼⣿⣿⠏⢰⣿⣿⣿⣿⡿⣹⣿⢱⡾⣇⡟⢹⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⢛⡇⣷⢈⣿⣾⣿⣿⣆⣿⣿⣿⣿⣬⣿⠀⣸⣻⠿⠋⠀⠘⠉⠽⠿⠿⡾⠟⢹⣸⠀⣿⡷⣻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⣿⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⢧⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡏⢹⡟⠋⠙⢶⠌⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣻⠿⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡃⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢀⡇⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣿⣤⠃⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⢹⠋⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⣷⢸⣿⢁⣀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⢀⡿⣷⠘⢸⡇⠀⡀⣏⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⠋⡀⠀⠀⢀⣿⠏⣼⠁⠈⠈⠉⠙⠲⢤⣠⡄⢸⠄ ⠀⠀⠀⡰⠋⠀⢻⡀⢿⡇⠀⢡⢿⠀⠀⠑⢦⣄⠀⠀⠀⠀⠠⠤⠤⠴⠊⠀⠀⣠⣿⣿⢠⡿⠄⠀⠀⠀⠀⠀⢠⠿⢉⣿⠀ ⠀⢠⠞⠀⠀⠀⢆⢇⢸⣷⠀⢺⣌⡇⠀⠀⠘⢿⣿⢷⡦⠤⣄⡀⠀⠀⠀⣀⢼⡏⣽⣇⣿⠂⠁⠀⠀⠀⠀⠀⠘⠀⣸⣏⠀ ⢀⡇⠀⠀⠀⠀⠈⣞⡄⣿⡶⡈⠙⣿⠀⠀⠀⠈⢿⡳⣄⠀⠀⠈⠉⠉⠉⠁⡸⢹⣿⣿⡏⡖⠀⠀⠀⠀⠀⠀⢀⣼⠏⠘⠄ ⢸⠁⠀⠀⠀⠀⠀⠘⢷⣼⣷⠹⣄⠘⢷⢄⡀⠀⠀⠙⠾⣆⠀⡀⠀⠀⠀⣴⡷⢿⡟⣿⠆⡇⠀⠀⠀⠀⢀⠆⣾⣿⡴⡴⠁ ⢸⡀⠀⠀⠀⠀⣠⡤⠈⢻⣿⣆⠈⢳⠘⢧⠉⠲⣄⡀⠀⠈⠙⠻⢆⣀⡜⠉⠀⠋⡰⠋⠀⣇⠀⠀⠀⠀⠸⠀⣿⣽⣾⡗⠀ ⢸⣇⠀⠀⣠⠈⠉⠀⠀⠀⠹⣟⢆⣀⣧⠀⢷⡀⢀⠉⠓⠦⢤⠀⣠⣿⣿⢿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⣷⠎⠀⠀ ⠀⢫⠳⣞⡁⠀⠀⠀⠀⠀⠀⠈⢣⠱⠜⣧⠘⣟⣄⠑⠢⠤⠄⣠⣿⣟⠉⠀⢹⡟⠲⢤⣀⠀⠀⠀⠀⠀⠓⠀⠘⣿⡀⠀⠀

⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠨⡆⠀⠀⠹⣧⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠘⡌⡄⣷⢀⠀⠀⣌⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⢀⣤⣾⢀⢹⡟⣧⣷⣧⢿⠀⢥⣀⢬⣻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⢠⣯⠀⣀⡾⣿⢿⡿⢺⣏⣽⣛⣷⣸⣴⣌⢗⠲⣽⡇⠀⠀⠀⠀ ⠀⠀⠀⢰⣇⢰⣿⣧⣼⣿⣳⢋⡟⠀⣾⠟⣿⣯⣼⠋⡏⡿⣔⡔⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣾⣿⣿⣏⣿⣿⡦⠀⠀⠈⠐⠊⠁⢸⠂⡇⠇⢈⡓⣜⠏⠀⠀⠀⠀ ⠀⠀⠀⣀⣿⡇⣻⣏⠟⠛⣿⣏⡄⠀⠀⠀⠀⠀⢸⠨⡇⠀⠀⣴⡟⠀⢀⠀⠀⠀ ⣄⠀⢿⠀⢹⣧⣿⠏⢆⠉⠉⠀⢇⣀⠂⠀⠀⠀⢸⠀⡇⠀⠀⣿⠯⠟⠛⠓⠀⠀ ⠀⠑⠨⢦⠀⡇⣿⠀⠀⠢⡀⠀⠀⠈⢀⣀⠀⠀⢸⣦⣇⠂⠀⢠⣄⡐⠲⠆⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⡆⠀⡄⠎⠂⢄⠀⠉⠁⠀⠀⢸⣿⡇⠀⠀⠘⡐⠙⣄⡀⡀⠀ ⠀⠀⠀⠀⠀⢸⠁⠇⠀⡇⠐⠊⠰⣹⡖⡤⡄⠤⢺⡿⡇⠀⡠⠈⠀⠀⠈⠢⡍⠛ ⠀⠀⠀⠀⠀⢸⢠⠀⠀⠃⠀⠣⡀⣻⣿⠁⢡⠀⢸⡇⠗⠊⠀⠀⠀⠀⠀⣰⡇⠑ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇⠀⠀⢰⣵⠇⠀⠙⠢⣼⣽⣢⠀⠀⠀⠀⢀⠼⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⣀⠔⠊⡜⠀⢀⣼⣿⣿⣿⣿⠗⡄⠀⡀⡡⠁⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⣿⣧⡀⠊⢠⠎⡘⢸⢀⡊⣽⣿⣿⣿⣏⠄⡚⠚⠚⠃⠀⠀⠀⠀

⢠⡿⡻⠙⢉⡫⠙⣡⢤⢠⡤⣜⢭⡢⡽⡻⡑⡩⣮⠻⡆⠀⠀⠀⠀⠀⠀ ⣮⡾⡐⡡⠻⠁⢜⠏⣹⡸⣿⢎⢢⠹⣘⣳⡜⡜⡌⠷⡽⡄⠀⠀⠀⠀⠀ ⣟⣧⣵⢃⠁⢸⠸⠀⠁⡁⠀⠸⡜⣷⡙⣷⣥⠰⣻⣌⢜⣧⠀⠀⠀⠀⠀ ⣿⣷⡜⢸⢀⡇⡄⠀⠀⡇⢺⡇⣃⢸⣾⡀⢻⡥⠹⡏⣯⡼⡆⠀⠀⠀⠀ ⡿⣿⡇⡌⢘⡇⡇⢰⠀⡇⣾⡆⢿⢸⡇⢇⢸⣧⠀⢻⡟⣷⡇⠀⠀⠀⠀ ⣿⣿⡇⢀⢸⡇⡇⣿⢠⣇⣹⡇⠀⣼⡇⢘⣦⣿⣷⢸⣇⠭⢼⠀⠀⠀⠀ ⢸⣿⡇⠘⡼⢠⣿⡟⢿⣿⡏⣧⣠⣷⠖⣯⣽⣾⣿⡇⡏⣿⣻⠀⠀⠀⠀ ⠈⠿⡇⣜⣧⣿⣏⣷⣿⣟⡇⢰⡿⠏⠸⠛⠿⡧⢻⡘⣷⢴⡏⠀⠀⠀⠀ ⠀⠈⢷⡿⣿⡿⣟⠿⣿⠗⠀⠁⠀⠀⠀⠀⠀⠀⢸⡿⣿⡞⠁⠀⠀⠀⠀ ⠀⠀⢸⡇⢹⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⣿⠈⠁⠂⢄⠀⠀ ⠀⠀⠈⡇⠸⡟⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡇⣿⠃⠀⠀⠀⠡⠀ ⠀⠀⡠⢻⢀⡇⠀⡇⠠⡀⠀⠀⠤⠄⠐⢊⠁⢀⣼⢣⡃⠉⠉⠒⢤⢀⠆ ⢀⠌⠀⢈⡌⣧⠸⣱⠀⠘⣷⢦⠤⢈⠉⠀⡠⡞⣟⡮⠃⠀⠀⠀⠋⣸⠀ ⡄⠀⠀⠀⢳⢻⣣⠙⣆⠀⠈⠓⡄⠀⠀⠁⣰⣽⣿⢻⠀⠀⠀⡀⣼⣁⠇ ⡇⠀⠀⡠⠄⠻⣧⠑⡜⢌⠢⢀⠈⠘⠢⢔⡉⠊⠎⢸⠀⠀⠀⠁⡯⡿⠀ ⢳⢤⡊⠀⠀⠀⠙⠗⠱⡈⣆⠢⢉⢀⣼⠟⠑⡦⢄⡘⠀⠀⠸⠀⢿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡘⣧⠀⠀⠀⠈⠀⠐⢿⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢹⡹⡆⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⡀⠀⠀⢦⠀⢸⡀⠀⣧⣇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⣿⣇⣄⠀⢸⡆⠀⣷⠀⢻⢹⠀⣀⠀⠀⠀⠙⢳⢤⡈⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠃⠀⢸⢼⣿⣿⣿⡀⢸⣿⡆⣿⡀⢸⢹⠀⠘⠲⠄⠀⠀⠈⠛⢿⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣟⠀⠀⣾⠘⣿⠏⢷⣧⣸⣿⣧⢹⡇⠸⣾⠀⠦⠤⣤⣀⠀⢐⡲⣤⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⢠⣿⣿⣿⣹⣿⢠⣾⠇⠀⣿⣄⣨⣿⣿⡏⣿⣾⡇⠀⣿⠀⠀⠀⢙⣺⠿⢭⠙⢶⡙⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣷⢏⠀⠀⠀⠀⢠⣿⡟⣾⣿⡿⣹⣾⣿⣶⠾⣿⠉⠁⠈⢿⠇⢸⣿⣷⠀⣿⣙⣷⣦⡀⢸⡿⠶⢶⣦⣙⢮⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⢀⣾⡞⣾⠀⠀⣤⣟⣿⡿⢠⣟⣿⢱⣿⡿⠋⠁⢀⣿⣶⣿⣟⣿⣿⣼⡿⢻⢰⣿⢿⢿⣿⣷⡾⠐⢦⣄⠹⣿⢮⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣼⢻⠀⠀⣴⣼⢧⣧⡇⣠⣸⣿⢿⣿⠇⣾⡿⠁⣾⡿⠁⠀⢀⣾⣯⣾⣿⣿⣿⣿⣅⡀⣸⠼⡇⢸⠀⢻⣿⡇⢰⣏⠈⢢⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢠⢧⣿⣼⢸⢻⢹⢹⣿⣼⣿⣴⡿⠁⣼⡟⠁⠀⠀⠸⣷⣿⠁⢻⣾⣿⣿⣿⡿⢹⠂⡇⢸⠀⢸⡇⠹⣼⣮⡷⠘⠀⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢸⣾⡏⣿⣿⣸⢸⡟⢿⣿⡷⢖⣶⣤⡀⠀⠀⠀⠀⠀⠚⠋⣀⣀⣹⢿⠛⠁⠀⢸⡆⡇⢸⠀⢸⡇⠀⠈⢻⠆⣰⠂⡿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡿⣟⣿⣿⣿⣿⢿⣇⣼⡿⣿⣿⡶⠽⠗⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⢸⡇⠆⢸⠀⣿⠃⠀⠀⣸⣼⠃⣴⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⠏⣿⣿⣿⡟⣿⣟⣿⡾⣿⣿⣿⣿⠷⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⢹⢸⡇⠀⠀⠀⠀⠈⠁⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠀⢸⣿⣿⣇⣼⠟⠋⠀⢿⣻⡿⣿⣁⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣸⡇⠀⠀⠀⠀⢠⡴⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡴⠖⠋⠩⣿⣿⣿⠀⢸⣏⣿⢿⣅⠐⣦⣤⣄⣽⡿⠛⠉⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⡶⣶⣶⣠⣉⠉⠀⠀⠀⡀ ⡄⠀⠀⠀⢻⡀⡇⠀⠀⢸⣟⣿⣇⢸⣿⣸⠀⠹⣆⠈⠉⠉⠀⠀⠀⠀⢧⡀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⣿⡇⠀⠀⠀⠀⠈⣿⣿⠿⠦⠼⠿⠿⠚⠛⠛⠂⠀⠉⠉⡉ ⠙⠷⣄⠀⠀⠻⣇⠀⠀⠀⢿⣿⠙⣾⣿⡇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠻⠷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣧⡇⠀⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇ ⠀⠀⠈⠛⠦⣀⡹⣦⠀⠀⠀⢻⠀⣿⣿⡇⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⡇⣠⠃⠀⠀⠀⠘⣧⣤⠤⡤⠤⠶⢒⣚⠛⠛⠋⠉⠁⠀ ⠀⠀⠀⠀⠀⢨⠙⠛⠳⠀⠀⢸⠀⣿⣿⠁⠀⠀⢀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⢴⣶⡶⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⠮⠿⣷⡒⠒⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⣻⣿⢰⡄⠀⣾⢠⠀⠀⣮⠻⢶⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⢷⠀⡧⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⡟⢸⡇⠀⠘⢸⡇⠀⢻⠀⠀⣈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠼⡇⠀⠀⠀⠀⠀⠀⢸⡾⠁⠀⠀⠘⣆⣄⣀⣠⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⡃⠀⠀⢸⡇⠀⠸⣦⡴⠃⠀⢠⠈⣻⢦⣄⡀⠀⠀⠀⠀⠀⠀⣠⢿⡿⣿⠀⡇⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠘⢧⡀⠉⠛⠶⢶⣺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⡇⢸⠇⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⢸⣤⡟⣷⣉⢛⣷⣶⡤⠤⠴⠚⠁⢸⣽⡟⢸⠇⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠀⠀⠀⢸⠀⠀⣤⣬⡦⢤⠀⠘⣿⣿⣿⣿⣾⠃⠘⣆⠀⠀⠀⠀⢸⣿⡇⣸⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢘⠀⠀⠀⠘⢃⣶⡀⠀⢯⣿⣿⣾⠏⠘⡒⢸⡆⠀⠀⠀⣾⣷⠃⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⡀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⠀⢨⠀⠀⠐⠄⠀⠀⠃⢀⣾⠛⢻⡿⠀⠀⠙⢦⣻⠀⠀⠀⣿⣿⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠘⡟⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡆⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⢸⣷⢿⣼⠇⠀⠀⠀⠈⠛⠷⣄⢀⣿⣧⣼⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠏⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠘⡇⢀⣤⠀⠀⠀⠀⣸⠿⢫⡟⠀⠀⠀⠀⠀⣠⣤⣬⣿⣏⣿⣧⣤⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⠇⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢿⢸⢻⠀⠀⠀⠀⠀⠃⠘⠀⣠⡴⠋⠁⢀⣾⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⢷⡀⠀⠀⠀⠀⡴⠋⢠⠏⠀⠀⠀⠈⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡸⣾⡆⠀⠀⠀⠀⣠⡴⠛⠁⣠⠄⢀⢿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⢳⡄⠀⢀⠞⠁⣴⡏⠀⠀⠠⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣏⣇⠀⢀⡴⠟⠁⠀⢀⣾⠁⢀⡞⢸⣿⠀⠀⢀⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⠤⠿⠴⠫⣬⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢛⠒⡒⠒⠀⣾⣿⣽⣿⡴⠋⠀⠀⠀⣠⣿⠇⠀⢸⠃⠀⢹⠀⣠⣏⡴⣚⣩⣿⢻⣿⣿⣿⣿⣿⣿⡧⠖⠋⣠⠞⡃⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢱⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⠂⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢳⣹⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣼⠀⣠⠀⠀⠀⣿⠃⡄⠀⠀⠀⣰⠋⠀⠀⣼⡀⠀⠀⠀⠀⡾⣿⡆⠀⠘⠀⢆⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢀⡟⢠⠃⠀⠀⢸⣿⢴⣠⠀⠀⣰⡇⠀⠀⢀⡟⢳⣆⠀⠀⠀⢹⣿⡁⠀⠀⠀⢸⠀⠀⡌⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠊⣹⠁⠀⠀⣼⡇⡼⡀⠀⢀⣼⣸⣿⣿⣤⣿⢻⣿⠀⠀⣸⠁⣈⣿⣶⡄⠐⡈⣾⡇⠀⠀⠀⡎⠀⠀⣷⣧⠀⠀⠀ ⠉⠒⠲⣄⠀⣿⣿⡏⡜⣹⠀⠀⢰⣿⢡⣿⠇⣠⣼⡷⣿⣿⣿⣿⠏⢸⣿⡄⢀⡟⠛⠉⠉⢿⣿⣆⢳⡘⣷⠀⢠⡆⣗⢢⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠈⠳⡧⣿⣇⣷⣿⠀⠀⢸⣿⣿⣟⣰⣿⡟⢀⠟⣸⣿⡏⠀⢸⣿⣿⣾⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⡇⢸⠃⣿⣄⣇⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡆⠀⣿⣿⢿⣿⣿⣿⣶⣾⣄⡛⠋⠀⠀⠈⠿⠿⠿⠀⣴⣿⣿⣿⣿⣿⣿⣤⣼⡇⢸⢨⡏⠀⠹⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡟⣹⡇⠀⢹⣿⡾⠟⢛⣿⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠠⠟⠹⣿⣿⣿⡷⠀⠀⢸⡇⠈⢸⡷⡾⠆⢻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠠⣿⡇⠀⢸⣇⡀⠀⠸⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠁⠀⠀⠀⡇⠀⢸⣧⠒⠃⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⡇⠀⣸⡀⠈⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢸⢃⡧⢴⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⣸⠧⠖⢛⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠁⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⠤⠚⡯⠒⢒⠿⠛⠛⢓⣆⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣼⣤⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡖⠁⢸⠁⠀⢰⡇⠀⢸⠀⠀⢷⠀⠈⢦⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⡇⠀⠈⠀⠀⢸⣧⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢆⠀⢣⠀⢘⡀⠀⡓⠀⠀⠸⠃⠈⠛⢤⣉⣙⡒⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⣰⣿⡇⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡀⠸⠀⠨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣿⠁⢸⣷⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⡀⠀⠈⣇⠀⠤⡤⠀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢀⡴⠋⠁⠀⠀⢻⡄⢸⠃⠀⢻⠑⢦⣀⠀⠀⠀ ⠚⠫⠭⠜⠊⠉⠙⠛⠯⠷⢿⡗⢲⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠞⠁⠀⠀⠀⠀⠀⢸⠁⡼⠀⠀⢸⠀⠀⠻⣍⠲⢤ ⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⣿⠸⣿⠘⣿⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣠⣿⡆⡇⠀⠀⢸⡋⠑⠦⡈⠑⠄ ⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢻⡇⢿⡄⢸⡀⠀⠀⠀⠈⢳⠒⠤⠤⣄⣀⣀⠀⢸⠀⠀⠀⠀⢀⡠⠞⠁⣿⣹⠁⠀⠀⢸⣷⠀⠀⠈⠢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⡞⣿⣾⣿⠀⢧⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣟⠀⣀⠤⠒⠁⠀⠀⢰⣿⡟⠀⠀⠀⡜⢹⠀⠀⢀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣹⡀⠀⠀⠀⠐⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⢳⠀⢹⣧⠀⠀⠀⠀⠀⠙⣿⡤⠤⠔⠒⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⣧⠈⡇⠸⣿⠀⠀⠀⠀⠰⣄⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠀⠸⢿⣿⣿⡀⣿⡆⣿⠀⣿⠀⠙⠂⠀⠀⠈⠻⣾⡆⠀⠀⠀⠀⠀⠀⠀⢂ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣶⣿⣿⡇⢀⡇⢸⡏⢹⣷⣿⣿⣼⠆⣿⠈⠁⠲⣦⣤⡼⣷⣜⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⡞⠀⠀⠀⢀⣾⣿⣿⡿⣷⣿⣥⢾⡟⠋⠻⡿⢸⣿⡆⣿⣒⣤⡀⢸⣯⢥⣬⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢠⡂⠀⠀⢠⣿⣹⠀⢠⣞⣾⡟⣼⡿⣱⣿⠋⠁⣸⣷⣾⣿⣿⣾⠿⣷⣿⢻⢿⣿⡾⠐⡦⡘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣇⠀⣰⣿⣟⡇⣦⣾⣿⣿⣡⡿⢡⡿⠃⠀⢰⣿⡟⢻⣿⣿⣷⣤⣟⠋⢸⠈⣿⢇⣸⢦⢱⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣭⣅⠈⠁⠀⠀⠈⠿⠁⣈⣿⡿⠋⠁⣧⡀⢸⠀⣿⠀⠙⣯⢀⢤⣯⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⡿⠀⢸⠰⠇⠀⠀⣧⠃⣼⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢻⣿⡏⢻⣿⠟⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠘⢸⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⠴⠺⣿⣿⡇⢸⣿⣷⡏⢁⣀⡘⣻⡿⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀ ⡄⠀⠀⢻⣸⠀⠀⢻⣿⣧⣸⣿⠇⠹⡄⠉⠉⠁⠀⠀⢇⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⣿⠿⠬⠿⠛⠛⠛⠃⠀⠀⠉ ⠈⠳⢄⡀⠻⡄⠀⠈⢿⠋⣿⣿⠀⠀⠘⣄⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠉⡒⠿⠦⠀⢸⡄⣿⡟⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⣿⣷⣿⡶⠁⠀⠀⠀⢻⣿⣽⠭⠅⠶⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠈⡇⣿⡇⡆⠀⡄⠀⠀⡟⠲⣄⡀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⢸⢐⠎⠙⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠃⡇⠀⠁⡇⠀⣧⠀⡠⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠀⠀⠀⠀⠀⢸⠏⠀⠀⠘⣶⠦⢤⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⡇⠀⠀⡇⠀⠈⠋⠀⠀⣧⣸⣟⠲⣤⣄⣀⣀⡤⠚⣿⣿⢸⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣤⡈⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠁⠀⠀⠀⠀⠤⣤⠀⠀⢸⣿⣿⣷⠏⠘⡅⠀⠀⠀⣿⡟⣸⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠁⠶⡄⢘⣿⣿⡟⠀⢑⢻⡀⠀⠀⣿⠇⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣄⣀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢇⠀⠀⠀⡄⠀⠀⠀⠀⠀⣼⣥⣹⠃⠀⠀⠻⢧⡀⢠⣿⢰⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠃⠀⣀⠀⠀⢀⡿⢟⡟⠀⠀⠀⢀⣤⣉⣿⣿⣿⣤⣿⣆⠀⠀⠀⠀⠀⠀⡰⢫⠃⠀⢸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⡆⠀⠀⠀⠀⢘⡠⠖⠉⢀⣼⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢳⡀⠀⠀⢠⠊⢠⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡠⠖⠋⢀⡖⠀⡞⣿⠀⠀⣠⠟⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣹⣄⣰⠁⢼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡒⠀⠄⠀⣾⣿⣿⡠⠊⠀⠀⣰⡿⠀⢸⠀⢹⠀⣴⣣⢔⣻⣿⣿⣿⣿⣿⣿⡥⠖⣡⠖⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠰⡾⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣰⠃⠀⠀⠀⠀⠀⢠⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢱⡹⡄⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⡟⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢷⢳⠀⠀⠀⠀ ⠙⣆⠀⠀⠀⠀⠀⢸⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⣼⠀⠀⣧⠀⠀⠀⢨⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⣮⡟⣇⠀⠀⠀ ⠀⠘⣦⠀⠀⠀⠀⣿⠀⠀⡼⠁⠀⠀⠀⠀⢀⣼⠇⠀⠀⢿⠀⠀⠀⢸⠸⣷⡀⠀⠀⠀⠀⠀⠀⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣽⣿⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⡟⠀⢠⠇⢠⣰⠂⠀⠀⡾⡏⠀⠀⠀⠸⡆⠀⠀⠘⡇⢹⣇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢹⠀⠀⢳⣿⡆⠀⠀ ⠀⠀⠀⠹⡀⠀⠀⡇⠀⢸⢀⡞⣿⠀⠀⢸⣿⣁⣀⡀⠀⠀⢷⣀⠀⠀⢷⠀⣿⣆⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠸⡸⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡶⠀⢸⣷⡇⠀⠀ ⠀⠀⠀⠀⠇⠀⢸⡇⠀⣾⣮⡇⣿⠀⠀⡟⡿⠀⠀⠉⠛⠳⢾⣾⡀⢠⠸⡇⠘⣿⢦⠀⠀⢆⠀⣿⡇⣿⡆⠀⠀⠀⠀⡇⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡆⢸⡇⠀⡄⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⠀⢸⡇⠀⢸⢹⢻⢻⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠹⣧⣸⣧⣻⡀⠸⣿⣿⣆⡼⡆⣿⣇⣿⣿⣦⠀⠀⠀⣿⡏⣇⠀⠀⠀⢠⠀⠀⠀⢸⠃⣸⣇⠈⡇⠀⡇⠻⡇⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⢸⡼⡟⡞⣇⠀⣿⣧⣤⣴⣶⡒⠶⠦⣤⠹⣿⣻⣿⣧⡀⢻⣿⣿⣿⣿⣿⡟⢻⡾⣽⣷⣦⠀⠘⣧⣿⡀⠀⠀⠈⠀⠀⠀⣿⢀⣿⣸⠀⣇⠀⢹⢰⠇⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠘⡇⠹⣿⣿⣔⣿⠋⠉⢹⣿⡿⣿⣶⣙⣧⠈⠳⣽⣿⣷⡄⢿⣿⠻⣷⣿⣷⠀⢻⣻⣽⣿⣧⠀⣹⣿⣿⡀⠀⡆⠀⠀⠀⣿⣜⢿⣿⠀⣿⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⢸⠇⠀⠀⢧⡀⢸⠋⠻⣷⠀⠀⢸⣧⣸⣿⣿⠻⣟⠃⠀⠀⠀⠉⠋⠘⠟⠀⠉⣹⣷⣤⣴⠿⢿⣻⣿⣧⡇⡾⢿⣇⠀⣷⠀⠀⢰⣿⠉⠙⠻⣄⣿⠀⣼⠇⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⢸⠀⡄⠀⠈⠃⣾⠀⠀⠘⣺⢧⣈⠛⠷⠿⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠾⠿⣻⣿⢿⣿⣿⢿⣷⡇⠸⣿⠀⣿⠀⠀⠀⡟⠓⢦⣀⠙⣿⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⢸⠀⡇⠀⠀⠀⡿⠀⠀⠀⠈⠙⠚⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣬⣿⡟⢿⣾⣃⠀⢹⡇⣿⠀⠀⢠⣧⠖⠒⢻⠀⠈⣯⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⢸⠀⠅⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠿⣴⣿⠿⠃⠀⠙⠿⠟⢹⣁⣿⣠⡇⢹⠁⠀⢀⡾⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⢰⠏⠀⠀⠀⢸⠀⠁⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠀⠀⠀⠀⢸⢹⣽⢸⠀⢸⠀⠀⣸⠃⣠⡟⠀⠀⠀⠀⠀⠀ ⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠘⠂⣾⠀⢀⣇⣴⡏⠀⠀⠀⠀⠀⠀⠀ ⢯⣀⡀⠀⠀⠀⢸⡀⢸⠀⠀⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣿⡇⠀⠀⣿⠀⢸⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠈⠙⠓⣦⣤⢸⡇⢸⠀⠀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⣸⡟⠀⠀⠀⡇⣰⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠁⢸⡇⢸⡄⠀⡇⠀⢻⣆⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⢸⡇⠀⣸⠿⣆⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⢸⡏⠉⢹⡆⠹⣆⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢸⡇⣸⡇⠀⢸⠃⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡞⠲⣤⡤⠤⠤⠴⠶⠶⠶⠤⠤⢤⣀ ⠀⠀⠀⠀⠀⠀⣾⢻⠀⡇⢻⡇⠀⢸⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠉⠒⢤⡀⠀⠤⠤⣤⣄⣀⣈ ⠀⠀⠀⣠⣤⠴⣿⠈⡆⢿⣾⣧⣄⣸⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀ ⡤⠖⠋⠁⠀⠀⢿⠀⢷⣾⢹⡇⠙⢿⣤⡀⠀⠀⠀⠀⠙⠿⠶⣦⣤⣤⣠⡤⠴⠶⠞⠛⣩⠵⠖⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡄⠸⣿⢸⡇⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⣿⠀⠙⢦⣀⡴⠛⠋⠉⠉⠛⠦⣄⠀⠀ ⠈⠀⠀⠀⠀⠘⠸⡇⠀⢹⣸⡇⠀⠀⠀⠀⠀⢉⡻⢦⣄⣀⠀⠀⣀⡤⠴⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⣀⡀⠀⠉⠋⣟⠀⠀⢸⣹⢀⣤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄

⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠜⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⡆⠀⠀ ⠄⠀⠀⢰⠀⡌⠀⠀⢠⢹⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣭⡄⠀ ⠈⠆⠀⡆⢰⢀⠀⢠⠇⠀⡀⠀⢱⡀⠀⠀⣶⡄⠀⠀⡀⠀⠀⠀⠀⠄⢠⠸⣇⠀ ⠀⠘⠀⡇⣤⣿⠀⡿⠒⠠⢷⡀⢃⢧⡀⠀⣿⡇⠀⠀⣳⠀⠀⠀⢀⢀⢸⢠⣿⠀ ⠀⠀⠆⡇⢸⣿⡌⣧⣤⣤⣤⠳⣿⡌⣿⣾⣿⢻⣧⡄⢻⡄⠀⠀⢸⣸⡆⠈⠹⠀ ⠀⠀⠃⠇⠘⣸⠛⢇⢸⣽⡟⠗⠈⠙⠘⠊⣻⣬⣿⣿⣌⢿⢰⠀⢸⡙⢧⢠⠃⠀ ⠀⡘⠀⠀⠀⢸⠀⠈⠓⠂⠀⠀⠀⠀⠀⠈⠁⢸⣭⡟⢻⡌⢾⠀⡴⠚⠆⡋⠀⠀ ⡠⠁⠀⠀⠀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⢀⣽⠀⡇⢘⡴⠁⠀⠀ ⡓⠤⡀⡆⠀⡟⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⡟⠀⣃⠻⠀⠀⠀⠀ ⠀⠀⠀⡇⡆⣃⡱⡀⠈⠓⢄⣀⣀⡀⠀⠀⠀⢀⠔⠁⠀⢸⠀⢀⡠⠃⠀⠀⠀⠀ ⠀⠀⠀⡇⡇⠀⠀⠑⡀⠀⠀⠀⠀⠁⠀⠀⢀⠃⠀⠀⠀⢸⠀⢸⠠⢀⠀⠀⠀⠤ ⣀⠤⠐⠸⣳⠦⡆⠀⠘⢤⣀⡀⢀⣀⡠⣤⢺⠀⠀⠀⠀⠈⠀⣼⠀⠀⠑⠀⠀⠈ ⠀⠀⠐⠆⢻⡇⠈⠓⢤⣀⠀⣀⠠⠐⠈⠀⠀⢱⣄⡀⠰⠇⠀⡇⡱⠐⠉⠉⠐⢄

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⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⠀⠁⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠁⢸⢠⠀⠀⡏⠆⠀⢠⠁⠀⣧⡀⠀⠸⣿⠀⠀⠀⠀⢡⠀⠀ ⡀⠀⠀⣀⡤⣺⠁⢀⡏⣆⠀⣸⣵⣾⣴⢻⡂⢰⣀⣻⣆⢠⢿⠀⠀⠀⠀⣿⠀⠀ ⠀⠈⠢⣿⣇⣽⠀⢸⣧⣏⣾⠏⢏⣿⠃⢸⣧⡎⠀⠀⣻⣷⣿⡇⠸⣦⣃⢸⠀⠀ ⠀⠀⠀⠀⢿⢿⡄⢻⣟⣿⣿⣾⣮⠉⠀⠘⠛⠃⡾⣿⣿⡟⠲⡇⠀⣇⢌⣿⠀⠀ ⠀⠀⠀⠀⠸⢼⠁⢸⠁⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠁⠀⣯⠒⡀⠀⠀ ⠀⠀⠀⠀⠐⣸⠤⢜⣄⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⠃⠀⠀ ⠀⠀⠀⢀⠔⡡⠂⡇⢈⠋⠉⠱⡀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠃⠀⠀⠀ ⠀⠀⠀⢯⠀⠃⠀⠇⢸⠀⢸⢄⡰⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢼⠀⠂⢀⠀⠈⠀⠈⠂⠒⠠⢀⠀⠀⠀⠀⡠⠊⡇⢸⢣⠀⠀⠀⠀ ⢠⠤⠤⠤⢤⣌⣦⣒⡂⠈⠁⠀⠀⠀⠀⠀⠀⠡⣀⠤⠊⠀⠀⡇⡏⠀⡏⠢⠄⡀ ⠀⠀⠀⠠⠀⠀⢸⡸⡏⡏⠒⠠⢀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡠⡇⠃⠀⣗⠢⢁⠢ ⠀⠀⠀⠀⠈⢂⢢⣧⣷⠰⡀⠀⢀⠈⠁⠒⠂⢸⢀⡠⠔⠉⢰⣷⠀⠀⠿⠀⢀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣀⣀⠀⡈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠀⠀⠀⠀⠈⠙⠲⡖⢤⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢆⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⡜⠑⡴⠃⠀⠀⠀⠀⠀⢸⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠆⠀⠀⠀⣸⠃⡜⠁⠀⠀⢀⡄⠀⢠⠃⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⢰⡏⡌⠀⠀⠀⢀⡾⠁⢠⠃⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⠟⠀⠀⠀⠀⡾⠁⣰⠃⠀⢀⡟⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⠀⠀⣸⠃⣰⢣⠆⠀⣸⠁⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⢀⡄⠀⡏⢠⣧⠏⠀⠀⡇⠀⠀⢰⠀⢀⡞⡾⠀⠀⢰⡏⠀⠀⠀⠀⠃⠀⠀⠀⢈⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⣷⣸⣿⣾⡟⠀⠀⣸⡇⠀⣦⠿⠀⣼⡹⡄⠀⠀⡿⡀⢀⠀⣰⡀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⡞⠀⢀⡇⠀⢸⡿⠿⣿⣿⠁⠀⢰⣿⢀⣠⡗⢀⣄⠈⠁⠇⢀⡼⢡⢀⢿⢉⠏⡝⡟⠓⢦⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠸⡇⢰⡾⠓⢳⣸⡏⠀⠀⣾⣹⣾⣾⣧⣼⣯⣹⠇⣤⡿⠁⣾⡏⢸⣟⣸⣓⡿⣦⠇⢀⡟⠀⡄⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠋⠀⠀⠀⣇⢸⣧⢠⢯⣼⠃⠀⢀⣿⠻⠉⠙⠉⠉⠙⠟⠓⠉⠀⠘⠉⠀⣾⡿⠿⠿⣿⣿⣾⡿⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⠚⠓⠺⠷⠂⠀⠀⢰⣿⡀⣿⣆⠨⣿⣄⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠃⠀⢋⣿⠀⢀⡇⠸⠀⢠⠦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠓⣘⡾⠋⢀⡼⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣸⡇⡇⠀⢸⠀⠈⠑⠢⢄ ⠀⠀⠀⠀⠀⠀⢸⡿⠔⢚⠏⠀⢠⣿⠄⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⡟⢧⠃⠀⢼⠀⠀⠀⠀⠀ ⢀⣀⣀⣠⡴⠖⣻⡇⠀⢻⡀⠀⠘⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⢿⡿⠀⠀⠸⡄⠀⠀⠀⠀ ⠉⠻⢿⣷⣶⠞⠁⢣⠀⠀⢣⠀⠀⠘⠷⠄⣈⣻⣄⠀⠀⠀⠀⠐⢦⡔⠒⠂⠤⢤⣤⠀⠀⠀⠀⣠⣿⠁⠀⡸⣸⠇⠀⠀⠀⠱⡄⠀⠀⠀ ⣆⠀⠈⣿⠁⠀⠀⠹⠄⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢄⡀⠀⠈⠉⠐⠒⠋⠁⠀⠀⢀⣴⡧⡏⠀⠀⣿⠋⠀⠀⠀⠀⢰⠋⠀⠀⠀ ⣿⣿⡄⠘⣷⣤⣀⠀⠓⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠀⠀⠀⠀⢀⣠⣾⣿⣿⣰⠁⠀⢀⡏⢳⡀⠀⠀⠀⡞⠀⠀⠀⠀ ⣿⣿⣿⣶⡘⣿⣿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣴⠟⠁⢿⣿⣿⡇⠀⠀⢸⣿⠀⢷⠀⢀⡴⠃⠀⠀⠀⠀ ⠻⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠁⣸⠀⠀⢸⣿⣿⡇⠀⠀⣸⡟⠀⢸⡄⢸⠃⠀⠀⠀⠀⠀ ⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡟⠒⠀⠀⠀⠀⢀⣿⣤⡀⠀⣿⡆⠀⠘⣿⡾⠁⠀⡎⣿⣧⣤⣠⣧⠈⠤⢺⡇⠀⠀⠀ ⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣞⠀⠀⠀⠀⠀⠀⣾⣿⠁⠑⠤⠏⢣⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣻⠀⠀⢀⡇⠀⠀⠀ ⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣻⢤⣀⠈⠑⠲⢤⣀⣰⣿⣯⣀⣀⠀⠀⢸⠀⢰⣿⡇⠀⣿⣿⣿⣿⣿⡏⣿⠀⢰⡋⠀⠀⠀⠀

⠀⠀⣠⡿⢞⣿⡿⢟⣿⠿⠛⣫⠗⢋⣩⠿⠓⠂⠀⠀⠀⠀⠀⠀⢠⣭⡉⠷⠲⣄⡈⢶⡙⢿⡏⠳⣄⠰⣕⢦⡉⢿⣦⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠞⣋⣴⠋⠉⠀⠀⣸⢃⡴⠛⠁⣠⣞⣷⢻⣇⠀⡖⢖⠛⢷⣤⠙⢯⡳⡌⢻⣦⡹⡄⠹⣆⠘⢧⡈⢷⣴⣆⠹⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢁⣾⠟⠁⣠⠞⢠⡜⣵⡟⠀⠀⢰⢫⡟⠃⠏⡹⢨⣿⣿⣷⢨⢿⣧⡀⡙⣞⢦⠸⡳⣝⣆⠙⣧⡈⢷⡀⠙⣟⣧⡈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⢟⡿⠁⣰⢃⢠⡟⢀⡟⠀⠀⢰⠃⣿⠁⠀⣀⡇⣸⠸⣿⣯⢻⣷⠈⢷⡹⡘⢿⢳⡱⡝⣾⣆⠘⢷⡈⣷⡄⠙⣎⢻⣄⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⡞⡆⢰⢃⢮⡿⠀⡜⠀⠀⢠⡇⢸⡇⠀⠀⢻⠇⡏⢠⠋⡏⠀⢿⡆⠸⣷⢳⡀⢳⡽⣷⡌⢷⡀⠘⣧⢸⣿⡀⠘⣆⠹⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⣸⢡⡏⡾⣼⠁⢸⠇⠀⠀⣿⠀⢸⠀⠀⠀⢸⠀⡇⢸⠀⡇⠀⠘⣧⠀⢻⡞⣷⡀⠹⡻⣿⡎⢷⠀⠘⡆⢿⡿⣤⡘⣦⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡜⢸⢹⡟⠀⣜⠀⠀⣰⡟⠀⡇⠀⢰⠀⢼⠀⡇⢸⡆⣧⢀⠀⢿⡇⠀⣿⣿⡻⡄⠁⢹⣷⢯⠷⠀⢹⣿⣿⠘⢷⡼⣇⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣧⣿⢣⡏⣿⠇⠀⡟⠀⢠⢽⡇⢰⡇⠀⢸⠀⠀⠀⡇⢸⡇⡿⢸⠀⢸⣣⠀⢹⣼⢻⣽⡄⠀⠹⣿⣇⠰⠀⢳⣿⡇⢾⣽⣮⢳⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣸⣵⣿⠀⢀⡇⠀⣼⣾⠀⢸⡇⠀⢸⠀⠀⠀⡇⢘⡇⣿⢸⡀⢈⣿⠀⢸⣿⡄⢻⡿⠀⠀⣿⣽⡆⠀⠈⢹⣿⣮⣿⣿⣧⡈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⡇⣿⢿⣿⠀⣸⠃⠀⡏⣽⠀⢸⡇⠀⢸⡆⢀⢸⣧⠀⡇⣻⣸⡇⢸⡟⠃⢸⡇⡇⠀⣿⡃⠀⢹⣯⢷⠀⠀⠈⣿⡧⣿⠏⣽⣟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⢳⣿⢸⡟⠀⡟⠀⢰⡇⣿⠀⢸⡇⢀⢸⡇⢸⢰⣿⠀⡇⣿⣿⡇⠀⡀⠀⢸⡇⡇⠀⠸⣧⡀⠸⣿⣞⡗⡄⡄⢹⣧⣟⢸⣷⣝⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⣾⣟⣾⡇⢀⠀⡄⢸⣧⢸⡀⢸⣿⢸⣿⡇⢸⣸⣿⡀⡇⣿⣿⡇⡄⣧⠀⣺⣇⡇⠀⠀⡟⢧⢠⣏⣿⣷⠃⣇⠸⣿⣿⢸⣯⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⣿⣿⣿⠃⢸⠀⣷⢸⢹⢸⡇⣾⣿⢸⣿⣿⢺⣿⣾⣷⣷⣿⡏⡇⡃⢹⢠⣿⢸⠃⠀⣀⣼⣾⣿⣿⣿⠹⣿⢿⠀⠿⡹⣎⣅⣈⠃⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣧⢸⠀⢸⡜⢸⡇⣇⡟⡿⣼⡇⣿⣾⣿⣿⣿⣿⡏⣿⣇⠀⡆⣸⡏⣾⣶⣿⠿⣛⣁⣿⣾⣿⣶⣿⡸⡀⢰⡇⢹⣹⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⡟⢿⢷⢸⠀⢨⡇⠈⡇⣟⣷⢣⣿⡇⠀⢿⣿⣿⣿⣿⠁⢸⣿⢠⣿⣿⣿⡿⠉⣰⣾⣿⣿⣿⣿⣿⢿⣿⡇⣇⢸⣷⢸⡿⢧⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣷⣿⢸⢸⠀⢸⣧⠀⣿⣻⣿⡌⠙⣷⣶⣿⣿⣿⢿⣿⠀⠀⣷⡾⣷⣿⡿⠃⣸⡿⢿⣿⣿⣿⣿⢋⣼⣿⡇⡿⡏⣻⢸⠀⣼⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⢘⣾⢸⢸⢨⣿⡾⣿⣏⣿⣧⣀⣿⣾⣾⣿⣿⣴⣿⡀⠀⣿⣣⠿⠛⠁⠀⠘⠃⠠⠭⠭⠭⠞⠿⠊⠀⣇⡇⡇⣿⣿⠞⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣾⣼⢸⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡈⠁⠚⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⡇⣿⡿⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡏⡇⠸⢸⡿⣾⠟⢻⣇⣈⠛⠿⢿⣿⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠃⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⣿⡜⢻⣷⡀⠁⠈⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢹⠐⢈⣾⡏⠉⡛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣷⠁⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇⣤⡇⠀⠀⠉⠙⠶⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢻⢸⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣿⡧⣼⠃⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣼⡄⠀⠸⡿⠛⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⢸⢸⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⡇⢰⠀⣷⠀⠀⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⢠⣿⢧⢸⡟⠓⢲⠶⠦⣄⣀⣀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⢀⡼⠿⣷⠀⡇⣽⠁⠀⢠⢸⡇⠙⠶⣄⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠴⠒⠋⠉⢀⡀⠀⠀⠀⢠⣾⡟⢠⣿⠁⠀⠀⠀⠀⠀⠈⠑⠒⣤⣖⠀⣼⠇ ⠀⠀⠀⢀⡴⠋⠀⠠⢿⡄⢧⢿⡇⠀⠸⡀⣇⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠤⣄⣀⡤⠖⠋⠀⠀⠀⣴⣯⣿⠇⣸⡿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠇⢹⣿⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⡜⣇⠘⣼⣧⠀⢰⣧⢻⡄⠀⠀⠀⠸⣿⣽⣗⡦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡏⣻⡿⢰⣯⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⠓⠀⣼⡟⠀ ⠀⣰⠋⠀⠀⠀⠀⠀⢱⣸⡀⠏⣿⢀⠀⢟⣎⢧⠀⠀⠀⠀⠹⣝⢮⡙⠂⠈⠉⠑⠲⠤⢤⣤⠴⠞⠉⡿⢠⢿⣧⣿⡇⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢿⡀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⢣⢷⠸⣿⢏⢧⠀⠘⣿⡄⠀⠀⠀⠀⠘⢧⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⢟⣿⡿⡿⠀⡇⠇⠀⠀⠀⠀⠀⢀⡄⢠⡞⡟⢀⠈⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⢿⣾⡈⢷⣀⠈⢻⡶⣄⡀⠀⠀⠀⠙⠢⣗⠀⢢⡀⠀⠀⠀⠀⣰⣷⡷⢛⡟⣼⡿⠀⡇⠀⠀⠀⠀⠀⠀⡸⠀⣯⢷⣡⢮⡴⠁ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠙⣮⢿⢧⠀⠙⢦⠘⢷⡀⠙⢶⣀⠀⠀⠀⠈⠙⠲⢿⣶⠀⢀⡼⠋⠁⠰⠋⢀⡿⠁⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⢈⣵⣿⡿⠀ ⢸⣇⠀⠀⠀⠀⣀⣺⠝⠋⠀⠀⠈⢿⣟⣆⠀⠘⣇⠈⠱⣄⠀⠈⠓⢦⣄⡀⠀⠀⠀⠈⢹⣟⣲⣦⠄⠀⠀⠋⠀⠀⠀⡟⠀⠀⠀⠀⠀⢠⠁⠀⣿⡟⣉⠔⠁⠀ ⠸⡿⣄⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠈⠻⣜⢦⡤⠻⣆⠀⢞⣆⠑⢦⡀⠀⠉⠛⠶⠀⣰⣿⣿⣿⠛⣷⣤⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣾⡄⠀⣼⣿⠟⠀⠀⠀ ⠀⠸⡙⢿⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⠆⢻⣦⠘⢏⢷⣀⢉⠳⠦⠤⢀⣴⣿⣟⡋⠀⠀⠈⣻⠋⠓⠦⣄⡈⠀⠀⠀⠀⠀⠀⢋⠁⠀⠃⣟⣧⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⣀⠀⠐⠢⢄⣈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⡀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠁⠑⢄⠈⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⢠⢅⠊⠀⢀⠀⡘⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⣎⠂⠀⢠⠏⡜⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢃⠈⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡅⠀⠀⡎⣘⠆⢰⠁⢀⠀⡠⠃⠀⡀⠀⠀⡀⠀⢸⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⡘⢨⠀⢸⢰⣶⡏⠀⡤⢠⡌⢠⣋⠀⠸⠁⠀⡄⠇⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠃⢸⢀⣸⢛⣿⠀⢸⣇⣸⢰⡤⡘⣠⢳⡜⡯⡍⣏⡐⢸⠀⢸⠀⠀⠀⠀ ⢀⢀⠌⠀⠈⡘⡇⢬⡇⠀⡟⠋⠋⠉⠻⠊⠁⠚⠰⣿⠿⡾⣷⡋⢸⠸⠀⠀⠀⠀ ⠀⠉⠁⠀⢸⠧⣫⠞⡱⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣸⡄⢰⠑⠠⢀ ⠀⠀⢀⣀⡟⢨⠁⢰⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠃⢸⠀⠀⠀ ⠚⢿⡿⠊⢁⠈⢂⠀⠳⠤⢳⡄⠀⠀⠠⢀⠀⢠⡄⠀⠀⣴⠃⢰⡼⠀⠀⢣⠀⠀ ⣷⡌⢧⣀⠈⠄⠈⠄⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢀⣤⣾⡙⠀⡘⢄⠀⠀⡌⠀⠀ ⣿⣿⣎⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⡰⠤⢴⠁⢸⣟⡇⠀⣿⠘⡀⡴⠁⠀⠀ ⡌⠻⣿⣿⣿⣿⣿⣿⣿⡏⢱⠂⠀⠀⢀⣧⡀⢸⡀⠸⣿⠀⣴⣯⣄⡇⠣⢲⠀⠀ ⣿⣦⡙⣿⣿⣿⣿⣿⠟⣗⡑⠂⠄⡀⣼⣇⣈⠁⡇⢠⡏⢠⣿⣿⣿⣎⠀⠌⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡜⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡞⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⣻⡀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⡞⠀⠀⡜⠀⠀⠀⠀⢠⠃⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢻⣣⠀⠀⠀ ⠙⡄⠀⠀⠀⢠⠃⠀⡼⠀⠀⠀⠀⢀⡎⠀⠇⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⢻⣿⡆⠀⠀ ⠀⠘⡄⠀⠀⢸⠀⢰⠃⢀⠀⠀⢠⡾⠀⠀⢸⠀⠀⢸⡘⣧⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡇⠀⢿⣷⠀⠀ ⠀⠀⠹⠀⠀⢸⠀⡼⣰⢿⠀⠀⣾⡃⠀⠀⠈⡇⠀⠀⣇⢹⣆⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⢸⣿⠀⠀ ⠀⠀⠀⠄⠀⡟⠀⣷⣻⢸⠀⢸⡿⠀⠉⠉⠒⢿⣆⢠⢸⡀⢻⣦⠀⢠⠀⣿⣿⣇⠀⠀⠀⣏⣹⠀⠀⠀⠀⠀⠀⡌⠀⡄⢸⠀⡆⣿⠀⠀ ⠀⠀⠀⢠⠀⡇⠀⣿⣿⣿⡀⢺⡇⠀⣀⣀⣀⡀⠹⣾⣷⣧⠈⣿⣿⣶⣷⣿⣼⣿⣧⣀⠀⢹⣿⡄⠀⠀⠆⠀⠀⡇⢰⣧⢸⠀⢫⢹⠀⠀ ⠀⠀⠀⢀⠀⡇⠀⢻⠸⣿⣧⣼⡟⠛⣿⣿⣿⣝⣧⠙⢿⣿⣧⡘⣿⡿⣿⣿⡀⢻⣿⣿⣧⠀⣿⣷⡀⠀⠀⠀⢀⣇⣿⣿⢸⡆⢸⡞⠀⠀ ⠀⠀⠀⡾⠀⡇⠀⠘⣆⢸⠛⢿⡄⠀⣿⣴⣿⣿⢿⡇⠀⠀⠙⠃⠛⠃⠉⣻⣤⣴⣿⣿⣿⣦⡯⢿⣇⢸⡆⠀⢸⡏⠉⠻⣸⡇⣼⠃⠀⠀ ⠀⠀⢠⠇⠀⡇⠀⠀⠈⣸⠀⠀⠹⢷⣬⡝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⣿⠿⢿⣿⣿⣿⠀⢿⢸⡇⠀⢸⢉⣑⣤⠙⣶⠃⠀⠀⠀ ⠀⠀⡞⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠉⢿⣶⢼⢻⡧⡄⢺⠋⠀⡘⠀⡸⠀⠀⠀⠀ ⠀⡸⠁⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠴⠀⠀⠀⢸⢸⡇⡇⠸⠀⢠⠃⡴⠃⠀⠀⠀⠀ ⡾⠁⠀⠀⠀⡇⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⡇⠀⡾⡾⠁⠀⠀⠀⠀⠀ ⠙⠲⠤⣀⡀⡇⠰⠀⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢹⡟⠀⠀⡇⣸⢱⠃⠀⠀⠀⠀⠀⠀ ⠓⠒⠒⠛⠁⡇⢠⠀⢸⠀⢳⡀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⣿⠀⠀⢠⠏⢁⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⢸⠀⣬⡀⣼⢷⡀⠀⠀⠈⠑⠦⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡇⠀⠀⢸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢸⠀⡏⠀⢸⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⢠⡿⡌⡇⡇⠀⢸⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠢⢄⡀⠀⠤⡀⠈⣉ ⠀⢀⡤⠖⢺⡇⡇⣿⡿⢤⡜⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢖⣻⡃⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡇⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀ ⠋⠁⠀⠀⢈⡇⢸⣿⣷⠀⠙⠶⣄⡀⠀⠀⠉⠙⠛⠓⠚⠋⢉⡩⠴⠊⠁⠀⢣⣄⠀⠀⠀⠀⢀⣼⠀⠀⢸⡟⢦⡀⢀⡤⠤⠤⢤⣀⠀⠀ ⠀⠀⠀⠀⠘⠇⠀⣿⣿⠀⠀⠀⠈⠙⠦⣄⡀⠀⢀⣠⠴⠒⠁⠀⠀⠀⠀⠀⠀⢹⣦⣄⡀⠀⠛⢻⠀⠀⣾⡇⣠⠟⠁⠀⠀⠀⠀⠈⠳⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣶⣄⠀⠀⣀⡀⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⠠⠀⠀⠉⠹⠽⣧⣭⣉⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠙⢦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣰⠃⠜⣰⠃⠀⠀⠀⠀⠀⠀⠀⢞⡅⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣰⣧⢆⡜⠁⠀⠀⠀⠀⢀⠀⠀⢠⠞⠀⠀⢀⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⡿⢀⠞⠀⠀⠀⠀⠀⣴⠟⠀⣠⠏⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣼⢀⡞⠀⠀⠀⠀⠀⣼⡏⠀⢠⠏⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡄⠀⠀⠀⠀⠀⢸⠀⠀⢀⡿⠾⠀⠀⠀⠀⠀⣸⠏⠀⣰⠇⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡟⠀⢰⠋⡄⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠀⠀⠀⠀⠀⡿⠁⢠⡏⣼⠁⠀⠀⡟⠀⠀⠀⢠⠆⠀⠀⡞⣿⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠃⠀⠀⣷⠀⢀⣷⢀⣾⣳⠃⠀⠀⢸⠁⠀⠀⠀⡼⠀⠀⣼⢣⡿⠀⠀⠀⣜⠏⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡾⠀⠀⢰⣿⡄⣾⣏⣼⣽⡏⠀⠀⢀⣾⡇⠀⣤⣸⢳⠀⣠⣏⡆⡇⠀⠀⢰⡟⡄⠀⡄⠀⢠⡆⠀⠇⡄⠀⠀⠀⠈⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠃⠀⠀⠀⠀⠀⢠⡷⠀⠀⣇⠀⠀⢸⣿⣳⣿⣿⡟⡟⠀⠀⠀⣿⣿⢠⠀⡇⠇⠀⡀⠀⠉⠁⡇⠀⠀⣾⢡⠁⢰⣿⠛⡟⣿⢻⠲⡧⣄⡀⠀⣶⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⠀⣀⣸⣿⣩⡉⢻⣿⠃⠀⠀⢰⣿⢿⢸⣲⣷⠐⢲⣷⠤⣤⠀⡇⢠⣾⠃⣸⣴⠏⣿⣼⢀⣇⣸⣄⡆⣸⠃⢀⣿⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⣹⣿⠉⣁⣻⢸⡿⠀⠀⠀⣼⣇⣸⣧⣿⣿⣶⣿⣽⣦⡟⠀⣧⢻⠃⢰⣿⠏⠀⣿⣧⣴⣥⣭⢹⣧⢇⢀⣼⡇⠀⢰⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⠟⠀⠀⠀⠀⢹⡄⢹⣿⠀⡠⡇⣼⡇⠀⠀⠀⣿⠛⠯⠉⠘⢁⠀⠈⠉⣿⠙⠃⠉⠀⠀⠋⠉⠀⣸⣷⠿⠿⢿⣶⣿⣕⣾⣻⢹⠃⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠶⢤⣻⣥⣤⠀⠀⠀⠀⣼⣇⠈⣏⣧⠀⣙⣿⠁⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠦⠤⠼⠇⠈⠟⢻⣿⠀⠀⢹⠀⡎⠀⠀⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣄⢹⡈⣧⡼⠛⢙⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠀⠀⣿⠀⡇⠀⢰⡇⠈⠢⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠄⢀⣤⡿⠋⠀⢠⠞⠁⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⣰⡇⢸⠀⠀⢸⡇⠀⠀⠀⠉⠓⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡵⠚⢩⠎⠀⠀⣠⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⡏⠀⠀⣿⠐⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡶⣾⡇⠀⠀⣿⠀⠀⠀⢻⣾⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢰⡏⣇⡏⠀⠀⠨⣇⠀⠀⠀⠀⠀⠀ ⠴⣶⣾⣿⣟⣋⣁⣴⠋⢹⠀⠀⠙⣆⠀⠀⠀⢻⣿⡀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⣸⢁⣻⠁⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⠟⠁⠀⢸⡄⠀⠀⠘⣆⠀⠀⠀⠙⠓⠒⠶⢬⣻⣦⠀⠀⠀⠀⠀⠈⠛⠯⣍⣉⠉⠉⠉⣓⡶⠆⠀⠀⠀⠀⢀⡞⣻⠁⠀⢀⡏⣼⡇⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⣧⠀⠀⠈⣿⠁⠀⠀⠀⠈⠇⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣴⣿⠂⡏⠀⠀⢸⣷⠛⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠀⠀ ⣿⣿⣧⠀⠘⣷⣦⡀⠀⠀⠰⠆⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⣸⠃⠀⠀⢸⠋⢳⡄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣀⠘⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⢀⣴⠟⠹⣿⣿⣿⣧⠏⠀⠀⠀⣿⣧⠀⢷⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⣤⣤⠶⢿⠃⠀⠀⣿⣿⡿⣸⠀⠀⠀⠀⣿⣿⠀⠈⣇⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣾⠀⠀⠀⢸⣿⡧⣿⠀⠀⢀⢠⣿⡏⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢈⣽⠒⠤⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣱⡏⠀⠀⣼⢸⣿⣇⣀⡄⣸⡄⠈⣂⣤⢾⡆⠀⠀⠀⠀ ⣿⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⢷⡀⢀⡏⣷⠀⠀⠀⣿⣿⠀⠀⢠⣿⣾⣿⣿⣿⣿⡿⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⣿⣿⣧⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠚⠿⠤⣀⣀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠉⠛⠁⢹⡀⠀⢀⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⡧⡟⠀⠀⢀⡴⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣄⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣙⣲⢤⣄⡀⠀⠈⠛⠢⢤⣀⣸⣿⣿⣇⣀⣠⡤⠀⠀⢸⡇⠀⣸⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣷⢰⣷⠀⠀⣟⠀⠀⠀⠀⠀⠀