⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣏⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡯⣕⡎⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⣓⠲⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣣⡝⣖⡣⡽⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣏⡟⡲⣍⡻⡽⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⢯⢏⡞⡴⣙⢦⠽⣜⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣼⠳⣥⢳⣙⢮⡝⡟⣦⡀⠀⠀⠀⠀⡼⡻⡜⢮⣜⢣⢏⣎⢗⡺⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢆⡟⡜⣮⢚⡇⠟⣻⣄⢠⡶⣴⡯⣕⢫⡳⢬⡏⣞⡜⡮⣕⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠴⠀⠀⡇⠀⠀⠀⠀⠀⣠⣴⠒⠉⠁⠀⠀⠀⠈⠁⠉⠻⢍⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣼⠝⣚⣥⢰⣏⣧⣻⣯⣷⢻⠥⡭⠧⢿⣶⣽⡦⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⡀⠀⠀⠀⠄⠀⠀⠀⣠⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠿⣿⡿⠛⠛⠻⣧⣄⠠⠛⠛⠛⡘⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⡤⠤⡀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⢶⡴⣶⢧⣀⠀⠈⠱⣄⠀⠀⠀⣀⡴⠛⡿⠀⠀⠀⠀⠀⠀⠀⠘⠢⡈⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠔⡙⢃⠤⠡⢉⠒⣈⠛⠷⡇⠉⢆⠡⠃⡄⣉⠻⣦⡀⠀⠀⠀⠀⠱⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣛⣮⡽⣯⡽⣞⣯⢟⣷⣷⣌⢿⡆⢀⡴⠋⠀⢸⠃⠀⠀⡀⠀⣠⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣾⣇⡴⠍⡰⠐⠌⡠⠃⢌⠒⡠⠘⡄⠢⢉⠄⢢⠑⡠⢂⠔⡠⠛⢷⡄⠀⠀⠀⠈⠢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣳⢟⣞⡷⢯⣽⡳⣏⣿⠾⣽⢿⣆⢳⠋⠀⠀⠀⡟⠀⠀⠀⠙⠂⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⡡⠌⠒⡠⢉⠰⠁⡜⢀⠆⢡⠑⡠⠃⡌⣐⡢⢁⠒⡈⠔⡠⠃⡌⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⢀⠞⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠷⣯⡿⠚⠋⠛⠺⠿⠝⠉⠙⠻⠿⢻⠀⢷⠀⠀⢸⠁⠀⠀⠘⠉⢸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠡⢂⠴⡅⢡⣂⠡⢊⠔⠠⠃⡌⢂⠜⠠⢡⠐⠨⠷⣧⡘⢠⠑⡠⢑⡈⢅⠸⣷⡄⠀⠀⠀⠀⠀⠀⠰⠦⠈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢸⡇⠘⣆⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠌⢡⢢⡞⡁⢾⡏⡑⠌⡄⠣⢑⠠⠃⢌⠂⠻⣮⡁⠆⡙⣷⡁⢆⠡⢂⠔⣈⢂⠹⢿⡀⠀⠀⠀⠀⠀⠀⢠⠆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⠴⠋⠀⠀⠂⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢠⠇⢸⠀⠀⠀⠀⠀⠀⡰⠀⣟⠀⢸⣷⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠤⠉⢤⡟⠰⣸⠋⣷⡈⢆⠰⢁⠊⣤⠉⡄⢊⠡⢿⢳⣌⠰⠘⣿⡄⢊⠄⡊⢄⢂⡒⣬⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠲⢶⣖⠒⠲⣾⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢀⣴⠏⠀⢸⠀⠀⠀⠀⠀⠔⠀⡼⠙⣄⣸⠉⠀⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡰⢈⢌⡿⣰⡽⠃⠀⠘⣧⡂⢌⢂⠡⢿⡖⢈⠄⢃⣾⠀⠹⣧⠜⠸⣿⡀⢎⠐⣂⠢⠄⣹⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⠮⣷⡍⠛⣶⣤⡤⠤⠴⠶⠶⢺⡏⠁⢀⣠⡴⠛⠁⠀⠀⡞⠀⢰⡄⠀⢂⣠⠞⠁⠀⠙⣏⠀⠀⠀⣧⣈⡳⠖⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠡⡈⣼⣽⣿⠀⠀⠀⠀⠙⢿⣆⠌⣂⠉⣿⡆⢸⣤⡏⠀⠀⠈⠻⣖⢻⣷⠈⡔⢠⠂⢅⣸⣻⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠃⠌⠛⣷⡀⠀⡆⢸⡗⠊⠉⠀⠀⠀⠀⠀⣸⡡⣴⠏⢀⣰⠟⠋⠀⠀⠀⢠⠇⠀⠀⢰⠏⠳⣄⡀⠛⠀⠂⠂⠀⠀⠀⠀⠘⢶⣤⣤⡼⢋⢰⢇⢻⣿⠸⣧⠀⠀⠀⠀⠈⠻⣶⡀⢣⠘⢿⣦⠟⠀⠀⠀⠀⠀⠈⢻⣿⡐⡐⢢⠘⢠⢸⡇⢿⣧⡙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡌⠄⢃⠈⢛⣦⣧⠘⣇⠀⠀⢀⣀⠀⠀⠀⠉⠚⠓⠶⠋⠁⠀⢀⣠⣤⣤⣾⡀⠀⠀⡾⠠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠞⣿⠄⢊⣿⣴⡏⢀⡀⠀⠀⢀⣠⡞⢻⡦⣞⣚⠳⣄⠀⠀⠀⠀⠀⢀⣼⠃⣅⣂⣡⡘⣲⣿⣁⢊⠛⠻⣿⡾⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣀⣀⡈⣧⣛⣿⣎⠠⢁⠂⡹⣿⣧⣹⣆⠿⠿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⣉⣽⠁⢰⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣠⠘⠿⢧⣙⣿⣷⣦⡉⠉⠉⠉⠀⠀⠈⢉⣩⣶⣾⣿⣶⡶⢾⣛⣻⣿⣿⣻⣿⡿⢯⠉⠉⠉⠉⠁⠀⠀⠀⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⢿⣍⠉⡉⢉⠉⡉⢉⠙⠛⢛⢾⣿⡎⠄⡡⠘⣿⣿⡔⠈⠓⠩⣹⣿⣶⣤⣶⣶⣦⠀⣀⣠⣶⠾⠿⣮⣥⣼⣰⣿⣧⣽⣦⡀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠷⣶⣖⡚⠣⠬⣉⡀⠀⠀⠀⠀⢀⣀⣠⠿⠟⣉⣁⡀⣄⢢⣹⢿⣛⢯⣿⠡⡐⠌⡳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣴⣈⠂⠡⢌⢈⠒⠄⠂⠌⠓⡐⠠⢡⣿⣿⣻⢿⣻⣟⡿⣯⣭⣤⣤⣍⣙⣛⣿⣋⣡⣶⢾⣻⣽⣿⡿⣷⣿⡿⠋⠙⠲⢤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣉⠻⢿⡲⡭⣝⢳⡖⣤⢬⣙⡓⠒⢊⣉⣡⢖⡞⢯⠳⣍⡟⣭⠳⡭⢶⣩⢖⣻⣷⡈⠔⠡⢄⡙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠳⢧⣄⣊⣄⣉⣌⣈⣡⣤⣷⣾⣏⠙⢯⣷⣻⣼⢳⡿⣼⣳⣛⡾⣽⣫⠿⣝⣻⢞⣯⢿⣟⣯⢷⣻⣿⡟⢤⣀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠡⢄⠺⣿⣹⣱⢎⡳⣜⡣⣏⠶⣹⡛⢯⢣⢏⡞⡼⣩⢗⣣⢞⣜⣳⣽⡶⠿⢻⣿⢋⠰⢈⠡⢂⠄⣃⠢⠌⡙⠳⢦⣤⣀⠀⠀⠰⠆⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⡿⢿⣻⢻⣽⡿⡳⢽⣦⣄⣙⣛⣾⣿⣟⣳⣭⣿⣽⠶⣯⣿⣝⣯⡟⣮⣟⣾⣽⣾⡿⠛⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⡋⠔⠡⠌⠢⣴⣾⠛⣍⡛⢷⣮⣵⠮⣝⡲⢭⣋⢮⣓⠮⣵⢓⣮⣳⡾⣛⠫⡔⣌⢣⢃⠻⣶⣈⠂⡅⢊⠰⢀⠆⡑⢨⠐⡂⠤⢉⠛⡳⣦⣄⠉⠁⠀⠀ ⠀⠀⠀⠀⠠⢦⣴⣶⣿⠛⠧⣍⡓⢧⣿⡗⢛⣭⣳⢎⣟⡻⣛⢯⣟⡻⣟⠯⣝⡇⠀⠀⠉⠉⠉⠛⠛⠀⠉⠉⣼⠀⠀⠀⡄⠀⢷⠀⠀⠀⠀⢀⣀⣤⡴⠞⡋⠰⡈⠔⡉⢄⢣⣵⢟⡰⣉⠦⣙⢢⢱⣿⢿⣶⣝⣧⢚⡵⢪⣗⣾⣿⡫⢱⡘⢤⠓⡜⢤⢃⢎⡱⢊⠿⣷⣢⠁⢆⠡⢂⠑⡂⢡⠘⠄⣃⠘⠄⠤⢉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⢿⡿⣿⣝⡶⢤⡙⢳⣾⣯⣭⡑⢯⡙⢮⡵⢫⡞⣿⣷⡭⢞⡱⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠠⠀⣼⢸⠀⠀⢀⣶⢋⠱⡀⠆⣂⠡⡑⢨⣰⢌⣶⠿⣡⢃⠖⣡⠚⡤⢇⣾⣟⡾⣏⣟⣻⣿⣾⡿⣹⢽⣼⣟⠤⡙⢦⡙⡘⢦⡉⢦⠱⣉⠖⣩⢛⣿⣄⡊⢄⢃⡘⠄⡊⠔⡠⠉⡌⢂⠅⡒⠈⢿⡄ ⠀⠀⠀⠀⠀⠀⠘⣿⣍⠿⣿⣿⣏⢿⣿⣹⣿⣯⣦⡘⢦⣜⢫⠭⢭⣽⣿⣭⢳⣻⡄⠀⠀⠀⠀⠀⣈⣭⣿⢿⣶⣤⣴⣤⠴⣿⣾⡀⠀⢺⡡⠌⢒⠠⡑⢠⢒⣼⣫⣷⠟⣍⠲⡡⢎⡜⢤⢋⠴⣩⣿⡟⠛⠺⣮⢷⠋⣿⣞⠷⠿⢾⣿⡬⡑⢦⠱⣉⠦⣙⢢⠓⣌⠚⡤⢣⠌⡝⢿⣮⣤⠐⡌⡐⢡⠐⡡⠂⡅⠒⡈⠥⢨⡇ ⠀⠀⠀⠀⠀⢀⡴⠋⠛⢚⣿⡟⠻⡿⣿⣿⡙⣿⣿⣽⣢⣸⣿⣿⣯⣝⣚⣿⣷⣹⣇⣀⣤⣴⡾⣿⢻⣏⣯⡿⠞⠋⠁⠀⠀⠁⠀⢹⠇⠘⢷⣌⠢⢁⠔⣡⣿⡟⢫⠔⡩⢆⢣⡑⢎⡜⢢⢍⠲⣽⣻⡇⠀⠀⢹⡿⣶⡟⠁⠀⠀⣾⡽⣷⡉⢆⠳⣌⠲⡡⢎⡱⢌⠳⣌⢣⠚⡜⢢⢍⡛⢿⣶⣆⠡⢂⠥⠘⣀⠣⠘⡠⢂⡇ ⠀⠀⠀⣀⡴⠋⠀⠀⣤⣿⢻⡇⠀⣷⢻⣧⢷⡈⢾⣹⣛⣿⡷⣎⡽⡹⢯⣝⡲⣥⢿⡿⣝⣧⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠙⢶⡃⠄⣿⠈⣿⣢⠙⡴⣉⠦⡙⢦⡘⢥⢊⣽⡿⣟⣿⠀⠀⣾⡻⣜⡿⠀⠀⣼⠷⡏⣿⣎⠥⡓⢬⠱⡑⢎⠴⣉⠖⡌⢦⡙⣌⠣⢎⡜⢢⣼⠟⠲⣥⣂⠱⢀⠆⠱⣀⡿⠁ ⠀⠀⠘⣯⠀⠀⠀⠈⠻⣮⣿⠀⠀⢸⡏⣿⣎⠿⣄⢳⡷⠚⢋⣽⢲⡝⣣⢮⠵⣎⡻⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⢻⡔⣼⠀⠉⢿⣜⡰⢡⢎⡱⢢⠍⢦⢹⣿⣸⡷⣹⢷⡄⣿⣳⡽⢃⣠⡾⣿⣹⢻⡟⣿⣢⠙⣆⢣⡙⣌⠲⣡⠚⡜⢢⠱⡌⠳⣌⣴⣿⠋⠀⠀⠀⢹⡆⠅⣾⣽⠏⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⢻⣦⡄⠀⣿⢹⣿⣽⠛⠀⢠⣾⢹⡎⣧⡟⢳⣮⠛⣴⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⡟⠀⠀⠈⣿⣬⠃⣦⠑⢣⠚⣴⣿⣿⣧⢻⣵⢫⢻⣿⣷⡟⣯⡏⣷⢣⡏⣷⢹⢻⣧⢹⠐⣦⢱⡌⢳⡄⢫⡜⢡⠓⡌⢳⣾⣿⠀⠀⠀⠀⠀⢸⣧⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠙⠻⠷⣿⣧⢿⣯⣤⡞⣧⡘⢷⣺⠝⢁⡼⣫⠽⣡⢟⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⣷⠇⠀⠀⠀⠘⢷⡫⢔⡩⢎⢲⣽⠟⣿⡜⣷⣽⣮⠷⠋⠳⢿⣼⣹⣎⠿⣜⢧⢿⣾⣿⣇⠳⡌⢦⡑⢦⢙⢢⠱⣉⢖⣹⠞⣱⡇⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠹⣟⡴⣻⣄⠉⢠⣞⡳⣭⢳⡹⢎⡞⡽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠀⢠⡞⢻⣦⡕⣊⣽⣿⡟⣯⢞⡵⣻⡄⠀⠀⠀⠀⠀⣭⡿⣹⢎⡟⣮⢷⡿⣻⣗⡸⢂⡍⢦⡉⣆⣳⠾⣟⠡⢊⢼⠀⠀⠀⠀⠴⢫⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣯⡴⣆⡙⢷⣜⣣⣝⢫⣜⢳⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠲⠯⠼⢿⣼⣿⢛⡿⣜⢯⡞⣵⢻⡄⠀⢀⣴⡿⣏⢷⡹⢮⡝⣮⢳⣻⣽⣿⢎⣱⣸⡶⠟⠋⠀⠀⠈⠳⠦⣞⣷⣄⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣷⣭⢳⢦⡈⠳⣎⡷⢪⡗⣼⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡻⣜⢧⡻⣜⢯⣟⡾⣟⢯⡳⣝⢮⡝⣧⢻⡜⣧⢏⣷⡿⠟⠋⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡿⣿⣮⣽⢳⢤⡙⠳⣝⣶⡱⣻⣆⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡽⣎⢷⡹⣞⡼⡳⣝⢮⡳⣝⢮⡝⣮⣳⣽⠞⠛⠁⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⡳⣯⣟⣿⣾⣽⣳⢤⣈⣙⡳⢽⣦⠀⢀⣴⣤⣿⡀⠀⠀⠀⠀⠀⣀⠤⠠⠤⠊⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡓⠻⠾⠵⠿⠼⠧⠿⢼⡷⠟⠋⠙⣆⠀⠀⢀⣀⣤⠶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣙⢄⠀⠀⠀⠀⠀⠀⡿⣷⣻⡵⣞⣧⢿⡆⠉⠙⠓⠯⢽⣷⣿⣷⣿⢿⣿⠿⠇⠀⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⣀⣀⣀⣀⣀⡎⠀⠀⠀⠀⠸⣶⣾⣹⣯⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣍⠦⡀⠀⠀⡄⡇⠘⢷⣿⣽⠾⠟⠃⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠿⠻⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠰⣄⡴⣄⣀⣀⣀⣀⣀⣀⠀⢀⡄⠀⡆⠀⣆⠀⡆⠀⣄⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⢵⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⠀⣿⣇⣸⡇⠈⣇⢸⢃⣹⣧⠿⠶⠶⣷⠀⠘⢧⣿⠀⣿⢧⡀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢳⠿⠇⠀⡇⠀⠛⠸⠉⠠⠏⠀⠠⠞⠉⠉⠙⢂⡟⠀⢿⠈⢳⣤⠟⠀