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

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