⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⢠⣀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⣹⣿⠻⢿⣧⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣮⢳⣟⣦⣀⣤⡀⣀⣤⡾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡽⣳⣄⣠⡀⣀⣤⣾⢻⡽⣷⣦⡀⣈⠉⡉⢉⠛⠛⠛⠶⠶⠶⢦⣤⣤⣤⣄⡀⠀⠀⣼⣟⢧⡟⣼⡳⣮⢽⡟⠈⢿⡽⣎⢷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢷⣏⢷⡿⠉⣿⢯⣳⡽⣣⣟⣼⣯⡿⠷⣴⣴⡆⠈⡔⢡⠂⢆⠰⠠⠄⡄⢠⠈⡙⣦⣾⣯⣛⣮⠽⣖⡯⣝⡿⠁⢀⠘⣿⣝⣮⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⢏⣾⡿⠁⠀⣿⡟⣶⣽⠷⠛⡉⢠⠐⡄⢂⠄⡠⢃⠰⡁⢊⠄⢣⠁⠎⡄⢣⠐⡁⣾⡿⢶⣫⢞⡽⣞⡵⣿⢃⣴⡄⠂⢿⡾⣜⡷⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣟⡞⣾⠃⠀⠄⣿⣿⠟⢁⠢⢑⡈⢂⠡⡈⢆⠒⡐⢌⠰⣀⠃⢌⠰⢈⠆⡐⢂⠡⢂⠸⣟⡯⣞⡽⣺⢵⣫⣿⣿⢻⡇⢀⠸⣿⢧⡟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢮⡽⡟⠀⣰⡴⠟⠁⡄⢃⠢⠡⠐⠡⠂⠅⠢⠡⠌⠤⠡⠄⡩⢠⠁⢢⠈⡄⠃⠌⠄⠂⢿⣽⢺⡵⣏⣾⣽⠿⣜⣿⠃⠀⡀⣿⣧⢟⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⠾⡿⠟⢋⠐⡌⠡⠌⢂⠌⡰⠉⢆⠱⡈⠥⢘⠠⡑⠢⡑⠄⢃⠈⠄⡌⠰⢉⠔⠨⠐⠸⣿⣣⢟⡼⣾⣏⠿⣼⣇⣀⡂⠀⣿⡷⣫⢞⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡄⢀⠸⢀⠜⣀⠃⠜⡠⠘⡀⠃⠄⢄⠣⠄⢃⠤⠘⡃⠤⢘⣤⣿⣿⣿⣧⠘⠄⡃⠇⡀⢿⣟⡼⣻⢧⡜⣿⣿⡿⣿⣧⠀⢸⣿⣣⢿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⢫⡿⣶⣔⠢⠌⡐⠌⠤⢁⣢⣼⣿⣾⣄⡎⠌⠢⣀⠃⡌⠰⣿⡿⣭⢳⣿⠃⡁⠆⠡⠌⡐⠈⢿⣷⡹⢮⣽⡿⣳⡝⣾⠇⠀⣼⡷⣏⢾⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣯⢗⡯⢿⣏⠻⣦⣅⡂⠌⠠⠸⣿⣿⣽⣿⣯⠘⡰⢀⠊⠤⢁⠻⠷⠟⢋⠁⣐⣠⣈⣐⡠⢈⠡⠀⢿⣝⣯⢳⡝⣧⣻⡿⢿⢿⣻⣝⢾⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡮⣟⡭⢿⣟⢿⡻⢿⠻⢶⣶⢾⣿⠿⣟⢓⠠⡁⠆⡘⡐⠢⡈⠄⣡⡾⠛⠋⠉⣩⣿⣿⣿⣷⣬⡘⢿⣼⢫⣾⣽⢿⡹⣏⡾⣵⢺⢧⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡞⡽⣽⢳⢮⢷⣹⠏⣰⣾⣷⢟⣿⠟⠷⣬⡐⣰⠈⠄⠡⠁⠄⣹⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠈⢿⣏⡟⣮⣳⢻⣜⣳⡭⣏⡿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡿⣝⣧⢯⣛⣮⣛⣴⢟⡾⢁⣾⠃⡐⢠⣹⣿⣫⣶⢿⡟⡿⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⣻⡇⢈⠻⣽⢶⣹⡳⢮⣳⡝⣧⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡿⣜⢯⢾⣶⢿⣥⣼⣷⣼⣧⣴⣾⣿⣿⣿⡳⡽⢮⣝⡳⢧⣟⣧⠀⠀⢻⣿⡿⠿⠛⠉⠀⢀⡿⠘⡀⢂⠉⠿⣧⣻⡝⣧⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣟⣮⢯⡇⠠⢀⢹⡀⠘⣟⠋⠉⠉⣼⡿⣽⣹⢳⡞⣽⢳⢮⣿⠳⣄⡈⠳⣤⡀⢀⢂⣡⠾⠓⠓⠈⠉⣉⣴⡿⣷⣿⣞⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢾⣥⣾⣷⣬⣕⡀⠹⣶⣈⣴⠏⣹⢶⣫⠷⣝⢾⡹⣾⡧⠖⠋⠉⠀⠈⠉⠉⠉⠁⢀⠴⢋⣴⠿⣏⡷⡽⢶⣭⢻⣝⡻⣟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡾⣟⡧⢷⢮⣽⣿⣷⣤⠀⠈⠙⠚⠷⣯⣟⣼⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣴⡿⣫⢟⣮⢳⡽⣳⣎⠿⣜⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠿⣿⡿⣭⢳⢯⡞⣯⣾⠛⠻⠿⠿⠷⣄⠀⠀⠀⠘⠻⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡻⣜⢷⣫⢞⡽⣺⢵⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣮⣽⡞⠋⢀⠠⠀⣀⣾⢿⣦⡀⠀⠀⠀⠀⠀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⣰⣿⡳⣽⡹⣎⣷⢫⣞⡿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢷⣦⣤⣴⣄⣻⡷⣺⣷⠀⠲⣤⡴⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣳⡝⡶⣿⣱⣞⡻⣎⠷⣝⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣼⢫⡟⡽⣷⣣⢟⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⢧⡻⣝⣻⡟⠳⠿⣾⡯⠿⠽⠾⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⡳⢮⣳⣽⣷⡿⣝⢮⢿⣆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠿⣼⣷⣿⡴⠚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⣾⣟⣽⡾⠟⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⠋⢠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠋⠉⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠃⠀⠀⠀⢠⡏⠸⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣟⣿⢿⡿⠀⣠⠴⠒⠋⠀⡀⢀⢀⡼⠃⠀⠀⢠⣾⠿⣟⡿⣶⣿⣻⣼⣏⣾⣽⡻⢿⡷⣶⡶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣟⣧⢻⡿⡽⣾⠇⠀⠈⠹⣶⠀⠂⡀⠄⣯⠀⠀⠀⣰⣿⣏⣿⣼⠟⠉⣡⣴⣎⢿⣹⣛⡿⣟⣾⢷⣯⣳⢭⡻⣝⡿⣻⢿⣦⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⡿⣏⢾⣿⢻⣵⡿⠀⠀⠀⠀⠸⠖⠋⠙⠳⠟⠀⠀⣠⣿⢷⠋⠀⡏⢀⣾⣟⡳⢾⣭⢳⣝⢾⣱⢾⣹⢻⠿⣧⣟⣾⢵⣫⢞⡵⣻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡽⣎⢿⡏⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⢿⠀⠐⢿⣾⢻⡼⣹⡳⣎⡿⣜⣳⢏⡾⣭⡻⣽⣹⢯⢿⣿⡷⣿⣜⣳⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡝⣾⣹⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠀⢸⣟⢮⣻⣧⡀⠘⢿⣧⡻⣵⢫⢷⡹⣎⢷⣫⢗⣧⣻⣜⣳⢯⡞⡽⣿⠌⠙⠻⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣉⣀⣀⣀⣀⣤⠖⠀⠀⠀⠀⢠⡇⠀⡏⠀⢸⡏⢷⣣⢟⡽⣿⣟⣿⣷⣭⣛⣮⢽⡹⣎⢷⣫⢞⡿⣷⠿⠾⠟⣻⣯⣄⢈⠐⡈