⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣸⣿⣿⣿⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡽⠀⣿⣿⣿⣿⣿⣧⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⠇⢸⣿⣿⣿⣿⣿⣿⡇⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡷⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣷⣻⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣝⡾⣷⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡽⣏⣿⡳⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣧⠈⣿⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡿⢾⣽⣳⠇⢰⣿⣿⣿⣿⠿⠛⣉⣤⣾⣿⣿⣇⠘⣽⡾⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡳⣏⣿⣻⢾⡝⠀⣼⣿⠿⠋⣡⣴⣿⣿⣿⣿⣿⣿⣿⡆⠸⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⢣⠿⣽⡶⣟⣯⡇⢠⣉⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⠈⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣟⣯⡿⣷⠛⠛⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⠐⠡⣉⠢⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠟⠳⠛⠈⠁⠀⡀⠄⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⢞⡱⡂⠡⢐⠢⡁⢎⠀⠀⠀⠀ ⠀⠀⠀⡀⢠⠀⢄⠂⠜⠠⢁⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡜⣣⢎⡵⢳⡀⠃⠤⡑⢂⠩⡀⠀⠀ ⠀⠀⡐⠌⠠⠌⡀⠎⡐⠡⠂⠌⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡴⢫⡜⡱⢎⣜⢣⠖⠈⡰⢈⠆⡱⠐⡄⠀ ⠀⠤⡁⡌⢄⡡⢐⢂⣁⠂⠥⠀⠸⠿⠿⠿⠿⠿⠿⠿⠟⢁⣀⣁⣉⣀⣉⣈⣁⠈⣁⠉⠀⣀⣁⣀⣀⣁⣀⣀ ⠈⠐⡡⠘⡄⢊⠅⣊⠤⡙⢌⠂⠐⣶⣶⣶⣶⣶⣶⣶⣾⢿⣿⣻⣯⣿⣟⣟⡿⣿⣿⠁⣸⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠠⢍⡰⠃⡜⢠⢒⡉⢆⠣⠀⢻⣿⢯⣿⣽⣯⣿⣽⣿⣳⣿⣽⣾⢯⣿⣟⣿⠂⢰⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠢⢄⠣⡘⠄⠦⡑⢊⠬⡁⠘⣯⣿⣟⣾⡷⣯⣷⣟⣯⣿⢾⣟⣿⠻⠞⠉⢠⣿⣿⣿⣿⣿⡝⠁⠀⠀ ⠀⠀⠀⠀⠀⠣⠑⡌⢒⠡⡉⠆⠥⠀⢻⣿⢾⣯⣿⢿⣽⣾⠿⠽⠛⠉⢀⡠⡐⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠡⡘⢢⠑⡌⢩⢒⡀⢸⡿⣟⣿⠾⠛⠉⢈⠠⡄⢦⡙⠦⡱⠀⣸⣿⣿⡿⠛⠹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠈⢢⠱⡈⠅⠒⢀⡀⠋⢁⡀⢤⠰⡘⣌⢓⡸⡐⣌⠣⠅⢰⣿⠟⢋⣄⠄⠀⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⡱⢆⠶⣙⢮⡱⡍⢦⡙⢢⢣⠱⡌⢦⠱⡱⢌⡃⠀⠟⣁⣴⡿⠃⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⢋⡞⣥⢲⡱⣃⠦⣑⠣⢎⡱⡘⢆⢣⡑⠎⠀⣼⣿⣻⢿⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠜⡴⢣⠵⣩⠒⡥⢋⠦⡱⣉⠎⠂⠀⠀⢰⣿⣞⡯⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣘⠧⢳⡡⢏⠴⣉⠖⠑⠀⠀⠀⠀⢀⣿⣷⡛⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡞⣥⢛⡜⠢⠁⠀⠀⠀⠠⠐⠀⣼⡿⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢏⣼⡆⠀⠀⡀⠁⡀⠀⣸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣟⣧⠀⠀⠀⠄⠀⢀⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢿⡀⠀⠀⡀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⢁⠂⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⠁⢂⠐⠠⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⢀⠘⡀⠘⡀⢃⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡁⢂⠐⠠⢁⠐⡀⢂⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⢀⠡⠐⠠⢈⠐⡀⢂⠐⡀⢂⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠃⠄⢂⠁⢂⠂⡐⢀⠂⡐⢀⠂⠌⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⡈⠐⠠⠈⠄⢂⠐⡀⢂⠐⠠⢈⠐⡈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⡐⠠⢁⠂⠡⠈⠄⢂⠐⠠⢈⠐⡀⢂⠐⡘⣧⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢀⠐⡀⠂⠌⠠⠁⠌⡀⠌⠐⡀⢂⠐⡀⠂⠄⡘⣧⠀⠀⠀ ⠀⠀⢠⠏⠀⠄⢂⠀⠡⢀⠁⢂⠐⠀⠄⡁⠠⢀⠂⠠⢈⠠⢀⠸⣆⠀⠀ ⠀⢠⠏⠠⢈⠐⠠⠨⢤⠂⠈⢄⠄⡁⢂⠠⠁⣀⠪⡆⢀⡂⡄⢂⠹⡄⠀ ⢠⠏⢀⠁⠢⠑⢑⠄⢐⠀⡁⡬⠃⢀⢠⠑⠣⢸⠸⢠⢰⠰⠐⡄⠠⠹⡄ ⢿⡀⠂⠜⣰⠈⡂⣃⠢⠀⠇⠣⠓⠠⠠⠈⣒⠜⡀⠣⠢⠣⡱⠀⢂⠁⡿ ⠘⣇⠐⡀⠉⠢⠕⠉⡀⠄⠠⠀⠄⠂⠂⠠⠍⠐⡁⠄⡀⠄⡁⠐⡈⣴⠇ ⠀⠸⣦⢀⠁⢂⠐⠠⠐⡈⠄⠡⠈⠄⡁⠂⠌⡐⢀⠂⡐⠠⢀⠡⣰⠃⠀ ⠀⠀⠹⣆⠈⠄⡈⠄⠡⠐⡈⠄⡁⠂⠄⡁⢂⠐⡀⠂⠄⡁⢂⣰⠏⠀⠀ ⠀⠀⠀⢹⣆⠐⠠⠈⠄⠡⠐⠠⢀⠁⢂⠐⡀⠂⠄⡁⢂⠐⢠⠏⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠡⠈⠄⠡⢈⠐⠠⠈⠄⠂⠄⡁⢂⠐⠠⢨⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡁⠌⠠⢁⠂⠌⠠⠁⠌⡐⠠⠐⠠⢈⢐⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⡈⡐⠠⠈⠄⠡⢈⠐⠠⠁⠌⡐⢠⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠡⠈⠄⡁⠂⠌⠠⢁⠂⣐⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢁⠂⠄⠡⢈⠐⡀⢂⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠌⠠⢁⠂⡐⠠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠐⠀⠂⡄⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠡⢈⠐⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔⢀⢢⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟⢀⣿⡄⠀ ⠀⠀⠀⠀⠀⣠⡴⠋⡴⠋⠀⢸⠈⡇⠀ ⠀⠀⠀⣠⠞⠁⢀⡞⠁⠀⠀⣸⠀⡇⠀ ⠀⣠⠞⠁⠀⣰⠏⠀⠀⠀⠀⡇⠀⣇⠀ ⣞⠁⠀⢀⡼⠃⠀⠀⠀⠀⢠⡇⠀⢿⠀ ⣿⠀⡞⣽⣧⠀⣀⡀⠀⠀⢸⢲⢰⢻⠀ ⣿⣰⠇⡏⢸⢸⠏⠉⢳⡄⡾⡞⡎⣸⡆ ⣧⡀⢰⣇⡞⣿⣾⣇⣴⣷⠃⠷⣿⡽⠃ ⢻⣷⣿⣽⣷⣿⠛⣻⣇⣠⣶⣶⡟⠀⠀ ⢸⠛⡿⢻⣟⣃⢠⣿⣿⣿⣿⣿⡇⠀⠀ ⢸⢰⣿⣿⣿⣿⢸⡟⠙⠋⠈⠛⠁⠀⠀ ⢸⣾⣿⣿⡿⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡿⠛⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠄⡈⠄⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠡⢈⠐⠠⢈⠐⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠄⠂⠌⡐⠠⢈⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡈⢰⠣⡔⠀⣅⢤⣊⠜⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢑⠓⢁⠉⠄⠋⡉⢈⢡⠎⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠙⡄⠈⠄⡈⠄⠡⠐⢠⠎⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠐⠠⠌⠠⢁⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢁⠂⠌⡐⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡐⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀