⡇⠀⠈⠉⠁⠒⢶⡤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡎⢉⠀⠉⠲⠤⣀ ⣧⠄⠐⢒⣤⣖⠦⣍⡀⢄⠉⠁⠐⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠹⡄⠉⠉⠁⠒⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⢁⡸⠊⠁⢠⣇⣀⣰⠉ ⡇⠉⠉⠳⡀⠈⠳⡄⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠉⠓⠢⡄⠀⢤⡽⠆⠀⠀⠀⠀⠀⠀⠀⠹⠒⠒⠒⠤⢤⣤⡤⠊⠀⠀⣀⣤⠄⠒⠂⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⢀⣎⣄⣀⠸⡄ ⡇⠀⠀⠀⠱⡄⠀⠈⢢⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⣈⡷⠒⠚⠓⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢾⣡⠔⠊⠁⡰⠃⠀⠀⣀⣀⣀⣀⠤⠚⠁⠀⠀⠀⡰⠋⡰⠃⠀⠈⠁ ⡇⠀⠀⠀⠀⠘⢄⠀⠀⠱⣄⠀⠀⠀⠙⠒⢠⠖⣀⠴⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠳⡀⠀⢸⠁⠀⠀⠀⠀⠉⣳⠆⠀⠀⠀⠀⣠⠞⠀⡔⠁⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⠋⠢⡀⠀⠀⣻⠋⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠉⠲⣬⠷⡲⠶⠒⠊⠉⠀⠀⠀⡀⣠⠖⠁⣠⠎⣀⣠⣴⠇⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣨⣦⣀⠀⠀⠙⠀⡰⠃⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⢴⡿⠋⠁⢀⣴⣷⣿⡿⢻⠏⠀⠀⠀ ⡇⠀⠀⠀⠀⣠⡶⠟⠛⠛⢯⡑⠀⠀⣷⠃⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⡴⢁⠞⠀⢀⣴⣿⣿⣯⣅⣴⠋⠀⠀⠀⠀ ⡇⠀⠀⠀⡴⠋⣀⣴⠞⢀⣤⣿⣲⠞⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡾⠀⣠⡄⡟⠢⠤⡄⠀⠀⠀⠀⠀⣤⡜⠏⠀⠀⠀⢶⡫⠉⠉⠉⠁⠀⠀⠱⡄⠀⠀⠀ ⡇⠀⠀⣸⢁⣴⣿⢃⣴⣿⣿⣿⢁⠄⠀⢠⣦⡀⣿⣷⠀⠀⢰⣰⣲⣿⠉⠒⢀⣤⣤⣤⣾⠁⠰⣿⢱⣷⡋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠙⣄⠓⠺⠶⣤⣤⣀⠘⣆⠀⠀ ⡇⠀⢀⣇⡎⣿⠇⣾⣿⣿⣿⠃⣿⡀⠛⠣⢤⢟⣿⣿⡆⠀⢸⣇⠁⣿⣯⠉⠀⠀⠀⣰⣇⠀⠀⣠⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⡏⠈⠑⠂⣿⣿⣿⣿⠿⠃⠈⢳⣄⠈⠙⠂⠀ ⡇⠀⠰⡟⢸⡿⠀⣿⣿⣿⣿⢸⢘⣿⡄⢲⠀⠀⢿⣿⣿⣦⡈⣿⣦⢻⣿⣆⠀⠀⢠⣿⣿⣿⡿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣿⣿⡀⠀⠀⠀⠀⢠⣹⡗⢄⡀⠀ ⡇⠀⠀⠃⠘⡇⠀⡿⢻⡿⣿⣿⡟⠻⣿⣦⣧⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣿⣿⣿⠟⠷⢤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠿⣿⠀⠀⠀⠀⠈⡏⢿⡆⠱⡄ ⡇⠀⠀⠀⠀⢧⠀⠁⠀⣿⣬⠉⠁⠀⠯⣿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡿⠋⣀⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣖⡽⠃⠀⠀⠀⣄⡀⠀⠀⠀⢳⣸⡈⢿⣄⠇ ⡇⠀⠀⠀⠀⠘⡄⠀⢀⣛⡁⠀⣀⣠⣴⣿⣿⣿⠿⣦⣄⣞⠀⢺⡟⡟⢿⣿⣿⠃⠋⠀⢰⠋⠁⠼⠒⣿⠉⠉⣛⣿⡿⢿⣿⣿⣿⠃⠀⠉⠉⠉⣹⠀⠈⠻⢶⣄⠀⠀⢫⣇⣜⡟⠀ ⡇⢀⠀⠀⠀⠀⢻⠀⠈⠛⠻⢿⣿⣿⣿⣿⡿⠋⠀⢁⠴⠃⡨⠫⣍⠁⠀⢈⡿⠀⡠⠄⢚⣩⠶⠓⠒⠋⣉⠛⠀⠀⠁⠘⣿⣿⣿⣗⣂⣀⣀⡴⠃⠀⠀⠀⠀⠻⣦⠀⠈⠉⡝⠀⠀ ⡇⠘⡷⠤⣄⣀⡼⠀⣠⠀⢀⣤⣿⣯⣁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠂⣤⣤⡤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢸⡃⠀⠀ ⡇⠀⢱⡅⠀⠀⣀⡴⢋⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡸⠆⠀⠀⠙⢻⡿⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⣶⣿⣟⡄ ⡇⠀⠀⠙⣲⠏⠁⢠⣿⣿⣿⣿⣿⣐⡶⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⢀⡀⠀⠀⠀⠀⠀⠀⠀⡎⠱⡄⢇⠘⢗⠦⢠⠞⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠱⠈⠉⠉⠀ ⡇⠀⢀⡞⠁⠀⠀⣿⠟⢹⣿⣿⣿⣿⣀⠾⢧⡀⡀⠀⠀⠀⠀⠀⠀⢀⣴⠝⠉⠀⠹⣕⣦⠀⠀⠀⠀⠀⢣⡀⠘⢎⣆⠈⢢⡏⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⡇⠀⠸⠀⣠⠀⠀⠛⠀⠀⢿⣿⣿⢿⣷⡒⠉⠀⠈⢆⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⣀⣴⠞⠀⠀⠀⠀⠀⠀⠉⣆⣀⡹⠥⠼⡷⠀⠀⠀⣠⣠⠇⠀⠀⣿⡀⠀⠀⣰⢻⠁⠀⠀⠀⠀ ⡇⠀⢾⢹⡏⠀⠀⠀⠀⠀⠈⢿⣿⠀⢿⡧⠤⠤⡀⠈⢳⣤⡀⠀⠀⠀⠸⡄⠀⡿⠀⡼⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⢰⠇⠀⢀⣶⣿⣿⠀⠀⠀⠘⣧⠀⠀⡇⠸⡀⠀⠀⢀⠀ ⡇⠀⠸⣼⢱⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠣⣤⠀⠈⠑⠚⠁⠈⠓⠤⣄⡀⠳⣄⠀⢰⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⢀⣼⡇⠀⣼⣿⣿⣿⡆⠀⠀⠀⠈⢦⡀⠙⠦⠬⠵⣲⠏⠀ ⡇⠀⠀⠈⠉⢣⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢏⢳⣤⡀⠀⠀⠀⠀⠀⠀⠹⡍⠛⠓⠛⠒⠉⢁⠞⠀⠀⠀⠀⠀⠀⢀⡔⣿⣿⡇⢰⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠑⠀⠀⡤⠚⠁⠀⠀ ⡇⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⣷⠀⠀⣼⡈⢿⣿⡦⣄⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣠⠞⠀⠀⠀⠀⠀⢀⠔⠋⠀⠸⣿⣿⡼⠘⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣻⠀⣰⠃⣱⣼⣿⣁⣠⣵⣦⣀⣀⣴⣯⣁⣐⣒⣈⣽⣧⠀⠀⠀⢀⡴⣇⠀⠀⠀⠀⠈⠻⣧⠀⠘⢿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⢸⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⡀⣀⣦⣷⣿⣿⣿⣿⢿⠘⠀⣧⠻⠈⠀⠀⠀⠀⣇⡴⢀⠀⠀⠀⣧⣽⣈⣒⣐⣁⣯⣴⣀⣀⣦⣵⣠⣁⣿⣼⣱⠃⣰⠀⣻⣀⠤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⠘⡼⣿⣿⠸⠀⠋⠔⢀⠀⠀⠀⠀⠀⠞⣠⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⣄⡦⣿⢿⡈⣼⠀⠀⣷⠀⠀⠀⠀⣄⠢⠙⠀⠀⠀⠀⠀⡇ ⠀⠀⠁⠚⡤⠀⠀⠑⠀⠀⠀⠀⠀⣷⣿⣿⣿⢻⢰⡇⣿⣿⡔⢀⠀⠀⠀⠀⠀⠀⠞⢁⠉⠒⠛⠓⠛⡍⠹⠀⠀⠀⠀⠀⠀⡀⣤⢳⢏⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⢣⠉⠈⠀⠀⡇ ⠀⠏⣲⠵⠬⠦⠙⡀⢦⠈⠀⠀⠀⡆⣿⣿⣿⣼⠀⡇⣼⢀⠀⠀⠀⠀⠀⠁⠚⡤⣀⠀⠀⠀⢰⠀⣄⠳⡀⣄⠤⠓⠈⠁⠚⠑⠈⠀⣤⠣⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢱⣼⠸⠀⡇ ⠀⢀⠀⠀⡀⠸⡇⠀⠀⣧⠘⠀⠀⠀⣿⣿⣶⢀⠀⠇⢰⠀⠀⠀⠁⠞⣤⢀⠀⠀⠀⠀⠀⡼⠀⡿⠀⡄⠸⠀⠀⠀⡀⣤⢳⠈⡀⠤⠤⡧⢿⠀⣿⢿⠈⠀⠀⠀⠀⠀⡏⢹⢾⠀⡇ ⠀⠀⠀⠀⠁⢻⣰⠀⠀⡀⣿⠀⠀⠇⣠⣠⠀⠀⠀⡷⠼⠥⡹⣀⣆⠉⠀⠀⠀⠀⠀⠀⠞⣴⣀⡀⣀⣀⢧⠈⠀⠀⠀⠀⠀⢆⠈⠀⠉⡒⣷⢿⣿⣿⢿⠀⠀⠛⠀⠀⣠⠀⠸⠀⡇ ⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⡏⢢⠈⣆⢎⠘⡀⢣⠀⠀⠀⠀⠀⣦⣕⠹⠀⠉⠝⣴⢀⠀⠀⠀⠀⠀⠀⡀⡀⢧⠾⣀⣿⣿⣿⣿⢹⠟⣿⠀⠀⠁⡞⢀⠀⡇ ⠀⠉⠉⠈⠱⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠁⠞⢠⠦⢗⠘⢇⡄⠱⡎⠀⠀⠀⠀⠀⠀⠀⡀⢀⡱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣒⡶⣐⣿⣿⣿⣿⣿⢠⠁⠏⣲⠙⠀⠀⡇ ⡄⣟⣿⣶⣿⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆⡿⢻⠙⠀⠀⠆⡸⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣴⢋⡴⣀⠀⠀⡅⢱⠀⡇ ⠀⠀⡃⢸⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⡿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠄⡤⣤⣤⠂⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣁⣯⣿⣤⢀⠀⣠⠀⡼⣀⣄⠤⡷⠘⡇ ⠀⠀⡝⠉⠈⠀⣦⠻⠀⠀⠀⠀⠃⡴⣀⣀⣂⣗⣿⣿⣿⠘⠁⠀⠀⠛⣉⠋⠒⠓⠶⣩⢚⠄⡠⠀⡿⢈⠀⠁⣍⠫⡨⠃⠴⢁⠀⠋⡿⣿⣿⣿⣿⢿⠻⠛⠈⠀⢻⠀⠀⠀⠀⢀⡇ ⠀⡟⣜⣇⢫⠀⠀⣄⢶⠻⠈⠀⣹⠉⠉⠉⠀⠃⣿⣿⣿⢿⡿⣿⣛⠉⠉⣿⠒⠼⠁⠋⢰⠀⠋⠃⣿⣿⢿⡟⡟⢺⠀⣞⣄⣦⠿⣿⣿⣿⣴⣠⣀⠀⡁⣛⢀⠀⡄⠘⠀⠀⠀⠀⡇ ⠇⣄⢿⡈⣸⢳⠀⠀⠀⡀⣄⠀⠀⠀⠃⡽⣖⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣤⣤⣀⠋⡿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⣿⠯⠀⠁⠉⣬⣿⠀⠁⠀⢧⠀⠀⠀⠀⡇ ⡄⠱⡆⢿⡏⠈⠀⠀⠀⠀⣿⠿⠙⠈⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⢤⠷⠟⣿⣿⣿⢀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣀⣧⣦⣿⠻⡟⣿⣿⡿⢻⡿⠀⡇⠘⠃⠀⠀⡇ ⠀⡀⢄⡗⣹⢠⠀⠀⠀⠀⡀⣿⣿⣤⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠃⡿⣿⣿⣿⢠⠀⠀⣆⣿⢻⣦⣿⡈⣦⣿⣿⢿⠀⠀⢲⡄⣿⢘⢸⣿⣿⣿⣿⠀⡿⢸⡟⠰⠀⡇ ⠀⠂⠙⠈⣄⢳⠈⠃⠿⣿⣿⣿⣿⠂⠑⠈⡏⣿⣴⢀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣠⠀⠀⣇⣰⠀⠀⠀⠉⣯⣿⠁⣇⢸⠀⡆⣿⣿⢟⢤⠣⠛⡀⣿⠃⣿⣿⣿⣾⠇⣿⡎⣇⢀⠀⡇ ⠀⠀⣆⠘⣀⣤⣤⠶⠺⠓⣄⠙⠀⠀⠀⣆⣿⢸⠀⠀⠀⠀⠀⠀⠀⠉⡋⣷⢱⣿⠰⠁⣾⣤⣤⣤⢀⠒⠉⣿⣲⣰⢰⠀⠀⣷⣿⡀⣦⢠⠀⠄⢁⣿⣿⣿⣴⢃⣿⣴⢁⣸⠀⠀⡇ ⠀⠀⠀⡄⠱⠀⠀⠁⠉⠉⠉⡫⢶⠀⠀⠀⠏⡜⣤⠀⠀⠀⠀⠀⡄⠤⠢⡟⡄⣠⠀⡾⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠁⠞⣲⣿⣤⢀⠞⣴⣀⠋⡴⠀⠀⠀⡇ ⠀⠀⠀⠀⠋⣴⣅⣯⣿⣿⣴⢀⠀⠞⢁⡴⢀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠃⣷⠀⠀⡑⢯⠛⠛⠟⡶⣠⠀⠀⠀⠀⡇ ⠀⠀⠀⠏⢻⡿⣿⣷⣴⢀⠁⠋⡿⢴⢀⠀⠀⠀⡀⢦⠑⠈⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠃⡰⠀⠙⠀⠀⣀⣦⣨⢀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠇⣴⣠⣀⠎⣠⠁⠖⣠⡀⠀⠀⠀⠉⠊⠒⠶⡲⠷⣬⠲⠉⠀⠀⠀⠀⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠁⠋⣻⠀⠀⡀⠢⠋⠈⠀⡀⠣⠈⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠁⡔⠀⠞⣠⠀⠀⠀⠀⠆⣳⠉⠀⠀⠀⠀⠁⢸⠀⡀⠳⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠋⠴⣀⠖⢠⠒⠙⠀⠀⠀⣄⠱⠀⠀⢄⠘⠀⠀⠀⠀⡇ ⠁⠈⠀⠃⡰⠋⡰⠀⠀⠀⠁⠚⠤⣀⣀⣀⣀⠀⠀⠃⡰⠁⠊⠔⣡⢾⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠓⠚⠒⡷⣈⠀⠀⠀⠀⠀⠀⠀⣄⠓⠈⠀⠀⢢⠈⠀⡄⠱⠀⠀⠀⡇ ⡄⠸⣀⣄⣎⢀⠀⠀⠋⡤⢀⠀⠀⠀⠀⠀⠂⠒⠄⣤⣀⠀⠀⠊⡤⣤⢤⠤⠒⠒⠒⠹⠀⠀⠀⠀⠀⠀⠀⠆⡽⢤⠀⡄⠢⠓⠉⠀⠀⠀⠀⠀⠀⣄⠓⠉⠀⡄⠳⠈⡀⠳⠉⠉⡇ ⠉⣰⣀⣇⢠⠁⠊⡸⢁⠊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⠒⠒⠒⠁⠉⠉⡄⠹⠀⠀⠀⠀⠀⡀⣀⢤⠦⠒⠐⠁⠉⢄⡀⣍⠦⣖⣤⢒⠐⠄⣧ ⣀⠤⠲⠉⠀⢉⡎⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⢶⠒⠁⠉⠈⠀⡇