⠋⠉⠉⠻⡉⠉⠓⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠉⢹⡾⣻⣩⠷⢦ ⣦⡤⠴⠶⠷⢤⣄⢸⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⡠⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢦⣷⠧⣴⣛⣽⣛⣄⣀ ⠛⠲⣄⠀⠀⠈⡏⠻⣄⡀⠘⢷⡄⠀⠀⢀⣤⣶⠶⠶⠶⢶⣶⣤⣀⡀⠀⠀⣀⣀⣀⣠⣤⣶⣿⣷⣶⣤⣤⣥⣬⣽⡖⠂⠀⠙⣷⡄⠀⠀⠀⠀⢸⡛⠳⢷⣟⣁⢀⣣⡽⠓⠛⠋⢀ ⡴⠞⠛⠛⢦⣼⠃⠀⠹⡜⠀⢸⣧⠀⣠⣿⠏⠀⠀⠀⠀⢀⣠⣬⣿⠿⠟⠛⠛⠛⠛⠉⣁⣀⣀⣀⣀⣀⠀⠉⠙⠛⠻⢷⣦⣄⡘⢿⡆⠀⠀⠀⢘⣷⡚⢉⡀⠙⠓⠋⢀⣀⣤⠖⣋ ⡇⣠⢴⣀⣰⡿⣀⣠⢾⣇⡴⠃⢹⢠⣿⠁⣀⣀⣀⣤⡾⠟⠋⢉⣠⠤⠶⢶⣶⡶⠿⠿⠿⠯⢤⣀⣀⠀⠉⠉⠒⠀⠀⠀⠈⠙⠻⣿⣿⠀⠀⢠⣏⣀⣉⣛⣓⣒⠛⠯⠭⠛⠊⢫⣠ ⢿⡣⣀⡏⠉⠉⠉⣡⡾⡽⠀⠀⣾⣿⠃⠈⣡⣾⠟⠋⢀⣴⠾⠋⢀⣤⢞⡿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠻⠒⢤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢷⣃⣤⣤⣄⣃⣤⢶⡲⠦⣶⣛⣁ ⡏⠙⠳⡿⠤⠴⠾⠿⠏⡀⠤⣾⢻⣿⢠⣾⢟⣵⣿⠎⠁⠀⢀⡴⠯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢹⣆⣀⠤⠤⠤⢾⣥⣄⣷⣀⣀ ⣧⣀⠀⢧⡀⠀⠀⠀⠀⣠⣾⠇⢸⣿⣿⣷⣿⠟⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⢻⠶⠶⡖⠒⢆⣧⡴⢚⣀⡒ ⣿⣷⠭⣭⣽⣦⣤⣴⣿⡟⠁⠀⣼⡟⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⣿⠗⢻⡀⢸⡏⡼⡥⠲⠨ ⣿⢹⣹⣟⡓⠒⠒⠂⠉⡇⠀⣼⡟⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡸⣟⠂⣇⣸⡿⣷⢳⡒⡪ ⡏⠙⣿⡀⠙⢧⡄⠀⣰⠃⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⣹⠱⣄⢀⠱⣦⡈⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣧⢿⣍⣁⣁⣹⣮⣓⣋⣒ ⠁⢠⡿⣆⠀⠀⠙⣿⠉⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡿⠀⢀⣴⣿⣧⠙⢄⠀⠙⣯⢦⡀⠈⢿⣦⡀⠀⠀⢰⡞⠳⠟⢻⡄⠀⠀⠀⣿⡌⠧⢤⣤⣤⡤⠶⠶⠟ ⠀⢸⠁⡇⠀⣠⣀⣸⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣾⠃⠀⣪⡾⠁⠈⠳⣦⣑⠂⠈⠳⣭⡒⠈⠳⣽⠢⣀⠘⢷⣄⣠⡾⣇⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠛⠚⠋⠀⠀⠀⣿⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⢁⡾⠀⣴⢏⣠⡾⠋⠀⠀⠀⠀⠀⠉⠛⠛⠳⠿⠛⠛⠷⠿⠿⢦⣍⣀⠈⠙⡆⣿⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠀⡔⠀⠀⠀⠀⢀⣾⣵⠾⠛⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⢹⡏⢿⠻⠿⢿⣄⠀⢦⢧⠈⢿⣆⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⡆⣇⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⡄⠀⠀⠀⡇⢸⣠⣤⣬⢻⡇⠈⣻⣷⡀⢻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢀⣿⣿⠶⢾⠋⡏⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⣠⡄⠀⢱⣾⡏⢈⡆⣸⡇⠀⠙⣿⣿⣆⢹⣧⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⣾⠏⣀⣀⢸⡄⡇⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⡤⠒⠒⢲⡀⠀⠀⠀⠀⠘⠛⠛⠁⠀⣿⠃⠛⢛⣴⡿⢡⠃⠀⠸⣿⣷⡈⣿⣹⠂⠀⢠ ⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⢀⡀⢀⠀⣿⡀⢹⡋⢻⢷⣿⠀⠀⠀⣀⠼⠛⠛⠋⠀⠀⠀⠘⣤⠚⣉⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⢿⠿⢋⡴⠃⠀⠀⠀⣿⣿⣇⣿⣿⡴⡞⠋ ⠀⠀⠀⣴⡟⠁⢀⡴⠶⣤⣼⡁⠘⣆⠙⣿⣌⡳⠞⠀⠻⡄⠀⠐⠛⠘⠛⠀⠀⠀⠀⠀⠀⠙⣲⢿⠖⢢⠙⣧⣀⡀⢀⣴⠶⠛⢶⡾⠃⡾⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡇⢰⠀⢠ ⠀⠀⣸⡟⠀⠀⡸⢷⡀⢀⣠⠇⠀⠈⠀⠀⠙⠻⡿⠾⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠉⠉⠁⠁⠉⠉⠛⠓⠿⣍⡇⣷⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠱⡀⡆⣯ ⠀⢀⣿⡇⢠⢎⣴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⢄⢹⡿⢷⣦⣤⣀⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡀⠘⣄⠀⠀⠀⠀⠀⢀⣿⡋⠸⣵⣀⣱⡼⠗ ⠾⢯⣽⣧⠁⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣾⠃⠀⠀⠉⢙⣻⣿⣿⡟⠛⣏⠀⢀⣀⣰⣿⠇⣠⣤⠀⣤⣄⠀⠀⠀⠘⡇⠀⣽⠗⠞⠛⣷⠀⣸⣟⣘⣠⡟⠋⢻⣧⣀ ⠀⠀⠈⣿⣴⡿⢻⣧⢄⠀⠀⠀⠀⠀⠀⠀⣴⠋⣀⡴⠞⠁⢠⣾⠿⢿⡛⠉⠹⣏⡁⠀⢻⣶⡯⣽⣯⣿⡍⣾⣿⣤⡿⠷⣤⡀⠀⢰⡇⠀⠹⣦⣀⣰⠟⠀⣿⣿⠉⢉⣧⣦⣞⠉⠉ ⢀⣰⣶⡿⠿⣅⠈⣿⡌⠄⠀⠀⠀⠀⠀⣼⠷⠾⠏⢻⠀⢀⣼⡷⣤⠈⢷⣤⠀⠈⠳⣦⣼⡇⢘⠓⢺⠉⣿⠀⣼⢻⡽⢿⣾⣷⣠⡿⣷⡀⣰⠃⠈⠁⠀⣼⣿⣿⣦⡴⣻⡼⡓⠤⡴ ⡎⣿⠿⣿⠿⢿⢳⡈⣿⡄⠀⠀⠀⠀⣸⠿⢿⣶⣴⡟⣰⣿⡃⠀⢙⣷⣮⣻⣦⣤⣾⠟⠛⠿⠿⠿⣷⣄⠿⠴⣿⡟⠛⠿⣷⣿⠁⡀⠘⢿⣧⡀⠀⠀⢰⠏⢿⣿⠹⣦⣠⣧⣀⡴⢟ ⣶⣿⣾⢇⡿⡟⢸⡟⣿⣧⠀⠀⠀⠀⣿⠀⠀⠀⢰⢀⣾⠏⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠠⠤⠚⣿⡄⢰⣿⣉⣩⠀⠈⠻⡟⠛⠒⠦⠝⣷⡄⠀⣿⠀⠈⢿⣇⠸⣄⣽⣫⠞⠁ ⢻⣝⡛⠒⢷⡧⠎⠉⢹⣿⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⣈⣩⣿⠀⠈⣿⡤⠒⠀⠀⠀⠘⠀⠀⠀⠀⠘⣿⡀⢻⠀⠀⠀⢻⣷⢟⣾⣡⣤⠤ ⠀⢡⣟⣏⣟⠽⢾⢦⣼⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢷⣶⣤⣶⣶⣾⠏⠀⠀⢈⣿⡾⣿⣥⣀⣄⠀⠀⠀⠀⢠⣿⠃⠈⠀⠀⠀⠈⣿⣟⣉⣀⡀⠀ ⠀⢸⡤⠒⠻⡍⢺⣷⡟⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠙⣿⣶⣤⣤⣴⣾⣿⠟⠳⢦⣤⣇⠀⠀⠈⢻⡦⣀⠀⢷⡟⠁⠀⠉⡿⢿⣿⠿⠶⠾⢟⡇⠀⠈⣆⡀⠀⠀⣿⢧⣄⡀⠈⣹ ⢶⣼⣿⢾⣶⣷⠿⠋⠀⠀⠀⣀⢀⡿⠁⠀⠀⠀⠀⠀⢀⡟⠀⢀⣼⠟⠉⢷⣄⡀⠀⢰⡿⠀⠀⠀⠀⣉⣉⡉⠁⠀⠀⠀⣼⠇⠈⠻⣷⡀⠀⠋⠀⠀⠀⢹⡘⠀⢸⣿⣄⡸⣿⠟⠋ ⣿⡾⣿⡐⠢⠄⠀⠀⠀⠀⣨⣴⠟⠁⠀⠀⣠⢤⣄⣠⠞⠀⣠⣾⠃⠀⠀⠀⠉⣻⢷⣾⡇⠀⠀⠀⠘⣽⢿⡙⠀⠀⠀⠀⣽⣦⠀⠀⠹⣿⡄⢀⠀⠀⢀⣿⣇⣠⣿⢻⣿⢀⣻⡀⠀ ⡛⢛⣿⡿⣶⣤⣤⣤⣶⣿⠟⠁⠀⠀⣠⠖⣇⡆⠙⢉⡇⣰⡿⠃⠀⠀⠀⢀⡼⢁⡜⠉⢷⣼⣰⣀⣼⠋⠀⣷⣀⠀⢀⣠⡿⠘⢧⠀⠀⠈⢿⣎⠂⣀⣾⣿⣷⣿⡇⢺⣇⠀⣸