⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠏⢄⠀⠀⠀⠀⠀⡰⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡡⠂⡆⠀⠈⠢⡀⡠⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀⠀⠀⠀ ⠀⠀⢀⠞⠀⠀⢠⠀⡠⠂⢉⠝⠛⠓⠢⣄⡀⠤⠤⠀⠀⠄⠀⡤⡢⢀⠬⠆⠀⠀ ⠀⢀⡀⠤⠄⠒⢒⡯⠄⠀⡇⠀⢠⠊⠉⢊⢣⠀⠀⢀⠔⠁⢸⢠⠁⠆⡜⠀⢀⠀ ⠀⠀⠑⢄⠀⠀⠘⢨⠧⠤⡘⢄⣘⠔⠶⣡⠄⢱⢴⠓⢄⠀⢘⢊⡘⡴⢀⠠⡀⠀ ⠀⠀⠀⠀⠈⠐⣰⢢⣀⡀⠼⢀⣀⡼⠊⡝⠀⣈⠢⡙⡤⢇⠌⠈⠒⢇⣩⡊⠀⢀ ⠀⠀⠀⠀⢀⠜⠈⡃⠀⠴⢖⣂⡁⠤⠮⠤⢔⠏⠀⠈⠳⡌⠀⠀⠀⠀⡱⠃⠃⠈ ⠀⠀⠀⢀⠊⠀⡠⣈⠰⡤⠤⠀⠠⡤⣴⣮⣥⣠⣄⣉⠁⠈⣖⣠⣠⣚⣄⣀⣀⠀ ⠀⠀⠀⠈⠀⠘⡀⢣⡀⢃⠀⠀⣰⣿⣿⡿⣿⠯⡟⠣⡑⡀⠹⠿⣠⣼⣿⠛⡿⠇ ⢰⣊⡁⣒⣢⠠⡈⠹⠬⠽⣄⡼⢝⠛⢿⠉⢫⡆⠀⠀⠘⡌⢂⡆⠀⠘⣿⣧⠀⠀ ⡤⠐⢢⠀⡄⠛⠅⠀⠀⠀⢹⡁⢹⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠁⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⣀⠤⣊⡥⡀⢀⣠⣼⣧⡘⣄⠀⠀⠀⡠⠒⠈⠀⢺⠈⠲⡀⠀⡸⠀⠀⠀ ⠀⠰⠭⠜⡈⢠⢳⣭⣿⣧⣾⠃⠑⡄⠑⠠⠎⠀⠀⠀⠀⠘⠀⠂⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠃⡾⡿⣿⣇⢡⠀⠀⢰⣴⣯⣼⣦⣀⣀⣤⣾⣿⣿⡦⣀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠊⢁⠀⡇⠀⠈⠑⠦⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢃⠀⠀⠀⠀⠈⠲⣄⣀⡞⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠸⡀⠀⠀⢀⡤⠒⠋⢉⡩⠭⠿⠶⢤⣀⢸⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣠⢤⡙⠂⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢧⢀⡔⠁⠀⠀⡴⠋⠀⠀⠀⢀⣀⣈⠳⣶⠒⠉⠉⠉⠁⠀⠀⠈⡹⠃⠀⡞⠁⡼⠁⢠⠎⢹⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠂⢹⣯⣤⡀⠀⠀⡇⠀⠀⠀⡼⠉⠀⠈⢳⣈⣣⡀⠀⠀⠀⠀⣠⠞⠁⠀⢈⠷⢴⠁⢀⣇⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠘⢯⡀⠀⠀⠀⠀⠀⠀⡟⠡⣴⠃⠀⠀⢳⡀⠀⠸⡇⠀⣀⢀⡼⠃⠈⠑⡄⠀⢀⡞⠁⠀⠀⠀⢸⡀⡆⠀⡼⠀⡏⠀⠀⠀⠐⠀⠀ ⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⢸⠁⢠⠟⠛⠓⠦⡀⠱⢤⣀⡽⠞⡿⠻⣥⣶⠆⠀⣷⠴⢏⡉⠑⢦⠀⠀⢸⠉⢇⡰⠙⡾⠀⣀⠔⢃⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣸⣦⣮⠀⠀⠀⠀⢘⡄⣀⠀⠀⣰⣡⠞⢹⠇⠀⠀⡟⠦⡀⠙⣆⣀⣇⠀⡜⠒⠛⠧⠴⡷⠊⢙⡖⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣇⡼⠗⠒⠲⠈⠉⠀⢃⣴⠾⠋⠁⣠⠏⠀⠀⣰⣷⠀⠈⠢⣘⡅⢈⡟⠁⠀⠀⠀⠀⠙⢲⠟⡤⠀⡄⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⠀⠀⠀⣴⣶⣖⡊⠉⢀⣀⡠⠾⠥⣄⡤⠞⡽⠃⠀⠀⠀⠈⢣⣸⠀⠀⠀⠀⠀⠀⠀⢈⡷⠉⠀⠃⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠳⢄⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⠴⠮⢤⡤⠤⠤⠤⠔⠚⠙⢄⣀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡴⢦⣀⡤⠞⡟⠒⠒⠠⠤⠄⠒⡖⣻⣿⣷⣿⣿⣯⣻⣦⣤⡤⣄⠀⠀⠸⣿⣍⣳⣶⣾⣭⣷⣤⣤⣤⣀⠠⠀ ⠀⠀⠀⠀⠀⠀⠓⠒⠒⢺⡀⠸⣄⠀⠀⢧⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⡏⣿⠟⢧⠈⢦⠀⠀⢻⣷⣾⢁⣀⣽⣿⡿⠿⣿⣿⣷⠀ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠳⣄⣨⠗⢄⡘⡄⠀⠀⢠⣾⣏⣿⣿⣿⡿⣻⣷⡉⠙⠛⠀⠀⠳⡄⠳⡀⠈⡏⠉⠺⠿⢿⣿⣿⣄⠘⠟⠈⠀ ⠀⡞⠉⠀⢘⣏⠓⢲⠦⢤⣀⣈⣹⡤⠤⣙⣿⣀⣴⣿⢍⡛⠛⢿⣷⠃⠈⢹⣶⡄⠀⠀⠀⠀⠙⡄⠙⢄⣹⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀ ⠀⠉⠉⡉⠁⠈⠉⠙⠲⣤⠏⠀⠀⠀⠀⠀⠈⢿⡞⠓⠢⡇⠀⠀⠙⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢹⡀⠀⠹⡄⠀⠀⠀⠘⡇⠙⠃⠀⠀⠀ ⢴⡊⠉⢉⣿⣉⣙⣏⣉⣈⠇⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠀⠀⠀⢀⡴⠛⢳⡀⠀⠀⠀⠀⢀⣸⢿⡆⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⢤⠇⠙⢦⣧⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠤⡞⢉⡦⠖⣟⢳⣄⣠⣤⡶⠛⢿⣿⡿⣆⢸⠳⣄⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠧⣄⣀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠺⣇⡀⠤⠋⠁⠀⢠⣋⣏⣴⣿⣿⣷⣤⢿⡿⠀⠈⢻⡀⠀⠑⠲⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠔⠋⢠⠇⣸⣿⣿⣿⣿⡇⠉⣏⠀⠀⠀⠀⢣⠀⣀⣤⣤⣹⡄⠀⠀⠀⠀⠀⠀⢀⣾⣶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⡿⢿⡿⣿⣿⣿⡄⠘⡄⠀⠀⠀⠈⣿⣻⣵⣿⣿⣿⣶⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣟⠦⢤⣤⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣆⢠⣞⣀⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡙⠓⠲⠤⣄⣀⡀⠀⢿⣀⣴⡶⠟⠛⠉⠉⠉⠉⠝⠻⢦⡀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢩⣶⣿⠟⠁⠀⠀⠀⢀⡴⠚⠉⠓⠒⠒⢯⣷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣴⣿⣯⡥⢶⡄⠀⠀⣴⠏⠀⠀⢀⣴⠟⠉⠙⣿⠿⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡿⡟⠁⢀⣠⠇⠀⢸⠁⠀⠀⠀⢸⣿⣦⣤⢼⠇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⣤⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⡇⣇⡴⠚⠲⣶⡄⠈⢣⣀⠀⣀⠀⢼⡋⠁⣼⣠⣤⣾⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⢰⠇⡿⠀⢠⠶⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⣿⡏⠹⣇⣀⣀⣹⡇⠀⢀⣨⡍⠉⠛⠁⠀⣴⣿⠟⢹⠈⠀⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡾⢶⠇⢠⠏⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣀⠀⠀⢹⡿⠋⠉⠙⢦⡀⠀⠰⢯⡀⢸⢀⣠⣴⣾⠟⠁⠀⣸⠀⠀⣸⡶⠖⢶⣦⡀⠀⠀⠀⠀⣾⢀⡇⣸⢁⡞⢠⠏⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠊⣧⡀⠀⠀⣸⣇⣀⣀⣀⣩⡯⠽⠓⠋⠀⠀⠀⣰⠏⠀⣠⣿⠃⠀⢸⡈⢧⠀⠀⠀⢠⡏⣹⣡⠃⣼⣵⠋⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡞⠋⠁⠉⢀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣞⣁⣠⠴⣻⠏⠀⠀⠈⣧⠸⡄⠀⢀⣿⣠⣿⢃⣼⡿⢁⡾⠁⣠⠴⢀⡀ ⠀⠀⠀⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⠈⠻⣆⡀⠀⠀⠋⠹⠶⠶⠶⠝⠛⠉⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠸⡆⢹⣴⠏⠀⠈⠓⢾⣁⣴⣯⠖⢋⣡⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡈⢷⡀⠀⠀⠀⠀⢀⡞⢸⡀⣇⣀⣼⣿⣦⣄⣈⠃⠀⣀⣤⠘⠃⣀⣤⡴⣿⣿⣤⣄⣀⡀⢤⠀⠀⢻⡛⠁⠀⠀⠀⠀⠀⠉⣻⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⣤⢤⡀⠀⠈⢷⡈⠳⣄⠀⠀⢠⡟⣀⡼⡇⢸⡙⠿⣿⣿⠈⠙⠛⠛⣿⣿⠟⠋⠉⠀⠀⠀⠙⢿⣿⣿⣿⡿⢷⠀⠈⢷⡄⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠳⣄⡉⠲⣄⠀⠹⣦⡈⠳⣄⡘⠉⠁⠀⢻⠀⢧⠀⠘⢻⠀⠀⢀⣾⣿⠇⠀⠀⢀⣠⣀⠀⠀⠀⠘⢿⡄⠀⠘⣧⠀⣸⣿⣶⣤⣴⣾⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⢠⡈⠙⠶⣄⣈⠙⠺⡿⣶⣬⣍⣹⠋⠓⠾⣧⣸⣄⠀⢸⠀⢠⣿⣿⠁⠀⠀⠀⢻⣶⣼⠀⠀⠀⠀⠈⣷⠀⠀⢹⣷⣾⣿⣿⣿⣿⣷⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠶⢤⣀⣶⠒⠚⠛⢛⡶⠶⠶⢤⣼⠃⠀⠀⠀⠀⠀⢹⣠⣿⣰⣿⡿⣿⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢿⡇⠀⢸⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠈⠙⠈⠉⠿⠿⠷⠾⠶⠦⠤⢤⠏⠀⠀⠀⠀⠀⠀⢸⣿⡟⣛⣯⣄⣹⣷⡀⠀⠀⠀⠀⢿⣟⡿⠀⡀⠀⢸⣿⠀⠀⢹⣧⡏⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠐⠠⠤⠤⢤⠤⠤⠤⠤⢾⣄⣄⠀⠀⠀⣀⣴⣿⣿⣿⣿⣉⣹⡟⢿⡗⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⠀⠘⣿⡇⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢚⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢺⣇⠀⠀⠀⠀⠀⠀⠀⠘⠃⣠⣾⣿⣷⡀⠀⢻⡇⠀⠈⣿⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⣹⣿⣿⠀⢻⡟⣦⡀⡋⠻⣦⡀⠀⠀⠀⠀⠀⠖⠋⠁⢸⣿⢻⣧⠀⠈⣇⠀⠀⠸⡆⠈⢿⡿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⣿⣿⣇⠀⢻⣿⣿⡇⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠻⣆⠀⢹⡀⠀⠀⣧⠀⠈⠃⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⢻⣿⣷⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠹⡄⠀⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⢿⡿⠧⠤⠤⠤⠌⢻⣷⣤⡤⠴⠶⣾⡶⣿⣷⠀⣹⡦⠼⠦⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⠀⠀⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⣿⣿⣻⡶⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣴⠟⠋⠁⠀⢄⣡⠀⠀⠀⠀⠉⠓⠯⣿⣦⣄⣸⣀⣀⣀⣀⣤⣤⣤⣤⡴⠶⠶⠶⢶⡦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⠴⠦⠀⠒⠒⠒⠠⠤⣀⡉⠻⡛⠻⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣼⣿⠏⢀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠈⢦⡈⢆⠀⠀⠀⠀⠀⢀⣀⣠⠋⠀⠀⠀⠀⠀ ⠠⡀⠈⠉⠉⠉⠉⠉⠁⣠⡾⠃⠀⠈⠆⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣠⠖⠒⠦⣤⣲⠄⠠⢷⣼⣦⠀⡆⠉⢩⠏⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⡀⠀⠀⠀⠀⢸⣿⠃⢀⠖⢦⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡝⢐⢶⡖⢿⣿⣦⢹⣤⢫⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⣶⡊⠉⢹⠇⢀⡎⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣼⡇⠀⢸⢷⣄⣹⡟⠺⡷⠥⣄⣀⣀⣀⡀⠄⠀⠀⢀ ⠀⣀⠀⠀⠀⠙⢿⣦⣼⠀⢸⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⡿⠋⢳⡘⠺⠦⠇⣹⢳⡦⠤⠤⣽⣄⣀⣀⣠⢴⡆⠀⢲ ⣤⣿⠀⠀⠀⠀⠀⠙⣿⠀⢸⠀⠀⢀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⣹⠟⢿⠀⢀⡜⠛⡦⠤⠞⢹⢸⠛⠀⠀⠀⠈⠙⠢⢤⡼⠀⣼⠀ ⠉⠁⠀⠀⠀⠀⢀⡼⠁⡇⢸⠀⢰⠃⠀⠉⠲⣄⠈⠢⣀⠀⠀⣀⠴⠺⠃⠀⡼⣠⣟⠀⠀⡇⠀⠀⡜⢸⠈⠳⡄⠀⠀⠀⠀⣠⠃⢠⣟⠀ ⢀⡠⠀⠀⠀⠀⡼⠁⠀⠰⠀⠁⢸⡀⠀⠀⠀⠈⠳⣄⠈⠉⠉⠀⠀⠀⠀⣼⠟⠁⠈⠑⢺⠇⠀⣠⢃⡇⠀⠀⣈⣤⣶⣶⣾⠛⠺⣿⣏⢀ ⠀⠀⠀⠀⢀⡞⠀⠀⢀⡠⢣⡄⠈⠛⢧⡤⠄⠀⠤⠽⠂⠀⠀⠀⢀⣠⠞⠑⣄⠀⠀⢀⡎⣠⢶⣿⣏⣀⣾⣿⣿⡿⣿⣿⣿⣀⠀⠙⣏⠀ ⠀⠀⠀⢠⡿⠀⠀⠐⠿⣀⢰⡇⠀⠀⠀⠱⣄⠀⠀⠀⢀⣀⡤⠖⠹⡄⠀⠀⠈⠓⢤⡜⠋⣠⢻⣿⣿⡏⣩⣭⠿⣿⣿⣿⡽⡿⣧⡀⠹⡆ ⠀⠀⠀⠙⠛⠓⠒⠒⠲⠾⠿⣿⢢⣠⠀⠀⠘⡟⠿⣍⠁⠀⢣⡀⠀⠈⢢⡀⠀⣠⠞⣀⣾⣿⣿⣿⣿⣿⣵⡆⣦⡿⢿⣿⠿⠗⠈⢷⠐⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡷⢤⡤⠴⣁⡀⠀⠉⠑⠒⠓⠦⠤⠔⢛⣫⣥⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢉⠇⢸⡆⠀⠈⠉⡍⠓⠒⠒⣲⢶⣿⣿⢟⣿⣿⣿⣿⣿⢿⡟⠉⢉⣀⣄⡈⠉⠛⠃⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡞⠀⠀⡇⠀⠀⠀⢹⠀⣴⠟⠁⢸⣿⣍⠿⣿⣿⣿⣿⣿⡾⠀⠀⣿⣿⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡎⠀⠀⠀⢹⡀⠀⢀⡼⠋⠀⠀⠀⠈⣿⣿⣿⣾⣿⡿⢣⣼⠁⠀⠀⠈⠛⠛⢹⣾⣿⣦⠀⠀⠀⠀⢀⠀⠊ ⠀⠀⠀⠀⠀⠀⢠⡞⠀⣠⠊⣀⡠⣤⡀⠘⣧⠔⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣿⣀⠀⠈⣙⣶⣤⡀⠀⠀⠘⠿⡿⠟⠀⢀⡄⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⣠⣞⣤⡼⠓⢉⣀⠤⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠉⠛⠛⠉⢹⠋⠙⡳⣦⣀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡀⠤⢀⠘⣠⠤⠖⠓⠢⢅⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢄⢠⡿⢥⠀⡔⠁⣠⠛⡿⢶⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⣿⡤⢪⡌⢄⣀⡹⢋⣡⠼⡇⡀⠀⠀⠀⢰⢠⠙⠠⡄ ⠀⠀⠀⠀⠘⠡⠄⣀⡗⠓⢌⠁⢎⣂⡤⠞⢁⠀⡧⢠⡄⠀⢸⡀⢌⠣⡳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡹⣖⠙⢀⡉⢁⣠⠤⠪⣼⠃⠈⡴⢀⠮⣟⠞⣕⡡⡠ ⠀⠀⠀⢫⢢⠀⠀⡜⡗⣨⣷⠤⣀⣤⣂⠤⠾⣥⣄⣄⢱⠋⠀⠈⣹⠕⠈⠀ ⠀⠘⢕⡄⢑⣕⠤⡈⣡⢃⠙⠀⣰⠏⠀⣤⠀⠈⢏⠘⣄⣷⣤⣾⡅⠀⠀⠀ ⡄⠢⠤⣘⣳⣒⡻⠁⠀⠈⣼⣼⢻⡀⠀⢩⣤⠀⢸⡄⢿⡿⣿⣯⡀⠀⠀⠀ ⠀⠀⠐⠒⠒⠒⠢⠄⣠⣴⣿⡯⠟⡗⠀⠀⠁⠀⢠⣇⠘⡇⢹⢿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠫⢽⣇⠩⣦⠙⢦⠀⠀⠈⠁⡟⡄⢃⠀⡄⠛⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢻⣇⣀⠳⣄⣀⣠⣼⡘⡌⠄⣁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠶⠖⠲⠶⠶⠦⢤⣶⠿⠞⠛⠋⠉⠛⠛⠶⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡾⢋⣀⡀⠀⠀⠀⣠⠶⠋⠉⠉⠛⣯⡙⠒⠒⠶⠶⢤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣰⠋⡼⠁⡀⢹⠀⢠⠞⠁⡤⠶⢤⡀⠀⠈⢳⡀⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣆⣴⠃⠀⡇⠀⠛⠋⢀⠏⠀⠸⣅⣄⠀⢳⡀⠀⠈⣷⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡀⣼⠓⢦⠀⠀⡾⠀⠀⠀⠉⠁⠀⠈⡇⠀⠀⠸⡆⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠖⠋⠁⡾⠀⠹⣧⠀⠈⡇⢀⡇⠀⠀⢠⡴⠶⢤⡀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢻⣄⡀⠀⠀⣇⠀⠀⢿⡦⣤⡇⠈⣧⠀⠀⡏⠀⠀⠀⠸⣆⣀⣀⣀⡇⠙⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠒⠤⠽⣦⣄⣾⣿⣄⡻⣆⠘⢦⡀⠷⣄⣀⣠⡼⠋⠁⠀⠙⡇⠀⠀⠈⠛⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢫⣙⣞⣮⠙⠺⢯⠽⠧⠤⠞⡟⢹⠃⠀⠀⠀⢀⡇⠀⠀⣀⣠⠴⠛⠀ ⠀⣠⣶⡋⠉⠓⢒⣿⠋⣰⣿⣿⣿⢳⣷⣄⢘⡆⠀⠀⢀⣴⣿⣧⣤⣤⣴⣯⣶⠚⠉⠉⠀⠀⠀⠀ ⠀⣧⡈⢷⡄⠀⠈⠙⢳⣿⣽⣿⣿⣿⣷⢿⣿⣿⢶⣾⡛⠉⠁⠀⠀⣸⡇⠀⠉⠉⠙⠉⠉⢳⢦⡀ ⠀⠘⢷⣄⡹⣦⠀⣀⣾⣿⣟⣿⣿⣿⣿⣸⠋⣿⣾⣿⣿⣶⣤⣀⣰⡿⢥⣀⡀⠀⠀⠀⣠⠟⠀⣿ ⠀⠀⠀⠙⠲⠼⠿⠟⠁⣴⡿⢹⣿⠃⣿⡟⢰⣿⣿⠹⣿⣿⡟⢻⣿⡅⠀⠈⡟⠀⠀⣰⠃⢀⣼⡿ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⣿⠃⣼⣿⠃⣾⠈⣿⠀⣿⠛⣧⠈⣿⣿⣆⠀⠻⣤⡞⠁⣠⣿⠟⠁ ⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⣿⠋⣼⣿⡏⢀⡏⡄⣿⠀⣿⠀⠸⣇⠘⣿⣞⣦⠀⠀⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠟⣠⣾⣿⠃⣰⣿⣿⠃⢸⠀⡇⣿⠁⣿⡀⠀⢹⡆⠹⣿⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢻⡄⣿⣿⡏⢠⣿⣿⡿⢀⡟⠀⡇⣿⡆⢹⡇⠀⠈⢿⠀⢿⡇⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⡀⠀⠻⣿⣿⡄⠸⣿⡿⠁⣼⠃⠀⣧⣿⡇⢸⣷⣤⣴⣾⠀⣼⣇⡼⠁⠀⠀⠀⠀⠀⠀ ⢲⢿⡟⣵⣹⣷⣶⣾⣿⣿⣷⣿⣶⡞⠁⠀⠀⠈⠻⣿⣄⡙⢿⣿⣇⣴⣿⣯⣤⠀⢀⣤⣦⡀⠀⠀ ⡟⠘⢷⣈⣹⣿⣿⠟⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠈⠉⣻⣾⣿⣿⣿⡿⣿⡿⠛⢿⣿⣽⣷⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⣻⠟⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⡏⠀⠀⠙⠒⠾⠛⠃⠈⣧⠀ ⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄ ⠀⠙⠷⢤⣀⡀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁ ⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣤⣤⣤⠤⠴⠚⠋⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⣄⠀⠀⠀⠀⣠⡾⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⣄⢀⡼⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣤⠶⠖⠛⠛⢲⡶⣤⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠤⠤⠤⠤⠤⢤⣿⠞⠉⠀⠀⠀⠀⢀⡟⠀⠀⠈⠻⣾⡤⠤⠤⠤⠤⠤⢤⣄ ⠘⣦⡀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣠⣤⣌⢻⡄⠀⠀⠀⠀⣰⠏ ⠀⠈⠳⣄⠀⠀⡾⠀⠀⣠⡴⠶⢤⡀⠀⡟⠀⢠⡟⠁⠀⠈⢷⢿⡄⠀⣠⠞⠁⠀ ⠀⠀⠀⠈⠳⣼⡇⠀⢰⡇⠀⠀⠀⢻⠀⣧⣀⣸⣧⡄⠀⢀⡼⢸⣧⠞⠁⠀⠀⠀ ⠀⠀⠀⢀⣴⢻⡇⠀⠘⢧⡀⠀⣠⡞⠀⠈⠉⠁⣸⠛⠚⠋⠁⢸⡟⢦⡀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⢷⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⠃⠀⠙⢦⡀⠀ ⢠⠟⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆ ⠘⠓⠒⠶⠶⠶⠒⠚⠻⣦⡀⠀⠀⠀⠰⣦⣷⠏⠀⢀⣤⠞⠓⠒⠶⠶⠶⠖⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣤⣤⠧⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠈⠙⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣦⣿⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠟⠛⠛⠛⠛⠛⢻⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠉⠙⠻⣿⣷⣤⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀ ⢰⣿⡟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⣿⡇ ⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁ ⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢀⣴⣿⠿⠟⠛⠿⣿⣶⣌⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀ ⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠹⣿⣧⢿⣿⡄⠀⠀⠀⠀⠀⣤⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢰⣿⠏⠀⠀⠀⠀⢠⣾⡿⠟⠋⠉⠉⠛⢿⣷⡄⠀⠀⣿⡟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⣿⣧⠀⠀⠀⣴⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣸⣿⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣿⡇⠀⠀⠀⠀⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢻⣿⠀⣠⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣿⣦⣤⣤⣶⣿⡿⢿⣿⠄⠀⠀⠀⢀⣴⣿⠏⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠉⠉⠋⠉⠉⠁⠀⣼⣿⣿⣶⣶⣾⡿⠟⠁⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⢹⣿⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⢀⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣾⡿⠋⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀ ⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀ ⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀ ⠸⣿⣧⣀⣀⣀⣀⡀⣀⡀⠀⢀⢀⣀⣀⣀⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⢠⣶⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣁⣀⣀⡀⡀⠀⠀⣀⢀⢀⣀⣀⣀⣤⣿⡇ ⠀⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣼⣿⣿⡿⠁⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⠋⠀⠀⢀⣀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣦⣤⣤⣤⣤⣄⣼⣿⣴⣶⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠰⣶⣤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠛⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢶⣤⣀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣿⠥⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⣦⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⣚⠭⢭⠭⠭⠭⠭⣝⣻⡿⢶⣄⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣾⠿⠚⠉⠀⠀⢄⡘⡄⠀⠀⠀⠀⠀⠉⠛⠪⢝⡻⣶⣄⣀⡇⠀⣀⣀⣀⣀⣀⣠⠤⠤⣤⣤⣤⣤⣖⣲⠾⢷⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣔⡿⠋⠁⠀⠀⠀⢀⠀⠀⢙⣃⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠻⢝⡻⠿⣟⠛⠛⠛⠓⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠉⠁⠀⠀⠀⠀⠉⠉⠓⠒⠤⣄⠙⢦⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣴⣶⢾⣿⡟⠁⢆⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡄⠘⣆⠀⠀⠀⣀⣀⣀⣀⣀⠤⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠠⣀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣾⠏⠀⠀⠈⢧⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠶⢦⣄⡒⣶⠀⠠⢽⣌⢞⢇⠀⢰⠀⠀⠀⡿⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠏⠀⢀⡤⣀⠈⠁⠀⠀⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢹⡏⠠⣄⡤⣝⢿⣞⣆⠘⣆⢀⡾⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠀⣀⣠⣤⠤⣿⡟⠀⢀⡞⠠⠜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⢀⡼⠀⡇⢈⣧⡈⠛⢿⣿⡆⢿⢋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢯⡿⣄⠀⠀⣿⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⠀⠀⠀⢠⣾⣧⠀⡇⢸⡹⣿⢦⣜⡏⠉⠺⠞⠒⢲⣤⠤⠤⠤⠤⠔⠒⠂⡁⠀⠦ ⠀⢀⡀⠀⠀⠀⠀⠹⣿⢳⣄⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢀⣀⣼⡿⠋⢸⣧⠘⠺⠧⠼⠀⣻⠟⣷⠦⠤⣄⣨⣧⣀⣀⣀⣀⣠⣶⡞⠀⠀⢾ ⣀⣸⣷⠀⠀⠀⠀⠀⠈⠳⢮⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠿⡏⠀⠀⢠⡿⢷⣄⣀⣀⡴⢹⠀⡏⡆⠀⠀⠀⠈⠙⠳⢤⣀⠀⣸⠁⢀⣾⠀ ⠿⠿⠏⠀⠀⠀⠀⠀⠀⢀⡾⢻⠀⢸⠀⠀⢀⡔⠂⠢⣄⡀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⡇⠀⣴⠟⠀⠀⡏⠉⠁⠀⢸⢸⡇⢤⡀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⣸⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠘⡆⠈⣇⠀⣿⠀⠀⠀⠀⠉⢲⣄⠀⠙⢦⣀⣀⣠⡤⠚⠋⠋⠀⠀⣰⣣⡾⢧⡀⠀⢠⡇⠀⠀⠀⡎⢸⠃⠀⠙⢦⡀⠀⠀⠀⠀⣠⣾⠁⢠⣷⡇⠀ ⢀⣠⠆⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻⡀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠈⠙⢾⠁⠀⠀⣼⢃⡟⠀⠀⠀⢀⣩⡴⣿⣿⣾⡿⠙⠻⣯⣾⢄⢀ ⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⣀⢧⠀⡄⠛⠷⣶⣀⣀⠀⠀⠀⢀⣻⡆⠀⠀⠀⠀⠀⠀⢀⠴⠃⣄⠀⠀⠀⠀⢀⡏⠀⣠⣾⣧⡾⠁⠰⣶⣾⢿⣟⣿⣷⣿⣿⡇⠀⠀⠙⣾⡉⠀ ⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⣠⡞⠁⢈⣿⠀⠀⠀⠈⠿⡄⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡠⡞⠃⠀⠀⠈⠳⣄⠀⢀⣾⠴⠋⣱⣿⣿⣷⣿⠯⠵⠿⢿⣿⣼⣿⣿⡻⣿⣷⡀⠀⠸⣧⠀ ⠀⠀⠀⠀⣰⡿⣅⠀⠀⠈⠙⠳⢄⣈⣿⡀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣠⠤⢶⠚⠉⠀⠻⣄⠀⠀⠀⠀⠈⠓⡾⠀⢀⣼⢁⣿⣿⣿⣇⣰⡶⡶⠛⢻⣿⣿⣿⠇⣹⡛⣿⣄⠀⠙⢇ ⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠒⠒⠒⠛⢻⡟⢦⢢⡀⠀⠀⠈⣯⠻⢯⣅⠀⠀⠈⢦⡀⠀⠀⠘⢦⡀⠀⠀⣠⠞⢁⣠⣿⣽⣿⣿⣿⣿⣿⣧⣶⡇⣷⣼⠿⣿⣿⡾⠟⠃⠈⢻⡍⠙⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⡷⣄⣀⣀⣴⠃⠀⠀⠈⠉⠓⠶⠦⠵⢤⣀⣀⡤⠽⠶⢋⣡⣴⣿⣿⣿⣿⣿⣷⣿⣿⠿⢿⣻⢷⡹⣿⡆⠈⠁⠀⠀⠀⠀⠀⢻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠤⡇⠘⣏⠀⠈⠙⠶⣶⠤⣄⣀⣀⣀⣀⣀⣠⣤⡤⣾⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⠿⠿⠆⠀⠉⠻⠷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣼⠁⠀⢿⡀⠀⠀⠀⠀⣇⠀⠀⣀⣀⡼⠛⣿⣿⣿⣫⣴⣿⣿⣿⣧⢿⣿⢣⡟⠀⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣰⠇⠀⠀⢸⡇⠀⠀⠀⠀⢿⠀⣰⡿⠋⠀⠰⣿⣿⣮⡻⣿⣿⣿⣿⣿⣷⣻⡿⠁⠀⠀⣿⣿⣮⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣡⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀⣸⠟⠋⠀⠀⠀⠀⢻⣿⣿⣿⣮⣹⣿⣿⢿⣄⡼⠃⠀⠀⠀⠈⠳⠿⠟⣫⣶⣒⣲⡄⠀⠀⠀⠀⠀⠀⠀⠠⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡰⠋⠀⠀⠀⠀⠀⢹⡄⢀⡴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⠻⣿⡿⠋⠀⠛⠱⢶⣤⡀⠀⠀⠀⠀⠀⢿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⠀⢀⠞⣀⡤⠔⠚⢟⣦⠀⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣶⣄⣂⣀⣴⣿⣟⢷⣤⡀⠀⠀⠈⠙⠛⠛⠁⢀⣠⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢛⣢⡴⠗⠊⢁⣀⡤⠖⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠉⠉⠉⠀⢠⡏⠀⠉⣛⢿⣒⣀⣀⣀⣠⣴⠟⡋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠿⢫⡏⠉⢍⣽⠗⢷⣀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣁⣰⡚⢓⣴⠏⠀⠀⣠⡽⠷⠚⠛⠛⢳⡶⢤⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣇⡎⠀⢗⡿⠁⢀⡴⠛⠁⠀⠀⠀⠀⢀⡟⠀⠀⠈⠛⢾⡤⠤⠤⠤⠤⠤⢤⣄ ⢸⡇⢀⣠⡟⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣠⣤⣄⢳⡄⠀⠀⠀⠀⣰⠏ ⠈⡇⢘⣿⠀⢀⡟⠀⠀⣠⠴⠶⢤⡀⠀⡟⠀⢠⡟⠁⠀⠈⢳⢻⡀⠀⣠⠞⠁⠀ ⠀⡏⣸⡏⠻⣾⡇⠀⢸⠃⠀⠀⠀⢻⠀⣇⣀⣸⣧⡄⠀⢀⡼⠸⣧⠞⠁⠀⠀⠀ ⣰⠛⠙⠻⡄⢸⡆⠀⠘⣧⡀⠀⣀⡞⠀⠈⠉⠁⣸⠛⠚⠋⠀⢠⡟⢦⡀⠀⠀⠀ ⢿⡀⠀⣠⠇⠈⣧⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⠃⠀⠙⢦⡀⠀ ⠀⠉⠋⠁⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣴⣧⠇⠀⢀⣠⠞⠓⠒⠶⠶⠶⠒⠒⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣬⣥⡧⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣶⣿⢿⡟⠛⢛⠛⠿⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠋⢉⣿⠁⠀⠈⣳⣾⠟⠋⠈⢻⣧⣤⣀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⠀⢀⡤⠼⠘⠤⣤⣾⡟⠁⠀⠀⠀⠀⣈⣽⣿⡶⠿⠿⠛⠛⠻⢿⣶⣦⣤⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⢓⣲⠂⢱⠄⣀⣴⡿⠋⠀⠀⢀⣠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠉⠛⠿⣶⣄⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⣸⡅⠀⠘⢛⣿⠟⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠈⠙⢿⣷⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦⡀ ⠀⣿⡇⠉⠁⠀⢠⣿⠋⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇ ⠀⣿⡇⠀⢰⣧⣿⠇⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⣴⡾⠟⠻⢷⣦⡘⣿⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀ ⠀⢹⡇⢀⣏⣿⣿⠀⠀⢀⣿⠃⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⠀⠀⠀⣿⠃⠀⠀⢠⣿⠃⠀⠀⠀⠀⠘⣿⡜⣿⡄⠀⠀⠀⣠⣾⠟⠁⠀⠀ ⠀⢸⣷⡌⢸⣿⣿⣤⣄⣸⡏⠀⠀⠀⢠⣿⠋⠀⠀⠀⠈⠻⣷⡀⠀⣿⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⡇⢹⣧⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⢸⣏⣠⣾⣿⠈⠉⢿⣿⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⣤⣤⣤⣼⣿⣿⡆⠀⠀⠀⣠⡿⠁⠸⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⢀⣼⡿⠛⠻⢿⣦⠀⠀⣿⡇⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠉⠉⠉⠁⠀⣿⠿⠷⠾⠟⠋⠀⠀⢠⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⣾⡏⠀⠀⠀⠀⢻⡇⠀⢸⣧⠀⠀⠀⠀⠻⢷⣦⣤⣤⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠙⢷⣄⡀⠀⠀⠀⠀ ⢻⣧⡀⠀⠀⢀⣼⡇⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠙⢿⣆⠀⠀⠀ ⠀⠙⠿⢶⡶⠿⠋⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⠇⠀⠀⠀⠀⣠⣾⠿⠷⠶⠶⢶⣶⣶⣶⣶⡶⠶⠶⠟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠸⠿⢻⣟⠁⠀⣀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⣤⣤⣤⣼⣿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢁⣔⣓⣓⣓⣓⣗⣿⡏⢢⡏⠲⢦⣦⡎⠁⠀⠈⠣⣺⣶⣶⣶⣿⣿⣿⣿⠀⠙⢿ ⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⠇⠀⠈⢧⠀⠀⠠⢠⣶⣿⣿⣿⣿⣿⣿⡿⠟⢣⠀⡈ ⠟⠋⠉⣹⣿⣧⣀⣤⣼⣿⡧⣀⠤⠼⢇⠀⠃⠀⢙⡿⢿⡿⠛⠋⠁⠀⣰⣿⣷⣿ ⡀⠀⠀⠘⢆⠀⠈⠉⠙⡻⠊⠀⠠⠇⠀⠉⠐⠂⠙⠀⠀⠈⢦⠀⠀⣴⣿⣿⡿⣋ ⣷⡌⠢⡀⠀⠱⣀⡠⠜⢰⠊⠉⠑⡄⠀⣠⠖⠒⠉⠉⠉⠢⢄⢱⣾⣿⣿⡿⠿⠟ ⢻⣷⡀⣧⠀⠀⢨⠀⠀⠀⠑⣤⡴⠁⠀⣿⠀⠀⠀⣀⠔⠒⠢⣫⢻⠋⠋⠀⠗⣿ ⡘⣿⣇⢸⡕⣤⢼⠄⠀⡀⠐⠉⢀⠀⠄⠈⠑⠢⠤⠿⢄⠤⠐⠛⠺⡀⠀⠀⠀⢀ ⠻⣿⠋⠉⠁⠀⢸⡄⠀⢹⠂⠀⠈⢄⠐⠀⠀⠀⠀⣀⠴⢁⠀⠀⠀⡿⣠⡀⠀⣯ ⠀⠘⠓⠒⠒⠒⠈⠷⡀⠀⠧⡀⡴⢰⢉⠙⣖⠒⠋⡉⢄⡾⠓⢠⢊⡰⣯⠀⠉⠋ ⠀⠀⠀⠀⠈⠲⡄⠔⠱⡀⠀⠈⠐⠣⠬⠰⠸⠸⠠⠓⠕⠁⣠⡗⠋⠈⠢⡀⣠⠀ ⠀⠀⢀⣀⠀⠀⢸⠤⣄⠈⠢⡀⠀⠀⠀⠈⠐⠦⠄⠤⢔⢽⣹⢤⣄⣀⠀⣽⠇⠀ ⢾⣾⣿⣿⣷⣄⠾⠀⠙⣿⢷⣿⣿⣷⡶⠂⢠⣤⡒⠈⠁⢸⠻⠿⠿⢵⣷⠷⢆⡀ ⣶⣟⣿⠛⠋⠁⠀⠀⠀⢻⣦⣽⠋⠻⠁⣤⠘⠏⠻⣄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁ ⠛⠛⢿⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠁⠀⠀⠄⠀⠀⢸⡷⣄⣧⣤⣄⠠⠤⠤⠤⠤ ⠴⢉⣈⣙⣆⣀⣀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣙⠛⣿⣿⡟⢛⣿⣦⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣠⣾⣥⠤⢤⣄⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠀⠀⢀⡽⣛⡉⠀⠀⢀⡤⠒⠛⠻⣟⠢⠤⠤⢄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⢠⠏⡞⢁⣸⠀⡴⠋⡤⠲⣄⠀⠘⢇⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣦⡇⢠⣄⡀⠁⡰⠁⠀⠷⠆⠈⡆⠀⠘⡆⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⣠⠴⠚⡿⠑⣏⠀⢳⠀⡇⠀⠀⣠⢄⣀⠁⠀⠀⣷⣮⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣄⡀⠀⣇⠀⢹⡦⢼⠀⢇⠀⢸⠀⠀⠈⣦⡠⢄⡏⠙⠢⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠑⠚⡶⢾⣟⡮⣧⣼⣦⠘⢲⣴⡾⠁⠀⠀⣱⠀⠀⠈⢳⣄⠀ ⠀⠀⣠⡤⠠⠤⣴⠎⣰⣿⣿⣷⣀⢩⠉⠉⠉⣠⣧⣀⣀⣴⣧⠤⠒⠊⠉⠀⠀ ⠀⢸⣈⠳⡀⠀⠙⢲⣿⣿⣿⣿⣿⣿⡷⣶⡛⠉⠀⠀⣹⠉⠉⠙⠒⠒⢲⢦⡀ ⠀⠀⠙⢦⣙⣤⣤⠿⢿⣿⣿⢿⣿⢹⣿⡿⣿⣷⣦⣴⠟⠢⣄⠀⠀⣰⠃⣰⡇ ⠀⠀⠀⠀⠈⠉⠁⣴⠟⣼⠏⣼⡏⡸⢿⡆⣿⢿⡀⢿⣧⡀⢸⣀⡴⢁⣴⠟⠁ ⠀⠀⠀⠀⠀⣠⡾⢋⣾⠏⣼⣿⠁⡇⣸⡇⣿⠀⢷⠘⣿⣷⡀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⢸⡏⣰⣿⠏⣸⣿⡏⢰⠀⣿⡇⢸⠀⠈⣧⠸⣏⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠳⣿⣿⠀⣿⡿⢁⡏⠸⣿⣧⢸⣇⣀⣼⠀⣿⣨⠇⠀⠀⠀⠀⠀ ⠀⡴⡟⣯⣷⣶⣾⣿⣷⣿⣷⠊⠀⠀⠙⢿⣌⡻⣿⣏⣰⣿⣥⡀⣀⣤⡀⠀⠀ ⢠⠃⠓⠤⠿⠿⠋⢹⣿⣿⣿⡿⠀⠀⠀⠀⢉⣿⣿⣿⡿⠿⢿⣛⣿⣿⢷⡀⠀ ⠘⣇⠀⠀⠀⠀⠀⠈⠉⠋⡟⠀⠀⠀⠀⠀⠸⣿⡿⠻⠃⠀⠀⠈⠉⠀⠀⣇⠀ ⠀⠘⠦⣄⣀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠢⠴⠶⠒⠚⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡟⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢠⠀⡇⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢧⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣱⣤⣾⣥⣤⣀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⡴⠞⠉⠁⠀⣠⡴⠖⠒⠚⠛⠶⢤⣀⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⡤⠶⡄⠙⠆⠀⣀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡴⠋⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢀⣀⣀⠙⢷⣖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⢰⠏⠀⣰⠇⠀⣠⠟⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⠴⢿⡟⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡶⠛⠉⠙⠻⣄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⣀⣠⠏⠀⢰⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⠶⠒⠋⠉⠉⠀⠀⠀⠀⢠⣿⠟⠛⣦⠀⠀⠀⣧⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⣿⠖⠺⢷⡀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⢠⡏⠉⡟⠀⠀⡼⠲⣶⠃⠀⠀⠀⠀⡠⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⡾⠃⠀⠀⠀⠸⣦⠀⠀⠈⢻⠀⢀⣤⢀⣴⠋⠀⠀⠀⠹⡆⠀⢀⣴⣋⡀⠀⠀⠀⠀⢸⣇⣠⡇⠀⢸⠃⢠⡏⠀⠀⠀⠀⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⡏⠀⣴⠿⠛⠛⠓⢦⡀⠘⢷⣄⣀⣘⡷⠏⣿⠞⢯⣤⣾⠖⠂⢀⣧⡴⢿⡁⠈⠙⢶⡄⠀⠀⢸⡅⠈⡇⣠⠏⠛⡟⠀⠀⣠⠖⢇⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⣧⣀⡟⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⣰⠃⣠⠞⣿⠏⠀⠀⢸⡿⣄⠀⠙⢷⡀⠀⢹⡀⠀⢸⠧⠤⠿⣇⡀⣸⣠⠶⠛⢇⡠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢓⣿⠙⢷⣀⠀⢀⣀⣤⠤⠟⢰⠋⠁⣀⣴⣫⠞⠁⢀⡟⠀⠀⠀⢸⡇⠈⠳⣄⠈⢳⡶⠚⢧⣀⡟⠀⠀⠀⠈⠉⢹⣇⢀⣴⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠹⣴⠞⠉⠉⠉⠳⠄⠀⠀⢈⣑⣯⠟⠋⠁⠀⣠⠟⠀⠀⠀⢀⣿⡟⠀⠀⠈⠳⣄⣇⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠉⢹⡋⢹⡆⠐⡞⠀⠈⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⡇⠀⠀⠀⢠⣾⣷⣖⡋⠉⠁⠀⠀⣀⡴⠾⣅⣀⣀⣤⠞⢋⡞⠁⠀⠀⠀⠀⠈⠻⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠉⠀⠉⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠻⣄⡀⠀⠉⠀⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⢀⣀⣀⠤⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⠀⠈⠙⠛⣦⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣫⡭⢭⣩⢭⣭⡉⠉⠉⠀⠀⠀⠀⠀⢙⣶⠤⢤⣄⠀⢀⡴⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡞⠙⣧⡤⠖⠋⢹⡇⠉⠉⠉⠉⠉⠉⠉⣽⢃⣼⣿⣿⣿⣿⣿⣿⣷⣽⣿⣝⣾⡓⢦⠀⠀⠀⠘⣿⡗⠦⢞⣿⠿⢶⣶⣿⣶⣶⣶⣶⣶⣄⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⢻⡄⠀⢷⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⠿⣇⠀⢳⡀⠀⠀⢹⣿⣿⡿⠁⣀⢀⣿⣿⠿⠿⠿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢹⣧⣀⠀⢹⠀⠀⠀⠀⠀⣼⣿⢻⣿⣿⣿⣿⡿⣿⣭⡍⠛⠷⠿⠆⠀⠈⢷⡀⠹⣄⠀⠀⢻⠉⠹⢮⣛⣿⣿⣿⣿⣦⠀⠸⣿⠉⠛⠀ ⠀⢀⡤⠴⠒⠒⣤⢤⣄⣀⣀⡀⠀⠀⠙⠳⣏⠀⠈⠛⢮⣧⠀⠀⢠⣾⠿⣿⣾⣿⣿⣌⣻⠁⠻⠿⢟⡀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢦⡀⠸⡄⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠈⠀⠀⠀ ⠀⢿⣀⣀⣀⣠⠿⣤⣀⣈⡏⠙⠲⢤⢤⠤⠼⠓⠒⠲⠬⣿⣆⡴⢻⠗⠲⣮⠁⠀⠻⣿⣿⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⡄⠈⠳⣄⣷⠀⠀⠀⠀⠀⢻⣿⢿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠛⠓⠲⣾⠀⠀⠀⠈⠉⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⢿⠀⠀⠀⠀⠀⠀⢧⠀⠉⠃⠀⠀⠀⠀ ⣠⠶⠚⠉⠉⢻⡓⠒⠒⣾⠋⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠘⠲⠶⠶⠶⠛⠒⠒⠒⠛⠒⢒⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠸⡏⢷⣄⠘⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⣨⢧⠀⠀⠀⠀⠀⢀⣠⣼⣫⣿⣦⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠉⢻⡁⠀⠙⢦⣳⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⢶⡏⢁⣽⠖⠛⣝⠉⣳⣀⣤⣴⣾⡿⠛⢻⣿⣿⠟⢧⡀⡟⠳⣄⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠙⠿⣤⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡏⠀⢀⣠⠟⠋⠀⠀⢠⠏⢻⢋⣭⣿⣿⣿⣦⣀⣶⣾⡏⠀⠈⢳⡇⠀⠈⠑⠦⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠁⠀⣀⡴⠀⢠⠟⠙⣿⣿⣿⣿⣿⣿⡟⠻⡶⠛⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⡀⣞⣀⣴⣿⣿⣿⣿⣿⣿⡇⠀⢻⡀⠀⠀⠀⠀⠀⢻⢀⣴⣾⠿⣛⣲⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣭⣛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⡿⠛⣿⡏⣿⣿⣿⣿⡄⠀⣷⡀⠀⠀⠀⠀⢸⣾⣛⣵⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣜⡛⠲⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀

⠋⠀⠀⣿⣶⣿⣮⣥⣮⣶⣿⣶⣷⣿⡞⢩⡸⠃⠳⣤⣅⣲⣄⣠⠞⠉⠀⠀⠈⠺⢷⠠⣼⣧⣤⣶⣶⣶⣾⣷⣶⣶⣿⣿⣿⠀⠈⠻⣿⣿ ⣠⣞⣿⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣀⣠⣿⡇⠀⠙⠙⣿⣿⠛⠂⠀⠀⠀⡀⠀⠠⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿ ⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⠄⠀⠀⠀⠠⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡄⠀⢀⠈ ⣿⣿⡿⠿⠿⠿⣿⣿⣿⠋⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠸⣦⡄⠀⠠⠄⠄⠘⠻⣿⣻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⢀⣾⣿⣦⢼⣷ ⠟⠁⠀⠀⠠⣬⣶⣿⠿⣷⣤⣴⣾⣿⣿⣿⣿⡞⣀⡤⠴⠒⠚⠛⢦⡀⠀⠀⠀⠀⢀⣸⡿⠿⢿⣿⠛⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣟ ⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⠉⠙⠛⠿⢿⣿⠟⠁⠀⠀⢀⣦⠀⠀⠉⠓⠲⠶⠒⠻⠏⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟ ⣇⠀⢀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢠⢾⠅⢀⣠⣄⣀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⠀⠀⠙⣦⠀⠀⣴⣿⣿⣿⣿⣿⣣⣤⣴ ⣿⣷⡀⠉⠲⡀⠀⠀⠈⢳⡀⠀⣀⡴⠋⢀⡶⠋⠀⠀⠙⢷⡀⠀⠀⢀⣴⡶⠛⠋⠉⠀⠀⠀⠉⠛⢦⣀⠈⢷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿ ⣿⣿⣅⠀⠀⢱⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠙⢦⡀⠀⠀⣸⠃⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠙⢷⡘⣿⣿⣿⣿⡿⠋⠀⣖⣴⣶ ⠸⣿⣿⣥⠀⢸⣇⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢹⣶⡾⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣠⡞⠋⠁⠈⠙⣦⣷⣼⡇⠁⠈⠀⠀⠀⠛⠻⣿ ⠀⢿⣿⣿⡀⠈⣯⠳⡄⢀⣀⣇⠀⠀⠀⠀⠀⠠⠚⠙⠁⢀⣀⠀⠀⠀⠙⠲⣤⣀⠀⠸⢿⡇⠀⠀⢀⡤⠾⠿⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⡘⣿⣿⣧⣄⣿⣤⠿⠛⠋⣿⠀⠀⠺⣧⡀⠀⠀⠀⠀⡇⠀⠀⢙⠆⠀⠀⠀⠈⠉⠉⠛⠛⠒⡻⠁⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⢠⣶ ⠻⢿⣿⠛⠉⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠘⡝⠂⠀⠀⠀⠸⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⠀⠀⠀⠀⢸⡟⡇⡄⠀⠀⠀⢸⡧ ⠀⠘⢻⣦⣤⣀⣀⣀⣀⠀⠀⣿⣇⠀⠀⠀⠹⣄⠐⠀⠀⡀⠈⠓⠦⠤⣤⣤⣀⣤⡤⠶⠟⠁⠀⣠⣷⣄⡀⠀⢀⡾⢁⡿⠿⠓⠚⠶⠛⡻ ⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠙⠛⣦⠀⠀⠀⢊⢦⡀⡼⠃⣠⠂⢠⠂⢸⠭⡍⢩⠀⢠⡄⠐⣦⣯⠏⠀⢈⡶⠋⣠⣾⢿⡷⠀⠀⠀⠈⠅ ⠀⠀⠀⠀⠀⠀⠀⠒⠲⢤⡀⠀⣰⠞⢧⠀⠀⠀⠁⠉⠒⠤⢁⣀⡏⠀⡞⢰⠇⢸⠀⣸⠡⢞⡡⠋⠀⢀⣼⣧⠞⠉⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡼⠁⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠈⠉⢂⣓⠛⠃⠉⠀⠁⠀⠉⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠘⣯⣽⣿⠀⠀ ⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠸⣷⣤⣤⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⣀⣤⡴⢞⣿⣏⣹⡦⢠⣀⡀⠀⠀⠀⣠⣿⡏⠀⠀ ⢀⣄⣰⣶⣾⣿⣷⣄⠀⠀⣰⡏⠀⠸⣿⣷⣴⣒⡹⣷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠠⣿⣿⣷⣿⣿⣿⠟⣷⣀⣿⣃⡀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣷⣼⠟⠃⠀⠀⠙⣿⣷⠻⣿⣿⣿⣷⣿⣿⡟⠀⠀⢻⣿⣻⣏⠁⠀⠀⠀⠀⡏⠙⠛⠛⠺⠿⠾⣿⣿⣿⠿⠃⣦⠀ ⣤⣌⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⣾⣿⡄⠘⣿⡿⠋⢿⡟⠀⣀⡀⠸⣿⡟⠻⣦⡀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⢀⡜⠁⠀⠻⠋⠀⠋⠀⠀⠙⢿⣆⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠋⠉⢽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠈⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⣿⠷⣄⣈⣷⣶⣖⡶⠀⠰⠦⠤⠤⠤⠤⠤⣤ ⢀⡠⠶⠒⠹⠷⠂⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀ ⠟⠛⢀⣀⣀⣀⣉⣛⣥⣀⣄⣀⣼⣿⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣄⣤⠠⠀⣽⣿⣿⣿⡉⠉⣹⣿⣿⣿⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠢⢀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢸⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⣠⠔⠁⠀⠀⠀⢸⠀⠈⢋⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠲⠛⠛⠻⢦⣄⡀⠈⠀⠀⠀⠉⢀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⡨⠀⠀⠀⠠⠌⣙⢟⢏⠉⠉⠉⠉⠀⢀⠎⠀⠀ ⢀⠀⠒⠒⠒⢒⡿⠁⢂⠀⢀⠌⠀⠀⠀⠀⠠⢤⣠⡄⢣⣥⠀⠐⢲⡲⠃⠀⠀⠀ ⠀⠑⢀⡀⠤⡿⢀⠢⠂⠀⡈⠀⠀⠀⠀⠘⠀⠀⣸⠀⣆⠻⣧⣗⠕⠁⠀⠀⠀⠀ ⢀⡀⠀⠹⣦⡇⠈⠀⠀⠀⠇⠀⠀⠀⠀⢰⣠⡴⠛⡔⠫⢉⢷⡤⠬⢍⡉⠤⠆⡰ ⠛⠁⠀⠀⡰⠃⠀⢠⠒⠠⡈⠢⡀⠀⡀⠴⠁⢇⡜⠈⠉⢁⠸⠠⡀⠀⠈⡱⢠⠇ ⠀⠀⠀⡰⠁⠘⡈⠸⣀⠀⠈⢢⠀⠀⠀⢀⢞⠁⠈⠹⢀⣌⠆⣠⣴⣾⣾⠉⢻⠄ ⠀⠀⣼⡀⠐⠅⣸⠀⠈⠢⣀⣀⠀⡄⠒⠅⠀⠑⠤⢋⣝⣿⣏⢭⢿⣿⣟⡷⡀⢧ ⠀⠀⠀⠀⠀⠉⢙⠙⢄⠀⡋⠑⠂⠴⠄⠈⢦⣒⣵⣿⣿⣿⠿⣷⣻⡙⠋⠁⠘⡄ ⠀⠀⠀⠀⠀⠀⡌⡹⠈⡄⠈⢹⠁⡤⢒⣿⣯⣿⣾⣿⡟⢡⣴⣤⠉⠁⠀⠀⠀⠸ ⠀⠀⠀⠀⢀⠌⡰⠁⠀⢇⠀⡠⠊⠀⠈⢿⢿⣿⠟⢝⡀⠈⠛⢻⣶⣆⠀⠀⡀⠐ ⠀⠀⠀⣠⣃⠤⢐⡠⡆⠘⠁⠀⠀⠀⠀⠀⠀⡜⠲⠴⢺⠓⢤⡀⢉⣁⠴⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⣿⠟⠛⠛⠛⠻⣿⣷⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣯⡶⠛⢳⣿⠀⠀⠈⠳⣤⣠⣾⡿⠟⠙⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠟⠁⠀⠀⢀⡟⣷⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠘⠻⠿⢿⣿⣄⣀⣠⣤⣤⣤⣾⣿⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⢰⡒⠚⠃⠙⠲⣢⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠛⠛⠉⠉⠉⠙⢛⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡟⠉⣉⡿⠈⢹⠆⠀⣠⣾⣿⠋⠀⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠈⠙⠻⢿⣷⣤⡀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡃⢸⡏⠀⠀⣼⡶⢻⣿⡿⠁⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀ ⠀⣾⣿⠙⠷⠷⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⡇ ⠀⢿⣿⠀⠀⠀⢀⠀⣰⣿⠏⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃ ⠀⢸⣿⠀⠀⠀⣿⣼⣿⠏⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢀⣴⣿⠿⠟⠛⠿⣿⣶⣄⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀ ⠀⠘⣿⡇⠀⣸⢻⣿⣿⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠙⣿⣆⢻⣷⡀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⣿⡇⠐⠃⣿⣿⣿⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣠⣾⡿⠛⠉⠉⠉⠛⣿⣷⡄⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⣧⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⣿⡟⡇⠀⣿⡟⢿⣿⣿⣆⣿⡏⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣿⣧⠀⠀⠀⠀⢻⣿⣀⡀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⠀⣠⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣇⣱⣞⣿⡇⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣿⣦⣤⣤⣶⣾⡿⢿⣿⠀⠀⠀⠀⢀⣴⣿⠇⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⠿⠿⣿⣿⣆⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠉⠙⠛⠛⠉⠁⠀⣿⣿⢿⣶⣶⣾⠿⠛⠁⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠋⠀⠀⠀⠀⠙⣿⣧⠀⠀⣿⣇⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠻⢿⣦⡀⠀⠀⠀⠀⠀ ⢸⣿⣆⡀⠀⠀⠀⣰⣿⡟⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀ ⠀⠙⠿⣿⣶⣶⣿⠿⠋⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣁⣀⣀⡀⠀⠀⠀⠀⢀⢀⠀⣀⣀⣠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⡿⠁⠀⠀⠀⠀⢀⣤⣾⡿⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢻⣿⠉⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⣤⣄⣀⣀⣀⣀⣸⣿⣦⣴⣾⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⣠⣔⣁⣀⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠠⡪⢅⢀⠔⣂⠙⢇⠒⠒⢤⠀ ⠀⠀⠀⠀⣶⢁⢅⠉⠎⠘⠆⢁⠀⠆⡠⠁⠀ ⠀⠠⣖⠁⡇⠸⣄⠲⠀⠐⠀⢂⣀⡘⠇⡀⠀ ⠀⠀⣀⢉⡨⣚⣷⠳⠷⠬⢖⠃⠀⡀⣀⠨⠆ ⠀⣏⢄⠘⢲⣿⣿⣷⣷⣶⡋⠉⡏⠉⠒⢒⢤ ⠀⠈⠓⠓⣩⢯⢏⡟⢿⣽⣿⢻⡍⢱⡠⢂⡾ ⠀⠀⢀⡼⣱⢏⣾⢱⢸⡿⡈⢎⢿⠆⠉⠁⠀ ⠀⣀⡈⠺⣿⢸⠏⡌⢾⡇⣇⣼⢸⡸⠀⠀⠀ ⠸⠫⠻⠿⢻⣿⣷⠀⠀⠙⣮⣿⡿⢷⢴⡷⡀ ⠸⣀⠀⠀⠈⠉⡇⠀⠀⠀⠛⡛⠀⠀⠀⠀⡧ ⠀⠀⠉⠀⠂⠉⠀⠀⠀⠀⠀⠑⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⣄⣰⣁⣀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠉⠒⠢⠤⢀⣹⣴⠞⠛⠉⠉⣀⣈⣉⣓⣤⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⣠⣿⣟⣁⠀⠀⢀⠜⠁⠀⣠⠴⠻⣿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠏⢁⣸⠀⢰⠁⠀⠀⢸⣿⣀⣴⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⢀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣿⣿⡴⠚⢻⣶⠀⠣⣄⣀⣀⠿⠁⣼⣴⡶⠟⡧⢀⠀⠀⠀⠀⠀⠀⡧⡇⠀⡞⡸⠀⡴⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣖⡉⠁⠀⠀⢿⣧⠷⢦⡔⠛⠀⡤⠲⠀⠀⣀⣼⠟⠁⡇⠀⢻⣀⣀⣀⠀⠀⠀⠀⡇⡇⢰⢋⠇⡼⣱⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢼⡅⠀⠀⣹⠀⠀⢙⣲⡶⠾⠛⠁⠀⣰⠃⢀⣿⠁⢸⡙⡄⠀⠀⢰⢳⣇⠇⣞⡜⣱⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠋⠉⠉⣉⠁⠀⠀⠀⣀⣤⣞⣁⡴⣿⠃⠀⠀⢇⢡⠀⢠⣏⣼⢋⣼⢟⡴⢁⡠⢂⡀ ⠀⠀⠀⠀⠀⣖⢲⡀⠀⠀⠀⠀⢠⢾⢠⠘⢧⣄⠀⢈⡙⠒⠛⢋⡉⠀⢀⣠⠞⠁⠀⠀⠀⠘⣌⡷⠋⠀⠈⠛⢥⡿⢋⡭⠖⠉⠀ ⠀⠀⢀⠀⠀⠘⢆⠱⣄⠀⠀⢠⠋⣸⠈⡶⣷⣿⡗⠶⢤⣴⣾⡤⠴⠚⠛⠻⢿⣷⣶⣶⣤⠀⢱⡀⠀⠀⠀⠀⣠⡟⠉⠀⠀⠀⠀ ⠀⠀⠸⣍⠲⣄⠈⠣⡈⠢⣀⠒⠊⠉⣇⢱⠀⠹⡇⠀⢀⣾⡏⠀⠀⣀⣀⠀⠀⠙⣿⠉⠘⣆⢀⣿⣦⣠⣴⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠈⠑⢦⣄⡙⠻⠷⠮⣭⠏⠑⠻⠬⣇⠀⡇⣠⣿⡏⠀⠀⠀⠿⠿⠀⠀⠀⠸⣇⠀⢸⣶⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀ ⣤⠈⠷⠶⢧⣄⣉⣹⣙⣛⣓⡏⠀⠀⠀⠀⢸⣾⣷⡿⠛⣧⠀⠀⠀⠀⣴⣶⡄⠀⠀⣿⡀⠘⣿⢿⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣉⣁⣉⣉⣀⣽⣀⠀⠀⠀⢀⣼⣿⣶⡛⢳⣿⣷⠀⠀⠀⠈⠋⠁⡆⠀⢼⡇⠀⢻⣇⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢲⣾⣿⣿⣿⣿⣟⠋⢰⣯⠀⠀⠀⠀⠀⠀⢃⡠⢿⣿⡀⠘⣿⠀⠸⡏⢻⣿⣿⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡴⣿⣧⠈⢿⣦⣠⠙⢷⣀⠀⠀⠀⠈⠉⠀⢸⡟⣧⠀⢹⠀⠀⢡⠀⢻⠻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠈⣿⣿⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣷⠈⣇⠀⠇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠘⣿⢧⠤⠤⠌⢳⣦⣤⣤⣤⣶⣿⣦⢘⣦⠸⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀

⠟⠀⠀⠠⣾⣧⣾⣷⣼⣥⣤⣵⣴⣽⣤⣼⣷⣯⡶⠋⡍⠘⡇⠛⣦⣌⡀⠰⣦⠀⢀⣴⠟⠉⠁⠀⠈⠙⢮⣷⠠⣤⢸⣧⣤⣤⣤⣤⣤⣶⣾⣶⣾⣶⣶⣶⣶⣾⡏⠀⠙⢿⣿⣿⣿ ⠀⣠⣴⠦⠋⠉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣿⣿⣿⠇⠀⢹⣧⡇⠀⠘⢏⢷⣿⣽⣷⣟⣡⠆⠀⠀⠀⠀⠀⠀⠈⠓⣬⡛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⢿⣿ ⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣇⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠰⠂⠀⢨⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠻ ⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠰⠶⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠟⠛⣋⣆⠀⠠⣄⠀ ⣽⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⢹⣆⣤⠀⠀⢀⡄⢠⡄⠸⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⣠⣿⣿⣦⣠⣜⣷ ⣿⠟⠉⠁⠀⠀⠀⠸⣝⣿⣿⣷⣀⡀⢀⣠⣴⣶⣶⣿⣿⣿⣼⡆⠀⠀⣀⣠⣤⣴⢿⣧⠀⠀⠀⠁⠈⠁⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣍⡿ ⠁⠀⠀⠀⠀⠀⠙⢿⡒⠻⠏⠙⠻⠷⢿⣿⣿⣿⣿⣿⣿⣿⢏⣴⠞⠋⠉⠁⢀⠀⠀⠙⢷⣥⣀⠀⠀⠀⠀⣠⣶⠿⠉⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶ ⡂⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⠋⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠎⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠃ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠅⠀⢀⣀⣀⣀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⢷⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣋⣠⣤⣤ ⣿⣾⡄⠈⠛⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡾⠃⠸⣤⠶⠛⠉⠉⠻⣷⡀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠟⠋⠉⠉⠉⠙⠳⣦⡀⠀⠈⢻⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⢱⡄⠀⠀⠀⠀⠙⢷⣄⣤⠖⠛⠁⠀⠲⣟⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⣾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⠋⢉⡉ ⢿⣿⣿⣄⡀⠀⢀⣷⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠀⠀⠈⠹⢦⡀⠀⠀⣰⡟⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠙⣧⣸⢻⡿⠿⠿⢿⣿⠋⠀⠀⣿⣼⣿⣿ ⠘⣿⣿⣿⣥⠀⠀⣿⡄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⡿⠿⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠉⢳⡘⣷⡸⣧⠈⠁⠀⠀⠀⠀⠀⠿⠸⣿⣿ ⠀⢻⣿⣿⣿⠀⠀⢸⣟⢶⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢛⠃⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣠⣿⣟⡃⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠈⣿⣿⣿⣧⠀⠀⣿⡆⠹⣦⣖⣦⣾⡷⠀⣀⣀⣤⡄⠀⠈⠁⠀⠀⠂⡔⠒⠒⠒⠤⡀⠀⠀⠀⠉⠛⠶⠦⣤⣬⣽⣷⣄⣠⡤⠖⠋⠉⠀⠉⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣆⢸⣿⣿⣿⣷⠴⢿⡷⠞⠋⠉⠀⢼⡇⠀⠀⠀⠟⣧⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡖⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣾⢻ ⠻⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⡝⠶⠀⠀⠀⠀⠀⢷⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣏⠘⠄⠀⠀⠀⠀⠀⠀⣿⠻⣇⢰⠀⠀⠀⠀⠀⢿⣣ ⠀⠘⠿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡄⠀⠀⠀⠀⢻⡀⠀⢰⠀⠀⠀⠀⠛⢦⣤⣀⣀⡀⠀⠀⠀⠀⣀⣠⠴⣛⣋⠀⠀⢠⣧⡀⠀⠀⠀⠀⢰⡿⠀⣿⢾⡼⠦⢶⡶⡴⣾⣷ ⠀⠀⠀⠘⠿⠿⠿⠿⠶⠶⠖⠦⠤⠤⢼⣿⣷⡀⠀⠀⠀⠲⡻⣄⠀⠀⢠⡾⠁⢐⡄⠈⣉⠙⣻⠿⠿⠿⠿⠛⠉⠋⠁⠀⡀⢐⡟⣿⠛⠲⢤⣠⡴⠏⠀⣸⣿⢸⡃⠀⠀⠸⠀⠰⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡀⠀⠀⠀⠱⣌⠳⣄⠞⠁⢀⡾⠁⢠⡏⠀⣸⠃⢸⠀⢸⠁⠀⣿⠆⠀⣧⠞⡼⠃⠀⠀⣰⡟⠁⣠⡾⣟⠻⠾⠃⠀⠀⠘⠀⠐⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠶⣦⡀⠀⠀⣒⡜⢷⡄⠀⡀⠀⠈⠀⠈⠓⠦⣬⣁⠀⡾⠀⠀⡟⠀⣿⠀⣸⠀⢀⡟⣠⠞⣡⠞⠁⠀⠀⢰⣿⣶⠞⠋⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⡾⠉⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠙⠲⠼⠷⠾⠷⠖⠋⠀⠉⠁⠔⠋⠁⠀⠀⣠⡴⣿⠟⠁⠀⠀⠀⠀⠀⠑⢶⡒⣒⣶⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⡀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⢞⡯⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠠⠈⡅⣄⡠⠄⠀⠀⠀⠈⣿⡟⠿⢷⣦⣄⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⠤⠴⠶⠟⣫⡴⠟⣷⣴⣿⢋⣰⣦⣤⣀⣀⡀⠀⢠⣿⡿⢿⠀⠀⠀ ⠀⣴⣀⣰⣷⣾⣻⣾⣻⣶⡀⠀⠀⢠⢿⠁⠀⠸⢯⣽⣧⢶⡞⣁⢻⣿⣷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠚⠋⠀⠰⣿⣿⣿⣾⣿⣿⣿⡿⢋⣿⠆⣰⣿⣁⡀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣡⣿⠞⠀⠀⠀⠘⢻⣿⣦⢿⣿⣇⢿⣿⣷⡽⣿⣿⣿⠃⠀⠀⢹⣶⣾⢿⡟⠉⠀⠀⠀⠀⠀⢸⡿⠙⠿⠿⠿⢦⣽⣷⣿⣿⣿⣿⣿⣿⠏⣠⡄⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠙⢿⣾⣿⣿⣿⣜⣿⠇⠀⠀⠀⠈⣿⣳⣿⣿⣆⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⠦⠹⠿⠀ ⣿⣶⣶⡿⣿⢻⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣄⣸⣿⠟⠉⠈⢿⠏⠀⣴⣶⣦⠈⢻⡿⠃⠈⢿⣷⡄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⣿⣿⣿⠋⠀⠀⣠⠏⠁⠀⠈⡛⠋⠀⠈⠁⠀⠀⠈⠙⣿⣦⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠙⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⢨⣿⣿⣆⠀⠈⣿⣤⣤⣤⣤⠄⢀⣤⣤⣤⣤⣄⣄⣤⣀⣄⣀ ⠀⠀⢀⣀⣉⠻⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣾⣿⣆⣽⣿⣶⣿⣿⣵⣾⣷⣶⣄⡀⠀⠀⠈⠁⠀⠀⠀⠉⠉ ⣠⣜⡛⠋⠀⠀⠉⢉⣤⣄⣀⣀⢀⠀⣀⠀⣤⣾⡿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠛⠛⢁⢤⣤⣤⣤⣤⣤⣛⣤⣤⣤⣤⣤⣤⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⢀⢠⣆⣠⡤⠠⠀⢰⣿⣿⣿⣿⣦⣀⠀⣠⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷

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