⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⣿⣿⣿⣿⣿⣭⣿⣿⣾⣿⣷⣾⣟⣿⣧⣛⠭⡉⠙⣟⣧⡙⣿⣌⢻⣿⣿⣿⣿⣿⣯⣉⣋⣻⣿⣿⣿⣿⣶⣄⠀⣀⣀⣤⣷⡶⡟⠛⢹⢹⠈⠉⡇⠁ ⠀⠀⠀⠀⣀⣤⡶⠿⣛⡿⣛⣟⡌⢫⣀⣄⣥⣶⣶⡥⠤⠤⠬⠽⠝⢻⣿⣿⣯⣤⣿⡸⣧⣿⡿⠄⢍⢛⣋⣭⡍⠻⠛⣿⣯⣿⣿⣿⣿⣿⣿⣟⣥⣿⠁⠀⣧⡇⠀⢸⢸⢀⣀⡇⣦ ⢀⡤⠔⠊⢉⣇⣴⣾⡿⠿⢿⣾⣿⣿⡿⣿⣛⣅⠭⡼⠀⠀⡀⣠⣐⣋⣁⡈⢻⡜⣽⣧⣹⣏⠙⠳⢲⡿⣆⣙⢿⣇⡿⣥⣩⣿⣗⣿⢿⣿⣿⣿⣿⣿⣆⣀⣸⣧⣴⣾⡾⠿⠟⠛⠉ ⠉⠀⠀⢀⣼⣿⣿⣧⣴⣾⠟⢫⣿⣿⣿⣷⣦⣈⡭⠗⡈⣢⡶⠛⠉⠀⠉⠻⣿⣷⣿⡏⢙⠿⣿⣷⣶⣦⣅⡝⣖⠛⣿⣿⣿⣿⣟⠻⢷⣯⡻⣿⣿⡿⢿⣿⠛⠋⠉⠀⠀⠀⠀⠀⣼ ⠀⢀⣴⣿⣿⣿⣿⠟⣋⣠⢞⣉⣥⢶⣿⣿⡿⠋⢰⣠⢞⡉⣠⠞⠛⢉⣹⡆⠹⡿⠛⡶⢬⡙⠳⣌⠉⠉⠛⢷⣿⣷⣼⣯⠻⣿⣿⣧⣀⣙⢿⡿⢿⣽⢟⠙⣿⣦⠀⣀⣠⣤⣶⡾⡇ ⣠⣿⣿⣿⡿⡛⠹⢭⠝⣩⠟⣫⠔⠋⣱⣿⣧⣼⣿⡗⣸⠁⢀⣴⣾⣿⣿⣿⣴⢣⣰⡇⠀⣿⣿⣿⣷⣄⣀⠀⢻⣿⣏⢿⣧⢹⣿⣆⢻⣿⡿⠿⢦⣿⣿⣿⣿⣷⣿⣟⣩⣵⠋⡇⡇ ⢿⡿⢋⣞⠑⢘⢓⣠⣾⣵⣾⣷⣤⡾⣻⣿⣿⣿⣿⠁⣿⣀⣾⣿⣿⠿⠿⣿⢃⣾⣿⡇⣀⣿⣿⣿⣿⢈⣿⡄⠀⣿⡻⣷⡘⣿⣿⡟⣷⣜⣾⠫⡍⣀⠨⣿⣿⣿⣿⣿⠀⢸⠀⡇⠃ ⠟⢀⡾⠀⣴⡿⠛⣭⣿⣿⡿⣩⣿⣶⠟⢩⠏⣽⣿⠁⣿⢛⣿⠟⢁⠴⠊⣿⣿⢹⣿⣧⡿⠿⡟⢿⠘⡏⡿⢳⡄⠸⣷⣙⢿⣿⡙⣿⡑⠂⠻⠿⠸⣾⠃⢻⣿⣿⣿⣿⠀⢸⠀⡇⢰ ⠀⣽⢀⡿⠁⢀⣞⡽⢋⡴⠂⢀⣿⢏⡶⣿⣾⡷⡟⠀⢻⣾⣷⠔⠁⠀⠀⣿⣧⢺⣿⣿⣇⠀⣧⠈⣦⡗⣇⢸⣷⠀⢻⣿⠿⢿⣿⣿⣷⡆⠀⠈⢳⠹⣿⣾⣿⣿⣿⣿⡆⢸⠀⢀⢸ ⢰⣧⡾⠁⢀⣿⠋⣠⠏⠀⢀⣾⣥⠞⡼⣿⠇⢴⡇⠀⣼⣿⢿⡄⠀⠀⠀⣹⡿⣿⢹⣿⣿⣤⡏⣧⢸⠗⢸⡸⣯⠀⠀⠻⡄⠀⢻⢷⠘⣷⠀⠀⡄⠠⠹⢿⣿⣿⣿⣿⣧⠘⡄⢸⢸ ⡏⣿⠃⣠⠋⠀⣼⠏⠀⢀⣾⢿⡟⢰⢣⣿⠀⣹⡇⢠⣿⡟⡏⣧⠀⠀⠀⢹⣇⢻⡀⢳⡉⢿⡼⡜⠺⣧⡀⢳⣷⠀⠀⠀⢳⠀⠘⡿⠀⠘⣇⠀⣿⡀⠀⢼⣿⣿⣿⣯⣿⠀⡇⢸⢸ ⣿⢿⢰⠃⠘⣾⣿⡀⣠⡟⡟⣼⡇⡞⣼⢿⠀⣿⣧⣿⣿⡇⢹⣺⡄⠀⠀⠈⣯⠘⡇⠈⢳⡈⢷⡜⣆⠀⢳⣄⢻⣿⣆⠀⠈⣇⠀⣧⡀⠀⢻⣤⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⡇⢸⢸ ⡏⢸⡀⠀⣸⠏⡏⣻⣿⣾⣷⣋⡇⣷⠇⢸⠀⣿⣿⡟⡟⣷⠀⢳⣳⡀⠀⠀⢹⣀⣧⣠⣤⣷⡾⢿⢿⣯⠉⢿⡷⣿⣿⣧⠀⡏⠀⠈⣇⡀⠈⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⠀⡇⢸⠸ ⡇⠀⡇⢀⡟⢀⣷⣿⠃⣸⣽⠛⡿⣿⠶⢼⡧⣾⣿⢧⣿⢹⠀⢆⢳⣿⠛⠛⠛⣿⣻⣭⠥⣄⣻⣌⢮⠻⣷⡌⢧⠘⢿⡟⣧⡷⠀⠀⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠈⡀ ⠀⠀⢳⢸⠁⠈⢱⡏⡠⣿⣿⣿⣿⣿⣶⡄⢳⢹⠹⣧⢻⢿⣇⠈⢣⡹⣷⣀⡭⠞⠻⣿⠛⠛⠿⣿⣿⣷⡈⢿⣦⣧⣸⣿⣼⡇⢸⣸⠿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢳⠀⡇ ⠀⠀⢸⣸⡇⠀⢸⢥⡾⠛⡏⠀⠘⣿⡙⠟⠈⣿⡆⠙⢿⡌⢿⣦⠀⠑⠈⠻⣄⢠⣤⣼⣦⠀⠀⠀⠙⠻⣿⣦⠙⢿⣿⣿⣷⡇⢸⣿⠠⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⠀⡇ ⠀⠀⣼⠷⣿⣤⣿⡏⠀⠀⠃⣰⣿⣿⣷⡄⠀⠙⠿⠄⠀⣝⡄⠙⠧⣀⠀⠀⠀⡿⣿⣿⠿⡇⠀⠀⠀⠀⠈⠛⠓⠆⠙⣿⣿⠃⢸⠁⠀⠀⠊⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⠀⡏ ⠀⣦⠟⠀⡏⢿⣯⡵⠀⠀⠀⢹⡀⠻⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢳⣀⣁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⢻⢀⡏⠀⠀⣀⠈⠑⢿⣿⣿⣿⣿⡿⡇⣿⣿⠀⢸⠀⡇ ⠀⠉⠀⠀⡇⠈⣿⠀⢀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠃⢸⢾⠃⢀⣴⣇⣀⣀⣘⢿⣿⡇⡟⢀⣇⣿⣿⠀⢸⠀⡇ ⠀⠀⠀⠀⡇⢀⣾⡇⠀⠲⠤⣤⠴⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠖⣦⠀⢀⡶⠚⠛⠀⠀⠀⠀⠀⠁⢠⡏⣼⣶⠟⠉⢁⡀⠀⠙⣿⡏⣷⡇⢸⣿⣿⣿⠀⠈⡄⢳ ⠀⠀⠀⠀⡇⣸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⢀⠴⡋⠉⠑⣤⢿⠀⣿⢳⢸⣿⣿⣿⣤⠤⣇⢸ ⠀⠀⠀⠀⡇⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⠹⣄⢀⡸⣸⠀⢿⢸⢸⣿⢸⣿⣤⣴⣾⣿ ⠀⠀⠀⠀⡇⣇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠹⡌⠉⢠⠇⠀⢸⢸⢸⣿⢸⣿⣿⣿⡾⢻ ⠀⠀⠀⠀⡇⢹⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢀⠇⢠⠏⠀⠀⢸⢸⠈⣿⢸⣿⡇⠀⡇⢸ ⠀⠀⠀⠀⡇⠀⢳⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣀⡤⠴⠋⣠⠏⠀⠀⠀⢸⢸⠀⣿⣸⣿⡇⠀⡇⠘ ⠀⠀⠀⠀⡇⠀⢸⡟⠿⣄⠀⠀⠀⠠⠖⠒⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⠤⣴⠚⠉⠀⠀⠀⠀⠀⢸⢸⠀⣹⢸⣿⡇⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢸⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⣿⡏⣿⡇⠀⢸⠀ ⠀⠀⠀⠀⡀⠀⠸⡇⠀⢸⣿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⢸⡿⣤⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⡟⡇⣿⡇⣿⣿⠀⢸⠀ ⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⣟⡟⡇⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠸⡟⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⡇⣿⣿⠀⢸⠀ ⠀⠀⠀⠀⡇⠀⠀⠁⠀⢸⣿⣷⣷⡇⠈⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⢻⠤⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⢽⡇⣿⣿⠀⢸⠀ ⠀⢸⠀⠀⡇⠀⠀⡄⠀⢸⡟⡟⣿⡇⠀⠃⠘⣿⣿⠳⣦⣄⣀⣀⣀⣀⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢠⠗⠉⣗⠀⣝⠲⢤⣀⡀⠀⠀⢀⡇⣿⠺⡇⣿⣿⠀⢸⠀ ⠀⢸⠀⠀⡇⠀⠀⡇⠀⢸⡟⡏⣿⡇⠀⢀⣄⣿⡿⠶⢻⠉⢫⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⡎⠀⣠⠋⠙⠚⠣⠤⣀⡉⠙⠒⠺⠧⢷⣾⣷⣿⣿⠀⠈⡄ ⠀⠈⠀⠀⡇⠀⣀⣇⣀⣸⠿⠿⠛⠓⠊⠉⠁⣀⣀⣀⡘⡆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⠀⠉⠉⠙⠓⠲⠧ ⠀⠈⢀⣖⣋⣉⣩⠤⠤⠖⠒⠒⣎⠉⠉⠉⠉⠀⠀⠀⠀⠘⡄⠀⠹⣄⠀⠀⠀⠀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⢄⣀⡀ ⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢹⠃⠀⠀⡇⠀⠀⠀⠀⣠⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⠀⠀⣰⠃⠀⠀⠀⡴⠁⠀⣀⠴⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠈⠢⣺⡀⡴⠃⠀⠀⢀⣠⠤⠒⢉⠖⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡞⠙⡧⠤⢒⡟⠉⠀⢀⠞⣽⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠖⠉⠀⠀⠀⠉⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀