⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢒⡾⠞⣹⢏⠋⣠⡒⡆⠀⠀⣀⠤⡺⣚⡽⣪⢊⢎⣼⡵⠈⣉⣶⠗⣨⣿⡞⡇⠀⠀ ⠀⠀⠈⡄⠀⢲⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠦⠤⠥⠤⠤⣴⣸⣈⣒⡷⠝⠁⢀⡿⣦⠴⡪⠊⣴⡖⢷⣿⠕⣊⡩⡥⣾⡩⠝⠁⡣⡇⠀⡠ ⠀⠀⣃⣀⣀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⠁⠀⠀⠀⠀⠀⣀⠤⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⡔⢊⠓⠉⣀⣴⠷⢾⡟⢁⠀⣿⠸⢤⣢⣟⢟⠀⢰⣡⠗⡡⣪⠏ ⠀⠐⠒⡴⠒⠄⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⣄⠀⠀⠈⠳⠊⣱⣊⡁⡠⣺⠵⢋⡠⠶⢍⡕⢏⣾⠃⡠⢞⡡⣪⠚⡡⠀ ⠀⠀⠀⢀⡴⠩⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠈⢆⠀⢀⠴⠒⠒⢄⠈⠙⢷⡚⠋⢀⣐⠁⣠⣞⠥⢊⡴⡫⠊⡠⠊⠀⠀ ⠀⠀⡰⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸⢸⣠⠞⢡⠖⠋⠀⠀⡠⠶⠀⢀⡤⠀⢀⡔⡫⡠⠀⠀⠀⠀⠀⠀⠀⠈⠶⠃⠀⠀⠀⣄⠳⡄⠀⠙⢖⠒⣢⡷⢻⢃⠴⡯⢊⡤⢪⢐⣷⠆⠀ ⠀⠀⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⣡⢞⣵⢀⠔⠀⠊⠐⠁⣠⠋⠀⡠⡫⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡆⠀⠈⢂⠘⣄⢀⠈⢆⢁⢴⢗⠥⢋⡴⠣⢊⢴⠝⠁⠀⠀ ⠀⠀⠈⠀⠀⠀⠈⠁⠰⣷⢲⡀⡠⢋⠖⢡⡿⢣⠂⠀⠀⢀⠀⡰⠁⠀⠜⡵⡁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡄⠘⡝⡄⠀⠀⢃⠘⣆⢵⡈⢖⠕⢁⠔⠉⣠⣴⠟⠁⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡜⡱⠋⣠⡕⢡⠇⠀⠀⠀⠁⣸⠁⠀⠀⡼⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⣷⣛⣷⡀⠈⠘⡄⠈⢎⡆⡈⣎⢣⠸⡜⠁⣠⠞⠛⠁⢀⡴⠋⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡰⡑⠁⢛⠆⠎⡄⠀⠀⠀⡰⡃⠀⠀⢰⠁⠇⠀⠀⢀⠏⠀⠀⠀⠀⢰⢰⠀⠃⠀⠈⢣⠀⣆⠁⠀⠈⠀⣇⠘⡌⢇⢁⠊⠀⠀⢀⠔⠉⡠⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡼⠹⡁⠀⡼⠀⠘⠀⠀⠀⢀⢣⠃⠀⢰⡏⢻⠀⠀⠠⠹⠀⠀⠀⡘⢀⡆⡎⢸⠀⠀⠀⠈⣆⠸⠀⠀⠀⢀⢸⠀⠹⡼⣼⡀⣀⠖⢁⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⡡⣺⢡⢷⡁⢀⠇⠀⠀⠀⠀⠀⡼⠘⠀⢠⢻⢸⣼⠀⢀⢇⡇⠀⠀⢰⢃⠏⠸⠀⡏⠀⠀⠀⠀⢹⠀⡇⡀⠀⢸⢸⣷⣄⠱⣿⡇⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣊⢤⡣⡜⡆⠀⢸⠀⠀⠀⠀⠀⢀⠇⠁⢀⢧⡇⡇⢻⠀⠘⢸⠁⠀⢠⠃⡜⢠⡇⣰⣀⣤⠤⠐⠒⠚⡄⡇⢡⠀⠀⠀⠈⣯⠳⣌⢣⡁⠀⠀⠀⠀⠀⢀⣄⠀⠀ ⠀⠀⠀⢀⡴⠋⠁⠀⣼⠃⣳⠁⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣌⡾⡇⢻⢸⠀⠀⠘⠀⠀⠎⡼⣁⣾⢿⠋⠁⢀⣀⣀⣀⠀⣧⣇⢸⠀⠀⠀⠔⣛⢢⣏⡏⠛⠦⠀⠀⣠⣴⢟⣥⠊⠀ ⠀⠀⢄⠋⠀⢀⠀⠀⢿⣸⠃⠀⡇⢠⢄⠀⠀⡄⠀⢸⠀⠠⣿⠇⡇⣼⠀⡆⠀⠀⠀⣜⣴⢟⠏⣌⣾⣲⣿⡿⠒⣶⡖⠒⢿⣿⢸⠀⢠⢠⡖⠁⠈⡟⣷⠀⠀⢰⠾⡫⠶⢋⡥⠊⠀ ⠀⠀⠀⣉⣶⣠⠨⠶⠈⠇⠀⠀⡇⢸⠸⠀⠀⡇⠀⣸⣤⣤⣿⢤⣴⣿⣀⢳⠀⡇⠰⢁⠃⠎⢸⣿⡟⢧⣰⡿⢄⣴⡠⠄⢸⠟⣾⠀⢸⣸⠀⡼⢀⡇⠈⣠⢔⠕⠉⡠⠔⢁⠄⠊⠀ ⡆⢀⣿⣿⣿⣗⠀⠀⢠⠀⡇⠀⡇⢸⡀⢆⡀⠇⠉⠙⠀⠀⣇⡀⠼⣿⠍⣈⣇⢀⡆⡞⣼⠀⠋⠀⠀⠤⠭⠟⠛⠉⠀⠀⠸⠀⣿⠀⣤⡇⢠⠃⣸⡰⠊⠃⠀⠰⠊⣀⣚⠁⠀⠈⠉ ⣬⣻⡿⡽⣤⢕⡵⡘⣾⢾⢳⠀⣧⡸⢧⠈⠃⢸⡀⠀⡇⢸⣥⡶⠶⠿⠶⣤⡘⢶⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⠤⠊⡰⠁⠈⠀⠀⠈⠠⠲⢒⠀⠈⠉⠐⠒ ⡤⣾⣷⣷⣝⣿⣧⣷⣿⣏⡉⢇⣿⠇⣸⣄⠀⠀⢣⠀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢿⢁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡻⣷⡝⡷⣮⣿⣿⣿⣿⣤⠌⡎⣰⠹⡈⢣⡀⠈⢦⢹⢻⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡈⢉⢠⠀⣠⠖⠉⠁⠀⠐⠒⠀⠤⠄⣀⡀⠀⠀ ⣷⣕⠚⣿⣻⣼⣻⣿⠻⣿⣿⣾⡞⢱⢸⠳⣄⠈⡲⢄⣻⣄⠁⠀⠀⠀⠀⠀⠀⠀⠸⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⢯⣾⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡠⠔⠋ ⠘⠹⣷⣭⣵⣟⢿⣟⣇⡿⢻⣿⣿⣿⣼⠀⢸⡶⡇⢀⢸⠻⡕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⡎⣼⡎⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⡰ ⡼⢾⣿⣾⡿⢿⢸⢎⡿⣣⣧⣀⣀⣸⢸⠆⢸⡇⣀⡼⣦⡓⠺⢦⡀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠊⣩⠝⠁⠀⠀⠀⠀⢀⠎⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⡰⠁ ⠻⣓⣷⣽⣒⣋⣯⢿⣛⠛⠳⣖⠒⢛⣋⠴⢾⣧⠟⠁⠈⠧⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠑⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠸⣦⡠⡄⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢠⠁⠀ ⢠⡏⡠⣠⢋⡷⣬⣆⣁⣀⡤⠴⢞⠛⠾⠒⢾⡇⠀⠀⠀⠀⠀⠀⠀⢠⡉⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡤⠊⢹⠃⠘⣄⣀⡠⢚⡟⠁⠀⠀⠀⠀⠀⠏⠀⠀ ⣿⣿⡦⣀⠈⠀⠸⡮⣄⠈⢫⢳⢶⡛⣽⠑⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⠄⣀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡠⠚⠁⠀⠀⡞⠀⠀⡾⠋⠀⠊⠀⠀⠀⠀⠀⠀⡸⠀⠀⠁ ⠈⣙⠆⠀⢳⠲⢄⡁⣿⠑⡦⢤⣀⣹⡊⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⣹⡖⠦⠖⠊⠀⢀⠔⠋⠀⠀⠀⠀⡘⠀⠀⡜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⡇⠀⠀⢸⡀⠀⠈⠉⠀⠛⣆⠱⣿⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⢶⠃⢣⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠰⠁⢀⠞⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⡿⢆⡀⡎⠈⠒⠒⠐⠚⠀⡇⠉⢻⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢁⠃⠀⠘⠶⠊⠁⠀⠀⠀⠀⠀⠀⢠⢇⣀⠊⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡠⠽⡄⠉⠀⠀⠀⠀⠀⠀⡰⠋⠉⠛⠺⠤⠼⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡜⠀⣠⠞⠛⠲⣄⠀⠀⠀⠀⠀⢀⠏⡰⢣⡀⢀⣠⣖⣭⠤⢤⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀ ⣾⡿⡧⡄⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡉⠁⠐⡲⠃⠀⠀⢠⣡⢺⠗⡲⠷⢅⡼⠙⠦⡀⠀⢀⡮⠊⠀⠀⠉⠉⠉⠀⠀⣰⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡭⣭⣧⣇⡀⠀⠀⠀⡰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠞⠀⠀⠀⣠⡞⠁⢸⢉⡹⠟⡶⠁⠀⠀⠈⢢⡞⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣁⠤⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠈⠑⢦⢩⡭⠽⢦⣀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣋⣀⠑⠠⣀⠞⡹⠀⢀⣼⢟⣷⡞⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⢀⣼⣭⣿⣾⡇⠀⠀⠀⠀⠈⡀⠀⠀⠀