⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢯⡽⡾⣭⢷⢯⣯⠿⣽⢯⡿⣽⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣾⣯⣷⣿⣷⣿⣾⣾⣿⣾⣽⣯⣿⣯⣽⣯⣿⣾⣷⣯⣿⣽⣿⣿⣿⣿⣟⣛⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡝⣯⣞⣵⣻⣼⣷⣿⣞⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡻⣽⢿⡻⢯⣳⢞⡶⣹⢎⡿⣹⣛⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⢞⣧⢟⡷⣚⡯⠽⠶⠿⣾⣿⢶⣯⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣽⡯⣗⡻⣝⢮⡻⣜⢧⡻⣜⢧⣏⠿⣜⢯⡞⣽⢻⣿⣿⣿⣿⣳⢏⣟⡾⢋⡵⢊⠱⣈⡥⢉⠖⡨⢌⠳⣟⢿⣷⡙⣿⡿⣟⠟⠉⠁⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⡸⠛⠛⠛⠛⠿⠛⠛⢻⣿ ⣿⣿⣿⣿⣿⣿⢿⡿⣵⢫⣽⢺⣭⢳⣏⠾⣵⢫⣞⡼⣻⢼⣣⢟⡼⡳⢮⣽⣿⣳⢯⣟⠟⢴⠉⣆⣡⡞⢩⠐⡣⡘⠔⡌⢒⢼⡆⠹⣷⠘⣿⡤⢲⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⠄⢢⠀⢄⠀⣿⣿ ⣿⣿⣿⣿⡵⣈⢾⣽⣺⡝⣮⢳⢮⡗⣾⡹⣎⠷⣎⢷⡹⢮⣝⡻⢾⣹⣿⡿⣧⢟⣱⠋⡜⢨⢱⠞⣅⡘⡦⡹⢱⣈⡶⠙⡬⢋⣇⣣⡝⡎⣹⣧⠟⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⠂⠀⠀⠡⠘⡄⢻⣿ ⣿⣿⣿⣿⣷⢌⢺⣷⡗⣯⢳⣏⢾⡹⢶⡹⣎⠿⠜⡓⠛⡓⠚⣯⡿⣿⣿⠟⣱⡾⣁⠣⡘⣴⢏⡘⣄⠖⣰⡧⢤⠤⠤⠚⣄⢰⡇⠤⣆⢣⠑⣿⣖⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢃⢱⢸⣿ ⣿⣿⣿⣿⣿⣎⢾⣟⢾⡱⣏⡞⢧⣻⠗⠉⠀⠀⠀⠀⠑⠪⣽⣏⠴⢫⠱⣘⣾⠃⣼⢁⣾⣷⣮⠟⣡⡾⢻⣶⠣⡘⢄⠣⣼⡸⢻⡄⣷⠘⡌⣷⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⠀⠀⠀⠸⢸⣿ ⣿⣿⣿⡿⣀⠹⣾⡿⣎⢷⡹⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⡿⡀⢇⡏⡷⡈⣾⢰⣿⣿⡶⠾⢇⣀⣾⣁⠶⢁⢎⣾⣿⠁⠱⣷⡏⣸⠰⢹⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⢸⠏⠀ ⣿⣿⡟⢰⢀⢣⡿⣙⢮⣳⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡫⢒⡿⡐⣡⡞⣸⢣⣼⣿⠰⣿⣷⢯⣤⣤⠞⣯⣱⣬⣶⣿⣿⠟⠤⠤⢿⡇⣼⢡⢫⣿⡿⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⣸⠃⡆⠀⠀⠀⠀⠀⠈⠀⠀ ⣿⡿⢈⠆⢂⣾⠳⣝⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⢸⣾⢡⡖⣼⠠⢿⣿⡿⣿⣧⡇⠈⠿⢿⠉⠃⠉⠯⠶⠛⢹⢿⣿⡿⣦⣼⣸⣿⢠⢻⡼⣗⣻⣦⠞⠋⠀⠀⠀⠀⢀⢼⠏⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⠇⢂⠌⣰⣏⢿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣗⣏⢃⢻⣼⡇⣿⡀⢿⣿⣶⣺⣿⡟⠦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠛⠀⡼⣻⣿⡏⡔⢺⣧⣿⡟⠁⠀⠀⠀⠀⠀⡰⢭⣟⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⡈⠄⡂⣼⣺⣣⡄⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠸⡜⣿⣷⣿⣿⣿⢿⣇⠚⣿⣿⣿⣿⡟⠦⠤⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⣸⣿⣿⣿⠱⣸⢻⣿⡿⣿⣤⠀⠀⠀⠀⠞⠋⠉⢿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡐⠠⢐⣏⢖⡞⠀⠀⠀⣀⡤⠤⠬⠶⡤⣄⣀⣀⣱⣶⢿⣿⣿⣻⢿⣿⣯⡜⢿⣿⣿⣿⢆⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣿⣿⣿⢃⢶⣿⣿⡟⣼⡿⠣⣛⢄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⡃⠄⠁⢸⢣⡞⠀⠀⢀⣼⣧⣼⢷⡿⢚⡱⢄⠣⡜⣰⣼⢾⣳⣯⢷⣻⣿⣿⣿⣷⣯⣿⣿⠀⡗⢄⡀⠀⠉⠉⠀⣀⣤⣶⣿⣿⣟⣥⣾⣿⣿⣿⣿⡟⠁⠀⠘⣎⢇⠀⠀⠀⠀⠀⡿⡀⠀⠀⢰⠀⠀⢠⠀⠀⠀ ⠀⠂⢁⣸⢻⠀⠀⢀⣸⣿⣿⠿⣧⢞⡡⠒⡌⢳⣹⣭⣷⠿⠛⠚⠛⠛⠿⢿⣿⣿⣿⡿⠟⠀⠞⠌⠻⣦⡤⠖⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠾⣽⣷⢦⣤⡴⣿⣞⠀⠀⠀⠀⢀⡇⡇⠀⠀⡄⠀⢀⠇⠀⠀⠀ ⠀⢈⡴⢏⣣⠷⣻⣿⠛⡯⡴⠀⣿⣿⣻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠀⣀⣸⠈⠢⣀⡀⠆⢈⣀⣀⠨⠔⠋⠀⠀⠀⠀⠀⠀⠈⢿⣝⡲⣝⡛⠲⠷⣄⠀⢀⣼⡣⢅⠀⢰⠁⢀⡎⠀⠀⠀⠀ ⠀⡘⠛⠋⠉⣏⣹⢨⣾⣷⡇⢀⣿⣶⢻⣭⠟⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣮⣽⣳⣧⡘⣻⣍⠞⣡⣼⡒⢞⠑⡜⠲⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣹⢿⠟⠛⠉⠀⣸⣼⣳⡿⢡⣿⣿⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⢻⣿⡽⣯⡻⣿⣾⡅⠐⡗⢺⣷⣄⣆⢹⣆⡇⠀⠀⠀ ⠀⠀⠀⡼⠁⠰⠁⠀⠀⠀⣰⡏⣉⣿⡑⣾⣯⡇⠀⠀⠀⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀⠀⢷⣿⡽⣷⠘⣯⣿⡆⠈⠓⠒⠩⢍⣉⢫⠐⠀⠀⠀ ⠀⠀⢀⡇⢀⠰⠀⠀⣴⣷⣟⣿⣯⢿⣼⡟⢻⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡄⠀⠀⠀⠸⣾⣳⡝⢀⣷⠧⢙⢢⡀⠀⠀⠀⠂⠀⢱⠀⠀⠀ ⠀⠀⠀⢱⠘⡄⠰⠀⠸⠉⡹⠋⠁⠙⢯⣧⣼⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢳⣿⣲⡾⠋⠀⠈⠈⠺⣢⠀⢀⠃⠀⠰⠀⠀⠀ ⠀⠀⠀⢀⢇⠐⠀⠃⠀⢳⠁⠀⠀⠀⠀⢈⠃⠀⡰⠁⢀⠤⠐⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠈⢢⡀⠀⠘⡆⠉⠀⠀⠀⠀⠀⢀⠏⠀⠈⠀⢀⠇⠔⠀⠀ ⠀⠀⠀⢄⠙⡄⠀⠀⠀⠈⢆⠀⠀⠀⠀⡘⠀⡘⠀⠰⢁⣴⣞⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡑⠄⣀⡑⡀⠱⡀⠀⢹⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡸⠊⠀⠀⠀ ⠀⠀⠀⠀⠢⢡⠀⠀⠀⠀⠈⢳⣄⠀⣼⠃⢠⠁⠀⡇⠸⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠇⠀⡇⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢾⣶⠘⠀⢣⠀⠈⢇⠀⠀⠀⢀⠜⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠠⡀⠹⡄⠀⠀⠀⠀⠀⠙⢧⡎⠀⢸⠀⢣⠐⠄⡀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡘⠀⠀⢰⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡸⢀⠆⡄⠀⠘⣆⢀⡴⠊⠀⠀⠀⠀⠀⡄⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠘⢆⢣⠀⠀⠀⠀⠀⠀⠈⢢⠀⠸⡄⠀⠑⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢣⡀⠀⠀⠈⠁⠒⠠⠀⠀⠀⠀⠉⠉⠉⡠⠊⢠⠁⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⢠⢁⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡎⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⢻⢆⠀⠀⠀⠀⠀⠀⢠⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡺⠋⠀⠀⠀⠀⠇⠀⠀⠀⠙⢳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠥⡘⣆⢢⠀⠀⠀⠀⠀⠈⠀⠀⢘⠀⣹⡶⠤⣤⣤⣤⡶⠚⢉⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢝⢗⢶⣤⣀⣀⣀⣀⡠⢴⣯⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡣⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣕⢄⠀⠀⠀⠀⠀⠀⠜⡴⠃⠈⠳⢔⣿⠉⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⠝⢿⡟⣀⠦⠐⠀⠘⠳⡘⠄⠀⠀⠀⠀⠀⠀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡕⡄⠀⠀⠀⣨⠞⣀⡠⠄⠀⠀⠸⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡾⠚⠁⠀⠀⠀⠉⠓⢽⣎⠢⠀⠀⠀⡄⣪⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣢⣄⣴⠷⠍⠤⡀⠀⠀⠀⠀⢹⡚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⡇⠀⠀⠀⠀⡠⠐⠒⠀⠽⢷⣕⠒⣊⡜⠁⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠫⡳⣄⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢉⡉⠌⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠔⡂⠒⠁⠀⢠⢮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢧⡰⡀⠀⠀⠀⢀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠂⠀⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣰⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⢷⣔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡐⠒⠀⠤⠂⢡⠞⡁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⣷⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢠⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⣧⠈⠀⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⣧⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡼⠃⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠘⣧⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡞⢡⠊⠀⠀⠀⠀⠀⢅⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠑⠜⢷⡈⠐⢄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢂⡞⡰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠮⡒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⢻⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠀⠀⡜⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢿⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠈⠂⠈⠀⠀⢡⣸⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡙⣄⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⣆⡀⣸⠀⣰⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⡆⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠈⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠹⣮⣽⣼⢃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀ ⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⢀⢞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸⣦⡏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡌⢼⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣧⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⡆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠐⠒⠤⠐⡀⠀⢑⠀⠀⠀⢿⡆⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⢦⠃⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠠⠁⠠⠀⠀⠱⣇⠀⡆⠀⠀⠀⠈⣿⡄⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢬⠏⠀⡔⠁⠰⠃⠀⠀⠠⠀⠐⠠⠀⠐⠀ ⠄⡁⠐⠀⠀⠀⠈⠀⢻⠀⠉⡄⠀⠀⠀⠘⣿⡆⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⢠⡟⠀⠰⠀⠀⠂⠀⠀⠀⠀⠄⠁⠀⠐⠈⠀