⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠼⢪⡺⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿⣔⠎⡱⡵⣝⢾⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⢝⢮⢮⡳⣝⢮⡳⣫⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⣨⡇⣗⢽⢕⣗⢝⢮⡳⣝⢮⣻⢤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢠⣰⢴⡳⡳⣝⢽⡸⡪⡮⡳⣣⡳⣝⢵⢝⢮⡳⣕⢯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣢⢺⡹⣪⢳⡹⡪⣎⢧⡫⣎⢗⡝⡮⡺⣪⢳⢝⢵⢝⢮⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡢⡋⣖⢵⡹⣪⢳⢝⢮⡪⡳⣝⢮⡳⣝⢎⢯⡪⡳⣝⢮⡫⣺⡪⡯⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡜⡀⡧⡳⣕⢝⢮⡳⣝⢮⡪⡳⣕⢧⡫⣎⢗⢵⡹⡪⣎⢗⣝⢮⢎⡯⣺⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠁⡮⡳⣝⢮⡳⣕⢝⢮⡳⣝⢮⡪⡳⣝⢮⡳⣕⢝⢮⡪⡳⡵⡹⡵⣝⢞⣞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡮⡸⣪⢳⢕⢧⡫⣎⢗⢵⡹⣪⢳⢝⢮⡪⣳⢝⣎⢳⢱⢙⢎⠯⢮⡫⡮⣳⡳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⡇⡯⣪⢳⢝⢮⡺⣜⢕⢧⡫⣎⢗⣝⣞⢮⣗⡯⡿⣜⢜⢜⢜⢜⢜⢜⢝⡮⡺⣯⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⡇⡯⡪⡯⣯⡳⣽⣪⡳⣕⢝⢮⡣⡳⣝⣗⣗⢯⢫⢣⢣⢣⢣⢣⢣⢣⢣⢫⢯⣺⡺⡽⣝⣗⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⢱⢱⢹⢾⢽⣺⣺⢜⢎⢗⢵⡹⡪⡚⡎⡎⠎⠌⡐⡀⢀⠂⠅⠣⡣⡣⡫⣳⡳⡹⣝⢞⡮⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣇⢇⢇⠣⠉⠊⠎⡎⡎⡎⡳⡽⡸⡸⡸⠨⠀⠁⣾⣞⣐⠀⠄⠐⠘⡜⡜⣵⡫⡺⡸⣕⢯⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⢗⡭⡪⢐⢐⠀⠈⢰⡌⠪⡪⡪⡪⡪⡪⡪⠀⠀⠀⣟⢮⣻⠌⠈⠀⠀⡇⡇⡷⣝⢜⣝⢮⢯⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣏⢮⣫⢣⢂⠀⠀⠀⢸⣻⣣⢱⢱⢱⢱⢱⢱⢁⠀⠄⠈⠛⢊⠀⠀⠀⢰⢱⢱⣻⢽⢽⣺⢽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣳⢕⣇⢇⢂⠀⠀⠂⠳⠝⠈⡎⡎⡎⡎⡎⡆⡂⠅⠀⠀⠀⠄⠠⡨⡪⡮⡯⠋⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣳⢵⢧⣇⢂⠠⢀⢈⢈⢀⢇⢇⢇⢇⢇⢇⢇⢇⡥⣱⣱⣱⢽⣺⡽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠷⠝⠺⢜⣆⣖⣔⣎⡎⡎⡎⡎⡎⡎⡮⡣⣣⣳⣳⢽⣽⣺⢽⣕⡳⠴⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡰⣤⡀⢀⠀⠁⠃⠓⠓⢿⢼⡼⡮⣞⢞⣞⢽⡺⣺⡺⡽⣺⡪⣗⣗⢽⡳⡦⡭⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣇⢂⢛⢊⠫⣮⡠⢜⡺⣝⢗⡽⡽⡽⣕⡕⡧⡫⡪⣪⢯⣺⡪⣗⢗⡽⣪⢯⡫⣞⢮⢷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢀⡦⣟⡮⣷⢐⢑⡱⣜⢵⡫⣞⢵⢝⣽⢽⡇⡇⡇⡇⡝⡜⣗⡵⣻⡞⠷⣝⢮⡳⣝⢮⡳⣝⢽⣆⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀ ⢨⡎⣵⣺⡳⢯⢳⢌⢳⢝⢮⡳⣝⢮⢯⠻⠊⢐⡇⡇⡇⡇⡇⡇⣗⢽⡪⣗⡀⢸⡳⣝⢎⢗⢝⢎⢇⢏⢮⢚⣪⡩⣩⢍⣓⡳⢤⣀⠀⠀ ⣳⢵⣻⢮⣻⢜⡜⣜⢬⢭⡳⣝⡮⠏⠃⠀⠀⢸⡪⡪⡪⡪⡪⡪⡮⡳⣝⢾⢽⣗⡟⡜⡜⡜⡜⡜⡜⡜⡜⣯⣞⡮⣗⢯⣳⢝⢧⣫⡳⡄ ⢸⣟⡞⡝⡾⣽⣺⣪⠮⠮⠞⠃⠁⠀⠀⠀⠀⢘⣧⡣⡣⡣⣣⢳⢝⡽⣪⢯⠟⣞⡇⡇⡇⡇⡇⡇⡇⡇⡇⡗⣆⠀⠀⠀⠈⢹⢧⡳⣝⡽ ⠀⣳⢕⢕⡯⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣺⢽⣞⣞⡮⣗⣯⢾⢽⢽⠀⡾⡸⣪⢪⢪⢪⢪⢪⢪⢪⢪⢳⠀⠀⠀⣬⢞⣗⣝⡮⡏ ⠀⡾⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡳⣝⢽⠞⠁⠙⢽⡺⡽⣝⣗⠀⠻⠼⠚⢱⡇⡇⡧⡣⡣⣣⢣⡻⠀⠀⢘⣗⡯⣞⡾⠉⠀ ⠐⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⡝⢮⢫⡳⣤⡀⠹⡮⣫⢞⡮⡄⠀⠀⠀⠀⠉⠉⠙⠚⠚⠉⠉⠀⠀⠀⠀⠈⠙⠁⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡕⡏⡇⡇⡇⣇⢧⣳⡻⠀⠻⣎⢷⢹⢽⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠮⣮⡪⣎⣞⠮⠋⠈⠀⠀⢠⢼⢣⢳⠱⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢤⢏⢎⢎⢎⢎⢎⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠽⠮⢞⢮⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀