⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⡽⣿⡽⣟⣿⣻⣟⣿⢿⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⢽⣳⣟⣗⣟⣗⣟⣯⢯⡿⣽⣻⣟⣷⢿⣻⢷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣽⡳⡯⣳⡳⡵⣳⡳⡽⣺⢽⢽⣻⣺⡽⣯⣿⣻⣟⣮⣟⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢽⢽⡺⣪⡻⣪⢞⣝⢮⢞⡽⡵⣻⢽⣺⣳⣻⣳⣟⣾⣽⢾⣳⣳⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⡽⣕⢯⡺⣪⡳⣝⢮⡳⣝⣞⢽⢵⣻⣺⣺⣺⡺⣞⡷⣯⢿⡽⡮⡃⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣻⢺⡪⡧⣫⡺⣜⢮⢳⡹⣜⢮⡳⣝⢮⢞⣮⡺⣝⣗⡯⡿⣽⢽⣫⠘⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣺⣪⡳⡕⡧⡣⡇⡧⡳⢵⢝⣜⢮⢺⡪⣏⢗⣗⢽⢕⣗⡯⣟⡽⡯⣗⢅⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣞⣜⢮⢺⢸⢜⢜⢌⢎⢎⢧⢳⡱⣣⡻⣜⢵⡳⡹⣕⣗⢯⣗⢿⢽⢽⢪⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡺⣜⢎⡇⡧⡣⡣⡣⡣⡫⡎⣇⢧⢣⡳⣕⢗⢽⡹⡮⣺⡳⡽⡽⡽⡽⡢⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣝⢮⡣⡳⡱⡱⡹⡸⡱⡝⡮⣺⢜⡵⡕⡇⣏⢞⡎⡯⣺⡺⡽⡽⡽⡽⢜⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣳⢳⡹⡜⡕⡕⡕⡕⢕⢕⣕⢽⢱⡳⣝⢜⢜⠮⣎⢯⢮⢯⣫⢾⢽⢝⢜⠨⠀⣀⢠⢒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢖⡾⣮⡳⡳⣹⣺⢽⣺⣺⢽⣳⡳⡯⣗⡝⣮⡳⣝⣽⣺⢽⠽⡝⣞⢽⢝⡽⡜⡄⢅⡘⡎⡂⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⢽⣺⢝⣞⢽⡺⣕⡧⣧⣳⣽⣺⡺⣕⢵⢏⢗⢿⡽⣞⣞⣮⡳⣵⣣⢷⢝⡮⣳⢕⠕⢑⢕⠔⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣟⡾⣝⢮⢳⢹⢳⢝⢎⢯⢞⡮⣏⢞⢮⢣⡫⣗⡿⣽⣳⣗⣯⡺⣪⢯⣳⣫⡳⡝⡆⢐⢱⢃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣾⢽⡺⡵⡹⡪⣳⢱⢱⢱⢝⢎⢮⢺⡱⡱⡱⣳⣻⣽⢾⣺⣞⢾⣕⢯⡺⣜⢮⡣⡃⢠⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡯⡯⡮⡳⡹⣜⢵⣣⣗⢵⡣⡗⡇⡇⡇⡯⣺⣽⢾⡯⡷⡯⡷⣝⢷⣝⢮⡳⣝⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢽⣎⢧⢳⢸⢸⢢⢣⢣⢣⢣⢣⡣⡳⣹⢺⣺⢯⣟⣯⢿⢽⣝⣗⡵⡯⡯⡮⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣞⢮⢺⡸⡸⡨⡪⣪⡳⡹⣜⢼⡸⣪⡳⣽⢯⣟⡾⡯⣟⣞⢮⣻⢮⢯⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣞⢵⢱⢕⢕⡝⣎⢮⣪⢞⣵⢕⣗⣝⡯⣟⡷⣟⣟⡷⣽⢽⣺⡳⡽⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢳⢕⡇⡧⣫⣾⢽⣞⣯⡿⣽⢾⣺⡽⣯⣟⣯⣯⢿⣽⣻⣺⣝⡎⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢏⢮⢎⣯⣟⡾⡯⡷⡯⡿⣽⣻⢽⣞⣷⣻⣗⡿⣽⢾⣺⢵⣳⢕⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡽⣕⢽⣺⣗⡿⣹⢸⡱⡹⣜⣮⣳⢽⣺⣳⣯⢿⣽⡽⣞⣗⡽⣎⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣯⣿⣻⣵⢻⣺⣗⣯⢗⣗⡽⣽⣳⢷⡯⣿⣺⢷⣻⣽⣾⣻⣝⢎⣟⣾⡳⣫⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣽⣿⣯⣿⣿⣗⣗⡯⣯⢷⣻⣽⣯⢷⣻⢽⣞⡿⣽⢯⣟⣿⡽⣷⣻⡾⡕⣕⣗⣷⣟⡽⣞⣟⣦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣮⣿⣿⣽⣿⣽⣿⣾⣳⡳⡽⣽⡽⣯⢷⡯⣟⣾⣻⢮⡯⣯⣟⡷⣯⣟⣯⣷⡻⣜⣞⣾⣳⡯⣿⢽⣳⡯⣷⣣⡀⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣯⣿⣾⣿⣽⣿⣾⣿⣺⣝⢧⡳⣻⣽⣗⡿⣽⢾⣺⡯⣟⣷⣻⣽⢿⣞⡿⣺⣺⣗⣷⣯⣷⢿⣽⢯⣷⣟⡷⣯⢯⣗⢷⣔⣄⢄ ⣿⣿⡿⣷⣿⣟⣯⣿⣯⣷⣿⣿⣺⢮⢷⢝⢮⡺⣷⣿⢽⣝⢷⣻⢿⣽⣻⣞⣯⢷⣻⣳⣟⣾⢷⣟⣾⢿⣽⢯⣷⢯⡿⣽⣻⣺⣳⣗⡯⣗ ⣿⢿⣿⡿⣟⣿⡿⣟⣿⣯⣿⣾⣯⢯⣳⣫⢳⡱⣳⡻⣿⣞⡷⣽⢽⣞⣗⡯⣞⢝⡾⣞⣯⣿⣻⣽⣟⣯⡿⣯⡿⣯⡿⣽⡾⣽⣞⣷⣻⢽ ⣿⣿⢿⣿⣿⣿⢿⣿⣿⣻⣯⣿⣯⣯⣺⡺⣕⡇⣇⣯⣷⡟⣟⢿⢽⣾⣺⢼⢜⣵⡿⣟⣯⣿⣽⢷⣿⣽⣟⣯⡿⣷⣟⣯⣿⣳⣟⣾⢽⢯ ⣿⡿⣿⣿⣾⣿⢿⣿⣽⣿⣟⣯⣷⣟⡶⡝⡷⣕⣿⢿⣗⣟⢺⣝⡷⣳⢽⡹⣝⢼⣿⣻⣯⣷⣟⣿⢷⣿⣽⣯⣿⣻⣾⣻⣞⣷⣟⣾⣟⣯ ⣿⣿⢿⣿⣾⣿⣿⣟⣯⣷⣿⣿⣟⣿⣺⣝⢞⢮⢾⣿⣟⣮⡳⡵⣫⢗⡗⡝⣜⣿⣽⣻⣞⣗⣿⣽⡿⣷⢿⡾⣯⣷⣟⣷⣟⣷⣻⣾⣽⢾ ⣿⣾⣿⣿⣷⣿⣷⣿⣿⡿⣟⣯⣿⡿⣷⣝⢮⢳⢽⡿⣞⡷⣕⡝⡼⡜⡮⡎⣞⢞⡗⣗⡵⣯⣷⡿⣟⣿⣟⣿⣟⣷⣟⣷⢿⣽⢷⣻⣾⣟ ⣿⢿⣯⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⡿⣿⣾⣽⡷⣿⣻⣳⢽⣗⢽⡪⢮⡪⡪⡣⢧⢻⣸⣽⣿⣯⣿⡿⣯⣿⣽⣯⣷⣿⣻⣿⣽⢿⣻⣷⢿