⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡎⠎⡜⡠⣑⣐⢐⢄⢅⢁⠑⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡣⡑⡜⣜⢮⣳⡣⣯⡳⣝⣞⡼⡔⡄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡢⡆⡇⡇⢎⢮⡳⣝⣞⢮⣗⢽⣣⡗⡽⡽⣕⡇⡜⢔⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢕⢵⢹⣪⢪⢊⠎⡞⡼⣕⡗⣽⢪⡟⡼⡽⣽⢪⡗⣽⢸⠘⡜⡕⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡣⢣⢣⢇⢇⢅⢣⢹⢪⠧⡯⣳⢹⣪⣻⢼⣳⡹⣪⠳⣕⠱⡘⢜⢜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⢣⠱⢀⠃⡜⡸⡱⡝⣼⣳⢽⣺⢪⣗⢧⣟⢼⣣⢳⠨⢐⠅⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠨⠐⡐⡜⡜⣜⢕⣗⢽⢽⡺⣽⡪⣗⣗⢽⣪⢪⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢣⢫⢪⡎⡆⡣⢪⢸⢸⢸⢱⡙⠩⡻⣼⡣⣟⢾⢼⢑⠑⡇⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠰⡱⢱⠱⠩⢃⢣⢫⢪⠢⡱⡱⡹⡜⡦⡴⣜⢷⣝⢧⢯⣳⢢⡪⡪⢢⢳⡀⠀⠀⠀⠀⠀⢀⢠⣪⢫⢝⢧⢳⣢⡀⠀
⠀⠀⠀⠀⠀⠀⢄⡃⡂⠢⡈⠪⢈⠔⡕⡎⡎⡌⡎⡎⢯⢽⣝⠧⢟⢮⢯⣳⠳⡝⡎⡎⠬⡪⡎⡄⠀⠀⢀⢀⠆⡇⢷⢱⠁⡃⠃⢇⠃⠀
⠀⠀⠀⠀⠀⠘⢔⠨⢂⢑⢠⢵⣻⣎⢪⢝⢖⠌⡎⡎⣗⢽⣺⣢⢡⣈⣈⡠⡼⣜⢕⠅⢝⢜⡕⣷⣰⢰⢱⢑⢈⠀⡁⠐⠀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠍⢜⠘⡌⠢⣝⣗⣗⣟⡆⡝⣺⠨⡪⡪⣎⡗⡷⣝⣗⣗⢧⣟⢼⣣⢳⠁⡇⣗⢕⢷⡕⢕⠨⡂⠅⠃⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠠⡑⠠⣝⡞⡾⣼⣳⣇⢣⢳⡑⢜⢜⡜⡽⣽⢺⣺⣪⡗⣽⢣⢗⡕⢱⢸⢸⢪⣟⡎⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢔⡜⣞⡼⡺⣝⣞⣞⡗⡌⢮⢪⠸⡸⣜⢽⡺⡣⡣⣳⡫⣗⢯⡳⡱⠡⡪⡣⡻⣮⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⢜⡞⡼⣝⡞⣼⣳⡫⡂⢏⢎⠪⡪⡎⡗⡕⡇⣽⢺⢮⣳⣽⡟⡎⠜⡜⡌⣟⣮⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⢳⢝⡞⡼⣝⣞⡮⣗⠡⡫⡪⡊⢮⢝⢜⢜⢜⢷⢽⢽⣺⣟⢽⡘⠌⣞⠸⡵⣳⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢽⢸⡣⣏⡟⣼⣪⢿⢜⠄⡇⡗⡸⣨⢳⢕⢕⢭⢳⢽⢝⣞⣗⡗⡕⢡⢇⢝⢽⣺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⡫⣞⢼⣹⢺⢮⢯⣓⠌⢎⢎⠜⡜⣮⢻⣔⢕⢕⢽⣣⢗⡗⣯⡊⡜⡜⣜⢽⣺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢼⢜⢮⢳⡳⡽⡽⣧⣓⠨⢣⢣⠣⡣⡗⣽⢺⡪⡪⡺⣜⣗⢽⡗⡆⡪⡪⡪⣗⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡎⣗⡝⡧⣏⡯⣟⣞⢖⢑⢕⢕⢱⢩⡝⣷⢹⢜⢜⡼⣕⣗⣿⣛⢆⢪⠪⡮⣗⣗⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⡹⡜⣎⡟⣼⢺⢷⣝⣇⠢⡣⡣⡱⡱⡝⡎⡮⡪⣞⢮⣳⣿⢳⡣⡣⢸⠪⡮⣗⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢇⢯⢧⢯⣳⣫⣟⡞⣖⠡⡣⡣⡪⡪⣇⢇⢧⢻⢼⡝⣾⣻⡳⣝⠔⢕⢕⢽⣺⣺⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⢻⢼⡕⣗⣗⣯⢿⣜⠘⡜⡎⡜⡜⣦⢃⢏⢽⢪⣟⢼⢧⣟⢼⠨⢕⢕⢽⣺⡺⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢕⢕⡗⡽⣺⢺⡮⡿⣜⡘⢼⢸⢸⢸⡪⣗⡕⡕⢽⢜⣗⢽⣳⣝⠌⡇⡇⣟⢮⣟⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡕⣝⢽⢺⢽⢯⣟⣎⠆⡝⣜⢸⢸⡪⣗⡗⡇⡧⣹⢪⡗⣷⣳⠡⡣⡣⡫⡿⣼⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢕⢧⡫⣏⢯⣟⡾⣜⢌⢎⢎⢜⢜⢮⣳⢫⡣⡣⡣⣟⣾⣿⢕⢅⢣⢣⢫⡟⣾⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⢣⢻⢼⢽⣪⣟⡖⡄⡫⡪⢢⢳⡱⡱⢱⠱⣵⢹⢧⡳⣕⢗⠄⢣⠣⢧⢯⣳⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢝⡜⡮⣳⢳⣣⡓⢌⢜⢢⢡⢣⡣⡫⢧⡻⣜⢽⡚⡞⡮⡪⠨⡘⢌⢗⢧⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⣝⢜⢧⣓⠂⢕⣂⠢⡱⢱⢸⢱⢣⡫⣪⢳⢹⢪⢪⡞⣖⠨⠊⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠸⡸⡮⣟⡮⣗⠈⠌⠘⠸⠘⠜⠘⠸⡸⡪⣗⢽⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⢯⡗⣯⡳⠀⠀⠀⠀⠀⠀⠀⠀⡇⡗⡷⣝⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣗⢧⡟⣮⡊⠀⠀⠀⠀⠀⠀⠀⠠⡸⢸⢸⢸⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⡱⡱⡱⡣⡫⡪⡂⠀⠀⠀⠀⠀⠀⠀⡐⡜⢌⢎⢎⢎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⢯⡞⣼⣸⣸⢪⡪⡆⠀⠀⠀⠀⠀⠀⠨⡪⣎⢮⢮⢮⣳⣳⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⢳⢕⠗⡏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠌⠳⠹⠸⠪⠓⠀⠀

⠄⠄⣿⣿⣿⣿⠘⡿⢛⣿⣿⣿⣿⣿⣧⢻⣿⣿⠃⠸⣿⣿⣿⠄⠄⠄⠄⠄
⠄⠄⣿⣿⣿⣿⢀⠼⣛⣛⣭⢭⣟⣛⣛⣛⠿⠿⢆⡠⢿⣿⣿⠄⠄⠄⠄⠄
⠄⠄⠸⣿⣿⢣⢶⣟⣿⣖⣿⣷⣻⣮⡿⣽⣿⣻⣖⣶⣤⣭⡉⠄⠄⠄⠄⠄
⠄⠄⠄⢹⠣⣛⣣⣭⣭⣭⣁⡛⠻⢽⣿⣿⣿⣿⢻⣿⣿⣿⣽⡧⡄⠄⠄⠄
⠄⠄⠄⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⢿⣽⢘⣿⣷⣿⡻⠏⣛⣀⠄⠄
⠄⠄⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⡅⣿⠚⣡⣴⣿⣿⣿⡆⠄
⠄⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣱⣾⣿⣿⣿⣿⣿⣿⠄
⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠑⣿⣮⣝⣛⠿⠿⣿⣿⣿⣿⠄
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄