⣯⢿⡽⣯⢿⡽⡯⡿⣽⢽⡽⣽⢽⡽⡽⣽⢽⢽⢽⢽⢽⡽⡽⣽⢽⢽⢽⢽⢽⢝⡽⡝⡽⡹⡙⡍⡝⢽⢽⢝⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⣽⢽⡽⡽⣝
⣿⢽⢯⡿⣽⢽⡯⡿⣽⢽⡽⣽⣻⣺⢯⢷⣻⢽⣫⢿⢽⣺⢯⡗⡿⢹⢹⢩⠣⡣⡱⡱⡨⡢⡣⣮⣺⡪⡝⢝⢝⠹⡨⡙⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⡽⣝⣗⢯⢾⣝⣗
⡽⣯⢿⡽⣯⢯⡿⣽⢯⡯⣯⢷⢯⢾⢽⡽⣞⣟⣞⡯⣟⢞⢱⡸⡜⡕⢕⢅⢗⢍⠪⡢⡺⡼⣙⢪⣢⢣⠣⡑⣅⡻⡺⣪⡢⡫⡯⡯⡯⡯⡯⡯⡯⡯⣯⣻⣞⡾⣯⢿⣺⡽
⣿⢽⡯⡿⡽⡯⡿⣽⢽⡽⣯⢿⢽⢯⢿⢽⣳⣻⢾⠝⡔⢕⢼⢜⠕⡜⢌⢎⢢⠱⣑⡽⡘⡔⡜⡪⡂⢇⢣⠣⡢⢳⡱⡡⡫⣆⠝⡽⣽⢽⡽⣯⣟⡿⣽⣞⣷⣻⡽⣯⢷⣟
⡯⣿⢽⡯⣟⣟⣯⢿⡽⣯⢯⡿⣽⣻⡽⣯⢷⢋⠎⡌⡎⡪⡱⡡⡑⢌⠪⣐⡵⣝⣗⡯⣧⠣⢕⢑⢜⢸⢸⡘⡌⢆⢳⠸⡰⡘⢎⢘⢚⢯⣿⣳⣯⣟⣷⣻⣺⣳⣻⣽⣻⣺
⣿⢽⡯⣿⢽⣻⣞⣯⢿⡽⡯⣯⢷⣳⢿⢽⢍⢎⢮⢺⢕⡕⡱⡐⣌⢦⢗⡯⣞⣗⣗⣟⡞⡜⠔⢅⠎⡆⡗⢔⢌⠢⡑⡇⡣⡨⢊⠢⠡⡙⢞⣷⣻⣞⣷⡻⡾⣽⣳⣻⣞⣗
⡿⣽⢯⡿⣽⣳⣟⡾⡯⡿⡽⣯⢯⡯⣿⠱⡑⡼⡱⡩⣗⢕⣵⣺⣺⢽⢽⣝⣗⣗⣗⢗⠕⣜⢪⢪⡪⡣⡇⢇⢇⠕⡌⢇⢎⢆⢣⡑⡑⢌⠪⡳⣳⣟⡾⡽⡯⣗⣟⣾⣺⣳
⣯⢿⡽⣯⣟⣾⣳⣟⡿⣽⢿⢽⣫⣯⢣⠣⢝⢜⢕⣽⣺⢽⣺⡺⡮⡯⣗⣗⣗⣗⢇⢇⢧⠣⣕⢮⠪⡪⣞⢜⢔⠱⡘⡌⡪⡇⡇⡚⡜⢜⢌⢮⡳⣗⡿⡽⣯⣟⣞⣗⣟⣞
⣯⢿⣽⢷⣻⣞⡷⣯⢿⢽⡯⣟⣷⣻⡢⡹⣘⡼⣝⣞⣮⡻⡮⡯⡯⣯⣳⣳⡣⡣⡣⣺⢕⡝⡎⡪⢸⠸⡵⣣⠣⡑⢕⢸⢘⡺⡌⢇⢕⢕⢱⡐⢯⡯⡿⣽⣳⣗⣯⢷⣻⣞
⣟⣿⣺⣟⡷⣯⡿⣽⣻⣯⢿⣻⣽⡇⣇⣟⣞⣞⣗⣗⢷⢽⢽⢽⣝⣞⡞⡆⡝⣜⡞⢵⠱⡍⡪⡒⣕⢕⢽⡪⡎⢎⠪⡪⢢⢓⢕⢕⢅⢯⢢⢋⢞⣽⢯⣷⣻⣺⣞⣯⢷⣳
⢿⡾⣷⣻⡿⣽⣟⣯⡿⣾⣻⣟⡾⣧⣻⣺⣺⣪⣞⡮⡯⡯⣯⣳⣳⡓⢕⢱⣣⢗⣯⢟⣯⣟⣯⢗⢇⠣⡱⣝⠮⣊⢪⢪⢎⢜⢬⢧⢹⡸⡕⡱⢹⣺⣻⣞⣗⣟⣾⣺⡯⣷
⣯⡿⣯⣷⡿⣯⣟⣷⣟⣯⡷⣟⣽⣺⣺⣺⡺⣺⣪⢯⢯⢯⣞⣞⡎⢎⠪⡊⡎⢕⠌⡓⢗⢕⡍⢕⢐⡑⡜⢼⡑⡆⣳⢯⡷⣵⡹⣺⢸⢌⣗⠍⢦⢹⢾⣞⣷⣻⣞⣷⣻⡽
⢯⣿⣻⣾⣻⣯⢿⣺⢽⣺⢽⣳⣳⣳⣳⣳⢽⣳⢽⢽⢽⡵⣗⢳⢘⢌⢎⢪⢊⢢⠑⢌⠢⡂⡪⢐⠅⡢⠣⡑⡕⣅⢳⢝⢝⢜⠳⡵⣝⢆⢷⠩⡢⡇⣿⣳⣻⣞⣾⣺⣗⣿
⣻⣽⡾⣷⣻⡾⡯⡯⣟⡾⣽⣺⢵⣻⢮⣗⣟⣮⢯⣯⢯⢏⢪⢢⠣⡊⡪⡢⡃⡪⢊⠢⡑⠔⢌⠢⡑⠌⢜⢐⢑⢌⠪⡱⠡⡊⢜⣞⣞⢼⢽⢘⢔⢽⣸⢾⣳⣟⣾⣳⣟⣾
⢯⣷⢿⢯⡷⣯⢿⣽⣳⢯⣗⢿⡽⡾⣽⣺⣺⢽⣛⢞⢕⢌⡎⣎⠪⢌⠆⡇⡪⡂⡅⢕⠨⡘⢄⠕⡨⡘⢄⠕⡐⡢⢱⠨⡊⢌⣞⣞⡎⣞⡝⢜⡬⡿⣽⢯⡷⣟⣾⣳⣟⣾
⣿⢽⡽⣯⢯⡯⣟⡾⣝⡷⣯⣻⣺⣟⣞⣾⣺⢧⢳⣻⢘⢔⡳⡸⡘⡔⡕⡕⢕⠔⡑⢔⠑⢌⠢⡑⡐⢌⠢⡑⢌⠢⡑⢌⠢⡑⣼⣪⡎⣖⢕⣽⢮⡿⣽⢯⣟⣯⡷⣟⣾⣳
⣺⢽⣽⣺⢽⡽⣳⢯⣗⣯⣗⡷⣻⣺⡳⣳⢯⣣⢷⣝⢆⢅⢷⢱⠱⡘⣜⡎⢆⡓⢌⠢⡑⢅⠪⡐⢌⠢⡑⢌⠢⡑⢌⠢⡑⣸⡺⣜⢎⡖⣯⡷⣿⢽⣯⢿⡽⣗⡿⣯⢷⢿
⣺⣽⣺⢾⢽⢽⣝⣗⣗⣿⣺⡽⣯⢷⣻⢽⡽⣼⣳⣳⠡⡃⣟⣎⡎⡪⡸⡮⡪⡸⡐⢅⠪⡐⢅⠪⡐⡑⢌⢢⠑⢌⠢⡑⣜⢮⡳⡱⣱⡏⣯⡿⣽⣟⣾⣻⣽⢯⡿⣽⣻⣻
⣗⡷⣽⢽⢽⡽⣺⣞⣵⣟⣾⢽⢯⢯⣗⢿⡽⣺⣺⡎⢎⢪⢞⡮⣎⠎⡜⡞⡆⡇⡇⡢⡑⢌⠢⡑⡐⢅⠅⠕⢌⠢⣑⣞⢮⡳⡇⡇⣯⡯⡷⣟⣷⣻⣞⣿⣺⣯⢿⣽⡽⣗
⢽⢽⣺⡽⡯⣞⣷⣳⢷⣻⢾⢽⢽⢵⡳⣯⢯⡷⡯⡗⡱⣱⡻⡺⣳⠱⡘⢮⢇⢇⢏⢮⢪⡢⡑⢔⠡⡑⢌⠪⣂⢗⣗⣗⡇⣯⢣⢣⢯⡿⡽⣯⢷⣯⡷⣟⣾⣽⣻⣞⣯⣿
⣟⣽⣳⢯⣿⡽⣞⣗⡿⡽⡵⡯⡯⣳⣫⡯⣯⢯⢿⢱⢑⡼⣎⡞⣵⣫⢸⢸⢽⢸⢜⢎⢮⢪⢝⢖⣵⣌⣆⢵⡺⣝⡮⣞⡎⡜⡦⣹⡯⣟⣯⢿⣽⢾⡯⣟⣷⣻⢾⣽⢾⣳
⣞⡾⣞⣟⣮⢯⣗⣯⢯⣟⣽⢽⣺⣳⡽⣽⢽⡽⣣⢇⠵⣝⣮⢱⢱⣳⡱⡨⣫⢎⠮⡣⡳⡱⣓⣯⢷⣻⢮⣻⡺⣕⣯⢗⣇⢕⢭⢺⣽⢯⣿⢽⣾⣻⣽⢯⣷⣻⣟⣾⣻⡽
⣷⣻⢽⢪⢷⣻⢞⡾⡽⣞⡾⣽⡳⡯⡯⡿⣽⡻⣼⢸⡸⣵⣳⢝⡮⣞⣎⠆⢯⢎⠜⣜⢘⠍⣮⣗⡿⣯⣻⡺⡺⣜⢾⢝⡮⡢⡣⢽⢾⣻⣾⣻⣗⡿⣾⣻⣗⣿⣺⣗⣯⣟
⡯⣞⡸⣜⣟⡾⣯⣻⢽⡽⣽⡳⡯⡿⣽⣫⢷⢝⣾⢢⢟⡼⣎⠣⡫⡳⣳⢍⢎⠧⡅⡇⣊⠪⡺⢸⡽⣗⡷⣝⡇⣟⣼⣫⢽⢌⢎⢎⢿⣳⣗⣿⣺⢿⣽⢾⣞⣷⣻⢾⣽⣞
⢙⠮⣞⡷⣯⣻⣗⣯⢯⡯⣗⡿⣽⣫⣗⡯⣯⣻⣺⢜⡯⣳⡻⡮⡰⣑⡽⡪⡢⡣⣕⣓⢔⡹⣌⠎⣿⢽⢽⣺⢪⣣⡷⣯⢗⡧⡣⡹⡜⣿⣺⣗⣿⣻⢾⡯⣷⣻⣾⣻⣳⢿
⢂⢇⢓⣟⡷⣗⣯⢿⡽⣽⢽⡽⣳⡯⡾⣽⣳⣻⣺⡕⣯⢗⣯⢟⣮⣂⡏⡧⡳⣕⢮⡺⣳⢹⡴⣹⢯⡿⣽⣺⠢⣗⣿⣽⣳⡻⡼⡌⣧⢳⣟⣾⣳⢿⣽⣻⡽⣗⡿⣞⣟⣿
⠢⡣⢱⢰⢹⡻⣞⣯⢿⡽⣽⢽⣳⣟⣯⢷⣻⣺⡵⡯⣗⡯⡯⣟⣞⡮⣗⡧⡫⡪⡚⢎⢗⠵⣻⢽⢯⣟⡷⡽⡕⡽⣾⢾⢮⡯⣯⢪⣺⢽⡽⣞⣯⡿⣾⢽⡯⣿⡽⣿⢽⣾
⣳⡪⡪⡸⡰⡩⣗⣯⢿⣽⢽⢯⣗⣷⣻⢯⣷⡻⣞⣯⢯⡿⡽⣽⢾⣺⢯⡇⡯⣫⢎⣪⡺⡘⣜⠿⣜⢆⢟⣯⣗⠭⡯⣿⣱⣟⡗⣕⣯⣗⡿⣯⡷⣟⣯⡿⣯⡷⣟⣯⣿⣳
⣲⣝⢵⣪⠪⣳⢪⢯⣟⣾⣻⡽⣾⣺⣞⣿⣺⢿⡽⣞⣯⢯⡿⣽⢽⣞⣯⣗⡿⡝⡱⡰⡣⡱⣹⢵⡻⣪⡪⢪⡺⣻⢮⢷⣻⣺⢝⣼⢾⣺⡽⣷⣟⣿⣳⣟⣯⣟⣯⣷⣯⢿
⣳⡯⡷⣎⢯⢮⡣⣻⣞⣾⣳⢿⣳⣟⣞⣷⣫⣯⢿⣻⣞⣯⡯⣯⣟⣞⣗⢷⣱⡑⡕⢜⢇⢕⡺⡵⣫⢗⡝⣆⢏⢮⠪⡻⣳⢯⣯⡯⣯⢷⣻⣗⣿⣺⣽⣽⢷⣻⢷⣻⣾⣻
⣷⣻⣻⡽⣯⡳⡝⣼⣗⡷⣯⢿⣽⢾⣽⣞⡷⣯⣟⣷⣻⢷⣟⣷⣻⢪⢣⣿⡺⡱⣸⠼⡸⡰⡝⡜⣝⡵⡽⡌⢧⡫⡇⡇⡮⣝⢾⡽⣯⣟⣷⣻⣞⣷⣳⣟⣿⣽⣟⡿⣞⣯