⣿⡿⡿⡟⢟⢛⠛⢟⠿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢘⢌⢎⢜⠸⡹⢕⢱⡱⡳⣝⠼⡸⠯⢇⢣⢣⢣⢛⣿⠻⡉⡆⣕⢕⢍⢊⠢⠡⠐⢀⠐⡀⠄⠂⡀⡂⡐⠠⠂
⡿⠩⢁⠂⢅⢐⠨⡐⠨⡐⡡⢋⢛⠿⣟⣿⡿⣿⡇⡪⡘⢔⢑⢌⠪⡘⡸⠨⡊⠜⠠⡁⡂⢅⢑⠌⡢⠡⢑⠨⢊⠜⡘⡘⡐⡐⡀⢂⠂⠨⢀⢂⠐⠠⠁⠄⢂⢐⠡⠡
⠅⠌⡐⠨⡂⠕⡨⠢⡱⢰⢘⢌⢆⢇⠇⠇⠝⡁⡂⠢⢊⠢⢑⢐⠅⡑⠌⠌⠄⢅⠑⢌⠂⠕⡐⠅⡊⢌⠢⠨⡐⡐⡐⢌⢂⠆⡢⡂⠌⠌⠄⡢⠨⡨⡈⡂⠅⡂⢌⢌
⠨⡂⡪⡐⢌⢊⠔⡑⡌⢆⢣⢱⢡⠑⠌⡨⢐⢐⠨⠨⢂⠅⢕⢐⢑⠌⢌⠪⠨⢂⢑⠔⡡⢑⠌⠢⡨⢂⠪⡨⠢⡊⡌⡪⢢⠣⡪⡨⢪⢘⠌⡔⡡⡂⢆⢊⠔⢌⢢⢱
⢅⠪⡐⢌⠢⡑⡌⡆⡣⡱⡡⡣⠪⠨⢂⢂⠢⡂⠅⢅⠅⠪⡐⢌⠢⡡⢡⢑⠅⢕⢐⡑⡌⢆⢕⢑⢌⢆⢣⠪⡪⡸⡨⡪⡪⡪⡊⡎⢆⢣⢑⠢⡒⢌⠢⠢⡑⢅⡣⢕
⣧⠂⢌⠢⡑⢅⢣⢊⢎⢢⢣⠣⠑⢅⢑⠐⢅⠢⠡⡑⢌⠪⡐⢅⠪⡐⡑⢔⠡⡡⡑⡌⢜⠔⢜⠰⡑⡜⢔⠕⡕⢜⢌⢎⢆⠇⡇⡣⡣⡱⢨⢊⢌⢆⢣⢹⢸⠸⡌⣇
⣿⡌⠄⡂⠪⡘⡌⡎⡜⡜⠔⠡⠡⡡⢂⠅⢅⠪⠨⡂⠕⡨⢂⠕⡨⢂⠕⡡⠪⡐⡌⡜⢔⢕⢱⢑⢕⠕⡕⡕⡕⡕⡕⡕⡱⡱⡱⡱⡑⡜⢔⢱⢘⢔⠕⡕⡕⣕⠵⣕
⣿⢧⠂⠌⢌⢢⢱⢸⠸⡈⠌⠌⡌⠔⠄⢅⢑⠌⡪⢐⠅⡊⠔⡡⢂⠕⢌⠢⡣⡑⡌⡜⡔⢕⢅⢇⢕⠕⡕⢅⢇⢣⠣⡣⡣⡣⡣⡣⡣⡣⢣⠣⡱⡡⡣⡣⡳⡕⡽⡸
⣿⢿⡥⢑⠨⢂⢕⠕⡡⠂⠅⢕⢐⠡⡃⢕⢐⠌⡰⠠⢑⠨⢂⢌⢂⠪⡐⡱⢨⢢⠱⡨⡊⡎⡆⡇⡕⡕⡕⢕⢕⢕⢱⢱⢱⢱⢱⢱⢱⡸⡂⡇⢇⢇⢧⢣⢣⢝⢮⢯
⡽⣟⣿⡐⡨⢐⠅⢅⢐⠨⢈⠢⣣⢪⠐⡅⡂⡊⠄⡊⠄⠅⢅⠢⡡⡱⠨⡊⢆⢕⠱⡘⡌⡆⢇⢕⢕⢕⢜⢜⢜⢜⢜⢜⢜⢜⢜⣼⣯⠫⡨⢪⢪⢪⡪⡎⡧⡫⣝⡽
⣝⢽⣟⣷⡐⢅⢁⠢⠐⡈⠄⡊⡎⢷⡕⡐⡐⠄⠅⡂⠅⠅⡅⢕⠬⡘⡌⢎⢊⢢⢑⢅⢇⢎⢎⢎⢆⢇⢪⢜⢜⢜⢎⢇⢗⣵⣽⡾⡕⡕⡸⡘⡜⡜⡜⡜⡎⡧⣳⣫
⡮⣳⣻⣟⣿⡐⠠⠨⢐⠠⠡⢘⢜⢔⠝⣆⢂⠅⠅⡂⢅⢑⠌⡢⢱⢘⢌⢎⢪⢊⢎⢪⠢⡣⡪⡪⡢⡣⡣⡣⡳⡹⣜⢵⡿⣞⣗⡯⡯⡎⡪⡪⡪⡪⡪⡪⡎⡾⡵⡽
⣝⢞⡼⣻⣽⣧⠡⢁⢂⠂⠅⠌⡎⡆⡃⡪⣗⡄⢅⢂⢂⠢⡑⢌⢢⢑⢕⢸⠰⡑⡅⡇⡇⡇⡎⡎⡆⡇⡇⡇⣗⡽⣞⣯⢏⣞⡮⡯⡯⣎⠪⡢⡣⡣⣣⢳⡱⣝⢮⣫
⣞⣝⣞⣿⣻⣿⡌⠔⠠⡁⡊⠨⡪⡪⡂⡪⡾⡅⠣⣂⠂⠅⡂⠕⡨⢢⠱⡘⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⣜⣮⢿⢹⣿⡳⣳⢯⢿⣝⡇⡕⡕⡎⡮⡪⣎⢞⢮⢗⣽
⣞⣾⣾⣻⣿⣽⡧⠨⡈⠢⡈⠢⢱⢱⢱⢐⢽⣲⡠⣝⢯⣆⢂⠅⠌⡆⡣⡣⢣⢣⢣⢣⢣⢣⢣⡣⡣⡣⣷⣿⣞⢘⡾⣗⡯⡯⣯⢷⡳⡑⡜⡜⡜⡜⣜⢜⡎⡯⣳⢳
⣿⣯⣿⣽⣷⣿⣿⡐⠌⠌⢌⠪⢐⢑⢕⢅⢂⠳⡯⡞⡡⢙⢶⣨⢈⠢⢱⢸⢸⢸⢸⢸⢸⢸⢱⡸⣜⡿⡽⣺⣟⣷⡿⡯⣞⣯⢯⡻⡘⢄⢇⢇⢇⢇⢧⡳⡹⣺⡪⣿
⣿⡷⣿⣯⣷⣿⢷⡇⠌⡊⠔⠡⡂⠢⢑⠕⢕⢅⢅⢂⢐⠔⡔⡝⢵⠨⢐⢘⢌⢎⢎⢪⢪⢪⢮⡟⡭⡳⣫⣗⡯⣟⣽⢽⣳⢫⠣⢂⢪⢪⢪⢪⢪⡣⡳⡱⣝⢞⡮⣟
⣿⣻⣯⣷⣿⣻⣿⣗⠡⢂⠅⠕⡑⣕⢔⠨⠨⡘⡘⠜⢒⠙⡘⠨⠐⠅⢅⢂⠢⡑⠜⢌⠎⡞⢕⠹⡸⢜⢎⢮⣪⢳⠝⢕⠡⡂⡎⣎⣾⢺⠸⡸⡸⣸⢱⢕⢗⡽⡽⣽
⣿⢿⣽⣯⣿⣯⣷⣿⠨⡐⠌⡊⡐⡸⢕⡣⣇⢔⢐⠡⢂⠅⡪⠨⡊⢌⠢⡡⡑⡌⣊⢢⠱⡘⡔⡱⡘⡔⢅⢕⢔⢡⢊⢆⢧⣺⡺⣯⠇⢕⢨⢪⡪⡎⡮⣪⢗⡯⣯⢿
⣿⢿⣯⣿⡾⣯⣿⣻⣇⢂⢑⠨⠐⢌⠪⣇⢆⢫⡗⡵⣅⡪⡠⢑⢈⠢⡑⢌⢢⢑⠢⡅⡣⡱⢨⠢⡣⡪⡪⡢⣣⣣⢯⣟⢝⢜⣞⢏⢌⢢⡳⡫⢪⢺⡸⣪⢗⣟⡾⣿
⣿⣟⣿⡾⣿⣻⣯⣿⢷⡂⠢⠨⠨⠠⢃⢘⢖⡕⣯⠨⡪⡩⡋⣷⠣⢧⢮⡪⡦⣕⣕⣜⣬⣪⢮⢾⣺⣞⢳⢹⢸⢸⢪⣟⢜⣼⢏⢢⡪⡣⢱⢸⢸⡺⣪⢗⣟⣮⣿⣻
⣿⣽⣷⣿⢿⣻⣽⣾⣿⢷⡡⠡⠡⠡⢑⢐⢁⠻⣼⡊⡆⡕⡱⣹⡝⡌⡲⡸⡸⡸⣗⡒⡲⡘⡜⡔⡵⡯⡪⡊⡎⡪⣺⡿⣞⠣⣱⠣⡑⢌⢪⢢⡳⣝⡵⣟⣞⣾⢷⣿
⣿⢷⡿⣾⡿⣟⣿⣽⣾⡿⣷⡡⠡⡁⡂⡊⡄⢅⠢⡙⠮⣪⡸⣸⡇⡇⡕⡜⡌⢮⢷⢱⠱⡱⡱⡱⣹⣏⢆⢇⣧⣫⡞⠝⢄⢣⠇⢅⢪⢸⢸⢜⢼⣪⢯⣟⣾⣟⣿⣽
⣿⣻⣟⣯⣿⣟⣯⣿⡾⣿⣻⣧⡑⡐⡰⢐⠸⡠⡑⢄⢑⢐⢙⢜⠻⠼⣜⣔⣕⣕⣿⣱⢱⣱⣸⣜⡾⡷⡳⠛⢍⢂⠆⡕⡱⡝⢌⢪⢢⡳⣕⣝⢷⡽⣯⣟⣷⣿⣽⣾
⣿⢯⣿⢯⣷⡿⣯⣷⡿⣿⣽⢷⣷⡌⡢⠡⣑⢑⡌⡢⢑⢌⠢⠢⡑⢅⢂⠢⡊⢌⢊⠍⡩⠊⢌⢂⢆⠢⣊⢪⢢⢣⢣⡳⡽⡸⡸⣜⣞⢮⣳⡽⣯⢿⣽⣾⢿⣞⣿⢾