⡪⡐⡑⡌⡢⢱⠨⡢⡃⢎⢌⢆⠣⡪⢸⠨⡪⡸⡨⡪⡸⡨⡪⢪⢸⢘⢌⢎⢪⢊⢎⢪⠪⡘⡌⡎⡜⡌⡎⡜⡌⢎⠜⡐⡐⡐⢀⢂⢂⠐⣐⣐⣴⢴⠶⡶⡶⡆⢂⠂⡂
⡢⢊⠢⡑⢌⠆⡣⢒⠸⡐⠕⢌⠪⡂⡣⡱⡑⡌⡆⡕⡌⡆⡣⢣⢑⢕⢅⢧⢱⣡⡣⡣⡑⢕⠱⡘⣔⡵⣜⣦⣣⣵⣴⡾⣶⢷⢶⢶⣳⢟⢽⡱⣕⢧⣻⡺⢉⠐⠐⡈⠄
⣮⢦⣵⡬⣦⣱⡬⣦⣧⣳⡽⣦⣕⣡⢱⡐⢡⣑⣐⢌⡦⡮⡬⢢⡣⣷⣳⣞⣗⣿⣲⢵⢪⡮⣳⢾⡷⣻⣽⣯⣿⢿⢽⡽⡽⡽⡽⣝⢮⣫⡳⣕⣗⠗⠃⠀⠄⢀⠁⡀⠀
⣗⢯⡺⡽⡽⡽⡽⣳⣯⣻⡻⣯⣿⣮⣟⣗⣻⢽⠽⡈⢳⠉⡀⡃⡽⣵⣳⢷⣳⣟⣞⡯⡯⡯⣟⡿⣞⣿⢿⣾⣿⢿⣽⣞⢽⢯⣟⡮⣗⢧⡳⠃⠅⠠⠈⢄⠨⠀⠄⠄⠂
⡑⠕⡇⣯⣺⢵⣯⣷⢿⢾⣟⣷⣯⣗⢿⣝⢮⡝⡑⠠⢀⠐⠀⠌⡜⣼⣺⡽⣷⣻⣺⣵⣻⣯⢯⢯⣯⢯⣿⣽⣟⣿⣟⣾⢯⣧⢳⣻⠮⠋⠄⠅⠅⢅⢑⢐⠨⢈⠂⠅⠅
⠐⠈⠄⡑⢎⢗⣳⢽⡽⣷⣟⣾⢮⣻⣺⢮⡳⡅⡂⠌⠠⠠⠁⢂⠸⡼⣾⢽⣻⣞⡷⣯⡷⣿⣽⣗⣷⢯⡷⣟⣿⣾⢿⣽⡿⣯⢏⠢⠨⠨⢈⠌⠌⡐⡐⡐⠨⠠⠡⠡⢑
⠀⠅⢂⠐⡀⠽⣯⣟⣽⣷⣳⡯⣟⣾⣳⢯⣷⣗⡄⠅⠅⡂⠡⠐⢈⠺⣺⢽⣗⣯⢿⡽⣟⣿⣾⣿⢾⣟⣯⣗⣟⡾⣿⣯⡟⡟⡐⠨⠠⢑⠐⠨⢐⢐⢐⠨⠨⠨⠨⠨⢐
⢈⠐⡀⡂⡐⠈⡜⣿⣗⣟⣮⢿⣻⣯⣿⣿⣷⣷⣣⢣⢑⠐⡐⠈⡀⠂⢕⢯⣳⢯⢯⡿⣿⣿⣻⣹⣿⣟⣯⢷⣯⣿⣳⣿⣩⠐⡠⠡⢁⠢⠨⠨⢐⢐⢐⠨⠨⠨⠨⡈⠢
⠀⡂⢐⠠⠀⠅⢸⣽⣯⡿⡽⡯⣿⣿⣻⣷⣿⣿⣷⠱⡢⢁⠂⡐⠀⠌⠠⢳⢹⣝⢷⣿⣿⣿⣿⣿⣿⣿⢺⡳⣽⡾⣷⣻⣞⠇⡂⠌⡐⠨⢐⢁⢂⢂⠢⠨⠨⡈⠢⠨⠨
⢀⢂⠐⡀⠅⠌⣈⢾⣳⢿⣝⣯⢿⣿⢿⣿⣟⣿⣽⡊⠢⡁⡂⡂⠡⠨⠠⢱⢝⣮⢿⡮⢿⣟⣿⣻⣽⣞⢽⢾⣻⣻⣷⡁⠢⠨⠠⠡⠨⠨⢐⠐⡐⡐⠨⡈⠢⠨⠨⠨⠨
⠠⠐⡀⢂⠐⡐⠠⢙⣽⣟⣾⣺⢮⣟⡿⡽⡾⣯⢿⢌⠊⠔⡐⠄⠃⢅⠨⢐⠹⡺⣯⢿⡧⣝⡽⣯⣗⣗⣯⣯⣿⣽⡿⡧⡡⠡⢁⠅⠅⠅⡂⠅⡂⡂⠅⡂⠅⠅⠅⢅⢑
⠐⠐⡀⠂⡂⠄⠅⠂⢽⣞⣿⢾⣳⡳⡝⡏⠯⠪⠹⢂⢅⢑⠀⢂⢁⠂⡂⠂⠌⠍⡯⡗⣯⢗⢽⣳⣳⣻⣽⡿⣷⢿⣽⡃⡂⠅⠢⠨⢐⢁⠂⠅⡂⡂⠅⡂⠅⢅⢑⢐⢐
⠠⠁⠄⠡⠐⠠⢁⢑⢺⢯⣟⣿⡳⡯⡣⠁⠅⠡⢁⠢⢂⢐⠈⡀⠄⢂⠂⠡⠨⠐⡑⡝⡼⡝⣽⠺⡳⡿⡿⣿⣻⢟⠿⡆⠢⠡⠡⡑⡐⠄⠅⠅⡂⡂⠅⡂⠕⡐⡐⡐⡐
⠈⠄⠡⠁⠌⡐⢐⠐⠨⡹⣳⣽⢝⢌⠄⠡⢈⠌⢄⢑⠅⡐⠐⠠⠨⠐⠨⠠⢁⠅⡂⢂⠁⡐⠈⠍⠏⡯⣟⣿⣻⣟⠡⠊⠌⢌⢂⢂⠢⠡⠡⡑⡐⡐⠡⠂⢅⢂⢂⢂⢊
⠌⠄⡑⠨⢐⢐⠐⠌⠢⢹⢝⡮⡫⡪⢈⠌⡀⡂⠡⢂⠅⡂⠅⠅⡊⠨⡨⠠⡁⡂⡂⠄⠂⠠⠁⠡⠡⡯⣿⢽⡱⢐⠡⡡⡡⠡⡂⡢⢡⠡⡁⡂⡂⢌⠌⡌⡂⡂⡂⡢⢂
⠄⡁⢂⢁⠂⡂⠌⠌⣌⢦⣳⣙⣮⠪⠠⠑⠄⡂⠅⠡⡣⡪⡸⡐⡌⡢⢪⠰⡐⡅⡂⠌⡀⠡⢈⠄⢑⢭⣺⡲⢿⡦⡃⢆⠪⡨⢂⠪⡐⢅⠢⡑⠌⡢⢑⢐⠌⡢⢑⠐⢅
⠄⡐⡀⢂⢐⠠⠡⣕⣗⢽⣺⠾⣺⢝⠌⡂⡑⠄⠅⠅⡪⢮⢮⡪⣪⢎⢮⣺⠪⠂⡐⡀⢂⢁⢂⠌⡐⡔⢗⢝⠕⡊⠢⠡⢂⠊⠔⡁⡊⠄⢅⠢⢑⢐⠡⢂⢑⠄⠅⢅⠅
⠡⢐⢐⢐⢐⠌⣪⢞⣖⡯⣯⣿⢻⢘⡨⠰⡘⢌⠪⢪⢐⢕⢝⢝⡮⣳⢝⠢⡁⡊⡐⡨⢂⠡⡢⡱⡱⡰⢅⢂⢑⠨⠨⢊⢐⠡⢑⠐⠌⢌⢐⠨⠐⡐⠨⢐⠐⠌⢌⠢⠨
⢑⠰⡐⡐⠅⢜⢮⣗⣗⢟⣭⡼⣺⢭⢂⠇⢕⢑⢍⢆⢇⢕⡜⣜⢜⣽⢜⡕⡕⡕⡜⡔⡕⡅⡇⡮⡘⠌⡜⡐⡑⠌⢌⠔⡠⡑⡐⡡⢑⢐⢐⠨⢐⠠⡁⠢⠡⡑⡐⠌⠢
⠢⡑⡐⠌⢜⢼⢽⡮⡾⣝⣼⢯⡧⡇⡣⡑⡕⡕⡕⡕⡕⡕⣕⢳⢝⣗⡽⡮⣳⢹⢜⡪⡎⣇⢗⢜⢜⢕⡈⢆⠪⡨⡐⡨⢂⠪⡰⠨⡂⠆⢅⢊⢐⠔⢌⠪⡨⢂⠢⠡⠡
⠅⡢⠨⡊⢼⣝⣗⣯⢿⢽⡵⣟⣯⢞⡎⢎⢪⡪⢆⢇⢇⡇⡇⡇⡇⡇⡏⣝⢜⢬⢇⢗⢝⢆⢇⠇⡆⠕⠌⠄⡑⠌⢆⠪⡨⡊⢔⢑⢌⢊⠢⡑⡐⢅⠕⢌⠢⡑⢌⢊⠌
⡑⡐⢅⢮⣻⣞⣷⢻⣝⣯⣟⣽⢯⡯⢎⢎⢎⢎⢎⢎⢎⢎⢎⢮⢺⢸⢪⡪⡳⡹⡪⡳⡱⡱⡐⠅⠢⢑⠡⢑⠰⡩⠢⡃⢎⢌⢢⠱⡐⢅⠪⡐⡅⢕⠸⡐⡱⡘⢔⢐⠅
⠌⡂⣗⣿⣻⡾⣺⣟⣷⣫⣾⣻⡿⣩⢮⡪⡪⡪⡪⡪⡣⣫⢪⡪⡪⡣⡇⡗⣝⢜⣕⢕⠕⡌⢆⠅⠅⠢⡑⢅⡂⠌⡣⢪⠢⡱⡐⢕⠸⡨⢊⢢⢑⢅⠣⡑⡌⡢⡑⢔⠡
⠅⠪⣾⣟⣿⣿⣿⣯⣽⢷⣳⣿⣻⣯⢷⠱⡱⡱⡸⡪⡺⡸⡜⣜⢜⢕⢵⢹⡸⡸⡸⡢⣃⠪⢘⢜⢌⢪⢀⠣⡊⡢⡑⡑⡌⢆⠪⡘⡌⡌⣊⢢⠱⡨⠪⡨⢢⠱⡨⠢⡡
⡊⢜⢺⣿⣽⣾⣿⣽⣾⣯⡿⣞⣿⢾⣗⡯⡣⡣⡣⡣⡫⡪⡪⣎⢮⢣⢳⢱⢕⢕⢕⢸⢸⢈⢔⢕⠡⡊⡢⠘⡌⢆⢣⠱⡘⠔⡅⡣⢊⢢⠢⢅⢕⢘⢌⢊⠢⡑⡌⡪⡐
⢌⢆⢳⣻⣟⣿⣿⣿⡿⣾⣟⣿⣽⣟⡷⣝⡜⡜⡜⣜⢜⢎⢇⢇⢧⡫⡎⡮⡪⡪⡂⡪⡪⡂⡪⡨⢢⢊⢐⠡⡪⡘⢔⠱⡘⡌⢆⠪⡊⡢⡑⡑⡌⡢⢅⠕⡡⠱⡨⠢⡊
⡑⢔⢱⢫⣿⢿⣻⢽⡫⡳⣕⢗⡽⡯⡿⡽⡸⡸⡸⣸⢸⡱⡕⣝⢜⢎⢎⢎⢎⢎⢎⢐⢌⢐⢐⢌⢢⢃⠆⢕⢌⢪⠸⡨⡢⡑⡅⡣⢱⠨⡘⡌⡢⡑⡅⡪⡘⢌⠢⠣⡑
⣊⠢⡑⡕⡍⡏⡎⡇⡗⣝⢼⡱⣝⢮⡻⣽⡣⡣⣣⢣⢇⢧⢳⡱⡹⡸⡱⡱⡡⡣⡣⡢⢘⠤⡑⣔⢕⢅⢣⠱⡨⠢⡃⡪⡂⠕⡌⢜⢐⢅⠕⢌⢢⢑⠌⢆⠕⡡⡱⢑⢅
⠢⡑⡑⡜⢌⠎⡎⡎⡎⡎⡎⣞⢼⡱⡽⣽⣎⢎⢎⢮⢺⢸⢱⢱⢹⢸⢱⢱⢹⢌⢎⢆⢕⢕⡝⣜⢎⢢⢑⠕⡌⢕⢱⠨⢌⢪⠨⡢⡑⡢⠣⡱⡐⢅⠕⡅⢕⢌⠢⡱⡐
⠣⡑⡌⡪⡂⡇⡣⡪⡪⡪⡪⡪⢮⣚⢮⢺⣳⡕⣕⢵⢱⢕⢕⢇⢗⢕⢕⡕⡧⡳⡱⡕⡜⡎⡞⡜⡜⡔⢅⠕⡜⢌⢆⢣⠱⡨⡊⡢⡱⡘⡌⢆⠪⡂⢇⠪⡢⡡⡃⡪⠢
⢑⠌⡆⢕⠜⡌⢎⢪⠪⡪⡪⡪⣓⢎⢮⢳⣹⡽⣮⢮⣎⡎⡎⡎⣎⢮⢣⡫⣺⢸⢕⢵⢱⡹⡸⡸⡸⡨⠢⠱⡘⡔⡱⡐⢕⢑⢜⢰⠨⡢⡊⢆⢣⢑⢅⠣⠪⡰⡘⢌⢪
⠢⡱⢸⠨⡪⡸⡘⡜⢜⢜⢜⢜⢜⢜⡕⡧⡳⣻⣽⣻⣞⡷⣝⢜⣜⢎⢧⢫⡪⡎⡞⣜⢕⡕⣝⢜⢌⢎⠜⡌⡪⡨⢢⠣⡑⢅⠆⡕⡱⡐⡅⢕⢌⢢⢑⢕⢑⢢⢑⢅⢕
⢌⢊⢆⠣⡑⢔⠱⡘⢜⠔⢕⢱⢱⢱⡱⡝⡎⡯⣟⣿⡾⣿⢽⣵⡪⡳⡹⡜⣜⢜⢜⢜⢜⢜⢜⢼⢸⢰⠱⡨⡒⡸⡐⡱⡘⢔⠕⡌⢆⢕⠸⡐⠕⡌⢆⢪⢘⠌⡆⢕⢌
⡐⠅⠆⢕⠌⢆⢕⠸⡐⢕⢱⠡⡣⡣⡪⡪⡺⡸⡪⡷⡿⣟⣿⣞⣷⡹⡸⡪⡪⡪⡪⡪⡪⡪⡱⡱⡱⡱⡱⡑⡌⡆⡪⡂⢎⠢⡃⡪⠢⡪⡘⡌⢎⠜⡌⡢⡑⡱⢨⢒⠌
⠨⠈⠌⡐⠨⠐⠠⢑⠈⡂⠅⡑⡈⡂⠅⡑⠡⠩⢘⠨⠙⠍⡋⡛⢚⠓⠕⠕⠕⠕⡑⠕⠜⠌⢎⠪⢊⠎⠪⢊⠪⢊⠢⠃⠕⡡⢃⢊⢊⠢⠑⠌⠢⢑⢈⠂⠅⠌⡐⢐⠨
⠠⠁⠅⠄⠡⠨⠈⠄⢂⠂⠡⢀⠂⠄⠡⠠⠡⠈⠄⠌⡈⢐⠀⡂⠂⠌⠠⢁⠁⠅⠄⠡⠈⠌⠠⠈⠄⠨⠈⠄⠨⠠⢈⠨⠐⢀⠂⡐⠠⠈⠄⡁⠡⠐⠀⠌⡀⠡⠀⠂⠐
⠅⠡⠨⠠⠑⡈⠨⠐⢐⠈⡐⢐⠈⠄⡁⠂⠌⠠⢁⠐⡀⠂⡐⠀⠌⢀⠡⠀⠂⠐⠈⡀⠁⠄⠁⠄⠁⠂⡁⠈⠄⠂⠠⠐⠈⡀⠐⡀⠂⠁⠄⠐⠠⠈⠐⡀⠐⡀⠁⠌⠀
⠡⠡⠈⢄⠡⠠⠡⠨⢀⠂⡂⠂⢂⠡⠀⠅⠨⠐⢀⠂⠠⠁⠠⠈⠄⠂⡀⠂⢁⠈⠠⠀⡈⢀⠁⠄⢁⠐⢀⠈⠠⠈⠀⠂⠁⡀⠂⠠⠈⠠⠈⡀⠂⡈⠄⠐⢀⠐⠈⡀⠂