⡽⡸⡭⣝⣝⣜⢧⣻⢨⢸⢕⠯⡹⡹⢝⡝⣕⢧⢡⠑⡝⣝⢎⢯⢎⡗⣝⢎⢗⢝⢎⢗⢵⢹⢜⢎⢞⢜⢎⢮⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⢪⠪⡊⡎⡪⡊⡎⡜⡌⡪⡘⡌⡪⢌⠪⡌⡪⡘⡌⡪⡸⡨⢪⢸⢨⠪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡺⡀⢘⠄⢪⢣⣣⢳⢱⢕⢝⡜⣎⢞⡜⡮
⡯⡝⣞⢞⣖⢵⣓⡯⡂⣳⢝⡽⣮⢯⣗⣗⢵⠵⣕⡕⡌⢬⡪⡪⣕⢍⡎⣕⣙⣘⣑⢓⢓⢕⠳⠹⠜⠵⢕⠵⡱⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢜⢌⢎⢪⢸⢨⠪⡪⡸⡨⢪⢘⢌⢆⢣⢣⠱⡑⡕⡕⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡜⡎⡎⡆⢐⠅⢸⢹⢹⢸⡸⡜⣕⢵⢱⢕⢟⡜
⣗⢝⢮⡳⣕⡯⡮⡯⡊⡮⣫⢿⡽⣯⡷⣟⢵⡫⡷⡵⡹⣕⢭⢯⢮⡳⣝⢼⡸⣜⢜⢎⢧⢣⡫⡝⡍⡇⡇⡗⡜⡆⡇⡎⡆⡧⠥⡥⡕⡥⢥⢥⢱⢡⣃⣃⣃⣃⡣⣃⠣⠣⡃⢇⠣⠱⠱⠡⠣⠕⢜⠜⡌⡆⢇⢣⢱⢱⢸⢰⢱⢱⢱⠱⡑⡕⢕⢜⠜⡜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⠄⠠⡁⢸⢸⢸⢱⢱⢱⢱⢕⢇⢯⢪⠮
⣗⢝⡮⣺⢵⢝⡮⣏⠎⡮⣫⢯⢾⣳⢯⢯⢺⣺⢿⣝⢞⢎⣗⡽⡯⣟⢮⡳⣝⣜⢎⢗⢵⡱⡕⣕⢕⢵⢱⢕⢕⢕⢕⢕⢕⢕⢝⢜⢜⡜⣕⢕⢇⢗⢎⢖⡕⣎⢮⢪⡫⢫⠊⢧⠉⡏⡇⢹⢸⠸⡒⡜⡔⡢⡣⡢⡢⡢⡢⠥⠬⡄⢥⢡⢡⢡⢡⢡⢡⢑⢡⢑⡁⣃⢑⢑⢑⢑⢑⠑⠕⠕⠕⠕⠣⡃⠠⡃⠸⠸⠸⠜⠼⡸⠕⠵⢝⠼⡱⢝
⣗⣟⣞⢷⢝⣗⢽⡇⢇⢯⢯⢯⢿⢽⡹⣪⡳⡽⣻⢞⢼⢕⣗⣯⣟⡮⣟⢞⢮⢮⢳⡹⣜⢜⢎⢎⢮⢪⡪⡪⡪⡪⡪⡣⡳⡹⡸⡱⣕⢵⡱⡝⣎⢗⣝⢵⢝⣜⢮⡣⡫⣢⠁⠈⠀⠑⠁⠘⠈⡸⠘⢨⢪⢪⢪⢪⢪⢪⢪⢣⢣⢣⢣⢣⢣⢣⢣⢣⠣⡣⡣⡣⡪⡪⡪⡪⡪⡪⡪⢭⠭⡍⡇⡏⡇⡇⠀⡇⡺⡸⡸⡸⡒⡆⡇⡗⣒⢖⣒⠦
⣗⣵⢽⢽⣕⣗⢽⡇⢇⢷⣻⣺⣯⣷⡿⣷⢿⣿⣻⣽⡪⡮⣶⡧⣷⢽⢼⢭⣝⣜⣕⣕⡣⣓⡓⡓⡕⠇⠧⡫⡺⠼⡱⡝⡮⣪⡳⣝⢮⡺⣜⡝⡮⡳⡵⣝⣕⢧⢳⡱⡝⡜⡆⠅⠀⠢⠁⡀⠄⠀⠠⠣⢣⢣⢣⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢸⢸⢸⢸⢸⢸⢸⢸⢸⢱⣱⣵⣵⣱⠱⡅⠀⡇⠐⡕⡕⡕⡕⡕⡕⡕⡕⡕⣎⢝
⣗⡽⣝⣗⡷⣽⣺⢇⢇⣟⣽⢾⡷⣿⣻⣻⡿⣿⢿⡷⣝⢮⣻⣿⡽⣯⢿⡽⣞⣾⣺⢮⣻⢮⢯⢯⢏⡯⡯⣮⣺⣪⣲⣪⡲⡲⣜⢔⢥⢕⡕⡭⣍⢭⣩⡪⣪⢪⡣⡳⡱⠣⠠⠀⠂⠁⢀⠀⠀⠀⠀⠀⢁⢘⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⢜⡜⣜⢜⢜⡜⣜⢜⡕⡕⡕⣝⣿⣿⣯⢮⢫⠀⡃⠨⡊⡎⡎⡎⡎⡎⡎⡞⡜⡜⣎
⣗⡯⣗⣗⣯⣗⢾⡣⡱⣻⣾⣻⣿⣻⣿⣻⣿⣿⣿⢯⡺⣪⣿⡾⣿⢽⣯⢿⡽⡾⣽⢽⣺⢽⢽⢽⢕⡯⡯⡺⡮⣺⣪⣺⡪⡯⣪⡳⣝⢮⢮⣳⡳⣳⡳⣝⢮⡣⡯⣎⠑⠀⠠⠀⠀⠂⠀⠀⡀⠁⠀⠂⠐⢲⢰⢒⢔⢔⢔⢔⠤⠥⠥⠥⡍⡥⢭⡨⣅⡣⡩⣊⢪⣑⣑⣑⣑⣑⡑⡑⡝⣛⣛⢳⢑⠕⠀⢪⠀⠇⠇⠇⢇⠇⠧⠣⡣⢣⠫⡲
⣗⡿⣽⣞⣗⡷⣽⢪⢸⣻⣾⣿⣽⣟⣯⣿⣿⣾⣿⡳⣝⢼⣷⣿⣻⣽⢾⡯⣿⢽⡽⣽⡺⡽⡽⡹⣕⢯⢯⢯⣻⣺⡺⣪⢮⣻⡺⣺⣪⡳⣳⡳⣝⡮⡯⣏⡗⣝⢮⣉⠂⠁⠈⠂⠈⠀⠀⠁⠀⠀⡀⠀⡀⡠⡱⡱⡱⡱⡕⣕⢭⢫⢭⢣⢳⡹⣕⣝⢮⣮⣯⣾⣵⣶⣷⡲⣒⡆⡇⡇⡯⣿⣿⣿⢕⢝⠀⡑⠀⡏⡭⡹⡸⡸⡩⡣⡣⡣⡳⡸
⣗⣿⣳⣟⣞⣗⣽⢪⢸⣿⣽⣿⣾⣿⣟⣿⣾⣿⡾⣝⢼⢵⢿⣽⢿⣺⢿⡽⣽⢽⣽⡳⡽⣝⢽⢝⡮⡯⡯⣳⡳⡵⣝⢮⣳⡳⣝⢮⡺⣺⡺⣮⡳⡯⣯⢷⣝⢮⡳⡳⠀⠑⠉⠄⠂⠁⠀⠂⠀⠅⠀⠀⠀⡄⡇⡧⡳⣕⢝⢼⢜⢮⡪⣎⢧⢳⢕⣗⢽⣿⣿⣿⡻⣿⣿⣾⡮⣺⣼⣼⣼⣿⣿⣿⡇⡯⡀⠸⠀⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡳
⣗⡷⣗⣟⡾⡵⣽⠢⢳⣻⣽⣾⣷⣿⣿⢿⣷⡿⣟⢎⣗⣽⣿⣻⣿⢽⡯⡿⣽⢽⣺⢽⢝⢮⢯⡳⡽⣝⣝⣞⢮⡻⡮⣳⡳⣝⢮⡳⣝⢮⢯⢮⡯⣯⡯⣿⢮⣳⡝⣪⢂⠈⢀⢀⠂⠅⠀⠐⠀⠀⠄⠀⠠⡠⡜⣎⢮⡪⡳⡱⡝⡜⣎⢮⢪⢳⢕⢗⣽⣿⣿⣿⢝⣿⣿⣷⣟⢾⣿⣽⣷⣿⣿⣿⣇⢯⠀⢸⠀⡪⡪⡪⡪⡪⡪⣪⢎⢎⢎⢮
⡗⡯⣻⢺⠽⣕⣟⢌⢽⢻⣿⣿⣻⣿⢿⣿⢿⡿⣯⡺⣢⢷⡿⣿⣽⣻⡽⣯⢯⣟⢮⢯⢯⣫⡳⡽⣝⢞⢮⢮⡳⡽⣝⡞⣞⢮⡳⣝⢮⢯⡳⡽⣾⣷⣯⢿⢽⡞⣗⡹⢔⢁⠀⢀⠀⠄⠐⠀⠐⠀⠠⠀⠀⠌⡜⣎⢧⢫⢎⢗⢝⢜⢎⢎⢗⢵⡹⡵⡽⡿⣿⣇⡗⡿⣷⣿⣿⢼⢿⣟⣿⣿⣿⣿⣗⣕⠅⡘⠄⡸⢸⡪⡟⣮⣪⡪⡪⡪⡺⡸
⣏⢮⡳⣝⢽⢜⣞⠌⡾⣿⣟⣿⣿⣻⣿⡿⣿⡿⣇⢯⡪⣿⡿⣟⣾⣳⢯⡯⣟⡮⡯⣏⣗⢵⢝⣝⢮⡫⣏⢷⢝⣝⢞⡞⡮⡳⡝⡮⣫⡳⣹⣻⣿⣿⡯⡿⡽⣯⢶⠋⢂⠂⠔⡁⠌⡀⡂⢀⠂⠈⡀⠐⢔⢜⢼⢘⢼⢮⢪⢣⢫⡪⡣⡫⡺⡸⡪⡮⣫⣿⣿⡎⡎⣿⣿⢿⣽⣺⣿⡿⣿⣷⣿⣿⣗⢎⠆⢈⠂⢸⢜⢜⢽⣯⣷⢱⢱⢱⢱⡹
⣎⢧⣫⡺⡜⡮⣇⠣⢽⣯⣿⣟⣿⣿⣻⣿⣿⡿⡕⡗⣝⣿⡽⣯⢷⣻⢽⣺⡳⡽⣝⢮⣪⡳⡳⣕⢗⡝⡮⡳⣣⢳⢕⢝⢎⢞⡜⡽⣸⢺⡪⣿⣿⣿⣯⢿⣝⢿⡇⠅⡂⡌⡀⡂⠅⠂⠐⠀⡂⢁⢀⢘⢦⢳⢱⠡⣹⣿⢸⢸⢸⢜⢎⢺⣷⣧⢣⢣⢪⣿⣿⡇⡇⣿⣻⣿⣿⢜⣷⣿⣿⣟⣿⣿⣿⢸⡁⢀⡃⢸⢸⢪⢪⣷⣿⡜⡜⡜⡜⣜
⢮⢺⢲⢵⡹⣜⡇⠅⣟⣾⣿⣽⢿⣺⣿⣷⣯⣯⢧⡫⡺⣞⣯⢿⣽⣺⢽⡪⡯⡫⡮⡳⣕⡝⡮⣎⢧⡫⣎⢯⢪⢣⢳⢱⢕⢕⢝⢜⢮⡣⣫⣿⣿⢣⠃⠅⠕⢽⢇⢁⢂⢂⢂⢂⠁⠌⠈⠂⢄⢆⡞⡜⡜⡜⡎⡎⢼⣿⢸⢸⢸⢸⢸⢘⣿⡷⡱⡱⢕⣿⣿⡇⡇⢯⣿⢿⣾⢕⣿⣿⣻⡿⣿⣿⣿⡪⡂⠐⡄⠸⡸⡱⡕⣿⣽⡯⡪⡪⡪⣎
⡝⣎⢗⣕⢧⢳⡣⡁⣗⢷⢿⣞⡯⡪⡎⡗⡝⡮⣪⢺⠼⣽⣺⢽⡺⣮⡳⡽⣝⢝⢮⡫⡮⣪⢳⢕⢵⡱⡕⣕⢕⢕⢕⡕⡕⡕⡝⣜⢕⢝⢜⣿⡇⠱⡱⠄⠀⡘⡈⡂⡂⡂⢢⠃⠠⠁⠅⠌⠀⠀⠀⠱⡱⡱⡱⡡⢺⣻⢜⢔⢥⣑⠕⢌⡇⢕⢸⡸⡸⣿⣿⡗⡅⢯⣟⣿⢿⡇⣿⣟⣿⣻⣿⣿⣿⡪⡂⠐⠔⠨⡪⡪⡎⣞⣿⡽⡸⡸⡸⡸
⡣⡳⡕⣇⢗⢵⡃⡂⡗⡿⡽⣺⢪⢇⢗⢝⢜⢮⢺⢸⢹⡪⡺⡽⡝⡞⣎⢗⢵⡹⣕⢵⢹⢜⢕⢇⢧⢣⢣⢣⢣⠣⡣⡣⡣⡣⡫⡪⡪⡣⡫⡱⡠⢄⠈⠂⠀⠀⠐⠐⠐⡠⠂⠂⠡⡈⠊⠀⠀⠀⠀⠀⡇⢇⢇⡃⢺⣿⢜⢔⠸⣏⠕⠅⡇⠢⡱⢱⢱⣻⣿⡯⡨⢪⢾⠽⡯⡗⡽⣫⢯⢟⡾⣿⣿⡇⡃⢀⢃⠈⡎⡎⡎⠮⡾⣝⢜⢜⢜⢜
⣣⢫⡺⡜⡕⣝⠆⡂⢏⢇⢏⢎⢮⢺⢸⢜⡜⣜⢎⢎⢇⢇⢏⢞⢎⢏⢎⢎⢎⢎⢎⢎⢇⢗⢕⢕⢕⢕⢕⢕⠱⡱⢸⢸⢸⠸⡸⡸⡸⠸⠀⠃⠊⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢜⠨⡘⣾⠪⡢⡑⢅⠕⢅⠣⡁⢎⢎⠎⣾⣿⣯⠨⡸⡐⢕⠱⡑⡕⢝⠜⡕⢝⣿⣿⡧⡃⠀⡢⠀⡇⡇⢏⢎⢺⢱⢡⢣⢣⡣
⡪⣪⡪⢮⢣⢺⡐⡀⢧⢳⢱⢹⢜⢎⢇⢧⢳⢱⢕⢕⣕⢕⠅⡇⡇⡇⡏⡗⡕⡕⡕⡕⡕⢕⢕⠕⡕⡑⡕⡸⡘⢌⢜⢜⢜⠜⡌⢆⢪⠪⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠅⢅⠣⡡⢘⢎⢇⢣⢊⠢⡑⠅⡣⠨⡘⢌⡊⣾⣿⣿⠨⠸⡸⡸⡸⡸⡸⡰⡱⡸⡨⣿⣿⡯⡂⠀⠪⠀⡕⡜⡜⡜⡜⡜⡜⡜⡜⡜
⢪⢲⡩⣣⢣⢹⠠⠀⣇⠇⡗⡕⣕⢇⢏⢮⢺⢸⢸⢸⢜⢎⢎⢎⢎⢎⢎⢎⢎⠪⡢⡱⢸⠨⡢⠣⡑⢌⢊⢦⣱⠡⡘⣎⢆⢣⢑⠅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠑⠌⡐⠅⢕⢑⠄⡣⡊⡢⠡⡑⠌⣎⠵⡩⢋⠣⠡⡑⡕⡕⡕⣕⢪⢪⢪⢪⢪⢻⣟⣿⢰⠀⡑⠀⡇⡎⡎⡎⡎⡎⡎⡞⡼⡸
⢱⢱⡱⡕⢅⢽⠀⠂⡣⡣⡣⡣⡣⡳⡹⡸⡪⡣⡣⡳⡹⡸⡰⡱⡱⢽⢸⡘⢔⢕⢑⢌⠢⡑⢌⢊⠂⡕⢌⢗⢭⢃⢪⢪⢊⢎⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⡊⡂⠆⢕⢐⠕⢄⠣⡈⡊⡢⡑⠌⡂⠅⠅⡂⡇⡇⡇⡇⡇⡗⡕⡕⡕⣝⠯⡿⡸⠀⢌⠀⡇⡇⡇⡇⡇⡇⡗⡕⡕⡕
⠌⡆⡗⡕⢅⢗⠀⢂⢕⢜⢌⢪⡣⡳⡹⡸⡸⡸⡨⡪⡪⡪⠢⡑⢌⠕⢅⠪⢲⢱⢐⠅⠕⢌⣦⡣⡁⡪⢘⡜⡜⢔⢸⢸⠨⡢⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢐⢌⢊⠢⡑⢅⠕⡨⡐⡑⠔⠌⢌⢐⠡⡁⡂⢇⢇⢇⢇⢣⢣⢣⢣⢫⢂⢐⠸⡸⠀⠢⠀⡇⡇⡇⢧⡫⡪⡪⡪⡪⡳
⢌⠪⡪⡊⡂⡇⠄⠰⠍⢆⢎⠔⢇⠧⠳⠹⠸⠸⠸⠸⡸⠌⡪⠨⠢⠡⡑⠌⢺⠘⡇⡕⠅⢕⢽⠎⠔⢌⠢⠣⠪⡂⢪⢎⢊⠢⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢑⠔⠅⢕⢘⠌⡰⡐⡌⡪⡘⠌⡂⡂⢅⢂⠂⡕⡱⡱⢱⠡⡣⡣⡣⡃⡇⡕⡱⡸⠀⢘⠀⡪⡢⡹⡸⢜⢎⢇⢏⠎⠮
⠀⠐⠀⢀⠀⡇⠠⠀⠠⠀⠀⢀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠀⠐⠈⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠂⠐⠀⠀⠀⢐⢅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢑⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⡨⠢⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡪⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠈⢐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⡀⠈⠀⡀⠄⠀⠀⠀⠀⡀⠈⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠐⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠄⠁⢀⠀⠄⠀⠀⠁⠀⠀⠀⡀⠂⢀⠐⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⣄⠀⠠⠀⠀⠀⠀⢁⠈⠂⠀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠐⠀⠠⠀⠂⡐⡈⠄⡈⠄⠄⡂⡁⡂⠀⠄⠠⠡⢐⠈⠄⢐⠨⢐⠀⠁⠀⡀⠄⠂⠀⠠⠀⠂⠀⠀⠀⠀⡀⠀⠀⢀⠠⠀⠐⠈⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀
⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠐⠈⠀⠀⠁⠀⠀⠀⡀⠈⠀⢀⡁⠘⢀⠀⠄⠂⠅⡑⠠⡑⢅⢕⠌⡔⣠⢡⠢⡒⡂⡒⠡⠑⡁⠅⠂⡁⢢⠂⠅⡂⢡⠡⡂⡂⢕⠀⠂⡌⡌⡐⠅⡑⡀⡪⠠⠁⠄⡂⡀⡀⡀⠂⠀⠂⠠⠐⠀⡁⠂⠄⡢⢑⢐⠀⡁⠈⠐⠀⢊⠀⡀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠠⠐⠀⠀⠀⠢⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠀⠐⠀⠀⠀⠈⠀⠀⠀⠄⠂⠀⠂⠁⠀⠀⢈⠀⠀⠂⠀⠈⠀⠐⠀⠀⢀⠰⡐⠔⡙⢈⠢⠡⡑⡐⡠⡠⡡⠡⡂⠆⡃⡊⡢⡡⢕⢌⢎⠘⡜⡄⢕⠀⢂⢇⢁⢎⢢⠪⢀⢎⢂⢐⢀⠂⠨⠠⠡⡃⡓⡜⢔⠤⡢⡠⡑⠰⠨⠂⡐⠀⠀⡀⠄⠀⡀⠀⠀⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⢈⠀⠀⠄⠁⡴⠀⠱⠀⠁⠀
⠀⠀⠀⠀⠌⠠⠐⠀⠀⠂⠀⠂⠀⠂⠀⢀⠠⠀⠠⠀⠌⡀⢀⠐⠀⠈⡀⠈⡀⠐⠀⡢⠋⢀⠁⡐⠠⢨⠰⢑⠩⡪⡪⡊⡎⠄⠅⡂⣐⢅⠇⡧⡱⣱⠁⢜⢆⠄⢘⠄⢇⢪⢂⢇⠅⢕⠰⠨⡈⡂⢍⠪⣔⢅⢕⠱⡱⠱⡑⢜⠄⢕⠑⠅⡂⠄⠐⠀⢀⠀⡀⠀⠄⠁⠀⡀⠄⠨⠀⠐⠀⠀⠂⠀⠁⠀⠀⠀⠀⠄⠀⠠⠀⠠⠀⠠⠀⠀⠂⠀
⠀⠀⠐⠀⠨⠀⠠⠀⠂⠀⠄⠂⠀⠄⠂⠀⢀⠀⠄⠀⠅⡐⠠⠐⠈⠀⡀⠠⠀⠄⢁⠪⢱⠰⡰⡐⢥⡑⡌⠢⡑⢕⢜⠜⡌⠮⡣⡇⡇⣊⣇⢳⡱⡱⡅⡪⡪⡨⡢⢋⠔⡱⡡⡣⠨⡪⡑⠕⠔⢜⠔⡕⡜⡎⡎⢜⢌⢇⢇⢣⢑⠅⠌⡀⡂⠕⡐⠈⢀⠀⡀⠄⠐⠈⠀⠄⠂⡁⠌⠀⠄⠀⠄⠀⠂⠀⠁⠀⠁⡈⢀⠐⠀⠐⠀⠐⠀⠁⡈⠀