⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠖⢆⡔⠑⢢⠊⠒⡒⠒⡒⠲⠒⡖⠒⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⠤⢔⢒⢒⠕⡦⡀⠀⠀⠀⠀⠀⢸⠀⡃⡕⡇⠌⢘⠀⠅⠂⡀⡘⢀⢈⠁⡂⢇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⢔⠡⡑⢅⠪⡐⡱⡑⡇⠀⠀⠀⠀⠀⢀⠁⡂⡁⡁⡂⠊⡒⡈⢁⢑⢈⢈⢐⢐⢁⢁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢑⢌⠢⡑⡌⡢⣑⢌⢎⢆⠵⠀⠀⠀⠀⡊⢀⡹⠈⢬⡈⡬⡫⠨⢘⠁⡉⡎⢈⠡⠁⡇⢡⠉⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡓⡒⡓⡍⡪⠩⢢⢱⢱⢱⠨⢇⠀⠀⠀⣂⠀⢸⠀⠺⡂⡇⡺⢨⠀⠁⠄⢁⠰⢑⠐⢃⠨⢀⠅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢢⢑⢌⠢⡊⡪⡪⡪⡪⡪⡪⢪⡀⠀⠀⠀⠁⠁⠈⠈⠀⠀⠈⠀⠁⠁⠁⠁⠁⠀⠁⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼⡰⡐⡑⣌⢮⢪⡪⡢⡣⡪⡲⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡐⣅⢞⣼⣽⢗⢕⢕⢕⢕⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢱⢪⢪⢕⢪⢪⢪⢪⢢⢣⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡳⡡⡣⡣⡣⡱⡑⡕⡕⢕⢕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡪⡪⡪⡪⢪⢪⢪⠪⡪⣞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢔⠜⡜⡜⢜⢌⢦⠋⢵⢯⣻⢴⡤⣄⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢤⣺⢽⢽⣎⣢⠵⠕⠕⠡⢢⢯⣳⢯⢿⢽⢽⣽⡳⣯⣻⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣪⢗⣗⢷⣵⣳⣻⣺⣕⣟⢾⢽⣅⠋⡨⢁⡾⣕⣏⣯⢿⢽⡽⣞⡽⡾⡵⣗⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡯⣻⢾⢽⣺⣞⡷⣽⢾⢼⣳⣟⡾⣔⠀⣲⡽⣞⡷⡯⣟⣽⢽⣳⣻⢽⢯⡳⣽⢝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣏⡯⣯⣟⢾⣺⢽⡽⣫⡯⡷⣯⢿⡽⣽⢽⢯⢿⡽⣫⣷⣻⢽⣳⢯⣻⡽⣝⣗⣟⡾⣲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⡳⡯⡷⣯⣻⢾⢽⢽⣳⢯⣟⣽⢽⣽⢾⣻⣻⡽⣽⣳⣳⢯⣻⣺⣽⣺⢽⣳⣽⣺⢽⡽⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣗⡽⡯⣯⢷⣫⡯⣟⡽⡾⣽⣺⢾⢽⡽⣯⣟⡾⣽⣳⢽⣺⡽⣳⣗⣗⡯⡿⣵⣳⢯⡯⡿⣝⣯⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢮⢯⢯⢷⣻⣳⢯⢷⣻⢽⣳⡽⣽⣻⣞⣗⣷⢻⣳⡽⣽⣳⢯⣗⡷⣫⡯⣯⣗⡯⣗⣯⢿⢽⣺⡽⡾⡽⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣜⣗⡯⣟⡽⡾⣽⢽⢯⣞⣟⡾⣽⣳⣟⣞⣷⣹⡽⣞⣯⢷⡯⣟⣮⢯⡷⣽⢾⠺⡽⣽⣺⡽⡽⣞⣽⢽⡽⣽⣻⢦⡄⠀⠀⠀
⠀⠀⠀⠀⣳⡳⣯⢯⢯⡯⣯⢿⢽⣺⢾⣽⣻⣞⣗⣟⣞⡾⡽⣽⢾⢯⣟⣗⡯⣟⡾⡽⠁⠀⠈⠑⠷⢻⡽⣝⡾⡽⣽⣺⢾⢽⠅⠀⠀⠀
⠀⠀⠀⠀⢮⢯⣗⡿⡽⡽⣝⣯⣟⣾⣻⢞⣗⣗⣯⣞⡗⢯⢯⢷⣻⢯⣷⣻⢽⡳⣝⡇⠀⠀⠀⠀⠀⠘⣗⢯⢮⣻⢞⡾⣽⣻⠀⠀⠀⠀
⠀⠀⠀⠀⢽⢽⣺⢽⡽⣯⣻⢞⣷⣻⣞⣯⢷⣻⣺⢾⣽⣫⢿⢽⣺⡽⣞⣎⢧⢳⢵⠅⠀⠀⠀⠀⠀⡮⣳⡽⡽⣞⡯⣯⢷⡓⠀⠀⠀⠀