danke
⠀⠀⢀⢐⢯⡣⣢⢠⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢪⢾⠵⣝⢆⢣⠃⡇⢎⢎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⡳⡝⢽⣸⡪⡢⡡⡣⣑⢑⢕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠉⠣⡣⡓⡌⢞⢮⢺⢜⢔⢌⢒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠂⢇⢇⢎⢜⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠜⡜⡌⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡪⡢⡱⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢜⢔⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⡪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢢⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡨⢢⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⡑⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠢⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡢⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⢑⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢌⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡕⢌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠕⡕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢌⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡐⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢌⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡢⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠄⠄⢄⠠⡀⡀⡀⠀⠀⠀⢀⠀⡄⡄⠤⠤⡱⢔⢌⣂⠀⠀⠀⠀⢀⢠⢠⢠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡢⠡⡑⡐⡔⡌⡌⡆⡆⡆⣆⢪⢘⠐⢅⢖⢍⢆⢎⣎⢖⣜⢔⡔⡄⢝⢢⣀⠦⣚⢔⣆⢖⣔⢔⢝⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡊⡢⡑⡌⡎⣎⢮⣪⣞⢮⡳⣝⣞⡼⡲⡐⡬⡣⣣⢗⣯⡻⡮⣟⣞⣗⡯⣞⡵⣕⢷⣝⡮⣗⡷⣻⢮⢯⡮⣇⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⡊⡢⡑⡕⡕⣕⣝⡮⣳⡳⡽⡽⣝⣗⣗⡯⣯⣳⢽⣪⢷⢯⣗⣯⢟⢓⢍⢍⡍⡍⡍⡝⡙⠳⢯⣗⣯⡯⠯⠟⢞⠷⣽⣪⣲⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠢⡑⡌⡎⡎⡮⡺⣜⣞⢮⡳⣝⢮⢯⢞⣗⣗⡯⣗⡯⣗⣽⣝⣗⢝⢦⡳⣝⡾⡵⣯⣳⢽⣪⢞⣜⢤⢙⢦⠠⢑⢕⢕⣕⢔⢌⢜⠱⢄⡀⠀⠀⠀⠀⠀
⠀⢀⠪⢨⢪⢪⢪⢪⢮⡻⣜⢮⢣⢏⢮⢳⡹⣕⢗⣗⢯⣗⢿⢽⣺⣺⣺⢽⣽⣺⣳⢯⣻⣺⣺⣽⣺⢽⣺⡵⣇⡇⢯⡠⡑⣝⢮⢯⣗⣗⢵⡡⡍⣆⠀⠀⠀⠀
⠀⡰⡑⢕⢕⢕⢕⣝⢞⡞⡮⡪⡣⡣⡣⠣⡣⡣⡣⡳⣻⣺⢽⢽⣺⢵⢯⣻⢾⣺⢯⣻⣽⡾⣽⡾⣽⣻⣻⡽⣯⡻⣧⣷⡪⡮⣯⣻⣺⣞⣯⣯⣟⣞⣷⣄⠄⠀
⠠⡃⡪⡪⡪⡪⣣⢳⢝⢮⡺⡸⡸⡐⢌⢊⢂⢎⢪⢪⣳⢽⡽⣽⣺⢽⡽⣯⢿⡺⣯⡻⡮⡯⣗⣯⢯⢯⡷⣿⣝⣿⣺⣺⣽⢽⣺⣞⣷⢽⢾⣞⡷⣟⣾⡽⡛⠀
⢨⠢⡱⡱⡱⡱⡕⡽⡹⣕⢇⡇⡇⡪⡂⢆⢕⢜⢜⢼⡺⣽⣺⣳⣝⣗⣟⡯⡿⣝⣍⡉⣽⣟⣻⣿⠿⢿⣯⠁⠁⠙⢺⣳⣯⣟⢾⢾⡟⣿⣿⣿⣏⠳⢳⣿⠅⠀
⡆⡣⡪⡪⡪⡪⡎⡯⣫⢮⡣⣣⢣⢱⢸⢸⢸⡪⣫⣗⡯⣗⡷⣳⣗⣗⣗⡯⣯⣻⢮⣻⣻⣿⣽⣿⣤⣴⡿⠀⠀⠀⠈⣷⣻⣺⠃⣿⣟⣻⣷⣠⣿⠂⡀⣼⠇⠀
⡇⡪⡪⡪⡪⡪⣪⢺⡪⡳⣝⣜⢮⡪⡮⡳⣝⣞⣗⣗⣯⣟⣾⣳⢗⣷⡳⡯⣗⡯⡯⡷⣗⣷⢽⣝⣟⢿⣳⢴⡴⣶⡻⣽⣗⢯⣟⣟⣟⢿⣻⢿⣗⢷⣻⠝⠀⠀
⡇⢎⢎⢎⢎⢎⢮⣚⢮⡫⣞⢮⣳⢝⡾⣝⣞⣞⣞⣾⣺⢾⣺⢾⢽⣺⣽⣫⢷⢯⣟⣽⢽⣺⢽⣳⢯⣟⡽⣯⣻⣳⣟⢷⢽⢽⣺⣳⢿⣻⣺⢽⣞⡿⣗⣦⠀⠀
⡇⢕⢕⢕⢕⢕⡕⡮⡪⡯⣺⢽⣺⢽⣺⣳⣳⢗⣟⣾⣺⢯⡯⡿⣽⣻⣺⣽⣽⣳⢯⢾⢽⣺⡽⣞⡽⣮⣟⡾⣞⢷⢽⢽⢽⢽⣺⣺⢽⢽⣞⣽⡺⣝⡷⣝⣧⡀
⢸⠸⡸⡸⡸⡸⡜⣎⢯⣺⢽⢽⣺⢽⣺⣞⣾⣻⡽⡾⣽⢯⢿⡽⣯⡟⡳⡻⢾⣺⣽⢯⡯⣗⣯⢷⣟⡯⡾⡽⣺⢯⢯⢯⢯⣗⡷⡽⡽⣝⣞⡮⡯⣗⢯⢷⡳⣱
⠐⡕⡕⡕⡕⡵⡱⡕⡧⡳⣯⣻⣺⢽⣳⣳⣗⣯⢿⡽⣯⢿⡽⣯⢷⡯⣎⢝⢮⢮⣪⡹⡹⡹⡺⡻⡮⡯⣯⡯⣯⢯⡯⣯⣻⢮⢯⢯⣻⣺⢮⢯⣻⣺⡽⣫⠚⠀
⠀⢱⢸⢸⢸⢸⢪⢎⣗⢽⡺⣺⣺⢽⣞⣗⣟⡾⣯⢿⡽⣯⢿⡽⣽⣽⣻⣻⣮⣮⡪⡹⡹⡺⡪⡮⢮⠮⡦⣧⣣⣫⢹⢩⢹⠹⡙⡏⡏⡏⡏⢟⢍⢇⣧⢻⠄⠀
⠀⠀⢇⢇⢇⢇⢗⢵⡱⡳⣝⢞⣞⣟⣞⡷⣯⢿⡽⣯⢿⡽⣯⣟⣷⣻⣞⣷⣳⡯⣟⣷⢧⣇⡇⡇⡇⡇⡇⡖⡕⡍⡏⡏⡏⡏⡏⡏⡏⡺⡹⡹⡹⡹⡸⠜⠀⠀
⠀⠀⠘⡜⡜⡜⡜⣎⢮⡫⡮⣫⢞⣗⣯⢿⣽⢯⣟⣯⣿⡽⣗⡿⣞⣷⣻⣞⣷⣟⣯⣟⣯⣯⣟⡿⡾⣾⣺⣼⡼⣼⢼⣜⡼⣜⡼⡼⡼⢼⠼⡼⠼⢜⠙⠀⠀⠀
⠀⠀⠀⠘⡜⡜⡜⡜⣎⢮⣫⡺⣝⣞⣞⡿⣽⡯⣿⢾⣺⡿⣽⣟⣯⡷⣟⣷⣻⡾⣽⣾⣻⣞⡷⣟⣿⢽⣞⡷⡯⣗⡯⣺⢜⡎⣎⢎⢎⢎⢎⠪⡊⡂⠁⠀⠀⠀
⠀⠀⠀⠀⠈⢎⢎⢇⢗⢵⢕⣝⢮⣺⣪⢯⢷⣻⢿⣽⡯⣟⣷⣟⡷⣟⣯⣯⣷⢿⣯⡷⣟⣷⣟⣿⢽⣻⣺⢯⢯⡳⣝⢮⢣⡳⡱⡱⡱⡱⡑⡑⠌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠣⡫⡪⣣⡳⣕⢯⡺⣪⢯⣻⡺⡯⡷⣿⣻⢷⣻⣽⢿⣽⢷⣻⣯⣷⢿⣻⣗⡿⣞⣯⣗⢯⣳⢝⡮⣳⢹⢜⢜⢜⢜⢜⢐⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠪⡪⡎⡮⣣⡻⣪⢗⣗⡽⡽⣝⣗⣟⡯⡿⣞⡿⣽⢿⣽⢾⡯⣟⣗⡯⡯⣳⡳⡳⣝⢮⢳⡹⡜⡎⡎⢇⢣⢑⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢎⢮⢪⡳⡳⣕⢯⡫⣞⣞⢮⢯⢯⡳⡯⡯⣳⢯⣻⡺⣝⣞⢮⢯⡳⣝⢽⡸⡕⡇⡇⡇⡣⡑⡱⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠸⢸⢪⢣⢯⢺⡪⣏⢷⢝⡽⡵⣫⢗⢯⣺⡪⣗⢵⡫⣇⢯⢪⢣⢣⠣⡣⡑⠌⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠣⠣⠣⣣⢳⢱⢹⠸⡍⡧⡣⡫⡪⡣⠣⡣⣃⡣⠱⠐⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀