⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠁⢀⡠⣲⢽⢜⠶⠢⡢⡐⡠⠀⢄⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢇⢧⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣞⢷⡫⡪⣐⠔⡜⣵⣑⢕⡸⡸⡨⡢⡓⡢⡔⣀⠀⠀⠘⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠫⣫⢦⣣⢢⣀⠀⠀⡠⣪⢯⣳⢽⢕⡧⢧⡑⡔⣑⢱⡱⡕⢕⢕⢜⢔⢕⠥⣙⠾⡪⠀⠄⠺⠂⠀⠀⠀⠀⠀⢀⠠⣐
⠀⠀⠀⠀⠘⣯⣞⡷⣵⡻⡽⣝⣗⡯⣗⣯⡇⣹⣗⣿⣯⡿⣝⠝⠘⣕⢥⢣⢣⢣⡣⡧⣷⣼⢬⢦⢰⡠⡤⡊⡔⠢⠣⡱⠚⠄
⠀⠀⠀⠀⠀⢱⠗⠏⢳⣫⢯⣞⢾⣝⣾⣳⢿⢾⣯⡷⣿⣻⡷⡽⣜⡮⡮⣳⣕⣇⢯⣟⣿⢾⡽⣵⢣⢈⢪⢆⡢⡱⢨⢒⢅⢰
⠀⠀⠀⠀⠀⠀⠀⢠⡳⡽⣕⣗⡯⣾⡺⣝⢽⡹⣷⡯⣗⣯⢿⣻⣗⣯⣞⣿⣪⢺⣯⢷⣝⣟⣯⢷⣟⣮⣣⡗⠇⢕⠱⢁⠊⠀
⠀⠀⠀⠀⠀⠀⠀⡮⡯⡯⣞⣗⢯⡗⡯⣞⢵⢯⡳⣻⢿⣽⣻⣳⣻⣺⢽⡺⡼⣕⢯⢷⣳⢷⢯⢟⣾⡺⣞⠬⡐⢄⢐⠄⡂⠅
⠀⠀⠀⠀⠀⠀⡘⣞⡯⡯⡷⡽⣝⢮⣫⢮⢯⣳⢝⡷⡏⣺⣺⣺⢵⡳⡳⣝⣞⢮⡯⣳⢝⡯⣟⢗⣟⡞⡕⡌⡀⠁⠐⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡎⣾⢽⢽⢽⣫⢗⣽⣪⢯⣻⢮⣻⢝⠬⢼⣺⣺⡯⣞⡽⣚⡮⣷⢯⣗⡯⣯⣯⡳⣕⣯⢺⡨⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢲⣽⣳⣻⣻⢽⣏⣗⢷⢵⣻⣽⡳⡏⢂⠀⠪⣺⢾⢽⡽⣾⢕⡯⣾⣻⢮⢏⣳⣻⣺⢵⢯⡳⣕⢄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡨⢗⡷⣻⢾⣞⣿⡪⣞⡯⣯⢷⣻⢹⡇⡀⢂⠁⢝⡎⢷⣝⡯⡿⡞⣞⢞⡏⠐⠜⣗⡯⡯⡷⣝⡇⣇⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠊⡢⡢⠢⡄⣄⡣⡯⡗⣟⣞⣿⣳⠷⣯⣻⡻⠾⣔⢝⠘⢞⣞⡽⠃⣽⡓⠑⠅⡁⢟⢯⢯⣻⢮⡇⡇⠹⡀⠀⠀⠀
⠀⠀⠀⠀⢨⢯⣞⣌⠆⣆⢗⢵⢯⢳⣳⣳⢫⠸⡣⢗⡗⡗⠈⠊⠂⡁⢏⢿⡄⡯⡼⡻⠛⢿⣦⢝⣗⡿⣽⢰⢁⠀⢣⠀⠀⣠
⠀⠀⠀⠀⡎⣺⡺⣺⣿⡪⣇⣓⡯⡫⣗⢮⠀⠂⢒⢁⠑⡁⢀⠂⠁⡀⠠⠀⠉⢞⢞⢟⠇⢈⡟⡞⡮⣟⣇⡣⡁⠀⠈⢦⣾⣿
⠀⠀⠀⡨⢢⢳⡽⣟⣞⡾⢏⡷⣯⡫⣞⡷⣅⠅⢂⢐⠐⡐⢀⠂⠁⠀⠀⢀⠡⠠⠑⠡⠐⡙⣜⣼⡹⡮⡎⠀⡂⡠⣾⡯⣿⡯
⠀⠀⡰⠨⡪⡾⣽⢯⣞⣏⡯⣯⢷⢝⡮⡇⠕⣅⠂⠄⠂⡐⠀⠄⢁⠈⡈⢀⠐⠠⠡⠁⢅⣿⡹⣧⡻⡎⠀⢀⣮⣻⢾⡟⣿⠇
⠀⡰⡸⡜⡵⣿⢽⡽⣾⣺⡽⣺⢯⡳⣻⡺⣄⠂⡑⠌⠀⠄⢂⠁⠄⠠⠠⠐⠈⡀⠅⢨⣺⣯⣗⣗⢡⠇⢰⣻⣕⡯⣯⢏⣯⣕
⡌⡶⠋⣸⣺⢯⢯⡿⣽⣪⢯⢯⢿⡕⡯⡾⣕⢕⠤⡀⠡⠐⠀⠄⢁⠈⠄⠂⢁⣠⣼⣳⣳⣳⢧⢷⣝⣤⣺⣳⡻⡾⣝⣽⡽⣞
⠟⠁⢰⣳⣟⡯⣿⢽⣳⣳⢽⢽⢽⡯⡪⣟⣗⢗⢭⢎⢖⠤⡁⠐⡀⣐⣔⡾⣽⢮⡺⡚⡺⣺⡙⠑⠝⠚⢳⣳⣽⢾⣳⢷⣻⣳
⠀⢠⣟⣷⣻⣺⣯⡻⡮⣯⡳⣏⢿⣽⣝⢜⣯⢗⡵⣕⣅⡇⡭⣣⣹⣗⣯⡯⡿⠿⡯⣳⡳⡽⣵⡁⢂⠡⢀⢻⣽⢿⢽⣻⣺⣳
⢠⡷⣟⣾⣳⢟⡮⡯⣯⡳⣝⢾⢽⣺⣳⢽⡸⡩⡫⢿⡺⣗⡽⡽⡣⡣⡢⣿⠹⡻⢶⣌⡍⠺⢮⣻⣲⢰⠠⡚⣽⢿⣽⣺⡳⡳
⣫⣟⣯⣗⢯⣻⣪⣟⢮⣺⣪⢿⣹⢞⡞⡷⡵⣵⠵⡵⣜⣔⣌⠢⡑⠕⣞⢼⠕⠠⠐⠈⠋⠷⣦⣊⠺⡳⣕⠬⣿⣽⢺⢜⢮⢝
⣟⣾⡳⡽⣽⢺⡺⣪⡳⡕⡯⠃⡪⡏⡊⠪⣟⡬⢙⠓⠦⣦⡱⡩⡹⣹⠓⢾⠴⣐⣈⡀⡁⠐⠈⠙⢷⠮⣳⡹⡸⡺⡹⣪⢳⢕