⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢞⡜⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣾⢻⣪⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣞⡽⣺⡠⠑⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⡯⣷⣳⢽⢵⣫⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⢮⢯⠳⠅⠂⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⢖⡯⣳⣝⣗⠯⡗⣗⢯⣳⣝⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢽⣕⠉⠀⠐⠈⠀⠀⠂⠐⠀⠀⣲⡲⣝⡮⣗⢗⡮⣳⢵⣳⡫⣞⣗⠵⠃⠀⠐⠘⠙⣺⣪⢯⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡯⡾⠑⠀⠐⠀⠐⢈⢠⢤⢄⢰⣳⡯⣷⢯⣞⡽⣺⢵⣫⢞⣞⡕⠃⠁⠀⠀⠄⠰⢽⣺⡺⣽⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣯⢗⠀⠄⠀⠠⠂⢁⢡⣢⢯⢯⣞⣞⢽⣝⢾⢽⣺⢵⡳⣫⢞⣞⡦⡄⠀⠂⠀⠀⣕⣗⣯⣳⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠸⣊⠂⠀⠀⠄⠁⡰⡼⣝⢾⢝⣵⡳⡽⡵⣳⡫⣯⣺⡳⣝⣗⢽⢮⡻⣽⣖⡀⠀⢢⢼⣺⡺⡮⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠨⡊⠄⠀⢀⠁⠀⣔⢯⣫⢾⢝⡽⣺⡺⣝⡽⣪⢯⣺⡪⣞⢷⢽⢵⣫⢾⢵⢯⡯⡄⡸⡯⣞⡽⡝⡌⢆⠢⣀⠀⠀
⠀⠀⠀⠀⡐⢅⠂⠀⡀⠂⠀⣸⣪⢗⢷⢝⣗⡽⡮⡯⣺⡺⣵⣫⢞⡾⣕⡯⡯⣳⡳⣽⡪⣗⢿⡽⡽⣝⣗⢯⡣⣊⣢⣣⡂⠀⠀
⠀⠀⠀⡌⡪⠀⡀⠂⠄⢂⢡⢗⣗⢯⢯⢯⡺⡮⡯⣞⣗⣽⡺⡮⣗⡯⣗⡯⡯⣗⣟⢮⣻⣪⢯⢯⣟⢷⣝⢧⠹⣺⣞⣷⡻⡆⠀
⠀⠀⢐⠌⠔⡀⢂⠡⡁⠢⣹⢽⡺⡽⡽⡵⡯⡯⡯⣞⣞⣞⡾⣝⡷⣝⣗⣯⣻⣺⣺⢽⡺⡮⣯⡳⣯⣻⣺⢐⠕⣗⣗⣯⢿⢽⠀
⠀⠀⢢⠡⠡⠐⡀⡂⡪⢘⣞⡽⡽⡽⡽⡽⣝⡾⡽⣺⡺⡎⢻⣳⢯⣗⣟⣞⡾⡵⣯⡳⣯⡻⣮⡻⡮⣗⣯⡷⣯⣗⡯⣾⣻⢽⡂
⠀⠠⢑⠨⠠⠡⠐⡐⢌⠢⣳⢯⢯⢯⢯⡻⡮⡯⡯⣗⣟⠄⠀⠘⠽⣞⣗⣷⣻⢽⣳⢯⣳⡻⡮⡯⡯⣗⡯⣟⡷⣯⣻⣺⢽⣝⡇
⠀⢈⢂⠪⢈⠄⡑⢌⠆⡂⢽⢽⢽⣝⣗⡯⣯⢯⢯⢗⠇⠂⠅⠄⠄⡈⡺⣾⣺⢯⣗⣟⡮⡯⡯⣯⣻⣳⣻⢽⡯⣷⣳⢽⡽⡮⡗
⠀⡂⠢⡑⡐⡐⡈⡆⡁⢀⠸⡸⣳⣳⣳⢯⣗⡿⡉⡞⠈⡀⠄⠠⠀⠠⠀⡈⠺⣻⣞⡮⡯⡯⡯⡷⡽⣾⣺⢯⣟⡷⣽⡳⡯⡯⣏
⠀⠠⡑⠬⡐⡐⠄⡣⣢⣠⣆⣢⡑⡟⡾⣽⠺⠁⠌⢀⠂⡠⣢⣵⡵⣿⢾⢶⠂⠄⣟⡾⣽⣫⣟⡽⣽⣗⣯⣟⡷⣯⢗⣯⢯⣟⡎
⠀⠡⡘⡜⢄⠢⡁⢇⢝⠥⡑⢿⡺⡗⠟⠹⡥⡁⡐⢀⠐⠡⠘⠷⡻⠽⡊⢐⠠⢡⣗⡯⣗⡷⣳⣻⣳⣟⡾⣞⣯⡯⣟⡾⣽⡺⡎
⠀⠡⢐⢜⢐⠌⠔⢅⢇⡂⢐⠐⡀⠂⠄⡁⠄⡁⢂⠠⠈⠠⠈⠄⠂⡁⠄⠂⢄⣟⡾⣽⣳⣻⢽⣞⡷⣯⣟⣯⣷⢟⣽⢽⣗⡯⡇
⠀⠅⡸⠠⢣⠡⡃⠕⡢⠣⠀⢂⠐⢈⠀⢀⠀⠄⠂⠠⠈⠄⡁⠂⡁⠠⢠⡱⢝⡾⣽⢞⡾⣽⢽⠾⢽⣳⢯⡷⣿⢽⣺⢽⡾⣝⠆
⠀⢂⠪⢊⠸⡐⠜⡌⡌⢕⠡⠐⣀⢂⠈⢄⢐⠠⡁⢌⠠⡅⡂⡁⠄⠨⢀⢴⢽⡽⣽⢯⣟⡽⣯⠃⣹⣞⣿⢽⡯⣟⢾⣝⣯⢗⠅
⠀⡂⢕⠡⠨⡊⢌⢂⢣⢑⠕⠐⠠⠑⠡⠱⠢⢑⠜⠄⠅⠄⠄⡀⡢⠕⡝⠝⣝⣯⢯⡷⡏⢢⡗⠀⣺⣞⣾⣻⣽⢽⢽⣺⡽⡽⠀
⠀⢌⠢⡈⡂⡪⡘⢔⢑⢌⠂⠀⠈⠠⠁⠌⠐⠠⠐⠐⡀⢂⠐⡀⢔⠨⢐⢡⣟⣞⡯⠏⠀⣼⠁⠀⣞⣾⣳⣟⡾⣽⡻⡮⡿⣝⠀
⠀⡪⢐⢐⢐⠰⡘⡌⢆⢣⠀⠀⠀⠀⠀⠁⠊⡠⠈⢄⢐⠔⠨⡐⠡⡈⡂⣾⣺⡳⠉⠀⢀⡇⠀⠀⣞⡾⣞⡷⡯⣗⡯⣟⡽⡇⠀
⠐⢌⢐⠔⡡⢈⢪⠨⡊⡒⢄⠀⠀⠀⠀⠀⠀⠀⠁⠕⡐⠌⢌⢐⠡⢂⣞⢗⠇⠀⠀⠀⠜⠀⠀⠀⣞⣯⡯⣿⣝⣗⣯⢷⣻⠇⠀
⢈⢂⢂⢪⠠⡑⢌⠪⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣠⣱⡰⣠⢅⢇⣕⣄⢇⠀⠠⠊⠀⠀⠀⠀⣟⡾⣽⣳⣳⢯⡾⡽⣞⡇⠀
⠰⡐⡡⢸⠐⠌⡜⢌⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡻⠺⡪⢏⢟⢜⠼⡻⡺⢏⡂⠀⠀⠀⠀⠀⠀⣷⣻⣳⣟⢾⢽⡽⣽⣳⠅⠀