⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠬⠻⢽⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡇⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢈⣉⠕⡁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣺⠃⢁⡀⡐⣄⡀⣁⣠⢪⡼⢉⠅⠎⠆⣜⠢⣔⢀⢐⡄⢁⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢫⢠⣕⠍⠄⡯⡏⡔⠤⣜⡧⣹⢣⣖⢋⠸⡮⣟⡩⢴⡎⣶⣲⢧⣗⣦⢈⣝⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⡲⡍⢕⢡⡆⡇⣵⢬⡿⣟⠿⠲⣓⣻⡜⡖⢞⠒⠗⢿⠎⣗⢞⢹⣷⣻⣭⢳⣟⡣⡾⠀
⠀⠀⠀⠀⠀⠀⠣⣄⣀⠀⠀⡄⢠⢐⠒⡾⡖⣷⡷⢧⣗⢵⠗⡓⡿⠇⠐⠊⠈⠁⠁⠈⠠⠏⠋⠀⠉⠀⠖⠑⠂⠒⡿⣞⡙⣆⣧⡟⢉⠀
⠀⠀⠀⠀⠀⠀⠈⠡⠬⠀⣥⠑⡏⡏⢃⣟⢏⢉⡚⠍⣑⠉⠀⠂⠀⠀⠀⡂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢁⡮⢜⠓⡏⡟⣆⠛⠆⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⢨⠯⡟⣓⢟⡣⠆⠀⠁⠀⠀⠒⠁⠀⠀⠀⠀⠅⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⡘⢷⠪⣉⡛⠏⠰⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣃⢣⠖⠽⠈⠁⠀⠃⠀⠀⠀⠈⡀⠁⠀⠀⠀⡨⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢁⢈⣽⡮⣝⢟⠞⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠆⣥⡝⣺⣍⡗⠁⠀⠀⠉⠊⠀⠀⠀⠈⠀⡡⡄⡔⡊⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⣄⡿⣿⠗⠏⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⢨⡖⠟⡮⠂⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠲⡆⡟⣿⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢂⣈⠕⢌⡜⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠄⠀⠀⠀⠀⠀⠄⠀⠌⠀⠀⠀⠀⠀⢀⡐⣮⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡈⠂⠮⣆⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠈⠈⠉⠀⠈⠀⠀⠀⠀⢀⠀⣠⣼⡇⣾⠰⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡢⡶⢥⠈⠀⠀⣟⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡠⠀⠠⡀⠀⠀⡀⢀⡦⣠⠀⢲⣔⣾⢿⠩⠻⡈⠉⣃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠢⠀⠀⠀⠀⠀⠃⠀⠀⠓⠥⠪⠗⠫⠒⠭⠃⠀⠢⡁⠤⣔⡌⠤⠃⣊⠚⢨⠗⡓⠃⢕⠒⠪⡶⢣⣘⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡵⠒⡁⡤⡣⠅⠀⠁⠁⠀⠀⠀⠈⠀⠠⣹⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢣⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀