⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⣠⡪⠚⡀⡤⡠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠜⡐⢄⢐⠄⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢄⢦⢢⡠⡀⡀⡰⡣⡯⣪⠲⢣⠫⡪⣫⢺⠼⡹⣔⢤⣀⣀⢠⢔⢕⢅⡕⡜⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡵⣝⢕⢯⢳⢝⠮⡫⣎⢗⠝⢔⠡⡑⢌⢌⣂⢆⣕⢌⡢⡣⣳⢪⡳⣕⢗⡗⡽⡔⠍⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠮⢎⠣⡃⡫⠨⡪⣺⢪⡳⡱⡕⡕⢌⢞⠮⡪⡧⠓⠗⢝⢞⢮⡳⣝⢮⡳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⣐⢜⢮⠍⡢⢑⢐⠌⡌⡞⡊⡣⢙⠸⡨⢢⢣⢱⢱⡹⠀⠀⠀⠀⠑⢧⡳⣕⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢇⢗⠼⡕⢗⡕⡕⣐⠕⠁⡬⠐⠀⠀⠠⠱⢰⢱⡫⡇⡇⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢏⢷⠀⠉⡈⠌⣢⠀⠀⠀⠀⣀⠀⠀⠀⡸⣸⢵⣹⢱⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡎⡮⡹⡱⡹⡱⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣯⢇⠦⠀⠀⠃⠀⡠⡎⡧⡳⡹⡲⡈⠽⣕⡗⡧⠇⠠⠠⠐⢈⠨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡭⡣⣣⢳⡱⡹⡜⣕⠕⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢮⡪⡳⣄⢀⢎⢇⢗⡵⡝⣪⡫⡀⡈⡧⢫⠨⠈⠌⡆⠌⠄⠢⠁⠅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡺⣝⢮⡺⠚⠈⠈⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠽⢸⢪⢣⣳⢽⢌⠮⣓⢕⡆⢆⢢⢜⠔⣣⢑⠨⢀⢅⡌⠌⠌⣐⢱⢱⡂⠀⠀⠀⢠⡀⠀⡴⣝⣝⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⢮⡨⡫⡕⡕⡕⡕⡝⡜⡮⡫⢢⠣⡑⡱⡬⠕⠕⣔⢄⢂⢍⡩⢤⢣⢣⢣⢫⢢⢄⡀⢆⢮⡛⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢆⢔⢧⣫⡳⡵⡕⣕⢵⢱⢱⢵⡹⢕⢅⠣⡑⢅⠣⡱⢁⠃⡀⡰⡓⠃⠉⠚⠘⠸⠱⡕⡵⡱⡱⡪⡪⡪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢀⢜⢜⢎⢗⣕⡞⠊⠃⠁⠀⠉⠉⠉⠀⠁⡑⣈⢃⠈⠀⢅⠘⢄⣂⠗⡠⡅⠀⠀⠀⠀⠀⠀⠈⠘⠊⣞⢜⢜⢜⢜⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠜⠀⢔⢕⡕⣕⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡄⠠⠀⠑⠐⠀⠂⠀⠈⠍⠍⢕⠅⠁⠀⠀⢀⡮⣳⠽⣸⢸⢣⠃⢲⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢂⠨⢠⢱⢱⡱⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣨⠀⠀⠄⠐⠀⠀⠐⠈⠀⢈⠨⠡⡁⢀⢠⡲⡝⠞⠀⠀⠈⠪⡪⣊⠄⠙⠜⠄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠔⠄⠂⡮⡪⡪⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⢤⢲⢱⢱⢡⡒⣶⣀⢤⡀⠈⡠⣀⡈⡇⡯⠍⡐⢐⠠⠉⠢⡀⠀⠀⠀⠀⠣⣣⢃⠡⢁⠅⡐⡁⢀⠀⠀⠀⠀⠀
⠀⡠⠐⡈⠄⠅⢮⢪⠮⠀⠀⠀⠀⠀⠀⠀⢀⠴⠝⣆⢇⢏⢎⢎⢮⢪⡣⣣⡻⡼⣕⡝⣄⢕⡕⡎⡎⣞⡀⢂⠰⠂⠣⢁⢒⠀⠀⠀⠀⠀⠰⠠⠀⡆⠂⢂⢂⠡⣄⠀⠀⠀⠀
⢰⠀⡁⠰⠈⢤⡣⣣⠁⠀⠀⠀⠀⠀⠀⠐⠄⢂⢁⠲⡱⡵⣹⢪⡳⣵⠹⠮⠚⠘⠊⠚⠪⠯⡎⣗⢝⢦⣳⠠⠰⠀⠅⡂⡪⢈⠄⠀⠀⠀⠀⠃⡂⡐⡁⢂⢐⢐⡯⣦⣀⠀⠀
⠈⠅⠤⢃⣡⢳⣹⠆⠀⠀⠀⠀⠀⠀⠀⠱⡨⢠⢢⢪⢚⢎⠺⡩⡂⢇⠔⡢⠤⡠⠀⠀⠀⠀⠀⠀⠈⠈⠚⢄⢃⠫⠺⡊⠅⡂⢒⠀⠀⠀⠀⢸⡮⡶⣬⡪⡯⣫⢺⢜⡮⡧⠀
⠀⢸⣝⢇⢧⡳⣕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠂⢅⠣⢪⠨⡢⠣⡑⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡑⣌⢂⠊⠅⡊⠄⠀⣎⢇⡗⠁⠈⢮⢣⡑⢕⢗⢽⣹⠄
⠀⠀⠀⠙⠑⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⣕⣍⣆⡇⢎⠪⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡐⠢⠡⠩⢐⠡⢀⠀⠀⠀⠀⠀⠀⢓⢵⢥⠑⠧⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⣻⢭⡳⡯⣪⢳⡝⣏⢇⢗⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠡⡑⠄⠅⠅⢅⠢⡀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢅⠑⠄⠅⢕⠡⠡⢊⢔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡶⣹⢹⢵⡹⣝⢜⢦⢳⣕⢖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠊⠓⠓⠱⠕⠙⠪⠓⠓⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀