⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡄⣄⢆⠦⡌⡆⡎⡔⡤⢔⢄⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣳⣳⢯⣞⢶⣲⡤⡤⡄⡄⠀⠀⠀⠀⠀⢠⡠⡦⡢⣇⢆⢑⢑⢕⠍⢕⠕⢅⠣⡑⡘⡘⡐⢜⢜⢒⢕⠤⡀⠀⠀⠀⢀⢠⢠⢤⢤⢦⣢⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠍⡾⡵⣫⢯⢞⡽⡵⣫⢏⣟⡽⡯⡯⣟⣽⣺⢽⡹⡜⢌⠢⢸⢸⢸⢨⠪⡨⠨⢢⠑⡐⢈⠢⠡⡱⡱⡑⡜⡽⢵⢯⢗⣗⢽⡹⡭⡳⡵⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢝⡮⣫⡳⣝⢮⡳⡝⣞⢞⡽⣽⡺⣺⡪⣗⢽⢜⢔⠡⡣⡳⣹⢪⢪⢨⠨⡢⡑⢄⠱⡨⠪⡸⣸⢪⢪⢪⢫⢯⢯⣞⣗⢝⡎⡯⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡪⣗⢝⢮⡳⣝⢞⣎⢯⢯⣺⡪⡧⡫⢮⢏⡗⡕⢌⢪⢺⢸⡱⡑⢔⢑⢜⢜⠬⡘⡜⡜⡜⢬⡫⡎⡎⡎⡯⣗⢷⢕⢇⢯⡊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣗⢭⡣⡳⡕⣗⠵⣕⣗⢷⢝⠵⠝⠕⠕⠇⠏⢎⢪⢪⡪⣎⢮⢢⢢⢱⢱⢝⢜⢜⢜⢜⢜⢮⡣⡣⡪⣎⢮⡳⡽⡜⡅⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡳⡙⣮⡳⣕⣝⣞⡮⡫⡃⠍⠨⠀⠅⢀⠁⠐⠈⠌⡚⡮⣫⡺⡔⡕⡵⡝⡮⡮⣳⢱⢱⡫⡞⡜⠨⢈⠪⢘⢙⢎⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢞⠮⢯⠺⢜⠮⡪⡪⡐⢈⠄⠁⠌⠀⠄⠁⡀⠂⢈⢺⢪⡫⣺⢪⢮⡫⡯⡾⢵⡳⡵⡝⡕⡅⠂⠐⠨⡐⣐⡕⡅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡫⡹⡨⡃⢅⢪⢎⣗⢅⠢⡁⠢⠀⠁⠄⢢⢐⠔⠐⡘⢜⢜⢎⢳⢹⡪⡳⡩⡣⡫⡳⡍⡇⡅⡂⡁⠡⡘⡔⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠰⡐⢔⠵⡝⡕⡕⢗⠧⡣⡣⡣⡣⡫⡸⣐⢅⠕⢠⢑⠅⡅⡣⡃⡇⡣⡱⠡⡣⠱⡹⢌⢆⠪⡪⡱⣪⡢⡇⡅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⢇⠇⡇⡕⢌⢊⠆⡣⢑⢁⢃⠕⡌⡪⣒⢔⣕⢵⢕⢕⠕⡑⠌⡂⠂⢂⠁⡂⡑⠠⢑⢌⢎⡪⣊⠲⡱⡱⡡⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢎⡢⣃⢪⠨⠢⠡⡑⠨⢂⠕⡔⣕⢕⠕⢕⠕⡕⠽⡕⣗⢕⠄⢁⠀⠡⠀⠂⡐⠠⢁⠢⢸⢜⢎⢆⢇⢕⠜⠄⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡇⢇⢇⢃⢇⠣⡑⠌⢌⢄⢇⣗⢵⢽⡹⡼⢸⢸⢕⢽⢸⢜⠬⡠⡂⡁⡀⠅⠐⡈⡐⡨⣪⢳⢕⡳⡹⡽⡊⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠪⡘⡌⢎⢒⠔⢅⠢⡃⢎⢪⢢⢎⡧⡯⣝⢵⡱⣕⢥⢣⡪⡪⡪⡢⡣⡊⢆⢆⠢⠈⠄⡂⢆⢇⢗⢕⣗⢵⢽⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠂⢅⢪⠨⡨⠢⡩⡪⡪⡸⡰⡱⡹⣕⢯⢯⡪⣣⢫⢪⠪⡊⡎⢜⢜⢌⢆⠕⡅⡢⡑⠡⢊⢔⠱⡸⡸⡱⣕⢕⡗⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡂⡊⠌⠰⡑⢐⠠⢁⠢⡊⡆⡇⡇⢏⢺⢸⢕⢷⢝⡮⡳⡣⣫⢪⢪⢣⢣⢕⢕⢕⢑⢑⠨⡐⡐⠔⡕⡕⣝⢮⢎⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢂⢊⢐⠨⡘⢌⡐⠜⡔⢕⠡⡑⡑⢜⢸⠸⡘⡜⡎⡗⡽⣹⣪⡺⡜⡮⡪⡪⡊⡢⡂⡑⡔⡱⡰⣑⢕⢕⣝⠮⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡂⣂⠢⡂⡢⢑⢑⠠⡑⢌⠎⢜⠐⢌⢊⠔⡑⢱⢨⠪⡪⡺⣜⢮⢮⢯⢮⡳⣕⣕⢕⢕⢕⣕⢕⡵⣱⡣⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠱⡐⢕⠰⠠⡱⡐⢅⢊⠢⢣⢑⢱⢐⠁⠅⠨⡐⠡⠡⡨⢪⢊⢪⢫⢫⣳⣫⣗⢷⢽⢵⣳⣳⡏⡚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⠕⡅⡣⢑⠑⢐⠨⠰⢐⢑⢅⢕⢐⠡⡨⡈⡊⢐⠈⡔⡌⡆⡕⡰⢡⢣⢪⡲⡳⣝⢽⠽⠚⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡕⡕⡌⡢⠨⠂⠅⠡⡂⠑⠐⠐⠠⡂⠅⢂⢂⠢⡑⠌⡊⠌⡪⡊⡂⢇⢇⠫⡪⡪⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢕⠌⢔⠨⡈⢌⠨⡈⠄⡁⠡⡑⡑⠔⢌⠢⡘⠜⡜⡌⡆⣑⢐⢐⢔⢱⢸⡸⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠱⡐⡡⠢⡁⡂⡊⠄⠌⡂⠢⡘⢌⠢⡱⢨⠨⣂⢪⢸⢰⢱⡱⣕⣝⣵⣻⡨⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠢⡊⠔⡐⢌⠢⠡⡈⠄⡣⡈⡢⡑⢅⢢⠣⡱⢱⠱⡑⠕⢝⢾⣺⣞⢮⢝⡒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡅⢌⠢⡨⡂⠔⠡⠢⠑⠔⠨⢢⢡⠱⠘⠀⠀⠀⠀⠀⠗⡧⡳⡱⡱⡸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡆⠕⢌⠢⡃⡑⠠⠡⠨⡪⡒⡕⡅⠀⠀⠀⠀⠀⠀⠁⠁⠉⠊⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢘⠔⠡⠢⢢⢑⢅⢇⢇⢇⢕⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡡⢅⠕⣆⢇⢇⢆⢗⡜⣖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢕⢕⢕⢕⢕⢜⢖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡪⡂⡑⡐⡔⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⢰⢜⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀