⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⢴⢔⣔⡴⡰⡠⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⢐⢠⢠⢠⣠⣳⡳⣫⢯⡳⣯⡺⡵⡱⡱⡱⡱⡸⡰⢠⠠⠠⡀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⠥⠡⠕⠅⠃⠂⡀⡨⡮⣳⡳⣳⢽⡺⡽⣺⢵⣫⢗⢕⢕⢕⠥⡱⡸⡨⡪⡢⡡⠨⠐⠈⠢⠢⣁⢢⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠢⠨⠀⠁⠈⠀⠀⢄⢼⡺⣝⣞⢮⢯⡳⡯⡯⣳⢯⢞⡝⡜⡜⡌⡪⡪⡨⡂⡊⡂⡪⡢⡀⠀⠁⠂⠀⠈⠐⢔⠀⠄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠕⠅⠕⡀⡂⠀⡈⡈⡮⣗⢯⡺⡮⣯⡳⡯⣏⢯⡳⡽⡵⣫⢪⢪⢪⠪⡢⠪⡪⡪⡨⡢⡢⡢⡀⡀⢄⠈⠔⠬⡐⠈⠔⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊⠢⠈⠐⠄⡽⣝⢮⣗⡯⣟⣞⢮⢯⢞⡗⢯⢫⢫⢺⠪⢎⢎⢎⢎⠮⡎⡆⣓⡢⢇⢎⡆⢆⡊⠈⢈⢐⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣟⢼⣳⡳⣝⣗⡽⡺⡩⡳⣜⣞⢽⢵⢱⢱⢱⢱⠩⡌⡇⡇⢎⠆⢕⠅⠕⢌⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣪⣗⢷⢝⢇⠗⢕⢕⡵⡯⡳⣕⡯⣻⡘⡜⡌⢎⢎⠪⡊⡪⠢⡣⡡⡑⠅⢕⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⣗⣗⢯⢇⢏⢪⢪⣺⢝⡵⡯⣳⣫⢗⢕⢜⢜⢔⢕⢕⢕⢜⠌⠜⡔⠅⠅⢕⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣞⢮⡳⣹⢂⠢⣪⣬⣙⠹⠽⡵⣫⠏⡸⡨⡪⡪⠢⢃⢁⢐⠀⠀⡇⠕⠅⢕⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢮⢗⡕⡽⡀⡣⠣⠳⠱⣫⡷⡬⣑⠳⡰⡑⡁⡀⠀⡂⠂⠀⠀⠀⡇⡣⠡⡑⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡯⣳⢱⢽⠐⡜⢍⠉⠒⠐⠨⡙⡘⠎⠆⠂⡂⡀⢄⢪⢀⠀⠀⠀⡧⡑⡑⠔⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢮⡳⣹⢼⠡⡹⣢⡑⢄⢀⡀⡀⡐⢰⠰⠑⠔⠒⡲⡽⡺⠸⠘⠐⣏⠪⡊⡊⠢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢽⡪⡞⣼⢑⠸⡹⣽⣲⢆⣖⢌⢬⢘⡆⠀⠠⠈⠌⡎⠄⠈⠀⠨⡎⡌⡂⠪⠨⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡺⡵⣱⡫⣞⠆⢌⢪⡚⢮⢦⡫⡫⡎⡮⡆⠀⠀⠀⢀⢇⠁⠀⠀⢸⢸⠨⡨⠨⠨⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡺⡕⡮⡪⣗⠕⡐⢄⢫⡪⡪⡺⣪⢳⡑⡑⡌⠄⠐⠐⡄⡀⠂⡈⡘⡆⢕⠌⠌⢌⢂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣝⢎⣞⢜⡧⡃⢌⢪⢢⡑⢝⢧⢕⡥⣅⡅⠥⠑⠠⠐⠄⠠⢀⠢⠸⡌⡢⠡⡑⡐⡐⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⢝⢔⡇⣗⡽⡌⡐⢌⢪⣚⠦⣍⠳⡝⣦⠡⡑⡈⠈⠈⡂⠀⠂⡐⢸⡂⡪⡂⡂⡂⡂⡂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡮⡣⣳⢕⡳⣝⠆⢌⢲⡰⡸⡹⢮⡳⣬⣢⢱⢐⢔⢌⠂⡂⢈⢐⠌⢸⠨⡊⡂⡂⡂⡂⠢⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣳⠣⣕⢯⢪⡺⣕⢇⠂⢆⠙⡮⣎⢕⢝⢜⢎⢗⢇⢇⢇⠂⢆⠐⡀⠂⢸⢑⢕⢐⢐⢐⠨⡈⠢⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⢗⡕⣕⢯⢣⢣⡫⣞⠆⠅⢕⢕⢌⠪⡻⣲⢵⣱⡱⣣⡳⡱⠨⡀⠠⠠⠡⢸⠢⡑⡐⡐⡐⡐⠌⢌⠂⠌⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣮⡳⡱⡵⣹⢵⢱⢱⡝⡵⡇⠅⢕⢧⡳⣕⢬⡈⡣⡓⠏⠎⢌⠌⢄⢂⠨⠨⢈⢸⢌⢂⢂⠢⡐⠌⠌⡂⠅⠅⠌⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡧⣻⣺⡪⡯⡣⣟⢜⢜⢮⡇⡿⣕⠡⢱⡱⡹⣪⠳⢵⢕⡵⣱⢱⢱⢑⢐⢐⠨⠈⠄⡪⡢⡂⠢⡑⠄⠅⠅⡂⠅⠌⠠⢁⠨⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⡜⡸⣸⣺⣳⡳⡝⣕⡽⡪⡪⣪⣟⢮⢺⡕⠌⡂⡳⣌⡊⡛⠬⣕⢫⢳⢝⢜⢌⠔⠄⠨⠨⢂⢪⠢⡈⠢⡈⡂⠅⠅⡂⠅⠡⠈⠄⢂⠐⡀⠡
⠀⠀⠀⠀⡀⡰⣸⢮⢳⢱⡃⡪⡮⡞⡮⡪⡪⣞⡎⡇⢮⣞⢾⢽⠸⣝⢐⢐⠑⢆⠳⣱⢡⠨⢈⠈⠌⢌⠢⠡⠁⠌⠐⡀⡣⡣⡈⡂⡂⡂⠅⠅⡂⠅⢂⠡⠈⠄⢂⠐
⠀⠀⡔⣔⢷⢝⢵⡫⡇⣗⢕⢕⢝⢪⢸⡸⣝⢖⢕⢌⣗⢗⢯⢯⡑⡕⡕⡀⡂⠌⡑⢆⢏⢷⢥⢥⡱⡱⡑⠅⠐⡈⠄⠀⡇⡂⡂⡂⡂⡂⠅⠅⡂⡈⠄⢂⠡⠈⠄⢂
⡄⣇⡯⡯⣫⢽⣜⢮⡳⣕⢯⡢⡣⡣⣳⢝⢎⢎⢆⣷⣫⡯⣗⢷⡱⡱⣱⢐⢘⢔⠐⢌⠘⠮⣎⡗⣽⣪⠪⠨⠀⠠⠁⠀⡇⡂⡂⡂⡂⡂⠅⠅⠄⢂⠈⠄⢂⠡⠈⠄