⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠄⠢⠐⢂⠊⢂⠒⡐⢁⠂⠢⠐⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢂⠑⠄⢌⠐⡁⢊⠐⡡⢈⠄⡡⢈⠄⡡⢁⠑⡈⢂⠢⠐⢄⠈⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠈⠂⢄⠑⢄⠑⡈⠂⠌⠠⠁⢂⠐⡀⢂⠐⡀⢂⠐⠠⠁⠌⠠⡁⠊⢄⢁⠊⡐⢄⢈⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠡⠀⠌⠢⠠⡁⢂⠐⠈⢄⠡⡠⠡⢄⠢⡐⠄⠆⠔⠤⠠⠅⠌⡐⡠⡀⠁⠢⢀⠁⠂⠔⠠⠑⢄⠈⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠀⠁⢄⠁⡊⠐⢄⠰⡀⡊⡑⢄⠑⡌⢂⠁⠄⠐⠀⠂⠐⠀⠂⠐⠀⠄⠠⢈⠁⠃⠆⠥⡈⢄⠁⡊⠐⠄⠢⠀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠂⠀⢀⠂⠐⢄⠌⠢⡑⠔⡨⢂⠜⡠⠃⠠⠀⠐⢀⠁⡈⢀⠁⡈⢀⠁⠐⠀⠂⠠⠈⡐⢀⠈⠂⢕⠢⢌⢄⠑⡈⢂⠢⠀⢁⠂⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠄⠠⡁⠜⡠⡑⠡⡊⢌⠢⡑⡌⠀⠂⠠⠈⠠⠀⠄⠠⠀⠄⠠⠀⡀⢁⠈⡀⠂⠠⠀⠄⠈⠄⡀⠓⡔⡡⠣⡄⡡⢈⠢⠀⠄⠐⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠂⢔⠨⢂⠆⡸⢠⠑⡌⢢⠘⢀⠈⡀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠄⠠⠀⠄⠠⠈⡀⢂⠈⡐⢀⠐⡀⠘⡌⡲⡈⠖⢤⠁⡊⠐⠄⠐⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠠⠀⠀⠄⠠⡃⢢⠑⡅⢪⠐⡅⠪⠀⠁⠀⠀⠄⠠⠈⡀⢁⠈⡀⢁⠈⠀⠂⠐⠀⠂⠐⠀⠂⠄⢀⠂⡐⢀⠂⡐⢀⠱⡌⡪⡱⡨⠪⡄⢑⢈⢂⠁⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⠀⠀⢂⢈⢘⢄⠣⡨⢊⠆⡕⢸⠀⠂⠀⠀⠀⠐⠀⠂⠄⠠⠀⠄⠠⢀⠁⡈⢀⠁⡈⢀⠁⡈⢀⠂⡐⢀⠂⡐⠄⠢⠀⣇⠪⡔⡱⡑⢜⠢⠐⢄⠡⡀⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢀⠀⠡⢀⠂⢔⠅⢕⢌⠢⡣⢊⢆⢣⠠⣁⠐⡀⠡⢈⠐⡀⢂⠐⡀⠂⠄⢐⠀⡂⢐⠀⡂⢐⠀⡂⢐⠀⡂⠔⡈⠔⡁⢂⢕⢕⢜⢌⢎⢪⠱⣁⠢⠐⢄⠀⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠄⠠⠁⢄⠁⡎⢜⢄⠣⡱⡘⢔⠥⡑⡕⡌⡲⠀⡂⢐⠀⡂⠐⠄⠨⡀⡁⢂⠐⠄⠢⠐⠄⠢⠐⠄⠢⠡⡈⠢⡈⠢⡈⢴⢑⢕⢪⠢⡣⡱⡑⡕⡄⠑⢄⠑⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⡐⠠⢁⠌⠢⡀⣇⢪⢢⠣⡕⣍⢎⢎⡪⡪⡪⡪⣣⠨⡠⠡⡈⢌⢂⠑⠄⢌⠄⡑⡈⠢⡑⢌⠊⢌⠊⢔⠡⡊⢔⠡⡑⢰⠣⡣⡣⡣⡝⣌⢎⢪⢪⡂⠑⠠⠑⠄⠡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠅⢐⠌⡢⢑⢌⠒⢄⠧⡱⡱⣙⢜⢆⡣⡣⡕⣕⢕⠵⣨⢣⠜⡐⢌⠢⡁⡊⠢⠢⡈⢆⠘⢄⠪⡐⢅⠪⡈⢆⠱⡈⢆⠱⣨⢣⢫⢪⡪⡪⢎⢖⢕⢕⢕⠌⠄⡁⢊⠐⡀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⡅⢨⠂⠕⠀⠂⠡⢈⡊⠪⡢⡑⡅⡣⢪⠪⡪⡢⣓⢕⢕⢕⢝⢬⢢⡑⢌⢌⢊⠢⡑⢌⠪⡐⢅⠪⡐⢅⠪⡐⢕⠨⡢⡕⡕⣕⢕⢕⡕⣝⢪⢣⢕⠕⡜⠠⡁⠀⠂⠐⡀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⡂⠱⡁⠂⠀⡁⠂⠰⡁⢇⠜⢔⢌⠪⡢⡓⢬⠪⡢⡣⡣⡣⡣⡣⣣⡙⢖⠦⣱⣁⠪⡢⢑⢌⠢⡑⢌⢢⡑⡬⡢⡫⡪⡪⡪⡲⡱⡣⡺⣌⢧⠣⡕⢕⠜⡐⠄⠈⠀⠀⠄⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂⠔⠀⠀⠨⡀⢘⢌⢢⢑⠕⣌⠣⡪⡊⢖⢕⢕⢪⢪⡪⣪⢚⡔⣝⢜⢕⢦⢕⢝⡜⡕⡭⡪⡝⡬⡣⡕⢎⢮⢪⡪⡪⢎⢞⢜⡕⡳⡜⡬⡣⢕⢕⠅⢌⠂⠀⠀⠐⠀⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠡⠀⠀⠐⠄⢨⠢⡑⣅⠣⡪⣊⢎⢜⢕⢕⢕⡕⡕⡮⣪⢕⡽⣬⢣⡏⣮⢳⢕⡝⣎⢞⡜⣎⢮⢪⢎⡳⡕⡵⣱⡹⡪⡳⣕⢝⢎⢞⢜⢜⢪⠢⡑⢄⠃⠀⠀⠈⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠀⠀⠀⢑⠐⡕⢌⢆⢣⢕⢬⢪⢎⢮⢳⢕⡝⣮⢳⣝⢮⡳⣵⡫⣞⡵⣫⢗⡽⣪⢗⣝⢮⡳⣕⢯⡺⣜⢵⢕⣝⢎⡗⡵⡹⣕⢭⢪⡪⡱⡁⢎⠐⠀⠀⠀⠌⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⠀⠀⠀⢊⠜⡔⢕⢕⢕⢕⢧⡫⣎⠷⡝⣚⢕⠭⠪⣕⠝⠬⠹⠬⣙⢕⡛⠾⠵⣯⡺⣵⡫⣞⢵⡝⣮⢳⡕⣧⢫⡺⣕⢝⡜⢆⢗⢜⢌⠢⡡⠁⠀⠀⠂⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠣⡊⢎⢪⢪⡣⡳⣝⠪⢊⠈⠄⢂⠐⣎⢉⡇⢐⠁⡂⠐⢄⢉⠙⡪⢲⡹⣪⢻⢞⣵⡫⣞⢵⢝⢮⢳⢕⠵⣍⢮⢣⢣⠣⡊⠢⠂⠀⠀⡀⠡⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢀⣄⣀⡀⠀⠈⠢⠀⠀⠀⡀⠈⠪⡢⢣⢕⢝⠆⠐⠄⡈⠐⡀⢸⣿⣿⠃⠐⠄⡈⢂⠢⡐⠡⢊⡎⢉⡶⡙⡎⢷⢝⡷⣹⡣⣏⢧⡫⣚⢦⢓⢕⠕⡅⡱⠁⠀⠀⡀⠐⠀⠀⠀⠀ ⠀⠀⡀⠔⢱⠨⡢⡢⡪⣘⠳⣢⡈⢂⠁⠀⠀⢀⠀⡔⢡⠡⡫⢀⠁⡐⢀⠂⠄⠘⠿⠋⡀⠑⠠⠠⡁⠢⡈⡊⢸⣿⣿⠃⢎⠜⡕⡝⢾⣝⢮⡳⣕⢵⠱⡕⡕⡕⠱⠈⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀ ⠀⡐⠀⠂⡸⢌⢎⡪⠪⠜⢕⢕⣝⠠⢡⡂⠀⠄⠨⡂⢕⢌⢲⠀⡐⢀⠂⡐⢈⠂⡐⠡⢈⠌⢂⠅⡨⢂⠌⡌⢚⠿⢏⢘⠄⡣⢪⠪⡪⣷⢫⡞⡼⡨⡓⡜⡌⠊⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠀ ⠰⢀⠑⢠⡓⡕⢁⠐⡀⠢⠀⢌⢪⡗⢄⡫⡢⢔⠨⡂⢕⠔⡱⢀⢂⠐⡀⢂⠐⠄⡌⢂⠢⡈⢂⠢⡐⢅⠪⡐⡅⢪⢂⠕⡌⡢⡱⡑⢽⡪⡗⡭⢪⠪⠊⠀⠀⠀⠄⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠠⣁⢗⢜⢀⠂⡐⠠⡁⢌⠢⡌⡷⣹⠔⡍⢖⢕⡪⡂⡓⢌⢆⠱⡑⣄⠂⡁⢊⢛⢗⢶⡬⣦⣕⣬⣢⣣⣪⡪⡢⡑⢌⢆⢕⢜⢌⠮⡪⡊⢎⠄⠀⠀⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢖⢕⢕⢭⡂⢅⢌⠢⡢⡊⢖⢱⡫⣞⢜⢜⡕⣭⢯⢈⢜⢔⢕⢕⠬⡢⡳⡈⢄⠈⢇⠣⡳⡸⣎⡿⣽⢟⡟⡱⢪⠘⢆⠣⡣⡪⢪⠪⣊⠜⡠⠂⠀⠄⠠⢁⠈⢀⣠⣀⣄⣠⢀⠀⠀⠀⠀⠀⠀ ⠀⠈⢎⠎⣖⢝⡦⣣⡓⣜⣌⠷⡭⠙⢮⡳⡵⣹⢎⢯⢐⢕⢕⢕⢕⢕⡕⡽⣡⢏⣪⣒⢆⠦⢬⣈⢍⡘⢕⠘⣌⢑⢕⢕⢝⡜⡵⣣⢫⡞⠠⣈⣄⢥⢲⠪⡣⡲⡫⢖⢕⠎⢦⢩⠓⢦⡀⠀⠀⠀ ⠀⠀⠀⠁⠊⠕⠽⡬⠫⠮⠊⠉⢠⠃⡢⢪⠪⡲⠑⠁⢎⡲⡱⡱⣱⡣⡻⡼⠈⠙⠲⢧⣯⣝⣕⢞⡲⡫⣎⢷⠰⣕⢕⢧⡳⣹⡪⡳⣕⢭⢯⡲⣪⢣⡫⡇⡵⡙⠌⠃⠑⠩⢢⢣⡙⡔⠍⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠢⡇⡱⣑⠝⠀⠀⢂⠸⣪⡪⡳⡵⣹⠺⣌⢟⠢⢦⡠⣄⢨⠘⠓⠽⠾⣾⣷⣿⣜⢵⡣⣏⢾⢜⡵⡕⢫⡷⣹⡪⣇⢿⡸⠌⡠⢀⠁⠐⢀⠀⠱⡌⡺⠀⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣑⠇⢮⢨⡃⠐⡠⢈⢆⠨⠺⢝⢎⡳⣝⡀⠙⢫⢖⢮⣌⡳⣙⠼⠢⡲⣔⢔⢦⢬⠳⣝⢮⡳⣝⢎⠼⡠⢟⣵⣫⢞⣧⢫⠐⠔⢄⢈⠢⡀⠢⡀⣏⢎⠠⡑⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⠞⡱⡑⡜⢦⢑⠔⡅⢮⢱⢛⠲⣡⢏⢔⢍⡓⣑⠙⢎⢎⢗⢝⢞⡝⡶⣲⣍⢧⣫⢆⠬⣣⢝⠴⡱⡑⢎⠌⠁⠉⠁⠘⣧⣋⠪⡢⡑⡌⡪⡘⡴⡱⣝⠰⡱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠨⡪⡪⣪⡣⠙⠨⢣⢕⡍⡫⡢⡣⡱⡱⢌⢬⢩⢑⢕⡑⡫⡚⡜⠵⢕⠮⣳⢍⡷⡱⣎⢎⢧⢱⡩⡊⠀⠀⠀⠀⠀⠘⢮⡳⡬⣪⢜⡬⡺⣜⢮⡺⡕⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⡐⢕⢝⢜⠖⠀⠀⠀⠈⢦⢱⢑⢎⢪⠪⡪⠂⠱⡐⢅⠎⡌⡮⣪⢜⢕⡱⡻⣗⢻⣳⣝⠸⡊⠒⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠎⡾⡜⠧⠫⠚⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠕⠵⠍⠀⠀⠀⠀⠀⠀⠁⠑⠁⠣⠑⠁⠐⡀⠪⡐⡕⠘⣮⢪⠷⠨⡽⣫⣛⣫⣓⡭⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠁⠀⢎⠐⢄⠈⠢⡈⡁⢊⠐⡹⣂⢧⢺⠔⡵⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⡁⠠⠠⡔⡵⢬⡱⡥⣩⢒⡔⣘⢔⡑⢔⢌⢚⠒⡫⡐⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠈⠢⡀⠀⠄⠠⠀⠄⠐⠀⠄⡁⠃⠪⠒⠥⡩⠪⡑⢍⢪⢓⢝⢪⢫⡚⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⡁⢄⠈⠢⡐⠀⠂⠠⢁⠐⠠⠀⢅⢈⠂⠢⡔⢓⢊⠢⡕⡡⡣⡱⡱⢌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠐⢀⢯⠢⣑⢄⢈⠣⢌⠢⠠⡁⡊⢐⠄⡢⢑⡱⡈⢆⠱⣡⠣⡪⡊⢖⠱⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠡⠀⢷⡈⢆⢣⣣⢊⢆⠕⣆⢢⢘⢄⢣⢘⠔⠵⣜⡬⣪⢒⢕⢕⢍⢎⢕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⢐⠈⡪⡳⣕⢮⢿⡺⣕⠮⢖⡕⡥⡣⡕⡝⢜⢆⢖⢕⢕⢕⢕⡕⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⠀⡁⢈⠠⢀⢅⠘⢔⢬⢳⢕⡽⠊⠀⠀⢹⡞⣵⢞⣜⡵⡱⡕⡵⣱⡣⣳⢊⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⢄⠐⡠⢂⠢⡐⢅⢕⢕⠧⡳⠁⠀⠀⠀⠀⢻⢜⡝⢮⢪⢫⢎⢝⢪⢓⢕⢅⢣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣌⠢⡱⡨⡪⡲⡱⣍⠞⠀⠀⠀⠀⠀⠀⠈⢣⡳⡐⡑⢕⢕⢕⠕⡥⡣⡱⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠵⠽⠜⠚⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⢌⢢⡱⡡⡫⡲⡱⡕⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠵⠮⠺⠎⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀