⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠏⢋⠠⠁⢻⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡺⠃⠂⠐⡀⠐⠈⡀⢫⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠋⠠⠈⠄⠁⠄⠨⢀⠐⢘⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⠟⢊⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⢊⠐⢈⠀⡂⠈⠄⢁⠐⠠⠐⠀⡷⣇⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡮⡯⠋⠂⡁⠄⠐⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⡲⡯⠏⠄⡀⠂⠄⠂⡀⠡⠈⠠⢀⠡⢀⣁⢿⢵⠻⠽⠻⢽⡳⣖⣦⢤⣲⡽⠞⠑⡀⠌⠠⠀⠂⣡⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠊⠯⠁⢂⠐⠀⠂⠄⠁⠄⠂⢁⠐⡀⡎⡎⡎⠎⠐⠐⠈⡀⡂⡎⡎⡎⡏⠗⢁⠡⠐⢀⠐⡀⠡⡸⡁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⠐⢀⠡⠀⠂⡁⠁⠄⠡⠐⠈⡀⡰⡱⡱⡱⠁⠂⢁⠈⢄⢢⢣⢣⢣⠃⠄⠂⠠⠐⠀⢂⠠⠐⣸⢡⡂⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡗⠃⡐⢀⠐⢈⠠⠐⠈⡀⢂⠈⠄⠠⡣⡣⡣⠡⠀⠅⡀⢢⢱⢱⢱⠱⢁⠐⢀⠁⠂⡁⢈⠠⠀⠂⢊⢁⡜⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢠⣻⠪⠀⠂⠄⠂⠐⡀⠄⠂⢁⠠⠀⢂⠈⠄⠣⠣⠑⠈⡀⢂⠀⡇⡇⡇⡇⠃⠄⠂⠐⢈⠠⠐⢀⠐⠈⠐⡀⠸⡔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣻⠝⢗⡟⡂⠂⢁⠈⠄⡈⢄⣤⡶⡾⡄⠠⠈⠠⠐⢀⠡⠀⡁⠂⡀⠂⠠⠘⠘⠘⢀⠡⠀⠡⠈⠠⠀⠂⠄⠂⢁⠁⠄⠂⠉⢦
⠀⠀⠀⠀⠀⠀⡴⡟⢓⠫⣿⣲⣄⣸⡪⠀⠄⠂⠠⠈⠠⠐⢀⢰⡾⣞⣟⣟⣯⠐⢈⠠⠈⡀⠄⠂⠠⠁⠠⢈⠐⢈⠀⠅⠠⠐⠈⡀⢁⢂⢁⠈⠄⡈⠠⠐⠀⠌⠐⢀
⠀⠀⢀⣴⠶⣖⢿⢐⠡⢊⠷⣻⣺⢾⡵⣔⡀⡁⠂⡁⠐⡈⠠⣿⢽⡯⣯⣯⢿⠀⠂⡀⢂⠀⠂⡈⠄⠨⠀⠂⠐⡀⠐⡈⢀⠂⢡⣲⢿⣽⣻⣻⢦⡀⠂⡈⠐⢈⠀⠂
⢀⣴⢟⠣⡑⡰⢐⠔⡡⠡⡊⢔⢸⣑⠻⡽⣻⢶⣔⡀⡁⠠⠈⢯⢿⣽⣻⡞⠃⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠄⠁⠄⡀⢂⡿⣯⢿⢾⣽⡽⣯⣗⠠⢀⠡⠀⠌⠐
⡿⡎⠪⡐⢔⢨⣢⢬⡢⡑⡐⠅⡢⠨⡃⠧⡍⣛⢞⢿⣲⣔⡄⠂⡈⠁⠅⢀⠡⠀⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠂⠐⣿⢽⣻⣻⣞⣯⡷⣿⠀⠂⡀⢂⠈⠄
⣿⢅⠕⡨⢲⡫⣮⢷⣻⢮⠐⢅⢊⠜⡜⢬⢨⠢⢣⢣⢫⢳⢯⢷⣤⡈⠄⠂⠀⠀⠈⠢⢄⠤⠜⠣⡀⠀⠀⣀⠖⠀⠀⠂⠁⠄⠙⢯⣟⡷⣯⡷⡟⡃⠄⠁⠄⡀⠂⠄
⣯⢇⠌⡂⢯⡺⣽⢽⣞⡟⢌⢂⠢⡑⡕⡕⡕⢭⢲⢨⢊⢎⢪⣙⢺⢽⢾⣤⡁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠁⠀⠀⠀⢈⠠⠁⡐⠠⠈⡉⢁⠑⠀⠄⠂⠁⠄⠂⡈⠀
⣿⡑⢌⢂⠅⡛⠮⡻⢪⠑⢔⠡⢊⢌⢎⢎⢎⢎⢎⢎⢎⢎⢲⢸⢘⢜⢜⡞⡽⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀⠐⡀⠂⡀⢂⠠⠁⠂⢁⠈⠄⠂⡀⠁
⣟⡎⡔⡐⡅⠪⣈⠢⡑⢌⠢⡑⡔⡜⡜⢜⢜⢜⢌⢎⢎⢎⢎⢎⢎⢎⢮⡣⡣⡗⡕⣟⢷⣤⡀⣀⣤⢤⣄⣀⠀⡀⠂⡈⠄⠠⠁⡀⠂⡐⠀⠄⡈⠐⡀⠂⠄⠁⠄⠁
⣿⢕⠕⡕⡌⡊⡲⡹⡐⡡⡱⡱⠱⡱⡩⡺⡸⡔⡕⡕⡕⡅⡇⡕⡕⡕⣕⢇⢇⢯⢪⢇⢇⡗⡻⣽⢽⢹⠺⡽⡯⣆⠐⡀⢐⠀⡁⠄⠂⠠⢈⠠⠀⡁⠄⠂⡈⠐⢈⠀
⡿⡕⡨⠨⡒⣌⣂⢪⢰⠸⡐⠌⡌⢢⢣⢣⢣⢣⡫⡪⣪⢪⢪⢪⢪⢪⢸⡕⡕⡽⡸⡕⡕⣕⢕⢧⢫⢳⢕⢕⠭⣻⡆⠐⢀⠐⢀⠐⢈⠀⢂⠀⢂⠠⠐⠀⠂⡁⠄⠂
⣿⡣⡪⡨⡐⢔⠠⡑⡐⠅⡌⡮⣺⡪⡮⣪⢺⢸⢸⢸⡸⣸⢱⢱⢱⡱⡱⡝⡮⣳⡱⡝⡜⡎⡎⣞⢜⢼⡐⡅⢍⠺⢵⡎⢀⠐⠠⠈⠠⠐⠀⠌⠀⠄⡈⠄⠁⠄⠐⡀
⠽⡽⣮⡪⡪⡢⡳⣢⢗⡽⣪⢮⣒⢭⠫⡞⣵⢳⢵⡱⡱⣪⢪⢪⢪⢪⢪⢺⢸⢱⠹⡝⡮⣣⢇⣗⢕⢵⢱⢱⢱⢱⢱⢟⡀⠄⢁⠈⠄⡈⠐⢈⠀⡂⢀⠂⠁⠄⢁⠀
⠀⠈⠑⠫⢟⣞⡮⣎⣕⢽⢪⣗⢽⡪⣗⢵⡱⡹⡱⢽⢕⣞⣜⢜⢜⢜⠜⡜⢜⢬⢹⢸⢸⡱⡹⢮⡺⡼⡸⡸⡸⡸⡨⣻⡆⠐⠀⡂⠐⡀⠌⡀⠄⠐⡀⠄⠡⣈⣠⢴
⠀⠀⠀⠀⠀⠈⠉⠻⢺⣻⣺⡼⣕⣯⡺⣕⢯⡫⣞⢼⡱⡱⡳⣝⢮⡲⣕⢕⢕⢕⢕⢕⢕⢕⢝⢜⢜⢝⢜⢜⢜⢜⢜⢜⣧⠠⡡⠀⢂⠠⠐⡘⢦⣁⠠⢀⢱⢏⠪⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⠷⣗⣟⣗⡯⣾⢵⢯⣺⢕⣗⢼⡸⣙⢮⣳⣣⢧⣣⣣⣣⡱⡱⡱⡱⡱⡹⡘⡦⣣⢱⡹⣾⠨⠢⡱⢠⢐⢐⢌⠢⡊⢝⢚⠝⡐⡑⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠐⠠⠐⡀⠅⢉⠊⣟⡮⠗⠋⢊⠁⠅⠨⠐⡈⠈⠈⠋⠗⡷⣕⡕⡕⡕⡕⣜⣯⢯⡟⢌⢊⠢⡑⢌⠢⠪⡨⢌⠢⡑⢌⠪⡨⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⡇⠈⠄⡁⠄⢂⠐⠠⢸⡍⠨⠈⡀⢂⠡⠈⠀⠀⠀⠀⠀⠀⠀⠙⠺⣮⣪⢪⢺⣺⢑⠅⢕⠡⡑⢅⠕⡡⡃⣊⠢⡱⢘⠌⡌⢆⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣺⠀⠅⢂⠐⠐⠠⢈⠐⢸⡅⠂⡁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣞⣞⣗⢅⠪⡂⡣⡑⢅⢊⠢⡊⢔⢑⢌⠢⡑⡌⡢⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣞⠈⠄⢂⢈⠨⠐⠠⢈⠸⣣⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡀⠓⡷⣥⢕⢌⠢⡊⡢⡑⡑⡌⢆⠕⡐⡅⠕⢌⠢⡊