⡆⡗⣎⢖⢕⢎⢖⢕⢮⡪⡪⡪⡪⡪⡪⡪⡪⣪⣪⣪⣪⣪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡲⡕⣎⢖⢕⢎⢖⢕⢎⢆⢗⢜⢆⢇⢎
⡪⡪⡪⡳⣕⢕⣕⣕⣕⢝⢮⣫⣫⣫⣫⣫⡫⡮⡮⡮⡮⣺⣪⣫⣫⣫⣫⣫⣫⡫⣺⡪⡮⣪⡪⡳⣕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕
⡪⡪⣪⣪⡪⡳⡵⡵⣕⢗⣗⢵⢵⢵⢵⢵⢝⣞⣞⢮⢯⣺⡪⡮⡮⡮⡮⡮⣺⣪⣺⡪⡯⡺⣺⣪⡪⡳⣕⢕⢕⢕⢕⢕⢕⢕⢕
⡪⡪⡮⡺⡺⡺⡺⣺⣪⣳⡳⡽⡽⡽⡽⡽⣕⢗⢕⠕⢕⠜⡌⠪⢊⢎⢪⠪⢪⢪⢺⡪⡯⡯⡮⡺⣺⣪⡪⡳⡳⣕⢕⢕⢕⢕⢕
⡪⡺⣪⣫⣫⡫⡯⣺⣺⣺⡪⡯⡯⡯⡯⡯⡪⡪⡂⡅⡕⢕⢌⢌⢔⢸⢐⢅⢢⢱⢡⠫⡯⡮⡯⡯⡮⣺⡪⡯⡮⡪⡳⣕⢕⢕⢕
⡪⡯⡮⡮⣺⡪⡯⣺⣺⣺⡪⡯⡫⡫⡫⡪⡪⡪⡪⡪⡪⡪⡢⡣⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡚⡮⢯⡺⡺⡺⣪⣫⡪⡪⡳⣕⢕
⡺⣺⡪⡯⡺⡪⠫⡊⠪⢊⠊⡊⠌⠌⠌⠨⠐⡈⡐⢐⠐⢐⠐⠐⡐⠐⡐⠐⡐⠈⠄⠡⠨⠈⠌⠌⢊⠊⡊⠝⠸⡘⢎⠮⡪⡪⡳
⡽⡘⢌⢂⢊⠄⠕⠨⠨⢐⢐⢐⢨⠠⡁⢅⠢⡐⡐⡰⠨⠠⠨⡐⢄⠅⡢⠡⠠⠡⡨⠠⠡⠨⠠⢁⠂⡂⠄⠡⢁⢐⢀⠢⠨⢈⢎
⢝⢮⢦⣣⡢⡪⡨⡨⡊⡎⢎⢓⠕⠡⡁⠅⠌⡀⡂⠄⠅⠡⢁⠔⠐⡐⠠⠁⠅⠡⠠⠁⠅⠡⢁⢑⠨⠐⢌⠨⣀⢢⢰⡨⡪⡪⡪
⢽⢕⣗⣗⢽⢽⢝⣞⢮⢮⢦⣢⢡⢑⠄⢕⢐⠐⡐⠨⡈⢌⢐⠄⢕⠠⠡⡁⠅⠡⢈⠌⠨⡈⢔⣐⣌⣎⢮⢯⣪⡫⡳⣝⢮⡪⡪
⢽⢕⣗⣗⢽⢽⢕⣗⢽⢝⢷⢽⣝⣗⢧⡑⢔⠡⡂⡅⡢⡱⡼⣜⣦⣣⣑⢄⢅⡑⡐⡈⡦⡯⣳⣳⣳⣳⡳⡳⣕⢝⢮⡪⡣⡫⡪
⢵⢵⢕⣗⢽⢽⢕⣗⢽⢽⢝⣗⢷⣝⢷⣝⢮⢯⢮⢮⢮⢮⢯⢮⢮⢮⢮⢮⢮⢮⢮⣺⡪⡯⣺⣺⣪⣺⡪⡯⡪⡳⣕⢝⢮⡪⡪
⡕⣗⢕⢗⣗⢽⢕⣗⢽⢽⢕⣗⣗⣗⣗⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢽⢕⣗⣝⣝⢞⢮⢮⡺⡪⡫⡫⡪⡪⡳⡕⡝⡜
⢝⢜⢕⢕⢕⣝⢕⢗⢗⢽⢵⢵⢕⢗⣗⣝⣝⣝⢽⢽⢽⢽⢽⢽⢽⢝⣝⣝⣝⢽⢵⢵⢕⢗⢗⢗⢕⢝⢝⢮⡪⡪⡪⡪⡪⡪⡪
⡱⡱⡱⡕⣕⢕⢕⢕⢕⢕⢕⢗⢝⢕⢕⢕⢕⢕⢗⢗⢗⢗⢗⢗⢝⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢝⢜⢜⢜⢜⢜⢜

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣭⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⣠⢖⢦⠀⠀⠀⠀⠀⠀⢤⣤⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣏⢫⡍⡇⢠⡄⢰⠂⠄⠀⣉⣠⠞⣴⡙⣣⡿⣹⠀⢀⠀⠀⠀⢠⣾⣿⣿⠦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⡞⢿⣿⡱⢗⡛⠤⠼⠄⠀⠸⢰⡄⢀⣿⣿⡿⡱⢃⣠⠤⠒⠚⠋⠳⡄⠙⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠱⡾⠚⠉⠀⢀⣤⣶⣷⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘⣆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⢰⣿⣿⠟⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⣶⣌⢻⣿⣷⣄⡐⠛⠋⢁⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⡀⡄⠛⠀⠀⠀⣿⠴⢛⣉⣥⣾⢸⣿⣿⡷⢠⡞⡇⠶⡢⢸⠁⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡀⠻⠛⠈⠠⢰⣂⢻⣤⣭⣭⣭⡟⣸⣿⣿⠿⢓⣈⣇⣉⡠⠊⠈⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⣇⣀⢀⣠⣶⣿⣿⢗⣭⣿⣿⣭⣾⠿⠟⠛⣀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣶⡇⠀⠀⠀⠁⠀⠀⠈⠣⢽⣛⣻⠾⠿⠿⣟⠛⠉⠀⠀⠀⠀⠀⠈⠑⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠹⡟⠋⠀⠀⠀⠀⠀⠀⣰⣴⠀⠀⣞⠀⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣶⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⢿⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡠⢦⠠⣴⣿⣷⡶⠀⠀⠀⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢒⠒⣊⣡⢸⡀⢸⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠐⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⣾⣿⣿⠿⠿⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⠀⠀⠸⢿⠟⠀⠀⠀⠀⠀⠀⠉⠀⢠⠞⣰⣶⣶⣶⣶⠟⣿⣿⣿⣷⠀⠁⠁⠀⠀⠀⢣⠹⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣒⠠⡀⠀⢀⡏⢸⣿⣿⣿⠟⡩⠚⣌⢿⣿⣿⡇⠀⠀⠀⢠⠀⠸⠇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣄⠀⠀⠀⢰⠱⠶⣾⣝⠀⢙⠋⠁⠈⠻⠿⢡⠊⠀⠀⠈⠢⢭⡭⠴⠚⠒⡄⣵⡧⠀⠻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠌⢿⣮⣝⠰⣄⠀⠀⠀⠀⣀⠜⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⢇⢸⣿⣺⡟⡾⠘⠂⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠓⢍⡻⢷⣬⡳⡄⠀⣰⠃⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣥⣛⡵⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣝⣈⠔⠁⠐⠛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀