⠀⠀⠀⡯⡯⡾⠝⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠘⡮⣣⠪⠢⡑⡌
⠀⠀⠀⠟⠝⠈⠀⠀⠀⠡⠀⠠⢈⠠⢐⢠⢂⢔⣐⢄⡂⢔⠀⡁⢉⠸⢨⢑⠕⡌
⠀⠀⡀⠁⠀⠀⠀⡀⢂⠡⠈⡔⣕⢮⣳⢯⣿⣻⣟⣯⣯⢷⣫⣆⡂⠀⠀⢐⠑⡌
⢀⠠⠐⠈⠀⢀⢂⠢⡂⠕⡁⣝⢮⣳⢽⡽⣾⣻⣿⣯⡯⣟⣞⢾⢜⢆⠀⡀⠀⠪
⣬⠂⠀⠀⢀⢂⢪⠨⢂⠥⣺⡪⣗⢗⣽⢽⡯⣿⣽⣷⢿⡽⡾⡽⣝⢎⠀⠀⠀⢡
⣿⠀⠀⠀⢂⠢⢂⢥⢱⡹⣪⢞⡵⣻⡪⡯⡯⣟⡾⣿⣻⡽⣯⡻⣪⠧⠑⠀⠁⢐
⣿⠀⠀⠀⠢⢑⠠⠑⠕⡝⡎⡗⡝⡎⣞⢽⡹⣕⢯⢻⠹⡹⢚⠝⡷⡽⡨⠀⠀⢔
⣿⡯⠀⢈⠈⢄⠂⠂⠐⠀⠌⠠⢑⠱⡱⡱⡑⢔⠁⠀⡀⠐⠐⠐⡡⡹⣪⠀⠀⢘
⣿⣽⠀⡀⡊⠀⠐⠨⠈⡁⠂⢈⠠⡱⡽⣷⡑⠁⠠⠑⠀⢉⢇⣤⢘⣪⢽⠀⢌⢎
⣿⢾⠀⢌⠌⠀⡁⠢⠂⠐⡀⠀⢀⢳⢽⣽⡺⣨⢄⣑⢉⢃⢭⡲⣕⡭⣹⠠⢐⢗
⣿⡗⠀⠢⠡⡱⡸⣔⢵⢱⢸⠈⠀⡪⣳⣳⢹⢜⡵⣱⢱⡱⣳⡹⣵⣻⢔⢅⢬⡷
⣷⡇⡂⠡⡑⢕⢕⠕⡑⠡⢂⢊⢐⢕⡝⡮⡧⡳⣝⢴⡐⣁⠃⡫⡒⣕⢏⡮⣷⡟
⣷⣻⣅⠑⢌⠢⠁⢐⠠⠑⡐⠐⠌⡪⠮⡫⠪⡪⡪⣺⢸⠰⠡⠠⠐⢱⠨⡪⡪⡰
⣯⢷⣟⣇⡂⡂⡌⡀⠀⠁⡂⠅⠂⠀⡑⡄⢇⠇⢝⡨⡠⡁⢐⠠⢀⢪⡐⡜⡪⡊
⣿⢽⡾⢹⡄⠕⡅⢇⠂⠑⣴⡬⣬⣬⣆⢮⣦⣷⣵⣷⡗⢃⢮⠱⡸⢰⢱⢸⢨⢌
⣯⢯⣟⠸⣳⡅⠜⠔⡌⡐⠈⠻⠟⣿⢿⣿⣿⠿⡻⣃⠢⣱⡳⡱⡩⢢⠣⡃⠢⠁
⡯⣟⣞⡇⡿⣽⡪⡘⡰⠨⢐⢀⠢⢢⢄⢤⣰⠼⡾⢕⢕⡵⣝⠎⢌⢪⠪⡘⡌⠀
⡯⣳⠯⠚⢊⠡⡂⢂⠨⠊⠔⡑⠬⡸⣘⢬⢪⣪⡺⡼⣕⢯⢞⢕⢝⠎⢻⢼⣀⠀
⠁⡂⠔⡁⡢⠣⢀⠢⠀⠅⠱⡐⡱⡘⡔⡕⡕⣲⡹⣎⡮⡏⡑⢜⢼⡱⢩⣗⣯⣟
⢀⢂⢑⠀⡂⡃⠅⠊⢄⢑⠠⠑⢕⢕⢝⢮⢺⢕⢟⢮⢊⢢⢱⢄⠃⣇⣞⢞⣞⢾
⢀⠢⡑⡀⢂⢊⠠⠁⡂⡐⠀⠅⡈⠪⠪⠪⠣⠫⠑⡁⢔⠕⣜⣜⢦⡰⡎⡯⡾⡽

⠀⠀⠀⣀⣤
⠀⠀⠀⠀⣿⠿⣶
⠀⠀⠀⠀⣿⣿⣀
⠀⠀⠀⣶⣶⣿⠿⠛⣶
⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
⠀⠀⠀⠛⠛


⠀⠀⠀⣀⣶⣀
⠀⠀⠀⠒⣛⣭
⠀⠀⠀⣀⠿⣿⣶
⠀⣤⣿⠤⣭⣿⣿
⣤⣿⣿⣿⠛⣿⣿⠀⣀
⠀⣀⠤⣿⣿⣶⣤⣒⣛
⠉⠀⣀⣿⣿⣿⣿⣭⠉
⠀⠀⣭⣿⣿⠿⠿⣿
⠀⣶⣿⣿⠛⠀⣿⣿
⣤⣿⣿⠉⠤⣿⣿⠿
⣿⣿⠛⠀⠿⣿⣿
⣿⣿⣤⠀⣿⣿⠿
⠀⣿⣿⣶⠀⣿⣿⣶
⠀⠀⠛⣿⠀⠿⣿⣿
⠀⠀⠀⣉⣿⠀⣿⣿
⠀⠶⣶⠿⠛⠀⠉⣿
⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⣶⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

⠀⠀⣀
⠀⠿⣿⣿⣀
⠀⠉⣿⣿⣀
⠀⠀⠛⣿⣭⣀⣀⣤
⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣶⣿⠛

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⣀⣿⣿
⠀⠀⠀⠀⠤⣿⠿⠿⠿

⠀⠀⠀⠀⣀
⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⣶⣿⣶
⠀⠀⠀⣤⣤⣤⣿⣿⣿
⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⣿⠉⠿⣿⣿
⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣿⠛
⠀⠀⠀⠀⠀⠀⣭⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

⠀⠀⠀⣶⣿⣶
⠀⠀⠀⣿⣿⣿⣀
⠀⣀⣿⣿⣿⣿⣿⣿
⣶⣿⠛⣭⣿⣿⣿⣿
⠛⠛⠛⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣀⣭⣿⣿⣿⣿⣀
⠀⠤⣿⣿�