⢀⠈⠈⠈⢈⢈⠄⡀⡨⠅⢁⢐⡑⢈⢪⠥⣃⣈⡱⢠⡮⡣⢬⢥⢌⢅⡸⢇⢬⢮⡇⡸⡕⡪⢱⢸⡍⡃⢸⡅⠨⡑⢘⠕⡑⡨⠅⠪⡌⡃⠅⠁⠨⠜⢌⢌⠨⠈⠈
⢐⠡⠠⠌⠄⠄⠁⡁⡥⡁⢈⠌⢌⠐⡕⡳⡡⢆⢒⢚⣕⡕⡸⡜⢣⣎⡅⢸⡎⡅⡅⠸⢜⡣⢆⡸⢣⡢⢌⡡⢰⡢⢔⠨⡂⣈⡌⠌⠅⠥⡂⠥⠢⡌⡔⡈⠁⡀⡀
⡈⠨⠨⠄⡀⠄⠂⠂⠲⡸⡨⠢⡎⠆⠫⡝⠧⠴⡭⢕⡣⢬⡲⡗⡪⠇⡸⠯⠓⠺⠧⠼⠧⢶⢏⡸⢣⠼⢣⢜⢕⡢⢌⡅⡈⠰⠃⡑⡡⢆⠁⢕⠬⡃⢕⢌⠂⡀⡈
⠌⡁⠨⠄⠄⠄⠄⡐⠨⣘⢪⡁⢨⢎⡌⢢⡎⡊⠸⢹⣇⢸⡋⠴⣉⡤⣲⣩⢶⣿⣿⣿⢶⡥⢄⣈⠉⠙⢼⣇⢢⡜⡓⡪⢣⡢⢄⡪⠃⡰⡑⡸⡸⡢⡅⢱⢂⢐⡀
⢡⢄⠑⡁⡀⢈⡁⠈⢔⡪⢜⠥⢧⠵⡒⡫⢎⡡⢸⡵⢉⠁⡰⢍⢴⢏⡕⠔⣸⣿⣿⣻⣀⣉⠉⠜⠓⠤⡀⠨⠺⣇⢸⠇⠣⠑⠪⢍⠐⣓⢅⠅⠢⡆⡕⠸⠰⠈⠁
⡂⢐⡀⠠⡅⢐⡀⡐⠸⢅⣘⠨⢜⢲⣇⢜⠼⣜⠋⢠⠃⠐⠔⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⢰⡀⠈⠲⣙⢧⡑⡢⠔⢨⠄⡂⡁⡢⢔⠣⢇⠜⢘⠂⠐
⡂⠨⣈⠐⠃⢊⡑⠈⢨⡸⡣⠈⡹⡕⡛⢓⠸⠞⢀⠁⠌⢜⠌⣿⣿⠿⠋⢡⢸⣿⣿⣿⡀⣄⡈⠛⠿⡃⠱⡀⡀⡀⡀⡀⡰⢨⢆⢜⡇⢸⡂⢸⢀⡌⢊⢐⡂⡆⣘
⡁⠨⡊⡀⡅⢊⠣⡀⢌⠇⠼⠂⡆⡎⡱⣜⠏⢠⡀⡀⡠⡊⡡⠤⣰⣪⢻⡧⢹⣿⣿⣿⡀⠯⢘⣺⡖⢠⢱⠁⠤⠘⡀⡀⠩⢱⡆⢔⠢⢮⠃⠁⠈⡨⡕⠜⠁⢆⢌
⣁⢐⢇⠠⡃⡢⡑⠠⠪⡘⡯⡨⢱⡇⢱⡯⡀⠃⠌⠪⠃⣸⡜⠴⣪⣞⣿⣗⣿⣿⣿⣿⡇⡱⡓⣻⡇⢜⡢⢫⢄⡀⠡⡀⢠⢇⠪⢆⡢⡎⢂⢸⢈⢌⢡⡲⢨⡐⠨
⡨⠰⡨⠠⡌⠱⠕⡀⡑⢜⢼⢨⢭⡜⡺⠁⣸⡀⡰⡀⢨⠎⢩⠅⡪⠧⣳⡝⣿⣿⡿⢿⣇⡳⡃⣫⣯⢇⢸⡀⢆⡀⡀⡀⠄⢻⢳⢣⡌⡪⠎⠣⠈⣑⡙⠕⡀⠡⠐
⢂⢐⠱⢐⡅⢢⡣⠄⠨⡂⡪⢪⡱⡮⡚⡀⡏⡀⡃⡀⣞⡨⡊⢎⣸⣱⣿⣆⣾⣗⡻⣳⣗⡲⢷⢹⠯⠵⢭⡀⡀⣂⠠⡀⡀⡀⠧⠵⠣⠌⠢⢌⠐⠍⠥⡂⠘⠅⠐
⢅⢐⠜⣃⡅⣊⡑⠂⣑⣘⡝⡣⣸⠜⡀⡀⠁⡀⠆⢠⡣⡃⣊⠳⡪⠝⣛⣱⠿⣊⣭⣉⠛⠿⣾⢕⠯⢎⣒⡂⠌⡀⠄⡀⡀⡀⢘⣒⡂⢒⡂⠌⡀⣒⡕⡠⢠⠒⡃
⢅⡃⠩⠆⢀⡊⣘⠄⡇⢨⢕⡮⡻⠸⡀⢨⡀⡀⡀⢹⠃⠜⢇⣃⠼⠛⢩⠐⣴⣿⣿⡿⣷⠘⡂⣉⡒⠻⣭⡇⡑⠠⡀⠘⠄⢠⠈⡝⡒⢃⢩⣒⣊⡕⡢⡐⠐⠊⣁
⢅⡌⢕⢪⠌⡊⡫⡑⠣⢬⡍⢺⠁⡀⡀⡆⢘⡨⠠⢼⠠⢠⢈⠄⠊⣁⣈⣴⢿⣴⣿⣶⣾⣿⣷⣶⣬⣁⡀⠈⢣⡀⣝⡀⡆⢨⡀⡀⡂⢐⡪⡱⡔⠌⡉⡑⢐⠐⢨
⠕⠇⣇⠲⢢⢜⡇⠖⠣⣜⡮⠏⡀⡀⡀⠅⢐⠁⡂⣮⡀⢁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠄⠈⠂⡄⠂⢸⡀⡀⠱⢒⢔⡰⣆⢪⡢⢑⢰⢑⢐
⢌⠱⠥⢪⣕⡎⡡⠌⠇⠱⡷⡀⡀⠁⡀⠆⡀⠠⢊⠇⢠⣿⣿⣿⣿⣿⣿⠿⣛⣭⣭⣭⣭⣭⡛⠿⣿⣿⣿⣿⣷⢘⡀⡀⠃⢸⡀⠂⡀⢪⡘⣑⣑⢜⡅⢌⢅⠢⡢
⠬⡑⡱⠔⠕⡇⢘⡸⢅⡸⠁⡀⡀⡀⡀⠅⡀⠤⠁⡀⣿⣿⣿⣿⠿⠉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢉⣿⣿⣿⠨⠳⠰⡀⠸⡀⠁⡀⡀⡜⢊⢜⠨⡢⠤⠌⠂⢆
⡂⠠⠌⠣⢌⠮⢅⢰⣎⠏⡀⡀⡀⡀⡀⡀⠈⡀⡧⡀⣿⣿⣿⣿⣗⡌⠛⢛⣤⣤⣶⣴⣶⣴⣦⠉⣾⣿⣿⣿⠃⣃⡆⣻⠃⡀⡀⡈⡀⡀⠘⢍⠱⠔⠰⢐⡂⢄⣘
⠅⠐⡈⠰⡂⢸⡆⠨⡣⡀⡀⡀⠠⡀⡀⡀⡀⡀⢸⠐⠘⣿⣿⣿⣿⣿⣦⣩⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡵⠋⡆⡕⡇⡀⡀⡇⡀⡈⡀⡀⢱⢱⠄⠐⠱⡘⠡⠈
⠌⢘⠡⠢⠁⢒⡃⢸⠇⡀⡀⡀⡀⡀⡀⡀⠐⣰⡿⡀⡀⠘⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡀⣧⠡⠨⡀⡀⢸⠄⠂⡀⡀⡀⠣⢂⢂⢐⡂⡑⢀
⡘⠒⠒⠪⠑⣊⣑⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡃⡀⠐⡀⠘⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⡇⣿⣿⣿⠟⡀⡀⡀⢸⠈⡀⡀⡀⡀⡀⡀⡀⠐⡀⣒⢑⠅⡀⢐⠄
⡡⡂⢁⠂⡈⡔⡂⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡀⡀⡀⡀⡀⠛⣿⣿⣿⣿⣷⡀⠉⠛⢋⢀⣿⡿⠁⠄⡀⡀⡀⢸⡀⡀⡀⡀⢣⡀⡀⠐⡀⡀⡀⢌⠬⠅⠆⠒
⢡⡀⢀⠅⠅⡔⣣⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⢨⡀⡀⡀⡀⡀⡀⠠⠈⠿⣿⣿⣿⣿⣿⣿⣿⠋⡀⡀⡀⡀⡀⡀⣼⡀⡀⡀⡀⠸⡀⠂⡀⡀⡀⠄⡀⢔⡂⢂⡀
⢅⠅⢀⢑⡠⠜⠇⡀⡀⡀⡀⡀⠂⡀⢸⡀⡀⠈⠈⡀⡀⡀⡀⡀⡀⠂⡀⠄⡀⠉⠛⠛⠛⠋⡀⡀⡀⢀⡀⡀⡀⡀⢁⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⠈⠠⠐⡂
⠄⠐⠠⠢⡂⡸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠘⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡰⡈⡀⡀⡀⡀⡀⡃⡀⡀⡂⠁⡀⡀⡀⡀⡀⠂
⡀⢀⠨⡑⢂⠃⡀⡀⡀⡀⡀⢐⡀⡀⠄⡀⡀⡀⡀⢇⡀⡀⡀⡀⣦⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⡀⡀⠸⡀⡀⡀⢁⡀⡀⡀⡀⡀⢀
⠂⡁⠨⡰⠊⡀⡀⡀⡀⡀⡀⡀⡀⠡⠅⡀⡀⡀⡀⡀⡀⡀⠰⠹⣼⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⡀⠠
⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⠰⢄⢀⡀⡀⡀⡀⡀⡀⡀⠳⣀⠘⢮⣛⣻⣄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣆⡆⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⠠⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡞⡀⡀⡀⡀⡀⡀⡀⠈⡀⠙⠦⠙⢿⣿⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⠎⣫⠁⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⠂⠠⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣌⠁⡀⡀⡀⡀⢀⡀⡀⡀⠈⠒⡀⠥⡀⠉⠿⣿⣦⡀⡀⡀⡀⡀⣀⠜⠈⡀⡀⡀⡁⡀⠅⢘⠁⡀⡀⡀⢃⠈⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡨⢐⡸⡀⡀⡀⡀⡀⢸⠠⡀⡀⡀⠌⠄⠁⠣⠁⢀⡀⡀⠋⣉⡀⣠⠊⡀⡀⡀⣠⡀⡀⠅⡀⠃⢄⢑⣊⢆⡀⠈⠐⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⠁⠢⠁⠌⡂⡰⡀⡀⡀⡀⡀⡀⡇⡀⠠⠐⡈⢄⡀⡀⠠⠈⡨⠪⢆⡀⡀⠈⠐⠦⣄⣀⣈⢁⡀⡀⢠⠁⠄⠂⠡⠒⠁⡆⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⢀⠁⠁⢀⠃⡴⡀⡀⡀⡀⡀⡀⢀⠙⠈⠄⣕⠈⠄⠑⠤⡕⡀⢀⠁⠨⠭⠄⡀⣀⡀⡀⡀⠈⡁⡀⡴⡀⢀⠁⠁⢪⡀⡀⠱⡀⡀⡀⡀⡀⡀⡀⡀⡀
⠄⡀⡀⡀⡠⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⢃⠬⠔⡀⡀⡀⡀⡀⡀⡀⠈⠒⠒⠒⠚⠒⠂⠁⡀⡀⡀⠂⡀⠰⡀⢀⡱⡀⢐⠄⡀⡀⢀⡀⡄⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡃⢐⠅⠐⢈⠪⡒⡠⡀⡀⠉⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢔⡀⡀⠁⡠⡠⠂⡀⡀⠘⡀⡅⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡜⠢⠠⠌⠨⠢⠄⠈⠑⡢⡀⡀⡀⠠⠐⠄⠂⡀⠤⠒⠁⡀⡀⡀⠌⠄⡀⠄⡀⠂⡐⡀⠂⡀⠂⡀⠅⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⢂⡀⠈⠑⠑⠃⠢⢑⡀⢆⢄⡀⠘⠁⡰⠉⡀⡀⡀⢀⠌⠅⡀⢔⡀⠐⡀⡀⡀⡀⠠⢀⡀⠅⡀⡀⡀⡀⡀⡀⡀