かわいい『ハム太郎』アスキーアート🐹💫【コピペ】

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⡒⡒⠒⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢡⢆⢢⢌⡘⡪⠱⢢⢔⡢⠓⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⢅⡨⡕⠸⢕⢸⡪⡕⡣⢢⢎⡣⢆⡙⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⢣⢆⡔⢎⡘⠱⢢⢌⡑⡪⢱⡪⢜⡱⢢⢌⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⢪⢌⡨⡜⡪⡜⡱⢢⢌⡑⠘⣁⡬⠥⠤⣌⠈⡀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢕⡆⡐⡪⢸⡪⢌⡨⣠⠞⠁⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⣠⢚⢅⡐⢊⡑⠢⢄⡙⢦⠀⠀⠀⠀⢀⣄⢀⡤⣤⡤⣤⣘⣐⢊⡅⡨⡕⠸⢕⠆⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⢀⠋⢘⢪⡱⢢⢔⡊⠡⠔⠸⢕⡙⡀⠀⢠⢋⠟⠴⡉⠢⠔⠢⢌⡰⢢⢌⡑⡣⢌⡕⣼⢡⠥⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢀⢃⡃⢐⡸⠕⢊⡡⠔⠪⠇⠪⢱⠊⡞⡝⢄⢡⢜⢪⢇⢢⡌⠕⢘⡱⢜⡑⠢⢎⡘⢡⢅⣒⠉⠀⠀⠀⠀⠀⠀⠀⡼ ⠀⡏⢕⡊⠨⢜⡊⢑⡊⠡⢌⡡⢌⣑⢸⢨⡢⢔⢸⡣⢆⡔⡢⡔⡘⠱⢣⡪⡅⠨⢕⢱⡣⠱⢪⢍⢦⡀⠀⠀⢀⠴⠟ ⢰⢈⠨⣑⣐⣘⣑⠜⢇⢢⢌⡡⢌⣕⢧⢆⢌⡑⠢⢌⡘⢑⢪⡌⡨⡌⢕⡸⠪⠱⢪⡸⢕⡘⠱⢢⡸⢪⡚⢭⠚⠁ ⢸⡴⠉⠀⠀⠀⠀⠀⠙⠦⠑⡢⠞⠀⠀⠙⠧⡢⢌⡑⢱⢕⡊⠡⢌⡘⠱⠜⢁⣴⣶⣷⣶⣦⡈⠱⢢⢌⡜⡑⠳ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⣒⣍⠎⠀⠀⠀⠀⠀⠀⠉⠚⢼⣱⢢⡌⡘⡊⡑⣴⠟⠁⠀⠀⠙⣿⣿⣷⠘⡪⡕⢎⡔⠹⡀ ⠈⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠅⡟⠀⠀⠀⠀⠀⢸⡟⠛⣷⠸⢕⢣⡱⢪⠹ ⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⢿⣿⠴⣢⢔⡎⢜⡑⢳ ⠀⠀⠀⠲⣄⣀⠀⠀⢀⣈⠀⠀⣠⣿⠋⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣄⣤⣾⣿⡀⠀⡟⠀⠀⠈⠛⢑⣁⠂⡄ ⠀⠀⠀⠀⠀⠈⠉⠛⠉⢹⠀⢰⣿⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⢀⠴⠊⠁⠀⠈⢮⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⣿⣶⣶⣿⠇⠀⠰⠭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣤⣿⣿⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠓⠒⠦⣄⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⡀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡗⠒⠒⠂⠀⠀⠀⠀⠳⡀⠀⢀⢯⠢⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡡⢜⢢⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⡎⢜⢱⢅⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⢆⡌⠄⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⡕⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠈⢷⣈⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢕⡎⢜⠀⠀⣠⠉⠉⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⢕⡽⠀⢰⠀⣀⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⠤⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠉⠉⠉⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⣤⣀ ⠀⠀⠀⠀⠀⢀⠶⡋⢰⡎⢱⡎⢱⡎⢱⡎⢢⡌⠳⣄ ⠀⠀⠀⢀⡾⡅⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡦⠙⣄ ⠀⠀⢠⢋⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀ ⠀⢠⢃⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢆⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡛⢅⡰⢖⡣⢔⡢⢌⡙⠲⣄ ⠀⡟⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢕⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢆⡉⢦⡀ ⢠⢀⡸⢃⣤⠶⠒⠒⠲⠦⣬⡃⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣷⢀⣠⡤⣤⠶⢙⢀⣠⣤⣄⠀⠀⠀⠀⠀⢠⢋⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡳⢗⡉⣦ ⢸⠨⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣬⠣⢜⡣⢜⡣⢜⡣⢜⡣⣠⠟⠅⣊⠞⣡⠞⢩⢒⣨⡥⠶⠓⠒⢦⠀⢀⠏⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢢⢷ ⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢕⡪⢕⡪⢕⡪⢌⡰⢕⡌⢔⡣⢆⡸⢇⡸⢎⡹⢇⡸⢇⢾⣀⣼⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡱⢷ ⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠓⣦⠾⠛⠉⣮⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢢⡅⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡆⡆ ⠀⢹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⠀⠀⠀⠀⠈⣎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢊⡥⠶⠛⠛⠛⠛⠲⢬⣑⢎⡱⢮⢹ ⠀⠀⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢕⠈ ⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢅⡛⢛⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠈⠾⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠶⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰ ⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢷⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣰⠁ ⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢠⣿⣿⣿⡿⠉⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠙⣮⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢽⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⠁ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢜⡣⢜⡣⢜⡣⠜⣡⣴⣶⣶⣤⣈⠱⡎⢱⡎⢱⡎⢳⠀⠀⠀⠀⣀⠶⣩⠛ ⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣾⡁⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡕⢪⡕⣴⣿⣿⠿⠿⠿⣿⣿⣿⣦⠘⢣⡜⢣⢬⢒⣒⣫⠭⠖⠉ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣿⣿⡶⠿⢿⣄⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣼⣿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⡘⡣⢜⡣⢸ ⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢹⣿⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠪⢕⡪⠅⡆ ⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣇⡆⡇ ⠀⠀⢨⠉⠉⠛⠲⢤⣀⠀⠀⠀⠈⠒⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⢀⣾⠁⠀⢘⣿⠀⢌⡸⢧⣿ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠉⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⡿⠋⠉⠙⢶⣿⣿⡰⢎⡱⠮⢻ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠁⠉⠓⢮⣱⢸ ⠀⠀⣿⠀⣀⣀⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸ ⠀⠶⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠈⠉⠉⠛⠶⠄⡿ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣀⡴⢧⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⣠⠋⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⣠⠁ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠃⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁ ⠀⠀⠀⠀⠀⣸⡰⡟⠀⢸⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⢀⠾ ⠀⠀⠀⠀⠀⡏⠟⠀⠀⠀⢧⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢴⢅⣧ ⠀⠀⠀⠀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢻⡘⡀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⠾⠀⠀⠀⠀⠀⠀⠀⢳⣧ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠛⠄ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞ ⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋ ⠀⠀⡤⠋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞ ⠠⣋⡤⠀⢀⠉⠲⠤⢤⣤⣤⣤⠤⠤⠤⠶⠶⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢯⡀ ⠀⠿⠴⢻⡁⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠳⡛⠋⠁⠀⢀⠈⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣀⢶⣄⠙⡦⠇

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀ ⠀⠀⠀⠀⣠⠖⡉⡀⢈⡁⠔⡢⡂⢉⠲⡀ ⠀⠀⢀⠞⠠⠢⠕⠆⢊⠐⠂⠂⢐⠅⠑⠌⣆ ⠀⢀⠃⢅⡂⢐⡂⢔⡢⢀⡐⢂⡐⢂⡐⡑⡘ ⠀⡟⠋⠉⠛⠦⡑⠊⢐⢄⡐⢂⡀⡂⠀⠂⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠦⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠳⡁⠠⠢⠢⠐⠂⠀⠑⣸⢔⡶⣋⡾⢒⣋⣭⣁⣀⠀⠀⠀⠀⢠⢋⠆⡑⡀⠠⠄⡠⠄⠄⠓⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠄⡂⣸⠮⠅⠌⡐⡀⠐⡠⢂⠠⢘⢛⠛⣭⣓⡄⠀⢠⢁⢌⡐⡁⢄⡂⢅⢄⡨⢀⠠⠄⢦ ⠀⢧⠀⠀⠀⠀⠀⠀⢘⡚⡰⠊⠀⠀⠹⢂⠎⠐⢂⡑⠁⢀⡐⠁⢈⢌⡠⡉⠳⣏⠑⢑⢊⡑⢂⡑⠑⠂⢑⡂⢀⡑⡀⡄ ⠀⠀⠳⣀⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠳⢅⡐⢂⡐⢂⢐⢕⡂⡐⢂⡐⢅⢡⡰⡂⢌⢨⢕⠢⢑⡂⢐⠨⢐⡂⠨⠐⢹ ⠀⠀⠀⠈⠻⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⡕⡠⢑⡈⠀⢅⡈⢈⢨⡑⢅⡨⢈⢅⢕⡨⢄⢌⡈⠁⠊⢁⡨⠢⢈⢌⡈ ⠀⠀⠀⠀⠀⠀⢀⠃⢚⣿⣶⠖⠒⢿⡉⠀⠀⠈⢧⠘⢁⠅⠨⢅⠅⠡⠨⠅⡨⢅⡢⠔⢀⣤⠒⠛⠉⠉⠉⠓⢦⡁⢈⢰ ⠀⠀⠀⠀⠀⠀⡏⣰⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣆⢐⢢⠅⠐⢐⠰⢊⠅⠨⠢⡢⠠⣕⠍⠀⠀⠀⠀⠀⠀⠈⡆⡾ ⠀⠀⠀⠀⠀⣸⠀⣷⣀⣿⡄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠙⢕⠂⠨⣂⣙⣄⠢⢐⠕⠪⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⢀⣀⡀⠀⣠⠁⠀⢿⠏⠀⢹⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⢻⣦⣈⠁⢄⠅⠀⠀⠀⠀⠀⠀⢀⠞ ⠀⠀⠀⠉⠳⣄⠀⠀⠳⠤⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠶⢨⡴⢽⣦⣤⣠⠤⠚⠁ ⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⠀⠀⠀⠀⣿⣦⡀⠀⣀⣾⠀⢻⠰⣨⡏ ⠐⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠀⢻⣿⡟⠀⠀⡇ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣤⠾⠋⠀⠀⠀⠁ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠦⠤⣄⢸ ⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⡏⠈⠓ ⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡼ ⠀⠀⠀⠀⠀⠀⣰⠈⠀⠀⠤⠒⠚⠋⢹⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠓⣀ ⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⣠⡤⡞⠁ ⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡤⠧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⢸⠳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⡇ ⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⡾⠀⣿⠛ ⠀⠀⠀⠹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠁⠀⡏⠎ ⠀⠀⠀⠀⠑⣄⢳⣤⠤⠤⠶⠶⠒⠒⠒⠶⠶⠤⠤⣤⣀⣀⡀⠀⠀⢀⠏⠀⡰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⢉⡉⢉⢙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢤⣍⡛⣟⣍⠍⣍⢭⡭⢥⡌⢩⡭⢭⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⠟⡀⡐⡐⠪⠪⢕⢅⡊⡊⢐⡈⠢⢉⠻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡯⢮⢗⣌⠺⣶⣇⠪⢮⢵⡹⡪⣝⡳⢯⢦⠳⣙⣳⢦⣍⡛⢿⡀⠨⠡⠅⠡⠄⠠⠅⠡⠄⠨⠅⠨⠌⡑⠡⢀⠻⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣝⡶⠶⡒⣒⡫⠺⣗⡮⣙⠙⡩⢮⣝⣕⣪⢦⠳⡙⡽⢮⡽⣲⣙⠦⣀⠪⠅⠨⠅⡨⡑⠈⢁⡤⡆⢑⠌⠌⠡⠹⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣕⡺⡵⢯⢵⢮⣝⡦⣙⠺⣝⡲⢥⣙⡫⠝⣝⣌⢦⢪⣪⣝⣝⡽⡲⡑⢄⠁⣀⡤⢖⣫⣮⠖⡀⠨⢐⡊⢑⠀⢻⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⡛⠻⣿⣌⢮⣞⣝⣝⣑⡥⠶⣚⡭⢮⣖⡭⣙⡒⠯⢭⣛⣓⣓⣒⣒⣒⣚⣛⣩⣭⠶⠒⡋⢉⠄⢂⡑⢂⡐⠢⢐⠂⠐⠸⣿⡇ ⣿⣿⣿⣿⣿⣿⠛⠁⠐⠢⠐⠢⠄⠠⠄⠨⠕⠕⠢⢈⢦⠯⢽⡳⢮⣕⡪⢝⡳⢮⣕⡪⢝⣝⡝⣊⢖⣥⢖⡲⣖⣲⢖⠳⡴⠁⠑⣈⡥⠴⠒⠒⠒⠒⠒⠤⣌⠢⡢⠀⣿⡇ ⣿⣿⣿⣿⠟⢀⡐⢊⡂⢐⡑⢂⡁⢐⡑⢂⡐⢐⡂⢈⡀⠙⢜⢗⣗⣗⡺⢽⣗⡪⢕⠪⣡⢖⢭⢮⣞⡽⡫⡫⡪⠝⣣⠋⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢸⣿⡇ ⣿⣿⣿⠃⢂⠅⡊⡑⠨⠡⠪⢕⢌⠅⡊⡑⠨⠡⠪⢕⡢⢂⢂⢉⠮⣙⢺⢽⣳⢮⣋⣕⣝⣝⣝⡽⣳⢮⠮⣊⠴⠋⡐⠁⡊⡂⠰⢤⠤⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇ ⣿⣿⠇⡨⡐⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⢔⡂⣴⢲⠠⠄⡑⢂⡉⠒⠥⣬⣊⣙⣙⣙⣙⡥⠴⠚⢉⡠⡢⠄⠠⠄⠠⢂⠠⠓⠤⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⣿⣿⠀⠠⠄⠨⠄⠠⠅⠨⠄⠠⠅⠨⠄⠠⠅⠨⠨⡾⠀⠀⠈⢦⠨⠅⠠⠄⠐⠐⠠⠐⠐⠐⠠⠅⠐⠨⠅⠠⠄⠨⠄⠠⠅⠡⠄⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇ ⣿⣿⡈⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡵⠋⠀⠀⠀⠀⠀⠈⢦⣐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⠝⡄⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡇ ⣿⣿⠀⢅⡊⢑⡈⢁⡊⢑⡈⠅⠊⠑⣁⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠅⠊⡑⢈⡁⢊⡑⢈⡁⢊⡑⢈⡁⠊⠑⠀⠂⠊⠅⠂⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⢁⠌⠡⢈⡁⡈⠁⠀⣨⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠉⠪⣡⠈⠡⠌⡁⢈⡁⢈⡁⠨⠅⣠⡾⠿⠿⣿⣿⣶⡀⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣦⠥⠥⠬⠥⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠉⢦⠀⠀⠀⠈⠓⠮⣬⣅⠨⢐⢕⠊⣾⠃⠀⠀⠀⠀⢿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢟⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⠀⠀⠀⠀⠀⠈⣿⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⢀⣀⡤⣒⣡⠀⠀⠀⢀⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢰⣿⠀⣿⡠⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⣠⠋⠛⣠⠇⠈⣄⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠱⣤⣤⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⢷⠀⠀⠃⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣛⣽⣿⡿⠁⠀⠀⠀⠀⠀⠒⠤⠚⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⠤⣤⣀⣀⣀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⡤⠤⠒⠒⠒⠒⠂⢰⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠⠋⠉⠒⠒⠊⠀⠀⠀⠀⠀⠀⠒⠒⠦⢤⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡹⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⡀⠉⢶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠀⠀⠀⠀⢀⠋⠈⠁⡿⢻⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢆⠈⠀⠱⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢄⠀⢀⡀⠀⠇⠀⠀⠀⠇⣼⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠑⠶⣒⡭⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣮⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠲⣀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⢰⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠸ ⠀⠀⠀⣏⠋⠀⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣣⠔⡩⣅⠤⣊⠼⣖⣲⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠈⢦ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠺⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⡀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠄⠀⣠⠋ ⠀⠀⠀⠀⠀⠀⠈⣢⣶⣿⡀⣀⡼⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠘⣀⠀⣰⣶⣦⣊ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⡽⠀⠀⣴⣿⠟⠉⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⣿⣿⡄⠀⠘⢁⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣾⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢹⣿⢿⣿⣿⣿⡟ ⠀⠀⠀⣀⠤⣌⣿⣿⣷⣗⡟⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣞⣯⣿⣟⣋⠤⣤⡀ ⠀⡴⠁⠀⠀⠀⠀⠙⣿⢼⠇⠀⠀⢿⣦⣼⣄⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⢀⣾⣤⣿⠃⠀⠀⣿⣽⡿⠁⠀⠀⠀⠀⠑⡀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠻⣀⠈⣿⣿⣿⣿⠋⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣸⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹ ⢸⠀⠀⢠⠚⠁⠀⡤⣲⣭⡦⣤⣀⣀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⣀⣀⡤⣿⣷⡲⡀⠀⠉⢦⠀⠀⢸ ⠈⡀⢠⠁⠀⢀⠃⣼⣿⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⡀⢣⠀⠀⢳⠀⡼ ⠀⠙⢼⠀⠀⠇⢰⣿⣿⡺⢟⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠾⣿⣿⢿⠀⡆⠀⢈⠔ ⠀⠀⠈⡀⢸⠀⣿⣿⣟⣽⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠚⠀⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣯⣝⣾⡿⡀⢸⠀⡼ ⠀⠀⠀⠈⠪⠀⠙⠿⣿⣻⣿⣿⠃⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢿⣿⣿⣿⡿⠛⠁⠼⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⢤⣤⣤⣤⣤⠤⠤⠤⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣶⣿⣿⣿⣿⣿⣿⣯⡳⣄ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠚⠛⠶⠶⠶⢦⣾⣚⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢷ ⠀⠀⠀⠀⢀⡶⣫⣶⣿⣿⣿⣿⣶⣭⡲⣄⠀⠀⢀⣤⠶⣛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣙⠷⣭⡻⣿⣿⣿⣿⣿⣿⣷⢷ ⠀⠀⠀⣴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣯⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣞⠛⠛⠶⣭⡻⡞ ⠀⠀⡾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡳⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⠀⠀⠀⠈⣆ ⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡀⠀⠀⣸ ⢀⡏⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣱⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡀⢠⠃ ⠘⡇⣿⣿⠿⣯⠶⠛⠉⠉⠉⠉⠉⠙⠲⠭⡻⢏⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠁ ⠀⢷⣿⣱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢭⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇ ⠀⠀⢷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣡⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠉⠶⣄⡀⠀⠀⠀⠀⠀⠀⣠⢞⣾⣿⣿⠿⣉⠴⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⡛⠛⠻⠿⠿⣿⣿⣿⢸ ⠀⠀⠀⠀⢀⠇⣦⣭⣍⣛⣛⣭⣵⣾⣿⠟⣩⢖⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⡥⠶⠚⠋⠉⠉⠀⠀⠀⣰⠀⠀⠈⠻⣿⣶⣍⣼ ⠀⠀⠀⠀⢸⣸⣿⣿⠟⣴⣸⣿⠟⣡⢚⣵⣿⣿⣿⣿⣿⣿⣿⠿⣋⣭⠶⠛⠉⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣷⠁ ⠀⠀⠀⠀⣿⢣⢸⠏⢯⢡⢋⠖⠥⣩⠯⣿⣿⣿⣿⡿⢛⣡⣶⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⡤⣿⣆ ⠀⠀⠀⠀⡇⠇⠌⣘⢃⢞⠕⡵⣫⣾⣿⣿⠿⣉⡴⢛⣿⡯⢿⣿⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⣠⡴⠛⠳⣿⠘ ⠀⠀⠀⠀⡇⡟⡞⡀⡗⢦⢫⣿⣿⡿⢋⡴⠋⠀⠀⠈⣿⣄⣠⣿⣿⣤⣀⣤⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣇⣀⠰⠁⠀⣇ ⠀⠀⠀⠀⠹⠃⢨⢄⡐⡀⣇⠟⣡⠞⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⡟⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⣖⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠖⠚⠉⠁ ⠀⠀⠀⠀⢸⠈⠲⣌⣑⢈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣀⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠘⠁⢸⡳ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢺⢓⠧⠤⣤⣀⡀ ⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⡟⢀⠃ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣤⠖⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣱⠁ ⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠁ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⠇ ⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣶ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦ ⠀⠀⠀⢠⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣸⡼⡇ ⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⡁⢠ ⠀⠀⠀⠀⠈⣷⠀⠀⡾⣿⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡐⡂⠅⢀⠇ ⠀⠀⠀⠀⠀⠸⡀⢰⠀⡂⢌⡑⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠢⠢⢠⠋ ⠀⠀⠀⠀⠀⠀⠹⣸⠠⠢⠪⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢊⠈⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⡀⢌⢌⠄⡏⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠚⣤⠴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⡑⣰⠦⠤⠶⠖⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣛⣛⣛⡳⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠿⠿⣿⣿⣿⣿⣷⠻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠉⠳⡻⣿⣿⣿⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣻⣿⣿⣿⠿⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸⠽⠯⣭⡻⣾⣭⠶⡚⣻⣽⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⣤⠼⠒⣋⣁⠀⠀⠀⠀⠈⣞⣿⣿⣿⣿⣝⣓⠿⣤⠀⠀⠀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣤⠤⡀⠀⠀⠀⠉⠳⠀⠀⠀⠹⠶⠶⠭⣙⠿⣿⣭⢿⣀⡶⣫⣶⣾⣷⣮⡻⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠟⠒⠶⠳⣬⡼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⢮⢿⣵⣣⣿⣿⣿⣿⣿⣿⣿⣮⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣠⠶⠂⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠈⣎⣿⣛⡭⠶⠾⣭⡛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢸⢽⣷⣤⠟⠀⠀⠈⢳⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢷⠂⠀⠀⠈⣆⠀⠀⠀⠀⠀⢼⠞⠳⣄⠀⢀⠏⠀⠀⠀⢀⣤⡀⠈⢦⠀⠀⣞⢸⠉⠀⠀⠀⠀⠀⣇⠇ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣯⣄⣀⠉⠙⢤⡴⢃⡉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠰⣌⠀⠀⠃⠀⢟⢸⠀⠀⠀⠀⠀⣠⠋ ⠀⠀⠀⠀⠀⣠⣛⣵⣿⣿⣿⠟⡴⣫⣝⢦⠀⠀⠀⡾⣘⠿⣿⣾⣶⣭⣓⠦⣌⠃⠢⡌⢄⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⠙⣄⠀⢰⣼⣸⣀⣀⣀⣤⠞⠁ ⠀⠀⠀⢀⢞⣶⣿⣿⣿⣿⣣⠏⠓⢭⡻⣷⡝⣲⢛⠦⣀⠉⠛⠮⣝⠿⣿⣿⣷⣭⡳⣄⠑⢨⡑⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠳⡏⣿⣙⣿⠁ ⠀⠀⣴⣣⣿⣿⣿⣿⡿⣴⣩⡳⣤⠐⠌⢓⠞⣾⣿⣿⣷⣭⣓⢤⡀⠉⠓⢬⡻⣿⣿⣷⣭⠶⣀⠑⠣⠢⠙⢤⣠⠤⣄⡀⠀⠀⠀⣧⠀⡾⣾⢣⠃ ⠀⣼⣴⣿⣿⣿⣿⣿⣴⣵⣿⣿⣿⣮⢓⠏⠙⠶⣝⠿⣿⣿⣿⣿⣶⣝⢦⣁⠌⠛⣬⠻⣿⣿⣶⡻⣄⠨⡘⡁⢦⠄⠀⠈⣦⠀⠀⢀⢞⣾⣣⠋ ⣸⣼⣿⣿⣿⣿⣿⢡⡑⣿⣿⣿⣿⠏⡏⣮⣝⠦⣀⠉⠶⣙⢿⣿⣿⣿⣿⣶⣝⢦⡀⢉⠶⣙⢿⣿⣷⣝⣦⠑⡈⠲⢦⠀⣸⣠⢶⣵⠿⣴⠁ ⡇⣿⣿⣿⣿⣿⡿⡿⡈⠓⣬⡻⣿⣸⣾⣿⣿⣿⣶⣛⣤⠀⠙⢦⡛⣿⣿⣿⣿⣿⣮⡳⣄⠨⠳⣝⢿⣿⣿⣝⣄⠂⡐⡠⠙⡝⠿⣡⠟ ⠨⣿⣿⣿⣿⣿⠇⢟⢦⣁⠂⡈⠳⣭⡻⣿⣿⣿⣿⣿⣿⣮⡳⣌⠈⠳⣍⢿⣿⣿⣿⣿⣷⡝⣄⠠⠛⣭⢿⣿⣷⡳⡐⡢⠪⠙⠛ ⡇⣿⣿⣿⣿⣿⣸⣼⣿⣶⣝⠶⣄⠂⢈⠳⣭⡻⣿⣿⣿⣿⣿⣷⣝⢦⠂⠙⣮⠿⣿⣿⣿⣿⣧⡳⣄⠄⠻⡹⣿⣿⡝⡌⢌⠄⡇ ⢿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⣓⣤⡐⢈⠳⣍⢿⣿⣿⣿⣿⣿⣝⢦⡀⡙⣮⢿⣿⣿⣿⣿⣮⠷⡀⠈⣎⢿⣿⡸⠀⣰⠁ ⠀⣧⣿⣿⣿⣗⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢤⡀⡙⢦⡻⣿⣿⣿⣿⣿⣭⢦⡀⠹⣜⢿⣿⣿⣿⣿⡝⣄⠄⣧⣿⡇⡶⠁ ⠀⠈⣦⢿⣿⣿⣧⠙⠶⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠶⡁⠌⠶⣛⢿⣿⣿⣿⣿⣝⢦⠀⠳⡹⣿⣿⣿⣿⣌⣆⠄⣎⡾ ⠀⠀⠀⠳⣝⠿⢸⢙⠦⣄⠉⠳⣭⠻⣿⣿⣿⣿⣿⣿⣿⣮⡳⣌⠈⠳⣝⢿⣿⣿⣿⣿⡝⣄⠘⣮⢿⣿⣿⣿⣎⣄⠟ ⠀⠀⠀⠀⠀⠛⢦⣧⢿⣷⣭⡳⣄⠉⠲⣍⠿⣿⣿⣿⣿⣿⣿⣷⣝⣄⠀⠳⣝⣿⣿⠿⠿⠲⢳⡀⢳⠻⣿⡿⣠⠋ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡻⢷⣭⠶⣄⠉⠳⣍⠿⣿⣿⣿⣿⣿⠷⣙⡤⠶⢓⣛⣩⣭⣵⣶⣶⣶⣭⠳⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⣷⣝⠦⣀⠙⢮⡻⡿⢋⡴⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠿⣶⣛⣤⢉⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡛⢣⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣍⣛⣛⣛⣉⣥⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⣶⠶⢶⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⣀⢖⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⣠⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣶⣿⣿⡶⣶⣤⣀ ⠀⠀⠀⠀⡴⣩⢟⣭⣶⣶⣶⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⡾⣥⣵⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣤⣴⣿⣿⣤⣶⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⡀ ⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣞⣿⡄ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠙⢿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇ ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⡿⠿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⣾⣿⣿⣿⠛⠉⠁⠙⢿⣿⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⣤⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠋⠻⣿⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⠃⠀⢸⣿⣤⣴⣿⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⢿⣿⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⢀⠇⠀⠀⢸⣿⣿⠛⠛⣷⣄⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⣿⡄⠀⣽⡆⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣤⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿ ⠐⠛⠒⢲⣷⣤⣀⠀⠀⠀⠻⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⣿⡄ ⠀⠀⠀⠘⠀⠀⠀⠉⠛⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣀⣠⣿⠋⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⣤⣄ ⠀⠀⣀⡤⢿⠛⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠿⠿⠻⠷⠶⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠰⠉⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⡶⠟⢷⣀⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣤⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆ ⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣄ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠙⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣤⠀⣠⠆⠀⠀⠀⠀⠀⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠙⠷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣥⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣫⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣭⢿⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣼⠷⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀ ⠀⠀⠀⠀⠀⠀⣠⣶⣟⣽⣾⣿⣿⣿⣿⣿⣷⣯⡿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣾⣿⣿⣿⣿⣿⣾⣯⣟⣷⣄ ⠀⠀⠀⠀⣠⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣄ ⠀⠀⢀⣾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣷⡀ ⠀⢀⣿⠾⣛⣿⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡇⠀⠀⠀⠀⢀⡤⠚⢉⣧⣠⣤⡀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣽⣷⣾⣯⣛⢷⢿⡀ ⠀⡿⣵⠿⠉⠀⠀⠀⠀⠙⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣠⠞⢉⠟⠁⡤⠚⠁⢀⠴⠚⠉⠉⠉⢓⡄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⠛⠁⠀⠀⠀⠀⠉⠻⣎⣷ ⣼⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄ ⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣱⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⣿⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⢿⣄⠀⠀⠀⠀⠀⢀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⣠⡾⠁ ⠀⠀⠈⠛⠿⢿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⠿⠿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⣿⠿⢿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⠉⠛⣿⣿⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣷⡀⢀⣿⣿⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣟⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⡟⡇⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⣯⣿⣷⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣾⣿⣾⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠿⣽⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠶⠞⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⣼⣀⡀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠛⠉⠀⠀⠀⣀⣀⣀⣇⣀⣀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣠⠞⠀⠈⠦⣄⣀⣀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠘⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣼⡀ ⠀⠀⠀⠀⠀⡴⠋⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠳⣄ ⠀⠀⠀⠀⠋⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣇⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⣿⣿⣿⣿⢟⣾⠟⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⢻⣎⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⣽⢯⡿⠁⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠹⣷⣿⣿⢿⣿⠋⠀⠀⠀⠀⢸⠀⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣄⠀⣤⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⣬⡾⠛⠀⠀⠀⠀⠀⠀⣾⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠀⠀⠉⢛⡶⠲⠶⠖⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⣛⠉⠁⠀⠉⠛⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣶⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢶⠈⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣷⣤⣀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣟⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⣿⣿⡿⣸⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⠀⢀⣴⣶⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢝⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣷⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⢿⣿⡿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣾⣿⣿⣿⢿⣿⡇ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣳⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⣋⣭⣭⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣶⣿⣿⣿⠿⠛⠿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⣿⣿⣿⣿⠁⠀⠀⠀⠈⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣤⣶⣤⣍⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢰⣿⠁⠙⣿⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠛⡉⠙⠻⣿⣿⣿⣆⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡌⣿⣶⣾⣿⣷⣄⣀⣤⣾⣿⢸⣿⡇⠀⠀⢀⠀⠉⠙⠻⣿⣿⢰⠁⠀⠀⠀⠀⢹⣿⣿⣿⣇⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢿⣿⠹⣿⣿⠀⠀⠉⣿⣿⣿⠋⣿⣿⠀⠰⣄⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⣼⣟⠀⢙⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⣀⣤⣿⣿⣿⣉⡀⠀⠹⣿⣍⠻⠆⠀⣼⡿⠛⣥⣿⡿⠁⠀⠀⠛⠟⠃⠀⠀⠀⣿⣿⢹⣿⣷⣤⣴⡾⠿⣿⣿⣿⡏⣿⣿⣿⣿⡇ ⠀⠘⠉⠉⣼⣿⣿⠁⠉⠙⠛⠀⠈⠻⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣧⠻⣿⣿⡏⠀⠀⢸⣿⠟⣼⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠙⣿⣿⣌⠛⠿⠆⠀⣛⣥⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠀⠻⣿⣿⣿⣿ ⠀⠀⣾⣷⡀⣇⡶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⢻⣿⣿⣿⣿⣷⣀⠀⠀⠀⣠⠇⠰⠀⠀⠀⠀⠀⠂⣀⣤⣶⣿⣿⣿⣿⣶⣤⡀ ⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣿⣿⠀⠀⠀⠁ ⢸⣿⣿⡿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⠀⢻⡟⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣶⣄⠀⣾⠁ ⠀⠀⣷⠀⠀⠀⠀⠀⠙⡆⠠⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⣷ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠁⢈⠉⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠟⠿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⠀⠀⣠⡿⠀⠀⠀⠀⠻⣿⣿⡇ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟ ⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⣤⣤⣤⣶⠿⠿⠛⠛⠉⠉⠀⠀⠈⠉⠛⠛⠛⠻⠿⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⠟ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⠉ ⠀⠀⠀⠀⠀⠙⠀⠉

⠀⠀⠀⠀⠀⢀⠴⣚⣭⣭⣭⣭⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣚⣭⣭⣭⣝⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⣛⣛⡒⠦⣄ ⠀⠀⠀⢀⢞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣎⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⣿⣿⣿⣿⣿⣿⣿⣷⣬⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣵⣿⣿⣿⣿⣿⣿⣿⣷⣌⢦ ⠀⠀⢀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⡄⠀⠀⠀⠀⠀⢠⢃⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠹ ⠀⠀⡏⣩⠶⡒⠒⠦⣙⠿⣿⣿⣿⣿⣿⣿⣧⡇⣤⣄⣞⣧⣶⣦⣀⡀⡏⣿⣿⣿⣿⣿⣿⡿⣋⡥⠶⠶⢬⣙⢹⠀⠀⠀⠀⠀⡿⡁⢸⡇⢠⡙⣌⢿⣿⣿⣿⣿⣿⣿⣧⡇ ⠀⠀⡼⢄⡸⢇⡸⢎⡠⠻⡙⣿⣿⣿⣿⣿⣘⣿⣿⢩⢰⣿⣿⢋⡍⣿⣷⣍⣿⣿⣿⣿⢑⠞⡔⢣⡜⢣⡜⢂⢧⠀⠀⠀⠀⠀⡇⢎⡱⢎⡱⢎⡀⣆⣿⣿⣿⣿⣿⠿⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣚⣛⣒⠤⣀ ⠀⠀⡇⢕⡪⢕⡪⢕⢂⣯⢿⢹⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⢸⡃⣿⡿⣿⣿⣿⣿⡇⣯⣲⠪⡕⢪⡕⢪⡕⠈⠀⠀⠀⠀⠀⡇⢎⡱⢎⡱⠎⢰⣼⢸⣿⣿⡏⣻⣿⡿⣛⣿⣷⣶⡿⠀⠀⠀⠀⢀⢞⡖⣿⣿⣿⣿⣿⣿⣶⡙⣄ ⠀⠀⢷⢊⡱⢎⡱⢎⠐⣭⣕⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⣿⣿⣽⢰⣿⡇⣿⣿⣿⣿⢰⠿⡽⢃⡕⢪⡕⢪⡕⣸⠀⠀⠀⠀⠀⠸⣄⠪⢕⡪⢅⢮⡞⢸⣿⡟⣾⣿⢟⡞⣴⣿⣿⡿⠷⠶⣿⡀⢀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢦ ⠀⠀⠀⢷⡈⠕⠪⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣦⠑⡪⢕⠊⣴⠃⠀⠀⠀⠀⠀⠀⠙⣷⣀⢾⣿⣿⣿⣿⣿⣸⣿⢏⡯⣼⣿⣿⢏⣺⠏⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡄ ⠀⠀⠀⠀⠙⠿⢲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡌⣿⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣖⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⣾⣿⣿⣿⣿⣿⡇⣿⣿⣾⣰⣿⣿⣣⣿⢋⣿⣿⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⠻⢿⣷⡇ ⠀⠀⠀⠀⠀⢸⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⢻⡇⣿⡇⠏⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣿⣿⣿⡇⣿⢇⠇⣿⣿⣱⣿⢁⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⠟⣡⠞⢩⡆⢰⡌⠛⡜⡇ ⠀⠀⠀⠀⠀⣾⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣸⣇⣿⢨⢰⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢏⣴⣿⣿⣿⣶⡙⣇⣿⣸⢸⣿⣡⡿⣠⣿⡿⢥⣾⣿⣿⣿⣿⣿⣿⢅⠿⣲⢐⡪⢕⡪⢕⡪⢸⠇ ⠀⠀⠀⠀⢀⠻⠿⠦⣿⣿⡿⠛⠉⠉⠉⠉⠙⠻⢿⣿⣿⠿⣿⠿⠋⠉⠀⠀⠉⠉⠺⣿⣿⣿⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣷⢂⡿⣿⠋⠀⠀⠀⣿⢸⣹⣿⣿⢃⠏⣴⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠭⠟⡨⢕⡪⢕⡪⠕⡼ ⠀⠀⠀⠀⣾⣷⡍⢖⣿⣿⠟⠛⠶⣦⣄⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣭⣭⣙⠛⣩⣿⠀⠀⠀⠀⠀⠀⠀⣯⠿⣿⣷⣿⠀⠀⠀⠀⣿⠘⣿⡇⡟⡇⢛⢥⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⠕⢪⡕⢪⡕⠊⡜ ⠀⠀⠀⢠⣬⡛⡇⣭⠿⠛⠋⠉⠉⠙⠓⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠷⠿⠶⠶⠶⢿⣿⣿⢰⢂⡄⠀⠀⠀⠀⠀⡾⠁⠀⢿⠀⣿⡀⠀⠀⣰⠟⠀⠀⢷⠾⠿⠿⠿⣟⣴⠿⠛⠻⣿⣷⣌⢿⣿⣿⣿⣿⢃⣁⣨⣥⠖⠁ ⠀⠀⠒⣾⠭⣤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⢻⣇⠀⠀⠉⠉⡹⠢⣀⠀⠀⠻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⠟⣼ ⠀⠀⠀⡏⣿⣿⠀⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢲⣒⣿⠒⠤⠀⠀⠇⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⢹⠛⣡⣿⣿⡆ ⠀⠀⠀⢿⠟⣇⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠀⠠⠒⠒⡒⠤⣄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠹⣧⣀⠀⢀⡴⢿⣼⡿⣣⣛⣫⡭⣢⣷ ⠀⠀⠐⠉⡱⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⣅⠃⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡀⢀⡿⠀⢻⣋⣤⣾⡿⢻ ⠀⠀⠀⠀⠹⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢿⣿⣿⠓⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⡶⠞⣡⣿ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠉⠉⠉⣿⣷⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠤⠶⠒⠒⠶⠤⢭⣛⣛⢛⠃ ⠀⠀⠀⠀⠀⠀⣏⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣡⠋ ⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣰⢻⣇⣛⣶⢷⠤⣄ ⢀⠞⣇⡖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡉⢿⣿⣿⢸⠨⣸ ⣇⢫⣡⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠔⢿⠠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢦⠀⣠⠖⢻⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢸⣰⠁ ⠀⡄⠁⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠉⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠙⠤⠓⠁⠀⠀⠀⠀⠀⢀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿ ⠀⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣙⣤⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰ ⠀⠀⠀⠀⠀⠀⢑⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠲⠤⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⢾⡴⢙⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⢭⠉⢦⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠥⠧⠖⠉⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠛⢒⠒⣲⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠗⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠁⢻⡀⣼⣵⣿⣿⣿⣄⠀⠀⠀⠀⠀⢿⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠀⣼⣥⠶⠿⠛⢻⣀ ⠀⠀⡾⠻⣿⣿⣿⣿⡿⠋⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⣇⣯⣀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣠⣇⣿⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇ ⠀⣼⠁⣠⠶⠛⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠙⠻⣦⠈⣇ ⠀⡏⣾⠁⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠿⣿⣿⡿⠛⠛⢛⠛⠉⠉⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⣹ ⢠⢱⠃⠀⠀⠀⠀⠀⠀⢠⣦⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣴⠋⠙⢶⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠸⣆⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣷⠂⠀⠀⠀⠀⠀⠀⢴⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣉⣽⠇⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁ ⠀⠀⠀⠻⣶⣶⡶⠶⠶⠿⠃⠀⠀⠀⠶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠶⠀⠀⠀⠀⠛⠿⠶⢶⣶⣶⡶⠋ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⡉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⣿⣿⡿⠉⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⡄⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣼⡿⠿⣿⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠀⠀⠀⠀⠀⣿⠉⢻⣿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣦⣴⣿⣄⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⣠⣿⣿⣿⣿⠂⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢿⣿⠏⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠈⣿⣿⠀⠀⢿⠀⠀⠀⡀ ⠀⠀⠀⠈⣆⣤⢿⠀⣏⣄⠀⠀⠿⣧⣀⣼⣿⣿⣿⠿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠻⣿⣿⣿⣿⣤⣤⡿⠀⠀⠀⣼⣆⠀⣸⠉⠳⣤ ⠀⠀⠀⠀⠙⠀⠀⢻⠁⠘⣦⣤⣀⠀⠉⠛⠛⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠉⠉⠉⣀⣴⠾⢶⣤⡇⣇⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠛⠷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⠛⠁⠀⠀⣀⣤⣴⣿⣶⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⣀⣠⣤⣤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣀⣀⣾⢛⢭⣲⢽⣪⢮⢞⡢⠻⡄ ⠀⠀⠀⠀⢀⡶⣀⣸⡏⢷⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡌⡮⡹⠚⠹⡺⣝⣝⡅⡇ ⠀⠀⠀⠀⣾⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣤⣾⣿⣿⢸⡪⢕⢰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⢃⣝⡵⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣄⠳⠋⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⡿⣿⠀⠉⠻⣿⣿⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠏⢻⣿⣿⠋⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠠⠔⣰⠃⠉⠗⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣈⣼⠋⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠿⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡌⠉⠉⣿⣿⡅⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣦⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣤⠈⢿⣿⣦⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣤⠀⠀⠻⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡩⡌⠛⢻⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⣿⡿⠛⠛⠛⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⡟⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⣿⣻⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀ ⠀⠀⠀⠀⠀⣤⠶⠛⠉⠁⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀ ⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠉⠀⠀⠀⠀⠀⣠⣿⠷⣤ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⡻⣦ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣤⣤⣾⣤⡶⠿⣷⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣮⣷ ⣸⣴⠟⠉⠉⠉⠛⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣶⢿⣾⢟⣵⣿⣛⣻⣭⣿⣗⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣷⣮⣽⡇⠀⠀⠀⠀⠀⢸⣿⣻⣵⡾⠿⠛⠛⠻⠿⣾⣹ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⣛⠻⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣾⣏⡀⠀⠀⠀⠀⠈⠀⠀⣻ ⠀⣿⡀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠋⠴⢾⡁⠀⠀⠀⠀⠀⠈⠀⣿ ⠀⠈⢿⣄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠈⣼⠃ ⠀⠀⠀⠻⣷⣄⠀⠀⡘⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠛⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⣴⣿⠃ ⠀⠀⠀⠀⠀⠳⣝⡟⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣤⠀⠀⠀⠀⣶⣿⠿⠋ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠉⣿⣿⣿⡀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠛⣿⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠿⠿⣿⣄⠀⠀⢀⣿⣿⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⢻⣿⡀⠀⠀⠀⣼⣿⣠⣿⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠈⣿⣿⣶⣶⣿⠛⠉⣿⣿⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⡿⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⡀⠀⠈⠁⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣶⣻⣭⣻⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠘⣿⣿⣯⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⢻⠦⣄ ⠀⠀⠀⠀⣿⢻⢿⣶⣶⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣴⣾⠁⠀⣿⡷⠶⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠉ ⠀⠀⠀⠀⢸⣶⢿⣯⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⡀⠀⠀⡏ ⠀⠀⠀⠀⠉⢿⡹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾ ⠀⠀⠀⠀⠀⠀⢿⡽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠉⡦ ⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣽⠃ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿ ⠀⠀⠀⠀⠀⠀⢰⣇⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣼⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣱⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣿⡇⠀⣽⢟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⢉⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⣿⣻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡏⠀⠀⠀⠻⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣯⡇ ⠀⠀⠀⠀⠀⠹⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣼⠁ ⠀⠀⠀⠀⢀⡾⡻⣷⣽⣛⣻⣿⣻⣛⣯⣭⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠓⠒⠒⠲⠦⠤⣶⣾⣛⠿⢿⣿⣿⣿⣿⣿⡿⢛⣵⡟ ⠀⠀⠀⢠⣿⠹⡚⢇⣩⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⡿⠿⡛⢥⢿ ⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣰⣷⣼⡷⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⣼⣿⡿⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠻⣿⣿ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⡄⠀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠈⣿⣧ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⡟ ⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⡿ ⠀⠀⠀⠈⠿⣶⣶⣤⣤⣄⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⣤⣤⣴⣶⣷⡿⠉ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣀⣴⣶⣿⣶⣦⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣾⣿⣿⠟⠉⠀⠉⢿⣷⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⣿⣿⣿⣄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠿⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠙⢿⡄⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣇⣀⣾⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢀⣿⣤⣼⣿⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢻⣿⣿⠛⠻⣄⣀⣀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣴⠟⠉⠛⣿⣿⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣿⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⣿⠃⠀⠀⠸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⣤⣴⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⠾⠁⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢀⣀⣀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⢺⠒⠶⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣾⣄ ⠀⠀⠀⠀⠀⠀⣀⠶⠋⠁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠉⠳⣄ ⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣠⡴⠋⠀⠙⠶⣤⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣠⣼⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡐⡆⡙⢷⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢈⡐⢰⡆⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⣬⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠶⠶⣶⣤⣴⠶⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠶⣶⡶⠶⠶⠛⠷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡥⢘⢊⡘⣡⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡁⠠⣄⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢿⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣾⣼⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣇⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣽⡻⡇⡟ ⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⠤⠤⠤⣄⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⣿⣿⣿⣳⠇⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣟⣟⡻⣏⣠⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣧⣹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⢸⣿⣿⣿⠿⢛⠉⠉⠛⣿⠟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⠻⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⢸⣿⡿⢁⠂⠀⢀⢂⡾⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⠀⠀⠀⢀⢀⠟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⢿⣿⣿⣿⣟⠋⠍⠀⠀⠠⢉⠛⢿⣿⣿⣿ ⠀⠹⡀⠄⢀⢀⡟⠀⠀⣠⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠢⠙⣿⣿ ⠀⠀⠙⣄⠂⣾⠀⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⠈⢿⠉⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿ ⠀⠀⠀⠀⢙⠃⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣦⠙⣄⠢⠀⠀⠀⠀⠀⠜⣼⠁ ⠀⠀⠀⠀⣸⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡈⣧⠢⢀⡀⠰⣀⡾⠁ ⠀⠀⠀⠀⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠷⠷⠟⠋⡆ ⠀⠀⠀⠀⢳⣿⡏⢤⣶⣶⣶⠚⠛⣿⣿⣛⣻⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⣤⣤⣤⣤⣀⣀⠀⠈⣿⣿⣄⠀⠀⠀⢿ ⠀⠀⠀⠀⢾⣿⠀⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠂⠀⢀⣿⣿⣿⣄⢿⣿⡀⠀⠀⢸ ⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⣿⣿⠀⠀⣺ ⠀⠀⠀⢀⣀⣱⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢸⣿⡆⠀⡟ ⠀⠉⠉⠀⠀⠘⠛⠉⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⣿⣷⢀⠃ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⣿⣿⣼⡇ ⠀⠀⠀⠀⠀⣧⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢰⣿⣷⠁⢿ ⠀⠀⠀⠛⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠖⣿⣿⣿⣷⣤⣀⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣾⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⣿⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⣿⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣖⣻⣿⣿⠀⣿ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣭⣛⣓⣒⣖⣦⣤⣄⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⣭⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⢧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⣷⡀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡗⣼⠁ ⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣄⠀⠀⣀⣠⡶⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠛⠒⠚⠛⠶⡴⠳⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣠⣌⣩⠿⠿⠿⠭⠭⠭⠗⣶⣿⣁⡇ ⠀⠀⠀⠀⠀⠀⢀⡾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣃⣤⠶ ⠀⠀⣀⣤⣶⣶⣏⡾⣀⠙⠶⣤⣤⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣠⠶⣷⣶⣤⣀⠁ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠄⣰⠹⡌⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠋⠉⠉⠁