Farm Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⡒⢄⠀⡀⡠⠊⡡⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠘⣿⠀⠀⠀⠀⡰⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣃⢾⣠⠊
⠀⠀⠀⠀⠀⢀⠀⡆⠀⣰⣴⡛⠀⠀⠀⢶⡅⠀⢠⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠟⠉⡫⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡇⢰⠟⣉⠙⢶⠤⠤⠀⠙⡶⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⡴⢋⢰⠈⠳⡈⢣⡀
⠀⠀⠀⠀⠀⢸⠘⡇⠛⠀⣈⠀⢸⣷⣶⡶⢶⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢾⠀⠀⠀⠛⡶⠃
⠀⠀⠀⠀⠀⠀⠭⣀⣄⣸⡇⣀⣸⣥⠤⠤⠬⠧⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⣏⡀⠀⠀⣿⠉⠀⠁
⠀⠀⠀⠀⠀⠊⠄⢀⠤⠚⠉⡉⠀⢄⠀⠠⡀⠢⡐⠄⠑⠀⠀⠀⠀⠀⠀⠀⠒⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢠⢂⡖⣄
⠀⠀⠀⠀⠀⠀⠘⠂⡿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠉⡐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⢰⢧⠺⢀⣤⠤⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣬⣆⡤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡼⠆⢰⠏⠈⢳⡤⠤⠤⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢙⣀⣹⣴⢯⣏⢳
⠀⠀⠀⠀⠀⠀⣀⡗⣆⠸⠀⡷⢸⡌⡗⢸⡇⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣸⣏⣿⢣⢺⣿⣿⣿⣼⢿⣯⠄
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⣀⣀⣼⣧⣧⣀⣠⣇⣀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣸⣯⠥⠼⠿⠾⠿⢿⣬⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⢀⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⠶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⢶⣶⡶⠶⣶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠⢄⣀⠀⠒⠀⢄
⣀⣀⣀⣀⡀⢀⡀⠤⠤⠤⠤⠄⠀⠀⠁⠒⠒⠒⠒⠒⠒⠐⠒⠒⠂⠙⠛⠲⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠤⠂⠈⠙⠉⠉
⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠈⠉⠉⠁⠉⠁⠂⠀⠁⠀⠀⠢⠄
⠀⠀⠀⣴⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠄
⠤⠶⠚⠛⠃⠑⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠀⠀⠰⠶⣤⠠⠴⠚⠈⠉⠁⠀⠈⠁⠈⠉⠂⠀⠀⠀⠀⡈⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠤⠤⠒⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠙⠛⣛⡋⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⠄⠤⠒⠒⠂⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠰⣾⣿⠟⠀⣿⣿⣿⡄⠀⠀⠤⠀⠐⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠠⠀⠛⠛⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢤⠤⠀⠀⠀⠠⠤⣤⣀⣤⣤⡀⠀⠀⠄⠀⠀⠀⠤⠄⠀⢀⣀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣶⣷⣿⠶
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣟⣽⣭⣒⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡿⡍
⠀⢀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣘⣨⣿⣊⣻⣽⣍⣡⣤⡄⣠⡶⢾⣷⣀⠀⠀⠨⡯⠃⠀⠀⠀⠀⣀⡀
⠀⢈⣤⣀⣀⡈⣉⠛⢿⣿⠿⣿⣿⣿⡏⣽⡯⣻⣿⣿⡿⣛⣛⣛⣶⠮⠵⢿⣿⠋⢉⣐⣿⣿⡗⠂⠈⠉⠉⠛⠃
⠀⢠⣤⣤⣤⣉⣩⣉⣒⣶⣾⣿⠿⠿⠇⠻⠓⣻⣟⠛⠛⠛⠛⠋⠛⠂⠀⠸⠿⠿⠿⢿⣻⣭⣽⣤⣤⣤⣄⣠⡄
⠀⠘⢟⡛⠋⡉⠉⠉⠀⣤⣴⣶⠀⠀⠀⠀⠀⢹⣿⣥⣤⣴⢤⠶⠒⣶⣤⠖⢠⣤⡄⢠⣽⡿⠛⠿⠿⠟⠛⠛⠃
⠀⢠⣾⣷⣶⣷⣴⣷⣾⣌⠻⣇⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡈⣿⣿⡇⣶⠀⣿⣷⡆⢁⣾⣶⣮⣠⣤⣠⣦⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠦⡤⢼⠄⠀⠀⠀⠙⠻⣿⣷⣇⡷⢹⣿⣤⣿⣭⣿⣬⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣄⣀⣀⣹⣿⣀⣤⣾⡄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣟⣿⣻⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠛⠋⠉⠉⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢰⣇⠀⣴⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⢠⣶⣾⣿⣿⡍⡅⠀⠀⠀⢠⡀⣼⣟⣩⣁⡀
⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⢿⣿⣿⣿⣧⣗⠀⠺⣿⣄⠀⢹⣿⣟⣋⣠⡐⢀
⠀⠀⣴⡈⢤⠄⠀⠀⠀⠀⠈⠁⠀⠉⠀⢻⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣟⣁⣀⣿⡟⢩⢹⣿⣟⣟⠩⢉⣯⡤⠆
⠀⠶⠿⣭⡤⠶⢖⠉⠉⠉⠁⠈⠃⠋⠉⠙⡛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠋⠀⠈⠙⠛⠛⠐⠊⠐⠀⠉⠀⣀
⠀⠀⠀⡔⣤⠡⢄⠀⣤⣀⡠⣤⠀⡠⠤⢠⢄⢄⠀⠀⠀⢀⣠⡄⢠⢀⠀⠀⠀⠠⣀⢀⡀⢀⡀⡀⡀⢀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⢹⡶⡌⢱⢛⠀⣿⡌⠉⣢⡽⢇⣦⡏⢀⢜⣮⣆⠀⢇⢁⠡⣉⣬⢠⣴⡧⣌⡅⣚⡤⣡⡶⠗⠠⠄⠀⠵⢹⣅⡠⡄
⠀⠀⣹⣽⣇⣷⢡⠲⣦⡆⢼⡣⡇⣻⡀⣧⠨⠞⢸⡟⠻⣤⡘⢹⣫⡍⣊⡡⢿⢳⣼⠽⢿⠾⠃⢜⡋⠦⠟⠃⢨⣏⣀
⠀⠀⢸⡇⡏⢾⢸⡟⢫⡇⢻⡟⣇⢺⣆⡟⢻⡯⢱⡏⠿⡳⢻⢾⣷⡄⣿⢠⣬⡀⢸⡷⣺⣧⡴⣦⢶⡖⡐⢺⣫⠌⠐
⠀⠀⣹⣏⡉⣺⠘⠒⢸⡇⢤⠮⣯⣼⠇⣷⢸⣋⣸⠎⠑⡟⡴⠛⢻⠂⠿⠠⠾⠉⣸⣏⠟⣻⣐⡗⣻⡿⠆⣶⠡⡆
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠚⠷⠤⠤⣭⣤⣄⣹⡅⠉⠈⣿⠀⠉⠃⣛⠄⠣⠀⢸⡇⢀⣹⣎⡟⣹⠛⠁⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠒⠒⠦⠿⣀⣀⡀⢸⡇⠀⠀⢸⡏⠈⠐⠋⡟⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠓⠒⠓⠠⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⡄⠀⠀⢀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⣹⡿⠟⠿⢦⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣶⣶⣿⠟⠀⠁⠀⢉⡟⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡛⠂
⠀⠀⡆⢸⠀⡆⡀⠀⠀⠚⠛⠛⠛⠛⠉⠙⢻⣿⣿⠋⠀⠀⠀⠀⣞⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⣄⣠⣼⣿⣿⣧⠀⠀⠒⠒⠶⠛⠀⣿⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣹⣿⣿⣿⡀⢰⡄⡦⠀⠀⠀⠉⢠⢜⣿⣿⣿⣯⣼⣿⣿⣿⠟
⠀⣀⣤⡤⠤⠤⢐⣒⣄⡨⣤⠤⠖⢒⣣⣬⣼⡭⢽⠛⠛⣿⣶⡶⠶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧
⢉⢩⣀⣤⢴⠞⠍⠉⢠⣦⣴⡶⠟⠉⣉⣡⣴⣶⡾⠟⢋⣭⣰⣤⣄⣼⣧⣯⣹⡟⣟⠛⠛⠉⠉⠉⠁
⠛⠛⠉⣀⣤⣤⠼⠚⠛⠥⣤⣴⣶⣿⠛⠙⡋⣠⣦⣼⣿⣿⠏⠛⠋⠉⠉⠀⠀⠀⢳⡝⡄
⣶⡞⡿⠿⠷⠶⠶⠶⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠄⠤⢤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣤⠎⠩⢞⠀⠅⠉⠒⠠⢬⣃⡉⠉⣹⠋⠐⠤⡀
⠀⠀⠀⠀⣚⠿⠦⠁⠡⠀⠋⠓⢒⠒⠃⠐⠌⠉⡁⠀⣤⡀⠈
⠀⠀⠀⢼⡛⣠⢡⠰⡀⡔⣲⠀⠀⢀⠬⣤⠀⠀⠀⠀⠊⠀⠀⠐
⠀⠀⠀⠈⠁⠁⠉⠷⠃⠂⠠⢸⣆⣁⢠⠰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠄⣠⠖⢀⡴⠋⣠⠞⠁⣠⠞⠁⣠⠞⠀⠀⡠⠂
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢤⠀⠀⠁⠀⠀⠉⠛⠁⠀⠀⠀⠀⢀⣠⣀⠀⠀⠉⠘⠁⠚⠀⠞⠀⠴⠋⢀⡜⠁⢀⡔⠁⢀⠔⠁⠀⢀⠘⠁⠀⢀
⢀⠀⠀⠠⣀⣠⡄⣤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⢦⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠜⠀⠀⢠⠂⠀⠀⣠⠋
⠈⠐⠱⣶⠟⠁⠀⠹⠛⣶⠖⠲⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⠋
⠀⠀⠠⠿⣧⣄⣀⣾⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢣⡿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠂⠀⠉⠉⠉⠛⠃⠦⠤⢯⣄⣀⡀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⢀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠃
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣤⣶⣿⣠⣴⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠈⠂⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠛⠀⠀⢁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡀⠀⠀⠀⠄⠀⢀⠀⢀⡠⠄⠐
⠀⠀⠀⠀⣀⣁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⣠⡀⠀⠀⡀⠄⠀⠅⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠁⠀⠈⠀⠅⡀⠀⠀⠀⡀⠀⠶⣆⠰⠀⠲⠐⢶
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡀⠀⠠⠂⠀⡀⠐⠀⠀⠁⠀⠀⠑⢦⡓⠙⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢠⠤⢤⠀⠀⠀⠙⠢⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠠⢀⠁⠐⠁⠀⠀⠸⠦⠼⠀⠀⠀⠀⠀⠈
⠀⠐⠁⠠⠂⠀⠓⠄⠀⢄⠀⠈⠁⠒⠀⠑⠀⠂⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠚⠂⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡠⠀⠄⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡤⢤⡼⠀⠀⠀⢲⡖⢲⡆
⠀⠈⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠂⠀⠀⠠⠄⠀⠀⣀⠀⠀⠂⠀⠀⠀⣿⣰⡆⠀⠀⠀⢸⢻⣼
⠀⢨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠂⠦⠴⠂⠀⠀⠄⠤⠄⠤⠄⠀⠀⢐⠈⡅⠀⠀⠀⠀⠀⢻⣏⡅⠀⠀⠀⢸⢸⣷
⠀⢈⡅⡉⠁⠉⠀⠀⠀⠁⠠⠈⠩⠀⡏⢁⠀⠠⠀⠀⠀⠀⠀⣀⡤⠜⠙⠀⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⢸⡟⢸⣇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠄⡐⠠⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⢒⠤⠉⢙⠀⠀⢀⠀⠀⣇⢀⠠⠀⠀⠀⠸⠑⠛⠒⠒⠀⠈⠉⠉⢉⡀
⠀⠀⡄⣀⠀⠀⠈⠀⠁⠀⢥⡀⢤⠀⡧⠄⠠⠖⠂⠀⠀⠀⠀⠈⠙⠀⠉⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⡍⠉⠉⠉⠀⠐⠂⠀⡀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⢈⠓⢧⢈⡂⡄⢠⡖⠍⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠩⣁⣨⡇⣨⡶⠈⡀⠒⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡰⠐⡐
⠀⢠⡌⠉⡳⣈⣤⣾⠫⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠘⠛⢙⠁
⠀⠀⡀⠈⢻⠷⠌⢶⠶⠘⣠⢅⣠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢻⣯⠏⠠⠁
⠀⠀⠉⠀⢲⠀⠀⠀⠁⢈⡋⠡⠀⠄⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⣠⡡⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⡁⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣈⣉⣩⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠁⠀⠁⠈

⣀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⢼⣿⣿⣶⠀⠀⠀⠀⠀⢀⡾⠥⠄
⣼⣿⣧⣌⣴⣆⠖⣶⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠴⢦⣤⣤⣤⣾⣷⣶⣦⡤⠀⡀⢠⣦⣴⣿⣷⣤⣀⠀⢀⣀⣀⠀⣀⡀⢠⣦⣤⣤
⢻⡿⠿⢿⡿⠿⠲⠿⠿⠧⠔⠀⠀⠀⠀⠿⠀⠀⠉⠉⠉⠙⠻⠿⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠉⠉⠉⠙⠋⠛⠛⡙⠉⠉⠉⠈⠉⠛⠛⠛
⡁⠐⣋⠤⠒⠈⢁⠠⠖⠂⡠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⡠⠀⠁⠀⠀⢠⠀⠘
⠴⠊⢁⡤⠒⠉⡠⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⡀⠂⠀⠈⠀⠄⠀⡠⠀⠀⡀⠐⠀⠀⠀⠀⢀⠔⠁⠀⡀⠀⠀⠂⠘⠀⡆
⡠⠖⠁⣠⠔⠀⣠⠀⠀⠐⠠⠄⢈⢁⠂⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠊⣠⠄⠈⢀⠔⠈⠀⠀⠀⠀⢀⠔⠁⠀⠀⡄⠀⠀⠆⠀⡆⠀⡇
⠀⢠⠎⠀⢠⠀⠀⠀⠹⠀⠀⠀⠉⠉⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠂⠁⠀⠂⠁⠀⠀⠀⠋⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠀⡇
⠀⠀⠤⠈⠁⣀⠒⠒⠀⠀⠋⠉⢀⣀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠁⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠁
⠆⠙⠂⠀⠤⠈⠁⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠒⠀⢀⠤⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣤⣴
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⣀⢀⣠⠀⠀⠀⠀⠀⠉⠛⢣⣀⣀⡀⣀⠺⢛⣿
⠤⡼⡿⠿⠧⠴⠶⠤⠶⢶⡦⠶⠾⠿⠿⠛⠛⠁⠢⠈⠻⠻⠿⠻⢿⣿⠿⠿⠾⠿⠀⠀⡄⠀⠀⠀⠰⣻⣿⣿⣴⣿⣷⣿⣿
⢠⠀⠁⢁⠀⠁⠀⡀⠁⠀⠠⢀⠀⠀⠀⠀⠀⠠⠀⢐⠂⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠠⢍⡈⠒⠭⣉⠁⠌
⡀⠀⠸⠀⠄⠀⢄⠈⠢⣀⠀⠀⠀⠀⠄⡀⠀⢄⠀⠀⠀⠂⠀⠤⠀⣀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢌⡑⠢⢄⡉⠒
⠁⡎⠀⡆⠐⡀⠀⢂⠀⠈⠣⡀⠀⠁⠀⠈⠓⢄⠉⠢⣄⠐⠤⠀⠈⠁⠀⠈⠀⠀⠀⡀⠀⠐⠂⠉⡤⠄⠂⢠⡈⠒⢄⡈⠲
⠀⡧⠀⣧⠀⢁⠀⠀⠳⠀⠤⠈⠂⠀⠀⠈⠂⠀⠑⣀⣈⠁⡀⠀⡀⠀⡀⢀⣀⢀⣀⠀⡤⠈⠉⣁⢀⠀⡏⠀⠀⢢⡀⠙⣆
⠀⠈⡀⠈⠀⠀⠀⠀⢀⠉⢀⠀⠄⠐⠌⠁⠀⠀⠰⠎⠉⠐⠈⠁⠉⠘⠤⢨⣤⠄⢤⢤⠠⣶⣤⠈⢟⣁⣉⠛⣫⣌⠯⡶⢋
⣀⠀⠄⠐⠢⠀⠉⠀⠈⣀⡀⠀⠀⠀⠀⠀⠐⠀⢠⠀⠠⠤⠶⠀⢀⠒⠂⠰⠀⠀⠀⢀⠀⠠⠤⠄⠀⢏⣁⣀⠈⠶⠋⣨⡭
⠈⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⢦⠀⠂⠀⠴⣄⠀⠀⣆⣀⡀⠀⢀⠀⠀⣄⣠⡄⠈⢏⣠⡄⠀⠈⠻⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢉⣁⣀⠀⠈⠁⠠⠆
⠀⠀⠀⠀⠀⠀⠶⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠤⠀⠀⠀⠠⡶⠚
⠀⠀⠀⢲⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⠀⠀⠀⣀⠤⠀⠀⠀⠀⠠⠖
⣤⣀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠤⠖⠒
⠉⠋⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠠⠤⠖⠒
⠛⠂⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠀⠀⠀⠀⠰⠖⠰⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢠⡤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⣀⣤⣖⣰⣤⢤⠤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠲⣄⠀⣷⢸⡇⢰⣶⣶⣿⣶⣶⣆⣀
⠀⠀⠀⠛⠛⠛⠛⠿⠴⠿⢿⣿⣿⣿⣶⣦⣄⠀⠀⠀⢠⣤⡀⢰⣾⣿⣷⣶⣤⠀⠀⠀⠀⢀⣾⢸⣏⣷⢘⠀⢸⣾⡗⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣷⡀⠀⡂⢀⣴⡶⣶⣤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣜⣓⢄⠀⣿⣿⢛⣉⣉⣠⣹⡁⣿⣿⣋⣲⣹⣧⣥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣂⢃⠈⢿⣿⣿⣯⣿⡉⠀⠀⠀⠉⠙⠛⠛⠻⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⠹⣿⣿⣍⢦⣼⣿⣿⣿⠿⢟⠛⠶⠦⣄⣄⣀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢈⠀⣿⣿⣷⢸⣿⣿⣿⣿⣶⣾⣿⣷⣶⣤⣄⡁⠘⠻⠟⠂⢀⣃⡄⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠀⣽⣿⣟⣼⣿⣿⣿⣿⣿⡿⣃⡿⣿⣿⣿⣿⣷⡄⠀⢸⣿⢽⣿⣿⠿⣷⣌⡆
⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⢿⣿⣿⣧⣠⣿⣿⣿⣻⣿⠀⠿⠿⠿⢇⣿⣿⣿⡒⠬⣿⣻⣷⡀⣹⣿⣻⣿⢇⠑⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠒⠦⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠘⣿⣛⡃⣛⣉⡴⢿⣦⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⡏⡀⣿⣿⣧⣿⠻⡿⠿⠛⠁⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⠇⠀⣿⢛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢼⣿⣷⠾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠃⠛⣂⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠉⠉⠈⣱⣾⣿⣿⣿⣿⣦⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠣⠆⠄⢠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣕⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣿⣶⣶⣦⣤⣶⣿⣿⣿⣿⣷⣿⣿⣶⣾⣿⣾⣿⣿⣿⣿⣾⣧⡄
⠀⠀⠀⢀⠀⠀⡄⠀⠀⠠⢼⣤⡟⣼⣧⠃⣿⡟⡟⠿⣿⡟⠛⢻⡜⠛⢻⡞⢻⣿⣿⢿⠿⣿⢿⡇⠀⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠟⠓⠒⠲⠤⡴⠲⠗⠛⠛⠻⠷⠷⠤⠤⠄⠀⠚⠋⠭⠍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⡒⠒⠒⠚⠁⢉⣉⣉⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⡷⡄⠀⠀⣀⡀⠀⠀⠠⠤⠀⠀⠀⠀⠀⢠⣞⠢⡿⠀⠉⠉⣶⣆⠻⡄
⠀⠀⠀⠀⢰⢻⠀⠿⢿⣛⣿⡟⠉⠛⠟⢩⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡿⠃⠀⠀⠀⠀⠀⠛⢱⠇
⠀⠀⠀⠀⡏⠈⡇⢸⣿⣿⣧⣿⠀⠀⠀⠀⡙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⢋⠜⠀⠀⠀⣀⣀⡀⡀⣺⡄
⠀⠀⠀⢰⠃⠀⢗⠈⠻⣯⣘⣻⣷⠠⠀⠀⠱⡌⢻⣧⢀⡀⠀⠀⠀⡀⠀⠀⢉⠰⠒⢦⢠⠄⠚⢰⠀⠀⠊⢁⠉
⠀⠀⠀⢸⡇⠀⠘⡆⡹⠙⠀⠈⢏⢛⠢⣀⡀⣈⣦⢧⠄⢉⠓⠀⢋⣉⣀⡀⠰⡇⠀⢺⡏⢀⣀⢎⣀⢰⡀⣦⣄⠀⢫⡍
⠀⠀⠀⠈⠀⠀⠀⢧⣀⠀⠀⠀⢺⡜⠀⠀⢧⣿⡀⠂⠀⡎⠀⠀⠀⠙⠉⠉⠻⠐⠂⠉⠋⠀⠉⠛⠁⠀⠁⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠰⠟⠞⠫⠞⠁⢢⣆⣷⣶⠀⢼⣽⡌⢆⡀⣇⣤⣴⢶⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠙⠁⠋

⣶⣶⣶⣶⠶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⡶⡶⣶⣶⢶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣤⣤⣤⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠒⠒⠀⠀⠰⠆⠀⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠰⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣎⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢊⠀⠀⠈⡄⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠘⢄⠀⠄⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀⡄⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠃⠀⠀⠈⠁⠀⠀⢨⠗⢄⠘⠁⢠⡄⠀⡆⠀⠀⠰⢣⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠈⠤⠀⠀⠀⠂⠀⢀⠴⠳⠀⠀⠀⢱⢀⡄⠀⢈⠈⢱⡌⡆⠀⠖⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⠀⠀⠀⠋⠴⠀⢀⡄⠀⢨⠀⠀⠀⠉⠀⠁⠀⠀⠀⢰⠁⡇⠂⠀⠀⠠⠀⢰⠆⠴⠀⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⡌⠀⠃⠀⠀⠀⠀⢠⠇⡀⠀⠀⠈⠁⠀⢸⠅⠀⠀⠀⠀⠀⠀⡀⠀⠘⠰⠿⣇⠀⠉⠈⠀⢨⣀⠀⠀⠛⠆⠁⠀⡁
⠀⠀⠀⠀⢠⠃⣆⠀⠀⠀⠀⢀⡇⣀⠀⠀⠘⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡏⢠⠄⢨⠀⣸⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠈⣢⣀⠀⠁⠀⠀⡾⠠⠀⠀⠀⠋⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠗⠂⠀⠂⠀⠁⠀⠀⠘⠀⡀
⢀⠀⠀⠢⣴⠉⠉⠛⠻⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡜⠢⠀⠀⠀⠀⠀⠀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠒⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈⠁⠒⠀⠤⠤⠤⠄⠀⠀⠀⠀⢱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠈⠁⠀⠛⠁⠴⠂⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠰⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠐⠂⠁
⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣈⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠋⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣀⣀⣀⣽⣄⡀
⠀⠀⠀⠀⠀⢀⡼⠿⠟⠛⠛⠉⠉⠉⠙⠛⣻⣥⡶⠦⠀⠀⠀⢀⣀⣀⣤⣤⣤
⠀⠀⠀⣠⡶⠋⠀⣀⣀⣀⡠⣤⣴⡖⢺⣿⣿⣧⢤⠀⠶⠚⠛⠉⠉⠁⠀⠀⢸
⠀⠀⠘⠛⠛⠉⢩⠏⠘⠛⠀⠈⡟⣷⠞⠁⢸⠀⣎⡄⠀⠀⠀⢀⣠⡄⠀⠀⢸
⠀⠀⠀⠀⠀⢠⣯⠤⢦⣀⡀⢰⣿⡿⢤⣤⢾⡄⢻⡄⣀⠴⠚⠋⢹⠃⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⣾⡿⢳⣄⠀⠈⡇⠀⠙⢦⣀⣀⣀⡟⠀⠀⢠⠃⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⣴⡟⠁⠈⣿⠣⡴⠞⠀⠀⠀⠀⠉⣹⣿⣿⣶⣾⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠸⣇⠀⠲⣦⡀⠀⠀⡰⠋⢑⠞⠉⠁⠀⠀⠀⠀⠙⢿⣧⡔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢻⣦⡼⠁⠀⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⣿⡁⠀⠀⣇⠀⠀⠀⠀⣠⣾⣿⠷⣫⠑⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⢇⣿⠶⣿⣿⣶⣴⣾⣿⡫⠕⡡⣐⡵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢸⢸⣡⡶⡟⢝⢝⡿⢿⣭⢖⠔⣊⠤⢚⣽⣷⡀
⠀⣠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡟⢸⡻⡌⣌⢇⠡⣻⣶⣿⣷⡫⣷⢯⣣⢿⡻⣧
⠀⠙⡟⠳⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⠝⣎⢂⣦⣷⡿⠟⠉⠘⢿⣕⢿⣷⠱⣒⣽⣇
⠀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢿⠧⡇⣿⣮⣶⠿⠛⠉⠀⠀⠀⠀⠈⢻⣯⢾⣿⡻⣝⣿⡄
⠀⠀⠈⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡹⡀⡟⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢻⣾⣷⡽⣧
⠀⠀⣦⡀⠈⣇⠀⠀⣀⣼⠀⠀⠀⠀⠀⢻⣗⡝⣽⣿⢷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣛⡭⢔⣿⡆
⠀⠀⠘⢏⢳⢸⡄⢀⡍⢙⡖⠀⠀⠀⠀⠀⠹⣮⣪⢿⢸⠟⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡛⠽⠧⠀⣀
⠀⠀⠀⣼⠈⣦⣧⢾⠀⣯⠀⠀⠀⠀⠀⠀⠀⣬⠇⣸⢸⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣠⣴⣶⣿⠿⡃
⠀⢳⡲⡈⣇⣹⣻⡼⡰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⡇⡎⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠋⠉⠀⣿⣿
⠀⢠⣷⣉⢫⣹⡟⡗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠾⣄⠧⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⣆⠀⢀⣠⢄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠘⢤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣽⠞⠛⠉⠉⣩⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣀⣤⣿⣃
⠀⠀⠀⠀⠀⠀⢛⣷⠀⡀⢠⠀⢀⠀⠀⣀⣐⣊⣼⣟⡀⢀⣀⣀⡀⠀⣼⠁⣠⡞⣠⠟⠀⠀⠀⠀⢀⣠⠿⠂⠶⠖⠠⢶⡟
⣀⣀⣀⣴⠛⠦⡼⠿⠜⢳⠿⣤⣯⠀⣸⣿⣿⣿⣿⣿⣿⣟⣁⠈⠉⣉⣉⡴⠛⠫⠿⢾⣥⣀⣰⣛⣉⣁⣀⣀⣠⣄⣠⣼⣥⣾⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠊⠙⠖⢒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠯⠄⠤⠦⠤⢤⣤⣶⣟⣿⣿⣷⣤⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣿⣿⣿⣿⣷⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠃⠚⠀⠒⣐⣤⣴⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣮⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⣷⣶⣶⣶⣆⣤⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⢦⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣥⡄
⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⣏⣁⣿⢸⣿⣹⡇⣿⣿⠿⡿⣿⣿⣿⡿⢹⠟⣜⢿⢸⠟⡜⠿⢻⣿⣿⢿⡿⡿⣿⡿⣇⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠈⠸⠃⠀⠈⠙⢧⣿⣿⣇⣛⣛⣛⠀⠿⢽⣈⣇⣿⣿⣿⣤⣄⣞⣽⡀⠀⢜⣛⣀⣸⣿⣿⠸⠯⠥⠿⠟⠋⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠽⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⣀⣀⠀⡀
⠀⠀⢠⣤⣤⣤⣦⣤⡤⢶⠆⠀⠀⢩⣥⣭⢄⣈⠀⠀⠀⠀⠀⠺⠀⢉⡉⠹⣦⠀⠀⠉⠙⠻⣿⣿⣶⡀
⠀⣠⣿⣿⣿⣿⣿⣿⣄⡞⢡⡀⠀⠈⠙⢿⣾⣿⣦⣄⠀⠀⠀⠀⠀⠈⠁⠸⠤⠂⠀⠀⢳⣌⠉⠉⠙⢿⡄
⠀⣿⣿⣿⣿⡿⣿⠿⡟⠃⣀⣠⠠⠀⠀⠀⠈⠟⠋⠀⠀⠀⢀⣤⣶⣿⣷⣄⣼⣧⡿⠂⠉⢁⠀⠀⠀⠘⠁
⠀⢿⣿⢿⣿⣻⢻⠿⣿⠿⣿⡧⠌⠷⠤⠀⠄⠤⠂⠀⠤⠀⠀⢙⣿⣿⣾⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⡇
⠀⣾⣿⣧⣮⣭⢠⣰⣿⣦⣴⢃⣀⣉⠋⢽⣶⡄⠈⠁⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⣹⢿⣿⠇
⠀⠻⣿⣿⣿⣿⡶⣿⣿⣿⡇⢸⣿⣿⣶⣾⣷⠄⡀⣝⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐
⠀⠐⣿⡿⠾⠿⣷⣿⣿⣿⣧⣠⣭⣭⣡⣬⣽⣷⣩⣿⣟⡀⣿⣶⣶⣶⣤⡼⠛⢻⣧⣸⣿⣿⣿⣿⠏
⠀⠀⢤⠀⡀⢀⠀⣿⡏⡽⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⡛⠳⡤⠜⠛⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠚⢿⣿⣅⣸⣇⠉⢿⡿⢿⣿⣿⣿⣿⡏⣦⠻⠿⠿⠟⠿⠙⠿⢯⣙⡶⠶⠟⡓⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠺⠷⠦⣘⣻⠿⣿⠿⠿⠗⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡛⠋⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠞⠶⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⠂⡀⠀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡿⠘⡇⠘⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢰⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣾⡏⢀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣿⣿⣿⣿⣿⣧⠋⠀⠘⢶⡄⣟⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⠞⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠂⠀⠂⠀⠀⠔⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⢿⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠀⠀⠀⠀⡀⠀⠈⣀⣠⣤⠤⡤⠀⠐⠀⠲⠛⢻⣿⣿⣿⣾⣿⠷⠶⠶⢦⡀⠠⠶⢖⠉⣀⡟⠁
⠀⠀⠀⠁⠢⢄⡋⠀⠀⠀⠀⠀⠀⠀⢉⡽⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⢰⡆⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡟⢻⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣇⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢹⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠘⣿⣿⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⡇⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⠇⠀⣹⠿⢿⣙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣦⣶⣶⣶⣶⣶⣶⣦⣶⠾⠿⠿⠛⠁⠀⣠⣤⣶⣿⣿⣾⡿⠃⣠⠾⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⣴⣿⣿⣿⢿⠟⠛⠁⢉⣁⡀⣀⣀⣀⣀⣤⣤⠝⠛⠟⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠐⠋⠈⠉⠁⠁⣠⠄⣠⣾⣿⢿⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠘⠡⠞⠱⠋⠁⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⣀⠀⠈⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢞⣥⠞⠉⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢻⡄⠀⠀⢀⡟⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠙⠶⠶⠛⠀⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢳⡀⠀⠀⠀⠀⠃⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠀⢣⠀⠀⡀⢠⣦⠀⠀⡖⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣼⡇⡠⢷⢂⡍⠉⠓⠛⢾⠤⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡼⠉⣿⠀⠀⠁⠀⠀⠀⠀⠸⢦⠀⠀⠈⢣
⠀⠀⠀⠀⠀⢀⣾⠃⠀⢲⡆⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠙⠢⣄⣸⢀⣀⡀⠀⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⡴⠛⠉⠈⣍⡳⡄⠀⠀⢸⠀⠀⠈⢷⡀⠀⣠⢾⣀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣾⣀⣠⡤⢜⡶⠳⠀⠀⠀⢸⠀⠀⠀⠈⢷⡞⠻⡄⠀⢠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠛⡶⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡸⢻⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⢸⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⡇⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡾⠀⢸⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⢱⡇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡎⠀⢸⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠃⠀⠀⣽⠋⠉⠉⠁⠈⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⡄⠀⢀⠀⠀⠀⠻⠖⠚⠛⠛⠒⠒⠋⠀⢀⡴⢇⣤⢤⡤⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⡠⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⣟⣀⣀⡀⠄
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠶⠶⢦⡀⠀⢰
⠀⠀⠀⠈⠛⠿⠟⢿⡏⠹⠁⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣈⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠔⢺⡙⢧⣴⡇⢙⡦⡀⠰⢊⡩⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣦⣤⣄⢰⣀
⠀⠀⠀⢠⡎⠀⠀⠈⠙⠲⣿⠟⡉⡀⠙⢲⡎⠀⠀⠈⠀⠀⠀⡀⠤⠀⠀⢀⠜⢡⠤⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⢄⣀
⠀⠀⠀⢸⣇⠀⠱⣦⣠⣶⠹⢄⣛⡤⠀⠺⠷⢤⡀⠀⣀⡀⠀⠀⠀⠀⠀⡀⢠⣤⠀⣤⠀⣬⠉⣭⣽⣛⠃
⠀⠀⠀⠘⣿⣄⡤⢿⣧⣿⣷⡿⣵⡛⠁⣀⣔⡿⣿⣿⣿⠀⠀⠀⠀⡀⠀⢀⣈⣉⣀⣉⣀⣿⣶⣿⣿⣿⣿⣦⣀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⢻⣿⣾⠟⠓⢦⡀⠀⠈⠁⠈⠉⠹⠛⢛⡏⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢿⣿⣷⣦⣀⡉⠓⠶⠚⠓⢛⣷⣰⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣤⣴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣾⠿⠾⣫⠀⠀⢠⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⡋⠀⠀⢠⡾⠀⢀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣾⡇⠀⣸
⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠟⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⠆⣀⣤⣤⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢛⣵⠟⠉⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣿⠇⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⢿⡆⠀⠀⠀⠀⢰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⢀⣠⡞⠀⣿⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⠀⠙⡛⠛⠉⠀⠀⠋⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠹⡆⠀⠐⠀⠀⠀⢠⠀⠀⡆⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢸⣇⠀⠁⢠⡶⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣸⡆⠀⢳⣰⡀⠲⠲⢾⣭⣤⣄⡸⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣰⢿⣧⡰⠋⠷⠤⠞⠀⠀⠀⠀⠈⣟⠛⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢰⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢶⣤⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠙⠓⣾⣧⠶⠶⢦⣀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢻⡄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢠⠞⠉⠀⠀⠰⢦⣌⢵⠀⠀⠀⠀⣷⠀⠀⠀⠀⢿⡄⠀⣠⡴⠻⣤⣤⠶⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣰⣇⡀⢀⣤⢤⣙⣷⠸⠦⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢿⡴⠋⢻⡄⠀⠀⣴⣾⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⢦⣬⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣠⣤⡀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⢏⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⡿⠸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⡄⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢰⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⣶⢸⡇⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡏⠀⠀⣾⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣮⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⠃⠀⢰⡟⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢿⠀⠀⠘⢿⣶⠤⠤⠤⠖⠈⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾⠃⠀⣀⣀⣀⡀⠀⠀⢀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣒⣦⠀⠀⣸⠇⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠛⠛⠉⠀⠀⡀⣴⠞⣤⣴⢦⣶⠖⢾⡤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠔⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠛
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠿⢿⢿⣿⡿⠿⢿⡿⠿⣿⠿
⣿⣶⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡋⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⣰⣄⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⣿⡿⣿⣾⡶⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀
⠉⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⢠⡴⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠴⠛⡀⡀
⠀⠀⠀⡄⢄⣀⣁⣄⠀⠀⠀⢐⡀⠉⢁⠀⡀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⡸⠀⡄⡦⢬⣄⣀⣙⡂
⠊⠒⠈⠁⠁⠁⣀⣀⣴⠔⠏⣅⠀⡈⢠⢀⠋⡨⢁⡀⠆⡊⠐⢉⠐⡈⡀⠄⡀⡀⡀⢱⠈⡚⠄⠈⠈⠙⠋
⠀⣀⣶⠶⠐⡋⢩⡆⠈⡁⠶⠐⢃⡅⣰⠘⣠⠁⠂⠴⢀⠉⠘⠄⢏⢡⠐⠀⡤⠆⠁⣤⢈⠁⠆⢠⠐⣀⠏
⠋⢍⢀⡤⠐⠃⢀⡶⠚⣁⠀⠟⡈⢁⣰⠀⡌⠀⠇⢤⠈⠡⠏⡀⠾⠈⢰⠀⣡⠘⠃⡄⠘⢠⠆⢠⢀⠉⠘
⢠⣶⠀⠁⣰⣇⠀⣰⡄⠛⢠⡄⠑⠀⣤⠀⠃⢰⠀⠉⢰⡆⠘⢣⡄⡾⢠⡀⠃⣤⠐⠃⡦⠈⢠⡌⠚⢠⡆
⣤⣤⣤⣶⣶⣤⣤⣤⣤⣤⣤⣽⣤⣤⣽⣤⣤⣽⣤⣤⣭⣤⣤⣾⣧⣴⣾⣧⣤⣿⣦⣤⣷⣤⣾⣧⣤⣾⣷

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⡃⢸⡟⠈⢻⣷⣆⠀⠀⠀⠀⢀⣀⠿⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢲⣶⣶⣶
⠀⠀⢰⡿⢻⠾⠧⢿⣸⣿⡷⠆⠀⠀⢴⣯⣥⠀⠤⣼⡿⠇⠀⠀⠀⠀⠒⠀⠀⠀⠐⣒⡮⠿⠲⠿⢛⠋⠉
⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠈⠀⠀⠀⠀⠘⠋⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢀⢄⣀⠀⠦⠴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣹⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡔⡑⢀⢙⣷⣦⡀⣀
⠀⠀⠀⠀⢀⣤⣾⣿⠁⠈⣿⣿⡿⠃⢀⣤⠀⣠⣤⣀⠀⠀⠀⠀⣤⢴⣻⣿⣧⣧⣽⣼⣿⢟⣝⡻⣷
⠀⠀⠀⠀⣉⠁⠄⠀⠀⠀⠛⠛⡃⠀⠰⠿⡀⣀⠉⠉⠃⠀⠀⠀⠀⠀⠁⠈⠐⠀⠀⣀⢐⣿⣿⣿⣅⡁
⠀⠀⠀⠀⠀⠐⠒⠒⠮⠮⠴⠥⠤⠄⠦⠶⠶⠶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠓⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣂⣂⣀⣀⣐⠒⠒⠒⢒⠒⠒⠂⣀⣐⠐⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣄⣀⣐⣂⣒⣂⣀⣐⣒⣒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣤⠤⢶⠶⣶⣶⠾⠿⠒⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⢛⣂⣶⣾⣽⢋⠙⣿⣻⣿⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣻⠫⢛⢛⢛⣛⣛⠛⣉⠛⠋⣩⣿⣿⣯⣙⡛⠛⡙⠉⡛⢛⡛⠛⢋⣙⠻⣛⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣛⣯⣯⠯⠿⣿⣞⡿⠯⠀⠀⠭⣿⣿⠿⣤⡉⠳⢾⣶⣌⡳⣮⣝⠳⢾⣍⡓⠶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣷⠶⢟⣛⣿⣿⡾⣞⣿⣷⠃⣶⠀⠑⣠⣿⣿⣿⡶⡇⢿⣷⣮⠛⢿⣶⣭⣙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣥⡶⣿⠿⣫⣿⣿⣿⣿⣿⡋⣸⢣⠊⢹⡟⢯⢻⣿⣷⡏⣯⣿⣿⣿⣄⠛⢿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣋⣵⣾⣿⣿⣿⣿⢿⡏⠙⢠⣿⡏⢠⡿⠋⠀⢻⣏⡉⠤⢝⣿⣷⡹⣿⣷⢷⣞⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⢹⡿⡏⠦⡸⣟⣼⣿⡇⣾⡇⢀⣧⠰⣿⣟⣇⡚⣿⣿⣧⠩⢻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣠⡎⡛⣑⡁⣞⣿⣿⣿⣿⠀⣿⢳⣾⣿⡀⣿⣿⣷⡍⣽⣿⣿⣧⠀⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⡿⠧⢭⣬⣷⣿⣿⣿⡿⢻⣤⣿⣿⣿⣿⣿⣿⣿⣿⢧⣳⣿⣿⣿⡆⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠭⢛⡦⡬⣾⣷⣿⣿⠟⠁⢷⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣦⣽⢿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠐⠙⠛⠝⠻⠋⠀⠀⠀⠉⠀⠀⠁⠁⠁⠀⠙⠿⠟⠛⠘⠛⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣀⣀⣀⣀⢐
⣤⣤⣤⣤⠀⠀⠠⠤⠒⠒⠒⠂⠀⠀⠐⠒⠚⠛⠛⠓⠐⠒⠒⠒⠘⠛⠛⢒⢒⣒⠂⠒⠒⢒⠒⠒⢒⠒⠂⠀⠐⠀⠀⠉⠉⠁
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⢀⡖⠀⡀⠀⣀⣀⣆⣀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠐⣤⠤⣄⡀
⠒⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃⠤⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠠⠤⠤⠄⠀⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣬⣤⡀⢠⣾⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⠿⠋⠀⢹⣿⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠂⠐⠂⠀⠀⠀⠀⠂⠒⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠋⠀⠀⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠊⢀⠀⠴⠀⠀⠠⠂⠀⠛⠂
⠀⠀⠀⠀⠀⡈⠀⠀⠄⠛⠀⠈⡀⠀⠀⠀⠘⠀⠒⠓⡛⠈⠁⠈⠀⠉⠋⠉⠀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⠀⠂⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠂⠀⡃⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣤⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠇⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⢀⠀⠀⠀⠈⠀⠀⠤⠄⠀⠈⡄⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡤⠀⠀⢠⠄⠐⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠀⠻⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⢰⠆⠀⡏⢰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣼⣮⣵⣦⣤⣦⣴⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢄⠀⠀⢸⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢳⡀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣇⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣠⠤⠜⠒⠒
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⣶⣾⠿⠏⠁
⠀⠐⠚⠒⠒⠒⠚⠻⠶⠖⢲⣶⠦⣤⠤⢤⣁⣀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠠⠴⠚⠋⠉⠈⠈⠃⠁
⠠⠀⠀⠀⠀⢀⡀⠄⠐⠊⠩⠐⠩⢔⠽⢊⡴⣩⢋⡏⣏⢻⠑⣶⠲⡴⠤⣄⢀⡀
⠀⠈⠀⠐⠀⢀⠄⠂⢀⠀⠀⠀⠀⠀⠔⠁⡰⠁⡈⠀⠇⠈⠄⠈⢆⠈⠂⡀⠀⠀⠈⠀⠐⠂⠀⠤⣀
⠀⠀⠠⠔⠈⠀⡠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠀⢲⠀⠀⠀⠀⠠⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠈⠀⢀⡀⠀⠀⠀⠉⠀⢀⠌⠁⠀⡈⠀⠀⠨⠀⠀⢀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⡟⢰⡇⢰⠋⠀⠀⠀⠀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⣰⣏⣿⢿⡶⣴⠖⢨⡙⢾⡇⢸⠀⣀⣀⠀⠀⢿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⣀⡀⣠⣶⣦⣄
⠀⠀⠀⠀⢠⣤⣿⣷⣿⠈⠛⠛⠀⠈⢡⠈⠇⠸⡆⠿⠿⢧⣤⣼⣵⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠴⢶⠦⠴⠿⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠸⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣻⠿⣿⣿⠉⡴⣋⣩⡆⠀⠀⡀⠀⡀⠀⠀⠀⠀⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢢⣄⠀⠀⢹⣷⣶⣶⣶⠿⠚⠋⠘⠓⠾⢿⣷⣶⣄⡳⠄⠀⠀⢸⣏⡄
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠠⠄⠀⠀⠚⠀⠋⢓⠦⠃⡞⢿⡔⢎⠻⢿⣿⣿⣶⢒⡄⠀⠀⠀⠀⠀⠉⠙⠓⠳⠀⠀⠘⣷⠁
⠀⠐⢢⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡃⠉⢙⠢⡀⢠⢿⣤⣤⢻⣿⣯⣤⣸⣿⣷⣦⣤⣐⠂⠀⠀⠀⠀⠀⠀⣀⣉⣠⣄
⠀⠀⠀⠀⠈⠉⠑⠬⠷⣦⡤⣀⠀⣿⠻⠀⠀⢈⣙⢦⢁⡞⣿⣿⣾⣿⢰⣮⣅⡉⢿⣿⣿⣿⣿⣷⣶⣤⣰⠞⠉⠁⠀⣠⣴
⠀⠀⠀⠀⠀⠈⠐⢠⣴⣾⣿⣷⡀⣿⢸⡇⠀⢠⣮⡳⠤⣿⣿⣿⣸⣿⣿⣿⢿⣇⡤⢭⢿⢿⣿⣯⠛⠿⣿⣿⣿⡿⠉⡿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⢻⡞⡅⠀⢸⣷⣝⣖⣿⣿⣬⣄⢳⡸⣕⠸⢿⣧⠀⢨⠹⣿⣿⡆⠀⢹⣿⣿⣟⠀⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡈⢿⣼⠀⣿⣿⣿⣿⣿⣿⣿⣨⣮⣻⣮⠻⡶⣍⠙⠸⡄⣿⣿⡇⠀⢸⣿⣿⣿⠀⣷⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡶⣦⡀⠁⢶⣎⣉⠿⡶⠘⣿⢿⣯⠀⠿⢛⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠻⢿⣿⡄⠈⢷⣿⣶⣷⣽⣯⣬⣿⣶⣿⣿⣿⡿⣻⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠈⣿⣇⣠⣿⣿⣿⠿⠟⣿⣿⣿⣽⣿⣟⣟⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡯⠁⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣾⣷⠀⠘⠈⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⣀⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢽⣿⡿⠿⠛


⣿⡿⡛⣿⠿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣥⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢰⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀
⣬⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠿⠃
⣿⣿⣿⣿⡧⠀⠀⣀⣀⣶⣶⣶⡄
⣿⣿⣿⣿⠇⠀⣴⣿⣿⣿⣿⣿⣿⢀⣀
⣿⣿⣿⣿⣃⠀⣿⣿⣿⣿⣿⣧⣂⣸⣿⣀⣴⣿⣧
⠿⠿⠿⠿⠧⠤⢿⣛⣋⣉⣯⣹⣿⣿⣿⣿⣿⣿⣟⠀⠀⣶⠀⢴⢶⠟⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠙⠛⠛⠓⠾⠭⠬⢝⣋⣁⣀⣀⣀⣀⣈⣀⣀⣀⡠⠤⠤⠐⠙⠋⠉⠉
⢰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠭⠟⠛⠋⠉⠱⣦⡀
⢼⣿⣿⣷⣷⣷⣿⣷⣶⣴⣤⣤⣠⢀⣀⣀⣀⢀⣀⡤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⢀⠀⠠⠀⣄⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠱⡈⠰⣡⣿⡇
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡠⢔⡡⢆⣿⣿⡇⢢⠑⣂⢹⣿⣇
⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠒⠥⠒⠭⠒⠥⠚⠥⠿⠿⠯⠄⠧⠘⠼⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣥⣧⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠗⠐⠉⠁⡟⠁⠀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣦⣤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⡀⣦⣠
⠀⠀⠀⠈⠃⡀⠠⠆⠀⠀⠀⢀⣰⠏⠀⠀⠃⠨⠀⠸⣦⠀⢀⠱⡀⠀⠀⠀⠀⢀⠠⡀⠀⡀⠸⠀⠀⢀⡇⠐⡄
⠀⠀⠐⠂⣄⠙⠷⡞⠛⣿⠽⠉⠙⢀⣀⢳⡗⣾⣻⣀⡘⣿⡟⣳⡿⡂⣀⣒⢂⣼⣶⣷⢀⣾⡀⠀⠄⠟⡁⣸⣧
⠀⠀⣀⡠⠈⢴⠄⠀⠀⣹⣀⠀⠖⢹⣽⣼⣿⣿⣏⠯⢗⡿⠴⠟⠒⠒⠓⠒⢰⠒⠒⠶⠂⠙⠃⠐⠒⠀⠐
⠀⢈⠈⢐⣒⢸⣾⠏⣷⢹⠟⠚⣿⣌⠁⠼⠀⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⢥⢤⠄⣀⠀⠀⠀⠀⠀⠀⠂
⠀⠅⠤⠠⠘⠿⠔⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠄⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⢀⣠⣤⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠻⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⢀⣀⡈⠁⠉⠀⠀⠀⠀⠀⠂⠄⠀⣰⡖⠛⠣⣸⣿⠟⢀⡴⢦⠀⠤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡞⣿⡏⢻⠇⠁⠀⣶⣶⣶⣤⣤⣀⣀⡀⠀⠀⢈⣤⣿⣵⣶⣿⣧⠀⠐⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢶⣆⢶⣮⠀⢀⣿⣿⡛⢻⣿⣿⠿⣍⡳⢤⣼⣯⣏⣽⣭⠽⢿⡄⣀⣶⡎⠀⠒⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠤⢀⣸⣛⣨⣏⢠⣭⠁⢸⣿⣿⣄⣸⣀⠠⠰⣿⣾⣿⡏⢁⣻⣿⣶⣷⡰⠛⣉⡄⠀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⣿⠄⣿⠆⣿⠂⣸⣿⣿⣂⣻⣫⣶⡴⢿⣿⡜⣤⣼⡽⢿⣆⢉⡴⠟⠛⠁⡴⠀⠳⡄⢹⣿⣿⠀⢀⡀
⠀⠀⠀⣴⡦⣶⣗⢾⡀⢘⠀⠘⠁⠀⠀⠀⠀⠀⠰⡇⢠⡅⠀⠀⠉⠈⠉⠈⠉⠛⠭⠉⠃⠉⠀⠒⣀⠙⠋⣠⣴⡆⢰⡇⠀⠀⢧⠀⣿⣿⡄⠿⠽⠶⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣷⠀⠇⠀⠀⠀⡀⣄⠂⢴⣲⣶⣶⣝⢳⡄⠀⠙⢷⡾⠋⢁⡄⠘⡇⠀⠀⡟⢀⡿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣇⣄⠀⠀⠀⠀⠘⢀⣿⠿⠛⠋⢹⣙⣫⣽⣿⠿⠿⣿⣏⢿⠂⢲⣤⣀⣴⠟⢁⠀⢳⣀⣰⠃⣸⠁⢀⣀⣀⣀⡠⠤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢺⣿⡇⠀⢸⣷⣾⠢⢤⣤⠴⠞⠛⢣⡤⣲⣿⡏⠀⣦⢹⣿⣾⣧⣤⣤⣉⣉⣴⠟⣤⠈⠻⠤⠞⠃⠀⣠⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣩⣿⣿⡶⣿⣿⣿⣶⣶⣶⣶⣿⣿⡗⣚⡽⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣉⣾⢏⣷⣄⣀⣀⣠⣴⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⢾⣿⢿⣿⣿⣿⡿⠟⠉⠉⠉⠙⠛⠱⣺⠿⣿⣭⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠾⠯⠟⠋⠋⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⣯⠷⣫⣖⢋⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡀⢸⣷⣸⣿⣷⣴⣤⣿⣧⢠⣤⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣸⣷⣾⣿⣮⣿⣿⣿⢻⣿⣿⣿⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣘⣿⣿⣿⣿⣿⣿⡹⣿⣽⣿⣹⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣷⣿⣿⣿⣽⢿⣯⣿⣷⠳⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠀⠀⠈⠳⣔⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣛⣿⣿⢭⣟⣿⣿⡻⣷⣯⢻⣿⣷⣿⣿⡿⣯⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢳⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣟⣏⣿⣟⢿⡜⣗⡿
⠀⠀⠀⠀⠀⢀⢄⣽⡯⡨⣿⣇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⡿⢿⣯⣷⠯⣻⣿⣝⣿⢏⣮⠻⠞⢞⠉⡈⠇
⠀⠀⠀⠀⠀⠰⠫⠋⠀⠁⣿⡯⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠛⠛⠋⠡⣶⠿⠾⠻⠟⠿⢾⣏⢮⠎⠙⣇⡄⢹⣢⡇⢠
⠋⠛⢛⡃⠄⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⣿⣸⠐⠘⣯⢱⣸⡇⣁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠯⠨⠓⠒⠒⠠⢤⣄⡀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠰⠶⠿⢿⣾⣿⠇⠀⠞⠹⠸⣿⣧⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢚⡽⠓⣲⣦⣤⣄⣀⠀⠀⠀⢰⣿⢹⠁⠘⠀⡌⠀⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠞⠋⠀⠁⠈⠀⠀⠀⠀⢔⡶⢲⣦⡀⠀⠀⠀⠀⠭⠽⢿⣿⣿⣷⣶⣾⣇⡄⣠⡀⢠⠁⢰⣽⣿⣿⠈
⠀⠀⢀⣀⣤⣤⣶⠾⠿⢛⠋⠉⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢸⣅⢃⣹⠃⠀⠀⠀⠀⠐⠢⣤⣿⣽⣿⣿⣿⣼⢠⡿⡇⠸⠧⢠⣟⣿⡧
⣶⣿⠿⠛⠉⠁⣀⠐⢋⡡⠔⠂⠉⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠖⠒⠒⠒⠂⠉⠉⠉⣉⡀⠀⠀⢹⣼⣿⢟⣧⢼⡇⠃⠀⢠⡾⢩⢿⡏
⣿⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⡀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡖
⠀⢀⡀⠠⢀⠀⠄⠀⠀⠀⡠⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠂⡔⠉⠀⠈⢂⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣿⠁⠁⠈⠘⠓⠂⠒⠀⠻⠦⠀⠀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⡀⠠⠄⠀⠈⠀⢳⡀⠰⡼
⠀⠀⠀⠀⠀⣠⣮⣤⠼⠷⠖⠂⠀⠉⠉⠀⣘⣛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣁⣤⣤⣤⠇⠠⠧⠅⡀
⠀⡠⠤⠒⠈⢉⣀⡠⠤⠴⠒⠒⠋⣉⣉⡡⠤⠤⠒⠒⣊⣉⠭⠤⠐⠒⢀⠎⠉⠉⠙⣟⣧⠀⠀⢠⣤⣄⣿⣷⠐⠢⠤
⠀⡠⠤⠒⠉⠉⢀⡠⠤⠒⠒⠉⢉⣀⠤⠤⠒⠒⠉⣉⣠⠤⠔⠒⠊⢉⠈⠀⠸⠏⠀⢸⣽⣿⡶⢩⡄⠙⡿⠿⣠⠄⡤
⠀⠀⠀⠄⠒⠉⠀⠀⠀⠠⠐⠊⠁⠀⠀⠠⠐⠊⠉⠀⠀⠀⠀⠔⠊⠁⠈⠀⠀⠠⠴⠓⠐⠂⠘⠂⠤⠼⠏⠜⠁⡞

⠀⠀⠀⠀⠄
⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢅⣴⡆⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢠⢄⡀⡀⠀⠀⢀⣀⠀⠤⣀⣄⡄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠤⠤⠠⠐⡒⢂⠐
⠀⠀⠐⠂⢤⣾⣹⡇⠈⠀⠈⠑⠢⣍⠱⢤⡉⠢⡌⠓⠂⠀⣙⠸⠿⡈⠌⠁⣦⡀⠙⢳⢤⠙⠄⠓⠒⠀⠈⠀⠀⠀⠀⠃⠘⠄⠁⠘⢃⠘⠀⠁
⠀⠀⠀⠀⠈⢽⠻⣿⠠⠤⢤⠀⡀⠙⣠⣜⠓⢰⡈⠐⠂⣼⠻⠇⠀⢟⡺⡇⢀⠀⢲⠄⣀⣈⣠⠲⡄⠄⢀⠀⢰⠀⢠⡄⠐⠀⢀⣤
⠀⠀⠀⠀⠀⠐⡄⠛⠴⠀⠄⢄⠉⠂⠀⡚⠛⢂⡑⠀⢀⢹⡇⠰⡆⢻⣥⠙⣷⠀⡘⣶⣤⠙⣿⠀⢵⠰⠀⢸⡈⠀⠈⢀⡁⠀⢨⡏
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠛⣵⡿⢯⣷⡄⢺⠿⣷⠾⢶⣭⣁⣙⡀⠈⠈⠸⠛⡋⡟⢿⠃⢻⡞⢻⢷⠷⠀⠻⠶⠚⠻⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠸⠀⠟⠀⠃⠆⠛⠉⠁⠀⣈⣁⠀⠀⢠⠀⡀⠀⡀⣠⢊⠀⠀⠀⠶⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠾⠂⢀⡄⠠⠀⠀⠰⡈⠀⠀⠀⠀⠦⠀⠀⠀⠐⠂⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡐⠀⢀
⠀⠀⠈⠑⠲⣶⣆⣄⠠⣖⠀⠀⢴⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⣘⣒⡉⠉⠐⠁
⠀⠀⠀⠀⠀⡼⣯⡽⠃⢩⣥⡄⠈⢱⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⢈⠀⢊⠀⠀⣠⣿⡽⢧⠘⠃⠀⢀
⠀⠀⢀⡀⠀⠹⠱⠀⢠⢸⠛⣦⣼⡈⢷⠃⡤⠆⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢶⠀⢈⠽⠷⡟⣁⠄⠒⠈⢻⢿⣿⣄⠀⢀⡀
⠀⠀⠀⠀⢠⠄⠀⢀⡀⠈⡄⠈⠹⠁⠀⠀⠀⠀⠀⠠⡄⡀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣌⣠⠿⣿⡷⠾⡤⠀⠈⠁⠺⠀⠈⠉⣀⡈⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⢀⣤⣀⠀⠄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠀⠾⢿⡇⠥⠀⠀⠃⠀⠀⠀⠀⠇⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠿⣷⣬⠁⠀⠀⠰⠀⠀⠀⠐⠀⠀⠀⡰⢃⠀⠐⠎⠁⠀⠈⢻⡂⠀⠀⠀⠠⠦⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠨⠦⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠚⠀⠀⠀⠛⠀⠤⠤⢦⡴⠶⣂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢹⠰⣦
⠀⢔⡲⣤⣤⣠⣤⣤⠤⠤⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣾⡗⣾⣦⠶⣆⠀⠀⠐⠃⠠⡀
⣛⠛⠛⠋⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⡒⠤⣄⡀⣀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⣆⣼⡌⢸⣥⣿⠁⠊⠀⠑⡦⠤⢤⣤⣴⠄
⠉⣉⣉⣉⣀⠀⠀⠀⠰⠦⠤⠤⠶⠦⠀⠢⠐⠄⠍⠙⠿⠆⠀⠤⠀⣀⡀⡀⠀⠀⢻⡿⠿⠿⠾⣿⠀⠐⠀⠀⠀⠀⠀⠒⢸⣇⣰⡖⢠⣤⣀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠒⠒⠲⠾⠿⠿⠯⣍⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⣄⢀⣤⣴⡄⢠⣾⣿⣄⣸⣦⣭⡷⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣃⣶⡶⠘⠛⢋⣉⣹⣿⠏⠛⠃⢄⠀⠀⠀⠀⠈⠉⠙⠓⠒⠻⠶⠒⠛⠾⠷⠿⠷⠾⠜⠙⠿⠿⠷⠿⠟⠀⠙
⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⠏⢸⡏⠀⠀⠀⠘⠻⠋⢠⡄⠐⣤⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡋⣿⠀⣼⣷⣶⣶⡄⠀⣀⠀⣸⡄⢐⡾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⢰⣏⡠⠿⠿⠤⠉⢫⡿⠻⡇⠼⠇⢰⣼⣏⣤⡄⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠉⠀⠀⠀⠀⠁⢸⠹⣏⠉⠁⠁⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢸⡟⣿⡝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠁
⠀⠘⠆⠀⠠⠠⢠⣌⣄⣿⣦⣀⣈⠀⠀⣀⣀⣸⣧⣀⣹⣂⠀⢀⢹⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠍⠙⠉⠉⠛⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣤⠀⠀⠠⠄⠂⠀⠀⠀⠒⠰
⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠴⠶⣾⠀⠀⠀⠐
⠀⠙⠁⠙⠈⠈⠁⠀⠀⠰⠐⠈⠀⠃⠋⠈⠃⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠒⠊⠛⠃
⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣄⢀⡀⠀⠀⠀⠀⢀⠀⠀⣀⠀⣠⣀⠀⠀⢀⠀⢴⠀⠄
⠀⠀⢸⠀⠀⢀⠈⣤⢰⣦⡷⠄⠈⠉⣴⠟⠋⠀⢠⠀⠀⠀⡸⠿⠿⠟⣿⡇⠀⠀⠀⠁⠈⠙⠁⠙⠀⠀⠈⢀⣤⣀⡀⠀⢤⡀⠀⢠
⠀⠀⠚⠀⠀⠉⠁⠁⠈⠉⠀⠀⡄⣲⠌⠦⡴⣴⣸⣧⣀⣄⣤⣀⠀⠀⠁⠀⠀⠫⢠⠇⢶⡄⠀⡄⡀⠀⠀⢨⡿⠿⡿⠁⢻⠞⣦⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠣⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⢀
⣿⣏⢭⣟⡛⣛⣛⠛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⢀⠈⠀⣄⡈⠉⠉
⠀⠀⠀⠐⠄⣀⣤⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⣀⣀⣀⣀⣀⠐⠁⡀⠀⠀⠠⡀
⠀⣀⣀⣀⣀⣈⣱⠄⢤⠙⡆⠂⠂⠀⢒⣐⡂⠠⡤⣤⢄⢐⠚⠋⠛⠉⠉⠁⠉⠀⠉⠁⠀⣄⡉⠄⠑⠍⠀⠀⠀⠿⠯⠁⠠⠄⠢⡀
⠀⠤⠀⠀⠀⠀⢼⠀⣙⠈⡃⠀⠀⠀⠛⠙⠛⠃⠉⠉⠈⠁⠀⠉⠈⠀⠒⠀⠤⠀⡀⠐⠚⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠪⠐⠢⣀⡀
⠀⠀⠀⠀⠀⠀⡸⠀⡨⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠒⠒⠂⠀⠀⠤⢠⡄⡀⠀⠁⠀⠈⠀⠐⢲⠄⠀⣠⣤⣌⡁⠀⠀⠀⡠⣄⡏⠉
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠑⢠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠋⠳⠒⠂⢀⠈⠀⠾⣈⠶
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠒⠉⠈⢂⠠⢤⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⠀⠈⠺⣆⢂⣠⡾⢤⡔⠂⠀⠀⡀⠀⢸⡀⢸⠀⠀⠀⡹
⠀⠀⢀⠀⣀⠀⠌⠀⠀⢀⡖⠃⠀⠃⠀⠘⠙⠆⠀⠀⢺⠀⠀⠀⠈⠀⠀⠀⢰⡟⢻⠀⠀⠀⠹⣎⠉⠉⠁⣹⠄⢀⡄⢱⡀⠀⢳⡞⢀⡄⠀⢀⡐
⠀⠀⠠⠤⠀⠀⠦⢠⡤⠄⠀⠚⠙⢂⠀⠀⠀⠀⠀⠀⢠⢀⠀⢠⠀⠀⠀⠀⢸⡥⠼⠆⠀⠀⠀⠛⠂⠀⠀⠐⠀⠈⠀⣄⠹⣄⠐⡴⢋⠀⠀⢉⠇
⠀⠀⠀⠀⠀⠂⡇⣠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡎⢡⣇⠆⠀⠀⠀⣀⣠⢤⡴⠶⠒⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⣌⣑⣉⢤⠖⠁⠀⡄⠁
⠀⠀⠈⠀⠀⠀⡟⡃⠀⠀⠀⣠⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠇⠀⠀⠀⠀⢸⢨
⠀⠀⡀⢀⣀⠀⣗⠇⡰⠂⠈⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠧⡀⡄⠀⠀⠀⢸⠸⢠⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢢⣤⢶⡓⠄
⠀⠀⠀⡀⠀⠠⠋⢢⡁⠀⠀⠀⢶⢄⠀⠀⡠⠂⠀⠀⠈⢤⠁⠇⠀⠀⠀⢸⠀⠌⠀⠘⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢹⠮⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠬⠇⡑⠊⠰⢞⡁⡀⠴⠤⠀⢴⢀⡄⠔⠚⠀⡖⡀⢙⠀⠁⠀⠠⠀⠀⠐⣖⣂⣀⡀⠀⠤⢤⠤⠀⠀⠐⠂
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡐⠈⠁⠀⢀⣤⣀⠄⠈⠀⠀⠀⠀⠀⠁⠁⠢⠀⠀⠀⡀⡂⣪⠝⣿⠌⣉⠉⠛⠒⠲⠤⠄⣀⣀
⠀⠀⢀⣽⠓⣦⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⣈⡽⢩⣱⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣠⠋⢶⠌⢃⡩⠤⠀⠀⠉⠁⠂⠒⠠⠄
⠀⠀⠈⠙⢂⠉⣴⣪⢍⣽⡉⢳⢠⡀⠀⣀⡇⠐⠿⠟⠈⠉⠌⠀⠉⠀⠀⢀⡀⣤⡜⠾⣃⠀⢁⣠⠤⠞⢉⣠⠴⢋⡠⠜⠂⣠⡤
⠀⠀⠀⠀⠀⠈⠑⠀⠙⠢⠞⠁⣽⡀⠀⠀⣎⡷⢦⡤⣤⡀⣀⣠⣤⢶⠝⡏⣙⡀⠀⣉⡤⠖⠉⣠⡠⠔⢋⡤⠔⠉⣠⡴⠓⢁⣠⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢓⠊⠗⢛⢤⠵⣈⣩⠋⢴⢏⠞⠉⠉⠀⠄⠘⡉⣤⣰⠟⣁⡤⠞⠋⢀⡠⠾⠋⢠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣶⣶⣶⣿⣶⣷⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣰⣿⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡏⠉⠋⠙⠈⠉⠙⠿⠿⠿⠙
⣯⣭⠿⣯⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠀⣈⠋⡀⢹⣿⠯⣛⠳⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶
⠟⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠱⣶⣿⠗⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⠀⣠⣶⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡀⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡃⣀⣹⣿⣿⣿⣿⣿⣿⡭⠉⠿⣿⣿⡏⠀⠀⠀⠀⣷⣦⣶⣳⡄
⠀⠀⠀⠀⠀⠀⢠⢀⣻⡗⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡹⣷⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿
⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⣿⠃
⣮⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠃
⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⠇⠲⣤⣶⡔
⠈⠞⢠⢴⣤⢃⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠠⣤⣦⣦⢑⢶⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣿⡒⢦⡀⠀⠀⠀⣠⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠠⢹⠻⣿⡟⠂⣤⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⢘⣷⠟⠰⠶⠀⢀⡀⡀⢀⡀⠈⠲⠻⣉⡙⠧⠀⢿⣤⣾⣿⣻⠇⠉⡿⠀⠉⠀⢀
⠀⠀⠀⠐⣾⣰⡾⢧⢩⣤⣄⡈⠹⣧⠒⣀⣧⡴⢬⠄⣬⠃⠀⠀⣶⣿⣿⣿⣯⣤⣮⣷⠀⠀⠷⠾⣀
⠀⠀⢠⣐⣮⢉⣷⣶⡶⠜⠟⢓⣤⣢⠁⠈⠛⠖⠚⠋⠁⠀⠀⠀⠀⠉⠉⠙⢎⠃⠉⠙⠲⣾⣤⣸⠏⠑⠂
⠀⠀⢸⣻⣿⣿⣴⢿⣷⡾⡾⢿⣆⠉⢷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣁⣀⢀⣀⣈⣙⣿⢛⣂⡀
⠀⠀⠀⢻⣿⣿⣽⣿⣯⣤⡛⣠⣥⢶⣾⠿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣞⡉⠋⠒
⠀⠀⠀⠙⠛⡋⣿⣿⣆⢛⠳⣤⢲⣼⣷⠤⠇⣿⣿⣿⣿⣿⣿⣿⠿⠟⠐⠃⠐⠒⠛⠓⠛⠛⣛⡛⡻⠿⣷⣀
⠀⠀⠠⠀⠀⠀⠈⠉⠀⠛⠒⠪⣷⠏⢑⣾⡇⠿⠟⠿⢿⠟⠉⢵⣶⠀⠀⠀⠀⠀⠀⠀⢀⣦⡈⢻⣿⣿⣮⡙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⢶⣧⡶⠀⢄⣄⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠈⠻⣧⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢠⡆⠀⠀⠀⢼⡟⡀⠿⠟⠻⣯⣾⣄⠀⠀⣤⣀⡀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠸⣰⢈⠋⠀⠀⠰⡾⡦⠡⠀⠀⠀⠆⢛⣡⣤⠤⠵⣿⠿⠛⠂⠀⣹⠿⠋⠉⠿⣶⢶⡖⢰⣶⣶⣤
⠀⠀⠀⠀⢀⡸⣿⣿⣤⣴⣶⣦⣴⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠛⣀⠀⢰⡔⠛⠉⠙⠐⠀⠈⠙⠻⠁
⠀⠀⠀⠀⠈⠈⠛⠿⠉⠛⠉⠉⠈⠁⠀⢀⡀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠸⠖⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡰⠀⠀⣤⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢐⡠⢠⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡿⠋⣀⣺⡧⠉⠉⢉⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠰⣾⣷⣿⠷⠛⠻⠆⠀⣹⠂⠀⠠⠀⠀⠀⠈⠀⠬⠄⢰⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠋⠀⣠⠀⠀⢁⠁⠀⠀⠀⠀⠀⠀⠀⢐⣲⣦⠔⢰⣽⣶⣶⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠄⣀⢺⣥⣄⠉⢘⠀⠄⠀⠀⠀⠀⠒⠻⠀⠁⠠⠚⠹⠿⠯⠙⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡖⠀⠀⠀⠀⠀⢀⣾⠃⣉⣳⣀⠀⠀⠀⠀⠀⠀⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣷⠀⠀⠀⠀⣴⠟⠙⠈⢸⠉⠈⢻⡀⠀⠰⠀⠀⠉⢻⣧⠤⠠⡤⠀⠀⠀⠀⢀⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⠀⠀⠾⠁⠀⠀⠈⠁⠀⠀⠀⠙⣦⣤⠀⠀⠀⣻⣧⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠸⠴⡹⣿⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⣄⣀⣀⠂⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢛⣋⢁⡉⢠⡄⠐⠒⡖⢲⠀⣶⠀⣿⣿⠀⠀⠐⢺⣿⣿⠿⡷⣟⣷⣶⡍⠛⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢃⣿⠸⠃⠈⠁⢀⠀⡇⢠⠀⠀⠀⣿⣿⠀⠀⠐⠺⠟⠛⠀⠀⠾⠙⠻⠟⠉⠓⣤⣀
⠀⠀⠀⠀⣀⠀⠤⠀⠒⠚⠋⠁⠠⠙⠉⠈⠁⠉⠋⠀⠀⠀⠀⠀⠠⠁⠉⠁⠒⠲⠴⠤⠀⠐⠶⠤⠄⠠⢀⠀⠈⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐



⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡛⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠐⢠⡄⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⣀⣀⡄⠊⠃⠀⠔⠀⠀⡠⠄⢀⠄⡠⠀⠢⠀⠀⠐⠊⠀⠈
⠀⠀⠀⠰⠀⠀⠨⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠒⢉⠀⠀⠀⠀⠀⠁⢀⢈⣤⣣⠤⠒⠲⠖⠒⠐⠢⠞⠿⠫⢅⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠁⠤⡄⢐⠨⠓⠉⣀⣀⠀⠂⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⢈⣖⡂⠀⠀⠀⠀⠀⠀⠀⠉⡒⠁⠡⠄⣀⠀⠀⠐
⠀⠀⠀⠀⢠⠊⠀⠀⢀⠀⠐⠀⢀⠀⢀⡨⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠷⠤⡼⠀⠀⠈⠒⢮⢠⣐⠀⡀⠂⢀
⠀⠀⠀⠀⠰⠤⠄⠠⠼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠌⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠐⠂⠀⡀⢈⠀⠀⠃⠂
⠀⠀⠀⠀⢀⠀⠀⠀⡤⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⢂⠰⠐⠀⠅⣀⠁⠀⢒⠩⠠⣀⠄⠉⠈
⠀⠀⠀⠀⠹⠀⠀⠀⣀⠠⠔⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡩⢁⠐⠀⠄⠉⠆⠀⢈⡁⠢⢌⠀⠀⡑⠄
⠀⠀⠀⠀⣨⠀⠐⢈⡡⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡒⠢⣀⠐⠭⠀⠢⢌⠐⠤⣐⠀⠤⡐⠀⠀⠂⢁⡀
⠀⠀⠀⠀⢈⡤⠒⠁⠀⠀⠀⠁⠀⠀⠠⠌⠉⢀⠖⣁⠚⡈⠢⢀⡂⠀⡌⢢⠀⠐⠄⡐⠄⠀⠠⣈⠂⢀⠀⠂
⠀⠀⠀⠒⠁⠀⠀⠄⠐⠀⠀⠀⠀⠀⠁⢰⠖⣉⠺⠁⠐⠢⡐⠀⢈⠀⢄⠈⠂⡐⠒⢌⠒⠌⠐⠄⠀⠀⠊⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢠⠀⠤⡀⠠⠈⠐⠀⠁⠄⠉⠂⠀⠈⠐⠈⢀⠈⠒⠉⠢⠀⠈⠲⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⡴⠇⠀⠚⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡶⣄⡞
⠀⠀⠀⠘⠛⢈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⡿⠀⠁
⠀⠀⠀⠀⠀⠀⢧⣶⣶⡆⠀⠀⠀⣠⣬⣗⣀⠀⠀⠀⠂⠀⠤⠄⠀⠀⠀⣀⠤⠒⠉⣿⣿⠏⢹⢳⡀
⠀⠀⠀⠀⠙⠒⠒⠛⠛⠃⢀⡠⠀⣸⣄⣉⣈⣷⣟⣒⣆⢀⠄⢂⣴⢖⠋⠁⠒⢴⢺⡿⠁⢀⡗⠂⣷⠤⠴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢫⣿⣀⠤⢼⡇⣿⠋⠸⡯⠿⠽⢾⣿⣿⡖⠒⠚⢁⣄⣀⣿⠃⣠⠚⠁⢸⣿⠀⢠⣼⣿⣦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣹⣾⣿⣧⣶⣤⣧⣤⣴⣁⣇⡈⣇⠀⠀⠀⠀⢸⢃⣴⡏⡀⠀⢃⣿⡄⢠⡏⠉⢹⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠂⣼⢏⣿⢻⢹⣿⠛⢿⠻⠿⡿⡿⡿⣿⣿⣷⣶⣾⣾⣼⣿⣇⣜⣺⣗⣽⣾⣗⣤⣼⡷⢲⣶⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⢷⡞⠈⠋⣿⣀⣌⣧⣖⣞⣎⣆⣆⠇⡇⡇⡏⢹⢸⠉⠏⡟⢻⢻⣿⣿⣿⣿⣿⣟⣽⣿⣏⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠿⠟⠿⣿⣿⡟⠒⠒⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣻⡳⠹⡽⣞⣦⣇⣧⢸⣸⡏⠁⠀⢺⠓⠻⡖⠊⠽⠷⠭⠄⠉
⠀⠀⠀⠀⠀⠀⠉⢁⣐⣶⣶⣤⣤⣤⡤⠤⠤⠤⠄⠀⠈⠉⠉⠛⠛⠛⠿⠿⣾⣬⣜⣌⣎⢋⢷⡈⠀⠘⠀⠀⠱⠄
⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣦⠷⠶⠶⠦⠤⣤⣤⣤⣤⣤⣉⣉⣛⣛⣻⣦⠇⢀⣀⣀⣠
⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣙⣂⣂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠰⡀⠀⢹⠀⢸⠀⠸⠀⢰⠃⠀⣠⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠈⠢⡀⠑⡄⠱⠀⠘⠀⠈⠀⠇⠠⠁⢀⠜⠁⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣀⠑⠢⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠄⠊⠀⠀⢀⣀⡤⠶⣎⣀⡀
⠀⠀⠀⠀⠀⠀⡨⠛⠒⠒⢤⡄⣀⠀⢠⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠉⠁⣤⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠡⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⣉⡁⣀⣿⣆⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠠⢀⠯⣕⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠈⠓⠚⣿⢷⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⢿⣾⣿⣦⣤⣄⣀⣾⣴⣿⣤⢤⠦⡤⢤⠤⣤⣠⣀⣈⡇⢸⣿⣿⡿⠿⢿⣿⣛⣿⣿⠿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠿⡟⡿⢹⢹⠃⡏⢰⢃⡇⡎⠸⠁⠏⠜⠔⠡⢋⠿⢛⡫⠍⣒⡨⠭⠥⢐⣒⣒⣒⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡏⡾⢸⠁⣋⣨⢤⢶⡲⡑⡝⢈⠝⡋⠔⣪⠔⣊⠭⠖⣊⡭⠭⠔⢒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠻⠙⡌⢎⢣⠱⢀⠔⡡⢊⠔⣊⠔⣋⠔⢊⡩⠔⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠊⠀⠐⠁⠚⠁⠊⠀⠐⠉





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣻⣿⣛⣻

⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦
⠀⠀⢺⣿⣿⣟⣠⣶⢿⢷⣦⣄⠀⠀⠀⠐⢚⣹⣿⢿⣿⡿⣿⣧⣭⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠄⢾⡗
⠀⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠐⠉⢉⡀⠘⢹⡎⠛⡂⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⢇⣾⣿⣿⣶⣄
⠀⠀⢸⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠈⠳⠀⣘⣏⠀⠙⠀⠀⠀⠀⠀⠀⢸⡿⠿⢿⡷⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠲⠆⠁⠀⠁⠀⠐⠇⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠹⣿⣿⣿⣿⠟
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⠄⠈⢃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠿⢉⡋⣻⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⡗⢦⡤⠞⢹
⠀⠀⢸⠀⣾⣻⣟⣻⡆⢶⠤⠀⠀⠀⠀⠀⠀⠀⡽⣧⣌⣡⣿⡛⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⣴⡆
⠀⠀⠘⠀⠹⣿⣿⡯⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢷⡸⣿⠅⠢⢤
⠀⠀⢨⡀⢰⣿⣿⣷⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣛⢃⣁⣴⠆
⠀⠀⠀⡇⢸⣿⢹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢎⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣉⡉⢽⣿⠟⠁
⠀⠀⢴⣷⣼⡿⢸⣿⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⢤⣿⠬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠙⢦⣤⡶⠒⡆
⠀⠀⠘⠛⢹⡇⠈⣏⠙⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⡱⣎⠀⠱⡑⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠈⢢⡇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⢀⣭⣄⣤⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠚⢻⠙⠸⠻⠻⠻⢻⠳
⠀⠐⣦⣤⣽⣿⣟⣿⣿⣤⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⢀⣿⣟⣿⣿⢿⠀⠀⠀⠀⠀⣀⡘⢱⠀⠉⠸⠈⠈⢱
⢜⣱⣿⣿⣿⣿⣿⣿⣿⣿⣧⣱⠄⠀⠀⠀⠉⠓⢤⣴⣿⣿⣿⣿⣿⣾⣿⡂⠀⠀⠀⠉⠀⢸⣀⡤⣿⣧⣄⣼
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣭⣗⣶⢶⡖⣶⣪⡅
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠋⢳⣿⣿⣷⠀⠀⠀⠀⠀⠀⢾⣵⣿⣽⣿⣯⣿⠇
⠀⠀⠘⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠉⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠳⠿⣾⣽⡮⡷⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠀⠀⠈⠉⠉⢐⣲⠠⠇⣰⣷⠀⣀⣦⣾⣧⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠁⠀⠀⠀⢀⡐⠿⠿⠾⠤⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⣀⠐⠂⠉⠉⠁⣋⡰⡦⡀⠀⠀⠀⠀⠀⣠⣭⣍⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠈⠒⠶⢦⡄⡀⠉⢉⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠁
⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠘⠙⠃⠺⠖⢰⡆⠘⠐
⠀⠀⠀⠀⠄⠒⠂⠦⠦⠤⢀⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣷⣿⣇⠀⠀⠀⠀⠀⢀⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢿⢻⣿⣿⣷⣶⣄⡀⣠⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⣀⣴⣾⡗⢀⣾⣿⠟⠙⠻⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⡖⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣤⣤⣤⣤⣶⣾⣾⣿⡿⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠒
⠀⠀⢠⡀⠀⣇⠀⣀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⢿⣿⠿⢟⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⡇⠀⠿⠀⠻⠐⠒⠀⠀⣈⣉⠉⠀⠀⢀⡐⠀⠄⢀⠠⣀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢳⠤⠤⡤⠤⠤⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⣤⣄⡐⢶⣭⣿⣿⣿⣷⠆⠐⠒⠒⠒⠒⢲⡖⠛⠀⢸⣿⡇⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⢿⣿⣿⣿⣿⡄⠀⠀⣀⠀⣀⠀⠀⠀⠀⠈⠛⠃⠀⠮⣶⣿⣷⣿⣿⠿⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠨⠯⠴⠶⠝⣿⣿⣿⣧⣄⣸⣿⣀⠛⠀⠀⠀⠀⠀⠀⢠⡞⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢁⢀⣤⣤⠴⢶⠶⠖⠒⠋⢩⣄⣀⣤⣦⠴⠶⠚⠓⢊⣤⣬⣼⣯⣭⣭⡭⠟⠛⠻⡿⡿⢿⡿⢿⣷⣷⣶⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠗⠿⠋⠀⡁⢀⣰⣤⡷⠻⠿⠋⠉⣄⡀⣅⣤⣼⡷⠛⠻⠋⠋⢉⣠⣄⣤⣷⣷⡾⠛⠛⢉⡉⢀⡀⠀⣿⣏⣛⡛⣿⣻⣿⣿⠿⠿⠿⠿⠛⠛⠛⠉⠁
⢠⣄⣿⣶⠾⠟⠛⠉⠈⣁⡀⣠⣞⣿⠿⠿⠋⣁⠠⣄⣴⣶⣼⣿⡿⠿⠟⠋⢀⡤⣞⣯⣼⣿⣾⣿⣾⣿⢯⠭⠗⠚⠧⢸⠆⣀⡀
⠋⠋⠉⠀⢤⣀⣶⣤⣶⡾⠟⠉⠉⡥⣤⣦⣮⣿⣶⣿⠟⢉⡈⠉⢠⣰⣷⣶⣾⣿⣿⣿⠯⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⡌⠦

⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢽⠏⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣄⠒
⠀⢀⣤⡀⠀⠀⢀⠀⠀⢶⣤⣤⡀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⣀⡀⠘⡟⢀⣀⣀
⠀⠸⠿⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⠸⠛⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⠂⠋⠈⠛⣛⠃
⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠈⠙⠛⢧⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣦⣤⣨⣿⡯⠼⣖⣢⣤⣶⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠛⠀⠀⠀⠈⠓⠀⠀⠐⠚⠛⠋⠉⠁⠀⠀⠚⠛⠛⠁⠀⠚⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⢤⠄⠀⠀⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄
⠀⠀⣄⠙⢡⣤⣤⣀⢸⣏⣰⣾⣦⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⡻⠟⠙⡟⣻⣄
⠀⠘⠿⠂⠀⠀⠉⠉⣘⣂⠉⢻⠋⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠤⡥⢯⣭⣷⣿⣿⣧⣶⠒⠛⠛⢻⣿⣿⣿⣿⣿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡶⡶⡦⣤⣤⣤⣀⣀⠀⠀⠀⠀⣼⣾⣶⣷⡾⡿⣻⣻⢻⢟⢟⢟⢟⡟⡟⡶⡺⡶⣭⣄⢤
⠀⠘⠛⠋⠉⠁⠁⠑⠙⠉⠈⠈⠈⠈⠈⠈⠈⠉⠋⠉⠙⠂⠀⠀⠉⠉⠉⠈⠈⠁⠁⠁⠁⠁⠉⠈⠈⠈⠈⠈⠈⠁⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⠠
⠀⣾⣧⠠⠀⠀⠀⢒⠀⠀⣼⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢈⣤⣤⡀⠀⠉⠡⠤
⠘⢻⣯⣤⣤⣤⣦⣤⣤⣤⣿⠛⢇⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠟⠿⠿⣿⣷⣶⣶⣿⣿⣿⡆
⠰⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠃⣾⣷⠀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠼⠿⠷⠀⠀⠀⠀⠅⠀⠀⠀⠈⠉⠃⠣⠈⠊⠀⠀⠀⠐⠒⠛⠋⠋⠋⠉⠉⠙⠙⠙⠙⠙⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⣶⣄⡀⠀⣀⣠⡶⢿⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠀⡄⢀⠀⠀⠦⣾
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡿⢹⣿⣿⣿⣿⡥⣤⡿
⠀⠘⠛⢿⡟⣧⣷⣼⣧⣼⣧⣼⢠⣶⣿⣦⡘⠿⡿⠿⠀⠀⠀⠀⡋⠉⣉⣉⠉⠉⠉⢉⠿⠛⣳⣶⣶⣿⣿⣿⣿⣿⣧⣤⣿
⢰⣶⣶⣿⣿⣿⣿⣿⣿⠿⠿⣋⣻⣿⣿⣿⣧⣤⣧⣤⣤⡀⠀⠀⡷⣠⣬⢾⢿⢲⡻⡻⡝⣝⢝⢟⢯⢻⡻⡳⡿⣽⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠈⠈⠀⠁⠁⠁⠉⠈⠈⠈⠀⠁⠁⠁⠉⠈⠈⠈⠉⠉

⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣠⠴⢶⣄⡀
⠀⠀⠀⠈⠉⢀⣨⣤⡄⠀⢭⠤⠄⠀⣸⡟⢲⠠⠆
⠀⠀⠀⠰⡉⠁⠀⠉⠀⠀⣠⡠⠂⠀⡈⠙⢳⡅⠘⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠒⠻⠁⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠤⢄⣠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⣿⣟⣿⡄⠀⢙⡛⠟⣶⣶⣤⢠⡍⢠⡿⣆⠀⣸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠞⠛⠛⠚⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢦⣤⣤⣤⣤⣤⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣌⡀⢰⠀⡀⠠⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠛⡟⣿⣿⡷⣻⣛⣏⣛⣷
⠀⡆⣴⢚⢹⣶⣄⠠⠀⡀⡀⠃⡿⡯⠾⠽⢿⣿⠝⠋⠈
⠀⣿⠀⢘⠉⠙⡌⢀⡀⠀⠀⠉⠀⢠
⠀⢹⣿⡀⠀⠀⢡⣟⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠐⠒⠂
⠀⠛⠋⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡿⣄⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⣤⣤⣴⡄⢀⡀⠀⠀⣀⠀⠀⠀⣠⣴⣿⣶⣤⣤⠀⡀⠀⣤⣤⣶⣾⣶⣤⣤⣤⡴⠆⣴⣿⠀⠀⠀⠀⠀⠀⠀⢀⢴⣶⣶⡔⣢⣦⣌⣠⢿⣿
⠛⠻⠻⠛⠛⠃⡙⠛⠁⢛⠛⠻⠛⠛⠛⠛⠙⠁⠉⠁⠀⠉⠀⠈⠉⠙⠉⠉⢻⠿⠛⠛⠋⠉⠉⠀⠀⠶⠀⠀⠀⠀⠘⠼⢿⡿⠷⠿⣿⣿⡿⢿⡿
⢠⠁⠀⡀⠀⠂⠀⠀⢀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⢄⡈⠑⠢⢌⡑⠢⠌
⡀⢰⠀⡇⠈⠀⠀⢄⠀⠑⢄⠀⠀⠠⠈⠐⠠⢀⠀⠢⢀⠀⠀⡀⠐⠀⠠⠤⠂⢀⡠⠄⠂⠀⠀⠠⠀⠀⠉⠀⠐⠀⠀⠀⠒⠤⡈⠑⠦⢄⡈⠑⢦
⠁⢼⠀⢠⠀⢠⠀⠈⢂⠀⠀⠙⢄⠀⠀⠑⠀⡀⠑⢦⡀⠑⠠⡀⠑⠤⣀⠀⠈⠁⠀⠐⠋⠀⠀⠐⠀⠀⠠⠐⠒⠁⣀⠤⠔⠀⠈⠁⢤⣀⠉⠢⣄
⠀⢸⠀⢸⡄⠀⠆⠀⠀⠳⠀⠀⠀⠱⠄⠀⠀⠁⠢⠄⠉⠢⠄⠈⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠲⠖⠄⠀⠀⠴⠂⠉⠠⡀⠈⠣⣄
⠀⠸⠀⠈⠷⠀⠒⠀⠀⠀⠁⠠⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠦⠄⠀⠠⠤⠀⠈⠆⢀⠈
⠠⠀⠐⠀⢀⠂⠀⣠⠀⠀⠄⠀⠢⠀⠂⠀⠁⠀⠀⡀⠀⠀⠁⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⠂⠀⠀⠤⠄⠀⠀⠖⠂⡀⠁⡠⠆
⢶⡀⠘⠀⠉⠃⠀⠀⡀⠀⠠⠴⠄⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⣤⠤⠄⠀⠂⣠⠤⠀⠀⠉⢀⣠⠄⠈
⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⠠⠀⠀⠀⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠀⠀⠁⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⣀⠄
⠀⠀⠀⠀⠉⠑⠲⠔⠀⠀⠀⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠓⠉⠀⠀⣀⡀⠀⠀⠁⢀
⢾⣶⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⠄⡀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠋⠉⠁⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠉⠉
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠒⠀⠀⠀⠀⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⣤⡴⠶⠒
⣿⢿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⣿⣿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⣀⣄⣄⣼⣰⣿⣾⣴⣾⣿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣇⠠⣀⣀⣴⣤⣶⣦⡿⣿⠿⠟⠛⠋⠉⠉⡈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢀⣄⣼⣿⣿⡷⡿⠿⠛⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢄⢰⢲⣼⡿⡿⠏⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠁⢠⢆⣷⡇⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⢐⠀⢀⣿⣀⣼⡟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠄
⢀⡆⢸⣿⡦⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣼⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠚⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠀⠄⠀⣀⡴⣄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⣀⣤⠤⠤⠲⢲⢥⣶⡂⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠒⣀⣴⣿⡠⣬⣳⢦⡀⠀⠀⠀⠐⠀⠀⠀⣿⡇⠀⠄⠀⢀⣠⣤⣤⢤⠤⠴⡇⠀⠀⠀⠠⠏⠉⠐⢲⡀⠀⠀⠀⠚⠉⠁⠁⠂
⠀⠀⠀⢀⠤⢄⠀⠀⠀⣀⣐⠁⠀⣠⡿⠛⠉⢀⣿⠀⠀⠹⣍⠉⠁⠛⠀⠈⠉⣻⣷⠶⠤⠤⢄⠀⢠⠕⢘⡐⠊⠙⣦⠀⠀⢠⠄⠀⠀⠀⣷⡆⠀⠀⢷⣤⢠⡀
⠀⠀⣤⡬⠀⠀⠥⠤⠤⠤⠰⢂⣼⡏⠀⠀⠀⠈⠀⠀⠀⠀⠘⣶⣦⡄⠀⠀⠘⣿⣿⣤⣀⣀⣀⡀⠈⣰⠁⠀⠀⠀⣘⣦⠀⡴⠀⣧⣄⣾⣿⣧⣤⣤⣾⣯⣤⠇
⠀⠀⠀⠀⢀⣀⠀⢀⠀⣀⠀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⣿⣗⣐⡇⠀⠀⠀⡀⢸⣢⠄⠤⠤⠟⠍⠩⢠⠤⠟⢛⠋⠡⠤⠤⠄
⠀⠀⠉⠉⠙⡊⠟⢉⣭⡾⠻⠋⢙⠁⣀⠀⠠⢤⡤⢤⠀⣤⡄⢸⣿⣿⠀⠀⠠⢾⣿⣿⣿⣿⡿⠟⣠⠐⠆⢦⣭⠽⠿⠋
⠀⠀⠀⠀⠀⢄⠀⢸⣶⡆⣿⠁⣶⠀⠛⠀⠀⢈⡇⢸⠀⠉⠁⢸⣿⣿⠀⠀⠤⣼⣿⣿⠅⠁⢀⠥⠙⠛⠲⣲⣧⡀
⠀⠀⠀⠠⠴⠞⠃⠰⠀⠠⠿⠆⣠⣤⠤⠤⠔⠘⠓⣺⠤⠄⠀⠼⠾⠧⣀⣠⣔⢋⠁⠀⢀⣠⡀⠀⠀⠀⠀⠀⠸⡌⡓⣠
⠀⠀⠀⠀⠀⠐⠒⠒⠚⠉⠉⣉⠀⠠⠤⠐⠒⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠉⠉⠘⠂⠒⠓⠋⠛⠉⠉⣉⠙⠛⠒⠶⠒⠶⢤⠤⢤⣀⣀⣀⡀
⠀⠀⠀⠤⠤⠂⢒⠒⠒⠀⠈⠉⠙⠲⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⡀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡈⠄⣤⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⡄⢠⡀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠀⡀⠀⠀⠀⠀⠐⠓⠎⠁⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⠉⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠚⠀⢁⠘⠛⠢⠄⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠤⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠑⠀⠐
⠀⠀⠀⠀⠀⠀⠠⢷⠆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠈⠠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐

⢲⣧⣶⡀⠀⠀⠀⠀⠀⣠
⣹⣿⡛⢃⣀⢠⣀⣠⡞⠉⠈⠀⠀⠀⠀⠀⣤⡀⣀⣀⢀⢀⣠⣄⣀⡀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⣿⣿⣿⣿⣧⣿⣿⣏⠃⠀⠀⠀⢰⠀⠀⠛⠓⠺⠿⣿⡟⠛⠻⠛⠋⠁⠊⠈⠛⠋⠛⠛⠳⠶⠾⠿⠷⠐⠚⠂⠻⠿⠿⠶
⡊⠄⢂⠩⠔⠊⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠴⠊⣁⠄⠒⢉⠀⠂⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠐⠠⢄⡀⠢⠀⠀⠀⠀⢀⠀⠀⡀⠐⠈⠀⠀⢀⡠⠊⠀⠀⠀⠀⠰⠀⡀
⠴⠊⢁⡤⠂⠠⠀⠈⠐⠠⠀⣉⡐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⢃⡤⠂⢁⠔⠈⠀⠀⠀⠀⡀⠊⠀⢀⠄⠀⢰⠀⢰⠀⠓
⠀⠔⠁⣀⠄⠀⠀⠘⠈⣀⡈⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⡄⢀⡇⠀⡗
⠀⣀⠒⠀⠠⡌⠉⢀⣀⠁⠀⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠂⠀⠀⠁⠐⠂⠤⠀⠄⠀⡀⠀⠀⠀⠀⠀⠄
⠁⠠⣄⠈⠂⠀⠀⣀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠚⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢀⠸⡀⠀⠠⠘⡀⢀⢤⠀⠀⠠⠄⠀⠀⠀⢠⣝⡾⢷⣫⣤⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡄⠀⢀⡀⠀⠀⠈⢁⠀⠀⣴⣙⣃⠈⠀⠈⢣⣄⠙⡄⠀⢘⡿⣷⡾⢿⡛⠯⠝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡀⠀⢠⠀⠈⡆⢰⢀⣀⣂⢺⣷⢷⠆⠡⢠⠐⡀⡂⡏⠁⠉⠉⠉⠉⠛⣿⡟⢻⠀⠀⠈⢹⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠰⢁⢀⡠⠑⠋⠀⠀⠀⢀⠤⠿⠚⠊⠑⠂⣚⣿⡠⢄⡅⠀⠄⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢀⠞⠤⠀⠀⡀⠤⠄⠀⠀⣀⣀⢀⡤⠖⠈⠀⠀⠉⠑⠯⣇⣤⡀⠀⠀⠠⣹⡅⢸⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⢐⠀⢀⡎⢠⠒⣀⡀⠀⠀⠀⠀⠀⠀⡰⣷⣶⠀⢀⠀⠀⠀⠀⠀⣤⣽⡳⡄⠀⠀⢹⡇⣸⠀⠨⠀⢆⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠱⠆⡋⠠⠁⠄⠁⠀⠀⠀⠀⠒⠂⣰⠁⠛⠛⠀⡻⢒⠶⡲⣦⠀⠿⠿⠸⣵⡀⠀⣸⣇⢸⠀⠀⢤⢒⠟⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠀⢠⣂⣀⣊⠁⠊⣁⣀⣀⣀⡀⣰⠃⠀⠀⠈⠀⢸⣏⣶⣡⣶⠀⠀⠆⠀⠙⣿⡁⣸⡇⢸⠀⠀⣾⡷⠚⣷⠁
⠀⠀⠀⠀⠐⠀⠈⢀⡠⠒⠘⠋⠉⠉⠭⢙⣱⣦⣌⠀⠈⠈⠉⣿⠀⢰⠆⠂⢿⢶⣶⣷⠖⣶⡖⠄⡦⠁⠐⡍⠀⣹⡧⢸⠀⠀⠀⢁⠰⣿⠀⠐⠂
⠀⠀⠄⠀⠀⠀⠀⠀⣿⠙⠙⠛⠛⠲⣷⠋⠁⠀⢹⢀⠀⠀⠀⢨⠀⢸⢁⠆⢸⣿⢹⡿⣛⢽⠀⡖⢹⠀⠀⡇⠀⣾⣇⣸⠀⠀⠀⠀⠀⠻⢦⡀⠣⡀
⠀⠀⠀⠴⠤⣤⣦⣴⣟⣿⠀⡀⠀⠀⠹⠀⠉⠁⣸⣼⣤⣤⣴⠼⠀⣼⣦⣄⠿⠿⠼⠧⢥⣽⣶⣀⣲⣀⣺⣿⣔⣿⠷⠿⠿⠶⠶⠾⠗⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠂⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⣠⡴⠿⠛⠶⠒⠦
⠀⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡄⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢠⡴⣮⣷⣾⣟⠟⠋⠉⠻⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣥
⠀⠀⠀⢀⣶⣿⣾⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⢂⠈⢻⡀⠀⠀⢠⢶⠋⠋⠡⡐⠆⣀⣤⡇
⠀⠀⠀⠠⣿⢻⣇⠀⠀⠀⠀⠀⠀⢘⢫⠛⡋⠀⠀⠀⠰⠀⠜⠀⠀⢿⡙⠿⣿⣿⣿⣿⣶⣤⣃⣙⢀⣧
⠀⠀⠀⠀⠈⠄⣵⠀⠀⠀⠀⠀⠀⢰⠒⠉⠁⠀⢠⠀⣀⣀⡄⠠⠄⢰⡆⣦⠊⠉⠉⠉⠉⠉⡙⡟⡴⣿
⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⣀⣠⡄⠀⠸⣿⠉⠃⠚⠀⡇⣿⡇⠘⠃⢸⡇⠁⠐⠀⠀⠀⠄⠀⠐⣇⡀⣿
⠀⠀⠀⠀⢼⢿⠿⢶⡴⠶⣿⣿⡿⠿⠸⠿⠤⠄⠀⠠⠷⠍⠁⠀⠀⠘⠁⠀⠀⠀⠐⠀⣷⣬⣬⡏⡯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠘⠛⢚⡇⠃⣿
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢰⠀⠘⠑⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⠀⣉⠀⢈⣉⢑⠉⣑⣲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⢀⣄⡀⠸⠄⠒⠒⠂⠂⢀⣀⠀⣿⣿⡀
⠀⠀⠀⠀⢤⣴⣤⣠⢄⣤⢤⣤⣤⣤⠄⣀⠀⠁⠀⠒⠚⠛⠋⡀⠀⠁⠀⠀⠂⠚⠁⠀⠒⠓⠂⠈⢠⢦⡄
⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣧⠇⢀⠤
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⠁⠀⠀⠁
⣇⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠁⠀⠀⠋
⡟⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢡⠀⠀⢀
⡗⠦⠠⣬⡤⠠⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡤⠤⠞⢈⣻⠓⠢
⣏⢑⣡⠊⠿⢩⠅⠀⠀⣁⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠡⠠⣤⣀⠩⣃⣣⢡
⣷⣶⣶⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣦⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢀⣿⣿⠟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠁⢰⠎⠉⠀⠀⠀⠀⠀⢴⡿⠃⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠘⢆⠀⣀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⡄⠙⠦⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠊⠀⠠⠀⠐⠀⠐⠠⠀⠀⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⡀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡄⢀⠀⠀⠀⡀⠀⣄
⢀⡖⣰⣇⣰⣄⣀⣠⢤⡠⣄⣺⠀⡞⢴⢀⣰⢇⣦⠑⣼⠁⢀⡸⢢⣶⣠⢀⣇⢰⢀⠨⣷⡐⣶⣠⢳⣆⣿⡇⢰⢾⣆⡀⡡⣆⣰
⣄⣇⣸⣟⣏⣻⣷⣿⣿⣁⣃⣟⣶⣷⣘⣹⣟⣻⣈⣘⣿⣀⣘⣇⣹⣻⣿⣿⣿⣸⣻⣢⣿⣀⣿⣿⣻⣉⣙⣃⣽⣿⣟⣇⣙⣽⣿
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣳⢇⡤⣥⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠓⠰⠾⣿⣿⣿⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠀⣸⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣶⣦⣴⣟⣻⣿⣷⡄⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡰⠉⠀⠈⡙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠂⣃⠰⡀⠀⠀⠾⣿⣿⣿⣿⡿⢃⠌⠀⠀⠀⣀⣠⣤⣤⡀⠤⣲⠈⠧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣦⣶⡄⠀⠀⢈⣻⣿⡏⠀⠀⢀⣠⣶⣾⣿⣿⢿⣻⣟⣾⣧⣾⣦⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡚⠀⠀⠈⢿⣿⣷⣤⡆⣸⣿⣿⡇⠀⠊⠛⠿⠿⠟⢛⣿⢻⣿⣿⠿⠟⠛⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⡩⠯⠀⠸⢃⣿⠟⣻⣼⣿⣿⣁⣀⣀⣠⡤⠶⠶⠟⠁⠀⢀⠄⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡵⠾⡐⢈⡼⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠠⠂⠀⠃⠠⢀⠄⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣥⡙⢟⣼⣧⣿⣿⢿⣿⡿⣿⣿⣿⣿⣇⠀⡀⠀⠀⣀⣤⢄⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣅⠁⠰⢛⣿⣯⣾⡿⢿⣽⣿⣯⣿⣿⣿⡄⠀⠀⠀⠉⠀⣈⡠⠶⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠛⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⡤⠀⠀⠀⠀⠀⡀⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢻⣿⣯⣭⣿⣿⠛⣿⣿⣿⣿⣿⣧⠀⠀⠇⠰⡶⠂⠀⠌⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣋⣬⣭⣿⡟⠀⢈⢿⣿⣿⣿⣿⣇⠀⢄⣃⡠⢁⣥⢠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢩⡒⠀⠀⢸⣿⣿⣿⣿⣷⠀⠹⠌⣿⣿⣿⣿⣿⡜⢔⡿⢡⣿⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠀⡀⠀⠈⣿⣿⣿⣿⣿⠀⡆⠐⣹⣿⣿⣿⣿⠃⣾⠇⠚⠛⣿⣷⡍⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠐⠀⢰⢛⣋⣻⣿⡿⠸⢀⠃⢸⠿⣿⣿⣿⠀⠋⢀⣴⣿⣿⡟⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣸⠀⠀⠀⢸⣾⣿⣿⣿⠃⣶⡟⠁⣹⠂⣿⣿⡧⢂⡇⣿⣿⣿⣿⠓⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⢀⡁⠀⠸⡛⠛⢿⣿⣾⡇⢹⠆⢛⠀⠟⢀⡄⡸⠁⡿⢃⠋⠋⢐⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣑⢮⣘⢳⣀⡿⠓⣿⣿⣟⣿⣾⣷⣿⠀⠀⢿⣱⢃⠀⠀⣬⠸⢆⢊⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⡛⠿⠿⢿⡇⠂⠂⠈⠄⢀⡟⣙⡟⠀⡎⢸⡁⠈⠀⠁⠹⠀⠟⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢞⣁⡹⠇⠉⣴⣜⢸⡷⣶⡤⣴⡝⢁⣁⡀⡬⠁⢀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⢀⣀⣤⠿⢶⡀⢈⡛⠁⠛⠃⠁⠻⠉⠿⣤⣤⣎⠑⢂⣈⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠛⠃⠀⠋⠋⠛⠛⠂⠀⠀⠀⠀⠀⠁⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠰⠂⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠐⠐⠁⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠄⠠⡆⠀⠐⢲⡂⠉⠉⠿⠀⠀⠀⠀⠾⠀⠀⢶⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠒⠂⠀⠤
⠀⠀⠀⠠⠶⣶⠶⠶⢶⠖⠶⠒⠚⠛⡟⠛⠛⠛⠻⣿⣶⣶⢾⣿⣿⡶⠶⠶⠤⠖⠐
⠀⠠⠀⢀⡀⠁⡀⠀⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠺⡿⠏⠘⢻⠿⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣀⠀⠄⠀⠀⠀⠀⠠⠦⠀⢀⣤⠄
⠀⠈⠉⠉⠁⠉⠀⠀⠁⠀⠀⠈⠀⠘⠒⠒⠒⠒⠒⠐⠒⠚⠚⠺⠷⠭⢄⡿⠧⠶⣢⠀⠀⠀⠰⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠄⠴⠶⠄⢤⡆⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⡀⣀⢤⡶⠦⠡⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⡌⢹⢻⠋⠀⠀⠀⠀⠀⠀⠸⠀⡀⠤⠄⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢰⠖⠀⠠⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢰⣇⡖⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣠⠔⠀⢠⣠⠂⠠⣿⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠘⠁⠸⣀⣦⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠛⣤⡂⠒⠀⠤⠉⣉⡛⠝⠉⡇⡰⠒⠠⣀
⠀⠀⠀⠀⠰⣹⣅⠂⠞⠁⠰⠢⠆⠤⢤⠈⠤⠐⠘⠉⠀⢀⠀⠁
⠀⠀⠀⢠⠽⠁⠂⡀⡌⠀⢄⡄⠀⠀⢀⡂⡀⠀⠀⠀⠈⠝⠀⠀⠠
⠀⠀⠀⠘⠓⠚⠐⢤⠼⠌⢊⠑⢠⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠄⢀⡠⠀⢀⠴⠀⢀⠔⠀⢀⡴⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⠀⠀⠑⠣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠎⢤⠊⣠⠞⢁⡴⠋⢀⡔⠁⢀⡴⠃⠀⡤⠋⠀⠀⡰⠃
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢲⠈⡿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢁⠀⠛⠀⠠⠎⠀⢀⡔⠀⠀⢀⠊⠀⠀⢀⡼
⠸⢀⢀⣀⣶⠞⠃⢸⣱⣄⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡟⠀⠀⢀⡞
⠀⠀⠈⣻⡄⠀⠀⢀⠀⠈⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢠⡄⠀⠀⠀⠀⠀⠾⠄
⠀⠀⠈⡉⠛⠲⠶⠾⣧⣤⢁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠲⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣣⠂⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠶⠞⠻⢿⠾⠿⠿⠶⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣢⣳⢳⢳⡞⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣄⣣⣣⣣⣜⣧⠿⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠉⣭⠉⠉⣥⡄⡿⠛⠚⢻⡤⣤⣴⡄⠀⠀⢀⣀⣀⣀⡀⣀
⠀⡀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣉⣁⣀⣉⠁⡇⠻⠟⢸⣧⣮⡃⡏⠉⠀⠀⠀⠀⢄⠐⢄⡀⠠⡀
⠛⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢸⠀⣲⣒⡗⣖⠀⡇⢰⣶⢸⠁⠈⠩⠁⠀⠀⠀⠄⠀⠀⠑⢄⠙⣆⠘
⠀⠀⠀⠈⠑⠲⢖⠊⠉⠁⠀⠀⠀⢸⡀⠈⠉⠉⠁⠀⡇⠀⠀⢸⣘⣁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢷
⠀⠀⠀⠀⠀⠀⢀⣉⡦⠤⠐⠒⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⡖⡒⢦⡀⠈⣧⠘
⠀⠀⢀⡠⠔⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠲⠾⠄⠁⠙⠂
⠤⠊⡡⠤⡇⢠⢂⠀⠓⠢⡀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⢤⡀
⠀⢀⠧⠀⠀⣠⠤⠀⠀⠠⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢄
⢰⡁⠰⣒⠆⠈⠈⠀⠰⠸⠂⡸⠀⠀⠀⠀⠀⠀⠠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠑⢄⠀⠀⣀⠘⠄⠃⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠘⣄⠈⠀⢃⡤⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠈⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠆⠇⠘⠉⢈⠉⠀⠐⠂⠟⠘⠁⠆⠀⠆⠀⠀⠸⠀⠯