Gelato Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠤⣄⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⢸⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⠀⠀⠀⠈⢧⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣄⠀⠀⠈⠙⠦⣤⣀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠙⢦⣀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠽⠛⠻⠿⠿⢿⣿⠿⠿⣿⠿⠟⠛⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣀⡼⣖⠁⠀⣠⡾⠋⠀⣀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠁⢀⣨⡿⠟⠁⠀⣀⡴⠛⢳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠞⠋⠁⠀⡀⠜⠻⣅⡀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠠⣀⠀⠀⠀⢀⣩⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠈⠓⢦⣖⠋⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⢙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⡳⢤⣞⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠛⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠁


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠠⠀⠀⠀⡀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡔⠈⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠱⠤⠦⠤⡤⠄⠶⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠠
⠠⡁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠑⠲⠤⢄⣀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡀⠄
⠸⡀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠂⠀⠀⠀⠀⠈⠉⠙⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲
⠀⠈⢢⡀⢤⠈⠁⠈⠡⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠠⣄⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠔⠐⠁⠀⠀⣉⠀⠀⠀⠀⠀⠀⡀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣫⣝⣹⣟⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠂⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠆⠀⠀⠢⠍⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⢤⠠⠄⠤⣉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⣀⠔⠋⠀⠀⠀⠸⠉⢆⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠠⠐⠉⠀⠀⠀⠀⢀⠄⠁⡠⠊⡆⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠔⠊⠁⠀⠀⣀⠠⠄⠒⢉⣀⡀⠊⢀⠰⠓⠎⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢀⠠⠄⠒⣛⠴⠖⠂⠀⠀⠈⢁⠄⠋⠁⠀⣠⢆⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⢀⠠⠒⠉⠀⠀⠀⣀⠤⠒⠉⠀⠀⣀⠄⠊⠁⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡠⠒⠁⢀⠠⠄⠂⠀⠉⣀⠠⠄⠒⠀⠁⠀⠀⢀⡴⠤⠐⠚⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠊⠀⡴⠊⠀⡀⠄⠒⠈⠁⠀⠀⠀⠀⢀⡀⠄⠒⠁⠀⠀⢀⡴⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⡠⠔⠉⠀⡠⠒⠒⠀⠀⠀⠉⠉⢀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⡉⠁⠈⠀⠈⠑⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⠀⠉⠉⠉⠉⠁⡒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⡉⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠤⠀⣀⡀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠒⠲⢈⠁⠀⠈⢉⡢⠴⢈⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣢⢄⡠⠤⠘⠒⠪⢄⣀⡀⠔⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢄⠀⠈⠒⣤⣠⠐⠂⠉⠉⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠒⠋⠛⠅⡀⠀⠉⡀⠶⠆⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⢤⡀⠀⠈⠛⠃⠠⣀⡠⠊⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⢈⣂⣤⣤⠔⠊⠀⢀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠙⠄⡀⠀⢀⠉⠖⠚⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠚⠙⠓⠀⠐⠒⠈⠁
⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⡟⠧⠀⠀⠀⠠⣿⠀⠀⢀⣠⡤⠤⡀⠀⠀⠀⣚⣳⣿⣛⣩⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠱⣤⣴⣤⣠⣶⣤⡆⠀⣠⠿⠤⠀⠀⠘⡆⠀⢼⣿⠯⠥⣿⠿⣛⡷⠀⠀⣀
⠀⢀⡔⠉⠉⠙⢳⡄⢸⣿⣄⣠⣼⡟⢠⣎⠁⠀⡤⠚⠓⠚⠳⡄⠸⣿⣷⣾⣿⣿⣧⠀⠀⡠⢻⣦⣤
⠀⢸⡄⠀⠀⠀⠠⣿⠀⣿⣟⣻⣿⠁⠸⣄⡀⣼⠁⠀⠀⠀⠀⢺⠀⢻⣧⣾⣥⣾⡟⢀⢀⣷⣣⡞⢫⣦
⠀⠀⠃⠀⠀⠘⠉⣳⠀⣿⣯⣹⣿⠀⠀⣇⣾⡍⢷⠀⠀⣀⣀⡼⠀⠀⣿⢷⣾⣿⠀⢈⣟⣵⠉⢧⣺⡿⠇
⠀⠀⢨⢶⡤⣿⡼⠁⠀⠘⠯⠼⠏⠀⠀⠈⠻⣷⣤⣯⣍⣰⡗⠃⠀⠀⢻⢾⣹⡿⠀⠀⢹⣿⣿⣼⢿⣿⠁
⠀⠀⠨⢻⣽⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡽⠀⠀⠀⠀⢸⣾⣹⡇⠀⠀⠈⣟⣏⣻⣭⡟
⠀⠀⠀⣳⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢛⣶⠇⠀⠀⠀⠀⠀⣯⣹⡇⠀⠀⠀⢻⣿⣹⣿⠃
⠀⠀⠀⢨⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠛⡜⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄
⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣦⣄⡀
⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣦⡀
⠀⣰⣿⣿⡿⠋⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆
⢰⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⠀⣴⣶⡄⠻⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢻⣿⣿⡄⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠈⢿⣿⣷⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿
⠀⠈⢻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣤⣤⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡟⠁
⠀⠀⠀⠙⠻⣿⣿⣿⠀⣴⣶⣶⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⣾⣿⣿⠀⣿⣿⡿⠟⠻⣿⣅⣠⣾⠟⠁⠀⠀⠈⠻⣷⣄⣨⣿⠟⠻⠿⢿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⣨⣿⣿⡁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣅⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣆⣠⣾⠟⠁⠙⢿⣦⡀⠀⠀⣠⣴⡿⠋⠈⠻⣷⣄⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠁⠀⠀⠀⠀⠙⢿⣧⣴⡿⠋⠀⠀⠀⠀⠈⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⣀⣾⡿⠋⠀⠀⠙⢿⣷⣀⣀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠹⣿⣤⡀⠀⠀⢀⣤⣭⠍⣹⣭⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠙⢿⣦⣴⡿⠋⠀⢠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⢀⣴⡿⢿⣦⡀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡿⠋⠀⠀⠙⢿⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⢰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣
⠀⠀⠀⠀⠀⠀⠀⢰⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠇⠄
⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠚⠃⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠀⠀⠀⠀⠀⠀⠄⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠲⠄⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡂⢳⠄⢰⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠀⠀⠀⠳⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠂⢸⣴⠀⠀⠀⠀⠀⡠⢠⠖⢀⡀⠀⠀⠐⠈⣀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⣿⠂⠀⠀⠀⠀⠀⠀⠀⢦⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢣⡀⠀⠀⠉⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠷⠛⠈⣇⣀⠀⠀⣀⡀⠖⢁⡸⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠔⡂⠀⠀⠁⠀⠀⢀⡼⠄⣤⣤⣴⠟⠂⠀⠄⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣠⢴⣿⡏⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠖⣋⡴⣎⠋⣻⡀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣥⠔⠒⠉⠂⠠⠀⠀⠈⣡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣄⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠁⠀⠀⠙⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⡖⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⣰⠂⢀⡖⢡⠆⣰⠂⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠛⠛⠛⠛⠛⠛⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⡛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠛⠛⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣧
⠀⠀⠀⠀⠀⢀⣼⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⡇
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⣼⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠟⢀⣿⣿
⠀⠀⠀⠀⠈⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⣤⣴⡿⠋⢉⣉⣀⣠⣾⣿⣟
⠀⠀⣀⣀⣼⡿⠋⠉⠉⠉⠀⠀⠀⠀⢀⣤⣀⣀⣠⣤⠂⣠⣄⣀⣉⣤⣴⠶⠿⢷⣤⣤⣤⣄⡀⢀⣀⣠⣴⠟⠋⠉⠉⢩⣙⠻⣷⡄
⢠⣾⠋⠉⠛⠃⠀⠀⣀⠀⠀⣤⣤⣴⡿⠋⠙⠋⠉⣀⣼⣿⣿⣿⠟⠀⠀⠈⠳⢶⣌⠻⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷
⣿⡇⠀⠀⠀⣼⣶⣿⠏⠀⣠⣉⠛⠉⠀⢀⣼⣿⠿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠷⠆⠸⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿
⣿⣇⠰⣤⣴⠟⣁⣠⣤⣾⠿⢿⣿⣿⡿⠋⠁⠀⠉⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿
⠸⣿⣦⣀⣀⣤⣿⣿⡟⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣼⡿⠃⣼⣿
⠀⠀⢰⣿⡟⠉⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣀⡀⣀⣴⣿⣿⣿⣿⣇⠀⢀⣶⡶⠆⠀⠀⠈⠛⠛⠛⠛⠛⢉⣠⣾⣿⠟
⠀⠀⠀⠻⠿⢿⣿⡟⠀⣀⡤⠶⠶⠾⠿⢿⣦⣼⡿⠋⣀⡙⠛⠿⠿⠛⠁⠈⠈⢿⣿⣿⠿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠘⢿⣇⣠⣤⣴⡶⢶⣶⣤⣄⣉⣡⡶⠛⣿⣿⣿⠖⢛⣷⣷⣶⣦⠀⠉⠀⠀⠀⣀⣀⣠⣼⡿⢛⣿⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣦⡈⠛⣁⣴⣿⣿⣿⣿⣿⣷⣶⣿⣿⣦⣌⣉⣉⣥⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⠟⢻⣿⣿⣿⣿⠃⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡈⠛⠋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠛⢁⣴⣿⣿⣿⣿⡟⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⠃⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⠙⢿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠙⠃⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣩⣿⣿⣿⣿⣿⣿⣉⠛⢿⣿⣿⡿⠋⣹⡿⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠋⣠⣾⣿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡏⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⠻⠿⠋⣠⣾⣿⣿⣿⣿⣿⡿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠙⢿⡿⠃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄⡀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⢉⣴⣿⣿⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⡛⢛⠛⠛⡛⢛⣛⣃⡘⠛⢻⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣏⣉⣭⣿⣏⣩⣿⣿⣿⣽⣛⣋⣉⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⢀⣀⡀
⠀⠀⠀⢠⣆⡀⠀⠀⡠⠛⠘⣢⣀⣸⡀⠀⠀⢀⣀⣀⠀⠀⢀⣴⣻⡿⠟⣳⠀⠀⠀⠀⠀⠀⠀⢠⣟⣂⣾⣯⣶⣷⣋⠂⠀⠀⠀⢀⣼⠉⢽⣀⠀⠛⣿⣿⣦⡀
⠀⠀⢰⡴⣻⢿⡄⣸⠀⢀⡾⠁⠀⠀⠩⡀⡴⠁⠀⠈⢱⡄⣶⣾⣛⣻⣿⣿⡄⠀⢀⡀⢀⡀⠀⣿⣾⢻⣯⠢⢣⢛⢿⡂⠀⠀⠀⢸⣿⡀⠈⢯⣠⣠⡟⢨⢙⣿
⠀⣸⣏⠍⢷⣼⣷⠎⣛⣞⢧⠀⠀⢀⣀⠇⠸⠀⠀⠰⠸⡇⢺⣷⣶⣿⣾⣏⢁⣤⠃⠀⠀⠈⣦⢹⣿⣤⣽⣤⣈⣠⣼⣿⠇⠀⠀⣹⣿⣯⣆⡀⠉⠈⣻⣾⣿⣿
⠀⠈⣿⣿⣼⣿⡿⠀⠙⢿⣦⣼⣍⣸⠟⠀⠀⣤⣄⣶⡴⠁⠘⢷⡾⢧⣾⠇⡏⠟⠆⠀⠀⠐⠏⠈⢿⣏⣿⡏⢻⡍⣿⡟⠀⠀⠀⢸⣿⣿⠿⢿⣶⣭⡿⣟⣿⡏
⠀⠀⢿⣯⣿⣽⠃⠀⠀⠘⣿⣿⠿⡏⠀⠀⠀⢳⢽⡗⠇⠀⠀⢸⣿⣿⣿⠀⠘⣷⡾⠶⢿⣾⠁⠀⠀⠙⢿⣿⢿⠟⠋⠀⠀⠀⠀⠀⣿⣟⡛⠻⠿⠞⠻⣿⡿⠁
⠀⠀⠸⣷⣼⠏⠀⠀⠀⠀⢿⣏⡿⠇⠀⠀⠀⢸⡞⠅⠀⠀⠀⠀⣿⣾⡇⠀⠀⢹⣿⢾⣿⠇⠀⠀⠀⣴⣾⡿⠼⣦⡤⠀⠀⠀⠀⠀⢿⣄⠀⠀⠤⠤⠄⣸⡇
⠀⠀⠀⢿⣾⠀⠀⠀⠀⠀⠨⣎⡽⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⢻⢾⡇⠀⠀⢸⣿⣻⣿⠀⠀⠀⠀⠈⠉⠓⠂⠉⢀⣴⡶⠒⠢⢀⠘⢧⣀⠀⠀⠀⣀⣿⠟
⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠹⠃⠀⣾⣿⠻⣶⠈⢰⡾⣷⡄⠀⠸⠿⠁⠀⠀⠀⠻⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠠⡄⠀⠉⠙⠛⠛⠉⠁
⠀⠀⠀⢰⡄⡄⠀⠀⣴⢶⣷⠦⡀⢰⣿⣍⣿⣧⠀⣽⠀⢸⡇⠀⣴⡿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠳⢀⠠⣾⣧⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠸⡀⢀⣿⣿⣿⣷⢷⢀⣿⣿⣿⠏⠀⡅⠀⢸⣧⢸⣿⠇⠈⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠻⣟⢳⣦⣴⠟⠛⠛⠛⠛⠛⠻⠿⢿⣷
⠀⠀⠀⠀⠀⠀⣇⢸⣿⣿⣿⣏⢸⢸⣿⣍⣿⣿⠀⣤⠀⢸⡏⢸⣿⠂⠀⢻⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢀⣠⣤⣭⡉⠀⡀
⠀⣴⡆⠂⢠⢠⣽⣨⣿⣿⣿⡿⢸⠀⣿⣿⣻⣷⠀⢸⠀⢸⡇⢸⣿⣇⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⢻⣾⣇⠀⢀⣤⠀⠀⠀⠀⠀⡀
⠀⢿⣀⣀⣭⣿⡿⢿⣿⣿⣿⣷⢸⠠⣟⢯⣻⡿⠀⢸⠀⣼⣷⠀⠛⠿⠷⣿⠿⠃⣠⣤⡶⣶⣭⡭⡵⡄⠀⠰⠉⡿⠛⢿⠻⣿⣿⠛⠋⠀⣧⠄⠀⠠⠪⠚⢻⠂
⠀⠀⠀⠁⠈⠁⠀⠀⠛⠛⠛⠛⠈⠀⠈⠛⢻⠁⠀⠘⠷⠿⠋⠀⠀⠀⠀⡇⠀⣸⣿⣧⣤⣾⣿⣏⣇⡏⢾⡀⢼⡅⢀⣀⣀⣛⡿⠀⢾⡦⢸⣶⣾⣷⣿⣿⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⢨⣿⣿⣿⣿⣿⣿⡋⠀⠀⠙⢻⣿⣭⣿⣿⡟⠀⠀⠈⣿⣎⢷⠃⢾⣿⠏⡟⣸⡄
⠀⢀⡠⠖⠲⢤⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣀⠀⠀⣦⡘⢈⣿⣿⠟⠿⡇⣰⠀⠀⠀⢶⠏⠀⠉⣹⠁⠀⠀⠀⣿⣿⣷⣻⣾⣷⣶⣾⣠⣾
⠀⡎⠀⠀⠀⠀⣷⠀⢠⠎⠁⠀⠙⢲⡀⢰⠋⠀⠀⠉⣧⢠⡞⠉⠉⠉⠹⡄⢻⣿⡿⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⣠⡄⣶⡉⠀⠀⠀⠀⠹⢿⣿⣟⢹⣿⢻⣿⡿⠃
⠀⣿⠦⠀⠀⣠⣿⠆⣾⠃⠀⠀⠀⣼⠃⣸⡀⠀⠀⣀⣿⠘⣧⡀⠀⣠⣾⡇⢸⣿⠀⠀⠀⠈⣿⣸⠁⠀⠀⠀⢞⠛⠓⢻⣤⠀⠀⠀⠀⠀⢀⣿⣿⡟⢾⡿⣿
⠀⠈⠓⠚⠛⠛⠋⠀⠈⠑⠂⠐⠒⠋⠀⠈⠓⠖⠚⠋⠉⠀⠉⠃⠐⠛⠉⠀⠀⠉⠒⠂⠔⠚⠛⠉⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠓⠳⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠉⡠⠄⠀⠀⠀⠀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⡠⠒⠂⠉⡀⠐⠁⠀⠀⠉⠀⠀⠠⠄⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠄⠀⠀⠐⠀⡠⠐⢀⠘⠀⠀⠋⠀⢠⠤⠶⠆⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢡⠜⠀⡠⠂⠀⠄⠀⣀⡴⠂⠀⠚⠁⢃⣬⡤⠴⢟⡻⣃⡀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠙⠁⢀⠜⠃⣠⠜⠀⠚⡁⠠⠔⠂⣠⠆⠁⠀⠀⠀⠬⢛⣩⣤⡀⢻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⡰⠋⠀⠐⠁⠀⠐⠃⡠⠀⠴⠛⠁⣀⠤⠀⠠⠀⢒⡹⣽⣶⢶⠆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢀⠰⠙⠁⠐⢀⡴⠂⠀⠒⠉⠀⢀⠀⡀⠀⡰⠾⣛⣿⢣⣼⡿⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣿⠀⠀⠀⠀⠉⠀⠀⠀⠐⠈⣱⠆⠀⠀⢀⣸⡁⢐⢳⠚⣉⡶⣟⢻⣽⣾⣷⣄⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢠⡀⠀⠀⢀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠇⢁⠴⠆⠺⢉⡧⣘⣿⣿⣛⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠒⠳⡔⢢⠀⡆⠀⠀⠀⠊⠁⠀⠀⠀⠄⣰⣀⣠⣿⣾⣷⣽⡿⣿⣿⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣼⣿⠷⣼⣠⣀⣧⣀⠀⣆⣤⣸⣿⣿⣿⣿⣿⣿⣏⡥⠄⢀⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⠁⠐⣆⠙⠛⠋⠹⠛⠛⢻⣿⠿⢿⡋⠁⠈⢉⣡⣶⣶⣯⣴⣖⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢤⣾⢷⣤⣀⣈⡵⠊⢀⣸⠇⠀⠈⠀⠄⣀⣿⣿⣿⣿⣟⡵⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄⠈⢻⣦⣴⡞⢡⡴⠷⠒⠒⠚⡉⢥⣿⣿⣿⣏⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠂⠀⠀⠀⠛⣿⡧⠞⢀⠠⣀⢐⣿⣷⠟⣻⣟⣭⣡⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠁⠀⠈⠁⢀⡀⠉⠉⠲⣿⡆⠙⣻⠛⡖⢲⢃⣙⣥⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠠⠀⠁⣠⢬⣉⣿⠟⠋⠉⠸⠙⠋⡆⡍⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠐⠀⠀⣶⣼⠞⠁⠠⠗⠐⢛⡗⠛⡩⣸⠁⢘⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣤⠿⠋⠀⠀⠀⠀⠘⢋⠉⢀⠛⢳⡙⠚⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣽⠃⠀⠀⠀⠀⠀⠠⠇⠁⣾⢛⢶⡏⡽⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡋⠀⠀⠀⠀⠀⠀⠐⠊⠘⣽⠋⡾⠋⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⠀⣰⡉⠲⡷⢎⡷⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠉⡁⡖⠳⡺⠓⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠄⠀⠈⠳⡴⡌⠢⠔⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⠁⠠⡐⠀⠠⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠁⠀⢠⠟⢤⠄⠀⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠦⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣦⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⡴⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠑⣤⡿⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣽⢟⡆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠣⣈⣌⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⣿⡄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣯⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢷⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠶⠛⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠶⠶⠾⢿⣍⠉⠛⠓⠂⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠉⠉⠛⠒⠶⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡦⣄⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⣠⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴
⢿⣄⣀⣄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣽⠃
⠀⠉⠉⠹⣦⡀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠚⠋⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣄⣀⣦⠀⠀⠀⠀⣠⣀⣀⣀⣀⣠⣤⣤⣤⡶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣠⡴⠟⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⡉⠙⠓⠋⠉⠉⠉⠉⠉⠉⠙⠛⠶⠾⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⣴⠋⠳⠶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠓⠚⠉⢹
⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢲⡏
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡇⢸⡇
⠀⠀⠀⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⡇⢸⡇
⠀⠀⠀⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣼⠁⣼⠃
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡼⠃⣰⠏
⠀⠀⠀⣾⠁⣀⡀⠀⠀⠤⠤⢤⣤⣤⠤⠤⠄⠀⠀⠀⢻⡄⠀⠀⢰⡏⠀⠀⠀⠈⠙⠒⠒⠲⠶⠒⠂⠀⠀⠛⠁⣴⠋
⠀⠀⠀⠈⠛⠉⠉⠓⠲⠶⠶⠦⠤⠤⠤⠴⠶⠾⠛⠓⠚⠁⠀⠀⠈⠛⠛⠛⠲⠤⣤⣤⣀⣀⣀⣀⣀⣀⣤⡤⣦⣈⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢛⣁⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣡⡟⡋⠙⡧⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⢻⠟⠛⠛⠿⠿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠤⠰⠀⠸⠄⠀⠃⠀⠴⠀⢲⠙⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠫⠀⠀⠓⠀⠂⠀⠀⠘⡀⠐⠂⠀⠀⠉⠀⠒⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠑⠠⠄⡀⠡⡄⠀⡈⠀⠀⠠⠀⠀⡀⠉⠠⠄⠀⠉⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢈⠀⠀⢁⠀⡀⠀⡙⠀⠂⠀⠀⢠⠈⠀⠀⠠⠄⠈⠃⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣆⣀⣀⣁⣈⣀⣂⣀⣁⣀⣠⣆⣀⣒⣀⣀⣂⣀⣒⣀⣁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠋⠉⠛⠉⠉⣉⣉⣉⣉⣉⣉⣉⡙⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢢⢰⠂⢰⡒⢠⠚⢰⣛⡆⣟⠀⣴⡆⢰⣶⡆⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠈⠓⠈⠓⠈⠓⠘⠉⠃⠓⠀⠃⠉⠈⠁⠃⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠷⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⠃
⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡁⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣿⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣛⡟⠧⠁⠀⠀⠠⢿⠁⠀⠀⣀⣤⠶⠤⣄⠀⠀⢀⣚⣯⣽⣛⣩⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣦⣴⣤⣰⣶⣤⡖⠀⢀⡾⠷⢤⠀⠀⢸⡆⠀⠸⣿⡿⠭⣴⡿⢿⣻⡗⠀⠀⣀
⠀⠀⡠⠒⠋⠙⠓⣦⠈⣿⣿⣈⣁⣼⣿⠁⣔⠋⠀⢀⡤⠾⠶⠚⠧⡀⠘⣿⣷⣶⣶⣾⣿⣅⠁⠀⣠⢳⣧⣄⡀
⠀⢸⣇⠀⠀⠀⠀⣼⡇⢸⣻⡟⢻⣿⡇⠰⣏⡁⢀⡾⠂⠀⠀⠀⠀⠴⡀⢿⣮⣼⣽⣡⣿⡇⠀⢘⣦⢏⡿⢏⣧
⠀⠀⡧⠀⠀⠀⠖⠺⡅⠈⣿⣞⠻⣿⠁⠀⢸⢹⡞⠳⠄⠄⠀⠀⠀⢸⠇⠀⢿⣯⣭⣿⡟⠀⢚⣾⣫⠛⣷⢸⣿⣷
⠀⠀⠰⣀⡄⣳⣄⡼⠃⠀⢻⡞⢹⡿⠀⠀⠘⢾⣧⣀⢑⡶⠒⢚⣍⠇⠀⠀⢸⣅⡗⣿⡇⠀⠙⣷⣿⣾⢽⣭⣷⡎
⠀⠀⠸⣫⢿⣽⣻⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⢷⢿⠃⠀⠀⠀⠘⣯⡿⣿⠁⠀⠀⢹⣿⡿⣿⠼⣿⠃
⠀⠀⠀⢥⣻⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⡏⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠈⣯⣷⢾⡷⡿
⠀⠀⠀⠸⣯⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣧⣼⢾⠁⠀⠀⠀⠀⠀⢸⣶⡿⠀⠀⠀⠀⠸⣿⣶⣿⠇
⠀⠀⠀⠈⠄⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⣹⡏⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢿⣧⡟
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣉⡠⠄⠒⠋⠑⡤⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠑⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢃⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⡀⠂⠉⠉⠒⣤⠤⢄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⣠⠖⠋⠻⢆⣠⣠⠤⣄⡀⠀⠀⢸⠀⠀⣉⣉⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⣸⣁⣠⠤⠤⠤⢤⡀⠀⠀⠉⠙⠛⢾⣤⠞⣁⡈⠑⠤⡤⢷⡀
⠀⠀⠀⠀⠀⣀⡟⠀⠀⣀⣀⣀⣀⣀⣀⣀⠠⠄⠀⠸⠧⣄⣠⠟⣁⡀⠀⠀⠀⠀⠙⠦⠴⠒⠺⣍⡽⠋⠉⠉⠉⠉⠓⢦⡀⡧
⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠀⠉⢳⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠓⠒⢤⡀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲
⠀⢀⡸⠇⠀⠀⠤⠤⠤⠤⣤⣤⡤⠤⠤⠤⠔⠒⠂⠀⠘⠛⠙⠳⣶⠒⠶⠶⠶⠶⠷⠶⠷⠶⠶⠶⣄⠀⢀⣠⠴⠦⣄
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠶⠶⠶⠶⠶⠶⠶⠖⠲⠒⠒⠚⠛⠛⠒⠒⠒⢾
⢨⡷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⢀⡇⠀⠀⠀⢰
⡏⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠶⠶⠖⠒⠒⠂⠉⠁⠀⠀⠀⠈⢧⣿⡇⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⢿⣧⡀⠀⠀⢸
⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⠁⠀⠀⣿⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⢸⡇⠙⣦
⠀⠈⣻⠒⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄⠀⢸⡇⠀⣿
⠀⠀⢸⡀⠀⢀⡴⠚⣆⠀⠀⣀⡀⠀⠀⠀⠒⠒⠀⠀⣠⣿⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⢸⡇⠀⡿⡇
⠀⠀⠀⠻⡶⠚⠁⠠⠜⢛⠋⠉⠙⠶⣶⢶⠀⣠⠶⣾⠁⢸⠈⡇⠀⢹⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⢸⠇⢰⠀⡇⢠
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡑⠤⠒⠁⠀⣹⢀⡏⣰⠃⠀⠸⡄⢿⠀⢸⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣸⠀⡸⢠⡗⠁
⠀⠀⠀⠀⢹⠀⠀⠈⠣⡀⠀⠀⡀⠖⢢⡇⢸⣧⠇⠀⠀⠀⢧⠸⡆⠀⣇⠀⠀⢹⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⡏⢠⠇⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠣⠁⠀⢀⡞⠀⣸⡏⠀⠀⠀⠀⠘⡆⢻⡄⠸⡀⠀⠘⡄⠀⠀⢸⠀⠀⠀⠀⠃⠀⠸⠁⡞⢰⡏
⠀⠀⠀⠀⠀⣇⠀⠐⣄⡀⠠⠄⠓⠙⠷⠞⡿⠀⠀⠀⠀⠀⠀⠹⣄⢳⡄⠱⡀⠀⠱⠀⠀⠘⠀⠀⠀⠌⠀⡰⢁⡜⢠⡟
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠑⢄⢀⠠⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣦⠈⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⣠⠏⣰⠟
⠀⠀⠀⠀⠀⢸⡄⠈⠒⠀⠉⠉⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠛⢦⣀⠀⠀⠀⠀⠀⣀⡤⠞⣡⡾⠋
⠀⠀⠀⠀⠀⠘⡇⠘⠀⡉⠙⠁⡀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣈⡉⠙⠛⠋⢉⣁⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣯⠀⢀⠈⠙⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠛⠛⢻⠉
⠀⠀⠀⠀⠀⠀⢹⠀⡈⠉⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡆⡈⠑⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠉⠉⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⢀⡞⠀⠀⠸⡄⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡀⠀⠀⠠⠋⠀⠀⠀⠀⠹⠀⠀⠀⠀⢀⣨⠗
⣀⣀⣀⣀⣀⣀⣀⣘⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣒⣲⣦⣤⣤⣤⣤⣤⣴⣖⣒⣉⣉⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡉⠻⠿⢿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣽⣿⡀⠀⠀⠈⠙⠛⠿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠩⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣤⣄⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⣧⣤⣤⣿⠏
⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢷⣄⡀
⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠘⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢷⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⣶⣶⣶⣦⣄⡀⣀⣿⠇
⠀⠀⠀⢀⣤⣽⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣄
⠀⠀⣴⡿⠋⠁⠀⠀⠉⠻⠿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡄
⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣶⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢷⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢷⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⠿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣶⣦⣄⡀⠀⠀⣼⡿
⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣾⣯⡀
⠀⣀⣼⠿⠿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣦
⢀⣿⠏⠀⠀⠈⠉⠻⢿⣷⣶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢷⣶⣶⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⢷⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⠿⠿⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠻⣷⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⣄⣀⢀⣀⣀⠀⠀⣀⣼⡿
⠀⠻⣷⣄⣰⣾⠛⠛⠿⣶⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣾⣿⠿⠟⠛⠻⣶⣶⡟⠋⠁
⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠒⠲⠆⠀⠀⠀⠛⠻⠟⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠘⠻⣷⣶⣶⣶⣦⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣶⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠛⠛⠛⠛⠛⠋⠉⠀⠀⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢻⣷⡀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⣠⣾⠇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠙⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠿⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⢀⣴⣶⣾⠟⠉⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣶⣶⣶⣿⣿⣀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⢿⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣧⡀⠀⠀⠀⢸⣿⣦⣶⡾⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠈⠉⠉⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣄⠀⢀⣼⡿⠉⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠋⠁⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣦⣀⣀⣀⣀⣀⣠⣶⡾⠿⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠘⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢰⣧⢀⣄⠀⠀⢀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⣸⠘⠾⠁⣧⠀⡞⠙⡆⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣾⣿⣿⣿⡆⣸⣿⣧⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⡏⠀⠀⠀⡿⠀⡇⠀⢹⠀⠀⠀⡼⢧⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⡇⠈⣿⠀⠀⠀⢰⣿⣿⣿⣿⠁⢸⣿⣿⠃⠀⠘⣿⣿⡇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣧⢠⡇⠀⡟⠀⠀⠀⢷⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⡄⣿⣿⣿⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⠀⢠⡇⠀⣀⡀⢸⡀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⡀⢻⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡏⢧⡸⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣧⣾⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠧⠞⠁⠀⠀⠀⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠓⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠇⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢯⠉⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢳⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢻⡄⣈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡇⣹⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⣧⠀⣾⣇⣽⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠇⠀⠛⡏⢻⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢀⠀⠀⡁⠞⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⡅⢰⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⠀⢠⡇⣘⠂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⢸⡇⢸⠃⣼⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡄⢹⣅⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣃⢸⣰⣟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⡴⡋⡉⢿⣿⢿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠠⣄⣀⣉⣉⠉⠠⡰⣙⣿⣇⠠⠀⣠⣼⠿⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⣻⢿⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠿⡿⠿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣗⣒⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣤⣀⣀⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠒⠤⢤⣀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⡠⠐⠂⠺⢷⣶⣶⣶⣶⣾⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠘⣏⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁⠀⠀⠀⠈⠙⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⡀⠀⠠⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⡷⠀⠀⠀⠠⠶⠒⠛⠉
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠚⠓⢢⡀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠸⡄⠀⠀⢀⠀⠀⠀⢀⣀⣀⡠⠄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠓⢦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠸⡀⢀⡞⠱⣤⠤⠢⣤⣤⡀⡠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠠⠄⠀⢨⡇⣇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠀⣀⠀⠈⣹⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠂⠓⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⠀⠤⠄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠑⠂⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢈⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠈⠻⣿⣿⣿⣶⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠙⠛⠿⠿⠿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡋⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⡴⠚⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⡇⠀⢀
⠀⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠁⣸⣿
⠀⠀⠀⠀⠈⠀⠀⡄⢀⠀⠠⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠄⠀⠀⠀⠀⡇⢿⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣧⠘⣇⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠛⠲⠶⠦⠤⠾⠁⠀⠀⢠⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣤⠤⠔⠛⠁⠀⠀⠀⠀⠈⠳⢽⡀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠐⠒⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢀⠀⡄⠀⠀⠀⠀⠁⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⡁⠀⠀⠀⠀⠀⠀⠀⠘⠛⡏⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠢⢊⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠾⠭⠍⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢸⠀⠁⠘⡄⠀⠀⠀⠀⢸⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢠⠚⢦⠾⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⡳⢭⣭⢧⡤⢄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸
⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣱⡎⠀⠾⠁⠀⠀⠀⠀⠐⡇⠀⠀⠀⣼⠀⠀⠀⠀⠄⠀⠀⢸⡀
⠀⠀⠀⠉⠐⠀⠀⠀⠀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⣷⣇⠀⠀⠀⣿⠀⠀⠠⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⢻⠀⠀⠀⢠⢤⡄⣴⢲⡍
⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣶⠶⡶⠆⡻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠟⣠⡖⢳
⠀⠀⠀⠀⡀⠀⠄⢿⣿⡦⡄⢐⠆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠤⠀⠀⠀⢸⡟⢀⡒⠀⡢⠁⠀⠀⠀⠁⠒⢤⡔⠒⠁⠀⠀⠀⠀⠻⣀⠵⠏
⠀⠀⠀⠐⠼⣀⣠⠀⡍⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠸⣎⡑⠮⣱⠢⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣩⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡖

⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⣸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⣰⠿⠛⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⣴⡄⠀⢰⡶⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢿⣿⣄⡁⠀⣀⣼⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⣻⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠀⡆⢀⠈⢻⣿⣿⣷⠀⠀⠀⠀⠛⠻⠿⠃⠀⠀⠀⠀⣻⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠷⠀⠀⢀⣤⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠚⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⠀⠀⠀⠀⣿⡿⠋⠉⠀⠀⢐⣄⠀⠀⢶⠇⠀⠀⣠⣾⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠃⢠⡀⣠⠆⡿⠋⠀⠀⢀⣴⣶⣿⣿⣿⣷⣦⣴⣴⣿⣿⣿⡇⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢰⣿⠟⠛⠻⢿⣿⣿⣿
⣄⡀⠀⠈⢀⡄⠀⠀⠀⠀⠨⠟⠉⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋⠀⠀⣤⣽⣿⣿⣶⣤⠀⠀⣠⡾⠇⠀⠀⠀⠀⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡤⠂⠀⠀⣠⣿⣿⠟⠁⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⠁⠀⠀⢹⡄⠀⠐⣦⡀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⠂⠀⠀⣰⣿⣿⠃⠀⠀⠀⠹⣿⣿⠏⠀⠀⢹⣿⣿⡀⠀⠀⠘⣷⡄⠀⠀⠁⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠸⠁⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠗⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠟⠛⠛⠿⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢀⣴⣿⠟⠉⢀⣤⣴⣦⠀⠀⠀⠀⢠⣤⣀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⠀⢠⣿⡿⠁⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠈⠛⢿⣷⣦⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⣾⡷⠀⠀⠀⠈⠻⣿⣆
⠀⠀⢀⣿⡟⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠹⣿⡆⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⣼⣿⠃⠀⠀⠀⣤⡄⠙⣿⣧
⠀⠀⢸⣿⠃⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⠀⠀⠀⣼⣿⠃⠀⠀⠰⣿⣆⠀⠀⠀⠀⠀⣀⠀⠙⠃⠀⠀⠀⠀⢿⣿⠀⠘⣿⣧
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠸⠿⠀⠀⣿⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⢻⣿⡀⠀⠀⣠⣾⡿⠃⠀⠀⠀⣀⡀⠀⠘⠿⠃⠀⢹⣿⡆
⠀⠀⣿⣿⠀⠀⠀⣰⣦⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠘⣿⡇
⠀⠀⣿⣿⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣄⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣤⣶⣶⣶⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠙⢿⠇⠀⠀⠀⠀⣿⡿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠻⠟⠀⠀⠀⣿⣿⠀⠀⢹⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⣿⣇⠀⠀⣠⣴⣶⣦⣄⠀⠀⣠⣴⣶⣦⣄⠀⠀⣠⣴⣶⣦⣄⠀⠀⣸⣿⠃
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⠋⠙⢿⣿⣿⣿⠿⠋⠉⠙⢿⣿⣿⡿⠋⠉⠙⣿⣿⣿⡿⠋
⠀⠀⣿⣿⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠹⢿⣷⣄⠀⣸⣿⠇
⠀⠀⣿⣿⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⠻⣿⣷⣿⡟
⠀⠀⣹⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣿⠃
⠀⠀⢹⣿⡀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠹⢿⣷⣄⠀⢰⣿⡏
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠙⢿⣷⣄⠀⠀⠀⠈⠻⣿⣷⣾⣿
⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⢿⣷⣄⠀⠀⠀⠈⢻⣿⠇
⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⠀⠀⠀⠻⣿⣷⣄⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣃⡀⠀⠀⠈⠛⣙⣣⣼⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠈⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢻⣿⣦⡀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠙⢿⣿⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⣏⢙⣏⢈⣛⠈⣛⠁⣛⡁⣙⡁⢉⡁⢈⡁⢈⣉⠀⣉⠀⣉⠀⢉⠀⢈⠁⠈⡁⠀⡁⠀⡉⠀⣉⠀⣉⠁⢉⡁⢈⡁⢈⡋⢈⣋⢈⣛⠈⣛⠁⣛⡁⣹⡋
⡋⢙⣛⢘⣛⠈⣛⠁⣛⠁⢙⠁⢘⡃⢘⡋⠈⡋⠀⠉⠀⠉⠀⠉⠀⠈⠁⠈⠁⠀⠁⠀⠉⠀⠉⠀⠙⠁⢙⠁⢙⡃⢘⡋⠈⡋⠈⣛⠈⣛⠁⣛⡃⣛⡋
⡛⢘⡛⠘⡛⠈⡛⠁⢛⠁⢙⠃⠘⠃⠘⠃⠈⠋⠀⠋⠀⠙⠀⠙⠀⠘⠁⠈⠁⠀⠁⠀⠋⠀⠙⠀⠙⠀⠙⠁⠘⠃⠘⠋⠘⡛⠈⠛⠈⢛⠁⢛⠃⢛⠋
⠟⠘⠟⠘⠟⠈⠛⠀⠛⠃⠛⠃⠘⠃⠘⠃⠘⠋⠀⠛⠀⠛⠀⠘⠀⠘⠀⠀⠁⠀⠃⠀⠋⠀⠛⠀⠙⠀⠘⠃⠘⠃⠘⠋⠘⠛⠘⠛⠀⠛⠁⠻⠃⠻⠃
⠟⠸⠟⠘⠟⠀⠟⠀⠻⠃⠺⠃⠘⠃⠘⠃⠐⠃⠀⠓⠀⠚⠀⠘⠀⠐⠀⠀⠀⠀⠃⠀⠓⠀⠚⠀⠚⠀⠘⠂⠘⠃⠘⠃⠘⠟⠐⠿⠀⠻⠂⠻⠃⠻⠇
⠗⠸⠟⠐⠿⠐⠿⠀⠿⠂⠺⠂⠸⠂⠐⠂⠐⠂⠀⠒⠀⠒⠀⠐⠀⠐⠀⠀⠀⠀⠂⠀⠒⠀⠒⠀⠒⠀⠰⠂⠐⠂⠐⠇⠐⠗⠐⠿⠀⠿⠂⠿⠂⠺⠇
⠗⠰⠷⠰⠷⠀⠶⠀⠶⠀⠲⠂⠰⠆⠐⠆⠀⠆⠀⠆⠀⠒⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠰⠀⠰⠀⠰⠆⠰⠆⠐⠖⠀⠶⠀⠶⠀⠾⠆⠶⠆
⠆⠰⠶⠰⠶⠀⠶⠀⠶⠀⠰⠀⠰⠆⠠⠆⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠀⠰⠆⠠⠆⠀⠆⠀⠶⠀⠶⠀⠶⠄⢶⠆
⡆⠰⡦⠠⡦⠀⠶⠀⠴⠀⠰⠄⠠⠄⠠⠄⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⠄⠠⠄⠀⠦⠀⠦⠀⢴⠀⢴⠄⢴⠄
⡆⢠⡦⠠⡤⠀⣤⠀⢤⠀⢠⠀⠠⠄⠠⠄⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⠄⠠⡄⠀⡄⠀⡤⠀⣤⠀⢤⠀⢠⡄
⡄⢠⡄⠀⡤⠀⣤⠀⢤⠀⢠⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⣤⠀⣤⠀⣠⠀⢠⡄
⡄⢀⡄⠀⣄⠀⣄⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣀⠀⣀⠀⣠⠀⢠⡀
⡀⢀⡀⠀⡀⠀⣀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣀⠀⣀⠀⢀⠀⢀⡀
⡀⠀⡀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢈
⡁⠀⡁⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠈
⠁⠈⠁⠀⠉⠀⠉⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠈⠀⠈⠁
⠃⠈⠃⠀⠋⠀⠉⠀⠉⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠋⠀⠉⠀⠘⠀⠘⠁
⠃⠘⠃⠀⠋⠀⠛⠀⠙⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠃⠀⠛⠀⠛⠀⠘⠃
⠃⠘⠃⠀⠓⠀⠛⠀⠚⠀⠘⠀⠐⠂⠐⠂⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠐⠂⠐⠂⠀⠃⠀⠒⠀⠚⠀⠚⠂⠺⠃
⠇⠰⠗⠐⠗⠀⠖⠀⠒⠀⠐⠀⠐⠂⠐⠂⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠐⠂⠐⠂⠐⠆⠀⠖⠀⠶⠀⠲⠂⠺⠆
⠆⠰⠷⠐⠶⠀⠶⠀⠶⠀⠲⠀⠰⠂⠐⠆⠀⠆⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠀⠰⠆⠰⠆⠀⠆⠀⠶⠀⠶⠀⠶⠆⠾⠆
⡦⠰⡶⠰⡶⠀⠶⠀⠶⠀⠴⠀⠰⠆⠰⠆⠀⠆⠀⠆⠀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠤⠀⠰⠀⠰⠄⠰⠆⠠⠦⠀⠶⠀⠶⠀⢶⠆⢶⠆
⡦⢰⡶⠰⡶⠠⣶⠀⣶⠄⢴⠄⢰⠄⠠⠄⠠⠆⠀⠤⠀⠤⠀⠤⠀⠠⠀⠀⠀⠀⠄⠀⠄⠀⠤⠀⠤⠀⠠⠀⢠⠄⠠⡆⠠⡦⠠⣦⠀⣶⠄⣶⠄⢶⡆
⣦⢰⣦⢠⣦⠠⣶⠀⣶⠄⣴⡄⢠⡄⢠⡄⠠⡄⠀⡤⠀⡤⠀⠤⠀⠠⠀⠠⠀⠀⠄⠀⡄⠀⣤⠀⢤⠀⢠⠄⢠⡄⢠⡄⢠⣦⢠⣦⠀⣴⠄⣴⡄⣴⡆
⣦⢠⣦⢠⣦⢀⣤⠀⣤⡄⣤⡄⢠⡄⢠⡄⢠⡄⠀⣤⠀⣤⠀⢠⠀⢠⠀⢠⠀⠀⡄⠀⡄⠀⣤⠀⣤⠀⣠⡄⢠⡄⢠⡄⢠⣤⢠⣤⢀⣤⠀⣴⡄⣴⡄
⣥⢨⣥⢠⣥⢀⣥⡀⣤⡀⣬⡄⣠⡄⢠⡄⢀⣄⢀⣄⠀⣄⠀⣠⠀⢀⠀⢀⡀⢀⡀⠀⣄⠀⣄⠀⣤⠀⣠⡀⢠⡄⢠⣄⢠⣥⢀⣤⢀⣬⡀⣬⡄⣬⣅
⣅⣨⣭⢨⣭⢀⣭⡀⣭⡀⣬⡀⣨⡅⢨⡅⢀⣅⢀⣅⠀⣀⠀⣀⠀⢀⠀⢀⡀⢀⡀⠀⣀⠀⣀⠀⣀⠀⣨⡀⣨⡅⢨⣅⢀⣅⢀⣭⢀⣭⡀⣭⡅⣭⣅
⣏⣨⣯⢈⣭⢀⣭⡀⣭⡁⣩⡁⣨⡁⢈⡁⢈⣁⠀⣁⠀⣉⠀⣈⠀⢈⠀⢀⡀⢀⡁⠀⣁⠀⣉⠀⣉⠀⣉⡀⣈⡁⢈⡅⢈⣍⢈⣭⢀⣭⡀⣭⡁⣽⣅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢂⡉⠤⠐⠒⠣⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠑⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢓⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢲⠆⠀⠀⠀⠀⠀⠀⠰⠸⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠆⡆⠀⠀⠤⠀⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠖⠲⢦⣰⣠⣀⣀⠀⠀⢸⠀⠉⣛⡋⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣰⣁⡤⠤⠤⢤⡀⠀⠈⠙⢒⣺⣤⢞⣁⡙⠢⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⢀⣠⣤⣤⣤⠤⠤⠀⠀⠿⠦⣤⣋⣡⣀⠀⠀⠀⠙⠲⠒⠚⢣⡼⠋⠁⠀⠈⠉⠲⡄⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠈⢧⡀⠀⠀⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠹⢇⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⣴⠯⣄⣀⣀⣀⣉⣙⣆⣀⣏⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⣤⣄⣄⣙⣦⣖⣉⣉⣹⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⣸⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⠒⠒⠒⠲⠶⠶⠒⠒⠂⠁⠀⠀⠀⠙⣦⣿⠀⠀⣿⠇⠀⠀⣿⠀⠀⠀⣿⠀⠸⣿⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⠈⣷⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠒⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠰⡏⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⣽⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⡼⠉⢳⣤⠤⠶⣄⣀⣀⠀⠀⣀⡴⢻⠀⡇⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢹⠀⠀⡿⠀⠸⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⢀⣀⠄⠉⢹⠀⡞⣸⠃⠘⡇⣷⠀⢿⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⣿⠀⢠⡇⢸⢆⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠂⠀⠁⠈⠢⠄⡾⢸⣡⠇⠀⠀⢷⢸⡄⢸⡄⠀⢸⠀⠀⠀⡇⠀⠀⠀⡟⠀⢸⠃⡞⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⠂⠀⠀⣼⠃⣸⠏⠀⠀⠀⠘⣆⢳⡀⢧⠀⠈⡄⠀⠀⠀⠀⠀⢠⠃⠀⡞⣸⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠤⡠⠀⠒⠉⠛⢚⡟⠀⠀⠀⠀⠀⠹⣄⢳⡈⢣⠀⠐⠀⠀⠀⠀⠀⠌⢀⠌⡰⢣⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⡀⠀⡠⠤⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠘⢦⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⡈⠠⣤⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡙⠲⠤⣤⣤⡤⠶⢚⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠴⠤⠂⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠦⠤⢶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠒⠂⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠃⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⣠⠎⠀⠀⢧⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡐⠁⠀⠀⠀⠈⠃⠀⣀⣀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣰⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡎⡧⠀⠀⠘⡒⠉⠀⠠⣄⠤⠦⠠⢹⠚⣨⣌
⠀⠀⠀⠀⠀⡾⢋⡟⡿⠇⣿⣿⣿⣿⣿⣶⡀⠀⠀⠠⣄⣀⣀⡀⠀⡘⢀⣀⠀⠁⠀⠠⠄
⠀⠀⠀⠀⠀⡇⠘⠃⢃⠶⣿⣻⠟⣟⢹⡉⠷⠀⠀⠀⠉⢹⡿⠁⣄⠁⠀⣈⠀⠰⠆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢿⠘⠀⠘⢀⣡⠀⠀⠀⠀⢐⣀⠇⠀⣍⠢⢤⡈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡅⢆⣌⣀⣠⣔⣫⠷⠀⠀⠀⠀⠀⠀⠀⠀⠟⡷⣦⣬⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⣡⠩⢻⣶⡇⠀⠀⠀⣤⣤⠀⠀⠈⡘⢀⢎⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⠏⠅⢊⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡖⡎⠌⡔⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣬⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⡁⠴⡁⢈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠩⢽⢉⠉⠉⣿⡿⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡞⡀⠱⢀⢉⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣶⣾⣼⠔⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⡻⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣎⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣯⣽⣟⣻⣿⣿⣻⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⣿⡿⠿⠿⠿⢿⣿⠿⣿⣿⣛⣻⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣽⣛⣻⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣟⣻⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣽⣛⣛⣻⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣭⣽⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⡻⢟⣿⣿⣿⣽⢿⣟⣽⣽⣽⣛⡻⣿⣿⣿⣿⡿⣻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣭⣵⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⡟⠳⣭⡿⣿⣵⣝⣿⣞⣿⡿⣵⣿⢟⣼⣫⡽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⣿⣶⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣩⣴⣶⣶⣦⣝⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠷⣤⢤⣤⣤⣤⢤⡤⣤⠾⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣘⠛⡛⣛⡛⢛⡛⢛⠛⣡⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣦⡜⢣⡜⢣⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠛⣧⡟⢧⡼⠋⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⢣⡜⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⡆⢧⡽⢯⡍⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⡄⡽⠯⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠼⠶⠶⠶⠷⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣤⡞⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⢤⡴⠃⠀⠀⠈⠉⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⣶⠶⠋⠉⠀⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⢶⣶⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⣤⣄⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠦⣶⣶⣦⠞⠧⣍⡉⠹⡄⠀⠀⢠⡇⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡴⠚⠁⠀⠀⠀⣩⠟⠻⠿⣷⣋⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠓⠦⣄⣠⠞⠁⠀⠀⢀⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣠⠞⠉⠛⠶⢤⣴⠋⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣄⡀⠀⢀⡴⠞⠉⠉⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⢙⡶⢯⣀⡀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀⠈⣩⢷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡴⠋⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠓⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡼⠃


⣿⣿⣿⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣟⣛⣛⣿⣛⣿⣻

⡀⢠⣄⣀⠀⠀⠐⠀⡀⠀⠀⠀⣟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⠴⠊⠀⠀⠀⠀⠀⠈⠈⠒⠲
⠉⠉⠘⠛⠿⠂⠀⠀⠀⠀⠀⠀⠈⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⠠⠶⠒⠁⠀⡀⠤⠤⢤⣠⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⡄⠒⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⡃⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠠⠒⠳⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠰⣇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣦
⠀⠀⠙⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢀⠀⡠⠈⠄⡀⠁⠀⢀⠀⠀⠀⠀⠀⠄⠙⡀⠸⡁
⡤⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣤⢀⡀⠀⠒⢓⡠⢒⠑⠈⠀⠀⠀⠰⠀⠄⠠⠄⠂⠀⠀⠀⠀⠈
⠹⡎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠹⠀⠀⠀⡁⠠⡉⠉⠀⠀⠀⠀⠀⠀⠀⠉⡀⠉⣀
⠀⠘⠦⠀⠀⠀⠀⠄⢠⠐⠄⠀⠐⠁⠀⠂⠀⠀⠠⣄⠀⡀⠀⢠⠟⠚⠀⠀⠀⠀⠂⡑⠈⢀⠀⠀⠀⠀⠁⠀⠂⣀⠀⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠘⠰⠀⠢⠀⠀⠈⠀⣄⠐⠢⠒⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠛⠈⠂⢂⠀⠀⠀⠀⠀⠀⡺⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⢛⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠉⠀⠀⠈⢣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠳⠴⣦⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢈⠓
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠖⠋⠏⠀⠀⠀⠁⠀⠈⠫⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡀⡀⠀⠀⡀⠐⠠⡤⠀⠤⠢⠈⢳⠀⠀⣌⣓
⠀⠤⠄⠀⠀⠀⡴⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠖⠀⡆⢀⠈⠀⠀⠈⠂⠀⢄⠀⠀⠀⠀⠈⠐⠀⠠
⠀⠀⠀⠀⡰⠚⠀⠀⠀⠂⠒⠓⠂⠀⠀⠀⠀⢀⠄⠠⠒⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠤⠂⠄⠁⠀⠀⠀⠀⠀⠀⠠⠀⠄⠁⠀⠀⠀⢀
⠄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠐⠀⠀⠀⣸⠒⣀⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠚⣉
⠔⠲⡀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣤⣼⣄⠤⠂⠉⠂⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠘⠀⠀⠀⠀⢀⠂⠄⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠚⣀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠆⠠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠺⣧⣦⡀⠀⠙⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡀
⠀⠀⠀⠀⠐⢄⡀⠈⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠈⠓⠟⢠⠀⠈⠀⠔⠀⠀⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠈⢧⠀⠓
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠷⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⡽⠀⠀⢣
⠀⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠑⠂⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠐⣥
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⡠⠃⠀⠈⠀⠁⠂⠐⠀⠒⠀⡠⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠘⠁⠈⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⡠⠀⠀⠀⠀⠲⠖⠎⠁⠀⠀⠀⠀⠀⠐⠂⠐⠄
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠐⡢⠁⠀⠂⠀⠀⠈⣧⠀⠀⠈⠀⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠄⠒
⠀⡀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⣠⠊⢀⡍⠒⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠂⣀⡐⢀⠀⠀⠀⠀⠐⠀⠒⠀⢀⠀⢀⠚⠁⠀⠀⠘⡀⡀⠀⠔
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠰⠟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⡧⠾⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⡟⠰⣖⠠⡄⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠆⣴⣾⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣶⣄⣀⠀⠀⠀⢠⣄⠀⢀⣀⡤⢶⡤⢆⣸⣿⣝⠿⣿⡿⠿⢿⣻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠿⢞⣉⣉⡙⠓⣦⡤⢸⡿⢷⣾⠟⠃⠈⠛⣛⣿⣿⣙⣷⣤⣶⣾⣿⣯⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡟⠿⠻⠿⣷⣼⣶⠀⣦⣸⣧⣶⣄⣠⣼⣿⣽⣿⣿⣿⣿⣿⠉⢙⢿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡽⠋⣹⣷⠂⠀⠉⠡⣿⣷⣦⣤⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡉⠋⢰⣷⡤⠈⠉⣿⣟⣫⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠿⠁⠀⠀⠀⠀⠈⠀⢀⡄⢀⡀⠛⠉⣿⣿⣿⣿⣿⢿⡷⠀⠘⣿⠂⠀⠀⠻⠛⣿⣏⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠁⣾⡇⠀⠲⠾⣿⣈⣹⣿⣿⣶⠂⢠⡁⠀⢀⣴⡆⢈⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⣶⣿⠄⣿⣿⣿⡏⠀⡈⠀⠀⠀⠉⠀⠊⢡⠸⡟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠁⠀⠀⠀⠀⢂⣀⠀⡆⠀⢀⠈⠟⣾⣿⣿⣿⣧⠀⠛⠆⠀⣠⡴⠶⢀⣤⠀⠶⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⣶⠎⠀⠀⠀⠀⢰⣿⠛⢛⠆⢀⡄⢀⣼⣿⣿⣿⣿⣿⣀⠀⠀⢀⠙⠁⠀⠀⠉⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠃⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠁⠀⣉⢀⣸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢘⣦⠤⣴⣷⠞⠻⢯⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⣴⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡘⠾⠙⢴⣿⣷⣾⣶⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⡀⠀⠀⠀⠰⢞⠁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣇⣼⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⢹⣿⣷⣦⣶⣦⣼⣶⣿⣿⣿⣿⠿⠿⢿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠿⣿⡟⢋⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡉⣩⡉⠉⣠⡄⣤⣼⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⢿⣧⣼⣿⣿⠷⠾⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠙⢦⣿⣿⣿⣿⡇⠉⠿⠟⢻⣿⠳⣿⣿⡿⠋⢽⣯⣱⣿⣾⣧⡞⢸⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠛⣿⡷⠀⠀⢀⣨⠿⠀⠙⠋⣴⠾⣾⡷⠈⢹⡿⢋⣽⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠀⠀⠙⣁⣠⣦⡄⠀⠈⢠⣿⣧⡈⢀⣾⣛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠋⠁⢠⡀⠀⠈⣁⣠⠟⠲⠆⢠⣾⣿⡿⣆⠙⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣧⠀⠈⠛⠁⢠⣤⣠⠀⢹⡏⢴⠋⡄⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠋⠀⢀⠀⠀⠀⠀⠙⣧⡄⠈⠱⠞⣠⣿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠹⣷⠀⠀⠠⠀⠛⢛⣤⡀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠀⠀⠰⣶⠿⢟⣷⡞⢁⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢁⣠⡄⣶⡀⠈⠀⣿⡿⠃⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢉⣿⡴⠀⡙⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠖⠀⠀⢠⠎⢀⠀⠋⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡆⠀⢀⣤⣠⣴⢿⣦⣂⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣠⣄⠰⡟⠋⣿⣾⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠹⣦⡉⢓⡉⠯⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠠⡔⠛⢁⣸⣅⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⢀⣶⠟⠹⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣤⣈⡡⠦⣴⣿⣛⠇
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡛⠁⠀⡜⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⡘⠃⣤⣴⣟⣻⠁
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⡀⢉⣽⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠾⠛⢿⣅⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠰⠾⠛⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣺⣹⠇
⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣶⣍⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣩⡿⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣰⠏⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠇⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⡟⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠷⡄⠀⢸⠁⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠘⢦⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠶⣤⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⢈⡙⠲⠤⠄⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⠙⠲⢦⣤⡀⠀⠈⠙⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⢄⠀⠀⠀⠤⢄⡀⢀⣀⡀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢦⠈⠙⠶⣤⣄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣠⡶⠛⣿⣇⠈⠑⠤⣀⠀⠀⠉⠛⠃⠤⠶⠦⠤⣀⣀⣀⣠⣿⣀⣀⣀⣼⠃
⠀⠀⠀⠀⣠⡾⠋⠀⣼⢿⡟⣤⠀⠀⠈⠑⠢⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠳⢦⣤⡀
⠀⠀⠀⣴⠛⠀⠀⣾⠁⠘⢧⡈⠳⣄⠀⠀⠀⠀⠈⠛⠛⠓⠶⠦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⢀⡟⠀⠀⢸⡏⠀⠀⠈⣥⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠶⣄⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠙⢦⡀⠀⠀⢼⠟⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⢼
⠀⠀⢸⡇⠀⠀⠀⣿⡀⠀⣠⠀⠀⠹⣤⠀⠀⠐⠛⠁⣨⡿⠛⢷⣶⠆⣤⣤⣄⡀⠀⠀⠙⠂⠀⠀⠀⢀⣼
⠀⣰⠿⣷⠀⠀⠀⠈⢷⡀⠀⠴⠦⠀⠈⠻⢦⡀⠀⠀⠉⠀⠐⠛⠁⣰⠟⢁⣸⠿⠛⠛⣷⣶⣤⣀⢀⡾⠃
⣾⠋⠀⠈⣧⠀⠀⠀⠈⠻⣦⡀⠀⠲⠶⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠀⠘⠁⠀⢠⠾⠋⠁⠀⠉⠻⣧⡀
⣿⠀⠀⠀⠈⢷⡄⠀⠀⠀⠈⠻⢦⡀⠀⠶⠶⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠈⢻
⠹⣆⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠈⢻⡄⠀⣠⠶⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂
⠀⢻⣆⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠷⠀⠀⠴⡶⠦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠙⠛⢻⣶⣤⣀⣀⣻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣭⣭⣽⡿⠲⠶⠖⠒⠀⠐⠒⠚⠓⠀⠲⠶⠶⠶⠶⠾⠿⢿⣯⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣇⡘⠋⠀⠀⠀⢴⡆⢠⡶⠆⠰⢶⡞⢛⣿⠟⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⠿⣇⠀⠀⠀⠀⠈⣷⡆⠀⠀⠀⠀⣸⣿⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢀⣠⡾⠃⠀⠈⢇⡀⠀⣠⠞⠁⠙⣤⠀⢀⡾⠃⠈⠳⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣏⠀⠀⠀⠀⠈⢱⡾⠉⠀⠀⠀⠀⣶⡏⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠙⣆⠀⠀⢀⡴⠛⠛⣦⠀⠀⣠⠞⠁⠘⠦⡀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⢢⣴⠟⠁⠀⠀⠈⢳⣾⠁⠀⠀⠀⠀⣹⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣰⠟⠳⣄⠀⠀⠀⣠⠟⠙⢦⡀⠀⢀⡾⠁⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠟⠁⠀⠀⠙⠦⣀⡾⠋⠀⠀⠀⢱⣶⡏⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⣰⠿⣁⠀⠀⢀⡴⠛⠀⠙⢦⣀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢦⣀⣠⠞⠁⠀⠈⢳⣤⠞⠁⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣠⠿⣧⠀⠀⠀⢀⠜⠛⠳⣄⠀⠀⣴⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠈⠳⣄⡴⠋⠀⠀⠀⠈⢳⣾⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠟⢧⡀⠀⠀⢀⡴⠋⠈⠳⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣠⡾⠉⠀⠀⠙⣦⣴⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡄⠀⠀⠀⣤⠛⠛⢦⣀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠙⣄⣠⠞⠁⠀⠀⠀⠙⣶⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⡾⠻⣄⠀⠀⠀⢀⡴⠋⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠈⠷⣀⡴⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⡴⠛⠳⣄⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣤⡴⠋⠀⠀⠀⠈⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠟⢷⣄⠀⠀⡠⠞⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⣶⣎⠁⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡴⠞⠀⠈⠻⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⣦⡀⠀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⣹⣾⣁⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣅⣠⡿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡿⠛⠻⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⣹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣹⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠟⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠛⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⢸⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢹⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢤⡀⠀⠈⠃⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠢⣄⠀⠀⠃⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠳⣄⠀⠀⠈⠛⠶⠤⣄⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠻⣦⡀⠀⠈⠙⠓⠶⠤⣄⣀⡟
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠈⠉⠳⣤⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠙⠢⠄⠀⠀⠀⠀⠀⠉⠛⢦
⠀⠀⠀⠀⠀⠀⣰⠏⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡏⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⡾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢈⡛⠻⠷⣶⣶⣶⣶⣶⣶⠾⠿⠛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠈⣫⡍⠉⢉⣽⠏⠁⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⣶⠶⣦⣤⡤⣀⣴⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠉⢀⣹⠶⠋⠁⣀⠼⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣭⣶⠙⣡⣾⣿⣿⠟⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠞⠋⠁⠀⠔⠛⢅⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣋⣴⣿⣿⢟⡋⢵⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠠⢄⠀⢀⣠⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣿⣿⣿⣷⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠙⠳⢤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣎⣛⠩⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠢⣄⡴⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣬⣚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢡⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⠀⠈⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⡄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠄⠀⡀⠂⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢀⠎⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢛⡰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠹
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠉⢠⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠎⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⢀⡴⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⠀⠒⠉⠀⠀⠀⣀⠤⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠙⢶⡶⠠⢤⡴⠶⠚⠉⠛⣇⠀⠈⡙⠁⠈⠳⢄⡠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⢠⡀⡴⠀⠐⠀⠀⠈⠳⡄⠀⠀⠀⢀⠌⠁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠀⠘⡀⠳⡀⠀⠀⣠⠂⠈⠂⠀⡀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⢨⡇⠀⠀⠘⢠⠜⠁⠀⠀⢀⡜⠁⢄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠐⠄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠞⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜⠂⠀⠀⠀⠀⠉⠰⣄⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⠀⠆⠀⠀⠀⠀⣀⠝⠂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢀⡰⠊⠀⠀⠀⠀⣀⠞⠁⠀⢠⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠑⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠒⢆⠀⠀⢀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠈⡲⠊⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠈⠀⠀⠈⠐⠞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠠⢀⢀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡠⠉⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠶⠈⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠖⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡟⠃⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠋⠁⠀⠀⠀⠐⠀⠀⠀⠀⢰⡠⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠊⠀⠀⢀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⢀⡔⠁⠀⠀⡸⢧⡤⠋⢱⡀
⠀⠀⠀⠀⠀⠐⠶⠀⠀⠛⠖⠀⠀⢀⣀⣀⢠⡤⢍⠈⢀⣈⠂⠀⠀⠀⠀⠀⠀⠂⠙⠦⠤⠒⠉⠁⠤⡔⠊⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣤⡄⢠⠀⠈⠀⠀⠀⠀⠘⢀⠋⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢠⠊⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡼⣀⠀⠀⢀⣰⠁⠀⠀⢀⣆⠀⠁
⠀⠀⡀⠄⣠⣤⢀⣀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠉⠋⠚⠋⠀⣳⠶⣶⣿⠁
⠀⠀⠀⠈⠁⠀⠀⢰⡃⠀⡤⠁⠀⡀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠠⠘⡳⢞⣷⡏
⠀⠀⠀⠔⣀⡀⠀⠀⠀⠈⠰⣇⠀⠀⠀⠁⣸⠒⠠⠤⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠀⢈⠐⢨⣕⣣⣼⠁
⠀⢀⠀⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠠⠐⠠⠄⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠐⠮⣭⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⠉⠒⠢⢀⣀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⢠⠛⠶⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⡡⠄⠀⠀⠀⠀⠁⡜⠻⢦
⠀⠀⠀⠀⠀⠀⠀⢋⣠⠟⠂⠐⠒⠆⠀⠀⠦⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣤⠀⠀⠌
⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠔
⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠐⠒⠀⠀⠀⠀⢈⡇⠘⡣⠄⠀⠀⠀⠀⠀⠀⠀⠰⠒⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠓⠋⠀⠃
⠀⠀⠀⠀⠘⠓⠆⠠⣄⣀⢀⡀⢀⣠⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠤⠒⠂⠀⠐⠂⠀⠀⠀⠀⠐⠒⠒⠚⠿⢿⠓
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠒⢈⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠠⠀⠠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠠⠀⠀⠀⢀⠀⣀⠠⠇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⡄⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⠀⠄⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠀⠀⠀⠀⠀⢠⢸⠃
⠀⠀⠀⢠⠄⠀⠀⣀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣼
⠀⠀⠀⠘⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠄⠀⠀⠠⠤⠔⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠶⠤⢤⣀⠀⠀⠀⣀⣠⣀⣀⣀⣙⣦⣰⠟⠉⠁⠀⠒⣁⠰⠟⣳⣴⡾⠛⠛⠙⠙⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡨⠛⣦⡀⠀⢀⡰⠜⠉⠉⢈⡧⠀⠀⠀⠀⠈⣉⣙⣿⠟⢧⣔⣄⡀⠀⠄⠐⠢⡌⢻
⠀⠀⠀⠀⠀⠀⠞⠀⠀⢀⡶⠛⠛⠛⡳⣏⠀⡠⣈⢿⡌⠁⠀⠐⠈⠁⣤⡠⡤⢤⣤⠤⣤⣤⣼⡉⠙⠲⠈⠈⣿⣿⣿⣷⣄⣨⣾
⠀⠀⠀⠀⠀⢀⡄⠀⠀⣎⠀⢀⣄⡠⠁⠈⣿⡍⢁⠄⢟⢁⣤⠶⢛⣁⡤⠀⠒⠒⠒⠒⠂⢸⡏⣉⠲⢦⣤⣾⠿⣟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠙⠻⠟⢻⣧⠀⡚⠈⠐⠁⣠⡾⠋⠡⢒⣭⣴⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⠢⣝⣿⣶⡄⠹⡝⠻⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣤⣴⠾⣇⠌⠠⠈⢠⣾⠉⡶⢾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣏⢿⣄⠘⡄⠘⣥
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣠⠄⢡⡞⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡿⣿⣕⢳⡤⠾
⠈⠢⡀⠀⠀⠀⠀⠐⠤⠦⠄⠤⠔⢒⠋⢠⡞⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣧⢹⢸⡏⠈⡟⢻
⠀⠀⠈⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⠷⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⢸⠆⣿⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠙⠓⠲⠒⠒⠖⠲⠋⢩⡉⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⢷⣾⣼⣷⢀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣫⣿⠋⣻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣆⢿⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢊⣴⣿⢁⡼⢡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣦⡓⣌⠛⢿⣿⣿⣿⣟⣻⣭⣾⠟⠉⣠⢞⣀⣟⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⣇⠹⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⠦⣬⣉⣁⣉⣉⣭⡤⢞⣛⣵⣿⣿⡟⣡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣥⣴⣷⠶⣿⣻⣻⣿⠛⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠉⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⢿⣥⢾⢛⡻⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠦⠀⠀⠑⠛⣷⣶⣾⣻⣟⣛⣿⣿⠿⣿⣟⣛⣛⣯⡷⣶⡛⣍⠿⠛⢗⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⢀⠀⠀⢈⡋⡾⠟⡻⢾⣯⣿⣿⣯⣿⣭⣭⠭⠷⠞⣙⣳⡶⠶⠾⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠠⢿⡗⠠⠀⡉⠀⠚⠉⠹⠄⢿⠄⠠⠞⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⢀⣠⡾⠋⢀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠛⢻⣿⠏⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⢿⣧⣴⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣦⣶⠾⠷⠶⠟⠋⠉⠛⢿⣄⠀⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠛⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⣸⠿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠾⠟⠁⠀⠀⠰⠏⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠛⠉⠉⠉⠉⠉⠁⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠙⠻⠿⣶⣤⣤⣀⣀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⣠⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣧⡀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠙⣿⣤⣀
⠀⢀⣤⣶⡿⠿⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⠙⠛⠛⢿⣦⡀
⢀⣾⠟⠁⠀⠀⠀⠀⠈⠛⢷⣶⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⢻⣦⠀⠀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠛⠻⣶⣤⣀⣀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⢷⡄⠀⠀⠀⠀⠀⠸⣿
⠀⢻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⣼
⠈⢿⣦⣀⣶⣄⠀⠀⠀⠀⢀⣀⣤⣶⠷⠶⣶⣦⣄⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⣶⣄⣀⠀⠀⠀⣀⣀⣴⣿⣀⣀⠀⠀⢀⣀⣀⣴⣿⣧⣤⣶⣿⠟
⠀⠈⢻⣿⠛⠛⠷⠶⠶⠶⠛⠛⠁⠀⠀⠀⠀⠀⠉⠛⠷⢶⡶⠶⠿⠛⠻⠶⠶⠶⠾⠛⠋⠈⠙⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⢸⡏
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⡿⠷⣶⣦⠀⠀⠀⠀⠀⠛⠿⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁⠀⠲⠿⠿⠷⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡆⠀⠀⠀⠀⠀⢀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣇⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠋⠀⠀⠀⠀⠀⠘⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⡾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠛⠉⣁⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠶⠷⠆⠀⠀⠀⠀⠀⣉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠈⠁⠀⠈⠀⠀⢠⠄⠀⠈⠀⠁⠠⠤⠀⠠⠤⠀⠈⠁⠠⠄⠠⠇⠠⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠠⣤⠤⠾⠀⠈⠀⠁⠀⠁⠰⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡷⠛⠻⣿⣿⣮⣵⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣼⣿⣿⣿⣽⣯⣿⣿⣿⡟⣿⣿⣿⢟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣻⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣯⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⠟⣩⣿⣿⣿⣿⣿⣟⠻⣿⠟⣩⣍⠻⣿⢟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠺⣿⣿⢿⣿⣯⣿⣿⠗⣀⠺⣿⣿⠗⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠌⠡⣾⣿⣿⠌⠡⣾⣿⣷⠌⠡⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣷⣌⠛⣡⣾⣷⣌⠛⣡⣾⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⣡⣶⣌⠻⠟⣡⣶⣌⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠻⣿⠟⣡⣌⠻⣿⠟⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⣀⠺⣿⣿⠗⣀⠺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠌⠡⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣡⣾⣷⣌⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠻⠟⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣡⣄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣳⣿⣿⢹⣿⣿⣿⢿⣿⣾⣿⣿⣿⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣣⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣮⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣿⣮⣵⣿⣿⣿⣿⣷⣛⣿⣏⣿⣿⣿⣷⣝⣯⣿⣿⣿⣮⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡿⠿⢿⣿⣿⣿⣿⢿⡿⣿⢿⡿⣿⠿⢿⡿⢿⡿⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡟⢻⣿⣿⠻⣿⡿⢻⣿⣿⡛⢿⡿⢻⣿⣿⡟⢿⣿⠟⣿⣿⣟⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡷⠀⠰⢿⣿⣿⡷⠀⠀⢾⣿⣿⡿⠆⠀⢾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠛⢋⣴⣿⣷⣄⠙⠋⣠⣾⣷⣄⠙⠛⣡⣾⣿⣦⡙⠟⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣈⠻⣿⡿⠋⣠⣄⠹⢿⡿⠟⣠⣄⠙⢿⣿⠟⣁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡦⠈⠠⣾⣿⣿⣷⠀⠁⢾⣿⣿⣷⠄⠁⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣾⣷⣌⠻⠋⣠⣾⣷⣄⠙⠟⢁⣴⣷⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⣠⡈⠻⣿⣿⠟⢁⣄⠙⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⣾⣿⣿⣧⠈⠁⣴⣿⣿⣷⠄⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡈⠻⠟⢡⣼⣧⡌⠻⠟⢁⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣀⡀⠻⣿⣿⠟⢁⣀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠈⠁⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⢁⣴⣦⡈⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢿⣿⣿⡿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠙⠋⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏

⣿⣿⣷⣄⠀⠀⠙⣧⡻⣴⠟⠒⢺⣠⡆⠍⣓⢭⢿⣯⣼⣻⣿⣿⣿⣷⢙⣿⣯⣭⡝⠃⠀⠀⣿⠋⢰⡆⠉⣿⡄⠙⠿⠈⠟⠹⣧⢶⣄⣾⠃⠈⠴⡟⠀⠈⡛
⣿⣿⣿⣿⣿⣶⣯⣅⢀⠽⠿⠁⠄⠽⢦⡄⠈⣷⣆⣿⡟⣭⣯⣿⣾⣿⡾⣟⣋⡮⣥⣠⠖⠖⢨⡆⠀⠠⠀⣈⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⢠⡀⠙⠄⠀⡸⢧
⣿⣿⣿⣿⣿⣿⠻⢿⣏⡙⣥⣤⠀⠀⠀⠉⠀⠏⠈⡍⢲⣭⣦⣿⣿⣥⣽⣬⣻⡹⢯⡝⠀⣀⣸⣷⢶⣆⣦⠈⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⡄⠁⢳⡘⠋⢠⣬
⣿⣿⡿⠛⠛⢛⣷⢾⣿⡟⢸⠟⠻⠟⠃⠀⠈⠀⢨⡟⠛⠦⠀⠉⠉⠀⠁⠈⠙⠛⠀⠀⠐⢯⠙⠙⣿⢏⠟⣄⢀⡸⢣⡄⠀⠘⠦⠀⠄⠀⠀⣠⣼⡷⠖⠟⠋
⣿⣿⣿⣷⣶⣿⡇⣸⣿⣧⣿⠿⢃⣠⢤⡃⠀⡴⠮⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⣠⠆⠰⠟⠚⠀⢀⣌⠁⠀⠀⠁⣄⣠⣀⠀⣀⠀⢹⠟⠀⠂⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣾⠷⠟⣭⢹⡶⠛⠛⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠉⡰⠿⠤⣠⠄⢹⡇⠀⠁⠀⠈⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⠚⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣱⣴⡇⢾⣇⣻⠁⠀⠀⠀⣤⠀⠀⠀⠀⢐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣿⣰⣧⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡔⢟⢭⣥⡿⣯⣯⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣀⣴⡄⠀⠀⠀⠀⠰⠒⠛⠛⠂⠀⠀⠀⠀⠀⠘⠂⠀⢠⡩⠶⠎⢾⡉⠝⠓⡾⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣥⠀⠀⠀⠀⠀⠘⠖⠠⠄⠀⠀⠀⠉⠀⢀⠀⠘⠦⠀⠀⠀⠘⣃⣠⢸⡇⠀⠰⠂⠀⠀⠀⠰⣿⡄⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣉⣥⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠒⠀⠀⢀⣤⡰⣎⠉⠀⠘⠀⠀⢀⠀⠀⠀⠀⠠⣼⠷⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⠖⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⣠⡄⢀⡴⠂⠀⠀⠀⠀⠀⠀⠴⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⣋⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠈⠁⢠⣄⠀⠲⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣵⠂⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⢠⣷⣿⡅⣘⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⡎⢸⡿⠋⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣦⠴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣶⡟⠟⠢⢠⢁⠀⠀⠀⠀⢀⣦⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠾⢫⣷⢥⣀⡀⡈⣇⣛⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠛⠋⣉⡁⣿⢡⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠇⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠛⢠⣆⣠⠀⠈⢿⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠓⠓⢹⣰⡟⢷⣽⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡉⢳⣶⣿⣯⣷⣶⡾⠿⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⣱⠺⠿⣍⢣⣴⣿⢧⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢀⢌⡻⠸⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣩⠉⠀⡀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀