Invertebrate Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢠⡄⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠐⢣⠀⠀⠎⠆⢀⡄⠀⢸⢸⠀⡇⠃⠁⠀⡇⠀⠀⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⢸⠀⠀⠄⡄⡀⢠⠀⠈⢸⢀⠀⠇⠀⠀⠇⠀⣠⠀⠀⠀⠀⡆⠠⢢
⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠈⠘⠀⣀⠀⡇⡇⢸⠀⡀⠐⠘⢸⢸⠀⠀⠀⡞⠀⡇⢰⠀⢀⢀⠃⡀
⠀⠀⠀⠀⠀⠇⢁⠀⠀⢸⠀⠀⢰⠀⠀⠀⡇⠸⠀⠀⠃⠀⠌⠘⠀⠀⡿⠀⠀⠃⢸⠀⠘⠀⠀⠅
⠀⠀⠀⠀⠀⡆⠀⡆⢡⠀⡇⠀⠈⠀⠀⢰⠀⠀⢀⢸⠀⠀⡇⡀⠃⢀⠃⠀⢰⠀⡆⠀⡄⠀⡘⠠⠓⢀⠎⡁
⠀⠀⠀⠀⠀⠸⡀⢱⠘⡄⢱⠸⠆⠀⢇⠸⡄⢀⡈⠸⠀⠰⣮⢹⠂⢰⢰⠀⡈⢀⠇⢰⠘⢠⢃⠀⠀⡌⠐
⠀⠀⠀⠀⠀⠀⢃⠀⢇⠱⠘⡀⢀⠀⢸⠀⣷⢸⡇⢠⡔⡀⣿⢰⢁⢸⠸⠀⡇⠸⠀⡆⠆⡆⡌⡜⠰⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠂⢥⣌⠷⠚⠁⠉⠉⠉⠉⠓⢾⣇⢸⠸⢸⠀⢰⠀⠇⢰⠸⠸⡰⠰⢡⢡⡢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠰⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣴⠀⣆⡺⡘⠀⣼⢃⢣⠃⠡⠣⠃⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠿⠲⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣻⠾⠧⠀⣿⣸⡆⡴⢁⡷
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⠂⠬⠍⠈⠉⠉⠩⠵⠶⠶⠦⠒⠉⠀⠀⠀⠀⠀⠀⡟⠓⢾⣡⠁
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡰⠁⠀⠀⠈⠁⠢⡄
⠀⠀⠀⠀⢀⠎⠉⢆⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⢊⠥⠊⠀⠀⠀⣀⣠⠔⠀⡸
⠀⠀⠀⠀⠸⡀⠀⠀⠑⠢⠭⠭⠀⠠⠤⠤⠔⠒⠒⠈⠉⠉⠑⠒⠒⠒⠒⠉⠁⠀⢀⡤⠖⢉⡀⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠉⠲⠤⠄⠀⢀⣀⣀⣀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠤⠴⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⣈⣁⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡘⣆⢠⠎⣠⢄⢡
⠀⠀⠀⠀⠈⠀⠀⠈⠁⠒⠌⡑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣜⣀⡮⢼⠞⠁⡴⠒⠚⢆⢳⠒⠀⠤⠤⠤⠤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢽⣲⣤⡴⠒⢒⡖⠉⠁⠀⠀⠀⡠⠛⠒⡠⠖⠁⢀⡎⠀⠀⠀⠈⢆⢣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⢷⠁⢧⠀⠀⢀⣀⠔⣠⠔⠋⠀⠀⢀⠎⠉⠉⠁⠒⠒⠚⢦⢣⣀⣀⣀⠠⣤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⡀⠣⢴⢿⢆⡘⡍⣾⡇⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠣⡤⠤⠔⠚
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠋⠀⠑⡶⢊⠾⣈⠧⢶⠛⠉⠉⠉⠁⠉⠙⠓⠒⠒⠒⠂⠈⠛⠟⠛⠓⢔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣔⠕⠁⠀⠀⠀⠈⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠙⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢢⡀⠀⠀⠀⠀⣠⠴⢦⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠿⣦⣠⣠⡿⢿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⣿⡏⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠙⠀⣀⣠⡷⠀⠀⠈⠣⢶⣒⠀⠁⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠈⠢⣀⠀⠄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠤⠀⠀⣀⡀⠐⣠⠄⣀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠃⢤⡇⠔⠊
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⠐
⠀⠀⢀⡞⠉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⡀⣼⣅⡝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠑⠬⠉⠐⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣶⠍⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠁⢪⡢⣀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⢀⠔⢢⠀⠀⠐⢤⡀⠀⠀⠀⠀⠉⢎⢂⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢠⣾⡀⠠⡧⠀⠀⠀⢧⡄⠀⠀⠀⠀⠀⠓⡡⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡟⡛⠀⠀⣃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠒⡥⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠉⠁⠀⠠⠇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⡁⠀⢀⠜⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠱⠚⠁⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠒⠒⠂⠐⠊⠉⠉⠀⠜⡉⠠
⠀⠀⠀⠀⢣⡀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠤⠂⢂⠩⠂⠁
⠀⠀⠀⠀⠠⡉⠻⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠁⠠⢍⠂⠠⠀⣀⡀⡀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠄⠀⡀⠀⡀⠀⠀⠀⢀⠀⣀⡀⠠⠄⠀⠀⠒⠂⠈⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡠⣤⡀
⠀⣀⣀⣀⣶⣶⣤⣤⣽⣶⣶⣦⣦⡀⠀⠀⠀⠀⢠⣶⠶⠶⠞⠀⠀⠀⠀⠀⠀⣷⡆⣘⠓⠀⠉⠉⠀⣼⠀⠀⠀⠀⠀⠀⠀⣷⡄⢛⡃⠉⠁⠀⢠⡄
⠀⠉⠉⠉⢿⠿⠛⠻⣿⠟⠻⠛⠋⠁⠀⠀⠀⠀⢾⣧⣤⣄⡠⣤⣤⠀⠀⠀⠀⠉⠀⠈⠁⠈⠳⠖⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠛⠓⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆
⠀⢤⡀⠀⢀⠀⢀⣶⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⣶⣆⣲⣂⡀⠀⠀⠀⠀⠀⢀⠀⢘⣿⡃⠀⡀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣤⣠⣤⣠⣴⡀
⠀⣸⡿⠿⢶⣦⣒⣾⣿⣾⣿⡿⣷⣶⠀⠀⠨⠿⠁⣀⣀⣉⠉⠉⠩⠿⢄⠀⠉⠓⠀⠀⠀⠀⢩⠿⠟⡿⠅⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠛⠘⠛⠛⠿⠁
⠀⠉⠀⠀⠘⠁⠀⠞⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠂⠀⠀⠄⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢰⡟⠧⠀⠀⠽⢷⡄⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⡴⠿⠧⠄⠀⠀⠀⢠⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣠⣶⢾⣝⣿⣷⡀
⠀⡤⢾⣷⣿⣿⣿⣷⣿⠶⣄⠀⠀⠻⠿⠿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣭⠉⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣿⡿⠟⢀
⠀⠰⠩⠻⠛⠛⠛⠻⠻⠹⠈⠀⠀⠀⠀⠀⠀⠋⠁⠁⠉⢿⣯⡁⠀⠀⠀⠘⠿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠉
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⢀⣠⡴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣛⣟⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠖⠛⠛⠃
⠀⣷⢦⣤⣿⣾⣿⣿⣿⣿⣟⣶⣤⠀⠀⣾⣶⣤⣾⣿⣿⣿⡿⠿⣿⣥⡄⠀⠀⢙⣶⠤⣜⡷⣶⣶⣿⣿⣿⣯⣿⣷⣶⡦⠀⠀⠀⡽⠇⢠⣀⠀⠰⡦⠄
⠀⠛⠃⠀⠿⣟⣿⣿⡿⠷⠿⠛⠉⠀⠀⠉⠉⠀⠲⢟⣟⣿⣿⠿⡟⠉⠁⠀⠀⠈⠀⠀⠁⠀⠛⠁⠀⠀⠁⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚
⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⢀⣠⡦⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣖⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⣷⡦⢤⠶⠶⠶⡿⢿⠿⡶⢶⡤⣤⠀⠀⠀⢳⣀⣠⣤⣶⣷⣿⠿⢿⣦⣤⣄⠀⠀⢀⣿⠶⢿⣿⣿⣿⣿⣯⣿⡿⠇⠀⠀⢰⡆⠐⠒⠚⠛⠛⠛⠛⠛⠓
⠀⠟⠃⠀⠶⠀⢤⡄⠀⠀⠐⠂⠂⠈⠀⠀⠀⠞⠀⠀⠉⣹⠟⠿⢿⡿⠟⠛⠋⠀⠀⠈⠀⠀⠀⠉⠛⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⡀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣤⠄⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣀⣀
⠀⣹⠖⠂⠈⡉⠉⠉⠁⠈⠭⠉⠀⠤⠀⠀⢀⣿⡇⠀⣀⠀⠀⠀⠠⡤⠀⡁⢠⠀⠀⠀⠤⠤⠤⠤⢴⣿⣿⣿⣿⣿⡧⠀⠀⠀⢨⡟⢐⣚⠛⠉⠉⠉⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠃⠀⠀⠰⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠖⠀⠉
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠂

⠀⣤⠀⣰⣴⡆⢠⣶⡄⢠⣤⣴⡄⣴⣶⡄⢀⣀⠀⠀⡀⢠⢠⡄⠀⣠⣤⣶⣶⣶⣄⠀⢠⣦⣀⠀⠀⠀⢠
⢰⣿⣦⢻⡿⢣⡌⠟⣡⡘⣿⡿⠀⣿⣿⠇⢸⡿⠀⢾⡏⢿⢈⡃⠉⣭⣥⣄⠈⢉⢉⠀⣿⠟⠋⡶⠁⣣⣴
⠘⡿⠛⠀⠰⠆⠁⣤⡌⣰⣮⠀⣛⣈⢩⣤⣤⠉⣤⣤⡄⠴⠞⢡⣄⡱⠄⠻⠀⠚⠈⣤⣍⠴⠂⢄⠐⣂⠈
⢠⣶⣿⣷⡆⢾⡷⠶⠗⠙⣛⡁⡾⠉⣤⣭⠹⠶⠨⠉⣥⢼⡷⠀⣠⣤⡘⠀⠛⠂⠩⠉⣒⣋⡁⠘⠰⢟⡃
⢀⣩⣼⣿⣤⣄⠛⡿⠿⢢⠙⡁⡇⣴⡎⠁⠘⠛⠓⠒⠒⠀⣦⣾⣿⣿⣿⡆⠉⠻⠿⣶⠈⠀⠔⠚⣁⣞⠓
⠘⠻⠿⠿⠿⠛⠘⠛⠈⡻⢿⢠⠃⠈⠁⠸⢿⣷⡷⠿⠇⢀⣹⣅⣈⣙⡁⠀⠒⠲⢤⠐⢊⣡⡄⠉⢁⣽⠔
⠀⣴⣿⣷⡄⢠⣶⣴⡥⠀⣴⡜⠀⠈⠀⠴⠖⠠⣴⣦⣄⢘⣽⣿⣿⠿⢏⠢⢤⣾⣾⣶⠛⠡⠖⠀⠛⢁⣀
⠀⠻⣿⠿⢃⡘⠿⠿⠋⠀⠿⠃⠀⣄⣀⡀⠀⢠⣦⡀⠀⠘⠋⠋⠙⠂⠀⠀⠘⠙⠛⢉⣀⢿⣂⠈⣋⠘⠛
⠀⣶⣶⣦⠙⢿⡆⢰⣿⡇⠀⣀⠀⠽⠿⠷⠄⠀⠉⠀⣥⡁⠀⠀⣤⠀⠀⢀⠀⠘⠀⠐⠉⠻⠃⠘⠛⣋⠄
⠀⠀⠀⠐⠾⠷⠂⢀⣤⣶⣿⠟⢠⣤⡤⢄⡠⠀⠀⠈⡁⠀⣤⡆⠰⠖⠀⠙⠃⠘⠻⠆⢸⠆⠐⠋⠀⠟
⠀⣿⣇⠈⠉⠋⣾⣿⡟⠋⠤⠀⠀⣰⠀⠈⣤⠀⠲⠾⡇⠀⣈⣀⠀⠀⠛⠁⣿⠀⠰⠆⣤⡀⠀⡀⠀⠙⠁
⠀⠈⠁⣾⣷⣦⢀⠀⢿⡀⠀⣸⠇⢹⣤⣤⠏⠠⣄⡀⠘⠀⢻⡿⢀⠀⢀⡀⢀⡄⠀⣷⠟⠛⠈⠉⢁⣀⣀
⠀⢐⠽⣿⣿⣿⣟⠣⠨⣷⣷⡯⠀⠈⢻⡟⢁⡘⢿⣇⠀⠀⡆⠀⠉⠁⠊⠁⠈⠃⠀⠀⠤⠄⠶⠒⠀⠉⠉
⠀⢀⣈⣈⠛⣩⠶⢦⡄⢹⣿⠁⣀⡀⠘⠁⣈⠱⣶⡦⠀⢠⡤⠀⠀⡀⠀⠠⠶⠶⢶⠀⠓⠂⠀⠉⠛⠚⠒
⠀⠺⠋⠉⠀⠠⠴⠶⠖⠀⢰⠟⠉⠁⠀⠟⠛⠷⠀⠶⣶⠈⢱⣦⠀⠀⠲⠤⡄⠀⠀⠛⠓⠲⢄⠴⠶⠤
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢿⠷⠀⠀⠀⠠⠞⡿⠅⠀⠀⠀⢀⣀⡀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠉⠁⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⡄⠀⠀⡀⠐⠀⠀⠀⠉
⠀⠀⠄⣒⣺⠻⣿⣷⣦⣄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠋
⠀⠀⠔⠉⠻⠿⢿⡿⠿⠿⠂⠀⠸⢉⣛⣿⡷⠦⣤⣀⣀⣀⠀⠈⠲⣼⡧⠐⠀⣀⣀⣀⣀⣠⠴⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠈⠙⠉⠑⠈⢻⡛⢾⣿⣿⠚⠛⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⣆
⠀⠀⠀⠀⠀⠀⢰⡀⢀⣄⠀⠀⠀⣀⣤⣶⡖⠒⡶⢶⣶⠿⣻⣿⢿⣭⡟⠿⠿⣿⣶⠶⠖⠀⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠲⣮⣿⠈⣿⠀⠀⠀⠉⠠⣶⣆⠉⠄⠀⠀⠀⠈⠁⠀⣽⡇⠈⠆⠀⢂⠀⠂⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⡷⠀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⡔⠂⡟⠛⢿⠇⢿⠀⠸⣇⠘⠁⠟⢴⣦⣄⡀⠀⠀⠀⠾⣻⠟⠀⠀⠀⣼⢸⣷
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⣿⣽⣷⣶⣾⣧⡊⠀⣻⠀⠀⠘⣧⠂⣵⣾⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢼⠪⣿
⠀⠀⠀⣰⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠎⢹⣿⣧⣿⠀⠀⠀⠀⣿⠀⠀⠀⠸⣦⡸⠿⣿⢫⠍⢹⡆⠀⠀⠀⠡⠂⠀⠀⠈⠦⠟
⠀⠀⠰⠯⢥⠁⠀⠀⢠⠀⠀⠀⠀⠀⣬⢦⣉⡩⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⣭⣶⣂⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠊⠀⠀⠀⠄⠀⠀⠳⣄⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⣀⠀⠀⠀⠈⠉⠉⠀⣰⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠹⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠈⠙⠅⡒⠒⣶⠲⠂⣡⠀⠀⠀⣄⣀⣀⣀⣀⠤
⠀⠀⠀⠘⠚⠾⠿⡿⣷⠷⢼⡿⠿⠬⠷⠾⠶⠶⠶⠒⠖⠂⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠽⠯⠿⠯⠵⣿⣿⣯⢯⣿⣯⣧⣬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢨⠀⠀⡔⢁⣇⡤⠒⠉⠀⡜⠀⠀⢀⣠⠤⠔⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⠩⣁⡌⣴⢸⠁⠀⣀⣀⠴⠔⠒⠉⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⡢⢄⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡸⢒⠏⣸⡄⡟⠒⠉⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡁⢾⠆⢻⡑⠢⠤⠄⣀⣀⣼⠶⠕⢲⠋⢠⢃⢱⠀⠀⠀⠀⢀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⢣⢴⣷⣦⠀⠀⣠⣾⠉⠉⡹⠃⠀⡞⢿⡏⠉⠉⠉⠉⠀⠉⠉⠉⠉⠐⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠛⢳⢞⡜⣙⣳⢟⡹⣰⣀⠏⠀⠀⡜⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠛⠁⠀⡴⡣⠊⠈⠁⠙⠉⠀⢸⡍⠳⠤⠺⢧⣰⣟⣠⣄⣀⣤⣀⠜⠂⠚⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⠀⠀⠙⠳⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢠⣶⣟⣻⢷⣄⠀⠀⠀⠀⠀⠀⢠⣠⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣆⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⢀⣤⡄⠀⠀⠀⠀⠀⢰⣾⡦⢨⣾⣷⡤
⠀⠀⣿⡱⢽⣷⡥⣿⡆⠀⠀⠀⠀⠈⠋⠀⠉⠫⣿⡤⠀⠀⠀⠀⠀⠀⢨⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⣡⣄⡘⠻⠃⠀⠀⠀⠀⠀⠀⠉⣁⣀⠹⠚⠉
⠀⠀⠙⢿⣟⣹⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠐⢿⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣯⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠆
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⡄⠄⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠶⢀⡀
⠀⠀⣼⣿⣿⡱⢎⣷⠀⠀⠀⠀⠀⠀⠌⣀⡀⢈⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣔⡿⣿⣮⠁⠀⠀⠀⠀⠀⣠⡾⢟⣛⡛⢷⣄
⠀⠀⢽⣿⡹⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⣽⠟⠶⠀⠀⠀⠀⠀⠻⣧⣘⣛⣃⣴⡟
⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖⠐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁


⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⣼⠛⣉⢿⡀⠀⠀⠀⠀⠀⠀⢠⠖⠊⢉⠲⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⠀⠀⠀⠀⠀⢠⡏⠉⠙⠆⠴⠏⠀⠀⠀⠀⠀⠀⠀⣿⠁⠘⣦
⠀⠀⠀⣾⠠⠠⢸⠇⠀⠀⠀⠀⠀⠀⢿⠈⠐⡀⡒⡯⠀⠀⠀⠀⠀⢠⡿⣯⣟⣏⣿⠇⠀⠀⠀⠀⠀⠈⠳⢦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡿
⠀⠀⠀⠙⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠉⠳⠥⠤⠚⠁⠀⠀⠀⠀⠀⠈⠻⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠈⠻⡤



⠀⠀⠀⠀⣶⠐⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣏⣶⣦⡀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡸⠂
⠀⠀⢀⣴⡟⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣞⢙⣏⣸⣷⠀⠀⠀⠀⠀⢸⡀⠂
⠀⠀⣾⡏⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣻⣏⣹⣿⠇⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⡀
⠀⠀⠘⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⡉⠁⠀⠊⠉⠉⠋⠉⢙⡳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⠞⡁⠀⢀⠢⠔⠶⠆⠤⣤⣤⡀⠠⠀⠀⠀⠠⠄⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⡴⠁⢤⠴⠊⠁⡀⣀⣀⡠⢄⡀⠉⠛⢷⣄⡐⠃⢀⡠⠒⢂⡙⢦⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⡜⠠⡴⢁⣤⠞⠋⠁⠀⠉⠙⠺⣍⠷⣆⡀⠹⣷⣔⠁⢰⡤⠐⠓⠈⢳⡀⠀⠀⠀⢸⠘⡀⠀⠀⠄⣿
⠀⠀⠀⢰⠃⢸⠁⣼⠃⢀⠖⠀⠀⠙⢷⣄⠈⢏⠻⣷⡀⠈⣿⣟⠁⠀⠀⠀⣴⠄⢱⠀⠀⠀⢸⡄⠉⠀⠀⠀⠛⢧⡀
⠀⠀⠀⢸⡑⣿⠀⣿⠀⢾⠐⡁⢢⢑⠀⣿⡇⡈⣷⣿⡇⠀⣿⡏⠴⠋⢶⡀⠀⢤⡘⣇⠀⢀⠎⠀⠀⠐⣀⠀⠀⢸⣷⡀
⠀⠀⠀⠸⡇⢹⡈⣿⣆⠸⢧⣍⣡⡞⢀⣿⠁⠀⣿⣿⡇⠀⣿⠇⠚⣁⣴⡄⠀⠀⣀⣻⣴⠃⠀⣴⣷⠾⠇⠀⢠⣾⡟⠉
⠀⠀⠀⠀⢧⡐⢷⡸⣿⣦⣀⡈⠀⣠⣾⠏⠀⣸⡿⠙⠀⢰⣯⣧⣴⣿⣭⣶⣶⣾⠿⠿⠃⢀⣾⣿⠟⣭⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠈⢳⣦⠙⢦⣙⠙⠿⠟⠋⢃⣠⣶⣻⠁⠀⣠⡿⣼⣷⣿⠿⣿⣿⣤⣴⣤⡶⢾⣩⣿⡟⣳⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠙⢷⣀⠈⠙⢛⠻⠛⠿⠿⠋⠁⣠⡾⢋⣼⡿⠟⠤⠀⠀⠄⠄⠤⠤⣖⣩⣪⣿⢨⣿⣿⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣬⡤⣤⡤⢶⣚⣫⣽⠾⠛⣁⢄⣄⣤⣶⣷⣴⣪⡿⣾⣽⣿⠟⢣⣿⣿⡱⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣚⣉⣭⣿⣽⣿⣿⣿⠿⠿⢶⣵⣷⣿⠟⣿⣿⣎⢨⡉⡻⠛⠛⠁⣠⣿⣿⡷⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣛⣫⣭⣼⣶⣯⣉⣈⣵⣿⣿⣿⣾⡒⠘⣈⣡⣿⣿⣿⣷⣥⣤⣤⡶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣝⣭⣍⣹⣩⣽⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⡀
⠀⠀⠀⢠⡄⠀⠀⠀⠀⢲⣿⣿⡖⠀⠀⠈⠻⠷⣿⣿⣤⣤⣤⠄⠀⠀⢴⣦⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠰⣶⣿⣷⣦⣄⠀⠀⠀⠀⠀⢂⣀⣀⠄
⠀⠀⢀⣿⣗⠀⠀⠀⠀⢈⣿⣿⣏⠁⠀⠀⠀⠸⣿⠇⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⡂
⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠁
⠀⠀⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⢠⣤⣀⡀⠀⠀⡄⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠒⠒⢴⣬⣔⡀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⢀⠀⠠⠀⣀
⠀⠀⠈⠻⣿⣿⣷⣶⣼⣿⣷⣶⣶⣿⣿⡿⠋⠀⠀⠠⣠⡾⠋⠁⢈⣿⠀⠀⠀⠀⠀⠀⢸⣿⣟⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⠷⠂⠿⠾⠾⠿⣅
⠀⢠⡀⠀⢈⡙⠛⠉⣿⣿⡟⡏⠛⠋⠉⠀⠀⢠⣀⣼⣿⣁⡄⠀⠀⡀⠀⢠⠀⠀⠐⠒⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠸⣿⡄⢾⣷⠀⠀⢸⣿⡇⠁⠀⠀⠀⠀⡤⣤⣿⣿⡯⣤⠀⠑⢄⠘⣀⣇⣠⠔⠊⠁
⠀⠀⢻⣿⣼⣿⡇⠀⠈⠿⠃⠀⠀⠀⣴⢷⣿⣿⣿⣿⢥⡀⠀⠐⢾⣿⣿⣿⡇⣛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠲⢿⣿⣏⣽⡀⠀⠀⠄⠒⠙⠉⠝⠣⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⡿⠀⠀⣶⠀⠀⠀⠀⠀⠉⠁⠁
⠰⣿⢿⣿⣿⡷⠶⠶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠙⠶⠾⠁⠀⠀⠀⠀⠈⠀⠘⠂⠀⠈⢉⣄⠀⠀⢀⡀⠀⠘⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢻⣇⠀⣾⠇⠀⠀⠀⠀⠀⢺⣿⡗⠀⠀⠀⠐⠾⢿⣿⣿⡿⠂
⠀⠀⣼⣿⢹⣿⡇⠀⠀⠀⠀⠙⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⡄⠀⠈⢿⢸⠏⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠈⢀
⠀⣼⡿⠃⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋⠀⠀⠀⢺⢂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣀⣴⣤⣤⣅
⠀⠈⠀⠀⠀⠀⠀⢀⣤⣶⠿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⣀⠀⠀⠀⣾⠘⣧⡀⢀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⡀⠀⣠⣤⣾⣿⣿⣷⣿⣶⣏⠀⠀⣸⡟⠀⢻⣧⠈⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⠝⡙⠫⠅
⠀⠀⠀⠀⠛⠛⠋⠀⣀⣤⣤⡀⢠⣀⣴⣿⣿⡿⠛⠇⠀⠈⢙⣛⡿⡿⠟⠿⠻⡇⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀⠵⠛⠁
⢀⡀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⣤⣶⡤
⠸⣷⡀⠀⠈⠛⠛⠟⠛⠛⠛⠙⠁⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣤⣀⠀⠀⠀⣿⣿⣿
⠀⠙⠻⠆⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠙⠛⠛⠛⠿⠛⠛⠛⠫⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣉⠁⠀⠀⠀⢻⣿⡏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣬⣭⣥⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠁⠀⠀⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡎⠀⠀⠀⠀⠀⠀⢱⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⡇⠈⠀⠀⠀⠀⠁⢸⡀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣸⡇⡀⠀⠀⠀⠀⢠⢸⣇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡇⠀⠀⠀⠀⠀⠀⢸⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠢⠄⠀⠀⠠⠔⢀⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⠠⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠻⢱⠀⠀⠀⠠⡌⠏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠰⠄⠀⠀⠀⠀⠀⠀⡔⠁⢠⠂⠀⠀⠰⡄⠈⢂⠀⠀⠀⠀⠀⠀⠠⠆⠀⠰⠁
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠈⢠⠀⠀⡄⠁⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀⠄⠊⠀⠈⠀⠀⠁⠀⠑⠠⢀⠀⠀⡠⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠒⠀⠂⠀⣠⠖⠊⠑⠲⣄⠀⠐⠐⠒⠈⣠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠒⠖⠒⠋⠁⠀⠀⠀⠀⠈⠉⠒⠲⠒⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣟⣿⣻⣛⣟⣟⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢸⠀⡇⢀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⣸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢈⠀⠣⠈⡃⠀⠀⠘⡄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡾⢠⡁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣜⠀⢼⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠢⣽⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⡀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡀⠀⢠⠀⠇⠀⠀⠈⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡠⠀⡠⠂⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠁⠈⢄⠀⠀⠀⠀⠀⣇⠦⡴⠼⠀⠀⠀⠀⠈⡰⠀⠻⢶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⢸⡀⠀⠀⠀⠀⡁⠁⢸⢛⠀⠀⠀⠀⠈⠁⠘⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣠⠞⠂⠀⠀⠀⠀⠛⠀⠁⠉⠁⠀⠀⠀⣨⣦⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢠⠂⢸⠀⠀⠀⠀⢀⠀⠘⠁⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⡀⡀⠀⠀⣀⠀⠀⠈⠓⠄⡟⡀⠈⠀⠀⠀⠀⠘⣥⠠⠒⠁⠀⣀⢀⡀⢀⠀⢀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠷⡀⠀⠀⠀⢰⢁⠁⠀⠀⠀⠀⢀⣀⣡⠀⠀⠀⠐⠉⠋⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠤⢀⡤⠤⠀⢠⣄⣐⡂⠠⣴⠦⠀⠈⠲⡂⣀⡈⡛⠀⠀⠀⠀⠀⠉⠈⠉⣠⣄⠔⠀⠀⠄⢰⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠐⢅⡀⠀⠙⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⡠⠖⠀⠀⠀⠑⠀⠛⠦⠀⠄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠶⠷⡇⠀⠀⠀⠐⢸⠀⠀⠀⠀⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠸⠖⠂⠀⠀⠻⠀⠰⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠆⠀⠀⠒⠂⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠊⠀⠀⠀⠀⠀⠀⠀⣤⠒⠰⢷⣄⣴⠂⠠⢤⣀⡀⠾⠀⢀⣄⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⢸⠄⠋⠀⠀⠀⠀⢠⠃⠄⠑⠀⠠⠀⠀⠀⠀⠈⠑⠀⣠⠀⠀⠀⠀⠀⠘⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⣀⠁⡀⠀⠀⠀⠀⠀⠈⠂⢆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢃⡀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡠⠈⡁⠄⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢻⠡⢀⠁⠰⠀⠈⠈⠱⢤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠃⠀⣽⠠⠄⠠⠄⠀⢠⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠠⠀⠸⠄⣀⡀⠤⠤⠤⠘⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢴⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⢀⣀⣤⣤⠤⣄⣀⣀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⣀⠴⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⢁⣠⡤⠖⠫⠙⡁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⣠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠡⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡆⠀⠀⠀⠠
⠀⠀⠀⠀⡀⣀⢄⠠⠐⠂⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠃
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣤⣶⡗⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⡀⠔⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠘⠈⡀⠀⠀⠀⡄
⠀⠠⠰⢺⠀⠀⡸⢰⡀⠀⠀⠀⠀⠀⠀⡅⣘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⢠⠾⢇⠙⠂
⡄⠀⠀⠀⠁⠀⡇⠸⠀⡇⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣼⠗⠓⠄⠀⢃⠜⣤⡾
⠃⠀⠀⠀⣄⠀⠃⠄⡘⢁⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⢉⠁⠄⠀⠀⢂⠾⣼⡏
⠀⠀⠀⠀⠘⡆⠀⡰⠡⢡⠚⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⢂⡀⢾⡦⠿⠁
⠀⠀⠰⡀⠀⠀⢈⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠽⠛⠉⠁
⠀⠀⠀⠉⠃⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢀⡀
⠀⠀⠀⠀⠀⢀⡀⠄⢪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⣼⠷⠄⣤
⠀⠀⠀⠀⠄⠀⠀⢀⠂⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠁⠀⠡⢄⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢟⠠⠄⡁⠠⢘⠠⡄
⠀⠀⠀⠆⠀⢐⠢⢄⡩⠤⣄⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢶⠓⢀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠸⣅⢂⠠⠈⠀⠀⠐⢂
⠀⠀⠐⡇⢠⡉⣵⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⡀⠀⠀⠀⠀⠳⣟⡆⠀⠀⠀⠀⣢⢼⡆⠀⠀⠀⠀⠈⠻⣄⣦⣁⠀⠈⠠⣤
⠀⠀⠀⠱⣰⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠏⢋⡛⣻⡛⠻⠿⠿⠶⣦⡀⢸⠟⠁⠀⠀⠀⠀⢶⣈⡅⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣗⡶⣚⡆
⠀⠀⠀⠰⡫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠁⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠤⠄⠄⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡑⠢⠍⠭⢽⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣶⣿⡇⠀⣼⣿⡆⠀⢀⣠⣬⣿⣷⣾⠻⠿⣿⣿⣾⣿⣿⣿⣷⣄⣀⣄
⠀⠀⠀⠀⠀⣾⢏⣿⣿⣾⣿⣿⠅⠀⢺⠋⠉⠙⢿⣴⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣦⣄
⠀⠀⠀⠀⠀⠋⠀⠃⣿⣿⣿⣿⡄⠀⠈⢇⢰⡿⣳⣿⡿⣟⣿⣍⣉⠍⠉⠙⠻⢿⣿⣿⣿⣿⡟⣧
⠀⠀⠀⠀⠸⠆⠀⢸⣿⣿⣿⣿⠁⠀⠀⣾⡟⢿⣷⣭⣼⣿⡿⣻⣿⡷⣦⣄⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⠙⠁⢀⣤⣤⣙⣳⣴⠟⠙⣛⣿⣾⣿⠏⣼⣿⢿⣿⣷⣾⣿⣿⡟⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣤⣾⡟⣻⣭⢠⣾⣿⣿⣿⣿⣿⠿⢞⡾⠟⠛⢿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣷⣿⣅⣻⣿⣷⡀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠙⠻⣧⣤⣷⣿⣿⣿⣭⣭⠇⡼⣦⣿⠁⠀⠀⢰⡏⠹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡛⠤⠀⠀⣾⠀⠀⢸⡇⢙⣉⠻⠟⣿⢻⣿⣿⣿⣶⣿⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠿⢂⣠⣾⠠⠄⡀⢀⡀⠠⠀⣿⠿⢿⣿⣿⣿⡟⢻⣷⣤⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠿⠟⠛⠛⠋⠻⠿⠟⠿⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠈⠀⠀⠀⠀⠻⠿⠆⠀⠀⠀⠀⢴⣄⠀⠉⠙⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⣀⡺⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⡄⢲⡭⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣟⣁⠀⠀⠚⠛⠃⠀⠀⠀⠰⣿⠷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⣿⠟⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢀⣀⠀⢀⣠⡀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⡆⠀⠿⠟⠀⠈⠙⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡛⠁⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣿⣿⣿⠷⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠛⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡜⠱⠟⠀⠀⠀⠀⠀⣀⣠⣄⣀⢀⣤⣄⣠⣤⣴⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠘⠃⢀⠏
⠀⠀⠀⠀⠀⣿⠛⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠻⠟⠛⠋⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⢹⣄⠈⠓⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠉⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠈⢿⡄⠀⢀⡀⡀⠙⠉⠛⠋⠙⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣾⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣦⣴⣦⡀⣠⣤⣀⣠⣄⢀⠀⠀⠀⠀⠀⠀⡀⡀⠠⢀⣴⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣾⣿⣿⣿⣿⣿⣆⣦⣦⣿⣿⣿⡿⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⢒⡿⠉⡁⡀⠈⡆⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣿⠽⣛⠿⢛⠀⠀⠀⠙⣄⠄⣶⢀⡇⠟⠾⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⣀⡀⢀⣞⡩⠽⣿⣷⡟⠁⠀⠀⡀⠁⣨⣥⣿⡤⠁⣼⣁⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢣⠋⠙⠉⠈⣹⣿⣷⠟⠁⠀⣀⡼⠟⣆⠀⣚⣴⣿⣟⢛⣩⣷⣾⣿⣏⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢻⣧⢀⣿⣤⣴⡲⠾⢿⣿⠇⠀⠠⠾⣩⣤⣿⣿⣿⡟⠟⣷⣴⣿⡟⠛⠒⠛⢺⡻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣴⣿⠿⠸⠛⠉⠁⠀⢀⣘⠟⠀⡤⠀⣲⣿⣻⣿⣿⣧⣿⡾⠿⢿⡿⠓⠒⠲⡞⠀⡟⠃
⠀⠀⠀⠀⠀⠀⠀⡴⢿⢏⠁⢀⡴⠾⣿⡏⠀⠀⠀⠀⠀⠀⣬⠧⠀⢼⡆⠈⣟⡉⣭⣼⣿⡿⡛⢲⣤⠀⠀⠉⣿⡴⠧⣼⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠇⣠⣿⣿⡇⢀⣿⠃⠀⠰⡀⠀⠀⣐⠛⡤⣥⣤⣶⠋⠉⠁⠈⣿⣿⡍⠀⠈⣻⡆⣠⣢⣟⣀⣴⠃
⠀⠀⠀⠀⠀⢠⣿⣿⣰⣿⠁⠀⣧⣾⠏⠀⠀⠀⠘⢓⣾⣯⣾⠏⠉⠉⠁⠀⠀⠀⠀⠀⠻⣿⣀⠨⣦⡟⠙⠁⠈⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡤⠖⠁⠀⠀⠀⠀⡴⢋⡞⠁⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡼⢿⢿⣿⣇⡤⠔⠒⠠
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⠀⠀⠈⠱⣤⣤⣖⡲⢛⡹⠶⠛⠛⠙⠁⢨⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣉⣉⣋⣙⣿⠛⠁⠀⠀⠀⣀⣴⡿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠛⠛⠉⢉⡽⠟⣀⠀⠀⣠⣶⣽⡟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⢤⡀⠀⠀⠀⡀⠤⠐⠀⠈⠃⢀⣩⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠵⣤⣴⣦⣤⣦⣤⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⢿⡟⢿⢿⡿⡿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣿⣶⣷⣷⣿⣷⣿⣼⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣶⣶⢿⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⢿⣷⡦⣄
⠀⠀⠀⠀⠀⠀⢠⡾⣁⣴⠏⣵⠋⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⠘⡏⣻⡌⢳
⠀⠀⠀⠀⠀⣰⣿⣴⡟⢠⡞⢀⡔⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠨⣆⢸⡄⢻⡎⣧
⠀⠀⠀⠀⢠⣿⣯⠴⠄⢸⡖⣋⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣈⣾⡅⣘⢻⣿⡀
⠀⠀⠀⠀⣾⡿⠄⠀⠻⣮⠛⣛⣿⡋⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣯⡉⣽⠖⠀⢛⣿⡇
⠀⠀⠀⢸⣿⠿⠤⠋⠉⠈⢸⣿⣿⡇⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣠⠖⠈⠀⠀⠀⣹⣿⣿⠁⠙⠉⣄⣹⣿⡇
⠀⠀⠀⠸⡹⣮⠀⡡⢰⣶⣿⣿⡯⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⠢⡈⠄⣠⢿⠇
⠀⠀⠀⠀⢿⣿⡟⠻⢿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠟⢳⣾⡷⠁
⠀⠀⠀⠀⠀⢻⣷⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠁⣾⡏
⠀⠀⠀⠀⠀⠘⢿⡂⢼⣟⣿⣿⣶⣀⣴⠾⢻⣦⠀⠀⣿⣿⠀⠀⣴⡟⠷⣦⣀⣶⣿⢿⣓⡷⢐⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠺⣭⣉⡽⣻⣿⣧⣀⠀⢻⣷⡾⢿⡿⠿⢾⡟⠀⣀⣼⣿⣟⢫⣉⡭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣷⣿⣿⣿⣶⣿⡅⣼⠀⢁⡻⣶⣿⣿⣿⣼⣿⡾⠋
⠀⠀⠀⢀⡀⠠⢤⣤⣤⡤⢄⣸⡃⠀⠉⠙⢿⣿⣟⣥⠁⠀⢠⣻⣿⡿⠋⠉⠀⢘⣇⡠⢄⣤⣤⡤⠄⢀⡀
⠀⢀⣴⣿⠟⠛⠋⠉⠙⠛⢿⣿⣵⣢⣀⠀⠀⣿⣿⣧⡟⢤⣼⣿⣿⠀⠀⣀⣀⣾⣿⡿⠛⠋⠉⠛⠛⠻⣿⣦⡀
⣰⣿⢋⣠⣴⣲⣶⣿⣯⣵⣾⡧⣄⡉⠛⢿⣶⠟⣫⠭⢭⡭⠭⢛⢿⣶⡿⠋⠉⣠⢼⣗⣪⣽⣷⣶⣖⣦⣄⡙⣿
⠉⣑⣭⡿⠋⠉⠀⠀⠉⠙⢻⡿⠶⢮⣷⣄⡽⣸⣿⡀⢸⠀⢀⠆⣄⣯⣰⣾⡽⠶⢻⡿⠋⠉⠀⠀⠉⠙⢿⣭⣊
⠞⠽⠋⠀⠀⠀⢀⢀⣠⣤⣿⣦⣤⣄⣈⣙⡇⣿⠃⢱⠠⠀⡆⠀⠿⢻⣋⣀⣠⣤⣴⣷⣤⣄⣀⡀⠀⠀⠀⠙⠯
⠀⠀⠀⠀⢀⣾⣷⠟⠋⠉⣿⠉⠉⠉⠉⠙⡇⠆⠀⠀⠀⠀⠀⠀⠐⣸⠋⠉⠉⠉⠙⣿⠉⠙⠻⢿⣷⡀
⠀⠀⠀⢠⣾⡟⠁⠀⠀⣠⣿⣶⣾⠶⠾⠻⣷⢨⣖⣀⣀⣀⣀⣀⠅⣿⠟⠶⠶⣿⣶⣿⣄⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠋⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢸⡿⣿⣿⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⢻⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠠⣿⣿⣟⣀⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡉⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⡇
⠤⠤⠤⠤⠤⠤⠤⢄⠤⣾⠇⠠⠤⢠⠤⠀⠄⣿⣿⣟⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷
⠁⡀⠀⠀⠀⠀⠀⢀⢀⣇⡀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻
⣉⠀⣀⢀⡀⣀⣀⣀⢨⡇⣀⢀⣀⡀⣀⠁⣂⢻⣿⡷⠶⢶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⢶⣿⢿⣿⡉⠛⣿⡿⣿⣷⢄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠞⢁⣿⠁⠈⣿⣧⢰⣿⠀⠈⣿⡀⠳⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⣧⣾⣿⣴⣶⡿⣿⣿⠿⣶⣦⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⣴⣶⠂⠘⠓⠒⠒⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠧⠀⠁⠉⡿⠻⢷⣦⣄
⠀⠀⠀⠀⢰⣯⠉⠁⠀⠉⠉⠒⠒⠦⣌⡑⠂⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣾⣄⡀⣠⠜⠉⢿⣷⣄
⠀⠀⠀⠀⣾⣟⠂⠂⠀⠒⠒⠤⠀⣀⣀⡈⠐⠢⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣛⡋⠀⣀⣤⠋⠈⣿⣷⡄
⠀⠀⠀⢠⣿⣭⣍⣁⣀⠀⠁⠒⠲⢤⣍⡙⠳⣄⣀⣝⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠉⣀⣀⡔⢁⣿⣿⣦⡀
⠀⠀⠀⢸⣭⡁⠀⣠⣈⣀⣈⠙⠛⠶⣮⣝⠻⣦⡙⢿⣷⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣀⠴⠛⠉⠀⠼⢑⣿⣿⣿
⠀⠀⠀⢸⢛⣛⣛⢉⠛⠛⠻⠿⣷⣦⡈⢙⣷⣮⡻⣦⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣝⡻⠿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⡼⠙⣿⣿⡇
⠀⠀⠀⢸⣏⣉⢉⣉⠉⠙⠒⠦⣤⣽⡻⣮⣙⣿⣿⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣶⣦⣼⣿⣿⣅⠀⠀⠀⠀⠠⢋⣾⡇
⠀⠀⠀⢸⣿⠟⠋⠉⠓⠉⠱⢶⣶⣭⣿⣦⡙⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⡄⢀⡀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⣿⠿⠦⠀⢤⣄⣀⠀⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⡿⢟⣋⣽⣶⡿⢛⡽⠋
⠀⠀⠀⠀⢸⣟⠂⡀⣼⣿⣙⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⠴⠋
⠀⠀⠀⠀⠀⢿⣦⣤⣾⣿⣿⣿⣿⣿⠿⣻⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠈⢿⣯⣡⣨⣿⣿⣿⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢶⣶⣶⠶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⡤⣻⣿⣋⠀⠻⠙⠉⣿⢿⡿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⠆⣴⢈⠉⠺⠀⣿⠙⠻⣿⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⣾⣣⣾⠁⠀⢠⠃⠀⠀⠘⢨⠃⢹⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢁⠎⠀⠀⠀⠀⠀⠀⢸⠇⠈⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣷⡏⠀⣠⣄⣀⠀⠀⠀⠎⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⠞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠞⠁⠀⡰⠃⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣠⡶⠛⠀⢔⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⡛⠛⠛⠛⠛⠟⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠈⠄⠀⠀⠀⠠⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠶⠶⢴⣀⠀⠀⠀⠀⠀⠘⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣞⡉⠉⠲⡄⠀⠀⠀⠈⠳⣄⠀⠀⠠⠂⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠈⠑⣤⡼⠶⠦⣄⡀⠀⠈⢳⡔⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠁⠁⠂⢄⠀⠀⢰⠃⠀⠀⢀⡾⠁⠀⢀⣀⠀⠙⣆⠀⠀⢷⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠒⠂⠄⡀⠙⢤⡟⠀⠀⠀⢸⠓⠒⠲⡏⠈⠃⠀⣸⡀⠀⣸⡇⠀⠀⠀⠀⢸
⣠⠖⡲⣄⠀⠀⠀⠀⢰⠋⣦⡌⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠑⢼⡇⠀⠀⠀⢿⠀⠀⠀⠹⣦⣠⡴⠋⠈⠉⢉⡇⠀⠀⠀⢀⣸
⣇⠶⠎⣸⠀⠀⠀⠀⠈⢢⡩⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⣸⠓⠂⠐⠊⠁⣼
⠈⠙⠉⢾⢆⠀⠀⠀⠀⣎⡇⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡠⠒⠻⣄⠀⠀⢸⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠈⣏⠣⣀⣠⠜⢸⡄⠀⠀⠸⡏⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠞⠀⠀⢠⠚⠳⢤⣼⣤⣤⡶⠛⠁⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢯⡲⠤⠤⠽⠦⢤⣤⣈⣲⣄⠀⠀⠀⠀⠀⠀⠸⣞⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⡴⠃⠀⠀⠀⠀⡠⢺⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣀⠀⠀⠀⠀⠘⢷⣄⣸⠀⠀⠀⠀⠀⠀⠀⣀⣱⣤⠶⠟⠉
⠀⠀⠀⢯⡉⢷⡚⠒⣫⢃⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⠤⠞⠛⠛⠛⠿⠶⠛⠿⣛⡋⠉
⠀⠀⠀⠀⠘⣄⠩⠭⠂⡜⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠐⠂⢤⡀
⠀⠀⠀⠀⠀⠈⠓⠒⠋⡤⠊⠁⠀⣀⣤⠴⠶⠶⠶⠶⠶⠦⠤⠴⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠙⠛⠓⠶⠶⠴⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠘⢻⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢺⠉⠗⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡌⢿⣿⣆⠀⠀⠀⣸⣿⡀⠀⠀⠀⣼⣿⠏⣸
⠀⠀⠀⠀⠄⠢⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠄⠀⠀⠀⠀⠘⣆⠛⣦⡹⢿⣿⣦⣼⣿⣿⣿⣦⣶⣿⠿⢋⡼⢋⡼
⠀⠈⠀⠀⠁⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠁⠀⠂⠀⠀⠰⣌⠳⣬⡙⠶⣬⣹⣿⣿⣿⣿⣿⣉⡥⠞⣋⡴⢛⣱⠂
⠀⠀⠀⠀⠁⠐⠤⢀⣀⠀⠀⠀⠀⠀⢐⡀⠤⠔⠀⠡⠀⠀⠀⠀⠀⠙⠳⢦⣍⣓⠶⢼⣿⣿⣿⣿⣿⠷⢖⣛⣩⠶⠛⠁
⠀⠁⠀⠀⠄⠈⠁⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠲⣤⣄⣀⣀⣉⣉⣽⣿⣿⣿⣿⣿⣍⣉⣉⣀⣀⣤⡤⠞
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⣿⣿⣿⡇⠀⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣽⣿⣿⣿⣵⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠟⠻⠿⠛⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⢀⣠⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠄⢐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠔⠋⠁⠀⠀⠀⠉⠙⢷⣀⠀⠀⠀⠀⠘⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠃⠀⠀⢀⣀⣄⡀⠀⢀⠀⠹⣆⠀⠀⠀⣼⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠡⠀⢉⠛⣆⠀⠀⣀⢹⣷⠀⠀⣿⣿⣦⡀⠂⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡘⠛⣸⣿⡿⢠⢾⠻⠈⣿⣦⣄⣥⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⠀⠀⠘⠻⣶⣷⣾⠟⠀⣾⣦⣤⢢⣿⣿⡟⠋⠉⠛⣫⡶⣢⣴⡶⠖⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡹⣄⣀⣈⡀⢀⣀⣠⣴⣿⣿⣿⠇⣘⣿⣿⣶⣶⣿⣻⡟⡛⢿⡿⢛⠄⣄⣪⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣼⣿⢿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⡿⠛⠻⠟⣟⡷⢛⠿⠵⡉⠔⠉⡿⢟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠛⠟⠛⠛⠉⠷⠿⠿⠟⠛⠷⠞⠓⠈⠛⠉⠡⠤⠍⠘⠁⠴⢧⡴



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢻⣿⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⣼⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⣇⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠈⠩⠀⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⡀⠘⠃⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢈⡁⢀⠀⡜⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠁⠀⠸⡰⣦⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣀⠀⣻⣞⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⡷⣻⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠃⠛⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣀⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡆⠀⡘⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⣰⣿⢃⡀⠀⠾⠀⠀⠀⠀⢀⠀⣄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣣⣷⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣿⠿⠟⣁⠈⠟⠊⠀⠀⠀⠀⠀⠘⣂⠘⠣⣔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣟⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣇⠈⠀⠉⠙⢀⡀⠀⠀⠀⠀⠀⢐⣏⠀⠀⣩⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠠⣤⣿⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⠖⢤⡤⣀⠀⢨⡅⠀⠀⠨⢋⣶⡀⠀⣄⣀⣌⢿⣿⣿⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠘⢿⡷⠞⠛⠋⠀⠈⣷⠿⣦⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣧⣽⣿⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⢀⣧⣀⠀⠑⢤⣸⡏⠀⢹⡄⠀⠀⠀⠀⢨⣿⡟⣾⣿⡿⠟⠋⠉⠀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡷⠆⠀⠀⠃⡙⠳⣄⡀⠉⡁⠀⣸⠀⠀⠀⠀⠀⣸⣿⡇⣿⣧⣤⡄⣠⣶⡴⢛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⣄⠈⠑⠊⠉⣿⠃⠀⢸⡀⢀⡀⡄⣰⣿⣿⡟⣿⣿⠿⠟⠋⢁⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠬⣻⢦⣀⠀⠈⡆⠀⠸⣷⣶⣾⣧⣿⣿⡿⣱⣿⣿⣄⠀⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠉⠀⠭⠿⣿⡇⠀⠀⠙⠋⠙⢫⠉⠋⣼⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠀⠀⠀⠀⣀⣤⣤⣤⡶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠢⠤⠀⢀⡀⣟⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⡟⠀⢀⣰⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠿⠉⣿⣠⣤⣤⣤⣀⣤⣿⣿⣿⣿⣿⣷⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣻⣿⠋⠉⢉⣙⣛⣉⣭⣿⣿⣿⣿⣅⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠉⠉⢉⡟⠁⠈⠉⠉⠉⠉⢿⣿⣿⣿⡟⠉⠉⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⢀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⠉⠉⠉⣹⣿⣿⣿⣿⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢨⣦⡄⢠⣤⣀⣀⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠤⠤⣤⣠⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠒⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⣨⣿⣿⣿⣟⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⡿⢿⣶⣿⣿⣿⣿⡟⢧⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡀⢸⣷⣾⣧⣄⣸⣿⣟⣀⣼⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠉⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠉⠡⠄⠚⣋⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡡⢒⣡⡜⠛⢉⡄⠞⠈⠉⠀⠀⠭⠉⠉⠁⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣴⠟⡴⠟⠁⠀⠀⣱⠁⠀⠐⠉⠁⠀⠀⠴⠶⠂⠐⠒⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⢀⣾⠏⠘⠀⠀⡀⡀⠀⠁⠀⣤⡆⠀⢰⣆⡡⠀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⢢⠋⠀⢸⠏⠠⣶⠀⠂⢇⢃⠀⠀⠀⣛⣧⣧⠘⢷⣿⡄⠀⢀⣐⣶⣶⠤⠉
⠀⠀⠀⠀⠀⠀⣶⠷⠀⢠⠀⠀⠀⣏⢀⠠⢬⣧⣮⡀⠀⣈⣶⣷⠦⢄⣻⡾⢽⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⡿⣤⠀⢺⣆⠀⠀⣻⣧⠢⠙⠛⣿⣷⡦⢽⡿⢿⣿⡷⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣸⣇⡘⢿⣗⣄⠘⢻⣧⠀⢲⣶⣽⠿⢾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢍⢽⡾⣿⣯⣷⠀⠭⠭⣿⡯⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠹⠍⠁⠓⠉⠁





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

⠀⠐⠀⢠⡀⠀⠀⠈⠀⢆
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡟
⠀⠀⠀⠀⠀⣀⠀⠵⠀⢠⡇
⠀⠀⠀⠀⡠⠌⠂⠀⠀⢀⣌⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠁⡀⢠⡀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⢂⠀⢀
⠀⠀⠀⠸⡽⠟⠁⠀⠀⠰⣤⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠒⠀⠒⢉⠥⠾⢠
⠀⠀⠀⠀⠀⣀⠈⠀⣀⠉⠛⠁⠀⠀⠁⠀⠀⢀⠉⠉⠉⠉⠉⠁⠉⡀⠀⠉⠀⠀⠀⠉⠀⠀⢰⠀⠄
⠀⠀⠀⠀⠀⠐⠈⢁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢄⡀⠐⠞⠀⠀⠀⡔⠁⠀⠀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣅⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠖⠂⠧⠀⡐⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠁⢀
⠀⠀⠀⠀⠀⠠⠄⠀⠤⠞⠀⢀⠎⠀⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠈⠁⠰⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⡀⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⢸⠀⣸⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⠜⠀⠈⠃⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠋⠀⢘⠴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠂⠄⠀⣀⠀⠀⢠⠎⠀⠀⠈⠃⠀⣀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠐⠏⠀⠀⠀⠀⠀⠀⢀⣀⣔⣻⡄⠈⣜⠀⠀⠀⠀⠀⠀⠈⠗⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠠⠀⠀⢐⠔⠹⠃⠿⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠊⠁⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃⠀⠀⠠⠤⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⢊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⣁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠊⠉⡄⠀⠀⠀⠀⠀⢀⡌⠉⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠁⠀⠀⠀⠀⠁⠨⠂⠀⠠⠀⠠⠆⠈⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠀⠸⠤⠄⠤⠄⠀⣄⠀⠰⠣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢄⡀⠀⠀⠀⠀⢀⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠓⠀⠤⣤⡤⠄⢊⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠠⠠⠄⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠄⠀⠀⠀⠤⠽⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠐⠳⠄⠺⠤⠤⠤⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⠤⠤⠎⠤⠀⠰⠰⠎
⠀⠀⠀⠀⠀⡟⣀⠢⢤⣌⣀⡀⠀⠤⠄⠠⠄⠀⠒⠉⠉⠉⠀⡀⠀⢢⡈⠁⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠒⠤⠕⠄⡀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⠁⠀⢡⠀⠀⠀⠀⡄⠀⢤⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⡀⠀⡕⠠⠆⡀⠤⠉⠀⠰⡉⠀⠀⡀⠄⠀⠀⢀⢉⡰⠚⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⣈⠀⠔⢀⡉⠀⡀⠠⣀⠈⠐⠢⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠰⠒⠒⠀⠀⠀⠀⠁⠂⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⢔⢒⣲⣿⣿⣿⡿⠛⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡛⣿⣿⣿⣷⠶⠶⠶⠒⠒⠉⠉⠉⢀⠀⣠⢄⣈⣿⣿⣿⣿⣿⣷⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⣈⠤⢲⣾⢉⣿⡇⢹⣿⣿⣋⣹⣀⣼⠿⠗⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⡬⢽⡿⢿⣿⣿⣿⣻⣿⢿⣟⣿⣷⣿⣅⠿⢿⡗⠿⣿⣿⣿⡿⢿⣅⡀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠁⣿⣧⠈⣿⣿⣿⣿⢻⡿⣯⣿⣻⣿⣿⠾⠿⠟⠓⠉⠀⠈⠀⠀⠀⠉⠓⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠀⠀⣀⣀⠨⠥⠆⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣼⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⠲⢶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣶⣤⣤⣀
⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠐⠚⢉⡿⠿⢿⡿⠛⢿⠙⡇
⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡾⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣶⣶⣶⠆
⠀⠀⢠⣄⣀⣠⣤⣤⣀⠀⠀⠀⢱⣿⠿⠻⠍⠛⠛⠀⠠⣤⣀⡤⠄⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡤
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⡿⠛⠲⠄⠀⠀⠀⠸⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⡀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿
⠀⠀⠀⠉⠙⠛⠋⠉⠉⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣄⣀⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣤⣀⠀⠀⠀⠛⠛⠋⠛⠛⣿⣿⡿⠛⠋⠉⠛⠓⠀⠀⠀⠀⣤⣤⣀⠀⣀⣠⡴⠆
⠀⠀⠀⡠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣯⣄⣀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⠛⠻⣿⡏⠉⠉⠉⠛⠂
⠀⠀⠀⠀⠀⡏⢸⡟⠉⢻⡿⠿⠿⢿⣄⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⣇⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣤⣴⣿⣿⣄⣀⡀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠲⢶⣼⣿⣤⣄⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⠿⠿⠷⡄⠀⢴⣿⣿⣿⣿⡧
⠀⠀⠀⡾⠛⢻⣿⠉⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⠟⠛⠋⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠲⢾⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠀⢀⣤⠤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⡀
⠀⠀⠀⠈⢷⡀⠀⢸⣿⣿⣿⣿⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠈⢷⣤⣼⣿⣿⣿⣿⣧⣴⡟⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⡿⠿⠓⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠉⣿⠿⣿⠻⣷⣍⣉⡀⠀⠀⠀⠀⠀⠈⠉⢉⣿⡿⣿⣦⡀⠀⠀⠀⠀⠉⠀⢀⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢠⠔⠁⠀⠈⠙⣶⡍⠉⠙⣷⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⠛⠿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣄⠀⢀⣶⣦⢀⣶⣦⡀⠀⢀⣤⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣍⠀⠀⠀⠹⣶⣿⡇⠈⠻⣟⣈⣻⡟⠀⠀⣿⣷⡾⠁⠀⠀⠙⠻⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡿⠛⢻⠛⠛⠿⣿⣷⡄⠀⠀⠀⠁⠈⣶⣿⣿⣿⣿⣿⣷⡎⠀⠀⠀⠀⢀⣴⠖⢶⡀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⡀⠋⣠⣾⣿⠿⠇
⠀⠀⠀⠀⢰⠿⠿⠿⡿⠛⠲⣶⠄⠀⠿⠛⠃⠀⠀⠀⠋⠉⠉⠉⠀⠛⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⣀⡀
⠀⠀⠀⠀⠀⠐⡀⣠⣴⣶⣿⣷⣤⡀⣠⡔⠀⠀⠀⠀⠤⢞⣄⠀⠀⠀⠀⢠⣤⣠⣿⣿⣿⣿⣿⣾⡀
⠀⠀⠀⠀⠀⠶⠂⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣸⢶⡝⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠟⠁⠙⠧⠀⠀⢒⣯⠅⠀⠀⠀⠀⠀⠀⠈⠻⢛⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠩⠷⣟⡄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡏⢀⡄⠀⠀⠀⠀⠀⠀⠈⠱⢿⠧⠀⠀⣴⣿⣿⣷⡀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⣧⣾⠀⠀⠀⠀⠀⠀⠀⣬⡿⡟⠃⠀⠀⠙⠿⢿⣿⣶⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣸⣿⠄⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⢿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢚⠛⢋⣩⣭⠭⠍⠉⠉⠛⢳⡟⠑⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⠉⠁⠀⠀⠉⠒⠊⠉⠉⠀⠀⠀⠀⠀⢸⡇⠠⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠲⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣿⡅
⠀⠀⠀⠀⠀⠀⠀⢠⡏⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⢰⡇⠀⢤⣤⡼⠇
⠀⠀⠀⠀⠀⠀⠀⣾⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⡴⠶⠛⠛⠛⠛⠲⢦⣀⡾⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⡏⠆⠀⠀⠀⠀⠸⠀⠀⠀⠀⣠⢞⠉⠀⠀⠀⠀⠀⠀⠀⠐⣝⢷⡐⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⠫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠴⣤⡀⠀⠀⠀⠀⠃⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡠⢢⡟⠀⠀⠀⠰⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣥⠶⠋⠀⠀⠀⠐⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣀⡠⠤⠀⣄⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⣀⡄⠀⠄⠀⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⢀⣀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠘⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠒⠤⠤⠠⠀⠂⠀⠀⠎⠀⢄⠆⠀⠀⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠋⠀⠀⠀⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠩⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠒⠠⠄⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠐⡄
⠀⠀⠀⠈⠁⣀⠀⠈⠁⠒⠀⠀⠀⠈⠢⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⢁⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡎
⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠌⠢⠄⣀⡀⠀⠀⠀⠠⠄⠐⠈⠁

⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠒⠶⠶⡶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣠⠴⠖⠒⠒⠓⠶⢦⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣠⠊⠀⢀⡤⠤⠴⢤⣄⠀⠈⠻⣦⡀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⠇⠀⣰⠋⠠⠔⡒⠦⡌⠳⡄⠀⠘⣷⡀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠁⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠀⡇⢰⡥⡇⣪⢳⢸⠄⢿⡆⠀⢸⡇⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣴⠃⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⡄⠀⠹⣄⠑⠨⠄⠂⡸⠁⣼⠀⠀⢸⡗⠀⠀⠀⠀⢿⢷⡄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠻⣄⡀⠈⠓⠒⠒⠋⣠⣼⠏⠀⢀⣾⡇⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⢿⣿⣟⣛⣹⣿⣿⠶⠶⠒
⠀⠀⠀⠀⠀⠀⣀⣀⣹⣆⡄⠀⠀⠙⠒⠷⠾⠶⠚⠋⠀⠀⢀⣼⠟⠀⠀⠀⢀⣴⢿⣿⢿⢿⣻⣿⣟⢯⣙⣴⣭⣣⣭⣷⣿⠿⠋
⣠⣤⣴⣶⣾⢿⣻⣫⣏⢻⣿⣦⣤⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠋⢂⣠⣴⣾⣹⢯⢷⠸⣗⣿⣿⣿⣾⣿⣿⠽⠿⠛⠋⠉⠁
⠈⠙⠛⠻⠿⣷⡛⠛⠿⠡⠤⠉⠟⠻⠷⠶⣶⣾⠾⠿⠿⠿⠻⠿⠿⠿⠿⠿⠖⠛⠚⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡤⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⣠⠶⠖⢿⠉⠉⢹⡏⠀⢸⡿⠉⠉⠉⠁⠀⠸⣁⠀⣀⠄⠀⠀⣲⠍⢁⣉⡁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⣠⣾⠋⢀⡤⠇⠀⠀⠉⠷⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢤⡾⡯⠀⠓⠚⠛⠒⠀⠉⠉⠀⠀⠀⠁⠐⠂⠄⠀⠘
⠀⢸⢇⢨⡟⠯⡀⢑⣀⡀⠀⠀⠸⣟⠡⢀⠀⠀⠀⠀⠀⢀⣠⡀⣠⣿⢋⡇⣢⠴⠖⠒⠂⠀⣀⡀⠂⣶⣋⣽⣿⡯⠯⢽⢀⣠
⠀⢸⡈⠙⠒⣤⠾⠍⠡⡄⢸⠆⠀⠉⢿⠓⢾⠶⣾⠒⠲⣛⣪⢹⡛⠿⠽⠥⠾⢥⣤⠔⢲⣾⡟⠀⠀⠀⠉⠁⠁⠒⠒⢈⡡⠃
⠀⠘⣿⠃⠘⠃⠉⠚⠂⠙⠀⠀⠀⠀⠀⠂⠈⠦⠈⡛⡄⢠⡉⠉⣓⡐⠒⠒⠒⠚⠲⠾⠿⠓⠿⠯⠶⠶⠶⠶⠶⠞⠊⠇
⠀⠀⠈⠣⣄⠀⠐⠒⠠⢤⡀⢠⡀⠀⠀⠀⠸⣆⠀⠨⢷⡈⠐⢦⡉⠙⠁⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢦⣀⠀⠀⣸⠃⠘⠀⠀⠀⠀⠀⠘⠀⠀⠈⡇⠀⠀⠙⣶⢄⠀⠐⢽⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⣀⠀⠀⠀⠀⠈⢣⣷⡀⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠂⠀⡝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⠀⠐⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢈⠀⡰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡖⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢲⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⡀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⢀⡀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⡄⠀⠀⠀⢆⠀⠀⠀⠀⢀⡴⠺⠚⠻⡖⢦⡀⠀⠀⠀⠀⡰⠀⠀⠀⢠⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠱⡈⢄⠀⠀⢀⡦⢄⠀⣠⠎⡠⠋⠉⠉⠛⢄⠱⣄⠀⡠⢶⡀⠀⠀⡰⢁⠎⡘⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⡈⢢⡬⠲⣗⡉⠉⠀⠀⡝⠃⠌⠀⠀⠀⠀⠀⠀⢣⠘⢫⠀⠀⠉⢉⣺⠔⢅⡔⢁⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠡⡈⢢⣕⢄⡈⠪⣕⢠⣎⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢱⡄⣪⠕⢁⡠⣪⡐⢁⠜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠢⣘⠯⡀⠑⠬⣺⣀⡍⠒⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠒⢩⡀⣗⠥⠊⢀⠽⣃⠔⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡱⠦⢕⠤⣋⡙⠐⠠⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠄⠀⢋⣙⠤⡂⠱⢎⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠑⠠⠀⢈⡸⠋⠖⠲⢴⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡦⠔⠲⠙⢇⡁⠀⠄⠊⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠂⠄⠀⣀⡀⠀⠈⠉⠐⠒⠒⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠒⠒⠀⠉⠀⠀⣀⣀⠀⠤⠐⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠼⣀⣈⣉⣉⣋⡁⠠⠄⠲⡀⣀⣀⣀⣀⣀⢀⣀⠖⠠⠄⢉⣹⣉⣉⣁⣀⠧⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠤⠤⠤⠤⠤⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠒⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⣀⣀⣀⡀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⡦⠤⠄⠀⠀⠠⠤⣖⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⢀⠎⠱⠀⠀⠀⠀⠀⢀⠉⢢⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠼⡀⠀⣣⡀⠀⠀⣠⡎⠀⢀⠦⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢲⣄⠀⠘⣬⡀⠀⠀⠀⠀⠈⠣⡀⠀⣠⣤⣤⠄⠶⠤⠠⠠⠀⠠⢄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⠛⠒⢢⣌⠙⢶⡀⢹⠧⠀⠀⠀⠀⣀⣤⣹⣾⠋⢴⢉⠑⠁⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠘⢋⣉⣉⣉⣑⣄⣀⣈⣧⣀⣷⡀⢾⡀⠀⣠⣒⠞⢛⣡⠻⡖⢦⡥⣀⣐⡂⣨⣄⡉⠈⠉⠛⠀⠀⠀⠀⣿⠃
⠀⠀⣰⣶⣶⣢⣀⣠⣤⣴⣶⣗⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⠷⣶⣾⣘⡶⠚⠁⠀⢱⠀⠈⢀⠌⠈⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⣸⠷⠆⣛⠱⠽⠟⢯⠿⠉⡟⠘⢏⠉⣸⠏⢙⡞⢹⡿⠿⢛⣿⠿⣿⠟⢿⣷⣾⣭⣿⣿⣶⣶⡿⣀⣴⠡⠐⡚⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⢣⡤⠁⢤⣤⡶⡦⠈⣇⠀⣮⠀⢸⡀⢠⡇⠁⢧⣾⠟⠠⣀⠁⠈⠹⠈⠈⢿⣻⣿⣿⣿⣩⣿⣿⡭⠤⠒⠊⡠⣠⣞⡍⡡⢂⠔⠀⠀⠀⠀⣿
⠀⠘⢷⣀⡀⠊⢹⡝⠴⠻⠄⠙⠷⠈⠓⠚⠷⣄⣼⡟⠀⠐⠀⠂⠀⠀⠀⠀⠀⣿⡿⣛⡩⣿⣟⡟⡏⠑⠒⠨⣴⣯⠫⣜⠐⠁⠀⠠⠀⠀⠀⣿
⠀⠀⠘⣟⢃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⣀⣀⣀⣀⣀⣀⣠⡶⠟⠛⠛⠉⠻⡏⢿⠇⠀⠰⠀⠀⠙⢷⣭⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣶⡆⡟⢺⠯⡙⣄⢀⡨⠛⣤⠀⢩⣞⠁⠀⠂⠀⠀⠠⣻⢯⣥⡆⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠁⢙⣾⣯⠝⣿⠙⢾⣧⣤⡂⣠⠏⠀⠀⠀⠀⠀⣠⣶⡡⠮⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⡶⠊⠁⢀⣤⣾⢽⡿⠁⣸⡇⠀⠀⠀⠘⢻⠯⠌⠻⠲⡠⠰⠂⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠋⡽⣇⡞⠁⠀⣽⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⣼⣿⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡬⢼⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠂
⠠
⠀⠡
⠀⠀⠡
⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢊⣸⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡴⢫⢧⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡿⡡⠋⠀⢨⠑⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠦⠒⠤⠄⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⣡⠞⠀⠀⢀⠏⣍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠈⠁⠀⠈⡏⣈⣵⢦⡘⠁⠀⢀⠤⠽⠶⠶⠦⠤⠤⢴⡫⠖⢁⡜⠁⠀⠀⠀⣾⢱⡭
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⢸⡀⠀⢠⢿⣆⠈⠳⢀⠄⡀⠔⠈⠀⡠⠋⠉⠒⠢⠤⣬⣇⣦⠃
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣀⣼⠹⢒⠏⠞⡏⣓⠤⡤⠋⠀⠀⢀⡼⠀⡀⠀⠀⠀⠀⠀⢸⡌⠁⠒⠠⠤⢀⡀
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠳⡿⡧⠚⢰⢠⣠⡽⠃⠀⠀⠀⡠⠚⢬⡐⠢⢉⠐⠠⢄⢀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠴⠶⠺⠋⠀⢀⠄⡪⠊⠀⢘⢰⠾⡠⣇⡀⠀⢀⠜⢁⠔⠁⢀⠈⠀⠤⢢⣀⢸⡝⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢄⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠊⠀⠀⠀⢸⡻⠀⠱⠥⠼⢾⡓⡶⢋⣤⠒⠁⡠⠂⢀⠌⢉⡷⣇⠤⣀⡀⠀⠁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣄⢴⡟⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠉⠓⠤⣍⡉⢻⠤⢶⢁⣠⢾⡟⢪⢳⣄⠈⠈⠉⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠊⠉
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠽⣿⠗⠚⠒⠤⢍⣐⢢⣄⣀⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠭⠴⠶⠤⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢷⢤⡀
⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢤⢐⡆⡲⠂⢆⣹⠀⡆⠄⠠⡆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡌⢛⣔⠱⣿⠿⣃⠔⡎⢘⠱⢄⡇⠀⡔⠉⡆⠂⢏⠍⠒⠤⣆⠀⡀
⠀⠀⠀⠀⠀⣀⢶⣿⣿⡀⠊⠈⢫⠀⢿⠀⠏⠀⠧⠘⡤⡼⠀⠠⠀⠀⠈⠁⠄⢈⠜⠀⠈⣛⣽⣠⡄
⠀⠀⠀⣠⢮⣷⣽⣇⠈⠇⠲⠀⢘⠀⠀⠀⠀⣨⠀⠀⡸⢁⠂⠀⠀⢠⠁⠒⣐⢁⣠⢆⡀⠛⠀⠄⠷⢲⠀⡀
⠀⠀⡼⣿⣿⡀⠀⢈⠃⠈⠀⠇⠉⠀⠀⡰⠀⠁⢐⡜⠁⣤⠄⠀⠀⡀⣤⡚⠕⠉⢁⣀⠀⠀⢀⡂⠂⣈⡹⠧⢤
⠠⣾⣿⡛⠏⣁⠀⡀⠀⠳⠀⢱⠈⠃⠘⠃⠀⡠⢮⠀⠀⠀⣀⠤⠚⠉⠄⠒⠁⢐⢉⠀⢐⡠⠌⠀⠈⠁⠀⠞⠛⢲
⢸⡏⣿⠿⢦⡈⠳⡏⠀⠀⠀⢈⠀⠀⠰⠆⠀⠀⣀⡀⠖⠂⠀⠀⠀⠀⠀⠒⠈⠀⠐⠀⠉⠀⠄⠀⡀⠠⠄⠚⠁⠉⡜
⢿⢈⡿⠿⠀⠉⠀⠂⠁⠙⠀⠈⢀⠀⠀⢀⡤⠬⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⣀⡀⢀⠀⠀⠀⠀⠀⡼
⠻⣬⣟⣀⡀⠙⠃⠰⠆⠀⠀⠚⠃⡀⢠⠟⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠠⠄⠀⠀⠀⠀⠀⠐⢀⣻
⠸⢷⡙⢿⡯⠀⠀⠀⠀⠀⠐⡠⢚⠉⣮⣤⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠰⢆⠀⠀⠀⠀⡠⠀⢙⢍
⠀⢸⡉⣷⡆⡄⠠⡄⡤⢀⡀⢧⡿⠀⢹⣿⣭⣷⣀⡀⠀⣀⠐⠦⣄⡒⠲⢤⣈⡉⠙⠓⠦⠤⠀⢀⡤⡄⢺⣧⣧⠸⣎
⠀⠀⠸⣿⣿⡤⢟⣀⠠⠘⠄⠀⠈⠀⢀⣻⡙⣷⡙⣿⣢⣌⣳⣄⡈⠙⢦⡄⠈⠙⢓⣦⠤⣶⡾⣻⣿⣀⠃⢣⡏⢸⠟
⠀⠀⠀⠀⠛⠲⡏⢁⢴⣦⣶⣦⣶⡶⠋⠀⡱⣌⡁⠘⠗⠘⣿⠿⣟⠁⠲⣝⢧⣈⠚⣿⣷⣔⣬⣸⣿⡯⠒⡟⣡⠟⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠿⣟⣟⣛⡉⠃⠛⠀⠄⠈⠛⠶⣶⣄⣉⣀⣀⣀⡀⣈⣳⣟⣶⣌⢨⠝⠻⣻⣿⣨⠞⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⠒⢪⡦⠤⣔⣤⣀⣠⣬⢉⢉⣭⣙⣋⡩⣭⣉⣭⡭⠿⠒⠛⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣼⣿⣭⣽⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⡀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢸⣤⡏⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⢀⡄⠀⠉⠸⢷⣶⣄⠀⠸⠿⠷⠀⠀⣴⣶⣄
⠀⠀⠙⣧⠀⠀⠀⠀⡷⠀⡷⠀⠀⢀⠀⠀⠀⡀⢧⣰⠀⠀⢠⠀⣘⠀⠀⠀⠀⠀⣾⣃⣶⣘⣿⣿⣿⡿⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀⠀⢀
⠀⠀⡌⠀⠀⠀⠀⠗⠷⠞⠁⠴⠃⠘⠐⢦⣀⣸⣾⣿⣦⣧⣾⣴⡏⣠⠞⠀⠀⢠⣿⣿⡟⢿⢿⣿⣿⠃⠀⠀⠂⢠⣿⣿⢿⣿⣇⠀⠀⠘⢸
⠀⢀⡥⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣭⡷⠿⠃⠀⠀⠂⢸⡿⠇⠡⠀⢴⣿⡇⠀⠀⠀⢀⣼⡯⣏⣾⣿⡿⠀⣠⣀⡊
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣻⣿⣿⠀⠀⠀⠀⠀⡄⢸⣿⣣⣄⣴⣾⡿⠀⠀⠀⠀⣼⣿⣿⢿⠟⡟⢡⠀⠿⣿⠟
⠀⢸⡇⠀⠀⠀⢠⣴⡶⠶⣦⡀⠀⠀⠀⠀⠀⣶⠚⠛⠉⠉⢹⣿⡏⠀⠀⠀⡇⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⢸⣿⠁⢮⡼⢣⣀⣤⣴⢿⢾
⠀⠀⡇⠀⠀⢰⣼⣿⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⢾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣣⣥⣴⣶⣿⣿⣿⡺⣾
⠀⢀⡇⠀⠀⣸⣿⢿⣶⡁⣿⠓⠂⠀⠀⠀⠀⣿⡄⠀⠀⠀⢰⣿⡇⡄⠀⠀⢀⣤⣴⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉
⠀⠻⠓⠀⠀⢼⣿⣾⣇⣧⣻⣿⡇⠀⠀⠀⠀⢻⣇⠀⠀⠀⣿⣿⠋⠁⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟
⠀⠀⠀⠀⠀⢨⣿⣎⠘⣿⣵⣿⠇⠀⠀⠀⠀⢨⡿⣆⣀⣼⡿⡧⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢙⠿⠷⣿⠟⠃⠀⠀⠀⠀⠀⠀⠁⠚⠉⠙⠂⠀⠀⠀⠀⠸⢿⣿⣿⣽⣿⣿⣿⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⢿⡯⣿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⢤⣀⣀⣀⣀⣀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠔⠿⣿⣦⣉⣛⣛⡩⣷⣿⡇⠁
⠀⣠⣤⣤⣆⠀⠀⠀⠀⠀⢠⣏⣰⡃⠀⠀⠀⢨⡟⠛⠋⠉⠀⢨⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣖⠀⡀⡀⠀⠀⠈
⠀⣿⡷⠉⠻⡇⠀⠀⠀⠀⣼⣿⢹⡿⠶⣀⠀⠈⠁⠀⠀⠀⢠⣥⣿⡟⢀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠛⠻⠟⠻⠿⠿⠾⠶⢆⢢⣤⣧⣤⣀
⠀⠙⠿⠿⠆⠀⠀⠀⠀⠀⠘⢿⣦⣝⡷⢮⣽⣷⣶⣄⣠⣶⡿⠿⠋⢀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⢀⠀⠀⢀⢀⡀⠀⠐⢺⣟⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡇⡟⡝⠉⣫⡏⡯⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⣷⢇⢇⣀⣷⣗⡷⣇⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡴⠋⠁⠀⠀⠙
⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⡄⠅⠀⢼⡦⠚⡤⢄⣠⠞⣛⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⠄⠂⠀⠀⠄⠈⠀⢇⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣷⣿⢷⣶⣦⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠁⠀⠀⠈⠀⢀⠤⢴⡾⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢠⢂⠀⠰⠀⠀⠀⡀⡀⣄⡞⠈⠳⣤⣀⣀⣠⣤⡴⢾⠀⠀⠀⣀⣤⠤⠤⣮⣭⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠺⢤⣹⣦⣾⡐⠊⠈⠉⠀⠀⣀⣾⣲⡶⠈⠻⣍⠀⠑⠀⢿⠟⠁⠀⠐⠐⠂⠉⠻⡆⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⡆⠀⣀⡴⠚⠍⠉⣿⠅⠀⠀⠊⠙⠳⠦⡈⠳⣄⠀⠀⠀⠰⠀⠈⠳⡶⠶⠒⠒⠒⠒⠒⠢⡄
⠀⠀⠀⠀⠀⢸⠃⢐⣾⣿⠿⠿⠛⠀⢐⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠁⢿⠀⠈⠙⠶⣤⣀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠛⠖⠊⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠉⠙⠲⠶⠤⣤⣀⣀⣁⣀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⡀
⠀⠀⠀⢀⡠⠤⢤⠾⠒⠢⣄⠀⠀⠙⡆
⠀⠀⢰⡯⠒⠒⢮⢠⣖⣄⠘⡆⠀⠀⣇
⠀⠀⢺⠀⢰⣷⠈⢦⣙⣃⣰⡧⠦⣄⠀⠙⠢⣄
⠀⠀⠀⠳⣄⣉⣠⠏⠀⠘⠲⢄⡀⠈⠳⣄⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠢⡀⠀⠉⠲⣄⠈⢣⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢢⡀⢳⡀⠀⠀⠘⢦⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠷⠴⠇⠀⠀⠀⠈⠓⢦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠲⠤⣀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⡴⠊⠁⠀⠀⠊⠹⡆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⢢⠀⢸⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡴⠊⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠙⠉⢿⠛⠙⠊⢹⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⡴⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣄⠸⡄⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠉⠀⠀⢠⠟⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⢍⡤⠃⡰⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠖⠊⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⢀⡤⠞⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⣀⣀⣀⣠⠤⠶⠋⠉⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠤⠖⠒⠲⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⠤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠖⠀⢤⡘⠃⡀⠀⠀⠀⣠⠂⠀⠠⢀⣠⡄⠀⠀⠀⢀⣾⣿⣿⣿⠃
⠀⠀⠀⠖⠈⠀⠀⠀⢀⣀⠌⠀⠂⠀⠀⠀⠀⠀⠠⢄⠀⢿⢇⡔⠀⠀⠀⠉⠛⠚⠛⠛⠁⠀⠀⠀⣴⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⣀⡤⢂⣤⣦⣦⠀⠀⠀⠀⠀⠄⡦⠂⠀⠀⠀⠰⣹⣿⡷⠀⠀⠀⠀⠐⠀⠀⠀⢀⠐⠄
⠀⢀⠀⠀⠀⣀⣤⡾⢫⣤⠌⣿⡚⢻⣷⡌⠙⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⡇⢠
⠀⠀⠉⠓⠛⠋⠁⠀⢨⣭⡞⣿⡿⢸⣿⠇⠀⠘⡄⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇
⠀⠀⠐⠁⠀⠀⠠⣠⣨⢟⡁⠀⡠⠺⠶⠶⠤⡀⠈⠑⠒⠊⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢸⠃⠈
⠀⠸⠀⠀⠀⠀⠀⠸⠁⣹⡇⠰⡁⠀⠐⠀⠀⠘⠈⠀⠀⠀⠀⠀⢳⠀⠓⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⢀⠼⠋⠉
⠀⠀⠀⠀⠀⠤⢀⣤⡾⠛⠀⠀⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢳⣄⢰⡄⠀⠀⠀⠀⠀⠀⠉⢩⠉
⠀⠀⠀⠀⠀⠀⠸⣥⠆⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠄⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢀⣀⣤⣴⣶
⠀⠀⠀⠀⢀⡤⡞⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣫⢗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⢼⣰⡆
⠀⠀⠀⠐⠁⠀⡄⣰⠣⠀⠀⠀⠄⢤⣬⣄⡃⠀⠀⠀⠈⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⢋⣠⡿⠉⢴⡤
⠀⠀⢠⠤⠶⠶⠋⠃⠀⠀⠀⠈⠀⠀⠀⠈⠓⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡰⠓⠣⢞⣋⣴⡷⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠘⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡠⠏⠭⢥⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠂⠀⠀⣠⣠⠤⠎⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠠⠐⠂⢀⡴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⢠⡤⠤⠞⠋⠀⠀⠀⠀⢰⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⡤⠴⠚⠉⠀⠁⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠫⣄⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⢻⡄⣸⠾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⡔⠉⣽⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⣠⣿⠋⢀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡾⠧⠤⣿⣄⣀⠀⠉⠻⣦⡀⠀⠀⠀⠀⣰⡟⢠⣶⠟⠉⠈⢹⡋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⠟⠛⠻⢷⣦⣌⡻⣦⠀⣀⢠⣟⣴⠟⠁⣀⣤⣴⡋⣹⡟
⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡼⠦⣤⣀⣀⣈⣙⣛⣾⣷⣿⣾⣿⣵⣶⣿⡿⠿⠿⢿⣍
⠀⠀⠀⠀⣼⣏⠉⠻⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣿⣿⠿⠿⣿⣿⠿⣿⣧⣼⣿⡟⠛⠛⠒⠲⢤⡴⠿⢷⡄
⠀⠀⠀⢰⡿⠿⣆⠀⠘⢦⡈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⣀⡴⠋⠉⠀⣸⣿⠉⣧⠙⣟⢦⡀⠀⠀⠀⢱⣦⣴⣧
⠀⠀⠀⣿⡧⣀⠈⠳⣄⠀⢻⣦⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡋⢉⡟⠀⠀⠀⢰⠇⡏⠀⠻⠀⠘⣆⠙⢦⣄⣤⣾⣄⣸⡅
⠀⠀⠀⢸⡇⠈⠻⣶⡼⠿⢦⣿⡍⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠋⢙⣦⣄⣴⠏⢰⡇⠀⠀⠀⠀⠘⢧⣀⡽⢧⣀⣽⣏⡀
⠀⠀⠀⢸⣿⠖⢶⣿⠀⠀⠀⠈⠻⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣞⠁⣸⠟⣤⡾⠀⠀⠀⠀⠀⠀⠀⠙⠳⡼⠿⠋⠉⢻⡗⢦
⠀⠀⠀⢸⣇⠀⠀⠙⢧⡀⠀⠀⠀⠙⡄⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⡿⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠘⢿⣦⣀⠀⠀⠙⢦⡀⠀⠀⢹⡀⣿⠀⠀⠀⠀⠀⠀⢰⣛⡟
⠀⠀⠀⠀⠀⠉⣛⣿⣶⣤⡀⠙⢦⡀⠀⢧⢿⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣴⣾⣿⡿⠿⠿⠿⠿⠿⣷⣤⡙⢦⡘⣾⡇⣠⣄⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠠⣿⠀⣏⠀⠀⠀⠀⠀⠀⣀⣉⡙⢿⣿⣿⣿⣿⣋⣤⣶⠾⣛⣛⣉⣁⣀⣀⣀⣀⣈⣛⣿⣏⣙⠛⠛⠷⣦⣀
⠀⠀⣿⣖⠻⢦⣤⣤⡶⠿⠛⠛⠛⢉⣩⣿⡟⣡⣿⣿⣿⣉⣉⠉⠀⠀⠀⠀⠀⠀⠈⠙⢿⣍⣉⠉⠉⠓⠒⠿⢿⣷⡀
⠀⠀⠨⣿⣤⣾⠋⠁⠀⠀⢀⣴⣾⠟⢉⣼⡟⣻⡟⣿⠻⢾⣍⡛⠳⠶⣤⣀⠀⠀⠀⠀⠀⣻⣍⠛⠲⢶⣤⣤⣴⡟
⠀⠀⠀⠈⢿⡍⢳⣄⣤⣴⡿⠟⠁⢠⣾⠏⠀⣿⠇⢸⣧⠀⠙⢿⣷⣤⡀⠉⠙⠛⠲⠶⢿⡉⠉⠓⢤⣀⣸⡿⠋
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⢠⣿⠋⠀⣸⣿⠀⠀⣿⡇⠀⠀⢻⣿⡿⣶⣄⠀⠀⠀⢀⣿⣦⡶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣿⡇⠀⠀⢸⡇⠀⠀⠀⣿⣷⠈⠛⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣸⣿⣄⣀⣀⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣙⣻⣟⣀⣙⣯⣥⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠛⠁
⣿⣏⢹⣟⠻⣿⢛⢟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⣶⠷⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢿⢶⡦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⣴⠏⣱⠏⢀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⠈⣇⢹⡌⢳
⠀⠀⠀⠀⠀⠀⢀⣾⣵⡟⢁⡾⢁⡔⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢇⠸⡄⢻⡊⣇
⠀⠀⠀⠀⠀⢀⣾⡿⠔⠆⢰⣟⣉⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣌⣶⠄⣤⢻⣿
⠀⠀⠀⠀⠀⣼⣿⠲⢀⣘⡧⠉⣩⣿⡁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣈⣵⠚⠀⣩⣿⡀
⠀⠀⠀⠀⢀⣿⡟⠓⢀⠈⠀⢨⣿⣿⠇⠀⠀⠀⠈⠄⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢨⣿⣿⡀⠈⠀⣤⣽⣿⡇
⠀⠀⠀⠀⠀⢣⣷⣌⣠⣀⣷⣿⡿⠟⠀⠀⠀⠀⠀⠈⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣀⡀⢂⡴⡻
⠀⠀⠀⠀⠀⠘⢿⣿⠉⣛⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠉⢹⣿⠟
⠀⠀⠀⠀⠀⠀⠈⣿⠃⢈⣻⣿⣆⠀⠀⠀⢀⣀⠀⠀⢸⣄⣼⠀⠀⢀⣀⠀⠀⠀⣠⣾⡟⡉⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣘⡿⣿⣿⣿⣴⡿⠋⠹⣧⠀⣸⣿⣿⡀⣰⡟⠉⠻⣦⣼⣿⣿⣭⣟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣾⣸⡟⣿⣦⣄⢹⣿⠉⣿⠛⢹⡟⢁⣤⣾⡿⣿⣸⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⠿⣿⣿⣿⣷⠠⠏⠀⢠⣽⣿⣿⡿⠿⠿⣯
⠀⠀⠀⠀⣠⣴⣤⣤⡿⢿⣧⣴⣾⣇⠀⠀⠈⢹⣿⣵⢃⡀⠀⢶⣿⣿⠁⠀⠀⢀⣿⣆⣤⣿⠷⣦⣤⣴⣄⡀
⠀⠀⢀⣼⠷⢋⡀⢀⣠⣤⠨⣹⡟⠛⠾⣶⣤⣘⣿⠿⢿⣥⣻⢿⣿⡇⣠⣴⠾⠟⢛⣯⡭⢤⣤⣀⡀⣈⠻⢷⣄
⠀⠐⠿⠣⢶⣿⠷⠛⠛⠻⠷⣿⣯⣅⣢⣄⠙⣿⢡⡖⠀⠙⠀⠀⠈⠻⠟⣁⣄⣪⣽⣿⡶⠿⠛⠛⠶⢿⣷⢌⠻⠃
⠀⢀⡖⣾⠟⠁⠀⠀⠀⠀⣀⣸⣇⠉⠙⠛⢿⡇⡿⡟⡄⢠⢀⠀⢨⣾⡷⠟⠛⠉⣁⣯⣀⡀⠀⠀⠀⠀⠙⢿⡷⣄
⠀⠀⠈⠁⠀⠀⢀⣴⣬⡾⠟⣿⠿⠿⠿⠷⢶⡇⠁⠀⠃⠀⠈⠀⠀⠐⡷⠶⠿⠿⠿⣿⠟⠷⣮⣶⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⣿⣄⣀⣀⣤⣼⡇⢀⡠⠀⠀⠀⠀⠀⢸⣧⣤⣄⣤⣀⣿⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠰⠋⠉⠀⠀⣴⣾⣿⠋⠉⠉⠀⠀⢿⣾⣿⣿⡿⠿⣿⣶⣾⠁⠀⠈⠉⠉⢻⣿⣦⡀⠀⠈⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⣿⠀⠀⠀⠀⠀⢸⣿⣿⣣⣄⣀⣼⣿⡿⠀⠀⠀⠀⠀⢸⡍⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡟⠀⠀⠀⠀⠀⢨⣿⣿⡟⠉⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⣿⣿⡟⠛⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠶⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢺⣿⡧⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡠⣶⡿⢿⣏⠉⢻⣿⢿⣶⠦⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠞⢀⡿⠀⠘⣿⡄⣼⡏⠀⢹⡇⠙⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣦⣾⡷⠶⠾⠿⠿⠿⠿⠶⠾⣿⣦⠇⠀⠀⠀⠀⠀⠀⠣
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠁⠑⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠳⡀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠀⠀⠀⡠⡘⣆⠀⢸⡄⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⢸⠀⠀⢪⠀⠂⠀⢀⡼⢃⠇⣼⠀⠈⣧⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⣶⡶⠛⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠈⢷⣄⠓⠒⠚⣁⡴⠃⠀⣸⣿⣶⣿⠿⣿⣶⣶⢶⣶⡶⠶⠿⠛⠉⠀⠀⠈⠳⠶
⠀⠀⠀⣀⣠⡤⠽⣆⡀⢀⠉⠛⠛⠛⠉⠀⢐⣶⡿⠛⢉⣤⣾⡿⠃⠀⠀⠀⠀⠀⢀⣠⠀⠐⠏⠉
⠚⠿⢿⣥⣴⣄⣁⣽⣿⣿⣦⣷⣤⣤⣤⣶⣿⡷⣶⠿⠿⠿⡿⢷⣶⣀⣴⣐⣤⣥⣶⣯⣄⣄⣠⣤⣤⣴⣶⣿⠟⠋⠁
⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉

⠀⠀⢀⡄⠀⡴
⠀⠀⡞⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⢲⠆
⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡿⠂⠑⢮⢴⡐⢺⡇
⠀⠀⠇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡥⡶⠋⠀⣠⢤⡵⡠⣯⠽⣆⢤⣠⣂⠢⢍⠈⢀
⠀⠀⢧⠀⠀⢳⡀⠀⠀⠀⣀⣤⣀⣀⣤⣄⡤⠤⠤⠤⠤⠔⠖⡶⢶⠶⠖⠖⠷⡚⣞⡣⡻⢑⡵⡟⡵⠒⣶⠹⠛⢊⢲⡩⡙⣀⡰⠔⠇⡁⠄
⠀⠀⠈⠳⡀⠀⠳⡀⢰⠏⣥⠤⡀⠙⡆⣠⡄⠠⠴⡂⠀⣠⡟⢳⠚⠂⣛⠐⣓⠊⡠⢊⡴⢋⢈⡞⢥⠪⠤⡄⡄⠈⡣⡻⣬⣒⣒⠭⠁⠈
⠀⠀⠀⠀⠈⠢⣀⠈⠯⢷⡹⣷⡷⢄⣿⠀⠙⡄⠀⡅⢰⡋⠹⡍⠉⢹⣻⡿⢣⠎⡴⠊⡠⣣⠞⣿⢻⢻⠶⣒⡖⠒⡟⢳⡿⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠚⢞⡇⠢⡀⠈⢿⣧⡀⠀⢀⣨⠿⢮⣒⣸⣤⡼⢧⣅⣱⢏⡠⢊⢼⠓⢻⡍⠛⡏⠒⢯⠛⢓⣫⠷⣷⡸⣄⣠⣄⣄⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠗⢶⣁⠀⠸⣬⡽⡿⢿⣵⣼⣁⣀⣀⣘⣋⣤⠴⠯⠹⡛⠓⠛⠒⠚⠋⠉⠛⠛⠚⠛⠀⠛⣤⣽⠑⠜⢦
⠀⠀⣴⠖⠚⠚⠓⠋⠉⠀⠀⠀⣩⠺⠁⠒⣂⠽⠊⠀⠉⠉⠀⠉⠁⠉⠀⠀⠀⠳⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢆⠣⡀
⠀⠀⠁⠀⠀⣀⠀⠀⠠⣐⠤⠒⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣱⣄⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠛⠓⠒⠶
⠀⠀⠈⠛⠛⠽⠲⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠋⠈⢻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠟⠏⠀⠘⠈⠻⠶⢲⢶⠶⣤⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⠉⠁⠀⣹⣷⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠰⡄⠸⡄⠸⡄⠠⠀⡇⢀⡴⠛⠉⠉⢉⣉⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇⠀⣸⣇⠀⠹⣄⢹⡄⠱⡀⣤⡿⠋⠀⠀⠠⣽⣶⠬⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠋⠀⠁⠀⠻⠏⠉⠓⠺⠶⠷⠖⠛⠁⠀⠀⢀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠴⠃⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠐⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⠉⠉⠀⠀⠀⠀⠀⢰⡀⠀⠢⡈⢷⣝⠦⡌⠒⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣀⠀⢢⡀⠀⠀⠠⠾⠃⠀⠀⡈⠲⣌⠓⠤⡀⣸⡇
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠃⠚⠋⠀⠀⢳⡠⡀⠀⠀⢀⣀⣰⡿⠀⠀⠁⠀⣤⠟
⠀⠀⠀⠀⢀⡠⢋⠀⠘⠁⡀⠀⠠⠾⠀⠹⣿⣄⡀⠀⠉⠉⠀⠀⠀⢠⡶⠋
⠀⠀⠀⠀⠿⠔⠋⠳⠶⠻⣅⣨⠿⢷⣄⣤⣬⡟⠛⠛⣦⣠⡴⢶⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠒⠒⠒⠒⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢹⠁⠀⠀⠀⣀⠀⠀⣎⡱⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠀⢸⠀⠀⠀⠸⣅⠇⠀⠀⠀⢀⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠨⣨⠇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠬⠃⠀⠀⢀⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢀⡀⠀⠀⠀⠘⣦⡤⠖⠒⠲⢤⣀⠀⠀⢀⡴⠒⠋⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡖⢢⠀⠧⠼⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢣⡴⠋⠀⠰⣉⡇⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⢄⠀⢀⠷⡀⠉⠁⠀⠀⠀⠀⣰⠃⠀⠀⢀⡠⠤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠲⡈⡀
⠀⠀⠀⠀⠀⣠⠤⠐⠢⢤⡀⢰⠃⡰⠊⠉⠲⡀⢃⡘⠀⠈⠳⢤⣀⠀⠀⢰⡇⠀⠀⠀⣾⠀⠀⠘⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠊⢀⠁
⠀⠀⠀⠀⡞⢀⠖⠀⠒⢄⠙⣼⡀⢇⠾⠆⢠⠇⡜⡇⠀⠀⠀⠀⠈⠉⠙⢻⠀⠀⠀⠀⠘⢦⣀⣀⣀⡴⢯⡀⠀⠀⠀⢏⡱⠀⠀⡸
⠀⠀⠀⠈⡄⠸⡀⠘⠟⡸⢠⠂⠑⠦⢁⣨⡥⠊⠀⡇⠀⠠⡊⣢⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠳⡀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⠢⠭⣒⡪⠔⢣⡀⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠸⣉⠆⠀⠀⠠⡖⢦⠀⠀⢸⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣸⡄⠤⠤⠧⠤⠤⠤⠤⠤⠤⠤⠀⢀⣙⣦⣀⡀⠀⠀⠀⠀⢉⣁⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠛⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠙⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠂⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⡀⠀⠀⠤⠤⠤⠤⠄⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣤⡄⠄⠀⠰⡆⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣶⣀⣄⡰⠋⠀⢦⠀⣀⣤⢤⠒⠶⠉⠈⠁⠁⠀⠰⡄⠀⠀⠀⣧⠀⢀⡋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢁⣠⣼⣿⣿⣿⣿⡦⣠⡾⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⣾⣥⣄⢻⣿⡌⣷⡆⣏⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⢀⣰⣾⣿⣿⡿⢠⠛⣥⠞⡹⠁⠀⠀⠀⠀⠐⠈⢦⣄⡶⣦⣿⣿⣷⣝⣿⣯⣸⣿⣧⡿⣣⣟⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢠⣤⢿⣿⣿⡿⠟⠁⠐⢸⠟⡔⣡⣼⣔⠁⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣻⣧⣶⣶⣭⣾⣿⠟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢠⣶⠟⣡⣿⣿⠏⠀⠀⠀⠀⣁⣼⡁⠍⣥⣡⣬⢲⣆⠀⢠⣿⣿⣿⣿⡿⢿⡉⠋⢉⡽⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣾⡟⢡⣾⣿⡟⠁⠀⠀⠀⠰⣊⣿⣿⣟⣽⣿⣿⣿⡿⣿⡳⡾⢿⣿⡋⠉⢶⣄⠹⠆⠸⣧⡈⢙⡭⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⣴⣿⡿⠋⠀⠐⠒⠒⠒⢺⡿⠿⠟⠛⠉⠛⠛⡛⠚⣛⣻⣧⠀⠙⣇⠀⢈⡿⢈⡇⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢣⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⢠⡏⠀⣸⠇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⠀⠁⠀⣤⡀⣰⠄⣤⠀⣶⣶⣿⣿⣿⣿⠃⢸⠇⢠⡅⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠙⢉⠉⠛⠻⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⣯⢻⣿⠟⢠⠟⠀⡸⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣩⣥⣶⣶⣶⣶⣷⣿⣿⣿⣿⠿⠛⠁⢠⣀⣠⡤⡲⠏⠘⡿⠟⠉⡴⠋⠀⠀⠁
⠀⠀⠀⣤⢀⠀⠟⣉⢉⡁⠠⠄⠻⠭⠬⠛⠛⠋⠁⢀⣤⣿⣿⣿⣿⡟⠷⠎⣸⠃⠀⠃
⠀⠄⠀⢿⣄⣁⠈⠁⣀⢀⢀⣀⣄⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⡿⢃⢁⣠⠞⠁
⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡽⠧⠴⠚⠉
⠀⠀⠀⠀⠈⠛⠟⣻⢿⣿⣿⣿⣿⣿⣻⡛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠁

⠀⠀⠀⠀⣴⣲⡄
⠀⠀⠀⠀⠘⣽⣿⣳⣄
⠀⠀⠀⢀⣠⡀⠙⢿⣿⣿⣦⣄
⠀⠀⠀⢨⣟⣹⣷⣄⠘⠻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠙⢧⡉⠻⣷⣦⣘⡻⣿⣿⣿⣮⣕⣢⣀⠀⣀⣀⣀⣷⣦⣤⣤⣤⣴⣤⣶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⡏⡟⣿⣿⣷⠆
⠀⠀⠀⣀⣠⣤⣤⣬⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⣿⣿⣧⣧⡿⠿⠙
⠀⠐⣹⣻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣧⡌⣿⣾⣿⣴⠛⠁
⠀⠀⣈⣉⣷⣿⣮⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣿⣿⣿⣶⣿⣿⣿⣿⡿⠷⠖⠤⣀
⠀⠈⠙⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣟⣿⡟⠿⠿⠿⣿⣿⣿⣿⠿⠛⠛⠛⠙⠛⠛⠂⠀⠀⠀⠀⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠤⠼⠛⠙⠓⠀⠐⠉⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠀⠁⠀⠀⡠⠆⢣⡀
⠀⢄⡀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⣆⡠⠎⠀⠀⠙⠠
⠀⠀⠈⠒⢄⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⠆⠀⠀⠁⡠⠊
⠀⠀⠀⠀⠀⠈⠒⢵⡤⠃⠀⠀⠈⠀⠀⠈⠀⠈⠁⢀⡜⠋⠉⠉⠁⠀⡠⠂⠁⠀⠠⠊⠁⠀⠀⠀⠆⠇⠀⠂⠐⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⣀⠄⠀⡄⠀⠀⠀⠀⠀⠟⠶⠖⢀⠄⠔⠉⠀⠀⠀⡔⠉⠀⠀⠀⠐⠒⣢⣍⣉⣈⣴⣬⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⢀⣷⡀⠀⠀⣀⠌⠀⡀⠀⡀⣍⠀⠀⢀⠴⠟⠚⠋⠉⠃⢈⠁⠉⣻⠀⠀⠀⠀⠴⣿⣽⡁
⠀⠀⠀⠀⠀⢀⠀⠀⢠⡄⠑⢣⡜⠇⠙⣮⠝⠉⠠⠐⣤⣁⣉⣉⠀⣘⢁⠀⡆⠀⣀⣀⡄⠈⠄⠠⣟⠇⠐⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠰⠤⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠤⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣤⠀⠌⡀⠀⠠⠀⡀⠤⠀⠄
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠢⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠀⠀⠒⠀⠈⠉⠀⠀⠈⢳⠀⠄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠨⠀⠀⠝⢤⡀⣀⠀⢀⣀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢈⡁⠤
⠀⠀⠀⠀⠰⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⡅⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠰⠀⠠⢄
⠀⠀⠀⠠⣎⠁⠹⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠩⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠀⠀⠀⠀⣶⡀⡡
⠀⠀⠀⠐⠀⠀⠐⠐⠀⠄⡈⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠶⠝⠤
⠀⠀⢀⠁⠀⠀⠀⠀⡁⠀⠢⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢠⠀⠀⠀⠁⢀⡀
⠀⠀⢨⠀⠀⠀⠐⠤⢢⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠐⠁⠀⠂⠀⠂⠔⠂
⠀⠢⠀⠰⠄⠀⡀⠔⠁⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢠
⠀⠈⠦⠂⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠁⠠⡀⠀⠀⢀⠂⠃⠀⠀⠀⠀⠀⠐⢇⠀⠀⠀⠀⡌⠀⠶⡄⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢳⠀⢀⡀⠀⠀⠀⠐⡀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣌⡀⠀⣀⠀⠠⠠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠠⠝⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠊⠋⠲⠸⠀⠀⠀⠀⠀⠀⢁⡌⡽⣈⠁⠀⣥⠻⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⠇⢂⠀⠸⢀⢏⣇⠀⠩
⠆⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠔⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠐⣬⢃⠄⠂⠙⢀⢛⠂⢁⠂
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣠⡆⠀⠀⠡⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣀⢀⣀⠀⠀⠀⠀⠀⢰⠃⠖⡤⠃⠀⠈⠄⠀⠀⠙
⢀⠀⠀⠀⠀⠘⢁⣤⡆⠀⢫⡇⠀⠆⠘⢀⣒⠀⠀⠀⠀⠀⠀⡀⣀⡨⠥⠥⢴⣚⢀⡣⠀⠀⠀⠀⠌⢸⠀⠀⡃⠊⡄⡀⠀⠀⠀⠀⠄
⠈⠙⣷⣄⣀⡀⢚⣀⡀⠀⠀⠀⠀⠣⢔⡥⠒⢋⡀⣀⠀⠀⣠⡥⠠⠈⣍⠑⢦⢁⠈⠀⠀⠀⠀⠀⠀⡀⠫⡄⠉⠀⠃⠁
⠀⠀⠀⠉⠉⠀⠈⠫⠇⠀⠀⠢⣤⣴⠾⠃⠀⠀⠀⠀⠀⠀⠐⠙⠀⠁⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀
⠀⠀⠀⠈⠂⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠅⠀⠀⠀⠀⠀⠀⠰⣶⣄
⠀⠀⠀⠐⢤⣘⣀⠀⠀⠀⠀⢀⠰⢒⢯⠁⢴⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠅⠀⠈⠀⠀⠀⠀⠘⣷⠟⢦⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⢑⠠⠙⠐⠛⠁⠀⠀⠀⠀⠀⠠⠊⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠃⣼⡧⢀⣾⢳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠔⡁⢂⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣖⠀⢠⠄⣠⣄⠐⠑⠂⠐⠄⠐⠀⠀⠀⠀⠈⠓⣶⡟⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⡡⠞⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣸⣿⠀⢷⡘⣷⣶⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣛⣡⣐⣛⣡⣿⣟⠛⢧⠀⠀⠐⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠻⠛⠿⠛⠛⠛⠛⠋⠙⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠲⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣾⣿⣷⣾⣿⣷⣦⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡞⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢏⣿⡆
⠀⠀⠀⢠⡞⡱⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢟⣿⡿⢣⣼⣿⣿⣿⣿⣿⣷⡻⣿⣿⡟⠋⢿⣿⡿
⠀⠀⢠⡟⡜⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢠⣿⡿⣴⣿⣿⣿⣿⣮⣿⣿⣿⣿⣯⠻⣷⡀⣸⣿⠁
⠀⠀⡾⣸⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣾⣿⣿⣿⣿⣾⣻⣿⣿⣟⣿⠛⠏⢸⣇⢻⣿⣿⠏⠐
⠀⢸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣀⣰⣿⣿⣿⡿⣿⣿⣿⣳⣻⡿⢸⣇⢠⣈⣿⢸⣿⡇
⠀⣸⢹⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⣴⣿⣿⣿⣿⣿⣿⣮⡿⣿⢻⣷⠀⣾⣇⢟⣿⣿⣾⣿⠁
⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢨⣾⢇⣾⣿⣶⣿⣿⣿⣿⠏
⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢐
⠀⠘⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠾⠛⢟⣋⣭⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠹⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣥⣶⣷⣿⠷⠿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠹⣿⣦⠀⠰⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠙⣿⠷⣄⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢭⣓⣲⠤⣤⣤⣤⣀⣀⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠖⠛⠙⠫⡉⠉⠋⠛⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣠⠴⠋⠉⠒⠀⠀⡀⠀⠀⠀⣀⠀⣠⡅⢀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢠⠞⠁⠀⠁⠀⢀⠀⠀⣡⣴⠟⠛⠉⣀⠀⠀⠈⠀⠑⠢⣄⣀⡘⢆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⡀⠀⠀⠀⣴⠃⠴⠉⠁⠂⢄⠀⣱⣾⠋⠀⣀⡤⢒⡥⠞⠚⠓⠒⠦⣤⡈⠱⣄⠀⢣
⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢠⢡⠁⠀⠀⡼⠁⠈⠉⠀⠲⢤⣀⣿⡟⠃⣰⣾⠭⡴⠋⢀⣤⠔⠂⠀⣀⠀⠱⣆⠈⡄⠤⡆
⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠘⢁⣸⠀⠀⢸⠁⠴⠤⠀⠀⣀⠀⣽⣿⠀⢀⣿⣏⡴⠀⣰⡟⢁⡤⢀⢠⠈⣆⠀⣿⠀⢱⣀⣿
⠀⠀⠀⡠⣾⡗⠀⠀⣀⠀⠀⠈⠻⠀⠀⡟⢀⠈⠀⠠⠇⠙⠃⠈⢿⠀⢠⣿⣿⡇⠂⣿⡇⢸⡘⠧⠔⢠⡏⠀⣿⠅⢸⠀⣿
⠀⠀⠀⠀⢿⣿⡀⠀⠿⢆⣦⡀⠀⢢⣰⠇⣀⠀⠀⠰⣶⣤⠁⠀⣾⡄⠀⢿⣿⣇⠀⠸⣿⡀⠙⠶⠶⠛⠂⣼⡿⢀⡏⢰⡇
⠀⠀⠀⠀⠈⢻⣿⣷⣔⡸⣿⣧⡀⠈⣿⢿⣶⣾⣿⣷⣶⣿⣷⡾⣇⣷⡀⠀⠘⢿⣄⠀⠙⢻⣦⣤⣤⣴⡾⠛⣡⠟⢀⡞
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⢿⣿⡷⣤⣈⠛⠻⠿⠿⣿⣿⣻⣿⣿⣿⣜⢷⣄⠀⠀⣽⣷⣦⣁⣈⣙⣙⣡⡵⠞⠁⣦⠟
⠀⠀⠀⠀⠀⠀⠸⣸⣿⣷⠘⣿⠗⡮⡛⠻⠶⠷⢷⡶⠷⠛⠿⢿⣿⣿⣦⣙⠷⣦⣀⠉⠑⠚⠉⡍⡉⠁⢀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢆⢿⣿⣇⢻⣗⣶⣬⣕⠂⣒⠂⠐⠐⠐⠂⠂⠻⠿⣿⣿⣿⣶⣭⣽⣓⣒⣖⣰⣐⡾⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣞⣿⣿⡆⠙⢿⣿⣿⣿⣷⣽⠶⡿⣧⣦⣦⣤⣄⠤⣈⢙⣻⣿⣿⣿⣿⣿⣟⣿⣿⣭⠭⢥⢴⢶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠈⠉⠋⢁⣸⣤⣾⣇⠇⠧⢏⢛⢻⣻⣏⣯⣿⣶⣍⣋⡯⠥⠷⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠂⠂⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣠⢋⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠰⡄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⡣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢀⡿⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⣰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢼⣥⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡄⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⢀⠀⢾⡇⠀⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠒⡎⠁⠀⠀⣔⡁⠀⡔⠛⣦⡄⢠⡶⠛⡄⠀⠀⢶⡄⠀⠑⠦⠤⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠈⠂⢠⡞⡟⢀⠎⠀⠸⠿⠀⠸⠟⡄⠈⠆⠀⠈⢻⡽⠀⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣿⣤⠊⠀⢰⠀⠀⠀⠀⠀⠘⡀⠈⣦⠴⣏⣀⢀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣋⣠⠃⠑⢤⡇⠀⠀⠀⠀⠀⠀⣷⠂⠉⢆⣈⣹⠏⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣹⠟⠦⠤⢼⠣⠀⠀⠀⠀⠀⢀⢻⠦⠀⠞⣯⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠄⣾⠀⠙⠇⠀⠀⠛⠁⢸⡶⠀⠀⢀⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡄⠀⠠⠴⣾⠀⠀⠀⠀⠀⠀⠀⢸⠷⠠⢒⠜⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⣀⠀⠀⠠⢾⡄⠀⠀⠀⠀⠀⠀⣸⠦⠐⡁⠚⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠀⢈⡒⠀⠠⠶⢷⣶⠒⠒⠒⢾⣿⠿⠒⠀⠀⠀⠉⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠁⠀⠈⠁⠀⠀⠀⢰⡿⠦⠌⠉⠿⣿⠀⠀⠀⠀⢀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⢸⣄⣀⡀⠀⣠⣼⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⢸⡉⠉⠀⠀⠀⣱⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠂⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣤⣳⣆⡀⢀⣴⣧⡄⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠂⠀⢹⡈⠉⠁⣘⠁⠀⢢⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣄⣀⣀⣧⣄⣠⣇⣀⣠⠼⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⣀⣀⡠⡤⢤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣠⢒⣦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡀⠀⢀⣀⡾⣿⣿⡆⣀⠈⢀⣤⡄⠀⠀⠀⠐⠐⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⡆
⠀⠀⠀⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠶⣤⣬⣵⣦⣿⡧⣽⣻⣿⣡⣾⣯⣤⣤⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⢉⣉⣩⡐⣶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣾⣤⣆⣀⡀⢀⢀⣀⣀⣤⣤⣤⣤⠄⠐⠒⠋⠉⠉
⠀⠀⠀⠀⠀⣴⡟⢳⠩⠃⢼⣐⠉⠉⢌⣁⢉⡉⢛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⠫⠙⠋⠁⡀⢼⠃⠻⠹⣟⡵⣦⡀
⠀⠀⠀⠀⠀⢫⡝⡞⣼⣆⣴⣣⣒⠢⣤⡴⠶⢒⠋⠿⣿⡽⣿⡿⢻⣿⡿⠿⢋⢿⣿⣿⣿⣿⣿⣟⡛⢦⣀⢛⡒⢠⡆⢓⡄⢂⡄⠣⠀⠉⡆⢹⠇
⠀⠀⠀⠀⠀⠀⠙⣷⢾⡋⢛⠑⠉⢠⡄⠀⠀⠠⠀⠈⢡⠾⠏⢀⢸⢻⣿⠉⠉⢛⣿⣿⣿⣿⠛⠟⠊⡒⠄⠀⠉⠀⠀⠃⠤⠐⠋⠓⠪⣴⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡆⢲⠀⠂⠀⠐⠀⠀⠀⢀⠴⠅⠀⠀⠀⡟⣿⠛⠁⠁⢹⠋⡿⣿⢿⡄⠀⠀⠀⠂⠐⠀⠀⠠⠀⠀⠢⠀⠐⡁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠂⠀⠀⢀⠄⠁⠀⠀⠀⠀⠎⠀⠀⠀⠇⠈⢿⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠄⠒⣿⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠠⠖⠒⣿⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⡿⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠛⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣻⣿⣿⣿⣭⣽⣿⣿⣿⣻⡶⣤⡙⢳⡀
⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⢠⣴⢿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⡼⣿⣿⡶⣅
⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⠻⣿⣿⣧⡀
⠀⠀⣿⡇⠀⣐⣶⣂⣀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢂⠌⢻⣿⢳⡀
⠀⠀⠸⣧⠀⠹⣿⠿⣯⣀⣴⣶⡿⣠⡿⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢻⣿⣷⠐⠢⣄
⠀⠀⠀⠙⢷⣄⡀⠀⠈⠉⠉⣉⣵⠟⠁⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⣿⣿⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⢸⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡧⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠈⠱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⢿⣿⢀⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡄⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣼⣿⣾⣣⠟⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣒⣂⣸⢇⣿⣿⣏⣳⣛⣡⣤⣶⡶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠡⠀⠚⠁⠀⠀⠀⠀⣀⣙⣾⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢸⣵⣛⣽⣿⣿⡷⣻⣿⣯⣽⣿⣿⢿⠿⡞⠁
⠀⠀⠀⠀⢀⡠⠒⠉⠁⠀⠀⡸⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣞⣿⣻⣿⣿⣻⣿⢟⣟⡁⣩⣤⣴⠾⠋⠉⠡⡄
⠀⠀⠀⢠⠋⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⡓⠛⠛⢛⣭⣵⣿⣿⣿⣿⣿⣯⣝⣾⡉⢠⠖⠒⠒⠚⠁
⠀⠀⠀⢸⡀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣟⣿⣿⣿⡿⠛⠛⠺⠝⣦⠙⡇⠘⠦⠄
⠀⠀⠀⠀⣿⣄⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢹⠇⢐⠀⠀⠘⡄
⠀⠀⠀⠀⠙⣌⠳⣤⣿⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠀⣀⣀⣀⠀⢀⣀⣴⠟⠀⠀⠙⠒⠚⠁
⠀⠀⢀⣤⣤⣈⡻⣮⢻⣄⠀⢸⠀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠈⠉⠉⠁⢀⣀⣀⣀⡀
⠀⠀⠈⢛⡿⣿⣿⣿⣽⣿⣦⠟⣿⡟⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠋⠉⠙⠛⢿⣦⡀
⠀⠀⡄⠈⠙⠷⣦⣤⣌⣹⣛⣶⣿⣧⠀⠻⠃⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠉⠉⠉⢲⠀⣼⠻⣿⣿⣿⣿⣿⣷⣶⣄⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠉⠀⠃⣾⠛⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠸⢄⡠⠔⠀⢿⡀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣤⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⢿⡿⠿⢿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⢒⠒⢼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠘⠱⠉⢿⣧⠀⡇
⠀⠀⠀⠀⠀⠐⠀⠂⠄⡀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠂⠉⢳⡄⠀⠀⠀⡇⠀⠁⠀⡇
⠀⠀⠀⠀⠀⢈⠦⠄⢀⣤⠌⠒⠒⠉⠉⠀⠀⠀⠀⠀⢀⡠⠃⠈⠢⣠⠔⠑⢄⠀⠀⠇
⠀⠀⢀⠤⠒⠙⠤⢀⣀⠀⠀⠁⠈⠉⠁⠀⠐⠒⢖⠊⢹⠀⠀⣀⠤⢻⡀⠀⠀⠑⠊
⠀⠀⠈⠢⠤⠤⠄⣲⠷⢝⢏⠐⠂⠤⠄⣀⣀⣀⠜⠒⠚⡏⠉⣏⠠⢼⡇
⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⣀⡑⢤⠤⠒⠉⠀⠀⠀⠀⠈⡇⠀⠉⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⡠⡤⡀⠀⠀⠀⠀⠀⢸⡇⠄⡤⠀⠐⠧⠌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠩⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠂⠈⠀⠠⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠀⠀⢀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢤⣠⠤⠒⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⢇⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⠚⠉⠉⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠴⠒⠛⠒⠒⠲⠶⠦⠤⢤⣀⣀⡀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⡈⢂
⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣆⢀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠈⡹⣧⠚⠃⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⠻⢵⡇⠀⠁⠎⠁⣰⡟⠓⠠⣍⣓⣒⠶⠦⠤⠠⠀⣀⣀⢀⣠⠔⠛⢃⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⡷⣾⣄⢫⠠⢴⣻⡏⠹⢶⣴⣬⣌⣐⠳⠒⠓⠋⠀⢄⣲⢽⠿⣫⠴⢯⡶⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢃⣹⡼⠛⢿⠃⣷⣶⠤⠿⢻⣿⡷⢂⠀⡄⢂⣉⡽⢋⣥⢋⣅⠚⡛⠛⠀⢀⡥⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣥⠀⠀⠙⠻⠯⢖⣾⣟⣿⣯⡤⣒⣵⣺⠟⢉⣴⣿⣤⣍⣀⡀⠀⠀⠈⡒⠁⠰⠾⢣⣀⣿⠃⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠎⠀⠐⣏⠀⠀⠀⠀⠀⢠⠟⢩⡏⠙⠛⢻⣋⠥⠞⠛⡻⠌⠀⢛⢉⣹⡟⠲⣦⡤⢤⣤⣈⣂⡀⠀⠛⠋⠙⢂⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠐⠀⠀⠀⠻⡀⠀⠀⠚⣯⣀⣀⡀⠀⢼⡷⠊⠛⠩⠷⠀⢹⠁⢺⡟⠦⣟⣹⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠉⠉⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⣾⠟⠿⢦⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⡴⠿⠻⣷
⠀⠀⠙⢷⣦⡈⢻⣦⠀⠀⠀⠘⣿⠀⢰⡿⢷⡆⠀⠀⠀⠀⢰⡿⢿⡆⢀⣿⠁⠀⠀⠀⣴⡟⢁⣴⡾⠋
⠀⠀⠀⠀⠙⣷⠀⢻⡇⠀⠀⠀⢹⣧⠘⠻⠟⠃⠀⠀⠀⠀⠘⠻⠟⠃⣼⠏⠀⠀⠀⢸⡟⠀⣾⠋
⠀⠀⠀⠀⢀⣿⠀⣸⡇⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⢸⣇⠀⣿⡀
⠀⠀⠀⠀⣾⠏⢠⡿⠁⠀⠀⠀⣸⡏⢈⣿⣶⣄⣀⣀⣀⣀⣤⣶⣿⡅⢹⣇⠀⠀⠀⠈⢿⡄⠹⣷
⠀⠀⠀⢰⣿⠀⣿⡇⠀⠀⠀⢠⡿⠀⣾⠇⣼⡏⢹⡿⢿⡏⢹⣧⠸⣷⠀⢿⡄⠀⠀⠀⢸⣿⠀⣿⡆
⠀⠀⠀⠀⢿⣆⠘⢷⣤⣤⣴⡿⠃⣸⡟⢀⣿⠁⣼⡇⢸⣧⠈⣿⡀⢻⣇⠘⠿⣦⣀⣤⡾⠃⣰⡿
⠀⠀⠀⠀⠈⠻⣷⣤⣈⣉⣁⣤⡾⠟⢀⣾⠃⣰⡿⠀⠀⢿⣆⠘⣷⡀⠻⢷⣤⣀⣈⣁⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣴⡿⠁⣴⡟⠁⠀⠀⠈⢻⣦⠈⢿⣦⡀⠈⠉⠉⠉⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⢉⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⡉⠻⢷⣦⣤⣀⣀⣀⣀⣀⣀
⠀⠀⣾⡛⠛⠋⠉⠉⢉⣉⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⣉⡉⠉⠉⠙⠛⢛⣷
⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀
⠀⠀⠀⢠⡍⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣭⣽⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢺⣿⡇⠱⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢁⣘⠿⠀⣿⣿⣿⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡈⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⡟⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⣿⣿⣿⣟⡶⠀⠀⣉⢻⣿⣿⣿⣿⣿⠛⢉⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⡟⠃⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣠⣉⠺⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣍⠑⠋⠀⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣧⣴⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⠿⡄⠀⠀⠀⠀⠀⠀⠈⠁⢘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢛⣛⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⢷⣶⣟⣀⠃⣀⢠⡜⠀⠀⣸⠟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⣾⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣆⣬⠉⠁⠀⠀⠀⠀⠀⢠⠋⠀⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡉⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⣼⢉⠃⠀⠂⠀⠀⠀⢀⠴⠛⠠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⢱⣟⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠧⣬⣁⣄⡀⠀⠶⠈⠁⠀⢀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢨⣟⠛⠖⡠⠇⠨⡇⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢶⣤⣤⣠⠀⣠⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣭⠸⠉⠖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣟⡀⠀⠀⠝⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠇⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡥⠄⠐⠀⠀⣰⡞⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣀⠀⠀⣱⣎⢿⣋⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣬⠍⣶⠀⢱⡋⣦⣹⣷⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡈⠓⠞⠻⣏⣽⣿⣿⣯⣿⣿⣿⡉⠛⠙⠛⠋⠙⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠛⣟⣱⠿⣷⣼⣿⣿⣿⣥⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⠿⠿⢿⡿⠿⠹⣿⣿⣏⣩⡴⠾⠙⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠁⠀⢘⣿⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⡀⢲⣿⣶⣝⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣦⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣧⠽⡍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⡸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⢀⡙⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢶⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⢿⣷⣌⠙⢿⣿⣿⣿⣿⢛⣿⣿⣯⡉⠁⠉⣭⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⡑⢋⡁⣾⣝⣷⣦⣈⠛⢿⣿⣿⣿⣿⡿⠃⢁⡀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠁
⠀⠀⠀⣠⣶⣾⣿⣿⡿⠋⠀⡙⠀⠀⠀⠈⢱⣿⣼⣿⣶⣮⣭⣛⣛⠓⠒⠷⠆⠁⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⠛⠾⣿⣿⣿⣶⣤⣄⣠⣤⣤⣼⣷⢸⣿⣴⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣬⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⢛⣽⡿⢻⡏⠈⢹⠁⠈⢈⣿⣷⢶⠤⢄⣴⡵⡗⣠⠀⢀⣴⣾⠟⣳⠤⢤⣀
⠀⠀⠀⠀⠀⣠⣺⠟⢿⠋⢡⠀⣡⡀⣼⠀⠀⣾⠟⠁⠊⠁⠀⠈⠀⢿⣟⡷⢉⢙⣈⡴⢯⡄⠀⠈⠑⠢⡀
⠀⠀⠀⠀⢀⡿⠋⡤⣒⣀⠿⣿⣿⢻⡛⣦⣾⠇⠁⠀⠀⠀⠀⠀⢠⠄⠉⠳⢾⠿⡋⠀⠈⢻⣦⣄⠀⢀⡈⠢⡀
⠀⠀⠀⠀⢺⠖⠊⣠⠏⠀⠀⠋⠘⠈⠃⢸⣿⡀⠀⠀⠀⠀⠀⢰⡃⢆⠀⠀⠀⠙⠪⡀⠀⠀⠈⠛⢤⣮⠻⣦⡘⣦
⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣳⡀⠀⠀⠀⠙⢧⣄⡁⠀⢰⢆⣠⣿⣤⣤⠀⠀⠀⠉⠳⣝⣝⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⠏⣹⠖⢲⡤⠀⠠⢤⣍⡲⠤⠥⣈⢿⠿⢿⣷⣄⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣴⣷⣊⢤⢴⣿⠤⠾⡿⡚⠛⠛⢿⡛⠻⡓⠛⢋⣉⣀⣀⣉⣤⣤⡤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⢸⢿⠀⠀⢀⣧⠀⠀⠸⣷⠀⢈⣙⣃⠉⠀⠀⠀⠳⠶⠖⠐⠉⠃⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⣾⠀⠀⠈⢘⣄⠀⠀⠙⢇⣯⣁⣀⡄⣄⣒⡁⣀⡀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠒⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⣧⠐⠆⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠄⢹⠿⢀⡃⠀⠀⠀⠀⠄⠀⢀⠀⠀⡧⡄⠀⠀⠀⠀⢀⣠⣄
⡄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠰⢧⣤⣄⣤⠴⡺⠋⠀⠀⠀⠀⣴⣿⣧⣿
⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⡀⠀⠀⠀⠀⠀⠠⡀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣰⡶⠤⣶⡛⣶⣿⡟⠷⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⠛⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣴⣾⠋⣶⡆⣬⣿⡈⢹⣿⣦⠀⠑⡀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠈⠠⡀⣀
⠀⠀⠀⠀⠈⠓⠦⢤⡾⠟⠁⠀⣈⣭⣴⢻⣿⡗⢠⣿⡏⠀⠀⠑⢄⣀⣀⣠⠞⠀⠀⠀⠀⠀⢮⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠪⡕⣿⠟⡀⠀⢠⠚⠷⠶⠒⠦⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠲⠛⠋⠀⠀⠀⢀⣀⠐⢄⠣⠀⡄
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠡⡼⠋⣾⡇⠀⡇⠀⠀⠂⠀⠀⠘⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⡠⠤⠌⠛⠛⠻⠦⢧
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡿⠃⠀⠑⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡧⣄⠀⠁⠀⠀⠐⠀⠄⠂⣰⡿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠀⠀⠀⢻⠀⠠⡀
⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡀⠀⠀⠀⠘
⢦⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠿⢶⣶⣄⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠳
⠀⠀⠀⠀⢨⠤⣤⡀⠀⠀⠀⠁⠈⠣⡐⠀⠀⠀⠀⠀⠀⠙⠿⢗⣹⣶⠿⠟⠃⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠰⡇⡀⠈⣹⣟⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠙⣆⠀⠀⢸⡇⠀⠀⠀⠀⡌⠻⢷⣀⢀⣀⠀⠁
⠀⠀⠀⠀⠀⠈⠑⢤⡘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⡤⠀⠀⡀⣠⠴⣊⣥⠶⠶⠦
⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢶⣦⣤⣄⣠⠀⠀⠀⠀⠀⠨⠥⣶⣦⣶⠾
⣶⡒⠀⠀⠀⡀⢀⡀⠄⠂⠀⠀⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠓⠷⠔⠂⠒⢌⡳⣶⣦⣶⡀
⠳⠀⠀⠀⢀⠈⠀⢀⣠⡼⠃⠀⠘⣿⣯⡄⠀⠀⠀⠀⠀⡈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠉⠁⠘
⠀⠀⠠⠄⠙⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠂⠀⢀⠀⠀⠀⠀⠸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣿⣿⣿⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠏⠀⠹⠛⢿⣶⣶⣝⠻⠿⣿⡿⣸⣿⣿⠏⢀⣿⠀⢈⣿⣿⡿⢸⣿⣿⠛⠉⠉⠀⠀⠁⠈⠹⣿⣿⣿
⠀⠀⠀⣿⠗⠀⠀⠀⠀⢸⣿⣿⢧⣾⡿⠁⠃⢻⣿⠀⠘⣏⠀⣸⣿⡿⠁⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠿⡛⣻⣿⡟⠁⠀⣧⠈⣿⡀⠀⠀⢠⣾⣿⡇⠀⠘⢈⣿⡄⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⣿⣄⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⠀⣿⣷⣿⣧⠀⠀⢾⣿⣿⣿⡀⠀⣾⣿⣿⡄⠀⠀⡀⠀⠀⢈⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡕⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣇⣸⣿⣿⣿⣿⣧⣆⠈⡐⢠⢾⣿⣿⣿
⠀⠀⠀⣿⠎⠉⠏⠁⢺⣿⣿⡿⠟⠛⠿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠟⠻⠿⣿⣿⣿⠛⢙⣿⠙⢻⣿
⠀⠀⠀⣿⠀⠰⣶⠐⢨⣿⠋⠀⠀⠀⠾⠆⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⠒⠀⢳⡄⠈⢿⡇⠀⠈⣿⣤⠀⣿
⠀⠀⠀⣿⡄⠀⠁⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣶⡆⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣇⠀⢸⣇⠀⠀⢸⣏⣠⣿
⠀⠀⠀⣿⣷⡀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⣿⠟⢿⣇⠀⠀⠀⠀⠠⡾⠋⠈⠀⢸⣿⡄⠀⢸⢛⣼⣿
⠀⠀⠀⣿⣿⣷⣤⣾⣿⣿⣧⠀⠀⠀⠀⢸⠟⠁⠀⣸⠋⢀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣸⣿⣿⣿
⠀⠀⠀⣿⣿⡿⠻⠏⠩⡔⢿⣷⣄⠀⠀⠨⠂⢀⣴⠃⠀⢸⠘⠟⢿⣄⠀⠀⠀⠀⢀⣴⡟⠛⠏⢹⠿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠐⠀⠀⣧⢾⣿⣿⣿⣶⣴⣾⣿⠁⠀⠀⣿⠀⠀⢸⡟⢿⣦⣤⣶⣿⣿⠀⡀⣿⡿⢎⠛⠛⣿⣿
⠀⠀⠀⣿⠟⡇⠀⠀⠀⡧⣾⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⠀⠀⣾⠋⡾⣿⣿⣿⣿⣿⠀⠀⠈⣷⢸⣇⣴⣿⣿
⠀⠀⠀⣿⣄⠃⠀⠀⡖⢀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⡆⣿⡆⡸⠃⣼⢿⡝⢿⣿⣿⡿⠂⡠⢴⡟⣿⣿⣿⣿⣿
⠀⠀⠀⣿⡿⠀⠀⠀⡅⠬⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣾⡇⠐⠈⠤⡻⣟⣮⣿⣿⣄⠀⣷⡾⣳⣿⠻⢿⢻⣿
⠀⠀⠀⣿⣶⠂⠀⣨⣇⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢈⣡⣬⣧⢹⣿⠁⠁⠀⢸⣿⠃⣼⣠⣿
⠀⠀⠀⣿⣿⡅⢰⢿⡟⠀⠪⣿⣿⣇⡤⠔⠂⠀⠂⠰⣿⣿⣇⠀⠀⠀⢀⣯⣿⣯⣿⡯⢄⣀⢠⣮⣶⣿⢿⣿⣿
⠀⠀⠀⣿⣷⣖⠌⠀⠇⠀⢸⣿⣽⣿⣶⠀⠀⢀⣠⣾⣿⣿⣿⡖⡀⢀⣾⣿⣿⣿⣿⣧⣾⣥⣀⡏⢻⣿⡿⣼⣿
⠀⠀⠀⣿⣿⣿⣇⠀⠀⢀⡮⣽⣾⣿⣿⣧⢁⣾⣿⡿⠟⠙⣿⠊⠀⠀⠹⣿⣿⣿⣿⣯⡏⠉⠚⠇⠈⠙⢳⣾⣿
⠀⠀⠀⣿⣿⣿⣿⡇⠀⣼⣁⣿⣿⣿⣿⣿⣜⡏⢿⡉⠀⠀⢷⣀⠔⠐⢀⣿⣿⣿⣿⣿⡏⡶⣠⢦⣖⣶⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣮⡀⠁⠀⠀⢺⣡⠆⣠⣾⣿⣿⣿⡿⠿⣿⣶⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢿⣟⣋⠛⠉⢁⡰⠀⣆⠐⣏⠛⢿⣿⣿⣦⡀⠀⢿⣣⣾⣿⣿⡿⠟⠁⣠⡆⠐⠀⠉⠉⠉⠙⠛⠿⣿
⠀⠀⠀⣿⠟⢁⣈⠁⠀⣸⠃⠀⣿⠀⠘⣆⠁⡀⠙⠻⢿⣶⣾⡿⢟⣋⣅⣶⣶⣾⣯⡁⠀⢀⠙⠆⠀⠀⠀⠀⢿
⠀⠀⠀⣿⢰⡶⠁⠀⢩⣏⡀⠴⣿⠄⠈⠙⣦⠀⠐⠀⠂⣾⣯⠘⣻⠟⣻⡿⣿⢻⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⠁⠀⠙⣿⠇⣀⢀⣿⡆⠀⠐⠛⣷⡄⢀⣾⣿⣿⡏⠁⣰⣿⣽⠃⣼⢡⡏⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⣿⣿⡇⠐⣶⡿⢠⡃⠀⢹⣿⣦⡄⠊⠛⣿⣾⣿⣿⣿⣿⣜⣿⣿⠋⢀⠃⠼⣇⠀⠀⠀⢱⠀⠀⣰⣿⣿
⠀⠀⠀⣿⣿⣧⣤⣼⣯⣶⠀⠈⢿⣿⣿⣧⣔⢊⣹⣿⣿⣿⣿⣿⣿⣿⣇⣠⣀⣀⡷⡿⠀⠀⣀⣽⣶⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⠖⣰⡶⣂⣴⣦⣄⡀
⠀⠀⠀⠀⠀⣠⢠⡟⢡⡾⢡⡾⢉⣴⡿⠛⣻⣿⣯⣙⢆⣠⣀
⠀⠀⠀⣀⢸⠏⣿⡄⣼⡇⢸⠇⢸⡏⢠⡞⠉⣠⠴⣿⣿⣿⣿⣷⣦⡀
⠀⠀⢠⡟⣾⡄⢿⡇⠘⣇⠈⠧⠊⡰⣊⡴⠚⠁⢰⣿⣿⣽⣽⡿⣿⣿⣷⣤⣀
⠀⢀⣏⣇⠸⣿⣄⠹⡆⢸⡀⢠⢊⣼⣫⠀⠀⠀⢈⣻⣾⣿⣝⣧⣿⣛⣿⣻⣿⣷⣤⡀
⠀⡞⣿⡻⣶⣄⠹⡄⢷⠈⢇⣤⣿⣿⡇⢀⣴⣿⡽⣿⣷⣿⣟⣿⣟⣿⣶⣿⣾⡽⣿⣿⣶⣀⡀
⠀⣧⡘⠿⢦⡘⣦⠀⠀⠙⢨⠿⣿⣿⣇⡞⣿⣽⡿⠟⣛⣭⣽⣿⣿⣽⣿⣿⣿⢟⣛⣛⠿⣿⣿⣶⣤⣄⡀
⠀⣟⠳⢦⣤⠙⠈⠉⠁⢀⣬⢠⣿⡟⡛⢛⣫⢵⡖⠉⠏⢩⡉⠁⠙⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣷⣶⡶⠿⢟⣒⠳⠤⠤⠤⢄⣀⣀
⠀⣛⠷⢦⣤⠶⠛⠒⠾⠛⣁⡴⢠⠘⢮⡺⣿⣿⣿⣄⠀⠸⡄⠀⣸⣭⠿⣿⣋⡉⢙⣛⣻⡿⢿⣿⣿⣿⣿⣿⣧⣤⣀⡀
⠀⠹⠷⢶⣤⣤⠶⠾⠟⠛⠋⢀⡿⠀⢸⣿⣾⣿⣿⣿⣷⣶⣦⣾⣿⢟⣻⣙⠻⣿⠿⠿⢦⣭⣿⣿⣿⣿⣷⣶⣞⡓⠨⠍⠑⠒⠢⠤
⠀⠀⣳⣶⣦⡴⠿⡟⢀⣴⠟⠋⢀⠔⢿⣷⡝⢿⣿⣿⡷⣎⡙⠃⠰⠿⢿⣿⣷⣿⢿⣷⣾⣶⣶⣮⣛⢾⡔⠂⠭⣻⣟⠳⠦⣄⠀⣀
⠀⠀⠈⢿⣍⣤⣶⠆⢸⡟⠀⣴⡟⠀⣸⠏⢠⡟⠉⢹⣿⣬⣒⠀⠀⠀⠐⠌⠻⣿⣦⣞⣿⣝⣟⢻⣏⠱⡝⣆⠀⠀⠉⠑⠢
⠀⠀⠀⠈⢛⡛⣁⣤⣿⠇⢀⣿⠀⠀⣷⠀⣼⡇⠀⠘⣷⠈⠻⡄⠀⠀⠀⠀⠀⠀⠹⡇⡉⡨⠈⣿⢿⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠻⠟⠛⢋⣠⣾⡿⠀⢠⣿⠀⣸⡇⠀⢠⣿⠀⠀⠘⠆⠀⠀⠀⠀⠀⠱⠈⡶⠏⠀⠠⣄⠀⠀⠀⠑⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠟⢋⣡⢤⡴⠟⠁⣰⡿⠇⢠⡾⠁⠀⣠⡆⠘⡀⠀⠀⠀⠒⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⢀⣴⣾⠟⠀⣰⣿⠁⠀⢰⣿⡅⠀⠓⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠛⠛⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⣃⠀⠇⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣷⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠛⢋⠁⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠈⠛⢍⠀⠒⠠⢄⡀⠈⡀⠐⢀⠦⣀⡄⢘⠆⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀
⠀⠀⠀⠈⠢⠀⠀⠉⠉⠣⢄⠘⠤⠤⠒⢀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠤⠽⠿⢿⣿⣳⣶⣶
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠑⠢⡐⢀⢯⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠄⠠⠀⣶⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⢠⠄⠛⢦⣛⢛⡿⠿⠶⠾⣞⠋⠉⠉⠀⠀⠀⢀⠀⠀⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡄⠀⠀⠈⠛⢤⣀⡀⠐⠈⠓⢄⡀⠀⠀⠀⠀⠈⠐⠠⢀⣺⠇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠉⠳⣄⣀⠀⠊⠉⠲⢤⣀⠀⠀⠀⠀⠀⣿⠃⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠙⠦⡄⠀⠐⠂⠀⠉⢒⡦⢤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠠⠀⠀⠈⠐⠤⡂⠤⠤⠀⠀⠀⠸⣿⠙⠓⠲⠤⣄⣀⣀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠐⠄⠀⠀⠈⠓⠺⣄⠙⠒⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡈⠂⢄⠀⠀⠈⠑⠦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠂⢄⠀⠄⠘⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡉⠢⢈⠂⢝⡿⣶⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣅⠂⠈⠐⠤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠗⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠋⢕⡢⢄⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡉⠒⢑⣤⠀⠈⠻⢶⡄
⠀⠀⣶⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⣿⣶⣄⠀⠙⣦⡀
⠀⢸⣿⠀⢸⣿⡀⠀⠀⠠⡀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣌⣻⡄
⠀⣿⡗⠀⢸⡿⡇⠀⠀⠀⠈⠢⢄⠙⢆⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⠋⠑⢦
⢸⡿⢇⠀⣾⠃⡇⠀⠀⠀⠀⠀⠈⠑⢌⢳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠈⡇
⢸⡇⠘⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⣟⢤⣄⣠⣄⣀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡠⢓⠰⣶
⣼⡇⠈⢸⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡆⠹⣯⠖⠻⠿⣦⢄⡀⢠⣿⠿⠉⠉⢡⠟⡄⢸⢧
⣿⡇⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⡡⠞⢲⣿⣆⠘⢿⡦⣄⡀⠉⠉⣻⣿⡇⠀⢀⣿⠀⢷⠀⣸⡀
⣿⡇⠀⠀⠘⡽⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢸⡸⣿⠀⠈⠻⣮⠙⠦⣠⣿⡿⠛⠷⣮⣴⠀⠺⡀⣿⡅
⣿⣧⠀⠀⠀⣷⠀⠀⠀⠀⠀⢰⡳⠁⠀⠀⣿⣿⢿⡇⠀⠀⠘⠷⡀⢾⢿⣧⡀⡐⠈⣿⠲⣦⡇⣸⡇
⢹⣿⡀⠀⢰⢳⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡿⣿⠈⢿⡄⠀⠀⠀⡇⢸⡎⣯⠛⢅⣨⡏⠀⣹⠛⣷⣇⡀
⠈⣿⣿⣷⣮⣦⣠⣤⠀⢀⣮⠃⠀⠀⠀⠀⢻⡹⣧⡌⠑⠶⠶⠚⣰⠟⣰⠋⢳⠀⠹⣄⣼⠏⡘⡾⠀⣙⠳⢤⣄⣤⠔⠛⠶⠂
⠀⠈⠻⣿⠋⠈⠉⠈⢳⣦⣥⣤⣤⣶⣤⣤⣤⣵⣝⠻⢶⣶⡶⢟⣫⡞⠁⠀⢸⡄⠀⠘⠏⡰⣡⠇⣼⠛⠉⠉⠈⠉⠓⠒
⠀⠀⠀⠙⠻⢶⣤⣤⣾⡿⠀⠀⠀⠀⣠⡤⣸⣿⣿⣿⣷⣶⣿⣿⣿⣧⠀⠀⠈⣧⣀⠀⢘⣿⢋⣾⠏
⠀⠀⠀⠀⠀⠀⢀⣽⠿⠿⣿⡿⠟⣿⣗⣛⠿⣿⣽⣿⡄⠈⠛⢿⣮⡻⣧⣄⡀⢘⣿⣷⣾⡧⣿⠃
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠊⢁⣴⠶⣿⠊⠙⢿⡶⢭⣽⣿⣄⠀⠈⢻⣷⣹⣿⣿⣿⣷⣿⣿⢿⠁
⠀⠀⠀⠀⢠⠞⠁⠀⣠⠶⠋⠀⣠⠇⠀⠀⠀⠈⠁⠊⠛⢻⣷⣄⣀⣿⣿⣿⣿⡿⠿⠟⠛⠛⡄
⠀⠀⠀⣴⠋⠀⠀⠀⠋⠀⠀⠀⠋⢀⣤⣀⣠⣶⣶⣾⣿⣿⣿⠿⣿⣿⢟⣽⠋⣠⡔⠂⢉⣴⣿⡆
⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⡽⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣫⣿⡩⠔⠚⠁⠠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣩⣤⠖⠊⠀⢀⣽⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⡋⠁⠤⠂⠀⠈⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⣀⡀⠴⠊⠛⣻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡠⠔⠊⠙⢙⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣠⣴⡏⠙⢿⣿⣭⡋⠋⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⠹⠀⠀⢻⠋⠳⣄⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⣿⡟⣿⣿⠁⠀⠀⢸⡶⠾⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠸⡇⠘⡿⣤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣾⠿⠛⠃⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣻⣏⣌⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣭⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠄⠀⢀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠀⠀⠀⠈⠙⠻⣿⣮⡙⣯⣦⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠐⠒⠒⠊⣉⣉⣁⣀⣠⣤⡰⠖⠚⠉⠉⠉⠙⠛⠻⠿⡷⠶⠾⣿⣶⠚⣽⡗⣶⡿⠃⠀⠀⠈⠻⣿⡿⠉⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠲⠶⠒⠒⠚⠛⠛⠙⠛⠛⠛⠛⠛⠛⠲⠶⠶⠒⠒⠒⠒⢾⣿⣿⣿⣾⣭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠻⠶⠶⠷⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠞⠛⠛⠉⠉⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢚⡽⣀⣤⢀⡄⢀⢠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠫⢎⣾⡜⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉
⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠄⢀⣶⣶⣦⡀⠈⠉⠁⠀⠀⠀⠉⠑⢢⡤⢶⣷⣿⣾⣆
⠀⠀⠀⠀⠈⠖⣧⠀⠀⣧⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⡆⢸⣿⠧⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡘⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⣧⡀⢸⣴⡄⢸⠀⠸⢀⡆⠀⢠⠀⢸⠀⡀⠀⠀⢀⡤⠂⡰⠃⠀⠀⠀⠼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⡀⠀⣄⠀⠉⢲⣼⢿⣾⣠⣆⣼⠀⣠⡏⠀⠘⣾⣁⠀⢀⡏⠀⢠⠅⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢪⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣷⣾⣦⢀⠀⠙⢻⣿⣿⣿⣗⣷⣿⣷⣚⠀⢻⣏⢰⣿⣇⠀⢸⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠐⠢⢰⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⡾⡄⠈⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⢹⠧⢠⢺⣸⣿⣿⣿⣿⠇
⠀⠀⠀⠁⢼⣿⣿⣿⣿⣿⣿⡂⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⡇⢰⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠀⠁⠀⣿⢾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⢀⣀⣴⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣃⣾⣿⣿⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⣾⢹⡏⡯⢻⣾⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠻⠛⠋⠙⠉⠁⠉⠉⠉⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⠀⠥⠀⠗⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⢊⠻⡍⣍⠩⡹⢄⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢯⣦⡐⢾⣦⡑⣿⠸⡆⢿⡌⡯⢨⣄⢸⡝⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⢷⣮⠻⣷⠙⢧⠘⡇⠁⣸⠃⣿⠞⢛⣼⠇⢰⠀⢙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣛⡛⢦⡙⣧⠘⡅⠹⡀⠃⡼⠁⡾⠋⣠⡾⠋⢀⡾⢡⡏⠀⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠻⣗⣐⣛⠮⢧⠘⣆⠙⣄⢀⡌⠁⣸⠇⠚⠋⣀⣴⠟⢁⣾⠇⡠⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣃⠀⠂⢀⣠⡌⠢⣍⣁⣸⣦⡸⡄⠈⢘⣃⠴⠃⣠⠴⠛⠉⣠⡴⠋⢁⡴⠋⣰⡟⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢶⣄⠃⠶⠂⠲⡀⡀⠈⠉⠛⠻⣿⡷⢾⣿⣴⣞⣋⠁⣠⣤⡞⠫⡤⠶⠛⠛⠾⠟⢀⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠄⠉⠆⣋⣛⢌⠰⢄⡇⠀⢄⠀⢠⠀⠈⣃⡀⣼⣿⢻⣟⠛⢫⡁⢀⣤⣤⣤⣤⣤⡤⡴⠞⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⢴⣑⢊⡅⣀⡟⠶⠙⠚⠘⣙⣀⣑⣘⣋⣉⣩⣥⡶⢿⣧⣏⣿⠳⣌⡛⠋⠉⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⢀⠀⠀⠀⢀⠴⠋⡠⢗⣞⠭⠁⠴⢶⡟⠋⠉⠉⠉⠉⠛⣿⣿⠛⠙⣵⠆⣹⣷⡿⡆⢹⡛⠑⢶⡶⡤⣤⣀⡀⠀⠀⢀⠀⠂
⠀⠀⣇⣯⠟⣉⣈⣁⣈⣁⣀⠀⠀⠂⢀⡄⢀⡀⠃⠀⠄⣰⡿⠿⢀⠜⠋⢸⡏⡟⠙⡇⠈⠳⣄⢀⡇⠀⠈⠀⠋⠉⠉⠀⠀⠀⢰
⢤⡐⢿⣷⣩⣉⣩⣹⣧⠦⠤⠶⠦⠀⠤⠬⣶⣤⠄⠤⠊⠉⢁⠀⠠⠀⠀⡼⢁⠇⠀⢻⠀⠀⠈⠙⠛⣦⠀⠀⠀⠀⠀⠠⠀⠀⡞
⢀⡬⣽⡾⢭⣍⣛⣒⡒⠾⢶⠖⣒⠒⢶⠖⠈⠀⠀⠀⠀⠀⠁⠀⠀⢀⡜⠀⡸⠃⠀⢸⢧⠀⠀⠀⠀⠀⠉⠀⠈⠈⠀⠀⠀⣰⠁
⠀⠉⠚⢻⣗⠶⢬⣭⣭⣙⣒⠦⠤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⡐⠁⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠈⢻⢶⣦⣤⢔⡲⣶⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⢸⣀⠀⠉⠙⠲⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠉⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠙⣦⢠⢿⣆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⢦⡈⠻⣾⠈⢧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⠟⠀⠀⢀⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⠀⢱⣄⠈⠳⣄⠳⣄⠘⢷⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⠖⠚⠛⠛⢻⠞⢫⢤⡌⢿⢥⣤⡴⠮⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⡏⡼⠳⣄⠈⠳⢽⣦⣀⣙⣦⡤⠶⠚⠿⠯⣥⣄⠀⠀⠀⠀⠀⠨⠀⣼⡀⠈⢿⠃⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⢸⢷⠇⠀⣈⣷⣄⠀⠙⢯⣅⠀⠀⠠⠄⠀⠀⠀⢙⣳⡦⣤⣤⣤⡤⠚⢠⣻⠄⠀⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣀⡿⠾⠟⠋⠁⠀⠼⢧⣀⠀⠈⠳⣤⢀⣀⡤⠶⢺⠉⠁⡬⣲⡤⠤⢀⣀⣠⠟⢦⡼⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡇⡟⠠⠀⠀⠀⠂⠐⠀⠀⠀⠻⣦⡀⠀⠀⠻⢧⡂⡃⠀⠀⠀⢼⡁⢸⢴⣤⣴⣟⡦⠬⢭⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣤⣸⢧⣇⣄⣂⣤⠤⡤⠦⠶⠚⠛⡉⠙⢿⣤⣀⡾⣭⣩⣭⣉⣑⣒⠚⣤⡿⠾⢻⡻⣍⠙⠲⠾⢳⡻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡿⢸⠀⣤⡀⠀⢀⢢⠀⠠⠄⠀⠁⠀⢐⣙⣿⣣⢹⣮⡤⠴⠾⣿⢋⣁⣀⣀⠀⠳⡜⢦⡀⠀⠈⢧⡘⢦⡀
⠀⠀⠀⠀⠀⠀⢴⡾⠷⣾⢁⡿⠖⠚⠷⠖⠲⠚⠲⠚⠛⠚⠛⠛⠋⠉⠉⠉⢿⣇⠀⠀⠀⠛⠛⠛⠉⠛⠃⠀⠘⠲⠿⠾⠶⠦⠙⠦⠿⠾⡶⠆
⠀⠀⠀⠀⣠⣴⣶⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⠀⡀⠀⠀⠠⢄⣀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⡀
⠀⠈⠀⢀⠀⠀⢮⣏⡉⠉⢙⠃⠀⠀⠀⠈⠢⡈⠣⡀⠀⠘⠓⠦⠀⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⢠⠄⠠⢄⡠⡈⢦⠀⣠⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠑⠦⢀⠀⠀⠀⢸⡵⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠈⠀⠀⡀⢀⢞⣲⠋⠁⠀⢀⠗⢈⡔⠀⡟⠡⠀⠑
⠀⢀⠄⠀⠀⢀⡠⣤⠤⠀⠤⠄⠀⠀⠀⠀⠭⠤⠤⠂⠀⠀⠒⡎⠃⠀⠀⡀⢀⠀⢠⠀⡀⠫⠄⠊⢀⠀⢋⡀⠀⠀⠀⢻⡀⠀⠠⡄⡀
⠀⠀⠀⣀⡀⠍⠁⠂⠁⢀⠃⠈⠀⠀⠀⣄⡀⠀⠀⣠⣾⣿⣿⢷⠂⠀⠠⠴⠆⠀⠈⣆⡣⢤⢒⣩⠥⠀⠀⠤⠆⠀⠄⠀⠳⢦⣴⡡⠃
⠀⠀⠔⢁⡤⠤⠒⢀⢊⠅⠐⠀⠀⠀⠀⠈⢻⣦⡐⠸⠯⠉⠑⠁⠀⠀⢀⠀⢀⠀⠀⠉⠒⠊⠁⠀⢀⠀⠤⠀⠠⠄⠀⠀⠀⡀
⠀⣠⣾⠿⠒⠛⠚⢉⣡⣰⣦⡴⡄⠀⡄⠀⠀⠻⣷⡀⠀⠀⠀⠤⢴⠞⠛⠳⢆⠀⠀⠀⢀⡄⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠙⠁⠀⠀⢀⣶⣾⣯⣽⣿⠷⠃⠀⠁⠀⠀⠀⠙⢷⠀⠀⠀⢸⡅⠀⠀⠀⣰⠀⠀⠆⠀⡆⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⡀⠀⠘⣝⠿⠿⠛⠁⠀⠀⠀⠘⡀⠀⠀⢰⡼⣇⠀⠀⠈⠙⠶⠶⠶⠟⠀⠠⠁⠀⠀⠀⠀⡟⠁⠀⠀⠀⠈⡦
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠙⢄⠀⠈⠁⠋⠀⠀⠂⠦⣄⣀⠠⠀⠂⠁⠄⠴⠐⡀⠀⠈⠢⢦⣤⠤⣞⠁⠁
⠀⠀⠖⢛⠙⠛⠓⠒⠀⠀⣔⢤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠖⡀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀
⠀⠹⡿⡇⠀⠂⠀⠈⣥⠀⠀⠁⠀⠀⠀⠀⠜⠀⠀⣀⣀⡤⠶⡻⠁⠀⡀⠀⠎⠀⠀⠀⠀⠀⠙⠀⠀⢠⣴⣶⣾⠿⠿⠿⠿⢿⣟⠛
⠀⠀⠈⠀⠑⠂⠤⣄⣉⣻⣦⠀⠀⢠⣤⠤⠶⠶⠟⢉⠀⠐⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠙⠻⢶⣤⣀⣄⣀⣍⣱
⠀⠀⠀⠀⠀⠉⠂⠂⠛⠙⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠃⠀⠀⠀⠀⠀⠀⠠⣼⣌⣮⡇⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡝⢶⣾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣷⣛⣁
⠀⠀⠀⢀⣀⡌⢀⠊⠻⠴⢄⣿⣿⣿⢿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⣽⣏⣟⡁⢠⡤⣄
⠀⣴⣿⣿⣿⣷⣆⣠⡄⣀⡀⠈⢻⣧⢇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠈⠀⠀⠀⠀⡉⠉⢀⣼⣧⡀
⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣷⣄⡀⠈⠉⠈⠒⠒⠒⠂⠉⠉⠀⢀⡤⠾⠐⣪⣭⣭⡥⠾⢟⢿⠋⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠄⠙⠛⠛⠛⠓⠲⠶⠶⡦⢤⣤⣶⣾⣷⣶⡶⠾⣿⠋⠉⠀⠀⠱⠧⠠
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣞⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡄⢳⣼⣹⢣⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⠙⢆⠙⠳⣄⠳⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⡴⣒⠲⣾⠟⠁⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡟⠀⡾⡷⣄⠈⠳⣝⣦⡀⠱⣄⣀⣀⣤⣴⣖⣚⠋⠉⠉⠀⠀⠀⠀⢰⠀⠘⣿⡇⢹⠚⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡇⢰⣧⠇⠈⠳⣄⠌⠙⢷⡛⠋⠩⠁⡀⠀⠉⠉⠳⣄⣀⣀⢀⣀⡠⢏⢳⡀⠉⣂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁⣾⣼⠶⠒⠋⠉⣷⡄⠀⠙⠷⣄⠀⢀⣀⡤⢖⠛⠉⡉⣍⣉⡉⠀⢈⡿⢏⣰⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡿⣾⠉⠁⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠈⠻⣯⠀⠀⠈⠀⠈⡞⠉⣧⣤⣭⣽⠦⣌⣛⣚⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⡇⣏⣀⣂⣀⣈⡤⠤⠖⠒⢛⠉⢻⣦⣀⣴⣎⣉⣁⣑⣒⡒⠻⣴⠷⠿⡟⢏⠙⠲⠶⢶⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⢹⡇⣠⡀⠅⠀⢆⠀⠠⠀⠈⠀⠀⣎⣻⣳⣹⣬⡤⠽⢿⣟⢋⣁⣀⠀⠹⣌⠳⡀⠀⠈⢧⡙⣄
⠀⠀⠀⠀⠀⠀⠶⠿⢷⢇⡾⠖⠚⠒⠚⠒⠛⠒⠛⠛⠛⠙⠛⠉⠉⠉⢳⣇⠀⠀⠈⠛⠛⠉⠉⠛⠀⠈⠳⠿⠿⠶⠆⠙⠾⠿⠷⠶
⠀⠀⠀⠀⣤⡶⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉


⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⠰⣦⡐⠂⢶⠀⣶⠤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠉⠀⠀⠁⠀⡀⠀⠉⠐⠡⠄⠛⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠐⠠⠿⠃⠁⢸⡆⠀⠀⠀⠀⠠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⠀⠂⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⡀⣄⠀⠀⠀⠘⢢⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠛⠂⠒⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠀⠄⡀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⡀⣤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡀⣀⡀⠀⢀⠆⠀⡀⠀⠤⠰⠆⠀⠄⠀⣀⡀⠀⠀⠀⠈⠄⠀⠀⡀⠖⠉⠀⠙⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠌⠀⠈⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢂⠀⠀⣀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⠂⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢡⠬⠀⠀⠀⠀⣤⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠘⠆⠰⠀⠃⢠⠄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⡄⠐⠤⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠀⠠⡀⢱⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⣹⠀⠄⠀⠀⠉⠱⠦⢄⣅⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠲⣸⠀⠀⡁⠀⠀⢀⢀⠐⠢⠄⠀⠀⠀⣧⢄⠀⠀⠀⡠⠣⠀⠀⠀⠆⡼⠀⠀⠁⠀⠀⠀⢀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⣀⠈⠠⡄⠈⠳⡀⠰⠀⠀⠀⠈⠀⠀⢠⠀⠂⠚⠈⢡⡤⠶⠹⣀⠀⠄⡻⣠⠔⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠐⡀⠀⠐⠦⢍⠀⠈⢱⠠⣐⡄⠤⠀⠀⠀⠀⠀⠀⠀⠶⢀⡾⠰⠏⠀⠲⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠚⠆⠓⠒⡤⠀⠠⠀⠀⠀⠀⠀⠠⠎⣠⣴⢩⠀⣀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠆⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠠⠔⠛⠋⠁⠂⠒⠦⡄⠀⠈⡀⣘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠣⣀⡄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠴⡀⠀⠄⠀⠀⢀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠋⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⣘⣠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣬⣿⠏⡿⠟⠻⠢⡤⠒⠶⠴⠶⢶⣶⣤⣤⣤⣤⣶⡎⠁⣤⣾⡟⢋⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⣫⡚⡁⠀⠐⠂⠠⠤⠝⢠⡄⣶⡎⠉⠈⢁⡤⠚⣿⡤⠀⡼⣿⣷⣶⠶⢶⣦⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠠⠟⠑⠦⣤⠀⢀⠀⠙⠲⣂⣤⠄⠀⠀⢀⡔⠋⠁⠀⠛⠂⣼⡅⠀⣴⣶⢶⣶⡆⠀⣘⣿⣈⣽⣿⡹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠔⠒⠂⠈⠁⠙⠓⠿⢻⡦⠖⢛⣃⣀⣠⣴⣿⣿⣟⣿⡒⣲⣼⠧⣤⣤⣈⣁⡀⣙⠛⢂⡉⠁⠀⠃⠀⠒⠋⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠙⢫⠟⠲⠷⠶⢯⣽⣭⣯⣿⠾⠁
⠀⠀⠀⠀⠀⠈⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠓⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠜⠧⢹⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⠲⣌⣑⠤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣶⡶⣶⣶⣶⣤⣄⡤⣐⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⡦⣄⣀⣀⣀⣨⣽⣿⠾⢿⣶⣾⣿⡿⣿⣿⣿⣽⡿⡉⢻⢿⡟⠃⢻⠙⣿⣿⠇
⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠴⠶⢐⢂⡼⠫⠋⠘⢏⠛⠻⠶⣦⣶⡿⣿⣿⣿⣿⣿⣿⠽⠟⣓⣛⣋⣽⠘⣿⣏⢓⣿⣴⣿⣿⡀⡠⠂
⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠰⣲⠊⠀⠀⠀⠈⠹⣿⠴⣦⣀⠈⠙⠛⠿⣿⣽⣶⣞⠛⣩⣉⣿⠁⠃⢳⣾⡟⣷⠸⣯⡽⠁
⠀⠀⠀⠈⠂⠤⠤⠤⠀⠀⠀⢀⡴⡁⣠⣶⣶⣶⣾⣿⣿⡿⠿⣿⠛⣦⣄⣀⠀⢌⣙⢻⣾⣷⣿⣿⢜⣠⣽⠿⠁⠉⠛⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡴⠫⠛⠀⠺⣿⣷⣿⣶⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠳⠿⠿⠿⠋⢉⡽⠁⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀
⠀⠀⠀⠀⠀⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠰⠊⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⣠⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢟⣥⣶⣿⣿⣿⣿⣷⣦⣝⠻⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡟⠛⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢡⣿⣿⠿⣛⣩⣍⣛⢿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⠏⣾⣿⣿⣿⣿⣷⡹⣿⣿⣷⠸⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⣿⣿⡄⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣜⢿⣿⣮⣙⣛⣩⣿⡿⣱⣿⣿⣿⢃⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣍⣛⡻⢟⣛⣩⣾⣿⣿⣿⠏⣼⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣚⠛⠛⣛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣷⣦⣍⡛⠿⠿⣿⣿⣿⠿⠟⣛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


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

⠿⠽⠿⠿⠿⠿⣿⠿⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤
⠀⠀⠀⠘⠢⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠮⣀
⠀⠀⠀⠩⠨⠀⠀⠀⠀⣸⠆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⡐⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠁⠒⢦⡴⠋⣴⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠂⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠦⢀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠑⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠐⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⠑⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⡶⠀⢀
⠀⠀⠀⠀⡀⠀⣀⠜⠠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⡄
⠀⠀⠀⠀⠨⡉⠁⣠⠄⠀⡠⠀⣰⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠢⠁⠈⠂⠚⠉⠋⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣾⣷⣶
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣽⣿⣽⣿⣭⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⡀⠀⢀
⠀⠀⠀⠀⣴⣶⣤⠴⡶⡤⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠈⢄⢀⣦⠄⠀⡰⠂
⠀⠀⠀⠀⠛⠿⠿⠷⠻⢀⠀⠀⠀⠂⠀⠤⡙⢿⠿⠶⠶⣾⣿⣿⣽⣿⣷⠖⠂⠤⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣤⠊⠉⠉⠀⠈⠈⠉⠁⠀⠀⠀⣤⡾⠿⠋⣹⣿⣿⣿⣏⠓⠄⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠃⠰⢺⣿⣿⢺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠂⠞⠻⢸⡟⣿⣸⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢸⠁⣿⣭⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⣿⠟⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠿⣿⣿⣧⠖⢶⡦⣀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠔
⠀⠀⠀⠀⠀⠀⡉⠑⠷⢤⣵⣝⣷⣦⣍⣒⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣾⡇⠀⡤
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣤⣼⣷⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤⡶⣿⣸⣿⡿⠟⠚⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⢿⣿⣿⣟⢹⣿⡻⠿⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠙⠻⠿⡏⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠘⡄
⡀⠀⠀⠀⠀⠀⣷
⠱⡀⠀⠀⠀⠀⢸⣆
⠀⠹⣄⠀⠀⠀⠀⢿⡄
⠀⠀⠙⣦⡀⠀⠀⠘⡔⡀
⠀⠀⠀⠈⢻⣦⡀⠀⠱⡱⡀
⠀⠀⠀⠀⠀⠉⠪⣢⣄⠑⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠷⢾⣮⣢⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠆
⠀⠀⠀⠀⠀⠀⠀⡤⢆⡉⠉⠛⢅⠀⠀⠀⠈⢳⠔⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⣠⢃⡠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⣾⠗⠂⠈⢢⠀⠀⢱⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⢀⠤⠊⣠⠾⠓⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢸⣿⣦⣴⡇⠀⠆⠀⠀⡆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⢄⣀⣀⣀⣀⣀⠀⠠⠶⠭⠤⡤⢀⠴⢊⡡⠖⠉⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠈⠿⠿⠛⢁⡜⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠓⠒⠒⠒⠒⠒⠐⠀⠉⣩⠝⠋⠁⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣈⡁⠀⣀⠔⠁⠀⠀⢸⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⣠⠎⠁⠀⣠⠞⠁⠀⠀⠀⣀⣀⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠤⠤⠄⠒⢒⡠⠟⠋⠁⠀⠀⢀⣀⡤⠊⠀⠀⣠⠞⠁⠒⢲⠂⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠓⠒⠒⠒⠒⠒⠚⠒⣤⡤⣀⣀⣀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⢀⡠⢴⠒⡩⠊⠀⠀⣠⠞⠁⠀⠀⠀⠘⡀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣆⡀⣤⠴⡒⠉⠉⠉⠉⠉⠁⠉⣉⣣⡉⢩⠟⠉⠀⠀⢀⡠⠔⠊⠁⠀⡸⠋⠀⠀⣠⠞⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢇⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⠊⠀⡰⠁⠀⠈⡆⢀⣀⠤⠔⠒⠉⠀⠀⠀⠉⠂⠤⠴⠮⢁⣀⡀⢀⡠⠊⠀⠀⡠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⣰⣀⡀⠤⠤⠚⠉
⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⢠⠃⠀⢀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⣠⣎⠽⢆⠀⠀⠉⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⡜⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⡠⠊⠙⠤⣀⡀⠑⢄
⠀⠀⠀⠀⢀⠴⠋⠈⡹⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⠉⠒⠛
⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠉⠉⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠦⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⡀⠙⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠔⠀⠀⠀⠀⠀⣤⡀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠄⠀⠀⠀⣀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠚⠣⠬⠁⣀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠒⠋⠉⠉⠉⠉⠀⠀⠈⠁⠛⢀⡂⠒⠁⠀⠐⠊⠁⠨⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡙⠀⠀⠀⠀⡀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠤⡀⠀⠀⠈⢣⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⣠⠀⠠⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢅⠀⠀⠈⠆⠀⠀⠀⣿⢁⠁⠀⠀⠀⢀⡠⠔⠉⠁⠤⠤⢤⠀⠀⢠⠊⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⠀⠈⢢⠀⠐⢄⠀⠀⠻⣘⣄⣠⡴⠚⡃⠀⠀⠀⠐⠠⣀⠀⠀⠀⢹⡄⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢃⠀⠸⡀⠀⠈⠃⠀⠀⠀⠉⠘⠜⠐⠀⡀⠀⠀⠤⠀⠈⠁⠠⠤⠊⠤⠐⠚⠉
⠀⠀⠠⠰⠂⢀⡎⠀⠑⢄⡀⠈⠦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⢀⠔⠁⢘⠖⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⡇⢀⠔⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠥⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⠛⠞
⠀⠀⠀⠀⠀⠀⠐⠠⡀⠠⢀⠤⡄⢠⢀⣀⠀⠰⠤⠀⠤⠤⠄⢀⢀⣀⡄⣈⠖⣡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠀⣦⢀⠀⢨⣂⠀⢠⣄⣀⣐⠂⡰⣂⡶⠖⢡⣾⢻⣶⣶⣤⢴⡆⣤⠤⢤⣤⠄⣤⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⣿⣈⠀⡸⢃⢻⡂⣉⠉⣭⠛⢉⠉⢀⡐⠻⠾⠘⣿⣯⣷⣾⡷⣶⣿⣿⣲⣶⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠍⠘⢛⠄⠉⢺⠶⠓⡷⠶⢦⠞⠵⣾⣟⣛⠁⠛⠾⡗⠳⠾⠛⡿⣿⣿⣟⣻⣿⣿⠣⣿⠷⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠁⠀⠐⠃⠀⠀⠀⢰⡒⠀⠀⠀⠀⠈⠉⠀⠹⠃⠰⣄⠐⠃⠄⠍⠉⠉⣭⢿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠐⠋⠉⠈⠓⠈








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠁⠀⢀⡀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡠⠂⠀⣀⣀⡈⠑⢄⠀⠙⢆
⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢠⠋⢔⣀⠀⢳⠈⢣⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠠⠄⡀⠀⣀⢀⣮⢠⠀⠀⡀⠀⢸⠈⡈⠉⠕⡸⠀⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣐⠀⠀⠀⠀⠀⠀⠀⠈⠦⡑⠄⠃⠀⠀⠑⠄⣀⡉⣀⠔⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣶⣦⣤⡤⣀⣀⣀⣈⠑⣺⣦⣀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠿⠿⠟⠛⠛⠋⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⠴⠶⠶⠶⠀⠀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠛⠳⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠤⠤⠄⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠊⠉⠠⠠⠆⠀⡀⠀⠀⠀⢀⠐⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠴⠁⠀⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⢠⠀⢀⠀⠀⠈⢃⡐⠒⣠⣠⡄
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⢀⠀⠀⠐⠙⠏⠁⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠜⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⣾⡅⢂⣠⣄⠀⠀⠀⠀⠀⠀⠀⢄⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣰⣄⢼⡍⢈⣒⠂⢠⣼⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠙⠁⠘⠀⠀⢀⠀⠀⠀⡀⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠰⠀⠀⠀⠀⠀⠈⠉⠉⠑⠚⠚⠛⠙⠉⠁
⠀⠠⠤⠐⠀⠀⠀⠀⢀⡠⠠⠴⠼⠦⠒⠆⠠⡀⠀⠀⠀⢨⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⢠⠖⢉⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠑⠬⡙⠂⠀⠀⠀⠀⠀⠀⢀⡖⠀⢉⢉⣀⠢⡀⢙⠢⣄
⠀⠀⠀⠀⠀⢠⠏⢀⠀⠀⢠⠀⠀⠀⠀⢶⠀⠐⠂⠑⠢⢀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡠⠊⠀⠊⠀⠀⠈⢢⠈⠪⠑⡌⠳⡄
⠀⠠⠉⠀⠀⠸⡄⠀⠀⠄⠁⠀⢩⣤⠀⠀⠁⠄⠈⠀⠀⠀⠉⠉⢀⡠⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⣀⠄⠀⡀⠈⠀⡄⢿⠀⡀
⠀⠀⠤⠄⠀⠘⠤⢄⣈⣀⣀⠴⠹⠁⠀⠀⠀⠀⠀⠀⠀⠚⢄⠀⣩⡀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡃⣾⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠄⢠⠃⠀⡀⡁⠀⠀⢀⠐⠂⠠⡀⠻⠜⠡⠀⠀⠀⢀⠹⡇⠐⠀⠀⠀⠤⠴⠞⠁⢀⡌⣸⢠⠇⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⣤⠀⢀⡠⢊⢀⡀⠂⠁⢀⠰⠁⠑⢄⡀⠀⡁⠐⠀⠰⡈⠂⠃⡘⠀⠀⠈⠀⠙⠪⢄⠀⠀⠠⠄⢀⣀⡤⠎⡡⠏⠀⠀⠀⠀⠀⢀⠴⠀⡠
⠀⠀⠀⠈⠓⠋⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢄⡓⠀⠠⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠠⠄⢁⠔⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠆⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠋⠀⠀⠁
⠀⢻⠥⠲⠦⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⡈⢩⣇⢵⡘⡀⢋⢱⢆⡀⠀⠀⠀⠰⠤⢠⡄⢀⠈⠀⣠⡈⠀⠊
⠀⢾⡥⣁⣄⣹⠦⠹⡿⠦⢄⣀⢰⠀⠀⢠⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠐⠀⠻⢿⣬⡰⢣⠖⣈⠹⡄⠀⠈⠉⢒⣺⣿⣦⢀⡀⠁
⠀⠈⢢⢹⢎⢵⠆⣠⡰⣦⣷⡿⣿⠓⠄⢋⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀⡀⠨⣿⣗⣥⣊⡥⣤⠹⠀⠀⢰⠋⣡⣾⣳⡐
⠀⠀⠘⣠⣿⡳⡹⣇⢛⣥⣿⢶⠏⡄⢠⡜⠀⠀⢀⣸⣅⠀⠀⠀⠀⢤⢺⡽⠇⣀⠀⢼⣯⣭⡛⣇⠨⠁⡀⠾⠊⠁⠳⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣟⣷⣇⣼⡋⠉⠁⠀⠀⢀⠃⠀⠨⢽⠟⠛⣱⡀⠀⠀⠠⠉⠀⠀⠉⠊⠃⣉⠹⢕⠲⡇⠀⠁⡘⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠘⡿⠙⠛⠋⠁⠀⠠⠀⠀⢰⡟⠀⠀⢀⠆⣰⠊⢹⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠃⡠⠋⠀⠀⣷⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠀⠈⠊⠁⠰⢡⠜⠀⠙⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡤⠲⠛⠳⠶⢿⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠒⠚⠋⢀⣀⣉⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⣠⠾⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⡿⠿⠛⠳⠔⣲⣶⠬⠅⢀⠤⠄⠀⠀⢀⠄⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠈⠙⠛⠓⠁⠀⠒⠒⠖⠂⠀⠀⠀⠀⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢄⣠⠄⢘⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠉⠀⠀⠀⡶⣠⡟⢀⡙⢶⠳⠀⠄⢀⠂⢠⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⠀⠤⠅⢈⣾⣦⢀⣀⡴⢾⣃⣸⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢂⡤⠊⠀⠀⠀⠀⠀⠀⠐⠊⠀⠐⠛⢀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠠⠀⠀⠀⣠⠜⠋⠛⣻⡿⠂⠩⡄⠀⣦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠿⠿⠁⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⢰⣟⠶⠦⠴⠖⠋⠀⠀⠀⠀⣾⠁⠀⢰⡾⠻⢆⠀⠀⢠⡇⠀⠛⠀⠰⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡰⠯⠤⠤⠄⠐⢿⠊⠀⢀⣤⣶⠃⢀⡀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⡀⣿⠁⠸⠀⢨⠘⣻⡗⠀⠀⢀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⢀⣠⡴⢋⣀⣾⣯⠋⠉⢀⣼⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⡗⢢⣹⡧⢀⠀⠀⠀⢰⠯⠄⠀⣠⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠬⠚⠛⣦⣉⣉⣉⣡⢴⣿⢷⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⡿⠟⠈⣙⣤⣶⠿⠒⣀⢨⠏⠀⠠⠁⢀⣾⣿⠋⣻
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠤⠶⠆⠙⠆⠋⠁⢸⠁⢀⡾⢃⡴⢷⣦⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⠇⢀⠀⢈⡟⠋⠁⣨⠋⡀⠀⠀⠀⢠⣿⡿⠏⠈⣹⡇
⠀⠀⠀⠀⠀⢠⣏⡀⠀⣀⡤⢤⣤⣀⣀⣀⣤⡗⠀⠞⠀⠺⠇⢨⣿⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣨⡟⠀⠀⠀⠀⡰⠁⠀⠀⠀⢸⡧⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⣡⣦⠄⠀⠀⠁⠀⠀⠀⢠⣄⠀⠀⢠⠞⠙⡄⡙⢇⠀⠀⠀⠄⠀⠀⠀⠀⣼⠑⠀⢠⠞⠀⣠⠖⠀⠀⠀⠊⠀⠀⠀⠀⢾⠂⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⢄⠀⠲⠬⠥⠞⠋⠀⠀⠰⡟⠜⡆⠀⠈⠀⠀⠀⢲⣾⡿⢀⣰⠏⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⣀⣀⣀⣘⠁
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠐⠘⢢⡀⠀⠑⠄⠀⢀⠖⠂⠀⠀⢸⠃⠈⢿⡀⠀⠀⠀⠀⠀⠀⠁⠘⠻⡖⠄⠀⠀⢀⠀⠀⢀⣴⣾⣟⡻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠄⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠈⠂⠘⠆⠀⠀⠐⠁⢰⡆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡽⣧⣿⣿⣿⡿⠋
⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣯⣀⡿⠿⠟⠉⠀⠀⣀⠀⢀
⠀⠀⠀⠇⠀⢹⡆⠀⠀⠀⠈⣇⠀⠀⠀⢀⣀⠁⠒⢲⠇⠀⠀⠀⠀⠀⠠⠤⠤⣤⣴⣶⠀⠀⠈⠉⠉⠀⠀⠴⢤⣄⡀
⠀⠀⠀⡆⠀⠀⠃⠀⠀⠀⢤⣍⢰⡏⠢⡀⠉⡛⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⣿⣶⣶⣤⣤⣤⣶⣀⡀⠀⠘⢦⠀⠀⠀⠀⢀⠔⠐
⠀⠀⠀⢁⠀⢜⠃⠀⡗⡀⠀⠛⠀⠉⠢⣈⠚⢉⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠉⠉⠀⠀⠀⠈⢉⣩⣿⣿⡀⠀⡇⠀⠀⡰⠁⠄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠈⠛⡄⠀⠑⣶⡅⢀⡀⠀⠀⠀⢹⣖⡘⠛⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡿⠃⢰⠃⠀⠀⠇⠀⠀⠀⢀⠀⠒⠀⣿
⠀⠀⠀⠀⠀⠈⠻⡛⢴⣤⠨⡷⠤⡄⠀⠋⠹⡥⠐⢉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣚⣉⠥⠚⠁⠀⠀⠀⢲⡀⠀⠀⠐⠀⢀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠾⢀⠀⣻⡄⠀⠀⠀⢀⣷⡈⠀⠉⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠒⣿⣯⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⣟⠁⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠘⠐⠈⠀⠀⠀⡀⢀⠀⠀⠀⠁⠘⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡀⠀⠸⣏⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠛⡓⠀⢠⠀⠄⠃⠀⠀⠀⠈⠀⠀⠒⠀⠀⠄⠀⣨⡇⡠⠀⠀⣰⣿⣿⡿⠋⢁⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⡇⠀⠀⠀⠀⠀⠘⠟⣿⣿⠛⣶⢁⣦⡚⣣⣄⢡⡶⢆⣰⡦⢤⣤⢤⣽⣾⣿⠀⠀⣿⠛⢉⣷⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣽⡖⢀⡀⢱⠀⠀⠀⠈⠉⠊⠉⠉⠉⠛⠛⠛⠋⠛⠚⠛⠃⠜⠛⠚⠛⠋⠁⠀⠀⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠻⡉⢈⣄⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠛⠦⠴⠛⠉⠁