Listening Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣚⡭⠭⠭⠭⣝⡒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣤⣤⡀⠈⠑⠦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⠀⠀⠀⢀⣿⡏⠛⢶⣄⠀⠘⢮⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡎⠀⠀⠀⠀⣀⣀⣸⣿⠃⠀⠀⣿⡟⠀⠈⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠸⢿⣿⣿⡿⠀⠀⢰⣿⡇⠀⠀⢸⣸⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠀⠀⠀⠂⠺⢼⡆⠀⠀⠀⣠⣤⡤⠀⢠⣶⣶⣾⣿⠀⢀⡤⠊⠀⠀⣉⣀⡀⠉⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⡙⣷⡀⠀⠈⠙⠛⠛⠋⢠⠂⠀⣠⡶⠿⠛⠛⠻⠿⣦⣄⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠹⠟⠃⠀⠀⠀⠀⠀⠔⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡅⡠⠒⢒⠀⠀⠀⠀⠤⣤⡄⠲⠚⣮⡓⠦⣄⣀⠀⠀⢀⣀⡰⠀⠀⣸⠃⠀⠄⡀⠄⠂⠀⠀⠢⠄⢹⡆⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠠⠄⠀⠀⠀⠀⠤⠀⠀⢣⡀⠈⠑⠲⠤⠭⠭⠥⠔⠺⢠⣶⣿⡖⠙⣉⡀⠀⠀⠀⢈⡑⠐⣾⣿⣦⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⠙⠁⠀⠀⠀⠙⠃⠀⣿⣿⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠀⠉⠁⢰⠇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⢿⠃⠀⠀⣦⣐⣒⣢⡦⠀⠀⢹⢿⡋⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠒⠂⠁⠀⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠣⡀⠀⠈⠛⠛⠛⠁⠀⡠⠊⠀⢩⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢶⢶⠶⠖⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠁⠂⡤⠀⢴⠒⠉⡠⣀⡠⠴⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠈⠘⠛⠤⢀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡤⠆⠉⠣⠀⠘⠉⠉⠀⢸⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⠀⠀⠀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⠞⡃⠀⠀⠀⠀⠀⠀⠘⢿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠌⠀⡅⠀⠀⠀⠀⠀⠀⡅⠀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣐⠢⠖⠠⣠⢤⡇
⠀⠀⠀⠀⠀⠀⠀⡔⢸⠄⠀⢰⣶⣤⣤⣤⣴⣶⠀⠀⢸⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⢿⣨⡟
⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢶⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡟⠀⢛⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠠⠆⠀⢸⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠾⠃⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠀⠀⢾⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⣤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⣾⣿⣟⡉⠁⠀⠀⠀⠈⠉⠻⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣁⣠⣶⣿⣿⣯⣾⣿⣿⣤⣤⣴⣿⣦⣀⣺⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⢐⣼⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢻⣿⡿⡇⠀⠀⠹⣿
⠀⠀⠀⢠⠀⢀⣾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠃⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠤⠶⠶⠶⣄⢀⡄
⠀⠀⠀⣰⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣷⣦⠙⣿⣿⣼⣿⡏⠀⠀⠀⢀⣠⣤⣴⡇⠀⣅
⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠋⠀⠀⠉⢿⣿⣷⡈⠙⠿⡙⣇⠀⠀⠀⠉⠉⣹⡿⠀⠀⠘⡄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡁⠀⠀⠀⣨⣿⣿⣧⢠⣤⣄⠈
⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢈⠀⠀⠀⠀⠉⠿⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣧⠸⣯⡷⡄⠀⠀⠀⠈⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⣌⠃⠀⠀⣀⣄⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡈⠻⢷⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⣷⣶⣤⣄⣀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⣀⠀⠄⠀⠀⢀⣀⣀⣤⣤⣤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⣁⠖⢀⣠⣶⣿⠿⠟⠛⠛⣛⠛⢟⢻⡅⢠⠔⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣨⣿⠟⠉⠀⠠⠀⠁⠀⡹⠀⠀⠀⢄⡀⠀⢦⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢰⣿⠗⢀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠉⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⡀⠁⡀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⠀⣐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢸⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠛⠒⠢⠘⣿⣀⢍⠖⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⢀⠸⣿⡤⢀⠀⠀⠴⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⡘⣷⡈⠉⠊⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⡀⠂⠙⢧⣜⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠶⠛⠁⢹⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⡀⠀⠘⠻⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⢀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⡜⠄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠉⠁⠇⠀⠀⠀⢹⡌⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢇⠀⠄⠐⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠔⢀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⢃⠖⠀⢠⠀⠀⠉⢀⠀⠀⠀⠀⠀⠄⠇⠀⠀⠀⠀⣠⡄⠚⠀⠀⠀⣷⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢄⡔⠀⠀⠀⠀⣻⣀⠀⠀⡆⠀⠀⠔⡕⠀⠀⠀⠐⡄⠀⠀⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠚⠀⠀⢀⠀⠀⠀⠠⠤⠄⠑⠀⠀⠀⠁⠐⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢸⡆⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⣿⠀⣰⣿⠋⠉⠻⣷⡀⣠⣴⡶⣶⣄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠉⠉⠛⢿⣿⡇⠀⠀⠀⢻⣿⡏⠀⠀⠀⠈⣷⠀⠀⣠⣤⣤⡀
⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣧⣾⠏⠁⠘⣷
⠘⣧⠀⣶⡄⠀⠀⠀⢸⣿⣦⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢸⡆⠀⣠⣤⡀
⠀⣿⠀⣿⣧⠀⠀⠀⠀⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣷⡿⠋⠀⠙⣄
⠀⢹⣆⣿⣿⡄⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣿⣿⡆⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢻
⠀⠈⣿⣿⡟⣷⡀⠀⣴⡿⠃⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⠀⢻⣷⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢸
⠀⠀⠘⣿⣧⠸⣷⣼⣿⠃⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠘⢿⣆⣿⣿⡿⠀⠀⠀⠀⣼⣿⡿⢧⡀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠃⠀⣼⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠛⢿⣿⠇⠀⠀⠀⣸⣿⡟⠻⣦⣳⡄⠀⠀⠀⠀⠀⠘⠁⠀⢸⡿⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⣿⡟⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣿⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣸⣿⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⣿⡃⠀⢠⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣿⠇⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢷⣿⣿⣄⣀⡀⠀⢸⣿⣿⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣧⡀⠀⢰⣿⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣿⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏
⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⢀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠐⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣤⣾⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠛⠛⠛⠛⠛⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠻⢷⣄⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣀⣤⣶⣶⣶⣦⣤⣀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣿⡀⠀⠀⠀⠀⠀⣾⡇⢀⣼⠟⠉⠀⠀⠀⠀⠉⠻⣧⡀⢸⣷⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⣿⡇⠀⠀⠀⣠⣠⣿⣧⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣼⣿⣄⣄⠀⠀⠀⢸⣿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⣧⠀⠀⠀⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⠀⠀⠀⣸⡇⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⣿⣀⣄⡀⠀⠈⠛⠋⠸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠙⠛⠁⠀⢀⣀⣀⣿⠃⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣿⡏⠙⢻⣦⡀⠀⠀⠀⠙⢿⣦⣄⣀⣀⣠⣴⡿⠃⠀⠀⠀⢀⣴⡿⠋⢹⣿⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠙⢿⣆⠀⠙⢿⣦⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⡿⠋⠀⣠⡾⠋⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠻⣷⡄⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢀⣾⠟⠁⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠿⠆⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠰⠿⠃⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢸⣷⠀⠀⣾⡇⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⢸⡿





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠰⠄⢤⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠆⠦⠀⠆⠸⠈⠑⠂⠀⠒⠒⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢐⠁⠂⠄⠠⠐⠄⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⡦⣀⠠⠀⠐⠠⢠⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠐⠓⠐⠦⠖⠥⠆⠶⠱⡔⠀⡆⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢠⠃⠈⠉⠢⢄⠪⡂⠑⢕⢄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠠⠃⠀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠐⢀⠎⠀⠀⠀⠀⠀⠙⢌⢂⠢⠡⠡⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠇⠀⢀⡀⠀⠀⠀⠀⠠⢄⠀⢰⠼⠢⡀⠀⠀⠀⠀⠀⠀⠀⢂⢊⢄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡖⡆⠀⠀⠀⠀⡀⠀⡆⠀⠁⡡⠋⠼⠍⠐⠒⡒⢀⠬⢍⠉⠖⠆⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⢣⠆⠀⠀⠀⠀⠀⠀⠄⢀⠄⠁⠂⠤⠀⠂⠀⠘⠂⠀⠀⠂⠀⠈⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠸⡀⠀⠀⢀⠀⠀⠀⢀⠉⠂⡀⠀⠀⠀⠀⠀⣄⠝⠂⠀⠀⠀⠀⣀⣈⡀⡀⢀⠀⠀⠀⠰⢁⡥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢄⠀⠀⠈⠁⠈⠁⠀⠀⢀⠂⠀⠐⣦⠀⠀⠀⠘⠀⠙⣣⡀⠀⠀⠀⠣⡀⠀⠀⡀⠂⠀⠀⠀⢠⢼⠐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⡈⠳⣄⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣿⡓⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡴⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⠠⡈⠋⠀⠲⢒⠊⡇⠀⠀⢀⢄⡰⠃⠀⠀⠀⠐⠀⡘⣷⡈⠓⢤⣀⠀⠀⠀⢀⣠⡴⠋⠀⢏⡃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠘⣾⣍⠪⢕⢤⠀⠁⢀⣭⠶⠾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠠⢻⠷⠒⠓⠆⠕⠝⠟⠽⣾⣷⣶⣾⣶⣶⢰⠂
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠪⡳⢄⣀⠉⡐⣞⡏⡀⠀⠁⠑⢄⡀⠀⠀⠀⠀⠀⡠⢸⠖⠒⠖⠆⠀⠀⠀⠀⠸⠿⠿⠛⢻⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠓⣽⡇⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣀⣀⡈⠟⢛⠻⡃⠀⠀⠀⠀⠘⠛⠿⠽⣛⣃⠙
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠔⠠⠐⠁⠔⡀⠐⠀⠐⡀⠀⠈⡆⡈⠔⡈⠄⠀⠀⠀⠢⠐⢈⠅⠀⠱⢀⡐⠀⠈⠂⠤⣂⡀⢄⠈⠀⠀⡠⠉⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⢈⠄⢀⠄⠈⠀⢊⠜⠀⠄⡈⠐⡈⠄⠀⠀⢰⠀⢀⠁⡠⣶⢅⣙⡦⠥⠶⠄⣃⡁⠠⠄⠐⡩⠀⢀⠀⡀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⡄⠀⠄⠐⠡⠐⡡⢐⡈⠀⠀⠀⢠⠔⣨⠖⠀⡈⠀⠀⠀⠀⡀⠐⠠⠂⠐⠀⠂⢀⠀⠈⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠠⠊⠀⠐⠀⠀⠠⠀⠄⠀⠔⡠⢀⠀⠀⠈⠐⠡⡊⢀⠅⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣢⣤⣴⣶⣶⣦⣤⣔⣅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠹⣿⣿⣿⣷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡢⢳⢻⣿⡟⠛⠛⠛⠋⠉⠀⠀⠀⠀⠙⣿⣿⡟⢻⠠⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢰⠀⢸⢸⣿⠀⠀⠞⠛⠦⠀⠀⠰⠚⠛⠆⠈⠻⡇⢸⠀⢡⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡠⠋⢄⢸⢸⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠎⢂⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠔⠀⠀⠀⢹⣾⡀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣾⠁⠀⠀⠡⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⠊⠀⠀⠀⠀⣾⣿⣷⣄⡀⠀⠀⠑⠠⠄⠊⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠑⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡰⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⣄⢀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⢄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠘⠠⢀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡈⠆⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠏⠀⠈⠉⠙⡟⠛⡏⠉⠁⠑⠄⣀⡀⠔⠁⠈⠉⢻⠻⠟⠛⠉⠉⠀⢙⠉⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⡌⠀⠀⠀⠀⢀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠀⠀⠀⠀⠀⢆⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢄⡀⠀⠘⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢆⠀⠀⡴⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠳⡞⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠋⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠆⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠻⢿⣿⣿⣿⣿⣦⣴⣴⣶⣆⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣶⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠉⠈⠉⠉⠹⢻⣿⣿⣿⣿⣿⠟⠙⠛⠣⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠀⠀⠀⣾⡇⠀⠙⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡶⠛⠉⠈⡇⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠉⢀⡀⣾⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⡇⠀⠀⠀⠀⢀⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠙⢿⣿⣷⣾⣿⣿⠟⢙⡆⡆⠀⢻⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣤⡅⠀⣴⡿⠃⠀⠀⠀⢀⡞⣰⡃⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠿⢦⡀⠀⢹⣿⡿⠁⢰⣿⣇⣹⠀⢸⣯⣻⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣸⢱⡟⠉⠉⠓⢄⠀⠀⠐⠋⠁⢀⣠⣀⣀⠀⠀⠀⠻⠁⢀⣿⣿⣿⠃⠀⠀⢹⡅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣀⡲⣋⡿⢶⡆⠀⠀⠀⠐⠋⠰⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⠛⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠇⢀⣀⣠⣾⣿
⠀⠀⢀⣠⠴⠛⢉⠀⠀⠀⠀⡿⠶⠄⠀⠀⠱⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠻⢦⣼⣿⣿⣿⠃
⠀⠀⢸⠁⢰⠀⢸⠀⠀⠀⠀⢿⠳⠤⠀⠀⠀⠙⠳⠄⠀⠢⠔⠛⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡥⠞⠁
⠀⠀⣟⢠⡾⠰⠏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢸⠉
⠀⠿⠋⠈⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣉⠙⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⠶⢖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡆⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣇⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⠻⠉⠙⠋⠉⠻⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠿⠟⠛⠛⠿⠿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣴⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⣷⠀⠀⠀⢀⠀⢸⡇⢠⡄⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⢠⣶⠀⣿⠀⣶⠀⣿⡇⢸⡇⢸⡇⢰⣶⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⢸⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠈⠟⠀⣿⠀⠛⠀⢿⠇⢸⡇⢸⡇⠘⠏⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⠞⠳⣄
⠀⠀⠀⠀⠀⢀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡦⠞⠁⠀⠀⢀⣄⡤
⠀⢀⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠗⠏
⠀⠘⣇⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢰⡿⠙⠁⠀⠀⠀⠀⣴⠆⠀⠀⠀⣿⣿⡆⢀⣴⣿⣿⣶⡀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠸⣿⣿⠇⢸⣿⣿⣿⣿⠃⢸⣿⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠉⠀⠸⣿⣿⣿⠏⠀⠈⠉⠁⠀⠀⢠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢹⣿⣿⣿⣿⣿⠇⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣾⣿⣿⣿⣿⣿⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠀⣿⣿⡿⢿⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠚⠿⠿⠂
⣿⡶⠻⠟⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣒⣲⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣫⣄⠀⠀⠈⠩⠔⢻⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣥⣤⣄⣀⣤⢀⡀⢐⣻⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⠉⣙⣫⣭⣿⣿⡿⠿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠛⠛⠿⠛⠿⠛⠋⠛⠉⠀⠀⢸⣿⣿⣯⣭⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⣿⣿⣿⡟⠛⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠳⣄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣄⡈⢻⡏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠘⣿⣿⡛⠋⠛⠣⡄⢹⠀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣛⣩⣿⣿⠂⠀⠀⠀⢉⡶⢶⣶⡤⢄⠀⠀⠀⠀⠻⠏⢠⣾⢻⠇⡀⢸⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠋⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠙⠊⠀⢉⠻⡟⠂⠚⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠤⠷⠦⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠚⠉⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡿⠀⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⣼⠃⠀⠀⠉⢛⠿⣦⣤⡜⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⢠⠃⠀⠀⠀⠀⠀⠑⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⣀⣀⣀⣠⣴⡾⠿⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠩⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠀⢠⡄⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⣠⣤⣀⡴⠋⠉⠉⠶⠞⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠘⡏⠉⠓⠀⠀⠀⠀⠀⠀⠀⢀⣀⡎⠀⠀⣈⣥⠶⠶⠶⠶⠶⢦⣤⣈⠓⠛⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠳
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠁⢁⡴⠟⠉⠀⠀⠀⢀⡀⠀⣀⡀⠉⠻⣦⡀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣴⠏⠀⣀⣀⡼⠓⠒⠋⠉⠉⠉⠓⠤⡖⠈⢻⣄⠉⢢⠀⠀⠀⠀⢠⣶⣶⣿
⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⣰⠋⠁⣸⠏⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⢻⡄⢸⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⡟⠀⠚⠋⠀⠀⣠⠶⣄⠀⠀⢀⡤⢤⡀⠀⠸⠤⠄⣿⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⢸⣿⣽⠀⠀⠀⠀⣷⣿⢾⠀⠀⢸⢸⣷⡇⠀⠀⢀⣿⣿⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⡆⠀⠀⠀⠙⠛⠋⠀⡀⠈⠓⠛⠁⠀⠀⣾⣿⣿⠀⠈⡇⠀⠀⠀⢰⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠜⣿⡿⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⡴⠃⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢻⢹⡀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣄⠀⠀⠀⢸⠁⣨⡟⠀⠀⠀⠀⠠⠶⠗
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠈⠓⢾⠼⢧⠀⠀⠀⠈⠫⣍⡛⠋⣉⡠⠃⠀⠀⠀⡟⠛⡯
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠸⡄⠈⢣⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢰⠃⠉⠙⠒⠒⠚⠋⠹⡄⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⣤⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠙⣄⠈⠑⠦⣄⡀⠀⠀⠀⣀⡤⢚⠕⠁⠀⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠉⠉⠉⠉⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤

⠀⣀⠴⠶⡄⠀⠀⠀⢀⣠⡖⠒⢶⠀⠀⠀⣀⠴⠒⢹⡆⡠⣖⠒⠚⠓⠒⠒⠒⠒⣆⢴⠊⠉⠉⠉⠉⡇⣠⡞⠙⠉⠹⡀⠀⡴⡎⠉⠉⡇⠸⡏⠉⠉⢹
⣞⣽⠀⠀⣿⠀⠀⠀⠸⢚⡇⠀⢸⠀⢀⣴⠃⠀⢀⡼⠣⣆⣷⣀⣀⡀⠀⠀⡠⣤⣿⣻⠀⠀⢀⣀⣀⣿⢵⡇⠀⠀⠀⢳⣸⣺⠇⠀⠀⡷⡏⣇⠀⠀⢸
⠗⠹⠀⠀⢹⠀⠀⠀⢘⣩⡇⠀⢸⠀⡜⣇⠀⠀⢻⡁⠈⠶⢥⣭⠜⡇⠀⠈⡷⠋⢸⠴⡇⠀⢸⣛⣋⢸⠋⠃⠀⠀⠀⠈⣯⢼⠀⠀⠀⡇⣧⢻⠀⠀⠈
⡧⢺⠀⠀⢸⠀⠀⠀⢸⣞⡇⠀⢸⡄⣇⠹⣆⠀⠀⠱⣄⠀⠀⢸⢊⡇⠀⠀⡇⠀⢸⢺⡇⠀⠀⠀⠀⣿⢪⡇⠀⠀⠀⠀⠸⣿⠀⠀⠀⡇⢺⢸⡄
⣗⢽⠀⠀⢸⠀⠀⠀⢸⣿⡇⠀⢸⡇⠈⠲⣌⣷⠀⠀⢹⠀⠀⢸⠟⡇⠀⠀⡇⠀⢸⣡⡇⠀⠀⣟⡻⢻⡵⡇⠀⢸⣆⠀⠀⠋⠀⠀⢀⡇⢸⡊⡇
⡧⢺⠀⠀⠸⣤⣤⣤⢀⣋⡇⠀⢸⡇⠀⠀⣸⠞⠀⠀⡞⠀⠀⢸⢊⡇⠀⠀⡇⠀⢸⡡⡇⠀⠀⣧⣤⣸⢜⡇⠀⠀⡿⡄⠀⠀⠀⠀⢸⠁⠘⣧⣩⣿⣟
⡗⣹⠀⠀⠀⠀⠀⢠⡏⣽⡇⠀⢸⣧⢺⡏⠁⠀⢀⡼⠁⠀⠀⢈⣯⡿⠛⠿⣧⡀⢸⣴⡇⠀⠀⠀⠀⣿⣪⣇⠀⠀⡗⢻⡀⠀⠀⠀⢸⠀⠀⣰⣏⠁⠈
⣿⣟⡶⣲⣲⢒⣶⠞⠡⣾⣓⣖⡞⢹⣹⠇⣶⣶⠛⠁⠀⠀⣠⡿⠋⣰⢾⢓⣝⣿⡄⡯⠳⠲⠶⢶⡾⢻⡻⠻⠶⢶⠻⣬⢋⠋⢛⢛⠏⠀⠀⢻⣌⣓⡶
⠈⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⡑⠀⣠⣾⠏⠀⠀⢸⢸⡆⠙⣎⣿⡍⠉⠉⠉⠉⠀⠀⣉⣉⡉⠁⠀⠀⠉⠉⠉⠉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⣦⡀⠰⠍⣠⣾⠏⠁⠀⠀⠀⠘⡇⢆⠠⠹⡞⣷⠀⠀⠀⠀⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠰⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⣩⡤⠴⠚⠹⣿⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠹⡘⡎⠑⢱⢹⡇⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⣤⡶⣾⠟⠛⢃⠀⠀⠀⠀⠀⠀⢀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠬⡟⣿⠀⠀⠀⠀⠉⠉⠉
⠀⢸⣿⠙⢹⡆⠀⠸⡄⠨⠄⠀⠀⠀⠸⡄⢀⡀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠱⣌⠚⣠⡟⠀⠀⠀⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣿⡀⠬⣇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠙⠦⣶⡶⠞⠛⡛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢀⣤⣤⣄
⠀⠀⢹⣗⠀⠹⣄⠀⠀⢳⠀⠁⠀⠀⠀⢀⡤⢛⣿⣄⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⠤⠶⠤⠼⣤⣀⡀⠀⠀⠀⣏⠀⢀⠌⡇
⠀⠀⠀⢻⣮⠑⠨⣓⣶⣿⡷⠤⠔⢒⣊⡩⠖⠁⠀⠙⢳⣄⠀⠘⠀⠐⠈⣦⣀⣀⣀⣀⣠⣤⠤⠖⢋⠥⠀⠀⠀⠀⠀⠀⣘⠟⠲⢤⣤⣹⠦⢵⠞⠁
⠀⠀⠀⠀⠙⠳⠚⠉⠀⣸⠏⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⡸⣿⣆⠀⠀⠀⠿⠓⠦⠬⠤⠤⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡂⢰⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤⣀⣁⣠⣤⠤⠔⠈⣀⠤⠊⣴⠃⢿⡄⠀⠀⢶⣤⡤⠶⠖⠒⠋⢁⣀⣤⠤⠶⠖⠒⠲⠶⢤⣀⠀⠐⠀⣼⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣯⣀⣨⣉⣀⣀⠤⠔⠒⠉⠀⠀⡴⢋⠀⠘⣷⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢿⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠬⠁⠂⠀⣀⠞⠁⠀⠀⠀⠈⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠙⢆⠤⡤⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣀⠤⠊⠁⠀⠶⢄⠀⠀⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⢯⣄⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⠃⣿
⠀⢠⡜⠙⢲⠆⠀⠀⠀⠀⢿⡆⠉⠉⠥⠀⢀⣀⠇⠀⠉⢉⠇⠀⠀⢠⢿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣄⠴⢦⠼⠀⠀⠀⠀⠀⠀⠀⣾⢠⡏⠀⠀⢀⣠⣄
⠀⠈⢷⠶⠞⠀⢀⡄⠀⠀⠈⣷⡀⠀⡉⠄⠙⠢⠄⠀⣀⣈⣣⠀⢠⠏⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠃⠀⠀⣹⡦⣼
⠀⠀⠀⠀⠀⠰⣌⣉⡖⠀⠀⠸⣇⠀⠀⠒⡀⠀⢰⠊⠀⠀⢀⡴⠃⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠧⣀⠀⠀⠀⣸⠁⡿
⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⢻⡄⠀⠠⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⡿⠀⠀⠀⡸⠣⣠⠀⠀⠀⠀⠸⢖⣼⠁⠀⠀⠀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡈⢀⡠⠞⠁⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠘⢧⣴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡤⣒⣋⣀⣀⣠⣤⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠲⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠐⠁⠀⠈⠄⠀⠀⠀⡀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠀⠘⠀⠢⣄⡀⠀⠀⠀⡀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠂⠀⠀⠀⠁⠠⠀⠤⠈⠈⠐⢄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠙⠛⠻⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠉⠙⠷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣷⣄⠀⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢀⣾⣿⠿⠿⣿⣿⣿⠇⠈⠻⢿⣿⣿⠇⠀⠙⠻⢿⣿⡿⡶⠚⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⢹⣿⡿⠀⠀⠀⢉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢧⠤⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠛⢉⠻⡇⠀⠀⠘⠛⠛⠛⠿⣶⡄⠀⠀⠀⠀⠘⠋⠉⠀⠀⢸⠀⡄⠈⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⡀⠇⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢣⢸⡀⠀⠀⠒⠢⠤⠔⠀⠀⠀⠀⢲⠀⠀⠉⠉⠁⠀⠀⡇⢸⠀⠀⢸⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢁⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⣇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠖⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣤⣤⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢿⣭⣤⡿⠁⠀⠀⠀⣾⣿⡿⠿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⡜⢷⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢾⠀⠀⠀⠉⠻⢿⡗⠒⠒⠦⠔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠙⠃⠀⠈⢦⡀⠀⠀⠀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡠⠇⠀⠈⠉⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠰⣶⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⠙⠿⣷⠀⠀⠀⠀⠀⢶⣾⡆⠀⠀⠀⠻⣾⣇⠀⠀⠉⠛⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⠀⣀⣠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢃⣀⣀⣀⡀⠙⠟⠀⠀⠠⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⠀⠀⠙⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠉⠀⠀⠈⠉⠉⠓⠲⠦⠤⣀⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣻⠶⠒⠢⠤⣄⣀⣀⣀⣠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠈⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⠋⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠐⠄⠀⡀⠠⡔
⠀⠀⠀⠀⠀⢸⠇⠀⣀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣨⠋⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣡⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠉⠢
⠀⠀⠀⠓⡆⠐⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠅⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣠⣼⡧⣤⣴⢦⠄⠀⠅⠀⠀⠀⠑⠁⠀⠨⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⢀⡤⠦⠠⢀⡄⡤⠀⠸⠀⠀⠀⠀⠉⠀⠀⠙
⠀⠐⠃⠘⠀⠂⠂⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠂⠀⠀⠄⠚⠀⠀⠀⠂⠀⠒⠂⠆
⢜⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⣀⣀⣀⣠⣤⣤⣤⡤⣄⡀⠈⠁⠀⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⣄⣀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣌⣩⣣⣝⣅⣄⣀⣀⣀⣉⣀⣙⣻⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣌⣭⣧⣯⣍⣄⣀⣀⣀⣈⣀⣈⣻⣆
⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣁


⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠟⠓⠒⠻⠈⠤⡇⠝⠒⠚⠻⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢹⠯⠿⠶⠏⢸⢰⠊⠷⠶⠿⢽⡉⡁
⠀⠀⠀⠀⠀⠄⠀⠑⠢⠤⠤⠔⠈⠀⠀⠂⠤⠤⠔⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠠⠠⠤⠄⠀⠈⠀⠂⠀⠤⠤⠀⠜⠁⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠙⢿⣿⣿⣿⣧⣴⣴⣶⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣞⣦⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⢹⣿⣿⣿⡿⠉⠀⢀⡄⠈⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⡤⠶⠛⡇⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠳⠀⢠⣾⣷⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿⣿⣦⣿⣿⡿⢻⡈⡄⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣤⠁⠰⠿⠃⠀⠀⢀⡎⣼⣀⡀⠀⠀⠀⢀⣠⠤⠔⠓⠤⠀⠹⣿⠏⢠⣿⣇⡇⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⢹⠃⣀⣈⣐⠀⠀⠈⠀⡠⢶⣤⡄⠀⠀⠉⠀⣾⣿⣿⠀⠀⠘⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣶⠁⠚⠙⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⣰⣿
⠀⠀⢀⣠⠴⠃⠀⠀⠀⡦⢄⠀⠀⢷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣼⣿⣿⠏
⠀⠀⡋⠠⠀⡀⠀⠀⠀⣿⠲⠄⠀⠀⠙⠧⠀⠀⠐⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣩⠕⠋
⠀⣠⠃⡾⠘⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠂⢠⠁
⠀⠉⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢗⡂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⢤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢐⢄⠃⡐⡔⠄⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠒⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠂⠠⠤⠤⠠⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠙⠢⢄⠀⠁⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡌⠀⠐⠀⠀⠀⠀⠀⠀⠘⣉⠁⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⡀⣀⠀⢀⠠⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠆⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠐⠌⠀⠡⠀⠐⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢩⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠈⣵⡀⠀⠀⠑⠄⠀⠀⠀⠀⠀⣰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠘⠢⠄⣀⣀⢴⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡞⢦⡀⠀⠀⠀⠀⠀⡠⠞⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠄⣀⠀⠀⢐⡦⢴⠚⠊⠀⠀⠀⠀⠀⠀⣿⠤⠼⠕⠤⠶⠶⣼⣧⣴⣬⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡢⢄⣈⡰⣘⠁⠀⠉⠀⢀⠀⠀⠀⠀⠀⣻⣒⠒⡂⠀⠀⠀⢘⠛⠛⢻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⡘⠉⠉⠁⠀⠀⠀⠈⠙⠙⠛⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣨⠒⣤⢀⡈⠰⠂⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢔⠤⠉⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡵⠚⢠⣴⢤⢘⢄⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠘⢧⣖⡜⠁⠌⢀⣾⡓⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠛⢤⠎⠐⠛⠀⠀⠓⣇⣀⠀⠀⠀⡸⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠆⠀⣃⣤⢡⡀⠠⠠⠤⣠⡩⠞⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣹⣾⢷⡦⠀⠊⢿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠄⡀⠀⠀⠀⠀⠀⠀⣿⠃⠉⠀⠀⢀⢸⣇⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡿⠈⠀⠀⠠⠁⠀⣿⣆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⣄⣀⠂⠀⠀⠀⠀⠈⡅⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠘⠀⡠⠈⡋⠂⠀⣼⢀⢀⠐⠦⠀⡴⢡⠀⡀⡆
⠀⠀⠀⠀⠀⠀⢰⣾⡍⣑⢄⠀⠁⣰⣦⣅⠀⠀⠀⠀⢸⡏⡁⠂⠀⠀⠀⠰⠀⠘⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣯⣍⣿⣧⠀⠹⢻⣯⣿⡅⠀⢰⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣮⣿⣗⢀⡤⣿⣿⣧⠀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡻⣿⡄⢸⣿⣇⠀⢿⡆⠀⣀⣠⣵⣋⣠⠐⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⢷⣿⣿⣷⡆⢸⠋⠈⠁⠀⣶⠙⠳⠤⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠈⠘⢿⣿⣷⣿⣦⣴⣤⣶⣾⣿⣶⣤⡀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠈⠉⠀⠈⠉⠙⠛⠻⣇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣥⣾⣿⣿⠿⢿⡛⢛⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠉⠀⠈⠀⠒⠈⣧⠠⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣿⡇⠐⠭⣄⠐⠀⠀⠀⡀⡸⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠸⡇⠐⠤⠊⡀⠑⢂⣀⠀⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣠⠕⢀⠀⠀⡐⡀⢉⣠⡠⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢈⡀⢃⠀⠈⡢⠶⠒⠈⠨⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⡀⠕⠚⡆⠀⢠⡀⠀⡀⣠⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣙⠒⣡⠟⡆⡈⢃⣀⠀⢀⢠⡃⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠀⠀⢸⠁⠀⠘⠁⠂⢸⡇⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡆⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠚⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⠿⣃⣲⣶⡆⢘⢯⠸⡀⣀⠒⠠⢅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠰⡐⠤⠃⠁⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠂⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠠⢬⠰⠀⠀⠚⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠸⣰⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢻⠀⠀⠀⢀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠀⠀⠀⠀⠐⠸⡆⠒⢊⠡⠤⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠑⠀⠄⣠⡴⠓⣖⠁⠀⠀⣀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⠶⠮⠚⠉⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣤⠶⠷⠚⠛⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⢩⠁⢀⡀⢀⡤⠀⠾⢀⠎⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢿⠄⠈⠀⢠⡄⠀⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠻⠀⢀⠀⠸⣷⡀⠀⢠⣤⡄⠐⠦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠴⢀⣀⠀⣠⡆⠀⠀⠰⠒⠃⠀⠴⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣾⣧⣬⣯⡄⢰⣿⠩⠵⣄⣀⠀⠆⢸⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⢦⣍⣛⠴⠁⢰⣷⣀⣼
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣿⣿⣷⣤⣀⠛⢆⠀⢀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⡿⡍⠳⠀⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣷⣸⡞⠃⠴⠃⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣅⣚⣚⡃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣏⠈⢰⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⡽⣿⣯⣿⣿⣿⣿⡟⢠⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢾⣽⣿⣿⡿⠛⡟⠋⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠋

⠀⠀⢸⣶⡖⠒⣶⣾
⠀⠀⢸⡟⠣⠀⠝⣿
⠀⠀⢸⣷⠒⠶⠲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣼⣦⣤⣶⣤⣠⣤⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⢸⣷⠴⠶⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⢠⡼⣿⣿⣿⣿⣷⠄
⠀⠀⢸⡿⠤⠴⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢰⣤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢋⣼⣿⣿⣿⠟
⠀⠀⢸⣧⣦⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣷⣉⣘⢤⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⠀⠈⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⡩⠕⠊⢰⡋⠍⠋⣞⣻⣽⣿⣿⣿⡿⠟⠛⠟⣿⣿⣥⣽⣀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣴⣾⣿⣿⣿⣿⡟⠉⢀⣠⣤⢞⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠿⢛⣿⣍⣿⢿⣿⡿⠀⢰⣿⣿⣯⣾⣿⣿⠿⢻⣧⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⣤⣒⣢⢤⣤⣴⣋⣼⣿⣿⣷⣿⣿⡄⢺⣿⣧⣼⣿⣿⡟⠀⡼⣿⣾⣿⣿⠷⠂
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠒⠢⠤⣀⣤⣽⣿⣧⣤⣾⣟⣙⣿⣿⣿⣿⣿⣿⡀⠈⠻⠿⠿⠿⠋⢀⡼⣡⣴⣿⣿⣅⡀
⠀⠀⠀⠀⠀⡾⠁⠀⠰⠶⡀⠀⠀⢠⣽⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⡀⣀⣴⣿⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣰⠇⠀⡤⡀⠀⠀⠉⢶⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣶⣿⣧⣀⠀⠈⠑⢤⡚⢻⣿⣿⣿⣿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖
⠀⠀⠈⣿⣿⣿⣿⣧⣄⣀⢠⣹⣮⣿⣷⠙⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠀⠉⠐⠻⠿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣷⣶⣶⣶⣴⣤⠞⠿⡿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠈⠉⠻⠿⠿⠿⠿⠛⠋⠁⢰⣾⣿⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣧⡈⢷⠒⢦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⢠⣴⢶⠦⠤⠀⠀⠀⣿⣿⢋⣉⠠⢸⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠛⠿⠟⠀⠀⠀⠜⠛⠛⠓⠀⠀⠀⠉⢁⡾⠹⠡⠬⡧⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠒⠲⠤⠀⠀⠀⠀⠀⠀⣸⢗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡿⠀⢿⣤⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠸⠁⠀⠀⠈⠙⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⣴⡾⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡤⠖⠋⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠁⢠⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⣀⠀⠀⠘⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⣀⣀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢃⠀⠀⠀⠀⡀⠄⠒⠂⠒⠖⠉⠀⠀⠀⠀⠀⣀⢀⠴⠃⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠚⠛⠀⠀⡐⠋⠀⠀⠀⠀⠀⠛⡄⢀⣀⣠⢴⠬⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡠⠰⢌⡤⡀⡠⠀⠜⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠐⠀⠈⠐⠡⠀⠀⠀⠀⣀⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⢆⠀⠀⠀⠀⠈⠀⠂⠨⡌⠒⠢⣀⠀⠈⢂⣈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠡⠀⢿⡉⠈⠉⠁⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⡲⢠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠢⠄⠀⢤⠤⠤⠔⠰⡰⠃⠒⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣒⠂⠀⠁⠀⠀⠀⠀⣶⣄⠧⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣩⢁⡕⢂⢤⢵⠀⡠⢀⠏⠠⠐⠈⠒⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢨⣀⠁⠴⠁⠀⠀⠀⢠⡄⢀⠀⢀⡔⠀⢀⣤⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢴⡁⠈⠄⠒⡡⠋⠐⢜⠄⢣⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠠⠆⠈⠊⠀⠀⠀⠀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠐⡉⠄⠀⡄⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠹⣀⠈⠀⠂⠠⠷⠖⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠔⠁⢈⠀⢄⠁⠔⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠈⢄⠀⠁⡀⠀⡘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡐⠄⠠⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡊⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠉⡛⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠋⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢰⣆⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠉⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠏⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇
⠀⠀⠀⢀⣠⣴⣶⣿⣿⣧⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣤⣤⣴⣶⣦⣤⣤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣷⡔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡈⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠟⠛⠋⠉⠉⠁⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣭⣿⣿⣜⣇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣅⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⠀⠀⠀⠠⣶⣿⣿⡿⠿⢷⣦⠀⠀⠈⢻⣿⣿⡿⠿⡿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⠋⠣⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⡜⣡⠏⠀⠀⡇⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠿⠷⠁⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⢸⢡⢹⠀⢀⠎⠘⠙⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢸⠀⠸⡀⠄⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠠⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⣇⠀⠙⠚⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⢷⣦⡤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⢒⣒⣊⣁⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠋⠀⠀⠀⡴⠁⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣉⣀⣠⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣣⣶⣾⣿⣿⣿⡿⠿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⠟⠛⠏⠁⢰⠊⢍⡊⢿⡏⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⢿⣿⠀⣠⠤⠀⢠⠀⠀⠀⠀⠈⢧⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢸⣿⠀⡐⠈⡆⠈⣄⠀⠀⠰⢠⠘⣆⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠈⢿⠀⠙⠚⠑⠄⠀⣁⣤⠄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⡜⠣⢄⠀⠄⡈⣄⢈⣀⣢⠖⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⡀⠸⠀⠀⠉⡲⠖⠒⠈⠀⠆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠑⣈⠱⠔⢳⠀⠀⣄⠂⢀⣀⣀⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠛⠢⠂⣸⢶⠀⠜⠇⠀⠀⠀⡀⡴⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⠊⠁⠈⢳⠉⠈⠳⠆⠤⠁⣿⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡺⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣦⣀⣀⡀⠀⠐⡀⣸⡷⣤⠔⠊⡁⠑⢒⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠛⡿⢄⠼⡿⢿⠰⠽⡇⠰⠀⣤⡈⠐⠺⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⢲⠐⠶⠃⠈⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠲⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⡴⠀⠀⢸⢸⠀⠀⠠⢶⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⢿⡃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠢⠄⠀⠀⠀⠸⡇⠀⠀⣠⠴⠒⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠑⢄⠀⠀⠈⠉⠈⣏⠉⠉⠔⠒⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡅⠀⠀⠀⠀⠉⠐⢒⣰⡶⠋⢻⣍⣀⠀⣀⣠⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠲⠾⠅⠛⠁⠀⠀⠀⠈⠉⠉⠉

⣀⣀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣠⠴⠶⢤
⠙⠚⠗⢠⠴⠦⡅⠀⠀⠀⢰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠹⢤⣰⡇⢤⣄⠀⠈⠣⠤⣄⠘⢧⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⣸⠀⠀⠈⡆
⠀⢠⣾⠇⠀⢿⣇⠀⠉⠁⠀⠀⠀⣈⣧⠈⣷⠖⢋⣡⠤⠲⠶⠾⢯⣍⣓⠒⠦⣌⠙⠦⣠⠔⢉⣠⣀⢀⣠⠇
⠀⠀⠀⠀⠀⠈⣿⡆⠀⢀⣀⡔⠋⠉⣠⠟⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⣹⢦⠙⣖⠋⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠸⡽⣴⠋⠉⠀⠀⡴⢃⡞⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡼⢳⠘⣆
⠀⠀⠀⠀⠀⠀⣠⢷⢣⠀⠀⠀⡼⢡⠏⠀⠼⠦⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠋⠛⢧⢹⡀
⠀⠀⠀⠀⠀⣰⠃⠘⡏⢇⠀⢰⠇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⢸⡌⣧
⠀⠀⠀⠀⢰⠇⠀⢠⡞⠉⢙⣾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢿⠀⣰⠓⠛⣧⡀
⠀⠀⠀⠀⣼⠀⠀⣈⠷⠖⠺⡉⢹⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⡴⠁⠀⣠⠞⠁⠀⢸⡀⡇⠀⠀⠙⣍⠓⢦⡀
⠀⠀⠀⠀⢹⠀⡼⠁⠀⠀⠀⢱⠘⠳⡄⢀⡾⣀⠴⠣⣀⣠⠔⠉⠓⠖⠊⠁⠀⠀⠀⠀⠳⢷⠀⠀⠀⡌⠀⠀⠙
⠀⠀⠀⠀⢸⣼⠁⠀⠀⠀⠀⠸⡇⠀⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⡏⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⡇⠘⣍⠀⠀⠀⠀⠐⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠐⢇⠀⢀
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⠇⠀⣿⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠶⢺⡁⠀⠀⢀⣾⣴⠋
⠀⠀⠀⡴⠋⠁⠙⢦⣀⠀⠀⡸⠀⢾⠁⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⣳⠀⠀⢀⡟⢻
⠀⠀⠀⠉⠛⠛⡿⠀⠈⢽⠛⠁⢀⡼⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⣤⠷⡀⠀⠀⠀⠀⠀⡿⠦⠴⡾⠒⠋
⠀⠀⠀⠀⠀⠀⠳⠤⠖⠻⣷⣋⣩⢴⣶⠠⣵⠦⡀⠀⠀⠀⠀⠀⠀⢇⠘⣂⠇⠀⠀⠀⣠⠞⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠳⡈⠳⣄⠉⠒⠠⠤⣤⣀⣤⣥⣥⡤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠙⠲⣌⡢⣄⣠⠞⣷⠋⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⡇⠙⠛⠓⠋⢠⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⢦⠀⠀⠀⢿⠂⠀⠀⢰⠋⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⢧⡀⠀⠸⡆⠀⠀⣸⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣍⣙⡿⠓⠚⢷⠀⠀⠛⣟⢿⠉⠓⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣽⠁⠀⠀⠈⠳⣤⡴⣿⠋⠓⢺⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢹⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣻⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⡀⢀⠀⠀⢠⡾⠋⠉⠉⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠞⠛⠓⠀⠀⣠⠴⠤⠀⠀⠀⠀⠀⠰⠀⡆⠀⠀⣼⣏⡀⠀⠀⠀⣰⠟⠉⠁
⠀⠀⡄⡇⠀⠀⠀⣿⣛⣷⠀⠀⠀⣿⣲⡆⠀⠀⠀⠀⠀⣼⠋⢀⠀⠀⠀⢸⡷⣦⡀⠀⠀⢸⡧⡄⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⣿⣩⡿⠀⠀⠀⣿⠽⠂
⠀⠁⠃⠁⠐⠀⠀⠹⣏⠁⠀⠀⠀⠘⣧⣀⡀⠀⠀⠀⠀⣿⡀⠏⠃⠀⠀⠸⣗⠛⠀⠀⠀⠸⣏⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠹⣧⣀⢀⡀⠀⠘⠧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠙⠷⠤⠔⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⣠⡤⠀⠀⠀⠀⢰⡟⠁⠀⠈⠀⢠⡖⠛⠒⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠁⠀⠈⠻⣆⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠈⠉⠳⣄⠀⠁⠀⠀⣹⣆⠀⠀⢤⢠
⢠⣿⢀⣤⡀⠀⠀⣿⣉⣿⠀⠀⠀⣿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠰⣏⣿⠀⠀⠀⢾⣏⣿⠀⠀⢀⣤⡄⢻⡆⠀⠀⠀⠀⠰⣯⣿⠀⠀⠀⢾⣍⣿⠀⠀⠸⢸⢠
⠈⣿⡈⠃⠀⠀⠀⠹⣧⡀⠀⢀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡀⠀⢀⣰⠟⠀⠀⠀⠀⢁⣿⠃⠀⠀⠀⠠⣤⠴⠋⠀⣀⠀⣀⣼⠏⠀⠀⠀⠀⠘
⠀⠘⢷⣄⡀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣄⡀⠀⠀⠴⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⡀⠀⠉⣹⡄⠀⣼⣉⠁⠀⣠⠒
⠀⠀⠀⠀⢀⣹⡆⠀⠀⠀⣤⣽⡇⠀⠀⢑⢸⠀⠀⠀⠀⠀⠠⠶⢤⡀⠀⠚⠉⠙⢶⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣻⠃⠀⠘⢳⡇⠀⣷⠛⠀⠀⢻⡋
⠀⠀⠀⠀⠘⢺⡇⠀⠀⠀⠻⢾⡇⠀⠀⡈⠸⢸⠁⠀⠀⠀⠀⢠⡶⣷⠀⠀⠀⣴⠞⣿⠀⠀⠀⣀⠈⣿⡄⠀⠀⠀⠈⠁⠀⠐⠒⠋⠀⠀⠈⠓⠂⠀⠀⠉
⠀⠀⠀⠒⠒⠋⠀⠀⢤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠀⠀⠀⠘⢻⡟⠀⠀⠈⠉⠃⣿⠇⠀⠀⠀⣀⠀⠀⠠⣤⡀⠀⠀⠀⣠⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠐⠶⠞⠋⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢈⣵⡀⠀⢠⣽⡆⠀⣾⣥⠀⠀⣰⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⣀⠽⠁⠀⠈⣹⠃⠀⢻⣉⠀⠀⠹⢍⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡴⠚⣒⣛⠳⠶⠶⢦⣤⣴⣦⣀⣀⠀⠀⠀⠀⠀⢠⡷⠒⢛⣿⠀⠀⠀⠀⠀⠀⡴⢒⣒⣷
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠷⠟⠛⠛⠛⠻⠷⣶⣄⠉⠛⢯⣿⣤⣄⡀⢀⣴⣾⠇⣶⣾⠇⠀⠊⠳⠆⠀⠀⣿⠉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠀⠙⡆⢽⣇⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⣶⣺⠇⢾⣭⠟
⠀⠀⠀⠀⠀⠀⣴⣟⣀⣤⣠⣄⣠⣀⠀⣀⠀⠀⠀⠀⣿⡆⠀⢷⢠⡿⠃⠀⠀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⢀⣴⢾⢇⠃⠚⠦⠈⠁⣨⠽⣍⡑⣤⠀⠀⡣⡇⠀⡞⢈⣿⠆⠀⠀⠀⠀⠀⣷⠶⠛⠀⢀⣀⡀⢀⡀
⠀⠀⠀⢀⣾⢁⢾⣻⢀⣀⠀⠀⠀⠀⠀⠀⠁⣌⠀⢀⣿⢧⣴⣇⣸⡇⠀⠀⠀⠀⢠⣤⡏⠀⠀⠀⠁⠀⠉⠉
⠀⠀⢀⡾⡇⢸⢠⣻⠀⠉⠁⠀⠐⠒⠒⠆⠀⣮⠖⢩⠖⡹⢆⠰⢻⣷⡄⠀⠀⠀⠈⠉
⠀⠀⢸⠃⢳⡸⡌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠻⣀⠇⣸⠃⡘⢹⡇
⠀⠀⡟⠀⠀⠑⣿⣼⡇⠀⡀⠀⠀⠀⠀⠀⠀⢱⠸⠀⠛⠀⠋⠀⢁⣾⣅
⠀⢰⡇⠀⠀⣸⠋⠘⢷⡀⠈⠓⠒⠃⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠘⢉⡿
⠀⢸⠃⠀⠀⡟⠀⠀⠀⣙⣷⣤⣤⣄⡀⠀⢠⡶⣿⠀⠀⠀⠀⠀⣰⠏
⠀⣾⠀⠀⠀⣷⣴⠞⠋⠉⠉⠉⠉⢻⠿⣠⡾⠛⢿⠀⠀⠀⣠⡾⠏
⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠊⠁⢠⠇⠀⠀⡸⢻⣆
⠀⢿⣄⣀⣀⣀⣠⢃⣀⣀⣀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠃⠀⠹⡆
⠀⠀⠉⠙⠛⠉⠙⠋⠉⠉⠉⢻⠀⠀⠀⠀⡜⠀⠀⠀⣬⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⠁⠀⠀⠀⠁⢳⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠸⣤⣀⣀⣀⣠⢼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠉⠉⠁⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⣿⣿⠻⠿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿