Disrespectful Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠐⠢⡀⠀⠀⠀⡐⠀⠣⠀⠠⡀⣀⠀⠀⠀⢚⠒⠂⣘⡈⠉⠛⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢀⡠⢂⡊⠦⡼⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⡅⡀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠉⢀⠀⠀⡀⠀⠀⢀⠄⠂⠙⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⣀⠀⣳⠘⠀⠀⠑⠠⢀⣀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡡⣤⠜⢹⠋⢿⠱⣆⣡⡀⠀⠀⢠⣄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠳⠏⠂⠒⠊⠀⠘⣏⡘⠀⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠤⢂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⣆⠈⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡠⠐⠀⠉⠈⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢀⡔⡄⣤⡘⣧⠀⠀⠀⠀⠈⢀⠔⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡇⢰⡐⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠉⠭⠤⠤⠀⠱⠼⠆⠠⠀⠀⡤⠁⠀⠀⠀⠀⢣⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢀⣀⣀⣀⣀⣀⣀⠀⡠⠊⠀⠀⠀⠀⡠⠀⠈⠄⠰⠀⠀⠀⠀⠁⠈⠉⠀⠈⢹⠀⠀⠀⡘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢄⡀⠃⠰⠀⠀⠀⠀⢀⠴⠞⠅⠀⠀⠀⠀⡴⠀⠀⠀⢹⡀⡃⠀⠀⠀⠐⡂⠀⠀⠐⠺⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠁⢀⡠⠀⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⣀⠊⠘⡀⠀⢀⣀⠇⠐⡀⢀⠀⢀⡭⠉⠉⠉⠉⠀⠀⢰⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠥⠼⠤⠬⠆⡀⠀⠐⠀⠀⠒⠂⠀⠤⠎⠀⣄⡊
⠀⠀⡀⠄⢠⠀⠐⠂⠐⠃⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠴⠦⠄⠀⠄⢀⠀⠀⠀⠀⣤⠚⠉⠁⠀⠀⠀⠄⠐
⠀⢮⠀⠠⠁⠀⠀⠄⠂⠀⣼⠂⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠀⠉⠉⠁⠀⠀⠀⠈⠉⠈⠙⠉⠉⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠐⠂
⢀⠁⠀⢀⠀⠀⠀⠀⠀⡴⠹⠖⠒⡖⡶⠒⠀⠰⠶⠀⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠠⠄⠠⠤⠤⠄
⠈⠸⠀⠀⠑⠂⠐⠢⠐⢁⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⢉⠠⠀⡤⢀⡀⠒⠁⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⡇
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠠⠀⡃⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠶⠤⠎⠀⢉⠴⠀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⠤⠤⠤⠆⢧⣄⠤⠄⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠠

⠀⠀⠀⠀⠀⣠⠶⠶⠶⠄
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠦⣈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢀⣤⣾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡉
⠀⣤⠙⣿⣿⣆⠐⣶⡄⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢀⢴⣓⠀⡀
⠀⣿⣄⠉⢻⣿⣭⣿⣯⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢺⣯⣬⣶⣡⣾⣿⢣⠈⠄
⠀⠻⣬⡆⠀⠙⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⣿⣿⣿⣿⣿⣿⠏⣧⣄⢀⠀⢀⢀⢄
⠀⠀⡝⢿⣦⡀⠈⠻⣿⡟⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⢩⣥⢀⣤⣬⣃⣾⣿⣿⣿⣿⣶⡆
⠀⢠⡧⠈⢻⣷⡄⠀⠘⢧⣿⠻⡇⠀⠀⠀⠠⢀⣀⣀⠀⣠⠏⠀⠀⠀⣀⠴⢷⣿⣼⣿⡯⠀⠀⣀⣬⡟⢉⣿⣿⣿⣿⣿⣿⡡⠂
⠀⢸⣿⣮⠄⠈⢡⣄⠀⠀⢿⡄⢧⣤⣤⣤⣷⣶⣦⣽⣽⣿⣤⣶⣤⣶⣤⣴⣿⣿⣭⣽⣿⣤⣨⣿⣿⣧⣿⣿⣿⣑⣘⣋⠁
⠀⠈⢰⢸⠀⠀⢰⠿⣿⢇⢨⡞⠈⠛⠛⠛⠛⠛⠛⠛⢋⠛⠉⠛⠛⠛⢛⣛⠛⡛⡛⢿⣛⠛⠛⡿⡶⠓⠀⠀⠀⠀⠀⠉⠉⠈⢹⠿⠂
⠀⠐⣠⡀⠀⠀⠀⠀⣟⣀⣩⠁⠀⠀⠀⠀⠈⠉⠉⢉⣉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡏⠉⡉⠉⠈⡹⣽⣟⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⣷⠀⠀⠀⢀⣿⠃⢹⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⣿⠦⠀⠀⢸⢿⣆⣈⣠⣤⣿⣶⣀⣤⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⡇⠆⠀⡟⣸⢯⢉⠁⢩⣿⣏⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⢸⡀⢸⣇⣛⠸⣾⣾⠚⣿⡏⠀⠐⣖⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉
⠀⠀⣸⣿⣷⣾⣿⣿⣶⣧⣄⡈⢹⣿⡇⠉⠉⠏⠉⠉⠉⠙⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⡀⠀⠀⠈⣿⡿⠿⠿⠟⠋⠙⠃
⠀⠐⠿⠿⠿⠟⠉⠉⠫⣿⣭⣽⣼⣙⠃⠁⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠒⠶⣶⣶⡦⠋⠉⠉⠋⠉⠈⠉
⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠈⠁⠀⠃⠀⠈⠁⠈⠀⠀⠀⠀⠁⠁⠑⠈⠁⠁⠃⠉⠁⠘
⠀⠀⡀⠀⢀⠀⠠⠀⡄⡀⢀⠠⠀⡀⢀⠀⢄⢀⠀⠠⠀⢀⠠⠀⠀⢀⠀⠄⠀⠀⢀⠀⣀⠀⠀⡠⠂⡄⡀⠠⢀⠀⡀⠀⠀⠄⠐
⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠁⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠈⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣷⣦⣄⠀⠈⠛⢛⣋⣠⣤⣴⣶⣾⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⢠⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⣤⣶⣶⣿⡿⠿⠟⠛⠋⢉⣠⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⣰⣿⣿⠋⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⠿⠛⠋⣉⣁⣤⡄⢠⣾⡿⣿⣮⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠘⢋⣉⣡⣤⣶⣶⣿⡿⠿⠟⠛⢉⣉⠀⢤⣴⣶⣶⣄⣿⡟⠋⠁⢸⣿⡀⠈⠁⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣈⣤⣴⣶⣾⣿⠿⠿⠛⠛⠉⢁⣤⣤⣶⡆⣾⡟⠻⠷⠸⣿⣄⣸⣿⢸⣿⡿⠿⠀⣿⣧⢀⣶⣷⠀⢹⣿
⠀⢠⣴⣶⣿⡿⠿⠟⠛⠋⣉⣤⣤⡀⣶⣿⠿⣿⡆⣿⣏⣀⣄⠻⣿⣶⣶⣄⢿⣿⠛⠋⠀⣿⣧⣴⣶⡈⠻⠿⠟⢁⣀⣤⣤⣶⣶⣧
⠀⠀⢉⣩⣤⣤⣄⠸⣿⡰⣿⡋⠙⠛⢸⣿⣤⣾⡟⢸⣿⡛⠋⠀⣤⣄⣸⣿⠸⣿⠄⠀⠀⠘⣉⣉⣤⣴⣶⣾⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠈⣿⡏⠙⣿⡇⢿⣇⠙⠿⠿⢿⣦⣿⣏⠹⣷⣄⣿⣷⡾⠿⠙⠛⢛⣁⣠⣤⣴⣶⣿⡿⠿⠟⠛⠋⢉⣀⣤
⠀⠀⠀⢹⣷⠀⢹⣿⠸⣿⡴⣶⣤⣾⡿⠸⠿⠀⠙⣉⣈⣤⣤⣶⣾⣿⠿⠿⠛⠛⠉⠉⢠⣤⣶⠆⠀⢀⣿⣿⠇
⠀⠀⠀⠈⣿⣷⣾⠟⠀⠛⠃⢈⣉⣡⣤⣴⣶⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⢀⣾⣿⡟
⠀⠀⠀⠀⢉⣁⣤⣤⣶⣶⣿⡿⠿⠛⠛⠉⢉⣤⣴⣦⣄⣀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠟⠁⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠈⠿⠛⠋⠉⠁⠀⠰⣶⣷⣦⡀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⣤⠾⠻⢶⣠⢟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡾⠋⠉⠳⠎⠁⠀⠀⢠⣯⠟⠶⣶⠀⠀⣠⡆
⠀⠀⠀⠀⢀⣤⡶⡖⠷⠚⠛⢀⡤⢾⠁⠀⢴⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⢔⣫⠾⠃
⠀⠀⠀⠀⢼⡏⡌⣶⡒⠚⠋⠉⠀⣸⠀⠀⠀⢨⡟⠋⠀⠀⣷⠿⣄⣀⠀⠀⠀⠰⠏⠲⣏
⠀⠀⠀⠀⠈⠻⠇⢹⠻⡄⠀⠀⢀⡟⠀⠀⠀⠘⢷⠄⡠⠚⠉⠠⡌⠛⠒⣆⣀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣆⠀⣼⢃⠀⠀⠀⠀⢠⡞⠀⠟⠰⠇⠀⠀⠀⠘⠟⡇⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⢧⣿⣸⠀⠀⠀⠀⢸⢠⣄⣑⣠⣄⠀⠀⠠⣄⣰⠃⢀⣹⠆
⠀⠀⠀⠀⠀⡀⢀⡿⠀⠀⠀⢸⣯⡼⢷⡀⠀⠀⠘⢦⡀⠀⠈⠉⠀⠶⣤⡾⠃⣤⠈⢷⡀
⠀⠀⠀⠀⣼⡏⠘⣧⠀⠀⢀⣏⡇⢹⡈⠳⣄⣀⠀⣤⡍⠳⠀⡤⢶⡞⠉⠲⠛⡉⢣⡠⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⢸⣿⢷⡛⡿⣇⠀⣼⠷⠤⣄⠙⠲⠤⣭⣉⡁⢹⡤⠖⠋⠉⠉⠙⠓⠶⡌⢆⡙⢌⢾⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣀⣤⣀⠙⢦⡀
⠀⠀⠀⠘⠟⠛⠛⠓⣿⣰⠓⠲⡄⠙⣦⠀⣀⣠⠞⠁⠀⠀⠀⣰⠏⣉⣉⣹⡆⢹⠈⠣⠈⠛⠋⢥⣄⠀⠀⠀⠀⢰⢋⡤⣠⡌⠋⢛⡛⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣠⠶⠷⢄⡈⠳⣯⠀⠀⠀⠀⠀⣴⣫⠎⠁⢀⢸⠏⣿⠙⢦⡄⠀⣿⣿⣿⠿⣷⣶⡀⢸⣄⣒⣈⣀⠀⠈⣻⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣫⠞⠁⣠⣀⠀⠉⠳⠘⢷⣄⣀⣠⠞⣱⠃⠀⢈⣹⣆⣀⣧⢀⣾⠇⠀⣿⣿⡿⢿⣧⣾⣷⡀⢳⡒⠛⠉⠀⠙⣽⠋
⠀⠀⠀⠀⣿⡀⡶⠋⢀⡴⢚⡁⠉⠛⠶⣤⣄⣀⡭⠟⢁⡼⠁⠀⠀⠈⠁⠋⠃⢁⣾⠟⠀⠸⣿⣻⣤⣿⢿⣎⠈⢿⣆⠉⢓⣦⠴⠦⠼⢦
⠀⠀⠀⠀⣿⣷⣳⠞⣩⡴⠁⣁⣂⣀⣀⣀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠉⠉⣿⠻⣷⣿⣷⠶⠛⣷⠋⠀⣀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠻⠟⠱⠮⢋⡶⠛⠉⠉⠀⠉⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠸⠀⣇⠹⡿⢋⡴⠚⣉⡷⢾⣇⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⡶⢦⣤⣄⡀⣠⣴⣶⠶⠶⢶⣶⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⠙⢁⣠⠞⠁⢀⣤⠟⠒⠀⣤⣤⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠉⠙⢋⣾⠃⠀⠀⠀⢹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣠⠾⠋⣠⠖⠀⠀⠀⣀⡴⣋⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⣀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣇⣠⠞⠁⠀⣴⠚⠋⠉⣻⠳⡌⠧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠘⠀⠅⢠⡿⠡⠌⠡⠄⠀⢤⠄⢻⠆⣿⠀⠠⠦⠀⠃⠠⠤⠀⠀⠘⠃⠰⠆⠑⠎⠠⠙⣧⣠⣤⣤⣤⣤⣀⣀⣿⣤⣝⠒⣲⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⡦⠈⠻⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡇⠙⠁⠀⠀⡀⠀⠀⠈⣧⠀⠀⢠⡇⠀⠀⠀⠻⠽⠏⢴⣶⡇⢠⣦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⡀⠀⡼⠀⣀⢀⡠⣄⠀⠀⠀⠀⠀⠘⠷⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠃⠀⠃⠀⣇⠀⠀⢘⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠴⠄⡄⠀⠀⢀⣤⣤⣤⡀⠀⠉⠲⠤⠜⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠁⠀⢠⣿⣿⣿⣿⣿⡆⠀⣀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠀⠀⠘⣿⡉⠙⣿⣿⠃⠀⠉⠁⠛⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣾⣿⣿⣷⣾⣯⣷⣿⣿⣶⣤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠙⠣⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣽⣿⣿⡇⣿⣿⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⣄⢀⣀⢀⣀⡆⢀⢀⣀⢀⣀⠀⣀⡆⣀⢀⣀⠀⣀⠀⣀⡰⢀⡄⢀⠀⡀⢀⠀⢠⡀⠀⡄⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠇⢠⣬⢥⣺⣽⠀⡟⡈⢹⠀⠯⣸⠀⣇⡿⣀⢇⣸⠀⣑⠸⣊⠵⢇⡸⢅⠇⠐⠮⠂⢁⡭⡇⡇⣗⡉⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣜⡥⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⢠⠞⢁⣠⠾⠭⢄⣠⠤⠤⢄⣀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⢀⣠⠟⠊⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠀⢀⠇⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⣆⠀⠀⡸⠀⠀⠀⠀⣠⠔⠁
⠀⡼⠁⠈⠑⢦⡀⢠⠞⠁⢀⠀⠀⠀⠀⠀⠈⣶⠰⠧⢤⣀⣠⠞⠁
⢰⠁⠀⠈⣻⡶⠄⠀⠠⠾⣛⠀⠀⠀⠀⠀⠀⢸⣧⡀⡠⠊⠉⠓⢤⡀
⡎⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢫⠀⠀⠀⠀⠀⠉⢢⡀
⢀⠀⠀⠀⠀⢀⡐⠂⠁⠲⣄⠀⠀⠀⠀⠀⠀⢸⡧⣄⣇⠀⠀⠀⠀⠀⠀⠙⢄
⢘⣄⡤⠖⠛⠉⣠⠄⠀⠀⣸⠀⠀⠀⠀⠀⢠⣿⡤⣸⡉⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠁⠹⣄⣠⠔⢋⡴⠂⠒⠊⠁⠀⠀⠀⢀⡴⠋⢸⡃⠘⡳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠐⠋⢓⡴⣏⣀⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⢐⡂⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠸⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣀⠤⠔⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠧⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⠛⠻⠙⡌⠉⠉⠙⡄⠀⣀⡠⣤⠶⡖⠒⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢤⣤⣄⣀⣀⣤⣄⠤⢞⠗⠋⠁⠀⠈⠀⠉⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠤⠤⠤⠔⠶⠖⠒⠛⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠤⡒⠒⠒⠒⠒⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡡⠖⣩⠴⠞⠛⢻⣧⠀⠀⠀⢀⣶⣶⡄⠉⠓⢦⣀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣣⠖⣭⣦⠀⢹⡀⠀⢀⣾⡏⠀⠀⠐⠋⡿⠀⢀⣴⣦⡀⠙⢷⡀
⠀⠀⠀⠠⡞⢁⠀⢀⡴⠊⠀⢠⡟⣿⡆⠈⣧⣴⣿⡟⠀⠀⠀⠀⠀⠇⠀⠸⣧⡼⠃⠀⢸⣿⡄
⠀⠄⡰⢙⣀⡬⢟⡵⣆⣠⣄⢸⡟⠹⠇⠀⢛⣻⡯⠄⠒⠂⠙⠛⠻⠿⣷⣶⣦⣄⠀⠀⢠⣯⡇⠇
⢠⠠⡇⠀⠀⠀⣮⣼⠟⣡⠏⠘⢃⣤⠶⣿⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⣾⣿⠇⠺⠆
⠀⢻⣧⠀⠀⠀⠈⣿⣶⠋⣠⢾⣟⠁⣸⠁⠀⠀⠠⡞⠙⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⣿⣿⠋⠠
⠀⠀⢻⣷⣄⠀⠀⠈⢛⣾⣿⠏⠈⠤⠇⠠⠀⠀⠰⠉⠀⠐⠒⢦⠀⠀⠃⢠⠀⢣⣿⣿⣃⢀⡤⡀
⠀⠠⠀⠻⣿⣿⣦⣤⣾⠟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⢤⡆⢸⣇⠀⠈⠀⠀⠘⣾⣿⣇⠸⣠⠆⣤
⠠⠀⠀⠀⠈⠙⠻⣿⣯⣷⣶⣶⡀⠀⢀⢞⣿⣿⣿⠿⣿⡀⠃⢸⣿⡀⠰⣤⣏⠀⣿⡿⠎⠛⠛⢿⣷⢸
⢡⠄⢠⠀⡏⠙⡆⠸⢇⣿⣿⡋⣳⠀⢈⠸⣿⣿⣿⣀⣸⡇⠀⢸⣟⣿⢦⡿⠙⣷⠈⠛⠤⢠⣾⣾⡟⣾
⠇⠀⠀⢀⠙⠒⠁⠀⠀⣿⣿⣿⡿⣌⠸⣆⢻⣿⣿⣿⣿⢿⠀⠈⠻⠿⠋⠀⢒⡟⠀⣠⣾⡿⣿⠿⠇
⠀⡄⠀⠀⠀⠀⠀⠀⡸⠾⠿⢛⣽⣿⣆⢺⣷⢿⣿⣿⡿⣫⣴⢶⣏⠀⢀⡆⢎⠀⣾⢯⣫⠔⠂⠀⠀⠀⡆
⠀⠰⣀⠀⢀⣀⠀⢀⡇⠀⠀⣼⡿⠻⠿⣧⠙⠻⠿⠷⠋⣿⡏⠀⠈⢳⠀⠀⢈⠇⠻⣮⢿⠀⠀⠀⠀⠊⠐
⠀⠀⠀⠉⡛⠻⠓⠀⢿⣷⣶⡄⠀⠉⠉⠉⠀⠀⠀⣴⣄⢙⣿⠀⠀⣼⡀⢠⠏⡀⣴⠟⡘⠀⠀⣤⣤⡤⠖
⠀⠀⠀⠀⠈⠓⡀⠀⠀⠙⢻⠃⠀⠀⢀⠀⢰⣶⣤⣼⣿⣿⡿⢀⣼⣟⡤⢘⣄⣿⣧⣤⣿⣦⣴⣧⣀⠈
⠀⠀⠀⡀⠀⠰⢿⡆⠀⠀⣼⣦⣿⣤⣼⣷⣾⣿⠟⠛⡏⢋⣁⣌⣉⣭⣀⣉⣩⣼⣿⠿⠿⠿⠿⣿⣿⣄
⠀⠀⠀⡨⠇⠀⠈⠀⠀⢸⣿⣿⣿⠛⢿⠀⠸⣿⠃⠀⢠⢤⣼⣿⣿⡿⠟⠛⠉⠁⠀⢦⣾⢷⡄⠈⠙⢟⢧
⠀⠀⠊⠀⠠⡀⠀⢀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣯⣿⡿⣻⠛⣷⣤⢤⣰⠛⣶⢸⡟⢸⣇⣴⢶⡌⢾
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢻⣿⣿⣿⣿⣦⣼⣶⣿⡿⠛⠁⠀⠙⣾⠉⣠⡾⠉⠙⠁⠀⠁⠺⢻⡟⠛⠃⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢫⡙⠛⠛⠿⣟⠟⡁⠰⣋⡷⡀⠀⠸⣟⣭⠶⢛⣏⠉⠛⠳⣄⠘⣧⣄⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠱⡄⢠⣤⡌⢿⡍⠳⡍⠛⢁⣴⠞⠉⠀⠆⠀⠁⠀⠀⠀⣽⠇⢀⡴⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢇⠀⢳⠀⠀⠛⣠⣦⡾⡿⠁⠀⢉⠇⠀⠀⢀⣠⣴⣟⡥⠖⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⢰⡘⢶⣬⣴⣶⣾⣟⡿⠏⠀⠀⠀⠋⠐⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣍⡙⠉⠋⠉

⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠄⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿
⠀⠀⠀⠀⣿⡷⢀⡀⢶⣩⣾⣦⠀⠀⠀⠀⠀⢠⣤⡄⠀⢠⣿⣿⡞⠁⠀⠀⠀⠀⠀⠍⡅⢨⡁⠺⣿⣿⣿⣆⡀
⠀⠀⠀⢠⣶⠞⠉⠀⠀⢹⣿⣿⡇⠀⠀⠀⢀⣼⣟⣡⣄⣼⣿⣿⣿⠀⠀⠀⢀⣰⣿⣷⣧⣿⣷⣶⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠸⣿⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⣿⡟⠉⠁⠀⠙⣻⣿⡿⠀⠀⣰⢻⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠂⠀⠀⠀⠈⣿⡏⠉⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠁⣿⠀⠀⠀⣻⡿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠛⠋⠁⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣤⡈⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠟⠠⠉⠀⠀⠀⠀⠀⣐⠀⠄
⠀⠀⠀⠀⠀⢙⣏⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢏⣹⠺⡿⠇
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠘⠁⣿⠋⠀⠀⠀⠀⠀⠀⢛⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠙⣿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠾⣿⡟
⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠃⠀⢁⡖⠀⠀⠀⣸⣿⣄
⠀⠀⠀⠀⢸⣿⡟⣳⣀⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷
⠀⠀⠀⠀⢸⣿⡏⠁⠉⢿⢛⡟⢹⡇⠀⠀⠀⠀⢰⢾⣿⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡿⣇⠀⠀⠈⠈⠁⠈⠁⠀⠀⠀⠀⠀⣻⣿⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⣠⣤⣤⣾⡷
⠀⠀⠀⠀⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⡿⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⡿⠃
⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢉⡑⠢⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣶⣄⠀⠀⡝⡍⡏⢆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣤⡖⠺⠧⠑⣄⠹⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠋⠛⢿⠷⣏⠱⢁⠀⠈⠆⠀⠀⠀⠀⠀⢀⣀⠀⠸⡃⢱⢄⡄⠮⠀⠈⠛⡇
⠀⠀⠀⠀⠀⣿⣿⠏⢥⡤⡘⣂⡀⢠⡏⢆⡀⠃⣀⡆⣀⣀⣀⠤⠤⠬⠥⠄⠀⢇⠀⣌⠄⢄⠂⢀⠎⠁
⠀⠀⠀⠀⠀⢍⠁⠿⡴⠒⠚⠁⣸⣸⡿⠆⢉⠁⠀⢃⠀⠀⠀⠀⠒⢒⠉⠀⠀⠈⠢⠜⠶⡮⠔⡏⠉⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠈⣿⣷⣼⣶⠮⠥⢾⡿⠡⠀⡸⠀⠀⠸⡀⠀⠀⠀⡀⠉⠀⡠⢖⢄⣇⠀⠈⡧⠔⠁⠀⠀⠤⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡩⠝⠉⠙⠤⣴⣿⣷⠀⠀⠀⠀⠀⢀⠅⠀⠀⠚⢀⡴⠊⠔⠁⡸⠈⠉⣻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠎⠀⠀⣀⠤⠴⡆⠀⢹⠀⢰⠤⠤⠐⠊⠀⠀⠀⠐⠁⠀⠀⠀⠀⢇⣀⣠⠃⢃⠀⠀⠀⡠⠒⠚⠂⡤⠃
⠀⠀⠀⠀⠸⠀⠀⠉⠀⠀⠀⢡⡠⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠷⠷⠧⠊
⠀⠀⠀⠀⠀⠑⠤⠄⠤⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠲⡤⠖⠋⠉⠳⣄⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⣴⠀⠀⠀⡜⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠁⠘⠦⠴⠊⢇⠀⣀⡄⠀⠀⢠⡇⠀⠀⡠⠲⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠊⣀⠀⡀⠰⣢⠀⠉⠀⢈⢶⠾⠁⠑⠒⠋⠀⠀⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⠀⠈⠛⢿⠄⠀⠀⠀⠀⠘⠁⢀⡄⢀⠀⠀⠀⢠⣇⣀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠘⠃⢰⣲⣾⠷⠄⠀⠀⠀⠻⠟⠛⠋⠀⠀⠀⠀⢀⣂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣫⡬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠢⣀⠜⠉⠁⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢆⠀⢸⠀⠀⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣤⠜⠀⣬⣤⠤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠴⡻⠤⠞⠀⠘⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠁⠀⠀⠀⠀⠘⢾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⡀⢷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢬⡙⠧⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⢈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⡀⠸⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢀⠔⠁⠈⢆⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞⠈⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⢄⠀⠀⣱⡄⠀⠈⣀⠤⣀⠀⠀⠀⢠⠃⠇⠀⢦⠸⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢎⢆⠞⡡⠃⠀⢰⡁⢐⡾⠤⠐⢶⠁⢸⣤⠉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠒⠊⠁⠀⠀⢠⢿⠁⠀⢀⡴⠋⠀⣾⡷⣊⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⠁⠀⠀⣀⡠⠄⢚⡶⠒⠊⠁⠀⠀⠀⠘⠹⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡄⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡴⠋⣀⠤⠒⠋⠉⠀⢀⡴⠃⠠⠀⠀⠀⠀⠀⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⢀⠔⠁⠀⠰⡁⡀⠀⣀⡤⠖⠉⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢣
⢀⣠⡄⣢⠄⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⢀⡞⠀⢀⠔⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢧⢀⡠⣒⡆
⠋⠈⠑⠪⢕⢕⢲⣠⠇⠀⠀⠀⠀⠀⡇⠀⠀⠎⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠳⢯⣏⠒⠀⠈⢇⣠⢿
⠀⠀⠀⠀⠀⠑⢵⣟⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠛⠀⢀⠜⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡀⠀⣠⠔⠁⢠⠂⠣⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠬⢷⡄⠀⠰⠶⠓⠐⠐⠒⠒⠒⠒⠒⠒⠒⢂⠖⠀⠀⠀⢀⠤⡤⠀⢄⠀⠀⠀⠀⢀⡀⠥⡞⣳⠎⠈⠑⠦⠃⠰⡄⠀⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠃⠀⠀⠀⠀⠣⢔⢻⠿⢸⠀⣀⣤⣯⠁⢀⡴⠁⠛⠁⠀⠀⠀⠀⠀⣷⢀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢎⠜⠫⡀⡭⠐⠈⠉⠹⢔⡝⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠟⠋⠙⢧⠀⡠⣫⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢰⡆⠀⠀⣶⠆⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡵⠁⠀⠀⠀⠀⢪⡀⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⡡⠛⢷⡬⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡰⢩⠋⠁⠒⠒⠂⢠⠤⠃⠀⠀⠀⠀⢎⣸⠐⢈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⢻⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠖⠳⠧⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢭⢸⠖⠛⠃⠀⠉⠓⣮⢦⣵⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣱⣄⠸⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠡⠃⠀⠀⠀⠀⠀⠀⠻⠞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⣛⣛⣷⠶⠖⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠿⠋⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢢⢰⡀⠀⡧⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠉⢉⣠⢴⠖⠂⠒⠁⠀⠀⠀⠀⠀⠀⢸⡁⢀⣼⢠⣠⡏⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢠⠔⡀⠇⡘⡆⠀⠘⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀⡀
⠀⠀⢀⠠⠄⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡉⢈⡲⠀⠀⠀⠀⠀⠀⣡⠇⠸⠀⡏⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠼⠓⠒⠁
⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉
⠀⠀⠀⠀⡴⠊⠁
⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣭⣋⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠉⠉⠁⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠐⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠉⠈⠉⠐⠀⠀⠀⠂⢴⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⡠⠊⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣤⡀⢀⣀⣁⣀⣤⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠆⠀⠀⠈⠛⠛⠀⡀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠙⢿⠿⠿⢿⡿⠃⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠃⠠⠃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡉⠈⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢴⣾⠿⠿⣷⣦⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠈⠑⠁⠐⠋⠈⡀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠉⠈⠑⢄⠀⠀⠀⠀⠀⢉⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠸⠀⠀⠀⢀⠀⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⢤⠄⠒⠄⣀⠠⠖⠃⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠤⠖⠀⠀⠉⠀⢀⡠⣄⡀⠄⠊⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⢠⣤⡇⠀⠉⢁⡀⠀⠄⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠈⠳⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⡀⠳⢤⡀⠀⠀⠀⠀⠀⢠⠄⠤⠠⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⡟⠂⠀⠀⠀⠀⠀⠀⠀⠐⠩
⠀⣉⣉⠀⠉⠀⠁⠀⠸⡀⠀⠀⠀⢠⠃⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⡅
⣠⠤⠶⠂⠀⠀⠀⠀⠀⣠⢤⣔⡒⢼⣦⡶⠉⠢⠀⣀⣀⣀⣀⣀⡀⠄⠮⣥⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠁⠑⠊⠀⠈⠫⡁⣝⠀⠉⠁⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠌⠳⠤⠤⣠⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠢⡀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⢤⠤⡤⠤⠤⠤⠬⠆⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠂⠀⡀⠀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢸⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⢈⠄⠀⠀⢅⠂⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠘⡂⠀⠀⠈⠑⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⠿⠋⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣦⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⣿⣴⣿⡿⠃⠀⠀⠀⠀⠀⡘⠘⠃⢻⡇⠉⠃⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⣤⣄⣰⣶⣾⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠏⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠁⠀⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⠿⠿⠿⠿⢿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠉⠙⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⢀⣤⣶⣾⠿⠿⠟⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣹⣿⣇⠙⢿⣦⣀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠹⣿⡄⠀⠙⠻⣷⣦⡀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠙⣿⣦⠀⠀⠈⠻⣿⣆⠀⢠⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⣤⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠸⣿⡄⢸⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣼⣿⡿⠋⠁⠀⢀⣀⣨⣭⣭⣽⣏⣉⣉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠈⠙⠿⣷⣄⣿⣧⣾⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⣠⣴⣾⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣶⡄⠀⠀⠐⠿⠟⠋⠉⠉⠉⠉⠛⠻⢿⣶⣤⡈⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⣿⣿⠃
⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⣀⣤⣴⣶⣾⣿⡿⣶⣦⣄⠀⠀⠀⢹⣿⡀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⣿⣏⣤⣴⣦⣄
⠀⠀⠀⠀⣾⡟⠛⢻⣿⠀⠸⣿⣏⠉⠙⠿⠟⠀⢀⣽⡿⠃⠀⠀⠀⣿⡇⠀⠀⢺⣿⣏⠁⠘⠿⠿⠋⠙⢻⣿⠆⠀⣿⡿⠛⠉⠉⣿⡇
⠀⠀⠀⠀⣿⣆⠀⢸⣿⠀⠀⠘⢿⣷⣄⣀⣤⣶⡿⠛⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠙⢿⣷⣤⣀⣀⣀⣴⣿⠏⠀⠀⣿⡇⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠙⢿⣦⣼⣿⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠁⠀⠀⢠⣿⡇⢀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣤⣄⣀⣀⡀⠀⣀⣀⣀⣤⣤⣶⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠟⠿⠿⠿⠿⠟⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⣴⡿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢿⣷⣄⠀⠀⠀⠀⠙⣿⣦⠀⢀⣾⡿⠁⠀⠀⠀⠘⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠛⠉⠀⠀⠈⢻⣷⡄⠀⠀⠀⠘⣿⣦⣿⠟⠀⠀⠀⠀⣠⣾⠟⠛⠻⠿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣶⣤⡀
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠘⣿⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⢀⠾⠽⣝⡀⠀⣀⡀⠀⡇⠀⠀⠀⢀⡠⢒⡪⣉⠭⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡏⠀⠈⠉⠹⠋⠋⡇⠀⢨⠂⠀⢠⠎⡫⣡⣤⣐⠶⢢⣾⣵⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡁⠠⠁⡄⠈⠀⠁⣃⡠⠎⠉⠐⢼⢈⢸⠩⠜⡝⢃⠀⢠⠘⢢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⠺⠙⡀⠀⠓⠀⠀⢠⠋⠀⠀⠀⠀⠈⡾⡘⡄⠀⠑⡄⠀⢀⠤⠄⠾⢠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇⠱⣀⠙⠁⡠⠃⠀⠀⠀⠀⠀⠀⠁⢹⢈⠆⠀⠸⠀⠀⠀⣠⠃⡇⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠃⠀⣰⠇⠀⠀⠀⡏⠀⢡⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠰⢣⠑⢄⢀⡰⠁⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠐⡖⠒⠒⠂⠒⠃⠀⠀⠀⢸⠀⢠⢇⣸⠤⠤⣀⡀⠀⠀⠀⠀⠑⣄⠀⠀⠙⡄
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⢆⠀⠀⠀⣀⡱⠖⠰⢄⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣿⡒⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢱⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠴⠓⠈⠁⠈⠉⠋⠒⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠊⠑⠊⠉⠉⠓⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠶⠄⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣈⣤⠶⠛⠀⠈⠁⠀⠀⠀⠀⠀⠁⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⢀⣉⠤⠶⣾⡇⠀⠀⠀⠀⢀⠀⠙⠂⢄⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣰⠋⠀⠀⠀⠀⢹⡠⢶⠂⡀⠸⠀⠀⠀⠀⠑⣄⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⡰⢋⡤⢤⡀⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⢠⠁⢈⠀⠀⠘⡆⠳⣀⠀⠀⣸⠁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢀⠂⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣜⠀⠀⠑⠠⠀⠀⠀⠈⠉⠁⠸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠄⠤⠐⠠⠤⠁⠒⠁
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢲⠄⡦⠐⠒⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢤⡀⠀⣠⠤⠴⠥⠆⠁⠈⣰⠋⢯⡲⠆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠲⠤⢀⣀⠀⠀⠀⠀⢘⡆⢖⢒⡒⠺⠿⠳⠤⠀⠠⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠁⠈⠉⠉⠈⡇⠸⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⡐⠁⢹⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⢘⠛⢢⡄⠀⢸
⠒⠶⠤⠤⠤⠼⣅⣀⡉⠒⠠⢀⡀⠔⠂⠈⠀⢱⡄⡇⠈⢠⠎⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⠤⠔⠲⣕⣸⡼⠟⢧⠴⠛⠒⠒⠒⠚⠳⠤⠤⠤⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢰⠃⠀⠀⠀⠀⠀⢿⣿⡟⠛⠡⠀⠀⠀⠙⢿⣿⣿⣿⣾⠋⠁⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⣷⡈⠀⣧⠆⠀⠀⠘⠿⠟⠋⢳⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⢸⠀⠀⠀⠀⠀⡴⠊⠉⠉⠉⠉⠉⠉⢳⠀⠀⠀⣀⠤⠤⢧⡀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⡜⠀⠀⠀⡴⠒⢲⡲⢶⡀⣦⠤⡾⠁⠀⠀⠀⠉⢢⠀⠀⠀⠘⡆⠀⠀⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠁⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠈⠷⠮⠔⠃⣸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⠀⡼⠁⠀⠀⠀⢸⡇⢀⣀⣀⣸⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢇⠀⠀⡆⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣵⠮⠒⠊⣆⠀⠀⡏⢸⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠉⢳⣤⣸⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡙⣗⢶⡒⠁⠀⣸⠁⠘⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠣⢴⠞⣹⢡⠊⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠸⡄⢈⣢⢀⠇⠀⠀⢳⠀⠀⠀⠀⢷⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠟⡇⠀⠀⡏⢀⠇⡼⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡄⢻⠉⠀⡘⠀⠀⠀⠘⡆⠀⠀⠀⠈⢧⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠈⡹⢠⠇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡇⠸⡄⢀⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢿⠀⠀⢀⠇⡸⠀⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⣸⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⡀⠀⢸⠀⡇⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⡀⢸⡇⣀⣀⠀⢀⣀⣀⣀⣈⣧⣄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⠀⠸⡇⠀⢸⠀⡇⠀⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡜⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉⠉⢹⠉⠉⠉⠛⢧⠀⣸⢠⠃⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆⣿⢸⠀⢠⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣴⣯⣧⣀⡀⠀⣀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠤⠀⠒⠒⠒⠒⠒⠛⠢⢄⠀⠀⠀⣇⣿⣸⣀⣸⣆⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠁⠐⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠳⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣀⣠⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠈⠛⠉⢅⣈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠐⠒⠒⡖⠋⠉⢁⠞⡔⠉⠑⠢⣄⠀⢀⠔⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⡏⠀⠀⠀⠀⡇
⢀⡤⠤⠀⠀⠒⠒⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡄⠀⠀⠀⢳⠀⠀⠀⢀⣼⣷⣤⣤⣀⣀⠷⡄
⠇⠁⣖⠆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⢧⡀⣠⠎⠈⢸⣄⣀⡤⠋⠀⠙⣆
⢰⡀⠀⣀⠀⠀⠸⡇⢠⡄⠀⠀⠀⠀⣠⠔⠒⠶⢤⣤⠇⠀⠀⠀⠀⠀⠙⠧⣤⣤⢾⠁⠀⠀⠀⠠⢄⡈⣇
⢸⣃⠈⠛⠀⠀⠀⠈⠛⣅⣷⠀⠀⠀⣇⠐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢄⣀⡠⠃⣸
⠈⠲⠦⠤⠴⠒⠒⠊⢻⡏⠈⢓⡶⠖⠋⠓⠒⠒⠋⠑⠦⣄⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⢀⢸⠀⠀⠀⢨⣠⠖⠋⠀⢀⡀⠀⠀⠀⢀⡄⠀⠀⠈⢙⠖⡶⠶⠤⢤⣤⠤⠴⠖⠒⠋⠙⠒⠒⠒⠂⠀⠤⠤⠤⠀⣀⣀⡀
⠀⠀⠀⠸⠘⡀⠀⢠⡞⠁⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⢀⠔⢁⣰⠧⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈
⠀⠀⠀⢀⡆⠧⢤⡏⠈⠓⠤⣀⠀⠙⢲⣶⣤⡤⣼⡤⠴⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢊⠠⠆⠁
⠀⠀⠀⠘⢅⡀⠀⠙⢦⡀⠀⠈⠙⠒⡟⠀⣹⣀⣏⡀⠒⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢊⠀⠂⢈⠀⡇
⠀⠀⠀⠀⢀⠋⠉⠒⢦⢬⣑⢲⣆⡒⠇⠀⡇⠈⠢⣼⢹⠒⠒⠤⢄⡉⠐⠂⠀⠤⢀⡀⠀⠀⠀⠀⠀⡠⠔⢈⠄⠊⠀⠠⠀⠀⡇⠁
⠀⠀⢠⣃⠌⠀⠀⠀⢰⢼⠀⠈⢳⣒⣀⡴⠃⠀⠀⠸⢸⠤⣀⡀⠀⠀⠉⠁⠒⠠⠄⣈⡉⠁⠒⡖⣉⠄⠊⠀⡠⠐⠁⠀⠀⠀⡧⠶
⠀⠀⠒⠊⠀⠀⠀⠀⠈⠉⠀⢀⣎⡇⡇⠀⠀⠀⣠⡟⢸⠀⢀⡼⠁⠒⠦⢄⡀⠀⠀⠀⠀⢹⢘⠋⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⡇⡟⠿⠛⡿⢯⠟⢸⠛⣯⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡜⢸⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡿⠢⠶⠀⡴⣷⢺⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠰⠿⠶⠒⠒⠒⠒⠒⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢶⠆⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⢀⣴⠟⠁⠸⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣐⠲⠦⠄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠴⠀⠉
⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠒⠉⢉⡐⠠⢄⣀⠀⢼⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣈⠑⠂⠬⠙⠲⢽⣄
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢰⡆⢀⡀⠀⠀⠰⠓⠈⠙⠲⢤⡄⠀⠈⠓⢤⡀
⣼⠀⠀⠀⠀⠀⠀⠀⣠⣔⠋⠁⠀⠀⠀⢸⠇⣸⠹⠟⠂⢄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠙⢄
⣙⠶⣀⠀⠀⠀⠀⠀⠀⠈⢙⣢⡄⠀⠀⠞⢀⡇⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡇⢀⡴⠶⢦⡈⢧
⣧⠔⡿⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⠳⡀⠀⠀⠀⠀⣷⡀⠀⣀⡴⠁⡞⠀⠀⢀⡇⠈⡇
⠈⠐⠧⠤⠤⠠⢄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠐⠠⡀⢀⣠⡟⠀⠀⠀⠀⠄⠀⠰⠒⠉
⠀⠀⠀⠀⠀⠀⢀⣁⡄⠀⢀⠼⠆⠀⠖⠢⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣰⠋⠀⢀⣠⣀⡇⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠹⡄⠈⠑⠒⠃⠻⣤⣀⣀⡀⠀⠙⠢⡀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠂⠉⡷⠦⡭⠻⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠖⠋⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠃⢀⠎⠉⠉⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡰⠃⠀⣸⠁⠀⣀⡤⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⣸⣄⢀⡀⢧
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⣱⠁⠀⣰⣃⡴⢚⡡⠀⣀⠀⠀⠉⠢⠤⣤⠔⠒⠉⠉⠀⠈⠓⢌⡙⣆⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠴⠋⠀⠉⠧⢤⣞⣁⣀⡦⣄⣤⠴⠚⠒⠂⠒⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠻⣿⡟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣽⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠉⠉⠐⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡦⣄⢀⣀⡬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⢄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠟⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠳⣄⡤⠴⠒⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⣶⢋⣉⣀⡀⠀⠐⠲⠎⣳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠁⠀⠀⠰⢡⡏⠀⠀⠙⠲⡄⢀⡞⠁⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⢸⡇
⣠⡤⠐⠒⠒⠒⠒⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡀⠀⠀⠀⢻⡀⠀⠀⠀⣰⣿⣶⡦⢤⣄⣸⠷⡄
⡇⠁⢞⡂⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⡀⣠⠞⠁⠀⣧⣀⣠⠴⠋⠀⠘⣆
⢫⠀⠀⣀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⠀⢀⠤⠶⠦⠤⣄⡼⠁⠀⠀⠀⠀⠀⠙⠧⣄⣀⣼⡏⠀⠀⠀⠀⠤⢄⠘⣇
⢸⣇⠀⠷⠁⠀⠀⠈⠑⢻⡠⡇⠀⠀⠀⡇⠠⠚⠻⠗⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡀⠀⣠⠇⢸
⠘⣼⣄⣀⣤⡤⠤⠤⠲⡶⡛⠹⠤⣤⡤⠞⠲⠤⠤⠴⠚⢦⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡴⠎
⠀⠀⠀⢸⠘⡀⠀⠀⠀⡇⣇⡤⠖⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠒⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠾⠭⠤⠄⣀⣀⣀⡀
⠀⠀⠀⠀⡄⡇⠀⠀⢀⡷⠋⠀⠀⠀⢐⠇⠀⠀⠀⠀⡏⠀⠀⠀⣠⠞⢡⡇⣀⠤⠜⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠲
⠀⠀⠀⠀⡇⢱⠀⢠⠟⢦⣀⠀⠀⠀⢼⣀⣀⠀⠀⠀⡇⠀⢀⣞⠥⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⡡⠐
⠀⠀⠀⠀⡷⡙⠛⢻⡀⠀⠈⠑⠢⣄⣀⣸⠛⢿⡟⢻⢟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⡁⢴⢹
⠀⠀⠀⠀⠑⢢⢄⣂⠉⠳⢤⣀⠀⣀⡈⡿⠀⢸⠶⡼⠦⣄⣈⠉⠐⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⡡⠔⠁⠀⢼⠀⡄
⠀⠀⠀⠠⢁⠎⠀⠀⠉⡖⢶⠬⣽⠧⠈⠃⠀⡏⠀⠈⠳⡇⡿⠈⠁⠒⠤⠤⣀⡈⠁⠒⠠⠤⣄⣀⠀⠀⠀⣀⠴⢊⡡⠔⠁⢀⠤⠊⠀⠸⠀⡇
⠀⠀⢠⢧⡌⠀⠀⠀⠀⡷⡏⠀⠀⢹⣍⣤⠴⠃⠀⠀⠀⡇⡷⠦⢤⣀⠀⠀⠀⠈⠉⠒⠒⠤⢄⡀⠉⢱⢊⡠⠖⠉⢀⡤⠂⠁⠀⠀⠀⠀⡖⡇
⠀⠀⠈⠒⠀⠀⠀⠀⠀⠉⠁⠀⢠⢯⡇⢀⠀⠀⠀⢀⣞⡃⡇⠀⣀⠞⠉⠐⠒⠤⢀⡀⠀⠀⠀⠀⡏⢹⠁⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣳⡇⢨⠿⣛⣿⠿⡽⠇⡟⠻⡅⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⡇⢰⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⠲⢴⠇⢠⣾⡦⣧⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠿⠿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⣰⡆⠀⠀⢠⡟⣠⣾⣇⣰⣾⣆⠀⠀⠀⠀⣤⡀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⢀⣼⣿⡾⠃⢀⣾⡿⠛⣿⣿⡿⣿⣿⣴⡿⠂⠀⢻⣷⡀⠀⠹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠾⠟⠉⠀⠀⠈⠉⠀⠀⠙⣉⡀⠘⠿⠟⠁⠀⠀⠈⣿⣧⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣠⣶⣶⣦⠀⢀⣴⣿⣿⣧⠀⠀⣠⡄⠀⣀⣤⠈⠁⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢀⣼⣿⠟⠙⣿⣷⣿⠟⠁⠘⢿⣦⣼⣿⣧⣾⠿⣿⣦⣿⣷⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⢠⣾⣿⠋⠀⠀⠀⠉⠀⠀⠀⠀⠈⠙⠉⠈⢉⣀⡀⠈⠛⢿⣿⣧⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠡⠶⢚⣻⣿⣿⡛⠻⠂⠀⠀⠀⠀⠈⠋⠉⣉⡙⠓⠊⢿⣿⣷⡄⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣧⠀⠀⢠⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠳⣄⠈⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⢿⣿⡄⠀⣿⡇⠈⠛⠋⣹⡇⠀⠀⠀⠀⢠⣿⠋⠻⠿⠟⠀⣿⠀⠀⠈⢻⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣷⣄⣸⣿⡇⠀⠹⣧⣄⣀⣴⡿⠁⠀⠀⠀⠀⣸⣟⠀⠀⠀⠀⣼⠏⠀⠀⠀⣾⣿⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠈⠛⢿⣿⡇⠀⠀⠈⠉⠉⠉⠀⢿⡄⠀⠀⠀⠘⢿⣦⣤⣶⠿⠋⠀⠀⠀⢰⣿⡇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⣠⣴⡜⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣴⣏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⠁⠈⠉⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⢿⣿⣿⡿⣻⣯⣤⣄⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⡀⢀⣄⣴⣶⣰⣿⣿⢷⡆⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡈⠀⠿⢃⣿⠟⠠⣏⠀⠀⢰⠟⠉⠀⠀⠀⠀⠉⢱⣿⣿⣿⢹⣿⠻⠏⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠛⠀⢀⡾⠁⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⣦⡄⠀⠀⠀⠀⠀⠀⢻⢶⣤⣄⣀⣀⣀⣀⣠⡼⣿⣧⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣸⡿⠂⠀⠀⠀⠀⠀⢀⣟⣄⣀⣈⣉⣉⣉⣉⣀⣠⣿⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⢸⠋⠛⠛⠛⠛⠛⠛⠛⠋⢩⡿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⢦⣄⡀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⡀⠀⠀⠀⠀⠀⠀⣠⢿⣇⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠙⠛⠲⠶⠶⠛⠋⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠛⠷⠶⠶⠶⠛⠁⠈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣤⣄⣀⣀⣀⣀⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠀⠀⣠⡿⠁⠀⠉⠉⠛⠛⠛⠛⠋⠁⢻⡆⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠉⣩⣟⣁⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣩⣽⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⡏⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢛⣛⣷⣶⠤
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⣚⡋⠉⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣯⡅⠀⠀⠲⣬⣉⠛⠶⣤⣄⡘⠿⣋
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⢦⣄⣉⠛⠲⠦⠌⠙⠳⢾⣦⡀
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⣤⠀⢀⠀⠀⠀⠀⣸⢿⠟⠛⠲⠦⣄⣀⠀⠀⠈⠛⢦⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⢰⣿⠀⣼⢳⣶⣤⣀⡏⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠙⢶⡀
⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠻⢤⣀⠀⠀⠀⠀⠀⢸⠇⢀⡇⠈⠉⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠙⢦
⠀⠀⡭⠟⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣤⠀⠀⠀⠛⠀⣸⠃⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀⡇⠀⣴⠞⠛⠳⣄⠈⢧
⠀⢸⣅⡔⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠠⠟⣦⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢀⡼⠁⣸⠃⠀⠀⠀⣼⠀⠘⡇
⠀⠈⠛⠀⣟⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣸⡏⠉⠛⠛⠉⠀⡀⠃⠀⣆⣠⠔⠁⠀⠀⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠲⡄⠀⠀⠀⠀⢸⣄⣀⡀⣀⡀⠀⠀⠀⠀⠈⠙⠶⠤⢖⡿⠁⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠦⠤⠤⢴⡞⢻⡅⢨⡏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⢀⣀⣀⣸⡇⠸⠀⠸⠀⠀⢀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠐⠫⣤⡴⠋⣷⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⣀⣀⣀⣀⣨⠿⣿⡛⠒⠶⣦⡤⠀⣨⠟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣰⠋⠛⣲⠋⠙⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠶⠚⠋⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠃⠀⣸⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣰⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡴⠁⠀⢀⡟⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⡾⠁⠀⠀⡼⠀⠀⣀⡴⠚⠉⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠞⠷⣖⠦⢤⣹⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣼⠁⠀⠀⣼⣁⣰⠚⣁⠤⠂⢀⡄⠀⠀⠀⠈⠓⠤⢴⡖⠛⠉⠁⠀⠀⠀⠀⠈⠓⣦⡈⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣠⠾⠁⠀⠈⠹⢧⣄⣴⠋⠀⠐⣦⣀⣀⣀⡤⠞⠓⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠀⠀⠀⠛⠛⠛⠋⠁⠈⠙⠁⠀⠂⠐⠀⠀⠂

⠀⠀⢀⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠰⣿⣇⣡⡄⢠⣼⡂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⡀
⠀⣾⣿⡈⢻⣧⣿⣯⡁⢠⣤⢀⠤⡦⠠⣜⣇⣠⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⢺⡿⣧⡀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⣿⣿⣧⠀⣿⣿⡹⣧⣿⣿⣿⣤⣿⣶⣿⣯⠉⢻⣿⣤⣳⡿⡀⢸⣧⣠⡶⠀⠀⠈⣠⡀⡼⢡⣿⣿⣷⡄⠀⠀⠁
⠀⠹⣿⣿⣃⠉⢹⣿⣿⢛⡿⠋⠀⡟⠛⣿⣷⡿⠄⣽⢟⢻⠀⢐⣿⣿⠗⢒⡀⠀⠀⢻⣿⡇⢸⣿⣿⣿⣿⣆⠀⠀⠀⠒⡆
⠀⣼⣿⣿⡟⢀⢠⣿⠂⣠⣏⠠⢀⠓⠠⠿⠉⠀⠀⠘⠀⠚⠛⠙⣮⡿⠀⣿⡀⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣏⠀⠀⠀⢤⡇
⠀⣿⣿⣿⣿⣾⣿⣄⠀⠈⣿⣿⣶⣿⣶⡄⠀⠀⠸⢢⣤⣴⡞⠶⢾⡿⠆⣹⡋⣀⠀⠀⠀⠈⠋⣿⣿⣿⣿⣿⡆⠀⠀⠀⡇
⢀⣿⣿⣿⣿⣿⣏⠸⠿⠿⠋⣿⣿⡯⣽⣧⠀⠷⢀⣴⡯⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣴⣳⣿⣿⣿⣿⢻⣷⣠⣶⣞⠇
⠸⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⣿⣷⣮⣁⠀⠂⣸⣿⣀⡀⠀⠀⠂⠄⠀⠀⠀⢐⣄⡄⢀⣏⣿⣿⣿⣿⠇⢀⣴⣭⣧⡄⡦
⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢐⣤⣽⣏⢥⣾⡆⠠⠉⠀⠀⠀⠀⢌⢲⣾⣼⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢄⣩⡿⠑⠀⠀⠀⡢⠀⢢⣸⣧⣹⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣾⣷⣖⢎⠀⠀⠀⠀⡐⠷⢤⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⣛⠏⠀⠒⠠⠶⠿⠿⢿⣿⠟⠛⠻⠶⠶⠦⢤⣼⣿⣿⣿⡟⠒⠛⠛⠋⠃
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠋⠉⠉⠉⠉⠉⠀⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⣠⣤⣄⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠻⣿⡿⠹⣿⣿⠇⠀⠚⠛⠚⠓⠒⠒⠀⠋⠒⠚⠓⠶⠒⠐⠒⠒⠁⠛⠚⠒⠚⠓⠒⠒⠀⣤⠀⠀⠀⠀⠰⠀⡁⣤⠀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠠⣧⠀⠀⠐⠃⠀⠀⠀⢴⡧⠉⠘⠇
⠀⠀⡶⠆⠀⣀⠃⠀⠀⠀⠀⠈⣆⠀⠀⠀⣠⡟⠀⠀⠀⢛⣅⠙⣧⠘⢫⡀⠀⠀⠀⠘⠻⢀⣿⡄⠀⠀⠀⠀⠼⠻⠀⢀⣼⣥⠄
⠀⢸⣷⢶⣿⢻⡿⣿⣿⣿⣿⠿⡟⠁⠀⠀⣿⡗⠆⠀⠤⠞⣿⢀⣿⠇⣼⡇⠀⠀⠀⠀⠀⢫⣿⠇⣀⣸⣷⣄⠀⠀⠀⠈⣿⢦
⠀⢀⡿⣦⠀⠸⣿⣿⣏⣉⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠈⣿⠀⢿⠀⠀⠀⠀⠀⠀⠉⠘⠓⠈⢉⣿⣏⡀⠀⠀⠈⠁
⠀⠛⠁⠙⠀⠀⠛⠉⠉⠉⠉⠙⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠰⠿⠿⠷⠿⠿⠂⠀⠀⢀⣿⡗⠚⠁⠀⠀⢀⡷⠀⠀⠀⠀⣲⡆⠀⠀⢰⣄⣀⠀⠀⠀⢀⣿⡆⠀⢀⣛⣀⣽⣇
⠀⢀⣶⣾⣅⠰⡇⠘⠀⠀⠀⠀⠀⠀⠸⣿⡉⠑⠂⠀⠀⣿⡇⠀⠀⠀⣾⠿⣖⠂⠀⣠⠜⣿⠃⠀⠀⢹⣿⡁⠀⠸⣿⡍⣿⣟
⠀⠈⠹⣿⣍⣧⣤⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⡆⠀⠀⢀⣿⣷⡀⠀⠀⢈⡗⠀⠀⠀⠀⢺⡁⠀⠀⠀⣾⢸⡇⠀⠀⣿⡇⣿⡇
⠀⠀⢰⠏⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠁⠀⢀⠉⠀⠉⠁

⠀⠀⢰⣆⡀⣠⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⢐⣿⣀⣠⠄⠀⠀⠀⠀⣀⠶⠆
⠀⠰⣿⣿⡍⠁⠀⠀⢻⣿⡗⠚⠁⣴⡆⠀⢀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⢻⠛⠁⠀⠀⠀⠀⠀⠀⣿⠓⠋
⠀⠀⠨⡏⣧⠀⠀⠀⢺⣿⡇⠀⠀⣿⡏⠀⠈⢃⣀⠀⠈⣿⣿⣶⠀⠀⠐⡿⣿⠀⠀⠀⢸⢺⡇⠀⠀⠀⠀⠀⠀⢸⡗⠛⠛⠓⠂
⠀⠀⠀⠇⠘⠀⠀⠀⠘⠃⠇⠀⠀⠻⠇⠀⠀⠀⠃⠰⠀⠿⠿⠿⠀⠀⠀⠃⠛⠀⠀⠀⠘⠘⠃⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠒⠉⠉⠉⠉⠙⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⢐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⣀⣀⣀⡠⢤⣄⣀⡑⠀⣤⠀⠀⠀⠀⠀⠈⢤⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠄⠀⠀⢀⡤⠒⠒⠲⠀⠉⢩⡋⠀⠀⠀⠀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⠶⠬⡶⡆⠀⡰⠋⠉⠓⢄⡼⠀⠀⠀⢧⡤⠞⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠑⣠⣔⠚⠁⠀⢇⠠⠤⠴⠊⡤⡖⠏⣄⣀⣊⣳⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠙⢢⡑⠀⠁⠀⠀⠀⠀⠠⢀⡎⠃⣀⣀⡅⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⠈⢯⠏⡐⠒⣒⢉⠉⢀⠀⠘⠣⣀⠖⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠄⢴⠉⠉⠉⠒⢷⡀⠀⢤⠖⠚⠦⠤⠚⠓⠤⠖⢺⣃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢈⠉⠉⠉⠐⢺⣄⠀⠀⠀⣤⡭⢏⡇⠀⠀⠀⠀⠀⣤⣤⠴⠟⠁⠀⢀⡉⠭⠝⠒
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢲⡉⠉⠻⣉⣽⣿⠇⢘⠦⢄⣀⣀⣀⣤⣿⠏⠉⠉⢹⠉
⣠⣤⣤⡤⠀⠀⠂⠚⠒⠒⠒⠠⠤⠤⠙⣓⣒⠛⠛⠁⠀⢺⡀⠀⠙⣄⣴⣿⠟⠐⠐⠀⢸
⠘⡄⠀⠀⢈⠉⠁⠒⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠛⠛⠛⠻⠋⠥⠤⠀⣀⢀⣸
⠀⢸⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠲⠒⠤⠤⠤⢄⣀⣀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠘⠒⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠀⠤⠄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠤⠤⢀⣀⡀⠀⢸⠀⢀⡀⠤⠒⠉

⠀⢀⣤⣤⡀⣠⣤⣄
⠀⢻⣿⣿⠗⢿⣿⣿⠀⠀⠔⠓⠒⠒⠒⠶⠂⠘⠑⠒⠚⠲⡶⠲⠀⠒⠶⠊⠹⠑⠲⠖⠒⠒⠲⠖⠀⢀⠀⠀⠀⠀⠀⡄⠀⠂⣠⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠈⠀⠶⠀⠀⠀⠀⣰⣇⠛⠀⡧⠈
⠀⠀⣠⡤⠀⠀⢠⠉⠉⠉⠉⠉⠉⡄⠀⠀⠀⠀⢰⡶⠀⠀⠀⢾⡆⠰⣷⠀⢾⡆⠀⠀⠀⠀⠰⢿⠀⢶⡀⠀⠀⠀⠀⠀⣻⢷⠁⠀⣰⡆⢀
⠀⢀⣾⣁⣤⡴⣷⣤⣤⣤⣤⣤⣤⣾⠆⠀⠀⢰⣿⣀⡀⠀⢀⣠⣿⠀⢸⡇⠀⣿⡄⠀⠀⠀⠀⠀⡴⢻⣿⠀⠀⣤⡄⠀⠁⠀⠀⠀⣿⣏⠁
⠀⠈⣿⣍⠛⠃⣿⣭⣿⡿⠿⣿⣭⣽⠀⠀⠀⠘⣿⠀⠁⠀⠉⢠⡟⠐⣿⠃⢺⡟⠀⠀⠀⠀⠀⠀⢸⠻⣏⠐⠶⢿⣿⡗⠀⠀⠀⠠⠞⠙⠂
⠀⣠⠟⢹⡆⠀⢹⡿⠿⠷⠶⠿⢿⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⢻⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡼⣿⠷⠄⠀⠀⠄
⠀⠈⠀⠀⠁⠀⠨⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣄⡀⢀⣀
⠀⠀⠀⢀⣤⠀⢛⠛⡛⠻⠿⠛⠁⠀⠀⠀⣼⣿⡋⠉⠀⠀⠀⢠⡟⠃⠀⠀⠀⣀⡿⠀⠀⠀⠰⢆⣤⡀⠀⠀⠀⣼⣿⡀⠀⢠⣭⣤⣼⣧⡀
⠀⠀⣾⣷⣷⡀⢻⠄⠉⠀⠀⠀⠀⠀⠀⠀⣿⣧⡉⠙⠂⠀⠀⣿⡟⠀⠀⠀⢰⡟⠿⡊⠁⠀⡠⠚⣿⠇⠀⠀⠀⣽⣿⠁⠀⢘⣿⡆⣹⣿⠁
⠀⠀⠙⣿⣇⣹⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⣹⠆⠀⠀⠀⠀⢸⡅⠀⠀⠀⢠⡇⢸⠀⠀⠈⣿⡇⢹⣿
⠀⠀⢀⡿⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠁⠈⠉
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣶⠄⠀⢀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⢀⡴⣶⡖⠚⠁⠀⠠⢾⣿⣧⡤⠀⢠⣄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣼⣷⣦⠀⠀⠀⣶⣿⡟⠉⠁⠀⠀⠀⠀⠀⣿⣬⠴
⠀⠀⠙⣿⣿⠀⠀⠀⠀⣼⣿⡆⠀⠀⢸⣿⠀⠀⢶⠀⠀⠀⠀⣷⣴⣤⡀⠀⠀⣹⣿⡿⠀⠀⠀⢸⣅⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄⣤⣤⡤⡄
⠀⠀⠀⣿⠸⡇⠀⠀⠀⢸⡿⡇⠀⠀⢸⣿⠀⠀⠈⠲⠆⠀⠀⣿⣿⣿⡇⠀⠀⢸⠹⡇⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠈⠁⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠀⠈⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⣀⣀⠀⠈⢧⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣾⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢱⠾⢯⢭⡭⣝⢷⠀⠀⠀⠀⠀⠀⢀⣔⣋⣙⣒⣦⠀⢸⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡇⠉⠉⠉⠉⠁⠀⡜⠀⠀⡇⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣯⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⡜⠁⠀⠀⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⡀⠄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠟⠇⠀⠀⢸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠃⠀⢃⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣿⡿⠀⠀⢀⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⡞⢰⡏⠀⠀⠀⠀⠚⠓⠤⠤⠤⠤⠖⠻⠂⠀⠀⡸⠉⠜⠀⠀⡎⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠑⠼⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡜⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢿⠀⠀⠀⠲⠾⠛⠛⠛⠛⣭⠿⠛⠒⠒⠋⠀⠀⠀⢀⠃⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠈⣆⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠉⠉⠙⡗⠛⠛⠛⠛⠛⠉⢉⡍⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⡴⠋⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⣶⣶⣶⣶⣶⣶⣾⣅⣀⣤⣤⣤⣀⡀⠀⠘⡄⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⡞⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢡⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠘⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⠤⠄⠀⠩⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠝⠁⠂⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣔⢀⣰⣃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢄⠀⠀⠀⠄⠀⠑⠀⢆⠀⡤⠀⠀⠀⠀⠉⠀⠴⠀⠀⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠦⠐⠁⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠰⠎⠈⠘⠁⠋⠀⠀⠀⠀⢀⡄⠀⢠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠁⣦⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠠⠃⠀⢀⠔⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⣶⢤⢌⡀⠄⠀⠀⠀⠒⠦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠒⢷⣺⡀⢁⡪⠃⠻⡾⠆⠐⠀⠔⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠱⡒⠠⠐⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠸⠁⠄⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠀⠀⢱⣄⠀⠀⠀⠉⠂⠀⢀⠀⠀⠀⠀⠀⠀⠊⠈⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠤⠊⠉⠚⢦⣻⡀⠀⠀⠀⢀⠜⠁⠀⠀⠐⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠁⠉⠀⠈⠈⠁⠀⠀⡠⠃⠀⠀⠀⢀⠀⢹⠉⢃⠀⠀⠀⠀⠀⠀⠄⠘⠳⠞⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡖⢀⡀⠀⠐⠒⢒⣒⣰⠊⠀⠀⠀⠀⠀⠂⠀⠀⢦⠤⠀⠀⠀⠀⢀⠀⠀⢀⣀⡃⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠂⢀⡀⠀⠀⠤⠄⠒⠉⠀⠈⠂⠀⠀⡠⢣⠀⠀⠀⠸⠀⢣⠀⠀⠀⠀⠆⠠⠤⠤⠄⠀⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠀⠀⠂⠀⠀⢰⡅⠀⠂⢠⠁⢸⢁⣀⡀⢀⠄⢀⠄
⠀⠀⠀⠀⡠⠀⡌⠀⠄⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⢀⣀⣈⣄⣈⡁⠀⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⢀⡀⣈⠈⠀⠐⠂
⢀⡀⠁⠐⠁⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠃⠀⠀⠘⠀⠰⠁⠤⠤⠤⠤⠤⡀
⠀⠁⠀⠀⠀⠀⠈⠀⢀⠺⣤⠤⣤⣀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢀⡀⢀⣀⣀
⠂⠆⠀⠑⠤⠀⢄⠠⠎⡜⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠔⠂⡀⠀⡀⢀⠤⠔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠁⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠤⣴⠀⠑⣠⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣄⣠⣠⡄⣮⣀⣀⠀⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠶⠶⢶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠛⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⣦⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⣶⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢀⣀⣤⣴⠞⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⡀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣠⣤⣴⣤⡄⠀⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⣶⣦⣄⠀⠀⠙⠻⣶⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⢻⡆⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠉⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠛⠛⠿⠷⠆⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⣷⠀⠀⠀⠀⠀⠀⠒⣶⠶⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⢰⣿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⣿⣛⡟⠛⠿⠷⠶⢶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢹⡇⢻⣄⡀⠀⠀⠀⠀⣀⣼⠏⠉⢹⡏⠉⠉⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⣾⠇⠀⠉⠛⠿⠿⠿⠟⠋⠁⠀⠀⠸⣷⡀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣼⡏⠀⠀⣀⣤⣴⡶⠾⠿⠛⠛⠛⢛⣲⣿⣿⣦⣀⣀⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢸⣧⡶⠟⠛⠉⣀⣠⣴⠶⠾⠟⠛⠛⠛⠉⠉⠉⠉⠉⠛⠛⠶⣄⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣴⠟⠉⠀⠀⠀⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣰⠋⠁⠀⠀⠀⢀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⡾⠋⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣴⠾⠋⠀⠀⠀⠀⠈⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⠛⠀⣾⣿⣿⣿⣿⡿⢿⣿⣿⡇
⠀⠀⢀⡴⠋⠀⠙⠛⠋⠀⠀⠀⠙⠛⠛⠉⠁⠀⣸⣿⣿⡇
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⢽⣷⣶⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠈⠃
⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⣿⢠⣿⣿⠀⠀⠀⠀⠉⠙⠓⠶⠤⣄⣀⠀⠀⠀⢀⣴⣿⢟⣥⣶⣶⣶⣶⣦⣄⠀⠀⠄
⠀⠀⠈⠉⠛⠒⠒⠚⠋⠉⠉⠁⠀⠀⠀⣸⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢿⠟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢨⣻⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣦⣌⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠤⠤⠴⠚⣿⣿⣿⡟⠈⢳⡀⠛⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⡟⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡷⠠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠋⠉⠉⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⢭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠉⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠇⠀⠰⠿⠿⠀⠀⠀⠀⠀⠠⠾⠿⠻⠃⠀⠀⠀⠠⠶⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠛⠙⢅⡐⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢙⢉⣭⣺⠷⠖⢲⠿⣾⠦⠶⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢨⠟⣿⢉⣑⣢⢟⢈⣟⣅⣠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠⣧⢤⣛⡿⡤⣿⠟⠻⡻⠿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢹⡿⢾⣰⡮⢽⣄⣠⣓⣺⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢑⣴⡽⣖⣾⠋⠉⠻⡿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢠⣉⣻⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⣀⠀⠀⠀⠀⢀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠻⡁⠣⠐⠈⠑⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢘⡄⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣴⢫⣵⠀⠀⠀⠀⠐⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡈⠈⠈⢀⡆⠀⠀⠀⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⢉⡠⠀⠀⠀⢹⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀⠈⢦⠀⠀⠀⢀⣉⣀⠀⠈⡄⠀⠀⠀⠈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠂⠀⠀⡱⣄⡀⠀⠀⠀⢉⡠⣷⠀⠀⠀⠀⠘⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠌⠑⠒⠒⢉⡜⠈⡆⠀⠀⠀⠀⢀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠚⠒⠐⣒⣉⡀⠀⢡⠀⠀⠀⠀⠈⠑⠺⠷⢶⣄⣀⣀⣀
⠀⠀⠐⠒⠀⠀⠀⢂⠀⠀⠀⠀⡐⢀⣆⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠒⠒⠚⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣂⣄⣀⣀⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⢠⢰⠂⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣦⣤⡀⠀⣿⠀⠀⠀⠀⠀⠠⢯⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠏⠈⠉⠉⠉⠁⠀⠹⡄⠀⠀⣤⡤⠿⠿⠏⢻⣿⣆⣿⠀⠀⢠⣖⢿⣿⣿⣿⢖⣦⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⡄⠀⠒⢀⡀⠒⠂⢠⠇⠀⠀⣿⠁⠀⢠⡟⢹⣿⣽⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣳⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠙⢦⣀⠘⠃⣀⡴⠋⠀⠀⠀⣿⠀⠀⣿⠁⢠⠞⠢⡀⠀⠀⠀⠹⣽⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠉⠉⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠣⣾⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠋⠀⠈⠙⢦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⡄⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⡿⠀⣹⠇⣄⠀⡦⠀⢿⠀⠀⠀⠀⣾⢹⣿⣿⠸⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⡯⡇
⠀⠀⠀⣇⣀⣰⣇⣿⣿⣘⣆⣀⢠⠀⠘⣇⡀⠙⠃⠾⠘⠃⢠⡜⠀⠀⠀⠀⠀⢸⡏⢿⡄⠀⠀⠀⠀⢀⠀⡈⢉⠉⢉⡉⡉⠁⣀
⠀⠀⠀⡿⠛⠛⢻⡟⢻⡟⠛⠛⢻⠀⠀⡠⡯⠓⠦⠶⠲⠶⠚⠀⠀⠀⠀⠀⠀⢸⡇⣼⠇⠀⠀⠀⠀⠘⠐⠛⠘⠘⠙⠖⠳⠂⠧
⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⢰⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠹⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣈⣐⣀⣿⣿
⠀⠀⠀⠘⣿⡿⠿⡟⡯⣽⣿⢦⡀⠀⠀⠀⠀⠹⢺⣿⡇⠀⠀⠀⠀⢠⡆⠀⢠⣏⢰⡆⣽⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢻⣟⣘⣷⣿⣿⠷⠞⠁⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⢸⡇⣤⣤⣤⣭⣥⣤⣤⣤⣴⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣀⣙⣛⣛⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡇⠀⠀⠀⠀⠸⡟⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣖⢆⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⣀⠈⠠⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣻⣿⢾⣷⡄⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠀⠀⠀⣰⣿⣿⣿⡿⠟⠙⢿⣷⡄⠀⠀⠀⢀⡟⣿⣿⡟⣇
⠀⠀⠀⢰⣿⠉⠉⢩⣤⣿⣿⢾⡇⠀⠀⠀⠀⢀⣙⣲⣿⣁⠀⠀⠀⢠⣿⠋⠉⢁⠀⢀⡀⠀⢸⣿⠀⠀⠀⠘⠁⣿⢿⡇⠙
⠀⠀⠀⢸⡏⠀⠀⣾⠁⠛⣻⠛⠁⠀⠀⠀⣴⡿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣆⠈⠁⢰⡄⠉⠀⣼⣿⠀⠀⠀⠀⠠⣿⢘⣷
⠀⠀⠀⠸⠧⠀⠘⠃⠀⠎⠀⠱⠀⠀⠀⠸⠿⠀⠿⠿⠿⠟⠛⠀⠀⠘⠛⠛⠓⠦⠤⠤⠔⠛⠛⠛⠀⠀⠀⠀⠀⠿⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⣤⡴⠖⠛⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣛⣁⣀⠉⠀⠀⠀⠀⣀⣠⣀⢻⣇⢹⣿⣿⣆⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠙⠛⠁⠀⠀⠀⠈⠙⠛⠁⠘⣿⣾⣿⣿⣿⣧⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣤⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠛⠿⠟⠋⠀⠀⣺⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⠋⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⠁⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠰⢿⡿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠶⠃⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⢿⣿
⠀⠰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠴⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⡙⢆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠱⡈⢷⣅⠙⠀⠀⠀⠀⠀⠀⡜⠁⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢤⡀⠀⢁⣀⠦⣀⡔⠀⣠⠚⡄⢡⠃⠀⠀⠀⠀⢀⠞⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⢦⢄⡱⠚⠁⠀⢀⣿⡤⠊⣁⠠⠕⠃⠀⡀⠀⠀⢠⠎⠀⡠⠃
⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠀⠀⢀⡀⢀⡤⠊⠁⠉⠉⠉⠐⠒⠙⢋⠙⣷⣆⣠⠴⠋⠀⢀⡼⠿⠁⠐⠦⣁⠀⠀⢠⠏⠀⡜⠁
⣜⣿⣿⣿⣿⡿⢲⡌⠉⠉⠀⠀⠈⡄⠀⣇⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠐⠀⠀⠀⠀⠀⣠⠜⠛⠉⠁⠒⢄⠀⢀⠇⢀⠎
⠉⠈⣍⠧⠦⠙⠉⠑⠠⢄⠀⠀⢀⠃⠀⠈⣲⠖⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢱⡆⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢌⡲⠎⣀⣠⠎⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣀⠤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠗⠂⠉⠀⠀⠀⠀⠤⠤⠠⠵⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠲⡀⠀⠀⠀⠘⠢⠤⠤⠐⠒⠈⡇
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⡰⣖⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢄⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⡤⠒⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⡠⠙⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠘⡍⠥⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡵⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠰⠁⠰⠚⣠⠀⣀⡣
⠀⠀⠀⠀⠀⠀⡈⣤⠀⢿⠐⠠⠤⠤⠤⠤⠞⡻⢿⡟⠉⢹⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠘⠤⠠⠖⠉⠣⣤⢤⡤⠔⠂⠙⠀⠀⠉⠲⢤⡀⠀⠜⢀⣀⠠⠤⠔⠒⠉⠇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠜⠊⠀⠀⠀⠀⠀⠀⠀⢩⢙⠉⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠈⠁⠠⢤⡀⠈⠙⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠛⢿⣇⠀⠈⠿⠖⠀⡴⣒⠂⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠸⣿⡀⠀⢀⠀⠘⠁⢉⣼⠥⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢻⣷⣄⣈⣉⣠⣴⠋⠀⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⠀⠙⠿⠿⠿⢋⣘⣄⡀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⢻⣿⠀⠀⠀⠀⢠⠎⠿⠿⠿⢻⡆⠀⠀⠘⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠿⠖⠒⠒⠚⠉⠀⠀⠀⠀⣼⣿⡄⠀⠀⠘⣄⣤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠻⢿⣷⡀⠀⠀⡏⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⡤⠞⠉⠓⠋⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢶⣤⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣠⣾⣿⠟⣻⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣰⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠙⣿⣿⣿⣿⡟
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢤⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⠄⢸⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡿⠀⠈⠾⢻⡇
⠀⠀⠀⠀⢀⡿⢋⣁⣉⠙⠿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠉⠀⠀⠀⣦⡾⠃
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠇⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠉⠻⢿⣿⣿⣿⣿⡿⠟
⠈⠛⠿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠉⣻⡶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠞⠛⢷⡄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣤⡀⠀⠉⠛⠿⠿⢿⣿⣿⣿⡿⢶⡶⢶⣤⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠙⢷⣶⠃⠀⠀⣰⣯⠀⠈⣿⠀⣿⡀⣿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠛⠿⢿⣍⡙⠷⠶⠿⠶⠛⠛⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣷⣦⣤⣀⣀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠙⠻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡟⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⢻⡇⣿⠟⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⢹⡂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣾⡉⣯⣹⠛⠛⠛⢿⡅⢸⠟⠛⠛⢻⣉⡏⣹⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣤⣼⣭⣥⣤⣤⣤⣤⣼⡇⣿⣤⣤⣤⣤⣤⣬⣭⣤⣤⣽⣷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣇⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠹⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠛⠲⠴⠚⠀⠀⠀⠀⠈⠓⢒⣉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⢀⡤⠴⠒⡞⠁⢠⠜⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠒⣏⠀⠴⠓⣇⠀⡏⠀⠀⠈⡆⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡞⣰⢊⣉⣉⣉⢱⣄⣀⢀⡇⠀⠀⡨⠇⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠈⣇⠘⠺⠧⢤⡶⠞⠻⠴⠾⠥⣀⣰⠀⣶⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⣤⠛⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⠀⠙⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡹⠓⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡠⠞⣠⣉⣹⠀⢀⠔⠋⣠⠞⠁
⠀⠀⠀⠀⢰⠀⠉⠉⠉⠁⢸⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢪⠃⠀⠀⡠⠊
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠆⣈⡀⠧⠤⠤⠤⠤⠤⠤⢿⠀⠒⠒⠳⣀⠧⢴⡋
⠀⠀⠀⠀⠸⠦⠖⠒⠒⠒⠊⠈⠁⠉⠉⠉⠉⠉⠉⣹⠀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠇⠀⠀⠀⣤⢿⡀
⣶⣶⣿⣿⢉⣉⠉⠉⢉⡉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡏
⣿⣿⣿⣿⢸⢾⣀⢶⣘⣁⡖⡆⡇⠰⡀⡇⠀⠀⠀⠀⠀⢪⠄⡀⡀⡀⣸⢰
⢿⣿⣿⣿⠈⠉⠈⠉⠀⠁⠉⠁⠉⠈⠁⡇⠀⠀⠀⠀⠀⠸⠄⠀⠀⠄⡿⠀⡂
⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡏⠀⠄⠀⣇⡲⠁
⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠓⣶⣶⡞⠁
⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠃⢧⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠑⣹⢋⠞⣿⢹⣿⣿⡿⣿⡄⠠⣄⣀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⡿⣻⢿⣟⡛⠅⠀⠀⠿⢺⣏⢹⣿⡏⣧⡿⡇⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⠿⠿⠿⠷⡀⢠⠾⠿⠿⢿⣿⡏⣿⢱⣏⠀⠀⢸⡶⢀⠀⠁⢄⣠⢘⢰⢀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠦⣴⠴⠚⠁⠈⠲⠤⣤⡴⣿⡇⣿⣿⣿⠀⠀⠸⠂⠘⠀⡀⡸⠙⠋⣿⢁⠞⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠱
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠠⠂⠀⠀⠀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⢤⣤⣤⢴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣀⣧⣷⣿⣿⣿⣿⣿⠀⠀⠀⢢⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠘⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⡀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⣇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣽⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢸⡇⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢹⠻⣿⠀⢸⣟⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣇⡇⢸⣿⢿⢸⢻⣿⣿⣿⣿⣿⢻⠇⣿⣸⠀⣿⠀⢸⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⢸⠀⣄⣿⡏⣿⢸⣿⣸⡆⣿⣇⣦⡏⠀⠈⢿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣇⣒⣈⣛⣛⡏⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣷⡀⠀⠀⠸⣿⣿⡿⠿⣛⣋⠱⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⣧⠀⠀⠀⠈⣴⣶⣿⣿⣿⣿⣶⣭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⢿⣿⣿⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⡄⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠙⠛⠋⠀⠈⠛⠛⠁




⣿⣿⡿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣾⣶⣶⣷⣾⣧⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡅⣴⠦⣖⡶⡄⠀⠀⠀⢠⣦⣶⣤⡖⢦⣤⣀⠀⠀⢀⣴⣦⣄⠀⠈⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠹⠗⠛⠉⠁⠀⢐⡏⣿⣿⣽⣻⣙⠀⢙⣿⣿⣶⣿⣿⣿⣿⠁⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢰⣿⣷⡯⣿⠷⠋⠁⠀⠘⠯⠻⣿⣿⣿⣿⣧⣀⠀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢠⠢⠀⠈⠙⡛⢻⡛⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡣⠐⡄⠀⡆⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⠀⠀⠀⠀⠈⠀⢈⠶⠦⠀⠀⠀⠀⠀⢀⠠⠀⠀⢼⡲⡇⢠⡿⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡔⠇⠈⠩⢌⡭⠃⠀⠀⢀⡞⠁⠀⣀⠀⡀⠑⡏⢸⡇⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⣡⣀⠀⡠⠄⡀⠀⠀⣰⡿⠀⠀⠹⠼⡥⠐⠀⠀⠠⢿⠇⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡂⠀⠀⠀⠙⢹⠸⣀⢀⠄⠀⣰⣻⠁⠀⡠⠔⠠⡀⠀⠀⠀⠄⢸⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⠀⠀⠀⠆⠠⠀⠀⠐⠘⠓⠋⢀⠀⠣⠀⠴⠀⠀⠘⡷⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠀⠀⠀⠀⣀⡀⠡⡀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⢠⠃⠇⡀⠈⢢⡄⣀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠸⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⣄⣰⠀⣃⢣⠃⢰⣿⣾⣿⠀⢠⠠⠠⢸⠀⠁⡇⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⠀⠀⠀⠀⠈⠙⠺⢾⠇⠀⠈⠻⣇⡤⠼⠤⠴⠶⠴⠚⠶⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡄⠀⠠⠀⣁⣤⡤⢣⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠄⠀⢢⡞⢿⠱⣾⠀⠙⢒⡴⠞⠃⠸⣷⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠰⠀⣸⠦⠟⠀⢻⣄⣀⡈⠁⠀⠀⣺⡍⢷⠛⣷⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠇⡟⠀⠀⠼⢿⠌⣥⢼⣭⢫⢰⡆⠘⠷⡯⣿⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠾⠤⡤⢐⣦⣴⠚⢹⡏⣡⣉⠀⠀⠀⠀⠆⢿⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⡇⣀⠀⣿⢰⢸⡃⢠⣿⠃⠉⢻⢁⣠⠴⢝⣼⡇⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣔⠆⢀⡀⠰⣿⣴⣾⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣷⣾⣷⣌⠀⠀⠻⢀⣿⣿⡏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠿⣿⣿⣿⣿⣷⣾⡖⣾⡆⢻⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣷⡐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠁⠀⠀⠲⠶⠶⠦⣤⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠈⢹⠷⠀⠰⠶⣤⣤⣀⣀⠀⢰⣿⠿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⣀⢠⡀⠀⠀⠀⠀⠀⠈⠙⢹⠏⠐⠛⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢰⣿⠲⠄⣒⠟⠂⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣓⠾⠟⠓⠤⠤⣤⣤⣤⠆⡰⡻⢿⢟⡻⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⢾⣏⠁⠀⣶⠃⠁⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⢸⡏⣠⠞⢡⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣧⠀⢀⣀⠴⠚⢣⠀⠈⠓⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣄⣀⣀⣤⡺⠦⠊⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠠⡉⠑⠂⠀⢀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⠑⠳⣄⣸⡁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⡿⠙⠶⣤⣄⣀⣠⡞⣀⣀⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠟⠉⠉⠉⠉⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠠⠀⠀⠀⠀⢰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢄⡀⠀⠀⠀⠀⠻⣶⠇⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢙⢶⣄⢀⣤⣶⡿⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⠃⠀⢀⣾⣿⣦⣄⣀⣀⣀⣀⣀⣤⣶⣦⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡛⢁⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡺⣸⢀⠀⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠁⠐⠀⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⠄⡀⡀⢾⣿⣿⣿⢏⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣤⣄⡈⠙⠛⠛⠛⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢎⠋⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡄⠈⠆⠀⠉⠋⠁⠻⠋⠛⢻⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠻⡆⠀⠀⠀⠀⢀⣸⡆⢀⡾⠟⢩⣽⣿⣿⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⣀⠀⡀⠀⠀⠀⠐⢾⣿⠿⠃⠼⢝⠬⣂⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣽⣿⣿⣿⡆⠀⢀⢠⠈⠁⣠⣶⣿⠷⢟⣾⣖⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⠟⠁⠀⣏⣾⡆⠀⠙⢃⣊⡡⣭⠥⠤⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⢞⣽⣤⣽⡄⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⣿⣿⣿⡿⠿⣆⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣏⣥⢀⣀⠠⠁⡀⠀⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢶⣀⠠⠞⢁⣼⣿⣿⣿⣿⣿⡟⣛⣫⠥⠄⠀⠀⠀⠀⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢛⣵⣾⡿⠟⠻⠿⣿⣿⣿⣿⣷⣾⣟⣏⣠⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢛⣩⣅⣀⣠⠤⠂⠀⣉⠙⠛⠻⢿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠏⡤⠖⠚⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣤⣾⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣦⡶⣶⠒⠂⠂⢄⠐⠄⠂⠀⠀⠀⠀⠉⠀⢤⣶⣿⣿⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠋⠁⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣿⣶⣿⣷⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠙⠿⠿⠿⠟⠻⢿⣿⣿⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡟⠋⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠙⣿⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣸⠁⠀⣀⡀⠈⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⢸⣋⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠉⠙⠃⠀⠀⠀⠈⠉⠉⠛⠉⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⢄⡀⠀⠀⠈⠉⠙⠀⠀⠀⠀⢀⣀⡤⠶⣻⡿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡠⠚⠉⢙⠓⠒⢲⡀⠒⠒⣚⠟⠉⠁⠀⠠⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢨⣷⡀⠀⠹⠛⠛⠉⠀⠸⣆⣠⣤⠵⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣵⠟⠙⠳⠦⢤⣤⣤⣤⠤⠎⠉⠉⢡⠥⠂⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⡽⠉⠙⠛⠛⠛⠛⢫⡉⠙⠒⢹⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠖⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⢰⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢛⣋⣡⠴⠖⠒⢛⠒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠗⢸⡆⠀⣞⣋⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⠀⠀⣀⡤⠶⠿⠉⠉⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡷⠐⣢⣾⣐⠤⠾⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⢀⠴⣃⡸⠀⡍⡇⠀⠀⠧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣀⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⡒⢤⠀⠀⠀⠀⠀⠀⠀⠂⣶⠀⡇⠀⡟⣳
⠠⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⡟⠲⣴⣡⣤⠇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠤⠔⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁
⠀⠀⠀⠀⣀⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠄⠀⠀⠀⢀⣠⣶⣶⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠥⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⢀⣿⣿⢿⣛⣛⡿⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⡟⣵⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢫⣩⢻⣿⡏⣉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣷⣿⣿⣷⣾⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣮⣭⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣝⢿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇






⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⣤⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⠷⠾⠛⠛⠒⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⡗⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⠶⠶⢦⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⡟⠛⣿⠛⣻⣶⣶⣶⡶⠶⢶⡶⠒⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⢻⡾⠋⢨⣿⡏⠙⣦⣼⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡇⠀⠀⠀⠀⣾⣿⡇⠀⠈⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠠⢄⠀⠀⠀⠀⠀⠀⢀⣤⢤⣄⡀⠛⡇⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠠⠀⢱⠂⠀⠀⠀⠀⢸⡇⠀⠈⠙⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠰⠊⠉⢣⡈⣥⣀⡀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢀⣠⢴⢻⠢⣉⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡂⠻⠏⢷⡌⠀⣢⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⠘⣄⢤⠒⠂⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠀⠐⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠤⠤⠤⠄⠈⠛⠷⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⡆⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⡇⢤⠴⣧⣄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⡐⠀⠀⠡⢀⢯⠂⠤⡄⠀⠀⠀⠡⡀⠀⠐⡖⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⣤⡚⢨⠄⠋⠳⠃⠀⠀⠀⠀⠈⢢⠀⠀⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠇⣸⠀⠜⠒⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠁⡈⠀⠀⡠⠀⠀⠀⡠⠔⠂⠉⠄⢀⠌⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠐⡹⡀⢀⠀⠀⠑⠢⢀⣀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢠⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⣀⡞⠙⡏⢱⡕⣷⡈⣆⠀⠬⠀⠀⣨⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠋⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢿⣥⠶⣌⠬⠔⠁⠈⢿⠋⡃⠀⠀⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡄⠀⠀⠀⠀⠀⠈⢷⡁⠒⠂⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠧⠐⠂⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠑⢄⠀⠀⣀⠀⡀⠀⠀⠀⠀⠔⠉⠉⠀⡀⠀⠀⠀⠀⢰⠁⢀⢀⠀⠀⠀⣀⡠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⣀⠞⠛⠹⠂⠈⠙⠀⠀⠀⠀⠀⠀⡶⠊⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠈⠂⠠⠤⠤⡜⠀⠶⠊⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠇⠀⠀⠀⠒⠀⠀⠛⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣷⣂⣠⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⢀⣀⡀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠁⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠠⡄⠤⠧⠴⠧⠤⠄⠀⠀⠀⣠⠄⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠲⠶⠆⠀⠀⠀⠶⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⢀⠔⠉⠀⢀⡀⠠⠤⠔⠒⠊⠉⠀⠀⠀⠈⠀⠀⠀⡰⠉⡆⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣓⠐⠒⠒⠒⠆⠀⠀⠀⠖⠠⠤
⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠐⠂⠒⠀⡆⠈⢹⡥⠤⠈⠀⢥⠀⠨⣅⣀⣀⣀⣀⡆⠀⡤⠤
⠀⠀⠀⠀⠀⠀⡄⢀⡎⠀⣰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠈⠉⠉⠁⠈⠉⠉⠁⠒⠄⠀⡠⠀⠆⠀⠀⠀⠈⠀⢀⠃⠐⠒⠀⠔
⠀⢀⠔⠊⢁⡟⠀⠈⠀⠀⠀⠀⢡⡀⣀⡀⠀⠀⠀⡥⠤⠤⠤⠤⠤⠤⠭⠭⠍⠉⠉⢉⠁⡀⢢⣄⣀⣀⣀⣸⣏⡀⢀⣀⣆⣀⣠⠊⣁⣈⢑⡀
⠀⠹⠂⠀⡎⠀⠀⠀⠂⠈⠀⢠⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⣀⡀⠀⢇⠀⠀⠂⠀⠀⢠⢃⡟⡟⠙⡟⢲⠂⠀⠀⢰⠲⠂⠀⠀⠀⠐⡖⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠖⠒⡖⠒⠒⠂
⠀⢠⠁⠀⠈⠑⠀⠀⠢⠔⠊⡸⠀⡇⠀⠀⢸⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠠⠞⠃⡠⠀⣀⠀⢀⠶⠔⠁⠀⠁⠀⢰⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠈⠋⠀⠛⠀⠙⠁⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⣀⣀⡸⠀⠣⢠⡀⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡊⠁⠈⠑⡀⡠⠊⠉⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠼⠈⠑⠚⠛⠛⠃⠛⠲⠖⠚⠱⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣒⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢦⠀⠀⢠⠄⠀⣠⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡟⠁⠀⠈⣇⠰⠋⠀⡼⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡄⠀⠘⢦⠀⠀⠀⠘⡾⠉⠉⢣⡀⠀⢀⣀⡿⠀⠀⠀⠀⠀⠀⠈⣹⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡷⢧⣠⠬⣕⢦⣄⠀⢧⣴⠒⠒⡿⠏⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⡇⢸⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣿⣦⠈⠳⠤⠴⡗⠒⠛⠒⠒⠒⠒⠒⠒⠒⠉⠉⢹⣸⠄⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠖⠲⠌⠀⠀⠀⠊⠀⠀⠛⠧⣀⠀⠀⠀⠀⠀⣀⢀⡠⠍⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⢶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣤⠒⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡊⠑⢧⡀⠀⢀⣤⠖⠻⡁⠀⢧⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⠉⢣⠔⠒⡄⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠭⠶⢀⠈⠑⠯⣘⡆⠀⢱⡤⠞⠉⡇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⣴⠒⠂⠀⠈⠦⠤⠤⠤⠤⠤⠧⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠉⠒⠯⣀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠤⠖⠊⠉⠉⠙⠃⠤⠒⠉⠉⠉⠓⠒⣚⠃⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⢉⠳⡄⠀⡾⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣴⠃⠀⢨⣾⡇⠈⠄
⣤⣶⣶⣾⡟⠉⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠁⠀⡌⡄
⣿⣿⣿⣿⡇⢸⣽⡆⢠⡄⡗⡇⡤⣄⣶⢀⡤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣿⣿⣿⣿⡇⠸⠼⠓⠯⠇⠇⠗⢦⠟⠻⠄⠽⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡽⢣
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⡖⠈⡻⠉⠉⠀⣸⢩⠈⠣⡄
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⣧⢣⣔⣀⡎
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣰⡃⠀⠀⡞⠸⡧⣮⠜
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢹⠋⠃⠀⢸⠁
⠀⠈⠛⢿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⢲⠂⣤⠤⠤⠤⠤⠤⠤⠤⠴⠓⠶⢖⣲⡳⠂⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣼⠷⢤⣤⣄⣠⣤⣤⠤⠤⠤⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠃⠀⣠⡤⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡏⠀⠘⠁⠀⠀⡀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⣠⠶⣿⣿⠀⠐⣎⠙⣿⡿⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠈⠙⠲⠞⠁⢤⣤⠌⠉⠉⣠⢤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢆⠌⠝⠄⠀⠀⣀⣤⣤⠀⠐⡍⠱⠑⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠑⣄⣀⣀⣀⣜⠁⠀⢤⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠗⡮⠤⡴⠋⠉⠉⠉⠈⠻⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣴⣃⡠⠄⠀⠀⠠⣤⣙⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠙⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠹⣦⣀⣀⡀⠀⠀⠀⠀⣀⣸⡗⠀⠀⠀⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡤
⠀⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⡀
⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠂⠀⠀⢀⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠤
⠀⠀⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⢰⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⡀⠊⡀⠀⠀⠈⠘⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠄
⠀⠀⠀⠀⠁⠄⠀⡄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠜⠢⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⣠
⠀⠀⠀⢀⡀⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠈
⠀⠀⢀⠀⠤⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠢
⠀⠖⠀⠠⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⢮⡀
⠀⠀⠀⠀⠈⠀⠀⠆⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⡇⠀⠁⠂⠄⢀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠑⠘⠀⠈⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⡰⠀⠀⠀⠉⡃⠀⠈⠀⠉⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣊⠤⠀⠀⠀⠀⠊⠀⠀⠠⠂⠈⠀⠁⠁⢨⠀⠀⠄⡀⠈⢠⡀

⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣄⠀⠀⠀⠀⣠⣶⣶⣶⣤
⢸⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿
⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠙⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠋⠀⠀⠀⠈⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠙⢿⣿⣿⣿⣿⣟⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣄⡀⠀⠚⣟⠃⠀⠀⠀⢴⣆⠀⠀⢰⣆⠀⠀⠀⠀⣶⠆⠀⠀⢀⣡⡄⠀⠀⣾⠅⠰⡄⠀⠠⣮⠄⠠⣤
⠀⠀⠈⣿⠀⠀⠸⣿⠀⠀⠀⠀⡼⡇⠀⠀⠸⡏⠀⠀⠀⠿⠿⠿⠁⠀⠿⠿⠿⠀⠀⢹⠀⠀⡟⠀⠀⣷⠀⢰⢿
⠀⠀⠀⠛⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠀⠁⠈

⠀⠀⣸⡆⢀⡀⣦⠀⠀⠀⢠⣶⢀⡀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡻⢃⡀⠀⠀⡸⠟⣀
⠀⠀⣿⡏⣿⠈⢚⡷⠀⠀⢸⣿⢽⡗⠀⠐⡻⠂⠀⢀⡔⠂⠀⠀⠀⢀⣿⠃⣀⡀⠀⠀⢹⡇⣈⣷⠀⠘⣿⢀⣹⡄
⠀⠀⠘⠃⠋⠀⠈⠃⠀⠀⠀⠛⠘⠓⠀⠀⠓⠀⠀⠘⠛⠐⠛⠙⠀⠚⠘⠀⠋⠙⠀⠀⠘⠃⠈⠋⠀⠀⠛⠀⠙

⠀⠀⢄⡀⠀⠀⢀⣄⡀⠀⠀⠀⢀⣯⣠⡄⠀⠀⣶⠀⠀⢠⣧⠐⣄⠀⠀⣆⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⡀⠀⢀
⠀⠀⢸⣟⠁⠀⢻⡿⠃⠀⠀⠀⠸⣿⢈⣿⠋⠀⣹⡆⠀⠺⣿⠛⣿⠀⠀⣿⠀⠀⠀⠰⣿⣿⠇⠀⢀⣿⠋⢳⡟⠂
⠀⠀⠘⠙⠀⠀⠘⠃⠀⠀⠀⠀⠀⠛⠘⠘⠀⠀⠛⠃⠀⠀⠋⠘⠙⠀⠘⠛⠃⠀⠀⠀⠛⠙⠀⠀⠘⠈⠁⠋⠑

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⢀⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣠⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⠞⠳⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⡄⣠⡴⠦⢄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡴⠋⠀⠚⠛⠁⠀⠀⠀⠀⠀⣠⡟⠒⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠘⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣻⣶⠄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⣴⣿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣧⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢸⠇⠀⣿⣶⠟⠋⢁⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢸⠄⠀⣿⠟⠀⢀⣿⣿⣿⡿⠋⣹⣿⣿⣿⠃⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣆⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣧⣀⣼⣄⣀⣿⠀⠀⠸⣿⣿⡏⠀⠀⢸⣿⣿⣿⡀⠘⣿⣧⠈⠛⢿⣿⣿⣿⠶⠂⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢹⡏⠉⢻⡋⠉⣿⠀⠀⠀⠻⣿⠀⠀⠀⠀⠻⣿⣿⣧⡀⠈⠻⣆⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢸⠆⠀⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠻⠿⠆⠀⠀⠀⠀⠀⠈⠙⠻⠷⠦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢸⡇⠀⣹⡅⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⡟⠛⢻⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢸⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⡇⠀⢺⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠉⠉⠉⠉⠙⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣛⣛⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⡤⠖⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢱⠀⠀⠀⢰⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠦⣄⠀⢸⠆⠀⠀⢾⠀⢀⡤⠖⠒⠒⢤⡀
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣴⣶⣄⠈⣆⢸⠀⠀⠀⢸⢀⡎⢀⣴⣶⣄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠹⣿⣿⠟⠀⣿⠏⠀⠀⠀⠈⢿⡇⠘⢿⣿⡿⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⣀⣀⣀⡤⠤⠤⠤⠤⠴⠶⠤⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠒⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠒⠶⣶⣾⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠂⠀⠀⠀⠀⢀⣠⣤⣤⠀⠈⠙⢿⣿⡿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣀⠀⣀⣤⡀⣤⡶⠀⣾⢻⣷⠈⢹⣿⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡆⣾⠇⣾⡻⠂⣿⣹⡇⣿⣤⢠⣿⠈⠉⠀⢸⣿⡄⠀⠀⠀⠀⢀⣼⣿⣿⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢻⡷⢙⢿⣆⣿⡟⠁⣿⣏⠀⣿⣆⣿⡇⢸⣿⡇⠀⠀⢀⣴⣿⣿⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⠸⣿⠟⠹⠇⠀⠻⠛⠃⠙⠛⠋⠀⠀⠉⠁⠀⣠⣾⣿⡿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⠐⠒⠒⠒⢒⣶⡒⠚⠩⠭⠭⠉⠉⠉⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠉⠉⠉⠉⠀⠀⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠀⠀⣿⢿⡆⣿⢰⡿⣧⢸⣿⡄⣿⢠⣿⡄⣶⣴⡶⢰⣦⢶⠄⡆
⠀⡀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣧⣿⡏⣿⣅⢸⣿⡇⣿⡜⣷⡄⣿⡟⣧⢸⠛⢸⠀⠃
⠀⠙⢬⡛⢿⣿⣿⣷⣤⡀⠀⠀⠀⣿⣿⣿⢸⡇⣬⢿⣼⣿⣇⣿⣀⣾⣷⣿⠀⣧⣸⣿⢸⡇
⠀⠀⠀⠈⠲⣍⠻⣿⣿⣿⣦⣄⠀⢿⣿⡿⠸⠇⠻⠿⠙⠟⠟⠛⠛⠙⠋⠙⠀⠉⠁⢉⡀⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣝⠿⣿⣿⣷⣤⡠⠤⠤⠤⠤⠀⢒⣒⣒⣤⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠉⠑⠒⠂⠀⠰⠦⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠦⠤⠤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠤⣄⣉⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣧
⠀⠀⠀⠀⠀⠀⠀⡠⠶⠀⠐⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣣⣄
⠀⠀⠀⠀⠀⠰⠋⢁⡀⠠⣌⣝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠸⢯⠳⣄
⠀⠀⠀⠀⢀⣀⡀⠠⠌⠉⠨⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠁⠀⠈⠁⠂⠀⠀⠀⠀⠂⠐⡘⣷⡙⠓⢄
⠀⠀⠀⠀⠈⣀⠉⡳⠀⠈⠘⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢻⡟⢤⠈⣆
⠀⠀⠀⠠⠆⠁⠉⠀⠓⢦⠀⣟⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡈⣿⣷⡀⡄⠈⡧
⠀⠀⢠⠇⠀⣠⡶⣶⣦⣤⠰⡏⠀⣠⣴⡿⠀⠀⣄⣤⡀⢀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠼⣿⣿⡑⠁⢸⡇
⠀⠀⠀⠀⠐⢿⡇⣯⣵⣿⠻⣷⣾⣿⢗⡞⠉⠁⠀⢀⡀⠀⠈⠑⠶⡄⠀⢀⣤⡴⠶⠲⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡿⣿⣿⣁⠸⡇
⠀⠀⠀⠀⠀⠈⢛⡿⣩⠟⠠⠟⠚⠛⡿⠛⣿⣿⣿⠟⠿⠛⠒⠒⠒⠻⢢⡿⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠳⢿⡿⠤⠄⡃
⠀⠀⠀⠀⡀⢡⠘⣾⣻⣄⡘⠀⠀⠲⢿⣄⣈⣉⣁⣤⣧⠚⠓⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠛⠛⠉⠉⠛⠶⣌⠻⣾⡏⠓⠻⡽⣤
⠀⠀⠀⠀⢣⢸⡄⣃⠛⣻⡇⠀⠀⠀⠒⠶⠭⢭⡥⠴⠂⠘⠂⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢸⡇⠀⢠⣯⣐⡀⢀⠀⠀⠀⠀⠀⢻⣿⢷⣤⡄⠈⢺⡇
⠀⠀⠀⠀⢴⢸⡟⠉⠳⡝⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠙⠂⠀⠀⠀⢸⠀⠠⢺⠛⢻⡛⢿⡟⢻⠟⠛⠛⠺⠗⠘⣿⣟⠇⠀⠉
⠀⠀⠀⠀⠀⠀⡅⢀⣀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⢀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠸⠷⠶⠶⠋⠀⠀⠀⠀⠀⠀⣬⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠉⠻⠟⠛⠛⠲⠖⣶⡖⠒⠛⠀⠀⠀⠈⠙⠒⠖⠒⠃⠀⠀⠀⠀⠀⢸⣗⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⣴⢾⣷⣿⣷⣿⣷⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣄⠀⠀⠀⠀⠀⠃⠂⠠⣥⠿⢿⣛⠂⠉⠉⠉⠉⠉⢉⣉⡭⢛⠷⠖⠇⠀⠀⠀⠀⡘⠁⡐⠀⣾⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠳⢦⣄⣀⣀⣐⣼⣯⠷⠋⠀⠀⠀⠀⠀⠀⠀⠃⢀⢣⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢹⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⣩⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⡷⠀⠀⠀⡀⠙⢷⣴⣄⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠱⠈⡌⠢⡙⢦⡀⠀⢀⠀⡠⠚⠉⠀⠋⠤⡀⢄⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⡄⠀⠀⠁⠄⠑⠆⠉⠂⠻⢆⡄⡜⠀⠀⠀⠀⠀⠀⢰⡼⠀⠀⣠⣤⡾⠋⠁
⠀⠀⢀⡀⠤⢬⡉⢉⡄⢀⡧⠀⠀⢷⠀⠀⠀⠄⠀⢌⠂⠁⠀⠂⣻⣧⠀⠀⠀⠀⢀⡀⢠⡇⡰⠾⠋⠈⡁
⠉⣀⠀⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠸⡧⠀⠀⠀⠀⠀⢀⣤⡄⠄⠀⠉⠓⠦⣄⡀⠋⠐⠃⠀⠀⠀⠐⢠⠃
⠁⠈⠑⠂⠈⠀⠀⢧⠀⢠⣾⡄⠀⠀⢷⣆⠐⠀⠃⢀⠀⢿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⠄
⡦⠀⠀⠤⠄⠒⠂⠙⣦⠀⣎⣧⠀⠀⠸⣇⢠⠀⣆⡈⠀⠀⠉⠛⠷⢦⣀⣀⣀⣀⡴⠀⠀⠀⠀⠀⣸⠋⠀⠀⢐⡃
⠐⠀⠀⠀⠀⠀⠀⠈⠛⠐⢦⣻⡀⠀⠀⠹⡞⢲⡀⠑⠆⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⡾⠑⠦⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢣⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡟⠀⠀⠑⠉⢸⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠚⠉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠧⢶⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠴⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣀⠞⠒⢋⢧⣞⠁⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⡴⠊⠁⠀⢀⡆⠀⠈⠳⡄⢴⡒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡎⠀⣀⣀⠀⢸⠀⠀⠀⠀⢸⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⡀⠀⢸⠉⠉⠽⠉⠇⡾⠒⡒⠒⠒⠒⠛⣲⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠯⠀⠈⠉⢉⣉⣉⡑⢧⡈⠁⠀⣠⠴⠚⢽⢡⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯
⠀⠀⠀⠀⠠⣀⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⢠⣤⡤⢯⡑⣎⠳⣠⡆⠙⠦⣄⠀⠀⠀⠶⠶⠶⠶⠦⠀⣀⡴⠋
⠀⠀⠀⠈⢹⣦⡇⠘⡞⣹⣃⠀⠀⠀⢙⣲⡄⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⢸⡶⠓⣀⣟⠁⠸⡉⠲⣤⠝⠋⠀⠀⠀⡀⠙⢤⣀
⠀⠀⠀⠀⠀⡝⠉⠉⠀⠀⠀⢸⠦⣍⣻⣤⠄⠀⠀⠳⣤⠀⣼⠃⠀⣀
⠀⠀⠀⠀⠀⣗⠒⠀⠀⠀⢛⠏⠀⣸⠁⠀⠀⠀⠀⡞⠁⢀⣼⣟⡋⠙⢳⡆
⠀⠀⠀⠀⠀⢹⠀⣀⡀⢀⠟⡞⠒⡇⠀⠀⠀⠀⠀⢳⡴⠛⠉⠀⣽⠀⠀⢳
⠀⠀⠀⠀⠀⠈⡇⠀⢀⡞⠀⠙⡆⢷⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⢃⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠹⣀⠞⠐⢯⣍⣀⣈⠣⣄⡀⠀⠀⡀⠀⠰⠯⠬⠭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠃