Dromedary Emojis & Symbols

⠀⣀⡠⠤⠤⠖⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠉⠉⠒⢄
⣞⠁⠀⠀⠐⠂⠀⠀⠘⡄⠀⠀⠀⠀⠀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢄⡀
⠈⠉⠉⠢⣀⠀⠀⠀⠀⠹⡀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠙⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠳⡄⠀⠀⢀⠀⠀⠀⢀⣀⣀⡠⠤⠒⠊⠉⡆⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠋⠱⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠘⢆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⢰⢤⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇⠀⠀⠀⠈⢣⠀⠘⡄⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠙⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡸⠀⠀⠀⠀⠀⠈⢇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣰⠁⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠳⡈⢆⠀⠀⠀⠀⠀⡸⢠⠃⠀⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⡆⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣀⣸⠀⢠⡒⠉⣠⠃⠀⠀⠀⠀⠀⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣡⠁⠐⣀⡁⠀⢠⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢈⡛⠁
⢀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠘⢃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠑⢄
⡧⢈⠂⢀⠐⠂⠠⠃⠀⠄⠁⢈⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢡
⡅⠀⠀⢩⠀⠀⠀⢀⠌⠀⠒⢉⠜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢁⠀⠀⣸⠀⠀⠀⢰⠁⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠈⠦⠤⠋⠦⣀⣀⠎⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠳⠤⠎⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢢⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠶⠶⢦⠤⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡇⠀⠀⠀⢰⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠁⢣⠀⠀⠀⡾⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⢳⠀⠀⢸⠉⠙⠛⠛⠛⠉⠉⢡⠀⠀⢸⠀⠈⢦⠀⠀⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢾⠀⠀⠈⢧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⡅⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀⠈⡆⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔⢰⠁⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡐⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⡄⠀⠐⠲⠀⠀⣠⠂⠀⠀⠀⠀⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⢣⠀⠀⡠⠁⠀⠘⢄⠀⠀⠀⠉⠉⠀⠀⠤⣤⠄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠀⣠⠠⠚⠀⠐⡀⠀⡂⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠗⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣘⣀⣕⣀⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⡖⠰⠂⣀⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⠟⡔⢰⠀⡾⣎⠟⠲⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠄⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠁⠀⠈⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢚⡟
⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠀⠀⠈⠀⡔⠀⢀⡾⠁
⠀⠀⠀⠀⢀⢎⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡼⠁
⠀⠀⠀⠀⢈⢋⡇⠀⠀⠀⢮⣢⡠⡀⠀⠀⠀⠀⠀⠀⣜⢦⣷⡀⠀⠀⠀⠀⠠⢸⡇⡆⠀⠀⠀⢀⣺⠗⡠⠊
⠀⠀⠀⣠⡎⢸⡇⠀⠀⠀⢸⣿⡿⣾⣷⣤⡀⠀⠀⠀⢌⣳⡿⠁⠀⠀⠀⢠⢇⡿⣶⠿⠶⠶⠞⠯⠒⠋
⠀⠀⡸⢱⠇⢸⡇⠀⠀⢀⣿⣿⣿⡷⠀⠉⠉⠙⠓⠒⠦⠍⡇⠀⠀⠀⣰⣿⣿⠀⢸
⠀⠀⠃⡸⠀⠸⠀⠀⢠⢾⣿⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⡜⠁⢻⣿⠀⢸
⠀⢈⠔⠁⣠⠃⠀⡴⠋⢀⡿⠈⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠁⠀⠈⢿⠀⢸
⠀⠀⠀⢰⡏⠀⢰⠁⠀⡸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡌⠀⠀⠀⢸⠀⣄
⠀⠀⠀⠸⡇⢀⡾⠀⠀⢷⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡃⠀⠀⠀⢸⡄⠘⡄
⠀⠀⠀⠀⣷⢸⠁⠀⠀⠈⢻⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⢰⠃⠀⠀⠀⠈⢻⣦⡇
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⢳⠸⡄⠀⠀⠀⠀⠀⠀⠀⡟⡡⠁⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠈⢇⠱⣄⠀⠀⠀⠀⠀⢰⢷⠇⠀⠀⠀⠀⠀⠀⠀⠘⣄⢣
⠀⠀⠀⢰⡇⠸⠀⠀⠀⠀⠀⠀⠸⣄⠈⠦⢀⡀⠀⠀⡞⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠃
⠀⠀⠀⠈⣷⠀⣧⡀⠀⠀⠀⠀⠀⠈⠧⣄⠀⠙⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⠀⠒⠒
⠀⠀⠀⠀⠙⢿⠆⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒
⣶⣴⣶⣦⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣤⣶⣤⣤⣶⣶⣤⣴⣴⣦⣶⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⠊⢹⣳⡿⠒⠒⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠉⢀⣀⡤⡶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⢀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡏
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⢸⠇⠀⠘⡇
⠀⠀⢠⣤⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣀⣀⣠⡾⠀⠀⢀⡇
⠀⠀⣸⠃⠰⡄⠀⠀⠀⣾⣿⣄⣐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠉⠉⠉⠀⠀⣠⡞
⠀⠀⣿⡆⢠⠀⠀⠀⣸⣿⢿⠟⠿⣿⣿⣾⣦⣄⣀⣄⣀⣄⠀⠀⠀⠀⣸⣿⣷⣶⣤⣤⡤⠾⠋
⠀⠀⣸⡇⢸⠀⠀⣰⣿⡇⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⡇⠀⠀⣰⡿⠋⠉
⠀⠀⢿⡇⣿⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡆⠀⢠⠏
⠀⠀⠸⠃⣿⠀⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⠀⣼
⠀⠀⠀⣼⡿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇
⠀⠀⣼⣟⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⢸⡇
⠀⠀⣿⣏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢇⣼⠃
⠀⠀⣿⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⡟
⠀⠀⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇
⠀⠀⣿⣧⣇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⢉⡀
⠀⠀⠛⠛⠻⣌⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠻⢅⣉⣒⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⣴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣷⣤⣤⣀⣤⣀⣼⡻⡆⢢⣀⣀⣄⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢻⠁⣹⣿⣿⣿⣿⣿⣿⡇⠁⣨⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁⠀⢹⣿⠃⠉⠛⠛⢋⠁⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡇⠡⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠸⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠸⠇⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁



⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡄⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢀⣀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡅
⠀⠀⠀⠀⠀⠀⠐⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠸⠇
⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣽⡄⠀⠀⠀⠀⠀⢀⣀⠀⢀⣼⠀⠀⠀⠀⣀⡀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢀⠀⠀⠉⠻⠦⣄⣠⡀⠀⢀⣥⣰⣼⣿⣆⢲⣳⠇⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠘⡿⡿
⠀⠀⠀⠀⠀⠀⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠀⠦⢀
⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⢀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠖⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠰⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠈⠀⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢲⡄⠀⠀⠀⠰⠖⠒⠒⠈⠁⢸⠀⠀⢣⠀⠀⠀⠀⡀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⡄⠀⠀⣷⡀⠀⠀⢧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡆⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡞⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠁⠐⣁⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡴⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠢⣤⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠘⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠋⠀⢈⣠⠦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠦⡀⠀⠀⠀⠀⠀⢀⡾⠀⠀⡞⠁
⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢧⠘⠓⠤⠤⡤⠶⠋⠀⢀⠜
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⡂⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⣟⣿⣄⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⠤⠴⠚⠉
⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠨⣿⣦⣠⣀⣀⣤⣂⣤⣀⣶⠀⠀⠀⡋
⠀⠀⠀⢀⣾⠟⢹⠟⠀⢧⠀⢰⠀⠉⠙⠛⠛⠋⠉⠀⢰⣿⣿⠲⣄⠈⢢⡀
⠀⠀⢀⡜⢁⠜⠁⠀⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠑⢦⠁⢀
⠀⠀⢺⣰⠃⠀⠀⠀⠀⠀⢃⠀⡆⠀⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠈⠡⠂
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠲⡱⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⣰⡗
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢔⢳
⠀⠀⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⣢⣄⠀⠀⠀⣇⣃⣀⡀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⣠⠐⠉⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠘⠛⢁⡄⠀⠀⠀⣀⣀
⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⢀⣠⣴⣶⡀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⢙⡿⠀⠀⣿⣿⣿⣿⣷
⠻⠿⠿⠇⢀⣀⣤⣶⡺⢟⡿⢟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⠙⠛⠛⠶⠆⠀⠀⡸⠃⠀⠀⠀⠀⠀⣴⡿⢁⣴⠀⣸⣿⣿⡏
⠀⠀⠴⠚⢿⡿⣟⡭⢞⣩⠖⠛⣠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠛⠛⠃
⣶⣶⢶⣲⠽⢋⡭⠞⢋⣤⡶⠛⣁⣠⡶⠶⠄
⠯⠗⣫⡵⠚⣉⡴⠟⠉⠠⣴⡾⠛⠃⣀⣼⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠦⠴⠂
⠞⣋⣥⠶⠛⠁⣀⣴⠼⠛⠁⣀⣠⣶⠟⠋⠀⣀⣤⣬⠛⠃⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠞⠋⠁⢠⣴⡾⠛⠁⣀⣀⣾⡿⠇⠁⢀⣠⣾⠿⠛⠁⣠⣴⣿⠿⠋⠓⣢⣶⡦⠄⣀⣤⠄⠀⢤⣄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣠⣾⣿⣏⣁⣀⣠⣴⣿⣟⣉⣀⣀⣴⣟⣛⣀⣀⣤⣿⣿⣿⣓⣀⣀⣾⣿⣋⣀⣴⣿⣿⣃⣀⣶⣶⣖⣠⣀⣿⣃⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣦⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⠤⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣰⡛⣋⠣⢾⣾⡶⢾⠨⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠉⠀⠀⠈⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣷⠋⠀⠀⢩⣷⡿⣾⣿⣟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠶⠖⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⣾⡿⠟⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⣤⣼⣯⣙⠻⣷⣄⡀⠀⠀⠀⢻⣇⢻⣿⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣴⡶⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣆⠀⠀⠀⢿⡌⢿⡘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠈⣿⣿⣿⣿⡆⠀⠀⠘⣷⠀⢳⡘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⣸⠀⠈⣷⢹⣷
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢸⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⣠⠈⢿⣿⣿⣿⣷⣤⣤⡿⠀⠀⢹⣾⣿
⠀⠀⠀⠀⣀⣴⠟⣿⠀⢸⣇⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⢹⣦⠈⣿⣿⠀⢉⡛⠋⢁⡀⠀⣸⣿⣿
⠀⣰⣾⠟⠉⠀⠀⢿⡆⢸⣿⣆⠹⣿⣿⣦⣄⣀⠀⠀⣀⣠⣿⠃⠀⠀⢹⠄⣸⣿⣆⣌⢿⣿⡿⠁⢀⣿⣿⡟
⠀⢻⣿⣧⡄⠀⠀⢸⡇⢸⠏⣻⣷⣮⣻⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⢀⡀⣿⡇⢹⣿⣬⣉⣀⣠⣾⣿⠟⠁
⠀⠀⠻⣿⣿⠀⠀⣾⡇⢸⣴⠏⢸⣿⣿⣿⣿⢿⣿⣿⣷⣶⣿⣧⡤⠀⠙⢁⣿⢃⣾⡟⠛⢿⣿⡿⠛⠁
⠀⠀⠀⠟⠁⠀⠀⡟⠇⣼⡏⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⢀⠀⡄⢸⣿⠟⣿⣿⣿⣏⠛⣇
⠀⠀⠀⠀⠀⠀⠀⣇⢀⡿⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⡌⠀⡇⣼⠋⠀⠈⠙⢷⣍⣀⢙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⣏⣼⠁⠀⠀⡸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⡟⠀⠀⠀⠀⠀⠈⠙⠻⣅⣙⢦⡀
⠀⠀⠀⠀⠀⠀⡟⠀⣿⠀⠀⣸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢸⠇
⠀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠀⠸⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠋
⠀⠀⠀⠀⠀⠀⡿⡿⠀⠀⠀⠀⠘⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇
⠀⠀⠀⠀⢀⡾⠁⣇⠀⠀⠀⠀⠀⢹⡞⢦⠀⠀⠀⠀⠀⠀⠀⠘⣷⢠⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁⡞
⠀⠀⠀⠀⠘⣿⢢⡏⠀⠀⠀⠀⠀⠀⢧⡈⢧⡀⠀⠀⠀⠀⠀⠀⣷⣼⠀⠀⠀⠀⠀⠀⢠⡾⠇⢸⡇
⠀⠀⠀⠀⣰⠇⠘⣆⠀⠀⠀⠀⠀⠀⠈⣇⣀⡽⣖⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣶⣻⣃
⠀⠀⠀⠀⢿⢲⣷⠾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢠⣇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣭⢿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠀⠀⠆⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠩⢤⣀⣀⡀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡤⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⠦⣀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠄⠈⠙⠒⠒⠒⠋⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠠⢋⣰⣤⠤⠤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣾⡿⢩⡭⠛⠲⠤⠤⠤⠤⠖⠦⠀⣿⠃⠀⣰⡤⠖⢻⡄⠀⠀⣤⣴⣦⡀⠀⠀⠀⢀⣴⣶⣤⣀
⠀⠀⠀⠀⠀⣸⠇⠀⣠⠴⣿⣿⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⠓⢄⠀⠹⣄⠀⠀⠈⢿⣧⣄⣤⣶⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⢀⡴⠋⡠⠊⠀⠀⢸⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣰⠃⠀⠀⠀⠑⢄⠈⢦⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠋⢀⡞⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠇⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⣴⠟⠙⣯⠀⠀⠀⠈⣿⠙⢷⡀
⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠸⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠀⠀⠀⢰⠃⠀⠀⠸⡃⠀⠀⢠⠟⠀⠀⢧
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢦⠀⠐⠃⠀⠀⠀⠘⠃⠀⠐⠃⠀⠀⠀⠘
⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣧⣀
⠀⠸⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⠀⠀⠀⠀⠸⠿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⠤⠶⠛⠙⠳⣄
⠀⠀⠀⠀⢀⣠⠞⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⢀⡶⠛⠛⢿⢡⡄⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀
⡼⠋⠀⠀⠘⡦⠲⠦⢦⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠹⣤⠶⣦⣸⠀⠀⠀⣼⠀⠀⠀⠙⢲⡀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠈⠳⢤⣰⠇⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⣀⣀⣀⣤⠴⠚⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠘⢧⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⢦⠀⠀⠀⠀⠀⠀⢰⣞⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡴⠖⠛⠛⠛⠛⠋⠉⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⣿⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⡇⠙⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⣇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡟⢹⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠞⠀⢸⡆⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠏⠀⠀⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠⠏⣰⠏⠀⠀⠀⢸⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢸⡆⠀⠀⠀⠀⣴⠛⠁⣰⡏⠀⠀⠀⢀⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⣧⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣴⣋⢀⣸⠃

⠀⠀⠀⣠⡖⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣷⡀
⠀⠀⠀⣿⣇⣸⣿⠆⠀⠀⢀⣴⠠⣦⡀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡄⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⢸⣷⢠⣿⠇⠀⢠⡄⠀⣄
⠀⠀⢠⡝⠋⠙⢋⡄⠀⠀⣾⣿⢀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣾⣿⠇⠀⣼⡇⢸⣇⠀⠀⠀⠀⠀⠈⠋⠈⠋⠀⠀⣿⡇⢰⣿
⠀⠀⠀⠙⠀⠀⠉⠁⠀⠀⣜⠛⠙⠛⣣⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⣿⣇⣿⡿⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠹⠟⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀



⠀⠀⠀⣼⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣦
⠀⠀⠀⢿⡇⣿⠇⠀⠀⠀⢠⡄⣠⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇⠀⠀⣰⣦⣶⡀⠀⠀⠀⠀⠀⢸⣿⣰⣿⠆
⠀⠀⠈⠷⠀⠰⠋⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⡇⠀⢰⣿⡇⣿⣷⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⢠⡆⢐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⠃⢛⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠿⠃⠈⠚⢀⡈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡤⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⢦⡙⢦⡀⠀⠀⠀⠀⢀⡴⠛⠁⠀⡜
⠀⠀⠀⠀⠀⠀⢠⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢇⠀⠉⠙⠚⠒⠛⠋⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⣇⣿⣆⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣿⣷⣠⣤⡤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⢸⣿⣆⣀⣀⣀⣀⠠⢀⣂⣀⢰⡄⠀⠀⠠⠏
⠀⠀⠀⠀⢀⣿⠟⠿⣻⠋⢳⡀⠀⢸⠉⠙⠛⠿⠿⠿⠛⠋⠉⠉⣿⣷⡦⢄⠀⠑⢄
⠀⠀⠀⠀⡿⠋⣠⠞⠁⠀⠀⢳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⠃⠀⠙⢦⣈⠓⢄
⠀⠀⢠⡎⣠⠞⠁⠀⠀⠀⠀⠘⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠈⠆⢨⠃
⠀⠀⢸⣥⠏⠀⠀⠀⠀⠀⠀⠀⢇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢂⠃⠀⠀⠀⠀⡐⡐⠁
⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⡄⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⢀⡜⡟
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢎⢻
⠀⠀⠸⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣳⣤⡀⠀⠀⠀⣻⣐⢤⣀⠀⠈⠚⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣽⣭⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠶⣶⠿⢶⡶⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢿⠈⣷⠀⣠⡿⠤⠼⣧⡀⢰⠏⣸⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠹⣆⠀⠈⣇⠸⣿⠻⣧⠀⢠⡟⢻⡟⢠⡏⠀⢀⡾⢉⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠋⠀⠹⣆⠹⣆⠀⢸⡄⢿⡀⢸⠛⢻⠀⣸⠇⣾⠀⢀⡾⢁⡞⠁⠈⣻⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠻⣌⢳⡀⠀⠙⣆⠹⡆⠀⣷⠸⣷⣼⣀⣹⣴⡿⢰⡇⢀⡾⢁⡞⠀⠀⡴⢋⡾⠋⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⠀⠀⠘⢦⠹⡄⠀⠹⣆⢹⣤⣼⣦⣿⣿⣉⣹⣿⣧⣾⣤⣼⢁⡾⠀⠀⡼⢡⠞⠀⠀⢀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣍⡛⢿⡄⠈⣧⣼⠶⠞⠛⣿⣏⣉⣉⣹⣿⣁⣹⣿⣉⣉⣹⣿⡟⠛⠶⢾⣤⡏⠀⣾⠟⣋⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠈⠉⠻⣿⠋⠁⠀⠀⠀⠀⢈⣛⣛⣛⣉⣁⣉⣁⣉⣙⣛⣛⣋⠀⠀⠀⠀⠀⠉⢻⡿⠋⠁⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠲⠶⢤⣽⡇⣠⣴⡶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠷⣶⣄⡀⣿⣤⠴⠶⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠲⠶⢤⣌⣿⣿⠁⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⢹⣿⣏⣤⠴⠶⠒⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⠤⣤⣄⣀⡀⣹⣿⠀⠉⠀⠀⣀⣉⡉⠛⠻⠆⠀⠀⠿⠛⠋⣉⣀⡀⠀⠈⠁⢸⣿⡀⣀⣀⣤⡤⠶⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠶⠶⣤⣤⣍⣿⢛⣿⡄⠻⢿⣟⢻⣿⡿⠷⣄⠀⠀⠀⢀⡴⢿⣿⣿⢛⣿⠿⠃⣼⣟⢻⣯⣥⣤⠶⠶⠾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⣀⠀⠀⠀⠈⢿⠈⢹⡇⠀⠀⠉⠙⠛⠛⠒⠙⠂⠀⠀⠚⠑⠚⠛⠛⠉⠁⠀⠀⣿⠙⡸⠋⠀⠀⠀⣀⣀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣥⣌⣉⣉⡛⠓⠶⠶⣧⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⡿⠶⠚⠛⣋⣉⣉⣥⣽⣷
⠀⠀⠀⠀⠀⢠⣿⣁⠀⠈⠉⠉⠙⠛⠛⠷⠾⣆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡾⠶⠟⠛⠛⠉⠉⠉⠀⢀⣻⣧
⠀⠀⠀⠀⠀⣾⡏⠉⠙⠛⠓⠶⠦⣤⣤⣀⣀⡘⠛⣷⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⡿⠛⣀⣀⣠⣤⡤⠶⠖⠛⠛⠉⠉⣿⡆
⠀⠀⠀⠀⣸⡿⠛⠻⠶⠶⢦⣤⣤⣄⣀⣀⢉⣿⣿⢻⡄⠀⠀⠀⢀⣀⣤⡒⠤⠔⣢⣄⣀⠀⠀⠀⠀⣼⢻⣿⣏⢉⣀⣀⣤⣤⣤⠶⠶⠞⠛⠻⣿⡀
⠀⠀⠀⢠⣿⣧⣤⣄⣀⣀⠀⠀⠀⠈⠉⢉⣿⢋⢹⡾⣷⡀⠀⠀⠈⠩⣅⣉⣑⣉⣁⡭⠉⠀⠀⠀⣰⡿⣿⢉⢻⣏⠉⠉⠀⠀⠀⢀⣀⣀⣤⣤⣿⣇
⠀⠀⠀⣸⣿⣀⣀⠉⠉⠉⠛⠛⠓⠶⢶⣾⢣⣿⡘⣷⣈⣿⣆⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣠⣾⣏⣸⡏⣼⣧⢻⣶⠶⠖⠛⠛⠋⠉⠉⢁⣀⣸⣿⡀
⠀⠀⠀⣿⡏⠉⠙⠛⠛⠛⠲⠶⠶⢦⣾⣧⣉⣛⣃⣿⡏⢻⡏⠻⢦⣄⡀⠀⠀⠀⠀⣀⣤⠞⠋⣿⠋⣿⣁⣛⣋⣥⣿⣦⠶⠶⠶⠛⠛⠛⠛⠉⠉⣿⡇
⠀⠀⠸⣿⣷⣶⠦⣤⣤⣤⣀⣀⣀⣠⡏⢩⡍⢹⡛⢛⠛⣿⡇⠀⠀⠉⠙⠛⠳⠚⠛⠉⠀⠀⠀⣿⡟⢛⠛⣻⠉⣭⠉⣥⣀⣀⣀⣠⣤⣤⣤⢶⣶⣿⡷
⠀⠀⠀⠈⠙⢿⣦⣄⣀⣀⣈⠉⠉⠛⠛⠻⠿⠿⠷⣿⠷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⠷⠿⠿⠿⠛⠛⠋⠉⢉⣁⣀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡙⠛⠛⠛⠛⠛⠶⠶⠶⠶⠶⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠴⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⣹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⣀⣀⣀⣀⣈⣉⣉⣉⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢉⣉⣉⣉⣀⣀⣀⣀⣰⣿⣁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢻⣏⠉⠉⠉⠉⠉⠉⠉⠛⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠛⠋⠉⠉⠉⠉⠉⠉⢉⣿⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣖⣂⣿⡏⠙⠛⠛⠛⠒⠒⠒⢾⡇⠙⠻⠶⣦⣤⣀⣀⣀⣠⣤⡶⠾⠋⠁⣿⠒⠒⠒⠚⠛⠛⠛⠉⣿⣇⣒⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠘⣿⡛⠛⠛⠛⠛⠛⠛⢿⡟⠗⢰⡄⣀⡈⢉⠉⢉⠉⣀⡀⣴⠘⢟⣿⠟⠛⠛⠛⠛⠛⠛⣻⡟⢆⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣎⢹⣷⡶⠶⠶⠶⠶⠶⣾⡏⢐⠠⠄⡉⢁⠛⠃⠛⠃⢉⡁⠤⢐⠈⣿⡶⠶⠶⠶⠶⠶⣶⡿⢉⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡙⢿⣶⡶⠶⠶⠶⣿⣷⡟⢰⡆⣤⢉⡌⣁⠉⡌⢤⡀⣶⠘⣷⣿⡷⠶⠶⠖⣶⣾⠟⣡⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣙⠻⣷⣦⣤⣿⣏⠀⠛⠀⠟⢸⡇⢼⠁⣿⠘⠇⠘⠃⢈⣿⣧⣤⣶⠿⢛⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣬⣙⠻⠟⡋⠸⠟⢰⣶⢠⣤⠀⢠⡄⢰⣶⠘⠿⢈⡛⠿⢛⣩⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣬⣰⣀⣆⡠⠁⠄⡌⢡⡐⣆⣲⣬⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁

⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣯⡰⠲⣯⣌⣉⣭⣍⣭⣉⣨⣭⣭⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⣶⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣷
⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠙⠻⠿⢿⣿⣿⣿⣿⡆
⣠⣤⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⣿⣿⡿
⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠴⠿⠟⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡁⠀⠀⠀⠀⠀⠀⠊⢹⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⠠⡄⠈⠀⠀⠀⡀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⠀⡐⠀⠁⠀⠼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐⠀⠀⠘⠒⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢸⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠄⡀⢰⣦⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠤⡼⣿⣿⣿⣯⣥⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣿⣿⣿⣿⣄⣀⣠⣾⣿⣇⣀⣀⣀⣼⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⣀⣀⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠛⠛⠋⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠢⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣩⣨⣀⢀⣀⡀⠈⣄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠊
⠀⠀⠀⢀⠠⠐⢐⠉⠉⠄⡀⠀⠀⠀⠀⠉⠉⠀⠒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠔
⠀⠀⢀⠁⠀⠀⠀⠑⠤⣀⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠄⡀⠀⠀⠀⠀⠔⠂⡀⠀⢀⠔⠈⠀⠀⠀⠀⡐⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢤⠠⠦⠐⠛⠈⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⠠⠤⢄⢀⡀⠀⢀⣀⠀⠁⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⣀⡔⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠢⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀⠐⢄⠀⠐⠀⠈⢅⠐⠤⡀⠀⢀⡀⠠⠤⠔⠒⠂⠈⠑⠄⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢢⣄⠀⠀⠑⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⠁⠀⠁⠢⢀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠱⠘⠀⠀⠀⢀⠝⠂⢄⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠡⠂⠀⠒⠁⠀⠀⠀⠈⠐⠄⣈⠢⣀⡀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣤⠤⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⣾⣶⣦⡀⠀⠀⠀⠀⠀⣠⣼⡟⡭⠒⢿⣶⣻⢄⣀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⡀⠀⠀⢨⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⣿⣛⡿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⢘⣿⠿⣷⣄⠀⠀⠀⠀⣿⡟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣡⡄⠀⠀⠀⠀⠀⠈⠻⣿⣷⣮⣿⣷⣄⠀⠀⠘⣷⠸⡏⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠙⣿⣿⣿⣇⠀⠀⠸⣇⠙⡌⢿⣿
⠀⠀⠀⠀⠀⠀⣼⠃⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⢿⣿⣿⣿⡄⠀⠀⣿⠀⢹⡜⣿
⠀⠀⠀⠀⠀⣰⣿⠃⢸⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣤⠘⣿⣿⡿⣿⣦⣴⡏⠀⠈⣷⣿⡄
⠀⠀⣀⣠⡶⠋⢿⡀⢸⣆⢻⣷⣄⡀⠀⠀⠀⠀⠀⢸⡿⠠⠹⣧⠘⣿⡇⠠⣍⣉⣠⠀⢠⣿⣿⠁
⠀⣾⣿⠁⠀⠀⢸⡇⢸⢿⣦⡙⢿⣿⣶⣤⣤⣤⣴⣿⠃⠀⠀⠙⢠⣿⢻⣴⡹⠿⠏⢀⣼⣿⡟
⠀⠹⣿⣿⡄⠀⢸⡇⢸⣰⠟⣿⣷⣿⣿⣿⣿⣿⣋⣼⣆⡀⠀⠴⢠⣿⢨⣿⣿⣶⣶⣿⠿⠋
⠀⠀⠘⠿⠁⠀⡿⡇⣼⡏⠀⢿⣿⣿⡿⠉⠉⠉⠉⠛⢿⠁⠀⠀⣿⣷⢿⣷⣶⡶⢿⡁
⠀⠀⠀⠀⠀⠀⣧⢀⡿⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠸⡜⢰⡅⡿⠃⠈⠛⢯⣙⠀⠳⡀
⠀⠀⠀⠀⠀⢠⣟⣼⠁⠀⢠⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠉⠙⠿⣉⡢⡀
⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡇
⠀⠀⠀⠀⠀⢸⣼⠁⠀⠀⠹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢀⡿⡿⠀⠀⠀⠀⢱⡽⡄⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇⠀⠀⠀⠀⠀⠀⣰⠋⡟
⠀⠀⠀⠀⣾⡄⡿⠀⠀⠀⠀⠀⢇⠘⡆⠀⠀⠀⠀⠀⠀⢿⣸⠁⠀⠀⠀⠀⠀⣠⡏⢸⠁
⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠈⡧⠈⣲⣄⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢷⡤⣾
⠀⠀⠀⠸⡧⣴⡼⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠀⣏⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠴⣻⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠄⢤⠐⠛⣻⣿⣤⣴⣦⣅⡀⠀⣸⡟⠀⠀⢻⣼⠟⠉⠙⢿⠻⣧⠉⠻⠏⠃
⣿⣿⣶⣶⣤⣿⣟⣻⣿⣿⣿⣧⣀⣿⣇⠀⣠⡾⠃⠀⠀⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠈⠉⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰
⡆⠀⠀⠠⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⠿⡯⠁⠀⠀⠀⢀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⡄⣄⠀⣿⣇⣤⣤⣤⣼⣿⡟⣿⣤⢦⣀⠀⠀⣾⡇⢸⣏⣼⣢⣸⣿⣦⡀⢀⣶⣆⣄⣼⣿⣿⣠⣦⡀⠀⢀⣀⣿⣦⣤
⢸⣿⣿⣿⠟⢿⡼⣿⣿⣿⣿⣵⣿⣿⣾⣿⡟⠁⠈⠀⠀⠙⢿⣿⡟⣿⠙⣿⠋⣼⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿
⣿⣿⡟⡿⢀⠀⠀⣿⣿⣿⣿⣿⡉⢻⣿⡏⢠⠀⢠⡄⠀⣠⣠⣤⡄⠀⠀⠘⡧⣻⣿⣧⢸⣟⢿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⠌⠓⢸⡟⣿⣿⣿⣿⣷⣾⣿⣧⣾⠀⠸⣿⠖⢟⣿⣿⣄⡄⠀⠀⢧⢨⣙⡋⠸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡶⣶⠙⠀⢠⠤⡻⣿⣽⣿⣿⣿⣿⡇⠘⠇⠀⢸⣿⣿⣿⠗⠀⠀⢸⠘⣿⡴⢃⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⠛⢚
⣾⣿⣿⣿⣤⣤⡄⣰⣄⣀⣾⣿⣿⣿⡟⢻⣿⡇⠀⡆⠀⠈⣿⣿⡿⠀⠀⠀⢸⣀⣿⣷⡟⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼
⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⠀⣧⠀⢀⣿⣿⡇⢀⡤⢀⣴⣽⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠉⢉
⣿⣿⠏⠹⢿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⣸⣟⣣⡈⣿⣿⠃⡟⠁⣼⣿⣿⣿⣿⠁⠀⢰⣽⣿⣿⣿⣿⣿⣿⣶⣶⣾
⣿⣷⣶⣶⣾⣿⣿⣿⣛⣛⡻⠌⠿⢿⣯⠘⠿⠿⢿⣿⣟⠸⣿⠟⢴⣵⡆⢾⡿⣿⢯⣽⣇⣁⠸⣿⣏⠙⢻⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⠃⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶⠿⡿⠿⣷⣦⣉⣛⡛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠟⠿⠿⠿⠛⠻⠿⠿⠿⠛⠀⠀⠀⠐⠉⠛⠓⠛⠛⠛⠚⠛⠛⠛⠛⠿⠟⠓⠶⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠰⢶⣶⣾⣃⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⡄⠀⠀⠀⡼⢷⣦⣀
⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⠇⢈⠿⠳⠀⠀⠀⠈⠛⠉⢻⣿⠛⠛⠛⢿⠳⡄⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠀⠺

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡀
⠀⠀⠀⣠⣶⣶⣶⣶⠟⠛⠃⠀⠀⠀⠀⢀⣴⣶⣶⣶⣾⣿⣿⡟⠉⠓⠀⠀⠀⠀⠀⣤⣶⣤⣶⣶⣦⣀
⠀⠀⠀⢸⠏⠛⢻⡟⠀⠀⠀⠀⠀⠀⠙⠚⠉⣻⡟⠛⠛⠿⣿⢷⠄⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⣿⡟⢿⣆
⠀⠀⠀⠌⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣟⠀⠘⡿
⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠳⣤⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢶⠄
⠀⠀⠀⠀⢸⣷⣄⣀⣀⣀⣀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠒⠋⠙⣿⡿⠿⠿⢿⡛⠳⡀⠀⠀⠀⠀⢿⣿⠁⠉⠉⣿⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠙⢷⠀⠀⠀⠀⠀⠘⢦⡀⠀⠤⠃⠈⠀⠀⠀⠀⠀⠀⡝⠄⠀⠀⣇⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⣵⣾⡿⣶⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣀⣀⣐⠸⣿⣿⣷⣼⣿⢼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⣿⣉⢿⢏⣉⣹⡿⠿
⠀⠀⡴⠛⠡⠉⠉⣴⡟⠿⡿⠟⣳⡎⠉⠉⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣾⣿⣿⣷⠄
⠀⢰⠙⣶⣿⠁⣸⠁⢀⣌⢉⣡⠀⠹⡄⢸⣿⡞⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣉⣹⣿⣿⡿
⠀⢸⣉⣿⣿⡄⠸⡀⢸⣿⣽⣿⠀⡰⠁⣸⣿⣏⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢣⠞⣷⣿⣦⡙⣿⣿⣿⣿⡿⢁⣼⣷⡟⢢⠎⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣷⣿⠇
⠀⠀⠀⠛⣴⢛⢾⣿⢿⡿⣿⣟⣿⣿⢾⠛⡬⠃⠀⠀⠀⠀⠀⠀⠰⠸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣛⣻⣿⠃
⠀⠀⠀⠀⠀⠙⠞⣹⣿⣿⣿⣿⣿⣉⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣨⢿⣟⣿⣿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠹⠉⣹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣧⣠⣬⣭⣤⣀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣠⣤⣬⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⡻⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣿⣿⣿⣿⡿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠹⠿⠽⠟⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢻⣿⣿⣽⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣸⣿⣿⣿⡄⢸⡇
⠀⠀⠀⠀⢠⣄⠀⠀⠈⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠘⠃
⠀⠀⠀⠀⠘⢿⣿⡆⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⢻⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠉⠳⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⣹⣁⣿⢈⣇⣸⣌⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣯⡻⡿⢿⣽⣶⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣭⣭⣅⣺⢿⣗⣬⣭⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠿⠃⠀⠴⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⢾⣿⣿⢸⣿⣿⡟⣱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢺⣿⣿⢼⣿⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⣼⣿⣻⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣭⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⠃⠀⠠⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⡀⠀⠀⠼⠾⠃⠀⠀⠀⠀⣤⠀⠴⠤⠄⣤⣀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢀⣼⢡⠂⠈⡆⠀⢀⡵⠈⠀⠀⠂⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠉⠈⠙⣁
⠀⠀⠀⠀⠀⣰⠿⠀⠸⡦⠁⠁⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡿⠃⠀⠀⣀⡄⢰⠄⠉
⠀⠀⠀⠀⠐⡏⠃⠀⠀⢠⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠛⠀⠀⠈⠉⠀⠃
⠀⠀⠀⠀⠀⣈⠀⠀⠀⢠⠄⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠻⠄⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠤⣠⠀⠀⠀⠀⠀⣀⡴⠋⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠠
⠀⠋⠋⠀⠀⠠⠤⠂⢈⡆⠀⡃⢁⠀⠰⠁⠤⠘⠋⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠁⠀⣁⠉⠁⠊⠀⠀⣀⠀⠀⠀⠡⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠖⠂⠀⠀⠈⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣀⣀⡀⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠹⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡰⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢀⠀⠀⡀⠀⠀⢠⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠀⣷⡿⠷⠛⠊⠗⠎⠿
⠀⠀⠀⠀⠈⡳⠀⠀⠀⠀⢙⠛⠁⠀⣈⣿⠳⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⣀⠀⡭⠁⠀⠀⠀⠐⠃⢸
⠀⠀⠀⠀⠀⣧⣂⠀⢀⠀⠀⡄⠀⠀⠉⠻⠄⠀⡉⠀⠀⠀⠀⠀⠀⠘⠀⡉⢰⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠀⣠⢸⡷⢂⣞⣀⠀⡀⠀⠀⠀⠀⢀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⢀⡅⢸⠂⠀⠈⠉⠙⢋⣤⠀⠀⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡀⠀⠀⠀⢠⠀⠀⣧
⠀⠀⠀⢈⡀⠈⠄⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢳⣄⠀⠀⠘⣆⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣚⡸⢷⣶⡄⡀⠀⠀⠀⢱⠀⠀⠀⠀⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠀⡞⣃⣹⣿⣷⡴⡛⠏⠀⢈⡀⠀⠀⠸⠀⠀⠀⠐⢿⣷⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⢶⣿⣿⣧⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡾⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠰⠇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⣟⠀⠘⢼⠁⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⠟⠷⠖⠒⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣾⡁⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣤⠀⠘⢿⡀⠀⠀⣀⣰⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⢀⣀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⣠⣄⣀⣀⣀⣠⣤⣾⡿⢋⣾⣧⢿⣧⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣧⣤⣀⡀⠀⢀⠀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⠿⠒⣿⣿⣿⠇⢯⡷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⣤⠀⢽⣾⣷⡿⣿⡟⠛⠛⠋⠁⠀⠀⠀⠸⢿⣿⡀⢬⣷⣾⡀
⠀⠀⠀⠐⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣿⣿⣧⡐⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⣷⠀⢸⣿⢷⠀⠀⢀⡠⢀
⠄⠀⡀⠤⡴⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⢰⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⢿⠋⠈⢠⡷⠊⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣿⠁⠐⠰⠋⠉⠀⠀⠂⠀⠀⢀⡠⠃⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⡀⢀⣀⣀⠄⠀⠀⠀⠀⣸⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠈⠂⠃⢀⠁⡠⠀⢈⡀⠀⠀⠀⢀⡺⢻⣏⣠⣿⣿⡄⣀⢀⣀⣀⣀⣀⣀⡐⢿⣿⣤⣤⣴⣿⣇⡀⢀⣀⠀⢀⣀⢁⣶⣦⣀
⠀⠀⠈⠀⠀⠈⠁⠀⠐⠊⠡⠄⠒⠀⠠⢤⠶⠶⠛⠛⠻⠷⢎⠹⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⢿⣿⠧⠿⠟⠛⠉⠉⠉⠉⠉⠀⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣷⣼⣿⡆⢰⢄⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⣉⢮⡿⠋⢀⣽⣇⠀⡎⠀⠀⢣⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠿⠏⠀⠀⠿⠋⣿⠰⠘⠀⣷⠀⡼⠃⠄⡃⢸⡄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠆⠀⠀⠀⢸⡇⣇⡤⣀⡼⡌⢠⡇⢀⣞⡥⠞⠻⢻⡿⠗⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣶⠷⣿⡷⡻⡁⠠⢎⣔⡾⠿⠣⠀⠀⠉⠀⠠⠚⠿⠁⠀⠉⠁⠛⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣆⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡧⠀⠈⣷⣅⣞⢪⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠘⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⣿⣻⠻⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡃⠀⠀⡁⠀⠀⠀⠀⠀⠀⣀⠀⡿⢤⠀⠀⠀⠀⠀⠈⠀⠀⢸⣧⡟⣿⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠳⢷⡈⠀⠀⠀⠐⠂⠀⠀⠀⣾⢾⡟⢻⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢤⣾⠀⠀⢀⣀⢰⣶⢛⣤⣚⢿⣷⣾⣿⣄⡄⠀⠀⠀⠀⢀⣾⣿⣾⢨⠄⣿⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣘⢹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡄⠶⣤⡼⡠⠋⠈⢿⣿⢸⡄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⣿⣿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠈⠀⠁⠀⠀⠈⢿⣸⡧⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡄⠀⠀⢸⣿⠙⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡀⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⢸⣻⣿⣺⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣷⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢼⡇⠀⠀⠸⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⠀⢹⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡃⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⡄⠀⠀⠀⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢟⣹⠁⣠⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣆⠀⠀⠀⠁⣄⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣯⣿⠿⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣿⣿⣛⣿⣿⠉⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣿⣷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡿⣿⡇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠹⣟⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶⣶⣤⣤⣞⣀⣀⣀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠛⠛⠻⠿⠿⣿⣿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣾⣿⣶⣿⡤⢤⣤⣤⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⠀⠹⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣷⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠻⠿⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣇⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⡶⠆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣴⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣏⣀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣛⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣛⣯⣽⣷⣾⡿⠿⠪⠿⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠟⣛⣯⣷⣾⣿⡿⣟⣻⣽⣷⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠋⠉⢸⣿⣿⣿⣿⣿⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠰⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠉⠁
⠀⠀⠀⠙⠷⣦⣀⣤⠶⠞⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢀⣀⡤
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣏⣵⣵⡟⠹⠃⢀⣤⠠⠤⠶⢶⠶⢦⡤⠤⣀
⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣋⣀⣾⡟⠂⠀⠈⠀⠀⠀⠀⣤⢠⠄⢈⡘⡿⠋⢛⡓⠲⡖⢦⠤⣤⠤⣤⣤⣤⣶⣶⣖⡒⢶⣦⣄⡀
⠀⠀⢀⢹⡀⠀⠀⠀⢠⠿⠏⠀⢉⠀⠘⢛⣿⢻⡇⢹⡅⠀⠀⠀⠀⠃⣀⡴⡤⠚⠛⠛⠳⡀⠛⡄⡆⠒⠉⠀⢃⠀⠀⠀⠈⠈⠉⠀⠀⠑⢤⠡⠀⠑⢄⡀
⠀⠀⢸⣽⣧⣀⣴⣯⣿⡶⠄⠀⢀⠀⠀⡌⣿⠁⢻⡀⠱⢀⢀⡄⣘⣴⠷⠶⠉⠀⠀⠀⢀⠃⢰⠆⠰⠀⠀⡄⠀⠀⠂⠀⠈⠀⠠⢄⠁⠀⠈⠃⢦⣀⠸⠿⣄
⠀⠀⠸⣿⣏⡿⣿⠋⠅⢶⡿⢓⠈⠳⣀⠀⢿⡄⢸⣥⠀⠈⣨⣶⣟⢯⢜⠋⠁⠀⠀⠀⣼⠧⡘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡄⠘⠂⠹⡀⣄⣹⡆
⠀⠀⠀⣿⣿⣶⣿⡥⢤⡴⠃⠄⠀⠰⢾⠀⣘⡤⢸⣿⡄⠀⢹⣿⠅⠲⠀⠀⠀⠀⢀⣼⣳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠙⡀⠈⠀⠳⠈⠁⣧
⠀⠀⣸⡏⢩⠵⠛⠓⣄⣩⢃⡄⣠⣰⣏⣠⣼⡇⣸⡏⠀⡆⠀⣿⠒⢰⢁⠀⠀⠀⠄⢹⡿⡆⠀⠀⢀⢀⡆⠀⣀⠀⠀⣤⠀⠀⠄⠀⢀⠎⠁⠰⠀⠂⢐⠀⢀⡟
⠀⠀⢿⣇⡤⢾⣶⣙⣯⣾⣯⣿⢿⣿⣿⡿⢿⣱⣿⠛⠀⠀⢠⣿⠎⠀⠈⠀⠄⠠⠀⢸⡷⠄⠀⠀⠀⠉⠀⠠⠁⠀⢰⠃⠀⠀⠀⠀⠌⠀⠀⠚⠀⢀⡀⢠⢂⡇
⠀⠀⠈⠛⠃⠳⠛⠋⠉⠀⠀⠀⠀⠙⢿⣿⡿⣿⡛⠀⠀⡴⠓⠴⠆⠈⠈⠀⠀⡀⠀⢸⣧⣻⣄⠀⠀⠀⠀⠀⡀⢀⠞⢀⠄⠀⡩⠦⠀⠀⣠⢺⡄⡰⢀⡞⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣇⢠⣊⣤⣀⣠⣀⠀⠘⠁⡐⣀⠀⠐⣿⡋⣹⡘⣇⣀⣛⣻⣝⡯⠒⡫⠵⠊⠚⠶⠰⣚⣱⣺⡿⣳⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣯⣻⡘⢻⣟⢿⣶⣤⣤⣄⣀⠳⢀⣿⣇⢸⠅⣟⣿⣟⣍⣿⣶⣆⡙⠿⢶⠂⣘⣞⣿⣿⣿⣿⢯⣳⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣦⣽⣬⣞⣯⣙⠿⢿⣆⠌⣿⣿⣿⣿⣿⣟⣿⣶⣦⣬⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⠇⠛⢑⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠘⣿⢩⣿⡐⢏⠀⡾⢋⡋⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⠿⡙⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠄⢹⣿⣗⣻⡼⠃⢈⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢀⠀⢽⣿⣿⢞⣧⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣅⠸⣿⣶⡥⢀⢀⠀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢦⢸⣿⡿⠿⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⢠⣿⠿⡿⢋⠀⣀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡷⡞⢸⣿⢣⡀⡈⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣟⡄⢹⣿⡁⠁⠈⠃⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣽⡇⡅⣾⣍⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡗⠛⠲⣤⣻⡽⠗⣠⠄⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡭⢵⣷⡿⢃⠀⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⣷⠇⠀⠁⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⣊⢀⣤⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⠉⠻⠿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⠛⠿⠿⠛⠛⠛⠛⠻⠟⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠌⣻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢻⣷⣎⠁⣿⣿⣿⣿⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣼⡿⡿⢻⠛⣋⣠⣤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⠛⠛⠛⠛⣛⣙⣫⠛⠛⠃⠀⣅⣤⣤⠶⠞⠛⣫⣩⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣒⠀⠀⠐⢋⣡⣤⣤⣤⡤⠀⢰⣿⠓⣒⣢⢔⣮⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⠀⠀⠈⠁⠙⠁⠉⠀⢀⣀⠳⣏⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⠛⣛⣭⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⣛⢛⣋⣭⣥⡦⠶⠚⠋⡩⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠺⠛⠛⢉⣁⣡⠤⠴⣒⣴⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢀⠀⠀⠀⣠⡴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠤⢷⣞⣿⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⡇⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⢿⣿⣷⣀⣀⣀⣀⣼⣿⡘⠻⣿⠿⣷⣟⣡⡿
⠀⠀⢀⣠⣤⣶⡶⠿⠿⠷⢶⣶⣤⣀⡀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠋⠁⠀⠀⠸⣇⠉⠛⠛⣿⣍⣹⣌⠻⠿⠋⠀⠈⣿⡏
⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⢛⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢈⣙⣛⠁⠀⠀⠻⠆⠀⢿⣇
⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣇⠀⠀⠀⠀⠀⠈⢻⣦
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣦⣀⠀⠀⣠⠴⠒⣿
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢀⣤⣼⣿⡿⢿⣅⣀⣉⣧
⠀⢿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⢀⡼⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠸⣿⢿⣇⠀⠀⠀⢀⣾⠟⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠤⠶⣿⠇⠀⢀⣼⠟
⠀⣰⣿⣿⣿⠀⠀⢠⣾⠃⠀⠀⣿⢿⣿⣄⠀⢀⣀⣤⣤⣤⣀⣹⣷⠀⠀⠀⢸⣿⠀⣠⣿⠃
⣼⡏⣸⣿⠟⠀⢠⣿⣧⠀⠀⣸⡿⠀⠻⣿⣶⠟⠋⠉⠉⠉⠉⠛⢻⣇⠀⠀⣼⣷⡾⣿⡏
⣿⣿⢿⣿⠀⢀⣾⠋⢻⣆⠀⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢠⣿⡅⠀⣿⠇
⠹⠃⠀⣿⡀⣼⡏⠀⠀⢻⣧⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣸⣿⣇⠀⣿
⠀⠀⠀⣿⡇⣿⠁⠀⠀⠀⢻⣧⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠋⣿⢸⣿
⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⢻⡇⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣿⠀⣿⡄
⠀⠀⢺⣇⠀⣿⡄⠀⠀⠀⠀⠸⣷⡀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢸⣿⣿⠀⢿⣧⡀
⠀⠀⠈⢿⣤⣬⣿⣦⡀⠀⠀⠀⠹⣷⣶⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣭⣿⡷⠶⠾⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡖⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣧⢤⣅⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⣿⣿⡄⠘⣿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠄⣼⣿⣿⣇⣠⣿⡟⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠋⠿⢛⣟⣼⣿⣿⣷⣿⣼⣄⠀⠀⠀⠀⠀⠀⣤⣤⡴⢲⡶⢒⣿⠻⠦⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣾⣫⢽⠉⠉⠻⣿⣿⣿⢻⣆⠀⠀⠀⢀⣼⡛⣡⠒⠻⠿⣏⣽⣈⣤⡶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣉⠅⣰⠃⣼⣆⠀⠙⣷⣘⣿⠂⠀⠀⠙⢻⣿⡟⠒⠊⢙⣿⣫⣿⠏⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣧⣴⣧⣾⣿⣿⣷⣄⠈⠻⡿⠳⡀⠀⠀⢻⣿⣾⣶⣶⣿⡟⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣏⠙⠿⠿⠿⠿⣻⣿⣿⣿⣿⣿⣴⣶⣦⡈⢢⡀⠘⢿⡎⢿⡿⣿⣿⣦⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢵⣻⣟⣫⣟⣶⣿⣿⡭⢟⡻⣿⣿⣿⣿⣿⣿⣉⠦⣈⢿⡌⢳⡈⢿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢹⣿⢖⣙⣦⢔⢦⣠⠳⡟⣈⣿⣥⠴⠒⣋⠿⡻⢟⡿⣿⡀⠈⠻⣿⡀⠹⣆⢻⣿⠎
⠀⠀⠀⠀⠀⠀⢀⣞⢃⣿⣿⣷⣥⣤⣙⣉⣙⣺⣿⣟⣽⠟⣷⣏⡱⢫⠞⢁⣴⣿⣷⣴⡆⢸⡇⠀⢹⣼⣿⡄
⠀⠀⠀⠀⠀⢰⣏⡘⣌⣿⣿⣿⣽⣟⣿⣺⣗⣿⣿⡿⣁⠘⠩⣿⡵⢋⣶⡿⣃⣇⣩⡛⣿⣿⠃⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⢨⣿⣷⣾⣿⡟⡿⣾⣿⣿⣽⣯⣿⣿⣿⠉⢠⣾⡿⣷⢻⣯⣵⣾⣇⠀⣉⣉⣁⣤⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣠⡾⢻⡇⢸⣿⡄⡄⣁⣉⣉⠉⠈⢈⠈⣿⣤⣿⣿⠁⠳⠾⠏⠀⣿⣿⣄⣌⢿⣿⠟⠀⣸⣿⣿⠃
⠀⣠⣶⠞⠋⠀⠈⣿⠘⣿⣤⣁⡁⠋⡿⠘⠙⠙⠋⣿⣿⡿⣿⠀⠀⠀⠀⠈⣿⡇⢻⣿⣦⣤⣤⣾⣿⡿⠁
⠀⣿⣿⣄⡀⠀⠀⢿⡇⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣿⣦⣀⠀⠚⢃⣿⣇⣾⡟⣛⣛⣿⡟⠉
⠀⠘⢿⣿⣷⠀⠀⣼⡇⢸⣷⠇⠸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠻⢿⠁⡀⠀⠈⣿⡿⢻⣿⡿⢿⡌⢻⡄
⠀⠀⠀⢹⠏⠀⠀⡟⠣⢸⡿⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣎⠃⢳⢀⡿⠁⠀⠈⠙⠶⣤⣄⣽⡦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⠃⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣶⠘⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢦⡮⢱
⠀⠀⠀⠀⠀⠀⠀⣼⣃⡿⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡏⠉⡿⠀⠀⢾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣰⠃⠀⠀⠘⢿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⣾⢿⠀⠀⠀⠀⠈⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣸⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⠁
⠀⠀⠀⠀⠀⠀⢠⠏⢸⡀⠀⠀⠀⠀⠈⢷⠈⢦⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠀⠀⠀⠀⠀⢸⣟⠁⣸⡄
⠀⠀⠀⠀⠀⠀⢻⡷⢸⠃⠀⠀⠀⠀⠀⠈⢷⡌⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⡽⠒
⠀⠀⠀⠀⠀⠀⣸⠇⠸⣄⠀⠀⠀⠀⠀⠀⠈⠧⠴⢯⡟⠃⠀⠀⠀⠀⡏⣹⡆
⠀⠀⠀⠀⠀⠀⣿⢦⣶⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⡽⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣆
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢹⣿⡿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⣀⣠⣤⣴⡟⢹⣿⣄
⠀⠀⠀⠀⣾⠋⢀⡿⢻⠏⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⠃⠀⠛⢀⡟⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢠⣽⣿⡿⢿⠟⠙⠛⠛⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⢿⣿⡿⠿⠿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⡄⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢺⢹⡁⠀⠀⠀⠀⠀⠀⣏⣇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠈⠀⠘⠳⣤⡶⣀⣼⣿⠀⠀⠉⠙⠳⠟⠂
⠀⠀⠀⠁⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠁⠙⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣷⠀⢦⡽⠀⠀⠀⢀⣠⣤⣶⣶⣾⣷⣶⣤
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⣷⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⡿⠛⠿⢿⣿⣿⣿⣿⠿⠟⠻⣿⡿⣷⡀
⠀⠀⠀⠀⢻⣿⡟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠙⣿⢿⡇⠀⠙⣿⣻⡿⠆⠀⠀⠀⠀⠈⠁⠀⢀⡴⠛⠉⢸⡇⠀⠀⠀⠀⢸⡇⠈⣷
⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢿⣿⠀⠈⠉⠛⠛⠃⠀⠀⠀⠀⠀⢀⣾⣿⣾⣥⣀⣠⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⡜⠁⠀⡿
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣾⣦
⠀⠀⠀⠀⠀⠀⡄⢠⢆⠄⡤
⠀⠀⠀⠀⠀⠀⢱⡏⠈⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⢧⡀⢳⣄⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣾⣷⣞⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⢠⡖⠋⠉⠛⠛⠛⣋⣀⣀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣴⡟⠁⠀⢰⡀⠀⠀⠀⣿⣿⣿⣦⣀⣀
⠀⠀⠀⠀⢀⣦⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠧⣤⣤⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣸⠟⢹⡟⠛⣿⠋⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠀⠀⠻⣿⢿⡄
⠀⠀⠀⠀⡏⠀⠈⣇⠀⢸⡄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⢱⣿⡟⠛⠻⠛⠛⢻⣿⣿⣿⠿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⠀⡇
⠀⠀⠀⠀⣧⠀⠀⠸⡦⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠉⢷⣆⠀⠀⠀⢼⣿⠀⠵⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⢠⣶⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠤⠔⢚⣛⣛⠒⠀⠀⠀⠀⠀⢻⣄⣤⣶⣄⡀
⠀⠀⣴⣿⣿⣿⣿⣶⣿⣿⣷⣄⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢒⡿⡏⠓⠀⠀⠀⠀⠀⠈⠛⣿⠿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠑⠐⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠉

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣤⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⡧⠃⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢠⡄⡁⠖⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠳⠳⣄⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡙⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⢀⣴⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⠀⠐⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⡿⣷
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠞⣿⠲⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⢸⠁⢱⡈
⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣧⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠘⠁⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠀⠀⠀⠉⠉⢦⣴⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠤⠿⣿⠃⠀⠀⠀⠀⠀⠀⣠⠄⢀⠶⢲⡶⠀⣤⣀⡀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⡤⠂⠐⠎⠀⠀⠀⢸⡆⠙⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁⠘⠉⠘⠓⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠹⢸⡇⠀⠤⠂⠀⠀⢸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⡴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠹⠀⠀⢻⠟⠀⠀⠀⢰⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⡋⠀⠀⠀⣀⣠⡾⠀⡸⠃
⠀⠀⠀⠀⠀⠀⢸⡍⠳⠀⠀⠀⠀⣤⠀⠈⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠈⠋⠀⠀⠀⠈⠁⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠜⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⡟⠁⣄⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⡄⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠈⠻⠆⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠀⠈
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠈⠁⡈⠃⡖⢀⠄⢀⡀⠀⠀⣠⣤⠶⠉⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠃
⠀⠊⠈⠁⠀⠀⠀⠀⠤⠶⠀⢀⣹⠄⠀⠋⠀⢁⠈⠀⠶⠀⠰⠀⠻⠁⠀⢀⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠉⠀⠃⢘⠀⠋⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⡀⣘⠆⠀⠀⠀⡄⠀⠀⠴⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠉⠁⠀⠀⠀⠀⢈⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠄⠀⠀⠀⠀⠀⠀⣠⣟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⠀⠈⢆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⢀⡈⠛⠛⠃⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⢀⠀⡆⠠⠀⢀⠀⣄⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄⢸⣷⣾⣾⡷⠾⠷⠸⡶⠶⠈⣧
⠀⠀⠀⠀⠀⠀⠤⣤⡠⠀⠀⠀⠀⠀⠤⣴⡶⠀⠀⠐⢶⣶⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄⢀⠿⡟⠀⠀⠀⠀⠀⠀⡄⠀⢴
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢄⠀⠀⠀⠐⠈⠀⠀⠀⣤⣾⣿⠀⠃⠀⣧⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠀⢰⠆⠈⡟⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣷⣘⣀⠐⠀⡀⠀⠀⢐⠡⠀⠀⠀⠈⠹⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣘⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰
⠀⠀⠀⠀⠁⠀⡀⠸⣯⡥⠆⣼⠃⠀⠀⠀⠁⢀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠛⢀⣏⠀⠘⠛⠶⠆⣠⣮⠤⡢⠀⠀⢰⣤⠸⠃⠈⢳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⡶⠂⢸⡁⠀⠀⠀⠀⠀⠀⢀⡀⣧⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠸⣆⠀⠀⠀⠀⠀⢰⡇⠀⠀⢿⣄
⠀⠀⠀⠀⠀⢀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠘⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠛⣦⡀⠀⠀⠀⠘⢧⡀⠀⠀⠛⠃
⠀⠀⠀⠀⠸⢿⣦⡀⠀⠦⣷⡄⠀⠀⠀⠀⠀⢧⠤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⠛
⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣿⣽⣽⣿⣾⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣾⣷⣶⣶⣾

⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠲⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤


⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣷⣶⣤⣤⣄⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣠⣤⣦⣄⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠈⢿⣿⣿⣿⣶⣄⡀⠀⠈⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣄⡀⠀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉
⠀⠶⢶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⣄
⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠠⠄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢥⣀⣀⣀⡀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⡠⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠉⠓⠒⠶⠒⠋⠁⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⢃⣤⣀⣀⡠⠤⠔⠊⠁
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⣿⠟⣍⡿⠶⢤⣤⣤⣤⠤⢴⡀⢰⡟⠁⠀⣔⡠⠾⣯⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⢰⡏⠀⢀⣠⢾⣿⡏⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡼⠛⠦⡀⠈⢧⡀⠀⠈⠹⣿⣆⣀⣠⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⠞⢁⠔⠉⠀⢸⣿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡼⠁⠀⠀⠈⢢⡀⠱⡄⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠁⡰⠃⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠁⠀⠀⠀⠀⠀⠙⠀⠙⡀⠀⠀⠀⠀⣴⠟⠻⣏⠁⠉⠀⠙⣿⠻⣧⡀
⠀⠀⡀⠰⠁⠀⠀⠀⠀⠸⣆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢸⠃⠀⠀⢻⠀⠀⠀⢀⠟⠀⠈⣇
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⡀⠀⠰⠃⠀⠀⠀⠸⠃⠀⠤⠋⠀⠀⠀⠸
⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣹⡄
⢰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⡀⠀⠀⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢳⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠞⠋⠀⠠⠞⠃⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠙⠋⠁⠶⢄⡀
⠀⠀⠀⠀⠀⢀⡾⠭⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆
⠀⠀⠀⠀⠀⠸⢤⣒⣠⣤⢄⣀⠀⠀⣀⡠⠂⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠙⢿⣏⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢰⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢨⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣾⡀⣀⣠⣤⠴⠾⠧⡀⠀⢦⣄⣤⣤⣤⣿⠟⣸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣼⠉⢏⠉⠉⣿⠀⠀⠀⠙⢄⠀⠙⠻⠟⢻⡿⣏⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣼⠃⠀⠈⡇⠀⢻⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡇⠈⠳⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠈⣧⠀⠀⠈⡇⠀⠀⢧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣼⠁⠀⠀⠀⠳⡄⠀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠈⢧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠏⠀⠀⠀⠀⠀⢳⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠸⡆⠘⡆⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣷⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡆⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⢸⡀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡀⠸⡇⠀⠀⠀⠀⠀⣸⠄⠀⣸⡆⠀⠀⢀⡟⠀⠈⡇⠀⠀⠀⠀⠀⣸⠃⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢁⣴⡿⠀⠀⠀⠀⣰⣃⣀⡼⠋⠀⠀⠀⢸⠁⠀⣠⡷⠀⠀⠀⠀⢰⣇⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠎⠀⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣶⣶⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣶⣶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⡀⡀⢀⠉⠙⢷⣦⡄⠀⠀⠀⠀⣤⣶⠟⠉⢁⡀⡁⡀⠀⠛⣧
⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⣱⠋⠙⠻⠷⠉⠁⠀⠀⠀⠀⠀⠀⠉⠹⠿⠛⠉⢳⡁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢸⡀⢲⡀⠈⢻⣆⠀⣵⡄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⡅⢀⣾⠏⠀⣠⠂⢸
⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠃⠀⠈⠑⢉⠀⠀⠀⠀⠀⠀⠀⠈⡑⠉⠀⠀⠃⠀⣸⠇⠀⣾
⠀⠀⠀⠀⠀⢸⣗⠀⠘⡇⠀⠀⠀⠀⠀⠈⢦⡀⢀⠀⢀⠀⣀⠾⠀⠀⠀⠀⠀⠀⡝⠀⢀⣿
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠂⠀⡀⠀⠀⠀⠀⠀⠃⠈⠑⠉⠀⠃⠀⠀⠀⠀⠀⡀⠀⠆⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣧⡇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢻⠀⠀⠀⠀⢠⠤⠤⠐⠊⠩⠌⠀⠑⡞⠳⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠲⠶⣤⣀⣀⣀⡀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡠⢼⠀⠂⠠⠀⠀⠠⠦⠀⠀⣦⣄⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠋⠀⠘⠃⠁⠃⠀⠀⠀⠘⠚⠓⠃⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⠀⠒⠒⠚⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⣼⠋⣆⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡜⠀⠀⡼⠁⠀⡀⣀⣀⣀⣤⣴⠾⢿⡀⢸⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⢀⡾⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠘⡃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⠁⢨⠞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡤⠋⠀⠀⠀⠀⠈⠀⠈⢦⠀⠀⠀⠀⠀⣧⠀⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠳⡀⠀⠀⠀⣿⠀⠠⡄⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂⠀⠀⣿⡆⠆⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠉⠉⠉⣿⠉⡏⠉⠉⠉⠹⡏⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡷⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠃⠀⢀⡿⠀⠀⠀⢆⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⣼⠃⠀⠀⠀⠸⠀⠀⢰⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡄⠀⠀⢀⡜⠀⢰⡏⠀⠀⠀⠀⢀⡇⠀⢸⠻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣁⠤⠒⠉⠀⠀⣿⠀⢀⣀⡤⠒⠉⠀⠀⢸⡄⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⠤⠤⠤⢤⡤⠤⠟⠰⠍⢥⠤⠤⠤⣤⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠄⠀⠀⠂

⠀⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⢇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠈⢿⣿⡿⢿⡇⠀⠀⠻⣴⣿⣶⣶⠀⠀⠀⠀⠀⠘⠋⠋⠁⠀⠀⠀⠉⠀⠈⠀⠀⠀⣶⣶⣾⡿⠃⠀⠀⢰⣿⣿⡿⠋⠃
⠀⠀⠋⠘⠀⠨⠙⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠂⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢠⣴⢶⣶⠞⠁⠀⠀⢻⣷⣶⣤⣤⣤⠀⠀⠀⠀⠉⠉⠉⠇⢠⡀⢀⣾⣿⣿⣿⣿⣿⠗⠀⢰⣶⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠜⠏⠀⠉⠀⠀⠀⠀⠀⠉⠟⠏⠹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠙⠋⠛⠋⠁⠀⠀⠘⠿⢿⣿⣿⡟⠿⢻⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠁⠀⠚⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⠆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣴⣿⠀⠀⣠⣾⣿⣿⣿⣷⣶⣶⡄⠀⠀⢠⢙⡆⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣿⣿⠂
⠀⠉⠲⣶⠶⡖⠀⠀⢼⡟⠛⢻⣿⠟⠃⠀⠰⣿⡿⣿⣿⠿⠿⠟⡿⣟⠀⠀⠘⠋⠀⣘⣿⣿⣿⡇⠀⢠⠿⠟⠻⢿⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠈⠅⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠁⠈⠆⠀⠀⠀⠀⠃⠁⠤⠁⠩

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡀⠀⠀⢀⠔⠐⠦⡀
⠀⠀⠀⠀⠀⢀⡰⡁⠀⠀⠈⠫⠑⢆⠀⠀⢐⡃⠀⠀⠈⢳⡀⡏⠀⠀⠀⠉⠒⠀⢄
⠀⠀⢀⠐⠀⠀⠀⠄⠀⠢⠠⠂⠀⠘⣄⠀⠘⡆⠀⠀⠀⠀⣻⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠒⠀⡀⣀⠀⠀⠀⠏⠁⠀⠀⠸⡄⡐⠁⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣑⠇⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄
⠀⠀⠀⠀⠀⠀⡬⠀⢀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⢰⠅⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠁⠀⠀⠀⠀⠀⣥⠀⡼⠐
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡸⡀⠀⠀⠀⠀⠀⢻⢳⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠐⠂⠀⠀⠀⠀⢸⡦⠀⢀⠀⠀⠀⠀⠀⢜⠣⣔⡨⠓⡄⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣠⠹⠖⠦⡴⣤⠮⠤⠴⠓⠚⠁⠀⠀⠙⡆⠀⠀⠀⠀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⢰⠙⣄⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢸⡆⠘⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢸⠀⢇⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⡀⡄⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠤⠒⠀⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⡸⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠦⠢⡀⠀⢀⣴⣫⡽⠶⣞⣛⣛⣛⡳⠶⢦⣍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣴⢯⠞⣭⡾⢟⣋⣩⣍⣙⣛⠻⢷⣮⣙⢷⣌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⣸⢧⣐⠚⣋⣾⢟⣭⣭⣭⣭⣛⡻⣶⣌⡻⣧⡙⣷⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⡁⣛⢛⣈⡡⠿⠧⠿⠯⠴⢶⣬⣝⠻⣦⡙⢿⣌⢿⡌⢷⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢲⣶⣶⣖⡢⠤⡀⠀⠀⢠⣽⣷⣌⢻⣮⢻⣎⢻⡜⣷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣽⣶⣶⢺⡯⠥⠝⢒⡲⠃⠂⣼⠻⣦⠹⣧⢻⣆⢷⠸⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠉⠁⠀⠀⠀⣾⠀⠁⣼⠻⣷⡜⢷⡙⣧⢻⡌⣇⢿⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠄⠀⠀⠀⠀⠀⠀⠀⣿⠱⣤⣟⢷⣌⢻⣮⢻⡜⣯⢿⣹⡼⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠠⠀⠀⠀⠀⠀⠀⢰⡟⠀⡇⡛⢷⣝⢷⣝⢷⡹⣜⣯⣿⣷⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⣠⡾⠁⠀⡏⡛⢦⣝⠷⣝⢦⡻⣝⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠶⢶⠖⠚⢿⡉⠀⠀⠀⡇⡛⠷⣬⡓⢬⡳⣝⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢔⡏⠀⠀⠀⣷⠀⠀⠀⣇⡛⠻⠶⣽⣳⣿⣮⣿⣿⣿⣿⣿⠟⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢗⢽⡀⣤⣤⠴⢾⠀⠀⠀⣟⣛⣛⣛⡛⠛⠻⢿⣿⣿⣿⣛⣡⣔⣽⠟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣿⣓⢕⡿⡀⠘⢬⢦⡈⡳⢤⣀⣿⣯⣭⣭⣭⣭⣍⣏⡿⠃⠀⠈⡍⠉⡉⣸⠿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠉⠉⢣⠀⠈⠈⠳⣉⡦⢄⣀⣿⣧⣬⣬⣭⣭⣽⣽⠑⡠⠀⡜⠀⡐⢠⠇⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢂⠀⠳⣄⠀⠀⠀⠙⠚⠤⣿⡷⠶⠶⣶⡯⠊⠁⠊⣠⠞⠀⡐⣠⠋⠀⠀⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢄⠈⠓⠤⣀⡀⠀⠀⠿⠿⠿⠛⠉⢄⣀⠤⠊⠁⡠⢊⡴⠁⠀⠀⠀⠀⠀⠀⠀⣯⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣁⠂⠀⠀⠁⠉⠁⠐⠒⠃⠉⠉⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣅⣀⣐⣐⣀⣀⡨⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣴⡉⠀⠀⠠⠊⠑⡢⢄⡀
⠀⠀⠀⠀⠀⣿⣿⣿⡶⣀⠀⠀⠈⠀⠀⠘⠑⢢⣀
⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣗⣤⡀⠀⠀⠀⠠⠊⠠⠍⠢⢄
⠀⠀⠀⠀⠀⠈⢯⣿⣿⣿⣿⣿⣵⣷⢆⣀⡀⠀⠄⠀⠀⣠⠟⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢯⡿⣿⣿⣿⣿⣾⠟⣿⣶⢠⡀⠀⠀⠀⠠⠊⠉⢰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣿⣿⣿⢀⢻⡇⣿⣿⣶⣄⣀⠀⠀⠐⠁⢠⠜⡰⠤⡀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⢀⠔⠊⠉⠀⠉⠁⠒⠠⢈⠙⠏⣾⡸⢱⣿⣿⣿⣿⣟⣷⣦⣄⡀⠀⠈⠀⠎⠀⠱⣦⣀⠀⠀⢈⠱⢄⡀⠀⠀⠰
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣤⣤⣈⠑⠢⢅⡸⠿⣿⣿⣿⣿⣿⣿⣿⣯⡶⣦⣤⣀⠀⠑⢵⡈⠱⠊⠁⠀⠀⢿⣯⡒⠿⣉⠂
⠀⠀⠀⢄⠀⠀⠀⣰⣿⡌⢙⣛⡉⢰⣿⣆⠀⠉⠖⠠⡉⠻⢿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣷⣶⡿⠆⠀⠀⠀⠀⠀⠻⣷⣶⡙⣄
⠀⠀⠀⠈⠢⣄⠀⢻⣋⣁⡻⠿⢟⣈⣙⣻⠀⠀⠀⠀⠀⠁⠢⠌⡙⠻⠭⠿⠿⠿⠮⣻⡿⠋⡀⠀⠀⠀⠢⣀⣴⣷⣬⣿⣷⡌⠢⡀
⠀⠀⠀⠀⠀⠀⠙⠢⢝⡻⠿⠆⠾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⣀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣿⣶⣮⣿⣿⣿⣿⣿⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⡀⣠⣜⠁⠀⣾⣿⣿⡿⠋⠛⣻⠿⠋⢀⠔⠁⢂⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⣧⣤⣿⣿⣿⣤⣶⣾⣤⣄⡀⠀⠀⠀⢹⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣷⣶⣦⣴⣶⣶⣾⣿⢿⣷⣾⣿⣿⣿⣿⣿⠛⠳⠕⠹⣿⣿⡏⠹⣶⡇⣶⣆⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠛⢿⣿⣿⣿⡿⠟⠁⢀⣩⣿⣿⣿⣿⠁⠀⠉⠒⠠⢤⡹⣿⡏⠂⢿⢁⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠢⢀⡔⠀⠀⠀⢰⡿⠟⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⣅⠄⠀⠀⠀⢸⣟⢃⣧⡀⡈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠐⠛⠓⠀⠐⠀⠀⠀⠀⠠⡀⢀⣤⣷⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣆⠀⠀⠀⠘⢿⣿⡿⠏⠈⠛⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⠀⡀⠀⠀⠂⠀⢄⠀⠀⢠⣴⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣄⠀⠀⠀⢀⣴⢎⣻⠋⣽⠆⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⠗⠀⢀⣠⠀⡠⠞⠛⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⢸⡶⠎⠽⢛⡁⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠤⠒⢚⣧⠾⠷⢶⣶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠚⠛⠀⢀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠅⢻⣿⣷⠶⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⠿⠃⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠣⣤⣴⣾⣟⣁⣀⣈⠀⠐⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠁⠀⠀⢀⡏⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠟⠀⠀⡇⠀⣠⣿⢡⡄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⢠⣷⣾⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⢣⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⠀⠀⠙⣿⣿⣿⠇⢸⣿⣀⣀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⡇⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⣿⣿⡿⠀⢺⣿⣿⣿⣿⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⢀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣿⣿⣧⣄⢸⣿⣿⣿⣿⣿⣟⣻⣿⢿⣿⣆⠀⠀⠀⣼⠇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣷⡄⢸⡟⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡿⠿⠶⣾⣿⠿⣿⣿⠛⠳⣿⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⢿⣷⡸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠉⠁⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠘⣿⣇⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⢨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠰⠀⠀⠀⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⣼⣷⡆⠀⠀⠀⠀⠀⢀⣄⡀⢤⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣤⣤⣶⣿⣿⣶⣿⣿⣧⣀⣀⣀⣀⣠⣬⣉⠉⠹⠤⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⣀⣀⡀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⣄⠀⢀⣀⣨⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠈⠻⢿⣿⠇⠀⠁⣈⠁⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⣨⣤⡜⠷⠄⠀⠘⢿⣷⣾⣿⣿⣿⣷⣬⠻⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠛⣿⡇⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣟⡛⠂⠀⠀⠠⠚⠟⠻⢿⣿⣿⣿⣿⡿⠁⠀⠘⡿⢠⠘⣷⠀⠀⠀⠀⠀⠀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣤⣤⡄⣣⣤⣄⣀⣨⣿⣿⣭⠉⠁⠀⠾⢆⠀⠸⡇⢹⡀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡯⠿⣿⣿⣿⣯⣭⣀⡀⢀⠀⠀⠀⠀⠀⣾⣀⣆⢱⠈⣧⠀⠀⠀⠀⣼⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣽⣯⣾⠀⢿⡀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠀⢸⣇⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡟⣰⣜⢿⡄⢸⣿⣦⣼⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠆⣿⣿⣦⡀⢸⣿⣿⣿⣿⠋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⡁⠀⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⣿⣿⡝⢿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠀⣿⣿⣿⣆⠀⠐⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠘⠻⠉⠉⠁

⠀⠠⢴⣶⡾⠃⣄⠹⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢠⣀⣀⣤⡀
⠀⢀⣾⠀⢸⣆⡼⠃⢀⠀⠀⠀⠀⢘⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠙⣇⢈⡀⠀⠀⠀⠀⠀⠂⠐⢏⡏⠁
⠀⠘⠛⠀⠈⠲⡀⡿⠦⢤⡴⠿⠄⢘⡇⠀⠀⠀⡀⠀⠀⣴⠂⠀⠀⢀⡾⠷⠖⠛⠂⣾⠏⠁⠀⠀⠀⠀⣤⣀⡀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠃⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠚⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⢠⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢀⣾⡶⢲⠀⠀⠀⢶⣶⣤⡄⠀⢀⠀⢠⡤⣀⡀
⠀⠀⣼⢛⣰⡶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣄⠀⣤⠀⠀⣈⡇⠀⠀⢸⡿⣧⣠⠀⠀⠀⠈⠺⣿⠀⠀⠀⠀⢀⡀⢘⡇
⠀⠀⠛⠀⠙⣧⢀⣄⣠⢴⡀⠘⠀⠀⠀⠀⠀⠝⠀⠙⠛⠛⠉⢻⣠⣼⠿⠳⠟⠃⠀⠀⠀⠀⠀⠹⢾⡗⠒⠶⠛⠛⡌⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣠⣀⣠⣤⠀⠀⠀⠀⠶⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⢰⠃⠀⠀⠀⠀⡀⠀⠸⠉⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠑⠒⠋⠁
⠀⠀⠀⠘⢠⠾⣄⣀⣀⣿⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢤⣦⡼⡄⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠦⠤⠴
⠀⠀⠀⡆⠀⠀⠈⠋⠁⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠀⠈⠿⠆
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠦⣬
⠀⠀⠀⠀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⠟⠛⠛⠉⠉
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢿⡀
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠟⠀⠀⠀⠀⢀⣘⣷
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡆⣤⠀⠀⠀⠀⠀⠀⠈⢱⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠤⢤⣤⡤⠴⠶⠛⠁
⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠉⠛⠓⠲⠶⠶⠶⠶⡖⠀⠀⠐⠀⠀⠀⠀⣼⠋
⣿⠀⢠⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡤⠀⠀⠀⣼⠃
⠙⢶⡿⣿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⡇⠀⠀⣸⠃
⠀⠀⢀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇⠀⢠⡏
⠀⠀⢸⠇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⠀⠀⣼⠁
⠀⠀⢻⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⠀⢰⡏
⠀⠀⠀⠻⣄⠀⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡏⡿⠀⣼
⠀⠀⠀⠀⠹⡆⢸⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡇⡇⠀⡟
⠀⠀⠀⠀⠀⢿⠀⢿⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢘⡆⠘⢿⠇⢰⡇
⠀⠀⠀⠀⠀⠘⡇⠀⢀⣀⣀⣸⠗⠀⠀⠀⠀⠀⠀⢾⣁⠀⠀⡀⠸⣧⣀⡀
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⠀⠀⠈⣹⡆
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠄⡾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠿⠿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠤⣶⢴⣿⡆⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠱⢻⣿⣷⣟⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣯⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⠀⠀⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠐⢻⢿⣿⣿⣿⠃⢀⠀⢸⣿⡏⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⡯⠀⠀⠀⠀⠀⠀⠰⠃⠀⡀⠀⠀⣠⣴⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠒⠊⠵⣮⣴⣿⣿⣿⣶⣶⣾⣿⣿⣇⠀⠀⠀⠀⠀⢿⣯⡀⢸⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣿⣾⣿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠙⠛⠛⠻⠿⠿⠯⠭⢍⣙⣛⣛⢀⣻⣿⣶⡄⠀⠀⠃⠱⣦⡀⣾⣥⣀⣀⣹⣿⣿⣿⣶⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣶⣴⣶⣷⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⢠⣈⣽⣿⣽⡟⡻⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⡧⣀⣰⠲⣦⣤⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣼⣿⣿⣭⣯⡬⣟⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠛⠛⠛⠛⠉⠩⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣬⣽⣿⣿⣿⣧⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠋⠁⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠂

⠀⣀⠀⠀⣀⠀⡄⠰⣤⡍⠲⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠳⢦⣀
⣜⣉⡁⠒⠉⠘⠛⠁⠦⠄⣿⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠈⠃⠘⠢⢔⣦⣀⡀⠀⣠⠈⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄
⠀⠀⠀⠀⠀⠈⠉⣿⢻⠸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⢳⣳⡀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⣤⡾⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⡼⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⣆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⡄⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣴⣶⠿⠿⣇⠀⠀⣠⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⣧⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⡄⠸⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⡀⠐⢟⣷⣀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣶⡾⠿⣿⣿⣿⠀⣷⠀⠃⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠸⣅⣸⣨⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⢡⠏⠀⠀⠈⢿⣿⡆⢸⡆⠀⠀⠀⡸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⡟⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣧⠀⠀⢸⣿⣧⠠⣽⡄⢀⡀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠆⣰⢿⡀⢻⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣾⠋⠈⠳⠿⢿⡈⠳⣱⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣯⡾⠁⠀⠙⣎⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⠀⠀⠀⠈⢷⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⢰⠟⠀⠀⠀⠀⢸⡎⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣼⡇⠀⠀⠀⠀⠀⠘⣿⡀⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢠⠏⠀⠀⠀⠀⠀⠐⡃⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠹⡽⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠋⠀⠀⠀⠀⠀⠀⠀⠱⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢷⠄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⡰⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣽⠆⠀⠀⠀⠀⢰⠞⣡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣥⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢎⠩⠽⠧⠀⠀⠠⣾⣭⡾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣡⣿
⣿⣿⡟⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⠀⠀⠀⠀⠄⣸⠍⠀⢀⣺⣷⣿⠛⠛⣻⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⣿⣿⣷⡾⠈⠁⠀⣼⠡⣤⣤⣭⣿⣟⡙⠓⠦⢠⣿⣿⣿⣾⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣡⣿⣿⠀⢠⣼⣥⣤⣶⣿⡿⠙⣿⠟⠃⢀⡈⠹⠿⡿⣿⡿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣿⡻⣿⠀⠘⠿⢆⠉⠘⠛⠁⠈⠀⠀⠀⠀⢀⣼⣒⣒⠂⠒⣒⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠉⠀⠁⡈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠄⣚⡭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡏⠀⠀⠀⠛⢤⣀⡀⣀⣀⢀⣀⣀⣀⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠉⠉⠛⡿⠿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣁⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⣈⣰⠋
⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⢠⡜⠁
⠀⣀⣀⠤⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⣼⠋
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⣀⡤⠖⠉

⠀⢀⣀⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⢠⠴
⠀⣹⠉⣦⡱⠈⠁⠀⠀⢠⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⢻⣿⠂⠀⠀⠐⠒⣦⠀⠀⠁⠤⣀⣀⡆⣤⠆
⠀⠙⠀⠘⠲⠟⠒⠚⠃⢸⠀⠀⠀⠀⢣⠀⠄⢤⠀⠀⠀⠀⠹⢴⠦⠤⠴⢶⠂⡀⠀⠂⠀⠈⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠳⡖⠒⠀⠀⡊⠧⠀⠀⠀⠀⢀
⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣰⡶⠆⠀⠀⠀⣠⠶⡴⠦⢰⠟⠂⠀⠀⠈⠀⢸⠒⠒⠛⢸
⠀⠀⠀⠀⠁⠀⠀⠀⠸⡄⢲⣀⣠⣷⠀⣀⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⣀⣀⣀
⠀⣸⢂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠐⢢⡀⠀⢡⡀⠀⠀⢀⠾⢣⠀⠈⠃⠰⠄⠒⣾⣿⠿⠇
⠀⠙⠈⠻⠤⠤⠴⣆⠈⠀⠀⠀⠀⠂⠲⣦⠰⠶⠴⠜⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⡶⠀⠀⠒⠦
⠀⠀⢀⠀⠀⡴⠀⠀⠀⠀⠁⠀⠀⢀⣀⣰⡄⠀⠀⠀⠢⡈⠉⢁⢀⠀⠀⠀⠈⢨⣿⣏⣀⣴⡀⣄⣴⣟
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠻⠉⠁⠸⠏⢱⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠘⠟⠙⣿⠉⠛⠛
⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⣝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣦⣄⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⢸⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⢻⡟⠻⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⣿⣿⣿⣯⣿⣿⣿⣽⣯⡿⣧⣿⣿⣿⡟⣿⣽⣝⣿⣿⣟⣿⣿⣻⣿⣿⣽⣟⣿⣿⣟⣿⣽⣿⣿⣽⣿⣿⣿⣽⣿⣽⣿⣽⣿⣿⣿⣭⣿⣻⣿⣿
⣿⣿⣯⣿⣿⣯⣽⣿⣧⣿⣏⣿⣽⣯⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⣿⣿⣿
⣿⣿⠿⣿⠿⠿⣿⡿⣿⡿⢿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⠿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢸⠉⢹⠀⠀⠋⠑⠋⡤⠤⠜⠛⠛⠁⠀⠐⢄⢠⡔⠀⠀⠘⠬⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣾⡀
⠀⠀⢠⣤⣦⣧⣤⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠄⡀⠀⢸⡁⠀⢠⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⢻⠁
⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠢⢼⣸⠀⠀⠻⡇⠀⠛⠀⠙⠒⠒⠒⠛⢀⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠒⠂⠐⠓⠀⠀⠀⠙⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠛⠛⠁
⠀⠀⢀⣴⣧⠀⠀⠀⠀⠁⣤⣄⠀⠀⣉⣁⠀⠤⠂⣀⣤⣤⣤⣀⠐⠂⠤⠀⠀⠠⣶⡄⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢨⣿⣦⣀⠌⠀⠀⢾⣿⣧⡀⠀⠀⠀⠰⠌⠁⢻⣿⡏⠠⠝⠖⠒⠀⠀⠀⣿⠃⠀⠀⠈⢹⣿⣶⣶⣶⣦⡀⠀⠀⠀⢻⡗⠀⠀⠀⠐⠀⠘⣷
⠀⠀⠀⢸⠿⣿⣷⡆⠀⠀⠘⣿⡷⣿⣤⡀⠀⠀⠀⠀⠸⡟⣄⠀⢀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⠿⡿⠿⡁⠀⠀⠀⢼⢿⠀⠀⠀⠀⣦⣸⣿
⠀⠀⠠⠎⠤⠯⠝⠁⠀⠤⠴⠷⠄⠨⠧⠄⠀⠀⠀⠀⠀⠁⠈⠒⠨⠑⠀⠀⠀⠀⠿⠁⠀⠀⠀⠐⠘⠃⠀⠃⠘⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⠿⠿
⠀⠀⠀⢠⡀⢠⡄⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠤⣀⡠⠄
⠀⠀⣀⣾⡟⠉⠁⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⢠⣿⣷⡀⠀⢀⣼⣶⣧⣶⣄⠀⠈⣿⡋⠀⣀⡀⠀⠸⣾⣿⣷⡾⠀⠀⣀⡀
⠀⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠛⠛⠟⠿⠿⢛⣿⣿⠀⠀⢋⣍⣹⡏⠁⠀⠉⢥⠸⡿⠇⢹⠀⠀⢻⡇⠀⠹⠟⠒⢶⣿⣿⣿⣷⠖⠞⠿⠁
⠀⠀⠰⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠞⠛⠛⠋⠁⠀⠀⠼⠿⠟⠛⠀⠀⢠⡮⣤⣤⣤⠈⠀⠀⠼⠇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⡀⠀⠀⠠⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⣄⠀⢠⠀⠀⠀⠀⢠⣄⣄⠀⠀⠀⠐⢶⠄⡀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢠⡏⠀⠀⠴⣾⣿⡍⠉⠀⠀⠀⣤⠈⠀⠀⢤⣠⣾⣿⠄⠀⠀⢀⣾⣿⡖⠚⠀⠈⠀⠀⠀⣀⠀⠘⠀⠀⠀⠿⣷⣶⣄⡀⠀⠀⢨⡟⣿⡦
⠀⠀⠉⢸⣷⠀⠀⣶⣸⣿⠃⠀⠀⢠⡄⣾⡆⠀⠀⢠⡄⢸⣿⠀⠀⠀⣼⢹⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠈⠋⠀⠀⣤⡱⢁⡀⣀
⠀⠀⣠⣴⠏⠀⠀⠘⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣃⣄⣀⡀⠀⣸⣿⡤⠴⡆⠀⠀⠀⠀⢠⣛⣆⠀⠀⠀⢀⣀⣄⡀⡀⠀⠀⠀⠀⣉⠅⣸⠁⢸⡆
⠀⠀⢠⡄⢠⡄⢠⣄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⣄⠀⢠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣾⡇⣸⡗⣸⣿⠀⠀⢰⣃⣸⣿⡀⠀⠀⠀⠀⠾⠉⣷⣄⠀⣴⠄⠀⠀⠀⡿⣿⠀⠀⢀⠈⣿⣦⡀⠀⠀⢨⣿⣿⣦⠸⠀⠀⠀⠠⣄⢀⣼⣷⣤⡀
⠀⢠⣿⣧⣿⣷⣿⣿⠀⠀⠀⠈⣿⡿⢻⡄⠀⠀⢠⣤⣤⣽⣿⣦⡿⠀⠀⠀⠁⢸⢿⡁⠀⠈⠉⠁⣈⠃⠀⠀⠀⢿⣝⣻⢷⡄⠀⠀⠀⢈⡍⢸⣿⠚⠃
⠀⢀⡈⣃⣀⣏⣀⢹⠀⠀⣙⠀⢋⣁⠐⠀⠀⠀⠀⢀⡰⡆⠀⠹⡦⠀⠀⠀⠀⡘⢸⠃⠀⠀⠀⢰⠇⣿⠀⠀⠀⢸⡟⠏⠹⣿⠳⠀⠀⢘⣇⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠁⠁⠀⠀⡀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠉
⠀⠀⢀⠀⠀⠀⢀⡀⠀⠐⢤⣤⣿⣦⡀⠀⠀⢻⣶⡆⣾⣾⠁⠀⠀⡀⠀⢰⣆⣰⣇⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⣽⠀⠀⠀⣀
⠀⢠⣾⣶⣀⣀⣀⡓⠀⠀⠀⠀⠛⠛⠁⢠⡀⠸⣿⣧⣿⡇⠀⣤⠀⣴⢾⣫⠟⣿⠿⣿⡟⠳⢦⣠⣤⣤⣄⠀⠀⢸⠏⠀⠀⢠⣿⠀⣿⡆⠀⠀⠹⣇
⠀⢀⣨⣿⣿⣿⣿⣿⡆⠀⠀⢾⠀⢦⡀⠈⢧⠀⢻⣿⣿⠁⢠⠇⠀⠙⠲⠄⣤⡹⠿⣯⡀⠴⠂⠉⠉⠉⠙⠀⠐⠿⢤⣄⣀⣸⣿⣶⣿⣧⣤⡤⠴⠟
⠀⠉⠉⠁⠀⢈⣉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠉⠉⠉⠉⠉⠁
⠀⢀⠀⠀⠀⣻⣿⠂⠀⠀⠀⠀⠠⣶⣷⣤⡄⠀⠀⠀⠀⠀⡏⠷⠀⠀⠱⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠉⠙⠂⡀⠀⠀⠀⠀⣶⣤⡀
⠀⠀⠳⣤⡞⣿⣿⣷⡄⠀⡀⠀⠐⠛⡟⠛⠁⡄⡀⠀⠀⠀⣧⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⡟⠀⠀⠀⠀⢶⣾⣿⣿⣿⣶⣤⡀⠀⠀⢙⣧
⠀⠀⠀⠀⠧⠙⠋⠉⠁⢼⣄⣀⣀⣀⣀⣀⣀⣥⡜⠃⠀⠀⢨⠁⠀⠀⠀⠀⡿⡏⠉⣹⠛⡇⠄⠀⢸⣿⡇⠀⠀⠀⠀⢀⣈⠍⠉⠉⠈⠉⠛⠶⠶⠚⠁
⠀⠀⠀⠚⠛⠛⠛⠓⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠘⠃⠀⠀⠀⠘⠁⠁⠀⠋⠘⠃⠀⠀⠛⠛⠛⠂⠀⠀⠀⠛⠉
⠀⠈⣯⣷⠀⣠⢤⡄⠀⣠⢤⡄⠀⠀⢀⡊⠁⡄⠀⠄⣀⣰⣦⡀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⢠⢢⣤⡐⠀⠀⠀⠀⠀⢴⡆
⠀⠰⢦⠍⠀⣿⢠⡇⠀⣿⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠿⠃⠀⠹⣿⣷⣆⠀⠀⠀⠀⠀⡼⢻⣿⢷⠀⠀⠀⢹⣿⣿⣿⡃⠀⠀⠀⡀⢰⣿⠃
⠀⢻⣿⠀⠀⣿⢸⡇⠀⣿⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⢠⠄⠀⠀⠸⣿⡿⣦⡄⠀⠀⢺⡇⠘⠛⠀⠃⠀⠀⠸⢿⣿⠿⠀⠀⠀⠀⢻⣿⣿
⠀⠈⠻⠷⠾⠃⠈⠳⠶⠋⠈⠳⠦⠀⠀⠀⠆⠀⠀⠀⠠⠃⠠⠂⠀⠀⠴⠿⠁⠙⠃⠀⠠⠚⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣾⠁⢀⢀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⢀⠴⢀⠀⠀⠀⢱⠀⡤⣄⠀⠀⠀⠀⠀⠀⣍⠀⠀⠘⠇
⠀⠀⠀⢶⡀⠈⢻⣄⣀⣀⣺⠋⠙⠿⣀⣿⡞⠀⠀⠀⠀⡇⢷⠀⠀⠀⠀⠈⢯⣻⠏⠀⡀⠀⠀⠀⠃⠈⢣⡾⣧⣾⠀⠀⠹⣤⣤⣴⠃⠀⢀⢀
⠀⠀⠀⠙⠁⢰⠀⠀⣿⣿⣿⠀⠀⣼⣿⣿⣤⢤⣤⣄⠀⠈⠸⠀⠀⠀⠀⠀⠈⠃⠀⠠⢆⣆⡸⣀⡾⠀⠀⢉⣿⠁⠀⠀⣬⣛⣿⠉⠀⢀⣟⣾⣶⠖
⠀⠀⢀⠀⠙⠛⠳⣿⣿⣿⠿⣆⣔⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡓⢻⡟⠑⠀⠀⠘⣿⠀⠀⠀⢹⠁⣿⠀⠀⢬⣿⡾⠿⠋
⠀⢧⣇⢀⣤⡄⠀⣿⣿⠀⢠⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⣿⠀⠀⠀⣸⠃
⠀⠀⠈⢻⣿⣇⣴⣿⣿⠿⣿⣿⣿⡏⢀⣶⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⣿⠀⠀⢀⡟
⠀⠀⠀⠀⣿⣿⣿⣟⣥⣴⣾⣿⣿⣷⣶⣿⣿⣿⣿⡄⣰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢻⡄⠀⠀⠀⢸⡇⠀⠀⠀⣼⡿⠀⠀⣸⠃
⠀⠀⠀⠀⣸⡿⢿⠿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠛⠙⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠸⣇⠀⠀⠲⠸⣷⢀⠀⠄⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠟⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣧⠀⠀⢸⢹⡄⠀⠀⡀⣿⠀⠀⠀⢸⣿⠇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢸⠸⡇⢀⠀⡅⣿⢠⠂⠀⢸⡟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⡆⣿⠸⡀⣇⣿⠀⠀⢀⣿⠁⣼⠇⡄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣧⠃⠰⣼⠀⣤⢹⡶⡃⠀⣾⡇⣶⡏⠰⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠣⣿⣾⢁⣿⠀⠇⢘⣼⢠⢸⣿⣷⡏⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠒⢿⣿⣼⣿⠐⠀⣼⣇⡏⣿⣿⣿⠅⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠌⢿⣿⣹⡇⣶⣿⣿⣳⡿⣿⢇⣾⣷⣶⣤⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣈⣿⣽⢤⡏⣿⣿⡾⣿⣯⣾⣿⣦⠿⠋⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠿⠿⠿⡿⠵⠾⠛⠛⠛⠛⠁⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⣀⠔⣁⠉⢂
⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠠⡀⠀⠢⣀⡠⢃⠜
⠀⢀⠠⠐⠀⠀⠉⢄⠀⠘⢿⠷⠂⠀⠀⠀⠈
⠀⠵⠤⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠄⠈⠁
⢠⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠤⠤⣀
⠐⣤⠄⠐⠂⠁⡀⠄⠒⠲⠀⠐⡆⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠉⠀⠀⠁⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⢀⡀⠀⢀⡀⣀⣀⢰⡄⠶⠛⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡄⠀⠀⢂⠀⠀⠀⠀⠄⠈⠃⠙⠈⠋⠈⠉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⡀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠠⡀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⡀⣀⣀⠀⠄⠃⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠡⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⢄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣆⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠁⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢧⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠢⠑⢆⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠥⠠⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠚⠒⠈⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⠁⠓⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠁