Invader Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠈⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠸⠇⠀⠀⠀⠈⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠟⠀⢰⡆⢠⡄⠀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⣤⣰⣆⣾⣅⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣶⠀⠀⢸⣿⣿⣿⣿⣀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⡋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⢾⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠉⠉⠉⠀⢀⡀⠘⠃⠀⢰⡆⠀⠈⣿⠉⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠘⠋⠀⠀⢰⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠸⣿⣿⣷⣤⣤⣤⣤⣤⠀⢸⣿⣿⣿⣿⣿⡇⠀⢠⡀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢠⣤⣤⣤⣤⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋

⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⣿⣿⣿⣿⡿⠀⠀⢀⣤⠄⠐⣀⠀⢀⡤⠐⠒⠂⠒⣄⢾⠀⢀⡀⢤⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠤⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠃⠐⠞⠉⢠⠶⣦⠅⠀⠀⠀⡆⠀⠀⣰⠟⠺⠀⣹⣤⣎⣀⠀⣧⡊⠀⠲⢾⡀⣼⠅⡀⠘⠠⠀⠀⠓⠠⠄⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠐⠀⠀⠙⠈⠀⠀⠀⠃⠐⠀⠐⠀⠀⠀⠈⠀⠀⠈⠀⠃⠈⠂⠀⠀⠁⠛⠀⠉⠢⠤⠤⠃⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⡠⠠⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡾⠀⠀⠀⢻
⣿⣿⣿⣿⣆⠀⠀⣠⢸⠇⠀⠀⠉⢇⢀⡸⠀⡊⠀⠀⢀⡅⢠⠖⠋⠉⢉⠆⡠⠚⠉⢁⠄⢀⠔⠋⠀⠆⣼⠳⣠⠟⢀⠀⠀⠘⠃⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠛⠤⠔⠒⠉⠀⠒⠒⠂⠁⠀⠳⠤⠒⠋⠀⠋⠀⠉⠀⠐⠆⠀⠠⠄⠀⣰⣿⣿
⢻⣿⡿⣿⣿⡿⣿⣿⣶⣤⣀⣀⣀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿
⠃⣿⢇⡘⠉⠳⠆⠈⠋⠁⠉⡙⠉⠛⠛⠻⠿⠛⠛⠿⣿⣶⣶⣦⣤⣤⣤⣤⠀⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⠿⡿⢿⣿⣿⣿
⠀⠹⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢿⣿⡆⣿⣿⠛⠉⠛⠛⠛⠛⠛⠙⠋⠉⠙⠛⠃⠈⠛⠁⠀⠀⠘⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢀⣠⠞⠋⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⢢⣠⠀⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢧⠀⡤⠃⠀⠀⠀⠀⠉⠉⠛⠒⠦⢄⣀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠰⣶⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠋⡀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⢰⠃⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠃⡌⠀⠀⠀⠀⡟⢷⣤⡀⠀⠀⡀⠀⣸⠄⠀⠀⢀⣤⣿⣿⣦⠶⠂
⠀⠀⠀⠀⢸⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠏⠀⠀⢀⡤⠴⠚⠁⠀⠙⢿⣶⣿⣇⣤⣿⣤⣴⠾⠛⠋⡉⢡
⠀⠀⠀⠀⠸⣧⣘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠣⠌⠀⠀⠀⠀⠀⠀⠀⡟⠻⢟⣿⠟⠉⢀⣀⣠⡼⠃⢸
⠀⠀⠀⠀⠀⢈⣿⡿⢷⣄⣀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠄⢆⠀⠀⠀⢀⡄⠀⠀⠀⠀⡸⠛⠚⠺⡇⠀⠦⠞⠉⠁⠀⠀⡜
⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⠀⠠⠜⠃⠀⠀⠀⣸⡷⣖⡶⢶⡇⣠⣶⡄⠀⠀⠀⣴⠃
⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠃⠀⡀⢀⣀⣤⣾⡿⠁⠉⠛⣿⣆⢃⣸⠇⠀⣠⠞⠁
⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠛⢷⣦⡈⠉⢉⣴⡟⠁⠀⠀⠀⣿⣿⢷⣤⣴⡾⠁
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢿⣿⣷⣾⣿⠀⠀⠀⠀⢀⣿⣇⡴⣿⠟⠁
⠀⠀⠀⠀⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢹⣿⣤⣾⣿⣭⣿⠉⠀⠀⠀⣠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠉⠙⣿⡦⣀⠀⠀⠀⠀⠀⠀⢠⡄⣀⠀⣰⢋⣽⣿⣿⣇⣾⣿⣧⣀⣀⣾⣿⡿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⡑⠀⢀⠀⠀⠀⠈⣿⡈⠳⡾⣾⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣇⡀⠀⠙⠿⣿⠧⣄⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠤⣠⣤⣴⠞⠁⢀
⠀⠀⢰⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠹⡟⠁⠐⠒⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⡴⠋
⠀⠀⢠⣧⣀⣠⣗⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⡂⢤⠀⠀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠋⠉⠑⠀⢉⠀⣀⡀⠀⠀⠀⣼⣳⣭⣾⡗⢀⢠⣿⣯⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠁
⠀⡶⣷⣀⡸⣶⣷⡏⠙⣿⡄⠀⠀⢸⡯⠽⠛⠉⠀⠘⡛⣿⣿⠀⠀⠙⠻⢟⡀⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋
⠀⣿⠳⢼⠃⠈⠀⠉⠀⠉⠁⠀⠀⣼⢀⠶⠀⠒⠒⢒⣷⡜⠻⠃⠀⠀⠀⠀⠉⠉⠀⠚⠛⠛⠛⠛⠉⠛⠀⠋⠀⠀⣀⠀⠀⡀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⡦⣤⣄⣉⣭⣶⣿⣷⣮⣤⣤⣤⣶⣦⣴⣦⠀⠀⢀⡴⠖⢳⣿⣦⣴⡆⣼⢁⣤⡜⠧⠙⣀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠉⠉⠛⠛⠙⣷⠾⠻⠟⠗⠸⠟⠻⠟⠀⠀⢀⣠⠤⡿⠻⣿⣿⠃⠻⡄⠛⠗⠠⠿⢟⣁⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠚⠈⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠛⠛⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⣀⣀⣀⠀⠀⠀⠈⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣛⢶⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⣶⣿⣿⣿⣿⣷⡀⠀⠀⢸⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠸⣿⣿⣮⠙⠦⣄⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⠇⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠁⠀⢀⡈⠑⢦⠀⠀⠀⣼⠁⠀⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⢤⣤⣄⣀⠙⠿⣤⠏⠀⠀⣸⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣄⣀⣀⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢿⣄⣤⣿⡍⠛⠒⠲⠤⣤⣭⠀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠀⣠⠟⠀⠀⠀⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⣧⣴⣿⡇⢀⣴⣾⢧⡀⠀⠀⠐⢿⣿⠿⢃⡤⠞⠁⠀⠀⠀⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⣿⣿⣷⣼⣿⣦⣤⣤⣤⣴⡖⠋⣁⣶⡦⠀⠀⠀⢸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣠⣾⣿⠏⠀⠀⠀⣀⣾⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣶⠸⡀⢸⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣤⡾⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢸⡄⡇⢀⡿⠛⣡⣾⠃⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⠟⠉⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⢸⡇⠿⢋⣤⣾⣿⣿⢸⣿⣿⣿⣿⠟⠁⢀⡴⢿⡃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣧⠖⠉⣿⣿⣿⡏⣸⣿⣿⡿⠁⢀⡴⠋⢀⣼⠃⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢣⣿⣿⠟⢀⣴⠟⠁⣠⠟⠁⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⠀⠀⠸⣦⣤⠞⣦⣀⠀⣿⣿⡟⣼⡿⠋⣠⠟⠁⠀⠘⠁⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠘⣿⠲⣟⠋⣿⣿⡿⣱⠟⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣦⡀⠈⢷⡈⠳⣍⢹⡿⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡽⢦⣈⣿⣄⣈⣛⣡⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣼⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⢦⣀⣁⣩⡉⣩⡽⠛⠀⠀⢀⣀⣀⣠⡤⣤⣾⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⢚⡵⢋⡼⣿⠟⢳⣾⣩⣭⠿⠷⠛⠉⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣋⡰⣏⣀⣟⠚⢿⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠉⠀⣿⠋⠙⠛⠈⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠒⠒⠢⢤⣴⡏⠀⣠⣴⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⣁⣀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠈⠉⠉⠙⠓⠲⠦⣤⣠⣷⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠛⠻⢶⣤⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠋⠀⠀⠀⠀⠀⠉⠻⣷⣦⣄⣼⡇
⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠇
⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠴⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀

⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⡀⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠠⡀⠀⠁⠀⠀⣠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠆⠴⡄⡀⢀⠀⠈⢆⠀⠠⠃⠀⠀⡠⠊⠀⠄⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠁⠀⠀⠀⢰⠁⠀⠀⠀⡈⠄⡐⠸⣓⠁⠀⠀⣀⡤⣃⡘⣏⠀⣨⡵⢙⣃⠀⠀⠀⠀⠈
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⢀⠠⠀⠀⠀⠤⣄⢠⡤⠀⢀⠠⠀⡠⠄⠀⣤⠀⠰⠀⠀⠀⡰
⠀⠀⠀⠐⠢⢤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠢⠀⠀⠸⠠⠀⠰⠀⠀⠰⠉⠠⠠⠅⠨⠤⠌⠀⠐⠀⠈⠁⠀⠃⠀⠔⠁
⠀⠰⠆⢀⠀⠀⠀⡚⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠋⠉⠉⠉⡙⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢀
⠀⠀⠀⠸⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠂⠀⠀⠀⢀⣞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠠⡇⠀⠀⠎⠡⠄⡀
⠀⠀⠀⡄⢰⠆⠠⠕⠀⠀⠀⠀⠀⠀⢠⠀⠢⢀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⢀⣀⡘⠀⠈⠣⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀⠀⡀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠵⢿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣜⣥⠶⢶⡄⢈⡀⠰⠀⠀⠀⠀⡰⢧⡿⠀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠰⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡈⠀⣸⣿⣿⣶⣿⣡⡄⢢⣀⠀⠀⠀⠀⠳⠜⠁⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⠿⠛⡒⣈⠉⠙⠉⢸⡟⢻⠊⠅⠀⠀⠀⠀⠀⠀⠀⠙⡉⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⢀⠀⠀⠀⢠⠁⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠁⠀⠀⠀⣸⣇⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢨⣀⣁⠒⠀⠀⠀⠀⢸⠀⠀⢀⡤⠖⢻⠏⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠀⠀⠀⠀⠀⠸⠖⠤⢞⡀⡶⣛⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠄⠀⠀⠐⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⡜⠋⠉⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒
⠀⠀⠰⣀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⡏⣡⡶⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⠂⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠙⠈⠀⠀⠀⠀⠀⠀⣰⠛⠉⠛⠻⢍⠸⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠙⠷⠄⠁⠀⠀⠀⠀⠀⠀⡼⠟⣹⠋⢻⠦⣀⠙⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠛⣄⡀⠸⠀⢈⡗⠚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠷⢰⠀⣤⠀⡀⠀⠀⠀⠄⡃⠤⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠹⠢⡴⣄⠀⢅⠀⠾⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠠⠀⠰⣀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠂⠂⠠⠇⠀⠀⠘⡇⡄⠈⢢⣰⡀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⢠⠀⢷⠄⠘⠀⠀⠀⠀⠀⠀⠈⠑⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⡇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤
⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⠞⠁⠈⣦⣤⡇⠀⠈⠳⢶⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠾⠖⠒⠒⠻⠿⠿⠶⠶⠒⠚⠒⠛⠛⠛⠙⠛⠋⠉⠁⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⣠⡿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣠⡴⣤⣀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡴⠞⠋⠁⠀⠀⠉⠛⠾⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢹⡇⢸⡇⠀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠠⠛⣿⠀⠸⣷⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠰⠀⢠⣤⠶⠋⠀⠀⠰⠛⠁⠐⢀⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣉⠙⠛⠒⠲⣶⢾⡀⠈⠂⡀⠀⠀⠀⠀⠛⢀⣾⡿⠹⡷⣆⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⢀⣷⠾⠓⠀⡀⠁⠀⠀⠈⣀⣠⣾⣯⢤⡤⠀⢛⠑⠆⠢⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠙⢧⣀⣀⡠⠤⢐⣒⣉⣩⣥⣿⡅⠀⣰⣃⣤⣿⡄⠂⠐⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡆⠀⣀⡽⠓⠋⠉⠀⠁⠀⠈⠛⠿⠷⣶⣿⣡⠐⣿⣹⢾⣛⡇⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⢿⣿⡶⢿⠿⣿⣶⡃⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡇⠀⢸⡏⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠉⠳⡀⢳⠀⣼⣶⣾⣿⣼⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣀⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⠾⣿⣿⠛⠁⠙⣿⣿⣿⠏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⣷⣤⣤⣤⣼⣿⡁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⢆⡀⠀⠀⠀⠀⢀⠞⠀⠀⠴⠓⢤⣤⣄⡀⠀⣹⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠙⠲⠶⡤⠞⠉⠀⣀⣶⣶⣾⣿⠿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠎⠀⠀⠐⠞⠀⠀⠀⢀⣠⡴⠞⠉⠀⠉⠙⠛⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣠⣤⣶⠒⣻⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠛⣤⣤⣤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢸⣿⣿⣿⢀⣦
⠀⠀⠀⢀⣠⣾⣿⣉⣿⣿⣿⣉⣿⣷⣄⡀⠀⠀⠀⠀⢠⣼⣿⣷⣴⣿⣿⣿⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⢛⣿⣿
⠀⠀⠰⠾⠿⠿⠿⣿⠿⠿⠿⣿⠿⠿⠿⠷⠆⠀⠀⠀⢸⡇⢸⡿⠛⠛⠛⠛⠛⣿⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠶⣉⠶⠶⠶⣉⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠛⠛⠛⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠉⠀⠉





⠀⠀⣀⣀⣴⣶⣶⣶⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⣀⣿⣿⡿⠿⢿⡿⠿⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣤⣤⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄
⠀⠉⣿⣿⣷⣶⣾⣷⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⢀⣼⣿⣧⣼⣿⣿⣿⣤⣿⣿⣤⠀⠀⠀⢀⣴⣿⣿⣿⣤⣿⣤⣿⣤⣿⣥⣽⣿⣿⣧⡄
⠀⠀⠙⠋⢻⡟⠉⠋⢻⡟⠛⠃⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠿⠿⠿⠿⠿⣿⠉⣿⠀⠀⠐⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠿⠇
⠀⣤⣤⠟⠁⠘⠛⠛⠃⠘⢣⣤⡤⠀⠀⠀⠀⠀⠈⠁⠸⠿⠶⠖⠀⠶⠾⠿⠀⠉⠀⠀⠀⠀⠀⠉⠿⠉⠀⠀⠉⠉⠉⠀⠀⠈⠹⠏⠁






⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣶⣷⣀
⠀⠀⢸⡇⢠⣼⣿⣤⣤⣤⣿⣤⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⣈⣵⣶⣶⣎⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⢿⣿⣿⣿⠿⣶⣀
⠀⠀⠘⢻⣿⣿⣴⣿⣿⣿⣤⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⣿⠶⣉⣿⣿⣿⣏⡱⢾⡇⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⣾⣿⣿⣿⣶⣿⣿⣶
⠀⠀⠀⠀⠘⠻⣿⠛⠛⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠉⠻⠿⠿⠏⢁⣸⡇⠀⠀⠀⠀⠀⠀⠈⠉⢉⡹⢟⣉⣉⣙⠿⣉⠉⠉
⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⡎⠱⠎⠉⠉⠉⠶⠉⠶


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠤⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⢀⣌⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⡆⣰⣿⣿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⢸⡞⠻⣿⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⡌⠉⠛⢿⣦⣄⠀⠤⡜⢀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⣧⣾⣿⣿⣿⣿⠁⠀⢀⣤⣾⣿⣿⣿⣿⠇⠀⠀⠀⢰⠁⠀⠀⠀⢹⣿⣿⣮⣵⠊⠑
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⣿⣿⠟⣽⡄⠻
⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⠛⠛⠋⠁⠀⠀⠀⠀⠉⠿⠛⠉⣁⠤⣤⠀⢀⠎⠀⣫⣦⠄⣠⣿⡿⠃⠀⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠒⠒⢻⣯⡉⠉⢱⣶⡂⠊⣿⣶⣤⣼⢃⡎⠀⣻⣿⣇⣾⣿⠏⠀⠀⠀⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣷⣤⣾⣿⣿⣶⣿⠿⠿⣶⣿⣏⠝⠃⣾⣿⣿⣿⣹⣿⣼⣟⠁⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠀⣿⢿⣿⠿⣿⣿⣿⣯⣀⡀⠉⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣰⣿⣀⣀
⠆⠀⠈⡍⣿⣿⣿⣿⣿⣿⣿⠃⡀⢸⡀⢸⣶⠀⠀⠈⠟⣿⣿⡿⣯⣿⣲⣤⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢀⣿⣿⣿⣿⣿⢟⠹⡾⠀⣸⣇⣸⣿⡀⠀⠀⠀⠀⠈⡾⣿⡿⣿⣣⡟⢿⣇⠀⣠⣼⡏⠛⠿⠿⠿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣤⣄⣀⣼⣻⡟⠀⢻⣿⣏⣻⣿⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⢸⣿⣿⣇⢄⡀⠀⠀⠀⠀⠈⢻⠛⣟⠛⠿⣿⣿⣿⣼⠟⠁⣠⣴⢿⣽⣿⣿⣿⡿⠃
⠀⡀⣾⣼⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠈⣙⣛⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣸⢿⣿⣿⣿⣿⣇⢄⡀⠀⠀⠀⠀⠀⠸⡇⠸⡄⣴⣾⣿⣿⡿⠟⠛⠋⣿⣿⣿⣿⣿⣿⣿⡇
⣛⣿⣷⣿⣼⢿⣿⣾⣵⠆⠀⠀⠀⣠⢀⣇⠀⣿⣿⣿⣿⣿⣷⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣧⣿⣿⣿⣿⣿⣤⣠⣤⣾⣿⣿⣿⠀⣿⠁⢩⡃⠈⠁⠀⡀⠀⣹⣿⡟⢛⣿⣿⠁⠀⠀⣀⣴⣶⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣇⠈⣷⣴⣀⣜⡁⣀⣿⣿⠀⢸⣿⣿⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⡏⠄⢿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡇⡄⠀⠀⠛⠃⠀⠀⠀⠉⠉⠛⠛⠛⠉⢧⠈⡀⢁⣽⣾⣿⣿⣶⡌⣿⣿⢀⣨⣿⣿⠙⠳⠾⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠛⠻⠿⠿⠿⠿⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣆⣾⣿⣿⣿⣿⣷⣿⠟⠛⠃⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⣾⡾⣿⣷⡄
⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠰⣦⣶⣶⡄⣀⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀⣾⣽⣶
⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⢀⠸⣿⣿⣧⣿⣿⣿⣿⣿⡿⣿⠟⣱⣿⣿⣿⣿⣿⣿⡼⣿⣇⠀⠀⢠⠋⠙⢿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣠⣮⣛⠿⣿⣿⣿⣿⣿⡇⢿⣿⠂⢀⡟⠀⠀⠀⠹⡄
⠀⠀⠀⠈⠛⠿⠿⠛⣁⠀⢀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣡⣸⡿⡿⣿⣿⣦⣍⡛⠿⣿⣷⣾⣧⠰⣾⡁⠀⠀⢀⣤⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣷⡟⣹⣿⣿⣿⡿⢋⢞⣵⣿⣿⣿⣿⠿⣾⣤⣿⠥⠍⢱⠇⣹⡤⠞⠋⠻⡟⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣻⣾⣿⣿⡿⠁⡴⣣⣼⣿⠏⠛⢿⡃⠈⠆⣰⠀⠀⠀⠿⠚⠉⠀⠀⡀⠀⢹⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⡟⢛⣿⣿⣿⠋⢠⣾⣿⣿⡿⠋⠀⢈⣽⣿⣿⣿⡐⢷⣼⠃⣦⡀⢉⢠⣤⠀⢺⣿⣾⣿⠿⠟⠙⠈⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⣡⣴⣿⡿⣟⣡⣤⣿⣿⣿⠟⡁⠀⣰⣿⣷⣭⣍⡙⠓⢿⣿⣷⣶⡎⠙⠚⠁⣠⣾⣿⣻⢿⡆⠀⠀⠀⢹⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣴⣾⣿⠟⣫⣾⣿⣿⠛⢿⣿⣿⣿⣿⣩⡟⡴⢁⣤⣿⣷⣶⣶⣾⣿⣷⠌⠉⠠⣿⣷⣶⣶⣿⣿⣿⣏⠁⣼⡇⠀⠀⠀⣸⢦⠀⠀⠹⣆
⠀⠀⠀⠀⣶⣿⡿⣣⣾⣿⣿⡿⠋⠀⠀⠉⠻⣿⣿⣿⡜⢡⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠻⠛⠀⢿⣿⣄⠀⢠⣹⣷⠀⠀⠀⠹⣄
⠀⠀⢀⣼⡿⢫⣾⣿⣿⣻⡿⠁⠄⠀⠀⠀⠀⠘⢻⡿⢡⣿⣿⣿⣿⣿⠟⣠⣶⡟⠁⠀⠀⠀⠉⠀⠟⠋⠁⠀⠀⠀⠀⠀⢹⣿⠀⠀⢿⡈⣇⠀⠀⢰⣿⠆
⠀⠀⣸⡿⣱⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣠⣦⡟⣰⣿⣿⣿⣿⣿⣵⣿⡿⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⣧⣹⡀⠀⣸⢣⠏
⠀⣸⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣴⠟⠛⠉⠉⠉⢻⣿⡟⠀⠀⠰⠄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣨
⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣼⣿⣀⣀⢀⣦⣰⣼⣿⡇⠀⠀⠀⠀⢸⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⢡⡏
⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⣟⣼⠿⠛⠛⠉⢻⢹⡿⠟⢻⣿⣦⣄⣠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣼⠃⡞
⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⠀⠀⠀⠀⠀⣸⠃⠀⠀⡇⠘⢻⡟⠃⠘⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢠⡏⡸⠁
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⠄⢠⢒⠁⠀⠀⠁⠀⠤⢾⠄⠀⣠⣿⣷⢺⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡞⢠⠁
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠁⠀⠈⠁⠀⠈⢫⠭⠽⠽⠝⠛⣻⣇⣠⣾⣿⣯⠋⢛⣼⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠹⣿⣤⣤⣿⣴⣤⣤⣤⣤⣤⣤⣴⣿⣷⡿⠟⠛⠉⠝⠛⢛⣋⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⣿⣿⣿⣿⣿⠿⣻⡿⠋⢹⣿⠽⣯⣿⣶⣶⣾⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⢠⣟⡔⠐⠁
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⢻⣿⣿⢏⣴⡿⠋⣠⣶⣤⣿⣈⣿⣿⢿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⠀⡟⠀⠀⠀⢸⣿⢿⣿⣯⣄⣀⣹⣿⡉⠉⠻⢿⣿⣿⣿⣿⣿⣛⣿⣴⠶⠂⠀⠀⠀⠀⠀⠀⣾⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠈⠁⢻⣿⣿⣿⣿⣇⡀⠀⠀⠈⠉⠹⣯⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⣿⣿⣿⣿⣶⣤⣤⣀⣈⣻⣷⣄⣀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠠⢯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⠉⠉⣿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠉⠀⠟⠋⠁⠁⡸⠛
⣤⣀⣀

⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣠⣴⡶⠟⠋⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦
⠀⠀⠀⠀⠀⠀⣸⣴⡾⠟⠋⠁⣴⠿⠛⠛⠒⠲⢤⡈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠉⠲⣄⠈⠛⢷⣄⠀⠀⣠⡾⠛⠉⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡇⠀⠀⠶⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠙⠻⣾⡉
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠠⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⡓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⣿⡇⠀⣀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⣀⡈⣷
⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠻⣖⠒⠚⠋⠀⠀⠀⣴⠾⠒⠋⠉⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢻⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢠⣀⡂⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡹⠛⠂⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢸
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⠿⠋⠁⢸⣿⡿⠛⠋⠉⠉⠉⠛⢷⣄⠀⠀⢲⠽⣿⠒⠶⠶⠞⠛⠁
⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣿⠟⠁⢀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣼
⠀⠀⠀⠀⠀⢸⠇⣿⣿⣿⡿⢁⣴⣾⣿⠀⠀⣿⣠⣤⠴⠶⢿⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⠀⣿⣿⢏⣴⣿⡿⢋⡇⠀⠀⠉⠀⠀⠀⠀⢸⡇
⢀⡀⢤⠀⠀⣿⢠⣿⣣⣾⣿⠟⠀⣼⠁⣀⣀⣀⣠⣤⠀⠀⢸⡇
⢸⣿⣆⠀⢠⡏⠸⢿⣿⣿⠃⠀⠀⠛⠛⠉⠉⠉⢠⡏⠀⠀⠀⣿
⠈⣿⣿⣆⣼⠁⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⡿
⠀⢹⣿⣿⡇⠀⢰⠐⣴⠖⠛⠋⠉⡀⠀⠀⠀⢠⡏⣠⡶⠛⠁
⠀⢠⣿⡿⠁⠀⡿⣀⠸⣄⣀⣀⣀⡀⠀⠀⠀⠼⠛⠁
⣴⠏⠀⠁⠀⢀⢱⢅⣃⣿⣿⡿⠿⠃
⠁⠀⠀⠀⠀⢈⠨⡄⣿⠉⠁⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⣿⣿⣿⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⠀⠀⠀⠸⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡾⠟⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠴⣏⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⢠⠞⠛⣶⢤⣄⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⢀⡏
⡞⠀⠀⠘⡆⠙⣏⠻⣦⣄⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⣸⠁
⡇⠀⠀⠀⢳⠀⢸⠀⢻⠘⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⡇
⡇⠀⠀⠀⢸⠀⢸⠀⡿⠀⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣸
⣧⠀⠀⠀⣸⠀⣸⢀⡇⣼⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠴⠀⢠⣯⣕⣒⣒⡲⠦⢤⣀⡀
⠘⣆⠀⢠⠃⣰⡧⠞⠻⡄⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣼⣿⣿⠛⠻⢿⣿⣶⣤⣍⡓⠦⡀
⠀⠈⠙⠋⠉⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣀⣽⠶⠤⠤⠴⠖⠉⠀⠀⠀⢀⣼⣿⣿⣿⣼⣀⣾⣿⣿⣿⠿⠟⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⢀⡤⠷⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⡶⠦⣤⣤⣤⠶⢶⣾⣿⣿⠿⠟⠛⠉⠁⢀⣀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢣⣽⠿⠟⣛⣋⣩⠥⠤⢶⠶⠿⠿⠛⠛⠒⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⡨⢿⠉⠀⢠⣾⣤⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣐⣢⡞⠇⢸⠀⠀⢸⣿⣿⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⣧⠂⢸⠀⠀⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⢤⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⡇⡃⢸⠀⠀⠸⣿⣿⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⣿⠀⢸⠀⠀⠀⠈⠛⠁⣷⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⣛⣛⡛⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⠙⢷⣶⣶⣶⣟⣀⣀⠀⠀⠀⢀⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠘⣿⣿⣿⣿⠀⠈⠉⠉⠉⠹⣿⣦⣤⣤⣤⣤⣤⣤⣴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠀⠀⠈⠻⢿⠿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇
⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢿⡴⠖⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⢤⡀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠤⠐⠒⠒⠠⠤⣀
⠀⠀⠈⢻⣧⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⠀⠈⠑⢄
⠀⠀⠀⠀⠻⣷⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈
⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠁⠀⠀⠀⠉⠉⠓⢦⡀⠀⠀⠙⠂⠀⢸
⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠦⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠤⠀⠉⠓⠦⠤⠀⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣦⣤⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠰⡿⠟⠫⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠙⠲⠤⢄⣀⣀⣀⡤⠔⠚⠁⠀⠀⠀⠀⠀⠀⣠⣴⡖⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⣯⠘⠃⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⣿⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢀⣠⢴⡟⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠐⣿⣅⢀⣽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⣤⣄⠸⣮⡳⠶⢚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢿⠓⣶⢿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⡆⢹⡾⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠈⢧⣬⡷⠋⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⢹⣿⡿⠁⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠀⠀⠀⣀⡤⠚⣿⣿⠇⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡶⠒⠋⠁⠀⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠄⠀⠀⠀⡄⢀⣀⣠⣀⣀⠀⠄⠀⠀⠀⠜⠀⡀⠀⠀⡠⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠠⡀⠀⠀⠈⢄⡠⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⣀⠄⠀⠀⠀⠀⠈
⠀⠀⠁⠀⢄⠀⠀⠀⠀⠈⠢⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡠⠂
⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠁
⠀⠀⠀⠀⠈⠀⠂⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣁⡀⠀⠄⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣟⠙⣷⡈⡆⠀⠀⠀⠀⡎⣰⡟⢙⣿⡇⡅⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⡄⠈⢳⡀⠀⠀⠀⠀⣰⠋⠀⣼⣿⡇⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠒⡘⢿⣿⣶⣤⣷⡀⠀⠀⣰⣧⣴⣾⣿⠟⡐⠂⠀⠄⠀⣀
⠀⠀⠀⠒⠀⠉⠀⠀⠀⠀⢀⠄⠒⠄⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⡠⠊⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠐⠠⡀
⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⡠⠊⠀⠀⡠⢂⠀⠀⢀⡀⣀⠀⠀⠀⠢⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡐⠀⠀⠡⠄⡀⠀⢀⡀⠔⠁⠀⠑⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠄⠀⠀⠐⡄⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠿⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⣆⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣀⠀⠀⠈⠂
⠀⠀⠀⠐⢄⣀⠀⠀⠀⠀⠀⠀⣤⣴⣾⠿⣛⣯⡥⠶⡂⢂⠀⢰⠀⠀⠀⠀⣀⠴⡏⠀⠰⠍⠂⠀⣀⠀⠀⠀⡠⠦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠴⢀⠀⠀⠐⠃⠀⢀⣴⠾⣛⣭⠶⠛⠋⢁⠀⠀⠱⡀⠷⢎⠀⠀⡔⠺⠁⠠⠑⠐⡀⠀⢀⠄⠀⡄⠀⠐⠀⠀⠀⠠⠘⠛⠀⠀⠤⠒⠀⠋⠠⠗⠛⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⢐⠘⠓⠛⠉⠈⢢⠀⠀⠀⣀⠀⠒⠀⠀⠈⠆⠀⠳⠄⠀⠀⠀⠀⠀⠀⠁⠠⠚⠘⡄⠀⠀⠀⠇⡀⡄⠀⡲⠀⣒⡀⣀⡀⢊⠀⢲⡀⠅⢀⠄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⢣⣀⠠⠐⠓⠒⠉⠀⠀⠀⠀⢀⡴⢃⢠⠑⡀⠀⡄⠀⠀⣀⣄⡀⠀⢀⣠⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⢩⣟⠁⠀⣿⣟⣆⠙⢠⣾⣏⣉⣽⠀⣸⣣⡆⠀⢀
⠀⠀⠀⠀⠀⠀⡐⠒⢄⠀⠀⠐⢤⣄⣀⠀⠄⠲⠋⠁⠊⢹⣯⠿⠃⣰⠌⠋⢩⡄⡌⠙⠛⠛⣵⡞⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡇⠐⠀⡄⠀⠀⠈⡲⢆⠢⠀⠀⠀⠀⠀⢀⡡⠐⠈⡁⢀⠈⣲⡀⢀⠀⠀⢀⡽⢃⠜⠁⢀⣀⡸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢰⠁⣸⣇⣀⡠⠀⠐⠈⠁⠀⣀⠙⠣⢙⠀⠄⠀⠀⠀⢀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢿⡌⠀⠀⠰⠆⠤⠒⠉⠀⣈⣴⡋⠀⣬⣭⡕⠀⣍⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠑⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠉⠙⣇⣀⣀⣤⡴⠾⠉⠀⢻⣷⠏⠀⠈⠃⠀⠀⠀⠀⠀⣙⣦⠀⠀⠀⠀⠀⣟⡺⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠦⣀⠜⠀⠀⠀⡤⠐⠀⠀⠀⠀⠈⣉⠽⠫⣀⠉⡇⠈⣧⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⣐⠶⣅⠈⢀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠰⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠧⠀⠀⠹⡜⠓⠀⣈⣇⡠⠚⡇⠠⠀⠤⠠⠀⡠⠋⠀⠈⠳⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⡉⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠸⡀⠀⢦⠀⢰⠄⠀⢠⠉⡀⢀⠠⡾⠆⠈⠲⢤⡟⠀⠀⠀⠀⠀⡦⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢎⡀⠀⠀⠀⠀⢂⠉⠁⢈⢣⡆⠀⠲⡎⠀⠀⠀⠀⠀⠀⢡⡀⠀⠰⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⢄⠈⠑⠖⠋⣼⡇⠀⠀⡋⠹⣶⣄⣀⠀⠀⢸⢱⠀⠀⢠⠀⠀⠃
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠀⠀⠀⠀⠙⠢⢄⣈⢀⢀⢉⠜⣿⠲⠚⠁⡌⠀⠀⠀⠃⠀⢨⡌⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠎⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠌⢣⣄⣨⡷⢤⡄⢰⡀⢀⡀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡐⠀⠈⠀⠀⡠⠠⣥⠋⣁⡀⠀⠀⡰⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠈⠐⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⠀⠠⠐⠈⠢⡴⠒⢎⠀⠠⣹⠀⡀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢤⠀⠀⠈⠀⠀⠀⣀⡄⠀⢸⡇⣠⠘⠀⠀⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇⠀⠀⠀⠀⠂⠀⡸⠂⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠤⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠄⠀⠨⢀⠴⠃⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⢦⡘⠓
⠀⠀⠀⠘⠑⠀⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠊⠀⠀⠀⠀⢆⠢⢈⠂⢀⠀⠀⢀⡀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣂⡀⠊⠉⠀⠀⠀⢀⡀⠈⡽⠰⠀⠀⠀⠀⠀⠀⢳⣀⢉⣀⢀⣀⡄⠈⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠿⠻⠿⠿⢿⡿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣞⣀⣀⣴⣦⣶⠶⠶⠶⠶⠿⣿⣿⡿⠿⠿⠿⠿⠷⠶⠶⠾⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⢿⠁⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠐⣧⣤⠶⠛⠉⠀⠀⠀⠀⢸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡽⠿⠿⠟⠓⠒⠶⠶⣤⡄⠀⠀⠈⡇⣼
⠀⠀⠀⠀⠀⠀⣠⣴⠿⠟⠋⠁⠀⠀⠀⠆⠉⠀⠀⢰⡿⠁⠀⠀⠀⣷⡏
⠀⠀⠀⢠⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣤⡀⠀⣿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⣽⢧⡀⢂⡠⠐⢴⣿⡟⠁⠀⠉⣿⣷⠀⡏
⠀⠀⠀⠀⣿⠀⢹⣄⠀⠀⢸⣿⠀⠀⢀⠀⠀⣿⡀⣧
⠀⠀⠀⠀⢹⣆⠀⠻⣆⠀⠈⣿⠓⠀⠁⠀⠀⣿⠀⣿⠀⠀⠀⠀⢠⠄⣄⡀
⠀⠀⠀⠀⠀⠻⣆⠀⢹⡆⠀⠹⣧⣄⣀⣠⠞⠁⠀⠸⣷⠷⣧⣀⣴⣦⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⠀⠈⣉⣠⠴⣶⠚⠛⢻⣻⣿⠿⠛⢦⠀⢈⠀⣀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠔⠊⠁⠀⣼⠋⠀⠀⠘⠃⢹⡏⠀⠀⣱⣌⠈⢉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⢽⣏⣉⠁⠄⢻⡆⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣾⣇⣀⣀⣀⣼⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠉⠉⠉⠉⠉⠀⠁⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡾⠿⠖⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⠀⠀⠄
⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⡄⠀⡇⢀⠔⠤⣀⡸⠀⠀⣼⠂⢸⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠠⢀⢰⠘⠃⡖⠀⠀⠈⢣⠁⠀⣧⠀⢈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠧⠀⠀⠀⠘⠰⠄⠁⠠⠿⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢙⠀⠀⠀⠀⢸⠁⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡀⠀⠈⣀⡀⠀⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠐⣄⠀⠀⢀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠔⠁⠀⠀⠀⠀⠈⠙⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢆⠀⠀⠀⠀⠀⠀⡘⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⢰⣧⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⣿⣷⣶⣄⡀⠀⡟⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⢶⣉⣉⣀⣄⠀⣉⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢻⣿⣇⣠⣤⡤⠀⣉⡌⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣿⣿⣿⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⣿⣿⠇⣷⣾⣿⡏
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⣴⣿⣿⣿⣷⡄⠀⢂⡀⠀⠀⠀⠈⠁⠀⠀⠀⣿⡿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠂⠀⠐⢻⣿⣿⣿⣿⠇⠠⠟⠋⠈⠁⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣥⡀⠄⢀⡠⠤⢚⣭⣍⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⢿⡟⢀⣼⣦⠀⠺⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣶⠂⠰⣾⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠁⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⡂⢐⡉⠀⠀⠀⠀⠀⠲⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣦⡀⠀⢰⡿⢿⣿⣶⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⣀⣠⣤⣶⡶⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⡿⠗⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣻⣭⠿⠟⠛⢻⡈
⠀⢠⣤⣀⣴⢾⣟⣧⠴⠖⠋⠁⠀⠀⠀⠀⠀⢧
⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣻⣛⣛⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡖⢚⡋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢉⡓⢲⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⣀⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣄⢵⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⣼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠧⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡤⢎⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡱⢤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⠞⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⠓⢖⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣞⢁⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣈⣫⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡤⢉⢜⡿⠚⢓⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⡛⠛⢿⡡⡌⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠙⠛⠋⣀⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⡉⠛⠋⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠺⣿⣿⣽⣯⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣾⣯⣿⣿⠛⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⣿⡿⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢿⢻⣆⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⡟⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠃⢻⣎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣱⠟⠘⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠹⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⠏⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⣿⣿⣧⡀⢀⣼⣿⣿⠃⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⢿⣿⣷⣾⣿⡟⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⣿⣿⣿⠏⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡟⠁⣠⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⢀⡞⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⢀⡴⠋⠙⢦⡀⠙⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠉⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠙⠻⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣈⠙⠿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠛⣉⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡙⠻⢿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠙⠻⢿⣿⣿⣛⣛⣭⠥⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢭⣙⣛⣻⣿⣿⡿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠙⠛⠛⠛⠛⠛⠿⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⣛⣛⣙⣛⣟⣻⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣾⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⢠⣿⡟⣱⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣃⠀⠀⣰⣿⡟⣴⣿⠏⠀⠀⠀⣤⣀⠀⠀⠀⠀⡛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⣿⢏⣼⣿⠃⠀⠀⠀⢰⣿⡿⣷⣆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣼⣿⢋⣾⡿⠃⠀⠀⠀⠀⠘⣿⣧⢻⣿⣆⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢣⣾⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣧⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣡⣿⡟⠀⠀⠀⠀⣀⣀⠀⠀⠀⠸⣿⣧⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣱⣿⠟⠀⠀⠀⢀⣼⡇⢼⣦⡀⠀⠀⠹⣿⣇⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣴⣿⠏⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠹⣿⣆⢻⣿⡄
⠀⠀⠀⠀⣠⣤⣤⣤⣄⡛⠋⣼⣿⠃⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⠁⠀⠀⠀⠀⠹⣿⣆⢿⣿⡄
⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣷⣮⡁⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣎⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⢹⡇⣻⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⡎⢿⣷⡀
⠀⠀⠀⠀⠀⣤⣶⣮⠉⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠸⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⢿⣷⡀
⠀⠀⠀⠀⠀⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣈⣭⣴⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢛⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⣴⣿⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠿⡆
⠀⠀⠀⠀⠀⠀⣿⣧⣰⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣠⣄⣤⢳
⠀⠀⠀⠀⠀⠀⢸⠿⡟⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⣀⡀
⠀⠀⠀⠀⠀⢀⣶⠟⠁⠀⠻⣿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣿⣧⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠛⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠛⢿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣤⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢻⡟⠻⣿⣿⡿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⢿⣿⣿⠟⢻⡙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢻⠄⠠⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⣴⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣯⣬⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠈⣿⣿⣿⡝⢏⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠳⠖⠶⠃⣸⣿⣿⣿⣦⣕⣦⡀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣲⣦⣷⣐⣏⣿⢿⣿⣿⣿⣿⣷⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠶⣎⠓⣮⠁⠙⣿⡝⢿⣿⡾⠋⢹⣏⠉⠉⣩⡿⢿⡿⠋⣰⡟⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣝⢦⠘⢦⣈⣦⢾⣻⠟⠂⠿⠠⠖⢙⣟⢻⠾⣍⠀⡴⢁⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠓⠾⣶⠿⡅⢸⡏⠀⠲⢲⠀⠘⠉⠀⠹⠀⣿⠏⣠⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣶⠟⣴⣧⣨⡥⠤⣤⣾⠤⠀⠠⠤⣤⡴⢃⣴⠧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⣯⣴⣿⣿⢹⡦⠴⢂⢹⠀⠀⣂⣠⡟⢡⣾⣿⣶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠹⣿⡟⠛⠛⠾⠷⠶⢤⣽⣥⣤⣽⣿⣷⣿⣷⠁⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣼⡏⠉⠉⠉⠉⠛⢓⣾⣟⡮⣅⡿⣾⠏⠙⢾⡅⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠯⠿⣽⣿⣿⢿⣿⣿⣿⣾⡿⠟⠀⣠⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣮⣥⣦⠿⠙⢿⣿⣶⣾⡿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⠲⣾⠻⣟⢀⣰⠟⠉⢹⠄⠀⠀⢉⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠉⠙⠲⣿⠾⠽⠛⡇⠀⠀⢸⡆⠀⠈⠁⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠛⠶⢦⣿⠀⠀⠀⡇⠀⠀⠀⣧⡀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢀⣴⢿⣿⡷⠤⠄⠀⠀⠀⠀⠀⠐⠦⣀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⣿⣿⣷⡄
⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣌
⠀⠀⠀⢀⡾⠋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿
⠀⠀⣠⠏⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠙⠓⠦⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠙⠆

⠀⠀⠀⠀⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷
⠀⢀⡴⢻⣿⣿⠟⠶⠤⠤⠴⠄⠀⠀⠀⠀⠀⠰⠚⠉⠉⣻⣿⡿⠶⠇⠀⠀⠀⠀⠀⠀⠠⣤⣹⣿⡇
⠀⠀⠀⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣧
⠀⢀⣴⠏⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⢷⡀
⠀⠾⠁⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠰⠞⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠈⣧
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀
⠀⢀⣴⣾⡿⠶⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢽⣷⣶⠊
⡠⠋⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⣾⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣥⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣷
⠀⢸⠏⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⡾⠟⠛⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠒⠛⠛⠛⠋⠙⠛⠛⠛⠒⠒⠶⢯⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⣀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢠⠞⠉⢳⡲⣤⣄⣸⡇⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⢠⡇
⡞⠀⠀⠀⢷⠀⠻⡍⢳⡦⣄⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣼
⡇⠀⠀⠀⢸⡆⠀⣧⠀⡇⠸⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⡇
⡇⠀⠀⠀⠀⡇⠀⡿⠀⡇⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡾
⣧⠀⠀⠀⢀⡇⠀⡇⢸⠇⣸⠇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡤⠀⢰⣗⡒⠲⠶⠤⣤⣀⡀
⠸⡄⠀⠀⡸⠁⣰⣣⡾⢾⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣾⣿⣿⠿⢿⣷⣶⣤⣍⡙⠲⢤⣀
⠀⠙⠢⠾⠷⠚⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣀⣀⣤⠖⠋⠀⠀⠀⠀⣼⣿⣿⣿⢠⠄⢸⣿⣿⣿⣿⣿⣦⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠐⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠹⣿⣿⣿⣋⣹⡿⠿⠟⠛⢉⣁⣀⣠⣤⡤⠶⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠷⢜⣛⣉⠥⠤⢴⠒⠚⠉⡟⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢠⠞⣿⠀⠀⢰⣿⣿⣴⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣄⣋⣴⠛⠀⣿⠀⠀⢸⣿⣿⣿⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⣽⢐⠀⣿⠀⠀⢸⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⢤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣿⠈⠂⢸⠀⠀⠸⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⡆⠀⢸⠀⠀⠀⠈⠛⠃⢸⡇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⠛⠓⠞⠀⠀⠀⠀⠀⠀⢸⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡶⠲⢦⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠘⣿⣿⣿⣿⡏⠛⠓⠒⠲⠖⢶⣿⣍⠁⠀⠀⠀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠤⠤⠤⠤⣤⣤⣤⠴⠞⠛⠉⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⣠⣤⣤⣄⠀⠀⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣬⣟⢧⡀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣶⣿⣿⣿⣿⣿⡇⠀⠀⣸⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠛⠿⠂⠈⠓⢤⡀⠀⠀⢰⠋⢠⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣀⡀⠸⠷⣰⠇⠀⢠⠏⠀⠀⠛⠻⠟⠛⠉⠀⠀⠀⠀⣼⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⣤⣀⣀⡉⠈⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢿⣤⢾⡏⠉⣛⠒⠦⢼⡀⠀⠀⠀⣠⣶⣶⡄⠀⣠⠟⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣾⣿⣇⣴⣿⢳⣄⠀⠀⠙⠛⣋⡴⢊⡁⠀⠀⠀⣆⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢃⣤⣾⠟⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠸⠀⢻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⠟⠋⢸⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠞⠉⡇⡇⢸⡿⢋⣴⡆⣿⣿⣿⣿⣿⠋⠀⢀⡴⠋⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣼⠋⠀⠀⡇⠟⣫⣴⣿⣿⢸⣿⣿⣿⠟⠁⢀⡴⣟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠁⣿⣿⡟⣼⣿⡿⠋⢀⡴⠉⣰⠏⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡄⠀⠀⣀⠀⢀⡀⠀⢰⣿⣿⢣⣿⡟⢁⡴⠋⢠⠞⠁⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠘⢿⣯⣹⠶⣼⣿⣟⣾⠋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡳⣄⠈⢳⡙⢦⡛⣿⡟⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣬⡷⣄⣿⣄⣙⣋⣴⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣼⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡎⢳⣄⣠⣤⣨⣝⢋⣀⣀⣀⣤⣤⣤⢶⣿⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡫⠊⣵⣻⣯⣭⡿⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠓⠸⠓⣶⠯⢬⡏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠤⠤⠤⣀⣀⡟⠀⢀⣤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠁⠀⠀⠀⠀⠀⠀⢹⢁⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠋⠀⠀⠉⠉⠙⠒⠲⠦⣤⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠉⠙⠓⠦⣤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣠⣿⠟⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⡇
⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠲⠶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⢠⣤⣠⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣟⠛⠟⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿





⠀⠀⠠⣄
⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠈⠳⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠖⠔⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⣄⡀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠈⢱⣏⣀⠟⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡇⠀⢶⣶⠿⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡀⠀⠳⣶⣮⣿⡗⣤⣤⡄⠃⠀⡀⢡⣶⠖⡎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢰⣶⡟⣵⣿⣿⢛⣭⢀⣥⣤⣿⡟⠉⣀⡁⠁⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣶⣿⡾⣿⣿⣿⣿⣷⣿⣿⣿⡿⠋⠉⢠⣿⣿⡟⠉⠉⠁
⠀⠀⠀⠀⠀⣸⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣶⣶⣾⣿⣿⣥
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⠟⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣄⣠
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⣧⠀⠀⠀⢘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⢸⣧⠀⠀⢠⣿⠋⠠⠀⣼⣶⣶⣦⡀⢀⠔⠁⢰⡇⠀⠀⠀⠀⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠈⣿⠀⣸⡇⠀⢸⣿⣄⠀⣸⠃⠀⠀⠀⣺⣿⠉⠻⣿⡀⠺⣤⣿⡧⠤⠤⡀⠀⠀⠈⠛⣧⡀
⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⢸⣿⡿⠀⠈⠀⠀⠀⠀⠈⢓⣦⣠⣤⡙⣦⣏⠁⡀⠀⠀⠙⣦⠀⠀⠀⠈⠃
⠀⠀⠀⠀⡀⢹⠀⢹⣇⡀⠈⣿⣷⣄⠀⣿⠀⠀⠀⠀⣿⡏⠙⠷⢾⡿⠻⢷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⢸⣿⡇⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠉⢿⣄⣄⢸⣿⣤⣄⡀⠀⠀⠀⠸⣿⡄⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠂⢸
⠀⠀⠀⠀⠁⠀⠀⠀⠛⣇⠀⠈⣿⣿⠟⠛⠃⠀⠀⢀⣀⣀⣉⣛⣻⣿⣿⣿⣿⣧⡀⠀⠰⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣼
⠀⠀⠀⠀⣈⡁⠀⠀⣀⢿⡄⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⡇
⠀⠀⠀⠀⢉⠙⠢⠀⠀⠈⢳⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⣿⠁
⠀⠀⠀⠀⠈⠁⠰⠟⣄⡀⠀⠁⢄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⠀⠀⣀⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⢠⣿⣿⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⢀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡸⣿⣿⣿⣿⠏⠀⣀⣤
⠀⠀⠀⠀⠀⠉⠉⠓⠄⠀⠀⠀⢐⣾⠋⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣟⠁⢘⣿⣿⣿⣿⣿⣿⣿⠇⠀⢻⣧⣿⣿⡿⢋⠴⣪⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⣿⡧⠄⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠁⣿⡿⠉⠻⢿⣿⣿⡟⠁⢀⣴⣿⣿⣿⡿⠃⠑⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⠫⠄⠀⢤⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⡿⠁⠀⠀⠀⠀⠉⣠⠞⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⣛⣲⡦⣤⣀⣻⣶⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⢙⠛⠛⠛⠻⠿⠿⠿⠿⠶⠶⠤⢤⣤⠶⠶⠿⠟⢛⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠋⠉⠉⠈⠁⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⢦⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⣠⠞⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⣴⠟⠉⠁⠀⠉⠙⢷⣄⠀⠀⠀⡞
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢸⠁
⠀⠀⠀⣯⠀⠒⠀⠀⠀⠀⠀⣿⠀⠀⠀⣯⠀⠀⠀⠀⠀⠐⠀⠀⢸⡇⠀⡏
⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⠃
⠀⠀⠀⠀⠀⠉⠓⠲⡞⠋⠀⠀⠠⢤⠄⠀⠙⠷⣤⣀⣀⣤⠶⠋⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⠃⠉⢸⡄⠀⠠⣞⠉⡡⠗⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣤⣶⡟⠙⠁⠀⢸⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠃⠀⠀⠀⢸⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠁⣷⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠘⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⠤⠶⠶⠶⠶⡟⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⠶⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠢⣄⠀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠓⠀⠀⠀⠹⠗⠀⠀⠸⡀⠀⠀⠀⠀⠀⠻⠇⡞⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠓⠢⠤⣀⡇⠀⠀⠀⠱⣄⠀⠀⢀⡠⠔⠚⠓⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠖⠁⠀⠀⣤⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡶⠆⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣛⢲⠆⠀⣠⡿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⣀⣨⡄⢈⠙⣛⢓⡖⢒⠲⢟⣿⣱⣿⣿⡏⢀⢰⡿⠁⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠛⠉⠉⠷⢾⠷⠾⢿⡿⣿⢧⣬⣽⣿⣿⣿⡇⢸⣿⣧⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡷⣹⣉⠿⣿⣿⣟⣻⡇⣾⠇⢻⡇⠀⠀⠀⣽⡷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣟⣿⣏⡥⡹⣯⡿⢰⡿⠀⠘⠀⠀⠀⢠⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣿⣦⣿⣿⣿⣰⣿⠿⠋⠀⣼⠇⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⢛⣿⣭⣭⣭⣀⣀⠀⢠⣿⠀⠀⠀⠀⣴⣶⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠉⠩⣿⣷⣺⣿⡟⠀⠀⠀⢉⣿⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⣠⣼⣏⣿⣽⣿⣶⣶⣶⣿⣿⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣯⣽⣿⣿⠛⠛⠻⠟⠋⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣮⣿⣿⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣐⣷⣿⣟⣿⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠙⢿⣿⣏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⣾⣿⡏
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠆⠀⣿⣿⣄
⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⢹⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠙⣻⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⠀⠰⠼⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠠⠾⣿⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⢴⣏⢴⣧⠾⡿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣿⣿⣷⣿⣟⣛⡛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣙⣛⣿⣿⣿⣿⣯⣭⣝⣛⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠷⣶⣬⡍⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⣟⣲⣿⠋⠉⠛⠛⢲⣮⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣟⡿⢋⣤⢮⡳⣄⣤⣿⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣹⠿⡿⢋⡴⠋⢀⣠⣴⣿⣿⣯⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠃⠀⣿⡉⣴⣾⣿⣿⣿⣿⣿⣷⡤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣉⣽⠀⢀⣀⡰⣟⣛⣛⣛⣯⣭⣽⣷⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣴⠊⠉⠈⠈⠁⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠈⠁⠀⠙⠈⠁⠀⣠⠴⣾⣷⣮⣭⣛⠻⣿⣿⣿⣿⣿⣿⠏⣼⠏⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣞⣻⠿⣶⣮⣭⣛⢿⣿⣶⣽⣿⣿⡿⢋⣼⣿⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠷⣮⣽⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠀⠀⠀⠀⠈⠻⣷⣄
⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢟⣩⣴⣾⡿⠟⠻⠟⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡿⠛⠋⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣭⠿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣯⣵⣶⢟⣩⣾⣦⣄⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢥⣿⣿⣿⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣴⣿⣿⣲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠶⢽⠻⢿⡿⢫⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣾⣿⠇
⣶⣶⣶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⣢
⠀⠀⠀⠀⠀⠀⢿⣤⣤⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣌⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⣾⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠑⢤⡀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡀⠀⠀⠀⡠⠊⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⢈⠶⠊⠁⢀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⡀⠈⠑⠲⡉⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣶⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠝⣶⣤⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣬⠳⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⠞⣡⡿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠙⢷⣌⡳⣌⠢⡀⠀⠀⠀⠀⠀⡴⣫⠞⣡⡾⠋⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠙⢷⣌⡳⣌⠢⡀⠀⡠⣫⠞⣡⡾⠋⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡳⣜⢪⡞⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣮⡳⣝⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⣹⡿⢿⣮⡳⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⣡⡾⠋⠀⠀⠙⢿⣮⡳⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⢞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠙⠿⣮⡳⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣮⡳⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⢕⣥⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⣕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣕⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣵⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣮⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⢆
⠀⠀⠀⠀⠀⠀⠀⠠⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡰⠁
⡔⠉⠙⢦⠤⠤⠀⠒⠒⠒⠒⠂⠸⠀⢰⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣀⣀⡀⠀⠤⠤⣀
⠻⣦⣼⠿⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣣⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⡀⠤⠄⠐⠂⠈⠉⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⣿⣧
⠀⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⣸⣿⣿⡆⠈⠻⠿⣿⣿⡿⠿⠋⠀⠀⠾⠟⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣷⣶⣶⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⡶⠒⢠⠀⠀⠀⠀⠀⠀⣠⠤⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⠰⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡄⠂⠘⠀⠀⠀⠀⠀⡌⣀⣠⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠤⠽⠒⠒⢠⠴⠘
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠗⠀⢠⠀⠀⠀⠠⣤⣔⣷⡜⠡⠯⠕⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡴⣶⠴⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠲⠠⠤⠒⠛⡋⢏⡋⠰⠓⠒⠒⠁⠀⣀⠀⠤⣠⠂⠈⠀⠀⠀⢀⠐⠚⣦⡟⠀⣰
⠀⠀⠀⠀⠀⠀⠰⢀⠫⣿⣦⡀⡑⠂⢳⣨⢥⢤⣩⠇⠉⠀⠀⠀⠘⠋⠀⠐⠁⠈⠄⠀⠀⠀⡀⠤⠶⠿⠇⠀⠘⢦
⠀⠀⠀⠀⠀⡴⡳⠖⠠⠿⠇⢞⠓⠈⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤⢈⣉⡉⠀⠀⣀⠀⡀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢳⣥⡆⠀⡆⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⣟⣤⡴⢋⠙⠲⡄
⠀⠀⠀⠀⠀⡿⣸⡇⢀⠁⠀⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠛⠁⠀⠀⢡
⠀⠀⠀⠀⠀⡇⠽⠇⠈⠢⢀⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡞⠓⠤⢄⣀⡤⠂
⠀⠀⠀⠀⠀⣇⠀⠀⠐⠂⠀⠁⠙⡿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⣷⣤⣴⣶⠖⣻⠃
⠀⠀⠀⠀⠀⠀⡾⠛⡿⠛⡟⠁⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣀⠔⠋⠛⠫⣋⣈⣩⠍⠲⢤⡀
⠀⠀⠀⠀⢀⡜⠀⠊⠀⠀⠈⠒⠀⠱⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠜⠹⠤⠊⠀⠀⠀⠈⠉⠈⠓⠲⠼⡂⠠⠄
⠀⠀⢤⣀⠣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣥⠍⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠉⠛⠒⠂⠀⠉⠛⠒⠶⠤⢤⣧⣤⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠖⠲⠞⠛⠛⠛⠉⠉⠉⠋⠉⠉⠉⠉⠉⠛⠒⠒

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠁