Zombie Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠚⠛⠛⠉⠉⠉⠛⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢤⡀⠀⢠⠎⠀⠈⠓⠦⠎⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⠀⠀⢀⠤⣄⠀⠀⡰⠃⡀⡀⠀⠉⣲⠃⠀⣀⡔⠰⢄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣴⠒⢄⡀⢠⠏⠀⠈⠑⠖⠁⡈⠀⠘⡄⠈⠁⠀⢘⣁⡀⠠⠞⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠜⠀⡄⠀⠈⡁⡔⠢⡀⠀⠠⢀⠃⠀⠀⠱⡜⠀⠀⡤⠀⠦⠔⠁⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠈⢛⠁⠀⢃⡇⠀⢡⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠤⠞⠁⠀⠀⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣇⠀⠀⠀⠀⣸⠃⠀⢀⣠⠤⢠⣤⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡤⠥⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡀⠀⠀⠀⠈⠓⠒⠒⢩⠏⠀⢠⠛⣸⡈⠓⠉⣉⠇⠀⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣡⠵⠶⣄⠀⠀⠀⠀⠐⠃⠀⠀⠸⣉⠏⠚⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⢠⢦⡀⠀⠀⠀⠀⣀⡤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⠀⠀⠉⠀⢀⡠⠤⠾⠿⠶⢏⡉⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣉⣐⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⡶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠀⠀⠀⠐⠒⣿⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠖⣤⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢇⣠⠔⠀⠀⠀⢀⡸⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣀⡤⠖⠊⠁⢀⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠎⠁⠀⢀⡤⠞⠉⠉⠙⠦⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⢸⣿⣦⡀⠀⡟⢷⠀⣠⢾⡇
⠀⠀⠀⠀⠀⠹⣆⠹⢦⣽⠀⣿⡏⢸⣿⣆⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢠⣶⣶⣿⣖⠻⠷⠈⠙⠁⠀⣀⡤⠄⠛⠛⠉⠉⠉⠉⠉⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⣉⠉⠉⠛⠛⠓⠶⣦⣀⠀⠀⠀⠀⣰⣿⠶⢻⡟
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢁⣈⡙⠻⣆⣀⣀⠀⠈⢙⡿⠛⢳⣴⠋⠀⠀⢾⡦⢤⣶
⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⡶⠟⠛⠉⠳⠞⠋⠀⠀⠀⠙⣆⢀⡀⠀⣴⣞⠁
⠀⠀⠀⢀⡼⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠘⢏⠁⠀⠀⠉⠙⣦⣄
⠀⠀⢰⡏⠀⠀⠀⢠⠁⠀⠀⠀⡤⢤⣤⡀⠀⠀⠆⠀⠀⠀⠀⠰⠋⠀⣴⠟⠁⠀⠀⠀⠙⢶⡀⠀⢸⣁⣤⠖⠒⠈⠉⠉
⠀⠀⢸⡇⠠⠀⠀⠀⢀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡖⢲⠀⠈⣷⠀⠸⣿⣤⣤
⠀⠀⢸⠇⠀⠀⠀⣰⠟⠉⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠉⠁⠀⣠⡏⠀⢰⠋⠰⣏
⠀⠀⣸⠀⠀⠀⢸⡇⣠⠦⣀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣀⠀⠀⠸⡿⣦⣤⣀⢀⣤⠾⠋⠀⠀⣼⠒⠀⣽⠀⢰⡾⣶⠿⣷⣶⣤
⠀⠀⣹⡀⠀⠀⢸⣇⠉⠲⠋⠀⠀⠀⢀⣼⡇⠀⠀⣼⢆⠀⣿⣥⠀⠀⠳⣤⡈⠉⠁⠀⠀⠀⠀⠀⣸⠶⠾⠋⠀⣼⡇⢸⡄⣿⠀⣿⣀
⣴⠶⠛⡇⠀⠀⠈⠻⣦⣀⡀⢀⣀⣴⠟⣹⠇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣿⢻⢸⡇⢸⡀⣿⠋
⢿⣄⠀⢸⡄⠀⠀⠀⠀⠉⠛⠋⠉⣀⠴⠋⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⡶⠶⣶⠚⣿⠉⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⡸⣴⣧⣸⣷⡏⣸
⠀⣿⡃⠀⣽⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢶⠀⢻⠋⠀⠀⠀⠀⡇⠀⢀⡄⠉⡄⠀⢀⡿⠁⠀⠀⠀⠀⠀⠹⣧⣀⣹⠛⢶⣴⡟
⠀⠈⠛⠛⠁⠀⠙⢷⣄⠀⠀⠀⠀⠀⠘⠉⢣⣠⠞⠳⠎⠀⠀⠀⠀⠀⠁⠀⠈⠃⠀⢡⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠷⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠦⢤⣤⣄⣠⡤⣦⡄⠀⢠⡶⠚⠋⠉⠉⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠾⡇⠀⢘⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⣷⠤⠤⠶⣶⠶⠶⠿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠛⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⣾⣧⣤⠤⡴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣽⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⢤⣄⡀⠀⣤⠶⠾⠛⠛⠃
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠛⣶⣤⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠏⠉⣋⠀⠀⢀⡋⠀⣿
⠀⠀⠀⢠⠟⠀⠀⢀⣴⠞⠉⣟⠀⢀⣠⣴⠎⠁⠀⠀⠀⠀⠀⢠⠀⠈⠉⠉⠉⠉⢃⡀⣿
⠀⠀⢰⡏⠀⠀⠀⣾⠃⠀⠈⠿⠿⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠀⠐⠖⠒⠚⢻⡏
⠀⠀⣾⠁⠀⠆⣾⠏⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⢻⡇
⠀⠀⢿⠂⢘⡆⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠿⢸⡇
⠀⠀⢸⡆⠈⠁⢻⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⢷⠆⠂⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢺⡏
⠀⣠⣴⡿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⣠⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠸⡇
⠀⠙⠛⣿⠀⣿⡂⣧⣨⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢻⣦⠿⣷⠿⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⢤⣤⠖⢢⣴⠛⠉⠛⢿⡷⠒⠂⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣣⠀⠀⣦⠀⠀⠀⠈⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⣿⠀⠀⠀⠀⣯⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⣤⢿⣧⠀⢀⣤⣿⣤⠤⠤⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡄⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⣼⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⣀⠴⠿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠈⠀⢀⠴⠶⢀⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣠⣤⣼⡇⠀⣇⠀⠀⠀⠀⣿⣀⣠⡈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠛⠉⠉⠉⠉⠉⠙⠛⠻⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⣀⠀⠀⠀⠠⠭⢿⣷⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⠏⠿⠟⢿⣿⣿⣦⡀⢐⣛⣻⣿⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢀⡴⢙⡇⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⠐⠒⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢸⣀⠾⠃⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠙⣿⡄⠨⠭⠽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣠⣾⠟⠛⠛⠻⠇⠀⠀⠀⠸⣇⠀⢚⣛⣿⡇⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⣾⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⢻⡀⢒⣲⣾⣷⡾⠛⠁⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⣀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⡟⠀⣴⠟⠉⠉⠉⠛⢿⣿⣿⣆⠀⠀⠀⠀⠘⣇⠨⢭⣿⠟⢀⣴⣶⠓⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⡉⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⢁⡾⠃⣰⣦⣀⠀⠀⢈⣿⣿⣿⡄⠀⠀⠀⢀⣿⢠⡾⠁⢠⡿⣋⣿⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠈⠉⠙⠒⠦⣬⣶⣤⡀⠀⠀⢀⣾⣇⠀⠙⠛⠿⠃⠀⣸⣿⣿⣿⠇⠀⣠⣴⡿⢃⡞⠁⢀⠏⠸⢫⠟⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣶⣶⣀⣀⣤⣤⣭⣻⣿⣶⣶⣿⠿⣿⣦⣄⣀⣀⣤⣾⣿⣿⣟⡟⣠⣾⠟⠋⠀⠀⣀⡀⠈⠀⣠⡶⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠹⣧⣀⣀⣀⣴⣿⠃⢹⡏⠁⠀⠀⠈⠙⠻⢿⣿⣛⣫⠽⣫⠞⠀⡏⠁⠀⠀⠀⢀⣨⠿⠿⡟⢉⠃⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠙⠯⠉⠁⠈⡝⠀⡿⢠⣶⣤⣄⡀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠁⠀⠀⢀⣴⠏⠀⠀⠀⢱⡀⠹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⣤⣤⣴⠈⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣦⣼⡆⠀⢸⣿⠀⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⡄⠸⣿⣿⠿⠟⠛⠿⠟⠀⠀⠀⠀⠀⠀⢺⡿⠉⣷⡀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⠀⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠛⠋⢁⡀⢰⣿⣶⣌⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣠⣤⠀⣿⣷⣾⡟⠀⠙⠉⣷⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠿⠟⠉⠁⠀⠀⠀⠀⢻⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠉⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣴⡆⠈⢰⠆⠀⠀⠀⣤⠒⠠⣠⡀⠀⠀⠀⠀⠀⣰⢗⣢⣄⡀⠀⠀⣤⣄⠈⡄⠀⠀⠑⢀⡀⠀⠀⠀⠂⠁
⠀⠀⢀⣀⢠⣦⣄⡙⠃⠀⠀⠀⢀⣬⣡⣝⣧⡀⠀⠀⢀⠾⣧⠭⢤⡀⠨⡂⠌⠿⠟⠀⠐⠀⠀⠀⠀⠁⡄⠀⠀⠀⣄
⠀⠁⠘⠛⠀⠉⢁⡄⣴⣶⣦⡀⣨⠛⠁⠈⠈⠉⠈⠆⠀⠀⠈⠀⠀⠉⠲⣤⡘⠃⠀⠀⠀⣀⣠⣄⣤⣄⢠⡄
⠀⠀⠒⣀⠀⣐⣷⣭⣌⣛⣻⠏⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠈⠀⠀⠀⠀⣽⣿⣿⡿⠘⢳⡧
⠀⠈⠀⠉⢙⠿⢿⣿⠿⠁⡆⣠⠄⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⡀⢈⢻⣿⡿⡿⠂
⠀⠀⠀⠀⠈⠦⣄⡈⠻⡇⢷⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⡰⢿⣦⠋⠀⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠛⠈⠛⠿⠄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⢱⠔⢁⠡⢠⣄
⠀⠀⠀⠀⠀⠐⢡⣴⡖⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢶⣆⠘⠟⠉⠀⡞⠸⢂⠀⠀⠀⠀⠀⠀⠃
⠠⠀⠀⠀⠄⠀⢼⣿⡏⢢⠁⢀⣰⡒⠐⢤⣠⣄⣠⠆⠈⢠⣴⡌⠉⣀⠠⠎⠁⠀⢶⠀⠀⣷⠐⠀⠑
⠀⣾⣿⡆⠀⠀⣰⣽⡇⠹⠄⠈⠹⢦⣀⡤⠼⡟⠙⠀⡀⠀⠈⠓⠺⣿⠃⠀⠀⠀⠈⠁⢠⡟⣴⡄
⠀⢼⡟⠁⠀⠀⢀⠸⣇⢶⣀⠀⠀⠀⠄⠀⠀⠀⠁⣀⣿⢆⠀⠀⠑⠄⠀⠀⠀⠀⠀⣆⠉⣼⣿⣿⠆⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠑⣼⡌⠺⠂⠀⠀⠀⠀⠀⠀⠀⣿⣟⠈⠷⡆⠀⠀⠀⠀⠀⠀⠆⢨⣴⣟⣿⡖⣒⠀⣾⣿⣧⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣶⡄⢹⠲⡄⠀⡆⠀⠀⠉⠈⠀⠀⠐⠀⠀⢀⡆⠀⠀⡐⢸⣿⠈⠙⣿⡿⠣⠙⠩⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠟⡛⣿⣿⣾⡄⠐⠀⢡⣀⠀⠰⡀⠀⠀⠀⠀⣀⡴⢷⠀⠀⠀⡾⠿⠂⠰⠾⣶⡃
⠀⢀⠀⠀⠀⠀⠶⢀⢀⣥⣽⣿⣿⣿⣦⡀⠀⣿⡴⣤⠀⡄⢤⠒⣲⣼⡇⢸⠀⠀⠈⡀⠀⠀⢄⣈⡙⠃
⠀⠈⠁⢀⣤⠀⠀⠛⠀⣠⡼⠿⡏⠹⢿⣿⣄⠙⠀⠘⠿⣷⠾⠟⢛⠉⠀⠈⠀⡄⠀⡇⡀⠈⠘⢻⣿⡀
⠀⠀⠀⠀⠉⠀⠐⠀⠈⠑⠀⠈⠇⠛⡌⠉⠀⠀⠀⢀⠀⠙⠀⠀⠈⠀⢀⠀⡀⢀⡠⠛⣷⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⠠⠆⡀⠀⠀⠀⡀⠢⠀⠀⠀⠀⢀⣀⣉⠀⠘⠃⢸⠅⠿⠀⠀⣄⠈⢂⠄
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⣿⣦⡄⠀⠀⠀⠁⠀⣡⡀⢄⠈⠀⢈⡁⠀⣰⡦⠜⠀⣠⣧⡀⠀⠠⠤⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠂⠐⠀⢛⣿⣿⣿⣾⠆⣹⡿⠁⡄⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⢉⠇⢀⡏⠱⠀⠀⠈⠄⠀⠊⠉⢅⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠑⠄⠀⠀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠄⠀⠠⠀⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠖⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠉⠉⠁⠀⠙⠻⠶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣰⣿⣶⣶⣆⣴⣧⣶⣴⣶⣤⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠛⠉⠉⠉⠍⠀⠀⠀⠐⣿⣤⡀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠘⡇⠀⠀⢠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣀⣀⠤⠀⠀⠀⠤⢄⡠⡺⠀⢀⡃⠀⡀⢀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠂⠐⠀⠐⠀⠠⢀⣤⣄⡀⠱⠀⢿⣋⠀⠡⢊⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣦⣄⣤⣿⣤⣤⣶⠟⠛⣿⣷⡄⡀⠘⡇⠀⣰⢏⣴⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⣸⡏⢹⢻⠻⣦⣤⣿⣿⢃⠄⠀⠈⠙⠛⣸⣿⢏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣷⣌⠈⡀⠀⣍⡉⢡⣊⠀⢀⣶⣿⣦⣙⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠛⣠⠈⢦⢠⣾⣽⣿⣶⡿⠏⣿⣿⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣁⣀⣀⢋⣜⣿⠿⣿⣿⡟⠁⠘⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣯⡯⠧⣾⣿⣿⡂⠘⡈⢠⠀⣼⢣⣸⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠭⢭⠋⡙⢩⠘⠁⢀⣄⣴⣿⠃⠈⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠈⠈⠀⣴⣿⣿⣿⡟⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣀⠀⠀⢐⢾⣿⣿⣿⡟⠡⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠈⣿⣿⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⢀⡀⠀⠀⣼⡄⠀⢀⡀
⠀⠀⠀⠈⣿⢢⡀⠏⠷⣠⠛⣧
⠀⢀⣠⣄⣸⣷⡙⠿⠀⠋⢀⣹⠷⠶⠶⠶⠶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠈⠉⠉⠁⠒⢤⣀⡠⠒⠁⠀⠀⠀⠀⠀⢀⣞⡛⠛⠒⠒⠤⣄⡀⠀⠀⠀⣰⡿⠴⡷
⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣍⠛⣦⣀⣀⠀⣹⠟⠛⣶⠋⠀⠸⠷⢴⠆
⠀⠀⠀⢀⡿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠉⠋⠀⠀⠀⠈⢣⡤⠀⠸⢧⣄
⠀⠀⣴⠋⠀⠀⡄⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⡔⠂⣠⠖⠛⠙⠓⢄⠀⠀⠧⢀⣀⠤⠬⠗
⠀⠘⣇⠠⠀⠀⠁⣀⣀⣄⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠰⡄⠈⡷⠀⢸⣫⣄
⠀⠀⡇⠀⠀⢀⠞⠉⠁⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠉⠀⢀⠟⠀⢸⠁⢾⠀⠀⡀⢀⡀
⠀⠸⡇⠀⠀⣿⠠⡒⡄⠀⠀⠀⢸⡀⠀⢀⡀⢰⣄⠀⠸⡛⠶⠦⠴⠞⠉⠀⠀⢏⣁⡾⠀⢸⢻⡏⣿⢻⡆
⢀⡴⢇⠀⠀⠹⣆⠀⠀⠀⢀⡴⢟⠃⠀⠺⠐⠀⠋⠀⠀⠉⠒⠀⠀⠀⠀⠀⢰⡟⠉⠀⢰⣿⡄⡇⢹⢸⡷
⢯⡀⢈⡄⠀⠀⠉⠛⠛⠛⢋⡡⠎⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠴⣶⠀⠀⢰⡞⠁⠀⠀⠘⣇⣿⣷⣸⣼⢁
⠀⣿⣀⣼⠶⣤⠀⠀⠀⠀⠀⢀⣠⡤⢲⡆⢹⠋⠀⠀⠈⠀⠀⡆⠉⡀⢀⡾⠁⠀⠀⠀⠀⢻⣄⣩⠛⣶⡿
⠀⠈⠉⠁⠀⠙⢷⣀⣀⠀⠀⠈⠁⠣⠎⠑⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣄⡀⠀⣀⣀⣀⡀⠀⠀⣠⠷⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡉⠭⠭⣿⠀⢸⠷⠶⠖⠒⠒⠒⠒⠒⢲⣤⠤⢤⣤⣤⢾⡚⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠀⠀⠘⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣀⣾⣤⠤⠴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⣀⣤⡤⠷
⠀⠀⠀⢀⣤⠞⠁⠘⣠⡄⠀⠀⠀⢀⡴⠀⠀⠀⠀⠐⠀⠂⠀⢉⠃⢸⠇
⠀⠀⢀⠎⠁⠀⣠⠞⢩⡇⢀⣠⣴⠋⠀⠀⠀⠀⢀⠂⠀⠁⠁⠈⢆⣸
⠀⢀⡟⠀⢀⣸⠇⠀⠈⠛⠋⢉⡟⠀⠀⠀⠀⠀⠈⠈⢣⠀⠘⠛⢈⣿
⠀⢸⡇⠰⢀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣤⣠⣤⡦⣿
⠀⠈⡇⠐⠴⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠃
⠀⡴⠛⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠘⢧⣴⡆⣤⢠⠙⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡟⠋⠀⠀⠀⢸⡇
⠀⠀⢸⣇⣿⣼⠿⠋⠀⠀⠀⠀⣾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⢀⣤⣼⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢻⠋⠙⠋⠀⠈⢹⡏⠁⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⡇⠀⠀⠸⡅⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠤⠤⢿⡄⠀⣤⠦⠤⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢸⡇⠀⡅⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠀⠈⡇⠀⡇⠀⠀⢀⡸⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠀⠀⠀⠀⣧⠀⡇⠀⠀⠁⢀⠤⢤⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣤⣤⣤⣤⣤⣤⠴⠿⠀⣇⣀⠀⢀⣿⣤⣆⣹⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠶⡶⠒⡒⡖⠒⠂⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠋⠁⠹⠀⠀⠀⠐⡃⢀⣄⣠⠋⠁⢠⠌⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠁⠸⢦⠀⢠⠆⠀⢱⠖⠚⠊⡁⠠⠀⣤⠀⢀⠀⠐⠃⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢱⠒⠒⠂⠀⠴⠧⠤⡔⠛⠒⠒⠨⢥⠴⠋⠒⠛⠳⣤⡥⠒⠊⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠁⠀⠈⠀⠀⠀⡆⢳
⠀⠀⠀⠀⠀⠀⠀⡔⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⢠⠄⡤⠠⠤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⣐⠦⣤⣤⣀⡄⠀⠤⣀⣀⡀⠠⣤⣤⣄⣀⡀⢀⠠⠀⠀⡀⠀⠀⢀⠀⠠⠀⠐⠀⡀⣸⠀⠰⢄⠓⠁⠐⠒⡸⠁
⠀⠀⠀⠀⠀⣠⣾⣥⡶⣀⠀⠈⠣⢠⠖⢿⣳⣕⢦⠀⠀⠉⢟⢿⠁⢀⠀⠀⠀⠀⢀⢠⠃⠀⠁⠀⠀⢁⠇⡠⠙⠀⠠⣉⠛⠒⠁
⠀⠀⠀⠀⠠⣦⣼⣿⣿⣼⡂⠀⠀⣿⣷⣿⣿⣿⡟⡇⠀⠀⢸⠀⠀⠻⢆⠰⣷⣠⡆⠃⠀⠀⠀⠀⢠⠎⠀⠁⠀⠈⠐⠤⡠⠎
⠀⠀⠀⠀⠀⢻⣿⣿⡿⡹⠁⢀⠄⠛⣿⣿⣽⡫⠞⠁⠀⡠⢋⠀⠀⠀⠀⡆⢨⣿⣿⠁⠠⠀⠀⡰⢋⡔⢁⠱⠖⡰⠢
⠀⠀⠀⠀⠀⠀⠙⠷⠊⣀⡴⠁⠀⠀⠈⡙⠳⠤⠐⠒⠉⠐⠁⠀⠀⠀⡴⢅⣈⠔⠁⠀⢀⡠⠊⠀⠊⢚⠂⢴⣀⠞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⣀⣀⠀⡸⠀⣠⠶⠿⠛⠿⣶⣤⣤⠞⠀⠀⠀⠀⠀⠘⡏⠀⣜⠍⠒⠤⢈⠒⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠓⠛⠛⠛⠻⠐⠊⡡⠄⠒⢠⠀⣼⠛⠀⠀⠀⠀⠀⠀⣠⠤⢂⠤⠃⡠⠉⠐⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⡍⢩⡙⣊⣍⡠⡤⠶⢛⡄⠙⡟⠀⠀⠀⣀⣬⠴⠅⠒⢌⠂⢄⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢩⣩⣶⠃⠀⠀⣠⢚⠉⠊⠀⡀⠀⠁⣨⠞⡔⠁⢆⠀⠢⡉⢢⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠂⠘⠠⢱⠀⠀⢰⠀⠃⠀⠀⠀⢐⡩⠿⢩⠀⠈⠲⣄⠑⠠⢃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⡀⠀⠀⢈⣣⡀⠀⢧⠀⠀⢠⡊⢩⡄⢀⠎⠀⢀⠄⠈⠃⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠠⡀⠀⢱⠀⠈⡍⠀⠀⢧⢿⠇⣎⡠⠔⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⡀⢀⠂⠁⠀⢠⢁⣈⠥⠊⠘⠆⠈⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠄⠀⠐⠋⠀⠣⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠿⠿⠿⠶⠖⠶⠖⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⣀⣀⡀⣄⠀⠀⣀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠹⣷⣦⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⡿⣿⣿⣿⠇⢾⣿⣿⣿⠿⠿⢿⣿⣿⣷⣀⣀⢿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⣠⡿⠋⠀⢈⠛⠟⠑⠀⠀⠀⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠮⠀⢠⡟⢠⣤⡀⠾⣥⡀⠁⠀⠀⠐⠛⣹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⡀⠀⢀⣿⣿⣿⣷⣌⠿⠀⠀⠀⠀⠘⢹⡿⣿⣿⣿⣿⣿⣟⠻⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠈⢻⣟⣩⠟⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣶⣾⣿⣿⣿⣷⣾⣷⠀⠀⠀⠘⡿⠏⢛⢽⣯⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡅⠀⠀⠟⣮⠉⠛⣉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠉⠉⠉⠛⠛⢻⣅⠀⠀⠀⠁⢠⠀⢸⠟⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣶⠦⣤⠶⣤⣌⠛⡤⠀⡄⠀⣨⡶⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⠀⢀⠀⠀⠙⣉⣁⣘⣯⣴⣿⠂⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠏⠐⠂⠀⠁⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠟⠋⠛⠛⠁⠀⠀⠀⡀⢀⣀⣈⣏⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠩⢽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢾⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠉⢁⡼⣿⣷⣂⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠛⠀⠸⠟⠁⠀⢁⣺⣧⡄⣀⠀⠀⠘⠁⠉⠀⠀⠀⠀⢀⠠⠤⠄⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⣤⣼⣿⡗⠀⠀⢸⡄⣠⠄⠀⠀⠀⠐⠂⠉⠀⣀⣠⡤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⣶⠆⠀⠛⠛⠛⠛⠛⠁⣀⣠⡾⠋⠁⠀⠀⣀⠀⣤⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠛⠛⠷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣤⣄⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠿⠿⡿⣿⡿⠿⠯⠿⠛⠒⠀⠁⠀⠀⠐⠀⠀⣬⣻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⣀⣀⡀⡀⠀⢠⣀⠀⠀⠀⢀⣀⣀⠀⠀⠤⠄⢌⣻⣿⣿⣭⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣼⣿⣿⣿⣿⣿⣿⡷⢠⣾⣿⣦⣼⣿⣿⣿⣿⣿⣿⣶⡄⢪⡦⣿⣿⣿⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠛⠛⢿⣿⣿⠃⠸⣿⣿⣿⣿⠋⠉⠙⠻⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣀⣠⣰⣾⡿⠁⠀⠀⣭⠻⠟⡉⠃⠀⠀⣀⣬⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣾⣶⣫⣽⠟⣠⣀⡐⢾⣿⣅⡈⠃⠙⠲⣶⢾⡿⢟⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠁⠈⠃⢰⣿⣿⣿⣦⣍⢻⣷⠂⠠⠀⠀⠊⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣶⡀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢀⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣍⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⠈⢿⣯⡦⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢀⠀⡀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣽⣿⣷⣿⣿⣷⣦⣾⣶⣆⠀⠀⠀⢺⣿⣿⢻⣿⣿⡟⣿⣿⣿⣿⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⠁⠀⣏⣿⡿⠿⢿⣿⡿⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⡏⠀⠈⠸⢻⣿⣦⢈⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠙⢋⡉⠉⠙⠋⠛⢻⣿⡆⠀⠀⠰⠃⢀⣶⠀⢿⡟⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣵⣄⣾⣦⣀⣽⢿⣇⣠⠀⡄⠞⢨⣏⣴⠘⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠉⠙⠉⠉⠙⣿⣷⠯⣅⣼⣷⣶⣼⣿⣥⠒⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣦⣄⣠⣄⣆⢴⣨⣷⣶⣶⣾⣿⣿⣿⣧⠈⠀⢀⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠛⠋⠰⠖⢂⣿⡶⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⣿⡿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⡱⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⢠⣤⠤⠂⣀⣀⣀⠀⠀⣀⠤⠶⠒⠛⠋⠉⠙⠛⢿⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣩⡘⣿⠿⠿⠐⠒⢉⡀⠀⠀⠀⠒⠒⠒⠂⠙⠻⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢡⡄⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠉⠀⠛⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠁⠀⠀⠀⢸⡶⠀⢿⣦⠀⠀⠀⠀⠀⠀⢴⠗⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠘⠀⠀⠀⠈⠀⠆⠐⣹⣿⢇⣠⣬⠁⠈⢴⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡈⠀⠀⠀⠀⠀⠈⠲⠇⢀⡾⠛⠁⢀⠀⠀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⡄⠀⠀⠀⠂⣶⠋⠳⠆⢀⠄⠀⠀⠀⠀⠾⠃⠀⢺⣧⠀⠀⠀⠐⠄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢱⣤⣒⣲⡶⠏⠉⠀⠤⠍⣼⠂⠀⠀⠀⠀⠘⣆⣾⠛⠈⠐⠤⣀⡀⠀⠈⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⠤⣤⡦⠄⣼⠁⠀⠀⠀⠀⠀⠸⣅⠀⠄⠀⠀⠀⠉⠻⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⢋⣰⣾⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⡶⠀⠀⠀⠀⠀⡏⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⣿⣿⠁⠀⠀⠀⡀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠛⠆⠀⠀⠙⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠌⠂⠖⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠂⢤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣠⢀⠈⠀⠀⠀⠀⠀⠀⡇⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣠⡴⢧⡄⠀⠀⠀⢀⣴⣷⣼⠟⡙⠣⠈⠈⣡⠀⠀⠀⠀⠀⠀⣿⠁⠙⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠘⠹⢯⠄⣿⠃⠀⠀⣠⠜⠛⡡⠤⠄⠀⣆⠈⠋⡀⠀⢀⠀⠀⢄⣂⣸⡿⠷⡌⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢈⡀⢀⠆⠀⠀⠀⠀⣄⣠⣾⡋⠀⡄⠑⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠐⠋⠉⠁⠀⠀⠀⢀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠲⡄⣨⡩⢆⠀⠀⠀⠀⣸⡿⠋⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠁⠈⠀⠐⠀⠃⠚⠀⠀⠀⠀⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠕⠀⠀⠀⠀⠀⠀⡜⠀⠤⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣠⠒⠉⠀⠀⠀⠀⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠇⠀⣠⠆⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⡓⢣⡀⢀⡏⠀⠀⠀⠀⠀⣸⣶⣶⣤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣿⠸⡇⢛⡿⠟⠀⠀⠀⠀⠀⠺⣿⠋⠀⡄⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠺⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡞⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢻⣇⡀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣷⣦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠻⣷⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⡤⣤⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢐⠀⠈⠠⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠉⢻⡲⢦⣀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⠶⢶⠛⠋⠁⠀⠀⠀⣹⣾⣿⡿⢿⣿⠇⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⣁⠈⡁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠻⠶⠾⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⠾⠛⠛⠛⠛⠛⠛⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠀⠚⠛⣿⠀⠀⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡀⠠⣤⠤⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣿⣦⡀⠀⣾⠟⠀⢀⣰⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣾⣿⠈⢿⡶⠙⣄⣰⠞⢁⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣁⣀⠀⠁⠸⠟⠁⣴⠿⢷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢀⣿⣧⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠶⠶⠖⠈⠉⠉⠉⠛⠀⠉⣿⠶⢆⡀⠀⢀⣠⠶⠆⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⣷⡄⠉⠙⣷⣀⣿⠀⠀⣀⣀⣀⠰⠶⠶⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠿⠃⠀⠀⠁⠶⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⠛⠁⠀⣴⠿⠿⠿⠗⠊⠈⠉⠁⠀⠀⠀⣀⣠⣤⣤⣴⡾⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠂⠀⢠⣿⣄⣀⣠⣤⣤⣤⣄⠾⠿⠟⠛⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠀⢀⠙⠉⠛⠉⣤⡍⠉⠛⢠⣤⣄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⣦⣾⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⢠⣤⠄⠠⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣼⣿⠀⠀⣿⠀⠀⣴⢙⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠸⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⢻⡄⠀⠿⣀⠀⠈⠉⠁⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠁⠀⠀⠀⠙⠻⣆⡀⠀⠀⠀⢹⠁
⠀⠀⢠⣤⣴⣾⢷⣶⣶⡄⠀⣸⡁⠰⢿⡆⠀⠀⠙⠷⣄⣀⡀⣀⣀⣴⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠘⠇⠀⠀⠀⠈
⠀⠀⠛⠉⢹⡇⢸⡇⢸⣇⠀⠙⢷⣶⣶⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣡⡆⠀⠀⢠⣾⠃⢀⡶⠆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠛⠻⠃⢠⡆⠀⠀⠀⢸
⣾⠿⣷⠀⣸⠃⠀⢷⡿⣿⡇⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠈⠉⠀⠸⠷⠂⠀⠀⠈⡹⢷⣄⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⢻⣷⣤
⢿⡀⠛⣴⡏⢐⣇⣸⣇⣸⡇⠀⠀⠀⠀⠻⣶⡀⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠛⠒⠲⠶⠿⠟⠁⠀⠀⠀⢀⠀⠀⠈
⠘⣿⣀⡿⢿⣿⠿⠃⢹⡿⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⡘⠉⠈⠉⠀⠙⠛⠛⠛⠛⢢⣤⣤⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠃⢰⡿
⠀⠈⣿⣿⠈⣡⣤⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢀⡟⠛⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠛⣧⣄⣴⠇
⠀⠀⢹⣿⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⠀⠀⠁⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠤⠛⠀⠀⠀⠀⠀⠀⣀⠀⣸⡟⠃
⠀⠀⢸⣿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠛⠛⠋
⠀⠀⠸⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡉⠉⠉⢱⣶⡄⠀⢀⣶⡶⠶⠤⠤⠶⠶⠶⠶⠞⠛⠋
⠀⠀⢠⣿⠋⠹⠿⠶⢶⣶⡶⠶⠤⣶⡟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠸⠃⠀⠸⡷⠦⠀⠀⢀⣀⣀
⠀⠀⠀⠹⠾⠧⣀⣀⣀⣬⣦⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠚⠀⠀⠀⠀⠀⠉⠙⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⠿⢶⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣤⣄⡀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⡆⠀⡼⠛⠁⠠⣧⣤⣤⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠙⠓⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⣷⠤⠤⣤⣤⠀⠸⠆⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢸⣿⠿⣄⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣄⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣄⣀⣈⣧⠀⠘⢳⡄⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠙⠛⠛⠋⠀⠀⠈⢿⣆⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⠿⠿⠶⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿⠗⠚⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢀⢠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠙⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⡞⢡⡀⣤⡄⢺⣷⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣷⣼⡃⣿⡇⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠳⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⠐⠒⠐⢾⡿⠟⠋⠙⢷⣤⠶⠂⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢀⡋⠀⠀⣿⠁⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⡌⠀⠀⠀⠀⢻⡇⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⢸⣇⡀⠀⠀⢀⣿⡇⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠙⠁⠙⠛⢻⡆⠀⣾⡟⠙⠛⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠇⠀⣿⡇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡆⠀⣿⡇⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⠀⠀⠀⢸⡇⠀⢿⡇⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠳⠂⡀⠀⠀⠀⢸⡇⠀⠘⠀⠀⠀⠀⠀⠀⣿⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣀⠐⠢⣀⠀⠀⠀⠀⠀⢸⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⠁⣀⣀⣹⣤⠀⠀⠀⠀⢸⠃⢸⣧⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⢿⣧⣴⣶⣶⣶⣞⠁⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠋⠙⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣄⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⣉⣬⡉⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠅⠀⠐⡫⠔⠒⠦⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠒⠲⣄⢰⠀⠀⠐⠀⢹⢆⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣂⣀⡼⠀⠳⢤⡤⠴⠣⠞⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣁⣀⣤⠒⡞⡖⠦⡀⠀⣰⢿⡗⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⢃⡩⢁⢍⣡⠞⣰⠁⠀⢣⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⠉⠉⣁⣀⣰⣻⠀⢃⠀⠡⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡝⠀⢀⡏⡆⠘⠀⠀⡇⠠⣄⠀⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⠀⢀⡞⢀⡷⠲⠦⢤⡁⠀⠀⢣⠀⠀⠀⣽⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣤⣎⠴⠋⣰⢛⡱⡄⠉⠒⢖⠊⠉⣶⠒⠛⠊⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠸⠷⠴⣶⡵⠟⣪⢄⡀⠀⢈⡆⠀⢸⠖⠲⠶⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⢋⡤⠚⠁⠀⢠⣏⣀⠜⠰⡞⣡⠚⠁⢿⡤⠚
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⠉⠀⡰⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⠧⢟⡀⡠⢾
⠀⠀⠀⠀⠀⢀⠠⠼⡆⢣⠁⠀⢣⠀⠀⠀⠀⠀⢰⣃⠀⠀⡗⠀⠈⠻⠀⢸
⠀⠀⠀⠀⠀⢸⠰⡺⣧⠞⡀⢀⡸⠤⡀⠀⠀⠀⠘⠁⢳⣱⠃⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢀⣾⡤⠃⣇⠸⣱⠘⢯⠓⠜⠀⠀⠀⠀⠀⠀⢹⠷⡤⣤⣴⣏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡡⠱⣠⠇⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠸⡄⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⡗⣄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠈⢧⠈⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡤⠾⠉⠸⠑⠂⣌⣇⡹⠓⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠛⢧⡒⠀⠀⠀⠀⠍⣏⠄⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠠⣄⠀⠀⠀⠀⠀⠑⣤⣭⡶⠂⢠⡬⣆⠠⠒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠑⠦⣀⠀⠀⠀⠐⠀⠀⠀⣈⣧⢐⣂⡭⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⣉⣑⡒⠒⠒⢒⣫⠵⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⢲⡀⢉⠛⠀⠒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠁⠀⠐⠊⠈⣇⡈⠀⠤⠀⠀⢈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠈⠀⡠⠀⠀⠀⠀⠈⢧⡀⠀⡀⠀⠀⠀⢹⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⣤⣀⡐⠀⠉⢀⠀⠀⡀⢀⣉⣄⣀⣹⣠⡄⣵⣺⠇⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⣹⡛⠓⠛⠛⠛⡟⠉⠉⠉⠀⠀⠁⠀⠀⠀⢸⢄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠐⠀⠒⢒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣰⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠐⠘⠔⠋⢀⣀⣀⣀⣀⡀⠀⢀⢀⣀⡘⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣧⡟⠘⠀⠘⠉⣽⣿⣯⠀⠄⠀⣼⠙⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢻⡇⠀⠀⠀⠓⠿⠿⠋⠀⠀⠀⠛⠖⠛⠋⠨⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠁⠤⠐⠀⡀⠀⢀⠔⢀⡀⠀⠀⠀⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⠅⠀⠈⠆⠀⢠⠀⠈⠀⠉⠉⠀⠀⠁⠁⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡀⠀⠉⠀⣶⣄⠀⠀⢂⠤⠄⠂⠀⣾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠈⠹⠛⠛⠿⡞⠖⠚⢻⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠰⠂⠈⠋⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⢠⠄⠘⠀⠀⠃⠀⠂⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⠒⠀⠀⠀⠀⠀⠢⠏⠀⠀⠄⠀⠉⠣⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡧⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣾⠌⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⡇⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⠬⠐⠒⢒⠤⡀⠀⠀⠀⢀⠤⡒⡒⠒⠼⣆⡇⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⡿⣇⠤⢓⠚⠚⠓⢷⡀⠀⡀⡾⠚⠃⠘⠒⢤⣸⠯⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠀⢸⡀⠀⠀⠀⠀⢘⡗⠠⢻⡇⠀⠀⠀⠈⣶⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⡈⢿⣀⡀⣀⣠⡾⢱⠐⠈⢿⡢⠀⠀⣀⡾⢁⡆⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡠⠸⡄⠈⠝⢋⠏⠐⣸⣀⠀⢀⠻⡙⠫⠁⢠⠇⢿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡇⠀⠈⠒⠒⠁⠊⡐⣥⢠⡕⡄⠡⣌⠒⠒⠁⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢦⣀⣀⡴⠁⠀⠈⠁⠈⠁⠉⣆⠈⠱⣄⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⣼⣿⠀⠀⠀⠀⠀⠀⢀⠂⢸⡂⠀⣹⢫⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⡇⠀⢸⣀⣀⣀⣀⣀⡑⠚⡄⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠀⠂⣿⣏⣩⣍⣿⡇⠀⡇⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠇⠉⠉⠉⠉⠉⠄⠀⢧⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠀⠠⠄⣀⣀⠀⠞⠈⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠘⠋⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢸⣟⢀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⢤⣄⠶⣄⠤⢄⣤⡄⠀⠘⣿⣷⣿⣶⣶⡏⠶⠾⣷⣄⠀⠀⠀⠀⠀⠀⠀⡠⣶⠖⠲⢦⡀
⣺⡎⠀⠀⠀⠈⢀⢸⣿⡄⠐⡟⣤⠚⠉⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⢈⠘⠁⢀⣁⠀⣹
⣟⡇⠀⡀⠀⠀⣿⣿⣿⡇⢨⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⠀⠀⣿⣧⣤⣤⣨⣄⣽
⣿⣧⣾⡆⣶⣶⠻⣿⣿⣇⣾⣿⡀⠈⠄⠀⠀⠉⠀⠀⣠⢼⣾⡇⠀⠀⠀⣿⣿⡿⢋⠿⠟⣿
⣿⣿⠿⣣⡦⢡⣤⣹⠷⣿⣿⣿⠁⢠⣦⣘⣁⣀⣀⠀⠻⣼⣿⡁⢀⠄⠂⢙⣿⣷⣶⣶⣿⠗⣦⣀⣀⡴⠖⠛⠉⠉⠴⠄
⠛⣛⣷⣿⣯⣦⡹⣾⡆⣰⣿⣿⣾⣿⣿⡿⠙⢿⣿⣿⣆⡯⣿⣿⣿⠀⠀⢸⣿⣯⣏⣿⠿⣹⡇⣸⠯⠀⠀⠀⠀⠀⢠⣤⣧⠐
⠀⣷⣏⣿⣿⣿⣷⡄⢾⣿⣿⣟⣌⢹⣏⣾⢷⡄⠙⣿⢿⢃⡘⠙⠳⢿⣧⣿⣿⡦⣽⣥⣶⣿⢠⣿⣐⠉⠀⠻⣯⣁⠀⢹⣿
⣦⣿⣿⣿⣿⣿⣿⠷⣾⣿⣿⣿⢿⣾⣿⣿⢧⣉⣼⣏⣳⣾⡏⣆⠀⠀⠈⠻⢿⣷⣿⠇⢙⣡⣿⣿⢱⣿⣿⣿⠿⣿⣿⣾⣿
⠻⢿⣿⣿⣿⣿⣿⣦⣿⡿⠛⠁⠘⡹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⡀⠀⠀⠀⠀⠉⢻⣦⣿⣿⡿⢿⡞⣟⣿⡷⣤⣝⣿⣿⠍⠒
⠀⠀⠈⠻⣿⣿⣿⣿⠏⠀⠀⠠⡀⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⢀⠀⡀⠀⠀⠀⠈⠁⠀⠀⣾⣿⣾⣿⣶⣯⣽⣿⣷⡆
⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠀⠀⣷⢿⡘⡝⣿⣿⣿⡿⢹⣿⣿⡀⢰⣼⡤⣇⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⣿⣿⣿⣿⣿⡿⠃
⣴⢀⡴⠀⠀⠀⢿⡇⠀⢦⣄⢀⣿⣼⣿⣷⣬⣛⣻⣁⣾⣿⣿⡅⠀⡄⠛⣿⠀⠀⠀⠀⢀⡠⠛⣿⣾⣿⣝⣿⡿⢿⣿⡇⠀⢠
⣷⣿⠁⡄⣀⠀⣸⡇⠀⡌⣿⠚⡃⠈⢿⣿⣿⣷⣶⣿⣿⣿⣿⣟⣿⡇⣀⣿⡾⠀⢀⠀⠈⢠⢰⣿⣿⡹⣿⣿⣶⣿⣿⠃⠐⣸
⣿⣿⣰⠀⠉⡑⢁⣼⣆⣸⣿⢀⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⣿⡏⣿⣷⣿⣠⢀⣿⠀⡀⢸⠀⢟⣻⣿⣟⣻⡿⢃⣾⣅⣰⣿
⣿⣿⣯⠀⠰⠁⣀⣉⣀⣉⠛⢿⣉⡉⣿⢹⣿⣿⣻⡟⢛⣿⡀⣿⠁⢹⣏⣽⢹⣾⣟⠀⠇⣾⠀⢸⣿⢸⣿⢿⠏⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠻⠿⠭⠍⢪⣿⣿⢁⡁⣏⠘⠃⠙⢿⡟⣿⣿⣿⠻⣿⣶⣽⣿⣿⣿⣿⣴⣿⡇⠀⠠⢉⣾⡟⢾⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠁⡘⠳⠒⢢⣤⡙⢿⠸⣿⣿⠟⠛⠃⡸⣿⠋⣿⡁⠀⣶⡟⡴⠃⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣻⣿⣷⣿⠇⠀⠁⠉⣽⣿⣿⠗⣤⡏⠘⠛⠀⡄⡇⡠⣿⣿⣷⣿⠿⢠⠼⢋⠉⠻⣟⣫⣾⣴⣶⣶⠷⢾⣛⣡⢿⣽⢿⠁⢸
⣿⣿⣿⣾⣥⡎⠀⣠⣾⣯⣿⠏⠀⢹⣆⣴⡾⢰⡇⣿⡇⠘⣀⣩⡥⢖⣡⡾⣟⣶⣤⡈⠿⣿⣿⣍⣉⠙⠂⠈⣞⣿⠟⠀⠀⢸
⣿⣿⣿⣿⣿⠃⠀⠹⣿⣿⠏⠀⠀⠎⠨⣷⡄⠀⠆⣿⣦⠠⡿⣿⣿⣿⣿⣿⠿⣿⡃⠙⠆⠘⣿⣿⣝⡳⣮⡢⣼⣇⣠⠂⠀⠘
⣿⣿⣿⡟⣋⡀⠀⠀⠹⣿⠀⠀⠀⣼⡆⢹⠇⠀⡀⣁⣽⣦⡛⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⢀⣿⣿⣿⣿⢿⣷⣿⣯⠅⣀⣴⠄
⣿⣿⣿⣫⣥⡶⣦⣤⡀⢿⡄⠀⠀⠻⠀⠾⠶⣿⣿⣯⢉⣽⣷⠘⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣌⠻⢿⣷⠾⠟⣋⣥⣊⣽⣿
⢹⣿⣿⣿⡟⠀⠾⣿⣿⣾⡇⠀⠀⠰⣷⣜⣋⡽⣫⣿⣞⠙⠿⣇⣄⠀⠙⠛⠿⠿⠟⠻⣿⣿⣿⣷⡈⢻⣿⣹⣿⣿⣿⣿⣿⡂
⢸⣿⣿⣿⡧⠎⣠⣿⠿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣤⣿⣿⣦⣝⣿⣧⣤⣤⣥⣤⡶⣾⣷⣜⢻⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡟⠁⠀⣿⣿⣶⡖⠀⠀⠀⢘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⡛⢿⢿⣿⣿⣿⣿⣿⣦⡀⠙⣿⣿⣿⡇⡇
⣿⣿⠟⠀⣠⠘⣿⡟⠋⠀⠀⠀⠀⠬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣷⣾⣿⡿⣥⣼⣼⠿⣿⣿⣿⣿⣿⣷⣦⠘⣿⣿⡿⠁
⣿⣡⠀⣰⡿⢠⣿⣷⣖⠀⠀⠀⠠⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠉⠿⠀⠀⠹⣿⣿⣿⣿⢿⡆⠘⠻
⢻⡟⣸⣿⡇⢸⣿⣿⣿⠂⠀⠀⡀⠀⢲⣯⣿⣿⣿⣿⣿⣿⣿⣛⠓⠶⠶⣿⣿⣿⣯⠀⠀⠀⠀⠀⠙⣿⣿⣿⡸⣷⠀⠆
⣿⣿⣿⣿⡇⢸⣿⣿⡿⠃⠀⣠⠃⠀⢹⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡷⣿⣇⣿⣄⢺⣄⠂
⡿⣿⣿⣿⠃⣿⣿⠋⠀⠀⠰⡏⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⠿⣿⡥⠆⠀⠀⠀⠀⠀⠀⢿⡇⣿⣿⣿⣿⡇⢯⡆
⣷⠻⣿⣿⣇⣿⣷⣶⠄⠀⠸⢀⣪⣩⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⠀⡇⠀⠀⠀⢠⣺⣇⢿⣿⣿⠊⣷⡞⢰
⣿⠀⣻⣿⣿⣿⣿⣿⣴⠄⣬⣿⣷⣿⣿⣿⣿⣿⠙⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠁⣸⣧⣱⠀⠀⣸⣿⣿⢾⣿⣿⢿⣿⡁⠈
⠏⠀⠹⠛⠿⠿⠛⠃⠋⠸⠏⠻⠿⠿⠟⠻⠿⠛⠀⠀⠀⠀⠀⠈⠿⠿⠿⠟⠋⠀⠰⠿⠿⠁⠀⠀⠻⠻⠿⠿⠿⠿⠀⠿⠗⠶
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠃⠈⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⠁⠈⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⣛⣉⣉⡉⢉⡒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠶⠋⠉⢀⣀⣀⣉⣉⠐⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⡾⠁⠀⠔⠛⢋⡉⢉⣉⣙⣿⣿⣶⣤⣈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣾⣧⣤⣀⣠⡞⠁⠈⠁⣀⣤⣤⣬⣉⡙⠿⣷⣦⣙⠲⢤⣄⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣀⣴⠋⠉⢙⠋⠁⠉⠉⠛⠳⢶⣴⡟⠉⠁⠀⠈⠉⠛⠳⣤⡙⠻⣿⠷⢶⣿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⣶⠾⠿⠛⠛⠛⠛⠛⠿⢾⣷⣧⣄⡀⠀⠄⠀⢽⢿⣷⣄⣠⣤⣤⣀⡀⠈⠻⣄⠘⢷⡄⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⣉⣡⠤⠶⢶⣶⣾⣾⣿⣿⣶⣿⣶⣯⣟⣿⣿⣤⡈⢈⣼⣿⣿⣭⣭⣭⣭⣟⢷⣄⠙⣧⡀⢻⣆⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⡡⠔⠋⠁⠄⠒⠂⠀⠀⢈⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣷⠈⣷⠀⢻⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣾⠋⡴⢋⡀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⣠⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣇⠘⣇⠀⢿⣎⣿
⠀⠀⠀⠀⠀⢀⣾⣿⠃⠎⡐⠃⡀⠤⠤⠶⠞⠛⠋⠉⠀⠀⢠⣾⠟⠉⠀⢀⣴⡿⢿⣿⣿⢿⡿⣿⡙⠻⣯⡻⣽⣿⣿⣿⣿⡆⣿⠀⣿⠀⢸⣿⣿
⠀⠀⠀⠀⢀⣾⢣⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣰⡿⠋⢠⣾⡏⠃⠈⠻⣎⠻⣄⠈⢳⡌⡾⣿⣿⣿⠃⣿⠀⣿⠀⢸⡇⠉
⠀⠀⠀⠀⢸⡏⠈⢀⡟⠀⠀⠀⠀⠐⠒⠲⢤⣤⣄⣤⠶⠋⠀⠀⠀⣰⠏⢀⣴⡟⢻⡄⠀⠀⠀⠹⡆⠙⡆⠀⢻⠀⢻⣿⣿⢠⡏⢰⠇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⣼⠇⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠞⣁⣴⣿⢿⣧⡀⠳⣄⡀⠀⠀⠓⠀⠰⠀⠈⠄⢸⣿⡟⣼⢁⡎⠀⢰⡏
⠀⠀⠀⠀⠈⣿⣀⣿⠀⠄⢁⣤⣶⣶⣾⣷⣶⣶⣶⣦⣤⣤⣴⣶⠿⠿⠋⠁⠀⠙⠻⣦⣄⠙⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⢷⡏⡼⠀⢠⡟
⠀⠀⠀⠀⠀⠸⣿⣿⠰⢠⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢀⠀⠇⠀⢨⢠⣿⣿⡾⡐⠃⢠⠏
⠀⠀⠀⠀⠀⠀⢻⣿⡄⡼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣆⢠⢀⣼⣾⣿⣿⠃⠁⢸⠏
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢹⡇⠈⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⠇⠀⠀⡿
⠀⠀⠀⠀⠀⣀⣠⣽⡟⠘⣘⣧⣮⣤⣤⣤⣍⡒⠄⣀⣀⣱⡖⠀⠠⠤⠀⣀⣠⣤⡿⠶⠶⡄⠀⠘⣿⣿⣿⣏⡿⢻⡏⠀⠀⢸⡇
⠀⠀⠀⢠⡟⠉⣉⣹⣿⡿⠛⠉⣁⣤⣶⣿⣿⣟⠷⠾⠶⢿⣧⠀⠲⠾⠿⣿⣿⣿⣿⣷⣶⣄⡀⢀⣿⢋⣀⠙⢧⣾⡇⠀⢠⣼⣧
⠀⠀⠀⢸⠃⠀⣼⣿⣿⣧⣶⣾⢿⣏⠀⠤⠀⠈⡷⡀⠀⠀⠈⠀⡄⣠⣾⠁⠀⠀⠀⢹⣿⣿⠟⠉⣿⣿⣿⠂⢸⢸⡇⠀⡞⢻⣿⣦
⠀⠀⠀⠘⣇⠀⢹⣿⣿⡇⠈⠙⠷⣿⢶⣤⣴⣾⣶⣿⠇⠀⣀⠘⡇⠻⣿⣻⠦⠤⠶⠛⠉⢁⡀⢸⣿⣿⡿⠀⠘⠈⣿⣴⡅⠀⠈⠙⠛
⠀⠀⠀⠀⠘⣧⠈⢻⣿⡇⠀⠙⠦⣤⣤⣤⣴⡾⠟⡡⢀⡴⠶⠂⠰⡀⢨⡛⠶⣤⣤⠤⠶⠀⣠⣿⣿⣿⠃⠀⠀⠆⠘⢿⣇
⣀⡀⠀⠤⢞⡽⠷⠊⠛⣃⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⡞⢀⣠⣄⠀⠈⠢⠉⠓⢒⣒⣂⣤⣾⠟⢿⡿⠃⡠⠀⢈⠀⠀⠀⠙⢦
⠈⠉⠉⠀⠀⠀⠀⠀⢰⠋⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⣧⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡶⠶⢶⣤⣌⢠⡀⠀⠀⠀⠸⣿⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠸⣿⣿⣿⣝⠆⠀⠀⢀⡴⠄⡤⢤⣀⡀⣠⣤⠄⢴⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣻⣦⡀⠙⣏⣙⡟⠀⣀⠖⣋⡔⢶⡶⣦⣌⣿⣿⣿⠷⠀⠀⠀⢀⣾⠏⠆
⠀⠀⠀⠀⠀⠀⠀⠊⢠⣱⠏⠈⠻⣷⡿⠍⠃⠙⠻⣿⠟⠛⠻⠟⢋⡉⣿⡯⠝⠀⠀⠀⢀⡾⣿⡐
⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠘⣿⣆⠀⠀⠀⠙⢦⣉⣁⣉⣩⣭⠟⠀⠀⠀⠀⣠⠏⠀⠙⢷⡆⡀
⠀⠀⠀⠀⠀⠀⢾⠋⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠉⠉⡉⠉⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠙⢄⢀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣾⢿⣿⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⠿⣦⣤⣀⣤⣄⣀⣤⣴⠾⠋⠁⢸⣿⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢈⠈⠋⠁⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡊⠀⠀⢸⣿⣿⠀⠀⠐⠂⠀⢸⠞⠃⠀⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣠⣿⡿⠃⠀⠈⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠁⠀⠀⠀⠐⠂⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢳⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠉⠀⠀⠙⠓⠤⢄⣀
⠀⠀⠀⠀⣠⠴⠛⠁⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⠀⠀⠠⠀⠀⠀⠀⢀⣴⣆⠀⠙⠀⢀⡔⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠑⢆⠀⢀⠛⠳⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⡴⠋⢹⣿⣆⠀⢹⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡄⠀⠚⠁⠿⠒⠤⢄⡠⢀⣀⣀⣀⣀⣀⡤⠴⠚⠋⠉⠀⠀⡀⠹⣿⣦⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⡀⠀⠀⠀⠀⢸⣿⠀⡱⠀⠀⠀⠀⢀⣠⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣿⠀⠀⠀⠀⢸⠿⠛⣇⠀⠀⠀⠀⣿⣟⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⢶⡄⠀⢙⣿⣿⣤⣀⣀⣴⠷⢀⠄⠿⢦⣀⣀⣤⠿⣻⡉⠀⢠⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣇⣴⣿⣿⣿⣿⣿⣭⣥⣶⠏⠘⢦⣤⣬⣭⣴⠎⢼⡿⣦⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⣴⣿⣿⣿⣮⣟⣻⣿⣿⣢⣄⠀⠙⠛⠋⠁⠀⠘⣷⣦⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⢶⡶⠄⠈⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠓⠒⠲⠦⢤⣄⡀⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⣿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⢿⠿⢿⠿⣿⣶⣿⣿⣷⣝⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡏⢹⡷⠙⠧⠀⠀⠀⠀⢀⡤⠀⠈⠁⣹⠉⣿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣥⣤⣭⣀⢲⣄⠀⢈⣶⣏⣀⣤⢆⣀⣤⡄⣹⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⣿⣷⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⡙⠻⠿⠟⠫⣿⣿⣿⣌⠋⠛⠻⠿⢛⣥⣟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡥⣤⣴⣶⣿⣦⣺⣿⢿⣿⠄⢠⣶⣞⣂⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠋⠇⠘⠇⠀⠀⠘⣿⣿⣿⡟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠾⢷⡷⡇⡶⡶⠶⣾⣿⣍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣛⢿⣿⣟⡓⡧⡧⠷⢒⣻⡿⠟⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣽⣿⣿⣏⠻⡇⠉⠉⠀⢀⣤⠞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡃⠘⣦⠀⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠟⠻⠶⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣗⣀⠀⠀⠠⠴⠶⠦⣄⢠⠆⠀⣄⠀⣤⠖⠛⠶⣤⡀⠀⠀⠀⡦⠃⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⢿⠀⠀⠀⠀⣢⡀⢈⠁⠀⠀⢩⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠸⠆⠀⠀⠀⠉⠀⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠛⠀⠁⡀⠸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⢠⡄⠀⣠⠀⣸⢧⠟⠂⠳⡀⠀⡄⢧⠀⠀⠀⢠⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣾⠁⣰⠟⠀⠤⣈⡆⣹⠀⠀⠀⠀⠀⢠⡏⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣇⠠⠀⠜⠉⠀⠀⢀⡁⠠⠦⣄⠀⢀⠠⠀⢄⠀⡟⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⣤⠀⠀⠁⠀⢀⠀⣄⠀⠑⠄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⡀⠀⡅⠈⢙⡄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠀⠁⠈⡀⠃⠈⠃⠀⠐⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠨⠁⡀⠀⠈⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠈⠉⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢰⣿⣿⣷⠀⢐⣶⣄⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⣶⣶⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⢰⣿⣿
⠀⠀⠀⠀⠻⣿⣿⠟⠀⠈⢙⣯⡀⠀⢀⣿⣿⡧⠀⠀⢠⣿⣿⠋⢀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⣴⣿⡿⠃⠈⣿⣿⡀⣿⣧
⠀⠀⠀⣴⣾⣿⣿⣿⣆⠀⢹⣿⣇⡀⣠⣿⣟⣁⣠⣴⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣧
⠀⠀⣸⡿⣿⣿⣿⣿⢿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢰⣿⡟⢹⣿⣿⣿⣿⣿⠙⢿⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠛⠛⠃
⠀⠀⣿⠃⣿⣿⣿⡇⠀⢿⡆⠀⠉⢹⣿⣿⣿⣿⣿⡁⠀⠀⢸⣿⠀⢠⣿⣿⣿⣿⣿⠆⠸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⢀⡿⣸⣿⣿⣿⣷⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢰⣷⠄⢺⣿⣿⣿⣿⣿⡀⠀⡽⣄⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⢸⡟⣿⣿⣿⣿⣿⠀⠿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠀⢸⣿⣿⡿⣿⣿⣧⠀⠀⠋⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⡟⠀⠙⣿⣿⡆⠀⠀⠀⠀⣸⣿⣿⠋⣿⣿⣷
⠀⠀⠸⣿⣿⡿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡟⠀⢹⣿⣿⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⢹⣿⣧⠀⠀⠀⠀⣿⣿⠃⠀⣿⣿⣿
⠀⠀⠀⣿⣿⡇⢸⡿⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢻⣿⡇⠀⠀⢀⣿⣿⠋⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠈⣿⣷⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⢠⣿⣿⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠻⢷⠄⢸⣷⡀⠀⠀⠀⢸⣿⣿⣧⣀⠀⢠⣿⣿⡄⠀⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿⣧⡀⢀⣽⣿⠿⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠘⠿⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣴⡆⢀⣽⣿⡿⢋⣽⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣼⣟⣋⠰⣿⣿⣿⣿⣿⣿⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⣻⣧⣴⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣿⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⢿⢻⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠏⠉⠛⠁⠁⡀⠀⠀⡎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠅⠠⠄⠀⠀⠀⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⡇⠀⠠⠤⣶⡖⠂⠀⢰⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⢫⢿⣿⣿⣿⣿⣷⠀⠀⠀⠉⣿⣆⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡏⠓⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⣸⣿⣳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⣰⡿⠫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣆⠀⠀⠻⣿⣿⣿⣿⣿⣿⠛⢴⡿⢋⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣄⠀⠀⣀⣉⣉⣉⣁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠻⣦⣠⣌⣉⠉⠉⣉⣥⣶⣼⣋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⢿⣿⣿⣷⣤⣾⣿⣿⡿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡿⠿⠿⠷⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠠⡽⠻⢶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠈⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⠁⢀⡦⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣶⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⢈⡿⠂⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠐⠀⡀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⡠⢾⣶⣦⡴⠊⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⠋⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⠿⡀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣀⣿⡿⠀⠀⠀⠀⢀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⡦⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡇⢸⠟⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⢦⣄⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⣄⠹⠏⣿⣄⣸⣿⣄⡀
⠀⠀⠀⠀⠀⢰⣿⡇⠈⠻⣿⣿⠃⠀⣰⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠋⠙⢻⣦
⠀⠀⠀⠀⠀⠈⢻⣇⠸⣧⣼⣿⠀⣸⡿⣿⣿⣿⠿⠿⠷⠶⣾⣤⣶⣤⣠⣾⡟⠻⣶⣄⣠⡀⣤⣤⣶⣿⣿⣿⣶⣤⡄⠀⢰⣿⢁⣤⠾⣾⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣦⢺⣿⣿⡆⢹⡇⣿⠈⠻⢷⣤⣤⣤⣾⣿⣿⢿⣿⡃⠀⣄⠙⡟⣽⣿⣿⡉⠀⢀⣸⣿⠟⣻⡿⡀⢼⡇⢸⡟⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣷⣿⣧⠀⠅⣙⣶⣶⣿⠗⣤⣼⣯⡕⢠⡿⡟⢠⣿⣿⢠⡇⠘⣿⣿⣿⣿⣯⡭⠔⡃⠘⣷⠀⠀⣷⣾⡦⢾⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⣿⣄⠉⠀⠰⠿⠿⠿⠏⢙⡿⢹⡿⡴⠋⠁⣶⣿⣛⣿⣷⡌⠀⠀⢙⣿⠷⣦⣤⣊⣵⣶⡛⠀⠘⠛⣿⣇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣼⣿⣷⣆⣀⣠⡀⠀⠁⠀⠐⢛⡇⠀⠀⠀⠾⠿⠋⠉⠻⠇⠀⠀⢪⠻⠆⠀⠀⠁⠀⢸⡦⢰⣶⠿⠛⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣏⠋⠀⣿⠃⣠⣴⣄⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⡟⠁⣾⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢦⣿⢀⣿⣥⣾⣿⣿⠈⣣⣄⡀⠀⠀⣀⣦⠀⢠⣀⣀⣀⡀⠀⠀⣠⠀⣠⠎⢰⢡⡆⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⠘⣿⣿⣿⣧⣿⣿⣯⣸⣿⣶⣟⢛⣿⣧⣸⣿⣏⣹⣿⣿⠤⣿⢾⣟⢀⣻⣸⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢻⣿⣇⣹⡿⣿⣯⣭⣴⣿⣿⣿⣻⣿⡿⣿⢿⣿⣿⣿⠿⣿⣿⣾⣷⣾⣻⣿⠟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣰⠰⣿⠃⢸⣿⣿⢿⠟⠁⡿⠟⠏⠉⠛⠱⠃⠀⠉⠙⢡⠠⠉⠻⠿⣟⡿⣽⡷⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡟⠀⢈⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠼⡇⠀⢸⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣇⠃⠀⠈⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⡞⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣼⣿⣿⣆⠀⡀⠀⢠⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣾⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣿⣿⣿⣿⣿⡆⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⣿⣿⣿⣿⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⢻⣿⣿⣿⣿⣿⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣭⣟⣀⣼⣿⣿⣿⣿⡇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡆⣁⠈⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⡇⠻⠀⢿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢰⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣼⠋⠀⠀⢸⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⢻⡟⣼⣿⣿⡏⠀⠀⠘⣧⢹⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣴⠟⠄⣀⣀⠸⢿⣿⣏⠻⣿⣧⠀⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣵⣿⠟⡐⡏⣰⡟⠃⡼⠀⠀⠀⠀⣹⣆⢿⣿⡄
⠀⠀⠀⠀⠀⢰⣿⠟⠉⠁⠀⡴⠉⠀⠀⠀⣿⠙⠁⠹⣿⣇⠀⠘⢉⣿⣷⣄⠉⠛⣿⠟⣻⣿⣿⠇⢠⡟⣰⡿⠁⠸⠃⠀⠀⢀⠀⠻⠏⢢⡽⣿⣄
⠀⠀⠀⠀⢠⣿⣿⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⠧⠤⠄⠘⢿⣦⡀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠪⣤⡀⠀⠀⠀⠘⡿⢷⣄
⠀⠀⠀⢠⣾⠋⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠘⣿⡟⠿⠟⠉⠉⢸⡟⠀⢀⡼⣹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢀⡈⠻⣷⣆
⠀⢀⣴⠿⠋⠀⣬⣿⣿⠷⣶⣶⣦⣀⣀⡀⣀⣄⠀⠀⠠⣤⣀⠹⣿⣷⡌⠻⡄⠀⠀⠀⢈⣠⣶⣿⣷⢃⡄⠀⠀⠀⢀⣀⣠⣤⣀⢀⣤⣴⣶⣟⣁⣀⠀⠙⣿
⠰⢿⣧⣶⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣦⣤⣤⣉⣳⣿⣿⣿⣷⣾⣦⣤⣾⠿⢿⣿⣿⣿⣿⣷⣦⣶⣾⣿⣿⠛⠿⠯⠉⠙⠛⠋⠉⠉⠉⢱⣾⠟
⠀⠀⠈⠙⠿⣷⣶⣆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⠶⠌⢙⣿⠛⠛⠛⠿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢷⣄⣾⡏
⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⣿⣷⣦⣤⣄⣀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⣠⡟⠁⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠶⠶⣦⣤⣤⣤⡀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠶⠿⠿⢷⣶⣶⡿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣈⣤⣤⣯⣄⣼⣀⣰⣷⣥⣴⣟⣱⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣖⢒⣶⣶⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣿⣿⣦⡰⣶⣦⣬⣭⣓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢷⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⡴⣚⣭⣭⣿⣭⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⣿⣛⠿⠿⠿⢿⣿⣶⣦⣤⣀⡀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠉⢻⢉⣿⣹⣿⡏⣩⣤⣤⣽⣛⠿⢿⢿⣿⣶⣶⣄⣠⣿⣛⣛⠿⠃⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢪⣳⣿⠡⠀⠿⣿⣷⣾⣿⠟⠉⣾⣟⣽⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣤⣄⣈⣩⡥⠀⣠⣶⣾⠙⠽⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⠙⣿⣿⣇⠀⠀⠋⠛⠀⣴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⣾⠃⢹⠂⠈⠻⡷⣶⠤⠀⢠⡤⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠠⡘⢶⣦⠰⢄⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⣀⣠⣾⣿⣿⣿⡶⢬⡙⠻⢷⣤⣤⣤⣶⡤⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣿⣿⣿⣿⣿⣷⣻⣦⡀⠀⠑⢮⡙⣿⣏⣦⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣿⣿⣿⣿⣷⡹⣿⣄⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣍⣿⣌⢿⣷⣄⡟⠙⣿⣏⠻⠛⣿⣿⣿⣷⣷⣄⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⡁⠀⢿⣿⡄⠀⢻⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⣺⣿⣿⣤⣼⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⡆⣶⢰⡆⡿⢳⠀⡟⠛⠀⣾⡆⢰⡟⣶⢸⣦⠇⣶⢰⡆⠀⢺⠀⠀⣿⠛⢰⡟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⣿⡇⡇⢸⠀⡷⠒⢠⣏⣧⢸⡇⣿⢸⣿⡀⣿⢸⡇⠀⢸⠀⠀⣿⠒⢸⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠃⠟⠹⠃⠷⠾⠀⠷⠶⣼⣿⣯⣭⣽⣟⢾⡋⠇⠿⠸⠷⠦⠺⠶⠆⠿⠶⠘⠇⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡖⣲⣶⣶⣶⠖⣶⣾⣿⣿⡿⠿⣿⣿⣮⣝⣶⡶⢲⣶⢶⣶⣶⡶⢲⣶⣶⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣫⣾⠿⠿⠿⠋⣼⣿⣿⣿⣿⢑⢀⠉⢿⣿⣿⡟⣴⣾⣃⣿⣿⣿⢡⢸⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇⣾⣷⡆⢺⣿⣿⣿⣿⣾⣦⣿⣶⣿⣿⣿⣇⣿⣽⣿⡿⣿⢯⣿⣦⡥⠸⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣿⢟⣴⣿⣧⢸⣿⣿⣿⣛⣛⢻⣿⣟⠟⣫⣽⣿⣿⡿⣟⣹⣫⢮⠏⢠⣾⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡏⣡⣴⣿⣿⡿⢋⣼⣽⣿⠏⢻⣿⣾⣏⣹⣷⣿⡿⣱⣿⣿⣌⣿⣇⣈⣤⣿⢿⡛⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣻⣖⣿⣿⣿⢿⡻⣌⠙⠛⠾⠿⣾⢿⣿⠋⣿⣿⣿⣿⣷⣽⣿⣟⣿⣣⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⣾⣷⣿⣿⢿⣿⣿⣷⣝⢬⡉⠙⢿⣶⣶⣾⢟⣾⣿⣿⣿⡏⣿⣿⣿⢟⡏⣿⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾⣶⣴⣶⣾⣿⡿⢃⣿⣿⣿⣴⣿⣿⣿⣿⣧⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⢻⡿⣯⠻⣿⣝⣿⠿⠋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣮⣿⢶⣀⣀⣠⣴⣿⣿⣾⣿⣿⣿⡟⣹⣿⣯⣿⣯⢽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣓⣚⣹⣍⣙⣿⣿⣿⣿⣿⣯⣿⠿⣿⣿⣿⣿⣷⣹⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣴⣿⣯⣵⣿⣷⣮⣽⡿⢼⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⢿⣷⣿⣿⣽⣿⣷⣿⡿⠿⣿⣿⢿⣟⣿⣦⣽⣿⣽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣿⣿⣿⣿⣿⣽⣿⣾⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⢋⠉⣩⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⠾⠿⠿⠿⠿⢿⣧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⣇⠿⠿⠧⠾⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠦⠴⠙⠂⠴⠠⠰⠆⠂⠆⠰⠀⠤⠆⠰⠠⠴⠷⠀⠰⠐⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⡄⢶⡀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢋⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣼⣿⣻⣆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⠃⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣼⣿⣍⣰⣿⣿⠛⠀⠀⠘⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡏⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠁⠀⠀⠀⠀⢹⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠛⢋⣉⣉⣉⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⣀⠀⠀⢸⢰⡇⣀⡀⠀⠀⠀⠀⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⠀⠀⣀⢸⡆⡇⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠙⣦⣾⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠘⡀⢀⠃⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣷⣴⠋⠁⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⢸⠀⠀⡤⢶⣤⡀⢨⡏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢡⡌⢀⡴⠋⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⢹⡅⢀⣤⡶⢤⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣆⠈⠀⣿⣿⣷⠘⣇⠀⠀⠀⣀⣷⣄⣀⣀⡆⠀⠀⠀⠀⠈⣷⢸⡇⣾⠁⠀⠀⠀⠀⢰⣀⣀⣠⣾⣀⠀⠀⠀⣸⠃⣾⣿⣿⠀⠁⣰⠁
⠀⠀⠀⠀⠀⠀⠘⣆⡀⢻⣿⣿⠆⠈⢿⣿⣿⠉⣿⣿⣿⣿⣿⣶⣤⣤⠞⣠⣿⣸⣇⣿⣄⠳⣤⣤⣶⣿⣿⣿⣿⣿⠉⣿⣿⡿⠁⠠⣿⣿⡟⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠙⣻⠀⠀⠈⣿⣿⣆⠹⢿⣿⣿⣿⣿⡿⠋⣻⣿⡿⠻⠟⢿⣿⣟⠙⢿⣿⣿⣿⣿⡿⠋⣠⣿⣿⠁⠀⠀⣟⠋⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠻⣷⣄⠀⣟⠣⠊⠓⢄⡉⠉⠉⠉⠀⠴⠟⠟⠁⠀⠀⠈⠻⠻⠦⡀⠉⠉⠉⢉⡠⠚⠑⠜⣻⠀⣰⣾⡟⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠊⠀⡇⠀⠀⣀⠀⠬⣥⣤⡤⠶⢲⡆⣜⣭⣐⣒⣬⣣⣰⡖⠶⢤⣤⣬⠥⠀⠀⠀⠀⢹⡀⠑⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⢀⣼⠓⢿⡟⣿⣥⡀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣟⢇⠀⠀⠀⠀⠀⢠⣀⣾⣦⣸⣧⣀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠸⡔⠿⠾⠟⠉⠋⠀⠀⠀⣨⠴⣿⣿⡯⠶⠲⢽⣿⣿⠦⣅⠀⠀⠀⠀⢀⡙⣿⣿⣿⠇⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣖⢿⣍⠀⠀⠀⠀⠉⠈⠁⠀⠀⠈⠁⠉⠀⠀⠀⠀⣩⡷⣺⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢸⡯⣑⠺⠺⡶⢤⡴⢄⣠⣄⡠⢦⡤⢶⠖⠗⣊⢽⡇⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⢸⣇⠈⠋⠶⢢⠤⣄⠤⡁⢈⠤⣠⠤⡔⠶⠙⠉⣸⡇⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢸⣧⢉⡖⢆⣈⠀⡇⠀⢸⡇⠀⢸⠀⣀⡰⢶⡉⣼⡇⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⢌⠢⣑⠆⣨⡉⢹⠀⢺⡇⠂⡏⢉⣅⠰⣈⠔⣡⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣌⠙⠢⠵⣉⣦⣎⣱⣴⣉⠮⠔⠋⡡⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠉⠓⠶⣶⣶⣂⣶⣶⣶⠶⠚⠉⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂⠀⠀⠀⠀⠀⠀⠻⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠸⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⢺⠴⠖⠀⠘⠀⠀⠀⠀⠰⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢂⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⢀⠈⢻⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣧⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣀
⡇⠀⠀⠀⠀⠴⠿⠀⠀⡀⠀⠤⠀⠀⠀⠀⠘⠀⡈⠀⠀⠀⠀⠐⠀⠀⠹⢧⠂
⡇⠀⠀⠀⠀⠂⠀⠀⢀⡉⠅⠀⠀⠀⠀⠀⢀⠂⠇⡝⠀⢠⡤⠆⠀⡄⠀⠰⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡇⠀⠀⠀⠀⠂⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠐
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠐⠒⠠⠄⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢰⠃⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⡀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠓
⡇
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢟⣛⣛⠛⠚⠻⠿⢆⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⡋⢰⡏⠃⠈⠓⠀⠀⠀⠀⠐⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠀⠺⠧⢈⣁⠀⢀⠉⠁⢤⣆⠀⢾⣿⡟⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⢀⠀⠹⠇⠹⣦⠀⣴⠠⠐⠋⠋⢈⣛⡛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⢤⣷⣤⣴⣄⠀⣤⣤⣤⡒⠒⠋⢻⣧⠀⠀⠈⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⢀⣠⣿⣟⠉⢁⣿⣿⣉⣿⡟⠲⠄⣸⣿⣇⡀⠀⣠⠞⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣤⡴⠿⠿⠟⠛⠲⣿⢟⣿⣿⣿⣷⣄⠀⠀⠈⣻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣶⣦⣈⡛⠛⠋⠉⠉⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⣭⢿⣿⣶⣶⣄⣤⣤⡤⠀⠀⠤⣠⠤⠂⠤⣤⣦⣤⣴⣦⡤⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣿⣿⣿⣤⣤⡁⠀⠀⠀⠀⣆⣀⣀⠀⢹⣿⣿⣿⣿⣷⡶⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢿⣿⣿⣿⣿⣷⡄⢀⣴⣿⣿⣿⣷⡌⣿⣿⣿⣧⣬⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢹⡈⢿⣿⣭⠽⠋⡇⠀⠙⠻⠽⠿⠿⠁⣿⣿⠿⠦⡁⠉⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠠⠶⠴⢦⣤⠤⠘⢦⣄⡀⠀⣿⣿⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣄⣠⣤⣦⣤⣤⣤⣀⣤⡽⢸⣿⡿⣄⡘⠠⠀⣀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠙⠿⣿⣿⣛⣿⡿⠟⠉⢀⡿⠋⡳⢄⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣆⠀⠀⠀⠉⠉⠁⠀⢠⣀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡼⣽⣦⣀⡀⠀⠀⢀⣀⡾⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣷⠙⣿⢹⣿⠗⠛⠉⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠈⠿⣤⣼⣿⣇⠀⠀⠀⠀⠀⣀⠾⠃⣼⡇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠹⠧⠀⢤⣄⡘⢻⡟⣿⣄⠀⠀⣤⠗⠂⣀⢮⠽⠒⠓⠄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠛⠷⢸⣿⡀⢻⠆⣠⠁⡐⠋⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣀⠀⣀⣀⣠⣤⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣽⣟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠹⡉⠈⠋⠀⠀⠉⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣄⣾⣭⡻⠦⢄⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⡤⢾⣿⢿⣿⠟⣿⣿⣦⣀⠁⠈⠀⠀⠀⢸⠏⠀⠀⠰⢿⣿⣷⣶⣤⣤⣤⣤⡼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣠⡶⠖⣻⠇⠘⣿⠀⡍⠀⠉⡿⢹⣿⡶⣦⣤⡀⢠⠟⠀⠀⠀⠀⠀⢧⠀⡈⠉⠀⠀⠈⠁⠀⢸⡇
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠉⡁⠀⠉⠀⠀⡏⢠⠀⠀⣠⠀⠀⢸⣇⣟⣛⠛⠋⠀⠀⠀⠀⠀⠀⠈⢧⡘⢢⠀⠀⠀⠰⠀⢺⡇
⠀⠀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⠘⡄⠀⠀⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠀⠀⢹⡇⠀⣸⠇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡇⢸⠇⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣷⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⡄⡆⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠸⢇⠹⢿⣶⣧⣿⡄⣠⡴⠟⣿⣇⡄⠀⠀⠀⠀⢀⣠⣴⡿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠹⠀⠀⢿⣿⠿⣿⠟⠴⠷⠿⠛⡏⠀⠀⠰⢴⠾⡿⠛⠁⠜⠀⠦⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣤⠄⡄⣠⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠋⠙⠛⠁⠋⠁⠀⠀⠀⠀⠀⠠⣿⡻⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠽⠇⠹⠏⠸⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣶⣶⣶⣶⡄⣠⣶⣤⣶⣾⣷⣶⣦⡄⠀⢹⣿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⣻⡟⠁⠙⢿⠿⠍⠀⠉⠻⣿⣿⣶⣏⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣇⢸⠿⢘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡍⠄⣸⢃⣀⡀⢼⣀⠐⠀⠀⠀⠛⢻⣿⣿⣿⣿⣽⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⠀⠀⣼⣿⣿⣦⣹⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⠻⣿⠃
⠀⠀⠀⠀⢰⣶⡆⣶⣰⣦⡖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⠀⠹⣿⡭⠟⠉⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⣿⡎
⠀⠀⠀⠀⠈⠃⠀⠃⠙⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⣀⣀⣠⡀⢀⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣴⠟⠁
⠀⠀⠀⠀⠀⣠⣄⢠⣀⡄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠛⠁⠉⣿⠿⣿⡿⠫
⠀⠀⠀⠀⠀⠿⠼⠠⠿⠆⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠿⠿⠿⠿⣿⡿⡂⠀⠀⡄⠀⠀⣹⣇⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣄⣀⣄⣀⠸⠆⡀⠀⠀⢘⣠⠉⢀
⠀⠀⠀⠀⠀⢸⣲⡿⠇⣟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠁⠉⠈⠉⢿⠊⢀⣿⣠⣿⠁⠀⢨
⠀⠀⠀⠀⠀⠚⠁⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣾⣶⣶⣿⣿⣿⣿⡿⠟⠠⠀⠈⢁⡄
⠀⠀⠀⠀⠀⣴⣦⢰⢦⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠛⠛⠋⠀⠀⠀⡀⣀⠀⣿⣥⠃
⠀⠀⠀⠀⠀⠛⠁⠘⠞⠃⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣠⠟⢻⡿⠐⠢⢀⣴⠀⠀⠀⠀⣤⠀⠰⠆⠐⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡁⢀⣤⣾⠛⠋⢰⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠉⣀⡭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡄⠀⠾⠿⠿⠿⠿⡀⢀⣼⠖⠋⠀⠀⡀⢀⣤⠶⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣭⣿⣿⣿⡿⠭⠐⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⣿⣿⣿⣿⣯⠂⠀⠀⢲⠀⢹⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠀⣾⣿⣦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⠐⢡⣷⣿⣿⣿⣿⣷⡝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣯⢹⣽⣿⣿⣿⣿⣿⣿⣭⣖⡶⢯⣙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣆⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣰⣿⣷⣮⣟⡿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣿⣿⣿⣿⣿⣿⡿⢿⠛⠻⠿⠿⣶⣤⣍⣉⡛⠛⠟⠻⠿⠛⠛⣿⣿⣿⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣿⣿⣿⣿⣿⣿⣷⡶⣴⣶⣦⣤⠄⣤⣤⣾⣿⡝⣿⣶⣶⣶⣾⣿⣿⣿⡇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⠃⡻⠿⠿⠟⣴⣞⠿⠿⠿⡂⢻⣿⣿⣿⣿⣿⣿⣿⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡛⠐⠿⠿⠐⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⣿⣿⡿⢛⣍⢻⣿⣷⣿⢸⣦⠤⠤⠤⣴⡟⢸⣧⣿⣹⠟⣹⡛⢿⣿⣿⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⣿⣤⡟⣿⣦⣿⣿⣿⣾⡙⠓⠠⠒⠋⣥⣾⣿⡿⢃⣾⡿⣻⣦⣿⢇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠳⡜⣿⢻⣿⣿⣟⢧⣻⣿⣿⣤⣤⣤⣼⣿⣿⡟⣡⣾⣏⣵⠟⡿⢫⠞⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠿⠼⠾⠄⠭⡅⢹⡷⠽⣝⣿⠿⣟⡻⢿⡿⣫⠾⣿⡇⢩⠭⠤⠷⠯⠿⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣳⣭⣤⢤⣐⣤⡻⣧⡒⠍⣳⣯⣵⡾⠍⢂⣽⢟⣤⣦⡤⣤⣭⡛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠸⡆⠙⢿⣿⡿⢾⣭⣷⣿⣿⣿⣿⣿⣽⠷⣿⣿⡿⠋⢰⠇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠳⠽⢿⣟⣛⣛⣻⡿⠯⠚⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢈⡷⢇⣤⠀⠀⠅⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⢀⢀⡀⣘⠀⠋⠁⠀⢀⣠⠀⣠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢃⡠⣤⡜⠒⠈⠐⣡⠀⠀⠈⠀⣄⡼⠃⠀⢀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣶⢠⡴⢀⡾⠀⠀⠀⠀⠘⣁⡀⠀⠀⠈⠻⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢯⣵⣾⠇⠀⠀⠀⠀⠀⠻⢟⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠄⠀⠐⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⡀⠀⠀⠀⠀⢈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⣳⡆⠀⠀⣴⠏⠚⠙⡑⢠⠔⠀⠀⠀⠀⠘⣄⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠀⡀⠈⠁⠉⡀⣤⠟⢀⠺⠈⠀⠁⠀⠀⠀⠂⠠⠖⠚⠁⠉⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠬⠕⡀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠀⡔⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⡄⢷⠶⠀⠀⠀⠠⣾⠟⢛⠓⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡐⠁⠀⠀⠀⠀⠀⠈⠀⢈⡚⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡠⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⢒⢤⣀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡔⠒⠏⠁⠀⠀⡠⠟⠛⠛⠛⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠴⢤⡴⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠈⠉⠀⠁⠀⠀⠑⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠲⠄⠀⠀⠠⠀⠀⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠀⠠⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠠⠆⠀⠖⠃⠀⠀⠁⠀⠋⠀⠀⣌⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⠀⡀⠃⠀⠀⠀⠀⠀⠀⠣⠀⠴⠆⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡤⡀⠀⠀⠀⠀⠀⠀⢀⠰⢠⠆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠖⠁⠒⢦⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡜⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠤⡁⠀⠉⠙⠀⡀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⠁⠘⠀⣀⠔⠡⠈⠉⠲
⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡻⣤⡽⠄
⢀⡀⠧⠤⠄⡉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⠴⡇⠇⠀⠀⠀⠀⠀⠐⠆
⠀⠢⠐⢂⠲⠦⠀⠁⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠐⠁⠀⡇⠰⠀⠀⠀⠀⠀⢀⡲⠄
⠀⠘⢍⡠⠔⠊⠶⠆⠀⠀⠀⡠⠉⢈⣀⡒⠒⠒⠺⠖⠲⠒⠚⢋⡤⠊⠀⠀⠀⠀⡗⠀⡀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠣⡀⠔⠁⠒⠈⠀⠀⠀⠀⠀⠉⠉⠰⠄⣀⠤⠚⠁⠀⠀⠀⠀⣠⡎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡀⢉⣠⡤⠤⠤⠀⠒⠒⠈⠁⣠⠏⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠉⠁⠈⠉⠠⠤⠤⠤⠤⠤⢬⠀⠀⣀⡀⠤⠄⠒⡝⠀⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠈⣠⠔⢀⢰⠰⠢⠤⠴⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⢤⠀⢼⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠃⠘⢨⠀⠃⠸⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠢⡀⠀⡏⠀⠀⠀⠔⢒⡶⠇
⠀⠀⠀⠀⠐⠠⠄⠀⠀⢠⠀⠑⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢄⣀⠈⠑⠃⣀⣀⠀⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⠔⠊⠀⠈⠉⠉⠀⠀⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢤⣀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡰⣎⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢦⡀⠌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠠⢶⠤⠤⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⢩⡄⠀⠀⠑⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢁⣈⣠⡄⠀⠐⠀⢀⣀⣀⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠈⠀⠀⠀⠀⠀⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠀⠀⠀⠠⠤⠤⠞⠧⠤⠬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣠⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢹⡆⠀⠀⠀⡄⠀⢠⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣀⠀⣷⢠⠀⠀⢇⡀⢸⢇⠀⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⢻⡄⠈⢧⡄⠰⢧⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣾⡱⣄⢸⣧⢹⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣀⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣼⠸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⢈⡩⠀⠀⠊⠁⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠹⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠿⣿⣩⣭⣽⠗⡫⢚⣤⣶⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⡦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⣿⣿⣅⣠⣀⣩⣤⣀⢛⣟⢩⣽⣷⠾⣾⣿⡿⣟⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣶⡉⠀⠀⠀⠀⠈⠛⠩⠣⣿⡖⢚⣛⣻⣾⡿⣛⣿⣿⣿⣿⠻⣯⠿⣬⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⢧
⠀⠀⠀⠀⠀⠀⢀⠹⡏⣿⣾⡿⡀⠀⠀⠀⢀⣤⣶⣤⣌⠙⣿⢿⠷⣶⣿⣿⠿⣿⠛⣡⣟⣹⣾⣟⣛⡱⢦⣬⠛⢮⢻⣿⣿⡿⣿⣈⡄
⠀⠀⠀⠀⠀⠀⠁⠸⢹⣿⣿⣿⣗⣀⣠⣈⠛⠿⠿⠿⠋⠀⢸⣷⣿⣿⣿⣿⠛⣻⣳⣏⣾⣋⣉⣉⠉⠙⠷⣌⠳⣮⠃⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⡅⢾⣿⣿⣿⣽⣿⣿⢷⡆⢀⠀⠃⢺⣿⣈⣿⣿⣿⠿⣿⣿⣿⣍⣛⣋⣛⣛⠿⣶⣵⣌⢳⡼⡇⣿⣿⣾⢿⣿⣿⡃⢀⣠⣀⡀
⠀⠀⠀⠀⢠⠊⠀⠀⡆⣸⢿⣻⣿⣿⣿⣏⣼⣷⣏⡷⠠⠘⣿⡿⠚⢻⣿⣷⣎⠻⣮⡛⣿⣿⣿⣿⣿⣮⣻⣿⣆⣴⣿⣿⡿⣿⣿⣿⣿⣟⣹⣿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⣿⣿⣿⣿⣿⣿⣿⣿⢂⣴⣾⣿⣟⣶⣾⣿⣿⣿⣦⣹⣷⢸⣿⡈⣿⣿⣿⣷⣹⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠸⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣷⣋⢛⣻⣶⣿⣿⣿⣿⣿⣧⣹⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣘⣿⣿⣟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣻⣯⡻⣏⢻⣻⣷⣿⣏⣉⣈⣉⣥⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣪⡿⠃⠀⠉⠛⠫⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢮⣿⣉⣀⠀⠀⠀⠀⢢⣿⣿⠟⠁⠀⠈⠁⠀⠀⢀⣼⠿⢋⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⣰⣿⠃⣠⣾⡟⣿⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⠀⠀⢀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⣾⠟⢁⣴⡿⠏⠀⠋
⠀⠀⠀⠀⠀⢀⡼⠛⠉⠁⠈⠀⣀⣴⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠴⠿⠃⠀⠀⢀⣠⣴⣿⡿⠋⠈⠉
⠀⠀⣴⣏⣀⡄⠀⠀⢂⣿⣿⡿⠋
⠀⣾⣿⣿⣿⡦⠀⠀⠸⣿⣿⣧
⠀⣿⡟⠉⠀⠀⠀⣀⢾⣿⠅⠻⡇
⠀⡿⠀⢀⣈⡄⣀⣿⡈⠟
⢀⠙⡄⣻⣿⠈⣿⠋⢷⡄
⢸⣶⢇⣿⣴⣇⣙⠀⢸⣷
⡐⢩⡆⢹⣶⠁⣿⡀⠀⣿
⠛⣦⡅⢸⡇⠀⠘⠇
⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠠⠄⢈⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠠⠀⠘⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠃⠀⠀⠀⠀⠀⠀⢰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠒
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠸⢿⣷⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⡀⠀⠁⠀⠀⠖⠀⠀⠘⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠴⠋⡾
⠀⠀⠀⠀⡀⢳⣄⠘⠀⢀⣠⡾⠁⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠻⣈⢧⣵⣗⢠⡏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⡅⠂
⠀⠀⠀⠀⠀⠏⠰⣿⠛⣀⠃⠀⠀⠀⠠⢀⡤⠬⠝⠷⢾⣦⣀⠀⣴⡟⠀⠀⠀⡎⠀⠀⢀⣤⠶⠋⠉⠛⠻⢷⣦⣄⠀⠀⠀⠃⠀⠀⢀⣿⡼⠋⠙⠿
⠀⠀⠀⠀⠁⢀⡀⠘⢷⣿⣰⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⠳⣄⠁⠂⠀⠀⠷⠇⠀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠀⢸⡟⠀⣰⡆
⠀⠀⠀⢠⠀⠀⢻⡄⠀⠹⣿⠀⠀⠀⠀⡀⠐⠃⢈⣷⡀⠈⢦⡀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠠⢤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⢀⣏
⠀⠀⠀⠀⠄⠀⢸⣿⠀⠀⣿⡄⠀⠀⠈⠀⠀⠀⠘⠋⠁⠀⠘⠋⢱⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⠏
⠀⠀⠀⠀⠠⡄⠀⠋⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣄⡀⠀⠀⢘⡀⠀⠀⠀⣿⠀⣴
⠀⠀⠀⠀⠰⠃⢀⠀⡀⠸⠆⡀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠂⠀⠀⡆⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆⠀⠛⠀⠀⠀⠀⠟⠀⠇
⠀⠀⠀⠀⠀⠀⠈⢸⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⢀⣀⠈⢴⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⡄⠀⣠⡄⠀⠀⠀⢀⣠⠀⠀⣸⡟⣠⡛⠙⢇⠈⢷⡄⠀⠀⠀⢰⡄⣷⡀⠀⠀⠀⠀⠀⠀⢀⠋⠀⣶⣾⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠛⠀⠛⠋⠀⢀⣴⡾⠁⠀⣰⣿⡇⠘⠃⠀⠈⣦⠀⠙⣦⡀⠀⠸⠃⠈⠳⡆⠀⡀⠀⠀⣠⢿⠄⠀⠻⠿⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⣰⣿⠏⠁⠀⠄⣤⡀⢘⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⡟⣀⠀⠀⠉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⣻⡇⠀⠀⠀⠀⠀⣠⠞⠷⠀⠀⠙⠁⠀⠰⠒⠀⠀⡌⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡇⢸⠀⢴⡄⠠⠉
⠀⠀⠀⠀⠀⠀⠈⠒⠦⠚⠹⣿⡀⠀⠶⠀⡾⠁⠀⠀⠀⠀⠀⠠⠤⣤⠤⠦⠶⠛⢶⣄⡀⠀⠐⣄⠀⠋⠀⠈⣦⠀⠀⡾⠁⢁⣿⠀⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⠳⡄⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⢠⠀⠈⠈⢁⠀⡀⠈⠙⢦⠀⠀⠈⢳⡀⠃⠀⠸⣧⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠠⠀⠀⠀⠀⠄⠀⢠⢀⣸⣀⣼⣧⠙⢄⠀⠀⠑⠠⡀⠀⠂⠀⠀⠀⠷⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠄⠐⠠⠙⡇⠈⢧⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠻⡄⠐⣧⠀⢸⡆⠀⢸⡇⠀⢠⠀⠀⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠃⠀⠉⠀⠀⠃⠀⠈⡁⠀⠿⠀⠀⠁⠛⠀⠀⠀⠘⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣀⡀⠀⠀⠀⣀⡤⠞⢀⡴⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⡀⠀⠀⠀⠀⠠⢤⣀⠁⠈⠁⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⡄⠀⠀⠀⠀⠀⠈⠙⠓⠤⠤⠴⢂⠉⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣼⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢦⣤⣤⠤⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠉⠀⠀⠀⠀⠀⣀⠀⠈⠉⠛⠳⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣇⣾⣷⣷⣶⣗⣠⣾⣵⣶⣴⣶⣶⣤⡄⠀⠀⠹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠛⠛⣛⠉⠀⠀⠀⠀⠼⣯⣁⠀⠒⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣻⡛⠃⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡆⠀⢠⡇⠀⠀⠀⠟⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠤⠤⠴⠒⠈⠀⠀⠒⠒⠢⡕⢼⠁⠀⣨⣄⡀⢠⠀⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠑⠌⢂⠀⠑⠂⠀⢄⣠⣤⣄⡀⠘⠄⠠⢿⣉⠀⠀⠜⢁⣠⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣄⡀⣀⣸⣧⣠⣤⣴⡿⠟⢿⣿⣿⡄⢀⠀⠸⡏⠀⢀⣾⢋⣴⣶⡎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠙⣿⠟⢻⣿⢿⣇⡐⣀⣿⣿⡇⢈⠀⠀⠙⠶⠾⠇⣿⣾⡿⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣵⣿⠀⢧⠸⡌⠙⠻⠿⣿⡿⢡⠆⠀⠀⢀⣤⣀⠰⣿⠿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣿⣿⣆⠀⢤⡀⠱⠶⢂⣬⣥⡀⣀⣴⣿⣿⣿⣷⣤⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣿⣟⢛⣰⠀⢹⡄⢰⣯⣶⣾⣿⣿⡟⠃⢿⣿⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠈⠀⢐⡺⢩⢛⣿⣿⢿⡿⣯⡎⠁⠈⣿⡇⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣙⣏⣏⣹⣭⡷⣿⠆⠘⠇⠏⢃⣀⣠⡿⡁⣿⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠷⡶⠷⡿⢛⢩⠆⠀⠐⠁⢃⣴⡿⠁⢷⠏⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡛⠹⠀⠐⡄⡫⠀⠀⣠⣾⣷⣿⣿⠇⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⣿⡏⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡋⡀⠀⠀⠀⣸⢾⣿⣿⣿⣿⡟⣠⢆⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠷⠶⠛⠁⠈⣿⣿⣿⠏⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⢪⣯⢴⣶⣖⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠥⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠂⠀⠀⠀⠀⠀⠠⠊⠉⠁⠀⠙⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠞⠓⠒⡠⣀⠀⡠⡀⠀⣀⡤⠤⠴⢶⣆⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠁⠈⡉⠀⢀⡟⠀⠀⠀⠈⠁⠹⣇⠀⡇⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣰⡇⠀⠘⢧⡀⠀⠀⠀⠀⣰⣿⠀⠘⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠲⠶⠾⣷⡎⣿⣦⠈⠻⢦⡤⠤⠞⠋⠂⢠⡄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠉⠁⠈⠁⢀⣀⠀⠀⠀⠐⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⣀⢴⣶⣿⣶⣾⣿⣿⠷⣄⢠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⠋⠈⢀⣀⡀⠀⠀⠀⠉⢉⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡩⢉⢹⠏⠉⣗⠒⠁⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⡞⢸⠇⠀⢋⠀⠀⢰⡞⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⡕⢹⠃⢸⠀⠀⠸⠀⠁⠀⢧⠈⠦⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠢⢌⠂⠘⢤⠤⠀⠀⠠⠤⠐⣒⠉⠸⠒⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣴⡀⢩⠀⠀⣸⠈⡩⠬⠤⢍⠁⠹⡀⠌⣀⠃⡸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠑⠈⠀⢰⠃⠸⠀⠀⠀⠀⠠⠀⢹⡀⠁⠐⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢣⡀⠈⠂⠀⠀⠀⢬⠇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠁⡄⢸⡀⠀⢀⡏⠁⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠠⠤⠤⠴⠃⠁⠈⠀⠀⠘⢣⣀⠀⠀⠀⣀⣷⠄

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣥⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣤⡁⣩⣤⠽⣾⢁⡆⢀⠀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⣦⠀⢯⠘⢿⣸⣟⡿⣷⣾⣷⣮⣦⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⡴⣦⣶⣿⣿⣸⣿⣻⣿⣿⣿⣿⡇⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡛⢷⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣌⢱⡴⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠻⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⣷⣿⡿⣿⣿⣿⠀⠀⡄⠀⠀⠀⢠⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⣿⣿⡆⠘⢧⡀⡀⠀⠀⣿⣶⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⣿⣿⣿⣦⠘⢿⣿⡄⣿⡿⣌⣿⣦⣴
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠟⢸⣿⣿⣷⡘⣬⡁⢠⣤⣉⢸⣿⡿⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣌⠻⠌⠿⣿⣾⣿⠃⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣞⢻⣦⣻⣿⣿⣧⡐⣦⢈⡉⠙
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣝⠿⣿⣿⣞⢿⣿⣿⡄⣸⠀⠀⠀⢳⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡘⠛⠛⢀⡿⣿⣧⣿⣆⠀⠀⠈⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣄⠘⢃⣮⠉⣿⣿⡄⠀⣦⠹⣦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⠆⡸⣿⣶⡀⠉⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢑⣃⣈⡛⠃⠀⠀⢻
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢁⡉⠙⠀⠠⣤⠘
⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡉⠛⠦⢠⣦⠈
⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⠀⠀⠸⠗⢄⣠⣿⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠐⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢠⠔⢋⡀⠀⠀⠐⠀⢿⡇⠉⢃
⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠶⠞⠟⠻⡏⣹⣿⣿⣿⣿⣿⣿⣿⠍⣠⣶⡿⢿⣆⠀⣀⠰⡜⣿⣿⣉
⣟⠷⢀⣉⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⣴⣦⣛⣿⣿⣿⣿⣿⣿⣽⡷⠘⠿⠉⠀⣸⣿⣄⠹⣷⡄⠉⠹⠿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡁⣀⣈⣿⣿⣿⣿⣿⡿⠟⢁⣩⣉⢁⡔⠀⢠⢀⣿⣿⣿⢧⡉⠉⡀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⣿⣿⣿⡿⣻⣿⣿⣿⣶⣿⣿⠟⠙⣿⣥⣶⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡛⠋⣹⣿⣿⡠⡧⢸⣿⠹⣿⡿⠋⠀⠀⣇⣴⣿⣿⣿⣿⣷⠆⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣿⣿⣿⣿⠻⣇⣠⣌⠻⠇⢠⣀⢁⣤⣾⣿⣿⣿⣿⣿⣿⣧⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠟⠛⠃⠈⠙⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⡄
⣇⠀⠀⠀⠀⡀⠀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣀
⡿⠗⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢾⣋⠄⡀⠈⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⣄⣰⡿⣿⣿⢿⡿⠿⠿⢣⢀⣴⢧⣿⣿⣵⡆
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡸⠟⠻⠟⠃⢻⣷⠂⠀⠀⠀⠛⠈⠁⠀⠀⠉⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣄⠀⠀⡼⣆⠀⠀⣠⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣹⡇⣹⣫⡕⢪⡿⡏⣸⣋⣠⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢢⡀⠲⢤⣤⠽⢾⣿⣦⣼⣿⠶⢯⣤⠤⢂⢀⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢶⡿⣟⠀⠀⣴⣶⣚⣽⣯⣿⣯⣳⣶⣆⠀⠈⣿⣷⢞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡖⣧⢾⣂⢜⣿⣿⣽⡿⣅⡨⣿⣭⣿⣟⠇⣸⡷⡜⢲⠁⡄⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠢⡠⣁⡏⣜⡏⣾⡟⢛⠻⠿⠾⠿⠿⢛⡛⣿⣧⠿⡄⢳⣡⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣱⡙⠋⣿⢸⡟⣃⠈⠐⠛⠆⢘⠓⠈⠀⡜⣿⢈⣿⠙⢁⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠁⢀⢻⡝⣚⢿⢸⣿⣞⡛⠳⣄⣄⣠⡼⠞⢛⢳⣿⢸⠿⣓⣹⠗
⠀⠀⠀⠀⠀⠀⢀⠀⠹⣾⡙⣮⡖⢸⡿⢿⣷⣦⡀⠀⠀⢀⣶⣿⡾⣿⡆⢶⡽⣱⣶⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⢿⣻⣿⠋⣿⡜⠻⣆⡻⣾⣧⣟⣼⠟⢶⡟⢸⣿⣏⡟⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠰⡦⠒⠺⣯⣗⢶⡎⣧⢰⣻⣟⣿⣿⣻⢻⠄⣾⢱⣶⣺⣿⠗⠲⢴
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⢻⠉⢫⠙⣧⣿⢿⣿⣿⣿⣿⣿⣿⢿⣟⣼⠋⠟⢉⡟⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⡤⢽⡘⢄⢻⡟⣟⣿⡀⣈⣿⡻⣻⡏⡞⣣⡧⢤⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢶⣼⢺⡛⢿⣿⣿⣿⣿⡿⢻⡟⣧⡆⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣯⢸⡌⢽⣧⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⠋⡟⡟⢟⠟⠛⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣤⣾⡿⣣⣿⣸⣿⣟⣿⡾⠶⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣼⣿⣿⣾⣵⣿⣿⠏⣜⣱⡗⠀⣿⣥⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢹⣿⣿⣿⡋⣼⣿⣿⣿⣯⢪⣿⡿⢱⣿⡟⢿⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣿⠀⣿⣿⣿⠁⣿⡟⣹⣿⡿⠛⣿⣿⣿⣿⣿⣿⣦⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⢻⡯⠇⢠⣿⣦⣿⣿⡏⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣇⣿⡀⢿⣿⣿⡟⣿⣿⣼⣿⣿⣗⣿⣿⣿⣧⣾⣏⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠹⠛⣸⣿⠿⠃⠘⣿⣿⣅⣿⣿⢯⣿⡿⢻⣿⣿⣿⣿⣯⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢹⣧⠀⣿⣧⣶⡆⣀⣿⣿⣿⣯⣵⣿⣿⣗⢸⣿⢻⣿⢿⣾⡟⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⡇⢻⣞⢿⡿⡿⣿⣯⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡾⢿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⡏⠀⣴⡟⠀⣤⣼⣛⣿⣿⣿⣿⣿⣡⡾⣿⣿⣿⣟⣻⣦⣹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⣿⣿⡏⢀⢘⣿⣿⣛⠻⣿⠻⣿⣷⣼⣿⢋⣾⣿⢿⣿⣿⣿⡿⣿⡟⣿⡦⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣇⣿⣿⡿⠿⠿⠿⣿⣦⣟⣸⣿⢿⣿⣏⣴⣿⠿⠿⢿⣿⣿⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣽⣿⢿⣿⣦⣤⣀⣬⣿⣿⣕⣻⣿⣿⣿⣏⣀⣀⣠⣾⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⡛⢿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣏⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⣡⣽⡿⣿⣿⢿⣿⡿⣤⡿⣩⣾⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣤⣤⣠⠏⣾⣿⣿⣧⣠⣧⣼⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣠⠀⢀⠄⡀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣀⣋⣹⣦⠭⠽⠿⢉⣴⣻⡟⣰⡟⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⢣⣤⡛⠉⠓⣁⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠝⠿⠿⢿⣿⣷⣶⣶⣾⣿⡿⢋⣿⣱⣿⢻⣿⣿⣷⣿⣞⣽⡟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠰⣾⣋⣭⣤⣭⢛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢐⡶⣾⣿⣛⣿⣿⣽⣿⣿⢻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣷⣄⣉⣛⣿⣻⣿⢿⣭⣆⠐
⠀⠀⠀⠀⠀⢴⡛⢋⣾⣿⣿⣿⣯⣭⣍⣭⣽⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣯⣩⣿⣿⣶⣿⣷⣄⡘
⠀⠁⠀⠀⢠⣤⣉⣀⣴⡛⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⢿⣿⣿⣿⣿⣿⣋⣽⣯⡍⢀⡀
⠀⠀⠀⠀⠄⢷⣿⠻⢿⣿⢿⡻⢟⡛⣯⣤⣶⣿⣿⣿⣿⣼⢿⡟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣮⡛⢿⢷⣌⢙⣛⣿⣿⣿⣿⣍⡙⠫
⠀⠀⠀⠀⠀⠌⠓⠽⠚⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣹⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⣠⢚⣿⣿⣿⣿⣷⣻⣿⣿⠷⠿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠫⠉⠉⣹⣉⣴⣾⣷⣿⣟⢻⣿⣿⢻⣿⣿⣯⣿⣿⣿⣿⡿⣿⣛⢿⣷⣾⣿⣷⢻⣿⣿⣿⣿⣿⣛⣛⣿⡧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠁⠉⠀⠰⠿⠟⠋⠉⠛⣿⡿⢿⣿⣿⡿⠿⢿⣿⡟⢿⠻⠃⠙⠀⠋⠉⠯⠛⠻⠛⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⡒⠦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣟⠋⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡶⠂⠀⠀⠀⠙⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣟⡤⠀⠀⠀⣀⡠⢷⣿⢧⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⡄⣲⡋⢹⡄⠀⣧⣿⣧⠤⣶⣾⡛⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⣈⣿⣾⠿⠒⠋⣁⣤⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣟⣛⣛⣉⣩⣭⣤⣴⡶⠞⠋⠙⣿⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣟⣛⠛⠉⠉⠉⢀⣠⣤⣤⣤⣽⠁⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠾⠿⠿⠛⠉⠀⣹⡏⣿⣿⣿⣿⣿⣶⠛⢶⣿⣿⣿⣿⡇⠙⢆⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠰⡋⠀⠈⠛⠛⠛⠋⣿⣾⡎⠝⠛⠛⠛⠁⣤⠌⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⡿⡆⠻⡿⠿⠀⠚⣽⣿⡏⠀⠀⠀⠀⠀⠀⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠀⠀⢀⣤⣿⠹⣿⣵⡇⠀⠅⠀⣀⣠⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢧⢀⡀⠠⠀⠀⢀⡌⢿⣿⠡⣙⣿⡀⢠⠀⠠⠠⢐⠟⠀⡛⠀⠀⠀⠀⡄⢀⡀⡼⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢋⢡⡤⣚⣾⣿⣿⣆⠙⢿⣮⣟⠿⠈⠑⠁⠁⠀⣠⣾⣿⣷⣒⡤⣅⡀⠀⠛⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⢿⣿⣿⣿⣿⣿⣿⣧⡘⠿⣿⢷⣄⣀⣀⣤⣾⡿⣿⣿⡀⠙⠻⣿⣦⡭⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡹⣿⣿⡿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣯⣄⡈⣿⣷⣶⣠⣼⢟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣻⢷⣼⣿⣷⡅⠀⡼⢿⣿⣿⣿⣿⠋⢹⡟⣿⣿⡿⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢭⣛⠿⣿⡄⠃⠘⣿⣿⣿⣿⡆⠈⠷⣛⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠺⠿⣿⣿⣿⡿⠯⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠂⠀⣁⠈⣉⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢤⠴⠤⠤⠀⠀⠀⠀⠈⠙⠻⠿⠟⠧⠴⢢⠄⠀⠒⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠘⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⡔⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⢀⠀⣀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃
⠀⡐⠀⠀⠀⠀⠞⡁⠄⠂⠁⠀⠀⢀⠻⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠒⠠⠄⠐⠂⠀⠀⠀⠀⠈⢠
⢠⠀⡀⠀⠀⠠⠂⢀⠀⠂⠁⠀⠀⠀⡑⠤⠀⣄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣜⣧⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⣇⠀⠀⠀⠈⠉⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠃
⠇⠈⠇⢠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⣄⠃⠠⠀⠀⠐⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠐⠖⠒⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉
⡇⠀⠀⠃⢁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠐⠀⠀⢀⠠⠀⠀⠀⠀⠁⠀⠀⠤⡁
⢳⠀⠀⠀⠘⡆⠀⠀⠀⠀⡀⠀⠸⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠸⡆⡀⠀⠀⠣⠀⣤⠀⠀⠀⠀⠀⠀⠀⡇⠆
⠀⢻⡁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠
⠀⠈⢧⢢⡀⠀⠀⠘⣆⠀⠰⠀⢀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢀⠉⠄⠀⠠⡤⠀⠀⠀⠀⠄⠀⠀⣼⠃
⠀⠀⠀⠀⠹⢦⡄⣄⢉⠶⠄⠀⠂⢀⡜⠀⠀⠠⢚⣣⠞⣣⡄⠀⠀⠀⢀⡆⠐⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠌⠀⠀⠘⠃⠀⠀⠐⠋⣵⡿⢟⡁⢠⡀⠀⢻⡇⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠔⣫⣿⢿⡇⠀⠈⠀⠀⠄⡐⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠙⣿⠈⠃⠀⠀⢀⠀⠀⡁⠀⠀⠀⠠⠀⢀⠀⠀⠀⠐⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⢦⡀⠁⠀⠀⠀⠻⠄⠀⠀⠀⠀⠘⠐⠃⠀⠐⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠁⢀⠠⠀⢀⠀⢐⠂⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⡔⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠩⣇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠻⣧⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡇⠀⠈⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⣦⣸⠇⠁⠀⠀⠀⠳⠶⠟⠛⢧⣄⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⣀⣀⠠⠀⠀⠀⠀⠠⠀⡇⢀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣾⡿⣿⠀⠀⠀⢳⢷⣴⣷⣾⠅⠀⠀⠰⣶⣤⣄⠀⠀⠀⠀⠀⠀⣾⣋⠑⠂⠐⠲⡂⠀⠀⠀⣷⠋⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠈⡷⢹⠀⠀⠈⠃⣠⠋⠀⠉⠀⠀⠀⠀⠸⠯⠻⢻⣦⠀⠀⢀⢶⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⡇⢠⡟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢂⠸⡄⠀⣄⠀⠛⢶⣦⠀⠈⠛⠐⠀⠘⠃⠐⠂⠙⠁⠀⠘⡆⠃⠀⢦⢀⣀⡴⠿⠁⠀⠀⠃⢸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠞⠀⢡⠀⠀⡇⡄⠀⡡⠄⠀⠐⠀⠀⠀⢀⣀⠀⠀⢀⠀⣐⡆⠀⠀⠱⣦⣈⠷⠃⠀⠈⢠⠰⠃⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠈⡀⠀⠁⣥⡄⠀⠀⠀⠀⠀⠀⠔⢻⣅⡀⠺⠁⠀⠈⠀⢸⣦⠀⠉⠁⠀⢠⡄⠀⠏⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣇⠀⠞⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠢⣀⠀⢠⠟⠁⠀⠰⠀⠀⠀⠌⡀⠀⡆⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠂⠀⠀⡆⠀⠀⠀⠀⣴⠉⠛⠙⣦⢄⣈⡉⢁⣀⣠⣀⠀⡀⠀⢀⢰⣃⢠⡧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⡇⠀⠘⠁⠄⠀⠀⠀⠀⣾⠟⠚⠢⢤⣇⡀⣉⣀⢩⣿⣧⣸⡦⠛⠀⢸⠸⠆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠠⢴⡀⠀⠀⠀⡀⠀⠀⢿⡤⢀⢰⠇⠈⠙⠋⠉⠈⠀⠀⢈⠁⠀⠀⠙⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣠⠀⠀⠛⡅⠀⠀⠀⠀⠀⢩⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⠀⠀⠁⠴⡆⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡀⠋⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠈⠆⣰⠂⠀⠀⠀⡀⣄⢠⡜⠣⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡴⣡⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢣⡴⠗⠂⠈⠁⠉⠀⠀⠀⠀⠃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⡁⠈⣠⠀⠀⠀⠀⠀⠣⡀⠙⣦⡠⠛⠶⡐⠒⠀⠀⠀⠀⠀⠀⡀⠀⡐⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⢋⡦⠀⠀⠀⠀⠀⠱⣄⠉⠀⠈⠀⠀⢀⡀⠀⠀⠀⠂⠱⠃⡰⠀⠀⠀⢀⡤⣄⡐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⣰⠁⠀⠠⢲⠮⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠛⠦⠶⢀⡀⠀⣀⣤⣤⡤⠞⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠂⠀⠀⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣮⣙⣿⣋⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⣽⣏⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡏⢻⣿⣟⡆
⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡇⠘⡟⠁
⠀⠀⠀⠀⣼⡟⢰⡿⢡⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁
⠀⠀⠀⢀⡿⠀⣾⠃⢸⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠇
⠀⠀⠀⢸⡇⠀⠋⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣀⣀⣀⣀⠀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀
⣿⠿⡿⢿⠿⡿⠟⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⠿⠿⠿⣿⠿⠿⢿