Scooby Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠀⠀⠀⠀⢠⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠲⡈⠑⢢⠀⢀⣤⣄⣀⠝⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⣤⠀⠘⠋⠛⠡⠌⠉⢙⣷⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⠄⠀⠀⠀⠼⠇⠨⠠⠆⢹⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠠⡤⠀⠀⠒⠊⠉⣰⣯⣥⣶⣶⣦⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠁⢀⠤⠀⠄⠀⠀⠀⠉⠻⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢹⠛⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠝⢆⣀⣠⡴⠞⠙⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣴⠀⠀⡞⠛⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣿⠀⠀⠀⠀⠉⢹⣿⠿⠚⠂⡂
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⣺⠀⢸⡄⠀⠢⠶⠚⠉⠀⠂⢻⡏⠁
⠀⠀⠀⡘⠀⡏⠀⠀⠀⠀⠀⢀⡤⢂⣴⠟⠉⠁⢀⣤⣶⣾⣿⣿⣶⣤⣤⣠⠤⣶⣿⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠰⠀⢰⠁⠀⠀⠀⢀⡴⢋⡼⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⡁⠙⣄⠀⠀⠈⠓⠶⠤⠤⠶⢛⡧⡀
⠀⠀⠁⠀⠃⠀⠀⠀⣠⠎⠀⣸⠁⠀⠀⠀⠀⠿⢿⠿⠿⠛⠉⠀⠀⠀⠀⢀⡀⣸⣆⠨⡃⠳⣄⣀⠀⠀⠀⢀⠨⠇⠁
⠀⠠⠀⠸⠀⠀⢀⡴⠃⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣦⢟⡶⢀⡀⠀⠈⠉⠀⠈⠁⣀⣤⡇
⠀⠀⣆⠀⠓⠀⠋⢀⡴⠋⢀⠇⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠖⠋⠀⠀⠈⠉⠓⠒⠚⠛⠋⠉⠀⠻⣆
⠀⠀⠈⠂⠠⠶⠖⠉⠀⢠⠎⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠠⣀⠀⠀⣰⠟⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠈⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢰⣿⡿⠂⠀⠀⠀⠘⡆⣼⠃⠀⠀⠀⣷⡀⠙⠲⣄⠀⠀⠀⠀⣿⠙⢻
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠠⠀⠁⢠⡄⠀⡀⣤⠰⠿⠃⠀⠀⠀⢸⡏⢻⠀⠀⠈⠛⠦⣄⣸⠇⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣦⠀⠻⠃⣾⢡⠔⠂⢀⡤⠀⢀⠀⠀⢳⡄⠑⠤⡀⠀⠀⠀⠉⠢⣄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣆⠀⠉⠛⠆⠀⠀⣷⠈⠀⠀⡊⠀⢐⡁⠀⠀⠀⣿⠀⠀⠙⣧⡀⠀⠀⠀⠈⠢⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣴⠟⠉⠀⠈⣷⠀⠀⡇⠀⠀⠘⢻⡀⠈⣇⠀⠈⢷⣀⣀⣠⠟⢀⣠⣶⠟⢻⣄⠀⠀⠀⠀⠐⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⠞⠁⠀⠀⠀⠀⣸⠀⠀⠙⠶⣄⠀⠀⠑⠶⠛⣧⢤⠾⠿⠽⠶⠞⠻⣏⢀⣴⠏⠙⢦⣀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⠤⠀⠂⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣆⠀⢆⠀⠀⠤⣀⣠⡿⠳⣤⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣀⣤⠴⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⡈⣑⡶⠴⠟⠁⠀⠀⠈⠳⣄⠀⠀⠹⣄⠀⠀⠀⠼⠛⠁⠔⠋⠉⠉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠙⣦⠀⠀⢄⣂⠘⠀⠀⣀⡠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢷⡀⠀⣿⠁⠀⠘⠁⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠻⣾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢦⡀⠀⠁⠀⣠⡴⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢻⡀⠀⢀⣤⡴⠞⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢃⠀⣼⠃⢰⣏⣁⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⠶⣿⠟⠛⠉⢉⡉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠓⠈⢉⣹⣉⡿⣧⣀⣤⢶⣶⡶⠶⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⡸⠛⠉⠛⠛⠋⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠐⢫⡀⠀⣀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠓⢻⡄⠀⠀⠀⠀⠀⠀⡸⢁⣴
⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣠⣤⣴⣱⡟⠁
⠀⣿⠋⠉⠉⠀⠀⠀⠈⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⢨⣭⣉⣸⠏⠉⠁
⠀⠹⢷⣤⣤⣶⠶⠶⠶⣶⡄⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣠⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠈⣿⣄
⠀⠀⠀⠀⢀⣾⠋⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⢶⣄⡀⠈⠙⠷⣦⣄⡀⠀⠀⠀⣿⣏⢿⣄
⠀⠀⠀⣠⡿⠁⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠀⢸⠟⢶⣤⡀⠀⠉⠙⠻⠶⠶⠿⢿⠳⣿
⠀⠀⣰⡟⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⡶⠿⡿⠋⠁⠀⠀⠀⠀⡰⠋⠀⠀⠈⠙⠳⢶⣤⣄⣀⠀⠀⡼⢷⣹⢦⡀
⠀⠀⣿⠁⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠟⠛⠛⠛⠋⠉⣩⠟⠀⠀⢰⠁⠀⠀⠀⢀⡤⠚⣁⠤⠒⠀⠀⢂⠀⠀⠀⠉⠉⠛⠛⣧⠶⡉⢢⢻⡄
⠀⠀⣿⡄⠀⠘⢿⣄⣀⠀⢀⣀⣴⡾⢿⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠲⠴⠶⠚⠁⢠⠞⠁⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠘⢷⣍⡚⣿⠁
⠀⠀⠘⢷⣄⠀⠀⠙⠛⢻⣿⡿⠋⢀⡟⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠁
⠀⠀⠀⠀⠙⠻⠶⢶⣶⣾⠋⠀⠀⠈⠳⠴⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠊⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⣰⡿⠀⣠⣴⣿⠋
⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣷⠟⠋⠁⣿
⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⡏
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠿⢷⣶⣶⣶⠿⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣿⠁
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢸⡇⠀⠀⣾⡏
⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⡇⠀⣼⡟
⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡇⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠻⣦⡀⠀⣼⠟⠁⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠈⢻⣾⡏⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣿⡟
⠀⠀⢀⣀⣀⣤⣄⡀⠀⠀⣿⠇⠀⠀⢀⣿⠻⣷⠀⠀⠀⠘⣿⣄⣤⠶⢦⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣸⡏⢸⡇⠀⣠⣤⣤⣄⣀⣀
⢠⣴⠋⣼⠏⢉⣽⡿⣦⣾⠋⠀⠀⠀⣾⠇⠀⣿⡄⠀⠀⢀⡼⠿⠻⢶⣄⢻⡆⢻⣆⣀⣀⣀⣀⣀⣀⣼⡇⠀⠀⢠⣿⠁⠹⠿⠛⠛⢶⡄⠈⢻⣏⢳⡄
⢇⣿⣸⡏⣰⡟⠁⠀⠀⠈⠃⠀⠀⣸⡏⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣿⣼⣧⣾⣿⡿⣻⠟⠉⠉⣉⣭⣄⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⣿⡀⢀⣿⣸⣿
⠈⠻⠿⣿⣿⣆⡀⠀⠀⠀⠀⣀⣠⣿⠃⠀⠀⠀⠛⠷⠶⠶⠶⠶⠶⠶⠿⠿⠛⣿⣿⠀⣿⠀⠀⣼⠏⠀⠈⠑⠀⠀⣿⡀⠀⠀⠀⣀⣠⣿⣤⡾⠿⠟⠋
⠀⠀⠀⠀⠙⠛⠛⠻⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣿⡀⠀⢿⡄⠀⣀⣠⣤⣶⠟⠛⠛⠛⠛⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣶⣟⣛⣟⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠃⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡄⢀⣀⣸⣆⣀⣀⡀⠀⠀⠀⣠⠞⠳⠤⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣿⠿⠿⠃⠈⠛⢿⣷⣤⡀⣰⠏⠀⡗⢤⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⣷⠔⠋⠳⣼⣿⠇⡹⠃⠀⢸⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠶⠶⣾⣟⢠⣶⡴⠋⠀⣀⠀⡈⠁⠀⠀⠀⠀⠘⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠉⠉⠁⠘⣜⠿⡠⠃⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠙⠿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣴⠇⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣰⠃⠀⢰⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣼⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡤⢛⣷⣤⣀⡀⠀⠀⠀⠀⢀⣠⠞⣹⠃⠀⢀⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡇⠘⢄⡈⠉⠛⠛⠒⠛⠋⠁⣰⠇⠀⠀⡼⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠉⠓⠶⠤⠤⠴⠶⠋⠁⠀⠀⣼⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣀⣀⣀⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠻⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣾⠟⠉⠉⠓⠒⠲⠶⠶⠶⠶⠶⠶⠒⠒⠋⠉⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠋⠿⢿⣿⠿⠓⠲⠦⠤⠤⢤⡤⠤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣾⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⡑⠒⣄⠀⠀⠀⠀⢀⡜⠁⣌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⠇⢘⡇⢰⣶⡦⠞⢀⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠀⠄⠂⡁⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣁⣤⠟⠀⠈⠋⢀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⣶⣶⣦⣄⠀⠀⡖⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⣿⣿⡿⠋⠀⠀⠑⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠉⡉⠀⠀⠀⠀⢀⡟⢻
⠀⠀⠀⠀⠀⠀⢀⡤⢰⠧⢤⡴⠷⢤⣀⣠⡴⠋⠀⣾
⠀⠀⠀⠀⠀⠀⡏⠀⠁⠀⣾⡛⠂⠀⠀⣠⠞⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⢘⠙⠒⠚⠛⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⣀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⢰⢿⣀⣀⠀⠀⣀⣠⡴⠞⢉⣠⡇
⠀⠀⠀⠀⠀⠀⢀⡼⢤⡟⠛⠛⠋⣉⣡⠤⠒⠉⠀⠙⣦
⠀⠀⠀⠀⠀⣰⢿⠴⡿⢿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣴⠃⢸⣧⣧⣼⠇⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢿
⠀⠀⠀⣸⡏⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⣟⣀⠀⠀⠀⠸⡆
⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⣿⣧⠀⠀⠀⠹⣄
⠀⠀⣾⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⠏⠀⠀⣄⠀⢸⣦⡀
⠀⠀⠸⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠉⠀⣀⣀⠹⣆⣸⣿⣷⣄
⠀⠀⠀⠈⠳⣝⢧⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠻⠏⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢻⣎⠻⣆⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⢻⣿⣿⣿⣿⣷⡀⡞⠉⠈⣉⠑⠢⣄
⠀⠀⠀⠀⠀⠈⢿⡀⠈⠳⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠈⠿⣿⠛⠻⣯⣷⠻⡀⠀⢍⠑⠂⠤⠃
⠀⠀⠀⠀⠀⣶⠛⢷⡀⠀⠙⢷⡄⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠀⠈⢻⣧⠙⣄⠈⠳⡀
⠀⠀⠀⠀⠀⢹⠀⠈⢷⡀⠀⠀⠙⢦⡀⠀⣸⠀⠀⠀⡿⠀⠀⠀⠀⣸⠇⠀⠀⠀⢻⡆⠈⢣⡀⠙⢦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⡄⠀⠀⠀⣿⡄⣿⠀⠀⢸⠇⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢳⡀⠀⠹⣄⠈⢳⡀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠹⡄⠀⠀⢸⢱⡍⠀⠀⡿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⡆⠀⢧
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠹⡄⠀⠈⣿⠃⠀⢸⠇⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⢻⡀⠀⡿⠀⠀⣸⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠁⣠⠏
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⣳⣄⡈⣇⠀⢷⡀⠀⢹⡀⠀⣈⣻⠶⣤⢤⣤⣒⣄⡀⠀⠀⠀⠀⣿⡤⠞⠁
⠀⠀⣠⠞⡹⠁⡜⢉⡜⠻⡞⠲⣍⡿⠀⢸⠃⠀⣀⣱⡾⠥⣷⢼⣡⠞⠉⠉⠉⠛⢷⣄⣀⡴⠃
⠀⠀⣏⡄⣇⠸⣇⣟⡇⢸⠀⡏⠈⠀⠀⡿⠀⠈⠁⠈⣧⠀⢸⡄⠏⣷⣠⡤⠴⠒⠋⠉
⠀⠀⠈⠉⠉⠉⠉⠛⠗⠺⠴⢧⣤⣤⠴⠷⢤⣀⣀⣀⣸⣄⣠⡶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠲⠀⠘⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢠⣶⣤⡄⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠸⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠃⠀⠣⣀⢀⠀⠠⠁⠂⠀⠁⠄⢀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⣀⣀⣀⠘⠉⡀⠜⠠⠊⠀⠀⠀⠀⠀⢨⠲⠄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠘⠻⢿⠟⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡴⠁⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠑⢂⣁⣤⠤⠔⠂⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠄⡀⠠⠐⠊⠋⠁⠂⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠚⠠⠀⠀⢠⡀⠀⠀⠀⠁⠂⠐⠂⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡈⢀⠷⢄⡄⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⡆⢀⠜⢀⢖⠣⣀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠱⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠊⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠀⠀⡀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠠⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠛⠲⠶⠤⠀⠦⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠉⠐⠢⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠀⠀⠤⠀⡰⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣠⠤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠈⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣶⠲⣽⣤⢴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣠⢀⠏⠲⠌⢩⠟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡈⡛⠃⠀⠀⢤⡀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠉⣧⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠓⢤⣼⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣴⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠒⠒⠚⡎⠁⠀⠰⢧⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡈⢐⣄⣠⣤⡄⡠⠊⣟⣠⠎⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢱⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢎⠁⠘⠉⠛⣭⢀⣿⡆⣾⣡⠀⠀⠀⠀⠀⡄⠀⠱⢄⠀⠀⠞⠀⡄⢨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⢳⡞⠁⣀⠠⡄⠀⠂⣹⡟⠛⣄⠀⠀⠀⠀⣤⠁⠀⠀⠀⠑⠂⠀⢠⡡⠊⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠈⣧⠰⣍⢠⠀⢀⣤⣤⣤⣿⣼⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣤⣿⢀⡍⠀⠁⠸⣿⣿⣿⡿⢻⡸⠳⣄⣼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣧⠘⢧⣀⣀⣀⣸⡏⢉⠴⡟⠁⢸⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⢧⡀⠀⠀⢲⣤⣗⢊⠜⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠙⠛⠚⠟⠁⣿⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⡼⠀⠀⠀⠀⠀⢀⠠⠒⠁⠌⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢦⡈⠙⠲⢤⣤⣄⡴⣼⢛⡃⠀⢣⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠉⠓⠦⠤⣀⣀⣠⣼⣟⣡⡀⢸⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢸⠀⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢣⣸⠇⠀⠀⠀⠷⠊⠀⠀⠀⠀⠈⡇
⠀⠀⠀⣀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡀⠸⣆⠀⠀⠀⠀⠀⠈⠙⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠀⢰⡆
⠀⠀⠀⠙⢦⡀⠙⣆⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢸⣿⡄⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣶⠤⠤⣄⣀⣀⡤⢞⠿⠣⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠙⡀⠘⡆⠀⠀⠀⣰⣯⠀⠀⠀⡰⠸⣿⣷⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⡟⢳⣿⠀⠀⠀⠀⡏⠀⠲⠖⣠⠀⣤
⠀⠀⠀⠀⠀⡼⠀⡰⠃⠀⠀⢰⣿⣿⡇⠀⣰⠃⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⡼⢡⡞⢹⡄⠀⠀⠀⡇⠀⢀⠛⠄⣱⣽
⠀⠀⠀⣠⠞⢀⡜⠀⠀⠀⠀⣾⣿⣿⡇⠰⣏⠲⣦⠀⠀⣰⠏⠀⠀⠀⠀⠀⣠⠞⣱⠋⠀⠸⣇⠀⠀⠀⡇⠀⢼⡠⠾⠋⠁
⠀⠀⣴⠃⢠⠎⠀⠀⢀⣀⠀⣿⣿⣿⡇⠀⢻⡀⠀⠀⢀⡏⠀⠀⠀⢀⣤⠞⠁⡌⠀⠀⠀⢀⡟⠀⠀⠀⣧⠀⠈⡇
⠀⢸⠃⠰⠏⠀⠀⢰⠏⠀⢳⣿⠿⠿⠀⠀⠘⣧⠀⠀⢸⡇⠀⢀⢾⠋⠀⠀⣼⠀⠀⠀⠀⣼⠁⠀⠀⠀⣇⠀⠀⡇
⠀⢸⡀⢸⡀⠀⠀⣼⠀⠀⢈⣿⠀⠀⠀⠀⠀⢹⡄⠀⢸⡇⢀⠇⡎⠀⠀⣼⠋⢂⠀⠀⠀⠿⣄⠀⠀⠀⡇⠀⠀⢰
⠀⠈⢧⠈⠳⡀⢀⡇⠀⠀⠈⢻⡀⠀⠀⠀⠀⠈⣇⠀⢸⡇⣼⢻⠁⠀⣰⠃⠀⢹⠀⠀⠀⢀⡞⠀⠀⠀⡇⠀⢀⣼
⠀⠀⠈⠳⣄⠈⡟⠁⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢹⠀⢸⡇⣿⡏⠀⢠⠃⠀⡾⠃⠀⠀⠀⡼⠁⠀⠀⠀⣷⠀⠈⣇
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⡇⠀⣇⢹⠀⢀⠇⠀⢸⠇⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⠀⠀⠹⡄
⠀⠀⠀⣀⣀⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⡇⠀⢻⣇⠀⡘⠀⣠⣟⣠⣴⣦⣰⢃⡴⠀⠀⠀⠀⢸⡆⠀⠀⠹⡄
⠀⡰⣫⠛⠏⢨⠿⠳⠦⢤⡄⢀⣄⡤⡾⢦⣄⣀⡴⠁⠀⡬⢧⠀⢹⡛⢉⣩⠕⣶⢹⡿⠊⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣽⣦⣤⣤⣤⡄
⠀⠘⢧⣼⣄⣼⣀⠀⢀⣀⣀⣤⣼⡜⢠⠋⢀⠬⡀⠀⠀⣴⡌⠀⠈⠉⠠⡌⢧⢘⣻⣶⣶⣤⣤⣄⣀⣀⣸⣷⡶⠾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠀⠘⠷⢧⣰⡇⠀⡀⠀⢠⡿⠷⣤⣤⣀⣤⣷⣬⣾⠾⠿⠿⠟⠋⠉⠛⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢉⡀⠀⡀⠀⠀⠐⠚⠛⠚⢢⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⡱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⢁⡀
⠀⠀⠠⠄⡴⠛⠀⠐⠀⢄⡀⠀⠠⠁⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⡆⠀⢠⠔⠀⢀⠐⢀⣤⠀⠀⠠
⠀⠀⠘⠂⣄⣠⣄⠀⠀⠀⠈⡆⢄⡀⠀⢸⠀⠀⣴⣿⣿⠛⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠂⢀⣀⠀⠆⢀⠔⠁⠀⠁⠁⠀⠂
⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⡰⠀⠀⠁⠈⠈⢋⣿⢿⢿⣿⣷⣀⣀⣰⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠀⠁⠀⠈⠐⡀⠀⢣⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠄⢔⡀⠴⠁⠀⠀⠀⡀⡄⠈⠋⠈⠁⠹⣿⣿⣿⡿⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢸⠈⠈⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠁⠰⠂⠜⠀⠈⠀⠀⠀⢀⠠⠉⠿⠟⠁⢨⣆⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣠⠞⠁⠀⢢⠄⠀⠀⡼⠀⠂⠈⠀⠀⢸⡿⣷⡆⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⢀⢀⣀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢈⣀⢤⠃⠀⢀⠄⢀⠐⠀⠈⠀⠀⢀⠄⠀⠀⣀⡀⢀⣘⣆⡀⡀⣀⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⡸⢠⠋⠀⡈⠠⠀⠄⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠁⠀⠀⠒⠀⢣
⠀⠀⠀⠀⠀⢠⠃⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⢀⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡏⠉⢉⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣁⡤⢾⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢋⣐⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⠶⢦⡀⠀⠀⣹⣿⠛⢛⡙⢻⣦⡀⠀⠀⢀⣤⣤⠟⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣄⠉⠲⢟⣉⡵⠾⠟⢛⠄⠀⠙⢦⡴⠋⠀⡠⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠶⠔⠚⠁⠀⠀⠘⠁⠀⣴⠆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠈⠻⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⣴⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠠⠶⡸⠇⠀⠀⢰⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠰⠞⠳⣄⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⣶⠟⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠙⠿⠒⠛⠉⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢰⡎⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢶⠶⣀⣴⠒⣄⣀⣀⣄⣠⡶⠞⠋⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢦⣤⡀⣈⠉⠙⣼⠋⠉⢉⣁⣠⡴⢶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠈⠉⢿⣿⣿⡾⣏⠉⠉⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⠀⠀⠀⠀⣾⠙⣋⠀⠈⢳⠀⠀⠀⠀⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⠃⠀⠀⠀⠀⠀⠀⠿⣮⣉⡀⢠⡟⠀⠀⠀⠀⠱⣆⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠞⠁⠀⠀⠀⠀⠀⠹⡄⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣿⠀⠀⠀⢀⣤⠴⠶⠖⠒⠲⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢰⡇⠀⠀⢰⠏⠀⠀⢀⡀⣀⡀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣸⠃⠀⠀⠈⠳⠖⠒⠉⠉⠀⠀⠈⠑⣆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠸⡇⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠉⠉⠑⢦⣄⣿⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⢀⡴⢪⡟⠁⠀⠀⠀⠀⠀⣼⣿⠃⠀⣀⣤⠖⢶⡄⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣤⠞⠉⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠀⠀⠀⠀⢢⡄⢻⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡾⠃⢈⡿⠀⢀⡴⠂⠀⠀⠀⣡⠀⠀⠀⠀⣠⡾⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠻⣼⣧⠀⠀⠨⣇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠏⠀⠀⡸⠃⣠⠞⠀⠀⠀⠀⠀⢿⣀⣠⡴⠚⠁⠀⢀⣤⠟
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⣿⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡾⠁⠀⠀⠀⢿⣶⠋⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⣆⠀⠀⠀⢠⡟⠀⠀⠀⣰⠟⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⠞⠋⠁
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡀⠀⣠⠟⠀⠀⢀⡾⠃⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⢀⣴⡯⠉⣭⠓⢦⣀⡉⠳⣤⡀⠀⠀⠀⠈⣷⠀⠀⠘⣧⢰⡏⠀⠀⣰⠟⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⣠⠞⢁⡤⠒⣀⠙⠂⠈⠁⠒⠊⠽⣦⡀⠀⣰⠇⠀⢀⡼⠋⣿⡄⠀⣴⠋⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⢰⡋⣤⠋⣠⠞⠉⠀⠀⣀⣀⣤⣤⣤⡴⠳⣾⡁⠀⠀⠾⢁⣴⠃⠀⠸⣇⠀⠀⠀⠀⢠⡾⠁⠀⠀⢀⣀⣤⣴⣿⡉⢁⡀
⠀⠀⠉⠛⠳⠿⣤⣀⣀⡾⢩⡟⠁⣴⠋⠀⢀⣠⣥⣤⡀⢹⡟⢁⣤⣾⠓⠻⣷⠛⢦⣴⣯⣤⠤⠖⠻⠿⠯⣭⣍⡉⠻⣎⠙⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣸⠇⢸⡇⠀⣠⠟⠁⠀⠀⠉⠀⣿⠉⠀⠈⢷⠀⢸⡇⢸⠇⣿⣀⡀⠀⠀⠀⠀⠀⠈⣧⠀⠈⣴⣃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⣷⣀⣀⣿⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⣸⠇⢸⣇⣿⠟⠁⠉⠉⠛⠓⠲⢤⣤⣤⠿⠦⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠷⣤⠶⠞⠋⠉⠉⠙⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠖⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠑⠄⠀⠀⣠⠃⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡆⠺⠊⢞⠉⡘⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣵⠀⠀⠀⣦⡆⠋⣦⢼⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡄⠀⠀⠀⠸⣿⣿⣿⣿⠏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠄⠀⠀⠉⠛⢻⠃⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⣀⡀⣤⠦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣶⠀⠀⠀⠹⣿⣅⠢⠀⠀⠀⡰⢒⠆⡶⠉⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠄⠀⠀⡀⠙⢉⡴⠀⠀⠀⡇⢨⠀⢇⠀⣰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠀⠀⠈⠢⠄⠀⠠⠿⠃⠀⠔⠀⠳⢄⡱⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠆⡀⠀⠀⠀⠀⢀⣀⣯⠠⠣⣀⡠⠶⡄⢀⡁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⢄⡈⠙⠂⠀⠐⠛⠛⣿⣤⣧⠤⣀⠀⠈⠀⢡⠀⠀⢆
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣡⡀⠀⠈⠑⠒⠀⠀⢶⣾⠻⣷⣤⠣⡀⠉⠢⢄⣨⠀⠀⠈⢄
⠀⠀⠀⠀⠀⢰⠁⠈⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠳⣝⣈⡏⠀⠱⠀⠀⠀⠸⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣴⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⡔⠉⠛⠋⠀⢿⣿⡇⠀⠀⠱⡀⠀⠀⠀⠀⠀⢠⠏⠈⠉⠈⠉⠉⠀⠈
⠀⠀⠀⠀⢀⠂⠀⡰⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⢠⠆⠀⣰⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠎
⠀⠀⢀⠊⠀⢰⠃⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢠⠁⠀⢀⠔⠁
⠀⠀⡌⠀⠀⠃⠀⠀⢀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠔⠁
⠀⠀⠇⠀⠈⡀⡰⠋⠈⢳⣿⡿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⢀⠂
⠀⠀⠘⡀⠀⢁⡷⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠎⡠⠒⠉⠉⠱
⠀⠀⠀⠱⡀⡸⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠁⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡔⣁⠤⣤⡀
⡠⣤⠤⣀⡀⠀⢄⡀⠀⠀⠀⠀⠀⡀⠤⠤⢄⠀⠀⡠⠁⠀⢸⠄⠴⠯⠞⣑⠃⣀⠋⣢
⡇⠣⠊⡡⠊⠉⠛⠉⠉⠁⠀⠀⡜⢠⠊⡡⠄⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⡃⡸
⠈⠳⢤⠁⠀⢀⡠⠤⠤⠀⠒⠂⠳⣆⠂⠆⠉⠉⠀⠀⠀⡿⠈⠈⠁⠈⠉⠀⠀⠈⠉
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⣀⣀⠠⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⢠⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⡀⢢⠀⣀⣜⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠸⠃⡨⢢⡈⣧⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠓⠊⠐⠋⠛⠋⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠇⢤⠀⠀⠂⠀⡴⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡘⠄⣀⢀⡴⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⢾⠀⠙⢕⡀⠅⢣⠀⠀⡐⠰⢂⠎⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢆⠀⠂⠌⣤⠀⠀⠀⢅⠠⡈⢠⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡄⠀⠀⠁⠒⠂⠙⡤⡸⡉⠉⣐⠈⠣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣈⠁⠢⠄⠀⠴⠶⣏⣠⡈⡉⠀⠀⠙⡀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠁⠒⠀⠄⠤⡖⠹⠤⠑⡀⠑⠠⣀⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠄⠀⠀⠀⠀⢠⠁⠈⠀⠀⠀⠀⠀⠀⠑⠄⡈⠀⠐⠀⠀⠀⢇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⢀⠬⣀⠄⠠⠊⡂⠀⢀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⣀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠁⠀⠀⢠⠂⠀⠀⠀⠈⠒⠁⠀⠀⠡⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠂⠀⠀⠀⠏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⢠⠁⢀⠌⠀⠀⠀⡘⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⠀⠀⠁⠸⠀⠀⠀⠀⠘⠀⠀⠀⠈⢠⠊
⠀⠀⠀⠀⠀⠀⠠⠀⢡⠀⠀⠀⠳⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠇⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢠⣠⣄
⠀⠀⠀⠀⠠⠲⢒⠤⣌⣠⠄⡀⠀⠀⠀⠔⢂⠐⠄⡀⠔⠀⢀⠖⠒⠓⠡⠘⠢⡈⢣
⠀⠀⠀⠀⠰⣔⡠⠊⠀⠀⠁⠀⣀⡀⢌⡐⠑⠈⠤⠀⠀⠀⡅⠀⠠⠤⠤⠀⠠⠷⠊
⠀⠀⠀⠀⠀⠈⠉⠒⠀⠊⠀⠀⠀⠀⠀⠑⠮⡀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠤⠴⠶⠶⢶⣶⣶⣶⡶⠶⠶⢶⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣆⠀⠀⢀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢺⣟⢛⢋⣍⣩⣤⣤⣤⣶⣦⣿⡏⠛⠋⣿⣿⣾⠯⣿⣿⣾⣿⡿⢿⣿⣷⣿⣿⢿⣿⣿⣇
⠀⠀⣀⠀⣼⣿⣤⣀⠀⠀⢀⡾⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣹⣿⠗⡤⠤⣄⢿⠋⠐⣾⣿⣿⣿⠂⡀⠀⣽⡁
⠀⠀⠻⢿⣹⣶⣿⣻⣿⣦⣼⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⣿⣮⠀⠀⠀⣾⢀⣴⡿⢻⣿⣿⣼⠿⢺⡏
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⢿⣿⡌⠉⢰⣿⡿⠛⠓⢇⢻⣿⣦⢊⠋⠁
⠀⠀⠀⠛⠻⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣟⡈⢋⣿⣿⣿⣿⣿⣿⡌⠀⠀⠴⢿⡿⢦⣾⡟⠃⠀⠀⠸⠟⢿⡼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣉⣿⣿⣿⣿⣿⣷⣥⣤⣬⣿⣿⣿⣿⣿⣷⡀⠀⠐⠀⣾⣿⣿⡆⠐⠀⠀⠀⠀⠈⣿⡙⠿
⠀⠀⠀⠀⠀⠀⢀⣿⠡⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⢿⣿⡿⢷⠠⠀⢀⠤⣤⣄⠸⣷
⠀⠀⠀⠀⠀⠀⣾⣧⣶⣾⣿⣿⣿⣿⢿⣟⣻⣿⣿⣿⣯⣽⣿⣿⣿⣿⣶⣴⣴⣮⣽⣥⣥⣤⣤⣬⣤⣽⣿⣧⣹⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⡆
⠀⠀⠀⠀⠰⡟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⣤⣤⡀⣿⣷⡀⠀⠀⢀⡔⢁⣠⣄⡤⢦⡀⠙⣄⠀⠀⠀⠀⣠⣾⣟⣠⣴⣶⠄⠀⢠⠏
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣀⣹⣿⡿⠿⣿⣷⢀⣠⣾⠀⠸⣄⡨⠧⡸⠓⣦⢸⣶⣶⣤⣠⣿⠟⠛⢿⣿⣅⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣇⠺⠿⢿⣏⠀⠀⢸⣿⣿⣿⣿⡀⢸⣁⡵⢲⣁⢻⠁⣸⣿⣿⣿⣿⣧⡀⠀⣸⣿⠛⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣸⣿⣶⣶⣿⣿⣿⣿⣿⣷⣄⡀⠳⠞⠉⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⠿⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⢤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢠⡾⢛⡍⡨⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⡄⠓⠀⠀⠀⠘⡟⣇⠀⠀⠀⠀⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢀⣀⣀⡤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢠⣀⠠⣷⠹⣧⡀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣌⠄
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢠⡿⠃⢸⣿⡆⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠛⠉⠀⡀⢀⡀⢀⣸⠁⠐⣿⣿⣿⡏⠤⠀⠀⠀⣤⣤⠀⠀⠀⠀⠁⠐⠒⠶⠲⠂⠐⠂
⠀⠀⠀⠀⠠⠄⠀⠠⠂⠀⠀⣈⣸⠀⠀⣼⣿⣿⣷⠀⠒⠀⢰⣿⣟⣛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣇⢀⠀⠀⠘⠏⠻⣿⣷⣤⡀
⠀⠀⠀⠀⡠⡤⠈⡓⠀⠀⡀⣄⠀⣿⣿⣿⣿⣇⣈⠛⠀⠀⠀⠀⠠⣿⣿⠿⠻⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠀⠛⠛⠹⠏⠉⣽⣿⣶⠰⠿⠆⠀⠾⠀⠀⠀⠀⡀⠉⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⡠⠖⠩⡴⣀⣀⣾⣿⠶⠶⠶⠶⠒⠛⠋⠉⠁⠠⠀⡴⠂⠀⠀⠀⣠⠀⢦⠀⠁⢀⣤⡏⠀⠒⣀⡀⠐⠂
⠀⠀⠀⠉⠉⠒⠾⢿⠉⡡⣠⡤⣶⣄⣀⢀⣠⣤⣤⣤⠀⢀⡀⠀⣀⡀⠀⠈⠁⠀⠌⢣⡀⠉⢹⡀⢀⡼⠋⠀⠸⠄
⠀⠀⠀⠀⣀⢀⠀⠀⣠⡄⠋⢀⣼⠟⢠⣬⠙⠧⢬⣻⢿⣻⣦⣶⣿⣧⣄⠀⠀⠀⠀⠀⠳⡄⢸⣷⡞⣀⣴⠴⠆⠀⠀⠂⠠
⠀⠀⠀⠀⢘⣿⣧⣄⣡⡁⠀⠀⠀⢀⣾⣽⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢳⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠰⣶⠙⠀⠙⠉⠀⠀⣴⣶⣿⣯⣭⢻⠟⣻⣿⣿⣿⡆⠀⣠⡄⢼⣿⡇
⠀⠀⠀⠀⠀⠐⣲⠈⢿⣿⡀⡝⠂⠀⠀⠀⠀⠀⠛⠘⣿⣿⣷⣴⣶⣿⣿⣿⣿⣷⣇⠁⠌⠀⢸⢿⣷
⠀⠀⠀⠀⠀⠘⢛⠁⠀⢀⡄⠳⢤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢤⠀⡀⢐⡛⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⢸⡏⠀⠀⠀⠀⢀⢀⠙⠻⠋⠙⠛⠛⠿⠟⠛⢠⣟⡧⢸⠃⣿⠿⣿⣿⡇⠀⣠⣤⣰⣶⣶⣶⣦⡄
⠀⠀⠀⠀⡶⠶⣶⣶⡂⠂⡐⠂⣧⡄⠀⠀⠲⢼⡗⣰⠃⠠⠠⠀⠄⠀⠀⠀⣨⠙⢋⠛⠸⢇⢤⣿⣿⣷⢈⣿⣿⡿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠑⠶⠶⠿⢳⠘⠗⢠⡿⠿⢧⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣾⣷⣄⣺⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠠⣆⣠⡖⣤⣠⡆⠀⠃⠈⠿⠀⠀⠈⠁⠀⠉⠐⠠⠀⠽⠿⠟⠛⠛⠻⠿⠛⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⣿⣿⡿⠿⣿⣿⣿⠿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣒⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠠⠄⣀⣀⣀⡀⠠⠀⠀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡤⠂⠄⠀⠀⠀⠀⢀⠀⠀⠐⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡂⠄⠀⠀⢀⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠈⠐⠀⠀⢔⡀⣀⠄⠊⡀⠀⠀⠀⢇⠀⠀⠀⠀⠈⢧⠀⣠⡀⠀⠀⠀⡘⠁⠀⢀⣠⠀⢁⣀⢀⣀⢀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⢸⡅⠀⠀⡄⠀⠀⠁⢂⢀⠏⠀⢀⣀⠤⢀⠒⢉⠁⠀⢸⠂⠀⠁⠀⠀⠀⢻⡉⠟⠤⡀⠀⠃⠀⠰⠪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈
⠀⠀⠀⠘⡅⢣⠀⣡⡀⠉⠀⢸⠀⠤⠐⠋⠀⠀⠳⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⢸⠁⠀⣥⠟⢁⠅⠲⠚⢁⠁⠂⠉⠀⠀⠀⠀⡺⠒⠀⠀⠀⡀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠁⠀⠐⠸⠯⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⢀⡂⢀⣧⠐⡠⠐⠀⠘⠱⠀⠂⠀⠴⣌⣐⢊⠀⠠⠀⠂⠉⠀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠈⡄⠂⠄⡀⠂⡀⠀⠀⠀⠄⠀⠀⠈⠉⠁⠀⢸
⠀⠀⠀⠸⣧⠦⡰⢤⢷⠀⠐⢐⡀⠀⠠⠐⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⢰⠂⡐⠓⢧⣠⠀⡀⠂⠀⠀⠀⠊⢌⠀⢸
⠀⠀⠀⠰⡄⢅⣴⠋⢉⣱⣰⣻⠉⠦⡁⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠁⣠⠐⠀⠀⠀⠀⠆⠒⠘⡇⠃⠀⣹⡢⠠⣐⠀⢄⡂⠀⠘⠒⠀⠀⠀⢸
⠀⠀⠀⠀⣗⣼⠑⡐⠂⠀⠍⠑⡀⠂⠡⡀⡠⠤⠒⠂⠒⠛⠚⠊⠉⠂⠀⠉⠀⠀⠈⢁⡀⠂⠀⠼⠁⠘⢹⣄⠁⠈⠀⠈⠂⠈⠐⠠⢐⠠⠀⠀⠈
⠀⠀⠀⠀⢛⣯⠊⠀⠀⢬⠀⡀⠹⡀⢂⠡⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠐⠈⠀⠀⠀⠀⢀⠀⠀⢿⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐
⠀⠀⠀⠀⣾⡹⠀⠀⢀⠂⡳⠒⡁⢀⠀⠀⠷⠗⠀⠀⠀⠀⠠⠈⣀⡀⠀⠑⠆⠀⠈⡁⠀⠀⠀⠀⠉⠁⠛⢤⣁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡯⣧⠀⠀⠉⠟⢁⠤⠠⠉⣃⢠⢭⠀⠀⡄⠀⣐⡠⠉⠁⠈⢂⠖⠻⠇⢀⡈⠀⠀⠀⠀⠐⠒⠂⠜⠁⠂⡌⠀⠀⠀⠀⠃⠐⠀⠀⠀⢨
⠀⠀⠀⢀⡹⣁⡈⠑⠶⢀⠀⠠⠄⠀⠂⠀⠈⠃⠀⠘⣛⣁⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠒⠈⢀⡠⠄⠀⠜⠩⠀⠁⠀⠀⠔⡩⠀⠀⢸
⠀⠀⠀⠰⠇⠀⢠⠃⠈⡅⠀⡂⠀⠘⡩⢠⠃⢻⢄⠄⠀⠈⠊⠀⠀⠀⠠⠤⠐⢄⠀⠀⠀⢰⠤⠀⠘⠉⠉⠀⠂⠁⠀⠀⣷⠖⠀⢀⠙⠁⠀⠀⢸
⠀⠀⠀⠰⠂⡜⠸⠀⠀⠀⠀⠀⠀⠀⠠⠈⠆⠈⠀⠀⠀⠀⠀⡤⠀⠀⢀⠀⠀⠠⡉⠂⠀⠏⠀⠀⠀⠀⠀⢠⠀⠠⠄⠈⠏⠀⡠⠂⠀⠄⠀⠀⠰
⠀⠀⠀⢠⡋⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠠⠤⠴⢥⡈⡦⡎⠀⠀⢀⠀⠁⠘⠆⠀⠀⠀⠀⠀⠆⡀⠀⢁⡴⣀⠀⠀⠀⡌⠒⠤⠤⠐
⠀⠀⠀⠘⢁⠸⢀⠀⠀⠘⡀⠰⠀⠐⠀⢠⡀⠀⣀⡡⡄⠀⠈⣆⡙⠣⡐⢲⠖⠴⠆⡀⠠⠤⠤⠀⡄⠀⠀⠉⢈⠀⢰⠀⠀⠑⠦⠂⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⡄⠠⠄⠀⠐⠄⢰⠀⠀⠨⠰⠀⠁⠀⠰⠕⡄⠐⠀⢘⠑⡠⢬⠲⢄⠑⢄⡀⠀⠀⠀⠀⠈⠒⠒⠐⠠⠀⠀⠀⠀⠀⠒⠀⢀⠀⠁⠀⠀⡅
⠀⠀⠀⠀⠂⠀⠂⠀⠀⣀⣐⠀⠀⢀⣐⣀⠈⠀⠀⠈⠸⢦⡠⠰⠶⠀⠀⠑⢄⡙⢦⣈⠂⠀⣀⡀⠆⠰⠀⡈⠀⠀⠀⠆⠀⠀⠀⡀⣀⠁
⠀⠀⠀⠀⠗⣀⠂⠒⠁⠸⠟⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠄⣈⠒⠊⠁⢁⡀⠤⠄⠠⠄⠀⠀⠀⠠⠠⠄⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡆⠹⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⠠⠤⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⣿⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡀⠀⠈⢦⠀⠀⠀⠀⠀⢠⠞⠁⢰⠃⢀⢿⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠸⠀⠀⠘⣧⠀⠀⠀⢰⡏⠀⠀⠸⣄⠂⣞⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣙⢀⡠⠤⣼⣶⣶⠦⣼⠁⠀⠀⠀⢻⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠿⠷⠀⠀⢉⠉⠻⠷⠈⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⠴⡄⠀⡖⠉⣙⣦⠀⠀⠀⠀⠀⠀⠋⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡴⢻⣡⣶⡎⠀⠣⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⣝⠒⠓⠋⠀⠀⠘⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠄⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠙⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠘⠦⣀⢠⠀⠀⠀⠀⠀⠈⠳⣄⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠈⠳⠦⣾⠛⡶⠦⢤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠑⡢⠶⠐⠒⠒⠒⠒⠚⠙⠛⠓⠒⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣮⣀⣀⣤⡤⠤⠤⠴⠒⠚⠙⠒⠒⠾⢧⣀⠀⠀⠀⠀⠀⣀⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢀⡤⠚⠉⢡⠆⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠉⠓⠚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢠⠏⠀⠀⠙⢌⣂⡵⠃⠀⠀⠀⠀⠀⠀⢤⡴⠃⠀⠀⠀⢀⡞⣀⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣸⠀⠸⣄⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢾⡉⠀⠁⠙⡄⠀⠀⠀⠀⠀⠀⠘⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⠀⠀⠨⣗⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣙⡶⣞⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢈⠀⠀⠀⠈⠙⠒⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣄⣤⣄⢀⣀⣀⣤⣄⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠟⠒⠒⠃⠒⠒⠒⠒⠲⠖⠒⠀⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠼⠄⠀⠀⣀⠀⠀⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣃⣀⣀⠀⣀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⢈⣍⠀⠀⠐⡆⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠠⠤⡆⠠⠤⠤⠤⠤⢤⢊⡁⠈⠀⠀⠀⣧⠀⠀⠀⠞⠁⢐⣶⠒⠆⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡸⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢦⣹⠀⡇⠈⠁⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠠⠀⡇⠀⠀⠀⠀⠀⠠⠄⠈⠉⠉⠀⠈⠉⠈⠙⠒⠒⠤⠔⠊⠀⠈⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣤⡖⢻⡟⠃⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠳⡄
⠀⠀⠀⠀⠀⠀⠚⢻⣿⢻⠧⠀⠀⠀⣿⢼⡿⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣠⣶⣆⢰⣶⣿⣾⡿⠆⠀⠀⠀⠀⠀⠾⣶⣶⣆⣶⣦⠀⠀⠸⢀⠀⠀⠀⠈⣦⡀⠘⣇⠀⠀⢠⠏⠁⠁⢀⡤⠀⠀⠀⠀⣸⡀
⢸⣿⣹⣯⡙⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠰⠓⠛⠀⠀⠰⠈⢿⣤⠀⠾⠿⠁⠀⠈⠧⠖⠁⠀⠀⠀⠡⠀⠀⠀⠀⠆⠳⢃
⠈⠈⠉⠉⠁⠀⠀⢀⠀⢀⣔⣰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠈⠁⢀⣠⠆⠀⠀⠀⠀⢀⡴⠀⡖⠒⠋⠀⠀⠀⠀⠰⠖⣿
⠀⠀⠀⠀⠔⠀⡠⠙⠒⠟⠂⠙⠒⠃⢀⠉⢢⡀⠀⡜⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠉⠙⠁⠠⢤⡀⠀⠀⠀⠘⠀⠻
⠀⠀⠀⡜⠀⡼⢡⣄⠀⠀⠀⠀⠀⣠⡄⢠⠀⢱⠀⠛⢀⢠⡀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠬⡎
⠀⠀⠀⡇⠰⠇⠀⢹⡷⢀⣄⠀⣾⡿⠀⢸⡆⢸⠀⠀⠈⠛⠑⠦⠟⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⠀⠀⠀⠀⠀⢠⡜⢀⠱⣄
⠀⠀⠀⢷⣴⡄⠀⢦⣀⠈⡙⢀⣈⡄⠀⢠⢇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠁⠀⠐⢶⣤⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠉⠛⠦⣾⠉⠻⠛⠏⣙⣀⣠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠓⠄⠖⠊⠀⠀⠀⠀⠀⢀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠈⠉⠀⠀⠀⠀⢀⡶⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⢠⡤⣠⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣶⠄⠘⠻⢿⣿⣿⣿⣿⣷⣾⠆
⠀⢀⠂⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠈⠀⢦⡀⠀⠀⠀⠀⠠⣦⣾⣿⢿⣿⣯⠀⠀⠀⣾⡿⠋⢿⣿⠁
⠀⣾⠀⠀⢠⢨⣿⠄⣿⡇⠠⡆⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⡹⣿⡽⢻⣿⣆⣀⣹⣿⣄⣀⣼⣯⣦⡀
⠀⢧⠀⢠⠈⠘⠛⢰⠌⠋⢀⠠⠀⠀⢠⢜⠇⠀⠀⠀⠀⠀⠀⣸⢇⠀⠀⠀⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⣠⡀
⠀⠈⠓⠶⠾⢠⣖⣐⣴⠀⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣿⣿⡄⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⠃⡄
⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⠀⠀⠀⠀⢀⡯⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠘⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣇⠀⢁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠘⠣⠠⠖⢦⢀⡀⣀⣸⣾⡇⠀⠀⠀⠀⠀⠀⢻⣿⢹⣿⡟⡋⣛⣿⡷⣾⣿⣥⡰⣏⣀⡽⣠⠂
⠀⠀⠀⢠⠔⢤⣀⠜⠀⠀⠀⠀⠑⢀⠀⠀⠀⠂⠀⡀⠐⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡿⠃⠒⠒⠘⣿⣿⣿⠛⣷⣏⣁⡴⠧⠤
⠀⢀⠀⡧⢦⡀⣭⠶⣦⡀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢸⣿⣇⢀⣀⣀⣀⣿⣿⣿⣶⡈⠉⠫⠄⠀⠁
⠰⠛⠛⠁⠈⠋⠁⣰⣿⠛⠛⠏⠐⡒⠆⣄⣀⠤⠄⠐⢒⡤⠤⠄⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣶⡍⠉⣻⣿⣿
⠀⢤⣀⣴⡶⠖⠛⠛⠛⠒⠐⠿⠓⢉⠁⢀⠀⣉⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠻⠿⠿⣿⣶⣦⣀

⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢶⣿⠛⠉⢸⡗⠓⠀⣿
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠄⠒⢲⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣶⡾⠿⠛⣿⡇⠀⢈⣿⢄⠀⢸⡧⣭⠀⠻
⠀⡇⢀⡄⠀⠀⠀⢀⠀⠀⣀⡀⢠⢴⡲⠊⠀⠀⠀⠀⢂⠁⠀⠀⠀⠓⢲⡖⠒⠒⠒⣞⠟⠉⠁⢹⣧⣤⢶⡾⠉⠀⠀⠀⣀⠱⠘⣿⠁⣠⣀
⣤⡇⣜⣁⠀⠄⠅⠀⢿⠠⡏⠄⢘⢸⣧⣶⣶⡆⠀⠀⠿⠷⠀⠀⠀⠐⠀⣷⠀⠀⠀⢻⠲⣄⣀⣸⡗⢿⠏⣀⠀⣛⠂⠀⠄⢷⡄⡇⢺⡏⡍
⠁⠙⣿⣷⠀⠀⠀⠀⠌⣆⣀⠁⠘⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡖⢀⢻⡴⠖⠚⠛⣯⠟⠏⠈⠁⡾⢀⣿⠀⠀⠀⠀⠐⢠⣄⢸⣿⠀⣄
⠃⠒⣿⣾⣄⢙⡆⡿⣳⢿⡀⠀⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠳⣦⠈⡷⣆⠀⠀⠀⡈⠀⠀⠀⢻⣸⣿⠀⠃⠒⠦⠀⣸⣿⡾⢏⣀⠤
⠚⠃⠀⠜⢌⣉⣽⡽⠿⠻⣠⢾⠘⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⣷⠀⠀⠁⢰⠁⠀⠁⠀⠁⣿⢿⠃⣄⣀⣀⢴⣿⡗⠉⢈⣁⢰
⠀⠀⠀⠀⢀⠀⢛⠀⠀⠀⡈⢾⢨⠶⣿⠉⢹⡇⠶⢤⣄⣀⠀⢀⣰⠀⠂⠀⠩⠐⠃⠒⢰⡇⢗⣠⠦⣅⠀⣠⡷⡔⣾⠕⠋⣡⣿⣿⠟⠀⠐
⠀⢀⣦⢠⠁⠊⠭⠀⠀⡀⡁⢸⣿⠀⣿⠀⠈⠁⠀⠈⡁⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⠉⣠⡏⠁⡴⣿⡟⠁⠀⠀⡏⡞⣼⡟⡿⠁⠀⠀⠈
⠀⢼⣿⢿⡇⢠⠀⠀⣘⡃⡿⠻⠛⠀⣿⠀⠀⠀⠀⠀⠇⠸⠀⠀⠀⠀⠀⣤⠾⡷⠶⣆⠜⢁⣐⣾⠷⢟⠠⠆⠀⡀⡇⣧⣿⠀⠀⢀⡀
⠉⠁⢻⠀⣱⢊⣤⡔⠋⠹⣷⠆⠀⠀⢿⠃⠂⠐⠂⠀⠁⠀⠙⠐⠖⠶⠾⣧⡀⢰⡞⠉⠙⣍⠃⠀⠀⠀⠡⣴⡞⡯⠦⣯⡿⣴⡿⢟⣻⠿
⡀⠠⢈⣺⣿⣽⣤⠤⠀⢀⡿⣿⣤⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⢻⠆⠀⠀⠁⠀⠀⠀⠀⠠⠼⢃⡅⣷⡸⡇⠀⢠⡤⠄⣄
⠤⢖⡗⣉⣿⣮⡉⠗⠀⠈⡏⢺⣿⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠔⠹⢄⣀⡀⠀⣀⠤⠶⣏⠀⠀⢜⢧⡹⡇⠁⠀⠈⣀⣤⠀⠈
⠀⠀⡇⡴⠋⠀⠀⠀⠀⠀⠁⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡇⢀⣰⣇⠀⣤⣄⠓⠱⣤⠈⠀⠀⠀⠉⠀⡀
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡗⠉⠀⠀⠀⡀⠈⠹⢦⡈⣎⠈⠀⠀⠀⠈⠉
⠀⠀⢇⣣⡖⢀⠤⠤⣤⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠘⠐⠵⠋⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣾⣆⠀⠀⠀⠒

⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠩⡜⠻⠆⠒⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢌⠃⠳⠶⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⢀⣤⣶⣕⠲⡈⢳⡄⠀⠀⠀⢀⣠⠶⢾⡛⡻⣿⠟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⣏⡬⣯⣇⠇⢻⡔⠹⡒⡇⠀⠀⣰⢋⡤⣸⣾⠷⣣⣰⠿⣇⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣐⣨⢟⣢⠽⢿⠿⢿⣳⢁⣟⣿⣿⣃⣘⡷⣿⢿⠀⢙⣯⣢⣯⡊⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⠦⠶⣾⡤⡄⣛⡿⢉⣿⡷⣁⣽⡇⠋⠨⠌⡟⡋⣿⣿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠉⣹⣾⣭⣞⣯⠹⢟⠊⠞⢮⡏⣛⠛⣒⣒⣺⣷⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠉⡍⣉⠉⣩⣿⣿⠿⣷⣉⢍⠢⡈⢆⢧⢨⠝⡛⠫⡋⣽⢻⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⠀⠀⢂⣠⣿⣿⠟⠁⠄⣿⣈⠣⡆⢁⠸⣎⠧⢤⠬⠒⢩⣭⣭⣺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠔⣀⠂⠔⣤⣼⣿⠟⢡⠄⡒⢠⠆⠨⠀⠟⢆⢤⠿⡍⢠⣼⠒⣁⣥⣸⣘⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠃⡴⠠⠘⢊⣽⡿⠋⠈⠊⠀⠀⠈⠁⢀⠀⢆⠸⠘⢩⡐⢻⡄⠀⠉⠀⣠⣤⣯⣛⣍⡉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡐⣄⠀⠛⠃⢀⣴⡿⠋⢀⡀⠈⡀⡠⠀⡠⠀⠀⠀⠸⡤⢳⣣⡩⠲⣧⠀⢀⣴⣿⡻⠿⠿⢉⠉⢸⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸
⢸⡾⠟⠲⠶⣄⠀⠔⢁⡿⢀⡔⢸⣿⣏⣳⣭⣭⣉⡛⠛⠚⠚⠳⠶⠷⠚⢓⣛⣊⣉⣳⣧⠘⠇⠉⣉⣠⣴⣶⣦⠀⡇⣎⣀⣤⣴⣶⡿⡟⠛⠳⣄⠀⢸
⠈⡟⠂⠀⠉⠀⡟⠀⣺⠁⡾⡇⢵⡟⠛⠓⠂⠁⠈⠩⠛⠿⣿⣿⣿⣿⠛⢻⠀⠛⠿⢭⡻⣆⣰⣿⣿⢯⢅⣼⠇⡜⣠⣿⡿⢿⢿⠟⢂⣠⣦⡰⠾⣆⢸

⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡞⢿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⢼⠀⣀⡤
⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣷⠀⣷⠀⠀⠀⠀⠀⠐⠓⠚⠁⠀⢈⡁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢾⣇⠶⠆⣿⠆⠀⠀⣠⣤⣤⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢲⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡤⡑⢦⡄⠀⠀⠀⠀⠘⢿⡷⠀⢀⣀⡀⠀⠀⠀⠘⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠷⢦⠰⡇⠷⠙⠀⠀⣴⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⡄⠀⠧⠄⠀⠙⠋⠉⠙⣿⣿⣾⡇⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢿⣿⣆⠉⠀⠀⠀⣨⣭⣦⠀⠀⣾⣿⡿⠋⠀⣶⡄⠛⠁
⠀⠀⠀⣾⡁⠀⠀⣯⡗⠀⠀⠀⠀⠀⢸⣿⣧⣶⣦⠿⣿⠀⠀⠀⠀⠉⢛⡥⣸⣿⣔⣄⠀⢀⢤⡉
⠀⠀⠀⠙⠆⠀⠀⠏⠙⠂⣀⠚⢠⠄⢸⠟⣰⠋⡏⢧⡀⠀⠀⠀⠀⠀⠘⠃⠉⠛⠛⠚⠀⠘⠛⢁
⠀⠠⣆⢶⣀⠀⠀⡀⠀⠀⢀⠆⠚⠀⠀⣰⡟⠀⣷⠘⣿⠀⠀⠒⠲⢤⡀⠿⣿⡿⠃⠀⠀⠀⠀⣿⣧⡀
⠀⠒⢢⡄⡧⠀⠀⣿⡦⣴⡿⠀⠀⠀⢰⣿⠁⠀⣿⡆⠘⠀⠀⠉⢹⡆⣇⠀⠀⢀⡀⠀⠀⠀⠀⠛⠉
⠀⠀⠈⠁⠘⠻⣾⠁⠀⠀⢹⡶⠶⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⣿⠀⢠⣟⣷⣾⠆
⠀⠀⠀⠀⠀⣠⣾⠦⣀⣠⢾⣆⠀⡀⠀⣾⢹⠀⠀⣞⣳⠀⠀⠀⠀⠁⠉⠆⠿⢿⣿⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠉⠱⢠⠀⠈⠉⠀⠀⠈⠁⠀⣤⠄⠀⠄⠀⠀⠻⣿⣟⠁⠀⣴⢀⠄⠱⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⡐⠘⡰⠂⠀⠀⠀⠀⠀⠀⠀⠁⠎⠀⠈⠀⠀⣼⣫⣝⢿⣴⡛⠚⠀⣀⣹⡾
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠰⠷⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡇⣟⢰⣌⡿⢻⣿
⠀⠀⣄⡄⠀⣤⠄⠠⣍⠠⠖⠀⠀⠀⠀⠀⠀⢸⣿⣃⠀⠀⣴⠛⣦⠀⠀⠀⠛⢛⠛⣸⠃⢱⣾⣿⣷⣿⣟
⠀⠉⠻⠓⠀⠀⠀⠀⠓⠀⠀⠀⠀⠧⠀⣶⣶⣿⠿⠿⠿⠃⢸⠿⣏⠀⠀⠀⠀⢸⣷⣿⠀⢻⠟⠙⠛⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣿⣃⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣈⣈⣈⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⣄⡀⠀⢀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀
⠀⠘⠛⠿⣿⣶⣿⠛⠀⠀⣠⣿⠋⠀⠀⣸⣿⡏⠀⣀⣸⣿⠀⠀⣠⣿⠃⠀⢀⣼⡿⠋⠈⣿⣿⡿⠉⠈⢿⣿⡟⢁⠈⠻⠿
⠀⠀⠀⠀⠀⠉⢻⣷⣤⣾⠿⠇⣲⡿⠋⠀⠈⠀⢰⣿⠋⠀⠁⣸⣿⠁⠐⠒⣿⡋⠁⠀⣴⣿⢅⣀⡀⠈⠀⠀⢀⠀⠀⠀⢮
⠀⢰⣶⣦⣤⣀⢀⣽⣿⠁⠀⢸⣿⡇⠀⠀⠀⠀⣿⡟⠀⠀⠀⣿⡇⠀⠀⢸⣿⡏⢶⣿⠟⠁⠈⣿⣿⡆⡀⠀⡞⠇⢠⣶⣿
⠀⠀⠀⠈⠙⠿⢹⣿⠇⠀⠀⢸⣿⡇⠀⠀⠄⠀⣿⣧⠀⠀⠀⢿⣇⠀⠀⢸⣿⡇⠈⠀⠀⢀⣼⡿⢋⠀⠄⠐⠘⣄⠀⠙⠟
⠀⠀⠀⠀⠀⠃⢸⣿⡀⠀⠀⠈⣿⣷⡀⠀⠀⢀⠘⢿⣧⡀⠀⡘⣿⣄⠀⠀⠻⣿⣂⣠⣶⡿⠟⠁⢈⣶⣶⡄⠀⠨⠃⢈⡇
⠀⠸⠿⠿⢶⣶⣾⣿⣧⠀⠀⠀⠘⢿⣷⣤⡀⠀⠓⣿⡍⠈⢻⣿⠈⠉⣷⡆⣤⣿⡟⠛⠉⠀⠀⣠⣾⣿⢟⠁⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⠀⠂⠀⡟⣿⣿⠀⠀⣿⡇⠀⢸⣿⠀⢀⠿⠋⠀⣠⣽⣦⣴⣶⣿⡿⠛⠁⠀⠻⠟⣀⠀⢙⠃
⠀⠀⣤⣤⣄⣀⣀⠀⠀⠈⠙⠷⣦⡀⠑⠿⢏⣀⣴⡟⠀⠤⢿⣷⡞⠁⠀⢀⣾⡿⠋⠁⠀⠉⣳⣄⣀⠀⣀⣴⣿⣀⣤⣤
⠀⠀⠛⠛⠛⠻⠿⢿⣶⣤⣀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣠⠿⠿⠀⠀⠀⠸⠿⢇⠀⠀⠀⣾⡟⠁⠈⢻⣿⡟⠋⠘⣿⣿⡇
⠀⢀⣠⠀⠀⢀⠀⠄⠈⣿⠛⠃⠀⠈⣉⠁⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢒⠛⠃⠑⠄⣀⠘⣿⠃
⠀⠀⠰⢆⡀⠉⠁⠀⠀⠛⠀⠀⠈⠀⠋⠈⠀⠀⠈⠃⠀⡀⠀⠀⠙⠁⠀⠀⠐⠘⠓⠀⠀⠀⠂⠀⠦⠀⠀⠀⢠⣄⠁⠨
⠀⠀⠀⠘⣦⠢⡆⢀⠈⣀⠀⠁⠀⠀⣀⠂⠀⡀⠀⡀⠂⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠠⠀⠁⠀⠀⠀⠐⠨
⠀⠀⡠⢤⡾⠀⠀⠀⠀⠉⠁⠠⠀⠀⠋⠁⠄⠀⠈⠋⠀⠀⠀⠂⠺⠂⢀⠀⠂⠐⠗⠀⠀⠐⠄⠰⠆⠀⠀⠀⢰⡆⢀⢀
⠀⡘⠀⠈⠧⡄⠀⠀⠀⠲⠀⠀⠀⠀⣠⡆⠀⠀⢀⣄⠁⠀⠀⠀⣀⡐⠀⠀⠂⢀⡀⠐⠂⠀⠄⠀⡀⠐⠁⠀⠀⡀⠈
⠀⡇⠀⠀⠀⠀⠉⠠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠠⠀⠀⡈⠉⠀⠂⠀⠁⠘⠃⠠⠀⠀⠘⠋⠀⠍
⠀⠧⡤⣄⡀⠀⠀⠀⠀⠉⠉⡤⢈⡅⢤⡆⠀⠀⢠⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣄⠀⠀⠠⠀⣀⡈⠁⢀⠀⢀⡄⠀⢀
⠀⠀⠀⠈⣱⣄⣀⡀⣤⠜⠋⠀⠰⠐⠀⠙⠢⠀⠀⠀⠀⠃⠀⠀⠀⢠⠐⠀⢀⠈⠁⠀⠐⠀⠀⠈⠀⡀⠀⠀⠈⠁⠀⠐
⠀⡀⡰⠎⠉⠉⠉⠀⠀⠀⠀⠀⡲⠀⠀⠀⠘⢀⠑⠶⢀⠀⠀⠀⠶⠀⠀⠀⠄⠠⡦⠀⠀⠤⠀⢴⠀⠀⠐⠀⢠⡆
⠀⣁⠁⠀⠀⠀⣠⡤⢤⣤⣤⠼⠁⠀⠀⠀⠆⢈⣧⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁
⠀⡃⠀⢀⡠⠊⠁⠀⠀⢹⡁⠀⠀⠀⠀⠈⣴⠟⣻⣧⠀⠀⠀⠀⢤⡄⠀⠀⠄⠠⣄⠀⠀⠀⠀⣤⠄⠀⠐⠀⢠⣄
⠀⡁⠐⠀⠀⠀⠀⠀⠀⠀⠙⠧⢤⣀⠀⡀⣻⠀⠀⠉⠑⢓⣀⣄⣀⣄⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⡉⠀⠆⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠐⠉⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠊⠀⢀⣧⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢉⡀⠤⠋⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠁⠀⠀⠣⠀⢐⠹⡆⠀⠀⠀⠈⣄⠀⠀⠀⠀⢀⠷⠠⠤⠤⠄⠲⠏⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠶⠖⠛⠒⠛⠂⠛⠀⣐⣯⢒⠙⠀⠀⠀⠀⡎⠀⢻⠲⢄⡀⠁⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠤⠈⠙⢉⣶⠄⢠⡄⢘⡛⣱⢃⠖⠀⠀⠀⠀⠇⠀⠈⢦⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⠀⠀⠀⣠⡆⠉⠉⢉⡠⠊⠀⠀⠀⠀⠒⠂⠉⠰⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠂⠀⠁⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣦⣤⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢀⠉⢈⣁⠾⠀⠀⠀⠀⠀⠀⢀⡴⢸⡎⡅⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⡤⣬⠅⠐⠃⡢⠀⣀⠤⠒⠉⠀⠈⢷⡐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣀⣀⣀⣤⡶⢂⡴⠾⠓⠋⠁⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣏⣤⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠻⢦⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⢠⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⠁
⠀⠀⠀⠀⠘⢦⡈⠢⠴⢤⡀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⢀⡀⠧⡀⠀⠀⠀⠱⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠔⢩⣆⠀⠀⠀⣸⢇⢰⠋⠲⡾⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⣖⢉⣴⠋⢨⠷⡀⡴⠁⠸⠃⠉⢶⠃⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡆
⠀⠈⢠⠁⣰⡏⢸⡇⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠈⠉⠀⠶⠊⠱⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⢰⡄⠀⣧⠀⡜⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹
⠀⣀⣀⣠⣀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠑⢶⡄
⡞⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⠽⠷⠒⠂⠀⠐⠒⠈⠉⠉⠉⠉⠉⣉⣉⣉⣙⡆
⠙⠳⢤⣤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠒⠛⠉⠉⠉⠉⠉⠛⣆
⠀⠀⠀⠉⠃⠀⠤⠤⠤⠤⠤⠀⠉⠉⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠞⠃
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠠⠔⢖⠒⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⢄⠀⠀⠑⢁⡀⢢⠀⠀⠀⠀⠑⠆⡠⠠⣶⡦⠀⠀⠀⠠⠀⠠⢻⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡌⢢⡀⠘⠁⠀⠀⠆⠀⠀⠉⠈⠙⣄⡘⠁⠐⠃⢠⠐⠀⠀⠀⢹⣧⠀⠀⠀⠀⠠⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⠄⠑⡄⠀⠂⠀⠀⡄⠀⠠⠤⠓⣂⣕⠀⡀⠐⡡⠂⠀⠀⠀⠀⢩⢃⠀⠀⠀⠀⠑⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠀⠞⠂⠂⢀⡈⠳⡀⠂⠀⠀⠤⣼⣿⣥⣯⢤⣀⡀⣀⠀⠀⠀⢆⢣⠀⠀⢀⣠⠘⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢉⠄⠐⠂⣼⠀⢆⣨⡔⠿⠓⣀⣷⣁⣈⣀⣉⣈⣀⣈⣈⣆⣩⡉⠁⠁⠀⣽⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠠⠀⠂⠈⠈⡀⠡⡘⠓⠋⠉⠉⠉⠛⠃⡉⠉⠩⢭⠉⠉⠩⠟⣿⠆⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⠚⠙⡅⠀⠀⠀⠈⠀⢀⢤⠀⡀⠀⠉⠧⠴⠶⠶⠂⠀⠀⢰⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠄⠂⣀⡇⠀⠀⠀⠀⠀⡆⠠⠰⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡞⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢸⡿⡝⠀⠀⠀⠀⠀⠀⢡⠀⡷⠀⢤⡖⢠⠀⠀⠀⠑⠀⡰⠁⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⡘⣞⡄⠁⠀⠋⡃⢇⣠⡀⢀⠠⡇⣀⢸⠀⢤⠀⠸⠣⡌⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⢡⡄⠀⡆⠁⢸⡿⠛⢻⡀⠄⡽⢙⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣖⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡀⠀⠃⠀⠃⠀⠀⠀⠀⣾⠉⠃⠀⠸⡀⠀⠆⠀⠀⠀⠀⠑⠄⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠘⠄⠀⣰⣏⠀⢠⠀⠀⠘⢄⠰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⡤⢠⢀⣿⣿⣄⢀⡀⢀⠀⠘⠀⠀⠐⣤⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄⢁⠀⠀⠀⠐⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⣿⣧⡈⣾⣿⣿⣿⡏⡅⡿⠀⢰⠗⠠⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠃⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⢿⠉⣱⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠁⠀⢠⣿⣿⡟⠁⢻⣿⣿⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠀⡀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢠⣿⡿⠋⠀⠀⠈⣿⣿⡀⠀⠀⠀⣾⣿⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⣰⣿⡿⠁⠀⠀⠀⠀⢘⣿⣇⠀⠀⠀⠛⠿⠿⣷⣄⠀⠀⠀⠂⠀⠔⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⣀⣴⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆
⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⠇
⠛⠛⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠙⣿⣿⡇⠀⠀⢸⣿⣿⠇⠀⠀⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡀⠀⠸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⢠
⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠙⢿⣷⡄⠀⢻⣿⠀⠀⣾⣿⠇⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠹⣿⡀⢸⣿⠀⣰⣿⠏⠀⢀⣾⣿⡿⠋⠀⠀⠀⢀⣾⣿⣿
⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⡘⣧⢸⡇⣠⡿⠃⢀⣴⣿⡿⠋⠀⠀⠀⣠⣴⣿⣿⣿⡿
⠁⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠷⠶⠶⢬⣑⢌⣌⠔⣋⣤⡾⠟⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⠟⠋
⠀⠀⢀⣠⣶⣿⣿⣿⡿⠟⠋⠉⠀⢀⣠⣤⠶⢒⡡⡻⠣⡚⠤⣤⣤⣤⣶⣶⣿⣿⣿⡿⠟⠛⠉
⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣾⡿⠋⠁⣴⡟⢰⡇⢷⡙⢷⣤⣀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⣿⠋⠀⢠⣾⡟⠀⣾⡇⠸⣷⡄⠉⠻⢿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⡿⠁⠀⢠⣿⣿⠀⠀⣿⣇⠀⠹⣿⣦⡀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛
⣿⠏⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⣾⣿⡇⠀⠀⣿⣿⡄⠀⠙⢿⣿⣶⣄⡀
⡏⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⢠⣿⣿⡇⠀⠀⢹⣿⣷⡀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣄⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣇⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠘⢿⣿⣿⣷⣀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠈⢻⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿
⣆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄⡀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣤⠄
⠀⠀⠀⠀⣄⡐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠃⠀⠀⢠⣤⠤⠀⠐
⣀⡀⠈⠀⠉⠸⠓⠂⠀⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠓⠀⠀⠀⠁⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠃⠄⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⣠⣐⠒
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⡄
⠀⠘⠁⠀⠀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⣴⣿⡿⢷
⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⡿⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⢶⡟⢛⡛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⢸⣏⠉⣿⣿⣿⣖⣼⣿
⠀⠁⠐⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⠀⠛⣶⡃⠀⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣿⣁⣄⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣛⣛⣿⢟⣩⣿⢿⣭⣭⡉⣩⡭⠋⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣼⡟⢻⣤⣟⣿⣙⡿⣿⣾⡟⢻⣯⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣿⣾⣿⣿⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡶⠶⠶⠶⢶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠠⠀⠀⠀⠀⠀⠀⢐⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⡀⠀⠀⠀⠀⠘⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡀⡈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠙⠋⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠽⠈⠏⠀⠀⠀⡀⠐⠄
⠀⠀⠀⠀⣀⠚⠓⢀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠛⢛⠋⠰⠀⠀⠀⠀⠀⡀⠀⠀⠆⡤⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢹
⠀⠠⠀⠀⣛⣛⣛⣻⠀⠁⠀⠀⠀⠀⠢⡈⠠⠉⠀⠤⠀⡀⠀⠀⠀⠀⠾⠀⡀⠀⠔⠀⠀⠘⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠃⠀⠀⢸⡀
⠀⠀⠀⠒⡿⣿⣿⡗⠀⠀⠀⠀⠀⠈⠄⠀⡄⠀⠄⠨⡌⠠⠀⠀⠀⠀⠀⠰⠿⢾⣶⣿⡂⠀⠈⠈
⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⣀⡀⠀⠀⠀⠀⡄⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡶⢶⣤⣴⠀⠤⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣿⣧⡑⠀⠀⠀⠠⠔⠀⠰⢠⡃⠀⠀⠀⠀⠀⣴⣿⠿⢿⣿⡄⠂⠀⠀⠀⠀⠀⠀⠀⣠⣷⣀⢐⣢⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁
⠀⠀⠀⠐⠀⡀⠀⠀⠸⠦⠃⣼⣿⠀⠀⠀⠲⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠈⠀⠈⠸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠈⠛⠛⠃
⠀⠀⠐⠀⠄⠄⠀⠀⠀⠀⢠⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⠀⣴⣠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤
⠀⠀⠀⠀⠀⡆⡱⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⠀⣀⠈⣉⠻⢿⣾⣿⣿⣴⣿⣿⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣦⡘⠀⠀⠀⣾⣇⣸⣿⡀⣸⣿⣧⠸⣿⣿⡧⣿⣻⡇⢿⣾⡟⠀⠀⠀⠉⠉⠋⠙⠋⢉⣠⡀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⡇
⠀⠠⠾⢿⣿⣿⣿⣷⡄⠀⠉⠁⠀⠀⠀⢿⣿⠙⣿⡇⣿⠛⢿⠆⣿⠉⠀⠿⠉⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⠿⠿⠓⠀⠀⡀
⠀⠁⠀⠑⠠⠾⠛⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⡀⢀⣀⠀⣀⣀⢀⣀⠀⢠⡄⠀⢀⣤⡀⣤⣤⣤⣤⣤⣶⣶⣶⡆⣾⣦⣿⠀⠀⠈⠂
⠀⠀⠠⠀⣀⠀⠤⠊⠀⠀⠀⠀⠀⠢⠀⠄⠀⠀⣿⣧⣼⣿⢰⣿⣿⣎⣿⣀⣼⣧⡄⣿⣭⡿⢿⣿⣿⡇⣿⣿⣿⡿⠧⠿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠿⠇⠸⠿⠘⠋⠙⠋⠛⠉⠉⠉⠁⠈⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠶⠶⠖⡀⣀
⠀⠀⠀⠀⠀⠦⠀⠀⠀⢠⠀⠀⢁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⣤⠄⣤⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠐⠿⠀⠀⠀⠙⠥⠛⠃⠀⠀⠂⡀⡀⠈⠀⠀⠀⢠⠀⠠
⠀⠠⡄⠀⠠⢀⠃⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣄⣀⣤⡤⠢⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⡄⠀⠀⠐⠀⠁⠀⠀⣠⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢉⣉⡉⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠢⠁⠀⠐⠊⠁⠁⠀⠀⠀⠠⡿⠁⢀⣉⠀⢹⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡛⠉⠀⠀⠀⠀⠤⠠⡇⠀⠀⠀⠘⠿⠁⠀⠀⢀⠰⣣⡄⠂
⠀⠀⠀⠀⠀⢠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⠁⠀⠂⠙⠂⠸⠁⠂⠀⠀⣤⣠⣀⠟⠛⠛⠛⠻⣇⣀⡀⠀⠀⠀⠀⠊⠀⢀⠀⢀⣠⠦⣀⡀⠀⡈⠀⠈⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠻⢿⣬⣀⢘⣤⡿⠟⠀⠀⠀⢉⣩⠏⠉⠥⠀⢠⠈⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⡂
⠀⠀⠀⠀⠼⠟⢛⣛⣋⣛⣀⣠⣤⡀⢰⠉⡡⢼⠁⠛⠀⠷⠠⠚⡆⠀⠀⠀⠀⠢⣤⣄⣀⣀⣤⡄⠁⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠀⠀⠀⠈⠉⠁
⠀⠰⢾⡿⠛⠛⠿⠿⠛⠉⠀⠉⠋⠀⠀⠀⣷⠀⠀⠛⠈⠀⣾⠀⠀⠀⠀⠀⢦⠰⣾⣿⣫⣳⣿⣄⠀⠀⠀⣾⣄⣼⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⣶⡄⢀⠀⢶⣷⢀⡀⠀⠀⢸⡧⠀⣷⡿⣾⡄⣿⡆⠀⠀⠀⠀⡖⠀⣿⣿⣿⣿⣿⣄⠂⠀⢸⣽⣿⣻⡇⠀⠀⠀⠀⠀⠀⣴⡆⠀⣠⣄⠀⢀
⠀⠀⠅⢲⣌⣉⣁⡛⢁⣤⣤⣾⠃⠀⠀⠀⠁⣴⣿⠄⢿⣧⡙⠀⠀⠀⠀⠀⡇⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⣹⣿⣽⡏⠀⠀⠀⠠⠀⣷⣬⣀⣃⣉⣩⡄
⠀⠀⠀⠀⠙⠋⠙⠿⠛⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠾⠖⠀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⡈⠛⠛⠛⠛⠋⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⡀⠀⢀⡜⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠓⠌⣲⠿⠀⢀⠄⠀⠀⠀⠈⠣⡀⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣆⠞⢀⡼⠁⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡄⣀⣸⠿⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠙⡶⠋⠀⣠⣟⣡⣀⣀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⠉⠃⢀⣀⣀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡄⠀⢄⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⢀⣴⠟⠁⣼⡇⠀⠀⠀⣼⠇⠀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣠⣾⢀⣠⠄⠀⢀⣀⣌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠃⠀⣰⣿⢁⣤⣤⣼⣿⣤⠀⡩⣀⣀⠀⣠⡀⢀⣤⡄⣸⡿⠁⣤⠀⣘⢻⡉⣰⡏⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⣀⣤⣿⢳⡿⢃⣼⣿⣿⡏⡰⣿⡟⡹⢣⣿⡴⢫⡿⢁⡿⠁⣼⠏⣰⡏⣸⣿⠏⣾⢋⡼⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⡏⠁⣼⣿⢾⣣⠏⢸⡏⢿⣣⠁⢿⣉⡔⠹⡿⠁⢿⣁⡼⣇⡴⣯⠜⢿⡼⣿⠏⡸⡏⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠘⠇⠀⢿⡟⠀⠁⠀⠀⠀⠀⣁⠀⣀⠀⣀⢀⣀⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⡯⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣿⢢⣿⠸⣧⣼⣿⡇⠈⣧⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠋⠀⠀⠐⠶⠶⣤⣴⣶⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⣩⡅⠀⠀⡀⠘⡿⣡⡄⠀⣶⡀⠐⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⠿⣁⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⣀⠀⠈⣿⢀⣆⠀⢠⡤⠀⠛⠃⠘⠛⠀⣶⡄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠻⠟⠁⢠⣾⣿⣿⣯⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠘⠿⣾⠏⢠⣿⠇⣸⠃⠀⢶⡿⢰⡟⠀⠀⠀⠀⠹⡛⠀⣿⣿⠀⠀⠀⠀⠀⠠⣍⡻⢿⣷⣶⣶⡄⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣷⡆⠀⠀⣤⡄⠀⠈⠙⢠⣿⡄⠀⠘⡇⠛⠋⣰⣆⠀⠠⣾⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣶⣍⡛⠿⢃⣾⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⢿⣿⡟⠀⣶⣦⠘⠋⠀⠺⣷⠆⠀⠀⠈⠿⠃⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⣶⣬⣍⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠈⠉⠁⠀⠙⠿⠟⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠙⠿⠿⠛⠁
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠀⠀⠀⠀⢀⡉⠁⢦⣤⣄⣀⠀⢀⣤⣤⡄
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣠⣴⡿⠃⠀⠘⠛⣡⣿⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠧⠀⠀⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠊⠀⠚⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⣴⣦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠸⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢀⠀⠀⠀⢰⠀⠦⡀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠁⢸⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⢼⣿⣿⣄⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⢿⣿⣿⣿
⣶⣄⣸⣿⣿⣇⠀⠀⠛⠙⠟⠓⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⠠⣾
⣿⣿⠘⣿⣿⣿⣿⠶⣿⣇⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠗⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⣼⣿⣿⣧⠉
⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠐⡀⠀⢀⡏⠈⢉⣁
⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⢼⣧⠀⠀⠀⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⠿⢿⡿⢀⣼⣿⡄⠀⠄⠀⣾⣿⣿
⣿⣿⣷⡙⠿⠿⣿⣿⣿⣿⠋⠉⢰⣯⡄⠨⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠘⢿⣿⣧⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠈⠛⠁⠀⠀⠈⣿⣵⣦⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⠋⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠄⠛⠛⠀⠀⠀⠛⠻⣿
⡿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⣴⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⢀⣀⠀⠀⠀⠀⠀⠘
⠃⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⣿⣿⣷⣦⡀⠀⣴⣦
⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠘⠿⠃⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⢾⣿⣿
⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠈⠿⠃⠀⣤⡄⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣿⣿⣿⣤⣦⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀⣀⠀⠛⠁⠰⣿⠇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠿⢛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⢀⢸⡇⠀⠆⠃⡄⠀⢀⠀⠀⠀⣄⠀⢠⢁⣊⠴⣫⠊⠀⠀⠀⠀⠀⠔⢠⠔⢠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⡁⠀⠰⢠⠃⠀⠈⠀⠈⢠⠏⢀⢀⡞⢁⡔⠁⠀⠀⠀⠀⠀⣀⠖⠁⠊⠀⢀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⠌⣇⠀⠀⡄⠀⠀⠘⠌⠠⢋⡰⢁⠊⠰⠋⠀⠀⠀⠂⠀⣠⡴⠋⡈⠀⠠⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠇⠀⢀⡄⠐⠉⢰⣶⣤⡁⠘⠑⠉⠀⢀⡄⠀⠀⠀⢀⡴⠁⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢿⢚⡄⢠⣶⣿⣾⣿⣿⡇⠀⠀⢀⠄⠋⠀⠀⢀⠔⠁⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠸⡆⠀⠀⠚⣩⣥⣿⣿⣿⣿⣿⡟⠁⠀⢀⢀⡤⠀⢀⡴⢃⣠⠒⡁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢣⡀⠘⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣦⡦⠎⢀⠴⠛⠊⠁⠀⠀⠀⠈⠂⠀⠈⡍⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠹⡀⢼⣤⡻⣿⣿⣿⣿⣿⣷⢿⣶⡗⢋⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡵⡼⡀⠙⢣⣿⣿⣿⣿⣿⣿⣼⣿⡟⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠘⠛⣵⠄⣸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠔⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠆⡴⢡⣾⣿⣧⣿⣿⣿⣿⣿⣿⣧⠀⠡⢄⣝⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣿⡿⣿⣿⣿⡟⢫⡶⠻⡶⠶⡿⣶⢇⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢿⣿⣿⢿⣿⣿⣿⣧⢸⣷⡾⢿⡂⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⣿⣹⣯⡿⣹⢾⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡀⢹⣿⢿⣿⣿⣿⣿⡆⢓⣮⣤⡲⢎⣹⠤⢀⠤⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⢻⡞⣹⣿⣿⣿⣿⣿⣷⠈⠒⣶⢲⡞⠁⠈⠀⠀⢴⠫⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⠷⣀⠘⠈⠃⣠⣬⣵⡀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⣿⣿⣿⡵⠋⠉⠉⠂⠐⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡌⣿⣿⣷⡆⢹⢀⣀⣀⠀⡸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⣿⣿⣇⢻⣿⣿⣷⣬⠠⡀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡇⠀⠀⢀⣿⣿⣿⢸⣿⣿⣿⣿⡁⠀⠄⠀⠀⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⣴⣶⠎⢉⣿⣿⠈⣿⣿⣽⣿⡇⠀⢀⠢⠀⠀⠀⠀⠹⣧⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⣿⣿⡇⠀⢸⣿⣿⢼⣿⣿⣿⣿⣿⢠⡆⠀⡘⠤⣀⠀⠀⢿⣧⠜⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡿⠤⠊⢿⣿⣿⡀⢸⣿⡿⣼⣿⣿⣿⣿⣿⣾⡇⠀⢦⠴⣽⠀⠐⡆⣟⠄⢀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⣚⣷⣾⣿⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⢀⡟⠀⡈⠰⣶⣴⣿⣿⡏⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈⢸⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣷⡟⠸⢁⡇⠀⢸⣿⣿⡟⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⡿⣶⣿⡿⣻⣿⣿⣿⣧⢻⡟⣿⡟⣿⣿⡟⢸⡀⢺⠁⣤⣾⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠃⠀⢨⠁⠐⣏⠉⠛⠻⠙⢧⡻⠙⠓⠹⣟⠷⣦⠁⡟⠀⠹⡈⠉⠁⠙⠲⣴⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⠇⠀⠀⠀⠀⠀⢧⠀⠳⠀⠀⠐⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⠈⡉⢣⡿⣽⢤⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢀⠀⠍⢈⡑⣆⡀⠀⣠⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣬⡙⠛⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢶⠆
⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠
⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠶⠆⡀⠰⠆⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠥⠦⠶⠁⠀⠀⠀⠹⠛⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠀⠀⣤⣤⣤⡤⠀⠀⠀⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⣆⣸⣵⡎⠁⡀⠀⠀⠀⠀⣰⣿⣿⣿⣶⠀⠆⢻⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠸⣿⣿⣿⡿
⠀⠀⠀⢰⠋⣾⠎⣄⡕⠄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣴⡾⠉⠁⠀⠀⠀⠀⠀⣠⠄⢀⣷⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠻⠶⣿⣿⣿⡇
⠀⠀⣠⣟⣹⠟⢺⡟⠛⠀⠀⠀⠀⠘⠛⠛⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣡⡈⡇⠀⠀⠀⠀⠞⠳⠀⡇
⠀⠀⣿⡟⠁⠀⣠⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⢰⡄⣄⣾⡧⠆⢸⡟⠿⠀⠀⠀⠀⠀⢀⡀⣽⡄
⠀⠀⢹⣧⣠⡾⡟⠋⣸⠀⠀⠀⠀⢠⡆⢸⡆⠀⠀⢸⡇⣧⢠⡇⢸⡷⠙⠛⠿⠃⠈⠁⠀⠀⠀⠁⠈⠈⠉⠁⠙⠋⠉⠉⠁⠀⠄
⠀⠀⠀⣿⠁⢀⡷⠚⠉⠀⠀⠀⠀⢸⣧⢾⡇⣾⣿⣼⣇⡿⠚⠓⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠒⠚⠃⠀⠀⠀⣤⡄
⠀⠀⠀⣿⣧⡞⠀⠀⠀⢀⡀⠀⠀⢸⡇⢸⡷⠏⠛⠘⠋⠁⠀⠀⠀⡀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡇
⠀⠀⢀⣿⡏⠀⠀⠀⠀⠛⠋⠀⠀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⣦⠀⣴⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈⠀⠀⣸⣇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⢒⣀⣸⠀⠀⠀⠀⠃⠀⠀⠛⠀⠈⠁⠀⠀⣹⣿⡄
⠀⠐⠛⠛⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠘⠛⠛⠋⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣿⣻
⠀⠀⠀⠀⣠⣤⣤⣤⣦⣤⣤⣀⠀⡀⠀⠀⠀⠰⣶⢆⡰⣿⠦⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠄⠠⠀⠀⠀⠻⠃
⠀⠀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣧⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠡⠤⠴⠤⣟⢲⣄
⠀⠀⠘⣿⣿⣿⣿⡿⢿⣿⢿⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠠⠀⠐⠈⠻⡏⠉⡇
⠀⠀⠀⠈⣿⣼⠏⠰⠞⠁⠀⠀⢹⡇⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠓⠤⡄⠀⠈⢹⠛⠛⢦⡀
⠀⠀⠀⠀⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣼⣷⡀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣀⣠⣀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⡆⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠻⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢽⣿⣿⣿⣿⣟⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠙⠋⢻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠉⠉⠻⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⢰⠄⠰⣓⠂⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡆⠘⣯⠅⠀⠀⠘⠁⠙⠚⠁⠀⠀⢯⣀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡈⠋⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠸⣤⠞⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⡀⠙⠋⠀⢀⡴⣾⠟⠒⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠠⠀⠀⠀⠴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠁⢀⡀⠀⣾⠸⡇⠀⠀⢀⠀⠀⠀⠀⠐⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠀⠀⠀⠁⠀⠘⢦⣉⣒⡶⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⢀⣦⡀⠁⠀⠀⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣆⡆⠀⠀⣼⡤⠀⠁⠀⠀⠀⠀⠀⠤⠀⣰⢿⣦⠀⠀⣀⡀⠀⠀⠀⠈⠟⠁⠀⠰⠂⠀⠉⣻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡈⠀⢀⠀⠘⠀⣠⣿⣄⠀⠂⠀⠀⠀⢰⠇⢹⡘⣇⠘⠃⢹⠀⠀⠉⠀⢠⣄⠀⠀⠀⠀⠈⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⡀⠀⢀⡼⠃⣼⠸⡆⠰⠆⠀⣰⠋⢀⡞⠀⠈⢁⡴⠋⠀⠆⠀⡴⠻⡏⢷⠀⠀⠀⠀⠓⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢹⡆⠀⢁⡴⠋⠀⢰⡇⠀⢹⣄⣠⠞⠁⠀⣾⣁⡠⢀⡞⣠⠶⡄⢠⠾⣇⢀⡟⠈⠳⣄⠛⠀⢘⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠄⠀⠈⢀⡄⠀⠈⢳⣴⠋⠈⠻⡄⠀⠈⠋⠉⠀⠸⡇⢻⡀⠡⡀⠀⠙⣾⠁⠀⣤⠈⠃⠀⢨⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠄⠀⢀⠾⡿⣆⠀⠀⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠹⣄⢳⡀⠙⠀⠀⠀⠀⡴⣿⢧⠀⠀⠛⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⢦⠀⠀⢠⣷⡀⠀⠀⢀⣤⣀⣀⣀⣀⡀⠹⢸⠇⢀⣿⡀⠀⢀⡴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⣠⢞⣟⢦⡀⠐⢫⣯⡓⠀⢀⡾⡴⠀⠀⢠⢠⣿⣆⠋⠀⢋⣿⡙⠀⢀⡾⣿⠳⡄⠰⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠀⡴⢛⣟⠢⡀⠐⣫⣯⡛⢀⣞⡁⠙⠓⠒⠋⡼⣻⣘⣦⠐⢫⣿⣝⠂⢠⠞⣿⡳⡄⠘⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡴⢛⣟⠳⡄⠜⣩⣯⡙⠆⢉⣉⣙⠛⠒⠞⠛⢋⣉⡀⠰⣫⣿⣝⠆⡠⢞⣿⡛⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣏⠳⢦⢚⣵⣷⣍⠂⠰⠆⣄⠰⠶⠶⠀⣀⠰⠆⠘⣡⣿⣌⠃⡴⢋⣿⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠑⠀⢋⣴⣷⣌⠓⠈⣼⣿⣄⢉⡉⣴⣿⣆⠁⢚⣡⣿⣮⡓⠀⠋⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⡷⣌⠓⢈⡴⡿⣆⠐⢀⡴⣿⢦⠀⠋⡴⣿⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠾⡿⢮⠀⠈⡼⡿⠦⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⣄
⠀⠀⢈⡁⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡄⢠⣾⣇⠀⠀⠀⠀⠀⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⣿⣿⣷⡀⠀⠀⣸⣿
⠀⠀⠀⠀⢠⣸⠡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠛⠄⠀⠀⢀⠀⣝⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⢀⣾⡿⠃
⠀⠀⠀⠀⠘⠻⡇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠘⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡜⣿⣴⣤⣤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⣧⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣆⣸⠵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣵⡏⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⣤⣤⣶⣿⣿⣿⠿⠟⠁⠀⢀⠀⣀
⠀⠀⠀⣀⣼⡆⣷⠀⣿⠀⢀⡀⠐⠄⠀⠀⢼⣿⣿⣄⠀⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠘⠛⠛⠉⠉⠉⠀⠀⠀⠰⣦⣘⣄⠙
⠀⠀⠲⣿⣿⡇⢧⣇⡿⠸⠈⠁⠀⠀⠀⢀⣼⣿⣿⣯⢸⣿⣿⣿⣧⡀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣤⣶⣷⡆⠀⢠⡀⠆⠠⡤⠀⠀⠉⠋⠁
⠀⠀⠀⣀⠉⢳⣌⣿⠧⠖⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⢸⣿⣿⣿⡿⣃⡀⠀⠈⠁⠙⠃⠀⠀⠸⠿⠿⠿⠁⠀⠘⢷⡾⠆⠀⠀⠀⣠⣶⣄⢀
⠀⠀⠀⠩⠤⠈⣏⡏⣠⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⡿⠘⢿⣿⣿⡇⠉⠛⠿⠟⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠙⠛⠛⠿⣷⣶
⠀⠀⠀⠲⣶⢶⡌⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠸⡿⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠈⠳⡁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠛⠂⠀⠀⠠⣄⠀⡆⢸⠀⡗⢰⠃⡴⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡶⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⢀⣈⠲⡌⠃⠀⣠⡿⢿⠟⢦⡀⠈⠠⠞⠁⠀⢼⣦⡀
⠀⢤⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⠀⠀⠀⣀⣴⣄⠀⠀⠀⠀⢰⣟⣿⡀⠀⠀⢿⣧⣀⣠⣾⠇⠀⡀⠏⠉⠁⠈⠉⠁⢀⣷⡖
⠀⠐⠈⠁⢣⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⡛⣰⠂⣤⣼⣯⣿⢿⣷⡀⠀⠀⠀⠉⠁⠁⠂⠠⠈⠛⠛⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻
⠀⠀⠀⠀⡄⢰⢞⠉⠐⠶⣾⣶⣍⠃⠀⠀⠀⠀⢙⣴⣯⣼⢿⣿⣋⠟⣻⣿⡄⠀⠀⠀⢠⠀⠀⣤⢰⣆⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠴⡄⣣⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⣾⣿⡾⠿⠿⠛⠋⠁⠈⠉⠁⣴⡄⠀⣄⣠⠴⠖⠀⠭⠀⢀⠀⠀⠀⠺⠻⣦⠀⠀⢀⣀⠄
⠀⠀⢈⠓⠁⠁⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠠⡿⠛⠁⠀⠀⠀⠀⠀⠻⡿⠀⠉⠁⠚⠛⠁⠀⠀⣺⣶⣇⠈⠀⠀⠀⠀⠀⠘⣧⠜⠉⠁
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⣜⡓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⡶⢶⣶⡶⢦⡀⠀⠀⠀⠈⠁⠾⢿
⠀⠀⢀⡀⢀⣰⢯⡿⣹⣼⡆⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⡀⠀⠸⠶⠟⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠠⠀⠀⠀⠀⣤⣴⢶⣿⠿⠷
⠀⠀⠠⠄⢢⡟⠈⠉⠉⠳⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣷⣶⣤⡀⠰⠀⠀⠀⠀⠀⣿⡛⠛⠁⢠⣾⠷⣶⣦⠀⠀⠀⠘⠈⢸⣿⠶⠖
⠀⠀⠀⠀⠀⠉⠀⠀⠂⠈⠁⣀⢛⠀⠀⠀⠀⠀⠷⠀⠈⠙⢿⡷⠀⠂⠀⠀⠀⢀⣰⠿⠟⠃⠀⣻⣿⠀⢸⡏⠀⠀⠀⠀⠀⠸⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⣆⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⢰⣯⣹⡗⠀⠀⢰⣟⣿⠷⠟⠃⠀⠀⠀⠀⢸⣻⡇
⠀⠀⠀⠀⠀⢰⣏⡶⠂⠀⠀⠀⠀⠀⠀⠘⣿⣧⣸⣤⣿⢀⠳⠀⠖⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⠁⠀⠀⠀⢸⣏⣷
⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⡿⢋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢿⠁⠀⢀⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠶⠀⠀⡞⠠⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠉⠐⢮⣁⣼⣧⣀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⢀⠀⢀⡀⠹⣯⡙⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣸⣿⣿⣿⡉⠀⠉⠀⠀⣾⣷⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄⠀⢻⡆⠀⣴⣿⣿⢿⣿⣷⣀⠄⠀⠀⢸⣿⣿⣿⣿⡆⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡦⠞⠀⣸⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠈⢿⣿⣿⡿⣿⣄⠋⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠀⢠⣿⣿⣿⡿⠛⠉⠈⠀⠁⠀⠀⠀⠀⠉⠙⢿⣮⡛⠃⠀⢿⣤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣾⣿⣿⣿⣿⠀⠀⠲⣶⣠⣀⣀⣠⣤⣦⣁⠈⢿⣿⣦⠀⢿⣿⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢿⣿⣿⠟⠁⠀⠀⠀⠀⠘⡃⣸⡇⠀⠀⢹⡟⠿⣿⣿⠂⢿⣿⣿⣹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠘⣿⠁⠀⠀⣰⠀⠀⠀⢰⡇⢹⢰⠀⠀⠀⣧⠀⢻⡟⠀⢸⣿⣏⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠻⠀⠀⣴⣿⣴⠆⣀⣼⡇⠀⣿⣆⠀⠀⢹⠀⠘⠀⠀⣸⣿⣽⣿⣿⢟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠀⢀⣾⣿⣿⠏⣼⣿⡿⠃⠀⣿⣿⠀⣿⠘⣧⠀⠀⢀⣿⣿⣿⣿⡿⣈⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⣿⠃⣴⣿⣿⣿⡏⢰⣿⠟⠁⠀⢀⡟⣿⡇⢸⣇⠘⣷⣦⣾⣿⣿⣿⣿⣿⣼⣿⣷⡇⣤
⠀⠀⠀⠀⠀⠀⠠⣬⣿⣿⣿⡿⡋⣸⣽⣿⣿⡟⢠⠟⠁⠀⠀⢀⡾⠁⢹⣧⠘⣏⠛⢉⡴⠀⠉⠛⠛⠿⢿⣿⣿⣁⣾⣿⡇
⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⣠⣿⣿⣿⡏⣴⠋⠀⠀⠀⣠⠈⠀⠀⠀⠿⡆⢻⣰⢣⠀⠀⠀⠀⢀⠀⠀⠉⠻⣿⣿⣿⡟⢠⣀⡀
⠀⣿⣦⣤⣼⣿⣷⣿⣿⣿⣴⣿⣿⡏⣽⢏⠜⠁⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠀⣀⣤⡴⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⡿⣯⡿⠻⠕⢸⡿⢰⡟⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⢭⠴⠞⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷
⠀⣿⣿⣿⠏⢽⣴⠏⠀⠀⢀⣿⠇⠘⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⣿⡏⠠⢄⡈⡻⣦⣾⣆⠾⠉⠀⠀⢿⡄⢸⣆⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿
⠀⢿⡤⣤⣴⣿⣛⣮⣿⣿⡄⠀⠀⠀⢸⣿⡌⢿⣿⣴⡀⢿⣄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿
⠀⣇⣻⣶⣤⣤⣭⣝⣿⡿⢿⣆⠀⠀⢸⣿⣿⡜⣿⣦⣦⡈⢿⣅⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣉⣿⣿⣿
⠀⠉⢱⣬⣿⠿⠛⠋⠁⠶⣾⣿⣶⠀⠀⣿⠉⣿⣸⣿⣿⣿⣾⡻⣷⣔⢤⠛⢷⣄⠀⠴⢦⣤⣀⣀⠀⢦⣄⠀⠀⠀⣈⠸⡅⠻⣿⣿⣿
⠀⢠⣿⠟⠷⠿⠶⣦⠤⡤⣠⣾⣿⣦⠀⠉⢠⠘⣿⠉⠟⢿⣯⠑⢘⣿⣿⣷⣠⣙⠻⣷⣶⡤⣤⣉⠉⡛⠻⠷⣦⣠⣇⠀⠁⢺⣮⡻⣿
⠀⣴⠟⠀⠀⠀⠊⣤⠀⠀⠈⠀⠙⣿⣧⡀⠈⢄⣸⡦⠌⠰⣤⡖⠉⠴⠛⠉⠁⠈⠑⠀⠉⠃⠈⠉⠀⠈⠀⠀⠀⣠⡴⠞⠻⣿⣿⣿⠎
⠀⣿⣶⣤⡀⠀⠀⣯⠀⠀⠀⠀⠀⢸⢿⣷⣤⣀⣹⢸⣆⣴⠇⠙⠶⠂⣄⣠⣤⠀⠠⢀⡀⠀⠀⣀⣀⠀⢤⡞⠙⠁⠀⠀⠀⠈⠢⠐⠛
⠀⠿⠻⣿⣷⣄⠀⢿⡄⠀⠀⠀⠀⠀⠾⣏⡉⣍⠝⢾⣿⣦⣄⣠⣴⣶⣿⠟⠁⠀⣴⠀⣅⣠⣿⣥⣤⣤⣽⣿⣂⡀⠀⠀⠰⣂⡴⣄⠐
⠀⠀⠀⢻⣿⣿⣅⠘⣿⣄⠀⠀⠀⠀⠀⠘⢿⡄⠦⡄⢛⢀⣿⠋⠉⢹⣿⠀⠀⢰⡟⠀⣇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠻⠿⣭⡿⠟
⠀⠀⠀⠈⢿⣿⣿⣆⢻⡙⣦⠀⠀⠀⠀⠀⢸⠇⢆⣿⢀⣿⣿⡀⠀⢼⣿⡆⠀⣿⠁⠈⠉⠛⠲⠶⣶⣤⣤⣤⣤⣤⣤⣤⡴⠂⠉⠄⣁
⠀⡀⠁⣄⠼⣿⣽⡿⢷⣤⣈⠳⣄⠀⠐⢤⣐⣶⣸⣿⡿⠋⠠⣿⡆⢨⡤⠷⡀⢞⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⡞⠁⠀⠀⣠⣿
⠀⣁⠀⠙⠳⣞⣿⣿⠈⠙⢿⣶⣌⡳⢄⡀⠀⣽⠇⢻⣱⣦⣶⠶⢁⠛⠀⠀⡇⢸⠀⠀⠙⢿⡷⠒⠠⢤⣤⡤⢤⣤⠬⣅⣤⣴⡟⠿⠿
⠀⠀⠣⠴⠀⢬⠙⣯⣦⡀⠀⠉⠉⠻⠦⠙⢲⡏⣠⠟⠁⠀⠀⢠⡀⣠⠀⠀⠁⣸⣄⣀⣀⣠⡹⣆⠀⠀⠀⠀⠸⠃⠀⠀⠙⠟⠁⢀⣴
⠀⠀⠁⠀⠀⠉⣝⣤⡹⠟⠷⠦⣤⣤⣤⢤⣼⠟⣯⠙⠷⠶⣦⠼⠃⠉⠀⠰⠚⠋⠩⠭⣉⡉⣁⣸⣷⣶⡄⠀⡀⠀⠀⢀⣀⣤⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠘⢧⣝⠦⠑⠀⠐⠋⠙⠇⠀⠃⠀⠙⠶⣷⣭⣤⣤⡠⢴⣤⣤⣀⡀⠀⠀⠀⠉⠉⠙⠋⠑⠊⣀⣤⣶⣿⣿⡿⢿⡟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠠⠄⠈⠀⠀⠀⠀⠄⠀⠀⠀⠈⠻⢷⠀⡁⠀⠀⠀⠉⠙⠛⠻⠿⠳⠞⠾⠛⠿⠿⠿⠛⠡⠈⠀⠁⠈⠉⠿
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠒⠂⠀⠀⠀⠚⠛⠒⠀⠀⠀⠀⠀⠀⠐⠑⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣐⣦⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣾⣾⣿⡏⠉⣿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣿⣿⣷⠀⣀⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣿⣦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣤⡄⠀⠀⠀⢠⣤⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡷⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣀⣶⣾⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⡷⠄⠀⠀⢤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⠉⠀⠉⣹⣷⣶⣀⣤⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⢀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⡁⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠛⣣⣼⣦⣤⣼⣿⣿⣿⣏⠁⠀⠉⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣆⣀⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠲⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠣⠤⣄⠀⣀⣴⢛⣛⠻⣯⡀⢀⠴⣲⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣀⠈⠷⠁⠀⡬⢉⡁⠀⠉⠁⣾⣿⣿⣿⣿⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠈⠛⠿⣿⠟⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣆⠀⠘⠒⡂⠀⠀⠀⠀⢀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠘⣇⠀⠀⠙⠢⠤⣤⠶⡏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠐⡦⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢧⣄⡀⠀⢀⣀⣀⣀⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⢄⣉⣉⡏⣋⣉⡠⠤⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠠⠞⠓⡿⡏⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠀⠀⠀⠰⡀⣀⡷⠟⠀⠀⠀⠀⠹⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣰⠇⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⢳⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡈⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢻⠹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣼⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠢⠤⣀⠀⠀⢹⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿
⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡠⠤⠤⢤⣀⣈⠇⠀⠘⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢹
⠀⠀⠀⠀⠀⠀⣰⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⣰⠓⠢⣄⠀⣿⡄⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣧⠖⠉⠉⡆
⠀⠀⠀⠀⠀⠀⣇⠀⢣⠀⠀⠀⠀⠀⡟⠀⠀⠈⠓⢿⣿⡄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⣸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠑⢄⠀⠀⠀⡆⠀⠀⠀⡀⠸⡏⠙⢦⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⡇⠀⢀⡏⡠⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠙⠲⢴⡇⠀⠀⠀⠘⢆⣸⠀⠈⠳⡄⠀⠀⢷⠀⠀⠀⠀⢸⠇⠀⣸⠞⠁⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣼⡇⠀⠀⠀⠀⠈⢿⡀⠀⠀⠙⢆⠀⠀⢣⡀⠀⠀⣼⠀⢠⠏⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⠳⡀⠀⢳⡀⢰⠇⠀⣼⠀⠀⠀⠀⣠⠞⠁⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠙⣆⠀⣱⢿⡀⠀⢇⠀⢀⣠⡚⠥⠔⠫⠌⠍⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣳⣤⣄⣀⠀⠘⢦⡀⠀⠀⣸⠀⠘⢦⣹⠀⠈⡳⠾⢤⠤⣄⣄⠀⠈⠲⡌⢂⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⣁⠎⢁⠖⠚⠙⠉⠛⢲⠟⡏⢩⠋⡹⠓⢤⡟⡠⠚⠳⢄⠈⢣⠈⣦⠷⠤⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠤⠾⣤⡤⠤⠔⠒⠋⠳⣧⡎⠠⡇⠀⠸⣇⡀⠀⠀⢨⣇⣈⡧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠉⠓⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⣶⣆⠀⡄
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣏⢠⡄⢄⣸⣧⣶⣿⣿⣿⣿⣶⣄⠀⣀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠉⠀⢈⣿⣿⣿⣿⣿⣿⣿⠿⣿⡆⡰⠂⠀⣀⡀
⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡄⢘⣿⣿⣿⣿⣿⣿⣿⡝⣿⠿⠃⠁⠀⠀⠈
⠀⢰⣿⣿⡏⣽⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡀⠒⠀⠀⠀⠀⠀⢀⣀⡀⠀⣸⣦⡀
⠀⣺⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣷⡄⠀⠀⢠⣿⣿⡇⠀⠛⠉
⠀⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡿⠟⠿⢓⠀⠀⣿⣿⣿⡁⠀⠀⠀⠀⠀⣑
⠀⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⡓⢴⣿⡌⠀⣶⣾⣿⣿⣿⠀⠀⠀⠀⠘⢻
⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣟⣁⡀⠿⣿⣿⣿⡏⠀⠀⠀⠀⣴⣾
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣟⣿⣷⣾⣴⣿⣿⣧⣤⣴⣶⣤⡄
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣋⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠧⣀⡀⠀⠀⠀⠀⠰⣍⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢠⠀⠙⣤⣤⡾⠧⣴⣡⡌⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠛⠄⠀⠁⢀⡄⢡⠀⡘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠘⠁⠌⠈⣁⡽⠦⢒⡶⢖⣒⣒⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠠⠌⠋⠀⠀⠀⠀⠀⠛⢾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠀⠙⣿⠿⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣤⣾⣿⣿⣆⠀⠀⠀⠀⠀⣠⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣾⣿⣿⣿⡿⡿⡀⠀⢀⣠⠜⢇⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡄⠀⢠⠿⢿⣿⣿⣿⢹⠀⠉⠉⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⡎⠀⠘⠻⣿⣿⠼⠦⡀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢇⠀⠣⠤⠴⠚⠉⠐⠶⣖⠁
⠀⠀⠠⠃⣸⠀⠀⠀⠀⠀⢀⡠⣀⣶⠟⠉⠁⣀⣤⣶⣿⣿⣦⣤⣀⣀⣠⣾⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠗⠄
⠀⠀⠆⢠⡏⠀⠀⠀⢀⡴⢋⡾⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⡂⠳⡀⠀⠀⠙⠶⠤⠤⠴⠚⣧⡀
⠀⠀⠀⠤⠀⠀⠀⣠⠎⠀⣾⠀⠀⠀⠀⠸⠿⡿⠿⠛⠉⠀⠀⠀⠀⣀⢄⣹⣀⢹⠶⠦⣀⣀⠀⠀⣀⡠⠗⡇
⠀⠀⠀⡀⠀⢀⡴⠋⢠⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣷⡿⣹⠦⢀⡀⠀⠉⠉⠁⠉⣀⣤⡇
⠀⠸⡀⠈⠂⠉⢀⠴⠋⢘⠇⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠊⠁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠻⣦⡀
⠀⠀⠈⠐⠒⠊⠁⠀⣰⠃⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢻⣻⣦
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠑⢄⠀⢠⡞⠁⠀⢀⠙⢦⡀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠿⠟⠃⠀⠀⠀⢸⣢⠏⠀⠀⠀⣸⢧⡀⠙⠦⣄⠀⠀⢰⡇⠉⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢰⡦⢀⠔⠒⣚⡋⠀⠀⠀⠀⢇⠘⣅⠀⠀⠈⠙⠢⣾⠁⠐⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠷⣾⡄⠈⠁⡞⢰⠁⠀⡴⠃⢀⠐⠀⠈⢳⡀⠙⢦⡀⠀⠀⠀⠙⢦⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⣴⠟⠛⣦⠀⠀⡇⠀⠀⢳⣼⠀⢰⡀⠀⢢⡀⠀⠀⣸⠇⠀⢀⣽⣆⠀⠀⠀⠀⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⢀⣴⠋⠀⠀⠀⢸⡇⠀⠳⣄⠀⠀⠙⢄⣈⣧⡀⢀⣷⣶⣖⣩⣤⡾⠛⢁⡼⢧⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡠⠜⠁⠀⠀⠈⠳⣤⡀⠀⠀⠘⢯⠉⠁⠉⠉⠁⠀⠙⠒⠋⠁⠀⠙⠲⠶⠤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠊⢀⠀⠀⣀⠀⢈⣿⣦⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣧⠈⠳⣤⣀⡽⠋⠁⠈⠻⣦⠀⠀⠹⣆⠀⠀⠀⢠⡾⠋⣡⠾⠓⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⢧⠀⠀⣍⡄⠐⠁⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢷⡀⠈⢻⠇⠀⠐⠉⠀⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠻⣴⡏⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢣⡀⠈⠁⠀⢀⡤⠶⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⢿⣿⣿⣿⣿⡿⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡎⢨⠸⣿⣿⣿⣏⢸⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣧⡀⠑⡌⠛⣋⡅⠚⢿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⢿⣿⠀⠛⠘⠋⠀⠀⠀⠉⠁⠛⠛⠛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢲⡉⠀⠀⠀⠀⠿⠂⠀⠗⠛⢈⣴⣿⣿⣿⣶⡌⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠃⢴⡄⠀⠀⠀⠀⠀⠈⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡆⠀⠀⠀⡆⠀⠈⢷⣄⣀⣀⣀⠀⠞⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⠀⠀⠐⣰⠂⠀⠈⠻⣿⣿⣏⠈⠢⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠀⠀⠈⠄⠀⠀⠀⠈⠛⠋⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣆⠀⠀⠈⠓⠄⣀⠀⠁⠀⣈⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡲⡙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⡀⠑⠂⠄⢀⣀⣀⣀⠠⠶⠶⣧⢹⡌⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠞⠑⠢⠄⣀⡀⠀⠀⠀⢀⣀⣠⠾⠯⣙⢦⡹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⣿⣀⠀⡿⠀⢷⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣡⠄⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⢸⡀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⢹⡘⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢹⡀⠀⢸⡇⣿⣿⣿⣿⣿⡿⡡⢿⡿⠃⠀⠀⣴⣿⣿⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⣼⠁⠀⢸⡇⣿⣿⣿⣿⡟⡰⠁⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡼⡆⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣰⠇⠀⢀⡾⣰⣿⣿⣿⡟⠰⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡞⢰⠃⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢠⠏⠀⠀⡾⢡⣿⣿⣿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡴⠋⢀⡟⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢁⡟⠀⠀⣼⢡⣿⣿⣿⣿⡇⣸⣧⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣾⠀⢀⡴⠋⠀⢠⠟⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⣼⠀⠀⣰⢇⣿⣿⣿⣿⣿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⡏⣰⠏⠀⠀⢠⠏⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢠⠇⠀⠀⡟⢸⡿⢛⡩⢭⡉⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢘⣵⡟⠀⠀⢀⡿⢌⡻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠸⡇⠀⠘⣇⠛⢰⠋⠀⠀⢳⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣿⢫⡇⠀⠀⡾⠀⠈⡃⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⢳⡀⠀⠙⢦⡟⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣧⣾⠃⠀⣼⠁⢀⡜⣡⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⠹⣄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⣿⡟⠀⢰⠇⠀⢨⢡⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡌⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠃⠀⡿⠀⠔⠁⠋⣅⠒⢮⠹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡇⠀⢸⡏⠀⠀⠳⣾⣈⣤⣤⠶⣽⣄⠇⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠟⠃⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠲⠦⠤⠞⠀⠀⢀⣤⡀⠀⠀⠈⠁⢶⡄⠻⠀⢘⠀⣿⣿⣿
⣿⣿⡟⠡⢐⠞⡹⠛⢋⡻⠖⠽⠟⠒⠲⠶⠖⠀⠐⠰⢡⠞⣩⠥⠶⠀⠀⠀⠀⡟⢻⡇⠀⠀⠀⠀⣸⣇⠾⠞⣋⣼⣿⣿⣿
⣿⣿⡁⢧⣈⠰⠁⢠⡋⠀⠀⠀⠀⠀⢀⣀⠠⠔⠳⣆⣈⢠⠃⠀⠀⠀⠀⣀⡠⠏⣤⣬⣤⣤⣤⣬⣤⣤⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣉⠛⠛⠚⠃⠤⠤⠐⢒⣉⣥⣤⣶⣿⣶⣬⣙⠛⠷⠶⢒⣒⣩⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣰⣴⣬⣧⠀⠀⣠⣤⣀⡀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠒⠲⣾⠫⣴⣶⣿⡏⠐⠲⣞⢠⡫⠁⠙⢷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠌⢸⡿⠋⠉⠉⠀⠱⣸⣆⡁⠀⢈⠋⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠃⠀⣼⠿⠶⢀⢞⠁⡀⠀⠀⠀⢠⣿⣿⡇⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⢴⡞⠉⠁⠀⢋⠂⡸⠃⠀⠙⣦⠀⠀⠸⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠜⠀⣿⠇⡀⠀⠀⣸⣴⣥⠄⡠⢶⡻⡧⠀⢠⣴⠎
⠀⠀⠀⠀⠀⠀⣇⡘⠀⢰⣿⢋⣀⠀⣤⡿⣿⠁⠊⠀⠈⠉⠀⢦⡀⠷⠸⡀
⠀⠀⠀⠀⠀⠘⠿⠇⠀⣼⠟⠋⡀⠀⠈⠻⣾⣆⠀⠀⢰⡷⠁⠀⢷⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣤⣾⡄⠠⠀⡠⠂⠁⠀⢀⢸⣥⡀⠀⠈⠻⣄⠀⠀⠙⠳⣤⣀⡀⢄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠿⣿⣣⣾⡁⠀⠀⠀⣼⡿⠉⠻⢗⢦⣄⣀⠉⠒⠠⠤⢄⣉⠳⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠉⠉⠉⢹⣷⣭⡴⠊⠀⠀⢰⠋⠀⠈⣿⡄⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠽⣿⡸⣿⣄⣠⢶⣯⣤⡴⠤⢉⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⢡⠉⠻⢿⠘⠁⢉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡶⣞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡼⢇⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⡾⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⠀⠀⣀⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣶⡏⡏⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⡁⠀⣀⣀⡄⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⠛⠛⠋⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠛⠛⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠤⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣷⣦⠀⠀⠀⠀⣠⠞⠛⠳⢦⣤⠿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠿⠟⠋⠀⠀⠀⠀⠈⠳⠶⠞⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⣤⣤⣤⣤⣤⣤⡄⠀⠀⢀⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⡴⠶⢦⡀⠀⠀⠀⠀⣠⣴⣶⣤⣀⣀⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠳⢦⣤⡴⠋⠀⠀⠀⠀⠻⢿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⢂⣰⣆⡐⠂⡀⢧⣤⢤⡀⠀⢀⠄⠀⠀⠀⡀⠀⠀⣠⠤⠶⠤⣄⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄⠀⠀⠹⠑
⠀⠀⠀⠈⠀⠀⠁⠀⠰⠉⠈⠓⠃⠀⠈⠀⠀⠀⠀⠀⠀⡼⡵⠋⠉⠙⢮⣳⡐⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⡇⣿⣷⠀⠀⠀⢦⡀
⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⠶⠂⢠⠞⠛⣇⠀⠾⠄⢠⠛⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠚⠃⠀⢀⠀⠀⢀⣀⡀⠈⠁⠃⠀⠀⠀⠹⣄⣠⠞⠀⠀⠀⠸⣄⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠤⠀⠁⠀⠐⠋⠭⠙⠂⠀⠘⠃⠳⠑⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠰⠈⠁⢚⠁⠀⢠⣤⢠⣤⡀
⠀⠀⢀⡤⢤⡀⠀⡀⡠⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣆⣢⣦⣞⣢⠄⠀⠀⠀⣴⣲⡄⠀⠀⠈⠙⣠⠀⡌⠁⠀⠀⠁⠀⠁
⠀⠀⢸⠀⠁⡇⠨⠏⣇⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆
⠀⠀⠸⠀⠀⠿⠀⠀⠈⠁⠀⠀⣰⠀⠀⣾⣶⡏⣟⢸⣗⢾⡇⠀⣾⢵⣷⢾⡷⣾⡷⣶⠚⡞⠀⠀⠀⠀⠀⢠⠖⠲⡄⠀⣃⢑⡗
⠀⠀⢀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠤⠀⠀⠘⠦⠶⠁⠀⠉⡀
⠀⠀⠀⢀⡉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣬⡙⠀⠀⠀⢷⣷⣵⠇⠀⠀⠀⣿⠃⣧⠓⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⡀⡀⠀⠀⠘⡋⠀⠉⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠁⠛⠁⠀⣤⡄⠀⠀⠈⠈⠁⢤⡀⠀⠶⠶⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⣿⠟⠀⠘⣥⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⢷⠄⠀⢰⠀⠀⠀⠀⠐⠀⠀⢷⠸⣦⠾⠁
⠀⠀⠐⠆⠶⠍⠰⠝⠃⠰⠀⠀⣼⠀⠀⠰⠋⠀⢠⢦⠀⢀⡴⢦⡄⣠⠶⣦⠀⠀⠙⠖⠛⠀⠀⣄⡄⠀⠀⠀⠀⠀⢀⢸⡆
⠀⠀⠀⠈⠴⠀⠀⠀⠮⠀⠠⡄⡀⠀⠀⡄⡀⠀⢹⠿⠀⠘⠷⠾⠃⠻⠶⠞⠀⢸⠟⣀⢹⡃⢀⡸⡼⠂⠀⠀⠀⠀⠀⢠⡙⠦⢔
⠀⠀⠀⠛⣿⠛⠛⠛⣿⠋⠀⠒⠋⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠙⡼⠃⠀⠀⣤⠀⣤⡬⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⡀⠀⢠⡶⠉⠀⠀⡀⠀⠀⢾⡁⠤⠒⠀⠈⠀⠀⠀⢀⡄⠁⠀⠀⠀⠈⠀⠀⠀⡀⠀⡠⠖⠒⢠
⣴⠟⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢸⣵⣠⣦⢀⡀⠀⠀⠀⠀⠑⢄⠀⣀⠀⢀⢌⠅⢀⡀⠀⢰⡄⡀⠀⠀⠰⡀⠘⣁⣠⡴⣤⢣⡀
⣿⣆⡶⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠉⢿⣦⣄⡉⠀⠀⠀⠀⠀⠀⠀⢀⢫⣴⣛⢀⡶⣻⣦⣶⠞⠉⠀⠀⠀⠀⣰⣾⢿⣡⡼⢩⣿⣧
⠉⢷⣴⣶⠻⣀⡀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠔⢠⠀⢨⠏⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣹⢟⣿⣦⡬⡈⠁⠀⠀⠀⠀⠀⡜⢿⡿⠚⡻⠶⠁⠀⠈⠛⡄
⡾⣿⡿⢾⣷⣛⣳⡦⠀⠀⢿⡞⠠⠐⠚⠁⢸⣿⣷⣾⣤⣤⡖⡆⠀⠀⠀⠀⠀⠀⡰⠻⠉⠻⠉⣩⠼⠇⠀⠀⠀⠀⠀⣸⠇⢸⡷⢤⣤⠀⢸⣆⠀⡆⠐
⠇⡌⠈⠀⡄⣹⣏⡐⢨⡒⢄⠀⠀⠀⠀⠀⠈⢻⡽⠉⢿⠟⠁⠀⠀⠀⠀⠀⢀⡄⠂⠀⠀⠂⠒⠁⠀⠘⠀⠀⠀⠀⢠⡿⠀⡀⣿⣯⡈⢀⣰⣟⠀⢩
⢰⣷⣀⡴⡁⠘⣾⣷⡮⠥⠤⠀⠀⠀⠀⠐⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⠞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣹⣷⡄⢉⠿⠀⣉⣴
⠞⢋⣁⣾⠃⠀⡆⣏⠀⠀⠀⠀⠀⠀⠀⠒⢸⠗⠲⠀⠀⠀⠀⠡⠀⠀⢻⣏⣻⠉⡋⡙⠡⠖⠀⠀⣯⠀⠐⠒⠀⠀⣿⠁⠀⡄⣿⣇⣈⣷⠸⠀⠘⢃⠜
⠈⢏⢱⣿⠰⡀⢠⠘⠈⢄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠸⣴⠆⠠⢉⣉⠓⡙⣉⣱⡀⢀⡠⠒⠀⠀⠀⠀⠀⢸⠀⠀⡇⠡⡿⠟⢀⡀⣈⡦⣬⠈
⣄⠘⡸⢿⡀⢰⣞⠀⣜⡀⣱⡄⠀⠀⠠⢶⢤⡟⠣⠄⠠⠄⠀⠀⠀⠀⠀⠀⠈⠉⠟⠾⠋⣲⠉⢀⠀⣀⡀⢀⢀⡀⠈⡆⢹⣧⢀⣅⡰⣏⠀⢎⢠⣄
⣷⡀⢣⠸⣟⢸⣁⣾⣿⠻⠉⠀⢰⠣⠊⢛⣻⢛⣛⠛⠒⠀⠀⠀⢀⣀⣤⠄⠐⠲⣷⣶⠞⠾⡇⠁⠀⠀⠀⠀⠀⠀⠀⣇⠾⠋⢨⣹⡿⡇⠀⢰⠞⠀⠜
⣿⣧⠀⡀⢸⠈⢸⡇⡿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠙⡇⠀⢤⣍⠙⠀⠀⠀⠘⢳⣆⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡠⠋⡀⢶⣿⠉⢡⠃⢀⠇
⣿⣄⠣⠙⠻⣠⠘⡃⠁⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣈⠈⠻⠶⠀⠀⠀⠈⠟⠀⠀⠀⠈⠵⠁⠀⠀⠀⠐⡀⠣⠻⢾⣫⠃⡸⠀⡘⠀⠀⠁
⠘⣝⣳⣢⣴⡙⣾⢣⣄⡷⠐⠿⠇⠤⠀⠀⠀⣈⠭⠀⠀⢠⣦⡉⠉⠀⠂⠀⠰⠂⠀⠀⠀⡠⠁⠀⠀⠀⠀⠰⠀⠀⠙⡄⠀⠠⡀⢀⢃⠞
⠀⡼⣹⣿⢀⣨⠟⢂⡁⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠸⠙⠁⠐⠀⠀⢀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠄⠀⠈⢇⠸⣦⣹⣆
⡼⠷⠞⠋⠀⠘⠶⢟⢮⡐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⡠⠂⠀⠁⠀⢀⡀⠈⠈⠀⠀⠀⠀⢀⣤⠐⠀⠀⠀⡀⢠⠀⠀⠀⠣⡀⢋⠘⣧
⢀⠀⢀⢴⠀⠀⣴⡀⠣⡀⣄⠀⠀⠀⠐⠂⢀⠀⠀⠔⠀⠀⠈⢨⠁⠀⠂⠀⠀⠳⡲⠄⠀⠀⠀⠀⣠⡿⢤⣠⡀⠠⡰⠛⠤⠸⢀⠀⠀⠀⡽⠊⢏⡂
⢨⠀⢁⡄⠸⠻⣷⠳⣶⠙⣟⢳⣄⠈⠓⠀⠀⠀⠀⠀⡰⠠⠆⠀⠀⠀⣰⡖⠀⠀⠈⠞⠀⠀⣠⣾⢻⣿⣷⡐⣿⣧⡶⠋⠀⠀⠀⠀⠀⠀⣠⠖⠀⢠⢰
⡄⠀⠉⠃⠂⠀⠈⠳⡝⠳⣄⡙⢌⠳⣬⡐⣤⡘⢓⣾⠿⢗⡄⢀⡴⢊⡼⠁⠀⠠⢤⣄⡤⠊⠁⢠⠎⣿⠋⠉⠍⠁⠆⢁⣀⠀⣀⣀⠀⢀⡈⢤⢁⣴⣷
⣄⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠙⠢⣌⠀⠉⠓⠮⣍⡉⢩⣿⢟⠁⣠⠋⠀⢠⡇⢸⢈⣿⣇⠀⢀⠄⣸⣿⡀⢀⣦⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛
⣿⡗⠂⣠⡐⠀⣀⢤⣽⣿⣷⣦⡀⠈⠙⠶⣄⡀⢀⡉⢕⡚⣶⡽⠃⠀⠀⡀⣫⣿⡿⢿⣿⠏⠁⢠⣿⣿⡟⠋⣹⣿⠈⠼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⣸
⣿⣵⣶⢋⡵⣛⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⠛⠟⠷⠦⣼⣭⣽⣶⠶⢁⣌⡙⠳⢾⡃⠧⠍⠀⣠⡿⠿⡏⣰⣶⣿⡟⢳⣄⣿⣿⣿⣿⣿⣿⣿⢉⣁⣴⣿

⠀⠣⠤⢲⠀⠀⣀⠄⡀⠀⢰⠒⠤⠂⠀⠘⠤⠔⢦⠀⠀⡀⢄⠀⠀⡔⠢⠤⠁⠀⠱⠤⠒⡆⠀⢀⠠⡀⠀⠀⠖⠤⠜
⢀⣀⣀⣘⠀⠀⢣⢠⡃⠀⢨⣀⢀⢀⠀⣀⣀⣀⣄⠀⠈⡆⢰⠁⠀⣁⣀⣀⣀⢀⡀⣀⣀⡇⠀⢸⡀⡜⠀⢀⣃⢀⣀
⢸⠀⠀⡈⠀⠉⠁⠀⠉⠁⠈⡄⠀⢸⠁⢡⠀⠀⠃⠈⠉⠁⠈⠉⠁⠸⠀⠀⡞⠈⡇⠀⢰⠀⠈⠉⠀⠈⠉⠀⢁⠀⢠
⠉⠀⠀⠓⠒⠓⡄⠀⠐⠓⠒⠃⠀⠀⠁⠁⠀⠀⠓⠚⢲⠀⠀⡖⠓⠚⠀⠀⠈⠈⠀⠀⠘⠒⠒⡆⠀⢠⠚⠒⠚
⠲⠀⠀⠋⠉⠊⠀⠀⠈⠒⠉⡇⠀⢠⠒⢢⠀⠐⠋⠑⠋⠀⠀⠙⠊⢙⠀⠀⡔⠒⡄⠀⢸⠉⠒⠁⠀⠀⠑⠉⠑⠀⢀
⠸⠀⠤⠴⠄⠒⢦⢠⠖⠂⢠⠤⠄⡸⠆⠧⠀⠤⡧⠀⠒⡆⢰⠒⠀⠼⠤⠀⠵⠰⠇⠠⠬⡄⠐⢲⠄⡴⠒⠠⡦⠤
⠀⢀⣀⢸⠀⠀⢇⣀⠇⠀⢸⠀⣀⠀⠀⠀⣀⡀⢠⠀⠐⣅⡨⠀⠀⡆⢀⣀⠀⠀⠀⣀⠀⡇⠀⠸⣀⡼⠀⠀⡃⣀⡀
⠀⢇⣈⣭⠀⠀⠀⡀⠀⠀⢈⣍⣀⡅⠀⠰⣁⣉⣅⠀⠀⢀⠀⠀⠀⣨⣁⣈⠆⠀⢊⣀⣩⡁⠀⠀⢀⠀⠀⠀⣭⣁⡸
⠀⠀⠀⢸⠀⠀⢎⠈⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡈⠀⠰⡃⢸⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⡱⠀⠀⡆
⢸⠉⠁⠚⠒⠒⠚⠘⠒⠒⠚⡃⠉⢹⠂⢏⠉⠁⠗⠒⠒⠃⠘⠒⠒⢺⠈⠉⡹⠐⡏⠉⢘⠓⠒⠚⠁⠓⠒⠒⠃⠉⠉
⠘⠀⠀⢧⠠⠤⡀⠀⢠⠤⢤⠇⠀⠘⠀⠊⠀⠀⣄⠤⢄⠀⠀⡠⠤⣠⠀⠀⠓⠐⠃⠀⠸⡠⠤⡄⠀⢀⠤⢄⡤⠀⠈
⢄⠀⠀⠴⠢⠴⠁⠀⠐⠤⠒⡆⠀⢀⠤⣀⠀⠀⠖⠤⠜⠀⠀⠣⠤⠲⠀⠀⡀⠤⡀⠀⢰⠂⠤⠃⠀⠘⠤⠔⠦
⢰⠁⠀⣀⣀⣀⣀⢀⣀⣀⣀⡃⠀⢸⡀⡜⠀⠀⣄⣀⣀⡀⢀⣀⣀⣰⠀⠀⣣⢠⡇⠀⢘⣀⡀⢀⠀⣀⣀⣀⣄⠀⠈
⠈⠉⠀⢨⠀⠀⡞⠈⡆⠀⢸⠁⠈⠉⠀⠈⠀⠀⠃⠀⢠⡃⢘⠄⠀⡈⠀⠈⠁⠀⠉⠁⠈⡇⠀⢰⠁⢣⠀⠀⡇⠀⠉
⠀⡖⠑⠚⠀⠀⠈⠉⠀⠀⠘⠒⠈⠂⠀⢠⠊⠒⠊⠀⠀⠉⠉⠀⠀⠓⠒⠑⡄⠀⡔⠑⠒⠃⠀⠀⠉⠁⠀⠀⠓⠊⢢
⠀⠙⠊⢹⠀⠀⡔⠒⡄⠀⢸⠉⠑⠁⠀⠀⠑⠉⠱⠀⢀⠖⠢⠀⠀⠏⠉⠊⠀⠀⠈⠊⠉⡇⠀⢠⠒⢢⠀⠀⡋⠑⠉
⢠⠂⠤⠼⠤⠤⠵⠰⠥⠤⠸⠤⠄⢠⠄⡔⠀⠄⡦⠤⠤⠇⠸⠤⠄⢴⠠⠀⢦⢠⡖⠠⠤⠧⠤⠬⠆⠧⠤⠤⠧⠤⠐
⡨⠀⠀⡄⠀⣀⠀⠀⠀⣀⠀⡇⠀⠸⣀⠼⠀⢀⡁⢀⡀⠀⠀⢀⡀⢘⠀⠀⠇⣀⠇⠀⢸⠀⣀⠀⠀⠀⣀⡀⣀⠀⠐
⠀⠀⠀⣨⣅⣀⠆⠀⢨⣀⣩⡁⠀⠀⠀⠀⠀⠀⡭⣁⡸⠀⠀⢅⣈⢭⠀⠀⠀⠀⠀⠀⢈⣍⣀⡇⠀⠰⣀⡨⣅
⢹⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠁⡱⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢎⠈⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠒⠂⢛⠈⠉⡹⠐⡍⠉⢸⠃⠒⠚⠁⠓⠒⠂⠏⠈⠉⠇⢸⠉⠁⠙⠐⠒⠚⠈⠓⠒⠘⡇⠉⢹⠂⢏⠉⠁⡇⠐⠒
⠀⡠⠤⣼⠀⠀⠑⠐⠃⠀⠸⡤⠤⡄⠀⢀⠤⢤⡴⠀⠈⠂⠘⠀⠀⢧⡤⠤⠀⠀⠠⠤⢤⠇⠀⠘⠀⠊⠀⠀⣥⠤⢄
⠀⡁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡧⣀⢳⡜⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣌⡲⣯⡳⣄⠙⠛⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠟⠟⡁⠀⠑⠑⠄⠙⢿⣿⣕⣿⣿⣌⠑⠴⠿⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣉⣉⣠⣴⣿⣧⣷⠶⠛⢶⣤⣀⡈⡙⠛⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣷⣤⣭⣻⣿⣿⣷⣶⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⢠⣄⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⠆⠀⢹⣿⠷⠀⠐⢲⣶⡖⠺⢛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢁⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠙⣉⠀⠀⠀⠀⠀⠀⣰⢏⡴⠒⠋⠙⢷⡸⣇⠀⠀⠀⠀⣠⠀⢰⣶⠦⣀⣤⡄⠀⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠛⠋⠀⠀⠀⠀⣴⠀⠉⣼⠇⠒⠀⠀⠚⣷⣌⣧⠀⢀⡈⠁⠀⠀⢨⣄⢻⣿⠇⠈
⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠲⡆⢠⡀⢧⢦⣻⢸⠀⠀⣤⣴⣄⢹⣿⢸⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣠
⠀⠘⠱⠆⠀⠀⣤⣶⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣿⠘⢨⡷⢸⣆⡈⢻⣿⡿⢸⣿⡟⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡤⣬⣡
⠐⠚⢠⠶⠀⣼⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢻⡟⡊⣿⣿⣿⡇⢀⣿⠻⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡦⠉⢉⡈⢦⡥
⠀⠀⠙⢴⣿⣿⣿⠃⠀⠀⠀⠀⢿⣶⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⢀⠈⣿⣷⣸⣧⠀⠈⠁⠀⠀⠀⣀⠤⠤⠤⢄⡀⠈⠉⠁⠀⣿⡟⣶⠂
⠀⠀⢺⣾⣿⣿⣿⣷⣶⣶⣶⣶⣤⣍⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡄⣤⣿⣿⣿⣿⣶⡇⠀⠀⢠⢊⠄⠂⠀⠀⠂⠌⢢⠀⠀⠀⠈⠛⠁
⠀⠀⢸⣿⣿⣿⣿⠟⠛⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠉⠉⠉⠉⠉⣀⠀⠀⠇⡎⠀⠀⠀⠀⠀⠈⠆⢧
⠀⠀⢸⣿⣿⣿⣧⣤⣤⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢸⣿⢸⣷⡀⢀⣴⡇⠰⣤⡀⠰⠸⡀⣀⣶⠀⠀⣀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⢡⣾⡿⠁⠀⠹⣿⣆⣤⣧⡿⢃⣶⣿⠟
⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣦⡁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠚⢧⣼⣇⣠⡄⠀⠀⠀⠈⢹⣷⣾⠟⣿⠉
⠀⣼⡿⠟⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢡⠄⣾⡏⠛⠦⠀⠀⠀⡿⠓⢠⣤⣄⠀⠘⠛⠀⠀⣿⠳⠄⠀⠀⠀⠶⢚⡿⣿⠻⠋⠀⣰⡇
⠀⠏⠀⢀⢠⡀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡀⠀⠀⠐⢶⣦⡀⠀⠀⠉⠉⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡆⠀⠀⢋⣴
⠀⠹⣿⠏⠀⠻⣶⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⣇⣶⣤⠀⠀⠿⠟⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠖⠘⣿⠁
⠀⠀⣀⣶⣿⠛⠻⠿⠇⣠⣶⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⢠⡿⣱⡗⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⣴⠆⠀⠈
⠀⢰⣿⠉⢹⣧⠀⣤⠀⠛⠿⠀⠀⠈⠉⠈⢷⡄⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠓⠀⠀⠀⠀⣶⡄⠀⠀⠀⠻⠶⠆
⠀⠐⠿⠷⠿⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣴⣶⣞⣿⣿⣷⣦
⠀⢠⣤⣤⣄⡙⢦⡀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⠳⣿⡿⣿⣿⠿⠋
⠀⠀⠀⠉⣩⠷⠾⠛⠀⣷⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⠀⠀⠀⢠⣄⠰⣦⡶⠀⡀⣠⢠⣇⣉
⠀⠀⣠⣤⡀⠐⠋⠉⠓⠾⢣⣤⣶⣄⣹⣷⣶⠿⠇⠀⠀⠀⠀⢀⣬⣰⣿⠄⢠⣿⣿⠂⡉⠀⢾⡁⠻⠦⠈⠁
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⢿⣇⣈⣿⣇⣈⠁⠀⠀⠀⠀⠀⠀⠘⠶⡹⣁⡀⣀⡉⠀⢀⢙⣦⠀⠉⣀⡀⠀⠀⠀⢠⡄⠀⠀⣀⡀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠉⠛⠀⠀⢘⣿⠉⠀⡤⠾⠛⣠⣶⣠⡆⠓⠻⣷⠘⣷⣀⣦⣠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⠈⠛⠀⠀⠁⠀⠀⠙⠻⠿⠁⠙⠷⠟⠀⢹⡿⠻⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠈⠐⠐⠀⠀⠀⠂⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠖⡟⣿⡥⢀⡀
⠀⠀⠀⠀⠀⡠⢔⣒⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⡟⣦⠀⣤⡘⠇⠀⣀
⠀⠀⠀⠀⢰⢡⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠀⣫⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⢾⠮⢧⣉⣋⡞⠀⠈⠁⠀⠀⠀⠀⣀⣠⣠
⠀⠀⠀⠀⠈⠢⡳⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢯⠇⣸⢺⣀⡪⠀⠀⠀⠀⣀⠤⠖⠋⠁⢦⠐⠉⠋⠲⠴⠂⣤⡄⢀⣀⠀⠀⢹⠙⠫⡼
⠀⠀⠀⠀⠀⠀⠈⢦⠱⡄⠀⠀⠀⠀⠀⠉⣡⠃⠀⣞⢲⡞⠠⠦⢀⠔⠋⠁⠀⢸⠃⠁⠀⠫⡴⢇⠀⣀⠴⠧⠤⢤⠤⠭⠜⢉⡀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⢸⠆⡇⠀⠀⠀⠀⠀⢠⠃⠀⠈⢻⣿⣿⣦⡴⠁⠀⠀⠀⡀⠈⢆⠀⣰⠀⠾⡀⠉⠁⠴⠠⡆⠀⠀⠀⠀⠀⠈⠁⠋
⠀⠀⠀⠀⠀⠀⣠⠊⠀⢉⣶⣤⡀⡤⠆⡞⡄⠀⠀⠈⠛⡟⠉⡇⣠⠴⠚⣩⠈⣷⠛⠋⠉⠳⡀⠰⡀⢻⡞⠏⡤⡺
⠀⠀⠀⢀⡔⠊⠁⠀⠀⠈⠙⢻⠿⠒⢚⡇⠇⣰⣦⣄⡤⣥⠎⠛⢡⠀⡴⠁⢠⡇⠀⠀⠀⠀⠈⢢⡘⡇⠁⠀⡜⠁
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢸⢃⢄⠑⠉⢰⢳⠸⡀⣀⣮⡾⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠑⠧⡴⠧⠕⠙
⠀⠀⠀⢧⡀⠀⠀⡲⣄⠀⠀⠈⣉⠀⠘⡞⣆⠙⠚⠏⢸⡷⡟⠛⠋⢳⠀⠀⡠⢼⠦⣄
⠀⠀⠀⠀⢹⠀⣻⠁⠸⡄⠀⠆⠈⠁⢠⠹⣬⠷⣤⠤⣾⣳⣷⡄⡴⠛⠢⣼⡝⠁⠀⡞
⢰⢿⠵⠤⠞⢰⠁⠀⠀⢹⣼⡀⠀⢀⢠⣢⠃⠀⢹⡔⠁⢝⠺⣷⡇⡀⠒⢻⡉⢳⡞⣇
⠘⢾⡊⠁⢀⡼⠀⠀⠀⣟⢈⢷⠀⠀⡻⠁⢳⠀⠋⡀⠑⣌⡷⠋⠄⠳⣄⣀⣇⣸⣼⡼
⠀⠀⠙⠒⠋⠀⠀⠀⠀⠈⠳⠚⡇⠀⠀⢀⢿⡀⠀⣸⠴⠋⠙⠦⡀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡞⠀⠙⠚⠁⠀⠀⠀⠀⠈⠲⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⢀⣴⣿⣦⡀⠀⠀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣿⣿⣿⣿⣿⣦⣴⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠙⢿⣿⣿⡟⠉⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠲⣄⠀⠀⡠⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠙⠋⠀⣀⣤⣾⣿⣿⣿⣿⣿⡋⠀⠀⠀⠈⠓⠐⠁⢀⡀⠌
⠀⠀⠀⠀⠀⢀⠔⠒⠄⠀⠈⢂⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⡔⠁⠀⠀⠑⠠⠔⠃⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠹⢿⡿⠃⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠠⠂⠐⢄⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠘⠿⢿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠡⢀⡀⠈⠢⠒⠁
⠀⠀⠀⠀⡔⠁⠀⠠⠒⠢⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣄⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠘⠢⠤⠊⠀⠀⠈⠢⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣷⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠁⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⠀⠀⠀⡚⠃⠀⠀⠀⠀⠀⠀⢀⡰⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⠀⠀⢠⣶⣶⡆⠀⠀⠸⣷⠀⠰⣁⣺⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠶⢿⠟⠋⠀⠀⣼⣿⣿⣿⡀⢠⠞⠋⢁⡀⠉⡛⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⣶⣄⠀⠀⠰⣄⣴⣿⣿⣿⣿⣷⣄⡆⠀⠸⣄⣾⡿⠀⠀⠀⠀⠀⠰⡇⡠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠈⣹⣿⣿⣦⣀⡀⠀⣿⣿⣿⣿⣿⣿⠀⢠⣤⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡀⠀⡄⠀⠀⠆⠠⠴⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠢⠸⡇
⠀⠀⠀⢠⠁⠘⣇⡴⠋⠀⠐⠞⢻⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡟⠆⠀⠀⠀⠀⠐⢧⣷⠠
⠀⠀⠀⢸⡀⢸⡟⠀⢰⣶⣶⣶⣾⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣤⡄⠀⠀⠀⠈⣿⡄⡀
⠀⠀⠀⠀⠑⢼⣇⠌⣼⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠓⣿⠏
⠀⠀⠀⠀⠀⢸⣯⠘⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣀⢰⡷⠀⣿
⠀⠀⠢⠘⢌⠙⣿⠀⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⢀⣿⠀⠋
⠀⠀⠀⠀⣾⠀⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⢸⡟
⠀⠀⣧⠄⢹⠀⢿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢺⠃⠀⣾⡇⠀⢰⠇
⠀⠀⢈⣧⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⢶⣶⣶⡶⢶

⠀⠀⠀⢰⣶⣶⠀⣴⡆⣖⠀⣶⠂⢀⣶⡀⣦⡆⡖⣢⠀⢦⢶⡆⡦⣶⡆⢲⢰⡶⠀⠰⣆⣴⠃⣖⢲⣴⢓⣴⣶⡒⡶⠀⢰⢲⣴⣒⣦⡒⡆
⠀⠀⠀⠈⠉⠈⠉⠁⠀⠈⠀⠀⠁⠈⠀⠁⠀⠁⠉⠁⠀⠈⠈⠀⠁⢀⠀⠈⠀⠉⡀⠈⠉⠈⠁⠈⢉⠈⠉⠀⠉⠀⠁⠀⠈⠉⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⢠⣶⡄⠀⡀⢀⠀⠈⢿⡃⢀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣣⣼⣿⣷⣶⣿⣯⣤⣿⣿⣿⡎⢳⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⠋⠠⣿⣿⠀⢸⣿⣿⡇⣼⣿⠭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⣿⣿⡀⣸⣿⣿⣆⢸⣿⣧⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢀⣿⣿⣴⣿⣿⣿⡃⢸⣿⡏⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡜⣻⢷⣿⣿⣿⣿⣁⣼⣿⣆⠀⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠰⢄⠄⢠⠀⠀⠀⠀⠉⠃⠄⠀⠘⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠙⠁⠀⠀⠀⠀⢈⡋⠀⠀⠙⠖⠀⠘⢏⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⢀⠀⡤⢆⡈⠂⠀⠀⠐⠁⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢀⠀⢀⠄⠐⠇⠠⠈⠁⠐⢀⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠂⠂⠀⠀⠠⡀⠄⠀⠠⠂⡀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠐⡆⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠰⠈⠉⠄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠊⠀⠀⠀⠑⠀⠁⠀⠀⠉⠁⠠⠔⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠙⠛⢃⢀⣴⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⠀⠀⠰⠆⣤⣶⣶⠖⠀⠈⠁⠀⠀⠀⠀⠀⠠⡤⠀⠀⡴⠂⠀⠀⠠⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠈⠀⠀⡀⠀⠀⠓⡄⠀⠘⠃⠀⢠⣤⡤⠤⠶⠛⠁⠀⢀⠠⢶⡶⣐⠦⣀⠀⠀⡇⢠⡄⠀⠀⠀⣠⡄⢸⠀⠀⠀⠛
⠆⠀⢠⡄⠛⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢀⡉⠸⡆⠻⡆⣈⠉⠁⠀⢳⡌⠁⠀⣿⠀⠈⢡⡞⠀⣀⠤⠶⠠⢀⠀⠐
⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠏⣁⠀⣀⠀⠰⠏⢠⡜⠃⢨⠀⠀⠀⠿⠀⠀⠀⡇⠀⠁⠀⠚
⠀⠰⢆⡀⠀⠀⠀⠀⠀⠃⠀⢎⡉⠀⠀⠀⠀⠀⢀⠀⠘⡋⣤⠉⣄⠀⠒⢀⠦⠀⠨⠖⠒⠀⠀⠀⠒⠰⠇⠀⠀⠀⠀⢀⡀⠀⠐
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⢄⠤⠝⠀⠉⢠⣶⡀⣰⣆⠙⠀⠀⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⢀⡀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣄⠀⠀⠈⠉⠉⠁⠦⠀⠀⠉⠁
⠈⣰⣿⣿⣿⣿⣟⠻⣆⠀⠀⠈⠐⠓⠈⠀⠘⠛⣿⣩⣿⣶⣦⣴⣦⣴⣶⣴⡶⣦⡦⣶⠀⠐⠀⠀⠀⠀⠀⠀⠰
⠀⣿⣿⣿⠀⠀⣻⡿⣿⠀⢠⡤⠤⠤⠤⣤⠀⣶⣭⡿⢛⣧⣾⡟⠋⠛⠛⠙⠛⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠹⣿⣿⣿⣿⣿⣿⠟⢀⠀⠁⠈⠛⠀⠉⠀⠀⠁⣠⣟⣽⣿⣡⣶⣶⡿⢶⡶⣮⣷⣦⠀⣠⡀
⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠛⠉⠛⠙⠋⠛⠁⠈⠛⠁⠀⠈
⠀⠀⢺⢶⠂⠀⢲⠶⠂⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⡖⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠾⠖⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⣖⣚⡥⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠹⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⢠⡄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⠆⠀⢸⣿⠷⠀⠐⢲⣶⡆⠻⢛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢁⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠙⣉⠀⠀⠀⠀⠀⠀⣠⢏⡴⠒⠋⠙⢷⡸⣇⠀⠀⠀⠀⣀⠀⢰⣶⠦⣀⣤⡄⠀⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠛⠋⠀⠀⠀⠀⡤⠀⠉⣼⠇⠒⠀⠀⠚⣷⣌⣧⠀⢀⡈⠁⠀⠀⠀⡄⢻⣿⠇
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠓⠀⠲⡆⢠⡀⢇⢤⡸⢸⠀⠀⣠⣴⣄⢸⣿⢸⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⣠
⠀⠘⠸⠆⠀⠀⣤⣶⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣿⠘⢸⣷⢸⣆⡈⢿⣿⡿⢸⣿⡞⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡤⢬⣡
⠐⠚⠠⠶⠀⣼⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢻⠏⡎⣿⣿⣿⡇⢀⣾⠹⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡦⠉⠉⡘⢦⡥
⠀⠀⠛⢴⣿⣿⣿⠃⠀⠀⠀⠀⢿⣶⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⠀⠈⣿⣧⣸⣧⠀⠈⠁⠀⠀⠀⣀⠤⠤⠤⢀⠀⠈⠉⠁⠀⣿⡛⣶⠂
⠀⠀⢲⣾⣿⣿⣿⣷⣶⣶⣶⣶⣤⣍⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡀⣠⣿⣿⣿⣿⣶⡇⠀⠀⠀⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⢸⣿⣿⣿⣿⠟⠛⠋⠉⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠏⠀⠀⠉⠉⠉⠉⠉⢀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠀⢃
⠀⠀⢸⣿⣿⣿⣧⣤⣤⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⢸⣿⡈⣶⡀⠀⣰⡆⠠⣤⡀⠐⠸⠀⢀⣶⠀⠀⣀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⠡⣾⡿⠁⠀⠹⣿⣆⣤⣦⡿⢃⣴⣿⠟
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣦⡁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠚⢧⣼⣇⣠⡄⠀⠀⠀⠈⠹⣧⣼⠟⢷⠉
⠀⣴⡿⠟⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢡⠅⣷⠍⠛⠦⠀⠀⠀⡿⠓⢠⣤⣄⠀⠘⠛⠀⠀⣻⠳⠄⠀⠀⠀⠶⢚⡿⣿⠻⠋⠀⣰⡆
⠀⠏⠀⠀⢠⡀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡀⠀⠀⠐⢶⣤⡀⠀⠀⠉⠉⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡆⠀⠀⢋⣴
⠀⠹⣿⠏⠀⠻⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⣇⣶⣠⠀⠀⠾⠿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠖⠘⣿⠁
⠀⠀⣀⣶⣿⠛⠻⠿⠇⣠⣶⠀⠀⢀⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⢤⣿⣵⡶⠀⠀⠀⠀⠀⡄⠀⠀⣄⣷⣤⠆⠀⠈
⠀⢰⣿⠉⢹⣧⠀⣤⠀⠛⠿⠀⠀⠈⠉⠈⢷⡀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⢀⣶⣦⠃⠀⠂⠻⣶⠆
⠀⠐⠿⠷⠿⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠊
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣤⣦⣞⣿⣿⣷⣦
⠀⢠⣤⣤⣀⡙⢦⡀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⠳⣿⡿⣿⣿⠿⠋
⠀⠀⠀⠉⣩⠵⠾⠛⠀⣷⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⠀⠀⢀⢠⣄⠰⣦⡶⠀⡀⣠⢠⣇⣉
⠀⠀⣀⣤⡀⠐⠚⠉⠓⠾⢃⣤⣶⣄⣙⣷⣶⠛⠃⠀⠀⠀⠀⢀⣬⣰⢷⠄⢠⣿⣿⠂⡉⠀⢸⡁⠻⠤⠉⠁
⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢿⣏⣈⣿⣇⡈⠉⠀⠀⠀⠀⠀⠀⠘⠶⠹⣁⠀⢀⡉⠀⢀⢙⣦⠀⠉⣀⡀⠀⠀⠀⢠⡄⠀⠀⣀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⡏⠙⠛⠀⠀⢘⣿⠋⠀⣤⠾⠛⣀⣶⣰⡆⠓⠿⣷⠙⣷⣀⣦⣠⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⠈⠛⠁⠀⠁⠀⠀⠙⠻⠿⠁⠙⠷⠟⠀⠹⡿⠻⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⢦⠴⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡝⠣⢠⠤⠊⡽⠀⠀⠀⠀⣠⢤⣠⡇⠸⡱⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠌⠠⢰⡀⠀⢀⡠⠊⢀⡀⠐⠀⠠⠂⣀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠰⣿⡿⢣⠔⢻⡀⠀⣸⡇⠀⠀⠀⠀⡇⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠠⡤⠤⡞⠁⠉⠒⢹⡇⠀⠀⠀⠀⡷⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠒⠀⢃⡠⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢄⡀⠀⠀⣇⠀⠀⠀⠀⢸⠀⢦⠀⠀⢸⠸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠐⠩⠝⠫⠽⡄⠀⠀⠀⡾⠀⠀⠡⠤⢸⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⠀⠀⠐⠀⠋⣆⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢸⡏⢇⠀⠀⠀⠀⣼⡄⠀⠙⡒⠒⠶⠒⣞⡄⢀⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⣠⣿⣷⡐⠆⢀⠎⠀⠀⢀⣼⠟⠀⠀⠀⡇⠀⠀⠀⡿⡣⠂
⠀⠀⠀⣠⠔⣊⠽⡶⢠⣷⠟⡿⠃⣇⠀⢸⠀⠀⡠⢊⡏⠀⠀⠀⢠⠁⠀⡇⠀⢇
⠀⠀⠀⠙⠉⢀⡜⡡⢫⠋⠀⢇⠀⢸⠀⠀⢠⠎⢀⠞⡘⠀⠀⠀⢘⠄⠀⡇⠀⡌
⠀⠀⠀⠀⠀⡞⢸⢁⠇⠀⠀⠈⢆⠀⠇⢸⡇⢀⠎⠀⡡⠀⠀⠀⡜⠀⠀⡇⠀⢇
⠀⠀⠀⠀⠀⠳⣌⡞⠀⠀⣀⣀⣨⡇⠸⠀⡇⡎⡠⠚⠁⠀⠀⡰⠁⠀⠀⡇⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠰⠮⣉⣱⢿⢛⠧⠀⡄⠻⡻⢩⣩⣷⣶⣿⣶⣦⣤⣧⣤⣶⣿⣶⣦⡀⢀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠒⠒⠑⠒⠋⠉⠉⠉⠈⠉⠁⠀⠉⠀⠀⠈⠉⠉⠉⠀⠉⠘⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⡤⠔⠉
⠀⢰⠤⠀⠙⣆⡀⠀⠈⠉⢁⡄⠀⠀⠀⠀⢠⢀⣀⣀⠀⠀⣠⢶⣂⢤⡀⠉⢁⣠⡴⡄⠀⠀⢀⡌⢀⡌⠀⣠⠖⠚⠁
⠀⢈⠀⠈⠠⡄⠰⠤⡄⠀⠀⠀⠶⠀⡀⠐⠀⠋⠙⠿⠁⠀⠈⠙⢿⣰⡏⠐⣋⡿⠑⠉⢉⣠⡈⢀⠂⠑⠄⠀⠸⢎⡁
⠀⠘⠀⠀⠀⢀⠤⠀⠛⠦⠀⠀⠀⠀⢑⣲⡀⠃⠀⠀⠀⠀⠀⢰⠈⠁⠀⠀⠉⠀⠀⢙⡍⡼⠁⠀⠀⠀⠀⠀⠄⠘⠃
⠀⠠⠀⠀⠠⠋⠀⢠⡀⠈⠁⠀⠀⠈⠻⣿⠉⠠⣄⠀⠀⠀⡀⠈⠀⠀⠀⠁⠈⠉⠀⠋⢿⡤⠃⢀⡀⠄⡀⠀⢀⡀⠄
⠀⢀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⣈⠉⠳⠎⠀⠀⠈⠖⣺⡟⠙⣶⡀⠀⠀⠀⢀⣛⠉⢀⠄⠐⠀⢀⣁⠤⡅⠠⠃⡈⠃
⠀⢸⠀⠀⠀⣀⠈⠁⠀⠀⣈⡀⠉⠀⣤⡶⠦⣼⣿⣞⡛⢿⡾⣧⠘⣧⡠⠴⠛⢛⣻⣻⣦⡀⠀⢻⣫⡜⠻⠁⠔⢀⡄
⠀⠰⠀⠀⣤⡉⢉⠀⠀⣼⠻⠮⡙⢄⠉⠁⠀⠻⠏⠈⢉⠿⣤⣿⡆⣩⣧⠤⢾⡭⢥⣬⣉⣿⣶⠀⠉⠀⠋⠈⢐⢋⡁
⠀⠰⠰⠦⠀⠀⠀⠠⠶⣄⡱⡿⢡⡄⠀⠀⠀⠒⠒⣒⡟⣺⠏⠃⠉⣉⣿⣦⡜⡖⡚⣃⣬⠿⣦⡄⢀⠀⠀⠀⠀⣬⠂
⠀⠰⠀⠀⠀⠠⠄⠀⠀⡛⠭⣃⡘⠙⣼⣤⠠⠾⠁⠀⠀⡎⠀⠀⠴⠀⡺⣹⠶⠦⡄⠤⠤⠁⢾⠗⠀⣆⣀⠋⠐⠀⡇
⠀⠘⠀⠀⣐⠚⠃⢀⡘⠙⢲⠏⣙⠛⠅⠉⣗⣴⡶⢚⠽⡆⠠⠄⢀⣴⡷⣳⣖⣒⡀⠰⠊⡙⢢⠤⢤⢁⠲⣤⡈⠹⠇
⠀⢰⢀⣐⠋⢡⣄⡈⠉⠁⢺⣃⣤⡘⢉⣴⣿⣿⣿⣤⢊⡌⣰⣾⣇⠠⡘⣿⣯⣿⣏⣤⠞⠀⠂⢸⠀⢾⡂⣹⣆⠑⡄
⠀⢨⠍⠀⣀⠈⠉⠉⠉⠉⢹⠁⠀⠀⣼⣏⣿⣿⠀⡙⠉⡱⠟⢘⠟⠶⢻⣯⣿⠁⠈⢹⣇⠐⠀⠀⢈⠀⣻⡇⠈⠆
⠀⢈⠀⠘⠛⠓⠒⠀⠒⠐⢾⡀⠀⠀⡾⠉⢿⣿⠊⡀⠨⠐⣥⣸⠐⠀⢸⣿⡯⠚⠠⣿⣿⠀⢠⠲⢾⣁⣉⣤⠂⠁
⠀⠸⠄⠀⢠⡀⠀⡀⠀⠀⣤⣧⡀⡼⠛⢤⡺⣿⠀⠀⠀⠑⡀⡉⢀⡔⢢⡿⠁⠀⠈⠿⢿⣷⣿⡄⠀⠀⢃⡠
⠀⢠⣄⡐⡜⡓⣀⠀⠀⣀⡄⠈⠉⠉⠓⠉⠀⢹⡇⠀⠀⠁⠀⠐⠁⠀⣿⠙⣦⣄⡐⠒⠉⠀⠀⢘⣦⡀⠈⡔
⠀⢈⣿⠷⣤⢺⣧⢽⡿⢢⡀⠀⢤⡄⠀⠀⣀⢀⣿⣄⠀⣀⣵⠦⠀⠐⢿⣆⣀⣙⠛⠺⣭⠦⠚⠋⠀⠓⠋⠁
⠀⢰⣸⢋⡿⢿⣧⣴⠋⠻⠇⠀⠠⣠⡷⠯⣽⣥⡈⠉⠉⠹⠿⢾⣀⡴⠶⠏⠀⣈⣤⣬⡯⢿⠭⢀⠀⠀⠀⠀⠀⠀⠁
⠀⢸⢛⢿⣔⣙⢣⣠⣤⣤⣀⡀⢴⡏⠀⠀⠀⡉⠉⠲⢤⣜⡶⠀⠁⠀⣠⣦⡾⠋⣠⠀⠀⠀⣸⡟⢀⡄⡀⠀⠀⠀⡄
⠀⢘⡙⢻⢯⣭⢿⠏⠁⠜⢰⠉⢈⣿⣶⡇⠀⠀⢀⡀⢀⠹⣴⣤⢦⣤⣞⣻⠀⠀⠀⢦⣤⠖⠹⢇⠀⠄⠐⠖⣶⠂⠂
⠀⠘⠁⣬⣲⣓⡾⠒⠒⣶⢃⠴⠋⠀⠉⠙⠗⠲⣦⡀⠀⠠⣙⢷⣞⠋⠀⠀⣦⡤⠶⠟⠑⣆⠀⢰⡔⠀⠰⠀⠀⠀⡄
⠀⠈⣰⢏⠀⠸⠓⠀⢀⣆⠙⠶⣈⠀⠂⠀⠀⠀⠀⡰⢳⠾⣅⠀⠉⡓⢾⡽⢯⡀⠀⠀⠀⠈⣆⠈⠓⠀⠀⠀⠀⡏
⠀⠈⠹⡀⠀⠀⠀⠀⡘⠉⠀⠉⢻⠑⢦⢄⣀⣀⢶⠠⣟⡢⠊⠛⠶⢍⡀⠻⣄⠻⣄⣰⣄⠿⠝⠀⠀⢹⠀⡞⠈⢱⡆
⠀⢠⣀⣿⠀⢠⠀⢘⠀⠀⠀⢀⣬⠉⠉⢻⠉⠿⡌⢻⣙⣯⣐⢰⡀⠀⠉⣷⣟⠱⠈⢿⠈⠁⢷⠴⠀⠺⠀⡇⠀⠀⡇
⠀⠈⢹⣯⣀⣳⠀⢹⠓⠒⠚⠋⡙⢚⢛⠏⣹⠒⣽⣻⠟⠛⠫⣟⠝⠻⢾⣷⢾⡽⠳⣼⠀⠀⠀⡀⠀⠧⢤⡷⠂⠈⠁
⠀⠐⡼⠂⠛⢽⡇⢸⠙⠁⠀⠀⠀⠌⣤⡵⢢⡄⠀⠘⣆⠀⠀⣼⠆⠀⠚⣄⣀⠤⠒⢚⣒⣉⣉⣉⡉⠐⠂⢸
⠀⢸⠁⠀⠀⡰⢢⡟⠠⣌⠄⠛⠀⣎⠹⣏⣓⠋⠀⢀⡼⢣⠉⢻⠆⠀⠐⡋⠀⠀⣋⠩⣁⢍⠹⣀⣀⣻⠁⠘⣷⠄
⠀⢀⠀⢀⣊⠀⠀⠈⠙⠟⠚⠛⠛⠛⠲⠤⠥⠴⠖⠋⠙⠊⠃⢸⡆⠀⠀⣱⢦⡀⠀⠈⣉⣈⣉⣁⣈⣀⠲⠁⠙⡆
⠀⠈⠉⢹⠟⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⣶⣞⣡⠞⡟⠛⣿⠉⠙⡆⠀⠈⣿⣁⣠⣀⣈⡟⢳⣀⠀⠀⢁
⠀⠀⠀⣼⠦⠄⠀⢈⣹⠗⠲⠦⠤⣶⣶⣾⣿⠛⣽⠁⠀⠀⠓⣶⣶⡿⠀⠰⣋⣀⣤⠀⠽⡇⠈⠉⠑⣙⣶⣶⠆⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠋
⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣙⣿⣿⣽⡍⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⡠⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠐⠀⠀⠆⢀⠆⠈⠀⠐⠀⠀⣰⠖⠀⠀⠈⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡁⠈⠁⠀⠀⠀⠀⠃⠀⠀⢠⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⣴⣿⣯⣭⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠉⢄⡀⠀⠀⠈⠣⡀⢰⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⠀⠀⠀⠈⠋⠻⢷⣄⡀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠅
⠀⠀⠀⠀⠀⣾⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣀⣀⣀⣀⡄⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⢀⣿⡆⠀⠀⠈⠑⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣄⡔⠉⠀⠀⠀⠙⠢⣀
⢀⠀⢀⠀⠀⣿⣿⣦⣀⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠑⢀⠀⠀⠀⠀⠀⠀⠑⠦
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⢀⠄⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠐⠚⠒⠒⠒⠀⠤⠤⠤⢤⠤⠤⢤⡄⠀⠀⠀⠀⠸⠄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢰⠇

⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢖⠒⠲⠒⠒⠒⠲⠒⠒⠒⠒⠒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠲
⣹⠀⠀⠈⠃⡀⣀⠖⠀⠀⠀⠀⠀⠐⠉⡐⠉⠉⠋⠃⠁⡜⠉⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠄⠙⡁⠀⠀⠄
⢹⠀⠂⠀⣰⣇⠉⠀⢋⠀⠀⣀⠀⠀⠀⠀⠠⠔⠒⠒⠏⠥⠐⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠤⠂⠀⠀⠄⠑⠀⠎⠐
⢸⠉⠀⢲⣷⠆⠀⠀⠀⡤⠂⠉⠂⠄⠀⢀⡁⠀⠀⠠⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠀⠰⠇⠠⠀⢘⣄
⢸⠀⠀⣸⣷⠙⠂⠀⢛⠉⠈⠲⠀⠀⠐⠘⡅⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⢢⠞⢠⡊⢰⡬⠉
⢸⣤⠤⣿⣧⡀⠀⢠⡾⠆⢀⣀⡄⠤⠀⠀⣉⠈⠀⠀⠆⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠐⠀⡐⣯⣉⠉
⢸⠀⡄⢘⣧⡄⣤⠞⢀⡴⠉⢁⠈⠐⠳⡀⢩⡶⠉⠙⠓⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠐⠀⠉⠀⠀⢁⡩⣦⠀⢂
⢸⣀⣷⡼⠷⠷⠥⠶⠊⢠⣄⠤⠐⠴⠃⠈⠉⠀⠀⠀⢀⣰⣯⣤⣀⡁⠀⠠⠈⠛⢿⡀⠀⠀⠀⠀⠀⠀⠈⢀⠑⡶⣩
⢸⠤⠤⠤⠤⣠⠌⠃⢒⠌⠁⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠠⠉⢬⠇⣽
⢸⠐⠂⠘⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠐⠋⠁⢻⣿⠻⢿⠟⠩⠿⣿⣿⣦⣄⠀⠀⠀⢰⠀⠀⠀⣟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⢐⡀⠀⢸⡿⠀⠐⠀⠀⠀⣿⣿⢿⣿⡷⠆⠀⠸⣇⠀⢀⡙
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠞⣀⣑⠄⡾⡇⠀⠀⠀⠀⣀⠈⠁⠘⠃⠠⢀⡀⠀⢹⣄⠛⢃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⣵⠀⠀⣠⠀⠀⠁⠀⢀⠄⠀⠢⡀⠑⣄⠀⠻⣯⠺
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠔⠾⢃⣤⡟⠁⠄⠀⠀⢠⠊⠀⠀⠀⠀⡀⠈⠂⠀⠀⠛
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢰⡄⠠⣠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠐⢁⠀⠀⣠⣿⠀⠀⠀⠀⠀⢠⡾⣿⣶⣬⡢
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡘⠀⠀⡸⠋⢀⡼⠷⣏⢧⠀⠀⠀⠀⠘⡿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢣⡴⣯⡝⠷⣍⠛⠀⠀⠀⠀⢠⡟⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡓⠀⠀⣴⡻⣦⡙⢶⣝⢃⡀⠀⠀⠀⢸⣛⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠄⠨⠉⢭⣿⠀⣿⡟⠤⣛⡾⣬⠛⣁⡀⠀⠀⢸⣽⣿⣿⣿⣇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣍⡑⠄⠩⠶⠀⠄⣦⣤⣤⣼⣿⣷⣬⣿⣷⢪⡽⡷⠛⢲⠭⠳⣦⠀⢹⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠀⢤⣖⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠁⢀⠉⠉⠉⠀⠀⠀⠀⠀⠢⠀⠁⢸⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣷⣶⠉⠡⠄⠠⠀⢾⣿⣿⣿⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠠⠀⠀⠀⢀⡜⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⢠⣤⣶⠯⣵⣿⢿⣷⣤⣀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⣤⣾⢇⣿⣿⣿⣿⡆
⢸⠀⠀⠀⠀⣮⣥⣬⣥⣥⣼⣿⣼⣿⣿⣿⣿⡂⣸⣿⣿⣿⡇⠤⠀⠤⠀⠀⠀⠠⠀⠀⣠⣶⣿⠟⣿⢸⣿⣿⣿⣿⠇
⢸⠀⠀⠀⠀⠸⣿⣿⣿⣦⢿⣯⣿⣿⣿⣿⣿⡅⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣽⣧⣛⡿⢸⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⢀⣠⣾⣿⣣⡟⣼⣿⢊⡶⢸⣿⣿⣿⣿⠆
⢸⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣺⣻⣿⠿⣿⡟⠀⠀⢹⣿⣿⣿⣀⣤⣤⣶⣿⢿⣽⣿⣷⣿⣾⣟⣏⡷⢸⣿⣿⣿⣿⡆
⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣿⣿⣻⣿⠇⠀⠀⠘⣿⣿⣿⣟⠉⢰⢎⡷⣿⣿⣿⡉⢹⣿⣿⣯⡗⢸⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⡇⠀⠀⠀⠙⠋⡏⠁⠀⢸⣯⡷⣻⣿⣯⣷⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⣯⣴⢻⣿⣿⣿⣿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣷
⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⡧⠤⡤⡿⢮⠽⢧⠾⠿⠭⠿⠽⠧⠷⠦⠼⠿⠿⢿⣿⡧

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠁
⠀⠀⠄⢰
⠀⠀⠀⠈⣄⡀
⠀⠀⠀⡞
⠀⠀⠀⢧⡤⡄
⠀⠀⠀⢾⠁⠁⠀⢀⡀
⠀⠀⠀⠘⣦⣀⣶⣮⠖⠒⢤
⠀⠀⢠⠞⠙⡁⠈⠁⣦⡀⠈⡇
⠀⠀⢸⠀⠀⣛⣀⣤⣶⡾⢀⠇
⠀⠀⣈⢧⣄⡈⢉⣁⣥⣴⣊⣤⣀
⠀⡜⠁⠀⢈⠙⠟⠉⠙⠋⠙⢷⡀
⢸⡇⠀⡀⠿⠇⠀⠀⣴⡆⠀⠀⢿⠠
⠈⢇⠀⠻⣷⣷⣶⣴⣶⠆⠀⢀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠳⣤⣄⣉⡀⢉⡁⣀⣤⣞⠛⠉⠙⢦⡀⢠⡀⠀⠠⡴⢄⣤⣀⣶⣊⣀
⠀⢈⣶⠋⠉⠟⠉⢉⠉⢹⠀⣠⡀⠀⠀⠀⢳⡍⢁⡴⠒⠲⠾⣿⠟⠛⠻⠉⠛⢦⡀
⠀⡿⠁⠀⠀⢰⣦⡀⠀⠀⡀⣿⣿⢄⡤⠦⢿⣷⣾⣀⣀⢀⣄⠀⠀⠀⣴⡄⠀⠀⢹⡀
⠀⣗⠀⠀⠀⠘⢛⣁⠀⣠⣤⣤⣴⡏⠀⠀⣈⠙⠉⠉⠋⠙⢿⣀⣀⢀⣭⣥⠀⠀⢸⠃
⠀⠻⣆⠀⠀⠘⠻⣿⣷⡟⢿⡿⠿⡇⢠⣜⣛⣀⠀⠾⠇⠀⠘⡿⠟⠿⠟⠁⠀⣠⠏⠀⠀⡔⠐⢢
⠀⠀⠙⢦⣄⣀⠀⢠⡀⠀⣠⣀⣀⣷⣄⠙⠻⠟⠾⠟⠃⢀⣼⣥⠴⠤⠴⠶⠚⠃⠲⠌⠤⠂
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠁⠁⠈⠙⠒⠒⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⡔⠀⢃⠀⠛⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠄⣠⣴⡾⠳⡦⠂⠉⠹⣿⣆⠊⠀⠰⠀⠧⡀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢸⡿⢋⠄⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣡⠒⠁⠀⠀⠠⠂⢄⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⢰⣦⠀⣠⡀⠀⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠢⠵⠶⠈⠁⠀⠙⠁⢀⡴⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣤⠔⠒⢀⣀⣠⣤⣤⣤⣄⣉⡓⠈⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣐⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠠⣀⣠⣴⣾⣿⠿⢶⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠿⠁⠀⠉⠀⠀⢀⠙⠋⠀⠀⢀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠐⠀⠈⠢⠤⠀⠄⠀⠀⠀⠀⠀⠀⡜⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢢⡌⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⡄⠀⠀⠈⠙⠶⣄⡀⠀⠀⠠⠄⠛⠀⠈⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠚⠔⠠⡀⠀⠠⢄⠀⠀⣀⣤⣶⡮⠒⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠛⠛⣷⡙⠄⠚⠉⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠤⣀⠀⠀⠸⣧⠀⠀⡀⠤⠒⠉⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠀⠹⢀⠀⠀⠀⣾⣤⣴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡘⠂⠀⠘⠂⠈⠈⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠠⠀⡀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠖⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⢿⡄
⠀⠀⠀⠀⠀⢀⡄⣀⡏⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠸⠃⠀⠀⠀⢠⡴⣶⣦
⠀⠀⠀⠀⣴⣿⡏⡃⠁⠀⠀⠰⡿⠿⣿⡇⠀⠠⣶⣀⣤⡖⠀⠀⣀⢀⠍⠧⠀⡀⢻⣿⠺⡏⡉⣿⣅
⠀⠀⠀⡈⢀⠉⠚⠃⡠⠆⣤⣦⣿⣲⣈⣳⣶⣟⣿⣿⣿⣆⠠⡊⢱⡌⠀⠂⡆⠡⠀⠙⠿⣟⣻⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣼⣧⣯⣿⣷⡿⠛⠛⣿⣿⣿⢧⠀⠁⠈⠀⠀⠀⠓⠋⠀⠀⣾⣽⣿⠟⢿⣆
⠀⠀⠀⠀⡀⣀⣀⣀⠻⠿⠂⡿⣿⣿⡟⠁⠀⠐⣿⣿⣿⡎⠀⠀⢀⠠⠀⠀⠀⠀⢀⣴⣿⣿⠡⠰⠾⠟
⠀⠀⠀⠀⢱⢯⠉⡇⠀⢴⣿⣛⠿⠟⡇⠀⠀⢰⣿⣿⣿⣷⡄⠀⢸⠀⠑⠒⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠈⡞⡄⢟⠀⠻⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⣿⠀⠘⣦⣤⣶⡂⠀⠉⠿⠿⠿⠁
⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⢀⣈⠉⡹⣦⣴⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣟⠃⠀⠈
⠀⠀⠀⠀⢠⠃⡇⠘⡆⠀⣼⣿⢆⡼⢫⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⢸⣤⡇⠀⡇⣴⠋⣙⣿⣧⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣼⣿⣿⣿⡀⠀⠀⠀⢀⢀
⠀⠀⠈⠙⠋⠉⠛⢿⣻⡏⠒⠋⠁⠈⠙⠛⠿⣿⣿⣿⣿⠿⠿⠾⠿⠻⠿⠻⠿⠶⠠⠞⠋⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠚⠛⠛⠛⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠂⠢⠤⢀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⣀⣀⠀⠀⠠⠤⠤⠤⠄⠈⠒⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⣀⡀⢰⣶⡆⢠⣄⣀⣤⠀⠀⣼⠓⠒⠒⡞⣷⡀⠰⢤⣴⡄⢰⣦⠀⢀⢀⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠆⢠⠏⠲⠟⠀⢥⣾⡁⣸⣟⠧⢸⣇⣼⣀⡀⠿⠙⣷⡿⢋⡉⢿⣾⣍⣧⣜⡏⣹⣧⠀⣠⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⣆⣤⣄⣤⡄⢤⣤⢼⣿⣸⣿⠈⠳⡏⠻⡟⢩⡌⢠⣸⡷⠻⣇⠘⠛⠀⠈⠙⠿⢿⣽⣿⣿⣏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣉⣛⠿⠉⢿⣯⣿⣿⡏⠀⠻⠿⠟⢓⠋⢠⣦⡏⢻⡇⠹⠟⠀⠄⠀⠀⠀⣐⡀⠀⠀⡤⣄⣈⢙⣫⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣸⣿⣧⣽⣧⢿⡏⢘⠿⣿⣟⡙⢾⣷⢯⣽⣧⠈⣧⠁⢲⡇⢤⣖⠈⣽⢛⣿⣯⣿⠀⢹⣿⢛⢿⣦⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⣿⣧⣬⣇⣸⣯⣿⣤⣤⣿⣿⣷⣿⣷⣖⠛⠛⢻⣿⣿⣿⣴⣇⣿⣾⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠛⠲⠿⠿⢿⣿⣿⣿⡿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⠀⠉⠙⠻⣿⣿⣟⣩⣤⣠⣴⠲⢲⣄⢀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡶⠿⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⣽⠒⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⠈⠝⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣰⠆⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⡋⠹⠉⠻⠃⣤⡐⠿⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠖⠉⠀⠀⠀⠀⢰⠇⣼⠀⠀⢸⠀⣇⠀⠀⠀⠀⠈⠉⠻⢷⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⣠⡟⠀⣿⠀⠀⠈⣧⠈⢣⡄⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⣤⣴⣿⣀⣀⡀⣻⣧⣀⣿⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠰⠒⠲⠆
⠒⠒⠀⠀⠐⠂⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠂⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⢀⠤⠄⠀⠐⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠔⡤⠤⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠏⠉⠉⠉⠉⠉⠉⠉⠉⢟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠀⠈⠀⠀⠄⠶⠂⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠠⠀⠀⠀⠀⠀⢀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⣭⠂⢠⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢠⠀⠀⠀⡐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⡴⠂⠀⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠉⠀⠀⡘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠤⠴⠈⠁⠀⠀⠈⠀⠀⠁⠈
⠀⠀⢰⠀⠀⠀⠔⠀⠐⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⡐⠢⠀⠀⠠⠰⠀⢀⠔⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⡐⠀⠰⠂
⠀⠀⢸⣤⡸⣌⢀⡀⠀⠈⠀⠈⠉⠐⠃⠐⡆⠀⠀⡇⠀⠀⠀⠒⠁⠁⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⢀⠈⢀⠀⡐⠀⠈⠲⠒⠀⠠⢤
⠀⠀⠘⢆⠀⠀⠀⠨⠓⢄⠀⠀⠀⠀⠀⢊⠈⠁⠈⠰⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢰⠉⢱⠀⠀⠀⠀⠀⠀⠁⠀⡀⡄⣀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠈⢦⡀⠐⠀⠀⠀⠑⠠⠀⡀⢱⣎⠀⠀⠀⠀⣁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠁⢀⡆
⠀⠀⠀⠀⠀⠉⠒⠪⠥⠒⠂⠀⡂⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠈⢎⡅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠊⠀⠀⠀⠐⠈⠈⢢⠀⣤⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⠸⠁
⠀⠀⠈⠀⠀⠀⠁⠁⡀⠀⡠⠉⡏⢈⣡⠭⠅⠤⠀⠀⠠⠤⠛⣿⠉⠉⠉⠀⠀⠀⢀⠡⠠⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠈⠠⢀⡀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠰⠂⠑⠒⠃⠀⠀⠀⠀⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠢⡀⠤⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⣆⠤⠈⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⣂⡆⠸⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠆⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡌⡁⠀⠀⢀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂

⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⡀
⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣄⡵⢃⣾⡙⠁⠀⠻⣿⣿⣿⡟⠀⠀⢾⣾⠟⠀⠀⠀⠀⠀⢰⡄⠀⠀⠙⠷⠄⢃
⠀⢠⣶⠄⠐⢘⣿⣿⣷⡄⢠⣶⣶⣦⢸⡿⠛⢻⣧⠀⠀⠀⠀⠙⠁⢟⡌⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠆⠀⠉⠛⠶⠿⠀⣰
⠀⢸⡿⠀⠳⢺⣿⠀⢹⣿⣿⡏⠈⣿⣿⠇⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠲⢀⠤⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢧⡴⠂⠀⠀⠉⠓⣄⣴⠇
⠀⠘⣿⣼⣿⠟⢿⣿⡿⠋⠻⣿⣾⡿⠁⠶⣦⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⡜⢣⣄⣀⡄⠀⠀⠀⠀⠀⠀⢀⢰⡇⠛⠶⠀⠀⠀⠀⠒⢦⡘⠛⣠⠴⠃
⠀⠀⠀⠉⠀⣠⣄⡀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠟⠂⠤⢤⡀⢀⣤⣤⣿⣦⡽⠋⠀⠀⢀⣀⠈⠳⣌⢻⡴⢃⡾⣿⣧
⠀⠀⠀⠄⢰⣿⣿⡿⠁⠠⣴⣾⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆⠹⣆⡤⡟⢠⣿⣿⡀
⠀⠀⠀⠠⣬⠋⠩⠄⠻⠃⠉⠀⠀⠘⣧⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⠛⠻⠿⠛⠿⠛⠉⠀⠈⢣⠤⠇⠀⠙⠻⠏
⠀⠀⠀⠀⠰⠇⠹⠆⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣾⣿⡿⠀⠀⣠⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣆⠀⠀⠀⢸⣷⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠯⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣸⣿⣆⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢀⢀⣠⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⡿⠉⡁⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⣿⣿
⠀⠀⠀⣶⣀⠀⠀⠀⠸⡏⡟⣨⣭⣙⠿⠿⣿⢛⡏⠀⠀⠀⢀⣀⣀⣾⣾⠁⠀⣶⣄⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠛⢿⠿⠃⠀⠀⠀⠀⠀⣀
⠰⠶⠰⣿⣿⣷⠀⠀⠀⠙⢿⣽⣿⣿⠿⠶⣿⡮⠀⠀⠀⠀⠈⠛⠉⣽⡏⣿⡆⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⠁⠀⠐⢀⠀⠀⠀⠀⠀⠘⠋⠙⠁
⠀⠀⣀⡙⠛⢫⣤⡀⠀⠀⠀⠈⠉⠛⠓⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣿⡇⠀⣿⣷⠀⠀⠀⣸⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠙⠄⡀
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣿⡏⠀⠀⠀⣿⣿⣿⡀⠈⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⣶⣤⣤⣤⣤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣸⣿⡇⠀⢻⡇⠀⠀⠀⠹⡇⡈⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⣾⡋⢻⡇⢠⡝⣙⡆⠀⠀⠈⣿⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢺⣏⢉⣿⣿⠃⠀⠸⣿⠀⠀⠀⠸⣿⡷⠀⣤⡄⢀⠀⠀⠀⠀⠀⠠⢤⣤⣙⠛⢀⣤⣄
⠀⠈⠛⠛⠁⠀⠀⠁⠁⠀⠀⠐⣿⠀⠀⢸⣇⣠⡟⠀⣴⡆⠘⠇⠀⠀⠈⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢃⣀⣠⣤⣤⣄⣀⠉⠉⠁⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢸⡟⢿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠈⠹⠋⠀⠀⣠⡾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠿⢁⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣼⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣤⡟⠁⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⡠⠒⠂⡈⢻⣿⣿⢷⣤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⠀⠀⠈⠻⠿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠈⠈⣿⣧⣈⣿⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⣿⡄⠀⢀⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠠⠀⠀⠀⠰⠀⡋⢻⣿⣿
⠀⢠⣤⣴⣤⠀⠀⠀⠀⠐⢿⣿⡄⠀⢻⡇⠀⢸⣿⠁⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⣿⡋
⠀⢀⣹⡿⠟⠁⠀⣀⠀⠀⠀⠙⢿⡄⣨⣷⣶⣾⣷⣶⣴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠓⢺⣿⣧
⢠⣿⣿⠟⠀⠀⠰⢿⣿⣦⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⢋⣿⣦⡴⠶⠶⠿⠷⠀⠀⠀⣠⡄⠀⡤⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣠⠤⡀⠀⣤⣾⣶⣿⠘⡏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⣿⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⡼⢧⣠⡏⢸⣿⠀⢈⣿⢯⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠉
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⡿⠿⢿⡿⠿⠿⠿⣿

⠀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⢾⡃⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠟⠟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢐⣄⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠑⠤⢔⠦⠖⠀⠀⠀⠀⡤⢊⣠⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⢄⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠁⡀⠘⣥⣦⡗⠉⠈⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣃⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢦⡔⠀⠟⠃⣰⡄⠘⠂⠀⠀⠀⠀⠀⣰⣻⣿⣾⣿⣿⣿⣿⣿⠿⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣵⠞⡁⠀⠀⠀⠟⡇⠆⠁⠀⠀⠀⠀⠀⠉⠉⠋⠙⠛⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⢾⢁⠄⡄⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠁⠈⠀⠉⠀⠀⠀⠀⠀⡄⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣷⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⡇⠀⣧⠀⡄⠀⡀⠀⡄⢠⠄⠀⢀⠀⠀⠀⠀⠀⣴⠇⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⡆⠀⠀⠀⣀⠀⠀⡇⠀⣼⠀⣇⠈⠇⠀⡟⠀⠀⠸⠀⡤⠀⠀⠀⠀⣿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠐⠈⠁⠀⠰⠞⢉⠀⠘⣇⠀⢸⠀⢷⠀⠀⢠⣇⢠⡄⠀⣸⠁⠚⠀⠆⡀⣿⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣠⢦⠀⠀⡀⠉⣤⣀⠘⡶⢸⡇⠘⠋⡗⠁⢸⠀⢻⣄⣏⠘⠛⠦⠠⣤⡟⢸⡄
⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠈⡆⠀⠁⠘⣇⠀⠙⢿⠈⠟⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠙⢷⡄⢶⣄⢸⡃⣸⣷⠀⠀⠁
⠀⠀⠀⣿⣶⣿⣄⠀⠀⠀⠀⠀⢹⠠⠆⠀⢸⡆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠃⠀⠘⢻⡏⠁⢿⡀
⠀⠀⠸⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣷
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡛⠐⠋⠉⠉⠳⠙⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢻⣷⠆⠈⠰⣶⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠜⠛⣴⡾⢧
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⢶⣶⣴⣦⣶⢆⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠾⠂⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠾⠙⠾⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣬⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠀⠀⠠⠀⠀⠀⠛⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣻⣾⠛⡛⢻⡋⢛⡛⣶⠄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠒⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢩⣍⠁⠌⣆⠀⠀⠀⠀⠉⠛⠑⠣⠶⠿⠘⠲⠿⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢉⣹⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠛⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠦⠤⠤⠤⡤⠾⠿

⠟⠒⣢⠤⡄⠴⢶⣶⢤⠶⢶⡷⠀⣸⠇⠀⠀⠀⠀⢄⠀⢸⠤⢤⡖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡋⢰⠀⡇
⠀⣀⠃⠀⠀⡀⠈⠁⣀⣠⣀⣳⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠁⠘⠀⠁
⠎⢙⣇⠀⢦⠿⡀⠀⠀⣮⣽⣷⠄⠀⢐⠀⠀⠈⠁⠈⠑⠀⠀⡙⢫⠀⠀⠀⠁⢐⣀⠀⢰⡀⢈⠀⠀⣀⠀⣀⠀⠀⠀⢰⣶
⠰⠋⠋⡁⠐⢤⣽⢀⠀⡏⢿⣿⣰⠀⠘⠃⢀⡀⡀⣀⢀⠀⡀⢫⡉⡃⠀⠀⣀⢘⣁⣄⡛⢀⠈⡀⠈⢳⣦⢾⡶⠀⠀⠀⠏
⠣⠀⢌⠦⣠⡜⢷⡎⠠⣇⢠⡀⢻⣼⢀⠠⣼⣧⣤⢻⣼⣼⢧⠾⢿⢹⣅⠀⢉⢉⣿⠁⠀⣤⠄⡶⠰⠘⠘⠊⡑⠄
⠀⠐⢿⠀⢂⠶⢈⣻⢂⡘⢇⣭⢉⠅⠈⠶⠿⣿⠙⠙⢿⢃⠘⠀⣾⡍⢻⣧⣌⠩⣟⣾⡖⢻⡇⠃⡇⣄⠐⣰⠁⣐⡚⠈⠰
⡆⠐⡀⢣⣀⠘⣀⠻⠛⠳⡘⠡⣘⣌⣴⠴⡶⣼⣇⠀⣺⢿⠀⠈⡿⠉⠉⡻⠟⣴⠓⢫⠇⠽⣤⢰⣧⣭⠶⣛⣥⣴⡀⢀⡀
⢱⣰⣛⣞⠧⠀⡤⠄⠀⢂⣿⡂⣤⣾⠴⠆⢹⣿⡏⠠⠈⢠⣴⣤⣠⡾⢶⡐⠠⡁⣴⡇⠖⣸⢁⡁⡔⠳⠄⠈⠯⠙⠷⣦⡽
⠛⠉⣆⠀⠀⢘⣧⡦⠀⠉⣭⣅⠃⡘⠂⠠⣬⢙⣿⠴⢴⣘⣦⣝⠨⠄⡰⠀⣈⢁⣭⡁⣬⡄⡀⠁⠀⢠
⣄⣴⡟⠄⠀⣁⡿⠈⢘⣧⡅⣠⣤⣆⣈⠷⠄⠭⠁⢠⣌⣁⣝⣇⠠⣦⢓⣆⣴⣰⣿⡀⣄⢠⣧⣀⣠⡴⣤⣴⣄⣠⡀⡆⠠
⣾⡿⠗⢀⡄⠈⣰⣞⣟⠙⠘⠩⢁⡑⠛⣀⠦⣤⣾⣿⣿⣿⣾⢹⣅⠾⣺⣵⠏⠟⠿⣷⡸⣿⡟⢹⣿⠅⣿⣿⣿⣿⣇⠇
⡩⠃⠀⢺⡤⠀⣸⣾⡻⢟⠙⣠⣬⡷⠞⣟⣂⣩⡛⡿⢡⣿⡏⡌⣿⡐⣄⣉⣴⡗⣀⣿⡾⣿⠀⣿⣿⢰⣿⣿⣿⣿⣿⣾⠻
⢕⣡⠀⢹⣿⡀⢼⡿⣿⠿⣷⣿⣿⢀⣿⣭⣭⣭⡟⠀⣏⣿⠇⡇⣿⡶⢩⡍⠠⠱⢈⡿⣷⣿⢰⣿⣻⢸⣿⣿⣿⣿⣿⣭⣤
⢿⣻⡆⢹⣟⡇⢸⠿⠿⣻⣿⣿⠗⣺⠙⣋⠛⠟⣟⢴⡿⣿⣤⣧⣷⣦⣿⣿⣵⣶⣶⣿⣯⣾⣿⣿⣯⣸⣿⣿⣿⣳⡿⠭⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸
⠀⠀⠀⢰⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⠀⠀⠀⢠⠋⠀⠀⠈⠐⠁
⠀⠀⠀⠸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⠀⠀⠀⠘⣄⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠲⡄⠀⠀⡌⣯⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣠⠞⠉⠁⠈⠉⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠊⠉⠀⠀⠀⢸⠃⢀⠼⣦⣌⢮⠫⠹⣦⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢒⣒⣛⣿⣂⢃⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⠳⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠁⢄⣺⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⢠⠚⣧⣀⢀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⢻⢒⠲⠲⠲⢶⠶⢶⣻⠃
⠀⠀⠀⠀⠀⠈⠓⢀⣊⢿⣬⢊⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣢⣡⣠⢠⢡⢂⣶⠁
⠀⠀⠀⠀⠀⡼⠋⠉⠁⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡬⠛⠛⢛⣛⠻⠄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠥⠒⠋
⠀⠀⠀⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⢏⢫⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⡟⡸⡷⣤⣀⢀⢀⣀⣤⢞⢧⣇⢀⠦⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⣠⣴⡧⠲⢄
⢠⠭⠸⣧⡑⡑⡑⡘⡉⠍⣌⠆⢌⡿⠿⣿⠌⠘⠞⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣀⣤⣶⠿⠛⠁⠀⠀⠀⠑⢄
⢘⣃⣀⢘⣳⣽⣐⡈⡀⣈⣋⣼⣟⣉⣉⣿⡌⠎⡜⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠸⣷⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠐⠠⠤⠀⠉⠛⠿⠿⠿⠯⠵⢦⡴⠒⢺⡷⡐⡠⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠈⠉⠀⠂⢩⣥⡬⠍⠉⠀⠀⠀⠉⣷⠱⡁⣱⣿⣤⣤⣤⣤⣴⣶⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡩⠳⡶⡤⢤⡤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⠀⣻⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⢥⣁⡙⡱⡀⠃⣸⠃⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠉⠭⠿⡿⡏⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣚⣋⢽⠿⢶⣷⣽⡏⣰⠇⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⢨⢽⣏⣬⠺⣇⠀⠀⠀⠀⢠⡾⡋⠠⠡⠀⠉⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢹⡁⠉⠙⠛⢫⠩⠭⣰⠟⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⣿⣣⠐⠹⣆⠀⠀⠀⣼⣵⣶⣥⣥⣤⣠⠄⢄⢾⡆⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣐⣒⠘⣷⣠⠀⠜⠷⣄⣠⠯⠥⢶⠶⠿⠿⣿⣆⠆⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡒⠚⢧⣆⠊⢌⣼⠃⠀⠀⠀⠀⠉⣈⣉⣿⣾⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠛⠋⠁⢠⡞⠉⠙⠂⠒⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⢤⠶⠶⠚⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢣⣶⠆⢠⠎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣻⡙⠘⠀⠂⠀⠌⡌⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠂⠀⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⡀⠀⠀⠈⠉⠙⠛⠶⣾⡾⡚⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣀⢻⣆⢌⡘⠙⣦⡀⠀⠀⠀⠀⠀⠀⣀⢴⠞⢋⢃⢃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⠀⠹⢿⡄⠀⠈⠟⣦⡀⠀⣠⡴⡟⠉⢀⡀⣦⢾⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠬⢿⣎⠌⡐⡙⡝⠛⠱⠐⣐⣰⣾⢛⣋⣹⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢙⣾⣝⣐⣄⣠⣤⡷⠛⣉⢭⠥⠄⣿⢇⢞⢳⣤⣀⣀⣀⣀⣤⡴⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠤⠀⠚⢛⡛⠉⠙⠋⠁⠈⠘⠑⢛⣛⣿⣦⢧⢠⢩⢁⢉⢋⣦⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠤⠶⠖⠒⠚⠀⠀⠀⠀⠀⠀⢀⣒⣛⣛⣛⣿⠷⠞⢋⣉⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠭⠥⠤⠴⠖⠒⠂

⠀⣤⣤⡤⣤⣤⣤⢤⡤⠤⠤⢤⡤⠤⠤⢤⣤⠤⢄⠄⠠⠤⠀⠠⠀⠀⣠⡤⠄⠀⠀⡀⢀⠤⠀⠀⠀⠀⠀⣤⠠⢤⠠⠀⠤⠀⠀⠀⠠
⠀⡿⠟⠋⢻⣿⣄⠋⠄⠀⠀⠈⠑⠸⠃⠀⡱⠋⠉⠉⠀⠀⠀⣠⠀⣴⡷⠁⠘⢆⠀⠀⡞⠀⠢⠀⠀⠀⢰⢇⡀⠀⠱⡀
⠀⣿⢿⣷⣿⣽⣷⢀⢾⡦⠐⠂⠀⠀⠀⢱⡦⠄⠀⠀⠀⢤⣤⣀⣶⠯⠁⠀⢀⠈⢆⠸⡑⠲⡄⠀⠀⢀⠋⡈⠈⠀⠀⠙⢦⠹⣄⠀⠘
⠀⠏⠳⣹⣿⠉⢰⠟⠸⠁⠀⠀⠀⠀⠀⠸⢧⣐⣀⠈⠀⠰⠮⣿⡣⠁⠀⠐⡟⡀⣨⢦⠀⠀⣘⠠⢰⡎⠦⠀⠀⠄⠀⠀⠀⠑⣌⠢⣼
⠀⠀⠀⠘⣷⢄⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠿⠿⠷⠤⠴⠌⠋⠹⠷⠄⠳⠐⠿⠋⡁⠿⠔⠤⠀⠠⠀⠀⠀⠢⠸⠧⢸
⠀⣧⣤⣥⣤⢬⣿⠄⠀⢤⣤⢤⡤⣄⠠⠤⠐⠤⠂⠴⢆⠐⣶⠶⠂⠶⠶⠶⠶⢶⣶⠶⠢⡞⡚⢦⣤⣲⣆⠲⡖⢰⣶⣶⣶⡶⠈⢶⡆
⠀⡿⣿⠀⡿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠳⡈⠀⠀⠘⠒⣦⣔⢼⢸⡤⢸⡇⣸⡟⠹⠿⠋⠳⣄⠘⠚⠋⠈⠙⠛
⠠⣧⡾⠛⣡⡇⠀⣷⠀⡄⠙⠦⢀⠀⠀⢃⣽⠶⠒⠀⠂⠈⣽⢶⡂⠄⠀⠠⠀⠸⢚⠀⠀⡇⢈⠄⢀⣰⣞⡀⢁⠀⢀⠤⣤⠤⣤⣤⡼
⠐⣧⡿⠖⣿⠇⠙⠛⢿⠿⠚⠐⠋⠑⢦⡙⠢⠔⠒⠒⠀⠀⣤⠤⠀⠀⠀⠀⠀⢸⢸⠀⠁⠋⠃⣵⣉⠀⠀⠀⠀⢶⡜⠀⠁⡴⠇
⠐⣴⣳⠀⠉⠰⠶⠶⣶⠠⠶⠤⠤⠴⠤⠭⢃⢀⣀⠰⠶⠶⠿⠀⠀⠶⠶⠶⠦⠾⠶⠆⠛⣧⠀⠿⣿⣖⡒⢒⣻⡇⠴⠶⢶⢿⡄⠐
⠐⡿⠋⡜⣡⣰⡶⠶⠷⢤⠀⣒⠀⣀⣐⠒⣉⡩⠃⣀⡀⠀⣀⣀⢀⣀⢀⣀⣀⣀⣀⠀⡂⠑⠲⣠⣤⠀⣀⢠⣄⣉⣩⣥⣬⣿⣦⡸⣡
⠀⣷⡜⠐⠻⣛⠷⠚⠁⡖⠁⠒⠒⠀⡶⠴⠲⡄⢲⢿⣶⢦⡀⠲⠟⣟⢷⠮⡍⢯⡴⢋⣤⣼⡁⠀⠀⢀⣤⣤⣤⣤⣤⣤⡅⢠⣍⠀⣭
⠀⡏⢹⢉⣡⠄⠼⢦⣤⣦⣀⡖⡬⠄⠠⠤⣀⢱⣌⣡⠄⠉⠙⠲⠦⢤⣼⣶⣆⣲⣀⣻⣛⣒⣖⣀⣀⣠⣠⣽⣖⠂⠀⠤⠔⢾⡆⠷⠤
⣤⣭⣤⣭⣭⣭⣭⣥⣭⣭⣭⣭⣤⣤⣤⣤⣬⣭⣥⣬⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣥⣬⣭⣥⣭⣭⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿