Apprehensive Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⠋⠉⠉⠉⠉⠛⠛⠛⠲⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠋⠀⠀⠀⠀⠈⣧
⠀⣸⠃⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣼⠁⠀⠀⠀⠀⢠⡶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⠀⠀⠟⠀⠀⠻⠀⠀⠀⢠⡶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⠀⠀⠀⠈
⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⡇
⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀
⢹⡀⠀⠀⠀⠀⠀⢰⡏⠀⠙⡇⠀⠀⠀⠀⠀⠀⠴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⣇⠀⠀⠀⠀⠀⡾⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⣸⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢻⡄⠀⣰⠏⠀⠀⠀⣟⣀⣠⣤⡤⠴⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢻⡴⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⣤⣤⡴⠶⠶⠒⠛⠛⠲⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠖⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡄⠀⠀⠀⢀⣾⢻⡆⠀⠀⠋⠉⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⣷⠀⠀⣸⠏⠀⢸⣏⣀⣤⣤⡶⠶⠞⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠹⣇⣼⠋⠀⠀⠙⠉⠉⠁⠀⠀⣀⣤⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠶⠶⠶⠛⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⡀⠀⠀⠀⠀⣈⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⠞⠉⠉⠉⠀⠀⠀⠀⠉⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⠖⠛⠲⣄⠀⢀⡴⠞⠛⢶⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣰⡇⠀⠿⠿⢸⠆⢸⡅⠐⠿⠇⣿⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡞⠁⠙⠦⣤⡴⠋⠀⠈⠳⢦⣤⠾⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢧⡀⠀⢀⡼⠁⠀⠀⠀⠀⠸⣆⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠉⠛⠉⠀⣀⣀⣀⣀⣀⣀⠈⢛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⡤⠶⠚⠋





⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿

⠀⢀⡤⠒⠚⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡴⠒⠋⠉⠉⠓⠦⣄
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⡇⠀⠰⡦⠀⠀⠀⠸⠇⠀⠀⣷⠀⡎⠀⠀⠀⢠⡀⢠⡄⠀⠀⠀⠀⡇⠀⢰⠃⠠⣤⠄⠀⠀⠀⠞⠂⠀⢳⡀⠀⡏⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⢳
⡇⠀⠄⠀⠀⠀⠀⠀⢀⡆⠀⡏⠀⡇⠀⣠⠀⠈⠁⠀⠀⠀⠒⡇⠀⡇⠀⢸⠀⢀⣀⣀⣀⣠⣤⡤⣤⡄⠈⡇⠀⣇⠀⢻⠀⣶⠆⠘⠛⢀⡇⠀⢸
⠸⡄⠈⠳⠤⣄⣤⠤⠋⠀⡰⠁⠀⠱⡀⠙⠐⠢⠴⠢⠴⠓⠊⠀⢠⠃⠀⠘⣆⠈⢿⡤⡧⢾⠒⣷⠟⠀⣸⠁⠀⠸⣄⠀⠳⢤⣄⣠⠴⠚⠀⣠⠏
⠀⠈⠲⢤⣀⣀⣀⣀⠤⠚⠁⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⢀⣀⠔⠁⠀⠀⠀⠈⠳⣄⣈⠉⠉⠉⣀⡠⠞⠁⠀⠀⠀⠈⠳⢤⣀⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢀⠤⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⢦⡀
⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⢦⡀
⡼⠀⠀⠀⠤⠀⠰⠆⠀⠀⡀⢹⠀⢠⠏⠀⢠⡀⠀⠀⠠⢦⠀⠀⠘⡆⠀⢰⠁⠀⠀⠰⠀⠐⠀⠀⠀⠀⢹⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⢸⠀⠀⠉⠁⠀⠀⣀⣀⣀⡀⠀⡇⠀⢾⠀⠀⠀⢀⣀⠤⠤⢎⣇⠀⠀⡇⠀⡇⠀⠰⠷⠀⠀⠀⠰⡶⠀⠀⣿
⢳⡘⢄⠀⠀⠀⠀⠀⠀⣠⢏⡞⠀⠘⡄⠘⢯⡭⠭⠭⠵⣲⠞⠀⣸⠃⠀⠸⡄⠠⠚⢯⠇⠀⠀⠀⠈⠁⣰⠁⠀⢳⡀⠀⠀⠐⠉⠳⠀⠀⠀⣠⠃
⠀⠑⢤⣉⠒⠢⠤⢒⣊⠵⠋⠀⠀⠀⠘⢦⣀⠉⠒⠒⠊⢁⣠⠔⠁⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠑⠦⣀⡀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⢀⡤⠖⠖⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠲⠤⣄⡀
⢀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦
⡼⠀⠀⢦⡄⠀⢐⣴⠀⠀⠀⢸⡄⠀⣸⠁⠀⢀⠀⢠⠀⢀⡀⠀⠘⡆⠀⢸⠁⠀⠠⠀⠀⠀⠐⠀⠀⠈⣇⠀⠀⡼⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⡇⠀⠀⠁⠈⠀⠈⠈⠁⣀⠀⢀⡇⠀⡇⠀⠘⠉⠉⠀⠀⠁⠉⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⣀⣀⣀⣀⣀⠤⠤⠆
⠹⡀⠀⠉⠉⠉⠉⠹⠽⠁⠀⡼⠁⠀⢳⠀⠀⠀⠀⢾⡷⠀⠀⠀⣸⠃⠀⠘⣆⠀⠀⠀⣠⠤⢄⠀⠀⢠⠇⠀⠀⢹⡀⠀⢹⡙⣿⠀⠀⠀⠀⠀⢠
⠀⠙⠢⣄⡀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠈⠳⣄⡘⠁⠀⢀⣀⠴⠋⠀⠀⠀⠀⠙⠦⣄⣉⠁⠀⢀⣀⡤⠖⠋

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠂⢄⡤⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠤⣀
⠀⠀⠀⡰⠋⢠⣦⠀⣶⡄⢰⡀⠀⠀⠀⠀⢀⣀⣠⣤⡤⣀⠀⠀⠀⠀⣻⣡⣰⠛⠈⡋⣀⢸⡛⠀⠀⢠⡾⠁⢠⣦⠀⠀⣶⠀⠑⢄
⠀⠀⠀⢣⠀⠘⠋⡤⠉⠁⣠⠇⠀⠀⢀⠔⠉⣀⠀⠀⡀⠈⠱⡄⠀⠀⢿⠀⡄⠐⠐⠓⡦⠈⡇⠀⠀⣾⠁⠀⠘⠟⠀⠀⠛⠀⠀⠀⣷
⠀⠀⠀⠀⠑⠀⠀⠀⡴⠚⠁⠀⠀⠀⠇⠀⠀⠛⠀⠘⠇⠀⠀⢰⠀⠀⠘⢦⣑⢤⣠⢜⡡⠞⠁⠀⠀⣇⠀⢰⠊⠉⠉⠉⠉⢹⠇⠀⣼
⠀⠀⠀⡴⡄⠢⠺⠿⠁⢀⣀⠀⠀⠀⡄⠰⣄⠀⠀⠀⢀⠖⠀⠄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠸⣆⡈⠣⣀⡀⣀⣴⠏⢀⣴⠏
⠀⠀⠠⡃⣩⣭⠭⠭⠭⣍⣿⠀⠀⠀⠘⢦⣈⠁⠀⠀⣀⡤⠂⠀⠀⠀⠀⠀⢀⣤⠖⠒⠒⠒⠒⠢⣤⡀⠈⠛⠢⠬⡭⠭⠴⠚⠁
⠀⠀⠀⠉⠁⢀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣾⣤⣤⣤⣤⣤⣤⣤⣈⣻⣄
⠀⠀⠀⡴⠚⠉⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢢⡀⠀⠀⠀⠀⡟⠻⠿⠿⡿⠟⠙⣿⣿⣿⡿⣿
⠀⠀⡜⠁⠤⢤⡄⠠⠤⢤⣤⠹⡄⠀⠀⠀⠀⠀⠀⠀⠁⢀⠇⡀⠀⠀⠀⣧⠀⢦⡀⠀⠀⠀⠀⡬⠉⢠⡿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢆⡀⠀⠀⠁⠀⡼⡀⠀⠀⠘⢆⠀⠙⠂⠠⠶⠚⢁⣴⠟⠁
⠀⠈⢧⠀⠀⠀⢀⣀⣤⠾⠀⡰⠀⠀⠀⣼⠀⠀⠁⠀⢀⠔⠉⠀⣸⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠋⠁
⠀⠀⠈⠓⠦⢄⣀⣀⣤⡴⠞⠁⠀⠀⢠⠘⠢⠄⠀⠀⠀⢀⡠⠚⠁⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⡴⠀⠀⢰⡇⠀⠀⣶⠀⠈⢢
⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠦⣄⣀⣤⠶⠶⠶⠶⢶⣏⣸⠀⠀⠀⡇⠀⠀⠘⠃⠀⠀⠋
⠀⠀⠀⢰⠃⠀⢺⠆⠀⢿⠂⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡼⠋⠀⠀⠀⠀⢀⣀⠈⢿⡄⠀⠀⡇⠀⢶⡀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⣯⠀⢀⣄⠀⢀⣀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡤⠶⣦⡀⢰⡏⠀⠀⠈⣿⠀⠀⠹⣄⠀⠑⠦⠤⠴⠚⠁⠀⡐
⠀⠀⠀⢻⡄⠘⠈⠓⠞⠀⠙⠛⣠⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⣰⠀⢠⡏⠀⠀⠀⠈⠓⠦⠤⣤⣤⠤⠔⠊
⠀⠀⠀⠀⠙⠳⠤⢤⣤⣤⠴⠞⠁⢀⣴⠞⠋⠉⠉⠉⠒⢄⡀⠀⠱⡀⠀⠓⠄⣠⣤⠴⢃⣴⠟⠀⠀⠀⣀⠤⠔⠢⠤⣄
⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⢀⡾⠃⠀⣾⡆⠀⢸⡇⠀⠙⢆⠀⠈⠐⠀⠤⠤⠀⠀⠉⠀⠀⠀⢀⡞⠁⣤⠀⢠⡄⠈⠳⡀
⠀⠀⠠⠊⢠⠀⢠⠀⠑⠀⠀⠀⢸⠇⠀⢀⣙⣁⣀⣈⣁⣀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠀⣈⣁⣀
⠀⠀⠀⢀⠀⠀⠈⡠⠀⠀⠀⠀⠸⡆⠀⢏⠀⠀⠀⠀⢠⡟⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠏⠇⢰⠐⣆⡇⢸
⠀⠀⠀⠄⣁⣀⣀⡠⠂⠀⠀⠀⠀⠹⣦⡈⠢⢤⣤⠴⠋⣀⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠉⠉⠉⠉⣁⡰⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢰⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀⠀⠀⠀⢻⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣀⣴⠾⠟⠛⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⣶⡾⢶⣦⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⣠⠶⠞⠲⡄⠀⠀⠀⠀⠀⠀⣸⠋⢩⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣰⡿⠋⠉⠉⠉⠉⠉⠙⠛⢷⡄⠀⠀⠀⠀⣿⠀⠶⠀⣿⠀⠀⠀⠀⠀⠀⠸⣦⣈⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣤⣀
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷
⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠙⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋
⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⣠⣤⣄
⣴⡾⢻⣿⠀⠈⠛⠿⠿⣧⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡶⠾⠿⠛⠉⠀⠀⠀⠻⣧⣿
⠛⠿⠟⠋⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣶⠾⠟⠻⣷⣤⡀⠀⠀⠀⣀⣼⠟⠻⣶⣤⣄⣀⣀⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠁⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⢀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣴⡾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠋⠉⠉⠉⠛⠛⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠤⠴⠺⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⢷⢀⡤⠄⠀⠀⠀⠀⠀⠀⠤⢤⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⢁⡘⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣠⠖⠛⢲⡘⣿⡷⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠁⠀⠀⠀⣷⡇⠀⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⢦⣀⣀⠀⠉⠀⠐⢯⠇⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⣧⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⡟⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠦⣤⣀⣀⣀⣀⣀⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠦⣄⠀⠈⠹⡯⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⢤⣀⠀⠈⠙⠲⣄⣻⣼⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⢻⡓⠶⢦⣠⡽⢿⡀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⢳⡀⠀⠀⠀⢸⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡏⠀⢹⠀⠀⠀⠀⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠼⠤⠤⠾⠤⠤⠤⠴⠧⠤⠼⠿⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⣤⣞⠤⠒⠩⠿⠒⠉⠵⠧⠒⠊⠉⡽⠁
⠀⢀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢺⠇⠀⠀⢸⣧⣿⣷⣟⣷⣼⣶⣼⡇
⠀⢸⠀⠀⠀⣀⢴⡮⢴⣖⣀⠤⢤⠆⠀⣀⣀⢠⣯⠀⠀⠀⠈⠋⠛⠃⠛⠛⠈⠟⠻⠁
⠀⢨⠀⡠⡪⠁⠤⣀⠈⠁⠀⠀⠚⠉⠉⠁⡏⢀⠏⠀⠀⢠⣤⣄⣠⣄⠀⠀⣤⣄⢠⡴⣤⠀⣄⢠⡄⡀⣄
⠀⢸⣿⠀⣠⠒⠢⡀⠀⠀⠀⣀⠔⠀⠂⢸⠀⡞⠀⠀⠀⠈⣿⠉⣿⣽⡇⠀⣿⣽⢿⡿⣯⣸⣿⣿⣿⣿⡟
⡜⠉⡽⢸⠛⠀⠀⢹⠀⠀⢸⠗⠒⠒⡲⢸⠋⢣⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠁⠈⠁⠀⠀⠀⠁⠈⠈⠁
⠳⣠⠇⠈⠢⣀⡠⠋⠀⠀⠘⠦⡠⠴⠁⠘⡄⡸⠀⠀⣴⣦
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⡏⠁⠀⠀⠟⠻⠂
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢰⠃⣀⣀⢀⠀⡀⠠⢀⠀⡀⠀⠀⠠⠀⡀⣀⠀⣀
⠀⠀⠘⢦⡀⢀⡀⠀⠀⠀⠀⠃⠀⢀⡰⠃⠀⠉⡏⢹⠶⣿⢰⣸⢷⡇⣿⣏⢰⣢⢷⡟⢸⣡⡄
⠀⠀⠀⠀⠙⢇⠙⠦⠔⢊⡩⣣⠖⠋⠀⠀⠀⠀⠁⠈⠀⠁⠈⠈⠈⠁⠁⠈⠈⠉⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⡗⠁⠀⠀⠀⠀⠀⡴⠆⢠⢄⠀⡴⠆⡤⠄
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠿⠉⠜⠺⠌⠷⠄⠯⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣙⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀
⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣶⣦⠀⠀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⣼⡿⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⢀⣾⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣧⠀⠀⠀⠈⢿⣿⣷
⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⣿⡇⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⣿⠁⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠸⣿⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⣿⡆
⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣶⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣶⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢻⣿⣿⠀⢠⣶⡿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠘⣿⣿⡆⢸⣿⠀⠀⠀⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⢹⣿⣿⡘⣿⡄⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠉⠻⠿⠶⣶⣶⣶⣶⣶⡾⠿⠿⠿⠛⠛⠛⠉⠉⠉⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣷⣶⣶⣶⣿⠿⠋

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣤⡀⢠⠟⢦⡀⢀⣀⡤⠞⠛⠁⠀⢺⡀
⠀⠀⢀⣀⡴⠊⠁⠀⠀⠀⠀⠉⠉⠓⠒⠊⠉⠓⢦⠀⠀⠀⢠⡞⠁⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⣷⠀⠐⠲⡄
⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡠⠋⠀⠀⡤⠤⣤⣄⣤⢤⡀⠀⠀⠀⢀⡤⣄⠀⠀⢸⣆⠀⠀⠹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢷⠀⠀⠐⠋⠀⠈⢷⣄⠀⠉⠛⢶⡄
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠈⠣⠤⣀⣀⡀⠀⠠⢄⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠉⠛⠀⠀⢸⡇
⠈⠦⣀⣀⡤⢤⣀⠀⠀⠀⣀⣀⣀⣠⠴⠶⠶⠃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢺⣀⠀⠀⠀⢀⣀⠀⠀⠀⢧⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⣀⡩⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⣆⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⣈⣉⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠞⠉⢩⠗⠴⣄⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠤⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⠀⠀⠉⠓⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⠀⣀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠙⢦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠶⠛⠉⠀⠀⠀⠀⢀⣴⠎⠘⡇⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⢠⠏⠓⡾⠁⠀⢹⡀⠀⠀⠀⡀⠀⠀⢀⡤⠶⠒⠲⣤⡀
⣠⣤⢠⣄⡾⠀⣰⡁⢸⣡⠀⣧⠀⢀⡴⠁⢀⡔⠁⠀⠀⠀⠀⠈⢷
⠷⢫⢩⣄⠀⠀⠀⠈⠳⡄⣔⣿⡆⢉⡤⠲⢾⢀⡀⠀⠀⠀⠀⠀⣸
⠀⠈⠁⠘⣆⢀⡴⠲⢤⡝⢮⠁⢹⡏⠀⠀⢨⡿⠟⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠈⠉⠀⠀⣀⣙⣭⡇⠈⠳⢤⡤⣾⠦⣄⣀⣀⣀⣴⣏⣀⣠⣤⡤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⡖⠲⢤⡀⡀⣄
⠀⠀⠀⠀⠀⠀⢰⠋⣭⣾⢭⠳⠀⡀⠀⠔⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢳⡀⣸⠳⠷⡏
⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣤⡄⠰⠵⠀⡠⢆⠀⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣏⣹⣿⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⠀⠙⠋⠀⣍⡆⠀⠀⠙⠲⢤⣀⠐⠠⠄⣄⢀⡀⣀⣠⠟⠀⠀⣠⢴⡁⠈⣯⡞⡫⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢨⣱⢀⠴⡀⢀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡖⠚⠒⢻⣹⠁⠀⠀⠀⠙⠀⣉⣽⣩⠧⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⡇⠀⠀⠈⠛⠁⠧⠇⠀⠀⠀⣀⣀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⡷⠴⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡛⠤⣿⡀⠀⠀⠀⠀⢀⡤⠶⡎⠙⠍⠳⡄⠀⠀⢸⣄⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⣹⠲⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⣐⠈⠉⠒⠒⠾⠭⠄⣀⣙⣦⣶⣚⣁⣀⠀⠈⣧⠿⠍⠉⠉⢧⠀⠀⣠⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠙⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠙⣶⣿⠀⢤⡀⠀⣸⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠉⠉⠓⠲⠤⢤⣀⡾⠀⠀⠀⠘⠀⠀⠳⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧⡠⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⡄⠀⢸⡀⠀⠀⠀⢀⣀⣀⣀⣤⡤⢤⡖⣲⠋⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠻⡀⠈⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⡜⢠⠇⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣎⠓⠀⢱⡀⠀⠀⠀⣀⣀⣀⣠⣎⣠⣋⣀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⢥⡄⣀⡜⠁⠀⠀⠀⠀⠊⠉⣿⣉⣉⡥⠤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⡒⠒⠒⠚⠹⣏⠉⠉⠉⠉⢉⡩⠕⠛⠧⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⠛⠛⠻⣝⢦⣀⣀⡼⡆⠀⠀⠀⡯⣀⣀⣠⠴⣒⡿⠿⢍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣒⣛⣛⣩⠬⠭⠖⠊⠁⠀⠀⠀⠑⠲⠤⣉⣉⡓⠒⠶⠤⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠲⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⣀⡴⠛⠉⡠⠒⢁⡞⣠⡴⠶⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢧⠞⠁⠀⣠⠊⠀⣀⠾⠋⠁⢀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡼⢁⣀⣴⣯⣤⡴⠛⠉⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡄⠀⣀⡤⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢠⡎⠈⠑⠦⡀⠀⠀⢰⣦⣟⠀⢸⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡠⠚⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠛⠀⢀⡾⠁⢈⡷⠋⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠛⠓⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⣤⠒⠒⣲⠄⠀⠀⣼⡀⢀⡜⠁⠀⠀⠀⠀⠻⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⢻⠀⠀⠀⠠⣔⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠹⠴⠛⠁⠀⠀⠀⡿⠌⢸⡇⠀⠀⠀⠀⣠⠞⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠀⠘⣇⠀⠀⠀⠈⠛⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠞⠹⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡆⠀⠀⣴⠉⠀⠙⣆⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡤⢿⠀⠀⠀⢿⣤⡤⠶⠶⠶⠟⢋⡇⠀⠀⠀⡄⠀⠀⢹⡙⠛⢻⠏⠀⢸⡍⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢇⠀⠀⠘⢧⡀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢳⡄⠀⠀⠉⠈⠁⠀⠀⢸⣇⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠷⣤⣘⡄⠀⠀⠀⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⠶⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣴⠾⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣰⣿⣿⣷⣭⣿⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢠⣇⡘⠻⣿⣿⡏⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢰⠋⢙⡷⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠁⠉⠙⠻⠿⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⡞⠙⠓⢾⠁⢀⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣛⡭⠿⠿⢷⣶⡦⠤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡆⠂⢴⡿⠤⡎⣀⡾⠁
⠀⠀⠀⣠⠶⠚⠛⠛⠉⢁⡴⠚⠁⠀⠀⠀⠀⠸⣤⣤⣬⠿⣤⣀⠀⠀⠀⠀⢀⣠⡴⣏⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⢀⡀⠠⠘⠁
⠀⠀⣾⠁⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⡼⠉⠛⠛⠛⠛⠋⣹⣦⢘⣷⠀⠀⠀⠀⢀⣤⠞⣡⡴⠋
⠀⠀⠉⢶⠁⢀⡀⢀⣀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡇⠀⢀⠀⠀⠀⠀⠌⢿⠟⠙⠻⢶⣶⣾⡯⠶⠚⠁
⠀⠀⠀⠈⠛⣿⡀⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠀⠀⣹⠗⢐⣶⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣘⠀⠙⠃⠀⠾⠏⢀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦⠀⠀⠀⠀⠀⢀⣿⣤⣀⣀⠈⠛⠛⠶⠶⠶⠶⠖⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣼⠏⡰⠃⢸⣇⠀⠀⠀⠀⢸⡗⠀⠉⠉⠙⠛⠓⠶⠤⣤⣄⣀⣀⣼⠁
⠀⠀⠀⠀⣠⡿⢡⠞⣀⣴⣏⣹⡄⠀⢀⣴⠞⢻⣇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣹⠏
⠀⠀⢀⣾⠋⡴⠃⠰⣿⡟⢿⡀⢻⣄⣼⣿⣄⠀⢙⡷⣴⣆⡀⠀⠀⠈⠙⠛⣺⡧
⠀⣰⠟⣡⠞⢦⢀⣴⠋⠀⠈⢷⣀⣩⡼⠋⠙⠛⠉⠀⠀⠈⠙⠳⠶⣤⡶⠿⣿⣟⡳⠶⣤⡀
⣼⣋⣴⣁⣠⡾⠟⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠆⢀⡿
⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣥⣼⣿⣶⣶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠧⣄⣀⣀⣙⠉⠁⠀⠀⡔⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⣶⣦⣭⣤⣭⣉⣉⣛⡓⠶⠶⡤⢿⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣙⣛⣛⣿⣷⣿⣇⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣛⣛⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⢊⣭⣍⢺⣿⣿⣟⣋⡥⠾⢿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⡘⠿⠟⣸⣿⣿⣿⡏⢼⣿⡇⢹⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣴⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⠟⣩⢹⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠟⣡⣾⣃⣚⣛⣛⣛⣛⡛⢦⡙⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣭⣭⢉⣭⣥⣾⣷⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠷⠶⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣛⣛⣛⣛⣃⣼⣿⣿⣿⣿⣿⣿⡿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣭⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⢀⣶⡦⠀⠀⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⣿⡿⠁⠀⠀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁
⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⢠⣾⡿⠃
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠻⠟⠀⠀⣠⣄
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⢰⣿⡏⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠉⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠉⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣷
⣼⣿⠁⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠉⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⣀⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⠿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠶⠿⠛⠛⠛⠛⠛⠿⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣇⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠈⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣠⠟⠳⠶⢤⣤⣄⣀⣀⡀⠀⠴⠶⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢋⡿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠰⢶⡦⣤⠀⢼⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠀⡆⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠀⠀⠀⠤⠬⣿⣷⣶⣤⣉⠋⠀⠘⠀⠙⠚⢋⣉⣀⣠⣤⣤⣤⠄⠀⠀⢸⠃⠘⡇⠁⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⣸⡏⢀⣀⡇⠀⠀⠀⠐⠒⠒⠚⠛⠛⠉⠀⠀⠀⠀⠀⠛⠛⠿⠿⣿⣟⣛⠛⠓⠀⠀⡿⠀⠀⣿⠀⠀⢀⣰⣿⣄
⠀⠀⠀⠀⠀⠀⠸⢧⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣧⠀⠀⣿⣀⣔⣭⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⢀⡁⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⡿⠟⢿⣄⣠⣄⡀⣠⠿⠒⢒⡿⠛⠿⣍⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠶⠖⠛⠋⠁⠀⠀⠀⠀⠉⠛⠿⠿⠷⠶⠶⠛⠁⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠞⣦
⢀⣠⣤⣾⠙⣦⡴⠞⠉⠈⢿⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠷⣄⡀⠀⠀⣀
⢺⣥⣌⠉⠀⠀⠀⢀⣤⡴⠟⣷⡀⢀⣠⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣇⠀⠈⠙⠶⠞⢹⣧⣤
⠿⢥⣴⠆⣠⠶⠛⠉⠀⠀⠀⠙⠛⠛⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⢦⣀⡼⠃⠈⠻⢦⣄⠀⠀⠈⢁⣤
⠀⠀⢿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠀⠀⠀⠈⠑⢦⠰⣦⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⠛⠛⠛⠲⠶⠶⠶⠶⠶⣤⣤⣤⣤⡴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡶⠶⠶⠦⢤⣤⣤⣤⣤⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⡀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠉⢉⣀⣹⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠉⠉⠉⠉⠈⠉⠉⠙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢾⠟⢛⠛⠻⡷⠀⠀⠀⠀⠀⣠⣴⣶⠿⠃⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠛⠛⢉⣠⣤⣀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⢰⡿⠋⠙⢻⣷⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠘⠿⢷⡾⠟⠃⠀⠀⠀⠀⠀⢻⣷⣀⣀⣼⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⣠⣾⠿⣿⡆⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⣼⡧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⡿⢃⣼⡟⠁⠀⠀⠛⠛⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⢗⣴⡿⠋⢠⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⡀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣿⠇⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⡯⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣀⣀⣀⣀⣈⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠻⣵⣦⣤⣤⣀⣀⣀⣀⣤⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠿⠀⢈⠋⠈⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣦⠈⣩⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠿⣿⡿⠏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠛⠻⠿⠏⠀⢹⣇⣠⣤⠀⣰⠛⠻⠿⠃⠀⠹⣿⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡷⠀⢀⣤⣤⣤⡀⠉⠁⢙⣿⣿⠆⢀⣴⣶⣶⣤⠀⠀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⣿⣇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⢹⡷⠀⠙⢿⣿⣿⠿⠁⢠⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⡀⠈⠛⠛⠛⠁⠀⣼⣿⣿⣧⣠⣤⡀⠀⢀⣀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣶⣦⣀⣼⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⣠⣾⡿⠋⢀⣤⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣴⣿⠋⠀⠀⠻⠛⠉⠉⠉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣦⣤⡀⠀⠈⢿⣷⡀
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠈⣿⣧
⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠿⠿⠿⠿⠿⠿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⢻⣿⡄⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠻⠟⠀⠀⢀⣿⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣿⣿⠀⠀⣀⣠⣤⣴⣶⣿⡿⠿⠛⣋⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣿⣿⣾⡿⠿⠛⠛⠉⣥⣴⣶⣿⠿⠿⠛⠁⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣹⣿⡇⠀⠀⠀⢀⣠⣴⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⠃
⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⠿⠿⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⣤⡴⠶⠶⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠞⠋⠉⠀⢀⣠⡄⠀⠀⠀⠠⣌⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠠⢾⣿⠁⠀⠀⠀⠀⠿⢋⠀⡠⠀⢠⡀⠘⠷⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢰⢃⣞⢣⠀⢰⢻⣦⣂⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠆⠀⢰⠄⠀⣸⣿⡏⢸⠀⢸⠘⣿⣿⣄⠀⠀⠸⣦⠔⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⢿⠀⠈⢳⡀⠀⡞⠀⢾⣆⠀⢰⠋⠀⢰⠀⣿⣞⣽
⠀⠀⠀⠀⠀⠀⡞⠡⡙⠦⠘⠋⠀⠈⠣⣭⠉⢀⡀⠈⢧⡉⠵⡋⠀⢸⠃⢹⣍⡇⠀⠀⡤⠖⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢻⡿⢹⣆⠀⠀⣿⠀⠉⠁⡀⢨⣤⣄⣀⠙⠲⣄⠀⠘⠃⠘⣿⠁⠀⠀⢀⡩⠴⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣀⢰⣿⠀⠀⣰⠃⠀⠀⠀⠈⠙⠒⢚⠀⠀⠀⠀⣿⠀⢀⡴⠋⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠘⠛⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣸⡏⣰⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣧⡴⠖⢒⣒⣀⠒⠲⢤⣸⠀⣴⡟⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠹⣧⡀⠘⢁⠀⠀⠀⠀⠀⠀⠀⢀⣬⠾⠋⠀⢸⡀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣝⡓⠲⣿⣦⣤⣤⣤⣤⡶⠋⠀⠀⠀⢀⡀⢉⢾⣤⣀⣀⠴⠋⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡜⡴⠓⣋⡤⣾⣧⢭⣽⣍⡗⢦⠀⠀⡰⣇⢙⢿⣁⡏⠀⠠⠔⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣿⠆⠀⠀⠸⢞⡟⣿⠓⠄⠋⠀⣯⡳⣄⣷⢈⠏⠀⠈⢳⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠁⢀⣀⣀⣠⡞⢁⣿⠀⠀⠀⠐⢿⡵⢉⡹⣌⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠠⣇⡀⣀⡴⠋⠀⠀⢸⣤⣾⣿⣧⣥⣤⣄⣸⡇⢾⠀⠈⢡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣤⡶⠶⠶⣶⡌⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢿⣙⢿⡃⢻⡇⠀⠀⣿⠁⣼⣋⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠭⠤⠖⠒⠚⠃⠀⠀⠀⠀⠈⠈⠷⠤⠤⣈⡓⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠿⠟⠛⠛⠻⠿⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⠁⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⣴⠾⠷⣶⡄⠀⠀⠀⠀⢰⡿⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠻⠃⠀⣾⠏⠈⢻⡆⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⣷⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⢿⡆⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⡦⠀⠀⠀⣠⣶⠟⠉⢀⣴⡿⠃⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⢀⣤⡾⠛⠁⣠⣶⠟⠉⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠙⢷⣄⠀⠘⢿⣦⡀⣀⣴⠿⠋⠀⠠⡾⠛⢻⣦⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠈⢻⣦⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⣤⣾⣧⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣄⡀⡀⠀⢀⠀⢀
⠀⠀⠀⢀⡂⠀⠀⠀⢀⡀⠄⠀⠀⠉⢀⣨⡄⣤⣈⠀⠀⠀⢀⡤⠒⠤⠀⠀⡤⠒⠤⠀⠰⡀⠉⢀⠁⠀⠀⡆⢂⠀⠀⠁⠘⠿⠗⠀⠁⠻⠿⠇
⠀⠀⢀⠻⠟⠀⠀⠀⠙⠃⡐⠀⠀⠀⢛⠋⠀⢈⣉⠁⠔⠀⠈⢴⡶⠄⠀⠀⠴⣾⠆⠀⠀⠀⠑⠊⢠⣤⡄⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠰⢤⣤⠴⠀⠦⣤⡤⠆⠀⠀⠀⠀⠀⢠⠐⠋⠀⠀⠀⠀⢄⡀⢀⠀⠀⠀⠀⣠⠀⠀⠈⠀⣽⣿⠀⠐⣶⣶⠀⠀⠐⠒⣢⡀⠀⡠⠀⠣
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⣀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠁⠀⠀⢖⠛⢋⠄⠀⠈⠓⢦⠃
⠀⠀⠀⠀⠉⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠲⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠃⠀⠀⠀⠀⠀⠀⠀⠬⠵


⠀⠀⠐⣈⣉⢀⡄⠀⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠤⠤⠀⠀⠀⠠⣀⢀⠀⠀⣀⣤⡀⠀⠀⡀⠄⠒⠅⠀⠀⢀⣀⠀⠀⠀⡀⢀⡑⠀⠀⠀⠄
⠀⠀⠀⠙⠻⠞⠃⠀⣿⡾⡋⠀⠀⠀⠀⠸⠿⠿⠅⠀⠀⠀⠀⠀⠻⠟⠀⠢⠛⠿⡃⠀⠀⠀⠘⠷⠀⠀⠄⠶⢀⠀⠀⢾⣾⣉⡇⠀⢠⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠙⠉⢀⣀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⡠⠄⠀⢀⣀⠠⠀⠀⢠⣒⡤⣦⡀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠂⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀
⠀⠀⠈⠙⠋⠀⠀⠉⢋⡠⠂⠀⠈⢿⣿⣾⠇⠀⠺⣿⢧⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⡶⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⣤⣶⣾⠿⠿⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠿⠿⠿⢿⣶⣦⣄
⠀⠀⣸⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠿⠀⠀⣀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣦⠀⠀⠀⢻⣇
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠈⣿⡄
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⡾⠁⠀⠀⠀⢹⣇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣤⣤⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠁⠀⠈⠁⠐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢰⠂⠀⠀⠠⢄⡀⠤⣀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠁⠘⠀⠀⢄⠀⠀⠉⠒⣝⠢⣉⠢⢕⣦⡀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠺⠃⠂⠀⠀⢀⠀⠀⢄⢠⡉⠢⢄⠀⠈⠑⠢⢕⣄⠙⢷⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠤⡀⢀⠂⠷⣄⣢⡓⢝⠲⢤⣉⠒⢄⡀⠀⠈⠑⠦⡉⢧⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠃
⠀⠀⠀⠀⠀⢀⠃⡄⠀⠀⢰⠋⠑⠉⠐⠂⠥⠝⢻⠷⢾⣿⣯⡢⣈⠢⡀⠀⠀⠈⠢⣃⠀⠀⠀⠙⠢⢄⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠈⠂⠀⠀⠠⡙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⣇⠴⠒⠲⠶⢤⡄⠀⠀⠀⢠⡴⠶⠒⠒⢿⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠉⠀⠀⠉⢒⡄
⠀⠀⠀⠀⠀⢸⠀⢃⠀⠀⡇⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠑⣄⠀⠀⠀⠀⢷⠀⠀⠀⠳⠖⠒⠒⠒⠋
⠀⠀⠀⠀⠀⡎⡄⢨⡄⡇⢰⠙⠃⠘⠛⠀⠁⠀⠀⠀⠈⠀⠛⠓⠈⠋⠀⠙⢧⠀⢡⠀⠈⡀⢧⣀⣩⡄
⠀⠀⠀⠀⠀⢱⢸⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠘⡆⠀⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣾⠀⢠⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⡿⢀⠏⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⢻⠀⢸⢰⠁⣻
⠀⠀⠀⠀⠀⠀⡇⢸⠀⢿⢻⡄⠀⠀⠀⠠⠀⣤⣤⣤⠀⣀⠀⠀⠀⠀⡏⣼⠀⣼⠃⡰⡃
⠀⠀⠀⠀⠀⠀⡄⠸⠀⠘⡘⣷⡀⠀⠀⠀⠲⢤⣤⡤⠖⠁⠀⠀⢀⢼⠁⡇⡰⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠱⠀⢣⡀⠇⡇⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢸⠀⡱⢁⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⠀⠃⡷⠃⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⢀⠁⠆⣾⠁
⠀⠀⠀⠀⠀⠀⢸⠘⡆⠈⡟⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⣼⣿
⠀⠀⠀⠀⠀⠀⡜⠀⣧⠀⢧⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢸⠇⢡
⠀⠀⠀⠀⠀⢰⠇⠀⡿⠀⡘⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⡄⠀⢣
⠀⠀⠀⠀⠀⡏⡇⢸⠃⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⢁⠁⠀⠁
⠀⢀⣀⠠⠄⠛⢅⡘⠀⡘⠡⡀⠷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣿⠀⢸⢀⠀⡀⠲⠄⣀⣀
⠉⠁⠀⠀⠀⠀⠈⣡⣼⣡⡔⠱⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⢨⠌⡀⠀⠀⠀⠀⠀⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠞⠉⠈⠉⠙⣧⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢹⡿⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⠻⢦⣄⠀⠀⠀⢀⣠⠾⠋⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠆⠲⠋⠀⠀⠀⡠⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠐⠀⠀⠂⠘⡆⠀⠀⠀⠀⠀⣸⠁⡀⠀⢀⠀⢳⠀⠀⠀⠀⠀⠀⡞⢐⠂⠀⠘⠈⣇⠀⠀⠀⠀⠀⢠⠋⢨⠀⠀⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠘⣄⠈⠓⠚⠁⢠⠇⠀⠀⠀⠀⠀⢹⡀⢁⠤⡌⠁⡼⠀⠀⠀⠀⠀⠀⢧⠘⠶⠶⠞⢀⡏⠀⠀⠀⠀⠀⠸⣄⠀⠰⠆⠰⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠂⠐⠈⢳⡀⠀⠀⠀⠀⠀⢠⠋⠐⠀⠐⠙⢧⠀⠀⠀⠀⠀⠀⡴⠻⠆⠀⠾⠙⡄⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠻⢿⡃
⠀⠀⠀⠀⠀⠀⢸⡀⠡⢀⠀⠜⢀⡇⠀⠀⠀⠀⠀⢺⡈⠀⢀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡇⠂⠀⠂⢀⠂⡗⠀⠀⠀⠀⠀⢸⡀⠐⠂⠐⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠘⡿⣇⣀⣀⡵⠋⠀⠀⠀⠀⠀⠀⠙⢦⣀⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⢤⣐⣂⡤⠎



⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⢰⣶⣋⣉⣉⣳⡦⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢙⢦⡀⠀⠀⠀⠀⠀⣘⡴⠺⠉⠉⠗⢆⣃
⠀⠀⠀⠀⠀⠀⢸⠁⣀⡀⢀⣀⠈⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⡏⢐⣀⢁⣀⡀⡇⠀⠀⠀⠀⠀⢹⠁⣆⣀⣀⣰⠈⡏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠠⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⣄⠐⠤⠐⣠⠞⠀⠀⠀⠀⠀⠀⠳⡌⢙⡿⠿⠳⠃⠀⠀⠀⠀⠀⠘⢧⣘⠛⠉⣁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉


⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⣸⢁⠁⠀⠈⠀⢳⠀⠀⠀⠀⠀⠀⡞⠐⠂⠀⠘⠈⡇⠀⠀⠀⠀⠀⢰⠋⡈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠘⣄⣄⠈⠉⠀⢠⠇⠀⠀⠀⠀⠀⢹⡀⢠⡤⡤⠀⡼⠀⠀⠀⠀⠀⠀⢧⠈⠒⠒⠊⢁⡏⠀⠀⠀⠀⠀⠘⡄⠙⠒⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠦⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀⢀⣀⠀⠐⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⣂⠀⠈⡉⠀⡽⠈⠉⠉⠐⠒⠚⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡇⢀⡀⠙⡄⠀⠥⢰⢁⡄⠀⠀⠀⠙⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠁⠈⠉⠀⠀⣯⠉⡀⠀⠐⠊⠀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡃⠀⢠⠃⠀⠈⢣⠀⢠⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠀⢀⠯⠇⠀⠸⡀⠀⠀⣀⣇⢉⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠔⠶⠄⠶⠄⠈⠀⢀⡀⠳⡀⠀⢁⡏⠉⠛⠒⠒⠒⠒⠒⠒⠒⠲⠶⠦⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠶⢶⠀⠀⣎⡁⠀⠈⠉⠕⠃⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⠀⠄⠀⡀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠠⡁⠀⠐⠄⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠉⠑⠒⠀⠤⠤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⣤⠄⠀⠀⢀⡠⡴⠆⠀⣲⡆⠀⢀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⠗⠁⠀⠀⠀⠊⠰⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠀⠀⡄⠀⠀⣀⣠⠂⠀⢠⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⠘⣂⢰⣷⣮⡏⢠⡃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠞⠀⠀⣿⣿⠟⢸⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠠⠎⡀⠀⠀⣇⡏⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡀⠰⠋⠁⠀⠀⣿⢠⡄⢷⠚⠲⢦⠤⣤⠴⣄⠄⣄
⠀⠀⠀⠀⠀⠠⡋⠇⠀⡸⡔⠀⠀⠀⠀⠀⠀⠀⡘⢁⠅⠀⠀⠎⠀⣀⢠⣄⠐⣅
⠀⠀⠀⠀⠀⠦⣋⠁⡈⠹⠀⠀⢀⡴⠀⠀⢠⠀⠁⡜⠀⠀⠀⢀⠃⠋⠉⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⢠⡜⠀⢰⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⡏⠀⠠⢷⣧⠁⠀⠘⡆⢠⠃⢀⠃⡜
⠀⠀⠀⠀⠀⢀⠀⡀⣸⡆⠸⡇⠀⠀⠆⠈⢹⠶⠞⠂⡞⠀⢸⠒⠃
⠀⠀⠀⠀⠀⠀⠘⠀⠧⠥⠀⠀⠠⠊⠀⠀⠘⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠄⠀⠠⠤⠤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣰⣿⠀⠀⡀⢀⡀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠙⠿⠿⠃⠀⢠⡇⢸⣇⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠉⠉⠉⠙⠛⠿⣦⡀⠀⠀⠀⢸⡧⢸⣿⡿⠁⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⣿⣆⠀⠀⠀⠀⠈⠋⠀⣠⡶⠟⠛⠉⠉⢉⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⢻⡄⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠠⣿⣿⣧⡬⠻⣆
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⣷⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⢹⡆
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣼⠃⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠙⠻⠶⣤⡀⠈⠳⣄⡀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⡀⠀⠀⠀⣀⣠⡴⢾⣿⠃⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⣈⣽⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⡠⠒⠉⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣮⣤⣤⡴⠶⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⣀⣀⡀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⣼⠋⠉⠙⠿⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⡀⠀⠀⠀⣰⣟⢁⣨⣿⠀⠀⠀⣄⠀⠀⠀⠀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠛⢻⡆
⣿⠀⠀⠀⢠⣆⣴⠞⠛⢷⣄⠈⣿⠟⠋⢻⣦⠀⠈⢻⡟⠉⠈⣿⠀⠀⢨⣿⠀⠀⠀⣾⣋⣁⠙⣿⢀⣴⠶⠶⣦⠀⣴⠶⠶⢿⡇
⢿⡄⠀⠀⣸⢿⡇⠀⠀⠀⣿⠀⣿⠀⠀⠀⣿⡀⠀⢸⡇⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⣾⡉⠉⠛⣷⢼⣧⣤⣤⣼⣿⡇⠀⠀⢸⣧
⠈⠙⠛⠛⠉⠀⠻⢶⣤⠾⠋⠸⠿⠷⠂⢠⡾⠷⢶⣼⣷⣴⠄⠹⣦⣤⠾⢿⣦⡄⠐⠿⠙⠛⠛⠋⠘⢷⣀⣀⣤⠸⣧⣀⣠⣼⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣿⣶⣶⣿
⣿⣿⣿⠍⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡤⠞⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⡾⠁⢰⣶⠀⢰⡦⠀⢹⡄⠀⠀⠀⢰⠃⠀⣶⠆⠀⣶⠄⠘⣆⠀⠀⠀⠀⡞⠀⢰⡶⠀⢰⡦⠀⢳⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⢀⣄⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⠀⠀⢸⠇
⠀⠀⠀⠀⠹⣄⠙⠢⠤⠴⠚⣡⠞⠀⠀⠀⠀⠈⢧⡀⠀⠉⠓⠀⢀⡴⠃⠀⠀⠀⠀⠹⣄⠞⠁⠀⠈⠓⣠⠟
⠀⠀⠀⠀⠀⠈⠙⠲⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡞⠋⡀⠀⢀⡉⠳⣄⠀⠀⠀⠀⠀⡴⠋⣁⠀⠀⣈⠙⢦⠀⠀⠀⠀⠀⢠⠞⢉⡀⠀⢀⠉⠳⡄
⠀⠀⠀⠀⡏⠀⠀⠇⠀⠘⠇⠀⢹⡄⠀⠀⠀⢸⠁⠀⡬⠟⠻⣅⠀⠈⣧⠀⠀⠀⠀⡏⠀⠹⠃⠀⠘⠏⠀⢹⡄
⠀⠀⠀⠀⣇⠀⠀⠀⣶⡄⠀⠀⢸⠃⠀⠀⠀⢸⡀⠀⡶⠶⠶⢶⠄⠀⡟⠀⠀⠀⠀⡇⠰⡤⠤⠤⠤⢤⡦⢸⠃
⠀⠀⠀⠀⠘⢦⣀⠀⠉⠁⢀⡴⠋⠀⠀⠀⠀⠀⠳⣄⡙⠒⠒⠋⣠⠞⠁⠀⠀⠀⠀⠘⢦⣈⠓⠶⠒⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⡟⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣦⣧⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀
⠀⡐⠡⠀⠈⢣⠀⣔⠥⣀⢌⡂⠀⠊⡀⢀⠉⠄⢠⢪⡤⢤⡕⡀⡐⠁⠀⠀⢡⠀⡜⢡⠀⡌⢂⢀⠊⠀⠀⠙⡄
⠀⠡⡐⠖⠖⡘⠀⢢⡉⠈⢈⠔⠈⢄⠢⠶⢂⠆⠘⡔⠧⠼⡢⠃⠡⡀⠒⠂⡸⠀⢃⠒⠙⢆⠌⠈⢄⠲⠰⢂⠃
⠀⠀⠈⣉⠁⠀⠀⠀⠈⣉⠁⠀⠀⠀⢉⡉⠀⠀⠀⠀⢉⡉⠀⠀⠀⠈⢉⠉⠀⠀⠀⠈⣉⠁⠀⠀⠀⢉⡉
⠀⡐⢉⠀⡈⢢⠀⢔⣁⣀⢌⠂⠀⠊⣁⢀⡑⠄⢠⠊⡀⢀⠑⡄⡰⢉⠀⢈⢢⠀⠔⣥⣠⣬⢂⢀⠊⡁⢀⠑⡄
⠀⢣⡰⣖⠖⡰⠀⢂⠙⠭⢊⡔⠈⢄⢶⡲⢂⠆⠘⡀⠀⠆⢀⠃⠡⡀⠒⠂⡰⠀⢃⠀⠸⢁⠌⠘⢄⠒⠲⢧⠇
⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁
⠀⡰⠉⠀⠉⢢⠀⡔⢉⠀⡉⢂⠀⠎⣁⢈⡑⡄⢠⢊⡁⢈⡑⡀⠠⠊⠀⠉⢢⠀⡔⢉⠀⡉⢆⢀⠞⠁⠈⠑⡄
⠀⢣⠠⠤⠖⡸⠀⢇⠀⠰⠀⡐⠸⡇⠶⠲⢊⠗⠘⣼⠷⠿⣧⠃⠡⡰⠆⠦⡸⠐⢟⠐⠐⠀⡿⠘⡄⠁⠄⢀⠆
⠀⠀⠉⠀⠉⠀⠀⠀⠉⠀⠉⠀⠀⠀⠁⠀⠁⠀⠀⠈⠁⠈⠁⠀⠀⠈⠀⠈⠀⠀⠀⠉⠀⠉⠀⠀⠈⠁⠈⠁
⠀⠠⠊⠉⠁⢢⠀⡐⢉⠉⡑⢆⠀⠔⠉⠉⠑⡄⢀⠂⠉⠉⠠⡀⠠⢊⡉⣉⢢⠀⡔⢉⠉⡑⢄⠀⠔⠉⠉⠑⡄
⠀⢃⠐⣶⠆⡸⠀⢟⠨⠲⠅⡿⠀⡀⠠⠂⢀⠄⠸⡀⠅⠨⢀⠃⢣⡈⠒⠃⠐⠀⠇⠶⠲⠆⡼⠸⡗⢶⣲⢖⡷
⠀⠀⠁⠒⠈⠀⠀⠀⠁⠒⠈⠀⠀⠈⠑⠂⠉⠀⠀⠈⠐⠂⠁⠀⠀⠁⠒⠊⠀⠀⠀⠐⠛⠋⠀⠀⠈⠛⠛⠉
⠀⠠⠊⠉⠁⢂⠀⡔⠈⠉⠑⣤⠀⠔⡉⢉⠐⡄⢀⢖⡉⢉⡢⡀⠠⠊⠉⠁⢢⠀⡐⢈⠉⡑⠄⠀⢔⡉⢉⡐⡀
⠀⢃⠠⠀⠤⡸⠀⢇⠴⠴⠄⡙⠀⡀⢄⣠⠄⠄⠸⡑⠪⠕⢃⠇⢂⠨⣀⡠⢸⠀⢇⠨⣤⠅⡘⠘⡘⠨⠕⠊⠇
⠀⠀⠑⠒⠊⠁⠀⠈⠐⠒⠈⠀⠀⠈⠐⠒⠈⠀⠀⠈⠒⠒⠁⠀⠀⠁⠒⠂⠁⠀⠈⠑⠒⠊⠀⠀⠈⠐⠒⠉
⠀⡠⢊⠀⡑⣤⡀⡠⠊⠈⠐⠄⠀⡔⠈⠈⠲⡀⢀⠔⠀⠁⢢⡀⠠⠂⠁⠑⢦⠀⡠⠊⠈⠐⠄⠀⠔⠈⠈⠲⡀
⠀⢇⠓⠋⠒⡹⠁⠆⠈⠀⠁⡠⠐⡀⢭⢬⠅⡄⠨⠀⠀⡄⢨⠝⢃⠈⠅⠍⢸⠀⡇⠨⠤⠅⡘⠘⡀⠥⢤⣆⡇
⠀⠀⠑⠀⠂⠁⠀⠈⠐⠐⠊⠁⠀⠈⠒⠐⠊⠀⠀⠁⠒⠒⠁⠀⠀⠑⠂⠒⠁⠀⠈⠒⠒⠊⠀⠀⠈⠂⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠻⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⢈⣁
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⣰⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣆⠘⣿⣿⣿⣿⣿⣿⡄⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⢈⡁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⠏⠀⣿⣿⣿⣿⣿⣿⡇⠈⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⣈⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⣤⣴⠶⠾⠿⠓⠀⠹⣿⣆
⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣴⣿⣿⣦⠀⠉⠛⠓⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠹⣿⣆
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⢹⣿
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠶⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠘⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⣠⡴⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠹⣿⣆⠀⠀⠀⣼⣿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠘⣿⣧⡀⢰⣿⡇⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠀⠀⠈⠻⣿⣾⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣭⣽⣿⡿⠀⠀⠀⠀⠀⣀⣴⣿⠿⠉
⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠶⠶⠾⠿⢿⣿⣟⠉⣁⣀⣀⣤⣴⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠠⣴⢿⣿⣿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣶⣤⣤⣤⣶⣶⣿⠿⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠛⠛⠛⠛⢿⡏⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⣠⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠟⠛⠛⠛⠛⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⣀
⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠛⠉⠉⠙⠛⠻⢿⣶⣄
⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧
⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡶⠂⠀⠀⠀⠀⠀⠀⣿⣿
⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠘⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⣀⣀⣤⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣤⣤⣤⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⢠⡖⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣿⡇⠀⠀⠸⣿⠟⠋⠉⠉⠉⠉⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠛⠛⠛⠿⢷⣦⣄⣀⠀⠀⠒⢶
⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣦⣤⣤⣤⣤⣤⣤⣶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠀⠀⠀⢸
⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠞⠁⠀⠀⢣⠀⠀⢸⡆⠀⠀⠀⠀⠀⡰⠁⣀⣀⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡞⠀⠀⠀⣠⣸⡆⠀⠀⠇⠀⠀⠀⠀⣠⠗⣩⣄⠀⠈⢳⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢸⠁⠀⠀⢰⣋⣿⣇⠀⠀⠀⠀⠀⠀⣰⠏⣸⠛⣿⡇⠀⢸⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⣰⡏⠀⢹⣾⣿⠇⠀⢸⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⡿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠀⠀⣼⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢹⢀⣠⡤⠾⠦⢤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠈⠓⢄⣸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⣀⠴⠖⠒⠉⠉⠉⠉⠁⠒⠢⢼⡀⠤⠤⠤⠤⠤⠏⣀
⠀⠀⠀⠀⠀⣠⡧⠤⠤⢀⡀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠉⠑⠤⡀
⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠈⠲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⢻⡶⢤⣀⡀⠀⠀⠀⠀⠤⠴⠚⠁⠀⣀⡤⠴⠖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢳⡀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠖⠋⠁⠀⠀⠀⢀⡼⣕⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡅⠀⠈⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠠⠴⠒⠋⠁⠀⢀⡞⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⣀⣀⡤⠴⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠠⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⢛⣉⣩⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣀⣠⣾⣿⣿⣷⣤⣾⣿⣿⣷⣄⠀⣠⣾⣿⣿⣤⣴⣆
⠀⠀⢀⣤⠶⢾⣿⣿⡟⠛⠒⢦⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⣰⠟⣡⡴⠾⠿⠿⠿⠶⣤⡀⠙⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢀⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⢹⣿⣿⣿⡄
⠈⣧⠙⢦⣴⢦⡴⢦⣴⢶⡞⢾⠇⣸⠇⠀⠀⢠⣿⣿⠀⡄⣄⠀⠀⠉⢉⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣷⠗⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠰⢿⡉⠛⢶⡄
⠀⠘⢷⣼⡷⠞⠷⠞⢳⡞⠛⢻⣶⠋⠀⠀⠀⢸⣿⡇⠀⠿⠋⠀⠀⠀⠸⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠙⠶⡴⠇
⠀⠀⠀⢈⡙⣷⠶⠴⣏⠉⠻⠏⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⡀⢹⣿⣿⡀
⠀⠀⢠⣿⡇⠹⢦⡀⠈⡷⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠛⠶⡄⢰⠶⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠘⣷⠇⠈⣿⣿⣇⡀
⠀⠀⠀⠉⠀⠀⢀⣹⣆⣀⣠⣤⣧⡀⠀⢀⡤⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧⢰⡏⠀⠀⡗⠀⠀⠀⠀⠙⠲⣶⣤⡀⠀⠀⠀⠀⠰⠾⣿⣭⣥⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⠤⠴⠖⢿⡀⠳⣄⣀⡇⠀⡄⢠⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⣧⠴⠟⠁⠀⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⣧⠀⠈⠙⡇⠀⠛⠋⠀⠀⠀⠀⠠⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠹⣆⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⢦⣀⣿⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸
⠀⠀⠀⠀⢀⣠⣴⠖⠀⠀⠻⣆⠀⠀⠀⠀⠀⠉⠹⣆⠈⠛⠀⠀⠰⠞⢦⣠⠴⢦⣤⠶⠶⠴⠟⠓⠛⠛⠂⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠰⣏⣴⠏⠀⠀⠀⠀⠘⢦⡀⠀⢺⣴⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠁⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠠⣄⡤⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⣠⠾⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣀⠀⠀⠀⠙⠓⠶⢤⣤⣉⣀⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉⠀⠀⠀⠀⠘⢧⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⡀⠀⠀⠀⣿⣤⢼⣿⣿⣭⣉⢈⡇⠀⠀⠀⠀⠀⠐⣦⣤⠀⠘⣧⠀⠀⠀⠻⣌⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠘⣿⣿⡏⠈⠉⠁⠀⠀⠀⠀⢰⡀⠈⠁⠀⠀⢸⡆⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢰⣿⣿⣷⠀⠀⣄⢀⡀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⣿⣿⣿⡄⠀⠙⠞⠻⣤⡖⠀⢸⣇⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⡦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡇⢻⠖⠛⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⡷⠶⠶⠒⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⣠⡄⠀⠀⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡷⡴⠶⠶⠋⢹⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠃⢈⣿⣿⣿⣿⣿⣿⡟⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠟⠋⠁⠀⠸⣿⣿⣿⣿⣿⠿⠋

⣿⢹⡏⣿⢹⠋⡟⢻⠙⡏⣿⢹⡏⣿⢹⡏⣿⢹⡏⣿⢹⡏⣿⢹⡏⣿⢹⡋⣏⣻⢹⡏⣿⢹⡏⣿⢹⡏⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⡾⠛⠉⠉⠛⠇⣿⣸⣇⣿⢸⡇⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⡼⠗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⡇⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⢸⡇⣿⠎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⡇⣿
⣿⢸⡇⣿⢸⠀⡇⢸⠀⣇⠿⠜⠳⠿⠾⣷⣿⣼⣧⡻⢼⣇⣷⢹⡏⣿⢲⠤⡤⢴⢺⡏⣿⢻⡏⣿⢸⡇⣿
⣿⢸⡇⣿⢸⠀⣇⡸⠂⠁⢀⣰⣤⣿⣷⣾⣿⣿⠯⠍⠁⠈⠉⠛⢧⣿⢸⠀⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⢸⣂⠟⠀⣠⠞⠉⠀⠀⠀⠀⠉⢻⣮⡀⠀⠀⠀⠀⠀⠀⠈⢻⡀⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⢸⠋⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⡔⠄⠀⠀⠀⠀⠀⠀⢹⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⡿⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣤⣤⡤⢬⡣⡈⢮⣦⡀⠀⠀⠀⠀⣼⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⠀⠀⢀⡷⠖⠒⠶⠀⠀⠀⠉⣡⠤⣤⣄⠀⠘⢶⠿⣷⠀⡆⠀⠀⢸⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⠃⠀⠀⣾⣷⡾⣻⡓⠀⠀⠀⠈⠀⠾⠒⠋⠀⠀⠈⠿⢻⢶⡇⠀⠀⢈⢧⣸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⠀⢸⣟⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⢸⡄⢸⡀⠹⣸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣷⢀⣿⡇⠀⠀⠀⠢⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⠉⠛⠂⠕⣄⠈⣇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⢸⠟⢳⡀⠀⠠⠀⢔⠀⠀⠀⠀⣤⠌⠂⠀⠀⠀⢸⢷⠿⣿⡦⡈⢦⠸⣆⡿⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⠈⠠⢡⢷⣄⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠸⠀⢣⡀⢀⣸⣰⣿⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⢀⠀⢀⣏⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⢸⣮⣢⣶⣬⣿⡿⢿⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⢸⡇⣿⢸⡦⡀⠛⠹⣟⣾⢳⡄⣀⢠⡴⣖⠉⠁⠀⠀⠀⢸⠀⢉⣿⣽⠉⡇⢸⢸⡇⣿⢸⡇⣿⢸⡇⣿
⣿⣸⣇⣿⣸⣄⣯⣽⣩⣏⣿⣸⣇⣿⣸⣇⣿⣦⠀⠀⠀⠀⣼⣴⣿⣿⣿⣤⣇⣼⣸⣇⣿⣸⣇⣿⣸⣇⣿

⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠈⢁⣀⡈⠀⠀⠀⡀⠃⢀⡀⠃⠁⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠠⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠈⣠⣄⠁⠀⠀⠀⠈⢁⣄⠈⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠁⢠⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢆⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠲⠶⠖⠲⠶⠆⠀⠀⠠⠆⠀⠔⠀⠀⠀⠁⠈⠂⠀⠄⠀⠀⠀⢸⠄⠀⡧⠀⠀⠀⠘⠾⠂⠻⠗
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠘⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠉⠉⠉⠉⠉⠓⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠠⠄⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⣾⠀⠸⠀⢀⢆⣠⠀⢀⣤⣠⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⡀⠀⠀⡷⢀⠛⣄⡌⣶⠁⠾⠀⣄⢆⢠⡆⠈⠟⣧⠎⠘⡃⠱⢟
⠀⠀⠀⠀⠀⢠⠐⢀⡠⠶⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠘⠀⠘⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠀⡘⠸⠀⠀⣠⠤⠤⣤⣔⠁⠀⠛⠀⠀⠙⣆⣀⣀⡐⣼⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠛⠳⢤⡀⠀⢠⢁⠐⣠⡮⠤⠖⠊⠀⠈⢳⠀⠓⠁⢠⠞⠁⠙⠦⣽⣆⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠠⠒⢢⠹⣤⡸⢀⠀⣏⠀⠀⠀⠀⠀⣾⠆⡇⠀⠀⡇⠀⠀⠀⢸⡇⢸⣸⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡧⠒⡆⠀⠉⠛⡘⠀⠹⡀⠀⠀⠀⠀⠙⡱⠀⠀⠀⢣⣀⠀⠀⠈⢁⠜⠳⣟⡮⠀⠀⠤⠤⢄⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢀⣺⡄⠀⠀⢀⠷⠀⠀⠙⠲⠤⠤⠴⠊⠀⠀⢠⠤⢶⠈⠛⠒⠚⠁⢠⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠄⠀⠀⡎⠐⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡀⢄⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠁⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣎⠔⠂⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠺⠀⢀⡠⠒⠉⠲⡀⠀⠀⠀⠀⠶⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠘⠖⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠋⠀⠀⠀⠀⠀⠘⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⠀⠀⠀⠀⠸⡀⠉⠉⠒⠒⠶⠦⣤⣤⣀⣤⣄⠠⠤⡔⠲⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠆⠀⢀⠀⠀⠀⠙⢄⠀⢀⠔⠚⠳⣧⡰⠗⢦⡀⠀⣠⠃⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠋⠀⢀⠃⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠸⠁⠀⠈⡧⠚⡅⠀⠀⠀⠈⣇⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⠦⢄⣀⡘⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢱⠀⠀⠀⠀⣸⡀⠀⠀⠀⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⠃⠀⠀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠀⡗⠒⠈⠉⠁⢇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠿⣦⣄⠀⠀⠀⣠⣴⣿⠿⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣼⡟⠋⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣤⠶⣾⣿⠃⠀⠀⠈⠛⠶⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠋⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡠⠄⠄⠤⠠⠠⠠⠄⠤⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠒⠚⠉⠉⣽⡏⠉⠙⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠉⠉⠙⠛⠒⠒⠶⠻⣷⠿⠷⠄⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠈⠀⠀⢠⣤⣦⣤⣄⠀⠀⢻⣦⡀
⠀⠀⠀⠰⠖⠚⣿⡿⠷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⣠⠞⠋⠁⠀⠉⢳⣄⠈⢉⢳⡄
⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⣠⠞⣡⠴⠚⠋⠉⠛⣿⠛⢧⡀⢣⣷
⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⢿⣄⣀⣷⡀⢻⣆
⠀⠀⣼⠁⠀⠀⢀⡴⠚⠁⢀⣀⠤⣶⠛⢻⣦⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢷⠀⢻⣆
⢠⠀⣿⠀⠀⠀⢸⣁⠴⠊⠁⠀⠀⢻⣦⣀⣿⣼⠂⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡇⠀⢿⢧⡀
⢸⢀⡏⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠈⠉⢁⡾⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣛⡛⠛⠉⠉⠉⢉⣠⡞⠀⠀⠈⣆⢳⡀
⣾⣼⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⡠⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠸⣼⡇
⣿⡇⠀⠀⠀⠀⠈⢧⡤⠤⠶⠒⠋⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⣿⣧⠀⠀⠀⠀⠀⠈⠛⠶⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠸⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣦⠀⠀⣷
⠀⠘⡜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⣿⠇⠀⢻
⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⢀⣴⠟⠀⢀⡿
⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁⠀⠀⣠⣴⡿⢷⣄⢠⣿⠃
⠀⠀⠀⠀⣏⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡄⠀⠙⠻⠶⣶⠶⠾⠟⠋⠁⠀⠀⠀⠰⠿⠋⠁⠀⢈⣿⡿⠁
⠀⠀⠀⠀⢸⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣾⠛⠃⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢪⣾⣿⣿⡁⠀⡄⢉⠸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣧⠀⠁⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢿⣿⣿⡟⢀⣴⡅⠰⢐⠖⠁⣹⣖⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠑⢾⣻⣧⠀⡚⠚⠉⡽⢌⣁⣁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠛⠟⠀⠈⠲⠊⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢩⠀⠀⠀⠀⠄⠀⢢⣄⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠠⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠁⠠⠄⠀⠃⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠁⠔⠚⠈⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠧⣀⠀⢆⣀⡠⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠖⠒⠚⢱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠹⠉⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠤⣴⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⡌⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠚⠁⠘⠧⢔⡒⠠⠤⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣁⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⡚⣃⡭⠳⡤⠋⡆⢹⠀⠀⠒⡖⠆⠀⢀⡠⠊⠓⢄⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢐⡇⠑⢄⠀⠀⡇⠀⢣⠀⢀⠀⠀⢠⠁⠀⢥⠂⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠁⠹⣯⡧⢠⠇⠀⢸⡆⠉⣀⠀⣸⡀⣀⠈⠘⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢒⠞⠀⠀⢀⣙⣞⣡⣴⠲⣻⠙⣯⣽⣼⢛⠋⣫⢀⣉⢠⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⠀⠀⠙⠛⠿⠿⠿⣯⠴⣷⣾⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⠿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠰⠛⠉⠉⠈⠉⠉⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠛⠛⠓⠀⠀⠀⠀⠘⣧
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣴⠛⢻⡆⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠳⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢻⣄⠀⠀⠀⣰⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠙⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠛⠉⠁⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⣤⠶⠾⠛⠋⠉⠀⠀⠀⣀⣀⣤⡴⠶⠚⠛⠉⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⢳⡀⠀⠀⠠⠶⠞⠛⠉
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠙⣧
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠋
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⣷
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⣀⣀⡀⡴⡀⣀⣤⣠⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠃⠃⠁⠙⠁⠋⠙⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠻⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣽⣿⣿⡏⡉⠀⠀⠛⠛⠃⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⢰⠃⢀⠀⠀⠀⢿⠄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⣿⣿⡇⠈⠀⠻⠇⠀⠀⠀⣀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⠿⡷⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡗⢻⣧⠀⠀⠀⠀⠀⠀⢀⣦⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⡀⠀⠀⠀⠀⠀⠸⠗⣠⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣤⣤⠖⠩⠶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠩⢽⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣠⠞⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁



⣀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡤⠀⡀⠐⡈⡉⠤⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠭⢑⡑⠧⠘⢀⠞⠁⠀⢀⣤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣁⣀⡀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⢡⠔⠂⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠔⠊⢉⡀⠀⢀⠠⠐⢈⡁⠄⠤⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢔⢞⡉⢠⠖⢁⠤⠊⠁⠠⠐⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠁⠀⢀⠷⢅⡐⠀⢸⡇⠴⠊⠙⠒⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠨⠑⠀⠀⠀⠁⠤⡴⠙⠂⠉⠉⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠘⠀⡇⠀⠀⠀⡀⣈⠀⢀⣀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⡀⡃⠀⢀⡾⠉⠉⢀⠎⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡤⣾⡿⡀⠨⠃⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠰⠉⣴⠋⠀⠙⠢⠄⠊⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠉⠈⠉⢀⡄⢀⠄⠀⠐⠒⠃⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⢀⠄⠂⠉⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⢷⣤⣀⠌⠀⠀⠒⠂⢤⠆
⠀⠀⠀⠀⠀⠀⢠⠤⣀⡱⡆⠹⣉⠒⠠⠤⠄⣤⠜
⠀⠀⠀⠀⠀⠀⠎⢠⠏⢩⢧⡀⠘⠝⠁⣎⠉⢽⠋
⠀⠀⠀⠀⠀⣸⢦⣴⣀⠔⠋⠳⠄⢈⠀⠈⠁⠁
⠀⠀⠀⠀⣴⠉⢈⡾⠍⡲⡶⢶⣤⢷⣄
⠀⠀⢀⣤⣴⣿⣷⣷⣶⣿⣶⣚⣋⣅⡀⢙⣿⣿⣷⣶⣶⣤⣤
⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣭⣭⣭⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣋⠭⢭⣻⣿⣿⣿⡿⠟⣻⣿⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⢡⣾⣶⢹⣿⣿⣧⡶⢋⣭⡛⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣦⣭⣥⣾⣿⣿⣿⣧⠻⠿⢃⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⡿⣡⡾⢣⣿⣿⣧⣶⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣷⣶⠶⠶⠶⠶⠆⣽⣆⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣙⡋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠿⠿⠿⠧⠤⢰⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣍⣛⣛⣛⣛⣩⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠎⠀⠀⠉⠁⠈⠓⠒⠓⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⢲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣵⡾⣿⣶⣄⢷⠀⣰⠇⣠⠞⠙⢦⡲⣄⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠫⢎⡥⠖⢺⡽⡏⠁⢧⠀⠀⠀⠀⠀⢩⡄⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⢠⣞⣉⡤⣇⠀⠀⣶⠀⢤⣀⡀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡟⠉⠈⢉⡁⠀⠀⠀⠀⣀⠈⠀⠀⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⡴⢿⠉⠀⠀⠀⠘⠋⠀⢀⡀⠈⠙⠀⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡞⠁⠈⠙⢲⡀⣦⠀⢀⡤⣤⡤⢤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠁⠀⠀⠀⠈⢳⡀⠀⠈⠓⠚⠓⠚⠁⠸⢆⡞⠀⠀⠀⡐⡆
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⢲⡤⣤⡄⠀⠀⠤⢶⠋⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠙⡾⠲⢤⣀⡤⢼⡁⠀⠀⠀⠀⠀⢈⡧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⡼⠁⠀⠀⢻⣀⣠⡽⣆⠀⠀⢀⡴⣫⣀⣀⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡞⠁⠀⠀⠀⠈⠁⠀⠓⠮⣷⣤⡮⠴⠏⠀⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠁⠀⣇⣀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠔⠋⠀⠙⢦⠀⠀⠀⡉⠀⢡⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⡁⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢀⡀⠀⠀⠀⢀⡤⠄⠠⡀
⠀⠀⠀⠀⠀⢠⠖⠁⠈⠓⠀⠀⠀⠕⠲⠠⠤⡄⠀⠀⠀⠀⠀⠉⠃⠀⠀⠊⠀⠀⠀⠘⠀⠀⠤⣤⡤⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⠆⠀⠦⠀⠀⠀⢀⡔⠒⠐⢦
⠀⠀⠀⠀⠀⠢⠄⠶⠋⠀⠀⠀⣀⢀⠀⣀⡀⠀⠀⠠⠤⡄⠰⠿⠀⠀⠀⠀⠀⠀⢀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⣠⣀⢀⡤⡀⠀⠀⢀⠴⠂⠲⠀⠀⠀⠀⢀⣤⠀⣄⡀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠔⠋⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠀⢄
⠀⠀⠀⠀⠀⠀⠐⠁⠠⢤⠀⠀⠠⠀⠈⡆⠀⠀⠀⡰⠀⡀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⡄⠈⠢⠀⠀⠀⡆⠀⢀⡀⠀⢀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠈⡁⠀⢨
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠤⠔⠁⡠⠁⠀⠀⠀⢁⠀⠀⠄⡀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠠⡀⠙⠒⠀⠒⠁⠀⠎⠀⠀⠀⠡⡀⠘⠿⠿⠟⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠐⠉⠀⠀⠀⠀⠀⠀⠒⠀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠉⠉⠐⢀⠀⠀⠀⠀⠀⡠⠂⠁⠈⠈⠉⠢⡀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠣⠀⠀⠀⠸⠁⠀⠆⠀⠀⠶⠀⠘⡄⠀⠀⠀⠀⡇⠀⢴⠄⠀⠰⡆⠀⢡⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣀⡉⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠈⡇⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠦⠤⠃⠀⡠⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠘⢄⡀⠙⠟⠁⠀⡠⠂⠀⠀⠀⠐⢄⠀⠀⠑⠊⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠈⠁⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡰⠄⠀⠄⠀⠀⠃⠀⠀⠀⡏⠀⠐⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⠀⠀⡌⠀⠠⠄⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠠⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡤⠒⠦⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⢠⣤⣤⡄⠀⠀⠘⠀⠀⠀⠇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠁⠈⠀⢀⠔⠁⠀⠀⠀⠈⠢⣄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠈⠁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣯⣭⣥⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠦⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⣠⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠠⣤⣜⡓⠘⠰⣶⣂⣀⣀⠀⢠⠋⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠃⠀⠈⠉⠉⠀⠀⠀⠉⠉⠛⠋⠁⢸⠀⣇⣠⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠀⠀⢀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠋⠉⠒⠶⠮⠜⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠢⠤⠚⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡦⡠⠖⠋⠙⠶⠊⡇⠀⠀⠀⠀⠀⠀⠀⡶⢄⠜⠲⢄⡉⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠒⠂⠤⠤⠤⠤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡼⠉⠉⠉⢹⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢤⡇⠀⠀⠀⠀⣇⡸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠓⠒⠚

⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⠛⠂⣾⣆⢸⡆⣾⣆⢸⡆⠻⣆⣴⠇⠀⠐⣿⠛⠂⢀⣾⣆⠀⣰⡾⠻⢶⢰⣿⠛⠂
⠀⠀⠀⠀⠀⠀⣿⣀⠀⣿⣛⡁⣿⠹⣿⡇⣿⠙⣿⡇⠀⢹⡇⠀⠀⠀⣿⠛⠁⣾⠧⢿⡄⢿⣄⣀⣤⢘⣿⣛⡁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠀⠉⠁⠉⠀⠈⠁⠀⠈⠁⠀⠀⠀⠉⠀⠈⠉⠀⠈⠉⠀⠉⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣴⠛⠛⠶⢸⣿⣛⠀⣿⣆⣿⡇⣿⣛⡃⣿⠛⣷⠀⣰⢿⡄⠘⢻⡟⠛⣴⠟⠛⢷⡀⣿⢛⣷
⠀⠀⠀⠀⠀⠀⢿⣄⣹⡿⢸⣿⣉⡀⣿⠹⣿⡇⣿⣉⡁⣿⢿⣏⢰⡿⠾⣷⡀⢸⡇⠀⢻⣦⣠⡾⠃⣿⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠉⠀⠈⠀⠉⠉⠁⠈⠀⠉⠈⠀⠀⠈⠀⠀⠁⠀⠀⠈⠉⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣠⣴⠶⠾⠿⠷⠶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣴⠶⠾⠿⠷⠶⣦⣄⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠘⠋⠀⠀⠀⠀⣴⠞⠓⢿⡃⠀⠀⠀⠀⠀⢸⣏⠀⠘⠋⠀⠀⠀⠀⣴⠞⠓⢿⡃⠀⠀⠀⠘⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠇⠀⠀⠀⠀⢿⡆⠀⠀⠀⡟⢎⠶⠟⡾⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢿⢼⡽⠾⣹⠾⡍⢾⠗
⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢶⣶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣄⣀⣀⣀⣀⣠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉

⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠑⠀⠀⠀⢠⠊⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠀⡀⠀⠀⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⣁⠄⣅⠀⠀⠀⠀⠀⠈⠀⠈⣤⣜⠀⠀⠀⢠⠀⠀⠀⡄⠁⠀⠀⡀⠄⠀⠀⠠
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠈⠀⠔⠀⠀⠀⠈⠀⢁⣀⠈⠀⠀⠀⠀⠀⠢⠀⠀⠝⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⡰⢀⡀⢀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⢧⠔⠾⠀⠀⠀⠀⠀⠙⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠢⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠄⠀⠀⠀⠀⡠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠠⠀⡆⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⢀⠁⠀⠀⠀⠀⡂⠀⠀⡜⠀⠆⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠘⢀⠀⠀⠀⡠⠁⠀⠀⠠⠀⠐⠃⢀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠁⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠊⠁⠀⠀⠢⠀⠀⠀⠀⢉⡀⢀⠈⠂⠀⠀⢠⠊⡀⠀⡄⠐⡄⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⢀⢊⣁⠀⣤⡕⠀⠀⠀⠠⠀⡀⠀⡀
⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠈⢥⣀⡼⠀⡀
⠀⠈⠒⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠔⠀⠀⠀⠀⠈⠂⠄⠠⠄⠀⠀⠀⠀⠀⠀⠉⠠⠊⠀⠀⠀⠈
⠀⠀⡠⠄⠀⠠⡀⠀⠀⠀⢠⠔⠂⠒⠢⡀⠀⠀⠀⠀⠔⠒⠢⢀⠀⠀⠀⠀⡠⠖⠂⢄⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠂
⠀⠘⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠰⠁⠄⠀⠐⠈⡇⠀⠀⠞⠀⠄⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⢠
⠀⠀⣄⠀⠂⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠆⢀⠔⠀⠀⠐⡄⠀⠀⠀⠀⠁⠀⠀⠡⡀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠶⠛⠛⠉⠉⠉⠉⠙⠿⢿⣦⣛⠓⣦⣄⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⠚⠛⢿⣆⠄⣨⠽⢦⡀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠐⠀⠁⠀⣀⣀⣀⣠⡤⠖⡡⣘⣿⡏⠀⠀⠒⠨⢦⡀⠀⠀⠀⠀⠀⠀⠀⡼
⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣠⠊⠀⠀⢀⠀⠒⠈⠉⠀⠤⠄⠭⠅⠐⠚⢵⣍⣾⣟⡛⠛⠉⠀⠈⠻⣄⠀⠀⠀⠀⣠⠛
⠠⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡜⠁⠀⠀⠂⢀⠠⠄⠒⠒⣀⣠⣴⣿⣷⡿⠿⠚⠿⢿⣿⣿⣿⢋⠑⠂⠄⠙⣆⣀⠠⠎
⠀⠁⠁⠌⠍⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡞⠁⠀⠀⠀⣀⠄⠒⠒⢉⣛⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣄⠀⠀⠀⠘⢏⠌⠀⠀⠀⠈
⠀⠀⠀⠐⡐⠀⠀⠉⠛⠂⠤⡄⣀⣀⢀⠀⠀⠀⠀⢠⠋⢠⡟⠀⠀⢀⡀⠂⢁⣠⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡂⠀⠀⠀⢘⡔
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⣤⠤⢤⠀⢠⡏⠀⠂⠀⠀⢀⣔⠔⣪⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠈⣵
⠀⠌⡄⢡⠡⢠⠀⠄⠀⠠⠡⢡⠉⡼⠀⠀⠀⣷⡾⠀⠀⠀⠴⢀⡾⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡧⠀⠰⠸⣇
⠐⡐⡐⢂⢂⢂⠂⠐⠀⠀⢂⢂⠒⡘⡙⠂⢚⣿⠇⠀⠀⡸⢂⣾⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠑⡀⠂⣧⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠚⠒⣀⠓⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⣿⣿⣧⢰⣿⢸⠆
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⡈⠀⢁⠀⠀⣼⠻⠦⠔⠹⣄⣿⣿⠠⠛⠛⠛⠛⠷⠶⠀⠀⠀⠀⠀⠀⠰⠛⢋⣉⣀⣀⠀⠈⠀⠀⠀⠀⠀⢿⣿⣿⣇⢿⣾⡄
⠀⢂⠂⡐⡐⡐⡀⢂⠀⠐⡐⡐⣀⢂⢂⠀⠛⣇⠀⠀⠀⣿⣿⣿⠀⢠⣶⣿⡿⠶⢭⡀⠀⠀⠀⠀⠀⠀⣰⡿⠻⠛⠛⠿⢶⠄⠀⠀⠀⠀⠃⠙⣿⡏⠐⣿⣄
⠀⠂⠂⠰⠐⠐⠀⠀⠀⠐⠐⠐⠀⠂⠀⠀⠲⢿⠀⡄⠀⠃⣿⣿⡆⠀⠈⠑⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣿⡁
⠀⠀⠀⠡⠁⠀⠁⠀⠀⠀⠠⠁⠉⠈⠀⠀⠠⣼⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠇⢹⡇
⠀⡀⡀⢂⢀⠀⠀⠀⠀⠀⢀⢂⠀⡀⠀⠀⠀⣾⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠿⠿⠾⣸⣃⡀
⠐⠐⠀⠆⠆⠀⠂⠀⠀⠀⠀⠆⠂⠰⠐⢀⣤⣿⣼⠇⡄⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡀⠀⠀⠀⢹⣿⣿⣿
⠡⠡⠉⠌⠌⠌⠄⠀⠁⠀⠈⣬⣼⣿⣿⣿⣿⣿⣿⡀⠃⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⢰⠀⠀⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠉⢻⣿⣿⣿⣶⡀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠙⡀⠀⠀⢸⠀⢃⣿⡏
⠀⠀⠀⠰⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠘⣿⣿⣿⣧⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⠀⢠⠀⠀⠀⠇⠀⠀⠈⠀⢸⣿⡇⢀
⠀⠌⠄⠡⠡⠡⠁⠈⢼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢹⢿⣟⣿⣷⡀⠀⠀⠀⠈⠙⠷⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⠀⠸⠀⠀⡀⢰⣸⣿⠇⣾
⠀⣈⡀⢡⢁⢁⠁⠀⣼⣿⡇⠀⠀⢠⡀⢱⡄⠀⠀⢿⣿⣿⡇⠈⠀⠈⢻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣤⣿⣿⣿⣼⡟
⠀⣸⡀⠀⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⢷⡄⢻⣆⠀⠘⣿⣿⣿⡠⠀⠀⠈⡽⣿⣿⣿⣷⡄⠀⣀⠀⠀⠀⣀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠓⠃⢸⣿⣿⣿⣿⡇
⠀⠽⠁⠄⠌⠄⠀⢠⣿⣿⡇⠀⠀⠀⠈⣿⣆⢿⣆⠀⢹⣿⣿⣧⢂⠀⠀⠀⠙⣯⣿⣿⣿⣦⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢺⢿⣿⠏⡀⠀⠀⣿⣿⣿⣿⣷
⠀⣳⢃⡘⡘⡈⣀⢠⣿⣿⡇⠀⢠⡀⠀⠘⣿⣾⣿⣆⠘⣿⣿⣿⡞⣄⠀⠀⠀⠹⡺⣻⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⣴⣿⣀⡀⢰⠐⢿⡼⠃⠀⠀⠘⢻⣿⣿⣿
⠀⢒⠂⠐⠐⠐⠀⢸⣿⣿⡇⠀⢸⣿⣦⡀⠹⣿⣿⣿⡆⣿⣿⣿⣿⣿⣆⢆⠀⠀⢻⣣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣧⣇⣼⠀⢸⡇⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠾⠄⠀⠀⠠⠀⢸⣿⣿⣿⢀⠸⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣾⣄⢣⠈⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⡔⠘⣷⡀⠀⠀⡀⠠⠀⣿⣿
⠀⡘⡀⢀⢀⢀⠀⢸⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡜⣧⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⢇⣿⣷⡄⢠⣧⠀⡆⢸⣿
⠀⣰⡐⢂⢂⢂⠀⠸⣿⣿⣿⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠀⢿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣼⣿⣴⣇⣸⣿
⠀⢸⠁⠄⠆⠄⠀⠰⣿⣿⣿⢸⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⡇⢈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠿⠛⠛⠛⠻⠿⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⣿⣆⠀⣈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠘⣷
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁⠀⠀⠀⠻⠋⢸⣿⡆⠀⠉⠻⢶⣤⣀⠀⠀⠀⢹⣇
⢸⡏⠀⠀⣀⣀⣀⣠⣤⣴⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿
⣿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⣀⠀⠀⠀⠠⡶⠾⠟⠛⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠷⠂⠀⠀⠀⠀⣴⡄⠀⢸
⣿⠀⠀⢰⣿⡇⠀⠀⠀⢠⡶⠾⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠿⠶⣶⠀⠀⠀⠀⢸⣟⣿⠀⢸
⢻⡇⠀⠹⣿⠟⠀⠀⠀⠸⣧⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⡿⠀⠀⠀⠀⠈⠙⠋⠀⣿
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⢰⡆⠀⠀⣶⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⣤⡄⠀⠀⢠⡿
⠀⢻⡆⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⣾⠃
⠀⠈⢿⡄⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣼⠏
⠀⠀⠈⢿⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⠾⠟⠻⣶⠟⠻⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⠟⠛⠛⠿⠿⠿⠿⢶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⣤⡶⠿⠟⠛⠛⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣠⡾⠛⢿⣆⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢀⣿⠁⠀⢸⡿⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣸⡏⠀⠀⢿⣧⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠀⢠⡿⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠸⠿⣶⣶⣦⣤⣤⣤⣶⣶⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠔⠚⠃⠀⠀⠈⠛⠲⠄
⠀⠀⠀⠈⣿⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⣤⡄⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠆
⠀⠀⠀⠘⠛⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⡖⡄⠀⠀⠄⢲⢂⠀⠀⠀⠀⠀⢾⠍⠀⠀⢩⡧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡤⠀⠁
⠀⠀⠀⢿⣦⡇⠀⢿⣢⡇⠀⠀⠀⠀⠰⢶⡽⠃⠀⠀⠶⣯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠸⣶⡂⠀⠀⠀⠻⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⢀⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⣹⣦⠀⠀⠀⣴⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⣐⡋⠀⠀⢑⣒⣊⠀⠀⠀⠀⠀⡴⡶⡄⠀⢰⢶⣆
⠀⠀⠀⠓⠂⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠈⠚⠃⠀⠀⠑⠋⠀⠀⠀⠀⠀⠺⠿⠁⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢠⣯⠗⠀⠠⣼⡼
⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠖⠒⠄⠀⠰⠒⠲⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠴⣦⡀⠀⡀⢲⣄⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⣤⣴⡎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠻⣾⣻⠇⠀⣷⣟⡾⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣟⡟⠀⠀⢣⣯⠇⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣸⣦⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠀⠀⠀⠀⠀⠋⠙⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢀⡴⠖⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠈⠀⢀⣴⣤⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⣽⣿⣇⠀⠀⠀⢀⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃⡴⠖⠶⡄⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⠤⣄⣴⠞⠋⠉⣉⣻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢠⡏⠀⣼⣡⠤⠖⠋⠁⢀⣨⢿⠄⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⡾⠀⠚⠉⠀⠀⠠⠖⠻⣍⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣠⡿⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠚⠁




⣿⣿⣿⣻⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣻⣿⣛⣟⣻⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⣄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣠⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣤⡀⠀⢀⣄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠀⠈⢁⡄⠀⡄⠀⠀⠀⠀⢿⠀⠀⠈⠁⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠉⣀⣀⡀⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠑⠲⠶⠶⠖⠋⠀⣼⠃⠀⠀⠀⠀⠸⣆⠀⠀⠀⠚⠛⠁⠀⢠⡟⠀⠀⠀⠀⠀⠹⣆⠀⠊⠁⠀⠈⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠆⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⠄⠀⢤⡂⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⡢⠀⠀⣔⠀⠀⢻⡄⠀⠀⠀⠀⢸⠃⠀⠈⠋⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢠⣶⣶⣦⠀⠀⢠⡏⠀⠀⠀⠀⠸⡇⠀⠀⣀⣄⣀⢄⡀⠀⣼⠁⠀⠀⠀⠀⠸⡆⠀⢲⣶⣶⣶⣶⡆⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠛⠛⠋⢀⣠⠞⠁⠀⠀⠀⠀⠀⠻⣦⡈⠁⠀⠁⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠹⣆⡀⠉⠛⠛⠉⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠛⢶⡄⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⣄⠀⠀⣤⡄⠀⢻⡆⠀⠀⠀⠀⣾⠁⠀⣴⡄⠀⠠⡦⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃⠠⠖⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⣴⣶⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠄⢠
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠋⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⡆⠀⠀⢿⣿⡿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠹⣄⠈⠒⠶⠶⠶⠚⠉⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠻⠇⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣠⣤⣴⣤⣄⡀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢠⣾⠟⢩⣿⠟⠻⢿⣦⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢻⣿⡀⢀⣼⣿⡆⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣽⡿⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠙⠻⠿⣿⣿⠁⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⣇⡀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠛⠿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⣶⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠸⣿⣄⠀⠈⠛⠿⣷⣤⡀⠀⢀⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠙⠻⢿⣦⣄⠀⠈⠙⠿⣷⣬⣉⠛⠛⠛⠛⠁⠀⠀⣴⡿⠛⠉⢉⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠉⢻⣿⣦⣄⡀⠈⠙⠿⣷⣦⣀⠀⠀⢠⣾⠟⠁⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⣿⡟⠉⠻⠿⠀⠀⠀⠀⠙⠻⣷⣶⡿⠋⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢋⣿⣿⣿⣫⢉⣤⣰⣶⣯⣟⣿⣿⠙⣿⣿⣿⣿⣟⡫⣡⣄⢶⣶⡉⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣮⣭⣼⣿⣿⣿⣿⣿⣤⣙⢻⣿⣿⣿⣿⣬⣥⣿⣿⣷⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠛⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⣻⢟⣛⣻⣵⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⡇⠶⢠⠆⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠉⠀⢀⣀⣀⡀⠁⠰⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⣠⠞⠁⠀⠀⠙⢦⡀⠀⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣰⠃⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠤⠀⠈⠓⠒⠒⠋⠁⢀⡀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡴⠃⠀⢠⠄⠀⡆⠀⠳⠀⠀⠀⠀⠀⠈⢕⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⢠⠋⠀⠀⠀⠈⢧⠀⠀⣀⡀⠛⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡽⣢⠀⠀⠀⠈⣆⡞⠉⠛⠳⣤⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⣾⣯⢽⡇⠀⠀⢠⢿⡉⠓⣦⡀⠈⠙⡦⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢳⡎⠉⢇⠈⠛⠲⠶⢶⠃⢤⡀⠰⠂⢻⡄⠀⣿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⣔⠊⠳⠤⠤⠤⠼⣄⣚⠁⠀⠫⡜⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠓⠶⠦⣤⠀⠠⠈⠈⠉⡉⠛⣍⠛⢁⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⠀⢁⠀⢸⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡋⠀⠓⠲⠲⠶⠶⠶⠖⠒⠲⠶⡖⠚⠉⢦⠀⠀⠠⠄⠀⢠⠿⣄⠀⡇⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠙⠢⣌⠀⣀⣀⣩⡤⠤⠴⠖⠒⠧⡀⠀⠀⠙⠦⡐⢂⡴⠃⠀⢣⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠙⠒⠚⠉⠉⠉⠀⢀⠀⠀⠠⠀⠀⠀⠘⣆⠀⠀⠀⠈⡟⠀⠀⠀⠸⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠭⣤⣄⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣤⠼⠤⠤⠶⠊⠀⠀⠀⠀⠀⠧⣌⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣫⣽⣿⣿⣯⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⢡⣿⣿⣿⣿⣿⡿⠋⠁⠀⣨⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠟⣋⠓⠀⣁⡀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⢻⡏⠀⠈⠉⠀⢠⡉⠁⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠈⣧⠀⠀⠀⠀⠰⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⢀⣠⠴⠶⠄⠀⠀⢀⡇⠀⠀⣠⢾⣿⠖⠉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠞⠀⠰⡏⠀⢀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡀⠀⣀⣀⡤⠖⠉⠀⢀⡜⢡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⢹⡏⠉⠀⠀⠀⠀⢠⠏⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡇⠀⠀⠀⠀⣰⠃⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠇⠀⠀⠀⡰⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡸⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⠛⠛⠳⢦⣄⠀⠀⠀⠀⠈⢿⣇
⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣿⡆
⢀⣿⠇⠀⠀⠀⠀⠀⠐⢤⣄⣀⣀⣀⣀⣠⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣹⣿⣭⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣖⠄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠟⠛⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠛⠉⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⢀⣾⣿⠃⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⣾⣿⠃⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⣼⣿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⣶⣦⣭⣛⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⣾⣿⠿⠛⠉⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⠄⢀⣀⣤⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⠃⢀⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠛⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⣰⣿⠏⠀⠈⠛⠉⠀⠀⠀⢴⣾⣿⣿⣿⣷⣦⣤⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣷⣄⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡏⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣀⣿⣿⣀⡀⡀⢀⣀⣀⣀⣠⣤⣴⣶⣾⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣴⣶⣿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⠐⠀⠐⠀⡀⠀⠀⠀⢀⠔⠂⠐⠢⡀⠀⠀⠀⠀⠄⠒⠀⠂⢄⠀⠀⠀⠀⡠⠐⠀⠐⠠⠀⠀⠀⠀⢀⠐⠂⠐⠢⡀⠀⠀⠀⢀⠄⠒⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠁⠐⠀⠐⠀⢘⠀⠀⠀⠈⠀⢐⣀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠂⠀⠁⠀⠀⠀⠃⣀⣂⣀⣀⠘⠀⠀⠀⠀⢀⣂⣀⣂
⠀⠀⠀⠀⢄⠂⠀⠔⠀⠂⠀⠀⠀⠢⡑⠀⠀⢂⠌⠀⠀⠀⠀⠌⠀⠀⠈⠠⠁⠀⠀⠈⢄⠀⠀⠀⡠⠀⠀⠀⠀⠣⡻⠋⠙⢏⠜⠀⠀⠀⠀⠈⠻⠿⠛⡠
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠔⠁⠀⠀⠁⠄⠀⠀⠀⡐⠁⠀⠀⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠠⡀⠀⠀⢀⠆⠀⠀⠀⠑⡀⠀⠀⠀⣰⣀⡀⣀⣀⣆⠀⠀⠀⠠⠂⠀⠀⠀⠢
⠀⠀⠀⠀⠀⣀⣀⣁⡀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢠⠀⠀⠀⠀⢀⠄⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠁⠀⡀⠀⠀⠀⡛⠛⠋⠙⠛⢛⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠙⠿⠛⠕⠁⠀⠀⠀⠐⠤⠀⠀⠀⠂⠀⠀⠀⠀⠢⠀⠀⠠⠈⠀⠀⠀⠀⠂⠀⠀⠀⠔⠁⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠀⠀⠈⠢⠁⠀⠈⠊

⠀⠀⠀⠀⢀⠠⠀⠤⡀⠀⠀⠀⠀⠀⡀⠄⠠⢄⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⡠⠄⠠⢀⠀⠀⠀⠀⠀⢢⠤⠤⠤⡆
⠀⠀⠀⠀⠁⠀⠀⠠⠀⠂⠀⠀⠀⠎⠀⡀⠀⠀⠡⠀⠀⠀⠐⠀⠠⠀⠀⠈⠄⠀⠀⠠⠁⠠⠀⠀⠈⠂⠀⠀⠀⠎⢴⡦⢴⡆⠱⠀⠀⠀⠐⠀⠠⠀⠀⠈
⠀⠀⠀⠀⡀⢶⣶⣶⠆⠀⠀⠀⠀⢄⠀⢠⡄⠀⡐⠀⠀⠀⠠⠐⠶⠿⠶⢀⠂⠀⠀⠰⡀⠔⠀⠐⢄⠄⠀⠀⠀⢄⠀⠀⠀⠀⡰⠀⠀⠀⢀⠠⠀⠀⠠⢀
⠀⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠁⠒⠀⠂⠁⠀⠀⠀⠀⠈⠐⠀⠒⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠁⠂⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠂⠀⠐⠠⡀⠀⠀⠀⠠⠀⠀⠀⠂⡀⠀⠀⠀⢀⠄⠀⠀⠐⢄⠀⠀⠀⠀⡀⠂⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠂⠁⠀⠀⠀⢉⠖⠂⠀⠐⢎⠁
⠀⠀⠀⠀⢠⣭⣤⣬⣥⠀⠀⠀⠀⠁⠀⠘⠀⠀⢸⠀⠀⠀⠈⠀⢀⠀⠀⠀⠃⠀⠀⠈⠀⠰⠀⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠦⠀⠆
⠀⠀⠀⠀⠠⠙⠀⠘⡡⠂⠀⠀⠀⠡⡚⠿⠿⢃⠌⠀⠀⠀⠘⢄⠀⠀⠀⠀⠁⠀⠀⠈⠄⢻⣿⡿⠣⠀⠀⠀⠀⠡⠀⠀⠀⢀⠌⠀⠀⠀⠐⢈⠂⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠊⢀⠀⠀⠑⠄⠀⠀⠀⡔⠁⡀⠀⡈⢂⠀⠀⠀⠠⠈⠀⠀⠀⠐⡀⠀⠀⢀⠂⠀⠀⠀⠗⡄⠀⠀⠀⡔⢰⣤⣤⡄⢦⠀⠀⠀⠰⠫⠤⡀⠬⠳⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⡈⠁⢠⠀⠀⠀⢀⠰⠀⣀⠀⠀⠄⠀⠀⢀⠀⣈⣤⣄⡀⡀⠀⠀⠀⡄⣾⠿⢿⡇⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠑⠤⠀⠠⠀⠀⠀⠀⠀⠘⠢⠄⠠⠄⠁⠀⠀⠀⠈⠂⠄⠀⠤⠊⠀⠀⠀⠀⠑⠬⠉⠩⠐⠀⠀⠀⠀⠀⠨⠔⠪⠕⠁⠀⠀⠀⠈⠂⠄⠀⠤⠊

⠀⠀⠀⠀⢀⠤⠀⠠⢀⠀⠀⠀⠀⠀⠠⠀⠠⢀⠀⠀⠀⠀⠒⡤⠠⠀⠤⡔⠂⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠠⢄⠀⠀⠀⠀⠀⡀⠄⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠄⠠⠀⠱⠀⠀⠀⠘⠀⠠⠀⠄⠘⠇⠀⠀⠐⠁⠠⠀⠠⠀⠂⠀⠀⠀⠊⠒⡦⠔⠶⠑⠀⠀⠀⠈⠐⠒⠖⠒⠈
⠀⠀⠀⠀⡀⠀⠀⠠⢂⠄⠀⠀⠀⢆⠑⠀⢤⠆⡐⠀⠀⠀⠠⡀⠀⠄⠀⢀⠃⠀⠀⠐⡀⠀⠀⠀⢀⠆⠀⠀⠀⢂⠐⠐⠒⠂⡐⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠈⠐⠀⠂⠁⠀⠀⠀⠀⠀⠁⠂⠐⠈⠀⠀⠀⠀⠀⠈⠂⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⢁⣴⠶⢮⣿⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉⢁⣾⡄⠻⣿⣿⡿⢸⠃⠀⠀⠘⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠻⠏⣼⡇⢸⣿⠇⠀⠈⠙⣇⡘⢧⣀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⠋⢰⠆⠀⠀⠀⠀⠈⠙⠲⠽⠷⣄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠘⠋⠀⢸⢿⣧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⣄⣼⠇⠀⠀⠀⢀⣿⡼⢻⡇⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣀⣤⣤⣤⡀⠀⠀⠀⢠⣾⣩⣤⡼⠁⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⣷⣄⡈⠉⠉⠙⠛⠀⣠⣴⣿⣿⣿⠟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⣿⣽⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⢉⣀⣀⣈⣉⣉⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⢉⣁⣠⣄⣀⣀⣀⡀⢨⣽
⠀⠀⠀⠀⠀⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠹⠟⠙⠿⣿⣿⡟⠉⣹⠿⣿⣿⣟⠛⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢈⠛⠋⠴⠟⠀⠀⢼⣿⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣅⣀⣀⢻⣶⣮⣽⢞⣻⣏⣹⡧⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣤⣦⢤⣀⠀⠀⠀⠻⣾⣥⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⣸⡥⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣽⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡞⢩⢿⣿⠟⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠺⠇⣴⣾⡯⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣸⣿⠁⠀⠀⠙⠉⠉⠀⠙⢿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣦⣴⣶⣶⣤⣼⣷⣾⣟⣿⣿⣧⣠⣼⣷⠶⣶⣶⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢉⣉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣴⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠁⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⣴⡦⢀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠟⠟⡀⠀⠀⠐⠀⠉⠁⠠⠀⠀⠀⠀⠀⠐⠋⠃⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⢶⠒⠾⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠐⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠙⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠢⠂⠀⠀⠀⣦⣤⣤⢤⣤⡴⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠈⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠐⠒⠓⠛⠃⠀⠀⠀⠋⠛⠁⠈⠉⠀⠀⠀⠀⠀⠒⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠶⠶⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠰⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠆⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⡏⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⠃⠀⣿⣿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⣴⣿⡇⠀⠀⠀⣸⠀⠀⢸⠀⠀⣾⣿⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠼⠧⠤⠿⠿⠧⠀⢰⡏⠁⠀⠀⠼⠦⠤⠿⠿⠦⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣾⣿⣿⣷⠀⢺⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣾⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠛⠛⠁⢀⡾⢤⣀⣀⣀⣀⣀⣀⡤⢧⡀⠘⠻⠟⠋⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠐⠋⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠙⠂⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠶⠶⠶⠒⠚⠋⠉




⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣤⣤⣤⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠶⠀⢸⠇⠀⠀⠀⠀⢸⡇⣐⠖⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣩⣿⡇⣼⣿⣿⣿⣿⣇⢸⣿⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠃⠸⡄⠀⠀⠀⠀⣠⠇⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣾⣇⢻⣿⣿⣿⣿⠟⣸⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⠿⠿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⡤⣶⡞⠁⠀⠉⠁⠀⠘⣳⡶⢤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣛⡉⢡⣿⣿⣿⣿⣿⣷⡌⢙⡛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡞⠁⠀⢸⣿⡀⠀⠀⠀⠀⢀⣿⡇⠀⠈⢳⠀⠀⠀⠀⢸⣿⣿⣿⣿⢱⣛⣻⠃⠘⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⡜⣿⣿⣿⣿
⠀⠀⠀⢸⡇⠀⠀⣽⣿⣿⣶⣤⣴⣶⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⡅⠀⠈⠉⠉⠙⠋⠁⠀⢸⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠧⣈⣳⡀⢠⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠐⢏⡩⠽⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢛⠻⢿⣿⡏⠀⠀⠀⠀⣶⠖⡤⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⣿⡿⠁⠶⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⢠⣿⠃⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡴⠁⢘⢷⡀⠈⢦⣉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡸⠃⠀⠀⠀⠀⠀⣤⡼⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⣿⠏⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⢷⣄⠀⠀⠀⠀⠀⠉⠀⠒⠙⠀⠀⠀⠀⠀⢠⡾⠳⣶⣦⣀
⠀⠀⠀⣀⡴⠖⠲⠞⠉⠀⢀⣀⣀⡾⠉⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡿⠠⣄⡼⠃⢙⢧⡀
⠀⠀⢸⡋⠀⠀⠀⠀⠠⡶⠋⠁⠉⣹⠖⠂⠀⠙⠿⢭⣿⣷⣶⠖⠒⠻⣏⠁⢀⡿⠀⠈⠓⢶⡁⣰⠇
⠀⠀⠀⢿⣀⡀⠀⠀⢀⡟⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡜⠷⠋⠀⠀⣴⠦⠴⠛⠁
⠀⠀⠀⠀⠙⢧⡴⠷⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠶⠞⠁
⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⢸⡦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣠⠞⡱⠋⢹⣆⡀⠘⣇⠀⠈⠉⠙⠛⠶⠦⣤⣄⣀⠀⢀⡟
⠀⣠⠞⡡⢊⡤⣴⠏⠈⠙⢦⣾⡳⣤⣀⠀⠀⠀⠀⠀⢠⠟⠻⣿
⣼⣣⠎⢱⣭⡵⠛⢦⡀⠀⠀⠈⠙⢲⡽⠛⠓⠶⠦⢤⡏⠀⠀⢈⡇
⠈⠛⠛⠋⠁⠀⠀⠀⠙⠶⣤⣤⠴⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢧⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠠⣀⠸⢭⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣅⠢⢍⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡾
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣿⣿⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡏⢀⣤⣶⣦⣄⣸⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⠋⢉⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠃⢠⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣤⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⠛⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠉⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣭⣍⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣅⣀⣀⣀⣼⣿⣿⣿⠟⣡⣶⣿⣿⣿⡿⢛⣡⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡏⣴⣶⣶⣶⣌⠻⣿⣿⣿⣿⣿⣿⡿⢋⣥⣾⣿⣹⣛⠛⢋⣰⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣷⣌⠻⣿⣿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣤⣌⢛⣟⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣷⣌⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣴⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢦⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣤⠶⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣶⣶⡄⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢾⣿⣿⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢠⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⣼⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⡇⠀⣸⣿⣿⡇⠀⠀⣴⠛⠋⠀⠀⠀⣻⡀⠀⣹⣿⣿⡀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠻⣤⣤⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⢸⡿⠋⠉⠁⠀⠈⠉⠙⢻⡇⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞





⣿⠿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣿⣿⣻⣿⣿⣿