Warer Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠒⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣀⡀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢧⡀
⠀⠀⠉⠉⠉⠉⠉⠛⠒⠲⢤⣉⠙⠲⣄⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⢄⡁⠢⣀⠀⠀⢇⢀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠙⢦⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢪⢂⠈⠳⡀⠘⡈⡄⠀⢧
⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠒⠲⢤⣌⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠇⢆⠀⠹⡄⡇⣷⠀⠸
⠀⠀⠀⠠⠁⠂⠈⠉⠉⠉⠓⠢⢄⡀⠈⠙⢦⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⠆⡀⠀⠀⠀⠀⢸⢸⠀⠀⣷⡇⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠘⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⢀⡇⣸⠀⠀⣿⠃⣹⡇
⠀⠀⠀⢀⣠⣤⣤⡀⡀⠀⠀⠀⡀⠀⠀⠹⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡜⢠⠇⠀⢀⡟⢠⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡈⢦⡀⠀⠙⡄⠀⠀⠈⢧⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⠎⠀⠀⡜⠀⡎⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠑⢆⠀⢹⡀⡀⠀⠀⠙⣦⡀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⢀⣀⡤⠚⠁⡴⠋⠀⢀⠞⠀⡜⢠⡇
⠀⠀⠀⠀⠄⡀⠀⠀⠀⠙⠒⠋⠀⠈⣇⠐⢄⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢀⡴⠊⠀⢀⡴⠋⢀⡜⠁⡾⠀⠀⣸
⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠸⡄⠀⠑⠤⣀⡀⠀⠉⠓⠶⢤⣤⣀⣀⣤⡤⠴⠚⠉⠀⢀⡴⠋⠀⣠⠎⠀⡼⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠙⢦⡀⠀⠀⢉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⣠⠞⠁⢠⠞⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⠀⠉⠙⠚⠉⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⠀⢠⡎⠀⣠⠴⠋⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠶⠶⠶⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡟⠻⠶⠶⠶⠿⠿⠿⠿⠾⠛⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡶⠞⠳⣶⣶⣶⡶⠷⢶⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⡻⢿⠶⠶⡿⠿⠷⣦⣔⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠻⣦⡀⢳⠀⠀⠀⠀⠀⠀⠀⠻⣿⠙⣏⠉⠉⠉⠉⠉⠉⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠘⣷⠈⡇⠀⠀⠀⠀⠀⠀⠀⢿⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣠⡟⢠⠃⠀⠀⠀⠀⠀⠀⣰⣏⣠⣇⣀⣀⣀⣀⣀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢈⣿⠿⢶⣧⣤⣤⣤⣤⣤⣴⠾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣟⠻⣧⡀⠀⠀⠀⢀⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠳⢭⣛⡛⠛⢛⣛⡥⠚⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣭⣭⣥⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⡆⠀⠀⠀⠀⠀⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⠀⣦⠀⠀⠀⣿⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇⠀⠀⠀⢹⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⠀⡇⠀⢠⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⠀⣿⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⣸⡇⠀⢸⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢿⡇⢸⢸⠀⠀⠀⣿⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⢸⡇⢸⠈⠁⠀⠀⢿⡄⠸⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⡇⠞⠀⢀⡄⠀⢸⠇⠀⠰⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣲⣦⣄⡀⢻⡇⠀⠀⢸⠁⠀⢾⡄⠀⣶⢶⠀⠀⠀⠀⣀⡤⠤⠄
⠀⠀⠀⠀⠀⠖⠒⠂⠀⢀⣼⣏⠁⠉⠁⠘⠃⠀⠀⠀⠀⠀⡼⠃⣀⡁⠀⠶⣦⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⢰⡋⠀⠀⣠⠤⠐⠦⡄⢠⠀⠀⠙⠀⢠⣿⣄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠈⢉⡀⠀⠃⠀⠀⠀⡀⠈⠓⢂⠀⠀⢀⣼⠇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠻⣧⣀⣀⣼⠇⠀⢿⣤⣴⠟⠷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠴⢂⡤⠠⠦⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⣻⠖⢂⢁⡴⠋⠀⠀⠀⠀⠀⢀⡀⠘⠶⢢⡀
⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠀⢃⠀⢰⠟⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⣷
⠈⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡯⠿⠠⠀⠖⢁⣯⣴⣄⠀⣀⠀⣏⠁⠈⠁⠐⠂⠲⠀⠃
⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⠀⡀⠀⣼⣾⡟⣿⡃⡴⠸⠇
⢻⣄⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠖⠀⣴⡿⣛⣩⢲⣆⡄⠀⠀⠀⠀⢀⣶⠾⠆
⣹⣁⣡⣄⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⢁⡄⠀⠀⠀⠀⠀⣿⣿⡟⡿⢻⣿⠃⠀⠀⠀⠶⣿⡥⣴⠀⠀⠛
⣿⣿⣿⢿⣿⣿⣶⣶⡂⣤⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠜⠁⠀⠈⣡⣸⠀⠀⠀⢸⣿⣯⠸⢳⣿⣿⠀⠀⠀⠀⠀⠉⢏⢣⠃
⣿⣿⣿⠶⠛⠉⣉⣙⣿⣿⣿⣿⡁⠀⢤⣤⣤⣀⢶⢆⣀⣴⡿⢿⠇⠀⠀⢠⣤⣼⡻⣃⠀⠀⠀⠸⣿⣿⣷⣿⡉⢻⡆⠀⠀⠀⠀⠀⠀⠉⢱⣴⣦
⠟⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⣶⣼⠉⠙⢿⣿⣯⣟⢋⣥⠠⠾⣶⣶⡾⣳⣷⣿⡏⠀⠀⠀⠀⠹⣿⡿⣿⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⢹⣿⣿⣿⣿⣶⣶⠀⠭⠉⠛⠀⢈⣻⣿⠽⣿⣴⣷⣿⣿⣷⡀⠀⠀⠀⠀⠈⢷⣾⣿⣿⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⣿⣿⣿⣹⣿⣗⢦⣄⣀⣙⣦⣦⣈⣠⣾⢭⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠛⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⣯⣩⣿⣿⣿⣷⣬⣉⠁⠉⠉⠉⢉⣡⠾⠟⣵⢞⣿⡟⠀⠀⠠⠀⠀⠀⠀⠀⠉⠙⠳⢶⣦⣽⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠄⠹⢿⣿⣿⣿⣿⣿⢛⣛⣻⣷⣿⠯⠿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣷⠦⠄⣲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠀⠒⠛⠋⠉⠀⠀⠀⠀⠜⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠠⢤⠍⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠙⠒⠿⠛⠋⠛⠋⠉⠋⠛⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣠⣶⣤⠶⣀⣀⣄⣀⣀⣤⡄⠀⠀⠐⠂⠐⠒⠄⠨⣯⣠⣤⣤⢤⣤
⠀⢀⡀⢤⣤⣤⡀⢀⣀⠀⠀⡀⠀⣀⣠⣤⣂⣤⡤⠀⠤⠴⠖⠒⠒⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⢄⣀⣀⣀⣀⣀
⣭⣥⣤⣤⣄⣐⣒⣠⣤⣶⣶⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠭⠍⠉⠉
⣛⣛⣛⣻⡿⠟⠛⠛⣿⣿⣿⣿⣿⡿⠒⣶⣶⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⣢⣤⣤⣤⣤⣤⣤⣀⣀⣀
⡉⠉⢸⣿⣿⣿⣯⣭⣭⣭⣭⣭⡟⠋⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⣉⣩⣭⣉⣉⣉⣉⣉⣩⣿⣿⣿⣶⠶⠶⠶⠶⣶⣖⣒⣐⣒⣒⣒⣒⣺⣿⣿⣿⣿⡿⠿⠿⠿⠿
⣿⣿⣿⣿⠿⠟⠓⠶⠶⠶⠶⠶⠶⣦⣤⣀⣀⡐⠒⠒⠒⢚⠛⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠿⢛⣛⣛⣉⣉⣉⣉⣛⣛⣛⣻⣿⣶⣶⣤⣤⣐⡒⠒⠒⠒
⠋⠉⠙⠒⠢⢤⣤⣀⣀⣀⣠⣤⣤⣤⣄⠀⠀⠀⣀⣀⣠⣤⣶⠶⣛⣋⣉⣉⣩⣥⣄⠀⣤⣤⣶⣶⣶⣶⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣻⣿⣛
⣒⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠙⣛⣛⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠷⠒⠂⠀⠉⠈⠉⢉⣉⣛⣻⣷⣶⣶⣶⠶⠶⠶⠶⠒⠛⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡥⠴⠶⠀⠀⢀⡀
⠉⠉⠀⠐⠓⠒⠒⠒⠒⠶⠶⠲⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣈⣉⣛⣀⣀⣛⣻⣿⡿⠛⠛⠛⠛⠋⠉⠉
⠛⣻⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⢿⣟⡓⠒⠀⠒⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣈⠛⢛⣛⡓⣒⣒⣛⣿⣷⣶
⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣭⣤⣤⣤⣤⣤⣶⣶⣶⠿⠿⠿⣿⣿⣿⣿⣿⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣉⣉⣉⣤⣤⠠⣤⣤⣤⣤⣬⣭
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠉⠙⠋⣉⣭⣅⣀⣀⣈⣉⡉⠙⠛⢛⣂⣀⣀⣉⣉⣉⣙⣛⣻⣿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠿⠛⠛⠛⠋⢉⣉⣁⣠
⣿⣿⡟⠛⠛⠟⠛⠿⠿⢿⣿⣿⣯⣭⣍⣉⣉⣉⣉⠉⠉⠉⠁⠀⠀⢀⣀⣉⣉⡉⠭⠭⠥⠾⠟⠛⠛⠋⠉⣉⣉⣉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠙⠛⠛⠛⠋⠉⠉⠁⠀⠈⣉⣉⣩⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟
⣉⣀⣀⣀⣀⣤⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⠿⠿⠟⠛⠛⠛⢛⣛⣛⣿⣿⣯⣭⣭⣭⣭⡽⠿⠿⠿⠿⠟⠛⠛⠛⠉⠛⠛⠛⠛⠋⠀⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣦⣶⣦⣤⣤⣶⣶⣤⣤⣤⣴⣶⣾⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣾⣤⣄⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⣀⣀⣀⣀⠀⣀⣠⣀⠀⠀⣀⡀⣀⣀⣀⣀⣀
⣭⣭⣭⣭⣤⠤⠤⣤⣤⣶⠶⠶⠶⠖⠒⣛⣻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠏⠉⠉⠙⠛⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠚⠉⠩⠉⣁⣒⣀⣀
⣿⣿⣟⣉⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠉⠉⠉⠁⢀⣐⣒⣒⣒⣚⣛⣓⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠴⣶⣶⣷⣿⣻⣛⣿⣟⣿⣛⣟⣿⣉⣉⣛⣛⣛⣻⣿⢿⣿⣿⣟⣟⣛⣛⣛
⡶⢶⣾⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠶⠷⠾⠿⠿⠿⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠠⠤⣶⣶⣶⠶⠖⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢉⣉⣙⣛⣛⣛⠛⠛⠻⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣾⣿⣷⣶⣶⣶⠶
⠀⠀⠀⢀⣀⠀⠀⠤⠤⠤⠤⠴⣾⣿⡿⠛⠛⠛⠻⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀
⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠒⠚⠛⠓⠒⠚⠓⠚⠛⠿⠭⠭⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣤⣤⣤⣤⠤⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⠿⣾⣿⣿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠠⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⢀⡂⢼⡉⠁⠓⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⢀⣁⠀⠀⠀⠀⢠⡀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⣀⠀⠀⠀⠰⠀⠣⠄⠀⠀⠂⠀⠀⠈⠀⠀⠆⠈⢴⡒⠁⠀⠀⠀⠠⠀⡐⠕⠀⠀⠠⠂⠀⢀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢢⠣⡀⠀⠀⠀⢪⠠⡀⠀⢀⠷⣚⠆⡀⠀⠀⠀⢆⢠⠀⡑⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣀⠂⠀⠀⠀⠈⠘⠋⡀⠀⠀⠂⠐⠀⠀⠁⡘⡰⢉⠆⠐⠊⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⠈⠠⢈⠀⡠⢠⢯⠏⢀⠀⡀⣂⣔⠀⢀⡂⠀⢙⡁⠁⠀⠀⡂⢼⠇⡬⠀⢀⢀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⣁⣤⣖⠊⠈⠷⠤⠔⠧⠤⡀⠀⢬⣡⡍⠔⠚⠒⠒⠊⠋⠋⡛⠹⣗⢲⠟⣦⣒⠆⠰⢒⠚⠈
⠀⠀⠀⢀⢄⠀⠈⠀⠀⠕⠮⣄⠀⠀⢀⡜⠑⢤⡶⠴⠃⠀⠀⣠⠢⣔⠀⣀⠬⣆⡠⢯⡀⠤⠺⠎⠸⡟⠉⠚⠂⠊⠀⠐
⠀⠀⠀⢀⡁⡀⡄⠀⡀⠠⠀⠨⠙⠤⠾⠒⢈⣠⡝⠁⠠⠆⢉⡁⠤⠠⢉⡉⠠⠌⠠⠐⠁⠀⠀⠀⠀⠀⡢⠀⠲⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠈⠄⠄⠀⠀⠀⠀⠀⢰⠀⠀⠻⠓⠢⠖⠀⠓⣯⣥⣈⣴⠂⢀⠤⠒⠉⡀⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⢡⡦⢄⠀⠐⠀⢀⠔⠠⠀⠀⠀⡄⠠⢆⢭⠉⠁⠈⢀⠄⢔⠀⠀⡀⡀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⢐⢠⣦⣤⠇⠀⠢⠤⠔⡛⠂⠀⠀⢠⠔⢣⠞⠚⠋⠐⠃⠈⠀⠠⠀⠆⠔⠈⠀⠠
⠀⠀⠀⠀⠀⠢⠹⡄⠀⠀⠠⣢⡄⠀⡀⠠⠔⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠔⠁⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠡⠀⠀⠀⡤⠚⠖⠐⠀⠀⠡⠀⠀⢀⢄⠄⠠⡀⠂
⠀⠀⠀⠀⠤⡎⠀⠤⠀⠤⠈⠠⠀⠄⠀⠁⠀⠠⠠
⠀⠀⠀⠈⠠⠈⠀⠀⠉⠠⠀⠀⠀⠄⠀⢀⣪⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠛⠉⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠞⠋⠉⢀⣀⣠⡤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣝⣌⣜⣧⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢈⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⢒⣚⣛⣛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣒⣲⣶⡶⠤⣴⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⡟⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠫⣿⣿⣟⣛⣒⣒⡒⠲⠶⠶⠒⣒⣒⣒⣒⣒⣛⣛⢛⡿⠋⢉⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣼⠁⠀⣼⢁⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⡤⠶⠶⠖⠚⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠓⠲⢶⠇⠀⢰⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣻⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡟⢳⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠒⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠥⠶⡾⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⣸⠃⠀⣸⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡟⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣰⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡟⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡾⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠞⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡈⠉⠛⠲⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣵⣲⡤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⣖⣚⣭⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣭⣔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠛⠿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡷⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠬⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⣰⣶⣤⣄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⣧⡉⠛⠻⢿⡇⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠭⠤⠀⠀⢀⠀⠊⠛⡄⣄⡜⠁⡈⢀⣀⠂⢀⡀⠀⠀⢀⣀⡀
⠀⠀⣀⠤⠄⡒⠖⠛⠉⠉⠁⣀⡤⠴⠖⢒⣋⣩⠭⠭⢉⡉⠉⢡⠇⠈⡧⠬⣩⣉⣉⡚⠒⠒⠦⣄⡈⠉⠉⠑⠋⠤⢀⡒⠠⠄⣀
⠐⠉⠀⡴⠉⠀⠀⠀⠐⡈⣼⠁⠀⣰⡾⠋⠁⠀⢰⠁⠀⠀⠒⠁⠀⣀⡐⢤⢀⡀⠨⡉⢻⣮⡅⠈⠻⢶⣔⠀⠀⠀⠀⠘⢲⣄⠀⠉⠒⠤⡀
⠀⠀⠀⣇⠄⡀⠀⠀⠀⡂⣿⠀⠀⠐⠷⣄⢀⠀⠀⠉⠒⠤⣤⡄⣀⡈⠉⣓⠱⠡⠐⠁⣼⠋⣳⠀⠀⢨⠙⡅⠀⠀⠀⡂⢕⢽⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠢⣄⡄⢄⢄⠀⠈⠺⣄⠦⠀⠀⠉⠚⠒⠬⠶⣶⣶⣦⣦⢿⣿⣶⣶⣶⢪⠬⠄⠊⢁⢔⠖⣑⠔⠀⠀⡐⡑⣌⠦⠋
⠀⠀⠠⢄⠀⠀⠈⠀⠈⠪⠦⣆⣄⣉⢁⠉⠈⠀⠪⠧⢶⣒⣲⣷⣬⣤⣆⣠⣀⢠⣀⣒⠞⠭⠅⠐⠋⡁⣄⣌⡴⠔⠋⠁⠀⣀
⠀⠀⠀⠀⠉⠐⠢⠤⠤⢀⣀⡀⠀⠈⠉⠉⠓⠒⠒⠐⠤⠤⠦⠾⠿⠶⠖⣍⣾⠤⠥⠤⠴⠖⠐⠒⠋⠉⢁⠀⠤⠄⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⠈⠤⠄⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠤⠄⠀⠀⠀⢀⡀⢀⣀⣉⣉⠉⡉⠉⠉⠉

⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠄
⠀⣀⣤⠀⠀⠀⠀⣳⣀⠀⠀⠨⠃⠀⠀⣀⠀⠀⠀⠍⢀⡀⠀⠠⠉⠀⠤⣆⣀⠀⠀⢀⡄⣀⠀⠀⠌⠁⠀⠀⢄⠀⠀⠀⠍⢀⡀⠀⠠
⡀⢀⢄⣴⣄⠀⠀⢡⡟⠀⡄⠡⡀⢀⡤⣨⣆⡀⠀⠩⣼⠀⢢⠉⢄⠀⣠⡀⣮⣀⠀⠀⢤⠇⢠⡌⢥⡀⢀⢄⣠⣄⠀⠈⠡⡝⠀⣄⠩
⠩⠓⠁⢀⣜⣠⠠⠄⠁⢀⡁⠀⠈⠝⠋⠀⣐⣁⡄⠤⠁⠀⣈⠀⠈⠹⠊⠀⢀⣊⡠⠠⠌⠀⣈⠁⠀⠋⠗⠁⠀⣘⣡⠀⠤⠁⢀⡉
⠀⠁⡄⢨⡇⠀⡀⢀⡇⠈⢀⠀⠀⠋⡠⢀⣭⠀⢄⠀⣧⠈⠁⡀⠀⠈⢡⠄⣨⡁⠀⡀⢸⡀⠉⣀⠀⠐⠉⡄⢨⡇⠀⡀⢀⣇⠈⢀
⠀⠀⠋⠁⠁⡄⢀⣎⡤⠀⢈⣏⠀⠀⢻⠉⠈⠤⠀⣸⣡⠀⢀⣫⡁⠀⠘⠟⠉⢡⠄⣠⣇⡄⠠⣘⡍⠀⠀⠫⠋⠉⡤⢀⣌⣠⠀⢈⣋
⠀⡌⠃⠀⠀⠀⢁⣕⠃⢤⠀⣭⠀⢄⠙⠀⠀⠀⠁⣨⠊⢠⠄⢩⡅⢠⡈⠂⠀⠀⠈⣈⡘⠁⡤⠈⡍⠀⡌⠁⠀⠀⠀⢁⣅⠋⢤⠄⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠒⠂⠈⠁⠀⠉⠁⣀⡀⠀⡁⠀⠑⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠤⠴⠀⠀⡀⣀⠹⠿⠄⠈⢀⣠⠀⣤⠤⠁⡙⠁⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⢆⣀⡀⠀⢀⣤⠖⠀⠙⢚⣙⠀⠀⠄⠀⠠⣤⣀⡁⠀⣀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⣠⢤⣾⠁⠀⠁⠯⡿⠀⠀⠀⠀⠀⠲⢂⣾⣶⣤⠄⢠⣽⡀⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠀⠀⠀⢐⠘⠃⣹⢷⡄⠀⠀⠀⣻⣧⠀⡀⠀⠂⠉⠱⡀
⠀⠀⠀⡀⠀⠀⠀⣠⡀⡸⠮⠲⡇⠒⠼⣷⣿⠏⠀⠉⣰⣦⣺⢿⣯⢏⠛⠰⠆⠤⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⡀
⠀⠀⠠⠀⠀⠀⠀⡙⠈⢡⠄⠈⠈⡒⠄⢈⣻⠇⠀⠀⠊⠉⢼⣾⠟⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠆⡈⢹⢿⢿⡗
⠀⠀⠀⣀⠀⠚⠁⠙⠚⠣⠇⠀⡀⠷⠌⠋⢉⣇⠀⠀⠀⠀⡼⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⣤⠄⣀⡀⡀⠠
⠀⢀⣍⣻⣿⡏⢀⣓⣶⢷⣶⡏⣯⣤⣤⣶⠂⣤⢶⣾⣷⣾⣶⣀⣔⡀⠒⠀⣀⣀⣀⡀⠀⣀⣀⠀⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠈⠉⠁⠈
⠀⠸⡷⢶⠄⠻⠻⣿⣿⠏⡟⠿⠐⢚⡷⠶⣿⣟⠙⠛⠀⠛⠻⣟⣩⣐⠂⠀⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠤⢄⣀
⠀⠀⠤⠤⠤⠥⠤⠭⠝⠛⠛⣁⣘⣥⠖⣖⣵⠀⠁⠀⠁⠀⢀⡘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠉
⠀⠀⠤⠤⠦⡄⢀⠀⠀⠀⠊⠁⠀⠀⠛⠠⠉⠁⠂⠀⠀⠀⠈⠃
⠀⠀⣀⡠⠎⠁⠀⢉⣤⡍⠀⠤⠢⣀⣀
⠀⢈⣍⠁⠚⠀⠀⠘⠓⢢⣤⡴⢠⣬⡍⢉⡂⠀⠄⠀⠀⠀⠈⠉⠁⢀⠄
⠀⠈⠁⠰⠄⠀⠢⠀⠈⠁⠀⠂⠀⠒⠘⠉⠀⠉⠁⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢏⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠶⠲⡠
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⣀⠀⠀⠀⠀⣤⠀⣿⣯⣤⡷⣶⡀⠰⣶⢂⢀⣀⣠⣤⣤⣤⣤⣶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠂⠚⢯⣤⣘⢿⣯⡦⠅⣤⡥⣾⣿⣿⢿⣿⣿⣿⣿⣷⡇⣠⡢⣼⢟⣻⠿⣉⣠⣴⣾⣶⣯⣭⠉⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠉⠛⠛⠿⠿⠿⠿⠿⢿⣿⠿⣿⡷⠿⠗⠒⠋⠉⠁⠈⠉⠀⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣤⣴⣶⣿⣿⠶⠀⠀⠀⠀⠀⠈⠒⠢⠤⠀⠀⢀⣀⡀⠀⠀⢠⣤⣤⣤⣤⣤⡤⠄⠀⠀⠐⠂⠉⠉⢉⣠⡄⠐⠀⠀⠀⠠⣤⡤⠄⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⠶⠾⢿⠿⠿⠷⠶⠶⠦⢀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⢀⣠⠀⠀⠀⠚⠛⠛⠋⠻⠉⠉⠙⢂⣤⣩⣴⣾⣿⣿⣿⣿⣿⣿⣦⣤⣤⣠⠄⠀⡀⠉⠉⠉⠱⣤⡖⠂⠀⠒⠠⢤⣴⣦⣤⣶⣶⣶⣶⣶⣶⣶⡤
⠐⠛⠀⠀⢤⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⢋⣩⣥⣶⣶⠿⠞⢁⣀⣤⣶⣿⣦⣤⣀⣠⣀⠀⢀⣍⢻⠟⠻⠿⠟⠛⠛⠁
⢾⣧⣶⣦⣶⣿⣶⣾⣿⣶⣦⣀⣠⣄⡀⠀⠀⢀⣀⡤⠰⠶⠒⠒⠶⣶⣤⣌⣋⣉⡉⠁⠶⠾⣿⣿⣿⣿⡿⠿⠟⢻⣿⠿⠿⢶⠶⠷⠴⠂
⣹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⠠⢾⣿⡟⠀⠀⣠⡖⢀⠀⠀⠀⠈⠙⠛⠓⠶⣤⣤⣤⣀
⣰⡟⣿⣿⣿⣿⣷⡿⠿⣿⣿⣿⡿⠙⣻⣵⡿⠋⢠⣄⣸⣿⣿⣿⣦⣼⣿⣶⣄⡀⠀⠀⠂⠂⠙⠋⠛
⠈⣽⠿⢿⠷⢿⡯⢐⠾⠗⠉⠀⠀⠛⠝⣫⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⣤⣤⣤⣤⣀⣤⣴⣾⣆⠀⠀⠀⢀⣀⡀
⣶⣦⣤⣤⡤⠋⠑⢤⣄⡀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣟⠉⠻⠿⠿⠟⠛⠛⠛⠛⠁⢀⣀⣴⣿⣿⣿⣦⣀⡀
⠻⡿⠛⠉⠀⠀⣤⠀⠙⠷⣦⣄⣀⠀⠀⢈⣘⡛⣿⣯⣛⠛⠻⠿⠍⠛⠓⢶⣶⣀⠀⠀⠀⠈⠻⠿⠄⠀⠀⣀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⢠⠶⠁⠀⠛⠀⠀⡀⠀⠈⠉⠛⢏⣀⠈⠉⠑⠿⠇⠠⠐⠂⠀⠀⣀⣠⣤⣴⣶⡶⠒⣚⣋⣁⣴⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⢰⡄⢠⣶⣄⢶⣾⣷⣾⣿⣿⣀⡀⠀⠀⠈⠙⠓⠲⢤⣤⣤⠒⢤⣄⠐⠛⠛⠛⢿⣿⣿⣯⣍⣉⣁⣈⡉⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠿⠛⠛⠁
⣿⢱⣿⣿⣿⣯⣛⠿⠛⢻⣿⣿⣿⠀⣷⣄⣤⣄⣀⠀⠈⠙⠻⠷⣤⣀⠀⠀⠙⠂⠈⠻⢿⣿⣿⣿⣅⣀⣀⠀⠒⠒⠖⠂⠠⠄⠐⠒⠀⠔⠂
⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⢋⣾⣿⣿⣯⡻⣿⣷⣶⣦⣄⣀⠀⠈⠘⠳⢦⣤⣀⣀⠀⠀⠀⠉⠉⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠎
⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣷⡜⣛⣿⣿⣿⣿⣿⣶⠶⣦⡀⣉⣉⠛⠿⠿⠷⠶⠿⢿⣿⣶⣶⣿⣯⠄⠀⠰⠟⠋⠉
⠈⢿⣌⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣥⣌⠻⢯⠋⣀⣤⣴⣶⣦⠀⣛⡻⠿⠿⣿⣶⣦⡀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠂
⢧⣮⣻⣿⣿⣶⣦⣉⠻⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣶⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀
⢈⠛⢻⣮⡉⠙⣿⣿⣧⠈⠛⠛⢈⠻⣿⣿⣿⣌⠻⠿⣿⠿⠓⠈⠻⡿⠿⢿⠿⠏⠙⠛⠛⠿⠿⠛⠋⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣾
⢹⣿⣦⣽⣿⣾⣿⣿⣿⣿⣾⣿⣶⣶⡄⠁⠀⠉⠉⠲⠦⣤⣄⠀⣠⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣆⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢒⣡⠼⠋
⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠀⠀⠀⠀⢀⠚⡆⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠢⢄⠀⠀⠀⠀⠀⡄⢠⡀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠈⠴⠃⠠⡓⠋⠀⠀⠀⠀⣀⠠⠔⡊⠠⠤⠴⠀⠤⠴⠀⠄
⠀⠀⠀⡠⡀⠀⠀⠈⢦⠐⢌⠓⠢⣀⡤⣀⡏⠀⣷⡀⠀⠃⠀⠀⠀⢰⠀⠀⡀⠤⠴⠣⣇⣀⣀⡤⠖⠋⢡⠤⠊⠀⠠⠃
⣀⠀⠀⠀⠜⠀⠀⠀⠀⢳⢠⠳⠤⢄⡀⢀⡀⠤⣀⡀⡑⢲⠀⠀⠀⢘⡉⠉⠀⠐⠀⠀⠈⠉⠠⡤⢤⠠⣇⡀
⠃⡁⠤⠤⠄⣀⣠⠖⠀⠁⢚⢄⡀⣀⡈⠉⡄⠐⠀⣤⢀⣾⡀⠀⠀⡘⠁⡀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠈⠑⢉⠉⠲⠶⠚⠉⢀⡤⣄⡒⢒⣲
⠀⠈⠐⣆⠠⣤⣤⠶⠒⠂⠛⠋⠉⠀⠍⣙⠶⠤⠤⠝⠋⠉⠉⠢⢴⡥⠞⣃⠈⢗⠤⠤⠤⠤⡒⠉⠙⠳⠤⠤⢂⡡⢐⣶⠾⠛⠋⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠘⠢⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠤⠤⢶⣆⣀⣠⠞⡁⠀⠀⠑⠐⠦⠴⠚⡁⠂⠒⠒⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠤⣤⡄⠴⠊⠀⠀⠀⠀⠉⠉⡁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠃⠀⠀⠙⠒⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠤⠄⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠊

⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣭⣷⣶⣦⣬⣭⠉⠉⡉⠛⠛⠃⣀⣈⣛⣈⠉⢁⣠⣤⣾⣧⣼⣶⣤⣭⣍⣉⣁⣠⡶⣴⠶⣶⡟⢾⡓⠮⣿⣵⣶⣦⣀⣠
⣛⡳⢒⣀⣉⣀⣀⣀⠈⠉⢠⡴⠟⠋⠉⠉⠩⠍⠙⣿⠟⠛⠛⣻⣻⣿⣿⣿⣿⣿⣿⣭⣷⠿⠍⠉⠙⠻⠛⠖⡩⢭⣭⠍⢻
⣛⣛⣛⣛⣛⡛⠉⠉⠐⢿⣿⣶⣖⡒⠒⢒⠛⣻⣿⣽⡷⠤⠴⠏⠿⠏⠑⠺⠃⠈⠁⢈⡀⠀⣀⠀⠀⢀⣉⣉⣗⠰⠊⣀
⠤⠼⠛⣩⣯⡴⠒⢚⣯⣿⣿⣏⣉⣹⣿⡴⠖⠀⠲⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠞⠓⠿⠻⣶⣿⣉⣉⣽⣿⣷⠶⠖⣛
⢶⣶⣶⡶⠟⠛⠿⠯⢭⣭⡉⠉⠉⠉⠛⠅⠀⠀⢀⣢⣿⣿⣿⠦⠀⠀⣠⣤⣤⣤⠄⠘⢋⣰⣶⡖⠚⠛⠓⢲⣾⠝⠲⣤⠟
⠀⣿⣿⠆⠀⠀⠀⠀⠀⠉⠉⣉⣙⣛⣚⣀⣈⠉⠉⠉⠀⠀⡀⠀⠀⠀⢨⡍⠙⢻⣶⣶⡿⣛⣉⣴⣴⠶⠛⣋⣥⡶⢂⡴⢚
⠀⠘⠿⣦⣄⠀⠀⠘⠿⣿⣿⡿⠟⠛⣋⣉⣭⣤⣤⣤⣴⣶⣶⠶⠤⠤⢴⣦⠄⣨⢽⣟⣉⣫⣩⠅⢲⢾⠛⠉⠀⠠⠶⠟⠛
⠄⣤⢀⣈⣻⣷⡦⠀⠀⣠⣶⣿⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⠷⠖⣒⣒⣭⣥⠾⠿⠶⠛⠛⢛⣭⣤⣴⣿⣷⣶⠖⠚⠋⠿⠿
⣀⣈⣱⣮⡉⢉⣤⣤⠤⠤⣭⣭⣉⣙⣛⣛⣛⣛⣛⣛⠋⠁⠀⣛⠭⠭⠶⠦⠤⠶⠶⠿⣿⣯⣽⣷⣿⣿⣿⣧⣶⣶⠶⠖⢲
⠉⠉⠛⠋⢀⣀⣙⠓⠆⠤⠀⣶⣒⣀⣀⠈⠭⠭⠟⢋⣴⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠛⢉⠀⠔⠉
⠀⠀⠀⣠⣾⣿⣿⠟⠛⠛⠲⠶⠶⢶⣶⣶⣶⣿⣿⣿⠟⠛⠛⣷⣶⣦⠀⠀⠀⠀⠀⠰⠶⠶⠶⠄⠀⠄⠀⠹⡗⠀⠀⠤
⣀⠀⠀⠙⠿⢿⣿⣦⣤⣀⣀⣠⣤⣾⡿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠙⣳⣦⣤⣤⣤⣴⣤⣤⣤⣤⣄⣠⣄⣠⣠⣅⣀⣀⣠⣔
⣛⠛⠓⠀⣀⣀⣀⣤⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣤⣴⣦⣤⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣤⣶⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠈⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠉⢲⣼⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡉
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣤⣤⣤⣤⣤⣁⣤⣤⣄⣀⣀⣀⣀⡀⣿
⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠉⠉⠉⠉⠑⠒⠀⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⣿⣿⡗⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠄⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣠⢤⣶⣾⡿⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿
⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⣴⡶⢛⣿⣿⣿⡏
⠀⠉⠉⠙⠛⠻⠶⢶⣦⣴⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⢤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣷⣶⣶⣦⠄⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⡀
⣤⣤⣤⣤⣄⣀⣤⣤⣶⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣠⠤⠤⠤⠴⠒⠒⠚⠙⢓⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠚⠉⠉⠉⢳⣉⠉⠀⠳⣖⡤⠶⢶⣾⣭⣽⣚⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⣠⡤⠴⠚⠁⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣩⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠂
⠀⠀⠀⠸⣔⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⢀⣈⠙⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⠟⢠⠴⣦
⠀⠀⠀⠘⠾⠃⢠⣞⡓⠒⣶⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⣶⣆⣀⢄⣠⠚⠛⠛⠁⠀⠈⠉⠁
⠀⠀⠀⠀⢠⠴⠶⠚⠻⢭⣀⣀⣀⠈⠻⢷⣦⣤⣰⣤⠤⣶⣋⣀⣠⠖⢻⠆⢉⡭⠽⡄⠀⠀⠀⠀⣖⣻⡿⠆
⠀⠀⠀⠀⠻⣄⢄⠀⠀⠀⠉⠉⠉⠛⠒⢦⡀⠀⠀⠀⢸⣥⣀⡀⡀⢀⣟⡠⠬⠭⣭⠵⠚⠛⣳
⠀⠀⠀⠀⠀⠈⠓⠮⠴⣶⠤⠖⢫⡭⠭⣭⣤⡄⠀⠀⠀⠀⠀⠙⠛⠋⠘⢶⣦⡤⠤⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠶⠦⠤⠤⠤⠄⠀⣀⣀⣠⣤⣴⠶⠿⠿⠷⠶⠶⣤⣤⡉⠉⠛⠛⠛⠒⠒⠒⠒⢚⣛⣉⣉⣁⣀⣀⣀⣀⡀⠀⠂⠒⠒
⠈⠉⠉⣈⠉⢉⣉⣉⣁⡒⠛⢋⣉⡉⠉⠉⣉⣭⣴⣶⣿⣿⣿⣿⣿⣶⣮⣍⣉⠉⢉⣉⣠⣤⠤⠶⠶⠶⠶⢤⣤⣄⡀
⠈⠉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⡒⠚⠉⠉⠩⠤⠤⠶⠖⠒⠒⠶⠮⢭⣍⡉⠙⠓⠲⠶⣦⣤⣤⣤⣴⣶⣶⣶⣶⡾
⠲⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⣀⣠⣤⣶⣶⣾⣿⣿⣷⣶⣶⣤⣄⡉⠙⠺⢖⠦⢤⣍⣛⠛⠿⠿⢛⣛⣁⣀
⣶⣤⣀⠠⠤⠤⠤⠤⠶⠖⠒⠋⠓⠚⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢀⡤⢶⣚⣩⣭⣭⣀⣀
⠙⠛⠛⠛⢁⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⢀⣀⣀⠀⠈⠉⠉⠙⠛⣛⠋⢁⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣶⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣝⣛⣛⣛⣋⣩⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣖⣒⣒⣒⣒⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣉⣉⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣉⣉⣉⣁⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿

⠀⠀⠀⠀⢰⠊⠀⠄⠂⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠘⡀⠀⠰⣫⡟⠀⠐⠀⢨
⠀⠀⠀⡀⠂⠈⠒⠙⠍⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢰⡆
⠁⠀⠀⠀⠑⠀⠢⢤⣤⠊⠁⢀⡔⠀⠀⡤⠀⠀⠀⠀⠀⡄
⢦⡹⢶⡆⠀⠀⠈⡆⡇⠀⡴⠋⢠⡒⠀⠀⠀⢀⡰⣿⢷⡄
⠀⠀⣸⠀⠀⠀⠀⢃⠃⡈⠀⠀⢛⣧⡾⠂⣱⣮⡿⠯⠿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⡀⢀⡇⡄⠀⠰⢠⡎⠖⢀⠈⣉⣟⣩⡴⠟⠋⠀⣀⠀⠠⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠁
⠁⢈⠌⠀⢀⠆⣾⢷⢋⠌⢡⠟⣿⠋⠀⠀⣰⠊⠉⠙⣆⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⢠
⢠⡏⠀⠀⠋⣼⠃⠊⠀⣰⠃⣼⠃⠀⠀⠀⡇⠀⡰⡦⠏⠀⢀⠀⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⠎⠀⣘
⣸⠃⠀⠀⡼⠃⢀⠀⣰⡋⣼⡇⠀⠀⠀⠀⢇⠀⠙⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡠⠶⣧⣀⠀⠈
⡇⠀⠀⠴⠚⡀⠃⠰⡟⢰⠈⣇⠀⠀⠀⠀⠀⠛⠀⡠⣤⠶⡾⣦⠀⢀⡀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡔⠘⡷⠀⠀⠀⠀⠀⠈⢳⠄
⡇⢀⠀⠀⣘⠁⠀⠐⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⣀⠀⠋⠉⢽⣷⣴⣣⡄⠀⠀⠀⠀⠞⣿⠇⠀⡘
⣦⢠⡊⠀⠇⠀⠀⢸⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⣩⠁⠀⠒⠀⠱⣆⢠⠂⠀⠀⠀⠀⠈⠓⢦⡀⠀⠝⠦⠉⣀⡀
⡿⠃⡁⡼⠂⠀⠀⢸⡄⠀⠀⠀⠀⠑⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣦⡴⠚⠁⠒⢀⡔⠋⡀⢸⠃⠀⠀⠀⠀⠀⢠⡤⢀⣽⠐⠄⠀⠀⠀⠈
⣇⠀⠰⠁⠀⢀⠀⠀⢯⠢⡄⠐⠈⠒⠈⠙⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠙⡀⢡⣹⡇⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠉
⣧⠀⠀⠀⠀⢸⠀⠀⡼⣅⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠐⠖⢋⠉⠀⠀⠀⠀⠀⠀⠐⢈⣀⠀⣀⠠⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢻⡤⠂⠀⠀⠠⠘⠀⠁⠘⣧⡠⠤⠤⠀⠤⠀⠀⠂⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠠⣀⡀⠱⠘⡂⠀⠐⠑
⠀⢡⠀⠐⢠⠀⡀⢠⠘⠀⢨⠙⢶⣒⠀⠠⡒⠄⣀⠀⡀⠈⢑⡲⠀⠀⠀⠀⢀⠔⡂⠀⠀⠀⠀⠀⠸⣆⢳⡆⠀⠀⠘⠶⠖⠠⠀⠀⢀⡀⠤⠞⠋⠉⠀⠠⡀
⠀⠈⠀⠀⠆⠀⢡⠀⠀⠀⠀⡄⠀⢉⠲⢶⣌⡁⠀⠁⡈⠔⠈⠀⠀⣀⠄⠚⠁⠊⠀⠀⠀⠀⠁⠀⠀⢹⣻⣧⠠⠀⠄⡀⠙⠢⠄⠀⡀⠀⠀⠁⠢⠀⠀⠀⠈
⠂⠠⠘⣈⠀⠀⠀⠆⠀⡄⠐⡈⠢⠀⠀⠀⠉⠛⠛⠛⠖⡰⠋⣹⠋⣀⠀⠉⠠⠀⠀⠀⢀⠠⠂⠂⠀⠀⣱⠹⡀⠁⠒⠂⠀⠀⠀⢀⡀⠐⠓⠒⡚⢂⡀
⠀⠀⠀⢹⣇⠀⡀⠢⠀⠈⠠⠀⠀⠀⠀⠀⢄⠈⠀⣠⠞⠀⠠⠁⠔⠁⠀⠀⠀⠀⡁⠀⠀⠀⢀⠤⠒⠈⠉⠙⠳⠀⠄⠀⢀⡀⠤⠤⠊⠐⠈⠁⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠙⢧⡍⠀⠀⠀⡑⠄⠀⠈⠀⠀⠀⡈⠁⠀⠀⠀⢁⠂⠀⢀⣀⡀⠀⠁⢀⡠⠖⠈⠀⠀⠀⠀⠀⠀⡀⠀⠲⣄
⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠘⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⣲⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠏⠛⠑⠒⠒⠊⠁⠀⠀⠉⢲⡀
⠋⠁⠀⠠⡀⠀⠀⠈⠓⣤⡀⠘⢦⡂⠈⠀⠀⠀⠤⢤⡀⠐⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢂⠀⠀⠀⡀⠀⢄⠀⠀⢨⡇
⠀⠀⠀⠀⠈⢆⠲⣀⡀⠈⠉⠺⢮⣷⣦⣤⣤⣉⣒⠤⠤⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠶⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⣿⣿⣷⣶⡿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣶⣶⣾⣷⣶⣶⣶⣶⣷⣿⣾⣶⣿⣿⣾⣿⣿⣿⣿⣶⣿⠷⣾⠶⢿⣿⡿⢷⣾⠿⠶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛
⠤⠔⠦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁
⣀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠷⠿⢿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠙⢦⡀⣠⡴⠖⠛⠛⠻⢦⣄⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⢀⣠⠞⠉
⠀⣀⣴⠶⠿⠷⠶⣦⣄⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⣀⣀⣀⣬⡶⠶⢾⣯⡁
⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠋⠉⠀⠀⠀⠀⠈⠻⣆
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⠴⠖⠲⠶⣤⣀⣠⡶⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠄⠀⠹⣷⡀⢀⣠⣤⠶⠶⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠙⠻⣤⡀⠀⠀⠉⠻⢶⣤⣀⣀⣀⣤⡶⠾⣿⠿⡋⠅⠀⡀⠀⠠⠤
⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣻⣦⣀⣀⡀⠀⠈⠉⠉⠉⠁⢠⡾⢁⠊⠐
⠷⠶⠶⠛⠛⠋⠛⠻⢦⡅⠀⠀⠀⠄⠀⠀⠀⠀⣀⣴⠿⠟⠈⠁⠙⠻⣦⣤⠴⢢⣤⣤⣿⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⠤⣦⣤⣤⣤⠾⠛⠁⠁⠀⠀⠀⠀⠀⠸⠻⠷⠾⠛⠛⢛⢷⣧⣀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠈⠙⢶⡄⠀⢀⣂⣀⠀⠀⠐⣀⠀⠀⠀⢨⠀⠠⠀⠉⠉⡉⠭⠭⣡⡿⠛⠋
⠀⠀⠀⠀⣀⣴⠾⠛⠛⠳⢦⣄⠀⠀⠀⠀⢀⣠⡿⠟⠛⠉⠙⠛⢶⡀⣀⣦⣬⣭⣋⡁⠒⠀⣀⡈⣉⣥⠞⡋⠈
⢶⣦⣴⣞⠋⠀⠀⠀⠀⠀⠀⠙⢷⣶⠶⠶⠟⠁⠀⠠⠀⠀⠀⢤⣼⡟⠋⠉⠉⠉⠙⠛⠿⣴⣴⠿⠋⠁⠀⠈
⠁⠀⠈⠙⢷⡌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠂
⠀⠀⠀⠀⠀⣻⣦⣴⣶⣤⣀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠄⣀⣤⡿⠶⠷⠶⣶⣤⡀⠀⠀⠀⡀⢀⢻⣇⡄⣀⣠⠔
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠹⣷⣤⣤⣤⣴⠦⠶⠟⠛⠙⠋⠀⠀⠀⠀⠀⢈⣨⣷⠶⠶⠶⣦⣎⣼⠧⣋⡉⠀⢀⣴⣿
⠀⣠⡾⠟⠀⠀⠐⠁⠀⠀⠐⠀⠻⣟⠒⠄⠀⠖⢠⠖⠂⠀⠄⠖⠁⣂⣴⢿⠍⣠⡤⠦⠌⠀⠙⠻⣶⠶⠶⠾⠛⠉⠉
⣴⡫⠀⠀⠀⠀⠀⡀⢀⣦⣾⣶⡿⣿⣿⣶⣶⣦⣄⣠⣴⣤⣶⣶⡛⠫⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠁⠀⠄⠀⠀⠈⢈⣴⣟⠟⠁⠈⠐⠀⠁⠈⠙⢛⠻⢿⣮⡉⡤⠛⢝⢷⣄⣠⣴⠶⡿⠛⢻⡷⣦⣄⠀⠒⠂⣀⡀⠠
⠀⠀⠀⠀⠐⣀⣿⣝⡀⠀⠤⠞⠉⡀⠀⠀⠀⠀⠁⣄⣽⣿⣷⣤⣶⣶⠿⡿⠞⠳⠉⠁⡀⠈⠃⢝⣷⣅⣦⡵⠶⠶⠶
⠀⣠⡶⠛⠻⠉⡉⢙⡙⣻⣦⣄⠔⠡⡈⢀⡲⣦⣾⠟⠉⠀⠉⠉⠉⡀⠀⠀⢀⠀⠀⠀⠠⢨⡀⣠⣾⡯⠗⠀⡀
⣾⣫⡄⢠⣴⡜⠛⠣⠟⣎⣃⣙⣷⣤⣚⣦⣿⡟⠅⢀⣖⣺⣍⣭⣭⣥⣤⣀⣠⣴⣶⣶⣤⣤⣹⡟⡌⠜⠁
⠋⠋⠻⢧⣗⡂⣩⣿⣿⣿⠻⠛⡻⢟⣿⣿⣿⠿⠿⣿⡿⠛⣿⣻⡭⢥⣽⠿⡟⠰⠀⢄⠈⠙⢿⣟
⠀⠁⠀⠀⢻⣿⣟⣯⣿⣽⣏⣉⠓⢧⣌⠹⣿⣷⣶⠶⢚⣀⣱⣮⣴⣟⣗⢱⠝⠁⢈⠀⠈⠦⠀⠻⢧⡄⡔⠀⠀⣠⣤
⣀⣤⣬⣤⣸⣟⡙⢩⠄⣩⠘⠚⠮⠴⣙⠯⠂⢈⠻⣷⣾⡿⠿⢟⠋⠉⠙⣳⣦⣤⣶⣶⣦⣄⡄⠠⠣⡝⣦⡴⠟⠉
⠉⠥⡌⠉⠭⢉⠛⠷⣮⡓⠁⠪⠣⡔⢿⠷⢘⡂⠩⠅⠄⠁⠉⣡⣶⢂⣾⢟⠃⠀⠁⠀⢠⡉⢻⣄⣱⣾⡋⠀⡀⠄⣁
⡁⢤⣀⠤⢂⠠⡢⣤⢌⡿⣯⡵⣲⣵⣲⣿⣿⣿⣷⣶⣿⡿⢿⣛⣿⣿⣿⣷⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣯⣽⣿⣿
⡃⠀⠀⠀⡉⢈⠄⠉⠻⡞⠻⣿⣿⣿⣻⣿⣿⢿⣿⣯⣷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡯⣵⣶⣟⣶⣮⣼⡽⠻
⡆⠀⠀⠀⠄⠠⢀⠹⣦⣮⡮⣝⢿⡿⢿⣽⣾⣿⣽⡿⢟⢯⣭⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢻⣿⢿⣮⡁

⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠾⠛⢒⠒⣒⣋⣉⣤⡴⠶⠛⠓⣒⣒⣚⣉⣡⡴⠶⠚⠛⣒⣒⡒⢛⣉⣤⡴⠶⠚⠛⣓⣒⣚⣋⣡
⠀⠀⠀⠚⢛⣉⡭⠭⠭⣍⣠⠤⠶⠛⣋⡩⠭⠭⢭⣀⠤⠶⠞⢋⣩⠥⠬⠭⣭⣠⠤⠶⠞⢋⣩⠥⠤⠬⣄
⠀⠀⠀⣩⣉⣀⠛⠛⠶⢦⣬⣉⣩⣉⣉⡙⠛⠲⠦⣤⣍⣩⣭⣍⣈⠙⠛⠶⢦⣬⣉⣩⣭⣍⣉⠙⠓⠶⠦
⠀⠀⠀⠶⢤⣉⣛⣓⡲⢖⣒⡒⠲⠤⣍⣙⣛⣒⠶⣒⣒⠒⠶⢤⣉⣛⣓⣲⢶⣒⣒⠒⠦⢤⣉⣛⣓⡶⣖
⠀⠀⠀⠳⠶⠤⠭⠤⢤⣬⣉⠙⠛⠶⠦⠤⠶⠦⣤⣄⡉⠙⠳⠶⠤⠭⠶⠦⣤⣌⣉⠙⠓⠶⠶⠶⠶⢤⣤
⠀⠀⠀⢚⣉⣭⣝⠒⠦⢬⡭⠭⠛⣋⣭⣭⡟⠲⠤⣬⡭⠭⢚⣉⣭⣭⡓⠲⠤⠬⠭⠝⣋⣩⣭⠝⠒⠦⠤
⠀⠀⠀⢉⣁⣤⡴⠶⠒⣒⣒⣚⡋⣉⣠⣴⠶⠚⢛⣒⣒⣛⣋⣉⣠⣴⠶⠚⢋⣒⣚⣛⣉⣀⣤⡶⠖⠛⣒
⠀⠀⠀⠭⠁⠲⠶⠖⣛⣩⡤⠶⠬⠍⠒⠶⠖⢚⣩⡥⠶⠖⠉⢑⠲⠶⠖⣛⣩⡥⠶⠖⠉⢐⠒⠒⢚⣋⣥
⠀⠀⠀⠛⣉⣉⣭⠭⢭⣤⡤⠶⠟⠋⣉⣭⠭⠭⣡⡤⠶⠞⠛⣉⣩⡭⠭⠭⣥⡤⠶⠞⠋⣉⣩⡭⠭⢥⡤
⠀⠀⠀⢋⣩⣐⣒⠒⠒⠦⣤⣐⣚⣋⣁⣒⡒⠒⠶⢤⣍⣚⣋⣩⣐⣒⠛⠒⠶⣤⣐⣚⣋⣩⣐⣚⠛⠒⠦
⠀⠀⠀⠶⢤⣌⣉⠛⠓⠶⠶⠒⠶⢤⣄⣉⡙⠛⠲⠶⢒⠒⠶⢤⣄⣉⠛⠓⠶⠶⣒⠲⠶⢤⣌⣉⣛⠓⠒
⠀⠀⠀⠛⠲⠬⠭⠭⠴⣬⣍⣉⠛⠲⠦⠭⠭⠴⠦⣭⣍⣉⠛⠲⠤⠭⠭⠴⠮⣭⣍⣉⠓⠲⠦⠭⠥⠶⢭
⠀⠀⠀⢛⣛⣓⣛⠲⠶⣤⣄⡉⢙⣛⣋⣉⡛⠲⠦⣤⣈⡉⢛⣛⣋⣙⡛⠲⠦⣤⣌⠉⣙⣉⣉⣛⠓⠶⣤
⠀⠀⠀⣉⣤⡴⠶⠛⠓⣒⡒⠚⣉⣡⣤⠶⠚⠛⣒⣒⠒⢚⣉⣡⡴⠶⠚⠙⣒⣒⣒⣋⣡⣤⠶⠖⠛⢓⣒
⠀⠀⠀⢍⡠⠤⠶⠚⣋⣩⠭⠭⢭⣀⠤⠶⠞⢛⣉⡭⠭⠭⢍⣡⠤⠶⠞⢋⣩⠥⠤⠭⣄⣠⠴⠶⠛⣉⡭
⠀⠀⠀⢛⣈⣉⣉⣉⣡⣤⠶⠛⠛⣀⣉⣉⣉⣩⣤⠶⠞⠛⢉⣈⣭⣝⣉⣩⣤⠶⠞⠛⣁⣈⣭⡭⣍⣥⠴
⠀⠀⠀⣉⣩⠤⣖⡒⠒⠶⣖⣚⣛⣉⣥⢴⣒⠒⠶⢶⣒⣛⣋⣡⠴⣖⣒⠒⠶⢖⣒⣛⣋⣡⠴⣒⣒⠒⠦
⠀⠀⠀⠤⠤⣤⣍⡉⠛⠳⠦⠬⠭⠤⣤⣍⣉⠙⠓⠶⠦⠬⠷⠤⣤⣌⡉⠛⠳⠶⠬⠭⠷⠦⣤⣌⣉⠛⠓
⠀⠀⠀⠓⠶⢤⣭⡭⠽⠚⠉⠉⠛⠲⠤⣬⣭⠭⠛⠉⠉⠉⠓⠶⢤⣭⣭⠽⠓⠋⠉⠙⠓⠲⠤⣬⠭⠝⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⣀⣠⣴⡾⠟⠋⣀⣀⣀⣀⠀⠀⢤⣀⣀⣠⣶⠟⠋⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠀⠉⠛⢿⣦⣀⠈⠉⠉⢀⣤⠖⠋⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣀⣀⣤⣶⡿⠟⠛⠛⠶⣄⠉⠻⠿⣶⠾⠛⠁⣠⣾⠟⠋⠉⠉⠉⠛⠛⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠠⠤⠴⣤⣤⣀⠁⠀⠠⢤⣤⡴⠿⠋⢀⣠⠴⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠈⠛⢷⣦⣀⠀⠀⢀⣠⡶⠛⠁⣠⣤⣶⣶⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠿⠛⠉⠉⠉⠉⠛⠳⢤⠀⠙⠻⠿⠿⠟⠋⢀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⣦⣤⣀⠀⠀⠤⠤⣤⠶⠟⠋⣠⡴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠉⠻⣷⣤⣀⠀⠀⣀⣴⠟⠁⣀⣤⣶⣶⣶⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠋⠉⠉⠉⠛⠶⣄⠀⠙⠛⠿⠟⠋⠁⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠁⡀⠈⠑⠢⢀⠀⠈⠣⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠠⠊⠉⠉⠙⣦⠀⠀⠑⠢⢄⣀⣠⠾⠃⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⡄⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢳⣀⠈⠛⠋⢁⣠⣤⣄⡀⠀⠀⠀⢀⣠⣤⣄⡑⠦⠤⠤⠤⠀⠀⠠⢤⣀⠀⠀⠀⠀⢀⣠⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠓⠶⠞⠛⠉⠤⣌⡙⠓⠒⠂⣠⡴⠶⠦⠍⠃⠐⠶⠶⠶⠶⣦⣄⣈⡛⠶⠶⠞⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠙⠛⠛⠛⠋⠙⠛⠲⢬⣉⠓⠐⠋⠁⠀⠴⠶⠦⢤⣌⡙⠳⢦⣤⣤⣤⠴⠖⢋⣁⣀⣉⡙⠓⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣈⠙⠒⣛⣛⣋⣉⣉⡓⠂⢄⣈⠁⣀⣤⡶⠞⢛⣉⣂⣀⡈⠙⠶⢤⡄⠀⠠⠶⢚⣋⣉⠉⠉⠙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠙⠓⠦⣌⡉⠉⠁⠄⠊⠉⠀⠀⠈⠙⠳⢦⣤⣤⣤⡴⠟⠋⠉⠉⠛⠲⢤⣄⣀








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⡠⢐⣀⠀⠀⠀⢄⠀⠀⢄⡀⢢⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠐⠁⢀⣴⠁⠀⠀⠀⠀⠁⠁⠰⠠⢀⡀⠏⠁⣾⣦⡽⣷⠦⡄⠀⠈⠀⡘⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⡼⠃⠀⢀⣀⠀⠀⠀⠠⣀⡀⢀⢳⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⢸⠀⡇⣶⣽⡇⢠⠃⣾⢡⣶⠟⠀⢉⣿⣧⠀⠄⢧⡄⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡆⣷⡟⠙⡇⢸⠀⣿⣿⡏⠀⠀⠈⠉⠙⢧⡢⢮⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠈⡇⣯⣇⠠⠁⠈⢧⡘⠯⠳⣄⠰⣄⠀⠀⠀⠳⣄⢙⠶⣦⡐⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣷⢛⢻⡀⠈⠀⠀⠹⡄⠀⠀⠁⠀⠉⠒⠄⠀⢼⣷⣧⣀⠳⣌⣉⢤⣤⣓⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⣿⡞⠈⢳⣄⠘⠢⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⣤⣄⣁⣟⣹⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠙⠓⠌⠒⠤⠤⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣻⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠔⠃⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠘⢤⠌⠄⠐⠂⠀⡈⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢃⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢈⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⣴⠃⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⡄⠀⢀⠀⠑⢤⠀⠘⠀⡀⠘⠀⠀⠀⠀⢸⢤⣴⢲⡶⢾⢿⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠦⣀⠠⢶⠀⠀⠈⠑⠐⢌⠀⠀⠀⡁⠐⠛⠠⠁⠌⠴⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⣂⣐⣂⡨⣤⡤⠀⢤⠽⣳⠾⢛⡀⢂⣄⠠⠤⠤⠆⠼⢤
⠀⢀⣀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⡉⠂⠀⠃⡀⠉⡉⠉⠈⠁⢀⣠⣀⠴⠀⠂⣀⠰⠛⣟⣶⡓⠓⠀⠀⠀⠀⠁⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠊⠁⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠍⠀⠐⠀⠄⠈⠉⠉⠍⠋⠁⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠩⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣠⣶⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣶⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣤⣄⡀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣷⡄⠀⣀⣤⣶⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠟⠋⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠙⠻⠿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢉⣭⣤⣤⣤⣤⣤⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⣯⣤⣤⣤⣤⣤⣭⡁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣭⣭⣭⣭⣭⣭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠼⠒⢶⠶⠂⠀⢠⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢠⣤⣄⣶⣠⣴⣾⣿⣶⣷⣿⣿⡿⠛⠻⠚⠛⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣘⣿⣿⣎⠛⠛⢻⣿⣿⣿⠻⢡⣿⣾⡟⡄⠠⠤⡴⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣷⠀⣦⣸⣿⣿⠿⠐⠀⣾⣿⡏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⠉⠀⠈⠻⣿⣿⣷⣿⣽⣿⣿⠇⣄⠀⣿⣿
⠀⠀⠀⠀⠀⣰⣾⣯⢫⡛⢿⡇⢰⡀⣄⣿⡿⠟⠛⠛⠻⣿⣦⡟⠀⢹⣿⡀
⠀⠀⢀⣤⣜⣿⠿⡻⡇⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣐⣯⣿⣥⡄⠘⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⣠⣦⣬⣿⣿⣿⡀⠀⠀⣼⣏⣩⠉⣭⡛⠋⠀⢰⣷⡦⢿⣿⡿⣿⣳⡀⠀⢹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣶⣶⣶⣶⡿⢿⠋
⣻⣿⣿⣿⣿⡛⣯⠀⢻⣿⣿⣿⣣⣿⣿⣷⡶⣿⣿⣥⠈⢿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣷⣶⣤⣤⣄⣀⣤⣄⣠⣴⣤⣤⣽⣿⣿⣿⠘⠉⠻⠳⡘
⣿⡀⢻⣿⣿⣇⣼⣤⣿⣿⣿⣿⡿⢿⢻⣿⣷⡙⠿⣿⣴⣿⠲⣦⣄⡉⠻⣿⣞⣿⣿⣿⣿⣿⣿⣿⣝⣛⣉⡉⣤⣿⡿⡿⠹⢯⠻⣧⠠⢳⣴⣷⣴
⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠈⠁⠈⠀⠉⠃⠀⠀⠸⡿⣇⣀⣈⠳⣿⣿⣶⣝⠛⣿⣿⣿⣿⣿⠿⠿⠿⢿⣹⣺⣧⣀⣀⣄⣨⣿⡾⠷⠟⠋⠉⠁
⢀⣀⣀⡀⡈⠀⠀⠀⢀⣀⣄⢾⣀⠀⠄⠀⠀⠀⠀⠀⠁⠈⢻⣿⣿⣌⣝⠷⣿⡟⣰⣾⠀⢾⡲⣿⣿⣿⣿⣿⣶⣬⣭⣍⠉⠁⠀⢃⠁⠀⠂
⠚⠟⣿⣻⣿⣶⣾⣿⡟⠛⣿⡌⣿⣇⣘⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⣿⣶⣮⣝⡻⢷⣷⣾⣿⣿⣿⣿⡿⣻⣿⣿⡏⢻⣿⣿⣿⣾⣷⣤⣶⣶⣄
⠀⠀⠁⠉⣿⣿⡿⡟⡋⠀⠇⠇⢸⡏⠚⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣝⡻⢿⣿⣷⣯⣽⣿⡿⠀⠀⢀⣼⡿⡿⠻⠟⢉⢿⣿
⠀⠀⠀⣾⣿⠟⠀⠀⠀⠈⠀⠀⠸⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣿⣿⣷⣦⣭⡟⠻⢿⣴⣦⣴⣿⣟⡐⣡⠀⠀⠀⢸⣿
⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⡷⣶⣠⣉⡉⢛⠻⠾⣿⣿⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡶⣖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠹⡌⠣⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠙⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⠔⢒⡶⠭⡉⠯⡱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢑⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠣⠤⢄⣉⡶⠶⣋⣸⣗⣀⠀⠤⠤⠤⠤⠔⠒⢒⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠰⣶⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⣄⠀⠀⡎⣱⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡟⠁⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢉⣛⢮⡻⣄⠙⠋⠀⠀⢀⣀⣀⣠⣤⣤⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡋⠢⡹⣜⣆⣠⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢻⣿⡶⠇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢡⢃⠎⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⡎⡎
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣯⣥⣿⣀⡀
⠀⠀⠀⢠⡞⠉⠉⠀⠀⣼⢰⠁⢨⠉⠉⠓⢦⡄
⠀⠀⠀⢹⠓⠦⣤⣤⣤⣟⣎⣸⣸⣤⣤⠴⠚⡇
⠀⠀⠀⢸⠀⣀⣠⡦⣼⠥⡯⠽⠭⢦⣦⡀⢀⡇
⠀⠀⠀⢸⡯⢅⣀⣉⡁⠂⠀⣒⣀⣀⣀⠬⣿⠃
⠀⠀⠀⢸⡇⢀⡀⢠⢀⠀⡄⠀⠀⣄⢠⠀⡿
⠀⠀⠀⠈⣇⠘⠶⠊⣀⣀⣳⡖⠰⠈⠉⢸⠇
⠀⠀⠀⠀⢻⣖⡉⠁⠏⠀⠀⠈⠉⠁⢲⡿
⠀⡀⠀⠀⠈⠳⢮⣕⣒⠀⠲⠆⣒⣬⠟⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠉⠉⠓⠲⠦⢤⣤⣤⣀⣰⡋⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣤⠤⠴⠒⠋⠉⠁⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⢀⣀⣤⠴⠖⠚⠋⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⢀⡷⠃⠈⠉⠙⠛⠲⠦⢤⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡶⢶⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠷⠾⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠋⠉⠉⠉⠉⠉⠉⠻⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⣹⣉⣋⡏⢹⠛⡟⢻⠛⡟⢻⠛⡏⢻⢙⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠋⠉⠉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡴⠞⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢠⡿⠁⠀⠀⠀⠘⣷⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⣼⠃⠀⠀⠀⠀⢰⠏⠀⢈⡿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡖⠲⠶⠤⢤⣤⣀⣀
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⢸⡇⠀⠀⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠈⢿⡀⠀⠀⠀⠀⢻⡤⠖⠛⠛⠛⠒⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⢷⣄⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠦⠴⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⠲⠤⣤⣄⣀⣀⣀⣤⡤⠶⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣤⣤⣤⣤⡴⠶⠞⠋⠁

⠀⢽⣶⣶⣦⣬⡍⠉⣉⠙⠋⠃⣀⣈⣃⣈⢉⣠⣤⣴⣿⣬⣷⣤⣭⣍⣁⣀⣰⢶⡶⣶⣾⣻⡓⠾⢿⣴⣶⣦⣄
⣙⣛⣂⣀⣠⣤⣤⡀⠉⣡⡶⠛⠉⠀⠀⠨⠉⢹⣟⠛⠋⣻⣽⣿⡿⢿⡿⣿⠿⡭⠿⠗⠁⠉⠛⢛⣃⡠⠶⡿⠉
⠭⣭⣽⣯⡭⠉⠀⣀⣛⣿⣿⣷⣍⣉⠩⠉⠿⢷⣿⠓⠒⠓⠚⠋⠈⠙⢁⡀⠀⣤⢀⣠⡀⣀⣠⣬⣤⣏⡐⠡⢄
⠒⠋⢁⣶⣿⣯⡭⣽⠿⣿⡧⣤⣾⣿⠟⠁⠀⠛⢿⣧⣄⡀⠀⠀⠀⠀⠈⠀⠘⣉⡙⠉⠛⢿⣦⣲⠾⢿⣟⠛⢩
⠻⣿⣿⠋⠉⠉⠉⠀⠲⠦⢤⣤⣀⣀⠀⠠⢤⡶⠾⠟⠛⠛⠂⠀⠶⠿⣿⣿⣀⣠⣤⡿⠏⠁⣀⣤⡽⠟⣀⡙⢒
⠈⢿⣿⡀⠀⠀⢀⣤⣤⣤⣶⣶⣶⠶⠶⠆⠀⠀⠀⣀⣀⣀⡀⠀⢐⣃⠀⠹⡿⠿⢭⠶⠞⢛⣫⣥⠶⠛⢋⣰⣭
⣀⠀⠉⠻⣦⣄⠀⠈⠉⣉⣭⠵⠶⠶⠾⣿⣿⣿⣿⣿⣿⣉⣉⠭⢽⣛⣤⣟⣹⢶⡶⠷⢅⣘⣵⣤⣤⣤⡬⢽⣶
⠀⠉⢵⣒⠛⢋⣀⣀⣘⣛⡛⠶⠶⠶⠤⠤⠾⠿⠿⠟⠉⠴⢖⣋⣛⣉⣀⣠⣥⣤⣶⣛⣻⣿⣿⣿⣏⣠⣤⣬⣭
⠛⠛⠿⠟⠀⠘⠿⠥⢀⡉⣯⠉⡉⠉⠛⣓⠺⠷⢂⣤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠿⠿⠋⠀⠔
⠀⠀⠀⣠⣿⣿⡿⠶⠶⠶⠮⠭⢭⣵⣶⣶⣶⣾⡿⠿⠷⢶⣶⣤⠀⠀⠀⠀⠀⠤⣤⣤⡄⠀⢄⠀⠺⡆⠀⢠⡄
⡀⠀⠈⠻⠿⣿⣷⣤⣀⣀⣀⣤⣾⣿⡿⠿⠿⠿⠗⠒⠚⠛⠛⣳⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⣁⣀⣀⣠
⣛⣛⣂⣀⣀⣀⣤⠽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠷⡶⠶⣶⠤⢾⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⠿⢿⣿⣿⣷⡶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⢀⣀⣀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣾⣿⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡬
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠒⠂⠀⠀⠒⠒⠈⠉⠛⣛⣭⣿⣶
⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠟⠃⠀⢀⣤⡤⣤⣴⣿⡟⠋⠁⠁
⠙⠛⠛⠿⠶⢦⣤⣤⣀⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠰⣿⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠷⠶⣶⣦⣤⣤⣤⣤⣤⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠾⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣆
⠛⠳⠶⠶⠶⠶⠶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⡄

⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣤⣸⠁⢀⣄⠠⠞⠀⠗⠌⠻⠯⣍⠀⠦⠀⠀⣠⣤⠀⠀⡰⠀⣜⡛⠛⣿⡏⠀⠀⠈⢶⣾⣿⣿⣷⣆⠀⠳⣤
⣿⣿⣹⡿⣿⣿⣿⡻⠻⠙⢙⣿⣿⢀⡄⠄⠦⠀⠀⡰⢦⣠⡄⠀⠀⠀⠀⣾⡆⢙⣤⡞⠓⠊⠉⠀⠈⢿⡇⠀⠀⠈⣿⣿⣧⣼⣿⡿⠄
⣿⣿⡿⠅⠙⠘⣿⣷⡀⠀⠈⢉⡦⢼⣽⣷⠀⠒⢈⣇⠈⢁⢶⣶⣤⣈⡜⠛⠁⠾⠆⢠⣶⣄⡀⠀⢀⡘⠁⠀⠀⠀⠘⠿⠻⢿⠋⠛⢀⡀
⡿⣻⡇⠀⠀⢰⣿⣿⣷⡄⠠⠿⣿⢾⡿⣿⣶⣶⠏⠁⠀⢰⣾⣿⣸⣿⠁⠀⠀⠀⠀⠈⣿⡿⣿⣿⣾⣧⣰⣇⡀⠀⠀⠀⠀⢀⠀⠀⠀⠊⠉
⠉⠀⠙⢠⣴⣿⡿⠛⠛⠳⠀⠀⠀⠘⢿⣿⣿⡿⢿⠉⢢⣬⣿⣿⡼⣿⡇⠀⠀⠀⠀⣰⣷⣿⣾⣟⢡⣿⣿⣿⣿⣿⣶⡾⣿⣉⣀⢤⡇⠄⢠
⠀⠀⠀⠈⡻⣿⣘⡢⠄⢀⡴⠰⠦⢀⠀⣿⣿⣿⣶⣴⣾⢟⣿⣿⠻⣿⡇⠐⠀⠐⠾⣿⣧⣾⣿⣿⣿⢟⠻⣿⣿⢿⣀⣁⡙⢿⣟⠒⠘⢳⣾
⣿⣶⣶⡠⢀⣿⣴⣿⣄⠊⣀⠀⠐⣄⣺⣿⠿⢿⠛⢿⡇⠈⠁⠀⠸⡞⣷⢤⣀⡠⠀⢸⣿⣿⡿⠿⠛⠂⢱⡄⢸⣄⠪⡝⢿⢟⠿⠃⡈⣨⢿
⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⢿⣷⣶⣏⣠⣼⡗⣸⡆⢸⡇⠀⠀⠀⢀⣼⠇⣀⠻⠆⠐⢭⠉⠛⢇⠜⠃⠀⢹⠀⠀⠁⠀⢁⡾⢉⣹⡘⢩⡶⣾
⠀⠉⠀⢸⡿⢿⡻⣯⢻⣿⣗⢻⡏⢹⡿⢧⡼⡛⣷⣟⢿⣆⠀⣀⡎⠀⠠⠈⢼⠷⠀⣸⣀⣤⣶⣦⣘⡦⡈⠆⠘⣧⠀⢠⠑⠆⡤⣽⢋⠘⠻
⡀⠀⢀⣈⣇⠀⠣⠘⢏⡻⠿⣯⠿⠎⣁⣀⢀⣿⣻⡉⣧⡉⡐⠋⢃⠀⡰⠾⠜⡓⠒⠏⠉⠸⠟⠉⣙⡷⣎⣶⣾⣮⢧⣿⣶⣾⣤⣦⠘⠻⣾
⠿⠂⣶⡼⢿⣧⠖⢦⡿⢶⡐⢨⠈⠴⠈⠋⠈⡯⢻⡌⣽⣇⡝⢙⡿⣿⣿⣤⠾⢁⣰⠄⢀⠀⠈⠠⡌⠋⠛⠛⠛⢯⣿⠿⣾⠇⠈⠁⠀⠀⠈
⣤⣀⣨⠟⠻⠻⣷⡷⠛⠋⣭⢾⣷⣶⠛⣤⠐⢿⢦⡀⠿⠟⠛⠊⠛⠿⣿⣧⡀⠈⠙⣷⣾⣧⣴⡗⠂⠀⠠⣶⣀⣠⣼⣿⣿⠀⠀⠀⠀⣤⣆
⠙⠃⠀⠀⠀⠀⠈⠀⠀⠀⠁⠛⠙⣧⢈⢻⡴⣧⠌⠁⠀⠀⠀⠀⠀⠀⢈⠙⣧⣤⣼⣿⣿⣿⣿⡟⠁⠌⢶⣿⣿⡟⣿⡙⣿⡀⠀⠀⣶⠉⠡
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣛⣷⣿⣧⣀⠀⠐⠁⠘⠀⢀⣄⠀⣠⣿⡟⡛⠛⠻⠿⣿⡿⢖⣶⣹⠿⣿⡿⢿⡟⣿⠗⢀⡼⠀⢀⡶
⠓⢤⣀⠀⠀⠠⠀⡇⠀⠀⡠⢦⣾⢏⣉⢀⣉⣿⡉⠀⠀⠀⠀⠀⠀⣿⡞⠉⠀⠀⠀⠴⠀⠀⠀⢺⣿⠟⠀⠀⠙⠁⠀⣈⠉⠀⠀⠃⠀⢸⠟
⠀⠀⠉⠻⣦⣄⣨⣷⣾⣠⠗⠀⠱⠂⠉⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⡟⢀⣥⠤⠖⠛⠆⠀⣁⣤⣿⣧⠀⠀⠀⠀⡤⢀⡆⠀⠀⠀⠀⠀⡄
⠀⡠⠀⠀⢸⣿⡿⣻⣏⠀⠀⠀⢀⡇⠀⠛⠊⠉⠣⡀⠀⠀⠀⣰⣾⣴⡾⠃⠀⠀⠀⢰⣦⣄⡀⠀⠉⢳⣾⡴⠊⢀⠿⠻⠆⠀⠀⠀⢿⡧
⡾⠀⠀⠐⠚⠛⠉⢹⠇⠀⠀⣀⣾⡇⠀⠀⠀⢴⢶⡿⣦⡠⣀⣝⠩⢟⢶⡖⠃⠀⠀⠀⠀⠈⠁⠈⠙⠀⣈⢀⣤⣴⡆⠀⠀⢘⡷⠾⢧⠀⠈
⠃⠀⠀⡀⠀⡀⠀⣞⠂⠤⠛⠉⠉⠳⣄⢘⣦⠀⠀⠀⠀⠀⠼⠅⢦⢺⢂⠥⠀⠀⠀⠀⡠⠒⠀⠸⠀⠀⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠰⠆
⠃⢠⣤⠤⢾⡛⣿⣿⣦⡀⠀⠀⠂⣀⠨⢿⠋⠓⢤⣤⣀⠀⠀⢢⡇⠓⠛⠋⠁⢀⠀⡿⠟⠀⣀⠀⠀⢐⣿⡿⠷⠄⣀⣠⣴⣶⣶⡀
⣹⣿⢻⣷⣿⢿⡿⠋⠹⣿⣿⣤⡞⠁⠀⠀⠀⠀⠀⠉⠉⠑⢂⡈⠀⠐⠊⠛⠻⠉⠙⠛⠻⢿⣷⣶⣿⠿⠿⣥⡄⠀⢻⣿⡿⢿⣿⡷⣄⡀⠐
⠿⠏⢀⢁⠺⢻⡀⠀⠀⠘⡿⠟⠀⠀⠀⠖⠀⠀⠀⣠⣶⠶⠛⠉⠰⢤⣀⠀⠀⠀⢠⡌⠀⠀⠙⢇⢧⣸⡀⢊⣿⡀⣼⡿⠁⠀⠈⠙⢿⡧⠟
⠐⠂⣾⢈⣀⣬⣁⠹⡀⠘⠑⣇⢠⡄⠀⠀⢠⣤⣾⣿⠁⠀⠀⠀⠀⠀⠉⢻⡗⠘⠋⠀⠀⠀⠀⢸⣿⢿⠿⡿⢿⣿⣿⡇⠁⠘⠆⢴⡋⠙⠛
⠀⠐⢳⡲⡟⠃⠈⢳⣿⠃⢔⡁⠀⠀⡉⠀⣠⡞⣽⣧⠄⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡦⠀⣄⠛⠿⠏⢴⣄⡟⠀⠛⢾⠁
⠸⢦⡇⠑⢠⣀⢛⣾⣧⢄⣉⡡⡤⢈⠉⠒⢠⣾⣭⡿⠂⠀⠀⠀⠀⠀⢀⣿⣭⠀⠀⠀⠀⠀⣀⡜⠋⣿⣧⣄⣤⣢⠄⠀⠠⢿⡇⣸⡤⠁⠈
⢓⣠⣽⣷⠞⢋⡴⣿⡦⣉⢉⡀⠀⠀⠙⠀⣴⣿⡿⠂⠀⠀⣠⣤⣤⠴⠰⠻⠏⠀⠀⠀⠚⠱⢏⣀⣼⣏⣿⣧⣥⣽⣶⣤⣤⢿⣯⣿⢹⣠⠎
⠁⠀⢀⣹⠋⣿⠳⠀⣀⠰⠎⠈⠁⠐⢷⡏⠈⣿⣷⣴⣂⣤⣿⡿⠁⠀⠀⠀⣷⠀⣀⣠⠀⣠⡖⠀⠀⠀⠀⢩⣭⣿⣿⠋⠀⠀⠀⠀⠠⡙⢤
⠁⠈⠉⠁⢀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠁⠀⣽⣿⣿⣿⣿⣿⣷⣗⣤⠖⢢⣼⣿⠟⠹⣇⣏⠀⠀⠀⠀⢀⢹⣮⣿⡟⠀⢂⠀⠀⠀⠀⠀⡄
⠀⠀⣠⠀⠛⢀⡇⠀⠀⠀⡁⠠⠀⠀⣀⠀⣴⣿⣿⡿⢿⢿⠯⣉⠿⣹⣆⡜⣋⣘⣉⣢⠿⠿⠓⢀⡀⠀⠈⢦⡝⣻⡧⠔⠻⠇⠀⠀⢀⡀⢀
⣴⣾⣧⣐⢠⣿⣧⠀⠑⠀⠈⡷⢶⣼⣿⣿⣇⡀⠀⠐⠀⠀⠀⠘⡿⢛⣿⡾⠋⠸⠿⠛⠀⠙⠚⣢⡄⣶⡶⠋⣌⣯⡀⠰⣄⠀⠀⠑⠎⡁⢀
⢹⣿⣿⣿⣿⡿⠋⢳⠆⠀⠀⠋⠀⠱⡡⠘⣟⠀⠀⠤⣆⣀⡀⠘⠡⣸⠏⠀⠐⠁⢀⠀⠀⠀⠀⡀⠄⠘⠻⢶⣿⡶⠒⠤⠈⠒⠀⠺⠶⡔⣿
⠴⠛⠉⠀⢹⠃⠀⠴⠀⢰⠶⠋⠀⠀⠀⠀⡇⠀⠀⢐⣹⣿⣿⣿⣿⣿⣦⡄⠀⣀⣠⢹⡇⣀⡷⠆⣨⠄⠀⢀⡈⠀⠲⠀⡀⠀⡚⠇⣡⡞⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣤⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣉⣹⣇⠀⣹⣋⣉⣉⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⢙⡇⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⢤⡀⠀⠀⠀⠀⢸⡧⠶⠶⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡟⠛⠛⠛⢻⠏⠀⠀⠀⠀⠈⢻⡛⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣤⠟⠒⠒⠒⠛⢧⣀⠀⠀⢀⣠⠞⠓⠒⢲⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⢀⣇⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⢸⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣹⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀
⠻⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠟⠛⠛⠛⠷⠶⠑⠊⠉⠙⠙⠋⠉⠉⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣤⣤⡀⢀⣀
⢠⣤⣤⣀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⣿⣿⣭⠤⠤⠤⠀⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠈⠉⠉⠉⠉⠀⠀⠀⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉
⣿⣿⣿⣿⣟⣻⣳⣶⣀⣐⣶⣖⣶⣶⣦⣤⣄⣤⣤⣤⣶⣤⠀⠀⠀⣤⣤⣶⣶⣶⣶⣤⣶⣶⣦⣤⣤⣤⣿⣿⣿⣤⣼⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠐⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⣿⢿⣿⣿⣿⣿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠺⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⠟⠿⠛⠛⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⢥⣀⣍⠹⠋⣛⡟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⢚⠿⠻⠷⠶⢷⣶⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣶⣤⣝⣲⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣭⣙⣛⡿⢿⣟⣛⣋⢻⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠲⠶⠖⠶⠶⣶⣤⣴⣶⣬⣍⠉⢿⣿⣿⣿⣿⠟⡛⠋⠉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣛⣋⣼⣟⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡔⣩⣤⣀⣿⣷⣬⣭⣤⣦⣤⣀⣉⣿⣿⣿⣿⣷⠦⠌⠙⢿⣿⣿⣧⣤⣬⣛⠿⢿⣾⣿⣯⣤⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠁⠀⣉⣁⣙⠛⠿⠿⠿⠛⠓⠒⠂⠀⠐⠛⠛⠻⠿⠿⠿⠿⢿⣓⣶⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⣄
⠀⠼⠀⣠⣀⡽⠁
⠘⠚⠋⠀⠸
⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠈⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄
⠀⠀⠀⠀⣰⣤⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠞⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠱⣆⠟⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣒⠧⣀⡀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠗⠬⣼⣃⢀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣚⠛⠛⠋⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢯⠥⡀⠀⣘⡁⣀⢠⡆⠀⠀⠀⣀⠤⠀⢿⡞⠐⠄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠂⠀⠀⠈⠁⠀⠈⠉⡄⠀⢀⡞⠁⠀⠀⠀⠙⢶⡋⠷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠏
⢀⡄⠀⠀⠏⣡⡽⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢳⣄⠀⡂⢀⣠⠞⠁
⡜⠗⠒⠛⠋⠀⠐⣆⠀⠀⢢⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⢩⣀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠡⡁⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⠦⠄⠶⠘⠋⠀⠀⠀⠀⠀⠙⠒⠖⠚⠋
⠀⢳⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢠⣶⣜⠂⡠⡶⠤⡀
⠀⠀⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡟⠀⠉⠋⠉⡖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠐⣖⢠⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠃⡈⠀⠀⠀⠀⠀⠀⠀⢸⡖⠓⠂⠉⠉⠙⣇
⠀⠀⠀⠀⠀⠀⡰⢻⠅⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⠾⠧⢾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡄⡀⠔⠁⠀⠀⠀⠀⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠲⢤⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣷⣤⠃⠀⠀⠀⠀⠀⠀⢀⣤⠶⣖⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠉⢻⣝⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠏⠀⠀⠀⠀⢠⠇⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⡠⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣤⡾⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠒⠒⠒⢰⠋⠉⢱⠄⠠⠤⠄⠀⠀⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣠⣀⣀⣤⡦⠼⠰⢽⣻⣶⣄⣀⣤⠀⠘⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠉⠑⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣼⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠚⢦⡶⠾⠶⣾⠷⢶⣄⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠾⠟⠛⡋⠉⠙⠛⣻⠁⠀⠀⠀⠀⣀⡎⠄⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⢜⠌⠀⣀⠀⠀⠀⠤⠈⠽⢧⣀⣀⣀⣾⠈⣷⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⢀⠔⠂⠉⠀⠀⠀⠀⠐⠒⠉⠁⠀⠊⠁⠀⠀⠀⠀⠀⠈⠐⠉⠉⠘⢹⣆⣿⣾⠀⠆⣠⣶⡴⡆⠀⠈⢿
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣈⠏⠃⠠⡄⠀⢠⣾⣿⣿⣤⠀⡀⣀⠀⠀⠀⠀⠀⢸
⠈⠀⠀⠀⠀⠀⠀⢀⣀⡯⣤⠦⣕⡀⠐⠀⠡⠉⠄⠋⢀⢂⣡⠷⠤⣼⣸⣿⣿⢿⢀⠡⠀⠀⠀⠀⠀⠀⡿
⠀⢀⠀⠀⠀⢂⢲⠋⠁⠀⠀⠀⠈⠙⢦⣄⣤⢀⣠⣀⡦⠋⠀⠀⠀⠈⠳⣿⣏⡏⠔⠒⢈⣁⠀⠀⠠⠀⡇
⠀⢸⠀⠀⠈⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢟⡠⡥⡀⠤⠶⠂⢀⣀⣼⠃
⢰⢸⠀⠀⠋⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⠻⠛⡇⢐
⡎⡚⠄⠀⢉⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠁⠨
⠣⣗⣀⢀⣠⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐

⠀⠀⡠⢣⡀
⠀⣐⠁⠈⠈⢆
⠰⠗⠀⢠⠤⣻⢇
⠐⠂⠀⣼⣶⣾⡻
⠈⠶⣠⣄⠍⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠢⣾⣿⣏⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⡆⠉⠛⢿⣧⠀⠀⣠⡀⣠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣶⣶⣿⣥⣶⡶⣄⠀⠀⠀⠻⠧⠀⠙⠿⣯⠱⣴⠿⣿⣄⡀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⢠⣤⣤⡴⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠙⠆⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠙⢶⠦⣾⡿⠿⠛⢟⠷⣤⣄⣤⠞⠋⠉⠻⠦⢀
⠀⠀⠀⠈⠛⠙⠇⠈⠻⠿⢁⣴⣿⣿⣿⠆⠀⠀⠀⠀⢀⣠⣤⣶⣶⢠⣀⠀⠀⠐⠀⢠⣄⣀⣀⠀⠀⢀⣴⠾⣿⣯⠙⠆⠀⠀⠀⠈⠙⠳⠤⠶⠒⠒⣦⣄
⠀⠀⠀⠀⠁⠠⣶⣾⢿⡄⠈⠻⣿⣿⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡇⠙⠻⠔⠄⠀⠀⠉⠉⠉⠃⠒⠉⠀⠀⢀⣿⠀⠀⠈⠂⠀⣰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠂⠄⠀⠙⢶⣶⣶⣾⣿⣿⣿⣿⠟⣻⢿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠘⠃⡜⠀⢠⠟⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠣⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⠔⠀⠐
⠀⠀⠀⢠⣀⣀⠒⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠉⠓⠀⣠⠀⠀⢀⡶⠛⢉⠀⠈⢀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣆⢀⠀⠀⠀⠸⣿⣿⣿⣤⡴⠂⠐⠃
⠀⠀⠀⢸⣿⣿⣷⡖⣤⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠐⠆⠉⢀⡠⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠻⠿⢿⠛⠀⢀⣻⣿⣿⣿⣿⣅
⠀⠀⠀⠘⠻⠉⠉⢙⣿⣿⣿⣶⣿⡆⣀⣄⢸⣿⣧⠀⣠⡀⠀⠀⠀⠉⠺⠿⣿⣿⡛⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⢀⢢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣿⢿⠀⠀⠀⢀⣴⡄⠀⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⣤⡀⠀⣀
⠀⠀⠀⠘⠷⢾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⡄⣸⣿⣷⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠛⠿⠿⠿⣿⡟⢿⣿⣿⣷⣿⣿⣿⣿⣷⣾⣧⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠁⠀⠈⠉⠉⠙⠛⠛⠻⠿⠧⠀⠀⠀⠾⠷⠾⠿⠟⠉⠉⠋⠙⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⡁⠭⠉⠩⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠀⢀⣴⠀⠠⠱⡄⠀⠀⠀⢀⠀⣄⣠⣴⡄⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠿⠆⠀⠈⠋⠀⢀⣠⣿⠓⠦⡀⠎⠀⠀⠁⠈⠀⢠⠀⠀⠀⣿⠀⠢⠀⢀⠄⢀⠊⠀⠀⠀⡠⠠⠀⢊⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠠⠈⢳⡄⠀⢀⣀⣴⢃⡄⠀⢴⡋⠀⠀⠠⠈⠀⡈⠄⠀⠀⣔⠓⣀⠔⢁⠠⠤⠊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢉⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡟⠩⠁⠀⠁⠀⠠⠟⡉⠀⠀⠀⡞⠙⠀⡤⠠⠺⠧⣌⡀⠀⠁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⢈⠠⠂⠡⠀⠰⠌⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣻⡄⡀⠠⠀⠀⠐⡀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠈⢦⣠⡀⠄⠀⢠⠀⠀⢉⠢⠅⣀⣀⠄⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⣹⡴⣄⢄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢋⠀⣀⡶⣫⣍⠣⠀⠘⠀⠀⠀⠈⠁⠀⠙⡀⠂⠒⣂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⡏⠲⢋⡊⢈⣀⣀⡰⠢⢄⠐⠀⠀⡀⠀⠀⠸⢧⣛⢛⣤⠁⠔⠀⠀⠀⠀⠀⠂⢲⡀⠄⠀⠠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⡯⠀⠀⠙⢆⠨⢳⣿⣟⠹⠃⠀⠤⠀⣴⡜⠉⠀⠀⠀⠘⠉⠋⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡽⠀⠀⠀⠀⠈⣆⠀⠀⠈⢳⡺⣴⣬⡻⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠖⠀⢆⠀⣨⢇⣤⣽⣦⡤⡤⢽⣇⢷⣲⢷⣔⡖⣢⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⣨⠴⡟⠑⢉⠉⣹⠆⠀⢹⣯⡳⣂⢻⡝⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⢀⠆⠊⢠⡆⠀⠠⠀⠈⢣⡱⣎⢯⠘⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠙⢾⣸⡧⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⠘⠙⠤⠌⠀⠀⠀⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠻⠀⠀⠀⠀⠀⡄⠀⢡⡄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⢧⠐⠆⠈⠃⠀⠀⠀⠀⠀⠀⡄⠠
⠀⠀⠀⠀⠀⡤⠰⠋⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠰⣙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢹⠞⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛⠻⠻⣧⡀⠀⢀⣤⣤⣄⣀⣠⣤⣄⣀⣀⣤⡾⠋⠘⠇⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣛⣿⡅⠉⠙⠛⠛⢸⣿⣿⠿⣤⣤⣀⠀⠀⢀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣶⡶⠛⠉⠉⠉⠉⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠙⠿⣶⣤⣷⣄⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⣿⠀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣶⣶⣾⣶⣶⣶⣶⣶⣿⣷⡟⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⠯⠭⠽⠿⠟⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣭⣵⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⣶⣿⠺⢿⣿⣒⠀⠀⠀⠀⠀⠀⣲⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠛⠻⠿⢶⣶⣤⣤⣤⣴⡶⠿⠟⠛⠉⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⡿⠀⣀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣾⠿⠏⠀⠉⠉⣉⢉⣉⣉⡉⠉⠉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠚⠉⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⡆⡀⠀⠐⣒⣲⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠻⣛⡛⠿⣉⠉⠉⠁⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢿⡇
⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⢸⡇
⠀⠀⠀⠀⠸⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡶⠟⠛⠿⣷⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣸⡇
⠀⠀⠀⠀⠀⣿⣁⠀⠀⠀⠀⠀⠀⠀⡄⣀⣠⣿⠋⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣰⠛⢿⣯⣀⣀⠀⠀⠀⡆⢐⣂⣛⣛⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠹⣦⣤⡀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠈⠙⠻⠷⠶⣦⣤⣤⣤⣤⣤⣾⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢻⠀⡄⢧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠘⣇⢳⣀⡁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⡇⠀⢻⡄⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣴⠘⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠂⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣦⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢼⣗⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⡀⠠⣇
⠀⢠⣙⣿⣀⣸⡇⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠰⣬⣿⣣⣭⣷⣒⡀
⠀⢰⣾⣿⣷⣻⣿⢁⣼⣿⡦⣸⣠⣠⣀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢄⣗⠀⠀⠀⣴⠀⠀⠼⣧⢀⣶⠀⡘⠶⣿⠶⢾⣿⢟⣂
⠀⣽⣿⣿⣿⢾⣿⡯⣽⣿⣟⡙⠟⠻⢿⣿⣇⣧⣷⣆⠀⠀⠀⠀⠀⠀⡀⢠⡄⢠⣼⡄⠀⢨⣓⣿⣤⣿⠠⣿⣧⢬⡽⡿⣼⣿⡆⠩⣿⣿⡿⣛⣿⣿⡥
⠀⢭⣿⣿⠟⣿⡿⠀⢺⣿⡿⠷⠀⠀⠀⠀⠀⠀⠉⣉⠁⠉⠉⠉⠉⣥⣿⣾⣧⣿⣾⣧⠀⠹⣿⣿⣃⣿⠮⣿⡯⠤⣽⣿⣛⣿⠛⣏⣻⣿⡷⡾⣿⣿⣛
⠠⠼⣿⣿⠀⠚⡅⠀⠈⠿⡻⠍⠀⠐⢶⣤⣀⠀⠀⠀⠀⠀⠘⠓⢤⢤⣄⡉⠉⠙⠉⠄⠋⠽⠿⠟⠛⠋⠲⠿⠇⠛⠛⢹⣾⡟⠀⢿⣿⣧⡛⢻⣿⡿⠯
⠀⠠⣾⣧⡐⠺⠙⠰⠞⠋⠁⠀⠀⢠⣈⠙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⠴⢠⠔⠲⣦⡀⠀⣀⠀⡀⠀⠀⠀⠀⠈⠑⠒⠛⠿⠭⠿⠿⠿⣿⡟
⠀⠀⠈⠁⠀⢀⣀⠠⠔⠞⠷⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠵⠼⠗⠗⢱⡆⠀⠀⣀⡆⣄⡀⠀⣠⠀⢀⡀
⢐⣶⠒⢆⠙⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠃⡑⢤⣿⡄
⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠈⠁⠀⠜⠃
⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠳⠠⠄⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠚⠊⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⢷⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣽⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠰⢿⣣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢯⣿⣷⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡉⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣾⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⡝⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⣿⣿⣿⣿⣇⣹⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⣿⡇⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣟⣴⡿⠁
⠀⠀⠀⠀⠀⠉⢳⣦⡀⠉⠻⣿⣿⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⠿⠿⠋⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⣈⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⢀⡴⠖⠶⣄⠀⢀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⡶⠦⣤⡀⠀⠀⠀⠀⣼⠁⠀⠉⠉⠉⢻⠁⠀⠀⢸⡏⠉⠉⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣦⠀⠀⠀⠘⢦⠤⠴⠶⠒⢻⠀⠀⠀⢸⠓⠲⠶⠦⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣤⣤⣼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⣧⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⢤⣤⣤⡼⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠞⠁



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⣠⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⢀⢀⠘⠀⡔⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⡈⠐⠀⠁⠠⠄⠀⣄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠆⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠄⠠⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣀⡾⢃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠢⡄⠀⠠⠀⠈⠲⠄⡀⠁⢠⠄⠘⠀⠀⠀⠀⢀⡧⢤⣎⢹⡟⣻⠯⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⢀⠐⠶⠆⠀⠈⠀⠉⠈⢈⠀⠀⠀⣉⠀⠊⠋⠄⠐⠆⠐⠦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⡀⠐⢒⣈⡁⣤⠄⠀⢠⠹⣑⠶⠟⣀⠐⡀⡄⢰⠒⠲⢇⢼⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠱⠀⠈⠂⠀⠉⠉⠉⠉⠈⠁⠀⢀⢀⣤⠄⠔⢂⠠⡒⢛⢋⣟⠛⠛⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠃
⠀⠀⠉⠀⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⢊⠒⠀⠤⢁⡀⠐⠛⠒⢚⠳⠒⠉⢉⠁⠀⠀⠀⠋⠁⠀⢈⠉⠉⠄⠠⠀⠀⠀⠀⠀⡋⢀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠐⠂⠀⠠⠀⠀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠿⢷⣶⣤⣤⣤⣶⠿⠋⠁⠀⠀⠈⠛⢿⣶⣤⣤⣴⣶⡾⠿⠛⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⠿⠟⠛⠛⠉⠉⠉⠉⠛⣷⣦⣤⣤⣤⣤⣴⡿⠛⠉⠉⠉⠉⠛⠛⠻⠿⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠉⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣤⣤⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡿⠛⠉⠉⠉⠉⠉⠙⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡛⠛⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠻⠿⠿⠿⠶⠶⠶⣶⣶⣶⣶⣶⣶⡶⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠶⠾⠿⢿⣿⣦⣄⣀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣶⣦⣤⣀⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣤⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠿⢷⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣸⣿⣴⡶⠿⠿⠿⠿⢶⣶⣤⣤⣄⣀⣀⣀⣤⣤⣤⣶⣶⠾⠿⠿⠟⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣤⣤⣴⣶⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠲⠦⣤⣄⣀⣀⣸⡆⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣟⡋⠁⠰⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠂⣉⠭⣍⣩⢶⡦⣄⠀⣤⣬⣽⣟⠉⠀⢎⢜⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⣊⣨⡇⠀⠈⠁⠀⠙⢶⣿⡟⠉⠋⠁⠀⠀⡆⢸⢘⠅⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⣉⢠⠇⠀⢀⠄⠀⠀⠀⢀⠀⠀⢀⠤⢄⠤⢣⡇⠘⠦⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡴⠛⡡⠴⠃⠀⠀⠉⠁⠀⠀⠴⠋⣁⡔⠒⣡⠤⢄⣀⡴⢁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡪⠂⠀⡠⠔⣋⣀⡼⠀⠀⠀⠀⠀⢀⠜⠉⠙⡄⢀⡠⠔⠋⠁⢠⠒⢢⠀⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠗⠉⠀⠀⠀⠀⡜⠀⠁⠀⡠⠤⣀⡠⠔⢻⠀⠀⠀⢸⣿⣰⣳⠀⡴⠋⠀⣨⠆
⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠲⠴⠚⠁⠀⠀⠀⠀⠘⠀⠀⠀⠈⢿⣷⣄⠀⠣⣀⠏
⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣶⣶⣤⡆
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠤⠂⢉⣆⠂⠉⠉⢂⡔⠒⠒⢆⡠⠖⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢢⠀⠀⠀⠀⢤⠀⠀⠀⠀⣿⣀⣀⣀⣾⣧⣀⢀⡘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⣼⣧⠀⢀⣀⢀⠤⣆⠀⢰⠁⠀⠉⠻⣿⣾⡟⠏⠁⢆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⡿⢿⣷⣿⡿⠏⠀⠀⠑⠄⢰⠧⢄⣀⣠⠞⠁⠙⠻⡄⠀⡸⠀⠀⢦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⡀⡸⠋⠋⠙⣆⠀⠀⢀⠄⢸⡀⠀⠀⠈⣄⠀⠀⡀⠋⠉⡀⠀⠀⢹⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡇⠀⠉⠐⢜⠂⢀⣻⣾⢾⣇⣠⡆⠀⠀⠁⢺⡀⣀⣠⠈⠆⡠⠋⠙⠏
⠀⠀⠀⠀⢀⠄⠀⢐⣂⠤⠵⣄⡀⣀⢠⡅⠀⠀⠀⣜⢀⣠⠾⣿⣿⠟⠁⠁⠠⢀⣀⣾⣿⣿⠁
⠀⠀⠀⠀⠱⠒⠋⠉⠅⠀⠀⠀⣙⣿⠟⣿⡶⠒⠻⢀⡏⠁⠀⠀⠻⡀⠀⠀⠀⠀⠀⢻⠋⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⢠⠞⠻⠻⡏⠀⠀⠀⠀⠷⡀⢀⣠⠁⠀⠈⠫⣄⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠘⠀⠤⠁⠸⠀⠀⠀⠀⠀⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠛⠿⡀⢀⣼⣿⣿⣇⠘⠛⠻⣯⣿⣿⣯⠤⡀⢸⣿⣯⣿⡀⠀⠀⠀⢀⣿⣿⣿⢟⣷⣿⣦⣴⣄⣠⡤⠀⢀⡄
⠀⠀⠈⢿⣟⠡⠀⠀⣀⢤⣀⠈⣿⣿⣯⣂⣼⣿⣿⡿⣿⡇⠄⠀⢤⣾⣋⣿⣿⣾⡾⢿⣿⣿⠙⠙⢿⣿⠍⠲⣭
⣶⣦⣄⠀⣯⣿⣦⠊⡁⠄⢀⣰⣿⠿⡟⢿⡏⠈⠁⠑⡿⡧⢀⣀⠀⢹⣿⣿⠿⠛⠈⣨⠉⣇⢹⠻⣾⡿⢂⡀⣻
⣿⡿⢻⣿⣿⣿⣿⣿⡿⣷⣾⣥⡴⢋⣧⢰⣇⠀⠀⠀⡼⠃⣈⢓⢈⠯⠉⠻⠘⢃⠀⠇⠀⡁⠈⢠⠋⢽⣌⣹⣺
⠀⠀⠐⡟⠻⡝⣾⣿⣧⢿⡌⠟⠳⢫⣽⡿⡟⠇⣠⡞⠀⢐⡔⣟⣁⡶⠔⣾⡿⣾⣗⢜⣠⣳⡀⣆⣁⡔⡚⣡⣉
⣦⢠⡒⣷⣄⢵⣸⣎⠹⢛⢉⠰⠆⠸⠷⡖⣛⡆⠦⣶⣶⣮⢩⡴⢈⡁⠀⠘⠀⠒⡿⠷⢿⣿⣿⣟⣿⠙⠃⠀⠙
⣀⢈⡷⠺⢷⣴⠿⠞⣲⣽⣤⠒⣀⢸⣦⣁⠿⠿⠧⠻⢿⣿⣏⠀⠛⣧⣿⣀⡶⠅⠀⢠⡄⣈⣽⣾⡇⠀⠀⢀⣄
⠛⠉⠀⠀⠀⠁⠀⠀⠁⠋⢻⣈⠻⡖⠆⠁⠀⠀⠀⠀⠀⠉⢻⣤⣴⣿⣿⣿⣿⠁⠐⣾⣿⣿⣿⡹⣇⠀⢐⡞⠉
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠿⣿⡦⠀⠈⠀⠁⠀⣦⣠⡾⠿⠉⠉⠙⠛⢟⣯⣿⠟⢻⡟⠻⠽⠏⠀⡞⠀⣸
⠈⠓⢦⣀⠀⢸⣀⢁⡎⠻⡏⠲⠐⠺⡇⠀⠀⠀⠀⠀⣿⠁⣀⣀⡤⡉⠀⠀⣸⡟⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠏
⠀⡀⠀⠹⣿⣿⣿⠋⠁⠀⣡⠀⠶⠘⠳⡀⠀⠀⠀⡤⣣⡾⠋⠀⠀⢠⣄⡉⠉⠛⢦⣆⠄⠋⡾⢧⠀⠀⠠⣶⡀
⠾⠀⠀⠚⠛⠋⡏⠀⢀⣠⣿⠀⠀⠀⠴⡿⣦⡠⣼⢻⣻⣶⠞⠀⠀⠀⠈⠙⠀⠙⢀⡁⣠⣴⡆⠀⠀⡶⠶⣏
⠀⠀⠀⢀⣄⣰⡍⠒⠉⠁⠉⠦⣬⣦⡀⠀⠀⠘⢛⢴⣕⣑⣆⠀⠀⣀⡔⠀⡘⠀⠈⣿⡿⠁⠀⠀⣀⠀⠀⠀⠒
⣭⣿⣮⣩⣏⣿⢿⣦⣄⢀⡤⠊⠛⠀⠙⠻⠦⠀⡈⠎⢉⡡⣤⡤⢤⣿⣥⣴⣀⣠⣼⣿⠉⠃⣤⣾⣿⣿⣄⠀⠈
⣿⠋⠛⢻⡞⠁⠀⠙⣿⠿⠀⠀⡄⠀⠀⢀⣠⡤⠞⠢⣀⠀⠀⠀⠀⡀⠈⠙⠏⢏⢍⠡⢻⡀⣿⡿⠉⠙⢯⣷⠢
⠒⢠⣍⣁⣘⡀⣆⠐⠳⡆⡀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠈⠙⢶⠔⠛⠀⠀⠀⠈⣿⢿⠿⣿⣷⣿⡀⠀⠖⣤⠛⠒
⠄⢙⠾⠏⢂⡙⣾⠇⣈⠁⠀⣈⠀⠰⣩⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻⣾⠆⢀⠙⠻⠁⢦⡜⢈⠑⠎
⡘⠫⣌⣰⡦⣹⣟⠢⠤⠐⠂⢤⠈⢺⣿⣟⠁⠀⠀⠀⠀⢰⣿⠆⠀⠀⣤⠤⠚⢡⢿⣶⠶⢴⡀⠐⢺⣧⣼⡂⢀
⠒⠛⢻⡧⣶⡽⠋⢁⡔⠂⠀⣤⡔⢻⣿⣤⣀⣠⣿⡟⠉⠀⢩⡆⠀⢀⠀⣁⠐⠛⠀⠛⣛⣿⣿⠟⠉⠛⠋⠙⢏
⠀⠐⠛⠀⣁⠀⠊⢀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⣴⣤⠤⣀⣷⡟⠻⣮⡁⠀⠀⠀⣀⣯⣿⡏⠠⡀⠀⠀⠀⢈
⠀⣠⠂⠊⣸⡄⠀⠀⡄⠀⠀⣀⣀⡼⠿⠿⠿⠿⢏⡹⣽⣦⣛⣍⣉⣶⠻⠛⠂⡄⠀⢱⡼⣻⠧⠚⠳⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⡶⣦⣼⣷⣷⣦⣤⣴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣤⣬⣭⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⣂⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣀⣤⣤⣤⠀⠀⡤⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠂⠉⠉⠀⢿⣯⣽⣿⣿
⠀⠀⠀⠀⢀⡴⠋⣠⣴⣿⣿⣿⣿⣿⣷⣦⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠏⢀⣼⣿⠟⠉⠉⠉⠉⠛⠛⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⡞⠀⣾⣿⠃
⠀⠀⠀⠇⠸⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⠀⠒⠲⠤⣤⣴⣶⣶⣶⣶⡶⠶⠶⠶⠶⢶⣶⣶⣶⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣶⡶⠶⣶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠉⠉⠉⠀⢀⠀⢀⣐⣒⣒⣶⣦⠀⣀⣠⣤⣤⣤⣴⣆⣀⣀⣌⣙⣡⣀⣀⣉⣉⣉⣩⣭⠭⠭⠭⠥⠴⠷⠶⠶⠶⠬⠭⠬⣭⡍⠉⠁
⠀⠀⠀⠠⠴⠶⠿⠟⠛⠛⠉⠙⠛⠉⠉⠙⠛⠃⠤⠤⠤⠄⢀⡀⠀⠀⢀⣀⣀⣠⠤⣤⣰⣒⡒⢒⣒⣂⣂⠀⣒⣀⣀⡲⠶⠶⠶⠶⣶
⠀⠀⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠊⠉⠙⠉⠉⠉⡉⠁⣄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁⠀⠈⠉⠁⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢄⠠⢤⡀⠀⠀⢀⣹⡄⠘⡆⠠⠤⠴⠶⠤⠀⠀⠀⠀⠤⠠⠤⠀⠀⠀⢀⡀⢀⢠⠁⠁⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠛⠀⠀⠈⠂⢉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⡉⡐⠀⣤⣿⣇
⠀⠀⠀⢀⣴⡆⠀⠀⠃⠀⠈⠙⣦⣸⣄⠐⢦⣼⡆⣴⣇⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣧⣿⣾⣿⣇⣿⣿⣿⣇⡀
⠀⢤⢲⠞⠻⢿⣾⣾⡆⠀⢀⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⡷⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠟⠛⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠚⠋⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⢣⡈⠳⣄⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠈⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣤⣀⡀⠀⣿⠀⠀⢧⠀⠘⢧⠀⣠⠖⠋⡠⢛⡀⠀⢠⠎⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠻⢽⡳⢾⡀⠀⠀⢧⡂⢘⡖⠁⠀⡴⠅⣿⠃⢠⡏⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠒⠂⠉⠉⠒⠢⣿⡀⠀⠀⠈⣦⣝⢆⡜⠉⠉⠉⠉⠳⣞⠀⠀⢻⣀⣿⡼⡤⠊⠀⠀⠀⢀⡼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠈⠹⣆⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⡈⢦⡇⠀⠀⠀⠀⠀⢘⢀⠠⢾⣿⣿⣿⣥⣦⠤⠴⠚⠉⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠤⠽⠖⠲⠤⣄⣀⣸⣿⣹⡾⠊⠁⠈⠙⢿⣄⡀⢀⡀⢠⠟⠀⠀⠀⠳⡏⠿⣿⣿⠄⠀⠤⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣛⡇⠀⠀⠀⠀⢄⣽⣿⡿⣿⣿⠀⠀⠀⠀⠀⡸⠯⢯⡭⠿⠷⣖⣶⣶⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⡀⠀⠠⣀⣺⡿⠿⠾⠠⠷⠤⣀⣀⣀⣤⢿⢿⣷⣾⣿⣇⣀⠀⠀⣠⡃⠀⠀⠁⠀⠀⠈⠁⣈⣹⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣐⡤⣤⠶⢳⡾⠋⠀⠀⠠⠟⣿⠏⠛⠈⠙⠢⣍⣁⠈⠉⠓⢦⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠒⠺⠋⠀⣀⡥⣒⠽⡄⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⠀⢸⠛⡙⠣⣄⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠦⠶⠤⣤⠞⡩⡏⠀⠀⢸⡀⠀⠀⠀⡰⠙⣆⠀⠀⠀⣀⣸⣄⠀⠀⠈⠉⠓⠌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠊⠀⠀⠀⠀⢀⡼⠋⠐⠊⠀⠀⠈⠁⠈⠉⠀⠀⠈⠉⠛⠒⠶⠶⠶⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠛⠒⠶⣤⠴⣾⡝⡟⠀⠉⠉⠉⠉⢙⠟⢿⠶⢤⠴⠖⠚⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⢻⠀⠀⠀⠀⠀⢸⢠⡆⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣇⡀⠠⠠⠤⠔⣒⣭⠽⠶⠺⡏⠸⡆⠀⠀⠀⠀⡇⢈⡗⠲⠾⣭⣑⡒⠤⠄⠀⠀⣨⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠹⣄⣧⣀⣀⣀⣸⢀⡞⠀⠀⠀⠀⠈⠉⠙⠓⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣏⣉⣉⣉⣉⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣉⣼⣁⣀⣀⣀⣀⣙⣄⠙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⢹⡟⠀⠀⠀⠀⠀⠀⣿⠁⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣼⣧⣤⣤⣤⣤⣤⣤⣿⣄⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣠⡟⢉⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠛⣉⣉⣉⠩⠍⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⡇⢸⠀⠀⡀⡀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⣠⠖⠋⣁⡤⠖⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⡇⡇⢸⢸
⠀⠀⠀⠀⣠⠞⢁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡇⢸⢸⢸⡇⡇⡇⢸⢸
⠀⠀⠀⣰⠃⣰⠋⠀⠀⠀⠀⡠⠂⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢛⣛⣿⣿⣿⡇⢸⢸⢸⠃⡇⡟⢸⣼
⠀⠀⢠⡏⢰⠇⠀⠀⠀⠀⣸⠀⢀⡴⠚⠉⠉⠉⠉⠙⠛⠳⠶⠦⣤⣄⣀⣀⣀⣀⠀⠠⢄⣒⣉⣭⡴⠖⠛⠉⠁⠀⠈⠙⣇⠸⢸⣻⢰⣷⡇⣿⣿
⠀⠀⣼⠁⡟⠀⠀⠀⠀⠀⡜⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣈⣛⣛⣛⣛⣛⡏
⠀⣠⡟⢸⠇⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⢸⡏⠅⣘⣒⠒⠂⢀⣀⣚⣓⣚⣻
⠸⣅⠀⢒⣖⣠⡬⡭⠭⠍⣶⣶⣿
⠀⠈⠉⠓⠒⠲⠶⠶⠖⠛⠛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿