Confuse Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢿⠇⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣠⣭⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⣠⡾⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠙⣿⣆
⠀⠀⠀⠸⣿⡀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠟
⠀⠀⠀⠀⠈⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠑⠢⣄⡀⠀⣧⠙⢦⣀⠀⢠⣄⠀⠀⠀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠲⡖⠒⠚⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠓⠚⠈⠳⣄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣠⠚⠉⠛⠢⡄⠀⠀⣀⣀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡇⠀⠀⠀⠀⢹⡀⡮⠄⠀⢱⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢤⣠⠏⠀⠀⠈⡇⠀⠀⠀⠀⢾⠁⠳⣀⢀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠈⢛⣓⣀⠀⠀⠀⠀⠘⣄⠀⠀⢀⠎⠀⠀⠈⢉⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⣆⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠠⢀⡠⠇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⠲⢤⣀⣀⠀⠐⠂⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢇⣀⡜⠀⠀⠀⠀⡏⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢾⠏⠀⡏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣭⠀⠀⣸⡀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠋⠁⢈⣙⡓⢲⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢿⠒⣶⣤⣴⠧⢶⡟⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠽⠛⠉⠙⠚⠭⠷⠾⠝⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠟⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⠀⠀⣹⣆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠴⠶⠚⠉⠁⣸⡷⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡤⠶⠖⣋⣡⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠀⢠⡿⠋⠉⣨⣿⡿⣯⠉⠛⠛⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⢺⡇⠀⠀⠙⠛⠁⣿⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⢀⣾⡿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠈⠿⣦⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⠛⠛⠛⠛⠿⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢤⡀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠧⠼⠃⠀⠀⠀⣾⡇⢤⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠀⠀⠀⠀⠀⣿⡇⠸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣿⠿⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢾⠿⣿⣦⣀⠀⠀⠈⠻⣆
⠀⠀⣠⣴⠾⠋⢹⡿⠀⠀⠀⣰⠃⠀⡟⡄⢰⠻⡄⠀⢀⡿⡆⢀⣾⠀⢻⡏⠙⠷⣦⣄⣀⣹⡇
⢶⣿⣉⠀⠀⠀⣾⠃⠀⠀⢠⠇⠀⠀⡇⠙⠟⠀⠙⣦⡞⠁⠳⠊⢸⠀⣈⣿⡀⠀⠈⠉⠛⠛⠁
⠀⠈⠙⠳⣤⢰⡿⠀⠀⠀⢿⡁⠀⠀⣇⠀⠀⠀⣼⠋⠙⣆⠀⠀⢸⠀⢠⢿⡇
⠀⣤⣄⣠⡟⣸⡇⠀⠀⠀⠀⠹⣄⠀⢸⠀⠀⣼⠃⠀⠀⠘⣦⠀⢸⢠⠏⠘⣿
⠀⠻⠟⠋⠀⣿⠁⠀⠀⠀⠀⠀⠈⠳⣼⠀⢸⣇⡀⠀⠀⢀⣸⡇⢸⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠿⣶⣶⣤⣤⣤⣄⣀⣀⣸⣄⣀⣉⣙⡛⠛⣋⣁⣀⣆⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡟⠛⠛⠛⠛⠛⠛⠛⢻⣟⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⣼⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⣤⠤⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠐⣿⣀⣰⣀⣀⣤⡌⢳⡄⠀⠀⠀⠀⣼⠋⣤⣤⣀⣰⣀⣤⡿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣥⣤⣿⣾⣧⣤⣤⣤⣤⣭⣿⣧⣤⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣁⣈⣉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡋⠉⠉⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⣠⠆⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⠈⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⡇⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠀⠀⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⠶⠄⠀⠀⠀⠀⠀⡞⠉⠙⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⡉⠒⠊⡇⠀⠀⠀⢀⠀⠀⣠⢒⡩⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠋⠀⠙⣦⠀⠀⠀⠀⢸⣄⣀⣀⡏⠀⣸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣟⠓⠈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⠀⡜⠉⠑⠂⠓⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⣻⠟⠀⠀⠀⠀⠀⠀⠈⣪⣉⢼⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡘⠒⠀⠀⠀⠀⠀⠀⠈⢁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠣⡀⠀⠀⠀⣀⠴⠊⠙⣿⠃⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠀⠀⠀⠀⠀⣀⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⣈⡩⠤⠖⡋⢸⣻⡄⠀⠀⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣀⣤⣄⠐⢯⣀⣨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡯⣒⡇⠀⠀⡏⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠽⢷⢶⡏⣀⡸⠀⠀⠀⣾⡕⠉⢱⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠖⠁⠀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⡼⠀⠀⠈⠙⠒⠶⢤⡟⠳⢤⡻⠔⠊⠈⢆⠀⠀⡔⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣀⣀⣀⢀⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠼⠀⠒⠒⠀⠀⢻⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠓⢨⡥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠓⠚⡄⡳⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⣧⣷⠇
⠀⠀⠀⠀⢀⣀⡀⢡⠀⠀⠀⠀⠀⢸⠁⢀⣤⠀⠀⢣⡞⠉⢙⡂⢠⡴⢦⠀⠀⣈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⡏
⠀⠀⠀⢰⠁⠀⢉⣈⡀⠀⠀⣠⣤⢤⣍⠀⠈⡆⠀⠀⠰⡖⠋⠀⠹⣀⠠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⡀⠀⡇
⠀⠀⠀⠈⢦⣤⠼⠁⢩⠀⠀⢯⡀⠀⣹⣀⣤⡥⠀⠀⠀⢣⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠷⣾⡤⣇⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⡇⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣯⣓⠢⢾⠰⠓⠉⠾⠭⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢤⣈⣏⣉⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣭⡷⢤
⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣙⣤⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⢀⣉⡷⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡜⢁⣠⡴⠞⠛⠛⠙⠙⠳⢦⡀⠈⠳⣄
⠀⠀⠀⢠⣴⣋⡉⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠛⠲⢦⣘⣟⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⡩⠋⠁⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠴⠶⢦⣄⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣸⡄
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠦⣬⡙⠷⡄⠀⠀⠀⢸⡇⠀⠀⢹
⠀⠀⠀⢀⣮⠔⡻⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⢷⡈⠀⠀⠀⢸⡇⠀⠀⢸⡆
⠀⠀⠀⠘⠁⠀⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠘⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣧⣀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡿⣙⡂⢠⡇
⠀⠀⠀⠀⠀⠀⡇⠘⣋⣛⣧⠀⠲⢤⣤⣤⡶⠶⠾⠿⠛⠉⠁⠀⢿⠆⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⣿⠇⠀⣸⠃⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢠⡟⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠸⡄⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠁⠀⠀⣸⠁⠀⠀⣰⣧⣤⣄⡀
⠀⠀⠀⠀⡴⠖⠒⠚⠢⣤⡤⠗⠀⠀⠀⠀⠀⠉⠛⠛⢛⣻⡿⠋⠀⠀⠀⠶⢶⡄⠀⠀⠉⠉⠉⠀⠀⠀⠘⠷⠶⠋⢁⣤⠖⠚⢻⡄
⠀⠀⠀⣼⠁⢀⡴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣽⡆⠀⠀⣿
⠀⠀⠀⢹⡄⠈⠀⣼⠙⣧⠸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠒⠠⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⢠⡀⠻⠀⠼⠃⠀⢠⡟
⠀⠀⠀⠀⠻⣄⠀⠉⠀⠉⢀⣷⠀⠀⠀⠀⠀⣴⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣦⡀⠀⠀⠀⠀⣼⠳⢦⣀⣀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠋⠘⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⣰⠏⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠙⢿⡟⠛⠛⠶⠤⠬⠥⠤⠽⠟⠛⠛⠙⣿⡿⠋⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠉⠓⠲⠤⠤⠤⢤⣤⣤⣤⡤⠶⠛⠉⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠚⠛⠛⠛⠉⠁
⡶⣶⢶⠶⠶⡶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⢶⣶⢶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⣀⣀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⢀⠤⠂⠈⠁⠀⠀⠀⠉⠑⠢⡀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⣇⣠⣾⣥⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⡇⠀⠀⢀⠀⢸⢧⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢰⣷⢀⣆⢸⠷⠿⣄⢳⡀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠲⠿⠤⠐⠃⡾⠚⠙⠟⠀⠀⠙⡀⢃⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⢀⣀⣠⣤⣤⡶⠟⠁⠀⠀⠀⠘⢷⣦⣤⣤⣀⣀⣀⠀⠀⠀⣇⢸⡀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠿⠀⠀⠀⠀⣨⠭⠄⠤⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡉⠁⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⢺⡟⠁⠀⠀⠀⠀⡞⠁⢀⣴⣶⠂⠘⣆⠀⠀⠀⢀⡜⣡⣤⡄⠀⠉⢦⠀⠀⠀⠛⢾⣇
⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠸⠁⠀⢸⣿⣿⣿⠇⢸⠀⠀⠀⢸⠸⣿⣿⣷⡶⠀⠘⡇⠀⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠾⣇⠀⠀⠀⠀⠀⠒⠤⢤⣉⣙⣁⣠⠆⠀⠀⠀⠘⢆⠙⣛⣛⣀⣀⡴⠀⠀⠀⠀⣼⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢿⡉⠛⢦⣀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠖⢶⡀
⠀⣀⠀⠤⠤⠄⠝⠲⠀⠈⠑⢄⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⡠⠔⠛⠉⣠⡐⠛
⣼⢛⣛⣛⡃⠀⠀⠀⠛⠓⣆⣸⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⢰⡃⣠⠶⠦⠈⠉⠙⣓⣒⡦⣄
⢯⠉⠀⠀⣀⣀⣀⣀⣀⣠⠟⢸⡀⠀⠀⠀⠀⢈⡟⣿⠒⠶⣤⠤⠤⠴⢴⡶⠛⣯⢳⡀⠀⠀⠀⠀⣼⠱⣇⠀⠀⠀⠀⠀⠲⠬⣭⣻⡆
⠈⠛⠋⠉⠉⠉⠉⠉⢹⡄⠀⠈⢧⠀⠀⠀⣠⠟⠀⡇⠀⠀⠈⠙⠒⠚⠋⠀⠀⢸⡌⠳⣄⠀⢀⡴⠃⠀⢈⡿⠓⠲⠶⠤⢤⣀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠙⠚⠋⠁⠀⣸⠇⠀⠀⠀⠚⠻⣿⣦⠀⠀⠀⣧⠀⠈⠉⠉⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⡤⠞⢹⠀⠀⠀⠐⣶⣿⣿⡿⠁⠀⠀⢸⡶⠤⣄⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠤⠤⠤⠤⠶⠶⠶⠶⠖⠒⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢲⡟⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠘⠁⠈⠉⡟⠒⠒⠒⠂⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣄⣀⣀⣀⣧⣀⣀⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠾⢧⡈⠉⠀⠀⢹⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣀⣀⣿⠀⠀⢀⣇⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢤⡅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡤⣀⣼⣾⠋⠗⣀⣀⠉⡻⢝⣟⣧⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢨⡅⠐⡐⠋⠁⠀⣀⠈⠁⠓⠢⢭⠘⢬⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃⡐⠐⠀⠀⢠⣾⣿⡿⣿⣷⡄⠀⠚⠹⠀⢀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣴⡷⠞⠀⠀⠘⠛⠛⠀⢨⣿⡷⠀⣢⡀⠱⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡊⠓⡀⢈⡤⢠⠇⠂⣰⣿⣿⠃⠀⠁⡐⠰⠖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⣀⢩⣾⣰⡞⠀⣸⣿⡿⠁⠀⠴⢲⡧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡙⣾⣭⠄⣉⣉⡁⢠⡆⠀⡌⠸⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡄⣴⣟⣿⡀⠿⠿⠇⢀⠞⠛⣁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠧⠼⠇⠁⠐⠐⠚⠉⠁⠅⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢨⡍⠀⢩⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠋⠉⠉⠉⠉⠓⠒⠒⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢰⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⣀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠐⢄⠀⠀⠈⠉⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠊⠹⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣧⡀⢀⠉⡇⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡹⠷⠷⠿⠀⠄⠀⠘⠯⠿⠻⠿⠼⠀⠀⠀⡧⠀⠠⢀⠇⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⣀⣀⡀⠈⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠳⡁⢠⠟⠳⡄⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠀⠁⠈⠛⠉⢠⠁⠀⠈⠀⠈⠛⠓⠀⠀⠀⠀⢩⡌⡤⠀⡃⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⠁⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠏⠀⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢠⡾⠥⠄⠀⠀⠀⠚⢷⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠘⠓⠐⣂⡁⠉⠀⠈⠈⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣏⠳⣄⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⢀⠔⡲
⠀⢠⡾⣯⡝⠉⠉⢡⡈⢳⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⢦⠶⠶⠶⡖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡰⠃⠲⡶⡶⣆
⠀⠘⠦⠤⠤⢄⣀⣀⡨⠞⣄⠀⠀⠀⠀⠀⢀⣠⢤⢴⣁⣶⡁⠀⡹⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡋⠁⠀⠀⣈⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⠜⢦⡀⠀⠀⣠⠞⡇⠀⠈⣹⣿⠃⠚⠀⠀⢠⡟⢆⠀⠀⠀⠀⡰⠅⠀⢩⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⢢⡴⠁⠀⡁⠀⢸⣿⡷⠀⠀⠀⢀⡘⠀⠈⠳⣀⡤⠈⠁⢀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢠⠇⢀⡴⡏⠀⢸⡿⠁⠀⠀⠀⡜⠙⢦⡀⠀⢹⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⠉⠀⢿⠀⠨⠁⠀⠀⠀⢰⠁⠀⠀⠉⠲⢬⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡞⢣⣀⣀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢱⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠘⣇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡯⣄⡀⣯⡶⢼⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⠒⠉⠁⣠⣄⠹⠋⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⢤⣠⢧⣿⠫⠭⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡼⢬⣿⠟⠁⠀⢠⢿⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡰⢲⣲⡮⠞⠋⠉⠉⠁⠀⠀⠀⠸⠋⠀⠀⣠⢶⣿⣿⣿⣿⣷⣶⠦⢄⡀
⠀⠀⠀⠀⢀⣴⣿⣶⣤⣽⠃⠀⠀⣀⣤⠴⠖⠒⠛⠿⠻⣯⡙⠛⠛⣛⡻⡿⢽⣷⣭⣙⠒⠤
⠀⠀⠀⣠⣾⣿⣿⣿⡿⠁⣠⠶⠋⠁⠀⠀⢀⡤⠤⠤⠶⠾⠄⠀⠀⠉⠀⠻⡆⠀⠉⠛⠿⣶⣄⡀
⠀⢀⣴⣿⣿⣿⣿⡟⢠⡞⠁⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠙⢿⡄
⠀⠘⠿⢿⣿⣿⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⣀
⠀⠀⠀⠀⠙⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡵⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠔⠂⠉⠉⠉⠙⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⣀⠤⠼⡖⠒⠠⢄⠀⡰⠁⠀⠀⠀⠀⠀⢀⡠⠼⠖⠒⠒⠒⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢘⡠⠚⠁⠀⠀⠀⠑⢄⡀⣀⣷⠶⠭⠉⠒⡲⠞⠛⠳⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠇⠀⠀⠀⡜⠀⠀⠀⠀⠈⡝⢢⠀⠀⠀⠀⠀⠀⠀⠀⠗⢄
⠀⠀⠀⠀⠀⠠⠁⢸⠀⠀⠀⠀⠀⢠⡞⠁⠀⡜⠀⠀⠀⠀⢇⠀⠀⠀⠀⣰⠁⠀⢡⠀⠀⠀⠀⠀⠀⠀⢠⠈⢆
⠀⠀⠀⠀⢀⠃⠀⠀⢧⠀⠀⠀⢰⡟⠀⢀⡌⠤⠄⠐⠒⠂⢄⠑⠒⠒⠈⣸⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠣⡀⠀⡞⣠⠾⠁⠀⠀⠀⢀⠔⠉⠀⡏⠱⡔⢊⠃⠀⠀⠀⠗⣀⡠⠒⠈⠉⠐⣦
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⢲⡏⠁⠀⠀⠀⠀⢠⠃⠀⠀⢀⠃⡌⣰⢂⡠⠔⠒⢲⢠⡏⠀⠀⠀⠀⢀⠃⠱
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⠑⠢⠄⣀⡀⢸⠀⠀⢀⣎⡠⣗⡝⠁⠀⠀⢀⣾⣿⠒⠒⠢⡀⠀⡸⠀⠀⢳
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⢀⠹⠀⠀⠀⠀⠀⠀⠉⢇⢉⠍⡠⠊⢧⠁⠀⠀⢠⠎⣸⠛⢄⠀⠀⡁⢠⠃⠀⢀⠛
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⡠⢛⠾⣁⣠⠛⣄⡠⠔⠏⡔⠋⠀⠈⠑⠤⣧⣆⡀⠔⠋
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠣⡀⠀⠀⡠⠎⢠⠃⠀⡰⠉⠉⠙⢄⣠⠋⠀⠇⠀⠀⠀⡸⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⠀⠀⣈⠤⡊⠀⢠⢃⡠⠊⠀⠀⣀⠔⠊⠑⡦⣼⢀⡀⠤⢊⠃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣖⣈⠩⠤⠤⠘⠓⡾⠥⠤⠤⠒⠈⠀⠀⠀⠀⢱⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠁⢱⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱⣄⠀⡰⠀⠀⠀⠀⣠⠊
⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠹⠓⠂⠐⠒⠈
⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⡄⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠌⢦⡠⠤⠒⠁⠀⠀⠀⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡠⠖⠚⣋⣽⢛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣲⣤⠉⠙⠒⠋⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡳⠄
⠀⠀⠀⠀⠀⠠⡯⠖⠒⡺⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⢶⡄⠀⢹⠳⢤⣀⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⠀⠈⠉⠁⠈⣙⠓⠦⢤⣀⡀⠀⠸⣖⠲⠤⢤⣀⣀⡐⠻⢟⡛⠓⠒⠲⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣼⠀⠀⠀⠀⠀⡩⠖⠶⢤⣄⠀⠉⠉⠓⠛⠃⡀⠀⢷⡈⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡏⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠳⣄⠀⣠⠴⠒⠛⢇⠈⢧
⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⢠⢃⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠘⡄⢀⡷⠲⣄
⠀⠀⠀⠀⣾⠁⠤⣤⢤⡉⠳⡞⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⣝⢃⣙⡆
⠀⠀⠀⠀⠹⣄⠀⠈⠓⠛⠀⠁⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⡤⣄⣸⢠⢲⣶⠀⠀⣼⠀⠀⠘⠢⣌⡵
⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠤⣄⣛⣿⠋⠙⠻⠿⠤⠞⢁⡴⠊⠑⡄⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⣀⡴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⢀⠀⣠⠴⠒⢺⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠁⡜⠀⠀⠀⠀⡟⠉⠓⢶⣒⡲⣧⣤⠥⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡧⢠⠇⠀⠀⠀⠀⡿⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢏⠙⢾⠀⢸⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⠅⠀⢀⡎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣙⣋⣉⣀⣀⣀⡤⡤⠶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠉⠀⠀⡇⣷⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⠘⠛⡟⠃⢀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠤⠤⢤⣤⢶⠞⡏⢉⣻⣤⣼⠇⠀⠀⠀⠀⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣗⣒⣒⣚⣓⣛⡋⠩⠝⠚⠉⠁⠀⠀⠀⠀⣤⣶⣶⣶⡶⠒⠀⠀⠀⠩⠍⠉⠙⠻⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠶⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠐⣀⢠⢤⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀
⠀⠀⡄⡀⠠⠀⠀⠠⠀⠠⠀⠀⠀⠄⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⢨
⠀⠀⠁⠁⠁⠀⠀⡄⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠀⠄⢀⣀⠀⠈⠀⠐⠀⠀⡀⠀⡠⠀⠀⠀⠀⠁⠰⡅
⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠄⢀⠀⠀⠈⠀⠂⠀⠐⠄⢀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠠⠀⠁⠀⠀⠄⠀⠀⠐⠂⠀⠐⠠⠀⠀⠀⠀⠓⣀⠀⠊⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⡇⠈⠀⠀⠈⣀⢨⡀⠀⡌⠉⡁⣀⠉⠁⠀⠂⠀⠐⠀⠀⠁⠀⠀⠠⢀⠀⡄⠀⠀⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠠⠰⠐⠈⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠄⠠⡶⡶⡦⢶⢤⡌⠀⠂⠀⡀⠀⠀⡀
⠀⠀⠀⠀⢠⡀⠀⠈⠐⠂⠈⠀⠂⠀⠀⠀⠀⠀⠀⢀⣾⡻⢃⣹⡷⠇⠠⠯⣦⡀⡀⠐⣁⠔⠰
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡋⠀⠀⠀⠀⠀⠀⠚⡞⡆⠠⠉⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠐⢦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠲⠒⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠠⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾⣇⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣾⣷⣤⣀⣠⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡈⣿⣿⣿⣺⣋⣻⡷⣽⣿⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣽⠯⢶⣟⣿⣿⣿⠀⠀⠀⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠰⢟⣷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠉⣿⡇⢀⣀⠤⠀⢀⣨⡥⠖⠚⢋⣉⣡⠤⠴⠒⠚⠋⠛⠟⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠟⠋⢁⡠⠔⠊⣁⣀⣤⣶⣚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢩⣭⡤⠚⣁⣴⣶⣿⣿⣿⣿⣿⡿⣣⣾⣷⣦⡀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡤⠚⢋⣴⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠻⣿⣿⣿⣿⣶⡀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣠⠞⢉⡠⢶⣿⣿⣿⣿⣿⡿⠛⠉⣁⣀⣠⠤⠄⠈⢿⠌⠻⡿⠿⠈⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⠋⠀⠸⣿⠛⢡⣿⠟⠀⠠⠄⠢⢬⡴⠞⠉⣀⠀⠀⢰⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣏⡴⠉⠴⢶⣦⠀⢿⡆⢸⡏⠀⢀⣠⣴⣶⡄⠀⣴⡾⢿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢨⣏⠀⠀⠀⣛⠉⠀⢸⡇⠀⠁⠀⡾⠋⠁⠈⠃⢀⠉⠀⠀⠀⠀⣸⡟⣻⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠈⠑⠂⠀⠉⢀⣤⢤⣿⠀⠀⠀⠀⠀⣤⡄⠀⠸⡆⠰⣿⠀⠀⣿⡟⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣄⠀⠀⣿⠀⠖⢻⣇⠀⠀⠀⠀⠙⣡⠄⠀⢻⡀⢦⣀⠀⣿⣇⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠸⣿⡄⠀⠀⠀⠐⠁⠀⣄⠈⡇⠀⠀⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣿⠃⠀⠀⠀⠀⠀⠀⢿⡉⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢉⣿⡀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠉⢹⡇⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣼⣡⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣍⣉⣭⣍⣠⣤⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠿⠿⠛⠻⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠄⣠⠀⠀⢈⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠺⠞⢷⠒⣴⠀⣀⣀⡀⠐⣒⢢⡀⠠⢀⠀⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢉⣖⠀⣠⣾⠽⣟⣹⣛⣉⣻⠿⣭⡉⢿⡷⠺⡄⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣴⠲⡄⠀⣰⣵⣄⢉⣨⣿⣿⣛⢶⣿⣛⣥⣭⣹⣶⣡⣤⠂⠀⠑⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠁⢊⣸⣏⠉⣤⡾⣿⣿⣿⣿⣿⣯⣛⣻⣷⣞⡙⡿⣆⠼⠾⣶⣨⡷⡈⠓⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡿⢶⣿⣿⣧⣤⠴⣿⣿⣿⣿⣥⣿⣟⣿⣻⣷⣼⣧⡸⡻⢿⣷⣚⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⣨⠀⣼⡷⢺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣷⣮⣿⣇⣛⢺⣹⣈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢡⠉⠀⣻⣷⡟⣏⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⡞⢻⡟⢸⡙⣄⠻⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠇⠺⣿⢿⣿⠟⢻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣾⣷⣾⠃⣭⣔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠁⠖⠀⠙⡆⢻⣬⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣀⠠⡎⠁⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢁⠀⠐⠀⣿⣎⠛⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠤⠜⣬⠿⣁⡜⠻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⢈⡎⠉⢻⣿⣔⣶⣭⣿⣿⣿⣿⣿⢛⣿⣿⡿⠋⠙⣆⣽⠏⠚⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢽⣤⠀⠙⣿⠛⠧⠐⠿⢿⠿⠿⢿⠟⣯⡰⣂⣼⡟⠉⢆⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠻⢟⡻⠓⠤⠴⢶⣀⣄⣀⠉⠀⠀⢈⣿⣋⡳⣄⣀⣈⣂⠠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣩⠂⢠⣿⡳⠶⢶⣎⢀⣘⠁⡄⠄⠲⠋⠀⠛⠀⠀⠜⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠎⠀⠀⠀⠀⠶⢦⡄⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⢀⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢀⠔⠉⠉⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⢀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⢀⣀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠢⢤⢄⣀⣀⣀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣼⠀⠘⠊⣽⡏⠲⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢤⡤⣀⣛⣁⠀⢸⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠁
⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠇⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠁⠀⠀⠀⣾⣭⣤⠤⠤⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⡀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠤⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⢀⣠⣤⣤⣤⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣶⠟⠉⠈⠛⢮⡙⠳⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⠿⠀⠀⠰⡄⠀⡀⠠⣄⠀⠀⠀⠀⠐⠒⠒⠚⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀⢻⡄⠀⠠⣶⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡀⢀⠀⢳⡀⢹⣄⡀⠉⠓⠒⠒⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠙⠦⣽⣦⣷⡾⠋⣛⡶⣦⣤⣤⣤⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣶⠚⠋⣡⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⣀⠀⢸⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⣠⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⢸⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⡟⠿⠉⣠⡴⠶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⣶⣌⠛⠋⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠀⠈⡇⢀⣼⠋⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠉⢳⡄⢸⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢿⣦⠀⡇⣼⠃⠀⠀⠀⠀⠀⣤⡄⠘⣷⠀⠀⠀⠀⣿⠀⠀⠀⠰⡷⠀⠀⢿⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⣀⠀⠀⠉⠿⢿⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⢻⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣠⣾⠷⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠈⣳⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠿⣷⠏⠀⣀⣀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⠋⢹⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣰⠏⠀⠁⣠⣾⡉⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⣄⡀⠀⠀⠀⠈⢷⣄⣀⠀⠀⠀⢀⣠⡾⠁⣴⠞⠳⢶⡄⠀⠙⠓⠶⠖⠛⠁⠀⠀⢠⠇⢸⡇⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣍⣉⠀⡇⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡼⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⡀⠀⠀⠀⣀⣀⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉

⣶⣶⣶⣾⣶⡷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⢷⣶⠶⠶⠶⠶⣶⡾⠷⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠻⠎⠙⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠠⠐⠀⠁⠀⠀⠀⠈⠉⠒⠦⢀⣠⠞⠀⠀⠀⠀⠀⠒⠈⢷⣄⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣀⣠⡤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠀⠀⠀⠈⣇⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢉⡥⠤⠄⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⠀⠀⠀⢰⠋⠀⣠⣴⡆⠈⢳⠀⠀⠀⠀⡴⢉⣤⣤⠀⠈⢢⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⡶⢸⡇⠀⠀⢰⠀⣿⣿⣷⣶⠀⠀⡇⠀⠀⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⠀⠀⠘⠲⠤⢌⢛⠋⣁⠜⠀⠀⠀⠀⠣⠙⠛⣛⢋⢀⡼⠁⠀⠀⠀⢀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣄⡀
⠀⠀⠀⠀⠈⢧⡈⠙⠦⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡤⠖⠋⣠⠟
⠀⣠⠤⠤⠶⠶⠞⠓⠀⠈⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠙⠂⠀⠀⠀⠀⣠⢞⡟⠉⠀⡀⠛⠷⠶⠤⢤⢤⡀
⣾⣃⣈⠭⠅⠀⠀⠈⠉⠙⡆⣜⠀⠀⠉⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⢘⡇⡔⠉⠉⠀⠀⠀⢭⣭⣁⣙
⢯⠁⣀⣀⣀⣀⣀⣠⣤⠴⠃⢹⡀⠀⠀⠀⠀⡽⠓⣶⢤⣤⣄⣀⣀⣀⣤⣤⡴⠶⣏⠁⠀⠀⠀⣸⠃⠳⢤⣤⣄⣀⣀⣀⣀⡀⢨
⠈⠉⠉⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣀⣀⣠⠞⠁⠀⣿⢢⡀⠴⣿⣿⡷⢄⡌⣿⠀⠙⢦⣄⣀⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠀⠀⣠⠞⣯⠀⠀⠀⢨⣽⡀⠀⠀⢸⣦⡀⠀⠀⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠤⠖⠚⠁⠀⡃⠀⠀⠀⠈⠛⣇⠀⠀⠈⡇⠉⠓⠦⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡿⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠒⢲⡆⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢰⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢯⡀⠀⠀⠀⠀⡹⠂⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣦⣤⣤⣷⣄⣀⣠⣾⣥⣤⣤⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢲⢰⠃⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⣏⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⣤⣶⣦⡄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⠋⠉⠻⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⡿⠋⢿⣿⣿⠏⠻⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⢀⣴⣄⠀⠀⢀⣦⡀⠈⠻⣿⣿⣿
⠀⠀⠀⠻⠿⣿⣷⣶⣤⣭⣥⣴⣶⣿⡿⠿⠃⠀⠀⠀⣿⣿⣿⣧⣀⡀⠈⠉⠛⠓⠚⠛⠋⠁⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⡀⢉⣿⣿⣿⣿⣿⣏⠁⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡼⠉⠉⠀⠀⢸⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣾⣿⣿⣿⣷⡹⣿⣿⣿
⠀⠀⠀⣼⣧⣤⣒⣒⣒⣼⣔⣒⣒⣢⣤⣿⡄⠀⠀⠀⣿⣿⣿⡟⠸⠿⠿⠭⠭⠟⠹⠭⠭⠿⠿⡇⢹⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠤⢤⣘⡶⢄⠴⠊⠉⠉⠉⠉⠉⠓⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠓⠄⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢿⠄⠀⠀⠀⣌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣸⣄⠀⢀⠸⣦⣄⡀⠀⢀⡀⠈⣆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⣠⠃⣈⠓⠦⢵⣷⠈⠉⠛⣛⠛⠛⢻⡂⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡴⠛⠁⠊⠉⠃⠀⠀⠀⠀⠀⠘⠉⠉⠀⠸⠿⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣃⠀⢠⠶⣿⣦⠀⠀⠀⠀⠀⠴⣾⣷⣄⠀⢸⣧⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠀⠀⢐⠿⠟⠀⠀⠀⠀⠀⠰⠿⣇⠀⠀⢸⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡇⠀⠈⠀⠁⠀⠈⠀⠀⢠⠄⠀⠁⠀⠀⣬⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢤⣤⡤⠤⢤⣔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⢀⠀⠄⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠇⠀⠀⠅⠀⠀⢷⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠤⣴⠀⠀⠀⠀⠀⠀⢸⡦⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡇⠀⠀⠀⠀⠀⠈⠀⣷⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⣼⡦⠀⠀⠀⠀⠀⠀⢄⡾⡦⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⡇⡏⠙⠓⠒⠒⠛⠛⠉⣇⠉⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⢰⠆⠀⠀⠘⣷⠂⠀⠀⢸⠈⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⢹⡄⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⠤⢤⡝⠘⢧⣤⡤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⠴⡇⠀⢸⢤⣄⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠃⢀⡇⠀⢆⡀⠛⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡰⠦⠋⠀⠀⠈⠣⣀⣀⡠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣠⣤⣀⣀⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡿⣛⡽⠛⠉⢉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠅⠈⠐⢶⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣾⣿⠿⠋⠛⠉⠉⠀⠀⠀⠀⡏⣠⡿⠛⠛⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⣠⣶⡛⠀⢠⠞⢁⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠀⣴⠶⣤⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠈⣰⠋⢀⣀⡀⢀⠀⣸⠆⠀⠀⠀⠀⠀⡇⠀⣿⣷⠀⠀⠀⠀⠈⢷⡀⢀⡤⢤⡀
⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⡼⠉⠛⠿⣿⠿⣏⠀⠀⠀⠀⠀⠀⢻⠀⢻⣿⡤⠤⠀⠀⠀⠈⢳⡿⠂⠘⡇
⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠙⠀⠀⠀⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⢚⠂⡇
⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⢘⡿⠧⠀⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠇
⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠻⠤⠖⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠶⠋
⠀⠀⠀⠀⣤⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠈⣇⣶⢌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠹⡾⢬⠟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣌⠻⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⠳⠞⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣴⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣶⣶⣶⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣿⣿⣿⣿⣿⣿⣿⣥⡾⣿⣿⣿⣿⣿⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣿⡿⣟⣿⠟⠁⠀⠀⠀⠈⠙⠛⠿⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⠞⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⢀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢀⣠⡤⠄⠒⠒⠒⠒⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠔⢉⡾⠃⢀⡖⠀⢀⠔⣁⠔⠊⠩⡗⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⣸⠀⢀⣾⠁⣰⢏⡜⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠒⠒⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡈⢻⠀⠘⠁⣴⠛⠏⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⢦⡀⠄⠀⠀⢀⡴⠞⠻⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠛⠿⠖⠲⠟⠒⠂⠀⠀⠀⢸⡇⣀⠄⠂⢠⠀⡾⠀⠀⠐⠒⠠⣀
⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡷⣾⠖⠀⠀⠿⠷⠀⠀⠀⠀⠘⢷⡅⠰⠆⡘⠀⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠤⠞⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠔⢁⣼⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠈⠁⠀⠀⣠⠴⠗⠊⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⢦⣤⣤⠶⠋⠀⣼⠛⡉⠈⢳⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⣄⠀⠀⠀⠀⢀⠆⢰⠋⠀⣠⠇⠀⠀⣀⡴⠛⠋⠁⢀⣉⠁⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣀⠀⠈⡾⡇⠀⢀⡤⢾⠀⠁⠀⠰⢛⡠⠔⠊⢀⡠⠔⠒⠉⠉⠛⠢⣤⣀⠻
⠀⠀⠀⠀⠀⢰⠀⢆⠀⠀⢀⠔⢃⡠⠀⢳⣤⣀⠀⣀⣠⡶⠊⠁⠀⠀⠀⠀⢀⠄⠁⠀⠈⢳⡀
⠀⢀⠦⠀⠀⠈⢆⠘⣤⠖⠁⠀⡼⠁⠀⣄⠏⠉⠀⠉⠈⠆⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⣇
⠀⠋⠀⠀⠀⡠⠾⠆⠈⢦⣶⣼⠁⠀⢐⣀⠆⠀⠀⠀⢻⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⣜⡁⢀⠀⠀⠈⢿⡇⣀⣀⡀⡠⠴⣄⣀⣈⣉⡀⠀⠀⠀⢰⠟⠀⠒⠌⣉⡱⠀⠀⡿
⠀⠀⢠⠜⡁⢀⣀⠀⢀⡴⠋⠁⠀⠀⠉⠀⢰⠀⠀⠀⠀⠈⠓⢦⡴⠃⠀⠀⠀⠀⠀⠉⠀⣰⠇
⢀⡔⠉⠰⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣤⣄⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⠤⠟⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠉⢢⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣼⣿⡇
⠈⠓⠶⠶⠶⠶⠶⠚⡟⠉⠁⠀⠀⠀⠀⠈⠳⠦⣤⣀⣀⢀⠀⠀⠀⠀⣠⢾⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠚⠁⠀⠫⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⠁⠀⠈⠉⠙⠛⠒⠒⠚⠛⠛⠛⠛⠒⠒⠒⠛⢉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠤⣉⠋⠭⣿⠁⣒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠤⠁⠆⠰⠁⠁⠚⠑⠀⠀⠈⠀⠐⠂⠐⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠄⠁⠊⠙⠂⠛⠀⠓⠛⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠛⠛⠛⠛⠛⠿⠶⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣾⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⢸⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣧
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣠⠾⡇⠀⠀⣸⡇⠀⠀⠀⠀⣶⠀⠀⠀⠀⢠⡀⠀⠀⠀⣿⢸⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠀⠱⠦⠾⠁⠻⢦⣄⣠⡴⠛⢦⣀⣀⡤⠞⢧⣄⣀⣰⠛⣾⡇
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡈⠉⠁⠀⢿⡇
⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⢀⠔⠉⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⢣⠀⠀⠈⣷
⠈⢿⡄⠀⠀⠀⠀⠀⠀⣤⠴⠃⠀⠀⠀⠆⠀⠀⣤⣤⠀⠀⢡⠀⠀⠀⠀⠀⡾⠀⠀⢰⣶⠀⠀⠀⡇⠀⠀⠸⣇
⠀⠈⢻⣄⡤⠶⠲⢦⣤⡟⠀⠀⠀⠀⠈⡆⠀⠀⠉⠉⠀⠀⡼⠀⠀⠀⠀⠀⢴⠀⠀⠀⠉⠀⠀⢠⠃⠀⠀⠀⣿
⠀⠀⠀⣿⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⢀⣀⠴⢁⡀⠀⠀⠀⣀⡀⠑⠤⢀⣀⡠⠴⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠘⢷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠛⢛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠠⠄⣀⣀⣀⣀⠀⢀⣀⣀⣠⣤⣤⠶⠞⠛⠉⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠷⢦⣤⣀⣀⠉⠉⠉⢿⣹⣿⠁⠀⠀⠀⠀⠀⠀⢠⡟⠁⠠⣉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣀⠉⠉⠛⠛⠶⢾⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣦⠙⣦⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠳⢦⣄⣀⡀⢸⡇⠀⠀⠀⠀⣀⣠⣴⡟⠁⢀⡄⢘⡷⠋⠳⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⢻⡏⠁⠀⢿⡞⠋⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠐⠳⠶⠶⣤⣤⣄⣀⣀⣀⣀⣀⣠⣼⡷⢶⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣩⠟⠉⠉⣼⠻⠄⣠⢈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⣿⠈⠛⢶⣤⡞⠙⢳⡄⢙⠛⣧⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣤⡟⠀⠀⠀⠀⠀⠀⠈⠷⠾⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣤⣤⣤⣄⣸⡇⢹⡄⠀⠀⠀⣀⣀⣠⣬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠹⠧⣤⡀⠛⠖⢿⠛⠉⠉⠉⠷⠶⠶⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡻⣶⣶⣶⠶⠶⠾⠛⣀⣀⢘⣧⣤⣤⣤⣴⣶⣶⣾⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠰⣶⡄⠀⠐⠦
⠀⠀⠀⠀⢀⣄⠀⠀⠠⡀
⠀⠀⠀⠀⠘⠋⠆⠀⠘⠃
⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⣿⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡇⠀⢰⡏⠀⠀⠀⠘⡇⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣇⣀⠀⢀⠀⢀⡠⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗⠿⠂⠀⠀⠸⢃⣀⣸⣿⣶⣶⣤⣤⣻⡆⠀⠀⠀⠛⣤⣄⣀⣀⣀⣀⣀⣀⡇⠀⠀⣸⣏⣿⡀⠀⢲⣼⠗⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠂⠀⠀⠀⢸⣿⣿⣟⠻⠟⠿⢯⣽⣿⣶⣶⣶⡟⠉⣭⣭⣿⣿⠭⣭⢿⣿⡆⠀⢸⡏⣩⠀⠀⠈⢳⡟⠂⠹⡇⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠶⠂⠀⠀⡇⠀⠹⣷⡽⠂⠐⠓⠊⠁⣼⢯⢦⣽⡄⠀⠀⠈⠘⠁⠀⢁⣼⣿⠀⠀⣿⣡⡿⠀⠀⢀⣞⣀⣤⣦⡳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠘⠃⠀⠠⡆⠀⢀⠛⢷⠤⠤⠤⠶⠞⠁⢨⠈⣅⠹⢾⣿⣦⣄⣤⣈⡿⢿⡧⠀⢠⣿⢫⡜⢛⡾⣿⠿⠿⢿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⠀⠈⠄⠀⠀⠀⠀⠀⠈⠀⠈⠃⠀⠀⠉⠉⠀⠀⠠⠚⣇⠀⠀⣿⣶⠷⣿⣿⠛⢷⣾⡖⣛⣿
⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⡴⢿⣿⠈⠉⣹⠉⠁⠈⠉⠙⠁
⠀⠀⡀⠀⠈⢉⡉⠀⢨⣉⡁⠀⠀⠀⠀⠀⢰⡇⡌⠀⡇⠀⠰⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡏⢘⣷⢺⡏⠀⠀⣿⡀⠀⣀
⠀⠀⠀⠀⠸⠤⠅⠀⠸⠋⠇⠀⠀⠀⠀⠀⠸⣷⡇⢸⠃⠀⠀⠸⣦⡀⠉⠉⠀⠀⠲⠶⠂⠀⠀⢀⣤⣶⢼⡇⢸⣿⢻⣧⣀⢠⣿⠁⠀⣿⠀⠀⠀⠀⢀⡀⣠⣤⣤
⠀⠀⠀⠀⠀⡐⠢⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⣤⣿⢳⣄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⣷⣿⠁⣾⣿⠸⣿⣿⣧⠙⠀⠀⣿⠀⠀⣴⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⡀⠀⢈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⢸⣷⣠⣿⠏⠁⠀⢻⣧⣀⣀⣀⣴⡿⢫⣾⣿⠻⡿⣿⠛⢹⣧⠀⢻⣿⣿⣷⣄⣾⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⢄⡀⠀⣨⡀⢀⣀⡀⠴⠤⣶⣾⣿⣿⣿⣿⠏⠀⢰⠀⠀⠋⣿⡿⠾⢿⣼⣿⡟⠡⠖⢻⡿⠇⢠⡟⠀⢠⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⡀⡄⢠⠀⡆⢉⠠⠄⠰⣾⣿⠃⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⡆⠀⠘⠇⠀⠈⠁⠙⢀⡼⠂⢸⣿⠀⣸⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⢰⡉⠀⠑⢻⠃⠀⢠⣾⣿⡆⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⡏⠀⠛⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠇⠙⠀⡾⢀⠷⠘⢿⣿⠇⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣴⠏⠀⠀⢰⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⢰⣾⣶⣷⠀⣤⠀⣾⡟⢠⣿⣿⣿⣿⣿⡇⠈⠑⠒⠤⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⢻⣿⣿⠀⠈⣶⠛⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠶⠛⠛⠳⢶⠶⢎⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠂⠹⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠏⡐⠻⡄⢴⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡠⠰⠟⠃⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢰⠇⠀⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠊⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⣯⠐⠂⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⣧⠘⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣶⠀⣿⠃⠀⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⣿⠀⠀⢺⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠐⣇⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⢻⠀⠀⢹⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡌⢀⡀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣌⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠐⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⠀⡀⠀⢀⠀⠀⢀⡼⡥⠀⣨⠎⠀⡒⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠔⠑⠊⠐⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠐⡱⠀⣠⡡⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⢒⠭⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠚⠁⠁⠀⠀⣀⠌
⠀⠀⠀⢀⠄⡰⠋⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⢀
⠀⠀⠀⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠍⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠢⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠠⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⢦⠀⡠⢀⠄⠀⠀⠀⠀⠜⠀⢀⠄⠀⠀⠀⠀⡤⠖⠁
⢄⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠚⣧⠧⠚⠠⢤⣀⣀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠁⠒⠀⠀⠈⠀⠀⠀⠀⠰⡀⡄⠀⠀⠀⢀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠑⠒⠄⠀⠀⠀⠁⠋
⠀⠢⠀⠀⢀⡀⠀⠀⠀⠀⠀⢣⠀⢡⡶⠛⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠦⣄⠀⠈⡇⠀⠉⠀⠒⢠⠆
⠀⠀⡐⠚⠋⠀⠀⠀⠀⡄⠘⠀⠀⠋⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⢎⠀⠈⠒⠊
⠀⠀⠈⠢⠀⠀⠀⠤⠚⠀⠀⡇⠀⠀⣼⠋⠀⣤⣤⡈⢂⠀⠀⠀⠀⠀⠀⠔⢉⣉⠉⢳⡄⠀⠀⣀⠄
⠀⠀⠀⠀⠁⠐⠂⢀⡀⠀⠀⡁⠀⠀⣏⠀⢲⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⡇⠀⣿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠻⡆⠐⠀⠀⠀⠹⣄⡄⠉⠉⠀⠈⠀⠀⠀⠀⠀⠘⠀⠉⠉⢀⡰⠃⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠁⠀⠀⢀⠠⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣐⣒⣂⣀⣀⣄⣀⣀⣒⣒⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⢩⣟⣃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧⣠⠖⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠙⢓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⣀⣤⣤⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣸⠆⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⣠⠞⠁⠀⠙⢮⡁⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢱⠐⣆⡑⠒⠤⠄⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢧⠀⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣚⣷⠿⣋⣽⡶⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠈⣏⣰⣾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣶⢸⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠛⢉⡴⠶⠶⠦⣄⠀⠀⠀⠀⢀⡴⠶⠶⣍⠛⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⣄⢸⢠⠏⠀⠀⠀⢀⠘⣧⠀⠀⠀⡟⠀⠀⣤⠈⢳⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⠀⠙⠾⡟⠀⠀⠀⠀⠙⠁⢸⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⢁⡼⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢨⢷⡀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣇⠀⠀⠀⠀⣸⠛⠏⣠⠴⠄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢯⣈⠁⠀⠘⢦⣀⠀⠀⢀⣠⠏⣠⠶⣤⡈⠓⠦⠴⠞⠁⠀⡸⢹⠆⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣭⣤⡇⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⠁⠜⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⣿⠴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⣤⣤⡤⠤⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠋⠛⠛⠓⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⢀⣀⢠⣤⣤⣤⣀⣀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠉⠑⢦⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⢻⣀⣤⣞⣁⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⠾⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⢦⣄⠀⠀⠀⢸⡇⠀⠀⠀⡀⢨⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⣸⡇⠀⣆⢸⡷⡾⣧⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣃⣀⣴⠏⣿⡼⠻⣾⠃⠀⠈⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢠⡶⠿⠟⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠃⠀⠀⠀⠀⠀⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣠⡾⠀⠀⠀⠀⢀⡤⠶⠒⠲⢬⣿⣦⡀⠀⠀⠐⠶⠾⣿⠯⠤⠦⢤⡀⠀⠀⠀⠀⠀⣿⣨⡇
⠀⠀⠀⠀⠀⠀⢀⡴⢾⡟⠁⠀⠀⠀⠀⣰⠋⠀⠀⣀⣤⡀⠈⢯⠁⠀⠀⠀⢀⠎⠁⣀⣤⠀⠀⠙⢦⠀⠀⠀⠀⠉⢹⣷⣄
⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⢰⣿⣿⣷⡆⠘⡇⠀⠀⠀⢼⠀⢸⣿⣿⣶⠆⠀⢘⡆⠀⠀⠀⠀⢸⡇⣿
⠀⢀⣀⣀⣰⠋⠉⠙⢺⡷⠛⠛⢢⡀⠀⠃⢀⣀⠀⠙⠛⠋⠀⡠⠀⠀⠀⠀⠸⣄⠀⠙⠛⠋⠀⢀⡘⠀⠀⠀⠀⠀⢘⣡⠏
⣾⠋⠁⠈⣧⠀⠀⠀⢸⡁⠀⠀⠐⡇⠀⠀⠀⠉⠉⠛⠓⠒⠊⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⢀⡟
⣟⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡾⠁
⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠺⡇⠀⠀⠀⣰⠟
⣿⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡠⠚⠁
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⢸⡄⠀⣿⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡋
⢻⠀⠀⠛⠛⠛⠉⠉⠉⢩⠟⠋⠁⠀⠀⠀⢸⡏⠉⠁⢹⠛⠛⠲⢶⣶⠶⠶⣶⡿⠛⠙⡇⠀⠀⠙⠳⣄
⢸⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⠀⠀⠀⠀⢈⣉⣉⠉⠀⠀⠀⣿⢦⣄⠀⠀⠈⢷⡀
⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣧⠶⢋⡟⠀⠀⠀⢰⣿⣿⣿⣷⡆⠀⠀⢿⠀⠙⣆⠀⠀⠈⣧
⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⡇⠀⠀⠀⠸⠛⠛⠛⠻⠇⠀⠀⢘⠀⢀⡟⠀⠀⢠⡟
⠀⢷⣄⣀⣀⣀⣀⣀⣬⣷⣤⣤⠤⠤⠤⠞⠁⠀⠀⢸⠁⠀⠀⠀⠀⠈⠋⠋⠁⠀⠀⠀⢸⡟⠉⠀⠀⣠⠞
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠤⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⢘⣇⢠⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢻⣤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣤⣀⣀⣀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠤⢀⣀⣼⡀⠀⠈⠙⣆⣀⣀⣀⠠⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣽⠁⠀⢸⠉⠉⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠒⢲⡖⠚⠃⠀⠀⠘⠳⠲⣶⠒⠚⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠲⢾⡇⠀⠀⠀⠀⠀⠀⠀⢻⡤⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⡀⣻⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⡿⣶⣦⣶⣦⠉⠉⠁⠀⠤⣤⣤⡀⠀⠀⠀⠀⠈⠙⠋⠀⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠘⠿⠃⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠙⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⣠⣶⡇
⢀⣤⣴⢤⣤⡀⢀⡀⠐⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠘⠿⣦⠀⠀⠀⠒⠂⠉⠻⠿⠛⠛⠂⢠⣤⠀⠀⠀⠀⠀⣀⠐⠋⠁⠀⠛⢢⣄
⠈⠛⠟⠀⠈⠀⣀⠀⠐⠲⡶⠿⠂⢠⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⣷⣦⡄⠚⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⢁⡿⢧⣀⠀⠀⠀⠀⠀⠀⠻⣤⡀⢀⣀⡀⠀⢾⣿⠶⠆⠀⠈⠉⣷
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠘⠀⠀⠙⢳⣄⡀⠀⠶⠦⠀⠙⠿⣏⠉⠁⠀⠀⢡⡄⠀⠀⠀⠀⠻
⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⢼⡟⠀⠀⠀⣰⡦⠤⠄⢠⡾⠿⢿⣷⣤⣄⡀⠀⠀⠙⢷⣄⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠀⠀⠘⠋⠀⠀⠈⠁⠀⠀⣻⡤⠈⠉⠛⠀⠀⢠⡌⠀⠀⠈⠋⣀⠈⠻⣶⣄⢠⣤⡼⢷⣤⣀⣹⣿⠆⠄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣧⠀⠚⠀⠀⠀⢸⡇⠀⠀⠀⣰⡿⠃⠀⠉⢁⠀⠀⠀⢀⡘⠛⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⡇⠀⠀⠀⠀⠸⣧⣀⠀⠂⠀⠁⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠈⣽⠛⠛⠒⠀⠀⢠⡤⠀⠒⠒⠊⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⠀⠈⠻⠀⠀⠀⠀⠀⠈⠻⠷⣀⣀⣠⣿⠆⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⠀⠀⠲⢦⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⢉⣄⠀⠀⠀⠿⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⣴⣎⣀⠀⠁⠀⠀⠀⠈⠛⣀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⣀⠀⠀⠀⠘⠃⠀⠀⠀⠠⡤⢤⣾⠉⠉⠉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠃⠈⠛⠛⠛⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠶⡶⠦⠄⣀⠀⠴⠶⠤⠀⠉⠉⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠐⠃⢠⡄⠀⠀⠀⠀⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢂⣄⠀⠀⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⣀⡀⠀⠀⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⣄⡀⠸⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⣾⣇⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣧⣤⣤⣄⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣠⣤⣄⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠋⠘⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣧⡙⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⡿⢣⣿⠟⡟⣹⠉⢯⣦⣾⣿⣿⣦⡌⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⣟⠀⠀⠈⣄⣱⣌⠲⢴⡄⠉⠉⢹⣿⡏⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣾⠄⠠⠤⠙⠻⠍⠛⠀⠀⠄⢀⠸⠙⣽⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣌⠻⠀⠖⠟⠂⠀⠀⠀⠀⠿⠶⠂⠀⠀⣹⣿⣿⠞⣹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⠝⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢴⣤⣧⡀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⢀⣮⡄⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠄⠘⠂⠶⠛⠹⣿⣦⣤⡌⠙⣒⠚⠁⣀⣀⣴⣿⣴⠶⠀⠀⠁⠈⠒⠂⠈⠠⡀
⠀⠀⠀⠀⠀⡠⠀⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠢⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣶⣿⣿⣿⣿⠂⠀⠀⠀⢈⠆⠀⠀⢠⠖⠛⠛⢵
⠀⠀⠀⠀⡤⠒⠁⠄⠀⠸⢑⠀⠀⠀⠘⠂⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠆⢸⠠⢀
⠀⢾⡖⠃⡀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣
⠀⠸⠃⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⢰⠇⠀⠀⠀⠀⠀⠀⢁⠸⡀⠤⠀⠠⠤⠴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⠤⠠⠠⠀⠘⠂⠀⠀⠀⠀⠃⠁⠀⠀⢠
⠀⠉⠀⠀⢀⠀⠀⠀⠸⣬⠳⠌⠀⠠⠄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠒⣊⣥⢔⣦⡶⢦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢁⡞⣱⡿⠋⡵⠟⠿⠛⠉⠙⠻⠿⣽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢹⡇⠈⢀⠏⢀⡀⡀⠀⢀⣠⣶⣤⣴⡤⢄⣂⣀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣸⣄⢧⣰⡌⣿⣿⣿⢡⣢⡿⠿⠿⠿⣿⣿⣯⣥⣤⡤⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣾⡏⠻⢿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣾⣿⡆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣆⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⢷⣦⠀⢰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⢠⣶⣤⣄⣀⡀⠀⠀⠢⠙⠾⠿⠛⠁⣀⠀⠀⠀⠀⢻⣛⡿⠗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠉⣉⣉⡛⠉⠁⠀⠀⠀⠀⠐⢑⣲⡒⠀⠀⠀⠀⢸⣿⢳⡗⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠁⠀⠀⠑⠒⠒⣒⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠿⠼⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠺⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣀⣡⣤⡤⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠚⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡛⢯⡉⠉⠛⠒⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⠷⣤⣤⣀⠈⠉⠉⠉⠛⠳⠦⠀⠀⠀⠀⠙⠲⣄⠀⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣞⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡭⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠴⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡁⠀⠀⠈⠉⠓⠀⠠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠯⣭⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢉⡤⠖⠚⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣶⠾⠿⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠰⣏⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣳⣤
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠶⠶⠦⣄⡀⠉⠉⠁⠀⠀⢻⣤⠴⠖⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⢛⣙⠛⠛⠻⣄
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⠦⣄⣀⠀⠙⠂⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠯⣭⠭⠿⠆⠀⡿
⠀⠀⠀⠀⠀⠀⣿⠀⠰⣶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣽⡶⠦⡄⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠖⠺⣏⣥⡞⠀⠀⠀⠀⠀⡴⠋⠀⠉⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠉⠙⠿⣍⡉⠙⠧⠤⠼⠃⠀⠀⢀⡾⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠈⠙⠦⣄⣀⣀⣀⡠⢤⡾⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⠈⠛⢮⣁⣤⠞⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⢸⡟⠡⣶⢀⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⣷⢀⡟⠘⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣉⠳⡀⢘⡿⠁⠀⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠋⠉⢷⣵⠾⢧⣄⡀⣾⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⠀⢀⡾⠋⠀⡀⠈⠛⠟⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠔⠚⠛⢿⣟⠛⠶⣤⡴⠁⠀⠀⡤⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣦⣤⣤⣤⣝⣷⡀⠈⠳⡀⢀⡞⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠙⢦⣀⣠⠟⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠲⠦⢤⣄⣀⣀⡀⠈⠁⠀⠀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⢒⣲⣾⣤⣼⣏⡉⠉⠉⠉⠉⠉⠉⣹⠏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣀⣰⠏⠀⠉⠃⠉⠓⠀⠀⠀⢀⡼⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣦⣀⠀⠀⠀⠀⢀⣠⠴⡋⢀⣛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠻⠤⠿⠦⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢩⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠈⠉⢉⣽⣿⣿⠀⠀⠀⠀⠀⠰⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣦⡄⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⡤⣀
⠀⠀⠀⠀⠀⠀⠘⠃⠛⢻⣿⣿⣿⡄⠀⠀⣿⡿⠃⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠲⠄⠀⠙⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⣼⣿⠁⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⣩⣿⠄⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠊⢻⣾⡇⠀⡄⠻⠟⠄⠀⠀⢴⡋⠗⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠉⢀⣤⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠈⠀⢀⠀⡤⠊⠀⠀⠀⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⠉⢁⡉⡧⠀⠀⠒⠀⠀⠀⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⡁⠠⠄⠀⠀⠄⣀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠒⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⢀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⣶⣶⣾⢿⣶⠶⣶⣶⢷⢶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣷⣶⣿⣶⣾⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠉⠉⠉⠉⠉⠉⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠲⢦⣤⣤⣀⡉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡉⠉⠒⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡒⠦⢄⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢠⠏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡙⠒⡶⠦⠤⢄⣀⣀⣀⠀⠀⠈⠳⢄⠈⠙⠢⢄⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⠿⠀⠀⠀⠀⠀⠤⠤⠒⠒⠛⠉⠡⠒⣸⠁⠀⢄⠀⠀⠀⠉⠉⠉⠛⠒⠚⠃⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠵⠃⠀⠀⠀⠀⠀⠻⡃⠀⠀⠀⠀⡴⠉⠉⠳⣄⡴⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇⠀⠀⠀⠸⡀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⢻⣟⣀⣀⣠⠇⣀⣀
⠀⠀⠀⠀⠀⠠⣁⠀⠀⠀⠀⠀⠀⢸⠉⠉⣉⡓⠊⠀⠀⠀⠀⠘⠦⢄⡠⠞⠀⠉⠹⠖⠉⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⢤⣤⡼⣄⠘⠐⠋⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠖⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⣗⢲⡶⠤⠤⠔⠒⠉⠀⠊⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡌⠉⠁⣉⡷⣀⡀⠀⠀⠀⡞⠋⠸⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠀⠀⠀⣸⣷⢄⡴⢁⡄⠀⡴⢮⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⡟⠚⠋⠉⠀⢈⣧⣤⠎⠈⢦⡃⣸⠑⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇⣱⠤⠒⠒⠋⠉⠀⠙⢢⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⢽⠘⠦⠴⠶⠶⡖⡖⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⡼⠋⠀⠀⡇⡇⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠁⠀⠀⠀⠀⠀⣀⣼⣴⠧⠄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢛⣻⡗⢦⣀⠀⠀⠀⠀⠀⠀⡭⠉⠁⣀⣭⡾⠿⢍⡓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣁⡔⢻⡀⠘⠞⠀⠉⠒⠤⢤⣄⣴⡓⠚⠙⠞⠁⢹⠦⣀⠙⣆⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠸⠿⠽⠭⠭⠭⠭⠭⠍⠉⠛⠓⠬⠭⠭⢍⣉⣿⣿⣏⣩⡯⠥⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⢶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⡒⠒⠶⢤⣀⣠⠴⠋⢁⡤⠴⠾⠯⠤⠤⠤⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠽⠷⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣝⠂
⠀⠀⠀⠀⠀⠀⠀⢰⡯⠴⠚⢛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠠⢄⠀⠀⢸⠒⢤⡀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆⠀⢸⡄⠀⠈⠑⠘⠂⠉⠒⠦⣤⣀⡀⠀⠀⠀⠀⢤⡄⢀⣀⠀⠀⠀⠀⠀⢤⡤⠤⠤⠤⠤⣀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠄⠐⣀⣀⠈⠉⠛⠂⠠⠀⠈⢳⣄⠀⠈⢹⡛⠒⠶⠦⣬⣷⣦⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⢀⡾⠋⠉⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⣤⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡟⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⢣⡀⢀⡤⠚⠉⠉⠙⡄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⣀⠀⡼⢡⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⠀⠀⠀⠀⠀⢸⠀⢀⡟⠒⢲⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⣤⣤⡈⠙⢷⡟⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⢸⠀⠈⡽⠛⠚⢳⡄
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠢⠽⢦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⡀⠀⡇⠀⢤⣤⡀⠀⠀⡿⠀⠀⠹⢯⣉⠙⡆
⠀⠀⠀⠀⠀⠀⠈⠂⠄⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⢤⣿⡞⠓⢴⣾⡿⠃⣀⡼⠃⣠⡤⢤⡀⢹⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⢒⡶⠞⠁⠀⠀⠉⠈⠉⠁⢀⡜⠁⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠞⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⠄⠀⠀⢂⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠀⠀⠀⠀⠀⠀⢰⡟⠓⠲⢦⠤⠤⣼⠃⢀⣓⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⣸⠁⠀⠀⠀⠀⢸⣥⠤⠶⠚⠓⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣾⢀⠋⠉⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠢⠀⠛⠀⢀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⠂⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⡉⠁⣀⣀⣀⣀⣤⣤⠔⢲⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡍⠉⠉⠉⠀⠀⡆⣰⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠤⠷⣿⠆⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣀⣠⡷⠦⠴⡞⠋⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣉⠙⠛⢉⣟⣍⣝⣀⣧⠤⢴⣿⡞⠿⠃⠀⠀⠀⠀⠀⢀⠉⠉⠙⠛⠛⠓⠲⠶⠶⠶⢤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⠭⠭⠭⠭⠭⠥⠔⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⢿⡿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠄⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠰⠰⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠄⠒⠒⠒⠒⠚⡗⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠤⠒⠉⠉⠹⡀⠀⠈⠑⣄⣎⡠⠤⢄⣀⣀⣠⡤⣖⠉⠉⡇⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠙⠢⢤⡶⡿⠛⠈⠉⠀⡠⠊⠁⠉⠉⠳⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢰⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⠎⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠼⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⡘⠀⠀⠀⢣⠀⠀⠀⢀⡿⠁⠀⣠⠧⠴⠒⠒⠒⠒⠢⣄⠉⠒⠊⢁⣸⠴⠆⠦⣖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠣⡀⠀⢸⢃⣴⠟⠁⠀⠀⠀⢀⠔⠉⠁⢸⠉⢢⡔⢩⠃⠀⠀⠀⡼⢢⢀⠤⠒⠉⠉⠑⢾⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣾⠉⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⢀⠏⣳⠃⣀⠤⠒⠢⡆⡼⠁⠀⠀⠀⠀⠀⡇⠙⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⢠⢃⣸⢖⡷⠊⠀⠀⠀⣸⣿⡿⠀⠤⢄⠀⠀⢠⠃⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠉⠁⠚⡖⠒⢲⠋⣡⠼⣡⠃⠀⠀⠀⡰⠋⡿⢆⠀⠀⠀⡇⢀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃⢡⠀⠀⠀⠀⠀⠀⠀⠈⡲⣁⠞⠁⢠⢇⠀⠀⡠⡾⢁⢼⠃⠈⠳⢄⠀⠇⡜⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⣠⠎⡰⠋⠁⡲⠃⠜⢖⠈⠀⡧⠋⠸⠀⠀⠀⠀⢹⠟⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠀⠀⠀⠱⣄⠀⡠⠚⠁⡐⠁⢀⠔⠁⠀⠀⢀⡱⢞⡇⠀⡇⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⡆⢀⣀⠤⠚⠛⢄⡀⣰⡡⠔⠁⠀⢀⡠⠖⠉⠀⠀⠟⠲⠂⠒⠒⠉⡸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠤⠄⠒⠒⠃⠉⠉⡛⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠢⡀⢀⠆⠀⠀⠀⢀⡠⠊
⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢈⠟⠒⠒⠒⠊⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠎
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣈⣢⣀⡠⠤⠒⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⡠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢂⣴⣤⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣟⣋⣀⠀⠀⠀⠠
⠀⠀⠀⠀⣴⣾⠀⠀⠀⢢⠀⠀⠀⠀⠀⣧⡸⣿⣿⣿⣿⣦⣮⠀⢤
⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⣰⣴⡠⢀⠀⣿⣾⣾⣿⣿⣿⣿⣿⣿⠾
⠀⢠⣿⠋⠀⠀⠀⠀⠀⠛⠿⠯⠥⠀⡼⠛⠛⠛⠉⠉⠛⢿⣿⣿
⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠀⠀⠒⢦⣄⣀⣐⡏⠁⢀⡤⠶⣦⢀⣠⠠⠀⢀⣀⠀⠤⠤⠒⠂
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠤⢄⡀⠀⠀⠀⠀⠀⠀⠋⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣗⢂⣤⣤⣤⣤⣤⣤⣤⡄⠐⠀⠀⢠⣿⡇⢼⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢸⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠄⠀⠀⠀⠉⠀⠀⠀⠰⣿⠠⢀⣴⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠘⠛⠟⠛⠛⠛⠛⠟⠻⢿⣬⣧⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠈⠀⠛⠻⠿⠛⠋⣵⣿⣿⣿⠿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠴⠿⠿⠿⠿⠿⠷⠿⠷⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣷⣄⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠤⠴⠿⠷⠶⠶⠾⠶⠶⠶⠤⠀⠀⠀⢘⣿⣿⠻⠂⠀⢹⠀⠀⡾⠿⠛⠛⡉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠉⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⠀⣦⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠟⠻
⠀⠀⠀⠀⠀⠙⣦⠤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⠉⣿⣿⠂⠒⠶⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⢀⣫⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⣸⣿⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⣡⣾⣏⠉⢣⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⣴⡉⠀⠈⠀⠈⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠱⠀⠀⡄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣧⣈⠁⠀⠀⠀⠀⠀⠀⠑⠠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠀⡤⠊⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢦⠀⡀⠀⠀⢀⡀⡀⡀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⠤⠀⠀⠁⠀⠀⠘⢿⣿⣿⠟⠃⠉⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠙⠶⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢭⣉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠰⠟⢻⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡷⡮⡿⠠⡄⠐⣶⣦⣤⣤⣤⣤⣤⡤⠀⠀⣄⡀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠠⠀⠀⠀⠀⢠⡄⠂⣀⣄⣬⣤⣤⣶⣶⣾⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⡾⣸⣿⡗⢶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢾⣡⣽⢰⣶⣶⣿⠘⣿⣿⣿⡿⠿⠿⠛⠛⠉⠭⡐⣾⣼⣿
⠀⠀⠀⠀⠀⡠⠚⠰⢿⣼⣧⣿⠄⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡈⣿⠿⣇⠛⠛⠛⠇⡟⠐⠀⡀⠚⠉⠀⠀⠀⠀⠈⠊⣝⡻
⣤⠄⢴⣶⣶⡴⢶⠴⢾⣭⣯⠉⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⣏⠓⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠔⣀⠄⠀⠉
⣿⡀⣸⠿⣿⣸⠛⣞⣳⣟⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⡸⡄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁
⣿⢁⡛⢻⡟⠉⠀⣹⣿⢛⣏⢀⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠒⣠⠖⠁⢷⠂⠀⠀⠀⠀⠀⠀⠀⠔⠉
⠋⠛⠋⠐⢻⡿⠿⣿⣿⠿⡏⠘⠁⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠠⡇⠀⠠⠀⣠⠟⡘⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢀⡴⠞⠿⠆⠀⠀⠀⠀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣔⣩⣄⡀⠀⠀⣀⡀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡾⠉⠀⠀⠹⣎⣻⠟⠛⠻⣿⠶⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠸⡇⠀⠐⠂⠀⣿⣇⠐⠶⠀⣹⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⢦⣤⣤⠾⠃⠼⢷⣶⣾⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣫⠅⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣙⣀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢀⣘⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣀⣠⣤⣴⣾⡿⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠋⢻⣤⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⢦⡀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠛⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⢻⣿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡇⢸⡇⠀⠀⠀⠀⠉⠉⢹⡏⠉⣿
⢀⣤⣤⣤⣤⡤⠶⠖⠛⠛⠉⠉⠉⠉⠀⠈⣷⡀⠀⠀⠀⠀⠀⢸⡇⠀⠾⠷⢦⣤⣤⣤⣀⣀
⠛⠶⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⢶⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⣮⣵⣍⡻⠿⠿⠿⠿⢟⣩⣮⣕⣢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣵⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣮⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠢⠀⠄⠀⠻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠠⢐⡇⠄⠀⠀⡊⠻⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡔⠁⠈⠢⢄⣀⣠⣊⣑⠢⠤⠒⠁⠀⠈⢮⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⡔⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⢀
⢠⠶⠶⠆⠺⢄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⡠⠗⠰⠶⠶
⢯⠉⠉⠒⠂⠘⢧⠴⠰⡞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢳⠄⠦⡼⠇⠐⠒⠉⠁
⠘⠒⠲⡆⠴⢣⠆⠀⠀⠇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡐⠀⠀⠰⣜⠦⢠⠖⠒
⠀⠀⠀⠈⠉⠑⠒⢺⠁⠸⡀⠀⠈⠑⠢⢤⣄⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠔⠊⠁⠀⢠⠃⠈⡗⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⣠⠏⠨⠈⠳⡈⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⠑⠢⢄⣀⣀⠜⠁⠀⠸⠀⠀⠈⢢⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡟⠐⠒⠒⠂⠠⠤⠤⠤⠀⣀⣀⣀⣀⡠⠬⠤⢄⣀⣀⣀⣀⠀⠠⠤⠤⠄⠐⠒⠒⠂⢺
⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣛⢞⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠈⠉⠉⠉⠀⠀⠐⠐⠒⠘⠢⢭⠍⠴⠃⠒⠒⠂⠀⠀⠉⠉⠉⠁⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢭⡁⠐⠒⠒⠒⠐⠀⠒⠒⠲⠊⠑⠖⠒⠒⠀⠐⠒⠒⠒⠂⢉⡩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⠄⠠⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠠⡖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣟⣻⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣟⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⣳⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣠⠞⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠒⣉⣀⣠⠔⠋⣆⣼⢻⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢶⠋⠉⠡⢾⢠⡥⠟⠳⡞⠀⠀⣋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠘⠀⠀⢃⣠⣷⠋⠑⠢⣈⠲⡀⣻⣬⡷⢄⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣖⡚⠉⠙⠻⣏⠐⡀⢠⠞⠉⠉⠛⠲⠾⣤⡀⠣⡀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠳⡄⠀⠘⣆⠑⢿⡿⠶⢤⣤⣀⣠⠆⠹⡄⠑⣄⠀⠀⠀⣏⠀⠀⠀⡄⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠢⠤⠄⢬⣟⣹⢽⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣿⡴⠚⠛⠓⢦⠀⢸⡇⠀⢸⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⠈⢦⠹⡆⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⣧⠈⣇⠀⠈⢷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠹⡆⠀⢸⡾⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⡄⢿⠀⠀⢸⡻⡇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⢤⡙⠒⠊⠀⣸⣷⠆
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠘⣇⡸⠀⠀⣨⠣⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠛⠛⠉⢿⣯⡇
⠀⠀⠀⠀⠀⠀⠿⡽⣶⣖⣛⣋⣁⣠⠴⠚⠁⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀⣠⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡤⠤⣠⣤⣤⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢋⠉⠙⡾⠛⠉⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠛⠛⠛⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡶⠶⠒⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢰⠹⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⢰⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠹⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢻⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠖⠚⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡧⣄⡿⠟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠻⣀⣌⡁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡱⠾⢭⠾⢱⡖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣷⣿⣛⣿⣶⡛⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣤⣴⠶⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠛⠉⠓⠒⠒⠁

⠀⠀⢀⣤⡶⠶⢶⣤⣄⣴⡾⠟⠻⠿⢶⣦⣄⣠⣴⠶⠛⠿⢶⣴⠶⠿⠛⠛⠷⣦⣤⣤⡴⠶⣦⣄
⠀⣴⡟⠁⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⢷⣄⣀⡀
⣸⡟⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢶⣄
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠘⢿⣄⠀⠀⠀⠀⣠⣀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⣀⣠⡴⠟⢿⣄⡀⠀⠀⠀⣀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠙⣷⠶⠶⠛⠉⠙⠛⠛⠛⠋⠉⠀⠈⠉⠛⠉⠉⠁⠀⠀⠀⠈⠉⠛⠛⠋⠉⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡤⠄⠀⠀⠀⠀⠀⠰⣿⡃
⠀⠀⠀⢸⣿⠀⢀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⢸⡿⠀⢸⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢸⡇⠀⡎⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣸⠁⢀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢸⡇⠀⠁⣶⣶⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢿⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⣿⡇⢠⡀⠈⠁⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠤⠒⠚⠓⠒⠾⣿⡀
⠀⠀⠀⣿⠀⠸⣇⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⣿⢣⡀⠀⠀⢀⡤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⣿⠀⠀⢧⡙⠒⣿⠃⡄⠀⠀⠀⠀⠀⢹⡄⠈⠉⠉⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠀⠀⠀⢸
⠀⠀⢠⣿⠀⠀⠀⠽⠟⠁⡰⠃⠀⠀⠀⠀⠀⠈⢿⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣿⠀⠀⣀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⢀⣾
⠀⠀⢸⣿⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⢸⣿⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣦⣶⡶⠾⠟⠋⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⢀⢿⣁⣀⣀⣀⡀⠀⠀⠀⠉⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠈⢧⣜⠁⢀⣀⣈⠉⠉⠉⠉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⢶⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠙⢷⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣶⡶⠶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣶⣤⣶⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠒⠲⠤⣄⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠈⠑⡇⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠃⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠀⢀⠀⠀⠀⠴⠤⠄⢀⡈⢧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠟⠀⠀⠀⠀⣠⠐⠈⠁⠀⠀⠀⠠⠊⣁⢤⣄⡀⠀⠀⢀⡤⠶⠚⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⣆⣀⡞⢀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠘⡄⠀⠀⣀⣀⡇⠀⠀⠠⣶⡏⢸⣼⡇⠈⣿⠶⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⢉⣉⣉⡛⠳⠛⠉⠁⠀⢇⠀⠀⠀⠈⠀⣼⠀⠳⡀⠀⠀⣀⣀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠒⠊⠉⠀⠀⠀⠀⠀⠈⠲⢤⣀⠠⠞⠁⢠⢠⡌⠑⠋⠀⢈⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠈⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠉⠓⠒⠤⢤⠤⠤⠤⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⣅⣀⣀⣀⢐⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢦⠘⠀⠀⠤⠄⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣰⢨⣀⣀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠊⠁⠀⠈⡏⡏⠉⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠒⢻⠛⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡤⠤⠤⣤⣤⣾⠢⢶⡓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠗⠓⠞⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⣛⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣠⣴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⢷⡄
⠀⠀⠀⢠⣾⠁⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⣮⣿
⠀⠀⠀⠀⠁⠀⠈⠉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢶⣤⣴⠶⠞⠛⠛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰⣆⠀⠀⢲⣄⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣸⠟⠻⠶⠾⠛⠛⠛⠛⠛⠻⣦⣤⣄⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⢰⡏⠀⠀⠀⣤⠀⠀⠀⠀⠘⠷⣦⣤⣤⣄⠀⠹⣧⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣸⡇⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣠⡶⠾⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣿⠃⠐⠟⢁⣀⡀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠙⠛⢠⡖⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡄⠀⠀⠙⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢦⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣆⠀⠀⠀⠀⠐⠋⠉⠉⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⣽⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣁⣴⠟⠁⠀⠀⠉⠻⠶⣶⣤⣤⣴⡶⠿⠋⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣰⡟⠁⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⣿⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⣁⣴⢶⣤⣤⣴⠾⠛⠉⠙⠷⢶⣤⣤⣴⠾⠋⠀⠀⠉⠙⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡿⠋⢀⣤⣿⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⠞⠋⢁⣸⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣶⠟⠉⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⢾⣂⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣠⣤⣤⣴⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⡿
⠀⠀⠀⢀⣤⡶⠛⠛⠉⠉⠉⠁⠈⠉⠉⠉⠉⠛⠛⠷⢦⣤⡀⠀⢀⣠⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣄⡀
⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆
⠀⢸⡇⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⢠⡿
⢀⣼⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣶⣦⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣾⣧⡀
⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⢶⣬⣛⠶⣯⠛⠿⣿⣿⣿⣿⠟⠋⠁⣀⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣍⣀⣠⣤⣤⣤⣀⣀⣀⣤⣶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠋⠉⠉⠉⠙⠓⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠐⠂⠒⠒⢒⠒⠒⠐⠶⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠛⡀⠀⠀⠀⡸⡀⠀⠀⡀⠈⢷⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠈⠐⡲⠞⠐⠈⠉⡉⠀⠀⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠁⡀
⢀⣀⣰⣒⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⢀⣔⣒⣀⣀
⡎⠀⠢⠀⠈⡆⡀⠄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⡀⡎⠀⠠⠂⠘
⠐⠤⠤⢠⡀⠈⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠈⠀⣀⠠⠤⠔
⠀⠀⠀⠀⠈⠒⢒⠟⣉⣉⡁⠈⠑⠢⠤⣤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠤⠒⠉⠀⣉⣉⡁⢓⠒⠊
⠀⠀⠀⠀⠀⠀⡘⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠘⡀
⠀⠀⠀⠀⠀⢀⠁⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⢁
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⣇⣉⠁⠀⠒⠒⠀⠠⠤⠄⠀⠀⢀⢀⢀⠀⠀⠠⠤⠤⠄⠐⠒⠂⠀⢉⣁⡏
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠉⠉⠁⠐⠒⠒⠂⠀⠠⠤⠴⠤⠤⠀⠀⠒⠒⠒⠀⠉⠉⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠐⠂⠤⠤⡀⣀⣀⣂⣆⡀⡀⡀⠤⠄⠒⠐⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⠆
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣀⣈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⣠⣤⣤⣴⣶⣶⣦⣤⣤⣄⠀⠀⣀⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢿⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⢤⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣄⣀⠀⠀⠀⠀⠈⠛⠙⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣧⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⣿⣄⣤⣤⢠⣿⣿⠟⢋⠀⣉⣧⣤⣄⣴⣿⠋⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⠞⠉⢀⣠⣴⣿⣿⣿⠻⣯⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠀⠀⠀⠀⠉⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣄⣀⣠⣤⣄⣀⣀⠠⣶⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣴⣾⣿⣿⣿⣿⣿⣍⠿⢿⣿⣿⡛⠛⠿⣏⢻⣿⡿⣿⣿⢿⣿⣿⣿⣧⡈⢿⣿⣦⡀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢊⣠⣴⣿⣿⣿⣛⠻⢭⡉⢨⣿⣷⣌⠛⡋⠿⠟⢂⡙⠂⣿⣧⢿⣿⣾⡇⠘⣿⣿⡟⣶⣿⣿⣿⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡛⠿⣿⣿⣿⡿⣶⣿⣆⢻⣿⣩⣿⠓⢬⣥⣿⣧⢸⠎⠛⠷⠉⠛⡙⢷⡘⣷⡏⢻⣿⣿⣿⣿⣿⣇⠘⣦
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣹⣿⣿⣿⣿⣿⡷⣬⣛⣹⡃⣈⣍⣛⣣⣤⣙⣿⣷⣤⣛⣩⣿⣦⣤⣴⣻⣶⣷⣽⣿⣽⣶⣴⡆⣯⣼⠿⠿⢿⣿⡇⠘⣧
⠀⠀⠀⠀⠀⣠⡎⢹⣿⡿⠛⢿⣷⡍⢛⡻⣞⢋⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⡍⠁⠻⠿⣿⢿⣿⠿⣛⣛⣷⣶⡈⢧
⠀⠀⠀⠀⠐⠏⣶⣿⣿⣷⣄⠒⢶⠅⣾⣭⣿⣿⣿⠿⠿⠟⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣃⣤⡨⣤⡄⠒⠶⣦⣍⠛⢷⣿⣷⡌
⠀⠀⠀⠀⠀⢰⣿⣿⣮⣛⢿⣷⣶⣿⣿⡿⢛⡩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠙⠿⣷⣜⣿⡿⢷⣌⢩⣶⡶⣾⣿⣧⡄⢠⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣠⣿⣿⠟⠋⠀⠀⠀⠀⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣻⣷⣶⣿⣿⡷⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⡿⠃⢀⣤⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠹⣿⣷⣼⡟⢛⣛⣛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⠟⢁⡴⠿⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠠⣌⢿⣿⣷⣌⠿⡿⢶⣴⣿⣿⣷⣤
⠀⠐⠀⠀⠀⠀⢸⣿⡟⢁⣴⣿⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢻⣿⣯⣐⣆⣈⣩⣽⣿⣿⡇
⠀⠀⠀⠐⠃⢰⣿⣯⣶⣾⣿⣟⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢧⣽⣿⣿⣿⣟⣛⠛⢟⣿⡇
⠀⣼⣿⣷⣦⣤⣿⣿⣿⣿⣿⣯⣁⡀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠋⠉⠉⠁⠀⠀⠂⠀⠨⣿⣿⣿⣿⣟⣉⣴⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠈⠉⠻⢶⣦⣿⣿⣦⣄⠀⠀⢀⣿⠀⠀⠀⠙⢦⠐⠄⠺⢿⣿⣿⣿⣶⡶⠖⠒⠶⠶⠄⠀⠄⠀⠀⠀⢨⣿⣿⣯⣥⣤⣤⣶⣿⣿
⢿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣭⣤⡶⠶⠞⠛⠋⠉⠉⠁⠀⣰⣿⡿⠀⠀⠀⢰⣦⠲⣄⠀⠀⠀⠀⠉⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣥⣦⣭⣭⣭⣿
⠈⢿⣇⣴⣿⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠇⠀⠀⠀⠈⠓⢄⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⠻⠒⠀⠀⠀⠀⠀⣿⣿⡟⠛⠉⠛⠻⢿⣿
⠀⠘⢿⣿⣿⣿⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⣠⡤⢴⣾⣿⣿⣿⣿⡀⠀⣠⣾⣧⡈⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣄⠆⠀⠀⠀⣀⣩⣭⣶⡶⢶⡦⢠⠈⣿
⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⣀⣠⡤⠀⠀⠀⠀⣾⡿⠻⣿⡟⠛⠛⠳⣾⣿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠉⣬⣿⣧⣀⠸⣿⠀⣼⠏
⠀⠀⠀⢸⣿⣿⣿⣟⣴⠾⢋⠐⠀⠀⣀⣼⣿⣿⣿⣿⣿⡇⠀⣀⣰⣿⣅⣀⣀⣽⣟⣡⠀⠀⠈⠉⢀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⡏⢀⢀⣾⠏
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⡿⣖⣖⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⡀⡄⢀⠀⠀⠀⠀⠀⠀⢀⣿⣷⢳⣿⠏
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⡿⢋⣠⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡄⠀⠀⠀⠀⠀⢰⡿⠿⠏⣹⡏
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣵⣿⣿⣿⣿⣦⣼⣷⣄⣀⣀⣤⣀⣤⡀⢀⣤⣤⡤⢈⡙⠻⠶⠛⠥⠒⠀⠀⠀⠀⠀⢀⣀⣀⣴⡿
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣁⠀⠻⣿⣿⣿⠿⠛⠛⣛⣻⡿⠋⠁⠀⠀⠀⠀⣀⠈⠐⡂⠄⣀⡤⠞⠀⠠⠀⠀⢠⣿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⡽⢿⣿⣿⣿⣿⣷⣀⠀⠀⠀⢀⣠⡾⣛⠍⠀⠀⠀⠀⡤⠖⢋⡡⢰⣾⠖⢛⡉⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠑⣚⣫⡵⠚⠋⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⡍⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⡷⠚⠀⠀⠀⠈⠁⣸⣿⡟⠁
⠀⠀⠀⠀⢀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣥⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣴⣿⡿⠟⠋⣁⠄⠀⠀⠀⢀⣤⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⠴⠒⠋⠁⠀⠀⢠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⡭⠁⠀⠀⢀⣠⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣟⣛⠿⠿⠿⠟⠉⠉⠀⠀⠀⢀⣀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡏⠉⣻⡿⣀⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠿⢿⡉⠉⠙⢿⡿⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⢃⣼⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⡾⠃⠀⠀⢸⡟⣶⣈⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣯⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⢰⣿⣛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠙⠻⢿⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠉⠙⣿⠙⣼⣿⠇⠀⠀⠀⠀⠈⠻⠿⠋⣀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣽⣿⠛⠀⠀⠀⠀⠀⠀⠈⠿⣾⣿⠇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⢀⣴⣿⡿⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡄⠀⠀⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⢠⣶⣿⣿⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⣿⣷⠀⢀⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣦⡀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣬⣉⣙⠛⠛⠉⠉⠉⠉⠀⢠⣿⣿⡇⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⠇⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢰⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣽⡗⠀⠀⣠⣶⣶⡾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣧⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠆⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⡿⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⢠⣴⡶⠶⠲⠶⣄⠈⢷⡄⠀⢠⣿⠀⢰⡿⢋⣉⠉⠻⠃⠀⠀⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠹⣿⣿⣿⡇⠀⠀⠿⠟⠁⢾⣿⠂⣈⣀⣈⠁⠀⠈⠁⠀⢀⣀⣼⣿⣃⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⣶⣌⠻⣿⡇⠀⠀⠀⠀⠴⠞⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠁⢩⠀⠀⠀⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⣰⡿⠁⣨⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢠⣴⣾⠟⢡⡄⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠀⠀⣀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣨⡿⠷⢶⣄⢻⡂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠺⠂⠀⠀⠛⠰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠁⣠⠀⠈⢿⣾⣿⣆⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠶⠿⠿⠶⣄⣸⣿⣿⣿⡿⠉⣿⡀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⢠⣶⣰⠆⠀⠀⠀⠀⠀⡤⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠤⠤⠤⢤⠄⢹⣿⣿⣿⡿⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡀⣀⡀⠀⣾⣿⣿⣿⠃⠀⠀⠈⣿⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⢸⣿⠀⠠⣤⣿⣏⠛⣠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⠀⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠻⣿⣿⣿⠟⠉⠀⣿⠀⠀⠀⣠⠾⣿⠀⠈⢻⣿⣿⣿⣷⣤⣀⣀⠀⠀⢀⣀⣀⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣿⡟⠀⠀⠀⢹⠀⠀⢠⠏⠀⣿⡇⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠇⠀⠀⠀⣸⠀⠀⡼⠁⠀⠘⢷⣄⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⠿⠛⠉⣿⡿⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣼⣿⠀⢀⣀⣴⡏⠀⢠⡇⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢈⣻⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡀⢤⣼⣿⣿⢰⣿⣿⡟⠠⠖⠻⠁⢸⠀⠀⠀⠀⠀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣠⣾⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢘⡇⠐⠿⣿⠇⠐⣿⡟⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⢠⡌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠾⠃⢀⣼⣿⣿⡇⣸⣧⣤⣄⣀
⠀⠀⠀⣠⣴⠖⠛⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣷⠀⠹⡄⠀⠀⠀⢠⣿⡟⠀⢹⣆⠀⠀⣀⠀⠀⠀⠀⣠⣿⠟⢿⣿⡇⣿⠀⠉⠙⠛⠛⠿⠷⣶⣶⣄
⣠⠀⠈⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣾⣿⡇⠀⠈⣿⡄⠀⢿⡄⠀⢀⣼⡟⠁⠀⠀⣹⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⣼⣿⡿⠀⠀⠀⠘⣷⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠻⣅⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠙⣷⣄⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣤⣤⡀⠀⠀⠀⢀⣷⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠙⠛⣿⣦⠀⢀⣈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠩⠁⠛⠃⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⠋⠉⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⡐⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠓⠒⠀⠀⠀⠠⠴⠶⠒⠆⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢀⠜⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⣠⠖⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠑⠶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⠀⠀⢀⣾⢏⣠⣴⣶⡶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣶⣦⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣯⣴⣶⣶⣿⣿⣿⣧⠹⠿⠋⢉⣉⣉⣙⣛⣿⣿⣿⣿⣿⠟⣠
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣿⣿⡿⠟⣛⡛⠛⠃⠀⠀⠾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠚⣽⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⠷⣦⠀⣴⣿⣿⣷⣶⣦⣀⠲⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⢃⣾⡿⠋⣡⣾⣿⣿⣿⣿⣿⣦⡀⢈⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣮⠻
⠀⠀⠀⠀⢀⣿⣿⣷⣿⡿⠁⣼⣿⡿⠋⠁⠀⠀⠀⠀⠁⠈⠉⠉⠙⢿⣿⣿⡿⣿⣾⣿⣿⡛⠿⣧
⠀⠀⠀⢠⣾⡿⠿⣿⣿⣡⣾⣿⡯⠶⡶⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡀⣿⣿⡇⢹⣿⣿⣿⣧⠀⠈
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⢛⣥⠞⢫⣴⡿⠿⠛⠛⠀⠀⠰⠇⠀⠛⠻⠿⣿⣟⠀⢿⣿⣿⠿⠷⠦
⠀⠀⠀⠀⠐⣛⡟⣫⡷⢾⢿⣿⡄⠛⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢿⣄⠈⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣹⣿⣿⡤⣾⠀⢻⡧⠀⢰⣧⠶⣾⠉⡗⠀⠀⣇⠀⢲⠒⢦⣤⣱⡈⠁⢹⢠⠏⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠈⣇⢻⡀⠸⠃⠀⠛⣄⡀⢀⣰⠃⠀⠀⠸⡄⠈⠣⣀⣠⠎⠀⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣇⠀⠀⠀⠳⣌⣉⠉⠀⢠⠀⠀⠀⠹⡄⢄⠀⠠⠾⠁⠀⣸⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣘⣧⠀⠀⠀⠀⠀⠀⠀⢿⣤⢤⣄⣠⣷⡼⠀⠀⠀⠀⢀⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⣷⡀⠀⠀⠀⠀⣾⣯⣭⣭⣿⣿⣿⡆⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⢰⡏⠻⣄⠀⠀⠀⠈⠉⢉⣁⣀⣀⣩⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⣿⠁⠀⠈⠳⣄⡀⠀⠀⠀⠈⠉⠉⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠳⢦⣄⡀⠈⠙⠳⠶⠶⠶⣶⡶⠶⠛⠃⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣠⣄⡉⠳⣦⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⠶⠛⠉⠀⠀⠉⠳⠌⢳⡴⠛⢀⡴⠞⠛⠉⠛⠛⠛⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⣲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣠⠊⣁⠤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠲⣄⠀⡴⠋⠀⠀⠀⣼⠵⠋⢀⣞⣡⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠼⠀⠈⠛⠀⣀⠀⠀⠘⠁⠀⠀⠈⠁⢠⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠠⠀⠑⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠓⠀⠀⡀⠀⣰⠇⡰⠋⠘⣤⠟⢆⢀⠞⠢⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠀⡜⠹⠜⠙⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠱⠆⠈⢆⢠⢆⠀⠀⣀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠆⠀⣰⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠈⣆⡀⠁⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⠀⡀⡇⠀⠀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⡀⠸⢣⠀⠀⢹⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠃⢰⠛⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠘⡄⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⢀⠄⢒⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣠⣤⣄⠀⠀⣧⣦⠷⡵
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⠼⠀⠀⠀⠂⠀⢺⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠃⠀⠉⠙⠓⢢
⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⡀⠀⠀⠀⢆⠀⠈⠙⠛⢁⠄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠁⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠑⠀⠀⠒⠁⠀⠀⠀⠀⠐⠢⡀⠀⠀⠁⠂⠀⠒⠁⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⠤⠶⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠂⠠⠄⣘⢂⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠶⠶⠒⠒⠒⠛⠀⠀⠀⠀⠈⠁⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠅⠈⠑⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⣀⠀⢀⠀⣧⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢂⠰⠄⠀⠀⠀⢠⣤⠤⠬⠶⠶⠒⠋⣙⡒⠤⢍⢳⣾⠋⠳⡤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠒⡄⠀⠀⢀⠴⢥⠀⠀⠀⣀⣴⡾⠿⠿⣿⡆⠀⠉⠉⠀⠀⢸⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⡁⠈⠀⠠⢊⣿⠟⠁⢀⡴⠟⠉⠀⠀⠀⠀⠈⢷⠀⠀⠀⢠⣿⣿⣗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠉⠀⠀⢐⡟⠁⠀⠀⠈⠀⢀⡤⠒⠛⣆⠀⠀⠈⠀⠀⠀⡸⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠁⢄⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢪⠖⠛⠛⢿⣆⠀⠀⠀⠠⢀⢡⡚⠢⢸⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠴⡄⠀⠀⢠⠴⢦⡀⠀⠀⣹⢹⡄⠀⠀⡇⢀⠋⠙⣆⢸⠧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡠⠂⠀⠠⠀⠀⠀⠀⠀⠘⠛⠲⣿⠏⣸⠃⠀⠀⡇⢰⣄⣀⠏⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠘⠂⠘⠐⠋⠀⠀⠓⠛⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣇⠀⠻⡀⠀⠀⠘⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⢀⡀⠠⠀⠀⢡⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⣄⢀⠈⠁⠀⣠⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⢀⠜⠓⠒⢤⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡬⠆⠀⡴⠋⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠖⠛⠛⢲⡷⠀⠘⡀⠀⠀⠀⠀⠀⠉⠲⣄⠀⢀⠎⠀⠀⣼⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢄⢠⢿⠃⠀⠀⠱⡀⠀⠀⠀⠀⠀⣀⡈⠉⠁⠀⠀⢀⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡈⠎⠢⠀⠘⡉⠁⠀⠀⠀⡴⠋⠉⠙⠖⠂⠻⢢⠰⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣧⠀⠀⠀⡾⠠⠒⢲⠒⠃⡄⢢⡏⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⢿⠀⠀⣰⠀⢠⡄⢸⠀⠰⠁⢈⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠒⠁⠓⠁⣑⣃⡐⠊⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠓⠺⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⠉⠀⠀⠀⠀⠀⠀⠶⠒⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠯⣁⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⡿⠿⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢀⠤⠄⠀⠀⠾⠛⠉⠁⠐⠲⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⡰⠛⢢⡀⠀⠀⠀⠀⡞⠉⠳⡄⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢳⣾⣿⡇⣀⠤⠤⣄⠳⣾⣿⠇⠀⣿⠟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣄⠻⠟⠀⠉⠉⠀⠁⠀⠶⠃⠀⠀⠀⠀⠀⠠⠟⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⣡⡀⠀⠀⠘⠢⣄⣀⣀⣀⣠⠜⠃⠀⢠⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠲⢤⣀⣀⡀⠈⠉⠁⣀⣀⠤⢚⠗⣤⠂⢲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡍⠉⠉⠻⣉⠀⢀⡼⢦⠀⠀⠜⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢵⣤⣤⣾⠿⠳⡘⣄⠀⠓⡄⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠈⠀⠀⠀⠙⣌⡳⠀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⡂⡤⠖⠒⠀⠉⢙⡀⡤⡻⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⢾⢱⡇⠀⠀⠀⠀⢸⡏⣷⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠇⠀⠙⠒⠒⠒⠒⠚⠀⠹⡄⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠲⠦⣤⣤⣴⠶⠚⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⡏⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⡆⠀⠀⠀⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣧⠀⠀⠀⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠺⢿⣷⠤⣤⣿⡤⠴⣿⡶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣀⠀⠀⠀⠀⠀⣀⡟⠀⠈⠀⠀⠀⢀⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣋⣁⣈⣙⣒⣲⣶⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠉⠉⠉⠛⠓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⣀⣴⡶⠿⠿⣶⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠤⢀⡀
⠀⠀⠀⠀⡀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣼⡟⠉⠀⠀⠀⢀⠁⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠶⣶⣦⣄⠈⠱⢦⡀
⠀⠀⡠⠂⢀⣤⣤⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⠔⠃⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠈⢃
⠀⣤⠀⢠⡿⠋⠉⠻⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⢠⡼⠋⢀⡼
⠀⠇⢀⣿⠃⠀⠀⠀⠟⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢀⣀⣀⣀⣀⣀⣤⡞⠃
⠀⣤⣀⣿⡀⠀⠀⣴⡀⠀⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢀⣴⠟⠛⠛⠛⠛⠋
⠀⠻⠟⠉⠀⠀⠀⠙⠿⣦⣄⠈⢱⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⢷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠋⠀⢲⣦⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠴⠚⠛⠛⠛⠛⠛⠛⠛⠓⠒⢠⣤⣤⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠛⠁⠀⠀⠀⠀⣀⣤⡶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⢶⣄⣻⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⢀⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡆⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⠀⠀⠀⠀⢀⣼⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠀⠘⠆⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢈⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠉⠁⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠁⠀⣈⠃⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠞⠁⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⡀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠻⠷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⣠⣄⣠⣴⢧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡴⣦⣄⣠⣄
⣀⠁⠀⠀⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠻⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣾⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠈
⣿⣀⣀⡀⠀⠀⠀⠈⣦⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠹⣿⡀⠈⠻⣦⡀⠀⠀⠀⠀⣴⠁⠀⠀⠀⢀⣀⣀
⠀⠉⠉⠉⠀⠺⣆⠀⠈⠿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢸⡇⠀⠀⣠⠿⠁⠀⣰⠗⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠙⢦⡴⠋⠙⢧⣄⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡼⠋⠙⢦⡴⠋⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⠀⠀⠀⠀⣠⡞⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣄⠀⠀⠀⠀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣀⣠⠞⠃⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠘⠷⣄⣀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠛⠛⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⢻⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⢀⣀⣀⣀⣀⡀⢰⣿⡀⣀⣀⠀⣀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠉⠉⠉⣿⠉⠉⠉⢹⣿⠉⠉⣹⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡿⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢀⣼⡇⠀⠀⠀⢸⣿⣄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠀⣻⡇⠀⠀⠀⢸⣿⣁⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣶⣷⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⠛⠋⠙⠟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⠀⠀⠀⠿⢻⡗⠀⣾⣷⠋⡉⡽⢳⠙⠉⣻⠏⣠⡠⢦⢻⣿⣿⣝⣿⣽⣿⣿⡿⣤⣉⠁⠀⠀⠀⠂⠀⠀⠀⢈⠉⠉⠉
⠀⠀⠀⠁⠀⠀⠀⠄⢊⣼⠿⠿⠀⠀⠹⣿⡀⣞⣄⣿⡶⠯⠼⠶⢸⣿⣿⣿⣿⣷⢿⣧⡆⠈⠙⠋⠀⠀⠀⠐⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠓⠚⠋⠁⠀⠎⠰⠀⠄⠀⡀⠀⠙⢿⣿⣄⠠⢤⣼⡟⠛⠛⠻⠟⠛⠛⠻⠦⠄⣀⢀⠉⠐⠢⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠉⠀⠀⠀⠐⠛⠛⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠀⠀⠀⠂⠁⠀⠰⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠤⠄⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣊⠀⠀⠀⠀⢀⠀⠀⢤⣀⠀⣀⡈⠀⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣿⣾⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣵⣄
⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣠⣤⣤⣤⠀⠀⠀⠀⢠⣶⣶⣶⡦⢤⣤⡀⠫⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡌⣾⣻⡿⢻⣿⣿⠀⠀⠀⠀⠘⠋⠹⠛⢿⣛⣻⡿⠆⠀⠀⠀⢸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠁⠈⠉⠉⠈⠁⢀⣀⣀⣀⣀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣷⣏⣙⣳⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠶⠛⠛⣛⣛⣛⣛⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡙⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣸⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⣤⣤⣤⡤⢤⡶⢦⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⢸⣿⡿⠿⠟⠋⠁
⠀⢀⢤⣄⣀⣉⠉⠉⣛⠻⡧⠐⣦⣀⣼⣿⣿⡀⠀⠀⠀⢈⣀⣿⣿⣦⣤⡤⣶⢶⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠔⡶⠆⢭⣭⠚
⠀⠊⠰⠉⢛⠁⠀⠀⠀⠉⠛⠀⠘⣿⣿⣿⠛⠭⠭⠯⠆⠈⠙⠉⣩⠭⠅⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡐⡉⠂
⠂⠀⠀⠂⢈⠀⠐⠀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠄⠀⡤⠶⠂⠁⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠒
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⣱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢓⡶⠀⠀⠀⠀⠀⢀⠀⢠⢤⠀⠀⠀⣐⠁
⠡⠬⠁⢄⡀⡀⠂⠀⠀⠀⡀⠁⠷⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠁⠋⠀⣤⣄⡐⠚⠁⣨⠖⠈⠁
⠀⠀⠀⠀⠀⠈⠙⠓⠛⠂⠘⠻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠸⠋⠛⠀⠀⠈⠀⠀⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄