Reindeer Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣴⠋⠀⠀⠀⣀⠀⠈⢲⡀⠈⣧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⠀⠀⡈⠉⠛⠻⡿⣶⣿⣌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣸⡄⠀⠳⣄⠀⣸⠇⢸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣦⡼⣿⣯⣴⣟⣡⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⡆⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣉⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣛⣿⣿⣿⣾⣦⣶⣶⣾⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⠟⠋⠉⢿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠸⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡆⠀⠈⣿⡿⠻⢿⣿⠟⠛⠛⠛⢻⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠉⠛⠛⠉⢹⣿⡏⣠⣾⡿⠃⠀⠀⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⠀⠻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣇⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⣿⠀⠀⠘⣿⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⢿⣄⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⠿⠆⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⣿⠀⠀⢠⣿⠃⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣾⡀⣀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢿⡏⠓⢿⣀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⣾⠛⠻⠿⣟⢆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣁⡴⠶⠦⢭⣿⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠈⢦⣿⡿⡄⠉⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡆⠀⠀⢯⣷⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡇⠀⠀⢰⡏⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⠀⠀⠀⠀⠀⠀⠀⢈⣾⣧⡤⣠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⢿⣦⣀⡀⠀⠀⢠⣺⡾⢋⣩⡾⠟⠋⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣵⣶⣌⣉⣙⣓⣪⡴⣫⣶⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣀⣤⣤⣤⣴⣶⣶⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠐⠟⢨⣿⣿⣿⣧⣿⢗⣤⣀⢀⢀⣄⣠⣤⣶⣿⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⠏⠁⠂⠐⠲⠝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠛⣟⢛⣏⣸⣿⣈⠉⠛⠛⠿⠻⢿⡟⣿⠟⠙⠉⠘⡃⠸⣿⣿⣿⣿⣿⣷⡄⠀⠀⢰⣌⢸⡿⢂⣀
⠀⠀⠀⢠⡄⡀⢀⠀⠀⠀⠀⠀⠐⠒⠒⠒⡻⡻⠻⠟⢻⣿⣿⣿⣿⣶⣤⣤⠇⠀⠀⠀⣧⢀⠀⠀⣥⣾⣿⣿⣿⣿⣿⣿⣷⣔⢧⣾⣿⣿⡷⠿⠿⠿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⡀⣠⣴⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣿⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⠿⠛⠉⠋⣧⡤⠆⠀⠰⣦⠀⠋⣹⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠁⠀⠀⠀⠀⢶⣤⠿⠟⠛⠛⠋⢻⣿⣿⡿⣿⣿⠟⠛⠛⠛⠛⣿⣿⡆⠀⢻⣿⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠴⠦⠤⣤⣤⣤⣤⣄⠀⠈⠂⣠⠸⡧⠤⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡏⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠉⠀⢹⠿⣦⣤⡶⣾⡑⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⡇⠀⢀⠀⠄⠀⠀⢸⣿⠃⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠰⣄⣷⡄⠀⢀⣀⠀⠀⢀⡏⠀⣀⣼⠑⠿⣇⠀⠀⠀⠀⠀⢃⡠⠠⣤⣬⣳⠟⢿⣿⡇⢸⡃⣼⣴⣷⣶⠧⠂⢸⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠠⢸⠟⠉⠙⠛⠺⢲⣿⣿⡿⣿⡿⠛⠳⣦⣨⠀⠀⠀⠛⠞⣷⣥⣾⣿⣿⣿⣤⣸⣿⢠⣼⠛⠉⠀⠀⠀⠀⠀⢻⠁⠀⠀⢀⣟⠠⠄⠀⢠⠄
⠀⠀⠀⠀⢠⠆⡇⠀⠀⠀⠀⠀⠌⠀⣿⡇⠈⠁⠀⠈⠀⠀⠄⣐⣥⣟⣆⣻⣿⠿⠛⠋⠉⠉⠈⣉⠀⢸⠀⠀⠀⢀⣀⣀⠀⣼⣤⣶⣶⠜⣿⢶⣶⣶⡆
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⠇⠀⠸⡇⢲⠐⣄⡤⣀⣀⣤⠘⠫⠙⠉⠁⠀⠀⠀⠀⠀⠀⣀⢻⠀⠀⣄⣀⣤⡾⣿⣥⣍⣵⣿⣿⣯⣍⣹⡿⠟⠋
⠀⠀⠀⢀⡃⡀⠀⣀⣤⣤⣄⠀⠰⢤⣤⠳⣼⣿⠿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠶⠿⠛⠓⠲⢯⣏⣉⣁⣀⣩⠟⠂⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠈⠀⠐⠂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⡔⠀⠀⢀⠀⠰⠀⠀⠐⠻⠿⠟⠋⠋⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠱⣿⣄⣤⣀⡀⡀⠀⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠚⠛⠛⠻⠿⣿⣿⣦⣦⣤⣠⣶⣶⣄⣀⣠⣄⣀⡛⢮⣀⡀⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⡀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡿⠯⠟⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠁⠈⠋⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠰⢁⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⢰⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠂⣀
⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁⠉⠉
⠁⠒⠂⠁⠀⠃⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣂⠥⣌⠂⠀⠤
⠀⠀⠀⠐⠀⠀⠊⠐⠄⣁⢀⠀⠀⠀⠒⠁⠀⠀⠀⢀⠔⠂⢀⠀⠀⣀⠤⠄⣀⡀⠤⠔⠊⠀⠀⠈⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠆⠀⠀⠈⠈⠣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢇⠀⠀⡤⠀⡀⠀⠀⣆⠀⠉⠉⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⡇⠁⠘⠳⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣀⠀⠀⣄⠀⠸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡶⠁⠀⠀⡌⠀⠀⠀⠀⠀⠘⡳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠁⠸⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡄⠣⡀⠀⢠⠔⠋⠉⠀⠉⠑⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢃⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠢⣀⠀⠀⢠⠁⠀⣸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠈⢳⠒⢁⠀⠀⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡄⠀⠀⢠⠀⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢁⠀⠀⢸⠀⢸⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢸⡄⠀⠈⠀⢸⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡧⠀⠀⠆⣀⠆⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃⠀⠁⠘⣅⣰⠀⠈⠁⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⡼⠃⠤⣤⣙⠉⠀⡴⠆⠀⠀⠀⠀⢠⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡴⠛⣀⠀⠀⠨⣥⡀⣆⠛⠀⠀⠀⢶⣦⢸⣇⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⡷⢛⡁⠀⠀⠁⠲⣄⣧⢚⣥⠄⠀⢢⡝⠞⣥⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣝⣷⠋⢐⣷⠘⣶⣤⠘⡇⣚⠅⢀⠸⣦⠙⣏⢉⣥⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⠉⠙⠳⠾⣇⡠⣤⣹⣴⡟⣡⠀⣾⠀⡀⢠⠷⠿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣧⡘⠖⠈⢛⣶⣭⣽⣦⣁⠀⢿⡄⢹⡿⠖⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡄⢩⣟⠛⣩⢅⡟⠁⢶⣭⣝⣿⣷⣾⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣼⠿⠃⠾⠋⠸⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣶⠿⡿⢀⡿⢛⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⢾⢟⣿⡛⢿⣿⡿⣿⢻⣶⣶⢶⠿⣻⢿⠇⣾⡽⠿⣾⣷⠿⠶⢿⣿⡟
⠀⠀⣴⣾⣿⣿⣟⣓⣛⠻⢭⡿⢿⡦⣧⣿⠧⠾⢛⣡⠾⣶⠏⡼⢡⢖⣛⢲⢬⣙⣛⣛⣿⠃
⠀⠸⠋⠉⢸⡿⢉⡵⣛⡓⢦⡹⣯⣿⠾⢷⣔⡛⠛⠒⣋⣵⣚⣷⡐⢜⡽⢢⡇⡌⣭⣿⠃
⠀⠀⠀⠀⢸⡿⡏⠸⡩⠿⢢⠇⣿⣿⠻⣳⣴⣶⡦⣤⣤⣔⠿⣿⡷⣔⢶⡟⣇⣿⣼⡇
⠀⠀⠀⠀⠘⣇⡇⢸⣬⢍⣭⣾⣿⣿⣿⣿⣼⣿⣿⡌⣧⡙⣷⣬⣿⢾⣇⣦⣿⣿⣿⣅
⠀⠀⠀⠀⢰⣿⢃⣇⣹⣶⣿⣿⣿⠃⠉⠙⠻⠿⠿⠿⠿⠿⠿⠛⢿⣿⣼⣿⣿⢿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠈⠉⠛⠛⢿⣿⡇
⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⡿⠃⠸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⢸⡟⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⣿⠃⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣶⡿⠃
⢸⣿⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠉
⠸⣿⡆⠀⠀⠀⠀⠀⠹⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⣀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣀⣼⡖⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡿⣯⣏⣽⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⡘⢑⡙⠎⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠠⡤⠄⠀⠀⢀⡀⠀⣀⣀⣀⣀⣠⢀⣀⣤⣭⡍⠛⠊⠻⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⢹⠄⠉⡀⢉⡖⠶⡈⠈⣃⢰⣿⠂⢹⠠⣿⣺⣇⣽⣿⣷⣤⣤⣴⣿⣿
⠀⠀⠀⠀⣾⢛⡁⠈⠀⠀⢂⠀⢆⠓⢠⡀⠠⠰⠀⢙⡯⢼⡛⠉⣗⡑⠘⠿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢸⣯⠘⣷⠀⠄⢀⠀⠀⠈⠃⠐⠃⠘⠃⢀⠉⠀⡉⠉⠀⠀⠃⢷⡀⠈⢻⣟⣿⡟
⠀⠀⠀⢸⡏⢠⠈⢷⡄⠀⠀⠀⠂⣸⣟⠂⠰⣯⣤⣍⣻⣧⣾⣶⣸⣷⣴⣷⡔⣻⣿⡿
⠀⠀⠀⠈⠓⠉⠀⠁⠈⠆⠀⢠⡿⠛⣿⣿⣾⡛⣷⡞⠓⢽⣿⣯⣷⠛⢳⣏⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⡴⢃⠀⢠⢒⠎⠀⠀⠉⠉⠛⠛⠓⠒⠒⠒⠛⠛⠙⣦⢻⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠂⡀⣠⠀⠐⢫⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠿⡆⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⣈⡼⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣧⢳⠀⠀⠀⠠⠖⠂⠀⠀⣰⠖
⠀⠀⠀⠐⢠⠃⠀⠀⠀⠀⠓⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠈⠁⠀⠉⠀⠀⠀⠀⣅⡈
⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡖⠐⠐⠋⠀⠉
⠀⠀⠠⠖⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠿⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠇⠀⠜⠃⠀⠀⠀⠀⠀⠘⠲⠓⠉⠁⠀⠀⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠘⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢠⠃⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⡞⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠷⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣷⠀⠇⡁⠀⠈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢰⠱⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⣴⢃⠀⠸⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⡠⢘⠀⠀⠜⣶⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢄⠘⡿⡄⠀⠙⢆⢦⡀⠀⠀⠀⠀⠀⠜⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⡼⡰⠃⢀⣾⣶⠃⡰
⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠤⠀⠑⢤⡌⠰⠄⠀⢠⡙⠆⠀⠀⠀⠀⠄⢧⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⢀⠀⠴⢋⠔⠀⣴⢟⣿⣿⡎
⠀⠀⠀⣀⠀⠀⡀⠀⢀⠀⠀⣀⠀⠀⡀⠙⢢⡴⢒⣒⠛⠓⠦⠌⠐⣤⣸⠀⠂⠀⠀⠀⠀⠠⠀⣃⣤⠂⢡⠴⠛⠛⢂⣲⣾⣿⣯⣾⣿⣄
⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠈⣌⣂⣀⡀⠢⣄⠈⢑⣦⠀⠀⠀⢀⣆⡈⢁⣠⠔⢀⣀⣂⣡⢰⣻⣿⣿⣿⣿⣯⣿⣆
⠀⠀⠀⠓⠀⠀⠃⠀⠘⠀⠀⠚⠀⠀⠃⠀⠐⠂⠀⠒⠠⠀⠀⠉⠳⠠⡙⡀⡀⢡⠀⣀⡄⠀⢀⠉⠠⠞⠉⠀⢀⡿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢁⡜⢅⠀⠼⢠⡅⠦⢀⡀⢃⠌⠀⠀⢀⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢑⡉⠀⠁⠀⠀⢰⠀⠁⣊⣦⠐⢀⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠳⣐⠆⠚⠓⠰⣀⠞⢠⠂⢀⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⢃⠀⠀⠌⠹⠀⡏⠀⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠆⠈⠛⠛⠂⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡆⠘⠃⠀⠀⠶⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠜⢂⠠⠴⠦⠄⠺⠣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠑⠐⠂⢊⠀⡠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠭⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠛⠠⣀⣀⠄⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⣒⣒⣒⣒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠠⠬⠭⠭⠭⠭⠭⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠸⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⠉⣤
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⢀⠿
⠀⠀⠀⠀⠇⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠆⠒⢸⡀⠀⡀⠤⢄
⠀⠀⠀⠀⠐⢄⡡⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣁⡠⠆
⠀⠀⠀⠄⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⠞⠁⠀⠉⠉
⠀⠀⠦⠀⠤⠄⠁⠈⠢⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣋⡀⠓⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠈⢀⠶⡈⠑⠆⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣉⡤⠚⠁⠈⠶⣄⠀⢀⡙
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠈⠉⠒⠒⠀⠈⠉⠉⠀⠀⠤⣄⠀⠀⠀⠀⠄⠀⢀⠐⢄⠀⠀⡤⠒⠀⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠞⠁⠀⠀⠀⠀⠈⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⢀⠀⠀⡠⠄⠀⠀⠀⠀⢀⡀⠒⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣤⡀⠁⠀⣾⠆⠀⠀⠈⠥⠄⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠇⠀⠀⠀⢠⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢠⠀⠀⠀⢆⠀⠀⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠀⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠠⠴⡿⠦⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣻⢢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⣀⡤⠄⠠⠦⡄⡀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⠣⡀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⠏⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⣄⡀⠀⠀⢠⠁⠀⠀⣸⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠛⠦⠒⢛⠀⠀⠀⠻⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢰⠀⢸⠀⠀⢰⠀⢡⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⠀⢸⠀⠀⢸⠃⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢢⠸⠀⠀⠈⠀⠈⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣄⠀⠀⠀⠀⠀⣦⠀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠘⠀⠀⢀⡇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⠀⡿⠀⣤⡄⢠⡠⠚⢁⠖⠀⠤⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⡇⠀⠀⠀⠀⢣⣀⡎⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠘⢷⣄⣀⣀⣀⣼⠟⠙⠢⠤⠤⠴⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣙⣿⠛⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⡜⠁⡏⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠸⡈⠳⡀⢀⠎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠲⠁⠸⡇⠀⡜⠁⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠳⡀⠀⡇⠀⠳⠋⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠞⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠓⠚⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠓⢄⡀⠀⠹⡦⢄⣀⣰⣄⡄⠀⠀⢀⡴⠃⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠓⢤⡀⠀⠙⣄⠤⠷⣄⠀⠈⠉⡿⠤⣤⡏⠀⢀⠴⠊⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠋⠉⠁⠀⡀⣉⠑⠢⣌⡶⠋⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠉⢶⣡⠔⠊⡉⣀⠀⠈⠉⠙⠒⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠁⠀⠉⠙⠂⡞⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢳⡐⠛⠉⠀⠈⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠴⠚⢹⠁⠔⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠣⠀⡏⠓⠦⣄⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣿⣛⣷⡀⠀⠀⠀⠀⠀⣾⣿⣹⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡻⠟⡢⠁⠀⣀⡀⠀⠀⢿⠿⢟⡜⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡈⠉⠀⣠⣤⣶⣶⢦⣄⠀⠉⢁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣨⣇⡀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠦⢤⣀⣑⣊⣀⡠⠴⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠏⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⢦⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⣧⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡇⠀⠀⣇⣀⣀⣸⠀⠀⢸⣷⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠃⠀⠀⠈⠿⣶⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠦⢄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⢶⣀⠐⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠈⠀⠀⠀⠀⠀⠀⠐⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢋⠃⠀⠀⠀⠀⠀⢠⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⢀⢔⡗⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡤⠆⣀⠀⠀⠀⢀⣲⠿⠛⠁⠀⣀⡠⢤⢎⣼⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⣀⣴⠀⠉⠙⠛⠓⠛⠛⠛⢿⣷⣄⢀⣷⣐⠥⢆⢀⡾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣛⢿⣿⣿⣿⣋⢵⣿⡟
⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠦⣽⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡆⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠘⢃⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡶⠿⠿⣿⣰⡿⢿⠃
⠀⠀⠀⠀⠀⣾⣿⣡⣴⠀⠤⠄⠐⠰⠤⡁⠀⠰⠶⢦⣀⣀⠀⠀⠀⠀⠀⠋⠹⠉⠁⠀⠀⠈⠛⠙⠋
⠀⠀⠀⢀⢸⣿⣿⠟⡽⣶⣮⣰⠷⠶⠶⠾⠀⠀⣰⣋⣩⣿⣆
⠀⠀⠀⠊⣼⡿⢁⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⣽⡏⠁⠀⠀⠉⠢⠄⠀⠀⠀⢀
⠀⠀⠀⡟⡟⢰⣋⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⡂
⠀⠀⠀⢹⡇⠀⢶⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢺⡄
⠀⠀⠀⢺⡇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠼⣧
⠀⠀⠀⠸⣇⢼⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⢶⣿⠿⠀⢸⡻⠀⠀⠀⢰⡇⠀⠀⣸⣧⠀⠀⠀⠀⣄⣠⠀⠀⢸⡆
⠀⠀⠐⠿⠟⠀⠀⠸⣿⣷⡀⠀⠈⠉⠂⠰⢿⣿⠜⠓⠒⠂⠁⠀⠀⠀⣾⣿⢆⡀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠶⠿⠗⠀⠀⠀⠘⠻⡷⠶⠂⠀⠀⠀⢠⣐⠠⣶⣩⣤⡥⠀⢈⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⣵⣦⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣷⢶⡀⠀⠰⠿⠁⠀⡠⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢇⡀⣐⣤⠐⣿⠉⠉⠧⠀⠀⢸⣞⡁⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢇⣱⠤⢄⣖⠰⠆⢴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⢷⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⣶⡛⣠⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠙⣿⣿⡿
⠀⠀⠀⠀⢀⣤⣶⣾⣯⣻⣵⣾⠩⢉⡁⠊⠸⣿⣿⣴⣾⣯⣉⣻⣚⣇⠜⢶⣟⣉⣟⡛⢹⣏⣽⣿⡃⠀⠠
⠀⠀⢀⠐⣾⠃⠞⣿⣿⠀⠀⠁⠀⠀⠀⠛⣶⢞⣿⡿⠟⣛⠘⠃⠿⠿⡟⣠⣤⡿⢿⣿⠛⣹⡾⢻⣿
⠀⠀⠻⢸⣿⠠⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⢰⠘⣷⣻⡟⠈⠙⠀⠂⠀⠘⠛⠻⣧⠿⣿⣽⢿⡛⣿⣿⠄⠀⠀⣠⣤⡆
⠀⠀⠀⢟⣿⡀⡀⢸⡟⠀⠀⠀⠀⠈⠉⠀⢀⠽⣏⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢛⣀⠠⣛⣵⣟⣠⠐⣾⣿⡟
⠀⠀⠀⠈⢻⣇⠡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣩⣿⠀⠀⠀⠀⠀⠀⠀⣰⣦⡾⠩⠄⢺⣏⣻⠿⣿⡟⡹⠋
⠀⠀⠀⠀⠀⣿⡄⠉⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⡽⠟⠀⠀⠀⠉⠉⠏⠀⠙⡟⠁
⠀⠀⠀⠀⠀⠸⣿⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠁⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠠⠄⠀⠀⠀⠀⠒⠒⢷
⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣀
⠀⠀⠀⠀⠀⠀⣤⡀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣄⣼⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡀⣆⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠜⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂
⠀⠀⠀⢐⠀⠀⠈⡈⠉⠈⡀
⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⡁⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢈
⠀⠀⠀⢸⡥⠤⠤⡿⢶⣏⡇⢠⢴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣸⡀⢀⡦⣤⡀⢀⣯⠒⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡠⢖⡥⠁
⠀⠀⢠⠤⡬⡬⠴⠰⡠⡇⢸⠉⠀⠀⡍⡇⠀⠀⠀⠀⠀⢀⡠⠔⠈⡅⠐⠙⠿⠿⠯⠿⠛⠀⢀⡠⠥
⠀⠀⠠⢠⡜⠀⠪⠀⠄⡜⢼⠀⠂⠀⡃⠁⠀⠀⣀⠔⠊⠁⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⢠⣨⣟⢄⣩⣨⣠⣌⣸⣀⣀⣀⣆⣇⠔⠊⠠⠇⡄⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠒⡆⠂⠀⠀⠀⠀⠙⡆⠀⠈⢤⡀⠀⠀⠁
⠀⠀⠆⠀⠀⠊⠁⠀⠀⠀⠐⠒⠀⠓⠂⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡆⢠⣿⠃⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⣠⡴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣦⣀⠀⢸⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠻⣷⣼⡇⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⢿⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠌⢿⣶⣶⣤⣤⣀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢀⣀⣴⣶⣿⣿⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠛⠻⠿⢾⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣆⠀⠀⠀⠀⢐⣼⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⢰⣞⠋⢹⣇⠀⠠⠊⠛⣿⣁⡀⠴⠶⠆⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣮⡿⠏⠁⠈⠉⠀⠈⢠⣿⡟⢡⣴⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠈⢿⡟⠁⠀⠀⠀⣄⣠⣄⠀⠘⠋⢀⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠐⠛⠛⠛⠁⠀⠀⠚⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣈⣿⣿⣿⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣭⣄⣀⣀⡀⠀⠀⣀⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠻⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡏⠀⢻⣿⣷⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⡋⠀⢙⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⣻⡯⠀⠀⠈⣿⣿⣿⠿⣻⣿⠃⣾⣿⡻⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡋⠀⠘⠿⠀⠀⠀⢿⣿⣥⣖⣺⣿⣵⣿⣿⣷⣮⣿⣇⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⠈⡓⠀⠀⠀⠚⢻⣿⣿⣿⠟⢳⣿⣿⣿⡿⢻⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣁⡀⣀⣹⣿⢰⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣿⠇⠈⡟⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⡟⣿⢻⣿⣿⡿⠀⢟⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⣿⣿⡿⠸⢿⠁⠀⠁⠀⠈⠁⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣛⣿⣿⠿⠰⢷⣶⣦⣤⡀⠀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣷⣶⣾⣮⣿⣿⣿⣶⣿⣿⣷⣶⣯⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣾⣝⣛⡛⠿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠳⣤⣴⢿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢧⠃⠂⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⢹⡷⡆⠄⣀⣀⠀⠀⢀⡻⠎⢀⠈
⠀⠀⠀⠠⢆⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠰⠻⠁⠀⠀⠘⠛⠻⠺⢙
⠀⠀⠀⠀⠈⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣄⣀⣀⣀⣀⣲⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⢈⠛⠀⢀⣤⣤⢀⣀⣀⣠⣄⣴⡆⠀⠀⣀⣶⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠶⣬⣽⠿⠀⢻⣿⣿⣿⣿⢿⣿⣿⣷⢀⡄⡹⣿⣿⣿⡼⢿⣿⠋
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠘⠙⡿⠁⠈⠀⡀
⠀⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⢢⣄⠀⠀⠀⢄⠆⣀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠲⣈⣤⡀

⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⢸⣠⠏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⢰⠃⠘⣄⠀⢠⠇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢻⡀⠀⢠⡏⠀⣀⠈⢶⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣾⠛⠋⠁⠀⢸⡆⠀⢀⣼⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢶⠦⣝⠷⣴⠀⢀⣼⠷⣶⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠷⡼⠳⠞⠛⢀⢑⢋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠋⠈⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢧⣀⡀⢀⣀⣀⣾⡯
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠷⠿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡄⠀⠙⡖⠤⠤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣾⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠰⣤⡀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡹⣿⡟⣇⣾⢳⡀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣿⠀⢻⣷⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠸⠇⢻⣧⣿⣿⡈⢃⡀⠀⠀⣷⣠⠀⠀⠀⢸⡟⢸⣿⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠈⣧⠀⢸⣧⠟⠄⠀⢠⢟⣠⣿⢿⣿⣇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⣸⣭⣤⣤⣶⡾⣿⣿⣷⣮⣿⣿⣧⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢻⡇⢿⡇⡰⠉⠉⠉⠁⠀⠀⠈⠻⣿⣿⣿⣧⡙⠻⣷⣤⡈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡻⣦⠀⠙⠫⣼⣟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢨⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⠀⠀⠀⠼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠⠊⠀⠀⢠⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠀⡀⠀⣰⣮⢖⣆⠆⠀⠐⠄⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠁⢀⣰⣿⠛⠉⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣬⡀⠀⠐⠂⠀⣸⡿⠁⡀⠀⠀⢀⠀⠰⠊⠁⠠⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⠓⠶⠶⣿⣿⣄⣘⣆⢨⣠⣤⣀⣀⠀⠀⠁⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⣿⣿⣿⣍⠙⠷⣄⣷⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⢿⣿⣶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠦⠂⠀⠩⢽⣷⣄⠈⠻⣁⠖
⠀⠀⠀⠀⠀⠀⢠⡶⢿⣿⣿⣿⡷⢿⢟⣿⣿⣯⣿⠋⡉⠛⠿⠟⡿⢿⠛⠛⠓⠒⠒⠶⣤⣄⡀⠠⠞⠀⠀⠀⠀⠀⠀⣀⡈⣻⡷⢀
⠀⠀⠀⠀⠀⢰⡟⣰⣟⣿⡿⢿⠐⠀⡀⠰⢻⣿⠟⠀⠀⠀⠀⠀⠀⠹⠓⡀⠀⠀⠈⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣵⣾⠁⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣷⠘⣆⠈⣧⠀⠈⢹⣯⣃⣀⠀⠀⠀⠀⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⠘⠀⠙⣷⢀⣀⣀⣉⠉⠑⠀⠀⠀⠙⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢿⣖⡷⢰⣅⡂⢉⣿⣿⣷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠠⠀⠀⢁⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣉⠘⣿⣧⠀⢈⡿⠛⠲⠤⣌⡉⠉⠛⠛⣻⣿⣶⣷⣤⣦⣤⣴⣾⣇⢀⣄⡠⠶⠛⠁
⠀⠀⠀⠀⠀⢀⠐⢋⣤⠟⠁⡠⣳⢿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢙⣿⣿⠛⠋⠁⠀⠀⠁
⠀⠀⠀⠀⡼⢋⡴⠋⠀⢀⣺⠏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⣿⢻⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠇⢸⣿⡇
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢻⡇
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⣧
⠀⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠸⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠛⠛⠒⠀⠀⠀⠀⠀⠘⠛⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⢤⣀⠛⠻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤
⠀⠀⠀⠀⣧⣾⣤⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⢼⣢⣆⡤⠄
⠀⠠⣤⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⢸⣿⣿⣿⣦⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣶⣦⣶⣶⣤⡄
⠀⠀⢠⡞⠛⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣄⠀⡀⢰⡄⠀⠀⠀⠀⠀⢸⣯⡛⠛⠻⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⢳⡀⠀⠀⠀⠈⠻⢿⣿⣿⠀⠀⠀⠀⠈⠻⢟⣺⣁⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⠀⠀⠀⠘⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢰⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⢹⡏⠉⠉⠹⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⣧⢾⣰⣦⠤⠂⠀⠀⠀⠀⠀⠈⢦⠸⡇⠀⠀⠀⢸⡗⠘⢷
⠀⠀⠀⠀⠀⠐⢶⣾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⠃⠀⠀⠘⠀⠀⠀⣿⡴⢉⡀
⠀⠀⢀⠀⢸⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣿⣿⡍⠉⠒⠒⠁
⠀⠀⡟⠙⡿⢿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠃
⠀⠸⡇⠀⠙⠆⠈⠉⠉⠉⢹⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣾⣿⣿⣿⡁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⡀⠀⠀⠀⠀⠒⢛⡭⠝⠛⠉⠉⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⣾⢃⠀⠀⠀⠀⠀⢀⢸⠀⢠
⠀⠀⠀⠀⠀⠀⣳⣄⠀⠀⠀⠀⣇⢸⡁⠀⠀⣻⣿⡟⣡⣴⣼⣧⠀⠸⠈⣤⢸
⢀⠀⠐⠃⠀⠀⢻⣿⠀⠀⠀⣎⢿⢼⣧⠰⠀⣿⣽⣿⣿⣿⣿⡟⡀⠒⢀⢿⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠀⡀⠁
⣸⣿⠀⠂⠀⠀⡏⣗⠀⠀⢸⣿⣿⣾⠛⠘⠀⠁⢹⣿⣿⣿⣿⡏⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠇⠘⣳⣶
⣿⣿⣄⠀⠀⠀⠁⠃⠀⠀⠀⢹⡿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠃⠀⠀⣽⡟
⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠟⠋⠁
⠸⠟⠿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠹⣿⡇
⠀⠟⠋⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⢿⡀⠠⣂⠀⡀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠵⠼⣍⠁⡇
⠀⢇⡵⠆⠉⢀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡉⠳⠄⡖⣠⠖⠚⠁⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠦⢬⣎⣳⡇
⠀⣯⠴⣖⠋⠉⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠓⢤⡄⣿⣡⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠈⢹⡇
⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⣿⣿⣿⡇⣿⣿⣷⣦⣄⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⢁⣀⣀⣠⣤⣤⠀⣤⣤⣴⣤⣤⣈⣵⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⡇
⠀⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣾⣿⠀⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠀⠀⠀⠀⠀⠀⣀⣀⣠⣥⣤⣴⣶⣾⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⢋⡀⠅⣨⣿⣿⡿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣤⣼⣮⠁⠀⠀⠈⣻⠃
⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣴⠃
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀
⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠙⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿
⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⠀⢀⣴⣶⣦⠀⡇⠀⡠⠊⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⢏⠀⠀⠀⠀⢅⠀⠸⡟⠋⠉⠉⠁⠒⠿⣿⣷⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛
⡇⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠑⠲⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠇⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠦⠤⠊⠁⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⡈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠉⠒⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⡇
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣤⣀⡀⠀⠀⠀⣀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠉

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣷⣖⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⡠⠤⡄⠀⢠⡄⠀⠀⢀⠖⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⡇⠀⠁⠀⠀⠳⡄⠀⠀⠓⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠈⠀⠀⠀⠀⠀⠘⢄⡀⠐⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⣿⣿⣿⣶⣄⣀⡀⠀⢀⣀⣤⣴⣾⣿⣿⣤⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣾⣿⣿⣿⣿⣿⣿⠿⣋⣼⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⠛⠛⠉⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⢻⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⢼⣿⣤⡤⠄⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⠀⠀⠀⠀⠄⠻⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠄⣁⢌⡠⡀⢸⠀⡀⢅⡤⠀⠞⠠⠂⡠⡸⡮⢁⠀⠀⡀⢂⣤⡄
⠀⠀⠈⠁⠘⠛⠙⠲⡾⠷⣮⢾⣀⣀⡧⠙⠚⠱⢿⣾⢀⠀⠀⠊⠛⠁⠀⠀⠀⠀⠉⠚⠐⠉⠀⠘⠋⠉⠙⣯⣦⣆
⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⣷⣀⡀⠀⠸⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌
⠀⠀⠀⠈⠙⠛⠛⠂⠀⠀⠀⣐⣿⣿⣿⣿⣕⣀⠀⠈⡧⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂⠐⠀⡀⠀⠀⠐⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⢻⣯⣿⣖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⡏⡰⠈⠠⠀⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠇⠄⠀⠀⠀⠀⠀⠀⠘⠀⣾⠀⡄⢠⡤
⠀⠀⠀⠀⢀⢄⠀⠀⠀⠒⣿⣿⣿⣿⣿⣻⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠐⠢⡇⠀⡇⠠⢀⠌⠒⠀⠀⠀⠀⠀⢀
⠀⣴⣖⣤⣿⡿⠁⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠘⠀⠀⠀⠀⢄⠀⠈⢆⣇⡜⠤⠀⠠⠀⠀⠀⠈⠚⠁
⠀⠉⠉⠉⢻⣿⡗⠀⠐⣼⣻⣿⣿⣿⣿⣯⢋⡽⢻⡗⢀⣈⠀⠀⠀⠀⠀⢹⠀⠀⡏⢀⠀⡴⠋
⠀⠀⠀⠀⠀⠉⠰⡄⢙⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢺⠀⠀⠀⠀⠁⠀⠳⠐⡇⠈⡠⠀⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⣿⠛⠹⢿⣿⣟⣦⠖⠈⠀⠀⠀⠈⠂⣰⠀⢰⡇⠸⠁⣸⠟⠉⠓
⠀⠀⢀⣠⠄⡀⠀⠀⢹⣿⢿⣿⣿⡿⡼⢂⣿⣿⣿⣷⡄⢀⡄⢀⠀⠀⡀⢈⠡⡈⣷⠗⣈⠀⢰⠆⠁⠀⠀⠀⠁
⢠⠼⠠⣴⡿⠃⠀⠀⠉⢺⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⢸⠃⠀⠀⠀⠀⠀⠄⠘⡇⢰⡀⠴⠡⠈⠁
⠀⠀⠀⠉⢺⣅⠐⡀⢠⢿⣿⣿⣿⣿⣹⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⢆⣧⠌⠀⢄⢀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠘⣿⠟⠀⢠⢿⣿⣿⡿⢻⡃⢿⣿⣿⠇⡠⠃⠠⠀⢴⡄⠀⠨⢦⠁⠘⣿⠀⢀⠴⠈⠀⠀⠀⠘⠙⠀⠠⠆
⠀⡐⠀⠀⠄⠀⠀⠀⠀⠊⠹⠛⠳⣼⣆⠔⠙⠛⣠⣴⣗⠐⠀⠀⠁⠀⠀⠀⠑⢤⣏⡴⢋⠐⣆⣀⣀⣀⣀
⢀⣷⣶⣦⠶⣿⡏⠀⠀⣠⣶⣀⠆⢹⡇⣤⡼⠛⠛⠉⠉⢛⡀⣠⣤⣄⣠⡾⣁⠸⣏⣰⡵⠾⠟⠋⠉⠙⠛⠶⠾⠷
⢨⣽⣵⣭⣭⣾⣧⠶⠾⠛⡁⠙⣻⣸⡏⣁⣴⣿⣄⣻⣶⣾⣽⡿⠿⠟⠋⠙⢳⠐⣿⠍⣀⣼⣷⣦⣤⣤⡀⠙⢶⣤⡄
⠈⠀⠚⠉⢉⣡⣤⡶⠋⡴⢀⡀⠈⢹⡷⣿⣶⣷⣿⣾⣶⣏⢀⣤⠖⢡⠦⠤⠈⠑⣿⣠⣤⢠⣤⣤⣤⣤⡁⢈⣀⣉⣙
⠀⣠⡄⠳⠿⠛⠋⠀⠆⠀⠸⣿⣿⣼⣇⣬⣉⠻⣿⣿⣿⡏⠛⠉⢴⠋⠀⢀⡌⡣⣿⢈⣉⡛⣷⣿⣿⣿⢿⠿⡛⠛⠛
⢀⣿⠆⠶⠦⠖⠀⣿⣯⡷⠈⠉⡉⢹⡏⢛⠛⠺⠿⢍⠀⢀⠠⠤⠀⠒⠒⠚⠛⠓⣿⠘⠛⠻⠿⠿⠾⢭⡅⢀⣿⣄
⢠⣴⣴⣤⣤⣤⠼⢴⣹⡶⠒⠛⠋⢸⡟⠛⠛⠛⠛⠓⠀⢠⢀⣴⣶⡿⠿⠶⠷⠀⣿⠶⠶⠾⠷⠲⠶⠦⠄⠸⣦⣿⡀
⠘⠛⣉⣭⠥⠀⠀⣦⢹⡇⠀⠀⠀⣾⡇⠀⠲⠀⠀⠀⠀⣾⠀⢉⠐⠀⢀⣠⣴⣾⣿⣶⣦⣄⠀⠀⠀⠀⠀⢸⣎⣿
⠀⠐⠄⠂⠀⠀⠀⣼⣿⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⣸⢫⡏
⠀⠀⠂⠀⠀⠀⢀⠟⡿⠀⠀⠀⣿⣿⠿⠧⠀⠀⠀⠀⠀⠈⡆⠶⠀⠙⠿⢿⠿⣿⠿⠟⠿⠟⠿⠄⠐⠒⢠⠏⡼⠋
⠀⠀⠀⠀⠀⣰⣯⡾⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄⠀⣠⡾⠃⠀⠀⠠⠀⠀⠀⠀⢠⣿⣼⠅
⠀⠀⠀⠀⢰⣿⡟⠁⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠟⠀⠀⠈⠀⠁⠀⠈⠀⢁⣾⡿⠁
⠀⠀⠊⠀⠈⠉⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⢄⠀⠀⠀⡀⠂⣀⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣲⣀⠙⠲⠍⠀⠈⠀⠠⡴⡎⢠⠜⠉⠢⠠⡒⢠⠖⠂⠠⠄⢀⡄
⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠰⠂⠚⢀⢀⠐⠀⢄⡄⠀⠀⠀⠀⠀⠀⠂⠞⠁⠈⠀⢠⣞⣅⢰⡚⠐⡠⠄⠉⠁⠉
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣔⠀⠀⡘⠉⠀⠀⠀⢑⣀⠀⠀⠈⠂⠀⠀⢂⣠⠔⠚⠀⠉⠂⣀⡁⠮⠗⢚⢦⣈⣻⠔⠾⢁⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⡀⢂⠀⢈⠵⠀⢠⣴⣞⠹⣯⠰⠁⠀⠀⠀⠀⠙⠁⠀⠐⣈⡼⠗⢨⣈⠉⢉⡜⢍⣣⣨⠖⣚⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠨⠲⠤⢿⡿⣿⣾⠉⠁⠀⠀⠀⠀⠀⠀⠆⠊⠁⢦⡴⣰⣛⡓⠨⢷⡾⠟⠛⢧⡑⣍⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⣺⡀⠀⠀⠠⠀⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⡦⠖⠉⠉⡓⣀⠀⢀⠜⠛⠟⠘⠋⣋⠩⠓⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠠⢔⠠⠐⠄⠀⠀⠙⢄⣠⡤⠐⠀⠀⠀⠀⠀⡀⠆⠋⠀⠈⠉⠑⢂⣄⠘⠒⠓⠂⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⢳⣆⠈⠒⢀⣄⡠⢻⣯⣹⣆⡈⠀⢀⠢⢠⠀⠀⠀⠀⠀⠀⠶⠏⠀⠁⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠨⠷⠦⡄⠡⢠⠀⠀⡀⣠⣷⣠⠋⠀⠑⠡⠂⠘⠉⠉⢋⣴⠽⠮⣙⡛⠓⠒⠒⠒⠫⠤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⡄⠀⠀⠈⠂⠈⠉⢹⠋⠄⢠⡀⠀⠈⠀⣀⡴⠃⠁⠀⠀⠀⠉⢏⠐⣤⣖⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠛⠷⢶⡠⠴⠤⡗⠸⠃⠐⠸⠷⠃⠀⡔⣀⣤⠤⢤⡆⠀⠒⠪⣙⣄⣀⣉⡠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠉⠀⠈⠃⠐⠁⠈⠑⠢⡀⠒⠈⢺⠀⠋⠁⠐⠀⠀⠁⠀⠀⠀⠈⠉⠹⠆⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡤⠀⣀⡀⠀⠀⣠⠀⠴⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⣦⡋⠰⢿⡂⢸⣠⡄⢻⣠⡷⢸⡃⠀⢹⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠠⠆⡀⠀⠹⡀⢀⠀⣅⢼⠈⠹⣠⢿⠀⠸⠇⠀⠼⠄⠐⠆⠀⠀⣀⠈⠀⠐⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡘⠄⠀⠀⠴⠀⠐⠀⠄⠰⠅⢄⠐⠐⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣥⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢿⣦⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⡧⠴⠤⠤⠤⠒
⠀⠀⠀⠀⠀⢀⣠⣤⡀⣿⣿⡇⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣆⣰⣿⡷⠶⠦
⠀⠀⠀⠈⠚⠉⠀⠀⠈⣿⣿⣷⣤⣾⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⣠⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢧⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⡀⢠⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⡈⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣤⡴⢊⣴⠿⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠄⠈⠢⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣡⣿⡥⢀⣠⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⣷⣾⠈⢳⣄⠠⣿⣀⣠⣤⣴⣦⣤⣤⣼⣿⣿⣿⡿⢡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣆⡀⠿⢷⡿⠟⣿⣿⠿⣿⡿⠿⣿⣿⡿⢛⣁⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⡿⠿⠄⠀⠁⠠⢀⣾⣴⣿⣴⠞⡋⣿⡇⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠘⣿⣿⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⢹⣿⣿⣿⣷⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠗⢉⣿⣿⡛⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠈⠀⠘⢻⡿⣷⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠉⠛⠏⣡⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⣀⣈⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⠟⠋⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⢀⠘⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣻⣿⡟⣫⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢦⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠁⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠉⠈⠀⠀⠀⠒⠈⢿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠏⠀⠀⠁⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠲⢋⡁⠤⣾⣿⢟⣉⠀⠈⠉⠀⠀⠀⠐⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢾⣿⣿⣶⣧⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠙⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⣀⠤⠈⠀⠀⠑⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣀⣀⣀⠀⠄⠈⠁⣠⠤⠀⢠⡞
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠁⢐⣄⢘⣿⣿⣇⣀⠄⢀⡀⠀⢀⣰⠎⠀⢄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⠃⠀⢐⠉⠉⠉⠛⠻⢿⣿⣀⣈⣀⣠⣿⡿⠎⠀⢸⠀⠀⠀⠀⠀⠀⣀⡀⢀
⢀⡀⠒⠀⠀⠀⠀⠀⠒⠀⠌⠀⠀⠀⠠⢕⡄⠀⠀⠐⠀⠈⠉⠙⠛⠉⠅⠀⠁⠠⠊⠄⡀⠀⠀⠤⠟⠛⠁⠀⡄
⠀⠳⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣀⠘⠐⢿⡦⠀⠈⠢⡀⠀⠀⠀⠀⠃⢰
⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⢠⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⡔⠀⠀⠈⡄⠀⠓⣻⡀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠊⡴⠁⠀⠀⡯⠀⠀⠀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠂⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠢⠖⠉⠙⢦
⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣤⠤⠤⠶⠾⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢉⡒⠃⠒⢤⠀⠀⠈⠑⣦
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠇⠀⠀⠀⠸⡃⢠⡀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⢀⣀⡴⠂⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠁⢀⠀⠀⠙⢦⣀
⠀⠀⠀⢡⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠵⢦⡀⠀⠈⠳⣤⡀
⠀⠀⠀⢦⠀⠀⢀⡤⢊⠀⠀⠀⠹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠙⢦⣄⠀⠀⠙
⠀⠀⠀⠀⠙⠛⠁⠀⠸⡀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠓⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠙⣆⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢦⡄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡤⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠈⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⣤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣴⣶⣶⣶⡄⠉⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣰⡀⠻⠿⠿⠟⠃⠸⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⠟⠀⠀⠀⠰⠆⠀⠀⠘⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⣿⠟⠀⠃⠀⠈⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠻⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⢰⠄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠺⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⠀⠀⠀⠀⣠⡀⠘⠋⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠺⣿⠗⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⣤⣶⠾⠃⠀⠀⠀⠈⠻⠿⠋⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠐⠂⠐⠀⠂⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠰⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡀⠀⣄⡠⠀⢤⢖⠀⢄⠀⠀⢰⣷⣀⣰⣸⡍⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠉⠚⢩⡅⠀⣤⠀⠑⠈⢛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡴⠋⠉⠒⠛⠛⠃⠀⠀⢨⡿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣄⠈⢂⠀⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢁⠀⠒⠂⠐⠂⠒⠒⠢⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢉⡷⠲⢀⠿⡿⢀⣶⣐⡖⠲⢄⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢈⢠⡾⠆⣀⣀⠀⡇⠀⠀⣣⣠⡝⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⣘⡇⠀⠓⠈⠉⠉⠙⡀⠀⠀⠀⠂⢀⠀⣀⠀⠉⠢⡀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⡀⢀⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠉⠰⡮⠀⠀⠀⠀⠀⠉⠑⠀⢱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠈⠁⠋⠁⠀⠀⡌⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠈⠀⠀⣠⠎⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⠦⠤⠐⠒⠚⠉⠉⠀⠻⣄⡀⠀⠀⠠⡄⠀⣠⣤⠞⠋⠀⠄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⢳⠠⠉⠀⠀⠀⠁⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠴⠒⢦⠀⣧⠰⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠸⡆⢿⣆⠀⠘⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⣀⣹⡀⢻⣆⣀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠉⠉⠀⠀⠬⠣⢀⡿⠙⢧⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠉⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠒⠈⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠓⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠃⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡄⠀⠀⠀⠀⠀⠈⠀⠐⠘⠂⠀⠀⠀⠀⠆⠀⠘⠓⠀⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎
⠁⠀⠀⠀⠀⠈⠓⠋⠉⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⠋⠁⠈⠀⠉⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢤⡤⢀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣤⡤⠄⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠙⣷⣿⣂⣀⣀⠹⡆⠋⠀⠁⠀⠉⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠂⠈⠁⠘⠉⠓⠐⠂⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠁⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠀⡀

⡀
⠃

⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠈⡏⠻⣷⣦⣄⣀
⠀⠀⠀⠀⠀⢃⠹⣮⡻⣿⡟⢫⡐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⡆⠹⣧⠙⣇⠀⠅⣺⠛⢿⠀⠀⠀⠰⣴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠔⣂⡴⢶⣦⣶⠟⣩⡽⠟⠛⠉⠉⠁⢨⡿⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠻⣇⠹⣆⡒⠋⠳⢤⣰⣠⠴⠃⠀⠀⠀⠀⣾⣿⣷⠒⠚⠷⣷⡛⠋⣴⣿⣿⣿⠟⠁⠀⢀⣴⡞⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠹⣆⢻⣾⡷⠒⢒⣿⣿⡍⣉⣁⣀⡀⠀⠛⠿⡏⠀⠀⠀⢼⡁⣘⠙⢻⠟⠁⢀⣴⣾⡿⠉⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠠⢤⢁⠈⡁⢠⣌⡫⢙⠀⠀⠀⠀⢠⣀⡀⠀⠠⣿⣷⠚⠃⠀⠰⠿⠛⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡰⠀⡏⢀⣧⢸⡯⢠⢞⠏⣳⣦⣤⣿⠙⣦⣁⡐⠋⡧⠠⠄⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⣼⢇⣼⡟⠾⣷⣥⣾⡿⠟⠙⠛⠻⣷⡿⣜⡇⢸⠀⡤⠀⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠞⣿⡩⠁⠁⠀⠛⠋⠁⢀⠄⠀⠀⠀⠈⠳⡿⣧⣿⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⡀⠈⠀⠀⠀⠀⠀⢁⣾⠟⢁⣠⣤⣤⣀⣄⠀⠀⠈⠾⣷⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡟⣿⣷⣿⠿⠿⠀⠀⠀⠠⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣙⡩⠀⠀⠀⠀⠀⣤⡾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢰⣾⠛⠉⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣹⣾⡟⠀⠀⢇⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣳⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⣤⣼⣿⣿⠛⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣨⣴⣾⣿⡿⠃⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡀⡠⢒⣿⣿⣿⢟⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣭⣿⣿⡇⣠⡮⠊⠀⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠋⠉⠀⠀⣰⣿⡿⢯⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠓⠙⠛⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣾⡆⠚⠘⠿⢙⠃⠰⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡌⠋⠸⠟⠘⠃⠰⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠘⣛⠹⣿⡇⠰⠂⠿⠇⠘⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠆⠙⡋⢻⣿⡆⠶⠐⠿⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣥⣤⢈⡁⠰⠆⢠⣤⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣥⣄⢉⠁⢰⡷⢠⣄⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠸⢛⡛⢈⢹⠀⣴⠀⣭⡤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠆⠸⢛⡋⢈⢸⠀⡔⢈⣭⡰⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠟⠀⢻⡿⠣⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠈⢿⡟⠁⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠰⣿⠲⠆⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⠟⠟⢻⣿⠇⠛⠙⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠛⠟⢱⣿⡆⢠⠄⣶⡆⠰⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡎⢓⡛⣴⢗⣦⠾⠆⢿⣿⠚⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⣠⣀⠙⠃⡄⠀⢀⣀⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡝⣣⣈⠛⠁⣾⣷⢀⡀⣾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠹⠿⠟⠘⢱⠀⣠⠈⣛⣨⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣌⢿⡾⠇⢰⠀⡴⢘⣋⢨⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⡗⠈⢾⣶⠇⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣾⣷⠘⣾⡾⠃⠻⠿⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠂⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠑⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣿⠆⠁⠀⠀⠀⠀⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢂⠀⠀⠀⠀⠘⠰⣷⡈
⠀⠀⠀⠈⣴⠋⡌⠀⠀⠀⠀⠀⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠄⠀⠀⠀⠀⢣⠹⣧
⠀⠀⠐⠀⠋⢸⠁⠀⠀⠀⠠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠄⠀⠀⠀⠘⡇⠙⠠⠂
⠀⠀⣧⠀⢀⠀⠀⠀⠀⠀⠃⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠐⠀⠀⠀⠀⠁⡀⠀⣴
⠀⢠⠃⢠⡟⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⡀⠀⠀⠀⢻⡄⠙⡀
⠀⠈⠀⢸⠁⠀⠀⠀⡄⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢁⠀⠀⠀⠘⡇⠀⢁
⠈⠁⠀⣿⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⣿⠀⠘
⣆⠀⠀⣿⠀⠀⢰⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⡆⠀⠀⣿
⣿⠂⠀⣿⠀⠀⠀⠀⢨⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢹⠃⠀⠀⠀⠀⣿⠀⠸
⣿⠀⣦⠘⡆⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀⢼⡤⠀⠀⠀⠀⠀⢰⠀⢸⠃⣴
⢿⣿⣿⡄⠱⠀⡇⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣦⠀⠈⠀⠏⢠⣿⣿
⠀⢿⣿⣷⡀⠈⢱⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣷⡄⠀⠀⣾⣿⡿
⠀⠘⢿⣆⠁⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⣴⡿⠃
⠀⠀⠀⠙⢷⣄⠀⠀⠈⠡⣄⣿⣶⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠀⡄⠀⠀⠀⠀⠀⠀⠀⣶⣿⣠⠌⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠙⢿⣶⣦⣀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠸⢾⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡷⠇⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⣀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⡈⠛⠄⣀⠀⠀⠀⠀⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠀⠀⠀⠀⣀⠠⠛⢁⣴⣾⣿⠟⠁
⠀⠀⠀⠀⢰⣿⣿⣷⣶⣶⣿⣿⣿⣿⣦⣀⠀⠉⠀⣉⡄⣸⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⣇⣠⡁⠀⠉⠁⣀⣴⣿⣿⣿⣿⣶⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢌⡉⠻⢿⣿⣷⣶⣿⣿⣿⣬⣿⣶⠷⠶⠶⢾⠿⠿⡷⠶⠶⠾⣶⣿⣡⣿⣿⣾⣶⣾⣿⡿⠛⢉⡡⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠰⣦⡀⠈⢻⣏⣻⣿⣿⣡⣶⣶⣶⣷⣶⣶⣄⣠⣶⣶⣾⣶⣶⣶⣬⣿⣿⣟⣹⡟⠁⢀⣴⠌⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⢰⣿⣄⡀⠘⠛⣿⣿⡟⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⠛⠁⢀⣬⣿⡄⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠘⠇⠘⠿⠏⠀⢰⣿⠋⣿⣿⢶⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⡶⣶⣿⠙⣿⡆⠀⠹⠿⠃⠼⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⢀⣀⣾⣿⣇⡿⠿⠚⠋⢸⣿⣿⡿⠛⠛⢿⣿⣿⡇⠘⠓⠿⢿⣴⣿⣷⡀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣿⣿⣧⣤⠀⠀⣼⠟⠁⢀⣤⣤⡀⠈⠻⣧⠀⠀⣤⣼⣿⣿⣿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣶⣾⣏⣄⣴⡟⠛⠛⢻⣦⣠⣿⣷⣶⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⣁⠀⣿⡝⣯⣿⣿⣿⣿⣽⢻⣿⠀⣈⠁⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣾⣿⡄⢿⣇⣽⣿⣿⣿⣿⣧⣸⡿⢠⣿⣷⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⣌⣿⡉⠀⠀⠀⠀⢉⣿⣡⣿⣿⣿⣿⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⣿⠁⠀⠈⣿⣿⠿⠛⠛⠿⣿⣿⠁⠀⠈⣿⣿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⢀⡄⠠⡔⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠓⠒⠒⠒⠂⠸⢄⢸⣄⠀⣸⣤⡡⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⣃⠀⠀⠀⠀⢀⣀⣮⣀⡉⠛⠁⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠉⠉⠉⠁⠁⣀⡬⠶⠈⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢐⢲⣾⣿⣿⣥⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠘⣄⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠐⣄⠐⠃⣠⠀⠀⠀⠄⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⠉⠐⠛⡄⠠⠟⢲⣂⠀⠤⢄⠉⠉⣠⠔⠊⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⣄⠀⠚⠇⠀⠘⣧⣀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⣠⠴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⣧⠀⠀⣀⡴⣇⢈⡗⢂⠔⠠⠄⢤⠐⠢⠀⠊⠁⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⣷⢀⠾⠉⠀⠙⠢⠁⡾⠁⠀⠀⠈⠀⢠⡀⠴⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢠⠁⠀⠨⠀⠀⡀⠄⢧⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢦⣀⠄⠀⠀⠀⠀⡼⠀⢸⠆⠈⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣧⡀⣞⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠁⡿⠀⠐⠰⠚⠀⠀⢹⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢹⣠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣨⠄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡼⢹⠇⠀⠀⠀⠀⠠⠚⢘⡇⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠉⠉⡀⠚⠃⠸⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡷⠀⠀⡀⠠⢤⡀⠐⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⡀⠀⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢻⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠐⠎⠡⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣤⡴⠞⠁⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠰⢦⣤⣀⣀⣤⠴⠂⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠸⡇⡘⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡄⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⣦⡀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠈⠙⠓⠶⠶⠞⠋

⠀⠀⠀⠂⠄⠀⠀⢀⠀⣿⢀⢀⠀⠀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠸⣿⡀⠀⠀⠀⠀⠄⠀⠀⣠⠿⡔⠠⢤⣶⣔
⠀⠐⠂⠀⠀⠠⠀⡀⢱⠇⠉⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣧⠀⠅⠀⠀⠀⣀⣴⠋⠀⠈⢷⠀⢹⠀⡀
⠐⠀⠀⠀⠁⢀⣼⠛⡄⠀⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣇⠀⠁⠀⡠⢚⡁⠀⠀⠐⠀⠑⠪⠀⠠
⢀⠀⠀⠀⢰⡿⠃⠀⠘⠦⡘⢿⣿⣆⠀⠀⠀⠀⠀⢀⠀⠀⣐⣶⣶⣿⣿⣀⠂⠈⠉⠽⠧⣶⡆⣶⣚⠁⠑⠂
⠀⠀⠀⠠⠾⡶⠀⠀⠀⣤⠤⠂⠘⣿⡆⠀⠀⣀⣴⣼⣗⣴⣿⣿⡿⠿⠿⣛⣛⣛⣻⣿⣶⣤⡀⢝⠙⠁⠄⠀⠈
⠀⠄⠘⣷⣙⣁⣶⠀⡔⠫⠂⠀⠀⢸⣿⣠⣼⣿⡿⠿⣛⣩⣥⢶⣾⣛⣿⠽⠿⠿⠟⠛⢻⣿⣷⠘⠏⠀⡀⠂
⠐⠀⠀⠁⠀⣴⣝⡀⣯⠢⢀⣠⣴⣾⡿⢟⣫⣵⢶⣻⡯⠷⠛⠋⠉⠀⠀⣀⣀⣤⠤⠤⣾⣿⡏⠀⠀⠆⠱
⠘⠀⠀⠀⠀⢈⣿⠀⠃⣴⣿⠟⣫⣵⢾⣿⡿⠞⠉⠁⢀⣀⡤⠴⠒⠛⠉⢁⣀⣠⣤⣴⣿⡏⠀⠠⠼⠀⡤⠑
⠀⠀⠀⠛⠉⠁⠸⠀⠀⣿⣏⣼⢫⡿⠋⠁⢀⣠⠴⣚⡩⠅⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠹⣿⡄⣀⠗⠀⣈⠳⠐
⠀⠀⠀⠀⠀⡢⠠⡀⣀⠈⠻⣿⣿⣷⣤⣞⣫⡴⠋⠁⣾⣿⠄⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⣿⡇⢐⣀⠠⣄⠋
⠀⠀⠠⣠⡼⠀⡐⣤⠏⢶⣂⠄⠙⠻⣿⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⣿⠇⣿⢿⡇⣡⣤⡀
⠈⠀⠀⢰⡿⣼⡅⠁⠀⠀⠋⢲⠀⠀⣿⡇⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⣼⡟⠀⣿⣿⡿⣋⣽⣿
⠀⠀⠐⡿⠁⠀⠭⡉⠁⣴⣿⠈⠀⠀⢸⣿⡤⣄⡀⠀⠀⠙⢿⣶⣶⣶⡾⢟⣁⡤⠤⠔⣿⣷⡶⠟⢻⣾⠟⡡⠈
⠀⠀⠈⣱⣇⠀⠈⠓⠂⣉⣋⣡⣶⣶⣿⣟⠙⢾⠉⠉⡷⠒⣶⠒⠒⠂⠘⡁⠀⣀⡤⠞⠛⠷⢭⣳⢜⣿⡆⠑
⠀⠀⠂⣾⣣⠀⣠⣾⢿⣻⠿⠟⠋⠉⠁⠈⢳⠞⠀⣸⠃⢀⡿⠤⠤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⠠⠄
⠀⠉⠃⠀⢃⣼⣿⣟⠉⠀⠀⠀⠄⠀⣠⠖⢁⡠⠶⠿⠴⠾⠦⠤⠤⢤⣤⣴⠶⠶⠶⠶⠚⠛⠛⠛⠉⢻⣷⠈⠄
⠀⠈⠀⣴⣿⡟⠉⠹⣧⡀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣧
⠀⠂⠀⢿⣯⡀⠀⠀⠈⢻⣶⣾⣥⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠠⠐⡌⠻⣿⣦⣤⣴⡿⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⡇
⠐⡀⠀⣸⠃⠀⢍⠉⠁⠐⡀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠰⣾⠋⠀⠀⠀⠉⠒⣆⠙⡀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟

⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣰⠀⢰⠀⠀⠀⢀⠀⠶⢀⡀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⢰⡀⠀⠀⢠⡀⠀⢠
⠀⠀⡅⠉⡄⠈⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠃⢠⠞⠉⠂⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢉⠀⠠⡐⠋⠘⠃⠈⠀⠏⠀⠈⠒⢀⠀⢨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠾⠒⠲⣄⠈⠳⡀⠀⣠⡄⠀⠀⠀⠀⠀⣄⠀⠀⠉⣤⣀⡂⠐⢤⣄⠀⠀⠘⠋⠁⠘
⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⡾⠃⠀⣤⢀⠁⠀⠀⢿⡆⠘⠀⠀⠀⠀⠠⠒⠉⠀⢠⠻⠋⣉⣹⣶⠀⠙⣷⠀⠀⠋⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠐⣏⠀⠀⠀⢱⠀⠀⠀⠀⠈⢡⠃⠀⠀⠰⠃⣠⠜⠀⠀⠚⠀⠷⠀⢷⡀⠀⢠⠀⠰⠛⢐⠤⠀⠀⠀⠀⠉⠀⢸⣧⠀⢸⡇⠀⠖⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⡤⠂⡲⣘⠛⣗⣤⠘⠣⠀⠙⠀⢀⣄⠙⠃⠀⠠⡀⠀⣠⡄⣠⡏⠀⣸⠃⠀⢤⡄⣩
⠀⠀⡇⢠⠆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⠀⠘⣠⠂⣠⠟⠁⠈⢁⣈⠁⠐⢀⡆⠀⠀⠛⢁⠑⡶⠀⠀⣿⡛⠿⠿⠋⢀⣰⠏⠀⠀⣀⡸⢿
⠀⠀⡇⠉⡆⠀⠀⠀⠰⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣥⠀⠐⠃⢰⣯⠀⠀⠀⠀⠀⢀⣶⡄⣥⠀⠀⠀⠈⠣⡀⣀⠀⠀⠑⠒⠲⠚⠛⠁⠀⠤⡀⠸⣀⣈
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠦⠀⡄⠀⠀⠀⢀⠀⣀⣾⠇⠀⠛⠇⠀⠐⠿⣿⡇⢸⣇⠀⣿⢆⣠⠀⠉⣀⠴⡂⢀⠂⡄⠀⣷⠀⡜⠋⠛⠉⡸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡖⠁⠀⠀⠀⠀⣰⣧⡟⢰⠄⠀⠀⡀⠄⠠⣿⢠⡇⣿⠀⠑⠈⠉⠂⡀⠋⣤⠈⣸⡇⣧⡜⠀⠐⠶⣠⣶⣾⢷
⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠘⠀⠀⢠⡟⠁⢃⣼⡀⠀⠀⠀⠀⣸⣷⡌⢃⠘⡆⢻⣏⣀⣀⡀⠚⠛⣦⠀⣤⡈⠁⣦⣽⣦⠟⢻⡇⢘
⠀⠀⡅⠀⠀⠈⠃⠀⠀⠀⠘⠄⠀⣠⣶⡏⠀⠀⠀⠰⡄⠁⣰⣶⠚⢅⠱⢦⣀⣤⣴⡉⠏⣛⠉⠴⣣⠀⢉⠉⠀⣄⢹⠀⠘⢦⠛⡧⠘⠃⠙⠃⢴⣬⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡶⠀⢻⣿⡌⠛⠂⠀⡀⢾⠀⣀⠀⠘⠋⢼⣿⠀⣉⣤⢷⡆⢸⡍⠛⣀⠙⢆⡀⠁⠀⢿⣥⡄⠀⡀⠀⠇⠘⠀⠀⢀⠾⢋⡀⢸
⠀⠀⣯⠀⠀⠀⠀⢈⡷⠀⡴⠀⠀⣀⣤⠐⠒⠋⢤⡈⠀⡀⠉⠀⠀⠀⢻⡇⠀⣨⡼⣷⣾⠕⠊⡙⠰⠚⠉⢂⡀⠀⠀⠰⣶⡅⡀⠀⠀⠀⠀⠈⢰⡾⠃⢸
⠀⠀⠉⠀⠀⠀⠀⠈⠁⠸⢧⠄⠒⠂⢠⠀⠳⢄⠀⠹⣆⠀⠀⠀⠈⠂⢸⣇⠀⢈⠀⢻⡃⠀⣹⡍⠂⢀⡤⠚⠡⣄⠀⠘⣶⣴⡍⠆⠀⠀⠀⠀⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡼⠖⠀⠀⠀⢋⣶⡄⠓⡀⠉⠳⢦⡁⢀⠀⢸⡟⠀⠈⠀⣸⠁⡂⢹⣇⡀⠂⣠⡈⣰⠛⣀⠀⠿⣤⠀⢄⠀⠀⠀⣠⠞⠁⡄⣠
⠀⠀⡄⠀⠀⠀⠀⡾⢠⣾⠃⢲⣶⣟⠀⠈⠁⣿⠀⠀⣠⣤⣄⠙⢦⡀⢨⡗⠂⠔⠸⢷⣈⣱⡞⢋⠀⣤⠼⠈⢉⡴⢇⠀⠂⠀⠀⢸⠁⠀⣐⠁⠀⠈⠓⠹
⠀⠀⡧⠤⠔⠀⠤⢇⣼⠟⠀⣿⢿⣿⠚⣤⠀⠙⣧⡀⢀⠋⠀⠛⠲⠷⣌⡛⠛⠛⠛⠂⡉⢡⡀⣹⣶⠏⠠⢠⡾⡇⠀⢣⡾⠦⣀⠈⣦⠀⡉⠠⠤⠤⠄⣸
⠀⠀⠃⠀⠀⠀⣴⣾⠇⠀⠀⣹⢿⣿⠐⢸⡄⠀⠈⢷⡀⠻⣷⣄⡀⠀⠈⠙⠛⠧⠼⠶⠷⠾⠿⠿⠟⠓⣐⠿⡄⠈⠒⡋⠀⠞⠛⠛⡤⠟⠀⠀⠀⠀⠀⢿
⠀⠀⡆⠀⠀⠈⢻⠋⠀⣤⠀⠇⢸⣿⠀⠈⠀⠀⠀⠈⠳⣄⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚⠟⣇⠈⡖⠀⠀⣾⠀⠘⣾⠤⠀⠦⠀⠀⠀⠀⣸
⠀⠀⡇⢠⠀⠀⠇⢀⡴⠉⠀⠃⣼⠇⠀⠀⢸⡀⠀⡀⠀⠻⣆⣀⠈⠛⢿⣶⣄⡀⠀⠀⠤⠄⢀⣀⣀⡀⠀⡈⠓⠀⡀⢸⣿⣧⣀⡀⠀⠋⠀⠀⠀⢀⠀⢨
⠀⠀⡁⠘⠆⠀⣀⡌⠁⠀⠁⠀⣿⠀⠀⠄⠀⣷⠀⠹⡀⠀⠙⢾⡦⠀⠈⠻⣿⣿⣷⣤⣤⣤⣴⡾⠋⣡⡞⠃⣠⡾⠃⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⢼
⠀⠀⠟⠃⠘⠃⢸⠀⢀⣿⣠⡄⢩⣷⡄⠀⠀⠘⣧⠀⠀⡀⠀⠈⠷⡼⢆⡀⠈⠙⠷⠾⠟⠉⠁⢀⣼⡟⠀⣠⠁⠘⠃⠸⣿⣿⠏⠠⠖⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠎⠀⠈⠁⠀⠶⠾⢻⣿⢀⡄⢻⣷⠀⠀⠀⢹⣄⠀⠘⠀⠀⠀⠈⠺⢏⠂⡀⠀⠀⠀⡀⠀⢠⡿⠀⡄⢙⡂⠀⠀⠁⠈⢡⣤⡀⢀⠀⠀⠀⠞⠁⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣹⣿⣆⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠀⠉⠀⠈⠀⣈⣡⠏⠱⠀⠀⠀⣠⣌⠟⠻⢮⣧⣆⣰⠇⠀⢀⣿
⠀⠀⠇⠀⠀⠀⠠⠀⠀⣰⠊⠙⢿⣿⣿⡟⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⡏⠀⢠⠀⢠⡎⠁⢈⣅⢠⣼⠋⠙⢿⡎⢉⠉⢻
⠀⠀⠄⠀⠀⢠⠆⣠⠎⡉⠁⠀⠀⠙⢿⡇⠀⢆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠒⠋⣠⣼⠟⠀⢠⡞⠂⠺⣁⠀⠸⢧⣸⣧⡀⢀⠸⢅⣸⣇⣤
⠀⠀⠆⠀⢸⡅⠀⠹⡄⠁⠤⠀⠘⠇⣠⠀⠀⠘⢄⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠠⡾⢂⠀⠛⣷⣤⣤⣠⡄⠀⠀⠀⢤⡄⠀⠆⢸
⠀⠀⠂⠀⠃⠰⣦⡄⠈⢑⣆⣠⣤⡄⢸⠀⠀⠀⠀⢂⠀⠀⠀⠄⡀⠀⠀⠀⠀⠈⠉⠿⠿⠛⠉⠀⠀⣠⠀⣷⠈⡆⠀⠸⠁⢘⡁⢀⠀⠄⠀⠀⠉⡀⠀⢘
⠀⠀⠁⠐⠂⠄⠘⢷⠟⠛⠋⠉⠀⠀⢸⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢱⡄⠀⣦⠎⠁⠐⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢾⣧⣀⡀⣀⣄⠀⠀⠸⢂⡀⠀⠀⢮⠀⣤⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⢀⡜⠀⠀⢸⠖⢲⠆⠀⠐⠛⠁⠀⠀⠀⣦⡀⠀⡤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠉⠁⠀⢠⡆⠈⠷⠀⠀⠆⠀⡏⠑⣄⣀⢀⠀⠀⠀⠢⠀⠀⠀⣠⡞⠀⠀⠀⡞⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⡄⠀⠀⠸⠁⠀⠀⢆⠀⠐⠀⡇⠸⠟⠉⠉⠻⠷⣤⣀⠀⠀⠈⠀⠀⠀⢀⡰⢿⠄⠀⡅⠀⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡄⠀⠀⠀⠐⡀⠀⠀⣀⣴⡄⠀⡇⠀⣿⡟⠳⠦⣤⣤⡾⠛⠙⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⣁⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⢰⣿⣟⠀⢱⡄⣠⠀⠀⢹⣿⠀⢀⠀⠀⠿⣿⠀⠀⠘⠁⡇⠀⢸⡆⠘⣷⠀⠀⡀⠤⠛⠀⠓⠀⠀⠤⠤⠤⢀⡀⠀⢨
⠀⠀⣙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠁⠈⠁⠀⠦⠀⠀⠛⠀⠸⠀⠀⠂⣿⠀⠀⠀⠀⢱⠀⢸⡇⠀⢻⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠄⠀⠀⠀⢳⣄⠀⠀⠄⡇⠀⠀⢹⡀⠀⠀⠀⢸⡀⠈⣷⠀⠀⢻⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠒⣰⣤⡀⠀⠀⢸⣿⠟⠉⠀⣷⠀⠰⣿⣧⠀⠀⠀⢸⠃⠀⣹⣦⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠞⠛⠁⠙⠁⠶⠚⠛⠦⠤⠴⠿⠀⠀⠿⠗⠀⠀⠐⠚⠓⠘⠛⠹⠶⢶⡴⠆⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⡀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡓⢴⡃⣴⠞⠁⠀⠀⡁⠀⠀⠀⢀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⢳⡄⢘⠀⢠⡄
⠀⠀⠀⠀⠱⡘⠟⠈⢧⡀⠀⠀⣇⠀⠀⠀⠸⡇⠀⠀⢀⡏⠀⠀⠀⠀⣠⠞⣧⣧⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠓⠶⠦⠿⢶⣦⣽⣦⠀⠀⢀⣿⣀⣤⣟⣀⣀⣤⣴⣾⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⣷⣶⣿⠟⢛⠛⣻⡿⠋⢉⠀⠀⢀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣞⠣⠟⢿⣿⣿⣿⣧⣜⠿⠃⠀⠀⠑⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⣠⢂⠀⠃⢀⡀⠀⠄⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢹⣾⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠈⠂⣀⣀⣦⢴⠐⠀⢀⠠⠆⢀⣧⠀⣀⣨⡠⠂⢀⢤⠀⢠⠛⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣠⡴⠛⠀⠹⠴⢦⠀⢀⠟⢻⣾⣿⢸⣿⠿⠆⠀⠉⣌⠀⠈⣰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠡⣀⠀⠶⡖⠁⠈⠀⠀⣩⣿⣟⢻⣿⣶⠀⠀⠋⡜⠀⣠⢭⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠟⠓⠀⠀⠀⠰⡽⣿⣿⡿⣿⣷⡀⠀⠇⣰⠋⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢽⡳⠌⣴⣄⣴⣒⣝⣿⣿⣿⣟⣽⣿⡅⣠⡞⠁⡀⠄⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠡⣈⠙⢿⣿⢿⠟⢻⣿⣿⡹⢿⢺⡿⣁⡀⠋⠀⠂⠀⠨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠉⠠⠈⠻⡟⡙⢿⣿⣿⡘⠪⡹⢣⣽⣇⣠⠈⠐⢢⡙
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡻⠨⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠣⣶⣿⣿⣽⣷⠈⢠⣿⣿⣿⣿⡧⠂⣴⡗⠠
⠀⠀⠀⠀⠀⣠⡀⠀⣠⠄⠀⠀⢻⣁⣤⡈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⠿⠵⣉⣬⢃⡏⣼⣿⣿⣿⣿⣿⣿⠁
⡀⠀⠀⠀⠀⠄⠆⢡⠀⠀⠂⡠⠀⠹⣾⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣴⡒⠄⣠⣽⡏⣾⢺⣿⣿⣿⣻⣿⡟⡉⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡂⠀⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠐⠂⣦⢹⣤⡿⠉⣃⣟⣹⢻⣏⣼⠙⢫⡟⠀⠀⠀⠄
⠀⠀⠀⠠⠀⠀⠀⠀⢋⡅⠻⠀⠀⠀⠈⢿⣿⡏⢿⣿⡿⠛⠛⠛⢿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣏⠀⠀⢠⡉⢡⣶⣽⣹⣹⣼⢛⣽⣿⣟⠭⠀⠈
⠀⠀⠀⠀⠀⣄⠀⢀⠀⠌⢀⠧⠙⠀⠀⠸⣿⣷⠜⣿⠇⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠙⠿⣿⣿⣧⡁⠆⠡⢸⠑⣾⣿⣷⣿⣿⣟⣩⠯⢀⠚⠉⠁
⠀⠀⠀⠀⠀⠈⠀⠈⡀⡤⢦⡡⢾⠤⢶⠀⢻⣿⢹⣿⠀⠀⢠⣄⡀⠀⠈⣿⣿⠆⠀⠂⠄⠈⡙⠻⢿⣿⡆⢀⣼⣿⣿⣿⣟⣹⣿⣴⣒⣁⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠒⢤⡀⣀⠀⠀⠀⠀⢁⣀⠈⣿⣿⡧⠄⠘⡷⣏⣣⣆⢠⡿⠛⠀⢢⣶⣿⣿⣷⣴⣮⠻⣿⠻⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀
⠀⠀⠀⠀⠐⠂⠀⢈⣂⡀⣀⡠⢀⠰⢟⠛⡷⣿⠸⣷⠀⠀⠘⡯⠙⡙⢿⠿⣶⣾⣿⣿⣿⣿⣿⣿⢿⣾⢽⣿⢿⣻⣿⣿⡿⢙⣍⠹⠿⢍⠑⠆⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⣈⠿⢦⠕⠄⠀⠀⣿⡠⢿⡇⢀⡆⠺⣧⠌⠌⠛⠻⠟⠻⠿⠟⠿⡟⠿⠚⣀⣠⣿⡿⠛⠛⠛⠻⠿⠓⠄⠂⠀⠁⣀⠄⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠘⡴⠂⢠⡀⢠⠼⠋⠀⠘⢿⠿⠋⢞⣛⣧⣤⣤⢸⡦⠞⣴⡄⠒⢐⣰⠞⠛⠉⣉⡅⠀⠒⠛⠀⢀⡀⠉⡀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡴⠻⡄⠀⠀⠴⣄⠃⠰⠐⠠⠴⣿⣿⣿⣿⣿⣷⣾⣿⣿⠞⢃⢀⣴⣻⠎⠉⢀⡄⠀⠀⠀⡨⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢺⠇⠀⢨⣿⡷⣥⠀⢄⡀⣄⠙⠉⠻⣿⣿⣿⢥⡖⠃⠾⢟⠁⣀⠀⠈⠃⡈⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠳⠀⠋⢣⡀⠀⠈⠀⠀⠀⢀⠼⠓⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠉⢣⡰⠉⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡆⠀⡇⢠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⡃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⢰⠁⠈⡇⠀⠇⠀⢀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⠀⣘⡠⠴⠦⢄⣠⡔⡑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⠀⢹⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢣⡀⠀⠀⢀⡜⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⣦⢍⣒⣒⢉⡴⡁
⠀⠀⠀⠀⠀⣀⠤⢤⣠⡤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠐⠒⠒⠒⠂⠀⠒⠀⠉⠐⠂⠀⠀⠀⣀⠡
⠀⠀⠀⠀⢰⢣⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠑⠂⠤⠄⢀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠈⠀⠔⠁⠀⡀⠔⠉⠠⠄⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠃⠀⠲⠁
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠐⠒⠒⠒⠒⠒⠒⠀⠐⠀⠀⠀⠀⠒⠐⠒⠂⠒⠂⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠒⠐⠓⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠂⣤⣶⣤⢲⣶⣷⣴⣶⣡⣾⣿⣿⡏⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣰⣿⠽⠫⣶⣾⣿⣿⣿⣿⡙⣿⣷⣿⣿⣿⣇⣠⣦⣴⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢶⣶⣟⠵⣿⣥⣿⣿⣧⣿⢻⣾⣷⣿⣿⣤⣍⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⠀⡀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡉⣰⣿⢟⣼⣓⡿⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠹⣿⣿⡟⡛⣿⣿⣿⣷⣞⠢⣿⣿⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⢸⣿⣧⣿⣿⣼⠿⠻⣿⣿⣶⣿⣿⣿⢿⡿⠁⢻⣏⢩⣟⠹⣿⣟⣃⡑⢾⡍⢲⡙⣿⣧⠸⣿⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⣠⡘⢿⣷⣿⣿⣿⣿⣿⢛⣶⣿⡿⢿⣿⣿⣿⣿⠀⠐⠆⣿⣿⣶⣽⠇⠀⠉⠉⠻⣏⠐⣧⣵⣹⣦⣀⣹⣷⢿⠆
⠀⠀⠀⠀⠀⠀⠀⣴⣆⣸⣿⢟⣹⢿⣿⣷⣿⣿⣾⣷⣬⣿⣿⣿⡛⠀⠰⠚⢻⣿⣿⠃⠀⣀⣤⠀⣴⣯⣹⣿⣿⣿⣾⣿⣿⣧⣾⡐⢦⡀
⠀⠀⠀⠀⠀⠀⡶⡄⢸⣿⣿⣿⢹⣯⣿⣿⡿⢿⣿⣿⣯⣍⠹⣿⣷⡄⠈⢙⡿⠟⣉⣉⣁⣻⠿⠿⣌⣿⡿⣿⠝⢭⣭⣹⣿⣫⡿⣦⣨⡧
⠀⠀⠀⠀⠀⢠⡿⠟⣶⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⠀⠎⢠⣾⡋⣿⣿⣿⣶⣶⣬⣬⣋⣩⣴⣾⣷⢽⣿⢯⣷⡾⠿⠇
⠀⠀⠀⠀⠀⠈⢹⣷⣾⣿⣿⣿⠿⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠆⠐⠌⢋⣡⣤⣬⣝⢿⣿⣿⣿⣿⣿⣭⣿⠿⣿⣶⣟⡟⣧⠆⡙
⠀⠀⠀⠀⢠⡴⣷⣤⣽⣿⣿⠁⠀⠀⣿⡆⠈⣿⡿⠛⢛⠟⢻⣿⡆⣀⠃⡀⠒⣾⣿⣿⣿⣿⣷⣿⡿⣿⣟⠠⢓⣭⣀⣠⣄⠫⣘⣿⣿⡟
⠀⠀⠀⠀⠈⢁⣴⣯⣽⣿⣿⣦⣠⢲⣿⣷⣶⡏⣰⣷⣾⡷⣆⠘⢄⣭⢺⣅⢠⣿⣿⣛⣿⡿⡿⢿⣿⣿⣿⠗⣿⠻⣟⠙⠛⣷⣿⢿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣏⡻⢷⡹⠿⣠⣿⡿⢋⣰⣿⢃⡈⠱⢿⣿⣼⣿⠏⠛⠋⠄⠀⢬⣿⣏⣿⣿⢿⠷⣼⣷⣟⠿⣽⣿⠟
⠀⠀⠀⠀⠀⢂⠘⢿⣿⣿⣿⣿⣿⣷⣾⣷⡞⣿⣿⣇⣙⣫⣥⣀⣱⣤⡌⡛⢹⣿⣤⠀⢠⡶⠖⢺⣿⣿⢨⣿⣿⣆⣹⣾⣿⣷⡏⣱⣀⣤
⠀⠀⠀⠀⠀⠘⢀⠈⢿⡟⣟⡙⠛⢟⣻⣿⣇⠻⣿⣟⣿⣤⣸⡟⣽⣿⣧⣇⣾⣿⢿⣶⣿⣵⣄⢉⣽⣿⣦⣿⡟⣿⡻⣭⢿⣷⣿⢾⣿⣉⣀⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣷⣌⣻⣿⣿⣷⣬⣅⠙⢻⣿⣿⣿⠇⣿⣙⣿⣿⣦⡈⠙⠹⣿⣿⣿⡌⢿⣁⠛⠻⣧⠘⠛⣿⣿⡀⠈⠝⣿⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣉⠙⢿⣿⣿⠿⢿⣿⣿⣿⣶⣀⣈⠛⠁⣸⣿⠿⠿⣿⣷⡌⣻⣷⣜⣿⣿⠹⣾⡟⢛⠁⢛⠟⠹⢿⣿⣷⠾⢿⣿⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⣷⣎⣹⣹⣷⣹⣾⣿⣿⣿⣿⣿⣷⡅⡟⠀⢠⣾⣿⣿⣧⢻⣄⡿⢿⣿⣶⡟⢹⡟⣉⡽⢳⣿⣿⣿⡟⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⡿⣁⢻⣿⢻⣿⣿⣿⣿⣿⡧⣽⠃⣧⡀⠈⣿⠋⠙⠟⡀⠘⠟⠂⣼⡟⠏⣿⢿⠿⢃⣙⢡⢷⡼⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣃⢿⣬⣿⣾⡿⠿⣿⣿⣿⠇⢘⠆⢿⣿⣟⠋⠀⠀⢀⣿⣷⡆⠀⣿⡉⢇⣴⢻⡴⠛⠉⣧⡾⣿⣬⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣶⣿⣿⣿⣷⣶⡿⠟⠋⢀⣍⣸⡆⠡⡻⣧⣠⠀⠿⠿⠟⠋⠀⣻⡵⢛⣷⣿⠛⠾⠛⠟⣧⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣶⣿⠉⠀⣴⣶⠏⢹⣿⡇⠘⠿⣮⣿⣧⣀⢀⣾⣿⣶⣿⣷⠺⣷⣿⣟⡛⠓⢶⣿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠹⣏⣩⡾⠟⣛⣉⠁⣠⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠏⣩⣶⣬⠙⣮⣛⡻⢦⣟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣷⣛⣛⣿⣆⠙⠛⢻⣷⣞⣿⣇⢀⣄⢸⣿⣿⠝⣿⣿⣿⢶⡶⠟⢿⡿⣇⠿⣻⡛⢦⣹⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢻⣿⡏⢹⡛⠛⠃⢠⣿⡿⣿⣹⡏⢻⡟⢻⣟⣿⣀⣿⠙⢿⣾⠃⠀⠀⠀⠀⠈⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⣼⡿⣾⡇⠀⢰⡄⢸⣇⣠⠙⣯⡾⢿⣿⣟⣿⣯⣯⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⣻⠿⣀⣙⣷⣄⣠⣿⠖⣸⣷⣄⡸⢇⣄⠛⠻⣿⣭⡍⣿⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⣈⣷⣾⣿⡅⠀⠛⢹⡿⠸⠛⣿⣿⠀⠘⠟⣴⣾⣿⣿⣿⢁⣷⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢿⣿⣿⡟⣫⣵⣀⣶⡟⠁⢤⣯⡙⠟⣠⣞⢶⣟⠻⣿⣿⡇⣀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⠉⠻⠛⠙⠟⠛⢋⣠⣆⠀⢀⣡⣾⣿⡛⢱⣤⡿⣧⠀⣿⣷⣾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠆⠟⣸⠟⣉⠷⠛⡼⠿⣿⣷⣽⣿⡿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣗⣾⢳⣄⣿⢿⣿⢿⣟⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢻⡟⠸⣿⣼⣯⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣵⠁⠈⢹⣿⡷⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⣄⠲⠻⢷⣿⢧⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣶⣋⠙⠂⠰⠾⠂

⠀⠀⠀⠀⠴⢠⣼⣿⠿⢛⣽⣿⣿⠟⣿⣿⡿⣿⣿⡟⠛⠉⠉⠉⠉⠉⠉⠀⢈⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⡛⣿⣿⣷⣤⣁⠛⠿⠤
⠀⠀⠀⠀⣦⣴⡶⠒⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣼⣿⣯⣿⣿⣿⣿⣌⣛⠻⠟⣶⣶⣤
⠀⠀⠀⠀⣀⣠⡴⠋⣽⣿⣿⣿⣟⣻⣿⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣮⡛⠳⢶⣶⠖
⠀⠀⠀⠈⠉⣁⠀⢺⣿⣏⠻⣿⡙⢿⣿⣻⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣠⣤⣿⣿⣿⡿⣿⣿⣿⣏⣿⡿⢻⣿⣿⣿⣛⣿⣿⣿⣷⡦⣬⡤
⠀⠀⠀⠰⠟⢣⣶⡚⠿⣿⡆⠈⠓⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⡿⠁⠀⣴⣯⡽⢿⣿⣯⣿⣿⣿⡿⣷⣗⡀
⠀⠀⠀⠀⢠⢠⣞⠻⢦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⣀⣀⣿⣿⣿⣿⡟⠀⠀⠈⠋⢁⣴⣿⣿⣶⣿⣯⣿⣷⡌⠋⡈
⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠘⣉⣩⣾⢻⣿⣆⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣹⣾⡿⢉⣾⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⣀⠀⠉⠉⢁⡀⠀⠀⠀⢀⣀⣀⣤⣤⣲⣿⣿⣿⣽⣿⣿⣿⣿⢳⡄⠙⠻⠛
⠀⠀⠀⠀⣠⠄⣩⢴⣽⣿⠿⢡⣿⢿⣿⣿⣿⡇⠁⠀⠀⠀⠉⢀⡀⠀⠘⠃⠀⠀⠈⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⣶⣠⣀
⠀⠀⠀⠀⣤⣾⡿⠟⠋⢡⡖⣿⣿⣿⣿⣿⣿⣧⢃⠀⠀⠖⡀⠻⠿⠦⠄⠰⠆⠀⠰⣸⣿⣿⣿⣽⣿⣿⣿⣭⣿⣿⣿⢿⣿⣿⣷⡈⠻⡶
⠀⠀⠀⠀⠉⢁⣴⣿⡾⢂⣺⣿⣿⣾⣿⣿⣷⣾⣧⣠⡀⠠⠇⡃⢲⢰⡎⠃⠀⢀⣵⣿⣟⣹⣿⣿⣿⢻⣿⣏⣿⣿⣿⣆⢭⣛⡛⠿⠦
⠀⠀⠀⠀⠚⠋⠛⢋⣴⣿⣿⣯⣿⣿⣽⣿⢿⣿⣿⣿⢻⣶⣤⣥⣍⣀⣤⣴⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣉⣉⠛⠗
⠀⠀⠀⠀⣠⢴⣎⣻⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⠟⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⢻⣿⣿⣿⠿⣿⣿⣿⢦⣿⣧⡈⣉⣡⡌⠛⠷⡄
⠀⠀⠀⠀⣺⣯⣿⠟⣋⣼⣿⣿⣿⣻⣿⣿⠋⠁⠀⠀⠀⠀⠈⣿⣽⣿⠁⠀⠀⠀⠀⠉⢿⣿⣷⢿⣿⣿⡯⣭⣽⣿⣿⣿⣦⣭⣈⣛⣢
⠀⠀⠀⠰⠊⢉⣀⣾⡿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⠇⢁⠀⠸⣿⣿⣿⣝⠷⠷⣟
⠀⠀⠀⠈⣱⡾⠛⣩⣾⣿⣿⣿⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣡⣀⣸⣄⣀⣈⣿⢿⣿⣇⣠⣍⣀
⠀⠀⠀⢀⣥⣴⣾⡟⠉⠓⣩⣾⣿⣿⣿⠏⠳⠤⣀⡀⠀⠀⠀⠈⣿⣿⣿⡄⠀⢀⡠⠴⠋⢻⡭⠭⡇⠀⠀⢸⠁⠀⠀⣿⠆⠛⢿⣿⣻⡆
⠀⠀⠀⢠⣴⣶⢶⡶⠂⣶⣿⣼⣿⣿⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣽⡿⠃⠀⠀⠀⠀⠀⠀⣿⡀⡇⠀⠀⢸⠀⠀⠀⣿⣗⡾⢶⣬⣉⠃
⠀⠀⠀⠰⠟⠋⣀⡴⣿⣭⣉⡉⠛⠻⢿⡀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡇⠀⠀⢸⠀⠀⠀⣿⣿⣿⣬⡙⠻⠿
⠀⠀⠀⠀⠶⣼⣿⣻⣿⠿⠿⠿⢿⣶⣼⠳⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣶⡇⠀⠀⢸⠀⠀⠀⣿⣿⣿⡾⣿⣢⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⡀⢀⣼⣿⠁⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠹⣟⠃⠀⠀⠸⠦⠐⠐⠉⠉⠛⠛⠻⠶
⠀⠀⠀⠀⢴⠶⠖⠓⢂⣀⣠⣽⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⡀⠀⠀⠀⠤⢀⣀
⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣶⣤⣤⣄⣉⣉⠐⠒⠒
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣶⡶⣯⣽⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢿⠿⠿⡿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡛⢋⢻⣛⡚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠈

⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢲⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿
⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣴⣿⣿⣷⣾⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣼⠟⢒⡆⠀⠀⠀⠀⣀⣀⣄⣀⣤⣾⡷⢿⣿⣿⡿⠟⠉⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣄
⡟⠀⣿⣵⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣄⣨⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⢿⡿⣷⡀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣟⠛⠛⠛⢙⡃⠀⠀⢁⣿⣿⣿⣶⣶⠶⠆
⠀⢠⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣟⠁
⣴⡾⡗⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀
⣽⠟⢿⣶⡆⠀⠀⠀⠀⠀⠀⢸⣟⣹⣿⣟⠁⠛⣿⡏⠉⠻⣿⣿⣿⣧⣀⡴⢾⣿⣷⣴⣾⢿⡿⣿⣿⣿⡿⠛⠹⢿⣟⢾⣿⣿⡇⠀⠀⠀⠀⠀⢦⡻⠄
⡟⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣾⣽⣶⣤⣭⣳⣠⣼⠺⣿⡟⣹⣿⡦⣴⣿⣴⠿⠇⣯⣿⣿⣫⣯⣤⠠⣤⣶⣛⡮⣿⡻⠀⠀⠀⠀⠀⠀⢾⣷⡀
⠤⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⢠⣽⣿⣿⡿⣏⣾⡟⢿⣧⣿⣻⣾⡀⢈⣛⢿⣿⣿⣿⣿⠿⢫⣙⢿⣿⡿⢛⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄
⡿⠂⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⣺⡿⢧⣌⢁⡀⠀⢿⢿⣿⣿⣶⣾⣿⣿⣟⡍⣤⣴⣿⣿⢛⣅⣀⣿⣧⣆⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠓⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡽⠧⢥⠡⣟⢢⣙⣿⣿⣿⣿⡿⣿⣿⣿⠿⠯⢽⣿⣿⣿⣿⣿⣈⣮⣿⠵⠼⣿⠵⠶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣌⣸⣶⣠⣿⡶⠿⣿⠿⠛⢛⣉⡉⢰⣿⣿⣿⣿⣿⡷⠀⠀⠙⠻⠿⠷⣷⣿⣾⣮⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣿⣿⡿⢀⣴⣇⠀⠀⠀⠀⢙⣿⣿⣋⣉⣁⣸⣟⡏⠀⠘⣛⡏⠀⢀⣉⣭⣿⣿⣿⣿⣿⣶⣄⢠⣀⣈⣿⣿⣻⣿⡿⣿⣾⣿⣿⠓
⢸⣿⣿⠇⣾⣿⡿⠀⠀⠀⠀⠀⠉⠛⢿⣟⠻⣿⣷⣶⡶⣶⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠋⠀⣭⡉⠉⠉⢁⣘⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀
⣾⣿⣿⣸⣿⣿⠇⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⢿⣿⣷⣗⣷⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣤⣤⣤⣤⣤⡿⣿⣿⠋⠟⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⣿⢿⣯⢹⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⡿⠿⣿⡟⣹⣶⣿⠟⠁⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⣿⠀⡙⢾⣿⠟⣿⣿⠁⡘⣿⢿⠋⣼⣯⣴⣷⡟⠩⣿⣿⣿⠀⠐⠋⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢶⡦⠀⠀⣠⠀⣿⠀⣀⣼⣿⣿⣿⣿⣾⡇⢹⠘⡀⣸⣽⣿⣿⣿⡿⠋⢹⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠤⠀⠻⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣱⣿⣿⣿⣿⣿⠄⠀⢸⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⣶⣿⡄⠈⢹⣿⣿⣿⡿⣿⣿⣿⠀⢿⣿⣿⠟⠉⠃⠀⠀⣸⣿⠈⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿
⣿⣿⣿⣿⡇⢀⣴⣦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠻⡿⠃⠀⠘⣿⣿⣿⡇⠘⣿⣿⣶⣾⡿⠁⠀⠀⢀⠀⠀⣻⡿⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟
⣿⣿⣿⣿⣧⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⣿⣿⣿⡇⠀⣿⢿⣿⠏⣹⣷⣷⡞⠁⠀⠀⠿⠁⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⣿⡇⠀⣿⡇⠁⠀⠹⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠉⠉⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠾⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠀⠔⢂⣈⡭⠥⠤⢤⣀⡐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡷⠋⠀⠀⣀⣤⠴⠄⠒⠋⠉⠁⠀⠀⡄⠀⠀⢉⠛⠆⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⡴⠖⠒⠉⣁⣀⣀⣤⣴⣦⣾⣴⣿⣿⣿⣷⣷⠟⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠯⢱⣤⠐⢠⡉⢹⣿⠟⠉⠉⠀⠉⠉⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣷⠂⠀⠀⡜⠁⠀⣀⠤⠴⠤⢄⠀⠀⠒⢓⣛⣒⣒⣚⣛⡒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣒⣸⡆⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠛⠋⡩⡭⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣨⢿⠞⢫⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠰⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡿⠀⢀⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⡄⠀⠀⠀⠀⢀⡾⠀⢰⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⡿⠟⠿⠷⠷⠼⢼⠟⠁⠈⢨⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠂⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠁⠀⠀⠀⡈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠸⠀⠀⢠⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⢸⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢆⠘⡀⢸⠀⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠱⠈⢆⠡⣨⣄⣇⡀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⡄⢆⠈⢂⠁⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⡠⢂⠕⢈⡌⢂⠔⡀⠀⠀⠀⡐⣒⠠⡀⠀⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⢊⠔⢁⠔⡱⠋⡦⠊⠀⠀⠀⠀⠈⠣⠤⠇⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⡠⠁⢠⠊⡜⠀⡘⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠂⠰⠁⢠⠁⡜⠀⢠⠀⠰⡁⢈⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠤⠤⠤⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠆⢠⠃⠀⠆⢰⠀⠀⠆⠀⢡⠁⠸⠀⠀⠀⠀⡠⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠀⡀⠀⠘⠀⠆⠀⢠⠀⡈⠈⠀⡄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⢠⠀⠀⡅⢀⠃⠀⡄⢰⠀⠀⡄⠀⠁⠃⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⡈⠀⢀⠀⢸⠀⢀⠀⠨⠀⠀⠁⢀⠀⠂⠀⡆⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⢸⠀⡀⠀⠰⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠀⡇⠀⢸⠀⢸⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⡇⠀⢸⠀⠀⠀⠃⠀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⠀⢠⠀⠆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⠤⠼⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⡿⠉⠈⠢⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠒⢤⡀⢸⡁⠛⠀⢀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠉⠋⠀⠀⠀⠀⠀⠊⠂⠉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠐⠄⠚⠒⠔⠰⣶⣶⣶⣶⣶⣾⣷⣦⡀⠀⠀⡆⣀⣸⣿⣿⣛⣏⣻⣿⣿⠆
⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠻⣿⣿⣿⣿⣿⣿⣿⠟⠂⠐⢿⠛⠻⢿⣷⣬⣦⡟⣿⠃
⠀⠀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢋⣠⠆⠀⠀⠀⢡⠀⠀⠈⠙⠛⠻⠿⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢁⠂⢘⣃⠀⠀⢘⠀⠀⠀⠀⠤⣦⣷⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠉⠀⠀⠈⡩⠂⠈⢢⡈⠀⢿⢷⣶⣶⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠀⠒⠁⠀⠀⠀⠀⠑⣠⣿⣿⣿⣿⡿⠣⠀⢰⣤⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⢛⠟⡟⠁⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠘⡂⠀⠀⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⢀⡀⠅⠊⠉⠀⠰⠗⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⠀⠤⠈⠑⠒⠒⠦⢆⡀⠘⢂⡀⣤⠈⠫⡒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣆⠀⢀⠀⢈⣡⣴⡴⠂⢀⣠⡅⣈⣳⣀⠉⠀⠈⠐⠐⢆⠀⠲⠿⢦
⠀⠀⠀⠀⠀⠈⢧⡃⣿⢂⣡⣶⠾⢁⡥⣄⠀⠈⠀⠀⠀⠈⢥⠀⠒⠠⡄⠈⠺⣆⠐⠀⠨⣷⡇
⠀⠀⠀⠀⠀⡸⠂⢻⡿⢻⢋⣀⡠⠁⠒⠐⠆⠉⠀⠀⠀⠀⠈⢣⡆⣀⣧⠐⠂⢼⠙⣦⠀⡼⣇⡰⣆
⠀⠀⢸⡀⢠⠀⡸⢟⡷⣟⢩⣀⣀⣠⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠴⢼⣄⢹⡁⡄⣿⣧⡟
⠀⠀⡄⢧⣊⢲⡟⡿⣼⠟⠉⠑⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠊⠦⣘⡁⠻⢷⣿⣸⣿⢠⠄
⠀⢣⠰⠞⣧⣟⡽⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢤⡀⣿⠹⣿⢲⡂
⠀⠈⣷⡀⢸⣿⡡⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣙⣿⡇⣿⣔⠇
⢶⡀⣏⢿⣾⣿⣼⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⢹⡟⣿⣿⠅
⠀⢻⣸⡎⣿⣿⠋⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⢾⣿⣿⠏
⠀⠈⣿⣧⣿⣿⢸⠟⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠈⠫⣼⣿⣿⡄
⠠⣿⡼⣧⣿⣿⡅⠀⣻⣟⡆⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡶⠷⣾⣿⡇⣷
⠀⢺⣿⡹⣿⣿⣧⠀⢊⣿⣷⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡿⢈⣿⣿⡇⡇⠀⠄
⠀⠀⠩⣾⠘⣿⣿⣧⠘⣿⡏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣽⡗⣾⣿⣿⣷⠁⠈
⠀⠀⠀⠙⣧⣿⣿⣿⣷⣜⣾⣿⣭⣶⣼⡆⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⣰⣶⢽⡟⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣯⣄⣻⣺⣿⣿⣦⠀⠀⠀⠀⠈⣻⠻⠾⠷⢧⣧⣯⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠙⢻⠿⢄⣀⢹⣿⣋⡉⠉⢉⠉⠙⠛⠻⣥⠋⢁⡔⢺⣓⣰⣿⣿⣿⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢿⣶⡞⣛⣶⣤⡔⣀⡤⣷⡺⠛⠉⠉⢉⣉⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠻⡟⠉⠝⠉⠂⠨⠃⠀⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣾⠟⣀⣀⣀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⢠⣄⡀⠀⣼⣿⠀⠀⠀⢀⣤⣤⣄⣽⠁⢈⣛⡋⠁⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣠⣤⡦⠈⢿⣿⣦⠟⠃⢀⣀⣀⡏⠀⠀⠀⠙⣆⠘⠿⠿⣦⡀⠀⣿⠟⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣦⣶⡿⢟⣋⣤⣤⣀⡀⢹⡀⠰⠿⠟⠋⢱⡄⠀⠀⠀⢸⡌⣳⣞⡉⠉⢻⡁⢠⡄⠀⣴⣿⠁⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⢀⣽⠟⠉⠉⠉⢉⠙⠛⠿⣦⣤⣀⠀⢾⣿⠀⠀⠀⣸⠿⣿⣿⡿⠀⣼⠃⠀⠙⢶⠟⠃⠀⠀⣾⡿⢀⡀
⠀⠀⢲⣦⡀⠀⢀⣾⣿⣿⠏⠀⠀⢸⠇⢠⣤⣤⣀⣻⢀⡴⠚⠓⠪⠙⢿⣮⡛⠀⠀⣰⠟⠀⣙⠛⢁⣼⣧⡤⣤⣤⠈⢠⣶⣦⣄⣿⠃⠘⣿⠀⠀⣀⣀
⠀⠀⠀⠙⢧⠀⢾⠿⠛⠁⠀⠀⠀⢸⣇⠀⠉⠛⠛⣻⢺⠀⠻⠟⢻⣦⡀⠹⣿⣦⣴⠃⠀⠘⢻⣷⠟⠁⣴⡇⠀⣈⣷⣦⠎⠉⠀⠘⠀⣀⠜⠚⢿⣿⡿⠟
⠀⠀⠀⠀⡆⢀⣤⣤⣤⠄⠀⣠⣾⡿⠉⠳⢦⣴⠞⠁⠘⣷⡀⠀⠘⢿⡇⠀⠸⣿⣇⢀⣠⣾⠟⣁⢸⣾⠟⠀⠀⣿⣿⣿⡇⣠⡴⢎⣁⢠⡖
⠲⣿⣿⡶⢷⡛⠿⠛⠁⠀⠠⠿⠛⠁⣠⡞⠉⠉⠉⠂⠀⠘⣷⣀⣠⣤⣄⡀⠀⢿⣿⣿⡿⠁⣀⣻⣆⠀⣤⣶⣄⠘⠛⢋⡞⠁⠀⢈⣽⣯⣄
⠀⠀⠀⠀⠈⠙⠶⠶⣶⣶⠶⠶⠶⣴⣿⠀⠻⢶⣤⡄⠀⣰⡿⠋⢀⣄⠀⠉⢧⣸⣿⣿⢃⣪⣷⡍⢻⡄⠻⠿⠏⠀⢀⡼⠁⣄⠀⠸⣿⣿⡟
⠀⠀⠀⣠⣶⣾⣶⣤⢮⣤⣤⡀⠀⢀⠹⣧⡀⠀⢰⠀⢠⡿⠀⠀⢸⣿⡆⠀⢸⢻⣿⣿⠀⣹⠛⠃⢸⡇⣀⣀⣤⠶⠋⠁⢸⣿⣆⡤⠈⠉
⠀⠀⠀⠉⠙⠉⠁⣴⣶⣿⠙⠋⠀⣿⠇⠈⠙⢻⠾⠷⢾⣿⡀⠀⠀⠙⠳⠀⠀⣾⣿⣿⠀⠛⣠⡶⠟⠛⠛⠛⠲⠦⣄⡀⠀⠛⢿⣃⠀⠀⠀⣿⣿⡧
⠀⠀⠀⠀⢀⣀⢀⡹⠿⠟⠲⣦⣄⣋⣴⡾⠀⠸⣷⢀⣤⠌⠻⣦⣄⣀⣀⣠⣾⣿⣿⣿⣶⡾⠉⠀⠀⠠⣿⣿⠇⢀⣠⣭⣭⣁⠀⠉⠁⠀⠀⠐⠙⠁⢠⣦⣦
⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠨⡍⠉⢰⣿⣶⠱⠛⠁⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢙⢣⡿⠋⠀⠀⠀⠈⠻⣦⣄⣀⣀⣠⣮⣀⠘⠟⠏
⠀⣤⣤⣸⢿⣿⣾⣿⡿⠀⣀⡴⠶⠿⠶⢤⣭⣥⠴⠷⠦⠤⣤⣤⣤⣀⠀⠘⣿⣿⣿⣿⡿⠷⠶⠤⠤⠖⢡⡿⠁⠀⣀⠀⠀⣰⣾⣶⠀⠉⠁⠀⠀⠀⣙
⠀⠀⠉⠉⢩⣛⣋⣤⡶⣾⠋⣠⠀⠀⠀⣴⠞⠉⠉⣿⣆⠀⠀⠀⠉⠻⣷⣶⣿⣿⣿⣿⠇⠀⠀⠀⢀⣴⡟⠁⠀⢾⣿⣿⠀⢘⠛⠉⠀⠀⠀⠰⣌⣧⣟⣤
⠀⠀⠀⢠⣿⣧⠀⠀⣠⣼⣞⠋⠀⠀⢰⡇⠀⠀⣰⣾⣿⣍⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣀⣤⣶⣿⣋⣀⠀⢀⣨⠟⠀⣐⣢⣿⠤⡀⠀⠀⠓⣹⢿⡻⠆⠁
⠀⠀⠀⢸⣿⡟⠀⠐⢿⣿⣿⠀⠀⠀⠸⣇⠀⠸⣿⣿⣿⣿⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠿⣯⣀⠀⠐⠥⢻⢿⣓⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁⠹⣦⡠⠒⠓⠻⣷⣤⣽⣿⣹⣯⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠋⠀⣰⣿⣶⠀⠀⢠⡙⡳⣦⡜⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⣶⡄⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠘⠛⠋⠀⡪⣿⣿⡳⠈⢷⠀⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⣼⣿⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⣿⣿⣿⢠⣿⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡾⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘

⠀⠀⠀⠀⣀⣀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠘⡄⠮⠐⠥⠣⣅⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠂⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠚⠉⡝⠁⢀⠀⠀⠀⠈⠷⢨⠇⠀⠀⠀⠀⠸⣴⠀⠀⠀⠀⠀⠑⡄⢤⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇
⠀⠈⣀⡇⠐⠀⠀⠀⠐⠂⠘⠦⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦
⠀⠸⣐⣛⢄⠀⠀⠀⠀⢠⠮⣤⠆⠀⠀⠀⠀⠉⠙⣇⠀⠀⠀⠀⠠⠽⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢘⠿⠒⠓⣘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠉⠻⡧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠸⡌⠉
⠀⠀⠀⠀⠈⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⢛⠳⣦⡞⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⣀⣤⢶⠂⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣆⣘⣗⡶⠄
⠀⣠⠴⢼⣶⠞⠛⠛⠷⣿⠚⠛⣦⠀⠀⠀⢰⡶⢶⣾⠟⡛⠛⠶⣾⣄⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⢐⡷⣤⣟⢻⣆⣏⡽⢇⣦
⠀⢧⣅⣾⠃⠈⠀⠀⢀⠘⣷⣴⠋⠀⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠸⣯⡽⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠙⠯⠼⣿⠛⢻⡶⠟⣺⠗
⠀⣰⠛⢿⡄⠀⡀⡀⠈⢠⡟⠩⣳⠀⠀⢀⣴⣋⣿⡄⠀⠀⠀⠀⣰⡟⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠟⣻⡷⣿⡻⣭⣿⣶⠆
⠀⠙⢦⠶⣿⡶⣦⣤⢶⡻⣟⠛⠋⠀⠀⠀⠀⠀⢹⡟⢶⣦⣶⢾⡟⠚⠛⠃⠀⠀⠀⠻⣿⠿⢿⠿⡿⠟⠀⠀⠀⠀⠈⢁⡹⢦⡧⣸⡵⡧⠀⠛
⠀⠀⠀⠀⢷⣤⡼⠛⠧⡷⠏⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠘⠉⠿⠂⠉

⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢘⠀⠈⣲⡃⠀⢘⡀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢣⣠⠔⠙⠁⠀⠀⠀⠀⠀⠀⠀⡤⢺⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⢦⣈⢝⡺⠂
⠀⡔⠛⠛⡶⠊⠉⠉⠑⢾⠁⠈⢱⠀⠀⠀⠸⡂⢚⡟⠈⠉⠉⠑⢶⠤⠤⣀⠀⠀⠀⢠⠊⢀⡇⠈⡆⠀⠀⠀⠀⣀⠟⢤⢏⠢⣄⡇⡌⢃⢲
⠀⠣⣀⣼⠀⠀⠀⠀⠀⠀⡷⠶⡁⠀⠀⠀⠀⡸⠞⠀⠀⠀⠀⠀⠀⣃⠔⠉⠀⠀⢀⡇⠀⠀⠁⠀⠘⡄⠀⠀⠀⠙⢙⠧⢀⢽⠊⠙⡬⣑⣮⠗
⠀⡘⠁⠘⣄⠀⠀⠀⠀⣠⡃⠀⣈⠀⠀⠠⠮⢀⣸⡄⠀⠀⠀⠀⡠⠋⢢⠀⠀⠀⠸⡇⠀⠐⠇⠀⠀⢸⠀⠀⠀⠀⢑⣪⠒⡙⡵⠞⡑⣤⣝⢪⠓
⠀⠈⠒⠒⡏⠑⠒⡶⠊⠉⢏⠈⠁⠀⠀⠀⠀⠀⠠⠈⣑⢶⡒⠊⠇⠈⠈⠁⠀⠀⠀⠑⠤⠔⢻⠢⠤⠊⠀⠀⠀⠀⠀⢁⠹⢢⠧⣜⠬⠦⠀⠛
⠀⠀⠀⠀⠳⠤⠔⠉⠢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⣛⣻⣿⢟⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡝⠟⢿⣿⣿
⣿⣿⢿⠿⣿⡿⣇⣻⢿⡟⣻⣛⢿⣿⣿⣿⡿⡿⣿⠧⠿⣯⣙⢷⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⢳⣗⣿⣿⣿⣿⣿⣿⢻⣿⢩⢵⣮⢭⣎⢱⠿⣿⣿
⣿⢵⣿⡷⣴⣿⣿⣿⣿⣮⢿⣿⢧⣿⣿⣿⣷⡻⡟⣴⣿⣿⣿⣿⣆⣭⣭⢛⣿⣿⣿⢧⣿⣿⣾⣿⣜⣿⣿⣿⣿⣫⣚⢢⣮⡓⣎⡝⣟⡫⢇⢻⣿
⣿⡶⣛⡑⣿⣿⣿⣿⣿⣿⢤⣤⡻⣿⣿⣿⡿⣫⡼⣿⣿⣿⣿⣿⣿⡘⣵⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⡫⣞⢿⡖⡿⡟⡶⣿⣋⢿⢻
⣿⡷⣿⣿⠝⢿⣿⣿⡿⣋⠻⠿⣏⣿⣿⣿⣬⣽⡇⣻⢿⣿⣿⡿⢫⣿⡮⢿⣿⣿⣿⡻⣿⡿⠙⢿⣿⢇⣿⣿⣿⣿⣯⣹⡛⢽⣾⡞⣽⣯⣮⢓⣿
⣿⣿⣾⣶⢾⣿⣶⣰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡯⠿⣻⣤⣲⡿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⢻⣶⣿⣿⣿⣿⣿⣿⣏⣓⠣⣶⣌⣾⣾⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⠒⠒⠂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠉⠐⠒⠂⠀⢴⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠒⢛⠀⠈⠑⢦⣄⣀⠀⣤⠶⢿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⢀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡦⣌⡐⠈⠲⢦⣤⣤⣠⣤⣴⡫⠥⠒⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠀⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣾⡆⠀⢀⣴⣤⠀⢀⣶⡄⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠘⣿⠟⠁⠈⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⢰⠇⢷⡀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠠⠔⠉⠐⠒⠚⡆⠘⡇⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠛⠒⣤⣀⡀⠀⠀⠀⠀⣳⣶⠗⠚⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⢯⠀⠰⢆⠀⢸⡈⠉⠘⡟⠉⠻⠀⢰⡀⠀⠀⣰⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⢆⡡⠀⠋⡀⠀⡗⢲⠒⣇⠀⠀⠀⠉⠻⠛⠈⠀⠀⠀⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⠳⠀⠈⠷⠀⠀⡇⠀⡇⠀⡄⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄
⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⣦⡀⠀⠀⢸⡁⠀⡇⠀⠇⢿⣤⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠁⠹⣄⣀⣼⡇⠠⡇⠀⠷⣤⣀⣉⡉⠙⠻⠋⠁⠀⠀⠀⡰
⠀⠎⠀⠀⠀⠀⠀⠠⠆⠀⢠⡶⠋⠁⠀⠀⠀⠀⢰⡄⠀⠈⠉⠉⠀⠘⠀⢀⣀⣀⣤⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣴⠋
⠀⠀⠙⠶⣤⣄⣀⣀⣤⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣠⠾⠿⠻⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠖⠛⠁⠀⠀⠀⠃⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠦⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⢤⡀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣠⡴⠶⠛⠛⠛⠓⠲⢤⡀⠀⠀⠀⣠⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⠀⠀⠀⠀⠈⠀⣠⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠑⣄⡐⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢦⠀⢸⠀⣠⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢸⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢸⠀⠘⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢖⠄⠀⡅⠀⣘⡀⠀⠇⢀⢐⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣴⠞⠉⠈⠉⠑⣶⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠘⢆⡀⠀⠀⡠⠂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠣⡆⡬⠉⠉⠤⠺⡀
⠀⠀⠀⠀⠀⢀⡤⠤⣄⡤⠤⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⡀⠤⠤⠐⠒⠒⠀⠀⠐⠒⠒⠈⠉⠈⠁⠒⠀⠀⠀⠀⣀⢡
⠀⠀⠀⠀⠀⡏⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢆
⠀⠀⠀⠀⢰⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠆
⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠁⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⢀⢤⠁⠀⠀⠀⣠⠂⠈⠉⠐⠒⠀⠀⠄⠇⠀⠀⢀⠀⠀⣀⠀⠒⢹
⠀⠀⠀⡄⠀⠂⠁⠀⡠⠐⠁⠀⠒⠁⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠑⠀⠀⢸
⠀⠀⠀⡀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠈⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠢
⠀⠀⠀⠠⠤⠴⠄⠤⠦⠤⠤⠤⠀⠠⠀⠀⠀⠀⠠⠆⠤⠧⠤⠄⠤⠰⠤⠴⠄⠤⠀⠀⠀⠀⠤⠄⠰⠤⠶⠤⠤⠤⠤⠤⠤⠤⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣸⣏⣙⣿⣩⣋⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑
⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠰⢶⠱⣾⡄⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⣆⠀⠠⡄⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⣦⡈⡵⡞⣧⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⢸⠛⠀⠘⠃⠸⠛⣧⠀⠐⠀⠀⠀⠀⠀⢀⣆⠀⠐⣇⠀⠀⠀⠀⡆⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⢈⢶⠀⠀⢠⣏⠀⢡⠞⣷⣿⡆⠀⠐⣢⣤⣴⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⠛⠀⠀⠈⣄⢀⣀⣠⢼⣿⣆⠠⠀⠀⣷⣇⠀⢃⣷⣿⣿⣿
⠀⠀⠀⠀⢘⡷⠰⠁⡁⠀⢸⠏⣷⣌⣘⠻⠂⢙⠀⡀⣹⣷⣯⡼⣦⠀⠀⠀⢸⠀⠀⠀⠀⠘⡯⠄⠀⣷⢦⣿⡏⠏⡌⠉⣿⠉⠟⠚⠈⢉⣵⠀⠈⠙⢻⣿⣿
⠀⠀⠀⠀⠉⠱⠀⢀⣿⠀⣿⣀⠫⠹⡿⣏⣼⣿⠀⣶⣿⣟⢁⡀⣻⣅⠀⠀⢸⠀⠀⠒⠒⢀⣭⣦⡴⠁⣴⡶⡀⠀⠁⠈⠀⠀⠀⣀⡠⣾⣿⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢍⡀⠈⠀⠡⠿⣽⢻⠀⠿⣿⠛⡏⠻⠿⣿⣷⠀⢸⠀⣴⡂⢰⡏⠉⣾⣋⡁⣿⣿⡇⠀⢸⣆⠀⠀⠀⠀⢠⣿⢿⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠉⠃⢀⠀⠉⠆⠀⠠⢠⠤⢥⢰⠀⠀⠀⠛⠙⠀⢸⡀⠛⢁⠈⠃⣴⠅⢸⣽⣿⣿⡿⠀⠀⠈⢷⡀⢀⣺⠖⣏⣿⡇⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⠇⠀⡀⠋⠀⢀⣶⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣼⡤⠆⠀⠠⠙⣯⣾⣿⡄⠀⠀⠀⣸⣿⡆⠀⠀⢸⣿⠅⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⢸⡇⠈⠀⣤⣄⣴⣶⣾⣿⣿⣿⣀⢀⣤⣾⠿⠋⠀⠀⠀⠈⠁⠀⠰⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠉⠓⠄⡠⠚⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⠀⢸⡃⢀⠴⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠄⠀⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⡠⡀⠀⡇⠀⠰⠂⠀⢡⠀⣀⢔⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢐⡥⠖⠋⠓⠲⣼⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⢸⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⡄⠀⠀⠀⠀⡸⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⢢⡌⡓⠒⠒⢊⣠⡊
⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠤⠤⢀⡠⠤⠰⠚⠊⢥⠙⠉⠉⠀⠁⢱
⠀⠀⡴⢉⡩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡄
⠀⠀⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣆
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠂⠶⠾⠃
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢡⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠰⠀⠀⠀⠈⢱⠂⠤⢄⣀⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠰⠁⢀⠔⠀⠀⠀⡠⠚⢀⣠⠀⡄⣰⠃⠀⠀⠀⠀⠀⠈⠉⠉⡆⠀⠀⡰⠠⠠⡔⠈
⡄⠀⠇⠀⡠⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠁⠀⠀⠈⠀⠀⢀
⠇⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠁⠀⠀⠀⠀⠀⠄⠀⠆
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⣃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠣⡀
⠀⠀⠈⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⢀⠀⠀⠀⠈⡅⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠑⠄

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣧⡉⠙⣀
⠀⠀⠀⢸⠃⠁⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠠⣽⠁⠰⡅⣄
⠀⠀⠀⠸⡃⠐⢶⠄⠶⠐⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢀⣸⡅⠈⠀⠀⠀⠀⠠⡴⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣧⠦⠀⠀⢤⣦⡀⣼
⠀⠀⠄⠀⠘⠆⠰⣦⠀⠀⢄⠀⠀⠀⠀⠀⠀⠻⡀⠀⣾⣟⠁⣀⠂⢀⣀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡁⣰⣾⣿⣷⡟⠈
⠤⠤⢍⠀⠘⡇⠀⠛⠀⠀⡎⠒⠀⠀⠀⠀⠀⠀⠱⡀⠹⡿⢠⣄⡈⢋⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣴⢷⠿⠟⠀⠈⡀⢠
⠀⠠⣴⣆⡄⠇⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⣀⣤⣴⣄⠀⢈⢋⡅⠙⡿⢷⠒⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⢸⡟⠍⠀⠀⠀⠀⠘⠂⠙
⠙⣷⢬⢽⣿⡀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠙⠢⣹⣿⣀⠴⣷⠞⣷⣤⠀⠀⠀⠀⠀⠘⠁⢀⣠⡌⢷⠢⢂⠀⠀⠀⣠⣤
⣀⣾⣿⠈⠄⠁⠀⢀⡸⠃⠀⠀⣠⡾⢇⣠⠈⢋⡀⠀⠲⠀⡟⣷⡍⠁⠀⠀⢘⣦⠀⠀⠀⡆⢠⣠⣶⣿⠟⢁⢈⡀⣸⠀⢀⠀⠹⠟⢰
⢨⣿⡿⠀⠈⠀⠀⠋⠰⠃⠀⠀⣿⣿⣾⣿⠀⠏⢀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠠⢿⠀⠀⠀⢃⣾⣷⣭⣤⣤⡴⣻⡆⢸⣶⡘⠆⠁⠀⠴
⣻⣿⣷⠖⠖⠃⠀⠀⡘⠀⢴⣾⣿⣿⡟⣿⠀⣶⣿⡀⠀⣼⡇⣿⠀⠀⢰⠀⠀⣾⠀⠀⢀⣿⣿⣿⣿⡇⣭⠀⠈⣷⣆⠹⠿⢿⣧⣄⣐
⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⣴⣿⡟⠉⠁⢹⠀⣻⡿⠻⠾⠿⠗⠛⠀⠀⠀⠀⠀⠿⠀⠀⣿⡏⢻⠟⡏⠃⢹⡇⠀⠶⣿⡇⠀⠀⡈⠙⢻
⣿⣿⠿⠃⠀⠀⠀⠃⠀⠸⢻⣿⡗⡞⠀⢸⠀⠂⢀⠀⠀⣰⡄⢲⣄⠀⠀⠀⠀⢆⠀⠀⣿⠥⠄⠀⠁⠀⠈⠀⠀⢰⠈⢻⡆⠀⠁⠀⣸
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠉⢼⡇⠀⢀⣾⠀⠁⠀⢠⣸⣿⠀⠸⣏⣶⡀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠺⠂⠘⠷⠸⢷⡀⣀⠀⣻
⣀⠀⣀⣀⠀⠀⠀⢀⠀⣀⠀⢰⡗⠀⠰⠸⠀⠀⣦⠈⢹⣿⡀⣶⣿⡇⢱⡆⠀⠸⣷⠀⠃⠀⠀⠀⠀⣰⡃⠙⠢⡄⢠⣄⣤⣿⠟⠋⣭
⣿⠀⣿⠀⣀⠋⠉⠄⠀⠛⠘⢋⠀⠀⠀⢠⠀⡀⠘⠆⢠⣿⠁⣦⢹⡇⠈⠀⠀⠀⢻⠀⣠⣠⣤⡤⢰⣿⠏⠀⠀⠀⣬⡖⠙⣷⣶⣂⠙
⣽⠰⢩⠀⠂⠀⠀⠀⠀⠀⠀⠈⣷⣀⡄⢸⢘⣿⢓⣄⢨⡿⡄⢹⣿⠁⢀⡀⠰⡔⢆⠀⠀⣥⡤⠄⣾⡏⢀⣾⠁⠀⠸⠃⠀⠀⣄⢿⠠
⣿⠉⢺⡬⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠈⣿⠺⣿⡾⣧⢣⡾⠃⠀⡀⢿⣆⠙⢄⠁⠀⢸⡇⢸⡟⠀⣸⣟⠀⠀⠀⡄⠀⠀⢀⠈⠐
⢿⢀⣸⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⢀⠈⠀⡈⣁⣿⣿⣜⡾⠃⠀⢧⢧⢧⠻⣄⠀⠀⠀⠀⣿⠸⠀⠀⣿⡏⠀⠀⣶⡇⠀⠄⠛⠃⠈
⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁⠈⠸⣧⢹⣿⣸⣿⡇⠀⣄⠀⠘⣯⠃⠙⢦⡀⠁⣁⣤⠀⠀⣴⣾⣷⣾⣿⣿⣤⣀⣤⠘⠷⢒
⡀⠘⣿⡇⠀⠀⠀⠀⢷⡀⠀⠀⠈⠃⠀⠀⢰⣿⡆⢻⣿⣿⡇⠀⠹⣆⠀⠘⣧⠀⠀⠉⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠘⠏⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠈⣿⣿⣄⠹⣿⠇⣴⡀⠹⣦⠀⠈⢷⣄⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢻⣿⠋⠀⣠
⣦⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⠚⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠸⣿⣷⡆⠘⢷⣄⠀⠙⢦⡅⠀⠀⣤⠀⢻⣿⣿⣿⣿⣿⠁⠀⢹⣧⠀⠟
⢻⣆⠀⠀⠀⠀⠀⢠⡷⡀⠄⠁⠀⠀⠀⠀⠀⢻⣿⣻⣿⠀⣆⠈⠛⠀⠀⠈⢻⣦⡀⠀⠁⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⢻⣶⣀
⠀⢻⡄⠀⠀⠀⠀⠸⡅⠟⠁⢰⠇⠀⠀⠀⠀⠀⠹⣿⣿⠸⣿⣷⣄⠀⠀⠙⢦⡙⣿⣶⡆⠀⠀⠰⠃⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿
⠀⠀⢻⡆⠀⠀⠀⠀⠙⢮⡷⠋⠀⠀⠀⠀⠐⣇⠀⣹⢛⣿⣛⢿⣿⣷⠀⢲⣤⡈⠨⡛⠇⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠈⣿⣶⡏⢸⣿⣿⣷⣏⠈⢶⣄⠉⠙⢂⡈⡅⠀⠀⠀⣴⡀⢽⣿⣿⣿⡇

⠀⠀⠀⠀⠀⢀⡠⠄⠔⠒⠒⠲⠦⣀
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⡏⠀⠀⠀⢀⣀⡀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠃⡱⠀⠀⠀⢸⠁
⠀⠀⠀⠀⢶⣄⠀⠀⠘⢠⠁⠀⠀⠀⠈⣠⠞
⠀⠀⠀⠀⠀⠙⢷⣦⣄⣈⣁⣠⣴⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠏⣽⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢿⣿⡿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠀⠀⡀⠀⣠⠄⠐⠀⠐⠂⠀⠈⠢⡀⠀⠀⠀⣠⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢢⡄⠀⠹⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠢⠀⢡⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠖⠂⠀⠀⠐⠚⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⠾⠤⠀⠤⠠⠄⠠⢠⡄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠇

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠆⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠑⠀⠀⠀⠀⢀⠃⠀⠀⠘⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠘


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣷⠀⢀⡼⣠⠞⣛⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣤⡶⠿⡇⣈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢋⡿⡿⣴⣄⣴⣿⡷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣮⠀⠼⠡⠙⣶⡾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢴⢻⣵⣈⢍⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⣖⠒⢲⡶⠦⠤⠀⠀⠀⠤⠤⠤⠤⢄⡀⢀⣀⣠⣤⡤⢤⣤⣤⣤⣤⣤⡆⠈⠉⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢢⡄⡞⣣⡀⠉⠁⠀⠈⢤⠤⢤⡄⠓⠘⠛⠀⣔⣺⢭⠀⣹⡄⢼⣷⠾⣿⠀⣵⣿⣿⣷⣄⣀⣀⣠⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣏⣴⠈⠸⣅⠉⠀⣀⠈⢀⡀⢳⡀⠀⠙⠀⠀⢩⡍⠑⣻⣶⡤⢸⣧⣤⠿⣏⡽⣋⠹⣻⢟⣿⣿⣿⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣿⢢⣤⡀⠀⠀⡀⠀⠀⡄⠀⢉⡄⠀⠐⣦⠄⢀⠨⠁⠀⡠⠶⠚⠻⣧⣉⣨⢧⡤⠀⠀⠋⢙⢿⡿⣿⣼⣿⣿⣿⠋
⠀⠀⠀⠀⠀⣿⣇⠈⢿⣖⠈⠀⡀⣀⢀⡀⠀⠀⠸⡆⠲⠟⠂⠙⠛⠈⡀⠉⠤⡈⣉⣀⠀⢀⠀⠚⠀⣿⡅⠈⠈⢻⣿⣏⣿⣿⠏
⠀⠀⠀⠀⠰⣿⡟⠀⠀⠻⣦⡄⠀⠈⠀⠀⠠⣄⠀⣴⣶⣔⡀⢀⣜⠂⠑⠒⠴⣯⠥⢸⣦⣤⢰⣧⣀⢈⣷⣄⣠⢼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⡇⣰⠇⠐⡙⠻⡄⠀⠀⠊⢀⣀⣥⣼⣯⣄⣀⢤⣿⣿⡯⠷⠶⠽⣿⣷⣽⣷⡾⢿⣙⡯⢺⣿⣃⣼⢿⣿⠋
⠀⠀⠀⠀⠀⠚⠒⠁⠀⠀⠁⠀⠐⠒⣀⡀⣰⣿⠟⢋⣽⣿⣿⣶⣛⣛⣿⣛⠛⠡⣾⣿⣿⣇⣿⡌⠉⠁⣿⡏⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠞⠀⠀⠀⠠⢆⠜⠀⠀⠈⠛⠛⠛⠿⠶⠶⠶⠦⠶⠶⠶⠶⠺⠗⠛⣧⡐⢿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠐⠋⢉⠐⠁⢀⣾⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⣇⣀⢀⡴⠁⠀⠉⣰⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣧⡸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢉⣰⠞⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣧⠀⠀⠀⠀⠀⢠⠔⠖⠈⡄⠀⠀⣴⡶⠒⠈
⠀⠀⠀⠀⠀⣐⠛⡷⠀⠀⠀⠀⠀⠀⢆⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣬⠘⠷⠚⠀⠤⠤⠀⠈⠁⠀⠀⢠⠃⠀⠜⠉
⠀⠀⠀⠀⠀⡀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠦⣄
⠀⠀⠀⠀⠀⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⢀⡄⠀⠠⠄⠀⠀⠁⠂⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⡶⠒⠂⠘⠋⠁⠀⠀⠀⠁
⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠖⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⢨⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠰⣤⣴⠈⠙⠛⢤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠠⠂⠄⠘⠃⠀⠠⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠁

⠀⠀⠀⡀
⠀⠘⡏⠯⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣲⠒⡶
⠀⠀⢱⡘⠾⡃⣽⡄⠀⠀⠀⠀⡠⢊⠹⣿⢂⡼⠁
⠀⠀⠀⠙⠳⢛⣿⠋⢁⡄⣠⠈⣢⣾⡚⡿⠚
⠀⠀⠀⠀⠀⠰⣧⡄⢸⠟⠙⣰⣥⡿⠂
⠀⠀⠀⠀⠀⠐⢻⠝⠎⡄⢼⣿⣼⠓⠂
⠀⠀⠀⠀⠀⠀⠈⣆⡐⣠⠸⣄⣿
⠀⠀⠀⠀⠀⠀⢠⡿⣾⣭⣷⣿⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠉⢉⣽⣾⢿⡗⠒⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢸⣇⣱⣿⣿⣿⣿⣻⣷⠂⠀⠀⠀⠀⠀⢀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣢
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣷⢉⣿⣯⢋⢐⠀⣰⠄⠀⣑⡛⢼⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⢢⣷⢈⣢⣐⣿⢮⣾⠷⣄⣠⡀⠀⡀⣷⠜⢀⣦⠏⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣏⠞⣿⣾⠛⣻⡇⠐⣤⣉⣿⣎⢩⣢⣀⣠⡀⠀⠀⡀⡀⠀⢀⠄⠿⣿⡷⣿⣿⣄⠟⠉⠁⢈⣿⣾⣷⣿⣯⡀⠈⣟⣰⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⠁⢰⣿⡁⢀⣽⡏⣻⣿⣿⣽⣿⣾⣿⣦⡴⢔⠙⣶⢀⢳⣾⣾⣷⣾⡿⠏⡐⡀⡰⢿⣿⣿⣿⣿⣿⣻⣾⢇⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣫⠻⣿⡿⢿⣍⡻⣿⡻⣍⢬⣿⣿⣿⢻⣿⣿⣿⣶⣻⣷⣽⣿⣿⣻⣿⣾⣿⡞⣌⣻⣿⣿⠿⣿⣾⣻⣽⡷⢏⣾⡟⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣹⣵⠿⣿⣯⣿⣿⣯⣿⠿⣇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣯⣟⣿⣿⢧⣿⡛⡛⠻⠟⠿⠻⢛⣟⠛⠙⠃⡤⣪⣶⣚⣿⣯⣽⣿⣿⣺⣾⡿⣛⣿⣿⡏⠀⣧⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣏⣿⣿⡿⠎⠉⠛⠲⠖⠦⣤⣄⡌⣡⣤⡤⠞⠛⠈⠉⠀⠱⣻⣿⣿⣿⢿⡽⢳⣿⣷⣿⡀⠀⢹⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⡟⣿⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠹⡟⣣⣹⣇⣿⣿⣟⠿⣷⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⢸⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠸⣧⠖⣿⣿⣿⣧⡿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢸⡁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣾⣿⣿⣯⡲⡜⢟⢷⡌⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⠀⢫⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⣾⣿⢇⡴⠙⠿⣾⡏⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣯⣼⠃⠀⠀⠉⢿⣷⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡟⠁⠀⠀⠀⠀⠀⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠁⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⠗⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡏⡄⠀⠀⠀⣸⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠨⢋⡀⠀⠀⠀⠀⠀⢠⣾⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣼⠇⠀⠀⢀⣾⢗⠀⠀⣀⠘⣆⠻⠗⡠⢤⣤⢤⣞⣡⣤⣴⠀⢀⠀⢀⣴⠻⠛⠄⠀⠀⠀⢀⢀⡀⡀⠀⠀⢀⣋⡟
⠀⠀⠀⠀⠀⠀⡀⠰⠒⠀⠤⢷⡧⠜⣁⣠⠶⢒⣾⣿⣽⠀⠒⢒⣫⣆⠈⠑⢉⣐⡋⠊⠀⠀⠁⢤⠀⢏⣠⡿⢁⣴⢎⣀⣾⣻⣟⣉⣭⡭⢟⠖⠀⢸⡿⣡⠇⣠
⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠈⠀⠈⠀⠴⠷⠾⠋⠁⠀⠉⠉⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⣠⣶⣤⣏⠐⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⢈⣥⣽⣁⠈⠷⠃

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⣪⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣶⣶⣰⣀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣾⣶⣆⣖⡀
⠀⠀⣀⢀⣄⣬⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⡄⣈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⠀⣹⣿⣿⣿⡷⣜⡾
⠀⠀⢐⣚⣽⣾⣿⣿⣿⣿⣿⣿⣿⣶⡖⠀⢐⠚⣥⢼⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢉⡤⣶⣿⣿⣿⣿⣷⣷⣦⠄
⠀⠀⠩⠟⢟⢿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⢩⡟⢏⢿⣿⣿⣿⣯⣯⣿⠧⣭⠀⠈⢩⠻⠊⢿⣿⣿⣿⣼⣾⡾⢂⡅
⠀⠀⠐⠀⠙⢻⡛⣻⣿⣿⣛⣿⠓⠍⠀⠀⠀⠀⠉⠾⡿⣿⣿⣿⢟⡷⠲⠉⠀⠀⠀⠀⠁⠟⠿⣿⣿⡙⠋⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀
⠀⠀⠀⠀⠀⠐⢒⢻⣷⣽⡪⢂⠀⠀⠀⠀⠀⠀⠀⠐⢀⢰⣷⡜⡂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠐⠠⠀⢰⣭⡾⣟⣿⡔⢢⡄⠀⠀⠀⠀⠀⠀⠑⣭⡽⡟⢯⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗
⠀⠀⠀⡠⣌⢲⣌⣳⣿⠟⡏⠂⡆⠁⠀⠀⠀⠠⡄⠐⣀⣒⣻⠉⣇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀
⠀⠀⠀⠁⠀⢠⣭⢿⣿⡖⢉⠎⠁⠀⠀⠀⠀⠀⠀⢀⠉⠽⣿⠄⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠐⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿