Stickiness Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠫⠙⠻⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠈⡿⣿⣿⣿⠀⢻⣿⣿⢸⣿⣿⡟⣿⣿⢣⣿⡿⠃⠀⡼⠋⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢷⡁⠈⢿⣿⠀⢸⡿⣿⢸⣿⣿⣿⡏⣿⡾⡿⠁⠀⠈⠀⠀⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⡇⣿⢸⢿⢹⢻⠁⣿⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢸⢸⢸⠟⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⢸⠘⠈⢸⠀⢈⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⣿⣧⠀⢸⠀⢸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⡏⡏⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠀⡇⠇⠀⢸⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡇⠀⣿⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⣇⣿⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠇⣿⡇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣇⢠⣿⡇⠀⠛⢰⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⠀⢠⡄⢀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠉⠉⠛⠿⣟⠻⣿⡻⠿⠿⠿⣟⡿⠛⠻⡿⠛⠛⠉⠉⠛⢻⣿⣿⠉⠟⠉⠻⣿⠙⢿⣽⡿⢿⣿⣿⣿⠹⣿⢿⡿⠛⠉⢙⣏⠁⠈⡿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⢹⡏⠀⠀⠀⠘⣧⢸⡟⠀⠀⠙⢺⢹⡘⢃⡿⠀⠀⠀⠀⢿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠈⣾⡇⠀⠀⠀⣾⠈⠙⣼⠁⠀⠀⠀⠀⠈⣧⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣾⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⠸⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⡇⣧⢸⡀
⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⠀⣷⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢷⡀⠀⠀⠀⣰⢑⣿⠈⢳⡀⠀⢀
⠀⠀⠀⠀⢀⣴⣇⠀⠀⣸⡇⠀⣷⣷⠀⠀⣷⡀⠀⠀⠀⠀⠀⣠⡀⠸⠄⢸⡀⠀⠀⠀⠀⠺⠿⠒⢈⣷⣦⣤⣶⣷⣾⣿⣶⣾⣿⣷⣾⣷⣤⣶⣄
⢠⣶⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣟⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⡿⠿⣿⠿⣿⡿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢟⣛⣿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠛⠛⠋⠉⠩⠥⠀⠆⠀⠉⠀⠀⠐⠒⠃⠀⠀⠀⠰⠿⡅
⠀⠀⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡴⣀⢶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠉⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡌⠀⠀⠀⠀⢸⣀⣀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢦⠴⣄⠴⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡸
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠓⠂⣤⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠙⢯⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠤⢼⠀⠀⠀⠈⡆⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢆⠀⠀⣰⣱⠃⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⠙⠋⠉⠀⢀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⡞⠒⠒⠒⠒⢲⠇⠀⢸⠒⠒⠒⠒⠒⠒⠒⡗⠀⠀⠀⠀⠀⠀⡇⠀⣀⡀⠉⠉⠉⠉⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⢀⠀⠉⠉⠉⠑⠒⠋⠉⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⠈⠉⠙⠒⠒⠒⠒⠒⠃⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠈⠲⠋⠣⠔⠒⢦⠔⢲⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡎⠀⠙⠒⠒⠤⠤⠤⠤⠒⠀⣼⠃
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠖⢦⡠⢦⣀⡤⣄⢀⣠⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢰⠃⠐⠲⠤⠤⢤⣤⡤⠤⠄⡸⡻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠀⠀⠀⡇⠀⠀⠀⠀⢀⡏⠀⠒⠢⠤⠤⣤⣤⠤⠄⣰⢃⠇
⠀⠀⠀⠀⠀⢰⠇⠀⠊⠈⠒⠋⠳⠖⠓⢤⠖⢢⡀⠀⠀⢰⠃⠀⠐⢶⣤⠾⠤⣀⣀⣀⠤⢤⡀⠀⠀⡰⠃⡜
⠀⠀⠀⠀⠀⢸⠀⢀⠴⣄⣠⣄⠀⣀⡀⠀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠯⣍⣑⣒⡒⠦⠤⠤⠿⠶⠊⠀⡰⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠁⠈⠉⠀⠙⠊⠉⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠙⠒⠲⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣶⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠁⠈⠛⠉⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⣿⣧
⠀⠀⠠⣿⡟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⢿⣷⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⠟⠉⠉⢛⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⢀⣴⣿⣿⣄⠈⠻⣷⣄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣴⣿⣏⠀⠈⠻⣷⣄⠈⠻⣷⣄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠉⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣷⣄⠈⣿⡂
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠉⠻⣷⣄⠈⠻⣷⣄
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣿⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠻⣷⣄⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⠀⠈⠿⣷⣤⣾⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣷⣄⣠⣾⡿⠋⣠⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⠿⠿⢿⣷⣄⣨⣿⡿⠋⣠⣾⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⣠⣾⠟⠁⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣅⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁

⡿⠿⠿⠿⡿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣠⣽⣧⣼⣷⣶⠶⠶⠛⠛⠛⠛⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠶⠞⠛⠛⠛⠻⣯⡉⠁⠀⠘⣷⡈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡴⠶⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢠⣄⠈⢿⣄⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠻⣦⠀⠻⣦⠙⣷⡀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠙⣷⡀⠹⣧⡈⢿⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢿⣤⣼⠇⠈⣿⡄⠀⠀⠀⠀⢻⡆
⣠⣤⣴⠶⠾⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⢸⡇
⢿⡄⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠸⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣿⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⠶⠶⠾⠛⠛⣋⣩⣭⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⣤⣴⠶⠶⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⣴⠶⠞⠛⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⣾⣶⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢻⣿⣿⡇⠰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢸⣿⡿⠀⢠⣾⣿⣿⡇⢠⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠙⠿⣇⢀⣿⡿⠋⢀⡀⠀⠀⠀⢠⣶⣷⣆⣸⣇⢠⣶⠄⠀⠀⠀⠀⠀⠀⣰⣶⡄⠐⣿⡧⠀⣸⠃⠀⠀⠸⣿⣿⣿⣇⠀⢻⣿⣿⡿⠃
⠀⠀⠀⠀⢠⣶⣤⣿⣿⣿⣦⡶⠈⠁⠀⠀⣀⡀⠻⣿⣿⣿⣿⣿⣄⣀⣀⣠⣴⣶⠀⠀⠙⠻⠿⣶⣿⣤⣴⣋⡀⠀⠀⠀⠈⠉⠉⣻⣷⣾⣯⣀⢠⣶⡄
⠀⠀⠀⠀⠀⢉⣡⣿⣿⣿⣿⠷⣶⣶⡄⠀⠈⢠⣾⣿⣿⣿⣿⣿⡟⠉⠀⣴⠄⠀⢠⣶⣶⡶⠶⢿⣿⠿⣿⣿⣿⠀⠀⠀⣴⣶⣾⣿⠛⣿⣿⡿⠀⠉
⠀⠀⠀⢠⣾⣿⣿⠃⣼⣏⠛⠀⠈⠉⠀⠀⠀⠈⠻⢿⣿⣟⠻⢿⠿⠀⠀⠀⠀⠀⠘⠿⠟⠀⢠⣿⣿⠀⠈⠋⠁⠀⠀⠀⠹⣿⣿⠟⠀⢀⣉⣀
⠀⠀⠀⠸⢿⣿⡟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣻⣻⣻⣛⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣭⣿⣭⣿⣿⣿⣿⣭⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠀⠀⠈⠁⠒⠒⠤⣄⣀⣴⣦⣀⡤⠔⠒⠂⠉⠀⠀⠠⠀⠀⠀⣀⡀
⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⡠⠄⠰⠒⢽⣿⣿⣿⣿⠕⠒⠀⠤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣄
⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⣷⡆⠀⠀⠐⠀⡼⣿⣿⣿⡿⡆⠐⠀⠀⠀⢶⡇⠀⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣧⡀⠀⠀⠀⢠⣶⢠⠎⠀⢿⣿⣿⡇⠘⢦⢰⣦⠀⠀⠀⠀⣠⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠈⠀⠈⣠⠋⠀⠀⢸⣿⣿⠐⠀⠈⢣⡈⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⡤⠊⣌⠔⠃⠈⢸⣿⣿⠘⠀⠓⢌⡌⠢⡴⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⢀⠀⠀⠀⢀⠆⢆⠀⠀⠀⢀⠀⠈⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠁⠀⠀⠁⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠛⠿⣿⣷⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣦⠀⠀⠈⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣀⡀⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡞⣽⣿⣿⣶⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠈⢷⣄⠁⠙⠻⣿⠀⣤⠀⠀⠰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⣀⡀⠀⠠⠤⠌⠐⢒⣀⣐⣐⣒⣒⡉⣆⢨⣸⠁⣀⠠⠤⡬⠁⠀⠀⣀⡀⢠⣀⣀⡀⢀⡀
⠀⠀⣀⠤⠖⣒⠭⠋⠉⠉⠀⡀⣠⡴⠶⠓⢛⣉⣉⠥⠤⠒⣀⡀⠀⢰⠇⢠⠷⠤⠬⣭⣉⣉⡉⠛⠒⠢⣤⣀⠀⠀⠉⠑⠐⠌⢁⡒⠒⠠⣄⡀
⠐⠉⠀⣠⠎⠀⠀⠀⠀⢔⠈⣞⠁⠀⢰⣾⠋⠁⠀⠀⢎⠀⠀⠐⠂⠁⠀⣀⣘⠢⡄⣀⠀⠬⡙⢿⢮⡅⠈⠛⢷⣤⡢⠀⠀⠀⠀⠘⣲⣄⠀⠈⠑⠦⣀
⠀⠀⠀⢯⡠⠀⠀⠀⠀⢕⡨⣷⠀⠀⠐⠽⣆⠀⡂⠀⠀⠁⠢⢤⣀⡀⣀⣈⣉⣑⡊⠎⠠⠔⠁⣼⠯⣻⠀⠀⠈⡍⣋⠀⠀⠀⢀⠢⡒⢽
⠀⠀⠀⠈⠲⣡⢂⢔⢄⠀⠈⠉⢶⡔⢄⠀⠈⠉⠒⠢⠦⣎⣦⣴⣮⣥⡤⢶⣲⣶⣆⣴⡶⣐⣑⠥⠚⠁⣠⢶⠕⣅⠎⠀⠀⢌⠢⠑⡬⠎
⠀⠀⠀⡀⠀⠀⠉⠉⠈⠊⢎⣆⡄⡈⠚⠊⠊⠃⠂⠠⣰⣒⡤⠤⢬⣭⣉⣊⣭⠉⡉⠉⡀⠠⠴⣶⣊⡪⠨⠖⠊⢁⢀⢊⣄⠦⠒⠉
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠉⠉⠙⠓⠲⠦⠤⠄⣄⣄⡉⣉⣉⣹⣻⣬⣭⠝⠻⢇⢙⢉⣉⣤⣤⠠⠤⠆⠛⠚⠈⠉⢀⡀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠀⠀⠀⠀⠠⠤⠄⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠄⠀⠀⠒⠒⠀⣉⡉⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣡⠀⠀⠀⢸⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⢤⣶⣶⣦⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠔⠃⡀⠘⠆⢸⢿⣿⣿⢿⠋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡠⠒⠂⡟⠂⢄⣟⡘⣙⠘⢻⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣇⣀⣀⣇⢀⠀⠀⡄⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⡀⠀⠀⠀⠈⢋⣭⡉⠉⠉⠁⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡙⠢⣤⡤⠴⠋⡍⠒⠀⠀⠀⠀⠆⢪⣥⣌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠷⠊⠁⣄⢀⠀⠁⠀⠸⠀⠀⠀⠀⣀⣸⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠋⠙⠃⠀⠠⡏⢹⠀⠀⠀⢠⠀⠀⠸⠀⣶⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡅⠀⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⡀⠀⣥⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡄⠀⢸⠃⢀⠀⡼⠀⠀⠠⠀⢀⠃⠀⠀⠀⡟⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠇⠀⠰⠆⢁⡼⠁⠀⠀⡀⠀⠸⠄⠀⠀⠀⡇⣄⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠺⠷⡶⠶⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢸⠇⢸⣀⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣇⣀⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⢨⣅⡾⠀⠋⢀⢠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠀⠀⠀⡏⢸⠀⠑⠛⠲⣶⡄⣀⠠⠀⠀⠀⣼⠁⠀⠀⡼⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡿⠺⣇⠀⠀⠀⠚⠑⠫⡄⠀⠀⡜⠳⡧⠀⠀⠷⠀⢠⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⢻⣆⠀⠀⠛⠀⠀⠀⣠⢾⠇⣾⠆⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⢰⠋⠀⡾⠋⡷⣄⣀⣀⣠⠞⢁⡎⣠⠁⠣⡉⢀⠙⡀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠈⢯⣸⠃⠁⡗⠛⡁⡸⠣⣤⡞⡰⠋⢠⠀⣧⣰⣦⢧⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⣸⠀⠀⡧⢀⡟⣁⢠⣿⠃⠀⠀⢸⠀⡟⠁⠙⠚⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⢧⣄⡘⡇⣰⢂⡇⠀⣼⠀⠀⣀⠋⠀⣋⣠⠴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠈⣧⠉⡱⠃⠸⢱⡀⠘⠳⠲⠟⠊⠉⠁⣤⢼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠒⠒⣶⠒⣿⣤⣌⣳⡀⢚⣠⡗⠀⠀⠀⠃⠀⠀⠀⢹⣹⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠴⠤⢤⣌⠭⠭⠥⠝⢙⠿⠭⠿⠶⠶⠶⠶⠂⠠⠴⠶⠤⢷⠤⠤⠤⠤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠤⠭⢤⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠂⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⢠⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠒⢐⣶⣶⡿⣷⣒⡆⠐⠂⠀⠀⠐⠀⠀⠐⠒⠂
⠀⠀⠑⢠⡄⠀⠼⡇⢸⡷⠀⠀⡄⠈⠀⠀⢀⠀⡼⠀⠀⠀⠀⠀⠐⠀⠘⠉⢿⠈⠉⠀⠂⠀⠀⠀⠀⠀⡸⠦⣤⠴⢇
⠀⠀⠀⠀⠐⠒⠓⠉⠋⠚⠃⠂⠀⠀⠀⠀⠘⣄⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠈⠀⠐⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⢀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠐⣀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠁⢂⣰⠉⢧⣀⠈⠀⠀⠀⠀⠐⢄⡁⠶⢈⡠⠄⠀⠀⠠⠀⠀⠀⠀⢸⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⢠⠘⠧⡙⠂⢛⡠⠃⡠⠀⠀⠀⠀⡀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣞⣆⡈⢿⠁⣰⣳⠆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠙⠒⠀⠈⠀⠐⠊⠁⠀⠀⠀⠀⠀⠑⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠂⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⣀⡀⢀⢠⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢠⠠⢤
⠀⠀⠀⠀⠈⠀⡿⠩⡇⠈⠀⠀⠀⠀⠀⠀⠐⢀⡠⠧⠀⠆⠀⠀⠀⠀⠈⡇⠀⠀⣀⣀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⢠⡚⠚⢢⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠬⠁⠀⠀⠀⠀⠀⢸⡄⣐⣿⣿⢂⢀⡟⠀⠀⠀⠀⠀⢸⡧⡞
⠀⠀⠀⠀⠀⠘⠄⠀⠜⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⢂⠀⠀⠀⠈⠸⣇⠈⠛⠟⠁⣰⠗⠃⠀⠀⠀⠀⢸⡓⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡇⠀⠀⠀⠀⠈⠀⠘⠂⠀⠀⠐⠃⠀⠁⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠂
⠀⠀⠀⠀⠢⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠄⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⢀⠯⠼⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠒⣋⠉⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠊⠇⠀⠀⠀⢤⡀⠐⠒⠀⣠⠄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠠⠀⢀⠘⠶⠃⡀⠀⡄⠀⠀⠀⠀⠀⠚⠑⠂⠱⠂⠀⠀⠐⠐⠀⠋⢈⠁⠀⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⣈⠁⢁⠈⢠⠇⠀⠀⠀⠀⠀⢠⠀⠀⠰⠈⠀⠀⠀⡀⢂⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠦⢤⠤⢚⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠰⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁
⠀⠀⠀⠀⠀⠈⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢰⡄⢀⢉⠛⠋⣉⡀⢰⠆⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⡄⠀⠀⠀⠀⠀⠑⢤⣆⠀⠀⣰⡤⠊⠀⠀⠀⠀⠀⢠⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⡸⡯⣴⣦⡽⢇⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣠⢶⢟⣶⣾⡿⣿⣶⣾⡳⡦⣄⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡁⢰⡿⣷⣿⡇⢸⣿⡾⢿⡅⢸⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡇⢸⠁⣿⣿⡇⢸⣿⡿⢈⡅⢸⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣩⣿⣽⣇⠸⣿⡇⣾⣿⠇⣸⣷⣿⣉⡙⢷⣄
⠀⠀⠀⠀⠀⣀⣀⡠⠤⠴⠾⠟⠁⢠⣯⣤⡄⠉⠙⢿⡦⡤⢤⢴⠿⠋⠁⢠⣬⣽⠀⠙⠿⠷⠦⠤⠄⣄⡀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⣷⢴⣾⡦⡿⣱⣮⢞⣰⠷⡖⢿⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢘⡯⣯⡽⣷⣌⢡⡆⢰⣾⢞⣳⣿⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢚⠛⣛⣿⣽⣯⢸⡆⣿⣗⣿⢹⠧⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⣃⣻⢤⣻⣹⡷⣏⡖⣟⣭⣤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⣙⣶⡢⡿⢸⡇⢺⢳⡇⡅⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡉⡍⠫⠃⢸⡇⠙⠫⣵⢛⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠙⠛⠓⠒⠛⠓⠒⠚⠛⠋⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠇⠀⠀⠀⠀⠀⢀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⡠⠔⠤⡐⠛⠀⠀⣰⠭⠏⡀⢀⢞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠉⠓⡄⠀⠀⠉⠀⠀⠱⠴⠖⠀⡠⠖⣋⠀⢀⠤⣈⢹⣗⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣠⡗⠁⠀⢀⡔⠒⣢⣀⡠⠔⢫⠒⠛⡾⠃⣞⡶⡿⠀⠉⠰⠉⠱⡄⠀⣎⣱⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠁⠀⡔⠁⣨⡷⠛⡇⠀⠀⠱⢤⡾⠃⣴⡌⠁⠀⣠⠔⠃⡤⠤⡘⣆⠌⢥⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢃⢌⣀⡳⠾⠃⡤⠒⣤⣤⡀⠀⢠⢄⠀⡞⠀⡠⠚⠣⣴⠃⠈⢦⣐⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢒⢦⣠⠴⠊⠁⠀⠳⠞⠉⡕⠀⡠⠗⠒⣿⠉⢀⡀⠈⠛⠀⡇⢨⡀⠀⡔⡐⠀⠀⠀⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠚⢇⠀⡀⡰⠘⡘⠸⣰⠀⠀⣅⢀⣴⡟⠀⢧⠯⠀⠀⠀⠘⡄⠉⠀⠉⠀⠀⠀⢠⣄⠱⣤⡄⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠒⠋⢰⢡⢁⢣⢁⠗⢣⠀⠀⠈⠁⠉⢠⠶⣽⠂⠀⠀⢆⡆⢨⢀⡄⠀⠀⣔⣢⠀⢡⠠⡟⠀⣠⠼⣄⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢃⢁⢃⠆⡌⡐⡜⠛⠋⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡠⠖⠶⡁⠘⠶⠀⠀⠉⠁⠂⢡⠐⢡⠀⢇⣠⢀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⢢⠀⠈⡘⡜⡸⢠⢱⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⢄⣼⢂⠀⠀⠀⢀⠀⡂⡄⠈⠀⣸⠀⠀⠉⠠⣎⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⡇⠀⠡⢂⠱⢁⢃⠇⡌⡜⡠⠀⠀⠀⠀⠀⣀⡀⠀⢠⣇⠀⢔⠌⠁⠿⠀⢀⢀⠰⠟⠁⠀⣶⠀⡼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⡄⠙⢢⡀⠱⣂⠘⡘⢠⢡⢠⠃⠀⠀⠀⠀⠮⣀⡼⠀⡆⠈⠉⠉⠀⢀⠀⠀⠐⠈⠀⠀⠀⣀⠘⠤⠃⡉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⠘⣷⡀⠀⠱⡈⠡⡀⠁⡎⡈⡌⠀⡠⢊⡹⣄⠴⡌⢀⡴⠁⠀⠀⢀⠰⠘⣀⢤⡀⡎⠉⢧⡀⡧⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠘⠤⡨⠇⠀⠙⡇⠀⠀⠳⡀⠀⠀⠀⠁⠁⠇⡇⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⣨⠔⠋⠀⢰⠁⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢇⠆⠠⡀⠘⣄⢀⠴⢦⡈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⡇⠀⣦⠂
⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⣁⡀⠘⠊⠣⡑⡀⠈⠁⠀⠀⠓⠔⠋⠀⢀⠄⢂⡠⠖⡆⠰⡇⠀⠀⠀⠀⠀⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢌⠂⠀⠀⠙⢌⠠⠀⠀⠀⠀⢀⠄⢂⡤⠚⠉⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠑⠢⡄⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢸
⠀⠀⢀⡠⢄⣠⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⡴⠒⣢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠎⠤⠌⠽⣃⣃⣘⢤⠀⢉⣒⣒⣀⣩⣯⡑⣤⣤⠔⢒⣈⠉⢑⣲⣤⠤⠌⠉⣭⠥⠤⠤⠔⠋⠀⢙⠦⠤⠤⢤⢄⠀⣄⠈⠂⢒⣚⠂⠀⠀⡤⠠⡖⠒⣄
⠀⠀⠀⠀⣆⡀⣀⣀⡠⠤⠴⡖⠒⠒⠒⢲⣒⣒⣒⡒⠀⢘⣋⣀⣠⡼⠧⣄⣀⣀⣀⣀⣀⣈⠉⠀⠉⠉⠀⢀⠀⠵⣎⣷⢮⡭⡥⢤⣬⡌⣓⡌⣁⡚⠉⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠄⠒⠒⣲⡶⢤⣀⢱⠞⠣⢀⣀⣬⠿⢍⣁⡚⠛⣮⠔⠛⠛⠛⢮⡘⠃⢘⠉⠙⠮⡛⠓⡎⠀⠀⠉⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⢰⣿⡆⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢶⣢⣶⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣖⣶⠄⡀
⠀⠠⢀⡐⣒⠚⠍⠁⠀⠁⢳⣿⡞⠀⠀⠉⠹⠓⣀⢀⡀⠄⠀⠈⢧⣕⣿⣯⣃⣹⢁⣸⠗⠠⢶⠂⠚⣏⡀⣏⣘⣽⣿⣚⣵
⠀⠀⣀⣀⠈⠁⠐⠄⠀⠂⢾⢛⡇⠐⠀⠠⠂⠉⠁⣀⡀⠀⠀⠀⠀⠀⣿⣿⣖⡠⣶⣪⣿⣷⣈⣼⣿⣯⣲⢄⣰⣿⣿⠃
⠘⠓⠒⠂⠀⠀⠀⣀⣁⡤⠜⣍⠢⢤⣈⣀⠀⠀⠀⠐⠲⠚⠀⠀⠀⠀⠉⠻⢿⢷⠏⢡⡟⣯⣟⣯⡟⡄⠙⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡄⠑⠊⢀⡟⡄⠙⠒⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢶⢄⠃⠀⠀⠈⠻⡶⣶⠞⠁⠻⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠤⠄⢀⣑⣾⣭⣿⣊⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⢿⣤⡿⠏⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⠇⢨⣿⡇⠘⣾⢃⠀⠀⠀⠀⠀⠸⣄⡀
⠀⠀⠀⠀⠀⢠⠀⡏⠀⠀⠀⢸⠀⣆⠀⠀⠀⠀⠀⠀⠁⠃⠃⢸⣿⣇⠈⠈⠈⠀⢸⠀⠀⢠⣄⠀⡇⠀⣰⠏⠙⠒⠂⢄
⠀⠀⠀⢀⣠⡤⠑⢮⡀⣶⣀⠥⠊⠠⣄⡀⠀⠀⠀⠀⠀⢀⡜⢻⣿⡟⢢⡀⠀⠀⠸⡗⠀⣼⣿⣿⣷⣶⣇⣠⠴⠓⠒⢤⡀
⠀⠀⠀⠀⠤⡤⠀⣀⣻⠭⣿⣁⠀⠤⠤⠀⠀⠀⠀⠈⠓⠋⠀⠀⠉⠀⠀⠙⠚⠁⠀⣈⡛⢻⣿⣟⢟⣿⣽⡷⠚⢧⡀⠀⠈
⠀⠀⠀⠀⢠⠘⠋⣩⣤⠛⣡⣍⠙⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠈⢉⣻⡿⣿⠿⠇⠀⠀⢱
⠀⠀⠀⠀⠘⠰⡄⠙⢿⣶⠿⠋⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⣰⡏⠘⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣻⣿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⡀⣀⡀⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣄⠀⠀⡴⠀⠀⠀⠀⠀⠘⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⢰⠁⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⢀⣿⠖⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡄⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣰⣵⠞⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠛⣷⣦⣴⢐⣟⣛⣤⣤⣤⣽⣾⣋⣀⣠⣤⡴⠞⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠊⠀⠐⠈⠂⠉⣿⠿⡯⢛⣩⠟⣻⠻⣯⣉⠉⠀⠀⠀⠀⠀⠈⠐⠛⠫⠤⠄⠀⠀⠀⠄⠀⠀⠀⠀⠑⠠⣄
⠀⠀⠀⠀⠀⠀⠈⡱⠀⠐⠠⠈⠀⠊⠀⣉⣙⣄⢿⠋⠅⢀⡿⠐⢀⢻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢾⠀⠀⢀⠀⠀⠔⠑⠛⡹⠏⢹⠘⠀⢁⡾⡇⠀⠠⠑⣽⠟⣿⡙⠋⠈⠉⠀⠀⠐⠒⠲⠶⠶⠒⠒⠀⠀⠀⠐⢆⠀⠀⠸⢇
⠀⠀⠀⠀⠀⢶⠀⠀⠒⠉⠀⠀⠤⠆⠛⠁⠀⢻⠇⣶⣻⠄⢠⡄⠀⠀⢼⡇⢽⡿⣶⣄⣀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠘⠂⠀⠀⢦
⠀⠀⠀⠀⠀⠘⠀⠀⠀⢈⡀⠒⡴⠀⠀⠀⡠⣼⠀⢻⡼⣢⠈⢷⡀⠀⠪⡇⠐⣽⢾⡏⢻⣍⠁⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡱⠄
⠀⠀⠀⠀⠀⣉⠥⣤⡀⠀⢨⣽⣁⣠⠂⠀⢊⣽⢄⢀⣧⣼⡆⠈⡱⡀⠀⠀⠌⠡⣿⣇⠀⡘⣧⢀⡠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠋⠀⠀⠈⠛⢷⠟⣁⣀⣀⡙⢮⣭⣞⠛⡼⣦⢝⣃⠔⠉⠁⠐⣷⡤⣷⠞⠋⠉⠛⠿⡏⠉⠙⢲⡀⣀⣀⣀⡀⠀⠀⠀⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡖⠉⠉⠉⠙⢾⣯⣜⡀⡇⡱⠚⡏⠀⠀⠀⠀⠀⢦⡏⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⢮⣁⠉⠀⠀⠀⠀⠀⣴⠆
⠀⠀⢀⣨⣄⠀⠀⣠⠤⠶⢄⡀⠀⠀⠀⢸⠀⠈⠻⣇⡵⣀⡥⠀⡀⠀⠀⢠⢾⠁⠀⠀⠀⠀⠀⠰⠂⣀⣼⢻⡄⠙⣷⣶⠂⠁⢀⠀⠘⣆
⡰⠉⠀⠀⠉⢻⡞⠀⠀⠀⠀⠘⣆⣀⠲⠃⠀⠀⠀⣿⣄⡼⠋⠉⠁⠂⢼⠟⠒⠓⢤⣀⣄⣠⠔⠛⠛⢻⠂⠘⣧⠀⠈⣠⠙⣦⣌⠀⠉⢯
⣧⡀⠀⠀⠀⣳⡆⠀⠀⠀⠀⠀⢸⠯⣍⡳⣀⣀⣤⣽⣬⢇⡀⠀⠀⠀⢀⡀⠀⠀⠀⠻⢮⡵⠚⠉⠉⠙⠢⣄⠸⡆⠀⠿⡄⠈⠙⡗⢀⠈⢳⡀
⢈⠷⠆⠐⢒⣭⣷⣄⠀⣀⠀⣠⠂⠀⠀⠘⢿⣷⠋⠀⠀⠀⠙⠄⢀⣠⣛⡁⠀⠀⠀⣼⠲⠗⠀⠀⠀⠀⠀⠘⣦⠀⣠⠢⠡⣤⣨⡝⣘⠢⠤⠙⣄
⢸⠂⠀⣔⠋⠀⠀⠹⢻⣿⠛⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣦⠈⠈⠉⠉⠙⢦⡞⠉⠑⢿⡀⢀⠀⠀⠀⣠⠌⠀⠀⠁⠀⠀⠈⠀⠉⠁⠚⠉⠉
⠈⢣⣴⠏⠀⠀⠀⠀⢸⠉⢧⣀⣀⣀⣤⣴⣿⣷⣄⣠⢀⣠⣾⡇⠀⠀⠀⢀⣀⠬⣆⣀⣀⣹⣯⠕⠻⠒⠊⠁
⠀⠈⠿⣄⠀⠀⠀⢀⠞⠀⠠⢤⠟⠉⠉⠛⢻⣾⣿⣿⣿⣿⣿⣷⣴⣀⣴⠋⠀⠀⠀⠹⡄⠉⢦⠀⡸
⠀⠀⠀⠈⠱⡖⠘⠉⢧⡀⠀⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠉⠛⣛⣿⣇⡀⠀⠀⠀⢸⡇⠀⢸⡋
⠀⠀⠀⠀⠀⠘⠢⠤⢚⠛⠛⢿⡀⠀⠀⢀⠜⠛⠛⢿⡏⠀⡴⠋⠁⠀⠀⠉⢦⣄⡴⠛⠃⠙⠛⢏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢍⠁⠘⠁⠀⠀⠀⠀⢳⣾⡀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⢸⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠁⢺⣆⡀⠄⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⢰⡋⠀⠀⣀⠄⢀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⡤⢴⠎⠁⢈⡜⠛⠉⠉⠙⢿⣿⣦⣤⣤⣄⣠⣿⣿⠟⠉⠉⠻⣏⣰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⣄⠀⣼⠀⠀⠀⠀⢠⠎⠀⠀⠀⠉⢿⣿⣿⡇⠀⠀⠀⠀⡉⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⠿⣆⡀⠀⠀⣨⡆⠀⠀⠀⠀⣸⠿⠛⠻⢦⣀⣠⠴⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢉⣹⠋⠀⠙⠢⠤⣤⣾⠁⠀⠀⠀⠘⣿⣿⠤⠤⡤⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡄⠀⠀⠀⠃⣸⣿⣆⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣤⣤⡾⠋⠉⠉⠛⢶⣾⡿⢿⡄⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣸⠃⠀⠈⠳⣶⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠤⢴⡃⠀⠀⠀⠀⣶⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣦⣤⣄⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⡇⠀⠀⠀⠀⠀⣤⣾⠟⠛⣿⣾⣯⣤⣤⡄⠀⠀⠀⠀⠀⠀⠘⠓⠲⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⢼⢻⣲⡄⠀⠀⠀⢸⡇⢹⠀⠼⣿⣿⣩⠽⣿⠇⠀⠀⡠⠂⠐⠊⠀⠴⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣯⢼⡯⣬⠇⠀⠀⠀⠀⣇⢸⣤⣾⡏⠉⠠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⡀⠊⣿⠦
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⢿⣶⠀⠀⠀⠀⠀⠸⡘⢇⣸⢿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠀⣮⢀⡆⠋⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣟⠉⠀⠀⠀⠀⠀⠀⢻⡿⢿⣭⣇⡃⠀⠀⠀⠀⠀⢀⠀⠠⠂⣷⣾⡇⢀⠃⣼⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⢻⡇⠀⠀⠀⠀⠀⠈⢀⣼⣆⠸⣿⠄⢀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⣶⡇⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⢿⡔⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡜⢿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⣦⣻⠃
⠀⠀⠀⠀⠀⠀⡔⣴⡔⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠛⣇⡫⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣾⡄⣶⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⢀⣶⣶⠘⠿⠋⣀⠉⢀⠈⠛⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠥⠤⠖⠀⠠
⠀⠀⠈⠀⠐⢌⠻⢿⡿⠂⢸⣿⣿⠿⠃⠀⠀⠀⠀⠁⠀⠀⢁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⢈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡁⡂⠐⡀⢐⠀⣂⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠅⠤⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⢌⢂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⡶⠄
⠀⠀⠀⠀⠀⢂⢐⠐⠂⠐⠀⡃⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠙⠋⠈⣡⣴
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⡀⠁⠠⠤⠄⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⠠⠆⠀⠤⡀⠣⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡅⢠⣳⡶⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠤⡅⠛⣀⠈⢀⠁⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠢⠀⠀⠀⠀⠆⠀⠀⠲⠒⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣴⣶⠦⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣄⣸⣶⡟⣹⡏⢿⡇⠀⠠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠂⠀⢸⡶⢋⣿⠛⣿⡍⢛⠂⠛⠃⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠈⠙⢦⡀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠐⠀⠁⠀⠁⠀⠀⠀⠀⣻⡲⠋⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⢀⣀⣤⠴⣻⣿⢷⣤⢮⡝⠒⠛⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⣠⣾⠟⠁⡌⡟⠀⡇⠀⠁⢀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠝⠁⠀⢠⢹⠃⠀⢷⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡣⠋⠀⠀⠀⡸⣾⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠁⠀⠀⠀⠀⡇⡇⠀⠀⠀⠹⡄⠀⠀⠀⠠⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⠁⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠁⠀⠀⠀⠀⠀⠀⡅⡇⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠇⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡸⠒⠒⠢⢄⡀⠀⠀⠀⢣⢸⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⢹⠁⡇⠀⢀⡀⠀⠙⣄⣀⣀⣸⡈⣇⣠⠴⠶⢤⣀
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠈⠀⠀⠀⠀⢰⣦⠚⠁⠀⠀⠀⢃⣹⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢸⠁⠀⠀⠆⡀⠀⠀⠀⠠⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⣄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠚⠛⠋⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠖⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢰⣼⠎⡿⠉⣋⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣿⢧⡿⣿⢙⡉⢈⡙⠳⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠲⣶⣤⡙⢿⣿⠷⠾⡟⠋⠛⡁⠋⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⡻⠿⢻⡾⣿⣶⡒⢞⠒⠲⢤⣬⠤⠤⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁⠈⠛⠂⠄⠰⠊⣽⡃⡘⠸⢛⣶⣌⠁⠀⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠈⣩⣡⡀⢠⡜⠤⠉⠠⢚⡯⠀⠁⠠⣉⠈⠛⢷⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣋⠔⠊⠉⠉⠀⠀⠀⠀⠸⣀⠀⢨⢇⠠⢤⡄⠀⢤⣀⠀⢛⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠓⠀⠊⠀⠀⠀⠈⠉⠙⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠒⡄⠐⢮⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣇⢀⠀⠀⢀⡍⣾⠁⣭⢻⣷⣟⡿⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠉⢭⠛⢀⣲⢞⣵⡿⣤⡞⡉⢩⡻⢷⣿⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⠁⢠⣿⣿⠙⠉⢹⣏⣽⢗⠷⣽⣿⣷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣺⢤⣻⣟⣯⠀⣐⣾⣏⢿⣿⣲⣶⣿⢯⢶⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠿⠻⢻⡗⠿⢷⣉⣹⣿⣿⣮⢷⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⢀⠛⣷⣻⣿⣿⣷⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⣭⢿⣿⣶⣿⣿⣹⣿⣽⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢯⣶⣿⣿⢟⠩⣽⡷⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⡿⣧⢼⣿⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠠⣍⣷⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠾⠟⠋⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣄⠀⠀⢤⠀⠀⡀⠀⢀⠀⠷⠀⠀⠀⡄⠀⡦⠀⢀⠀⢰⡄⠀⢀⡀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⡀
⠚⢰⡀⠈⠀⠀⠇⠀⠸⠆⠀⠀⡆⠀⠁⠀⠀⠀⠘⠀⠈⠀⣄⠘⠇⠀⠀⠀⠋⠀⣤⠈⠃⠀⠐⠖
⠀⠈⠁⠀⢸⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⣆
⢲⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⣆⠀⢲⠀⠈⠀⠀⡄⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠀⠗⠀⠸⠀⠀⢈
⠈⠀⠀⠋⠀⢰⡄⠀⢰⠀⠀⠁⠀⠀⡀⢀⡀⠠⣧⣀⡀⠀⠀⠛⠀⠀⠀⢲⠀⠀⠘⠀⠀⠀⡀⠀⡀⠘
⠀⢀⡆⠠⡆⠀⠀⣀⠤⢐⣠⠻⢛⠥⠢⠐⠀⠀⢈⡄⠂⠌⠉⠙⠒⠶⣤⡬⠀⣀⠀⠀⠀⠸⡥⠀⣥
⢀⠀⠋⠀⣠⣔⠚⠉⡴⡫⠡⢊⠩⡂⠈⠀⠀⠀⠀⠐⠈⠂⠉⠀⠀⠀⠈⠙⠲⡠⠈⠁⠢⢄⡀⠀⢠⡄
⠸⠀⡠⠊⠀⠁⠀⡜⢘⠨⡂⢑⢅⠂⠁⠀⠀⠀⠀⠀⠁⠁⡀⠀⠈⡀⠀⠀⠀⠘⢦⠀⠀⡀⠈⠢⡈⠁
⢀⢎⣢⠴⠀⠀⢰⢐⠕⠨⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⡀⢀⢀⠀⠀⠀⠈⣧⢐⠀⠀⡄⢝⡄
⠟⠉⠀⠈⠉⠀⣬⡵⠖⠓⠉⠈⠉⠉⠈⠙⠓⢦⣤⡀⢠⢠⣤⠴⠿⠓⠂⠡⠠⠤⠾⢜⡵⠚⠉⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣗⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣉⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠁⠀⠂⠀⠀⠂⠔⠄⠠⠢⠠⠈⢄⠁⠌⠀⠨⠢⢀⠕⢔⢄⢀⢀⠀⡠⡂⡠⢀⢄⠔⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⠶⠿⠿⣛⣛⣛⠿⣿⣛⣛⣛⣉⣽⣿⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢾⣿⣛⡭⠵⠾⣛⣋⢷⠴⠿⠗⣚⣻⣭⣝⣛⣀⣹⣯⠭⠿⠭⠟⠛⠛⠛⠛⠛⠋⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠻⣿⣻⣦⠭⠷⠒⠒⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⠀⣠⡴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣇⣠⣤⡤⠤⠐⠒⠒⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⡀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⡀⠴
⢩⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣫⣁
⠈⠉⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⣿⠞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡙⠈⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡿⠇
⠀⢀⠠⠒⣀⡰⡖⠀⠀⠘⡀⠀⠰⢦⣀⠐⠢⠀⠀⠀⠀⠀⠊⣌⠋⣬⠁⠀⠀⠀⢀⠠⠒⣀⡐⡖⠀⠀⠈⠀⠀⠲⢦
⠀⠁⠀⠀⠀⠀⠀⠐⡇⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⣀⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣄⡀⠀⢀⠀⡀⠀⠀⣀⣤⣤⣦⡄
⣩⡽⣻⣿⠟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡽⣦⣍⡓⢄⢤⡤⣒⣩⡽⣻⣿⠟⠀⠀⠀⠀⡀⠄⢀
⣦⣼⡿⠃⠀⠀⠀⠀⠀⣤⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣶⠛⣩⢤⡙⠳⣦⣼⡿⠃⠀⠀⠀⠀⠀⣤⡀⢠⣄
⣤⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡞⠹⡜⡌⣦⣮⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⣟
⠾⠋⠀⠀⠀⠀⠀⠀⠀⠠⠃⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠩⠃⠘⠏

⣀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⡀⠘
⢵⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⢵⣥
⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿⠋⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠢⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⡏⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⠃⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣸⣿⠀⢹⠀⢀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠻⠀⠈⠀⡾⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⠛⠉⠀⣠⡤⠶⠚⠛⣻⡆⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣀⠤⠴⠚⠉⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣤⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠘⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⡿
⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⢀⣴⠟⠋⠀⢀⣤⠴⠖⠒⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣤⣤⣤⣤⣴⠟
⢠⡟⠁⠀⠀⠜⠉⠀⠀⠀⠀⠶⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⠟⠁
⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠰⣶⣤⣤⣤⣤⣴⡶⠾⠛⠉
⠀⠈⠻⢷⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣸⠁⢀⡆⠀⠀⢿⡇
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣦⡀⠀⠀⠋⠀⣼⠁⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⡏⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠘⣇⣰⠏⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠈⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⣾⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠖⠒⠒⠐⢦⣤⣄⣀⡀⠀⢀⣀⣀⠀⢀⡠⢐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠋⠁⠀⠀⡀⢀⣠⣴⣿⣛⣿⣿⢿⡿⠛⠉⠉⠀⠀⢉⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⣀⣭⣻⡿⠿⠛⠋⠉⠀⢀⡜⠁⠀⠀⠀⠀⠠⣺⣿⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⣼⣾⣿⠟⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣰⡾⠁⣼⠁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⡠⢞⣿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠀⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣀⣼⡷⠛⠘⠀⠀⠀⠀⠀⢀⠀⣠⠞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣸⡤⠀⢒⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡾⠟⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⡁⠀⣴⡿⣿⡇⠀⠀⠀⣤⢀⣤⠿⠛⠉⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠐⢿⡄
⠀⠀⠀⠀⠀⠀⠇⡼⠋⠀⣸⣀⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣻⡄
⠀⠀⠀⠀⠀⢰⣞⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⣏⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠟⠛⠙⠛⠛⠛⢋⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⢹⡀⠄⠂⠀⠀⠀⠒⣿⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠆⠀⠀⠀⠀⠀⠈⠀⠘⢞⢻⣿⣿⣿⣿⡄⠀⠀⢠⢸⠁⠀⠀⠀⠠⢤⣶⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⠤⢠⣴⣿⣿⠿⢛⣻⣿⣤⣄⣸⣼⠆⠀⡀⠀⠀⠀⠀⠉⠁⠀⠈⠻⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠡⠘⠛⠃⠉⠹⢿⣿⣿⣿⣿⣷⣿⣄⣀⡀⠀⠀⠀⠀⠀⠎⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⠃⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣧⣿⣆⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣄⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢒⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣾⣿⣿⣿⣿⡇⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠙⠘⢧⣆⠀⠀⠀⠀⠀⠀⠀⠤⢒⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⢀⣄⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢰⠆⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⠀⢀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⢀⣻⠁⠀⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠤⢤⣤⠶⠋⠁⠀⠀⠒⣩⣄⠀⠀⠀⠈⠪⡆⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣨⡉⠀⠀⠀⠀⢿⣖⠁⠀⠀⠀⠈⣲⡿⠀⠀⠠⠐⡄⢻⣔⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣡⣦⣉⢀⠐⠤⣀⠈⠻⢿⣶⠂⠈⣽⣿⡀⠀⠠⠀⡝⠄⠹⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣷⣤⣈⣷⡀⠈⠛⢻⣿⢩⣙⣿⡄⢠⡀⡀⠀⠢⡄⠀⣴⢒⣈⠥⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠦⠾⠿⣿⣿⣿⠿⠾⠿⣄⣠⣼⣿⠀⣽⣿⡀⠀⢻⣧⠀⠀⠹⢄⡇⠀⠀⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠻⡄⠀⠀⠀⢻⡟⠀⢠⣿⣿⠀⠐⠀⠈⢷⡄⠐⡌⣧⠀⠠⠏⣰⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠹⡄⠀⠐⣼⣷⣰⣾⠏⠤⠀⠁⠀⠀⠀⠙⢷⣦⡘⠄⣀⠖⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠙⠂⣶⣿⡟⢿⠃⠀⠒⠀⠁⠀⠀⠀⠀⠀⠈⠙⠆⠐⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⡿⠟⠁⠀⢡⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢻⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠁⠀⠀⠀⢤⣻⡇⠀⠁⠀⠠⠖⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣻⡿⠃⠀⠀⠀⠤⢊⣥⠠⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣀⠘⠟⠃⠀⠀⠀⠀⠖⠋⣶⣦⡄⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠠⣿⣿⠀⠀⠀⠐⠀⠀⠐⠋⠀⠀⠀⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡖⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⣿⣾⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠛⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠔⠂⠀⠀⠀⠀⠺⣇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢸⠠⡀⠀⠀⠀⠠⣺⠆⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⠀⠉⠛⠷⠿⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠐⠻⣦⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢶⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⠲⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⣰⠋⠃⠒⠂⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠁⢰⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠛⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣐⣤⢀⣽⠃⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⢀⡀⠀⡀⠀⠠⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠐⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠂⠐⣀⡀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠉⠄⡄⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⢄⡀⡀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠰⠠⠀⢈⠀⠁⠐⠄⢔⠀⠉⠛⠲⠒⠺⠁⠀⠀⠑⢔⠀⠁⢅⠔⣐⡀⠁⠈⠁⠀⠈⠮⠤⡀⠀⠀⠉⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠞⠉⠱⠒⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣄⡴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡉⠣⠀⠅⠈⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁
⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣄⡤⠀⠠⣊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠀⡄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠋⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠐⠀⠈⠉⠀⠀⢀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠤⠀⠠⠄⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠁⠀⠀⡀⢀⢀
⠀⠀⠀⠸⠔⠀⠀⠆⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢈⡀⠀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⢥⠀⠀⠀⠀⣀⠀⠀⡄⠀⠚⠀⠀⠁⠈⡁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠃⠀⠉⠀⠀⠌⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⡆
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⡇⠀⢸⠤⠤⠤⠄⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⠀⡗⠒⠒⠚⠓
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡝
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⢀⡜
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢀⠎
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠋
⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠶⠶⠶⠤⠤⠤⠤⠤⠴⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢀⢨⢿⠠⠶⣾⣁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣼⣿⡎⠀⠀⠀⠐⣿⣿⡄⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢆⠀⣿⣿⣷⢀⢀⠀⣨⣿⣿⡇⠀⠀⢀⡴⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⡆⠈⢛⣾⣾⣾⣷⣿⣭⣤⣁⡀⢀⢾⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠟⠙⠛⠉⠁⠉⠉⠙⠹⣿⣻⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢊⣶⠔⢀⡀⠀⠀⠀⠀⠀⣀⢠⣿⣤⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⣤⡴⠊⡐⡂⣺⢿⣿⣾⣤⣴⣆⡄⣄⣮⣷⣿⣭⠭⢳⠀⠈⠳⣤⣄⣄⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠚⠓⢚⠍⠁⠀⡰⠃⠉⢉⣹⣿⠻⠿⡏⡿⣟⠿⢻⣙⣓⠚⠃⢣⠀⠀⠈⠛⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⢁⣞⣯⣽⡃⠀⠀⠁⠀⠈⠁⣀⣠⡏⠿⣭⣛⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠈⢠⡙⣆⠋⠹⠓⠶⠠⠖⠒⠚⠛⠉⠁⠘⠄⢀⡀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢠⠁⠀⠈⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠇⠀⠰⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠞⣽⠟⠒⠀⠄⠄⠀⠀⠤⠠⠐⠊⠈⠙⠀⢲⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢇⡾⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣧⠀⠀⠻⣝⡂⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠿⠾⠧⡀⠀⠀⠀⠀⣀⣀⡥⠘⠏⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢀⡰⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠶⠤⢄⡀⣄⠤⡤⠾⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣼⡏⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⡠⢊
⠀⠀⠀⠀⠀⠀⡰⠥⡰⠄⢠⠋⠉⢲⠈⢋⠀⠘⠀⠀⠄⠀⠀⠀⠀⢠⠀⡠⠂⠀⠄⠀⠚⡎⠀⠑⢧⡀
⠀⠀⠀⠀⠀⠀⢇⠠⠀⠀⠀⡇⠀⢼⠁⠀⢱⠂⠁⠀⠀⠀⠀⠰⡁⡸⠀⢇⠀⠐⠀⠀⠀⣼⠀⠀⠇⠀⠀⢰⠀⢀
⠀⠀⠀⠀⠈⠂⠢⡀⡀⠂⠺⣄⠀⡈⠁⢰⡋⠀⡃⠙⠀⠀⠀⠀⠀⠑⠀⠌⠀⠀⠀⠕⠉⠸⡄⠠⡗⠠⣤⠂⢀⠸
⠀⠀⠀⠀⠠⠃⢆⠀⡱⠠⣴⠋⠀⠑⡶⠛⢳⠈⢳⠈⠀⠀⠀⠀⠀⠀⠀⡌⠰⠀⠘⡀⠀⢠⠃⠀⠇⢀⠃⠀⠜
⠀⠀⠀⠀⠀⠂⠎⢈⠄⢀⡼⠒⢤⠖⠓⣔⠚⠄⠚⡀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠄⡠⠘⠀⠀⢈⠅⠀⡸⠀⠁
⠀⠀⠀⠀⠀⢰⠁⢡⡀⡨⠃⢠⠸⠀⠀⠾⣈⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⠀⠀⠀⠇⠉⠐⣀⠇
⠀⠀⠀⠀⠀⠀⠑⣞⠀⠣⡀⠼⡒⠉⢰⠰⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣱⠀⠪⡄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢨⠆⠸⣄⢀⡜⠂⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠣⡀⠠⣅⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠘⡦⠠⡄⠀⣰⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠐⠀⠀⡇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠙⡆⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡂⢈⢠⠃⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢰⠖⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠓⠈⠁⢀⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡐⠀⠀⡸⠀⢱⡀
⠀⠀⠀⠀⢀⠰⠀⠀⢀⡀⠤⠒⠉⠀⠀⣠⠃⠀⠀⢣
⠀⠀⠀⠀⠠⡣⠖⠋⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡎⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠡⡀⠀⠀⠐⠊⠀⠀⠙⠢⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠲⣄⡀⠀⢀⡠⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⠲⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠠⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠀⠰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠐⠂⠀⠀⢀⡆
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⣀⣀⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⣄⣀⢀⣀⡠⠖⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⢠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠈⠻⣿⣿⡇⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⣷⡀⠀⠘⣿⡇⠀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣷⣤⣤⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠤⠴⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠺⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣿⡏⠀⠈⠻⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠒⡄⠀⢀⡤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⢁⡔⠉⢰⠃⠀⣠⠔⠊⠉⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠢⡀⠀⠀⠀⠀⡇⠀⢸⠏⠀⠀⠸⡤⠞⠁⠀⠀⢠⠏
⠀⠀⢸⠉⠉⠛⠒⠲⠤⣀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⡎⠀⠀⠀⡇⠀⢀⢿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠉⠉⠓⠲⠦⣄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠃⠀⠀⠀⢇⡰⠃⣼⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠈⠉⠓⠻⢤⣸⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⠠⣀⣀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢯⠉⠀⠀⠈⠉⠲⣴⠋⠁⠀⠀⠀⠀⠉⠳⣄⡴⠊
⠀⠀⠀⠀⠀⢈⣲⠄⢀⣀⣀⣀⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠈⣳⠤⠤⠤⠤⣀⠀⠀⠈⢧
⣖⠚⠉⠉⠉⢁⡴⠊⠉⠀⠀⠀⠈⢇⠀⣀⠴⠖⠒⠒⠲⠤⣀⠀⠀⣸⣤⣤⣤⣀⡰⠊⠁⠀⠀⠀⠀⠀⠙⢦⡀⢸⡆
⠈⠓⠤⣄⣀⠎⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⡏⠀⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⣘⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡠⠔⠒⠛⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣯⣀
⠀⠀⢀⠔⢻⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠇⠈⠑⣄
⠀⡴⠁⠀⠈⢦⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠈
⢸⠁⠀⠀⠀⠈⠓⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⣠⠧⣄⣀⡠⠤⠚⠁
⢸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠔⠒⠉⠈⠓⠤⣀⣀⣀⣀⠤⠚⠁⠀⠀⠀⢳
⠈⢇⠀⠀⠀⠀⠀⢀⠜⢦⡀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠣⣄⠀⠀⢀⡏⠀⠀⠉⠓⠒⠤⠔⠒⠋⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡞⠲⠤⠤⠤⢤⡖⠋
⠀⠀⠀⠀⠉⠛⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠓⠦⢤⣤⠤⠴⠚⠁⠀⠉⠒⠒⠒⠲⡉⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⣀⣀⠤⠔⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⢀⡠⠞⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠉⠉⠉⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⢀⣀⡤⠳⣄⡀⠀⠀⠀⠀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠉⠀⠀⠀⠀⠉⠑⠒⠒⠊⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠉⠓⠂⠤⠔⠒⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⣀⡠⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠑⠤⣀⠀⠀⠀⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⢀⡖⢚⠀⣀⣀
⠚⠲⢤⣀⣀⣀⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⡆⢒⠀⠀⢀⡀⠀⠀⢸⡈⣁⠀⠀⢀⡘⡦⢶⢤⢾⡇⠿⠯⠋⠁⠁
⠀⠀⠀⠈⠀⠚⠠⠍⣅⡐⠒⠀⠀⠀⠀⢀⡶⢺⡗⣤⣀⣀⣀⣴⠀⠚⠗⢺⡩⠉⠩⢹⡅⠀⢘⠯⣬⢸⠛⠻⣇⠁⢠⠰⢸⣷⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⠀⣿⡇⢤⠚⠏⠀⠀⢠⣉⡣⠀⠀⠉⠛⢿⡀⢰⠿⡄⠈⢀⡽⡏⠀⣠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢈⣇⠄⠀⠀⢀⡀⠀⠀⣠⠂⠀⠀⠈⠀⠀⠀⠉⠉⡄⠘⡀⣸⠀⢧⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠓⣾⣿⠛⠀⠀⠀⠐⠀⠀⠀⡀⠃⠀⢹⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠖⠸⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠭⣀⠀⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠄⡅
⠀⠀⠀⠀⠀⠀⠀⢐⠁⣰⠒⡄⢱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠠⠜⠉⠁⠀⠉⠙⢇⡇⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠘⢌⡑⠒⠲⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡦⠴
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠂⡈⠀⠀⠃⠒⠂⠀⠚⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣀⡀⠄⠀⠀⠀⠄⠀⠴⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣠⠆⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣄⠀⢠⢏⣠⠖⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⣤⣀⢰⡏⢿⡙⠿⣯⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⣛⣻⣿⠃⠀⢳⡀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢷⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⣇⣀⣀⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⠞⠋⠉⠉⠉⡿⠉⠉⠉⠛⠲⣄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠐⠲⠤⠷⠶⠂⣀⡤⠶⠞⠓⠺⡗⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡤⣤⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠉⠉⡽⠉⠉⠙⠓⢦⡀⠀⠀⠐⡇⠀⣸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⣄⣀⣼⣡⠄⠀⠀⠀⠀⠙⣆⠀⠀⣧⠀⠸⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⣴⢻⠆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠻⣆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡾⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣀⣤⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⣤⣤⣤⣄⣀⢀⣿⣿⣷⣄⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⣤⣀⡀⣸⠄⠙⢦⣄⣀⣠⢤⡀
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠉⢭⣀⠀⢢⠈⠉⠁⠀⢷
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣠⣶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠓⢮⣇⠀⠀⣤⢸⠀⠀⢀⣴⡖⢦⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⣰⣏⡀⠛⠓⠒⠲⠿⣦⡀⡟⢸⣠⠞⠉⠀⢳⡶⠃
⠀⠀⠀⠈⢉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⣉⡭⠷⢤⣀⢀⣀⣀⣳⠃⣼⠋⠀⣠⠾⠯⣤⣤⣄⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⡿⠋⣽⣿⠿⣿⣿⢿⣷⡀⠀⠀⠀⡾⠁⠀⠀⢀⡟⠉⠁⠈⠉⢻⡁⣠⠞⢩⠟⡥⢦⢰⡦⡝⢦
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣶⣿⣷⣤⣿⡟⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⣿⠉⠓⢾⡜⠧⠼⣱⠇⣹⢸
⠀⠀⣼⣏⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠙⣿⠛⠛⠋⢠⣾⡿⠁⠀⢀⡏⠹⣤⣀⠀⣘⡦⠖⠒⠲⢤⣰⠃⠀⠀⠈⣿⠛⠛⠁⣴⢃⡞
⠀⠀⢻⣿⣦⣶⣿⣿⣟⠉⠀⠉⣿⣿⣿⣷⣤⣶⡿⠀⠀⠀⠈⠉⠀⠀⠀⠈⣧⡴⠖⠛⢿⡏⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠏⠀⠀⠀⠈⠉
⠀⠀⣾⣿⣿⣿⣿⣿⣷⣁⣀⣤⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣸⠶⠶⠞⠛⣆
⠀⠀⣿⣿⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠶⣤⣤⡤⠞⢧⠀⠀⠀⠀⢸
⠀⠀⠈⣿⣷⣾⣿⣿⣿⠋⠙⢿⣿⣿⣿⣷⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣤⣤⡤⣟⠀⠀⠀⠀⠀⠈⡇⠀⢀⣠⠏
⠀⠀⢸⣿⡿⠿⣿⣿⣷⣄⣤⣾⣿⣽⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡼⠋⠋⠉
⠀⠀⠘⣿⣦⣤⣿⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣼⠛⠒⠚⠋
⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠛⣛⠒⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣀⡁⠀⠐⠚⣂⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠀⠀⠀⢘⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⡶⡄⠀⢀⠖⠂⢸⠖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡈⠉⠁⢀⡴⠁⠘⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣈⠀⠸⠑⠒⠒⠁⠀⠀⠀⠠⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣠⠄⠀⠲⣄⠀⠀⠀⠀⢀⣀⠀⠀⢃⣠⣤⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠐⠁⠀⠈⠑⠄⢀⠎⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⡜⠀⠀⠐⠒⠤⠀⠀⠀⠙⠦⣤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠢⡀⠰⢻⢡⣄⣀⠀⢀⣀⣀⣀⣀⡤⠖⠋⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⠣⡅⠀⠀⠈⠉⠀⠁⠀⠀⡠⠀⠀⠀⠘⢦⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠂⠤⢄⣐⠀⠁⠒⠒⠀⠀⠀⠉⣠⠔⢁⠀⣀⠤⠓⠁⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢄⡀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠈⠀⠔⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢍⣉⠓⠢⢄⠀⠀⠁⠀⠐⠒⠒⢤⡀⠊⠁⠀⠀⣀⠀⠀⠀⡠⠀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⡒⠄⠀⠀⢄⠀⠠⠀⠀⢱⠀⠀⠀⠊⠁⠀⣠⡬⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠢⡄⢣⣸⠊⠀⠒⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⣀⡤⢤⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠙⢋⡀⡙⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣩⣻⡆⠀⠀⣀⣀⣠⠤⠷⣄⡘⢧⣐⣛⣦⣼⡵⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢇⡬⠖⠚⠉⠉⠀⠀⠀⠈⢻⣙⡞⠃⢹⠞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣦⠽⡶⠒⠒⠚⢛⡽⣿⠀⠀⠉⠀⠉⠉⣇⠀⠀⠰⡏⢭⡉⠉⠉⠉⢹⡛⠾⠟⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠊⢻⣦⠘⡇⠀⡔⠲⠋⢠⠇⠀⠀⠀⠀⡠⣄⢻⠀⠀⠀⢻⡀⠹⣄⠀⢀⣼⠇⠀⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⣿⠀⣧⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠓⠊⢸⠀⠀⠀⠀⢷⠀⠘⡆⣏⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡿⡏⠀⡏⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⣷⢹⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⣿⠇⠰⣇⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⢯⡽⠀⡇⠀⠀⠀⠀⠸⡄⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⣄⣀⣀⣀⣀⣤⣤⠴⠶⠶⡶⠶⠶⠶⡶⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡄⠀⠀⠘⡇⡴⢡⠜⠛⠛⠛⢻⠀⠀⢰⠋⠉⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⠀⢰⣧⡄⠀⢸⠃⡇⠈⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠘⠿⠁⠀⠸⣴⠃⠀⡟⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⡼⠒⠒⠛⠛⠃⠘⠛⠛⠛⡟⠀⠀⠀⣠⠋⠉⠉⠹⣄⣀⠀⠀⠈⢯⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣭⣝⣛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⣀⣠⠖⠒⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⣀⠤⠀⠀⡤⣀⢐⠉⠂⠲⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠⣀⡀
⠀⣅⠳⢤⠔⢄⠀⠠⠹⢀⣀⣣⠞⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⠢⠏⠡⠡⠈⡀⠸⢹⡞⠀⢆
⡠⠃⠀⢀⣠⠛⠃⠀⠀⠢⠜⢸⠧⡄⢠⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⡁⣠⣘⢄⢀⢇⢀⣇⣰⡼⢻⡖⠊
⠃⠤⠊⠣⣀⡱⢦⡡⠌⣐⡰⠃⠑⠒⠂⠀⠀⠤⢀⠐⢌⣭⣔⡒⡒⢄⠀⠉⡧⠃⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠥⠤⠤⠴⠄⢻
⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠤⢀
⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠰⠀⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠤⠅⢁
⠀⠀⠀⢸⡄⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠊⠀⢄⠱⠄
⠀⠀⠀⠈⢌⠒⠄⢉⠒⠀⠐⢊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣀⠄⠂⠠⢀⣀⠀⠈⢈⡀⠀⠀⢀⢠⢖⡀
⠀⠀⠀⠀⠈⠱⠤⣀⣀⡩⠝⠁⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠢⠀⢈⣁⠀⠀⡀⠐⠈⡄⠀⠀⠈⠀⡑⠏⣠⠲⠊
⠀⠀⠀⠀⢀⠃⡐⠀⠀⠀⠀⠀⠀⣀⠠⠚⠒⠀⠘⣤⣄⠀⠀⠀⡀⠈⠐⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢀⠎⡘⠀⠀⠀⠀⠀⢴⡋⠄⠀⠀⠀⠀⡊⠀⠈⠉⠁⠚⡍⢣⠀⠷⠊⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⢄
⠀⠀⠀⢎⣠⠀⠀⠀⠀⠀⠀⠠⢈⠑⠈⠀⠙⠉⠈⠖⠉⠙⠆⠀⡠⠸⠁⠀⠀⢀⠔⠊⠁⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠚⠀⠈⠓⠀⠉⠓⠈⠀⠀⠀⠀⢀⠏⠀⢀⠔⢋⠑⡦⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⣄⠀⠀⠀⠀⠀⠸⡀⠉⡇⠀⣭⠤⠣⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠲⢚⢉⠉⢫⡤⢀⠃⠀⠀⠀⠀⠀⠙⢤⡛⢮⣀⣀⡧⢏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠂⠉⠀⠑⠄⠀⠈⣎⡤⠊⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢂⠠⡀
⠀⠀⠀⠀⢲⠠⠠⠅⠀⢂⠑⠄⡄⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⢆
⠀⠀⠀⠇⠀⡑⢒⠔⠣⠤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃

⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⡅⠀⠀⢀⡗⠀⠀⠀⣠⡤⢠⢀⢄⣠⣀⢄⢠⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢢⠀⢻⢛⡛⢿⠃⡀⠀⠀⠙⢦⡀⢢⣾⡷⣿⣦⠂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠣⢼⣯⣽⡯⠔⠁⠀⠀⠀⠀⠹⣦⣀⣹⣋⣠⡼⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢎⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠀⢀⣺⣿⣷⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠸⣶⣧⡶⠄⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡠⣼⠿⢿⢤⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣯⡧⠀⠀⠀⠀⠀⠈⡜⢹⣄⣸⢱⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠈⠁⠈⠻⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣽⣷⣇⠀⠀⠀⠀⠀⢐⣛⡂
⠀⠀⠸⣿⠇⠀⠀⠀⢀⣿⣷⣾⣧⠀⠀⢀⡜⠻⡿⠛⡀⠀⠀⠀⣿⣽⣿⣯⡟⠀⠀⠀⠀⠹⣿⣿⡐⠄
⠀⠀⠀⣉⠀⠀⠀⠀⢸⢀⢠⢇⣭⡇⠀⠀⣵⣦⣶⣶⡉⠀⠀⠪⡇⠈⠛⢀⣶⡅⠀⠀⠈⠁⢸⡏
⠀⠀⠀⠉⠀⠀⠀⠀⠰⠻⠾⠾⠣⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠰⡹⣴⣶⣿⢿⠃⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣟⣛⣛⣛⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠉⠕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⠈⡄⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠜⠒⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠑⠒⠒⠢⡤⠒⠚⠀⢀⠂⠄⠔⡠⡠⢃⢊⠎⠀⠀⠀⠀⠀⠀⡄⢣
⠀⠀⠀⡠⠄⠠⢼⠀⠀⠀⢀⢀⠄⡠⢀⢀⢀⠄⢄⣄⣐⣆⣐⣀⣀⡀⣠⣠⡥⠚⠘⠺⡴⠋⠁⠳⡎⠀⠀⠀⠀⠀⠀⠀⠄⠸
⠀⠀⡜⠀⢀⢤⢀⢄⠔⡀⠡⢂⠜⡴⠥⠆⠚⠈⣩⠜⢋⢩⠉⠉⠙⠩⢍⣉⠒⠲⢤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠑⠤⠤⠤⠤⠀⠂⣒⠶⠂⠁⠀⠀⢀⡤⠊⠀⠀⠀⠂⢣⠀⠀⠈⠐⠀⢙⠢⣕⠀⡨⢉⠐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠈⡆⢁⠄⠀⠀⠂⠠⠈⠓⢄⠑⡡⢂⠄⢉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠋⠐⠄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡐⢍⡀⠀⠀⠈⠒⠤⠀⠑⢄⠕⡨⠐⡨⢐⣌⣲⣄⠀⠀⠀⠀⠀⠀⠓⠢⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢀⠜⠀⠁⠀⠀⢀⣀⣀⣀⣀⣀⠠⠀⠇⠀⡂⠤⠄⠒⠒⠒⠀⠠⢈⣢⣀⠕⠊⢁⠀⠄⠈⢀⠂⠄⡀⠠⠀⠀⠀⡅
⠀⠀⠀⠉⠉⠉⠁⠒⠠⢁⡬⠔⠒⠈⢉⠄⠍⠀⠀⠀⠀⢿⠁⠁⠚⠁⠀⠀⠀⢠⠀⠀⡠⢀⠀⠌⡙⡰⠡⠂⠌⡰⢠⠂⠎⡐⠡⢂⢂⠂⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⣀⣀⣻⣏⣐⣁⣊⡐⠀⠁⠂⠈⠀⠀⣁⣊⣈⣀⣀⣁⣈⣀⣁⣁⣈⣐⣀⣁⣀⣈⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡤⠀⣠⠀⠀⠴⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠄⠀⢀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣜⠇⢀⡀⢸⡃⠀⠀⠸⠁⢰⡌⠀⠰⠊⠀⠀⣢⠆⠀⢰⡁⠀⠀⠗⠀⠀⠗⢠⠃⠰⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢀⡀⠁⢰⡥⠀⠸⢀⠀⢠⠚⠀⠀⠀⠰⠂⡜⠁⠀⢀⠀⠀⢀⠴⠀⣀⡒⠀⢀⡶⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡀⠀⠀⢈⡸⠀⠘⠃⠀⠀⠸⠊⠀⠀⠀⢀⡭⠀⠀⠘⠃⠀⠉⡀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⢸⢻⡀⢀⡀⢀⠴⠀⠀⣀⠀⢀⠄⢀⣈⠁⢀⠀⠀⠼⠃⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⡀⠂⠈⠁⠀⢰⠄⠀⠛⠀⠈⠁⢀⡪⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⡀⠀⠠⢀⠀⡀⠀⢀⠀⡀⠀⠀⢀⠀⠀⢀⠀⡠⠀⠀⡀⢀⠀⡠⠀⡀⠀⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠉⠂⠁⠊⠔⠨⠊⠔⠄⠈⠔⠡⠊⠔⡡⢂⠅⢊⠔⠡⢊⠄⡥⢊⠔⠨⠔⡡⡪⢂⠁⢊⠔⡡⢊⢔⠡⢊⠔⡥⢊⠂⠕⠊⠠⢊⠄⠔⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⡠⠤
⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠦⡤⠠⢄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠠⣄⠀⣠⣄⣀⡀
⠀⠀⠀⠀⢾⣧⠀⠀⡙⠀⠀⠀⠁⠉⠙⡄⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⡿⠿⠍⠀⠀⠀⠀⢤⠌⠑⠀⠄⡉⠹⣦
⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠹⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⣄⠇⠍⠀⠀⠀⠀⠀⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠃⠀⠂⣵⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢄⡠⣇
⠀⠀⠀⠀⠀⢄⠀⣦⡄⠁⠒⠒⢆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⠚⠒⠚⠓⠋⠘⢄⣀⠠⠄⢰⠞⠋⠀⠀⠀⡘⠁⠈⢦
⠀⠀⠀⠀⠀⠈⠶⠾⠿⣾⣧⣠⠜⠀⠀⠀⠄⢀⡀⠀⠀⠀⣀⣩⡽⠗⠒⠒⠈⠁⠀⡀⠀⠒⠁⠀⠀⠀⡠⠊⠀⠄⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡀⠀⠀⠀⠐⡈⠉⠉⠉⢉⢁⣠⠶⠛⠐⣒⠴⠎⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠈⠓⠢⠴⠾⡟⠁⢠⡴⠋⠁⠀⣶⡀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢰⠋⠀⠀⡀⣸⣾⠇⠀⠀⠀⣠⣇⡀⠀⠀⠀⠀⠀⠀⠱⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢰⠃⠀⣦⣰⡷⠿⠋⠀⠀⠀⠀⠈⠉⢁⡦⠀⢀⣇⢷⣄⡀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⣦⡤⡀⣰⠀⣸⣧⣝⡀⠄⠀⠀⠀⠀⠀⠘⣴⣴⡿⠛⠉⠀⠀⠀⠀⢠⣤⣀⣀⣶⡞⠀⠀⠈⠉⠀⢸⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⣆⣀⣼⠏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢷⣄⣀⠀⢀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⠤⠔⠒⠉⢱⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡀⠀⠀⠀⠸⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠻⣿⣿⠿⠿⠿⠿⠿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠛⣿⣿⣿⠸⣿⣿⡿⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣖⠿⣿⡟⠀⢾⣿⣶⣦⠉⠁
⠀⠀⠀⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⡈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⣿⣿⣿⢶⣿⣿⣿⡌⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣋⠀⠛⣿⣟⡁⢠⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢶⠀⠀⢀⣿⡆⠀⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⢼⣿⣿⣿⡛⠿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠁⠀⠘⡟⠀⠈⠙⣧⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡛⣿⣿⣿⠛⣿⣯⣔⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⡀⣴⣷⣀⠀⠀⣽⡶⠂⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⢙⡿⠋⢰⣿⣿⣷⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⠀⠈⠁⠀⠀⠈⠀⠈⣿⠁⠀⠀⠈⣇⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⢇⣬⣟⠿⢿⣽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⡤⢤⠀⠀⠀⠀⠀⠀⣀⠈⠉⢁⣀⠀⠰⢏⠋⢑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⣾⣿⣿⡆⢻⠟⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠁⡼⢁⠀⠊⠀⠀⠀⠁⠀⠐⢘⣄⢀⡠⠟⠀⠀⠘⠦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⣫⣄⡿⡻⡿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠁⠈⣹⠆⡀⠀⡁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠀⠀⠀⠀⠀⠀⠑⠆⠴⠃⠀⠀⢰⡁⢘⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⠴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢾⠉⡋⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡖⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠛⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⠶⠶⡶⢶⣶⡶⠶⢶⣶⢶⡶⠶⣶

⠀⠀⠄⠀⠀⠀⣤⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⣶⠄⠀⠀⢀⠊
⠀⠀⠘⡂⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⣀⠀⠀⠀⠀⣠⡴⣦⡄⠀⠀⠀⣀⡤⠔⠂⢀⣯⡄⡀⠀⠀⠠⠦⠀⠀⠀⡠⠃
⠀⠀⠀⠈⢆⡀⠀⠀⠐⠀⠀⠻⠱⡂⣄⡀⠂⠨⢉⣓⣼⣏⣥⣼⣧⣉⣾⣴⡫⢛⠀⠀⠰⠬⠛⠊⠀⠀⠠⠀⠁⠀⠠⠔
⠀⠀⠀⠀⠀⠱⠄⢆⠀⠀⠀⠀⣠⣀⣀⣀⣀⣈⡠⠾⣤⣘⣿⣷⣿⣟⣃⣽⠷⣤⢤⢄⣠⣤⣄⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠙⢢⣿⣿⣿⡛⢻⣿⣿⣿⠂⠁⠉⠁⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⡿⣿⣿⣟⢿⢿⡋⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢣⣿⠿⣿⡿⢿⡗⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⠛⠂⣽⡀⠙⡑⠏⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⡿⠿⢿⣋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠑⣒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡤⠴⠒⠋⠁⠀⠀⣀⡤⢾⡇
⠀⠀⠀⠀⠀⢸⠒⠚⠉⠉⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠈⢦⣠⣤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠴⢶⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢝⢢⣀⡠⠴⢲⠶⠦⣄⡀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⡅⠉⠀⣰⠋⠀⣰⠃⠙⣎⣇⠹⣄⣀⣠⣄⣀⡀⠀⠀⣠⠴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣰⠒⠀⠀⢀⡏⠀⢰⠇⠀⠀⠘⢻⡶⢫⠇⠀⣾⠀⠉⢲⠞⠔⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢼⣘⣿⣠⠴⢦⠀⢸⠀⠀⣾⡋⠉⠭⣛⠿⠀⢸⡀⠀⢹⠀⠀⠀⠐⣃⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡄⠀⡏⢳⡄⠀⠒⠀⠀⠀⣇⠀⠸⡆⠀⠀⢀⠀⠩⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡟⠀⡪⠀⣄⠀⠸⣄⠀⠹⡄⣠⠏⠙⠲⠯⠥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⣢⠞⠉⠙⠲⠾⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠁⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢸⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⡄⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡇⠀⢀⣀⡸⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠛⠋⠉⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣀⣠⠤⠄⠒⠘⠛⠉⠉⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⣀⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠄⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠸⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡔⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⡄⢸⣷⠀⢿⡏⠁⠀⠀⠀⢱⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⣰⣶⣦⠀⠸⣿⡀⠀⢸⣷⠀⣿⡇⠸⣿⣀⣀⡀⠀⠈⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢷⠀⠀⣿⡇⠹⠃⠀⣿⡇⠀⠀⣿⡄⠸⣿⠀⢻⣿⠛⠋⠀⠀⢸⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⡀⠀⢹⣧⠀⠀⠀⢸⣿⠀⠀⠸⣧⠀⢻⡇⠘⣿⠀⠀⢀⠀⠀⢇⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢣⠀⠘⣿⡀⣴⣶⡀⣿⣇⣀⡄⢻⣦⣼⣿⠀⠻⠿⠿⠿⠃⠀⢸⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⡄⠀⢹⣧⣀⣽⡇⠸⡿⠟⠋⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢰⠀⠀⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠶⠶⠖⠒⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢦⡀⠴⠚⠉⠁⠀⢀⣀⣤⠤⠶⠒⠚⠋⠉⠉⠉⠉⠍⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⣂⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣤⣄⣀⣀⣀⣀⣀⣉⣁⡀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⡶⠶⠶⣶⠶⠶⢶⡶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡙⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢡⠤⠤⠤⠔⠒⠒⠲⠾⠌⠉⠉⠙⠶⠒⠒⠂⠤⠤⠤⢤⠃
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢀⣀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠄⣀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⢦⣀⣠⠤⡶⠛⢄⡀⠀⣀⠄⢠⣀⡀⣀⡠⠿⣦⢄⣀⡠⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢀⢉⠿⠛⠂⠀⠛⢿⡁⡀⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡦⠄⠀⠀⠀⢴⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⠤⠀⠀⠤⡤⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣬⣄⣠⣀⣠⣤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢹⣿⣿⣿⣿⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡇⢻⠃⢻⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢻⠀⠈⠀⢸⠀⠘⠀⠀⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄⠀⢠⠎⢣⡀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⠀⡸⠀⠸⡇⠀⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⡧⠀⠀⣇⢀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠰⣇⠀⢀⡿⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⢸⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠟⠀⠀⠀⠘⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⢄⠀⠀⠀⠀⢀⣤⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⣤⠃⠀⣀⣠⡴⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⡽⠉⠉⢹⡏⠀⠀⠘⢯⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠔⠀⠘⣷⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢶⣦⡀⠈⣧⠀⠀⠀⠀⠠⠐⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢛⣦⣟⣰⣾⣆⣾⣿⡎⠀⡆⣜⣋⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⣿⣷⣿⡿⠋⣽⣿⠙⣋⣿⡃⢠⣾⣝⣿⣶⣌⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣫⣀⣶⣿⡿⠯⣴⣿⣿⠗⡿⠿⡿⠻⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠤⠉⣹⣿⣋⣴⡿⢋⣭⣧⣾⣁⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠒⠘⠿⠟⢩⣿⣷⣾⣿⣿⠗⢩⣿⣟⣣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠐⢿⡿⢩⣼⣯⣷⠋⣿⡿⠟⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢉⣶⡶⢛⣯⡻⢟⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⣿⣿⣥⣿⠿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣧⣾⣿⠇

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠐⠤⠤⣀⣀⣀⣀⢀⣀⣀⠀⣀⣀⠠⣤⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠢⠀⠀⠀⠁⠀⡀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡠⠤⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠚⠉⠁⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⣠⡾⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⣠⡾⢋⠔⠀⣼⣷⠶⠛⠛⠛⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢻⡟⢀⠎⠀⠀⠀⢀⡠⠤⠒⠂⠀⠀⢀⣠⣽⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠳⢦⣄⠀⠀⠀⠀⢀⡿⠁⠀⡜⠀⠈⠀⠘⠀⣠⠔⠊⠁⠀⠀⠀⢀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡉⠳⣦⡀⠀⣸⠇⠀⠀⡅⠀⠀⢀⠔⠫⠤⣀⣀⣀⡀⠀⠸⠿⣥⣤⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⠀⠈⠛⢦⡈⠻⣆⣿⡀⠀⠀⢱⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠿⡷⠀⠈⣉⠛⠷⣦⣀⠈⠻⣦⡙⢿⡇⠀⠀⡰⠛⠤⠤⠤⠤⠐⠒⠀⣠⣶⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡋⠁⠀⠠⢄⣀⠀⠀⠀⠈⠑⢄⠀⠙⢷⣄⠈⢷⡌⢻⡄⢰⢁⣠⣤⣄⣀⣤⣤⣤⡀⠈⠉⣛⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣀⡠⠤⠄⢹⠖⠐⠒⠂⠤⣧⣀⠀⠙⣷⡈⣿⣤⢿⣿⡏⠁⠀⣹⠟⠁⠀⠎⢿⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠐⠉⠀⠀⣀⠔⠁⠀⠀⠀⣠⠔⠁⠀⣹⠶⠛⣿⠏⠀⠀⠈⢻⣆⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣾⣁⣠⣤⣤⣤⡄⠀⠈⠁⠀⠀⠀⠀⠊⠁⣠⡶⠾⢿⣤⡀⢻⡄⠀⠀⠀⠀⣿⣀⣿⣄⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠀⣰⠟⠁⣀⣠⣴⣾⠂⠀⠀⠀⣸⡇⠀⠈⠀⠈⠻⣾⣷⣄⠀⠀⣠⣿⠛⠉⢉⢻⣿⡿⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⢉⣾⣃⣤⣤⡶⠟⠻⣧⠀⠀⠀⠀⠀⣻⠟⠻⢿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣼⠷⣤⣀⣀⣴⡟⠀⠀⠀⠹⣿⣿⣄⡀⢀⣰⣿⡄⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⣿⣿⣿⣆⡀⠀⣠⡿⠛⠉⠻⣿⣿⣿⠿⠷⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢀⣿⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⢸⡿⠁⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡟⠁⢠⡞⠋⠩⠍⠻⣧⠀⠀⠀⣸⡇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⠀⢸⣷⣶⣶⣿⣿⣄⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣼⣷⣄⡀⠀⣀⣼⣿⣿⣿⠏⠀⠀⢈⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠋⠁⠈⢻⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢠⣿⣦⣀⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣶⣿⠟⠛⠻⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣰⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠹⢦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⣿⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠖⠋⣁⡤⠴⠒⡦⠀⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠒⢋⣡⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡄⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠃⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠴⠚⠉⢉⡤⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣶⡶⠋
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⣤⣀⣀⣠⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⡀⠀⠀⢠⠇⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠀⠀⠀⡏⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠐⣇⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠞⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠶⠶⠶⢦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⣀⣠⣤⡴⠶⠶⠟⠛⠿⢯⣙⠉⠉⠉⠉⠙⠛⠛⠓⠲⠶⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⢀⡴⠛⠁⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣤⣀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⣴⠋⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠈⠻⣆
⣸⠃⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠹⣇
⢿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢻
⣼⣧⡀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠶⠶⠶⠶⠶⠒⠒⠒⠒⠲⠶⠶⠶⢶⣶⣾⣦⣤⣤⣀⣀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⣸
⣿⠈⢷⣄⠀⠀⠀⠈⠙⠷⣤⣖⡚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣲⣤⠾⠋⠁⠀⠀⠀⠀⠀⣰⢿
⣿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⢸
⣿⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠁⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠶⠶⣤⣤⣤⣤⣴⢶⠶⠶⣶⣶⠶⠖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⡶⠾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⣲⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣤⠤⣤⠤⠴⠖⠒⠛⠓⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠉⠛⢲⡉⠋⠀⠻⣔⣀⡤⠤⣴⣒⣓⣲⡚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⣀⣈⣡⠴⠚⠉⠁⠀⠈⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⢰⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠮⣭⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⢀⣀⣀
⠀⠀⠀⢰⣒⡦⠀⣀⣤⣤⣄⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⣀⣴⣶⠿⠚⠀⠻⠶⠟
⠀⠀⠀⠀⠉⢀⣀⣓⣶⡤⠾⠃⠀⠀⢳⣤⣀⠀⠀⢀⠀⠀⢀⡴⠋⠉⣀⣤⡘⠮⠶⠭⡖⠃⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⢰⠋⠉⠁⠈⠙⠲⠤⠤⢤⣀⣈⠛⠛⠛⠛⠛⢫⠟⠒⠒⠚⠁⢰⠃⠀⢾⡭⠽⣀⣠⣤⡀⠘⠓⠒⠋
⠀⠀⠀⠀⠈⠳⣕⠤⣀⣀⡀⠀⣀⣤⣤⣭⡿⠀⠀⠀⠀⠘⠷⠶⢦⣄⣠⢿⡖⠛⠛⠒⠛⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠋⠁⢶⣛⣒⣶⠿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⠗⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿⣿⠏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠃⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⡀⠀⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠈⠀⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⠲⠤⠤⠴⠃⠀⠀⠀⠀⢶⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡿⣃⣴⣯⣤⣽⠿⢛⣷⣶⣤⠀⠀⠀⠄⣀⣀⣀⣀⣻⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠂⣀⣤⣄⠀⠸⣿⠿⡧⠀⠀⠀⠀⠀⠀⠀⢸⠙⣶⢄
⠀⠀⠀⡠⠄⠶⡀⠀⠀⢰⠃⠀⠀⠿⣿⣿⣷⡄⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡄⠸⡄⣥⣴⣤
⠀⠀⠀⠄⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠨⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠔⢸⣿⡿⠏⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⢠⣾⣿⣿⠜⠿⡇
⠀⠀⠀⠀⣾⣷⢦⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠂⠀⡇⠀⠀⠐
⠀⠀⠀⣼⣿⣿⡟⠿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢠⡔
⠀⠀⠀⠘⠻⠟⡿⠀⣠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡁
⠀⠀⠀⠀⠸⣰⠃⢘⣿⣿⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⢳
⠀⠰⣶⣷⣆⢿⡔⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠆⠠⢼⣧⣶⣾⣆
⠀⠰⠿⣿⠟⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠙⠛⠋⣀⠴⡏⠘⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣠⡀⠀⠀⢰⣦⡄⢀⠀⠀⠀⠀⠀⢠⣼⣿⣷⢀⣾⣥⡄⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠂⣀⡤⠤⢄⡀⠀⢶⣿⣿⣿⠀⢸⣿⣷⡌⠀⠀⠀⠀⠀⠀⢹⠿⢟⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠑⣄⣬⣛⣿⣁⣀⠘⠿⠿⠃⠀⠀⠀⡀⠀⠀⢀⣀⠼⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⠀⠙⠿⣿⣿⣿⡍⠳⢤⣘⣆⣀⠔⠋⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠉⢉⣬⣯⣄⠀⠀⠀⠀⡹⢄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠂⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⢆⣤⣐⢒⠂⣠⣺⣟⢙⣷⣷⣶⢶⣤⠀⠀⠀⡀⣤⣴⣶⣞⡟⡟⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠲⠋⣻⡉⠁⠚⢀⠛⠀⠀⢦⣁⠛⢓⣼⣿⣯⣿⣷⡿⢿⣻⡍⠂⠀⣰⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠐⠛⢻⠶⣯⣯⡀⣼⡤⣶⣽⡿⣿⣷⡝⠻⣉⣵⣿⣟⢹⣧⡗⢡⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠈⠓⠛⠛⠛⠀⢒⣾⠓⠖⠚⢿⠝⣪⠟⠛⠘⠷⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠄⠂⠛⠀⠀⠀⠀⠀⠀⢀⡴⠋⣇⠀⠀⠠⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠈⠙⠆⠘⠉⢿⣿⠚⣖⣖
⠀⠀⠀⠀⠀⠀⠀⢉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠈⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠱⡝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⢉⣉⣶⠋⠀⢁⠊⢊⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⣀⠤⠒⠊⠁⡰⠃⠀⠀⠈⢸⠀⠎⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢀⡤⠚⠉⠀⠀⣀⡴⠊⠀⠀⠀⠀⠠⡸⠀⠸⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠔⠁⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⢀⢂⠇⠀⠀⣞⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠁⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣢⠊⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡵⠁⠀⠀⠀⣌⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠜⠁⠀⠀⣠⡴⠒⠛⠛⠛⠒⢦⣜⣾⠴⠒⠒⠒⣶⣹⠤⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠋⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣠⠎⡎⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠾⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣀⣀⣀⣀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠤⡤⠴⠶⠚⠋⠀⠀⠈⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠢⢶⣤⢀⢄⡀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠑⣇⣚⢡⡞⡥⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⢢⠃⠙⠙⢇⡇⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣸⠀⠀⠠⢀⡷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠉⠉⠁⠓⠀⠁⠸⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠁⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⡱⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠇⢠⠁⠀⠀⠀⣨⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣄⡁⠀⣀⡤⠄⠗⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠉⠀⠂⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣨⠀⠀⠀⠈⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠐⠠⠰⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠂⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣧⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⡘⢀⠢⠃⠀⠀⢀⠄⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠉⠉⠛⠀⠀⢀⡇⠀⠀⠀⠀⡠⠈⠀⢼⣄⣀⢀⠔⠁⠰⠀⡸⡊⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠀⠀⠀⢃⠀⢀⠊⠀⠙⠊⠀⢀⡶⢂⢫⡑⢄
⠀⠀⠀⠀⠀⠈⠒⠀⠀⡀⡀⠀⢀⣦⡴⠋⠠⢔⣶⣶⠒⣲⠗⠀⠀⠀⠀⣀⣀⠴⢏⣠⣈⣄⠝⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡁⢤⣤⡤⢎⣉⣀⠿⠉⠓⠲⡦⢀⠀⠀⠀⠀⠀⠻⣭⣹⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠼⠿⠇⠼⢿⣏⣉⣶⡆⠐⡏⠀⠙⠛⠛⠛⠙⠻⠿⠀⠿⠧⠼⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠄⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⣾⣟⣼⠄⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⣠⡐⡦⣀⠀⠀⠀⠀⠀⠀⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠘⣷⢣⢠⡍⠀⠀⠀⠀⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⡰⣟⡲⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⣀⢸⡶⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⠀⠀⠀⠀⠿⠮⠙⠁⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠰⣬⡳⠁⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠃⠀⠀⠠⣿⠊⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠻⢿⡿⠏⠀⠀⠀⠀⣸⣷⡿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠾⣟⡀⠀⠀⠀⠀⣴⢿⣿⣷⡄⠀⠀⠀⠀⣀⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⣶⣤⣴⣦⣶
⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠀⠘⠁⣾⣿⣿⡿⠀⠀⠀⠀⠉⠛⣛⣽⠃⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⢀⠄⢼⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⢀⠮⠁⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⢀⣯⡀
⠀⠀⠀⠀⠠⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠂⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⣠⣤⡔⠿⠟⣠⣤⣄⠀⠀⠀⠀⢀⣤⡴⣾⠀⡷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆
⠀⠀⠀⠀⢸⣿⣿⣷⡇⣰⣿⣿⣿⠆⠀⠀⠀⣿⢿⣷⣾⠀⣷⣿⡟⣿⠀⠀⠀⠀⠀⢠⣶⣆⡻⢛⣴⣶⡄⠀⠀⠀⠀⣠⣶⡺⡅⡟⣶⣦⡀
⠀⠀⠀⠀⢸⣿⣿⠛⠃⠛⠻⣿⣿⠀⠀⠀⠀⡿⣿⣯⡿⠀⣿⣿⡿⢿⠀⠀⠀⠀⠀⣻⡁⠀⢠⠁⠀⢸⡇⠀⠀⠀⠀⣿⣿⠿⠇⠿⢿⢿⡇
⠀⠀⠀⠀⢸⡟⢻⢤⡄⣤⣀⡏⣿⡇⠀⠀⢠⣄⠹⡿⡃⠀⢻⢿⠃⣸⠀⠀⠀⠀⠀⣿⡇⣶⣮⣷⣶⢸⡇⠀⠀⠀⠀⠛⢸⣶⠄⣴⣎⠘⠃
⠀⠀⠀⠀⣾⠇⢸⣿⣧⣾⣿⡇⢸⡇⠀⠀⢸⣿⢀⡷⠀⠀⠀⢾⡀⣿⡆⠀⠀⠀⠀⣿⢀⣿⣗⣿⣯⠘⣷⠀⠀⠀⢸⡿⢠⠟⠀⠸⣧⢰⣷
⠀⠀⠀⠀⣛⢰⣿⣿⣿⣿⣿⣿⠈⡇⠀⠀⠸⠇⢨⣦⣄⢀⣤⣮⡁⠹⠃⠀⠀⠀⢰⡏⣼⣿⣿⣿⣿⣦⢻⠀⠀⠀⢸⠇⣽⣦⣀⣤⣾⡄⣿
⠀⠀⠀⠀⠟⠘⣿⣿⡛⢻⣿⢿⠈⠇⠀⠀⢸⠆⢸⣿⣿⣿⣿⣿⡇⠴⡆⠀⠀⠀⢨⠀⣿⣿⡟⢿⣿⣿⢨⡄⠀⠀⣘⢀⣿⣿⣿⣿⣿⡇⢘⡀
⠀⠀⠀⠀⠀⠀⡌⣿⡇⢹⣿⣰⠀⠀⠀⠀⠀⠀⢉⣿⣿⠈⣿⣯⡅⠈⠀⠀⠀⠀⠈⠀⣷⣿⡇⣾⣿⡇⠀⠁⠀⠀⠋⠘⣸⣿⡇⣿⣯⡀⠈⠃
⠀⠀⠀⠀⠀⠀⣿⣿⠃⢸⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠃⢿⣿⡇
⠀⠀⠀⠀⠀⠀⡀⣹⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⢸⣻⡇⠀⢻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸⢻⠇
⠀⠀⠀⠀⠀⠀⣇⡿⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⢸⣦⡇⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⢀⡰⠈⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠸⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤
⠀⢣⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⡀
⠀⠀⢑⡆⠀⠀⠀⠠⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⢐⡊
⠀⠀⠈⢷⡀⠀⠉⠀⠈⠦⣀⣙⢦⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣶⠆⠀⠀⠀⠀⠰⣾⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⡴⣋⢀⠴⠁⠀⠉⠀⢀⡾⠁
⠀⠀⠀⠈⢿⠤⠀⠲⠦⣄⣘⠛⢣⡷⣄⠀⠀⠀⢠⠞⠀⠈⠉⠑⣤⣶⣶⣶⣶⡴⠊⠉⠁⠀⠳⡄⠀⠀⠀⣠⢾⡜⠻⣓⣠⠴⠖⠀⠠⡿⠁
⠀⠀⠀⠀⠘⣀⣀⠀⠀⠀⠀⠤⡆⠐⢌⢣⡀⠀⠸⣄⡀⠀⠀⣠⡿⣿⣿⣿⣿⢿⣄⠀⠀⢀⣠⠇⠀⢀⠜⡩⠂⢰⠤⠀⠀⠀⠀⣀⣄⠃
⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠋⠃⠀⠀⡀⠙⢦⡀⢸⣿⢀⣾⢽⣾⣿⣿⣾⣿⣷⡯⣷⡀⣿⡇⢀⡴⠋⢀⠀⠀⠈⠙⠂⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠙⣦⡹⢿⣿⣤⣿⣿⣿⣿⣿⣿⣤⣿⡿⣏⣴⠋⣠⠖⠁⠀⠁⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠴⠶⠿⢿⣷⣾⣿⡛⡿⠟⢛⣿⣿⣿⣿⡛⠻⠿⢛⣿⣷⣾⡿⠟⠶⠦⠀⠀⠀⠰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠔⠉⠛⣿⣿⡿⡀⠀⢘⣷⣿⣿⣾⡃⠀⢀⢿⣿⣿⠛⠉⠢⠄⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⢀⠈⣸⣿⡇⡀⠀⡚⣿⢿⡷⣿⢃⠀⢈⢸⣿⣎⠁⡀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠈⣸⢻⡇⠀⠠⠋⢻⣼⣇⡗⠙⠄⠀⢸⡟⣇⠑⢀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⣼⣿⣿⡇⠀⠀⠼⢻⣻⣟⡿⠇⠀⠀⢸⣿⣿⣧⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣷⡇⣿⣇⠂⢀⠀⡐⣿⣿⢂⠀⠀⠈⣸⣿⢸⣾⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⣿⣾⣄⠓⢿⣿⣿⡿⠚⣠⣷⣿⡟⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠉⠻⠶⠶⠟⠉⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢴⣾⣿⣿⡄⠈⠂⠙⠛⠀⠀⠐⠀⠀⠀⠀⠎⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠋⡿⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣼
⠀⡠⠒⠃⠀⠒⢀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⢀⣾⣟
⠞⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠉⠉⠤⠤⠤⠄⢀⡴⠒⠒⠒⠠⡀⠀⠀⠈⠃⡀⠀⠀⠀⠄⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⣶⣿⡟⢉
⠂⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⣄⡀⢈⢢⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠐⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢯⣿⣿⢿⣿⣿⣯
⠷⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⡠⠒⠀⠀⠐⢉⣿⡿⠄⠉⠏⠛
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢵⣤⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠈⡟⠒⠠⠀⠀⠀⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠙⠧⠀⢀⠀⠀⠀⠒⠤⢤⣿⣿⣿⡇⠀⣿⣇⣠⣴⢅⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠠⣤⡼⣿⣿⣿⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⢈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠠⠀⠀⠀⠑⠀⢀⡎⠀⠄⠺⠃
⠀⠚⠀⢤⡀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢔⣾⠿⠛⢿⡇⠐⠦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠈⠐⠛⢧⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠄⣀⣀⣀⡀⠤⢰⠞⠋⡠⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠁⠀⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠒⠻⣷⢶⣷⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣀⡄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⢆⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠁⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⢸⣇⣸⣀⣠⣾⠿
⠀⠀⠀⢀⡇⠉⠉⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢱⣄⣆⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣽⣧⣾⣿⣿⡿⠿⠃
⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⡜⠁⠀⠀⢀⣴⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⡁⠀⠀⠀⠐
⠀⠀⠀⡀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢤⣀⠀⠀⠀⠀⢻⣿⣷⣀⣠⡄⠀⣤⣿⣿⠟⢀⡀⠀⠀⠀⠀⠢⡄⢀⠍⠀⠂⠉⠷⣁⠂⠤
⠒⠀⡉⠁⠀⠈⠀⠀⠐⠄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠈⠙⢿⣿⡛⠃⢰⣿⣿⣩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣶⣶⣉⡄⠓⢦⣹⣿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠈⠞⠛⠙⠋⢻⡿⢿⠅⣠⣆⠋⣼⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠳⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⣀⡧⢴⡖⢋⣉⠉⠉⡉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡁⠒⠉⠉⠉⠙⠫⠉⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡀⣸⠙⠲⠤⢤⣤⡤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡞⠀⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡼⠀⠀⣇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠁⠀⠀⢸⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠀⠀⠀⠈⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣼⠀⣾⣀⣀⠀⠀⠀⢳⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠻⣀⠯⠄⠈⠳⣄⠤⠼⡆⠘⣇⡤⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠲⠿⠴⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠤⠴⠖⠛⠦⣄⣀⠀⠀⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠒⢛⡉⠛⠒⢦⣀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠔⡡⣫⡟⢀⡤⠛⢦⡀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⣾⠫⠞⣵⣹⡏⢰⣿⣆⡇⠀⢰⠀⢷⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⡞⠁⠀⠣⣭⠽⠳⢤⣭⠞⠁⠀⢸⠀⢸⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⣰⠏⣠⠴⠒⠚⠋⠉⠉⠛⢲⡄⠀⠀⢸⠀⠈⣇⢸⣤⠖⠒⠒⠲⢤⣀⠀⠀⠈
⡏⠀⢧⣀⠀⠀⠀⢀⣀⣤⠾⠁⠀⠀⢸⠀⠀⢻⠘⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠐
⠻⡄⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠙⢦⣄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣏⠛⢦⣄⠀⠈⠢⠄⣤⠘⣆⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⡟⠀⠀⢸⡟⠶⣤⣀⣠⣴⠏⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠸⡄
⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠈⠁⣯⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡀⠀⠒⢮⡁⢚⠄⢣
⠀⠀⠀⠳⠶⠚⠁⠀⠀⠀⠀⠀⠘⣾⢦⣤⠴⠞⠁⢀⡠⠖⠋⠉⠉⣧⡤⠤⢷⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠻⡄⡖⠒⠚⠉⠀⠀⢀⣀⣼⠁⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢤⠇⡇⠀⠀⠀⠀⡞⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⠃⡇⠀⠀⠀⠀⠙⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡗⢀⡇⠀⢀⣀⣀⠀⠀⠉⠓⢤⡀⠈⢦⡀⠀⡐⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠘⠣⡀⣇⠀⢌⠟⠉⠉⢁⣒⣛⡂⠒⠛⠢⠈⠓⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣇⣀⡇⠀⠀⡇⠈⠑⢾⣀⡄⣞⠀⣫⠈⠉⠉⠙⠓⠒⠦⠾⠀⠳⣌⡑⠒⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⡇⠰⡇⣹⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣇⢸⠀⠀⠀⠀⡇⠀⠷⢣⣏⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⢦⡑⠿⢸⠀⠀⠀⠀⣇⡴⠲⢤⠞⠲⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡤⠾⡄⣀⣀⡔⠻⡇⠀⠸⡄⠀⠘⢦⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⡴⠛⢾⠁⠀⣿⠁⢸⡀⠀⢳⠀⠀⠹⡄⠀⠈⠳⢶⡛⠋⠉⠙⠻⢄⠀⠀⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠷⣸⠃⠀⡏⠀⠀⡇⠀⢸⢧⠀⠀⢧⠀⠀⠈⢦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠘⢯⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⡽⠋⣹⠀⠀⡇⠀⠀⢻⠀⠘⡎⢧⡀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⣿⡀⠀⢻⡀⠀⠈⢇⠀⠘⢆⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⡍⠲⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⢏⢧⠀⠀⠱⣄⠀⠈⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⢧⢀⡘⢿⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡳⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⠀⢸⣸⡏⢳⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠚⢧⠜⠁⢹⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢀⡉⠀⠀⠀⠀⣧⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠉⠙⠒⢲⠒⠒⠋⠁⠀⠀⠀⠘⡟⡟⠉⠉⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀
⠀⠀⣀⣀⣀⣀⣀⣀⣠⣞⠉⣴⣛⣀⠀⠀⠀⠀⠀⠀⣠⣴⣗⣶⣶⣦⣴⣏⢁⣾⣯⣄⡀⠀⠀⠀⠀⠀⣤⠾⠽⠷⠶⠶⠶⣏⢁⠶⠷⣦
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⢸⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⡟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠳⡖⠒⠒⣶⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻⢏⠛⠛⢻⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠢⡄⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣯⣀⣳⣄⣸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠲⠶⠟⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠯⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣤⢤⣄⣀⣔⢒⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡏⠉⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢷⡆
⠀⠀⡏⠉⠉⠉⠉⡍⠉⡏⠉⠉⠉⡷⡄⠀⠀⠀⠀⠀⡇⠀⠀⣧⣤⡏⠉⢹⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⠒⠺⡇⢸⡗⠒⠒⠒⢶
⠀⠀⡇⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⡇⠘⠛⠒⠀⠀⠀⢸⡇⠀⣧⣤⣄⠀⠀⠀⠀⠀⣿⠀⢠⣤⣤⣏⣻⣥⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠒⠒⠒⠒⠒⠒⢸⡷⠶⠇⠀⣸⠀⠀⠀⠀⠀⣿⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⢸
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠐⠒⠒⠒⠒⠃⢸⡉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠰⠶⠶⠶⠶⣶⣶⣶⣀⣸
⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣠⣠⣤⣼⠉⢉⣉⡁⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣠⠞⠁
⠀⠉⢿⣤⣤⠤⠤⠤⣤⣤⣤⡤⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⠉⠁⢻⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠶⠶⠖⠚⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠈⠛⠳⠛⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣿⣄⡀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣁⡽⢀⣀⠈⠛⣦⡴⠞⠋⠁⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣀⠀⠀⠠⡏⣹⠇⢀⡼⣧⣠⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠀⣏⣈⡷⠀⠀⠉⠁⠀⠈⠓⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⢋⠀⠀⠉⡴⢤⡀⠠⡞⢳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣏⣹⠀⠀⠙⠦⠇⠀⠉⠉⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠈⠁⠀⠀⠀⣀⡤⣄⠀⢰⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡤⠇⠀⣞⣹⠆⠐⢧⡤⠏⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⣸⣷⡀⠀⠀⢁⣤⣄⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⣠⡾⠋⠀⠙⠷⢦⣼⡧⣾⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠛⠉⠻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣛⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾