Chili Pepper Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⡴⢋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠙⢿⣯⣡⡀
⠀⠀⠀⠀⠠⡾⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⣧⣾⣷⣼⣿⣻⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⢿⣯⣓⣶⡤⢤⣤⣤⣤⡴⠶⠛⢉⣠⣤⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣦⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢠⠔⠉⠡⡶⠚
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿
⠀⠀⠀⢺⡛⠛⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⢫⣴⣷⣙⣿⣏⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⠓⡶⠦⣤⣤⣤⣤⡴⠶⠛⣋⢡⣤⡼⠧⢓⡳⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠑⢦⣄⣠⣤⣴⣸⣦⣻⣜⡣⣾⢧⢶⣵⡞⠷⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣜⣻⠹⠟⠛⠚⠒⠓⠛⠉⣙⣩⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⣀⡤⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃
⠰⣏⣴⠶⣤⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡀
⠀⠈⠁⠀⠈⠻⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠈⢧
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⢦⡀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠤⣄⣀⣀⣀⣠⡤⠿⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⢀⡴⠋⠀⢀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⢸⣃⣀⡀⢀⣄⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣼⠳⠦⠤⠤⢶⠞⠛⠒⢤⡔⠉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡤⣄⡿⠀⢀⡞⠁⠀⣭⡏⠀⡌⠁⢹⡆⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⠀⠶⠀⠀⣷⠘⠃⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⡟⠀⠀⠀⠀⠘⣇⠀⠀⠀⣷⣄⣀⣀⠜⠁⣠⠀⢸⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠣⣀⠀⢀⡠⠛⡦⠤⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣾⠀⠀⠀⠀⠀⠀⠈⣳⣶⣏⣁⣤⣤⠴⠒⠋⢹⠀⢸⠐
⠀⠀⠀⠄⠀⠀⠀⠈⢧⡀⠘⡗⠢⠭⢥⣤⣀⣀⡠⠤⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣿⠀⠀⠀⠀⠠⠂⠀⠸⣄⣀⡀⠀⢀⣀⠠⠒⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢱⣄⣀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⢉⡀⠠⠀⠊⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠂⠀⠀⠀⡼⠳⣤⣀⡀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠟⠋⠉⠉⠹⡍⠉⠻⡇⠀⠀⢀⡤⠒⠒⠾⡁⠀⢀⣈⠉⠉⠋⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⡏⠀⠤⠀⠀⢸⠎⠉⢀⠉⠳⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⡀⠀⠀⠀⣇⠀⠀⠈⠀⠀⡇⠀⣰⠃⠀⠢⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⣆⠀⠀⠀⠀⠀⣰⠃⠃⠀⠀⠉⠒⢲⠋⠙⠦⣀⣀⣠⠔⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⠈⠑⠒⣲⠖⠊⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠀⠀⠂⠚⠂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣤⣤⣴⣶⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠹⠉⠉⠛⣿⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠆⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠖⠛⠶⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⣀⣤⣤⣀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⡴⠟⣻⣿⠟⢉⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢠⠋⢀⡴⠟⠀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠰⣃⣴⠿⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡟⠃⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠊⠻⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠙⠷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⠖⠉⠀⠀⠀⠀⢀⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⣀⡿⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⢀⣤⣾⣿⣿⣿⡙⡉⠉⠠⠀⢹⠟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣾⡇⠀⠀⠸⠃⠐⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠛⠀⠉⢿⣧⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⢀⡏⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡈⠀⠀⠀⠀⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⡀⠀⢠⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠛⡏⠸⠋⠈⠉⠀⠀⠀⠀⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣄⣠⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠿⠻⠗⢿⣿⠁⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠋⠋⠀⠀⠀⠀⠀⢈⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠧⣒⡄⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⣿⣿⣿⠋⠘⢯⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢈⠁⠋⠀⠀⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠋⠁⠀⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢰⣿⣿⣿⢇⣀⣤⡿⠛⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠢⢄⠀⠀⠚⠁⠙⠋⠻⣌⠓⠫⠹⠦⠑⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠙⡆⣀⠀⠀⣀⣤⣔⠉⠤⠠⡤⠀⢠⠤⢍⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠛⠉⠉⠉⠁⠈⠁⠉⠀⠉⠉⠉⠙⠒⠦⢤⣐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣦⣤⣄⣀⣠⣠⣄⣠⣀⡘⠂⠀⠀⠀⠀⢀⠞⠁⣀⡀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⢳⠀⠀⠀⠀⠀⡄⠾⣧⠹⠷⠆⣶⠋
⠀⠀⠀⠀⠀⠁⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢝⠱⠾⠛⠀⠁
⠀⠀⠀⠀⠥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠋⣿⢤⡝⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠈⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠠⠚⡽⠀⠀⠀⠀⣴⡏⣹⠿⠀⣶⡞⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠩⠖⠀⠀⠁⣠⠞⠀⠀⠀⠀⢶⣶⠦⠿⠉⢀⣭⠀⠉⠋⠱⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠘⢦⣄⣀⣀⠄⠊⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⢆⡀⣀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠿⢿⣤⣀⣀
⠀⠀⠀⠉⠉⠀⠘⠿⣦⣀⣀⣀⣀⣤⣴⠴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⣤⣄⣄⣄⣀⣠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠊⡽
⠀⢸⠀⡇
⠀⠘⡆⢧
⠀⠀⠘⢎⠢⠄⢀⣀⣀⠤⠄⣒⣒⣒⡒⠒⠀⠤⢀⣀
⠀⠀⠀⠀⢱⠀⠉⠛⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⣆⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡒⠝⡻⡸
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠋⠉⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢭⡒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡯⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⣍⣒⡒⠤⠤⢤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⡠⠲⡄⡄⠀⠠⡄⣇⢰⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣥⣧⣼⡇
⠀⠀⠀⢸⡇⠀⠀⢹⠈⡇⢻⢸⠈⡇⠀⠀⠀⠀⢀⢀⡀⠀⠀⢀⣾⡿⠋⠀⠀⣹⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠰⣿⡦⠔⠸⠆⠙⠸⠃⡥⢉⡠⣄⢠⠒⡌⡇⠀⠀⢀⣾⡿⠁⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠛⠙⢿⡷⡄
⠀⠀⠀⠀⠈⠠⣴⠒⡆⢀⡀⢇⠙⡎⣧⢘⡞⢧⡀⠘⢀⣠⣿⠟⠀⣠⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠀⣄⠘⠘⡶⠃⢾⡄⠀⠀⣠⣤⣿⣿⣏⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⢀⣠⣴⣶⣾⢄⣔⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠿⠄⠈⠁⠀⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣠⣿⡟⠉⠉⠙⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⣼⣿⠋⠀⠀⠀⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠂⠀⠀⠀⠀⢠⣾⠿⠃⠀⣤⣤⣶⣿⣿⣿⣿⡟
⠀⠀⠀⣶⣶⣦⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⠛⣛⣩⡿⠟⠉⠀⣀⣀⣀⣤⣤⣶⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠻⢿⣿⣭⣽⣿⣿⣿⡽⠷⠶⠶⠛⠋⣉⣤⠶⠿⢛⣿⣿⣿⣻⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣋⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠉⠀⠐⠂⠀⡀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⢀⣤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠁⠈⠈⠀⣈⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠦⣀⢜⠻⡟⢹⢿⡿⠟⠛⠉⠉⠉⠉⠫⢿⣿⣿⡟⠻⢶⣤⣤⣤⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⠿⣶⣾⣺⣅⣀⣀⣀⣤⣠⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡼⠿⠚⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣹⣰⣶⡵⢿⣟⡿⠿⢦⡀⠀⠀⠀⠀⠀⢛⢆⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⣹⠛⢟⠁⠀⠀⠙⢳⡀⠙⠟⣆⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⢀⡄⠀⠀⢟⠀⡈⢾⣷⡀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡧⠀⠀⠀⠀⠳⡆⠀⠀⠁⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⡀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠎⢷⢀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠙⠶⢄⠈⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡎⢷⢓⣠⠀⠈⠠⡀⠀⠀⠈⠠⡈⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠁⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡊⢝⠤⢀⠀⠀⠀⠀⠀⠀⠀⢂⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⠀⠀⠀⠂⠀⠀⠈⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⣀⠀⠈⠀⠀⠀⣙⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣨⣧⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⣀⠈⠀⠘⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⢣⠃⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠛⠒⠻⠶⠤⣜⣽⢝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠺⣄⠀⠀⠠⡙⠃⠁⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠠⣈⠓⠠⡄⣀⣀⠀⢤⠀⠈⠀⠀⠀⠀⠀⣠⣴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠸⢤⣭⣍⣉⠃⠀⠒⠀⠈⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢲⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠆⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢄⠀⠘⡣⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⢴⡈⠐⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠉⠀⣍⠉⠀⠀⠀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢈⣦⠁⠀⠀⠀⠀⠀⣀⠄⠲⠼⣠⠋⡐⠠⠄⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡖⠈⠀⠀⡀⠀⠀⠀⡀⠀⠀⡈⠁⡓⢴⠉⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠁⠀⠿⠀⠀⠐⠀⠰⠔⡌⢡⡄⠠⠅⠀⡀⢅⠀⡈⠁⠀⠀⠀⠀⠀⠦
⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⢔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠐⠒⡆⠀⠀⠁⠀⠀⠑
⠀⠈⢠⢈⠤⡀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⡰⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⡃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⠦⠄⡈⠀⠀⢀⠙⠻⡀⠀⠀⠀⡰⠁⡁⢴⢔⡄⠀⠀⠀⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠹⣄⢀⡔⠁⠀⠀⢐⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠄⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⢴⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠴⠄⠠⠤⠴⠴⠦⠤⠴⠤⠤⠄

⢀⣴⠟⠻⣆
⣼⠇⢀⡾⠃
⣿⠀⣿⠁
⢻⣆⣿⣀⣀⣀
⢀⣿⠋⠉⠉⠙⠻⣦⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣀⣀⣀⣠⡴⣷⡀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣠⡿⠁
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠒⠒⠒⠛⠻⣦⣀
⠀⠘⣷⡀⠀⠀⣾⠲⠶⠤⢤⣤⡽⠆⠀⠀⠀⠀⠀⠙⠷⣄⡀
⠀⠀⠈⢷⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠙⢷⣄⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠉⠻⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⢶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⢀⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⢦⣄⠀⠀⢀⡀⠀⠀⠀⢰⣿⣦⣴⡇⣥⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⠁⠀⠀⠀⠀⠀⠀⢰⣾⣶⡆⣾⢫⣶⡿⠛⢿⣷⣝⣷⡀⣿⡇⠀⠀⠀⢸⣿⣿⢡⢳⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣾⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢸⡏⣿⣿⣧⠀⣾⣿⣿⢸⡇⢻⡇⠀⠀⠀⠈⣿⣿⢸⠸⣿⣇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⡹⣿⣿⣆⢻⣿⢟⣾⠃⢸⡇⠀⠀⠀⠀⠘⣿⣼⡀⠈⠿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠻⣮⣭⣟⣯⣵⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⢠⡰⡄⣎⡦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⠼⣰⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⠆⡦⡖⠂⢀
⠀⠀⠀⠀⠀⢀⡾⠃⠁⢀⠠⡄⠈⠈⢳⡄⠀⠀⠀⠀⠀⠀⣴⠜⠚⢁⡠⢆⠉⠒⠡⣆⠀⠀⠀⠀⠀⠀⢠⠙⠟⠁⣀⠤⡉⠀⠋⢥⡀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⠟⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠃⠀⠀⢸⣿⡟⠃⠀⠀⠸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⡿⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⠀⠀⠀⠘⣿⠠⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⣧⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠘⢿⡄⠀⢀⡼⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⢻⣆⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣨⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣥⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣡⡴⠞⠁



⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢟⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⡿⢟⢿⡿⣛⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⡿⢟⢿⡿⣛⣿⠿⡻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⡇⠀⣼⡀⠠⣾⣿⣿⣇⠀⠀⠀⠀⢰⣿⡇⠀⣼⡄⠠⣾⠀⣠⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣷⡀⢿⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣷⡀⢿⣧⠐⣿⣆⠻⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣬⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣬⣿⣷⣼⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣬⣿⣷⣼⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠋

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠠⠒⠉⠉⠁⢀⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⡠⠖⠚⠛⠉⠛⠒⢤⣀⡀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣀⢀⡇⣿⣷⣿⣯⣿⣿⣉⣉⣉⣭⣙⣛⣳⢦⡀
⠐⡇⠀⠀⠐⠒⠒⠒⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣹⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⡙⣆
⠀⡟⢤⣄⣀⣀⠤⢶⣾⠟⠉⠀⠀⠀⠀⠀⢠⢾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⢧⣀⣀⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⢀⠔⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡕⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠃⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠞⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢟⢦⡀⠀⠦⠀⠀⠑⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡙⢄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠢⠥⠀⠀⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠠⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⡄⢀⡀⠀⠀⠀⠑⠢⠀⣀⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢋⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡰⠆⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⢉⠷⠦⡀⠀⠀⠀⠀⠁⢸⣿⡀⠉⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⢄⠀⠠⡚⢾⢌⠑⠦⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⢇⠸⠁⣤⠀⣄⠀⠀⠀⠀⠆⠀⠿⢷⠀⠘⣿⡿⠻⠛⠃⠀⠀⠀⣠⣮⠎⡡⡀⠘⠂⠋⢵⢆⠂⢵⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠘⣱⠂⣡⡈⠳⠢⢀⠀⡠⠒⢢⠊⠉⢣⠀⣿⡠⢐⡒⢄⠀⢀⠔⠀⠰⣾⠀⠀⠀⠀⠀⠂⠉⠘⠙⠉⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠡⣴⡇⠀⠀⠙⠀⠀⢨⠀⠀⢀⠀⠙⠀⢁⣠⡾⠶⠊⢀⡠⠂⠔⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⡈⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⣠⣀⣤⣤⡤⠔⠒⠠⢀⡴⠂⠈⠉⠈⠳⠤⠌⠀⠀⠈⣿⠦⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠸⢿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⣦⣤⣀⡀⠀⢩⡐⠘⠁⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡤⠖⠠
⠀⠀⠠⠄⠀⠀⠀⢀⣞⣠⣄⠀⠙⢄⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢿⣿⣿⣿⣿⣶⣼⣇⡇⠡⡀⠙⣧⠀⠀⠀⠀⠀⠰⡁⠈⡎⡆⠀⠀⡀
⠀⠀⠠⢤⡄⠐⠂⠈⠃⠀⠨⠁⠀⡌⠁⠀⠚⠂⠤⠶⢆⣠⢀⣀⢉⢀⡠⠊⠙⠛⠿⣿⣿⣿⣿⣿⣄⠘⠄⠈⠻⠗⢄⡀⠀⠀⠈⣵⢠⠠⠀⠀⡄
⠠⠞⣀⠄⠀⠰⠦⣀⠀⠀⣘⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠈⠑⢠⠋⢹⠿⢿⣿⣷⣌⠽⠃⠀⠑⡿⠆⠀⠀⠣⠄⠣⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠁⢀⠈⠑⢢⡴⡄⢀⣀⣀⡤⣴⠀⠀⠀⠀⢠⣄⡀⠠⠎⠀⡸⡀⠶⣷⠀⠉⠈⠢⠠⠀⠸⠿⠷⠄⣶⠄⠀⢀⠄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⣸⠀⠀⢸⠀⢠⣠⠤⢷⠀⠀⣠⠲⠤⡄⣠⠊⢀⠀⠀⢠⠇⡄⣶⣼⣄⣀⡀⠀⠀⠀⠀⠀⠀⠮⠤⣄⠀⠈⠧⠢⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⠀⣸⠀⠀⡤⠂⡛⠀⢀⠃⠈⠤⢁⡌⠔⠁⠀⣴⣿⠾⠠⠆⠤⣇⠀⠀⠀⠂⠀⢄⠀⠰⠀⢠⡄⠑⠊⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣴⢏⠠⠊⠀⠀⠝⠁⠀⠳⣀⡀⠀⠀⢀⣤⠊⣡⣴⣾⠋⠈⡐⢾⠀⠀⠀⠀⠄⠀⠹⡘⢂⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⠿⣦⣆⠘⢡⢂⡀⡄⡲⢶⣼⠂⠁⠀⠀⠀⠀⠀⠈⠁⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣣⢸⠷⣮⣝⢰⣘⣂⣂⡅⠷⢶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠒⠒⠒⠒⠒⠒⠒⠶⢤⣦⣶⠶⠠⢒⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠘⠧⣄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣶⡆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⣠⠞⠀⠀⠈⠓⣦⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠏⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠓⣄⠀⠀⠀⣖⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⠤⠞⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣀⣀⠀⠀⠀⠀⠀⠋⠁⣀⣀⣀⠀⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⣤⣤⠤⠤⠶⠶⡶⠋⠁⠈⠙⣖⠒⠒⠒⢲⠎⠁⠀⠈⠳⡖⢲⠇⠀⣸⠷⠶⠤⢤⣤⣄
⠀⠀⠀⠀⡏⠉⠉⠉⠉⠙⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⡇⠀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢸
⠀⠀⠀⠀⣧⠘⣇⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⣠⠇⡟
⠀⠀⠀⠀⢹⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠋⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣸⠃
⠀⠀⠀⠀⠀⢳⡀⠀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠳⣄⠳⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠣⡤⠞⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⡔⢲⡄⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⠏

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⣟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⣟⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡂⠄
⠀⠀⠀⠀⠀⠀⡰⠋⠀⢰⣿⠟⡤⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⣾⡟⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠞
⠀⠀⠀⠀⠀⡼⡁⠀⣀⢵⣿⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠠⣿⣰⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠏
⠀⠀⠀⠀⡼⡑⠁⠀⠴⣿⣿⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣾⣷⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⣸⢡⠁⡄⢔⣿⣿⢷⠌⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⣺⣿⡟⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡟
⠀⠀⢠⡇⣄⡾⢐⣭⣿⣏⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠃⣨⣿⣟⡙⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣿⡑
⠀⠀⢸⢀⢪⣟⣿⣿⣟⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣛⣸⣿⣽⡱⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⡳
⠀⠀⢸⢸⣾⣵⣛⡽⣾⢡⠎⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⢰⣥⣿⣿⢣⢁⠔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣾⣿⣿⣿⢣⠁
⠀⠀⢸⣜⣽⣿⣿⣽⠖⠁⢀⣠⠦⣤⢾⣿⣏⢷⡄⠀⠀⣎⣿⣿⣿⣩⠗⠀⠀⣠⠴⣤⣾⣿⣏⢳⡄⠀⠀⠘⣿⣿⣿⣿⡶⠂
⠀⠀⠀⠙⠛⠛⠋⠁⠀⢀⡏⠀⠀⠘⣿⢻⣿⠈⣷⠀⠀⠈⠙⠛⠋⠁⠀⠀⡎⠀⠀⠈⣷⢻⣿⡀⢷⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⠀⢸⡷⣟⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠸⣷⢿⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⡀⡂⢸⣷⢻⣷⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠀⠀⣿⣹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢧⣃⠈⣿⣟⠉⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢧⢀⠀⢹⣿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⣹⠀⣿⢛⡄⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣸⠀⢸⣿⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣠⠀⣿⣿⡟⢀
⠀⠀⠀⠀⠀⣀⡤⢤⣀⠀⠀⠹⣷⣻⠂⣿⢿⢡⡿⠀⠀⠀⠀⣠⠤⣄⡀⠀⠀⠘⣿⢃⠂⢸⣿⢃⡿⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠘⣿⣿⡗⣿⣿⡇⡀
⠀⠀⠀⠀⣞⢡⢷⠲⣮⣦⠀⠀⠹⣧⡜⣷⣿⢿⠃⠀⠀⢠⡞⡁⢆⠢⠽⡄⠀⠀⠙⢧⡜⣹⣿⣾⠃⠀⠀⠀⠴⠱⢿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣩⠗⣨⡟⡟⡟⡆⠀⠀⠈⠛⠾⠿⠃⠀⠀⠀⣼⣨⠂⠹⠚⢰⢹⠀⠀⠀⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠙⠻⠿⠁
⠀⠀⠀⡟⣼⡫⠜⠁⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢜⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⠀⠀⠀⣧⢾⡠⢂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢋⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⢸
⠀⠀⠀⡷⣞⡴⡆⡀⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣃⡶⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⣧⣯⠿⢷⡷⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠻⢶⠔⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡆⡠
⠀⠀⠈⣏⠁⢿⣿⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠺⢿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠁
⠀⠀⠀⠘⠷⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠓⠚⠚⠻⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠄⠐⠀⠈⠻⣝⠒⠛⣚⡚⢧⡄⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡏⢀⡤⢤⣉⠈⢷⡀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣔⣦⡀⠀⠀⠀⠀⠀⠀⢸⠹⠏⢱⠁⣾⣷⠈⣧⠈⣱⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢣⠁⠙⣄⣄⠀⠀⠀⠀⢨⠟⠚⠿⢄⡻⠏⣀⠟⠀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠛⠧⠉⠀⢷⢄⠈⢦⣦⠀⢀⣀⣱⠦⠀⠀⠈⠉⠀⠤⡚⠓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣆⠀⠐⢦⡤⠌⠁⠑⠿⠝⠒⠒⠦⣀⠀⠀⠀⠈⢉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⢲⠛⡖⡦⢤⡨⡙⠦⠤⣉⣀⡀⠻⠀⣀⢳⡢⠄⠈⢳⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠤⢤⣘⣖⣢⠣⣼⡠⢷⡀⠀⠀⠉⠉⡍⣖⣈⠂⠀⠀⢀⡜⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣑⠦⠤⠲⣤⣜⡉⢉⡟⠀⠀⠀⠀⠀⠳⣄⠈⠉⠉⠉⢉⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣉⣉⣁⣐⡢⠖⢋⠀⣀⣒⠀⠀⠀⢀⠜⠉⠉⢹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⠤⢤⠤⠤⠤⠔⠲⡃⢀⡠⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣎⣠⠀⠀⠀⠀⠈⠁⠀⠀⣇⠀⠲⠤⠤⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣟⣒⠒⠢⣌⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣰⠟⠉⠈⡇⠀⡟⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣤⣀⣠⠏⠀⠀⢠⡞⣛⣚⠁⠞⠙⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠱⡀⠀⢾⣸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠞⢅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠃⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠇⠀⠀⠀⡸⠃⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠈⠀⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠈
⠀⠀⢨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢻⡇⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢰⡁
⡀⠀⠀⠀⠳⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠳⠀⠀⠀⢰⣿⣿⡆
⣁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣸⣁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⣿⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⣇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⣇
⠃⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⡸⠃⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠈
⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢻⡇⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠳⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠳⠀⠀⠀⢰⣿⣿⡆
⣁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣺⣁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⣿⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡇

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⢠⠒⡀⠉⢙⣆⣠⠤⣄⠀⠀⠀⡀⡤⢄⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⠶⠚⠐⠃⢰⠋⡞⠁⢠⠸⡄⠀⢀⣠⠔⠃⠀⠀⠁⠄⡀⠀⡡⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡴⠋⠁⠀⠀⠑
⠀⠀⠀⠀⡜⢀⣪⠉⢠⠟⡜⠁⠈⠃⢀⠁⠀⠀⢀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢸⣅⠁⠀⠀⢀⠀⠀⢀⣴⠟⠀⠀⠀⢸⡁⠀⣀⠀⣀⠀⠀⠠⡄
⠀⠀⠀⢠⠇⠺⠀⢦⠀⣞⠀⢢⠀⠀⣾⠀⠀⡔⡩⠀⠀⠀⠐⠁⠁⠀⠀⢰⠁⠀⠀⢄⠂⠀⠀⢀⡾⠁⢀⠤⡀⠀⠀⠑⠚⠁⠀⠈⢋⠀⠀⠁
⠀⠀⠀⠘⡄⠀⡠⢪⠎⠀⢠⠀⣸⡤⠏⠀⠀⠳⣅⠀⠀⠀⢸⣀⠀⠀⣠⠛⠃⠀⠀⣸⢤⡤⠴⠋⡀⠀⡶⠀⠈⠲⠤⠤⠂⠀⢢⠀⠈⠳⠖
⠀⠀⠀⠀⠀⢤⣁⠈⢀⡎⠁⡸⠁⠀⠀⠰⢩⠆⠀⠉⠓⠒⠚⠋⠀⠀⣇⠀⠀⢀⠔⠁⠀⠀⠠⡏⢦⠀⠘⣄⠀⠀⠀⠀⠀⠰⠋⠀⣀⢄⢀⠂
⠀⠀⠀⡄⢀⠀⠉⠒⠒⠒⠉⠁⡠⠀⠠⢄⠀⠀⠀⠀⣠⡴⠛⢿⡄⠀⠈⠁⠈⢁⠴⠒⠉⠀⠀⠈⠁⠀⠀⠈⠁⠂⠀⠀⠐⠁⠀⠊⠁⠃⠰⠂
⠀⠀⠀⠉⠉⠀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠐⠛⠀⢀⣼⠋⠀⠀⣸⠇⠀⠀⠀⠀⠘⠒⠂⠁⠀⠀⠀⠀⠠⣶⠙⠉⠀⠀⠀⣀⡠⠄
⠀⠀⠀⢠⠔⢿⠁⠂⠰⡆⠀⠘⠎⠀⠀⣠⠞⠀⣼⠃⠀⠀⠀⠉⠀⠀⣠⢔⣶⠀⠀⠀⠀⡼⠁⢀⣀⠀⠀⠀⠀⠀⣰⢏⠁⢀⠀⠄⠈⠀⠱⡄
⠀⠀⢠⢿⡇⠈⠀⠀⠀⢳⠀⠀⠀⠉⠉⠀⠀⠀⠻⠤⠄⠐⠲⣆⢀⣰⠵⢛⠵⣲⢄⣠⣼⠃⡴⠋⣿⠀⠀⢀⠔⠉⠀⠘⣦⠀⠄⠐⠀⠀⠀⢹
⠀⠀⠘⡈⢧⡀⠀⢡⣀⢌⡄⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠣⢠⡿⠞⠋⣿⠡⠏⢸⠁⠘⠁⠀⣰⠣⠐⠋⡀⢀⡸⣆⠀⠀⠀⢊⡴⠃
⠀⠀⠀⠈⠚⠟⢛⣋⠡⠚⠁⠀⠈⠀⠚⠁⠄⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠂⠐⠀⠈⠀⠀⠀⠑⢆⠀⠀⠈⠒⠢⠬⠴⠖⠻⢍⡤⠤⠚⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠲⠀⠀⠘⠦⣤⣤⠶⠋⠁⢀⢤⠀⣠⡀⡄⢠⢤⡄⠀⠙⠓⠁⠀⠾⡀⠀⠀⢀⠀⢀⠔⡄⠀⣀⣀⠀⠓⠁
⠀⠀⢀⠔⠙⠪⠉⠑⣮⠀⠀⡀⠶⡄⡄⠀⢀⠀⠀⢀⠀⠀⠀⠟⠞⠠⠏⠿⠁⠿⠚⢁⣤⡀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠧⠞⠁⠀⣏⠢⠑⢤
⠀⠀⢼⠤⠀⠁⢦⡀⢸⠢⠤⠀⠰⠞⠁⠰⠇⠇⢀⣿⢁⡤⠶⣆⠀⣀⠀⣀⠀⠀⠀⣾⠏⠀⠀⡰⠊⣿⠆⠀⠀⠁⢰⣒⡨⠀⠀⢧⠀⠁⣀⠱⡀
⠀⠀⠘⢷⡀⠄⢀⡨⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠊⠀⣼⡇⣼⡏⢰⡟⠀⠀⣾⠟⠒⠂⠀⢣⡈⠋⠀⠀⠀⠀⣀⡀⠀⣀⠀⠘⠦⣄⢠⡰⠃
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡎⠠⠚⠄⢸⠀⠀⠀⣼⠃⠀⢰⡿⠀⢿⠔⠙⠧⠐⠀⢏⠀⠀⠀⢆⣀⡿⠀⠀⠀⣴⠎⠉⠐⠂⠀⠌⡳⠢
⠀⠀⠀⣠⣲⣵⡶⠀⢱⡄⠉⠠⠀⠀⠜⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⣁⣀⡀⡀⠀⢏⡛⡩⠅⠠⢤⠤⠊⠀⡠⠂
⠀⢀⡾⢋⠞⠁⠀⠀⡰⠃⡠⠐⠀⠀⠀⠂⢀⠀⠠⠒⠒⠂⠀⠀⠀⠀⠀⡰⠚⠁⠐⠀⠀⠀⠀⠳⠔⠂⢀⠀⠀⠉⠈⠉⠉⠀⣀⠀⠀⠀⠉
⠀⠈⠛⠁⠀⠤⠖⠋⠀⠀⠃⠠⢤⣤⣀⣤⣤⡇⠀⠀⠁⠁⢠⠞⠉⠣⡀⠙⠋⠁⠀⠄⠀⡐⠀⢀⠀⠰⡷⠀⠀⢀⣤⡖⠨⠯⠈⠉⠿⣷⠢⡀
⠀⠀⠀⠀⡠⠀⢀⡔⠒⢠⣄⡀⠀⠀⠈⠉⠉⠀⢠⣂⡂⢠⡏⠀⠀⠀⢱⠀⠀⠀⠸⡆⠈⠀⠀⢠⠆⠀⠀⠀⣰⢋⠏⠆⠰⢀⣀⠶⢒⠿⢻⣇
⠀⠀⢴⣿⡄⠀⠉⠀⠀⠤⢴⠟⠀⠀⠀⠀⡀⠤⢀⣤⠤⣿⢀⠤⠒⠶⠺⣤⣀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⢰⠙⣇⢖⠀⠀⢔⡅⢈⡈⠖⣮⣿
⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣠⠞⠉⠀⠀⢸⣇⠀⠀⠀⠀⡄⠉⣏⢢⡀⠀⢠⢴⡏⠁⢠⠀⠸⢦⣶⡤⣀⠤⠣⢀⣠⢀⣞⣽⡟
⠀⠀⠀⠀⠀⠑⠀⣇⠑⠄⠀⠀⣠⠁⠒⠉⠀⠀⠀⠀⠀⣼⣻⢦⣀⡈⢀⡀⠀⠘⣆⢇⠀⠀⠘⠀⠀⠀⠁⠀⠘⣥⣞⠡⠄⠘⠩⢑⣮⡿⠟
⠀⠀⠀⠀⠢⣀⠀⠈⠂⠀⠀⠀⠓⠒⠒⠂⠦⠴⠶⠷⠚⠁⠈⠙⠪⠭⢭⣭⣑⣊⣩⠜⠀⠑⠚⠂⠄⠂⠀⠀⠀⠈⠘⠋⠣⠍⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠙⣦⡀⠀⠐⠉⠉⠻⣷⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⢿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⢀⣾⣿⣷⣤⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣄⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡄⠨⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣀⡠⠂⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠤⠤⠄⣠⢀⣂⠀⠄⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⢀
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠿⠀⠀⠀⢄⠀⠈⡜⠀⠀⠀⠀⠀⢂⠀⠀⠀⡨⠀⠀⡀⡜⠁⠀⣠⠎
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠄⠀⠀⠀⠐⠂⠀⠀⠞⠁⠀⢀⣼⠇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠹⣿⠂⠀⠂⢤⡀⠀⠀⠓⠦⡴⠿⠟⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠢⣀⡀⠀⠰⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣤⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⣤⣤⣶⡶⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠉⠁⠀⡊⠐⡀⢸⠀⢱⡀
⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⢄⠀⠔⠉⠀⠀⠣⠤⠇⠘⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠠⠤⢄⡀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠀⠊⠀⠀⠀⠀⠀⠉⠁⠀⠀⠢⠀⠹⡕⣿⢙⢶⣄
⠀⠀⠀⠀⠀⠐⡀⠀⠙⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠐⠀⠅⠰⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠈⠻⣦⣥⣮⠇
⠀⠀⠀⠀⠀⠀⠈⠢⠤⠜⠂⠀⠀⠀⠀⠀⠀⢀⣠⠾⠆⠁⠀⠠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠀⠀⠀⠀⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠢⠤⠔⠊⠉⡀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠔⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠐⠀⠀⡴⠉⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠐⠄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⢃⠌⠀⠀⠀⠀⠑⢤⡀⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢰⠀⠈⠂⠤⠤⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠑⠠⠤⠤⠤⠃⠀⠀⠀⠀⠈⠑⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋⠋⠉⠙⠓⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢏⣤⣀⣠⣀⣀⡀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃⠈⠀⠀⢽⠎⠁⠐⠦⠙⣇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⡠⣶⠾⡤⢪⣭⠒⡄⠸⢆⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⠓⡄⡀⠀⠀⠀⠀⢳⠭⢴⣇⢻⣿⠁⡸⠀⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡴⠷⡖⠃⢰⣌⠙⢆⣄⠀⠀⠘⣤⡀⠈⠑⠒⠊⢁⠴⠣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣤⡀⠈⢤⣅⡈⠋⠲⠿⡛⠦⠤⣀⠀⠀⠀⠐⠛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⢴⢳⠦⡤⣄⣙⠲⢄⣉⣀⡀⠲⠀⡀⢶⠤⠀⠑⡄⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠦⠤⢼⣞⣶⣣⣎⠼⡆⠀⠀⠉⠉⡭⢶⣙⠈⠀⢀⡰⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡸⢍⣒⡒⠳⠤⠯⠉⡹⠃⠀⠀⠀⠀⠱⣄⣀⠉⠉⢉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⠭⠭⡝⠋⡆⠠⠭⠄⠀⠀⢠⡊⠀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⢲⠗⠒⠒⠋⠙⠤⠤⠚⢱⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣚⡴⠂⠀⠀⠀⠀⠀⠀⠘⠦⢬⣍⣉⡚⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠒⢦⠈⡁⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⢀⠎⠉⠛⢩⠤⠤⠇⡠⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠸⠞⠑⠲⡀⠀⣻⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠿⡁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠋⠂⠀⠀⠀⠀⠀⡵⠃⠀⠀⠀⠺⠉⠉⠉⠀⢠⣄⠀⠀⣠⠏⠀⠘⣏⢂⠀⠀⠚⠊⠁⡔⠀⠀⢰⠏⠀⠀⠈⠓⠦⠕⠀⢩⡁⠀⠀⢯⡄⠀⠉⠋
⠀⣀⠀⠘⣇⠀⠀⠀⢀⣄⣠⠾⠀⠀⢰⣀⢠⡈⢇⠀⠀⠁⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠹⣤⠀⠸⠄⠀⠀⠀⠰⡄⠀⠐⣸⠃⠀⠀⣄⠠⣆⡀
⣨⠟⠀⠐⡼⠀⣤⠀⠀⠉⠀⠀⢀⡀⠀⠈⠉⠁⠀⠀⠀⢤⣄⣤⣄⠀⠀⠀⡴⠒⠗⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⣷⠀⠙⠃⠠⣠⠞⠁⠀⠀⠙⠛
⠀⠀⣀⡀⠀⠀⠈⠳⠶⠀⢀⣀⡼⠃⠀⠀⠀⠛⠶⠶⠒⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠋⡳⣄⠀⠛⠂⢀⡤⣀⠉⠀⣀⠀⠀⢠⡔⠚⠃⢀⡶
⠀⠀⠑⠭⡷⠀⠀⢠⣤⣄⡀⠁⠀⠀⠈⠳⠤⠤⠀⠀⠠⠖⠒⠶⠀⠀⠘⢧⡂⠀⠀⣀⠀⠈⠁⢀⣤⡀⠀⠙⠲⠖⠀⠉⠳⡄⠈⠀⠀⠚⠋⠀⣀
⡳⣄⠀⠀⠀⢠⡀⠀⠁⠒⠋⠀⢠⣄⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⣀⡀⠀⠙⠂⠀⠉⢳⣄⢰⡋⠈⠀⣠⡀⠀⣀⠀⠀⠈⠃⠀⢤⣀⣀⣠⠄⠈
⠈⠉⠀⢀⡀⠘⢦⣀⠀⢰⠀⠀⠀⠈⢳⡀⠚⠒⠚⠉⠀⠀⡽⠀⠈⠋⠍⠳⠀⠸⡲⢤⡀⠉⠀⠀⣴⠆⠈⠉⠉⠉⢠⡀⠀⠀⣀⣠⡀⠀⣄
⠶⠀⠀⢼⠁⠀⠀⠉⢀⣸⢀⡀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠚⠃⢠⢄⠀⠀⠀⣀⣀⠀⠉⣅⠀⠀⢰⡇⠀⠀⠀⢀⡀⠀⢣⠀⠘⠓⠂⠁⢸⡋⢀⣠
⡀⠀⠀⠘⠆⠀⢠⠄⠈⠁⠀⠉⠓⠲⠃⠀⠀⠀⠊⠃⠀⠀⠀⠈⠳⢬⡄⠈⠃⠉⠝⠀⠈⣇⠀⠀⠀⠘⠓⠚⠉⠀⠀⠙⠀⠀⢀⡤⠦⠘⠃⠈⠁
⠍⠀⠀⠀⠰⠵⠋⠀⠀⣰⠆⠀⢀⣀⠀⣠⠖⠋⢀⡀⠀⠚⠛⢒⠄⠀⠀⢹⠀⣠⣄⡀⠀⠋⠀⠶⠚⠻⠆⠀⠐⠒⢤⡀⠀⠰⠍⠀⠀⠀⠀⠀⢀
⠀⠘⢳⡀⠀⠀⢀⠀⢸⠁⠀⢠⢊⡏⠀⠁⢀⠀⠈⠙⣢⠀⠀⢀⡀⠀⠀⠛⠀⠀⠐⠹⠆⠀⠀⠀⠀⠀⠴⢶⣄⠤⠀⠃⢀⢐⡆⠰⢦⣤⣤⠤⠸
⡤⣄⡀⠃⠀⢠⠏⠃⠀⠀⠀⠈⠋⠀⠘⠋⠋⠛⠀⠀⠀⠀⠀⣎⠁⠠⣆⣠⣤⠄⢀⡄⣀⡴⠀⠘⢝⢢⡄⠀⢀⠤⣠⠄⠗⠋⢀⡀⠀⠀⣀
⠈⠈⠉⠠⣄⠈⠁⠀⢀⡴⠚⠃⠀⠀⠀⡶⠀⠀⠸⣆⢀⠀⠀⠿⠀⢀⡀⠀⠀⠀⠀⠉⠁⣠⡄⠀⠀⠈⠀⠀⠛⠋⣁⠀⠀⠀⢠⠇⣠⣠⠞
⠀⢶⠀⠀⢈⢳⡀⠀⠛⢀⡀⠀⠀⠴⠊⠀⠀⣰⠀⢀⣉⠁⣤⠀⢠⡏⠁⠀⠉⢢⡀⠀⠎⠀⠀⠰⠥⠤⠟⠀⢀⡀⠉⢳⣄⠸⠟⢀⡈⠀⠀⡟
⣄⠏⠀⠀⠀⠉⠁⠀⢠⠏⠃⢠⣄⠀⠀⠶⠞⠁⢠⣋⠝⠀⣇⠀⠸⠇⠀⣤⠀⠈⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⡸⠁⠀⠀⣉⠀⠀⠈⢉⢦⠀⢧
⠀⢀⠀⣤⡶⠵⠃⠀⠘⠂⠀⠀⢈⣧⠀⠀⠤⠤⣬⡀⠀⠀⠉⠀⠀⠀⠀⢻⡀⠰⢦⡀⠉⠉⢁⣄⡦⠝⠀⠛⢁⡀⠀⣀⡟⠀⠀⠀⣀⠉⠁⠀⣤
⡰⢋⠃⠀⠀⠀⠀⠀⣀⠤⠀⢀⡠⢤⠄⠀⠀⠉⠀⠉⢀⡀⠀⢰⠀⢠⢄⠀⠀⠀⠐⠹⠆⠀⠀⠀⢠⠀⠀⢠⠏⠁⠈⠋⠀⠄⡸⠃⠹⡕⠀⢠⢸
⠧⠁⠀⢴⡤⠟⠃⠴⠑⠁⠀⠛⠐⢁⡀⠀⡦⡀⠮⠖⠚⠁⠀⣸⠀⠈⢧⡀⠀⠈⠙⣆⠀⠙⠛⢉⣉⠀⠀⠸⠀⠀⣠⡀⠘⠚⠁⣀⣤⠈⠋⠈⠋
⠀⠀⠀⢠⣀⡀⠀⢀⡀⠀⠀⠀⠀⢸⠁⠀⠙⠯⡄⠀⣦⠀⣀⠁⠀⠀⠈⠁⠀⣶⠈⠺⠀⢀⣠⡄⠉⠙⡆⠀⢄⡴⠋⣀⠀⠀⠴⠅⠀⢠⡄⠄⡀
⣀⣤⠄⠀⠀⠙⣦⠀⠉⠒⠚⠀⠀⠈⠃⠀⠀⠀⠀⡴⠃⠀⠙⠝⣶⠀⠀⠀⣠⠏⠀⠀⠴⠉⠀⢀⣀⠀⠀⠀⠀⠀⠰⡝⢰⡟⡄⠀⠀⠀⠈⠓⠶
⠁⠀⠀⢀⡀⠀⡤⠀⠀⠀⠀⡷⠀⠀⣀⠀⢿⠀⠀⠀⢠⠔⠦⠀⠀⠀⣀⠀⢀⣄⠀⠀⡀⠀⣴⡵⠋⠘⠛⠙⡳⠀⠛⠁⠀⠷⠁⢲⡄⢺⡢⡀
⠀⢠⡞⠙⠃⠀⠙⢦⡄⠀⠴⠃⡠⣠⠏⠀⠘⡄⠀⠀⠟⠈⠀⠀⣤⠴⠁⠀⢠⡌⠉⠉⠁⢀⡀⠀⢀⢴⠄⠀⠀⢀⡤⠲⠂⠀⠀⢠⡇⠀⠳⣴
⣀⠀⠀⠰⢤⠀⠀⢀⡀⣀⡀⠀⠛⠁⠀⠀⢀⡀⠀⣀⣠⠾⠃⠀⠀⠀⠀⠐⣸⠃⢀⠀⠀⢠⡇⠼⠁⠈⠀⣰⠆⠘⠀⠀⠘⢦⡀⠀⢠⡤⠶⡶
⠪⢳⠀⠀⠁⢷⠀⠈⢙⠛⠋⠀⢀⡴⠒⠂⢸⠁⠀⠉⠀⠀⠀⠛⠓⠲⡄⠈⠁⠀⠉⢳⣄⠉⠀⠀⠠⡄⠀⣧⠁⠀⠀⡆⠀⠐⠽⠀⣠⠀⠀⣀
⡄⠀⢴⠒⠲⡦⠀⠀⠈⡇⠀⠀⠋⠀⠀⠀⠈⠧⠀⠉⠓⠴⠆⠀⠀⠀⣠⠚⠦⣤⡄⠀⢀⡀⠀⣠⠞⠀⠀⠀⠀⡤⠎⠀⠀⠀⢠⡴⠋⠀⡼⠁
⢜⡆⠀⠀⣀⣀⡀⠀⠀⠿⠀⣠⢴⠂⢠⣤⠀⣠⡀⢀⣠⢤⠄⠀⢄⠴⠋⢀⡔⠂⠀⠀⠀⡙⣆⠉⠐⠦⣄⣤⠀⢀⡤⡖⠖⠀⠀⠀⠀⠘⠃
⢀⡤⠶⠀⠉⠀⠉⠃⣤⠀⠘⠁⠁⠀⢀⣈⠉⠉⠀⠈⠀⠁⣦⠀⠀⠀⠀⠸⠂⠀⡠⣰⠆⠈⠛⠀⣀⠀⠀⡄⠀⡈⠁⠀⡀⣠⠟⠀⣶⠐⣶⡢⠄

⣤⣤⣤⣤⣤⣤⣤⣤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡐⢶⣤⣀⣀⣤⡶⢖⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣯⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⣉⣈⣍⣉⣉⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡟⠿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⡿⠟⠛⠛⠛⠿⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢀⡀⠀⠀⠀⢹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣤⠎⠈⠳⣤⡄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⣿⣷⠀⠀⡇⠀⠀⠀⠀⠃⣸⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠹⣿⣷⣄⡈⠒⠲⠖⣁⣴⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣄⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣶⣤⣀⣀⡉⢹⣅⣀⣠⣤⣶⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡙⠿⠿⠛⠓⠚⠉⠉⠉⠻⡋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⡎⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠑⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⠟⠀⠀⠀⢀⡼⠛⠛⠛⠻⣿⣧⡀⠀⠀⠀⠀⠈⠢⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠓⠤⠤⠒⠋⣿⠇⠂⠒⠠⢀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣤⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠎⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⢤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠆⠀⢀⣴⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⢀⣾⠏⠀⠀⠀⠈⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⠃⠀⣀⣤⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡏⣠⡾⠟⠋⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠀⠀⠿⠷⠄⠀⢀⣤⣀⠀⠀⣴⡆⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠀⠀⠀⠀⠀⠤⣀⠈⠻⠿⠿⠆⢛⠠⠾⠛⣫⣴⡖
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡲⠴⠤⠄⠘⠷⠀⠀⠈⠉⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⢀⣛⠂⠀⠀⣀⣀⢀⣀⠺⠿⠷⠂⢀⣴⣾⠆⠀⠀⠀⠙⠲⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡙⢛⢋⣉⣛⠻⠆⠸⣧⠘⠋⢡⣾⠇⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠞⠀⠙⠛⣁⣤⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠆








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣊⡀⠘⠄⠱⠀⠀⡀⠀⠀⠀⣠⠊⠁⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠴⠴⣌⠀⠑⢄⡌⠉⠉⢲⢃⡆⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⢀⠤⠤⣽⡇⠀⠀⢡⠀⠀⠾⡆⡁⠤⠊⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠠⢀⣂⠑⢤⠀⠀⠐⠌⣩⠈⠁⠀⠀⠀⠑⠀⠘⠓⢒⡒⠈⠉⠉⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠈⢢⡰⠁⠀⢀⠔⠁⠀⠀⣀⠤⣀⡖⡰⠂⡤⣈⡁⠂⠀⠀⡤⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣗⡤⠐⠁⠀⢀⡤⠊⢀⠀⠀⠈⠑⠚⠤⢆⡨⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠹⣇⠀⠀⢠⠿⢦⣀⠄⠺⣀⢀⡐⠀⠘⠀⠟⠀⠤⠠⡀⢄⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠋⠁⠀⠀⠀⢃⠢⡀⢗⠈⠦⠔⢨⣠⣋⠀⠈⠠⠒⠉⠑⠄⠣⠀⠀⠉⠁⠀⠈⠁
⠉⠤⢀⠄⢒⡤⠛⢉⡹⠔⠚⢆⠀⠀⠀⠀⠀⠀⠀⢂⠙⠦⡑⠛⠫⠧⠇⠚⡤
⠀⠀⠒⠐⠙⡀⡴⠋⠀⠀⠀⠀⠑⢄⠀⠀⢠⢄⠀⠈⠑⠒⣬⠒⠀⠀⣠⢎⠑⠒⡰⣆⠀⠀⠀⢰⡡⣬⡂⣤
⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠈⠢⣀⣮⠁⠀⠀⠀⠀⠸⢅⠼⠳⡀⠀⠀⠀⠘⠐⢮⠥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠘⠓⠂⠄⣀⡀⠠⠌⣈⣄⠀⠀⠀⡠⠁⠰⠀⣕⡹⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⡀⠈⢦⣀⠤⠤⠤⣤⠀⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⢀⡀⠔⢹⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⣀⡴⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠤⠤⠦⠀⠤⢤⠦⠴⠦⠤⠤⡤⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⣦⣴⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡝
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠈⣱⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣵⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣷⣴⣦⣴⡟⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢣⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠻⡇⠸⣿⣿⣿⣧⣤⡈⠻⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣥⣾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣆⣼⣿⢹⣿⣿⣿⡀⠉⠙⠿⣿⣷⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠆⠀⣠⣾⣿⡿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢿⣿⣿⣿⣮⣿⣿⣿⣧⣀⣀⠀⠈⠙⠻⠂⣭⣽⣿⣷⡦⢂⣀⣀⣠⣶⣶⠖⣀⣀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢓
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠉⠻⡿⢿⣿⣿⡉⠻⠿⣿⣿⣿⣿⣷⣶⣿⣽⡁⠀⠀⣀⣉⣉⢁⣀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣾⣧⣀⡀⠛⠛⠿⣿⣿⣿⣦⣾⣿⡿⡿⠿⠿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⡀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣷⣶⣤⣤⣥⣀⣿⣿⣿⣿⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣠⡄⣀⠜⠳⢿⣿⣦⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠶⠛⠁⠀⠀⡀⢹⣿⣷⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠠⣉⠃⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡟⠁⠀⢀⣴⠿⢾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⣷⣶⣤⣄⣨⣬⠷⡦⢤⣄⣀⣤⡴⠶⠶⠶⠶⠿⠛⠛⠛⣯⣤⣠⣴⣯⣤⣠⣾⣿⣿⡹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣬⣍⣙⣿⡶⢦⣤⡈⠉⠁⠀⠀⠒⠃⣠⣠⣴⣾⡿⠛⠏⢉⣶⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣷⣶⣦⣾⣿⣿⠲⢾⣿⣿⣯⡭⢉⣤⣾⣿⣤⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢢⢠⢤⠀⠀⠾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⡠⠃⠤⢀⣦
⠀⠀⠀⠀⠀⡸⠁⠋⠰⢆⠀⣉⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢈⣶⡆⢰⠾⡏
⠀⠀⠀⠀⠀⢁⣯⠁⠀⡀⠀⠁⠀⠒⡨⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⢀⣠⣈⠈⠉⠀⡅⢈⠘⠁⠁
⠀⠀⠀⠀⠙⠴⠄⠀⠂⠀⠡⠘⠒⠞⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠡⠄⠘⠚⣀⡄⣡⠋
⠀⠀⠀⠀⢠⣐⢄⠨⠄⡤⠂⠢⢉⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡕⠀⠂⢀⣤⣤⣤⣈⣁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢀⠈⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣹⠀⡤⠰⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⡤⡀⠱⡅⢄⣨⠼
⠀⠀⡀⡀⠀⠴⠀⠁⡀⠊⢀⡀⢀⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠠⡈⠙⠖⡂⠮⢑⠀⢠
⠀⠘⠀⠑⠈⠀⠀⠅⠙⠂⠠⠝⠁⠀⠉⠠⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠁⠐⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⡄⠀⠀⠀⠀⠀⣴⠀⠘⠃⠀⠜⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠸⡆⠀⠀⠀⠀⣟⢧⡀⠙⠤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣌⠇⠀⠀⠀⠀⢳⡨⢘⠦⣄⠀⠑⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⠀⠀⠀⠀⠀⠀⠈⢖⡡⢂⠠⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡡⠹⡄⠀⣠⠀⠀⠀⠀⠀⠳⣅⠪⢀⠤⠛⢆⠀⠀⠀⠀⠀⠀⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠑⠪⢒⠩⡇⢰⢳⠀⠀⠀⠀⠀⠀⠈⢲⠁⡊⢔⠨⢣⠀⠀⠀⢀⠔⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡐⠅⣊⠑⣺⠃⠘⢌⠳⣄⢲⣤⣀⠀⠀⠀⢹⡔⠅⣢⡜⡇⠀⠀⡎⡰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠐⡩⠐⠥⣻⠀⠀⠀⠑⠺⠄⢳⠍⢣⡄⠀⠀⠇⢊⡀⢀⢽⠀⠀⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢕⠀⠷⡀⠐⢧⡀⠀⠀⠀⠀⣜⠠⠲⣷⠀⣜⠁⠸⡁⢀⡸⠀⠀⡴⣷
⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⠀⠀⢹⡡⠀⢇⠈⠢⡀⠙⢆⠀⠀⡼⠑⠀⠀⣷⠞⠁⡠⠁⡆⢀⡇⠀⠀⡏⢸⡆
⠀⠀⠀⠀⠀⠀⠹⡀⠹⠲⣄⠀⠀⠀⢫⠄⠘⣄⠀⠙⢢⡈⢳⣞⠉⡰⢣⠀⠋⢀⠜⠁⠰⠁⡼⠀⠀⣸⡡⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⡘⢆⠀⠀⠀⠳⣄⠈⢆⠀⠀⠱⠀⠁⡜⠀⠈⠄⡴⠃⠀⢠⠃⣼⠁⢀⡴⠏⠀⠡⢸⠀⠀⠀⠀⢀⣻
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣌⡙⠀⠀⠀⠀⠘⣧⠀⢂⠀⠀⢣⡘⠀⠀⢰⠋⠀⠀⢠⠃⣴⣧⠶⠛⠀⣀⠀⠨⣼⠀⠀⠀⡰⠋⣲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡉⠒⢤⡀⠀⠀⢸⡄⠈⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠇⡘⠋⢀⡠⠔⢊⠃⠀⣠⠇⠀⠀⢎⡠⠖⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠕⠈⠹⡄⠀⢸⡃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠀⡠⠊⠁⠀⡰⠁⢀⡰⠃⠀⠀⠘⢁⡤⠞⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠗⡄⢹⣄⣾⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡜⠀⠠⡞⠁⣠⠤⢀⡴⣃⢢⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⡆⠘⡄⠿⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡟⢠⠾⣟⢀⣞⠁⠒⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢠⠁⠀⠶⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⢀⣷⠝⠂⢟⣼⢃⡾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⢸⠀⠀⠘⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇⠈⡇⡼⡇⢻⠟⡎⢠⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠣⣠⠀⠱⡈⢰⠁⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠒⠀⡘⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠌⢲⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⢚⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠉⠐⠂⠤⠤⠀⠀⢀⣀⣀⣀⣀⠀⠠⠌⠑⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠒⠈⠄⠂⠡⠐⡈⠔⢊⠡⠐⡀⠄⣀⠤⢐⠀⢀⡠⠄⡂⠄⣂⠀⢂⠠⢀⡀⢤⡒⢄⠂⠐⡂⠤⡰⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠈⠀⠈⠁⠈⠀⠈⠀⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣼⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠻⣅⠀⠀⠈⠁⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣠⠴⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⣿⠀⠀⠀⠉⠛⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠲⠶⠶⠶⠶⠶⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠚⠛⠉⠉
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢶⣤⣀⣀⣢⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣃⠀⠀⠈⠉⠉⠉⢉⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡗⢀⡄⣤⠐⢋⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠃⠸⢻⣿⠞⠃⠈⢀⣾⢃⡘⠋⠀⠀⠀⠀⠀⠀⠀⢀⡶⠾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠟⠁⠀⣀⢠⣾⣿⣿⠟⠠⣄⡀⠀⠀⣠⣋⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠋⠀⣀⣀⣙⠛⢿⣿⣧⣄⣀⣈⡉⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⡿⠀⢘⣿⣿⣿⣿⣿⢻⠿⠆⣸⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⢁⡠⡿⠛⣇⠀⠉⠛⣿⡀⠀⡿⠋⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠇⠀⠀⠀⠀⢹⣆⠀⠀⠙⣿⣠⣶⣦⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠗⠠⣄⠀⠀⠀⠀⢙⣄⠀⠀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠸⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣷⣴⣿⣛⣿⣛⡗⠀⠀⠀⢀⡃⠀⢠⣴⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠁⠀⢸⢻⣾⡿⠟⠛⠛⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⢿⠇⣤⣿⡇⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠈⢻⣿⡳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⠀⠉⠀⠀⠑⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣲⠀⠀⣾⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡠⠈⢻⣧⠀⠸⣇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⣷⣌⢻⣦⣤⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣶⣾⣿⣿⣯⡛⢻⣷⣽⣶⣿⣷⣦⠀⠀⠀⠀⠸⣠⣀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣼⡟⠀⠙⢿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⣶⣶⡆
⠀⠀⠀⠀⠀⠀⣤⣶⣾⣷⣶⣾⣿⣷⣶⡾⠁⣸⣿⣿⣷⡄⠀⠛⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⢀⣤⠺⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣴⣦⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠰⣌⡿⢿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⣼⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⡇⠀⠈⠉⠁⠈⠉⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠙⠿⠶⠖⠛⠋⠉⠉⣻⣿⣿⣿⠟⠀⠉⠹⠿⠿⣿⣿⣿⡆⡀⠀⠡⠀⢠⠀⠀⠀⠀⠀⠉⠻⢿⡋⠙⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠹⣿⡄⠀⠀⠀⡀⠀⠀⢿⣿⡇⠘⣷⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⢳⠀⠀⠸⣿⡧⡄⣹⣿⣿⡁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣿⣇⣿⣿⣿⣏⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣼⣿⡍⠙⠻⣇⠀⠀⠉⠛⢷⣶⣦⣤⣤⣤⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡏⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣾⣿⡇⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡆

⠀⣠⣿⣄⣀⣩⠶⠛⠉⡠⠴⠶⢿⣷⣦⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⢢⡀⠈⢑⠪⣐⣌⢦⣄⡀⠀⢀⣀⣴⠿⠷⠖⣲⣶⡿⠶⢷⣕⣄⠹⡟⠉⠐
⠴⠯⢄⡼⠋⠁⠀⠀⠀⠀⣢⢝⣻⡎⠁⠀⠀⠀⢀⣤⠒⠋⠀⠀⠒⢞⣀⠴⠖⠐⠛⠋⢉⣩⠟⠛⠋⠁⠀⠀⠀⣡⠜⠋⠉⠉⠙⠳⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣴⠋⠀⠀⠀⠀⠀⠒⠉⠐⢁⠒⠁⣀⣠⠤⠴⠿⢧⣄⡀⠀⠀⠐⠂⠁⢀⡀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⠖⠁
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠔⣊⠵⠛⠋⠁⠀⠀⠀⠀⠀⢮⣿⡂⢌⡓⢿⣰⠋⢿⣶⣤⣧⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⠲⢶⠋
⣷⡤⠔⠋⠉⠐⠲⣤⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣽⡇⠀⠉⡞⠁⠀⠀⠁⠀⠈⠻⣷⠀⠒⠒⠂⠠⠼⣇⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠳⣶⠶⠦⣤
⡈⠁⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⣀⣀⣤⣪⣿⡿⠃⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠠⣀⠢⣍⠲⡴⢳⠶⣿⣋⣀⠀⠀⠀⠀⠀⠀⠘⠋
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠒⠂⠉⠀⠀⠀⠀⠈⠢⣄⣤⠬⠧⠄⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡀⠀⠙⠂⠩⣿⡧⠊⣡⢿⠋⢻⡦⢄⡀⠀⠀⠀⠇
⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠺⡁⠀⠀⠀⠈⠑⠬⣀⠄⣸⣷⠰⠃⠈⠀⢸⡧⡀⠍⠢⣀⡀⣂⣀⣀
⢳⡀⠙⠳⣤⣀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠛⠛⠛⠒⢦⡀⠠⢀⣅⣋⣻⣽⠏⠀⠀⠀⣠⠟⠡⠈⠢⠀⠙⡙⠁
⢸⣧⡶⠛⠁⠀⠀⠀⠐⠖⠒⠛⠳⠶⢶⣶⣶⡿⠿⠖⠚⠛⠛⠻⢿⡄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠶⣦⣤⠴⠿⠟⠒⠐⠃⠚⠻⠦⣄⠀⠀⠑⠀⠐
⣼⠃⠙⣄⠀⠀⠀⠀⠀⠀⣀⡵⠖⠋⠩⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡈⠁⣾⠀⠀⠀⠀⠀⠀⠀⢀⣿⠚⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠁
⡋⠀⠀⠈⢷⡀⠀⠀⠀⡟⠁⠀⠀⠊⠀⠀⢀⠒⠲⢦⡤⣄⣴⡟⠁⠈⠛⠛⢷⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⣠⣼⠛⠛⠳⢦⡀⠀⣀⣠
⠿⣳⢶⢦⡄⠙⠷⠄⠨⠳⣤⡀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠠⠛⢊⠉⢹⠷⣶⣿⡁⠀⠀⠀⠀⠀⠀⠈⠟⠛⠛⢿⠋⠉⠀⠀⠀⠀⠘⣿⠎⢉⠄
⡴⢃⠃⣨⠿⠀⠳⡦⠀⠀⠀⠙⠳⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠡⡢⠊⡠⠂⢁⢾⣽⢀⢻⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⣟⠀⠠⠊
⠁⣴⡿⡁⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢀⠂⢀⠄⠀⠂⠀⢀⡇⠀⠈⠉⠉⠙⠓⢦⣤⣤⣄⡀⠑⠀⣼⣷⣶⣶⣤⣤⠀⣠⡿⠁
⢸⠃⡀⠀⠑⠄⡁⠀⠀⢉⣻⠷⠒⠒⠒⠀⠒⠂⠓⠦⣤⣀⣤⢴⠃⠀⠂⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡈⠙⣻⠞⠋⠉⠁⢀⢖⡿⠾⠟⠁
⢺⡀⠈⠁⠀⠀⠈⠓⢄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣬⣑⡄⠀⠀⠀⠠⠀⣠⡾⠋⠉⠀⠀⠀⠢⠀⠀⠀⠀⢸⡷⠚⠁⠀⠀⠀⠠⢂⣞⠁⠀⠀⠀⠂⠀⢀⠔
⠀⢳⡀⠀⢤⣦⡀⠀⢌⠀⠘⢧⡀⠀⠀⠀⠀⠄⡀⢠⡄⠀⠉⠇⡄⠀⠀⢀⣼⠏⠁⠂⢄⠀⠀⠀⠀⠈⠢⣠⡶⠛⠁⠀⠀⠀⠀⠐⣱⠋⠈⢰⣆⣄⣀⣠⠄
⠀⠀⠙⠶⣄⡀⠀⠀⠀⠢⣑⣄⠙⣦⡀⠀⠀⠀⠈⢹⠂⠀⠀⠈⠻⠿⠟⠛⡇⠀⠢⠀⠀⠁⠢⢄⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⣴⠞⡁⠀⠀⡇⠀⠉⠛⠉⠒⠢⣄
⣦⠀⠀⠀⠈⠙⠳⣦⣌⣣⣬⣹⡷⠽⠿⢶⣄⡀⠀⠆⣦⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢄⠀⠀⡀⢇⠀⠈⢢⣷⠴⠂⠐⠚⠛⠀⠀⡈⠲⠼⠁
⢸⡗⢛⠉⠉⠉⣻⡿⠟⠋⠁⠀⠀⠀⠉⠁⠈⠙⣳⠶⣶⡶⣀⠀⠀⠀⠀⣼⠏⠙⢦⡈⠉⠁⠀⠈⠢⡐⣄⠈⣿⡇⠀⠠⠀⠀⠀⠀⠈⠐⢤⡄
⠟⢱⢶⣄⣠⡛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⡐⠀⡎⢲⠠⠄⣴⡟⠀⠀⠀⠙⠳⢦⣄⡀⠶⣎⠺⣧⡘⣇⢀⡠⣄⡀⠤⠀⢘⠀⠈⣿⣦⣀⠀⠀⠀⢀⣠
⠀⢡⠀⠈⠛⠉⠛⠳⢦⡄⠀⠀⠀⠀⢀⠀⡊⠰⠠⠀⠃⠀⣃⡀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢈⠟⠻⠿⣿⣿⣿⠿⠋⠀⠉⢀⠎⠀⣤⣷⣾⠿⣈⡙⢿⣗⡞⠋⠁
⣀⠄⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢀⣤⢾⡇⠀⡀⠀⠀⠈⠉⠉⠙⠺⣷⡾⠷⠦⠤⠤⠴⠖⠁⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⡐⢒⣶⣷⡟⢉⣛⠻⠿⢿⡿⠃
⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣴⠿⠞⠻⠋⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⣴⢋⠀⠀⠚⠁⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⢀⡴⠛⠛⠋⠀⠀⠀⠀⠙⢢⡢⢌⣻⡿⠛
⠀⠀⠀⠠⡀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⢰⡿⠅⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠻⣿⡄
⠀⠀⣀⣠⡼⠶⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⣦⡀⠀⠀⠀⠀⠀⠉⠛⠶⣶⡶⢶⣿⣛⣧⠀⠀⠀⣀⡴⠚⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠑⠪⣕⣀⢿⡇
⠛⠋⠉⠉⠀⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠋⣸⣶⠿⠛⠲⣤⣀⣀⣀⣤⣀⣀⣹⡆⠀⠉⠉⠉⢳⡖⠋⠈⠓⠒⠒⣟⡲⠶⠶⠶⢾⣿⣍⡀⠑⠦⢬⣭⣧⣾⡟
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡤⠤⠤⠤⠊⠁⠀⢹⡀⠀⠀⠀⠀⠈⠉⠉⠠⢍⡣⡍⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⠀⠀⠉⡆⠀⠐⣄⣆⠈⠙⠓⠶⠶⠞⠋⠀⢳
⠉⡿⣿⠀⠀⠀⠀⠀⣄⣵⣼⣦⡀⠀⠀⠀⠀⠀⣀⠽⠶⠆⠠⠤⡀⠀⢄⡀⠀⡁⠘⡄⠀⠀⠀⠀⠀⠈⢳⣄⠐⠚⠂⠀⠑⢌⢀⠀⠺⣿⡄⠀⣀⡠⣤⠶⠖⠚⠋

⠀⠀⠀⢀⠄⠊⠀⣿⣿⣷⡷⠛⡇⢀⢶⡄⢀⣼⣿⣿⣶⣄⡀⠱⠀⠀⠀⠀⠉⠒⢄⠈⣀⣀⣀⠀⠀⠁⠀⢤⠀⡛
⠀⣠⠞⠁⠀⠀⣰⠛⠛⣉⠟⠉⠁⠀⠀⢁⣼⠿⠛⠁⠀⢻⣿⣶⣥⠀⠀⢠⣖⣩⣍⣙⣧⣤⣤⣬⣉⣙⣲⡄⠀⠁
⠚⠀⠀⠀⣠⡼⠁⣀⠔⠁⠀⢀⡄⠀⢀⣾⡟⠀⠀⠀⠀⢿⣿⠋⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁
⡤⠴⠶⠋⠁⣠⠔⠁⠀⠀⠀⠋⠀⠀⣾⣿⠁⠀⠀⢀⣴⡿⠁⠀⢀⠠⠄⠀⠘⣞⣀⠿⠈⠹⠉⢻⣀⣿⠁⢀⠆⣠⣮
⠇⠀⣀⠴⠋⠀⠀⠀⠀⢀⠀⠀⠀⠐⢿⣿⣷⣦⣤⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠈⠣⠸⠟⠻
⠄⠊⠁⢀⡠⢰⠀⠀⢠⣿⣿⣿⠀⠀⠈⠑⠻⠿⠿⠏⠀⠀⠀⠀⣠⡀⣠⣶⣀⢠⠀⠄⠀⢀⡀⠀⣀⠀⠀⠀⠀⠔⣼
⠁⠠⣦⣭⣠⠊⠀⠀⢸⣿⣿⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⣦⣖⢩⣠⡤⢼⠏⠚⠺⢭⣶⣠⠌⠑⠢⡀⠈⣅⠀⠀⠀⠙
⠀⠀⡇⠀⢸⠁⠀⠀⣼⣿⣿⡟⠀⠀⢨⡀⠈⠆⢀⢀⠊⠥⣽⠟⠁⠀⠀⠀⠀⠀⠀⡈⠙⢦⠀⠀⠁⢀⠸
⠀⠀⠧⠤⠼⠀⢀⣴⣿⣿⡿⠁⠀⡰⠋⣸⠋⠀⢈⠞⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⠒⠁⠀⠀⠀⡄⠀⠀⠀⠡
⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠀⠀⠰⣁⠀⡏⠀⢠⡿⣿⡟⠁⠀⠀⠀⠀⢠⡤⠄⠂⠉⠀⠀⣀⡀⠀⠀⠀⠁⠀⢠⢀⡀
⠒⠀⡀⠀⠟⠉⠀⠀⠀⠀⠀⢀⡄⠈⠉⠀⠀⠸⠸⣸⡇⠀⢀⠢⠔⠊⠁⠀⠀⠀⢀⠔⠫⡳⡌⠓⣂⡄⠀⠀⠘
⠄⠂⠉⠀⠀⣠⠀⠀⠠⠀⠐⣠⡬⡙⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠀⢠⣾⡀⠀⠀⢧⣀⣀⠴⠋⠀⠁⠀⠀⠀⠀⠅⢀
⣄⠀⠀⠀⠀⠃⢂⠀⢀⣬⣁⣀⣿⣿⠳⠤⡀⠀⠀⢠⠄⠀⢢⣄⣀⣀⡀⠀⠀⠀⠀⠉⠀⢀⡠⠤⠴⠒⢒⣒⢲⠴⠧
⣿⠃⠀⡀⠁⠀⠸⠀⠑⠈⢛⠙⠛⠛⢧⠀⠈⠓⣄⠀⠃⠀⠀⠙⠻⢿⣿⣿⣷⣦⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠃⡤⠨⠁⠒⠉⠀⠀⠀⠀⠀⠑⢄⠀⠘⢦⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⢻⡽⢻⡟⢻⡟⠛⣟⢻
⣤⢀⣀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠑⢤⡀⠷⢦⣀⡀⠀⠈⢢⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠙⠒⠶⠦⠥⠶⠶⠖
⠀⢣⠈⠁⠈⠁⡜⠀⠀⠀⢨⠱⠀⠀⠀⠑⠦⡀⠈⠙⣿⣿⣟⠷⡖⢀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⣀⠠⠄
⠀⠀⢦⠀⣠⠜⠀⠀⠀⠀⡞⣠⠖⢄⠀⠀⠀⠈⠑⠦⣽⡿⣯⢡⠀⡀⠀⠀⠀⠀⠙⠍⠁⠀⠀⠀⠰⠤⠄⣀⠀⠓⡀
⠀⠀⠐⠒⠁⠀⢀⣤⠀⠀⠛⢇⠀⠀⢱⡄⠀⠀⠀⠀⠈⠦⠽⠇⠀⠀⠀⠀⣀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠚⢀
⠀⠀⣀⡤⢢⡀⠀⠋⠀⠀⠀⠀⠉⠲⠋⠀⠀⢀⠰⠀⠀⠀⠀⢰⣍⡱⠀⠀⠐⠃⠀⠀⠀⠈⠁⠀⠘⠾⠂⠀⢀
⠲⡞⣁⣀⡤⠇⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡖⠁⠈⠀⠀⠀⢀⠠⠔⠂⠆⠀⠀⠀⠀⠀⠀⡰⠋⠆⢀
⠠⠏⠉⠀⠀⠀⢀⣤⡿⣁⢠⡀⠀⠀⢴⠄⠀⠠⣄⠤⠔⠪⣑⠤⠂⠀⣤⡊⠀⠀⠀⠠⠀⠀⠀⣀⠠⠒⠑⠀⠀⢃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⡔⠁⡀⠀⠀⠄⠀⠁⢀⠌⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠁⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢈⡠⠔⠊⠁⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡤⠤⠤⣶⡌⢥⠈⡢⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠈⢣⡀⠶⣅⠙⠦⠌⣠⢆⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⣤⠐⠟⠁⢉⠉⠁⠂⠀⠊⣉⠢⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠈⡄⢠⡀⠀⠘⠀⠀⠀⠄⠀⡓⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠁⠀⠰⠋⠙⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡩⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢈⢀⠀⠊⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠠⠄⠲⠎⠀⠀⠀⠀⠀⠀⠘⠆⠀⠓⠄⡠⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠒
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠠⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠐⠠⠀⠀⢀⠀⠀⠓⡀⠀⠀⠀⠦⠐⠊⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⣉⣆⠀⢀⠄⠰⢤⡀⠀⠀⠸⡀⠀⠀⠀⠐⢰⢔⠋⢤⡄⢀⡹⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡢⠐⡉⠠⢨⡗⠁⢀⠴⠈⠀⠀⠀⠀⠳⡀⠀⠀⡀⠀⢀⡤⠐⠁⢠⡇⠈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⠋⠐⠁⠀⢠⠔⠁⢰⠁⠠⠂⠀⠀⠀⠀⠀⢱⡀⠀⠑⠒⡁⠈⠑⣀⠈⠦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠈⠀⠀⠄⠠⠈⠀⢀⠊⢀⡔⠀⠀⠇⠀⠀⠀⠀⠀⢀⠊⠉⠈⠁⠘⠂⠙⠁⠁⠀⠀⢹⠹⠒⠠⢤⣀⡀⠀⠀⠀⠣⠀⠀⠀⡀⠀⡈
⠀⠀⠀⠀⠀⠀⣀⠐⠀⢁⠀⠠⠾⠛⠰⠛⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠂⠀⠂⠒⠒⠀⠀⠀⠀⠀⠈⣆⢀⠀⠀⠘⠉⠙⠦⣄⠁⠐⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠑⢄⡀⡀⠀⠀⢠⠔⠊⠀⠀⠀⠀⠀⡴⠁⠀⠑⣀⠀⠒⠒⠀⠀⠀⠀⠀⠀⢈⠇⠑⢄⠀⢀⠀⠀⠙⠦⣀
⠀⡀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⠰⠛⠒⣀⠴⠃⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⢱⠤⣉⣉⣁⣀⣤⠴⣶⡒⠃⠀⠀⠀⠀⠀⠁⠲⣞⠀⠈⠲⢤⣄⡀
⠀⠁⠀⠔⠀⠀⠀⠀⡈⠀⠀⠀⠀⢠⠄⠀⠀⠆⠀⠀⠀⣠⠎⠉⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠙⠢⣴⠂⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⠚⣛⣳⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠔⡁⢦⡀⢴⠀⠀⠀⠀⢦⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⡄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠖⠁⠀⢿⣳⣤⢴⠀⠀⠀⠀⠸⡆⠀⠜⢀⠎⠀⠀⠀⠀⠀⠀⠰⠉⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⢢⠀⢸⠟⠁⢸⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⡇⠈⠙⠦⣄⡀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠸⡰⠋⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠟⡇⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠴⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢠⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠠⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣥⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡆⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣤⣴⡇⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢨⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣦⣄⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣄⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⠿⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠑⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠙⠟⢶⣄⣀⡀⢀⣀⣀⣀⣤⡤⠶⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠁⠀⠀⠋⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣤⣠⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢢⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠓⠒⢦⣄⠀⠀⠀⣸⠀⢀⣴⣋⡁⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⢻⠀⠀⠀⠀⠳⣄⡀⠐⣽⡀⠀⠀⣿⡴⠛⠻⣄⣀⣀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢦⡀⠀⠀⡟⢀⠄⢀⡟⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⢦⣸⠟⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣇⣀⡤⠟⠷⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⢻⣌⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠙⢧⡉⠙⢷⣄
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠉⠛⣦⠀⠘⣷⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣀⣸⡇⠀⠀⠙⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣤⣬⠃⠀⠀⠀⠈⣧⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣤⣦⡴⠋⠀⠀⠸⡇⠀⠀⠀⢠⡏⠀⠀⠀⠠⡿⢿⣟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢾⣿⠏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠔⡾⢸⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⣄⠀⠀⠀⠐⠟⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢻⣄⠀⠀⠀⠘⡇⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉




⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡆
⢀⡴⢛⡙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇
⠈⠓⠋⠙⢷⡄⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢇
⠀⠀⠀⠀⠀⠹⡆⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠈⢆
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠒⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⠤⣄⣀⣀⣠⠤⢷⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣠⠏⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣉⣠⠞⠁⢀⠤⠬⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⠀⢘⡧⠤⢄⡴⠤⠀⢠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠩⠋⢀⠈⠑⡅⣠⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡴⠛⠚⠁⠀⡏⠀⠀⠻⡄⠘⠀⢠⠇⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠠⡀⠉⠀⢀⠧⣀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢰⠁⠀⠀⠀⠀⠙⢦⣤⠔⠛⠒⢒⣡⠔⢋⠀⡇⡀
⠀⠀⢀⠀⠀⠀⠘⣆⠀⢲⠬⣐⣂⣁⣈⣀⣀⡠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⠀⠀⠀⠀⡀⠀⠸⡉⠉⠉⠉⠀⢀⠤⡾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣄⣀⠀⠀⠉⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢻⠉⠉⡉⠀⠠⠒⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠀⡼⠳⢤⣀⣀⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣟⠉⠁⠈⢻⠀⠉⡇⠀⠀⡠⠊⠉⠘⢇⢀⡠⠬⣉⠉⠉⠈⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠀⠀⡇⠀⢸⠀⠈⠀⠀⠸⠁⠀⠠⠀⢣⠀⢀⡇⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⡇⠀⠀⠀⠀⠀⡇⡄⠀⠳⠄⣀⡤⠶⡀⠀⠀⢀⠜⢀⠞⠀⠠⠁⠄⡠⠀⠀⠀⣧⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠙⠤⠀⣠⠤⠚⠁⠀⠀⠀⠀⠸⠃⠀⢈⠁⠈⠩⠆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⣤⣤⣤⣾⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠹⠋⠙⢻⠇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠙⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠠⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣛⡏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡁⠙⠻⣿⡃⠀⠀⠀⠘⢧⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠈⠙⠿⠆⣈⠛⠉⠚⣆⠠⡀⠹⣿⣿⣾⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠏⠐⣄⠰⣧⡘⢿⣿⣦⡄⠸⣧⡹⣷⡿⠟⠡⠀⣠⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡉⠉⢉⣤⡈⠛⢧⡌⠻⣦⡈⠛⣿⣷⣌⡿⠛⢿⠀⠀⣠⡟⣁⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⡴⠂⡠⡌⢳⣄⠀⠻⣦⡈⠻⣿⡆⠉⣫⠅⠀⠀⣦⣴⣿⠿⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠢⠀⠙⣷⡀⠈⠀⠀⣿⣠⡄⠀⡌⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣗⣤⡞⣿⠟⠃⠀⠀⠀⠹⡧⠀⠀⠀⠙⠟⠿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠐⠂
⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⡀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⢿⡀⠄⢀⠤⠐
⠀⠀⠀⠀⠻⣿⣿⣷⣾⣦⡀⠀⠀⠺⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣾⣦⠰⣿⡆⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⣆⣉⣍⣴⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⣀⡀⠠⣌⠳⢤⡐⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠘⠟⣿⡟⠀⠀⢀⣴⠻⣏⠶⡻⣟⢦⣻⢿⠛⣠⡀⡆
⠀⠀⠀⠀⠀⠻⣆⠺⠟⠀⠀⠀⠈⢙⡁⣹⡧⠹⡞⠋⢿⣄⡾⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢚⠉⠁⠀⠀⢠⢀⠀⠀⠋⢀⠀⠠⠴⠒⠒⠒⠂⣤⠉⡹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠀⠈⣡⡆⠀⠐⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠂⠁⣿⣿⣆⠀⠀⠀⠀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⢀⣤⡴⠾⢧⠶⣶⣦⣄⣀⠀⠐⠦⣤⣀⣀⣀⣠⣀⣉⡘⣡⣒⣹⢄⣦⣽⣿⣽⠦⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⠾⣻⠤⠐⠂⠈⠉⠉⠉⠉⠛⠛⠣⠆⠽⣿⣿⠋⠻⠿⠛⢫⣍⣀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢠⠏⣠⢞⡽⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠉⠉⠐⠒⠉⠁
⠀⠀⠀⠀⠀⡰⢋⢘⡗⠁
⠀⠀⠀⠀⣼⣿⠟⠋
⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠻⠿⣿⣿⡿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⣀⣀⠀⠀⢀⠁
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⣿⣿⣷⡎
⠂⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣶⣵⣿⣿⠀⠀⠀⠀⠹⣿⣿⠇
⠈⡄⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠘⠿⣿⣿⣿⣦⠀⠀⠀⠀⠉⢿
⠀⠈⢄⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⠀⠀⠀⡀⠠⠐⡸⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⡄⠠⢀⡀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠑⡀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈
⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠁⣀⡀⠀⠀⠀⠀⣀⡀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⣀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠂⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡤⠴⠒⠛⠉⠉⠉⠉⠛⠒⠶⢤⣀
⠀⠀⠀⣠⠞⠉⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⢠⡞⠁⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠉⠙⠓⢤⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠈
⢀⡟⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⡖
⣼⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⢀⠇
⢻⢶⠶⠟⠀⠀⠀⠀⠀⠰⣟⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠤⠔⠉⠒⠒⠉
⢸⢸⠀⠀⠀⠀⠀⠀⠀⣀⡬⠗⠒⠧⢤⣀⠀⠀⠀⠀⠀⠀⠀⡔⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⢀⠇
⢸⡸⡄⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⢠⡇⡏⠀⠀⠀⠀⢀⠤⡶⠀⠁⠀⠴⠂⠒⠁
⠀⢧⢳⡀⠀⢀⣠⣯⣤⡶⠶⠾⠿⠿⠿⠿⠿⠶⢿⣦⣤⣀⡞⡼⠁⠀⠀⠀⢰⠃⢀⠿⠊
⠀⠈⢣⣽⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣅⠀⠀⠀⠀⢿⠀⢸
⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠲⣦⣄⡀⠀⠀⠀⠈⢷⣄⠀⠀⢸⡀⠀⡇
⢠⡿⠀⠀⠀⠀⠀⠀⣠⣤⡾⠿⢥⡀⠀⡠⠖⠊⠛⠻⣗⠶⠀⠀⠀⢻⣆⣠⡼⠁⢠⡇
⢸⡇⠀⠀⠀⠀⠀⠀⢰⢋⣤⣤⡀⠈⣾⢁⣺⣿⣦⠀⢸⡆⠀⠀⠀⠀⣿⠁⠀⢀⡾⠁
⢸⡇⠀⠀⠀⠀⠀⠀⢻⣰⣾⣿⡟⠀⡾⣞⠿⠿⠟⢀⡼⠃⠀⠀⠀⠀⣿⠶⠚⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⣮⣭⠴⠞⠁⠈⠛⠒⠾⠟⠋⠁⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣴⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⣄
⠀⠀⠀⠀⠀⠀⣸⡯⠿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⢷⣦⡀
⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣗⡪⣝⡻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢧⠻⡝⣿⣿⣿⣿⠿⣾⣿⣷⣬⡛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣦
⠀⠀⠀⠀⠈⢣⡙⢾⣿⣿⣿⣷⣮⣙⣿⡿⣿⣷⣽⣿⣯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⢹⣧
⠀⠀⠀⠀⠀⠀⠈⠲⣍⠻⢽⡛⠿⣮⣝⡿⣶⣍⡛⢿⣿⣿⣮⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣷⠀⠀⠀⠀⠀⠀⠸⡇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢍⣓⠦⣍⡛⢿⣿⣿⣶⣽⣿⣿⣧⡳⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣇⠀⠀⠀⠀⠀⠀⣷⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠭⣝⣺⢿⣿⣿⣿⣿⣿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠻⠀⠀⠀⠀⠀⠀⢻⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠭⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢀⡀⠀⢸⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠻⣶⡾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⠔⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠞⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡸⢡⠏⠀⠀⠀⠀⠀⠀⠀⢡⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣯⠍⠉⠩⢭⣭⣽⣛⡻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠀⠀⠀⠀⠀⣠⡴⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠮⠙⠆
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⡄⣴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⡼⠁⠀⠀⠀⠈⠳⠌⢀⠐⠲⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣠⡿
⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⢀⡴⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣬⣉⣛⡛⠻⠿⠿⠿⠛⣛⣋⣥⡾⠛
⠀⠀⠀⠀⠀⠀⠀⢧⢸⡀⠀⠀⣠⢖⡭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠓⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢷⡈⣻⠷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠾⠟⠁⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠿⠦⣤⣌⣉⠛⠶⣦⣄⠀⠀⠀⢀⣠⣤⡤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠈⠙⠻⢶⣄⠉⠛⠶⠶⢿⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠻⢦⣼⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠲⠶⠒⠒⠒⠒⠲⠶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣄⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⡟
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣶⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠁⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣾⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠈⠙⣓⠤⣶⠋⣿⣖⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣼⠁⠀⠀⣈⠴⢋⣡⡀⠻⡢⣟⠢⢄⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠀⠈⠀⢒⡴⠺⠣⠆⠀⡀⠠⠰⠘⡝⡄⠀⠑⠆⡀⠀⢵⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢊⠔⠃⠀⡠⠀⠁⣰⡵⠠⡀⡽⠁⡀⠀⠇⢤⢸⡀⠠⠀⠙⠢⡄⠘⣦
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⣠⢞⠀⠀⣰⡏⠀⡀⢘⠕⠊⠀⢈⠁⡞⠀⡁⠀⠀⠀⠀⠙⠢⣀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢠⢀⢎⠁⠀⠀⡜⡼⠂⠀⠘⡫⠒⠂⠲⠁⡸⠁⣰⠋⠲⡄⠦⣀⣀⢠⡈⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢼⠞⣁⠒⣀⡰⢡⠅⡀⠈⡦⠃⠀⠀⠀⡀⠀⢰⠇⠀⠀⣗⠀⢹⠀⠁⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡛⠀⠈⢖⠁⠀⠁⠂⣰⠁⢀⠛⢆⠀⠀⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⠀⢂⡝⠒⠀⠆⡠⢘⢠⠂⠀⠈⠳⢤⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠅⠑⡞⡂⠖⣡⣜⡠⡠⠃⠀⠀⠀⠀⠀⠑⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣊⡥⠴⠭⠅⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡀⣀⡀⢀⢀⡀⡀⡀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠃⠁⠹⠘⠸⠸⠰⠀⠃⠃⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⠒⢀⣉⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠋⣻⣿⣿⣅⣴⣛⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣠⣾⣿⣷⣿⣿⡿⠁⠀⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⢶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⣯⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠐⣉⣴⣿⣿⡿⣿⣿⣿⣿⡇⢀⣠⣤⣀⣽⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⡫⠍⢠⡿⠋⣿⠁⠙⠻⠿⢋⠀⢸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣶⣾⣿⣧⠀⣹⠀⠀⠀⠀⠀⠀⠈⠻⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⣩⠾⣿⣿⣿⣿⠀⠀⠀⣄⠀⠀⠀⢀⣴⣿⣿⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠖⣋⣡⢾⣿⣿⠟⠉⣷⣄⠀⠈⠙⠛⣿⣿⣿⣿⠇⠜⠀⠀⠀⠀⠀⠄⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠉⣉⣠⣼⣿⡇⠀⠀⠸⣿⣷⣶⣶⣾⣿⣿⠏⠉⠀⠀⠀⠀⠀⣴⣀⠚⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⣿⣿⣟⡯⢿⡿⠙⠐⡂⣀⢀⣀⣿⣿⡟⠛⣿⠀⠀⠀⠀⠀⣰⠷⠖⢮⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠖⠒⠂⠀⣨⣭⣍⣐⠛⠁⠀⠀⠠⠏⠀⠸⣿⣿⠀⠀⣿⠀⣸⠇⠀⢰⣿⡐⠳⠀⢀⡔
⠀⠀⠀⠀⠀⠀⣀⣀⢈⣁⡈⢀⡀⣀⣤⣀⠁⢀⡀⠀⠈⠑⢈⣀⡀⠀⠀⢀⢀⢹⣿⣦⣷⣟⢠⣿⡂⣠⣿⣿⣆⡀⢀⣘⡀⢀⠀⢀⠀⣀
⠀⠀⠉⠁⠁⠈⢁⡽⠈⢁⠜⢉⡼⠛⠉⠁⠁⠀⠉⠉⡁⠁⠈⠻⢽⢾⣦⣬⣭⣽⣿⣿⣿⢩⠟⠏⠉⣿⣯⣿⣿⣉⢉⡍⠉⠈⠀⠀⠈⠈
⠀⠀⠀⠀⠀⢰⠋⠀⣰⠏⠀⡾⡇⢀⣄⡀⣠⣤⡀⠀⢹⣤⠀⠀⠀⢣⠹⣿⣿⣿⣿⣿⣿⡞⠀⠀⢰⣿⣿⡌⠀⠉⣉⡅
⠀⠀⠀⠀⠀⡾⠀⢰⡏⠀⣸⢧⣷⡘⠿⣿⣿⠟⠁⠀⠀⣿⡀⠀⠀⠈⡇⠙⢿⣿⣿⣿⠃⢹⠀⠀⠸⠈⣿⣿⠀⠈⣼⢳
⠀⠀⠀⠀⠀⢷⣼⣾⢣⣾⣿⣇⠻⠳⡀⠈⠁⠀⠀⠀⠀⣿⣷⡄⠀⠀⢣⠈⠢⠹⣿⡏⠀⢸⡄⠀⠀⠀⠸⣿⣆⠀⠃⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠙⠄⠀⠨⡆⠀⢀⠹⣷⠀⢸⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⠀⢢⣾⣾⣿⡀⠀⠀⠀⢳⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⢠⣿⠏⠀⢠⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⢰⡿⢹⡀⠀⠀⢳⡸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⢀⡄⢿⣿⠙⢷⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢻⣿⡀⠃⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⢀⢀⣿⡜⡿⠀⠀⠙⣆⠀⠀⠀⠀⣷⣠⠊⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠈⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠼⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢋⣉⣤⣴⣶⣶⣶⣦⠹⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⣡⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣡⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⣿⣿⣦⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠘⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⡄⠀⠈⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣶⣦⣼⣿⠟
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣇⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣌⣉⠛⠛⠿⠿⠛⠛⣉⣤⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣼⣿⡟
⠀⠀⠀⣿⣿⣧
⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠈⠉⠻⣿⣄
⠀⠀⣾⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢾⣽⢿⡁⠀⠀⠀⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⣦⠀⠀⠀⠀⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⣧⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⢠⣿⣿⣷⣄⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡄⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢾⣧⣴⡶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡽⣿⣾⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣻⣷⠟⠁⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢁⣴⠟⠀⠀⢀⣴⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⣴⡟⠁⠀⠀⠀⢸⣿⣿⣿⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠿⢱⡶⢄⠀⠀⠀⠘⢸⣿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣟⣻⠃⢠⣿⣇⠘⠃⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⢏⠋⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⠀⠀⠀⠀⣼⡏⠘⠀⢰⣿⣿⣿⣿⢴⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢻⣿⣿⡇⠀⠀⣼⡟⠀⠃⠀⢸⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣿⣿⣇⠀⣾⡿⠀⢠⠀⠀⣿⣿⣿⡿⣆⡈⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⠿⠆⣿⠃⠀⢸⠀⢰⣿⣿⡿⠛⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢧⣾⡇⠀⠀⠁⠀⠀⡀⠀⣾⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⠀⠀⠀⠀⢰⡀⠀⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢣⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⡿⠁⠀⠀⠀⠀⠆⠀⣸⣿⣿⠃⠸⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣤⣿⠃⠁⠀⠀⠀⠀⢀⠀⢠⣿⣿⠏⠀⠀⠀⠀⣹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡟⠀⠀⠀⠀⠀⠀⡌⠀⣾⣿⠟⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⡼⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⢀⠎⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⡠⢎⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⣀⣴⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡿⣿⣿⣿⢿⣿⡿⠻⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⣠⢾⢻⣿⢻⣿⣿⣦⡀⠀⠀⢠⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣿⡇⣿⡇⣿⣿⣿⣿⣦⣄⣉⣭⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⣛⣽⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣴⢟⣠⣴⣤⡛⠉⠁
⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⣰⣯⣭⣿⣿⡿⠃⠀⠀⠀⠙⠻⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠹⢿⣿⠟⢰⣶⡆⠀⠀⠀⠀⠤⢄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠿⠛⢉⣡⣶⣾⣿⣿⣿⡆⢠
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⢀⣠⡴⠟⠉⠁⠈⣉⣉⣉⣀⠈⠂
⠀⠀⠀⠀⠛⠻⠿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⢉⣩⠴⠶⠶⣶⣶⣶⣾⣿⠟⢁⣠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡀⢢⠀⣶⡿⠛⠛⠿⢿⣶⣦⣤⣴⣶⠾⠋⠁⠀⠀⠀⣀⣠⣭⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠸⡄⠁⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠁⠀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠿⠛⠛⠛⠉⠉⠉⠉⠙⠛⠛⠻⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠛⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢤⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠱⣀⠞⠁⠁⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡄⠀⡟⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⡴⠃⠘⢧⣄⣀⣠⠞⠁⠀⠀⡀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⢆⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⠞⠁⠀⠀⣸⠇⠀⠀⠀⠀⢠⠶⢦⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠚⠁⠀⠀⠀⢠⡟⠀⠀⣠⠶⢤⡏⠀⠀⡏⠀⠀⣽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢣⡀⠀⠹⣄⡘⠄⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣷⠀⠀⠀⠱⠀⠈⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢈⡷⠀⠀⢀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣠⠞⠁⠀⣠⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠶⠶⠖⠛⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣀⣤⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠶⠤⠤⠶⠒⠋⠁
⠀⠀⠀⠀⢀⡼⠁⠀⣠⠞⠉⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡼⠁⠀⢸⠃⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣠⠖⠃⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⡞⠁⠀⣀⡀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⡞⠀⠀⡼⢻⠹⣄⡀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠳⠤⢾⣅⡼⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛⡟⢳⡟⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠈⡇⠀⡇⢸⡇⢸⠃⢀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠇⠀⡇⢸⡇⠸⠛⠉⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⡗⢺⣤⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡿
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣿⣧⡶⠟⢋⣁⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡶⢶⣄⠘⢿⣛⣥⣤⣾⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣯⡿⢟⣽⣷⡄⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⣤⠖⣊⡤⢚⣩⡶⢟⣫⣵⣾⣿⢿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢪⣤⡾⢋⢔⣷⡿
⠀⠀⠀⠀⣀⡘⣷⠚⣛⢉⡥⢞⣵⠶⠋⣡⣶⣿⣿⢿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣊⣾⣿⢿⡿⣯⡾⠋
⠀⠀⠀⠀⢿⠉⢿⣽⠻⡧⠞⠋⣁⣴⣿⡿⢿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣾⡿⢏⡴⢫⣾⠟
⠀⠀⠀⠀⢀⣄⣀⠻⡆⣻⣶⣿⣿⠟⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣾⡿⢛⣷⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠛⠻⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⣀⠠⣄⣾⠟⠋⣸⡿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠘⠏⢿⠿⢿⣶⣾⡿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠰⡆⠀⠌⣩⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠤⠌⠳⡀⣿⢀⣴⠟⠋⠀⢒⣶⡶⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠈⠱⣶⣶⣶⣽⡉⢻⡿⠷⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢿⣯⢿⢯⣀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⠛
⠀⠀⠀⠘⠃⠈⠀⠀⠀⠤⠶⠟⠛⠉⠐⢁⡏⢿⡀⠙⠙⠛⠷⠞⠓⠀⠒⠀⠀⠀⠀⠀⠘⠾⢿⠿⠿⢿⠿⠟⠟⢿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠃⠘⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠚⠒⠈⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠓⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⢄⡊⠀⡁⡀⠀⠀⠀⠀⡐⢊⢀⡠⣦⠀⢠⡄
⠀⠀⠀⠀⣀⢲⡔⠀⠀⠀⠀⣀⠐⠀⠘⢐⠀⠀⠈⠀⠀⠀⠀⠜⠽⣈⠐⠏⠀⠀⠀⠀⠀⠘⠋⢉⠁⠁⠄⡀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠨⠄
⠀⠀⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⡀⡀
⠀⠠⣀⡀⢄⠠⠉⡀⠀⠀⠀⢀⠚⢰⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠈⡁⠈⠉⠀⢪⠀⠀⠀⠀⠀⠀⡆⢀⡄⠄⠹⠀⢠⠀⠀⠀⠀⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦⠠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠁⠐⠄
⡈⢀⣄⢉⢠⠀⠠⠄⠀⠀⠀⠀⠠⠄⠐⠒⠀⠂⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠗⠀⠒⠂⠀⠀⠀⢀⠚⠀⢀⡘
⠀⠊⠙⠊⠂⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡆⠂⢂⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⣰⡡⠀⠀⠀⠀⠀⠀⠀⠨⡀
⡘⢙⣠⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠤⡠⠍⣂⣁⣀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⢿⣿⣿⠖⠀⠀⠀⠀⠀⠁⢀⠀⠠
⠑⠩⠄⠠⠨⠭⠐⠁⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠰⠂⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀
⠀⠀⠈⡀⠄⠀⠀⡀⠀⠀⠀⠀⠊⢑⡀⠠⠐⠲⠀⠀⠀⠀⠀⠀⠀⢂⠀⣠⣄⡁⠀⠀⠀⠀⠈⠠⡀⠠⠀⢀⡀⠀⠀⠀⠉⠀⠀⠁⠀⠁
⠁⠀⠂⠀⡘⠄⠀⠐⠀⠀⠀⠀⠈⡀⠠⠐⢄⡠⠆⠀⠀⠀⠄⣀⡴⠂⠾⡀⠀⠙⠀⠀⠀⢃⡦⠀⠀⢖⠀⠈⠄⠀⠀⠀⠀⠠⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢾⢔⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡶⠟⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣳⡿⠂⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣡⠄⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⣀⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⠇⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠲⠖⢏⢡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣿⠊⠁⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠉⠀⣠⣶⠾⢹⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡝⣋⣀⣵⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⣠⣿⡯⣁⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠃⣠⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠁⢀⣿⢏⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢋⣋⣥⣶⣶⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠀⠘⣟⣷⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠰⣶⣿⣯⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⢠⣽⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⣸⠧⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠾⣁⠒⠻⠄⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠛⣋⣉⡉⣛⣿⣻⣷⣯⠵⠒⢉⡁⣶⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣛⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⠉⠉⠀⠀⠀⠈⠉⠉⠛⠾⢯⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠩⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠄⠀⠐⠂⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠒⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠒⠒⠒⠚⠉⠉
⠀⠀⡀⠀⠀⣀⣀⣤⠮⠤⣘⣆⣀⡠⠴⠒⠉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠓⠛⠛⠉⠉⠀⠀⠀⠀⣀⡀⠠⠚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠒⠒⠒⢀⡢⠏
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⢣⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡴⠛⢉⠽⠒⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠸⢧⠤⢬⣷⣠⣿⣀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡈⠺⢖⣤⠶⠾⣯⡉⠑⣝⣧⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⡴⠃⠀⠀⠀⠐⣿⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠰⣤⢁⡾⠧⣱⡀⠤⠌⠀⣾⠃⣰⣿⡤⢄⣠⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠸⠛⣷⠀⠀⠀⠻⡄⢿⠉⠙⣦⣭⣉⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡾⡟⠢⠀⠛⢠⣷⣤⣄⡐⠾⣿⢮⡑⡄
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠢⣄⣻⠀⠀⢸⣿⣿⣿⣿⡇⠀⣹⠀⢈⡄
⠀⠀⠀⠀⠘⡇⠀⢀⠀⠀⠀⠀⠉⠃⠀⠈⠉⠀⢈⣿⠃⣸⠃⣾⡿⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣐⢁⠀⠙⠶⣤⢄
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⢠⠀⠀⣠⣴⣿⣿⣿⣿⣷⣅⠈⠇⠘⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣀⢠⣠⣾⣿⣿⣿⣿⣿⠟⠉⠉⠓⠄⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⠤⠔⠒⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⡾⠁⢠⡤⠄⠀⠀⠀⠀⠀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁