Alcoholic drink Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠠⣤⠀⢀⣀⠀⠀⠀⢀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠴⣶⣀⣀⠀⢻⡏⠀⠀⠸⡄⠘⠂⠘⣷⡶⠀⢰⣾⠁⠀⣤⣀⡄⠀⢉⣀⣀⡀⠀⠸⠿⠉⠁
⠀⠀⠀⢈⠃⠀⠀⠘⠿⠃⠀⣿⣧⠀⠀⣰⣶⣶⠀⠘⢿⣧⠀⢸⣿⠀⠀⣿⣹⡇⠀⣿⣿⣿⣷⠀⢸⣹⡆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠹⣿⡿⠀⠀⠈⠀⠀⠸⠟⠀⠀⣷⣾⡇⠀⢿⣿⣿⡟⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡀⠀⣤⣤⢄⢰⣶⡾⠓⠀⢀⠲⠀⣠⢤⣤⣤
⠀⠰⣶⣶⣲⠀⣿⣿⣿⢀⣀⣀⣀⠀⣤⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⠀⠘⣿⡇⠀⣿⣿⡇⠀⢧⢾⢸⠁
⠀⠀⠈⠉⠁⠀⣿⣿⣿⠀⠉⠋⠁⠀⡁⠀⠷⠦⠭⢀⣿⣿⣿⡆⠀⣿⣿⡤⠀⠙⠃⠀⡿⠿⠇⠀⠸⠿⠞

⠀⠀⠀⢠⣤⠀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢀⣤
⠀⢀⣴⣾⣇⣸⣛⣛⣛⣃⢘⡂⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠻⡿⠃⣭⣭⣭⣭⣭⠈⣅⠀⠀⠀⢸⣿⡟⠀⣀⣀⠀⠀⠀⠀⠀⠈⡆⢰⡆⠀⢰⠀⣰⢿⡄
⠀⠀⠀⠂⠀⣛⣛⣛⣛⣛⠐⡋⢲⣶⣶⢸⣿⡇⠀⢿⡯⠀⠀⠘⠀⠀⠀⡇⢸⡇⠀⠈⠀⣿⣶⡇⠘⠿⡿⠖
⠀⠀⠀⠀⠀⢹⣛⣛⣛⣛⢘⡃⠀⠉⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⢿⣏⣉⣉⣉⣉⣉⣉⣉⣹⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣭⠶⣶⠾⠿⣯⣟⡳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢹⡄⢰⠏⣨⡿⢮⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣽⣤⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣼⣧⣯⡴⣯⣠⡼⢷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⢾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣠⢾⣿⠶⣤⣀⣸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠞⠁⠈⢻⡷⣄⣉⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡔⠁⠀⠀⠀⠀⠱⣼⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠹⣿⣿⣿⣿⣿⣿⣿⡿⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠻⣿⣿⣿⡿⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠉⠉⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠖⠒⠒⢿⠀⠘⠗⠒⠒⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣄⣀⠀⠀⠀⠀⠀⠘⠒⠚⠁⠀⠀⠀⠀⢀⣀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠿⠟⠛⠁
⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⢤⢠⢠⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⣍⠁
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢮⣯⣯⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆
⠀⠀⠀⠀⠀⠘⢿⣿⣿⠗⠀⣤⣦⡀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⠏
⠀⠀⠀⠀⠀⠀⣤⣿⣧⣴⣶⡍⠉⠁⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠙⠧⢟⠛⢻⢏⠃⠀⠀⠀⠀⠀⠀⠀⠲⡖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡇
⠀⠀⠀⠀⠀⢰⡐⠂⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣦⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢰⣤⣤⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴
⠀⠀⠀⠀⠀⠀⠙⣿⠏⣵⣾⣄⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⢀⣹⣀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠂
⠀⠀⠀⠀⠀⠀⣸⣿⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⢠⠄
⠀⠀⠀⠀⣤⣦⠈⢻⠋⣴⣿⣶⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⣿⣿⣭⡀
⠀⠀⠀⠀⠈⠙⠐⠛⠓⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠚⠁⠀⠀⠀⠀⠀⠀⠒⠿⠓⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠻⠛⠀⠁

⡿⠿⠿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣂⠤⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣀⣀⢀⡞⠕⠁⠀⠀⠀⠈⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⣾⣉⢥⠦⢤⣄⡀⣾⠁⠀⠀⠀⢂⡴⠇⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡸⣿⠃⣸⣶⣀⠈⣷⢸⡄⠀⠀⢀⢐⣄⡄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣵⡾⠀⠁⠈⠉⠿⣧⡄⠑⠀⠀⢠⣤⠾⣧⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠸⠉⠊⠓⠒⠒⠀⢈⠑⠒⣻⣿⠶⠀⠀⡇⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡷⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡝⡂⠠⢄⠀⠀⠀⢠⣾⣿⣿⢗⡜⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⢇⣀⡃⣤⣴⡟⣿⣿⣏⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢄⣿⠃⣿⢟⡇⣯⣴⡆⠘⠓⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡆⢸⣟⡃⣶⣟⡃⢏⣉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣦⣷⣦⡸⣿⡇⣴⣿⡅⣸⣿⡅⣀⣼⢽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⡷⢾⢜⡻⠶⣬⣭⣥⣬⣥⣈⢻⡷⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣶⣯⣽⣿⣛⣛⣿⣿⣥⣾⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⡿⠉⠁⠀⠀⠉⣉⡀⠦⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⢸⠒⠈⠉⠁⠀⠈⠩⠖⠂⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠘⠁⠀⢀⠀⠀⠁⠀⣖⠁⠉⣉⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⣀⡇⠀⢤⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⢡⠁⢣⡀⠉⠄⠂⠀⣀⣠⡿⠤⠤⠀⢀⡀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⡟⠐⠂⠤⠠⠤⠤⠄⠀⠒⠂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣿⠀⠠⠤⠀⠀⠀⠄⠀⠀⠁⢀⣡⠤⠀⠖⠂⠀⠀⠀⠀⡀⠠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠤⠀⠀⠀⠀⠊⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠄⠀⡀⠀⢠⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣈⣀⣈⣁⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡇⠀⠀⠀⠀⠀⠐⠃⠀⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡉⠉⠁⣸⡧⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⡇⠐⠊⠃⠀⠄⢒⠀⠁⠀⠀⠀⣀⠀⠀⢸⠷⠀⠀⠀⠂⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⡰⠀⠀⠈⡄⢰⠀⠘⡶⠖⠒⠒⠋⠁⠀⠀⢸⠰⡀⠀⠀⠀⠀⠀⠀⢀⠄⠸
⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⡰⠁⠀⠀⠠⡇⠈⢀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠊⠙⠒⠲⠶⠖⠚⠉⢢⡇
⠀⠀⠀⠀⠀⠀⠘⠦⣄⣈⢀⣀⡠⠄⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠤⠖⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠉⠳⡆⠀⠀⠀⠀⠐⠲⢤⡐⡆
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡎⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢲⣷⣶⣶⠂⠀⠀⠀⠀⢣⢻
⠀⠠⣤⣤⣤⣤⣤⠜⠒⠒⠀⠀⠀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠘⣾⡆
⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⢠⠞⠗⠀⣶
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣦⠄⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⢘⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⠀⠀⠀⢸⡏⠀⠈⠃
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢙⠁⢈⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⡄
⠀⠀⠒⠛⠻⠟⠒⠀⠀⠀⠀⠀⠀⠒⠻⠿⠗⠒⠀⠀⠀⠘⠛⠿⠛⠁⠀⠀⠀⠀⠀⠐⠚⠿⠒
⠀⠀⢀⣀⣀⡀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⣶⣶⣶⣶⣶⣶
⠀⠀⢸⣿⣿⠇⠀⠀⠀⠹⣿⣿⣿⣿⠏
⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠈⢹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠠
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⣶⣾⣿⣶⡶⠀⠀⢰⣿⠟⠻⠛⠻⡇⠀⠀⢰⣶⣶⡏
⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⢀⣸⣄⡀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⢈⣹⣿⣋⠀⠀⠀⠸⣷⣤⣴⣦⣤⡇⠀⠀⠸⠿⠿⠇
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢿⣦⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣴⣦⣤⡀⠀⠀⠀⠀⠐⠖⠒⠂
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⡀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠈⡇⠀⣶⣶⣶⣷⣶⣶⣶⣾⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠶⠴⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣤⣿⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⢺⢯⡀⢊⠉⢿⡁⠀⠠⡇⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⠉⡁⠀⠈⢧⠀⠀⠀⢸⣿⡍⠶⠖⠌⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠿⠅⠀⠀⠀⠀⠀⠀⠠⣯⡤⣿⠣⣀⡾⠀⠀⠀⢸⣿⣆⣀⡈⠀⠠⢴⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣂⡀⠀⠊⠙⠈⣻⠏
⠀⠀⠀⠀⠀⠀⠀⡿⠲⠶⢲⣦⠀⠀⠂⠰⠞⢿⡿⠖⠊⠀⠀⠀⠀⠐⣿⡶⣍⠙⣈⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠀⠟⣃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣾⣦⡈⣃⢤⡀⡀⢈⠠⣷⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃⡉⣶⠉⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡓⠠⢩⠎
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣛⣛⠙⢊⡙⠛⠋⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣻⡷⠒⣬⠟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⠀⠀⠀⣿⠀⠰⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣦⡀⠀⡈⣃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡇⠀⠄⢸⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡛⠋⠙⠺⡄⠨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠺⠇⠀⠀⠈⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣴⣆⠀⡑⠟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣃⠐⠃⢰⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡙⠛⠛⠛⠛⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠤⠎⠉⠙⡄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⡄⣀⣈⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿⠛⠛⠀⠀⢀⢦⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣧⡀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠤⠀⣐⢢⡈⢱⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢘⣿⠀⠀⠀⡅⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣾⣯⡥⠛⠻⠿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠶⠾⠇⢸⠄⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣖⡂⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣏⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⢑⡊⠅⠠⢜⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠊⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⡤⢦⢂⠀⣠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠘⢄⠙⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡄⠀⠀⠠⣴⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⠛⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⢀⣿⣛⠛⠛⠂⠐⠋⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠚⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠰⢆⠀⠐⣄⠀⢠⠊⠀⢠⠀⠀⠆⠀⠐⠁⠙⠀⠀⠸⠀⠠⠀⠀⠀⠸⠀⠀⢆⠀⠁⣅⠀⣠⠊⠁⢠⠀⠀⡄⠀⠘⠃⠙⠀⠀⠸⠉⠠⠃⠀⠀⢠
⠀⠠⠀⠀⠈⠉⠉⠀⠀⠀⠘⡄⠀⢀⣢⣬⠃⣀⠂⠀⠀⣀⣴⣇⠀⠢⠀⠀⠠⠂⠀⠈⠉⠁⠀⠀⠀⠘⡅⠰⢀⢁⣬⠃⣠⠂⠀⠀⣀⣰⣇⠀⠠
⠀⠀⠀⠀⠀⣰⠦⢶⡄⠈⢌⣁⠄⠀⠀⠜⠀⠃⠀⠀⠘⠉⢉⠽⡄⠀⢐⠐⡲⣒⡂⠀⣴⠶⢶⡄⠐⠈⠀⠀⠀⠰⠌⠄⠃⠶⠀⠸⠉⢉⠸
⣊⣷⣘⡄⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠢⣀⡠⠂⠀⢠⡀⠈⢐⡇⠀⢠⣈⣳⣘⣤⠀⠰⡀⠰⠀⠀⠀⡇⠀⠀⠀⠡⣀⡀⠀⠀⢘⡀⢈⢐
⠁⠀⠑⠃⠀⡄⡀⠀⠀⠀⠒⠑⠂⠀⠀⠀⠸⠅⠀⠀⠀⠉⠀⠈⠀⢀⠘⠀⠁⠋⠊⠀⠄⡀⠀⠀⠀⠒⠐⠂⠀⠀⠀⡸⠀⠀⠀⠀⠁⠀⠉⠀⡄
⣄⡄⠀⠠⠤⠬⠤⢄⣀⠠⡏⠉⠉⡵⠀⠈⠁⠉⠀⡒⠒⠐⠀⠀⠂⡞⠐⣄⡄⠀⠠⠤⠥⠤⢄⣀⠠⠏⠉⠉⠷⠀⠈⠁⠉⠀⠆⢲⢰⠀⠠⠀⠎
⠞⠁⠀⠐⢄⣀⣠⠞⠈⠀⠠⣞⠗⠀⠀⠆⠰⡆⠀⣇⣽⣬⠀⠀⢃⠤⢰⠟⠁⠀⠐⢄⣀⣀⠖⠀⠀⠣⣎⠇⠀⠰⠄⠒⠆⠀⣥⣽⣸⠀⠀⡄⢼
⠀⡀⠀⢀⠈⠉⠁⠀⠀⠀⠐⠀⠐⠀⠀⠦⠴⠃⠀⠠⠿⠝⠀⠀⠘⠈⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠀⠐⠀⠀⠦⠴⠂⠀⠢⠿⠏⠀⠀⠐⠉
⠀⠂⠀⠸⠀⢀⢁⣈⢡⠀⢰⣧⠀⣶⣷⠦⠀⡤⣀⠁⠀⠀⢐⠒⣒⣲⠀⠀⡆⠀⢒⠀⣐⢁⣀⢡⠀⠠⣧⠀⣾⣿⠦⠀⡤⣀⠁⠀⠀⢐⠒⢂⣒
⠀⠐⢶⠀⠀⠈⢠⢤⠊⠀⠀⠸⠀⠉⠋⠛⢏⠝⠁⠀⣀⡀⠨⠒⠤⠀⠀⠀⠀⢶⠂⠀⠐⠠⠤⠈⠀⠀⠀⠀⠉⠛⠙⢯⠝⠁⠀⣀⡀⠈⠒⠤
⠀⠠⠍⠤⠀⠀⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⡸⡀⠀⠀⡁⡇⠀⠌⠀⡄⠀⠀⠠⠌⠤⠀⠀⠉⠈⠁⠀⡂⠀⢱⠀⠀⠀⡘⠀⠀⠀⠁⡅⠀⠎⠀⡄
⠦⡀⠀⢠⠐⠂⠢⡀⠀⠀⡄⢸⠀⠀⢀⠀⣁⠉⠀⢀⠀⠠⠀⠀⠀⠀⠎⠦⡀⠀⢀⠐⠂⠢⡀⠀⠀⡁⠁⢘⠀⢀⠀⢁⠁⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠁⠀⠄⡄⡤⢂⠾⠄⡀⠡⠤⠤⠀⠸⠀⢨⠀⠀⠐⠂⠄⠀⠀⠀⠏⠀⠀⡁⠈⠄⡄⡠⠂⠾⢢⠀⠯⠤⠼⠀⢈⠀⠘⠀⠀⡒⠂⠄⠆⠀⠀⠈
⢈⡀⠀⢀⠁⠉⠈⡸⠚⠀⠤⠤⡀⠀⠀⠄⢼⠀⠀⢠⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⢂⠃⠉⠀⠰⠚⢀⠤⠤⠀⠀⢸⠄⢤⠀⠀⢠⠄⠂⡇⠀⠀⠈
⠈⠑⠀⠀⠓⠒⠚⠀⠀⠘⢰⠂⠃⠀⠔⢀⡤⠀⠠⠀⠀⠀⢠⡄⠀⡌⠉⠁⠑⡄⠀⠑⠒⠚⠀⠀⠘⢰⠂⢃⠀⠴⠀⡤⠀⠠⠈⠀⠀⢠⡄⠀⠈
⠀⠈⠀⡀⠀⢀⣄⣀⠀⠠⠠⠅⠀⠘⠊⢳⣀⣖⡀⠀⠠⠧⠭⢵⡀⠀⢀⠀⠈⠀⠀⠀⢀⣀⣀⠀⢀⠠⠏⡐⠘⢈⢻⡀⣞⡀⠀⢠⠦⠭⢧⠀⠈
⡐⣮⠳⡂⠀⠘⠀⠐⠂⠀⠑⡖⠁⠀⠀⠅⠀⠀⡀⠀⠀⠀⠐⠈⡇⠀⢐⠐⣎⠷⣂⠀⢛⠀⢐⠃⠀⠑⡒⠁⠀⠈⠄⠀⠀⠀⠀⠸⠀⠐⠈
⠂⠛⠒⡧⠀⠀⠒⠀⠀⠀⣀⢃⡀⠀⠀⠈⢲⠎⠀⠀⠘⠲⠒⠖⠁⠀⢸⠒⠛⠒⠿⠀⠀⠒⠊⠀⠀⣀⢃⡀⠀⠀⠈⢲⠊⠀⠀⠘⠒⠒⠖
⠀⠀⠀⠀⠀⡡⡂⠀⠀⢀⣤⡐⡲⢄⠀⠠⠎⠲⠀⡀⣠⢐⠀⠀⡀⣹⠀⠀⠀⠀⠀⠀⡅⡀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠎⠲⠀⡀⣠⢐⠀⠀⡀⣁
⣿⠆⠀⢀⠀⠀⠀⣸⡰⠈⠃⡠⣄⠋⢀⣀⣀⡀⠀⡆⣖⢐⠀⠀⡄⢁⢀⣯⠗⠀⢀⠀⠀⠀⣱⡀⠈⡀⡠⡄⡀⢀⣀⣀⡀⠀⠂⣺⢰⠀⠈⠀⣀
⠁⠀⠀⠀⠱⠶⠞⠁⠀⠀⢈⣉⣠⠀⠀⣅⣈⡇⠀⠛⣿⢿⠀⠀⢰⢭⡼⠁⠀⠀⠀⠱⠶⠚⠁⠀⠀⢉⢉⣁⠁⠀⣅⣀⡀⠀⡟⣿⣾⠀⠀⢃⣭
⠀⣂⣀⢰⠀⠀⠐⠂⠀⠀⢀⡄⠀⣠⣤⡀⠀⢀⠠⠈⠉⠁⢀⠀⠀⢀⠀⠀⣀⣀⣐⠀⢀⠀⠒⠄⠀⠀⡄⠀⣠⣤⡁⠀⢀⠀⠈⠉⠁⢀⠀⠀⢀
⠀⠠⣀⠈⠀⠸⡀⢀⡸⠀⠘⢻⠀⠻⠿⢭⡰⢫⠂⠀⠀⠀⠰⣤⠀⠘⠀⠀⠣⣀⠔⠀⠲⡀⠀⡸⠀⠈⠛⠀⠻⠿⢍⡰⠫⠃⠀⠀⠀⠰⢤⠀⠒
⠀⠀⠽⡀⠀⠀⠼⠹⠄⠀⡐⠈⠄⠀⠀⠀⢱⠁⠀⠀⠎⡆⠈⠠⠉⠀⠀⠀⠀⠸⡀⠀⠀⠴⠱⠄⠀⡄⠀⢂⠀⠀⠀⢹⠀⠀⠀⡎⠆⠀⡠⠉⠈
⡀⠈⠀⠉⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠠⠎⠶⠀⠀⠂⠃⠀⠁⠀⠁⡀⡀⠈⠀⠈⡀⠀⡀⠀⠀⠀⠂⠀⠸⠀⠀⠀⠎⠶⠀⠀⠇⠃⠀⠁
⠠⠆⠀⡚⡀⠀⡈⣢⠀⠀⡇⠘⢀⠀⢸⠉⢹⠀⠀⢰⠀⠈⠀⠀⠀⡮⠠⠬⠆⠠⡒⠀⠀⡈⣢⠀⠀⡆⠀⢰⠀⠸⠉⠹⠀⠀⣈⠀⠈⡄⠀⠀⠴
⢠⣀⣀⣁⣇⣗⣀⣉⣈⣂⣀⣀⣀⣀⣈⣀⣘⣀⣀⣀⣀⣁⣀⣀⣀⣡⡀⣠⣂⣀⣁⣇⣳⣀⣉⣘⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣁⣀⣀⣃⣀⣀⣰
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣶⡀
⠀⢰⠆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠄⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠠⠀⢰⠆⠀⠀⠀⠀⠁⠠⣶⡿⠁
⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟⠀⠀⠈⢃⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⠉⡼⠁⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⠙⠺⡤⡴⠚⠁⠀⠀⠀⠀⠈⢳⣴⡿⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠘⢾⢿⡞⠀⠀⠀⠀⠈⠙⠺⠤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⡉⠁⣀⡀⢊⠀⠰⠉⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⢿⡟⠚⠖⠁⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠁⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠈⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣊⡥⠐⢲⠄⠠⡐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠎⠀⢊⢂⡈⠀⡠⠊⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇⣸⠀⢀⡀⠂⠁⠡⠎⠄⠀⣁⢰
⠀⠀⠀⠀⠀⠀⠀⡟⠢⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣁⣀⣠⣼⠵⢳⡜⢇⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠁⠀⠀⢸⠈⠢⣢⠔⡡⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⣀⠥⠊
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠒⠒⠒⠈⢁⠩⠳⡦⢄⡀⠀⣀⡠⠔⠂⠉⠉⠉⠲⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡘⡀⠀⠀⠠⠂⠁⣠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡄⠀⠁⠀⠡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢁⢁⠀⠀⠠⠀⠀⠀⠀⢀⠸⠁⢀⠀⠀⠀⠀⠀⠀⠀⢘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⠀⠀⠀⠁⠁⠄⠂⠁⢠⠀⢀⠁⠀⠁⠀⠀⠀⠀⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⢈⣀⠀⠀⠀⠀⢠⠀⠀⠀⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡰⠀⢀⠆⠀⠈⠓⠀⠀⠀⠀⠂⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⠀⠀⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠰⡀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠀⢀⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢬⡑⠒⠶⠤⠤⠄⠴⠂⢒⣩⠔⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡈⠉⠁⠒⠒⠒⠊⠉⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠂⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣄⡄⣄⣀⠀⠀⠀⠀⠀⢰⠀⢡⢀⣰⡆⠀⠀⠀⠀⠁⠈⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡟⢓⣛⣿⠀⠀⠀⠀⠀⢠⠀⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣿⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡅⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⡒⢀⡀⢀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠋⠀⢉⢉⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠘⠂⠁⠟⠃⠀⠀⠀⠀⠀⠘⠂⠠⠴⠛⠃⠀⠀⠀⠀⠛⠀⠈⠛⠁⠀⠀⠀⠀⠀⠂⠡⠴⠟⠀⠀⠀⠀⠀⠀⠓⠂⠤⠤⠤⠚⠛

⠀⠀⠀⠀⢀⣀⠀⠀⢠⣠⣀⡀⠀⠀⠀⢀⠠⠀⠀⣀⠀⢤⠀⠀⢠⡔⠀⠒⠒⠀⢢⡄⠀⠀⢀⡤⠤⠠⠤⢤⣤⣀
⠀⠀⠀⠀⠘⢯⠀⠀⠘⢳⡾⠁⠀⠀⠀⠨⠀⠀⠀⠀⠀⠸⠀⠀⠀⠱⡀⠀⠀⢠⠞⠁⠀⠀⠸⠀⠉⠉⠉⠉⠉⠋⠀⠀⠀⠄⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠀⡀⣠⠄⠀⠀⠀⠀⠀⠑⡄⢀⠊⠀⠀⠀⠀⠀⠑⠀⡀⢀⡀⠀⠀⠀⠀⠸⠀⠃⠀⠀⠻⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠁⣼
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡶⠃
⠀⠀⠀⠀⠀⢀⠀⠈⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠄⠚⠃⢀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢂⠀⠀⠀⠀⢸⠄⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢀⣀⠄⠄⠀⠀⢤⡄⠀⠀⠀⠀⢠⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠒⢢⡄⠀⠀⠀⠀⢀⠀⡀⢀⣀⣀
⠀⠀⠀⠀⠸⡁⢀⠀⢀⡉⢙⡇⠀⠀⠀⠀⠉⠙⠛⠛⢙⡿⠀⠀⠀⢘⠀⠀⠁⠀⡗⠀⠀⠀⠀⠸⠀⠀⠀⢹⡇⠀⠀⠀⠀⡿⠒⣲⣀⣶⠛⣿
⠀⠀⠀⠀⠀⢃⠀⠀⣀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⣧⢚⠩⡿⢻⡀⣿
⠀⠀⠀⠀⠀⠸⡆⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠀⠀⠇⠁⠲⠄⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠷⠂⢀⡴⠇⠀⠀⠀⠀⠀⠘⠆⠀⠤⠾⠀⠀⠀⠀⠀⠇⠐⣠⡾⠁⠀⠀⠀⠀⠀⠣⠀⠀⠼⠀⠀⠀⠀⠀⠷⠤⠀⠀⠒⠶⠇

⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⢉⡉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡀
⠀⠀⠀⠀⠀⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⢸⣶⣶⣶⣶⡆⠀⠀⠀⡠⠈⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡷⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⡁⠀⠀⠀⠀⣏⠃⠀⣧⣀⠰⠶⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⢀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢣⠀⠀⠀⢰⡟⠀⠀⢿⠉⢁⠀⢻⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⣟⠀⣀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠞⠀⠀⠀⠘⠉⠉⠑⠇⠀⠀⠀⠠⠐⠒⠚⠁⠀⠘⠯⠾⠿⠟
⣶⣖⣶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⢈⣭⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⠀⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⡠⣾⣿⣿⣿⣿⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⠛⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣀⠙⢿⣿⣿⡟⣿⡽⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⡽⣿⣟⢿⣿⣿⡇⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⢿⣿⣿⣿⣿⣿⣷⣄⠙⢛⣬⠻⣿⣮⣝⣃⡸⠿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣭⣿⣿⣿⣭⣽⣾⠿⠋⠀⠀⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣬⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠴⠋⠉⠀⣰⠿⠿⢿⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠔⢁⣤⣶⣶⢌⠻⢷⣊⠈⠙⠧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢠⢣⠀⡀⢀⡠⢂⣉⣤⣾⠻⣿⣿⣿⣿⣿⣿⣦⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣇⣾⣿⣵⢋⠴⠋⠈⢿⡟⠆⠸⣿⣿⣿⣿⣿⣿⡛⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⡈⣱⠊⠀⣀⠀⢈⡇⠀⠀⢹⣿⣿⣿⣿⣿⡇⠏⢹⡀
⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⠘⠛⠁⠙⠛⠛⠛⠀⣤⣾⣿⣿⣿⣿⣯⠇⢸⣽⠃
⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣶⠶⠆⠀⠂⠀⠀⠉⠻⣿⣿⣟⣿⡏⠀⣾⡏
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢻⣿⣄⣀⣀⡀⢀⣀⠀⠀⠀⠙⣿⣿⣿⡶⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡔⠀⠀⠀⠀⠀⠀⠀⠻⢦⡽⡿⠋⠉⠁⠀⠀⠀⢀⠀⠀⠙⣷⠟⠁
⢈⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠈⡀⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠻⣦⣬⡉⠛⠛⠛⠛⠛⠛⠛⢉⠉⡤⠀⣾⠀⠈⠀⠀⠀⠀⠀⠀⠸⣤⢀⠀⡀⠀⠀⠀⠀⢶⠀⠀⠀⠈⣧⣄⡠⠒⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⣷⠄
⠀⠀⠈⠙⠲⠼⠄⠀⢀⣃⠈⠈⠄⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢄⣠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠦⣤⣤⡄⠀⠀⡀⠀⠀⠀⠙⢦⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⠀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀
⠀⠀⢀⠎⢾⣿⠷⣯⣗⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠟⠿⣿⣶⣯⣿⣶⣄
⠀⠀⢸⣶⣾⣿⣷⣮⣟⣶⣶⣶⣶⡶⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢙⣻⣿⣿⣿⣷⣆
⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣦⣷⣶⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠎⠉⠛⠿⣿⣿⣿⣿⣶⣏⣝⢦⣄⠀⢀⠀⠀⠈⠙⣯⣁⡀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⡴⠁⠘⣦⣤⠤⠽⠛⠛⠿⠛⠿⣷⣮⣷⣦⠛⠆⠀⠀⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠑⢆⣔⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣭⠀⠀⠀⠀⠀⠀⢀⣒⣀⣾⠿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⡠⠁⠀⠀⢹⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣠⣌⣽⣻⣿⣿⣿⣿⠟⠁
⠀⠀⢠⠃⠀⠀⠀⠸⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⣀⣀⠀⠀⠀⢀⣼⣦⣬⣶⣿⣿⣿⡿⠛⠁
⠀⠠⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠁⠉⠁⠀⠘⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠠⠙⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠚⡇⠀⠀⠀⠀⠀⠀⣠⠎⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⡀⠀⠀⠀⠠⠖⠋⠉⠉⠉⠙⢒⣏⡀⠃⠀⠀⠀⣀⡤⠞⠁⠀⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣠⣿⡋⠉⠀⣀⡠⠔⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠣⣰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⡬⡄⠨⢍⡙⠒⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣾⢀⠉⠉⠀⠀⢀⠉⠀⠀⠈⠂⠐⠠⠤⣉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⢋⡅⠀⠶⢂⢀⠀⡬⠵⣆
⠀⠀⠀⠀⠀⣸⠹⡌⠓⠀⠀⠀⠀⠀⠂⠀⣄⡀⡀⠀⠀⣫⠀⠀⠈⣳⣤⡀⠀⠀⠀⠀⣀⡴⠛⡁⠐⠎⢡⠀⠀⢈⡴⠃⠀⠀⠠⠚⢿⡆
⠀⠀⠀⠀⠀⡏⠀⠹⣆⠠⡀⠀⠀⠀⠀⠤⠴⣿⡞⠳⣞⣋⣀⠀⠀⠘⢣⠙⣆⠀⣠⠞⢋⠠⠸⣤⣀⡀⣸⠦⣶⣏⣀⡀⠀⠀⠈⢁⡞⡧
⠀⠀⠀⠀⠀⡇⠀⠀⠈⠃⢈⠁⠀⠀⠀⠀⠀⠀⠶⠒⢟⠻⢭⡉⠁⠒⠀⠠⡈⢳⡁⠶⠄⠀⣀⣨⣭⣿⣄⠎⠿⡁⠀⠀⠀⠐⢀⠘⢁⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⢀⠀⠀⠀⠈⣇⠀⠈⠲⣄⡀⠠⢨⡄⡇⠐⠊⠉⢉⡴⠋⠰⡏⠁⠀⠑⡈⠀⢀⡴⠋⠀⣸
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣙⡀⠤⠀⠘⢦⡀⠀⢀⠙⠀⠀⣱⠃⡀⢀⡴⠋⠀⠀⠀⠁⣠⠠⣂⣠⠖⠉⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⠬⠤⠤⠀⠒⢈⣿⣛⠀⠈⣴⠀⠄⢀⣀⡤⢴⠛⠉⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣼⠫⣝⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⠛
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣴⡿⠃⠠⠉⠲⣶⣦⣤⣤⣤⣤⠤⠤⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠛⠋⠉⡱⢹⡇⠀⢀⠀⠀⠀⠀⡀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⡹⠁⠀⠀⠀⠀⢰⠁⢈⡇⠀⠈⠀⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡼⠀⠘⣇⡀⠀⠀⠙⢄⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠜⠀⠀⢸⠁⠳⡄⠀⠃⠀⠹⡀⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣀⡀⠚⠀⢀⡠⠃⠀⠀⠈⠓⢄⠀⠀⠀⢦⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠴⠁⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⢸⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢰⠃⠘⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⡏⠈⡇⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⠒⡄
⠀⢀⠀⠄⠄⠄⠀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡃⠀⠀⠀⠀⢀⠇⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢸⡒⠒⢺
⠀⠱⠦⠐⠄⠠⠄⠄⠲⢅⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠣⡀⠀⠀⢸⣶⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⢰⢦⠑⡀⠀⠀⠀⠀⠀⡏⣀⣀⣀⣀⢱⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⢀⠇⠀⠀⠀⠀⠀⢧⣿⣿⣿⣿⡌⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠥⠊⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⠋⡇⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡞⡼⡡⠀⠀⢜⢆
⠀⠐⢄⣀⣀⣀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣠⠇⠀⠀⠘⢆⣀⣀⣠⠆⠀⠀⠀⠀⡎⢸⢡⠁⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣼⣤⣤⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⠤⠤⠤⠤⠤⠤⢤⠀⠀⣿⣿⣿⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢠⢂⡈⠉⢉⣀⢦⠀⠀⠰⣶⢶⠒⠛⠒⠻⣿⡆⠀⢸⠰⣖⣲⣶⣶⡶⢸⠀⠀⣿⣿⣿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⣿⣧⣤⣤⠜⠛⠁⠀⠀⠣⡹⢿⣿⠿⡡⠃⠀⠀⣿⣿⣿⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠑⡖⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⡇
⠅⠀⠀⠀⠅⠀⢸⠀⠀⡖⠁⣴⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⣿⣿⡿⠿⠃⠀⡇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢿⢸⠀⠀⠀⠀⠇
⠀⣀⣠⣾⠀⠀⠀⢤⣤⣾⣿⡿⠇⠀⠀⠀⠴⣶⣶⣷⣶⡶⠀⠀⠀⠀⠰⣉⣉⣋⣉⡱⠀⠀⠀⠯⣍⣛⣒⣒⣂⣀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣒⠒⠒⠒⠒⠒⠒⠲⠶⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠚⠧⣬⣉⣉⡉⠙⠛⠛⠛⠛⣉⣉⣉⡽⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡿⢶⡶⢦⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⡶⢾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡧⢸⡇⢸⠀⣿⠀⡇⢸⠁⣿⠀⡇⢸⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠾⢷⣼⣤⣿⣤⣧⣼⣥⣿⣤⣷⡾⠷⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢾⣷⣶⣶⣶⣶⣶⣶⣾⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣈⣉⠉⠉⠉⠉⣉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢉⣛⠛⠛⠛⠛⠛⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠀⠀⠀⠀⠀⣠⡾⡛⢳⡄
⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣀⣀⠀⠀⠀⣿⠀⠉⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠀⣿⡀⠀⠀⢠⡾⠻⢌⢁⣴⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⢈⡇⠯⠝⣧⠀⠀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡆⠀⣿⡀⠀⣨⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣶⣶⡾⠋⠀⠀⠙⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠛⠁⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠫⠭⢻⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣾⣶⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⣚⣉⣭⠭⠭⠤⠶⠶⠶⠶⠶⠶⠶⠤⠬⠭⣭⣍⣛⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢦⣙⠲⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⠲⢦⣭⣍⣛⣓⣲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⣒⣚⣩⡵⠟⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠐⠒⣠⠖⠋⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⡴⠶⢦⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⢰⣯⣀⠀⠠⠤⣀⣀⣀⣀⣠⡤⢞⣿⠔⠋⢀⣀⣀⣈⢳⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡾⠈⠉⠛⠓⠲⢶⠶⠾⠧⣤⣤⡾⠧⡤⠤⠤⠴⠶⢒⡶⢿⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠳⣄⠀⠀⠀⠀⣼⢀⣠⠞⢻⡟⢧⡀⠀⠀⣀⡴⠞⠉⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠑⠦⣄⣀⣿⠟⠁⠀⣿⠃⠀⠙⢷⡞⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⠞⠉⠢⣀⠀⠸⡇⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣟⡠⠊⠁⠀⠀⠀⠈⠙⢶⡧⠔⠋⠀⠀⠤⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⢄⡀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⢤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣠⠤⠴⠶⠖⠚⠛⠛⠛⠓⠂⠀⠀⠀⠀⠐⠲⠤⢤⣀⡀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠠⢄⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠈⠉⠙⠛⠲⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠖⠒⠊⢁⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠈⠉⠙⠒⠦⣄
⠀⠀⠀⣰⢿⠃⠀⡴⠒⠚⠄⠀⠀⠈⠒⠐⠠⣈⠙⢦⣀
⠀⠀⣸⠇⡇⢀⠼⢥⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢱⡀⠙⢦⡀
⠀⢀⡟⢰⠀⣜⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢳⡀
⠀⢸⡇⠘⡆⠹⣤⣤⣤⣤⡀⠈⠑⠂⠀⠔⠁⠀⠀⠀⠀⠐⠈⢧
⠀⠘⡇⠀⢧⠀⡆⠀⠀⠀⠀⢀⠔⠁⠦⢆⠀⠀⠀⠀⠀⠈⠀⢸⡄
⠀⠀⢷⠀⠈⢧⠘⢄⠀⢀⡔⠁⠀⠀⡇⠀⠢⡀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⠀⠒⠒⠒⠶⢤⣄⡀
⠀⠀⠈⢆⠀⠈⠳⡀⠉⢧⠀⠀⠀⠀⡇⠀⠀⠈⢄⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠈⢂⠀⠀⠈⠢⢄⠑⠢⠄⣀⡇⠀⠀⠀⢀⣱⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠉⠒⠠⣀⣀⡈⠀⢉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⠀⠈⠉⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣠⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠚⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠈⠀⠐⡏⠁⠀⠀⠀⠰⠀⠀⣀⠀⠀⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⡄⠀⢤⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠃⠀⢛⠁⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠂⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡖⠀⠀⢀⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀⡀⣰
⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠴⣀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡾⠟⠛⠻⢷⡄⠀⠀⠀⠀⢀⡾⠟⢿⡀
⠀⠀⠀⠀⠀⣀⠜⠛⠙⣄⡀⠀⠀⢀⣤⣇⣿⣿⣦⠀⠀⠀⢀⣀⠀⢀⣠⣰⠀⢐⠀⠀⠀⢰⠆⠀⣎⠀⣀⡀⡀⠀⣿⠀⠀⠀⢀⣤⣤⣤⣤⣽⣶⡄
⠀⠀⠀⣶⣿⣷⣴⡶⠶⢿⣿⣷⡆⢀⠺⠟⠛⠻⢿⡇⠀⠐⠿⠲⠟⠋⠀⣿⠀⠐⠀⠀⠀⠀⠁⠀⣿⠾⠛⠛⠿⠷⣿⠀⠀⠀⣜⠋⠀⠉⠉⠙⠿⠃
⠀⠀⠀⣀⠤⠀⠠⠤⠰⢰⣀⢸⠇⠈⣤⡀⠠⠀⣼⡇⠀⠀⣀⢤⣠⠄⡀⢹⠀⠀⠀⠀⠀⢀⡁⠀⡏⠀⠀⠀⠀⠀⣿⠀⣾⢸⠃⠀⠠⠀⠄⠤⠈⣿⡆
⠀⠀⠀⠹⣶⡍⠛⠋⢰⣿⣿⣿⠀⢀⡇⠀⠀⠀⢸⡁⠀⠀⠈⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⠸⠇⠀⣧⣀⣀⣀⣀⣀⣿⠀⢩⣼⣧⣀⠀⠀⢀⣀⣴⣿⡇
⠀⠀⠀⣼⣿⣿⠟⠓⢬⣯⣾⣿⡄⠀⠗⠶⠶⠶⠾⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠤⠀⠻⠿⠿⢿⠿⠿⠏⠀⠀⠙⠻⠟⠏⠀⣽⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⣶⣿⣷⠄
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⣿⣿⣧⡟⠛⠛
⠀⠀⠀⠀⢀⡾⠟⠛⣋⣉⣶⣾⣿⣿⠹⣷
⠀⠀⠀⣀⣤⣶⣴⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⢠⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⠇⠀⡀⠒⢶⡶⠀⠀⠀⠀⢦⣾⣷⢛⣧⡔⠛⠁⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠉⠀⠀⠘⠛⠛⠗⠀⢐⠈⠀⢀⣘⣯⣿⣿⣿⡡⣾⠃
⠀⠀⠀⣿⣿⣿⣿⠟⣛⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⣤⣀⣤⣶⠟⢿⡿⠟⠁⢿⣁
⠀⠀⠀⢹⣿⣿⣿⡌⠉⢓⡈⠉⠋⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢀⣬⠟⠉⠙⠀⠘⠃⠁⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠈⢿⣿⣿⣿⣄⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⡂⠀⠀⠂⠀⠠⠤⢠⣄⣤⡶⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⠀⠙⠳⢤⣀⣀⣀⠀⠀⠀⠀⣠⣤⣴⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠙⠛⠻⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠤⢄⣀⠤⠒⠚⠠⣀⣀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠣⢤⣀⣀⣀⡀⣀⣀⣀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠛⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⠤⢤⠄⢰⠒⡩
⠀⠀⢠⣦⠀⠀⠀⠀⠐⠟⠀⢲⠤⠀⠀⢠⠟⠁⣀⡤⠒⠋⡐⠁
⠀⠀⠀⠈⠙⢖⣤⡀⠀⡠⠂⠀⠀⠀⡴⣣⡴⠋⠉⠉⣠⠞
⠀⠀⠀⠀⠀⠈⣇⡉⠙⠳⣦⣤⣤⡴⠿⣿⣓⣈⣉⣁⡀⣤⣖⣚⡉⠛⠳⠶⣄
⠀⠀⠀⠀⠀⠘⣿⠙⢦⡀⠀⠙⢦⠀⠀⠀⠉⠑⢤⣀⢀⣸⡀⠁⠙⠲⢄⡈⠉⠳⣤⣄⡀
⠀⠀⠀⠀⠀⢰⠉⢷⡈⠳⣀⡴⠾⣶⠦⣄⠀⢀⠞⠾⠋⠀⠉⠛⠦⣄⠀⠈⠙⠺⠠⠤⠭⠟⡚
⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⢹⡇⠀⠀⠁⠫⡹⣞⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠀⣇⠀⠀⠀⠀⠀⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⣠⠇⠀⠀⠀⠀⠀⠐⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠀⠀⠀⠀⠀⠀⠀⡿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⠳⢄⣀⣀⣀⣠⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⣤⣀⡀
⠀⠀⠀⢶⣄⠀⢠⠞⠁⡡⠦⠼⢄⠀⢀⠤⠤⣄⠀⠰⣿⣿⣋⣽⠀⠀⠀⠀⠀⠀⣰⣿⣴⡿⡿⢿⣍⠁⠀⠀⢀⣾⠁⢿⡄⠈⢻⢯⣷⣄
⠀⢤⡿⣷⢫⣇⠺⣄⣸⠁⠀⠀⠐⡄⡇⠀⠀⢸⡇⣿⣟⣻⣟⡿⠇⢀⠄⠀⠀⡄⢿⣿⠻⡇⠡⠅⢻⣤⠀⠀⢸⣿⡦⡈⠳⠦⢿⣐⣬⣿
⠀⢺⣾⣎⣿⣿⠁⢾⣇⢁⡤⢰⡶⠁⢀⠀⢈⣨⠇⢹⣟⣿⣻⡟⡴⢿⠀⠀⠀⡿⠸⣿⢿⡿⢷⡞⣻⡟⠀⠀⠸⣿⣿⣷⣦⡤⣾⣿⣿⡏
⠀⠀⣿⣻⣺⡇⠀⠀⢿⣿⣿⡟⠀⠀⠘⣝⡿⡏⠀⠀⣿⣿⣿⠁⠱⣦⡤⠴⣶⠆⠀⠙⠿⣿⣾⡷⠟⠁⠀⠀⠀⣿⡷⠾⢽⡭⠿⣾⣿⠃
⠀⠀⢹⣭⡿⠀⠀⠀⠸⣿⡳⠆⠀⠀⠀⣷⠃⠀⠀⠀⢸⣯⡿⠀⠀⢻⡶⣶⡏⠀⠀⠀⣴⣿⠭⣦⡄⠀⠀⠀⠀⢹⣄⠀⠠⠄⠀⢸⡇
⠀⠀⠘⣷⠇⠀⠀⠀⠀⢯⣽⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⡗⡇⠀⠀⢸⣟⣻⡇⠀⠀⠀⠉⠉⠀⠉⣠⣴⠖⠒⠀⠘⢧⣀⡀⢐⣀⣼⠏
⠀⠀⠀⠉⠀⠀⠀⠀⣀⠈⠃⠀⣿⣯⣻⠆⢰⠟⢿⡄⠀⢛⣃⣀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⢀⡂⠀⠈⠉⠉⠉
⠀⠀⠀⠃⢰⠀⠀⣾⣿⣟⢦⠘⣿⣮⣿⠆⢸⠀⢸⡇⢰⣿⠛⣿⡷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣁⠂⣺⣿⣿⣿⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⠹⢀⣿⠿⣿⡄⢸⠀⢸⡇⣿⡇⠀⢻⣷⣷⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⢈⣓⠿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠛
⠀⣤⠀⠀⠀⣹⢸⣿⣿⣿⠰⠈⣿⣿⣿⡅⢸⠀⢸⡇⣿⣇⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⡿⣦⣾⠀⠀⡀
⠀⣯⣁⣀⣿⣿⢿⣿⣿⣿⠀⠀⣿⣟⣿⠇⢸⡀⣼⡇⠘⠿⣷⣾⠿⢃⣠⣤⣤⣖⣶⢤⠀⠀⠎⣿⠟⡿⢷⣿⡛⠓⠈⣧⠀⠀⠔⠴⢳
⠀⠀⠈⠉⠉⠀⠈⠛⠛⠛⠁⠀⠉⠛⠋⠀⠘⠓⠟⠃⠀⠀⠀⡁⠀⣼⣿⣤⣼⣿⣿⣿⠃⣇⣤⣇⣀⡀⣬⣿⠇⢸⡆⢹⣶⡿⣾⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⢿⣿⣿⣿⡿⠁⠀⠈⢙⣿⠷⣿⣿⠃⠀⠀⣿⣮⢾⡸⣿⠃⢏⠼⡀
⠀⡴⠊⠉⠑⣆⠀⢀⡤⠤⢤⣀⠀⢀⠤⠂⠤⡀⠀⣠⠴⠶⢤⡀⣷⣬⣼⣿⣏⣛⣧⡆⠀⠀⠘⠋⠀⣠⠏⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣾⠇
⠀⣧⡀⠀⠀⣺⡀⣼⠀⠀⠀⢸⡆⣮⠀⠀⠀⢸⢸⡁⠀⠀⣠⡇⢸⡿⠉⠉⠛⣿⢻⠁⠀⠀⢠⢾⢇⣟⡀⠀⠀⠀⠈⢹⣿⣶⣿⣴⣿⠋
⠀⠛⠭⠴⠾⠟⠁⠙⠤⠠⠤⠟⠀⠻⠤⠤⠶⠛⠀⠛⠆⠴⠟⠃⠘⠳⠤⠀⠤⠿⠛⠀⠀⠀⠈⠒⠀⠛⠁⠀⠀⠀⠀⠘⠻⠽⢬⠷⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣦⣄⣀⣀⣀⣀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣉⣨⡀⣲⡞⣿⣿⡯⠥⠤⠄⠀⠀⠀⠀⠁⠀⣉⣉⣉⣉⣉⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⣝⣿⣿⣿⣟⣄⣒⣒⣒⣂⣀⣀⣀⣠⣽⣿⣿⣯⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣛⡻⣟⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣿⣽⣷⡄⠀⠀⠠⡶⢛⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⣀⣀⣥⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⡿⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢈⡋⠔⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⢠⡀⣠⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣷⣿⡆⣰⣶⢠⡶⠒⣿⠁⣂⣴⢶⡄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠏⠘⠇⠷⠿⠸⠇⠀⠿⠄⠿⠿⠘⠇⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣿⣷⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠻⠿⠿⠛⠃⠀⠀⠀⢹⣯⣭⣭⢱⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠒⣤⣤⣤⠤⠄⠀⠀⢙⣫⣭⡵⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠦⠄⣀⠀⣀⠄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡶⠿⠁⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⣀⡴⠚⠉⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⡀⠀⠀⡆⢸⣸⣦⣶⣾⣟⣋⠀⠀⠀⠀⠀⠀⢢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣧⣀⣰⣡⣿⡿⠟⠛⠛⠙⠋⠀⢀⢉⡑⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢇⠀⠀⠀⠀⠁⠀⠉⠃⠒⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠐⠢⢤⠤⢤⣴⠾⠃⠀⢸⣿⣉⣉⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⢾⠟⢋⠟⠀⠀⠀⢘⣹⢿⡅⠀⠀⢀⣈⣑⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠉⠉⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸⡇⠐⢳⡄⠀⠀⠀⠈⠉⠙⠦⡀
⠀⠀⠀⠀⠀⡴⠁⠐⠀⠀⣤⡦⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠟⠖⠀⠀⠀⠐⠶⠶⢿⣦
⠀⠀⠀⠀⢰⠁⠀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⠀⠀⠀⠀⠀⠤⠶⢾⣷
⠀⠀⠀⠀⣼⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣹⣄⡸⠀⠀⢳⣄⠀⠀⠀⠀⠈⠙⠇
⠀⠀⠀⠀⠿⢅⡀⢀⠀⣀⢀⣀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⢁⡀⡀⠀⠉⠉⠙⠧⣤⣀⠈⠱⡄⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⣇⠀⠀⡴⠻⠿⣆⠀⠘⠳⣄⠀⠀⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠖⠈⠀⠀⡈⠀⠂⠀⠠⠀⢀⠁⣐⡡⠀⠀⠈⢷⣄⣢⡙⣿⣶⣞⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠰⢇⡀⢒⠀⠚⠀⠀⢡⠀⠀⠀⢈⠠⠁⠁⠀⠀⠀⠀⣀⠀⠙⢿⠍⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠠⠃⠀⠁⠀⠀⠉⠘⠆⠰⡀⢀⣀⣾⣥⠆⢀⠀⠒⠃⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣈⢓⣐⠀⠄⢤⡀⠀⢀⢳⣀⣿⡟⠁⣀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡎⠀⠶⠺⠦⣤⠶⠦⠢⢬⡅⠉⠈⠿⠯⡶⠛⠋⠁⠐⠚⠠⢌⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠎⠉⠃⣻⠡⣄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄⠁⡀⣸⠆⠀⢀⠈⣰⠆⡇⠀⠀⠄⡀⢔⠢⠀⠀⠀⠀⣴⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠒⢊⡠⠾⠒⠀⠀⠠⡛⠀⠀⠀⠀⠠⠙⢄⠓⠂⠀⠲⡴⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠹⡀⠀⠀⢀⠄⠐⠋⠁⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡈⠐⠄⣀⣀⣠⠎⠀⢀⡘⡀⠀⠀⠀⠀⠀⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠚⠛⠁⢀⣀⣠⡶⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠃⠀⠠⠶⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⣠⠴⠖⠒⠂⣠⣄⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⢤⡀⠀⠀⠀⢀⣠⠤⢤⡤⡤⢄⡀⠀⠀⠀⠀⣠⠴⠒⢒⡲⠦⣄⠀⠀⠀⠀⠀⢀⠤⠆⣶⠦⣄
⠀⠀⢰⣁⡤⠴⠚⠉⠁⢀⡇⠀⠀⢠⡗⠒⠒⠒⠒⠒⢒⣿⠀⠀⠀⣿⡀⠀⠘⡐⠀⠀⢹⡆⠀⠀⠀⡷⣦⣝⣃⣀⣠⡴⡇⠀⠀⠀⠠⣟⠓⢲⡟⠒⣨⡇
⠀⠀⠘⢝⡓⠲⠶⠖⢚⡻⠁⠀⠀⠘⢏⡓⠒⠒⠒⠚⣉⠜⠀⠀⠀⠳⢌⣙⣛⣓⣒⡨⠝⠀⠀⠀⠀⠳⣄⣀⣀⣀⠤⠔⠃⠀⠀⠀⠀⠳⠅⠛⠻⠿⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⢀⢜⢧⠀⠀⠀⠀⠀⠀⡠⢆⠀⠲⡄⠀⠀⠀⠀⠀⡴⡡⠒⠒⠪⠣⠀⠀⠀⠀⠀⠀⢠⢮⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠕⠁⢸⠇⠀⠀⠀⠀⢸⡀⡨⢶⠁⢸⠀⠀⠀⠀⠀⡗⡀⠀⠀⢀⢆⠂⠀⠀⠀⠀⠀⡇⠀⠙⠦⣄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡊⠁⢀⣠⠎⠀⠀⠀⠀⠀⠀⠙⠤⠤⠗⠁⠀⠀⠀⠀⠀⠙⠾⣦⣐⡭⠊⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⣀⡠⠄⡀⠈⠉⠉⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢤⡀
⠀⠀⠀⢀⣴⣊⠁⠀⠀⢈⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⢿⠀⠀⠀⢀⡠⠒⠉⠀⠈⠃⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⣠⡚⠁⠀⠀⢀⠇
⠀⢀⡔⠁⠀⠈⢳⢀⡴⠋⠀⠀⠀⣠⠊⠙⢵⣄⢀⠴⣫⠞⠀⠀⣰⣟⡳⣦⠀⠀⡠⠂⠀⠀⢠⠞⠁⠀⠀⠀⣠⢞⠕⠁⠀⠀⠀⣠⠊⠀⠑⢤⡀⡠⠊
⠀⢸⠀⠀⢀⣠⠞⠋⠀⠀⠀⢀⡜⠁⠀⢀⡠⢟⡵⠊⠁⠀⠀⣜⣿⣺⣽⣽⡧⠚⠁⠀⠀⢠⣇⡀⣀⡀⢔⡫⠚⠁⠀⠀⠀⠀⢰⡃⠀⠀⢀⠔⠋
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⢦⣤⠖⠉⠊⠁⠀⠀⠀⠀⠀⠙⠾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠓⠁⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⠢⣄
⠀⠀⠀⡠⠴⠤⠶⠤⠶⠦⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⣎⠀⠀⠀⢱⠈⡇⠀⠀⠀⠀⢠⢶⣒⡉⠉⣏⢉⣀⢶⡄
⠀⠀⠀⠳⠤⠄⣀⣀⣠⠶⠞⠀⠀⠀⠀⢯⠲⠤⣤⣤⠤⢶⠃⠀⠀⠀⠀⠘⡧⠬⣭⣃⡭⠥⢊⠇⠀⠀⠀⠀⠘⠦⠤⠤⠥⢤⣤⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠐⠉

⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠉⠉⠑⠒⠦⣄⡀
⠀⢀⡔⡟⠁⢀⡤⠔⢆⠉⠀⠉⠐⠄⠤⢀⠙⠳⣄
⢀⡾⢸⠀⢀⣏⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠙⢦⠈⠳⣄
⣼⠁⡆⢀⠇⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠘⣧
⡟⠀⡇⠘⡄⠀⠀⠀⠀⠈⠒⢄⠀⠀⡠⠊⠀⠀⠀⠀⢠⠘⣇
⣇⠀⢻⠀⢈⠉⠉⠉⠉⠁⠀⡠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢻⠀⠈⢧⠘⣄⠀⠀⠀⡠⠊⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠈⡇⠀⠀⠀⠀⠀⠤⠤⣤⣀⣀
⠘⣆⠀⠈⢧⡈⠂⠤⠋⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣦
⠀⠘⢄⠀⠀⠑⢄⡀⠳⢄⠀⠀⢸⠀⠀⠀⠀⠑⢄⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠈⠢⡀⠀⠀⠉⠢⢄⡉⠀⠚⠀⠀⠠⠤⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠈⠑⠒⠦⠤⠤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠴⠒⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣷⣶⣶⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠼⢧⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠠⠂⠀⠀⠀⠀⠈⠁⠀⠙⠢⡀⠀⠀⢀⡤⠴⠖⠒⠒⠦⢤⣀⡤⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠞⡱⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⡀⠓⠘⣦⠚⠡⠀⠀⠀⠀⠀⠀⠀⠸⣌⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠅⡴⢁⠞⠁⠄⠈⡆⠀⠀⢠⠎⣀⠘⡄⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⢐⡽⠻⡌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇⠄⡼⢠⠊⠀⠀⠀⡀⢰⠀⠀⠏⠀⠀⡆⠱⡀⠀⡿⡄⠀⠀⡠⠦⡑⠄⠀⡜⠀⠀⠱⣾⢄
⠀⠀⠀⠀⠀⠀⢀⡜⠁⡎⢈⡜⢁⠎⠀⠈⠀⠀⡇⠸⠚⢨⠀⠀⠀⠈⢄⠙⠒⢃⡇⢀⢰⠁⠀⢰⠀⠠⡇⠀⠐⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⣾⠀⡞⠀⠀⠀⠀⠀⠑⡀⠇⠸⡀⠀⢠⠀⠀⠁⣀⠀⡷⠀⡟⠀⡀⠸⡈⣱⠁⠀⠀⠀⢀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹⣝⠋⠀⠀⠀⡄⠀⠀⠀⠐⣘⠦⠃⠀⠀⠀⠀⠀⠁⠀⣇⡴⠃⠀⠀⠀⠉⠁⠀⠐⠀⠀⠀⣠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠉⠓⠒⠦⠤⢄⣀⡘⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣼⠗⢢⡴⠚⠛⡆⠐⠀⣀⡠⠴⠖⠋⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠢⠤⠤⠤⠿⠦⠾⠽⠶⠚⠓⠛⠉⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⠲⠦⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠔⢀⠔⠀⠀⠉⠉⠉⠉⠋⠉⠙⠉⠛⠛⠛⠛⠛⠉⠋⠉⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠐⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣴⡁⣀⠀⠠⠂⣠⡮⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡴⠦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⡒⢶⡲⣟⠻⠹⢟⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡊⠷⡹⣄⠙⠪⠅⣀⡨⢵⡽⢊⡿⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣔⣁⢊⠶⠍⣴⡒⡒⡈⡕⢎⠡⡈⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠒⠶⠦⠶⠶⠾⠖⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠓⢄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⢳⣇⠀⢀⡄⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢻⠀⡜⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⣷⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⡇⠀⢰⠏⠀⠀⠀⠀⠀⣠⠤⠀⠢⣤⠤⢄⡀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠉⢔⡢⢄⠀⢀⣼⠁⠀⠀⠀⠁⠈⠁⠚⠍⡲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢗⣼⣿⠈⠀⠀⠀⠀⢠⠀⠀⠀⠘⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢆⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⡴
⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠸⡀⠀⠀⢘⠨⡀⠀⠀⠀⠀⢀⠰⢢⠲⡶⠶⠘⠂⠠⠤⢈⢶⠄⣀⠀⠠⠀⠀⠴⣾⡝⢁⡂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⡄⢣⠀⠀⠀⠂⠁⠀⠆⠀⠁⠀⠈⠀⠀⠀⡜⣸⠀⠀⣉⣐⣶⠶⢏⠁⠀⠀⠀⠀⠀⠬⢔⣦
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠒⠱⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠛⢿⠛⠋⠛⠀⠀⠀⠈⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⠉⣷⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣼⢿⣿⣷⡖⠁⣠⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠂⠀⠉⠻⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⢈⠿⠿⣿⣿⣿⣿⠿⠋⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣤⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⡀⠀⠀⠉⠻⠿⠷⠶⢄⠙⠲⠻⢦⣀⠀⠀⢀⠔⠀⠀⠀⢰⣟⣉⡙⠀⠀⠀⢿⣿⣿⣿⣤⣤⣬⣼⣋⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⢸⣿⠻⠓⠦⠤⠤⠖⠒⠄⢺⣿⣶⢶⣤⣉⠳⡄⠀⢻⣦⡴⠀⠸⠉⠙⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⠯⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠀⠀⠀⠀⠀⠀⠀⢀⠛⠋⠄⠟⢙⣛⡛⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⡜⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠘⠃⡶⠋⢝⣣⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣄⡀⠀⠸⢀⣤⣶⢦⣤⣶⣿⡿⠟⠋⠉
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠚⠛⠉⠉⠁⠀⢺⡏⡟
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢬⡁⣿⢣⡀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠱⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⣤⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⣤⡿⠘⡧⠀⠀⢀⣀⣤⠶⠚⠁⠀⠀⢀⡜⠳⣄
⠀⠀⠸⠀⠀⠀⠀⣠⠞⢋⠔⠁⠀⢀⠗⠐⠦⠤⣤⣄⣀⣀⣀⠀⢀⣀⠴⠚⠉⠀⠀⣀⡾⢼⣷⡀⣀⡾⢫⠀⠀⠀⠀⣀⠤⠒⠋⠀⠀⠈⠑⢄⡀
⠀⠀⠠⡀⠀⠀⠈⠁⠠⣃⣤⣴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣠⣴⠿⢆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⣤⡀
⠀⠀⠀⠑⢦⣀⠀⠀⠐⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠙⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣀⡀⢀⡾⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣼⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣾⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⠾⢁⣴⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡴⢋⣴⣞⣃⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣀⣴⣿⣿⣿⣽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠉⠉⠉⣉⣀⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⣧⣸⠏⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⣡⣾⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡤⣶⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣴⣿⠋⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢰⣯⣴⣿⣱⡿⠟⠘⢴⣀⣀⠤⠐⠀⠂⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠟⠋⠀⠀⢀⠜⠉⠤⠀⠈⠀⠈⠀⠁⠠⠈⠂⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⠏⠰⠁⠀⠀⠀⠃⢀⠐⠀⠀⠀⠀⠐⡀⠀⠠⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠡⠀⠀⠀⠀⠄⠠⢀⠀⠈⠀⠀⠂⢸⠶⢶⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠄⠀⠤⠀⠐⠣⠠⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⡠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⣈⣡⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢂⠥⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠠⢌⣀⠀⠀⠀⠀⠠⠤⠤⠔⠀⠀⢐⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠂⠀⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⢀⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠑⠒⠒⠀⠀⠀⠀⠀⠀⣸⠠⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⠉⠀⠐⠂⠀⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⠉⠉⠁⠀⠐⠄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⢀⣀⣠⠤⠤⠔⠒⠚⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣀⠜⠀⣀⡀⠰⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢐⢁⡤⠄⠀⠀⠀⠀⠉⣠⠴⠋⠁⠈⢧⠁⠀⠘⢦⠀⠀⠀⠀⠀⠀⠸⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠈⠀⠀⠀⢀⡠⠖⠋⠀⠠⠔⠊⠉⠀⢣⠀⠀⢀⠱⡀⠀⠀⠀⠀⠀⡇⠀⠘⡀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⣨⣠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠰⠀⡇⠀⠀⠀⠀⠀⡇⠀⡄⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢣⠀⠀⡇
⠀⠀⠀⠀⢨⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⠀⠀⠀⠀⠀⠀⢧⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⠃
⠀⠀⠀⠀⠀⠱⣄⠈⢢⠀⠀⠀⠀⠠⠶⠤⠄⠀⠀⠀⠀⠀⠱⣌⠀⠀⠀⠀⠀⠀⠀⠉⠢⣴⠀⠰⠤⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠆
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⠤⠤⠖⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⠲⠂⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⡊⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠶⠶⠶⢾
⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠚⠛⠋⠉⠉⣉⣠⠴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⡎⠀⠀⡀⠄⠘⠓⠀⢀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⢀⣀⣠⠴⠖⠛⠉⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇
⠈⠉⠉⠀⠀⢀⡴⠛⡏⠀⠠⣯⠤⠤⠤⠤⠶⠶⠚⠛⢉⠡⠄⠀⠀⠀⢈⢭⣭⡙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣇
⠀⠀⠀⠀⢰⠋⠀⣸⠃⠀⠀⠹⣦⡀⠀⠀⣀⣤⡶⣯⡀⢀⣤⠴⠶⣦⢀⣀⣬⢿⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢿⣄⣴⠏⠀⠀⠀⠀⠘⢿⣤⣾⣟⣁⣀⣨⣵⣯⡴⠶⠖⢛⣩⢥⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣯⠉⠉⢉⣵⠞⠛⠶⠶⣆⢻⠀⠀⢹⡧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠋⡏⠀⠀⠀⠀⣿⠀⠀⣐⡚⠁⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠰⠶⢶⠇⣴⠋⠉⠉⣋⡴⣿⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣁⣤⣥⡴⠶⠛⢉⣠⠟⠀⠀⠀⠀⣼⠵⠒⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⢉⣀⣠⡤⠔⠚⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠒⠒⠒⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣤⡾⠚⠛⠻⢦⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢹⡄⠀⣀⣀⣀⡴⠞⠉⠀⠈⣷⠀⠀⠀⣠⠞⠻⠷⠊⠀⣿⠀⣠⠤⣄⠀⢻⡄⠀⠀⡇
⠀⠀⠀⢠⣶⢨⡇⢸⡏⠉⠉⠀⠀⠀⠀⠀⠘⠷⠤⠖⠁⠀⠀⠀⠀⠀⣿⠎⠀⠀⠘⡆⠀⡇⠀⠀⡇
⠀⠀⠀⠛⢋⡜⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⠀⡏⠀⠀⢻
⠀⠀⠀⢠⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⣸⠁⠀⠀⢸
⠀⠀⠀⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡼⠁⡴⠃⠀⠀⠀⢸
⠀⠀⠈⢧⣤⣤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠋⣠⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠠⠖⠀⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⡷⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⠛⠋⠁
⠀⠀⠀⣠⣤⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠿⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠸⣧⠈⠙⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣤⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣿⣿⣿⠛⠋
⠀⠀⢀⣼⣿⣿⣿⣿⣯⣿⡍⠸⠙
⠀⠀⣾⣻⠿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠚⢲⠆
⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣀⡒⠀⠤⠀⠀⡀⠀⢠⡀⡀
⠀⠀⠈⢿⣿⣿⡁⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⢤⡀⣀⠀⢀⣅⠀⠀⠀⠀⠀⣠⠸⠷⡄⣥⡂
⠀⠀⠀⠀⠻⣿⣷⣆⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⢟⣀⣶⣶⣶⣆⠀⠶⠶⠇⣻⠇
⠀⠀⠀⠀⠀⠈⢿⠋⠀⠈⠳⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠪⠙⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⣆⢠⣀⣀⣀⡤⠦⣄
⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠟⢹⠀⠁
⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⣄⠀⠀⠀⠀⠀⠀⠀⠢⢄
⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢄⠀⠀⠀⠀⠆⢹⣄⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠉⠢⢄⣀⡘⡄⢷⣕⠦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠙⠿⢦⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⢶⣶⣶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠴⠂⠀⠀⠀⠒⠒⠒⠒⠲⠤⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⡿⣃⠰⣯⠗⠀⣈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠒⠀⠀⠀⠒⠛⠛⠋⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⡾⢿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣤⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣏⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⢿⠳⣿⠀⠀⠠⠤⠤⠀⠀⠀⢤⡄⠠⠠⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠙⠚⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⡀⢀⣠⣿⣾⣿⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠠⠾⠾⠲⠷⠞⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣴⣞⣻⣿⡿⠋⠉⠉⠉⠉⢹⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣙⣛⢿⣦⣄⡀⠀⠀⢴⣟⡛⣩⣿⣏⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠿⠿⠿⠿⠿⠿⠿⠯⠉⠁⠀⠀⠀⠀⠀⠠⣔⣲⠀⠀⠸⣯⣵⣤
⠀⠀⠀⢀⡀⢀⣄⡤⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣄⠀⠀⠀⠀⠀⢀⣀⠀⠈
⠀⠀⡐⠁⢀⡀⣹⣷⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠿⠀⠀⠀⠸⢿⡷⠿⠆
⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⠀⣴⣦⠀⢠⣶⣦⣄⢰⣦⣶⡦⣤⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⢄⠠⠤⠤⣤⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⣿⠀⣿⢻⡆⢸⣇⢀⣿⠀⢸⡇⠀⠸⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠆⠀⠀⠲⡶⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠋⢰⣇⣸⡇⢸⡟⠻⣧⠀⢸⡇⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢼⠏⠙⣿⠸⡇⠀⣿⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠒⠒⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⣤⡄⢠⣤⡄⠀⢠⣤⡄⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠉⠀⣿⡇⢸⣿⣷⠀⣼⣿⡇⢸⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠤⠶⠶⠾⣮⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⡇⢹⣷⡏⢸⡇⢸⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠉⢀⠀⢀⣀⣀⠐⢷⠶⠤⠭⢒⠒⠤⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡇⢸⡇⢸⣿⡇⣿⡇⢸⣿⣤⣤⡄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠑⣄⠀⠀⠀⠈⠁⠀⠀⠉⠁⠈⠁⠀⠉⠀⠈⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⡆
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠠⡆⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠀⠀⢀⠀⠀⢠⠜⠛⠀⠁⠐⠄⠀⠀⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡏⠀⠀⠀⠀⠀⠈⡶⠀⠀⢀⡠⠂⠠⠴⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡼⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠂⠊⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⡶⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣦⠀⠀⠀⠀⠀⠙⠓⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡅⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢻⣄⠀⠀⠢⣤⣀⣀⠛⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⣸⠐⡇⠀⠀⠀⠀⡠⠊
⠀⠀⠈⠛⢷⣆⡀⠀⣿⣿⣷⣦⣌⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⢩⡄⠀⡠⠊⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⢿⣦⣌⣿⣯⣉⠂⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣻⣾⣄⡀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⢏⢿⣿⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣱⡏⢸⣙⣦⣺⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡤⣛⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠔⠒⠋⠀⢀⣰⠃⠀⠀⠀⠰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⡀⠀⠀⣠⣾⡇
⣼⣤⢀⡀⢀⡀⡀⠀⠀⠐⠊⠁⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠁⠲⠦⠴⣱⣶⣿⣿⡿⠃
⢿⣿⣌⠉⠀⠤⠀⠀⠀⢀⣀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣐⡒⠖⣻⡯⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢹⠽⠟⠋
⠀⠉⠛⠿⠶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣀
⠀⠀⠀⢀⣶⠾⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⢟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⡀⠀⠤⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠘⢦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣾⣴⠎
⠀⠀⢸⣧⡤⡴⠒⡶⡀⠀⡄⠀⠀⠀⠀⠀⠀⢻⡨⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢸⣯⣧⡬⡤⠤⠿⡄⢧⠀⠀⠀⠀⠀⠀⠈⣷⣿⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣿⡅⣿⠀⠀⠀⠀⠀⠀⢸⣯⣭⠉⠁⠀⠀⠀⠀⠐⠐
⠀⠀⠘⣷⣟⠀⡀⢀⠀⣤⣐⠀⠀⠀⠀⠀⠀⠀⠸⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢿⠀⠀⠀⠀⠀⠀⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠹⣿⡴⡿⠿⡣⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠷⣾⡄⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠙⢶⠖⠛⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣰⣾⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⡽⠄⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠶⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡀
⠀⠀⠀⠀⠀⣀⠠⣤⡤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠰⠄⠠⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣿⣿⣷⣦⡂
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠻⣷⣆⠀⠀⡄⢀⡀⡀⡀⢊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⡟⠀⠀⢿⣤⡭⠕⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢰⢱⠁⠀⠀⢸⠛⠉⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⠀⠈⠁⢹
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠅⠀⠀⠀⠀⠀⠳⡄⣀⣀⣀⣿⠃⠀⠀⠀⢸⠷⠤⠴⠦⢤⡇⠀⠀⠀⠀⡄⢀⣠⣤⣘⡗⠀⠀⠈⣿⢣⣤⣾⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉
⣿⢿⠿⠿⡿⣟⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⡚⠉⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⡭⠖⠉⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣋⠴⢚⡩⠀⠀⠀⠀⠀⣀⣤⣶⠾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠐⣈⡤⠚⠁⠀⠊⢁⡤⢖⡫⠝⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⣀⡴⠚⠁⠀⠀⣀⡴⣞⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⡵⠊⣀⠴⠚⢁⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⠈⢧⡀
⠀⠀⠀⠀⣠⠴⢋⠵⠊⠁⠔⠊⠁⠔⠊⣡⣴⣿⠟⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡟⠀⠀⠈⣿⡄⠈⠳⣄
⠀⠀⠀⢯⡁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣷⣤⣤⠾⣻⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠳⣄⠀⠀⠀⣀⣴⡿⠟⠉⠀⠀⠀⠀⠀⣠⠤⠖⠶⢤⡤⠶⠦⢤⡴⢛⡟⢿⣞⣋⠁⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠈⠳⣤⢞⠕⠋⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠲⠤⢬⣷⠀⠀⣿⠀⢰⡇⠀⣿⠀⣩⡶⠶⠶⣦⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣀⣠⡤⢾⡷⣴⠒⢻⣷⣴⣷⣞⡃⣼⠁⠈⢢⣤⠿⡆⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⣿⠑⣄⠈⢳⡄⢸⠁⣧⡴⠋⢻⠀⠈⣪⡽⠿⠿⣟⣉⣡⢴⡧⠶⠶⣤⡀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⢹⡹⣄⡈⠳⣸⡇⢘⣧⡘⢷⣤⡾⠀⢰⡟⠶⠴⠤⣼⣧⠀⣸⡀⠀⠀⢈⣷⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⠳⣬⣽⡿⠋⣠⢾⠈⠙⣍⢳⣠⡶⠾⣿⣛⣛⣫⠵⠋⠀⠻⣍⣛⣛⣻⠇⠀⠀⢀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠹⣌⠓⠦⣬⣾⠹⣗⢦⡈⠻⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠉⡿⠲⠚⠉⠹⡎⠳⣽⣤⡾⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢸⡘⢦⣄⣀⣼⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⢹⡆⠀⠀⠀⢀⢴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠙⠲⠶⠾⠋⠀⢀⣀⣀⠀⠀⢺⣧⡤⠴⣾⠇⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⡴⠉⢹⠉⢳⡄⠀⠉⠛⠉⠁⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⢰⣧⡀⣸⣀⣾⠇⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⠻⠿⠯⠽⠋⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠾⠟⠛⠻⠿⠷⠶⠶⠶⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⢻⣿⠟⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⣿⡦⠾⠿⠿⣿⣿⠿⠿⢶⣤⣄⣀⣠⣤⣶⠶⠶⠛⠋⠁⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⠉⢉⣉⣀⣠⣤⣤⣴⣶⣶⠿⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⡀⠀⠀⠘⢿⣿⣿⠏⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠘⠿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠉⠉⠉⠉⣁⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⢶⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡆⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣀⣀⣠⣄⣀⡤⠴⠒⠋⠉⠉⠉⠉⠙⢿⣷⣤⣶⣤⣄⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠘⣿⣿⠀⠀⠀⠀⠀⣀⣠⣾⠯⢤⣤⣀⣀⣀
⠺⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠒⠻⠿⢿⣿⣿⣿⣿⣶⣿⣿⣦⣤⡤⠖⠛⠉⠉⠁⣀⣀⡤⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣛⣋⣉⣁⡤⠖⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠁

⠀⠀⣀⣀⣠⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⠶⠶⠤⣤⣤⣤⣄⣀⣀
⣶⡛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛
⠈⠻⣿⠓⠶⠶⠶⢦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠶⠶⠶⠚⣻⠟
⠀⠀⠈⠳⣄⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣀⣀⠀⠤⠤⠤⠄⢠⠶⠶⠶⢂⡉⠉⠉⠉⠙⠛⠛⠓⠒⠒⠂⠀⠀⢀⣠⡤⠤⠤⠄⢀⣀⣀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⢬⡄⠀⣀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡧⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡙⢀⠀⠀⠈⠉⠙⢻⠒⠂⠀⠀⠐⠀⠠⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⡠⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡐⠄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠢⡀⠀⠀⠀⠙⠆⣀⠀⣸⡣⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⡀⠀⠐⠉⠀⠀⠀⠀⠀⢀⡔⠂⠉⠉⢁⣦⡀⠀⠀⠀⠀⢀⡔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣔⢦⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠁⢜⠀⠀⠀⡠⢪⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡝⢄⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⠆⠀⡠⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢦⡀⠈⣄⠀⠀⠀⠀⢀⣰⢎⡠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠢⣀⠑⠀⠄⠛⢫⠋⠉⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠒⠲⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⠾⠃⠀⠀⠘⠳⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠩⢉⣡⠾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠈⠉⠙⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠀⠀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⡛⠳⠶⠶⣤⣥⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣥⠶⠶⠞⢛⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⣤⣤⣤⣍⣉⣉⣉⣉⣉⣉⣉⣉⣩⣤⣤⣤⠤⠶⠖⠚⠉⠁
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣁⣀⣀⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⣠⢷⣇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠐⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠉⢤⢐⣲⣦⣶⡔⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣾⠙⠛⢻⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠐⢾⣿⣏⠟⣟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠃⢉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠅⠀⢨⣞⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⢠⣼⣷⠦⡄⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⣈⠛⠿⢿⣷⣾⡿⢟⣱⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⡷⠀⠀⠀⠠⡀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⢤⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠖⠦⠤⠴⠿⠿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠠⠤⠤⠤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠸⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠐⠄
⠀⠀⠀⠀⠀⠠⡦⠠⣦⣤⣶⣤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⢀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠰⡇⠀⠙⠿⡿⠋⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⠶⠦⢤⠀⢰⠆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠉⠉⠉⠛⠛⠒⣚⣛⣺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠰⣾⣿⢄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠶⣿⠋⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠋
⠀⠀⠀⠀⠀⠀⠀⡆⡄⠐⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣟⠂⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡭⠉
⠀⠀⠀⠀⠀⠀⠀⣷⣞⡃⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣆⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣴⣶⠞⠠⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⣯⣽⣭⣭⣉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠈⠁⠀⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⡉⠉⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⡡⠒⠉⠀⠀⠀⠈⠁⠂⠽⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠅⠊⠁⠀⡠⠴⠚⠉⠑⠲⣄⠀⠀⠸⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢜⣄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⣉⢖⠵⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢌⠻⢖⠠⢀⠀⠀⠀⢀⠤⡪⠔⠁⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠃⠀⠉⠂⠑⡤⣀⣀⡠⠔⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⠀⠠⠀⠀⠀⠀⠈⠁⠀⠠⠊⢀⠔⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢈⠀⠀⠠⠂⠀⠀⢠⠈⠀⠀⡠⠣⠀⣠⣂⡾⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠓⠤⣀⠀⠀⠀⢸⢀⠀⠈⣀⢔⣬⠟⠉⠀⠀⠀⣀⡴⡒⠟⠛⠭⣙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣍⣢⡠⢾⠐⠄⣪⠷⠋⠀⠀⠀⣠⡴⡛⠅⠊⠀⠀⠀⠀⠀⠑⠤⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠳⠾⠶⠋⠁⠀⠀⢀⡴⡻⠕⠀⠀⡀⠔⠐⢉⠐⠢⣄⠀⠀⠀⠁⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣒⡋⠉⠩⠉⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⢇⢀⠀⠪⠀⡠⠀⡁⠀⠀⠀⠙⡢⠄⡂⢸⡟
⠀⠀⠀⠀⠀⢠⡶⠚⠉⠀⠊⠀⠀⠀⠐⡰⠁⣿⠀⠀⠀⠀⠀⠀⠀⢹⠈⠓⢝⠠⠀⠀⠀⠀⠀⢀⠠⢒⡩⠔⠀⡀⢸⡇
⠀⠀⠀⠀⣠⢏⠁⠀⣀⣤⠴⠖⠒⠂⠉⠀⣀⢹⡀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠈⠉⠛⢶⡤⠬⠑⠊⡁⠀⠀⠀⡇⢸⡇
⠀⠀⠀⢰⡟⠈⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⢷⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⢸⠇⠀⠠⢊⠀⠀⠀⠀⢈⣼⠁
⠀⠀⠀⠘⣿⡀⠸⡄⠀⠀⠠⢂⢀⠀⠀⠀⠀⠘⡈⣧⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⢀⢸⢰⠀⠀⠡⠊⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠘⣿⡄⢃⠀⠐⠑⠡⠂⠄⠀⠀⡰⢀⢇⡿⠀⠀⠀⠀⠀⠈⠳⣌⡐⠲⠤⠞⢸⠸⡀⢀⠠⣲⡽⠋⠁
⠀⠀⠀⠀⠀⠘⣿⠘⢄⠀⠀⠀⡀⠤⢐⣈⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣼⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠉⣁⡤⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠲⣔⣆⣠⣬⡇⠠⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠴⠎⠀⠀⠀⠀⡀⣡⣶⣾⣾⡎⠙⠿⠿⠷⢦⠱
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⢯⠙⠀⠀⠀⠀⠐⣄⢧⠤⠜⠛⠋⠿⠽⠛⠋⠁⠀⡀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣍⣂⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠉⠳⠤⠤⣄⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠣⡀⠀⠀⠀⠐⡇⣀⡒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⡀⠈⠁⠒⠒⣤⡘⣿⡇⠀⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠎⠸⡀⠀⠀⠀⢰
⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠈⠢⢄⣀⣀⡷⣝⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠦⣀⢀⣸
⠀⠀⠐⠉⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡂⠤⠩⠝
⠀⠈⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⡄⠀⠀⢀⣴⡵⠖⠀⠀⢀⣀⣀⣀⠑⣠⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢸⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣧⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣬⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⡀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⣻⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣇⢤⡀⠀⠀⠀⠀⣚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣩⠿⣷⡵⠪⢟⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⢇⠹⠦⠀⠀⠀⠠⠐⢺⡇⠀⠀⠀⣠⡤⣶⠛⠒⠶⣄⠀⠀⠀⣀⣉⣭⣴⣾⣯⣥⣴⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣴⣀⣦⣤⠠⣴⣦⣕⣶⠀⠀⠀⣴⣷⣦⣄⠈⢀⠀⢙⡆⠀⠀⣸⣿⣿⣯⣥⣤⣶⣿⡿⢚⣿⠆
⠀⠀⠀⢀⡤⠴⠲⠶⣤⣄⠀⠹⢿⣿⡟⠙⠚⠛⣿⣿⡏⢀⣴⠟⠁⠀⠀⢈⣱⣤⣤⣼⣇⠀⠀⢰⣿⣯⣤⣤⣭⣭⣶⢾⡛⢙⠀⠀⠀⣺⣥⡄
⠀⠀⣰⠏⠀⠈⠰⠀⠁⠹⣷⡀⢺⣿⡷⢶⣶⣿⣿⡇⠀⡾⢦⠀⠈⢀⣼⠋⠁⠀⠁⠀⠉⠳⠄⠀⣿⡿⡿⢶⣶⡾⢿⣿⣿⠂⠀⢠⡖⣇⠿⣿⡿⣦
⠀⠀⣿⣄⠀⠀⠀⠀⠀⠰⣿⡇⠈⣯⣿⡏⠛⣿⣿⠁⠀⢿⣀⡀⠀⣾⢍⡁⠀⠀⠀⠀⠀⠰⣻⠀⠻⣿⣷⣾⣾⣤⣼⣿⠏⠀⠀⣘⣷⠟⣤⡿⢷⣸⣦
⠀⠀⠘⡧⠀⠀⠀⠠⡾⠶⢿⡁⠀⣟⣷⡾⠻⣾⣿⠀⠀⠀⣟⢹⡶⠿⣦⡀⠤⠀⠁⠀⠀⠈⣿⠀⠀⢸⣿⣯⣉⣽⣿⡟⠀⠐⠷⣟⠛⡚⠿⣗⢨⡿⣻⣷⠄
⠀⠀⠘⢠⠀⢀⠀⣄⡈⠡⣼⠇⠀⠻⣯⣽⢶⡭⡷⠀⠀⠐⢧⣼⣿⠀⡌⠦⣠⣀⠠⡤⠴⢶⡋⠀⠀⠠⣽⢉⣿⣽⣿⡇⠀⠰⢽⣧⣻⣡⡚⠻⡞⢿⣍⡿
⠀⠀⠀⢨⣶⣮⣤⣿⣷⣼⠁⠀⠀⠈⠿⠧⠤⠷⠁⠀⠀⠀⠈⠛⣿⣿⣧⣶⣦⣄⢀⡼⣿⠊⠁⠀⠀⠀⣿⣶⣇⣼⣿⠃⠀⠀⠈⣿⣿⣿⣯⣽⠿⣿⣻⡇
⠀⠀⠀⠘⢡⡞⢳⣞⣥⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢿⣾⣿⣿⣿⣾⣻⠁⠀⠀⠀⠀⠀⢹⣶⡿⢮⣽⠀⠀⠀⠀⢹⣾⣿⠿⣿⡞⢿⡿
⠀⠀⠀⠀⣧⠚⣿⣧⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣻⡛⠳⠇⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⡟⠀⠀⠀⠀⠈⣧⣿⣶⣿⣷⣿⡇
⠀⠀⠀⠀⢰⣻⢇⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⡏⢹⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣽⡇⠀⠀⠀⠀⠀⢹⣹⣧⣨⣷⣾
⠀⠀⠀⠀⠈⡟⢋⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⣯⣿⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⠇⠀⠀⠀⠀⠀⠀⢿⣾⠻⣿⠇
⠀⠀⠀⠀⠀⠸⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿