Automation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠋⠉⠉⠙⠁⢺⡿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠛⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣀⠀⠀⣀⣼⣿⣿⣧⣀⠀⠀⣀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⣾⣿⣷⣿⣿⡿⠿⠿⢿⣿⣿⣾⣿⣷⡀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⢻⣿⣿⠟⣡⣶⣿⣿⣶⣌⠻⣿⣿⡟⠁⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⣿⡏⣸⣿⢿⣿⡿⢋⣽⣇⢹⣿⣷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣇⢸⣿⣦⣉⣴⣿⣿⡇⣼⣿⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠿⠿⣿⣿⣦⣙⠻⠿⠿⠟⣋⣴⣿⣿⠿⠿⠁⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣰⡆⠀⠀⠿⣿⣿⠟⠛⠛⠻⣿⣿⠿⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠇⣀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢸⣿⡇⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⣿⢸⣿⡇⣿⣿⣿⣋⡄⠀⠀⠀⠀⣸⡿⣫⣍⠻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠦⠭⠵⠿⠿⠿⠿⠇⠀⠀⠀⠘⢿⣇⠿⡿⢃⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡿⠿⠿⠿⡿⠿⠿⠿⡿⢿⣿⣿⣿⠇⠀⠘⠛⠷⡾⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⠿⠟⡋⣴⣿⣿⣿⣿⢩⡍⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⢸⡇⢼⡿⠿⠿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣮⣅⡛⠃⣿⢸⡇⣿⢡⣶⢸⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢸⡇⣿⢸⣿⢸⡟⣛⡛⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠇⢿⠸⡿⢸⠇⢿⠇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢐⣒⣒⣒⣒⣒⣒⣒⣒⣚⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛⠋





⡶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢶⡆⠀⠀⠀⠀⠀⠀⣾⠁⣾⠁⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠳⠞⠛⠁⠀⠀⠙⠳⠾⠛⢦⡀⢠⡿⠃⠈⠛⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣠⡴⠶⠶⢤⣄⠀⠀⢈⡿⠋⢀⡴⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⣧⣴⠏⢀⣴⠻⣦⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⣇⠀⠀⢀⣤⣤⣴⠟⢁⣴⢿⣥⣀⠀⠉⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠻⣦⣰⡟⣡⣄⡁⢠⡟⠁⠀⠀⠙⢷⡀⠀⠸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠙⠟⠁⣨⡷⣠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⢦⣤⡀⠀⢐⡿⠞⠻⣄⡀⠀⢀⣠⠟⠀⠀⢠⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠾⢷⣄⠀⠈⠉⠛⠉⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢳⣆⣀⣰⡞⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠰⢀⠀⠀⠄⠠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢤⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠤⠤⣄⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢄⠀⡇⠀⠀⢸⠀⣠⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡆⠀⢮⡀⠀⠀⠙⠁⣀⣀⠘⠚⠁⠀⠀⡱⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠁⣀⣀⣹⠀⢀⠔⠉⡀⠀⠉⠢⡀⢠⠊⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡎⠀⢸⠉⠓⣦⠀⢱⠀⠉⠉⠉⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠒⠢⢤⠀⠱⡀⠀⠖⠊⠁⢀⠞⣠⠤⠤⠠⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⡴⠋⠀⠀⠈⠒⠤⠤⠒⠉⠀⠘⢦⡀⠀⢰⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣠⠔⢹⠀⠀⠀⡎⠳⡀⠀⡠⠇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣄⣀⣀⠇⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠯⠤⢀⣀⣀⣀⠤⠴⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⣶⢰⠐⡆⣔⢒⢰⣦⡆⣰⡆⢲⢰⢰⠒⡆⡦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠁⠈⠉⠈⠉⠀⠁⠀⠀⠈⠀⠉⠀⠁⠉


⣟⠉⣻⣛⣛⣛⣛⣟⣛⣛⣻⡛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣿⣿⣟⣻⣻⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣶⡾⠟⠃⠘⠻⢷⣶⠿⣦⡀
⠀⣴⣾⠿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⢀⡀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⠿⢿⣶⣄
⣼⡿⠁⠀⠀⠀⠈⢻⣷⣀⣀⣀⣀⠀⠀⣤⣼⡟⠀⠀⢠⡾⠛⠛⢷⡄⠀⠀⢻⣧⣤⠀⠀⢀⣀⣀⣀⣾⡟⠁⠀⠀⠀⠈⢿
⣿⣇⠀⠀⠀⠀⠀⣸⣿⠛⠛⠛⠛⠀⠀⣿⣥⡄⠀⠀⢻⣇⠀⠀⣸⡟⠀⠀⢠⣬⣿⠀⠀⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⣸
⠘⢿⣷⣤⣀⣤⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠙⠻⠟⠋⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⣀⣠⣴⡿
⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣁⣤⣄⡀⠀⠀⢀⣠⣤⣈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⢻⣧⣼⡟⠋⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠟⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⣤⣾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⠀⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡙⠋⠉⢁⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠴⠤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⠴⠖⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⣴⠃⠀⠀⣀⣀⡀⠐⠈⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠳⠀⢰⠇⠀⠀⠃⠉⠉⠛⠤⠀⠈⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠃⠀⠀⠀⠀⡄⠀⢀⡿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⣠⣶⡶⠻⣄⠀⠠⣶⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⠋⠁⠀⠀⠈⠛⠶⠦⠤⠶⠞⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠶⢤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠶⠶⠶⠦⣤⣤⣤⣄⣀⣀⣀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


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

⠀⠀⠀⣀⠀⠀⡤⠲⡀⠀⠀⠀⠀⢀⣀⠀⠀⢰⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣸⡾⣫⡳⣄⠉⠋⠀⠀⠀⢀⣿⢟⣝⢧⣄⠚⠁⠀⠀⢀⣷⢟⣝⢦⡀⠀⠀⠀⠀⢀⡷⣫⣝⢦⡀⠀⠀⠀⠀⢀⡷⢻⣝⢦⡀⠀⠀⠀⠀⢸⡷⣫⡻⣦⡀
⠾⣫⣾⣿⣿⣮⠳⠀⠀⠀⠀⠟⣵⣿⣿⣷⡝⠇⠀⠀⠰⢟⡵⣟⣛⢷⡝⠆⠀⠀⠰⢫⣼⡟⢻⣷⡝⠆⠀⠀⠰⢟⣼⣿⣹⢷⡝⠆⠀⠀⠰⢫⡞⣫⡝⣮⡻
⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⢸⣿⣷⣲⣿⡇⠀⠀⠀⠀⢸⣿⣧⣼⣿⡇⠀⠀⠀⠀⢸⣿⣝⣻⣼⡇⠀⠀⠀⠀⢸⣧⣝⣷⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣴⡄⠀⣀⠀⠀⠀⠀⠀⠠⢠⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⡀
⠀⡞⣛⢛⡛⣿⠿⣷⠀⠀⠀⠀⡅⣟⡇⠲⣿⠒⠀⠀⠀⠀⠨⢸⣿⠐⠒⠒⠂⠀⠀⠀⣿⣿⣸⡿⠿⠇⠀⠀⠀⠸⠿⣤⢯⡼⠿⠀⠀⠀⠀⠘⠋⠛⣛⣛⡂
⠀⣇⠚⠀⠃⣿⣭⣿⠀⠀⠀⠈⢡⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣾⣿⡄⠀⠀⠀⠀⠀⠀⣬⣽⣷⢻⣷⡄⠀⠀⠀⠠⢷⢛⣞⢳⡾⠀⠀⠀⠀⠨⣙⣫⠭⠶⠂
⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠈⠻⠟⠋⠘⠟⠃⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠐⠶⠖⠛⠉⠁

⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⡤⠤⠤⠤⠤⠤⠤⢤⡄⣤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⢐⣀⣐⠀⡀
⠀⢸⡁⢨⠆⠀⠀⠀⠀⠀⢤⣴⡏⣤⣧⠀⠀⠀⠀⠀⣿⡇⡇⠀⣴⣿⠻⣷⠀⢸⡇⣿⠀⠀⠀⣿⣿⠀⣾⣷⡶⡆⠀⠀⣞⣽⣿⣿⠄⠀⠀⢠⡏⠀⠈⣣⠠
⠀⠀⢧⡏⠀⣀⣤⣶⠀⠀⠀⠈⠓⠀⢃⣠⣴⡆⠀⠀⣿⡇⡇⠀⠹⢿⡾⠟⠀⢸⡇⣿⠀⠀⠀⣿⣿⣮⣤⣤⣵⠁⠀⠀⠘⣾⣿⠏⠀⠀⠀⠐⠱⡀⢰⠃
⠀⢀⣤⣶⣿⣿⣤⣿⠀⠀⠀⣠⣴⣾⣿⣧⣼⡇⠀⠀⣻⡃⠛⣛⣛⣻⣿⣛⣛⠛⠁⣿⠀⠀⠀⣿⣷⣾⣿⣿⣯⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⢿⡇

⠀⠀⠀⢖⣓⡲⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢰⣶⣧⣶⡄⠀⠀⠀⠀⠠⢤⣤⠹⢣⣤⠤⠀⠀⠀⠀⣼⠉⠉⣧⠀⠀⠀⢸⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⣿⡿⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⠤⣿⡇⠀⠀⠀⢠⡀⠴⠞⠃⠛⠶⠄⠀⠀⠀⠐⣾⡖⢲⣷⠂⠀⠀⠘⠀⠐⣾⡖⢶⣶⠂⠀⠀⠀⣿⣽⣿⣿⣿⣯⣇⠀⠀⠀⡇⣴⣎⣉⣶⡄⣇
⠀⠀⠸⠿⠿⠿⠃⠀⠀⠀⠈⠿⠷⠶⢾⡷⠀⠀⠀⠀⠀⠠⠿⠷⠾⠿⠄⠀⠀⠀⠀⠠⠿⠧⣾⠟⠀⠀⠀⠀⠛⢻⠿⠿⢿⠇⡿⠀⠀⠨⡿⢿⠿⠿⢿⠏⡿

⠀⠀⢀⢀⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⢀⡽⣫⣮⡻⣦⡀⠀⠀⠀⠀⣾⣶⠿⣶⡇⠀⠀⠀⠀⠀⣿⠩⠉⣿⠀⠀⠀⠀⢰⠟⢁⣤⡈⠛⡀⠀⠀⠀⠠⠐⣸⣯⠂⠅⡂⠀⠀⠀⣼⣿⡄⣴⠏
⠀⠋⣾⡁⠆⣿⣮⠋⠀⠀⠀⠀⣾⠃⠲⠘⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠻⠀⢾⣿⡇⢸⡇⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠉⠋⣼⢏⣠⣷
⠀⠀⠿⠿⠿⠦⠟⠀⠀⠀⠀⠀⠼⠤⠤⠤⠧⠀⠀⠀⠀⠀⠿⠿⠿⠿⠀⠀⠀⠀⠘⠻⠶⠤⠶⠋⠀⠀⠀⠀⠠⠶⠿⠿⠶⠆⠀⠀⠀⠀⠀⠼⠋⠘⠋⠘

⠀⠀⡖⠒⠒⠒⢶⠀⠀⠀⢰⠒⠒⡒⠒⢒⣒⡲⡆⠀⠀⠀⣿⣻⣟⣗⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⡇⣴⣷⣄⣼⠀⠀⠀⢸⠠⣿⣿⡦⢸⣓⡻⡇⠀⠀⠀⠿⢰⡮⡧⠀⠀⠀⠀⠘⣟⣛⠿⠿⠛⣂⡀⠀⠀⢸⡏⢴⣆⢹⡇⠀⠀⢠⡀⢛⣠⣥⣤⣤⣘⠁
⠀⠀⡇⠛⠉⠃⣸⠀⠀⠀⢸⣀⣛⣘⣃⣐⣛⣨⡇⠀⠀⠀⠲⣾⣷⣶⡆⠀⠀⠀⣀⠀⢹⠟⠙⠃⠿⠀⠀⠀⠈⠻⣦⣴⠾⠁⠀⠀⠀⠰⣏⢸⡱⠆⣹⣈⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡁⠰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣈⡷⢦⡴⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⢀⣤⠞⠉⠀⠀⠹⡄⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢛⣩⣍⠳⣤⠶⠋⠀⠀⠀⠀⠀⠀⠹⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢾⠀⢈⡇⣹⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣙⣋⣴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠶⠞⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠄⠴⠶⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡠⠤⡠⣤⡤⢤⣤⠤⡠⣄⠀⠀⠀⠀⠓⣀⣀⢄⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡖⢲⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⡗⠿⠍⠭⠇⠛⠿⠛⠽⢺⠀⠀⠀⢠⠊⣶⣼⣯⢲⡕⡍⠀⠀⠀⠀⡿⡫⣿⠝⠿⠹⠿⣿⣟⣿⠀⠀⠀⢸⠛⠋⣶⢶⡍⡛⣻⠀⠀⠀⠀⠰⢶⠖⡲⠂⠘⠯⠿⡽
⡇⠛⠛⠛⠗⢾⣛⣋⣿⢺⠀⠀⠀⢿⢟⡼⣩⢷⡟⣥⡇⡀⠀⠀⠀⣧⢃⢉⣴⡄⣭⣤⣽⣟⣿⠀⠀⠀⢸⣿⢷⡍⠍⠱⠟⢿⠀⠀⠀⠀⠈⠴⠫⠤⠄⠀⣀⡲⡀
⣥⣤⣤⣤⣤⣭⣭⣭⣭⣭⠀⠀⠀⣈⣮⣳⠶⢣⢟⣴⡁⠀⠀⠀⠀⣿⣚⣬⣭⣵⠋⢩⣯⠍⡅⠀⠀⠀⢸⠶⣻⡇⢄⣐⣻⣿⠀⠀⠀⠠⠨⡍⠭⠭⠥⠴⠷⠓⠏
⠀⠀⠀⠤⠬⠥⠄⠀⠀⠀⠀⠀⠀⠈⢡⠌⠉⠁⠁⠀⠘⢦⠀⠀⠀⠛⠛⠛⠛⠛⠁⠀⠛⠀⠃⠀⠀⠀⢸⣛⣻⡇⣭⣭⣿⠛⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠁
⠀⢀⣄⢀⣤⠠⢰⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⡄⠀⠀⣠⣠⣄⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⢀⣤⡴⣤⢠⡶⣤⡄⠀⠀⠀⢀⣠⣄⣤⣤⣤⣤⣤⣤⣤
⠀⠣⢼⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠋⢀⠔⠁⠀⠀⠿⢿⡏⣥⡘⢠⡜⣢⣿⣿⠀⠀⠀⢀⡽⠶⠿⠸⠶⠟⡁⠀⠀⠀⢸⢟⣫⣅⡛⡿⢻⢿⡿⣷
⠀⡀⠀⣉⠶⠦⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡤⠙⠀⢰⡃⡠⠆⠀⠀⣌⣰⡌⣴⠄⢸⡷⠶⣤⣤⠀⠀⠀⠀⡵⡜⢩⣬⠩⠾⠄⠀⠀⠀⢸⡳⢧⡼⠇⣿⣻⣿⡛⣿
⠀⣧⣌⢯⣍⠿⢿⢹⣿⠀⠀⠀⠀⢀⡀⠋⠀⠀⡀⠀⡈⠀⠀⠀⠀⠿⠿⠷⠶⢼⡴⣼⣥⠶⠶⠀⠀⠀⠀⡻⠣⡬⠩⠴⠹⠀⠀⠀⠀⠸⠿⠷⠶⣿⣿⣿⣿⣿⣫
⠀⡧⡜⢫⣶⣿⣶⢼⣿⠀⠀⠀⠀⣀⠤⠄⡀⠘⠇⠀⠗⠀⠀⠀⠀⠉⠉⠉⠉⠩⠉⠉⠉⠉⠁⠀⠀⠀⢀⣼⣋⣿⢸⣋⣷⡄⠀⠀⠀⠀⠉⠉⠉⠉⠩⠉⠉⠉⠉
⠀⠓⠒⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉


⠀⠀⠀⠀⠀⠀⠀⣼⢿⣇⠀⣿⡇⠀⣿⡇⠛⢻⣿⠛⢃⣾⠟⠻⣷⡄⣿⣿⡀⣿⣿⠁⢀⣾⢿⡆⠘⠻⣿⡟⠃⢸⣿⠀⣾⠟⠻⣷⡄⣿⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⡄⢿⣇⣀⣿⠇⠀⢸⣿⠀⠘⣿⣄⣠⣿⠇⣿⡏⣿⡇⣾⡆⣼⡿⣾⣿⡀⠀⣿⡇⠀⢸⣿⠘⣿⣄⣠⣿⠃⣿⡏⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠉⠉⠁⠀⠀⠈⠉⠀⠀⠈⠉⠉⠁⠀⠉⠁⠉⠁⠉⠁⠉⠀⠀⠉⠁⠀⠉⠀⠀⠈⠉⠀⠈⠉⠉⠁⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣿⡛⣿⣿⣿⣿⡇⠀⠀⡴⢢⠰⠖⠺⠗⠻⠭⠀⠀⠀⠀⠀⠀⡤⡤⢤⣤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣀⠸⠤⠇⣄⡀
⢀⡀⢸⡟⠟⢻⢻⡇⣀⡀⠀⠀⢸⣿⢸⣿⣿⡇⣿⡿⣿⣿⡇⠀⠀⠈⠉⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡱⣟⡋⣍⡛⢟⠀⠀⠀⠀⠀⠀⣤⡔⠉⠀⠀⠀⠀⣨
⠓⣖⢸⠃⣃⡾⠸⡏⣓⠂⠀⠀⢸⣿⠘⣛⣫⣼⣿⡇⣿⣿⡇⠀⠀⠀⢀⡤⠉⣥⡤⣤⣄⠀⠀⠀⠀⠀⠀⢟⡧⢧⡴⠇⣳⠄⠉⠀⠀⠀⠀⠑⠋⣤⠀⣤⢀⣤⠁
⠀⠛⠘⠛⠛⠛⠚⠃⠛⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⠇⣮⢻⡇⠀⠀⣤⣍⢥⠍⣤⣄⢬⢍⣤⣄⠀⠀⠐⠂⣞⡿⢷⣶⣟⣵⡇⠒⠀⠀⠀⢶⣲⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠴⠶⠶⠶⠶⠶⠿⠼⠇⠀⠀⠛⠋⠀⠈⠛⠋⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠈⠉⠉⠉⠉⠸⠟

⠀⢸⢟⣫⣝⡻⣟⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠀⠀⠀⠀⠀⢸⣉⣟⣿⣿⡿⢿⣿⠀⠀⠀⢀⣤⠤⣤⣤⣤⢤⡤⣤⡤
⠀⢸⠺⢧⡼⠅⣷⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣒⣀⡀⠀⠀⠀⠀⠀⠀⢰⠥⢸⣈⡡⠀⣀⣀⠀⠀⠀⠀⢼⢛⡑⢒⡚⠒⢈⣿⡄⠀⠀⠸⢃⠛⠘⣿⡷⠺⡗⠾⠶
⠀⢸⣞⠇⣾⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⢹⢫⢭⣻⡇⠀⠀⠀⠀⠀⠀⠈⠉⣠⣔⠏⠀⠙⠒⠀⠀⠀⠀⢼⣬⣵⣎⡍⢶⡍⣵⠃⠀⠀⢸⣙⣶⣃⣿⣟⢺⡗⣻⡛
⠀⢸⣯⡛⣻⡮⢸⢿⡇⠀⠀⠀⠀⠀⠀⢸⣜⡖⣹⡇⠀⠀⠀⠀⠀⠀⣠⠾⣘⣪⠷⣄⠀⠀⠀⠀⠀⠀⣿⣋⣿⣁⣷⣾⣾⣿⠀⠀⠀⢸⠟⢿⠉⣿⣟⢛⡟⢻⠛
⠀⢸⣿⣭⣉⣟⣘⣸⡃⠀⠀⠀⠀⠀⠀⠈⢉⣦⠙⠁⠀⠀⠀⠀⠀⠀⢷⣛⣼⣦⣚⡸⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣩⣿⣿⣿⠀⠀⠀⠈⠛⠛⠚⠛⠛⠛⠛⠛⠛
⣿⣿⡿⠻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠣⠖⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢴⠒⠒⠀⠀⠀⠀⠀⠒⠒⢰⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣶⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣲⢾⣿⣿⣿⣿⣿⡷⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣜⣿⣣⣦⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠈⠉⠉⣿⠍⠉⠁⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠻⢿⣵⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⣿⣯⣿⣿⣾⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣶⣿⡇⠀⠀⣠⢶⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣭⣿⣿⣻⣿⣭⣿⣿⣻⣿⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡘⣿⣿⡇⠀⣰⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠻⠿⠿⠿⠟⠻⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡖⠢⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣟⣿⣿⣿⣿⣿⢿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣶⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⠿⡧⣿⣿⣿⢿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣛⣟⣿⢿⣽⣿⣿⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⢿⣭⣿⣿⠶⠶⢾⣿⣿⣿⣷⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣿⣿⣮⣼⢿⣿⣿⢫⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣫⣾⣿⠇⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠶⠿⠿⠆⠀⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⣿⣿⣿⣯⣽⣿⣿⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠿⠿⠿⠿⠛⠁

⡤⣠⣤⣤⢤⣀⡤⣤⡤⡠⡄⠀⠀⠀⢙⡤⡤⣠⠤⣤⠆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡏⠉⠉⢉⣯⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⣇⣒⣞⣂⣧⣚⣲⣆⣨⡇⠀⠀⣰⣳⡋⠙⠖⣪⠳⡱⠏⠀⠀⢸⠀⠐⡤⣂⣀⡰⣀⠀⠠⠈⡇⠀⠀⡇⣴⣴⠃⡉⢱⣤⡄⡇⠀⠀⢰⣟⣟⣿⢧⣶⠘⠗⣤⡴
⡇⣅⢀⡀⣄⣇⢢⣶⣆⣩⠃⠀⠸⣿⣧⠜⠴⣊⢣⡞⡇⣷⡄⠀⢸⠈⢹⢶⠛⠘⠗⠛⠂⠰⠀⡆⠀⠀⡇⠀⡈⠓⠒⠊⠀⠀⠃⠀⠀⠘⣷⣻⣵⣛⣿⣀⠴⠯⢦
⣗⠒⠒⠒⠒⠚⠒⠒⠛⢒⡇⠀⠀⣸⢞⣦⢉⡴⢡⣟⢼⡉⠀⠀⢸⠀⣦⠟⠀⠋⢰⣖⠀⣺⣺⡇⠀⠀⡇⣈⡄⢠⡤⠤⠄⠀⡇⠀⠀⢸⣳⢲⣖⣒⣛⣋⣀⣤⣸
⠈⠉⠉⣤⣛⣚⣓⣬⠉⠉⠀⠀⠀⠉⢚⡽⠋⠈⠋⠉⠻⣍⣦⠀⠘⠒⠒⠒⠒⠒⠚⠛⠒⠛⠚⠃⠀⠀⡇⢤⠄⢸⣷⠒⠂⣤⠇⠀⠀⠀⠙⠒⠁⠀⠀⠀⠈⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠁
⠀⡀⠰⣤⠴⣖⣶⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠖⠄⠀⢀⡴⠶⠶⠶⢦⡶⢶⡶⠶⢦⡀⠀⠀⢰⠒⢀⡒⡖⣀⡒⢲⡄⠀⠀⢠⠶⠶⠶⢶⠶⠶⠶⠶⢶
⠀⠣⢋⡼⣁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⡰⢋⡴⠃⠀⢸⣀⡄⢀⡏⠻⣝⢻⡜⢀⠀⡇⠀⠀⢸⢶⣈⣁⣇⢉⣡⡞⡄⠀⠀⢸⣠⠖⡻⢤⢀⡄⠄⣠⢸
⠀⡀⠀⡱⢎⣉⡧⣀⠀⣀⠀⠀⠀⠀⠀⢀⢈⠷⠟⠀⣏⣠⠖⠀⢸⠳⠟⠙⡏⣹⣎⣀⣉⠛⠛⠃⠀⠀⢸⢿⠳⡖⠛⣖⢉⡻⡅⠀⠀⢸⢸⣙⣃⣹⠠⠄⠠⠄⢸
⠀⣗⡛⠿⠛⢧⣠⢸⠀⠰⠀⠀⠀⠀⡰⠗⠁⢀⣤⣀⡤⡀⠀⠀⢸⡄⣀⡀⣉⠵⠮⡹⠞⣉⢩⡇⠀⠀⢸⢦⣼⢛⣖⢋⣷⡿⡅⠀⠀⢸⢀⣈⡉⠦⠶⠬⠥⠬⠼
⠀⡯⡟⣶⠋⠁⠈⢹⠀⠐⠀⠀⠀⣤⠶⠲⠦⣴⣤⡿⣤⡇⠀⠀⠈⠑⠂⢐⡰⠶⠶⢖⡒⠒⠊⠁⠀⠀⢸⠛⠰⠆⡇⠲⠎⠻⠃⠀⠀⠈⠒⠒⢒⠲⠶⠶⣒⠒⠒
⠀⠓⠂⠒⠒⠒⠒⠂⠀⠋⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠒⠒⠒⠛⠒⠒⠚⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠀⣀⡀⠀⢀⣀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡀⠀⠀⢀⣀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣸⡿⣷⠀⢸⣿⠀⢸⡿⠘⠛⣿⡛⠃⣾⡟⠛⣿⡆⢸⣿⡇⣸⣿⡇⠀⣾⢿⣧⠘⠛⣿⡟⠋⢸⣿⠀⣾⠟⠛⣿⡄⣿⣿⣆⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⠷⢿⣧⠸⣿⣤⣼⡟⠀⠀⣿⠃⠀⢿⣧⣠⣿⠇⢸⡇⢿⡟⢸⡇⣸⡿⠾⣿⡆⠀⣿⡇⠀⢸⣿⠀⢿⣦⣠⣿⠃⣿⡏⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠈⠁⠈⠀⠈⠀⠉⠀⠀⠈⠁⠀⠉⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠈⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄
⠀⠀⢀⡀⣀⣀⣀⢀⠀⠀⠀⠀⢘⠐⢲⠖⠒⢲⠒⠒⠒⠒⢸⠀⠠⡪⡭⣫⠽⠧⠦⠟⠦⠀⠀⠀⠀⢶⣰⢒⠒⠒⠒⠒⢒⡲⢶⡆⠀⠀⠀⠀⣀⠔⣣⣛⠾⡓⣤
⡀⠀⠌⠀⠠⣦⢰⢸⡇⠠⡄⠀⢸⠀⠈⠀⠀⢸⠤⢤⡤⠤⢸⠀⠀⠉⠛⢍⡦⠤⠀⠀⠀⠀⠀⠀⠀⣤⣽⠿⢠⠒⠓⠲⠀⠇⡘⠃⠀⠀⠀⡴⣿⠋⠀⠀⠀⠨⠛
⠱⡒⠲⢴⠆⡇⣼⣸⡗⢲⠃⠀⢸⠀⢠⠔⠒⠋⠀⢸⡀⠀⢸⠀⠀⠀⡀⠊⡽⣏⣉⡏⠚⡇⠀⠀⠀⠾⢸⣽⢸⣥⣚⣼⢂⡇⠸⠆⠀⠀⣀⢀⣱⣒⣦⣒⣖⡛⣦
⠀⠓⠛⠒⠒⠒⠚⠚⠓⠃⠀⠀⢸⠀⢘⣀⣀⣀⣀⣸⠋⢃⠸⠀⢠⠞⠙⣎⣱⠒⠚⣏⣲⠛⠲⡄⠀⣴⢻⡙⣀⢀⡍⣴⣋⣘⢳⡄⠀⠸⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠬⠭⠭⠭⠭⠬⠥⠬⠴⠀⠈⠓⠒⠁⠈⠓⠚⠁⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠋⠉⠉⠉⠉⠧⠴
⠀⢀⡄⠀⠀⠠⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⡀⠤⢀⠠⠤⠠⢀⡀
⠀⢸⢰⠶⣚⠶⡄⡒⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠲⡗⠃⠀⠀⠀⠀⠀⡇⠒⢒⣀⡀⢠⡄⠀⣿⠀⠀⢐⢛⡻⡛⠛⢛⣟⢻⡛⣛
⠀⢸⢸⣭⣛⢼⠆⠀⢠⠀⠀⠀⠀⠀⠀⡴⠚⠛⠛⢢⠀⠀⠀⠀⠀⠀⠆⢯⣟⡚⠫⡷⣤⠤⠀⠀⠀⠀⡇⡔⢿⣿⠳⣖⡟⣦⣿⠀⠀⢸⢾⣶⣿⠀⠀⣥⢨⡄⣬
⠀⢸⠐⢦⠏⠠⠤⡀⢸⠀⠀⠀⠀⠀⠀⡇⠐⣩⡳⢸⠀⠀⠀⠀⠀⠀⠀⣡⢞⣓⢽⡋⠉⠉⠀⠀⠀⠀⡇⠑⠃⢘⢚⡇⢱⠁⣿⠀⠀⢸⠳⠭⠜⠀⠠⡶⠰⠆⠶
⠀⢸⠀⠲⠶⠨⠯⢤⢸⠀⠀⠀⠀⠀⠀⡄⠸⣇⡟⢸⠀⠀⠀⠀⠀⢀⢆⠥⡕⢞⡤⡕⡄⠀⠀⠀⠀⠀⠇⠘⠀⠚⠀⠁⠀⠀⣿⠀⠀⢸⠴⠴⣿⠀⠐⡖⠰⠆⢶
⠀⢸⣀⣈⣛⣃⣁⣊⣸⡀⠀⠀⠀⠀⠀⠉⠚⣉⡟⠈⠀⠀⠀⠀⠀⠈⢞⣒⣋⣈⣓⣢⠃⠀⠀⠀⠀⠀⢆⣀⣀⣈⣛⣀⣀⣀⡟⠀⠀⠈⠒⠒⠐⠒⠒⠒⠒⠒⠒
⣿⣿⡿⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⢸⡟⠉⠣⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⣙⣿⣃⡀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠉⢉⣉⣷⡟
⠀⠀⠀⢀⣁⠀⠀⢈⣢⡑⢄⢀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢸⣾⣿⣾⡇⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢠⣼⣤⢠⣴⣾⣿⣿⣯⡄
⣠⣤⠀⠈⡉⠀⢀⠘⠛⡈⠢⣿⣿⠀⣠⣤⠀⣠⣤⠈⠛⠛⠁⢀⠘⠛⡛⠛⠁⡀⠘⢋⠛⢀⣤⡄⠀⣤⡄⠘⢛⠃⠀⡀⠈⠛⡋⢺⣿⣿⠛⡉⠛⢡⣤
⠙⠟⠠⠈⠁⠄⠈⠀⠄⣡⣾⣿⠟⠤⠙⠟⠀⠛⠟⠀⠈⠁⠠⠈⠠⣤⢥⡤⠠⠁⠄⠨⠀⠌⠻⠃⠈⠻⠃⠠⠈⠠⠀⠁⠀⠈⠁⣿⣿⣿⣧⣭⠀⠸⠟
⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠳⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿
⡛⠛⠛⠛⠛⢻⣿⣿⣿⣛⠛⠛⠛⢻⣿⣿⣿⣟⠛⠛⠃⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⡛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛
⡇⠀⠀⢠⣤⣔⠶⠾⠻⠻⠂⢀⣤⣔⠶⠾⠻⠿⠃⠀⠀⠀⠰⠏⠈⠉⠏⠉⠉⠏⠉⠈⠷⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣤⠖⠶⠛⠛⠃
⡇⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠿⠥⣀⡀
⣧⡤⢤⡤⣤⠈⠙⢦⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯
⣿⡷⣟⣷⢾⠀⠀⠠⣿⠄⠀⠀⠀⠀⠀⠠⢿⠄⠀⠀⠀⠀⠀⠀⢊⣔⣀⠐⠒⠐⠒⠒⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⡇
⣿⣷⣾⣶⣿⣀⠀⢰⣶⡆⣰⣶⠀⣶⣶⢀⣶⡆⠀⠀⠀⠀⠀⠀⢒⣿⣽⠇⠀⠰⠽⠀⠀⠀⠀⠀⡅⣀⡸⠿⠇⠀⠸⣿⣇⣀⣀⣀⣀⡀⠀⠸⠿⢇⣀
⣿⣿⣿⣿⣿⡿⠿⠇⠴⠀⠀⠄⠀⠰⠄⠀⠴⠀⢰⣿⡇⠀⠀⠈⠢⢉⢉⠈⠋⠙⠉⠋⠀⠀⠀⠀⡟⣿⠗⠀⠰⠂⠀⠀⣒⡒⠒⠂⠸⠀⠀⠆⠀⠺⣿
⣿⣿⣿⣿⣿⣿⣀⣀⢰⣿⣿⣾⣿⣿⣾⣿⡆⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⢿⡿⣿⣿⣀⣀⣀⣀⣀⣈⣿⣿⣿⢿⣿⠁
⢿⣿⣿⣿⣿⡇⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠉⡏⢽⢹⡋⡏⢉⣿⠿⡍⢹⢹⡏⡿⢹⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⢠⣤⣤⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠐⢻⡟⠂⡖⠚⢫⠛⠠⡆⠚⣿⠓⢰⣦
⣶⣶⣶⣶⣶⣶⠶⠶⠶⢾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣠⣤⣤⣤⣤⣴⢶
⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣍⠁⠀⠈⠉⠉⠉⠹⣿⣿
⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡋⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⣷⣶⡟⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣶⣷⣿⡆⠀⠀⢰⣿⠚⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠞⠀⠀⢠⣤⡾⠟⠁
⠀⢿⣿⣿⣿⡄⢀⠀⠀⠀⢀⣀⠀⠀⠸⠿⠃⠀⠸⠿⠇⢀⣀⠛⢿⣿⣿⠁⠀⠀⠘⡿⠆⠸⠃⢀⣀⠀⠻⠟⠠⠟⠇⠀⠀⠀⢀⣀⠙⣾⣿⣿⡆
⠀⠀⠀⠙⣿⣿⣿⣿⡆⠀⠿⣿⡀⣘⣂⣀⣘⣀⣀⣚⣀⢸⡿⠃⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠻⡿⢀⣘⣃⣀⣐⣀⣀⣒⣀⣹⡿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡧⣿⠀⠀⠀⠀⣿⢸⡇⠀⠀⡆⢸⣟⣿⣻⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⡇
⣀⣀⣠⣴⣿⣿⣿⣿⣷⣤⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣀⣸⣗⣿⣀⣀⣀⣀⣿⣻⣇⣀⣀⣃⣸⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣰⣿⣿⣿⣿⣆⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⡤⠟⠀⠘⠧⣀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣠⣼⣿⣿⣤⣀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⣀⠤⠤⠤⢄⣠⠁⠀⡽⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⣛⣛⣛⡻⠟⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠎⠁⠀⠀⠀⠐⠛⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣱⣿⣿⣿⣿⣯⣤⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⣾⠀⠘⠃⠀⠀⠛⠀⢸⡆⠀⠉⡇⠀⠀⠀⠀⣿⣿⣿⢰⣿⣧⣼⣿⣿⣤⣿⣷⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⡀⠘⢀⣀⠒⠶⠖⠃⠀⡼⠀⣰⠛⠃⠀⠀⠀⠀⠉⢹⣿⣦⣿⣿⣭⣙⣩⣽⣿⢇⣾⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠻⠻⠤⣤⡤⠴⠊⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⣔⡛⠿⠟⣛⣥⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⠒⠤⣄⠀⢀⡤⠖⠲⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠿⢿⣿⣿⠿⠟⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡆⢰⢠⠂⢢⠰⡀⡆⣰⡆⢲⠀⣦⠂⢢⠰⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠈⠀⠁⠁⠀⠁⠀⠁⠀⠈⠀⠁⠁⠁⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠛⠛⠛⢻⣿⣿⣴⣿⡗⣤⣤⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠘⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⣶⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⢹⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡔⣶⣿⣷⡆⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣛⡁
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠛⠀⠉⠉⠉⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⢰⣦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠐⠒⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠰⠶⠶⠶⠶⠶⠶⠆⠀⠘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠶⠶⠶⠶⠶⠶⠆⠀⠀⡇⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⢰⣤⡄⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠤⠤⠀⠀⡃⠀⠀⠀⢀⡠⢴⣿⣶⣶⣿⣿⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⡠⠄⠒⡦⠤⠤⠴⠶⠷⠶⠶⠶⠆⠀⢀⠇⠀⠀⠀⣇⠠⠄⠼⡞⠉⠉⠙⢻⣽⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢻⠋⢉⣉⣉⣙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⣩⣷⡶⠶⠿⣯⡉⠑⡆⠀⣿⣿⣤
⠀⠀⠀⠀⠀⢰⣶⣴⣶⡿⣧⣼⣀⣈⣉⣉⣉⣉⣑⣢⣤⣀⣀⣠⣤⣄⡀⠀⢣⣀⣀⣛⣹⠒⠀⠉⢙⣁⣀⣧⣼⣿⠏⠉
⠀⠀⠀⢀⣀⣾⣷⠟⠉⠉⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠇⠀⠀⠈⡀⠀⠀⡌⡀⠀⡿⠻⣿
⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⢃⠃⠀⡇
⠀⠀⠀⠀⢈⣿⣻⣄⣀⣀⣠⣾⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⢳⡄⠘⢸⠀⢸⢸⠀⡇
⠀⠀⠀⠀⠙⠋⠛⢿⣯⡿⠿⢿⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠙⣦⡈⡇⠈⡎⡄⡃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢸⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢈⣧⢧⠀⢳⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⣠⠟⠘⡸⠀⠸⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠅⠆⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠉⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢢⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻


⣏⠉⣹⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠛⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⠏⠀⠙⠳⢶⣤⣤⣀⣀⣀⣤⣴⠶⣆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⡏⢠⡶⠶⠶⣦⡀⠀⢩⡽⠷⠶⢦⡀⢹⣆⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⣿⠀⠀⠀⢸⡟⠛⢻⡇⠀⠀⢸⡟⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠘⠳⠶⠲⠛⠁⠀⠈⠳⠶⠶⠟⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⣤⡀⠀⠀⠀⣀⣤⠶⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⠙⠛⠛⠛⠉⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠟⠙⢷⡄⠀⠀⠀⠀⠀⢠⡾⠋⠻⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠛⠛⠋⠉⠁⠹⣆⠀⠀⠙⢦⡀⠀⢀⡴⠋⠀⠀⣰⠏⠈⠉⠉⠛⠛⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢹⣶⡟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠳⣄
⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣴⣿⣭⣿⣦⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡆
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠛⠛⠷⢦⡀
⠙⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠹
⣶⣶⣶⣶⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣦⣦⣤⣴⣶⣶⣶
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⠀⠁⠀⠁⠀⠀⠀⠀⢠⡞⣟⢷⡀⠀⠀⠀⠀⣠⠴⣶⡶⢤⡀⠀⠀⠀⢠⣶⣾⠒⢲⠀⠀⠀⠀⢀⣀⣀⠴⠦⡀
⠀⠀⠰⠴⠶⠶⠆⠀⠀⠀⠀⠈⢷⣶⣿⡇⠀⠀⠀⠀⠀⠫⠿⠯⠃⠀⠀⠀⠀⠘⡏⠙⣶⡾⠀⠀⠀⠀⠘⠛⠈⠢⢴⡃
⠀⠀⠛⠛⠀⠚⠛⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠤⢤⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⢰⡶⠶⣶⣶⡆
⠀⠀⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⢸⣿⣽⠀⠀⠀⠀⠀⣽⣟⣿⣿⣿⡅⠀⠀⠀⠀⠸⠀⠝⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⣴⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣾⠛⠻⣷
⠀⠀⠁⢰⠚⡆⠀⠀⠀⠀⠀⣰⠞⢾⣻⣢⠀⠀⠀⠀⢾⣿⣿⠆⡠⠁⠀⠀⠀⠀⢸⣸⣿⡇⠀⠀⠀⠀⠀⣷⣈⣤⣿
⠀⠀⠂⠀⠛⠐⠒⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠿⠶⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣀⣀⢀⡀⡀⣀⢀⠀⠀⠠⠀⣀⢄⡀⠀⢀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇⠀⠀⠀⠀⢠⣤⡤⠞⠛⠃
⠀⠀⠁⠉⠉⠉⠈⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣷⡤⣤⡇⠀⠀⠀⠀⠈⠋⠓⢦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣟⣛⣿⣛⣛⣿⣭⢯⣽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⠿⠛⠁⠠⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⠿⢿⣿⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⠇⠀⠀⣿⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⣿⣤⣄⠀⢿⡿⠀⠀⠀⢸⡿



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠛⠛⠻⠿⠿⢶⣶⣶⣦⣤⣄⣀⠀⠀⢈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⢀⣠⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣆⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣴⠿⠛⠉⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠶⣶⣶⣦⣤⣄⡀⠀⠀⠙⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠠⡀⠀⠀⠀⠉⢻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢀⣤⣶⣶⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣤⣀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣠⣤⣶⡶⠶⠶⠶⠶⣦⣤⣄⡀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠋⠉⠉⠉⠉⠙⠛⠷⣶⣄⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠋⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⣟⣷⣶⣶⣤⣄⠀⡀⠀⠀⠀⠀⣾⣻⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⡄⢀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣀⢀⡀
⠀⢸⣿⣏⠛⠛⠻⠓⢾⣧⡀⠀⠀⠈⣿⣿⡛⠛⠛⠛⢾⣷⠀⠀⠀⠀⢿⣿⣿⣿⣟⢿⡗⠀⠀⠀⠀⡏⢈⡉⠉⡉⠀⡇
⠀⢀⣿⣿⣦⡀⠀⠀⠘⢆⠇⠀⠀⠀⣿⣿⣧⡀⠀⠀⠘⡇⠀⠀⠀⣾⣿⢻⣧⢠⣿⣏⣿⣷⠀⠀⠀⡇⠨⠀⠤⠄⣠⢧⡀
⢰⢾⡿⣿⢿⢷⡆⠀⠀⠀⠀⠀⠀⡾⣿⢿⢿⡿⣆⠀⣠⣦⠀⠀⠀⠀⣽⣮⣳⣤⣾⣽⣯⠀⠀⠀⠀⡇⠘⠁⠁⡞⣀⡴⠊
⠼⠷⠷⠿⠾⠷⠷⠀⠀⠀⠀⠀⠰⠷⠿⠾⠷⠷⠿⠄⠽⠿⠄⠀⠀⠀⠉⠉⠹⠿⠏⠉⠁⠀⠀⠀⠀⠓⠒⠒⠒⠛⠮⠤⠞
⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⣴⣶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦
⢀⣴⡟⣏⣯⣻⣽⣿⣷⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⣭⣅⠀⡀⠀⠀⠀⠀⠀⠀⢠⣭⣥⣀
⢸⡇⠀⠿⣿⠟⠀⠀⠀⣿⠀⠀⠀⠈⢩⣿⣯⣯⣿⣽⣿⡍⠀⠀⠀⠀⢰⢿⣿⡟⠛⣛⡀⠀⠀⠀⠀⢠⠿⣿⣿⠉⢸⣿⡿
⢸⡇⢀⣀⢋⣀⣀⣀⠀⣿⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣞⣿⣿⣻⣻⣟⣟⣿⡷⠀⠀⠰⣾⣟⣿⣿⣻⣿⣟⣟
⣼⣷⣾⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀⠀⠀⠛⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠴⡶⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠴⠦

⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⡄⣠⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⢠⠞⣡⣴⣶⣤⡙⢷⡀⠀⠀⠀⢸⠃⠖⠒⣿⣗⣨⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠀⠀⠀⠰⣿⣷⡿⠻⣷⣿⡇
⠀⡟⠀⠁⠀⣈⣻⡵⠈⡇⠀⠀⠀⢤⣾⣿⣿⣿⠝⢋⠉⠸⡀⠀⠀⠀⠀⣤⣴⣾⣿⣿⡇⠀⠀⠀⠀⣶⣿⡟⠀⡄⢸⣿⣷
⠀⢻⡀⠀⢾⣽⠏⠀⣰⠇⠀⠀⠐⢿⣿⣳⣸⣿⠗⠈⣀⡾⠀⠀⠀⠀⢴⣿⡉⠈⣿⣿⠃⠀⠀⠀⠀⢉⣿⣿⡶⣠⣾⣿⣏
⠀⠀⠙⠶⢤⣤⠤⠞⠁⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠙⠁⠀⠀⠀⠀⠀⠀⠛⢿⡟⢿⠿⠀⠀⠀⠀⠀⠀⠙⠉⢻⣿⠋⠛⠁

⠀⢠⠒⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣀
⠀⢸⢸⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏
⠀⢸⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣶⣴⣦⣶⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣻⣻⣟⣿⠀⠀⠀⠀⢀⣴⣮⣍⣈⢁⣈⣽⣶
⠀⢾⢻⣿⣿⣿⣿⡿⣷⣿⡆⠀⢸⣿⠛⣿⡟⢻⣿⣿⠿⣶⡀⠀⠀⠀⢀⡯⣩⢩⡍⣍⡀⠀⠀⠀⠀⢸⣿⣿⣿⡌⠛⠋⢹
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣩⣿⣯⣹⣿⣿⣴⣿⠃⠀⠀⢠⣭⢡⣭⢨⣭⣨⣥⡀⠀⠀⠀⠘⠿⣿⣿⡇⣀⡤⠞

⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡤⠔⠚⠉⠁⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠔⠋⠁⠀⠀⢀⠀⣠⠚⡁⢀⡠⠤⠤⠤⠴⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠳⣦⠀⠲⠤⠀⠘⠈⠉⠁⠀⠀⠀⠀⠀⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⡸⠠⠀⠈⠳⣄⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡎⠁
⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠈⢷⣀⠠⠀⠀⠒⢀⠀⠀⠈⠉⠋⠉⠉⠀⡈⠙⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠇⠒⠀⠀⠀⠈⠀⠉⠲⡀⣀⠀⢈⡀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⡠⡄⠀⠀⠐⠂⠙⢢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠄⠊⠁⡟⠀⠀⢀⠠⠀⢠⠾⠣⡀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠄⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣈⠀⠀⠀⠀⠀⠀⠂⣠⡄⠀⠀⠀⠀⠀⠀⠀⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄⡔⢸⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠁⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⡀⠀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢀⡤⠐⠊⠀⠀⠀⠈⠅⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣠⠋⠀⡇⠀⢀⣀⠈⠀⠀⠀⢀⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠀⠳⢄⣠⠴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠾⠤⠤⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⢠⠎⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⠀⡔⠉⠉⠑⠦⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⢀⠀⠠⡒⠟⠁⠠⠄⠁⠀⠀⠓⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⡇⠀⠀⠉⢠⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠒⠚⠂⢠⠀⠀⠙⠹⠤⠀⠀⢁⠀⠀⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠙⠶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡈⠀⠀⠀⠀⠀⠰⠈⢇⠀⡀⠈⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⠂⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⡀⠀⠀⡀⢻⠁⠀⠀⠀⠀⢠⠋⢀⡀⡄
⠀⠀⠀⠀⡖⠿⢢⡀⣇⠀⠀⠀⠀⠀⠀⠈⡄⠖⠀⠀⠀⠀⠰⠆⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠈⣧⠀⠀⡀⢘⡋⠁⠀⠀⡼
⠀⠀⠀⠀⢃⠀⠀⠑⠏⠀⠀⠀⠀⠐⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠄⠀⠀⠀⢹⡄⠀⠀⠈⠀⢀⡠⠊
⠀⠀⠀⠀⠘⡆⠀⠀⠒⠠⠀⡦⣤⡔⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠁⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠤⣀⡀⠀⢿⠀⣀⡤⠒⠉
⠀⠞⠈⠓⢤⡟⠀⠀⠀⠀⠀⡳⠊⠉⠀⠀⠀⠀⠀⠀⠀⡀⠐⢏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⣏⠁
⠸⠂⠀⠐⠀⠀⠀⠀⠀⣡⠞⠑⠀⠀⠆⠰⠂⠀⠀⠀⠀⠀⢀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⡇⠘⠀⠀⠀⠀⢠⡞⠣⠄⠀⢀⡈⠀⠀⠀⣀⣄⣀⣀⣀⣀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⢰⠀⡀⠀⠁⣤⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢧⠀⢀⡞⠁⣀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡄
⠀⠀⠈⣴⠋⠀⠈⠀⠀⠢⠁⠲⡉⠛⠀⠒⠶⠦⠂⠒⠋
⠀⢀⡞⠁⠉⠓⠦⢄⣀⠃⠀⠀⠈⢲
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢦⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠛⠛⠛⠀⣀⠀⡂⠀⠠⠤⡽⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢺⡉⠛⠁⠀⠀⠀⠀⠀⡰⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡤⠶⠢⢤⡀⠀⠀⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠖⢤⡀⠀⠀⠀⢨⠁⠉⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠉⠈⡇⠀⠀⠀⢰⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠦⠤⠤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⣠⣧⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣄⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⣀⡀⣼⠁⠈⠁⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⠒⠒⠚⣿⡯⠗⠛⢻⡄⠀⠀⢀⡿⠦⠮⣬⣄⣒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢤⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⡀⠍⢛⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠫⠷⣤⣄⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⣊⣩⠴⠞⠋⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠙⠓⠶⠤⣧⣐⡒⠀⠤⢀⡀⠶⢈⣩⡴⠖⠛⠉⣠⡀⢰⠂⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡋⡓⠰⠦⣤⣄⣈⠉⠛⠓⢶⠖⠛⠉⠀⢀⠔⠄⢈⡄⡆⢘⠁⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠁⠘⠲⠦⣤⣉⡙⠓⡆⢘⡇⠀⠋⡁⠀⠆⠇⠀⠄⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣠⣤⣤⣤⠖⢤⡀⠀⠈⠉⠁⠘⡁⠀⡋⠁⠀⠃⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⠿⠟⠛⠫⠁⠀⠀⠂⠉⠓⠦⣀⠀⠸⡇⠀⠀⠀⠀⢀⠤⠔⠂⠁⠠⠒⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠍⠻⠋⠉⠠⢀⠐⠄⠀⠀⠄⠐⠀⠀⠠⡀⠂⢌⢑⣶⡇⡠⠀⠂⠀⣀⡀⠰⡊⡃⠀⠃⠇⣿
⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⢁⣀⡀⠈⠲⢄⡀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠂⣀⣠⠤⠖⠊⠁⠀⡃⠀⡤⢄⠐⡇⡆⠀⡁⠇⠀⠁⠀⡟
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡧⠭⢉⣳⡄⠉⠲⣄⡀⠀⢀⣀⣠⠤⠚⠋⠁⠀⠀⠀⢀⣀⠀⡇⠀⠇⠾⠀⠄⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠑⠒⠾⠁⠀⠀⠀⠙⡖⠋⠁⠀⠀⠀⠀⠀⡤⠄⠀⠳⠚⠀⡇⠀⠃⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠒⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⣖⡆⠀⠙⠁⠀⠀⠀⠠⡇⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠐⠠⠄⣀⠀⠉⠐⠒⢤⡀⠀⡇⠘⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠴⠚⠉
⠀⠀⠀⠀⠀⠀⢭⣀⡉⠐⠠⢀⣀⠈⠀⠂⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⡀⠁⠂⠀⠄⢸⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠸⠀⠀⡇⠀⠀⣠⡴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⡧⠖⠋⠁

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣬⣧⣴⣤⣴⣮⣤⣾⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⡠⠁⠀⠰⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠰⠌⠉⢴⠀⠀⠀⠀⣴⠁⠀⠀⡤⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⣰⠀⠀⢀⠀⠀⠋⠄⠇
⠀⠀⠀⠁⠀⠀⠀⠶⠋⠀⠘⠋⠀⠀⠀⢀⠀⠁⠉⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⣅⠀⠡⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⢠⡂⠀⠉⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⣀⠠⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⡄⠀⢀⣀⣥⠶⠛⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢰⠂⠎⠁⠀⠈⡄⠀⠀⠀⠀⡶⠟⠛⣄⠀⠀⠈⠻⠛⠋⠉⠁⠀⠀⠐⠾⣦⠀⢄⠀⠀⠁⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣰
⠀⠀⠀⠀⡀⠀⠰⡆⠀⠐⠁⠀⠀⠀⠀⢠⡀⠀⠛⠁⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢡⢣⠞⡆
⠀⠀⠀⠀⣧⡄⠀⢀⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠖⠀⠀⠀⠁⠀⠸⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢲⣭⡝⣈⣲⡁⠀⢠⠁
⠀⠀⠀⣠⠃⠁⠄⠠⠤⠀⠀⠀⠘⠃⡀⠰⠃⠀⠀⠐⠀⢰⡆⠁⡍⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠺⡥⠀⢨⡏⠁⠀⠈⠳⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢆⠋⡀⠻⠂⠀⠀⠈⠆⠈⠇⠀⠀⠀⠀⠀⠀⠄⠀⠾⠆⠀⠀⠂⠠⠀⣠⡀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠠⢿⡇⠀⢀⣶⣶⣄⠀⠈⠊⠛⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡔⠇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠀⠶⠀⠀⠀⢀⣠⠤⠂⠐
⠀⠀⠀⡀⣸⠁⠀⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⢰⡆⠀⣶⠀⣶⠠⢦⣤⡤⣤⡄⣤⢠⡆⢀⣴⢠⣆⣴⠀⠉⠀⢴⠀⢀⡀⠀⠈⠁⠁⠀⠀⠀⠈⠐⠀⢀
⠀⠀⠀⠉⢉⠇⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⠀⣿⠀⢸⡇⠀⣿⡀⡟⢸⣷⣾⡇⢸⣿⣿⠀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⣀
⠀⠀⠀⣦⡏⠀⠀⢠⠃⠀⠀⠃⠂⠀⡀⠀⢸⡟⢿⠀⢿⣀⣿⠀⢸⡇⠀⢻⣧⣷⢸⣿⣿⡇⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠉
⠀⠀⢰⣾⠁⠀⠀⡞⠀⠀⠀⠀⢠⢢⡀⠀⠈⠀⠈⠁⠈⠉⡁⢀⠀⠁⡀⠈⠉⠁⠀⠁⠉⡉⣀⠀⠈⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢸⠇⠀⠀⠘⠀⠀⠀⠘⠀⠚⠫⠀⠀⠁⠀⠀⠃⠈⠀⠀⠈⠈⠃⠀⠀⠐⠈⠃⠁⠀⠁⠉⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⠀⠀⠀⠋
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣤⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⢀⡀⠀⠀⠀⢀⡴⣚⠟⠱⣦⠀⠀⣇⣀⣴⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⠃⠀⠀⠀⠀⢀⠀⣠⠄⠀⠨
⠀⠀⣰⣿⣿⣷⣦⠀⠘⠙⣿⡇⠫⢘⠇⠀⠙⣿⣿⣿⠆⠐⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡼⠶⢤⣀⠀⠲⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⢿⠿⠛⠋⠀⠀⠀⠀⠃⠛⠓⠛⠀⠀⠀⠀⠉⠉⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠈⠛⠀⠐⢄⡀⠀⠀⠀⠘⠁⠢⠀⠀⠂⠁
⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡄⠐⢈⡀⠀⠀⠀⠀⠀⠠⠀⠀⠰⢆⠀⠠⠀⣀⠀⢢⡀⠀⠀⠀⢀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⢀⣦⣴⣿⡿⠿⠛⠁⠀⡰⠄⢢⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢠⠋⠉⠙⠣⠖⠀⣄
⠀⠀⠀⠀⣾⣿⣿⣯⣧⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠃⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⠦⠉⠉⠃⢀⠀⡐⠀⠀⢀⠀⠸⠸⠀⠀⠃⠀⠀⠀⠀⠀⠘⠆⠐⠂⢀⠆⠀⠀⠀⠀⠀⠠⠙⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⡄⠃⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠉⠁⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠄⠀⠘⠀⠀⠀⠀⠀⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡯⡄⢠⠀⠙⢿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠸⡿⠷⠆⠀⠻⠿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⣟⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢂⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠾⠷⠆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⡅
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⠀⠀⠀⠀⠠⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠴⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⣿⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣯⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣧⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠻⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣷⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠁⠛⠀⠄⠙⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠣⡀⠀⢻⡀⢠⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⣀⣀⣀⡀⠀⡄⠀⡄⠀⠀⠘⠂⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢱⣦⡀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⣾⣽⣿⣿⣿⡎⠀⢐⡃⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠘⠳⣦⠀⠀⠀⠀⡜
⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⢸⡇⠀⠀⣀⡆⠀⠀⠀⠀⠀⢀⠀⢠⡆⠂⠀⠀⠓⢀⡈⠂⠀⠦⠀⢰⠃
⠀⠀⠀⠈⢿⣿⣿⣿⠄⠀⠀⠧⡞⠉⠉⠁⠀⠀⠀⠀⠀⠘⠊⠛⣷⣆⠈⠂⠀⠀⠉⠠⠄⠀⢠⠇
⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠐⡀⠀⠀⠀⠁⣀⡀⠠⣤⠄⠀⠟⢻⣾⠃⠀⢠⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢹⣿⡿⢀⣀⡤⠄⣐⣓⣤⣦⣭⣭⣥⣴⠄⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⣠⠿⣛⣩⠶⠚⠋⠉⠤⠀⣸⣿⡉⠁⣀⣀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠓⣿⠉⣡⣶⣿⣿⣿⣿⢗⣿⣿⣿⣿⣷⣶⣧⣄⠀⠀⠻
⠀⠀⠀⠀⠀⢀⣿⠀⣹⡿⠿⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣿⣿⣷⡶⣾⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⡟⠋⠉⠉⣱⡋⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡴⠋⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠁⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠐⠂⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠉⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠠⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠁⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⣈⣳⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣴⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠁⠀⠀⠀⣷⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣿⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⣀⢠⡄⠀⠀⠀⠀⠀⢀⠔⠁
⠀⢀⣀⡀⠀⠄⠐⠂⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢦⡀⣿⠀⢠⡞⢁⣀⡤⠶⠒⠉⠉⠀⠀⠈⠀⢀⠀⠀⠀⠄
⠀⠀⠉⠉⠁⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⢓⡶⠦⣿⣿⣶⠿⠚⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣿⡃⠤⢀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠉⠐⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠒⢀⠀⠀⠀⠀⣀⠄⠂⠁⠀⠀⢹⡇⠀⠀⠈⠑⠂⠤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠉⠢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠅⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄

⠀⠀⠀⢠⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣄⣀⣀⣀⣤⣤⣤⡀
⠀⠀⠐⣿⠁⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢉⣿⠼⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠛⢷⡤⣾⢹⡶⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⣿⠿⣿⣄⣀⣀
⠀⠀⠀⢀⡶⠲⣤⢻⣄⢀⣼⠃⠀⠀⠀⠀⠀⠀⣴⣶⣦⣧⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠳⣦⠀⠀⠀⠀⠀⠀⠀⡏⠀⣯⢸⣿⣿⣿⠁⠉⡁
⠀⠀⠀⠈⢧⡤⠞⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣒⣿⣏⠉⠉⣻⡏⠉⡇⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⠙⠻⡗⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣿⠶⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⢸⣿⣿⣯⠀⢠⠏⢳⠀⡇⠀⠀⠀⠀⠀⠰⣿⣿⠀⡿⡀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⡭⢍⠉⠉⠉⠉⡇
⠀⠀⢸⣿⣿⡇⢀⠎⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⢾⠒⡄⠀⠀⡇
⠀⠀⢸⣿⣿⡿⠚⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⡿⠁⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠭⠤⠤⠴⠇
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣠⡄⣨⣧⣤⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⣠⡞⣭⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠶⣆⠀⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⠿⠿⣤⣤⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣭⡦⠮⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⢸⣤⣤⣤⣀⣟⢰⠇⠀⠀⠀⠀⠀⢀⣸⡟⠔⠁⠈⠦⢻⣅⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣏⣻⣧⡟⠀⠀⠀⠀⠀⠀⠘⢿⡌⢭⢈⠀⣅⢸⡟⠃
⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢇⢸⣿⣬⣯⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⠦⣥⣬⠶⣿⠇
⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋


⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣶⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢤⡀
⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⡟⠁⢾⠇⠈⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⢲⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡾⠛
⠀⠀⠀⠐⢘⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠻⣇⢴⣿⣿⡆⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣉⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛
⠀⠀⠀⠉⠈⠛⠟⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⠛⣻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠚⠀⠀⣠⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡰⠞⠛⠋⠛⠛⢶⣄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣰⠎⠳⣆⠀⠀⠀⣠⠞⠙⣧⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡟⠀⠀⠈⠳⣤⠞⠁⠀⠀⢸⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢻⣤⣤⣤⣤⣤⣾⠁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣗⠲⠶⠤⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡁⠸⣏⣉⣛⣛⣺⡇⠀⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡜⠁⠀⠻⣍⣉⣉⡽⠁⠀⢯⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⢠⡄⠈⠉⠉⠀⠀⠀⠈⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢤⣜⡧⠤⣤⣤⣀⡀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠉⢧⡀⠈⠓⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠻⢤⡀⠀⠀⠀⢠⠇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠙⠚⢉⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⡬⠬⣄⠀⠀⠀⠀⢴⣿⣿⣷
⠀⢸⡇⣀⣀⣀⣀⡀⠀⠀⢀⣤⣿⣧⣤⣼⣷⣀⣀⠀⠀⠀⠐⠃⠗⠐⠂⠓⠀⠀⠀⠀⠀⢺⣷⣶⣶⣶⡆
⠀⣿⣭⣯⣽⣭⣯⣽⠀⠀⢨⡭⣭⠭⡭⢭⣭⣭⣭⠀⠀⠀⢠⣔⣏⣉⣗⣤⠀⠀⠀⠀⠀⢸⣟⢣⠚⣿⡅
⠀⣿⠛⠛⣿⣶⣷⣾⠀⠀⢸⣧⣿⣤⣧⣼⣿⣿⣿⠀⠀⠀⢀⣠⣃⣀⣣⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⢰⡛⠛⠛⢳⠀⠀⠀⠀⠛⠀⠛⠃⠘⠛⠛⣳⡀⠀⠀⠀⣀⣶⠶⠖⠒⠆
⠀⠀⣀⠀⢀⡀⠀⣿⡇⠀⠀⣠⣏⢳⡄⣴⢋⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣷⠀⢀⣀⡀
⢠⣾⣿⣷⣿⣿⣦⣿⣧⠀⠀⣺⣒⢸⡇⣿⢐⣺⡇⠀⠀⣤⣶⣾⢠⣴⣾⡆⣿⡇⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿
⢸⣇⣇⣸⣸⣘⣇⣿⣿⠀⠀⢺⠒⢸⡇⣿⠐⢺⠃⠀⠀⣛⣛⣛⣘⣛⣛⠃⣿⡇⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⠛⠛⠛⠛⠁⠛⠛⠛⠁
⠀⠺⣦⠀⣀⢠⣤⠀⠀⠀⠀⢸⣿⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⣀⣀⠀⡠⠢⡀⠀⠀⠀⠀⢸⡟⠛⠛⢻
⠀⠀⣾⣆⣿⣸⣿⠀⠀⠀⠀⢸⣿⡶⢶⣿⣿⣿⡷⠀⠀⠐⣿⣿⠀⡇⣇⢰⣷⠀⠀⠀⣰⠟⡀⠀⠀⠈⢳⡄
⠀⣴⠿⠿⠿⡿⢿⢧⠀⠀⠀⢸⣿⣟⣻⣿⣿⣿⣏⠀⠀⢸⣿⣿⣦⣿⣿⣽⣿⠀⠀⢸⡇⠀⡷⠶⣿⠀⠀⢹
⠀⣿⠉⠉⠩⡯⢿⢽⠀⠀⢠⣼⣿⣯⣭⣿⣿⣿⣧⠀⠀⣸⣿⣿⣏⣹⣿⣸⣿⠀⠀⢸⡇⢀⡷⠒⣿⠀⠀⣸
⠀⠉⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⢀⣄⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⣀⣛⣛⣛⣛⣛⣛⡀⠀⠀⢀⣀⣤⣷⠒⠻⢿⠀⠀⢸⣿⢰⣿⣿⢀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿
⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⣼⢿⡆⠀⢸⠀⠀⢸⣿⣸⣿⣿⡍⠹⣿⠇⠀⠀⢀⣤⣤⣤⣴⣿⣿⣿
⠀⠘⠻⣿⠟⠿⣿⠟⠀⠀⢰⣿⣴⣿⣾⣿⡀⣸⠀⠀⢸⣿⣿⡀⢸⣷⠶⠛⠀⠀⠀⠸⢼⠤⡧⠾⢼⠤⣿
⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠈⠉⠁⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠛⠛⠲⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠏⠀⠀⠀⠀⠀⠈⠉⠉⠙⢦⡀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡄⠀⣯⣀⡿
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣉⣀⣀⡀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⢸⡏⠉⢹⡇⠀⠀⠀⡟⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠶⠾⣆⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⢸⣇⣀⣸⡇⠀⠀⠀⣧⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⢸⡏⠉⠨⡇⠀⠀⠀⡏⠈⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⢴⡇⠀⠀⢰⡷⠶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣸
⠀⠀⠀⠀⠀⢤⣤⢤⣤⠤⠤⣤⠤⣤⠤⠀⠀⠀⣶⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠚⠛⠒⠒⠚⠓⠒⠒⠛⠓⠒⢲
⠀⠀⠀⠀⠀⠀⡧⠀⡇⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠀⢸
⠀⠀⠀⠀⢀⣀⣟⣀⣇⣀⣀⣿⣀⣿⣀⠀⠀⠀⣿⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠿⠀⢸
⠀⠀⠀⠀⢸⠉⣭⣭⡍⠉⠉⣭⣭⣍⢹⡇⠀⠀⣿⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡦⠀⢸
⠀⠀⠀⠀⢸⠀⠷⠴⠇⠀⠀⠿⠤⠿⢸⡇⠀⠀⣿⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠗⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⡶⠶⠶⣦⠀⠀⢸⡷⠶⠶⣿⠶⠶⠶⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⣇⣀⣀⣿⠀⠀⢸⡇⢀⡴⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⢠⣤⣬⣭⣬⣥⣤⡀⢸⡧⣾⠀⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠄⢹⡦⣤⡀⠀⢸
⠀⠀⠀⠀⢸⠀⢺⠀⠀⠀⠀⠀⢸⡇⢸⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠈⣷⠀⢸
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⣸⠀⣸⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣸⣿⣷⡀⠀⠀⢀⠔⠋⠉⠙⢢⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⡰⠚⠉⠉⠲⡄⠀⠀⠀⢀⣿⣁⠀⠀⠀⠀⠀⢰⣿⣿⣦
⠀⠀⠀⣘⣿⣟⡀⠀⠀⠘⣌⠁⠉⢈⡰⠃⠀⠀⠘⢿⣿⠛⠀⠀⠀⢧⡉⠈⠀⣁⠆⠀⠀⢰⡎⠉⢹⡦⠀⠀⠰⣶⣿⣿⣿⠇
⠀⠀⠿⠿⠇⠿⠿⠇⠀⠀⠘⠋⠉⠉⠀⠀⠀⠸⠷⠜⠏⠾⠷⠀⠀⠔⠋⠉⠉⠁⠀⠀⠠⠾⠷⠤⠾⠷⠆⠀⠀⠉⠛⠏⠁
⠀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⡇⠀⣄⠀⠀⡇⠀⠀⡏⠩⠭⠍⢹⠀⠀⠀⡏⣩⣬⡉⡆⠀⠀⡔⢒⠛⠓⠲⡆⠀⠀⣴⡄⠁⠀⠀⡁⠀⣠⣇⣀⣀⣀⣧⡀
⠀⠀⣧⣤⣬⣤⣤⡇⠀⠀⣇⣀⣀⣀⣸⠀⠀⠀⡟⠿⠿⠋⡆⠀⠀⡇⠘⠈⠛⠀⡇⠀⢸⣿⣯⣿⣿⣽⣿⠀⣿⡿⠿⠿⠿⣿⡇
⠀⠀⠀⠠⠿⠧⠀⠀⠀⠰⠿⠿⠿⠿⠿⠆⠀⠀⠳⠰⠦⠶⠁⠀⠀⠙⠻⠛⠛⠟⠁⠀⠈⠿⠏⠛⠛⠛⠋⠀⠀⠣⠤⠤⠤⠃
⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⢠⠤⣄
⠀⠀⣿⡷⢀⡲⡝⡄⠀⠸⠿⠉⠉⡹⢿⠆⠀⢠⡏⠀⠀⠈⣆⠀⠀⠀⡇⠀⣀⡇⠀⠀⠀⢰⢸⣤⣧⡦⠀⠀⢀⣀⣤⠴⣒⣺
⠀⠀⠙⢷⣄⣠⣤⡀⠀⠀⠀⢘⣁⡇⡆⠀⠀⠘⠋⠀⠀⢀⠟⠀⠀⠀⣇⣚⣛⡇⠀⠀⠀⠈⠾⣛⠯⠃⠀⠀⠘⢻⣻⠿⢿⣿
⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠘⠒⠒⠒⠃⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠓⠓⠓⠃⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠤⠤⡀⠀⠀⠀⡴⡀⠀⢀⢦⠀⠀⠀⣀⡤⠤⣀⡀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⢀⡤⠤⣀
⠀⠀⡾⠟⠁⢠⣿⡆⠀⠀⢧⠇⣛⠸⣸⠀⠀⣴⠉⡜⠛⡌⣳⠀⠀⠀⣿⣦⡝⠎⠇⠀⢰⠊⠀⣀⠀⠈⡇⠀⢔⠉⠀⠀⠀⢙⠆
⠀⠀⢧⡰⣷⠆⣸⠇⠀⠀⠀⣰⣟⣆⠀⠀⠀⠸⣹⡖⠖⣟⡝⠀⠀⠀⢈⠻⠿⠆⠀⠀⠀⠉⢡⣿⡇⠉⠀⠀⠈⠉⢺⣿⠊⠁
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠈⠛⠘⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⢠⣒⣒⣒⣀⠀⠀⠀⡔⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠦⢤⠀⠀⠀⢠⣴⡶⣦⣄⠀⠀⠀⣀⣀⣠⢄
⠀⠀⢸⣿⠋⢻⣿⠀⠀⠀⡇⠍⠅⠄⢹⠀⠀⢨⣛⢿⣿⢟⣥⠀⠀⣜⠨⠭⠭⢈⡇⠀⢠⣿⡵⣯⢲⣻⡆⠀⠀⠒⠒⠲⠔⠁
⠀⠀⢸⣏⣀⣉⣿⠀⠀⠀⡇⠭⠭⠅⣸⠀⠀⢸⣫⣷⣶⣯⣻⠀⠀⡿⣻⣮⣶⣛⡇⠀⠀⠻⣬⣾⣷⡿⠁⠀⠀⠾⣿⠶⠿⠆
⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁
⠀⠀⢠⡤⠤⠤⠤⡄⠀⢀⠔⣒⠒⠒⢦⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⣠⠖⠒⠲⣄⠀⠀⢠⣴⣤⣤⣤⣦⡀
⠀⠀⠹⣐⣂⢒⡀⡅⠀⢸⠀⢬⡙⢦⠀⡇⠀⢰⣷⣖⠉⠉⠉⠀⠀⣿⣙⣉⣩⣹⡿⠀⢰⡧⠘⠶⠊⠬⡇⠀⢈⣉⡏⡏⡏⣿⡇
⠀⠀⣈⠻⠿⠈⠇⡇⠀⠸⣄⠃⠙⢘⣢⠃⠀⠀⠉⠀⠙⣿⣷⠀⠀⠈⠹⠟⠋⠋⠁⠀⠀⠳⣄⣀⣠⠜⠁⠀⢸⣇⣇⣇⣇⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠳⢄⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡉⠃⠁⠀⠈⠘⡄⣠⠖⢳⢚⠋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢌⠀⠓⢠⠆⢀⣇⡇⠀⠀⡦⠐⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠭⠭⢍⣒⢤⡀⠀⠀⣴⣾⡇⠀⠀⠀⠘⠳⣒⠛⠢⣠⠔⠹⡐⠀⢁⣜⠁⣖⡩⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠰⠷⢶⡦⡀⠈⠑⠮⡓⢄⠘⣷⣾⠀⠀⠀⠀⢀⣈⣷⡤⡧⠤⢼⠤⢔⣈⣀⠔⠁⢀⠖⠉⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡇⡇⠀⠀⠈⣞⡄⠀⠀⠈⠳⣕⢾⠻⣧⡴⠖⠋⠉⢀⠴⠁⢺⠐⠄⠑⠀⠂⠁⠈⢻⡛⠆⠠⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢇⢇⠀⠀⠀⡸⡇⠀⠀⠀⠀⠈⠹⣷⣟⡄⠀⠀⢰⠃⢀⠔⢁⢦⠀⡞⢳⠀⢸⠉⠘⢍⠓⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠪⣗⣒⡪⠝⠁⠀⠀⠀⠀⠀⢀⣿⣫⣻⡄⠀⠸⢾⠁⢠⠁⣠⡀⠹⡼⡆⠀⣦⢤⡬⠆
⠀⣀⣀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⠵⢭⠹⣆⠀⠈⠢⡿⣔⠀⡼⠦⠇⠙⠛⠒⠦⠇
⡼⠁⠀⠁⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡫⠘⡆⣥⣕⣋⢊⣧⡀⠀⠀⠈⠑⠃
⢧⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢀⣤⡶⢞⠛⢟⠳⡶⢾⢛⣿⢿⠳⢶⠟⢛⠟⠛⡛⠻⣦⢶⣶⠶⣦⣤⣀
⠈⠳⣤⣤⡤⠞⠋⠀⠀⠀⠀⣠⣾⣋⣩⠑⡄⢡⢀⡦⢤⠸⣌⣛⠝⢀⠆⡐⡡⢚⣽⢢⢀⢹⠂⢀⢲⠃⢠⢟⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⡏⣖⣿⠦⣸⢀⡾⡿⡸⠅⣒⣀⢂⡁⢻⡇⢧⡘⠾⡛⢤⡜⠢⠘⣾⡀⠻⠷⠇⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⢄⠳⠬⠵⠔⢁⡾⢁⠭⡂⡡⠨⠠⠣⠤⢠⡯⠔⢍⢛⠙⠓⡴⠓⠒⢿⡝⠲⠒⠎⢱⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⠑⠄⣁⡒⠒⣶⣿⠃⡈⠶⠁⡠⠒⡉⢉⠙⢺⡇⡘⣸⠰⢶⡾⡴⢿⣷⠌⣷⣠⡧⢒⠲⢾⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⠔⠊⣄⣀⠈⢸⣿⡆⡀⠀⢸⢁⢡⣺⣟⢮⢸⣯⠐⠸⡅⠖⠒⢴⠚⠛⠲⢿⠋⢹⠾⢿⠋⣷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠋⣡⣬⡙⣾⣧⣈⣔⣁⣈⣦⡈⠳⠚⣸⢻⡇⣠⠾⠛⠲⢌⡃⠻⠉⠑⣿⠃⠚⢯⣭⠜⢉⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⢟⣳⣣⣿⢁⣀⡈⠑⡌⠪⠙⢍⣉⡌⢺⣿⠁⢠⣶⣶⠀⡗⠡⡐⢀⣿⡠⡪⢶⣶⠬⠕⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡙⢴⣁⢈⡡⣻⡏⣞⡿⠀⡼⠀⡁⠘⢛⠗⣸⡯⠂⠸⣝⣊⣴⡷⠒⠛⢛⡿⢊⢄⠐⡐⢤⡟⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢔⣈⠍⠩⢙⣟⠲⠶⣎⡤⠬⣀⡜⠠⢈⢾⡇⠕⡑⢰⣷⢼⡀⣿⡿⣺⡧⠚⠓⢦⡈⢆⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣉⠔⣛⢢⢹⣠⠟⠁⣀⣄⡠⠹⡆⠳⡸⠰⣬⣤⣁⢀⢃⠓⠖⢲⠿⡁⣿⣷⡄⢹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣽⣤⣏⡤⢸⠱⣙⡗⢰⠇⠀⠐⡼⢡⣦⡈⢷⡡⡎⠀⠈⢀⠛⣖⣮⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢷⣤⣴⣯⣤⠶⠞⠻⠾⢿⣧⣼⡴⠶⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⢠⣁⣀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⢀⠄⢰⠞⠉⠻⣏⠀⠀⠈⣷⠶⠦⠀⠀⠄
⠀⠀⠀⠀⢀⣀⣀⣀⡀⢹⡁⣀⠀⠀⠀⡀⠘⠀⠀⠀⣀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠸⣤⠙⣾⣄⣠⠜⠁⠀⡀⠴⣠⠔⡿⠛⠛⠂⠀⠀⠠⠀⠀⠠⠋⠀⠀⠀⡖⠐
⠀⠀⠀⠀⢀⠐⠛⡻⠗⠺⣿⠿⡿⢷⣦⡀⠀⠀⡀⠒⠀⠀⠀⠠⠀⢀⠉⠑⣶⠣⣅⣹⠾⠿⠉⠙⡄⠀⠓⠀⠀⠋⠀⣇⠀⠀⠀⠀⠀⢀⡄⢀⢀⠀⢀⡠⠾⠛⠆
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡻⠀⠸⡄⢹⡝⡄⠠⠉⠀⠀⠀⠐⠀⠀⠀⠀⢀⡝⠸⠃⡇⠀⠀⠀⠀⡼⢀⠰⠀⣦⡀⠸⠉⠉⠁⠀⠀⢤⣿⠟⣟⡻⠒⠀⠀⠀⠀⠈
⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⣴⠄⠀⠀⠀⠁⠀⠀⠀⠀⠒⠉⠤⠼⠦⡘⠂⠀⠀⠾⠙⠀⡀⠀⣷⠇⠰⣀⣀⣀⡠⠖⠺⣿⣷⠿⠋⠀⠉⠀⠈⠙⠧
⠀⡀⡇⠀⠀⠇⠀⠀⠀⢠⣷⡏⢀⣇⣠⣏⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠋⠀⠀⠀⢀⠊⠀⠁⠀⠀⠀⠀⣀⡀
⠀⠙⢷⡀⠠⠀⠀⠀⠀⠞⣾⠟⢿⡉⠳⢦⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠂⠀⠘⠓⢓⣤⠀⠀⠀⡏⠀⠀⠑⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⡙⢇⠀⠀⠀⡠⠗
⠠⠀⠀⠀⠀⡾⠀⠀⠀⠀⢃⠀⠀⠀⡇⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠤⠚⠃⢀
⠀⠀⠀⠀⠠⠂⠀⠀⠠⠦⢨⣦⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠂⠀⡠⠄⠉
⠈⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠀⡄⠀⠈⠠⠀⠀⠀⢸⡶⢠⡖⢸⢸⢰⡦⠀⢸⡇⢶⡄⢸⠀⣦⡄⡶⠶⢰⢲⠀⠀⠀⢠⠀⠀⣤⠀⠄⠂⠃⢀⠄⢀
⠀⢀⠀⠀⠀⠂⠀⠁⢠⣰⢤⣀⠁⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠁⠀⠈⠀⠀⢤
⠀⠠⡄⢐⡾⠋⠛⢿⡇⠀⠀⠈⣷⡶⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⣀⠀⠀⢠⡄⠀⠐⠇
⠀⣠⠶⠚⠧⠀⠀⠀⠁⠀⠀⢀⠟⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢍⢦⡀⣠⣴⣾⠿⠿⠿⣭⣙⠢⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⣀⡾⢦⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠻⣿⣟⠉⠉⠲⢦⡀⠉⠳⣌⢧
⢠⠟⠒⠦⠄⠀⡀⣠⣾⣷⣶⢶⣂⠐⠈⠁⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣠⠤⠃⠀⣥⣼⢷⡋⠀⠈⠓⣄⠀⠀⠙⢦⠀⠘⣦⡇
⠈⠀⠀⠀⠀⢀⣈⣿⣿⣔⣧⡮⠄⠀⠤⠀⠠⣤⡀⠀⠀⠐⠉⠐⠂⢀⠀⢸⠀⠀⠐⠀⠀⠀⠸⠀⢠⠤⣤⣿⣤⣤⣝⢠⠁⠈⠇⠀⠀⠀⠈⢳⡀⠀⠀⢱⡄⢻⣿
⠈⢳⡴⠶⠒⠉⠉⠙⡻⠛⡍⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⠀⣽⠀⠆⠀⠠⡀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠻⠈⠱⣆⠰⠀⠘⡀⠀⠀⠀⠀⠹⡄⠀⠀⣦⢸⡿
⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢⡤⠂⠀⣠⠆⠀⠀⠀⠀⠿⠀⣀⠁⠀⠁⠄⠀⠀⠀⠀⢰⠃⠀⠀⠘⡇⠀⢸⡆⡁⠀⠑⡀⠀⠀⠀⠀⢱⡀⠀⣾⡟⠁
⢀⢀⠄⣀⠀⣠⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⢢⡀⣀⠀⢸⠀⠀⠀⢠⠇⠀⣿⠴⠀⠀⠀⠙⠄⠀⠀⠀⢸⣷⡾⠋
⠄⠀⠠⠃⠈⠙⠄⠀⠀⢀⡰⠛⠂⠀⠀⠀⠀⠈⡁⢀⠂⠀⠀⠀⠀⢠⡘⠀⠀⠀⠀⠀⠀⠛⠈⠑⠾⠧⣤⣤⠿⠶⠚⠉⢀⠈⠲⣄⠀⠀⢑⣶⠄⠚⠁
⣿⣿⣿⠿⣿⠿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠟⠻⢿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⢨⣿⣿⡇⠀⠀⣿⣿⡇⢀⡀⠀⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⣬⣙⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣦⣌⣙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⢈⣿⣿⡇⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠟⠛⠻⣿⣿⡟⠛⠛⣿⣿⡿⠛⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣤⣄⣤⣿⣿⣧⣤⣄⣿⣿⣧⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⣀⣤⠀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣤⣄⡀
⠀⠀⠀⢀⡘⣿⡙⠷⠟⢸⣧⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠋⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⣿⣙⠛⢡⡶⠶⣦⠉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⣨⡾⠛⠛⠛⢷⣄⠀⠀⢹⣆⡀
⠀⠀⠀⣩⡽⠇⠸⣧⣤⠿⢀⣙⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠻⣆
⠀⠀⠀⠹⡷⠞⣷⢀⣴⣄⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠁⠀⠀⠸⣧⠀⢤⣴⡄⠀⣼⠃⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠘⠻⠾⠃⠹⠛⠁⣶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣿⢰⡞⠁⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣦⣀⣿⠀⢀⣿⣠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢰⡾⠷⠿⠾⣷⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠉⠁⠀⠀⠉⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⡛⢿⡄⠀⠀⠀⠘⠿⣾⠿⡷⠟⠀⣼⠛⠛⠉
⠀⠀⠀⠀⠀⢠⣤⣤⣴⠟⠀⢠⡾⠛⠛⢶⡄⠈⢿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⣨⡗⠈⠻⢶⣤⡴⣦⣀⡀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⢿⡄⠀⠀⢸⡇⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⣩⡷⠀⠈⠛⠶⠾⠋⠀⠀⣿⡉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⢾⣏⠀⣠⡶⣤⠀⠀⣴⢦⣄⠈⣻⡦⣠⡶⠛⠉⠉⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⣿⠀⢀⣿⠀⠙⠿⠋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠰⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣠⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢠⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄
⠀⠀⠀⠀⠀⢠⣄⢀⡤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡇⠀⣀⣀⡀⣠⣤⡀⠀⠀⠀⣴⠶⠾⠋
⠀⠀⠀⠀⠀⢀⡭⢨⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⡏⠉⠿⠋⢀⣿⠆⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣨⡿⠃⠀⠀⠘⣧⣀⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⠀⠉⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣷⠄⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠈⠻⣦⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣧⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣼⡇⠀⠀⠀⠈⠻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠊⠁⠀⠀⠀⠀⠀⠀⠃⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠋⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠐⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠑⠢⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠋⠒⠊⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠣⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠣⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁⠀⠀⠀⠀⠀⠀⡀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠢⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⡔⠓⠈⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⡀⣀⣈⣷⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣴⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠁⠀⠀⠀⣿⠀⠀⠀⠀⢡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣂⣠⡤⠐⠀⠀⠀⠀⢀⠔⠁
⠀⣀⣀⣀⠤⠤⠒⠂⠉⠁⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠙⢦⡀⣿⠀⢠⡾⢁⣀⡤⠶⠒⠋⠉⠀⠀⠈⠀⢀⡀⠤⠀⡌
⠀⠈⠉⠉⠁⠒⠒⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠋⠉⠙⠛⢓⡶⠦⣿⣿⣶⠿⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠔⣿⡗⠤⣀⡀⠀⠀⠀⠀⢰⠉⠀⠀⠉⠐⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠥⠤⠴⠒⠒⠒⢦⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⢻⡇⠀⠀⠈⠑⠢⠤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠥⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⣠⣴⣶⡿⠿⠿⢿⣶⣦⣄⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠉⠀⣀⡀⢀⠀⠀⠉⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢰⡶⣛⣛⢿⣥⡀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢰⣿⠁⠀⠀⢿⡗⣿⣿⢇⣿⡅⠀⠀⠀⠈⣿⡆⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠀⢀⣜⣟⣶⡶⢿⢽⠞⣓⢷⡄⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⡏⣶⢝⡇⣠⣤⣹⣮⣋⡼⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠙⠖⠛⠙⢿⣻⠇⠈⠁⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣶⣶⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋



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

⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⣿⠉⢙⡛⠛⠲⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠶⠶⠶⠶⠆⣠⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⢠⡀
⠀⢀⠼⣿⠀⠀⠙⠗⠀⡇⠀⠀⠀⢀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿
⠀⠘⠀⠛⠛⠛⠛⡛⠛⠃⠀⠀⢀⠈⣶⡾⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠀⠈
⠀⠀⢸⣇⠈⠩⠉⣭⣭⣧⡄⠀⣿⠀⠉⣶⣾⢻⡇⠀⠀⢀⠀⠸⠆⢀⣷⣦⣤⣀⢀⣀⠀⠀⣉⠀⠀⠀⠛⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⣿⠛
⠀⠀⢸⣿⣷⡄⠐⠊⠳⣟⣿⣦⡘⠂⠀⠉⡿⠾⠆⠀⠀⣿⡗⣴⣶⣮⠉⠉⠉⠉⣉⣿⠀⣀⡀⡀⢀⣀⣀⠀⣀⣀⡀⢀⣀⣀⠀⣀⣀⡐⣾⣿⣿⠖⠛⣷⠄
⠀⠀⢸⣿⣿⣿⡦⢢⡄⡄⣤⢤⠭⠆⠀⠀⠀⠀⠀⠂⠘⣿⡇⣿⣿⣿⠀⠀⠀⠀⣭⣽⡁⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⠙⠉⠁⠲⠴⡟
⠀⠀⢸⣿⣿⣿⡇⠎⢱⣥⣍⣿⣅⣣⣤⡀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⢠⣶⣶⣶⣶⣶⣶⣿⣿⣷⣼⣿⣿⣶⣿⣿⣷⣾⣿⣿⣶⣿⣿⣷⣶⣶⡆
⠀⠀⢸⣿⣿⣿⡏⠚⠛⠛⠛⠛⠛⠋⠉⠉⣴⣶⣶⣶⣶⣶⣶⣶⡶⣶⡄⣴⣿⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⢠⢸⣿⣿⡿⣧⣀⣀⣀⣀⣀⣀⡀⠀⠀⠛⣿⢿⣿⣿⠟⠛⠛⠓⠛⠃⢿⣿⠈⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠛⠛
⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄
⠀⠛⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠃⠀⠀⠘⠛⠉⠉⠙⠛⠃⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⢿
⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⣤⣤⣤⣴⣶⣶⣶⡏⠋⢠⣤⡄⢡⡀⠀⠀⠀⠀⢀⠄⠀⠀⣀⡤⢀⠀⠀⠀⡶⢻
⠀⠀⠀⠀⢸⡿⣿⢿⡇⠀⠀⠀⣿⡿⠿⢿⣿⠿⢿⡆⠀⠀⠀⠰⣿⡷⡹⠿⠿⠿⠿⠿⠛⠓⠂⡈⠋⢁⣼⣷⡀⢀⡠⢂⣭⠐⠿⠂⠧⢆⡸⠋⠉⠀⠛⣾
⠀⠀⠀⠀⠘⠀⠀⠈⠃⠀⠀⠀⣿⡰⡿⢂⡇⢾⣿⡇⠀⠀⠀⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣽⣷⡡⣶⣿⡿⠛⠀⠀⠀⠀⠀⠁⠀⠀⢾⣸
⠀⠀⠀⠀⠀⡠⠀⢄⠀⠀⠀⠀⣿⣷⣶⣾⣿⣶⣾⠇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡝⠋⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠻⣛⠟⠀⠁⠀⠰⠛⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⠀⢀⣶⡀⠀⢰⣆⠀⠀⣰⣆⠀⠹⠋⣴⠶⣦⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡆⠀⠀⣠⠀⠀⡘⣷⣝⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢾
⠀⢰⠏⠀⣰⠉⠯⠉⠉⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠾⠇⠀⠰⠿⠀⠀⠁⠂⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣤⣤⣤⣥⠤⠤⠤⢤⣤⣤⣦⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠓⠒⠛⠒⠒⠚⠛⠓⠒⠛⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⢀⣴⡆⣦⣄⢠⣶⠶⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣦⣤⣤⣤⣿⢿⢿⠀⠀⠀⢠⣄⣤⣤⣤⣤⣤⣤⣤⠀⣤⠶⡄⠀⠀⠀⠀⠀⠀⠀⢺⠿⢁⠻⢿⢸⣧⣣⣤⣿
⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⢙⡋⠚⠛⠛⠛⠛⠛⠛⡀⠛⠶⠃⡀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⠉⠘⠉
⠀⠀⠀⠀⣿⣿⡿⣿⢿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⢿⣿⢿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⣿⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⡙⠷⠟⡀
⠀⠀⠀⠀⣿⣿⠇⠿⢼⣿⣿⠀⠀⠀⠀⣿⣿⣶⣴⣽⣿⣼⡿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⠀⠀⠀⣶⣿⣿⣷⣶⣾⢻⣿⣶⡄
⠀⠀⠀⠀⠛⢛⣛⣛⣛⣻⠛⠀⠀⡄⠀⡹⠛⣻⠛⡟⢻⡋⠠⡀⠠⡀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣇⡀
⠀⢀⣠⣴⣾⣿⣿⡿⠋⠁⠀⡠⠊⢀⡜⠁⢠⠃⠀⡇⠀⢣⠀⠙⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⢸⣿⡆⠀⠀⢐⣟⠂⠀⠀⠀⣿⣿
⠀⡏⠩⢉⠙⣿⣿⠀⣾⢻⣿⢻⡟⣿⡿⣻⣿⢻⣿⢻⣿⢻⡿⢻⡟⣿⡟⣿⡟⣿⡄⠀⠀⠀⢀⣀⣀⣿⣇⣀⣀⡀⠀⢸⠿⡇⠐⠂⣭⣭⠁⠈⠀⢠⡿⣿
⠀⠓⠒⠒⠚⠉⠛⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢉⣵⠟⢹⡏⠻⣮⡉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⡞⠁⠀⢸⡇⠀⠈⠻⣄⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⢸⡇⠀⠀⠀⠹⣆⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡆⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠗⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠤⠤⣿⠤⠤⠤⠤⠤⢼⡧⠤⢀⣴⠞⠛⠛⠛⠶⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇⣰⠟⠀⠀⠀⠛⠳⣄⠈⢷⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠸⣇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡄⠀⠀⠀⢸⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠻⣆⠀⠀⢸⡇⠀⠻⢦⣄⣀⣀⣀⣤⠾⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠙⢷⣄⢸⡇⣠⡾⠃⣈⣭⠉⠉⠁⠀⢼⡋⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠿⠿⠚⠛⠉⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀⣀⡀⣀⡀⢀⣀⠀⣀⢀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡿⣾⠀⣿⠀⣿⡂⢸⢾⡃⣿⣾⠃⣿⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠈⠀⠉⠁⠈⠀⠁⠁⠈⠀⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣴⡄⣠⣤⣤⣌⣭⣍⣩⡁⠀⠀⠀⠀⢸⣿⢣⣿⡿⣱⣿⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣰⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣷⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣴⣶⣶⣶⣶⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣻⣟⣛⣛⡋⠄⠀⠀⠀⠀⠀⠀⠀⢠⣴⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⣴⣿⢻⣽⣿⢗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠃⠀⠀⠀⢰⡟⢛⣦⠻⠓⠈⠁⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⣷⣿⢀⣀⡀⠀⠀⠘⠻⢿⣋⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠾⠶⠿⠿⠿⠆⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⡇⢤
⠀⠀⠀⠀⠀⠀⠠⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠀⠀⢸⣿⣿⡇⠼
⠀⠀⠀⠀⠀⠀⠠⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠥⠤⠤⠬⠭⠭⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣼⣤⡀⠀⠀⣀⣠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⡿⠿⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠦⠠⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠛⠒⠲⠶⠦⠤⢤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⣠⠜⠋⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣤⠀⠀⠀⣾⠁⠀⠀⣠⣤⣄⠀⠁⠘⢷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢸⡇⠀⠀⠉⠀⠀⠉⠱⠄⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠀⠀⠀⠀⢠⠀⠀⢰⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣠⣶⡾⠻⣄⠀⠀⣼⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⣿⠋⠉⠀⠀⠈⠛⠦⢤⣤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠷⠶⠶⠶⣦⣴⠶⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠈⠁⠈⡇⠀⠀⠀⠀⡠⠔⠢⣀⠀⣀⠄⠒⡄⢀⡠⠖⠙⢆⠀⡠⠔⠢⡀⠀⡠⠖⠁⠈⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢘⡒⡀⠀⠀⠀⠓⢒⠶⠒⠁⠀⠀⣀⠜⠋⠀⠀⡀⠘⠁⠀⠀⡀⠔⠉⠀⠀⣠⠜⠉⠀⠀⢀⡠⠊⡅
⠀⠀⠀⠀⠀⡤⠖⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⢨⠇⠉⠈⠉⡸⠚⢅⠀⠀⠀⡠⠪⡀⠀⠀⡠⠛⡄⠀⠀⡰⠫⡀⠀⠀⡠⠊⢆⠀⠀⢀⠔⡁⡌⠀⡆
⠀⠀⠀⢀⠎⢀⠔⠀⠁⠉⠘⠒⠠⠤⠤⠄⠒⠊⠁⠀⠀⢠⠎⠀⠀⠈⢣⣤⠊⠀⠀⠘⣤⡎⠀⠀⠈⢦⠎⠀⠀⠙⣤⠎⢀⢀⣀⣧⠔⠁⠠⠀⠀⠀⠃
⠀⠀⠀⠸⠀⢸⠐⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠢⠸⠘
⠀⠀⠀⡇⠀⢼⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠒⠚⠋⠐⠤⡀⠀⠈⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⠀⣀⣀⣀⣀⣠⠁
⠀⠀⠀⡇⠀⢸⠈⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢢⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠸⠸⠀⡀⠀⠀⠑
⠀⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢂⠀⠀⠀⠎⣠⠞⠀⡖⢁⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡠⢒⢠⠀⡇
⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣀⠄⠠⠀⢀⡀⠀⠀⠀⠈⠆⠀⣨⠄⠀⡘⠀⡄⠀⠀⡇⢠⠀⠀⠀⠤⠀⠀⠖⢀⠅⠀⠘⡄⠃⠤⠌⢀⠁
⠀⡠⠤⠃⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠸⠘⠤⠤⠤⢴⠀⡶⠀⠐⡇⢸⠒⠒⠒⠒⠒⠀⠀⠉⠀⠀⠀⢨⠃⠒⠒⠁
⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⡄⠀⠘⠀⢸⠀⠁⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠸⣄⣀⣀⣀⣠⣀⣀⣀⣀⣆⠀⠀⡊⠀⠀⠈⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⡇⢀⡴⠒⠺⣄⡰⠒⠒⠧⠠⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠓⠶⠶⠒⠲⠒⠒⠒⠒⠒⠚⠒⠒⠖⠛⠁

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⣶⠿⠛⠛⣿⠛⠛⠿⣶⡶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢀⡴⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⡀⠉⠓⢦⣄
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣼⠃⠀⠀⠀⣀⣀⣀⣀⣿⣀⣀⣀⡀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠻⣄
⠀⠀⢀⡞⠁⠀⠀⠀⣀⣼⠧⠶⠚⠛⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠙⢛⣤⡶⠿⠛⠛⠛⠛⠿⢶⣤⡀
⠀⢠⡟⠀⢀⣤⠶⠋⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⡾⢠⡶⠋⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⢸⣷⠋⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⠤⢤⣤⣤⣤⣤⣼⡧⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣿⢤⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⢹⣧⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏
⠘⣏⠳⣄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣄⣠⣤⣤⡶⣿⣿⡿⢋⣤
⠀⠹⡆⠈⠛⢦⣄⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠍⢉⣩⠴⠂⠈⢡⣾⣿⣿⣷⡄
⠀⠀⠙⣄⠀⠀⠈⠙⠳⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣤⡿⠚⠋⠁⠀⠀⣰⠊⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⢧⠀⠉⠉⠛⠛⠓⠒⠒⣿⠒⠒⠚⠛⠋⠉⠉⢀⡾⠁⠀⠀⠀⢀⡾⠁⠀⠀⠘⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠻⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠏⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣬⣿⣦⣄⣀⠀⣿⠀⣀⣠⣴⣫⡥⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⣤
⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⡘⠁⠀⠀⠀⠘⠁
⠀⠀⠐⠠⠀⠀⠈⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠁⠀⢀⠑⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠒⠀⣀⠂
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠
⣈⠀⠀⠀⠀⠐⠆⢀⠐⠄⠀⠀⠀⠀⠀⠘⠖⣠⣀⠀⠀⠡⠄⠔⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠄⠀⠀⠀⠀⠀⠀⠫⠚⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣤⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢈
⠀⠀⠀⠀⠘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠄
⡠⢀⠄⠀⠀⠀⠀⣰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠃⠀⠀⡀
⠣⢀⠜⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠰⣨⡀⠀⠈
⣶⣷⠶⠷⠿⣿⣿⣶⣶⣶⣿⣿⣶⣶⣶⣿⣿⣿⣾⣿⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⢰⡟⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢠⣶⡟⠋⠀⠀⠀⢠⡿⠀⠀⠀⠉⠛⣶⣤⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⡀⠀⣾⠃⠀⠀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⣿⣇⣀⢀⣉⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣶⠶⠶⠾⠷⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠉⠀⠀⠉⢻⣿⣿⣇⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣷⣀⡀⠀⣀⣼⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⣿⣿⠏⠁⠈⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡹⠛⡟⢯⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢅⡀⡼⠁⠀⡇⠀⢳⣀⣠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢹⠛⠒⠲⡗⠒⠛⣏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢺⠒⠒⠲⡗⠒⠒⣿⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⠼⡖⠒⠚⡟⠂⢶⠦⠤⣄⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⢳⡀⠀⡇⠀⠸⡆⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣙⣤⣧⣞⡥⠳⠋⠲⣌⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⡗⢺⣧⠄⢸⣀⡀⡀⢀⣾⠀⢀⠀⠀⡇⠀⢰⠀⠀⠀⣀⣀⣀⡀⡇⠀⡇⣇⣂⣶⡀⠀⠀⢀⣠⣸⣸
⠀⠋⠷⠾⠿⠇⠸⠿⠿⠇⠸⠿⠿⠿⠖⠀⠿⠿⠿⠶⠇⠸⠿⠯⠽⠿⠿⠈⠿⠿⠟⠿⠁⠭⠤⠽⠿⠿⠿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠰⠀⠀⢀⣀⡀⠀⠀⢀⠀⢰⡆
⠀⣾⣷⣤⣄⡆⢀⣠⠶⣷⡆⢀⣦⣠⣼⡄⠀⣤⣿⣞⠃⣴⣾⣵⣶⡄⠀⣼⣿⣿⢩⡏⣽⡄⢘⣻⣿⣇⣠
⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠉⠉⠉⠈⡉⡉⠁⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠠⠀⣤⡄⡆⠀⠀⣤⠀⠀⡆⠀⠀⠀⠀⢀⡆⠀⣀⠀⢀⣀⠀⠀⠀⢀⡀⣿⡇⠀⠀⢀⣧⣶⣾
⠀⣾⣾⣶⢸⡄⣿⣿⣧⣄⠀⣿⣤⣶⡇⠀⣾⣶⡗⣼⡇⢰⣿⣦⣼⣿⣦⡄⢠⣿⡗⣿⣧⡄⢠⣾⣶⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⡇⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⣀⡴⠖⠛⠛⠛⠓⠶⣄⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⠀⣠⠞⠁⣀⡀⣰⡖⣶⡀⣀⡀⠙⢦⡀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠏⠀⠸⣏⠙⣩⠤⢬⡙⢉⡿⠀⠈⢷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡀⣿⠀⢰⠞⠃⡞⠁⠀⠀⠙⡆⠓⢦⠀⢸⡇⣠⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⠳⣆⠳⡀⠀⠀⡰⢃⡶⠋⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠘⣧⠀⠸⣧⡴⢬⠉⢩⡴⣤⡿⠀⢠⡟⠰⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣈⢳⡀⠀⠀⠘⠓⠛⠀⠀⠀⣴⢋⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣙⣛⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢽⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠶⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠁⠈⠀⢀⢀⢄⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⢦⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠈⢀⠈⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠛⢳⠆⠈⡾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⢀⢀⠆⢀⠄⡀⣄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢶⠈⠠⠞
⢴⡉⢒⢸⠃⠐⢠⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠶⠁⠌⡧⠢⢐
⢹⡛⠣⡾⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢃⢷⠄⠛
⢃⡅⢀⠆⠀⠈⣷⣄⢀⣀⣀⣤⠴⠟⢣⣶⣖⣀⡀⠀⠀⠀⢀⣀⣀⡀⡀⡀⢛⡉⠣⡀⠀⠀⠈⠀⠀⢰⡠⡀
⡉⠀⠌⠁⠸⠛⢁⢨⠗⠉⠁⠀⠀⠀⣼⠀⠑⠏⡟⣡⠱⠆⡿⡍⡟⣦⠣⠀⠖⠃⠀⠉⠀⠀⠀⠀⢴⠊⢷⣶⡄
⠀⠀⠀⠀⠶⠒⢩⣾⠀⠀⠀⠀⠀⠀⣿⠀⡀⢠⣞⠏⣈⢀⠛⠾⠁⠸⠀⠱⣒⠀⠀⠰⡄⠀⠀⠀⠜⠀⢦⠉
⠀⠀⠀⠀⠲⠀⠸⠌⠆⠀⠀⠀⢀⡼⠉⠰⣤⡀⠀⢰⠉⢿⡇⠐⠄⢼⠂⠠⡍⠐⠀⠦⡀⠴⠔⠃⠀⠀⠀⠟
⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⣠⡜⠣⠉⠁⠀⠊⠀⢦⡀⠀⠀⢠⡛⢢⠝⢢⠄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡄⠸⠄⠀⠀⠀⠀⠐⠃⠀⠀⠀⢠⠉⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⢥
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠊⣃⠀⠀⠀⡀⠛⢢⠠⡀⠠⣌⡀⠘⠁⠀⢤⡀⠀⠀⠔⠀⠀⠀⢰⢀⡀⠀⣀⡒
⠀⠀⠐⢥⠀⢀⡀⠀⠀⢠⣙⠄⠀⢒⡂⠀⣁⠀⣄⣐⠉⠳⠁⢴⡆⠀⠈⣄⠂⠀⠀⠀⠀⠈⣦⡅⣀⣁
⠀⠀⣴⣆⡀⣎⠀⠀⠀⠀⠉⠀⢀⣈⡙⢀⢻⢀⠹⣡⠀⣆⠞⢻⢠⠀⠀⣿⠀⠀⠀⠀⠀⣀⠇⠟⠉⡁⠀⢀
⠀⠀⠉⡝⠯⠁⠀⠀⠀⠀⠙⢆⠀⠏⠑⠀⣏⡐⢧⣼⡄⢍⠠⡛⢘⣷⣦⣏⢀⣀⠤⠶⠚⠛⠦⡴⠋⠁⢠⠃⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠐⢀⣠⡄⠀⢀⠤⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣼⣿⣦⣄⣀⣼⢠⠁⣠⠛⠒⠪⣕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⠀⢸⠹⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠐⣾⣿⣿⡯⠿⣿⣿⣿⣿⡟⠀⢤⠃⠀⠀⠚⢴⠃⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⠤⠼⠧⠀⠀⠀⢸⠀⠈⠹⡾⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠧⣀⣸⣿⣿⣿⠀⠀⣯⣿⡿⠛⡇⠀⠀⠀⠔⠚⠋⠉⠓⢄⠀⢷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⠄⠠⠬⣍⣛⡟⠀⠀⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠁⠙⠊⡌⠣⡀⢀⣿⣿⡇⢸⡷⠖⠒⠒⠮⠀⠀⡀⢀⡦⠴⠃⣰⠞⢳
⠀⠀⠀⠀⠀⠀⢸⣯⢁⠎⠀⠐⠄⠀⠀⠀⢘⡞⠛⢻⡇⢸⡇⠀⠀⠀⠀⠀⢀⡍⠉⠁⠀⠀⠻⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠌⠙⢀⠔⠈⠀⠀⠀⠘⣷⠀⠈⡇⢸⡇⠀⠀⠀⢰⡴⠊⠀⠀⠴⠒⠢⡄⠀⢼⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢄⠤⠐⠀⠀⠀⠹⡄⠀⠃⢸⣷⠶⠶⠶⣏⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⣤⣤⡇⢀⠄⠀⠁⠀⠀⢸⡇⠀⠀⢀⠈⠙⠒⠒⠒⠋⠀⣶⠋⣸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣷⣷⡇⠈⠒⠀⢈⠀⠀⢸⡇⠀⠀⣸⠷⠤⠤⠾⠦⠤⠤⠻⣦⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠧⣍⡇⠀⠄⠀⢸⣴⣷⣼⡇⠀⣰⠏⠀⢰⣄⣠⠖⠒⢦⡀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣦⢬⡑⣴⠁⣠⠂⢀⡏⢻⣿⣿⣧⠾⠯⡤⠔⠋⠈⣷⠀⠀⢀⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡙⣧⡰⢋⣴⣾⣷⣿⣿⣿⡇⠀⠀⢤⣄⣴⠾⠋⢀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⣿⣿⣿⣿⠏⡷⠶⠛⡋⠉⢀⣆⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠋⠀⠘⠦⠶⠿⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣤⢤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣥⣷⣥⣿⣌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⡿⢫⣿⣛⣛⣛⣛⣛⣿⣛⣻⣿⣝⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⡧⢿⣿⣮⣿⣭⣭⣭⣭⣿⣭⣿⣯⣿⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣭⣽⣛⣛⡱⢸⡿⢫⣿⣿⢏⣿⣯⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣼⣿⣮⣿⣯⣾⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⢟⣵⣿⡿⢫⣿⣿⢏⣿⣯⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢾⣶⡷⢻⢻⠿⣿⣮⣿⣯⣾⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣭⣶⣿⣿⣿⡌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡶⣿⣿⣿⣿⣿⣷⣭⣾⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⣿⣿⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⣷⠀⠀⠀⣿⣿⣿⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣭⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣤⣤⣤⣽⣿⣯⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⢛⣿⡿⠋⠉⣿⠉⠙⠻⣿⡛⠻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⢠⣿⠋⠀⠀⠀⣿⠀⠀⠀⠙⢿⣄⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣘⣿⣀⣀⣀⣀⣀⣘⣿⣆
⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⢻⣟⠛⠛⠛⠛⠛⠛⢿⣆
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⠇
⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣷⣶⣤⣈⡁⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡉⠉⠉⠉⠉⢻⣏⠉⠉⠉⠉⠉⣿⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣀⠈⢻⣦⡀⠀⠀⣿⠀⠀⢀⣴⡟⠀⢹⣿⣿⠟⠙⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢶⣿⣿⣶⣤⣿⣤⣴⣿⣿⣶⠷⠀⢿⠏⠀⠀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁


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

⠀⠀⠀⠄⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⡸⢇⠀⠀⠁⠀⠀⠀⠀⠀⢀⡲⠀⠀⠜⠀⠆⡀⠀⠀⠀⠀⠀⢀⡀⠀⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠈⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⡁⠀⠀⢆⡀⠀⠀⠐⠖⠚⠒⠒⠒⠒⠒⠒⠒⠓⡖⠀⠀⠀⠀⠀⠀⢣⡬⠃⠘⣦⠟⠀⢣⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⢸⠀⠈⡇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⡀⢀⣀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⣆⠁⠀⠀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠡⣇⣹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⡀⢰⠀⠀⡀⠀⠀⡀⠀⢀⠀⢐⣦⢠⣤⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡂
⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⡶⠆⠀⣁⠼⣧⠀⠀⠀⢠⠄⢨⠀⢄⠤⠸⢀⡅⠠⠠⢄⢠⡿⠘⠉⢉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⠗⠚⠇⠀⠀⠀⠈⢻⠦⡟⠁⠙⡷⢼⠋⠀⢻⠇⡟⠃⠘⡿⢺⠋⠁⢓⠀⠀⠀⠀⠀⠀⡀⠘⠢⠜⠁⢀
⠀⠀⠠⡄⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠠⠤⠭⠥⠤⠤⠬⠯⠤⠤⠤⠽⠥⠤⠤⠬⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣠⠀⠀⣀⡐
⠀⠀⠀⠠⢀⢀⠀⠁⠀⠀⠀⠀⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢀⡀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠒⢂⣀⡀⣴⠋⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠦⠀⡀⠀⠀⡤⠀⠄⠀⠀⠀⢀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠂⠀⠠⠠⠤⠜⠙⢷⣋⣀⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠹⠀⠀⠀⠆⠀⢲⡀⠀⠐⠃⠀⡂
⠀⠀⠀⠠⠀⠀⣒⡒⢒⣀⢀⣓⠒⣂⡀⣀⡀⢀⣀⢀⣀⠈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⣂⡀⣐⡢⢜⣂⢐⣀⠒⣀⡚⢀⡀⢓⣢⠰⣛
⠀⠀⠀⠀⠀⠀⠘⣗⡺⠁⠀⢻⣚⠏⠀⠈⣗⡺⠁⠀⢹⣓⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⡻⠁⠈⢻⣚⠏⠀⠙⣗⡻⠁⠈⢻⣚⡏
⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⣀⢠⠔⠒⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⠉⠑⢦⢀⡀
⠀⠀⠀⡀⠔⠉⠀⠁⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠁⠀⠂⠤⠤⢄⠀⠀⠀⠀⠀⠀⠘⠂⠁⠢⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠤⠤⡀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠤⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠑⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡆⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⣀⣀⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⡖⠒⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣒⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣠
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⣀⠀⣀⡀⢀⣀⠀⣀⣀⠀⣀⡀⢠⣶⣶⣶⠀⠀⠀⠀⠀⣃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡆
⠀⠀⠀⢈⣉⠀⡉⡁⢈⣉⡁⣉⣉⢀⣉⡁⢸⣿⣿⣿⠀⡇⠀⡇⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠃
⠀⠀⠀⢨⢨⠀⣍⡅⢠⣩⡄⣨⣥⠀⡍⡄⢸⣷⣶⣾⢀⠀⠀⡇⠀⠀⠀⣒⣒⡆⠀⣖⣒⡂⠀⢰⣒⣲⠀⢰⣒⣒⠀⠀⣒⣒⡆⠀⡇⠀⠀⠀⠂
⠀⠀⠀⠤⠠⠀⠄⠄⠠⠠⠄⠤⠤⠠⠄⠄⢸⣗⣒⣺⠸⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⠀⢰
⠀⠀⠀⠐⠰⠀⠖⠆⠰⠶⠂⠲⠶⠐⠂⠆⠸⠗⠒⠺⣄⠀⠀⡇⠀⠀⣗⣒⣚⡇⠀⠀⣼⠩⠩⢳⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸
⡔⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣑⣄⣀⣀⣀⣄⣀⣀⣇⣀⠀⠁⠀⠀⠁⠀⠀⠹⡆⠀⠟⠀⠀⡇⠐⡁⢸⢐⡉⢹⢸⡉⢱
⠑⣤⠤⠤⠤⠤⣤⠤⠤⠤⢤⣤⠤⢼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⣀⣀⣀⣀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠁⠁⠀⠁⠁⠀⠁⠁
⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⢈⠈⡇⣈⢈⡇⣈⢈⡇⢸⠀⠀⠀⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠋⠀⠀⢀⣇⣠⣀⠀⠀⡇
⣴⣿⣷⣶⣶⣶⣿⣶⣶⣶⣾⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡔⡾⠻⡗⢦⠀⠀⠀⠀⣠⠞⠳⣶⠀⠀⠀⠀⠀⢠⢞⠟⠓⣄⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀⠀⢀⣠⠚⠉⠓⠤⣄
⠀⠀⡞⠉⡟⠉⡟⠉⡇⠀⠀⠞⣡⣾⣷⣌⠳⠀⠀⠀⠀⢸⡈⠀⢀⡝⠀⠀⢾⣏⣿⣹⣏⣿⡇⠀⠠⣤⡻⣿⣿⣿⡿⠀⠀⢻⣀⣀⣀⣀⣀⡼
⠀⠀⠹⣏⣯⢉⣏⡽⠁⠀⠀⢸⣿⠉⠉⣿⡇⠀⠀⢠⣾⡟⠉⠉⠉⠀⠀⠀⢨⠿⠿⠿⠿⠋⠀⠀⠀⠙⠻⠷⡿⠛⠁⠀⠀⠀⠀⠸⣿⡷
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⢠⠀⢀⣀⠀⠠⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢰⣝⢿⣿⢟⣵⡄⠀⠀⠰⠋⠭⠭⠹⠆⠀⠀⢀⣾⠫⣗⢪⢻⡆⠀⠀⠘⠀⠈⣟⠀⠰⠁⠀⠀⣠⣉⠙⢷⣄⠀⠀⠀⠀⣠⣄⠴⠚⠛⠁
⠀⠀⠸⣫⣶⣶⣮⡻⠅⠀⠀⣿⡦⡉⢉⢴⣿⠀⠀⠈⢿⣑⡭⣬⣾⠇⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⢀⡉⢻⡄⢹⡆⠀⠀⠀⠙⠋⠳⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠞⠛⠛⠳⠉⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠐⠋⠉⠙⠀⠀⠀⠀⠙⠁⠀⠋⠀⠋⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠌⡀⣐⠀⠀⠀⠀⠀⠀⠀⠁⣷⠉⠀⠀⠀⠀⠀⠀⣴⢂⢶⡄⠀⠀⠀⣀⡀⢀⣼⣇⣀⡀⠀⠀⢸⣿⣿⣷⡆⣿⡆⠀⠀⣀⣠⢿⣆⣀⡀
⠀⠀⠀⠁⠸⣿⣷⠂⠀⠀⠀⠀⣦⣿⣿⣶⠀⠀⠀⠀⢠⣦⣙⣰⡆⠀⠀⠀⣿⡇⣿⣿⣿⣿⠃⠀⠀⠿⢿⣿⡿⠇⠿⠇⠀⠈⠻⣷⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠉⠙⠷⠄⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠈⠿⣿⡿⠃⠀⠀⠀⠛⠃⠛⠛⠛⠛⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠰⠟⠛⠻⠇

⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢀⣴⣶⣶⡆⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⢰⣶⣤⣤⣄⡀⠀⢠⣶⣦⣠⣶⣆⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⣶⣰⣿⣾⡇⠀⢢⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⣿⠟⣩⡛⣿⣷⠀⠀⡖⠚⠚⣚⠒⣾⡏⠀⠀⣽⣯⣬⣿⡅⠀⡀⠀⠀⣿⣿⠈⠙⣿⡇
⠀⠀⠉⠈⠻⣿⡇⠀⠂⠀⠀⢠⣾⡇⠸⡿⠇⠀⠀⢸⣿⣎⣛⣣⣿⣿⠀⠀⣧⣾⣷⣤⣦⡟⠃⠀⠀⣿⣿⣿⣿⡇⢿⡇⠀⠀⠻⣿⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⣤⠤⠤⠤⠤⠤⡄⠀⠀⣤⠤⠤⠤⠤⣤⠀⠀⠀⢠⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠀⠀⠀⠀⡤⠤⠤⢤⣄
⠀⠀⣿⠀⠰⠦⠀⠀⡇⠀⠀⣿⠀⠰⠆⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⣶⢸⣿⣷⣶⣶⣶⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⡇⣉⣉⣨⠙⡆
⠀⠀⠻⠶⢶⣶⠶⠶⠇⠀⠀⣙⣶⣶⣶⣶⣏⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢹⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⡇⣒⣒⣒⠀⡇
⠀⠀⠀⠰⠾⠿⠶⠀⠀⠀⠐⠿⠿⠷⠾⠿⠿⠂⠀⠀⠘⠿⠟⠿⠟⠀⠀⠀⠘⠾⠿⠿⠿⠿⠟⠀⠀⠘⠿⠿⠿⠿⠃⠀⠀⠀⠳⠶⠶⠶⠶⠃
⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⣠⣮⣀⣀⣀⣧⡄⠀⠀⠈⣧⣤⣤⣤⣤⠄⠀⠀⢀⣀⣀⢻⣽⠇⠀⠀⠀⠀⣠⣾⠅⣸⠂⠀⠀⢠⠞⠋⠋⠲⡄⠀⠀⠀⢰⠁⠀⠈⡃
⠀⠀⣿⡿⢿⣿⡿⣿⡇⠀⠀⠀⢹⣿⡿⠿⠟⠀⠀⠐⣾⠟⢻⣷⠀⠀⠀⠀⢠⠞⣟⣡⣾⠇⠀⠀⠀⢿⡀⠀⠀⢀⡟⠀⠀⠀⠀⢣⡀⡰⠃
⠀⠀⠉⢣⣘⣓⣠⠟⠁⠀⠀⠀⠠⡶⠠⣶⠀⠀⠀⠈⠻⡷⢿⠛⠀⠀⠀⠀⠸⢤⣬⠟⠁⠀⠀⠀⠀⠈⠓⠴⠶⠚⠁⠀⠀⠀⠀⠀⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⡏⢉⣉⣉⠉⣿⣿⡿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠟⢁⣄⠉⣁⣼⣿⣿⣆⣈⢁⣤⡈⠻⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣅⠰⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⠂⣼⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠺⠟⠀⣾⣿⡿⠋⣠⣶⣦⣄⠙⢿⣿⣷⡀⠛⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⣿⣿⠁⣼⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣟⢙⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠇⡆⡔⣦⡔⡆⡖⡰⡄⡖⡖⡆⡖⡖⡆⣤⠖⣤⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠙⠃⠁⠉⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠛

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣸⡀⠀⢀⣀⡀⣾⣿⡇⠀⠀⣵⣶⣄⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢦⣿⠄⠀⠘⢿⣷⣿⣿⣥⣶⡆⠙⠻⣿⠅⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⠰
⠀⠀⠀⠐⣾⣧⠄⠀⠻⢿⣿⢿⣿⣿⣍⠀⣤⣼⣿⣿⣀⣤⣠⡌⢻⣿⠀⠀⠀⠀⠀⠀⠌⠀⠀⠄⠀⢬⠔⠂
⠀⠀⠀⠀⠈⠉⢀⣴⠀⠈⠁⠈⠛⠉⣉⣠⣀⣬⠀⠈⠛⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⡀⠔⠈⢠⡼⠀⠀⡠
⠀⠀⠀⣿⣆⢠⣿⡟⠀⠀⠀⢀⣰⣾⣿⣿⡿⠇⢀⣤⣾⣇⠀⢰⣷⡄⠀⠀⠀⢀⠀⢡⠂⠘⢦⡀⣸⠧⠖⠊⠀⡴⠈⠁
⠀⢀⣀⣹⣿⣿⣿⣴⣶⡤⠀⠺⠿⢿⠿⠟⠋⣰⣿⣿⣿⣿⣧⠘⢿⣿⠀⠀⠀⠀⠁⠺⢄⠀⡀⠹⡏⠀⣀⣜⣁⣀⣀⡀
⠀⠀⠉⠉⠛⠻⣿⡉⠉⠀⢰⣶⣦⣠⣴⡆⠀⠘⠛⠿⣿⣿⠟⠠⡄⠀⠀⠀⠀⠀⠀⠐⠲⠛⠳⣼⣿⠟⠡⠀⠈
⠀⠀⠀⠀⢀⣀⡈⠛⠀⠀⢈⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⡀⠀⣿⣏⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⢠⣾⣿⣿⣷⣆⠐⠿⢿⣿⣿⠟⠛⠉⠀⠀⠀⣿⡟⠈⣿⣗⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠛⠿⠿⠟⠂⠀⠸⠿⠃⣀⠀⠀⠀⠀⡀⢛⣁⠀⠹⠿⠹⠍⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷
⠀⠀⠀⣠⣾⡷⣀⣤⣤⠀⠀⠀⠀⢠⣿⣿⣷⠀⣼⣿⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠈⠁⠀⠙⠋⠙⠿⠛⠛⠀⠘⢿⣿⠟⠀⠻⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠙⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣴⡆⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠋⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠨⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣤⣤⣤⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠉⠉⢹⣿⣿⣟⠉⠉⠉⢹⣿⣿⡟⠉⠉⠉⢹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣀⣀⣸⣿⣿⣿⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣸⣿⠀⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣇⣀⣀⣀⣸⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣈⢁⠈⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠎⠘⠓⠆⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶
⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉
⠀⠀⠀⠘⣷⣾⢻⢘⡢⡾⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⡄⣄⢤⠔⠂⡤⠰⡄
⠀⠀⠀⠀⠘⠃⠈⠈⠁⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣻⣮⢻⣽⡟⣟⣸⣿⣟⣽⣧⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠛⠛⠻⠛⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⢐⡞⠀⡀
⠀⢸⡒⡆⢰⣄⠰⡔⡇⢙⢵⢴⡆⢠⡆⠀⠀⠀⠀⠀⠀⠸⣷⡿⠑⠂⠀⠀⠀⠀⠀⠀⠀⣄⡄⡄⡀⣠⢤⡀⡄⠲⢀⣤⣰⡀
⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠝⢓⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠃⠉⠉⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣰⢶⠐⡠⢲⠂⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠁⠁⠈⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠉⠐⠢⠒⠊⠉⠉⠁⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⢸⡀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⢀⡠⠞⠁⠒⠒⡲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁
⠀⠀⠀⠀⠀⠀⡏⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⣀⢀⡠⠊⠉⠐⠒⠉⠑⠤⢀⣀⣀⡀⠤⠊
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⣶⠒⠲⠶⣦
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣇⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⣷
⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣸⣄⣼⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀
⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢻⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠸⡇⠀⠀⢀⣠⡴⠖⠋⠁⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡧⠶⠛⠉⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⢸
⣿⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⢲⠒⠒⠒⠂⠐⠒⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⢻⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⡀⣀⢀⣀⣸⠀⠀⠀⠀⠀⣸⢀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⠻⠿⣲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠃⠀⠃⢸⡶⡇
⠀⠀⠀⢀⣠⠤⠤⠤⠤⠧⠤⣤⣀⣀⣾⣈⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠤
⠀⠀⡞⠉⡇⠀⣴⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣈⠉⢹⡟⠉⠉⠉⠉⠁⠒⠒⠒⠶⡴⠽⠋⠰⠚⠉⢉⣉⣉⣉⣉⣲⣤⡀
⠀⠀⡷⣾⣧⡀⢻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠇⡇⠀⡄⠀⠀⠀⠀⣤⠱⠞⡡⠄⠐⠊⠉⠓⡒⠋⠉⠙⠛⠳⠈⠉
⠀⢰⠀⠛⢠⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⢀⠃⠀⣌⣉⡉⠉⢉⣯⠄⠀⢡⠀⠀⠀⢀⡴⠃
⠴⣇⡀⢀⠾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⠀⡇⠸⠀⢰⠀⠀⠀⠀⠠⢿⣇⠀⠸⡀⠀⠀⡏⠐
⠀⠀⠈⢋⢀⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡆⢸⠁⢸⠀⠀⠀⠀⠀⠀⠉⠉⠸⢳⣴⠃⢀⠔⠓⣤⠤⣄
⠀⠀⠀⢸⣿⢧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠃⡎⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⡆⢸⡀⠀⣸⣉⣈⣇⣀⣀⠠⠤⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠘⠉⠁⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢰⠃⠀⡇⠀⠀⠀⠀⠀⣀⣀⣰⡏⢩⡙⠇⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡸⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⠀⠀⡇⠀⠀⠀⡴⠋⠁⠀⠀⠱⡈⢉⣠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⣗⡖⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠀⢰⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠈⠉⠀⠱⡀⠀⠙⢏⠒⠠⠤⢤⣀⣀⣀⣀⠤⠤⠐⠉
⠀⠀⠀⠀⣿⣿⠀⠻⠛⠛⠛⠛⠛⠛⠿⠿⠿⠇⢻⠀⢸⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠘⠙⢻⠉⠉⠉⠉⠉⠙⠻⠛⠯⠟⣟⣋⠀⢸⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠞⠲⡄⠈⢆
⢰⢖⠒⠒⢞⢯⡙⢃⡲⣱⢆⡶⡰⢆⠶⣶⣶⡛⢝⠷⣾⠀⠶⠐⠷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠤⢛⣛⠉
⠈⠲⣷⣄⠀⠑⠿⠖⠛⠚⠛⠛⠛⠛⣻⠟⠇⠈⠓⢵⣿⣶⣶⣖⣉⡥⠷⡆⠀⠀⠀⠀⠀⠀⣠⡀⡿⠀⠸⣍⣁⢙⠆
⠀⠀⠈⠻⣍⣉⣉⣉⣉⣁⣀⣀⣐⠒⢺⠦⣸⠆⠀⠈⢻⢻⠛⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⢇⣯⠇⠀⣾⠭⠉⠈⢹⡆
⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⢠⠚⠛⠢⡬⠂⠀⠀⢸⢸⠈⠁⠀⠀⠀⠁⠀⢀⠖⠒⠊⡇⠀⢏⢀⣴⢣⡤⡄⠀⠀⠁
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠇⠀⠀⠀⠘⢸⠀⠀⠁⠀⠀⡖⠒⢡⠀⠀⠐⠗⠛⣜⢷⡟⠉⠳⣸⣳⣀⡶⢦
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⡀⠈⠀⠀⠀⠈⢠⡦⢰⠎⡀⠀⠀⠀⠀⠈⠛⠀⢰⡤⣈⡇⠀⢸⠃
⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣅⣥⠴⠒⠊⠉⠉⣱⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡘⣧⡀⢈⠇
⠀⠸⣟⢕⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠈⠀⠀⠉⠉⠙⠛⢛⠒⠒⠒⠚⠋⠛⠁⠀⠈⠉⢱
⠀⠀⠈⠓⢝⠯⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠠⢤⣤⠶⠮⣤⡤⠄⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠑⢌⢢⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠀⠀⠀⠒⢿⡷⡲⢶⠒⢺⠏⠓⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢴⣒⣊⣉⣉⣻⣗⡺⠿⡭⠥⠖⠤⠤⠈⢹⡍⣚⡱⢏⣀⣄⣐⣤⠤⠖⣶⠋⣉⣉⣐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠽⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡀⢸⡠⠀⠀⠠⠒⠀⠀⠠⠀⠀⠀⣀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢾⠠⠀⠀⡀⠇⠐⠀⢈⣁⠑⠲⢅⠐⠀⢠⠀⡦⣄⢀⠄⢀⠌⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⢘⡠⠄⠈⠁⡔⠆⠾⠚⠛⠛⠀⠈⠁⠀⢀⠀⣤⠁⡤⠐⠉⠏⠀⠀⠷⠠⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡒⠀⠀⠀⠀⢀⣤⠸⠏⢁⡄⣀⠀⠀⠀⠀⢴⠀⠁⢨⡀⠠⠴⠁⠈⠀⡄⠐⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠄⠀⠀⢡⠌⡁⠰⠶⠿⠓⠙⢁⠄⠆⠀⢀⡍⠀⠀⠀⠀⠈⠀⠆⡀⠥⠄⠐⠁⠒⠐⠁⠀⠀⠀⠊⠠⡂
⠀⠀⠀⢠⠀⢃⠠⠀⠒⠰⠁⠐⡖⢰⠘⡁⠀⡇⢸⠀⠄⠀⠀⠨⠁⠀⢠⠜⢀⠙⠀⠨⢐⠀⡠⠀⢀⠉⢈⠑⡤⠄⠀⠠
⠀⠀⠐⠁⠀⠘⠄⠠⠀⠃⠠⠼⠁⣎⠀⠈⢐⠃⠸⠀⠀⢀⠀⡂⠀⠀⣀⢀⠡⢂⠐⢀⠠⢱⠢⡑⠂⠖⢙⠐⠆
⠀⠀⠀⠀⠀⢂⠁⡎⠐⠉⠒⡶⢠⠄⠀⠤⣭⠀⡄⢀⠀⠘⠁⠀⠀⠀⠀⠉⠙⠠⣘⢒⡆⡏⠑⠢⠀⠀⠀⠊⠤⠒
⠀⠀⠀⠐⠀⠀⣠⠅⡀⠀⠀⡇⠘⠀⠠⠄⠃⠀⠀⠊⠀⠀⠀⠀⠀⢠⠀⠐⢄⠀⠈⠺⠁⢁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⢠⡄
⠀⠀⠀⠠⠀⠀⠘⠒⠠⣤⣘⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡀⣀⡀⠦⠄⠘⠒⠂⢂⠖⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢊⠢
⠀⠀⠀⠀⠀⠐⠀⠐⠙⡀⢠⡀⠀⠀⠀⠀⠀⢸⠀⠀⠖⠐⠀⠀⠀⢂⣠⠔⠀⠀⠀⢀⡄⠊⠀⠑⠀⢄⡀⣀⡠⠴⠎⠅⠄
⠀⠀⠀⠀⠀⠀⠀⣄⣠⠁⠅⠀⠀⢀⠐⠀⠀⠘⠀⠀⠀⢐⡁⠜⠛⠈⣀⠀⠤⠐⣇⠀⠀⠀⠀⢀⠀⠀⢢⠀⠀⠐
⠀⠀⠀⠀⠀⠠⠀⠈⣘⡠⠔⠄⠀⠤⠔⠀⢀⠀⠀⡠⠛⡙⢄⠠⠶⢃⢷⠀⢀⡴⠃⠈⠒⠠⢀⠈⡄⢰⠆⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠠⠄⢚⢉⠉⠀⠀⠀⠀⠀⠀⠋⣀⡐⢀⠀⠀⢀⢀⡤⠀⠀⠈⠀⠠⠆⠀⠀⠀⠀⠠⣛⠁⡸⠀⠀⡴⠉⠀⠂
⠀⠀⠀⠀⠀⠈⠢⡤⠁⠀⠀⠀⠈⠊⠈⢁⡞⠀⢠⣾⣀⡠⠬⢀⠀⠉⠀⡠⠀⠀⠀⠀⠀⠁⡖⠁⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠿⡘⠃⠰⠂⢠⠄⠋⣴⠀⠃⢀⠓⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⢁⡅⠀⢀⠠⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢆⢳⡐⣀⢀⠰⡆⠄⣸⠀⠈⠃⠐⡃⣠⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠂⠀⠹⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡐⠨⣥⠖⠉⢂⠀⠑⠪⢍⠵⠁⡼⠓⠢⣅⣂⠠⠀⠀⢀⠟⠠⠆⠸⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡙⠒⠂⠕⠴⢤⠀⡀⠂⠀⡀⠀⠂⠀⠉⠐⠒⠋⢢⠀⠐⢉⠝⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠒⠁⠀⡂⠉⠀⢀⠀⠀⣀⠟⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠘⠀⠀⠀⠀⠐⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⡽⠟⢻⠛⢿⣍⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⣰⠟⠁⠀⢸⠀⠀⠙⢷⡀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣼⠃⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢻⡄⠀⠀⠀⢸⠀⠀⠀⠀⣼⠃⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠹⣆⠀⠀⢸⠀⠀⢠⡾⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣈⣳⣤⣸⣠⣴⣋⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣧⡇⢹⡏⣾⠍⢸⣽⠂⣷⣾⢸⡯⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠁⠈⠁⠉⠉⠈⠈⠁⠁⠉⠈⠉⠀⠉

⠀⠀⡖⠉⠙⢦⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠲⡄⠀⠀⠀⠀⠀⠀⡤⠤⠞⠙⠤⢦⡀⠀⠀⠀⢀⣀⠘⣆⡞⣀⡀
⠀⠈⢧⣀⣀⡜⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⣠⠏⢠⠞⠓⣆⠘⢤⠀⠀⠀⣀⡴⠛⢯⠋⢣⣀
⢠⠖⠒⠬⠴⠒⢢⡀⠀⠀⠀⠀⠳⣄⣀⣀⡴⣇⠀⠀⠀⠀⠀⠈⣦⠘⠦⠤⠋⢰⠋⠀⠀⠀⠉⣇⠶⡼⠰⢠⠏
⠘⠦⣤⣤⣤⡤⠔⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⠄⠀⠀⠀⠀⠙⠛⠢⡴⠚⠚⠀⠀⠀⠀⠐⠏⠓⠲⠒⠉⠆

⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡤⡄⢠⡄⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⢧⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠁⠈⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⢭⠇⠀⠀⢸⡇
⠀⢰⠖⠒⠲⡗⠒⠒⣦⠀⠀⠀⠀⠀⠀⠀⢶⠀⢸⠀⢸⡆⢸⣱⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⢀⡇⢄⢸⡇
⢠⠼⢦⠀⡴⠧⡄⢠⠿⡄⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢸⠁⠋⢸⡇
⠘⠓⠚⠀⠓⠒⠃⠘⠒⠃⠀⠀⠀⠀⠀⠀⠛⠀⠘⠀⠳⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚⠁

⠀⣠⡶⠒⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⡆
⡾⠷⣃⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣖⢸⢰⠄⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠐⡆⠀⠀⡇
⡇⢼⣏⢹⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣋⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠇⠰⠃⠀⠀⡇
⡇⠈⠛⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣹⣿⣿⣉⠉⠉⠀⠀⠀⠀⠀⠀⠼⠭⠭⠭⠭⠭⠭⠭⠭⠷

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸
⠀⠀⠄⣡⠆⠐⢄⠠⠀⠀⠀⠀⠄⡥⠂⣄⣀⡀⠀⠀⠠⢀⡴⠶⢦⡅⠄⠀⠀⠀⠠⢀⢔⠀⡢⡀⠄⠀⠀⠀⠰⢉⠞⠒⣷⣈⠂⠀⢸
⠀⠀⠐⡃⠀⠀⢀⠀⠂⠀⠀⠐⠀⡀⠀⢈⣿⠁⠀⠀⠂⢸⡁⠀⢀⡂⠐⠀⠀⠀⠂⢀⢆⡋⡠⡀⠐⠀⠀⠰⣈⢀⠀⠀⠀⡇⣁⠆⢸
⠀⠀⠀⠑⣀⣠⠃⠀⠀⠀⠀⠀⠀⠱⣀⠟⠉⠁⠀⠀⠀⠀⢩⣙⡙⠁⠀⠀⠀⠀⠀⠀⢃⣿⡘⠀⠀⠀⠀⠀⢠⡀⢂⣀⡜⣀⡆⠀⢸
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢈⠠⠀⠀⠠⠀⠀⠂⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⢄⢀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠌⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠃⠀⠀⠀⠀⠢⠄
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠊
⠀⠈⠪⡁⠀⠀⠀⢀⡀⠀⠸⠀⡄⠀⠀⡆⢀⠀⠀⠀⠀⠤⡐⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠠⡀
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⡈⡇⠈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠠⠂
⠀⠀⠀⠀⠀⢡⠀⠄⠀⠀⡀⢀⠀⠀⠈⣇⠀⠀⠀⡰⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⡁
⠀⠀⠀⠀⠈⠃⠠⡀⠀⠀⠈⠳⣄⠀⠀⣇⠀⢂⡜⠁⡀⠀⠀⠰⠆⠀⣀⠠⠀⠀⠄⠀⠀⠰⡉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠅⠀⠀⠂⠈⠑⣄⢻⢠⠞⠀⠀⢀⣀⣤⠐⠂⠁⠀⠀⠀⠀⢀⡀⠤⠀⠘⠂
⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠐⠂⠀⠤⠌⣿⣯⣷⣒⡋⠉⠀⠀⠁⠀⠀⠀⢠⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠢⡀⠈⠉⠉⠒⠲⢤⡀⠀⠀⠀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠑⡄⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠀⠳⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠐⡘⠀⠀⠀⢐⠀⠈⠒⠈⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠢⠄⠀⠀⠀⠀⡄⠩⡒⣂⠥⠀⠣⠄⠚⢃⠀⠀⣄⠀⠙⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⡇⡇
⣈⠔⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂⠉⣀⠠⠄⠒⠁⠀⠀⠙⠐⠒⠒⠁⠀⠀⠀⡝⠀⠀⠒⣊⡡⡣⠀⠀⠠⡀⠴
⡉⣦⠄⢻⠂⠀⢀⠔⣊⠩⠤⠤⠍⣑⠢⡀⠀⠀⠑⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠘⠓⠛⠋⠉⠁⠀⠀⠀⣵⠀⡦
⢡⠠⠄⡜⠀⠰⡡⡪⢒⠩⠥⠬⢅⠢⡑⠬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠋⠉⠉⠀⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢣⡠⠰
⣢⡴⠔⠀⠀⠀⠘⠔⡡⢊⠉⠉⡒⢝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢨⡇⢀⣋⣀⣘⠀⠀⠀⠀⠀⢠⡐⠊⣩⡞⠉⠀⠀⠀⣠
⠉⠀⠀⠀⠀⠀⠀⠀⠉⢡⠂⢲⠈⠁⠀⢀⠤⠠⠔⠒⠚⠉⠉⡆⠀⠈⠋⠀⠈⠀⠰⠄⢠⠄⠀⠀⠀⠀⠀⠀⠈⣏⢔⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⢰⠀⠀⢀⢀⠂⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠤⠐⠢⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠂⢖⠏⠫⠆⠀⠀⠀⢀⡠⠄
⡐⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠌⠂⠄⡌⠉⡄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠄⢒⡢⠉⢰⠊⠙⣞⠀⠀⠰⡄
⠈⠀⠀⢸⠄⠀⢠⡋⠉⠒⠘⠀⠀⠀⠀⠀⠀⠀⠚⠓⠊⠉⠉⢀⢀⠤⡖⡀⡰⠠⣀⠀⠀⠈⡄⠩⢐⡂⠁⠀⠦⠤⠘⠇⠀⠀⠇
⠀⢤⠉⠀⠁⠀⠀⠉⢀⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣁⣤⠰⡊⢢⠠⠘⠥⠀⠀⢡⠈⠒⠂⠈⣀⡠⠄⠒⠁⠀⠀⢃⠒⢀
⠂⠉⠛⠀⠀⠀⡔⠉⡍⠑⣤⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠱⡀⠴⠖⢙⡀⡥⢤⠀⠀⠀⠀⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢰⠀⠀⠃⠀⠏⠀⠀⣪⠓⠀⠁⠀⢾⣇⠀⠀⠀⠀⠑⢄⡜⠣⣱⠄⠀⠀⠀⠀⢀⠠⢐⡂⠀⢐⡂⠄⡀
⠤⠀⢠⡀⠀⠈⠑⠂⠤⠚⠀⠀⠀⣹⠀⠀⣠⠀⠸⡹⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⡔⡡⡪⠕⢐⣒⠒⠬⡑⢌⡢⠀⠀⠀⣀⡠
⠀⡤⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠁⠀⠀⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠔⡩⠔⣒⠨⢕⠬⠂⠀⠀⠀⡐⠁
⠐⠃⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⣀⣀⠤⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⡡⠤⡉⠒⠀⠀⠀⠀⠀⡤⠥⠈
⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡠⠴⠶⠛⠃⠀⠀⣀⡀⣀⡀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠃⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣒⣒⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⣤⠐⢒⢤⢄
⠤⠤⠄⠔⠀⠀⢠⢊⢔⡨⠐⠀⠐⠠⢅⠢⣑⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⢀⢇⢀⡕⢣⠆⡦⠴⠄⠀⠀⢠⠀⠄
⠂⠀⠀⠀⠀⠀⠈⠡⡡⢊⠥⠀⠠⢍⡢⠕⠀⠀⠀⠀⠀⠀⡀⠙⠻⡛⠹⢉⡙⠙⠀⠂⠀⠀⠀⢰⣀⣨⣁⡛⢰⠇⢀⡡⠀⠀⢸
⡀⣀⣀⠂⡄⠀⠀⠀⠀⠣⢊⠥⢍⠓⠃⠀⠀⠀⠀⠀⠀⠘⠢⠤⠴⠥⠤⠤⠁⠀⠀⠘⠁⠀⠀⠈⠧⣘⣸⠕⢣⡠⠊⠃⠀⠀⢸
⠇⢉⠉⠁⠐⡄⠀⠀⠀⠀⠘⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⢯
⠀⠘⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠉⠉⠀⠀⠀⣀⠠⡄⢒⣂⡲⡄⠀⠀⠓⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣰⢶⠀⠀⠀⠀⣀⡠⠤⠐⠒⢏⠏⠯⢇⠀⠀⠀⠀⠉⣡⠘⠀⠀⠀⣇⠁⠀⠀⠀⠸⣽
⠀⠀⠀⠀⠀⠀⡀⠈⠢⡤⢪⠃⠈⠀⠀⠀⢸⡀⠤⣐⠈⠉⠰⠈⠉⢶⠀⠀⠀⠰⠁⣼⠈⢻⠄⠀⢹⠀⠀⡞⠄⠀⣿⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠀⠀⠀⠀⠀⠸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢀⡖⠛⠓⠒⢦⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⣀⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⣀⣴⡆⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣴⣾⣿⣿⡇⣠⣴⣾⣿⣿⠂⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣟⠛⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⡏⠉⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣧⣤⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡟⣉⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⣧
⠀⠀⠀⣠⡶⣦⣀⣤⠶⠞⠛⠀⠀⠛⠳⢶⣤⣀⣴⢦⡀
⠀⠀⠸⣯⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣿⠂
⠀⠀⠀⣼⠃⠀⠀⠀⢀⣤⡶⠶⠶⢦⣤⡀⠀⠀⠀⠹⣧
⠀⠀⣸⠇⠀⠀⠀⣴⠟⠁⠀⢠⣤⣤⣬⣿⣆⠀⠀⠀⢹⡆⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠛⠛⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡆⠀⠀⠀⠛⠛⣷⠀⠀⠀⠀⢀⣤⢦⣄⠀⠀⠀⠀⠀⠀⣿
⠿⣤⣤⠀⠀⠀⠸⣇⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠀⠀⣤⣤⡿⠀⠀⠀⠀⢸⣇⣀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⣆⠀⠀⠀⠻⣦⡀⠀⢸⡇⠀⢀⣴⠏⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠐⠛⠉⠉⠙⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⡆⠀⠀⠀⠈⠙⠳⠾⠷⠞⠋⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿
⠀⠀⠰⣟⠁⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢈⣿⠆⠀⠀⠀⠀⠀⠈⣿⠶⠶⣾⡋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠻⠛⠉⠛⠳⠶⣤⠀⠀⣤⠶⠞⠋⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠁⠀⠀⠀⢻⣆⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠛⠛⠛⠛⠛⣿⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡄⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣴⠛⠉⢹⡏⠉⠙⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠈⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠷⠶⠾⠷⢶⡶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⢀⣠⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣾⣿⣥⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠟⣫⣴⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠻⣿⣿⣿⠛⣡⣾⣿⣿⡿⢋⣴⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⠉⠁⠚⠻⠿⠿⠏⠐⠛⢋⣡⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣿⡿⠃⣴⣿⣿⣿⣶⢂⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠹⠟⢀⣾⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⠏⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠺⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⠏⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢀⣶⣤⡈⠻⢿⣿⢸⣿⣿⣿⣿⣿⠟⠁⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣶⣤⡁⠙⠻⢿⡿⠟⢁⣴⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃⠟⢛⣀⣤⣦⣬⣭⣭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢴⣶⢰⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⢿⣟⠻⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠘⠓⠹⠇⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⣀⣤⠴⠛⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠶⣶⠶⠶⢶⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠋⠀⠀⠈⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⡉⠀⠀⡀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡏⠢⣀⢸⣿⣿⢴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⢙⡇⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣷⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⠀⢰⣿⣿⣦⠼⠛⢻⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿⣿⡤⠞⠋⠉⠀⠀⠀⢸⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠸⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠼⠶⢿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠻⣿⣿⣿⣿⣿⣷⠀⡚⢠⣤⠤⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⣘⣿⡿⠟⠉⡰⠛⠠⣁⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⢲⣷⣶⣿⣄⣀⣀⣈⣡⣴⣿⣿⣿⣿⣿⣽⣿⣿⡍⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠇⠘⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠂⠀⠀⠁⡄⠀⠀⠀⠁⠀⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⡀⠀⠂⠀⠀⠀⢀⠁⠀⠨⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⠀⡀⡋⠀⠀⣀⡄⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠠⠂⠀⠀⡀⢀⠀⠁⠐⠀⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠂⠰⠄⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠈⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠿⠿⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⣿⠉⠉⠉⣿⠀⠀⢀⣤⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢀⣴⠟⠙⢿⡶⠿⠛⠀⠀⠀⠛⠿⣶⡿⠋⠻⣦⡀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣴⠿⠛⠛⠛⠿⣦⡀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣾⡟⠛⠛⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠛⠛⢻⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠙⠛⠻⣷⡀⠀⠀⢻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣿⠛⠛⠃⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⠀⠉⠛⠷⠶⠿⠛⠁⠀⠀⠀⢾⣇⡀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠟⠙⠛⣷⠀⠀⠀⣿⠛⠉⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠐⠿⢷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⢶⣶⣶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇

⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠚⣩⡤⠶⠦⣬⡙⠂⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⢀⡀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠁⠴⢚⠲⠄⠁⠀⠀⠀⠀⠀⢀⠂⠀⠋⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⣀⣠⣿⡇⠀⠀⠀⢀⠀⠀⠤⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠽⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠼⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠽⠿⠿⠀⠒⠐⠃⠐⠂⠿⠿⠿


⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣒⣒⠴⠶⣂⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⣲⠁⢈⠆⢘⣒⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣍⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀⡢
⠀⠀⠀⠼⠷⠤⢤⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⢸⣿⣟⣉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠪⠭⣕
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠿⠛⠛⠃⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⣶⣤⠚⣿⠳⣴⣶⠀⠀⠀⠀⣀⣤⣶⣶⣄⣀⠀⣤⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⣶⠖⣿⣿⡿⢶⡶⠀⠀⠀⠘⠿⠿⢻⠟⠿⠟⠈⠛⠛⢻⡟⠛⠛⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠸⠛⣿⣧⣠⣄⣀
⠀⠀⠀⠀⢠⣤⣭⣄⡄⡀⠀⠀⠀⠀⠀⢀⣐⢴⠀⠀⠀⠀⠀⣀⣲⠀⠀⠀⠀⠀⢸⣦⣍⣉⣵⣿⠀⠀⠀⠀⠀⠀⢸⡟⠿⠿⢿⣿
⠀⠀⠀⠄⢤⢤⡤⡤⡌⠄⠀⠀⠀⠀⠀⠀⠀⡭⠀⠀⠀⠀⠀⠁⠭⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⡩⡀⠀⠀⠀⠀⠀⠾⡷⠤⠤⢬⣷⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⡟⠙⢂⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣙⢒⠂⣾⣿⠈⢳⠀⠀⠀⠀⠀⣖⢂⣐⠁⢤⠤⠐⢂⡁⠇⠀⠀⠀⠀⢸⠐⠩⠃⡇
⠀⠀⢀⣴⣆⣿⣿⣿⣿⣴⣦⠀⠀⠀⠀⠀⠀⠲⣒⣆⢇⠀⣿⡟⠀⠀⠀⠀⠀⢄⠀⡶⠔⠒⠀⢀⠁⡦⠆⠀⠀⠀⠀⣸⢖⠤⡖⠇
⠀⠀⠀⠙⠁⠈⠙⠋⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠈⠒⠚
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠌⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉⠉⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢣⢰⠆⠰⠆⠰⡆⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⣀⡀⠀⠀⢀⡠⢤⠀⠀⠀⣀⡀⠀⠀⠀⣀⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⣅⣀⣀⣀⠄⠂⠁⠀⠙⣦⠔⠊⠀⠈⡢⠔⠉⠀⠀⢱⠄⠊⠁⠈⢢⠤⠊⠁⠀⠀⣈⠶
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠠⠤⠠⣠⡔⠊⠀⠀⠀⣠⠔⠊⠀⠀⢀⡔⠈⠀⠀⢀⡄⠊⠀⠀⠀⡠⡖⠁⠀⠀⠀⡠⠊⠄⢘
⠀⠀⠀⠀⢠⠊⠉⡀⠀⠀⠀⣌⠀⠀⠀⠀⠀⣀⣠⠜⠀⠀⠀⣠⠎⠀⠙⣄⠀⣠⠞⠁⠱⡀⠀⡴⠁⠘⢆⠀⡴⠁⠘⢄⠀⠠⠊⠀⠘⠄⢀⠄⠊⠀⠘⠀⢸
⠀⠀⠀⢠⠃⢰⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠘⠚⠁⠀⠀⠀⠘⠚⠒⠒⠒⠚⠛⠒⠒⠒⠚⠛⠓⠒⠒⠒⠚⠁⡘⠈⠁⠀⠀⢸
⠀⠀⠀⠘⠀⢸⢨⠉⠉⠉⠉⠉⠉⠁⠀⠀⢹⠀⢀⣀⣠⠄⠒⠒⠂⠄⡀⠀⠀⢈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⢉⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⠀⡗⠀⢸⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠋⠉⠀⠀⠉⠐⠠⡀⠀⠀⠠⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠂⠰⠀⠤⠃
⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠐⡌⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⠀⠀⢁
⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠸⠀⠀⠀⡌⢠⠞⠃⢰⠁⠰⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⣤⠉⠅⡄⢸
⠀⠀⠀⡧⠀⢸⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⠤⠀⠒⠀⠠⣀⠀⠀⠀⠀⢡⠀⡤⠇⠤⠠⠁⠸⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠃⢀⠆⠀⠀⢆⡀⠲⠖⢁⠆
⠀⡤⠐⠃⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠆⠓⠲⠒⠲⡇⢸⠂⠀⢸⠀⢘⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⢠⠋⠈⠉⠁
⢸⠇⠀⠀⠀⢸⠀⠀⠀⠀⢠⠁⠀⠀⡜⠀⠀⡠⡀⠀⢀⠤⡀⠀⢳⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠸⣆⣀⣀⣀⣸⣀⣀⣀⣀⣸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢀⡤⠒⠒⠣⠠⠓⠒⠚⠄⠜⠃⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠜⠀⠀⠈⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣀⡀⠔⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡔⢄⡠⠁⠀⠀⠀⠀⢀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⢀⣀⠄⠙⠀⠀⠀⠁⠀⠀⢃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⠊⠀⠀⠀⢸⠀⠀⠐⠀⠀⠐⠀⠐⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⠓⠂⠀⠀⠀⠀⢀⠊
⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⡀⠀⠀⠀⠀⡔⠁
⠀⠈⠩⡓⠒⠤⠄⣀⠀⠀⠀⢀⡇⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⢀⠌⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⣀⠠⡄
⠀⠀⠀⠈⠢⡀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢺⠀⠃⠀⠀⠀⠀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠩⠈⠉⠁⠀⠀⠘⠉⠉⢁⠔
⠀⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠑⢾⠀⠀⠀⠀⢀⡾⠥⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⢤⡂⠀⠁⠀⠀⠑⢤⡚⠀⠀⠀⢸⠀⢀⠀⣠⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡤⠴⠄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠐⠛⠲⣄⠀⢸⡀⢈⡴⠃⠀⠄⠀⠀⠀⠉⣐⡤⠖⠚⠁⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠀⠀⠈⠀⠀⠈⢷⣸⣇⣞⠁⠀⢀⣠⡤⠶⣎⠉⠀⠄⠀⠀⠀⢀⡀⠤⠐⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠒⠒⠚⠒⠂⠒⠀⣽⡿⠶⣿⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠐⣄⠀⠁⠈⠉⠑⠒⠦⣀⠀⠀⠀⠀⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠈⢆⡀⠀⡀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢣⢰⠀⠀⠘⢄⠔⠉⠐⠤⠐⠈⠁⠈⠁⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣤⣿⣿⣦⣤⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠉⠀⠀⠈⠙⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⢀⣤⣤⣄⠙⣿⣿⣿⡄⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡏⣤⣄⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⡿⢠⣿⣿⣿⠃⣴⣶⣿⣿⣿⣿⢃⣩⣍⡘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⡀⠀⠘⢛⣋⣴⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣿⣧⠙⠻⠟⢃⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠛⠻⣿⣿⠿⠛⣋⣥⣦⣙⣡⣾⣿⣿⣿⣿⣿⡟⢰⣿⣿⡄⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢃⣿⣿⣿⣷⠸⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣤⣤⣤⣤⣤⣄⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣦⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢀⣭⣭⣭⣭⣭⣭⣭⣭⣅⢸⣿⣿⠿⢂⣹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠸⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠟⠘⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠙⠛⠋⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠄⠲⠰⠀⣇
⠀⠀⠀⠀⠀⠀⣿⣛⣛⣛⣛⣛⣛⣛⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⢩⣍⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⢀⡤⢠⠤⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⣤⣤⡤⠤⠿⠀⠀⣴⣷⡆⠀⠀⠀⡠⠤⡀⠀⠀⣿⠀⠀⠘⠢⠜⠠⠊⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠈⠉⠁⢠⢤⡀⠓⠔⠃⠀⠀⣛⣒⠲⢶⡶⡶⠲⠲⠶⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢀⣀⠀⣀⠀⢀⡀⠈⠋⠀⣀⣀⡀⠀⢘⢱⡮⣧⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠈⠉⠈⠉⠉⠀⠁⠀⣴⡛⢿⣈⡿⢻⡎⠓⠒⠁⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⣤⣤⣤⣤⡼⣿⡿⣿⢭⣷⣿⣿⣦⣤⣤⣼⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠾⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣤⣤⣤⣼⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠆⠀⠀⠰⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠄⠀⠀⠴⠶