Inquire Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠖⠒⠒⠚⠛⠛⠒⠒⠒⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢋⠉⣤⡄⣴⡄⠾⠆⠺⠇⠻⠇⠺⠇⠾⠆⢴⡆⣠⡄⢉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⣠⠖⢋⣁⢰⡦⠙⢃⡨⠥⠐⠒⠂⠈⠉⠉⠉⠉⠉⠉⠀⠒⠒⠠⠭⣁⡛⠃⣦⠀⣈⠓⢦⣀
⠀⠀⠀⢀⡴⠋⠁⣴⠜⢛⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢌⠛⢴⡦⠉⠳⣄
⠀⠀⣠⠞⣀⡸⠟⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠿⣀⡈⢧⡀
⠀⣰⠃⣠⡉⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⣣⡀⢳⡀
⢠⠇⣠⡍⢡⠃⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢡⠉⣡⡀⢷
⣼⠀⣬⡁⡆⢸⣟⣛⠛⠃⠀⣿⣦⠀⣿⠀⣀⠐⠛⣷⡀⢸⡇⠀⠈⡇⠀⣿⠀⢸⡟⠛⢻⡄⠀⠹⣧⣠⠾⠃⠀⡇⢩⣁⢸
⣿⠀⣭⡀⡇⢨⣟⠙⠀⠀⠀⣷⠙⣷⣿⠀⣿⡀⣠⣼⠁⠘⣅⠀⢘⡇⠀⣿⠀⢸⡿⠛⣿⠁⠀⠀⠘⣿⠁⠀⠀⡀⣨⣅⢸
⢸⡀⣩⡄⢂⠘⠛⠛⠛⠂⠈⠛⠀⠈⠛⠀⠈⠛⠛⠿⠀⠀⠙⠓⠛⠁⠀⠛⠀⠘⠃⠀⠐⠃⠀⠀⠈⠛⠀⠀⢀⠃⣨⡁⢸
⠈⢧⠈⣥⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣤⡍⢁⡏
⠀⠘⢧⠉⣴⡄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣴⡌⢡⡞
⠀⠀⠈⠳⣄⠸⠗⣈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢋⡐⠶⢂⡴⠋
⠀⠀⠀⠀⠈⠳⣄⠛⢡⣦⢈⡑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⣀⢠⣦⠙⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡘⠋⢶⡆⣠⡈⢁⠒⠐⠂⠀⠤⠤⠠⠤⠄⠒⠐⢂⠉⣡⡀⣶⠌⠛⣁⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣍⣁⡛⠃⠿⠇⠾⠆⠾⠆⠾⠂⠻⠇⠛⣃⣉⣥⠴⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣓⣒⣒⣒⣒⣚⣛⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀
⠀⢰⣿⣿⣿⣿⢟⣽⣾⣿⣿⣿⣿⣿⣷⣯⡻⣿⣿⣿⣿⡇⠀⠀⢠⠔⠋⠁⠀⠀⠀⠀⠈⠙⠢⡀
⠀⢸⣿⣿⣿⢣⡿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⡜⣿⣿⣿⡇⠀⢰⠃⣀⡀⡀⡀⢀⢀⣀⣀⠀⣀⠘⡆
⠀⢸⣿⣿⣿⢸⣇⣧⣭⡘⢨⣘⣿⣒⣄⣇⣿⡇⣿⣿⣿⡇⠀⢿⠠⠯⠿⢿⣽⠻⠼⠿⠿⠧⠷⠀⡇
⠀⢸⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⣿⣿⡇⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⢸⣿⣿⣿⣿⣿⣮⣝⣻⣿⠿⣿⣟⡿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠙⠲⠤⢤⣀⣀⡤⢄⡀⠻⣄
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠠⠀⠀⠀⢀⣀⠠⠠⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⢀⡤⡄⠂⠀⠁⠐⠀⠀⠁⠠⠊⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠀⢁⠀⠠⠀⠈⡂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠊⠈⡀⠀⢀⡀⠀⠔⠂⠔⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠑⠄⠄⠀⠀⠠⠠⠔⠁⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⡀⠀⠀⠀⠀⠈⠀⢐⠀⡀⡐⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢠⣶⠂⠀⣠⣶⡀⠀⠀⠁⠀⠀⣼⣦⡀⢠⣾⣿⡄⠀⡴⠀⠰⡆⠀⠂⠔⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠱⠆⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣄⣀⡀⠁⠀⣰⣿⣿⣿⠿⣿⡟⠀⠀⠐⠀⠀⠀⢴⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠋⢀⣾⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠉⠉⠉⠹⠀⠀⠀⠀⣾⣿⠿⠟⠛⠋⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠀⠠⠤⠀⠀⠤⢀⠀⠀⠜⠉⠀⠠⠐⠀⠁⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢄⠡⠈⠂⠐⠀⠀⠈⠀⠀⢐⡀⢀⣀⠀⠀⡉⠀⢉⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣥⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡔⠀⠀⠀⠀⠀⠀⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⣢⣴⣿⠷⠀⠀⠀⠀⠀⠀⠂⢀⢀⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠂⠀⠁⠀⠀⠀⠀⠈⠘⠋⠛⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣿⣻⣿⣟⢯⠿⢻⢛⢙⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

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

⠀⠀⠀⡆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⡖⠂⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲
⠀⠀⠈⡏⠉⡍⢁⠀⠀⢤⠀⠀⠀⠀⠀⣶⠾⠰⠆⡇⠶⠰⠰⢲⡆⠀⠀⠀⠀⠀⠈⡏⢉⠍⢅⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⡠⠀⠸⣀
⠀⠀⠀⡇⠸⣶⡶⠂⠀⠀⡀⠀⠀⠀⠀⣿⠘⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡇⠸⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣀⣀⣀⡇
⠀⠀⢠⣧⣤⣤⣤⡄⢾⡿⡧⠀⠀⠀⠀⠿⠚⠛⠒⠛⠓⠚⠛⠺⠇⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢰⠏⠁⠉⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡇⡉⠈⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⡄⠉⢢⡀
⠀⠀⠀⠀⠀⣸⣦⣄⣤⠟⠀⠀⠀⠀⠀⣏⠀⠀⢠⠦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⣶⡇⣆⣀⡇⠀⠀⠀⠀⠀⠀⢼⠐⠳⠌⠁⠻⠇⡇
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠈⠀⠒⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣄⠺⠆⠸⠗⣠⠃
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣠⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣦⣤⢛⠁
⠀⠀⠀⢠⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⡋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠐⠢⠬⢿⣿⠧⠄⠆
⠀⠀⠠⡜⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣽⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⢡⡉



⠀⠀⠀⢀⣔⠉⠟⠟⣑⡄⠀⠀⠀⠀⠀⠀⡀⠀⡭⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠉⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⠀⠁⠉⣄⠀⠈⠦⣐⣂⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣁⣀⣀⡀⢠⣤⣴⡀⠀⠀⠀⠀⠀⠀⠚⠀⠈⣄⢀⠨⠄⡀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠂
⠀⠀⠈⠻⠿⠛⠀⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡴⠖⠛⣋⣽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠯⢭⡉⠙⠳⠤⠞⠁⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⢀⡞⣁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠧⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠞⢀⠀⠀⠐⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⢷⠀⠀⣷⠈⠛⠦⣽⣟⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢀⣀⠌⠉⠛⠲⠦⣤⣀⡀⠹⣏⠙⠛⠲⣶⠤⣤⣈⣛⣦⣄⠉⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣩⠖⠚⠓⠶⣤⡀⠀⠀⠈⠉⠉⠁⣀⠀⠹⡄⠀⠀⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠙⣦⠀⢀⣤⠖⠒⠛⢧⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⡾⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⠀⠀⠀⠘⡇⠀⣹⠦⠤⡄
⠀⠀⠀⠀⢠⡟⢁⣀⣀⣀⠙⠻⣵⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢉⠟⠒⠳⡄
⠀⠀⠀⠀⠈⣇⠀⠀⠙⠮⠿⡄⠙⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡀⢠⡇⢠⣤⣄⠀⠀⢸⡇⠀⠈⢷⣉⠛⣧
⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣯⣿⡿⠣⣷⣾⡿⢀⣠⠟⢀⣠⠤⣄⠸⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⢙⣓⣶⠞⠁⠀⠀⠉⠉⠉⠀⠠⠋⠀⠀⣸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⢀⡄⢀⡴⠒⠛⣚⣧⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⠀⣼⠀⠀⠀⠀⢠⡏⠉⠙⢲⣒⣒⣾⣤⣬⠵⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣇⣠⡇⠀⠀⠀⠀⢸⡗⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠚⢧⡞⠀⢸⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡑⠀⠁⠀⡞⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⠤⠤⠞⠁⠀⠀⠀⠀⢀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣦⠤⠶⠶⠶⠒⣾⢻⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⣸⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠀⠉⣹⣉⣁⣼⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠢⠤⠤⢴⢶⢖⠟⣻⢀⣈⣷⡤⣾⠇⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢝⣒⣒⣒⣛⣛⣚⣉⡩⠥⠖⠋⠉⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⠒⠒⠀⠠⠤⠬⠭⠉⠉⠻⠿⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠯⠭⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠖⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡇⢸⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡴⠋⠀⢸⢸⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⡇⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣸⠁⠀⠀⢸⠘⢚⡥⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢸⠀⡇⡇⢸⠀⠀⠀⢀⢇⡀⠀⠀⣿⡀⢠⡀⠀⢣⠀⠀⠀⢹⠀⠀⢹⢀⣀⠀⠸⠚⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⡇⢸⢸⠀⡇⡇⢸⠀⠀⠀⢸⢸⠁⠀⢠⡧⡵⣌⡏⢶⢬⣇⠀⢸⠈⡇⠀⠀⡏⠉⡇⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⣀⣧⣸⣇⣇⣸⣸⣀⣇⣇⣸⣀⠀⠀⢸⢸⠀⠀⡾⠰⠀⠈⠉⠀⠆⢹⠀⢸⠀⡇⠀⣠⠕⠸⢵⡒⠒⠚⠉⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡆⢸⡇⠀⠀⠠⠄⠀⠀⢸⡆⢸⢀⡇⠀⠛⠚⠒⠚⠃⠀⢀⣀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠳⡙⣾⠙⢤⡀⠻⠟⢀⡴⢋⡹⣼⡞⠀⠀⠀⠀⠀⠀⠀⢀⡷⠾⢤⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⠸⠬⢷⠀⠀⠀⠀⠀⠈⠳⠞⢦⡏⠑⠊⢹⡤⠚⠓⠙⠀⠀⠀⠀⠀⠀⢠⢴⡏⠀⠀⠀⠹⡽
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡇⢐⣒⣒⡂⢸⠀⠀⠀⠀⠀⣀⣠⡴⢻⠁⠀⠀⣈⣟⠦⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠈⠙⡇⠈⠭⠭⠅⢸⠀⠀⡰⠋⠉⠁⢼⠀⡏⠀⠀⠈⠀⢸⠀⣹⠈⠉⠓⣄⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⣤⡤⢤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠷⠶⢶⠶⠖⠚⠀⠀⡇⠀⠀⢀⡜⠁⡗⠒⠒⠒⠒⢻⠈⢣⡀⠀⠀⢸⠀⠀⠀⡷⠒⠒⠒⠒⠒⠒⠛⠓⠲⡇
⠀⠀⠀⠀⢠⠜⠃⠀⣄⢸⢀⡄⠀⠸⢤⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡏⠀⡘⠀⠀⠀⠘⡃⠀⠀⡇⠀⠀⠠⡏⠉⡆⠀⠀⠀⡇
⠀⠀⠀⠀⢏⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡇⠀⠀⡼⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⢠⠃⣰⠃⠀⡆⠀⠀⡇⠀⠀⡇⠀⣀⣀⣉⣉⣓⣀⡀⠀⡇
⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⢧⠈⡇⠀⠀⡼⢠⠏⠀⠀⡗⠀⠀⢻⠀⠀⡇⠀⠭⠭⠭⠭⠭⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠘⡆⢻⠀⢰⠇⡞⠀⠀⢰⡇⠀⠀⢸⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡀⣸⡀⣀⣀⣸⣸⣆⣜⣼⢀⣀⣀⣸⡀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡇⠉⠈⠁⠉⠉⠈⠁⠉⠁⠁⠉⠁⠉⠉⠉⠉⢹⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠯⠥⢜⣦⣠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣿⡹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣶⠟⠁⠀⠀⢀⡧⣙⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠤⠤⠤⠴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠑⠠⠑⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠠⠀⢐⠀⠂⠀⡠⠀⠁⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠰⢁⠠⠀⠀⠂⠀⢀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠂⠈⠁⠀⡇⠨⠭⠍⠀⠀⠂⠀⠀⠀⠂⠈⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠊⢁⠁⡀⠀⢀⡈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠤⠤⠄⢘⠃⠀⠘⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠈⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠤⠠⠤⠀⠠⠄⠤⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠊⠀⠒⠀⠘⠀⠒⠂⠀⠀⠀⡆⠙⠑⢄⠀⠀⠀⠀⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⢀⡀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⡀⡠⠠⡀⠀⢈⡁⡀⣉⡄⡄⡄⠀⠀⠀⠄⠃⠣⠜⡠⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⡀⠁⡀⠀⠀⠀⠁⠀⠁⠄⠀⢠⡀⠄⠀⠀⠑⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠅⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠒⠒⠁⣇⠈⠀⠀⠀⠀⠀⡀⠀⠑⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣆⠀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠛⠉⠁⢀⣤⣤⣤⣉⡻⢿⣿⣿⣷⣌⠻⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⡄⠀⠁⠀⠀⠉⣙⣿⣾⣿⣿⣿⡏⠁⠘⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⣸⠀⠀⠀⢠⣾⡟⠛⣿⣿⣿⣇⣾⡇⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡀⠀⠸⣄⠛⠁⢸⣿⣿⡿⢙⣿⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢦⣤⡙⠿⡲⣿⣿⣿⣷⠞⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⡄⣤⢒⢀⠀⠠⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣉⡟⣷⣧⡞⣫⠤⣰⣼⡟⣾⣛⣿⣷⡢
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣾⣿⣿⠻⣴⡶⠀⡸⠟⣯⢽⢩⣟⢿⣿⣏⠈⣀⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣄⢠⢰⣎⡄⡆⠄⡠⡀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡪⠑⣺⠇⡇⡿⠀⢘⢹⣷⡇⡖⣧⡟⣦⡦⡠⠀⠀⠀⠀⠀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⣷⢄⣂⡄⠱⠂⡁⠒⠀⢸⠂⠘⠁⠼⠃⠥⠧⠷⠶⠀⠀⠀⠀⠰⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⢯⢥⡽⠧⡀⠀⠗⡆⣠⢸⡇⠹⡆⢠⡀⢷⠀⢒⣛⠀⠉⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⠰⠂⠌⣁⠬⠉⠀⠀⠂⠁⠐⠀⢱⠀⢻⡄⠁⠘⢆⣨⡥⠢⠄⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣣⠄⠒⠀⠧⢈⠁⠒⡐⠌⠁⠐⠃⠀⠡⠜⠁⠀⠀⠤⠄⠰⠂⠀⠀⠹⢸⠇⠀⠀⠈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⡨⠀⠁⠀⠀⠀⠌⠉⠀⠀⠅⠀⠀⢈⠀⠐⠀⠀⣀⠘⠂⢣⢀⠗⢁⣍⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⢻⣼⠊⠀⠉⠀⠀⢠⠀⣤⢀⢠⡌⡤⠱⠀⠆⡈⠰⢈⠐⠀⡞⣭⠤⡀⣀⣠⡿⡿⡄⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠢⢆⠐⣀⢀⡀⠀⠢⠉⠀⠨⠐⠀⠂⢁⠤⠤⣸⠓⢿⠀⠧⣇⣽⣽⣧⢘⡙⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢪⠓⠀⠡⢀⣀⠤⡤⡐⣶⡞⡏⣳⢿⠸⣿⠆⠻⠋⠠⠀⣶⠋⠼⣹⣎⠡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⢾⡖⢣⢸⢸⡇⣟⠀⢾⣻⣳⣝⠺⣓⡶⠳⣆⠀⠛⡭⠌⠶⣔⠈⡥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢻⡌⢿⡴⠞⣜⣹⣾⠬⢕⣺⣭⣭⢵⡖⢋⣏⠀⣿⡀⡴⣧⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠈⠁⣴⣺⣟⡭⠳⠂⣻⠋⡍⢃⢈⣀⣧⣉⡽⠶⠶⠛⠛⠓⠀⠀⠠⢖⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠊⠀⠀⠀⠈⠁⢁⣈⣷⣣⣐⢋⡶⢰⡞⢻⣣⢭⣶⠮⠎⣠⡀⠐⠀⠀⠀⠀⠀⠉⠊⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣥⢆⢀⣙⣀⣀⡁⣗⣭⣥⡖⣾⡿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⢋⡭⣭⡻⠩⡊⢧⣸⣲⣵⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⣝⣓⣝⡃⣀⣁⡁⡤⣵⢛⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣮⣝⣲⣥⣬⠿⠓⡲⠏⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⣠⣤⠴⠟⠂⠉⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⣀⣀⣠⣤⠶⠞⠋⢁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡉⠉⣁⣀⣠⡤⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠏⠉⢀⣀⡤⢤⠶⠤⢤⣄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠖⣋⠥⠚⠈⠁⠁⠈⠘⠛⠶⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠞⡥⠋⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⣇⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠁⠀⢲⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠃⠀⢄⠿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⣂⣠⠔⠋⠀⡠⣪⠛⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠁⠀⠀⢄⡮⠞⠉⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣠⠞⣳⠲⠤⣤⣀⣀⣀⣀⣤⠤⠔⢚⠉⢁⡸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠂⠀⢀⡠⢺⢀⠖⠉⠑⠲⠤⢦⣼⣄⣥⣰⡤⠦⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠊⠀⢀⡴⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⢋⣠⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⡔⢃⡤⠊⠁
⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⢁⡴⠋
⠀⢀⡴⣉⠀⠀⣠⠞⢁⡴⠋
⠀⢸⠀⠀⠙⡎⣡⠞⠁
⠀⠀⠓⢧⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠉⣉⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠐⠢⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⠿⠿⠿⠛⠛⠛⠋⣉⣉⡉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⢙⣛⠶⣦⣀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣴⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⡠⠴⠚⠋⠉⠉⠉⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠆⡐⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠳⠤⠖⢊⣉⠉⠉⠲⣄⠀⠠⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠁⣰⣿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠊⠉⠉⠉⠉⠲⣌⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄
⠀⠀⢀⣿⡏⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣄⣀⣀⣀⡠⠜⠃⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡆
⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⢀⣠⠞⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠋⠛⣋⣉⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡠⠂
⠀⢀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⡄⠂⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣋⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⠟
⠀⠈⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⠞⠁⢀
⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣀⣤⡇⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠕⠊⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⣴⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠄⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠶⣦⣀⠀⠀⠀⠸⣆⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⢷⣦⣀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠛⢷⣦⣘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠹⣄⠀⠀⠀⡤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢶⠒⠤⠤⣀⠀⠀⠈⣇⠀⠀⢰⠋⠀⠀⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠽⢳⡄
⢸⠀⠀⠀⠸⣀⠀⠀⢸⠀⠀⠈⡇⣠⠖⠉⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣶⡚⠛⠛⠒⠒⠃
⠸⣆⢤⣀⠀⠀⠑⠢⣼⠀⠀⠀⠙⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠉⠒⠤⡀
⠀⠁⠀⠈⠑⠦⣄⠀⠀⡖⢦⡄⣖⢴⡆⣰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠆⠀⢠⠎⠀⠈⠲⡀⠀⢑⠦
⠀⡠⠛⠦⠤⠤⠬⠿⠦⢦⣤⢰⣇⢲⠂⠑⠒⠒⠦⠤⠞⠳⣄⠀⢠⠖⠒⠲⠤⣄⡀⠀⠀⠀⠀⣠⠖⠒⠒⠲⣤⡠⠴⠒⠛⠓⣆⡴⠋⠀⢀⣀⠤⠼⠀⣌⢳⠆
⠾⣅⡀⢀⣀⣀⣄⠤⠤⢤⡄⠀⠀⡨⠤⠤⣄⣀⣀⡀⠀⠀⠈⢢⡘⢦⣂⡀⠀⠀⠈⠉⠓⠲⠤⣽⣄⡀⠈⡷⣯⠄⠀⠀⢀⡼⠃⠀⠀⣠⣿⡶⠚⠓⠦⠉⠃
⠀⠀⠉⠚⠀⠀⠀⣀⣀⡞⠀⠀⡰⠁⠀⠀⠀⠀⠀⢹⣀⠴⠚⠁⠀⠀⠈⠙⠓⠲⡦⠤⠤⠤⠤⠷⠂⠉⠉⢳⣄⣀⣠⠶⠋⠀⠀⣠⠾⠿⣏
⠀⠀⠀⠀⠀⠀⠀⢳⠉⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄⠀⠀⢀⡞⡵⠶⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠚⣻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣰⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡰⠥⠾⣇⠀⠲⢄⡀⠀⠀⠀⣠⠴⠋⢀⡴⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢒⣼⣆⠀⠀⠀⢀⡤⠚⠁⢀⡴⠋⠀⠀⢀⠀⠀⠙⠖⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⢯⣮⣬⣧⣠⢖⡉⠀⠀⡰⠋⠀⠀⣄⠀⠀⠣⡀⠀⠀⠀⠈⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⡏⠉⠁⣎⣿⣧⠀⠙⠢⠞⠁⠀⠀⠀⠈⣆⠀⣠⠟⠀⢀⡤⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢚⣿⣿⢀⣴⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⡿⣧⠴⠋⢀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠿⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡜⢆⢠⢫⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠤⢤⣤⣤⣤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠘⢦⡛⠉⣈⣉⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⣌⣢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⠙⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠋⠽⣛⣙⣿⣿⣛⣷⠶⠶⠖⠒⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⠉⠉⠉⠀⠒⠤⣀
⠀⠀⠀⠀⣠⠖⠒⠁⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠈⠁⡀⠀⠀⢀⡤⠤⠤⣄⣀⠤⠒⠀⣀
⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡔⠁⠀⠀⠀⠀⡇⠀⠀⠀⢈
⠀⠀⠀⠸⠀⠉⠗⠤⢠⣀⣀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⡸⠀⣧⠀⠀⠀⠀⠀⡘⠦⣄⢠⡎
⠀⠀⠀⠀⢀⢼⣀⠔⠁⠀⠴⢠⠃⠀⠀⠀⠀⢀⠤⠂⠈⠁⠀⠀⠑⢄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢰⠁⠀⢇⠙⠚⠓⠤⣀⡷⡀⠀⡟⠉
⠀⠀⠀⠘⡐⢼⠁⠢⡀⠀⠉⢸⠀⠀⠀⠀⡰⠁⠀⠠⠤⠤⠤⠤⠤⠄⠝⠶⠠⠤⢠⡀⠠⠤⠒⠢⣀⣀⡣⠀⠸⠈⠀⠀⠀⠈⢱⠆⡰
⠀⠀⠀⠀⠈⣦⡀⠀⠈⠻⣹⠁⠀⠀⠀⠀⡁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡸⠀⠀⢀⢾⠊⠁
⠀⠀⠀⠀⢠⠋⠛⠲⠦⡴⠊⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠋⠁⣸⣀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠉⠀⠈⠳⡀
⠀⠔⡕⠒⠢⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠦⠤⠤⠒⠒⠒⠀⠄⠀⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⢀⠀⠸⡀
⠘⠘⠀⠀⠀⠘⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠁⠀⠀⠃⠀⢃
⠀⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠙⠞⠀⠀⢟⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢠⠁⠀⠀⠀⠀⠀⢸
⢠⢃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⡠⢲⣗⠥⠂⠀⠀⠀⠀⢱⠴⣗⠠⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸
⢸⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣠⠖⠁⠐⢋⡴⠃⠀⠀⠀⠀⠀⠀⠑⢌⡁⠀⠑⢄⠀⠀⠀⠀⠸⠀⠰⠀⠀⠀⠀⠀⠆⠀⢸
⠸⠀⢇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣀⠠⠔⠊⢁⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢄⡉⠀⠐⠠⢠⣄⠆⠀⠀⠀⠀⡌⠀⠀⢸
⠈⠀⠈⡄⠀⠀⠀⠀⢀⠧⠒⠉⠁⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠈⠢⠀⠀⠀⡰
⠀⠀⠀⠘⡄⠀⠀⠀⠎⠀⠀⢀⣠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠢⠄⣄⠀⡐⠁
⡄⠀⠀⠀⠘⢄⣀⣼⠠⠔⠊⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⠤⣀⣀⠤⠒⠒⠲⠤⢤
⠸⡆⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⡝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡄
⠀⢰⠁⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢡
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠈⢷⣦⣤⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢈⠟⠛⢛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣶⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⢿⣑⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢧⠀⠀⡎⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⢤⣄⣀⣀⣠⠷⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠠⠤⢀⠀⠀⠀⢀⠤⠒⠀⠈⠉⠉⠁⠐⠢⢄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠐⠀⠀⠐⠆⠁⠉⢂
⠀⠀⠀⠀⠀⠈⡆⠠⡄⠄⠤⠞⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣤⠀⠀⠀⠀⡦⢀⢠⡎
⠀⠀⠀⠀⠀⠐⠇⢰⠀⠈⠄⡆⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢀⠔⠉⠑⠄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠈⡀⠀⠑⠚⠂⢄⡧⠀⡛⠁
⠀⠀⠀⠀⠈⢬⠂⠀⠐⢶⢲⠂⠀⠎⠄⠠⠒⠂⠤⠤⠤⠄⠐⠊⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠀⠀⠉⠠⡀⡄⠀⠀⣟⠴⠁
⠀⠀⠀⠀⠀⠀⡑⠠⠄⢠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢥⠄⠊⣃
⠀⠀⠀⠀⣠⣊⡉⠂⠴⠊⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠊⠀⠑⡄
⠀⠀⠀⡼⠁⠀⠈⡄⠀⠀⠀⠘⡡⡀⠀⠀⠀⠀⢀⡴⣟⣦⠞⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠄⠀⠑⠘⡄
⠀⠀⡜⠀⠀⠀⠀⠃⠀⠀⠀⠀⠇⠈⢆⠀⡠⠂⠁⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠆⠀⠀⠀⡇⡆
⠀⡘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⢯⠂⢀⠀⠀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠁
⠀⠂⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⠑⠀⠀⡀⠘⠀⠁⠀⠀⠀⡐
⢠⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠐⡄⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠤⢰⡀⡠⠁⠀⠀⠈
⣆⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⡴⠶⢶⣶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⣿⣿⣿⣿⣶⣾⣿⣿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁⢀⣠⣬⣤⣤⣿⡿⠉⠁⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠀⢀⣫⣥⣤⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠋⣁⣠⠤⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⠴⠒⢋⣡⣤⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⡶⠟⢛⣯⣷⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣋⣥⣶⣿⠿⠟⢋⣽⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡝⠟⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⣠⠶⢛⣽⣽⣿⠇⢄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡜⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋⠉⠉⠇⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡹⠟⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⣾⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣴⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣟⡿⠋⠁⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠲⢶⣄⠀⠀⢴⣏⠭⠛⢶⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⢍⠢⡈⠀⠈⠻⣦⠀⠀⠀⠀⠈⠻⣶⣄⢀⠄⡠⡘⢶⣄⣀⣈⣿⣷⡄⠹⣧⣀⣤⡿⠀⠀⠸⠟⠶⣆
⠀⠀⠀⠀⠀⣴⣿⣿⢿⡙⠨⠂⠑⠁⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠈⠙⢷⣦⣈⣫⣲⣿⣿⣿⠿⠿⣿⣆⣈⠛⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣼⡿⣏⠢⡕⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⢘⡯⣻⣿⣿⣿⠁⠀⠀⠀⣿⣿⣃⡄⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣰⡿⣕⠮⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠀⠀⢫⣾⣿⡯⠽⣿⠀⠀⠀⠀⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⣿⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⢿⣷⣦⣴⣿⣿⣧⢖⣫⡿⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠄⠉⠛⢿⣿⣿⣿⠿⣇⠀⠀⠀⢀⣠⣽⣿⡿⠀⠀⠀⠀⠀⠀⣼⠃
⠠⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡿⢋⣡⠴⢿⠀⠀⢠⣾⣿⣿⣿⣿⣷⣤⣄⣀⣀⡼⠃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠋⠀⠀⠘⣇⢠⣾⡿⠛⠁⠀⠀⠀⠀⠈⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡈⠙⠲⢤⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠋⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢿⠀⠢⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠉⡒⠤⣄⣀⣰⠙⢟⠢⡀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠈⢀⡼⠃⠀⠈⢧⠙⢆⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⢤⣀⡴⠋⠀⠀⠀⠀⠈⡆⠈⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡒⠒⠒⠒⠒⠒⡄⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣲⣒⣶⣒⣖⣲⠇⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣀⣀⣀⣠⠎⠀⠀⠀⠀⣠⠃⢀⠇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⢺⠁⠀⠀⠀⠀⡗⠒⢒⡲⠖⠁⡠⠋⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢉⣁⣠⠴⠊⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠭⠟⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠷⠶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠽⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢁⣤⣄⣀⠠⠶⠶⡄⠀⠀⠄⢰⠂⠈⠀⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣾⠋⠉⠓⣄⡀⠀⠀⠀⠑⢄⡀⢰⡀⡀⠈⢠⠒⠒⣤⣄⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢄⠉⠠⠀⠈⣷⣄⠀⠀⠺⠂⠉⠉⠈⠹⢸⠏⠖⠒⠀⣾⠐⠮⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡉⠀⠀⠄⠀⠙⠷⣦⣤⡄⠀⠀⠰⠊⠉⠉⠙⠤⠒⢳⡈⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠻⢄⠀⣄⠀⢀⠠⡤⢬⠤⠶⢾⡦⠤⡲⡄
⠀⠀⠀⠀⠀⠀⠀⣎⡤⠴⢤⡤⠀⠀⠀⠀⠁⠀⠀⡔⠀⠀⠂⢀⣄⠀⠈⢣⣶⣽⣉⠀⢀⡄⣱⠗⠸⢁⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠜⠈⠋⡓⢯⡵⠋⠙⠂⢠⣀⠀⢺
⠀⠀⠀⠀⠀⢠⠞⠛⠳⣶⣤⡄⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢨⢁⡞⠧⡈⠓⣄⣤⠄⢉⢠⢯⡆
⠀⠀⠀⣠⠐⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠀⠘⠀⢀⡀⢐⣦⣀⣀⠀⢀⠀⠰⣈⡂⠑⡌⠲⣄⡉⢠⠄⠀⠈⠉
⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠖⠋⠀⢹⣤⢈⡆⠢⢼⠳⣄⣸⠞⠈⠃⠀⢰⠂⡀
⠀⠀⠀⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣾⡏⣹⠶⠀⠫⣰⡆⠉⡘⢷⡄⢴⠴⠂⠀⠀⠀⠁
⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡟⠀⠈⠀⠐⠏⠀⡀⠀⢸⠄⠈⢰⡃⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⣰⠋⡾⠀⠀⠀⠀⡀⢀⠶⣄⠀⠀⠀⠀⠛⠲
⠀⠀⠀⠀⠘⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⢃⡜⠁⠀⠀⠀⢠⠉⠛⠀⠀⠉
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠱⠤⣄⣀⣀⣀⣀⣀⣠⣄⣀⠀⠀⠀⠀⡰⠀⠐⠀⠀⠀⠀⠔⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⣃⡆⢤⣀⡀⠀⠇⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠴⠿⠶⠆⠲⠶⠶⠶⠷⠶⠄⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣾⣷⣄⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣄⠀⠈⢻⣿⣧⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⢹⣿⣧⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⢿⣿⡆⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⡇⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⡇⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⣿⣿⠃⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⣼⣿⡏⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⣾⣿⠏⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⣋⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡿⢧⣀⠀⠀⠀⢿⠹⡇⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣠⡖⠏⡑⢯⣀⡞⢉⣷⡄⢀⠞⢿⣾⡀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⢀⣼⠯⡂⠁⠀⠀⠙⢦⡞⠀⠿⠈⢢⢻⡇⢱⠀⠀⠠⡞⠒⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣛⢿⣦⣄
⠀⠀⠀⢠⠟⡂⠅⠀⠀⠀⠀⠀⠈⢛⡀⠁⣠⣚⣚⡏⠉⠀⠀⠀⢇⠀⣠⣇⣶⣴⣷⣿⠁⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣦⡀
⠀⠀⢀⡿⢑⠂⠀⠀⠀⠀⠀⣄⢲⢹⠃⡔⠋⠀⠀⡇⠀⠀⠀⠀⣀⣧⠉⣻⢿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⣿⣻⡽⣿⣦
⠀⠀⢸⠯⠐⠀⠀⠀⠀⡞⡧⠛⠄⠁⠀⡇⠀⠀⠀⠃⠀⣠⣴⠟⣽⣼⢊⡴⣩⠛⠢⣀⠀⠀⠀⠀⠀⣠⡾⢿⣛⠽⠗⠋⠉⠁⠨⡲⢕
⠀⠀⢸⠭⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠀⠰⠖⣩⣿⣿⢠⡿⠀⣫⢖⡁⠜⢴⣚⣦⣠⢴⣲⠿⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠨⡑
⠀⠀⢸⡅⠀⠀⠀⢸⠦⠽⢧⠀⠀⠀⠀⢣⢀⣠⣴⣿⣿⣿⡇⢸⡵⠊⣀⡼⠀⠀⠚⢿⣿⡏⠉⠀⠀⠀⠀⠀⢀⣴⣿⢿⣶⣄
⠀⠀⢈⡧⠖⣒⣶⣬⣯⣉⣚⣷⠀⠀⠀⠘⢿⣿⠿⠟⣿⣿⣧⢊⡤⠊⠁⠀⠀⠀⠀⠀⢻⣷⠒⠒⢶⠒⠒⡞⡿⡈⠁⡀⠙⢮⠇
⠀⠀⡞⢸⣿⣿⡿⣿⢿⣿⣄⣽⣇⣀⣀⣀⠀⠀⠀⠀⣸⣿⠱⠋⠀⠀⠀⠀⢠⣆⠀⠀⣸⣸⠀⠀⠀⠀⠀⣇⣱⠣⡀⢉⣰⠞⢦⡀
⠀⠀⢣⡼⠟⢁⡀⠉⣸⡇⢣⠀⠀⠠⠞⠛⠳⣤⠞⣶⣿⡇⠀⠀⠀⠀⠀⢰⠁⣸⠀⡠⣿⣿⠀⠀⠀⠀⣷⠀⠈⣳⠋⢋⣡⣰⣴⣽⣄
⠀⣴⣿⣟⢳⣌⢀⣠⣿⢃⢸⠀⠀⠀⠀⠀⡾⠓⠚⠉⠉⣇⣀⣀⣤⠔⠒⠉⠉⢀⣠⡿⣟⣽⢶⣒⠒⠒⢿⠀⡴⠃⣠⡎⠳⣄⣀⣀⣀
⣼⣿⣿⡟⠛⢻⣿⣿⣻⠏⠛⠇⠐⡄⠀⠀⢹⠀⠀⢦⣤⡟⠀⣢⢰⠀⣠⣾⢿⡻⠕⠊⣿⣟⣩⡖⠒⢲⣾⠟⢀⣼⣻⠁⠀⣾⣿⡛⠛
⣿⣿⠏⠉⣿⠾⣿⣿⣿⠀⠀⠀⠀⢳⡀⠀⠈⡆⠀⠀⠛⠛⣿⣿⣿⣦⣷⣾⡇⠀⠀⠀⢿⣿⡝⡇⠀⢸⠁⣠⣾⣏⡇⠀⣸⣿⡦⡝⢦
⠸⣿⠀⢸⣿⣷⡼⣿⣿⡆⠀⠀⢀⣿⣿⣋⣥⣷⠖⣶⣶⣿⣿⣿⡿⠿⠛⠓⢻⠀⠀⣠⣿⣿⣷⡁⠀⣸⠾⠛⠋⡽⠀⢠⣿⣗⠭⠂
⠀⢿⠀⠘⣿⣿⣧⣦⣿⣧⣀⡤⠾⠛⠋⠉⠀⡟⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣀⣰⡿⠿⠛⠋⣇⠀⠙⢦⣄⠰⣇⠀⣼⣿⡪⠕⠀⢸
⠀⠘⣷⡶⠿⠿⢷⡿⣿⣉⣹⣀⣠⣤⣴⣶⣿⢟⣶⣷⠤⣄⣀⣀⣀⣀⣀⣀⡸⠏⠀⠑⢄⡀⠀⠈⠙⠛⢿⡿⠀⢳⣝⣿⡳⢮⣀⠀⣿
⠀⢠⣿⣁⣀⣀⣸⣄⣀⣀⣈⣉⣿⣿⣯⣽⣾⣿⣸⣿⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣙⣦⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣷⣭⣻⣿
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠶⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣀⣀⡠⠤⠄⠀⢀⣀⡀⠀⠀⠀⠉⠁⠶⠆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢾⠏⠉⠉⠉⠳⣄⠀⠀⠈⠉⠉⠶⢦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠶⠶⠀⣀⣴
⢀⣠⣤⣀⣀⠀⡀⠐⠒⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⣦⠀⠀⠀⠀⠘⠻⣶⠶⠶⠄⣀⡀⠀⠀⠀⠀⣀⠴⠋⠉⠰⠆⣀
⠈⠻⠃⠈⠁⣀⡀⠐⠲⠶⠖⠀⣼⣆⡀⠀⠀⠀⠈⠀⠀⠈⠶⡀⠀⠀⠀⠀⠘⠧⠀⠀⠈⢩⣶⣄⠰⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠿⢧⣀⠀⠀⠀⠀⠀⢹⣤⣀⣠⣀⠀⠸⡿⠒⠂⠀⠈⢹⡆
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠈⠀⠀⠉⢳⣤⡀⠚⠓⠀⠉⠻⣄⠀⠀⠀⢰⡆⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⣦⡀⠀⢀⡄⠀⢻⡇⠀⡄⣼⠗⠚⠀⠺⠋⠙⣿⠟⠢⣤⡀⠀⠈⢳⣄⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠂⢀⡌⠀⠀⢸⠀⠀⠀⠈⣶⡄⠘⠿⠃⠛⠋⠙⠻⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣷⠀⠀⠀⠀⢸⡄⠀⠀⠘⠋⠀⠀⠀⠆⠀⠀⠀⠁⠀⠘⠛⣦⣤⠤⠄⠀⠀⡀⠀⠤⠤⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠻⡆⠀⠀⠀⠀⠙⣷⣄⣀⠀⣴⡄⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⢤⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢋⡄⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠉⠙⢿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⢶
⠀⣴⣇⡀⠉⠀⠀⠀⠈⢣⡀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠁⠁⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠈⠁⠀⠀⠀⠶⠶⢾⣉⠉⢉⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⣀⣀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⢀⠀⠀⠂⠈⠉⠁⠈⠉⠉⠁⠲⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⢾⡷⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢀⣀⡀⠀⠀⠀⣀⡀⠀⠶⠦⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡆⠀⠉⠉⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠒⢀⣀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢂⣀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠘⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣤⣤⣦⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠻⣑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠮⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⣟⠪⣙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⡞⢍⡑⢌⠣⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠰⠆⢶⣑⢮⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⢉⣉⣀⣀⣀⣀⡀⢸⣍⠲⣙⢦⣙⡮⠶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢌⠳⣌⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣞⠔⡡⣫⢞⡝⡩⢳⣗⢌⡳⡎⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠦⡙⠦⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣡⣪⣎⣔⣥⣫⣿⣿⣃⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⡉⠢⣙⠢⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⡉⠢⣌⠢⣈⠓⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠻⣍⠢⣌⠢⣌⠳⢌⡳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠣⡈⠣⣌⠳⣌⠓⢌⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡈⠢⡈⠳⣌⠓⣤⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⠦⡈⠢⡈⠲⣄⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠥⠀⠀⠀⠀⠀⠀⠀⢘⠢⣈⠢⡈⠳⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠨⠀⠀⠀⠀⠀⠀⠀⢸⡑⢌⠳⣌⠳⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣭⡍⣤⢀⣀⣠⣀⣀⣸⣝⠢⡑⢮⡑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣡⢊⡔⡡⢊⠜⡠⢋⠗⣬⡲⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢈⠁⠉⠉⠉⠑⠛⠚⠓⢷⢮⣴⣽⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⢦⡴⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠑⢌⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⡙⢦⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠶⣌⠢⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡝⣹⢋⡝⣹⢋⢏⡝⡩⡱⣌⠳⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣊⣔⣱⣣⣎⣴⣵⣱⣡⣻⣦⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⠤⢐⣀⠤⠔⣀⡠⠤⠄⣀⠠⠄⢀⣀⠤⠀⣀⡀⠀⠀⣀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠐⠊⠁⠀⠒⠈⠡⠔⠊⠩⠔⠒⠩⠥⠒⠪⠭⠒⢈⡩⠔⠒⡩⠅⢒⠤⠔⣢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⠓⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠐⣖⠔⠶⢶⣖⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠖⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⠆⠀⠀⢀⡀⠀⣣⡀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⡈⠋⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⠿⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠲⢄⣠⠖⠤⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⡠⠃⠈⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠑⣄⣓⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⣀⠀⠀⠈⠛⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⡏⠁⠀⠀⠀⣀⣀⣀⠴⠂⠀⠀⢈⡥⠎⠀⠀⠐⠔⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⡜⢀⢉⢪⠃⠀⠀⠀⠸⣀⣀⡀⠀⠀⢠⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⠀⠀⠀⢸⠀⠀⢠⠃⣸⠷⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡀⠀⠀⢸⠀⢠⠯⣲⠃⠀⠀⠀⠀⠀⢀⣴⣶⢿⡻⣿⡟⣻⣷⡶⣦
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⡇⠀⠀⢸⢀⡏⠀⢸⠇⠀⠀⠀⠀⢀⠞⣗⡀⢉⣼⡿⣿⡤⡨⣼⠋⠲⣄
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⠀⢸⡞⠀⢀⡟⠀⠀⠀⠀⠀⡞⠀⡌⠳⠋⢿⠃⠽⠌⠛⠃⠀⠀⠸⡆
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢷⠀⠀⠸⠁⠀⡾⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⣴⠂⢀⣠⡄⠀⠀⢸⠀⠀⣷
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡏⠀⠀⢣⠎⠛⠙⣾⣿⣾⠅⠀⡎⠀⠀⣿
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡏⠀⠀⠀⠀⢠⠞⠀⢀⡴⢁⡠⠔⠒⠋⠉⢉⠆⡼⡇⠀⠀⣿
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡷⣤⠞⠀⠀⠀⠀⢠⡏⠀⣠⠊⡴⠉⢢⠘⡃⠀⠈⡟⡼⠁⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢈⠇⡖⢁⡜⠁⠀⠈⡇⠋⠀⢲⠂⡇⠀⢹⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠣⠜⠀⠀⠀⡼⢙⠋⠀⠙⡅⢳⠀⢻⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⢀⡜⠁⡈⠁⠀⠛⡇⠈⢧⠸⣃⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉⠀⠀⠈⠸⡄⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⣄⠀⠀⠀⣠⠾⠋⣠⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡈⠢⣈⣷⣶⣿⠥⠤⠶⣤⣥⣀⡈⢳⡀⢀⣀⣤⠴⠒⠋⠉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⣀⣸⢃⣠⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⡉⠀⡀⠄⠂⠘⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠤⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢀⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⠀⠐⣟⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠂⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣿⢣⡀⠀⢀⡤⠞⠉⠉⠀⣈⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⣧⡈⠀⠀⣯⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠄⠀⢀⠀⢸⣄⠙⢦⠎⢀⣠⠶⠛⠛⠙⠛⠳⢦⣷⠀⠀⠀⠀⠀⠀⣿⠑⠀⢀⣀⠉⠓⠦⣤⣀⡀
⠀⠀⠀⢠⡴⠚⠋⠉⢀⡀⠠⠄⠐⠂⠀⠉⠳⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⠐⠤⠀⣠⠟⠃
⠀⠀⠀⠀⠙⢦⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣤⣤⣤⣤⠴⠚⠁⠀⠀⠀⠀⢀⣼⡇⠀⢀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⣼⠁⠰⡀⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠆⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠶⠶⠒⠚⣉⣤⠞⠁⠀⠀⠀⠀⠀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡴⢊⠵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠄⠘⣷⡀
⠀⠀⠀⠀⠀⠰⠯⣄⡈⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠤⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢁⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⡿⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠌⠀⠀⡀⠤⠀⠀⠂⠀⣼⠏⠀⠀⠀⢹⡄⠀⠀⠜⠑⠀⡀⠀⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠐⠂⢀⣀⣀⣀⡀⠀⠘⠀⣿⣄⠀⠈⢀⣼⡇⠀⠊⠀⣀⠀⠀⠑⠲⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠖⠚⠋⠉⠉⠁⠀⢻⡄⠀⠐⠙⣯⣝⣛⣭⢿⣌⠀⠀⣼⠋⠉⠙⠓⠲⠶⠤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣴⠟⠉⠀⠉⠀⠀⠉⠻⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢄⢀⣤⣴⣯⣶⣿⣿⣿⣧⡄⠂⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠙⣷⣿⣾⢿⣿⣿⣿⣯⣿⣿⣿⣿⣵⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⣙⢵⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣁⣾⣭⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⣧⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⡿⣶⠒⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⢠⣬⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⡁⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠓⠛⢷⣞⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⠏⠓⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⡀⡼⠧⠏⢻⣿⣿⣿⣿⣿⣿⣿⣷⠴⣿⣿⡉⠿⠃⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠛⠚⠋⠿⣿⡯⣉⠗⠙⠾⣁⠙⠖⠂⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⢈⠈⠑⠃⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣶⣦⣴⡁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣻⣟⣏⠿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠠⢀⣨⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⢿⠉⣀⡀⢛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣷⣦⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣷⣴⣿⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⡀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⣶⣤⡀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠁⠀⠀⠈⠙⠻⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢤⣍⣙⠛⠿⠛⣋⣩⣤⡶⠶⠿⣿⣿⡧
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢠⣶⣦⣬⣉⢋⣩⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⣀⣀⣠⣴⣾⡿⠏⣰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⢠⣴⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⠇⠀⡀⣫⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⡿⠈⢿⣿⣿⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣏⣀⣜⣳⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣇⣀⣈⣻⠏
⠀⠀⠀⠀⠘⠿⣿⠿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤
⣿⣿⣥⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡠⠏⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡤⢄⣀⣀⣀⣀⣤⠤⠖⠒⠳⠬⠙⠃⠉⠀⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠓⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠿⢝⡂
⠀⠀⠀⠀⠀⠀⠻⣖⣒⣒⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡴⠃⣀⣤⠴⠶⠶⠦⣄⡀⠙⢆⡀
⠀⠀⠀⣀⡴⠚⠉⢉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠤⣄⣹⣞⡴⠚⠉⠀⠀⠀⠀⠀⠈⠹⣄⠀⠙⢦⡀
⠀⠀⠀⠈⠉⢉⠟⠁⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠹⠏⠀⠠⠶⢤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⣳
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢬⣙⠳⡄⠀⠀⠘⡇⠀⠀⣧
⠀⠀⠀⣼⠖⢹⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠁⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⠶⠒⢸
⠀⠀⠀⠀⠀⢸⠠⠤⢼⡄⠀⣀⣀⣀⣀⣤⣤⣴⠾⠛⠋⣴⡄⠀⢠⣆⠀⠀⠀⠀⠀⢀⣿⠀⢠⡏⠑⠂⢸
⠀⠀⠀⠀⠀⢸⠀⠈⠉⡇⠀⠈⢻⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣼⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⢳⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⣤⡿⠁⠀⢠⡇⠀⠀⣰⣧⣄⡀
⠀⠀⠀⣠⠶⠒⠚⠢⠤⠼⠂⠀⠀⠀⠈⠉⠛⠛⣟⡿⠋⠀⠀⠠⠖⣦⠀⠀⠉⠉⠉⠀⠀⠀⠳⠶⠊⣡⡴⠒⠙⣆
⠀⠀⠀⡏⢀⡴⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⣿⠀⠀⢹
⠀⠀⠀⢷⡀⠀⠼⠈⡧⢸⡀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⠂⠁⠐⠒⠒⠤⣄⡀⠀⠀⠀⠀⢠⣆⠙⠀⠋⠀⢀⡿
⠀⠀⠀⠀⠛⢦⣄⣀⣠⠼⢧⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣠⣤⣾⣿⣿⡆⠀⠀⠀⣼⠉⠛⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⡀⠀⠘⢿⢿⣿⢿⣟⣋⣛⣛⣛⣿⣿⠿⠿⣿⣿⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠲⠤⢄⣀⣀⣉⣁⣀⣀⣠⠴⠞⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠚⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣄⡸⣰⡿⠭⢗⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣇⣿⣵⠿⠁⠀⢀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣼⣡⠾⠿⠒⠛⠁⠀⠀⠀⢸⡞⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣁⡈⢻⠏⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣶⡶⠶⠾⢯⣾⣿⣿⣿⠿⣟⡳⠦⣍⡁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠀⢀⣤⠖⠛⠉⠁⠀⠀⠘⠁⣈⣻⡇⠀⠀⠴⠖⢺⣭⠙⠛⠿⣷⣦⣈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⣠⡾⠋⠀⠀⠀⠀⠀⢾⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠉⠻⢿⣦⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠈⠛⠛⢿⣿⡿⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠛⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⠁

⠀⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⡏⡴⠋⠉
⠀⠀⠀⢻⡸⡄
⠀⠀⠀⠀⢣⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠹⡅⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⠹⡄
⠀⠀⠀⠀⠀⡟⢿⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡞⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢱⡘⣧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣆⢰⣆
⠀⠀⠀⠀⠀⠀⢧⢉⣁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠉⠛⣿⣿⣿⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⣀⣾⣿⢸⣿⣤
⠀⠀⠀⢀⣤⣶⣾⣿⣟⡁⢷⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠟⠛⣫⠛⠷⠶⠚⢻⣿⣿⡿⠀⠀⠈⢳⣦⠰⠖⠛⢡⣿⣟⣸⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣬⣇⠀⠀⠀⠀⠀⠀⢸⣀⡘⠛⡸⠁⣇⠸⠗⠀⣼⡙⡿⠁⠀⠀⠀⠸⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠿⣿⣿⣿⣿⣿⠛⠡⠼⡀⠀⠀⠀⠀⠀⠀⠉⢩⠉⢥⡄⠉⠉⠉⠛⣯⠜⠁⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡆⠤⣶⠴⠂⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣉⣁⣤⠞⠁⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⠀⠀⠀⢹⡍⠂⢄⡀⠀⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡤⠦⠤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠁⡼⠀⠀⠁⠀⠙⢦⠀⠙⣄⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠓⠒⠚⠀⠀⢳⣄⣀⡀⠶⣒⣨⡇⢀⣜⠀⡟⠺⢄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇⠀⠀⠘⠂⢰⡄⣿⣿⣿⣿⣿⡟⡔⠁⠀⢹⠃⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⢀⠎⠀⢀⡀⠀⣠⠏⠀⣿⣿⣿⣿⡟⠀⢹⡀⠀⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⡞⠀⠀⢸⡇⡰⠁⠀⠀⣿⣿⣿⡟⠀⠀⣠⠃⣸⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡼⠁⠀⠀⣸⠃⠸⡀⠀⠀⣿⣿⡿⠀⢀⡜⠁⢠⡏⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⠀⠱⡀⠀⣿⣿⠁⣰⠋⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⢀⡞⠀⠀⠀⠀⠱⣘⣿⢇⡼⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⢹⣿⠞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢰⠇⠀⣠⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢀⡼⠃⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠳⣄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⡼⠁⠀⠀⠀⣀⣠⠤⠤⠤⣄⡀
⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠛⢦⡀⠀⠀⠈⠳⠖⠋⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡼⠃⠀⠀⣠⠞⠁⠀⠀⣀⣀⠀⠉⠳⡄
⠀⠀⢀⡞⠁⠀⣴⠚⠛⢲⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⢀⡞⠁⠀⠀⢀⠇⠀⠀⢀⠞⠉⠉⠙⣆⠀⢹
⠀⠀⢸⠁⠀⠀⣇⠀⠀⠀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠈⠛⠓⠒⠚⠀⠀⠀⢀⡿⠀⣼
⠀⠀⠘⣆⠀⠀⣹⡄⠀⣰⠇⠀⡾⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠖⠋⢀⡴⠃
⠀⠀⠀⠈⠳⠚⠁⠀⢰⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⣀⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣤⠇⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⠴⠊⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⡆⠀⠀⠀⠀⠀⡴⠛⠉⠉⠹⣆⠀⠀⠀⠀⢠⡏⠁⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣠⡴⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠈⠳⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣒⠚⠂⠀⠂⠤⠀⠀⠉⠈⠁⠐⣢⡀⠀⢀⣀⢀⡔⢒⠞⠑⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡼⠄⠀⠀⠀⠀⡜⠁⠠⠀⢀⡀⠀⠀⠸⠓⡨⠀⠭⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡠⢞⠓⠊⠀⠀⠀⠀⠀⣸⡵⠟⠁⢑⠢⠄⠑⠂⠜⣁⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⣠⡔⠴⠛⠁⠀⠀⠀⠀⢀⣀⢀⢨⠀⠠⠴⠀⠂⢡⡯⠖⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠥⠤⠚⠪⡢⣀⣄⡄⠀⠚⠔⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⣴⡂⠖⠓⠒⠁⠀⠀⠀⠀⠈⠀⠀⢐⡂⠀⢀⠀⠀⠀⠄⠀⠀⠃⠀⣀⠒⠀⠀⠀⠀⠲⠦⠤⣤⣤⠤⢀⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠒⠏⠀⠀⣆⣆⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠜⠃⠀⠀⢀⠀⠀⠀⠸⠀⠡⠄⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡤⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠂⠛⠉⣣⢤⠨⢀⠀⠀⢠⡆⠂⠀⠀⠐⡄⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠊⠉⠐⠀⠀⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢹⡀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠈⠵⠦⡀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠀⢀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⡅⠀⠀⠀⠀⠒⠁⠀⠀⠘⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠈⠁⠙⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠬⠀⠀⠀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⠀⣀⠤⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⡀⠸⠴⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⢛⣛⣛⣳⣶⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠞⠁⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠉⠻⣕⠢⡀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠏⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢢⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠷⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⡰⠃⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⣠⠞⠁⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢀⡴⠊⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⠔⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠞⠁⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡎⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣲⡼⠖⠚⠛⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠭⢤⣀⣀⡤⠖⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⡇⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠗⠊⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⢀⣿⠋⠁⢹⠀⠀⠀⠀⠀⠀⢀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⡜⠹⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⢀⣾⡿⠀⠀⢀⣠⣄⡰⠀⠀⠉⠀⠀⠀⠀⠀⡀⠠⠆⣤⡄⠰⠖⢀⡆
⠀⣀⣀⣀⣀⣀⣷⣿⣿⣁⣀⣀⣻⣿⣿⣃⣀⣀⣀⣀⣬⠠⠤⠤⠬⠞⠀⠀⠀⢉⠠⠄⠃
⠀⠉⠉⢉⣽⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⡖⣄⠰⠆⠈
⠀⢀⣰⣿⣿⣋⣹⣆⣀⣀⣀⣀⣀⣠⣤⣤⠤⠤⢤⠦⠤⠒⠒⠚⠿⡃⢈⡤⠄
⠀⣹⣿⠟⠉⢉⣽⣿⣶⣦⣄⠀⠀⠀⠀⡰⠚⢛⡎⠀⠀⠀⠀⢀⣦⠏
⠀⣿⣏⣀⣠⣿⣟⣻⣛⣿⣿⣧⣤⠤⠤⠬⠿⠿⠒⠒⠒⠋⠉⠙⡏⡆
⠀⢻⡏⠉⢹⡏⠉⠸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡤⠜⡇
⠀⠀⢳⣄⣀⣛⣄⣀⣧⣠⣼⡿⠤⠤⠴⠖⠒⠒⠛⠉⣉⣁⡀⠁⢀⡆
⠀⠉⠉⠉⠻⠭⢥⣤⢿⠖⠋⠀⠀⠀⠀⣶⣿⡆⠀⣐⣿⡿⠷⠒⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣼⣧⠤⠤⠴⠶⠒⠛⠛⠋⠉⠁
⠀⠉⠉⣹⣿⣿⣇⠀⠀⣧
⠀⠀⠀⢻⣿⡿⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⠿⠃
⠀⠀⠀⠀⠉⠛⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠀⠂⠀⠄⢀⠀⠀⠀⠀⠠⠄⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢺⣿⠆⠀⠀⣀⠐⠓⠋⠀⢀⣀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣤⣌⠁⠂⠄⢀⠀⠀⠀⠁⣴⠏⣷⠀⣴⡄⢠⠀⢠⡲⢶⡿⢹⡇⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡿⠃⠀⠀⢀⠃⠀⡄⠰⣿⣴⠇⣴⣿⡅⠀⣥⠈⢶⣁⣀⣸⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠆⠀⠀⠀⠒⣤⣄⣈⠛⠾⠀⠀⠁⠆⠀⠉⠛⠁⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠒⠤⠀⠀⠀⢾⠆⠀⣼⣤⢄⡀⢀⡜⠿⠁⠀⠈⠑⠚⠀⠀⠘⡀⢀⠠⣤⣴⠈⠉⠀⠀⠀⠀⡀⠤⠄⠐⠒⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠤⠴⠀⠉⠋⢥⣬⠞⠒⠂⡀⠀⠠⣄⠀⠀⠀⠁⠀⠀⠘⠹⠀⠀⠀⡆⠀⠀⠀⠠⣤⠒⠲⡄⢡
⠀⠀⣀⡀⣀⠀⠀⠠⠤⡀⠀⠐⢐⠢⡀⠀⠀⠙⣍⠠⢀⡀⠀⠈⠠⡈⠆⡀⠀⠀⠠⠀⠔⠁⠀⠀⠀⢰⠀⠄⠰⠆⣀⣰⠒⠻⢧⢄⣀
⠀⠀⠁⠀⣠⠀⣄⠀⠀⠁⠘⡀⢠⣄⡄⠀⠀⠀⠈⠑⠀⣌⢢⠀⠀⠈⠢⠈⢠⠂⣴⠁⠀⠀⠀⠀⠀⣠⡆⠂⠐⠒⠉⠙⠀⡀⠐⠚⢤⢉⠉⠑⠆
⠀⠀⠀⠀⢻⣿⣿⣻⡷⢸⣿⠹⠦⢌⡃⢄⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠃⡞⠛⠡⢀⠂⠤⣂⠅⠛⠙⣄⣀⡀⠤⡆⠀⡇⠰⠶⠄⣗⠀⠘
⠀⠀⠀⠀⠘⠿⠿⠿⠇⢸⠀⠀⠀⠀⠈⣂⠷⠠⡄⣠⠜⢡⡀⠀⠀⠀⠀⢀⡄⠃⣀⠀⠀⠉⠴⡷⣄⠀⠀⠀⠀⠀⠰⠀⠈⢀⣷⣾⠋
⠀⠀⠀⠦⠄⠀⠀⠀⠐⠋⠀⠀⠀⢀⠔⣡⡶⠆⠀⡌⢠⣟⠋⡼⣣⣴⣤⣬⡙⢎⡠⠤⣙⡞⣀⢰⠃⣄⡀⠀⠀⠀⠦⠀⣀⠈⠙⠃⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣽⠀⠋⢁⠔⡙⠇⢸⠛⣦⣌⠃⣬⡗⠡⣼⣦⣢⡼⢉⠇⡀⡾⠀⠛⠫⠐⠤⣀⠠⠐⡻⠏⠉⠐⠒⠒
⠀⠀⠀⠀⣀⠴⠲⡄⠀⠀⢀⠰⠷⠀⣤⣡⣤⡄⢇⣈⣤⡙⠛⠋⣣⠘⠋⠳⣦⣤⡤⢶⣧⡤⢋⣴⣧⢀⡀⠈⠑⠶⠆⠊⠀⢀⢀⣀⡀⠀⠠⠶⠴⡆
⠀⡠⠐⠉⠠⠀⠀⠀⢦⣾⠄⠂⠁⠒⢄⠙⢮⣻⡊⢹⠋⢉⠟⡟⢴⠀⠀⢠⢏⠳⣚⡺⠷⣝⢯⡹⠁⢆⡆⠂⠀⠀⠀⠀⡏⠀⢀⠒⢄⠀⢀⡀⠀⡇
⠻⡀⠀⢠⠊⠈⢂⠠⠈⢃⠀⠀⠀⠀⠀⠉⠐⢶⣶⣡⢞⣉⠁⡾⢃⣜⠳⢭⣒⡷⢈⣄⢀⣍⣷⠑⣶⣯⣴⣷⠐⠒⠤⠿⠇⠀⠙⠂⠋⡠⢒⢉⠴⡇
⠀⠡⡀⠀⡂⠐⠀⠐⠀⢀⠃⠀⠀⠀⣀⠀⢨⣽⣯⣇⣉⣻⠟⣰⣿⣿⡷⣦⠙⣿⣾⡟⢿⣿⣾⢀⣿⣿⣭⠉⢋⠁⠀⠀⢠⠀⠀⠀⠸⡐⠉⠋⠀⠇
⠀⠀⠁⡀⠀⣁⠤⠒⠉⠀⠀⠀⠀⢠⠁⠉⠒⠩⠙⠛⠛⠿⠾⢧⣼⣏⣴⣿⣰⣿⣵⣿⣤⡿⠧⠾⠟⠛⠩⠐⠉⠀⠀⠀⠸⡀⠀⠰⠶⠧⠤⠄⠀⠚
⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⣀⠣⠤⠤⠤⣈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠉⣑⠂⢄⠠⡂⢤⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢾⠀⠀⠾⠁⠀⠀⠀⢠⡀⠙⠃⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠉⠺⠦⠀⣿⢀⣖⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⣦⠠⠀⠀⢠⡾⠛⡢⣼⡗⠻⠳⡀⠀⠀⠀⠀⠀⠀⣰⠾⡖⣶⣶⡦⣶⡄⠀⠅⡻⢬⣶⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠋⠀⠀⠀⠀⠑⠢⠤⠐⠊⠠⠐⠁⠀⣄⠀⠀⣦⠀⠁⠦⡀⢋⣛⣂⠤⠃⠀⠀⢵⠠⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠴⡎⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿⠀⢦⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠀⠀⠀⢀⣰⠧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠶⠶⠟⠛⠐⠃⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⣈⣐⡠⠈⠁⠐⠢⡄⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠾⡯⣭⣄⣤⣀⣀⣈⣉⣉⠐⠚⢷⡄⠀⠀⠀⡀⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠰⣀⠙⠳⢬⣭⣡⣽⡽⠟⠛⠛⠋⠀⠀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⣀⡄⠈⠀⠀⠀⠀⢐⠑⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢆⣀⡀⠀⠀⠀⠀⠀⠀⠉⠘⠙⠋⠉⠀⠀⠀⠀⠀⠀⣀⢾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠚⠃⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠣⢄⣀⠀⠀⠀⠀⠀⣠⡀⠄⢠⡟⠀⠄⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠌⡙⠛⠓⠰⠴⠴⠤⠞⠋⠀⠌⠀⠀⢀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠘⠀⠐⠀⠃⠚⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠠⠀⠐⠖⠀⠞⠑⠞⠳⠶⠳⠞⠰⠗⠿⠞⠷⠋⠞⡑⠟⠺⠒⠷⡺⢞⠶⢃⠾⡚⢟⠳⠛⠚⠛⡛⠟⠻⠟⠛⠀⠆⠀⠂⠀⠀⠀⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⡋⠁⠁⠠⠈⠉⠭⠑⠒⡛⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣸⡃⠀⠀⠀⣌⢀⡤⣌⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠰⠀⠀⠸⣇⢹⠀⠀⠀⠈⠁⠀⣀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣧⠼⠀⠀⠀⢜⣩⡤⠤⠔⠊
⠀⠀⠀⣠⠴⣒⠲⢄⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠠⠴⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⣬⡅
⠀⠀⠀⣇⣸⠉⣹⢀⠆⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⢀⣞⡵⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠁⣐⡒⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⢡⡦⠀⠀⠀⢀⣀⠤⠔⠒⠚⡳⡦⠀⣬⠀⢀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠇⢇⣀⠬⠀⠸⢸⠧⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡄⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠈⢸⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⢦
⠀⠀⠀⠀⢀⣏⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⡝⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣇⢠⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢠⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢹⡌⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢸⠀⠀⠀⠻⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠉⠉⠀⢘⣗⡿
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠉⠉⠙⠓⠲⠤⢄⣀⣀⣧⠀⠀⠀⠀⢧⠠⢤⣸⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠘⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢳⡖⠒⠒⠒⠲⠶⠶⠤⠤⠤⠤⢿⡄⠀⠀⠀⢸⡥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⠂⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⢈⣿⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⣰⣿⡿⠁⣠⡾⠁⠀⠉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⣿⠏⢀⣴⠏⠀⠀⢀⣼⠋⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⡟⠁⣠⡾⠁⠀⠀⣠⡟⠁⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣾⣿⠋⢀⣴⠏⠀⠀⢀⣼⠋⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⣿⣿⣿⡟⠁⣠⡞⠁⠀⠀⣰⡟⠁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⢀⣼⠋⠀⠀⢀⣼⠋⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠟⠁⠀⠀⣰⠟⠁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢀⡾⠋⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣰⠟⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⡾⠋⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣴⠟⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢠⡾⠃⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⣴⠟⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⣿⣦⣄⣠⡾⠃⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠛⢿⣿⣦⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣀⣤⣶⣾⣿⠿⠛⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠻⡄⠀⣠⠴⠂⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠴⣾⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡴⡿⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⢃⡴⠚⠙⠲⣤⡀⣾⡟⠀⠀⠀⠀⠀⠹⣆⠀⠚⠉⡉⠈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠙⢯⡿⢦⡀⠀⠀⠀⠀⠙⢧⡀⡿⠙⡟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣿⡄⠀⠀⠀⢀⣀⣭⡇⢀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠦⢤⣽⣷⣿⠤⠖⠚⠉⠉⠀⠙⠛⠓⠞⠷⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠴⠶⠶⠶⢦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⢦⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⠶⢾⣷⣤⣬⣵⣤⣤⣵⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⣙⢦⡀⠀⣠⡟⠀⠀⠶⠖⣻⣿⠟⠓⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠁⣿⠂⢙⡾⠋⠀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡶⠟⠁⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠀⠀⠸⣧⠶⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣄⣤⠶⡿⢲⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣽⣷⣭⡙⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⣈⡝⢿⡀⠙⢿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣇⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣠⣶⣶⠾⠷⠿⠿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡯⠀⣿⠷⢼⡇⢰⠜⠃⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⢹⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠠⣾⣥⣤⣤⣤⡴⠛⣻⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢳⠀⠸⡇⠈⡇⢸⠀⢸⡿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢷⣜⣧⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⢷⠀⣿⢸⠇⢸⣇⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⣄⡈⠻⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠸⡇⢸⡿⠀⠈⣿⢹⣆⣿⣤⢴⣶⡤⠶⣶⣆⢹⣷⠤⢀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠛⠋⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡀⠀⠸⡇⠀⣿⣸⣧⣤⠶⠛⠉⠉⠀⠀⢰⣿⠀⠀⣿⡽⠦⠿⠄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠛⠶⠖⠲⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠃⠀⠀⢿⡤⠼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣀⢹⡗⣶⠶⢆⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣒⣚⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣧⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣉⡚⣣⡇⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠙⠓⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠸⣿⡃⠀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡟⠉⠉⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⡏⠙⣿⠉⢻⣏⣉⣠⡤⠶⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⢿⣆⣠⣿⠀⠘⣏⠉⠀⠀⠀⠀⣿⣤⠤⠤⠴⠶⠶⠶⠖⠚⠛⠛⠛
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⡇⠁⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠂⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣧⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⠤⣤⠼⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠛⢛⣻⣿⣿⣿⠿⠧⠤⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠒⠒⠂⣉⡿⠋⠀⣮⠈⠛⠓⠶⠶⢠⡿
⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⢀⣀⣀⣤⣤⣤⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣀⣤⠴⠶⢿⡷⠻⠛⠒⠒⢠⡄
⠻⣤⣀⣀⣈⠹⣦⣹⣯⣭⡿⠿⠛⠛⠋⠉⠁⠀⠀⠉⠉⠐⠶⠾⠶⠧⠶⠶⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡋⢹⣿⡋⣻⣿⠉⣿⣿⣿⣿⠄⠀⠀⠈⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠈⠛⠶⢤⣤⣤⣤⣤⣤⣄⣺⡏⠁⠀⠀⠀⣠⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⢸⣿⣿⣿⣿⡟⠿⢿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⡿⠿⢻⣿⣿⣿⣿⡇⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠙⠿⠿⠷⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠾⠿⠿⠋⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣿⣿⣿⣧⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⣼⣿⣿⣿⣿⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣿⣿⣿⣿⣿⡏⠉⠙⢿⣿⣷⡀⠀⠀⢸⡇⠀⠀⢀⣾⣿⡿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⣿⣧⠀⢸⡇⠀⣼⣿⣿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣿⣿⡇⢸⡇⢸⣿⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣻⡿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠁⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣘⠋
⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⣦
⠀⠀⠀⠀⣼⡏⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠹⠷⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡗⠦⣀⠀⠀⠀⠙⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢋⣤⡄⠀⠀⠀⣀⡀⠀⢀⣹⠀⠀⠙⠲⠤⣤⠼⠀⠈⠳⣄⠀⡷⢦⡀⠀⠀⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠈⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃⠀⠀⠀⠀⠀⠀⣈⡃⠀⠀⠀⠀⠄⠠⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡴⠋⠉⠉⠓⣆⠀⠀⣠⣤⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠘⡆⢸⠱⠀⠈⣧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠦⣀⡞⠀⠀⠀⠸⡄⠀⠀⠀⠀⢿⡇⠘⣆⠀⢀⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠛⠓⣌⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡼⠀⠀⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⢆⠀⠀⠀⠀⠀⠈⠦⠒⠚⠁⠀⠀⣈⠀⣸⠂⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⠦⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡔⠀⠀⠀⠉⡷⠒⠶⠴⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢲⠞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣍⡛⠃⠀⡞⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣂⣀⡴⠧⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠉⠁⠀⠠⢤⠬⢍⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⠉⢻⣙⣒⣶⣶⢟⡒⣻⠋⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠟⠚⠉⠈⠑⠛⠽⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠚⠛⠛⠛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣶⣿⡿⠁⠀⠀⢹⣿⣶⡄⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠉⣿⣿⣄⣀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠻⠟⢻⣿⡿⠛⠿⢁⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⣶⡟⠛⢿⡖⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣠⣼⢧⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⣉⣉⡉⠛⠓⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⣠⠴⠂⠀⠀⠀⠀⠀⢀⣴⠛⣧⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡴⠋⠁⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠘⣆⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⢀⣀⠀⠀⠘⣦⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠉⠉⠛⠲⠎⢳⣄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠴⠶⠚⠋⠉⡙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠷⣄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡏⠀⠀⠀⣀⡻⣤⢷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣶⡾⣤⢟⣀⠀⠀⠈⠙⢿⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⢸⠃⠀⠀⠀⠈⢻⠃⠸⢿⡿⠹⡆⠀⠀⠀⢠⡏⠻⣿⠇⠈⣿⠀⠀⠀⠀⠀⠈⡇⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡴⢻⡟⢿⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⣸⡇⠀⠀⠀⠈⢧⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡿⢻⡟⢦⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠷⣼⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢹⡇⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣯⠼⠁⠀⣸⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⡶⣶⠿⣶⠶⠶⣶⡶⢶⡶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠁⠈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⡤⠀⠤⡀⠀⠀⠈⢳
⠀⠀⠀⡀⠤⠐⠀⠀⠀⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠼⠶⠯⠓⠁⠀⠀⢀⣾⠟
⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⣀⣀⣀⡠⠔⣩⠏
⡌⠀⠀⠀⠀⠀⡔⠒⠀⠒⠄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢀⠤⢑⠂⡤⠴⣫⡴⠶⠶⠶⠛⠁⠁⠀⠄⠀⠒⠒⠒⠀⠠⡀
⠇⠀⠀⠀⠀⠀⠻⣍⠛⠒⠦⣐⠀⠀⠀⠀⣷⠀⠀⠀⢠⡄⠁⠀⠀⠈⣷⡶⠓⠀⠀⠀⠀⠀⠰⠈⠂⠀⠀⠀⠀⠀⠀⠀⠨⠳⡄
⠀⠀⡀⣀⠀⢀⡴⢿⠄⠀⠀⠉⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠁⠐⠠⢎⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⢀⣲⣉⣭⣍⠂⠀⠀⠀⢁⡧
⠐⠄⠘⢥⡔⠁⣢⠧⠀⠀⠐⢄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠁⠊⠴⠟⠂⠀⠀⠀⠀⢀⠀⠂⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⣠⢾⠇
⠀⠈⠀⣼⡴⠛⠁⠀⠀⠀⠀⡄⠑⢄⠀⢀⡡⣾⡥⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠐⠀⠀⢀⡠⠔⠒⠢⠤⠤⠤⠐⢊⡥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣨⣍⡞⠁⠀⠀⠈⢑⣄⠀⠀⠀⢀⠔⠀⠀⠈⠂⢬⢒⣩⣴⡾⠿⠿⠻⠶⣶⣿⠯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠢⢒⣠⠴⢹⠗⠀⠀⠀⠈⠐⠠⡀⢀⡔⣿⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢘⣠⣴⡋⠀⠀⠀⠀⠈⠀⠀⠀⣯⠞⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄
⠀⠀⠀⠀⠀⠀⢸⣠⣾⠃
⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⢀⣾⠟⣁⣷⣤⣄⠀⠀⠀⠀⢠⠶⠚⢻
⠀⠀⠀⠘⣿⠰⡟⢹⡍⢻⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠢⢭⣪⣷⠞⠁⠀⠀⠀⣤⠇⠀⠛⠃⠀⠀⠘⡳⡄
⠀⠀⠀⠀⠀⣠⣤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠻⠿⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⠀⠀⢠⣀⠀⠀⠀⠀⢸⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⢸⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠘⠛⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠐⢢⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⢔⠑⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠠⢄
⠀⠀⠐⠀⡀⢀⠀⠄⠀⠀⠀⠈⠂⢩⠒⠉⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠄⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⠂⢄⠀⡇
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠦⡐⣃⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠤⢚⡤⠞⣠⠇
⠀⠀⠀⠀⢠⠋⡢⠀⠀⠀⠀⠀⠀⠀⢨⣀⣨⠇⠀⣀⠑⠀⠀⠀⠀⠀⠀⠈⠐⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠠⠄⠂⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠄⠀⠀⠠⠁⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⣀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠈⠀⡐⢢⠈⠄⠀⠀⠀⠀⠐⢂⠀⠀⢀⠔⡀⠌⠂⠀⠀⠀⠈⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⢆⢁⠊⠀⠀⠀⠀⠀⠀⠈⠓⡀⠈⠢⠥⠀⠀⣠⡤⠄⠠⠄⠄⠁⠀⠀⠀⢀⠀⠀⡂⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠊⠀⠘⠍⠧⡄⠀⠀⠀⠀⢀⡠⢠⡀⡓⠊⠀⠀⠀⠀⠀⠬⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⡐⠀⠀⢆⠀⠀⠀⠀⠈⠀⠱⣠⠉⢒⠁⠀⠀⠀⠀⠁⠤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠂⢀⠄⠀⠀⠀⠀⠊⠐⠲⠚⠃⠀⠀⠀⠀⠀⠀⡨⠃⠉⠀⠀⠀⠀⠀⠐⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⠠⠀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⡠⠀⠂⠄⠀⠀⠀⠀⠀⠀⢐⢀⡆⠀⠀⠀⠄⠀⠀⠰⠐⡤⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢄⡀
⠀⠀⠀⠀⠀⢀⡐⢑⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢯⣰⠖⡆⢹
⠀⠀⠀⠀⠀⠀⠨⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠄⠒⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢉⠕⠋
⠀⠀⠀⠀⠀⠀⠠⡉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠖⠉⠡⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⢢⢈⠀⠀⠀⠀⠀⠀⣀⡂⠒⠂⢤⡠⠐⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢀⠊⠀⠀⠀⢠⠂⠁⠀⠀⠙⠄⢸⠇⠁⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡆⠀⠀⠀⢧⢀⣀⣀⡀⠀⠈⣩⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠐⠀⠻⠟⠩⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠢⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠿⢿⣿⠿⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⢙⡁⣤⣶⣾⣾⣷⣶⣬⡄⠀⠀⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠈⢉⡽⠟⠛⠉⠁

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⣶⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⣟⠉⠉⠉⠉⠉⠉⠁⠀⠀⢻
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣠⣤⠤⠶⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡉
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢌⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢄⠁
⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠛⣻⢆⣤⣄⢀⣠⣀⡀⠀⠟⣀⣀⠀⣠⣴⡇⢠⢤⠀⣦⠞⠀⠀⣿⠢⡀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⢯⡁⠸⣏⡉⠰⡏⡟⣷⢸⡇⣿⠉⡇⢯⠞⣇⠘⢯⠀⠻⠀⠀⠀⣯⠑⠄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠁⠀⠈⠁⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡱⠄
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢆⠙
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢫⡈⢢⠁
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣾⡟⢯⠙⢄⠑⢄
⠀⠀⠀⢰⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡉⢦⠑⣄⠳⡈⠳⡀
⠀⠀⠀⠀⠀⠉⠉⢯⠻⡉⢻⡙⢟⠛⢿⠛⢟⠛⣟⠛⣟⠛⢏⠉⢣⠘⢆⠑⡄⠱⡌⢢⡙⠄
⠀⠀⠀⠀⠀⠠⡌⠆⠣⠱⠄⠱⠌⢢⠀⢣⡈⢣⠘⣆⠈⢆⠈⢣⠀⠳⡈⢦⠈⠦⠈⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢌⠀⠀⢠⣼⠂⠀⠤⢐⠺⣵⠤⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢀⣀⡴⠀⢸⣧⣶⡿⢩⠷⠆⠐⠒⢙⠛⣟⠩⣿⣿⣦⡀⠐⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠶⡯⠐⣚⠛⢻⡷⣔⠉⠐⠋⠛⠳⠄⢲⣍⠁⠾⡖⢋⡕⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠢⢼⡇⠁⠈⡌⠉⠁⠀⠀⢈⣀⣀⡀⠀⠈⠀⠉⠲⣷⣀⣓⣧⡴⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢾⠣⠐⠦⠘⠄⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠂⠾⠫⡥⠀⠀⠘⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⢀⣰⣇⢠⠎⠀⠀⠀⣾⣿⣿⣿⠋⠉⢻⣿⣿⡇⠀⢠⠀⠈⠠⣄⠐⠻⠖⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣉⡾⣝⡋⠛⠂⠀⠀⠀⠉⠉⠉⢁⠀⠀⣸⣿⣿⡏⠀⢈⡿⣅⡀⡽⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠻⢬⠩⠤⠀⠀⢹⢀⡄⢔⣢⡤⠂⢀⣴⣿⣿⣿⠃⠀⠈⠁⠡⡆⣱⡶⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠐⣧⠄⡸⠃⣀⣚⠁⠂⢠⣿⣿⣿⡿⠁⠀⠀⡀⢀⡞⠀⠀⣄⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠉⣀⣡⠠⣶⣹⡀⢿⡁⠀⠀⣿⣿⣿⡏⠀⠀⠄⠒⠋⢻⡟⠢⢁⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣽⣇⠂⠀⠻⣤⡏⣁⡀⠈⠛⠛⠉⡡⢀⣴⠒⠐⢂⡉⠸⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢯⠠⠔⢃⣿⣿⡟⠃⠀⣿⣿⣿⡄⠀⢛⢡⣀⣼⠀⠀⠉⠋⠓⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⣇⢠⣿⢿⣹⣿⡄⠀⠿⠿⠿⠃⢀⣞⠚⡉⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢋⣼⣇⣹⣿⡥⠃⠀⠤⠠⠖⠞⠉⠛⠉⡙⠉⠙⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢈⣁⣀⣁⣤⣤⣄⣠⣄⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠉⠉⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠤⡄⠀⣠⠤⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⣷⠀⠀⠀⣾⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡏⠉⣠⣌⠈⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣅⠸⢿⡿⠀⣼⠿⠿⣿⠟⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠻⠴⣄⣰⡶⠿⠀⢀⣀⣀⠀⠛⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢠⣶⡄⠙⣿⣄⠀⢰⣿⣿⣿⣷⡀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⠈⡛⢁⣨⣿⡏⠀⠘⢿⣿⣿⠟⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⢀⣀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠟⠛⠛⠛⠋⠉

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠀⠀⠀⠀⠈⠑⢦⣠⣴⣶⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⡞⣠⠖⠒⠖⠒⠊⠁⠈⠻⢿⣿⣿⣿⣿⣿⢿⣿⣦⣀⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠘⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⡿⠃⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠋
⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢿⠀⠀⡄⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠈⠧⢼⡃⠀⢸⠀⠀⢹⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⠀⠀⡇⠀⠀⡷⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡇⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡴⠶⠶⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠛⠈⠛⠛⠛⠛⠀⠛⠒⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡏⠀⠀⠀⣬⢻⡄⠠⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⠻⣦⡾⠁⣸⠇⠠⡤⠤⠤⠤⠤⠤⣤⠄⢀⣿⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠶⢤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠐⠒⠶⢦⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠞⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣀⣀⣀⣀⢸⡇⠐⠶⠶⠶⠶⠶⠶⠶⠞⢧⣀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀⠀⠀⢀⡼⠁⠐⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⠁⠒⠒⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⠀⠀⠈⢳⡄⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠛⠛⠛⠛⢸⠇⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠧⣶⡄⣶⣠⣶⢄⣶⢰⠆⡖⠂⡗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠉⠀⠉⠈⠉⠈⠀⠉⠁⠁⠁

⠀⠲⡀
⠀⠀⠈⢆⠀⠀⠀⣀
⠀⠀⠀⠀⠑⢄⣼⡿⣆
⠀⠙⢄⠀⠀⢸⡟⠤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠑⢤⣸⠁⣠⣿⠓⠢⢀⣀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠶⢶⠀⠀⠀⠀⠀⠀⢀⡀⠠⠖⠀⠀⠐⠂⠋⢀⠀⠒⠀⢠⡀⠀⠠⠄
⠀⠀⠀⠀⠀⣨⣷⣿⣇⠀⠀⠀⢸⠉⠁⠀⠀⠚⠉⠁⠰⠛⠂⠀⠀⠀⠀⢠⠄⢠⠄⠈⠀⠀⠐⠃⠉⠁⠀⠀⢈⣠⡔⠂⠀⠈⠀⠐
⠀⠉⠲⣤⣴⣿⢿⠁⠀⠉⠐⠒⢸⠄⠠⠀⠀⠐⠂⠀⢀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠃⠀⠀⠈⠁⠀⠖⠂
⠀⠀⢠⣿⠟⠓⣸⣤⣄⣀⠀⠀⢸⠉⣿⡀⠀⣀⡆⠀⠈⠉⠁⠀⣾⡷
⠀⣀⣿⡏⠀⣼⠿⣿⠻⢿⣧⠉⠹⠋⠁⠀⠐⠿⠃
⠀⠈⢹⡗⠶⢯⣤⣼⣄⣈⣿⠤⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠙⢦⣀⠁⢀⣧⠴⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⠿⠋⡄
⠀⣀⣀⣀⣀⣈⣉⣉⢽⡤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⠠⡄⠀⣤⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠰⠆⠁⠰⠃
⠀⠀⠀⠀⣼⣿⣧⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢹⣷⠰⠀⠛⠁⠀⣀⢀⣄⠘⠋⠜⠛⠀⠀⡉⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠻⢿⣋⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡟⠀⠀⠀⠀⠈⠉⣈⡁⠀⠀⠀⠀⠀⠀⡘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠉⠉⠙⠛⠃⠀⠀⠀⠠⠀⠀⠀⢀⠉⠓⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣤⠀⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠻⠏⠙⠃⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠄⠂⠀⠈⠉⠉⠀⠒⠢⢄⠀⢀⡼⠇⠀⠀⠀⠀⠀⠤⢱⣄⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠦⣄⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⡄⠀⠀⠀⢳⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠒⠚⢛⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠚⠉⢀⣀⡉⠓⣄⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⣽⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣧⣤⢸⡄⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⣣⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠈⢧⣀⠈⠿⡿⠿⠋⣸⠃⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡼⠀⠀⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡆⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠀⠒⠁⠀⠀⠀⠀⠈⠂⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣴⠲⢦⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠴⠲⡄
⠀⠀⠀⠀⠀⠙⢦⣄⠉⠳⢤⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣫⠴⠛⢁⣤⠞⠁
⢀⣴⢒⡛⡏⠉⠉⠉⣤⣤⡀⠹⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠞⣽⠁⢀⢤⡌⠉⠉⠉⣿⣿⡲⣤
⣿⠥⠤⠒⠒⠀⠀⠀⠀⠀⢹⢸⡅⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠂⠀⠀⣽⢠⡁⠀⠀⠀⠀⠀⠒⠲⠦⢬
⢳⣀⣤⠤⠤⠤⠤⠴⢶⡖⠋⠀⢧⠀⠀⠀⠀⣠⠏⠉⣟⠲⠶⠦⣤⣤⡤⠶⠶⣾⠛⢯⡀⠀⠀⠀⢠⡏⠀⠓⣶⠶⠦⠤⠤⠤⠤⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢧⣄⣤⠞⠁⠀⢠⡏⠢⠤⠚⢿⣿⠟⠢⠄⢹⡀⠀⠙⠦⣤⣠⠞⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⢰⣼⡄⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠖⠒⠒⠚⠉⠀⠀⡇⠀⠀⠀⠈⢙⣧⠀⠀⠀⢣⠈⠉⠒⠒⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢿⣿⡯⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣶⠒⠲⡆⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢰⠀⢸⠇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣠⠞⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣟⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣬⣧⡀⠀⠀⣴⣏⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣾⣿⣛⣛⣻⠿⠛⠶⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢶⣥⣀⡀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡐⠂⠈⠙⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⠁⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣎⠁⠀⡈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠉⣩⡿⠟⠉⠁⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠡⠄⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡀⠀⠤⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠸⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⡀⠤⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣤⣀⠀⢸⡏⢈⣠⣴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠐⢺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠤⢤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⠤⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠤⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⢂⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣥⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠥⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⣴⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡿⠟⠻⠟⡛⠛⢉⣋⣽⠟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣁⣀⣠⣈⣤⣦⣴⣾⠟⢋⠤⠊⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠛⠛⠋⠉⠉⠉⠉⠀⠀⣿⠊⡠⠔⢈⠤⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠠⠒⠡⢂⣽⠇
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢐⣠⠾⠋⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⣠⣤⣤⣼⡷⠟⠁
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⣀
⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⠁⠉⠛⠆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢿⣻⣿⡂⠀⠀⠀⡰⠋⢁⣠⣤⣄⠈⠻⡄
⠀⠀⠀⠀⡜⠁⠀⡤⠶⠶⣄⠀⠀⢸⠀⠀⠀⠀⠀⢸⢿⡟⠁⠀⢹⣩⣹⠃⠀⠀⠀⠁⠠⡃⠀⠀⠈⠇⠀⠘
⠀⠀⠀⠀⡀⠀⡌⠀⠀⠀⣸⠀⠀⡸⠀⠀⠀⠀⠀⠸⣾⣷⢀⣴⣿⡿⠋⠀⠀⠀⠀⢦⣤⠵⠄⢀⣀⠞⠀⢠
⠀⠀⠀⠀⠙⠚⠁⣤⠖⠚⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢡⡻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢉⣁⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠚⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⠇⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⢸⠉⠁⠀⣀⣤⣄⡀
⠀⠰⠊⠉⠑⠄⠀⡇⢸⡀⠀⠀⠀⠀⠘⠉⠙⢧⠀⠀⠀⢹⣿⠦⠀⠀⠀⠀⠯⠈⠙⠄⠀⠸⢬⠆⠀⠸⠅⠀⠀⢙
⠀⠀⠀⠀⣠⠆⠀⠘⣒⣃⠀⠀⠀⠀⢀⡤⢤⡾⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⣀⠄⠀⠰⣋⠀⠀⠀⠀⢀⡤⠎
⠀⠀⠐⠉⠁⠀⠀⠀⣁⣨⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢈⣛⣁⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠘⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠰⠀⠀⠀⣠⠶⠛⠉⠉⠉⠛⠗⢦⡀⠀⠁⠀⣀⣤⣶⣶⣶⣶⣦⣄⠉
⠀⠀⠀⠀⢠⠞⠋⠉⠉⠉⠛⢷⠀⠀⠀⠀⠀⢸⠁⢠⣾⠛⠲⣤⡀⠀⠀⠁⠀⠀⣼⡿⡟⠛⠛⠛⢿⣏⠙⡆
⠀⠀⠀⠀⢫⣀⡴⠚⠛⢆⠀⢈⡁⠀⠀⠀⠀⠘⢤⣠⡜⠀⠀⠀⡇⠀⢀⡖⠀⠀⢼⣟⣿⠀⠀⠀⢸⣿⣴⠃
⠀⠀⣀⣄⡀⠀⠀⠀⢀⠎⣰⠟⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠉⠁⠀⠀⣴⣿⠟⠁⢀⣀⡀
⠀⢨⣀⠀⠙⠀⠀⠀⡞⢸⠁⠀⠀⠀⠉⠉⣻⠀⠀⠀⢀⠴⢋⠔⠊⠁⠀⠀⠊⠙⠢⠀⠀⠀⢸⡟⠁⠀⠀⡁⠀⠈⡆
⠀⠀⢀⡤⠖⠀⠀⠀⢻⡞⠀⠀⠀⠀⢸⠉⠉⠀⠀⠀⠘⢶⠃⠀⠀⠀⠀⠈⢁⠤⠎⠀⠀⠀⣘⡁⠀⠀⠀⠀⠊⠉
⠀⠀⠠⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠸⣌⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢀⡄⠀⠀⠀⠤⠤⠤⠠⠀⠸⠥⠀⠀⠀⠀⠀⠒⠛⠶⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠠⠅⠴⠆⠒⠒⠒⠂⠀⠀⠀⢺⠁⠀⠀⠀⣶⠆⠀⢠⠠⠠⠤⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠓⡆⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠄⠀⠀⠠⠄⠠⠄⢴⠖⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠈⠀⠀⠀⠀⠀⠐




⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⡀⠀⠀⢐⢦⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⣁⡀⠠⠼⠤⠤⢤⣤⢄⣙⣀⣉⢁⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠐⢸⡡⠶⡄⠀⠐⠒⠚⠓⠢⣤⠤⢬⣍⣉⣙⣛⠒⠒⠶⠦⠤⠤⢤⡶⠤⠤⠤⠤⡤⠤⠤⠒⠒⣲⡃⠉⠛⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⢀⢵⡚⠃⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠛⠒⠂⠀⠀⠀⠉⢀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠸⠀⠀⠀⣀⣠⠤⠤⠴⠶⣶⠶⠷⠤⠤⣄⣀⣀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠤⢴⡿⠶⣾⠿⠟⠿⠯⠭⣖⣒⠒⠶⠬⢭⣄⣀⡀⠀⠀⠀⠉⠉⠙⠛⠒⠦⠤⢤⣄⣀⡉⠉⠉⠉⣉⣡⡄⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢤⣉⣙⡒⠶⠤⣄⣚⡁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠒⠒⠮⠭⠿⠶⠶⠮⠤⠴⢤⣀⣀⢠⠤⠤⡾⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⡎⠀⠀⠀⠀⣀⡤⠀⠸⡇⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠴⠀⣀⡸⠀⠀⣠⠖⠋⡁⠠⠆⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⢀⡶⠀⠀⠚⢀⠀⠘⠟⠃⠀⠈⡀⠴⠀⣡⠤⣤⡤⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠌⢆⠀⢾⠁⠀⡾⠀⠀⢠⡄⠀⠀⠄⠈⠁⠀⣀⠡⢮⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠉⠠⠀⢁⣦⠀⠀⠀⠈⠁⠀⠂⠂⠐⢏⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⡌⠀⠐⠁⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡤⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⢠⡄⠀⠀⠀⠀⡠⠛⠛⠳⢶⠄⠀⠀⠀⢻⣄⠛⢶⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠤⠀⣠⠀⠀⠀⠀⠺⠷⠃⢀⣤⣠⠂⠀⠀⠀⠀⠀⠉⠋⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠀⠆⡞⣵⡢⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⣤⡄⠘⢃⡙⠀⢉⡎⠁
⠀⠀⠀⠀⣀⡀⢠⡀⢠⡞⠁⣄⠁⢄⡈⠉⠀⢀⠈⠁
⠀⠀⠀⢀⡉⢩⠉⢉⠉⣃⠘⠋⠀⠀⠶⠀⠠⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⣢⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣏⣋⢳⠀⠀⠀⠀⠀⣠⣤⡴⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠂⣄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣦⣈⡭⠓⣄⠀⠀⠀⠀⠉⠀⠀⣀⡇⠀⠀⠀⠈⡒⢭⡀⢀⡉⡤⢀⣠⠀⢀⡴⠁⠴⢀⡀⠒⠀⠄⠤
⠀⠀⠀⠀⠀⠉⠀⢠⠖⣒⠦⠐⠀⠀⠀⠀⠛⠀⠀⠀⢴⡾⠀⠈⠛⠁⠀⠀⠀⠀⠙⠚⠱⠎⢠⠀⠛⠛⠀⠈⣀⠛⠀⠈⠁⠛⠠⡤⣀⢚⡀
⠀⠀⠀⣤⠀⠀⠰⠆⠋⠒⣀⣤⠀⠀⠀⢠⡁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢠⡄⢀⡄⠀⣀⡴⠚⢁⠀⠖⠀⠀⠀⠀⠀⢛⠁⠀⢀⡀⠻⠃⠐⠂⠀⡄⠒⠒⢀⡙⠆⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠘⠃⠀⢉⠠⠆⠉⠀⠀⠀⣠⠾⣷⠄⠀⠀⠀⢛⠁⢀⣴⠄⠀⠄⠱⠚
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠶⠀⠘⠁⠀⠲⠟⠁⢰⢨⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠡⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠆⠀⠀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢡⡀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⠈⡀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠬⠁⡼⠀⠀⠀⠠⢤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠠⠈⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠠⠀⠀⠤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠄⠀⠈⠀⠀⢠⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣀⡠⠀⠠⠀⠀⠀⠤⠤⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⣦⠀⠄⠀⠀⠀⠀⠀⠈⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⢿⣿⣿⣿⣿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡴⢋⡙⠳⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠉⢀⣀⠀⢛⡟⢠⡤⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠘⣇⠺⠼⢀⡗⣼⣿⣦⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠸⠿⠀⢠⣿⡤⣤⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠈⠓⢒⡯⠦⣝⠟⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣠⣤⣟⠁⣤⡀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢸⡸⡽⣸⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⣠⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢧⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠁⠀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣁⠀⠀⠀⡀⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣾⣿⣿⣶⣄⠀⠀⣀⣀⣀⡀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠒⠚⠉⠀⠙⠋⠻⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⣾⡀⠀⣀⣰⡏⠁⠀⠀⡘⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣼⣿⣿⣇⠀⡄⠀⠙⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⠕⠶⠶⠂⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⠀⠀⠀⢹⣿⣩⣔⠒⠶⠶⠄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢰⣦⣀⢰⡀⢛⣴⡀⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠶⣶⣤⣤⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠀⠀⠈⠙⣿⣿⣷⣿⣌⣿⠀⣅⣽⡜⢷⣤⣼⠿⣿⣿⣆⠀⠀⠀⠉⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⣴⡆⠀⢉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢻⣎⣿⣿⠀⠈⠻⣿⣶⠀⠀⣼⠋⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢻⣿⠗⠊⠙⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠷⣈⠛⠲⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣤⠄⠈⠁⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠙⢶⣷⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⢿⣿⣿⣿⣷⣶⣠⣤⣾⣿⣿⣿⠟⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡿⠿⢿⡿⡁⢀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⡿⠟⠉⠀⠀⢈⠁⣠⡄⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⢸⣴⠀⠀⠀⠀⠀⠀⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⣀⣀⠀⣧⣴⣿⡏⢠⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢄⢰⡆⠀⠀⠀⠀⣙⣿⣿⣿⣾⣶⣶⣶⣆⡀⠀⡀⠠⠦⠀⢠⡇⠀⠻⣿⣿⣿⣿⣿⣱⣮⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⢀⡀⢀⣦⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⣞⠛⣧⣴⣿⣿⣵⣤⣤⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⠀⠀⠀⠘⢷⣽⣿⣿⠿⢛⠛⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣯⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠁⢀⣦⠐⢦⣈⣾⣿⣴⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣰⣿⣿⣧⣿⠿⠛⣡⣿⣿⣿⣿⣿⣿⣿⡿⠇⠠⣿⠏⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠻⣿⣾⣿⣧⣄⠀⠀⢼⣿⣿⣿⣿⣿⡿⢀⣶⣾⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⠀⠙⠋⠁⠀⠚⢿⣿⣿⣿⣿⣷⡏⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⢯⡀⠀⠀⣸⣤⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⡤⠀⠀⠀⢉⡥⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣄⠀⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣠⣤⡜⠻⠟⣻⣿⣶⠶⠀⠀⢹⣿⡟⢿⣿⣿⣿⣿⣿⣀⡈⠙⠂⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠈⠄⠀⠈⠛⠛⠀⠀⠀⠀⢈⠟⢡⣦⣨⣿⣿⣿⣿⣿⣿⣶⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢤⣼⡃⠁⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⡗⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣿⡧⠀⠀⠠⣶⡄⠀⢀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣟⣷⠙⢷⣄⣀⡀
⠀⠀⠀⠀⢠⡖⠶⠞⠾⠟⠻⠝⠁⠤⠀⠛⠿⠿⡤⠶⠀⠀⠀⠀⠀⢀⠙⢦⣄⣀⠀⠀⠀⠚⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣦⡕⠠⠀⣀⡀⠄⢤⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣄⠉⠻⣶⣷⣼⠿⠋⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣤⣤⣬⣝⣛⣙⣿⡿⣿⣷⡆⢀⣸⣟⣿⣿⠛⢿⣦⣤⣤⡤⢶⣦⣶⣶⣶⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣾⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣁⣈⣉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡋⠉⠉⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⣠⠆⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⠈⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⡇⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠀⠀⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⠶⠄⠀⠀⠀⠀⠀⡞⠉⠙⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⡉⠒⠊⡇⠀⠀⠀⢀⠀⠀⣠⢒⡩⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠋⠀⠙⣦⠀⠀⠀⠀⢸⣄⣀⣀⡏⠀⣸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣟⠓⠈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⠀⡜⠉⠑⠂⠓⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⣻⠟⠀⠀⠀⠀⠀⠀⠈⣪⣉⢼⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡘⠒⠀⠀⠀⠀⠀⠀⠈⢁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠣⡀⠀⠀⠀⣀⠴⠊⠙⣿⠃⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠀⠀⠀⠀⠀⣀⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⣈⡩⠤⠖⡋⢸⣻⡄⠀⠀⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣀⣤⣄⠐⢯⣀⣨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡯⣒⡇⠀⠀⡏⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠽⢷⢶⡏⣀⡸⠀⠀⠀⣾⡕⠉⢱⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠖⠁⠀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⡼⠀⠀⠈⠙⠒⠶⢤⡟⠳⢤⡻⠔⠊⠈⢆⠀⠀⡔⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣀⣀⣀⢀⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠼⠀⠒⠒⠀⠀⢻⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠓⢨⡥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠓⠚⡄⡳⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⣧⣷⠇
⠀⠀⠀⠀⢀⣀⡀⢡⠀⠀⠀⠀⠀⢸⠁⢀⣤⠀⠀⢣⡞⠉⢙⡂⢠⡴⢦⠀⠀⣈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⡏
⠀⠀⠀⢰⠁⠀⢉⣈⡀⠀⠀⣠⣤⢤⣍⠀⠈⡆⠀⠀⠰⡖⠋⠀⠹⣀⠠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⡀⠀⡇
⠀⠀⠀⠈⢦⣤⠼⠁⢩⠀⠀⢯⡀⠀⣹⣀⣤⡥⠀⠀⠀⢣⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠷⣾⡤⣇⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢠⢶⡀
⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⡿⠋⣼⣿⣿⢙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⣸⣼⠇⠀⠀⡷⡄
⣿⣿⣿⣿⣿⣶⣿⣿⣿⠏⣠⠾⢿⣿⡛⣸⣿⣿⡏⣩⣿⡇⠀⠀⠀⠀⠀⢸⠉⣀⡇⠀⣾⢿⣅⡀⠀⢴⡿⠀⠀⣾⠗
⣿⣿⣿⣿⣉⣸⣥⣼⣿⡀⣷⣶⡆⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⠀⠀⠀⢴⡾⠘⠻⠃⠘⣿⠏⡏⢻⠆⠀⠀⠀⠘⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠚⣧⣾⣿⣿⢿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣵⢻⠉⠀⣀⡀⢀⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⢠⣴⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠙⠛⠋⠀⢸⠟⠃⢸⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠑⠢⢍⣛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠑⠦⣌⣉⠒⠤⡉⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣑⠢⢭⣑⠢⢍⡙⠒⠤⣀⠀⠀⠈⠙⢷⣄⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠓⠮⣍⣒⠦⢍⣓⠢⠄⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣭⣷⣦⣌⣁⠐⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣯⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣄⣠⣤⣴⣟⣁⣤⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢻⣿⢿⣿⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢛⣛⣛⣻⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡜⠘⣯⠉⣿⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠁⠀⠘⢧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⢶⡟⣀⣠⣤⣴⣦⣬⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⢤⣭⣉⣉⣉⣉⣉⣉⣛⣛⣛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⢶⡾⠿
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠒⠒⠤⠬⠭⠭⠭⠭⠭⠍⠉⠁⠀⠀⠀⢠⡟⠳⢤⣀
⣼⠃⠀⠀⠀⠉⠑⠢⠄⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣒⡒⠒⠒⠢⠤⠤⠤⠤⢬⣭⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠄⢀⣀⣀⣀⣀⣈⣉⣉⣉⠉⠉⠉⠉⠉⠉⣛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⣤⣽⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣭⣭⣭⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⡦⠄⠤⠄⠀⠀⠀⠉⠁⣀⣀⠀⠀⠙⣟⠛⠋⠉⠉⡟
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣉⣩⣭⡿⠿⠟⠛⠛⠛⠛⠛⠒⠶⠶⠾⠿⠛⠀⠀⠀⢸⠃
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠛⠉⠁⢀⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠶⠒⣛⣉⣉⣤⡤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣈⡳⣭⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁

⠀⠤⠂⠉⠉⠉⠐⠢⢄
⡌⠀⠀⠄⠒⠠⢀⠀⠀⠑⡀
⢇⠀⠸⠀⠀⠀⠀⢡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⠃
⠀⠀⠀⠀⡀⠊⠀⠀⡠⠊
⠀⠀⠀⠘⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡙⢄⠀⠀⡔⠄⠀⢀
⠀⠀⠀⢠⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠄⠁⠀⠀⠁⠀⠀⠀⠃⠈⠰⠁⢆⠰⠄
⠀⠀⠀⠈⢄⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠨⠀⠢⠀⠀⠀⠀⠀⠀⠀⡠⡶⢠⠄⠀⠤⢀⠀⠀⠀⢀⡀⠠⢤⡀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠄⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢰⡄⠂⠀⠂⠀⠀⠐⠂⠐⠠⠀⠀⠀⠀⡠⢤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣸⢠⣖⠒⠢⡀⠀⢠⣄⠠⢄⠀⠀⠐⠎⡠⠂⡆⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⢄⡀⡁⢻⠘⠥⠀⠔⠇⠀⠫⣉⣀⠜⠀⠀⠀⠀⠑⠀⠇⣠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠀⢀⠈⠙⢸⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠸⠀⠀⡀⠀⠀⠁⠄⠤⠀⠀⠀⠀⠀⠀⠀⢘⡁⢀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠁⠀⠀⢃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⠐⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠠⡀⣀⠀⠤⠀⠈⠀⠀⠀⠀⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠈⠐⠀⠤⠄⠤⢴⠀⠠⡀⠀⠀⠀⠀⠀⡠⠂⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⡰⠤⡒⠉⠀⠀⠀⢀⠄⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠐⡠⠚⢠⢀⡘⢆⠀⠠⠂⠁⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠂⠀⠀⠒⠀⠀⢀⠂⠑⢄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠊⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠚⠀⠢⡀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⡀⠀⠀⠇⠀⠀⠀⢈⠀⠈⢢⣤⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡘⠀⠀⠀⠀⠀⠂⠄⠉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠄⢤⠀⠀⢠⠀⠀⠀⠀⠀⠄⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠉⠉⠉⣛⣃⠀⢀⣀⡉⠍⢖⡒⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢠⡠⠀⡠⠖⠉⠀⠀⠀⠀⠀⠈⠉⠲⣌⠉⢦⡀⠈⡁⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡤⠊⢀⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⢣⡀⢸⠃⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢀⡠⠃⢀⡏⠀⠀⢀⠴⠶⠉⡾⣩⡛⣄⠀⠀⠀⠄⡇⠈⢆⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢱⠀⢸⠀⠀⠀⠈⢆⠉⠀⠉⠀⢰⠃⠀⠀⠀⡀⡀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠶⣁⠄⠈⡆⠀⠀⠀⠸⡀⠀⠀⢀⠃⠀⠀⠀⡐⢀⠇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢈⡆⠀⢳⡀⠀⠐⠠⣇⠀⠀⡜⠀⢀⢀⠠⢁⠜⠐⠀⢈⣦⠀⠀⠀⠀⠀⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠛⠠⣆⠀⡱⢄⠀⠀⠃⠁⣀⡁⠄⠘⢈⡠⠊⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠁⠒⢤⠀⢇⠀⠀⠀⠀⠀⠀⠨⠤⠒⠂⠉⡢⠶⢤⣼⣧⠒⣊⡉⠀⣀⠤⣀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⢀⠀⠀⢠⠀⠸⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⢘⡷⠤⠴⢚⣡⡃⠀⠈⠲⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠣⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠊⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡶⠄⠖⠛⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡎⠀⡌
⠀⠀⠀⠀⠀⢠⠊⠉⠁⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠻⣤⣴⣾⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠃⢀⠎
⠀⠀⠀⠀⠀⠘⠦⣐⢐⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡠⠀⠀⠀⠀⠀⠈⠲⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡀⠇⢁⡴⠁
⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠔⠠⡠⠀⢀⠀⡀⠀⢀⢀⠀⠄⡄⢰⢀⠅⠃⢁⠴⠋
⠀⠀⠀⠀⠀⠘⢄⡀⢀⠜⠀⠀⠀⠀⡟⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⢍⣈⡐⠁⠃⠊⠘⠘⣀⣁⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠀⠀⡅⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠃⠔⠢⡀⡇⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣷⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⡐⠏⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⡌⢐⠕⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣏⢺⣅⠄⢕⡤⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣅⢒⠥⡊⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡪⣂⠽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⣨⡗⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢝⡏⡇⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⢹⠁⠇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⣠⢄⠤⢂⢔⡠⢂⠠⣂⠔⡠⠔⡠⢂⡴⣂⠔⡠⢐⡠⢀⢄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠔⣇⣼⡫⢶⠿⣤⣸⡇⣂⢔⡠⣀⢴⠔⠤⠠⠀⠄⠀⠀⠀⠁⠈⠀⠁⠀⠀⠈⠀⠈⠀⠁⠀⠀⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⠉⠉⠉⠙⠒⠒⠰⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣀⠤⠤⠤⠤⠤⠀⣀⣀⡀⢀⢀⣀⡴⠊⠀⠰⡄⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢤⣤⣤⡄⠀⠀⠀⡤⣴⣦⣦⢀⠀⠀⢸⠓⠠⠀⣿⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠈⠉⠉⠁⠘⠄⠀⠉⠉⠉⠉⠉⠀⠀⠸⡡⠀⣠⣧⡀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠂⠺⠶⠀⠀⠀⠀⠂⠲⡶⠤⠀⠀⠀⠙⣄⢋⠀⠇⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢀⡇⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡼⠁⠀⠻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣰⠯⠤⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠙⠂⢈⡉⠈⠀⠌⠈⠀⠀⠀⣠⠞
⠀⠀⢀⣀⣀⣸⣌⠢⡀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⢠⠞⡱
⠀⢰⠟⠒⠃⠀⠐⠦⢈⡄⠀⠀⠀⠀⠀⠈⠉⠙⣳⠞⡛⠛⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⠌⠁⠙⠟⠟⣆
⠀⠈⠓⠒⠒⠒⠠⡔⠋⢳⡀⠀⠀⠀⠀⣤⠒⠚⣧⣾⣆⣀⠜⠓⠦⣄⠀⠀⠀⠀⠀⡠⠓⠧⡀⠤⠤⠤⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠁⠙⢦⡀⢠⠞⢸⠀⠀⣴⣿⠠⠀⠀⠀⠸⠋⠳⡀⠀⠀⠴⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⡁⠀⣰⠆⠀⣿⡟⠀⠀⠀⣰⠢⡀⠀⠙⡖⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⡤⠞⠁⡇⠀⠛⠀⠀⠀⢠⡇⠀⠈⠢⣄⠃⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠛⣄⣀⡠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⢹⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⢉⠓⡾⠉⠙⡇

⠀⠀⠈⣧⠀⣴⣷⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠸⠿⠏
⠀⠀⠺⠿⠀⠈⠁⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⠀⠀⢀⣤⡾⣿⡇⠀⠀⠀⣰⢿⡷⢀⣾⣷⠀⠀⠀⣼⠃⠀⠀⠈⠉⠯⣽⠟
⠀⠀⠀⠀⢀⣶⡀⠀⣠⢼⡂⠀⠀⣳⡾⠁⠀⠀⠀⠛⠔⠁⣀⠀⠀⠀⣰⠃⠀⢀⡟⠀⠀⠀⠀⢀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⡆
⠀⢠⣶⣴⠯⠞⠁⠀⠚⠏⠃⠀⡴⢛⣤⣤⡀⠀⠀⢀⡀⣰⠇⠀⠀⠀⠛⠲⠦⠞⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⢀⡔⣢⡀⠀⠀⢀⣤⣄⠀⢀⣿⡅
⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⠀⢸⡇⣏⠱⠈⣿⠀⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣀⡀⠀⠹⠬⠞⠋⠉⠀⠀⢠⡞⠛⠋⠀⠘⠛⠁
⠀⠀⠀⡴⢢⣤⣞⣹⠀⠀⠀⠀⠳⠬⣤⡾⠋⠀⠀⠀⠀⠀⠀⣮⠬⠃⠀⠀⢠⡞⣹⠗⠀⠀⢸⢩⡟⠀⠀⢠⡀⠀⠀⠀⠀⠋⠀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠈⠋⠀⠉⣠⣄⠀⠀⠀⠀⠶⣆⠄⠀⣠⠦⠤⣤⠀⠀⢻⠀⠀⠀⠀⢀⡽⠃⠀⢀⣤⡾⠋⠀⠀⠀⣾⠁⠀⠀⣴⣶⡄⣰⠿⠟⠀⠀⡷⠚
⡦⠀⠀⣴⣤⣠⠞⠁⠈⢳⣄⠀⠀⠀⠀⠀⢀⡟⠀⠀⡟⠀⠀⠘⠀⠀⢠⣶⡌⠀⠀⢰⢏⡴⡿⢶⡄⠀⢠⡾⠆⠀⢰⣏⣉⣠⡏⠀⢀⡄⠀⣿
⡁⠀⠀⠈⠋⠀⣾⣶⠖⠋⠈⢷⡀⠀⢀⣤⣼⠁⣶⣾⠃⠀⠀⠀⣶⡶⠈⢿⡀⠀⠀⠸⣌⠃⢃⣰⡏⠀⠈⠁⠀⠀⠛⠒⠶⠟⠀⢀⡞
⠉⠀⠀⡀⠀⠀⠀⣡⣀⣠⠴⠋⠀⢀⡀⠙⠉⠀⠈⠁⠀⠰⣿⠇⠘⢧⡀⣠⠿⣄⠀⠀⣬⠛⠛⠉⠀⠀⡴⣲⠆⠀⠀⡶⢄⠀⠀⢾⣷⠄⠀⠀⠐
⢀⡠⢾⠁⠀⠀⠀⠙⠛⠁⢀⣀⣠⢿⡷⠀⠀⠀⠀⢀⡀⠀⠙⣆⣠⠴⣻⡵⠚⠁⠀⠀⠉⠊⠀⠀⣖⣲⠞⠁⠀⠀⠀⣻⠘⠀⠀⢀⣀
⠈⠀⠉⣀⣤⡀⠀⠀⠀⠀⠻⠟⠉⠉⠀⠀⠀⢀⠴⣻⠀⠀⠀⠈⠳⠞⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣁⣀⣀⠀⠀⢯⡹⠀⠀⣰⠋⠉⢹⡆
⢀⣄⠀⠙⠲⣽⡀⠀⠀⠀⠀⢀⣠⣴⣶⡀⠀⠀⠈⠁⠀⢠⠤⠤⣤⠀⠀⠀⢀⣠⣴⠛⠉⢧⡀⠀⠈⡿⠭⠽⡇⠀⠀⢠⣤⣼⢃⣀⣠⠏
⣛⡿⠀⠀⠀⢿⡿⠀⠀⠀⠐⠋⠁⠈⠉⠀⣤⣤⠀⠀⠀⣾⠋⠉⣿⠀⠀⠰⡉⠀⠘⣧⠀⢈⣷⡀⠀⣷⣶⠀⣧⠀⠀⠈⠛⠁⠈⠛⠋⠀⠀⣠⣤
⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⢀⣶⣦⢸⡏⠉⠀⢀⣠⡇⢰⣶⡏⠀⠀⠀⠹⣄⠺⠿⠃⠘⠟⠃⠀⠈⠁⠀⢻⣿⠆⠀⠀⠀⠀⡴⣆⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⡀⠀⢸⣏⣁⣸⡇⠀⠀⠙⠛⠁⠀⠀⣀⡄⡀⠀⢴⣿⠆⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡀⠀⠑⣻⡄
⠀⣶⢼⡂⠀⠀⠀⠀⠈⠧⠃⠀⠸⠷⠶⠞⠁⠀⠀⠀⠀⠀⠀⠰⢫⡟⠃⠀⠀⡀⠀⠠⣴⠲⡄⠀⠀⣠⣷⠀⠀⣀⣀⠀⡿⠿⠀⠘⠤⠃⠀⢀
⠀⠺⠉⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣀⣤⢤⣤⣀⣴⣚⣷⠄⠀⠀⢀⣀⡀⢾⠿⠂⠀⠈⠙⣯⡄⠈⠛⠋⠀⠀⡟⠛⠀⡇⠀⠀⠀⠀⠀⣤⡾⠂
⠀⠀⠀⢠⠄⠀⠀⣷⠐⠁⠀⠀⠀⢸⠡⠖⡳⣾⡉⠉⠉⠁⠀⠀⠀⢸⡟⠃⢸⡀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⣟⣻⣿⠇⠀⠀⠀⠀⣤⢿
⠀⣠⣠⡏⠀⠀⠀⣿⠀⠀⠀⢰⡶⢸⣦⣊⣠⣾⠃⠀⠀⣰⠇⠀⠀⠘⡇⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠛⠛⠀⠀⠀⠀⠈⣀⣀⣀⡀⠁⠁⠀⠉⠉⠀⠀⠀⢠⠟⣳⠂⠀⠀⠛⠛⠉⠀⠀⣠⣶⣆⠀⠀⠀⢻⡲⡀⠀⠀⣀⣴⠀⠀⠀⣸⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢩⡇⠀⠀⠀⠀⠀⣠⣄⠀⠉⣻⠃⠀⠀⣿⣦⠀⠀⠀⣰⠋⠉⠁⠀⣀⠀⠘⠛⠀⠀⣠⣿⠀⠀⠀⠀⣿⠀⠀⣿
⣰⣿⡦⠀⠀⢀⣀⡾⢀⣤⣼⠀⠀⠀⢀⣤⡄⢻⡏⠀⠀⠋⠀⢀⣤⡗⠃⠀⠀⠀⠁⠀⠀⠀⠘⢯⣳⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠻⠿⠀⣯⣄
⠃⠀⠀⠀⠀⠘⠿⠃⠈⠛⠃⠀⣠⣶⠈⢿⡁⠀⢹⣆⠀⠀⠀⠘⠛⠃⢀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠟⡆⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠘⢯⠀⢀⣽⣞⣩⠞⠃⠀⢠⠒⣤⣴⣋⠇⠀⠀⡾⠭⣭⡿⠀⠀⠉⣁⠀⠀⠘⣧⠜⠀⠀⠀⢀⡞⠙⠲⣤⣄⡀
⠀⢀⣤⠶⠺⡍⠀⠘⣆⠀⠀⠀⠀⠈⠻⣯⠴⠋⠁⠀⣀⠀⠀⠉⠁⠈⠁⠀⣀⣸⠁⣤⣴⠃⠀⠀⣿⣿⠄⠀⠀⣿⠀⠀⣠⣄⡞⢀⣀⡼⠁⠈⣹
⣀⣈⣳⣀⣀⣻⣄⣀⣽⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣇⣀⣀⣀⣀⣀⣘⣿⣃⣀⣉⣉⣀⣀⣀⣙⣈⣀⣀⣀⣈⣀⣀⣙⣛⣀⣙⣛⣁⣀⣰⣃
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠦⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠦⡀⠀⠀⠀⠀⠀⣠⠔⢲⢰⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⡆⡇⠀⠀⠀⠀⠀⣼⠕⠂⢀⠀⢠⠂⠀⠈⢆⠀⠀⠀⡜⠁⠀⢸⢸⠴⣚⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢸⠀⡇⡇⠀⠀⠀⠀⡸⠁⠀⢠⢇⡴⠃⠲⡀⠀⠘⡄⠀⠀⡇⠀⠀⢸⠔⠊⠁⢀⡇
⠀⠀⠀⠀⠀⠀⡞⢳⢸⠀⢸⠀⡇⡇⠀⠀⠀⢀⠇⢀⡴⣷⢍⠀⠀⡠⣈⢦⠀⠱⡄⠀⢹⠉⡣⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⢀⣧⣸⣼⣠⣼⣄⣧⣇⣤⡀⠀⢺⠊⣏⠀⠐⠆⠀⠀⠰⠀⠀⣳⢄⣹⢀⡼⠃⠯⡖⠒⠊⠁⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣷⡀⠀⣐⣂⠀⢀⠟⡏⢀⡞⠈⠉⠉⠉⠁⠀⡤⡄⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢹⢦⡀⠀⠀⠀⠹⣄⣇⠙⡦⢍⡡⡴⠋⢠⢃⡟⠀⠀⠀⠀⠀⢀⡴⠋⠙⢢⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠭⠬⠉⡇⠀⠀⠀⠀⠈⢁⣹⡇⠀⠀⣸⣾⡓⠋⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡴⠚⠉⠓⡇⠀⣛⣛⠀⡇⠀⢀⠔⢺⠉⠉⢣⡈⢲⡞⢁⠇⠈⠙⡶⠦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠰⡁⠀⠀⡀⠳⠤⢤⠤⠄⠇⠀⠆⠀⣸⠀⠀⢘⠑⢻⡟⠋⠃⠀⠀⡇⠀⢹⠀⠀⢸⠖⠖⠖⠒⠲⠚⠳⠲⡇
⠀⠀⠀⢀⠔⠁⠀⢄⣇⡠⠀⠘⢦⠀⠀⢰⠀⠀⢻⠀⠀⠘⠖⠑⣞⠒⠂⠀⠀⡷⠀⠈⡄⠀⢸⠀⠀⠰⣉⣱⠀⠀⠀⡇
⠀⠀⠀⠸⣄⠀⠀⠀⠉⠀⠀⠀⢠⠇⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣧⠀⠀⡇⠀⢸⠀⠤⠤⠤⠬⠤⠄⠀⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣇⣀⡀⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⢳⠀⢸⣀⣉⣉⣉⣉⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠒⠬⣷⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣟⡩⠭⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡞⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣇⠀⣠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢼⣄
⠀⠀⠀⠀⠀⠀⠤⢤⡴⣫⡿⠓⠒⢾⢶⡥⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣳⣯⣻⣦⡤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠺⠛⡏⠀⠀⣀⠜⠓⠚⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠒⢄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠐⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀
⠀⠀⠀⠂⢀⠄⠀⢢⠀⠀⠀⠀⠡⠄⢚⡤⠚⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⣀⡀⠀⢳
⠀⠀⠀⠀⢨⠀⠀⠌⠀⠀⠀⠀⠀⠀⠘⣄⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡸⢄⣨⠀⣸
⠀⠀⠀⠀⠘⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠘⣦⠀⠀⠠⢄⠀⠈⠉⠉⠁⠀⠐⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣘⠁
⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⢰⠎⠀⠀⠀⠀⠀⢀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡭⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⡠⠐⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⢰⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⢄⡀⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⢉⡀⢠⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⢰⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠈⠓⢢⠀⠀⣴⡶⠒⠀⠀⠐⠀⠀⠀⠀⠀⢤⠂⠈⠅⠀⠀⠂⠀⠄⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⠄⠹⠤⠀⠀⠀⠀⢀⢠⠌⠰⣀⠏⠁⠀⠀⠀⠀⢘⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡉⠀⠀⢋⠀⠀⠀⠀⠀⠁⠀⢢⣐⠉⢒⠁⠀⠀⠀⠀⠈⠠⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⡘⠊⠁⠠⠬⠃⠀⠀⠀⠀⠀⠀⢀⡹⠋⠁⠀⠀⠀⠀⠀⠀⠣⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠐⢀⠀⠤⡄⠀⠠⠄⠒⠈
⠀⠀⠀⠀⠀⢀⡠⠄⠠⡀⠀⠀⠀⠀⠀⠀⢠⠉⢢⠀⠀⠀⠀⠀⠀⠀⢠⠨⣄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⡔⠀⠈⡄⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡈⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠉⠓⢁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⢀⠠⠄⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠔
⠀⠀⠀⠀⠀⠀⠀⠩⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⡀⠄⠓⠒⠲⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢠⠂⠀⠀⠀⠀⡀⠀⠖⠠⣀⠈⢸⡆⠡⠰⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠂⣠⠃⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠕⠀⠀⠀⠘⠂⠤⠀⣠⣀⣀⣀⣠⡀⡀⠀⡀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣓⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣆⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠋⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠋⠉⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⡛⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣸⣶⡿⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠿⠿⠏
⠀⠀⠀⠀⠀⣠⣾⡿⡏⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢾⣿⠟
⠀⠀⠀⠀⣾⡿⠋⢀⣹⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃
⠀⠀⠀⢸⣿⠃⢀⡾⠻⡍⠉⠻⣷
⠀⠀⠀⠈⢿⡆⠈⢇⠀⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠈⠻⢦⣄⣀⣱⣤⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡄
⠀⠀⠀⠀⠀⣰⣶⣦⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠘⢿⣏⡤⠞⠀⠀⠀⠀⠀⠀⢾⡿⠟⠀⠀⠀⢿⡿⠋⠀⠀⠀⠸⣿⠿⠁⠀⠀⢾⡿⠟⠀⠀⠀⢾⡿⠟

⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⡜⠁⠀⠀⠀⠙⣿⣆⠀⠀⢾⡦
⠀⠀⠀⢧⣾⣿⡦⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠈⠙⠛⠁⠀⠀⢠⣿⡟⠀⠾⠗⠀⢸⠀⠀⠀⠀⠀⣀⣧⣼⣶⠀⠀⠀⠀⠀⠷⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⢸⢀⣀⠀⠀⠀⠛⡏⢹⣀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⢸⠉⣿⠇⠀⠀⣴⣷⣿⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠁
⠀⠀⠀⠀⣀⡤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠴⠋⠀⠀⠀⠉⡇⠸⠀⠀⠀⢰⣿⡿⠃⠀⠀⣴⣿⡿⠀⠀⠀⣾⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⢉⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠠⠖⠂⠠⡄⠘⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⠔⠁⡠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠒⢆⣮⠭⠄⠂⠀⠀⢠⠀⠀⠀⠀⣀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠈⠪⡢⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢄⡲⣶⠖⠀⡀⠉⢸⠀⠀⠀⠰⠐⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠁⠀⠈⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠘⠀⣀⠈⡢⠀⠀⢀⡴⡁⠀⡠⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠚⡀⠀⢀⣈⠑⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠋⣓⠴⢗⢄⡀⡠⠔⢁⣄⡒⠲⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡅⡡⠬⡑⠒⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢴⠠⠀⠑⣜⣆⢀⣰⠜⠗⠉⠛⠛⣋⠀⠀⠀⠀⠀⠀⠀⠀⢎⢉⣉⡆⠀⠀⣔⡟⢠⠁⠀⡸⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣂⠊⢆⠀⠀⠘⠛⠛⠁⠉⢀⣀⡤⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡍⠉⠳⢀⣼⠼⠥⠊⣀⠴⠋⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠬⠠⢂⠓⢀⣀⣀⡠⠄⠊⠀⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⢀⡷⣤⠀⣀⣀⣠⠤⠚⠭⠊⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠄⢀⡄⠈⠓⠒⠒⠒⠒⠤⢀⠠⠆⠀⠀⠀⠐⠂⠐⠂⠒⠒⣌⡡⠌⠒⠋⠉⠁⠀⢁⠤⡖⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⢠⠮⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⠀⠈⠛⠻⣿⣿⠿⠋⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⣈⠐⠐⠐⠀⠀⠀⠀⠀⠀⠸⢀⠈⡆⠀⠀⠀⡟⡇⠀⠀⢀⠀⠀⠀⠙⠓⠂⢠⡒⠖⠴⠲⠚⠒⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣈⣉⣉⡓⢒⠒⡄⠀⠸⠀⢀⢏⡀⠸⠀⠀⠀⡁⡇⠀⠀⠸⡀⠀⠈⠁⢡⣦⢸⣷⡆⠀⠀⠐⠒⠒⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⠀⠀⠀⠀⡙⠠⠁⠠⠀⠀⣚⠀⠄⠀⠀⠀⠀⠆⡇⠀⠀⠀⠣⠀⠰⠞⡋⡥⠀⢯⡇⠀⠀⠀⠀⢀⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠀⠀⠀⡘⠀⠀⠀⢀⣈⠁⣀⡈⣈⡂⠀⠉⠉⠱⡅⠀⠀⠀⢰⠀⠀⠈⡐⠠⠸⣽⡇⠀⠀⠀⠀⢰⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⠀⠀⠀⠐⡄⠀⠀⡇⠀⠀⠀⠀⠀⢩⢖⡴⡂⣱⢋⢀⣀⣀⠎⣀⠔⢡⠃⠀⠁⢘⠄⠀⠀⠀⠀⠘⠂⡂
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠴⢘⠒⠠⣄⠠⢽⣦⣀⣰⠄⡄⠀⢘⠀⢉⡛⠫⢚⠃⠳⢚⠚⢫⡦⠠⣔⣁⣤⠴⢻⣭⡖⠢⢐⠀⢠⢀⣦⣇⢀⡀⢄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠀⠉⠀⠈⠀⠈⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡔⣄⠠⠀⠀⠁⠀⠀⢠⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡖⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠈⠂⡀⣜⣂⠀⠀⠀⠀⠀⠘⡄⠠⠤⣄⡰⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢸⡀⣀⢰⣟⠤⠟⠰⢾⢫⡤⣴⣶⣤⡔⠁⣈⡽⠼⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡈⠻⠯⠉⠀⠻⠤⠴⢟⣾⣿⠗⠛⠉⠛⢋⣿⡃⠀⠀⠀⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢭⠷⠆⢁⣾⢦⣤⡔⢪⣟⢧⣧⡆⠉⠛⡀⠈⠙⢳⢠⣀⣤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣾⣿⣿⣆⠀⠁⠐⠊⢹⢦⠼⡱⡌⠊⠏⢸⣿⠛⢙⡿⠴⣦⡄⡈⣷⠦⡠⣤⢎⠉⠙⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠂⠃⠀⠵⡓⠀⠀⠠⠈⠀⠨⣟⠉⠉⠀⠱⢀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣋⣀⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁
⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀