Vacay Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡏⣿⣿⡟⣽⠟⣿⡿⢡⣾⣿⢟⣽⢙⣿⡟⣽⣿⢹⣿⣿⣿⠀⠀⠀⠀⡆⠀⠀⡴⢒⡦⠀⣰⠋⠀⢀⠖⢲⡄⠀⡴⢀⢰⡆
⣿⣿⣿⣇⣿⣿⣧⣿⣇⣿⣷⣸⣿⣿⣮⣿⣸⣿⣦⣿⣿⢸⣿⣿⣿⡀⠀⠀⠀⢇⠀⠀⠓⠀⣇⠔⠻⠄⠐⠈⠂⠸⡁⠈⠃⠀⣸⣇
⣿⣿⣿⣿⠋⣿⡟⢻⢻⣿⢫⡻⣿⢩⡻⣿⠛⣽⣿⣿⡟⣼⣿⣿⣿⠀⠀⠀⠀⢤⣆⠀⣦⢠⡄⢠⠶⡄⢰⠶⡄⢠⡖⠀⠔⠁⡼
⣿⣿⣿⣿⢻⣿⡇⣦⡎⡇⢸⡇⣿⢸⡿⣹⢰⣾⣿⣟⣽⣿⣿⣿⣿⠀⠀⠀⠀⢡⠀⠀⡏⠛⡇⣿⠀⡇⢸⠀⣹⢸⡏⠁⠄⠔⠁
⣿⣿⣿⣿⣷⣿⣧⣿⣧⣿⣜⣵⣿⣸⣵⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠇⠀⠃⠙⠖⠁⠻⠖⠁⠘⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠳⣆⠀⠀⠀⠀⣴⠛⠉⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢹⡀⠀⠀⣼⠃⠀⠀⠀⠡⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⠶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠘⣇⠀⢸⡇⠀⢰⡇⠀⠐⠀⢀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠉⠀⢀⠀⠀⡀⠀⠀⡀⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡟⠀⢸⠇⠀⡿⠀⠀⢀⡾⠋⢻⣾⠁⠀⣰⠟⠙⣧⠀⢀⡼⠋⢻⣾⠃⠀⣼⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠃⠀⣼⠀⣸⠃⠀⢀⡾⠁⠀⣼⡇⠀⢰⡏⠀⢰⡏⠀⣾⠃⠀⣸⡏⠀⢠⡏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⡼⠃⠀⢠⡟⢠⡏⠀⠀⢸⠇⠀⢰⣿⠀⠀⣿⠀⠀⠛⠀⣰⡇⠀⢠⣿⠁⠀⣼⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⣿⠀⢀⣿⡇⠀⣸⣿⠀⠀⠀⣰⣿⠁⢀⣾⡟⠀⣰⣿⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⣧⠟⠀⠀⠀⠀⠹⠶⠟⠉⠷⠾⠃⠙⠶⠶⠟⠁⠸⢧⠞⠁⠿⡴⠋⠻⠴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣁⣀⣀⣈⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⠀⠈⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣧⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠙⠛⠋⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠉⠉⢉⣀⣀⣀⠀⠀⢀⣉⢍⣉⠉⠁⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⣴⣿⠁⠀⢹⣿⡄⠀⢸⣿⡇⠀⢹⣿⡄⠀⣿⣿⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⡆⠀⢸⢿⣿⡇⢰⣿⣟⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠸⣿⣷⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡆⠀⢸⠈⣿⣷⠀⡇⣼⣿⡇⠈⣿⣿⠀⠀⢠⣿⡟⠀⢸⣿⡇⠀⠀⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⠁⣾⣿⡇⠀⠈⠛⠧⠤⠾⠋⠀⠀⢸⣿⡇⠀⢀⣿⣿⠀⣿⣿⡧⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⢿⡏⠀⢽⣿⡇⠀⢀⡖⠉⠉⠳⡄⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣸⠀⠀⠈⠁⠠⠿⠿⠧⠀⠸⣤⡄⠀⠀⣷⠀⠀⠼⠿⠧⠠⠾⠛⠀⠠⠿⠿⠧⠤⠼
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⢩⠟⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠒⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠞⠁⠀⠀⠀⠀⠀⠈⠉⣓⣦⣀
⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠛⢦⡀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠁⠑⢦⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣞⣽⠟⠉⠉⠀⠀⠀⠙⢦⡀⠀⢀⣴⠃⠀⠀⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠔⠒⠆⠀⠀⠀⡴⠦⣄⡈⢑⡍⠢⠤⢚⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠈⠀⠀⠀⠉⠉⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢟⠉⠀⠀⠲⠤⣤⣀⣀⣀⣀⢀⣿⡏⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢞⣫⡵⠞⠉⢀⣠⠄⠀⠀⠀⠈⠉⠉⢉⣿⡟⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⢛⣉⣥⠴⠚⠋⢁⣠⠴⠚⠉⠀⢀⣤⠖⠃⠀⣠⡶⠟⠛⠋⠑⠢⡄⠀⠈⣷
⠀⠀⢤⡶⠒⠒⠚⠋⣉⣩⣤⠤⠶⠒⠛⠉⠁⣀⣤⠴⠚⠉⠀⣀⣤⠶⠚⠉⠀⣀⡴⠞⣉⡤⠤⠤⠤⠴⠚⠁⠀⠀⢻⡄
⢀⡴⠚⠙⢦⣀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠁⣀⣠⡤⠖⠛⠉⠀⣀⡤⠖⠋⠁⡠⠊⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⠄⠄⠚⠁⠈⠓⢦⣄⡀⠀⠀⠀⠀⠴⠖⠚⠋⠉⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⡤⠒⠉⣀⣾⠃⣀⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣦⣤⡀⠒⢀⣉⣡⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢾⣿⣿⣤⣤⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣁⣀⣈⣴⣞⣉⣥⣤⣴⣞⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣦⣄⣀⣉⣉⣀⣠⣞⣁⣜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠤⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣆⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⢠
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢀⡇⠀⠀⣆⠉⠁⠀⠀⠀⣶⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⠀⠀⠀⠀⠀⠆⣷⡄⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⣿⣷⣤⣄⠀⠀⠀⠀⠀⠼⠿⠿⠿⠆⠀⠀⠀⠀⠀⠛⠁⠛⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⡆
⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⢀⢂⠀⠀⠀⠀⠀⠀⢰⡆⣠⣴⣶⡆⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⢰⣿⣏⣿⣧⠀⠀⠀⠀⠀⢡⡾⡆⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⠀⠀⠀⠀⡀⣾⠟⠁
⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠛⠱⠙⠓⠀⠀⠀⠀⠸⠇⠿⠿⠇⠇⠀⠀⠀⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⡆
⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠉⠁⠉⠉⠈⠁⠀⠀⠀⠀⠀⡇⢩⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣶⣶⣶⣶⠶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⢶⣶⡶⡶⣶⠶⡶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣼⠟⠛⠃⠀⣰⡟⣿⠀⠘⣿⣟⠀⠀⣻⣿⠂⠰⣶⠆⢻⣿⠂⠻⣿⡇⠀⠀⢲⡶⠆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠀⣿⡆⠀⣿⣿⡀⢠⣿⣿⠀⠀⣿⠀⢸⡟⠀⠀⠘⣷⡀⣰⡿⠁
⠀⠀⠀⠰⢦⡀⣿⠀⠀⠀⣸⡇⠀⢻⡇⠀⣿⢻⣇⣼⠏⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⣿⡟⠀⡀
⠀⠀⠀⠐⢒⡃⣿⠀⠀⠀⣿⣧⣤⣼⡇⠀⣿⠈⣿⡿⠀⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣸⡗⣋⣁
⠀⠀⠀⠐⠋⠀⣿⡟⠛⠀⣿⠁⠀⢸⡇⠀⣿⡄⠙⠃⠀⣿⡄⠀⣿⠀⢸⡇⠀⢀⠀⠀⣿⡗⠶⡄
⠀⠀⠀⠀⠀⠀⣿⣇⠀⢀⣿⡄⠀⣸⡇⢀⣿⡇⠀⠀⢀⣿⣇⢴⣿⡄⠸⣷⣤⣾⡇⢠⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠉⠁⠀⠛⠛⢨⣭⠁⠀⢀⣠⣉⠀⠀⠀⠀⢠⣾⠀⢰⡆⠀⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢰⣷⡀⢠⡴⠲⣼⣿⠀⢰⣿⠁⠹⠇⣠⡶⠛⣾⣿⠀⢸⣿⠀⢀⣿⣿⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣾⡟⠳⣿⡇⢠⣿⣿⠀⢸⣿⠀⠀⢀⣿⡇⢠⣿⣿⠀⢸⣿⡄⣼⠏⣿⣷⠞⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⢿⣧⠟⢹⣿⠀⣾⣿⣆⢀⡾⠻⡷⠟⠘⣿⡄⣾⠉⠛⢉⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡖⢄⠠⡰⠈⢿⣾⠇⠈⠛⠋⢀⢶⡀⠀⡀⠻⠿⠃⠀⢀⣾⢣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡔⡁⠀⠘⢄⠀⠠⠀⠤⠒⠤⠔⠁⠀⠉⠉⠑⠤⠤⠦⠤⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠉⠉⢀⡀⠐⠂⢰⣴⢰⣰⣐⠐⠀⠲⠆⠐⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠒⠈⠉⠮⠁⠡⠺⠀⠢⠐⠐⠄⠂

⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⣰⠁⠈⢷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄
⠀⠀⠀⠀⡇⠀⠀⠘⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠿⣷⣾⣼⣾⡿⠿⠷⠆
⠀⠀⠀⠀⡇⠀⡜⠀⣿⡄⠀⢀⡇⢀⣀⠀⠀⢀⣀⠀⠀⣀⡀⠀⣀⠀⢀⡀⢠⣾⠟⠻⡟⠛⢭⣳⣄
⠀⠀⠀⠀⠙⠊⠀⠀⢸⡇⠀⣸⢡⡟⢹⡇⢠⡟⢹⠇⣼⠋⣿⠀⣿⠀⢸⡇⣿⡁⠀⠀⣷⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠇⢸⡇⣿⡇⣸⡇⠀⢀⣿⢰⣿⢀⣿⠀⣼⡇⡜⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠘⠛⠉⠛⠉⠳⠶⠋⠛⠋⠙⠋⠙⠚⣹⡏⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢹⡇⠀⠀⢰⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⢀⠀⢀⣀⠀⣀⣀⢀⣀⠀⠀⢸⠁⠀⣼⢣⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢩⣽⣽⠆⣿⣉⠸⡝⠃⠀⠈⢂⣚⡁⢛⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⠙⣦⣿⠀⠀⠹⣆⠀⣴⣿⣿⣿⡆⢼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢸⢿⣤⠟⣿⣀⣶⣤⡟⠀⠈⠿⣿⠛⠃⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⢦⣀⣤⠖⠲⣤⣀⣀⣤⠶⠲⢦⣀⣠⠶⠲⢦⣀⣀⡴⠶
⠀⠀⠀⠀⠀⠀⠲⠶⣄⣀⣠⠴⠶⢤⣀⣈⣩⠽⢦⣄⡀⢀⣨⡵⠦⣄⡀⣉⣥⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⠀⠀⢠⡄⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⢻⡆⠀⠀⠈⣿⠀⠀⣿⠃⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡀⠀⠻⠀⠀⠀⠛⠀⠀⠁⠀⠀⣰⠟⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠈⠻⠄⣀⣤⠴⠶⠒⠲⠶⢦⣄⡈⠁⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄⠀⣠⠞⠉⠒⠉⠉⠉⠉⠉⠀⠈⠙⢦⡀⠀⠀⠀⣀⣤⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣦⣤⣀⠀⡼⣣⣶⣶⣶⣶⣦⡄⣤⣶⣶⣶⣶⣦⡙⠄⠐⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠉⠉⠉⢰⠃⢻⣿⣿⣿⣿⠟⠀⠘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠤⢶⣶⠄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣶⡈⡄⠀⡠⢀⣤⣤⣾⡀⠀⢍⠉⠉⠀⠀⠀⢐⠒⠬⣍⠉⠁⡠⢀⣤⣤⣤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠃⠙⠛⠉⢻⣿⠄⠀⠀⠀⢀⣴⣿⠿⠿⣷⠆⠱⠀⠃⠙⠛⠉⢻⣿⡄⢀⢀⣿⡇⠀⠀⣠⣤⠈⡄
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢀⣿⡇⠀⠀⢀⣤⣶⣶⣾⣿⡷⠈⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣷⠈⠘⣿⡇⠀⠀⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣼⡿⠁⠀⠀⣿⣟⠁⢠⣿⡇⠀⠀⠀⠀⢹⣿⣤⣀⣀⣤⣦⠀⠀⣿⣟⠁⢠⣿⡇⠀⠀⠀⠻⣿⣦⣠⣿⡇⠸
⠀⠀⠀⠀⠀⠸⡈⣿⣧⣾⡿⠁⠀⠀⠢⡙⠿⠿⠿⠿⣿⣾⠆⠸⠰⣿⠟⠛⠛⠛⠋⠉⠀⠠⡙⠿⠿⠿⠿⣿⣾⠆⠀⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠁⠘⠿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣶⣀⣀⢀⣠⣤⡈⠢⠀⠀⣠⣤⣤⣌⠂⠀⢀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢀⣤⣴⣤⣁⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠛⠛⣿⡟⠙⣿⡄⠀⣾⡟⠁⠉⢿⡇⠐⢡⣶⠿⢿⣿⠏⢀⠄⣴⣴⣿⣋⣠⣽⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠃⠀⣿⡇⠀⢿⣇⠀⢀⣼⡏⠀⣿⡇⠀⠸⣿⡀⠀⠑⠈⢻⣿⠛⠋⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠿⢏⡀⠀⠻⠃⠠⡈⠻⠿⠿⠋⠀⠀⠘⠻⠿⠿⠿⠿⠾⢆⠕⠈⠛⠿⠿⠿⠟⢋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⣿⢿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣟⣛⣛⣿⣿⣿⣿⣿⡻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣲⣤⣄⠀⠀⠀⠀⠀⠀⢘⡾⠿⡏⣗⣶⡄⠀⠀⠀⣀⢀⣤⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢿⣿⢿⣼⠇⠄⠄⠀⠀⠀⠘⠁⢁⠈⣷⣷⢣⡀⣀⠻⣾⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣛⣻⣿⣿⠗⠀⠀⠀⠀⠈⣂⢀⣶⣾⣿⣣⢞⣇⣐⠃⣿⣷⣿⣛
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡡⠉⠉⠉⠁⠁⢁⡀⠀⠀⠉⢉⢅⠙⠉⠉⡨⠉⠀⢉⡙⠛⠫⠃
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⣀⡀⠀⠀⢀⠄⠀⢌⢀⠀⢤⣤⣤
⠀⠀⠀⠀⢀⣤⣼⣎⡉⠥⠀⠀⢠⠄⠀⠀⠀⠀⢀⠀⠀⣠⠤⡀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠉⢠⡞⣸⣷⣻⣧⣤⣀
⠀⠀⠀⠀⠙⢯⣽⣿⣟⣻⣷⡀⠙⠀⠀⠀⠀⠀⢺⠀⠀⠁⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⠠⠞⣉⣿⣻⣿⣿⣭⠟
⠀⠀⠀⠀⠀⠀⠘⠛⣫⣿⣻⣿⡦⠀⡄⢀⠀⠀⠈⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣨⠍⠉⣉⡻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢓⠀⠇⠸⠀⠀⠰⠀⠀⠠⠀⠄⠀⣄⠸⠀⠧⢀⣠⡤⠆⢀⢠⠢⣤⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣶⣶⣶⢾⣦⡀⠂⠀⠀⠀⣀⡠⢤⣴⣦⣶⡤⢶⣎⣉⠛⠑⠂⠉⠞
⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⡿⡾⠘⠋⠀⠀⠀⠀⠀⠁⠀⣽⣿⢹⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠹⠾⠝⠾⠟⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢠⣤⠀⠀⣠⠀⢠⣤⠀⠀⢀⣤⡀⢀⣤⡀⠀⠀⣤⡄⠀⣠⣤⣤⣄⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠛⠀⢸⣿⠀⠀⣿⠀⢸⣿⣇⠀⣾⣿⡇⢸⣿⣷⠀⣸⣿⡇⠀⣿⣿⠉⠁⠀⣿⣿⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⠀⢸⣿⠀⠀⣿⠀⢸⣿⣿⣼⢿⣿⡇⢸⡿⣿⣦⡟⣿⡇⠀⣿⣿⣶⡦⠀⣿⣿⣠⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣿⡇⢸⣿⡀⠀⣿⠀⢸⡇⢿⡿⢸⣿⡇⢸⡇⢹⣿⠁⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⠟⠀⠈⠿⢷⡾⠏⠀⠸⠇⠸⠃⠸⠿⠇⠸⠇⠀⠏⠀⠿⠇⠀⠿⠿⠶⠶⠀⠿⠿⠀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠂⠀⣀⠀⠀⠀⢲⣶⣶⣶⣶⣦⣴⡤⠠⠤⠀⠀⣶⡆⠀⠀⣠⡀⠰⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠐⠈⠋⣉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⢀⣤⡤⠀⠘⠃⠀⠀⠠⠄⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⡀⠂⠀⠀⠀⠉⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠐⠉⠀⢀⣤⠀⠄⠀⠃⠰⣤⡈⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣶⡔⠓⠀⢸⣀⠀⣄⠀⠀⠠⣄⡀⠸⣿⣿⣿⡇⠀⠀⣴⡟⠁⢠⠄⠀⠀⢠⡄⠉⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣶⡸⣿⣿⣶⠀⡀⠀⠉⠲⣿⣿⣿⡇⢀⣾⠏⠀⢀⡏⠀⣀⠀⠀⠙⠀⠀⠐⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⠀⢺⣿⣷⣿⣿⣿⣶⣄⠀⠀⢰⣿⣿⣿⣷⣿⣿⠀⠀⠘⠀⢠⠇⠀⠀⡀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠈⠀⠻⣿⣿⣻⣿⣿⣿⣈⣿⣾⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠹⡄⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡴⠃⠀⠀⢠⡌⠙⠌⠉⠹⣿⠋⠉⠉⠙⠻⣿⣿⣿⣧⣼⠀⠀⠀⠀⡀⢄⡀⣧⢇⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠆⠀⠀⠃⠀⠀⠀⣼⣿⣴⠃⠀⠀⣀⠀⠙⢿⣿⣿⣷⣄⣧⣾⣿⣷⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣧⡀⡌⢀⡀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠐⠀⠀⢻⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣼⣯⡅⠀⢰⡿⠛⢉⣉⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢠⠀⠀⠀⣨⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⡅⠀⠚⣠⣾⣿⠟⣫⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⡇⠀⠀⢸⣿⣿⣵⣿⠟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠉⠛⡝⠹⠇⠈⠀⠀⠘⠛⣽⣿⣟⣵⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠑⠆⠀⠀⠂⠀⠀⠰⠶⠒⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣠⡀⠈⠠⣤⣤⣤⣤⣽⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠉⠻⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣄⠀⠉⠉⠉⠉⣉⣵⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠃⠀⠘⠁⠀⠀⠒⠀⠈⠛⠿⠿⠿⠿⠿⠄⠠⠀⠙⠛⠂⠠⠴⠾⠋⠛⠋⠙⠿⠿⠿⠿⠇

⠀⠀⢠⣶⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⢀⢀⡀
⠀⠀⠘⣶⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈
⠀⠀⠀⠀⢸⡆⠀⢠⠀⣸⡇⠀⣴⠖⡆⠀⢸⡇⢠⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⡅⠀⠘⠢⢀⠀⠀⠀⠀⠊⠀⠈⠃
⠀⠀⠀⠀⠀⣿⠀⡟⢀⡿⣇⢸⡟⠀⠀⠀⡿⣷⠀⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⢡⡏⣿⢰⡏⠃⡞⣹⠇⡖⣸⡇
⠀⠀⠀⠀⠀⢹⣧⠇⢸⠛⣿⠸⣧⠀⡴⢸⠛⣿⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠉⠙⠊⠳⠊⠉⠘⠞⢋⢸⡏
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠛⠀⠉⠚⠁⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡂⠉⠠⠀⠄⠉⠀⣷⡿
⠀⠀⠀⠀⢰⣶⠀⠀⣴⡆⣰⣤⣆⠀⣶⠶⢤⡀⢰⡖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠁
⠀⠀⠀⠀⢸⣿⣇⣸⢿⡇⠸⢿⡟⠀⣿⠀⠈⣿⣼⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⢢⡄⠀⠀⠀⣤⠐⠲⠾⠂
⠀⠀⠀⠀⢸⡇⢻⡟⢸⡇⢸⣳⢮⣆⣿⠀⣠⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠂⢿⡀⣿⣧⡏⢠⣆⡏⢰⠟⠀⠱⡟⠂
⠀⠀⠀⠀⠈⠋⠀⠀⠈⠟⠈⠾⠑⠏⠻⠋⠁⠀⠘⠗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠿⠸⠏⠓⠀⠉⠓⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠉⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢂⡞⠁⠌⠀⢀⠀⣀⡀⡀⣤⢠⡆⡴
⠀⠀⠘⣧⢀⠇⡤⣴⢀⡶⡆⣠⢤⡆⣠⢠⡆⠀⠋⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣾⣇⡜⣴⣡⣏⢾⡤⠾⠶⠗⣻⣺⣃⡀⣀
⠀⠀⠀⢻⣼⠘⠧⢻⡸⣇⣠⠿⠜⣇⠧⢺⡧⣒⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⣠⠜⢀⠀⠀⠀⠀⢠⡞⠛⠃⠈⠉⠉
⠀⠀⠀⣈⠃⠀⣦⢠⣄⠶⣴⢠⣴⠀⢐⡽⠋⠿⡿⣿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢁⡴⣇⣰⠋⡠⢠⣠⢰⡏⣴⣛⡄
⠀⠀⠀⠹⡇⠀⠟⠋⠿⠴⠻⠜⠻⠀⠀⠀⠀⣸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡟⠸⠇⠿⢀⣛⣃⣛⣉⠅⣩⣵⢶⣤⡀
⠀⠀⠀⠀⢷⠀⡄⠋⠑⢤⣚⡉⠢⣴⣋⠓⢤⣂⠀⠀⠀⠏⠘⠉⠉⠉⠈⠉⠈⢀⣸⡵⠶⠒⠛⠉⠉⠉⠀⠀⠀⢸⣿⣍⣈⣿⣷
⠀⠀⠈⠑⠛⠋⠀⠀⠑⠉⠀⠉⠉⠁⠈⡟⡩⡠⠁⠀⢠⠄⣄⣠⡀⠀⢀⢤⢠⢨⠁⠀⢠⢠⡄⡄⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠈⠈⠁⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⡀⠀⢰⠃⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⡟⣾⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⡇⢀⡏⣼⣹⡖⣸⠇⢁⣴⣫⡷⢰⡆⡎⣷⡠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢸⣿⢱⠋⠖⢹⡏⣼⣿⠋⢔⢉⡟⣹⢳⠸⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⡼⠀⠉⢸⡷⠙⠛⠁⠈⠸⡧⠙⠛⡰⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡌⢃⣿⣷⣇⢚⣷⣬⣾⣷⣯⢘⣷⣤⢟⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢶⣶⠶⢶⣦⣤⣤⡶⡶⢶⡶⢾⣵⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⣉⣉⠛⢛⠛⢋⣉⡉⢉⡃⠞⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠮⠇⠘⢷⣾⡗⠛⠀⠛⢷⣷⡾⠃⠀⣶⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠁⣩⣴⣿⣦⡌⡈⢁⣾⣿⡏⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⡄⢠⣦⠀⠀⡀⠀⠀⣶⠒⠲⣆⠀⣶⠒⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⢻⡿⠙⣿⣿⣿⣿⣿⠉⣭⣍⠻⣿⠋⣭⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢻⡼⣿⠀⢾⣿⡇⠰⣿⠀⠀⣿⢸⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠠⡎⢃⡆⣿⡅⠀⢸⣿⠀⣿⣿⠀⣿⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠁⠿⠀⠀⠁⠀⠀⠿⠤⠼⠋⠘⠿⠤⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣠⣿⣿⣇⣿⣿⣿⣿⣿⣀⣛⣋⣴⣿⣀⣛⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠌⠨⠁⡇⠰⠀⣴⠃⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡥⣄⢀⡀⡰⠇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣄⣐⠲⠂⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⡋⠠
⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠒⠳⠀⠀⠀⠀⠀⠀⠁⠁⠐⢀⠀⡀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⢀⠃
⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠀⠸⢳⠳⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡀
⠀⠀⠀⠀⠀⠙⠷⠤⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣈⣨⣤⣀⣀⡀⠤⠀⢀⠈⠁⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠐⠘⠤⣀⠠⠀⠄⠀⠄⠠⣠⣤⡎⠞⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠂

⠀⠀⢀⡀⡀⢀⡠⡀
⠀⠀⢸⡀⢸⠊⣀⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠓⡄⢀⡀
⠀⡠⠆⠛⣿⣿⠿⠿⠛⠿⣿⣦⣤⣤⣴⣶⣾⡿⢿⡿⠻⣶⣤⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣣⣀⡟⢁⡸
⠀⠙⠒⠚⣿⡗⠀⣴⣶⡆⢸⣿⣿⠿⠿⠿⣿⣷⠾⡇⠀⣿⣿⣿⡿⠛⠛⠻⢿⣿⠟⢿⣿⠟⢿⣯⣉⣉⡢
⠀⠀⠀⠀⣿⣿⠀⠉⠁⣠⣾⣿⠁⣴⣶⠀⢹⣿⠀⡇⠀⣿⣿⡿⠁⣴⡷⠀⣾⣿⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⣷⣄⠈⠻⡏⠀⣿⡟⠀⠘⣿⠀⡇⠀⣿⣿⡇⢰⣿⠇⠀⢻⣿⣇⠈⠁⠀⣿⣿
⠀⠀⠀⠀⠙⢿⣶⣿⣿⣷⣤⣿⣄⣉⣠⣶⣤⣿⣀⣧⡀⠛⠙⣧⡈⠉⣠⣶⣤⣽⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠉⣁⣴⣿⠇
⠀⠀⠀⠀⠀⣼⣿⠟⠛⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣯⣬⣧⣼⣾⣽⣼⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠀⠀⠀⠀⣿⣿⠀⣾⣿⠿⠁⣼⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣤⣤⣤⠉⣿⠁⣴⠆⢸⡟⢠⣶⡄⠘⣿⠏⣠⣄⣙⣿⠀⠿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⢿⣿⡆⠹⠿⠿⠛⢀⣿⠀⢤⣴⠾⡇⠸⣿⠃⠀⢿⠀⣿⣿⣿⡇⢀⣶⡆⠘⣿⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠻⢿⣶⣶⣶⣾⣿⣿⣷⣤⣤⣴⣿⣦⣤⣴⣷⣾⣧⣈⣉⣨⣧⣼⣿⣇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠉⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⡿⠟⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠈⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠗⠀⠀⠀⠠⠀⠀⠄⡄⠈⡅⠀⠀⠠⠀⠀⠀⢠⢀⡃⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠀⠀⣀⠀⠀⠇⢴⡤⠀⢀⠀⠀⠀⠀⡈⠌
⠀⠀⠀⠀⠀⠀⠄⠀⠉⡀⠈⠁⠘⠃⠀⠀⠀⠄⠀⠀⠀⠠⠤⠀⢀⡐⠁⡼⠀⠤⠤⡄⠀⣠⠇⠀⠹⢠⠁⠆⠀⠰⣀⣀⠀⠴⢴
⠀⠀⠀⠀⠀⡐⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀⣰⣭⠀⠄⠾⠀⠞⠑⠀⣂⢀⡦⠴⠆⠑⠚⠁⠗⠐⠂⠂⠈⠍⠀⠐⢀⡆⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠹⡃⠀⠀⠤⠀⠀⠐⠂⠀⠀⣘⢁⠍⠁⠀⠀⠀⠀⠀⠌⠀⠉⠉⠀⠀⠤⠴⠀⠀⠀⡰⠄⣀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⣀⠠⠐⠢⢀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⠁⠐⠀⠠⠔
⡠⠀⠂⠁⠀⠀⠀⠀⠀⠉⠐⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠉⠀⠂⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠄⢠⠴⢦⡤⠀⢀⡤⢦⡀⢀⡴⢦⡴⠀⢶⠷⠆⡤⠀⢀⡤⠦⡄⠀⢠⡤⠶⡄
⠀⠀⠀⠀⠀⠀⡼⢀⣠⠏⢰⠃⠀⣼⠁⢠⠏⠀⠘⢡⠏⠀⣰⠃⢀⡏⠀⣰⠃⢀⡞⠀⣠⠇⢠⡟⠀⢰⠃⢀
⠀⠀⠀⠀⠀⢰⠃⣸⢯⡤⣏⢀⣰⡇⣠⢿⡀⠀⣠⣿⠀⣰⡏⢀⣾⠀⣰⡏⢀⣾⠀⣠⢯⣤⡞⠀⠀⡏⢀⡞
⠀⠀⠀⠀⠀⠈⢉⣡⣤⣤⣈⣩⣤⣍⡁⠀⠉⠉⠁⢈⡉⠁⢉⣍⠈⠉⡁⠉⠁⠈⠉⢁⣠⣤⣅⣀⣤⣭⣍⡀
⠀⠀⠀⠀⠀⢠⠿⠟⢛⣿⣿⣿⣿⣿⣷⠀⠀⣀⡀⢨⣿⠆⠾⠿⠠⣶⡿⠀⢀⡀⠀⣾⣿⣿⣿⣿⣿⡛⠻⠿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⣿⡻⣿⡍⠀⡀⢹⡟⣨⣶⣾⣿⣿⣷⣶⣄⠻⡿⠃⠀⢩⣿⢟⣿⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠛⠋⢸⠁⣿⡇⠙⠇⠙⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣷⡶⠸⠛⢸⣿⠈⣇⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠸⠇⠀⢠⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣄⡀⠀⠸⠇⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣄⠀⠀⠀⠀⢈⣩⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣝⠉⠁⠀⠀⠀⢠⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣤⣀⠀⠀⠛⠛⢃⡹⣿⣿⣿⣿⣿⣿⣿⣿⢟⡘⠿⠶⠀⠀⣀⣤⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠰⠿⠿⠊⠙⠛⠿⠿⠛⠋⠁⢿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⢀⣶⣶⡆⠀⢀⣠⣶⣶⣶⣶⣤⡀⠀⢰⣶⣶⣶⣶⣦⣄⡀⠀⢰⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⢀⣾⣿⣿⡇⢀⣾⣿⡟⠋⠙⠻⣿⣷⡄⢸⣿⣿⠉⠉⠻⣿⣷⡄⢸⣿⣿⣉⣉⣉⡁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⠘⣿⣿⠃⣿⣿⡇⠈⢿⣿⣷⣤⣤⣾⣿⡿⠁⢸⣿⣿⣤⣤⣾⣿⡿⠁⢸⣿⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠘⠛⠛⠀⠙⠋⠀⠛⠛⠃⠀⠀⠉⠛⠿⠿⠛⠋⠀⠀⠘⠛⠛⠛⠛⠛⠉⠀⠀⠘⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣤⡄⠀⢀⣤⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⣤⡄⠀⢠⡄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠀⣾⢿⣇⠀⠀⠀⢠⡿⠉⠀⠀⠀⠀⢸⡿⣷⠀⠈⢻⣆⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⡇⠀⢰⡿⠈⣿⡀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣿⠃⢻⡇⠀⠀⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠁⠀⣾⡇⠀⢹⣇⠀⢸⡏⠀⠀⠀⠀⠀⢰⡟⠀⠘⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡏⠀⢛⣿⠛⠛⠛⣿⡀⠘⣿⢀⠔⡄⠀⠘⣿⡟⠛⠛⢻⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⢸⡟⠀⠀⠀⠸⣧⠀⠙⣿⣄⣇⡀⠀⣿⠀⠀⠀⠈⢿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⢸⡇⢩⠉⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⠇⠆⠀⠀⠀⠀⠀⠀⣸⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠆⠀⠀⣍⠀⣿⡔⠀⠀⠀⠀⢀⡠⡄⢿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠃⠸⠀⠀⣸⡇⠀⣿⠃⣠⣦⠀⢀⣾⠃⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠠⠂⢸⡇⠀⢻⡤⠃⢻⡇⢸⣿⠀⠀⠈⣿⡄⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠁⠀⠀⠈⠧⠈⠀⠁⠀⣿⠁⠀⠙⠓⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢽⠏⠀⠀⠀⠀⠀⢰⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠙⠿⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⣷⣟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣱⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣎⡳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣵⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣷⣤⡀
⠀⠀⠀⠀⣠⣴⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣽⢦⣄
⠀⠀⠀⠀⠉⠹⠋⠁⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠻⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⢀⣀⡀⢶⡶⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢀⣀⣻⠿⠟⠃⠀⠈⣛⠁⣴⣦⣀⠀⠘⠿⠿⣟⣀⡀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣶⣤⣴⣾⡿⢻⡏⠻⢿⣷⣤⣶⣿⣿⣿⣷⡄⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⡟⢿⣿⣟⠛⠁⠀⣼⣧⠀⠀⠙⢛⣿⣿⢻⣿⣿⣿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢰⣿⣿⣿⡇⠀⢹⣿⣀⣀⣀⣿⣿⣀⣀⣀⣸⡿⠁⢸⣿⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠈⣿⣿⣿⣇⣀⠀⠀⠻⣦⡀⠀⠀⢀⣼⠟⠀⠀⢀⣸⣿⣿⣿⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠙⠿⠿⢿⣿⣿⣿⠆⠘⢿⣄⣰⡿⠁⠰⣿⣿⣿⡿⠿⠿⠋⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠽⠿⠿⢿⡯⢀⣿⡟⠀⠀⢠⡿⣯⡀⠀⠀⣿⣿⠈⢿⡿⠿⠿⠯⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢸⣷⣾⣿⠃⢀⣴⠟⠁⠈⢻⣦⠀⢸⣿⡇⣿⡇⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣼⣯⣽⣭⣤⣾⣯⣤⣤⣤⣤⣽⣷⣤⣽⣥⣿⣧⣤⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢻⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠝⡡⠃⡇⢸⠈⢎⠻⡢⣄
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡟⡿⡟⠻⢻⡟⠛⡟⢻⠟⠛⠛⡇
⠀⠀⠀⠀⠀⢸⡏⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⢠⡱⠀⡇⣌⠇⢀⠃⢸⡄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢻⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⢀⢧⠃⡸⢰⡟⠀⡸⠀⣆⠇⠀⡎
⠀⠀⠀⠀⠀⡠⡿⠛⡹⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡜⠀⣎⠇⢠⠃⣾⠁⢠⠃⢰⢹⠀⢠⠃
⠀⠀⠀⠀⡰⢱⢱⠀⠇⠘⣌⢪⡢⣄⠀⠀⠀⠀⠀⡰⠁⡜⠀⣜⠎⢠⠃⣼⠇⢀⠎⢀⠆⡆⠀⡜
⠀⠀⠀⡜⢀⠇⢸⠀⠸⠀⠈⢆⠙⢦⠑⢄⡀⢀⠜⢀⠎⢀⢎⠎⢠⠃⡼⡏⢀⠎⢀⠎⡘⠀⢰⠁
⠀⠀⠚⢟⠻⡿⣯⠻⡿⡥⠶⣼⠷⠶⡷⠶⣝⢯⡴⠁⡠⣣⠊⡰⠁⡜⡜⣠⠋⢠⠊⡜⠀⡠⠃
⠀⠀⠀⠀⠙⠿⣎⢢⡑⣌⢦⡈⠢⡀⠈⠢⡈⠢⡙⢮⣴⣡⠞⣠⣾⣯⠞⢁⡴⡡⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠿⣮⡳⣝⠢⣈⠢⢄⡈⠲⢌⡓⢮⣓⠿⢿⣿⣥⣶⣿⣫⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠮⠽⢶⣭⣶⣤⣍⣓⣮⣽⣳⡶⠭⠝⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠈⠑⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣶⢰⣗⣿⣴⣸⣧⣿⣸⡧⣆⣾⣾⣷⣼⣧⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡇⡀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠿⠿⠟⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠛⠀⠀⠉⠀⠀⠀⠀⠀⣤⡀⢹⣏⡤
⠈⠉⠉⠙⠛⠿⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣈⣩⡷⠒
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠒⢂⡓⠒
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠛⠦⠭⣽⣿⣒
⠀⣀⣶⡄⣀⣘⣃⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⣽⠆⠸⢾⣉⢻⣟⣡
⠘⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢍⠴⣾⣛⣁⠀⣉⠙⣟⣡
⠀⣿⣿⣿⣿⣿⡿⣧⣦⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⠀⠀⠭⣽⣿⠥⠶⠀⢈⣿⣿⣥
⠀⠻⠿⢿⣿⡿⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠷⡿⠾⠅⠐⠚⠻⠃⠈⠐⠫⠟⠻⠯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⢄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠈⢆⠀⠀⠀⠀⠀⠀⠈⠀⡀⠄⠀⠀⠀⠀⠐⠊⠉⠁⡀⠀⠀⠠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠘⠢⠑⢄⠀⠀⢠⡄⠀⠀⠀⠀⠱⠀⠀⠸⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣕⠀⠀⠀⠀⢐⣲⡶⠖⠉⢐⠂⠀⠉⠉⠉⠀⠀⠁⠉⢠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠢⠀⣀⡤⠒⠋⠤⠙⠸⡂⣸⠀⠐⠀⠠⠤⠤⣤⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠈⠀⠳⡀⠀⠉⠁⠈⢁⣿⠀⢀⣀⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⡹⢏⡀⣨⠷⠶⠦⠴⠃⠌⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠄⠀⠴⠶⠶⠶⠶⠄⢶⠀⠘⠒⠚⠋⢿⠙⠙⠛⠛⠛⢻⠛⠃⠐⠃⠁⢰⠄⠤⠴⠶⠶⠦⠤⠤⠤⠤⠀⠀⡀
⠀⠀⠀⢠⣖⢉⠉⣛⠁⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⣒⠀⠐⠒⠒⠒⢘⠂⠀⠀⠒⠒⢺⠀⠂⠀⠐⠂⣒⠐⠒⠀⠀⠂⢘⠛⠋⣰
⠀⠀⠀⠀⠘⠉⠑⠛⠢⠤⠤⠤⢤⣴⣤⡤⠤⠀⠀⢼⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢼⠀⠄⠀⠀⠀⠤⢤⠤⠤⠤⠄⠚⠒⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣠⠏⠀⠀⠀⠀⠀⠀⠸⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣂⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠐⠒⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠄⠂⠀⠁⠘
⠀⠀⠐⢀⡀⠤⠤⢀⠀⠰⢄⠈⠀⡀⣀⠀⢂
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⢤⠈⠅⠠⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠱
⡇⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡂⠈⠐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁
⠁⠈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠈⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠐
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⣠⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠁⠀⠈⢆⠰⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠂⠀⠀⢆⡈⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠁⠄⢄⢂⠄⠘⠠⠬⣃⡑⣀⣀⠿⢉⣤⢤⠤⢤⠀⢸⡟⠝⠛⠛⡏⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠦⣞⡦⠔⣂⠴⠚⠩⡦⠀⠀⣀⣤⣀⠀⠀⡾⠉⠈⢄⣠⡄⠀⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⢠⠔⠂⠀⠐⠉⢄⠀⠀⠀⠀⠀⠃⣧⣀⣼⠀⣰⣿⡤⠖⢊⠁⠐⣰⡧⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠘⣿⠠⠓⣀⡥⠖⠋⣿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠲⣦⣅⣀⡀⢰⡇⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠁⠰⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠐⠀⠩⠞⠋⠉⠀⠀⠘⠛⠋⠉⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠑⣀⠀⠠⠃⠉⠉⠉⠉⠉⠙⠀⠀⢠⠁⠐⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡀⠀⠀⠐⡀⠀⠖⢀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠉⢁⠔⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠦⠀⠀⠃⠀⠀⢄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⢶⡤⠺⡿⣧⣴⡆⠀⠀⠀⠡⠀⠀⠀⠀⠁⠀⠤⠄⠀⠀⡉⠀⠁⠀⠀⠂⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⡖⣷⡀⣏⡉⣿⠏⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⠤⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠠⣆⢁⠀⣿⣿⣿⣀⠉⠀⠀⠀⠀⠀⠃⡀⠀⡴⠄⠀⠀⠀⠀⡌⠀⠟⣧⠠⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢠⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠘⠢⠀⠈⠄⠀⠀⠐⡄⠠⢋⠞⣰⠃⣠⢆⡕
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠈⠀⠀⠀⢤⡀⠀⡜⣕⡡⠾⣁⠜⠀⠋
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⢼⠟⠺⢅⡲⢼⣯⠆
⠀⠀⠀⠀⠀⠀⠨⣀⣂⠰⣏⠀⣹⣏⠀⢙⣦⣤⡤⣤⡤⠾⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈⠲⠉⠂⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣤⣴⠆⠀⠀⠀⠀⠀⠀⣀⣘⣧⣀⡀⠀⠀⠀⢠⣤⣿⡀⠀⠀⠀⠀⠀⠰⣦⡾⠙⣿⣿⣿⡇
⠀⢀⣀⣿⣿⣉⢳⣀⣀⠀⠀⠀⠀⠀⠙⣯⠉⠉⠁⠀⠀⠀⠘⣿⣿⠙⠃⠀⠀⠀⠈⠛⢻⣷⣀⠘⠿⣿⡇
⠀⢾⠀⢈⣧⡟⣏⠀⢈⡆⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢠⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⢷⠘⠇⠀⠙⠇
⠀⠈⠉⠉⠈⠀⠈⠉⠉⠀⠀⠀⠘⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠘⢦⣿⡴⠃⠀⠀⠀⠀⠀⢀⣠⣤⣠⠀⠀⠀⠀⠀⢰⡆⢤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣦⣄⡀
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠈⠓⣀⣤⣀⠀⠀⠀⠀⠀⠙⠉⠛⠉⠛⠉⠛⠁
⠀⠀⠀⣸⠀⣟⡀⠀⠀⠀⠀⠀⠙⡿⠿⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠰⣝⢦⣄⢀⣀⡀
⠀⠀⣀⣽⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠾⠿⢿⡿⠁⠙⠿⠄⠀⠀⠈⠳⠽⡯⠭⠽⡤


⠀⠀⠀⠀⠐⣿⣿⠂⠀⠀⠀⠀⠀⢠⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢤⡛⣤⡀⠁⣀⠀⠀⠀⠀⠀⣠⣿⢸⣷⠀⠀⠀⠀⢰⣦⣠⣾⢿⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣷⢐⡀
⠀⠀⠉⠪⣻⣛⣉⣛⣂⠀⠀⠰⣾⣿⣾⣿⣶⠂⠀⠀⢽⣷⣿⠋⢸⣿⣿⣏⠀⠀⠀⣶⡿⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀⠀⠀⠁⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⠶⣦⣠⣤⠀⠀⠀⠀⠀⢸⣁⣀⣏⣀⣸⣿⡟⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁
⠀⠀⡀⢀⣶⣿⡿⠟⠓⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣤⣤⣾⣯⣭⣭⣤⡆
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠙⠚⠉⠉⠉⠉⠑⠊⠀⠀⠀⠀⠀⠀⠉⠙⠟⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢢⡄⢠⡀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢚⣂⣄⣠⠧⣤⣒⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠔⠃⠀⡉⠁⠃⣀⢈⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠲⡀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⠱⠞⣠⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁⣈⢁⡐⠸⣦⡶⠓⡖⣒⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣤⡶⠈⠁⡀⡤⡈⠀⢃⡄⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⡄⣀⢠⡄⣻⠃⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⢠⡇⢸⣣⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠻⣰⢃⡾⢀⡿⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⢀⡵⢃⡞⢁⡾⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣠⡶⢋⡴⢋⣠⡾⣴⠛⠁⠀⠀⠗
⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⣀⣀⣤⡷⠶⢞⣋⣥⠞⣛⡿⢟⡁⠼⠋⣰⠆⠲⡄⠄⠀⢄⡀
⠀⠀⠀⠀⠈⠻⣭⠭⠭⠭⠭⠵⠶⢒⣛⣩⡥⡞⠛⣉⡴⢾⠶⠀⠀⠉⠀⠀⠉⠀⠀⠶⡇
⠀⠀⠀⠀⠀⠀⠐⢖⣒⣚⣛⣋⣩⣭⡥⠴⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣀⣰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠸⠿⠄⠀⠀⠀⠀⠀⠀⠠⠿⠇
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⣀⣤⣤⣾⣿⣷⣤⣴⣶⣶⣿⣯⣀⡀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⡿⠋
⠀⠀⠈⠙⠷⣦⣤⣀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠰⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣀⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠈⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣶⣦⣤⣤⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⡿⠛⠉⠉⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠈⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⡏⢹⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡷⢹⡀⠀⢰⠁⠈⡆⠀⢀⡠⡎⡟⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢓⢤⡀⠀⠀⡇⡄⢧⡀⡸⠀⠀⢇⡰⢉⠊⡜⠁⠀⢀⡤⡚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⢌⠓⢤⣧⣘⠤⢽⣇⣠⣄⣸⡧⠼⣀⣇⡤⠚⡡⢊⠞
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠙⣄⠑⢄⣈⠗⠊⠉⠀⠀⠀⠀⠉⠑⠺⣁⡠⠊⣠⠋⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⢍⠒⠒⢺⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡴⡟⣉⠭⠉⣙⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⣉⣇⡎⠀⠐⣋⣭⡛⢦⡀⢀⡴⢛⣭⣙⠂⠀⢱⣸⣠⠞⠉⠁
⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠒⠊⠉⣹⠀⠀⠸⢯⣿⠟⠀⡇⢸⠀⠿⣿⡿⠇⠀⠀⣏⠉⠑⠒⠒⠢⠤⢤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⢄⣀⣹⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆⠀⠀⠀⠀⠀⠀⣏⣀⡠⠤⠤⠔⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⡏⢇⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⡸⢹⣉⡑⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣫⣍⣀⣒⣉⣼⠞⢣⡀⠀⠀⠈⠩⠭⠭⠍⠁⠀⠀⢀⡔⠳⡧⠤⠤⣑⠵⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠊⡠⠊⢉⡶⢄⣀⠀⠀⠀⠀⣀⡠⢴⡉⠑⢄⠙⣄⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⢊⡤⠚⢹⠉⡖⢺⡏⠙⠋⢹⣗⠒⡍⢻⠓⢤⡑⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡬⠚⠁⠀⢀⡜⡠⣁⠎⢱⠀⠀⡎⠈⢳⠘⢸⠀⠀⠈⠓⢥⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣼⡸⠊⠁⠀⠸⡀⢀⠇⠀⠈⣇⢾⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣇⡸⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⡞⠀⠐⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⣠⠊⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣐⠦⠔⠃⠘⡠⠃⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢄⠈⢄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⡐⠁⠀⠀⢀⡝⠶⠒⠉⡸⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⡹⠋⠀⠀⠆⡰⣡⣤⣿⣦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⠟⠛⠛
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠄⠚⠀⠒⢒⡒⠘⠛⠛⠛⠛⠛⠓⠴⠦⠤⠼⠦⣘⣻⠂⠀⢓⡀⠄⣢⡆⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠄⠀⢀⢷⠏⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢈⠔⠀⡸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠴⢄⠠⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠺⣮⠄⣞⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⣀⣑⡛⠋⠺⡡⠃⠸⠂⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀⠀⠁⠂⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠉⠁⠉⠉⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠉⠢⠀⠀⠀⠀⠀⢀⡤⠤⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠑⠀⠀⠉⠀⢀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠠⣀⠄⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⡡⠀⠀⠁⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠁⡠⠴⠊⠁⠀⠀⠄⢀⢠⡅⡀⠀⡆⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⡐⠊⣷⡄⠨⠄⠑⠄⡀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠋⠠⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠢⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠐⠒⠒⠒⠒⠒⠒⠒⠶⠖⠒⢒⠒⠒⠠⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠤⡤⣄⣀⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢲⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⠉⠉⢻⠛⠛⠛⢛⠟⠛⠛⠯⠒⠒⠢⠤⠶⡶⠶⠶⠶⠶⠶⠶⠶⠆⢠⠀⠀⠀⠘⠀⠤⠤⠄⠈⠑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⢚⠩⢹⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⢀⡤⠇⠋⣉⢡⡀⡀⣨⠀⠀⠄⠆⠙⠥⠾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⢰⠉⠀⠀⠈⠉⠉⠁⠑⢲⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⠠⠼⠽⠹⠦⠀⢀⠸⠀⠀⠀⠀⢰⡀⢠⠇⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠔⠁
⠀⠀⠀⠀⢸⠀⢁⣋⣘⢀⣁⠀⢨⡻⠰⠄⡀⠨⢤⣤⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⠀⣀⣘⣚⣒⣁⡀⢸⡟⠱⠊⠈⠁⠰⠏⠙⠃⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡠⠤⠤⠠⠤⠠⠊
⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠁⢸⣧⢤⠰⠤⠤⠤⠤⠴⠦⡆⢐⠂⠀⢀⣀⣀⠀⢘⢒⣀⣐⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⡀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⣤⠀⢠⣸⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠠⠀⠉⠉⠩⠀⠀⠂⠠⠂⠀⢠⢀⡁⠀⠈⡇⠀⢤⣀⡄
⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠈⠲⠚⡈⢀⠀⠀⠀⠆⠐⠈⠂⠀⠄⠀⠐⠿⢄⠀⠀⡇⠀⠀⢁⣠
⠀⠀⠀⠀⠀⠀⠰⢀⡀⠴⠉⢉⡠⠌⠀⡈⠥⠀⠘⠎⠤⠴⠅⠀⠀⠴⢾⡞⣤⠡⠀⠙⠳
⠀⠀⠀⠀⠀⠠⠂⠈⠩⠌⠠⠞⠤⠄⡀⠀⠶⠤⠬⠠⠠⠥⠄⠀⢤⡶⠐⠂⢠⣢⠄⣠⡤⣤⣤⠀⠐⡀
⠀⠀⠀⠀⠁⠀⠁⠈⡠⠤⠄⠀⢈⠃⢩⠈⢈⠀⡀⡉⡀⡀⢉⠀⠘⠁⠘⢠⠯⣎⢇⠩⣅⣤⣄⠀⠸⠀⠠⡅⠘⢶⣥
⠀⠀⠀⠈⡆⠐⠀⠀⡀⠴⡖⠓⠈⠠⣂⠀⢀⠀⠀⣦⡄⠀⠀⠀⠀⢔⡀⡟⢀⡍⣦⠁⠀⠀⢌⠂⠀⢀
⠀⠀⠰⠀⠘⢦⣈⡀⠀⠐⢓⠐⡂⠂⠀⠀⠀⣔⡂⠁⠀⣈⠀⠀⣀⡄⠀⡄⠠⠀⠣⠀⣡⡀⠈⢆⠠⠈⠄⠈⡀
⠀⠀⠀⢐⠀⠄⠀⠠⠸⢉⡹⣿⣉⠀⣨⠉⡍⡅⢠⢈⢻⡉⢀⢀⢉⠉⡭⠠⠆⠀⠀⠐⣰⠔⣸⠆⠉⠁⢀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢀⢀⠀⠀⠀⡥⠀⠎⠬⠄⢧⠠⡄⠘⠀⠍⠰⡆⠀⠠⢲⠅⠈⢈⣢⣬⡜⠆⡄
⠀⠀⠀⣀⠠⠀⠀⠀⠂⠘⠆⠐⠠⣀⠾⠄⠀⢰⠀⠄⠢⠘⠆⢤⠐⠀⡁⠂⠀⢂⡈⡆⠰⠆⠞⠛⢉⣀⣟⣇
⠀⠀⢰⢣⠈⠆⠀⠘⠀⠀⠀⠀⢀⠇⠀⠀⠀⠛⠓⢆⢀⠀⠀⡸⡤⠈⢀⡠⢤⡈⢷⡀⠠⢨⡐⠴⡉⠀⠉⠉⡆
⠀⠀⡆⠀⠀⣸⠂⢀⢲⠌⠼⡐⢊⠀⠀⠀⠀⠀⠀⠀⠁⠨⠘⠃⠓⢌⣿⡜⠏⡻⠀⢷⡀⠤⠈⠀⠙⠒⣤⠔
⠀⠀⠀⠀⠀⠘⠀⠯⣅⡩⢂⣙⢈⡀⠀⡀⠀⠀⠠⠘⠀⠀⠀⠀⠠⠒⠈⠋⠊⠁⠀⠀⠳⡄⢀⠐⢒⠖⡀⢠
⠀⠀⠀⠐⠀⠀⠀⠘⠆⠈⠼⠏⠙⢃⢶⠗⢻⠂⠀⡀⠢⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⠘⠔⡏⡛⢹⢣⠏
⠀⠀⠀⠠⠀⠐⠀⣤⠤⢀⠤⢤⠞⠐⣿⠃⠚⠀⠀⠀⠀⠘⠙⠠⠀⠀⡀⠠⠴⠖⠞⠋⠉⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠉⢧⠴⠃⠈⡀⢄⡠⣏⢠⣀⠀⠀⠀⠠⠀⠒⠑⠀⠀⠀⠠⣄⣘⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⡀⠀⠘⠗⠁⠀⠀⠐⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⢠⡆⠁⠀⠒⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠓⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⡎⡰⠠⣀⠈⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⣀⣄⠀⣐⣟⣦⡽⠧⠶⢤⡉⠢⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠤⢄⡠⢔⣏⡛⢷⣷⣞⢯⠀⠲⡀⠀⠀⠹⠓⢄⠑⢄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⠎⠀⠀⠀⠀⠀⠉⠉⣉⣿⢠⡃⣡⠀⡇⠀⣀⡾⠀⠀⠑⡌⢢⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠔⠚⡄⠀⠀⠀⠀⠀⠪⡀⢸⠁⠯⡄⠀⠱⠜⠀⠀⠀⠀⠀⢈⡄⢡⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠃⠠⡄⢼⡄⠀⠀⠀⠀⠀⠀⢶⣘⣾⡀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⠤⡇⠸⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠊⡠⠤⠤⠤⢄⠉⠆⠀⠀⠑⣦⡀⢀⠔⠒⢲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠃⢰⠀⢸
⠀⠀⠀⠀⢀⡄⠘⠀⠃⠀⠀⠀⠘⠂⠒⠀⣄⠀⠀⠑⠼⠦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⡆⢰⠀⠄
⠀⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠈⢻⠊⠉⠁⠀⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠁⠆⠀⠄⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢠⢭⣶⣤⣤⣤⣤⣤⣠⣧⡼⠤⠾⠖⢺⠿⢛⡛⠮⡛⠛⠛⠛⠛⠛⢋⡇
⠀⠀⠀⡈⠀⠸⢄⣿⡀⠀⣀⣀⡀⣿⡀⠜⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠰⠡⡿⢋⠿⡗⡘⡄⠀⠀⠀⠀⢸⢠
⠀⠀⠀⡇⠀⠀⠀⠻⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢨⠀⡠⠔⠉⡐⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢠⠐⢵⢆⣠⡳⠁⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠤⣀⡀⠀⠀⢸⢀⠁⠀⢀⡇⡗⠢⠄⠀⠀⢀⡀⢨⡄⠤⠐⠈⢣⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇⡆
⠀⠒⢲⠀⠀⡔⠉⠉⠉⠉⠉⠉⠉⠉⠉⠱⠀⠀⠹⠛⠲⠠⠄⣉⡁⣈⣉⣈⡉⠠⢼⢡⠔⠂⠀⠛⠀⠐⠲⠇⠀⠀⠀⠀⠱⡀⠀⠀⡌⠀⠀⠀⠀⢀⡀⠴⢁
⡆⠀⠘⠀⠀⠃⠴⠲⠀⠤⠤⠤⠤⠄⠴⠀⡇⠀⢸⠀⡠⠆⠤⠤⣀⢀⡀⠀⣤⠤⠸⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡵⡄⢠⡏⠀⠈⠉⠁⠀⠀⠐⠸
⡏⠁⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡄⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⢸⠀⣄⠀⡠⠫⢦⣼⣆⣄⠀⠀⠀⠀⠀⠀⠀⡅
⢇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⢀⠃⠠⠤⠤⠤⠤⠤⠤⠤⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⡆⢀⠔⠑⠂⠀⣾⠁⠙⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠙⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠏⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠜⠈⢸⡄⣀⣀⣀⠀⠤⠐⢋⠀⢀⣀⣀⣀⣠⣤⠤⠦⠤⠤⠤⠤⠤⠤⠼
⣤⣤⣬⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢷⡀⢣⠘⢷⡄⠀⠐⣄⠀⠀⠸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣤⢀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⢀⣤
⠀⠀⠀⠀⢀⠙⣆⠳⡌⢿⣦⡀⠈⡆⠀⠀⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣰⣿⣷⠈⠂⠀⠀⢰⠏⠀⠀⠀⠀⠀⢠⠤⠀⡀⢀⣴⠏⢠⡿⠁⠀⠀⢀
⠀⡄⠀⠀⠈⢣⠘⠀⣿⠸⣿⣅⠆⠀⠀⠀⠹⣄⠀⠀⠀⢸⡟⠀⠀⠀⢹⢈⡟⢢⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣀⡰⠁⣾⠁⣠⠎⡄⠀⢀⣴⣿
⠀⠀⡀⠠⠀⠀⠑⣸⠋⢤⣟⠉⠺⣦⠀⠀⠀⠈⠃⠀⠀⠈⣷⠄⠀⠀⢨⢘⣿⡆⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠋⠀⢰⡏⠰⠈⠆⠀⣴⡿⠛⢡
⠀⠀⢀⣤⠀⠀⠀⠀⢇⠈⢹⣆⠐⠟⢷⣀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢸⠸⣇⠴⢀⡾⢃⠀⠀⠀⠀⠀⠴⠁⡄⢠⡟⠀⣧⡘⠀⣸⠏⣀⣴⣿
⠀⠠⡀⠀⠈⠳⣌⣠⣿⡀⠀⠻⡄⣇⠈⢳⡄⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡾⣰⠏⢸⣼⡧⠀⢠⠜⠀⡀⠐⠀⠀⣰⣿⠇⢀⣿⠁⢠⡏⣰⢋⣼⠇
⠀⠀⠈⠂⠐⠢⠤⢁⡍⢻⡄⠠⡘⡀⡆⠀⠗⠀⠀⠀⠀⠀⢹⣧⠠⠀⠀⡆⢹⠀⣧⣿⠁⣄⠄⠀⢰⣰⠃⠀⢠⣿⠏⠀⣼⠋⠠⢋⡴⣧⠟⠁
⠀⠀⠀⠠⡄⠀⡀⠀⠘⡄⣿⣄⡐⢰⡷⢄⠐⠀⠀⠀⠀⠀⣿⡁⠀⡄⢠⠃⣼⠀⢻⡅⠀⣇⠀⢀⡟⠀⣠⠀⢫⠇⣰⣟⣡⠎⢠⠋⠘⠁⠀⠔
⠢⣄⠀⠀⠘⣂⠈⢦⠀⠘⢬⡛⢿⡄⠳⣈⡇⠀⠀⢀⠀⠀⢈⣿⣶⠑⠈⢾⢃⣴⠿⢃⣼⠟⢀⡾⠃⢾⠁⡠⠋⣠⡷⠋⡸⢀⡄⠀⠀⠐⠂⣄⡴
⠀⠘⡃⠈⠀⠹⢆⡀⠂⣀⠀⠉⣿⠃⠀⠠⡉⢦⡀⠀⠀⠠⣿⣿⣇⡀⠐⢹⣿⡇⠀⣼⠁⢠⡿⢀⡶⠃⠈⢠⡾⠋⠀⠀⢠⡟⠁⡰⣂⣤⠞⡝⢣
⠀⠀⠈⠲⣐⠀⠀⠙⠂⠙⢦⡄⣿⣇⠀⠀⠈⠜⠽⣢⠐⠀⠈⠙⣿⣿⣦⠈⠹⣿⡀⣿⣴⡿⠁⡀⠁⢲⣶⠟⠃⠀⠀⣠⢞⣠⠀⣴⢋⡤⣞⡶⠆
⠀⠈⢢⣁⢨⣇⡀⠀⠐⢦⠘⣯⠈⠻⣷⣦⣄⣀⠠⣽⣀⠁⠀⠀⣼⣿⣿⡇⠀⣿⡇⢹⣿⠁⠰⣁⣠⣾⠃⠀⠀⢀⠞⣁⣾⡥⢾⣿⣩⡶⠋⡠⠖
⠀⠀⠈⣏⠉⠙⢿⣅⠀⠈⢣⠙⠲⣤⣀⠈⠻⢿⣷⡌⢻⣷⢇⣴⣿⣿⡿⢠⣾⣯⣎⣾⡿⠀⠀⣿⠉⡠⠀⠀⡀⢀⣴⣾⣏⣴⠾⠛⢁⡀⢈⣤⣾
⠀⠶⢤⣈⡛⠛⢆⠨⠳⣄⠘⠳⣄⠀⢸⡇⠀⠘⣿⡿⢸⡟⢻⣿⡟⣿⢡⣿⣿⣿⣿⣯⣤⣾⣤⡿⠀⠃⡠⢂⣤⡾⣻⡿⠏⠁⣤⠔⢃⣼⣾⠷⠉
⣄⡀⠀⠀⠙⠶⠾⣟⢿⣉⢓⣦⠸⣄⣀⣙⣶⣴⣿⠁⣾⣷⠙⣿⣇⢿⣿⣿⣿⣿⣿⣿⡟⣛⣉⣡⡾⠋⣰⣿⠍⣰⡟⠀⠴⣉⣤⣿⡿⢋⡁
⠀⡉⠑⠄⠀⠀⠀⠘⢦⣙⣿⣿⣷⣤⣄⠀⢹⣿⣿⣧⡘⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⢋⣭⣭⣥⣾⣯⣥⠾⠫⢤⣾⠿⠿⢛⡿⠛⠋⠁⠀⡠
⢦⣄⡀⣈⠁⢀⡀⣄⠀⠀⠀⠙⠛⠛⣿⣇⢿⣿⣿⣿⣿⣿⠟⠋⠩⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣟⣁⢠⣶⣶⣟⣡⡶⠾⠋⣀⣠⡔⣂⣻⣷
⣀⡀⡀⠀⠈⠁⠉⠛⠷⠶⠶⠾⢶⣄⡹⢿⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣤⣼⡿⢿⣛⣿⣭⣭⠿
⣋⡉⠁⠂⠉⠛⠶⠶⠶⣦⣤⣤⠶⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣭⡿⣧⠿⠶⠟⣉⣉⡄⠐⠂
⠙⠾⠶⣿⣁⠴⠶⣤⣤⠴⢦⣄⣀⣬⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⢛⣉⣹⣧⣤⣴⡚⢛⣷⣾⣧⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣏⠉⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⠟⣿⠟⣛⣛⠋⣻⣿⣟⢉⣉⠙⠿⠿⢛⣁
⠠⠀⠄⠤⣀⣀⣀⡀⣀⣽⠷⣦⣌⣛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠛⢿⣛⠛⡿⠿⢿⠿⠿⣟⣛⣛⣋⣩⣍
⢀⡤⠌⠀⠉⠛⠑⣉⠉⢡⣶⣄⠉⢉⣼⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⢻⣬⡟⠲⢦⣉⠛⠛⠳⠾⠓⠚⠛⠛⠓⠢⠀⠄
⣀⣀⣤⢶⠾⠟⠾⠛⠳⠿⡥⠈⠟⠿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣶⣤⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣮⡛⠿⣦⣉⡉⠛⡢⣤⢀⣀⡀
⠋⠉⠀⠀⠀⠀⠀⠀⠐⠀⣁⢀⣶⠶⢿⢠⣼⡿⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣌⠉⠻⣿⣿⣷⣌⡙⢻⣶⣤⣠⡀⠀⠈⠛⠿⠛⢣⣶
⠀⠀⠀⠐⠉⠁⠀⢀⡄⣴⠏⠉⣁⠔⣤⢶⣿⣴⣟⣸⡏⣿⣏⣿⠏⢘⣯⢿⣿⡟⢧⡻⣿⣿⣧⣀⠈⠙⠳⠦⡷⢶⡍⢻⣯⡉⠤⡀⠠⢀⡈⠀⠈
⠀⠀⠀⠀⣠⡤⠴⠏⠀⠀⠔⠉⠰⠞⣁⣼⡏⢁⣼⠏⢀⣾⣏⣿⠀⢻⣇⢨⣿⢃⠸⡋⣿⣯⡛⢻⣷⣄⡀⠀⠀⠁⠙⠦⠹⣿⣤⡈⠉⠠⠀⣀
⠀⣄⡲⠿⠋⠀⠀⠀⠀⣠⢴⠿⣋⣾⣿⠛⠐⡏⠁⠀⣿⢹⣿⠃⠀⠸⣯⠹⣷⡘⢆⠙⣋⢿⠿⣿⣿⣿⣿⣌⡲⣦⡀⠑⠢⣝⠻⡿⢶⣶⣄⡀
⠚⠁⠀⠀⠀⠀⠀⠀⢈⣡⣁⣼⣿⠏⠉⠂⡔⢁⠀⢀⣾⣦⣿⠀⠀⢰⣿⡇⠈⢻⡎⡆⠹⡈⠀⠈⣿⣿⡏⢿⣷⣜⢷⡄⠀⠻⣄⠘⠊⢻⣏⠻⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠋⢉⡟⢻⡉⠠⠀⡠⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⣿⠇⣀⣾⡃⢨⡀⠁⠀⠀⢻⣎⡳⣤⣙⠿⢷⡍⠻⣦⠀⠙⣦⡈⠉⢷⡌
⠀⠀⠀⠀⡀⢨⣿⢀⣸⡏⢀⣭⠋⠀⣼⠀⠀⠀⠠⢾⣿⡅⠀⠀⠀⠈⢻⣤⡙⡯⣿⠘⣧⡀⠀⠘⠙⢈⠙⢦⠈⢇⠀⠰⡆⣹⢷⣄⡘⠷⣄⡀⠈
⠀⠀⢠⣤⣤⣿⠁⢾⣩⣾⠟⠁⢀⢾⡏⠀⢀⣦⣴⢾⣿⠟⠀⠀⠀⠀⠀⣿⠟⠁⣼⠃⠈⣿⣦⡀⠀⠈⠀⠈⠂⡀⠐⠄⠀⠘⠷⣄⡙⠳⡀⠹⣧
⠀⢀⣿⠁⠀⠀⢈⣾⠛⠋⠀⢀⡟⢸⡇⢠⢻⠉⠀⢀⣿⠀⠀⠀⠀⠀⠀⣹⣷⡄⡈⠃⠄⠈⠚⣿⡆⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢌⠻⣆⡡⠀⠻
⡰⠟⠋⠀⠀⢠⣞⠅⠀⡀⢠⠊⢠⡇⠀⠸⠀⣧⠀⢸⠇⠀⠀⢀⡠⠖⠈⢿⡟⢧⣁⠀⣴⡀⠐⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠌⣻⢷⣄
⠁⠀⠀⠁⠀⠼⠃⠀⢠⡸⢀⡤⢿⠀⣠⣴⠾⠛⠀⡞⠀⠀⢀⡏⠀⠀⠀⣟⢧⡘⠏⠐⠨⣿⣄⠀⢦⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙
⠀⠈⠀⠀⠃⠀⠀⢤⠋⢠⢸⡴⠃⢸⡏⠀⠀⠀⠸⠇⠀⠠⠊⠁⣄⠀⠀⢹⠆⠣⠈⢠⡄⠀⢻⡆⡘⠌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠈⠛
⢠⠄⠈⠀⡀⠀⠰⠃⠀⢸⣼⠃⠀⢼⡇⠀⠀⠠⠀⠀⠠⠀⠀⢠⡁⠀⠀⠹⢦⡀⢣⠈⠉⢦⢼⡇⣶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠁⠀⠀⠀⠀⠀⠀⣠⠞⣱⠏⢀⠔⡘⠀⠀⢠⠀⠀⠀⣰⠀⠀⣸⡇⠀⠀⠀⠀⡅⠈⢄⠀⠸⡈⢿⠻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⡞⠁⡼⠃⠐⠁⠖⠁⠀⠀⠃⠀⠀⡀⢙⠂⢀⢳⠈⠇⠀⠀⠸⡃⠀⠀⢠⡀⢸⡇⢣⠀⡄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣜⠷⠈⢰⠀⢿⠀⠀⠀⠑⠀⠀⠀⠇⠸⢷⡠⡋⠡⡀⠁⠀⠀⠀⠀⠈⠋⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠙⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⣾⡄⠻⡀⠀⠀⠀⠀⠀⡃⠰⠒⠂⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⢀⣄⣠⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿
⠀⠀⠀⠀⣨⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣤⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⢚⣿⣿⣿⣿⣿⡿⢿⣿⣶⣶⣄⠀⠀⢤⢰⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄⣤⡄⠸⣿⣿⣿⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣿⣳⠛⢿⣿⣧⣄⠈⢹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠼⠶⠂⠀⠟⠛⢻⣿
⠀⠀⠘⡻⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿
⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⡆⠀⣀⣀⣤⣄⣤⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠀⠀⠀⠈⠻
⠉⠛⣻⣿⣿⠏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣶⣶⣆⠀⢸⣿⣿⣦⣄
⠀⠀⠈⠉⢣⣾⣿⣿⣿⣿⣿⣿⠛⣿⣿⠿⠛⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣷⣼⠟⣿⣿⣿⡀⠀⢈
⠀⢀⠀⠀⠸⠟⠙⠉⣿⣿⠛⣛⠂⠀⠀⠀⠀⠀⢸⣇⠽⢛⣟⠻⣿⡿⠿⠫⡏⣸⣿⠝⢛⣿⣿⠿⣿⢿⣆⣽⣿⣿⣇⠀⢨
⠀⣿⣇⣠⣀⠀⠀⠀⢸⣟⢠⣿⣶⡄⢰⣿⡄⠀⢸⣿⡗⢺⣿⠖⣿⠀⢃⡀⠁⠙⣿⡆⠀⢸⡇⠀⠉⣾⣿⡿⢿⣿⠃⠀⠠
⠀⣿⣯⡸⣿⣂⡀⠀⢸⣿⣄⢻⣿⣧⣿⣿⠆⢴⣿⣿⣿⡞⡿⠇⠛⣰⣿⣿⣧⠀⡟⢇⠀⠀⠁⠀⠀⣹⡉⢽⣖⣿⣀⡀
⠀⢹⣿⣼⣿⣿⣷⠀⢸⣿⣿⣸⠿⣿⣿⣿⣆⡏⢹⣿⣯⠹⡄⠀⠀⣽⣿⣿⣿⡐⠗⠘⠃⠀⠀⡔⠉⢹⠈⠛⣯⣿⣅⠈⡆
⠀⠸⡿⠏⣿⣿⣿⡇⢀⣿⣿⣿⠃⠈⣿⢿⡟⠃⢸⣿⣿⠀⠁⠀⠀⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⣆⢀⡜⠀⠀⠾⠿⠤⠜
⠀⠀⠁⠀⣿⣿⡟⠃⠉⣿⣿⡟⡇⠀⣿⠈⣧⠀⠀⣿⡏⠀⠀⠀⢸⠇⣿⣿⣇⢻⡄
⠀⠀⠀⠀⢿⣟⠀⠀⠀⣿⣿⡇⠁⠀⢻⠀⠹⠄⠀⣿⡇⠀⠀⠀⡟⢸⣿⣿⣿⠈⣧
⠀⠀⠀⠀⠸⣿⠀⡀⠀⢹⣿⣧⡀⠀⠈⠀⠀⠀⠀⠛⠃⠀⠀⢠⣇⠈⣿⣿⡏⠀⠉⠀⠀⢠⡀⠀⢀⡀⠀⢠⠀⠀⡀⠀⡀
⡇⢸⠀⣿⢴⡿⠧⣷⠀⣿⣿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⣿⠀⠀⠀⠀⠀⢸⡗⠒⢺⡗⠒⢺⡗⠚⣗⠒⣿
⠇⢸⠀⣿⠐⡗⠐⣿⠒⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢸⣿⣀⣼⣿⣤⣿⣿⣿⣿⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⣇⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⣰⣖⡲⠥⣀⠠⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠤⠀⢯⣛⣷⠻⠄⠀⠀⠈⡓⠈⠢⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠥⠀⠀⠀⠀⡄⢛⢰⡈⠐⡠⠘⠁⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠆⠀⠀⠀⠀⠃⢠⠰⠀⠀⠀⠀⠠⣦⠷
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠷⠾⠀⠀⠁
⠀⠀⠀⡠⠰⠬⠀⠀⠘⠄⠠⡄⠈⠀⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜⣈⣠⣀⣀⣠⣤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⢀⣆⠀⠀⠀⣶⠐⠀⠄⠀⠀⠀⠀⠢⠀⠀⣈⠉⠉⠉⠉⠉⠋⠉⠀⠐⡵⠒⢦⠀⠀⠀⠀⠰
⠀⠀⠁⠀⠀⠃⠀⠀⠀⠋⠀⠀⢠⡀⠀⠀⠀⠀⠠⠂⠀⣄⠀⠀⠀⠀⢀⠀⠀⢁⠙⠤⠞⢀⠀⠀⠀⠀⠁
⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠦⡄⠐⠀⠐⠂⢐⠈⡄⠠⠀⠐⠀⠬⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡥
⡇⠈⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠒⠀⠠⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠇⠀⠀⢀⠓⡀⠇⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⢀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠰⠄⢙⡟⠲
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣠⣀⢘⣁⣀⡀⠤⠤⠼⠤⠤⠤⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣬⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⢿⣿⣷⠻⡖⠄⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⡀⠀⠿⣟⠁⣙⣿⠇⠀⢀⣾⣴⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣾⣿⣷⠀⠀⠑⡀⠈⠁⠀⠙⣌⢻⡟⢦⣸⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠈⠀⣼⡟⢻⣟⣍⠳⢹⡁⠀⠀⠙⢆⠀⠀⠀⠀⠛⠻⢻⣿⣽⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣾⡄⠀⠫⠟⠄⠘⠋⠑⠘⢿⠄⠀⠀⠈⠁⠀⠀⠀⢤⡀⠀⠙⠀⠘⠟⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢛⣿⣛⠯⡳⠄⠀⠀⠀⠀⠀⠀⠠⣈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⢯⣻⣟⠣⠈⠀⠀⢀⠀⠀⠀⠀⠀⠈⠑⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⢤⡀⠠⣠⡀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⡠⢊⡀⠓⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢄⠀⠈⠀⠀⢀⣴⣶⡠⣀⣀⠀⠁⠠⣄⠀⠈⢀⡀⠀⠀⠀⠙⣦⣄⡀
⠀⠀⠀⠀⠔⠁⠀⠃⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡠⢄⡤⢴⣾⣿⠛⢣⡴⢌⠀⠴⠞⠻⣿⣿⣨⠉⢉⣱⡦⣀⣀⡠⠈⣉⣩⣵⣦⣄⡀⠀⠈⠙⠲
⠀⠀⠠⠖⠶⠶⠶⠒⠒⠛⠉⠙⠻⢿⣿⣶⣆⠤⠊⠈⠁⠀⠀⣈⠥⢠⣤⠎⠁⠀⠀⠀⠀⠀⠉⠉⣉⡽⠚⡿⠟⠁⠀⠀⠉⠙⠋⠯⠭⠭⠷
⠀⠀⠀⠀⠐⠒⠒⠒⠶⠦⢤⣶⣶⣯⣭⣵⣆⣒⣒⣒⣒⣒⣊⠒⠲⠾⢁⣐⣛⣛⣛⣛⣛⡁⠀⠀⠉⠀⠀⠠⠤⠄⠀⣤⣤⠤⠤⠤⠤⠤⣌⣉⣀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠉⠁⠩⠤⠵⠖⠒⠒⠂⠃⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠠⠀⠈⠉⠀⠀⠀⠀⠒⠂⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠄⠀⠀⠀⢀⠀⠀⠉⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠘⣧
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠹⡆
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠲⠚⠛⠛⠛⠛⠛⠛⠶⠖⠀⠀⠂⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⢠⠿⣄⢀⠞⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⣠⠏⠀⢸⢿⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣄⣀⣀⣀⠀⣀⠀⠀⠚⠛⠛⣉⣉⣉⣙⠛⠛⢻⡀⢀⡼⠶⣷⠄⠠⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣉⣉⣉⣉⣉⣉⣛⡋⠁⠀⠰⠦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠋⡀⠀⠼⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠠⠀⠀⠀⡄⢠⢿⣷⡀⠁⠀⠁⠀⠐⡀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣤⡀⠀⠂⠀⠀⠀⠿⠸⢿⣇⠀⠀⠀⠀⢀⡴⡫⣷⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠹⡌⢎⢳⣤⠐⠀⢀⢸⠁⠀⣆⢹⡀⠀⠀⣰⠞⢱⢣⡟⠀⠀⠀⠈⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠐⠀⠀⠀⠸⡇⠈⢄⠟⣷⡆⠀⠇⠀⠀⡇⣼⣷⠀⡴⠃⢀⣏⢎⡟⠀⠀⠀⠈⠀⣀⠈⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⢿⡳⣴⣄⣀⠀⠐⣇⠀⠘⣞⣰⣽⣿⠤⠤⠶⠻⠿⠿⡿⣅⢀⡞⡿⣜⡟⠀⢁⣠⠤⠚⣡⢾⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢮⠪⣝⣗⢶⣾⣀⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⠔⠋⠁⣠⢞⣵⡏⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠄⠐⠠⡀⠀⠘⢧⠀⠙⠪⣪⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣠⣞⢕⣿⡏⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠘⢧⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣀⡄⣠⡤⠤⠶⢦⣴⡶⠂
⠀⠀⠙⠻⣿⠯⣟⣻⢏⣓⠿⣖⣻⠿⠀⠀⢀⡤⢴⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣀⣀⠀⠀⠀⠹⡅⠀⠀⣀⠤⢒⣭⠾⠛
⠀⠀⠀⠠⠉⠓⢦⡉⠙⠛⠿⢶⡿⡀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣟⢷⡀⠀⠀⢀⡴⠟⣥⣀⣀⣴⣉⣀⠀⠀⠀⠀⠸⣦⠛⣠⣴⠞⠋⠀⠄
⠀⠀⠤⠄⠀⡀⠀⠉⠳⢤⡀⣼⠁⠀⠀⠀⠀⠁⠀⣻⣿⣿⣇⣽⣿⣷⠀⠀⣼⠻⠓⠛⠹⣿⣿⡟⣨⡗⠠⠀⠀⠀⢻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⣿⡄⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠠⠀⠸⡅⠉⠙⠓⠶⠆⣠⣀⠀⠁
⠀⣀⣠⣶⠶⠞⠋⠭⣭⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣧⣤⣤⣶⣶⣶⣶⣴⠿⠖
⠀⠉⠿⠏⠩⢉⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣶⠖⠚⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠑⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⢐⣰⢿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⢀⠈⠲⢦⡀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⡴⣏⡬⠗⠋⠉⠙⡄⠈⠀⠀⠀⠀⠀⠀⠀⠲⠔⠓⠒⠦⠤⠚⠛⠛⠒⠒⠀⠂⠀⠀⠀⠀⠀⢠⣿⣷⣿⣟⣾⣥⣂⣽⣷⣄⠂
⠀⠀⠀⣠⣾⣗⣋⡥⢤⠤⠴⠖⠶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣄⣀⠋⣤⢊⠂⢀⠀⠀⠀⠀⢀⡴⠉⢻⡀⠁⠀⠉⡁⠉⠙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⠫⡫⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠠⠐⠀⠀⠀⢀⣴⢿⡢⡀⠀⠩⡄⠈⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⢀⠄⠊⠀⢀⣼⡋⣠⠞⠁⢀⣹⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣀⡤⠞⢿⠷⣴⣝⢮⡲⢄⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⢁⣠⢖⠋⠘⣯⢋⣻⠋⠛⢳⣶⣦⣤⣤⠤⠴⢶⣶⣿⠋⠄⠀⢸⡄⠌⠉⠻⠿⢦⣕⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠵⠞⡁⠀⠀⠀⢸⢇⢈⠇⠀⣰⠋⢸⡏⢿⠀⠀⠀⡜⠘⠿⣆⣌⠄⠈⣏⠂⠀⠀⠀⠀⠁⡉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⢀⠀⠀⢸⡏⡌⠀⡞⠀⠀⠈⣿⢸⠈⠀⢰⠁⠀⢠⠘⢿⡌⠄⢧⠀⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣾⡝⡰⠃⠀⠀⠀⠀⠘⣷⢠⢀⡇⠀⠀⠀⠀⠀⠹⣤⣬⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡀⠀⠐⠀⠀⠀⠀⢻⣼⡘⠃⠀⠂⠀⠠⠈⡄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠂⠈⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠠⡀
⠀⠀⠀⣧⣤⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠠⠀⠉⡌⠄⠀⠀⠀⠀⢀⡤⢒⡆⢲⡞⡉⠳⣄
⠀⠀⠁⠁⠒⠺⠁⡃⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⢤⣊⣤⢞⣝⣭⠓⢾
⠀⠀⡂⡰⢒⠒⡀⠃⠀⠀⠀⠀⠀⠀⠀⢀⢡⠠⠶⣄⠈⡢⠄⠀⠀⠀⠀⠈⢌⠠⡀⣀⣀⠄⠣⠂⠀⠀⠀⠀⠀⠀⠙⢦⣉⠐⠚⠉⠁
⠀⠀⠐⠶⠞⠶⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠈


⢠⣤⠀⡀⠤⠠⢀⠀⠠⡀⠀⠀⠀⠀⠀⡤⠶⠶⠾⠯⢉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠋⡆
⠈⡙⠊⠀⠐⢆⢶⠂⢠⠁⠀⠀⠀⠀⠀⡇⠀⡤⢤⡀⠀⡇⠀⠀⠀⠀⠀⢰⣛⠉⣡⠶⣄⣛⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃
⠀⡅⢄⠣⣥⢧⠇⡀⢸⠀⠀⠀⠀⠀⠀⠇⠀⣖⣂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⠓⠀⡁
⠀⠃⠀⠑⠒⠂⠈⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠄⠈⠉⠮⠁⠘⠓⠃⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠤⠀⠄⣀⣀⡬⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⡀⠈⠄⡍⠉⢹⢆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣒⣐⡄
⠀⠀⠀⠀⠀⠁⢲⠈⠀⠀⠀⠀⠀⠀⢂⡀⠄⠀⠀⢀⡴⠃⠃⠀⠀⠀⠀⠀⠣⡀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠖⠆⠉⠉⠙⠋⠁
⠠⢀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠀⠀⢀⣬⡄⢰⠉⠉⠉⠒⢀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠢⠤⢀⡀⠠⡄⠈⠁
⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⢄
⡀⠠⠤⠤⠜⠶⠖⢁⢐⠄⠀⠀⠀⠀⠀⣀⡐⢢⠀⠊⠱⣵⠀⠀⠀⠀⠀⢀⠔⠲⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⡇⠀⠀⠀⣠⠔⢂⠀⠈⠀⠀⠀⠀⠀⠀⣼⡇⠀⠈⣁⣀⢉⠀⠀⠀⠀⠀⠀⠁⠈⠀⡋⠳⠆⠢⡄⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⡂⡄
⢁⠀⠀⠀⠁⠚⠉⣀⡸⠀⠀⠀⠀⠀⠀⠻⣗⣶⡶⠥⣭⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⢣⣀⠀⣀⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠿⠻⠟⠶⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢤⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⣐⠗⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⣶⡶⣿⣛⠳⠶⣄⠀⠀⠀⠀⠀⠉⣰⠟⠉⠉⠻⣆⠛⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡾⣻⠋⢷⣀⣩⡷⠖⠛⠁⠀⠀⠀⠺⠂⣿⠀⠀⠀⠀⣿⠰⠆⠀⠀⢹⡆
⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠃⣻⡴⠞⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠳⢤⡤⠞⠁⠦⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠞⠋⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠐⠓⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠻⢧⣤⠖⠛⠛⠳⢦⣤⠶⠛⠛⠳⢦⣼⠷⠛⠛⠓⢦⣤⠶⠛⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣠⣄⣀⠀⠀⢀⣀⣤⣀⠀⠀⢀⣀⣤⣀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⠋⠀⠀⠉⠛⠚⠋⠁⠀⠉⠛⠚⠋⠁⠀⠈⣻⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⡄⠀⠀⢀⡀
⢠⡄⣇⡆⢠⢸⡧⠀⢰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠸⣿⣿⡧⢸⣾⡷⢸⣿⡇⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀
⠀⠈⠉⢻⡾⠿⣿⣸⣿⣇⣿⢸⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠙⠉⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⢿⣾⢠⡀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡀⠰⡆⠸⡇⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣩⢠⢵⠀⡁⢠
⠀⠰⠃⢄⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢂⣤⢌⢠⡯⠷⠠
⢨⡇⢾⣍⣈⣰⣖⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢨⡈⣰⢦⣄⣫⡷⣾⣙⠈⠄

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠂⢤⡀⠀⠀⠀⠀⢀⡠⠔⠂⢉⠀⠀⠉⠑⢢⡀⠀⠀⠀⠀⠀⢀⠔⠊⠉⡁⠀⠡⡐⢀⠀⠀⢀⡀⠀⠀⢀⠔⠈⠣⠄⠠⠜⠁⠢⡀
⠀⠀⠣⡀⠀⠈⠐⠂⢀⠍⢠⠀⢁⠚⠥⠈⠀⠁⠈⠁⠀⠕⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⠑⢆⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⠜⠂⣈⠕⠀⠈⠀⡡⠐⠒⠢⢄⠀⠀⠀⠀⡀⣀⠜⠁⠀⠀⢸⠠⠈⢈⡈⡀⠀⣠⠀⠔⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠘⠒⠫⠤⠄⠄⡤⠊⢀⠀⢀⡠⠚⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⠀⠀⡆⠁⢀⠀⡘⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠮⠤⠴⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣢⡈⢲⡰⠁⠀⢘⠖⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⣀⡀⡠⠔⠢⢄⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⣀⠀⠀⠀⣀⠀⠀⠈⠒⣄⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠇⢯⡱⢸⠒⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⡤⠴⠎⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠛⠁⠀⣠⠄⠒⠒⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁⣠⡀⡄⠀⢡⣧⠀⠀⠀⢨⠉⠉⡇
⠀⠀⠀⡀⠀⠐⠚⠀⠀⠐⠻⣄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⢰⠃⠀⣙⡷⠃⠀⣿⠇⠀⠀⠀⠈⠳⠞
⠀⠀⢰⠁⠀⠀⠀⠀⠠⡄⢠⠀⠃⠀⠑⠐⠊⠉⠉⠐⠢⠤⠀⠤⠔⠊⠀⠀⢀⠀⠀⠀⠇⠀⠐⠇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⠂⣠⣀⡀⠀⠀⣼⠇⠀⠀⠀⠈⠁⠀⣀
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠲⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠈⠁⢐⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡧⠀⠐⠒⠒⠀⢤⢄⠈⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠚⠉⠢⣄⠀⠀⠀⠀⠀⠙⠶⠶⢥⣤⣤⡾⠁⠀⠀⠀⠀⡚⠓
⠀⠀⣇⠀⠀⠈⠀⠂⠈⣾⠘⠃⡅⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣄⣴⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀⣠⣖⠠⠀⠐⠀⣷
⠀⠀⠉⡄⠀⠀⠀⠀⠀⠙⠐⡀⡇⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠙⠋⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠄⠀⢀⢸⣿⣿⡇⠀⠀⢸⡅
⠀⠀⠀⠲⠶⢤⠤⠤⡾⠡⡾⠐⠁⠀⠀⠀⠀⠀⠀⣀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠈⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⠛⠶⠶⠶⢴⣄⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣉⠀⢀⡂⠀⠀⠀⠁
⠀⠀⡀⠀⣀⠠⠖⠒⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠀⠠⠔⠒⠂⡄⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣤⣀⣀⣀⡀⢈⠀⠀⠀⠀⠀⠀⠀⢀⢄⠤⠄⠀⠀⠄⠀⠀⠰⠂
⠀⠀⢸⡀⠀⠀⠒⠡⡐⠀⠰⡀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⡄⠕⠁⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⡃⠀⠐⠂⠚⠁⠀⠀⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⡈⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⡀⠀⠀⠀⡧⡀
⠀⠀⠀⢣⠀⣤⠴⠖⠚⠀⠀⡁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣄⢣⣤⠇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠂⠀⠒⠊⠁⠈⠒⢄
⠀⠀⠀⠈⠆⡀⠀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠘⠻⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠉⠉⠐⠲⠀⡀⠤⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠈⠀⠉⠉⠉⣥⢻⣶⣶⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⣀⠐⠖⠂⠀⠦⡶⠋⠙⠲⢿⣷⣿⣷⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣤⣤⣄⣠⣤⣀⠿⠿⠇⣉⠠⠾⣯⣎⡢⡀⠀⠈⠉⠛⠿⣀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠶⠯⢉⠐⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⡖⠀⣼⣿⡌⠪⡢⡀⠀⠀⠀⠀⠉⠒⠦⢀⠀⢀⠔⠁⠀⠀⠀⠀⣦⠏
⠀⠀⠀⠀⠀⠀⠀⡰⢱⡾⠟⢻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢠⣦⡌⠋⠀⠀⠻⣮⠢⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠰⠃⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣾⣿⣿⣿⡄⠀⠀⠀⠈⠪⡢⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠻⠀⠀⠀⠀⠀⠀⠊⡠⠂⠀⠀⠀⠀⠀⢀⠔⢃
⠀⠀⠀⠀⠀⡰⠔⠂⠉⠡⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢂
⢀⣠⢔⣊⣁⣀⣀⣀⣤⣄⣡⣈⣻⣿⣿⣿⣿⠛⠛⢻⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⣠⡐⡁⠀⠀⠀⠀⠀⢆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠤⣤⠊⡀⠀⠀⢀⣠⣾⣿⣿⣮⡢⡀⠀⠀⠀⠈⠆
⡇⠀⠀⠀⣀⣤⢤⡤⣤⣀⠀⠀⢸⣿⠀⠈⠉⠙⠳⣄⠀⢀⢀⣀⠔⠁⠀⠀⡰⣡⡾⠋⡠⠔⠙⠿⣿⠿⠿⣿⠁⠈⡢⡀⠀⠀⠈⠄
⡇⠀⢀⡾⢥⡿⢼⡧⢽⡬⢷⡀⢸⣻⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣄⡒⠺⡫⠔⠉⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠪⠢⡀⠀⠈⡄
⡇⠀⢸⣤⣼⣤⣼⣧⣤⣧⣤⡇⢸⢯⠡⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡐⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠪⡦⡀⠘
⡇⠀⠸⣄⣸⣄⣸⣇⣠⣇⣠⠇⢸⢽⡆⠡⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⢃⠠⠊⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⡇⠀⠀⠙⠦⣷⣼⣧⣾⠴⠋⠀⢸⣺⡥⠖⠓⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⡠⠁
⡇⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⢸⢿⡄⠍⢣⠰⡀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⠔⠈
⡇⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠀⢸⢸⣿⡌⠄⢣⠱⠀⠀⠀⢸⣿⠁⠀⠀⠀⢀⡠⠔⠊
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡿⢛⠨⠑⠈⠀⠒⠀⠀⠛⠐⠒⠈⠉
⢇⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⡸⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⣄⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⠀⢹⣷⣄⠀⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡈⢻⣿⣿⣿⡆⣾⣿⣿⣴⣿⣿⡏⠀⢀⣾⡇⠀⠀⣠⣾⣿⠋⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡿⠀⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣶⣶⣾⣿⣶⣤⣀⠀⠹⣿⣿⣿⢿⣫⣽⣶⣶⣶⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⣿⣷⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⡿⠟⠉⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣿⣿⣏⣾⣿⣭⣥⣭⣝⣿⣿⡿⠿⠻⠿⣿⣧⢻⣿⣿⣷⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⣿⣿⢹⣿⣿⣿⣟⣧⣿⣿⣿⣾⣿⣿⣻⣾⣿⡟⣿⣿⣛⣉⣀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣯⡉⠉⠙⠛⠛⠋
⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠉⢁⣴⣾⣿⣿⣯⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣾⡿⠟⠛⢋⣿⣿⣶⣽⣛⣿⠿⠿⣿⣛⣭⣾⣿⣿⣿⣿⡛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⢸⣿⣿⠏⣿⣿⣿⠏⢿⣿⡆⠀⠀⠻⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠸⣿⠃⠀⣿⣿⣿⡄⠀⠉⠛⠶⠄⠀⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠹⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡖⠊⠉⠦⠒⠞⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⢀⣤⠤⢤⣤⠂⠁⠈⠀⠐⠃⠀⠀⠀⠀⠀⠢⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢨⡏⠀⠀⠀⢹⡆⠀⠀⢀⠀⣎⠀⠀⠀⠀⠀⢢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢧⣀⠀⢀⣼⠧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⡖⠚⠛⠹⠉⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠢⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠢⢄⠀⠀⢀⠴⠒⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠥⠰⡃⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⡰⠉⠉⠱⣄⠀⠀⠀⠀⢀⡜⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠉⠒⠒⠚⠁⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣂⡠⣀⣀⡀⠀⠀⠀⠀⠀⡳⠀⡠⣶⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣠⡤⠤⡀⠀⢘⠀⠀⢺⡓⢢⡴⠶⢦⡠⢒⡆⠀⠀⢀⠀⢀⢀⠈⡀⠐⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢨⠀⠘⡂⠀⡤⠀⣏⠀⠀⢀⡇⠈⠀⠀⠀⣤⠂⠉⠄⠀⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡈⡓⣀⣐⣉⠠⠔⠁⠈⠓⠃⣘⠲⠶⠚⡁⠬⠷⠀⠀⠂⠀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠛⠀⠳⠇⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⣢⠔⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠴⠔⠒⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠨⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢾⣍⡁⠀⠀⠀⠀⠒⠀⢠⡀⠀⠗
⠀⠀⠀⠀⠠⣀⢐⠀⠀⢀⡄⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠚⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠠⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠐⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠠⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⢀⡖⠉⠈⠙⠁⠀⢹⣄⡀⠀⠀⠀⡀⠀⠀⠀⡐⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⣄⣀⠀⠀⢢⠀⠀⠀⠀⠱⡄⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠻⡀⣀⣄⣀⣀⡠⠃⠀⠀⡰⢠⠒⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠠⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠋⠍
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠛⠒⠦⡀⠀⠀⠀⣀⠤⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⣀⣀⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠋⢱⠄⠀⠀⠙⡆⠀⠀⠀⠀⠀⡀⠆⠀⠈⠀⠀⠀⠀⠰⠶⠿⠺⣧⠀⠀⢸⡇⢠⡤⡼⢧⢬⣽⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠘⠒⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠤⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠿⠀⠀⠘⠃⣼⡇⠀⠀⠀⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢧⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠲⠈⠰⡶⠀⠀⠀⠒⠺⠃⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠄⠚⠁⠀⠀⠀⠀⠀⠈⠀⠀⠊⠀⠀⠀⠀⠀⠒⠀⠴⠾⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⢠⠂⠀⠀⠀⠀⣀⠤⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢄⠀⠀⠀⠀⡠⠴⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠠⢾⣅⠉⠀⡼⠇⠀⠀⢀⡔⠊⠀⠀⠀⠘⡉⢢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⠴⠀⠀⠒⠊⠤⠄⠀⠞⡀⠀⢀⠂⢀⠄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠚⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⡑⠀⠈⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠃⠂⠠⠀⠀⠀⣹⠀⠀⢶⡀⠀⠀⠀⠀⠠⢐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠒⠒⠊⠁⠀⠀⠀⠑⠢⠤⠄⠤⠖⠋

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠸⡌⠡⠀⠀⠤⣡⡧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠉⠛⠒⠶⠤⣤⣉⡙⠓⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠛⠲⠄⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠦
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂
⠠⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠏⠄⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⣋⣻⢀⡾⠉⣀⡀⢀⣀⠀⣀⣀⢀⣤⢀⡆⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠉⢹⡟⠁⢾⣽⣇⢿⣭⢼⣭⣯⢼⡏⢼⡵⣯⡽⢼⢫⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⠀⠀⠀⠀⠀⠢⠀⢠⢌⣀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢠⠀⠀⠠⠀⣀
⠀⠀⠀⣀⣈⡐⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠏⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⠹
⠀⠀⣀⠛⠉⠉⠈⠛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠻⣷⠆⠀⠰⣿⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⡿⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠈⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠷⠀⡂⡄⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠘⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⢀⠀⠐⢄⡀⠀⠀⠀⠠⠀⠀⠁⢀⠀⠈⠁⠢⢀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠡⡀⠀⢀⠁⠀⢀⠒⠀⠈⠁⠊⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠄⣡⠔⠊⠀⠀⡠⠀⠀⠀⢉⡄⠠⠤⠄⠀⠒⠁⠀⠀⢸⠈⠀⡀⠂⢀⠰⠃⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠉⠉⢠⠋⣀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠸⠀⡀⠀⠀⣀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⢀⠀⣀⠀⠀⠀⠘⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠐⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠐⠁⣒⠄⡆⠀⠀⠄⠀⠀⠀⠀⠀⠛⠃⠀⠀⠁⠀⠀⠀⠈⠢⣀⣠⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠣⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈
⠀⠀⠈⠋⠀⢠⠄⠀⠀⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡀⡄⠀⣼⠄⠀⠀⢈⠉⢉⠁
⠀⠀⢀⠀⠀⠈⠀⠀⠐⠳⢄⠀⢰⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠄⠀⠨⠝⠀⢈⡟⠀⠀⠀⠀⠑⠋
⠀⠀⡆⠀⠀⠀⠀⠀⠆⠀⠀⡆⠀⠉⠀⠀⠀⠈⠐⠂⠒⠀⠁⠀⠀⣠⠀⠀⡘⠀⠀⠁⠀⠀⣜⠇⠀⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠐⠲⠢⠀⢀⡏⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⠀⠠⡦⢄⡀⠀⠀⠀⠀⠰⣄⣀⣀⡀⢀⡼⠁⠀⠀⠀⠠⠄
⠀⠀⠄⠀⠀⠀⠀⠚⣴⢸⠀⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⠀⠒⠀⢀⡀⠀⠀⠀⢠
⠀⠀⠠⠀⠀⠀⠀⠀⠹⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠟⠁⠀⠀⠀⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⡈
⠀⠀⠀⠴⠤⡤⠤⡼⠥⡮⠈⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠓⠒⠶⠖⠤⠄⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠈⠉⠀⠘⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⡄⠀⠈⢀⠈⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⢲⠄⠤⠤⠀⠀⠀⠀⠀⠀⠀⡐⠊⠁⠀⠉⠀⠀⠀⠁
⠀⠀⢰⠀⠀⡀⠨⠂⠀⠘⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠈⡀⢀⡀⡠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠜⠉⠠⢀
⠀⠀⠀⢡⠈⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠓⠊⠹⠶⠀⠀⠀⠀⠞⠀⠀⠀⠈⠀⠀⠀⠒⠀⠤⡀⢀⠄⠄⠠⠂

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠠
⠀⠀⠈⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⠀⠀⢰⠈⠀⡘⠂⠀⠀⠀⢀⣀⠀⠐⠀⠀⠀⠄⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⢿⣿⠐⣿⡷⠀⠀⠀⠀⠓⠀⢀
⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⠀⡀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡹⠘⣿⡟⣾⣯⣸⠀⢹⣹⣼⢉⣿⢸⢰⣿⣿⡇⠀⠀⣀⠰⡀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠋⠛⠘⠁⠉⠙⠘⠁⠈⠁⢉⠋⠈⢈⠈⠉⠉⠁⠀⠀⠡⡂⠁⠀⠀⠩
⠀⠀⡤⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠆⠐⠡
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠐⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣼⣧⠀⢀⣶⡆⠀⠀⣄⠀⠁⠀⠀⠀⢀⣶⡗⠛⣦⡀⠀⠀⠀⢀⡄
⠀⠀⠀⢹⠐⢆⠀⠀⠺⢱⣿⣿⡄⠈⠛⠁⠀⡖⠛⠀⠀⠀⠀⠀⢸⡟⠀⢰⣿⠇⢠⠖⠊⠛⡙⠀⠀⣀⡀
⠀⠀⡠⠄⠧⢘⡂⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠙⠒⠛⠋⠀⠀⠁⠒⠊⠀⠀⢡⣦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⣀⡄⠀⢸⡶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠖⠀⣤⣀⡀⠠⡇
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠆⠀⢻⡇⠀⠀⠻⠁⠀⠀⠀⠂⣦⠀⠀⠹⠆⠐⠀⠀⠀⣓⡪⢭⣓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



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

⠀⠀⠀⠀⢀⡔⣰⡖⢶⡄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀
⠀⠀⠀⢠⡟⢰⣿⡇⢸⣿⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠸⡇⢸⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢢⠀⠀⠀⠀⣤⢾⡼⢦⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠘⠿⣷⣶⣤⣄⣀⣠⣤⠤⣤⣤⣄
⠀⠀⠀⠀⠻⡈⣿⡇⣸⡿⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⠟⢻⡇⠀⣿⣶⣶⣾⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣏⣹⣧⣬⣿⣤⣿⡿⠟
⠀⠀⠀⠀⠀⠈⣎⣓⣛⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⣿⣄⣼⣿⣿⡇⠀⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⢻⣿⡿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣸⣀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣿⠿⣤⣿⡇⠀⣿⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣾⣿⠇⠀⠙⠿⠻⠟
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⠟⣿⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⢠⣄⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠿⠿⢿⡦⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄
⠀⠀⠀⠀⣿⣿⠂⠙⠉⠀⣠⣤⣤⣤⣶⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⢤⣤⣀⣤⡤⠀⢠⣿⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⡿⠿⠛⢻⣿⣧⠀⠀⠀⠀⠰⣿⡿⢿⡛⠆⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠘⠋⠀⠀⣰⡿⣽⣿⣿⣿⣇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠉⠀⠈⣧⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣿⣯⣭⣭⣴⣶⣶⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠰⢿⠇⣿⣿⣿⣿⣿⣶⣶⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣼⣛⣛⣋⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣒⣒⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⢟⣭⣽⡻⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠆⣉⢐⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢺⣿⣿⢇⣿⠀⠀⢸⠋⠉⠛⡗⠀⠀⠀⠂⠭⠀⠀⠀⡝⠀⠈
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⢀⣆⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣮⣵⣾⣿⠀⠀⣿⣀⠀⢀⡇⠀⠀⠀⠀⠀⣀⣀⣀⣧⣀⡀
⠀⠀⠀⠀⠀⢠⣿⠛⡛⠻⣿⣿⣆⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣉⠉⠙⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣇⠀⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⣿
⠀⠀⠀⠀⠾⠿⠿⠷⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⢶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⠀⠀⣸⣿⠀⠀⡀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢿⣤⡄⣿⣿⠀⢰⣇⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢳⣔⣦⣿⣿⣦⣼⣿⣿⣿⣿⣦⣿⣿⣧⣿⡿⠁⢀⡄⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣻⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣇⣴⢟⡆⢀⣤⣶⡿⠟⠁
⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠐⢦⣔⡶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣤⣀⡈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⣤⡶⠚⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣀⣤⣤⣤⣶⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⡶⠦
⠀⠠⠴⠶⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣽⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⢿⣿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⢶⣤⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⣨⡿⠛⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣯⡉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠮⠻⢦⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢻⡟⠀⣿⣿⢿⣿⡟⠻⣿⣿⢿⣻⣆⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠚⠀⢠⣿⡟⠈⢻⡇⠀⢻⣿⠀⠁⠹⠄⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⢊⣠⡀⡄⠀⢀⡀⠤⠒⠀⡀⢀⣀
⠀⠀⠀⠻⣿⣷⣤⣀⣴⣿⣽⣿⣟⡴⠋⡼⣻⣡⠜⢁⡴⠁⣴⣱⣄⢪⠁⢬⡂
⠀⠀⣤⡾⣻⣿⣿⣿⣿⣷⣾⣿⠋⢀⣼⡽⠠⢃⣴⡿⠁⣞⢹⡿⢮⠂⢹⡄⠱⡄⡠⣄
⠀⠀⠀⣰⡟⠃⢿⡏⢻⢫⣼⡇⡞⢸⠷⢱⠔⢳⣽⢃⣞⡌⠁⣷⠆⠀⠀⠹⣌⠥⠈⠙⠷⡄
⠀⢀⣀⠛⠀⠀⣾⠁⢸⣛⠙⠋⠀⠈⠀⠀⠀⠀⡟⣸⡌⠀⠀⡟⢀⠀⠀⠀⡬⣉⡆
⠀⢂⢻⠿⠦⢬⢩⠀⢸⡙⠀⠠⢼⢤⣀⡀⠀⠀⣾⠡⡄⠀⢰⡟⠙⠀⠀⠀⠀⣄⠃
⠀⠢⠀⣀⣀⠢⡞⢄⢼⣟⡂⠀⡬⠆⠈⠛⠂⠀⢹⠄⡗⠀⣼⡏⠀⠀⠀⣀⣀⣀
⠀⠀⠲⠰⠌⣀⣀⣈⣀⡟⣧⠀⣩⠵⠴⠒⠐⣶⣦⣄⡈⠓⣾⡇⢨⠟⣛⡛⠛⠛⠋⠉⠁⠂
⠀⠀⢀⠈⠓⣑⠉⠈⠈⠋⠀⢰⠁⠛⠻⠿⠣⡉⠉⠛⠃⠀⣿⣤⠄⠀⠀⢀⢠⠀⠀⠀⠀⠐
⠀⠀⠀⠗⠓⠉⠁⠀⠀⠀⠀⢸⣠⣴⣞⣿⡗⠁⠠⣶⠆⢰⣟⣒⠂⠀⠄⠳⠈⠂⠀⣤⠤⡄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣿⣿⢿⡀⠀⠀⠀⠐⠀⡼⠀⣴⠀⣄⣰⢀⣴⡆⢀⡀
⠀⠀⠀⠀⡄⣹⣶⠞⠁⠀⠀⢀⣀⣬⣷⠈⠀⠀⠈⢛⠀⠁⠠⡖⡤⠀⠙⠋⠋⡐⠊⠤⡤⡀⡀
⠀⠀⠀⠰⠀⣿⣿⠀⢰⡀⠀⢈⡟⡷⡇⠀⠀⡮⣑⠋⠀⠀⠄⢀⡥⠁⡂⠀⠂⠀⠀⠀⠢⡀⠈⠁⠠⢀⣀
⠀⠀⠀⠰⠚⠿⣿⠣⠀⣇⣐⡞⠀⣀⡸⠛⢢⡀⠠⣙⡓⢶⡀⠀⣙⠋⠁⠀⠐⡆⠀⠀⠀⠈⠢⣀⣤⣾⣃
⠀⠘⠁⠙⠦⣻⢿⣤⣃⡟⠘⣤⣄⣉⡇⠀⠉⠈⠳⠇⠈⢠⡹⣄⠈⠻⣌⠀⠒⠁⠀⠀⠀⠀⠀⣚⣉⣈⣩⡀
⠀⠀⠇⠀⢁⠈⠳⣌⡙⣟⠛⠃⢫⣤⣄⡀⠀⠀⠀⠀⠀⠀⣇⠈⣷⠄⠈⠀⠀⠀⠀⠀⠀⠀⡠⠿⡇⣿⣿⡏
⠀⠀⠸⣠⠾⣄⠀⢸⣿⡟⠁⠀⠀⠁⠀⠉⢢⣀⣠⣀⡀⠀⠹⡼⠁⠉⠉⠀⠀⠒⠒⠒⠒⠈⢠⣿⠧⠈⠉⠙⠦
⠀⠀⠀⠑⢄⠀⠑⢌⣿⣧⠀⠀⠀⠀⡀⢠⡿⣏⣽⣻⣿⡄⠀⠈⣢⢀⣀⣀⡀⠠⠔⠒⠒⡠⠖⠁
⠀⠀⠀⠀⠀⠑⢄⠀⠙⢿⣧⠀⠀⠀⢹⠸⣿⣿⣿⡿⠿⣀⢤⣺⡝⠣⠄⡀⠀⠀⠀⠤⠊⠀⠀⠀⠀⢀⡴⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠙⢷⣄⠀⠀⢳⡚⠉⠁⠀⠀⠈⢢⣁⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢀⣴⡿⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠉⠃⠀⠀⠑⣄⠀⠀⠀⠀⣜⣽⣿⣻⡟⣯⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣀⡤
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡆
⠀⠀⠀⠀⠀⣠⣤⣤⠀⠠⠀⠤⠂⠐⠤⠿⠿⠄⠤⠤⠤⠤⠤⠤⠄⠼⠿⠇⣄⠀⣤⠠⠄⠄⢤⣤⣤⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⡄⠒⢠⠑⠀⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠘⠉⢿⣏⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠉⢂⠀⠀⠀⠀⠣⢀⠼⢀⠀⣿⣉⣿⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡸⠀⠀⠀⠈⠂⠀⠐⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⠀⠈⠁⠈⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣸⠀⠀⠰⠈⣉⣀⣉⠀⠀⡅⠀⢨⠀⠀⢀⡁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢶⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⠤⠀⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢶⠧⣼⡤⣷⠞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠁⠀⣿⡿⢋⢞⣼⣷⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢾⠤⢾⠦⢼⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠃⠁⠀⠀⠛⡁⠁⠙⢙⠉⠂⠀⢈⣀⡀⣀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠾⣖⠃⠀⠻⢦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡡⢐⣂⣐⡀⠌⠐⢄⠘⠓⠚⠛⠀⠀⠀⠀⢰⠀⠀⢰⠆⠀⠀⠈⠳⠿⣤⢤⡬⠏⠀⠀⠀⡇
⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠐⠠⢢⡞⠉⢉⣩⣿⣶⡀⠄⢂⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠷⠀⢰⠶⢶⠶⠞⠁⢾⣶⣶⣶⣶⠀⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⣴⣉⠹⣿⣿⣿⠰⠈⠀⠀⠀⠀⢀⡀⠀⢐⠀⠈⣻⠇⠔⠒⠋⣀⠖⠷⠲⠶⠶⠶⠂⠀⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⢀⢻⣿⣿⣿⣿⣿⣿⡟⡈⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⢄⠀⢝⠻⠿⠿⠟⠩⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠁⠀⢄⣁⣈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡠⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠂
⠀⡤⢊⠄⠀⠀⠀⡀⠠⠀⠀⠀⡡
⠀⠄⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⡆⠄
⠀⠠⠀⠀⠀⠀⠀⠈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⡇⡄⠀⢀⣶⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣷⠁⠀⠀⢿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡾⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠃⠢⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣄⡀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠞⠉⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⠀⠀⠀⠀⠀⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⣷
⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⢿⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢿⠲⢤⣀⣀⣀⣀⣀⣤⡶⠀⠀⢀⡇⠀⠀⠀⠀⠐⠛⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⠤⣀⣉⣉⣩⠵⠋⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠈⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⢀⠭⠤⠤⡄⠒⠒⠂⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠃⠠⠀⠂⠒⠺⠈⠈⡀⠥⠤⠤⠄⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠒⢲⠀⠀⠀⣀⠀⠀⢘⣉⣙⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠂⠒⠂⠀⠈⠉⠉⠉⠉⠭⢭⣤⡤⢀⠀⣀⠠⠬⣉⣁⡒⠤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠊⠁⢲⢡⠨⠭⠋⠑⠒⠄⠀⠏⠠⢊⠄⠀⠠⣔⠅⠂⠐⡔⠆⢠⡔⠒⠤⠄⠈⠑⡌⢢
⠀⠀⠀⠀⠀⠈⠉⠆⣗⠀⠔⠁⢉⢰⠖⡜⠀⡄⡡⠔⠀⠒⠼⠤⠶⢦⡧⠼⠀⣃⠄⠂⠁⠐⠈⠘⡀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣼⣅⠹⡁⡠⡇⠠⡌⠀⠐⠆⢚⠔⠀⠀⢀⡗⢚⡄⠁⠀⠋⠰⣢⠊⠄⣦⠴⢤⡄
⠀⠀⠀⠀⠀⢀⠸⠀⠒⠸⠡⠤⠤⢎⣌⡇⠀⡏⣲⠊⠀⠈⠐⠦⠀⠀⠈⡄⡇⣈⣀⣔⡊⢐⡖⢒⣩⠐⠀⠓⠒⠀⠈⠁⢢
⠀⠀⡀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠛⡔⠀⠄⠐⠒⠈⠉⠨⢅⠈⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠸⠉⡩⡉⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠑⠒⠊⠀⢠⠀⠀⠀⠀⠀⢀⠠⢖⣒⠠⢄⠀⠀⠀⠀⡇
⠀⠀⢣⣊⣱⠰⠀⠀⠀⠐⡪⠑⣼⠀⠀⠀⠀⠀⡠⣶⠶⠓⠚⠶⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠊⠉⠀⠉⠲⡐⣄⠤⠠⠄⡀
⠀⠀⠈⡀⠁⠐⠀⠀⠀⠀⠁⠝⢸⠀⠀⠀⠀⢎⡞⠁⠀⢀⣀⠀⠀⠱⣵⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠊⠙⡆⠀⢡⡇⠀⠀⠀⠄
⠀⠀⠰⠉⠉⠁⠒⠀⠤⠄⠀⣀⠀⠧⠄⠀⢸⣸⠀⠀⠎⠀⠀⠃⠀⠀⡇⣃⣀⣀⣄⣀⠀⠤⣿⠀⠘⠦⠴⠃⠀⡼⠳⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠐⠒⠈⠀⠀⣰⡟⠀⠀⣀⣀⣀⠀⠠⠴⠓⢄⣀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠒⠃⠠⠤⠄⠒⠈⠁⠑⠤⣄⣀⣀⡠⠔⠁⠉

⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠂⠀⠀⠈⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠉⠀⠀⡇⠙⠀⠀⠀⠀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠁⠭⠀⠀⠀⠀⠀⠀⠀⠠⠘⠄
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⡜⢹
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡘⠀⠸
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠁⢠⠃⠀⡏⠀⠠⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠚⠀⠠⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡤⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠉⠉⠁⠈⠹⣁⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠒⢠⣧⠔⠀⠀⠀⠀⠁⢀⠓⠀⠀⠀⣁⠀⠀⠖⠦⠏⠁⠈⠉⠀⠀⠀⠀⠀⠀⢀⡉⠁
⠀⠀⠀⠐⠁⠔⠀⠈⠛⠀⠒⠠⠀⠀⠔⠁⠀⠀⠀⠀⢨⠂⠀⡄⠤⡤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡀
⠀⣀⡠⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⠀⠀⠀⠀⠅⡂⠀⠀⠀⠀⠐⠍⠩⠑⢄⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠈⠁⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠃⠉⠀⠌⠀⠀⠀⢠⠀⠀⡇⠀⢌⠆
⠀⠀⠲⠬⠃⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠞
⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⢺⢂⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠈⠉⣽⡀⠀⠀⠀⡌⠀⡇⠀⡀⠀⠀⡀⠀⠀⠙⡛⠓⠛⠦⢀⣀⢀⠀⡄
⠀⠀⠀⠨⠇⠀⠀⠀⠀⠇⠀⠀⠘⠀⢧⡀⢀⠋⠁⠀⠀⡐⠀⠠⣡⠀⠿⣀⠈⣡⢈⡇⢰⡃⢀⡄⣴⣀⠝⡿⢠⣁
⠀⠀⠀⠀⠐⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠂⠀⠙⠂⠀⠉⠉⠉⠉⠁⠈⠉⠀⠁⠈⠁⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠊⠉⠀⠀⠡⡀⠈⠀⠲⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡀⠀⢀⠀⠀⠄⠀⠂⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⠠⠄⠒⠈⠠⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣀⠠⠀⠘⠀⠀⠀⠀⢸⣇⢀⠀⠤⠃
⠀⠀⠀⠀⠀⢀⣐⡁⠀⠀⠀⠀⠀⣀⡀⠀⠉⠢⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⣄⣀⣀⡀⠀⠀⠀⢸⣿⣿⣦⣀⠐⠦⠀⠁⢀⠑⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣶⣤⣿⡟⠛⠛⠛⠆⠀⠂⡐⠷⢦⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠈⢂⠀⠀⠀⢠⣿⣿⣿⣿⠟⠋⠁⠀⠈⠙⣷⣦⡀⠀⠀⢑⠠⣤⠉⠀⠉⡠⣦⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠈⠀⠘⢦⢀⡀⠠⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢘⢃⠀⡴⠉⠀⢠⡀⠠
⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠀⢏⠀⢳⠌⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠂⠈⢁⠀⠀⣤⣀⠉
⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠲⣶⣦⣤⣀⠈⠉⠓⠒⠲⠖⠒⠛⠒⠵⠖⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠋⠀⠄⠚⠤⠀⠃⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠉⠙⠛⠛⠓⠶⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠠⢂⣠⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉



⡿⠿⠿⠿⡿⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⢀⣴⡆⣀⡐⣞⣇⣀⡀⣠⣤⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢆
⠄⠀⠉⠉⠤⠋⠖⠘⠚⠙⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⣀⡀⡀⣄⠉⠠⠠⠀⢀⣀⣤⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠠⠤⠀⢀⠀⠀⣈⠉⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣀⡀⠀⠀⢀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡑⠀⠀⠀⠁⠀⠀⠈⠈⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢹⡐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡪⡟⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄
⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠄⠤⠂⠂⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠀⢀⣀⡀⠀⠈⠛
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠉⠁⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠁⠀⠀⢠⡎⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣤⠀⠀⠀⢠⠀⢶⠴⣶⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⠂⠀⠀⡇⠠⢤⣄⣀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠦⠴⠶⠾⠶⠦⠀⠚⠓⠚⠛⠛⠋⠉⠁⠀⠀⠧⠤⣄⣀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣔⣒⣓⡖⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣉⢀⠉⠁⠐⠒⠀⠀⠀⠠⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠐⠂⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠿⡇⢰⠀⠈⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠂⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠓⠖⠉⠑⠋⠉⣁⡄⠀⠀⠀⠀⠀⠀⠔⠀⠘⠢
⠀⠀⠀⠀⠀⣀⠀⠀⠤⢀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⠉⢢⠂⠃⠀⠀⠠⠀⡀⠘⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠨⣄⠀⠀⡰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠨⠠⢀⡀⢀
⠀⠀⠀⠀⠀⠀⡀⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠀⠈⠋⠉⢃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⢀⡀⢁⡃
⠀⠘⠀⠓⠈⠢⡀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠐⠀⠠
⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢄⠀⠁⠦⠄⠂
⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⢀⡀⠀⢀⠄⠀⠀⠰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐⠀⣀⠀⠄⠐⠀⠀⠀⠨⠀⠀⠈⠀⠀⠠⡂⠀⠀⠀⢳⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠃⠀⠄⠀⣸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠦⠐⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠀⠀⠀⠀⠀⠀⠈⡰⠄⠠⠀⠀⠀⠀⠰⡀⣠⢃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠉⠀⠀⠀⠖⠀⡌
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⢀⠀⢀⠀⠀⠀⠀⣠⠔⡡⠀⠀⠀⠀⠀⠀⠔⡀⠍⠒⠀⠁⠢⠁⠀⠀⠀⢀⡀⠠⢀
⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠊⠍⠛⠓⠒⢚⠉⠕⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠒⠁⠁⠀⠀⠡⣀⠀⢁
⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠑⠂⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊
⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⣠⠀⠀⠀⠠⡀⠑⠀⠀⠀⠀⢀⡀⢀⡐⠂⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠜⠈⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢀⡈⠃⠚⠄⡸⢧⠀⠀⠈⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠰⣁⠆⠀⡠⠉⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠂⠀⠀⠀⢲⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠂⠰⢦⡄⡀⠙⠀⠶⠥⠟⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠂⠀⠀⠙⠻⠷⣤⣀⠀⠀⠀⡐⠀⠐⠡⠀⠀⠀⠀⠀⠀⠀⡂⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠀⠔⠀⠀⡀⠀⠂⠀⠘⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆
⠀⠀⠀⢀⡀⠀⠀⠈⠐⠀⠄⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠱⠊⠠⠈⠤⠂⡀⢀⠠⠀⣠⠀⡀⠀⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠒⠈⠆⠀⠁⠀⠐⢈⠀⢰⣆⡀⢀⢀⠀⠀⠈⠉⠀⠒⠐⢨⠡⠀⠃⠈⢂⠀⠈⠁
⠀⠀⠀⠁⢂⡐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢉⢢⠀⠀⠀⠀⠀⠂⠀⠠⠑⠀⠀⠀⠀⠐⠄⡀⠈⠉⠁⠛⠛⠒⠗⠶⢲⣦⡆⠀⢌⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠇⢁⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠊⠡⠙⠤⠒⡐⢆⠠⠀⢤⠄⡀⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠐⠂

⠀⠀⠀⠀⠀⠠⡄⠀⢀⣼⡀⢀⣀
⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿⣷⣼⣿⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠠⣷⣾⣇⣾⣿⣿⣿⣿⣿⣿⣿⢷⣽⣝⣶⣤⣀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⠙⢿⣿⣿⣦⣿⣲⡤⣀
⠀⠀⢠⣾⣿⣿⣿⣿⣹⣿⢻⣿⣿⣷⣿⠸⡿⣷⣤⡙⡟⠿⣿⣿⣿⣦⠙⣦⣀⠀⠀⢠⡤⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠦⢤⠤⠤⠴⠖⠒⠛
⠀⡴⢫⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⠸⣧⣿⠛⣿⠻⣮⡀⠈⢿⣿⣿⣧⠘⢿⣷⣄⠀⠀⠀⠒⠚⠉⠉⠀⠀⠀⢀⣀⠀⠀⠒
⠊⢠⢟⣿⡟⢸⢻⡿⡇⠀⣿⣿⣿⣿⡆⠹⣿⣤⠹⣷⣮⡻⣆⠀⢻⣻⣿⣇⠈⢿⣿⣷⣄⠀⠀⠀⠀⢠
⠀⢋⣾⡿⠁⡟⢸⠃⠀⠀⠿⢹⣿⣿⣇⠀⢻⣿⡆⡏⠻⣟⠦⡑⠲⣿⠛⠹⠲⣾⢿⣿⣿⣷⡄⠀⠐⠂
⠀⢸⡿⠁⢠⠃⡿⠀⠀⠀⠀⠸⢹⣿⣿⠀⡈⣿⡟⣿⣷⡘⣷⣌⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣿⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠂
⢀⡞⠀⠀⠀⠀⠁⠀⠀⠐⠂⣤⢼⣿⣿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣉⡁⠈⢿⣆⠀⠀⠀⢤⣤⡀
⠈⠀⠀⠀⠀⠀⠀⣠⣶⠾⢟⣠⡯⣿⣿⠃⠀⠈⣿⡟⣿⣿⣯⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠃⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠰⠒⠯⠉⣠⣄⣬⣬⣄⣇⣬⣤⡴⢤⣦⣷⣷⣿⣿⣷⣿⣿⣿⣶⣤⣶⣶⣶⣶⣦⣠⣼⣧⣤⣦⣜⣦⣄⢐⣤⣠⣤⣀⣀⣀⡀
⠀⠀⠀⠒⠟⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠓
⠀⠀⠀⠀⠰⠶⠟⠛⠉⢹⡏⠙⠿⠻⣿⢿⡿⠿⡿⠛⣿⠛⠛⢿⠏⢹⣿⠋⠉⠉⠛⢻⣿⣏⠻⣿⠻⠿⠟⠙⢹⣟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠸⡇⠀⠀⠀⡇⠀⠀⠘⣿⢸⣿⠀⠀⠀⠀⢈⣿⠉⠀⠀⠀⠀⠀⠀⢸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⢠⣶⣶⠘⣿⠀⠀⠀⠀⢀⡇⠀⢰⣶⡶⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠀⡇⠀⠀⢠⡄⠀⣈⣿⠉⠀⣿⠀⠀⠀⠀⢸⡇⠀⠘⠯⡉⠂⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠰⠂⢸⡇⠀⠀⠴⠃⠰⡇⠀⠀⣸⡷⢻⡿⢾⠓⡂⣿⠀⠀⠀⠀⣠⡇⠀⢠⣿⣥⣶⡆⠀⢸⠇⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⢰⣿⣿⣟⠺⡛⠒⣞⣻⣿⣿⡶⠖⡲⢻⡓⢂⣼⠟⣿⣿⣷⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡇⠀⠀⠀⠀⠺⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣛⠁⡰⢋⣹⣿⣿⣧⣀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠁⠉⡍⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⣿⠿⠿⣿⣿⣿⡏⣼⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠉⠁⠚⠛⠃
⠀⠀⠀⠀⠀⠀⢠⣄⢳⢸⣿⡆⣷⣵⡄⢨⡇⠀⣸⡟⣿⣿⡇⠀⣿⣿⣿⣾⠿⢿⡟⣻⣿⣶⡿⠟⢿⣿⣿⠏⢸⡄
⠀⠀⠀⠤⢶⣶⣜⠿⣗⠈⢩⠅⠻⠛⠛⢺⣷⣶⣹⣶⣿⣿⣷⣴⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣶⣶⣦⣼⣿⡆⢼⣧⣤⣀⡀⠁
⠀⠀⠀⠀⠙⠛⠛⢂⣼⣶⣤⡖⣽⣉⡈⠙⠷⢶⣾⠿⢿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⣩⠉⣙⠀⠛⠛⠛⠛⠋⠉⠀⠃
⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣇⣙⡻⠻⣿⣿⣧⠙⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠘⢹⣿⣿⡷⠀⠡⠿⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠉⠑⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠐⠹⣀⡀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⢂⡀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣖⠁⠐⠀⠈⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠳⣄⣀⠠⠂⡄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⢻⡱⠮⣿⢻⢄⠀⢀⠌⣉⠿⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠘⠒⠒⠊⢸⡞⠛⣡⣎⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠳⠀⠀⠀⠀⠈⣋⠉⣁⣀⣁⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⠀⠀⠀⠀⠀⡠⠤⠐⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣾⠀⠀⠀⠀⠀⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠀⠀⠀⠀⠀⡗⠠⣄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡴⠚⡛⠓⠧⡌⡄⠀⠀⠀⣀⣀⡃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠇⠀⠈⢓⠀⠀⡆
⠀⠀⠀⠀⢸⠁⡀⠀⠀⠀⠘⢢⠀⡠⠊⠀⠀⠀⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠙⡏⢣⠈⠳⣀⠤⠼⠦⠮⣄
⠀⠀⠀⠀⠘⣎⠀⠘⠄⠀⢀⣺⣸⠀⠀⠀⠀⡸⠁⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡔⠁⠀⣷⣠⠁⠀⠀⢀⣀⣈⣆⣀⡀
⠀⠀⠀⠀⠀⠈⡱⠦⠒⠒⠻⣴⠉⡄⠀⠀⢖⡃⠀⠀⢰⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⡀⠀⣉⠆⣠⡛⠶⢤⡴⡐⠉⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡷⠜⡱⢲⣤⣧⣤⣖⠋⢰⠃⠀⠀⣩⣽⣲⠆⠀⠀⠀⢰⠒⠉⠙⡌⢠⠖⠒⠼⢎⠀⠉⡲⠊⠠⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡠⠖⠒⠋⠉⠳⡒⠚⢤⠖⡡⠋⠀⠀⠀⠀⠙⠻⡇⠰⢀⡿⣡⠞⠀⠀⠀⠀⡼⣤⠀⠀⡸⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⢧⠀⠀⡷⠗⠒⠒⠒⠒⢤⣀⢀⡽⠿⠋⣰⠃⠀⠀⠀⠀⠀⢧⠙⢦⡔⡧⢄⡰⢀⣀⣀⣀⣇⣀⣀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⠄⠀⡇⠀⠀⠀⠀⠀⠸⡎⢻⡐⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣀⠜⢱⠉⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢷⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠇⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⣨⠞⠛⢵⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣛⡓⣨⠐⠿⣾⠦⡀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⢃⡘⠟⠀⢩⣦⡀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⣿⣿⣿⣿⣷⣄⣼⣿⣶⡀⠀⠉⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⢀⣀⡀⡘⣿⣿⣿⡿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢀⣤⣾⣿⣿⠦⡀
⠀⠀⠀⠀⠀⢠⣖⣟⣟⣗⣦⠀⢸⠀⠀⠀⠙⢢⣴⣶⣦⣄⠀⢠⡞⠁⠆⠀⠈⠛⠉⡟⠀⠉⠦⡀
⠀⠀⠀⠀⠀⡧⢼⠤⡧⢸⠤⡇⢸⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠳⡼⡄⡧⡼⡤⠃⢸⠇⣠⡀⠀⠀⠈⢻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣬⣭⣭⣭⣀⣄⢸⣍⠀⠀⠀⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢸⣿⡄⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠞⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⠈⠀⠈⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠴
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠛⠛⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀
⠀⠠⠾⠿⡤⢬⡤⠷⠺⡦⠶⣠⢾⡝⠿⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠉⠉⠃⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠂⠀⠀⠀⠐⠚⠡⠋⠈⠉⠁⠁⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠁⠐⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠤⠄⢄⣀⣀⣀⠤⠄⠤⠀⠄⠀⣠⣄⣤⢤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⠤⠄⢀⠀⠀⢀⠘⠉⠩⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢽⣯⡳⠄⠀⠀⠀⠒⠒⠠⠁⠀⠓⠃⠀⠈
⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢭⣛⠷⡆⠁⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣆⠀⠀⠀⠀⠀⠈⣃⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣂⡍⡰⠀⠀⠀⠀⠀⠀⠀⠁⢬⣄⠀⠀⠘
⠀⠢⠄⠐⠠⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠀⠈⠀⠀⢀⡤⠄⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠉⠀⠀⠀⠀⠤⠤⠄⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢆⠀⣀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠒⠒⠀⠉⢠⡔⠒⣦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠋⡇⠂⠀⠀⠀⠀⠀⢠⣌⣤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠠⡄⢀⣀⢀⣤⣀⠀⣀⣒⣿⣿⠀⠀⠀⢸⠈⠛⠛⠒⠶⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠈⠋⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠘⠒⠶⠦⢤⣄⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠈
⠀⠀⠀⢀⠀⠄⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣀⠀⠴⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠒⠦⠤⢄⣀⡀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠐⠒⠂⠀⠬⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⡀⡈⠀⠀⠈⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡆⣾⣿⣴⣿⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⣿⣦⣿⣷⢸⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡹⠟⣼⣫⠟⠁⠀⠀⠈⠻⣿⣯⣽⣿⠟⠀⠀⠀⠈⢿⣝⣧⠻⢏⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢀⣠⣤⣤⣤⣭⣭⣤⣤⣤⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣾⣿⣿⠗⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠸⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣌⣛⠿⢿⣿⣿⡿⠿⣛⣡⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣚⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠒⠉⠙⠛⠿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣤⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⣴⣦⢀⡀⠀⠀⠀⠀⠀⢨⢟⠙⡏⢾⡼⣷⢀⠀⠀⠀⣤⢠⢶⣴⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣛⣿⣟⣷⣾⡇⠀⠀⠀⠀⠀⠀⠉⠀⠠⠄⣱⣯⡞⣦⠀⡠⠙⣿⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⣟⢛⣻⣿⣿⠗⠀⠀⠀⠀⠀⢉⣂⠀⣲⣾⣿⣟⡴⣻⣇⣘⠁⣿⣷⣾⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠟⡈⡉⠉⠛⠃⠁⠙⡀⠀⠀⠀⠙⢉⣉⠙⠛⠋⠁⣉⠉⠁⠘⡛⠛⠿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠉⠈⠁⠀⠀⠈⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡠⠤⠄⠀⠒⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠊⠀⠀⠀⠒⠁⠀⠁⠒⠂⢈⡿⢻⣟⣤⣤
⠀⠀⠀⠀⠠⣶⣿⣿⣷⣦⣘⣀⡀⠀⡞⠁⠀⠀⠀⠀⠀⡖⠀⠀⡞⠙⠢⢀⠄⠀⠀⢰⠊⠉⠁⠀⠀⠀⢀⣿⣥⣿⣯⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠘⠿⣻⣿⣯⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡃⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠋⣠⣤⣿⣽⣿⣿⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠵⣿⢫⣿⣿⠇⢠⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⠠⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⣤⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡃⠘⠆⠸⠀⠀⠀⠀⠀⠀⠣⠀⠂⠀⠠⡤⠃⠈⠀⠀⠠⡤⠃⠀⡀⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣶⣶⣶⢾⣷⣄⠐⠂⠀⠠⠀⢀⡀⢤⣤⣶⣤⣤⣤⠤⣤⣀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠂⠄⠀⠀⠀⢸⣟⣿⣿⣦⡇⠟⠃⠀⠀⠀⢀⠀⠉⠀⢈⣿⡏⢻⣿⣿⣿⡿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⡇⢧⣾⡻⣼⡿⢿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠲⣵⣈⣁⡁⣈⣧⣄⠀⠀⠀⡀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢊⣿⠁⠀⠀⠀⠀⡟⣿⣦⢷⡊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⣿⡶⠒⠚⠋⠋⢰⠄⠼⣷⡈⣀⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡟⠀⠀⠀⢠⢰⢰⠀⠀⢿⣷⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⡇⢠⣿⠀⠀⣀⣀⡤⠼⡼⢤⡀⡄⣹⣄⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠘⡘⣄⣠⡷⣾⠗⢚⣹⣬⠅⠠⠄⠚⢺⡅⠀⠘⢿⡄⠈⡱⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢧⠐⣼⠅⣶⠟⠉⠀⢸⣇⣀⣀⠬⠬⣦⣧⣤⣀⢘⣧⢀⡧⠤⠒⠒⠒⠒⠚⣿⡡⢚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠳⣼⣠⣷⡰⠊⠉⢀⡏⠘⠀⠀⠊⠀⡀⠉⠉⠉⢿⡏⠁⢒⠀⣀⣀⡠⠒⠒⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣫⢩⣽⠛⣷⣤⠤⢸⠀⡆⠀⢸⠀⠀⡇⠀⠄⠀⠈⣶⠘⠌⢀⠇⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⣾⡏⣸⣼⠥⠖⢺⠀⡇⠀⢸⠀⠀⣿⠀⠀⣒⣲⣿⡀⠀⢸⠓⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⢻⡿⠋⢻⠀⠀⠀⠸⠀⣃⣀⣼⡠⠤⠿⠓⠒⠂⠀⢺⣷⠒⠚⠒⠰⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⢿⠁⠀⢸⣲⡄⠤⠚⠋⠉⠁⠋⣀⠤⢤⣤⢖⡒⠒⠚⣿⠒⠒⠒⠠⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣿⡧⠔⠒⠉⣀⣤⡤⠶⠶⡆⠀⠀⢱⣈⡍⠀⠀⠐⠢⡀⣿⡏⣉⠉⠒⢷⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡘⣻⣽⣶⠖⡆⢮⢠⣟⡶⠚⡛⣷⠀⠀⠈⡇⠀⠀⡀⠀⣠⠗⢳⣿⠈⠓⠒⡈⣧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡱⡿⠿⡟⠚⢻⢸⠐⡜⠁⠈⠀⡷⡇⠀⠀⢿⠒⠒⠚⣫⣉⣀⣻⣿⣐⣀⣐⢀⡛⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡠⠰⠀⡇⣀⣓⣀⡼⠘⠦⠶⠒⠒⠒⠋⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠾⠳⠓⠊⠉⠉⠀⠀⣀⡀⠀⠀⠀⢠⠖⡋⢲⣒⣒⡒⢐⡀⠁⣀⣀⣀⣻⣹⣖⣖⣒⣒⣒⡀⠀⠰⣷⠐⠄
⠀⠀⠀⠀⠀⡠⢚⣁⣤⣤⡶⠶⠖⠒⠉⠁⠀⠀⠀⠈⠉⢠⠾⠏⠁⠉⠳⣄⠂⠉⠀⢀⠠⠐⡀⠨⠿⠧⣤⠤⠀⠀⠠⠄⠉⢿⠋⢂
⠀⠀⠀⢀⣼⡟⠛⠉⠉⠉⠑⠢⣤⠤⠄⠀⡀⢀⠀⠀⢴⠏⠀⠀⠀⠀⠀⠘⡆⠀⢌⡀⠀⠒⠭⠾⠶⠁⠉⠀⠐⠚⢛⠈⠉⢹⠀⠘
⠀⠀⢠⣿⠋⠁⠀⡀⣀⠀⠀⠀⠘⣦⠉⠀⠤⠤⠀⢒⡟⠀⢀⣄⠀⠀⠀⠀⢹⣀⠀⠀⢁⡐⠒⠒⠂⠀⠀⠤⠤⠤⣤⡄⠀⢸⠀⢀⡇
⠀⡠⢠⡟⠀⢠⡾⢀⡄⢳⡀⠀⠀⠘⣄⣀⠀⠀⠠⣼⠃⢀⡟⢸⡇⠀⠀⢀⡸⠇⠬⠭⡏⢰⠶⠶⠒⠒⠲⠒⠶⠲⡇⢰⠤⠼⣄⢸
⠀⠇⢀⣇⠀⣾⠣⡇⢹⠀⣧⣀⣀⣀⡿⠀⠀⠠⠤⠾⠤⠸⡇⡏⢸⡄⢀⣫⣄⣀⣀⣀⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⡇⣬⣀⡀⠀⠃
⠀⠀⠀⠀⠀⠸⠀⠳⡟⢀⡅⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡾⠀⡘⠀⠀⡼⠀⠀⠈⠙⠋⠁⠀⢸⠀⠀⠀⡎⠈⠀⣰⠁
⠀⠀⠀⠀⣀⣀⣧⠀⢀⣜⣀⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣄⣀⣰⢁⣀⣰⣧⣤⣤⣤⣤⣤⣤⣤⣬⣄⣀⡼⢁⣀⣰⣃⡀
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠰⡀⠀⠀⠁⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄⣠⣶⣶⣷⣶⣶⣦⡀⠀⠀⠙⠒⠀⠂⠁⠤⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⡿⠃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠋⠀⠀⢿⠆⣤⢸⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣰⣿⣤⡄⠀⠀⠀⠀⠘⣿⣿⣷⣶⡀
⢠⡶⠂⠀⠀⠀⠀⠀⠻⠃⡠⠀⢀⢀⣤⣤⣀⠀⢠⣿⣿⣵⣶⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣣⠀⠀⠀⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉⢰⣶⣶⣴⣶⣤⠀⣉⠋⠀⠀⠀⠀⠀⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢿⣿⣿⣿⡦⡤⢤⣀⡀⠀⠀⠀⢀⣸⣿⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠒⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣸⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠒⠀⢀⠒⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠢⠈⠀⡀⠀⠀⠀⠀⢈⠀⠀⢁⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠑⠂⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠈⠀⠀⠁⠄⠄⢀⠀⠄⠀⠀⠀⢁
⠀⠀⠀⠀⢀⠀⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠈⠖⠀⠀⠁⠀⢀⠂
⠀⠀⠀⠀⡅⠀⠀⠀⠁⠂
⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠁
⠀⠀⠘⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡈⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⡄⢡⠀⠂⠀⠀⠀⠀⠰⠄⠠
⠀⠀⠀⡀⡀⠰⠀⠀⠀⡀⠀⢀⠠⠀⠀⠀⡀⠀⡀⠀⠀⢂⡀⠀⠀⢈⠀⠂⠀⠀⢢⠡⠀⠂⠀⠔⠀⠀⠀⠀⠤⠀⢇⠀⣁⢀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠤⠀⠈⠀⠀⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠉⡀⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⢂⠃⠙⠆⠀⠀⠀⡄⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠉⠀⠀⠄⠂⠀⠀⠀⠀⠀⠠⠏⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢀⠠⠆⠀⠤⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣴⣻⣏⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⢀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠀⠀⠠⠄⢘⠀⠀⠀⠒⠘
⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠂⠁⠀⠐⠀⠀⠀⠃⠠⠤⠀⠀⠀⠀⠸⠁⢜⠀⠀⠀⠈⡤⠊⠀⠀⠁⠀⠀⡈⠀⠈
⠀⠀⠀⠀⠠⠂⠀⠢⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠈⠀⠀⠀⠀⠁⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠘⠀⠀⢀⡆⠦⡀⠀⠀⠰⡄⠰⣤⠀⠀⠀⠀⠀⢀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢀⡐⠈⠏⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⡰⠁⠀⠀⠀⢀⠘⢝⣂⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⠂⠍⠀⣵⣀⠀⠀⠀⠈⠿⠁⠀⠂⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠚⢀⣼⣿⣿⣿⣦⣄⣠⠂⠣⡈⡴⠑⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⡀⢄⠔⠥⠂⠰⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠑⠢⡀⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⢠⠀⠀⠂⠀⠀⠹⠤⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠺⠟⣿⡀⠘⡟⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣐⠀⠈⠶⢤⠢⡀⠀⠆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⠇⠤⡉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠓⢁⣀⣘⡆⠀⠘⢀⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠀⠀⠉⠚⠠⠟⠀⠀⠟⠛⠉⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠎⠉⢹⣿⡖⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢂⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⢁⠀⠀⠆⠀⢠⣤⠀⠀⡻⢃⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠁⠀⠀⠀⠈⠀⠀⢢⠀⡇⠀⣠⠀⠀⢀⠠⡀⠈⡄⠀⢦⠀⠀⠐⠶⠔⠁⠸⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⢈⢢⠁⠞⠁⠀⢀⠌⠀⢳⡀⠀⠀⠀⠇⠀⡌⢀⠐⠀⢀⡄⠀⢠⣃⣠
⠀⠀⣀⣤⣤⣤⠃⠀⢠⣼⣀⠇⠀⠀⠀⢀⠀⣮⡜⠀⠀⠀⠀⡌⠀⠀⠀⠱⡄⢀⡀⣀⠐⠀⣰⠀⠀⢀⢙⣈⢉⣴⠟
⠀⠘⠻⠿⠿⣧⣤⣶⣿⣿⣿⠀⠒⣻⣿⠁⢀⣿⡇⠀⠀⠀⣼⣿⣷⣦⡀⠀⣈⠃⡈⠀⡤⠊⠑⢄⣀⣤⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢠⣿⣷⠀⢾⣿⡇⠀⠀⢰⣿⣿⣿⣟⡁⠀⠀⠀⠀⠂⠋⡆⢠⠞⠛⢿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢷⣾⠛⠇⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠴⠃⠘⠀⣠⠂⠈⡁⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠢⣄⠒⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠁⢀⠀⠈⠲⢤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡁⠰⠃⡡⠄⠀⠀⠀⠀⠑⣄⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣱⠀⠤⠄⠁⠀⠀⠀⠀⠀⠏⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡔⠒⢄⡐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢡⠀⠘⡄⠤⠒⠠⠎⠀⢀⠆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⠰⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠆⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠈⠁⠂⠀⠀⠀⠀⠀⡀⠂⡄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢁⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡈⠐⠠⢀⠤⠂⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠈⠐⠊⢦⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠊⠱⠆⠐⠀⠀⠐⢂⠀⣠⠄⠀⡴⠀⠐⠘⠀⠉⠉⠀⠀⠀⠀⠀⡀⣁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠒⠉⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠢⢀⠀⡖⢀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠠⠂⣡⠁⠀⠁⠂⠠⢀⠀⠠⠀⠀⠀⢀⠀⠐⠒⠁⠢⡀⠀⡇⢀⣠⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⢠⡀⠀⠀⠀⠀⠈⠀⡱⠊⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⣀⡀⠠⠓⠂⠐⠒⠆⠀⢡⡄⢀⠀⣀⣤⣤⢤⡀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⠀⣰⡀⠀⠀⠀⡇
⠀⠀⠀⡄⠉⠉⠉⠉⠉⠉⢉⢉⠉⠉⢉⠛⠙⢫⢙⡟⡒⠡⢸⢻⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⡇
⠀⠀⠀⡇⢤⠀⠀⠰⣠⠞⠛⠛⠳⣦⢦⠒⠒⠂⠰⣳⠂⢠⢄⣜⡃⠀⠀⠏⠀⠀⠀⠀⠀⠀⢀⠠⠀⠛⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠉⠀⠀⢼⠃⠀⠀⠀⠀⠈⣧⠂⠀⠀⠀⠛⠵⠷⠚⠋⠀⠀⠆⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠉⠁⠀⠀⠈⠐⠀⠀⠀⡃
⠀⠀⠀⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠐⠊⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠘⠪⢳⠶⠶⡞⠋⠂⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠦⠀⠄⠀⠀⠀⠀⠁⠀⠐⠃⠀⠀⠀⠀⠀⡠⠀⠠⡄
⠀⠀⠀⢀⣥⣤⣶⣶⣄⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⣉⠤⠐⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⠄⠄
⠀⠀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⡰⠀⠀⠀⠄⠀⠀⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⣸⠇⠀⠀⢘⡒⠲⠎⠀⢀⣀⡀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠀⠀⡆⡀
⠀⠀⠀⠐⠖⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠉⠛⠓⠚⠻⠿⠶⠞⠁⠀⠀⠚⠓⠐⠒⠀⠀⠐⠒⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⡠⢀⡀⢀⣠⣤⣤⣴⣶⡆⢺
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠋⡽⠉⠹⠈⠈⢡⡈⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠤⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸
⠀⠀⠀⠀⠀⠀⠔⠶⠾⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠠⠠⠔⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠄⣠⣀⣀⣠⣀⣀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⣴⠃⣾⡆⢳⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⣪⠭⢭⣒⢄
⠀⠀⠀⢰⣶⠄⠀⠀⠀⣴⣶⠀⠀⠀⣿⠀⣿⡇⢸⡇⠀⠀⠀⠀⠘⣛⡃⠀⠀⠀⠀⡎⡞⠁⢦⠀⠈⣎⠇
⠀⠀⠀⠘⠛⠁⠀⢀⠀⠛⠛⠀⠀⠀⠘⢦⣿⡧⠞⠀⠀⠀⠀⠀⢈⣋⡁⠀⠀⠀⠀⢇⢧⡀⠘⠇⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⢀⣬⣭⣥⣀⠀⠀⠀⠈⠫⢝⣒⣒⠭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⢻⣆⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⢀⣶⣶⣶⣶⣄⠀⠀⠀⠀⢿⣧⣤⣾⡏⠀⠀⢀⣇⣀⠀⠀⠀⢀⣸⡆⠀⢤⣤⣴⣿⣷⣾⠟⠁
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢿⣿⡟⠀⠀⠀⠈⢇⡀⣈⠛⢅⣀⡠⠃⠀⠀⠀⢹⣿⠿⣿⡄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⣀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠴⣻⡿⡿⣿⡻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢹⣿⡏⣵⡿⣷⡍⣿⠀⠀⠀⠀⡿⠀⠠⠘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠿⠷⠮⠛⢫⠶⢿⠀⠀⠀⠀⠁⠀⣸⠀⠀⠀⠀⠀⠀⢠⣤⠃⠀⠀⠀⠀⠀⠀⢀⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠂⠀⠀⠀⠀⠐⠛⠚⠒⠒⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠤
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣴⣿⠿⠟⠂⣿⡂⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠠⠁⣷⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⣿⣷⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⠛⢲⢷⣄
⠀⠀⠀⠀⠠⠁⣤⢹⣧⠀⠀⠀⠈⠃⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣆⠻⣷⡄
⠀⠀⠈⠀⠛⠛⠛⠛⠛⠃⠈⠀⠀⠀⠀⠐⠚⠛⠋⠀⠀⠀⠀⠀⠙⠋⠙⠃⠀⠀⠀⠀⠀⠀⠐⠛⠿⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡨⠄⠤⠤⢀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡀⠐⠀⠄⣠⠀⠰⠆⠚⠓⠃
⠀⠀⠴⣄⡦⠀⠉⠉⣸⣯⣄⣠⣤⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⢀⢠⢠⣆⡠⣽⣗⠒⠛⠣⢖⠴⠢⢀⠘⠂
⠀⠀⣜⠿⠁⠠⡄⠺⠗⢻⡈⢷⡍⠐⠃⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠝⠙⢋⠝⣿⢶⢋⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠋⠁⠀⠉⠂⠀⠀⣸⡏⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢛⠋⠀⣸⠯⢹⡃⠐
⠀⠀⠀⠀⠀⠸⠂⠀⠀⡛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠀⠀⡘⠀⠀⣼⠋⠊⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠦⠶⠒⠞⠀⠀⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣅⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠐⠂⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣏⠈⣉⣉⣉⣐⠉⠉⠒⢶⣛⣗⣳⣀⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠈⠯⢭⣬⢭⠭⠍⠀⠀⠉⡁⠄⣻⢼⣥⠮⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠉⠀⠀⠀⠀⠑⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁