Annoyed Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠛⠛⠛⠛⠻⣶⣠⣤⠶⠶⠶⠶⢶⣦⣤⣀
⠀⠀⠀⠀⢀⡤⠶⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⡀
⠀⠀⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇
⠀⠹⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠈⠙⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⣀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⢶⣶⠶⠟⠳⠦⣤⣤⣄⣀⣀⣀⣀⣤⡶⠟⠋⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢶⣤⣄⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣦⣀⣄⢀⣀⠀⠀⠀⢀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠿⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣻⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⢸⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡀⠀⠀⠹⣿⡇⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣶⡄⠀⢠⣾⣿⣿⣿⣿⢿⣁⠀⠀⠀⣿⣧⠀⠀⢰⣁⠀⠈⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⡜⢁⡤⠚⢛⢿⡿⠋⠀⠈⠻⠿⢻⡛⣦⡀⢙⡆⠀⠈⢁⣮⣽⣖⣉⣄⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠙⣦⣀⣀⣜⣉⣭⡙⠆⠀⠀⢣⠘⣄⣳⣿⠞⡇⠀⠀⠀⢸⣄⠘⠻⠟⠁⣠⡇⠀⠀⠈⢃⡰⠃⠀⠈⠓⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⢀⡠⠔⣎⠹⠀⢃⡀⠀⠀⠀⠓⠶⠿⠶⠞⠀⠀⣀⣀⡀⠙⠧⢤⠖⠓⠋⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣄⠀⣈⡗⠀⠈⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠠⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠁⠐⠒⠒⠀⠨⠛⠛⢦⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⣀⡀⣀⣀⡀⣀⣀⣀⡀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣛⣛⣛⣛⣛⣓⣒⣒⠒⢒⣒⣚⣋⣉⣁⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⣴⣿⣿⡟⠁⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⢿⣿⣿⣷⣆⢸⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⢠⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠻⢿⣿⣿⣤⣶⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠀⠀⣨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠒⠌⠙⢿⣿⣿⣿⣿⣿⠿⢿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠙⠒⢶⠀⠀⠀⠀⠀⢰⣾⣶⠈⠀⠀⠙⣿⡿⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠻⠇⢠⠇⠀⠀⠀⠀⠈⠈⠛⠋⠀⠀⣀⡠⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⢀⡤⠋⠀⡀⢀⣀⣀⠀⣀⠀⠉⠉⠁⠀⠀⢸⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⢠⣤⠚⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠹⠿⠇⠙⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠐⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠋⠉⠉⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢨⠢⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠃⠀⠈⠒⠄⣹⡢⣄⠸⢄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣴⠁⠀⠀⠀⠀⠀⠀⠁⠀⠉⣃⡳⣄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡤⠒⠉⢹⣮⣷⠂⠀⠀⠀⠀⠰⣖⣷⡏⠀⠈⢻⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢣⠀⠀⠈⠛⠋⠀⠀⡖⠀⠀⠀⠙⠋⠁⠀⠀⡜⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⡄⠀⠀⠀⠀⣠⣶⣦⣶⣶⣄⠀⠀⠀⠀⣰⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠙⣦⡀⠀⠀⠓⠒⠂⠒⠒⠚⠀⠀⢀⡴⠃⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⢻⣕⣤⣀⡀⣀⡀⣀⣀⣤⣾⡏⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣯⣽⡇⠀⠀⠀⠀⢸⣯⣽⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢫⠁⡇⠀⠀⠀⠀⣸⠈⡍⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠡⠀⠀⠀⠀⡆⠈⠑⠢⠔⠊⠀⢰⠀⠀⠀⢀⠎⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡜⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢠⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢰⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⡄⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢘⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉⠈⠉⠙⣿⣯⣼⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⣿⣭⡼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣭⣭⣍⣀⠾⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣮⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⣛⡉⢙⣛⣛⡛⠛⢭⣭⣬⣿⣿⣿⣿⡿⠟⢿⣿⣟⣿⡿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣽⣶⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣌⣉⣿⣿⣉⣡⣶⣶⣄⣿⣿⣿⣿⣿⣿⣶⣾⣭⣓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⠟⠿⠾⢻⣿⠏⢹⣿⡿⠳⠿⠿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡆⠀⠻⣄⡀⠀⣸⣛⠁⠈⣛⣇⠀⢀⣠⡟⠀⢸⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⡄⠀⠈⠿⠛⠁⠀⠈⠳⠖⠁⠀⠈⠛⣿⡁⠀⢠⣽⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡎⠀⢀⡇⢀⣴⠞⠛⠿⠿⠛⠳⣤⡀⢸⡀⠀⢰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⣿⣿⣿⣿⢠⠀⠀⡇⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⢸⠃⠀⡄⣿⣿⣿⣿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡽⣿⣿⣿⣿⣎⠀⢀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡀⠀⢸⣿⣿⣿⣿⣟⣾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠨⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢆⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣻⣿⣿⣧⢳⠀⡀⠀⠀⠀⠀⡘⠁⠀⠀⢀⠀⡾⣼⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⣮⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⣷⣿⣿⣿⡏⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⢿⣿⡄⠀⡄⠘⠄⠀⠀⢀⢿⣿⢿⣿⠎⠀⠀⣀⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⠟⠻⣆⢘⣆⢀⡎⢠⡟⠻⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢹⠏⠡⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣖⠤⣀⣀⠀⣀⡠⢂⣦⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣠⣾⡿⢛⢛⣛⣛⠚⢻⣿⣿⢋⢭⣭⠭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡠⠬⢍⠛⢿⣿⣧⣀⣈⣛⣀⣁⣼⣿⣿⣄⣬⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠊⠈⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⡛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⠀⠊⠈⠒⠁⠈⠒⠁⠈⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⣀⣀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣀⣀⣀⣀⡀⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠁⠀⠉⠀⠀⠈⠁⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠄⢀⠀⠈⠀⠈⠄⠀⠀⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⢤⢀⡌⠀⠐⣊⠀⠀⠰⠄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⡀⠀⠋⠀⠁⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⢃⠀⠀⠀⠐⠄⠀⠀⠀⡀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠴⣀⠀⣠⡀⠠⠄⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢯⣤⠧⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⡀⠀⠀⠀⠀⠀⢀⡀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣁⠈⠀⠐⠀⠀⠀⠀⠀⠊⠈⠰⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡜⠀⠡⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠛⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠤⣴⣆⠀⠀⠀⠈⠛⠋⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣿⣶⣄⡀⠀⠀⠉⠲⠆⣀⣀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⣼⠿⠿⠛⠚⠛⠿⢶⣤⣴⠂⢀⣉⠉⠈⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣧⣤⡀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡝⠛⠷⢶⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⣴⢆⠀⠀⠀⣠⣄⣀⣀⣀⠀⠀⢀⣼⣧⡈⠙⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣼⣧⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⠻⣷⣄⠙⢧⡀⠈⠉⠉⠁⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠙⢷⣦⣱⣄⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣈⣹⣿⣷⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠉⢻⣏⠉⠉⠉⠻⣿⣿⡛⣩⡿⠋⣿⠉⠉⠉⠙⢿⣿⣯⠉⣿⡏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢷⣤⣄⣀⣈⣭⣿⠟⠁⠀⠈⠻⣦⣤⣄⣈⣩⣭⡿⠋⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠈⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢰⠟⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⣤⣄
⠀⠀⠀⠀⠸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠹⠶⠶⣿⡇⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⣤⣤⣶⣶⣤⣤⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣶⣦⣤⣤⣀⣀⣀⣀⣄⣀⣠⣤⣤⣶⣶⣶⣶⡶⠶⠶⠶⠟⠛⠛⠋⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡜⢫⡀⠀⠀⠀⣿⠉⠀⠀⠀⢹⡏⠁⠈⣿⠃⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣷
⠀⠀⠀⠀⠀⢠⡎⠀⢸⠁⠀⠀⣠⠋⠀⠀⠀⠀⠈⡇⠀⢠⡟⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣿⠇⠈⣿
⠀⠀⠀⠀⢀⡜⠁⢰⡃⠀⠀⠀⣿⠀⣠⡄⠀⠀⠘⠗⠀⣿⠇⠀⠀⠀⣤⣄⣸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠘⠃⠀⠸⠇⠀⠀⠀⡿⠻⣯⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⢀⣼⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣷
⠀⠀⠀⢀⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⣸⣿⠃⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠤⠤⠤⢾⣿⠀⠀⢸⣿
⠀⣴⠊⣹⠟⠋⢀⣴⡿⠿⣦⠀⠀⠀⠀⠹⣧⠀⠀⣿⡏⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⢀⣠⣴⢶⣾⣿⠀⠀⠈⣿⣀⠀⡀
⠀⣹⠾⠁⠀⣰⡞⠁⢀⣴⣿⡀⠀⠀⠀⢀⣸⣧⣤⣿⣧⣠⠴⠾⠿⠶⠶⠶⠶⠶⣶⣮⣉⣀⣀⣸⣿⠀⠀⠀⣿⣏⣀⣁⣤
⣤⠟⠀⢀⣼⠋⠀⢰⠏⠁⢈⣿⠖⠾⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⣤⡶⠿⠋⠉⠉⠉⠉⠙⠿⠀⠀⠀⢹⣯⢈⡉⠉⠿
⠻⣤⣰⣿⠁⠀⡸⠃⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⠛⣿⡄
⠀⢸⡿⠀⢠⡼⠋⠀⣴⣿⣦⣤⣶⣤⣶⡶⠞⠛⠛⢻⡏⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⠶⠶⣿⣧⠈⠢⣄⣀⣹
⠀⠸⣷⣄⢘⣷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠰⣦⡼⠛⠃
⠀⠀⠈⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠀⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⡇
⠀⠀⠀⠀⠸⣷⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⠿⠿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⢻⡟⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣤⠼⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠖⠊⠉⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠿⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣀⡀⠀⠀⠉⠻⠿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⣠⣤⠞⠛⠉⠉⠀⣠⣴⣿⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢀⡻⠿⣦⣤⡀⠀⠀⠀⠉⠙⠛⠛⢦⣤⣤
⠀⢠⣶⣤⡘⠋⣀⣀⣀⢤⣶⡾⠛⠋⠀⠘⠿⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠈⠛⠛⠛⠲⠶⠶⠶⠶⠄⠛⠛
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⠿⠛⢻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣦⡀⢠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⢠⣴⣶⣶⣼⣿⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⠙⠃⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣦⡀
⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⣿⠀⠀⢰⡆⠀⠀⢹⣷
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⣿
⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢰⡇⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⢸⡿⣆⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⡇⠀⠀⢸⡇⢹⡄⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⣹⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⣼⠁⠀⠀⣾⠁⠀⣷
⢿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡄⠀⢀⡴⠋⢸⡇⠀⠀⠀⣰⠟⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⡾⠁⠀⠀⠀⢠⠿⣄⣠⡼⠃⠀⠀⢸⡄⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠛⠋⠀⠀⠘⢧⣤⡴⠟⠁⠀⢷⣤⣤⡴⢿⡀⠀⠀⠀⣠⢿⡇⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡅⣼
⠈⣿⡆⠀⣠⣤⣤⣆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠛⠶⠶⠛⠁⠈⠳⣤⡴⠾⠋⠀⢀⣀⣀⠀⠀⠀⠀⠘⠁⣿
⠀⢻⣷⠘⣇⠀⢠⣉⠳⣤⣼⠇⠀⠀⠀⠀⠀⠀⢀⣉⣙⣲⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣏⣉⣉⣀⣀⡀⠀⠀⠀⣾⡿
⠀⠘⣿⡀⠙⢶⣄⣹⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⣉⣭⠿⠛⠁⠀⢀⡤⣤⡶⢶⣴⠶⣤⡶⣤⠀⠀⠈⠻⢦⣉⠉⠉⠉⠁⠀⠀⠀⢻⡇
⠀⠀⣿⡇⠀⠀⠈⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⣸⡏
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⣾⡟⠀⠀⢀⡀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⢸⣿⠁⠀⣰⠟⠀⠀⠀⣶⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋
⠈⠛⠷⠿⠻⣧⣤⣤⣴⣿⣤⣀⣀⣷⣄⣀⡀⠉⠙⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠙⠛⠛⠿⠾⣷⣤⣤⣍⣉⣿⠷⣦⡀⠀⠀⠤⢤⣤⣤⣤⣤⣤⡶⠶⠟⠛⣩⡁⢀⣶⣄⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⠿⢷⡀⠈⠛⢦⣄⣀⣀⣤⠞⠁⠙⢷⣤⣴⣿⡾⠛⠻⠟⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢻⡏⠀⠀⠀⠀⠙⣦⡀⣠⠞⠻⣯⡀⢀⣠⡶⠋⠉⠙⣿⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢻⡄⢀⣤⠀⠀⠈⠛⠉⠀⠀⠈⠛⠋⠁⠴⢶⣄⢠⡟⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⡀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⢻⣧⢠⣄⡀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠈⣿⠧⣀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⣾⣋⡄⢹⣇⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢀⣰⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠙⠷⠾⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⠛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣈⣉⣉⣿⠟⠉⠉⠉⠉⠉⠉⠉⣿⣭⣭⣤⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠉⢉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣦⣴⡾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠂⠈⠉⠉⠉⠁⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠒⠠⡤⠂⠈⠁⠀⠐⠢⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡤⠄⢐⡒⠒⠒⠂⠀⠤⠬⢄⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠋⠀⠀⠀⠤⢀⡀⠈⠁⠒⠀⠄⡀⠀⠀⠁⠒⠠⣀⠀⢃⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠉⠂⢄⡀⠀⠀⠉⠚⢄⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⢘⢻⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⡀⠈⠑⠤⡀⠀⠀⠈⠒⠄⡀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢣⡀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⢈⡑⠠⣀⠀⠀⠈⠢⢄⠈⡄
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡃⠀⠀⠑⣄⠀⠀⠈⠑⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠭⠒⣤⣀⣀⡑⠜⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡐⠀⠀⠀⠀⡌⠛⢦⣀⠀⠀⠀⠈⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠼⠛⢳⠑⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠜⠀⠀⠀⢀⠜⠀⠀⠀⠉⠛⢔⡢⠄⣀⡀⠀⠀⠉⠁⠒⠠⠤⠄⢀⣀⡀⣀⣀⣠⠤⠄⠒⣛⡴⡢⠔⠃⡆⠑⢄
⠀⠀⠀⡰⠁⠀⠀⢀⠔⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠌⢁⣐⠒⠂⠀⠀⠀⠒⠒⢈⣁⡠⠤⠤⠂⣉⣁⠀⠤⠄⠪⢄⠀⠀⠁⠂⠉⠉
⢀⠔⠊⠀⢀⠠⠒⠁⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⢀⠤⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠁⠒⠂⠤⠄⠀⢠⠤⢤⠒⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠙⠯⠥⡤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡦⣀⠀⠀⢀⡠⠔⠁
⠀⠀⢀⠌⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⠀⠉⠉
⠀⠀⠊⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡
⠀⠀⠣⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠊
⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠠⠀⢀⣀⣒⣀⣀⣂⡁⠀⠠⠤⠀⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠙⢿⣷⡄⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⣠⣿⡦⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠉⠁⠀⠀⣠⣿⣄⠀⠀⠈⠉⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⣀⣠⣶⡿⠃⠹⣶⣄⡀⠀⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⣿⠃⠀⠀⠈⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠻⠷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣦⣤⣀⣀⣀⣀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⡀⡀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠉⠉⠉⠒⠒⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⡠⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⡖⠋⠀⠀⢀⣠⠖⠋⢀⡴⠊⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢀⡠⠶⡋⠁⢀⡠⠴⠚⠉⠐⢀⣠⠴⠒⡽⢀⡤⠖⡏⠀⠀⡴⠋
⠀⠀⠀⠀⢀⣠⠔⠋⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⠤⠒⠋⠁⠀⠘⠒⠋⠁⠀⠀⠀⠘⠃⠉⠀⠀⠈⠃⠉⠀⣸⠁⣠⠎
⠀⠀⠀⠚⠋⠲⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠚⠉⠀⠀⠐⠶⣤⣀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠞⠳⢶⣤⡀⠀⢠⢇⠞⠁
⠀⠀⠙⣓⡦⠤⠤⠤⠤⠤⠔⠒⠂⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⡐⠁⠀⣹⠿⣶⣤⣾⠀⢀⡴⢫⠴⣲⣦⣼⠀⠁⢀⡾⠁
⠀⠀⠈⠙⠢⠤⠤⣀⡤⠀⠀⢀⣠⠤⠶⣄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐⢵⣄⡀⠙⣋⡟⣁⣈⣻⡁⠀⠀⣸⣿⣿⡟⠀⠀⢸⡃
⠀⠀⠀⢀⣤⣴⣚⣉⣀⣀⡔⠋⢀⡀⠀⠸⠀⣀⠵⠀⠀⢀⠠⡤⠤⢬⣀⣙⣛⣉⣡⠄⠀⠀⠈⣿⢦⣤⡭⠿⠛⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⣔⢹⡆⠀⠋⠁⠀⠀⣀⣠⠄⠀⣀⠀⠀⠈⠉⠁⠙⠧⣤⡤⠶⠋⠐⠬⣄⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠈⠁⠀⠀⢠⣶⣾⣿⣇⠀⢀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠘⣿⣿⣿⣿⣷⣧⡀⠀⠀⠀⠈⠉⠙⠒⠒⠶⠦⠤⠤⢶⠖⠛⠉⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢎⠈⠻⣏⠉⠉⠉⠻⣿⠿⠿⣿⣿⣷⣶⣶⣷⣶⡖⠛⠋⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠳⣄⠉⠳⣄⡀⠀⠈⢧⠀⠈⠻⣿⣿⣿⣿⣿⠀⢤⡀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠉⠓⠦⢤⣀⣀⣀⢈⣻⣿⣿⡯⠇⢀⡹⠆⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⠲⠦⢤⣤⣤⣠⣤⠤⠔⣚⡭⠔⠛⠛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣤⡤⠴⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⣿⠀⠀⢀⣠⣤⣤⣴⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⣸⣿⣧⣴⣾⣿⣿⣿⣟⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⣿⣿⣿⣿⠟⠉⠛⠋⠹⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠋⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⠻⠛⠁⠀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⢀⣴⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇⠸⢿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⣿⣿⣧⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠁⠙⡟⠀⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⢹⣿⣿⠏⢸⡿⠛⠻⢿⣿⡀⢀⡆⠀⠀⢀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⢀⠔⠒⠚⣿⠿⠟⠁⠀⠀⠘⠿⡿⢗⡛⠉⠙⣦⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠠⠃⠰⡾⠂⢠⠀⠀⠀⠉⠁⠀⠀⠤⠀⠛⠋⢀⡼⠃⠀⠀⣿⣿⣤⣀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣧⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⢰⣿⡇⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠘⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⣡⠴⠶⢦⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡔⠉⠉⢳⣹⡿⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠈⠉⠃⠀⣀⠀⠀⠀⠀⠀⢸⡇⠸⠓⠲⣄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢠⠋⠉⠛⡇⠀⠀⠀⠀⠀⠘⠤⠤⠄⠀⠀⠰⠆⠔⠋⠀⠀⠀⠀⠀⢸⠁⡀⠀⢀⠏⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⠷⣤⡤⣷⠀⠀⠀⠐⠀⠀⢀⣀⣀⣀⣀⣀⣐⡀⠂⠀⠑⠀⠀⠀⢹⣀⣈⣉⣥⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣼⡀⠀⢀⠀⠀⣰⡏⢉⣏⣉⣹⣍⣉⣭⣉⣛⡇⠀⠀⠀⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⣟⢫⣉⣯⣤⡼⠦⠶⠶⠾⠿⠇⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣇⠀⠀⠀⠙⠛⠉⠀⠐⢂⠽⠛⠂⠀⠠⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⣀⠀⠀⠀⠀⢠⣧⣼⣷⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠷⠶⠦⣾⣿⣿⣿⡷⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠠⠄⠀⠀⠀⠄⢀⡀⣠⣤⣤⣤⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣀⡀⠀⠀⠠⠄⠀⠈⣻⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠤⠀⠀⠁⠐⠀⠄⡀⠈⠉⠛⠿⣿⣧⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠁⠂⢀⠀⠀⠙⠢⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢫⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⡈⠂⢄⠀⠀⠁⠢⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠆⠀⠳⡀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠐⡠⣀⠀⠑⠌⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⡘⠀⠀⠀⡘⠲⣄⠀⠀⠈⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠒⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⢀⠌⠀⠀⢀⠔⠀⠀⠀⠙⠣⠀⠠⠀⠀⠀⠈⠁⠂⠀⠀⠤⠀⣠⠤⠤⠀⢒⣫⠶⠆⠚⡀⠘⢿⣿⣿⣿
⣿⣿⠟⠁⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠌⠡⠄⠀⠀⠬⠀⠠⠔⡒⠛⠀⠀⠐⠂⠈⡰⠀⠀⠈
⣿⣥⣤⡐⣈⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡉⢃⠀⠀⠀⠀⢀⣴
⣿⣿⡿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣶⣶⣾⣿⣿
⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠈⠉⠁⠀⠉⠉⠀⠖⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠘⢶⣄
⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠒⠒⠈⠳⠸⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠑⢤⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢆⠀⠀⢠⠄⢀
⠀⠀⢀⠊⠀⠀⣀⣀⣠⡄⠀⠀⠁⠠⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠁⠀⠀⠀⡈⠀⠀⠀⠚⣋⠉⠛⡀⠠⡿⠀⢀⠀⠀⢰⠤⠈
⠀⠀⣦⡄⠂⠒⠟⠀⠀⠀⢀⠶⡆⠀⠈⠦⠀⠀⢀⡀⠁⠀⠀⠀⠀⣤⠀⠉⢰⡇⠀⠀⠀⣤⠉⢀⠔⠀⠀⣈⠉⠁⠀⠀⠐
⠀⢰⡀⣀⡀⠀⠀⠐⣄⣀⠻⠄⠁⠀⠀⠐⢀⣀⠄⠁⡀⠀⠀⠀⠀⡿⠠⠤⣤⠁⠀⠀⠀⠀⠉⠁⠀⠀⠐⠊⠤⠀⠀⠀⡇
⠀⠘⡷⢉⠿⢃⣀⠀⠈⠉⠁⠀⠀⠀⠀⡀⠉⠁⠀⠀⠇⠀⠀⠀⠀⠹⣄⠀⣶⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠀⠀⠀⣀⠀⠤⠄⠀⠀⠀⠀⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠢⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⢱⡀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⣀⡀⠀⣀⣀⠀⠄
⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢹⠀⣄⣠⡀⠐⠂⠂⢀
⠀⠀⠀⠀⠀⠉⠑⠒⠲⡖⠒⠀⠋⠀⡀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠢⢤
⠀⠀⠀⠀⠀⠀⡀⢠⠀⠡⠀⡸⠀⠐⢃⠀⠀⠢⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⠉⠙⠛⠛⠃⠁⠀⠀⠀⠀⠂⠀⠀⠀⠹⣄
⠀⠀⠀⢀⠤⢂⠀⢸⠀⢀⠂⠀⠀⠀⠌⠓⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡀⠀⠤⡄⠄⠀⠀⠀⡠⠶⠦⠤⠤⠙⢦
⠀⠀⡐⠀⠀⠀⠙⠺⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⡠⠀⠀⠀⠀⣠⠊
⠀⠸⠇⠀⠀⠶⠆⡀⠈⠑⠢⡀⠈⠐⠂⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⣀⢠⠎⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠐⠲⠖
⡄⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠑⠂⠀⠀⠈⣇⣲⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣸⣷⣮⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠇
⠧⠄⠐⠂⠈⠁⠀⠀⠀⠈⠢⡀⠀⠀⠠⣤⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⡟⠒⠒⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⠌⠁⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⣼⠙
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠰⠃⠇
⠀⠀⠀⠀⠘⠖⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠻
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠈⠓⠦⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠀⣤⠀⣤⡄⢠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⡀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠸⣇⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢸⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⢻⣇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠾⢟⣧⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠀⢉⣀⣈⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⣀⠒⢂⣀⣀⣀⣀⣈⣻⣄⣸⠂
⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⢳⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⡩⠀⠀⠀⠀⠀⠁⠀⠂⠀⠘⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣤⡄⠀⡀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡤⠊⠀⠀⠀⣠⠀⢀⣴⣿⢀⣴⣫⡴⠋⠁⢿⡀⡇⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣀⣴⣊⣥⠶⠋⠀⠿⠟⠋⠁⠀⠀⠀⠈⢷⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⡶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣿⠦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇⠀⠀⠉⠙⠳⢤⡀⠀⡄⠀⢀⣀⡴⠛⠉⠀⠀⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⢠⣿⣷⡦⠀⢸⠃⠀⠀⠀⣴⣶⣶⠀⠀⢸⠀⣆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⣙⣛⡅⢀⡟⠀⠀⠀⠀⢙⠿⣋⠄⠀⢸⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠧⣤⡀⠀⠀⠀⠉⠁⠀⠀⢸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡄⠤⠤⠶⠶⠶⠶⠶⠀⠆⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⡟⠙⡟⠛⠛⠉⠉⠻⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠛⡿⠁⢸⡀⠀⠙⠀⠀⠀⠀⢠⡇⠈⣿⠓⠶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠀⠀⠀⠀⢸⠇⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁⠀⣻⠀⠀⠀⠀⡀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠐⡄⠀⠀⠀⠸⡇⠀⠀⠀⠱⣄⠀⠀⣠⠞⠁⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠘⡄⠀⠀⠀⠷⠖⠻⡇⠀⠈⢳⠾⠋⠀⢸⠛⠺⠃⠀⠀⠀⠌⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣼⣤⡴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠌⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠸⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⠙⠲⢤⣄⣰⡆⠘⣇⠀⠀⠀⠀⣰⠇⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣤⠴⠚⠉⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠛⠶⠶⣤⣽⡇⠀⠈⠙⠲⠖⠋⠁⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⠶⠾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠒⠶⠾⢷⣤⣄⣀⣀⣤⣤⣤⣤⣀⣀⣀⡇⣿⢀⣀⣀⣤⣤⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⢻⡄
⣤⣤⣤⣤⣤⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⣬⣭⣭⣿⠿⠿⠿⠛⠛⠻⠶⢶⣶⣲⣄⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⣻⠀⠀⠀⠀⠀⠀⠀⠀⣬⡻⣧⡀⠀⠀⢀⣠⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣤⣤⣄⣀⠀⠀⢀⣒⠶⣝⢮⣻⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣯⣿⣾⡷⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⣺⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⢀⣤⠴⠚⠉⠁⠀⠀⠀⠘⠛⠛⠋⠉⠙⠛⠒⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⣠⣤⣤⣤⣄⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⣴⠟⠁⠀⠈⠳⣌⠁⠀⢀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠁⠀⠘⡆⠠⡀⠓⠤⣤⣀⠀⠈⠉⠀⣠⡾⠃⠀⠀⠀⠀⠀⠸⡆⠀⢻⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⢄⣢⣽⣤⠟⠲⣤⣀⣀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣴⠞⠛⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢹⡀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡇⠸⠏⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⣇⠀⡇⠀⠀⠀⠸⣧⠀⠀⣀⠀⠀⠀⢤⡀⠀⣸⡟⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠀⠈⠙⢶⠇⠀⠀⠀⠐⣿⣿⠏⠁⠀⠀⠀⠀⠉⠿⡿⠇⠀⠀⠀⠀⣼⠀⣸⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠉⢀⣀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⡞⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡅⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⡳⢤⠄⡀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠛⠛⠛⠛⠛⢷⡄⠀⠀⠀⠀⠀⡎⢠⡇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠦⣿⠀⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠘⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣋⣠⣤⠽⠷⠶⠚⠛⢿⡇⠀⠀⠀⠀⣿⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣯⠤⠶⠖⠚⠛⠛⠛⠙⠛⠻⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⠶⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⢤⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣸⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠓⠀⠈⠀⠀⠙⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣘⡰⠋⢀⡤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠛⠶⣤⡀⠀⠀⠾⢀⠞⠉⣠⣖⣩⡤⠔⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡀⠠⠤⠤⠀⠤⠄⣀⡀⠀⠀⣼⠗⠚⠁⠀⠀⠀⠀⠀⠁⠈⠻⣦
⠀⠀⠀⠀⢀⡼⠃⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢀⡞⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣾⠔⠁⠀⠀⠀⠠⠶⠚⠋⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡤⢤⣀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢤⡀⠙⢦⡀⠀⠀⠀⠀⢠⡞⠀⣠⢞⡀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣙⠦⣀⠙⠦⠀⠀⠀⠛⢀⠞⣵⣿⣿⣠⠀⠀⢹⠀⠀⠀⠀⠀⢸⡛⣦
⠀⠀⡏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣿⣿⣤⡌⠳⡄⠀⠀⠀⠐⣏⠀⠹⢿⣿⠟⠀⠀⣼⢠⡤⠀⠀⠀⢸⡇⣹
⣰⠒⣇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⠿⠾⠟⠀⢠⠇⠀⠀⠀⠀⠈⠠⣄⡤⠴⠒⠛⠁⠀⠀⠀⠀⠀⠀⢸⣧⠟
⣯⠀⢿⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠘⢦⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣀⣀⡀⠀⠀⠀⠶⠶⠿⢷⡀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠉⠁⠀⠀⢀⣀⣀⣀⣀⣀⣳⡀⠀⠀⠀⣰⠆⠈⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢰⣥⠤⠴⠒⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠠⠼⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠉⠻⣦⠀⠀⠀⠀⣀⣨⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠛⠲⠦⣤⣄⣀⣀⣀⣀⣀⣠⣤⡴⡖⠚⢉⠔⢀⡏⠀⢀⣘⣧⠀⠀⠛⠉⢀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠙⠻⣬⣉⠉⠩⠙⡇⠀⠈⠲⠋⠀⣸⠁⡶⠋⠁⠙⠶⠶⠖⠒⠲⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⣤⣤⣤⣤⠤⠿⠚⠀⠀⠀⠀⠠⡴⠶⠶⢶⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢈⣉⣡⠟⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠀⣭⣻⣿⣿⣿⡟⠚⠛⢛⣻⣧⣤⡿⠋⠉⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠉⠚⠙⠟⠿⠧⢄⣴⠟⡉⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢻⡾⠃⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣤⣠⡴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⣤⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣙⣶⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠠⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣤⣾⣦⣙⠟⠖⢁⠘⣆⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⢀⣤⡿⠛⠋⠉⠉⠁⠀⠻⠓⢀⡀⢌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠉⠀⠀⠀⠀⠤⠀⠈⢦⠀⡈⢶⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠙⢧⡠⠊⠀⢀⣀⣠⣤⡀⠀⠀⢳⣀⠈⠣⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠚⠁⠀⠚⠋⠁⠀⡁⠈⠦⢀⠀⣽⠆⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠆⢀⣼⣶⣶⣿⠡⡆⠀⢙⠶⡀⢀⠸⠟⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠚⠉⠉⠉⠙⠩⠀⠀⢤⣾⡆⢠⠻⣶⠾⣦⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠣⠀⠀⠀⠤⠸⠄⠀⠀⠀⢩⢀⣻⣤⢿⣂⢏⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠐⠀⢀⣀⣠⡐⠄⠐⠋⠈⠛⣀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠴⠄⢳⣽⣿⣦⠀⠀⢠⣾⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⢻⡇
⠀⠀⠀⣿⠀⠀⢀⢠⠀⠆⡄⠀⡄⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⢰⠴⢿⠙⠏⢫⡀⣰⠟⠻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡠⠛⢀⠃⢸⡇
⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⡇⠀⠀⢂⢸⠀⢸⠀⢸⡀⡄⠀⠄⠀⠉⡀⠵⡀⠈⢣⠇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡴⠀⢀⡎⢀⡞⠰⠀⡎⠀⢸⡇
⠀⠀⠀⣿⠀⠀⢀⠀⣶⠀⠀⢳⢠⡈⠀⠂⠈⠀⠈⡀⠁⠀⠀⠐⠂⡀⠀⠑⠄⠈⡀⠀⡀⢈⠀⠃⠀⠀⠀⠀⠂⢀⠟⠁⠀⠞⢀⢎⢛⡀⡜⠀⠀⢸⡇
⠀⠀⠀⣿⡆⠀⢸⡆⣿⣧⠀⢸⣇⣷⣦⠀⣀⢠⣦⢳⣿⣷⣔⣶⢆⠃⠀⠀⠐⠀⢽⣄⡁⣡⣶⡆⣠⣀⢀⣄⡴⣫⠆⣠⡶⢠⠋⣤⣮⠠⠀⡼⠀⢸⡇
⠀⠀⠀⢸⣿⢠⣼⣿⣿⣯⣦⣦⣻⣿⣿⣷⣿⣶⣿⣿⣿⡿⠋⠁⠊⠁⠢⡀⠀⣤⠀⢿⡿⡌⠱⣿⣿⣷⣿⢏⣴⢋⣴⢟⠀⠚⡰⠋⣿⠄⣸⣇⢀⣿⠁
⠀⠀⠀⠘⣿⡎⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⡿⢙⢯⠷⠛⢻⣄⠠⠄⠀⢀⣈⢰⣿⠀⠊⢿⡽⣦⣑⢿⣿⣿⣿⣷⣿⣷⠋⠀⠀⣧⠀⡍⢰⣟⣿⣿⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡻⡕⠁⠀⠀⠀⠈⠙⣄⢀⠔⣱⡉⠈⠁⣱⡶⢯⢿⣼⡿⣿⣷⡍⣿⣿⣿⠟⢀⠀⠀⣯⡞⢠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣡⠇⠃⠀⠀⡄⠀⠁⠙⡤⣪⠿⣿⠃⠈⠟⠀⠀⢻⣿⡅⠈⣇⢻⣼⣿⣧⡟⠀⠀⠀⣿⠁⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢂⡟⠀⠀⠀⠀⣱⠀⠀⠀⠀⠁⠀⢸⣧⡶⠁⠀⢀⠀⠿⣛⠡⠟⠘⣿⠿⢫⠄⣰⢦⢴⡇⠐⣻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⡞⠀⠗⠆⠀⠀⡧⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠘⠀⢀⠀⠀⠂⠂⠙⠋⡤⠒⢛⠙⠼⡇⢰⣿⢏⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣟⠇⠀⠀⠀⠀⠀⢀⢠⣧⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠀⠀⠀⠠⠒⠂⠐⢠⣠⣏⢷⠙⠓⠀⠀⠆⢩⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠉⠀⣠⣢⡀⡄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣠⣾⣿⣧⣿⢻⣩⣁⠀⠁⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣡⠘⠥⢷⡄⠀⠠⣽⣷⠐⠂⠠⠤⠀⠽⠤⠶⣴⠃⠀⠦⠀⢠⠉⠙⡇⢹⡿⢼⣏⣉⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣈⣿⣶⣾⣤⡴⠾⠻⢦⡀⠀⠀⣀⢻⠀⡀⠠⣠⡟⠃⢸⠃⠈⣷⣾⠿⠉⣽⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⡉⠉⠤⠀⠈⠈⠀⢈⡏⠁⠀⣽⢸⣧⢶⠛⠉⠀⢀⠋⠀⠘⢱⣻⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡀⢠⣼⡇⠀⢀⡀⣰⠇⠠⠀⠀⠉⣰⣄⣀⠠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⠶⠤⣤⣬⠤⠶⠶⠶⠛⠋⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣽⣿⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣿⣿⣶⣶⣶⣿

⣿⣿⣿⣿⣿⣿⡿⠟⠃⠾⠟⣿⣻⣿⡿⠿⢿⣿⣿⣧⢹⠻⠷⣏⣛⣦⣍⠐⢰⣨⡯⣯⣽⣏⣿⣷⣿⠗⠸⣗⣞⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣷⣾⣿⣷⣏⠻⢿⡿⠇⠘⠙⢃⠈⠻⠿⢞⡧⣾⣿⣶⡉⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡋⣯⣭⣿⣾⣶⣦⣿⠹⢳⣾⡸⢋⣄⠻⣷⢸⣷⣿⣶⡈⣿⡿
⠃⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣍⢻⢻⣿⣻⣿⣿⣿⣁⢘⢫⣝⣻⣍⣻⣦⠀⠀⣽⣏⣿⡌⢹
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣹⢿⣿⣟⣿⡿⣵⣿⣸⡇⣮⣿⣿⣿⣭⠘⢶⣌⡛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⠿⣶⣤⣿⠹⣿⣿⣿⣿⣾⡟⢸⣷⣾⣟⢮⡛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⢟⣰⣷⣿⣿⢿⣷⣿⣽⣿⣿⣿⡖⣽⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⣶⠶⡶⠀⢀⣼⣿⡳⢻⣿⣿⣻⡟⢿⣿⣬⣽⡿⣿⢻⣿⣥⣿⣿⣷⣽⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢸⣿⡿⢰⣾⡿⣋⣻⡿⣷⣘⠻⢿⣿⡿⣼⣿⠛⢿⣿⣇⣴⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣧⠀⠀⠀⠸⠏⣴⢺⣿⣿⣿⣿⣿⣷⣼⣃⢘⡿⢧⣻⣿⠁⣿⣾⣏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢿⣿⣿⢿⣿⡛⣿⢿⣧⣸⣷⣾⠀⡽⠒⢻⣿⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡟⣿⣻⣏⠙⣨⢹⣧⣦⡈⢻⣿⣷⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣉⣣⣹⣷⠿⢾⡵⠂⣰⣿⡙⢿⣧⣾⣿⡛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢀⡀⢀⣼⣿⣿⡟⢫⣶⣾⡇⣼⢿⣿⡟⣦⠙⣿⣿⣿⣦⣉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣾⣿⡿⢿⣷⣿⡎⣿⠈⡆⣿⣿⢾⣅⡿⣿⢿⣿⣿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣫⣴⢿⣽⣿⣧⡀⢾⠰⠿⢃⣽⡽⠇⣀⡰⣿⣾⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣊⡿⣿⣷⠷⣾⠿⡛⠋⢠⠠⠀⠸⠋⣥⣾⣏⢻⣿⣽⠏⠙⣛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠁⠼⢛⣚⣉⠁⠀⠸⣀⣟⡀⠀⠀⠶⠆⠾⢨⣯⣏⢨⣭⣼⡄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣻⣋⠃⢠⣞⠿⢻⣩⣤⣴⣶⣯⠘⠇⣀⣹⡁⡆⣀⡘⣻⡿⠘⠿⣧⡶⢡⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢈⠹⢷⠔⢻⠟⣾⢻⣽⣿⣾⣦⠟⣿⡆⠉⠸⣣⣼⣿⣦⣷⠆⠀⣾⡿⡇⢨⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠁⡜⢻⠟⢼⣟⣭⡙⣿⡾⣇⣾⣿⣷⡏⣿⣮⣛⢹⣷⡆⢞⢠⣷⣿⠇⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣦⣿⡆⠉⠩⣿⣿⣿⣯⡙⠣⢾⣿⡏⢇⣿⣿⠟⠀⠉⣾⠉⢸⣧⣿⣷⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡿⣿⠰⠆⠉⣋⣥⣾⡧⣔⢻⣿⡇⡀⢄⢰⣶⣾⣤⢰⣤⣼⣯⣿⡇⣿⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣙⣠⣭⣤⡝⠶⢿⢿⡽⠛⣡⣦⣼⣿⣿⡟⣡⢸⣿⣿⣿⡧⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠉⣣⡀⠐⠨⠈⣵⡿⣿⠿⣛⣿⣿⣿⠙⡄⠻⣛⣥⡄⣾⡷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣭⣝⣷⡀⠚⢷⡟⠿⢗⣭⠹⠿⠟⡀⠃⡀⢿⣿⠃⣿⣱⣾
⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣽⡲⣿⣿⣿⣿⠿⠿⡗⣈⠂⠛⠀⠉⠐⣒⡛⢃⠀⣼⣌⣿⣅⣿⣾⣿
⣞⣿⣿⡏⣿⢷⣄⡀⠀⠀⠀⢀⢠⣴⣯⣛⣛⣫⣭⡤⣄⠀⠈⡁⠤⠶⣶⣷⣬⣰⣿⣷⣽⣛⣿⣤⣿⣿⣾⣹⣿⣿⣿
⠛⢛⠛⠓⢙⣛⣹⣿⣶⣶⣾⡿⢿⣿⣿⣻⣿⠶⠛⢩⣔⣿⣷⣶⣶⢦⣙⣛⠿⣿⣿⣟⢰⣿⣧⠙⣿⣿⢿⠏⢻⣿⣿
⢠⢈⡆⣠⣻⢸⡿⣿⣿⣿⣿⣼⣿⠿⣛⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢳⣿⣿⣛⣿⣽⣿⡄⣷⣾⡘⢻⣿⣿⣿
⣄⣨⣀⣋⠉⣾⡾⣿⠿⠟⡁⢭⣶⣞⣿⢟⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⣿⢳⡾⣿⣿⣿
⣈⣉⢁⣿⠀⣼⡆⣴⡶⣴⣶⣿⣿⣿⣝⣽⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣆⣾⣦⣟⣿⣿
⣿⣒⣞⣿⣧⣿⣷⣜⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡆⣽⣿⣭⣭⣽⣭⣩⣭⣿⣹⣿⣷⠰⣎⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣦⠀⠀⢀⡤⠤⠤⠖⢺⠃
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡔⠁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠘⡤⠤⠖⠚⢄⡀
⠀⠀⠀⠀⠀⢸⣶⣶⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⡿⠛⣿⣿⣿⡿⢹⣿⣿⣿⣿⡿⠟⠁⠉⠛⠿⣿⣿⣷⣦⡷⢄⡀⠀⠀⠙⣲⡤
⠀⠀⠀⢀⠔⠚⣿⣿⠿⠿⠛⠛⠉⠀⠀⠉⠉⠀⠀⣰⣿⠿⠋⢀⣾⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡏⠲⡌⠉⠉⠉⠁
⠀⠀⠀⡎⠀⠀⣿⣿⡆⠀⠀⠀⠀⠤⠶⣦⣤⣀⠀⠉⠀⠀⠀⠈⠁⠀⠀⢀⣤⣴⡶⠦⠄⠀⠀⠀⠀⣿⣿⠁⠀⢸⡀
⠀⠀⠀⢇⠀⠀⠹⠟⠁⠀⠀⠀⠀⠚⢻⣽⠟⠛⠳⠀⠀⠀⡾⠀⠀⠀⠰⠛⠛⢯⡿⠛⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⠁
⠀⠀⠀⠈⠢⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⣄⢀⣄⢀⠀⠀⢀⣠⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡆⠀⠀⠀⢻⣿⡆⠀⠀⠀⢀⣠⢤⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣷⣄⠀⠀⣶⣿⣿⣿⣿⡿⠿⣅⠀⠀⠀⢸⣿⣇⠀⠀⠀⣇⠀⠀⠁⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣸⠁⣠⠖⠚⠛⣿⡿⠏⠀⠀⠙⡿⠿⡿⠛⣦⡀⠈⣧⠀⠀⠈⢠⣮⣽⣖⣋⣀⡀⠀⠀⣀⣠
⠀⣠⡤⠖⠛⠓⣦⠀⠀⣰⠚⢭⡙⢷⠀⠀⠀⢻⠀⣇⠲⠴⣗⠞⡇⠀⠀⠀⠀⣇⠀⠻⣿⠿⠁⢀⣿⠀⠀⠀⠘⠃⣸⠇⠀⠈⠳⠶⠶⠟⠁
⢾⡁⡀⠀⠀⠀⠉⢉⡩⣽⠻⡏⣹⠀⠀⠀⠀⠈⠳⣬⣙⣫⣥⡴⠁⠀⠀⠀⠀⠙⢷⣄⣀⣠⠖⠿⠁⠀⠀⠀⣶⠚⠁
⠀⣿⠁⠀⠀⠀⠚⣯⠀⠘⠦⣥⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⠓⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠈⠙⠻⠦⠤⠞⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣒⣀⠉⠙⠛⠿⢷⣦⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠑⠄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠒⠒⠒⠲⠶⠶⠶⠶⠖⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⡄⠀⣀⣀⡀
⠀⠀⠀⠀⢀⡀⠻⣦⣀⣠⡾⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠹⠊⠀⠀⠈⡆⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠙⣧⠀⠉⠁⢠⡞⠁⠀⠀⠠⣄⡀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡜⠁⠈⠖⠊⠓⡆
⠀⠀⠀⠀⠀⣠⡟⠀⢀⠀⠸⣧⡀⠀⠘⢶⣌⠛⠶⠞⢡⡾⠃⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⢀⠔⠚⠀⠀⠀⠀⠴⢥⡀
⠀⠀⠀⠀⠘⠋⣴⠞⠉⠛⢦⡈⠋⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⢀⡴⣄⢸⠉⠉⠀⠀⠈⠢⢤⡄⣀⠀⠀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣡⡶⠲⢦⣌⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⢦⡇⠀⠀⠀⠀⠀⢸⠖⠙⢄⣠⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⠎⠀⠀⣠⡀⠀⠈⢦⠀⠀⠀⠞⣛⣓⣒⠾⠽⢶⡀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣤⠀⠀⠙⣄⠀⠀⠠⢟⣛⣓⡲⠯⠽⢦
⠀⠀⠀⡏⢀⡠⠞⠁⠙⠢⣄⡀⡇⠀⠀⣠⡇⢐⡄⠀⣔⠀⢳⡀⠀⠀⠀⠀⠀⢰⠃⣀⠤⠊⠀⠑⢤⣀⠘⡄⠀⢀⣼⠀⢢⠄⠠⡔⠈⣇
⠀⠀⠀⣧⢻⠀⠾⢁⠘⠇⢠⢷⡇⠀⠀⠺⡇⠈⠁⠂⠉⠀⡼⠎⠀⠀⠀⠀⠀⢸⡜⣇⠀⠏⡀⠹⠀⣼⣢⡇⠀⠘⢾⠀⠈⠠⠀⠁⢀⡧⠃
⠀⠀⠀⠹⡉⢣⣀⣔⢠⣠⠎⣩⠃⠀⠀⠀⠙⢄⡢⠀⣁⡴⠁⠀⠀⠀⠀⠀⠀⠀⢧⠙⢆⡀⠀⢀⡴⠋⡼⠀⠀⠀⠀⠳⣄⠐⠂⣠⠞
⠀⠀⠀⠀⠙⢦⡜⢋⠛⣦⠔⠁⠀⠀⠀⠀⠀⣴⠛⡍⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠟⣉⠻⡤⠊⠀⠀⠀⠀⠀⢀⣞⢩⡍⢷⡀
⠀⠀⠀⠀⠀⡾⠑⠊⠒⠹⡆⠀⠀⠀⠀⠀⣸⠁⠉⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠂⠉⠂⢱⡀⠀⠀⠀⠀⠀⡞⠀⠁⠈⠀⢳⡀
⠀⠀⠀⠀⡼⠀⠡⠀⠠⠁⠸⡄⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢂⠀⡐⠀⢡⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢀⡇⠀⠀⠑⠁⠀⠀⣇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⢱⠀⠀⠒⠀⠐⠘⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡾⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⡄⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⡀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠃⠁⠀⠀⠀⠀⠈⠀⠃
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠀⠀⢀⣠⡄⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡏⠘⡇⠀⠀⢠⡇⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢤⡀⠀⡼⠀⠀⠱⣄⠀⠸⠴⠋⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⠉⠊⠁⠀⠀⠀⢹⡄⣠⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠼⠚⠁⣧⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠙⠆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣞⣠⠜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢄⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⣀⡉⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡍⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡜⠱⢶⠶⣦⡀⠀⡀⠀⣰⣟⠛⣬⠙⠃⢸⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠁⠀⢧⡀⠻⣻⠞⠙⢾⡻⠟⢀⡼⠀⠀⣸⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠁⠀⠀⠀⢈⣩⠥⢤⣀⠀⠉⠉⠉⠀⠀⠀⡏⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢰⡀⠀⠀⠈⠀⠀⠀⠙⠳⠶⢳⠀⠀⠀⢸⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠤⠤⠤⠤⠴⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡤⣔⡉⠉⢉⣒⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡜⡠⠔⠛⠈⣙⠶⠄⠐⠚⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣏⣀⠤⠒⠉⢀⣠⢒⠘⣿⡶⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠤⠤⣼⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠤⠐⢲⡉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠠⠐⠈⢈⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡊⣤⠀⠀⢀⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⣠⠤⣰⠂⢉⣉⣉⠁⢻⡃⣁⠊⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠆⠈⠁⡐⠋⠉⠩⠳⡀⡉⠈⠀⡧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢇⠙⣀⠷⣇⣇⡄⣄⣄⡷⢇⡜⢁⠋⠢⠈⢒⠢⣄⣀
⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠱⡉⠢⢠⡜⡷⡟⣤⢠⠋⡳⠁⠀⢰⠀⠸⠀⠘⠀⠑⠆⠤⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠑⠲⢌⡖⢅⠕⣯⠴⠊⠀⠀⢀⠆⢠⠃⠀⠸⠀⠀⠀⠀⠀⠑⢄
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⠎⢠⠃⠀⠀⠆⠀⠀⠀⡇⠀⠀⠀⠡⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡐⠁⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⢡
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠊⠀⠠⠃⢠⠀⠀⢀⠃⠰⠀⠀⠀⠀⠀⠀⡆
⢃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⠔⠁⠀⡰⠁⢀⠃⠀⠀⡌⠀⠇⠀⠀⢰⠀⠀⠀⢰
⠀⠢⡀⠀⠀⠀⡀⠴⠚⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⡠⠒⠁⠀⢀⠊⠀⠠⠃⠀⠀⡐⠀⡌⠀⠀⠀⠨
⣤⣤⣬⣥⣬⣥⣤⣤⣤⣤⣤⣤⣤⣼⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣾⣶⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠼⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠃⠀⠘⢦⡀⠀⠀⢟⢄⡀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠇⠀⢤⠀⠀⠉⠲⠄⣈⣆⠉⠒⠤⢀⣀⠀⠀⠈⢆⠣⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡠⣼⠀⡴⠊⢷⡀⠀⠀⠀⠀⠉⠁⣠⣤⣖⠚⠉⠁⢲⠼⠄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣀⠗⡿⠃⠣⠘⣿⡟⠀⠀⠆⠠⠴⣏⣽⠆⠈⣷⠀⠀⢸⠀⢀⡠⠤⢄⡀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡒⠁⡜⠁⢠⠁⠀⠀⠀⠀⡠⠤⠀⠀⠀⠐⠈⠋⠒⠒⠃⠀⣠⠞⠐⢁⡤⠤⡀⢡⠀⣀⠈⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣁⠔⠉⢆⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⢰⠁⠀⡆⠈⠇⠀⢀⠎⠀⢹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⡆⠀⠈⠣⣀⠀⠀⠀⠀⠈⠓⠤⠄⡀⠞⠀⠀⠀⢸⠀⢠⠧⠤⠤⠒⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⠣⡘⠀⠀⣠⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣸⠳⡀⠀⠀⠉⣁⡰⢶⠒⠈⢉⠜⠓⠤⡀⠀⠁⠀⡠⢻⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡲⠒⠉⠀⠀⠸⡤⠒⠁⢀⠀⠀⠈⢆⡠⠞⠁⠸⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠤⣠⣁⠀⠀⠀⢀⣴⠂⢆⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢡⣞⡉⠈⠉⠙⠒⢯⡲⣝⠎⠉⢑⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠈⠣⠀⢠⠎⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⣀⣠⠔⠛⠢⣄⠀⠀⢀⡴⠃⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠟⢿⣯⢸⣿⣿⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⣀⣾⣿⣿⡿⠟⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣠⣿⣿⣿⣿⣷⣄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠑⠊⠉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡐⠁⠀⠀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣤⣴⣿⠟⠋⠙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣥⡀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣟⠀⢀⣾⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣧⡘⠉
⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠿⠻⠿⠷⢶⡟⡛⠻⠏⣉⡛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠛⢛⣙⣃⣘⣿⣿⣿⣷⣦⣽⣷⣦⣼⣿⣦⡘⢿⠾⠟⠛⠻⠿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠟⣛⣫⣴⣾⡿⢟⣛⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣶⣿⣿⣥⣶⡶⣈⣽⠇
⠀⠀⠀⠀⠀⠀⠸⣧⣄⡲⠿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣛⠲⢦⣬⣽⣶⣿⣿⣿⠟⠽⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣌⠻⠶⢶⣄⡀
⠀⠀⠀⠀⠀⢰⡟⢡⣾⣿⣿⣿⣿⣿⡟⠋⢠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡦⠀⢹⣿
⠀⠀⠀⠀⠀⣿⢡⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢉⠍⣩⣿⣿⣿⣿⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⡟
⠀⠀⠀⠀⢸⣏⠈⣸⣿⣿⡿⣱⣿⣿⣿⣿⣿⣯⣾⣫⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠙⣷
⠀⠀⠀⠀⠀⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣍⠱⣾⡏
⠀⠀⠀⠀⠀⢸⣇⢻⡟⣹⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⡏⢩⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠻⣦⡄⣿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡹⡾⠿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠛⠻⡯⠙⢿⡿⢉⠀⢸⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠹⡏⠈⢿⠉⠛⠻⠿⠿⠯⠭⠽⠟⠛⠛⠛⠭⠙⠛⠀⢀⠤⠀⠘⠧⠈⡠⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢣⡀⠀⠀⠁⠐⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⢄⢰⢃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠱⡐⢄⡃⠀⠀⠀⠾⠛⠿⠿⠟⠋⠀⠀⠀⠘⠛⠛⠿⠏⠹⠂⠀⠀⠀⠈⢸⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣭⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⣈⠠⢤⣄⠀⠀⠀⠀⠀⠀⡸⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢈⣆⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣤⣶⣿⣿⡄⠀⠀⠀⠀⠴⣁⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⠖⠁⠈⢆⠀⠀⠀⠀⢀⣿⣿⠛⠻⠟⠙⣿⠿⠇⠀⠀⡠⠊⠀⠀⠙⢎⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⠃⠀⠀⠀⠀⠀⢄⡀⠀⠸⠏⣿⣦⣤⣤⣴⣿⠇⣀⣠⠚⠀⠀⠀⠀⠀⠈⢃⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠃⠀⠀⠀⠀⠀⠀⠀⡍⠓⠶⠠⣂⠉⠉⠩⠍⢐⡜⠻⠀⠀⡆⠀⠀⠀⠀⠀⠈⡀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠠⡀⠉⠀⠐⠂⠁⡠⠃⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⡞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠲⣤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠴⢶⢋⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡼⢿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⠀⠀⢸⡇⠳⠭⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠰⠄⢀⡀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⢫⡆⠈⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣇⣷⢀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡇⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⢦⠀⢁⠆⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣿⡇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣸⠺⠈⡇⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢰⣿⣷⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢈⠀⠀⡁⠀⠀⠀⠀⢀⣿⣿⣟⠙⣻⣷⣦⣄⣀⣴⠀⠀⣀⣀⣀⣀⠈⣿⣿⣏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠃⠀⣀⠀⠀⠀⠹⠛⠻⠷⠈⣿⣿⡿⠟⠃⣴⣿⠿⢿⣿⣿⣿⣿⣿⡫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣴⠶⣶⣯⣧⣧⡤⠿⡀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⡀⠀⢀⣀⣰⣯⠀⢀⣿⣿⣿⣿⡄⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢰⢡⠞⢉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⠇⣰⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⢀⡙⣄⠀⠀⠀⠀⠈⢨⡞⣿⣅⠚⠿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣓⣉
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠤⠊⣣⡀⠀⠀⠀⠈⠁⢾⠄⠒⡐⠒⠚⠋⢀⡼⠡⣿⣿⣿⣭⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⡀⠀⠀⠀⠀⠦⣀⣁⣩⡴⠝⢁⣾⣿⡿⠧⣍⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠓⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡦⣀⣀⣀⣀⣀⣴⣿⣿⠿⣍⡓⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠉⠿⠿⣿⣿⡻⣝⠳⣮⠑⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢋⠀⠳⡈⠳⣌⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠠⠄⠀⠀⠀⠄⢀⡀⣠⣤⣤⣤⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣀⡀⠀⠀⠠⠄⠀⠈⣻⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠤⠀⠀⠁⠐⠀⠄⡀⠈⠉⠛⠿⣿⣧⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠁⠂⢀⠀⠀⠙⠢⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢫⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⡈⠂⢄⠀⠀⠁⠢⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠆⠀⠳⡀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠐⡠⣀⠀⠑⠌⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⡘⠀⠀⠀⡘⠲⣄⠀⠀⠈⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠒⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⢀⠌⠀⠀⢀⠔⠀⠀⠀⠙⠣⠀⠠⠀⠀⠀⠈⠁⠂⠀⠀⠤⠀⣠⠤⠤⠀⢒⣫⠶⠆⠚⡀⠘⢿⣿⣿⣿
⣿⣿⠟⠁⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠌⠡⠄⠀⠀⠬⠀⠠⠔⡒⠛⠀⠀⠐⠂⠈⡰⠀⠀⠈
⣿⣥⣤⡐⣈⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡉⢃⠀⠀⠀⠀⢀⣴
⣿⣿⡿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣶⣶⣾⣿⣿
⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⡿⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⡀⠨⠭⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⡉⡉⠉⠁⠩⠅⣀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡏⠀⢨⠀⠔⠈⠀⡀⠚⠛⠁⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠢⠀⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠊⠀⣠⠨⠐⠀⢁⣶⣤⠀⠀⣤⣶⡈⠀⠀⠀⣄⠀⠑⠂⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⠦⡍⠽⠀⠀⠯⢩⠴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢾⣷⡄⢠⣿⡷⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠝⠀⠀⠫⡈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠠⣀⠀⠀⣀⠄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⣤⣠⣤⡔⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠦⡤⠞⠁⣀⣀⣠⣤⣾⣷⡆⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣠⣴⣶⣶⣶⠶⢀⣠⠌⠙⠛⠛⠛⣭⣴⣿⣿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢠⡞⣉⠈⠉⠋⢁⣴⠋⣠⣶⣦⣀⣀⣀⡈⠉⠉⠑⠶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⠀⢠⡏⣾⠁⣀⣀⡀⢸⡏⣼⣿⣿⣿⣿⣿⣿⡟⠠⣄⡳⢶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⢸⡆⢿⣸⣿⣿⣧⡸⠇⠿⠿⠿⠿⠛⠻⢿⣷⡄⠈⠙⠛⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠛⠛⢶⣄⠀⠛⠊⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢦⣄⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣼⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣷⠀⠀⣿⣧⡈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠚⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠹⡆⠀⢨⡻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿⠀⠀⠹⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠲⣿⣿⣧⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣉⣀⣀⣀⠀⢹⣿⣿⣿⣒⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢠⣾⣿⡀⠀⣀⡴⠶⠒⠲⠶⢤⣤⣀⡀⠀⠀⣀⢰⡟⢁⣤⣾⣿⠛⠛⠋⠀⠀⢻⣖⢶⣽⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⡇⢸⣿⣿⣷⡀⠉⠀⠀⠰⣶⣶⣶⣄⣈⠙⢷⡈⠉⢿⡇⠉⠀⠉⠙⠛⠁⠀⠀⠀⢸⣿⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣎⠻⠿⠛⠁⠀⠀⠿⠿⢙⣿⣯⠄⠉⠀⠈⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠘⢿⣧⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣭⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣼⠆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠚⠛⠀⠛⠁⠀⠰⠀⠀⠀⠀⠀⣿⣿⠿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⢳⣿⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣿⣿⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣽⣻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠿⢛⣻⣿⡟⠉⠀⠀⠀⣸⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣧⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠒⠛⠋⠁⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠒⠒⠒⠒⠲⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡠⢦⣠⠤⡀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠤⠤⣀⣠⢷⡀⠹⡄⠱⡄⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⣹⠀⠱⡀⠱⡀⢹⢡⢾⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⡎⠀⠀⠀⢸⠈⢣⠀⢣⠀⢇⠈⣧⠘⣤⠗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢺⡇⠀⠀⠀⣈⣆⠀⢧⠘⠂⠀⠀⠛⠀⡿⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡇⠀⠐⠢⢄⣸⠀⠘⠀⠀⠀⠀⠀⢠⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣵⢢⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀⠉⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠑⣄⠀⠀⠀⠱⣄⠀⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡏⠱⣄⠈⠩⠭⠵⡌⠁⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⢧⠀⠀⠀⠀⠀⠈⢯⠉⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢣⠀⠣⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠉⠉⠉⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⣀⣀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠲⢅⠀⠙⠢⡀⠀⠀⢀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣄⠈⠑⢦⡀⠈⠲⣄⢁⡤⢤⠀⠀⠻⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⢸⡄⠈⠓⢄⡀⠙⠂⠀⠈⢿⠀⡏⠀⢠⡶⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡟⠦⣄⠀⠉⠀⠈⠀⠀⠀⠀⡇⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⡼⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⢹⣦⡈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡇⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠡⣤⣤⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠳⣄⠀⠀⠀⠀⠀⠀⢿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⢀⡠⠔⢒⣉⣀⢀⣀⣀⢀⣀⠤⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⠀⠀⢘⠷⡄⠀⠈⠉⠛⠛⡿⣿⣿⣿⣶⡄
⠀⠀⠉⢢⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⠤⠚⠁⠀⢹⠀⠀⠀⡰⠋⠀⠈⢻⣿⣿⡇
⠀⠀⢀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡯⠞⠊⠁⠀⠀⠀⠀⠈⡇⢀⠎⠀⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠙⣄⢣⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⠀⢀⣀⡀⠀⠘⠇
⠀⠀⠀⠀⠈⢆⡇⠀⠀⢀⠴⠒⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣶⠿⠛⠓⠒
⠀⠀⠀⠀⠀⠘⡇⡠⠞⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⢆⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣰⠞⢩⣿⡛⢿⡷⣦
⠀⠀⢠⣏⣰⣿⣿⣿⣶⣿⡟⣷⣄
⠀⠀⢀⣟⣹⣯⡼⢻⣿⢻⣧⣿⢹
⠀⠀⢸⡟⢿⣟⣿⢿⣿⣾⣿⣷⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠈⢷⡈⠻⢭⣽⣿⡿⠿⠿⠃⠀⠀⠀⣀⡴⠞⠋⠁⢀⣀⣤⣤⠀⣀⠀⣉⡙⠳⣤
⠀⠀⠀⠀⠉⠛⠛⠹⣇⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⣶⡿⠿⠛⠉⠉⢠⢚⣼⡿⡑⠄⣤⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⡾⠁⣀⣰⣿⠟⡁⢅⠂⡥⠌⣠⣴⠿⠋⢂⢃⣼⣿⣦⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⢤⣾⢟⡠⡔⢁⣐⣬⣶⡿⠛⢁⠌⠒⣡⣾⡟⠀⡙⣿⣤⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣱⡿⠃⣪⣴⡾⢟⡛⢉⠑⠐⠎⣣⣬⡾⠋⠀⠻⣶⣔⠈⢿⣦⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠸⠟⣠⡿⢋⡁⢒⣠⣤⣶⠶⠶⠟⠋⠁⠀⠀⠀⠀⠈⢻⣮⠘⢿⣆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣌⢇⣾⢟⡔⣢⡷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢲⡀⢀⡀⠀⢻⣯⠸⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⣼⡏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⢻⡇⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣹⣟⣼⠋⠀⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤⠀⠀⠘⣿⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⣿⠁⠀⠀⢿⡀⠀⣿⠀⠀⠀⣠⠄⠀⠀⠘⣇⠀⢠⡟⠀⠀⠀⣿⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣿⠀⠀⠀⠈⠛⠛⠁⠀⠠⣾⣁⠀⠀⠀⠀⡈⠛⠋⠀⠀⠀⠀⢿⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠈⠁⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⣾⣿⣭⣙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⡇⠀⠀⢠⡾⠛⠙⠓⣦⠀⠀⠀⡗⠀⠀⠀⢠⣿⠐⡩⡻⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⡻⢷⠶⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁⠈⠛⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠛⠛⠛⡛⣛⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⣍⠙⠛⠁⠀⠈⠋⢋⣽⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⣤⡀⠀⠀⠀⡾⠀⠊⠀⠙⠷⣦⣀⣀⣠⣾⠛⠁⠈⣠⠈⣷⠀⠀⠀⣠⡴⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣬⠿⠛⠀⠀⢹⡆⠀⢀⡇⢨⣄⠀⠀⠀⣿⠉⠉⠈⣿⠀⠀⠀⣠⡀⢹⡄⠀⢰⡃⠀⠀⠛⠻⣯⣀
⠀⠀⠀⠀⢠⡾⠋⢀⣠⣤⢶⡞⢛⢿⡄⢸⡇⢸⡏⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢿⡇⢸⡇⢠⣿⡛⢲⡶⢦⣄⡀⠙⢶⡀
⠀⠀⠀⠀⠻⠴⠞⠋⠁⠀⠀⢿⡀⠊⣿⡄⡇⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⣇⣾⠣⠀⡾⠀⠀⠈⠙⠛⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠜⣿⡇⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢺⡇⢸⣿⠫⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠃⠘⣷⣸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣾⣧⣾⢃⠇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⠀⠽⠛⠿⠄⠀⠐⢿⠀⠀⠀⡿⠀⠀⠂⠿⠛⠋⠐⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠉⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⡈⠛⢿⣷⣶⣤⡀⠀⢀⣀⣤⣶⣿⠿⠋⠁⠀⠀⠈⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠌⠀⠀⠀⠈⠛⠿⠟⠀⠈⢿⡿⠋⡁⠀⠀⠀⠀⢂⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠤⠀⢿⣿⡇⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢸⠀⠈⠠⠆⠀⠀⠀⢸⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠨⡀⠀⣀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡰⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠎⠀⢸⣿⣿⠋⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠀⠒⠂⠈⠑⠤⠀⠔⠀⠁⠒⠀⠐⠊⠁⠀⠀⠀⠀⢠⠤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⡰⠊⣁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠈⠐⢄⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡜⠘⠁⠀⠀⠉⠂⢀⡀⠀⠐⠂⠀⡂⠀⢀⠀⢂⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠐⠀⠀⠀⠣⢀⠀⠀⡀⠀⠂⠠⡁⠀⠈⠀⡘⠀⣠⠖⠁
⠀⠀⠀⠀⠀⣠⠤⣄⢀⠀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠐⠂⠒⠁⠀⡄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⡜⠁⠀⠈⠀⠀⣈⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢀⠄⠰⠏⠀⠀⠙⢆
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠉⠒⠤⠤⣤⣄⡀⠤⠤⠤⠒⠈⠈⠁⠀⠀⠈⠒⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣷⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⠀⠿⠿⠿⠿⠿⠈⠿⠿⠿⠿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⣤⠄⠀⠀⠀⠙⠉⠉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⣉⣙⠻⢿⠀⠀⠀⠐⠒⣶⠖⢄⠀⠀⠆⢀⠤⣶⡖⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⠄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⣀⣀⣀⠤⠊

⣴⣶⣶⠆
⣿⡿⢡⡀⠣⠀⠘
⠟⠁⠀⠄⠁⠀⠺
⠀⠀⢄⠀⢠⡀⢰⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⡀
⠀⠀⢘⢀⠸⡀⢸⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠙⠄
⠀⢂⢈⠰⠈⡅⢸⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠓
⢀⢀⠘⠀⠈⣃⠐⡇⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⢌⠘⠀⡐⢃⠀⡇⠰⠆
⢀⠌⢸⠀⡃⡡⠀⡇⠰⠆
⠈⣠⠒⡀⡇⢡⠀⡇⠠⠄
⢈⢸⠀⡁⠇⡡⠀⡇⣀
⠈⣤⢰⠁⡆⡁⠀⣧⣤⡇
⠸⢇⢠⠃⡅⡃⠀⡏⢉⡇
⠰⠎⢠⠂⡃⣡⢀⡇⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⢰⡌⢠⠀⡇⡱⠀⡇⡀⣿⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⣀⣀⡀
⠈⠃⢨⠀⡧⠴⢠⡇⡇⣿⠀⣧⠲⠀⠀⠀⠀⠀⠺⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠚⠋⠉⠉⠁⠀⠀⠀⠙⠛⠛⡉⠉
⢀⠀⣀⠂⡧⠔⢸⡇⡇⣿⡇⢹⠈⠓⣂⠀⣠⠞⢀⠔⢀⠀⠀⠀⣀⠤⠒⠊⠉
⠘⠐⠁⠆⡇⡄⢸⡇⡇⣿⣇⠘⠈⣉⣴⠟⢁⣴⠁⠆⣀⡤⠖⠉⠁
⠰⠩⠇⠀⠂⡖⠸⡇⡇⢿⣿⣶⣿⠟⢁⣴⣟⣿⠖⠋⠁⠀⡀
⠠⣒⠄⠀⠀⠋⠀⡇⡇⢸⠿⠋⢱⣴⣣⠜⠋⠀⠀⢀⠠⠤⣥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠖⢶⣶⠀⡇⣇⠠⣠⣞⡥⠋⠀⠀⠀⠄⢒⣈⣩⠤⠤⠤⣤⣍⣀⡀⠀⠀⢀⣠⠤⠸⠟
⢠⡰⠀⢰⣾⠿⢇⣧⢴⣎⡼⠋⠀⢀⣠⡤⠖⠚⣿⣿⠁⠀⢀⣴⣿⡿⠋⣉⣵⣾⡉⢠⢲⣆⠰⣶
⢀⢻⣦⣤⣤⠶⠛⣇⡼⠋⣀⡤⠟⠋⠁⠀⠄⡅⣿⡟⠀⢠⣿⠟⢁⣠⣞⢯⡷⠟⢛⠣⠙⣯⡆⣿⠀⣤
⠈⠚⢋⡉⣠⡿⣠⣟⢠⢞⣫⡥⢼⣥⣄⣀⠀⠀⢹⡇⢰⡿⢃⣴⢿⣹⡾⠋⡴⠞⠻⣷⠀⢸⡇⣿⠀⠁
⢰⢂⡟⣱⡟⡵⣣⢿⡄⠽⠶⠒⠒⠲⢤⣌⡑⢧⡈⣷⠟⣠⡾⣍⡶⠋⠀⠀⠀⠀⢠⡟⠀⢸⣧⡏
⠀⣸⢱⡟⡼⣱⡏⣸⡇⠼⣥⣶⡈⢳⣅⣀⣈⣓⣂⡈⠚⢻⣿⠏⠀⠀⠀⠀⠀⢀⡾⢁⢀⣾⠟
⢠⢝⡟⢼⠁⠉⠁⣿⡇⢀⣄⢀⣱⣌⢤⣭⣉⣉⣉⠙⠸⠇⠉⠀⠀⠀⠀⣀⡔⣫⠔⢣⡼⠃
⠐⢸⣇⡆⢈⢆⠀⣿⠁⠀⡈⢨⣿⡉⠀⠀⠀⠉⠉⠙⠛⠀⠀⣆⠄⠀⠀⠆⠁⡄⠘⠉
⣿⠈⡇⣃⠈⠂⠀⢾⠶⡦⣉⢸⡿⠈⠃⠂⠀⠀⣘⣉⠴⡱⣺⢻⠀⠀⠀⠠⡆⡠⠀⠈
⣿⡀⠀⠈⢀⠀⣥⣬⡄⠘⢋⡠⣍⡥⣾⠷⣀⠂⠀⠒⠊⠐⠁⢁⠠⢀⣠⡄⡇⢓⠁⣤⠀⣦⡀
⡻⡇⣤⡀⠀⠀⢸⣿⢱⡤⠈⠁⠦⠄⠁⠚⠛⣀⠘⡟⡃⠀⢀⣠⣶⣿⣿⡇⣧⠸⠀⣿⣷⡌⠁
⢻⡇⠿⡷⠀⣀⠀⢿⠀⠀⠐⣣⠖⣁⣀⣦⣤⣤⣴⣧⣷⣤⣠⣅⣩⣍⡽⠴⣿⣶⠶⠖⣖⣶⠖⠶⠶⠖⠤⠴⠦⠤⠤⠀⠶⠄
⠁⠭⠥⠨⠤⠽⠧⠤⠤⠒⠀⠁⠀⠀⠶⠀⠀⠶⠈⡿⠃⠐⠒⠒⠒⠂⠘⠀⣿⢙⠙⠀⠁⠐⠶⠶⠔⠦⠸⠆⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣤⣤⣴⣶⣶⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣆⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⢀⡀⠄⠀⠈⠉⠙⠛⠛⠛⠿⠹⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠐⠁⢀⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⠐⠁⠀⠄⠀⠀⣠⠎⠀⣀⣀⣀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡿⠁⠀⠀⢀⠄⠀⠀⠔⠈⡹⠿⠿⠛⠋⠉⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⠀⠀⠀⢀⠂⠀⡀⠁⢀⠔⠁⠀⡀⠀⠀⠀⠸⣿⡛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠀⠀⠀⠀⠀⠀⠘⠀⢀⠊⠀⠀⠀⠈⠉⠀⠀⠀⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠠⠀⠀⠀⠀⠀⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⣠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⡴⣇⠀⠀⠀⠀⠀⠀⣀⠜⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠁⠁⠀⠀⠈⠁⠀⠀⢸⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢰⠣⢀⣀⢀⡀⠀⠀⠀⢀⣀⡠⠴⠊⠁⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠈⠈⡏⠀⠀⠐⠉⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠲⠤⢤⣀⠃⠐⢀⠃⠈⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⠏⠀⢠⠟⢳⡶⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣀⣏⠐⠋⢀⣤⠞⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠀⠀⠀⣀⣤⠶⠚⠛⠛⠉⠉⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⠈⠛⣷⡀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠟⠁⢀⣴⣋⣡⡴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠁⠠⠾⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡿⠁⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢹⣷⣄
⠀⠀⠀⠀⣠⡴⠟⠉⠘⢧⣠⣴⣯⣴⠶⠚⠛⠛⠛⠛⠛⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣦⡀⢸⣇⠘⢷⡄
⠀⠀⢀⣼⠏⠀⠀⠀⣠⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⠀⠀⠀⢰⣷⡀⢀⣶⠀⢿⡿⠟⠻⣧⡈⢿⡄
⠀⠀⣾⠃⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠻⣇⣸⠟⢷⣾⠃⠀⠀⠘⣷⡀⢻⡄
⠀⣼⠇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⣤⡤⠞⠁⣴⠿⠃⠀⠈⠁⠀⠀⠀⠀⠘⣧⠀⢷⡀
⠀⣿⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣇
⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⠶⢶⡆⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿
⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⣠⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⢿⣤⣿⡄
⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠛⠉⣠⡤⢤⣉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⣼⡿⠃⢀⡼⠋⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⢹⡿⣦⡀
⠀⢹⡇⠀⢀⣼⠏⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⠷⣄⠈⠛⢷⣄⠀⠀⠀⣸⡟⠁⣴⢟⣀⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧
⠀⣈⣿⣴⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣴⣦⡌⠻⣦⡀⠁⠀⠀⠀⠈⢠⡞⢱⣿⣿⣿⣄⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏
⣼⠏⢸⡅⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⣴⣿⣿⣶⣦⡀⢠⡄⠀⠀⠀⠀⠘⢧⠘⢿⣶⣿⡽⠀⣀⣠⣴⡿⠶⠛⠃⠀⠀⠀⢸⣿⠈
⣿⡀⠘⣧⠀⠀⠀⠀⠀⣀⠀⢻⡄⠀⠀⠀⠘⠿⢿⠿⠛⠀⣼⠁⠀⠀⠀⠀⠀⠀⠛⢦⡽⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠘⢷⣀⣻⡆⠀⠀⠀⠈⠉⠛⠚⠛⠛⠛⠛⠓⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠙⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠋⠉⠉⠉⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⡀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠠⠤⣤⣴⡀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⣿⣏⠀⠀⠀⠀⣤⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠉⠛⠻⣿⠶⠶⠶⠶⠶⣶⣿⡿⠿⠋⠁⠀⠀⢸⡟⣧⡀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⣀⣠⣄⢀⡀⠀⠀⠀⠘⣷⣸⣇⠀⠰⠾⠛⠉⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠙⢶⣤⣶⣬⣿⣿⠿⠽⠆⠀⣠⠞⠉⠉⣿⣤⣤⣤⣤⡟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠿⠿⠆⠾⠋⠀⠀⠀⢀⣀⣀⣀⣀⣿⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⠶⢶⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣈⣉⣙⣛⣿⣿⣿⣿⣿⣿⣷⠶⠶⠶⠶⠟⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠛⠛⠛⠋⠉⠉⠉⠉⢉⣽⠟⠋⠙⠉⠁⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⣿⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠶⠶⠶⠤⣾⣇⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⡴⠟⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⠷⢶⠶⠟⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣶⠶⣦⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⢻⣦⣤⣤⣴⡴⠶⢶⡶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠾⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠷⣤⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⢀⡴⢒⣶⠶⣶⢦⡀
⠀⠀⠀⠀⠀⣾⣠⣿⣿⣿⣼⣿⢳⣦
⠀⠀⠀⠀⠀⣿⣹⣯⣞⣿⡟⣿⣸⢻⠆
⠀⠀⠀⠀⠀⣏⢻⣯⣟⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢦⣝⣳⣾⠟⠛⠛⠁⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⢀⡴⠋⢀⣠⣴⠶⠿⠶⢶⣤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⣴⠟⠉⢀⣀⣤⣄⣀⠈⠻⣦⡈⠑⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⡀⣀⡴⠃⠀⠈⠁⣠⡾⠛⠉⠉⠉⠉⠻⣶⡘⠃⢀⣤⣤⣀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⡉⠉⠀⠀⠀⠀⣴⠟⠀⠀⣠⣶⣶⣶⣤⡈⠛⠀⠈⠉⠈⠙⣷⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⢶⣤⣤⣤⡾⠋⠀⠀⣰⠿⢦⣍⠳⡌⠻⠄⠶⠶⠶⣄⠀⢹⡇⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⣀⠈⠉⠀⠀⠀⢀⣼⠋⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠘⣧⠈⢿⡀⣧⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠃⢨⡟⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞⠀⢸⣆⡈⠳⠦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⠀⠘⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡼⠛⣿⠀⠀⠈⣇⠀⣸⠁⠀⢀⡴⠀⠀⠀⠸⡀⢀⡾⠀⠀⠀⣿⠛⢷⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣤⣿⠀⠀⠀⠈⠉⢁⣀⠀⠛⠶⠀⠀⠀⣀⡉⠉⠀⠀⠀⠀⣿⣤⡼⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⡀⠀⠀⠀⣰⠋⠁⠀⢀⣀⣀⡀⠀⠈⠙⢷⠀⠀⠀⢀⣿⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⡄⠀⠀⠘⠀⠀⠰⠏⠁⠀⠙⠦⠀⠀⠘⠀⠀⢀⡾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⣶⡶⢶⣶⡖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⠾⠏⠉⠉⠉⠽⠒⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⡞⠁⢀⠹⣧⡀⠀⠀⠀⣠⡾⠁⠆⠙⣧⠀⠀⠀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣽⠷⠂⠀⠙⣆⠀⢸⡇⣠⡥⠠⠌⠛⠛⠾⠛⠋⠐⡄⢠⡁⢹⠀⠀⣾⠁⠀⠐⠿⣯⡀
⠀⠀⠀⠀⢠⠞⠉⣀⣤⠶⣾⠛⢻⣆⢸⡇⣿⠁⢣⡄⠀⠀⠀⠀⠀⠀⢈⢸⡇⢸⡆⣰⡟⠛⡶⠶⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠘⣆⠀⢻⣼⡇⣿⡄⡆⡁⠀⠀⠀⠀⠀⠀⠈⢸⡇⢸⣷⡟⠀⣸⠃⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⢿⡇⢿⡇⢁⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⡐⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⠌⢿⢼⡇⢈⠀⣀⠀⣂⡒⠂⠀⢂⣸⣷⡟⠐⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢦⠤⠽⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠿⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠢⣀⡛⣄⠀⣀⠸⡓⠀⠀⡠⠔⠒⠃⠀⠀⠀⠀⢠⡤⠒⠋⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠾⠱⣿⡄⠀⠧⢤⣈⠀⠀⠀⠀⠐⠺⣜⣠⠤⠖⠛⠒⠛⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⡤⠔⠊⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣒⠿⠛⠉⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠠⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠈⡙⢲⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⡙⠁⠘⡆⠈⢶⢤⣀⠀⠰⡶⢄⠀⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢦⠀⢸⡀⠀⠇⠀⠘⣆⠈⠉⠐⠛⠈⢺⠥⠤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⠀⠀⠃⠀⠈⠀⠀⠘⠆⠀⠀⠀⣰⡃⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡧⠤⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢾⣿⡀⢿⠿⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⣖⡀⠛⢁⡀⠳⡄⠰⠒⣻⠁⠀⠀⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣇⣠⣅⠀⢠⠇⠀⠀⠀⠀⠈⠒⡛⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠦⣀⠀⠀⠈⢑⣿⠉⠬⠤⠞⠢⠄⠀⠀⠀⠀⠘⢅⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠛⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢅⣂⣩⣭⣍⠉⠛⠛⠲⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡴⢋⠇
⠀⠀⠀⠀⠀⠀⢰⣆⢄⡀⠀⠀⠀⠀⣰⠃⠚⠭⠗⢒⡂⠀⠀⠀⢀⣄⠀⠄⠀⠀⠀⣹⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⠀⣿⠀⠀⠈⠭⠵⠆⠀⠀⠀⠈⠙⣷⡄⠒⣠⠞⢛
⠀⢶⣒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠁⠀⠁⣤⡘
⠀⠀⠉⠉⠉⠙⠓⠲⠀⠀⠀⠀⠀⠀⣇⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡇⠀⠀⠀⠀⠔⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡤⠤⠂⠀⠀⠀⠀⣠⠔⠂⠁⠙⠤⠤⠔⢧⠀⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢰⠕⠂⠈⠁⠘⢐⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⠈⠠⠄⠴⢄⠂⠈⠀⢀⡞⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠈⠑⠀⠄⣀⠀⠀⠀⢀⠠⠔⢋⠀⠀⠀⠀⠓⡒⠠⠶⠐⠦⢤⣀⢀⠴⠚⠫⠉⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠙⣧⠀⠀⢠⠏⠀⠀⠀⢀⡤⠥⠀⠀⠀⠀⠀⠀⡍⠀⠀⢀⣏⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠒⠁⠀⠀⣙⠤⠤⠤⠤⠔⠛⠃⠀⠀⠀⢀⣀⣠⠋⢂⠀⠀⠀⠀⠀⠀⢀⠙⡦⠐⠯⠤⠤⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠐⠁⠠⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠉⠉⠀⠦⠗⠲⠤⠴⠶⠛⠉⠉⠓⠦⠴⠖⢊⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡀⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡤⠟⠓⠓⠤⠴⠴⠖⠚⠉⣁⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣗⠀⢀⡀⡀⣠⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⢠⡤⢤⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠘⢲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠆⢠
⠀⠀⠀⠀⠀⠀⢸⡄⢿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢤⡴⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠘⣧⠈⡟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠛⣋⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠁⢠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢤⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡇⢰⠋⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⣼⠀⠘⠄⠀⠀⡀⠄⠒⠚⠉⠉⠉⠁⠀⠈⠉⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠡⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡴⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠲⠶⠶⠶⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠀⠀⢀⡴⠚⠛⠓⢦⣄⢀⣠⡤⠖⠚⠛⠛⠛⠶⣄⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠀⣴⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠙⠳⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⢀⣴⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣇⠀⠀⣠⠶⠒⢶⠖⢶⠖⠶⢶⠖⢚⣛⣫⣭⣤⣤⣤⣤⣤⣤⠴⠶⠛⠁⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣀⠻⢤⣤⣼⣤⣼⠧⠶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⢀⣠⣴⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣩⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⡿⠿⠶⣤⣀
⠀⠐⠚⠉⠉⠉⣿⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⣤⡄⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⡿⠿⠛⠋⠉⢹⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣾⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠘⠧⠴⠿⠋⠀⠈⠉⠙⢻⡏⢿⡋⠉⠹⣇⣀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⢻⡏⠉⠉⠀⠀⠀⠀⢸⡏⠉⠉⠙⠓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠛⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡍⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⣤⣤⠿⠤⠴⠶⣶⠶⠶⠾⠷⠶⠒⠒⠒⣶⠟⠛⠛⠛⠋⠉⠉⣹⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢰⣿⠹⣦⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣀⠀⢰⡿
⠀⠀⠀⠀⣆⠀⠘⣿⠀⠈⢷⣄⣀⣤⠴⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠲⠦⠤
⠀⠀⠀⠀⢻⡄⠀⠙⠳⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠙⠶⢤⣤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠩⠿⣁⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣎⠒⠶⢤⠘⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡨⢠⠈⢀⡰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⠁⠀⠈⠑⠢⢤⣠⡏⠀⠀⠁⠃⠀⠨⠓⢄
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢴⡾⡋⠢⠤⠄⠀⠀⢀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⢀⣠⠖⠋⠁⣀⠐⢱⠀⠀⠴⠆⠑⠂⢄⡀⠀⠈⡌⠀⠀⠀⠀⠀⠀⠜⢀⡀⠀⠑⡀
⠀⠈⢻⣄⠀⠘⠄⠸⠃⠈⠢⡀⡀⢀⠤⡪⠀⣈⡴⢻⠁⠀⠀⠀⠀⠀⠘⠀⠀⠑⠀⠀⠈⠠⡀
⠀⠀⢸⠈⠓⢤⡀⠀⡀⠈⢆⣀⠍⠓⣨⠴⠚⠓⠂⠣⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢄⡠⠣⡀
⠀⠀⢸⠀⠀⠀⠙⠢⡉⠀⢀⣠⠖⠋⠁⠀⢀⠴⠋⠀⠀⠉⠓⠂⢀⡴⡀⠀⠀⠀⠀⠀⠀⢑⡢⡈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⢹⠚⠉⡇⠀⠀⢺⠚⠁⠀⠀⠀⢀⣠⠔⠚⢁⣀⡜⠀⠀⠀⠀⠀⠀⠐⠠⠬⡀
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⢖⠈⣿⠀⠉⠉⣏⢸⡇⠀⠀⠀⠀⠀⠈⠒⠤⠥⠃
⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⡜⢆⠀⠀⠈⡄⣿⠀⠀⠀⡿⠈⡇⠀⠀⠀⢠⣶⣻⣛⡏⣻⢙⣓⡄
⠀⠀⠈⠳⡄⠀⠀⠀⢸⠀⠀⣿⠀⠀⡇⠈⢆⠀⠀⠸⡇⠀⠀⠀⡇⠀⣷⠀⠀⠀⠈⣿⣟⣏⣹⣉⣯⣿
⠀⠀⠀⠀⠙⢦⠀⠀⢸⠤⠒⠋⠉⢹⠀⠀⠈⢧⠀⠀⢣⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡀⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⣄⢸⠖⠒⠋⠉⠁⠀⠀⠀⠈⢧⣀⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣾⣆⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣰⣷⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠾⠇⠙⠃⠙⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠋⠘⠋⠸⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠈⠳⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠞⠁⠀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠀⢀⣀⣀⠈⠀⢀⣴⠶⠞⠳⠶⣦⡀⠀⠁⣀⣀⡀⠀⠨⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠉⠀⣴⠏⠀⠀⠀⠀⠀⠀⠹⣦⠀⠉⠻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠆⢸⡇⠀⣀⣀⡀⢀⣀⣀⠀⢸⡇⠰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢻⡾⠋⠉⢻⡟⠉⠙⢷⡟⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠟⠁⠀⢀⣼⣧⡀⠀⠈⠻⣦⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠁⠀⠀⣠⡞⠁⠈⢳⣄⠀⠀⠈⢷⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠼⠋⠀⠀⢀⡾⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣧⣤⣤⣤⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣼⣧⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠈⠙⠛⠀⠀⠀⠐⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡔⡉⠉⠉⢢⡀⠔⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⣔⠀⠂⠀⠀⠿⢹⢠⡆⠀⢀⡃⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠊⠈⠢⡉⠀⠀⠠⠠⠚⠁⣄⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠔⡁⠄⠀⢌⠢⡀⠀⠀⠀⠀⣀⣀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⡄⠀⠀⠀⠠⢡⡆⠀⡍⠒⠀⣀⠀⠄⢊⢀⣠⢠⠄⣷⡀⠀⠀⠀⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠆⣸⡗⠒⢃⠐⠂⣒⠰⠂⢸⠉⠸⡖⠂⡙⢷⠀⠱⡀⠀⠀⢀⣀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣄⣠⣤⡀⠀⠀⠀⠘⠀⢹⡏⣠⢸⠰⠶⠘⡠⠚⠛⠈⠁⠁⠈⠁⠈⡇⠀⡇⠀⠀⠈⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠰⡀⠈⠣⡀⠘⠀⡠⠞⠀⠀⠀⠀⠀⠈⠐⠀⠐⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠲⠤⢤⣈⣁⡀⠀⠀⠀⠀⢀⡀⠤⠔⠊⠀⠀⠀⠀⠀⠰⡷⢤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠷⠚⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠻⣉⠉⠀⠀⠀⠀⠀⡀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢉⠃⠀⢁⡀⠀⠀⠀⠀⢀⡀⢈⠄⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢅⡀⠐⠄⢐⡲⠀⢈⠀⠀⠀⠀⠀⠽⠀⠤⠐⠀⣩⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢈⠆⠘⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣶⡄⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⣐⠸⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠒⠀⠀⠈⠉⠀⠂⠂⠀⠀⠀⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠞⠛⠛⠛⠛⠳⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠁⣸⠖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢸⠀⡟⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⢸⠀⡇⠀⢀⡟⢳⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣿⠘⠀⠀⠇⠀⢸⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟⠀⠀⠀⠀⠀⠀⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠲⢄⠀⠀⠀⠀⠀⣰⢿⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣸⠃⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⣤⠞⠋⢀⡼⠃⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣤⣾⣧⣤⣤⡶⢞⣋⣁⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠇⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠀⠀⣀⣤⡴⠶⠞⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠳⣦⣤⣤⣤⣤⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⢀⡾⠛⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣸⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠓⠶⣼⢷⡀⠀⠀⠀⠀⠀⢠⠷⠤⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢰⠇⠀⠙⠦⣄⡀⠀⣰⠋⠀⠀⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡾⠀⠀⠀⣀⣤⠤⣶⠃⠀⠀⠀⣼⡽⠟⠉⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣼⠃⢀⡴⡟⠁⠀⣰⠃⠀⠀⠀⣰⠏⠀⠀⢀⡴⠞⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣰⣣⠶⠋⢸⡇⠀⣰⠇⠀⠀⠀⢠⠏⠀⢀⡴⠋⠀⠀⠀⠀⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢠⠟⠁⠀⠀⢸⡇⢠⡏⠀⠀⠀⢀⡟⢀⡴⠋⠀⠀⠀⠀⠀⣴⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠠⠟⠀⠀⠀⠀⣸⣇⡞⠀⠀⠀⢀⣾⡴⠋⠀⠀⠀⠀⢀⣠⠞⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣿⠃⠀⠀⠀⡼⠉⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣿⠀⠀⠀⠼⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣍⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡆⠀⢬⣁⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢰⢁⣀⡢⣰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠨⠔⢇⠸⡷⢩⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄⡘⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⢀⡎⠀⠀⠴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠜⠓⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⢒⠎⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁⢒⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁⡜⡀⠀⢀⠊⢉⠦⡀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠲⠊⠊
⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⢀⠞⠀⠀⠀⡀⠀⠗⠢⡈⢢⡀⠀⠈⠢⣀⡴⡑⠀⠀⢀⡌⡰⠁
⠀⠀⠀⢀⠃⠀⠀⠀⢀⡤⠂⠀⠀⠈⠒⠁⠈⠀⠀⠈⢊⢿⣄⠀⠀⠈⢢⡇⢢⣀⠞⡟⠁
⠀⠀⠀⠀⠓⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⡉⠫⠿⣦⠀⠀⠀⠁⠸⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠒⠤⠼⠀⠀⠐⠀⡆⠀⠀⠀⠙⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢠⠃⢰⠁⠀⠀⠀⠀⠀⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡰⠃⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠚⣤⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡝⣿⠢⡍⢡⠔⠀⠀⠀⠀⠀⠀⢀⠜⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠱⡎⢹⣺⠟⠁⢙⣟⢄⢃⠀⠃⠀⠀⠀⠀⠀⡠⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠚⠤⠇⡇⠎⡇⠀⠀⠈⠀⠙⣿⣶⠆⠀⠀⢀⡠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡊⣬⠶⠳⠋⠀⠀⠀⠀⢄⡀⢀⠍⠑⠒⠘⣇⡔⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠦⢄⣀⠌⠹⠀⡈⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠶⠟⠒⠊⠉⠴⠌⠙⠛⠛⠉