Bribery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣶⠒⠒⠒⠒⠲⠶⠶⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠉⠉⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢀⣸⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣠⠴⠚⠉⣿⢠⣿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢿⡇⠀⠀⠀⣽⢿⠃⢀⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠘⣿⡄⢤⣴⠃⠈⠛⣻⠃⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠘⣿⡈⠁⠀⠀⣼⣫⡿⠦⣄⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⣷⡀⠀⣾⠁⠀⠀⠀⠈⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠹⣷⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⡾⠁⠀⠙⠦⣄⠀⠀⢀⣠⠴⠚⠁⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠳⢶⡏⠁⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣾⣧⣤⣤⣄⣀⣀⣀⣤⣤⣤⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⣻⣧⠶⠟⠁⢀⡴⢛⠲⣤⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣬⣾⠁⣰⠚⠛⠉⠸⠿⣶⡆⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢠⣿⣽⢟⣡⠞⠁⠀⠀⠀⠀⠀⠋⠁⢰⠇⠀⡴⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠊⠉⠀⠈⣄⡿⢟⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠓⠃⢠⣴⣶⢋⣴⣟⣡⣤⡆⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠄⢰⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⠄⠀⢸⣿⠉⠙⣶⣿⣧⡀⠁⠀⠀⠀⠀⠀⢠⢞⡅⠀⠀⠈
⠀⠀⠀⠀⠘⠙⣿⣿⣶⣶⣶⣤⣤⣤⣀⣀⣤⣤⠾⠋⠀⠀⡇⢸⠄⣸⡇⠀⠀⠀⠉⠙⠻⠾⣿⣿⣦⢀⡴⣣⢾
⠀⠀⠀⠀⠀⠈⡿⠻⠛⠋⠙⠛⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⢧⣴⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡝⠻⢼⣇⣸⢠⣶⣆⢀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀⣘⡟⡿⠁⠀⠈⣹⣻⢻⣯⣼⡄⣄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠙⠻⢶⠤⠀⠻⠟⣿⣀⣠⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠐⠛⠻⠶⣦⣄⣀⣀⣀⡸⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢸⣿⠀⠀⣀⡀⢠⣿⠀⠀⣠⣤⣤⣴⣋⠉⢻⡟⠃⠉⢹⡇⠀⠦⣤⣀⣀⠀⠀⠀⠉⡏⠉
⢀⣀⣶⣀⣼⣿⣦⣼⣿⣿⣿⣿⠋⣻⠋⢀⣿⡿⠁⠀⣿⠁⠀⠀⣾⠛⢳⡆⠀⠈⠉⢻⡗⠂⠈
⢿⣿⡿⢿⣿⠿⠛⠛⠛⠛⠛⠁⠀⠓⠎⠛⠉⠣⠽⠕⡇⠀⠀⣰⠃⠀⣰⠛⠶⠦⠄⠜⠁
⠁⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠛⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣶⡄⠀⠙⢷⣄⠀⠀⠀⠀⢀⣠⣶⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣝⢷⣤⡄⣴⣾⢿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⠻⠿⣿⡿⣿⣿⣷⣝⢿⣜⣿⡯⠿⠟⠙⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠛⣯⣿⣿⡿⣇⡙⢿⣦⡀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠛⠿⠛⠎⠃⠀⠙⢿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⠀⠀⠀⠀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⣂⣂⣓⣒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠶⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠏⢄⠀⠑⢌⠢⡀⠀⠀⠀⠀⢀⡔⠊⠁⠙⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢸⠀⡰⢷⠦⠄⠓⢌⠢⣄⡠⢾⡱⠘⡄⠀⠀⡇⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢘⣐⠁⠌⠀⢀⡤⠊⠑⢌⠳⣄⠱⡀⠈⣆⡠⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⡄⠉⠑⣖⣁⠄⡀⠀⣠⡗⢌⡳⣝⠉⠀⢠⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠈⠑⢮⡔⢰⣳⡼⠚⠑⢮⡓⠤⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢍⣐⣒⣒⣂⡩⠄⠚⠁

⠀⠀⠀⠀⢀⢀⢀⣀⠀⡀⡀⣀⡀⡀⢀⢀⣀⢀⡀⡀⢀⣀⢀
⠀⠀⠀⠀⠣⠤⠸⠤⠃⠓⠇⠗⠇⠧⠼⠸⠊⠀⠇⠇⠣⠜⠺⠹


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⣤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⡦⠘⣿⣹⡇⠠⡆⠀⠀⠀⠘⠿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⣼⣆⠸⠽⢂⣾⡄⠀⠀⠀⠀⠉⠉⠉⢍⠉⠉⠁
⠀⠀⠀⠀⢰⣧⣲⣿⣿⣷⣤⣷⠀⠀⠀⠀⠀⣃⠀⢤⣀⡁⠀⠀⠀⠀⠀⢿⡏⠉⠈⠉⣿⠇⠀⠀⠀⠀⠠⢤⠄⡄⢤⠠⡀
⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠈⠛⠛⠻⡋⠒⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⡇⠀⠀⠀⢰⣥⣬⣤⣧⣬⣧⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠈⠈⠁⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣠⠞⠀⠀⠀⢂⢰⣧⣲⢒⡠⣷⢰⠆⠀⠀⠰⠷⠆⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠸⠿⢳⠺⠆⢰⠿⠿⠀⠀⠀⠀⠀⠀⠀⠙⠀⢦⣦⠀⠀⠀⠀⠿⠁⠀⠀⠘⠀⠹
⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢲⡶⣒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⢀⣦⣤⣤⠀⠀⠀⠀⠂⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⣈⠀⠀⡇⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⣿⣷⠞⠋⠉⠿⠋⠀⠀⠀⣰⠚⠃⡀⢶⣿⣆⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠃⠀⢀⣀⠠⠀⠂
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀⠀⠀⠘⢦⡴⠃⠙⡻⣟⣷⠀⠀⠀⠀⡂⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⣄⣨⣯⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠁⠈⠁⠀⠀⠀⠀⠂⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⡄⠠⠤⣀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦
⠀⠀⠀⠀⣀⣀⣠⣰⠀⣽⣀⣀⠀⠀⠀⠀⠀⠃⠀⢄⠀⡅⠀⠀⠀⠀⠀⠀⠀⡟⠆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠈
⠀⠀⠀⠀⠛⠛⠛⡛⠀⠉⠙⠛⠀⠀⠀⠀⣤⣶⡦⡤⣶⣧⡀⠀⠀⠀⠀⢀⣠⡜⣼⣤⣀⠀⠀⠀⠀⠀⢀⣠⡜⣜⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠾⠿⠿⢿⠀⠀⠀⢀⣿⣿⣧⣤⣿⣿⣇⠀⠀⠀⠀⣿⣿⣧⣧⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢲⡿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠖⠁⠉⠀⡜⠁
⠀⠐⠀⡀⠀⠀⠀⠀⣀⠄⢀⡀⠀⠀⠊⠁⠠⢺⡀⠚
⠀⠀⠈⠀⠀⠀⢀⣼⠅⣰⣂⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠈⠀⠀⠀⣼⡓⢠⣋⡥⣦⠄⠐⢍⠀⠀⠞⠀⡜⠉⠒⠀⣄⡀⡀
⠀⠀⠀⠀⡀⢰⣟⢡⢸⣶⡶⠒⠋⠀⠀⠀⠀⠀⡜⠀⠀⠐⠂⠈⠉⣉⠁⠀⠒⠢⣤⠄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⢸⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠷⣤⣤⣤⣄⣉⣀⣀⣡⣤⣤⣄⣤⣤⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠇⠉⠀⠀⠀⠀⠀⠀⣠⣀⣷⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⡿⢻⠻⠖⡖⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠀⠈⠁⠀⠐⠀⠠⠤⢤⡀⠀⠀⠀⡸⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢠⣺⠇⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⢨⣠⣄⣧⣤⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠷⠶⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⡇⠀⠠⠈⠀⠀⢀⣾⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⢰⡄⠀⠀⠀⠀⠠⣿⡇⢿⣟⠃⠀⠀⠀⠀⠀⠸⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣴⣿⡛⣛⠿⠟⢿⣿⣿⣿⣦⡄⠀⠀⠀⠙⠷⠀⠙⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠻⣿⣶⠚⢢⠀⢈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⢛⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⡄⣠⠾⢿⠞⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⢛⠻⣭⣾⣟⠋⣿⣦⡞⠀⠀⠀⠀⣿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣢⠄⢯⡿⣻⣶⣯⣤⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⠀⠀⠀⠀⣤⣰⡄⠀⠀⠀⢀⢿⡀⢻⣿⣿⢀⠸⠟⠻⣿⣿⣿⣦⣄⠀⠀⣿
⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⢸⣼⡇⠈⠉⠁⣭⡄⠀⠀⠸⣿⣿⠋⠁⠀⠀⣿
⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⢠⡼⢿⣷⣾⣆⠸⣿⣿⡤⠖⠲⣿⣷⠀⠀⠀⠀⣿
⠀⠀⠈⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣼⠇⡄⠉⠓⠾⣇⣈⡛⠓⠀⠀⠘⡿⢦⡀⠀⠀⣿
⠀⠀⠀⣾⣿⣶⡔⢿⡿⠛⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣀⢄⣴⣧⣷⣾⣿⣿⣁⠀⠀⠀⠀⠘⠁⠀⠀⣿
⠀⠀⠀⠹⣿⡟⢡⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣿⠏⣾⣿⣿⣿⠿⠻⢿⣷⣦⡆⠀⠀⠀⠀⣿
⠀⠀⠀⢀⣿⣧⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣯⢟⣿⠀⢸⣿⣿⠙⣦⣀⣤⣿⢿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⢠⣿⡁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢸⣿⣨⡟⠀⣾⣿⣿⠀⠘⢻⡿⣿⡜⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣾⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣷⡼⣿⠙⣿⠄⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢺⣿⣧⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡾⣿⣦⡄⠀⠻⠟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣌⣷⣿⣿⣷⣄⠀⠀⠀⡾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⢻⠛⡃⢀⣀⣀⣠⣤⣤⣤⣶⣶⣿⡉⠉⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⣥⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠐⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠉⠐⠈⢁⢿⣿⡿⣿⣿⣿⣭⣄⣈⣿⣿⠶⠄⠀⠀⣿
⠀⠀⠀⢀⣿⣿⣷⣀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣷⠄⢀⣀⣀⡀⠿⣼⣿⣤⣴⣿⡿⠛⠛⣯⣽⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠠⠈⠭⠍⠥⣤⣾⣿⣿⣭⣽⣿⣷⠾⠿⠏⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠄⠄⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⢀⣤⡀⡴⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣀⡄⢻⠆⠹⠘⠶⠇⠳⠾⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣀⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢠⠀⠀⠀⠐⢶⡶
⠀⠀⠀⠀⠀⠀⠀⢠⡄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢁⣸⣥⠀⣀⠀⢈⡁
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃

⢰⣲⠄⡀⡀⠀⡤⢰⢀⠀⡀⡀⠀⣆⣀⢀⢀⠀⡀⢀⢀⠀⠀⢀⢀⡀⡀⣀⢰⠀⢠⣆⡀⡀⣀⢠⢀⠀⡄⠀⢀⠀⢀⢀⢀⡀⣀⢀⠀⡀⣀⣀⢠⡄⡂⣀⣀⢀⣀
⠸⠼⠚⠥⠁⠀⠧⠸⠀⠇⠧⠁⠀⠇⠸⠘⠬⠁⠁⠣⠼⠀⠰⠼⠘⠀⠇⠣⠼⠀⠰⠀⠇⠧⢼⠸⠀⠃⠧⠀⠣⠄⠣⠼⠸⠁⠁⠘⠤⠇⡧⠼⠀⠄⠇⠣⠼⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠃⠀⠂⠀⠂⠀⠀⠀⠀⠂⡄⠂⠀⠀⠒⠀⠀⠀⠂⠐⠀⠁⠀⠂⠀⠂⠀⠘⠀⠀⠐⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡄⢠
⣿⣿⡿⠿⣿⠿⢿⢿⡿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣶⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠳⠦⣤⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⣴⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⣤⣤⠟⠁⠀⠀⢈⣙⠶⣄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠛⠉⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⡾⣣⡾⠛⠶⠞⠛⠙⠳⣮⣙⠷⣦⣤⣤⣤⠦⠶
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⢠⡟⣠⡾⣫⡾⠋⠀⣀⣀⠙⠷⣤⡀⢀⠉⢻⡦⠙⠻⢶⣤⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠉⠛⠿⣾⣋⡶⠋⠀⢀⠀⠻⣯⡛⢶⣌⠙⠿⠀⠸⣇⠀⠀⣠⡞⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠰⣟⠛⢷⣌⠛⠶⣽⠆⠀⠀⣠⠿⣣⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⣤⣘⣷⠀⠀⠀⣠⠾⣫⣾⡋⢿⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠉⠀⣠⠞⣡⡾⢫⡾⠃⠀⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⢟⣡⠞⠁⠀⣿⠀⠀⣠⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢿⣡⣤⠶⢛⣩⡴⠟⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⣤⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠻⣶⡞⠋⠁
⣿⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠈⣷⠟⠉⠉⠉⢻⣄⣤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢳⣶⠶⠶⠶⠶⠶⠶⠶
⠙⠛⠛⠛⠛⠛⣻⠟⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⣿⡶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⡾⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⣷⠈⠛⠶⣤⣀⡀⠀⠀⠈⠛⢦⣀⠀⠀⠙⠷⣄⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣧⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢰⣇⣀⠀⠀⠀⠉⠛⠳⢦⣄⣀⠀⣈⡷⢦⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⢿⣇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣾⣯⣉⠛⠛⠲⢶⣦⣤⣴⠟⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠋⠙⠷⢦⣤⣴⠏⠀⠙⠻⢦⣄⣸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠙⠀⡵⠁
⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠈⠁⠤⢧⠐
⠀⠀⠀⠀⠀⣰⠇⢰⠥⠀⠀⡀⠀⠀⡸⠀⣀⡀
⠀⠀⠀⠀⢠⡿⠀⣇⣚⣫⠄⠁⠀⠈⢀⠌⠀⢀⠐⠶⠤⠀⢀⣀
⠀⠀⠀⠀⢸⡷⠓⠛⠁⠀⠀⠀⠀⠀⠸⠶⠦⣤⣀⣀⣀⠂⠀⢠⣉⣁⢀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⠣⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠤⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠈⠋⠂⢄⠀⣠⠆⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠡⠀⢸⡄⠀⢰⡸⠀⠰⢰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠄⡀⠈⠔⠀⠘⠐⠀⠂⠂⠀⣆⠆⢀⠌⠜⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠢⡀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⡀⠈⠀⠀⡠⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠑⢄⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠁⢀⠔⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⡲⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣂⠥⠊
⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀⡈⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠠⡴⣂
⠀⢠⣤⣤⣤⣤⣤⣤⣤⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣯⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⢸⣿⠀⠀⢀⠀⣀⠀⢀⣀⣀⣀⢀⠀⠀⠀⢀⣀⡀⢀⣀⡀⣀⣀⠀⣀⣀⠀⡀⢀⡀⣀⣀⢀⣀⣀⠀⡀⣀⣀⢀⡀⠀⡀⣿⡇
⠀⢸⣿⠀⢀⢿⡄⢸⣆⢸⠀⢸⠀⢸⠀⣀⣀⢸⠀⠙⣾⠀⣿⣇⣨⡅⣇⣨⠗⡇⢸⣺⣁⣸⠀⢸⠀⠰⣁⡇⠈⣿⣶⡀⡇⣿⡇
⠀⢸⣿⠀⢸⠛⢧⣹⠘⣿⠀⢸⠀⢸⠀⠀⠁⢸⡀⣠⢿⠀⡿⡏⠉⡧⡏⠘⡶⡇⢸⢹⠉⠀⠀⢸⠀⠀⡏⣇⢀⣿⠈⠿⡇⣿⡇
⠀⢸⣿⠀⠈⠀⠈⠉⠀⠉⠀⠈⠀⠈⠀⠀⠀⠀⠉⠁⠈⠉⠁⠁⠀⠁⠁⠀⠁⠉⠉⠈⠀⠀⠀⠈⠀⠀⠁⠈⠉⠈⠀⠈⠁⣿⡇
⠀⠘⠛⠛⠛⠛⠛⡛⠿⠟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢻⣛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠒⠁⡠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠈⠉⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⣠⠄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⡀⠈⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣔⠁⠀⣀⡔⠀⣈⠉⠛⠛⠛⠛⠛⠛⠛⠉⢁⢄⠀⠠⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠌⠀⡰⠰⠀⢀⡸⠀⢂⡃⠀⡌⠄⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠆⠇⠀⠈⡁⠀⠰⠄⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣯⣿⣽⣽⣯⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣭⣽⣿⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠿⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⢠⠾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣆
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢀⣠⠴⠚⡇⣰⣯⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣏⠀⠀⠀⡿⣟⠀⣼⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⣆⢴⡾⠁⠈⣹⣏⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⣎⠀⠀⣰⠧⠞⠓⢦⣀⣠⠏⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿⡄⢰⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠈⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢀⠞⠉⠛⢤⡀⠀⠀⢀⣠⠴⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⡰⠋⠀⠀⠀⠀⠙⠢⣴⠋⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣠⡞⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⢀⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣄⣠⣴⣶⡾⣿⣯⣿⣿⣿⢆⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡏⣩⣊⡇⣬⡿⣿⠓⢋⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⠿⠛⠉⠉⠈⠉⠻⣿⣿⡪⣝⢿⣿⢿⣿⡿⣧⡴⠺⣿⡉⠉⠻⠋⠉⠉⠉⠙⠻⣿⣿⣿⡄
⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣿⢿⣾⣿⠇⢠⣈⣿⣤⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢿⣿⣷⣿⠛⣭⣤⠒⢩⠝⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⡂⠙⠿⣿⣷⣹⡻⣿⣁⣰⣠⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡏⠀⠶⠿⣷⣶⣦⡄⠀⢹⣿⣿⣿⢯⣶⣼⢿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣶⣶⣾⠛⠛⠆⠸⣿⡯
⠀⠀⠀⡈⣿⠀⠀⠀⠫⣿⡿⠷⠔⡆⢸⣿⢋⠴⠾⣿⣇⣈⣿⡿⢿⣿⣿⣽⣿⠳⠁⠤⠹⣿⣏⠂⠀⠀⠋
⠀⠀⠀⠆⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⠶⢿⡏⣿⣿⡾⡶⢻⣟⡻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠊
⠀⠀⠀⠀⠿⡄⠐⠀⠀⠀⠀⢀⢀⠀⠀⡏⠀⠒⠈⢰⣿⣿⣴⡇⣰⢬⠓⢈⣾⠀⠀⡀⠀⠀⠀⠀⠀⢘⠛
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠘⠬⠆⣴⣯⠀⠀⠀⣰⡿⠏⣹⠃⠀⠘⠃⣸⣿⡶⠆⠃⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⣠⣄⣠⣿⣄⣀⣨⣿⠀⢀⣼⡀⠀⠀⠰⢛⢧⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠿⠿⢿⣿⡏⣿⠉⢻⣦⡿⢿⣧⣤⣴⣯⣥⣾⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣏⣼⠟⠀⠀⠉⠀⢼⣇⣾⣋⣿⡿⡇⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣄⣹⣟⠳⠤⣁⠐⣂⣴⣟⣿⠟⠋⠁⠀⠅⣀⣀⠤⠶⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣹⣷⣾⣏⣻⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠸⠧⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⠀⠀⠀⠁⠙⣆⠀⠰⠀⠀⠈⠀⠀⣠⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⢠⡤⠴⢛⡧⠀⣀⠒⢦⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣷⡿⠙⢇⠘⠓⢅⠈⠀⣠⠟⣇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣤⣴⣶⣶⣾⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⢰⠃⠀⠀⢰⣿⣣⠀⠀⠉⠀⠀⠀⠀⡐⠀⢻⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠙⠛⠛⠻⠿⠋⠉⠉⠙⠋⡌⠀⠀⠀⢸⣿⡞⠀⠀⠀⠰⠁⢀⠀⢀⠐⣼⡇⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢻⣧⣀⢠⡄⠌⠶⣿⣓⠈⣷⡿⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡴⠂⡄
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠽⢿⣷⣿⣂⡋⢈⣹⡵⠟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣧⠀⠀⠀⠀⡀⣐⡀
⠀⠀⠀⣶⣮⡀⡀⠀⣰⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⣾⣣⡤⠀⠀⢹⣖⡤⠾⡄⠘⣿⣿⠆
⠀⠀⠀⢘⡿⣧⡘⡄⠀⠀⠉⡂⠀⠀⠀⠻⠀⠈⠀⣐⣲⠀⢷⣴⣀⣀⠤⣿⠀⠀⠀⠀⠀⢁⣻⠁⠈⢻⡄⢹⡀⠀⡟⣠⡾⠿⢀⢸
⠀⢀⠞⣉⠉⠁⣉⠇⠤⠒⢠⠀⠀⠀⠀⠢⡀⠂⠀⠀⡼⠛⠛⠟⢛⡅⡼⢀⠁⡄⠀⠀⡔⡙⠤⢃⠀⢀⠝⠈⣥⢹⣞⡫⣦⡀⠘⠾
⠠⡙⠂⠹⣇⠘⣷⡶⢖⠀⡆⠀⠀⠀⠀⢄⠀⢦⡀⠀⢳⡀⠚⡿⠿⢡⡇⣬⠀⢠⠀⢸⠟⢿⡄⠸⣿⠃⠀⠀⠘⣿⠯⡁⣸⡇⢱⡀
⠄⢉⠠⢸⣟⣀⣧⡐⣿⡀⠀⠀⠀⠀⠀⢈⡦⢄⠀⠀⣀⠿⠂⠀⠀⠀⡆⢿⡆⢠⣄⠌⣰⣿⣄⣠⠀⠀⠀⠀⣰⣿⡓⣾⣬⡧⣼⡊
⠀⠀⠐⠚⣋⣸⡟⡇⠘⣇⠀⠀⠀⠀⠀⣯⣥⣤⡖⠃⠉⢻⡛⠺⡃⠀⣧⣸⠃⠀⢯⣦⣽⣯⠙⠉⠀⠘⣧⣤⢹⣯⠇⢹⣿⡞⠬⠁
⠀⠀⠀⣶⣆⠀⢷⣄⣀⣹⡀⠈⣇⠰⡄⢻⣇⠘⡇⠀⢠⣿⡿⡄⢣⡀⣹⡇⠸⡄⠈⣙⣿⢗⣷⡔⠊⠀⠈⠡⢸⣿⠀⠈⣿⡄⠀⢀
⠀⠀⠀⣿⠙⢦⠨⡏⠀⠘⠁⠀⠈⠀⠤⠄⢻⠀⠹⠀⠈⢸⣇⢹⠆⡇⢸⡇⠀⣿⠁⠀⡶⠌⠈⡇⠀⠀⠀⠀⢸⣧⠀⢀⣿⣿⡄
⠀⠀⢠⡿⠀⠘⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠤⡀⠀⡟⢸⠉⠂⠱⣸⠁⠀⢀⣄⣄⡇⢀⡐⠁⠀⢀⠀⣤⡼⠇⠤⣾⡿⠘⣷
⠀⠀⢻⠃⠀⠀⠙⢄⠈⠉⠉⠀⠀⠀⢀⢀⣀⠆⢰⡃⠐⠂⣸⡂⣒⣤⡀⠁⠼⠧⠡⠬⠭⠄⠼⠦⠥⢀⠀⠀⠀⠀⠀⠻⠇⠀⠙⢶
⣀⣀⣾⣀⣀⣒⣢⣬⣆⣀⣀⣀⣀⣀⣰⣤⣌⣀⣱⣉⣨⣁⣉⣉⣁⣀⣄⣀⣀⣠⣤⣤⣤⣀⣀⣦⣸⣯⣤⣶⣀⣄⣄⣲⣤⣤⣶⣤
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠰⢚⣻⢶⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠈⢀⡽⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠹⣭⠿⡖⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢐⢠⡀⠀⠡⣴⢈⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡆⠀⠀⠀⠀⠃⣨⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⣀⠀⠀⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⠀⠠⠔⣿⣤⡁⠶⡀⠀⠀⠀⠰⠂⠸⠷⠯⠉⠀⠀⠘⠍⣻⣦⣤⡝⣌⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⡀⠈⠁⠀⠀⠀⠉⠛⢂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠛⠉⣹⣷⣾⣏⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣑⣒⠂⠖⢤⣀⣱⣿⣴⣃⠀⠠⣀⣤⣖⡀⠀⠀⠀⠀⢠⠀⠴⣤⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣴⡷⠂⠀⠈⠙⠲⠄⠈⠿⠀⠀⡀⠁⠀⡿⠛⠿⢿⣼⡆⠂⠂⠊⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣴⠖⠚⠻⠛⠶⣄⡁⠀⢀⡴⠆⠒⠀⠀⠀⠀⢀⣩⣤⣤⡴⠗⠂⡠⡶⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⡀⠀⠀⠀⠀⠘⢿⣦⡇⠠⠂⢐⠀⠉⣥⠈⠁⠀⠀⠘⠀⡠⠊⡔⢁⠞⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⣿⢻⣧⡀⠀⠀⠀⠀⠀⠝⠓⠠⡈⠀⠤⠈⣿⡆⠀⠀⠀⠀⣾⡄⠀⠆⠀⠀⠀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣿⢸⣧⢻⣦⡀⠀⠁⠀⠀⠀⡠⠁⠑⠲⠸⠛⡁⠀⠀⠀⠀⠰⣏⠀⢌⠀⣠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⣿⡆⢯⡟⣦⣤⠶⠀⣈⠄⠀⠀⠀⠀⠈⠉⠀⢊⠹⣠⠀⢸⠀⠀⠀⠹⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣇⠀⣟⣀⡜⡇⢣⢉⢲⡄⠁⠀⠀⠀⠈⠠⠌⠠⠐⠾⠄⠐⠀⡈⠇⠀⠀⠀⠀⠀⠀⢠⢅⡀
⠀⠀⠀⠀⢀⡀⠈⠻⣄⠾⢙⣽⣿⣿⣷⣤⡀⠀⢣⠀⣶⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⢞⠀⠀⠐⢠⠇⠀⢿⣾⣿⣤⣶⢒⣦⣶⣶⣶
⠀⠀⠀⠀⠀⢀⣤⣴⠠⣴⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⠈⠋⢻⣧⣀⢀⡀⠀⠀⡄⠀⣇⣐⣂⣸⣃⡐⣛⣸⣦⣄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠈⠈⠩⣙⠛⠉⣿⣟⢿⠿⣿⢿⣿⣿⢓⣀⠀⠀⢸⣿⣿⣾⣿⣿⣷⣶⢂⣽⣽⣿⣿⠭⠄⠉⠉⢣⠀⠈⡶⠟⣿⣿⣿⣿⣿⡏⣁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠘⠃⠀⣴⢿⠿⠋⠉⠁⡴⠀⣾⣿⣿⣿⣿⣿⢿⠯⢭⣟⣻⣿⣿⠀⠀⠀⠀⣴⣽⣟⣢⣶⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠐⠁⠀⣈⠁⠐⡀⠀⠀⠀⠓⠠⢭⣥⣀⠮⠹⠿⢿⡄⠂⠀⢠⢿⠇⠸⠯⣛⠊⠑⢒⣶⣿⣟⣛
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢀⣃⣠⣶⣦⣮⡷⠶⠀⠋⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⢀⣠⣾⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣦⡀⡶⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠦⠈⠷⡀⣠⣴⣾⠿⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⢀⡙⢂⡓⠢⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡠⣄⣀⣀⠀⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣧⠀⢀⣤⣰⣶⣾⣏⡿⣿⣿⡄⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠟⢋⠅⡇⣙⣿⣿⠯⢾⢻⣝⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣿⣿⣝⠷⣿⣿⣶⣿⣷⣟⣠⣼⣿⠟⠛⢻⡿⠛⠛⠛⠛⠿⣿⣿⣿⣷
⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣽⣿⣮⣷⣬⣿⣚⣿⣯⣾⡏⠀⠙⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧
⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣯⢿⡽⠟⢋⡁⠜⠻⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿
⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⡙⢿⣿⣿⣄⠿⣽⣦⠜⢁⠇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠃⢀⣤⣤⣀⣀⠀⠀⠐⣿⣿⣷⣵⡄⣉⣻⣿⣾⣷⣽⣾⣾⣾⣷⣇⠀⢀⣀⣀⣤⣤⣤⠀⢻⣿⡏
⠀⠀⠀⠻⣿⡇⠀⠋⡩⣽⣿⣿⡛⢀⠀⢺⣿⠟⢓⣻⣿⠋⠹⣿⣿⣿⣿⣿⢿⣿⡿⡴⠙⠻⣿⣦⢄⠈⠁⢸⡟⠁
⠀⠀⠀⡂⢹⠁⠀⠀⠀⠛⠛⠋⠉⠘⠀⣼⣿⠘⣉⣹⡿⣷⣴⡻⣛⡩⣿⣿⣿⠻⡇⠁⠁⠁⠛⠛⠎⠀⠀⠀⣄⠠
⠀⠀⠀⠉⣸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠐⣉⡹⢠⣿⣿⠏⡍⢹⠷⣮⠹⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁
⠀⠀⠀⠀⠉⢣⠀⠁⠀⠀⠀⠀⡄⠄⠀⠘⡇⠀⠁⠀⢸⣿⣷⣿⡇⠘⠳⡄⢡⣿⠁⠀⢠⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠚⡀⠀⠀⠀⠀⠀⠈⠉⠒⢻⡇⠀⠀⣆⡼⠟⠑⢼⠁⠀⠈⠀⣸⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣠⣴⣶⣦⣾⣿⣦⣬⣼⣿⠀⣠⣾⡄⠀⠀⣐⣫⢝⣦⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠛⠛⣿⣿⢃⣟⠀⢹⣴⠟⢻⡷⢶⣾⣿⣶⣿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣄⡾⢃⡀⠀⠀⠀⣺⣇⣾⣥⡽⠟⠟⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠤⠤⣿⣏⡒⠢⢄⣈⣃⣾⣏⣿⠏⠉⠀⠀⠈⠀⠠⠤⠖⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣹⡷⣿⣍⣻⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡤⠤⠤⠤⠤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⢀⡴⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⡏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣀⡇⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⢿⡄
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡴⠞⠉⠁⣧⣾⠓⣦⠀⠀⠀⠀⠀⠀⡴⠃⠀⠸⣧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⢿⡀⢀⣠⠏⠧⢴⡏⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⣷⡹⠃⠀⢠⣞⣦⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠘⣷⡀⢠⡏⠉⠀⠈⠙⠲⠏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠸⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢠⠞⠺⣅⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⡴⠋⠀⠀⠈⠳⢄⣠⠖⠉⠁⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠞⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣻⣤⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠶⠶⠶⠶⠶⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢘⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡖⠀⠀⢤⢀⡕⠀⣹⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠻⠆⣿⣧⡀⠀⠁⠀⠁⢀⣿⣿⡿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⢻⣿⣧⣾⣿⡏⠻⣷⣦⣶⣶⣿⢿⣿⣿⡉⢽⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠐⢌⢢⣿⣿⣿⣿⣇⠀⢈⡍⣍⠉⠁⣸⠛⢿⣷⣸⣿⡏⠁⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠘⡆⠘⣿⣾⣿⣿⣿⠻⢷⣬⣣⣄⠙⠋⣰⣞⣤⣶⣿⣿⣿⣿⣷⡿⠻⠥⣸⣧
⠀⠀⠀⠀⠀⠀⢶⣿⠄⢌⣿⣿⠏⠀⠈⠀⠀⠉⡛⡶⠟⠋⠑⠋⠙⠻⠟⣿⣿⣿⣄⢀⡀⢀⡟
⠀⠀⠀⠀⠀⠀⢆⣹⣷⣿⠏⢿⣆⠀⠀⠀⠀⠀⠈⡯⠀⠒⠀⠀⠀⠀⢀⣻⣿⠋⠻⣷⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⡈⠻⢦⣀⠀⠀⠀⠀⢏⠀⠀⠀⠀⢔⣢⣾⣿⣿⡇⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠄⠀⠀⠈⠙⠲⠦⢤⣏⣤⡤⠾⠟⠋⠉⠘⣿⣿⣿⣿⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣦⣄⣀⠀⠰⠀⠀⠀⡀⢄⣠⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡭⣿⣿⣿⢻⣿⣿⠟⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⣤⣿⣿⠃⠈⡏⠹⠋⠐⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⢒⣿⣿⠀⢸⡁⠀⠀⣰⣏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢨⣿⡏⠀⢸⡇⠀⠀⢹⡇⢠⣬⣛⠂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣑⠀⠀⢀⣿⣷⠄⢸⣷⣆⣠⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣋⣤⡽⠿⠿⠟⠉⠀⠀⠀⠛⠛⠛⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣧⣤⠤⠖⠚⠉⠙⠻⢯⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⠇⠀⠀⠀⣰⠛⠉⠓⠞⠀⠀⠀⠈⣹⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⡾⣄⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠏⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⡠⢋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠵⠊⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡴⠦⣄⠀⠀⢸⡉⠉⠳⢦⣀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢼⣧⣈⠙⠦⣌⠳⣄⣀⡽⠀⠀⠀⠈⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡉⠛⠲⠞⠛⠉⠁⠀⢀⣀⡀⠀⠿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠴⠶⠒⠛⠋⠉⠉⠉⠓⢿⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠉⠉⠉⠉⠉⠉⢹⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣴⢦⣤⡴⢦⣠⠾⢷⣴⠟⠷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠉⠁⢀⠉⢀⣄⡁⣠⡀⠁⣠⣤⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⠾⠛⠻⠟⠉⠛⠉⠙⠟⠁⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢰⣷⣤⣤⣼⣭⠀⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⢠⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢁⣠⣿⣿⣿⣿⣿⣿⣿⣆⢛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠎⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⢙⣿⣿⣿⣿⣿⣿⡿⠛⠉⣽⣿⣿⣿⣿⡆⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠤⠤⠴⠿⠿⠿⠿⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⣀⣠⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⠉⣉⣉⣉⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡃⠀⣿⣩⣭⣽⣿⡿⢿⣿⣯⣭⣭⣿⠃⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠀⣄⠉⠋⠙⠋⠁⠀⠉⠉⠉⠋⢁⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⡧⠀⠐⢡⣀⣀⡔⠀⠀⢾⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠂⠀⡀⢀⣙⣋⡀⢄⣠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣄⠘⣄⣴⡶⠴⠦⣴⡧⣰⠗⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠁⣰⠀⠈⠻⣦⣤⣀⣠⣀⣀⣹⡿⠃⠀⢸⣆⣮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠋⣱⣾⣿⣷⣿⣧⠀⠀⠈⠙⠿⣿⡿⠿⠋⠀⠀⢠⡾⣿⣿⣿⣧⡈⡙⠿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⠁⠀⣠⣾⡛⢻⣿⣿⣿⣿⡃⠀⠀⣠⣾⡻⢷⣆⡀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣆⠀⢀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣾⣿⣿⣿⣶⣿⣿⣿⡹⡇⣠⡾⠙⢿⣿⣾⡿⠱⢦⡀⣾⢹⣿⣿⣿⢟⣫⣿⣿⣷⣿⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣽⣾⣿⣿⣷⣿⢀⠀⠀⢸⣿⣾⠁⠀⠀⠁⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡻⣿⢿⣿⣿⣿⣿⣷⠀⣼⣻⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⣜⢿⣷⣿⣿⣆⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣫⣾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠽⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡰⠋⢠⠗⢀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⣠⢞⡤⠊⡤⢞⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⢠⢞⠕⣩⠔⠈⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠰⡆⠀⡈⠉⠑⠕⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡔⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠂⠀⠠⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣀⣀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠸⢤⡀⠀⠈⠀⠀⠀⠀⠈⠅⠲⠆⠔⠀⣀⠀⠀⠀⠀⠀⠘⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣠⠆⢀⣀⡐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣩⣍⣹⣝⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠂⠒⠐⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡠⢀⡀⠀⠀⣤⠀⠀⠀⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡷⢈⣤⣴⣿⣶⣦⣄⣤⣠⢥⣴⣶⣶⣤⣕⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⢾⣿⣿⣿⣿⣯⡥⢰⣾⣾⢿⣿⣿⣿⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⠿⠿⠷⠾⠿⠿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣶⣾⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠵⠒⠂
⠀⠀⣀⣀⣀⣠⣶⣤⠶⠿⠿⠿⢿⣿⣿⣿⣍⣻⢷⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢹⢻⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠸⠉⠉⠩⣭⡄⣾⣿⣿⣿⠗⣈⠙⣛⡂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡤⣄⣂⡠⠄⠁⠈⠙⠍⡿⠋⠀⠹⣆⣤⣾⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡘⣿⣿⣶⣦⢧⠰⠠⡦⢴⠠⣴⡞⡻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⠋⠉⠉⠉⠓⠃⠉⠉⠉⠸⡇⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡛⢿⣥⣤⣀⣀⠀⢤⡿⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠉⠙⠋⣙⡛⠋⠙⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠾⡥⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⡔⡄⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⠀⢡⢘⡀⠀⡧⠆⠀⢀⣥⠆⠀⢠⢃⡖⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡀⠘⢄⠃⠀⠇⠱⠀⠸⠘⠀⠀⡆⡘⠀⢀⣞⡼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠈⠉⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠈⠀⠠⠎⠈⠀⠀⣨⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⣄⠀⠀⠱⠄⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠔⠁⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠑⠄⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠔⠉⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣍⠲⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢰⢊⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣀⠠⡴⢖⡀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣺⣍⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣰⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⣿⡇⠀⠀⢰⡆⠀⡶⡀⢰⡔⠶⢶⠶⠆⣤⠀⠀⠀⠀⣴⠶⣄⢠⠶⢦⢀⡶⠶⡄⢐⡶⢦⡄⡄⠀⢠⡀⡶⢶⡄⠶⢶⡶⠆⢰⢀⡴⢶⣄⡶⡀⢰⡄⢸⣿
⠀⠀⣿⡇⠀⠀⡼⢷⠀⣷⣧⢸⡇⠀⢸⠀⠀⣿⢀⣀⣀⢸⡃⠀⠉⢸⠀⢸⣿⣇⣀⡟⢸⣇⣸⠇⡇⠀⢸⠅⣇⣠⡇⠀⢸⠀⠀⢸⢸⡇⠀⢸⣿⣧⢸⡇⢸⣿
⠀⠀⣿⡇⠀⢰⡿⢿⡆⣿⠘⡿⡇⠀⢸⠀⠀⣿⠀⠉⠉⢸⡃⠀⣤⢸⠀⢸⣿⡏⠈⣳⢸⡏⢸⡇⣇⠀⢸⠄⡏⠁⠀⠀⢸⠀⠀⢸⢸⡇⠀⣸⣿⠘⣿⡇⢸⣿
⠀⠀⣿⡇⠀⠚⠀⠀⠛⠛⠀⠘⠂⠀⠘⠀⠀⠛⠀⠀⠀⠀⠙⠞⠋⠈⠓⠚⠀⠃⠀⠛⠘⠃⠘⠃⠘⠓⠋⠀⠃⠀⠀⠀⠘⠀⠀⠘⠀⠛⠚⠃⠛⠀⠘⠃⢸⣿
⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠩⢝⣉⡋⠭⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠫⠭⠭⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⠤⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣐⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⠤⠊⠁⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠙⠢⢍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⠀⠈⠑⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢀⠔⠁⠀⠀⢀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠈⠳⡄⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠂⠀⡠⢠⠎⠀⡠⢢⠀⢀⠀⡉⠉⠉⡉⠉⢀⢄⠀⠰⠒⡄⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠃⠀⢠⢃⡎⠀⢈⣥⠁⠀⢣⣩⠀⠸⠈⡇⠀⢀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⢾⣸⠀⠀⣇⣹⠀⠀⢇⠗⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁