Shoat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠇⠼⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠄⢂⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠁⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⠀⠀⠀⠀⠀⠀⠁⠀⣽⠋⠀⠝⠀⠀⠀⡆⢠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠐⠀⠀⠀⠀⠃⠀⠉
⠀⠀⠀⠠⠂⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⣠⡤⠀⠀⠀⠀⠐⠀⠀⠴⠦⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠐⠀⢐⡖⠀⠁⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⡀⠀⡀⠈⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢀⢰⢂⠩⠜⢉⣴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⢸⠐⠐⡀⠁⠀⠃⠀⢠⠀⠀⠀⡠
⠀⠀⠀⠀⣀⢧⠘⠓⢰⠶⠋⢠⣼⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠠⡄⢥⢀⠀⠇⢠⠇⠀⡀⡇⢠⢃⠌⡠⠀⠀⠔
⠀⠀⠀⠀⠟⢰⡶⢛⣁⣡⠽⠋⣀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡄⠘⠆⢣⢸⣾⠁⡰⢠⣱⠧⢋⡜⠁⠀⠀⢀⡀
⠀⠀⠀⠀⡟⢣⣔⠚⣍⠀⠤⡞⣭⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⡀⠈⢚⠀⣿⢠⠃⡾⠋⡰⢋⡴
⠀⠀⠀⠀⠯⣙⢬⡛⣮⣷⢶⡻⣍⢦⡅⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠮⣣⡱⣦⣸⠀⣿⠇⢸⠇⡞⣡⠾⢃⠠
⠀⠀⠀⠀⠘⢾⣕⠻⣵⢽⣠⣳⣾⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣦⣌⠙⠻⢿⣆⣾⢀⣾⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣵⣾⠙⢯⣿⠦⣆⠈⠁⠣⣄⡀⠈⠙⠛⠻⣿⣷⣦⣄
⠀⠀⠀⠀⠀⢀⡞⣠⢞⣴⣿⠟⠋⠀⣤⠉⢁⣈⡀⠀⠀⠈⠻⣅⡀⠀⠀⠨⣹⣻⣿⣷⡄
⠀⠀⠀⠀⠀⣮⡔⣡⣿⡟⠁⠀⡀⠀⡿⣌⣻⠿⢿⠀⠀⠰⣄⡘⠿⣿⣶⣦⣤⣙⣿⣿⣿⡄
⠀⠀⠀⠀⣼⣿⣿⠟⠋⣀⡠⠀⠃⠀⣷⣼⣿⣿⠿⠗⢸⣶⣬⣿⣿⣾⣷⣿⣿⣿⣿⣾⣿⣿⡆
⠀⠀⠀⠘⣿⣿⣿⣷⣿⣟⢀⡆⢸⣷⣶⣽⣿⣿⢿⣾⣟⣿⡿⣿⣿⣿⣿⣿⣤⣭⣿⣿⣿⠟⠿⡄
⠀⠀⠀⢀⣼⣿⣿⣿⡿⢫⡿⣿⣸⡿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡄⣿⠁
⠀⠀⠀⣾⣼⣹⣸⣯⣞⣽⣾⣿⣿⣿⣈⠻⡿⢿⠿⠋⠛⢮⣽⣥⣾⣤⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠛⠁⠀⠀⠀⠀⠘⠛⣿⣾⣿⠜⠁⠙⠻⣿⣿⣿⣿⣿⣻⢷⡄⡀
⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣟⠉⡜⣽⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⢿⣿⣿⣿⣿⣿⣷⣧
⠀⠀⢀⣂⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⣯⡜⢻⣿⣿⣿⣿⡿⣥⡄
⠀⣼⣫⣽⣞⣿⣿⡟⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣠⣤⡾⠛⠋⠀⠀⠀⠀⡿⠗⣿⣿⣿⣾⣿⡟⢻⢟⣿⡌⣷⠀⡀
⠠⣿⠏⢛⣼⣿⣿⣿⣾⣿⣛⢻⣿⣆⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⡀⢀⣀⠀⠀⢰⣿⣿⣿⡿⢿⣧⣾⣾⣿⣧⣤⡀⣰
⠈⣿⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⠛⠛⠃⠀⣾⣿⣿⣿⣇⠀⣅⣿⣿⣿⣿⣷⡿⠛
⠀⠙⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠘⠉⠙⠶⠞⠁⠀⠀⠀⣼⣿⣷⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢀⣾⣯⣿⢁⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣶⣟⣻⠟⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠘⣿⣿⣿⣿⡿⣿⣿⣷⣶⣤⣤⣴⣶⣿⢿⣿⣯⣽⣭⡄⢸⣾⣟⣃⣹⣿⣯⣽⡆
⠀⠀⠻⣿⣿⣿⠋⢻⣿⣿⣿⣿⣤⣛⣿⡿⠟⠻⢭⣿⣯⣀⣀⣀⣀⣀⣎⣨⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠿⣿⣟⡀
⠀⠀⠀⠀⠉⠀⠀⠈⠟⠈⣿⠟⢱⡿⣿⢷⣴⣶⣿⡿⠉⠉⠛⠛⠛⠉⠉⠁⠈⠻⣿⣿⣿⡟⠿⣿⠿⣏⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠸⣿⣾⡟⣹⡏⠀⠀⠀⠀⠀⠀⢠⠠⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠈⣷⢷⣿⣿⡂⠀⢀⠠⠐⠂⠁⠀⠉⠁⠈⠀⠀⠲⠄⠀⠀⠐⠉⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠶⠊⠀⠀⠀⣠⠊⡄⠀⢠⡀⠀⠀⢐⠊⠀⢀⠀⠐⠁⢸⣧
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣿⠘⠂⠄⢈⣴⣀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠁⠈⠘⠛⠈⠁⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠖⣒⣒⣒⣒⣒⣒⣒⣒⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⡴⠚⣀⣠⣤⣤⣤⣴⣶⣠⣤⣤⢬⣉⡑⠢⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⡙⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢀⠴⡇⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⠉⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠀⠐⠂⠀⠀⢰⠛⠉⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⢉⠇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠧⠔⠋⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠊⠉⠘⡆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⡤⠞⠁⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⢀⡀⠠⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⡉⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠐⣋⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠤⣈⣉⡁⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⢒⣒⣉⡩⠥⠤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡧⠅⢠⣒⠀⡤⠲⡄⡤⢠⡔⢢⢠⡒⠀⣔⠂⡠⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠐⠀⠃⡗⠐⠁⠃⠈⠃⠂⠐⠀⠃⠂⠛⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣰⣄⣤⣠⣤⣶⣴⣴⣦⣤⣄⡇
⠀⠀⠀⠟⠰⣿⣻⣿⣿⣿⣿⣿⡿⣻⣿⢲⠄⠀⠀⠀⠀⠂⠀⠂⠀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠛⢻⣿⣾⢛⢻⣿⡷⡷⠶⠟⠀⠀⠀⠀⠂⡀⠡⡀⠄⠀⠀⠠⠁⠌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠠⢌⠀⠀⠌⡀⠀⠂⠊⠐⡡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠁⠂⠈⠉⠀⠠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠉⠉⠉⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⡄⠀⠀⣀⠀⠠⡀⠀⠀⢀⣀⣾⣖⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⣀⣤⣄⠤⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠓⠄⠀⢀⣀⠀⡇⠀⠀⠀⠀⠋⡏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⡤⠋⡉⡀⠀⠀⣁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠠⠔⢁⢼⡀⠉⢢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠘⠀⡀⠀⢀⠀⠆⣨⠟⠁⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⣀⠃⠀⣀⠸⡀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣾⣆⠠⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⠴⢡⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⢀⣨⠀⡙⠂⠀⠀⠀⠀⠠⢸⠦
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⠀⠚⠁⠀⠸⣠⠼⠾⠯⣴⢊⡴⠲⡶⡀⠀⠀⠀⠀⠀⢠⣢⢃⡴⠋⡠⠖⠃⢲⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢩⠷⠒⢈⡠⡄⠀⡀⠘⡗⠾⣛⠀⡹⠲⢤⣀⠀⢠⠎⢧⠎⠴⠊⢁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⠀⠑⣺⡧⠖⠋⢉⣱⠀⢧⠤⢤⣉⠧⣄⠀⠀⢰⠃⠀⠀⠀⣠⠔⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠑⢦⣰⠃⠀⣀⣴⠃⠈⡇⢾⠀⠀⠀⠙⡶⠒⠲⠼⠦⣄⡤⠞⠁⠀⣠⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⠀⠀⠙⠚⠉⠀⢰⡴⡞⠙⠋⠉⠉⠙⢲⣇⣀⣀⠀⠀⠀⠀⠀⠴⠊⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢙⡖⠀⠐⣲⠿⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡏⠉⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡀⠀⠀⠻⣦⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⣦⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣴⡌⢷⡀⢀⣀⣀⣠⡾⣡⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡟⠻⠄⠉⠉⠉⠉⠉⡼⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠒⢀⣀⡀⠒⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠾⡇⠀⠀⠀⢀⣻⡇⠈⠛⠁⣘⣓⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠁⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠞⠛⠛⠛⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠶⠶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⣭⣭⣈⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢠⡾⠉⠀⠀⠈⠻⣆⢹⣤⣤⣄⡀⠀⠀⢀⣀⣠⣤⡤⠴⠶⠶⠖⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠶⠶⠾⣷⠶⠛⠋⠉⠁
⠀⠀⠀⠀⣴⠏⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⡼⠃
⠀⠀⠀⣼⠃⠀⠀⣿⠛⠶⢤⣤⣤⣤⣤⠤⠶⠶⠚⠛⠉⣁⣠⣤⣤⣤⡀
⠀⠀⠀⣿⠀⠀⠀⠘⢷⣄⣀⡀⠀⢀⣀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠘⠷⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠦⢤⣤⣤⣤⣤⠤⠴⠶⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠴⠤⠴⠶⠤⠤⠤⠤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢥⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠁⢁⡀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢰⠂⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠔⠖⡄⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠀⠄⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⠶⢴⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠐⡒⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠲⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠖⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠴⡶⠶⠶⠖⣿⡛⠛⠚⠓⡷⠶⠶⠤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠒⠤⠤⠬⣅⣁⣀⣀⣀⣀⠤⠤⠖⠛⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡌⠑⠀⠁⠀⠀⠀⣀⣠⣬⡧⡒⠀⠀⠐⠒⠘⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⠪⢆⠄⠐⠰⠡⠥⠩⠥⠄⠂⠂⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠠⠠⠠⠀⠀⡀⠀⠠⠄⠄⠀⢀⣂⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠚⠋⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣢⠆⠈⠉⠉⠉⢹⠁⠃⠈⠁⠈⠒⠒⠢⠤⣀⣀⡲⣎⣻⣅⣲⣂⢲⡄⢠⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣾⣿⣿⣥⣤⣶⣶⣶⣶⣾⣶⣦⣶⣶⣦⣤⣤⣤⣀⠀⠈⠉⠛⢍⣻⣍⣿⣍⣻⣛⣻⡛⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡳⢦⣄⠀⣮⣷⣤⣷⣤⣿⣍⣻⣙⡄
⠀⡆⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣟⣿⣿⣿⠟⡹⠏⠀⠙⣷⣿⣿⣿⣆⣶⡤⢿⣬⣭⣉⣆
⢢⠑⡀⠀⠀⠀⠈⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣴⣶⣶⣵⣾⣴⢟⠟⠋⢻⣿⣦⣶⡤⢷⣤⣵⣄⣦
⠀⢢⠰⡈⢀⠉⠀⠀⠘⢷⣌⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣭⡶⢣⠊⣠⣾⣿⣿⣿⣿⣶⢿⣤⣹⣄⣱⡀
⠀⠀⢢⠰⠄⠠⠄⠤⠤⢤⣹⣷⣄⠀⠀⠉⠙⠋⠉⠛⠛⠛⠛⠛⠉⠛⠋⠉⢁⣾⣾⡫⠔⠡⠊⠉⠀⠺⣿⣿⣿⡿⣯⣷⣄⣨⣄⣙⣄
⠀⠀⠀⠑⠒⠲⠲⣶⡶⠶⠿⠛⠉⠁⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣋⡁⠀⠀⠀⢿⡄⠀⠴⠿⢟⣫⣾⣿⣤⣽⣤⣈⣅⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠽⡳⢤⣀⠀⠀⠀⠈⠀⠂⠒⠪⠭⣭⣭⣭⣾⣿⡿⠿⠿⢛⣫⠽⠛⡩⠝⠋⠀⢛⣹⣯⠽⣧⠤⢷⡤⢼⣤⣬⣥⣄⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠄⣠⣤⣤⣤⣶⣾⠛⠛⠉⠉⠁⠀⠀⠀⣀⠥⠔⠂⠉⠀⠀⠀⠀⠀⠡⢿⣷⣿⣷⣾⣷⣶⡾⠦⠴⠷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠒⠚⠓⠒⠒⠒⠚⠓⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⣀⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠧⠤⠤⠤⠤⠤⠤⠤⠬⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⢚⣩⡡⣔⡒⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⡉⠱⢠⠂⡏⢇⢣⠙⢂⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢰⡖⣶⡂⡖⡆⡆⣰⢀⡦⠀⣰⡆⢸⠀⡇⠀⠀⠀⠀⠀⠀⢱⢦⣬⣤⣥⣼⣶⣿⣟⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⠁⠛⠂⠛⠓⠛⠛⠋⠛⠒⠋⠙⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⣀⣤⠭⠭⠭⠭⠥⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠸⡗⠦⠤⠤⠤⠤⠤⠔⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠲⠤⠤⣄⠤⠤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠋⠓⠤⣀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⣄⠭⠖⣨⢙⠲⢤⡑⠶⠤⠤⠤⠖⠋⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⠒⠋⠀⠈⢻⣦⡊⡵⢡⠃⡆⡌⡑⠢⣄⠀⠾⠂⢠⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣬⣘⣃⣃⣉⣤⠟⣀⠀⠰⠀⠀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠈⠀⠀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣦⡸⡍⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣅⣀⡂⠐⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣥⣀⣐⠒⠈⠉⠉⠀⠀⠒⠚⠿⠿⣛⣿⣿⣟⢃⣀⣉⠻⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣧⡀⠀⠁⠈⠉⠉⠀⠈⠉⠉⢉⣠⡬⠿⠟⠁⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡀⠸⣿⣿⣿⣟⠛⠂⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣍⣻⣧⠀⢻⣿⣿⣛⢂⣠⣤⣶⣶⣦⣄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣤⢭⡥⢀⡙⠻⣵⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠞⠚⠁⢤⠘⢻⠿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣤⣤⣤⣤⣤⣀⣬⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠿⠻⠗⣭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣸⣓⣺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⢀⡠⢤⠄⠐⠒⠒⠒⠒⠢⣤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠉⢃⠈⢁⣀⣤⣤⣤⣤⣄⣈⣀⡘⠉⢠⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⢨⢶⠢⡤⠈⣀⣀⠀⣬⢿⣿⣟⣯⣝⠒⡍⠀⠀⠀⠀⠀⠀⠀⠃⢛⠙
⠀⠀⠀⠀⠈⠸⣷⣴⠀⠀⠀⠀⠀⠀⣀⣬⠿⠃⣴⠇⠀⠀⠀⠀⠀⠀⠀⣉⣹⡁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⡿⠤⠂⠀⠀⠀⢹⠀⠀⠀⠀⡀⠀⠀⢠⣥⡀⠠
⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⣯⡉⠀⠀⠀⠀⠀⢸⣴⣮⠞⡒⢓⡂⠀⠷⣾⣧⡤⠦⣤⣄⡀⡀
⠀⠀⠀⠀⠀⠘⢿⠋⢁⡨⣿⣿⣖⠂⠀⡠⠖⢓⣇⠉⠉⣆⠙⠂⠀⠀⢀⣻⣷⣷⠈⠶⠿⣻⣿⣿⣽⠗⡠
⠀⠀⠀⠀⠀⠀⢸⡀⡸⠿⣿⣿⡏⠉⢠⣧⠀⣚⠀⠈⠐⠼⠃⠀⠀⢀⣈⣉⣉⣭⣄⣀⠨⢛⡻⠯⠓⠉⠁
⠀⠀⠀⠀⠀⠀⢠⡹⠷⠖⣾⣿⣇⠀⠘⠿⣾⡏
⠀⠀⠀⠀⠀⠀⠘⣥⣤⡀⠛⡛⠛⠋⠐⣦⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢠⣤⣄⠀⠠⢶⣄⠀⠚⢷⣄⠈⠻⣿⣦⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⠀⠤⣶⣤⡀⠐⠿⣿⣦⣀⠈⠻⢿⣦⡀⠉⠻⣷⣤⡀⠙⢷⣤⡀⠙⠷⠄⠈⠙⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠠⣶⣄⠀⠛⢿⣿⣦⡀⠙⠻⣿⣿⣦⣄⠈⠻⢿⣦⣄⠈⠛⢿⣷⣤⡀⠙⠿⠶⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⡀⠙⠻⣿⣶⣄⠈⠛⢿⣿⣷⡤⠀⠙⠛⠓⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠶⠄⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣹⣿⣥⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠻⣿⡉⠉⠻⣿⣿⡛⠛⢿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠈⠻⣿⣦⡀⠙⢿⣷⣄⠙⢿⣷⡀⠙⢿⣷⡄⠹⣿⣯⡉⠙⢿⣿⣟⠛⢿⣿⣟⠻⢿⣿⡿⠿⣶⣶⣶⣶⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣦⣿⣿⣦⣤⣽⣿⣦⣈⣻⣿⣦⡀⠙⢿⣷⣄⠙⢿⣧⡈⠻⣿⣦⡈⠻⣿⣦⡈⠻⣿⣎
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⡍⣩⣙⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⣬⣿⣿⣦⣼⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⣭⣭⣙⣛⣛⣛⣛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⣛⣛⣛⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⠿⠸⢿⣿⣿⣿⡇⣿⣿⣿⣧⣾⣿⣿⣿⣿⣌⡻⠿⢛⣴⣿⣿⣿⣿⣩⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠿⠿⠿⠿⠿⠿⠶⠿⢿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠿⠿⠿⠿⠿⠿⢛⣛⣛⣛⣛⣛⣛⣛⣫⣭⣭⣭⣭⣭⣭⣭⣥⣴⣶⣶⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣥⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢸⡏⣰⣾⣿⡿⠟⠛⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⡄⠹⢷⡈⠀⠸⠶⡄
⠀⠀⡞⠽⠈⠁⣿⡏⡞⠀⢀⢠⣶⣿⣿⣿⣿⣿⣿⠟⢋⣼⣿⣿⠘⠙⣿⣿⣿⣿⣧⣭⢿⠃⠀⢶⡄
⠀⠀⢿⣦⣤⣶⢟⣤⢀⣾⣿⣧⣽⠟⠛⣛⣿⡟⢁⣴⠿⣿⠋⠁⠀⠀⠘⢿⣷⣿⣿⣧⣏⣤⡀⠉⠀⢀⣀
⠀⠀⠀⠉⠉⠁⣟⣿⣾⣿⣏⠁⢰⢠⡾⠛⠻⣧⣿⡋⠀⢿⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⣿⠇⣠⣀⠀⠘⡆
⠀⠀⢰⡀⠀⠆⠈⣛⣷⣬⣛⠛⡋⢸⣷⠀⠀⠉⠉⠛⠚⠛⠁⠀⠀⠀⠀⠟⢿⣿⣷⡖⢋⣡⣄⣿⡿⠀⠐⡷⡄
⠀⠀⠘⠿⠿⢿⣿⣿⣿⣻⣿⠀⢙⣛⣋⠀⠀⠀⠀⠀⠀⠴⣾⣿⣟⡓⠀⠀⠀⢸⣿⢿⣾⣿⣿⣿⣧⣄⠀⠁
⠀⠀⠀⠀⠀⠀⣹⠇⣹⡍⢻⡆⠉⣩⣭⣤⡀⠀⠀⠀⠀⠾⢻⣿⠟⠋⠀⠀⠀⠀⢙⡿⣿⣿⣇⡿⠈⣿⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠈⣙⣻⡟⠃⣼⣇⠀⠋⠸⣿⠁⠀⠀⠀⠀⠀⠑⠓⠉⠀⠀⠀⠀⢠⣌⢀⣿⣿⣿⣷⣾⠈⠂⡤⡞⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⡄⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣿⡩⣟⣻⡄⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠙⠏⠻⣿⣿⣿⣷⠀⠀⠀⠀⠳⠖⠶⠛⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣿⢯⣄⡀
⠀⠀⠀⠀⠀⢠⡿⣷⣀⣤⣿⢿⣿⣦⠀⠀⠀⠀⣀⣤⠤⠤⠴⠒⠀⠀⢀⣴⣿⣿⣿⣿⣦⣘⡿⣿⡿⡫⠃
⠀⠀⠀⠀⠀⡏⠀⠙⢿⣿⣿⣀⣙⣿⣷⣦⣀⠈⠁⠀⠟⠃⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⠷⠖⠃
⠀⠀⠀⠀⠀⠈⢁⠝⢠⣇⣡⣿⣿⣿⣿⣌⢻⣿⠶⠤⠀⣀⣠⣾⣿⣿⠋⠀⠙⢿⠛⠛⠻⠿⠕⠉⠲⠶⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠈⠻⠿⠿⠿⢛⣻⣿⣿⣿⣄⣀⣀⣀⣉⣁⣉⣁⣠⠀⠀⠉⠉⢷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠄⠀⠀⠀⠉⢿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠛⠛⠫⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⣿⡿⢿⣿⣿⣦⣤⣀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠉⠉⠋⠩⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣬⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠰⣿⣿⣿⣿⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣚⣩⠭⠭⠭⠭⠅⠀⠀⢤⣄⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠛⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠀⠉⠍⠢⣄⣀
⠀⢀⣀⡤⠤⠴⢞⣡⠔⠂⠀⣄⠀⡀⠈⠡⣠⠆⠀⡀⢀⡠⣀⠈⡇
⠀⣏⠀⠀⣠⡔⠋⠑⣤⠀⠀⢈⠿⣅⠠⠀⠀⠀⠠⠈⠁⣀⣠⢴⠇
⠀⠘⡶⠦⢤⣌⣳⣉⡀⢈⣂⣀⣀⡠⠴⠒⠛⣋⣉⣉⣉⡡⠴⠋⢀⣀⣤⣔⣪⣿⣯⣵⣖⡒⣒⢤⡀
⠀⠀⠈⠷⣤⣀⣀⣈⢉⣉⠉⣉⣁⡤⠴⠊⠉⠁⠀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⡿⣛⣁⠛⣿⣎⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠤⣒⣯⣵⣶⢶⢟⣳⣦⣼⣷⣿⣾⣿⣿⡕⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠟⣷⠫⣝⣾⠿⢯⣭⡭⠿⠭⢿⣿⣿⣿⣟⣸⡿⢥⡾
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣞⢠⣿⡇⠀⣿⣿⡇⠀⠀⠀⢹⣿⡦⢀⣀⡠⠟⠁
⠀⢀⡴⣫⣶⣦⢰⣍⠒⠤⢤⣄⣀⣀⣀⣀⣈⣉⠁⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠋⠉⠉
⠀⣾⣴⣿⣿⣿⠸⣿⣿⣿⠿⢃⣶⣶⣶⣶⣤⣍⣙⠢⣄
⠀⡇⣿⣿⣿⣿⣆⠠⣭⣀⠒⠛⠛⠛⠛⢛⣉⣭⣭⣶⢘⡆
⠀⣇⠹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣥⣾⡇
⠀⢹⣦⣝⡛⠟⠃⣸⣿⣿⣿⣿⣿⠟⣫⠴⠋⠁⣠⠴⠛⠀⣀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢿⡄⠉⠛⠒⠬⢭⣭⣭⣭⣶⣿⣿⣤⠔⠋⠀⢀⡔⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠊⠁⠀⠈⠓⠤⡀
⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠓⠤⣀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠀⣀⣠⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⠀⣶⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠁⣐⡂⠀⠀⠐⢒⢖⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣈⢣⠒⡟⠘⣇⡖⡄⠀⠀⠀⠀⠀⠀⡜⠠⣀⠔⢂⠀⢈⣦⠴⠓⡄⠀⠳⣄⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⢱⣠⡄⡂⢀⡸⢹⣠⡆⠀⠀⠀⠀⢰⡧⠀⠙⣦⡴⠚⡍⠀⢱⣤⠞⠣⡀⢈⠦⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠾⠞⣹⡻⡁⣄⠙⢉⠘⡿⡄⠀⠀⠀⠸⢈⠀⠈⠉⢶⣀⠝⢿⡁⢈⣧⡔⠉⠣⡀⡨⠶⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣧⣿⣿⣿⣯⠾⡍⢐⡀⢸⣦⠀⠀⠈⠃⣱⣀⠀⠋⠱⣄⡠⠓⣏⠀⢙⣦⠐⠉⠂⣠⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠿⠛⠋⠃⡀⠀⢻⠚⠓⠊⠘⠂⠀⠈⢿⢁⡃⢄⣀⣉⠃⠀⠬⠓⠉⢀⣠⠴⠋⠀⠈
⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁⠀⠀⠀⣶⢉⡓⣚⣹⠃⠀⠀⢐⠀⠀⠀⠁⠀⠀⢈⡉⢋⠉⠉⠉⠉⡉
⠀⠀⠀⠸⠉⠉⠉⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣦⡃⠀⠀⠘⠀⢱⣦⡦⠘⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀
⠀⠀⠀⠀⣤⣤⣤⣴⠷⠤⣤⣀⣠⣤⣤⡄⢀⣀⠀⠀⠘⠝⠙⠀⠀⠀⠀⣪⡙⣷⡴⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣡⠶⠺⣕⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣟⣦⢄⡒⣛⣸⠑⢦⣄⡐⢝⣀⡠⣄⡀⡈⠓⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣧⠈⡀⠈⠹⣿⠘⣇⡀
⠀⠀⠀⠀⠀⠀⢀⡙⠏⠞⠃⠢⠀⡁⠰⡵⣸⡏⠀⣷⢟⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢋⠴⣊⣬⢿⡮⡅⠀⠀⠉⠀⢇⠄
⠀⠀⠀⠀⠀⠀⠠⠙⠲⠽⣟⡳⢀⣺⣡⣎⠉⠀⠀⢡⡼⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠷⣾⢛⣼⡿⠉⠈⠱⡄⠀⠀⠀⠾⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢻⡿⠺⢖⣤⡀⣠⣬⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢁⣴⠾⣓⡯⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠙⠮⣭⢱⣎⡀⠄⠚⠁⠀⠀⠀⠀⠀⣀⣤⠔⠋⣉⠠⢚⣩⠔⠛⢉⡴⠀⠀⠌⠀⠀⠀⠈⠀⠀⢀⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢀⣀⣤⣶⡷⠷⠒⢒⣩⡴⠞⠉⠀⠀⠀⢸⣿⣄⠀⠀⢶⣀⠂⠈⠐⠀⠁⠀⠎⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣧⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⠓⠀⠀⠀⢹⣇⠀⠀⠀⣨⢀⣴⠇
⠀⠀⠀⠀⠀⣠⠖⠀⠂⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀⣀⣀⣰⣿⣯⣻⣿⡶⠦⣦⡄⠀⠄⠠⣀⣺⣟⣾⡿⢷⡄⠀⣀⣼⣟⢃⣠⠜⣡⠞⡟
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠭⠿⣾⠿⠿⣭⣉⣉⣙⣙⠿⢿⣦⣭⣠⣡⡤⠶⣊⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠿⢶⣭⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢦⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⣬⣿⣦⣧⠀⠀⠀⠀⠋⠀⠈⠐⠓⠒⠒⠉⠉⠁⠀⠀⢱⣄⡀
⠀⢲⡻⣷⣿⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⢸⣾⣇⣿⣼⣅⣿⡾⠀⠀⠴⢄⣀⣀⡀⠀⢀⣀⣀⣠⣴⡆⠀⣾⠇⠁
⠀⢻⣭⣻⣢⡦⢰⡲⣯⡳⣽⡏⠀⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠈⠙⢿⣇⢸⡿⠿⠿⣿⣦⠸⡟
⠀⠀⠙⠻⣿⣷⣶⣿⣮⣽⠟⠀⠀⠀⠈⢢⡻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢺⠹⣸⠀⠀⠀⢌⡏⢠⠇
⠀⠀⠀⠀⠈⠻⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣩⡭⡯⠍⣹⡄⠀⠀⠀⠀⠀⠈⠈⠢⠋⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⡘⠀⢤⠀⠀⠀⠀⢰⠋⠛⠤⡷⠞⠋⢳⠀⠀⠀⢀⢾⢀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣧⠀⠀⠸⡧⠀⢠⡿⡟⣿⡄⠀⢠⡴⣻⣭⣵⡽⢿⣷⡆
⠀⠀⠀⠀⣀⡄⡰⠁⢀⢂⣤⣀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠘⠷⣷⠷⠃⠀⣵⡞⣿⣿⡟⣿⣯⠻⣿
⠀⠐⣿⣶⣌⣿⡇⠀⠀⣹⣏⣠⣶⡷⠀⠀⢀⠀⠀⠀⢆⡀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢠⣁⣾⣿⣧⣿⣻⢄⡿
⠀⠀⠈⠉⠋⢻⣿⠀⢠⣿⠏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠾⣼⣿⣷⣠⡀⠀⢸⡿⣽⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠘⣿⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⡀⠀⠀⠤⢤⣴⡏⠀⠀⢠⡷⣱⡿⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠱⣥⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⣭⠄⠀⠀⠀⠀⢸⡇⠀⠀⠸⣟⣫⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠁⠙⣆⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣈⢳⣄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣠⠤⣍⠉⢳⠒⠒⣇⠀⠀⣾⠛⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⡀⠀⠉⠒⢠⡀⣈⣀⣠⠷⣄⢸⡟⠉⢛⡶⢤⡀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣵⣤⣤⣤⡁⠀⠀⠀⢮⡷⠬⠉⠀⠰⡇⢠⣬⣙⣷⣶⣤⣀⣀⠀⢹⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠏⠈⠑⠂⠖⠋⠀⠀⠀⠀⠀⠐⣄⣀⡸⣄⠀⠀⠈⡿⢋⢹⣻⡙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡌⣿⠉⠙⠓⠲⢇⣸⣈⣱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢧⡟⠀⠀⠀⠀⢀⡿⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡇⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣀⣀⠈⣳⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠾⠶⠶⠶⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠙⠻⠷





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠚⠉⠓⠢⣄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠔⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣧⡀
⠀⠀⠀⠀⢀⡴⠋⡠⠒⠀⠐⠈⠍⣻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣷
⠀⠀⠀⠀⣼⠁⡎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡶⠦⣤⣤⣀⣠⣤⣤⣖⡯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⢠⡿⠀⢧⠀⠀⠀⠀⢀⡴⠖⢒⢶⡄⠙⢢⡀⢀⡤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⢸⣇⠡⠘⢆⠀⠀⠀⡞⠀⠊⠉⢳⣿⠀⠀⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⣿⡀⢁⠘⢆⠀⠸⡇⡆⠀⢀⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼
⠀⠀⠀⠀⠸⣧⠀⠣⡈⢣⡀⠳⣝⣒⣋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⣿
⠀⠀⠀⠀⠀⠙⣧⠀⠈⠢⡱⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎⢰⡟
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠪⣳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠚⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠈⠓⢌⡉⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢚⡡⠔⠉⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠑⠒⠨⠵⣲⡶⠶⠶⠶⠶⠖⠖⠒⠒⠚⣉⡥⠔⠚⠁⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⠁⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⠟⠛⠛⠛⠛⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢀⠸⡀⠀⠸⠘⡀⣀⢤⠀⠀⠀⠀⠀⠀⠀⢠⣝⡾⢷⣫⣤⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠈⠁⠀⠀⣴⣑⣁⠈⠀⠈⢣⣄⠙⡄⠀⢘⡿⣷⡾⢿⡛⠯⠝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡀⠀⢠⠀⡈⡄⢰⢀⣀⣄⢺⣷⢷⡆⠁⠠⠐⡀⡂⡏⠀⠉⠉⠉⠉⠋⣿⡟⢻⠀⠀⠈⢹⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠰⢃⢀⡠⠐⠉⠀⠀⠀⢀⠤⠿⠚⠂⠑⡃⣚⣿⡠⢄⡅⠀⠀⠀⠀⠀⠀⣿⡧⢸⠀⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡶⠤⠀⠀⠀⠠⠄⠀⠀⣀⣀⢀⡤⠖⠉⠀⠀⠉⠑⠫⢧⣤⡀⠀⠀⠠⣻⡅⢸⠀⠀⠀⠚⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⢐⠀⠀⡎⠠⠂⢀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣶⠀⠀⠀⠀⠀⠀⠀⣤⣽⡷⡤⠀⠀⢹⡇⢸⠀⠨⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠂⡋⠠⠁⠀⠐⠀⠀⠀⠀⠐⠂⡰⠁⠛⠻⠀⣾⢒⠶⡲⢦⠀⠿⠿⠙⣽⡀⠀⣸⣇⢸⠀⠀⢠⠒⠟⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢠⣆⣀⣈⠁⠊⣁⣀⣀⣀⡀⣰⠃⠀⠀⠈⠀⢸⣯⣶⣡⣾⠀⠐⠖⠂⠙⣿⣿⣿⣿⣿⣷⣃⣾⣷⠾⣷⣷⢦⡀
⠀⠀⠀⠀⠐⠀⠀⢀⡠⢒⠘⠊⠉⠉⠭⢙⣳⣧⣍⠀⠀⠈⠉⠻⠀⢰⠖⠒⢿⢳⣶⣴⠖⣾⡗⠒⡂⠑⠒⡛⠋⣛⡛⣛⠛⠓⢈⣕⡺⣿⣿⣞⢧
⠀⠀⠄⠀⠀⠀⠀⠀⣛⠙⠙⠚⠓⠺⢶⠋⠁⠀⢹⢀⠀⠀⠀⠀⠀⢸⠁⠆⢸⣿⢹⡿⣛⢽⠉⡞⢹⠀⠀⡏⠉⣿⡏⣹⠉⠉⠉⠉⠁⠻⢯⡁⠣⡀
⠀⠀⠀⠴⠤⣤⣤⣴⣟⣰⠀⡀⠀⠀⠰⠀⠉⠁⢸⣸⣤⣄⠴⠴⠀⣸⣦⣀⠾⠿⠾⠧⢥⣼⣶⣀⣲⣀⣺⣷⣴⣿⡷⠿⠿⠶⠶⠶⠗⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠀⠁⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⡴⠟⠻⣦⣤⣤⡀
⣼⠀⠀⠀⠁⠀⠈⢻⣄⣀
⠻⣤⣤⣄⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠈⠻⠦⢦⣤⡀⠀⠀⠀⠀⠈⢙⡷⠶⠾⠿⠷⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠶⠾⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⣉⣤⠤⠶⠶⠶⠒⠒⠲⠦⢄⣉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣤⢾⡄⡀⠀⠀⠀⢀⡴⠋⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠙⢦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢿⡀⠀⠉⠀⠀⠀⣠⢏⡴⠉⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠟⠁⠀⠀⠸⡇⠀⠀⠀⠀⣴⢣⠏⠀⠀⠀⣠⡤⠶⠶⢤⣀⠀⠀⠀⡴⠊⠉⠀⠀⠈⠉⠙⠢⡀⠀⠀⢸⡆⢿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⢣⠆⠀⠀⣴⠟⠁⠀⠀⠀⣠⠈⢳⠀⢸⡁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡇⢸⡀⠐⢯⣄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡆⠀⢠⢇⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠴⠃⠈⠧⣄⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⢸⠁⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣿⠃⠀⠀⢸⣇⠀⡟⣸⠀⠀⡼⠁⠀⠀⠀⠁⠀⢠⠎⢁⡤⠶⢤⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠃⠀⠀⠀⠀⣿⢰⠇⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⡏⠀⢸⠁⠀⠀⡿⠀⢹⠀⠀⠀⠀⠀⠀⢀⡟⠀⡼⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢰⡇⠀⢸⡀⠀⠀⠀⠂⠀⠀⢧⠀⠘⠦⠤⠞⠁⢠⡆⠀⠀⠀⠀⠀⢀⡞⠀⡼⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⠋⢀⡼⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⣧⠀⠀⠘⢦⣀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⠞⠁⣠⠎⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠁⢀⡴⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣉⣙⠒⠒⠶⠶⠶⠒⣒⣊⣩⣥⠴⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⡶⢖⢲⠛⠛⠋⢉⡍⢍⡝⡻⠛⡳⠒⣶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡚⠫⣍⠳⢌⠢⡙⢌⠀⠇⠀⡇⠸⠀⠜⠔⣡⡞⠡⢊⡡⠖⣋⠤⠞⢉⠹⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠲⢌⡑⡂⠍⡒⠅⠢⣈⣤⣬⣄⣡⠞⠛⠲⠞⠉⠉⠳⠴⠶⣭⣴⠶⡶⣄⠒⣩⡷⣤⠉⡓⣦⣀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠳⡄⠁⠀⣴⣾⣿⣿⣿⣿⣿⡴⢶⢶⠶⣶⠖⣶⡶⠒⢿⠾⠶⢷⣿⣰⡿⠧⣿⡟⠉⠁⠈⠳⢦⡀
⠀⠀⠀⣠⠞⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠶⣾⣿⣿⣿⣿⣿⣿⡿⠶⠶⡶⣶⢶⡾⠁⠀⠀⠀⢱⡄⢸⣿⢹⡇⠈⣿⡇⠀⠀⠀⢀⣠⠿⢦⡀
⠀⠀⡼⠃⠀⠀⠀⠁⠀⠀⢄⣠⣤⠞⠁⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣈⣓⣙⣙⣈⣻⠇⠀⠀⠀⠀⠀⣧⢸⣿⢸⡇⢰⣿⡇⠀⠀⠀⠈⢡⠀⢈⣷⡄
⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣟⣏⣙⣁⣛⣘⣃⣸⣤⣤⣤⣀⣀⣠⣯⣸⣿⣼⣅⣈⣿⣇⣀⣀⣀⣀⠀⠀⠈⠀⠻⡄
⣸⣷⣶⣶⣶⣦⣤⣤⣀⣀⣀⣠⣤⠤⠤⠶⠶⣟⣛⣿⡿⠿⡟⢛⣛⣯⠿⠟⠛⣋⣭⡤⠶⢚⣫⡭⠖⠋⠁⣠⡴⠛⠉⢀⣩⠟⠉⡽⠉⣟⠛⣟⠲⣶⢿
⣿⠢⠬⢭⣅⣉⢉⣙⠛⠻⠻⡿⣿⣶⣦⡶⠟⢉⣁⣀⣤⠾⠛⠉⠁⣀⣤⠶⠛⠋⢁⣤⠞⠋⠁⠄⣠⡴⢛⠁⠀⢀⡴⠋⠀⠀⡾⢁⢰⣗⢀⣹⣄⣈⣻
⣏⠑⠮⣄⡠⡉⠙⠓⢦⣴⣠⣠⣴⢛⡩⢀⣤⣞⡋⠉⠉⣀⣤⣶⣻⣥⣤⣤⣤⣞⠋⠀⠀⠀⣠⡾⠋⠀⢁⡀⢠⡟⣁⣤⠶⠟⣩⠉⠉⠉⢉⣉⣁⡤⢾
⢻⢳⢤⣤⣉⣳⣷⣿⣛⣫⣯⣥⣬⣩⣿⣿⣟⣉⣹⣻⣿⣽⣽⣭⣭⡁⠹⠛⠟⢻⢧⣀⣠⡾⠋⠀⠀⠀⡚⣵⠿⠭⠕⠒⠉⠀⠀⠀⠀⠠⢝⣛⣓⣟⣿
⠈⢿⣭⣼⣻⣿⣿⡿⣿⠷⣿⣷⣾⣷⣿⣿⣿⣿⡻⣿⣿⣿⠿⣿⣯⣟⡿⣷⢶⣤⣈⣻⣿⡟⣽⢳⣠⢄⣼⣟⣿⣟⣷⣖⣶⣦⣀⣤⣤⣀⣀⡈⠉⣨⠏
⠀⠈⢷⠦⣠⡠⠍⢿⣟⣷⣾⣅⣇⢉⢻⣷⡿⡻⣿⢤⢿⡿⣶⣿⣻⣿⣿⣿⣯⣽⡟⣛⣮⣏⡙⠾⢯⣿⣿⣽⢧⡿⣿⢻⣭⡟⣽⣛⢷⢶⡭⠽⣽⠏
⠀⠀⠀⠳⣄⠹⣯⠭⠇⡹⢤⢿⠿⣿⣦⣻⣶⣻⣫⢿⣷⣟⡻⣯⣿⣟⣯⣟⠿⡽⣷⢿⣆⡿⣓⣾⢧⣸⡟⣛⣧⠹⡷⣟⣲⡧⠯⣝⡟⣼⣭⡿⠁
⠀⠀⠀⠀⠈⠳⢿⡅⣢⢍⡛⣿⡁⣹⣿⡇⣿⣿⣟⣏⢿⣾⣷⣛⣟⣳⣝⣯⣾⡟⣫⣻⣞⢿⣭⢿⣦⣯⣿⣧⣞⣷⢛⡟⢾⣓⢦⣈⣳⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⣐⢢⣟⡙⣿⣿⣿⣿⣼⣿⣭⡑⢿⣚⣿⣴⣿⡷⢿⢯⣿⣫⣿⣿⡛⣾⡷⣾⣩⣿⣝⣿⣟⣿⣟⣽⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣥⣼⣿⣿⣿⡟⡷⢮⣉⠟⣾⡿⡻⣼⣗⡿⢳⣿⣿⣮⣽⣛⣷⣿⣿⣯⣴⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠿⢶⣟⣚⣇⣿⣯⣍⣽⣷⣿⣿⣿⣿⣭⣭⠾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠰⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠶⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣭⣤⡾⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠉⠀⠈⠉⡠⣤⣤⣤⣒⣒⣢⣤⣤⡤⠤⣤⢤⣤⡤⠤⠤⠤⠤⠤⠦
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠑⠀⠀⡀⠀⠀⠀⢨⠯⠉⠋⠉⠉⠁⠀⠀⠀⢀⠀⠂⠁
⠀⠀⢀⠀⠀⠀⠑⡶⠖⢚⣩⠉⠀⠀⣾⣥⣀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠈⠄⠀⠀⠈⠳⣞⡟⠁⠀⠀⣰⡟⠿⠿⢷⣶⣤⣴⡶⠚⠛⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⣴⡟⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠈⠀⠈⠳⣄⡀⠀⣠⣾⣿⠁
⠀⠀⠀⠠⠀⠀⠀⠈⠻⠿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⣻⠿⠟
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠐⠒⠦⠴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣫⣽⣶⣶⠒⡠⣔⣫⠽⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣭⣾⡿⠛⠛⠛⢁⣦⡉⣓⠾⣭⣿⣓⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⠏⠁⡰⣜⢮⡿⣷⣽⣾⣧⠈⠻⢿⣓⣶⠾⢤⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣉⡁⣴⣿⣿⣮⣳⣝⡮⣷⣿⣿⡬⣧⣄⠺⣭⣽⣛⡂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⣮⣳⡜⢿⡯⣟⢮⣗⢿⣚⠩⣿⣣⢿⣾⣦⠙⢳⢯⣟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠻⣿⣧⠈⢿⣮⣟⡮⣝⡾⢈⣓⠾⣽⣲⠏⠀⠈⣓⢏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠻⠃⠄⣶⣝⡲⣝⡛⣭⣐⠮⣝⡆⣬⣛⠂⣐⢎⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃⣼⠀⢿⣿⣝⡲⣽⡷⢮⣙⠾⣱⢰⣝⡷⠌⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⣿⠀⣷⣽⡻⣽⣻⢏⡳⣭⣳⣇⡻⣮⠃⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⡿⢠⡹⣿⣿⡳⢍⡳⣝⢮⡻⣯⡻⠀⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⢃⣺⣷⣝⢟⢿⡳⣝⢮⣳⡽⠎⢁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡾⠏⡰⣝⢮⣿⡇⠠⠅⠈⠀⠁⢀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣶⠁⣰⣿⣾⣯⠗⠀⠀⠀⠀⣀⣴⢸⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠟⡃⣾⣯⣿⡿⠃⠊⠀⣠⣴⡇⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⡙⠙⠛⢋⣀⣠⡆⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣇⣷⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠒⢠
⠀⠀⠀⠘⠢⠐⣄⠀⠀⠀⠴⠢⡄⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⡀⢠⣤⠀⠀⣀⠀⠀⣀⣤⣄
⢰⣤⣤⠴⠶⠤⠾⠶⠾⠀⠀⠀⠒⠂⠛⠓⠰⠿⠧⠴⠷⠾⠦⠤⠤⠴⠆⠀⣤⠤⢤⡄⠁⠀⠀⢰⣋⣁⡀⠉⡿⠔⠢⡄⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠋⠙⠁⠛⠋⠁⠠⠾⠿⠿⠿⠶⠤⠤⠤⠧⠄⠘⠛
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠉⠀⠀⠠⣴⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⡀
⠄⡀⠀⡀⢠⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⡉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠁⠁⠁⠈⠉⠉⠁⠉
⡆⣄⡷⠀⡼⣄⠀⢀⡀⠀⣸⠡⢛⣀⣧⣻⣽⣇⣀⣀⣀⣀⣀⠀⣀⣀⣴⡷⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡆⠏⡟⢡⣟⣾⣾⢀⣇⣆⣟⠰⠮⡉⠁⣀⠀⠀⠀⠂⠀⠀⠀⢠⡇⠀⠘⣻⢿⣯⡆⠆⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠘⠀⡄
⠟⢰⣰⡧⣩⡎⠙⠞⠒⠈⠀⢀⡠⠔⠈⠀⠀⠀⢀⠐⢀⡠⣤⡚⠀⠀⠈⠻⢿⣷⢣⢸⡌⠆⢠⠀⢹⠀⡅⢀⠀⢀⠀⠰⢀
⣟⣸⡿⠛⠊⠁⠀⢀⣠⡴⠚⢉⠀⠄⠀⠀⠀⠄⠁⢀⠞⡤⠺⠁⠀⠀⠀⢀⣤⣶⢟⡋⢿⢀⢈⡄⡄⣀⢣⡈⠀⣸⠃⠀⣾⠈⡀
⠁⠀⠀⠀⢀⡤⠴⠋⢁⡀⠢⠀⠀⡠⣂⠄⠀⠀⡰⠋⠘⡽⠀⠈⢠⠀⠀⠀⢈⡿⣸⡅⣻⣈⡌⢰⡟⢋⠀⡇⠁⠇⠀⠂⢸⢸⣷
⢀⣠⠴⠚⠁⠀⢀⡸⠁⠀⠀⣐⣄⠣⠀⠀⠀⡜⢡⢠⣼⠃⠀⠀⣾⠀⠀⠀⢈⣸⣛⣛⣋⢿⣃⡘⣧⠄⠀⣷⢠⠀⡼⠀⡖⢨⡾
⠉⠀⠀⣠⣶⠙⠋⠀⢀⢠⣳⠹⠌⠀⠀⢠⠌⠄⣠⡻⠇⠀⠀⠐⠇⠀⠀⠀⠩⠑⠛⠋⢉⢴⡇⣧⢸⣧⠀⠁⡿⢡⣻⠀⡿⡘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣼⣷⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠿⠒⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣭⣴⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣥⡈⣡⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠴⢾⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡯⠀⠐⠀⠀⣀⡠⠤⠄⠒⢚⣶⣠⣤⣤⣶⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⢀⣴⣿⠏⣰⣿⣿⣷⡄⢹⣿⣿⣿⣛⣳⠾⢠⡖⠋⢡⣠⡄⣠⣶⣼⣿⡹⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠛⠟⠀⠙⣿⣿⣿⣧⡸⣿⣿⣿⡿⠁⠀⢿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⣶⣦⣶⣿⣿⣮⣿⠿⠶⢤⣥⠾⠁⠀⠀⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⣠⠆⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⢻
⠀⣠⠞⠁⠀⠀⢀⣄⡻⣿⣿⣿⡟⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣰⣿⣿⣻⡆
⣸⠇⠀⠀⠀⢠⡾⠉⢳⣿⣿⣿⠀⢀⣴⣿⣷⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⢻⡗
⣿⠀⠀⠀⠐⠋⠀⠀⢾⠟⠋⣿⣤⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠷⢻⡆
⠙⠳⠶⠦⢤⡴⠚⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠐⠻⣿⣿⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣄⣀⣾⣿⣿⡇⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣻⣿⣿⡿⠿⠿⠿⠿⠿⠿⢟⣛⣋⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠛⠂⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠈⠀⠀⠀⠀⠀⠀⣆⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⡉⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⢀⣀⡤⠔⠚⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠛⠻⢿⣯⣛⢿⣿⣿⣿⣋⡴⠟⠉⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⣿⣿⡎⠿⠛⠛⣫⣾⣷⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠘⠇⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣶⡀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⣠⠞⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣭⠶⠞⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡾⠛⠋⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⣽⣿⣿⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣶⣤⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⠛⠋⠙⣛⣡⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠛⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⠛⠛⠻⠿⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣴⡿⠿⠿⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⣦⣤⣤⣤⣴⡿⠝
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⣬⣿⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⡿⢿⠿⣿⠿⡙⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠛⠛⠛⠻⠟⢿⣿⡿⠿⠿⠿⠿⠿⣿
⣿⣶⣷⣶⣾⣶⣷⣶⣿⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⢶⣳⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠠⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⡞⠉⣩⣆⠈⠛⣿⣄⠀⠀⠀⠀⠀⠀⠓⢄⠀⣑⡈⣳⣤⣶⡛⠋⠁⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣨⠇⠀⠎⠛⠁⠀⠀⠀⠛⡆⢀⠀⡀⠀⠉⠻⣅⢠⣶⠟⣉⠙⡛⠛⠉⠈⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣶⣄⣀⠀⠀⠉⠲⣄⠀⠀⢲⣄⣼⠦⠶⠃⠄⠀⣈⠀⠀⡀⠈⢉⡟⠉⠛⠉⠙⠋⠀⠐⠋
⠀⠀⠀⠰⠂⠀⠀⠀⠆⠀⢾⣿⢁⠹⣜⢦⠀⠀⠙⠶⣽⡮⠹⣿⣍⣷⠶⠶⠟⠿⠿⢷⣬⡤⠀⠁
⠀⠀⠀⠀⣨⠥⠀⠀⡤⠀⠈⢿⣟⣷⡜⢿⡇⠀⢀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠐
⠀⠀⠐⡤⠿⠔⠀⠀⢅⠀⠀⠸⣿⣿⣿⣛⣣⡄⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡦⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠡⣀⠀⠄⠀⠀⠀⢄⡀⠈⠻⠿⣿⠟⠁⠀⠁⠀⣀⠤⠀⠀⠀⣠⠠⢲⠇⢰⡆⢀⠀⠀⠀⠀⠀⠈⢶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⢠⠊⠀⠀⠀⠄⢀⠘⣠⣷⣤⣼⣿⣿⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⣀⠀⣈⡄⢦⣤⠀⢄⡀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣷⡦
⠀⢀⠀⣀⡿⠟⣹⢧⣭⣶⣛⣳⠛⡆⠀⠀⠀⠋⢒⠘⠃⡀⣿⣿⣷⣿⡿⣟⠙⠙⠏⠙⠢⣅⣾⠁⠀⠀⠀⢀⠔
⠀⠘⣿⢿⠳⢞⢧⢺⣿⣟⠻⡿⣷⢤⣀⠀⠀⠐⠚⠒⠶⠚⠛⠛⣁⣈⠉⠻⡗⢲⠖⣢⣴⣯⣿⣦⠒⠆⠀⠁⠐⠶
⠀⠀⢰⣾⡖⣸⢋⡧⠌⠹⠇⢰⡜⣧⣌⣧⣄⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⠓⠴⠼⠿⠟⠁⠀⠀⠀⠂
⠀⠀⠈⢛⣿⣽⡿⢶⠐⣆⡀⢈⡷⣼⠟⣿⣟⣆⠀⠀⢀⣄⣴⠰⣾⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡤
⠀⠀⠀⠨⠙⢛⣛⣛⠁⣬⣿⣟⣿⣯⣯⣿⣿⠷⠂⠀⠀⠙⢿⠂⢩⠃⠈⠉⠉⠀⢧⣤⣡⣶⣿⣿⣧⣄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠈⠁⢲⣍⢡⠀⡀⠀⠀⠿⢻⣧⣽⣷⢾⣤⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⡓⢸⠂⠀⠀⠀⠼⡦⠀⠁⠀⢀⡄⠈⣿⣿⣿⣸⣯⡐⠀⠀⠀⢠
⠀⠀⣀⠀⢀⡤⠴⠶⠚⠓⣒⠈⢉⠀⠀⠀⠀⠀⠸⣿⣷⠲⡤⣤⡤⠀⠁⠲⠂⠀⠀⠐⢃⡟⣿⣯⣿⣷⣷⡖⠀⡐⠀⡀
⠀⢠⣏⢳⣛⡅⠶⠾⠿⣷⡎⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠤⠂⢉⡭⣿⣇⠀⠀⠀⠩⡰⠛⣿⣿⣿⣿⣷⣵⣤⡟
⠀⠀⣿⣿⢽⣷⣿⣾⣿⡟⠑⠁⠀⠀⡠⠞⠀⠀⠂⠘⠂⠀⡰⣯⣿⠿⠷⠛⠁⢀⠀⠀⠀⠠⠾⣛⠛⠿⢿⣛⠷⠚⠁
⠀⠀⠘⣿⣵⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠈⠐⠀⠒⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢷⠀⠀⠀⠀⠾⢥⣶⣴⠟⢿⣦⡀⠀⢀⠀⠀⠀⠀⢀⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡒⢉⣡⢤⡾⠀⠀⣴⣤⣀⠂⢤⡀⠀⢾⠿⣿⠟⠻⣷⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⢰⣏⢱⠍⠐⠋⠀⠀⢶⡶⢶⣿⢿⣦⣈⠿⠛⠳⢤⡀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⢤⣉⠂⠠⠊⠀⣠⠶⣯⣵⡿⠟⠋⠀⣀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣳⣦⡀⠙⠧⠀⠈⠀⠤⡉⠻⣿⣶⡆
⠀⠀⠀⠀⠠⢌⠲⢠⣰⡾⣱⣾⡽⠋⠀⠀⠀⢀⠀⠈⢰⣶⣾⣿⡷⠤⡀⠀⠀⠀⠀⠈⠙⠛⠦⠘⢦⠀⠀⣀⣀⡁⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠒⠿⠾⠛⠁⠀⠀⠒⠂⢀⣷⣮⣓⣞⣟⣛⣻⣥⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠈⠻⠲⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣯⣒⠚⠛⠛⠛⠻⣿⣿⣿⣿⠟⠎⢀⠀⠀⠀⠀⡄⡠⠀⠀⠈⠓⠠⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⣾⣿⣷⣷⡶⣞⣾⣶⣾⠗⡶⠁⠀⠀⢀⣻⣴⡌⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠛⠿⠇⠒⠋

⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⢉⡉⣁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡈⠙⠛⠙⣶
⠀⠀⠀⠀⠀⡤⠚⢿⡀⣁⣈⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠮⠭⣤⣀⣻⠏
⠀⠀⠀⠀⠀⢫⠀⢸⣿⣼⣿⣿⢏⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠢⡄⠀⠀⠀⠀⡰⠆⠰⠂⣹⠟
⠀⠀⠀⢀⡔⠩⠆⢸⠉⢹⠉⣸⣇⠀⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢨⠃⠀⠀⠀⠀⢸⢗⡶⣶⣿⡎
⠀⣠⣖⠯⡤⠒⠛⢻⠉⠉⠉⠑⢻⡀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠀⠀⠀⢀⣤⡼⣿⣿⣿⠟⢣⣄
⣼⠏⠀⢀⣧⣤⣤⡼⠀⠀⠀⠀⢸⣧⡀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣿⠀⠀⢰⡟⠇⠋⢳⠏⠉⢚⠕⠉⠡
⠻⠷⠶⠛⠁⢿⡏⠁⠀⠀⠀⠠⢬⠀⠘⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡏⣄⡀⣸⠃⠀⠁⠉⠉⠁⢸
⠀⠀⠀⠀⣀⣸⣷⣄⣒⣤⡔⣀⡎⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠶⢤⣏⣈⡆⠀⠀⠀⠀⠀⠸⡇
⠀⠀⣀⣀⣀⠀⢀⣤⣤⠖⠒⠋⢉⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⠛⠇⠀⠀⠀⠀⠀⣰⠁⠀⢀
⣰⣾⣿⣛⣯⣵⣏⠀⠸⣤⡤⡴⢋⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠸⣄⡀⠀⠀⢀⡉⠐⣲⡾
⠹⠿⠛⠛⠛⠁⠘⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠨⢉⡻⠖⠉⢘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣦⣤⣤⣤⡤⢅⣀⣴⠃⠀⡆
⠀⠀⠀⠀⠀⢀⡤⠒⠦⢤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢠⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⣿⠶⠒⠒⠚⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠖⠶⢾⡅
⠀⠀⠀⠀⠀⠀⣿⡈⠁⠘⠋⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢁⡉⢸⠇
⠀⠀⠀⠀⠀⠀⢸⣧⡐⠖⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣾⡿⣿⣿⢿⣶⡤⢤⡀
⠀⠀⣠⢤⡖⡶⢏⠣⢼⣿⠿⢫⢷⠶⣄⣀⠀⠀⠀⡜⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣿⡇⠉⠛⠓⠁⢹⡇⠀⢹⡄
⠀⡜⠁⢠⡇⣯⠈⠑⠋⡏⠛⠁⢸⢠⠃⠈⢳⣀⠞⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡏⠳⠤⠤⠤⠤⠚⢳⠀⠀⢱⡀
⢰⠃⠀⢸⣧⣸⠀⠀⠀⡇⠀⠀⡏⢸⠀⢠⡼⢃⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇
⡏⠀⣎⠉⠉⠉⠳⢦⣤⣧⡤⠞⣠⢼⡤⢮⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⠴⣾⠀⠐⠀⠀⠀⠐⠀⠸⣷⠤⠴⢿
⡇⢠⠟⢉⡷⠒⠒⠒⠛⠉⠉⠉⠀⠀⢈⣿⢏⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢻⠂⠀⠀⠀⠀⠀⠐⠘⡇⠀⢀⡟
⢸⣇⡀⣸⡀⢀⣀⣠⡤⠖⠾⣟⣳⣴⣋⣨⣮⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⠉⠦⣤⣄⣀⣀⣀⣤⠤⠏⠓⡞
⠀⠙⠛⣿⣿⡿⠋⠁⠀⠀⠀⠉⠉⠙⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣀⣸⡟⠻⠿⣿⣟⣇⣠⣰⣛⡄
⠀⠀⠀⢹⣿⠀⡀⠀⠐⠒⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡵⣿⢦⣄⣀⣉⣛⣿⣿⡿⠃
⠀⠀⠀⠀⠉⠑⠒⠲⠶⠶⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣿⣾⣷⡟⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⣤⣤⣴⡄⢀⡀⠀⠀⣀⣀⠀⠀⢠⣤⣿⣧⣤⣤⠀⡀⠀⣤⣤⣴⣾⣷⣄⣤⣤⣴⠦⣠⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣶⣤⢖⣤⣤⣡⣸⣾
⠛⢻⢻⢛⠛⠃⡛⠛⠓⢛⠛⠻⠛⠛⠛⠛⠛⠃⠉⠁⠀⠈⠀⠈⠉⠙⠉⠉⠛⡿⠟⠛⠛⠉⠉⠀⠀⢰⠆⠀⠀⠀⠸⡭⠿⣿⣿⠾⣿⣿⣿⠿⣿
⢠⠁⠀⡀⠀⠢⠈⠀⢈⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠒⠂⢀⡀⠈⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠲⢤⡀⠉⠒⠤⣀⠒⠤
⡘⢰⠀⡧⠘⡀⠀⢄⠀⠑⠄⡀⠀⠢⠈⠁⠢⢀⠀⠢⢄⠀⠀⢀⠀⠂⠀⠤⠄⠀⣀⠤⠂⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠐⠦⢀⠙⠲⠤⣀⠙⠲
⠁⢼⠀⢰⠀⢠⠀⠀⢂⠀⠀⠙⢦⡀⠀⠁⠀⡀⠙⠢⡀⠙⠢⣀⠁⠦⣀⠀⠈⠉⠀⠀⠚⠀⠀⠐⠂⠀⠠⠔⠒⠈⣀⡠⠤⠂⢀⠁⠲⣄⠈⠑⢤
⠀⣼⠀⢸⡄⠀⠇⠀⠀⠳⡄⠀⠀⠹⠄⠀⠀⠈⠢⠄⠈⠲⠄⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠐⠖⠆⠀⠠⢠⠒⠈⠁⢄⠈⠙⢦⡀
⠀⠸⠀⠀⠧⠀⠘⠀⠀⠀⠡⠬⠍⠀⠀⠀⡀⠤⠈⠀⠀⢀⡐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠶⠆⠀⠀⡤⠤⠀⠳⠀⡀⠃
⠠⠀⠐⠀⠀⠂⠀⣀⠀⠠⡄⠀⠢⠀⠒⠀⠁⠀⠀⡀⠀⠀⠉⢀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠒⠀⠀⠠⠤⠀⠀⠲⠒⢀⠉⢀⠤
⢶⠀⠘⠀⠉⠁⠀⠀⡀⠀⠠⠤⠄⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠐⢀⣤⠄⠀⠈⠁⣀⡤
⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⣀⡄⠀⠀⢀⣠⠄⠀⠀⠈⠀⠰
⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⡀⠀⠈⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣀⠀⠀⠀⠀⣠⡴⠆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠
⠀⠀⠀⠀⠉⠙⠒⠤⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠊⠁⠀⠀⣀⠀⠀⠈
⢾⣶⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠰⠓⢤⠄⡀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠉⠉⠉
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠉⠁
⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠚⠂⠀⠀⠀⠀⠀⠰⠗⠂⠂⠒⠀⠀⠀⠀⠚⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⢤⡤⠤⠖⠂

⢀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠂
⠐⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠄
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⣄⣤⠛⠁⢠⡴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⢄⠀⠀⣁⠔⠀⠀⠀⠀⠀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠅⠀⠄⠈⠈
⠀⠀⠀⠀⠅⠀⠸⠒⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠁⠀⠀⡀⠀⢀⣼⠉⡪⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⡀⠀⠀⢄
⠀⠀⠉⠀⠀⠄⠀⠠⠀⠀⠁⠀⡰⠋⠑⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠘⠀⢠⡀⠊⠀⠀⠀⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢱⠋⠋⠀⠴⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⣿⢆⠂⠀⠀⠼⠊⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣤⣈⣈⣁⣁⠂⠠
⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠉⠉⢀⣀⣀⡀⠉⠉⠉⠛⠳⠶⢦⣭⣀⡀
⠀⠀⠀⣠⡾⠛⠁⢂⣠⣴⣾⣯⣽⣿⣿⣿⣟⣛⣓⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⣀
⠀⠀⠘⠻⢷⣖⡔⡫⢚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀
⠀⠀⠀⠀⠈⠘⠛⠑⢿⣿⣿⣿⣿⢏⣽⣶⣿⣾⡇⠈⣉⡙⢛⠳⣦⣄⣀⡂⢀⣀⠀⠀⠀⠀⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⣮⣿⣿⣿⠏⢱⣿⣿⣿⡶⠲⣿⣿⣿⣿⣿⣿⣷⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢉⡉⠀⠀⠻⠿⠛⠀⣠⡾⠟⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣦⣄⣴⣠⢥⣀⣿⣃⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢠⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠸⠷⠉⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⢀⣀⣠⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡅⠉⠩⠉⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⠢⠬⣯⣤⠀⠈⣄⠐⠐⠊⠀⠀⠀⠀⠘⠛⠛⠂⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣄⠛⢿⣿⣦⡀⠐⠀⠀⠀⢠⣿⢃⣦⣄⢀⠈⢲⢢⣀⣘⣿⣩⣤⠂
⠀⠀⠀⠀⠀⢀⣾⣆⠙⠿⣽⣷⢦⣉⡙⠻⣦⣤⠀⠀⢹⡿⢸⣿⡿⢹⡦⠀⠒⠀⠉⠹⠗⠔
⠀⠀⠀⠀⠀⠈⠟⢿⣷⣦⣈⡁⠙⠟⢽⢷⣦⣝⠳⡄⠸⡏⣼⡿⠁⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠻⠶⣤⣄⡀⠉⠷⠜⠂⠇⠋⠀⣸⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⢀⣤⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠈⠉⠁⠄⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⢀⡴⠾⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⠀⠀⠄⠒⠂⠀⠀⠀⠘⠉⠉⠉


⠀⡀⠄⣠⠄⣀⡀⠀⡀⠀⣀⠀⡀
⢦⡈⠲⢄⡉⠒⢭⡑⠂⠤⢀⠋⠥⣂⠢⠤⣐⡂⠤⢀⣀
⠀⠙⢦⡀⠙⠢⣀⠈⠓⢦⣀⠉⠲⢤⣌⡁⠂⠬⣉⠓⠲⠭⣝⡲⠤⠤⣄⡀
⢳⡀⠀⠙⣦⠀⠈⠳⣄⠀⠈⠳⢶⣀⠈⠙⠳⢤⣀⡉⠑⠶⢤⣍⠙⠒⠦⣭⣙⠒⠦⠤⣄⣀
⠈⢻⣤⠀⠈⢳⡄⠀⠈⠻⣤⠀⠀⠉⠳⣤⡀⠀⠈⠑⠶⣤⣀⠈⠙⠲⢦⣀⠉⠙⠲⢦⣄⡉⠛⠲⢦⣄⡀
⠀⠀⢷⡀⠀⠀⠙⣤⠀⠀⠈⢣⣄⠀⠀⠈⠻⣦⣄⠀⠀⠈⠙⠷⣤⡀⠀⠉⠛⠶⣄⡀⠈⠙⠲⣦⣀⠈⠉⠛⠶⣄⣀
⡇⠀⠈⢿⡆⠀⠀⠙⣷⡀⠀⠀⠙⠷⡀⠀⠀⠀⠙⢷⣦⠀⠀⠀⠈⠛⢷⣤⡀⠀⠈⠛⠷⣤⣀⠀⠉⠳⢦⣤⣄⡈⠙⠳⢦
⣿⣶⠶⠾⠿⣶⣶⣶⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣾⣿⣿⣿⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸⣿⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⠀⠸⣿⠀⠀⣧⡈⠳⣄
⠀⠀⠀⠐⡄⢀⡤⠖⠉⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⢞⡥⣸⡷⠀⠀⠀⢿⠀⣄⣿⣧⡄⠈⣳⡄
⠀⠀⠀⠀⠘⠾⡀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣤⡴⠋⢠⢸⡇⣿⡇⠀⠀⣠⠀⢰⣯⣿⡟⢃⢞⠝⠁
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⡑⠈⢿⣧⠹⡄⢸⢸⡇⣿⡇⠀⠀⣿⠀⢸⠛⣃⢔⠕⠁
⠀⠀⠀⠀⠀⠀⣈⡆⠀⢐⠆⠰⡁⠘⣆⠈⡿⠛⠛⣆⢼⡇⢹⠀⠀⠀⡟⢀⣠⡾⠗⠁⠀⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢳⡀⢹⣄⣸⠖⠃⠀⠀⠈⢆⠁⢸⠀⢀⣠⡶⢟⣋⠴⢒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡾⠛⠉⠀⢘⠇⠀⠏⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡎⠀⢀⣸⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⢤⣤⣄⣀⣠⡤⠶⠒⠚⢛⣒⣚⠛⢧⠀⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣥⣤⣍⡉⠉⣤⣤⣄⠲⣶⣶⣶⣶⣶⣿⢃⣾⣿⡿⣋⣴⣿⢀⡟⣷⠇
⠀⠀⠀⠀⠀⠀⣼⠁⠾⣿⣶⣯⣽⣿⣦⡘⢿⣿⣷⣮⣿⣿⣿⡿⠃⣚⣻⣻⣿⣿⣿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠶⣿⠗⠲⠶⠤⣭⣛⠿⣿⣿⣌⡛⢋⣭⣭⣭⣍⠐⢋⣭⣭⣭⣭⡭⠀⢀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠆⡖⢩⣛⠶⣌⡙⠻⠶⣦⣭⣭⣭⡴⠿⠟⣋⣉⣥⠴⠞⡻⢟⣼⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡲⠶⣾⣿⣑⠈⠉⠛⠒⠶⠶⠶⠖⠚⠋⠉⠉⠀⠰⠖⣋⡵⢛⡁⠦⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠁⢀⠍⠙⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠛⠋⠇⠀⠢⠀⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠙⠛⠉⠉⣉⠁⠁⠀⢀⠠⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠉⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠁
⠀⠀⠀⢀⠆⠁⠀⠀⠃
⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⢀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡄⢀⢀
⠀⠀⠉⠒⠒⢩⠃⠀⠀⢉⡁⢠⡁⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢯⠀⠀⠀⠈⠋⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠏⡄
⠀⠀⠀⠀⠀⠸⢌⡁⠀⠀⠸⣦⡄⠀⠂⠒⡄⠀⠀⠀⠀⠀⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⣐⠀⠠⠀⠀⠀⠀⠀⡄⠒⡀⠀⢄⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⢀⡀⠦⠀⡝⠆⠄⠀⠀⠑⣄⠰⠐⠂⠁
⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠈⠀⢈⠠⠀⡀⢠⢠⠂⠰⠀⠀⢸⠀⢐⠀⠀⢀⠀⣠⣄⠲⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠗⠈⠀⠀⠀⠀⠀⠀⠀⢨⢥⠢⠆⠀⢅⠈⠙⠛⠘
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⡔⠀⠀⠀⠀⠀⢀⠐⠋⢇⣈⠇⢀⠆⠄⠀⠀⠈⡀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠⡁⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠤⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⢈⡁⠀⠀⠀⢸⠀⠀⡁⠀⠀⠀⣧⠀⠀⢸⢸⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠊⠁⠀⢠⠀⠘⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠇⠉
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠜⠢⠄⠈⠀⠀⠀⠠⠈
⠀⠀⠆⠀⠀⠀⠀⠀⠄⠊
⣷⣿⡿⢿⠿⠿⣿⡷⣿⡿⢷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣾⣿⣷⣿⣿⣿⣷⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⢤⣄⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠒⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠋⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠉⠳⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠁
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠧⠤⠤⠤⠤⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢳⡀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣒⡒⢦⡀⢸
⠀⠀⠀⠀⠀⢀⡷⠚⠛⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣭⡍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢀⡇⠘⡆
⠀⠀⠀⠀⠀⡞⢀⡴⠒⠲⢄⠙⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠯⠞⠀⠀⢳
⠀⠀⠀⠀⠸⡇⠘⠀⠀⠀⣼⣧⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⣠⠶⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣛⣉⣉⣁⣀⣀⣀⣀⣠⣤⣴⡟⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⢙⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠂⠈⠉⠒⠤⣀⠀⠀⠀⢲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⡵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣰⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⢿⠑⠒⠢⠵
⠀⠀⠀⠀⠀⠀⢰⠁⡠⢠⠃⠀⠀⠀⡆⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⡇⣰⠃⡆⠀⠀⠀⢠⠁⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⢃⢨⠀⠀⠀⠀⠀⢡⠈⢇
⠀⠀⠀⠀⠀⢠⣠⡏⠀⠀⠀⠀⠀⡌⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⡆⠸
⠀⠀⠀⠀⠀⠘⢿⠇⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡠⠤⠐⠒⠉⢋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠛⠓⠐⠒⠒⠤⠤⢀⣀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠈⢿⠁⡇⠀⠀⠀⢠⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢐⠇⠀⠀⡠⢀⡔⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠃⠀⠀⠀⣠⣬⡉⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⡜⢀⡠⠊⠰⠊⠀⢄⣀⠎
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⣼⣿⣿⣿⠀⠀⢡⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆⠀⠀⠑⡄⠸⠤⠑⠒⠀⢀⡤⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠳⡀⢰⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠰⠋⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡾⠟⠛⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠈⠛⠯⠄⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⠒⠒⠒⠒⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠈⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢶⠴⠇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡺⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⡶⠓⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣄⣤⣀⣿⡀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⠛⢻⡿⢿⢟⣿⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⡐⠀⠀⢰⡤⢸⡿⢿⣿⣶⣿⣿⣾⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠖⠠⡀⠀⠰⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣂⣼⣶⣦⣄⢠
⠀⠀⠈⠀⠀⢀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠉⠁⠀⠀⠈⣯⠛
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⠛⠿⣛⠿⡿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠖⠒⠒⠒⠒⠒⠛⠋⠙⠛⡒⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠀⠀⠉⢀⠉⠓⠲⣄
⢀⡤⠴⠖⠚⠛⠉⣥⡴⠞⠉⠀⠀⠳⣄⢀⡔⠀⠀⠢⡴⠋⠀⠢⡀⢀⠴⠃⢄⠀⣼
⢸⠀⠀⠀⣡⣴⠛⠁⠈⢢⣤⠀⠀⠀⡨⠻⣄⠠⠖⠁⠀⠀⠀⠤⠈⠁⢀⣀⡤⢾⡇
⠈⣷⢤⣤⣀⡈⠙⢦⡚⠁⠈⠑⠄⠀⠀⠀⢈⣡⡤⠖⠒⠒⠒⠒⠚⠛⠉⣁⡴⠏⠀⠀⢀⣀⣠⠔⣫⣽⣭⣓⣒⠤⠤⠤⢄⡀
⠀⠈⢳⣄⣈⠉⠉⠛⠓⠶⠖⠲⠖⠒⠚⠛⠉⢀⣠⠴⠖⠒⠚⠛⠋⠉⠉⠁⠀⢀⡴⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠆⣿⣶⣌⠳⣄
⠀⠀⠀⠙⠛⠷⠴⠤⣴⣤⣤⣤⣀⡴⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣘⣻⣿⣛⠿⠿⣛⣛⣿⣛⣡⣶⣶⡆⣹⣿⣷⣜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⣫⣽⡶⢿⡿⠿⣟⣩⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣿⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠿⡗⠮⣍⣲⣟⣿⣯⣭⣭⠭⠽⣯⣼⣟⣛⣛⣛⣿⡿⣃⣿⣋⣥⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡄⠀⡿⠀⣾⣿⠁⠀⢸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣧⡉⠉⠉⠁⢠⡿⠃
⠀⠀⢀⡴⢒⣛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠚⠳⠶⣿⣿⣥⣤⣼⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠧⠶⠒⠚⠉
⠀⣴⢋⣾⣿⣿⣇⢸⣧⣄⣉⠓⠲⢶⠶⠶⠶⠶⠶⠶⠦⣤⣀⡀
⢸⢃⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⠿⠋⣰⣿⣿⣿⣿⣶⣶⣤⣉⣙⠶⣄
⣿⢸⣿⣿⣿⣿⣿⡄⠈⣉⣉⠁⠴⠾⠿⠿⠿⠿⠟⠛⠋⣉⣉⣩⣤⠘⣆
⣯⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠋⣠⣿
⢹⣆⠹⣿⣿⣿⣿⡟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⠤⠶⠞⠻⣿⡏
⠀⣿⣷⣬⣉⡛⠋⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣡⡖⠋⠁⠀⣠⡴⠞⠋⠀⣀⡤⠔⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠸⣿⡀⠈⠙⠓⠲⠬⣭⣉⣉⣉⣭⣴⣾⣿⣿⣧⣠⠖⠋⠁⠀⢀⡴⠊⠁⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠛⠉⠁⠀⠀⠉⠓⢄⡀
⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⠞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣤⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⠉⠓⠒⠚⠛⠉⠉⠀⠀⢀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⣠⡤⠴⠒⠚⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⡿⠿⢿⠏⣨⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠈⠃⠀⠘⠂⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣶⣶⣶⣷⡾⠧⠀⠀⡀⠀⠀⠀⠀⠀⠀⢾⡇⣁⢠⣿
⠀⠀⠀⠀⡀⠀⠇⠀⠀⠐⠇⠐⠐⠀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠼⠟⠛⠻⡏⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋
⠀⠀⠀⠐⠿⣷⣶⣶⣶⣶⣶⣶⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠢⠰⠐⠆⠆


⠀⠀⠀⠀⠀⠀⠐⣾⣷⣿⣿⣷⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢶⣦⠀⢠⣶⣾⣶⣄
⠀⠀⢠⣀⠀⠀⠀⠿⠛⠛⢹⡇⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣿⣽⠇⢺⣇⣤⣰⣿
⠀⠀⠾⢿⡏⣛⢗⣛⢲⡖⠚⢳⠛⣏⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠶⠖⠀⣳⣾⠋⠰⠶⠀⠀⡆⠀⠀⠀⢀⣴⣶⣶⣄⠀⢀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠎⠈⠈⠳⣄⠀⠀⠀⠁⠀⠀⠀⢸⣏⡀⣀⣹⠇⢾⣋⣀⣈⣿
⠀⠀⢀⡀⠀⠀⠀⢾⣿⣿⣿⣶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠀⠈⠻⠿⠟⠋
⠀⠀⣼⣿⡖⠲⡶⠾⢦⡶⠷⢶⠖⡒⣾⣿⡄
⠀⠀⠀⠈⠉⠛⠚⠛⠚⠓⠚⠚⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠐⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠀⠀⠀⢀⣀⣀⠀⠀⡇⠀⠀⠀⠀⠀⣧⣤⣤⠀⣿⡇⠀⣿
⠀⠀⢠⣄⣀⠀⠀⢻⣿⡿⠛⠉⠀⢀⣀⣤⠀⠀⠀⠀⢸⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⡇⠀⠀⠀⠀⢀⣿⣿⣿⠀⣿⡇⠀⣿
⠀⠀⠺⢿⣏⣙⣿⣹⡫⡟⣛⣹⣉⣍⣿⠿⠂⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣿⣿⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠿⣿⣦⡀⠀⣴⣿⠿⠋⢁⣠⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠙⠻⣿⣦⡀⢀⣴⣿⠿⠛⠛⠛⠿⣿⣦⡀
⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆⠉⢁⣤⣾⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣈⠉⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⣿⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⢀⣿⡏⠀⠀⠀⠀⢀⣴⣿⠿⠋⢁⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡌⠙⠿⣿⣦⡀⠀⠀⠀⠀⢹⣿⡀
⠀⢸⣿⡇⠀⠀⠀⣰⣿⠟⠁⠀⢠⣿⡟⠁⠀⠀⠀⢠⡶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠛⠳⠄⠀⠀⠀⠻⣿⣆⠀⠈⠻⣿⣆⠀⠀⠀⢸⣿⡇
⠀⠘⣿⣇⠀⠀⢰⣿⠏⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠹⣿⡆⠀⠀⣸⣿⠃
⠀⠀⢻⣿⡀⠀⢸⣿⠀⣀⣤⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣤⡀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣀⠀⣿⡗⠀⢀⣿⡟
⠀⠀⠈⣿⣷⠀⠸⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⢸⡁⠶⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⠇⠀⣾⣿⠁
⠀⠀⠀⠘⣿⣧⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⣼⣿⠃
⠀⠀⠀⠀⠹⣿⡎⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢷⣿⠏
⠀⠀⠀⠀⠀⢿⣿⡈⠻⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⠟⢁⣿⡿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣸⣿⠇⠀⣼⣿⠃⠘⣿⣧⡀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣠⣴⠶⠛⠁⠀⠀⠀⠀⠀⣴⣿⠏⠘⣿⣧⠀⠸⣿⣇
⠀⠀⠀⠀⢠⣿⣟⣠⣾⡿⠃⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠘⢿⣷⣄⣻⣿⡄
⠀⠀⠀⣠⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣄
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⣴⣶⣦⣶⣶⣄⡀⠀⠀⠀⢠⣶⣾⣿⣶⣾⣿⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠿⠻⠗⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⢿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠣⠀⠀⠠⠴⠶⠦⣄⠀⠀⠀⢠⡴⠶⠒⠀⠀⠀⢸⠯⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⠛⠄⠀⠀⡤⣤⣤⠄⠀⠀⠀⠀⢤⣤⣄⠀⠀⠀⠟⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⢀⣀⣀⣀⣀⠀⡀⣠⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠢⢄⣈⣀⠤⠀⠀⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠁⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⢀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠄⠐⢲⠒⠉⢹⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡭⣽⣿⣆⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠀⣠⡄⠤⢼⠒⠂⠛⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⡿⣻⣛⡃⣿⣽⣥⣿⣿⣿⡿⢟⡅
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠀⢸⣀⣀⣤⠤⠀⠂⢀⠴⠊⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⡿⠿⠿⠇⣿⣿⣿⣿⢟⣭⣾⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡴⠃⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⢟⣵⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠑⠦⢄⣀⣀⣀⣀⡤⠔⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣻⠿⣿⣿⣿⣿⠿⣛⣵⣿⠟⠁
⠀⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡤⠤⠄⠀⢤⣤⡤⠀⠤⢤⡶⠚⠉⣁⣴⣶⣿⠟⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣠⣶⣯⣴⠶⠞⣿⠟⠁⠀⠀⣰⣿⣡⣴⡾⠿⣽⡿⠁⠊⠀⣀⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠶⣶⠟⠛⠉⠁⠀⣠⡾⠁⠀⣀⣤⣶⠿⠟⠋⠁⠀⣰⠋⢀⣠⣶⣿⡿⠋⢀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡾⠃⠀⠀⠀⣠⣾⣿⡴⠾⠛⢻⡟⢁⡤⠀⠈⣠⣾⣧⡶⠿⠛⣡⡟⠁⠈⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡋⣀⣠⠤⣶⠾⠋⡁⠀⠀⢠⣼⠏⢐⣁⣴⣶⠟⠛⠛⠁⠀⠀⣼⣿⣥⡶⠶⠶⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⣠⠞⠁⠀⠀⠀⣠⣞⣩⣴⠞⠉⣼⠟⠁⠈⠀⢀⣨⣤⠞⠉⠡⠀⠀⢀⡾⠃⣀⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠻⣄⠀⠀⣀⣠⠞⠛⢩⠄⠂⣠⡜⢁⡠⠔⠒⠋⢉⡼⠃⠠⠄⠂⠈⣠⠎⢀⣠⣾⣿⠀⠈⠲⠦⠞⠀⠴⠺⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣪⡟⠁⠀⠀⠀⣠⣾⣿⣾⣿⣗⣶⣶⣶⣿⣤⣤⣄⣐⣦⣾⣧⣶⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⣿⣧⣠⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣑⣟⣹⠟⣿⣷⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⣿⣧⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⠆⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣸⣻⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣐⣚⣍⠴⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠚⠋⠉⠉⠀⠈⠉⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⠿⠿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠙⣯⣀⣤⣤⣤⠤⠤⣤⣤⣤⣈⣉⠛⠳⢤⣀
⣰⠞⠛⠛⠛⠲⢦⣤⡾⠋⠀⠀⠀⠀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣦⣍⠳⣄
⠹⣄⠀⠀⠀⠀⠀⢨⣅⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣌⢷⡀
⠀⠘⠷⣄⠀⣀⣴⣿⡟⠙⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣎⢷⣻⣆
⠀⠀⠀⣸⡿⣹⢏⡾⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠘⣯⣿⣿⣧⡀
⠀⠀⣰⣿⣷⠏⣼⠁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⣿⣿⡏⢧
⠀⢀⡟⣾⡟⢰⠇⠀⠀⣸⣏⣀⣀⣤⣤⡤⠤⠶⠾⠻⠶⠶⠶⠶⢶⣶⣶⠾⢿⡄⠀⠀⠀⠘⣿⣷⠘⣇
⠀⣼⠁⠈⢀⡟⠀⠀⢰⡏⠉⠝⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠑⠄⢹⡄⠀⠀⠀⠸⡏⠀⢻⡀
⢀⡇⠀⠀⣼⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⡀⠘⣇
⢸⠇⠀⢠⡏⠀⠀⣼⠁⠀⠀⣴⠞⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⢦⡀⠀⠀⢻⡀⠀⠀⠈⣧⠀⢿
⣼⠀⠀⣼⣥⡶⠞⠋⠀⠀⠙⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠁⠀⠈⠷⠦⣤⣤⣹⡄⢸
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠀⠸
⣷⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⣄⣀⣀⡀⢀⣀⣀⣠⡤⠶⢦⡀⠀⠀⠀⠀⠀⢀⡟
⣿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢷⡶⢤⣤⣉⣉⣉⣉⣉⣉⣤⡤⢶⡾⠀⠀⠀⠀⠀⠀⣼⠃
⠛⠶⠶⠤⣤⣄⣻⣄⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠈⠉⠉⠁⣀⣠⡴⠋⠀⠀⠀⠀⠀⢀⣼⣃⣀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠚⠉
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠑⠲⠋⠉⠑⠚⠉⠒⠦⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢤⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⡤⢄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣀⠜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠶⠒⢆⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⡠⠾⡄⠀⣰⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⢦⡀⠀⠀⠀⣮⣀
⠀⢸⠀⢀⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⢏⠁⠈⡆
⢠⠇⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡀⠀⣠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠸
⡇⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡇⠀⠀⠀⠀⠀⠀⢀⠜⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⣀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢾⡿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠐⠀⢤⣀⣰⣤⡄⠀⣤⣀⣀⣀⡀⠀⠠⣀⣀⡀⠀⢀⣀⣀⣠⣀⣀⣸⣷⣀⣀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠙⠉⠉⠉⠉⠉⠙⣉⡉⠉⠋⡛⠛⣻⣻⡿⠟⢉⡉⠭⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠻⠿⠫⠿⢤⣤⡄⣹⣶⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⡀⢀⡀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄⢚⡿⣾⣦⣀⣀⢀⢀⣤⡀⠀⠀⠀⠀⠀⣴⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣳⣿⣿⣿⣙⣶⣿⣿⡿⠿⠋⠀⠀⠀⠀⡠⠼⡀
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠴⣖⡖⢲⣾⢀⡌⣤⣥⣴⣾⣦⡄⡀⢀⡀⢄⡣⠀⠈
⣀⣀⣀⣀⣀⣿⣟⣒⣠⣳⣖⣺⣿⣿⣽⣗⣛⣛⣿⣟⣋⣷⣘⣛⣛⣘⣳⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣽⣿⣿⣿

⠀⠀⠀⠀⣠⠴⠂⠉⠉⠛⠉⠐⠢⢄⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠲⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠐⡄
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣊⡿⠂⠄⠀⠒⠒⠈⠎⣧⢀
⠀⠀⠀⠀⠁⠒⠤⠄⠤⢴⠞⠛⠉⠉⠀⠀⠀⠀⠀⣈⠀⡌⠐⡢⠄⠀⠀⠉⠀⠈⠃⠎⡆⠀⠀⠀⢀⣀⣀⡤⠤⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⠁⠀⠀⠀⡇⠀⠀⠀⠀⡆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡐⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢤⣀⣀⣠⣴⡎⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠀⠀⠀⠋⠙⠁⠈⠁⠀⠀⠀⠌⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠅⣀⢠⠀⠘⠛⠄⠀⠀⠀⠀⡠⠃⠀⠢⣀⠀⠀⠀⠀⣀⣀⡠⠀⠑⢂⠀⠀⠀⠀⠀⡇⢀⣀⠀⠤⢄⠇
⠀⠀⠀⠀⠀⠸⠠⡌⠁⣲⠂⡜⠀⠀⠀⠀⡸⡑⠁⠓⠀⠘⠳⣠⠤⢺⠁⢀⠦⡎⠀⠀⢣⠀⠀⠀⠀⡏⢉⣀⣀
⠀⠀⠀⠀⠀⠈⢗⡁⠀⡢⠀⠑⣄⠀⢀⣴⠟⡅⠀⠁⠀⠰⠆⠉⠐⠾⠀⠁⠀⠃⠄⠀⠀⢣⡀⡏⠛⠧⡜⢉⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⠀⠀⠀⠙⡽⠃⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠘⠀⢀⢌⣵⠿⠂⢲⢹⠤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡐⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠁⠐⠁⠀⠀⢸⠈⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⡀⠐⠂⠀⠀⠀⢀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⣢⣤⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠐⠐⠀⠀⡰⠋⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠒⠀⢠⠐⠒⠐⠒⠂⠒⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⢀⣇⠀⣀⠤⢤
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣀⣀⣀⡀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⣴⢟⡥⠖⠋⠉⠁⢀⣄⣉⠙⠲
⠀⠀⠀⠀⠀⢠⡟⠀⢀⣴⠞⠋⠉⠉⠉⠙⠳⣄⠙⣧⠀⠀⠀⠀⠀⣼⡷⠋⠀⣠⠖⠋⡀⢢⠀⠁⠀⠀⣦
⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⣿⣄⡼⠐⠶⣧⠴⠛⣷⢸⡇⠀⠀⠀⠀⢻⠃⢠⡞⢡⣰⡼⠁⠊⠒⠛⠛⢛⠁
⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣿⠃⠀⠀⠀⠀⠸⣤⠏⡴⠋⠉⠠⠤⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⢿⡀⠃⠀⠰⠷⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠠⠃⠀⠀⠒⠛⠂⠀⠖⠚⢛⣧
⠀⠀⠀⠀⠀⠈⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠘⡇⢢⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⢹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠐⣒⠆⠀⣠⡾⠁⠀⠀⠀⠀⣤⣀⡇⠀⠱⡄⠀⠀⠀⠀⠠⣖⡆⢠⣏⢈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠘⠻⣢⢀⡷⢿⠀⠙⠦⣄⠀⠀⣰⠏⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠙⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠎⣁⣠⠴⠚⠿⠗⠲⢦⡉⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢰⡏⣏⠚⢋⡤⠀⣄⣠⠖⠁⠙⣆⢳⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⣴⠞⠋⡹⠿⠛⠛⠢⡀
⠀⠀⠀⠀⠀⢸⡄⣀⠐⠩⠄⠀⠀⠀⠀⠈⣆⢸⡼⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣾⡟⠀⣀⡀⣴⢀⡤⣞⣿
⠀⠀⠀⠀⠀⠈⡇⢿⠀⠛⠁⠀⠀⠘⠋⢀⡏⣸⠃⠀⠀⠀⠀⠀⠀⢻⠀⠀⡾⢸⡇⢀⡈⠛⠑⠚⠀⣻⡇
⠀⠀⠀⢠⡻⠶⠁⣸⣆⠀⠀⠀⣀⠀⠀⠸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⡗⠘⠁⣤⡄⠀⠀⢀⣀⣿⣵
⠀⠀⠀⠢⣍⠀⢀⡟⠈⠳⢤⡀⢉⡤⠞⠀⢨⣳⣴⠇⠀⠀⠀⠀⠀⠀⢻⣄⢇⠀⠀⠀⠀⠀⠀⠈⣹⢻⠦
⠀⠀⠀⠐⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⠌⠠⠚⠀⠀⠀⠀⡰⠢⢞⣈⡀⠲⣄⠀⠐⠶⢂⣴⡇⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⡭⠞⠞⠁⠈⠓⠢⠔⠋⢿⡈⠋⠁


⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢻⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣀⣉⣉⣉⣁⣀⣤⣴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠃⠓⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠂⠀⣒⣒⠲⣂⠀⠓⣀⣒⡂⠐⣖⣚⡀⠛⣂⣙⣂⡛⣆⠐⢂⣘⣳⠀⣲⣘⠃⠠⠓⠈⢻⠂⠛⢂⡼⠏⢻⡧⠛
⠂⢀⡒⠀⠀⢹⡆⠀⠘⢳⠀⠀⠉⣷⠆⠀⠈⠳⡀⠀⠒⣃⡀⠚⠃⡀⠘⠁⢠⡘⠃⠀⣬⡋⠀⢀⣍⠀⠀⣍
⣀⠘⠉⠀⠀⡈⠉⠀⠀⢘⣳⣀⠀⠉⢉⣥⡀⠈⠙⢀⣄⣉⠉⠀⢈⣹⡁⠀⠈⠍⠀⠀⠉⣁⣀⠀⠈⢀⣴⣤
⡛⢓⠄⠦⠀⢹⡓⠤⠒⠀⠍⢉⡁⠀⠈⣁⡈⠀⣀⠭⠉⢉⠁⡀⠈⢙⠋⡄⠈⠙⠣⠀⠀⢙⣙⡂⠄⠠⠉⠉⡄
⣿⣿⣾⣷⣶⣾⣿⣷⣾⣾⣾⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣾⣿⣿⣷⣾⣿⣷⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠲⢦⣄⡀
⠀⠀⠀⠀⣴⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⢸⡄⠀⣀⣤⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣆
⠀⠀⠀⠀⠘⣧⠀⠉⠉⠉⠉⠃⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣀⣤⡴⠶⢺⡟⠉⢹⡆
⠀⠀⠀⠀⠀⣿⢦⣄⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⢷⡀⠈⡇
⠀⠀⠀⠀⢀⣏⠀⠀⠉⠉⠉⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⢷⣀⡇
⠲⠤⠖⢻⡟⡏⠉⠛⠒⠒⠒⠒⠚⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠸⡇⠃⠀⠀⠀⠀⠀⠀⢠⠃⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠷⠄
⠀⠀⢀⡴⠃⢰⠀⠀⠀⠀⠀⢠⠃⢸⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⣤⣤⣤⣀⠀⠀⠀⣠
⠀⣰⠋⠀⠀⢸⡄⠀⠀⠀⢠⠃⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠉⠉⠉⠉⠁⢀⡼⠋
⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠋⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⢧⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⢳⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠹⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣀⣤⣤⣤⣀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠉⠉⠉⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⣀⣀⣀⣀⣴⠋⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⠉⠁⠀⢀⣠⠆⠉⢹⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡷⠶⠶⠶⠶⠶⠶⠞⠋⡽⠀⠀⣸⠇⠈⠙⠛⠶⢦⣤⣀⣀
⠀⠀⠀⠀⠀⣤⢐⣤⠞⠛⠛⠛⠚⠛⠉⣧⢷⠀⠀⠀⠀⠀⠀⠀⢰⣃⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀
⠀⢀⣤⣿⣼⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡌⡆⠀⠀⠀⠀⠀⠀⡏⢹⣖⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢻⡀⠀⠀⠀⠀⣼⠀⠀⢻⡤⠴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢿⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢷⠀⠀⠀⢠⠇⠀⠀⣴⡿⡞⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠘⣇⠀⠀⡞⠀⠀⠀⠀⠀⣟⣋⣁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢹⡆⣸⠃⠀⠀⠀⠀⠀⠨⣟⣉⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⠀⠀⠀⠀⠀⣤⡄⢸⣅⣡⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠛⠉⠉⡿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠋⠀⠹⣅⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣎⡄⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⡠⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡳⠊⠁⠀⠀⠀⠀⡎⠛⠀⠀⢠⠂⡓⡠⠊⠐⠄⠀⠀⠠⠂⠱⠉⡠⠂⠀⠀⠀⠐⠔⣊⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡠⠐⢁
⠀⠀⠀⡀⠀⠀⠀⠺⠂⠀⠀⠐⠀⠳⠀⠘⢴⠁⠀⢀⠀⢀⠈⠀⣀⡄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠂⣁⠀⡠⠀⠀⢀⠼⠀⡀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠶⠀⠀⠀⠀⠌⠰⠀⠠⠠⠀⠀⠀⢄⣨⠀⠀⠀⠀⠂⢨⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠟⡌⠀⠀⢠⠁⠀⠀⠀⡔⠀⡆⠁⠌⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠈⢀⢄⣀⢂⡆⠀⣀⣀⣀⣀⠀⡖⠀⠀⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠘⠃⠨⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠔⠚⠀⠄⡀⠀⢡⠀⠀⠀⡀⠀⠁⠀⠉⠀⢐⠁⠀⡐⠀⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡌⠀⠀⠀⠀⠈⢢⢀⠄⢰⢠⠃⠈⠀⠀⠀⢀⠌⠀⠀⠀⠀⠰⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠒
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠀⠀⠀⠀⡁⠀⣠⠌⣀⠠⢆⠀⠀⠄⠀⠂⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⣆⠀⠈⡠⠈⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⡁⢀⠓⢄⠀⠢⡄⠄⡀⠀⠂⢀⢼⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠌⠇⠀⣗⠀⠀⡀⠔⢚⠴⠶⠀⠀⠣⠁⠀⠀⠑⠄⠇⠀⡆⠀⠂⠀⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠀⠀⠀⠀⠀⠀⢀⠂⠀⡰⠠⠂⠂⠀⠀⠀⠀⠰⠀⠀⢠⠀⠀⠐⠀⠀⠃⠀⠄⡀⠀⠀⠀⠀⠀⡅
⠀⢨⠀⠀⠀⠤⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠂⠄⠀⠊
⠀⠀⠉⠀⠀⠀⠒⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⣠⠤⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⢀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⡎⣱⢉⡁⣠⡀⢀⡀⠀⣀⢀⡀⡆⠀⠀⠀⠐⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠄⠐⠤⠀⠴⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡌⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡊⠀⠈⡆⠀⠀⠀⠀⠀⢀⠀⢤⠈⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡏⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣀⣄⣀⢤⠔⠄
⠀⠀⠀⠀⠇⠀⠀⠐⢠⡤⢐⠂⠉⠀⠀⠀⠒⠀⠀⠁⠂⠄⠀⠀⣀⡀⣠⠔⠈⠔⠠⠠⡓⠄⠈⢄⡠⠄⠀⣀⢄⣠⠊⠒⠦⠠⠀⠀⠓⠊⠀⠀⠉
⠀⠀⠀⠀⢠⠀⠐⠀⢨⠑⠢⠌⡁⠒⠀⠄⠀⠀⠀⠀⠀⠄⠂⠈⠤⠿⠃⠀⠁⠸⠀⠀⠈⠢⠀⠀⠑⠀⠲⣁⣀⣠⣤⣤⣤⡤⠖⣶⢒⡲⣖⣲⣒⠒⠐⠄
⠀⠀⠀⠀⠀⠒⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠚⠀⠖⠈⠀⠀⠀⠀⠀⠈⠢⣀⠂⠀⠀⣀⡠⠔⣂⡥⠙⡊⠕⠋⡁⠔⠊⢁⠠⠐⡠⠒⡁⠔⡡⠔⠉⠩⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠀⠘⠁⠀⠐⠳⠆⢉⡅⠊⢁⠠⢰⣍⣠⠔⢁⡠⠐⠈⡠⠐⢁⠄⠊⡠⠊⠀⢀⠔⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠬⢑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⠃⠀⢰⠆⣁⡠⠒⢁⠠⠂⠁⠔⠁⠀⡠⠂⠁⡠⠈⢀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠑⡀⠁⠂⠄⡀⠀⠀⡀⠀⠈⠉⣨⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣠⣰⠀⠈⢉⡘⡧⢤⡊⠁⡀⠔⠁⠀⡠⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠂⠒⠒⡈⠁⢀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠑⠋⠈⡁⠠⠀⠂⣉⣙⠈⠱⠒⡰⠣⡄⣠⠂⡠⠔
⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠃⠀⠀⢀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠈⢉⡁⠠⠂⡰⠀⠀⠀⠀⠀⢀⠠⠒⠉⢄⡒⠢⣌⣉⠒⠩⢴⡒⢬⠉⡑⢄⡈⣑⠒⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⡧⠀⠒⡿⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠀⠠⠒⠈⠀⠀⠐⠀⣠⢊⡀⠎⡉⠒⠠⢍⣉⠒⠒⠅⣓⠢⠬⠢⣒⠆⢅⠙⠠⡁
⠀⠀⠀⠀⠀⠘⡗⠀⠁⠀⠀⡇⢀⣠⣿⠀⢀⠤⠐⠀⠁⠀⠄⠂⠁⠀⠠⠀⠀⠀⡠⢒⢊⠣⣈⠦⡑⡂⠚⢷⡤⢀⡈⠓⠢⢤⡁⠒⢄⠈⠣⢄⠈⠓
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠰⡏⢁⡠⠚⠀⠁⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⢀⣤⣊⣀⠛⠩⣉⠲⠤⡀⡉⠂⠤⣍⠢⢉⡐⠢⠄⢈⡃⠂⢌⡐⠤⡁⠒⢀
⠀⠀⠀⠀⢀⡠⡇⠀⡁⣀⠤⠊⠁⠀⢀⠠⠂⠀⠀⠀⢀⣀⡄⠂⠀⠰⠐⢈⣘⠆⠁⡑⠦⠄⢉⡒⢄⢉⠒⠤⢈⠐⠢⠬⡉⠒⢢⡈⠒⠠⢈⠑⠢⢕⡂
⠀⠀⠀⠀⠀⢀⣡⠆⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⠌⠀⠀⣠⠟⢁⡘⠉⡀⠱⡄⣈⠑⠂⣤⠜⣠⢄⠉⠲⢄⡙⠢⠀⡈⠢⢄⡉⠢⢀⡀⠉⠠⢀⡉
⠀⠀⠀⠀⠴⠛⠁⠀⠀⡀⠈⠐⠀⠀⠀⠀⠀⠀⠘⠀⢰⣤⠞⠃⢾⡁⠈⠢⣌⠒⢄⢀⠙⠂⢄⠀⠘⢄⠑⠢⠤⡈⠢⣄⠉⠢⡀⠈⠉⠂⢌⠠⢄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡞⠀⡎⠉⠦⡀⠑⠠⡀⠑⠆⣀⠙⠢⡀⠙⢤⡀⠉⠒⠢⣈⠒⠤⠉⠒⣌⡒⠤⡀⠀⠈⠢⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠀⠉⠒⠀⠘⠂⠀⠀⠑⠀⠈⠐⠀⠈⠂⠀⠀⠈⠀⠀⠂⠀⠀⠁⠀⠉⠂⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣦⡀⠀⠀⣈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⢈⢿⣿⣿⣷⣄⠀⠀⠀⠂⠈⠑⢄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠈⢢⡈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡒⠲⡄
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠐⠐⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⣹
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠐⠘⢦⣀⠀⠀⠀⠀⢀⣠⠏⠀⢰⣏
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢀⡤⣄⠀⠀⠀⢀⣿⣿⠀⡀⠀⠀⡠⠀⠀⠀⡀⠈⠈⠉⠓⠒⠚⡿⠀⠀⠀⠘⠈⠳⡄
⠀⠀⠀⠀⠈⣿⣿⡄⠀⢠⡏⡞⢢⢳⠀⠀⣸⣿⡏⢀⠇⠀⠀⣇⠀⣠⠀⣇⡤⠂⠀⠀⠀⣀⣽⠤⠤⣄⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠘⣿⣷⡀⠘⣇⢧⡼⡸⠀⣠⣿⡟⠀⡼⡠⠊⠀⣿⠞⣁⡴⠿⠒⠚⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠉⠉⣁⣴⣿⠟⢀⣠⠏⢁⡠⢚⣧⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⣟⠥⠒⢁⣮⣔⡫⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⠟⡿⠉⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠙⠋⠁⠘⠁⠀⠉⠛⠿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣭⡝⣆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⡇⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠋⠉⢱⡌⠻⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠃⠀⠀⠀⢀⣀⣀⠀⠈⠛⠉⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠜⡐⠀⠀⠀⠉⠉⢢⡖⡠⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⡀⠈⠱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠁⠪⡈
⠀⠀⠀⠠⡀⠀⠀⢀⡄⠀⠀⠀⠀⢠⣲⣀⣢⣀⣀⣀⣀⣀⣀⡠⠈⠀⠀⠀⣠⣈⣁⣂⣀⡀⣀⣰⣀⡖⠂⠀⠀⠀⠀⠐⠢⢄⡀
⠀⠀⠀⠀⠁⠀⠤⠤⠆⢀⠠⡀⠰⡥⢼⠦⠴⠧⠤⠤⠤⠤⠠⢇⠀⠀⠀⠚⠤⠤⠤⢬⠦⠤⠤⠍⡂⣇⡀⠀⠀⠀⠀⢀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠊⠃⠅⠀⠀⠀⠀⠰⠊⠁⠘⡄⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠀⣠⠃⠊⠀⠀⠀⠀⠀⠣⣀⠀⢀⡀⠀⠀⡀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢄⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠩⡁⠈⢉⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠕⢀⡀⡔⠁⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠘⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠔⡒⠁⠀⠀⢠⣀⠀⠀⢀⠇
⠀⠀⢠⠆⠁⠈⠉⠚⢊⡖⠀⠀⠀⢠⠊⠀⠀⠀⣄⠀⢀⡟⠟⠀⠀⠀⡠⠂⢀⢀⠀⠀⡏⠁⢠⡥⠀⠠⠇⠀⠀⢠⣀
⠀⡈⠃⠀⡠⠊⠐⡀⠀⢱⠀⠀⠀⢸⡀⠀⠈⢠⠃⣽⢈⣇⠀⠀⠀⡞⠀⠀⠀⠈⠀⢠⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢓⠄
⠀⢑⠀⠀⠱⠖⠐⠋⠀⢠⠃⠀⠀⢰⠇⠀⠀⠀⠧⡔⢠⠃⠀⠀⠀⠳⡀⠀⠀⠀⠀⠠⣁⢀⠊⠒⠀⠰⠀⠀⠀⠐⠊⠁
⠀⠘⢄⣀⣄⠀⣀⠀⡀⠎⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠎⠈⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⡷
⠀⠀⠀⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⣬⡦⠀⠀⣀⡠⢻⠟⠃⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⣱⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡀⠤⠤⡄⠠⣄⡀
⠀⠀⠀⣠⠰⠊⠉⠓⠦⡀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⢀⢀⡭⢲⠂⠀⠀⢀⡀
⠀⣀⢰⠁⢀⠴⡀⠀⠀⡇⠀⠀⢐⠁⠀⢀⠄⠄⢒⡀⠀⠀⠀⣃⠀⠀⠀⡠⠂⠉⡀⡀⠈⠉⠦⡀⠃⠀⠄
⠀⢹⠊⢠⠁⡰⠁⠀⠀⢹⠓⠒⡊⠀⠀⠘⣒⡐⢸⡃⠀⠀⠚⡞⠙⠀⢠⡇⠀⢠⠁⢈⡲⠀⠀⡇⠈⠉⠀⠀⠀⠀⠀⠉⠑⠦
⠀⡁⠀⠑⠒⠁⠀⢀⠠⠊⠀⠀⢠⠀⠤⠂⠀⠄⠈⠁⠀⠀⡜⠁⠀⠀⠸⡀⠀⠈⠐⠉⠀⠀⢀⠇⠠⠤⠤⠀⠀⠀⠀⠤⠄⠊
⠀⠈⠒⠐⠉⢠⠍⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠦⡀⢀⠤⠐⠻⠆⠀⢒⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⠐⠒⠂⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠛⢉⣱⠆⠀⢻⠋⠀⠀⠀⠀⠀⠀⠈⢹⠃
⠀⠀⢠⣀⣀⣀⣠⣤⠀⠀⢀⣠⡀⠀⠀⢤⡀⠀⠀⠀⠸⠀⠀⠀⣿⠀⠀⠀⠳⣬⡭⠥⠬⢗⣸⡿⢃⣀⠀⠀⣀⣀
⠀⠀⣸⠩⡉⢉⣧⣿⠀⢰⣿⡟⠓⠲⠖⠒⢷⠀⠀⠀⢠⡀⠀⢠⡏⠀⠀⠀⠀⠙⢧⣄⡀⢀⡽⢁⠋⠉⠉⠉⠉⠻⡆
⠀⠀⢻⡅⠀⠀⠁⣿⠀⣸⣯⣀⣀⣀⡀⠀⢸⡀⠀⠀⢸⡧⣧⣼⡇⠀⠀⠀⠀⠀⠀⠙⡤⠏⠀⡌⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠸⣧⠀⠀⣰⠇⠀⣿⠋⠉⠉⠙⡇⠀⢸⡇⠀⠀⠘⠇⠠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠙⢻⣿⠏⠀⠀⢿⠀⠀⠀⠀⠃⠀⣸⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⣀⣀⣿⣿⡿
⠀⠀⠀⠀⠁⠈⠀⠀⠀⢸⡀⠀⠀⠀⢦⣤⡿⠀⣰⣫⣭⣅⣀⣁⣀⣨⣆⠀⠀⠀⣀⡀⠴⢤⠄⡀⠈⠉⣙⣛⠛⠉⢰⡆⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣿⠇⠀⣿⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠁⠒⠚⠓⠐⠁⠀⠀⠀⡊⠀⠀⢸⣷⡀⠀⠀⠀⠤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢨⣿⠀⠀⣿⣷⣦⣤⣴⣶⡄⢰⣿⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣧⡀⢀⣀⣀⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡏⠀⠀⡏⠀⠀⠈⠉⣻⠀⢸⣿⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⡟⢿⣿⡷⣾⣿⣿
⠀⠀⠀⣀⡤⣤⣀⡀⠀⠀⢸⠀⠀⠀⣸⡇⠀⠀⡇⠀⠀⠀⠀⢹⠀⢸⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠚⠷⠾⠟⠧⠀⡇⢸⡏⠀⢻⡏⡿
⠀⠀⠂⠘⠓⠚⠒⠊⠁⠀⢸⣷⠶⠾⢿⣧⠀⢠⡇⠀⠀⠀⠀⣸⠀⢸⣿⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠀⢸⣇⡀⠀⠀⣠⣿⢀⣸⣿⡶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣇⠀⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⠿⠿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠿⠶⢿⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠿⠥⣉⣹⣿⡤⠴⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠋⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠟⣋⠉⠩⠍⣉⠛⠻⠿⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⠀⡠⢾⣅⡀⠀⠀⠀⠀⠉⠒⠤⡀⠉⠒⠄⡈⠑⠠⣀⣀⡀⠀⠈⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⣰⣿⡿⠋⠀⡊⢣⡈⠑⠢⢄⡀⠀⠀⠀⠈⠑⠤⣀⠈⠐⠤⣀⠙⠻⣦⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⣿⡟⠀⠀⠠⠁⠀⡹⢦⣀⠀⠀⠁⠒⠤⢀⡀⠀⠀⠉⠐⠂⠀⣬⠴⢺⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⢀⠟⠀⢀⠔⠁⢀⠔⠁⠀⠁⠪⠅⡒⠠⠤⠤⠀⠠⠭⠡⠙⠛⢁⣤⣖⣩⠃⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠴⢅⣤⣒⡁⠤⠂⠁⠀⠀⠀⠀⠐⡀⠀⡙⠁⠒⠐⠒⠂⠒⠚⠩⠄⠀⣠⣬⠃⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⣿⣿⣿⣿
⣿⣿⣿⠟⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⠘⣿⣿⣿
⣏⠉⠁⠀⣀⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣄⡀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠠⢀⠠⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⣠⡆⠀⢀⠆⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠒⠒⠀⠁⣹
⠀⠨⢰⣤⢠⠀⠀⠒⠐⡭⠛⠀⠀⠘⠃⠒⠈⠀⠀⠠⠀⠀⠀⢠⡾⠛⠛⠚⠀⠀⠊⠀⠀⠲⠆⠀⠀⠀⠊⠉⣀⡁⠼
⠀⠀⠙⠁⠘⠀⠐⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠴⡮⠁⠁⠀⠀⠀⢀⡀⠀⢀⢠⠔⠆⠀⠀⠀⠀⠀⠤⠄⢒
⠀⡤⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣷⠸⠁⠀⠀⠰⠀⠐⠀⠀⠐⣂⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⢤⣤⣀⣀⠀⠀⠀⠀⠔⠸⠂⢸⠀⣆⠀⠀⠙⠳⠤⠗⠀⠀⠀⠀⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠉⠈⠻⠛⠀⠀⡒⠂⡃⠘⠂⢸⣴⣿⠀⠀⠀⠀⠀⠀⢠⢋⠔⠡⠈⡠⠊⡠⠂
⠀⠀⢰⣄⠀⠀⣀⣀⣀⣀⡄⠀⠁⠠⡀⠀⠀⠀⠉⠉⠉⣋⠈⣣⣞⡧⠁⠀⠀⠒⠷⣶⡄⠈⠟⠶⣣⢆⣀⠞⢠⠊⢠
⠀⠀⠈⢿⣯⠁⣯⣹⠁⠣⠃⠀⠀⠀⠈⠁⠀⠀⠈⠻⢷⣾⣮⠿⠈⠀⣤⡄⠀⠀⠐⠁⠙⠃⠀⠀⠈⠈⠛⠛⢷⡶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢰⠀⠀⣿⠀⢰⠇⠀⣰⠂⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠙⢦⠀⠹⡀⠀⠘⡇⠀⡏⠀⡼⠀⢠⠃⠀⢀⡞⠁⠀⠀⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠙⢦⡀⠳⡀⠘⠀⠀⠃⠀⠃⠀⠃⢀⠃⠀⡠⠋⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⠉⠢⢄⠙⠦⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⠁⢀⠴⠊⠀⠀⠀⠀⣀⣤⠴⠾⣭⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠲⣤⣀⡈⠁⠀⢠⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠤⠔⠚⠩⠋⢀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠞⠙⢆⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠂⠀⢼⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⣶⣲⣆⣾⣾⣿⣦⣼⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢼⣆⠀⠀⠀⠀⠐⢰⠑⢺⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣇⣀⣀⣀⣼⣿⣫⣿⣿⣿⣿⣿⣿⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣶⣶⣤⣄⣠⣯⡴⣯⠷⡶⢶⠗⡶⠲⡶⢦⡤⣤⣤⣦⣼⡀⢸⣯⣿⡽⠷⠿⣟⣛⣛⣿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡟⣿⢩⠇⣿⢁⡏⢠⡏⣼⢁⡇⣸⠁⡾⢠⠏⠴⠡⠞⣱⠯⢛⣫⠥⠖⣂⣩⡭⠤⠔⠒⣒⣒⣒⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣸⢰⡇⣸⠁⠾⠀⣋⣨⡤⢤⠲⡖⢦⠒⡺⠖⣉⠔⢊⡩⠔⣚⣩⠥⠒⢒⣉⣉⡭⠭⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⣉⣴⢲⡙⣏⠳⡜⢆⠳⠈⡠⢊⡠⢊⡠⠚⣩⠔⢋⣡⠴⠚⣋⡩⠤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠷⠘⡆⢱⡘⢠⠎⡠⢋⡴⢋⡴⢋⡤⠚⢉⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠉⠀⠉






⡿⢿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠘⢖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠭⠍⠠⠬⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠠⠄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠩⠅⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠑⠒⢶⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡳⣄⠀⠀⢀⣀⣀⠤⢴⣾⡍⠷⣤⣤⣾⡿⠛⢳⣦⡤⣀
⠀⠀⠀⠀⠀⠀⠀⢾⡉⠀⠀⠀⠈⠳⣞⠉⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠳⡄⠀⡀⣼⣿⣿⠶⣶⣶⠶⣶⣶⠾⣿⣿⣄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⣀⡬⠖⠺⠿⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⡿⠟⠒⠤⡄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡞⣹⠋⡤⠀⠀⠀⠀⠈⠙⠛⠛⠒⠿⠿⠶⢉⣀⣈⡁⣀⣺⣄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⢻⣧⣊⡄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⠏⠀⠙⠲⠚⠛⠁⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠀⢸⠇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⡄⠀⠀⠀⠀⣀⣠⣤⣴⣶⠾⣿⣿⠿⣶⣤⣤⣤⣟⣠⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣶⡟⢻⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⠛⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠛⠐⠛⠛⠀⠛⠛⠂⠛⠛⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⠤⠤⠤⠤⠤⡤⠤⢤⣤⣄⣀⣀⣀⣠⡤⢤⣤⣤⡤⠤⢤⠤⠤⠤⠤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢂⡤⠂⠀⢀⠀⣰⠀⠀⢀⡀⠀⠐⣆⠀⡀⠀⠀⢄⡀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠢⠐⠂⠊⠀⠁⡼⠁⠆⣰⠈⠁⣆⠰⠈⢧⠀⠀⠑⠀⠂⡐⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡑⢄⠐⢊⠊⠁⠚⠀⠙⡄⢠⠏⠀⠃⠈⠕⡑⠂⡠⢊⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⠿⣦⣍⠀⢥⠀⠐⠀⠀⠁⠈⠀⠀⠂⢀⡨⠀⣩⣴⡿⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢰⣦⣤⣭⣍⣛⣛⣚⣒⣒⢒⣒⣒⣛⣙⣩⠍⠁⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡄⢹⣧⣿⠀⠉⠙⢛⢛⣛⢛⡛⠛⠋⠉⠀⠀⢠⠀⣸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣇⣼⣿⣻⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⢿⣖⣾⢦⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣇⡀⢠⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣻⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠉⣭⡛⢛⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⣿⢹⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⡇⢠⣿⡇⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⢸⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣇⢸⣿⡇⠘⡆⠀⠀⢀⠄⠀⠀⠀⠀⡇⢸⡏⣾⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⡀⢿⡇⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣧⡟⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣧⠀⡇⣇⣀⡀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⠶⢿⣯⣥⠄⠈⠉⠉⠀⠀⠀⣸⣿⣿⣿⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣬⣙⠲⠬⣥⣉⣉⣁⣀⣀⣀⣴⣿⣿⣿⣿⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡌⠉⠤⢤⣄⣀⣀⡀⠀⠀⣿⣿⣿⢟⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡑⠢⢤⣀⣀⡀⠠⠶⢖⣚⣿⠿⠗⢋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣭⣭⣭⣭⡥⠴⠖⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⣤⣀⣤⣤⣤⣤⣄⡀⠀⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⡞⠁⢸⠁⠀⣀⣀⣉⣹⡇⠀⣿⣛⣻⣟⣻⣫⣋⣹⣭⣻⣿⣿⡏⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣶⣾⣿⣿⣿⣶⣶⣾⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⠻⣿⡯⠿⠿⠿⣿⣿⡛⠃
⠀⠀⠀⠀⠀⢀⡤⢞⠛⢻⣿⡄⢀⣤⠴⠒⠒⡏⠉
⠀⠀⠀⠀⢠⠟⢠⣿⣷⣿⠟⠁⢯⠻⠀⠀⢀⠃
⠀⠀⠀⢠⡏⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣾⠃⢸⣿⣿⡏
⠀⠀⣰⣿⠀⢸⣿⣿⣧
⠀⢰⡿⠿⠶⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢢⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⢋⠁⢿⣿⡠⡄⠀⠀⠤⠤⠒⠂⠉⠒⠀⠶⠒⠒⠂⠀⠀⠀⣤⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢶⠀⣤⠈⣿⣶⠀⢀⡀⠀⠉⠀⡲⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠶⠟⣤⢸⠦⣄⡤⠀⡀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⣰⣂⠄⠀⠸⠉⠁⠀⠀⠸⡏⠀⠄⠀⠀⠀⠨⠷⡚⠀⠀⠀⡆⡄⡄⡤⡄⠀⠀⢤⢠⢠⣤⣤⢠⣄⢀⢀⣀⡇⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠙⠻⠾⠀⠋⡉⠙⠂⠀⣸⠃⣾⠂⠀⠀⠀⠠⣿⡃⠀⢀⡆⣟⢇⢿⣏⡇⡆⢀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢹⠁⣀⠤⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣦⣄⣠⠀⡀⠸⠤⠗⢠⣿⣿⡁⠀⠀⠀⠁⡇⠵⠛⠏⠾⠜⠀⣀⠀⡀⢀⠏⢠⣞⠋⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠏⠚⠛⠒⡈⠉⢉⠉⡛⡟⠧⢥⣟⣂⡇⠇⠇⣶⢦⠆⡼⠁⠼⢀⠎⢠⣴⡙⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⢸⢧⠆⠥⠳⠸⠘⢇⣷⠳⣠⡆⢌⠑⠲⣄⠀⠀⡬⠀⡦⢡⠞⠐⢦⡤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣡⣤⣦⠀⠀⠀⢠⣾⣯⣴⣦⣤⣌⡄⢤⠀⣄⢀⠀⢬⡤⠣⠳⠄⠒⡐⡂⢠⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡀⠀⠀⡸⠛⠉⠉⠉⠉⠛⠷⢦⣬⡍⢹⡃⣾⢂⠶⠀⢓⡟⠛⠓⢸⡀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠍⠆⠀⠀⠙⠂⠸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⡶⠃⠀⠀⢪⠇⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⢸⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⢀⠇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣛⣿⣁⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣻⡟⠁⠀⢀⠜⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⢰⣿⣶⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠂⢄⠀⡐⢀⠔⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠒⣒⡶⠒⠂⠳⠶⠷⠆⡀⠁⠁⠀⠠⠘⢧⠀⠀⠀⠀⣠⠴⢚⣭⠟⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⠂⠐⢄⠀⠈⢢⡀⠀⠀⠀⠈⣧⠀⣠⠞⣁⠀⠉⠉⠉⠙⢦⡀
⠀⠀⣠⣒⣉⣉⢉⣉⠩⠉⠙⠲⢄⠀⠀⢀⣴⠏⠀⠀⠀⢀⡴⠚⠉⣷⠀⣴⠀⡇⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⠸⡶⢣⡾⠁⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠈⠉⢉⡽⠋⠀⠀⠀⠀⠀⢠⡝⠙⢣⡏⠀⠀⢀⡴⠋⠀⠀⠀⠘⢆⣾⠑⠾⠦⠀⢸⠀⡼⠀⣼⡄⠀⠀⠀⠀⢿⠀⠙⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⢸⠀⠀⣠⠏⠀⣠⠶⠿⠿⠃⠀⠙⠦⠀⠀⣠⣃⣜⣠⠞⠁⠈⢢⣄⠀⠀⢸⡀⢣⣽⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⠋⢰⠋⠦⣿⡟⠀⠔⢹⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠻⠿⠷⢤⣸⡄⠁⠀⢸⡧⠎⠉⢳⡀⠀⢀⡜⣼⠁
⠀⠀⠀⢸⡄⠀⠀⠀⢰⢿⠀⡿⠀⠀⠈⡇⠀⢠⡆⠀⣴⠟⠛⢛⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⣦⠈⠳⣄⠀⢸⡇⠀⠀⠀⡇⣠⢾⡿⠁
⠀⠀⠀⠀⢳⡀⠀⠀⡿⠈⠳⡇⠀⠀⠀⣧⠀⠀⡧⢼⡇⢀⢀⣸⣿⡧⠀⠀⠀⠀⠀⠀⠀⡋⠀⣻⣆⠘⣇⡠⣯⠀⢸⠀⠀⠀⡼⠛⣡⠟
⠀⠀⠀⠀⠀⠙⢦⣀⡇⠀⠀⠀⣠⠞⠋⢻⡄⣸⠁⠀⠇⠸⣿⣿⣿⠃⠀⠀⠀⢀⣀⡀⠀⢿⣿⣿⡟⠀⠃⠀⠹⣄⣸⠖⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢰⡇⠀⠒⢲⣷⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠁⢠⠟⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⣡⠄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢰⠛⡆⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠦⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⠦⠴⠒⠒⠊⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣂⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⣇⣂⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⢀⣤⣽⣿⣿⡍⡁⠀⠀⠀⢠⡄⢠⣿⠋⡉⡀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠈⣿⣿⣿⣿⣇⡽⠀⠰⣿⣌⠉⠙⣿⣿⡟⣋⣄
⠀⠀⢠⠔⢡⡄⠀⠀⠀⠀⠀⠒⠀⠐⠂⠰⢿⣿⣿⣿⣶⣶⣛⣿⣿⣿⣿⣿⠂⠀⢹⣿⢛⠛⣿⣿⢿⠟⡛⢒⣃⣀⡄
⠀⣠⣿⣗⣊⢡⣤⠐⠒⠒⠒⠒⠲⠰⠒⠲⠾⠿⠿⠿⠾⠿⠿⠾⠿⠟⠻⠿⠿⠿⠿⠟⠘⠀⠿⠿⠿⠇⠤⠏⠍⠀⠂⠐
⠀⠀⠀⢉⠁⠀⠈⠁⢁⠀⠀⣀⡀⠀⣀⠀⢒⢀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⢲⣍⡙⢆⣭⠂⢲⣝⢻⢼⣳⣾⢈⡱⡇⢁⢧⢲⡀⢀⡔⠊⠒⠾⣘⠈⢀⣴⠐⢺⠠⣆⠴⢂⣰⣔⣂⠀⢁⡀⣖⠢⢀⡀
⠀⠀⢼⡇⡇⣜⡴⢠⡉⣻⠀⣸⣹⢡⡞⢹⡇⢪⡽⢻⢷⣆⠑⢰⢪⠷⠿⠸⠏⣣⣇⡁⠔⣿⣌⡿⠀⡦⢄⣠⢼⠁⢻⠟⠉
⠀⠀⢺⡇⣷⢾⡏⡤⣽⣿⢨⡷⣽⢒⣷⢸⣧⣬⡴⢼⡔⣼⣍⡦⣼⣞⠃⣶⠊⡘⠎⠹⣧⣩⣮⠁⣨⢛⣉⡁⢀⢠⠞⠒⡂
⠀⠀⠼⡧⢿⢸⣝⡇⡀⣿⠀⢛⢼⠆⣿⠸⡇⢿⡏⣸⠣⢅⣮⢘⣽⣿⡃⣻⠘⢛⡦⠠⣿⢴⢿⡟⣻⣫⣾⣴⢀⣫⢚⡠
⠀⠀⠚⠓⠂⠼⢧⣤⣥⣏⣈⡋⣽⠓⠛⠰⡇⠽⠴⣽⠄⢌⠧⣧⠀⣽⡅⣭⠘⣭⠂⢲⣿⠈⢰⡧⣾⡤⣿⣭⢨⣏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠚⠓⠒⠶⠼⠤⢤⣀⣿⣀⠀⠀⢴⠁⠈⠀⠐⣿⠀⠲⠿⣾⠤⠏⣀⣰⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠴⠤⣠⣯⣀⣀⡀⢻⠀⠀⠀⢸⡅⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⣀⡤⠀⢀⣀⠀⠀⠀⡀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣀⣒⣣⣤⣴⣶⣶⣿⣿⣿⣷⣿⣷⣏⠀⣸⣿⣗
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣤⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣥⠀⠀⠉
⠀⠀⢀⣞⣯⣭⣵⣶⣾⣿⣯⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠋⠉⠉
⠀⠀⠈⠉⠉⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⡟⠉⠀⠀⣿⠁⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⠀⠀⢀⡿⠄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠿⠟⠛⠛⠉⡀⢀⣀⣀⣠⣤⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣶⣶⢸⡗⢸⡏⣿⠋⣿⠁⣿⠇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣤⣉⣾⡷⣿⣷⣿⢰⣿⢀⣿⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⢠⣄⣹⡏⣿⠃⣿⠹⣿⠾⠏⠘⠟⠀⠛⠁
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢋⡁⢩⠀⠰⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠙⡿⠛⠛⠛⠛⠛⡋⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠴⠍⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⢀⣀⠶⠤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⣀⠤⠊⠉⠀⠀⣰⣛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⢐⣥⣶⠿⠛⠛⠛⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠋⡩⠤⡀⠀⢀⠤⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠴⠖⠄⠀⠠⠶⠲⠀⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⠀⠂⠐⠂⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠈⠛⣶⠋⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠄⠐⠖⣰⠙⡀⠐⠠⠀⠀⠀⡘⡶⠤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠁⠁⠀⢀⣿⠘⡆⠐⠤⡀⠢⢞⠄⣿⠀⠈⠁⢤⠑⠐⠢⡄
⠀⠀⠀⣀⣠⠴⠯⠀⠠⠀⠀⠈⠀⠀⢸⡟⠀⠁⠃⠀⠈⠒⢈⠠⡿⠀⠀⠀⡀⠀⠀⠀⠀⠓⢀⡀
⠀⡴⠋⠉⠛⠓⠂⠀⠀⠀⠀⠀⡝⠀⠘⡇⠀⠐⢰⠘⠀⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠐⣣⠞⠓⠙⠒⣀⠀⠀⡤⢾⠉⠁⠀⢰⡇⠀⠀⠐⠀⠢⠀⠀⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⣀
⠀⡏⠀⠀⠀⠀⠈⣇⢠⠃⠀⢧⠁⠀⢸⡇⠀⠄⠖⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠁⡤⢄⠀⠀⡀⠀⠀⠀⠀⠀⢨
⢀⡇⠀⢀⠀⠀⠀⠘⠣⡀⠀⢸⠀⠀⠜⢀⠓⠢⢧⡅⢀⣀⣤⡾⠁⠀⠀⠀⠀⡄⠀⠀⢹⡂⢠⠞⠀⠀⠀⠀⠸
⠀⠑⠒⠤⣀⠀⠀⠀⠀⠈⠢⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠑⠀⣀⡀⠀⠀⠀⠉⠱⡀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠔⠁⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣲⢠⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⢀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠐⠀⠀⠀⡀⡀⣀⡀⡟⢦⣀⠀⠠⠀⠁⠀⠀⠆⠀⠀⠁
⠀⠠⠤⠤⠤⠄⢀⣠⣄⠬⠀⠀⠀⠀⠀⠀⠈⠃⢿⡙⢿⠃⠄⠉⢱⡄⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠶⠧⢄⣞⣁⠚⢚⢉⣀⡀⢀⣨⣅⣈⢛⠧⠀⠄⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢺⠁⠁⡰⡅⠀⠐⠲⠶⠶⠖⠒⠀⠘⠙⠶⡀⠀⠀⣉⠿⣀⣀⣀⡜⠰⠤⠶
⠀⠀⠀⠀⠀⠐⠦⣌⣧⡀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⡤⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣆⡧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠐⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⢿⡿⣤⡀⠀⠢⠀⢀⡀⢀⢀⡀⠀⡀⡠⠐⠀⣀⣼⠷⠁⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣩⡳⢄⠑⠚⣀⣀⡀⣀⣠⠌⠁⠰⠚⠉⢉⠜⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⣀⣰⣿⡾⠛⠛⠉⠀⢀⠄⣠⠈⠳⣤⡙⣷⡀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⠘⣦⣸⡀⠠⠿⢿⡿⠿⣿⣛⣫⣤⢖⣩⢪⠏⢠⠰⡌⢻⣿⣿⣦⣄⢹⣦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⢸⡇⡀⢈⡻⣾⣿⣿⣿⣿⣿⠿⠿⢟⣫⣭⡶⢛⣵⠏⡴⣸⡇⠙⢄⠹⣿⣿⣿⣿⣿⡆⠀⢳⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣍⣭⣭⣥⣶⣶⣶⣾⡿⠟⠋⣡⣴⠟⠁⣰⢡⣿⣷⠀⢸⡆⢹⣿⡿⡝⢿⣿⣆⢸⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⢉⣠⣴⡿⠟⠁⢀⡾⢣⣾⣿⣿⠀⠀⣿⠀⢿⣷⡝⠄⠻⣿⡄⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢋⣵⣿⠿⢋⣠⣶⠿⠛⠉⡠⢂⣴⠟⣡⣿⣿⢣⣿⠀⠀⣿⠀⢸⡇⢻⡀⠀⣿⠃⣡⡏
⠀⠀⠀⠀⢤⣤⣤⣴⣾⡿⣿⠟⢉⣴⡿⠟⣡⡶⠟⠋⢀⡠⠔⣉⣴⠿⣡⣾⣿⣿⠏⣼⡟⠀⣄⣿⠀⢸⡇⢸⣧⠀⠉⠨⠛⡀⠀⣀⠀⢸⣾⣤⡔
⠀⠀⠀⠀⠀⠀⠈⣹⢏⡼⠋⡴⠋⠊⠠⠚⠁⠀⠀⠀⣡⣴⡾⠟⣡⣾⢿⣿⣿⠏⣰⣿⠃⡐⣸⣿⡄⣸⠃⢸⣿⠄⠘⣄⠦⣄⣀⠙⣶⣼⣿⣿⡥
⠀⠀⠀⠀⠀⠀⣼⠏⡼⠁⠈⠀⠀⠀⢀⠀⣤⣴⡾⠿⢛⣩⣴⣿⢟⣥⣿⡿⠁⣰⣿⠃⠀⢠⣿⡟⢠⠏⠀⢸⣿⠀⠀⠸⢷⣮⣻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢰⠇⠸⠁⠀⠀⠀⣄⣀⣀⣈⣡⣤⣶⣾⣿⠟⢋⣵⣾⠿⠋⢀⣾⡿⠃⠀⢠⣿⡟⠐⠋⠀⢠⡟⠜⡈⠀⡄⠀⠙⣿⣿⣿⡭⠴⠒
⠀⠀⠀⠀⠀⡾⠀⡃⠀⠀⠀⠀⡿⠶⠶⠶⠟⠛⣋⣩⣴⣾⠿⠛⠁⣠⣾⡿⠏⠀⠀⣰⣿⠏⠀⠀⢀⣰⠏⠀⣰⠃⠀⢿⠀⢦⠸⡇
⠀⠀⠀⠀⠀⠇⢰⡇⢰⣦⠀⢀⣏⠀⠐⠒⠚⠛⠛⢋⣉⣠⣤⣶⣿⠿⠋⠀⢀⣤⣾⠟⠁⠀⠠⠖⠋⠁⣀⡼⠁⠀⠀⢸⡄⢸⡆⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⠀⠀⠈⢙⣛⣻⣿⣿⣿⣿⡿⠿⡿⢋⣀⣠⣤⡶⠿⠋⠁⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⢸⡇⣾⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢧⢸⡇⢀⠀⠀⠀⠐⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣿⢷⠇
⠀⠀⠀⠀⢀⣴⣶⣦⣸⡇⠸⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢠⠏⣸⢟⣴⣶⣦
⠀⠀⠀⠀⢸⣿⣏⠈⠁⠻⡀⠀⠀⠀⠀⠀⠺⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠛⠃⠀⠀⠀⠀⠈⠰⠋⠈⢉⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⢠⣶⣦⡀⠀⠀⠀⠀⣠⣀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⣠⣀⠀⠀⠀⠀⣠⣶⣦⢸⣿⣿
⠀⠀⠀⠀⠀⠻⣿⣿⡇⠈⣿⡀⠀⠀⢲⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣿⣷⡂⠀⠀⢰⡟⠀⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⠘⣁⠀⠀⠈⣥⣿⠀⣻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⠟⣯⡬⠀⠀⠀⡸⠃⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡦⠀⠀⢦⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣵⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣖⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠤⠤⠄⠀⠀⠀⠀⠀⠲⠾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠉⠉⣉⣉⡉⢛⣲⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⠄⢂⠉⠤⠄⣀⠄⠒⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠓⠀⢀⠔⢀⡆⠀⠀⠀⠀⡌⠀⣰⠋⣀⣀⣠⣤⣴⣶⣖⠲⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠘⡰⢃⠚⠁⠙⢆⠀⠀⢐⢁⡼⠋⠉⠁⠉⠀⠀⠀⠀⠀⠀⡀⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⠃⡇⠀⠀⠀⠀⠑⢄⣦⠞⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠞⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠀⢧⡤⣤⣠⠀⠀⣼⠋⠀⢀⣠⣤⡴⠦⠓⠛⠉⠀⠀⠀⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠆⣷⢰⠈⢿⡑⠚⡛⠛⠋⠉⠉⠉⣀⡠⠤⠤⠖⠂⠀⠀⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣸⠘⣀⠈⢷⡀⠸⠄⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣇⠈⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠤⠀⠂⠁⠀⠀⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⠎⠀⢳⡀⢠⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢳⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢣⠀⠀⠀⠈⠢⠐⠁⠀⠀⠐⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠳⣄⠀⠀⠀⠀⠂⠀⠀⣀⡼⠃⠀⣨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣬⡓⠶⠶⠀⠀⠐⠚⢉⣀⠤⢾⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠚⠛⠛⠒⠶⠶⠊⠉⠁⣄⠀⢱⣼⠄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣨⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⣤⡤⠴⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣶⣶⣾⡿⠟⠛⠿⠿⠟⠻⡿⡿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⣠⠊⠉⠟⢋⣿⠿⡿⠿⠿⠻⢻⣿⠉⠀⠀⠀⠀⠀⠀⣈⠥⠀⠒⠛⠉⠁⠀⡀⢀
⠀⠀⢸⣷⣿⣿⣳⣿⠋⡞⠁⣠⠆⣴⠎⢠⠆⣠⣂⠀⠤⠒⠈⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠉⠛⢿⣿⣿⣶⣄⣼⣇⣪⣼⣶⣿⣿⣿⠟⠁⢀⡀⢰⢋⣄⠄⠀⠀⠀⠀⠀⠀⡰⠁⠀⣃⣆⡃⢂
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠀⠼⣏⠁⡄⠀⠀⠀⠀⠀⠀⠰⢃⣄⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⠀⠠⠀⡀⣰⠆⠁⠀⠑⠀⡴⠆⢉⡀⣤⣤⣀⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⢿⣀⠀⣨⡴⢷⡀⠁⢀⡤⠀⠀⠛⡛⠷⠾⣿⣿⣉⣀⣀⣠⣄⡀⠤⢶⣤⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣫⡍⢙⢻⡄⠀⠷⢡⣷⡟⢩⠧⢴⡖⢈⢁⠠⠔⠀⠂⢉⣫⣙⣷⣾⣿⣟⡋⣴⣴⠦⠓⢒⠼⠀⢠⡟⠿⢶⡄⠀⢦⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠙⣿⣷⣄⡈⠺⠿⠿⣿⠻⣜⠖⣬⡾⣿⣛⡯⣝⠻⣤⣅⠀⠒⠂⠂⣁⣠⣶⣏⡄⡈⠎⢀⣰⣿⡿⡾⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠀⠙⠫⢿⣓⣀⣁⢀⣀⣴⡙⠯⠾⠾⠾⠛⠋⠉⠉⣀⣠⣴⣶⣿⠏⠹⠚⠋⢁⣠⣴⡿⠧⠒⠋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣉⣁⣀⣀⣤⢤⣴⢶⠾⠿⠿⠻⠛⠛⣉⣁⣠⣤⣤⣶⣶⠿⠟⠛⣉⣡⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠘⠶⠤⠴⠶⠖⠒⠚⠛⠋⠙⣯⣉⣉⣡⣬⡤⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢳⡆⢰⣿⡆⠀⣿⠳⣦⠚⢷⡟⠒⣷⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⠒⠒⠒⠒⢲⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⡇⣸⠙⣇⠀⣿⣤⡟⠀⢸⡇⠀⢹⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠈⠉⠙⠃⠅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⣿⠶⣿⠀⣿⠈⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠀⣀⡠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⠙⠁⠋⠀⠛⠀⠘⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡟⠛⢸⡇⢸⣿⣧⠀⣸⣿⡇⢸⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⢸⣿⣿⠀⣿⣿⡇⢸⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣠⣤⣤⣴⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⢸⣿⢹⣦⡟⣿⡇⢸⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠉⠀⠀⠀⡀⠼⡧⠤⣁⡒⠠⢄⡀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⢸⣿⢸⣿⡇⣿⡇⢸⣧⣀⣀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠁⠀⠀⠀⠁⠠⡈⠱⡄⠀⠀⠀⠉⠁⠀⠈⠁⠈⠉⠀⠉⠀⠉⠁⠈⠉⠉⠉
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡆
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠁⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠠⠀⠀⠁⠀⣼⠀⡀⠀⠀⠐⠇⡁
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡏⠀⠀⠀⠀⠀⣎⡈⠀⠀⠈⡁⠀⢀⠇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠇⠀⠀⠀⠀⠀⠜⠁⠀⣤⠊⠁⠈⠉
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡾⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⢀
⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠇⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢎⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠠⠰⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠢⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠿⣛⣚⠭⢗⣛⠿⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢮⢎⠕⡭⢄⠀⢰⢙⠆⢉⠲⣵⠷⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⢷⢣⠃⠀⠑⢌⡆⢸⡞⣴⠟⠋⠀⠀⠀⠀⠀⠀⣀⣉⣩⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⡇⡇⢏⣉⣲⢤⣽⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢇⢇⢀⣴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠼⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣶⣚⣉⡉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣓⣦⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢱⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⡗⢺⣆⠧⠔⠀⠀⠀⢀⡜⡏⣿⠋⢀⡴⢾⣟⣭⣿⣿⣿⣧⠀⠀⠀⢹⣧⣄⠀⠉⢳⡄⠀⠀⡇⠀⡃⠀⣇⠀⡃
⠟⠊⠁⠀⠀⠀⠀⠀⠈⢷⣿⣯⣤⢻⠽⣴⣻⣮⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢿⣿⡇⠀⠀⢧⣄⢰⡀⠱⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠓⠒⠚⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⣴⣶⣾⣭⣴⣟⠙⢫⡿⠀⠀⠈⠂
⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⣴⣿⣥⠙⢦⣭⣏⡘⣆⠀⠀⠉⠻⠏⠿⠯⠽⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣠⣾⣧⣿⣷⠀⠀⠀⠀⠀⢰⣿⣟⢿⣧⡄⢸⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡀⠀⠀⢀
⢠⡞⢹⣿⡯⢞⠛⠀⠀⠁⠀⠀⢸⣏⠛⠊⠉⠸⠿⠁⠀⠀⠀⢀⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⡿
⣇⢨⡴⠋⠂⠀⠀⠠⠁⠀⠀⢠⣟⢁⡀⣠⡼⠃⠀⠄⠀⣠⣬⣶⣤⡾⢳⡖⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢮⣾⠃⠀⠀⣾⡜⢻⡿⠉⠢⠀⠀⠀⢰⡟⠀⠿⠋⣼⣷⣶⣏⠽⣷⠄⠀⠀⠀⠀⢠⠏
⣠⣤⠖⣦⠠⣾⠇⡏⠀⠀⠐⢯⢕⡈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⢻⣿⡏⠷⠴⣯⠘⢦⣀⠀⣰⠏⢀⣀⣤⣤
⢏⠁⠀⣀⣠⣡⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢢⡀⠀⠉⢯⣀⣘⣃⠛⢻⣯⣄⣘⠿⣷⡒⣨⣿⠋⢠⣾⡟⠛⠻
⡄⢀⢈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠈⠛⠯⣽⣏⣚⣷⣶⣿⡿⠟⠁⢠⣿⡅⣳⠆⢂
⣶⡿⣫⣿⠏⠀⠀⢆⠀⠘⡄⠀⢢⠀⢃⠘⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣿⣱⡀⣠⣼
⣸⣿⠟⠁⠀⠀⠀⢠⣡⠀⣇⡀⣸⡆⢨⡄⣱⠀⠀⠀⠰⡈⠿⣷⠶⣦⣄⣀⣀⣀⣀⣤⣤⡀⠀⠀⢿⣿⣆⣩⡌
⠋⠁⠀⣤⡀⠀⣶⡛⢿⣶⡉⡙⡋⠙⣋⣻⣿⠿⠇⠀⠀⠈⢷⣍⠓⢮⣭⣭⣭⠷⣶⣶⣈⣿⣦⠀⠈⣙⣛⣩⣵
⠀⠀⣴⣹⡿⠀⣻⣧⠀⠛⠿⠷⠲⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠙⠳⣔⣏⠉⠈⠒⠈⠛⠻⣿⢿⣶⡄⡀⠈⠉⠉
⡼⠋⢉⣽⠁⣰⠋⠋⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⠀⠀⠀⠀⠛⠀⣰⡏⣿⡄
⣤⡶⣼⡇⠀⣿⡒⠠⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠈⢳⡀⠀⢀⠐⣊⣼⣶⡿⠁⠀⠀⣴
⣸⢿⣿⠁⠀⠘⢿⣄⣉⣈⠻⢀⣄⣠⣠⡭⡴⠾⠋⠀⠀⢠⣶⡜⠺⢿⣷⡦⠀⠹⣗⣧⣌⣤⠾⠟⠀⠀⠰⠘⣿
⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢉⡀⠀⠀⠀⠀⠀⢀⣇⠁⠀⠈⠁⠁⣝⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙
⠄⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣖⣴⣾⡿⢻⣿⣿⣷⡶⣄⠈⠋⠙⢹⣄⡀⠔⢦⡾⠇⠀⠀⠀⡠⠂⡠⠀⡀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⠀⠀⠐⠌⢀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢀⠀⠀⠀⠈⠂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⡄⢀⡟⠀⠂⠀⠉⠣⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠁⠀⠱⠂⠀⠀⠀⠀⠀⢠⣀⠑⢤⠀⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠤⡀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠉⢅⠂⠀⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠰⡄⠀⠀⠂⠸⡆⠠⢀⠀⠀⠀⢀⡄⠤⠀⡀⠤⠹⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠀⠀⠑⣤⡄⠀⠀⣄⣀⡋⠓
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢀⠀⠔⠈⠘⢃⠀⠀⠈⠉⠁⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⠀⠀⠀⠂
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠂⠀⠈⠁⠀⠁⠀⠀⢄⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⠀⡀
⡀⠀⠀⠀⠀⠐⠠⢀⢠⣞⡣⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⣀⣡⠛⠈⠀⠀⠢⢀⠀⠀⢆
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠄⠈⢀⢠⠄⢻⡀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢑⣀⣎⣅⣳⡠⠧⠤⠰⠖⢒⢘⡻⠛⠛⠛⠻⢄⡉⠑⠀⡉⠁⠠⡀⠀⠐⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠁⠀⠀⠀⠀⠀⠴⠋⠉⠐⠒⠀⢤⣀⠀⠝⠲⠀⠄⡐⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⢐⠂⠂⢄⠀⠀⠀⠂⠈⠓⠀⠄⠉⠉⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣂⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣤⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠟⠉⠉⠙⠟⠉⠉⠛⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣀⠀⣀⡠⠤⠄⣀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⠜⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠄⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢀⣀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣿⣿⡟⠁⠀⠢⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⣀⠤⠎⠉⢿⣿
⣿⣿⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⣿
⣿⠏⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠹
⡇⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⣧⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠒⠤⠤⠤⠂⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣶⡶⣿⠛⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠈⠁⠀⢰⠃⢠⠊⠁⠈⠑⠦⡈⠑⢄⡀
⢠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠈⡆⠀⠙⢆
⡏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠂⠀⠀⠀⢀⠞⢀⠞⠓⣄⠑⡄
⢻⣄⠀⠀⠾⠷⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠙⠲⠤⣤⠏⣠⠋⠀⠀⠈⢦⠘⣆
⢀⡟⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠉⠒⠢⠤⢍⣉⡐⠒⠒⠚⠀⠘⡄
⣾⠀⠀⠀⣼⠛⠛⠻⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⡀⢳
⠘⠷⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠱⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡦⢄⣀⠀⠀⠀⠀⠙⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠀⠀⠀⠈⢣⡘⢦⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠙⢦⡙⠦⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⣦⣤⣀⣀⠙⢦⡈⠓⠦⣄⡜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢿⣷⣤⣀⣠⠏

⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠉⠉⠙⠛⠿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⠋⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠘⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠛⡇⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠒⢤⡆⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣴⡆⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⣸⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢸⣿⣿⣿
⣿⠿⠟⠁⠀⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠹⢿⣿
⣦⣄⣀⣤⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠙⠀⢉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⡒⠒⡁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠈⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠧⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡞⠋⠻⣶⡶⢞⠿⡕⢦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⡇⢰⣯⣝⣛⣫⣄⡇⠘⡆⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⡇⢠⣍⡍⣭⢩⡍⣅⢠⡸⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⣸⠃⣸⢹⡇⣿⢸⡇⣿⢸⣇⣷⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣿⢯⡆⣿⢸⣿⣿⢸⡇⣿⠊⠀⢉⡗⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠉⠛⠻⣾⠃⣾⢠⡟⣿⢹⡇⢸⡧⠃⠀⢀⢞⡼⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⣀⡀⠀⠈⠑⠻⢼⣇⣿⣸⡇⢼⣁⡀⢠⢏⣾⣧⣤⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣦⣍⣩⣍⣛⣲⣒⡤⠀⠀⠀⠀⠈⣿⡷⠛⠩⢭⡲⢤⣀⣨⣉⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⢽⣦⣉⣿⠙⠿⣿⣿⣿⣏⣄⣤⣾⣿⣧⠀⠂⢶⠄⠀⠙⣿⠟⢛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠲⣦⠻⢷⣦⣴⣿⣿⣿⣟⠿⣟⡻⢷⣦⣄⣀⣈⣴⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⠛⢦⣬⡿⣿⣿⣭⣲⠭⣓⣯⣗⢝⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢯⣿⣌⡛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣼⡿⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⣿⣷⠾⠛⢉⣀⠀⠀⢀⣤⡀⠀⣄⠀⣀⡀⢠⡥⢰⡟⠀⠀⣀⣄⣀
⠀⠀⡆⠀⠀⠀⠀⢎⣓⠲⠴⠾⠇⠀⠀⠀⠀⠀⠀⣸⣷⠀⢰⣾⠟⢻⣇⠀⢰⣿⡝⠀⣾⠋⣸⠇⣸⡏⣠⡿⢀⣿⢃⣾⠇⢠⡾⢁⡾⠁
⠀⠀⢦⠀⠀⠀⠀⢹⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠁⠀⠘⣿⡀⢸⡟⠀⣸⣿⢀⣿⡼⣿⣰⢻⣧⠞⣿⠋⣿⡠⣿⣡⣿⠃
⠀⠀⠈⢦⡀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠻⡧⠚⠳⠔⠉⠙⠛⣿⢁⣙⣁⣀⣀⣀⣀⣀⣈⠀⠻⠁⢻
⠀⠀⠀⠀⠙⠦⠌⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⠴⡶⠶⠟⠛⠀⠀⣯⠈⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠐⡄⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡠⠀⠀⠀⠀⠀⡼⠘⠀⢀⠀⠀⢀⡀⠀⠒⠄⠐⠠⠁⠀⠀⢀⢀⡇⠀⢀⠾⡩⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣝⠂⠀⠠⠴⢞⣁⠇⠀⠈⣧⡀⠀⠀⠀⠀⠁⣀⣀⡀⠤⠊⠀⣸⠃⠀⠘⣇⠀⠀⠀⠀⠈⠀⠒⠒⠊⠁⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠉⠉⢹⠁⠀⠀⠀⠀⠈⢧⣉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠙⢶⠖⠀⠤⠤⠄⠠⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠀⠛⠂⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣤⣤⣀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡀⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠁⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢦⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠘⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⠋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳
⠀⠀⠀⠀⠀⡼⠀⠀⢀⠀⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢹⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⡀⠐⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠁⢀⡰⠛⢦⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠓⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠘⡆⠀⠓⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠋⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⣸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡶⣤⣄⣶⣾⣷⣶⣶⣶⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⠃⠺⣯⣿⡿⣿⣿⣿⡿⡿⢿⣲⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠉⠿⢿⣏⣹⠿⠯⠟⠛⠃⠀⠀⢀⠈⠠⠀⠂⠀⠠⠐⠐⡠⢁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠅⠂⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢈⠀⠉⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⡀⠀⠐⠀⠈⡆⠀⠀⠐⢲⢿⢶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⠴⠞⠉⠉⠡⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣐⢀⣀⠔⢱⠀⠃⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠁⠀⠉⠁⢀⠉⣻⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⡱⠀⢉⢱⠀⢰
⠀⠀⠀⠀⢠⣧⣀⡀⠀⠀⠀⠀⠀⠱⣄⣉⣁⡜⡅⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⢘⠀⡓⠄⠀⠀⠀⠀⢠⣶⠤
⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⢀⠀⠜⠀⠀⢇⣠⠷⠷⢤⠔⣡⠖⡦⡀⠀⠀⠀⠀⠀⣴⡴⣠⠞⣡⠴⠃⢦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢹⠶⠒⣉⢠⠀⣀⠀⢿⠲⣛⠀⡹⠢⢤⣀⢀⣤⠠⡄⠁⠀⢃⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡀⠀⠑⣿⠕⠊⢉⣤⡆⢸⠤⠤⢍⡣⠄⠀⠀⣼⠀⠀⠀⣠⠴⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠙⠦⣼⢁⣀⠤⠎⠀⣱⢸⣁⣀⠀⠈⡗⠒⠒⠚⠦⠤⠞⠁⢀⡠⠞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢤⣀⠀⠈⠉⣀⣀⣗⣿⠉⠉⠀⠀⠉⠹⠧⠤⢄⣀⣀⣀⡀⠐⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠋⠀⠉⡟⠋⠈⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⡹⠗⠈⠁

⠲⣾⣴⡶⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒
⢺⡟⡿⠿⡷⠀⠀⠀⠀⠀⠠⠞⠛⠒⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⣾⣿⣟⣤⣰⣾⣦⠛⣶⣿⣿⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣚⣳⣶⣶⣦⣾⣿⣿⣷⣶⡶⠀⣠⠀⢶⣶⣾⣾⣿⣶⣆⣀⣀⣤⣠⣄⡀⣀⣤⡀⢰⣷⣶⣶⣂⡀
⠻⣿⠿⠿⣿⠿⠿⠳⠾⠿⠿⠤⠁⠀⠀⠀⠀⠸⠆⠀⠀⠉⠉⠉⠉⠉⠿⠏⠁⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠏⠋⡉⠁⠉⠉⠉⠉⡉⡍⡛⢛⠋
⡋⠤⠚⣁⠤⠖⠊⠉⣀⠴⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠠⠉⠈⢉⡉⠀⠒⢀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠡⠀⢈⠀⠈⠀⠂⠠⢀⠀⡀⢆
⣠⠔⠋⢁⡠⠴⠒⢉⡠⠔⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠠⣄⠀⠐⠀⢀⠀⠀⢀⠄⠂⠀⠠⠄⠈⠀⠀⠀⠀⠀⠄⠁⠀⠐⠀⢀⠀⢸⠀⠇⠸
⢀⣠⠔⠉⠀⡠⠀⠉⠀⠠⠄⣀⡀⠑⠒⠤⠄⡀⠁⠐⠀⠀⠀⠐⠂⠀⠉⠋⠀⠀⢀⡤⠀⢀⠠⠊⠁⡀⠔⠁⠀⠀⠊⠀⠀⣠⠞⠀⠀⠀⠌⠀⢀⠄⠀⡀⠀⢷
⠋⠁⢀⠔⠋⠀⡀⠚⠀⢤⠀⡀⠉⠠⠶⡶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠖⠉⢀⡠⠊⠁⣀⠄⠁⠀⠀⢀⠞⠀⠀⠀⣠⠋⠀⠀⠐⠀⢀⡇⠀⣸
⠀⠐⠍⠀⣠⠎⠀⣀⣀⠀⠁⢀⣄⡄⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⡀⠂⠀⠀⠀⡄⠀⣼⠀⠀⡿
⠀⣀⠐⠢⠀⠠⣄⡈⠉⢀⡀⠀⠐⠀⠠⣤⡖⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠀⠁⠀⠚⠀⠤⠀⢀⠀⠀⡐⠀⠀⠄⠀⠠⠀⠀⣀⠀⢀
⠣⠈⠁⠀⠐⠦⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⡀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⣀⠀⠁⠀⠘⠃⠀⠰⠖⠀⡤⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁⠀⠈⣿⠏
⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⢸
⠀⠀⠀⠀⠀⢀⠿⠛⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣭⡓⡄⠀⠀⠀⠀⠀⠀⢾⣾⣷⣱⠸⡀
⠀⠀⠀⠀⠀⡜⠰⠉⠑⣦⠙⢿⡟⠀⠀⠀⠀⠀⠀⠻⢿⠧⠃⠀⠀⠀⢀⣀⠀⠈⠙⠛⠁⠀⢣
⠀⠀⠀⠀⠀⢱⠀⠀⠐⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠳⢄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⣤⣄⣀⣤⠤⠤⠄⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⣀⣀⣀⠀⠀⠀⠀⢤⣀⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣬⡤⠠
⣶⠶⠶⠆⠀⠀⠐⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠉⠭⠅⠈⠉⠩⠍⠁⠠⠈⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⠤⠼⠇⠐⠀⠐⠐⠓⠒⠒⠀⠀⠀⠀⠒⠒⠀⠄⠀⠠⡄⣀⠀⠠⠄⠒⠂⠀⠚⠛⠒⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⠛⣛⡋⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠒⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠺⣿⠋⠀⣿⣿⣧⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡊⢍⠉⡩⠷⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠔⠓⠒⠒⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⢖⣦⠄⠀⣤⠴⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡁⠀⠁⠀⠘⠉⠉⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⣉⡁⠐⠛⡁⠀⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠐⠒⠀⠀⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⢹⡄⢈⠓⢤⣤⣤⣾⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁⢸⠃⠀⣷⠀⠑⢄⣀⠜⠁⢸⡟⢹⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡁⠀⠀⠀⠀⠏⢤⠀⢹⡀⡴⢻⠋⢂⣠⠋⠁⢈⠆⠀⠀⠈⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⡸⠇⠀⣀⠀⠀⠰⡄⠀⠀⢧⠀⣼⡇⠀⡆⠀⠖⣺⠀⡆⠀⣸⣴⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡈⢻⠀⣘⠟⠓⠑⢎⡽⢦⠀⠘⡆⣿⣧⢰⠀⠀⡴⢹⠀⠁⠰⠏⠇⢸⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠱⡀⠀⠹⠠⠠⠔⣈⠀⢀⡉⣉⣉⠉⠁⢉⡀⠀⠀⠘⡇⠀⣠⠜⠠⣿⣵⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠉⣀⠀⡝⢄⢈⣠⠃⠀⢀⠀⠀⠙⠙⠀⠀⣰⡴⠀⢿⡀⣿⠀⢀⡿⠃⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣨⣯⠭⠿⠒⠋⠉⠀⠀⡇⠀⣠⣟⠙⡄⣼⠀⠀⠀⠀⢠⡟⡰⣧⠀⣸⣏⢸⡄⠋⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣶⠃⢆⠰⠀⠀⠀⠀⠀⠀⣏⡔⣡⠞⠁⢻⣸⢳⡄⠃⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢯⡟⠀⠈⢆⢣⢀⠀⣀⠀⠠⢋⠀⠁⠀⠀⠘⠿⠎⢃⠠⣀⣀⣀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠤⣚⣯⡴⠞⠋⢡⣸⣡⠎⣀⠤⠖⠋⢦⢣⠀⠀⠉⠓⠛⢰⡆⠀⠀⣠⢶⡺⠋⠛⣒⠒⠂⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠉⠀⠀⠀⠀⢸⣿⢃⡜⠁⠀⠀⠀⠀⠹⣧⠀⠀⡔⢋⡴⢾⡇⢠⢸⣍⠀⠀⠀⠈⢁⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣠⣤⣤⣄⣀⣾⢿⠏⠀⠀⠀⡀⠀⠀⠀⠀⢀⡎⣰⣿⣜⣵⡶⣣⢦⠞⣷⠀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⢀⠀⠀⠀⡠⠀⡐⠁⠀⠀⠚⢉⠀⠤⠀⢀⡴⣫⣾⣿⣿⣿⣿⣿⣧⣵⣿⠟⢻⣿⣿⣷⡒
⠀⠀⠀⣀⡴⠚⠉⠐⢁⠔⠁⠀⣐⠼⠁⡴⠳⠤⠦⠤⣀⠀⠀⠀⡠⢪⣾⣟⣿⠿⢿⣿⣿⠭⠙⢛⠉⠀⠀⠹⣿⣿⣿⣆
⣠⡴⢋⣁⣀⣀⣠⣂⣁⣈⣀⡘⠁⣠⠊⠀⠀⠀⢠⠆⠀⠙⠒⠢⠂⠛⠿⠛⠛⠋⢩⠀⠀⠀⠀⠀⢣⠰⠄⠀⠈⢻⣿⠏
⣿⣿⣿⣿⡿⣿⡿⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣖⣒⣒⣺⣗⣂⣐⠶⠶⢾⠷⠶⠶⠶⠶⡷
⠙⠀⠀⠀⠀⠘⠈⠩⠭⠤⠤⠤⠼⢧⣤⣤⣤⣼⣧⣤⣤⣤⣤⣭⣭⣭⣽⣭⣭⣭⣽⣭⣭⣭⣭⣭⣽⣿⣿⣿⣀⣀⠃
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣤⣤⠴⠶⣌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⢁⠔⠊⡀⠈⠆⠀⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡒⠋⠉⠀⠀⠀⡠⠞⠁⠀⢠⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣦⣤⣤⡴⠭⠤⠤⠤⠤⠤⠤⠤⠤⡤⠬⠦⡤⢤⠤⠤⡤⣤⣤⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣺⣍⣒⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⣂⡭⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠖⣂⠈⠉⠓⠒⠢⠬⠭⠝⣒⣒⠒⠒⠒⠫⠽⠒⠋⠉⠉⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣬⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢤⣄⣀⣀⣀⣀⣀⣠⣤⡾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠉⠉⠉⠀⠀⠀⣉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠅⠀⠀⠀⢀⡀⠀⠀⠀⠂⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⡂⠀⠚⠋⡉⠉⠛⠂⠀⠭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣶⢾⠶⠾⣶⣷⣦⣤⡶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣀⣤⣤⣄⣀⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠙⠋⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠆
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⡇
⠀⠀⠀⠀⠀⢀⡹⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣉⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⢘⠄⢷
⠀⠀⠀⠀⠀⡎⢠⠒⠒⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠊⠀⠸⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠒⠋⠒⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠒⠊⠉⠉⠉⠀⠉⣹⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠛⠉⠁

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