Drugs Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠲

⠀⠀⢀⣀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⠀⣿⣯⣬⣉⣉⣥⣾⠗⠚⠛⠀⠀⠀⠀⠀⠰⠄⠀⠀⢻⡏⢉⠀⢼⣇⣦⠀⣿⡅⢻⠁⣺⠏⢍⠈⣯⣔⠢
⠀⠀⠛⠛⠛⠛⣛⣋⣡⡄⠀⠀⠀⠀⠀⠀⠐⣦⡄⠀⠀⠈⣿⡶⢀⣼⣧⣦⡀⢸⡇⠞⡀⢻⣾⡟⠂⢬⣝⣿⡀
⠀⠀⠀⠀⠀⣻⣷⡿⠿⠷⠶⠒⠐⠒⠒⡐⠀⠉⠀⣤⡆⠀⠛⠉⠀⠈⠁⠈⢩⠀⠉⠋⠁⠀⠉⠋⠀⠈⠛⠋⠁
⠀⠀⠦⠃⠀⠀⠀⠀⡀⢄⡀⡀⠀⠘⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⡀⡀⠀⠨⠀⠀⠀⠀⣰⣎⠑⠠⢾⡿
⠀⠀⠂⠉⠀⠑⠀⠉⠉⠁⠀⠀⠀⠀⢰⣻⣿⣿⣻⣿⣿⣧⡁⣈⣑⣖⡀⠀⢠⣴⡄⠀⢉⣀⠶⠴⠊⠀⡄⠒⠠⠇
⠀⠀⠀⠀⣼⠄⠀⠀⠀⠉⠉⠁⠉⠉⠈⠛⠛⠛⠛⠿⠿⠷⠦⡯⠝⠋⠀⠀⠺⠞⠀⠀⢰⠯⠇⣠⣤⣄⠈⡅⠀⡀
⠀⠀⣶⡀⣿⠀⣠⡆⠀⠀⠀⠀⢒⣈⡉⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⡀⢀⠀⣄⠀⠀⠀⠀⢀⣠⣈⠉⠉⠉⠀⢀⡰⠠⠤
⠀⢠⣽⣷⣿⣾⣿⣶⠏⠀⠀⠀⠉⠠⠂⠀⠀⠀⢀⡴⠋⠉⠀⠉⢙⣃⣘⠷⣌⣙⠀⠀⣾⣿⣿⡿⠀⠀⣾⡓⠊
⠀⠀⣙⣿⣿⣿⣿⣭⡄⠀⠀⠀⣤⣾⠻⣼⡄⢀⡎⠀⢠⠤⣤⢤⣿⣿⣻⣷⡍⠋⠀⠀⠀⠋⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⢿⣦⣉⣛⡿⠁⠀⠀⠀⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⢠⠂⠒
⠀⠀⠀⠀⡄⠀⢀⣶⣄⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⠈⠟⠟⠟⢋⣠⡾⠋⠀⠀⠀⠀⢱⠤⠄⣴⣶⢃
⠀⠀⠀⠀⠀⠀⡘⣿⣽⢉⣼⠟⠆⠀⠀⣼⠉⠢⠀⠀⠀⣿⡿⠀⠀⣠⠀⠀⠉⠑⠀⠐⠈⠀⡀⠁⠀⠀⠈⠉⠹⣆
⠀⢠⣬⡀⡀⠈⣛⢻⡿⣿⠁⢀⠀⠀⣨⡍⡆⢠⠦⡀⠀⠿⠃⠀⠀⠀⠄⡀⠠⠀⡀⠀⠀⠀⢳⡀⠀⠀⠀⡀⢀⠜⠉⠉
⠀⠘⠿⠷⠖⠀⢹⣟⠀⠈⠻⡿⠃⠀⢹⣶⡷⢏⡇⠀⠀⠀⠀⠀⠀⠆⠆⠉⠠⠘⠁⠀⠀⠀⢾⡗⠐⠶⢾⣷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⠿⠿⠛⠛⠘⠓⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠻⣿⣶⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠈⠙⠻⣿⣿⣟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣦⣄⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠻⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡿⠿⠿⠶⠶⠾⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡏⠻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣴⣿⠟⢸⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣄⡀⠉⠛⠿⢿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣽⣿⡿⠋⠁⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠁⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠉⠛⠒⠒⠶⠤⠴⠤⠶⠶⠖⠚⠛⠃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠢⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡠⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣧⢸⡇⠀⢾⣉⣈⢿⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⣇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢀⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠉⠉⠉⠉⠀⠀⡷⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⣴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠒⠲⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠛⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡙⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤
⡞⠋⠉⡟⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠹⠉⠓⢦⡀
⠉⠒⠲⠦⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠁⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⣭⠇⠀⠀⡼⠁⠀⠀⣸⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠚⠋⢿⡄⠉⠉⠋⠛⠓⠒⠒⠒⡖⠒⠒⠛⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⠳⣄⠈⢳⠶⢤⣤⣄⣀⣀⣀⣀⣃⣀⣥⣤⠴⡞⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢷⣸⡄⣀⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣷⣞⠉⠉⠉⠉⣙⣷
⠀⠀⠀⠀⠀⣀⣴⠷⠛⢿⡓⢦⠀⠀⠀⠀⠈⢿⡇⠀⠉⠉⢙⣛⠛⠛⣷⠀⠀⠀⢀⣿⣈⣉⣉⣉⣉⣉⡼
⠀⠀⠀⠀⣰⢫⠇⠀⠀⠀⠹⡌⢷⡀⠀⠀⠀⠘⡇⠀⠀⠀⣯⡬⢃⠀⣿⠀⠀⠀⢰⠏⠀⠉⠉⠉⠉⠀⠙⡖⠶⢤⣀
⠀⠀⠀⠀⡇⢸⠀⠀⡠⠖⠲⣿⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⠉⠽⠫⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⣇⠸⡆⢀⡵⠶⣞⢹⠀⡟⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠉⠒⠶⠶⠶⠶⠖⠋⣿⠀⠀⠀⠀⢠⠞⠉⢳
⠀⠀⠀⠀⠸⣆⢿⡁⣠⠟⢉⡟⣸⠃⠀⠀⠀⠀⣿⠲⢤⣀⣀⣀⣀⣀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡖⠀⢀⡎⢠⠂⠛⢢⡄
⠀⠀⠀⠀⠀⠈⠳⠯⠿⠶⠿⡚⠁⠀⠀⠀⠀⠀⣻⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣇⡇⢸⠀⢻⣄⣰⣷⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠬⣟⠲⠶⠶⠖⠛⠉⠉⠓⠦⢤⣤⣤⣤⡤⠤⠖⠋⠹⣶⠤⣀⣀⣀⣀⣀⣴⠏⠀⠈⠙⠛⠓⠋⠀⠉⠁⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣋⠀⢘⣀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣒⣲⠶⢦⡀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠶⠷⠚⠉⠀⠀⢀⣤⠤⠤⢤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢧⣀⣀⠃⠀⠈⢻⠉⠁⠀⠀⠀⡠⠴⢶⠶⢤⣟⠲⠤⠤⢞⢇⣠⠶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡇⠀⠉⡧
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⢸⠆⣀⣎⣀⡴⡏⠉⠛⢋⠟⠋⠉⢆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠓⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠶⠚⠁⠀⠀⣯⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣩⡛⣉⣝⣙⣯⣏⣿⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠒⠒⠲⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢿⠒⠦⠤⠤⡤⡤⡤⢤⠤⠴⢾
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠙⢦⡘⡶⠤⠤⢤⣀⣄⣤⣤⠤⢴⢋⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣯⣤⣄⠀⠀⠀⠱⣟⠐⠤⠤⠤⠤⣄⠀⠀⢸⡿⠤⠤⠤⢽⡆
⠀⠀⠀⡜⡏⠀⠈⢣⢳⡀⠀⠀⢻⠀⠀⢰⡵⡀⣿⠀⠀⡸⠋⠙⠛⠋⠙⡶⠤⣀⡀
⠀⠀⢸⡀⡇⠠⣊⡹⡇⡇⠀⠀⢸⠀⠀⠀⠊⠁⢸⠀⠀⡧⢀⣀⣀⣀⣀⢼⠀⠀⠉⢑⠦⡀
⠀⠀⠀⢧⢳⢈⡼⢳⢣⠇⠀⠀⢸⠦⣄⣀⣀⣀⣸⠀⠀⡇⠀⠀⠉⠁⠀⢸⢠⠀⢠⢃⠄⠧⡀
⠀⠀⠀⠀⠙⠛⠛⠻⣅⣀⠀⣀⣨⢦⣀⠀⠉⠁⠀⠀⣀⣇⠀⠀⠀⠀⠀⡽⠾⢤⣼⣸⠦⠾⠳⢤⣀
⠀⠀⢀⣀⣀⣠⠒⢋⣹⠈⠉⠁⠀⠀⣈⢭⣭⡙⠉⠉⠀⠙⠿⠷⠶⠶⠟⠃⠀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠒
⠀⠀⠧⢄⣅⣈⣹⠉⠀⠀⡠⠐⡖⠲⣟⣒⣖⣧⣤⠒⣦⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⢀⣆⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣒⣓⡾⠃⠀⡜⠁⢀⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⢀⡤⠤⠦⠴⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢸⣉⣉⣀⣉⣉⡇⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀⣀⣀⢀⣻⠀⠀⠀⠔⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢼⡁⠀⠀⠀⠀⢀⡴⠃⠈⠀⠀⠀⠀⠈⠳⢄⠀⠸⡣⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠒⡂⡐⠈⡇⠀⠉⠒⠦⠤⠤⠒⠋
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠆⡬⠀⠙⠒⠐⠀⠀⡀⡀⡇⠀⡴⠒⠒⠛⠛⠻⣿⣿⣿⣶⣆
⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⡇⠄⡋⠀⣀⣾⣆⡀⠀⡘⠀⡇⠸⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠠⠃⠀⠉⢿⠏⠁⠀⠅⠂⡇⠀⠉⠛⠒⠒⠒⠛⠛⠛⠛⠉
⠀⠀⠀⣼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠙⠤⠤⡠⠤⡠⠔⠁⠂⡇⠀⡔⠋⠉⠉⠉⠉⠉⠉⠉⠒⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠈⠓⠖⢂⡈⠡⡃⠂⠀⡇⠘⡅⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣻⠀⠀⠀⠀⢶⣿⠶⠀⠀⠀⠀⡇⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠈⠉⠛⠓⠒⠒⠒⠒⠋⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠤⠲⠤⠠⠴⠲⡤⠤⠶⠒⠖⠲⠖⠒⢲⠲⠶⠒⠒⡶⠦⡀
⠀⠀⠀⣿⣶⢶⣦⣶⣦⣤⣤⣶⣶⣶⣖⡇⠀⠀⢀⡞⢡⣀⠀⠛⣄⡀⠈⠃⢥⡄⠀⠉⢠⣤⠀⠈⠀⢦⠀⠀⠁⡼
⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⢀⠎⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡄⢀⠀⠀⣠⠀⠠⠀⠀⣀⠀⡰⠁
⠀⠀⠀⢻⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⠇⢠⠋⢠⣤⠀⠋⢤⠄⠈⠁⢢⡆⠀⠀⠰⠖⠈⠈⠀⠲⡖⠈⠈⣰⠃
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠒⠛⠉⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⠴⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⠉⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⠵⠊⠁⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⠥⢖⡩⠔⢀⠀⠀⢀⣠⢴⡺⠟⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢀⡤⠖⠋⠀⠀⣁⡴⣚⠽⠊⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡫⠀⢀⡤⠞⠉⠀⠀⣀⣴⡾⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡠⢞⡩⠖⢋⠤⠚⢉⠤⢊⣠⣴⡾⠛⠁⠀⠀⠀⢀⠀⠀⠀⢠⡞⠋⠉⢳⡄⠈⢧⡀
⠀⠀⠀⡞⠉⠐⠉⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣇⣀⣠⡼⡷⠀⠀⠹⣦⡀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣀⡤⠤⣄⣀⣤⣤⣀⡤⢶⠿⣿⠷⠊⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠙⣦⡴⡪⠟⠁⠀⠀⠀⠀⠀⠀⡞⠢⠤⢤⣌⣿⠀⠀⣾⠀⢸⠀⢸⡏⠙⣢⠤⠤⣄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣄⣀⣠⡴⣿⣤⠖⢿⣦⣼⣦⡞⢡⡎⠉⠲⣤⡾⡆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡼⡏⠣⡈⠙⣦⢰⡇⢿⡴⠋⣷⠀⠘⣬⠿⠿⢾⣋⣩⠴⡧⠶⠶⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢷⠳⣄⡙⢆⡿⠈⣧⣈⣳⣤⠟⠀⣾⠓⠲⢖⣰⢿⠀⢸⡄⠀⠀⣸⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠳⠮⠽⠟⢡⠾⡀⠉⢍⢱⣴⡟⠻⣿⣭⣭⠵⠋⠀⠘⠮⣭⣭⡽⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⢧⣉⠓⢶⣿⡘⢿⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣽⡉⠁⠀⢸⡆⠑⠿⠞⠃⠀⢀⠤⠶⢤⡀⠀⠀⠀⠀⢀⣴⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢧⣙⡲⢶⡿⠁⠀⠀⠀⠀⢠⣇⠀⠀⣨⡇⠀⠀⠀⢐⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠉⠀⣠⠴⡶⢤⡀⠈⠻⢿⡭⠟⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢰⡇⠀⡇⢀⣿⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠸⣿⣶⣷⣻⠏⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠉⠉⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣵⢂⠀⠀⠀⠀⡈⠀⠘⢶⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠃⠀⠀⠀⠀⠶⣀⠻⠟⢂⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠂⠀⠀⡀⢠⡤⠜⠛⢯⡉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢆⠀⠠⠀⣀⡀⠀⠀⠰⠂⠉⠀⡄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣪⢀⠀⢀⠉⠀⠐⠀⠀⠀⢠⠀⣠⡄⠀⠀⡠⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⣁⡨⠀⠀⢀⡁⢀⣤⣄⠀⠀⠀⠙⡃⡀⢠⡙⠧⠘⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠤⠈⠀⠈⡂⠒⢨⠁⠘⣹⣦⡂⠀⠀⠀⠠⠌⢦⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⠛⠟⢻⣿⣿⣶⣿⣷⣶⣿⣤⡉⢠⣄⠊⢡⡄⠀⠀⠀⠀⠀⠓⠀⠀⣠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣽⠱⣄⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⡟⢸⡟⠁⠄⠀⠐⠀⠒
⠀⠀⠀⠀⣠⠞⠉⠻⣿⡁⠀⠑⣌⠣⡀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⠛⣥⡠⠶⠀⡀⠀⡀
⠀⠀⣠⠊⠀⠀⠀⠀⠙⢿⣆⠀⠈⠳⣌⠢⡀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣾⣃⡁⠀⠂
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠈⠳⣌⠢⡀⠀⠀⠀⢈⣿⣿⣿⣿⣮⡑
⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⢷⣝⢆⠀⢀⣹⡿⣿⣿⣿⣋⡑
⠀⢸⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠙⢷⣟⠉⠀⢐⣿⣿⣯⠼⠀⠓
⠀⠈⢧⡀⠉⠒⠤⠀⣀⡀⠀⠀⠀⣀⡀⠹⣧⢀⣠⠤⠛⠀⢀⣴⣿⠟⠅
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠶⠤⠤⠤⠤⡴⣶⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣤⢤⡄⣤⣥⣾⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣮⣭⣵⣿⣭⣍⣩⠼⣯⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠉⠀⠐⠃⠉⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠣⠄⠁⠀⣤⣀⠀⠈⠐⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⠁⠀⠈⠉⠀⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠟⠛⢳⡖⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡔⠀⠀⠀⣸⢿⢈⡽⠓⠶⣤⡴⠆⢀⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠷⣴⣉⡠⠈⠸⠊⠁⢀⠔⠁⠀⣀⣽⣯⣽⡷⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣤⣉⣁⠓⢤⣰⣶⠃⠀⠀⠚⠿⣿⡿⣉⣃⡈⠑⡀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠿⠍⠉⣙⠁⠰⣶⣿⢰⠀⠛⠁⣀⠘⢿⣿⣭⣿⣿⡟⠛⣤⡀⠜⡿⣾⣇⠀⠀⢀
⠀⠀⠀⠀⢠⣶⣾⣿⣯⡖⠶⠓⠒⢒⣼⠿⢿⣥⣠⣮⢹⣶⣆⠀⣩⡗⠐⠀⣸⣿⡿⣷⡿⢅⡥⠂⣠⢞⣿⡆
⠀⠀⠀⠀⠈⢲⣭⣭⣭⣭⣭⣭⣥⣤⣴⡖⠁⠀⠉⠻⡞⢿⡙⣧⠍⠉⠐⢀⣈⣽⠛⣡⠛⠿⣧⣽⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⡛⡛⠩⠍⠙⠀⠀⠀⠀⠀⠘⠂⢛⢿⣄⡰⢶⣆⣍⡠⠊⠁⣡⢞⣽⢿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠰⠛⠠⣼⠀⡘⠑⠛⠉⠐⡛⠛⢹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⢀⡄⡙⠒⠇⣀⣰⡛⠋⠁⣰⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣀⡠⢾⠿⣋⡄⣶⣾⣿⠧⣼⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡔⠛⠛⢡⡾⠿⠿⠚⣿⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠏⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣬⣍⣈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠣⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⠉⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⡆⠀⠀⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⡀⠀⠀⠀⠀⠉⠻⢷⣤⠀⣀⠔⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣾⡃
⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣧⡀⠀⠀⠀⠀⠀⠀⢙⠶⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠊
⣾⠃⠀⠀⠱⡄⠀⢀⣀⡀⠀⠀⠀⠸⡆⠙⠿⡄⠀⠀⢀⡤⠊⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠃⠀⠀⠀⠈
⢷⡀⠂⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⢦⣀⣀⣤⣄⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠂
⠈⢷⡀⢠⡀⠀⣱⡀⠀⠀⠀⠀⠀⠀⡖⣤⠀⠀⠀⢀⣠⣀⠀⠀⢀⡀⠀⠀⠀⢘⡜⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠋⠀⠀⠀⠀⠀⢠
⠀⠈⢷⣴⣿⠉⣿⣿⡄⠀⠀⠀⠀⣸⡿⣾⢀⡴⠢⠎⠝⢭⢗⣶⣴⢾⣥⣶⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠟⢋⣩⡄⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠘⣿⣿⣧⠈⢿⣿⡄⠠⠤⠴⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠛⠻⠻⣛⣤⠀⠀⠀⠀⠀⠀⠀⣏⢉⣁⣤⣾⣿⣿⣧⣤⡴⠖⠋⠉
⠀⠀⠀⠘⣿⣾⣧⠘⣿⣿⠀⠀⠈⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠘⢿⣿⣿⡁⠋⢠⠆⠄⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢠⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠑⣼⣿⣷⣄⠀⠀⠐⠒⠒⠒⠛⠋⠁⠀⠀⢀⢴⣿⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢄⡈⠛⢶⣤⣿⡏⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢷⣤⣤⣀⣀⡀⠠⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢄⠉⠻⣿⣷⣆⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⡄⠀⠈⠛⢿⣿⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠸⠷⢤⣀⣠⢀⡀⣠⠔⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢧⣽⣿⣷⣴⣼⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⠀⠀⠈⠉⠙⠢⣄⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡾⠁
⠀⢀⡤⠶⠶⠶⠦⢤⣄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⢰⡏⠀⢠⡀⠀⢄⠀⠈⠙⠲⣼⡟⠛⠒⠒⠚⠛⠛⠉⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⣿⢇⠀⠀⠙⢢⡀⠱⣄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⢿⠈⢆⠀⠀⠀⠈⠢⡈⠳⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⣴⠃
⠘⢧⠈⠳⡄⠐⠠⠀⠈⠳⣌⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⢀⡼⠃
⠀⠈⠳⣄⠈⠲⢄⣀⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠈⠙⠦⣄⣈⡉⠛⢛⣋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠉⠁⠀⠀⣀⣠⣤⠤⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢀⣤⠞⠋⣉⠀⠀⢀⡠⠖⠋⣀⠽⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⡠⠖⠉⣀⠴⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⢤⣤⣄⣀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠔⠁⢀⡤⠚⠁⠠⠂⠀⣠⢺
⠀⠀⠀⠀⣠⡞⠛⠳⢤⣀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢴⣎⠁⢀⡴⠋⠀⢀⣀⡤⠔⠋⣠⡞
⠀⠀⠀⡾⠁⠉⠓⠦⣄⡈⠙⠲⢤⣀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡈⠉⢉⣉⣉⣉⣀⣤⠴⠞⠉
⠀⠀⠀⣷⣄⠀⠀⠀⠀⠉⠓⠦⣄⡈⠙⠲⢤⣀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⢻⡌⠑⠢⢄⣀⠀⠀⠀⠀⠉⠓⠦⣄⡈⠙⣲⠞⢻⡆
⠀⠀⠀⠀⠻⣄⠀⠀⠈⠉⠒⠒⠲⠶⠶⠖⠚⠋⠉⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣓⣶⣶⣦⣶⣶⣖⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠋⠉⠉⠑⠒⠲⠦⠤⠤⣄⣀⣈⠉⠉⣛⣻⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣾⣛⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠿⢻⠉⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣟⣉⣀⣀⣀⣀⠀⠀⠉⠉⠉⠙⠓⠒⠢⠤⢤⣤⣤⠶⠛⠉⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠉⠁⢹⠁⠀⠀⠀⠈⠉⠉⠉⠉⢙⣻⣷⣶⣶⣶⣦⣤⣶⣟⡉⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⣾⣯⣥⣤⣿⣽⣶⣿⣿⠀⠈⠹⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠀⢀⣠⣴⣞⣋⣥⣸⣿⣷⣶⣖⣺⣿⣿⠿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⣠⠶⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿⠟⠋⠁⣾⠭⠤⣀⣈⣹⣧⣴⠛⠛⠛⠛⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⣦⣤⣄⣀⣉⣛⣒⠶⠖⠛⠙⠷⢭⣭⣭⡭⠾⣿⠀⠀⠀⣿⠀⣀⡴⠞⠉⠀⠀⠀⠀⢀⣠⠶⠛⢉⣉⣛⢦⣄
⠀⠀⠀⠀⠀⠀⠸⣇⣠⠶⠛⠁⠻⣿⣿⡻⠛⣿⡟⣿⠛⠲⠶⠶⣤⡴⠞⣿⠀⠀⠀⣿⠞⠋⠀⠀⠀⠀⣠⡴⠞⠋⢁⣤⠶⢿⣿⣿⡇⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⠤⣤⣤⣀⣈⣉⠉⠉⠀⠈⠛⠛⠛⢛⣫⠴⠛⣿⠀⠀⢀⡿⠀⠀⢀⣠⠶⠛⠁⢠⡞⢛⣻⡿⠿⠟⢉⣡⣶⣒⣲⡮⠙⣦
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠲⠶⠚⠋⠛⠒⣲⡿⡴⠶⠛⢁⣠⠶⠋⠁⣠⡴⠶⣾⡿⠿⠛⢁⣠⣾⣯⣝⣿⠟⠋⣡⡶⠋
⠀⠀⠀⢰⠛⠛⠛⠓⠶⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⢀⣠⠶⣋⣡⣤⣀⣸⡧⠴⣖⣿⣁⣀⣰⣯⣥⣤⣿⠏⢁⣴⠞⠉
⠀⠀⠀⠸⠧⢤⣤⣀⣀⡀⠀⠀⠈⠉⠛⠓⠶⣤⣀⠀⠀⠀⣠⠞⠉⠀⢀⡴⠛⠁⣾⣋⣀⣀⣭⣿⠉⠉⣹⣟⠉⢉⣹⡏⠉⢉⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠶⣤⣤⣀⣀⠈⢷⣠⡾⠋⠀⠀⠀⠀⠻⣦⡀⠛⠶⠶⢶⣿⠷⠶⠶⣾⠿⠿⠿⠟⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣶⠖⠶⢦⣌⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⢿⡳⠤⠶⣚⡿⠀⢀⣤⠞⠉
⠀⠂⠀⠀⠀⠀⠀⠀⣾⠧⣄⣀⣏⣇⡤⠔⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠉⠛⠋⠉⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⣤⠶⠞⠋⠀⣠⡴⢶⣶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠥⠤⠧⠿⠴⢒⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠋⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠈⠁⠈⠉⠛⠛⠛⠒⠒⠒⠒⠛⠻⠿⣻⣿⣿⠫⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⣛⣎⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⢤⣄⣀⣀⡀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⠃⡇⡦⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣽⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⣐⣺⣗⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣴⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡜⡇⠱⠦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⡤⡦⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⠈⢳⡀⢸⠀⠳⣿⡃⠀⢃⠀⠀⠀⠀⡄⣴⢷⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⣠⠲⣼⣧⣨⣿⡏⠀⣰⣢⠀⠀⢸⣧⠟⠀⡂⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠙⢷⣹⣧⣼⡵⠟⠚⢳⠁⠁⢀⠦⢡⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⣹⣿⠋⠀⣀⣴⣿⡀⠀⣐⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠿⠿⠿⠿⣥⠿⠿⠿⠿⠛⠋⠁


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

⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠙⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠣⠤⠤⠤⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠠⠄⠀⠐⠀⠉⠍⠀⠀⠀⠐⠀⣆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠉⠀⠀⠀⠈⠀⠣⠀⠀⠀⠀⠀⠀⠀⣀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠐⠘
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⢀⠔⠈⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠠
⠤⠄⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⢀⠄⠀⠠⣄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤⠂⠀⠀⠀⡀⠈
⠠⡀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠐⠈⠁⠀⠐
⠁⠐⠀⠀⠑⢀⣠⠄⠊⠀⠀⠀⢀⠀⠀⡐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠐⡀⠀⠀⠀⢠⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠀⠒⠋⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⣀⡀⠀⠀⠀⠀⠐
⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠠⠎⠁⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠐⠤⠀⢀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⠀⠀⠀⠀⠁⠀⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣄⣂⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⣿⣿⣿⢩⡍⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⢩⣭⣼⣧⣭⡍⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣶⣦⢸⡇⣶⣶⣿⣿⡇⠀⠀⣿⡇⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⠿⠿⠿⠿⠶⠶⠿⠿⠿⠿⠇⠀⣠⡿⠟⠉⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠞⠛⠙⠛⠛⢻⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠤⠤⠤⠤⠤⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⢷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠲⠿⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠂
⠀⠀⠀⠰⠤⠄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⡁⠀⠀⠀⠀⠐⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠠⣀⠀⠀⠀⠐⠃⠀⠀⠀⢉⠀⠀⠀⡘⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠒⣀⠀⠀⠛⠀⠘⠀⢈⡀⠀⠴⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠈⠦⡀⠚⠀⠀⡀⢈⡁⠐⠃⠀⠀⠀⠐⠀⠀⢀⡀⠒⠈⠀⠀⠀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠱⡄⢃⠀⢠⠀⡀⠚⠀⡀⠀⡜⠀⡄⠒⠀⠀⠀⠀⢀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠢⡘⠧⡖⢰⠈⢉⡁⡰⢁⢎⡔⠃⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠱⣄⡈⢂⠻⡡⣬⣡⡀⣁⠾⣀⠄⢊⡀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢤⡄⢠⠠⠤⠤⠀⢀⠄⠀⠀⠂⠠⠀⠀⡀⠀⠀⠀⠀⠙⠢⣁⢵⣽⡤⣶⠽⠎⠐⢈⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⠚⣾⠿⣿⡑⠒⠚⠓⠚⠀⠁⠈⠁⠁⠘⠂⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠒⠂⠀⣸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣂⣡⣠⡠⠓⠐⡟⠸⣌⠑⠉⠳⢒⠰⠠⠆⠤⠠⠄⠠⠠⠄⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠿⠭⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⠀⠠⠈⢣⡄⠀⠂⠐⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⣸⠈⠁⠄⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⢄⣀⡠⠀⠀⠀⢀⣀⣀⢠⡤⠤⠤⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢯⣠⣾⠏⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠤⠔⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⡌⢢⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⢀⠀⠸⠀⡀⠀⠀⠐⠁⠀⢸⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠒⠊⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⠀⠈⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡿⡟⣻⣿⣿⣿⠃⠀⠐⡾⡀⠰⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉
⣼⣿⣿⣿⡿⣹⠀⠛⠹⠃⠁⠘⡘⠉⢀⠀⣀⣰⠃
⣿⣿⣽⣿⣷⣇⠀⠀⣴⣶⣾⣾⣿⢠⣼⣴⣻⣿
⣹⡿⢿⣿⣿⣿⠀⠀⢨⡧⢼⢹⢻⠠⣏⠿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⡇⢾⣿⣿⠗⠀⠀⠈⠀⢸⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⠀⠀⠀⠀⢠
⣿⠀⢘⣿⣿⣧⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⡉⠀⢸⠃⠀⠀⠀⠀⣦⡤
⠃⠀⠀⠹⣻⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠧⣀⠈⠀⠀⠀⠀⢀⠟⠁
⠀⠀⠀⠀⢹⡿⠿⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠊⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣶⡜⣧⠄⠰⠨⠁⠀⠀⠀⠀⠀⠀⣤⣤⣂⣤⡄⣀⣤⣴⡧⠤⢤⡟⠟⠚⠋⢋⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡆
⠀⠀⠀⣿⡀⠉⣄⡀⠀⢠⣤⣀⣰⡀⠀⠈⠉⣉⣅⠉⠀⠉⠉⠈⠋⠁⠀⠀⣤⢠⡀⠀⠀⣤⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠂
⠀⠀⣼⣭⢷⢸⡿⣧⠀⣼⢿⣿⡙⢇⠀⠀⠀⢿⣿⠀⢀⡀⢠⡀⠐⣾⠀⠀⣭⣿⡁⠀⠀⣿⠀⠀⣀⣀⠀⠠⠗⠀⣀⡄⠋⢸
⠀⠀⡿⠿⠀⣿⠁⠉⠀⢁⣈⣿⡇⠀⠀⠀⠀⡶⣿⡀⠘⠃⣼⢇⣼⡽⠗⠈⣿⣽⡋⠀⣰⣏⣁⣤⣖⠃⣠⣶⠀⣼⠷⣦⠀⠃
⠀⠀⡀⠀⠀⣿⠀⢰⣇⣸⣿⣿⣿⡇⠀⠀⠀⠀⢸⡏⠀⠠⢹⡟⢿⣷⣶⡴⢿⣿⣧⣼⣿⡿⠛⠛⠛⠓⠖⠈⠀⠀⠀⠇⢸⢀⡄
⠀⠀⠀⠀⠀⣿⢠⣿⣿⣿⣿⡟⠛⢃⡀⠀⢠⣄⢰⡗⠀⠀⢨⡀⠾⢿⡇⣴⠟⠛⠛⠛⣿⡆⠀⠀⠀⠰⠖⠀⠀⠴⠂⠀⣤⣿⣥⡀⣠
⠀⠀⢀⡀⠀⠉⠘⠻⠟⠻⣿⣿⣿⣿⣿⡇⠈⠛⠈⠁⠀⢀⣀⣡⠀⠸⢇⣿⠀⠀⠀⠀⣿⠀⠂⠀⣀⢤⣤⣀⣴⣀⣀⠀⣿⣿⣿⣏
⠀⠀⠟⠃⠀⠀⠀⠀⠀⣤⣿⠿⠿⠿⠿⠀⠀⣾⡷⠈⠶⠂⠉⢽⡀⠰⣦⣿⠰⠂⠠⠆⣿⡹⢄⣂⣠⣶⣾⣏⢼⣿⣿⡆⢻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠠⠀⢠⡛⣁⡀⠀⠀⠀⠀⣰⣿⣷⣸⣿⣦⡀⣉⡤⠰⣿⣿⣷⣶⣶⣿⡇⣠⣶⣿⣿⣿⠟⣡⣾⣿⣿⣿⡜⢿⣿⣿⡆
⠀⢀⠀⠀⠀⠀⣀⣴⣿⣽⣿⡿⠀⠀⠀⡀⠻⣿⣿⣷⢿⣿⡇⠙⠥⠀⠜⠛⠋⠉⢉⣵⣿⡿⠛⢇⢙⣵⣿⣿⣿⣿⣿⣿⣿⡈⢿⠟⠁
⣶⣶⡶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣿⣿⣶⣶⣷⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡷⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠛⡿⠁⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢛⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⣌⣉⠛⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣬⡙⠳⣦⡀⠙⣆⠀⢀⡀⠀⡀⣀⣼⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡈⢿⢆⠈⣷⣴⣧⣦⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⣤⣴⠄⢸⣿⡟⠉⠙⠋⠛⢿⣿⣿⡄⠆⠀⢹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠉⠀⠀⠻⡆⠀⠀⠀⠀⠀⠇⡘⣿⣷⢀⢈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢱⣄⣠⠔⡿⣿⡿⢸⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣒⣢⣤⣀⡀⠀⠀⠈⠱⣤⣈⡉⣁⣰⣿⢃⡾⠁
⠀⠀⠀⠀⠀⢰⣖⣠⡽⠟⠛⠃⢀⠀⠈⣿⡆⠀⠀⠀⠀⠈⠉⠙⠉⠁
⠀⠀⠀⠀⢀⣿⡥⠾⡄⠀⢤⣶⣿⢆⣤⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡉⠉⣑⡀
⠀⠀⠀⠀⣸⣿⠀⠀⠈⢙⣿⠋⠁⠈⠙⣞⣸⣧⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⠿⠟⠁
⠀⠀⠀⠘⢸⣿⣷⣤⣶⣿⣷⣄⠀⣀⣤⣾⣿⡟⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊
⠀⠀⠀⢸⡘⠹⡟⠚⠛⠛⠛⠛⠛⠻⢿⣿⡿⡻⢳⠇⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠄⠀⠀⠈⠯⣶⣤⣶⠇
⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢊⣴⠏⠀⠀⠀⠀⠀⠀⠀⢷⣀⡀⣀⣠⡆
⠀⠀⠀⠀⠀⠙⢷⣦⣤⡄⡀⡀⠀⣈⣥⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉

⣿⣿⠻⢿⢻⠿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⡤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡧⢥⣸⣨⣅⣇⠧⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠂⠠⠤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣶⣽⡖⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⢀⡠⠔⣊⠡⣾⣲⠏⠉⠁⢠⡶⢮⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠻⢄⣘⠯⠟⠀⣀⣀⡸⠽⠟⠈⡡⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣈⠉⠁⠀⠀⢀⢤⢄⠀⠉⠲⢄⡙⠚⢃⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⠋⠘⠿⠃⠀⠘⠋⠛⢠⣶⣦⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠤⡄⠀⢀⣈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠨⠒⠁⠘⢅⣸⣈⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠛⠈⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⠿⢫⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣼⡿⢿⣿⠟⠋⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⠴⠟⠉⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠋⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⢛⣷⡟⠀⠀⠀⠀⠀⢀⢲⣀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⣿⠋⠻⡃⣘⡧⠴⠛⠉⠀⠀⠀⠠⢌⡑⢾⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⢿⡿⣿⡿⡿⠀⠉⢻⠀⢹⣀⡼⠤⠐⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⣍⠳⣜⢿⡿⠉⠉⠉⠁⠉⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⣥⡤⠄⠆⠀⠀⠊⠁⠀⠀⢀⢀⠀⠀⠐⠄⠀⠁⠃⠀⠀⠀⠀⠀⠉⠣⡸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠿
⠿⠍⠀⢀⣀⡀⣀⠀⠀⠀⠉⠀⠀⡄⢤⢠⠀⡄⠀⠀⣷⠸⠈⠀⠀⠀⠀⡀⠈⠠
⠀⠀⢠⣿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠸⠸⢸⠀⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢸⣿⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠱
⠀⠀⠻⠹⠐

⠀⠀⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠛⠀⠀⠉⠁⠀⠀⠀⠀⡦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⢱⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠖
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣂⡀
⠀⠀⠀⠂⢀⠀⠀⣀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠚⠳⠤⠀⠀⠄⠀⠀⠀⠀⠐⠁⠈⡄

⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣤⠄⠠⠤⠄⣤⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠦⢀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⠀⠀⠀⠀⢠⣤⠀⠶⠆⠘⠛⠂⠲⠖⠠⢦⡄⣀⠀⠀⠀⠉⠀⠀⣠⡾⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠚⠁⠀⠀⣠⡄⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⣠⡾⠋⠀⡾⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠁⠀⠀⣴⠆⠁⠀⠀⣀⣤⠶⠖⠛⠛⠉⠉⠉⠛⠃⠀⠀⠀⠀⣀⣤⣤⡾⠋⢀⠀⢸⣇⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⠀⠀⣴⠆⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢀⣤⣶⠒⠶⣤⡴⠟⠉⠀⣸⠇⠀⠘⢣⡀⠉⠉⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⢀⡶⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡁⠘⢧⡀⠈⠳⣄⣀⣴⠋⠀⠀⠀⠀⠙⣀⠀⠀⠩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⡦⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢧⡈⢳⣄⠀⠙⢦⡀⠈⠹⣇⠀⠀⢀⡀⠀⠀⠙⠂⠀⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣌⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⣴⣟⠙⣧⡈⠳⣄⡉⠳⠄⠀⠙⠶⣄⣻⠀⠀⠈⢷⡀⠀⠀⠹⠆⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢘⠃⠀⠀⡿⠀⠀⠀⠀⠀⢀⣴⢿⡅⠹⣦⡈⠳⣦⡈⠛⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠈⣧⠀⠀⠀⣶⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠸⠁⠀⠘⠃⠀⠀⠀⢀⣴⠟⢳⡀⠹⣦⡈⠛⠦⠀⠁⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⣶⠀⠀⠀⠀⣤⣀⡤⠻⡅⠀⠀⠹⢦⡀⠙⠂⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢘⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⡀⠀⠀⠀⠈⢿⡀⠀⠹⣄⠀⢶⣄⠉⠀⠀⠀⠀⢀⡶⠋⣠⡴⠞⠛⠛⠛⠛⠲⢦⣀⠈⠀⠀⠀⠸⠁⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠈⠁⠀⠀⠀⠀⠈⣷⣄⠀⠈⠳⣄⠙⢧⡀⠀⣠⡾⠋⢠⡾⠋⢀⡴⠞⠛⠛⠲⢦⡀⠙⢧⡀⠀⠀⠟⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣽⢦⣄⠀⠈⠻⢦⣿⡾⠋⠀⢀⡟⠀⣰⠏⠀⠀⠀⠀⠀⠀⢻⡄⠈⣷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣦⣠⠞⠁⣰⠞⠁⣠⠟⠳⢦⣤⡾⠋⠀⠀⠀⢸⡇⠀⢿⠀⣀⣄⡀⢀⣄⣀⢀⡗⠀⢸⡇⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠳⣄⠘⠁⣠⠞⠁⠀⠀⠀⠈⠻⠆⠀⠀⠀⠸⣇⠀⢸⡿⢧⡴⢏⡻⣤⡽⢿⠁⠀⣼⠁⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣾⡁⠀⠀⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠓⢲⣆⣉⣁⣰⠖⠛⠀⣴⠃⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣬⠟⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠆⠈⠳⣤⣀⡉⠉⠉⣁⣀⡴⠟⠁⠀⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠁⠀⠀⣴⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⠀⠀⠀⠉⠀⠛⠓⠰⠶⠆⠶⠶⠀⠛⠀⠀⠀⠀⠀⢀⡠⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠶⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠋⠘⠛⠃⠙⠋⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠖⠒⠒⠒⠒⠒⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⣉⣍⡉⠉⠉⠉⢹⠀⠀⠀⠀⢀⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⡇⢸⣇⣀⡀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠐⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠧⠤⡄⢀⡤⠬⠇⠀⢸⣀⡴⢯⡀⠀⠀⠀⠠⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢧⣼⠇⠀⠀⢀⡼⠋⠀⠀⠙⢦⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⢶⠶⠿⠶⠶⠶⢶⠶⠶⠟⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⣤⡴⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠸⠂⠸⠨⠀⠨⠀⠸⠘⠲⠸⠂

⠀⠀⠀⢀⣀⣤⣶⠶⡄⠀⠀⠀⠀⠀⢀⡆⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⢸⣫⣵⡾⠿⠃⠀⠀⠀⠀⢳⣼⣇⡼⠁⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⢀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠈⢹⠿⠿⢟⠉⠀⠀⠀⠀⢸⣧⣼⡇⣄⡆⠀⠀⠀⠀⣨⠿⠟⠁
⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁

⠀⠀⠀⠀⢠⣤⣴⠀⠀⠀⠀⠀⢀⣔⠲⠶⣢⡀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⢀⡀⢴⠦⠤⠤⠤
⠀⠀⣠⠞⠻⣿⣿⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⡿⢀⠀⠀⠀⠀⢸⣧⣴⡄
⠀⠀⠻⣿⣦⠜⠁⠀⠀⠀⠀⠀⢶⣶⠖⢰⣿⣷⠀⠀⠀⠀⠀⣙⠶⠶⣉⠀⠀⠀⠀⠀⠸⣿⡿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡉⠤⠀⠀⠀⠀⠀⠀⠀⣯⣩⣭⠇⠀⠀⠀⠀⢠
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠠⣄⠹⣷⡀⠓⠀⠀⠀⠀⠀⠀⡇⡀⠈⡇⠀⠀⠀⠀⢠⣥⡆⠀⠀⠀⣀
⠀⠀⣘⣁⣀⣀⣀⠀⠀⠀⠀⠀⠘⡀⠑⠿⠀⠃⠀⠀⠀⠀⠀⣇⡅⢰⡇⠀⠀⠀⠀⠀⣽⡷⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠖⠒⠒⠒⡇⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⣤⣀⣤⡅⠀⠀⠀⠀⢠⠊⠙⢿⠟⢁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠇⢀⣀⣤⠴⠖
⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠢⠔⠁⠢⠊⠃⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠸⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠆⠀⠀⠀⠰⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣿⣿⣿⣿⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢻⣿⣿⣿⡟⠛⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢈⡉⢠⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⢶⣿⠃⢀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣷⡄⠁⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠿⠀⢻⣷⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⣀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣭⣤⠀⠀⠀⠀⢀⣼⡿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣶⣶⣶⣶⣶⣶⣶⢶⡶⡶⠤⠤⠶⠶⠶⠶⠦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⢤⣴⣶⣶⣷⣿⣿⣿⣷
⢸⣿⣿⡿⠛⠓⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠞⠛⠛⢿⠿⠟⢿⣿⣿
⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡀⣧⡸⡧⢿⠀⡿⢸⢧⡏⣸⠂⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢦⡹⡆⠻⠈⡀⢡⢸⡀⡇⣨⢨⢀⡋⠸⢁⠟⣰⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠸⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣤⠙⠌⠡⣀⣦⠵⡚⠛⣭⣍⣉⣭⡙⢛⡲⢧⣆⡔⢁⠞⣡⠞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⢸⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣈⠳⢈⠑⢌⡷⠋⢰⣴⣿⡞⠿⠟⠛⠟⠲⠿⣩⣷⠎⣓⢅⠖⡠⠚⣫⡴⠂⠀⠀⠀⠀⠀⢰⡤⠀⠀⢸⡇
⠀⢸⠁⠀⠀⠀⠀⠈⠳⣤⣀⠀⠰⢦⡝⠛⢬⡽⣫⣼⣷⡞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠼⣯⣤⡱⡅⠎⡁⠴⠖⢁⠀⣠⣴⠶⠋⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡦⢈⣙⡞⣥⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣃⡘⡎⠤⠐⢛⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣄⣹⢡⣟⡿⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡿⣻⢹⣠⣴⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⣛⠉⣿⡏⣘⣛⠃⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⣀⣀⣀⢀⡀⠀⠀⢚⡟⡇⡿⢿⡁⡈⠛⠻⠷⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡴⠏⡇⠉⠾⡇⠀⠐⢵⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⢳⠀⠀⣰⣰⡇⡇⠈⢳⣿⣷⡄⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡍⣿⣷⣴⣷⠙⠿⡇⠀⠀⡆⠙⠟⠋⠃⣾⣿⣯⠙⠋⠟⠙⠙⠀⢀⣞⣛⢳⣧⣤⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠾⣿⣥⠀⠂⢀⠈⢦⠀⠿⠿⠷⠀⢀⠀⢤⠄⠀⣼⣯⡟⣾⣿⣿⣿⡿⠘⠀⠀⠀⠀⠀⠀⠁⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⡿⢆⠿⣡⣵⡀⠀⠀⣦⣄⢀⣄⢀⣀⣬⠇⠀⣀⢶⣯⢟⣜⣿⣿⣿⡿⠱⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠝⣀⠈⠳⣍⠡⣾⣟⣤⣬⠃⡃⣀⡀⣩⣅⣦⡞⢿⢗⡵⠏⣀⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠇
⠀⢸⡇⠁⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠞⢀⡌⠓⠮⣘⡻⠋⢾⡿⣿⣿⡻⠯⣘⡣⠖⢫⡄⠳⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⢸⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⢺⡟⣤⣸⠗⢠⣍⡙⣓⠒⠒⣒⢛⣉⡥⠰⣧⣄⠻⣷⠌⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠞⣹⠟⣠⣾⣿⣠⢿⣿⣷⡿⣎⣹⣷⡄⠹⣯⠳⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠃⣿⣿⣿⣿⡈⠛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡄
⠀⢸⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠉⠀⢸⡿⣿⣿⣿⣧⠀⠉⠂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⢸⣿⠓⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢛⣛⠃⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣠⣄⣀⡤⡀⢤⡄⡄⢸⣿⣿
⠀⢸⣿⣶⠀⣠⠀⠀⠄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠖⠺⠯⠽⠷⠛⣾⠀⡇⢸⣿⣿
⠀⢸⣿⣿⣦⣿⣧⣤⣤⣿⡤⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⢤⣤⣾⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠿⠿⠿⠟⠻⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⢶⡴⠶⠶⠶⠶⠿⠿⠿⠿⣿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢰⣿⣟⡑⠐⠒⠒⣩⣴⣶⣴⢾⠷⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⢰⣶⠒⠲⠄⢸⣿⢩⡍⠂⣿⡆⢰⡖⢂⣴⡟⣛⠢⠸⡟⠭⣅⡀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠘⢻⣇⣙⠀⠈⣿⢘⠋⠀⢹⡇⢨⡇⠘⣾⣡⣼⣆⠈⠿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣤⢶⣶⣶⡆⠀⠀⠀⠀⣀⠀⢀⡀⢙⠿⠃⠀⢀⠀⢺⣿⣟⠠⠚⣿⠻⢷⣄⠘⢷⣙⣡⠆⠙⢿⣗⡤⠈⢿⣶⣿⡗
⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⠛⠛⠋⠁⠉⡉⠉⡀⠀⠀⠀⠘⢶⠟⠀⠀⠉⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠉⠁
⠀⠀⠹⠜⠁⠀⠀⠀⠀⢀⢀⢄⡀⡀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⡀⠀⠀⠇⠀⠀⠀⠀⢀⣰⣍⠘⠀⠴⣿⠟
⠀⠀⠐⠐⠓⠊⠁⠊⠁⠛⠛⠂⠀⠁⠀⠀⠀⢠⡟⣿⣿⣟⣿⣿⣿⣷⣐⠒⠘⠳⣴⠀⠈⠀⢀⣤⡄⠀⠈⠉⠁⢴⣀⠴⠋⠀⡤⠤⠒⣸
⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠐⠒⠒⠂⠐⠒⠂⠹⢿⣿⣿⣿⣿⣿⣿⣿⣟⣀⡟⣛⠿⠍⠈⠠⣭⣥⠃⠀⠀⣞⡟⡆⠀⠀⠀⠀⠳⠆
⠀⠀⢀⡀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠉⠁⠰⠿⠽⠧⠤⠛⠀⠱⡄
⠀⠀⢸⣿⡄⣿⠀⣴⡿⠀⡀⠀⠂⠀⢨⡤⠤⠄⠀⠂⠀⠀⠀⠀⢀⣠⡤⠴⣦⣤⣤⠀⣤⠒⢦⣄⡀⠀⠀⣀⣤⣶⣶⡄⠀⠀⢀⡀⢀⠴⠋⠉⠉
⠀⠰⣶⣿⣾⣿⣾⣿⣾⣿⠃⠀⠀⠁⠀⠀⠒⢁⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⢈⣁⣤⡙⢷⣄⣬⡁⠀⠸⣿⣿⣿⡿⠃⠀⠰⣿⣣⠁
⠀⠀⢙⣻⣿⣿⣿⣿⣭⣥⡀⠀⠀⠀⢠⣰⣿⢻⣵⣇⠀⣠⡋⠀⠀⡤⣄⣤⢠⣿⣿⣟⣿⣦⠙⠋⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠙⠛⠋⠟⠻⠏⠉⠉⠀⠀⠀⠀⠈⢿⣿⣄⠙⠿⠿⡻⠁⠀⠀⡃⢸⡇⢸⣷⢿⣭⣟⣿⡇⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀⠈⡥⠤⠤⠤
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠛⠁⠀⠀⠀⣧⣼⡇⠘⣿⣿⣶⣿⠟⠀⣠⡶⠀⠀⠀⠈⠉⢣⡀⠀⠀⢀⣄⣼
⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⠶⣶⠰⣠⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⣿⡇⠀⠁⠁⠈⠀⠰⢿⣏⠃⠀⠀⣠⠀⠀⡠⠋⠉⠁⠻⣿⣬⡄
⠀⠀⠀⢀⡀⠀⢀⣤⣹⣷⣧⣠⣾⠋⠙⠀⠀⢀⣾⡁⠈⠃⠀⠀⠀⣿⣿⠇⠀⠀⢰⠂⠀⠀⠀⠀⠈⠀⠁⠀⠠⣴⠁⠀⠀⠀⠀⠀⠈⠻⣆⣀⣀
⠀⢀⣮⣤⢀⡀⠀⢉⡙⣿⢟⣟⠁⢀⣀⠀⠀⣴⢄⢿⠁⣴⠲⡀⠀⠹⠟⠀⠈⠀⠀⠰⢂⡀⠰⠀⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⠀⡰⠋
⠀⠈⢷⣿⣶⠖⠀⠙⣿⡃⠀⠈⢻⣾⡿⠀⠈⢻⣦⣼⢴⢽⡆⠀⠀⠀⠀⠀⠀⠀⢤⠰⠈⡇⠡⠸⠇⠀⠀⠀⠀⢼⣷⠀⠦⠦⣾⣷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢉⠀⣠⣄⣼⣿⣿⣶⣿⡷⠶⠆⣶⠄⠀⠤⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠈⠉⠹⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⣭⣽⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⣿⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣿⠀⠀⣿⣿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣤⣤⣬⣽⣿⣄⠀⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣤⣬⣭⣽⣙⣩⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⣿⣿⣿⣿⠟⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣥⣿⠅⠀⢴⣿⣿⣿⡿⢧⡈⠻⢿⡿⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠀⠙⠀⠀⠁⠀⠀⣈⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⣽⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⢻⣿⡶⢿⡾⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣏⣿⣷⣯⣽⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣼⢿⣌⢁⠾⣧⣾⣟⣿⣯⣤⠀⠀⠀⠀⢼⠷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⡟⣿⣷⡚⢛⣧⢛⣹⣿⣿⡄⠀⠀⠀⠘⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣴⢻⣷⡉⣿⣷⡋⣹⣿⣯⣾⣿⣆⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⡿⣷⣀⣿⣿⣯⣽⣯⣼⣿⣿⠀⠀⠀⠀⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣶⣦⣵⣶⣦⣽⣿⣶⢿⣷⠿⣿⣷⣿⣿⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣾⣿⣿⡀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⣼⣿⣿⣿⠛⢻⢿⣿⣿⡟⣿⣸⣿⣁⣟⣿⡯⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠄⠻⠁⠀⢸⣿⣿⣧⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡏⣾⣿⣿⣼⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⡙⡏⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⣿⣿⣿⣛⣿⣌⣙⠟⠃⠸⢟⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⣦⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣿⢶⣶⣿⣧⣴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠋⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣈⣙⡛⠿⠿⠻⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⣉⣁⣴⣾⣿⣿⣿⠟⠉⣹⠙⠋⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡿⠟⠛⠒⠦⠤⠦⠀⢴⠶⣶⠟⠛⠛⠛⠻⠿⠿⠿⠟⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣷⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶
⣿⣿⣿⡏⠀⠉⠀⢀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⡄
⠰⣿⣿⣿⣿⠿⡟⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣰⡿⡶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢿⣾⣿⡇
⠀⣿⣿⣻⣿⡟⣽⢿⣟⡟⢿⣿⡄⠀⠀⢀⠀⠀⠘⠛⠿⠿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⡼
⠀⢻⣿⣻⣿⣷⣽⣿⣿⣿⣼⠻⣷⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⣿⠛⠃⣼⠁⢀⣾⣷⣆
⠀⢸⣿⣻⣿⣿⣿⣿⣴⣿⣿⣧⣿⡇⠈⠿⠟⠀⢤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢻⡀⠈⠛⣿⠛
⠀⠀⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠻⠆⠀⠀⠘⢷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⣧⠀⠀⣸
⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠿⠄⠰⠏
⠀⠀⠰⠀⠇⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣴⢿⣿⣿⡟⣿⣷⣄⠀⠠⡖⠻⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⣶
⠀⠈⠀⠀⠐⠄⠸⠟⠃⠀⠀⠠⠂⠀⢀⣾⡟⡸⢹⣾⣿⣿⣻⣿⡀⠱⡉⠓⢌⢌⡄⢰⡶⢶⠲⠞⣿⡟⠋⣉⠁⣦⡽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⡤⣟⣿⡟⠏⣿⣿⡇⠀⠱⣀⠺⠃⠁⢸⡇⡄⠙⠀⠻⠇⠀⢿⡟⡮⠙⣶
⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣧⣿⣿⣿⣿⠠⣤⡀⠀⠀⠀⠀⠸⡇⢁⡀⣄⣀⣀⣄⡀⣀⣄⣠⡿
⠀⠀⠀⣀⠁⠀⠀⣀⠀⠀⠀⠀⡀⠀⠸⣿⣿⣿⣿⣹⣿⣽⡿⠃⠀⣿⡇⠀⠀⠀⢀⠀⠛⠉⠉⠉⠉⠁⠈⠉⠉⠀⣀
⠀⣤⣤⣤⣤⣤⣬⡿⠁⠀⠸⠒⠉⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⣠⣿⣇⣠⡾⠇⠈⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣤⠋
⠀⠀⠀⠀⠉⠉⠀⠀⣀⡠⢤⠀⠀⠀⠀⢰⡄⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣯⠀⠀⢠⡶⠀⠀⠀⠀⠀⠈⠉⠘⢿⣿⣇⠛⠃
⠀⠀⠀⣠⠤⠒⠊⠉⠀⠀⠀⣣⠀⠀⠀⢸⣿⡄⠀⣰⡟⠀⠀⠘⣿⣿⣿⠃⠀⣀⣀⣀⣀⡀⠀⠐⠂⠰⠀⠠⠇⠈⠁
⠀⠀⠀⢃⠀⢀⣀⡠⠤⠒⠋⠁⢶⣤⡀⠈⢿⣷⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⢛⢿⣿⣿⣿⠀⠘⠀⠐
⠀⢀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣌⣿⣾⣃⣤⣶⠟⠃⠀⠀⠀⠀⣿⢸⡾⣿⣿⣿⠀⠘⠀⠈⠀⠀⣀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢾⣿⠿⢯⣅⠀⠀⠀⠀⠀⠀⠀⢿⣼⣧⡇⢷⣿⡆⠀⠀⠀⠀⠀⠀⠈⠑⡄
⣴⠖⠚⠋⠽⣦⡀⣠⡶⣄⠀⠀⠀⠀⠀⢀⡞⠁⢠⠀⠈⠓⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠈⣿⠗⠀⢠⠈⡛⠿⠻⣿⡀⠀⠀⠀⢀⣈⡀⠀⠈⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⢠⡀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆
⠀⠈⠳⣴⠂⠀⠐⠀⠀⣿⠉⡉⠙⡏⠉⡝⣷⡀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡜⣧⡜⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠹⣿⠲⢠⡀⠁⠀⡄⠐⣦⠀⢰⣈⣷⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⣿⡘⠷⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⡁⠀⠀⠑⠀⠀⠠⠂⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣧⢠⣶⣶⡀⠀⣠⣶⣶⡀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⢀⠒⢧⠀⠀⠀⠐⢄⠀⠀⠀⠀⡀⠂⠀⠀⠐⠄⠀⠛⠋⠁⢠⣿⣒⣄⠀⠀⣿⣿⣿⠈⢻⣿⣿⣶⣿⣿⠟⠀⠀⢸⠄⠀⡇
⠀⠀⠀⠀⢀⠂⢀⠂⠀⠀⠀⠀⠀⠁⢢⡄⠈⠀⠀⠀⠀⠀⠊⠀⢱⣶⢦⡻⠿⣿⠏⠀⠀⣿⣿⣿⠀⠀⣹⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⢀⣿⣷⠃⠀⠀⠀⠀⡠⠔⠲⡅⠈⢄⢀⠴⠶⠀⠀⠑⠠⢿⣿⣿⢷⣶⡀⠈⠀⠀⣿⣿⣧⢀⣼⣿⣿⠿⣿⣿⣦⠀⠀⢸⣄⣠⡇
⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠁⠀⣠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠧⠐⠁⠀⢿⣿⣿⠈⠻⠿⠃⠀⠙⠿⠟⠀⠀⠀⣿⣿⠃
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠂⠀⠀⠀⠀⠀⠰⣄⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣮⢥⡤⠄⠼⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠔⠋⣈⠷⡀⢸⡇
⠀⠀⠀⣦⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡅⠰⠚⢀⠠⣤⠣⢸⡇
⠀⠀⠀⠉⠀⠚⠉⢀⠀⢀⠲⢶⣶⠶⢖⠀⣸⠟⠁⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠠⠴⠃⢉⣀⢆⡓⠋
⠀⠀⠀⣀⣀⠀⣀⢀⡀⠀⠉⠀⢦⣉⡉⠀⠐⠀⠼⢋⡼⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⣁⡠⠐⢺⡔⠺⠉⠠
⠀⠀⠀⡇⠈⠉⠉⠈⡇⠀⡄⠀⢨⠳⠇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠟⠈⢋⣌⠙⠁⠀⠀⠀⠀⡀
⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⡇⠀⢘⡓⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣿⠃⠀⡐⠀⠀⠀⠀⠀⠁⠝⠁⠀⠀⠀⠀⢀⢠⣌⠀⠳⡀
⠀⠀⠳⢧⢶⡴⠒⠞⠁⠀⠑⠖⠾⠥⠂⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠿⡄⠀⠘
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠂⡠⣄
⠀⣾⣀⠀⠴⢂⠘⣢⠀⠀⢤⣄⠈⣥⠞⠋⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⣠⠁⠀⠀⠀⠀⠠⠤⡤⠦⠐⠃⠀⡜⢠⠁⣼
⠀⠈⡛⠟⠣⣤⡾⠟⠀⠀⠀⠈⢉⠹⠦⠀⠈⠁⠀⠀⠀⠀⡀⠀⢀⠈⢳⡀⠀⠻⣷⣿⢿⣮⡁⠀⠀⡈⠬⠭⠄⠁⠀⢀⡀⠤⠊⠀⣘⢀⡇
⠀⠰⣦⣤⣤⠆⢠⠀⠀⢠⠀⠀⠘⠓⠂⠠⣤⡤⠀⠀⠀⠘⠟⠃⣸⡟⠁⠃⠀⠒⣫⣴⣿⣿⡿⠀⠐⠀⠀⣀⣤⣦⣴⣶⡄⠀⠀⠀⠇⢸⠃
⠀⠀⠀⠈⠀⠀⠘⠻⠶⠟⡀⠀⢀⣾⣷⠄⠀⠀⠀⠀⠸⢿⣦⠀⠙⠃⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠸⣷⣷⡟⠛⣷⣿⡿⠃⠀⠀⢠⢓⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢦⡈⠁⠙⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣷⡤⠀⠀⠀⠀⣀⣀⡀⢀⣌⣿⣷⠶⣾⣿⡇⣀⡀⠀⠸⣭⡇
⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠛⠛⠃⠀⠛⠛⠉⢠⡄⠘⠿⣿⡿⠂⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠃⠈⠻⣦⡀⠀⣾⠟⠋⢀⠠⡄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⢽⣿
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢈⢁⣀⡀⠀⠈⠁⠀⣧⠀⡀⠶⣠⣴⡁⡐⠚⢸⣿⠑⠊⠉⡇⠀⠀⢀⣿⣧⠀⠀⠀⠀⠸⣼⡇
⠀⡇⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⢰⣴⢶⡜⣦⡆⠀⠀⠀⢀⡀⠮⣩⣞⣃⠶⣠⠴⠤⣸⣿⠀⠀⠀⡇⠀⢠⡋⣼⣿⣷⠀⠀⠀⢰⡟
⠀⣇⠀⠀⠀⡸⣤⣀⣀⣀⣆⠀⢸⡿⢾⡇⢿⡇⠀⠀⠀⠈⠙⡛⠦⠈⠋⢛⠷⠀⠉⢹⣿⣤⣀⣴⡇⠀⠸⣿⣿⣿⡿⠀⠀⠀⣼⠇
⠀⠀⠉⠉⠉⠀⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠖⠈⠁⠐⠒⠂⠙⠛⠛⠛⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢰⣶⣾⣿⣿⣶⣶⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⣏⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣿⣿⡿⠟⣠⣴⣶⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⡶⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡶⠛⠁⠀⠙⡿⠿⠛⠻⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡏⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⡟⠛⠛⠓⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠸⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⡄⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣧⣤⣤⣤⣤⣤⠞⠁

⢰⣿⣿⣿⣿⠷⠟⠛⠛⠒⠒⠓⠒⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠂⢐⣶⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠉⠙⣿⣿
⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⣦⢰⠀⣆⣰⢠⢀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡸⡜⠇⠋⢈⠈⡀⡅⡉⠈⠘⠱⠃⠞⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢢⡜⢆⠁⣀⡤⠶⠛⢫⣍⣩⣍⠓⡳⢦⣆⠄⡡⢋⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢰⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣌⠓⣈⢢⢕⡉⢶⡾⠿⠛⠋⠙⠋⠺⠧⣷⠎⣕⢄⢢⠐⣩⠴⠂⠀⠀⠀⠀⣰⠄⠀⠀⣿
⠀⠘⠀⠀⠀⠀⠈⠓⢶⣄⣈⠳⠌⣉⡶⢣⣾⠻⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⠳⡊⠄⢚⣩⣄⣤⡾⠋⠁⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠐⠾⢱⣿⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣱⡐⣀⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠿⣷⡇⠿⠿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢧⣿⣿⠛⠻⢶⣦⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣠⠟⡕⠩⡗⠀⠠⣴⣾⣿⣦⠀⠀⢰⣿⣿⣶⣧⠀⠀⢍⡾⡇⠘⢶⣷⡄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣷⣼⡇⠻⢟⠀⠀⠌⠻⠛⠉⣼⣿⡎⠛⠻⠛⠑⠀⢠⣛⡋⣇⣤⣿⡟⡿⠀⠀⠀⠀⠀⠀⣿
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡜⣻⡧⠀⠀⠤⠑⠀⠛⠛⠃⠀⡀⠰⠂⠠⣾⡿⣽⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠛⣌⠴⠾⣠⡀⠘⡦⡴⠂⠠⠰⠚⢀⣤⡿⢟⠝⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢈⡏
⠀⢸⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣥⣂⡌⠳⢜⡻⢽⡿⢣⣦⣶⣦⣶⠞⠇⣙⠵⠫⣐⢮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢐⠙⠫⣶⢋⣠⠍⣓⠲⠬⠭⠭⠭⠽⢒⠫⣅⠘⣶⡝⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⢸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⡟⢠⣿⣋⡼⣶⣶⢧⣙⣿⡄⠻⡟⠎⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⣼⣿⣿⣧⠙⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁
⠀⢸⣅⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢠⡟⣿⣿⢻⡆⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠓⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⣾⣦⣟⣥⣰⠖⠀⣿⣿
⠀⣸⣿⣇⢾⣄⡈⢀⡄⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁⠉⠉⠉⠁⠛⠐⢀⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣯⣤⣤⠤⣴⣶⡶⠶⠤⢤⣤⣶⣴⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿
⠀⠈⠉⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⢿⣿⣿⣿⣿⢿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣿⣾⣿⣿⣿⣿⣦⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣚⣉⣀⡘⢦⣄⣀⣉⢋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡋⠉⠉⠉⠀⠉⠉⠁⠈⠁⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠟⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠂⠘⠛⠉⠉⠻⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣷⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢀⣶⣶⣶⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠙⠛⠛⢿⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣻⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢹⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⢀⠀⢠⣷⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣷⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣴⣾⣿⣿⣘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣛⢋⠉⠉⠉⠛⠛⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣏⣛⠙⠛⠛⠛⠛⣛⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⣤⣿⢉⣉⣉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠉⣉⣉⡉⠉⠙
⠀⠀⠀⠀⠀⣿⣸⢸⡧⣾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⣷⢴⡃⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣿⡆⠃⠘⢧⡶⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠇⠘⠀⠳⣴⠀⢇
⠀⠀⠀⠀⠀⣿⣷⣧⠀⠀⣈⣉⣀⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⢀⣉⣁⣸⣀⣀⣀
⠀⠀⠀⠀⠀⣿⣿⣮⣲⣾⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣑⡴⠚⠛⢛⠻⠿⠟⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⡆⠀⡖⠀⣶⠀⣶⠀⢰⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣧⣤⣧⣤⣧⣤⣿⣤⣿⣤⣼⣤⣼⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠉⢉⣉⠉⠉⠉⠉⠉⠁⢸⡇⠀⠀⠀⠀⡠⠊⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⡏⠉⠙⡆⠀⠀⠀⠀⢸⡇⠀⠀⡠⠊⠳⢄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣟⠛⢻⡁⣠⠀⠀⠀⢸⡇⠀⣼⠁⠀⠀⢈⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠁⠀⣠⠟⢧⠀⠀⠀⢸⡇⠀⠘⠦⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠉⠉⠀⠈⠉⠉⠉⠀⢸⡇⠀⠀⠀⢠⠴⠒⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠉⠉⠀⠈⠉⠉⠉⠀⢸⡇⠀⠀⢰⠃⠀⠀⣠⠞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠂⢸⡇⠀⠀⠸⣄⣠⠞⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠃⠀⠀⠀⠘⠳⠤⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⡀⠀⠀⠀⡀⠀⢀⢀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠘⠀⠚⠀⠂⠈⠁⠈⠁⠈⠀⠀⠒⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡄⠀⢠⠀⠀⣤⠀⢠⡄⠀⣤⠀⠀⡄⠀⢠⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⠀⠀⣟⠀⢸⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠓⠒⠛⠓⠒⠛⠒⠚⠓⠒⠛⠒⠚⠓⠒⠚⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣯⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡾⠛⠓⢶⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠾⣧⡀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⣿⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠞⠁⠀⠈⠻⣦⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡏⠀⠙⢷⣄⣴⠆⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⢀⣴⠟⢧⡀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠤⠤⠄⠀⠤⠤⠤⠤⠤⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣀⣀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣿⠀⠀⠀⠀⢠⠞⠉⠁⠀⠈⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠈⠉⠀⠀⠈⠉⠉⠉⠁⠀⠀⣿⠀⠀⠀⢀⡏⠀⠀⠀⣠⠞⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⠀⠀⠀⠘⣇⠀⣠⠞⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠘⢿⣅⡀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⢀⠄⢀⠀⢀⠀⠀⠠⡀⡀⠀⡀⢀⠀⡀⡠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠘⠊⠸⠀⠈⠑⠐⠤⠀⠓⠀⠃⠃⠁⠐⠀⠈⠀⠜⠘⠱⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠙⠓⠂⠤⠤⠍⣉⡉⢛⣲⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠫⠤⠤⠤⢄⣀⣀⠀⠀⠀⢀⣠⠶⠛⢩⠀⠀⡇
⠀⠀⠀⠀⠀⡴⠚⢻⠛⠛⠛⠛⠒⠒⠒⢶⣤⣤⣤⣄⣨⣽⢻⠉⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⢰⡇⠀⢸⠀⠀⠀⢀⣠⢴⣾⠭⠼⣿⣶⣿⡇⠈⢻⡀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⢸⣤⠴⣺⠟⠒⠺⢿⣻⣿⡿⢿⣿⡇⠀⢸⡇⠀⠀⠀⣸⠴⠋⠁
⠀⠀⠀⠀⠸⡇⠐⢯⣄⣀⣙⣺⡿⠿⠛⠿⢴⣶⡶⢿⡇⠀⢸⡇⣀⡴⠚⠁⠀⠀⣀⡤⠖⣛⣲⣤⡀
⠀⠀⠀⠀⠀⣧⡖⠋⠁⠻⠿⣭⠿⠟⢿⣛⣒⣲⠖⣻⡇⠀⢸⡟⠁⠀⢀⣠⠴⢚⣁⣴⣚⣿⠿⢃⣉⡲⣄
⠀⠀⠀⠀⢀⡬⠟⠉⠛⠒⠒⠶⠦⠤⢤⣤⠤⠶⠯⣠⣇⣠⠜⢀⣠⠖⢋⣀⣰⣿⡶⠟⢉⣵⡶⣿⠿⠏⡨⠃
⠀⠀⢰⠚⠛⠒⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢀⣠⢖⣫⣤⣀⣏⣄⣾⣃⣀⣾⣭⣽⠟⣡⠴⠋
⠀⠀⠈⠓⠒⠶⠤⣤⣀⣀⡉⠉⠓⠦⡄⢀⡴⠁⠀⠰⡏⠀⣯⣤⣐⣾⣃⣁⣿⣥⣤⡿⢈⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠤⡬⠭⣝⡓⠒⠿⠋⠀⠀⠀⠀⠈⠳⣄⠉⣾⠭⠤⣼⡇⢉⣡⠞⠁
⠀⠀⠀⠀⠀⠀⣟⠤⠤⠿⠄⣊⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠉⠉⣉⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠋⠁⣠⣖⣻⣻⣉⠽⣦⠀⠀⠀⠀⠀⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠒⠋⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶