Pelvis Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠂⠲⠶⢶⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⠛⠉⠉⠉⠑⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦
⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢠⡎⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠙⠿⢀⢈⣦⠤⢤⣬⣤⡛⠀⠀⠈⠳⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧
⢸⡇⠸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⣼⣛⣤⠄⡤⢀⣨⣿⣶⡀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠙⠆⠹⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⣀⣤⣶⣾⠏⠙⢿⡛⣿⣿⣿⣿⠻⣿⣆⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸
⠀⠀⡄⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⣿
⠀⠀⠳⣤⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣯⣟⡻⡏⠀⢂⣿⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢀⣴⠿⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡷⣴⣿⣿⣿⣿⣿⡿⠻⢆⣼⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠸⡟⠙⠛⢻⣿⣿⣶⣠⣿⣿⡿⣿⣿⣿⣵⣾⣿⣿⡿⢿⠟⠙⣷⠀⠀⠀⠀⠀⠀⣠⣶⢿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣴⠆⠀⠀⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⡇⡾
⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⢻⣷⣄⠀⠸⣧⡀⠀⠀⠀⢻⣿⣯⣿⢙⣿⣻⣿⣿⠟⢠⠃⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣏⣼⠿⣿⣷⡀⠘⣿⣦⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣏⡀⠃⠀⠀⠀⣾⠟⣠⣾⣿⣶⡆⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣭⣿⣙⣿⠿⣿⣿⣄⣼⣿⡇⠀⠀⠈⠙⠶⠡⠀⢀⠙⠋⠁⠀⠀⢀⣴⡿⠾⠋⠉⢸⣿⠁⣾⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠙⢿⣿⣿⣿⣡⡈⠛⠟⢿⣦⡀⠀⠀⠒⠀⠐⠋⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⣀⣿⡿⣸⣿⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⣿⣿⢿⣿⡿⠳⠶⠶⣼⣿⡶⠦⠐⠻⡾⠃⠀⣶⣾⣏⣁⠠⠤⠤⣾⣿⣿⣿⣴⣿⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠈⣿⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⡇⢠⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠘⣿⠄⠀⠀⠀⠀⠀⢸⣿⠿⠆⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠛⣷⡀⠀⠀⠀⢠⠾⠟⢀⡼⠃⠾⣿⣿⣧⣄⠀⠀⠀⢀⣰⡀⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠉⠒⠖⠊⠁⠀⣠⡞⠀⠀⠀⠈⢿⣿⣿⣿⡿⠖⠛⠁⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⣀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣩⣤⣀⡬⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⡟⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠈⠉⠉⠉⠉⠉⠛⠓⠦⣄
⠀⠀⠀⣠⣖⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⢄⠀⡀⣠⣤⠀⠀⢐⣦⠀⠀⠀⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⡴⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⡿⠟⠋⢠⣤⡉⠈⠛⠻⠿⠛⢾⡃⠋⠉⠀⠀⢀⡸⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⢸⢁⣿⣿⣿⣿⣿⡿⢀⡀⠀⠀⠀⠀⠀⠁⣸⠟⠀⠉⢉⠀⠀⣠⣄⠀⠀⠀⢙⡄⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣾⡟⠉⠀⠀⠀⠀⢠⠀⠃⠀⠀⣠⣾⣷⣤⣽⣷⣾⣧⣤⣾⣷⣆⣀⠀⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⣦⣿⣷⠀⠀⠀⣿
⠀⠃⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⡔⠃⢀⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⢶⣯⣠⣏
⠀⠘⡀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣿⡿⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣦⠊⢹⡁⠀⢀⡀⠀⠀⢀⣖⡀⠸⣍⣿⡇
⠀⠀⠇⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⠏⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⢿⣷⠀⢁⠶⡈⠉⣉⣷⠋⠻⠃⢀⣴⡿
⠀⠀⠈⠳⢿⣿⣿⣿⣿⣿⡄⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡦⠈⣶⢇⣴⡿⣯⡴⠿⠶⠟⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡟⡄⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠛⢻⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡷⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠈⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠿⢛⠿⠛⠉⠀⠀⠀⡟⡀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⢠⣿⡟⠻⠀⠀⠀⣠⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡻⠟⠓⡀⠀⠀⠂⢙⣴⡃⠄⡀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⢀⣤⠿⠋⠀⠀⢹⣴⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣤⣀⣀⣋⣈⠁⠀⠁⠐⠦⣤⣤⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣅⣀⣀⡀⠀⠘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⡏⠉⠀⠈⠉⠉⠻⣿⣦⣤⣄⠐⠂⢀⣤⣼⣿⡿⠛⠉⠉⠙⠋⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢧⡀⠀⠀⠀⠀⣴⣿⣿⣿⡤⠀⠀⠾⢿⣿⡿⠷⢄⡀⠀⠀⠀⠈⣹⡟⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⣩⠋⡀⠀⠀⠀⠀⠙⢦⠀⢀⣿⣦⠀⠀⠀⠈⠁⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠘⠻⢿⣿⠆⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠞⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⣶⠛⠉⠉⠁⠐⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠀⠈
⢀⢴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⠀⠀⠀⣤⣀⣀⡠⠠⠀⠠⠀⢺⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⣿⣼⠿⣟⣸⠀⠀⠀⠀⠀⠀⠀⢸⣳⠄⠀⢀⣰⣦⣭⣤⣤⣤⠀⠀⠀⢤⠽⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿
⠐⢿⡀⠹⣿⣄⠀⠀⠀⠀⠀⢀⣾⡁⣠⡾⠟⢛⣹⣿⣿⠧⠾⠟⠲⠀⠀⣀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⣰
⠀⠀⠉⠢⡙⣿⡇⠀⠀⠀⢰⣿⣿⣿⢋⠴⠛⡛⠋⢿⠍⠀⠛⠁⢢⣰⣿⣿⣇⢀⠀⠀⠀⠑⠂⠀⠐⠉⠁
⠀⠀⠀⠀⢹⢼⣇⠀⠀⠴⢼⣏⠉⠛⢇⡈⢹⠿⠦⢤⡤⠘⠟⠓⠘⠛⠛⠉⠛⠁⠀⠀⠀⣶
⠀⠀⠀⠀⢀⣾⣥⣀⣠⣄⠀⠈⠑⠠⣤⡹⠟⠚⠓⠐⠀⠐⠲⠸⠇⠀⠔⠋⠀⢀⡴⣀⣀⣰⡇
⠀⠀⠀⠀⠸⢿⡿⠿⣿⣿⠧⠀⣠⠤⠀⢽⡶⠃⠀⠀⠀⣠⣶⣾⡿⠷⠄⠀⡰⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⢀⡀⠈⣿⣷⢾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠾⣿⠟⠀⠀⣾⢦⣿⣿⠿⠋⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣾⣿⡆⢼⠟⠁⠀⠀⠀⢠⠖⠀⠸⡯⡀⠀⠀⠳⠻⣿⣷⡄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠈⡀⠀⠠⠂⡴⠁⠀⠀⠀⠟⣿⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠁⠀⢠⠞⠁⠀⠀⠀⠀⠈⢮⡀⠀⠀⠀⢸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣄⣀⣀⣠⣥⡤⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠈⠉⣺⡿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⡤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⠖⢀⡻⢷⣿⢻⡟⢳⣶⠶⠀⠒⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣤⣿⣾⣄⣀⣀⣠⠴⣾⣶⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣴⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣭⣛⠛⠉⠋⠑⣚⣿⣶⣼⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⡀⠀⠀⠀⠀⠀⠰⠋⠉⠉⢻⣿⣿⣿⣿⡟⠻⣿⠍⠛⠋⣿⠋⠉⠈⢻⡄⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡙⣸⡻⣵⣦⡶⠞⡉⠀⣇⠀⠀⠀⠸⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⢀⠈⠀⣸⣿⡳⡅⠀⣷⣿⡷⠀⠁⠀⣸⡄⠀⣀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣷⠀⠄⡁⠄⠀⠙⠲⣿⠋⠉⠙⢷⠼⣩⠴⠿⠃⠈⢿⡿⠞⠁⠀⢀⣴⣶⡿⠷⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⢀⣼⣿⡇⣿⣆⠀⠈⣠⡄⠀⢀⣀⣄⡀⠀⠀⢷⢦⡎⠀⠀⠀⠈⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠁⣿⣿⢾⣴⣷⣾⣿⡿⠿⣏⠛⠒⠒⢚⣼⡖⠒⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⠤⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⡿⢿⡏⠉⠉⢿⣿⣶⠏⠋⠀⠀⠀⡘⡉⣇⠀⠀⠸⣿⣀⣠⣀⣡⣿⣿⣧⣄⣀⣀⡤⠈⠋⢸⡷
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢿⠋⠀⠘⡧⠀⠀⠀⠈⠉⠀⠀⠀⡠⠊⠀⠀⠈⠣⡀⠀⠃⠤⢭⠄⠌⠀⠉⣩⠍⣿⣿⠇⢀⠐⢹⣅
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡆⠀⠀⠙⠤⣀⣀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⢀⡠⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⡖⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⣤⢄⠀⠀⠀⡀
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣟⡀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⣿⢵⡖⠄⠀⠀⠀⠈⠁⠂⢤⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠘⣿⡿⠃⠐⠆⠀⠀⣦⠀⠀⠀⠀⠀⠲⡆⠀⠀⢰⣯⠀⠀⢟⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⠋⠖⠃⠀⠀⠀⠀⡂⠐⠃⠀⠀⠀⠀⢄⠀⠀⠋⠉⢳⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⡀⠀⠀⠀⢰⢻⡼⠀⠀⢀⣀⣀⣈⡀⠀⠀⠀⠀⢀⣤⣿⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠹⣿⣿⣿⣿⡟⡛⠉⠀⠀⠀⠀⠀⠸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣤⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⣀⣿⡿⣿⣿⣿⣿⣿⣷⡂⠀⠀⢰⡿⠁⠀⠀⠻⠛⠿⣟⣻⠙⠿⠟⠋⣿⡹⠿⣿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣾⡿⠁
⠀⠀⠀⠁⠀⠀⠈⠀⢻⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣼⠋⠀⠀⠀⠀⡈⠰⣰⠇⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⢀⣾⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠙⠛⠿⢶⠒⠒⢚⡭⠞⠋⠀⠀⠀⠀⣠⣾⠇⠀⣰⡏⢴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠺⣿⣍⡀⠀⠀⠀⠀⠈⠻⣿⠆⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠀⠀⢻⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⢠⡀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡄⠀⠑⢂⣤⣤⣤⣀⢼⠰⠀⣠⣤⣤⣐⡟⠉⠀⠀⢨⣿⡏⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠹⠆⠀⠀⠉⢤⡤⠈⢿⣿⣾⣿⣿⣿⣿⣦⣤⣤⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠖⠉⠀⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣲⣒⣃⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣻⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⣠⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠉⠉⠑⠂⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠸⣾⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⢠⡆⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠟⠁⠙⠦⠄⠀⠠⠀⠠⢤⣄⠰⠀⠊⠑⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣆
⠘⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⢸⣊⠀⠀⠀⢀⣀⣵⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠈⡀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣤⢆⠃⠉⠛⠛⠟⣿⣿⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿
⠀⠀⡇⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣿⣿⣿⣗⣀⣀⣀⡀⠛⣻⣿⣿⡟⡓⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣺⡿
⠀⠀⠙⢦⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⣄⠈⠿⣺⣯⣭⣍⠉⠉⠀⠀⠉⢻⣿⣯⣛⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣧⣼⠿⠿⠿⠛⠿⣿⠆⠠⣶⣟⠿⠿⠛⠁⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⠀⠀⠀⠀⢹⠀⠈⠙⠟⡿⣿⣤⡊⠀⠀⠀⠋⣵⣼⡿⠇⠀⠘⠘⠁⢰⠀⠀⠀⠀⠀⢀⢄⡾⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠗⠄⠀⠀⠸⡄⠀⠀⠀⠀⣽⣛⡒⠶⠲⠲⡿⢛⣛⠗⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠃⡄
⠀⠀⠀⠀⠀⠀⣄⣸⣶⣿⣿⠀⠀⢶⣄⠀⠹⣦⡀⠀⠀⠨⣉⣵⣃⢀⠀⠈⠳⠍⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣛⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣿⣮⡛⠏⠀⠄⢈⣿⢢⠀⠘⢿⡆⠀⠀⠱⢯⠉⠙⠀⠠⢁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠐⡦⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠛⢶⣼⡄⠈⠈⠓⠈⢈⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠠⣭⢀⣾⣿⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢻⣷⣀⣀⢠⣀⠀⠈⠁⢄⣀⣀⢀⡀⠀⠀⠀⣀⡠⠔⠁⠀⠀⢀⣀⣀⠼⠋⣼⡿⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣿⣿⠉⢻⠏⠀⠀⠀⠐⠲⢯⣍⡀⠘⠃⢀⣤⣿⣷⠖⠀⠉⠀⠘⡟⢥⡶⣿⣿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠸⡇⠀⠀⠀⠀⠀⢀⠙⢷⠀⠄⢸⣿⣿⠋⠀⠀⠀⠀⠀⠃⠁⠀⣸⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡼⠀⠀⡀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠐⠀⠤⠔⠊⠀⠀⠞⠁⠀⠈⠻⣿⣷⣤⡄⠀⠀⠀⠀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠛⣋⠀⠀⠀⠀⠀⡈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠐⠂

⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⢢⡲⠒⠀⠀⠀⠐⠂
⠀⠀⡄⢀⣾⡏⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀
⠀⠀⠄⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢈⣢⠀⠀⣀⣀⣠⡤⠺⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⠉⠴⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠆⢰⠻⣿⣿⣟⡀⠀⠀⢀⢀⣠⣴⣦⣄⡀⠀⠀⢀⣤⣤⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠳⡍⢻⣿⠁⠀⠀⡟⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠱⡘⣿⡆⠀⢰⠋⠀⠀⠮⣿⡟⠳⡾⡲⡟⠻⣿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠈⠝⠉⠢⠚⠐⠙⢻⠃⠀⠀⠀⠐⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢠⠾⠀⠀⠀⢢⠘⢄⠀⠀⠀⠀⠘⠠⠶⠞⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⢀⣶⣟⠁⠀⠀⠀⡸⠃⠂⠀⠀⠀⠀⠀⠒⠀⠚⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠂⢀
⠀⠀⢸⠟⢣⠀⠀⠀⣠⢃⡘⢦⠤⠦⢄⣀⠀⠀⠑⠐⠀⢀⣴⡆⠤⢴⣎⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣨⡄
⠀⠀⢸⣾⠈⠀⠀⣼⣿⣯⠾⠋⠀⠀⠀⡈⠳⠌⠦⠀⠠⣾⣟⡾⠒⠖⢸⣿⠷⠤⠀⠀⠀⠀⠠⠀⠀⠀⠑
⠀⠀⠈⣿⡆⠀⣾⡏⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣅⠈⠀⢀⡴⠋⢰⡇⠀⠀⠀⠀⠃⠀⠀⢀⡞
⠀⠀⠀⢸⡏⣀⣿⠃⠀⠘⣿⡄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠻⣧⣰⠞⣿⠆⡸⠀⠀⠀⣾⡀⠀⠀⠀⡼
⠀⠀⠀⢸⡇⣽⡟⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠓⠊⠀⠀⠀⠀⠈⠃⠂⠀⢐⡇
⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡤⠖⢛⣛⣛⣛⣓⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢚⣛⣛⣛⣛⠓⠦⣄
⠀⠀⣴⠋⣠⠞⠋⠉⠉⠉⠉⠉⠙⠒⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠔⠚⠉⠉⠉⠉⠉⠉⠛⢦⡈⢳⡄
⠀⣼⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻
⢰⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡌⢷⡀⠀⣏⠙⠷⣄⠀⣀⣀⠀⡠⠊⠉⡇⠀⣰⠏⡼⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⠺⢷⣄⡿⠀⣧⡈⠋⠀⠈⠉⢀⡀⠸⣇⣴⠿⠊⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠉⠀⡏⠀⠁⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠐⠛⢶⣄⣀⠀⠀⣀⠤⠞⠛⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⢻⣄⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⢴⠦⣀⠀⠀⠀⢀⡀⢲⠤⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⠀⠙⠻⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠠⠾⡏⢀⠀⠀⠀⢀⠈⡽⠦⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠛
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣥⠴⠾⡅⠀⠀⠈⢀⢠⡀⠀⠀⣠⣲⠆⠀⠀⠀⡽⠶⢤⣵⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⢳⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠘⡄⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⡀⠀⠀⠭⠐⠂⠠⠤⠚⠨⠅⠀⠀⢸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡇⡜⠀⡿
⠀⠀⠀⠀⠀⠀⠘⢧⣀⣿⣇⠀⠀⠀⠀⠀⠀⢻⡓⢤⡀⠀⠑⠲⠤⢤⣀⠀⠀⠀⢀⣠⠤⠤⠒⠁⠀⣠⠔⣻⠁⠀⠀⠀⠀⠀⢀⣿⣇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠳⣴⠃⠀⠀⠀⠀⢀⡽⠗⠒⠒⠿⣄⠀⠀⠀⠀⠀⢳⡴⠃⠀⠀⠀⠀⢀⣴⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠸⣦⣀⣀⣀⣠⡾⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣾⣅⣈⣀⣽⣆⣤⣤⣴⠞⠁⠀⠀⠀⠀⠀⢀⡾⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠙⠳⣶⣶⡶⠶⠦⢤⣄⡉⠓⠄⠈⠏⠁⠉⡏⠀⠔⠋⢁⣤⡤⠤⠶⣶⣶⡶⠛⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⠾⡏⠉⠱⡀⠀⠀⠈⠙⣦⠀⠼⡇⠀⠀⡿⠆⠀⡞⠁⠀⠀⠀⣰⠃⠉⡿⠶⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⠀⠀⢳⡄⠀⢀⡴⠃⠀⡰⣧⠀⢠⣷⡀⠀⠳⣄⠀⠀⡰⠃⠀⠸⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠐⠛⠒⠉⠀⢀⢄⡤⠛⠓⠛⠳⣕⣄⠀⠈⠛⠛⠃⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣐⡵⠋⠀⠀⠀⠀⠀⠈⠳⣕⡄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠂⠀⠀⠂⠀⠐⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠃⠋⠀⠂⠀⠘

⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀
⠀⠀⠀⢀⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠸⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠆⠀⠀⠀⠀⢀⢀⣄⣰⣿⠃⠀⠈⠿⢿⣿⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠹⣜⠇⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢉⣼⣿⣿⣿⣿⡆⠈⠀⠙⠀⠂⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⣈⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⣙⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠠⠻⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠟⢧⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣿⣿⣿⡿⠋⠀⠀⡠⠊⠀⠈⢉⣠
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⣀⡀⠈⠻⢿⣿⣿⣿⣿⠟⠁⠤⠄⠀⠀⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣿⣿⣶⡞⠉⠙⢦⣤⣤⣭⣿⣭⣥⡤⠴⠋⠉⢹⣟⣟⣛⣿⠏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⠀⠀⠀⢈⣿⣿⣿⠿⢏⠀⠀⠀⠀⠀⢀⠛⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣠⣼⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⣤⡀
⠀⠀⠀⡠⢊⣤⠖⠀⠙⠛⠒⠲⠭⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠐⠀⠀⠘⠓⠦⡍⠢⡄
⠀⠀⡰⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹⡄
⠀⢠⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⢠⡀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧
⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⢤⣦⠀⡇⢠⠱⣤⠖⢦⡴⢣⠀⡇⢠⣏⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠛⠃⡞⠓⠂⠤⠄⠒⠛⡆⠛⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⣿⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠐⠳⣤⣀⣀⣀⣠⡴⠛⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⡇
⠀⠸⣄⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⢶⢢⣌⣉⣉⣠⣲⠦⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣀⡼
⠀⠀⠈⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⡀⠀⠘⠻⠓⠂⠀⠐⢶⡝⠛⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠙⣦⢆⠀⠀⠀⠀⠀⠀⢸⡟⠊⠉⢳⡀⠀⠁⠶⠓⠀⠀⠳⠇⠀⠀⣼⠋⠁⠚⡿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⠀⢢⢰⠀⠀⠀⠀⠀⡇⠀⠀⠈⡀⠀⠀⠐⠦⠀⠀⢔⡂⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠀⣾
⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⡀⠀⠀⠀⠀⠹⡲⣤⠀⠛⠶⠤⣄⡀⠀⠀⣠⡤⠴⠞⠃⢠⡴⣾⠃⠀⠀⠀⠀⣸⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣦⡀⠀⠀⠀⠻⣞⠀⠀⠀⠀⡴⠛⠑⠙⠳⡄⠀⠀⠀⢘⡾⠃⠀⠀⠀⣠⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣧⠀⠀⠀⠀⠘⢦⣀⠀⠀⢹⡆⠤⠄⣾⠁⠀⢀⣠⠞⠀⠀⠀⠀⢠⡟⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⢦⣤⣤⣤⣀⣀⡉⠻⢟⠛⢿⠛⢺⠛⢛⠿⠋⣁⣀⡀⣠⣤⣤⠟⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤⣟⠉⢣⠀⠀⠉⠳⡄⢠⣆⠀⠀⣧⠀⡰⠊⠉⠀⢠⠊⢙⡧⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠸⠀⠈⢧⡀⢀⠼⠁⢀⢿⡀⣰⢧⠀⠑⣦⡀⣠⠆⠀⠸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠉⠉⠀⢀⣤⡴⠋⠁⠈⠳⣇⣀⠀⠉⠉⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣴⡬⠷⠋⠀⠀⠀⠀⠀⠈⠳⠧⣤⣄⣀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠢⡀
⠀⠀⠀⠀⣽⣿⣿⡿⠉⠉⠉⠛⢹⡿⣿⣿⠛⢣⡀⢰⣄⠀⣰⡄⠀⠰⣦⡘⢃⣴⡙⡆⠄⠀⠀⠀⠀⠀⠀⠀⠊⣳⢹⣆
⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⣿⣷⡿⢡⣤⠾⠁⢦⡏⢨⡁⢀⢀⠰⣽⠶⠛⠚⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⡟⣼⡿
⠀⠀⠀⠈⣿⣿⣿⣿⣶⡀⠀⣴⣿⣿⣿⣏⢁⣤⣤⣦⣀⡛⠛⣙⣩⣴⣿⣦⠀⢠⣼⣿⡗⠀⠀⠀⠀⠀⢀⡀⣹⣿⡟
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣿⣿⡟⠸⣼⠿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣐⠈⢷⡃⠀⠀⠀⠀⡀⣸⣋⣿⠏
⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⠋⠻⠋⠙⠻⡿⣶⡆⠀⠉⢿⢿⣿⡿⠛⠋⠙⠛⠂⣷⣄⡀⡀⠀⢄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⠶⠀⠠⡴⠟⠋⠁⠀⠀⠀⠀⢠⢇⠪⠁⡄⣰⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⢻⠉⠛⣿⣄⠀⠀⠀⠈⢻⠠⠀⣴⣯⠀⠃⠀⠀⠀⠀⣰⡷⠁⣶⣟⢠⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⢇⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠘⠍⠀⠀⠀⠀⢠⣾⠟⠀⣠⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⣬⣁⡿⠟⢧⡀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⢀⡴⢋⣀⣴⣿⡿⠛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢈⣿⣿⠂⠀⠙⢷⣦⠄⢀⠀⣀⠀⢀⢄⣾⡿⠛⠛⢻⣿⡟⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⡆⠀⠀⠀⢻⢿⣶⡆⢰⣶⣶⠟⡏⠀⠀⠀⣸⣏⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⡿⠤⣤⣴⣤⣠⠟⠁⠈⠻⣳⣾⣷⣄⣀⣀⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⠀⠀⠀⣠⠆⠁⠀⠀⠀⠀⠈⠙⢧⡴⣈⢹⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⢀⡴⡂⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⢺⣷⣾⣿⣿⣿⣶⣤⣤⣤⣼⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⣀⣹⣛⣿⣿⣿⣿⣿⣄⣀⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⡴⢿⠟⠛⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⢀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠈⠛⢿⣄⣤⣤⣀⠀⣨⢶⣀⠀⠠⣤⠄⠀⠀⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣿⡏⠠⠘⠋⠀⠀⠀⠀⠀⠀⢠⠏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⢀⣀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠠⣤⣀⠀⠀⠃⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣠⣴⣚⣽⣵⣶⣶⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠐⠒⠒⠒⠲⠤⣀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠋⠀⠀⠈⠁⠈⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠸⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⡾⣿⡆⠤⣀⠀⢠⠀⠀⠀⠀⢢⡀⠀⢤⣁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣
⠀⠀⢶⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠈⢱⢄⠉⠉⠉⠙⢆⡄⠀⠀⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣
⠀⠀⠈⠂⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⣀⡞⠳⣾⣾⣷⣿⣿⣿⣷⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⢰⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⣶⣿⣿⣶⣧⣂⡠⠎⣽⣿⣿⣶⣿⣿⣶⠄⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿
⠀⠀⠀⠈⢦⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⡀⣿⠿⣟⣯⣛⣿⣿⡏⠹⢿⣿⣿⣛⠻⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡁⠀⠀⠀⠀⢠⣿⣿⣴⡿⠿⠿⠟⢿⣿⡤⣤⣶⡿⠿⡟⠛⠁⣠⣯⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠈⡏⠈⠉⢷⣞⣿⣤⡎⠉⠂⢾⢫⣤⣿⠟⠀⠘⠛⠋⢹⠀⠀⠀⠀⠀⠀⣰⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢫⠘⣿⣿⠂⠁⠀⠀⢳⠀⠀⠀⠉⢞⣋⡟⠛⠿⠛⠟⢉⣛⠒⠂⠀⠀⠀⣸⠀⠀⠀⠀⠀⣟⢏⣸
⠀⠀⠀⠀⠀⠀⠀⣠⣚⢷⣿⡿⢀⠙⢷⣄⠈⢳⣄⠀⠀⠸⣭⠾⣧⢠⣆⢈⡳⠀⠸⠀⠀⢀⣰⠏⠀⢀⠀⠀⠀⢫⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣍⣃⠈⠁⠨⡟⢦⠀⠙⣇⠀⠀⠘⠣⠘⠋⠉⠉⠷⠐⠀⠀⠀⢸⠋⠠⠀⠈⡇⠀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠉⠑⠀⠀⠀⠀⠑⠈⠻⢆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡆⢰⣿⢟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠠⡠⢤⣤⠤⠀⠠⢀⣁⡠⠤⠐⢀⠀⠀⢠⣶⣋⣁⠤⠤⠴⣶⢿⣉⣴⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠒⡅⠀⣋⠀⠀⠀⠀⠈⠉⠱⡆⠈⠀⣼⣿⣿⠋⠀⠀⠀⠀⢏⡿⢋⣹⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠈⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⢀⣀⡴⠊⠀⠰⠂⠈⠱⢶⣶⣤⣀⠀⢀⠔⠀⠀⣠⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠈⠀⠀⢀⠔⠀⠀⠀⠀⠈⠻⡿⡖⠀⠀⠀⠀⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⠤⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡒⠚⠓⠾⠃⠶⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣒⠿⣛⣀⠀⢶⣀⣤⣵⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣉⣀⣀⣀⣈⠉⣯⡉⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠛⠻⢿⠉⠛⠿⠷⣄⠀⠀⠀⠀⣡⡶⡞⡛⠋⠉⢿⣿⣿⣿⣿⣿⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡾⡷⠈⠀⠀⠀⠂⠈⣽⡳⣤⡈⠀⢉⡡⠤⠄⡠⢮⣿⣿⣯⡙⢁⡄⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⢸⡄
⠀⠀⠀⠀⠀⠈⢀⠱⣿⣿⣿⣿⡆⠤⠀⠀⠀⢀⠀⠘⣋⣾⣿⣿⣶⡾⣙⠓⠒⠐⠛⠀⠓⣹⣿⣿⣿⣷⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡞⠡⢿⠇
⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠨⠉⢛⣾⣯⣤⣤⣤⣶⣿⡟⠛⠿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⢠⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠐⣿⢄⣡⣴⣾⣿⣿⣼⣯⣿⣿⣿⣿⣏⣷⣤⣤⡀⠱⢤⡀⠀⠀⠀⠀⠀⠂⠀⠀⢰⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣿⡿⣿⠄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢂⡸⠩⡁⠀⠀⠈⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢸⣿⣿⡤⠀⢀⣼⣷⣽⣿⣿⣿⣿⣿⣾⣿⠿⠋⠻⠷⢿⠳⣦⣴⡿⢃⠭⣶⡆⢹⠀⠀⠀⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⣷⣿⣣⠀⢸⡟⠉⠙⠛⠺⣿⣿⢿⠶⠿⠤⠓⠲⠚⠻⠾⢟⣛⡵⠶⠞⠉⢷⣟⡁⠀⠀⠀⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠁⠀⠸⣧⡀⠀⠀⠀⠻⣵⡾⢿⡡⠠⠀⢤⠀⣬⠿⠿⡿⠁⠀⠀⢀⡾⣣⢤⠖⠻⠟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡀⠀⠀⠁⠛⠦⣀⠀⠀⠈⣊⢉⣀⠃⠈⡀⠘⢠⣍⡞⠁⢀⣠⠔⠃⡀⠀⠀⢀⣴⣿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣦⠀⠈⢷⠐⣀⣑⣦⣖⠶⠤⠄⠀⢀⠀⠠⠝⠻⢓⣤⣾⣥⠶⣿⣷⡆⣰⣿⣿⣧⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣿⣶⣶⡿⠛⠉⠀⠙⢻⡟⠛⠲⡋⠀⠀⢰⣾⣿⢿⡏⠁⠀⠀⢈⢻⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣣⣿⠰⣿⡆⠒⠀⠀⢀⠗⠀⠀⢡⣴⠄⢸⣣⣿⠿⣄⠀⠀⠉⢻⣸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⢻⡇⠀⠀⠀⠀⢀⡤⠂⠁⠘⠂⠀⠉⠺⣕⣿⣷⣄⠀⠀⠹⠿⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠁⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠷⠃⣸⢎⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⢄⣀⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣇⣾⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠉⠛⠲⣄
⠀⠀⣠⢖⣭⠖⠒⠒⠒⠒⠈⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠚⠉⠉⠑⢦⡈⠳⡄
⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⡄
⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻
⢸⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⣯⠉⠳⣄⠀⠀⠀⠀⢀⡴⠖⣦⠀⠀⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸
⢸⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠻⣄⣘⡇⠀⠈⠷⠒⠒⠶⠋⠀⠀⣿⣀⡼⠃⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸
⣼⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠉⠁⢠⡶⠲⠦⠤⠤⠶⠟⢶⡀⠉⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⣿⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠙⠳⠚⠉⢻⡅⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠿⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠧⢤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠛
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⢀⣾⠀⠀⠀⢠⡏⡀⠀⠀⠀⣿⠀⠀⠀⠀⣰⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠒⠉⠘⣷⠀⠀⠈⡿⠋⠉⠓⠚⢿⠀⠀⠀⠀⣯⠀⠀⠙⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠘⣷⣦⣀⣀⣀⣸⡇⠀⠀⢠⡟⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⡄⢰⡇
⠀⠀⠀⠀⠀⢀⡇⠀⢲⠀⠆⠀⠀⠀⠀⢻⡄⠀⠀⠙⠷⠤⠤⣧⡀⠀⠉⠉⣨⣿⠤⠴⠞⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢾⣥⡼⠃
⠀⠀⠀⠀⠀⠀⠙⠒⠾⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣿⠶⠲⠾⣥⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢯⡀⠀⠀⠀⣨⠗⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢢⡀⠀⠀⠀⠀⠀⠙⢳⡖⠚⠛⣻⠦⠤⣼⣧⣤⣤⣠⠴⠋⠀⠀⠀⠀⠀⣀⠴⠋⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠓⠦⣤⠤⠤⠤⣤⣀⠉⠀⠀⣇⠀⠀⣸⢇⡴⠛⢁⡤⠶⠒⠒⠚⢳⡏⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡤⠾⢏⠈⢧⡀⠀⠀⠈⢻⡆⢀⣿⠀⠀⣯⠈⠀⣰⠏⠀⠀⠀⣠⠂⢀⡿⠶⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠂⠘⣇⠀⢀⣠⠾⠃⠀⢹⡇⠀⢹⡆⠀⠙⢦⡀⠀⣰⠇⠀⠘⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⠶⠏⠁⠀⢀⡴⠋⠙⠓⠛⣧⠀⠀⠀⠙⠒⠋⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⠼⠃
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⢀⣉⣿⣿⣏⡁⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⡉⣿⣿⡏⣡⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠹⣿⣿⡟⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⠀⠙⠟⠁⣀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣾⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⢿⡄⠈⣻⢿⡁⢀⣿⠏⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⠋⠁⠀⠙⠛⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣽⣫⣍⣉⣟⣻⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⢈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⠧⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠉⠉⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠐⡂⠀⠀⠐⠂⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠖⠒⠒⠦⣄⣀⢈⠁⢉⢀⣀⡤⠴⠒⠒⠢⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡄⡌⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠀⠀⣠⠞⠁⠙⢦⡀⠀⠈⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⠀⠉⠓⠒⠚⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡔⢆
⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡇⣿⠇⠐⠒⠒⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠾⢿⣿⣿⣿⣿⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⣿⣿⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠛⠈⠻⣷⣔⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⣤⠋⢀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠦⣄⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⠁⠐⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⡂⢰⣤⣠⣿⣿⣿⣿⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣹⣿⣿⣿⣧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠈⠙⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⡿⣋⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠛⠛⠛⠛⠋⢉⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⣾⣻⣭⣥⠴⠶⣦⣹⣦⣄
⠀⠀⠀⠀⠀⢰⡿⢃⡀⠠⠤⠶⠾⣿⠇⣹⡀
⠀⠀⠀⠀⠀⣸⠃⢏⣀⠀⠤⠤⣤⣾⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠒⠒⠒⠒⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣿⠀⠈⠁⠐⣦⣤⡤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠐⠦⣤⣤⣤⠶⠟⠉
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠙⣧⣴⢟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⣷⠀⣶⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⣿⠀⠛⠶⠶⠶⢋⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡴⢒⡦⠖⣻⠓⠆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠻⡻⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣿⣤⣘⣵⣋⡉⠉
⠀⠀⠀⠀⠀⠀⢻⡀⢢⡀⠀⠀⠙⣦⠙⣧⡀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣟⢷⣄⠐⢶⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⡀⠀⠀⠈⠃⠈⢷⣄⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣆⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⠃⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣧⣄⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠛⠦⣌⠙⠻⠷⢶⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢠⡿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠸⣄⠀⣿⣿⢧⣀⣀⡀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢸⡇⣸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡎⠒⠀⢹⡄⠑⠚⠒⠊⠀⠀⠀⠀⠀⣿⣿⢯⠐⠦⣤⣤⣤⣴⠾⠋⠀⡠⣞⠄⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⣤⠾⠃⢹⡄⠀⠀⠀⠀⠀⠀⢄⠀⡼⡼⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠛⠷⠶⢶⣤⡤⠤⠄⠀⠀⠸⠃⢰⡄⠀⠀⠀⠉⠢⣭⣥⣷⠄⠀⢀⣾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⠋⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠙⠦⣤⣤⠤⠀⠈⠁⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⡀⣀⣠⣴⠾⠛⠛⠋⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠋⢃⠞⠈⣀⠸⠗⢐⡶⠣⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠓⠀⠸⡗⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⢿⣖⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⣠⠴⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠃⠀⠲⠛⡁⠀⠀⣧⣙⣛⢊⣿⣷⣀⣠⣴⣶⣏⡟⢡⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙
⠀⠀⠀⠀⠀⠀⡀⠂⠐⣤⣀⣶⣿⠆⠀⠀⠀⠀⣿⣿⣇⢠⣿⣿⣿⣷⠷⠿⠛⢠⣿⣿⣿⣿⣿⡇⠈⠙⠻⠛⠿⢿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⢤⣄⣨⣽⠋⠁⠀⣠⣾⠇⠀⣿⣦⡁⠀⢹⢿⣿⣻⣣⠀⢠⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠉⠳⠦⠜⠛⠈⠀⢸⣿⣿⢳⣤⣄⣾⣿⠿⠃⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣀⢰⣾⣿⣿⣟⣯⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣰⡄⠀⠀⠀⠀⠀⢸⣿⠁⠈⢀⠈⠉⠁⠠⢶⣿⣿⣿⣿⣿⣿⣟⠙⢧⠀⠀⢿⣿⣿⣾⣿⣟⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢿⠁⠀⠀⠀⠀⠀⢸⡿⠆⢀⠘⠀⠀⠐⢀⣸⣿⡻⣟⣿⣿⣿⣿⣷⡜⢸⣧⡄⢉⣟⠟⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⡇⠀⠠⢀⠀⠐⢸⡇⠀⡤⠀⠀⠔⠀⣸⡏⣈⠧⣿⣽⢮⣿⣿⣿⣷⣿⣿⣃⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⢀⣠⣤⠤⠸⣆⠈⣿⡀⢀⣈⠀⠀⢸⡁⠀⣂⠀⠒⠀⣸⣿⣿⣿⣶⣷⣿⢿⣿⣿⣿⠁⣀⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⡶⠁⠀⠈⠀⠻⠀⠙⢷⡌⠁⠀⢸⣾⡆⠈⠁⠆⠀⣰⣿⣿⣿⠇⠀⠈⠛⠻⣿⣿⣿⡇⠸⣿⡏⠛
⠀⠀⠀⣼⡇⠀⠀⠀⠐⠀⠈⠀⠹⡱⢶⢜⠘⠹⣿⣿⡆⠈⣼⢟⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⠘⠁⠀⢿⣇
⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠔⡯⣴⠇⣶⡆⣿⡅⢀⡴⢿⣎⢾⣿⣿⠀⠀⠀⢀⠀⠀⣿⠦⠀⠀⠘⣿⣶⡀
⠀⠀⢸⣿⡧⠀⠰⠀⠀⠀⠀⠄⠀⠀⠸⢠⠻⠟⡝⢡⣿⠜⠧⠈⠈⢽⣿⠀⠀⠀⠂⠀⢰⡿⠄⠀⠀⠠⣿⣳⣷⡀
⠀⠀⠀⢻⠇⢀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠂⠒⢣⣶⠶⠦⡵⣤⠀⠀⣸⣷⣷⡄⠀⠀⠀⣿⡄⠀⠀⠀⣶⠟⢿⣿⢷⡀
⠀⠀⠀⢀⣴⠇⠀⢀⣦⡀⠀⠀⠀⠀⠀⠁⢒⠟⠁⠀⠀⠀⠀⠀⠀⠉⣸⣿⠯⣽⡆⢼⣿⣿⣄⣀⡸⠃⠀⠀⣿⠘⣧
⠀⠀⢀⣿⠁⠀⠘⢿⣿⣶⣴⣀⠀⠀⠁⠀⣈⣀⡀⠀⠀⠀⠀⣀⠀⠜⢀⡙⣇⠈⠁⠸⣿⣿⣿⣿⣧⡀⠀⠀⣼⠀⠹⣧⠤⠲⣦⡀
⠀⠀⠈⠁⠀⠀⠀⠈⠋⠹⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⠞⠁⠀⠠⠀⠘⣌⢧⡀⠀⠈⢻⣿⣿⣿⣷⡜⣴⡟⠀⢨⡍⠀⠄⣿⣷
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣿⣿⠂⠀⠀⢠⣿⡇⠀⠀⠀⠘⣆⡀⠄⠀⠀⠀⠈⡄⢷⣄⠀⠈⣿⠙⢿⣯⠟⠉⡀⢀⣿⣷⠲⣾⣿⣿⣇
⠀⠀⠀⠐⠂⠠⠐⠶⠿⠛⠉⠉⣀⡤⠤⠾⠿⠧⠤⣄⡀⠀⠀⢁⡐⠐⠂⠢⠄⠈⣠⡘⡗⠂⢿⠀⠀⠀⠤⣗⣣⣟⣼⡗⢄⡤⣼⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀⠀⠀⠀⠀⠀⢸⠗⠙⠇⡴⠃⠀⠀⠀⢰⠉⠉⣽⠏⢠⣾⣿⣿⠟⠁⠀⠀⠈
⠀⠀⠀⠀⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣤⠔⠀⠀⠀⠀⠀⠀⡼⠃⠀⢠⠾⢶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⢰⣿⣋⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡋⠙⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠴⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡯⠿⠛⠛⠻⠿⠟⠽⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣴⡿⠿⠟⠉⠋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠎⢠⣿⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠘⠀⠳⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠛⢹⣷⡆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠉⠀⠀⣿⣿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⡿⠉⢆⢣⠀⠀⢶⣿⣿⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⠁⠂⣤⡽⣿⡷⡄⠀⠀⣀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡀⠃⠀⠀⠈⡰⣆⠰⣾⣿⣶⣄⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⡆⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⠀⠈⣷⠄⠀⠀⠄⠉⠛⠿⣿⣿⡿⠿⠞⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣧⠄⢀⣄⠚⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠈⠑⠓⠄⢁⣤⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠳⠀⠀⠀⠀⠀⣀⣄⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢠⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⡧⢀⣠⣾⣿⣿⣿⣿⣿⡿⣇⣸⣻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣠⢟⣴⣿⣿⣿⣿⣿⡿⣿⡏⠀⡟⠉⠉⠉⠛⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡵⢿⣿⣿⣿⣿⣿⣿⣿⡜⠁⠈⠋⡀⠉⣁⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣵⡟⠰⣿⡏⠉⠉⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢻⣻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠾⠃⠀⠙⡿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⡄⣠⡀⣠⣿⣿⣿⠁⠀⣀
⠀⠀⠀⠀⠠⠆⠆⢰⡆⠀⠀⠛⠋⠀⠀⠀⠇⠀⠀⠀⠶⠆⠀⠀⠀⠻⣿⣿⣍⠹⢿⣿⠿⢿⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡷⡄⠸⠐⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣄⡀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠈⣿⠀⠁⠀⠀⠀⠀⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠉⠛⠒⠦⠄⠂⠐⠛⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠙⠛⠿⠿⣿⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣤⣀⣠⣤⣶⠶⠚⠁

⠀⠀⠀⢰⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⢠⠒⢺⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡗⠒
⠀⢼⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢀⣠⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⢄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡶
⣤⢸⡀⠀⡇⠀⠸⣒⡒⢒⣒⣒⣇⢠⡠⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠂⡤⢠⡁⠀⠀⠀⢈⡇⠀⢸⡇⠀⡇
⠛⠀⡇⠀⡇⠀⠀⠁⠀⠀⠀⠀⠙⣆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣴⠋⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇
⠀⠒⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⢤⣤⡄⠀⢀⢤⡖⠲⠤⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠉
⠀⠀⠣⠤⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠘⠉⠀⠈⢑⠈⠉⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠒
⠀⠀⠀⠀⠣⠄⠤⠃⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⣀⠀⠎⣤⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠀⠀⠀⡄⠘⠛⠀⡆⠉⠁⢀⠃⠀⠀⠈⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⡠⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠖⠂⠀⠃⠠⠃⠀⠔⠀⠀⠀⠀⠀⠀⠼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⣀⡉⠦⠀⠀⠀⠐⠤⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡤⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠑⠒⠒⠒⠉⣿⠀⢹⡏⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢂⠀⢀⡹⠂⢎⡀⠈⡐⠉⠈⠲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣴⣺⣛⣲⢭⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡫⣰⡿⣿⠿⣿⣿⣿⣯⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣹⢡⡏⠉⣨⣶⣿⣿⡿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠉⠉⠙⠻⢦⣠⣿⣿⣿⣿⡟⣿⣿⣿⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⢸⣟⣯⣽⣿⣷⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠲⡄⠀⠀⣠⠞⠁⠙⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⣷⠃
⠀⠀⠀⠀⠀⠀⣾⣗⠀⠀⢴⣿⣿⡏⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⣼⣿⣿⣿⣟⡯⣫⡾⠋
⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠘⣻⣿⠻⣄⣀⡄⠀⢀⣼⣷⣄⢀⣼⣿⣿⣿⣯⣵⠞⠉
⠀⠀⠀⠀⣰⣿⣿⡅⠀⠀⠀⢳⡄⠀⠈⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣼⣿⣿⣿⣗⠀⠀⠀⠐⣧⣤⣶⡿⠿⠋⠀⠀⠀⠀⠀⠀⢻⣿⡧⠃⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⣿⣿⡿⣿⣯⡇⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠻⣿⣷⣤⣰⠉⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠸⣿⣿⣏⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠑⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢹⣿⣷⠛⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠀⠒⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠈


⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣹⠳⡀
⠀⠀⠀⠀⠀⢀⡞⠁⡟⠀⢠⠃⠀⡇
⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⡎⠀⠀⠃
⠀⠀⠀⠀⢰⠇⠀⡟⠀⢰⠃⢀⢰
⠀⠀⠀⠀⣸⠀⢰⡇⠀⡾⠀⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠤⣀
⠀⠘⠀⠠⡿⠀⣸⠀⢀⡇⢠⡿⠧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡸⠀⢸
⠀⠀⠀⠀⡇⠀⡿⠀⢸⠁⢸⣿⠃⠐⠂⠀⠨⢍⠋⣰⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢠⡇⠀⣸⠑⣆
⠀⠀⠀⠀⡇⠀⡟⠀⢸⠀⢸⢋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠐⠚⠀⠬⢐⡂⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠀⡼⠀⢠⡇⠀⡏
⠀⠀⠀⠀⡇⠀⡇⠀⣾⠀⠀⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠤⣤⡉⣿⠆⠀⠀⠀⠁⠒⠇⡀⡐⠀⠄⠀⠀⡜⣼⠇⢰⠃⠀⡾⠀⢰⠃
⠀⠀⠀⠀⢃⠀⡇⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢄⡉⠈⠛⠑⠀⠈⠑⡄⠀⠀⢀⡴⠀⠀⠈⠑⠂⠨⣙⡟⢀⠏⠀⣸⠃⢀⡟
⠀⠀⠀⠀⠈⠉⢧⠀⢧⢠⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢄⠀⠀⠀⠀⠠⣼⡤⠔⠋⠀⠀⠀⠀⠀⢀⢱⡿⢀⡞⠀⢰⠏⠀⡼⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢶⠢⢲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠞⠁⡜⠀⢠⠏⠀⡼⠁⠂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠉⣽⣦⣄⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼⠁⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠻⠿⣿⣿⠿⡇⠑⣄⠀⠀⡀⠈⠀⡎⠀⡜⠀⣠⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣿⣦⣤⣀⣀⣴⡇⠀⠈⡠⠊⠀⠀⠀⣇⠎⢀⡴⢇⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡈⠙⠻⠿⢻⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠷⠶⠞⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠠⢠⣜⣡⣥⣤⠦⠠⠀⠁⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⠾⠟⠋⠙⠫⠿⣿⡊⢿⣆
⠀⠀⠀⢀⠀⢀⣿⢋⡽⠋⠀⠀⠀⠀⠀⠀⠈⣿⣶⣄⠀⣼⣶⣄⠀⠀⠀⠀⣠⣶⣆⠀⢠⣄⡰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⣿⡄
⠀⠀⠀⢾⠀⢸⣷⣿⡝⠀⠀⠀⢀⡄⠠⠔⣻⠁⠈⠙⢿⠟⣛⢛⣀⣀⠁⠀⠛⠙⡿⠞⠋⠉⠁⢹⡇⠀⠀⠐⠀⠀⠀⠀⢀⣿⠀⣿⡇⡀
⠀⠀⠀⢸⡏⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣵⣶⣶⣦⣦⣴⣶⣶⣾⣆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⢀⣿⡇⠁
⠀⠀⠀⠈⢿⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⣤⣳⡀⢀⣴⣿⣿⠿⡿⣿⣿⢿⣿⣟⣛⣿⣷⣶⣄⡂⣿⠀⠀⠀⠀⠀⠀⠀⣾⢟⣿⡟⠋
⠀⠀⠀⠀⠀⠈⠙⣝⢿⠿⡏⢢⣁⠀⢠⣿⣧⣿⣾⣿⣿⣿⣿⣿⣷⣷⣿⣷⣿⣿⣿⣿⣻⣿⣧⣿⡀⠀⠀⠀⠀⠀⢸⡃⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠰⣿⣦⣝⣯⣻⣿⣿⣿⣯⣿⢿⣿⣯⣉⣘⣽⣻⣙⣿⢩⣿⣋⣩⣿⣿⠟⢿⠀⠀⠀⠀⠀⠘⣿⡁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠘⣇⣯⠉⠘⢿⣿⣿⡇⠉⠉⢻⣿⣿⣭⠿⡿⠿⢿⣿⣿⠿⣿⣿⡿⠁⡄⠀⡼⠁⠀⠀⠀⠀⣠⣭⡅⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡀⠀⠀⠉⠙⠷⣄⠘⠀⠹⠿⢿⣄⠛⣶⣾⣿⣷⢿⣵⡿⠁⠀⣀⠜⠁⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⢀⠀⠀⠀⠉⠂⠀⠀⠘⣾⣷⣾⣿⣿⣿⣿⣾⢿⡡⢴⠞⠅⠠⠠⢤⢀⢰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣯⣁⣈⠉⠟⠋⢀⣤⣴⣶⣿⠂⢐⣲⣿⣿⣦⣾⣿⣿⠇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⢾⢿⣿⣿⣿⣏⠉⠉⠻⢿⣿⣿⣿⡆⣧⡅⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⡟⠀⠀⠀⣨⣿⣿⣿⣇⣿⡇⣿⣿⣿⣧⣀⡀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣀⣤⣾⢟⣾⡿⠋⠁⠐⠄⠈⠙⢿⣿⣿⣿⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣫⠞⡁⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁

⠀⠀⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⣴⣴⠀⠀⠀⠀⢠⣤⣄
⠀⠀⣠⣿⣿⣄⣄⣼⣿⣧⡄⠀⠀⠀⣰⠛⢻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠿⣿⠁⠀⢸⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣶⣄⣀⣀⣰⣶⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⢠⣥⡄⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⣤⡄⠿⠏⢉⣯⡹⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣹⣏⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠻⣿⠅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠘⢷⠂⠀⠀⢠⡾⠏⠀⠀⠀⠀⣀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠄⢀⠤⣀⢰⣄
⠀⠀⣤⣾⣶⣶⣶⠾⢧⡀⠀⠀⠀⠈⣿⠀⠉⠉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢿⣯⣼⣿⣿⣄⣠⠇⠀⠀⠀⠸⠿⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⣿⣿⣤⣄⣾⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠙⢻⠉⢹⣿⡍⠉⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣄⣅⣸⣿⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇⠀⡇
⠀⠀⢶⣶⣶⡶⡶⣶⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠼⠄⠨⠿⠄⠤⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣦⠀⠩⠀⠈⢹⢩⣷⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠦⣶⣶⣤⣄⡀⠀⠀⠀⠀⠙⠒⠛⠳⣿⠀⠀⠀⠀⢸⠈⠛⡿⠟⠛⠛⠓
⠀⠀⠀⠀⠀⠀⢀⠴⠏⠋⠓⠉⠻⠀⠈⠛⣿⣿⣦⡈⠠⠀⡀⠀⠀⠀⢀⣮⠀⣠⠀⠀⣾⣶⣿⣧
⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⣿⣶⣄⣶⠛⠢⢄⣼⣉⡛⠁⠀⠀⠉⠉⠻⣿⣀⣤⢶⢦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣷⣦⣶⣿⣏⠉⠒⠆⠰⠶⣶⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣰⣿⣿⡄⠀⠀⠀⠀⣐⣿⣾⣿⣿⣿⣯⡉⠉
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣠⣾⣷⣿⣦⡁⠐⠂⠀⠐⠿⠛⣻⣽⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡦⣪⣦⣆⣀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣾⡦⠤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡧⣄⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⠿⢟⣿⡧⠄⢠⣼⡻⠿⠿⢷⠙⠃⠿⠟⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣳⣿⣾⣧⣀⡀⠾⣦⣦⡄⠈⣡⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⠀⢠⡀⠀⠀⠀⢸⣿⣦⠸⡿⠭⣙⠋⠉⡀⢙⠉⢤⣼⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⠿⣿⣿⣒⠀⢼⣧⠀⠀⠀⢸⡿⠛⣧⢷⢶⣻⡂⢪⠓⠞⠁⣾⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢲⣰⣞⣳⠛⠈⣿⣧⠀⢀⢼⠣⢈⣭⣿⣯⣼⠗⢶⣍⢀⣤⣬⡋⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⣿⡖⠀⠉⠛⠻⢿⣷⣮⠉⠛⠩⠿⢿⣍⠈⡿⠛⠻⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⢠⡶⠀⠀⠀⣸⡏⢀⠉⣍⠢⣄⣀⠀⠈⠙⠧⣀⡀⠀⠀⠀⢆⠅⠀⠀⠀⢀⠀⠉⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠠⠀⠀⠟⠀⠀⠀⠀⣿⣧⣴⣶⣿⢿⡟⠲⠾⠃⠒⠠⣌⠉⠑⢦⡦⣼⣤⡤⠔⠂⣠⣴⣛⠿⡟⠓
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢰⣿⢿⣟⠟⢷⣾⠁⠀⠀⠀⠀⠀⢨⡉⢹⡄⠳⣼⡿⢁⣾⣿⣿⠛⠻⢇⠄
⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣿⠀⠈⣿⣄⠀⠀⠀⠒⠒⠉⠀⠘⠃⣼⣿⣿⣸⣿⣿⣿⣄⣓⠀⣠⢄⡀
⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢅⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⠠⣄⣠⠤⠖⠚⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣿⡆
⠀⠀⠀⠀⠀⢰⠁⠀⠀⢽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡠⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⡠⡠⠒⣀⣡⣠⡄⢈⠑⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠿⡛⣿⣷⠝⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⠟⡿⠋⠉⠀⠀⠀⠀⠀⠘⣿⣤⣀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣀⣤⡀⠀⢀⡀⢠⣾⠟⠁⠁⠀⠀⠀⠀⠀⠈⠛⣷⠘⣿⡄
⠀⠀⠀⢸⡆⠐⣿⣵⢟⠆⠀⠀⠀⢀⠀⢀⡠⢶⠏⠙⠛⣷⣾⠿⠿⠇⠀⠀⠂⠸⠿⠿⣷⣤⠾⠿⠧⢹⣦⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⢸⡷⢰⣿⢿⡿⣆⠀⠀⠀⠈⠀⠀⠀⡟⠀⠀⠀⠈⢓⣜⣓⣛⣒⣒⣀⣀⣠⣴⡋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠀⣿⣇⠂
⠀⠀⠀⠀⣿⡌⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄⣀⡀⢀⢸⠆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⡿⠋
⠀⠀⠀⠀⠈⠛⢿⡿⣿⣿⣿⢄⠢⠀⠀⠀⣿⡞⣧⣤⣾⣿⣿⣭⣝⣽⣛⣏⣿⣛⣷⣶⣿⣿⣿⣿⣇⣸⡀⠀⠀⠀⠀⠀⠀⢰⠟⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡛⣹⣆⡹⣦⣤⣼⣿⣿⣿⣿⣿⣿⣾⣿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⠾⣿⣷⣿⣧⡄⠀⠀⠀⠀⠀⡼⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⡿⡿⢶⣷⣾⣿⡟⠿⣿⣾⣝⣿⡿⢶⣶⣼⣾⣶⣾⣶⣼⣯⣥⣶⡿⠟⠋⢉⣧⠀⠀⠀⠀⠀⠈⣿⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣬⣇⠀⠀⠻⣾⣿⣇⠀⢠⡘⢿⣿⣿⡞⢺⣛⡋⣻⣿⣟⣛⠟⣿⡟⠀⠆⠀⡼⠁⠀⠀⠀⠀⢀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⡄⠀⠀⠀⠈⠛⢦⡈⠀⠈⢛⡛⣷⠤⣨⣿⣿⣿⣿⣻⣿⡟⠀⢀⣠⠞⠁⠀⠀⠀⢀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣀⡀⣀⣀⠀⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⣺⠛⠑⠐⢒⣳⠶⠄⣻⣿⣿⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡻⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣾⣤⣤⣄⢨⠋⡁⣠⣬⣼⣿⣿⠋⠙⢛⣻⣛⣛⣚⣻⣿⣿⠁⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢾⢿⡽⣿⣿⣯⠁⠀⠙⠻⣿⣿⣿⣿⢸⣬⡁⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⠀⠠⠀⢀⣿⣿⣿⣿⣠⣿⡅⣿⣿⣿⣷⣄⡀⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣠⣶⡿⣳⣿⠟⠋⠁⠰⠀⠈⠙⢿⣿⡿⣿⣷⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢟⡴⢛⠁⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠛⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⣀⣠⢀⣆⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠙⠶⣾⣷⡶⠞⠁⠀⠀⠀⠀⠀⢰⣿⠻⠦⠄⣴⠂⠀⠀⠀⠀⠀⠠⠞⣿⢦⣠⢀⡿⠀⠀⠀⠀⠘⠐⣆⡶⣠⠆⠛
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⢶⣭⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⡀⣸⠇⠀⠀⠀⠀⠀⠀⢘⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢹⠶⠿⠻⣗⠀⠀⠀⠀⠀⠀⢠⣭⣥⣴⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡳⢄⠀⠀⠀⠀⠀⠀⠀⠐⢲⡂⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣃⣀⡽⠂⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀⠀⠀⢈⣭⣀⣠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣥⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠟⠂⠀⠀⠀⠀⠀⠀⠻⣿⣥⣄⠈⣻⡇⠀⠀⠀⠀⠀⣠⠿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⣤⣬⣿⣏⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⠁⢻⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡟⣷⣿⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢠⡴⣿⣿⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣆⠀⠀⠀⠀⠀⠀⠠⡾⣿⢧⡀⢀⡾⠃⠀⠀⠀⠀⢶⠎⣷⣦⣤⣄
⠀⠀⠀⠀⠀⢰⠀⣿⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣮⡅⠀⠀⠀⠀⠀⠀⢹⡟⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡙⣷
⠀⠀⠀⠀⠀⠈⠢⡌⣿⠴⠁⠀⠀⠀⠀⠀⠠⠴⠚⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⣄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⡶⣻⠄⢀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣷⡘⠟
⠀⠀⠀⠀⠀⠀⠸⢿⣟⢻⠆⠀⠀⠀⠀⠀⠀⠀⠸⡶⢛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣾⡿⢻⡄⠀⠀⠀⠀⠠⣔⣛⡯⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠈⢠⣾⣷⣶⡀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣎⢿⣆
⠀⠀⠀⠰⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⢈⡟⠀⠈⠢⢤⣧⣼⣆⠀⢐⠀⢠⡀⢸⣆⢀⡴⡆⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣿⡄
⠀⠀⠀⢠⠐⠘⣿⡆⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⣬⣿⡁⠡⠤⠤⠀⠨⠅⢀⡙⠋⠁⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⡾⠀⣿⡇⠀⢀
⠀⠀⠀⠀⣇⠀⢛⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣿⠁⠀⠈
⠀⠀⠀⠀⠈⠻⢮⣷⣄⠀⠀⠀⠀⠀⠀⠂⣆⣴⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⢀⡴⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢉⠣⡀⠀⠀⠀⠀⣻⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⠏⣰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠓⠀⠀⠀⠐⢿⡀⠀⠘⢿⣿⣯⣿⣿⣿⣿⣿⣟⣻⣿⣿⠿⠋⠀⡿⠀⠀⠀⠀⠘⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠀⠈⠀⠱⢄⠀⠈⢿⣿⠿⣿⣿⣿⣿⠿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⣿⡦⡠⣤⣤⡤⠤⣤⣤⣶⣦⣉⠉⠉⠉⣉⣠⣤⣤⠖⠒⢶⣤⡀⢂⣾⣿⡏⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣩⡿⢿⡟⠀⠀⠈⢿⣿⣿⣧⣤⣴⣼⣿⣿⣿⠃⢠⠀⠉⣿⢷⣯⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣻⡇⠀⠀⢀⡠⠈⣿⠟⠘⠻⢿⣿⢿⣧⣀⠀⠀⣀⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢼⣷⣤⣶⣏⣴⠞⠁⠀⠀⡄⠀⠙⢿⣧⣽⣷⣾⡻⣑⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠟⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠟⠉⠩⠤⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠌⠀⢀⣦⠁⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⡎⠁⠀⠻⠄⠀⠀⠸⠋⠀⠉⠆⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⡇⠀⣠⠚⡏⠁⠉⣿⢲⡄⠀⡨⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠊⠉⠀⠈⢆⢥⠀⢀⣅⡜⠀⠈⠉⠂⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣕⠀⢀⡀⠀⠀⠘⠴⡂⣰⠖⠀⠀⠀⠀⠁⢠⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⡀⠐⠀⠀⠀⠀⠃⡋⠀⠀⠀⠐⠀⡀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢰⠀⠀⠠⠀⠀⠘⠁⢀⠠⠂⠀⢸⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⣠⢤⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⡟⠋⠉⠙⠂⠈⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠞⠉⠁⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀
⠀⠀⠸⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⢠⡇⢠⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡟⠁⠙⠦⠀⠀⠠⠀⠠⢤⣄⠳⠠⠊⠑⢦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣆
⠘⣇⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⢸⣚⡄⠀⡄⣠⣨⣵⣦⡀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢹
⠀⠈⡄⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣴⢶⠃⠉⠛⠟⠿⣿⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠐⡇⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⡇⢐⣿⣿⣿⣿⣷⣦⣀⣀⣀⣻⣿⣿⣿⣿⡛⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⡿
⠀⠀⠙⢦⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣤⠈⠿⣻⣿⣭⣍⠉⠉⠀⠀⠉⣻⣿⣯⣟⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠟⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⣼⣿⣧⣼⣿⠿⠿⠟⠻⣿⠆⢠⣶⣿⠿⢿⡟⠃⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣧⠀⠀⠀⠀⢹⠀⠈⠙⠿⣿⣿⣤⡎⠉⠀⠀⠋⣵⣼⣿⠇⠀⠘⠛⠁⢠⠀⠀⠀⠀⠀⢀⣤⡿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⡄⠀⠀⠸⡄⠀⠀⠀⠉⣽⣻⡷⡶⢶⡺⠿⢟⣻⠷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠃⡎
⠀⠀⠀⠀⠀⠀⣄⣺⣶⣿⣿⠀⠈⢷⣆⠀⠻⣦⡀⠀⠀⠸⣭⣽⣃⡀⠀⠚⠷⠍⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⣛⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣿⣿⡛⠇⠠⣄⣜⣿⣧⠀⠘⢿⡆⠀⠀⠻⣿⠩⠛⠀⠰⢡⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣶⠀⢀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠻⢷⣼⡇⠙⠋⠓⠈⢨⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠠⣿⢀⣿⣿⢟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣻⣿⣀⣀⣠⣢⠤⠈⠙⢦⣀⣀⢀⡀⠀⡀⠀⣀⡠⠔⠉⠀⠀⣀⣀⣠⠾⢋⣼⡿⠣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⠉⢻⠏⠀⠀⠈⠙⠲⣯⣅⡀⠙⠃⢀⣤⣿⣷⠖⠀⠉⠀⠸⡿⢥⡶⣿⣿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⡇⠀⠀⠀⠀⠀⢠⠙⣷⠀⡇⢸⣿⣿⠋⠀⠀⠀⠀⠀⡇⠉⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⣼⠀⠀⣀⠆⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠐⠠⠤⠔⠊⠀⢀⠞⠁⠀⠈⠻⣿⣿⣶⡄⠀⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠘⠟⣿⠁⠀⠀⠀⠀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠊⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡈⡟⠁⠀⠈⠉⢩⣟⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢰⣾⡿⠛⢉⠀⠈⢳
⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⡋⠁⣬⠐⠻⣆⣤⠄⢠⡖⠀⢀⡌⣤⢠⣼⡄⠀⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠠⠁⡾⠁⠀⠀⠈⠀⠉⠀⣀⠀⠀⠙⢧⠈⠻⠇⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣳⣤⠤⣂⣀⣿⣤⠀⠄⣦⠛⠚⠊⣹⣧⡄⢠⣷⣄⠈⠆⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⢿⡛⣿⠉⠈⢳⠰⣿⠀⠀⠀⣾⠟⣱⠁⠈⡟⠀⣠⢾⣿⡀
⠀⠀⠀⠀⢀⠀⢠⠞⠉⠹⠄⢻⡈⠳⢤⣤⣯⠙⠀⣀⠀⢛⣃⣇⣤⡞⢰⣾⠃⠴⠁⠙⠂⣀⣠⠒⢢⡀
⠀⣰⠃⢀⠈⢻⡦⢀⠀⠤⢇⡼⠡⡖⠈⠓⣂⠀⠀⣉⠒⠀⠁⠉⠉⠉⢲⣧⡀⢤⣤⡀⠂⠀⢖⠀⠀⣷⡀
⠀⣯⡀⠉⠃⠸⡷⠋⠀⠀⠀⠀⠀⣯⠀⠀⠋⠁⣠⠜⠠⡄⠀⢄⡀⡀⢈⣻⡇⠀⠀⠙⠆⠀⠀⠀⠀⣹⠃
⠀⠘⢿⠀⠠⡄⣇⠀⠀⠀⠀⢳⡀⠈⢁⣠⠶⠂⠀⠀⠀⠈⠨⢟⡿⡿⠠⡡⠁⠀⠀⠀⢰⣄⠀⠀⢼⠃
⠀⠀⠈⡇⠰⡇⠇⠀⠀⠀⠀⠀⠑⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸
⠀⠀⠀⡧⠐⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡏
⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡆
⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢀⡇
⠀⠀⠀⠸⢬⣤⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡤⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣷⣶⣶⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠠⣿⡛⣻⡟⢟⠛⠛⢻⡧⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢻⣿⡀⠀⠀⠀⠀⠀⠀⣦⡼⢧⠀⠀⠀⢘⣄⠀⠀⠁⠘⡓⣿⠋⠀⢀⠜⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⣿⣷⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠈⠁⠚⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⣿⣧⢀⣾⠀⠀⡄⢀⡤⠤⠤⣤⡄⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣆⣀⡀⢸⠃⣿⣿⠀⢀⠜⠛⠇⠀⠀⠀⠀⠘⠋⠳⠄⠀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠙⠿⢿⠗⡀⣴⣝⣿⣄⣤⡤⠖⠀⠀⠀⠀⠀⠀⠢⠀⠀⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⡟⠛⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠛⢷⣦⡘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢹⣹⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢻⣄⣀⠴⠃⠀⠀⠀⠀⠀⣼⣏⣼⣿⡄⢀⣈⡲⠶⣤⠤⣄⣀⠄⠠⠤⠖⣊⡀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢄⠀⠀⠀⠀⠀⢰⢶⡶⠯⠄⢹⡇⠀⠀⠀⠙⢷⣶⣆⣺⢿⠀⣠⡶⠊⠁⠀⢈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⠠⠙⢿⠟⠸⣾⠿⣅⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠰⡀⠀⠀⠸⡦⠐⠂⠁⢀⠔⠁⠀⠀⠀⢀⡨⣷⢢⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠈⠢⣀⡀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠙⠻⣟⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠉⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣾⡿⠋⠁⠀⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣿⠟⠛⠛⠛⠛⢻⣷⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⡆⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⢠⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣦⡀⠀⠀⠀⠙⢿⣿⣧⣄⣀⣀⣴⣿⣿⠟⠁⠀⠀⢀⣴⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⠀⣶⣶⣤⡈⠉⠉⠀⠈⠉⠉⣡⣴⣶⡄⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⢿⣿⣿⡧⠀⠀⠀⠀⠀⠠⣿⣿⣿⠇⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠈⠛⠛⠁⣠⣶⣶⣶⣦⡀⠙⠛⠋⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣤⣾⡿⠃⠀⠀⠹⣿⣦⣀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⢀⣀⣀⣀⣤⡶⠆⠀⠀⠀⣀⠤⠖⠒⢢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢖⡒⠚⠓⠒⣤⢄⢣⣀⣀⢀⣈⣰⠘⢴⡦⠆⠞⠀⠀⠀⠀⠀⠙⠎⣆
⠀⠀⠀⠀⠀⢀⠔⠁⠐⠈⠁⠀⠀⠀⢳⠃⠀⠈⠐⠴⠴⠿⠃⣔⠉⠀⣦⡀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠎⡀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠘⠲⡤⠤⡤⣖⡇⠀⠀⢣⠇⠀⠀⠀⠀⠀⢰⢁⡇
⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠙⢷⠎⠋⠁⠤⠁⠀⡘⢤⡄⠀⠀⠀⠀⠁⡼
⠀⠀⠀⠀⠈⢮⣦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠁⢢⡀⠰⠂⠀⢒⠀⢸⠃⠀⡁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠰⡀⠀⠀⠀⠀⠣⡀⠀⠀⠘⣄⢁⠀⠉⢰⠃⢀⠜⠁⠀⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠓⣀⣰⠋⠀⠋⠀⠀⣀⣠⡖⠫⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⡀⠱⠀⠀⠀⠑⠮⣀⠀⢀⣀⡨⠗⠊⠀⠀⢀⡞⢅⠀⢹⠖⠠⣓⡓⢒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⡈⠀⠉⢁⠄⢰⠚⠓⠢⣄⠸⣄⡀⠠⢒⡒⠛⠂⢾⣐⢬⣭⡃⠀⠀⡔⡡⠃⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⠀⠐⢹⡀⠀⠣⡀⠘⠚⢀⡤⠉⠓⠢⣉⠒⠒⠈⠪⣕⣂⣬⣱⠀⠀⠁⢱⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣹⠀⠀⠈⠑⠚⠉⠀⠀⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠙⢀⠀⡇⠞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⡤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠟⢿⠛⢟⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⣿⣷⣶⣶⣶⣶⣿⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠉⡛⠛⣿⠛⠛⠏⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⣿⣿⡿⣿⢷⣤⣿⠁⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠰⠀⠙⠓⠋⢥⡁⣈⠈⠄⠉⠓⠋⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣄⠀⠀⠀⠀⠀⠀⠸⣋⡿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠁⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠓⠂⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠚⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⢰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⣀⡆⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⡷⡴⠂
⠀⠀⠀⠀⠀⣞⡷⠀⠀⠀⠀⠀⢀⣯⣍⠁⠀⣻⣇⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⢀⣀⡿⣇⢣
⠀⠀⠀⠀⡀⠘⠃⢀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢏⠉⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⢠⡄⢠⣼⣼⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡟⠀⠀⠀⠀⠀⠀⡞⣿⡦⠓⠀⠀⠀⠀⠀⠀⣠⡾⣷⡄
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⠿⣬⠁⠀⠀⠀⠀⠀⠀⠓⣿⡄⠀⠀⠀⠀⠀⢀⡼⢻⡄⠸⣿⡀
⠀⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠏⠀⠞⠀⠀⠻⠇

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⣀⣤⠟⠻⢿⠀⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⣶⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠾⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⠠⢠⡄⡄⡦⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠙⢾⡗⠋⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⡎⠋⡇
⠀⠀⠀⠀⠀⡃⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠓⠂⡄⠀⠀⠀⠀⠀⡞⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀

⠀⠀⠀⠀⠀⠀⢀⣠⣄⠤⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡤⣀
⠀⠀⠀⠀⠀⢀⣏⣾⠃⠀⠀⠀⠈⠋⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣲⣮⠟⠛⠘⠛⡿⠀⠀⢨⢧
⠀⠀⠀⠀⠀⢸⡘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢿⣀⠤⣄⢠⡄⠀⠀⠀⠀⣤⣀⠀⠀⡜⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠈⠻⣍⠳⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡿⠁⠀⠈⢳⣿⣿⣒⡲⠿⠀⠁⠀⠘⣇⠘⠆⣤⠤⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⢰⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢱⡜⢀⢠⠴⠄⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣄⠀⠀⣠⠀⣸⣿⣄⠀⠀⠀⢀⡀⠳⠆⠀⠐⠒⠻⠇⠀⠀⢀⣼⣁⠀⠉⢣⡀⠀⠀⢐⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡻⢛⣩⣤⣶⣼⣿⠿⠷⡄⠈⠁⠽⠇⠀⠀⠀⠀⠿⠿⠿⢀⡸⠿⢿⣷⠀⠈⠀⣀⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠶⢮⡁⢙⣿⠁⠀⠀⠹⡖⠻⣿⠄⠀⠀⠀⠀⢴⠟⠀⡟⠀⠀⢀⡇⠀⢀⣠⠶⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⢿⡀⠹⣆⠘⢷⣄⣀⠀⢹⡚⠛⠃⠀⠀⠀⠰⠾⠂⣸⠁⣀⣴⠫⢠⢢⡞⠁⢠⠏⠉⢹⢄⡀⠀⠀⡠⠤⢤⡀
⠀⣠⠖⠈⠉⠓⠰⠊⠉⠀⠀⠀⢈⡇⠀⣻⠀⣀⣈⣉⣛⣉⠉⠀⠀⠀⣶⢀⡀⢐⣃⠩⣿⠿⠶⣤⣲⣾⠁⠀⢈⠀⠀⠀⠀⠉⠂⠊⠁⠀⠀⢳⡄
⣸⡧⡎⡀⠀⠀⠁⡖⠀⢠⠴⠒⠺⢧⡴⠋⢻⣿⠀⠀⠈⢡⠀⠀⠀⠀⣈⠈⠀⠀⠀⠀⠁⠀⠀⡏⣿⣯⣦⣤⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣟⣰⡷⠋⠀⠀⠀⣧⡔⠁⠀⠀⠀⢸⠁⠀⢨⣿⡀⠀⢀⠜⠀⠀⠀⣀⠾⢴⡤⠀⠀⠀⡀⠀⠀⣤⠉⠱⣿⡇⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠁⠈⣹
⠹⣿⣆⠀⠀⣄⠀⢹⠁⠀⠀⠀⠀⠀⢣⠀⠀⠙⠧⠐⠃⠀⣀⡴⠊⠀⠀⠀⠀⠰⡐⠤⣬⡒⠢⠇⢘⠿⠉⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡼⠃
⠀⠘⣿⡀⠀⢘⡀⣮⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢹⣠⠂⠀⠀⢸⠃
⠀⠀⢸⡇⠀⠺⠇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⢸
⠀⠀⠘⣧⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⣾
⠀⠀⠀⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⡆⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠁⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅⠀⠀⢠⡏
⠀⠀⠀⣿⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⢸⡇
⠀⠀⠀⣿⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⢸⡇
⠀⠀⠀⠸⣄⣢⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣠⠼⠃
⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀
⣿⣿⣿⣿⣿⣿⣿⡏⠟⠙⢹⠩⢙⣿⠩⠙⠋⣭⠙⠙⠏⡋⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⣿⣿⣿⠿⠿⠿⣿⢦⠷⣴⡼⣼⢿⢿⠬⡴⢦⣭⢶⠼⢦⠦⣬⢽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⢿⡷⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠤⠄⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⡀⠋⠀⠀⠃⡀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠡⠀⠠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢢⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠐⢀⠀⢀⠑⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⢀⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⡣⠀⠠⡂⠀⠀⠀⢀⠆⢀⠀⠁⠂⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠢⣠⡀⠀⠀⠠⡦⠁⠀⡧⠀⠀⠀⣠⠠⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠐⡀⠐⠀⠀⠉⠓⠀⠀⡈⢦⠞⠀⠀⠐⠋⠁⠀⠔⠀⠐⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⡉⠢⡀⠀⠁⠀⠆⠀⠀⠲⠔⠲⠄⠁⠀⠴⠒⡤⠂⠀⠀⠆⠀⠀⠀⡠⠚⠩⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠎⠀⠘⠀⠀⠀⠀⠠⠂⠀⠸⠀⠀⠠⠀⠀⠀⠀⠘⠀⠀⢲⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠁⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⡌⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠠⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡛⢶⣄
⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣆⢻⣧⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⢶⣆⣚⠛⠛⠻⠉⠙⢻⣿⣿⣿⡇⢸⣿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣷⡌⣷⡄
⠀⠀⢸⣿⣿⣿⣤⣾⣼⣿⣿⣿⡇⢸⣿⠀⢠⠋⠻⠿⠿⠿⠶⢶⣶⣶⣶⣤⣤⣤⣤⣀⣤⠚⢿⣿⣿⣿⣿⣿⣷⠸⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣧⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⡁⠀⢯⣀⣈⣿⣿⣿⢀⣿⣦⣤
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣡⣿⠏⠀⡇⠀⢳⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⠀⠀⠀⠀⢷⠀⠘⣿⣿⣿⣿⡿⣸⡟⠉⠁
⠀⠀⠀⠀⠈⠛⠿⣿⣯⣵⣾⠟⠁⠀⠀⢸⠀⠀⢳⡄⠀⠀⠀⣾⣿⡟⠁⡤⠙⡄⠀⠀⠀⠸⠁⠀⣿⣿⣿⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠻⣄⡀⠀⣿⠋⠁⠀⠁⠈⣧⠀⠀⢀⣇⡀⠀⡝⠻⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠱⣄⣘⡇⠀⣀⡀⢈⣧⣠⡔⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣀⡀⠉⠑⠲⣤⡙⠛⢷⣄⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⠛⠆⠀⠀⠸⣷⡀⠀⠙⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⡀⠀⣿⣿⣿⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⠟⠉⠀⠀⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⢰⠂⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣾⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡦⠰⣤⣀⣀⡀⠀⢠⠛⠙⠒⠉⠉⠀⢸⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⡸⣇⠀⠀⠉⠗⠁⠀⠀⠀⠀⢀⡴⠻⣓⢀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡏⠉⠉⠳⢤⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⠟⠉⠉⠉⠉⠉⠓⠶⠶⠊⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠛⠳⢦⡄
⠀⠀⠀⢀⣠⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡆
⣼⠃⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠛⠛⠋⠉⠉⠀⠸⣇
⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣤⠀⠀⠀⢸⡆⢸⡆
⢸⡇⠀⠀⠀⣀⣤⣤⠿⠀⠀⠀⠀⠹⠂⠀⠀⠈⠁⠘⣧
⠀⢷⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢿⡀⠀⠀⠀⢀⣠⡴⠶⠞⠛⠶⠶⣤⡀
⠀⠘⢷⡀⠈⠷⣤⣄⠀⠀⠀⠀⢀⣤⡴⠞⠛⢉⣿⠀⢸⡇⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠙⠢⣤⣤⣿⡀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠃⠀⣿⠀⠀⣼⠃⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⠈⢿⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡟⠀⠀⠀⣾⠁⠀⠀⠀⢻⡆⠀⠀⢸⡇
⠀⠀⣠⠀⠀⠀⠀⠀⣠⠿⠳⢦⣤⣤⣤⣤⡴⠾⢯⡀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⣀⡾⠁⠀⠀⢸⡇
⠀⣼⠋⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠙⣦⡀⠀⠹⣆⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣠⡟⠀⠀⠀⣸
⢰⡏⠀⠀⠀⢠⡟⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠷⣤⡀⠘⣧⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠉
⣼⠁⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⡀⠀⠀⠀⠈⢹⡟⠛⠛⠛⢻⡍
⣿⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣨⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠸⣇
⠉⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⢀⣴⠏⠀⠀⣴⠏⠁⠈⠉⠙⢷⣼⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣄⣠⡾⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣰⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⢷⣶⣤⣀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠈⠉⠛⠳⠶⣼⣧⣀⣤⠾⠃
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠶⠶⠶⢾⡃
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡐⠄⠀⠀⠀⠀⢇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠁⠈⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠉⠁⠀⠢⡀⠀⠆⢐⠠⠀⠀⠤⡤⠄⠜⡂⠱⠀⠀⠔⠀⠈⠉⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠇⠀⠀⠀⠀⠀⢀⢀⠠⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡁⠲⠂⠭⠀⠐⠀⠬⠐⠡⠊⡐⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⢀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠢⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠳⠄⠀⠀⠀⠀⠆⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠐
⠀⠀⠀⠔⠁⢁⡠⠂⠀⠀⢸⠄⠀⠀⠀⠐⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠄⠀⠀⠀⠀⣾⠀⠀⠀⠢⡠⠁⠑⡄
⠀⠠⠊⠀⠀⠀⠀⢀⠠⠀⠌⠂⢢⠀⠀⠀⠈⠢⡀⠀⠈⠐⢀⠀⡠⠒⠁⠀⢀⠀⠀⠀⠀⠀⡐⠒⠃⢀⡀⡀⠀⠀⠀⠀⠈⢢
⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠈⠀⡀⠤⠂⠁⠀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢠
⠀⠀⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠉⠐⠤⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠐
⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰
⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡞⠁⠀⠀⠀⠙⠁⢩⣙⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⣬⡾⡿⠑⠛⠉⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣇⢸⣦⠀⠀⠀⠀⠀⠀⠀⢹⠛⠇⠈⠛⢀⡤⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⠙⠋⠈⠛⡚⠀⠀⠀⠎⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢯⣛⢧⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⡿⠀⠀⠙⢤⣿⡗⠒⠀⣾⠈⠈⠀⠰⣿⡸⡇⢠⣿⣿⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣇⠀⠀⠀⠀⠀⡦⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠁⠭⠆⠀⠀⠀⠀⡆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⠀⡄⠀⠀⣿⡀⠀⠀⠀⠀⡀⠠⠤⠤⠤⠖⠿⠇⠀⠀⠀⣰⣃⠀⠀⢢⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠿⢚⠉⢤⣦⣠⣿⠿⣷⡀⠈⡈⣿⠆⠀⠀⠀⠰⣿⣿⣷⠀⣠⠿⢿⣷⡀⠀⠁⠀⣰⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠦⣍⠈⢳⣿⠁⠀⠀⠱⡔⢲⣶⡀⠀⠀⠀⠠⣶⡖⠂⡜⠁⠀⠀⡟⠀⠀⣀⣽⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠛⣇⠈⢷⡄⠹⣦⣀⠀⠀⢷⠖⠺⠆⠀⠀⠀⢠⣶⠆⢸⠃⠀⣠⣞⢁⡄⣼⠋⢀⡼⠉⠹⢆⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⡀⠀⠀⢰⠀⡄⠈⠋⠀⠀⠀⢹⠀⠀⣟⠀⠈⢙⣛⣛⠛⠃⠀⠀⠠⣤⠀⠀⠐⣒⣛⣾⣿⣷⡀⠀⣴⠃⠀⠈⠁⠀⠀⠀⠀⠒⠴⠋⠀⠀⠹⣄
⠀⠀⣾⠁⠀⡤⠀⠙⣿⡷⠀⣀⠠⠶⠾⢀⣴⠇⠴⠛⠁⠀⠙⢉⠀⠀⠁⠀⡀⠘⠁⠀⠉⠀⠀⠀⠀⠀⢸⣯⣢⣀⡰⣶⣦⣄⠀⠀⠀⠐⠅⠀⠀⠀⣽⣆
⠀⢸⡋⠀⠨⠓⠆⠀⣹⣤⡞⠁⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠸⠊⠀⠀⢀⡭⡀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣿⡇⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠛⡿
⠀⠈⣿⣦⡀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⣄⠀⠀⠛⠦⠀⠂⠀⢀⡠⠜⠉⠀⠈⠙⢦⠀⢤⣕⡲⢤⡇⠀⣶⢛⠇⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠈⢿⡇⠀⠀⡆⠘⣏⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠲⢭⡛⢯⠏⠐⣠⠞⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡿
⠀⠀⠀⠀⣿⠀⠀⣾⠰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢿⡀⠀⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢸⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢸⠆
⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣇⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠉⠓⠿⠾⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠔⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠘⢿⣦⠀⠐⠀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⣀⢠⣤⡄⠀⠀⠀⢼⠟⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢡⠐⡀⠡⣤⡤⡘⠷⠀⠁⠀⢰⡾⠀⢴⡶⠎⣑⣾⣦⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠐⣿⠈⠠⣀⣀⡀⠠⣤⡵⠀⠐⣦⡤⠀⢀⣤⡤⠈⠡⡿⠁⠀⠀⠀⠀⠶⣚⡚⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠘⠛⡀⢈⡙⠁⣠⠄⡀⠀⠀⠀⠁⠀⢈⣉⡀⠈⠛⠢⠀⠀⠀⠀⢀⣀⠉⡀⠉⡀
⠀⠀⢠⡤⠄⡉⠛⠋⢁⠀⢀⡁⠀⠀⠀⠁⣉⠉⠛⠛⠁⠴⢤⠀⠀⠀⠀⠈⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠠
⠀⠀⠀⣀⠐⠾⠟⠒⠀⠀⢀⡅⠀⠀⡥⠤⣄⣐⠒⠻⠗⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠘⠉⣠⣴⡦⠄⠀⠀⢸⣇⠀⢀⣿⡀⢀⠀⠤⢴⣦⡄⢹⠀⠀⠀⠀⠸⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡀
⠀⠀⢰⠂⢀⡁⠐⢊⣡⠴⠐⠻⠀⠙⠷⠰⣦⣉⡓⠂⣀⡀⢻⠀⠀⠀⠀⠀⠘⠴⡦⠸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑
⠀⠀⠀⠌⢉⡑⠛⠋⠀⠀⣀⡈⠂⠊⢤⣤⠀⢀⡙⠳⣉⡉⢯⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘
⠀⠀⠀⠠⠙⣀⠀⡀⠀⠈⠀⠀⠒⠒⠀⠀⠀⠀⠀⢀⡈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⡀⠐⠃⠛⢀⠆⣀
⠀⠀⠀⠀⠞⠉⠠⠀⠀⠀⠀⢀⠤⠤⠁⠀⠀⠀⡀⠈⠩⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠈⢠⡄⠀⠀⢠⡄⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡊⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠰⠚⠻⠶⢂⠓⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⡀⠀⠚⠻⡆⠀⠀⠀⡶⠂⣄⠀⣀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⡈⠀⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠀⠈⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢷⡀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⢀⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠑⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⡄⢉⡀⢀⠾⠡⡤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠑⠅⠲⠤

⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⣿⡇
⠀⠘⢿⣿⣿⡟⠻⣏⡉⠉⠉⣉⠉⠉⢉⣩⡟⠹⣿⣿⣿⠏⠁⠈⢻⣿⣿⣿⠙⣯⣉⠉⠉⣉⡉⠉⠉⣩⡿⠉⣿⣿⣿⡏⠁
⠀⠀⠈⠛⠛⠁⠀⠙⢿⣦⣸⣿⣆⣴⡿⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠈⢻⣷⣤⣿⣧⣤⣾⠋⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⠃⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣄
⠀⠀⠀⣴⣮⣿⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣯⣶⡄
⠀⠀⢸⠉⡇⢸⠀⣿⣿⣿⣿⣷⡀⠤⠤⠤⠐⠒⠒⠒⠒⠒⠒⠠⠤⠤⠄⣰⣿⣿⣿⣿⠇⢸⠀⡏⢹
⠀⠀⣸⠀⡇⢸⠀⢸⣿⡟⣧⣴⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠷⢶⣶⣤⡟⣿⣿⠀⢸⠀⡇⢸⡀
⠀⠀⢳⡆⢡⠀⡆⠈⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⡏⠀⡆⢠⠁⣾⠃
⠀⠀⠀⠱⡈⣆⣰⣠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣰⣀⡎⡰⠁
⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁