Cantaloup Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣠⣰⣶⣾⣷⣤⣤⣠⣤⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡼⣿⣿⣷⣿⠿⣿⣿⣿⣟⣿⣟⡿⢿⠿⣿⣀⡛⣀⣤⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣛⣶⣯⣝⣉⠉⣥⠙⢿⡭⠬⡍⠉⣿⡿⠟⢻⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡿⣿⣿⣏⣿⡟⢿⡟⠻⠀⠟⠁⡐⠀⠘⢁⡌⠐⡴⠃⢠⠌⣿⣣⠊⢿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⢿⣏⣯⣽⣥⢍⣀⣠⡤⠶⢈⣾⠇⢲⢀⣁⠀⠐⠒⢞⠂⠹⣿⣬⣿⠉⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡞⢻⠿⡯⠀⣴⡖⢈⠴⠤⠰⠐⠀⠈⠁⠀⠘⠫⢶⣏⣹⢶⣻⡇⣿⣻⢱⡟⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣶⠄⣾⡉⠿⠉⠐⠃⠴⠶⠀⢉⠶⠀⠀⠀⠀⠉⣛⡳⣿⡿⠿⢷⣾⢢⡈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⡖⠯⢠⣾⠇⠴⠋⠘⢀⡄⠰⢄⠀⠙⠂⠀⠀⠀⢌⣈⣿⣷⣄⠹⣅⢽⠶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡙⠷⠀⣦⣶⠆⠀⠀⣼⠁⢙⣢⣌⡿⣷⣄⠺⣭⡍⠻⣽⡝⢻⣿⣧⠙⣶⠀⠉⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡁⢼⣿⡴⠶⠂⣀⣠⣼⡿⠯⢃⠺⠐⠇⠉⡠⠠⢀⡹⠌⢿⠷⣿⡻⠧⠹⡧⣀⣄⣈⡄
⠀⠀⠀⠀⠀⠀⠀⣀⢈⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣷⣟⣿⣿⣥⣌⣵⠂⣴⠄⢷⡉⠒⠁⠘⠁⠘⠃⢰⣄⡎⢀⣦⡞⣷⠺⣯⢻⣇
⠀⣤⣠⣤⣶⢤⠼⣇⡈⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡼⢀⡓⠈⢥⣀⠀⠉⠁⠀⠦⠔⡀⠀⡌⢙⡿⣥⣦⣭⣽⡝⣟⣿⡻⣏⠧
⠀⠘⠋⠉⠻⣷⡄⠀⠉⠳⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⡿⢀⣛⣬⡥⠒⠃⠤⢦⠠⠺⢦⠀⢘⡷⣀⣿⠿⣅⠜⠣⣼⡿⢿⡞⣿⣷⣿⣏
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣦⣀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣄⡀⢻⣿⡆⠈⡛⢰⡦⣶⠦⣾⠆⠀⣼⣻⡿⠦⢈⣃⢸⡋⣿⢿⣽⣿⣧⢱⣾
⠀⠀⠀⠀⠀⠑⣦⣠⣦⣤⡼⠉⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣛⠈⠶⠋⠁⢀⡉⢶⠀⢃⣾⣿⡏⢹⡤⠶⠨⠁⢈⣁⠝⢟⣿⠻⣟⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⣧⡀⠘⣆⠀⠀⠘⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣧⣴⣶⡷⠤⣨⣷⣎⣴⣿⣅⢸⡏⡀⠛⢶⢦⡉⠛⠹⣾⣿⣧⡾⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣿⡿⠷⠈⢢⡄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠛⣤⣞⣿⣿⢿⣷⠙⠏⣰⡶⣯⣤⣠⡈⠋⡤⣼⣟⣯⡉⠳⢜⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣿⠳⣦⡀⠀⠹⣆⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣾⠊⣭⠀⣿⣯⣥⣾⣯⠙⣧⣴⣶⣾⣽⣿⠋⠠⡾⣻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⢶⣄⠘⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡙⣿⡇⠘⣿⠀⠘⢻⠶⣬⣏⡜⣽⣇⠈⠘⡾⣵⠿⡾
⠀⢄⣀⣴⣴⣷⣶⣶⣶⡄⢤⠤⡀⠀⠀⠉⢻⣿⣿⣇⠈⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣄⣥⣤⣰⣅⡛⢛⣿⣭⠾⡯⠸⣿⣶⣿⣆⣦⠁
⢼⣿⣿⣿⣿⣿⣿⣷⠛⣙⣿⣷⣿⣷⣦⠶⠞⠋⢿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣾⣿⣿⣾⣻⡗⣠⣾⣿⣶⣏⣥⣞⣿⣿⠇⠹
⠀⢸⡿⣿⡿⠿⠟⠹⢿⣿⣿⡻⠉⠉⠉⠀⠀⠀⢸⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢿⣿⣿⣿⣿⠿⢿⣿⢟⣝⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⠀⠀⠈⠻⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⣿⣿⣾⡷⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⡟⠀⠀⠀⠀⠀⠀⠀⠑⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣠⣤⣤⣼⣿⣎⣀⣤⣤⣤⣤⣤⣴⣶⣦⣶⣾⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⡛⢻⠛⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠨⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠧⠼⠾⠃⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣀⡀⠤⠒⠂⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠛⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠁⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠠⣢⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠟⠙⠀⠀⠀⡙⢿⡂⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠔
⠀⠀⠔⠀⠀⠉⡇⠀⠀⠀⠘⡄⠀⠀⠉⠙⢢⢷⡤⠀⠀⢀⣁⠀⠤⠀⠀⠘⠀⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠁⡀
⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠋⠀⠀⠈⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢰⠊
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠒⠓⠃⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠏⠀⠁⠀⠀⠀⣀⣰⣿⠃⠀⠀⠀⠉⠉⠒⠖⠂
⠀⠀⠀⠀⠀⠘⠁⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣠⣿⣤⣶⣶⣶⡿⠿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠐⠞⠃⢀⡼⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣉⠤⠊⠉⠉⠉⠉⠁⠀⠀⠀⠻⡀
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢙⠛⢳⣶⣶⣦⣴⣶⣶⣶⡾⠛⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢤⡀⠀⠈⠐⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⡀⠨⠀⠀⠈⠰⢀⠘⢨⡙⠐⠀⠀⠄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢸⡤⡀⠆⠀⠀⠄⢀⠁⠆⣀⠟⣀⡗⡥⣱⠣⠀⡌⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣷⢶⠄⢀⠈⡀⡄⢇⡹⠶⣺⡙⣫⣴⠷⠣⣳⢒⡖⢀⢄⡀⠄⣸
⠀⠀⠀⠀⠀⠀⠹⣷⣶⢉⣅⣤⢠⣨⣔⡘⣽⣣⣭⣿⡟⣽⣞⣞⣶⡡⢀⣷⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⣼⣟⣫⣭⡝⣦⣻⣿⣿⣿⣿⣿⣿⣿⡱⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣾⣿⣘⣽⣿⣿⣿⣿⣿⣿⣿⠟⡀⠀⡀⢤⢤⣶⣎⢂⠜⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡟⢉⣉⠉⠵⣻⡿⣇⣿⢶⡽⡷⠟⠋⠡⠐⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠽⡄⠀⠈⠉⠉⠐⠚⠁⠉⠁⠁⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⡈⠀⠀⠀⠄⠀⠀⠀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢠⡄⢁⢀⣒⣨⢡⠀⡃⠰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠌⣬⡰⢴⣞⣯⣾⠾⡖⣓⣲⣩⣀⡄⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢃⠒⢷⠲⡾⣷⠿⠟⣃⡻⢟⣛⣆⣧⠏⡄⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢁⠢⠘⣛⣯⢿⣛⣟⣻⡭⣗⣹⣷⡽⡞⣇⡂⠃⡀
⠀⠀⠀⠚⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠱⠂⣷⢻⡍⣋⣯⡽⣷⣸⡯⢿⢮⡥⢡⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠊⠀⠁⠀⠈⠁⠀⠈⠁⢸⣷⡷⢻⢬⡕⣋⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠈⠀⠀⠀⠀⠀⢀⡘⣧⠩⠰⠆⠶⠫⢁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠐⠂⠸⠈⠥⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡉⠀⠂⠂⠈⠀⠀⢀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠀⠄⠒⠈⠉⠀⠀⠀⠁⠀⠁⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣶⣦⣄⣤⣴⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣻⠿⠿⢟⢿⣟⠻⠿⣭⣾⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣹⡿⠾⠟⠹⠁⠊⠐⡉⠠⠔⠩⢳⣾⡻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡟⢒⡶⢖⠃⡛⠋⠆⠂⣬⣉⢧⣜⣷⢿⣮⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⡿⢡⡞⠷⠀⠂⠴⠐⠢⠀⠀⠉⢛⢿⣿⠾⣷⣏⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢾⡎⢐⣟⠐⠁⡁⢆⠓⣤⣉⣀⡀⣬⣽⣿⣎⢣⡟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣵⣿⠭⣀⣈⣷⠞⠻⠭⡙⡨⡅⢸⢽⣾⣿⠇⢳⣀⣈⡆
⠀⠀⠀⠀⢀⢀⡴⠻⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢶⠽⡆⠆⢡⠁⡀⠉⠘⠡⣿⢏⡷⣿⣿⣯⣧⡀
⠀⠀⠐⠟⠛⣮⠉⠒⢄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣲⠤⠍⢤⠀⢦⠈⢶⢀⣷⣏⠻⣽⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢈⣧⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣀⠇⠶⠶⠺⢂⣼⣿⢛⠨⠤⠏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢘⣿⣿⣯⠀⢇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣷⣬⣥⡀⣦⣽⣴⡟⣿⠈⢯⣅⠰⠶⣼⣿⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠊⠰⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣳⣾⣿⣿⡟⣃⡶⢧⣤⡌⠣⢸⣿⣭⠓⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠳⣄⠙⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢹⡗⠻⣧⣽⣟⣿⡟⠳⣼⣿⡟
⠀⠀⣠⣴⣶⣶⣶⣶⣤⡠⣀⠈⢻⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⢻⣶⣷⣾⠁
⠀⠀⢻⣿⣿⣿⢿⣷⣿⡿⠟⠛⠉⠀⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡟⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠻⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠫⢟⠏⠉⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⠱⠏⠙⠀⠐⠁⢀⣤⣤⣤⡄⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⠎⡼⠛⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠐⠛⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡴⠮⠤⠐⠒⠒⠤⠬⢉⡒⠤⣼⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠈⣦
⠀⠀⠀⠀⡠⢒⡩⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇
⠀⠀⣰⢋⠔⠁⠀⠀⠀⠀⠀⡀⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣱
⠀⣰⢃⠎⠀⠀⠀⠀⠀⠀⠀⣿⡄⢹⡿⣷⡶⢀⡀⠀⠀⠀⠀⠀⠘⢆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡏⠸⠀⠀⠀⠀⠀⠀⠀⡚⠩⡙⠱⣰⣶⡿⡆⣱⡦⠀⠀⠀⠀⠀⠀⠳⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⣀⠠⡤⡄
⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⣿⠓⢌⣦⡘⣄⢑⡈⢇⠒⠀⠀⠀⠀⠀⠀⠀⢱⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣴⣿⠇⠀⠀⠈⠎⢦
⠀⡧⢸⠀⠀⠀⠀⠀⠀⠀⢻⣭⢶⣋⢡⡈⢆⠁⣼⠛⣫⠀⠀⠀⠀⠀⠀⠀⡇⠇⢀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣴⢶⣿⣿⣿⢿⣿⠋⠀⠀⠀⠀⠘⡈⣇
⠀⣷⡀⢇⠀⠀⠀⠀⠀⠀⠀⢶⣃⣙⣟⢷⣌⣆⣀⣠⡄⣤⡀⠀⠀⠀⠀⠀⡇⢸⣿⠿⠛⠉⢻⣾⣿⣿⣿⣿⣿⣧⣿⢿⣏⡾⠃⠀⠀⠀⠀⠀⢠⠁⠸
⠀⠸⣷⡌⢆⠀⠀⠀⠀⠀⠀⠀⠙⣇⣾⠃⠒⠠⢤⡠⢌⡍⢉⣉⡉⠓⠒⠒⠳⠾⢭⣄⣀⡀⠀⠈⠙⠛⠚⠛⠺⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⡏
⠀⠀⠱⡝⣮⠳⡀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠱⣡⡗⠮⠣⠐⠉⡙⠿⣶⣶⠦⣄⣤⣈⣉⠑⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡸⠁
⠀⠀⠀⠙⢆⡑⢬⡲⢄⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⠀⠙⢇⠊⢻⡠⠹⠍⠄⠒⠩⢧⠴⣾⠬⠭⣩⣩⠒⢄⠀⠉⠒⠤⣀⠀⠀⣀⠤⠔⠊⠀⡠⠊
⠀⠀⠀⠀⠈⠳⣄⠌⠢⢝⡢⢄⡀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠑⠫⢽⡟⠷⠰⡚⠃⡨⠔⡞⡀⡿⣩⣿⠾⠊⠑⠒⠢⢤⣠⣟⣩⣤⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠧⣔⡈⠁⠛⠷⢿⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢦⡀⠦⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⡆⣸⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠣⠦⠦⠴⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠬⠍⣐⣲⣔⣒⣒⣂⣉⠡⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣤⣀⣀⡀⢰⣤⣄⡀⡇⣴⢤⡠⣴⠄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠓



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⢀⣀⣠⠤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠞⡫⠭⠭⠍⣛⣿⣿⡥⣚⣽⠶⠿⣉⠛⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣒⣶⣤⠲⠾⠛⠽⠿⠿⣛⠛⣻⡿⣷⣾⣏⡁⠀⠀⢀⠀⠐⠒⠤⠐⢄⣢⣀
⠀⠀⠀⠀⠀⠀⢀⣐⣵⣿⠕⣿⢡⠀⡀⠀⠀⢁⢤⣌⣭⣿⣿⣯⢿⡩⡿⣷⣤⡀⡀⠀⢀⠠⢘⡂⡙⣤⢖⡄
⠀⠀⠀⠀⠀⢰⣿⣿⣫⢛⡾⣽⢣⣾⣇⣠⣎⣵⣸⣿⡟⠈⠃⢙⡄⢋⢿⣿⣿⣷⡌⠀⠈⠙⣮⡽⣷⣿⣿⣽⣦
⠀⠀⠀⠀⢠⣿⣿⣿⣷⣷⣿⣿⣿⠁⠋⢁⠁⣿⣿⡟⠀⠀⠀⣜⣵⠝⣿⣾⣿⣿⣷⠘⢰⣄⢽⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣾⣿⡧⣶⡂⢚⢾⠷⣿⠁⠀⠈⠀⡘⢳⢺⢿⣿⣿⣿⣿⡆⠈⡁⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⡟⣿⣴⣧⠙⠼⠏⢹⡇⠀⠀⠠⡞⣀⠀⠙⣋⡿⢽⣿⣿⣷⣜⢿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣷⣲⡸⣿⡇⡀⠀⡰⡀⠈⢤⢀⣸⢻⣼⣿⣿⣿⣿⡾⣷⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⣼⣿⡏⠃⡠⣡⣍⠀⠄⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣇⡸⠁⣀⣠⣼⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠀⠘⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠽⠃⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠞⢛⣿⠟⢿⡟⠓⢠⠀⠀⠈⠙⠻⢦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡸⠋⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠂⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⢒⡀
⠀⠀⠀⠀⠀⠀⠐⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢷⠀⠁
⠀⠀⠀⠀⠀⠀⠤⣜⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⡈⣷⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠆⠰
⠀⠀⠀⠀⠀⠸⢹⣟⠀⠀⠀⡠⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⠀⡙
⠀⠀⠀⠀⠀⠘⣋⣿⡀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠸⠃
⠀⠀⠀⠀⠀⠀⠨⣿⣷⠆⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠂⢸⣧⠞
⠀⠀⠀⠀⠀⠀⠀⡿⣿⡆⠀⠀⢸⣿⡆⠀⠀⠐⠀⠀⠀⢢⠀⠀⠀⠀⣸⣿⠀⠐⣀⢢⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣼⣠⡣⢻⣿⣧⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣾⡟⠡⣖⡈⢸⡟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣀⠘⢿⣿⣇⣀⠀⠀⢀⢸⡆⠀⠀⢰⣿⣃⣰⠟⣼⠟⠀⠀⣀⡤⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣼⣿⣿⣿⣿⡂⢠⣿⣸⣏⢐⢳⣾⣟⣿⣯⠟⢁⡤⠒⠉⠀⠀⠀⠀⠀⣀⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⢁⠔⠃⠀⠀⠀⠀⠀⣤⡖⢳⣦⣄⣘⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⣤⣠⣿⣏⣱⠼⣿⡅⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠠⠏⠼⠦⠧⠶⠞⠃⠀⠀⠀⠀⠀⠀⣠⢾⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣞⣱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⡔⠂⠐⠒⠂⠐⠀⠀⠀⡀⠀⠂⠛⠀⠀⢠⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣷⣀⡀⠀⠀⢀⠀⡀⠀⢀⢀⣤⣞⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠦⠮⠶⠿⠿⠖⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠠⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⠀⠀⠀⠀⢣
⠀⠀⠀⢄⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢝⠈⡾⠃⠸⠆⠀⠸⠀⠀⠀⠀⠀⡀
⠂⠀⠲⡠⠀⠀⠀⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢨⡇⠀⠠⠂⠁⠸
⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠢
⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀⠀⣀⠈⠀⠀⡠⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠈⠢⠀⠀⠈⠁⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠾⠦⢄⡀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⡀⠐⠶⢤⠤⡤⢄⣈⣦⣤⡀⠀⠈⠛⠴⠤⠀⠀⠀⢀⣤⣤⠖⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣉⣉⣈⣉⣁⣀⣀⣉⣑⣛⣾⣶⣶⣬⣤⣀⣀⣉⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⠴⠚⠉⠀⢀⠀⢀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠖⢶⡄⠙⡄⢰⣏⠁⠀⢰⣿⡄⠀⠀⠀⠀⠀⠑⠒⢆⠀⢀⡬⠖⡻⠂
⠀⠀⢀⠞⣁⣀⣠⠿⠶⠛⠋⠙⠋⠉⠛⠓⢤⣈⣷⡄⢀⣀⠀⠀⠀⠸⠦⠾⢃⣼⡇⢸⣿⣦⡀⢘⣿⠃⠀⠀⠀⣰⣆⣦⣀⣀⠘⠯⣁
⠀⢠⣇⣴⠿⠋⠉⠀⢀⣀⣤⣴⡶⡶⠣⠖⠶⣿⣭⣿⡏⠀⠀⠀⠀⠈⠒⠒⠛⠋⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠘⡿⢁⢤⡀⠙⢎⠳⣮⠑
⠀⣼⠟⠁⢀⣀⣴⣿⡾⠛⠋⠈⠀⠀⠀⣀⠖⢋⡟⡯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢨⣿⡀⡘⢀⣿⠂⠤
⠀⣿⣀⣶⠾⠏⠁⠀⠀⠀⠀⢀⣼⣿⡿⠏⠀⣾⡧⣷⢻⠴⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡆⢸⣏
⠀⢹⡟⠁⠀⠀⠀⠀⡀⣶⣶⣿⠟⠛⠀⢰⣾⣿⣴⣿⣿⠀⠚⢰⢃⡆⢠⠀⡄⢲⡘⠆⠀⡰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣈⡿⠁⢠⣿⡄
⠀⠈⣧⡀⢀⣦⣴⣾⠟⠛⠃⠀⣀⣠⣷⡿⢟⣻⣿⣿⣏⠳⣄⠀⠈⠁⠙⠀⠛⠈⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡇⠀⢸⣿⠇
⠀⠀⠘⢿⡟⠛⠋⠀⠀⣤⣤⣶⣿⠿⢋⣘⣷⣿⡿⠁⠙⠳⣬⡐⠲⠤⢄⣄⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠁
⠀⠀⠀⠀⠙⠶⣾⣿⢿⠿⠛⣋⢃⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⢀⣷⡤⠀⣇⠀⠀⠀⠀⢄⠀⠤⢡⣆⡾⠈⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⠿⡇⠀⢯⡤⣀⡀⠌⢆⢾⣾⣻⣿⣇⣆⠢⢂⢄⠀⡆
⠀⠀⠀⣠⣆⢀⡀⣵⡘⠳⠀⠘⠦⣄⣀⠀⣀⠀⠀⠈⠁⠀⠠⠀⡰⠋⠀⠀⠄⠀⠈⢿⣷⣶⣷⣾⢾⣻⣷⣿⣽⣿⣿⣗⣾⡟⠁
⠀⠀⠀⠉⠀⢰⣇⠀⠙⠢⢦⠀⠀⠈⠿⣇⠀⠀⠀⠀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣿⣿⠿⢿⣿⣿⣯⣤⣤⣴⠾⠿⠈
⠀⠀⠀⠀⠀⠀⠙⠱⢄⠀⠀⠑⡄⠀⠀⠀⣿⣟⠛⠉⠁⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢯⠰⡀⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠐⠻⠇⠀⠈⠛⠦⣤⣀⡠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒
⣿⢿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢂⣩⠥⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣈⣥⣴⠰⡆⠈⢳⡒⠒⠒⠖⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠩⣂⠘⠒⠒⠉⠐⡊⠀⠀⠄⢀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡑⠀⠀⠂⠂⠄⠁⡕⢠⠁⠈⡀⠁⠀⠄⡀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⢀⠐⠢⠀⠀⠉⢀⠀⠨⡀⠂⠅⠂⠂⢌⡁⢰⠀⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠈⠄⠈⠁⣀⠂⠐⠊⠀⠋⠀⡢⠀⠄⢠⠂⠄⠈⠠⠐⠀⠐⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⢠⠀⠀⢐⠀⠀⠇⠈⠀⢌⠄⠀⠉⠀⢧⠂⠉⢁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠁⢀⠀⠀⠄⠀⠀⢀⠀⠐⠄⠁⡐⠠⠀⠡⠄⠀⡄⡐⠀⠂⣈⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⡀⢉⡁⠀⡔⠂⠀⠎⠁⠈⡄⢢⠀⡔⠂⠈⢀⠤⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⣤⠀⠀⠀⢱⠈⢉⠆⠀⠀⠁⠜⢀⠀⡀⠀⢄⠨⠅⠈⠡⠢⡈⠀⡄⡌⠀⠀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣦⠀⠘⣆⠀⠐⠀⠀⠀⠔⢂⣁⡠⠒⠘⠒⠒⠠⠔⢀⠀⠀⠀⠀⢨⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠛⠛⠛⠓⠚⠛⠓⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇⠅⠂⢀⠄⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠤⡀⠘⠐⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⢿⠀⠀⢃⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠥⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢤⣀⣀⣀⣀⣀⣠⣤⣤⡴⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⡠⡄⡄⡄⡆⡠⡄⣧⠤⡄⠀⡄⡤⣄⣤⠄⠀⡧⣰⣂⣤⢰⣠⢠⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠁⠉⠁⠁⠁⠉⠀⠉⠁⠃⠁⠁⠀⠀⠁⠀⠀⠁⠈⠉⠉⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡊⠉⣍⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠉⠀⠀⠀⠀⠙⡳⢄
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⣄
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡠⢀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡠⠦⠁⢀⠄⠀⠀⠀⠀⠀⢰
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠈⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡜
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠤⠐⠀⠈⡈⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⡂⢀⠀⠀⠀⠀⠄⠄⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠘⣆⠀⠘⡀⠀⢔⠈⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠈⢦⡀⢷⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠙⢾⣧⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣈⣙⣲⣦⣤⣤⣤⣴⣿⣿⣛⣋⣛⣛⣛⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠘⠟⠻⠿⠛⠿⠶⠚⣶⡿⢶⣄⡀⢉⡀⠢⣄⡀
⠀⠀⠀⠀⠀⢀⠠⠚⠀⢀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣤⡀⢈⠙⢱⣦⡀
⠀⠀⠀⠀⣐⣥⡶⠖⠳⠿⠷⠾⠿⠿⠿⠿⠿⣷⣿⣤⣦⣀⠀⢀⠀⠀⠈⠙⢻⡄⠀⠙⢏⠂
⠀⠀⠀⡰⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠐⠛⠶⢖⣤⣄⡀⠉⢲⣆⠈⣡⠣
⠀⠀⢀⡏⢠⣤⣴⣶⡾⣤⢦⡠⡄⢀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠈⠙⠳⣤⡌⢆⢨⡇
⠀⠀⢘⠷⠟⠁⠀⠀⠉⠉⠉⢶⠈⠁⠊⠛⠋⠉⠉⠀⠚⠋⠑⠒⠚⠛⠛⠂⠤⣀⠀⠙⢆⠆⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣷⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂
⠀⠀⠀⢿⣄⣀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣀⡠⠶⠒⠋⠾⡥⠉⠐⠒⠂⠀⠀⠀⠀⢀⡨⠟⣁⠸⠀⠀⠀⠀⠀⠰⢀⠈⠀⠘⠂
⠀⠀⠀⠀⢎⠙⠿⠛⠿⣷⣾⣳⣶⢾⣶⣋⣡⣀⣀⣀⣀⣀⣀⣀⢤⣤⣤⣤⣤⡤⠞⢋⠴⠑⢸⠇⠀⠀⠀⠀⠀⠀⠁⢠⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠳⣄⠀⢀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠀⠋⠁⠁⣠⠴⠞⢁⠐⢠⠂⠀⠀⢀⡐⠀⢠⠀⡤⠨⠁⠀⠈⠿⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠙⠿⡻⠶⣤⡄⣀⣀⣀⣀⣦⣀⣀⣀⣀⣀⣀⣤⣤⠴⠞⠋⠁⠀⠜⢃⡔⠀⠀⠀⢀⡀⠀⠐⠧⣀⠃⠀⠁⠀⠀⠀⣀⡤⠚⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡈⠀⠀⠈⠈⠛⠋⠙⠃⠉⠁⠀⠀⠀⣀⡤⠆⠋⡠⠔⠁⠀⠀⠀⠀⠀⠈⠓⠢⠤⢀⣈⣁⢀⣉⣉⡉⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠦⠤⢄⣠⣤⣀⣤⣀⣂⡉⠥⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⠛⠛⠛⠛⠿⠿⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⠁⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣰⣷⣤⣬⡿⠷⠜⠳⡶⠛⠛⢷⣿⢦⢀⡈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣼⣷⣶⠿⡟⠋⠉⠁⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠈⠳⣦⣽⣿⠧⣀⡦⠝⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣼⣿⠋⠁⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠷⣿⠇⠤⠒⠛⣶⣿⣶⣴⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⢠⣾⣶⣼⣿⡿⣿⠉⠉⠃⠀⠀⠀⠀⠀⢠⣴⠏⣹⠿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣤⣤⣿⠿⠛⢿⠀⠀⠀⠀⠀⠀⢤⡀⠀⣰⣶⠊⠀⠐⣿⠀⡟⢸⣷
⠀⠀⠀⠀⠀⠀⢸⡇⡀⢰⣶⡮⠍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠉⠀⠑⣿⡿⢤⣿⠞⣿
⠀⠀⠀⠀⠀⠀⠘⣷⣽⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣾⣿⣿⣿⠋⠀⢠⣀⣿⣿⡁⣲⣿⣥⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⠀⠀⠀⢠⣄⣰⣿⣿⡿⠟⠛⠀⠀⠀⠀⣼⣿⣿⢿⢱⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣳⣤⣠⣿⣿⡿⠛⠛⠿⠀⠀⢀⠀⣠⣽⣿⡿⣿⣃⢻⣿⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⡿⢿⡿⠃⠉⠀⠀⠀⠀⠐⣌⣼⣿⣿⣿⠋⠣⣔⣪⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⢀⠀⣀⣠⣿⣶⣾⣿⠿⢟⠉⠀⠒⠀⠛⠛⠛⠻⠁⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⣶⣿⣿⣿⣿⠿⠟⠛⣯⡆⢸⡥⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠤⣧⣤⣤⣴⣿⢰⠈⣧⠀⠀⣴⠆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⣄⠐⠀⣸⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⠸⠄⠀⠀⢠⡶⠀⡤⠀⡒⠀⠰⠀⠐⠀⣌⠁⢢⡀⠈⠻⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣹⡄⠲⣤⠀⡈⠁⠾⠃⣼⠃⢠⣆⠀⣴⡀⢻⡇⠘⠟⠀⠀⡜⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣹⣆⠘⢷⡀⡀⠀⠀⠋⠀⠘⠟⠀⠻⠃⠀⠁⠀⠀⠀⠜⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠙⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣈⠙⠓⠢⠄⣤⣤⡤⠀⠄⠀⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⠤⠤⠤⠒⠊⠁



⣿⠿⠿⡿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⢠⠊⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠀⠸⠊⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⠤⠤⠤⠤⠤⣤⣤⣤⢄⣀⠀⠀⠀⠀⢹⡉⠉⠙⠳⢮⢍⠒⠦⡀
⠀⠀⠀⠀⡠⠔⠊⠉⠩⠀⠁⢈⠀⢂⠀⠠⠀⠀⠈⡏⠉⠓⢦⡉⢢⡀⠀⠀⢣⠀⠀⣠⠀⠑⠌⠢⡈⠢⡀
⠀⠀⡠⠋⡀⠃⢀⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡤⠆⠈⢎⢢⠩⢦⠀⠘⡄⠀⠀⠠⠆⠀⠂⠑⡀⠱
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠱⠀⠀⠀⠀⠀⠸⡠⠤⠈⡄⢇⢀⢣⠀⢃⠀⣠⠀⢀⣀⠀⢀⢱
⡘⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⢣⠀⠀⠠⠀⠀⢣⢀⡄⠁⠘⡄⠈⡆⢸⠀⠐⠂⠀⢀⠀⠀⠀⡄
⡇⠀⠠⠀⠰⠀⠀⠀⠠⠀⠀⢈⠀⠀⠀⠈⠄⠀⠀⠄⠀⠘⡀⠀⠈⠀⡇⢠⡇⠈⡆⠠⠤⠈⠁⠀⠀⢀⠁
⡇⠀⠠⠀⠐⠀⠀⠀⢠⠀⠀⠈⠄⠀⠀⠀⠃⠀⠀⠰⠀⠀⡇⠠⠄⠀⡇⠀⠇⠀⡇⠀⠀⠀⠉⠀⠐⢈⡴
⢃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠠⠀⠀⢻⠀⠀⠀⠇⡸⠀⠀⢠⠀⠀⠢⠄⣠⡿⠋
⠘⡄⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠰⠀⠀⢠⠀⠀⢸⠈⠁⡘⡰⠃⠀⠀⢸⠀⠀⣠⠴⠋
⠀⠐⡄⠀⠁⠀⢡⠀⠀⠐⠀⠀⠈⡀⠀⠀⠰⠀⠀⠀⠀⠀⢸⢀⣴⠔⠁⠀⣠⡀⠐⠚⠋⠁
⠀⠀⠈⠢⡀⠡⡀⠡⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠟⠁⠀⡲⡄⢸⣈⠆
⠀⠀⠀⠀⠈⠲⢌⣂⣡⠀⠀⠡⡀⠘⠀⠀⠃⡀⠁⣀⠤⠚⠁⠀⠀⠀⠓⠁
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣷⣶⣶⣶⣶⣶⣾⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡸⡿⢸⣞⢇⠟⡦

⠀⠀⠀⠀⠀⠉⣀⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⣴⣤⡀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⠀⠀⠀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⣿⣿⣗⠀⢀⣼⣿⡿⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣸⠀⠀⢀⢶⠿⠈⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠠⢤⡴⠟⠁⠀⠀⠙⠿⡿⠿⠃⠀⠺⢿⡿⠖⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⠤⠞⠃⠀⠀⠨⢄⣀⠤⠂⠀⠈⠹⢿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠁⠈⢩⣄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⡀
⠀⠀⠘⠢⠀⠀⠀⠀⢆⠀⠀⠀⢀⢴⠞⠁⠀⠀⠀⠀⠀⠀⠉⢻⡆⠉⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠄⣈⣲⣤⣴⢊⠇⠀⠐⠏⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠜⠀⠀⠀⢄⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⢾⡇⠀⠀⠀⢀⠴⠖⠀⠀⠀⠀⠚⢶⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⢈⡿⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⣳⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠠⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠖⠀⠀⠀⠀⠀⠀⠒⠁

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠤⠀⡀⡀
⠀⠀⠀⠠⢧⣬⠤⠀⠀⠀⠀⠤⠌⠀⠀⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⢀⠠⠄⡀
⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⢀⡐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠠⠤⠄⠉⠈⢠⣾⡆
⠀⠀⣰⣷⡀⣀⣀⡀⢀⠀⠀⠐⢿⣦⣦⡤⠄⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⣠⣄⡀⠈⡟⡁⣤⣤⣤⣄
⠀⠀⠿⡿⠗⠐⠐⠀⠀⠀⠠⡀⠀⠐⠀⠀⠀⢸⡟⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⠆⡎⠀⠈⠛⠛⠛⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣀⡀⡀⠀⠸⢿⢟⣉⣯⡥⠬⢀⣀⣤⣤⣼⣤⣤
⠀⠨⠈⠉⠁⠈⠅⠀⠈⠁⠉⠀⠀⠀⠀⠈⠲⣄⠀⠉⠲⣄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⣠⣶⣶⢶⠿⠿⠛⠛⢛⣻⣿⣿⣿⠿⠛⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠠⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢼⡧⠀⠀⠠⣀⠄⣾⡷⠀⣠⣄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⢿⣿⣿⡧
⠀⠀⣰⣧⠀⠐⠖⠒⣶⣶⡄⠛⠷⣼⣿⣿⣿⡤⢄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢭⢭⢙⣀⣀⣽⢡⣶⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠛⠿⠂⠁⠀⠀⠀⠀⢀⣉⣋⠀⠉⡏⠉⣼⡆⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠿⠶⣤⠼⣤⣤⣿⣿⣿⣿⣧⣾⡟⠛⠛⠋⠉⣽⣭⣭⣭⣭⣭⣭⣍⡉
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣾⣿⠿⡿⣻⢟⡿⣻⢛⠟⡳⢻⠟⡷⣲⢾⡷⣖⣓⣒⣒⡂
⠀⠀⢿⠿⡿⠿⠻⠝⠏⠫⠙⠍⠮⠳⠝⠮⠢⠑⠜⠮⠳⠝⠭⠫⠻⠗⠶⢤⠀⠀⠀⠸⠿⠟⠿⠋⠟⠱⠋⠞⠴⠣⠎⠼⠡⠋⠞⠱⠃⠞⠴⠡⠏⠼⠡⠋⠟⠲⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠒⠁⠢
⠀⣴⣿⣆⠠⠄⠤⠀⠀⠲⠒⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢁⣤⣤⡀⠀⠀⠉⠑⣤⡄
⠰⣿⣿⠟⢀⢀⣀⣈⣉⣉⣁⣀⢀⣾⣿⣿⡆⠑⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠈⢁⣴⣿⣿⣿⣿⣶⣄⣀⣠⣐⣶⣶⣶⣦
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠒⠀⠀⠀⠉⠀⠐⠠⠄⠂⠉⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠿⠿⠿⠿⣿⣿⣯⠉⠉⠉⠉⠉⢸⣿⣿⡆⠤⢄⣤⡤⣤⣤⢤⢤⠦⡦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠈⠙⠂⢧⠣⠑⡑⠄⠀⠀⠀⠖⠚⠙⠉⠋⠋⠑⠉⠊⠒⠑⠊⠊⠓⠙⠊⠋⠙⠙⠋⠛⠛⠛⠛⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠁⠀⠀⠀⠄⠠⠠⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶
⠀⠀⢠⣼⣿⣿⣶⣀⣀⣤⣤⣾⡟⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣤⣠⣦⣠⣄⠄⡀⠻⢸⣿
⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠙⣿⣿⣿⣿⣿⣿⡤⣤⣬⡿
⠀⠀⠻⠿⣿⡿⢿⣉⣯⣸⣿⣄⣼⣧⣠⣿⢀⣤⣾⣷⣀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⢚⣛⠛⠋⠛⠉⠛⠛⢛⣛⣛⣛⡷⠷⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣇⣀⣻⣶
⢀⣤⣤⣤⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠆⠀⢸⡆⠀⠀⠀⠀⠀⠀⢲⡀⠀⠩⠭⣭⣭⣭⣥⢶⡶⣦⢦⡾⣿⢿⡯⣭⣯⣭⣟⣻⠿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠀⠀⢨⡭⣾⢻⡙⢏⢳⡙⣎⢳⡙⣎⢳⡙⣎⢳⡙⣎⢳⡙⣎⢻⡙⣟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣠⣰⡈⣩⡿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠩⠳⠎⠛⠿⢻⡾⠙⣿⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⣀⣀⠀⠀⠈⡑⠰⢤⣀⣀⣠⣤⣴⣾⠟⠋⠛⠛⠤⠉⠉⠁⠀⠠⠤⡤⠄⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡐⠋⠉⠓⣲⣤⣦⣶⠿⠛⠋⠉⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢈⡩⠝⠚⢋⣧⣶⡿⡿⠋⠩⠇⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠜⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⡀⢀⠚⣶⠒⢛⠓⣶⣲⡾⡟⠉⢀⠀⠀⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠀⢦⣄⣀⣈⣠⣾⡟⠉⠠⠀⠀⡼⠀⢀⠃⠀⠋⠀⠀⢀⣀⣀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠉⢉⡉⢡⣾⠟⠉⠀⠀⡜⠀⢠⣃⢀⠎⠁⠀⠀⠀⢈⠐⠀⡽⠛⢴⠛⢦⣼⣦⠀⠀⠀⠀⠀⣤⣿⣿⡃
⠀⠀⠀⣴⣴⣿⣿⣿⠟⠃⠀⠀⠀⢰⠀⠀⢼⠊⠁⠀⠀⠀⠀⢸⠁⠀⡼⠁⠀⣞⠢⣼⣿⣟⢳⣄⠀⠀⡾⠛⣿⡷⠈
⠀⠀⢰⣁⡽⢯⡿⠁⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠠⠤⣤⣞⠀⢰⡇⢀⣢⣿⣈⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⡟⠢
⠀⠀⠸⢀⣀⡜⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠀⠈⡿⠟⢻⠏⠉⡇⢽⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⡀
⠀⠀⠐⡋⣽⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣠⣾⠀⡄⠀⡇⢸⡄⢘⣿⠨⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⠛⠢⢄
⠀⠀⠀⢩⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠃⠘⠛⠃⢰⠀⣾⣷⡞⢻⣷⣾⣿⣿⣿⣿⣿⣿⣇⢼⣿⢄⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⣆⣶⡄⢲⡎⢘⡟⢹⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡾⠋⢳⡟⠀⣸⡇⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢷⣿⣷⠀⣠⣷⣤⣿⣇⣼⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡔⠋⣁⣠⡀⠀⠀⠀⢸⠋⠙⠿⣿⠉⣿⠛⡟⠛⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⢸⣎⣿⠿⠂⠀⠈⠉⠻⠀⠀⢢⠘⣤⣦⢀⡇⢀⣿⠀⡆⢠⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⠀⠀⣴⠃
⠀⢀⣾⡟⠀⠀⠈⠉⣧⣤⣄⡀⠱⢄⠀⢀⠀⠈⠂⢹⣷⣾⢻⣶⣿⣤⣿⣾⣿⣼⣿⣿⣿⣿⣼⣧⣼⣿⡏⣾⣿⠀⢸⡇
⠀⠈⠹⣷⡀⠀⠀⠙⠿⣿⣟⠀⠀⠈⢳⣴⡅⠀⠀⠸⣿⣿⣧⣿⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣿⡆⢻
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⢿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣎⢆
⠀⠀⠀⠀⠀⠀⠚⢆⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠓⠻⠿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣁⡀⢀⣀⣈⣙⣷⣦⡀⠀⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣻⠋⠉⠉⠉⠉⠉⠿⠯⠸⣧⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⡀⠀⠀⠀⢠⣶⡆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠟⠋⠁
⠀⢀⢄⠰⠾⠁
⣶⣿⠿⠷⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⢀⡄⠀⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣠⡴⢊⣤⠠⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠵⣦⣤⠠⢀⣀⠀⠀⠄⢶⣀⠹⡍⢻⠆⡀⠠⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠌⣀⡠⠄⠀⠉⠉⡁⢃⠘⠹⡟⠈⠙⡄⢐⡔⢢⡤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⠉⠀⠀⢀⣠⡶⠛⠁⠀⠰⣇⡀⠀⠀⠀⠑⠈⠻⣄⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠐⡠⠋⠁⠀⠀⠀⡤⠞⣿⣿⣶⠀⠀⠀⠀⠘⠛⢷⣌⠸
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⠏⠀⠀⠀⠀⠁⠀⠀⠀⢀⡜⠁⠀⠀⠀⣭⣿⣿⡄⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⡀⢠⠏⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢦⡄
⠀⠀⠀⠀⠸⣾⡇⡠⠁⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣿⣼⣿⣄
⠀⠀⠀⠀⠀⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠜⡙⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢐⠘⣋⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣬⠀⣼⢁⣿⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣸⣿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠐⢲⣿⢿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠐⠟⣐⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⠀⠀⠆⠀⠀⠀⠀⠈⠀⠙⠻⣿⣿⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠀⠀⠀⠀⢀⡀⠀⠂⡰⣶⠟⢿⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠈⠁⠀⠀⠀⠀⠀⢀⡄⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠶⣶⣿⠰⢶⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⡀⣀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢒⡆⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣦⣰⣿⣟⢀⢀⡀⠀⠠⠀⠀⣀⠀⠡⠄⡀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣧⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠈⠑⣅⡞⠀⢊⠁⠀⠀⠀⠀⣠⣤⣾⢃⡆⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠉⣽⣿⣇⡇⡰⣆⠙⠘⢃⠀⠀⠀⠀⠀⠠⢸⡄⠀⢨⠀⠀⢀⣠⣴⣿⣛⡿⠏⠀⠀⢱
⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡀⠁⣖⣯⣸⣿⣿⣿⣿⡹⠳⢤⢼⣇⠀⠀⠀⢰⡀⢸⡏⠁⢸⣀⣰⣟⣧⠨⣿⢫⡑⠉
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠇⠘⠉⢹⣽⣏⢿⣿⣿⠱⣇⢎⡾⢻⢷⣶⣶⣾⣷⣾⣧⡐⣋⠡⠀⠀⠀⣤⠘⢴⠠⢀
⠀⠀⠀⠀⢠⠀⠐⠀⡆⠀⠀⠀⢀⠀⣠⣀⢹⡎⢢⠀⡹⠟⣷⣾⣿⣿⡧⣿⠬⢤⣉⢾⣿⣿⠟⣿⣿⣻⣧⣿⢤⡶⢤⣠⠘⣏⡀⢡⠜⢦
⠀⠀⢠⠀⡶⡀⠐⠀⢡⣤⢴⣾⣿⣄⠻⣯⢀⣹⡲⣄⠀⣻⣿⣿⣿⣿⣿⣏⣷⢢⣤⣼⣿⡏⢣⣿⣿⣿⣿⣿⣚⡏⠎⠹⣷⠨⣁⣴⡁⠈
⠀⠀⣌⢨⠶⣄⣥⠈⠨⡷⣆⡏⠃⠫⢸⢴⣶⣶⣇⣲⣿⣿⣿⣿⣿⡟⠿⠙⣿⣡⠔⢻⣶⢳⡌⡿⢹⢾⠟⣟⣷⣄⠀⣐⣿⣿⢧⠈⠁⠂⠀⠀⠀⠤
⠀⠀⠙⠉⢺⣾⣷⣤⣴⣶⣾⣶⣾⣶⣶⣷⣿⣿⣿⣿⠈⠹⠯⡟⠙⠐⢀⠇⠸⠶⣶⣾⡷⣌⢷⡷⠋⠀⠀⢿⣹⠿⠺⠿⢛⡛⠄⠀⠐⠂
⠀⠀⠀⠀⠂⠾⢻⣛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠴⠀⠁⠀⠀⠁⠀⠀⠀⠄⠀⠈⠀⢡⠄
⠀⠀⠀⠐⠀⠀⠉⠉⠉⡁⠢⠐⠚⠉⠁⠛⠛⠉⠛⠛⠛⠋⠿⠿⠟⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⠐⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣿⣿⣾⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠀⠀⠀⣀⣀⠀⣀⡀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠬⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡠⠒⠈⠀⠀⣀⠤⠀⠀⠤⠤⠒⠒⠒⠀⠀⠒⠢⠄⣀⣀⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠞⠀⢀⡠⠠⠊⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠄⢀⡀⣀⠈⠓⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠀⠘⠀⠀⡠⠃⠀⠀⠀⠤⠊⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣂⣌⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⠀⢂⠂⢉⠀⠔⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠤⢀⡀⣀⠤⠒⠒⠀⠐⠉⠀⠀⢹⠒⣌⡇⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢂⢒⠠⠔⠁⡀⢀⠤⠒⠒⠐⠊⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠂⢸⡆⣟⢧⣈⠗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⢘⣋⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠤⠐⠀⠒⠁⠀⠀⠀⠀⢀⢾⠁⠘⠲⠶⠚⠁⠀⣠⠶⠚⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠓⠶⠾⡇⠀⣿⠢⢄⡀⠁⠁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⣾⢀⣠⠖⠚⢛⠉⠉⠁⢀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢲⠞⠁⠀⠰⡀⠀⢿⡀⠀⠑⠀⠀⠑⠤⠤⢄⡀⠀⠀⠀⢀⡞⠙⠓⠒⠒⠒⠲⠖⠛⠛⢛⠛⠶⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠒⠢⡄⠳⣆⠈⢧⠀⠀⠁⠐⢄⠀⠀⠀⠈⠉⠉⠀⣿⠁⡇⢸⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣤⡴⠃⠀⠌⡑⠨⢧⡀⠀⠀⠀⠈⠈⠈⠒⢄⣀⣸⠟⠀⢳⠸⠀⠀⠃⠀⠀⠀⠆⠀⠀⠀⠀⣁⠀⠀⢀⠀⠀⠀⡁⠀⠀⠠⠀⢈⢰⠇
⠀⠀⠀⠀⡧⠀⠐⠠⠄⣠⠄⢒⠂⠉⠉⢉⠿⢦⡀⠀⠑⠒⠤⡀⠀⢀⡏⠀⠀⠸⡀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⡌⣸
⠀⠀⠀⠺⣄⠀⠀⢀⠊⠀⡠⢁⡤⠶⢴⡁⠀⠀⠉⠳⠦⣤⣀⣈⠐⢺⠃⠀⡀⠀⢣⠐⡀⠀⠃⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢠⡏
⠀⠀⠀⠀⣸⠀⡠⠀⠀⠐⢰⠋⠀⠀⠀⣷⠀⠀⣇⠀⠀⠢⡀⠉⠛⠻⡆⠀⠀⠀⡀⢣⠐⠄⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡴⢡⠎
⠀⠀⠀⣴⣯⣀⣀⡤⠤⣤⡟⠀⠀⠀⢠⡏⠀⠊⠸⣄⡀⢰⠏⠉⠙⣆⠹⣆⠈⠄⠐⠄⠑⢌⠢⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⢀⡠⠔⣩⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠈⣺⣧⠀⠀⠈⠛⠛⠳⢦⣀⠈⠂⠈⠳⢄⠁⠂⠠⠤⠀⣀⣀⣀⠠⠤⢔⣊⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠦⣭⣶⣶⣤⣤⡤⠶⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡔⣶⡿⣷⡶⢿⣷⣤⡶⣦⣾⣯⣭⠉⠑⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠙⠻⡷⣿⢷⣶⣞⡁⠀⠘⠻⢆⣄
⠀⠀⠀⠀⠀⡠⢚⣩⣠⣤⣴⣭⣤⣴⣤⣴⣧⣤⣤⣄⣴⡀⢀⠀⠈⠂⠀⠈⠉⠻⢶⣶⡀⠀⠻⣷⢄
⠀⠀⠀⠀⡰⡖⠛⠋⠁⠈⠉⠉⠉⠙⠋⠉⠈⠉⠙⠟⠛⠻⣿⣶⡆⣤⣆⣀⣀⠀⠀⠈⠿⣄⠀⠈⢦⠱⡀
⠀⠀⠀⢸⠅⠀⠀⠀⢀⣠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠫⣿⠶⣦⣀⠈⠻⠄⠀⢿⡑⡀
⠀⠀⠀⡿⢀⣾⣶⠿⣿⣟⣶⣳⡴⠶⣦⢤⣄⢠⣄⣀⣀⡀⢀⣀⣴⠀⠀⣀⣠⣀⠀⠀⠙⠳⢶⡘⢆⢸⡁⠂
⠀⠀⠀⡟⡟⠉⠠⠀⠀⠀⠈⠉⠹⡇⠉⠈⠈⠉⠁⠀⠁⠈⠈⠙⠉⠙⠛⠉⠙⠙⠓⠒⠤⣀⠀⠙⣜⢌⣇⣾⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⢆
⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣘⣞⢊⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠌⠁
⠀⠀⠀⢸⣧⣀⡀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡶⠒⠿⠽⣯⡞⠉⠶⠖⠂⠀⠀⠀⠀⠀⣀⡽⠿⣁⡸⠀⠀⠀⠀⠀⠀⠴⢀⠉⠀⠘⠃
⠀⠀⠀⠀⢱⡛⠻⡶⠿⢿⣷⣶⣶⣴⣶⣷⡶⠛⣉⡀⠀⡀⠀⡀⢈⠀⢀⣤⣀⣀⣀⣠⣄⡴⠖⢫⡜⡃⢹⠇⠀⠀⠀⠠⠈⠀⠐⠃⢠⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠱⣔⠐⠀⠀⠘⠋⠉⠉⠁⠉⠉⠉⠘⠙⠛⠻⠿⡿⠿⠿⠓⠉⠟⠉⠋⠉⣡⣴⠚⠁⠜⢀⠌⠀⠀⠀⠠⠂⠄⡐⠀⡀⢘⠃⠀⠀⣿⡆⠀⣆
⠀⠀⠀⠀⠀⠀⠘⢳⣦⣬⣤⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠁⢀⡶⠃⡤⠊⠀⠀⠀⠀⠃⠂⣴⡇⢼⠃⢠⠂⠀⠀⠀⠀⢀⣨⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣉⡛⠣⠖⠚⠛⠟⠿⣿⠾⠶⡏⠶⠶⠚⠛⠛⠙⠁⢀⡀⡴⠂⢀⡰⠋⠀⠀⠀⠀⠀⠳⢤⣄⠈⠙⠒⠠⠄⠤⠤⠴⠶⠞⠋⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⡤⠰⠚⢋⣁⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠐⠒⠒⠂⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠖⠲⠶⠷⠘⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢠⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢠⣥⣭⣽⣄⠀⣠⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡠⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⡆⣾⢁⣿⣿⣿⣿⣿⣯⣭⠭⠭⠿⠻⠟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠀⢠⠙⢴⡄⠀⠀⣀⡀⠠⠔⠛⠁⠉⠛⠛⠋⠉⠙⠉⠁
⠀⠒⠚⠓⠛⠛⠛⠛⠲⠖⠒⠒⠒⠛⠛⠓⠚⠒⠒⠛⠀⠀⠀⠁⠉⠘⠛⠛⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠤⠒
⠀⣤⡥⠴⠖⠐⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⡀⠔⠀⠄⠀⠄⠀⢀⠀⠀⠀⢀⣔⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠈⠉⢀⡤⠒⠁⠄⡠⠀⣠⢄⠄⢀⠄⠁⢀⢀⠔⠁⣠⡮⠊⣠⠖⡠⢆⠅⣠⠔⠡⡠⡂⢚⢕⢕⣽
⠀⠀⠤⣑⠢⢄⠑⢍⠢⣤⣾⠾⠛⠉⠀⠀⠀⣠⢶⢋⡠⢂⣔⢉⣠⢞⢗⡕⡴⡃⡄⢰⡟⡵⡢⡴⡫⡪⡀⡫⢊⠖⣡⢞⡵⣫⣪⠊⢔⢕⡵⡫⣪
⠀⣀⠀⠄⠑⠢⣹⣾⠟⠋⡠⠀⠀⣠⠀⣠⢞⠕⣱⣛⣔⢝⢕⠕⡵⡡⢪⢊⣮⣾⣪⣪⣪⢮⢾⢟⢎⢪⢞⠔⣵⠞⡱⣫⢞⢝⢅⡴⡡⣪⢎⣔⣵

⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⢄
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠺⣦⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⡀⠀⠀⠀⠈⢆⠐⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠸⡄⢀⠀⣀⡰⠞⠁⠀⣤⠀⠀⡇
⠀⢀⡾⠁⠀⠠⣤⡀⠀⠙⠂⠀⠀⠀⠈⢆⢷⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⣼⠁⢀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⢎⣧⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠐⣦⠀⠀⠀⣼
⠀⡏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠈⢟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠧⠤⣀⣀⡘⠓⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠈⢎⢳⡄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠈⠉⠉⠋⠒⠒⠢⠤⠄⣀⣀⠀⠀⠈⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⢸⡆⠀⠀⠀⠀⠳⠄⠀⠈⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠉⠈⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠚⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⣠⢶⣾⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⢀⠔⠊⠁⠈⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢴⡾⠟⢉⣴⠊⢀⡞⠀⢷⡝⣬⡛⢿⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠀⢀⢔⡥⡄
⠀⠀⠀⠀⢠⠞⣱⡟⠁⣶⡿⠁⠐⣿⣇⠀⣸⡇⢸⡇⠈⣷⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢣⢰⠀⠀⠚⠁⠀⢰
⠀⠀⠀⡰⣡⣾⠏⠀⣾⡟⠁⠀⣾⡿⠋⠀⣿⡇⣸⡷⠀⢻⡇⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠈⢄⠀⠁⠀⠀⠀⢀⡤⠂
⠀⠀⡰⣽⡿⠋⠀⣾⡟⠁⠀⣠⣿⠇⠀⣼⣿⠘⣿⡇⠀⠻⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⢅⠀⠉⠙⣄⠈⠆⠀⠀⢀⠔⡡⠐⠢⡀
⠀⠀⡇⣽⠇⠀⢠⣾⡟⠀⢀⣿⣧⠀⢸⣿⣏⠐⣿⣧⠀⠀⣿⣿⠈⣿⣿⡄⠀⠀⢀⠔⠒⡄⣇⠀⠀⠈⠓⠃⠀⠀⠦⠔⠁⠀⠀⢸
⠀⠀⢀⣿⠀⢀⣼⣿⠇⠀⣿⣿⠟⠀⢸⣿⡟⠀⣾⣿⡀⠀⣸⣿⠀⢸⡇⡇⠀⠀⢌⠀⠀⢂⢀⡕⣄⠀⠀⠀⡄⠀⠀⠀⠰⠖⠒⢡
⠀⠀⡞⣿⡀⢿⣿⡏⠀⣠⣿⡿⠀⠀⣿⣿⡁⠀⢹⣿⡇⠠⣿⣿⠀⢸⣿⡇⠀⠀⢔⠛⠂⠀⠁⠰⡌⢱⡀⢰⠀⡔⢒⢶⡢⠶⠴⡁
⠀⠀⢧⣿⣇⠘⣿⣷⠀⢻⣿⡆⠀⢀⣿⣿⣿⠀⢸⣿⡇⠀⢹⣿⠇⣼⣿⠀⠀⠀⠈⠉⠐⠢⣄⠀⠙⣼⠀⢏⢊⠔⠁⠀⠀⠀⡠⠆
⠀⠀⠘⣎⣿⠀⣿⣟⠀⢸⣿⡁⠀⠀⣻⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⣿⠃⠀⠀⠀⠀⡤⠂⠉⠈⠁⠀⠀⡜⠈⠁⠀⣀⠤⢄⣀⡑
⠀⠀⠀⠈⢿⣆⠈⢻⡇⠀⢿⡅⠀⠀⢹⣿⠂⠀⢸⣿⡷⢀⣼⠏⡠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢺⠓⢄⠀⠀⠉⠒⠲⡄
⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠈⢷⣄⠀⣼⡿⠀⣀⣿⠋⢀⣿⡣⠞⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⡏⠀⠀⠙⠦⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣷⣄⠘⣷⣿⣧⣾⣟⣋⡤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠉⢍⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠙⠒⠘⠃⠀⠀⠀⠈⢿⠦⣀
⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠳⡄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠄⡀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡠⠴⠉⠀⡠⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⡈⠁⠁⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⡼
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠠⠄⠒⠈⠃⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠙⠅⠀⠀⢀⠀⢀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠹⡄⠀⠀⡆⠀⠀⢀⠠⠒⠉⠀⠀⠀⠐⠤⠦⣐⣐⠨⠤⠥⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠹⣄⠀⢰⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡤⠚⠁
⠀⠀⠀⠘⢦⡈⣇⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣶⣦⣤⣴⣾⣛⣛⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⡿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣾⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡎⠳⣤⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡁⢦⢸⣅⣿⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣀⡄⠸⠏⠁⡀⣿⠟⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⢲⠈⠁⣠⠉⠏⠲⣀⣤⠟⠋⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡴⠶⠈⠀⠀⠀⠀⠀⠀⠀⣷⣼⡶⠟⠁⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⣶⣷⡶⠛⠉⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠰⢦⣶⣁⡿⣀⡔⡠⠀⠀⢀⠀⠀⠀⡀⣀⣠⡼⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠉⠙⠛⠛⠓⠶⠖⠛⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠀⠤⠤⠤⠤⠴⠖⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠑⠢⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠤⠤⠤⠀⠀⠤⠤⠄
⣶⣶⣶⢶⠶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣰⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⢠⡾⢿⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⣿⣄
⢀⣴⠏⠀⠀⠙⢦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠃⠙⣧⡀
⢾⡁⠀⠀⠀⠀⠀⠙⢶⣄⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢀⡴⠋⠀⠀⠀⠈⢻
⠀⠻⣦⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢁⣠⡾⠋⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠉⠛⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠾⠛⠉⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣤⣀⣈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣁⣀⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣉⣉⡉⡉⠉⠛⠛⢿⣿⡿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣛⡛⠻⠿⣷⣾⣷⣦⣤⣄⡀⠀⠉⠛⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣷⣶⣄⠈⠛⠛⠿⣿⣿⣧⡀⠀⠀⠀⠙⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣦⡜⠻⢿⣿⣿⣿⣷⣆⡀⠈⠉⠻⢿⣿⣶⣄⠀⠀⠈⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⣿⣿⣿⣿⣿⣦⠈⠙⢿⣿⣿⣿⣿⣿⣦⣄⡀⠙⠻⣿⣿⣦⣀⡀⠈⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣀⠈⠛⣿⣿⣷⡄⠀⠛⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⡇⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠋⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡰⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣷⡀⠀⠋⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠉⠹⢿⣿⣿⣿⣿⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠙⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣦⣀⡀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣦⣤⣄⣀⠻⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣈⠉⣩⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⠛⠛⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠄⠠⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠠⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⢠⡀
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡄
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢐⡴⡶⢳⡄⠀⣀⠀⠀⣣
⠀⠀⠀⠔⠄⠀⠀⠀⠑⠤⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠋⡪⢐⠟⠁⠀⠟⠀⠀⢱⠀⠀⠀⠀⠀⠠⡀
⡇⢀⠉⠢⠌⠀⠁⠀⠁⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠊⠁⠀⠓
⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⢆
⠘⡀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢂
⠀⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠓⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠚⣁⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⠐⠁⠀⡀⠀⠀⠘
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⡀⠀⠀⠀⠀⠂⡈⠀⠐⠂⠁⠁⡸⢣⠀⠀⠀⠃⣀⠀⠀⠀⠴⠐⠊⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⡄⠀⠀⠀⠀⠈⠐⠀⠀⠀⣀⠀⠈⢃⠀⠀⠀⠈⠃⠠⠀⣀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⡀⠀⠀⠀⡀⠄⠀⠪⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠛⠚⠢⣄⢈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠥⣔⠀⠙⠗⢶⡲⢤⠤⣤⣼⡶⢴⣀⠀⡀⢉⠊⠔⡤⠤⠄⠀⠠⢤⣴⠶⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣉⣉⣉⣉⣁⣀⣀⣀⣈⣙⣛⣶⣷⣶⣦⣭⣍⣁⣀⣈⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠠⢄⣀⡠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢷⡌⠻⣤⠈⠛⣶⣆⠉⠓⢤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣿⠃⠘⢷⡀⠙⣧⡀⠀⠉⢿⣄⠀⡳⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⣿⠀⠀⣸⣏⡀⠀⣳⡆⠀⠀⢿⣄⠀⠘⢦⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠂⠲⢿⣆⡀⠘⢸⣇⠀⠀⢷⡆⠀⠈⠻⣄⠀⠘⡆⢃
⠀⠀⠀⠀⠀⠀⢸⠀⣿⡀⠀⠈⣿⡅⠀⠁⢸⣗⠀⠀⣳⡄⠀⠀⢹⡦⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢿⣷⡄⢠⠾⣿⡀⠀⠲⡿⣇⠀⠙⣷⣄⡀⢸⡇⠀⠬⠘⠀⠀⠀⠀⠀⣤⠀⡉⡀
⠀⠀⠀⠀⠀⠀⠈⣇⠘⢿⣧⠀⠀⣨⡿⡆⠀⠁⢹⣆⠀⠹⡿⠁⠘⠃⠀⠀⠀⠀⠀⠀⠐⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢿⡀⠀⠉⠘⣻⣇⡀⠄⠹⢀⠤⠑⠀⠀⠀⠀⠀⠀⢀⡀⠀⢦⠄⠶⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠛⢦⣀⠀⠛⢹⣧⡀⠀⢳⡀⠀⠀⠴⠀⠀⠀⠀⠈⡁⠀⡀⠲⠄⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣍⡙⠶⢦⣌⣙⣷⡄⠑⢄⠀⠀⠀⠘⠂⠘⠂⠛⠀⠙⢀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠀⠀⠀⢀⡠⢔⠯⠊


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⣿⣸⣷⡰⢰⣰⡆⣺⠃⣴⠲⢰⡖⠒⡶⢶⢲⡆⣴⠲⠀⡇⣴⠲⡆⣶⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⠃⠸⠞⠇⠹⠂⠛⠆⠘⠇⠀⠇⠸⠘⠇⠙⠦⠈⠇⠙⠼⠃⠻⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⣤⢸⣭⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠄⠀⠲⣣⣏⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠐⢻⣷⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡈⠟⡃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢰⣄⠀⣀⣀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠐⠸⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⡠⠈⠁⠋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⢠⢴⠀⠠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠼⣀⢸⠘⠀⠠⠧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠢⢀⡏⠈⠁⠀⠈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⢆⡀⠀⠁⠰⠊⠀⠀⠀⠀⠀⠘⡐⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠹⠈⣀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠛⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⣶⡽⣟⣷⡂⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠄⠀⠀⠀⠀⠁⠂

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⣶⣿⣽⣷⣿⣿⣷⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⣀⠴⠚⣫⠵⢊⡷⢣⡏⢹⡙⠫⣉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣤⠾⠋⢠⡾⠃⠀⣿⠁⠘⡗⠀⢱⡆⠉⢧⡈⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣄⡾⠁⠀⣰⡿⠀⠀⣼⠋⠀⢰⡇⠀⠐⣇⠀⠈⢳⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⢰⠏⠁⠀⣾⠏⠀⠀⢠⡏⠀⠀⢨⣟⠀⠀⣿⡆⠀⠀⣷⡄⠸⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢠⣿⠀⠀⢰⡿⠂⠀⠀⢸⡿⠀⠀⢀⣿⠀⠀⢻⡇⠀⠀⢹⡇⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⣾⠁⠀⢠⣾⡇⠀⠀⢀⣾⠇⠀⠀⢸⣿⠀⠀⠠⣧⡄⠀⢸⣇⠀⠰⣿⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡷⠀⢀⣾⣿⠀⠀⠀⢺⣿⠀⠀⠀⢀⣿⠀⠀⠀⣿⡄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⢻⠇⠀⢻⡇⠀⠀⢿⡟⠀⠀⠀⢸⣧⠀⠀⠀⢸⣏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⣿⡗⠀⠀⠀⣸⣿⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠸⣿⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⡆⠀⢠⡀⠀⢀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠦⠠⠤⠖⣀⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢈⡠⣼⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣀⡠⠖⢋⣠⣌⣀⣤⣬⡐⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠶⠞⠉⠉⠉⠋⠉⠉⢻⣼⠤⣽⣿⣇⣒⡒⠂⠠⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠉⠉⠉⠛⠛⠳⠶⠶⢾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣿⠀⢢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⢾⣿⣿⣿⣃⣾⣿⣟⠿⣿⣿⣿⡷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⡿⠿⠛⣱⡿⢣⣬⣽⣬⣿⡇⠹⣿⣟⣿⡛⣾⠻⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣭⣻⣿⡆⢳⣿⡿⢁⣾⣿⣴⣍⣯⢹⣇⢻⣿⣟⣀⠛⠻⢆⠳⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣣⣾⣿⣼⣯⠓⣿⣿⠓⠿⢙⣯⣼⣛⠟⣴⣿⠀⢹⡯⣿⢣⣾⡘⢧⡈⢿⡽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣴⣿⣾⣿⢅⡸⣿⡯⣿⡹⠿⣿⣾⢛⡇⠈⣿⡌⣧⣾⣿⡮⢷⠈⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣟⡟⣿⣿⢿⣯⢾⣶⣧⢴⣮⣷⡷⣾⢯⣇⣶⠾⠿⡛⢿⠀⢹⣿⡏⠹⢿⣷⡞⡃⠸⠷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣿⠟⢹⡾⣵⢷⣾⢟⣼⣧⣿⣾⡻⣿⠇⣤⡉⢿⠆⠘⣿⡽⣯⠲⠀⢺⣷⠐⡷⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢠⣿⣿⢛⣿⡿⣶⡭⣿⣼⢉⣸⡏⠛⡷⢿⢞⣥⠛⣨⠄⠀⣿⣿⣏⣷⡤⣶⢻⡈⢫⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣷⣾⣿⣟⣾⠋⡷⣿⠀⣯⣿⣟⣟⣶⣎⣡⣿⣾⢻⣿⣿⣀⢁⣿⣽⣿⡋⢘⠁⣿⢁⣿⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⢿⣿⣿⣯⢿⣏⣹⡆⣿⡿⠉⠉⠛⠻⠿⡟⠻⣿⣿⣿⢿⣿⣿⣿⣟⡛⣿⢿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣿⣾⣿⣿⣿⣧⣇⣽⣴⣿⡷⣶⠶⡴⠶⢶⣷⠶⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣴⣶⢿⣴⣤⢤⣦⣶⣴⡿⣿⠿⢿⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⣿⣿⣿⣿⣼⡷⣿⣿⣼⣋⣾⣿⣿⣙⣻⢿⣿⣼⣿⣿⣯⡿⠷⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣤⣿⣿⣿⣿⣆⣿⣿⣿⢿⣿⣿⠿⣹⣯⣾⣿⣿⣿⣿⣷⠻⣶⣷⣾⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣻⣟⢻⠿⣿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⢀⣀⠀⣀⡀⣀⠀⡀⣄⡈⣤⣌⢀⡀⠀⠀⢹⡇⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⣿⣆⠀⠐⠀⠀⠀⠀⣸⣠⣤⡷⠁⠀⠀⠀⠀⣴⣿⣾⡇⢣⣿⣾⣷⢶⡇⢀⡸⠄⠀⠀⠻⡄⠱⣦⠄⠀⠠
⠀⠀⠀⠤⢀⢿⡿⠻⣆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣴⢛⣾⣿⣷⣾⣷⣯⡀⠀⡀⡀⠀⠲⠀⡁⣤⡄
⠀⠀⠸⣲⣯⡟⠁⠡⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣾⠰⢟⣟⣿⣿⡿⡻⣤⡅⠀⢢⢠⡀⠉⠈⠁
⠀⠀⠀⢽⣿⣿⣽⣧⣶⣈⣃⠛⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣿⡿⣿⡾⠟⣋⣽⣯⣿⣿⣿⢀⣠⣋⠈
⠀⠀⠀⠈⢿⣿⣿⡿⣁⢸⣿⠟⢸⡿⢿⢿⣿⢿⣿⣿⣿⣿⣿⡿⡟⠭⡯⠍⠤⡭⠿⠉⠶⠑⠚⠂⠛⠀⠙⠀⡀⠋
⠀⠀⠀⠀⠀⠁⣉⣠⣃⣌⡭⡲⠶⠟⠀⠈⠀⠀⠉⠉⠉⢙⡦⠘⠁⡂⠀⠀⠄⠀⠀⠀⠴
⠀⠀⠀⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠡⠐⠀⠀⠃⠀⢀⡀⠐⡆⣤⣴⠐⡥⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⣲⠩⠂⡎⠀⠀⢄⣢⣴⣺⡱⣼⡾⠮⣶⣢⡘⣶⢀⠰⠀⡀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⠄⡄⠂⣀⣄⡌⣙⢳⠖⣢⣯⢄⣴⣬⣽⣾⣿⣴⣶⣿⣼⣇⢧⢘⠤⢀⣠⡀⣴
⠀⠀⠀⠀⠀⠀⠀⢀⢩⠄⢀⡀⠠⣰⡄⣀⢙⡂⢿⡯⣟⢿⣢⡽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣛⠱⢎⣟⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣽⣴⣶⣿⣷⡾⣿⣿⡜⣻⣗⣛⣿⡿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠝⠛⣻⣾⣿⣿⣷⣿⣿⣿⢻⣧⡿⣴⣿⣿⣽⣿⣿⣿⠿⢿⣿⣿⣿⢿⠟⡵⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣽⠋⠽⠘⣿⠀⠉⠐⠋⠁⠉⠟⠾⠟⡷⠍⠙⠉⠘⠠⠌⠋⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⣿⣻⣿⣻⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠒⠈⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡾⠓⢆
⠀⠀⠀⠀⠀⠀⠀⣤⣦⢄⠄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠠⣀⡤⠖⢲⣶⣾⡞⠁⠐⢀⠂
⠀⠀⠀⠀⠀⠀⡰⡿⡿⢋⡘⠀⠀⠄⠀⠀⠀⠀⠀⠂⢠⡔⢦⣼⡿⠿⠿
⠀⠀⠀⠀⠀⢰⠠⠙⡰⡷⠀⣀⠰⠀⠀⠁⠀⠀⢀⡰⢯⣵⣾⣿⣷⠚⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡏⣼⣳⠁⣰⢁⠄⠀⠀⠀⢀⢀⣬⢗⣟⣛⠤⠋⠉
⠀⠀⠀⠀⠀⢸⢸⣿⣿⡇⣿⠊⠁⠀⠀⠠⠘⣧⣽⣟⣻⠇⠂⠐⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣼⡇⢻⣎⣿⡟⠀⠀⡄⠲⡾⠗⠛⠋⠀⠈⠰⠊⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢣⣾⣟⣿⣟⣇⡀⠀⠸⠙⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣽⡗⣩⣍⣡⢼⠁⡠⠄⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⡏⢽⣿⣿⣯⡿⢃⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣽⣿⣅⡺⢧⣿⠇⠴⢆⢀⠀⠀⠠⠂⠓⠂⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢧⣾⣣⣞⣯⢴⣎⣠⣤⡦⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢱⠀⠀⣠⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢦⡈⢣⣼⠀⣼⣁⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡖⠊⠁⠀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⢷⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠒⠚⠉⠉⠀⠀⢳⠀⠀⠀⠁⡇
⠀⠀⢠⢤⠤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⠶⠖⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉⣟⠀⣠⣆⠀⣸⢆⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠈⠃⠀⠀⠀⢠⠀⠀⠀⡀⡇
⠀⠀⢸⢰⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠢⠼⠀⠰⠠⡀⠀⠀⠄⠀⠀⠀⢃⡇
⠀⠀⢸⡀⡄⠀⠀⠐⠀⠀⠀⠀⠀⣖⠃⠀⠀⡠⡄⠀⠀⢀⡄⠀⠀⠀⠂⡀⠀⠀⢆⡱⠀⠀⠀⠀⠀⠀⠑⠃⠀⡐⠀⠀⠀⠈⣸
⠀⠀⠀⢧⢁⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⠣⠃⠀⠀⠠⡼⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠈⡑⠆⠀⠀⠀⠀⡐⠀⠀⠀⢀⢣⠇
⠀⠀⠀⠈⣆⢆⠀⠀⠀⠱⡀⠀⠀⢎⡅⠀⠀⠀⢀⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠉⠁⠀⠀⢀⠜⠀⠀⠀⠀⢄⡏
⠀⠀⠀⠀⠘⣎⢢⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⢸⢱⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⢊⡞
⠀⠀⠀⠀⠀⠘⢦⡱⡀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠱⣌⠢⡀⠀⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⠀⠀⠀⢀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣩⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣑⡢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⣋⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠭⣭⣁⣐⠒⠂⠀⠀⠀⠒⠒⣂⣉⣩⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⢝⠛⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠐⠀⠣⣀⠸⢗⠠⠀⠀⠀⠙⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⠀⠀⠑⣌⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠳⣄
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢧
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡠⠖⠋⠱
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⡤⠖⠓⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠲⡉⠀⠈⢁⡰⠖⠃⢀⠄⠀⠀⠀⠀⠀⠀⠀⣸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠱⠂⠁⠀⠔⠊⠁⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠈⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠒⠂⠀⠉⠃⠋⠃⠀⠀⣈⣠⠔⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⠏
⠀⢹⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠈⣅⠂⡀⠈⠀⢀⢠⡐⠠⠠⠒⢁⣀⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡴⠃
⠀⠀⢳⡀⠀⠀⢸⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠑⠛⠢⠥⠴⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡥⠋
⠀⠀⠀⢳⡄⠀⠘⡌⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣂⠴⠋
⠀⠀⠀⠀⠙⣦⡀⢳⡀⠀⠀⠙⠻⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣠⠵⠊⠁
⠀⠀⠀⠀⠀⠈⠛⢮⣿⡄⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⣀⡀⠀⠀⠀⢉⣟⣷⣶⡶⠶⠶⠶⠦⠤⠶⠶⠶⠖⠒⠚⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⡖⠂⠒⠒⠐⠐⠂⠒⠆⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠉⠁⢀⣀⡤⣤⡀⢀⡤⠤⢤⣀⣀⠀⠉⠓⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠀⠀⠠⡜⠉⠉⠀⠧⠻⢰⠂⠀⠀⠡⢋⠇⢠⠤⣤⡀⠡⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⠈⢀⡖⡚⠲⣘⣆⠀⢎⡱⢷⣯⠇⠀⠂⡨⡺⡦⡀⠉⠈⠻⢦⡀⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡞⠃⠀⠑⠈⢳⣽⢺⠀⠀⢣⡞⠉⢻⡾⣱⢠⠀⠄⣊⡌⠼⢷⡄⠉⠀⡄
⠀⠀⠀⠀⠀⠀⢰⡃⠀⠐⠛⢀⠀⠁⢀⣧⣀⡻⣝⡄⢀⠘⡇⢀⡟⣰⢑⡀⠐⠩⠨⠡⢁⡩⠇⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣸⠂⠀⠈⣁⣴⢤⣦⣺⡀⠈⠙⢯⠈⣁⠠⠈⢩⡀⢷⣳⠵⠧⣵⡾⣛⠛⡒⠚⠹⣆⠈⣭⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡂⠄⠁⠑⣑⡮⢽⣷⡄⢈⠁⠀⠀⠀⠁⠂⢠⠞⠛⠐⠢⣔⣀⠐⠀⠂⣿⡀⠐⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⣀⣄⣧⣠⣤⣀⣁⠀⢀⣀⡀⠀⠘⠉⣈⢰⣶⡤⣖⣻⣀⠈⢀⡊⣼⠃⠘⠙
⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⣠⠞⠉⠉⠁⠠⠀⣡⣩⡴⢦⠑⣀⠈⢀⣌⣟⠓⠾⣛⡩⠉⡢⢙⠳⡈⡁⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠹⡇⠄⠁⠡⣵⠾⢿⠃⣀⣯⣾⠋⠐⡼⢜⠊⢳⣦⣟⢂⠕⠂⡀⠉⢸⠃⠠⣔
⠀⠀⠀⠀⠀⠀⠀⢻⢆⡁⠀⠙⠐⢪⠾⠩⠀⡂⠛⣹⡿⣟⠀⢀⣷⡸⠤⢀⠠⠹⣧⣂⡰⠈⣢⠞⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢮⢳⣆⠄⠀⠷⣌⠀⠀⠀⢠⢏⡄⡝⢗⠋⠏⡇⠀⢆⠠⠁⡸⠉⠘⠛⠁⠀⢬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⣮⣂⠠⠈⠳⠬⠐⢨⠄⠜⠐⡘⡐⠠⠿⠀⠠⠂⣠⡴⠞⠀⠀⠐⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣶⣦⣠⠀⠀⠈⠲⠶⠶⢥⡤⠤⠁⠙⠛⠛⠁⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠩⣛⡷⣤⣀⣀⣀⣂⢀⣆⣷⣠⣦⣤⣧⠶⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠉⠉⠭⠙⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⣀⢠⠇⠀⠉⠑⠢⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠙⢣⡀⠀⠀⠘⢠⡁⠙⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠡⡈⠙⢤⡀⠀⠈⢃⠀⠁⢀⡉⠍⣙⣙⢒⠖⠒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠄⢁⠘⠑⠦⢤⠤⣈⡋⠉⠐⠁⠀⠀⠀⠀⠀⠀⠠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠑⠑⠂⠒⠊⠘⠁⠉⠒⠤⢀⠀⠀⠀⡠⠔⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡻⠔⠂⠁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢅⡐⠠⠤⠤⣀⣠⠤⠤⠔⠊⣁⠴⠓⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠦⠔⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠒⠮⣉⡽⢁⠜⣰⠋⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⢞⠀⡞⠀⠉⣆⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠤⠒⠀⠉⢙⠗⢖⠋⠁⠀⠀⠀⠀⠢⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⡰⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡖⠁⠀⠀⠉⡰⠖⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⠻⣕⣲⠔⠓⠒⠉⠉⠉⠉⠉⠘⠁⠀⠀⠒⠂⠤⠤⠤⠄⠀⣀⣠⡀⠀⠀⠁⠀⡄⠀⠳⡶⠶⡏⠈⣶⠓⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢲⣼⡦⢬⣷⣀⢰⠀⢤⣀⣀⡀⠀⣀⣠⣤⣤⣤⠤⠴⣖⠈⠉⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⢠⠛⡋⠙⣏⠁⡿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢲⠤⡀⠀⠀⠉⠙⢦⡈⠁⠉⠉⠡⠉⠐⠀⠉⠉⠒⢤⣈⠁⠐⠂⠀⠀⣀⡀⠸⠊⣸⠦⣾⠓⡋⢻⡉⢹⣦⣼⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡈⠲⣄⠀⠀⠀⠈⠳⢤⡀⠠⠀⠀⠀⢀⠀⠄⠀⠈⠛⢿⡃⠀⠀⠀⣠⠖⠛⠛⠒⣿⡂⠙⠳⢾⣉⣤⣼⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠐⣄⠀⡙⢲⠤⣄⠀⠀⠑⣦⣄⣀⠀⠀⠈⡀⠀⠄⠀⠂⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⣯⠉⡤⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂⢾⡖⠓⠒⠒⢾⡀⢈⠂⠐⢈⠉⠒⢤⡈⠳⡉⠓⠦⣤⢀⡤⢤⣬⣠⣐⡠⣳⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠦⢿⠄⡟⢢⡆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⡗⠤⢄⣄⠨⠻⣷⠶⠶⠶⣛⡯⠭⠤⣼⣾⡇⠤⠤⣀⠀⠀⢀⡞⠁⠀⠈⠓⣏⣹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡊⠀⢀⠂⡁⠀⠈⢳⣄⣉⠁⠀⠈⢧⠀⡜⠁⠀⠀⠀⠀⠿⠄⠀⠀⠀⢱⣴⠟
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢧⡙⢦⣄⡀⠀⠀⠀⢀⠻⣟⠛⠳⠶⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠓⠤⣌⠳⣌⠛⢶⣀⣠⠂⢁⠈⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠤⣤⠴⠛⠁⠀⠀⠀⠙⠲⠼⣆⠀⠉⠙⠛⠶⠖⠞⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠒⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠀⠀⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⡀⠘⠃⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⣿⣿⣿⣿⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⠇⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⡿⠿⠿⠿⠛⠁
⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣄⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀
⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠘⠀⠀⡀⠀⠡⠄⠀⠀⠀⠀⠀⢸⣧⡀⠰⠤⠽⠶
⣸⣟⠀⠀⠀⡆⠀⡷⢀⡆⠀⠀⡰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢀⠀⠘⠻⠀⠈⠉⠃⠀⠀⠄⠀⠀⠀⠀⢿⢽⡅
⣼⣛⡄⠀⢸⣷⠸⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠧⠤⠄⢠⠀⡄⠀⠁⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠀⠠⣿⣎⡒
⣶⢻⡆⢀⣿⣿⡄⢀⡀⠀⠀⠀⢀⡐⢦⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠤⠄⠘⠷⢄⡃⠀⠠⢤⠀⠀⠀⠀⠀⠀⢀⣻⣿⣇⡻⠀⠀⠀⠀⣴⠆
⣾⣛⣧⠄⠉⠉⣀⣬⣤⣮⡀⢀⠉⠘⡆⠳⠄⠈⠁⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠴⠀⠉⠀⠀⠠⠄⠀⠀⠀⠀⠈⢉⣠⣤⡄⠀⠀⢹⡤
⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⢀⣠⡇⠀⠀⠀⠿⠷⠦⠤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⠶⣿⣿⣽⣭⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⢀⣀⣀⣤⠤⣿⢶⣤⣄⡀⠉⠉⠐⠂⠀⠀⠠⠀⢀⡸⠛⠛⠈⠉⠉
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣦⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠈⠛⠿⢛⣳⣦⣤⣤⣴⡶⠟⠛⠉
⠀⡆⠀⣀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⢀⠀⢀⣠⣴⣦⣴⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣈⡴⠋⠛⠛⠋⠉
⢠⣤⡴⢸⢰⠈⠀⠀⢠⠀⢓⠰⠀⠄⢀⣶⣾⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢾⣿⣷⣮⣾⠓⢞⢀⣁⣾⣞⣻⣿⠿⠿⠉⠛⠋⠋⠁
⠀⡇⠀⠚⢻⣿⣿⡛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⠤⠀⠂⠠⢄⠀⠀⠀⠀⠀⢰⠀⢨⠅⠀⢇⢃⢰⠙⡀⢇⡄⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠘⠐⠐⠀⠘⠘⠈⠈⠒⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠱⡐⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⠛⠉⠙⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⢹⠀⠀⠀⠀⠀⡠⠤⢄
⠀⠀⠀⠈⣀⡀⠀⢀⠀⠀⡜⠄⣱⣖⣆⢸⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢺⢄⠀⠀⠐⠄⡅⠀⠀⠀⢸⣺⡷⡾⠁
⠀⢀⠐⢤⣁⣥⡆⠸⠄⠘⣏⠐⢫⢩⠁⡾⢸⠁⠀⠀⠚⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⣀⠪⡒⢨⣾⡄⢳⠀⠀⠀⠒⠀⠀⠀⠈⠰⠵⠃
⠀⠀⠡⠛⠉⠉⡛⠛⠀⠀⠘⠤⣶⣤⡿⠔⠁⠀⠀⠘⠄⠄⠀⠉⠀⢠⡄⠀⠀⠀⠀⠈⡀⠑⣄⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⢀⢀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⡀⠀⠀⠉⠒⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀
⠀⠀⠀⠀⣄⠀⠀⠀⠆⢠⡄⠀⢠⠖⢉⠉⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⡀⢀⠀⠀⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⣮⢣
⠀⠀⠀⠀⠈⠑⡦⢄⡔⠀⠀⢀⣧⡞⡉⠁⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣀⡇⠀⠈⠀⠮⠀⢜⠁⣆⠀⠀⠀⠀⢠⠈⢤⣁⡸
⠀⠀⠀⠀⠀⠀⣗⠠⡈⠙⢍⠉⠙⠒⢄⠀⣹⠓⠢⢄⠉⠳⣄⡀⠀⠀⠀⠘⣯⣖⣀⣃⣀⣍⣐⣐⣂⣰⣽⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⢦⠡⡴⠚⠖⠤⡀⠚⠋⠀⠉⠒⢄⣈⠐⠂⠘⠃⠀⠀⠀⢿⣿⣹⣿⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠃⢡⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣯⣿⢻⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡜⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⢻⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠳⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡇
⠀⠀⠀⢿⡄⠀⢿⡄⠀⢰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠀⠀⣼⠇⠀⣼⠇
⠀⠀⠀⠸⣷⠀⠘⣷⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⡟⠀⢰⡿
⠀⠀⠀⠀⠹⣧⠀⠘⣷⡄⠀⠘⠿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⠟⠀⠀⣴⡟⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠹⣷⡀⠈⠻⣦⡀⠀⠀⠀⢾⠇⠀⠀⣴⡄⠀⠀⢿⠆⠀⠀⠀⣠⡾⠋⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣠⣴⠿⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠈⠙⠛⠷⠶⠶⣶⡶⠶⠶⠟⠛⠉⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣈⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣥⣬⣽⣤⣶⢦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⢿⣯⠻⡏⢣⠘⡰⣦⠿⣿⡲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⣷⣿⣏⠞⠠⠵⣿⠀⢻⠂⠘⣇⠈⠳⣌⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣯⣿⡟⠥⠂⢰⠂⢻⡄⠈⣷⡄⠠⠛⡷⠸⠈⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣾⣿⣷⢤⢿⡿⠒⢺⣿⢶⣿⠁⠀⠡⣧⡀⢦⣽⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⡅⣘⢸⡧⠀⢌⣿⠃⢠⣿⣦⠔⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡣⣾⣷⠀⣹⣯⠀⠀⠹⣿⠀⢹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡗⣿⣯⡙⢿⡧⡄⢰⣾⣧⠄⣾⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣷⣊⣿⣃⠴⣸⣿⢳⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉

⢀⠄⠀⠀⠁⠀⠐⠀⠀⡀⠀⠀⢀⣤⡄⠀⡀⠀⠀⡴⢾⡿⢿⠿⠉⠛⠓⠶⣤⠀⠀⠀⠠⠤⠀⡀⡠⠂⠉⠻⣶⡄
⣾⠀⠀⠀⢀⣀⡤⡄⢀⠈⠐⠶⠤⠀⠠⠚⠁⡰⠋⠀⡜⠁⢘⠀⠀⠀⠀⠀⠀⠑⡂⡑⠒⠀⠋⡜⠀⠀⠀⠀⢹⢿⡄
⢿⠑⠄⠀⠈⢿⣿⣷⣈⠃⠀⠀⢠⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿
⠘⣧⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡃⠀⠀⠀⢳⠀⠀⠆⠀⠀⡀⠀⠀⠀⠇⢹
⠀⠈⠳⣦⡀⠀⠀⢤⣀⣀⣀⡤⠂⢀⣻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢺⠠⢀⠀⢰⠇⣧⣤⠀⠀⠂⢘
⠀⠶⢀⠀⠉⣙⣛⣛⣛⠋⠉⠀⠀⠠⢿⠄⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣜⡌⠘⠀⢀⣴⢟⡺⠀⠀⠀⣸
⠐⠀⣥⣶⡿⢿⣿⣭⡻⠟⢶⣤⡀⠀⢾⣧⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡧⠀⠀⠀⢸⣼⡾⠆⠀⠀⠀⣽
⢠⣾⡯⠙⠅⠀⠀⠉⠛⢦⠀⠉⢳⣄⠘⢿⣄⡀⢻⣦⠀⠀⠀⠰⠀⠀⢐⡿⢀⠠⣿⠇⠀⠀⠀⠀⠰⠛⠀⠀⠀⢰⠇
⣸⣏⣿⡄⠀⠁⠀⠀⠀⠀⠙⠀⠀⢻⠀⠘⢿⣯⣘⣿⣦⡀⠀⣐⡆⠀⣸⣇⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡟
⢿⡌⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠉⠛⢿⣿⣷⣼⣿⣧⣼⣿⡿⠛⠁⠀⠀⠀⠀⠄⠀⠀⠀⠠⣴⠏
⠘⣧⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⡀⢀⠅⠀⡀⠤⠤⠤⢈⡉⢉⠉⠉⠉⠁⠀⣠⣄⡀⠀⠀⡀⠀⡀⠀⣴⠟⠁
⠀⠋⢢⠀⠀⠈⠀⠀⠀⠀⠀⡀⣇⡜⣰⠋⠀⠀⠀⠀⠀⠀⠙⠲⣄⠠⣀⠀⠉⠉⠁⢠⡼⠁⠀⠈⠉⠁⠀⠰⠾⠂⢀
⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⣀⠿⠋⢠⡷⠀⠀⠀⠀⠈⠉⠓⠦⣤⡬⣷⡈⠑⠒⠒⣂⣉⣤⠤⠤⢤⣤⣀⡑⠤⠤⠔⠋
⠀⠀⠀⠀⢀⣉⣑⣒⡚⠋⠁⠀⠀⠸⠑⠄⠀⠀⠀⠀⠀⠀⢀⠈⠙⢿⡇⢀⣴⠿⠿⠛⠀⠀⠀⠀⠀⠀⠉⠛⠦⣀
⢀⣴⠾⠛⠉⠀⠀⠀⠉⠉⠓⢦⣄⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⠇⡞⠁⠀⠀⠀⠀⢠⣶⣠⣤⣀⠀⠀⠈⠙⢷
⢋⠀⠀⠀⠀⠴⠶⣶⣶⠆⠀⠀⠈⠳⠀⠑⢦⣀⠀⠁⠒⠶⡷⣿⡿⠋⠀⠐⢄⠀⠀⠀⠈⠭⠉⠿⠽⠍⠁
⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣚⣿⣛⣛⣉⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡇⠀⣹⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣚⣉⣉⣭⣭⣤⣤⣬⡙⢦⣝⠷⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣴⠾⠿⠛⠋⣉⣭⣭⣭⣿⣿⣷⣽⣦⡟⣸⣛⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⣹⣿⣷⠾⠟⣻⣯⠁⠀⠐⢲⡞⠋⢟⢳⠼⠩⣝⣻⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣴⡾⠋⢁⣠⣤⣾⡟⠉⣠⣾⣿⣿⠃⣠⠟⢸⣇⢢⡸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣡⡶⠶⠿⠋⠀⣸⣵⣿⡿⠛⢁⣿⣾⣏⣀⣾⢻⡟⣷⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡟⣡⣿⡿⠀⠀⣠⣴⣾⡿⠋⠁⠀⢀⣿⣿⠏⢹⣿⠋⢘⡇⢸⡇⠻⣏⣷
⠀⠀⠀⠀⠀⠀⠀⣶⡿⠋⠀⢀⣴⣿⡿⠋⠀⠀⣀⣴⣿⡟⠁⠀⣾⡟⠀⣼⡇⣸⣇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣤⣿⡿⠉⠀⠀⢀⣼⣿⡏⠁⠀⠀⣴⣿⠀⠈⣿⠀⣹⡟⢠⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣐⡿⠿⠿⢿⣄⡀⣐⣿⡿⠋⠁⠀⢰⣿⣿⠁⠀⢰⣿⡄⣿⢀⣟⣟⣠⠤⠤⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠙⣿⣿⡿⠇⠀⠀⣰⣿⣿⣃⠒⠒⠛⠛⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⣼⣿⡿⠀⠀⠰⠿⣿⢣⡎⣿⠇⠀⠀⠀⠀⠘⠋⢴⠾⢦⣴⡄⢶⠴⠎⠛⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢿⣟⠃⠀⢀⣴⡾⠋⢸⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠂⠻⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⣿⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣥⣒⠤⠤⣄⣀⣀⠠⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⣀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⣾⣿⣷⣤⣿⣿⡋⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠃⠀⠀⠛⠃⠀⢰⣦⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⣿⣀⣿⣿⡟⢻⣿⣉⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣤⠀⠾⠇⠀⢠⣤⠀⢶⠆⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣷⣾⣿⡿⠻⣿⣷⣿⣿⣿⣏⣈⣿⡿⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠉⠀⠀⣤⡀⠀⠁⠀⠀⠀⠿⠂⢀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣹⣇⣸⣷⣶⡿⣿⣿⣀⣿⡿⠿⣿⡄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⠗⠘⠿⠀⠉⢁⡀⠀⠾⠇⠀⣠⡀⢛⣯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⣶⡶⠾⠏⢻⡿⠿⣿⣤⣾⣿⡿⠿⣷⠶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠉⠉⢉⣉⣠⣧⠀⣠⡀⠛⠃⠀⠀⣀⡀⢉⣅⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠻⣿⣿⠀⠀⠀⠀⠑⠖⡻⢿⢹⣏⠷⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⢰⠀⠀⣸⣿⣿⣿⣷⣋⡥⣀⠆⠀⢂⡙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢱⣿⣿⡄⠀⠀⢀⠀⡀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠹⣿⠀⢠⣬⣥⣥⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢰⠀⢹⣿⠛⠚⠛⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠈⣿⣿⣿⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡆⢸⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠐⠂⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠢⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⠀⠀⠑⠀⢤⠀⠈⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⢤⠐⡀⠀⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠈⠙⠀⠀⠀⠒⠈
⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⣆⠰⣄⠩⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠇⠀⠈⡀⠀⠀⠀⠀⠀⠀⠸⣦⢓⠀⢱⠀⠀⠀⠀⡆⠀⠀⠀⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⢀⠀⠀⠀⠀⠀⠀⠄⢒⠃⠀⠀⠀⠀⠨
⠀⠀⠀⠀⢀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⢐⢀⠐⠀⠠
⠀⠀⠀⠀⠀⠢⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠈⠀⠀⠠⡤⠄⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠐⠢⣔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢔⠠⠃⠼⠭⠝⠒⠰⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠴⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⡠⠋⠔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠻⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⠄⠀⢀⠤⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢰⠃⠁⠀⠀⠀⠀⠐⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠓⢃⠀⠀⠐⠀⠀⠀⠀⠰⢰⡀⠀⠡⢠⠀⠀⠂⠀⠀⠀⠀⠀⡅⡃
⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠐⠲⠀⢠⠁⠀⠀⠀⢸⠂⠀⠄⠈⢃⠀⠀⡀⠁⠀⠀⠀⠀⢀⠻⢛
⠀⠀⢸⠁⠀⠀⠀⠀⡦⡄⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠍⢸⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠎⠃⣈⠀⠀⠀⠀⠀⠀⡌⠀⢸
⠀⠀⠠⠄⠀⠀⠀⢠⡖⠀⠀⠀⠀⠁⡀⡟⠀⠀⠀⠀⡼⢀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⡤⠀⠚⠉⠀⠀⠀⠀⢀⢘⠀⠀⡺
⠀⠀⠀⢅⠀⠀⠀⠘⢯⠀⠀⠀⡀⠔⠛⠀⠀⠀⠀⡔⢀⡎⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⣰⠃
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠠⠀⠊⠁⠀⠀⠀⠀⠀⡂⢠⠎⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁⢖⡠⠄⢤⠄⠴⡒⠮⠁⡁⠀⠀⢀⠦⠋
⠀⠀⠀⠀⠀⠀⠉⠠⠤⢤⠀⣤⣤⡥⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⢨⢤⣄⡤⠠⠔⠐⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⡷⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠤⢄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇
⠀⠀⠀⠈⠁⠐⠒⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢞⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠠⠀⠀⠄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⢠⣿⡟⠳⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠐
⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠟⠁
⠀⠀⠀⠈⠐⠠⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⣤⠀⠀⠀⢠⠀⠀⠀⢀⣼⡧⠄⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⠞⠉⠩⡟⠀⠀⠀⢸⠄⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠑⢾⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠬⢴⠟⠁⡤⣶⠊⠀⠀⠀⠀⣸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢂⠀⠀⠀⠀⠀⠈⠋⠯⣳⠶⣶⠄
⠀⠀⠀⠀⠀⣰⡿⢁⣀⡿⠋⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳
⠀⠀⠀⠀⠀⠉⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠐
⠀⠀⠀⠙⠥⠄⢀⣀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡑⠤⡀⠀⠀⠀⠀⠀⣀⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣭⣿⣷⣭⣬⠖⠊⠁
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠥⠤⠠⠠⠤⠦⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣽⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⡄
⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⠀⠰⣤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠟⠉⢯⣧⣤⣶⣞
⠀⠀⢰⠀⣃⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠸⠀⢀⣒⡁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⣿⣆⠀⠀⠀⢨⣿⣿⡏
⠀⠀⠈⠁⠙⠺⠀⠠⠐⠓⠀⠀⢘⠁⠀⠉⠉⠙⠓⠂⠄⠄⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⢾⣿⣿⣿⣿⣷⣤⠼⢿⣽⣧
⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢿⣿⣿⣿⡿⠙⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠓⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠿⠻⠟⠁
⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠛⠀⠀⢀⣀⣀⠀⠠⠤⠴⠾⠷⠄⠀⠀⠀⠀⣀⣀
⠻⣷⡀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣾⡶⠦⠐⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿
⠀⠀⠘⠄⣠⣄⡀⠀⠀⣠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇
⠀⡄⠀⠀⠉⠻⠟⠘⠷⣷⡄⡀⣀⣶⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠶⠶⠤⠤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠁⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠚⠃⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⢴⣦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠉
⠀⠄⠀⠀⠀⠀⠀⣠⣐⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣰⢯⣖⡀⡀⠀⠀⠀⠀⣀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⢲⣿⣿⣿⣿⣿⣾⣷⠀⠀⠉⠁⠀⠀⠀⠀⠀⠐⠚⠒⠂⠀⠀⠈⠁⠉⠈⠀⠴⠤⠄

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣠⣾⣿⡟⡼⢿⠟⡿⢿⣿⣆
⠀⠀⠀⣿⣿⣿⡇⢲⣶⣶⣿⢾⣿⡟⠄
⠀⠀⠀⠘⣿⣿⣶⣈⠏⣏⠁⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠻⣿⣵⣿⣿⣟⣼⡿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠳⠾⠛⠀⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠚⣡⠞⠁⠀⣠⠀⠀⡆⠀⠙⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠄⢀⡾⠁⠀⣠⢻⢄⠀⠹⡀⠀⠰⣄⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣧⣮⢲⣿⡃⠀⠀⣿⢰⡇⠀⠀⢳⠀⠀⠘⡄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡁⠀⠀⣻⡞⠃⠀⠀⢸⡄⠀⠀⣫⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣾⡀⢸⣿⠀⣆⠀⠀⢼⡷⠀⠀⣾⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⡿⠄⢠⡼⣷⠀⢰⣭⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣧⣏⣷⣘⣿⣍⣲⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⢠⠃⣼⣿⠿⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⣀⡀⠀⠤⠶⠚⠋⠁⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡴⠃⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⢿⡇⠀⣇⣤⣀⠀⣿⡗⠀⣀⠀⣄⠀⢀⡀⠀⠀⠀⠀⢀⣀⢰⣯⠏⠀⢀⡀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡞⠘⣇⠀⡿⣿⣸⣇⣿⠀⣼⡽⠇⢺⡇⣾⡿⢹⡞⣷⢀⣿⠽⢻⣯⠀⣰⣿⢿⣾⡷⢹⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠚⠁⠉⠁⠉⠹⠄⠉⠛⠁⠈⠁⠈⠁⠈⠁⠈⠉⠉⠋⠀⠻⠟⠁⠉⠉⠈⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⣠⣶⡄
⠀⠀⠀⢀⣄⢠⡤⢴⣿⣿⠄⣴⣿⡷⠖⠚⠓⠒⠓⠾⠿⢿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⣀⠀⠀⢀⣀⢀⣤⣄⠀⠀⣀⣀⡀
⠀⠀⠀⣿⣿⣧⣄⢸⣿⣿⣷⣿⠋⠀⠈⠀⠀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠀⢉⡽⠚⠁⠀⠉⠻⣿⣿⣿⣿⣦⣀⠀⣤⣴⣦⣷⣦⣵⠍⠉
⠀⠐⠒⠛⠛⢻⣟⣳⣿⡟⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠾⡿⠿⠿⠷⠶⠶⠄⢠⠀⠀⢀⡀⢠⠈⠉⡉⠉⠉⠉⠶⠿⠿⢿⠿⠿⠿⠧⠄
⠀⠀⠀⠀⠀⠘⢻⠹⠿⣾⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠐⠐⠀⠀⠤⠖⠀⠀⠀⠀⢀⣴⣶⣀⢺⣷⣶⡀
⠀⠀⠀⠀⠠⠼⠼⠤⠀⠿⠄⠄⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡙⠿⠟⢴⢿⡄⠐
⠀⠄⠄⠒⠚⠂⠀⠀⣠⣄⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡎⠇⢀⢀⣼⠄⠇⠐⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⡠⠄⣀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢠
⡀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠟⠠⠐⠀⠠⡕⠊⠂⠀⠈⠀⠀⠈⢻⠀⠀⠀⠒⡒⢂⠒⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠃⠀⠀⠀⠀⠀⠋⠂⠤⠥⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢂⣄⠀⠀⠀⠠⠧⠀⠃⠀⠀⠀⠀⠀⠸⠯⠤⠄⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡵⠔⠶⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢼⣢⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢀⣁⣄⠀⠀⠀⠀⠚⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣀⠀⢠⣴⢹⣧⣿⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠉⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⡄⣀⣠⣿⣦⣼⣿⣿⡿⠟⠋⠁⠠⠁⠀⠀⠀⢀⠀⠀⠀⠲⠀⠀⠈⢀⠀⠚⠀⠀⠀⠘⠃
⠀⠁⠀⠀⢀⠈⠀⢀⠀⠀⠀⠀⠈⣀⠀⢠⣾⣸⣧⣿⣿⣿⣿⣿⠟⠙⠉⠀⢀⡈⠉⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⢠⣾⣿⣦⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⡀⠒⠈⠁⠀⠀⠀⠀⠀⣐⠂⠀⡄⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠸⠁⠀⠀⠉
⠀⠀⢀⠀⠀⡀⢠⢄⢠⢀⣼⣾⣿⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⢡⡟⠆⣴⣽⢸⡟⣼⣿⣿⣿⣟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡿
⠀⠈⠛⠀⠛⠋⠚⠃⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⣀
⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⣶⠶⠶⠶⠶⣶
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠳⣄⠀⠼⠁⠀⣤⠀⠀⡄⠀⢠⡄⠀⠻⠄⢀⡴⠃⠀⠀⠀⢀⡟
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠳⢦⣄⣀⡁⠀⠀⠃⠀⠀⣁⣀⡤⠖⠋⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⢤⣤⣤⣤⣭⠿⠶⠶⠤⣤⣤⣤⣤⣤⣤⡤⠴⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣄⠄⠉⠑⠂⠀⠀⠶⠀⠀⠀⢀⣀⡀⡀⠈
⠦⠀⠀⠀⠀⠠⠂⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠁⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠂⠀⠀⢺⠀⠀⠀⠀⠀⠐⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡠⡀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⢀⣢⣾⣼⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⣀⣼⣷⣼⣿⣿⡿⠋⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣶⣸⣾⣷⣿⡿⠿⠟⠉⠁⠀⢠⡀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⡄⠀⠀⢀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣦⣶⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃
⠀⠀⡄⠀⠀⡀⣠⡀⣄⣴⣿⣿⡿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⡇⠁⣭⠅⣟⢽⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠘⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣾⣿⣿⣷⣿⣶⣷⣾
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠙⠓⠢⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠋⠀⠀⠀⠀⢀⡠⠄⢋⡋⢈⣃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣴⣾⠧⠖⠋⠉⠛⠋⠉⢣⡽⢽⣿⣦⣒⣀⠠⠤⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡟⣻⣶⡿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⢿⢛⣿⠟⣬⣽⣿⣿⡈⢿⣟⣿⢿⡻⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢛⣿⢻⣶⣸⣿⣏⣼⣿⠷⣾⡏⣷⠘⣿⣧⣌⢙⢣⠺⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢻⣏⣽⡟⢨⣥⣾⢿⣿⣽⡿⡇⢻⣟⢯⣻⣦⣷⡘⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣿⡿⣟⣿⣽⣹⣆⣯⣿⣾⡗⣬⣿⡗⢿⠀⣿⣿⠻⣿⣯⠷⠸⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢾⣿⡟⣻⡿⢾⣿⢛⣿⣿⣷⡿⡿⣣⣍⢻⠂⢸⣿⣯⠚⠐⣿⠐⡗⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣸⣿⣋⣿⣟⡗⣿⣼⣠⣿⣈⢿⣟⣽⣎⣵⢂⢸⣿⣧⡾⣲⢿⠆⣵⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡾⢥⡯⢧⢻⡿⠛⠟⠻⣾⡿⢿⣻⣿⣿⣽⣿⣿⢷⣷⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣯⣏⣿⣿⣧⣤⣮⣦⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⣶⣻⣦⣠⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⣿⣷⣿⣻⣿⣿⣼⣿⣿⣯⣟⣿⣿⣿⣿⣿⣙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⡿⣿⢿⣿⣧⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉