Tagline Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣿⣷⣿⣥⣄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣶⠄⠀⠀⢀⣤⠀⠀⢰⣿⣧⡀⠸⢿⣿⣿⠛⠛⠉⠀⠀⠀⣰⣿⠋⣿⡿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠁⠀⢸⣿⡏⢰⣾⠀⢸⣿⠀⠀⣾⠟⢿⣿⣦⡿⣿⣿⠀⠀⠀⣠⡀⢠⣿⡇⢀⣿⣧⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⣾⣿⣀⣼⠏⣶⣿⠟⠋⠀⢹⣿⣦⣀⣴⡿⠁⠀⠻⠿⠟⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢿⣿⡇⢸⣿⣾⠟⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⢠⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢸⣿⠃⣤⣙⣩⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⢀⣿⡟⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠋⠀⠘⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠊⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⠂⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠻⠒⠚⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣾⣿⣿⣦⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⢛⢿⣿⣿⣿⣿⣿⡧⠀⠀⠠⠶⣧⣄⣀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣛⣿⣿⣿⣿⡿⠋⠀⠀⠀⡀⠀⠈⠙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢡⣭⣽⣿⣿⡟⠉⠀⢀⠀⡀⠺⠝⠀⠀⠰⣟⡛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⠿⢶⣿⣿⠏⣠⠀⠀⠀⢀⠸⢦⠀⣁⡀⢍⣉⣵⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⣦⣽⣿⣿⠏⢀⠃⠀⠀⢠⡈⠳⡄⣠⣍⢻⣾⣿⣿⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⠟⠋⠁⡀⠂⠀⣀⡒⠀⠻⠄⢤⣤⣹⣿⣿⣿⠟⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠁⡠⠚⠛⠛⢷⣄⠐⢶⣸⣿⣿⣿⠃⡼⠃
⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⢹⣿⠀⣀⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠡⣀⡀⠀⠀⠙⣷⣼⣿⣿⠿⠃⡼⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⡀⠈⠁⣼⢛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠉⠛⠀⠂⠛⠛⠉⢁⡴⠞
⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⣿⣿⣶⣿⣾⡧⢠⡶⣷⡄⣴⣤⠾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣸⣿⣿⡁⠀⣿⣷⣋⣴⣿⡇⢠⣿⣁⡾⢃⣀⣀⠀⢀⡶⣶
⠀⠀⠀⠀⠀⠸⣿⣷⣤⣤⣴⣾⠟⠁⠹⠷⠞⠋⠙⠉⢠⣿⣿⠟⠛⠋⣴⠟⠛⢻⡇⢸⡇⣿⠀⠀⠀⠀⠀⣀⠀⢀⣠⣤⡀⣶⣴⣶⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⠀⠀⢸⣿⠀⠀⠀⠀⢼⣷⢯⣾⠻⣷⣤⣼⢿⣄⢸⣧⠞⣡⣿⡇⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡟⠀⠀⠘⣿⣦⣄⣀⣤⣼⣯⣨⡿⣴⠟⠐⠋⠾⠟⠋⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠉⠛⠉⠉⠀⠈⠁


⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣽⣤⣦⣤⣾⣦⣼⣯⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣷⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⠁⣶⣄⠀⣠⣶⠈⢻⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⡀⢠⣤⡄⢀⡄⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⢿⣶⣿⣶⡿⠃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣷⢦⣝⣿⣫⡴⢾⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⢿⡿⢻⢤⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⢸⡟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣭⣍⣉⣛⣛⡛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⣛⣛⣛⣉⣩⡍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣭⣭⠤⠶⠶⠶⠒⠒⠒⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⢤⣭⣅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢀⠈⠐⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⣀⠔⠉⠉⢢⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠐⣲⠒⠐⡀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢳⠦⣠⢠⣦⠦⣌⠉⠢⡀⠀⠀⠀⠀⠈⢺⣢⠖⣴⠦⠀⡇⠈⣻⠆
⠀⠀⠀⠀⠀⠀⢸⠩⣇⠈⢀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⣾⠜⣴⠃⢢⢀⠀⠰⠁⠀⠀⠀⠀⠈⠊⠁⢻⠿⠿⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠚⣦⠉⠧⠿⠽⢳⡎⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⢸⠿⠿⡲⠈⠋⠡⢀⠀⠀⠀⠀⠀⠀⠰⣶⢾⢲⣦⣾⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡐⢦⣸⢠⢤⠸⣶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⢐⣒⣢⡄⠀⣀⢀⠛⠘⠃⠀⠀⠀⠀⠨⢦⡌⢸⣯⣬⣤⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⡄⢾⢦⣿⣾⣷⣪⣿⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠃⠉⠉⡩⢟⠁⠀⠀⠀⠀⠀⠀⠀⢶⠀⣬⣍⢓⠂⢀⡤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡏⢿⠛⢻⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣁⡎⣸⢣⣔⣅⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣙⡛⢛⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠉⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢰⠀⠠⢐⠈⠈⢈⠑⠀⠀⠀⠀⠀⠀⠀⠈⣹⡤⣿⣚⢬⠝⢶⠄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⣧⠀⠀⢸⡄⠀⢠⠆⠀⠀⡀⠀⠀⠀⣾⠛⢻⢺⠒⡀⣝⠖⡚⠛⣓⣿⠀⠀⠀⠀⠀⣶⠂⠏⢨⣈⡉⠀⠫⠀⢰
⠀⠀⠐⣄⡀⠰⠓⠤⡔⠉⠂⠀⢉⡑⠐⠛⢆⣠⡴⠁⠀⠀⠀⠹⣄⣸⠃⠻⠖⠃⠉⠻⠔⠗⢛⣀⠀⠀⠀⠀⠻⢲⠀⢰⣶⠠⣶⡎⣿⢸
⠀⠀⠀⠈⢄⢲⣦⡄⢨⡟⣒⣒⣘⣚⠋⠶⡖⡰⠁⠀⠀⠀⠻⣷⣴⣤⠶⠆⠀⠟⠷⠾⠞⠆⠟⠁⠀⠀⠀⠀⠨⠸⠴⠼⠛⠀⠿⠇⠿⠘
⠀⠀⠀⠀⠀⠾⡷⠾⠛⠛⠙⠙⠛⠛⠻⠿⠶⠁⠀⠀⠀⠀⠀⣄⢒⡖⠀⢀⡀⢉⣉⣉⣍⡉⠉⣽⠄⠀⠀⠀⢠⢀⡌⢀⣨⣁⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣿⣯⣽⣯⣭⣿⣶⣷⡶⠾⠆⠀⠀⠀⢻⢀⣽⣿⣞⣉⣾⡗⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠁⠀⠋⠁

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠀⠀⠁⠀⠀⠀⠀⢀⠠⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠈⠁⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⢀⣤⢦⣄⠀⢀⣀⣀⠀⠈⢀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣼⠏⠉⠹⣷⠀⣼⡇⠀⣿⡄⢸⡟⠛⢿⣦⠀⠈⠀⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠
⠀⠐⠂⠀⠀⠀⠀⠀⣠⡾⠛⢻⡇⢠⣿⠀⠀⢠⣿⠀⣿⠁⠀⣿⠃⢸⣇⠀⠀⣿⠀⠀⠈⠀⠀⠀⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⣰⡟⠀⣀⣀⡀⢸⣿⠀⠀⢸⡏⠀⣿⣇⣠⡿⠀⠘⠿⠿⠟⠛⠀⠀⠈⢄⠀⠀⠀⠀⡀⠃⠀⠀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠟⠻⣿⢸⣿⠀⠀⣾⠇⠀⣘⡛⢋⡿⢷⠀⣰⡟⠉⢳⠀⣶⠶⣤⡀⠀⠂⠉⠉⠉⠀⠈⠁⠈⠛⢀⡤⢦⡀⠀⠀⠆⠀⠰
⠀⠀⠐⠛⠂⠀⠀⣿⠈⠋⠀⢸⡟⠀⠿⠷⠾⠋⢠⡟⠁⢹⡏⠀⣿⢀⣿⠀⠀⢸⠀⡇⠀⣸⠇⢸⣇⡴⢿⡆⢘⠀⣦⡾⣷⢸⠁⠀⠃⠀⠀⠀⠀⠠⠁
⠀⠀⠭⠭⠿⠀⠀⣿⠀⠀⣠⡿⠁⠀⠀⠀⣀⠀⠸⡇⠀⢸⡇⠀⣿⠀⣿⠀⠀⣸⠀⣿⣾⡁⠀⢸⡿⠀⢸⡇⢸⠀⣿⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠻⣶⡾⠋⠀⣠⣤⠀⠀⠉⠀⠀⢃⣀⣈⣁⣀⠈⠃⢙⠷⠶⠃⣴⠇⠈⣷⠀⠈⣇⠀⢸⡇⢸⠀⣿⠀⣿⢸⠀⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠉⠀⢠⠴⠒⠉⠩⠁⠀⠀⣉⡇⠀⡞⢧⠀⠀⣶⠒⠤⣬⣒⠀⠷⠀⢸⡇⢸⠀⣿⠀⣿⢸⡄⠀⣇
⠀⠀⠤⠦⠠⠤⢈⠄⠀⢀⣠⠴⠚⢋⡇⠸⠤⠖⢲⠀⢰⡏⠉⠉⠀⣸⠑⠘⡆⠀⣿⠈⡶⢦⡈⢳⢠⠤⣌⣣⠸⠀⣿⠀⢿⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠂⢀⡴⠋⣠⠴⣚⣉⡀⠀⠀⠀⢸⠀⢸⡇⠀⠀⢰⠃⢻⠀⢣⠀⢿⢀⠳⠞⠋⡸⠻⢤⡀⠨⠙⠶⣄⠀⢸⡜⣇⢀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠉⣉⡉⠀⢈⠹⡄⠀⢸⠀⠘⡇⠀⢀⡏⠐⠾⢂⢸⡄⣿⠈⠀⡘⢯⡀⠀⠀⡇⠀⣴⠦⢞⣠⠤⠿⣜⠛⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠉⠉⡷⠠⢀⡇⠀⢸⠀⠀⡇⠀⣸⠀⣰⠳⡄⠈⡇⣿⠀⢰⣌⠂⢳⠀⠀⡏⠀⡟⠀⢺⡀⢰⡖⢮⡑⣄⠐⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⠴⠋⢀⡠⠞⠀⠀⠸⠶⠚⠁⠀⡙⠛⠃⠀⠉⠉⠁⠙⠓⠛⠈⠳⠼⠇⠰⣇⣰⡇⢠⣖⣯⣻⠝⠒⢝⠁⠀⠀⠀⠀⡄
⠀⠀⠠⢄⠀⠀⠀⢠⠞⠉⣀⡤⠖⠋⠀⠀⠀⠀⠐⠢⠀⣰⠋⠀⠀⠀⠰⡄⠀⣌⠀⣠⣇⠀⠀⢰⣀⡀⠀⢀⡀⠀⠉⠛⠧⣤⣤⠴⠃⠀⠀⠀⠈
⠀⠀⠒⠀⠀⠘⠀⠸⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠦⠴⢿⣄⣴⠇⢰⠏⠈⢹⠉⠁⠀⢸⠏⢹⡄⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠻⡆⠀⠀⢀⣴⠖⠒⢦⡀⠀⠀⠀⣀⣀⠈⠓⠀⠈⠳⠶⠂⠛⠀⠈⠃⠀⠀⠀⢀⣴⠖⢦⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⢸⡇⠀⢀⣾⠋⠈⠃⠀⢠⣴⠶⡄⠀⠀⣀⡴⠶⣄⠀⢠⣿⠃⢀⡞⠀⢀⠠
⠀⢀⠀⠀⠀⠀⠓⠀⣿⡇⠀⠀⠀⢀⣠⠞⣿⡇⠀⠀⢀⡞⠠⠚⣿⠟⠢⣄⠀⢀⣿⠃⠀⠀⠀⣼⠏⠀⢀⡟⠀⣾⠃⡠⠊⠀⠀⠀⠀⠠⠀⠁
⠀⠈⠆⠀⠀⠀⠀⠀⢿⣆⣠⣤⠶⠋⠁⠀⠻⣧⣤⠴⠋⠀⠀⣼⡟⠀⠀⠈⠙⣿⠗⠚⠁⣀⣼⡿⠴⠚⠉⠀⣰⣿⠋⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⢃⡀
⠀⠀⠀⠠⠀⠀⠈⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠛⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⣿⡀⢀⣀⡤⠚⠉⠻⠶⠶⠞⠋
⠀⠀⠀⡀⠀⠤⠖⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢀⠀⠀⠉⠈⠀⠐⠀⠀⠀⠀⠀⠃⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⢀⠈⠀⠀⢀⣀⡠⠄⠀⠀⡀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⡘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢿⣿⣻⣿⣻⣿⣻⣿⣻⣿⣻⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⣿⣽⡿⠞⠛⠉⠉⠉⢉⡀⠉⠉⠉⠙⠛⠾⣿⣽⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢠⣶⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣰⣿⣿⢿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⣉⣨⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⢿⡿⠃⠀⠀⠀⠀⠀⢰⣾⣿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣧
⠀⠀⠀⣸⣿⣿⣻⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣧
⠀⠀⢠⣿⣿⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢠⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⡆
⠀⠀⣸⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣿⣧
⠀⠀⣿⣿⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿
⠀⠀⣿⣿⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿
⠀⠀⢹⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⠛⠛⠻⢿⣿⣿⣷⣿⡞⠀⠄⠀⣿⣻⣿⡟
⠀⠀⠘⣿⣿⣟⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢔⠠⠀⠉⢉⠀⠀⠀⣸⣟⣿⣿⠇
⠀⠀⠀⢻⣿⣿⣻⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⡀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣶⢣⣿⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣽⣧⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣽⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣽⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⢟⣼⣿⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣳⣯⡻⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⣿⣿⠿⣫⣶⣻⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⢷⣮⣝⣛⡿⠿⣿⣿⣿⣷⠄⠀⣀⣠⣭⣶⢿⣯⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣾⣿⣽⣿⣻⣿⣻⣿⣻⣿⣹⣿⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⠀⠘⡇⠀⠀⡶⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠈⠳⠀⠘⠀⠀⠓⠀⠀⡇⠀⡆⠀⡏⠀⡔⠀⣰⠃⠀⢀⡄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⣴⣶⣶⣶⣶⣦⣤⣤⣀⣁⠈⠁⠘⠃⠰⠃⡴⣠⠏⢀⡞⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠁⠰⠋⠴⠋⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠦⠤⠀⠘⢛⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠀⠀⣾⠿⠛⢻⣶⠶⠮⣭⣝⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⢠⠏⠀⠀⠸⠁⠀⠀⢻⠁⠉⠙⠛⠳⠶⣭⣽⣛⡿⠿⣿⣿⣿⣷⠀⠐⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⡀⠀⠀⡘⠀⢠⣴⠆⢀⡄⠀⡇⠀⠀⡰⠀⠀⢀⠂⠈⠉⡛⠻⠶⣬⡍⠃⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡇⠀⣾⣿⠀⣼⠃⣰⠀⠀⢿⠇⠀⣴⡎⠀⠀⢠⠃⠀⠀⡸⠀⠀⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠀⠀⢸⡇⠀⠉⣿⡀⠀⣰⡏⠀⣴⡞⠀⣀⣽⠁⠀⢻⡏⠀⣀⣰⠃⠀⠀⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠶⠶⠄⠀⠀⣾⣿⡶⠀⠁⢻⣿⡿⠉⠙⣿⡧⠤⣿⡇⠀⠶⡾⠀⠀⢹⠇⠀⠀⠛⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⢠⣿⠏⠠⣾⠀⢸⣿⠇⠀⠀⢿⠇⢰⣿⠁⠀⢴⠃⠀⢷⡟⠀⠀⠓⠶⢤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢴⣶⣤⠀⢸⡿⠀⣿⠀⠘⠀⣿⠇⢀⣶⣆⠑⣄⡼⠁⠀⠰⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠉⠀⢠⡏⠀⠀⠈⣿⠀⣼⡇⣸⣿⡆⠀⣸⡿⠀⣼⣿⠟⠀⣼⠃⠀⠠⣄⣀⠀⠉⠓⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠴⠶⠖⠀⠀⣸⠀⣸⡇⢠⡇⠀⣿⠋⢹⡟⠳⣤⠿⣧⣤⡤⠠⣶⣿⠇⠀⠀⢤⣀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡇⢠⣿⡀⡼⠀⣸⡇⠀⡿⠀⣸⠇⢠⣿⣿⠁⣰⣿⡏⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼⣿⣿⠇⠀⠙⠀⣸⠃⢠⡏⠀⣾⣿⠇⢠⣿⡟⠐⠀⠰⢤⡄⠈⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠀⠀⣸⠀⣿⢿⡿⠀⠀⠀⢠⡟⠀⣾⠀⣸⣿⡟⠀⣾⡿⠁⠀⠰⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠖⠂⠀⠀⣿⠀⠃⢠⠇⢠⡆⠀⣼⠁⢸⠇⢠⣿⣿⠁⣸⣿⠁⠀⠲⢤⣀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⢻⡀⢀⣾⠀⣾⠃⢰⡏⢀⡿⠀⣼⣿⡏⢠⣿⠃⠀⠐⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠙⠻⠷⣤⣿⣀⣾⠀⣸⠃⠀⠉⡽⠀⢈⠁⠀⠤⢤⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⠞⠁⢠⠇⣰⠀⡌⠉⠙⠛⠿⠶⢤⣴⣥⠴⠋⠀⠐⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⢀⡇⠀⡿⠀⣶⠀⣤⢠⠀⠀⣄⠀⠙⠲
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⢻⠀⠛⠘⡇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢸⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣿⣿⡇⠀⠛⣹⠃⠀⠀⣼⣿⡿⠃⠀⢠⣆⠀⠀⠀⠀⠈⢀⠀⠁⣀⠀⠐⢄⠀⠀⠀⠀⠈⣨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠃⠀⠀⠀⠈⠿⠃⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠳⠀⠀⠀⠀⠁⠂⠼⠇
⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⢐⡀
⠈⠁⠀⠉⠀⠀⠐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⡄⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠃⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢀⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣧⠸⣿⣷
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠄⠀⠀⠀⠍⡟⢀⣼⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢻⣿⡆⠹⣿
⡆⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠼⠛⠿⠃⠀⢀⠀⠀⠀⠀⠀⢀⣿⢅⡅⢠⣤⠘⣿⣷⠀⢿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢈⠆⠀⠀⣈⡓⢦⡀⠀⠀⠘⠛⢸⡇⠸⠏⠀⠹⣿⣿⣿
⣿⣇⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⣥⠈⠀⠀⠈⠁⠉⠢⡉⠀⠀⢠⠆⢸⢿⡆⠀⠀⠀⢿⣿⣿
⣿⡿⡄⠀⣾⠀⠀⠀⣄⢠⡆⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡄⢀⠏⠀⠀⠀⠀⠀⠂⠤⠁⠀⢀⣦⠀⢿⣾⡇⠀⠀⠀⠸⣿⣿
⠸⣾⣧⡀⢯⠀⠀⠀⠈⠋⠀⠀⠈⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠻⠀⠀⠀⠀⠀⢻⣿
⠃⠙⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢰⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⡀⢁
⣠⣿⣿⠏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠿⢋⣼⣷⡈⠁
⣿⣿⡿⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡜⠃⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⣰
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡤⠀⠀⠀⢸⣿⣿⡿⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⢹⣯⢿⠇⠀⠀⠀⠀⣴⣿
⣿⣯⠀⠀⠀⠲⠋⠀⠠⠶⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⣾⣿⣿⠃⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣶⠀⠀⠀⢾⣿⡟⠁⠀⣼⣇⣼⣿⡏⠀⠀⠀⠀⢴⠿⣿
⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢠⣾⣿⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠟⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠸⠆⣴⣿
⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢁⠂⠐⣉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⡇⠀⠀⢠⣤⠀⠀⣠⣼
⣿⡇⠘⠃⠀⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⡞⠠⠰⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⣴⡿⠁⠀⠀⠻⣿
⠍⠑⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⡼⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡴⣀⣀⡀⠀⡀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⣾⣿⡿⣸⣟⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⢀⠐⠁⠀⠀⢀⡀⣀⠀⠀⠀⠐⢄⠀⠀⠠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣿⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣷⣁⣀⣀⣘⣄⣈⣠⣀⣀⣀⣄⣀⣀⣤⣀⣀⣀⣀⣺⣿⣇⣀⣀⣀⣀⣠
⣿⣿⡟⠛⠿⠛⠻⠻⣟⠟⣿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠣⡀⠈⢢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢌⠂⣀⡸⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⣀⡸⠈⢃
⠀⠑⠦⢀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⢀⣠⠚⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡈⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡈⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠁⢀⠜⡢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠐⠊⢀⠜⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠋⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠰⠉⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠮⡔⠋⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡔⠉⢀⠜⡡⠊
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠑⢲⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢒⡡⠊
⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⢉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡔⢉⢇
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢
⠠⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢌⠲⣀⠙⠦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢌⠲⡄
⡀⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡄⠙⠆⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌
⢌⠲⣀⡸⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣀⠸⠉⢃
⠀⠑⠧⢀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⢀⣠⠚⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡘⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡘⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠃⢀⠜⡢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠃⢀⠜⡢⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡔⠃⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠉⢠⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠮⡔⠊⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⡤⠃⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠑⢲⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢲⡡⠊
⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢉⢇
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠤
⢠⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀⠈⢢⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯⣳⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⡿⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢠⠏⢠⠞
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡰⠁
⢠⠞⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠉⠳⣤⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⡴⠃⠀⣀⠞
⢸⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠉⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢸⢉⡄⢸⡾⠁⠀⣰⠋
⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⢀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⢤⢼⠟⣷⠋⠀⢠⡞⣁⡞
⢸⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡙⡛⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡁⢸⡾⠁⠀⣴⢏⠞⠕
⢸⡇⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠤⠤⠤⣤⠏⠀⢀⣼⠁⠘⠃
⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡶⠃⠀⢠⠟⠽
⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⢻⠀⢀
⢸⡇⢸⣿⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⡃⠀⢀⠞⢀⣿⠀⠈
⢸⡇⢈⢻⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣠⠊⠀⢈⣁⠀⣤
⢸⡇⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣠⠞⠁⠀⠀⢿⣨⠀⣿
⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠁⠀⠀⠀⠀⢼⡏⠀⠉
⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿
⢸⡇⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿
⠀⡇⠀⠻⡦⠀⠀⠠⠤⠤⠴⠦⠰⠶⠖⠒⠲⠒⠒⠒⠒⣾⡴⠒⠂⠐⠶⠂⠀⠰⠦⠀⠤⠤⠤⠤⠤⠤⠤⠾⠇⠀⡃
⠀⠙⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠁⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠐

⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢹⡀⡄⢀⠂⠀⠂⠢⠀⠀⠀⠀⠀⠀⠺⣄⣤⠤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠦⠆
⠀⠀⠀⠀⠀⣞⠛⡗⣗⡠⡕⣒⠛⡳⡇⠀⠀⠀⠀⣤⠘⠋⣘⣋⠑⠌⢀⠀⠀⠀⠀⠀⠀⡦⠴⠶⠷⡦⠄
⠀⠀⠀⠀⢀⡘⠤⠇⡈⠋⣁⣈⣒⡉⣩⠄⠀⠀⠀⠙⢲⢰⣷⢰⣶⢹⠉⠀⠀⠀⠀⠀⢀⢄⣐⣂⣛⢠⢤
⠀⠀⠀⠀⠈⡛⢛⠋⠉⠀⠍⠍⠅⠅⠭⣄⠀⠀⠀⠀⢈⠉⠠⠄⠉⠈⠀⠀⠀⠀⠀⠀⠘⠀⠉⠼⠀⠂⠉
⠀⠀⠀⠀⠀⢻⣘⣣⣶⣒⣞⣾⣯⣷⣤⣧⠀⠀⠀⢰⢘⣶⣌⣋⣴⠀⣤⠀⠀⠀⠀⠀⣄⢀⣓⠚⣚⠀⠀⣠
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠛⠋⠀⠙⠙⠛
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠣⠼⠘⠆⠇⠀⠀⠀⠀⠀⠀⠀⠘⠟⢳⠟⠿⠾⠀⠀⠀⠀⠀⠀⢀⡖⠊⡉⣡⣐⡄
⠀⠀⠀⠀⣰⣿⠀⣴⢄⠉⢁⡤⠷⣷⡄⠀⠀⠀⠈⠁⡏⣠⣠⣄⣀⡆⠀⠀⠀⠀⠀⣀⣋⠁⣁⠉⠉⠉⡀
⠀⠀⠀⠀⢻⣷⠈⢷⡺⠜⢋⠣⠰⡿⠇⠀⠀⠀⠀⠀⠉⠑⠛⠧⠴⠀⠀⠀⠀⠀⠀⠀⠒⣶⢒⢒⠶
⠀⠀⠀⠀⠀⠉⠀⡟⢃⣰⢩⡀⠀⠀⠀⠀⠀⠰⠆⠎⣡⡖⡇⣰⡀⣏⢐⠂⠀⠀⠀⢠⡌⢙⠛⡈⢠⠄
⠀⠀⠀⠀⠀⠀⠠⠑⠚⠿⠛⠋⠔⠀⠀⠀⠀⠀⠀⢌⠡⠁⠁⠒⢂⡷⠀⠀⠀⠀⠀⠈⡟⠺⠎⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠔⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢸⡀⠸⠞⡆⠀⣿⠁⠠
⣀⠀⠀⠀⠀⠀⠀⣿⡙⣷⣾⣔⠰⣀⣀⡤⠤⢤⡶⠀⠀⠀⠀⠀⠀⠀⠠⠘⠷⠖⡂⢘⡀⠻⠀⠈
⠘⣿⡙⠲⣗⡢⠿⡭⣬⣥⠤⠤⠒⠉⣿⠁⠐⡿⠓⠀⠀⠀⠀⢰⣿⣇⢀⢠⢤⠀⠁⠉⠃⣀⣐⣿⣾⣦⡄
⠉⠻⣯⡀⣇⡽⠾⡴⣤⡴⠶⢶⡖⣛⣿⡤⠞⠁⠀⠀⠀⠀⠀⣻⣿⡃⠀⡿⡉⣴⡆⣶⣪⣿⠁⠈⣻⣿⠇
⠀⠀⠈⠙⠛⠉⡷⣶⣶⡖⢲⡮⠽⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠀⢑⣯⡙⠊⠝⢱⠘⠒⠈⢿⠟⠁
⠀⠀⣠⡄⣶⠒⠰⣤⢠⡖⢠⢠⢰⡂⣯⡈⠧⣄⠳⠁⠀⠀⠀⠀⠈⠁⠀⢸⠜⠅⠀⡼⢉⡀
⠀⠀⠈⠁⣏⡀⠰⠻⡜⣧⠼⣦⠀⣼⠻⡴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⣺⣇⣯⣏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠉⠉⠙⠇⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⡠⠄⢨⣯⢰⣄⡆⡂
⠀⠀⠀⠀⠀⠀⠑⠒⡘⠉⡉⠈⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⢻⠁⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⢸⡯⣉⣿⢩⠭⠉⢩⣭⣏⣹⣁⣤⣸⣁⣀⣼⢗⠰⠶
⠀⠀⠀⠀⠙⢣⡄⣀⡀⡉⡅⡐⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⡤⠈⠀⠀⡀⠀⠀⠀⣤⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠂⠁⡤⠒⢠⡀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣀⢳⣀⣤⠈⡏⢠⡖⢀⡯⡄⢀⠁⢸⡇
⠀⠀⠀⠀⠀⢰⢰⣼⣇⣭⣻⢡⣖⣿⣤⠀⠀⠀⠀⠀⠀⢸⡇⠳⠋⠚⠛⢊⣌⣨⡍⡩⡅⠃⠓⣁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠋⢙⣉⡥⡅⡴⡆⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠑⠌⠿⠘⠙⠧⠶⠥⠴⠐⠇⠀⢸⡇
⠀⠀⠀⠀⠀⢀⠈⢻⠸⠷⠧⢟⣡⣦⣆⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠹⠲⡶⡶⢶⠶⠞⠛
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡟⣆⡠⣤⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡩⢄⡏⣣⣊⣑⢊⠃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⡀⠑⣞⢁⣉⠉⠉⠛⣡⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⢸⣧⡾⢦⠀⠀⡴⣤⣒⡯⢆⣐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠃⢀⠘⣘⠛⣠⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢿⠸⣇⢸⣶⡶⡡⠾⡕⠾⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡗⢻⢸⡋⠀⠳⣄⠸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠉⠈⠪⠶⣉⠀⢀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠨⢟⣁⣈⣬⣷⣥⣴⣯⣤⡱⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠀⡴⢢⣠⠀⡀⣾⠁⠇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⣾⣶⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⡄⣾⠉⣸⣿⣠⡇⢻⡾⣾⢹⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⢉⣿⣁⠘⠁⢉⠨⠽⡅⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢛⣿⡿⠿⠿⢿⠛⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⢠⢠⡀⢀⡤⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆⢠⠂⠘⠶⠴⠾⠿⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡆⣇⠀⢸⡎⣧⠄⣿⠂⠀⣾⣇⡤⢲⠆⠀⠀⠀⠀⢯⡴⠀⣷⢸⡤⢀⣀⡀⢿⣄⠀⡠⣇
⠀⠀⠀⠀⠀⠐⠭⣉⣹⣾⣇⠻⠐⠊⠃⠘⡁⠙⠂⣠⣿⣟⠭⣁⠀⠀⠀⠀⠀⠀⢠⡌⣹⢻⣁⣿⠼⣥⠞⣏⣸⣤⣿⡀
⠀⠀⠀⠀⠀⠀⢠⡎⠔⣫⡥⢤⡀⠀⠉⠉⠁⣤⡤⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⢤⡿⣋⠀⣍⢠⣤⣴⣦⠨⠄⠈⣽⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⠘⠉⣱⡴⣿⡾⡞⢦⡠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈⢨⣍⣬⡀⣤⡀⣤⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⣾⠀⢉⣻⠆⢐⡖⠁⢰⣶⡯⢃⣤⣄⣠⠀⠀⠀⠀⠀⢀⣀⣉⣘⣥⣿⣵⣯⣧⣼⣬⣁⣀
⠀⠀⠀⠀⠀⠀⢴⣾⣿⣷⣄⡙⡏⢁⣤⣿⠰⣟⣀⣩⣿⣿⣿⠿⠛⠀⠀⠀⢀⣠⣼⣿⢿⡯⣿⢿⣿⣿⣿⣿⡿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⣏⣻⠿⢷⡶⢤⣤⡶⠟⣿⣥⠋⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣄⣴⣿⠶⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠃⠀⠢⠐⠐⠙⠃⠊⠈⠘⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠰⠒⠐⣀⠀⠀⠸⠃⠀⣠⠒⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠎⠀⢀⠞⡁⢀⠄⠀⠀⠀⣤⢐⠐⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⡌⢀⣤⡈⠀⠀⠁⢀⢰⠃⠀⡟⡜⠉⠀⠀⠀⠀⠐⢄⠂⠀⠀⠄⠠⠚⠁⠒⠂⠀⠈⠒⠚⠁⠀⠀⡠⠀⢀⡠⠄⠐⠂⠀⠁⢨⠀⡀⠀⠀⡄⠐⠀⠤
⠀⠀⢱⠘⠂⠻⠄⢄⢀⡜⠈⣇⢀⠇⢧⣀⡞⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠐⠒⣨⡉⠀⠀⠐⠀⠒⠀⠁⠀⠀⠁⠀⡀⡀⠀⠀⠀⠸⠀⠇⠠⠐⠁⠀⠀⠀⠠⠀⢀
⠀⠀⠈⠀⠀⢀⢤⡀⠁⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣉⣤⡀⠀⣺⠀⡄⠀⣄⠑⠂⢀
⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠊⠀⠠⠀⠠⠀⠠⠁⠀⠀⠀⠀⠀⠀⠄⠕⣀⠀⠠⠀⠀⠀⢀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢾⠁⠄⢹⠸⡇⠀⠊⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠰⡄⠇⠀⠂⠰⠀⡠⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠅⠼⠁⠎⠜⠣⠟⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⢠⡆⠀⢸⠀⡀⣸⠀⠈⠀⢡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡀⠀⡠⠀⡔⠁⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⡴⢀⢀⡄⢀⡤⢄⠀⠀⠀⢀⠀⠀⠀⠀⢰⠰⡼⠠⠴⠃⠀⠐⠁⠀⣀⢀⣸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠚⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢠⣤⠞⠐⡏⠊⣧⢾⠀⡀⡀⡈⠐⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠄⠂⠀⠀⠀⠈⠉⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⡄⢜⠫⠴⠃⢆⣼⠘⠦⠴⠓⡁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠥⠄⡂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠁⠀⠀⠂
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠽⢷⣷⡹⣶⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣉⣽⣦⣀⡀⠈⠙⠻⢷⣶⡄⠀⠳⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠄⠀⠉⠠⣾⠛⠛⠻⢿⡀⣀⠀⠀⠀⠀⠉⠳⢤⡈⠂⡀
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⣀⣼⣯⡀⠀⠀⠀⠀⠛⢿⣶⣰⢄⡄⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠂⠀⠀⠀⠀⠀⠙⠿⣿⠦⢥⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⠇⠀⠀⠀⣲⣤⣄⠀⠀⠀⠈⠑⠶⢽⣷⣦⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣴⢶⡀⢀⠋⠻⢷⣦⣰⡠⠀⠀⠀⠘⡿⢿⡷⠖⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣼⡆⡴⣶⣶⠀⠈⠈⠻⣾⣧⣄⣼⠀⣙⣿⣷⣶⣶⣬⣥⣀⣿⣦⡀
⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⣽⣻⡿⣦⣤⢘⠉⢻⢿⢿⣿⣾⣿⣿⠿⠛⠛⠋⠁⠀⠈⠻⢦⣀
⠀⠀⠸⠿⠿⢿⢟⣿⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀
⠀⠀⠀⠈⠉⠉⠁⠉⠀⠉⠛⠻⠿⠿⠻⠿⠿⠿⠟⠿⠓

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⠸⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣌⠣⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠂⢑⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⣦⡀⠸⢷⡄⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⠘⢿⣦⡀⠠⡀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠢⣄⠀⠀⠀⠈⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣹⣷⣄⠙⢷⣦⡄⣀⣀⡀⠹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢻⣸⣿⣷⡀⠙⢿⣿⣿⣧⠀⠀⢣⡀
⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿⣦⡀⠹⣿⣮⢷⠀⠀⢳⡀
⠀⠀⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢢⡆⠉⢐⣸⢿⣷⣿⡖⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⣶⣬⣳⣤⡀⠀⠀⢀⢀⣀⠀⣀⡀⠀⣀⣀⣀⣐⣘⣉⣠⣉⡻⠦⠀⢏⠀⠀⢙⣿⣿⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣿⣿⠿⠿⣿⡿⠿⢿⣿⣛⣿⣿⣷⣶⡾⠷⠿⣜⢿⣇⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢠⣤⣐⢷⡶⢛⣫⡵⠟⠉⠁⠙⠛⠛⠻⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠭⠟⠦⣤⠞⠳⣌⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣽⠟⣉⣥⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣀⠈⠳⢾⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁




⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢡⡠⠤⣀⣠⠄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠⠲⢀⡄⢒
⠀⠀⠀⠀⠀⠘⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣚⣒⣀⠀⠀⠈⠑⡄⢸⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠒⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⣤⣴⣦⣤
⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠚⠛⠓⠒⠻⠿⠀⠀⠀⠳⠄⠀⠲
⠀⠀⠀⠀⠀⠐⠰⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⡀⣀⡀⠀⠀⠀⠀⠠⠀⠤⠤⠂⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⠂⠀⠀⡄⡀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠐⠂⠐⠠⠀⠀⠀⠀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠒⠃⠋⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠈⠛⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⢘⡆⠀⡀⠀⠀⣚⠄⠀⠀⠀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⢈⣀⣁⣀⡀⠀⠀⠀⠀⠀⠽⠁⠀⡇⠀⠀⢼⠄⠀⠤⢤⠄⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⡀⣰⣷⢠⣦⢰⣿⠀⠀⢀⡶⣳⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠀⠀⣾⣿⣷⢿⣿⠈⠿⢾⣿⠤⠄⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⡏⢹⡿⢸⣿⢠⡞⢹⠏⠀⠀⠀⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢶⣦⠀⠀⠀⠀⠀⠈⠉⠁⢾⣠⣿⣀⡠⠤⠴⠒⠒⠒⣾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣴⡆⣠⢛⣶⠀⣠⣶⠀⣴⢦⣶⠀⣿⠃⢠⣶⡄⢠⡤⡀⣸⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠯⢞⣿⠏⠁⣾⠏⢀⣿⢋⣼⣯⣾⡏⢸⡏⣠⣿⢋⣠⢻⣷⠊⣿⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡟⠀⠀⠛⠒⠉⠉⠁⠀⠀⢿⡠⠋⠉⠁⠈⠉⢰⢉⣿⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢪⡾⢻⠀⣰⡟⡇⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠇⢠⣿⡰⢡⡤⠀⣴⠶⢸⣿⠉⣠⡍⣤⢀⣄⠀⣤⠦⣾⡆⣴⠲
⠀⠀⠀⠀⠀⠀⠀⠦⢴⣿⢥⣄⣼⡟⢁⣿⠟⡠⣿⡆⠈⣿⡖⣿⢠⣿⢻⡿⢸⣏⢜⣿⢋⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠼⣿⠈⠓⠋⠙⠊⣴⢹⠇⡼⢻⡇⠙⠁⠉⢸⡧⢃⡔⢹⡏⠸⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⣀⠀⠀⢀⠀⢈⠁⠀⠳⠛⠀⠀⠀⠀⠀⢀⢘⣒⣋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⢠⡟⠙⡇⣰⠟⡇⣿⠀⠀⣿⠀⠀⠀⣿⣆⢰⣿⢸⡏⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠠⠴⠒⢂⢸⡇⠀⣄⣿⢶⡇⣿⠀⠀⣿⠀⠀⠀⣿⠻⠟⣿⢸⡗⠒⠀⢐⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠈⠷⡾⠋⠿⠀⠇⠿⠤⠄⠿⠤⠄⠀⠿⠀⠀⠿⠸⠷⠶⠄⠈⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⡀⠀⠀⢴⡞⠲⡄⢠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣷⢾⣧⢨⣿⠂⡶⢺⣿⢟⣿⡔⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡏⣾⡇⡼⣟⣠⠃⢸⡿⢸⣿⢰⡿⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢿⡼⠁⠈⠀⠀⠀⠀⠀⠀⠘⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⢰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⡇
⠀⠀⢸⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⣀⣤⣤⣄⠀⠀⣤⣤⣤⣄⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⠉⢻⣿⡀⢰⣿⠏⠙⣿⣧⠀⣿⡏⠙⣿⡇⢸⣿⠉⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠘⣿⡇⣿⣿⠀⠀⢸⣿⡀⣿⣷⣴⣿⠇⢸⣿⣷⣶⠀⠀⣄⡀⠀⢸⣷
⠀⠀⢸⡇⠀⣀⣶⠀⣿⣿⠀⢸⣿⠇⢻⣿⠀⠀⣼⣿⠀⣿⡟⠉⠁⠀⢸⣿⠀⠀⠀⠀⡟⠛⠀⢸⣿
⠀⠀⢸⡇⠀⠉⠃⠀⢿⣿⣶⡿⠏⠀⠈⠿⣷⣾⡿⠃⠀⣿⡿⠀⠀⠀⢸⣿⣶⣶⡶⠀⠁⠀⠀⢸⢹
⠀⠀⢸⡇⠀⢀⣤⣤⣔⠲⣄⠀⡠⠴⣦⣄⠀⣠⡶⢲⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣴⠖⠆⠀⢸⢸
⠀⠀⢸⡇⠀⠊⠸⠀⠈⢇⣿⡟⠀⠀⢸⡿⢰⣿⡡⠃⠀⢀⠀⠀⠙⠇⠀⡀⠀⣰⣿⡣⠊⠀⠀⢸⢸
⠀⠀⢸⡇⠀⢄⢠⠈⡇⠸⣿⡇⣀⣤⠞⠁⣼⡏⠀⢀⡾⠁⢸⣿⠀⣰⠏⠈⠂⣿⡯⠒⣦⠀⠀⢸⢸
⠀⠀⢸⡇⠀⠈⠉⠛⠐⠁⠿⠃⠀⠈⣷⠀⢻⡇⠀⣸⡇⢀⢾⡏⢠⣿⠀⠀⡰⣿⢤⡞⠃⢰⠀⢸⢸
⠀⠀⢸⣷⠀⠹⢏⠀⠀⠀⢎⠈⣃⣼⠟⠀⠈⠳⠔⠁⠉⠁⠈⠷⠊⠙⠧⠐⠁⠈⠀⠻⠔⠁⠀⢸⢸
⠀⠀⢸⣿⢠⣤⠀⣤⡄⢠⣤⠈⢁⣤⣤⣄⠀⢀⣤⠀⠀⠀⣤⡄⠀⣠⣤⣤⡀⠀⢠⣄⠀⢠⣤⢸⢸
⠀⠀⢸⣿⢸⣿⠀⣿⡇⢸⣿⠀⣾⡏⠀⣿⡇⢸⣿⡇⠀⢰⣿⡇⢀⣿⠃⢹⣷⠀⢸⣿⡀⢸⣿⢸⢸⡆
⠀⠀⢸⢸⢸⣿⢰⣿⣧⢸⣿⠀⣿⡇⠀⣿⡇⢸⣿⣿⠀⣼⣿⡇⢸⣿⠀⢸⣿⠀⢸⣿⣇⢸⣿⢸⢸⡇
⠀⠀⢸⢸⠈⣿⢸⡿⣿⢸⡏⠀⣿⡇⠀⣿⡇⢸⣿⣿⣦⣿⣿⡇⢸⣿⡀⣸⣿⠀⢸⡟⣿⣾⣿⢸⠘⡇
⠀⠀⢸⢸⠀⣿⣿⡇⣿⣿⡇⠀⣿⡇⠀⣿⡇⢸⣿⢻⣿⡏⣿⡇⢸⣿⠛⢻⣿⠀⢸⡇⠸⣿⣿⢸⠀⡇
⠀⠀⢸⢸⠀⣿⣿⠁⢸⣿⡇⠀⠹⣿⣴⣿⠃⢸⣿⠈⣿⠁⣿⡇⢸⣿⠀⢸⣿⠀⢸⡇⠀⢿⣿⢸⠀⡇
⠀⠀⢸⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣠⡇
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣀⢐⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠐⠒⢀⠀⠀⠀⠀⠆⠠⠂⠴⠀⠀⠀⠀⠊⢀⠀⠉⠂⠀⠀⠂⠖⡀⢠⠧⠉⠀⠀⣞⢐⠠⠄⢻⠀⠀⠀⠀⠐⠆⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠰⠄⠀⠀⠠⠄⠀⠈⠀⠄⠁⠄⠀⠉⠀⣤⡿⠿⠿⠿⣶⡄⠀⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⢠⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⡀⡀⠀⠀⢀⠡⠂⠄⠂⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⢀⢠⡄⣀⣀⠀⠀⢈⣈⡀⠁⠄⠥⠀⠀⠈⠀⠃⠂⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠒⠤⠄⠀⠀⠀⠀⠲⠀⡀⠀⠀⠀⠀⠒⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠴⠤⠴⠦⠴⠀⠀⠀⠰⠖⠠⢠⠀⠀⠀⠀⠤⠈⠤⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠸⠨⠍⠙⠀⠀⠀⠀⠸⠋⠒⠀⠀⠀⠀⢠⠂⠀⠀⠶⠀⠀⠀⢀⣤⠀⣄⡀
⠀⠀⠀⠀⣐⢢⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⢀⢳⠞⠀⠀⠀⠀⠀⢠⠀⠂⠆⠀⠀⠀⣶⠉⠛⠓⠖⠀⠀⠘⣽⣿⣿⣟⣭⡇⠀⣀⣾⣠⣆⣴⣶⠄
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠊⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠉⠓⠓⠒⠁⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠈⠛⠉⠉⠉

⠀⠀⢀⠤⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠰⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⠀⢶⠄⠀⠈⠶⠆⠀⠀⠀⣙⠈⠀⠀⠀⠀⠀⠉⠃⠈⠋⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣴⣄⠀⠀⠀⠀⠀⢈⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠠⠁⠄

⠀⠀⠀⠀⠀⠀⣀⡀⡀⢠⡀⢀⢠⢄⠀⠀⠀⠀⠀⠀⠠⠆⡀⠤⢦⡀
⠀⠀⠀⠀⠀⠸⡆⠀⢰⢸⡙⡇⢸⡠⠁⠀⠀⠀⠀⠀⠠⠻⠷⢶⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣽⠚⣟⣁⢠⣈⢩⢡⡄⠀⠀⠀⠀⠀⠀⠉⠭⡉⡀⠀⠀⠀⠀⠀⣠⡂⢰⢅⣀⡠⠄⡤⣆⢦⣤
⠀⠀⠀⠀⠀⠀⢹⠁⣸⠈⠉⠴⣻⠋⠀⠀⠀⠀⠀⠐⠺⠿⡚⠟⡇⢂⠀⠀⠠⠴⠛⢳⢦⣤⡤⢠⠤⣭⣼⠶⠛⠲⠄
⠀⠀⠀⠀⠸⣿⣷⠎⠀⠐⠀⠚⠒⠘⣿⣿⡇⠀⠀⠀⢨⣮⡁⠈⠀⣀⠀⠀⠰⠮⠤⣠⠀⡸⠱⣏⡷⠉⡏⢀⠤⠥⠄
⠀⠀⠀⠀⠀⠙⠋⠰⠋⠉⠛⠋⠋⡗⠈⠉⠀⠀⠀⠀⠀⢯⣍⢉⣩⠝⠁⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠐⡋⣀⡀⠀⣈⠓⠀⠀⠀⠀⠀⠀⠘⣐⡤⣩⣠⡤⣬⠑⢄⠀⠀⠀⠀⠀⣹⣒⣝⣓⡨⠠⠼⠃
⠀⠀⠀⠀⠀⠀⡄⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣦⡎⠐⣄⡀⠊⠀⠀⠀⠀⠀⢠⣠⣯⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠳⠈⢓⠛⢻⠘⡙⠀⠀⠀⠀⠀⢀⣊⡁⢘⣛⠙⡃⠁⠀⡤⠀⠀⠀⠀⠀⣤⡉⣿⣭⡭⠡⠖
⠀⠀⠀⠀⠀⠀⠀⣱⣛⣾⣦⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⡆⠞⠓⠚⢶⠂⠀⠀⠀⠀⠀⠀⢲⡠⣭⣈⣁⡴⣺
⠀⠀⠀⠀⠀⠀⠈⠈⢙⠛⡛⢿⠝⠀⠀⠀⠀⠀⠀⠀⢀⣁⡖⡴⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣽⣿⣽⣿⣽

⠀⠀⠀⠀⠀⠀⣀⡀⡀⢠⡀⡀⢠⢄⠀⠀⠀⠀⠀⠀⠰⢂⡀⡤⢆
⠀⠀⠀⠀⠀⠸⡄⠀⢱⢸⡑⡇⣎⠸⠀⠀⠀⠀⠀⠀⢘⠻⠶⠶⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣟⠚⣟⣉⢭⣉⢩⢡⡄⠀⠀⠀⠀⠀⠀⠉⢯⠁⠀⠀⠀⠀⠀⢀⣀⠂⡾⡄⣀⡤⢰⢴⡰⣤⡄
⠀⠀⠀⠀⠀⠀⢹⠁⡹⠈⠋⠜⡻⠉⠀⠀⠀⠀⠀⠒⠻⡿⠸⢻⠕⡂⠀⠀⠠⠞⠛⡷⣦⣤⡬⣠⢬⡥⡷⠞⠓⠢
⠀⠀⠀⠀⢸⣿⣷⠏⠀⠒⠐⠚⠂⠘⣿⣿⠇⠀⠀⠀⢡⣏⠁⠈⠀⣀⠀⠀⠴⠥⢄⡀⠀⡏⢸⣩⠏⢹⠁⠠⠬⠤
⠀⠀⠀⠀⠀⠙⠃⡸⠛⠃⠛⠋⠫⡇⠈⠁⠀⠀⠀⠀⠘⣯⣉⣉⣩⠛⠀⠀⠀⠀⠀⠉⠁⠀⠒⠒⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢠⣤⠤⠴⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⡋⣀⡀⠀⣘⠃⠀⠀⠀⠀⠀⠀⠚⢠⢬⣁⣠⡤⡜⠠⡀⠀⠀⠀⠀⢀⡿⢪⣞⣂⠉⠠⠟
⠀⠀⠀⠀⠀⠀⡔⡆⠂⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣲⡏⠠⣀⠀⠃⠀⠀⠀⠀⠀⣀⣼⣍⣭⣤⠄
⠀⠀⠀⠀⠀⠀⠳⠈⣳⠟⢳⢙⡃⠀⠀⠀⠀⠀⢀⣊⡁⢘⡋⠙⠀⠁⡡⡄⠀⠀⠀⠀⠠⣌⢹⣯⣭⡍⡵⠃
⠀⠀⠀⠀⠀⠀⠀⣱⣻⣾⣌⣿⡦⠀⠀⠀⠀⠀⠀⠀⢰⡶⠛⠆⠓⡶⠀⠀⠀⠀⠀⠀⠀⣇⢴⣍⣉⣀⠖⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠛⢿⠝⠀⠀⠀⠀⠀⠀⠀⢀⣃⣖⣖⣕⣃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠥⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠠⠀⣎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⡀⣿⠀⣟⢶⢰⣶⣶⣶⡆
⠀⠀⠀⠀⠄⣠⢄⣤⣀⣨⣌⣡⣀⣤⠄⠠⠀⠀⠀⠀⣤⠈⣥⢀⣠⡀⣉⢩⡝⡈⣠⠄⣘⣡⡀⠀⠀⠈⠋⣤⠭⣤⢭⠬⠬⢭⡅⠩⢁⣴⡀
⠀⠀⠀⠀⠀⢙⡦⡟⠻⢿⡸⢻⠗⢿⡄⠀⠀⠀⠀⠀⣿⠀⣿⢸⡇⡐⢻⣸⣇⡇⣿⠀⣿⣞⠁⠀⠀⢠⡯⣹⢓⡟⣸⣇⡟⠛⢱⢷⣯⢉⡅
⠀⠀⠀⢤⣦⡄⣦⣀⢦⡶⣤⠶⣴⠶⢄⣰⡀⠀⠀⠀⠉⠀⠉⢁⠌⠀⣌⢡⡍⠀⣭⠁⢉⡈⠁⠀⠀⠘⠓⢛⣞⣲⠛⠃⠛⠀⢙⡻⡙⣛⡂
⠀⠀⠀⣈⢋⢁⣉⢉⣈⣋⢈⢃⣙⠈⡈⢛⢁⠀⠀⠀⢰⣿⡆⣿⢰⡄⡇⢸⣷⡀⣿⠀⢾⡷⠀⠀⠀⠈⡏⡽⠆⡄⢩⡉⢁⣤⢤⠰⠹⡸⡃
⠀⠀⠀⠟⠸⠆⠿⠸⠿⠘⢾⠸⡸⠻⠲⠻⡾⠀⠀⠀⠀⠀⠀⠈⠉⠠⠥⠌⠈⠡⠍⣠⣤⠀⠀⠀⠀⠘⠓⠻⠒⡂⠀⡀⠀⡀⠐⠐⠛⠒⠛
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⡀⢰⣷⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠛⠛⠀⠀⠀⠀⠀⠺⠿⠸⠳⠹⠿⠨⠗⠚⣾⠸⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⠀⡤
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢧⠸⡇⣿⢠⡇⣰⠃⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⠠⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢤⡳⣌⣧⢳⣿⣸⣱⢣⢞⡡⠆⠀⠀⠀⠀⣄⡀⢺⣠⡇⡀⣠⡄⣿⡀⠀⢠⡀
⠀⠀⠘⣧⠘⡇⠀⡞⠀⢻⢸⡃⣟⠰⡏⣿⠀⠀⠀⠀⢠⢀⢩⣈⢬⣨⢌⣠⢁⣥⡉⣠⠄⠀⠀⢀⡤⣟⢁⠸⠈⠃⠃⢻⡇⡋⠷⠀⢾⣿⢇
⠀⠀⠀⡜⣧⣁⢰⡆⡀⠀⢀⡦⢸⣆⣠⠌⠁⠀⠀⠀⠸⠼⠤⠻⠤⠻⠯⠹⠼⠷⠃⣬⠗⠀⠀⠈⠳⣆⣞⣴⣆⣴⣎⣴⡾⣵⣾⢸⣆⣶⣯⡆
⠀⠀⠀⣙⢿⣃⠘⢂⣓⡁⠀⣃⠘⣑⠛⣀⣀⡀⠀⠀⢀⡤⣾⢩⠀⢢⡤⣃⡤⣱⢺⣼⠆⠀⠀⠙⠚⠉⠉⡉⠉⠁⡉⠉⠉⠉⠉⠈⠉⢉⠁⠉
⠀⠀⠘⣿⠋⣿⢶⣿⠉⣿⣼⣿⣆⣿⢸⣿⣉⠁⠀⠀⠘⠒⠓⠛⠊⡿⠘⠙⠛⢨⡆⠛⠂⠀⠀⠀⠀⠀⠘⠛⢐⡭⠒⠋⠉⠙⢪⠢⠤⠜
⠀⠀⠀⣿⣋⣿⠜⣿⣀⣿⠑⣿⠹⣿⠈⣿⣉⡀⠀⠀⠀⠀⠀⢰⠒⢷⣲⢶⡶⡆⠀⢠⡦⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠠⠠⠜
⠀⠀⠀⠁⠈⠁⠀⠀⠉⠀⠀⠁⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⡇⠀⢀⠄
⠀⠀⠀⣀⠀⣾⡇⣲⡀⢀⠁⣀⠀⢃⡀⢱⣆⡀⠀⠀⢠⡌⠟⢿⢱⣄⢠⢀⣤⣄⣦⣬⡋⠀⠀⠀⠀⠀⠄⣀⠢⠁⠀⠀⠀⠂⠔⣀⠤
⠀⠀⠸⣏⣱⠏⣼⠉⣻⣾⢟⡿⣰⡿⢋⠎⡾⣡⠀⠀⣤⡀⠀⠀⢸⡏⢹⠻⣗⡁⣿⢾⠀⣤⠀⠀⠀⢀⣀⢠⣉⣀⡀⢒⡀⢂⢁⠠⣀⡀
⠀⠀⠀⠟⠙⠋⠛⠚⠁⣛⠈⠛⠙⣳⠋⡀⠛⠁⠀⠀⠇⣿⡆⢛⡴⢦⣰⢄⡦⣠⢶⡶⣸⠏⠀⠀⠀⣸⣟⢸⣿⣟⡇⡏⢿⢹⣾⣑⡯⡟
⠀⠀⢠⣰⣆⡥⣾⢱⡆⣷⢘⣷⡆⣿⠠⣀⣆⡤⠀⠀⠀⣿⣰⠻⠧⠞⢿⣾⠵⠿⠺⠷⠿⠎⠀⠀⠀⠙⠛⠙⠛⠛⠋⠛⠛⠛⠘⠋⠓⠛
⠀⠀⠐⠛⠛⠂⢙⡿⠃⠿⠸⠻⠇⠛⠀⡛⠛⠃⠀⠐⡓⠈⡁⣀⠀⡂⠺⡋⠀⣀⢀⡀⢐⡃⠀⠀⠀⡇⣴⢎⡱⣧⢼⠀⠘⢇⡙⣼⣿
⠀⠀⠀⠀⠄⠐⠀⠀⠉⠉⠀⠀⣀⠀⣺⣿⠇⠀⠀⢰⣧⣿⣿⡏⣽⣧⣿⣿⣿⡏⠹⣏⠻⣍⠀⠀⠀⠀⣴⣤⢠⠤⣬⣤⢤⣤⠠⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠃⠙⠉⠁⠉⠁⠁⠛⠈⠋⠈⠋⠀⠀⠀⠀⠉⠁⠘⠂⠋⠙⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡄⠟⠞⠳⠇
⠀⠀⠀⠀⢀⣰⣁⠰⠗⣆⣀⡲⠒⣸⢞⡥⠿⢴⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠂⠀⣠⠆⠀⠀⠀⠀⢰⢄⣹⡋⣭⠉⣩⣩⣉⣏⣩⣹⣏⣉⡽⡒⠶⠶
⠀⠀⠀⡤⠾⠗⢶⣿⣀⣄⣀⣀⣀⣮⣥⣾⡷⡞⠓⠶⠤⠀⠀⠀⠙⢢⢀⣀⡘⠇⡸⠃⠀⠀⠀⠀⠀⢸⠀⡀⢠⠀⠀⠀⡄⠀⠀⢰⠀⢻⡿⢿
⠀⠀⢀⣌⣂⠀⠈⠀⠉⡟⢡⡞⢱⡌⢳⡟⠀⣀⣀⣃⡀⠀⠀⠀⠀⠀⠀⢠⢒⣠⡄⢀⡆⠀⠀⠀⠀⢸⠈⣧⡜⣦⣶⡈⢇⢼⣃⢾⣶⡠⠀⢸
⠀⠀⠀⠀⠉⠉⠻⠌⠔⣁⣈⣓⣚⣀⣨⠥⠤⠃⠀⠉⠁⠀⠀⠀⠀⢰⡷⣼⠴⠽⠴⠶⠷⠂⠀⠀⠀⢸⠀⠉⢈⡡⣤⢶⢶⢠⡲⠀⡈⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⣞⣇⡾⢃⣀⠀⠀⠀⠀⢸⣤⣠⣤⣥⣬⣤⣤⣭⣭⣭⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣥⣀⣩⣬⡽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⢖⣟⠛⣛⠛⡛⠛⢻⡿⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢰⡄⠠⡴⡄⢰⣂⠀⢠
⠀⠀⠀⠀⠘⡀⣧⠗⣡⣟⣟⣇⣘⣃⣠⡼⠛⠁⠀⠀⠀⠀⠀⠀⢰⡏⣷⢞⣿⠆⣏⣹⠀⠀⠀⠀⠀⠀⢠⠐⣂⣼⡟⣇⡀⠇⠳⠸⠧⢄⣿⣾⠛⠁
⠀⠀⠀⠀⠀⠉⠉⠉⢻⠷⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡹⣏⣍⣍⡽⠋⠀⠀⠀⠀⠀⠀⠀⣠⠪⢛⡭⣄⠀⠘⠚⢁⡤⠈⠉⠑⠋
⠀⠀⠀⠀⠀⠀⢲⡴⣾⢳⣴⢸⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⣭⣤⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠉⣹⠶⠷⢿⠓⠄⣠
⠀⠀⠀⠀⠈⣢⢀⠃⢙⣞⣉⣋⣉⢉⣱⠾⠀⠀⠀⠀⠀⠀⠀⠀⣦⠷⢶⣿⣰⣶⣡⣸⡅⡇⠀⠀⠀⠀⠀⢈⣫⣿⠋⢠⡼⢃⡼⢃⡀⠿⣯⣴⣶⣶
⠀⠀⠀⠀⠀⢉⣛⠂⠸⡟⣛⣩⠧⠌⠉⢠⡄⠀⠀⠀⠀⠀⠀⢀⠉⣿⡆⠰⠄⠰⠀⠿⡆⠀⠀⠀⠀⠀⠀⠿⠿⢿⡷⣶⣦⣉⣛⣉⣶⣾⣻⠟⠉
⠀⠀⠀⠀⠀⠘⣷⡰⣽⢧⢤⣄⡤⣴⠛⣹⠃⠀⠀⠀⠀⠀⠀⣨⢰⣳⣷⣶⠦⡴⣤⠸⣣⠨⡆⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣯⣉⣽⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣍⣉⣉⣤⠞⠃⠀⠀⠀⠀⠀⠀⠈⠉⣶⠁⣤⠰⡶⠗⢠⡄⢠⣄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡉⡿⠟⠿⠿⠿⠻⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠙⡾⠋⡏⠀⣷⢸⠀⡷⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢀⠄⠀⠿⣤⣴⣼⣾⣴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠚⠁⠈⠂⠋⡀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣩⠉⢷⢸⢀⡀⠀⠀⠠⣶⡄⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢺⡟⠓⠓⣠⡐⠟⣻⡛⢺⡇⠘⡓⠒⠆⠀⠀⠀⠀⠀⠀⠉⢀⡐⢺⡾⡟⢰⣟⣿⠁⡽⡿⢠⡏⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⡷⠆⠺⣟⣡⣜⡇⣴⣦⣸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡾⠁⠳⠞⡉⠈⣉⡀⠓⠊⠙⠳⡿⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⢾⠦⣠⠦⠨⠵⠀⣀⣉⠀⠀⠀⠀⣀⠀⠀⠀⠚⢹⣏⠰⠆⡾⠆⠿⠻⠻⠟⠈⠃⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⢿⡷⠒⠙⠙⠟⠋⠀⠿⠳⠇⠀⠐⡍⠙⠛⠛⠛⠀⠿⠟⠀⠀⠀⠈⠁⣠⠰⣶⢶⣶⢠⣷⡌⢺⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⡿⠟⢷⠟⠳⠛⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣥⣬⣥⣭⣥⣥⣬⣤⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠚⠛⠊⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠿⣿⢽⡿⣿⣯⣝⣿⢻⣿⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⢡⣶⠆⢻⡋⢳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡟⣧⢲⣴⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣥⣤⣬⣭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⣰⣃⠀⠈⢈⣀⠀⣄⣠⠆⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣾⡇⢸⡵⣾⢡⢴⠤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣜⢦⢂⡉⠘⠆⠲⠜⠉⠓⣪⠼⣞⣉⡛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⣝⣓⠘⢁⣘⡊⢠⣄⠀⠀⠀⠀⠀⠀⠐⡖⠛⠛⠹⠿⢧⣤⣤⡤⠤⡤⠤⣦⠶⣿⠿⡟⠉⠙⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⡂⠀⠀⡁⠀⢸⡏⢡⡟⠙⣧⠙⢲⡏⠀⣇⣀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣽⣳⣤⢤⣴⣤⣶⣿⡤⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣇⣈⠚⣁⠈⠳⠞⠃⣀⣘⣣⣤⠌⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣨⡉⠉⣁⣠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠋⠉⠛⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣏⣀⣀⣀⣸⣿⣀⣀⣀⣿⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠙⠻⣷⡄
⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⣿⡇⢀⣤⣶⣦⡄⠀⠘⠿⠀⠀⠀⢠⣴⣶⣤⡀⢸⣿⠀⠀⣠⣄⡀
⠀⠀⠀⢀⣠⣼⣿⣿⠏⠀⠀⠀⣿⣷⣾⣿⡀⣸⣿⣶⣶⣶⣶⣶⣶⣿⣇⢀⣿⣷⣾⣿⠀⠀⠈⠛⠿⣶⣾⣷⡀
⠀⠀⠸⠿⠋⠁⠈⠉⢀⣤⣤⣄⣤⣤⣤⣽⣿⣿⣥⣤⣤⣄⣠⣤⣤⣬⣿⣿⣯⣤⣤⣤⣠⣤⣤⡀⠀⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣦
⠀⠀⠀⠀⠀⣠⡾⠟⠀⣴⣿⡿⢻⣿⠟⠿⠿⠿⠿⠻⣿⡟⢿⣿⠿⠿⠿⠿⠿⠻⣿⡟⢿⣿⣦⠀⠻⢷⣄
⠀⠀⠀⣠⣾⠟⠁⣠⣾⠏⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠻⣷⣄⠈⠻⣷⣄
⠀⢠⣾⡟⠁⣠⣾⠟⠁⠀⣿⡇⢸⣿⡀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⢀⣿⡇⢸⣿⠀⠈⠻⣷⣄⠈⢻⣷⡄
⠐⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛⠛

⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⡟⢻⣿⠟⢿⡿⠛⠛⠛⠛⣿⡿⢿⣿⠛⠛⠛⢿⣆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⣿⠇⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⡇⢀⣿⠇⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⢷⡾⢿⠷⠿⡿⠶⠶⡶⠶⠿⡿⡿⣿⠶⢶⡾⠿⠃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣿
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣴⣤⣦⠀⢴⡴⠶⠛⣠⠠⠤⠤⣤⠄
⠀⠀⠘⠳⡍⠉⣿⣓⣶⣞⣶⣅⢒⣶⢲⣉⢩⡭⡇⢀⣘⡡⠄
⠀⠀⠀⠚⠒⠒⠛⠙⢻⠉⠸⠋⠘⣛⣀⣙⡠⠥⠉⠁⢰⠂⠀⠀⠀⠀⠀⣠⠞⣳⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⣠⢆
⠀⠀⠀⠀⢙⣶⣤⣴⡦⠉⠛⠻⠛⠚⡃⣀⢀⣠⣤⢰⡛⢥⠀⠀⠀⠀⠳⡧⠶⠋⠀⠀⠸⣸⢀⠀⠀⢤⣾⣿⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠆⠀⣾⣵⣀⡏⢹⣈⡟⠙⣇⡌⠻⣜⣋⢳⠀⠀⠀⣠⣄⠈⡏⠙⣦⣾⠡⣿⠃⣬⢰⢲⢠⠉⣦⣜⠆⡰⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⢰⣟⡂⠺⡁⠻⣍⠓⠲⠋⠀⠀⠀⢸⣿⣦⣌⣶⣿⡽⢷⡙⣖⡙⣚⡗⣉⣚⠁⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠷⠎⠓⠂⠘⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠿⠁⠀⠀⠀⠙⠁⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠠⢸⠃⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣼⢃⣀⣀⡴⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣰⣧⡶⣆⠀⢰⢦⣴⡮⢅⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢷⡟⢿⣹⡏⠀⢷⠟⠁⣶⠆⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡿⣇⣼⢶⠫⢚⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣉⢁⡌⠁⠈⠉⠀⠀⠀⡾⡇⢠⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠚⡡⡀⢠⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⣼⠁⢀⢀⡄⡀⢀⠀⣿⡃⢻⡏⠀⠀⠀⠀⠀⠀⢠⡼⡇⢠⡯⢱⣶⢠⢸⣁⣁⢾⡇
⠀⠀⠀⠀⠀⠀⠀⡔⢡⡏⣰⣟⡿⢻⣇⣾⡾⢏⣹⠟⣧⡄⠀⠀⠀⠀⠀⠸⣥⢧⠼⣧⠏⠿⠻⠞⢫⡟⠘⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠉⠉⠁⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⢞⡵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣄⣤⣤⡤⠐⣡⣶⡋⢀⣾⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⣡⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⣉⣴⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣾⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣉⣖⣫⣾⣿⡿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣠⢻⡤⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣀⢟⡽⢷⣤⣤⡆⢀⣀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⢀⢀⠛⠋⠀⠀⠙⠛⠋⠹⠿⢻⠿⠿⠛⠛⠛⠛⣛⠛⠻⢿⣿⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣇⠀⢻⣿⣿⣿⣿⣷
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⢿⡿⠟⠛⠛⠛⠋⠛⠛⠉⠁⠀⠀⠀⠀⠀⢄⣸⣇⢿⣿⣟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠁⠀⠙⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⣀
⠀⠀⠀⣀⠘⠔⠃⢁⡁⣤⠀⠀⢿⡛⢛⡃⠀⠀⠐⠋⠓⠀⠑⠊⠀⠀⠀⠀⣛⣛⢛⣺⣟⠃⠀⠀⠀⠣⠼⠅⠠⠶
⠀⠀⠀⢀⠈⣛⢈⣬⡅⠄⠀⠀⢘⣈⣛⠁⠀⠀⠈⣀⢀⢁⣁⣀⠀⠁⠀⠀⣭⣉⢜⣻⣄⡆⠀⠀⠶⠷⠶⠶⠶⠾
⠀⠀⠀⠈⣉⢈⠤⠤⠄⠖⠀⠀⠘⠛⠉⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠁⠀⠰⠌⠀⠀⠀⠀⢀⠀⡄⢀⣀⠀⠀⢀⣀⣀⣀⣀⢠⡀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠠⠜⠂⠂⠃
⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⣆⠠⡄⡀⣁⠉⡀⠀⢠⣉⡩⡭⣭⣸⣥⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠆⠂⡁⢠⠅
⠀⠀⠀⢠⣿⡿⠛⣿⣷⠀⠀⠀⠀⠠⠤⡤⠀⠀⠀⠈⠉⣧⣴⣤⠍⠈⠀⠀⢈⡈⠐⡉⣉⠀⡀⠀⢀⡉⡍⠠⠤⠃
⠀⠀⠀⠘⠙⠁⢀⣉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣄⡠⡨⠤⠄⠀⠀⢠⣿⣶⣯⣿⣻⣿⢿⠀⠀⠀⠀⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠆⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⠦⠀⠀⠐⠒⠀⠀⠀⠂⠀⠖⠐⠀⠀⠀⠓⠒⠐⠒⠂⠀⠀⠒⠲
⠀⠀⠀⠀⠀⢽⢿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡀⠀⠀⠀⢀⡀⣀⢀⢀⡀
⠀⠀⠀⣀⣸⠿⢿⣿⣻⡀⡀⠀⢀⡀⠀⠀⠀⠀⠘⠂⠋⠃⠀⠀⠀⠀⠛⠁⠀⠻⠃⠀⠀⣤⣭⣍⣭⡥⣭⡥⣠
⠀⠀⠀⠛⠛⠘⠛⠛⠛⠛⠃⠀⠀⠁⠀⠙⠀⠀⠈⠀⠀⠃⠈⠀⠀⠀⠀⠺⠷⠀⠀⠀⠀⠀⠀⠈⠦⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠀⠰⠦⠀⠀⣀⣀⠀⠀⣮⡹⠷⡀⠀⠀⠀⠀⠀⣦⠀⡄⣀⡀⣀⠀⣀⠀⣠⢤⡀⠀⠀⣶⣤⡤⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣶⣦⡀⡇⠀⠸⣯⣿⡇⠀⠉⠑⠀⢃⡀⠀⠀⠀⠀⣿⠿⡇⣿⠀⣿⡀⣿⡀⣷⣴⡇⠀⠐⢿⣿⠿⠄⢸⣿⢛⣻⡇⠘⠃⢹⣭⣿⡇⢰⣿⣿⢛⣿⡇
⠀⠀⠀⠀⠿⠿⠟⠁⠷⠶⠰⣦⣼⠇⠀⠀⠀⠀⠀⢉⣈⡆⠀⠀⠛⠀⠃⠉⠁⠙⠋⠙⠛⠈⠉⠀⠀⠀⠀⠁⠀⠀⢸⣟⠶⢹⡇⢰⡆⢸⡜⢿⡇⠈⠛⣿⠘⣿⡇
⠀⠀⣶⠀⠀⢴⡶⢠⡖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡀⢸⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢹⣷⣦⠘⠓⠘⢿⣾⠟⠀⢰⣄⣤⠆⠀⠀⠀⢀⣤⣶⣶⣿⣿⣶⣶⣤⣀⠀⠐⣿⣄⠀⠀⠀⠀⠀⠀⣠⣽⡃⠀⠀⠀⠀⠀⣌⡉⠉⠉⠉⠉⠉⠛⠛⠛⠛
⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⠷⠀⢀⣼⣿⣿⣿⣿⣿⡟⢿⣿⡿⢿⣷⡀⠋⠙⠿⣶⣤⣤⣴⠀⢨⣭⡍⠀⠀⠀⠀⠺⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣾⣿⡅⢶⡇⠿⢸⡆⠾⢿⠀⡠⣿⣷⠀⠀⠀⠀⠘⠋⠁⠀⢈⣹⡧⠀⠀⢸⡇⠀⠄⢠⡆⢰⡦⠀⣿⠀⣠
⠀⢨⡀⠠⡦⡄⠄⣠⠀⠰⢦⣄⢤⠤⠀⠀⠀⢿⣿⡷⠶⠿⢶⠿⡿⢶⡾⠷⠲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠷⠆⠑⠘⠧⠎⠳⠆⠿⠶⠛
⠀⠀⣁⡀⢀⣀⠀⣤⠀⢀⣤⡄⠀⣀⠀⠀⡄⠈⢿⣷⣶⣵⣶⣤⣿⣭⣤⣴⣼⡿⠃⠠⠄⠀⠠⠄⠀⠀⠀⢈⣹⡇⠀⠀⢰⣶⣦⡖⣤⣤⠤⠔⣶⢲⢢⡦
⠀⠀⣙⡆⢸⠟⢡⡟⡇⢻⣇⣀⢸⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⠿⠟⠋⠀⣠⠀⠀⠉⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠛⠉⠙⠑⠃⠉⠈⠙⠓
⠀⠀⠈⠀⠈⠀⠈⠁⠁⠈⠉⠉⠀⠉⠀⢀⡖⠁⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⣶⣦⠀⢀⣠⡄⢀⠿⢏⠉⠯⠉⠁⣤⠤⢤⣀⠀⢰⡶⠶⢠⡀⢀⠀⣤⣴⢀⣌⣤⠁⡆⢰⠀⢠⠀⠀⠀⠀⠀⢀⡤⠀⣤⣄⢰⡆⢀⣴⠶⠀⣠
⠀⠀⠀⠀⠈⠁⠀⠈⠻⠇⢐⣄⡔⢀⣤⣀⡀⠿⠤⠴⠛⠀⢸⡏⠀⠸⣇⡼⠀⡿⣿⠸⡿⣿⠀⢙⡾⠀⣀⢀⡀⡐⢀⡀⠠⣽⠆⡟⠉⣾⢻⠘⣷⣤⠀⣏
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⠉⠙⢧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠋⠘⠃⠿⠌⠛⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⣿⣶⣦⠀⣯⣉⡧⠀⣾⣁⣹⡇⠀⠀⠁⢸⣧⣼⡇⣴⠒⣦⢰⣦⣶⡆⡶⠦⠻⣿⠗⣾⡃⣶⠖⣦⢾⡛⠀⠀⠀⠸⠃⠸⣇⠀⡄⡿⣧⣿⠆⢹⣤
⠀⠀⠀⠛⠛⠋⠀⠉⠋⠁⠀⠈⠛⠋⠁⠀⠀⠀⢸⡏⠙⡟⢿⣤⣿⢸⡿⣿⠣⣍⣷⠀⣿⠀⢿⡤⣻⣿⡁⢦⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠘⠃⠘⠛⠈⠛⠁⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⠀⠻⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠐⠆⠀⣄⣤⡄⠀⢀⣴⣿⠉⣿⣿⢿⣿⢿⣿⠟⣿⣿⠉⣿⣿⣦⡀
⠀⠀⣖⠂⢰⣶⡄⣿⡇⢠⡿⠛⠀⣴⠀⠀⣿⣿⣷⣶⣶⠶⣶⣶⣶⣴⣤⣤⣤⣤⡄⠀⣙⡁⠠⠤⣤⡄⢀⣾⣿⣿⠀⠿⣿⢻⣇⢰⣷⡄⡾⢿⠠⢿⡇⣼⣷⡀
⠀⠀⠶⠇⢸⠉⠠⡿⢳⠘⣿⣶⠄⠿⠄⠀⢻⣿⣈⣹⣺⠀⢯⡐⣯⣚⣸⣨⢙⣽⡇⠀⢈⡃⠰⠶⣭⡄⢸⣿⣿⣿⣶⣶⣿⣷⣿⠦⣼⠷⣶⣿⣶⣶⣿⣾⣿⡇
⠀⢀⡀⣀⠀⣀⣰⢄⡄⢠⢠⡄⡀⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⢿⣿⣿⡇⠀⢈⠍⢈⣥⣤⡀⠀⢿⣿⣿⢹⡏⠹⠇⣭⠠⣇⠛⢀⡇⢸⠹⡆⣼⡿⠁
⠀⠘⠂⠛⠒⠋⠸⠦⠛⠋⠘⠃⠓⠛⠀⠀⢸⣿⣎⣯⣽⣿⣧⣧⣶⣸⣦⣹⣷⣿⡇⠀⠐⠀⠘⣃⣈⠃⠀⠀⠻⢿⣾⣷⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣉⠉⠁⠀⠀⢈⡋⠈⠁⠉⠀⠀⠀⣄⣀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⢰⣶
⠀⢲⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀
⠀⢾⣿⠉⣿⣿⠋⣿⢹⣿⡝⣏⣋⣿⣷⠀⠀⠀⠀⠀⠀⣆⢠⣄⠀⢶⣠⠤⠀⢸⢻⣰⣎⣲⢰⣎⣶⢸⣿⠀⠀⠀⠀⢠⣾⠛⢸⡇⢰⡗⠺⣿⠃⠀⣾⣿⡿
⠀⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⠀⠉⣉⡀⠀⠀⠀⣤⠀⠀⠿⠶⠄⠿⠾⠃⠀⠿⣶⠇⠻⣯⠶
⠀⣿⣇⠾⡇⢀⣹⠀⢻⡁⢴⣾⡏⣹⣿⠀⢰⣤⣴⡄⠀⠀⠀⣾⡀⣶⡆⣼⠃⠀⢰⣀⣼⡤⣟⠃⣼⡃⠀⠀⠀⠀⠀⠠⣤⣄⣤⣠⡀⣴⠀⣶⠀⣰⣦⣶⡦
⠀⠿⠷⣶⣧⣿⣧⣼⣼⣧⣤⣼⣧⡽⠿⠀⠘⠻⠟⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠁⠛⠙⠀⢠⣦⠀⠀⠈⠀⠉⠛⠉⠁⠺⠃⠙⠖⠛⠗⠛⠓
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢰⣶⠀⠀⠀⣰⡿⢷⡖⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠘⣿⣷⣾⣿⡆⠹⢿⣿⠟⣿⡇⠀⣿⠟⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⡀⢿⡏⠻⢹⣷⠀⢼⡟⠀⣿⡇⣸⣟⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠨⣿⣤⣿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⢴⣿⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⣲⢆⠈⠉⠁⠀⠀⢠⣶⠆⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠙⠛⠱⣖⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣾⠃⠸⠀⠀⠴⠒⢰⣿⠿⠆⠤⠶⠖⠛⠁⢠⣶⠆⠀⠀⠀⠀⠀⠇⠘⣷⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢀⣴⣿⠏⠀⢀⣴⠞⣷⠀⢠⣿⣿⠊⠉⣷⡀⠀⣠⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢉⣻⣷⠚⢁⣾⡟⠀⣠⣿⠷⠚⢁⣰⣿⡿⢁⣀⣼⡿⠒⠋⠹⣿⡀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣠⠖⠁⢸⣿⠀⢸⣿⣠⠞⢿⣇⣀⡴⠋⣼⡿⣗⣡⡾⠋⠀⣤⠖⠒⣿⣷⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣯⠀⢀⣾⠏⠀⠈⠉⠁⠀⠀⠉⠁⠀⣼⡿⠁⠈⠀⠀⠀⠐⣇⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⠀⢹⣿⡇⠀⣽⣿⡏⠀⣿⣿⠿⠿⠿⠀⢸⣿⠟⠻⣿⣦⠀⣿⣿⠁⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⠈⠀⠈⣿⣧⠀⣿⣿⠀⠀⣿⣿⣴⡆⠀⠀⢸⣿⣄⣠⣾⡿⠀⢻⣿⡆⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠿⠀⠀⠀⢿⣿⢠⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠟⢿⣿⡁⠀⠘⢿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⡀⠀⢸⣿⣿⣿⠃⠀⠀⣿⣿⣤⣶⣾⡂⢸⣿⠀⠈⣿⣧⠀⠀⣤⣤⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣴⣿⡀⠀⠈⠿⠿⠛⠀⠀⣀⣭⣭⣭⣭⣉⠀⠘⠛⠀⠀⠿⣿⡄⠀⣿⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢀⣀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣻⣇⠘⡇⠀⣸⣿⣶⣤⣈⠉⠁⠀⠀⠀⠀⠀⠀⣿⣷⠀⠘⣿⣿⠀⢸⠃⣸⣟⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠾⠓⠀⣰⣿⡟⠙⢿⣿⡆⠀⣼⣿⣿⣿⣿⡄⢸⣿⣇⠀⣿⣿⣇⠀⠚⠷⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣿⡿⠁⠀⣾⣿⡇⢠⣿⣿⣀⣹⣿⣇⠀⠻⢿⣿⠟⣿⣿⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣤⣾⣿⡟⢀⣾⣿⠿⠟⠻⣿⣿⡄⠀⢠⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠉⢀⣾⣿⡿⠀⠀⠀⢻⣿⣷⡀⠈⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⣠⠄⠀⢸⠂⠀⠀⠀⣅⠀⠲⢀⢀⡆⠐⢀⠀⠀⠓⡄⠀⠱⠀⢠⠄⠀⠀⠀⡄
⠀⠀⠀⢁⢀⡄⠤⣹⡀⠈⠁⠈⢠⡄⡎⢷⠂⣄⠄⠈⠀⠆⠀⠢⠀⣆⠘⠁⠚⢠⠃⠀⠀⠀⠀⠀⠀⡠⠈⢇⠀⠳⠃⢀
⠀⠀⠀⠈⠑⡀⠀⠠⡽⠀⠸⠀⠀⡀⠀⣼⠀⠁⠀⠠⠐⠆⡀⠀⠠⠿⡄⣌⣦⡈⢄⡘⠂⠔⠐⠁⠀⠠⡀⠁⡄⢸⡀⠈
⠀⠀⠀⠠⡄⠠⠀⠻⣷⡶⣄⠀⠀⣜⣻⠇⢰⠀⠀⠀⡠⣠⢥⣀⠀⠀⡄⠙⠋⠙⣆⠠⣴⠀⠀⠀⠡⡁⠁⠀⡇⢁⣄⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠙⢦⣀⣿⡏⠴⠅⡈⠁⣰⠇⠀⠀⠈⠑⠪⡁⠠⠂⠀⡄⠳⡙⡴⠆⠄⡤⠠⡊⢀⡆⢈⠈⠂⠁
⠀⠀⠀⠀⠀⠙⠂⢈⣠⡀⠀⠈⣿⣿⠀⠀⠀⣶⠾⠷⠦⢀⠀⠀⠀⠀⡈⠷⣄⠠⠤⠑⠉⣄⠓⠒⠀⠠⠟⠉⠡⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⣄⠀⢹⣿⠀⣠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⠁⠰⣾⡇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣿⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⣀⣈⡓⡷⣶⢴⠤⠴⠷⠻⣉⣡⡐⠒⠒⡲⠆
⠀⠀⠈⣑⠆⠀⣏⣥⣶⣵⣷⡌⣽⡍⢯⠇⡆⣿⣀⠨⠕⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⣉⠉⠁⠁⠏⢀⣛⣀⣩⣥⠬⠤⠒⠁⠀⣰⡃⠀⠀⠀⠀⠀⡜⢉⡗⠀⠀⡠⡄⠀⠀⠀⠀⣦⣤⣳⣀⡀
⠀⠀⠀⠀⠨⡓⠶⣿⠂⢈⢉⡉⣉⣩⣤⠤⣴⠶⣸⣎⠒⠀⠀⠀⠀⢹⣗⣋⠀⣀⣀⣧⠇⡄⠀⠐⠿⠛⢛⡛⠿⣧⡀
⠀⠀⠀⠀⠈⠀⠐⠧⠳⡼⠀⢧⣼⢁⣻⢚⢈⡯⠥⣸⠀⠀⠀⢶⣧⠈⢇⣈⡷⣧⣺⡏⣸⡇⣯⣇⢇⡽⢾⣛⡜⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡀⣿⣏⢈⣶⠈⡷⠈⢉⠁⠀⠀⠀⠘⠻⣷⣶⡿⠿⠙⠳⠈⣶⢠⡞⠲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡉⠈⠉⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠃⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡾⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⢃⣄⠀⠀⣀⢀⣠⣖⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣼⣷⠿⣷⠋⢾⣹⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⢻⠙⣾⢿⠈⣧⡴⢣⢟⢭⠶⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⠛⠀⠛⠃⠀⠈⢡⣤⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠈⠛⠁⠤⢔⡉⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠿⠃⡿⠀⠀⢀⠀⠀⠀⣿⡏⠶⡟⠀⠀⠀⠀⠀⠀⢀⣸⠀⣠⡖⣤⡄⣀⡎⡐⢨⣿
⠀⠀⠀⠀⠀⠀⢀⠔⣸⠇⣼⢿⡿⣾⣰⣧⣿⢛⡶⣇⡀⠀⠀⠀⠀⠀⣿⣘⣇⣿⣰⠻⡷⢧⠿⣻⠅⢿⠄
⠀⠀⠀⠀⠀⠀⠘⠶⠛⠚⠙⠋⠀⠛⠁⠁⠈⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠓⠢⠀⠐⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢿⣶⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⢸⣿⡇⠀⠀⢸⣿⣦⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣶⡄⠀⢻⣿⡇⣼⣿⠃⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⢸⣿⣿⣿⣧⣤⣤⣀⠀⠀⢁⣤⣶⣶⣦⠀⠀⠀⣾⣿⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⠻⠁⠀⢸⣿⡿⠋⠉⠀⢹⣿⣷⡀⣾⣿⠋⣰⡿⠀⠀⠀⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣼⣿⢹⡇⠀⠀⢀⣼⣿⡇⠀⠀⠀⣸⣿⣿⢻⣿⡿⠛⠉⢀⡾⠀⠀⠙⠉⠁
⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢠⣿⡟⢸⡇⠀⢠⣿⠉⣿⡇⠀⠀⣰⣿⣿⠏⠈⢿⣿⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣠⣤⣤⣄⣀⣸⣿⠇⠀⠀⣸⣿⡇⢸⡇⠀⠈⢿⣄⣀⣀⣴⣾⣿⠟⠁⠀⠀⠀⢈⣉⠉⠀⠀⠀⠀⠀⢠⣶⣆⠀⣸⣿⡀
⠛⠷⣤⣤⣭⣿⣿⠓⠒⠲⣿⣿⡷⠾⠃⠀⠀⠀⠈⠉⠙⠉⠉⢰⣦⣴⡟⢻⣦⢸⣿⡆⢀⣴⠶⣶⡄⢸⣿⣿⠀⣽⣿⣇
⠀⠀⠀⠀⢀⣿⣿⠀⠀⢀⣿⣿⠇⠀⠀⢠⣶⣿⠟⣿⣆⠀⠀⣿⣿⡟⣀⣼⡿⢼⣿⣿⡿⠁⣀⣿⡟⠙⣿⣿⣦⣿⣿⣿⣤⠴⠒
⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⢀⣴⣿⣿⡏⣼⣿⣿⠀⣼⣿⣿⣿⣽⠿⠁⠈⣿⣿⣧⣞⣵⡟⠁⠀⠀⠉⠉⢀⣿⣿⣇
⠀⠀⠀⠀⠸⠿⠃⠀⠀⢸⣿⣿⣴⠟⢹⣿⣿⣿⠇⣿⣿⣰⡇⣿⣿⣇⠀⠀⠀⠀⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⣰⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠈⢿⣿⡟⠀⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⣿⡟
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢸⣿⣿⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⢀⣴⡖⠰⠂⠘⠿⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⡤⠔⠚⠉⣁⣠⠼⠛⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⣀⣛⠋⠀⣾⣼⣠⣿⣖⣲⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠻⣟⠯⢭⣁⣀⠀⢀⡤⠖⠚⣛⡶⠒⠀⣠⠴⣋⠽⠛⣁⣼⠿⠯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠳⡀⠀⠹⣝⠻⢟⠛⠛⠲⢶⡶⠾⣿⣛⠛⠋⠙⠛⠒⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠼⠂⠀⠈⠓⢤⣑⣄⠀⠀⠈⠓⠲⠶⠽⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣸⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠂⠀⢰⠃⠀⠉⠙⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠌⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡘⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠉⠉⠛⠛⠶⠶⠶⠶⠖
⠀⠀⠀⢸⠀⠀⠀⠐⢄⡰⢀⣀⣼⣠⣤⣼⡧⠴⠚⠁
⠀⠀⠀⠸⠄⠀⣠⡤⠾⠟⠉
⠀⠀⠀⠀⡴⡫⠁⠀⡆
⠀⠀⠀⢠⣧⠣⣀⣀⠄⠀⠀⠀⣠⣤⠤⢤⣄⣀⣀⣀⣀
⠀⠀⠀⢸⡀⠙⣲⠒⠒⡖⠋⠉⠓⠢⣵⠯⣀⣀⠈⡍⠙⠒⠦⣤⣤⣀⣀⣀⣀⠀⠄
⠀⠀⡀⠀⠙⠚⠑⠠⡜⠳⢄⡤⠤⡀⢸⠀⠀⠈⠻⡓⠒⠠⢤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠴⠶⠶⠶⠶
⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠀⠉⠑⠚⠚⠼⠁⣐⣠⠇⡊⠘⣸⠃⠀⠈⠉⠓⠒⠒⠒⠒⠛⠉⠉⠁
⠀⠀⠈⠁⢩⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⣿⠋⠁⠀⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠋⠀⣿⠀⢀⣴⠏⠀⠀⠀⠀⢠⡶⠋⡁⠀⡀⠀⡀⠀⣠⡄⢸⠁⡠⢀⠀⠀⣀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠟⠁⢀⣀⠀⠀⢰⠟⢀⡾⠁⡼⢁⠀⠈⢰⡷⠃⠼⣏⣴⠏⣑⢰⡇⣸⡇⣰⠇⣠⠖⠆
⠀⠀⠀⠀⠀⠀⠴⣿⠉⠑⡆⣴⠏⠀⠀⠀⡟⢀⡾⠁⣼⠃⣼⠀⡇⢸⣀⠎⡀⣿⢺⡀⠀⡾⢡⠟⣰⠏⣼⠃⢁⠠
⠀⠀⠀⠀⠀⠀⢠⡇⢀⠜⠁⣇⡠⠂⠀⠀⠓⣹⠃⠀⠻⠀⠻⡴⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠞⢠⡏⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠔⠀⠀⠀⠀⠀⠀⠀⢆⣀⡼⠃⠀⣠⠖⠀⠀⠸⠃⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣄⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠄⠀⠀⠉⠀⠀⢠⡏⠐⠀⠀⠀⢰⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡄⠀⠈⢀⣰⠞⢣⠀⠀⢿⠀⠄⣾⠀⠀⣠⣄⠀⠀⢸⡁⠀⠀⢀⡀⠸⡄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⠀⢰⡇⢀⡞⠀⠠⠹⣇⢰⡇⠀⣼⠧⠊⠀⠀⢻⠀⠀⣰⠣⠀⠀⢷⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣇⢀⠁⢸⠃⢸⠇⠀⠁⠰⡗⢸⠃⢰⡏⠀⡀⠀⠀⢸⡆⠀⣿⠀⡠⢁⢼⡄⡜⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠹⠆⠀⠈⠁⠸⠄⠀⠄⢸⠇⠸⡠⠙⠧⠊⠀⠀⠀⠀⢧⡀⠘⠋⢠⠂⣼⠁⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡼⠁⠂⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⢇⡀⢀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⢸⡇⠀⠀⢀⠀⠀⢀⣶⠀⣀⠀⢀⠔⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣧⠀⢹⡇⠀⣼⠃⣵⡆⢸⡇⠀⣿⡄⠁⠀⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⢸⡇⢠⣿⢀⣿⠀⠜⢧⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡿⠀⠀⠳⠂⠙⠃⠘⠞⠀⠀⠠⢻⡇⠀⠀⡠⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⠠⠄⠀⠀⠀⠀⠠⠀⣾⡆⠀⢀⡂⣼⠃⢀⠌⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠡⠞⡉⠀⢀⠀⢰⡆⠀⢠⡅⢠⣿⠀⢀⡂⠙⠁⢀⢋⡤⢠
⠀⠀⠀⠀⠀⠀⠀⣿⢇⣀⡀⢅⡄⠈⡄⠈⢷⡄⣿⠃⢸⡏⠀⣾⠃⣼⠃⢢⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠢⠐⣿⠇⠸⣷⢺⡇⠀⠇⢠⠚⡇⢹⣄⢿⡇⠀⣿⣠⢿⡌⢸⡇⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣞⡏⠈⠓⠊⠀⠘⠘⠁⠀⠁⠸⡇⢸⠀⠁⠈⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⢀⢀⠌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡁⠈⣿⣈⡷⣧⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⣰⣥⠆⠨⡏⡙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⠋⢉⡄⢠⣿⣧⡥⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠃⠀⠹⠞⣏⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠆⡅⢀⣴⡿⢿⠁⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡋⡻⠟⠀⠇⢱⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣷⣆⢲⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢹⣿⣯⣤⡂
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⣄⣠⣎⣧⠀⢀⠀⣀⠤⠄⠀⠀⠸⠞⠚⣉⡿⣠⢆⠑⠢
⠀⣠⣾⣾⣵⣶⣶⡴⠾⠷⠾⠻⠿⢽⠛⢳⢞⡔⣠⣤⡴⣯⣤⠄⢀⣦⡐⠂⣠⣛⣀⣀⣐⣀⡸⠿⠶⠒⠖
⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⡀⡀⠠⠄⠀⠀⠈⠈⠈⠉⠁⠈⠓⠒⠚⠛⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⢛⣟⡛⢛⡛⢛⠛⠛⢛⡿⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⣯⡾⡿⠷⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠘⣇⡿⢏⣸⢺⠳⠀⠀⠇⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⢘⠓⢻⢿⢻⢉⡏⣽⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠒⢺⣿⣿⣟⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⡘⢊⠉⢁⡳⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡔⣧⡄⣤⢠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣄⡠⢭⡍⢁⣠⢅⠒⡖⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⣿⢹⡇⣿⢿⣸⡿⡿⡅⡀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡹⢉⠹⠙⠑⠛⠛⠚⣲⡓⠙
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣤⡈⠀⣾⣥⣴⢤⣴⠀⣦⡟⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⠇⠘⠛⠁⠉⠀⠛⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠙⠀⢿⠭⠯⠤⠃⠀⢀⠀⣶⠄⠀⠀⠀⠀⠀⠀⡅⢸⢹⣿⣶⡲⢶⡶⣶⠰⣣⡆⢵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡔⢯⡿⣦⣠⣄⡤⣴⡟⢉⡿⠀⠀⠀⠀⠀⠀⠛⠁⣎⠃⣤⠠⣤⠾⠦⢀⡤⠀⣤⡸⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣉⡙⠊⢙⣥⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠈⠀⠀⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣋⡄⢀⣢⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡞⣿⢩⠄⣶⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣤⣴⡴⣶⣷⣦⣄⢄
⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⣛⠁⣉⣈⡉⣉⠈⢛⡀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣀⢀⣤⣘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⡥⠄⣙⣝⠙⣨⢠⡠⢦⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⣨⣩⣄⡍⡍⢤⠖⣔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣿⣿⠉⢸⣾⡇⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠧⡘⠘⡛⢓⣋⠑⣩⡈⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠓⠓⠏⠙⣀⠘⠽⠧⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠸⠒⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣬⠁⠀⣉⡉⡀⠤⠨⠤⠄⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠷⠻⠿⢶⠣⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠣⣶⢾⣩⠏⢏⣰⣇⠆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⢣⢶⣶⢲⡀⠰⣯⣦⣤⣤⡄⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⣎⡽⡿⣷⠶⠒⢻⡳⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠁⠉⠈⠙⠻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢞⡀⢠⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⣰⣶⠶⠦⠐⠶
⠀⠀⠀⠀⠀⠀⡀⢠⠿⡹⡵⠰⣋⠛⠀⠀⠀⠀⠀⠀⠧⠖⠒⠻⠶⠦⠀⠀⠀⠀⠀⠀⠘⣋⡉⢀⡦⡂⣀⠀⡆
⠀⠀⠀⠀⠀⠸⡯⡐⢀⣲⠂⣂⡀⣄⡾⠀⠀⠀⠀⢠⢤⣀⣃⣈⡃⣴⡄⠀⠀⠀⠀⠀⠘⠽⠛⠛⢫⢗⠿⠯⠷⠧
⠀⠀⠀⠀⠀⠀⡇⣇⣈⣿⠁⣿⡇⡇⡀⠀⠀⠀⠀⠈⠂⠉⠰⠆⡒⠈⠁⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⢥⠐⡆⣀
⠀⠀⠀⠀⠀⠀⡃⣉⠉⠐⠂⠀⠑⠁⠁⠀⠀⠀⠀⣀⠀⠙⠒⢒⠃⠀⢀⡀⠀⠀⠀⠀⠺⠺⣶⣄⡖⢲⡀⡇⠉
⠀⠀⠀⠀⠀⠀⡇⢙⣶⡮⠛⣥⡆⠀⣥⠀⠀⠀⠀⠀⠿⠛⠂⠙⠛⠻⠎⠁⠀⠀⠀⠀⠀⠀⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠑⠛⠛⠉⠉⠃⠀⠛
⠀⠀⠀⠀⢀⠀⣄⠀⠐⠴⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⡄⢠
⠀⠀⠀⠀⠀⢁⢸⢟⡶⠆⢗⣤⣇⠀⠀⠀⠀⠠⡤⢤⡄⣨⠇⠛⢓⡠⢶⠂⣰⠇⠀⠀⢀⡄⠀⠓⠩⠬⠈⢀⣀⡀
⠀⠀⠀⠀⠀⠲⠅⢰⡒⢒⢀⠀⠒⠀⠀⠀⠀⠈⠻⣨⣿⠶⢤⠤⢤⣖⠿⠴⠃⠀⠀⠀⣿⡏⢰⣛⡤⣤⣰⠊⢻⣿
⠀⠀⠀⠀⠀⢠⣬⣽⣿⣿⣶⣧⣄⡀⠀⠀⠀⠀⠀⡀⡅⢉⠛⡋⡛⢉⢤⠰⣀⡤⠀⠀⠛⠟⠀⣧⠉⢨⠆⠁⠘⠋
⠀⠀⠀⠀⣾⣿⠿⠿⠿⠿⠿⠿⢿⣿⡅⠀⠀⠀⠈⠉⠇⠘⠧⠧⠣⠀⠿⠤⠊⠀⠀⠀⠀⠀⠘⣁⣤⣇⣖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠈

⠀⠀⠀⠀⠀⣤⡶⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠸⠟⠀⠀⠠⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠐⠤⠊⠀⠈⢆⡀⠀⠀⠀⠀⠀⠠⡤⠤⠶⠦⠤⡤⢤⣄
⠀⠀⠀⠀⡨⡉⠩⠉⠅⠄⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡼⢻⠼⢴⡟⠛⠂⠈⡆⠀⠀⠀⠀⢀⣯⣛⣝⣗⣀⣇⡠⠟
⠀⠀⠀⢈⣖⠷⡤⣤⢴⣀⢿⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢹⣧⣿⡀⢣⢤⠀⠁⠀⠀⠀⠀⠀⢀⣀⣏⣉⣡⣤
⠀⠀⠀⠀⠙⡄⢹⠍⡉⢞⣨⡌⠀⠀⠀⠀⠀⠀⠀⢔⣁⡀⡘⠍⠉⠩⠤⠠⠵⠦⠀⠀⠀⠀⢂⡘⠟⠿⢛⡚⠛⣢⠇
⠀⠀⠀⠀⠀⣬⣌⣶⣤⣮⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠞⠓⠚⡳⡗⠀⠀⠀⠀⠀⠀⠈⡍⢀⡚⠹⠝⠈⣁⣤
⠀⠀⠀⠀⠈⢈⠛⡝⢿⠿⣟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⡃⡔⣰⢂⢔⡁⡂⠀⠀⠀⠀⠀⠀⠹⣾⡛⠷⠶⢞⣡⠇
⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡴⡀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡆⠠⡡⠀⣀⡍⢃⠀⠀⠀⠀⠀⠀⢈⣷⣺⣯⢱⠏⠷
⠀⠀⠀⣧⠀⠀⣷⠀⠀⣼⠀⢀⡎⠀⠀⡄⠀⠀⠸⡏⠙⡏⣏⠤⡍⣯⡍⢩⢾⠀⠀⠀⠀⠀⣿⠸⠁⠦⠤⠄⣉⣀⣴
⠁⠆⠐⢉⠑⠪⣄⣈⡉⢤⣨⢉⣑⠒⡞⠀⠀⢀⣠⠑⠴⠃⡈⠋⣁⡀⣑⣉⢉⡥⠀⠀⠀⠀⠃⣷⠀⣿⠃⣿⡇⡏
⠀⠈⢄⣟⣋⣴⣯⢥⢥⣤⣤⣬⣝⡜⠀⠀⠀⠀⠙⠛⣛⡋⡋⠀⠅⠭⠭⠬⠬⢅⡀⠀⠀⠀⠀⢈⠍⠡⠤⠁⠡⠁
⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⡷⠺⣤⣴⢶⣼⣴⣞⣳⣀⣸⡅⠀⠀⠀⣧⠸⣤⣎⠗⢇⡦⠀⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣁⣸⣟⣛⣋⣉⣓⣀⣿
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⣠⡞⠁⠀⠼⠃⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠰⣿⡀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⢀⣼⡿⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠙⠳⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⠀⢀⠈⠁⠀⢀⣾⣟⡡⠚⠁⠀⣠⣴⠟⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡀⠀⠀⢀⣀⠀⢀⡠⣤⠀⡰⠊⢀⣼⣿⠃⢰⣿⠇⠀⢀⣾⡿⠉⠀⠀⢠⣾⡟⢁⣠⠞⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⢀⣾⠏⡰⠋⣴⢯⠎⠀⢠⣾⡿⠁⢠⣿⠏⠀⠀⣼⣿⠁⠀⠀⢠⣿⡟⠋⠉⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠈⣿⣿⠀⣼⡟⡜⠀⣼⣿⠃⠀⢠⣿⠟⠀⠀⣼⡿⠀⢠⢾⣿⡇⠀⠀⢀⠾⣿⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⣿⠏⠀⣿⡟⠀⠀⢿⠃⠀⢠⣿⡏⠀⢀⠎⠈⠻⠖⠁⢸⣿⡇⠀⡠⠋⠀⣉⣛⣛⠁⠀⠀⢠⣾⠄⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣠⠾⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠿⣧⡤⠋⢀⡴⢋⠇⠀⠀⠻⠿⠛⠁⠖⠛⠉⠉⠉⠙⠓⣶⣿⡏⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⢁⣀⣀⠀⢠⡤⢤⡄⢀⡄⣠⣤⡀⠀⠀⠀⣴⠟⡠⠋⠀⠀⠀⠀⠀⣀⣀⠀⣠⣴⠖⠁⡆⣰⣿⠏⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠸⣄⠁⠀⣼⠁⡼⠳⣾⡾⠓⠚⠁⠀⠀⣼⡿⢊⡤⠶⣦⡀⢀⣴⠟⢁⠔⠰⣿⣇⠀⠚⢡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠐⠤⠟⠀⠀⠃⠘⠃⠘⠉⠳⠴⠋⠀⣠⢴⣿⡱⠋⢀⡀⢼⡗⣾⡟⠀⠀⠀⠀⠹⣿⣦⠀⣸⡟⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠴⣶⡄⠀⠀⣀⢤⣄⠐⠒⠉⠀⣼⡿⠁⡖⠁⡠⠟⠀⢿⣇⢀⡔⢁⡀⢀⣿⡟⠀⢿⣇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⡔⠁⣰⣿⠃⣠⠚⢁⣼⡿⠀⣀⡀⠀⠘⠃⠀⣩⠟⣳⠀⠀⠈⠉⠉⠀⠀⠉⢉⡁⠀⠀⣀⠉⣡⣄⡠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢧⠎⠀⣰⣿⢇⠞⠁⢀⣾⡟⠑⠋⠉⠉⠙⠒⢲⡾⠗⠊⠁⠀⠀⣀⣤⢤⡀⠀⣴⡿⠃⠀⣾⠏⣰⡟⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢰⣿⣿⠋⠀⣠⣿⡟⣠⡶⠋⠙⣦⡄⢠⣿⡥⠚⠙⡿⣠⡾⠋⢀⠜⢀⣾⠟⠀⠀⣼⡏⢰⡟⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢠⣿⣿⠃⠀⢰⣿⠏⣼⠏⠀⠀⣼⡟⢠⣿⣋⡠⠤⠊⢱⣿⠗⠚⢁⡄⣸⠏⠀⠀⣼⡟⢠⡿⢧⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣾⣿⠃⠀⢠⣿⡟⢸⡏⠀⠀⣴⡟⠀⣼⡏⠙⢻⣦⡀⠈⠻⠦⠔⠋⡀⢿⠀⢀⠜⢹⡇⣼⣃⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⡇⠀⠀⢸⣿⠃⠸⢧⡤⠊⢿⡤⠜⣿⠃⠀⠀⠙⢿⣦⣤⣤⣤⠞⠁⠈⠓⣁⡤⠴⠒⢻⣅⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠘⣿⣆⠀⣀⠀⢀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠈⠉⢁⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠳⣤⣤⣄⣀⣤⣤⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣯⡽⢶⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀
⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠦⣦⠞⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠡⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠐⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠄⠀⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠉⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣿⠃
⠀⠀⠀⠀⡀⢴⡿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢍⠀⠀⢸⡿⠋⡐⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠑⠂⠉⠛⠛⠉⠁⠀⠀⠀⠀⢤⡀⠀⠈⣇⠈⠁⠀⠁⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⣀⢹⣁⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡏⠐⠦⢽⣄⣀⣠⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠀⠀⠀⠀⡇⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣜⢂⡀⣄
⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠑⠪⣐⠠⡄⠀⣨⡥⠮⠀⠂⠁
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀⠀⠀⠀⠀⠁⠒⠉
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠻⢿⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢀⡀⠀⠀⠀⠀⠀⢀⢀⢀⡠⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠍⢳⣾⣶⣖⣊⠂⠁⠂⣀⡌⠓⣗⣲⣾⣴⠟⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠹⠁⢻⡄⢋⠏⢻⠈⢁⣤⠈⣽⢁⡟⠁⠈⢸⡏⢯⠓⣰⠋⢹⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⣷⡟⠀⠀⠀⢩⡏⢙⣿⢿⣄⣴⡄⠀⠀⠈⣷⣿⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣷⡌⠁⢀⡀⠀⠀⠛⠛⠋⠘⠛⠛⠀⠀⢀⡀⣫⣥⠄⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣽⡿⠀⣸⡏⠛⠷⠀⢠⣾⣷⡄⢀⣶⠿⢟⡇⢹⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠭⢿⣥⡀⣿⡷⢾⠆⠀⣿⣅⣸⢷⢸⡏⠀⠈⠁⢨⣿⣴⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⣿⣇⣀⣶⢠⣿⡍⢸⣿⣼⣷⣀⣜⡆⢰⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⡿⠃⣿⣛⠉⡁⣠⠀⢠⣄⣄⣀⡉⠉⣙⡀⠿⣿⣄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠿⡟⢉⣤⡶⠦⠈⠀⠇⠿⠂⠟⠛⠘⠸⠇⠈⠩⢥⣤⣄⡁⠘⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣞⣀⠛⢋⣴⠃⢰⣴⢠⣶⣰⡖⣲⣶⣲⠶⣴⠀⠲⣬⠻⠇⣘⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡿⠻⢿⣾⡁⢋⡈⠈⠙⠙⠛⠋⡁⠋⠁⠈⠋⠈⣃⡉⣴⣿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣷⢸⡇⠀⠀⠀⢠⣿⢻⣧⠀⢠⣾⠿⢟⡇⣿⣿⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣠⣴⣿⠇⣼⡇⠀⡀⠀⡾⣧⣼⣿⠀⣿⡇⠀⢀⠀⣿⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠋⠁⠀⣿⣧⣼⡇⠠⠿⠿⠹⠿⠆⠹⣿⣶⣽⠀⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡄⠀⠀⠀⠉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡉⠀⠻⣿⣦⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠛⠁⠀⣴⣾⣿⠟⢋⣽⣿⣶⠚⠓⣶⣿⣿⠟⢋⣩⣷⣦⡈⠙⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡄⣼⣟⣋⡤⠞⣉⣿⣿⣿⡇⢸⣿⣋⣤⠞⣋⣽⣿⣿⣧⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠆⢻⣿⣿⣷⣾⣿⣿⡿⠋⠁⠈⠙⢿⣷⣾⣿⣿⣿⣿⡟⠰⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⣀⣼⡆⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⠀⠠⢘⡈⠁⠁⡉⠒⠀⠀⠀⠀⠀⠀⠀⠈⠣⣆⣰⡧⠄⣒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠃
⠀⠀⠀⠀⠀⠀⠠⡾⠛⢿⢺⠗⣃⣘⢲⠶⠿⠓⣺⡇⠀⠀⠀⠀⠀⢠⡄⠸⠏⠎⠓⠃⠫⢆⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡤⠤⢶⣷⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠆⠳⡧⠿⠘⠹⣄⠼⠜⠧⢀⠀⠀⠀⠀⠸⡇⡌⠀⣿⡝⣩⣤⠠⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢤⠀⠶⠌
⠀⠀⠀⠀⠀⠀⣶⣤⣭⣍⣤⣄⠀⣶⢶⢰⣶⢲⢰⠾⠋⠀⠀⠀⠀⠀⡆⣧⣀⡟⡇⢸⢿⢠⡇⡇⠀⠀⠀⠀⠀⠀⠀⢰⠳⠶⠶⠲⠶⠆⠏⣿
⠀⠀⠀⠀⠀⠀⠈⡉⠍⡉⠡⠥⠤⠔⠐⠂⢒⠒⠐⠆⣤⠀⠀⠀⠀⠀⡇⣀⠂⠀⠲⠀⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⢐⠀⠟⠁⡉
⠀⠀⠀⠀⠀⠀⠈⡳⠚⠷⣤⣴⠶⣶⢧⣿⣞⣻⣂⣘⣯⠀⠀⠀⠀⠠⡇⠸⣤⣞⡿⢏⣰⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠖⠗⢖⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠁⠪⠟⠟⠗⠋⠹⠃⠸⠿⠀⠀⠀⠀⠀⠀⠀⠁⣾⡿⠧⠐⠿⠶⢶⣶⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⢀⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠸⣄⣸⠘⡦⢸⡃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⢿⢯⠿⣿⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⣉⣡⠘⢂
⠀⠀⠀⠀⠀⠀⣠⣦⠀⢀⣀⠐⠲⠶⠀⠀⣴⣴⣄⠀⠀⠀⠀⠀⠀⠖⠒⡶⠒⠁⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠦⠿⠹⠿⠻⠿⡾
⠀⠀⠀⠀⠀⢰⣿⡏⠀⣾⠋⣤⢄⡤⣺⡋⠉⣻⣿⡇⠀⠀⠀⠀⠀⠀⡸⡡⠼⢶⠷⠷⠾⡞⠂⠀⠀⠀⠀⠀⠀⠲⠒⠓⠂⠒⠒⠐⢚⠓⠛⠂
⠀⠀⠀⠀⠀⠘⠿⣿⠂⢑⣇⡙⠊⠛⡎⠃⠂⢿⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠉⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣻⣛⡿⢛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠞⠀⢠⠏⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⢸⠋⣀⣶⢾⠀⣾⡀⢹⡅⡒⠂⠀⠀⠀⠀⠀⣤⡘⠘⠛⠓⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣀⣼⣿⡸⢿⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠺⠃⡋⡘⣂⣋⣃⣘⡃⠉⠁⠀⠀⠀⠀⠀⢻⣷⣸⣰⡟⣧⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣅⣀⣁⣀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢠⣴⢥⡄⠁⠀⠉⣷⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢢⡀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⢀⡄⠀⡀⢀⡈⠀⠀⠤⠛⠈⠁⠀⣄⠀⠀⣾⣿⣿⢿⣻⠀⠉⠃⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⡄⠀⠀⠀⠘⠛⠀⡘⠛⠃⠀⠀⠘⠁⠶⠀⠀⢀⠀⠀⠛⠛⠛⠋⠁⡀⠀⠀⠘⢡⣿⡦
⠀⠀⠀⢀⢀⡀⠀⠀⠠⠀⢰⣿⣆⠀⠀⠀⠀⠉⠄⠀⠀⢀⡀⠀⠴⠀⠀⠂⠀⠀⡉⠀⠀⠀⠠⢀⠕⠛⣈⡃
⠀⠀⠀⠙⠉⠁⠠⠄⢠⣤⠘⠋⠉⠀⢠⣶⡖⠀⣤⣄⠀⠿⠟⠁⠀⠀⠀⢰⠀⠄⢀⠄
⠀⠀⢈⠂⠀⠀⢀⡀⠈⠙⠀⠶⠿⠀⠿⣿⠀⢠⣿⡇⠀⠾⠀⠀⠁⠈⠊⠄⡠⠀⠠⠄⠀⡀⠀⠁⠀⠀⡂⠀⠀⠈⠁
⠀⢀⡠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⢨⡍⠉⣀⠀⠀⠀⠁⠀⣦⠀⠀⠀⠀⢀⠂⢀⡄
⠀⠀⠀⠁⠀⠀⢀⠀⠀⢀⠀⠄⠄⠀⠃⠀⢸⡇⠀⢨⠗⠰⠄⣦⠀⣿⠀⠹⢢⡇⠀⣰⣾⣧⠀⠀⠀⠀⠀⣠⣶⡈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠁⠀⠀⠀⢸⡇⢀⠸⣀⠀⡆⣿⠀⣻⡄⠀⣾⠁⢀⠀⠉⠛⠀⠰⢦⣤⠀⠻⠟⠁
⠀⣀⠤⡀⢴⡆⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠙⣁⠀⠙⠋⠈⠉⠉⡀⣉⠁⠴⠟⠀⠘⣿⣶⠂⠰⣿⣷⣷⠀⡾⠂
⠀⠄⠄⠇⠈⠙⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠚⠁⠛⠃⠀⢀⠀⠀⠀⠀⢀⣟⣾⢾⣮⠁⢀⣬⣄
⠀⡀⠅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠄⠀⠠⠊⠀⠀⠠⠆⠀⠀⠘⠣⠄⠀⠸⣭⣿⣿⡗⠀⠈⠛⠋
⠀⠀⠀⠒⠒⢒⠂⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⠀⠀⠀⠰⠂⠓⠀⠀⣛⣳⠶⣶⠅⠀⠀⠀⡾⠖
⠰⠶⠓⠒⡓⠒⠓⢈⠀⠀⠂⠠⠤⠀⠘⠀⠀⡤⢠⡠⣄⠛⠿⠟⠉⠀⠀⠀⠠⠀⣴⡆⠠⢼⣭⣭⣟⠀⠀⢠⠒⣀⡀
⢈⡙⡒⠘⠀⠀⠠⠀⠀⠈⠉⣁⡳⡀⠀⠀⠀⠀⠄⠈⠃⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⠀⠼⠒⠱⠹⡛⠀⠀⠘⠀⠡⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡝⢿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠻⢶⣤⣀⣠⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⣀⣤⣠⣾⣿⣿⡿⠋⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣠⡴⢟⣽⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣀⡀⢰⡶⠶⠶⠶⢶⡆⠀⠀⠈⣿⣿⡀
⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣠⡾⢋⣴⣿⣿⣿⠟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⣷⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⡇
⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢠⣾⣫⣴⣿⣿⣿⠟⠁⠀⣠⡾⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣧
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⡇⠀⢀⣾⣿⣿⣿⣿⣯⣥⣤⣤⣘⣫⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡞⣁⣠⣾⠟⠛⠛⢿⡍⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⡟
⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣧⣀⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⣄⠀⣸⡇⠀⠀⣼⣿⡇
⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⡻⣿⠟⠉⠉⠛⠛⠛⠷⠶⠶⠶⢶⠶⠶⠶⠶⠿⠶⢶⣤⣤⣤⣤⣶⡶⠶⠶⠿⠆⢰⡏⠺⣧⡽⢃⣿⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢀⡘⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠃⠀⠀⣼⣿⡟
⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⢀⡀⠈⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣿⣧⠀⢰⣟⠁⢀⣠⣴⠾⠛⠉⠉⠙⠻⣦⣄⣀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠠⠤⡀⠀⢝⢤⡀
⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠴⡶⠴⠂⢀⣀⣂⡀⠀⠀⠈⠀⢀⠐⢁⡔⠐⠄⠀⠀⠀⠈⣏⢳
⠀⠀⠀⠀⠀⢂⠝⠁⢀⠜⠁⠀⠀⠀⠀⠀⢀⠀⡀⡠⠀⠀⢀⣖⢻⡓⢼⡽⠷⠆⠀⠀⣐⠀⡎⠀⠀⠀⡇⠀⡇⠀⢸⡈⡇
⠀⠀⠀⠀⢁⠀⠄⢴⡏⠀⢀⣀⣀⡀⡠⢀⠂⠐⠐⢁⡀⢠⣿⣭⡆⣏⣀⡈⠓⢀⠀⠀⢨⠀⢇⠀⠄⣀⠇⢈⡇⠀⢸⡤⡃
⠀⠀⠀⠈⠃⠠⠀⡘⠈⠉⠀⠀⠀⠈⠀⡈⠀⠀⠁⠉⢀⣿⡈⡿⢤⠋⡉⠲⣻⣷⣀⢄⠈⠧⡀⠉⠈⢁⣠⠎⠀⢠⡟⣸
⠀⠀⠀⢀⠀⡆⡇⡇⣀⣀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠀⣨⡷⠊⣤⠞⢿⡇⠀⣉⣹⠈⠂⣠⣄⣀⣉⠀⢉⣁⣠⡾⡏⠔⠁
⠀⠀⠀⢀⣇⢳⠁⠁⠀⠀⠀⠀⠀⠀⠀⢁⣨⠀⠇⠀⡹⠁⣾⡴⠒⠻⡿⠞⠻⡕⠀⠀⠈⠁⡬⠭⢍⡭⠏⠐⠂⠁
⠀⠀⠀⠀⠘⣌⠶⣔⡀⠀⠀⠀⠀⠀⠀⠰⠰⣆⢂⠀⠘⣿⣻⣾⣲⡂⢰⣾⠶⣇⣀⣀⣂⣤⡬⠀⠀⢠
⠀⠀⠀⠀⠀⠊⣺⣷⣷⣄⣀⠀⣀⡀⡀⢠⣣⡣⣊⣢⡀⠘⢿⣿⡿⡂⢯⡹⠂⣠⣤⣤⠀⠀⠙⢳⡖⠢⢁⣀⡰
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠀⠃⠉⠙⠋⠽⠉⠁⠻⡻⣻⡇⣼⣶⣞⣯⣭⣏⡙⢻⣻⠏⠛⠒⢭⣍⣉⠂⠐⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠈⣣⣌⡀⠙⠾⣟⠧⣍⣘⣥⠾⢛⠛⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠛⠉⠉⠙⠦⠤⠀⠀⠐⠘⠁⣰⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡈

⠀⠀⠀⠋⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠂⠐⠀⠀⠀⢀⠒⢀⠠⠀⢀⠀⠀⡠⡄⠀⠀⠘⡈⠀⠀⠀⠀⠀⠠
⠀⠀⠄⠀⠀⠄⠀⠀⠀⠢⠀⠀⠀⣴⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠈⠈⠀⠉⠀⠀⠥⠤⠤⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⡡⠤⢌⡁⠀⢀⣶⣤⡤⣀⠀⢀⡀⡀⣀⡀
⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⠀⠀⠙⠛⠛⠃⠀⠙⠛⠛⠋⠁

⠀⢀⡂⠀⢂⡀⠀⠀⠠⠠⠀⠀⠀⠒⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠈⠉⠒⠲⢤⣄⣀⠀⠀⠀⢀⣀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⠚⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⡀⠻⢬⢝⡞⠿⣧⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⢉⣤⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠻⠷⢶⣾⡿⢷⡶⠶⢟⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣤⠖⠋⣡⣦⡶⠖⠋⠁⢀⣠⣴⣾⡿⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣿⡶⠟⠋⠁⠀⣀⣤⠶⠛⢩⡟⢱⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⢀⣠⡴⠟⣻⣀⣀⣠⡾⠀⠈⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⢴⡚⠁⠀⠀⣀⣴⠾⠛⢻⡏⠉⠙⣛⡿⠟⠃⠀⣀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⠤⠺⡙⣆⠀⢻⣤⣶⡟⠛⠛⠃⢀⡼⣡⠔⠋⠁⠀⠀⠀⠀⠈⣽⠃
⠀⠀⠀⠀⠀⠀⠀⡟⣴⠛⠙⣆⠀⣹⣽⠶⠛⠁⠈⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠀⠀⠀⠀⠀⠀⣼⠃⢧⣀⣠⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⢿⣈⡟⣆⢹⠀⠀⠀⠀⠀⠀⠀⢀⡸⡛⣛⠟⠿⠿⠅
⠀⠀⠀⠀⠲⡖⢤⡄⢴⣛⣊⡙⠡⠳⡞⠡⡿⠀⠀⠀⣠⣦⠀⢈⡀⠒⠶⠀⢠⣤⣄⡀⠀⠀⠀⠈⢠⢏⣤⣤⣄⣤⡆
⠀⠀⠀⠀⠉⠻⣼⣯⢓⠶⠴⢒⣶⡻⠷⠚⠀⠀⠀⠀⣿⣏⠀⣟⣱⢆⣖⢾⠉⢹⣿⠇⠀⠀⠀⠀⠀⠉⠐⠓⠦⠴
⠀⠀⠀⠀⠀⠀⡀⡤⢉⡛⣃⣘⢉⡥⡄⢆⡠⠄⠀⠀⠛⠿⠀⣹⡆⠁⢩⠎⠁⠘⠋⠁⠀⠀⢰⠆⠏⣰⡶⡆⣰⡀⣿⢰⡆
⠀⠀⠀⠀⠀⠈⠁⣇⠠⠣⠣⠼⠄⠹⠧⠔⠃⠀⠀⠀⠀⠀⠀⡏⢠⣴⢧⣶⡀⠀⠀⠀⠀⠀⠀⠠⡝⠥⠁⠁⠉⢄⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠹⠉⠉⠐⠃⠀⠀⠀⠀⠀⠀⠈⠓⠒⠖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠠⡔⢨⡧⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡸⢧⠤⣄⣠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⠀⣠⠀⠀⠀⠀⠀⣤⡐⢶⢒⡒⢒⣒⡒⡖⢒⣲⢒⠒⠂⠤⢴⠀⠠⣏⠀⣿⡟⡿⠾⢷⣽⠂
⠀⠀⠀⠀⠀⠀⠈⠳⠠⠄⠑⠘⠁⠀⠀⠀⠀⠀⢿⠈⠉⡍⠉⠉⡉⠉⠉⣭⠉⣿⣿⡋⠀⠀⠀⠀⠙⡓⡘⣛⢛⡀⣨⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣴⢂⣸⡀⠀⠀⠀⠀⣼⢸⣠⣳⣤⡎⢏⢰⣂⠿⡆⠈⠈⡇⠀⠀⠀⠀⢌⠏⠿⢏⠋⡱⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⣥⣰⠄⠀⠀⠀⠀⠀⣿⠈⠁⢍⢤⡶⢶⣂⡲⢀⠠⠄⠀⡇⠀⠀⠀⠀⣠⣿⣿⣿⣯⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠤⣌⣉⣥⡿⠃⠀⠀⠀⠀⠹⠤⠤⠤⠤⠥⠤⠤⠭⠥⠤⠤⠴⠇⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠚⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⡞⢹⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠘⢧⡙⢦⢹⡸⡴⢋⡼⠃⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡘⢵⡼⡝⠀⠀⠀⠀⠀⠉⠚⢿⡿⠓⠉⠀⠀⠀⠀⠀⢣⣣⡫⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠟⠀⠀⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢹⠀⠀⡏⠀⠀⢾⠆⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠣⡀⠸⣤⠎⡅⠀⣠⡤⡀⠰⡖⠂⠀⣤⣄⠀⠐⠂
⠀⠀⠀⠀⠀⡞⠛⠲⢤⡀⠀⠀⠀⢰⣦⡜⠀⠀⣠⠇⠀⠯⢊⠄⠀⣸⠆⠀⠉⠁⢀⡤⠖⠛⢳
⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠦⠄⠀⠀⠉⠰⠿⠩⣧⣀⡤⣠⣤⡀⣤⠀⣤⠀⠠⠴⠛⠋⠙⠛⠋
⠀⠀⠀⠀⠀⠀⣶⣫⠽⠂⢀⠀⠀⣠⡖⠋⣹⡆⠈⣿⠀⢻⣼⡇⢻⣠⡟⠀⠀⡀⠐⠯⣝⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡝⠀⡜⠸⠀⠀⠈⠁⢀⣉⠀⠀⠉⠀⣠⣉⠀⠀⠀⢫⡳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣣⠞⠀⠀⣇⢣⠀⠀⠀⣼⠏⣨⡇⠀⣠⡟⠉⢻⠀⣤⠀⠀⠳⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠺⠷⠶⠊⢙⣚⣁⣛⣿⣃⣃⣀⡘⠛⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠂

⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢀⡀⢠⣄⣼⠂⡀
⠀⢰⡞⠋⠁⠀⢷⠀⢻⠳⡄⡟⠀⡏⠈⢳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣿⠋⠈⠃⢬⠟⠁
⠀⠀⢿⡁⠀⠀⠸⠆⢸⣀⣙⡇⠀⣇⠴⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣹⠰⠌⡷⣟⡤
⠀⠁⠈⡷⢶⣚⣯⠍⠉⠉⠉⠉⠉⠛⠒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶
⠀⠀⢶⡿⣀⡤⢷⠔⣾⢘⡷⠺⣇⣿⣀⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣐⠛⣂⠀⣀
⠀⠀⠀⣾⠁⠀⣸⠀⠈⠉⠀⡴⠚⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠦⣇⡇⡿⠀⣷⢳⡇⡧⠶⠆
⣴⣶⣤⣜⣲⠖⠋⣀⣀⠀⣤⢱⣋⡅⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⡁⣥⣉⡄⠉⣡⣹⠁⣴⣄
⢻⡿⣿⣿⠟⢀⠀⠉⠈⠀⠈⠀⠀⠁⢀⠸⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⠀⠈
⠈⠳⠿⠃⠀⢽⠻⠝⠣⠿⠯⠟⠷⠛⣻⠄⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣿⡶⡴⡶⠶⡴⣾⢟⡔
⠀⠀⠀⠀⠨⠜⠀⠀⠀⠀⠀⠀⢐⣋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣅⣍⠉⢉⡄⣤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠩⠟⠉⠙⠏⠉

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣴⣿⠟⠋⡍⠍⢙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠐⠢⣄⡴⠉⠀⠀⠙⡆
⠀⠀⠀⠐⠿⠃⠀⠠⠂⠰⠈⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣦⢦⢠⡄⡀⣤⣦⣤⠉⠹⠤
⠀⠀⠀⠀⠛⠘⣙⣛⢃⠁⡄⢃⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⡋⠸⡊⠏⡽⠏⢄⠈⠉⠀⢀
⠀⠀⠀⡏⣸⠇⠈⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⢻⣇⣷⡇⠀⠘⣤⢦⠀⠁
⠀⠀⠠⣷⡔⠛⣟⣾⣟⣻⣧⡞⣗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠸⠏⠟⠻⠟⠀⠁⠀⠓⣤
⠀⠀⠀⠈⣑⠄⢸⡄⠉⡀⢺⣁⢸⡌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠃⣒⣒⣳⣤⠄⡉⣍⡍⡈⠉⠉
⠀⠀⠀⠀⠈⢛⠎⣇⣏⠯⡜⢹⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠟⠘⠚⠚⢉⣿⡟
⠀⠀⠀⠰⠌⠻⣾⣾⣿⣛⣿⣵⡟⢧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠇⣠⠤⣠⠄⢁⡼⠀⠠
⠀⠀⠀⠀⠉⢄⠁⡱⠸⢻⠋⠻⣇⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡖⡦⢿⡰⢏⣼⣣⡶⡆⠫
⣀⣀⣀⣀⣀⣀⣁⣁⣢⣌⣐⣃⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠖⠈⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠶⠀⠀⢀⠲⠆⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠂⠄⠂⠆⠀⠀⠀⠆⢡⠀⠀⠀⠀⠀⠀⠀⢁⢈⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠆⠃⠐⠰⠂⠀⠀⠐⠐⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠨⠄⠄⠀⠀⠀⠀⠀⡠⠤⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠀⠀⠀⠀⠙⠀⠁⠃⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠐⠊⠀⢀⠘⠃⠀⠀⠀⢠⣲⣀⠂
⠀⠀⠀⠀⣈⣉⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠏⠁⡀⠀⠀⠀⠀⢰⠀⠁⠃⠀⠀⠀⢴⣆⣀⠀⣰⠶⠀⠀⠀⠀⡀⢂⠀⢠⡄⠀⠀⡀⣀⠀⢀⠈⠁
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡈⡁⠀⠀⠀⠀⠀⡀⠁⠀⢀⠀⠀⠀⠀⢀⠒⠀⠒⠴⠀⠀⠀⠀⡀⠃⠂⠀⠠⠀⠀⢠⡄⡀⠀⡠⣄⠀⠀⠀⠀⠉⣉⠁⠀⠀⠀⠀⠀⠠⠀⠤
⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠄⠈⠀⠠⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⢀⠁⡀⠈⢈⠀⠀⠀⠘⠂⠄⠈⠀⠋⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣐⠀⠲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠄⠤⣄⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⡠⠊⠁⣀⣀⣀⣀⣠⣤⢶⣻⠿⢿⡉
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠔⣀⠀⠈⠐⢤⡞⢠⡠⠚⣣⣽⣻⣫⢵⠚⡍⠀⠀⠀⠈⠢⣀
⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⣀⡀⠀⢀⡠⠆⢈⡄⠚⠁⡠⠂⠀⣜⣠⣾⣷⡿⠟⢻⠩⢳⢀⠣⠂⠀⠀⠀⠀⠀⠈⠓⢦⠀⣤⣀⡀
⠀⠘⠢⢅⡀⠀⠀⠀⠀⡦⠒⠁⡄⠒⠀⠠⠊⢁⡀⠒⠁⣀⣴⡾⣿⠉⠢⡀⠈⠑⠛⠒⠓⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣿⣷
⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⢀⡀⠒⢁⡤⠀⠉⡠⠔⠁⠈⠀⠀⠲⠟⠷⠶⠾⠤⣤⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠈⠀⠔⠋⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠶⣤⠤⠴⠶⠤⢤⣴⡇⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠈⣿⣇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠊⠁

⣻⢿⢿⣿⣿⣿⢾⡿⣝⢻⣛⣷⢿⡋⢔⣬⣶⢫⣿⣿⣿⢿⣿⡷⣽⠿⣽⢷⣟⣴⣯⣿⣟⣿⢻⣿⣿⣿⣿⣻⣿⣷⣗⣵⣿
⣷⢋⢿⣿⣿⣽⢿⡟⡻⣷⣽⣷⡽⣷⡏⣽⣇⡿⢿⣿⢿⡷⣿⣤⠻⣻⣿⢚⣽⡷⣿⣻⣿⣾⣾⣷⣽⣷⣴⡿⣿⣽⢿⣿⢯
⣿⣿⡻⣿⣿⣿⣛⢿⣿⣾⣝⠻⡇⣿⡿⢟⡴⣷⣿⢿⣜⠾⣿⣹⣷⠻⢣⣟⣿⣆⣭⡞⣿⡍⣿⣿⣯⣿⣿⣻⣟⣻⣿⣿⡵
⣮⣽⢹⡜⢿⣿⣯⣿⣿⣿⣿⣧⡄⢿⣣⡿⢠⣿⣿⢿⣽⣷⡝⢿⣿⢀⣟⡵⠿⢟⣯⣿⣿⣿⡜⣿⣿⣿⣿⣟⡿⣿⣋⣽⣾
⣟⢺⣍⢻⣆⢋⢫⣿⣿⣿⣿⣿⣿⡆⠻⢡⢿⣿⡏⣾⢡⣼⣿⣾⠇⠸⣏⣴⣾⣿⣿⣿⣯⣿⢠⣿⢿⣿⣷⣿⢺⣿⣿⡿⣷
⢻⣾⢻⡇⢼⡎⢣⡞⢻⣯⡻⢿⣿⣿⢀⣿⣏⣷⠠⣷⣿⣿⣿⡏⢀⣞⣿⣿⣿⣿⣿⣾⣿⡇⢸⣛⣿⠟⣯⣾⣿⣻⣯⣝⣛
⠀⠻⣷⣝⢸⡇⣿⣷⡀⢿⣿⣮⡻⣿⢸⣿⣯⣾⡼⣿⣿⣿⡟⠸⣿⡝⣹⣷⣿⣿⢿⣿⣿⡟⢸⡿⢋⣾⣿⣿⣿⣿⣙⡫⣷
⠓⠎⡈⠻⣭⠇⣿⣙⠓⠈⠙⢿⣿⣦⠘⣯⣭⣽⡁⢿⣿⡿⠁⣸⡿⣇⣽⡿⣿⣿⣿⣯⣻⡏⢈⣴⢿⡇⣾⠾⢛⣿⣫⣷⡟
⠉⠉⡰⠦⠀⠀⠷⡬⠷⠿⣶⠀⡙⢿⣇⢹⣿⣿⣷⡈⠻⠃⢰⣿⡻⣏⣿⢟⣿⣿⣿⣿⣿⣧⣾⣯⡟⢀⣵⡞⣿⣯⣿⣕⣾
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡝⢦⡉⠀⢿⣿⣿⡇⠀⠀⣿⢹⡿⣿⡞⣸⣿⣻⣿⣅⣿⣷⠉⢻⣶⣿⣿⡼⣿⣽⣷⡯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⣿⣶⠈⢿⣿⡇⠀⠀⣿⡈⢿⣿⢁⣿⣾⣿⣿⣿⣿⣿⠀⣾⣿⢟⣭⡞⣼⠿⢳⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠻⣧⠀⠘⣿⣿⣎⠃⣾⣿⣿⡿⣿⣿⣿⡿⢀⣿⣿⠿⢋⣰⣾⣿⣻⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣄⠀⠀⠈⠃⢐⣿⠙⡿⢰⣿⠸⣻⣿⣿⣿⡿⠃⠘⢋⣁⣤⣼⣟⣻⢿⣟⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢷⣄⠀⠀⠀⢽⣷⠃⢘⣵⢚⢻⣿⡿⠋⣠⣶⣾⣿⣿⣿⣿⣻⣿⣿⣻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⣆⠀⠀⢸⣏⢰⠏⢊⣿⠟⠉⣠⣾⣿⣿⣿⣿⢿⣎⣿⡿⣿⢧⢿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣿⡄⠀⢠⠨⣿⣆⣁⣤⣴⣿⣿⣿⣿⣿⣴⣿⣤⣿⣹⣯⣿⡾⠼⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⠁⢀⣾⣿⣷⢰⡆⠀⢻⣿⣿⣿⣿⢿⣿⠏⣞⣻⣿⣽⣿⣿⣿⣟⢟⣝⢛⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡟⠀⠸⢟⡿⠁⠈⢃⠀⢹⣿⣿⣿⠻⠟⠻⣾⣿⢧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡾⠀⠀⣸⡾⠁⢸⡇⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣴⠟⠁⢠⣿⡇⠀⠀⣴⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⡠⢾⣿⡇⠀⠀⠛⢷⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⣠⣿⣿⠃⠀⣄⡀⠘⣷⣄⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡛⠝⠋⢠⡿⣿⠿⠦⠈⠻⢿⣷⡬⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀
⠀⠀⠀⠀⠀⠐⢡⠎⠘⣆⡅⡆⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢲⠃⢀⣴⠀⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⠓⡁⠓⠀⡇⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢸⠄⠀⡀⢀⡄⠠⡀⠠⠀⠀⠀⠀⠀⠻⣸⠀⠸⠸⡀⠃⠀⠘⢆
⠀⠀⠀⠀⠀⢀⠀⢨⠀⡸⠺⠀⠘⠀⠐⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⡿⡇⠸⠇⠀⠺⠀⠀⠀⠀⠀⡀⠘⠀⠣⠀⠀⢉⠀⣴⠀⡼
⠀⠀⠀⢀⣠⣼⠁⡄⠀⣤⡄⣲⠀⡀⡆⡄⣰⠛⡄⠀⠀⠀⠀⠀⢸⢻⠀⠀⠃⡔⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⣀⢰⡆⣷⢸⠀⣽⠐⠁
⠀⠀⠀⢼⢾⢺⡇⢧⣼⢻⠁⠓⣾⡇⡇⠐⠧⠐⢻⠀⠀⠀⠀⢀⠄⠘⠆⠠⠀⠤⡅⢀⠔⠀⠀⠀⠀⠀⡇⠀⣿⠈⠁⢧⢸⠀⠸
⠀⠀⠀⠀⠘⠌⠃⠀⠀⠀⠁⠐⠘⠃⠀⠀⠀⢀⡞⠀⠀⠀⠀⡈⠰⡇⡇⢰⠠⠁⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⠈⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⡊⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡼⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢺⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠸⢓⡘⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠠⠔⠂⠀⡀⣀⠀⠀⠀⠀⠀⠀⢸⡀⡀⡟⣰⢠⢻⢸⢸⡀⠀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠠⡜⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠆⠀⠀⠘⠉⢇⠀⠀⠀⠀⣀⠀⠈⠆⠁⠓⠉⠀⠈⢸⠈⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠹⡂⢠⡆⠀⡧⠉⢶⣄⠀⠀⠀⢰⠀⠁⠠⠄⠀⡄⣾⠀⢲⢠⢀⡆⠀⡏⠀⠀⢰⡀⠀⠘⡆⣤⡄⢸⡇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠀⠁⠈⠃⠀⠑⠀⢰⠁⠀⠀⠀⢸⡀⢀⠄⢹⠀⠇⣿⠀⢸⠀⢸⡁⠀⠇⠀⠀⢺⡅⠁⢸⡃⠓⡇⠀⠠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡔⠳⡄⠀⢠⠀⠀⡴⡏⠀⠀⠀⠀⠈⢳⠈⠀⠙⠀⠀⠘⠄⠸⠀⠀⠉⠀⠀⠀⠀⠈⠆⠀⠀⠁⢀⠉⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢵⣖⠻⣋⢻⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⡞⠈⢲⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠘⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡞⣻⣟⠛⣉⡉⡍⠉⠹⣿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠘⣽⢫⣿⣆⣸⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣇⢸⡼⠛⣥⢟⡏⣆⣀⣓⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢉⠉⡝⡏⣍⣽⢹⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⠿⠿⠽⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢣⣉⣀⠀⣌⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⣹⢦⣰⡄⣶⣯⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣤⣒⣶⢀⣤⡖⡄⣾⢨⡂
⠀⠀⠀⠀⠀⠀⠀⢦⣀⠹⡇⠿⣼⠛⠧⠟⠟⠓⢠⣎⠀⠀⠀⠀⠀⠀⠀⠐⢙⣄⡃⣁⣉⢩⡉⢹⣯⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣻⣦⡀⢸⣷⣾⠟⡶⠣⠾⠊⠀⠀⠀⠀⠀⠀⠀⢠⠆⣘⣛⡄⡈⠁⠀⡀⡉⣽⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⢠⢬⡅⠚⠚⠀⠀⣨⡭⣽⠇⠀⠀⠀⠀⢀⣰⠇⢳⠹⠻⠃⢙⣗⠛⠓⠓⠏⢘⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⠚⠹⣷⣗⣮⠿⢏⣰⡟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡆⠘⠏⠉⠁⠾⠀⠺⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣶⣤⣤⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣤⣖⡗⡒⣒⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⣀⣰⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠟⠳⠎⠷⠧⠛⠥⠆⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠋⠉⠙⠙⡋⠿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⣿⡧⢐⣂⠰⠷⠶⠜⠂⡀⣃⡀⣼⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠛⢂⠙⠛⢂⣠⣐⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿⠀⢸⣾⡗⠚⡇⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠰⡇⠟⠿⠿⠽⠻⠜⡈⢃⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠴⠼⠛⠃⠀⣇⡇⢸⠇⡌⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠘⠀⡿⠥⢈⠉
⠀⠀⠀⠀⠀⠀⠀⢨⡇⢄⡰⠄⠘⠚⠂⢀⠘⣂⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⡶⣶⠼⡠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣥⣴⡎⡿⢻⢀⣆⡄⠀⣣⠀⠀⠀⠀⠀⠀⠀⠷⣠⣤⡶⡄⠀⣶⣧⣄⣀⣀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠃⣴⢫⣿⣿⡤⠴⠟⣾⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠎⠁⠉⠀⠈⠙⠉⠙⠻⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠒⠠⠤⠥⠐⢪⠕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⣆⠈⢁⠀⠀⢀⣀⠀⡀⠀⠠⢀⡤⠄⣿⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢷⡀⠀⢹⡄⢸⡇⢠⡏⠐⢰⡇⢀⢱⡏⠀⠁⠈⣩⡟⠀⢀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢸⡇⠀⢸⡏⢸⡇⢸⡇⠀⢾⡇⡐⢸⡇⠀⠀⢀⣿⠀⠀⠛⠇⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠘⠃⠸⣇⠈⠓⠈⠀⠛⠃⠀⠈⠀⢠⡜⣇⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⠀⢸⡇⠉⠀⣰⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠘⣧⡀⠀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠘⣧⡀⣿⠀⠀⣀⠐⠀⣸⡆⠀⠀⣾⡇⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⡔⠈⣶⢹⡆⢿⠀⢰⡯⠀⠃⢹⡇⠂⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡀⢌⡿⢸⠇⢸⣇⡜⢧⠘⠀⣸⡇⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠑⠀⠔⣋⠀⠀⠉⠀⠀⠀⠀⣿⠁⠠⡀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿⠀⠀⠀⢀⡀⠀⠀⢸⠁⠀⠀⠀⠀⢀⠀⠀⠉⡀⠀⡇⢠⠆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⡿⠀⡞⢰⡌⠓⣶⠀⢰⡄⢸⢀⡆⠀⣿⢰⡇⣿⠀⣿⠐⠃⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠷⠀⠧⢸⡇⠀⣿⠀⠸⠇⣼⠘⠇⠀⠛⠈⠇⠈⠀⢿⡄⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠉⠀⠻⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊




⡿⠿⠿⢿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⣤⠖⠒⠀⣇⠀⡷⣄⣸⠀⡏⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⣰⠗⠸⠏⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⣀⣗⣘⣏⢰⣧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⠿⠞⠷⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢽⠒⠯⡿⠋⠉⣉⠉⡉⣉⢓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢟⡥⠒⢻⠘⢧⠽⠉⣷⣿⠬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠉⣧⣠⡄⢀
⠀⠀⠀⠀⠀⠀⣀⣀⠘⣅⣀⡾⠀⠀⠀⢾⠥⠞⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠛⠹⠿⠿⠁⠟⠸⠇⢉⡁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠒⠃⠘⠊⠛⠃⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠚⢸⡛⠓⠐⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠘⠾⠟⠁⣸⠶⠾⠰⠷⠶⠶⠶⡦⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠰⣟⣷⣤⣤⣤⣤⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠀⢰⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣭⠉⣩⣠⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠉⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⢀⠔⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠨⠀⠔⠀⠻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠲⣤⡝⡅⣠⣤⣄⡹⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⣚⡘⡀⣀⢐⡘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⣖⠚⠻⠿⡉⠛⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡩⣇⠀⢀⠀⡀⠰⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠹⣯⡿⣇⡀⢻⠶⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠉⠧⠿⠭⢟⡎⢫⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⢀⡀⣀⣋⠉⠑⣃⣀⡀⣌⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦⣸⣂⢤⠈⢶⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⡇⣠⠶⣠⡰⠶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢼⣥⣿⣿⢿⣎⣿⡟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢁⡀⣀⠠⢊⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠊⡋⢿⡿⠿⣇⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⢼⡠⣏⣴⣩⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠑⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣀⠀⣤⡀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡀⡄⢠⡤⣠⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡟⣷⢿⠿⢿⣅⠀⠀⠀⠠⠋⠿⡈⠈⠲⠀⠀⠀⠀⠀⠘⣧⢿⣿⡗⢷⣤⣚⡸⠀⠀⠠⣄⣀⠀⣤⣤⣶
⠀⠀⠀⠀⢸⣇⣭⣀⣹⣼⣿⠀⠀⠀⠘⠀⢠⣀⢇⠄⠂⡆⠀⠀⠀⠀⠠⢆⡆⠷⡜⡆⣷⡆⠀⠀⠀⢻⡿⡆⢿⠿⠏⠆
⠀⠀⠀⠀⢸⣾⣬⣧⣾⣿⣿⠀⠀⠀⠀⠙⠌⠟⠈⠁⠈⠀⠀⠀⠀⠀⣶⣄⣶⣲⣰⢠⡤⢰⠀⠀⠀⢀⠀⠀⠀⢠⠐⢄
⠀⠀⠀⠀⢸⣿⠿⣏⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠛⠈⠃⠚⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⣶⣴⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣧⡆⣶⡆⢰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⣦⣤⣶⠀⠄⠀⠀⠀⠀⠀⣯⣥⠩⠭⠭⠭⣭⣽⡄⠀⠀⠀⠀⡤⢤⣤⣤⡄⠀⠀⠀⠀⠀⢠⢤⡄⢰⣤⠀⠆
⠀⠀⠀⠀⠀⣀⡀⡀⢰⣖⣿⠀⠀⠀⡐⡃⡐⡛⡁⣀⢘⢂⡀⠀⠀⠀⣼⠓⡒⡶⠞⠞⣦⡀⠀⠀⠀⣾⢸⣷⣿⡸⣶
⠀⠀⠀⠀⠀⣿⡏⢷⣿⠿⠙⠀⠀⠀⣿⢱⣷⣏⢏⣿⢻⢸⠇⠀⠀⠘⠿⢧⣇⣧⣄⣽⣼⠗⠐⠀⠀⢘⣉⠏⠈⢡⡏
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣿⣼⣿⡇
⠀⠀⠀⠀⠀⣤⠀⡄⠀⠀⡠⡤⢤⡄⢀⠀⡄⡀⠀⠀⠀⠀⠀⡠⣤⣄⠀⣤⣠⣤⣀⢀⡀⠀⠀⠀⠀⣴⢱⣮⣯⣯⣧
⠀⠀⠀⠀⢸⢿⣰⣇⢷⢼⡣⡧⣿⡿⠼⠔⡟⠏⣧⠀⠀⠀⠈⠿⠭⠟⠀⠛⠙⠋⠃⠚⠁⠀⠀⠀⠀⢸⡜⠇⠃⠸⠵
⠀⠀⠀⠀⠈⠸⠇⠉⠀⣠⣀⠥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⣏⢰⢃⢸⠙⡇⣾⢺⡅⠀⠀⠀⠠⣬⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠈⠃⠈⠃⠘⠀⠃⠋⠐⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⡀⠂⠀⠈⠠⠈⠐⢉⠂⠈⠅⠀⡐⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠌⡠⢀⢀⠀⢀⠘⠂⠀⠀⠀⠱⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠈
⠠⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⠀⠈⠀⠡⢠⣉⠢⠁⠐⠇⠑⠘⠀⡀⠉⢁⠁⠀⠀⠀⠀⢣⡐⠶⡄⠂⠀⠆
⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⣀⢘⣤⡤⡌⠂⠀⠀⠀⠀⠀⢀⡠⡄⠀⠀⠂⠈⠉⠀⠀⠀⠀⡀⠠⢄⠒⠀⠸⠉⠁⠀⠀⠃⠀⠐⠀⠲⡀⠉⠀⠁⠁⠄
⠙⠁⢀⠀⠀⠀⢒⠐⣿⣀⡩⠺⠟⠓⠃⠁⠀⠀⠠⠚⠀⠀⠀⠀⠁⢂⡁⠂⠈⠐⠀⠑⠀⠀⠄⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠀⠀⠂⡠⠄⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⡀⠊⡠
⠂⢄⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠠⡠⠀⡁⠁⠀⡤⠂⠀⠀⢀⠉⠃⡐⣰⡤⠠⠤⠄⠈⠁⠀⠀⠈⠀⠐⠀⠒⡈⢀⡀⠄⡀
⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡀⠀⣀⠀⠠⠂⠀⠀⡋⠀⡕⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠉⠈⠀⠑⠀⠀⠔⠈⠀⠀⠀⠀⠀⠈⠀⢁⠂⣸⠍⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠁⠂⠀⡆⡒⠂⠇⠀⠈⠀⠀⠀⠀⠀⠫⡈⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠁⠂⠀⠠⠀⠄⠃⠀⠀⠀⠀⠀⠤⠌⠄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⢈⠀⠀⠀⡀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠈⣀⠐⠁⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⡀⠀⠀⢀⠀⠐⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⢐⠂⠨⠙⡌⢢⡱⠀⠀⠠⠀⠀⠔⠁
⠀⠑⠄⠀⠔⠀⠀⢀⠐⠀⠀⠀⠠⠀⡠⠀⠀⠀⠉⠀⠂⠀⠁⠀⠀⠀⡐⠀⠀⠠⠀⠄⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠀⠨⠐⠅⠈⠠⢈⠁⡁⠀⠀⠀⠀⠁
⠀⢀⠀⢀⠁⠀⠉⠀⠀⠀⠠⠄⡀⠚⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠈⠂⠀⠑⠘⠂⠀⡀⠀⠀⠀⠀⠀⢠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠈⢀⢀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐
⢀⠀⠀⠒⠒⠂⠀⠒⠒⠐⡀⠀⠀⠀⠀⠀⠀⠨⠿⠃⠹⢠⡍⠉⡹⣷⠆⠃⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡄⢀⡠⢀⠄⢀⡀⢀⡀⠀⢊⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠁⠀⠱⢉⠀⠐⢃⠠⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢌⠄⢀⠀⣀⠀⠀⠁⠉⣤⠀⠀⡐⠀⠄
⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢸⠁⡈⠘⢠⢄⠡⢡⠲⠀⠸⠀⠬⠦⢀⠀⠀⠂
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⡀⠀⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠒⠛⠋⠉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠙⠛⢿⣿
⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠐⠒⠛⠉⢁⠀⠀⠀⢶⡄⢀⡀⠀⢀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠉⣓⠀⠘⢿⣿⡆⠀⠀⣰⠋⠀⠀⢰⠞⢋⠟⢁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⢸⣿⣿⣿⣿⣿⣿⠟⡀⡀⠀⠀⠀⠈⠉⠛⠒⠂⠀⠀⠀⠀⠀⠀⠛⠃⠘⠁⠀⠈⠁⠀⠀⠀⠀⣠⣶⣶⣆⠀⢦
⠀⠈⣿⣿⠛⠀⠚⠁⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⢀⣾⣿⣿⣿⣿⣷⣾⣿⡆
⠀⠀⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡄⠐⠂⠀⠠⠀⠀⠀⠀⢀⣾⣿⣿⠟⠋⠉⠀⢸⣿⡷
⠀⠘⣿⣿⡿⠿⣿⠛⠉⠁⠠⠀⠒⣶⣶⣾⣿⣿⣿⠟⠿⢿⠟⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠁⠀⣰⠆⢈⣿⡇
⠀⠐⣿⣿⡄⠀⣹⡆⢠⣶⡆⠀⠀⠻⠋⢉⣹⣿⣿⡧⠀⢤⣄⠞⠁⠀⠀⠠⠀⠀⠀⢀⣾⣿⣿⠁⠀⢀⡀⠿⢠⣾⡿
⠀⠀⣿⣿⣠⣂⠈⢿⣿⡻⠃⠀⠀⠀⠀⢻⣧⡹⣆⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⣀⢼⣿⣿⡇⠀⣄⠀⠈⣠⣿⣿⠃
⠀⢠⣿⣿⣿⡏⠀⠀⠙⢧⢀⠴⠔⠂⠀⠈⠻⣧⣨⣤⠤⠞⠃⡀⠁⠰⣮⡉⣻⡿⣿⠰⣿⣿⠁⠀⠘⣿⣿⣿⣿⡏
⠀⠈⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⡗⠀⠀⠠⡼⠃⣸⠀⠀⠀⠙⠓⣿⠀⣿⣿⠄⠀⠀⠈⣹⣿⣿⢳⣄⡀
⠀⠀⣿⡄⡀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠘⠿⣯⣬⡿⠛⠀⢠⡏⠀⠀⠀⠀⠀⠈⠀⠻⠻⡆⠀⠀⠀⣹⣿⡇⡌⢏⡿
⠀⠀⣿⣇⢃⠀⣴⠀⠀⠀⠀⠈⢠⠈⠀⠄⠀⠐⠒⠃⠀⠀⠀⠘⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⢠⡇⠜⡡
⠀⠀⠁⠹⣼⡄⣸⠀⠠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣠⣴⠀⠊⣴⢨⡏⢁⣾⠇
⠀⠀⠀⢠⣝⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣼⣧⡾⢣⣿⣵
⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡟⠀⢀⣿⣟⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠖⠀⡀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⢧⡀⢸⠇
⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠙⣦
⠀⠀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠀⠉⠀⠀⠈⠃⢀
⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠟⠳⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡇⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣞⣀⡀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠀⠟⠸⠀⠀⣠⠀⣼⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠂⠀⠀⠀⠀⣠⠄⣡⣾⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠈⠑⢶⣦⣤⣤⣤⣤⣤⣶⠟⠁⠀⠀⠂⠀⠀⢀⣴⣾⡿⣀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡠⠀⠀⣴⣿⢇⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢈⠙⠿⠏⠋⢀⠀⠐⠀⠀⠀⠆⠾⣧⣿⣿⣿⣿⡻⣿⣿⣿
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠟⠛⠛⠛⠛

⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⢠⡟⠉⠀⣤⣍⠻⣦⠀⠀⢀⣶⠛⠉⢩⣉⠻⣦⡀⠀⠀⢀⣾⠛⠉⢠⣍⠛⣦⡀⠀⠀⣴⠟⠉⢀⣬⡙⢷⡄
⠀⣿⠀⠀⠀⠿⠿⠇⢸⡇⠀⢸⠃⠀⠀⢸⣿⣧⢸⡇⠀⠀⣼⠁⣀⣀⣼⣿⣧⢸⡇⠀⢸⡇⢸⣿⣼⣿⣿⠀⣿
⠀⢻⣆⠀⠀⠀⠀⢠⡾⠁⠀⠸⣧⠀⠀⢸⡿⠋⣼⠇⠀⠀⠹⣦⠙⢿⣿⠿⢃⣼⠃⠀⠈⣷⡈⠿⢿⡿⠟⣰⡟
⠀⠀⠙⠻⠶⠶⠾⠋⠁⠀⠀⠀⠙⠳⠦⣤⡴⠟⠃⠀⠀⠀⠀⠙⠻⠶⠶⠶⠟⠁⠀⠀⠀⠈⠛⠷⠶⠶⠟⠋

⠀⠀⣠⣴⣶⣶⣶⣦⡀⠀⠀⠀⢀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄
⠀⣰⣿⣿⣿⡏⠉⢿⣿⡆⠀⢠⣿⣿⣿⡟⠙⢻⣿⣆⠀⠀⢠⣿⣿⣿⡏⠉⢻⣿⣆⠀⠀⣾⣿⠿⣿⠉⠛⣿⣷
⠀⢿⣿⣿⣿⣷⣶⣾⣿⡇⠀⢸⣿⣿⣿⡇⠀⢀⣿⣿⠀⠀⢸⣿⡟⠛⠃⠀⢀⣿⣿⠀⠐⣿⣯⠀⠈⠀⠀⣽⣿
⠀⠈⢿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢿⣿⣿⣧⣤⣾⡿⠃⠀⠀⠈⢿⣿⣦⣤⣴⣿⡿⠃⠀⠀⠹⣿⣷⣤⣤⣾⣿⠏
⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁