Clips Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣀⣠⣀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠁⠀⠈⢣⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⠙⣄⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠈⢦⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⡠⠤⠤⠤⢤⣷⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡷⠃⢀⡠⠤⠤⣀⠀⠱⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣇⢀⡏⠀⠀⠀⠀⠙⢦⠱⡄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢆⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⢣⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡁⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⡄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢆⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢧⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠭⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢳⡀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠉⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢇⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⣀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠈⠲⠤⠔⠒⠉⠁⠀⢀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⣀⣀⡠⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡴⠂⢀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⢤⡘⠒⣉⢤⢀⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣴⣩⣶⣤⡆
⠀⠀⠀⠀⠀⣀⠀⣧⢠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢬⠁⠾⣹⣾⣯⣁⣩⠏⠀⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⡯⢋⣀
⠀⠀⠀⢀⡼⠟⣁⣬⠚⠀⠀⠀⠀⠂⠀⠀⠤⣶⡘⠚⣶⡀⣷⣽⣾⠶⠫⠷⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠠⣾⣽⠇
⠀⠀⢠⡾⠁⢰⠋⢠⣎⣉⣉⠀⠀⣀⠀⠀⢲⣭⣼⣉⠩⢼⠯⣿⣿⣶⣶⣶⣖⣱⡀⠀⠀⠀⠀⠀⢀⣠⡎⣀⣀⡀
⠀⠀⣸⠃⢤⡜⢶⡟⠁⡌⠀⠇⠀⠌⠀⠀⠘⣿⣶⡟⠒⠂⠲⠟⢺⣞⣏⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⢢⡄⡀
⠀⠀⣧⣴⢷⣤⢟⣱⠾⠀⠀⠀⣩⡀⠀⠀⠀⠈⢺⣿⣿⣖⡷⠖⡏⠀⡆⠁⣁⠀⡦⠠⠉⠀⣀⣿⣿⣿⣿⡿⣿⢻⡇⠈⢰⡟⣀
⠀⠠⣿⡿⣻⣿⣼⠋⠂⠄⠀⠀⠉⠙⠢⡀⠀⠀⠀⠈⠹⠟⣷⢾⣿⡏⢈⡖⠿⡛⠁⡀⢰⣤⣿⣿⣿⣿⣿⣷⣷⡊⠀⠀⠀⠼⠏⡀
⠀⠀⢻⣿⣿⣿⣾⣿⡎⠀⠛⠀⠀⠀⠀⠀⢀⠀⠎⠁⠀⢀⠀⠈⠋⠃⢸⡷⠀⢀⠐⣿⣿⣿⣿⣿⣿⣿⢟⢘⣻⡷⠀⠀⠀⠀⠐⠁
⠀⠀⠈⠻⠟⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⣃⣾⡟⠀⢀⣷⡀⠀⡇⠀⡼⠀⠸⢿⣿⣿⢿⣯⣵⣶⣤⣟⡗⢉⠀⣀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⣄⣰⠷⣄⣈⠙⠿⡟⠻⡄⣄⣸⣿⣇⣀⢓⡼⠁⢢⠀⢻⣿⣿⣿⣿⡿⡿⣿⠏⠁⠀⢲⣤⡉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣿⣿⣿⣿⣿⣏⠑⠂⣵⡀⣇⣿⣿⣿⣿⣿⢸⠃⠀⢀⡷⠉⢹⣥⣮⠟⡀⠁⡜⡇⠰⢠⢰⣼⡿⠓
⠀⠀⠀⢰⣄⡀⠀⠀⠀⢀⣉⣹⣿⣿⣿⣿⣿⣼⣧⢈⡣⣸⣿⣿⣿⣿⡏⣿⠀⣠⠋⠀⢠⡎⠈⠳⠾⢃⡸⣧⢷⡜⠞⠓⠉
⠀⠀⠀⠀⢿⣿⣀⢈⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡌⣿⣿⣿⠁⣟⣼⠋⠄⠀⡾⢰⣞⣦⠀⠀⠀⠁
⠀⠀⠀⠀⣤⣤⣽⢿⣤⠂⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣳⣼⣿⣿⢖⡽⠃⢀⡆⠀⡃⣸⠟⠁⠀⡴⣀
⠀⠀⠀⠀⠉⠛⢁⣾⡀⠁⢢⠀⠀⠼⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠛⣯⣠⣥⣿⣀⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣘⢷⡟⢂⣉⣁⣠⣄⣀⣁⣤⣼⣿⣿⣿⣿⣿⡧⠐⣀⣤⣾⣿⢻⣿⣿⣿⣿⣴⡦⠖
⠀⠀⠀⠀⠀⠀⠖⠾⠁⠺⢃⣹⣯⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠛⠃⣼⣿⣿⣿⢧⡞⡼⠛⠙⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢿⣿⣿⣿⣿⣿⠟⢛⣷⣬⠟⠁⢠⣶⣶⣝⠻⣿⣏⣼⣡⣶⣿⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠋⠁⢠⣿⣿⡿⠒⠀⢠⣉⣛⣿⡄⠿⣸⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠽⣿⣿⡟⢰⣿⣿⣛⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠿⠿⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⡲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⣐⠀⠛⢠⡄⠀⠠⠄⠀⠀⢠⠀⠀⠀⣠⡄⢈⡀⠀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠰⡕⢢⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠤⠁



⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠈⠦⡄⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋
⠀⠀⠀⠀⠀⡜⣂⡈⠉⠉⢹⠏⣐⣒⡒⠚⠯⠤⢤⣠⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⡀⣀⡤⠠⠖⠀⠀⢀
⠀⠀⠀⠀⠀⠘⡴⠃⠀⠀⠀⠀⠚⠁⠈⠉⠉⠉⠒⠒⠖⠒⠒⠛⠒⠀⠰⠃⠀⠀⠀⠘⢁⣀⡠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⣀⣀⣀⣘⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀
⠀⠀⠀⠀⠀⠀⢠⣦⣤⣴⠶⠶⢖⣫⡭⠤⠤⣞⣀⠀⠉⠉⠙⠒⠒⠾⠥⢄⣀⡀⠐⠂⠒⠒⢒⡋⠉⠀⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⢑⠚⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠭⣙⣒⠢⠤⣜⣁⠀⠀⢠⡄⠀⠈⠀⠛⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠚⠛⠛⠒⠒⠒⠒⠂⡔⠂⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠖⠛⠛⠒⠒⠆⠀⠈⣙⣳⣦⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠓⣂⣤⠴⢖⣛⠋⠉⣩⡄⠀⠀⠀⠰⠶⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣥⠾⠛⢉⣀⠀⠈⠉⠀⢀⡈⠀⠀⠛⠃⠀⠀⠒⠀⢠⠎⠀⠀⡠⢔⠦⡀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⠠⡶⠀⣀⠁⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠘⢧⣛⡣⠃⠀⢀⣠⣤⡴⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠘⣡⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢠⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⢁⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⠏⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣉⡩⠤⠄⠉⠉⠑⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⣰⢏⠀⣿⠀⠀⢀⣠⡤⠤⠀⠀⠀⠀⢀⣀⣀⣤⣽⣧⡤⠒⠀⠀⠀⣠⣄⣀⣀⣀⣀⣤⣤⡴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣏⢰⡏⠀⢰⡯⢐⠀⠀⠀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠙⠶⠧⠶⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢾⡇⠀⠘⢶⡥⠞⢁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾⠉⡷⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⠇⠀⣀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⣀⡴⠋⠀⣄⠈⢳⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠋⠉⠀⠠⡀⢘⡶⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢆⠀⢻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠄⠂⠒⠀⠉⠉⠉⠀⠒⠒⠒⠤⢤⢤⣀⣀⣀
⠀⠀⠀⠠⠒⠶⠌⣉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠲⢦⣤⠄
⠀⠀⠀⡇⠂⠀⠀⠀⠀⠈⠉⠙⠒⠒⠦⠤⢭⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⠉⢩⠇
⠀⠀⠀⠱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⢤⡤⠔⠒⠋⠉⠀⠀⠀⠀⠀⣈⣆⣀
⠀⠀⠐⢶⣿⣉⡉⠉⠒⠒⠦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠤⣤⣀⠀⠀⣀⣤⣶⣟⡋⠥⠤⠀⠛⠒⡄
⠀⠀⠀⢸⠀⠀⠉⠓⠲⠤⣀⡀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣄⣀⣀⡀⢻⠀⣀⣬⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⡤⠶⠖⠒⠛⠉⠉⠁⠉⠉⠛⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⣀⣸⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⣖⣺⣶
⣼⡏⠙⠛⠷⢦⣽⣻⣷⣦⣀⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⣒⣊⣩⡭⠴⠶⠒⠛⠋⠉⢹⡇
⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢷⣦⣴⣁⣦⡤⠴⠶⣒⣛⣫⣭⡭⠴⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠘⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠓
⠀⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣀⡼⡄⢀⣀⣀⣤⣤⡶⠶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠭⣓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢑⡢⠭⣀⠈⠙⠓⢦⣄⠀⠀⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⢴⣪⠥⣒⠁⠀⠈⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠬⠿⠶⣥⣀⡀⠀⠀⠀⠀⣼⠀⠀⢀⣀⣠⡤⠶⠶⠿⠯⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠿⠗⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⣶⢶⣶⠶⠶⠶⠶⠖⠒⢒⣒⣒⣒⣶⣶⠶⠶⠓⠓⠒⠛⠛⡞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⢳⣸⡟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⣀⠀⠀⠀⠀⠐⠊⠙⢦
⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃⣀⣠⣤⣿⣷⣶⣶⣶⣖⣒⡚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⢀⡴⠞⠛⠉⠁⠀⣿⠟⠉⠀⠀⠀⠀⠐⠋⠭⠭⠭⠭⠭⠍⢉⣛⡛⣛⣛⡒⠒⠒⠒⠲⢶⡾⠓
⣰⠋⠀⠀⠤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣈⠉⠩⠭⠭⠭⠤⠄⠀⠀⠀⣼⠉⠓⠦⣄⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⣀⣀⣉⣉⣉⡀⠐⠒⠒⠒⠠⠍⠉⠉⠉⠀⠀⠀⠀⠀⢇⠀⠀⣀⣀⣹⡷
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣈⣻⠉⠉⢠⠇
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⣠⠴⠖⠒⠛⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸
⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡙⢷⡠⠀⠀⠀⠀⠤⠤⠶⢖⣒⣛⣯⡭⠭⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⠞⠁⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⠤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠓⠶⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⣀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡤⠒⠒⠤⡀⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠠⠤⠨⡇⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⠦⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡨⠦⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢊⡠⠞⠁⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⢤⣤⣤⣤⠤⠴⠿⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠔⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⡠⠴⠊⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢑⡄⠀⠀⡠⠔⠉⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠤⣄⡲⠃⠀⣞⡀⠀⠀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠑⠢⣄⣀⡀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋

⢀⠢⠁⠀⡄
⢌⡁⣃⢀⡼⠠⣶⣆⡀
⠀⠁⡉⡅⠀⣶⣿⣷⣄⡀
⠀⢔⠋⡂⠁⠌⢿⣿⣿⣿⣦⡀
⠀⠀⠉⠁⠀⠀⠀⠙⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣿⣿⣿⣷⣄⠀⣀⣀⡤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠛⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢆⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠉⠄⠠⠑⢠⣖⡒⢤⡙⢦⣄⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠚⡉⠉⡇⢻⣄⠈⠉⣛⠋⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⢹⡶⠲⠦⣄⠀⠀⠀⡖⢶⠀⠘⢀⡰⠞⠊⠁⠀⠙⠦⣌⡭⠃⠀⠀⠈⠙⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣀⣤⣄⡈⠳⣄⠀⢳⡄⠀⠰⠋⠐⢀⠀⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠳⡜⢦⠀⠙⣦⠀⠀⠀⠀⠐⣌⡶⠚⠁⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢘⠆⣀⠘⡇⠀⠀⠀⠀⠳⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡋⠀⠙⠚⠁⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡈⢣⡀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢦⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⢦⠳⡄⠀⠀⠀⢀⠞⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⠙⢦⡀⢧⠈⢢⣠⠖⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⢧⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⣨⣟⠉⢃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠙⢦⣄⣧⡀⠀⠀⢀⣀⣠⡴⠖⠋⠁⣘⣆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠛⠛⠛⠋⠉⠁⠀⣠⡴⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣒⣶⣤⣤⣤⣴⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⢀⣯⣽⣿⠀⠀⢀⣀⣾⣿⡿⠛⠓⠀⠀⠀⠀⠀⢀⣴⠂⠀⣤⣀⠀⠀⠀⣠⡤⠀⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠘⣿⣿⣿⣏⠀⠀⠘⠛⠙⢻⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⣬⣷⡀⠀⢸⣟⢷⣤⣿⡀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠘⣧⠀⢄⡀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠹⣄⢸⣮⣿⣿⠟⣷⠀⠀⠀⢀⠀⣴⣿⣮⣇
⠀⠀⠈⢹⣿⣿⣿⣧⠀⠀⠀⠀⢻⣇⠀⢙⣦⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢨⣿⡛⠉⠀⠀⣿⠀⢀⡴⠋⠀⠈⣿⣿⣿⡆
⠀⠀⠀⣾⢼⣿⣿⣿⣷⡀⠀⠀⢴⣿⣶⣬⣿⣧⣀⠀⠀⣾⣿⡟⠀⠀⣰⣿⠇⣓⣴⣀⠀⣿⣠⠟⠀⠀⣠⣶⢟⢻⣿⣿⣆
⠀⠀⠀⣿⡎⣿⣿⣿⣿⡣⢤⡀⢸⣿⣮⣿⣶⠛⠛⢷⡀⣿⣿⡇⠀⣴⣿⠏⠀⠹⣿⣿⣷⣹⠁⢀⣴⣿⠟⢱⣿⣞⣿⡿⠋
⠀⠀⠀⣿⣷⣶⢰⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣢⡀⠀⠀⠀⣾⣿⣷⢮⠿⢿⡇
⠀⠀⣤⢀⠀⠀⠀⠀⣀⠷⣿⣿⣶⣆⠀⢸⣿⣿⢠⡆⡰⡇
⠀⠀⢺⣿⣴⢐⣤⡀⢉⣹⣿⣿⣝⢻⣄⢸⣿⣿⣴⣦⣶⣧⡤⠤⢤⣤⣤⠤⢤⣤⡤⡠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⣿⢿⣿⢷⣌⣹⣿⣯⣿⣊⣯⣾⣯⣿⣿⣭⣽⣧⣜⣻⣣⣤⣼⣟⣏⣅⠖⡗⣊⣍⠶⠶⣉⣹⠾⠶⣹⡱⠶⢦⢹⡱⠦⢄⣛⣫⣭⡝⣏⣩⣭⡞
⠀⠀⢤⡘⣿⣿⣥⣄⢹⠛⣿⣿⣯⢿⣿⣾⣿⣟⣆⡀⣠⣤⡈⣀⣨⣀⣈⡘⣉⣉⠠⡉⠈⠁⠛⡌⠉⠉⠙⠛⠉⠉⢍⠹⠍⠉⠉⠋⠉⠅⠩⠈⠉⠠⠀⠛
⠀⢠⣿⣿⣬⣿⣿⣿⣯⣹⢸⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄⠺⡦⠬⠮⠦⠄⠥⠦⠀⠢⠯⣼⡷⣽⣿⡬⢭⣭⠌⢥⣀⡈⣁⠉⠃⣄⢄⠀⡀⢃⢙⡙⢐⡀⢂
⠀⢈⢻⣿⣿⣿⣿⣷⣿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⡸⣁⡀⣁⣈⣀⠓⣙⣄⠂⢓⣳⣙⣛⣖⣂⡂⡒⡒⠐⠒⠲⠐⡐⠂⠄⠀⠄⠠⠀⠸⠤⠀⠄
⠀⢈⣿⣿⣿⣿⣿⡿⣿⣿⣶⡟⠳⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⢉⠽⠬⠏⠯⠍⠦⠨⠄⠁⠄⠈⠉⠭⠈⠀⠂⠁⠁⠀⠀⠀⠈
⠀⠀⠘⣿⣯⣿⣿⣿⣿⣭⣛⣿⣖⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢻⠛⠛⠛⠿⠿⢿⠿⠿⠿⠿⠿⡿⠿⢽⠽⠯⣯⠯⠿⡿⠿⢿⠿⠿⣿⠿⢦⠾⠿⣿
⠀⠀⠀⣘⣛⢿⣿⣿⣿⣛⡻⢿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠠⠘⣃⠠⠘⠁⠀⠐⡋⣀⠘⣡⠁⡐⣠⠀⠃⠄⠾⢈⠁⠒⡀⠐⢂⠁⠶⢨⠀⠂⢁
⠀⠀⠀⠈⢻⣿⣿⣷⣛⣟⡾⣯⣽⡛⣻⣻⣿⣿⣿⣿⣿⣿⣿⡇⠈⠱⠀⠸⡂⠚⡋⣛⣀⣱⠀⣈⠱⢀⠱⣆⢰⣟⡻⠆⣠⠄⠀⠄⢁⠀⣆⢀⣸⢻⡷⢀
⠀⢀⣿⣷⣎⣿⣿⣿⣝⣿⣿⣿⣿⣷⣿⡤⣯⢿⣿⣿⣿⣿⣿⡏⠉⠁⠊⣀⣿⣿⣿⡿⣿⣿⠀⢠⠟⢩⡀⣿⣿⢿⣿⣿⣿⠀⣁⠰⢤⠀⢸⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣯⣿⣯⣽⣏⣿⣿⣿⡿⣿⣍⣿⣿⣿⣿⣿⣿⡇⢚⠠⠒⠐⣿⣷⣾⣿⣿⣧⠀⢆⡁⠶⡂⣿⣿⢾⣷⣿⣿⠀⠄⠀⠆⠀⢸⣾⣷⣿⣾⣿
⠀⠀⣠⣙⠻⣿⣿⣿⣿⣿⣿⣷⠿⣄⢻⣿⡴⣹⣿⣿⣿⣿⣿⡇⠈⠀⡈⠂⣿⣧⣼⣥⣾⡇⠀⠂⡁⠂⡀⣿⣶⣰⣦⣾⣿⠀⡀⠁⠀⠁⢸⣾⣤⣯⣬⣿
⠀⠀⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣎⢶⡻⢿⣿⣿⣿⣿⣿⣿⡇⠀⢘⢡⠈⣿⣯⣿⣧⣿⡇⠀⡱⠀⡡⠀⣿⣿⣼⣯⣿⣿⠀⠀⠁⡀⠂⢸⣿⣭⣿⣽⣿
⠀⠀⠘⢿⣿⣿⣿⣿⣥⣏⣙⣿⣬⣙⡻⣮⣤⢻⣿⣿⣿⣿⣿⡇⠀⠈⠀⢠⣛⣛⣛⣛⣛⣃⠀⣡⢂⡀⢠⣿⣛⣛⣛⣛⣻⡆⠁⠂⠁⠀⣼⣿⣿⣟⣿⣿
⠀⠀⠀⢠⣌⡹⡿⣿⣿⣻⣿⣙⢻⢿⣶⣟⠛⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠂⢀⠁⠐⡀⠈⠀⠰⠀⠀⠂⡖⢃⠔⠀⢶⡂⠰⠊⠀⢜⡲⠖⡒⠆⠀⡶
⠀⠀⠀⠀⠙⠿⣿⣯⣿⣿⣾⣻⣏⣭⢿⣋⠹⠦⣿⣿⣿⣿⣿⠄⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠂⠀⠂⠁⠊⠄⠐⣀⠁⠐⢈⠀⠀⡐⠀⣩⢤⡀⠰
⠀⠀⠀⠀⣽⣦⡻⢿⣿⡿⠿⣷⣯⠺⠿⣿⣽⣦⣿⣿⢿⡷⣿⠄⠀⠀⠀⠠⠀⠀⠒⠒⠀⡠⠈⠀⠀⠀⠨⠄⠄⠓⠦⠅⠤⡅⠂⡓⠠⠃⣠⣔⣧⣾⡣⣄
⠀⠀⠀⠀⠨⣿⣿⣿⡿⢿⣿⣽⣿⣷⡛⣧⣏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣷⣶⣾⣷⣿⡇⠀⠐⠀⠀⠀⣿⣶⣾⣷⣿⣷⠀⠀⠀⠀⣬⣿⣽⣿⣿⣯⣯
⠀⠀⠀⠀⠀⠹⢿⣿⣷⣿⣻⣾⣶⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠠⠀⣷⣶⣾⣷⣿⡇⠀⠀⡁⠀⢀⣿⣷⣾⣷⣿⡷⠀⠀⠴⠘⢷⡿⣉⣍⢁⣈⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⢻⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣯⣭⣭⣍⣭⡇⠀⢁⠁⠀⠰⣭⣥⣭⣥⣭⣯⠀⢄⡙⠄⣹⡟⣩⡇⢨⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡘⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣯⣯⣽⣭⣿⡇⠂⡁⠄⡡⢸⣽⣏⣿⣏⣿⡇⠀⠂⡥⠃⣽⡇⣿⡇⢸⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⡡⠿⠿⠿⠿⠿⠇⡀⠁⠂⡔⢸⠿⠷⠿⠿⣿⣧⡀⠁⢄⠁⢸⠃⣤⡄⢠⣤⢿

⠀⠀⠀⢀⣠⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⡀⡀
⠀⣴⡞⠍⠚⡉⠀⠀⠋⠀⠁⠀⠀⠀⢠⠂⠙⠃⠐⡀⢠⠀⠀⠆⠀⠀⠀⠠⠀⠀⠈⠀⠈⡇⠀⠀⠁
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⡤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠐⠀⢀⠀⠐⠐⠐⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠏⠀⠀⠀⢀⠐⠁⠀⢀⡀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠠⠎⡬
⠀⠀⣢⡶⡤⠄⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠣⠩⣶⣄⠀⠀⠀⠂⠀⡀⠀⠀⢀⠴⠀⠁⠐⠀⠀⠀⠀⢀
⠀⠀⢟⣿⢿⡃⠀⠀⢼⣚⣭⠀⠀⠀⠀⡀⠀⠀⢌⠔⠊⠀⠸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠉⡅⠉⠀⠀⠘⠉⠒⠁⠠⡀⠀⡀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠂⠀⠀⠁
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢠⡄⡀⠀⠀⣀⣀⠈⠁⠐⠀⠐⠁⠀⠀⢀⣀⡠⠀⠀⡀⢀⠐
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠁⠂⠄⠀⠀⠐⠈⣡⠁⠠⠞⠀⠈⠉⠀⠀⠀⠢⠀⠀⠀⠈⠈
⠀⠀⠀⠀⢀⠀⢈⠀⠀⠄⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠀⠘⠀⠅⡈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠤⡀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠐⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣪⢯⡔⠆⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡀⠀⠒⢈⠷⠃⠀⠀⠀⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠴⠦⠤⣀⣀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣁⣭⣿⣿⣾⣿⣿⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣉⢻⣿⣿⣿⡿⠟⠉⣙⡛⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡆⠻⠞⢛⣋⢠⣴⣾⣿⣿⣿⣷⣜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢀⠛⢻⡿⠟⠋⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠑⠽⠿⠿⠖⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠙⠲⠀⠀⠀⠀⠤⠖⠢⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣤⣤⡲⠀⠀⡴⣠⣤⣀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠛⠁⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣁⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⣹⣷⡆⠀⠀⠰⣞⠛⠛⢳⣦⠀⠀⠀⣷⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡄⠀⠀⠉⠛⠛⠋⠁⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣟⠻⣿⣶⣬⣝⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠙⣿⣧⠀⠀⠀⠉⠉⠉⠙⠋⠻⣿⣿⣷⣞⠙⢿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⣿⣏⣸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡻⢿⣇⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠉⠺⢿⣿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⣲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢟⠿⠟⠋⢡⣴⣞⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠠⡑⡄⢈⠿⠋⠙⣷⣄⠀⠀⠀⠀⠀⠌⠀⠀⠖⠀⠐⢛⣻⢯⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⣀⡀⠀⠀⠐⣤⣀⢈⠉⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠸⢫⠉⠀⠀⠀⠛⠋⠐⡄⢸⣿⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⢘⠁⠨⡽⡆⠀⣠⣤⣄⣸⣿⣿⡟⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣹⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⡋⠑⠚⢿⣿⣿⡆⠀⠀⠀⢈⣀⠔⢀⡀⠀⠀⠀⠀⢠⡝⠛⠉⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢀⠀⠘⠀⠠⣯⡇⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠈⠠⢤⠄⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⠿⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⣄⠋⠄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣿⡏⠀⠀⠀⣿⠿⠋⣰⡿⠿⠦
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠐⠿⡿⢱⣦⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⠾⠿⢿⠁⠀⠀⠘⠃⠀⣰⡿⠁
⠀⠀⠀⠀⣀⣤⠀⡎⠏⠀⠔⠺⠛⠁⢸⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠑⢤⠀⠀⠀⣰⡿⠁
⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡸⣼⠆⠀⣰⡿⠁
⠀⠀⠀⣯⣿⣇⠀⠀⠀⠂⠠⠀⡠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣷⣷⠀⣰⡿⠁
⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⢀⣾⣣⣿⠷⣿⢯⠯⢭⣵⣿⢿⣫⣿⣿⣿⠟⠋⠀⣼⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣾⢝⣾⡟⣸⣇⠃⠠⠿⠟⠖⠋⢱⣟⠟⠁⢀⠀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢆⠑⠀⢀⣶⠛⣯⣿⣿⠃⢹⡽⡣⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣸⢻⣻⡿
⠀⠀⠀⠀⠀⠢⡀⠸⣏⣾⣿⣇⢟⣴⡷⠉⠈⠁⠀⠀⠀⠀⡄⢀⠀⡐⠀⠀⡏⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⠈⠉⠿⢿⢶⠫⠿⠁⠀⠀⠀⠤⠊⡀⠂⠈⡆⠀⠀⠀⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⢳⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡤⠀⠀⠀⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢤⡀⡀⠀⠀⣀⡀
⣀⣾⡞⣧⣀⠀⠀⢀⠀⣠⢹⡆⠀⢸⡄⠀⠀⠀⣶⠹⡦⣤⢀⣠⣧⡄⠄⣾⣆⣀⣷⢸⡇⠀⡄⣿⠉⠙⣿⠄
⠙⣿⡧⠿⠟⠶⠿⣾⣷⣿⣿⠃⣴⣾⣇⠀⣠⣼⢿⣾⡿⡋⠅⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⣷⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣿⡿⣋⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣍⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⡇⠀⣀⣠⠴⠶⠤⠤⡀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⢉⠛⠋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⣄⢀⡀⠇⡼⠉⢀⠃⣃⡝⡲⡙⢦⠒⣀⣀⣼⠏⠀⡠⣤⣤⡄⠁⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣖⠍⡂⢶⣿⠀⠛⡰⣯⣷⡒⣦⢸⠿⠿⢿⡇⠀⢘⠉⣟⣷⡘⠀⢸⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠺⠤⠼⢿⣆⠐⢆⣸⣈⡴⠏⡈⠀⣀⣈⣧⡀⠘⢄⢘⡉⠌⢠⠈⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠲⠤⠄⠐⠛⠛⠿⠿⠟⠛⠛⠢⠤⠤⡤⢴⠾⠾⠿⠿⠋⠁

⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠛⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⡈⠘⢿⣿⣿⣿⣿⣷⡦⣤⣀⣾⣿⣍⢿⣿⣿⣿⣶⠆⢶⣶⣶⣶⣦⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⢿⣿⣷⣿⣿⣿⡿⢋⣱⣾⣿⣿⣿⣿⡆⣿⣿⣿⣿⠀⢼⠏⣵⠄⢿⡿⠿⠋⢿⡷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣒⣒⣒⣒⣲⣿⣿⡿⠟⣡⣰⣿⣿⣿⣿⣿⣿⣿⠰⣷⣿⠿⢿⠀⠸⣧⣙⣣⠎⠁⠀⣐⡾⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⢭⣽⣿⠟⢡⣴⣿⣿⣿⣿⣿⣿⣿⡿⣁⣳⠿⢏⠀⠈⠀⢄⠀⠉⠀⠀⠀⠀⠃⠛⠒⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠂⠉⣉⣵⣿⠟⠡⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠶⠄⠀⠀⠀⠀⠙⡆⠀⠀⠀⡄⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠒⣊⠭⣿⣿⠏⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⡄⠀⠀⠀⠀⢳⣀⠀⠀⠒⣤⠖⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⡀⠀⠀⠠⠴⠒⠳⢤⣈⣙⡷⠛⠁
⠀⠀⠀⠀⠀⠉⠁⠪⣻⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠡⠸⠽⠠⣄⡀⠈⠁⠀⠐⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣿⡏⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣾⣷⣀⠀⠀⠀⠁⠀⠁⠁
⠀⠀⠀⠀⠈⠠⢈⣽⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠞⠿⡟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣤⣤⣴⠛⠉⠁
⠀⠀⠀⠀⠀⢀⣴⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣻⣿⢿⠀⢠⡞⣰⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠐⠉⢛⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣾⡿⢯⡷⡁⢰⣹⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⢀⠞⢯⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠶⡔⠙⣯⡵⣦⣝⡹⠛⠁
⠀⠀⠀⠀⠀⠄⠀⣾⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠂⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⢠⠈⠉⣧⠸⣿⣿⣿⣿⣿⣿⣿⡾⣡⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⣿⣿⣭⣛⢿⡛⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⢄⣠⠛⡄⢹⣿⣿⣿⣿⣿⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠀⠀⠀⠀⠈⠉⠛⢷⣝⢿⡿⣿⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠐⣷⡄⠓⣄⢿⣿⣿⣿⣿⣿⣯⢟⠴⣭⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠑⠙⣷⢳⢤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠉⣜⣻⣿⣿⣿⣿⣿⣿⣽⢃⠄⠀⠀⠀⢀⣤⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠜⠸⣼⡄⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠆⣿⡇⠹⢿⣿⣿⣿⣿⣿⣾⣳⢆⠐⢶⣟⣛⣛⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⡇⠀⠀⠀⠀⣠⣾⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⢸⣦⣻⣿⣿⣿⣿⣿⣯⣿⢂⠀⠉⢋⠀⠀⠚⠳⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠞⣉⢻⣧⣶⣶⣿⢟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠡⠀⣿⢶⣬⡛⢿⣿⣿⣿⣿⣿⣧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢰⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠊⢠⣀⢿⣳⠈⠹⠿⢿⣿⣿⣿⣿⣵⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣠⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢠⣄⣄⡀⠉⠙⢿⣿⢿⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣷⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠲⠦⠶⠶⠿⠽⠿⠿⠾⠿⠟⠛⠛⠉⠁

⠀⠀⠀⣀⡠⠤⢖⠂⠶⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⢀⠄⣠⣶⣣⣴⣄⡀
⠀⠰⣭⠤⠂⠈⠘⠃⠉⠧⠶⡦⠤⠤⠃⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣿⡿⣿⢭⡹⠁⠈⠹⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⢤⠌⠀⠰⠶⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡩⠭⠔⠗⠰⠯⢭⣽⣳⠆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠈⠉⠁⠠⠂⠄⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⡠⠀⠀⢀⢀⣉⢛⡂⢠⠁⠱⠀⠀⠀⠋⠆⠀⠀⠀⡴⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⢶⣋⣠⡤⠶⠾⢦⣟⠃⠐⠋⠛⠋⠉⠉⠈⢡⠀⠉⠀⠚⠀⠐⠐⠀⠠⠅⠀⠀⠀⢃⠐⠐⠀⡆⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⢉⣡⣤⡴⠶⠶⠇⠀⠆⠀⠀⠈⠈⠉⠈⢠⡴⠁⠒⠒⠀⠰⠠⠤⠤⠄⠀⡀⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⣤⣈⠙⠤⡤⠤⠤⠶⠶⠀⠠⠆⠀⠄⠀⠀⠀⠀⢖⣣⡄⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⡀⠹⠆⢠⣤⣤⣤⣤⣴⠀⠀⠈⢀⠄⠀⡀⠐⠻⡌⢳⡈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠰⢴⣄⠈⠀⠰⠶⢦⡀⠻⠀⠀⢠⣀⣀⣠⣀⣤⡄⠀⠈⠁⠀⠀⠀⠀⢠⡟⡸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⢸⠀⢠⠀⠀⠘⢳⢀⠀⠀⠀⠟⠀⠀⠀⢠⣤⣬⣥⣤⣀⣠⠀⠀⠉⠈⠁⠀⠁⠉⢀⠀⠀⠀⠀⠀⠀⠤⠤⠇⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣾⣦⣤⣶⣶⣶⡆⠀⠁⠀⠀⠀⢠⣶⠀⡀⠀⡖⠰⢻⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢠⠀⠀⠀⠀⠀⠁⠈⠳⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⢠⠀⠀⢰⠉⢯⠃⢀⢹⣾⣏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠎⠐⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢈⡀⠸⠇⣧⣾⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⠀⢸⣿⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠉⢺⣠⢦⣀⣤⢠⡀⣀⠀⣀⢀⣄⡈⢁⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡆⠠⠤⠠⠼⠀⢼⢿⣿⣧⠀⠘⣿⡇⠠⠀⢀⣀⡴⡀⢀⠛⡿⢟⠀⡀
⠀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣯⣟⣿⠛⠛⠛⠙⠏⠀⠀⠀⠀⣼⣯⣶⣿⣾⣶⣾⣧⠀⣿⡿⣿⣿⡄⠀⣿⣷⣿⣾⣿⣽⣾⣵⣿⣷⣿⣿⣿⣧
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠉⠉⠉⠉⡉⠉⢠⠋⠁⠹⠿⠇⠀⠛⠠⠌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠤⠔



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣤⢦⣤⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠙⠒⠾⣿⡿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠀⡠⠀⠀⠀⠀⣠⣤⣄⡄⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⡠⠿⣧⠁
⠀⠀⠀⠀⠨⠔⣏⣿⠋⠛⠀⠀⠀⢀⣤⣰⣦⠀⠀⠀⠀⠑⠤⢤⠦⠉⠀⠀⠀⢿⣿⡟⠁⠀⠀⢾⠿⠣⠀⠀⠀⠀⠀⠀⠀⢸⣯⠰⡀
⠀⠀⠀⠀⠀⠀⠈⣿⢀⠀⠀⠀⠀⢿⣿⢿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠈⣭⡆⠴
⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠘⠿⡿⣿⣻⠃⠀⠀⠀⠹⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠐⠛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⠀⢨⠷⠞⠀⠀⠐⢸⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣆⣶⣞⠇⠀⠀⡀⢣⢀⣄⠠⡀⠀⠀⠱⠀⠀⠀⠀⠀⠊⠁⢀⠁⠀⠀⠀⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⠋⠉⠁⠀⠀⠀⡀⠀⣙⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⢴⢨⡀⠀⠀⠀⣀⠀⠀⠀⣄⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠰⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠰⠆⢤⡄⠀⠀⠺⠿⠂⠀⡠⣪⡄⡚⠁⠀⠀⠀⠄⠀⠀⠀⢀⣤⣤⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠤⢘⣃⣤⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⢱⣆⠀⠀⠠⠀⠀⠀⠀⠀⠈⢸⠟⠀⠀⠈⠛⡓⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡀
⠀⠀⠀⠀⣡⠞⠿⢛⢷⢤⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡛
⠀⠀⠠⠋⣀⣤⣴⣈⠂⢸⣿⣟⠀⠈⣧⠀⠀⠀⠀⣾⣮⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠙⢖⡀
⠀⠀⠀⠀⠉⠁⣀⠀⠀⡀⠉⠙⠢⠒⢾⣷⠶⣶⣯⣍⡛⠺⠶⠤⠤⠀⠀⠀⠠⣤⡄⠀⠐⠒⠓⠳⠴⠦⢠⡶⠿⠓⣻⡄⠁⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣉⠉⣛⣿⠷⢶⡶⠦⣀⣹⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠒⠒⠛⠀⠀⢀⣠⠤⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢠⣶⣆⣈⡈⠳⣄⡙⠂⠤⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠶⠶⠶⠠⣦⣤⣤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⠋⢠⡀⠈⠹⠖⢶⣶⣦⡿⣷⡀⠀⠀⠀⠀⠀⢀⡴⠛⠈⠛⠙⠻⠶⠛⠙⠟⠋⠀⠒⠚⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣟⡿⠋⠀⠊⢉⡐⠒⣀⡁⠈⠢⡀⠀⢀⠴⠏⠃⠀⠀⠘⢧⡀⠀⠤⠀⢠⠄⡀⠀⢠⡟⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠀⠀⠀⠀⠀⠄⠿⠀⠀⠁⠸⠾⠭⠁⠉⠀⠐



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣌⠻⠛⣉⣥⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢠⣌⡙⠻⢿⣿⣿⣿⣿⡿⠿⢉⣁⣤⣶⣾⣿⣿⠿⠟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠛⢿⡷⢤⣈⡙⠋⢤⣶⣾⣿⣿⣿⡿⠛⢁⣀⣤⡴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣎⢻⡏⢶⣤⣉⠛⠛⣫⣥⣶⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⠀⠙⣿⢶⣄⢋⣉⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢸⣾⣿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⣛⢷⣆⠀⢸⠃⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⠿⠿⢿⣿⣈⢻⣆⠘⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣼⣾⣿⣿⣿⣿⣿⡆⠀⠀⣧
⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⢀⠀⠹
⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣭⡄⠀⠀⠻⠿⠁⢻⡟⠹⣿⣿⠀⠃
⠀⠀⠀⠀⠈⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠁⠀⠀⠀⠀⠀⣸⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⣤⡰⣿⠏⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣠⣆⠀⠀⢠⡿⣫⡞⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢪⡻⣿⣶⣶⢟⣵⡟⠀⠀⠀⠀⠀⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠀⠀⠀⠰⢦⡀⠀⠀⠁⠀⠈⠻⣮⣷⣶⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠖⢶⠿⠏⠛⠓⢦⣀⠀⠙⠣⣴⠀⠀⠀⠀⠈⣉⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⣤⣴
⠀⠀⠀⠀⣀⣀⣠⡤⠶⠶⠿⠿⠿⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡈⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠛⠯⢭⣙⡛⠂
⣶⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣀⠤⠄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣠⣤⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠂⠀⠀⠀⣠⣴⣾⣯⠥⠤⠄⠆⠀⠀⠀⠈⠙⠿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⢀⣤⣶⣿⣿⣋⣡⡤⠤⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣦⡀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠒
⢤⣄⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⣀⣤⣶⣾⠟⠛⠋⠉⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⣶⣾⣿⣿⣦⡀⠻⣿⣿⣿⣿⣧
⠀⡈⠛⠉⠁⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣧⠤⠶⠶⠖⠒⠒⠚⠋⣩⣍⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣿⣿⡇⠀⠀⢀⣦⠤⠤⠤
⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⡽
⢀⣤⣶⣿⣿⣿⣿⣿⣥⣤⣤⣤⠤⠤⠤⠴⠒⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⢿⣶⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⠃
⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣧⣀⣈⣻⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣀⣀⣀⡀⢀⣀⣀
⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛
⣷⣦⣤⣤⣶⣶⣶⡶⠶⠶⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠙⠻⠿⠟⣿⣿⣭⣽⣿⣿⣿⣿⣿⡏
⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⢉⣽⣿⣿⣿⣧
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣇⣀
⢀⣀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀
⠿⠿⢿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛
⠀⠀⠘⠛⠻⠿⠿⠿⠟⠛⠉⠈⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣻⠟⣁⣠⣤⣄⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⡈⠙⠃⠉⠉⣽⣿⠛⣾⣿⣆⣨⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡅⠉⠀⠀⠀⣼⣯⣈⣰⣿⢀⠄⣮⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡿⣼⣿⣟⡁⠁⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣼⣧⣿⣿⠉⠻⢦⣄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣿⢩⣻⠝⠿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣼⣟⢻⣜⢋⣿⡶⠤⢛⣿⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣶⡟⣹⠛⢳⡾⠛⠀⠀⢉⡿⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⡸⠛⢻⣿⡍⣤⠈⣁⡾⠀⠀⢀⠁⠀⣩⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡝⠁⠀⠘⣁⣿⣽⣾⣏⣁⣠⡠⠾⠗⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⣛⣿⣿⣷⣦⡀⠀⢻⣷⣿⣿⣿⢿⣿⣿⣦⣶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣣⣿⣾⠏⠿⣆⢸⣿⣿⢿⣿⣷⠋⠉⡀⠙⢻⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠀⢸⣦⠀⠻⣿⡿⠃⣨⣯⡁⠠⣏⢉⡇⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢻⣿⣷⣿⡟⠁⣠⣿⡿⢿⣤⡈⢉⣀⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠙⢟⠳⡿⠁⣈⡻⠿⣿⠗⢾⣿⣷⡽⠃⠈⠉
⠀⠀⠀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠸⣅⡽⠀⡀⠀⢀⣽⣦⣤⡀
⠀⠀⣼⣿⣿⠟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠿⠟⢰⡦⠀⠀⠘⠋⠀⣾⣿⣿⠈⠻
⠀⠀⢻⣿⣷⣄⣀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⡏
⠀⠀⠀⠙⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠁⠀⢀⠈⢀⠈⠀⠀⡀⠁⡀⠀⠀⢐⠈⢐⠀⠀⠀⡀⠁⡀⠀⠈⢐⠈⢀⠀⠀⠁⡀⠁⡀⠀⠨⢀⠈⢀⠀⣀⣁⣠⣤⣦⣤⣬⣀⣨⣀⣥⣀⠁⡀⠁⠈⠀⠨⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢈
⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠠⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⢀⢠⣼⣿⠿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣯⢻⣆⠀⢐
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⢀⣾⡿⣣⣾⣿⣿⠟⠋⠉⠉⠙⠛⠛⠛⢿⣿⣝⢿⣰⣿⠀⠐
⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡠⠤⡀⠀⣼⢻⣳⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢾⣿⣿⡇⠠
⠄⠀⢐⠠⢐⠠⠀⠄⠀⠄⠀⠀⠀⢐⠠⢐⠀⠀⠀⠂⠄⠀⠀⠠⢐⣀⣐⠀⠀⠸⣄⣀⡸⢀⣿⣼⡿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⠃⠠⠀⠠
⠀⠀⠐⠠⠐⠀⠀⠀⠀⠀⣀⡴⠶⠒⠛⠛⠛⠒⠂⠂⠄⡠⠖⠉⠉⠉⠉⠉⠒⢄⡂⠁⠀⠰⣿⣿⢧⣿⣿⠠⠦⣄⡀⠀⠀⣠⠴⠛⠃⠀⠀⢿⣿⢿⣿
⠀⠀⠠⠀⠀⠐⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢨⣿⣿⣼⣿⡷⠖⣾⡟⠣⠀⠈⠑⠺⣿⠟⠗⠀⠈⡅⠉⡟
⠀⠀⠈⠀⠈⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⠀⠐⠀⠐
⠀⠀⠀⢀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣵⣿⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣿⣆
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠨
⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⢿⢿⠟⠁⠀⠀⣠⣾⣿⣿⣿⣇⠛⠈⠀⠈
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⢾⣿⣿⣿⣿⣿⣿⣦⢈
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⢰⣝⣯⣻⣿⠟⠻⡎⢳⠒⠒⠋⠀⢸⣿⣯⢿⣿⣹⣿⣿⣷⣨⣀
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠁⠀⠀⠀⠀⠉⠉⠛⠻⠟⠃⠀⡴⠁⠀⠁⠀⠀⠀⠀⠙⠻⣧⣿⣷⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠒⠒⠒⠒⠒⠒⠈⠁⠁⠀⠘⠟⠀⠀⠀⠀⠀⠀⣈⣿⢹⣿⣧⠟⣿⣷
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡀⢀⣀⠀⠤⠤⠔⠒⠒⠈⡅⠀⠀⠀⠀⠀⠀⣠⡴⢁⡼⢿⡏⠀⠛⣿
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣀⣀⠄⠴⠈⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⢾⣿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⣀⠠⠠⣶⣷⠀⠀⠀⠘⠄⢔⡈⠒⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠉⠉⠀⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷
⠀⠀⢀⠈⢙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⠛⠢⣀⠀⠀⠀⠀⡄⢀⠞⣿⣿⠋⠙⣿
⠄⠀⢐⠠⢀⠠⠀⠍⡉⠍⡃⠘⠊⢐⠠⢘⠢⣄⡀⠀⠀⠀⠀⢀⣠⠠⢀⠤⠤⠤⡤⠶⣷⠀⠀⢸⠀⠀⠀⠀⠀⢳⣿⣿⣷⣶⣿⣷⣄⢣⣸⢠⣷⣾⣿⣿⣷⣾⣿
⠀⠀⠐⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠉⠛⠛⠛⠙⠉⠐⠀⠐⠀⠀⠀⠀⠀⠘⡀⠀⢸⠀⠀⠀⠀⠀⠈⡋⠉⣿⣿⠋⠉⣿⣦⣿⠉⣿⣿⠋⠙⣿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣌⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣌⠹⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⡈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠛⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠹⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡈⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⣿⣷⣄⣀⣀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠙⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀⠀⠀⠀⣀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡴⠶⠶⣤⡀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣠⡞⠉⠀⠀⠀⠈⢻⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄⠀⣠⡟⢁⡾⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⢣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣰⠏⣰⠏⣠⡟⠁⠀⠀⠀⠀⣰⠏⣹⠇⢀⣼⢃⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣰⠏⣼⠃⣰⡟⠀⠀⠀⠀⠀⣼⠋⣰⠏⢀⡾⢁⡾⠁
⠀⠀⢀⣤⡴⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣴⠏⣼⠃⣰⠏⠀⠀⠀⠀⢀⣼⠃⣴⠏⢠⡞⢁⡾⠁
⠀⣴⠟⠁⣠⣤⣤⣤⡀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⠃⣸⠇⣰⠏⠀⠀⠀⠀⢀⡾⠁⣼⠋⢠⡟⢀⡾⠁
⣼⠃⢀⡾⠋⠀⠀⠈⠙⢦⡀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡾⠃⢠⡟⢠⡟⠀⠀⠀⠀⣠⡟⢁⣼⠃⢠⡟⢀⡾⠁
⣿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠹⣦⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡾⠁⠀⢸⡇⠸⣇⠀⠀⢀⡼⠋⢠⡾⠁⣠⡟⢀⡾⠁
⢻⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⠀⠈⣷⡀⠙⠳⠚⠋⢀⣴⠏⠀⣰⠏⢀⡾⠁
⠈⢷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⠀⠀⠀⠀⠈⠳⣤⣤⣤⡶⠟⠁⢀⣼⠋⢠⡟
⠀⠈⣷⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⢷⡀⠀⣀⣴⣆⠀⠀⠀⠀⠀⠀⣯⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣰⠟
⠀⠀⠈⢷⡹⣦⠀⢰⡞⢳⣄⠀⠀⠀⠀⠘⢷⡀⠻⣄⢻⡄⠙⣧⡀⠀⠀⠀⠀⢻⡄⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣼⠋
⠀⠀⠀⠘⣷⠘⣧⠀⢻⣄⠹⣆⠀⠀⠀⠀⠈⢿⡄⠹⣆⢻⡄⠈⢷⡀⠀⠀⠀⠀⠻⣆⠈⠳⣦⣀⠀⠀⠀⠀⢀⣤⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠘⣧⠘⢷⡀⠻⣆⠹⣦⠀⠀⠀⠀⠈⢻⡄⠹⣆⠻⣆⠈⢻⡄⠀⠀⠀⠀⠈⠳⣦⣀⠉⠛⠳⠶⠞⢋⣁⣴⠟⠁
⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠹⣆⠘⣧⡀⠀⠀⠀⠀⢻⡄⠹⡆⠹⣆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠹⣦⠘⢷⡀⠀⠀⠀⠀⢻⡀⢿⡀⠙⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢻⡄⠘⢧⡀⠻⣦⡀⠀⠀⢸⡇⢸⡇⠀⠘⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢻⣄⠈⠻⣄⠈⠛⠶⠶⠟⠀⣼⠃⠀⠀⠘⣧⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣆⠀⠘⠷⣤⣀⣀⣠⡾⠃⠀⠀⠀⠀⢹⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠙⣧⡀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡉⠳⠶⠴⠶⠶⠛⢉⣠⡶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠋⠉⠉⠉⠛⠓⠠⢄⢀⣠⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⣤⣼⣧⣄⣀⣀⣀⣀⣠⣏⠀⢀⣀⣀⣀⣀⡉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⡾⢛⣿⡿⠻⠛⣻⡟⠛⠛⣿⣿⣿⣿⣟⠛⢉⣉⣍⣙⡳⢦⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠋⢀⣿⠁⠊⠹⣿⣿⣿⠇⢡⠇⢾⡷⢠⣿⣷⡗⠈⠚⣿⣿⣧⡈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠸⣿⠀⣀⣀⣀⢞⠃⢠⠃⠀⠀⠀⢸⠀⠀⠹⣄⠈⢸⣿⣿⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠱⣭⣾⡿⠶⠋⣰⠇⠀⠀⠀⠀⠸⠀⠀⠀⢹⣿⠛⠛⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣀⠀⢀⣀⠠⠄⠠⠀⣀⣀⠌⠙⢦⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⠶⠶⠞⠋⠁⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠰⠶⣦⣤⣀⣀⣤⣤⠴⠀⣀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣶⣦⣤⣀⡀⠀⠙⠛⠋⢉⣁⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠛⠛⣋⣩⣤⣽⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠠⠩⠍⠑⠲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠐⠒⠒⠒⠚⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠻⠶⡶⣤⡤⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⠶⠤⠄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠲⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠖⠺⣿⡀⠀⠀⠀⢦⡈⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠈⠉⡏⢸⣏⠀⠀⠀⠈⠛⠳⠂⠀⠀⠙⠲⠦⣄⡈⠙⢲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠻⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣄⠀⢣⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⣉⣈⣉⣉⡀⠺⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⢣⡄⢀⡀⣀⠀⠙⢿⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠙⠬⢷⠀⠈⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠈⢢⡀⢸⠃⠀⠈⡆⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠀⡀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⢠⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠉⠀⠀⠀⠀⣸⠀⠀⠀⢠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢧⠀⠀⢸⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⢀⡀⡇⠀⠀⢀⠃⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢨⡆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡴⠂⠐⢦⠀⡇⠀⡴⠃⠀⠀⠀⠃⡈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠁⠀⠀⠀⢣⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢱⡇⠜⣁⠀⠀⠀⠀⠀⠘⠀⣡⠀⠀⠀⠀⢀⠐⡰⠀⠀⠸⢸⡦⠀⠀⠈⠄⠈⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡥⠀⠀⠀⠀⠘⢇⡼⠋⠉⠓⠚⠛⠙⠛⠛⠣⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠙⠆⠈⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠋⠀⠀⠀⠀⠀⠀⠈⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣆⠠⠛⢚⡲⢤⣀⣤⡤⣤⠆⠀⠀⡴⠂⠔⠁⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣉⠲⢤⡴⠶⠶⣤⣤⠖⢾⠠⣤⣶⣦⣄⣀⣤⠖⠊⠉⠀⠐⠒⢦⣤⣤⣬⣤⣀⣀⣰⠆⣀⠦⠤⠶⠦⣤⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣤⣀⣀⣀⣠⣤⣄⣀⣈⡆⢾⠀⠄⠈⠉⢸⠀⠀⠉⠳⠠⠂⢢⡀⠀⠄⠀⣏⣉⡡⠶⢀⣤⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠆⢹⡉⠉⡅⠁⡤⠀⠀⠈⠀⠐⠲⠒⠚⠳⠞⠀⠀⠀⠀⠀⠚⠉⠙⠓⠖⠰⢇⠀⠀⠀⠀⠀⣸⣋⢉⢀⡀⠐⢄⡀
⠀⠀⠀⠀⡀⠠⠀⠛⠙⠛⠷⠛⠚⠦⠶⠆⢠⡇⠀⠀⠖⠒⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⠈⠀⠀⠘⠀⠀⠀⠁⠀⠁⠈⠃⠀⠉⠐⠠⣄⡀
⠀⠀⠈⠉⠀⠀⠴⠂⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠠⠤⠤⣀⣠⣄⢀⣀⣀⠀⠀⠀⠁⠈⠤⣤⠄⠠⢤⣤⠤⣤⣤⡿⠦
⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡙⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⢸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣌⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠁⠀⠀⢀⣴⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⣷⡈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⣰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⣿⣿⣷⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⠁⢀⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⢿⣿⣷⣿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣅⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠙⢿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣦⣴⣿⣿⡿⠋
⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⢙⣿⣿⣿⡿⠋
⠀⠀⣾⣿⣿⠟⠉⠉⠉⠉⠙⠻⣿⣿⣿⠀⠀⠀⢀⣠⣴⣶⣾⣿⣶⣦⣄⣠⣾⣿⡿⢿⣿⣿⣶⣿⣿⡿⠋
⠀⠀⢿⣿⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⡟⠀⠀⣰⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣏⠀⠀⣹⣿⣿⡿⠋
⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣼⣿⣿⠋⠀⠀⠀⣠⣾⣿⡿⠻⣿⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢀⣀⣠⣾⣿⡿⠁⠀⠀⣠⣾⣿⡿⠋⠀⠀⣨⣿⣿⣿⣏⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠿⠋⠀⣠⣾⣿⣿⣿⣿⣷⣄⣠⣾⣿⡿⠛⣿⣿⡇⠀⠀⢸⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠁⠀⣀⣀⣠⣤⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⢰⣿⣿⠏⠉⠉⢻⣿⣿⣿⡿⠋⠀⠀⣿⣿⡿⠀⠀⢸⣿⣿⣇⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⢀⣸⣿⣿⠋⠀⠀⠀⣠⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠁⠀⣿⣿⣿
⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⢀⣤⣾⣿⣿⠏⠀⠀⠀⢸⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠟⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠈⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣄⣀⠀⣀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⣾⣿⣿⠛⠉⠉⠉⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣤⣀⣀⣀⣠⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣷⣦⣤⣤⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⡿⠿⠋

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⣿⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⣠⢶⡿⠇⣠⡔⠶⣖⠀⠀⠀⠀⠀⢀⣤⣶⡶⠆⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠈⣁⠉⠚⢠⣦⠈⠀⠉⠀⣶⣿⣿⡻⠆⠀⠙⠃⠀⣶⠟⠋⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⢠⠈⠉⠠⡿⠀⠀⠀⠠⠀⠉⠉⠁⠰⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠈⠄⠀⠈⡧⡀⠀⠀⢀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠰⠃⠈⡀⢀⣬⠀⠀⠠⡄⠀⠁⠀⠰⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠁⢁⣤⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣴⣾⣿⢟⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⠁⠚⠟⠋⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⢠⡄⠤⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠗⠈⠛⠘⠇⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢨⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠐⢠⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠠⣤⠉⠙⠋⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⣤⣤⣼⡇⠀⢠⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠀⠀⢁⣼⣿⡶⢾⣯⠟⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠞⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⠴⠦⠶⠶⠾⠿⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⣣⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠋⠀⢁⡄⠀⣷⠀⠀⠀⢠⡤⠘⠉⣀⣭⢴⠀⠀⠀⢰⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢷⣄⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠄⠀⠀⢺⡇⠀⣿⠀⠀⠀⢀⠀⢠⣾⣿⣦⡇⠀⠀⠀⢸⡟⠀⠀⠀⣠⣄⠈⠛⠛⠃⣤⣶⣤⣤⣄⠘⡃⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠠⣄⠸⠣⠀⣿⣶⣄⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠛⠉⠁⠀⢀⠀⠀⠛⠛⠉⠻⡧⡇⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡄⠀⢠⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠁
⠀⢸⣿⠀⠀⠀⠀⣤⠀⠀⠸⠧⠀⠰⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣬⣍⣄⣀⣉⣧⡀⠀⠀⢸⣠⣤⣀⣤⣀⣶⣦⣼⣿⣿⣿⣿⣦⡀⠙⢷⣆⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠟⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠏⠀⠠⠐⢂⡀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠲⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⠀⠀⠀⠈⠀⠈⡀⢠⣈⠻⣶⣤⣤⣤⣤⣦⣴⣤⣴⣾⠏⠁⠀⠈⠃⠀⠀⣿⠄
⠀⢸⣿⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⢰⣷⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠇
⠀⠘⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠴⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠐⠒⠚⠉⠉⠁⠀⠀⢀⣀⣠⡴
⠀⠀⢀⣤⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠐⠒⠊⠁⢀⠄⠀⠀⠀⠀⠀⠀⣠
⠀⢰⡸⠻⣆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⢸⠀⠀⠀⢀⠀⢠⣿⣔⣄⠄
⠀⠘⡿⡌⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠂⡰⡄⠀⢸⡄⠀⠀⠈⢂⠘⢿⣿⢇⣾⠅⡀
⠀⠀⠀⠸⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⠀⠀⠁⡇⠀⡜⢹⡤⠤⣄⠀⢂⠈⢹⣵⠿⢛⣆⣀
⠀⠀⠀⠀⠱⡀⢻⡀⠀⠀⢦⠀⠀⢸⡆⠀⢉⠀⢸⠀⠀⢦⡇⣸⢱⢋⡇⠀⠈⡧⠀⠡⠈⠑⠨⠔⣛⠷⠂
⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠈⣷⡀⠀⡇⢰⢿⣳⠎⢣⣀⡸⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠡⡀⠈⢭⣿⠯
⠀⠀⣶⣿⣧⠀⠹⡄⢳⡀⠀⢸⡙⢦⢹⠸⡆⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⡟
⠀⢹⣿⣷⣤⠀⠀⠱⡀⠁⠀⠈⠇⠈⠻⡄⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⢘⣿⠿⢿⣦⡀⠀⠱⡀⠀⠀⢸⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠤⢒⣿⠽⣫⣆⡀⠰⣵⡄⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠡⢖⣫⣽⠿⣗⠀⠀⠻⡧⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠉⢽⣿⣿⢿⡥⣢⠀⠹⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠠⢄⠂⠉⣿⠃
⠀⠀⠀⠀⠸⠛⠵⣪⣵⣿⣗⣠⡵⡀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⣀⣠⠵⠖⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⠃⠹⣄⠐⣄⣀⡤⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏⣀⣀⣤⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⠃⡴⣽⡋⠀⣈⣩⣇⠀⠈⢣⠀⠙⢧⠈⠙⢿⣍⠉⠻⠷⣄
⠀⠀⠀⠀⠈⠋⡙⢛⠛⠿⡛⠛⠻⢻⡟⠛⠛⢿⡿⠻⠻⠟⠛⡿⢻⠿⠿⠛⠿⡷⠛⠿⡷⡾⢛⡿⣷⠶⠲⢾⠿⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠙⠄⠠⣠⣱⡄⠀⠈⢣⠀⠀⡀⠀⡇⠘⠸⠀⠀⢐⠀⣀⣜⡡⢒⠥⠖⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠰⡁⠀⡅⠀⡇⠀⡂⠀⣰⢏⣨⡾⠕⠊⠀⠀⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠈⠉⠳⢤⠀⢦⠀⣷⣠⣧⣾⠿⠈⠉⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣸⢧⣯⣧⠀⢀⠂⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⢣⣿⣼⢬⡛⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢟⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡥⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠛⠛⠛⠛⠲⣶⢤⠶⠶⠖⠒⠒⠚⠛⠋⠉⠙⠛⠷⣄
⠀⠀⠀⠀⠀⠀⣠⠊⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⢀⣀⠶⠖⠒⠶⠶⠾⣷⣄
⠀⠀⠀⠀⠀⣼⡷⡫⠛⠉⠩⠍⡙⠶⣖⣁⣤⠴⠁⠈⠛⠶⠶⠖⡒⠋⢀⣠⣤⣤⣀⠢⡀⠀⠘⣆
⠀⠀⠀⠀⢠⠏⠀⢀⣴⡾⠻⣿⣶⣧⡈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⡛⢿⣯⣣⠉⢿⡄⠀⡀⠘⡆
⠀⠀⠀⠀⣼⠀⡀⣿⢸⣿⣶⣿⣿⢏⣷⢀⡤⡒⠶⠒⣙⢲⢄⠀⢺⡹⣿⣿⣿⣏⣠⠞⠀⢠⠃⢀⡇
⠀⠀⠀⠀⢿⠀⢣⡈⠛⠿⠿⠿⠛⠉⢠⠊⠒⠙⠒⠒⠉⠉⠀⠱⡄⠈⠛⠛⠛⠋⠁⢀⡴⠃⠀⣼⠁
⠀⠀⠀⠀⠈⢧⡀⠙⠲⠤⠤⠤⠒⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⡀⠂⠐⠊⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠈⠻⢦⣈⣀⢀⣤⠎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠻⢶⣶⡦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡇⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠉⠑⠒⠤⠄⠠⠄⠒⠊⠁⠀⠈⢀⠜⠀⣎⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⣤⣤⡤⠶⠶⠛⡇⠀⠀⠙⠢⡄⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠜⣧⠀⠀⠀⠁⠈⢦⡀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠤⠤⠄⠠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠔⢿⠀⠀⠀⠀⠀⢠⠦⢄⢸⣼⠋⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠀⠀⠀⠀⡠⠚⣧⣄⣀⡀⠀⢸⡆⠀⣨⠇⠀⣠⡔⠊⠉⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠲⠎⠳⠀⠀⠀⠒⠈⠀⠀⠔⠀⠀⠀⠉⠉⢻⡇⠔⡟⠀⡐⡞⠀⢠⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠞⠉⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠸⣇⠸⣀⡔⠳⣯⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠘⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢡⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡡⠀⠀⠀⠀⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁⠂⠌⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠌⠰⠁⠀⠀⠀⠀⠐⢌⠢⠀⠀⠀⠐⠁⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐⢈⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⠔⡁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢁⠂⠀⠠⠐⢂⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⢤⣤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠨⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⣛⣋⠁⠘⠛⠋⠡⠄⠀⠀⠀⠀⠀⠒⠶⠿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠉⠉⠉⠙⠓⠆⠀⠠⠤⣄⠀⠀⢀⣠⡴⠶⠿⠿⠿⠿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠤⢐⡦⠿⠶⠦⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⢄⣀⣤⡴⣤⣤⡄⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡰⢋⣾⣶⣶⣶⣄⣠⡙⡿⠲⠒⠒⠁⠀⠀⠀⡙⠶⢶⡴⢚⠏⢁⣈⣉⣛⣤⡉⢷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠁⠸⡏⣾⣟⣿⣿⡟⡇⢸⡆⣸⠿⠾⠆⠀⠐⣒⠅⢸⢠⣷⡾⣿⡿⣿⣿⡝⣧⢸⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⠳⠿⣿⣿⣿⠔⠁⡜⠀⡵⢊⣁⠀⠀⣉⡙⢳⡀⢢⠻⣄⣿⣿⣟⣿⣷⢁⡌⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⢶⡶⣊⣫⠵⢛⡫⡊⠜⠣⠟⠉⠀⠘⠙⠿⠌⠱⡈⠣⠈⠉⡉⠉⠻⢗⠉⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠤⠀⠀⠔⡩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠠⣌⣙⠋⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⠀⢠⠎⣟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢬⣳⠲⣜⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⣄⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣈⡉⠓⠶⣶⠶⠟⣋⣉⣤⡴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠉⠙⠛⠛⠛⠋⠉⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠁⠀⠀⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⣄⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠴⠳⣈⠑⠀⠀⠀⠀⠀⠀⢈⠹⠷⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠀⠀⠈⠙⠋⠉⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠂⠒⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠉⣉⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠙⢷⣆
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣈⣿⣧
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡼⠋⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠚⡄⠀⠘⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠎⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢁⠶⢀⣁⠐⡄⡍⠐⣁⠄⢀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⣈⣌⠈⣚⣠⣬⡦⠶⠖⠶⡶⠬⣤⣘⡊⢀⣆⢢⠀⠀⠀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠥⣨⡕⠋⢻⠁⠙⢃⠆⠀⠀⠀⠀⠀⠈⠹⠳⣮⡀⢜⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⣀⢈⡦⣠⢞⡡⢄⡡⠊⠉⢺⡉⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠝⣶⡠⣆⢭⡁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⡕⣡⠄⡼⠃⢺⢂⡱⡱⠀⠶⡣⠀⡱⠀⠀⠀⠀⠀⠀⢦⠀⠤⠰⠖⢿⣄⢤⠃⠛⠹⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⡈⡾⣁⣤⠊⠑⠈⡑⣄⣀⢜⠉⠀⠀⠀⢀⠀⠀⢀⡍⠌⢂⢁⢊⡭⢹⡆⢀⠤⠀⠐⡥⢌
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠙⢸⣇⣓⣧⣈⠴⡣⣀⣬⣁⣨⡀⠈⠀⢀⠀⠀⢀⡰⠐⡒⢦⡔⡡⡢⠑⣻⡘⠐⠼⠉
⠀⠀⠀⠀⠀⠀⠠⠈⠠⠝⣸⠡⡎⣬⣝⣤⡄⠟⠀⠀⠁⡀⢀⠀⠀⠀⠰⡎⡸⠋⠉⠋⡜⢌⡔⠑⢸⡅⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡛⠙⢄⢎⠃⠀⠠⠀⠀⠀⠀⠀⣐⠨⢆⣾⡷⢽⠂⣤⢘⡈⠰⡀⣰⢩⠇⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⣹⣇⡄⠈⡀⠠⠀⠖⠉⡾⠓⡆⠡⠀⣰⡛⠃⠀⠏⢨⠸⢣⢨⠀⡼⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠙⠛⠄⠀⠖⠝⠁⠀⠖⠐⠂⠘⠓⡖⠈⠁⠀⣠⠖⠀⠘⢦⢣⢦⡶⣠⠏⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢾⠷⠀⠀⠀⠀⠄⠂⠘⢀⠀⢘⠑⠀⠀⠀⠀⠊⢁⢀⢢⠴⣮⠁⠁⠰⠏⠘⡍⠁
⠀⠀⠀⠀⠀⢠⣤⣤⠄⡏⠠⢠⠂⠀⣆⠀⢹⠀⢀⠗⠀⠀⠀⡰⠚⠣⡂⠀⡀⠿⠀⠉⠀⠒⠁⠌⠚⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡐⡘⠀⢢⣧⡀⠈⠢⣀⢄⠀⡀⠔⠒⠀⠱⡤⠜⠁⠀⣠⢖⠒⢎⠀⠞⠐⠉⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⢒⢫⠀⠀⠉⢰⠀⠀⢸⠀⠀⠴⠎⢀⡄⠀⠤⡔⠣⢈⠈⠏⢰⡃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡘⠉⢀⠄⠁⠒⠁⠐⠤⣠⣼⠁⠀⢹⣤⣆⠂⢀⢇⡀⠀⠑⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠏⠀⣰⠀⠘⣆⠀⠃⢌⡳⠶⣪⠀⠀⡀⠀⠀⠧⣀⣀⡼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠀⠁⠈

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

⠀⠀⠀⣀⠄⢒⣀⠉⠭⠭⢁⣐⠂⠤⣀
⠀⠠⠊⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠠⡑⠠⡀
⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⠢⡀
⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⢦⡀
⠇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢆
⠸⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄
⠀⠣⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄
⠀⠀⠑⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⡈⠢⡑⢄
⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢊⠄⠒⠈⠁⠒⢤⡑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠂⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠱⡄⠀⠀⠀⠀⠀⠂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⠀⠰⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⢆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠢⡈⢢⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢆⠑⢈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢌⠢⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠑⢌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠑⢄⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠳⡄⠱⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡈⠢⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠑⢄⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡑⠢⠄⠀⠤⠚⡡⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣶⣦⣤⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣥⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠈⠉⣹⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣭⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣉⣤⡾⠃⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢄⡀⠈⠀⠎⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠉⠄⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠐⢠⠈⠁⠒⠦⠠⠤⠌⠭⠒⠒⠠⠤⠬⠀⠀⠀⠐⣧⡀⠀⠙
⠀⠀⠀⢀⠈⠃⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠔⣿⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠁⠰⢉⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣤⠟⠉⠀⠀⢀⡠⠤⠐⠈
⠀⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⠀⡅⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢄⢀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢰⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣀⣤⡟⢹⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⡈⠀⠘⠈⡄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠃⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠐⠀⠠⠃⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠖⠀⠄⢀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⣸⠀⠃⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⣤⠐⠢⡄⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠓⠚⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂
⠀⠀⠦⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠈⠀⠀⡀⠀⠂⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠃⠠⠆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠀⠀⠢⠀⠀⠠⠀⠂⠀⠀⡀⠀⠀⣠⠀⠀⢀⠖⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⢀⡇⠀⠀⠀⠾⡁⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠁⠀⠀⣧⢀⠀⠀⠀⠀⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠈⠆⣨⡁⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⠀⠘⠁
⠀⠀⠀⠀⠀⠀⡀⠸⠃⠉⠀⠀⠰⠂⠀⠀⠐⠁⢀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠘⠀⠀⡀⠤⠀⠉⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠰⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣐⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡰⠒⠒⠢⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡝⠀⠀⠀⢀⢿⠀⢀⠠⠤⠤⡀⠀⠀⠐⡄⠀⠀⠀⠁⢠⠊⠉⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡌⡄⣠⠋⠀⠀⠀⡸⠀⠀⠀⣧⠒⠀⢐⣺⣾⣦⣤⢄⣀⣀⡑⣦⡀
⠀⠀⣀⣀⠀⠀⢸⠃⠀⠀⠀⢠⠁⣿⠃⠀⠀⢀⢳⠁⠀⠀⠀⣿⣀⡀⣇⠈⣾⠀⠘⢿⣍⠐⠚⠋⠽⢷⣄⣀
⠰⠋⠀⠀⠙⢦⣧⠀⠀⠀⠀⡌⣰⠃⠀⠀⢀⣮⠃⠀⠀⠀⠀⠿⣆⠀⠉⠉⣿⠒⠂⠤⠭⢷⣄⡀⠀⠀⠙⢷⢍⡆
⠘⢄⡀⠀⠀⠀⠙⢷⣆⠐⠊⢰⠏⠀⠀⠀⣼⠎⠀⠀⠀⠀⠀⢰⡈⣁⣂⡩⡼⠤⠴⡒⠢⢄⠈⠙⢯⣁⠒⣒⠏⠙⢢
⠀⠀⠙⣦⡀⠀⠀⠀⠙⢦⣠⢫⡀⠀⢀⡼⡞⠀⠀⢀⣶⡶⠾⣟⠉⠙⠒⠈⠁⠀⣀⠜⠀⢀⡇⠀⠀⠉⠣⢄⣀⣀⠴
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢟⢆⠉⠉⠉⡼⢠⠔⠊⢋⠀⠀⠀⠀⠑⣦⣤⣔⡒⠭⠄⠒⠊⠉
⠀⠀⠀⠀⠀⠘⢮⠢⣀⣀⣠⠟⠓⡖⠋⠀⠸⣀⠀⠀⢑⣢⠶⡞⠛⠋⠉⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⡜⠀⠀⠀⠀⠉⠉⠁⠀⠐⠪⠝⡒⠤⣀⠀⠀⠀⠈⠙⠳⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣒⣒⣊⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠫⢶⣤⣀⣀⣠⠇⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠰⠊⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠒⠒⢄⠀⠀⠉⠒⠤⠄⠠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣘⣦⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⣀⣰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⣟⠁
⠀⠀⠀⠈⣹⠿⡟⢀⣴⣶⣶⣤⡀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠗⠐⠀⠀⠀⠄⠀⠀⠀⢀⢀⣰⡟⠏⢿⣟⢦⣶
⠀⠀⣀⣀⣁⣀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠉⢀⠀⠀⠀⠀⠀⡄⠈⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣿⣏⢻⡏⢻⡿⠙⠀⢀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⡀⠻⣟⠻⣮⠻⠏⠀⠀⠀⠀⡞
⠀⠹⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⣤⡰⠋⠀⠀⠈⢢⠙⠂⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠙⠻⢿⠿⠋⠀⠀⠰⡾⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠠⠀⠰⠀⠀⠀⠀⢚⣠⣄⠀⢸⡿⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡆
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⠀⣴⢶⣤⣴⣶⡶⣦⣤⣤⣴⡶⣦⣿⣯⣽⣷⠶⢶⣄⠀⠀⠀⢠⡔⠁⠀⡀⠀⠀⠀⠈⠀⡀⡠⠂
⠈⠀⠀⠀⠠⠆⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡏⠀⠛⠁⢸⠀⣸⡇⢹⢃⣴⢀⣿⠁⣿⠁⣴⣦⡿⠀⢠⣶⠿⠁⠀⠀⡇⠀⠀⠀⠈⣡⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡂⠀⢸⡇⣰⣶⡆⢸⡄⣿⠇⢸⣌⠛⠿⣿⠀⣿⠸⣿⣀⡀⠀⠀⠀⠀⠀⠠⠶⠀⠀⢠⡶⠀⢰⣀⣀⡘
⠀⢰⣶⣿⠂⠀⠀⢦⡀⠀⠀⠀⠈⠀⠀⣾⡇⣸⣿⡄⢸⣇⠀⢀⣾⡟⠿⠀⣹⠀⣿⡄⠛⢛⣿⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠋⣀⣀⠹
⠀⠀⠙⠃⣠⡊⠳⠈⠁⠀⠀⠀⠀⠀⠀⠙⠷⠟⠙⠻⠟⠛⠷⠿⠋⠻⠶⠿⠛⠿⠟⠻⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠤⢤
⠀⠀⡴⠢⡄⠉⠀⣠⠄⠀⠀⠀⣾⡇⢺⡇⠀⠀⢸⡇⢸⡇⣾⡇⠀⠀⣾⡇⣿⠇⠀⠀⣿⠆⢺⡇⣿⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠴⠂⠤⢬
⠀⡀⠙⠃⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⠸⠇⠀⠀⠸⠇⠿⠇⠿⠇⠀⠀⠻⠇⠿⠀⠀⠀⠿⠀⠺⠇⠿⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⡤⠶⠶⢄
⢠⡄⠈⠁⠂⠄⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⣐⣀⣀⣈
⠈⢡⡖⠠⣁⠢⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠸
⠀⠦⢤⡝⠢⣑⢄⡣⠀⢀⠀⠀⣴⣾⣷⣶⣯⣿⣿⠀⣘⣦⡄⠀⠶⠀⠈⠉⠉⢹⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡒⠒⢒⠳
⠀⠀⠀⠈⠫⡉⣌⣥⠳⠊⠙⠃⠹⣿⣿⣿⣿⣽⠃⢠⠽⣿⡿⠁⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠰⠀⣔⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⢠⣼⠙⡏⣀⠀⠀⠀⠈⠓⠿⣿⠁⠀⠀⠀⠉⠇⢀⠀⠀⠀⢈⠁⢸⠟⠀⠀⠀⡀⠀⣠⠐⠀⠓⠂⠀⠂⠀⠉⠀⠀⠉⠉⠉⢸

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣄
⠀⠀⠀⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡟
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⢀⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⢠⡀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣧⣤⣄⡀
⠀⣸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡿⠁⠀⠀⠁⣰⠀⠀⢀⣤⡤⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣇
⠀⣿⠁⢻⣿⣿⣿⣿⠀⠀⠀⠀⣰⡟⠁⠀⠀⡀⠐⠻⣇⣰⠟⠀⠀⠀⠀⣿⡟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢰⡿⠉⣿⣿⣿⡏⠈⣿
⠀⢿⡄⠈⠟⣛⣿⣿⡆⠀⠀⠀⠘⣷⠀⠀⠁⠙⢰⡖⠻⠁⠀⠀⠀⠀⠀⣿⡁⢹⣿⣿⣧⣀⠀⠀⠀⠀⠀⢸⣷⠀⣹⣿⡟⢃⡀⣿⠇
⠀⠈⣿⠀⢼⣿⣿⣿⡧⠀⠀⠀⠀⠈⢧⣀⠀⠀⠸⡇⢠⠀⠀⠀⠀⠀⠀⢹⣷⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠹⣯⠀⠋⠉⠠⡐⡟
⠀⠀⣿⡆⠈⣽⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣁⡀⠁⠀⠀⠁
⠀⠀⠈⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⣀⡀⠘⠒⢠⠀⢢
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠂⠉
⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢰⡟⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⢀⡾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⣿⠃⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠰⣿⠃⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⣰⡅⠀⣴⡀⠀⠀⠀⠀⠰⠂⠀⠀⠸⠂⠀⠀⣀⣤⠁⠀⡤⠀⠐⠀⡴⣃⠉⠀⠀⠀⢸⣶⣧⡠⢻⡷⠀⠸⠀⣆⢻⠘⡄
⣤⡀⠀⠤⠂⠀⠚⠀⠈⣆⣀⠉⠏⠸⣿⣿⣤⡀⣰⣿⣶⠀⠀⠘⠁⠀⠀⠊⠀⢀⠀⠃⣀⠀⠀⣰⠱⠁⠀⠁⠁⠀⠀⠰⠟⣰⡆⡖⠛⠈⡇⢱⠈⡇⢸
⠁⠀⠀⠀⠀⠐⢂⡀⢸⣿⣿⣷⡀⣀⣤⡽⠟⠁⠚⠛⠛⡄⠀⠀⠐⠃⠠⠆⠀⠀⠀⠀⠐⢶⡾⠃⠀⠀⠀⠀⠀⠀⣢⣤⡅⠀⠈⡇⠸⠀⡇⢸⠀⢷
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠿⠿⠿⠟⣀⠀⠀⠀⠁⠀⠟⠀⠀⠀⠀⠀⠈⠀⠀⠠⡔⠋⠀⠀⠀⠀⠀⠺⢣⠈⠛⣫⠀⠀⣸⡀⡆⢀⡇⢸⠀⢸
⠈⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠚⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠀⠀⠀⠀⢂⠀⢠⠁⠸⠚⡿⠻⠟⢸⠃⢙⠢⢼⡀
⠀⠀⠀⠀⠀⠈⠉⡽⠟⠋⠀⠲⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡋⢰⠟⠀⠂⣼⠁⠀⡀⣸⠀⠐⠀⣾⠙
⠀⠀⠀⠉⣀⣠⠀⠀⠀⠐⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠄⣀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠞⢤⣿⢄⠏⠀⠀⠈⣧⣠⣄⠀⡿⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⡤⠊⠡⠀⠀⠀⠀⠠⢋⣵⡾⠋⠀⢠⣾⣿⣿⣿⡧⠀⠀⠀⡠⠁⠔⠀⠀⢀⠎⠀⢈⡯⡜⠀⠀⠀⢸⠿⢿⡋⢠⡧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠀⢂⣠⠿⣿⣿⣿⣿⣃⣀⣀⣄⣠⣊⡀⠀⢠⠊⠀⠀⠀⣰⠁⢀⠀⠀⣯⣾⡿⠈⢾⡀⢹
⠀⠀⠀⠀⠀⠀⡤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⣰⣿⢟⡴⠂⡐⣀⣈⢿⣿⣿⣿⣿⣿⠿⢢⠃⠀⠀⠀⢠⠃⠴⠾⠀⣼⠛⢅⠀⠀⡟⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢟⠔⢀⠌⣁⠀⠀⡰⠁⠀⠀⠀⢠⠏⠀⠘⠀⢰⢿⠠⠬⣣⣼⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠛⠻⠋⠩⠟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⠁⡸⣧⣴⣿⠉⠁⠀⡐⠁⠀⠀⠀⢀⠎⠀⠀⠀⢀⡞⠀⢳⣿⣿⣿⣆⣠⠇
⠀⠀⢀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠉⣤⣤⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢰⣿⣿⣿⠿⢃⠜⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡼⠁⠀⠈⠛⢻⠿⠟⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠐⢟⠀⠊⣰⡿⠿⠊⠀⠀⠀⠀⠀⣠⣶⠀⢀⠔⠁⡡⠊⡀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⡾⠀⠀⡇
⢠⣤⡤⠄⢀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⡼⠿⠁⡰⠋⣠⠜⠀⠀⠃⠀⡰⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⠏⣳⣠⡀⠀⢰⠇⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⣿⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⣸⠂⣷⡀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠈⢷⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠛⠉⠉⣽⠉⠉⠉⠛⠻⢾⣿⣇⠀⠀⠀⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣿⢇⠘⣷⠀⠀⣀⣴⠾⠛⠉⠀⣿⠀⠀⠀⠀⠘⡆⠀⠀⢀⡀⢸⡏⠿⣦⡀⠀⣸⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣿⡃⢀⣿⣴⠟⢛⠃⠀⢀⣀⡀⠋⠀⠀⠀⠀⢘⠀⠘⠥⠞⠀⡰⠂⠀⠈⠻⣦⣿⠀⢸⣿⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣏⣷⡿⠋⠀⠀⠀⢳⡄⠈⠙⠦⠀⠄⠘⢦⡀⠀⠱⡄⠀⠀⢸⡁⠀⠀⢀⠀⢙⣿⡄⠘⢸⡇⢀⡟⢹
⠀⠀⠀⠀⣸⡇⠀⠀⠀⣯⣷⣿⣡⠴⠖⢁⣀⣀⣈⡀⠀⠀⠘⠲⠃⠀⠀⠉⠛⠛⠁⣀⠀⠀⠙⠦⣄⠈⢢⠸⣌⣿⡄⠈⣷⣸⡇⣼
⠀⠀⠀⠀⣿⡇⠀⠀⣠⡿⣋⣩⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣍⣉⣉⣀⣒⠒⠠⠤⠄⣀⠐⠠⢄⢳⠈⠛⠃⣠⢤⣉⣿⡄⠘⡿⢁⣿
⠀⠀⠀⠀⣿⣷⠀⣴⡿⠛⢯⡉⢅⠀⣄⠠⡄⠀⡄⠀⡄⠀⡍⠉⡉⢉⡛⢛⠛⡷⠶⣶⣤⣥⣀⡌⠀⢀⠀⠘⠤⡀⠙⣿⡀⠑⢸⣿
⠀⠀⠀⠀⢹⣿⣦⣿⡤⣑⠦⣽⣦⣵⣮⣷⣽⣦⣼⣦⣼⣦⣼⣦⣧⣸⡆⣿⢰⡇⢀⠇⠀⡏⠉⡿⠳⣶⣬⣐⠦⣜⣄⢹⣷⠀⢸⣿
⠀⠀⠀⠀⠀⢻⡻⣮⠻⣦⣭⣽⣿⣟⡛⠳⠿⣿⣶⣭⣝⣽⡽⣉⣛⠿⣻⡷⢾⣤⣞⣀⡴⠁⣰⠃⣰⠂⠈⡟⠳⣮⣘⠝⣿⡄⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠳⡾⣷⣿⡟⢿⣯⣿⣿⣷⣦⣄⠈⠻⠿⣿⣿⣿⣿⣯⣵⣶⣯⣭⣉⠻⢿⣾⣥⡞⢁⡠⢚⣀⡴⠉⣹⣷⣿⡇⢸⡏⢣
⠀⠀⠀⣤⠀⠀⠀⢷⡈⠣⠙⢶⣦⣭⣛⢿⣯⣽⣻⠷⣶⣿⣿⣿⣿⣿⢿⠿⢿⠿⠶⢞⡓⠲⠯⣿⣿⣿⣿⡷⠶⠛⢁⣈⣿⠇⣾⠁⢸
⠀⠀⠀⢹⣧⠀⠀⢸⡁⣲⡖⠴⠷⣬⡉⠻⠶⣿⣟⠻⣷⣿⣿⣿⣿⣟⣿⣿⣶⣾⣷⠶⠶⣿⣶⠶⣿⣿⡯⣉⣉⣉⣭⡿⠋⠀⣿⠀⣾
⠀⠀⠀⠈⢿⣧⣀⣼⣦⣽⣷⡂⠒⠀⠭⢤⣷⠀⠙⣿⣿⣿⣿⣿⡟⢩⣿⡟⢻⠛⠻⣿⣿⣿⣿⣿⣿⡛⣿⡟⣿⣩⣿⣾⣿⣷⣿⠀⣿
⠀⠀⠀⠀⠈⣿⠏⢦⡌⠉⠹⢿⣷⣤⣀⠤⢈⡳⡆⠈⣿⣿⣿⣿⡇⣿⡂⣿⡎⠀⢀⣿⠿⢿⣿⣿⣿⡇⢻⡇⣿⣿⣿⣿⡉⢿⣿⠀⣿
⠀⠀⠀⠀⣼⠋⠁⢈⠄⠐⢥⣤⡹⣮⡉⠻⢦⣄⠻⣶⣿⣿⣿⣿⡇⣾⣳⡿⠀⠀⣿⠁⠀⠀⠻⡿⠟⠁⢸⡇⣿⡟⠁⠀⣿⠸⣿⢠⣿
⠀⠀⠀⣰⠋⠋⠀⠀⠀⠀⠀⠴⠁⠨⢷⣄⠈⢻⡌⢻⣿⣿⣿⣿⡟⠋⠉⣀⠀⢰⣿⠀⢀⣠⣶⣦⡀⠀⠈⢻⣿⠃⠀⢰⣿⢰⡟⠘⣿
⠀⠀⢠⣟⣀⣠⣶⣤⣖⣺⣶⣿⡞⠛⢛⣿⣷⡈⢻⣾⣿⣿⢉⣿⣟⠛⣛⣿⣇⢸⣧⣾⣿⣿⣿⣿⡇⠀⠀⠀⢹⡄⠀⣿⡏⣿⠁⢶⡼⣧
⠀⢹⡾⠫⠷⢬⡽⠿⢿⠿⠟⢷⣾⠏⢄⣻⣌⣻⣼⣿⣿⣿⠆⣽⣿⡟⠉⠆⣸⡇⠛⣽⣿⢿⣿⣿⠃⠀⠀⢠⣼⡇⠀⢿⣷⣿⠀⠈⠙⣿
⠀⠘⣿⡄⢠⡾⠻⢦⣹⣾⢀⢻⣿⣂⠄⣘⣯⠻⡞⣿⣿⣿⠀⣹⣿⠃⠀⣼⣿⠃⢀⣿⠃⠘⣿⣿⡀⠀⠀⢘⣿⡇⠀⣿⣿⣿⠀⠀⠀⢹⡄
⠀⠀⠩⣿⣏⣿⡈⠤⢻⣏⣇⡸⣿⣿⣷⣤⢿⡝⠻⣿⡿⢿⡆⠁⣿⣧⢢⣿⢻⡆⣼⡏⠀⢸⣿⣿⡇⠀⢀⡿⠿⠁⠀⣿⣿⠏⠀⠀⠀⣰⠗
⠀⠀⢀⡟⠉⣘⣀⣂⣀⣹⡿⣾⣿⣯⣭⣭⣿⣿⡇⢾⣷⢿⣡⠞⠘⣿⣿⡟⢈⡧⢸⡇⠀⣾⣿⣿⡷⠀⣿⠀⠀⠀⠀⢿⡇⢠⡇⠀⢸⡅
⠀⠀⢸⡷⢛⣫⣿⣿⣯⣽⣿⡭⠷⠶⢶⣶⢾⣿⣿⣶⣿⣠⣏⡤⠃⠘⢿⣆⠸⣧⢸⣧⢠⣿⣿⣯⡀⠀⢸⣧⠀⠀⠈⠈⢻⣿⣧⢰⡌⢷
⠀⠀⠈⠉⠛⠋⠻⣯⣿⡿⠾⠟⠛⠛⣛⡙⠛⡛⠛⠿⣿⣇⠼⡆⣈⠄⠈⠻⣶⡇⢿⣿⠸⣿⣿⠀⠈⢠⣿⠋⠀⠀⠀⠀⠀⣿⣿⠸⡇⢸⡇
⠀⠀⠀⠀⢳⣤⡀⢻⣧⣄⣀⣈⢱⣾⣿⣿⣷⣶⣶⡾⠛⢿⡄⢛⠀⠚⠁⠀⠙⣷⣾⡏⠀⢿⣿⣦⣀⠚⠟⠛⠶⣤⡀⢀⠀⢻⣿⠃⣷⣸⠁
⠀⠀⠀⠀⠀⢹⠙⣿⣿⣿⣭⣙⠛⣻⣿⢹⣿⣧⣙⣧⡈⢙⣷⡈⢒⠀⠈⠐⠄⠈⢻⣿⡄⠈⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⡆⡿⠀⣸⡏⣿
⠀⠀⠀⠀⢠⡋⡴⠞⣛⣛⣛⢿⣿⢾⣿⣇⢻⣿⣿⢿⣷⣦⠹⣷⡌⢆⠐⡀⠈⢦⡈⠹⠿⣦⣈⠀⠀⠀⠀⠀⠛⣿⣿⣿⠛⠃⣼⣿⠇⣿
⠀⠀⠀⠀⢈⡿⠟⠋⠉⠉⠉⠛⠻⣦⣝⢿⣧⣘⢿⣦⣭⢋⠛⠿⣿⣄⠠⡈⠡⡀⠙⢤⠈⢻⣿⣿⣦⣀⢀⣠⣴⣿⣿⡟⠀⠀⣿⣿⠀⣻⡄
⠀⠀⢀⣠⣏⣀⣤⣤⣤⣶⣤⣤⣤⣌⣿⣾⣿⣿⡷⣭⣻⣿⣾⣄⣂⠻⣷⡘⢖⠝⢦⠀⢙⠦⡱⣫⣿⡿⠟⠻⠿⡿⠟⢁⠀⠀⢻⣿⣷⠙⣧
⠀⠀⠈⢻⡿⣤⣤⣤⡴⢷⣶⣷⣚⣿⣟⣩⣷⣿⣿⣿⣿⠿⣷⣿⣿⣷⣾⣿⣦⣕⠄⠑⣄⡀⠸⣿⡁⠀⠀⠀⠀⠐⢶⣿⠀⠀⠀⠙⢿⣇⡿
⠀⠀⠀⠀⠙⢯⣉⡉⣣⡈⠛⢿⣯⣿⣿⣿⡿⠿⠿⠟⠛⠛⣛⣻⠛⠻⠿⠿⢿⣿⣷⣦⣀⢈⣤⣿⠗⠀⠂⠀⠀⣀⣼⠏⢀⣀⣀⣨⣇⣿⠃
⠀⠀⠀⠀⢀⣤⠼⠾⢯⡙⠶⠶⣶⣶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠙⠛⠛⠛⠛⢶⣾⣍⣻⣿⣯⣥⣤⣤⣤⣀⣀⣈⣭⡶⠟⣛⡛⠛⠛⠛⠁
⠀⠀⠀⠰⢿⡥⠤⢶⣾⡿⠗⠂⠀⣠⠖⠛⢸⣇⠀⠀⠀⣠⡖⣛⣦⣄⠀⠀⠉⠉⠉⢉⣩⣤⣤⣄⡀⠈⠉⠛⠉⢁⡴⠟⠉⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣒⣾⣬⣥⣴⣶⣿⣯⣻⠆⠈⠉⠉⠉⠉⠉⢁⣀⣀⣠⡴⠋⣁⣠⣼⣿⢷⣤⠤⠀⠚⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄
⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠁⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣯⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢷⣄⡴⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢻⡟
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣾⠇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣾⠏
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⠉
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠶⠶⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠻⣤⣤⠤⠴⠶⠶⠶⠶⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠤⠄⠀⠀⠀⡀⠄⠀⠀⠀⠀⠄⠀⡀⢀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠴⠂⠒⠀⠄⠀⠀⠀⠀⠀⠐⠀⡀⠈⠈⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡼⠂⠐
⠀⠀⠀⠀⠀⠀⠄⢠⠀⡔⢡⠐⠀⠀⠀⠀⠀⠃⢠⣶⣤⡀⢀⠀⠙⡌⠺⠿⣿⣿⣷⣦⡄⠀⠀⠀⢀⠀⠤⠄⠀⠰⠋⠀⠰⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⢀⠀⠈⡀⠘⣉⠀⢆⠘⠀⠉⠉⡁⠀⠣⠸⠀⠀⠘⠛⠛⠹⣿⡆⠠⠊⠠⠀⠀⠀⠠⡘⠄⡀⠀⢀⠄⠀⢌
⠀⠀⠀⠀⠀⠊⠀⠀⠈⡄⠀⠆⠀⢁⠀⠀⠤⠀⡙⠲⣆⠀⠁⠂⢀⢳⡀⠀⠀⠀⠠⠄⣿⣿⠁⠀⠀⠀⠌⠐⡔⠁⣀⢁⠀⠠⠛⠂⣄⠢⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠱⡀⠐⠀⠀⠄⠀⠐⠂⠀⢀⠙⢷⣶⠈⠀⠂⠴⠂⠲⠂⠲⠾⠛⠛⠀⠀⠀⠴⠀⡰⠀⡀⠈⠀⡆⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠄⠈⢂⠰⣰⣶⣧⠀⢉⠀⠐⠂⠀⠋⡀⠈⢢⡀⠻⡄⠀⠀⣆⠀⠀⠀⠂⠀⠀⠠⠖⠢⠈⠀⠘⠀⡀⠀⠀⠀⡗⠀⠠
⠀⠀⠄⠀⠀⠜⠀⢦⡙⣿⣿⣇⠀⠠⠀⠈⠀⠀⠀⠠⢤⣷⠀⣽⡄⠂⠈⠐⠂⡀⠀⠀⢰⠀⢀⢀⢉⡙⠀⡀⢀⠈⠈⠈⠛⠄⠀⠠⠈⠀⡀
⠀⠀⢠⠀⠀⠹⠁⢉⠷⣌⢩⣉⠁⠀⠀⠀⠐⢀⣠⣾⠟⠡⢾⣿⠀⢀⡠⠉⠠⡀⠁⠁⢸⠀⠀⠈⡳⠉⠰⠆⣧⠀⠀⠀⢀⡎⠀⠀⠁⠀⠁
⠀⠀⠐⠂⢀⡂⣬⣏⢰⣿⣦⡙⣧⢸⣷⣶⣿⣬⣉⣄⠚⠷⡀⢙⣿⠟⠋⣈⣢⡀⠀⠀⣸⠀⠀⢐⠆⢠⣃⣡⠾⣦⣀⡄⠊⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠸⣇⢻⣿⣮⣭⣿⣷⠄⣼⣿⣾⠟⠁⠀⠀⠀⠢⡘⢊⠁⠙⠶⠙⣿⢁⠃⡰⠃⠀⢂⠀⠭⠁⠉⠁⠀⣿⠏⡣⣄⢀⠔⠂⠁
⠀⠀⠀⠀⠀⢾⣦⣉⠛⠛⣋⣡⣾⡌⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠦⠞⢁⠶⡉⠀⠀⠀⠂⠌⠀⠀⠐⣠⣼⠏⠀⡡⠂⡀⠀⢀⡀⠀⠂
⠀⠂⠀⠀⢁⠀⠙⠛⠛⡛⠋⠉⢻⡃⢀⠀⠀⠐⡀⠒⠀⠃⢀⡀⠀⠐⠄⠀⠀⠀⠀⠈⠀⠤⡀⠀⢠⢠⡞⢿⠃⠀⠀⡀⢀⡔⠀⣀⣠⠂
⠀⠀⠀⠀⠀⡠⢀⣬⣤⠀⢺⣿⣴⡧⠀⠁⠀⠀⠀⠉⢀⠈⠀⠀⠐⡄⠀⡁⠀⠈⠀⠀⠒⠤⠀⠀⠂⢸⣿⡆⣇⠀⡆⠆⢩⣐⠀⠀⣿⡇
⠀⠀⠰⠀⠀⠀⣹⡿⠋⠑⠀⢈⣉⣠⣾⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡰⢧⡀⠀⠒⠄⠀⠀⢀⠀⠀⢰⣶⡇⡸⢌⡻⣿⡥⠠⢄⣴⠟⠃
⠀⠀⠀⠀⠀⠐⠀⠁⠠⡘⠈⠆⡿⠛⠉⠀⠀⠆⠀⠑⠠⡉⠒⡈⡠⠚⣊⠁⡰⢦⡀⠐⠀⠀⠀⠀⢠⡾⠟⣠⡃⠈⢟⡌⢷⡴⠈⠁
⠀⠐⠀⠀⠀⠄⠓⣶⣯⠀⣀⢤⠀⢠⠀⣠⡀⠄⠈⡰⠔⠉⠀⠀⢤⠤⠀⢉⠐⡅⠉⠙⠒⠀⠘⠚⠧⠰⠚⠠⠁⠐⣦⠽⡀⡆⠀⠀⣀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⡏⣴⠋⠡⢂⠀⠐⢀⠙⠣⠂⡀⠠⢄⠀⠀⠀⠉⠁⠀⢼⠒⠈⢣⢀⡤⡄⠀⡀⢀⢠⠀⠀⢦⠌⡙⢻⠃⡅
⠀⠀⠈⠀⠂⠀⠀⢰⠂⠊⠀⠈⠢⣀⠁⠀⠀⣀⢀⣿⡏⠀⠀⠄⢐⠀⡀⠀⠦⠐⡀⠂⠀⢀⡑⠂⠀⣱⣤⠆⠑⠁⢀⡜⡐⢀⠂⠌⠠⠁
⠀⠀⠂⠊⡔⡩⠅⡂⢐⠀⠀⠌⣱⣿⣿⣿⡟⣿⠸⣿⡀⠀⠀⠐⠿⢇⠀⠀⠀⠀⣅⠀⠀⠨⠱⠃⠈⢹⢋⣽⣤⡤⢊⣼⠃⠀⠄⠄⠠
⠀⠀⠀⠀⠣⢁⠂⢃⢸⠀⠀⡀⠟⣻⡟⠉⠻⣿⡄⢻⡷⠎⠀⠈⠀⠀⠀⣰⣤⡀⢠⣷⣤⡈⠁⠀⡔⡘⠦⢩⣥⣶⡿⠁⠠⠉⠄
⠀⠀⠌⠈⠀⠀⡠⠉⡌⢅⠀⠐⠈⠯⣵⠾⠀⣿⣿⣦⡀⠨⣁⣰⣶⣶⣾⠿⠋⣠⣿⣿⣿⣿⡷⣄⡀⠀⠡⠂⠈⢉⠀⠠
⠀⠀⠈⠂⠨⠁⠀⠈⠀⠀⠲⢄⡀⡀⢀⠠⠀⠙⠉⣹⣿⣶⠤⠭⠉⣅⠀⠀⠀⠈⢙⠴⠉⠙⠾⣿⣿⣾⠃⠤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠐⠀⡠⠀⠀⠈⠉⠐⠀⠀⢄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢩⣿⠋⢠⣽⡿⠝⣻⣿⣿⠀⣻⣿⡇⠙⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⣴⡿⠁⢠⣾⡟⠀⢠⣿⣿⠉⠀⣿⣿⡇⠀⢹⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣿⡟⠀⢠⣾⡿⠀⠀⣾⣿⡇⠀⢀⣿⣿⣿⠀⠀⣿⣿⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣽⡿⠁⢀⡿⣿⡇⠀⢠⣿⣿⠇⠀⢐⣿⣿⣿⠀⠀⢻⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⠁⣼⣿⡇⠀⣼⣆⣿⠀⠀⢸⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⢸⣯⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠠⣾⡟⠀⣿⣿⠁⢀⣿⣿⡏⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠨⣟⣿⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⡇⢀⣿⣗⠀⢸⣿⣿⡇⠀⠀⣿⣿⣯⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⡇⠐⣿⣿⠀⢸⣿⣿⡇⠀⠀⣿⣿⣯⠀⠀⢸⣿⣿⣿⠁⠀⢐⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⠀⠘⣿⣿⡇⠀⠀⢻⣿⣿⠀⠀⠈⣿⣿⣿⠀⠀⢸⣿⣿⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣄⣹⣿⣤⡀⣿⣿⣿⠀⠀⢸⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⣼⣿⡿⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⢼⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣴⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣆⣠⣼⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⣿⠇⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣿⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠛⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠄⠀⢠⣀⡄⣤⣤⣦⣠⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠆⠀⠸⣿⣷⣿⣿⣿⠟⠣⠄⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⣤⡰⡦⣤⠰⠇⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⣤⠙⠘⣃⢀⡸⠦⠺⡎⠾⡀⢭⡸⢇⡤⠿⣀⠿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣬⢃⡜⠃⣺⡂⡬⣥⠌⣛⢈⣟⠀⢹⡅⢶⡄⣼⠆⣤⡝⢺⣧⠍⣤⢰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠵⠎⠘⢱⢆⡈⣍⢣⢺⣃⢩⡡⠿⠀⡍⠾⡡⣑⠛⢰⠖⠶⡄⣿⢢⡷⠀⣘⢣⡄⡴
⠀⠀⠀⠘⣃⠿⢠⡆⡉⣤⡛⣥⡔⢼⣃⠉⠸⡌⣱⢎⡃⢙⡋⢱⡾⡶⠋⣡⢀⣟⢓⣇⣽⠃⣀⠷⡙⢯⣑⠟⢠⡆
⠀⠀⠲⠎⢩⡥⠣⣜⢣⡖⣤⢀⡛⠁⢸⡏⢹⣿⢦⣘⠃⣮⠙⣼⢈⣛⠀⣍⢤⡍⡾⠴⠂⣤⢙⢞⡑⠶⠉⢴⢠⡖⣠⡄
⠀⠀⠈⢫⣤⠚⠋⠾⡟⠲⢬⣬⣋⡻⢂⣤⠀⠑⠶⠛⣷⣤⠞⠑⠶⠁⢈⡋⡺⢼⡇⣐⠷⣨⢯⡜⡣⢴⢠⡄⣤⠚⡆
⠀⠀⠶⠔⢦⠺⠜⠗⣘⡯⠖⣛⢩⣻⣦⠀⠿⡈⡶⠟⣽⡏⣠⠻⢆⣀⡘⠋⢇⣼⠁⢙⣰⣯⣼⢯⣤⠙⠀⢁⡨⣄⠟⣸⡋
⠀⠀⠐⢛⣥⢠⡌⣦⢷⢙⡓⢙⡠⣭⢹⣧⠸⠃⣇⢠⣿⢋⣥⢠⠃⣉⣡⣴⣿⠷⢿⣿⣉⡤⠙⢋⡠⡶⢷⠘⣃⠤⠰⠯⢡⠖
⠀⡈⢿⣄⠷⠎⡀⠁⠶⠎⡛⢈⡃⠰⡆⢻⣿⠓⠹⣾⡿⣠⢄⣿⡾⠟⣭⡅⣚⢣⣠⡦⢈⣱⠶⣸⠷⣚⡻⠯⢠⡴⡦⡶⢰⢖⣤
⠀⢙⡂⣦⠸⣆⣇⡻⠸⠇⢻⣈⣥⣴⠶⢾⣿⣷⣄⣹⣿⢈⣾⡟⣠⡝⠆⣤⢛⡨⢕⡱⠮⢉⣼⢫⠖⣩⠄⠳⣮⠀⣄⢶⣛⣅
⠰⠮⠉⠀⣩⢠⡎⣩⢙⡟⢩⡅⡶⠀⡛⢣⡀⢉⠻⣿⣿⣿⣿⢡⡶⠸⠇⣵⠋⠲⢎⣉⣤⡾⠟⠛⢛⡛⢫⡉⣮⢛⠉⠰⠦⠉
⠀⢟⡙⠇⢙⡄⣶⢉⡌⣣⡌⣀⠲⠆⠛⠬⢧⣘⣃⣈⠻⣿⣿⣇⠀⠀⣼⣿⡿⠟⢛⠋⣭⠰⡇⠸⠎⠃⣬⡁⠀⠘⠃
⠀⠘⠁⠀⠘⠁⠁⠈⠁⠉⢈⡍⠶⠃⣶⠸⢦⡆⣩⢉⡟⠿⣿⣿⣧⣾⡿⠁⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠏⠀⠀⠀⠀⠉⠘⠃⠀⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⣠⠴⠛⣻⣶⣶⣶⣶⣶⣿⣿⡿⣿⠿⣿⣤⣀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢁⣠⠞⡩⠤⡴⠛⠉⢀⣴⡟⠀⣿⠀⠙⢿⣿⠶⢦⣤⣶⣚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠋⠀⠀⠞⠁⣤⠾⡿⠉⢇⠀⠙⣷⣄⠀⠙⠳⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠜⠀⠀⠀⢀⣼⠁⢠⡇⠀⠀⠀⢀⡟⠈⠑⠄⠀⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⡜⠰⠁⠈⠀⠀⠐⠁⢣⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢸⣧⣤⣤⣤⣤⣤⣤⡿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⢿⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⢀⣴⠟⠙⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢃⠀⠀⠈⠹⣶⡇⠀⢰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢣⡀⠀⠀⡸⠗⠒⠛⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢻⡞⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢥⣾⡹⣄⠀⠀⠀⠀⣠⣤⢤⡾⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⡉⠻⣦⠀⢀⠾⠛⢻⡦⠿⣆⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠃⠀⠀⠇⠀⠹⣇⣿⣦⠀⡘⠉⢄⣹⡆⠀⣰⠃⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⣿⡟⠉⡟⠁⠁⢸⣿⣧⣴⡟⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⠀⠀⢹⠁⠀⡇⠀⢀⡼⢿⡛⠿⣧⡀⠀⢀⣀⡴⠷⠴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠀⠀⠀⡆⠀⢸⡆⢰⠁⢠⡏⠒⣾⠓⢶⡌⢻⣶⣿⠇⠀⠀⠀⢸⣽⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣿⡿⠀⣸⠁⠀⢡⠀⠀⠱⣿⢯⡁⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣾⣇⠀⠀⢰⠀⠀⢿⡏⢀⣿⡁⠉⠉⠃⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣴⣦⡙⠋⠉⠁⢹⣷⣶⣾⠀⠀⢸⡇⣼⣿⡇⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡷⡄⠉⠉⠛⣾⣧⡈⠙⣦⡀⢸⣿⣿⣿⡟⡉⠳⣄⠀⡀⣋⠀⡆⠀⢀⡀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣷⣽⣦⡀⠀⠈⠀⠙⠣⣌⠙⢿⣿⣿⣏⣴⠛⠇⢹⡆⢻⣿⣴⠷⢾⠋⢳⡀⠀⠁⠀⠇⠀⠀⠀⠀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡛⢉⣉⣿⣆⡀⠀⠀⠀⠈⠢⣈⣿⣿⢿⡇⠀⣸⠟⣷⣼⡟⠁⠘⢇⠀⠀⢳⣴⣷⠀⢸⣀⣤⣤⠎⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣟⠋⠁⠈⠙⢦⡀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠈⢠⣿⠏⢁⡀⣀⣀⡄⠀⠈⣿⣿⣤⠟⠁⠟⢹⠀⠀⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠑⢄⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡏⠀⠈⠁⠁⠈⠀⠀⣸⣿⠟⠁⠀⠀⠃⠀⠀⠀⠁⢾⡇
⠀⠀⠀⠀⠀⠀⢀⡿⢻⡌⠻⣦⡀⠀⠀⠀⠑⢄⠀⣿⠇⠀⠀⠀⠂⢸⠇⡀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠠⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡴⠿⣶⠿⢷⣄⠀⠀⠀⠀⠑⣿⠀⠀⠀⠀⡇⣼⡆⠀⠀⠀⠀⠀⡴⠁⡠⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⢈⣻⣄⣹⣄⠀⠙⢧⡄⢀⣀⣀⣯⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⢀⣾⡷⠊⠀⠀⠀⠀⠀⠀⢀⣴⠉
⠀⠀⠀⠀⠀⠀⢀⡿⠛⢿⣿⣿⣦⠀⣼⣷⣄⠈⠉⠉⠛⢛⣶⠚⡛⢻⣶⣄⣰⣰⣿⡟⠛⠋⠈⠛⠻⣷⣾⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠦⣙⠛⠛⠿⣉⣿⡿⣧⡀⠀⠀⠈⠉⠀⠠⣈⠉⠛⣿⣿⠁⠀⠀⠀⢀⣶⡦⡨⠿⠧⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣤⣄⡉⢁⣈⠳⡆⠀⠀⢀⡠⢤⣿⣷⠀⣽⠃⢀⡴⠐⠆⠚⣠⡴⠃⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢣⠀⠹⣀⣀⣠⣄⡈⢀⣠⣄⣤⣶⣦⡀⣀⠀⠾⠓⠀⠋⠐⠁⣼⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠤⠚⠓⠊⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠿⠶⠶⠿⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠶⣤⣴⠎⠉⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣧⣼⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠉⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠈⠁⠠⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠁⠀⠄⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣷⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠠⠿⡀⠈⠁⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠐⠶⠟⠃⢀⣇⠀⠀⠀⠀⢀⡀⢠⡇
⠀⠀⠀⠀⡀⠀⠀⡀⠀⠠⠤⢤⢰⡶⠞⠋⠀⠙⢶⣴⡰⠊⠀⢰⡇
⠀⠀⠀⠀⠁⠀⢁⣀⣥⣴⠖⠀⠀⠀⠀⠀⠀⠀⢘⠗⠀⠀⠀⠘⣿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠒⣠⣳⣦⣿⠃⠀⠀⠀⠀⠀⠀⣠⡘⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⢈⣉⣭⡄⠀⠀⠀⠀⠀⣠⣾⡋⠀⠀⠀⠀⠀⣼⡏⢡⡄⠀⣴⠉⡞⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⢁⣾⣿⡿⢀⠀⠀⠀⠀⠀⣿⣇⡈⣦⠚⠈⣑⠇⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇⠀⠀⣴⡿⣱⡿⠁⠀⠀⠀⠀⠀⠀⠧⠋⡿⣿⡶⠾⠛⠀⢠⡀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢽⣿⣿⡏⠁⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⢈⣿⣟⠀⠀⠀⢻⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢅⢠⠀⠀⠀⠀⠈⠀⠀⠄⠈⠀⠀⠀⠈⢇
⠀⠂⠀⠀⠀⣾⣿⠟⡄⢀⣼⡍⢸⡯⠄⢠⠀⠀⣓⡂⢀⠆⢐⠿⠙⡤⠄⠀⠀⠆⠈⡀⠘⡄⠀⢠⠱⡄⠘⣧
⠀⠀⠀⠀⢀⣿⣿⠀⢠⣿⠁⢀⡿⠃⠀⣬⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠀⠘⡆
⠀⠀⠀⠀⢸⣿⡏⠀⣾⣁⠀⣼⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⣿⣿⠀⣼⡿⡜⢰⠇⡜⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣿⣷⣠⣿⢡⠁⣾⢦⡄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⣻⣿⣿⣏⡞⣽⠃⠀⠇⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠙⣛⣿⣛⠁⣿⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⡇⠀⢀⣶⣄⠀⠀⠃⠀⠀⠀⠀⡀
⠀⠀⠀⡈⣾⣿⣿⣇⣰⣧⡀⠀⢸⠋⠀⢀⡴⢤⡀⠀⠀⠀⠀⣾⡆⢹⠳⣤⣀⣀⠀⡎⢇⠀⠙⠀⢴⣀⠄⠢⠀⠁⢀⡀
⠀⠀⠐⣇⢻⣧⣹⣿⣿⣿⣿⠄⢐⣷⠎⣿⠃⢸⠁⢲⡤⢤⣴⣿⡇⠈⡆⢰⠘⡿⣄⢷⠈⡆⠀⠀⠘⠉⠀⠀⠀⠀⠀⠃
⠀⠀⢸⣿⣦⡙⠿⠿⠿⢟⡋⣼⡿⣿⠀⣿⠀⢸⠀⢘⡇⠀⠀⢼⢷⠀⢧⠈⠀⢡⠘⢾⣇⠹⡀⠀⠀⠆
⠀⠀⢀⣿⣿⣿⣷⣿⠿⣿⢑⣿⢹⡏⠀⡿⠄⢸⠀⠈⡇⠀⠀⢸⢸⡄⢸⡄⢠⠀⠆⠰⣿⡆⢇⠸⠀⢦⠀⡆
⠀⠀⢸⣿⣿⡿⢹⠏⢰⡇⢸⡿⢸⡇⢸⡗⠀⢀⡆⠀⣿⠀⠀⠀⢈⣧⠸⣿⠈⡇⠀⠀⢹⡇⠈⠀⠃⠈
⠀⠀⢻⣿⣧⡀⡀⠀⡞⠀⠞⠀⠟⠁⢸⠷⠆⠸⠗⠀⠈⠁⠸⠀⢸⡤⠀⡇⠀⣃⠀⣀⣠⣧⣀⣤⣀⣤⣴⣤⣤⣶⡶⠊
⠀⠀⠸⣿⣿⣿⣿⣿⣷⣾⣶⣶⣤⣼⣧⣤⣤⣦⣤⣤⣷⣿⣧⣴⣾⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠂
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠋⠉⠉

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠂⠀⠢⣀⠀⠀⠀⠀⣄⠤⠒⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠸⠀⠘⠀⠀⠀⠀⠢⡀⠀⠈⠳⢄⠀⠀⠀⡀⠐⢄⠀⢀⠀⠀⢀⠀⢠⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠑⠦⡀⠈⢆⠈⠱⠀⠀⠀⠀⢠⠃⠀⡴⠃
⠀⠀⠄⠂⠁⣰⡵⠃⠂⠆⠀⠀⢀⡄⢠⠀⠀⠀⠀⠀⡀⠱⣦⡤⣀⣈⣂⡀⢁⣀⣀⠀⣀⡈⠙⣦⡜⠃⠈
⢫⠀⠐⠒⠁⠊⢡⡞⠉⢲⠀⠈⣨⡄⠼⠀⠀⡠⠤⠀⢰⠋⠈⠿⢭⡉⠛⢩⠋⠉⠻⠳⡜⣯⠉⠾⣧
⠈⠀⢀⠔⠁⠀⠈⢧⠀⠈⣇⡠⠋⠈⠳⡤⠊⡠⡲⠶⡙⢄⣀⣀⣠⣀⣴⣇⣀⣀⣰⡱⠃⠘⢷⢠⠟⢦
⠀⠀⡀⡀⠀⠀⠀⠘⡆⢀⣼⠀⠀⢀⡜⠀⡰⠋⠀⠀⢀⠀⠀⠀⢀⣼⠋⠀⢈⣽⠋⢉⠉⠉⠉⠣⡀⢀
⠀⠘⢀⠃⠀⠀⠀⠀⣡⠟⠀⠂⢠⡞⠀⠈⠀⢁⠊⠉⢺⡀⠀⢀⡾⠁⠀⢀⡞⠁⠐⢄⣑⣤⠤⠂⠉⠉⡆
⠀⣸⠀⡁⢀⡀⢀⣴⠋⠀⠀⣴⠋⠐⡄⠀⠀⠸⡇⠀⠈⣇⡠⠁⢇⣀⣰⠯⠀⠰⠚⠉⠉⠀⡀⣀⡠⠄
⠀⠙⠀⣟⡠⣤⣣⡰⢄⡠⡾⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⣁⠈⠀⢠⢎⠀⠀⠐⠀⡤⠖⠓⠋⡏⠸⠄
⠀⡇⠀⢻⠑⣅⠘⢜⣦⡎⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⢠⡟⡗⠗⠒⠁⣈⣉⠳⣉⣁⡀⡀⠀⡀⠇⠘⠃⣁
⠀⡇⠀⢸⠐⢌⠳⣞⠻⣉⣢⠖⠒⠲⡄⠀⠔⠋⢀⢯⠀⢁⣄⣠⢀⡊⠁⠀⢹⠁⠠⣈⣎⠑⢄⡗⠈⠁
⠀⠁⠀⠈⠀⠈⢷⡈⠃⡙⣧⠀⠀⠀⣋⠀⠴⠚⠓⠒⠋⣉⣉⣈⣺⡥⠤⡀⡜⣤⡔⠉⠙⣷⡎⢀⡄
⠀⠃⠀⠀⠀⠀⠀⠹⡄⠨⢻⡳⡒⠒⢼⡉⠐⠒⠒⠢⢟⠉⠉⠁⣽⠉⠓⣾⢶⠉⢷⣤⠞⠁⢻⣌⠀⠀⠒
⠀⠀⡀⠀⠒⠄⠀⠀⠐⢄⠈⣧⠀⠀⢸⡇⠀⠀⠀⠐⠀⠀⢁⢻⠷⠤⣬⣟⠈⢃⠞⢻⣆⠀⠀⠹⣆
⠀⠀⢢⠀⡠⠈⢦⡀⠀⠀⠈⢻⡀⠀⢨⣷⣀⣀⡀⠀⠠⠀⠀⠸⠁⠀⢸⠓⠚⠁⠀⠁⢹⣆⣂⣠⠇⢢
⠀⠀⠀⠁⣦⠀⠀⠱⣄⠀⠀⢸⡇⠀⠀⢿⡅⢀⠔⠛⢟⠻⢦⣧⣀⣀⠬⠀⠀⠀⠀⠀⡴⠱⡌⠀⠀⠀⡳
⣀⠀⠀⢀⠍⠳⣄⠄⠚⢣⡀⠀⢣⠀⠀⠈⡗⠦⢀⣄⣨⡆⠀⠙⠈⠻⡁⠖⠠⡀⠀⠀⠏⠀⡟⠢⠤⠼⡁
⠁⠀⡠⠎⠐⠁⠘⠳⡂⠁⠈⠀⠘⣄⠀⢀⠆⣦⠀⠀⠙⡟⠲⠦⣤⠔⠁⠀⠀⡁⡠⠴⢄⠀⠁⠀⠀⠀⠁
⢀⡞⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢈⡉⠁⠀⣿⠀⠀⢸⡇⠀⠀⠀⠉⠐⠒⠊⢸⠀⠀⠀⣆
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⢆⢠⠴⠚⡉⢽⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠫⡙⠉⠈⡉⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⢨⡟⠀⠀⢠⡾⠀⡉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠽⢦⡀⠆⠈⢀⠈⢷⡀⠀⠠⠲⢤⣀⠸⡇⣿⣿⠀⠠⠈⣼⠃⢀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠙⠣⣄⠀⠀⠀⠙⡖⠀⣰⣦⣬⣉⠻⢿⡿⠐⠀⣴⣃⣀⡀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠉⣳⣤⣀⡞⠀⣰⣿⣿⣿⣿⣷⣤⡷⢟⡉⠉⠉⠉⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣾⠟⠋⠿⡿⠀⢠⣿⢿⠿⡛⢻⡸⣶⣒⣾⣿⣿⣿⡆⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⢶⣿⣿⡇⠀⣠⣶⡇⠀⡞⠹⡌⢿⠁⠀⢹⣿⣿⣞⣹⣿⣿⡇⢸⡟⠉⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠉⠒⠒⠒⠦⣌⣿⣿⡇⠀⣿⣿⣷⣮⣾⠀⠙⢾⣀⡴⠾⣯⣉⠀⣈⢿⣿⠇⣸⠇⠀⠀⡼⡁⠤⠒⠚⠉⠛⣲⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡉⠻⣷⣶⣿⣿⣿⣄⠈⢿⣿⣿⠟⠀⢀⡼⢻⡇⠀⢣⠈⠓⠿⠼⣿⣞⣁⣀⠄⣰⣧⣶⡶⠖⢁⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⢉⠛⣻⢣⡿⠿⣿⣷⠀⠉⠳⢤⡒⠉⣠⠞⠀⠀⠈⠳⢤⡤⢴⣾⣿⣿⡭⠞⠉⠛⢯⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⡴⡶⢚⠋⡿⠀⠀⢠⣿⡍⠛⠒⠶⠤⣍⡻⠤⣶⣶⣦⣤⣤⣴⢠⣿⣿⣿⣿⡗⠀⠀⢀⠀⠳⡄
⠀⠀⠀⠀⢀⠞⢡⠤⢺⠛⠁⡰⠁⠂⢸⡇⠀⠀⢸⣿⣿⣦⣀⢠⣤⣤⣽⣦⡈⣙⣛⣿⣿⣵⣿⣿⣿⣿⣿⡥⠀⠐⢋⡠⢾⡁
⠀⠀⠀⡠⠞⠊⠣⣄⡁⠀⠐⢀⣠⠶⠺⣇⠀⠀⠈⠻⣿⣿⣿⣷⣯⣟⣻⣿⣿⣿⡿⢿⣿⣧⣈⠉⠉⣉⣡⣶⣶⣿⣿⣦⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠈⠑⢦⡀⠀⢀⣉⡻⣿⣿⡿⠦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏⠠⣌⠛⣿⠿⠟⢉⣀⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠈⠻⢿⣿⣿⣿⡿⠅⠀⢀⣠⣿⣿⣿⣿⣿⣿⠃⠀⣿⠆⣟⣀⡴⢋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⣿⠓⠤⣀⣀⣤⠶⠒⢶⣶⣿⣿⣿⣿⣿⡿⠟⠁⠀⠜⠋⣰⠿⣄⢀⠁⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠟⣩⡏⢀⠄⡈⢱⡇⠀⠘⢧⡹⠿⣿⡍⠉⠁⠀⠀⠀⠀⢀⡼⢁⠀⠈⠳⡄⠁⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣃⠤⠊⢹⢃⠅⠊⠀⣼⠀⠂⠀⠀⢹⣆⠀⠀⠀⠀⠀⣀⣠⣴⣿⡀⡀⡀⠀⠀⡉⢳⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⢸⡀⠔⢀⠠⡇⠈⠀⠀⠀⢸⠏⠓⠒⠚⠉⠀⠈⡇⢸⣿⠙⣧⡀⠀⡀⠃⠀⠙⢄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⠁⢸⡏⢄⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⣇⢸⡟⢠⠏⠙⠶⠤⣤⣤⣄⣈⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡾⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡗⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⠀⢀⠀⠀⣀⡀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠄⠀⠀⠀⠆⠀⠀⡀⠀⠀⢀⡀
⠀⢀⠀⢸⣿⣿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⣄⡘⠿⠃⠀⠀⠀⢀⣾⠀⠀⡼⢀⡔⠁⠀⠀⠀⡀⢀⣽⡆⠓⠀⠀⢠⣦⡄
⠀⠀⠀⣼⣧⣜⠿⣛⣩⢿⣿⣦⠀⠀⠀⠀⣀⣿⡟⠀⠀⠀⠀⢠⣿⣿⠀⣸⣷⠏⠀⠈⢀⣤⠞⡁⠘⠟⡁⢠⠶⡄⠘⠛⠁
⠀⢀⣿⣿⣿⣿⣯⣷⣶⣿⡯⠥⠀⠀⠀⢸⣿⣿⣧⡄⠀⠂⠀⠘⠿⢿⣷⣿⣿⣧⣶⣶⡿⠋⠀⠀⠀⠀⠀⠈⠛⠁⠰⠤
⠀⠨⠁⠀⠙⠻⠿⠟⣿⡇⠈⠀⣀⠀⠀⢸⣿⣿⣯⣷⠀⠀⠀⠀⠸⣯⣿⡭⠉⠉⠛⠉⠀⠀⠀⠀⠄⠘⠷⢶⣶⣶⡀⠠
⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢈⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⡀⢠⣴⣄⣀⣤⣤⣄⣰⠂⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠁⠠⠄
⠀⠀⠀⠂⠀⢸⣆⠀⠈⡆⠀⣠⠂⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⠂⠀⠠⠀⣤⠶⢯⢤⣀
⠀⢳⣤⣄⠀⣸⣿⣧⠀⣿⡾⠁⠀⠀⠀⠀⠜⡛⠟⠦⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣭⠁⢀⠀⢤⣤⡖⣣⢨⣤⢒⡽
⠀⠀⢻⣿⣿⣌⢻⣿⣷⡿⠡⠀⠀⠀⠀⠙⠛⠒⠛⠛⠃⠀⢠⠶⣿⣿⢿⣿⡿⠋⠻⠟⠃⠀⠠⠀⠉⠁⡀⠀⢅⣂⡴⠀⠂
⠘⠀⠀⢀⣼⣿⡧⣿⡟⣵⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⣊⠁⠀⠀⠙⠉⠘⠈⠃⠈⠀⢀⡄⠀⠀⠀⠈⠛⠃⠀⢐⢿⡓
⠀⢤⠀⠀⠻⢿⣅⣿⠕⠃⠀⠻⣿⡿⠀⠁⠀⠈⠓⠛⠋⣀⠘⢁⠀⠠⠀⠀⠀⢐⠀⠿⠇⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡠⠡⠈⠀⠀⠠⠄⠐⠂⠐⠟⠭⢀⠀⠀⠀⠀⠀⠄⠀⠐⣀⠀⠀⠀⠆⠀⠀⠀⢠⡴⢦⡀⠀⠁
⠀⡀⠁⠀⠀⣀⠀⣜⣻⣾⣶⣿⣷⡄⠀⠀⠙⠀⠈⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡃⠿⣷⡾⣥⣤⡀
⠀⠁⠠⣀⣿⣿⣿⡬⠛⠛⠻⢿⠛⠋⡁⠀⠄⠀⣤⡄⠀⠀⠀⠀⢠⣄⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠈
⠀⠀⢄⣈⣯⣿⢁⢀⣶⣦⡀⣀⢱⠀⠀⠀⡴⠒⠉⠳⠮⠁⠀⡀⣠⡟⢣⠶⣄⠀⠀⠴⠀⠀⢉⠀⠐⠂⠀⣿⡏⠐⠂
⠀⠟⢲⣿⣿⣿⡏⣘⠽⡯⣣⣹⡿⠀⠲⣾⡅⢰⣛⠆⠘⠀⠘⠛⣼⣧⡜⠶⢻⣄⣀⣀⠀⠀⣾⡄⠀⡠⢀⣿⠁⠀⠀⠀⡉
⠀⠀⠀⠙⠻⠟⣿⣨⠟⠚⢳⣸⡇⠀⠀⠠⠳⠤⢄⡤⠎⠈⠁⠀⠉⠻⠿⠇⣾⣬⣾⣽⡇⠀⠉⢧⣬⣀⣼⣿⡀⠀⢤⣾⠃
⠀⠄⠀⠉⠐⠿⠋⠛⠿⠾⠟⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠘⠃⠛⠙⠛⠋⠃⠀⠂⠀⠘⠋⣥⠙⠛⠛⠋⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠔⠀⠁⣉⢁⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⡀⠀⠀⠀⠀⠘⡉⢃⡀⠀⣠⠤⠠⠤
⠀⠀⠀⠀⢠⡿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠄⠀⠐⠂⠬⢀⠀⠁⣠⣼⠁⠌⠠⠊⡱⠃⠀⠀⠃
⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠌⢀⠐⢾⡿⠁⠁⡒⠀⠀⠻⠛⢁⠔⢁⠌
⠀⠀⠀⠀⢸⣀⣾⡏⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠈⠰⢁⠔⠁⠀⠀⠀⠬⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣼⣿⠿⠀⠐⠀⠀⠀⠂⠂⠡⠄⢀⣄⠀⠀⠀⠀⠀⡠⢃⠀⠁⠂⡀⠁⠀⢀⢖⡅
⠀⠀⣴⣿⠟⢳⠀⠂⠀⠀⠀⠠⠿⢇⠀⠐⠀⠏⢧⡀⢰⣶⡿⠀⠂⡐⠈⠀⠀⠀⠀⠀⠉
⠀⣸⡿⠁⣠⣾⣷⣾⣤⡀⠀⠀⠀⠀⠀⢀⣈⡃⠐⠀⠀⠀⠀⠀⠀⢱⣄
⠀⢻⡇⠰⡟⠁⢗⠉⢻⡇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠈⡀⠀⠀⠀⠀⢁⠜⠆
⠀⠈⢧⡀⠑⠄⢸⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇
⠀⠀⠀⠉⠓⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣠⣤⡄⠀⢹
⠀⠀⠀⢻⣿⠋⣀⡜
⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⢤⣒⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⡽⠟⡠⢐⡵⠞⠉⠁⠈⠁⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡵⠞⡩⢔⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡭⠞⡉⢔⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣭⠞⡋⢔⣬⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣪⠞⢋⢔⣨⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣨⠖⢋⢄⣪⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⡿⢀⢄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣪⠶⢋⢄⣪⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⡭⠞⡩⣢⡵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣪⠶⢋⠥⣪⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡥⠞⡩⢐⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣪⠵⠋⠁⢀⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣬⠞⡫⢔⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣢⡵⠛⠁⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣬⠞⡋⢔⡭⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡠⣒⡵⠛⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣨⠞⡋⢔⣭⠞⠋
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣨⠖⡋⢔⣬⠞⠋
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⣀⠀⠀⠀⠀⠀⣀⢔⣪⠖⣋⢔⣪⠞⠋
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠽⣗⣒⣲⡭⠖⡋⢔⣪⠖⠋
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣨⠖⠋
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣬⠞⠋
⠀⠀⠀⠀⠨⡳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣭⠞⠋
⠀⠀⠀⠀⠀⠈⠑⠚⠭⢟⣒⣶⣶⣖⣒⡭⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠉⠛⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⡆⠀⠀⠀⠀⠀⠀⣿⢠⣶⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣴⣶⣶⣤⣀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⢠⣾⠋⠁⠀⠀⠉⢻⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡧⢸⡇⠀⠀⠀⠀⠀⠀⣿⡂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⣾⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣇⣹⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣇⠀⠀⠀⠀⠀⢀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⣦⣄⣀⣀⣤⡾⠋⢸⣿⠀⠀⠀⠀⠀⠀⢸⡧⣿⡇⠀⠀⠀⠀⠀⠀⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠛⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠋⣾⡇⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦⣤⣀⣠⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣀⣤⣴⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠈⠉⠉⠒⡄⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⢠⠏⠉⠀⠉⢲⡀⢀⢔⢡⠪⠓⢄⠀⠀⡀⠀⠀⠀⡌⠀⠀⠀⠀⢀⡠⠴⠔⣚⣋⡭⠭⠩⢴⡖⠲⡞
⠀⠀⠀⢀⡤⢬⡣⢄⡀⠀⠨⢇⢔⣼⢆⠁⢖⣀⠑⢎⡖⣡⣶⣮⡅⠀⠀⠀⠀⠈⠉⡟⢹⠀⠀⠐⠀⠀⠀⡇⠈⡇
⠀⠀⠀⠙⠓⠚⠁⠀⠈⠹⡕⡹⣫⣷⢟⣷⣌⠁⠀⢈⠳⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⢰⠀⠀⠀⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡫⣪⡿⣋⣼⢦⠀⠐⢆⠘⢏⠉⠉⠀⠀⠀⠀⠀⠀⢿⠈⣆⣀⣸⡤⠤⠔⠚⠊⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⠙⢯⡪⢛⣵⢟⣳⡀⠈⢳⡈⢆⠀⠀⠀⠀⠀⠀⠰⠏⠭⠭⠄⠠⠒⠒⠊⠉⠹⣶⣶⣦
⠀⠀⢠⠈⠀⠀⠑⠒⠀⠛⢛⡀⠀⡀⠹⣯⡴⢟⣯⡿⣄⠀⠀⠘⣦⣄⣐⣂⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁
⡔⠀⠉⠀⠀⠀⠀⡔⠉⠉⠀⠀⠀⣈⠀⢈⣦⣽⣿⡶⣻⣆⠀⣀⠸⠀⠈⠀⣀⢀⢠⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿
⠑⠀⠠⠀⠀⠀⠀⠈⠓⢦⣀⢀⣀⣇⣈⣠⠋⢯⣴⡿⠟⣳⣀⠩⠕⠀⢠⢌⣸⠆⣋⠁⠲⣤⣶⡀⠛⢻⠋⠛⢟⠛⠉⠉
⠀⠀⠀⠉⠑⠤⣀⡀⣠⡪⠛⣆⠸⠀⠢⠋⠈⠘⣷⣾⣿⠉⠀⢀⡠⠔⠉⢮⠳⡀⠀⠀⣠⠏⢻⣿⣄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⢨⠛⠃⠀⠲⡦⢰⣿⣿⢋⠥⠊⠁⠀⠀⣀⡠⣆⡗⣶⡉⣳⠄⠀⣿⠃⠀⠀⠀⠀⢀⣀⣑⣄
⠀⠀⠀⠀⢀⡠⠒⠂⠈⠉⠒⠃⠀⠀⠀⠀⡁⡨⠟⠋⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⣏⢼⠀⠀⠀⠀⢸⠉⠉⠁
⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⢀⡠⠴⢏⡀⠀⠀⠀⢠⣾⢿⣿⣷⡄⠀⠀⠈⠑⢁⠄⠀⠀⠀⢨⣀⠀⠿⠂
⠀⠀⠀⡆⠀⢀⠀⢠⡊⠉⢲⠀⠀⠀⠘⢦⡐⠊⠉⠀⠀⠀⡈⠲⠀⠀⢿⣷⢇⢈⣿⡹⠒⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⢱⠀⣿⡆⠈⠣⢄⠔⠀⠀⠀⠀⠀⠉⢻⣶⣶⣦⣄⣁⠀⠀⠀⠀⠙⠶⠿⠿⠁⠀⠶⢁⠢⡀⠀⠀⠀⢠⠿⠿⠋
⠀⠀⠀⠀⣇⠹⡽⠀⠀⠀⠀⠀⠀⠔⠉⢹⣿⣿⣿⣿⣿⠋⠉⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣀⢀⠌
⠀⠀⠀⠀⠈⠑⠤⢀⣀⣀⣀⠄⠈⠀⣀⠼⠛⠋⠉⢿⣿⣶⣤⣾⣿⣷⠀⠀⢀⣀⠠⠄⠤⡀⠀⠈⠉⠉⣛⡢⢄⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⢀⠄⠀⠠⣄⠀⢻⣿⣿⣿⣿⣿⣷⡿⠛⠁⢀⡀⠀⣈⠑⢄⡀⡸⠀⠈⠋⠱⡀⠀⠉⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⢀⠀⠀⠀⠀⡇⠀⠻⣿⣿⡿⠟⠁⠐⢏⠉⢠⠁⠀⣿⠟⠃⠸⠓⠤⣀⣀⡠⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠑⠤⠤⠔⠃⠀⠀⠹⡋⣀⠤⠤⠤⡈⣦⠃⠀⠀⠀⠀⠀⠀⠑⠀⠠⡄⠀⠀⢀⠞⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠒⡄⠀⠀⠱⡑⢀⡈⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠈⢈⣁⣤⣴⣾⠁⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⢛⡿⣛⡛⢻⠛⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠑⡅⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⣀⠘⠁
⠀⠀⠀⠀⢀⠀⠀⠠⠄⠤⠢⠤⠠⣀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠤⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠂
⠀⠀⠀⠀⢀⠐⠀⠀⠄⠐⠀⠀⠀⡀⠀⠠⡀⢀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠔⠉⠘⠁⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉
⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢂⠔⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⠶⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠈⠤⠐⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⣤⠠⠚⠁⠀⠀⠛⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡐
⠀⠀⠀⠔⠀⣠⠀⠈⢉⠈⠈⡀⠀⠀⠀⠀⡤⠀⠀⠀⠄⠀⠉⠁⠀⠠⠀⠉⠢⡤⠀⠀⠁
⠀⠀⡐⠀⠰⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠁⢠⠀⠀⠀⢀⠀⠀⠐⠀⠈⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠁⠐⠀⠀⠐⠀⣄⠘⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠋⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⡦⠀⠀⠀⠀⠐
⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠛⠣⠀⠈⠑⠠⠀⢰⠀⠀⠀⠀⠈⠈⠂⡀⠀⠀⠠⠄⠠⠀⠀⢀⡠⠈⠈
⠀⠀⠀⠀⠀⠀⠈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⠄⠤⠄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠀⠈⡥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡃
⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡀⠨⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠡⣄⠈⠢⠀⠀⠀⢀⠀⠠⠈⠁⡴⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠈⠑⢄⣠⣠⡁⢀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁⠈⠋⠀⠀⠀⠀⡀⠀⠀⠨⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⣀⡀⠀⠀⠀⠀⠀⢴⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⠷⠆⠀⡐⠒⠐⠶⠘⠃⢠⣤⣔⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣿⣟⣓⣒⣲⣶⣯⣭⣭⣭⣭⣭⣤⣽⣿⣿⣛⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⢀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠛⡿⠉⠉⢁⡄⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠤⠠⢶⣛⣑⣦⡀⠀⠀⠀⣀⣤⣒⣠⡀⠀⠀⠀⢹⣿⣿⡿⢿⣽⣿⣿⣿⣿⣖
⠀⣠⣯⣿⣿⣿⣨⡿⢿⣿⣿⠿⠛⠉⠀⠀⡠⠿⣿⣛⣛⠗⠄⠀⠰⠛⣛⣛⣿⠿⠦⣀⠀⠈⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿
⠀⢿⢿⣾⠛⠿⠿⣿⣤⠍⠁⡖⠀⠀⣠⡞⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡸⠳⢄⣀⠐⠂⢻⣽⣯⣿⣿⣿⣿⡆
⠀⠈⠻⢯⣶⣿⣷⣶⣤⠄⣼⡄⠠⢘⣋⣄⣼⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⡇⠀⠀⠚⠶⢇⣸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⠿⢿⣶⡿⣔⡁⠃⡰⠉⡉⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⡛⣹⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠘⠷⠈⠀⠈⠗⠀⢄⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣿⢦⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠂⡾⠟⠓⠠⡄⠀⠱⠾⠻⣦⣀⠀⠀⠀⣠⣴⣿⣿⣶⣿⠋⠀⠀⠞⠉⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂⠀⣴⠄⠈⠉⠉⠉⠀⡈⢠⠟⡿⡏⠀⠀⠀⢀⡴⠃⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣂⣀⣠⣤⣂⣠⣄⠀⠲⡟⠁⠀⠀⠀⠀⠀⢀⠖⠉⢀⡀⠈⠛⠿⣿⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠈⠉⢱⡟⠁⠈⢀⣀⣀⡼⠝⠳⠬⠗⠀⠀⠀⠀⠀⠀⣧⣄⣠⠊⠀⠀⠔⠀⠀⢰⡀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡤⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣉⣃⡀⠀⠖⠀⠀⠀⠀⠈⠆⠘⢢⡀⡀⠛⡅
⠀⠀⠀⢀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣆⠀⠘⣧⠨⣩⣤⠀⣂⡀⢀⠀⠂⠀⠠⣤⠀⠝⠁
⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠀⠃⠀⠋⠈⢡⠆⠀⠸⠆⢠⡗⠀⠀⠀⡠⠀⠀⠄
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠀⠀⠀⠀⠀⢀⡄⠚⠀⡤⠂⠀⢀⠂
⠀⠀⢀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⢊⣀⡀⣤⠄⠖⠁⠒⢀⡤⠐⢄⣀⠀⠀⠈
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠹⠟⠋⠱⡇⠖⠀⠀⠀⠀⢨⠇⠀⠉⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠂⣿⣿⣿⣿⣿⠟⢿⣄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠂⠀⢠⣿⣿⣿⣿⣿⣿⡿⢿⣆⠀⣀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣴⠟⠉⢻⣿⣿⣿⣿⠃⠀⠻⠿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⢨⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠿⢿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⡀⠉⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠃⠀⠀⠀⠀⠲⢶⢶⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢀⣠⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⠋⢰⣿⣿⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣀⣀⣀⣈⣿⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⣿⣿⣿⣿⣿⣿⠿⣿⡀⠀⠀⣾⣷⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠉⠛⠿⠿⠷⢶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠀⣿⣿⣿⣿⡿⠁⠀⠻⣿⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠁⠀⠀⠀⠀⠀⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣇⠄⠀⠀⠀⠀⢰⣶⣦⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡠⠀⠀⠀⠐⠂⠐⠄⠀⠀⠀⠀⠄⠤⠂⡀⠀⠀⠰⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⣀⡀⠔⠁⠀⠀⠀⡀⠉⠐⠠⠂⠀⠐⠌⠡⠄⠑⠀⠀⠀⡔⢢⠄
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠂⠑⠂⠈⢀⠙⢉⠀⠁
⠀⠀⠀⠀⠀⢇⢂⠳⠰⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠄⠨⢅⠢⡀⠀⠀⠀⡠⢒⡎⡑⢄⡠⠂⠙
⠀⠀⠀⠀⠀⠀⢂⠂⠀⠁⠀⠀⠀⡀⡀⢠⠀⠀⢀⢀⢃⢊⢂⠅⠀⢕⡱⣊⠔⠂⠥⣊⠽⡆⠁⠈⢀⠂⢰⠖⠂⢐
⠀⠀⠀⠀⠀⡠⢂⡣⢠⠂⡀⠐⠀⠁⠀⠀⠀⠀⢀⣀⠉⠓⢇⠀⠀⠀⠈⠂⠅⠀⠨⡰⠒⠉⠉⠁⠓⠴⡕⣈⠔⠁
⠀⠀⠀⢠⢊⢔⢍⠔⠡⠊⠀⣴⡄⠀⢠⣀⣀⡆⠘⠛⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠐⠀⠐⠃⢠⢤⡀⠀⠈⠄
⠀⠀⠀⡃⠀⠀⠆⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠁⠙
⠀⠀⠀⠐⡌⠎⣪⠃⠀⠀⠀⠀⠀⣀⡀⢤⡄⠐⠂⠀⠋⠁⠈⡀⠀⡃⠈⡀⠀⢀⡃⠀⠀⢀⠀⠀⠀⠀⢠⢂⣠⠂⠌⠠⠤⠤⡀
⠀⠀⠀⠀⠈⠑⠨⠀⡀⠠⡀⠈⠄⠀⣀⠠⠥⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠁⢀⠂⠙⠐⠀⡄⠠⠀⡀⠔⠁⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠉⢀⠀⠔⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡁⠒⠠⠉⠰⠄⠒⠉⠀⠀⠀⠠⠃⠂⠄⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠦⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠈⡀⡠⠀⠤⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⠀⡤⠀⠀⡄⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠠⠤⠂⠀⠀⣀⠀⢲⠮⣐⠃⠀⠀⠀⠐⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠰⠶⢠⡤⣄⠀⣈⠀⢈⠘⠁⢀⠐⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠄⠤⣀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈⠉⠀⠀⢂⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⡀⢠⠈⢆⠀⡀⠀⠀⠀⠀⡀⠀⠠⠀⠀⢄⠄⠀⠰⠠⠀⠅⢠⢊⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠆⠀⠀⢀⡏⠄
⠀⠀⠰⡉⢉⠑⢀⡣⠘⠉⠉⢁⠒⢄⠈⢚⢀⠄⠀⠀⠀⠐⢀⠀⠈⡥⡀⢠⠀⠀⡐⠅⠀⠂⠀⠈⡄⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠂⢬⠏⠀⢀⡠⠄⠙⠁⠐⠱⡅⠀⠁⠀⠀⠀⠈⠐⠈⠀⠈⠀⢸⡆⠀⠁⢂⠀⠀⠀⢀⠂⠃⠀⠀⡄
⠀⠀⠀⠀⠀⢈⠀⠶⠈⠁⠁⠀⠀⠀⠀⣇⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⢢⣁⣀⠠⠀⠀⠅⠀⠀⠅⠀⠀⠀⢠⠁⢀⠄⣊⠐
⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⡧⠔⡀⠖⣒⡊⢷⡍⡠⠤⠄⡢⡆⢄⢠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠀⠶⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠠⢠⠁⡈⠔⠁⠀⠀⠑⢌⡚⠄⠬⢚⡴⠢⡠⠁⠀⠀⠀⠀⠂⠀⠀⠊⠀⠢⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⢀
⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡤⠶⠚⠛⠉⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⣀⣙⣤⣤⠤⠤⠶⠶⣦⣤
⢀⠠⡠⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⣉⣤⠴⠚⢋⣉⠀⣀⣀⣀⣀⣤⣤⡇
⠈⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡡⠽⠛⣁⡤⠴⢶⣿⠟⠉⠉⠉⠉⣿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡩⠖⣫⡴⠾⢋⣁⡤⠤⠶⠒⠒⠚⠛⠓⠲⠾⠷⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠄⡨⢔⣽⡖⣉⠤⠖⢋⣉⣤⠤⠤⠶⠶⠶⠶⠦⢤⣤⣄⣀⠀⠀⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢘⠡⠐⠥⢒⠡⢘⣉⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦
⠀⣠⠆⠀⡀⠀⠀⣀⠀⠀⠀⠶⠀⠀⣥⠐⠿⠐⠊⠁
⠘⠟⡳⠸⠉⠀⠀⠁⠀⠘⠁⠀⠀⠈⠋
⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀⣀⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢴⡻⣏⢹⡿⣿⢿⠉⢉⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣶⢲⣿⣿⣦⣄⠙⠋⢀⣼⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⠛⠂⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⢿⣿⣿⣿⡿⣿⣳⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠙⣿⣿⣦⣤⣴⡀⣩⣽⡇⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠡⣾⣻⣿⣿⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⢨⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⣘⡀⠴⠟⠁⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡈⣸⣿⡶⢶⣿⣷⠠⣄⡀⠀⠀⠀⠹⣿⠃
⠀⠀⠀⠀⠀⠐⠃⠐⠂⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣶⣶⣿⣿⣿⣿⢷⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢻⠛⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡛⢻⡟⠛⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣀⡈⡀⠀⠀⠀⠀⣀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣾⣿⣟⣉⠉⠀⠉⢙⡖⠁⠀⢩⣿⣾⣿⡄⠢⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠰⣾⣦⣀⠀⠀⠀⣀⠛⠛⠛⠿⠻⠷⠦⠀⠀⠼⠦⠿⠿⠿⢿⣿⣆⢦⡀⠀⠀⠀⢘⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⠀⢠⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣦⣠⣾⣿⣿⣿⣿⣦⣴⣾⣿⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡻⣿⣿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠄⠆⢿⣷⣤⣤⣀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣀⠀⠀⠈⣛⡛⠛⠿⠿⠿⠿⠿⠿⠿⣿⡏⡇⠤⠐⠛⠇⠸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⠧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣠⣶⣶⣦⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⡿⢿⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡤⠙⠻⣿⣄⠀⠀⠠
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⢻⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⢃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢹⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⠐⠘⠛⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣦⠠⢿⣿⣯⣶⣤⡀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣸⣿⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣮⣝⣤⠾⠛⠻⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⠘⠇⢶
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢨⣿⡟⣿⣿⣿⣿⣿⡟⠁⣠⣶⣶⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⠀⠀⢸⣷⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠟⠁⠿⠟⠿⠛⠏⢀⣾⣿⣿⣿⣿⣦⠈⣉⠁⠀⠂⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠀⠁⠀⠻⢏⠀⠐
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣾⣿⣿⣿⣿⣿⣿⣆⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉
⠀⢺⣿⣿⣿⡇⠀⠀⠀⣀⣸⣿⣷⣿⠁⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣾⣿⣿
⠀⠙⠛⠛⣿⣇⠀⠀⢀⣿⣿⣿⣿⠃⢀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⢸⣧⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠻⠿
⠀⠀⠀⠀⠿⠟⠀⠀⠘⠿⠿⠿⠟⠀⠸⠟⠀⠿⠿⠿⠟⠿⠿⠿⠟⠀⠗⠀⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠶⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠛⢉⣉⣙⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⡞⠋⠿⠯⣝⢷⣝⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡏⢠⡟⠀⠀⠀⠀⠀⠳⡝⣮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⠘⣇⠀⠀⠀⠀⠀⠀⠙⡜⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘⠘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡹⣧⠈⢿⣿⢷⡀⠀⠀⠀⠀⠀⠘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣧⠘⣿⡎⢷⡀⠀⠀⠀⠀⠀⠘⣧⢻⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣻⣆⠘⣿⡌⣧⠀⠀⠀⠀⠀⠀⠘⣧⢻⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⣿⡜⣧⠀⠀⠀⠀⠀⠀⠘⣧⢻⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⣿⡜⣧⠀⠀⠀⠀⠀⠀⢹⡆⢿⣇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠘⢿⣾⣧⠀⠀⠀⠀⠀⠀⣿⠸⣿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠈⢿⣿⢷⡀⠀⠀⠀⣰⠏⠀⣿⠹⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠈⢻⣷⡙⠳⠶⠚⠋⣠⢱⡇⠀⠹⣯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠻⣿⢶⣶⣶⣪⡵⠏⠀⠀⠀⠹⣯⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠹⣆⢈⠉⠁⠀⠀⠀⠀⠀⠀⢹⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠈⢻⣝⢄⠀⠀⠀⠀⣀⢸⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠙⢶⣝⣲⠶⢒⣠⠟⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣈⠉⠉⠉⠁⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⢄⣴⡄⠒⠲⠗⠚⠉⠉⠤⠂⠀⡀⢠⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢄⠀⠉⠒⠔⠀⠀⠀⠀⢀⣶⠉⡀⠄⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣀⣠⣄⣯⣨⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢊⡁⢀⠊⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢛⣉⣀⣠⣤⣄⣀⣀⢀⣤⣴⣶⡾⠿⠿⠁⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢈⠉⠁⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠲⡀⠌⠔⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⢰⣦⣄⡀⠀⠀⠐⢠⠁⠀⢀⠂⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⢬⡀⠀⡄⠀⣤⣤⣤⡄⠂⠀⠒⠀⠀⠀⢨⠀⠈⠭⠀⢀⠁⠺⠬⠄⠘⠓⢠⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⢙⣉⣉⡉⡈⠀⠀⠀⠀⠀⠈⠛⠂⢰⣤⠀⠀⠀⠀⠀⠀⣀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠉⠈⠁⠙⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠞⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⡄⠀⢀⣦⡶⠀⠀⠀⠄⠀⢀⠋⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠇⠀⢨⡷⡟⠀⠀⠐⢀⣀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢏⠀⠀⠀⠉⠀⠀⠀⠺⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠿⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠄⢷⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣠⣿⣿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢯⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⡏⡀⢠⡌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⣉⠁⠀⠀⢠⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠆⣄⢀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠈⠉⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⣩⠉⠄⠰⣿⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⡂⠀⠠⣄⠀⣿⡆⠀⣙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠈⢳⡀⠀⠉⠀⢸⣷⠀⠋⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢁⣀⠈⢻⣦⣄⣀⢸⣿⣤⣆⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡅⠋⠁⠹⠚⠛⠻⡿⣿⣿⡿⢯⣦⡜⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠁⠀⠀⠀⠀⡤⠂⡰⠋⠀⠀⠄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣡⡀⠀⣀⠀⠐⠁⠀⠃⠈⣷⡀⠀⠀⣶⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠡⠞⠁⢀⠃⠀⡼⠲⣼⣿⡟⣾⠃⠹⠏⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣤⠁⢠⡖⠀⠈⢻⠂⢠⡇⠀⡈⣿⡇⢻⣇⢀⡀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⢁⣤⠏⠀⠀⣰⠿⠀⣾⡇⠀⠁⣿⣧⠸⣿⡌⠃⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣤⣶⠿⠉⡀⣠⢶⡄⠂⢠⣿⣇⢀⠈⣹⣿⠀⣹⣧⠸⠖⡀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠸⢠⣾⣿⣿⠤⢾⣿⡿⠂⠈⠥⣆⠦⠂⢠⣿⣿⡿⠸⠐⢻⣿⠄⢽⣿⣆⠀⢁⠜⣿⣇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢰⢀⣿⣽⡿⢶⠶⣶⡟⠀⠀⠐⠂⠙⠀⠀⣼⠷⢿⠇⠀⠐⠀⣿⡆⠀⠘⣿⡆⠻⣷⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⣯⣿⣻⠿⠉⠀⠀⠠⣰⣸⠆⠀⣘⠃⠀⠁⠀⠀⠈⠁⢹⡇⠀⠡⡼⣿⡄⠘⢷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢄⣿⣿⣿⣿⡟⣁⣴⠞⣡⣤⠴⠟⠋⠀⣼⣿⡏⢘⠀⠀⠀⡀⠀⢸⣇⠀⢀⠀⠘⣿⣄⠘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣡⡾⠋⠁⠐⣇⣠⣿⢀⣠⣾⣿⣿⡀⠸⠀⠀⠀⢱⡀⢹⣿⠈⡄⠀⠀⣿⣿⣆⠸⣿⣷
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⠄⠀⢀⡼⠻⠄⣉⣿⡏⢸⠋⣧⡄⠀⠀⠀⢙⠃⢸⣿⠀⣿⣦⡀⠈⣿⣿⣷⡿⣿⡇
⠀⠀⠀⠀⢳⣿⣟⡟⣋⢶⡿⠄⠀⠟⠉⠁⢴⣾⣿⢻⠇⢾⠀⢹⡇⠀⠀⠀⠘⠀⢸⣿⡀⡟⠺⣷⠆⢛⣻⡙⢷⣿⣷
⠀⠀⠀⠀⣴⣿⢟⣷⣿⣃⡝⠐⠆⠀⢀⣠⠾⢋⣿⡆⠀⡀⠀⣀⠇⠀⠀⠀⠀⠀⣸⣿⠇⣡⠀⠀⠀⣨⣿⣯⠈⢿⣿⡇
⠀⠀⠀⢀⢿⣿⡙⠿⢿⣹⠇⣌⢀⣾⡿⢡⡀⢿⡏⢿⣄⡵⡧⠬⣦⡀⠀⠀⠀⠀⢹⢻⡇⣽⣄⠀⠀⡙⠿⣗⣻⡄⢻⡇⡀
⠀⠀⠀⣿⣦⠙⠿⠃⢸⣿⠟⣣⣿⣿⡷⠈⢷⡌⠃⣸⣿⣆⠁⠀⢎⣁⣄⣼⣁⠀⢸⠘⡇⢉⣻⣤⠐⠛⠀⣾⠿⠇⠀⣾⠃
⠀⠀⢰⣿⣿⣷⣶⣶⣶⣶⡈⠿⣾⣿⡇⠸⣦⣱⣶⣿⣿⣿⣷⣀⠈⠉⢠⠟⢉⡄⣿⠀⡇⢈⣟⡿⠋⣠⠆⠀⢲⡇⠀⣿⡃
⠀⠀⣸⣿⣿⣿⣿⣿⣷⠸⣷⠀⣿⣿⡄⠀⠙⢻⣿⣿⣿⠇⣿⡿⢷⣤⣀⠀⠘⠃⣽⠀⣷⠀⠈⣡⡴⠃⠀⢀⣾⣿⡀⢸⣷⡆
⠀⠀⣿⣿⣿⣿⣿⠟⠙⢧⠀⢼⣿⣿⣿⡄⠀⠀⢻⣿⣿⢠⣿⠃⠀⠛⠛⠛⠶⢤⣽⠄⢻⠶⠛⢉⡇⠀⠞⠉⢸⣿⠃⠸⣿⡇
⠀⠀⠛⠛⠻⣿⣤⣤⣀⣀⣀⣼⣿⣿⣿⣧⡈⠀⠈⣿⣿⡎⠁⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⣺⣇⢀⡍⠀⢸⣿⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠐⠛⠻⠟⣻⣿⣿⣿⣽⣯⣿⣇⣠⣴⣿⣿⣷⣶⣦⣤⣄⣈⣀⣀⣀⣀⠀⢀⣀⣰⣾⣿⣄⣀⣠⣼⣷⠤⠞⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣽⣟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠈⠉⠉⢻⠿⠿⠟⠛⣿⠿⠻⠿⠛⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣏⣽⡛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣤⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣾⣟⣻⣗⠀⠀⠀⠀⢠⣶⣶⢿⣿⣿⣏⣠⡄⠀⠀⣹⣿⣇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣪⣿⡇⠀⢀⢻⣾⠿⣴⢇⡀⠀⠘⠻⠟⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣟⣿⣯⣤⠀⠀⣻⣿⣟⡴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⢤⣘⣿⣿⣿⣻⡿⣡⡤⠀⠠⠴⢾⣿⣿⣿⢿⣿⣟⣯⣿⣹⣿⠛⠟⠂⠀⠠⣿⣿⣻⠤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⠿⠿⠟⣿⠿⠿⠿⠂⠀⠀⠐⠉⠁⣨⣿⣯⣿⣿⡿⢿⣷⡦⠀⠀⣠⣶⣿⣿⣿⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠒⣾⡿⢿⣷⠖⠀⢀⣶⣿⣿⣿⣦⠀⠀⢀⣤⣠⣤⠈⠉⣽⣻⡟⠉⠀⠈⠙⠓⠀⢠⣧⣿⣿⣿⣯⣷⣺⣿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣏⠀⢠⡾⣷⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣦⠘⠋⠁⢀⣤⣴⣶⣦⣤⠄⠈⣿⣿⣿⣿⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⣿⣿⣿⣿⣿⣿⣻⡄⠈⠙⠿⠏⠀⠀⠀⠀⠀⠘⢿⣶⡿⠇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠈⢛⣿⣿⣿⣿⣾⡏⠀⣀⣀⣤⠖⠀⠀⢀⡶⠒⢶⡄⠹⠏⠁⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣈⣙⠿⠛⣟⣉⣱⣿⡿⠟⠛⠉⠀⠀⠘⡧⣿⣼⠃⠀⠀⠀⠐⠂⠀⢻⣿⣿⣿⣿⣿⣯⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠙⠷⣯⣿⣿⣽⣿⣽⡯⠿⠃⠀⠒⠀⠘⠻⠿⠿⣭⠿⠿⠟⠂⠀⠀⠀⠀⢠⡛⠛⠿⠛⣋⣉⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⣶⣤⣿⣴⣻⣶⠆⠀⠀⠀⠀⠀⢙⣴⠒⠋⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⢸⣿⣷⣦⡀⠀⠀⢠⣆⠀⠈⢛⣿⣻⣻⣿⣿⣁⠀⠀⣰⡄⠀⢰⠋⠀⡧⠀⢠⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⠷⠀⢠⠀⠈⠻⢷⣿⣷⡀⠀⠻⣽⠃⠰⢿⣿⢿⣿⡿⣿⣿⣅⠐⣯⠟⠀⠘⠲⠖⠁⠀⣿⣏⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠈⠉⠁⠀⠀⠘⢦⣄⣈⣁⣼⣿⣧⣈⣙⣋⣴⠃⠀⣠⣤⣤⣤⣀⠀⠙⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣾⣟⣿⣷⣿⣳⣶⡀⢀⣀⣀⡀⠀⠉⠛⠛⢿⣿⡿⠛⠛⠉⠀⠀⠘⠿⣿⡿⠿⠋⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣷⣼⣿⣯⣿⡽⣿⣿⣿⠟⢿⣻⡾⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⣤⣄⡀⢀⣀⡀⣠⣶⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣿⣿⣷⣽⣿⣟⣿⣫⣿⣿⠾⠋⠀⡀⠀⠀⢀⣠⣄⣤⣘⣍⡀⠈⢿⣿⡿⣯⣧⡿⢿⣿⣭⣟⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣶⠝⣛⠛⢿⣿⣿⣿⠿⠿⡀⢴⣶⣿⡥⠀⣠⣿⡿⣛⢿⣿⡛⠁⡀⠀⠙⢙⣿⡿⣿⣛⡞⣿⣿⡀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡤⣄⣉⣉⣁⡤⣼⣿⡟⠉⠁⠰⠮⠼⣿⣷⣭⣾⣿⠁⠀⠀⢀⣾⣿⣵⣿⣮⣭⣾⣿⣞⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠻⠥⣿⣼⣼⣯⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⣀⠀⠀⠈⠉⣽⡷⠏⠉⠈⠉⠹⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⢘⣆⢠⣾⠆⠛⠋⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⣾⣆⣀⣀⠀⠀⠀⠀⠸⠿⠃
⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⡞⣷⠀⠀⠀⢀⡤⡞⠿⠗⠀⠀⢀⡾⠿⠂⡼⠿⠆⠀⠀⣾⠁⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡴⣦⠀⠰⣞⡇⠀⠀⣵⠏⠀⠀⠀⠈⠙⠁⣤⠀⠀⠀⡜⠁⠀⡼⠁⠀⠀⠀⠠⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣹
⠀⠸⣿⠞⠚⠁⠀⠈⠃⠁⢀⡞⣽⠶⢶⡄⠀⢀⣤⣴⠃⠀⠀⠀⠉⠙⠚⠁⣀⠀⠀⠀⠀⠀⠀⡤⢄⣰⣩⠆⠀⠀⢠⣶⣦⠀⢰⣿
⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠸⣆⠧⢁⣸⠇⠀⠈⠙⠃⠀⡠⠤⡀⠀⠀⢀⣴⣏⠀⠀⢀⡤⣄⠀⠙⠊⠉⠀⠀⠀⣠⠏⠈⠁⠀⠈⠁
⠀⠀⠀⠯⠵⠫⠖⠃⠀⠀⠀⠈⣙⠛⠁⠀⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠻⣴⠋⠀⠀⣸⣼⠃⠀⢀⣶⠀⠀⠀⣀⠀⢀⣴⣄⠀⢠⣖⡦
⡀⠀⠀⣀⠀⣀⡴⠛⢦⡀⠀⠀⠉⠋⠀⢠⠏⠉⢹⠃⠀⠸⠀⠀⢀⣀⠞⠁⠀⣰⢞⣽⣄⡀⠀⢘⣧⠀⠀⣼⠻⠃⡼⠉⠁⠀⠸⡇
⠃⠀⠀⠻⠟⢡⣤⣠⠜⠻⣄⠀⠀⠀⣀⡼⢀⣄⡟⠀⠀⠀⣠⣄⠻⡟⠀⠀⠰⡇⠏⠀⢨⡇⠀⠘⠀⠀⠰⢿⣗⣺⠃⠀⣼⠃⠀⠃⠠
⠃⠀⠀⠀⠀⠈⠛⡁⠀⣠⠞⠁⠀⠘⠿⠃⠈⠛⠁⠀⣴⡆⠻⣅⠀⣹⣆⠀⠀⢙⠲⠶⠛⠁⠀⡤⣤⠀⠀⢠⣄⠀⠀⣸⣧⠀⠀⠀⢰
⠀⣠⣖⠁⠀⠀⠘⠿⠋⢁⡀⢠⢞⡆⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⢾⡥⠞⠁⠀⠙⠓⠁⠀⡔⢠⡟⠁⠀⠀⢸⡸⠃⠀⠈⠉
⠈⠁⠋⣀⣀⠀⠀⠀⠀⠸⠿⠋⠉⠀⠀⠀⣠⢾⡅⠀⠀⠈⠯⠖⠋⠀⠀⠀⠀⢀⠀⠀⠀⠈⣉⠀⠀⠀⠰⣉⠇⠀⢠⠏⠙⢲⠆
⢀⡀⠈⠓⢮⣇⠀⠀⠀⠀⢀⣠⣴⣦⠀⠀⠀⠉⠀⢠⡤⠤⣤⠀⠀⠀⣀⣤⡞⠉⢳⡀⠀⠸⡯⠭⢽⠀⠀⢀⣤⣴⠋⣀⣠⠏
⣻⠏⠀⠀⠸⡿⠃⠀⠀⠐⠋⠀⠈⠉⢠⣶⡄⠀⠀⢸⠋⠉⣿⠀⠀⢺⡁⠀⣳⡀⢀⣷⡄⠀⣷⣦⢸⡇⠀⠀⠉⠁⠈⠛⠋⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⢠⣶⡆⢸⠉⠀⢀⣤⡿⠰⣿⠇⠀⠀⠀⢳⡐⠿⠃⠈⠛⠁⠀⢀⠀⠀⠿⠗⠀⠀⠀⠀⡞⣇⠀⠀⠉⠋
⠀⠀⡀⠀⠀⠀⠀⠘⡷⢄⠀⢸⡥⠤⣾⠀⠀⠀⠉⠁⠀⠀⣤⣆⠄⠀⠿⠗⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣤⡀⢈⠽⡄
⠀⣷⣿⠄⠀⠀⠀⠀⠛⠃⠀⠈⠛⠉⠉⠀⠀⠀⢀⣀⠀⠘⠱⠋⠀⠀⣤⡄⠀⠺⣝⣦⠀⢠⣶⡇⠀⢠⣶⡄⢸⠋⠁⠈⠊⠁⠀⣄
⠀⠉⠈⠀⠀⠀⢠⡒⡄⠀⠀⠀⢠⠖⣛⣛⡶⠾⡥⠾⠃⠀⠀⢠⣦⠀⡟⠁⠀⠀⠀⣿⡆⠀⠉⠀⠀⢸⣉⣤⣿⠀⠀⠀⠀⠀⣿⠋
⠀⠀⢀⡞⠀⠀⢸⡇⠀⠀⢀⣀⢿⠈⠁⢛⣷⠀⠀⠀⡄⠀⠀⢸⡁⠀⢻⠀⠀⠀⠀⠈⠀⠀⣤⣄⠀⠘⠒⠒⠋⠀⠀⠀⠀⠟⠙
⠐⣿⡟⠀⠀⠀⠘⠃⠀⠀⠈⠫⠘⠛⠲⠛⠁⠀⠀⣼⣥⡀⠀⠘⣧⠴⠞⠀⠀⣀⡀⠀⠀⠀⣿⣉⠀⠀⠀⢀⡄⠀⠀⢠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠛⠒⡆⠀⠀⠀⠀⠀⠀⠀⠸⢧⡞⠀⢠⣦⡀⠀⠀⠀⡴⠛⠛⠀⠀⠀⠸⠜⠀⠀⣰⡟⠁⠀⠀⣾⠀⠀⡇
⢠⣶⡄⠀⠀⠀⢰⠇⣀⣸⠃⠀⠀⢀⣀⠸⣿⠃⠀⠞⠀⠀⣀⡯⠇⠀⠀⠘⠁⠀⠀⠰⣖⢦⠀⠀⠀⠸⠉⠃⠀⠀⠀⢿⣶⠀⣇
⠋⠉⠁⠀⠀⠿⠟⠀⠻⠛⠀⣠⣤⠸⣟⠀⠘⣦⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢀
⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠙⣏⠀⢈⣶⣚⡭⠇⠀⢠⠤⣄⡴⣻⠆⠀⢰⠯⣟⣷⠀⠈⠛⡁⠀⠀⢸⡭⠃⠀⠀⢀⡞⠓⢦⣤⣀⠈
⠀⢀⡤⠖⢿⠉⠈⢧⠀⠀⠀⠀⠈⢿⣭⠞⠉⠀⣀⠀⠀⠉⠁⠉⠁⢀⣀⡏⣠⣤⡏⠀⠀⣿⣿⠀⠀⠸⡇⠀⢠⣄⡾⢀⣄⡾⠀⢉⡟
⣀⣈⣧⣀⣈⣧⣀⣨⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼⣻⣇⣀⣀⣀⣀⣀⣻⣟⣀⣈⣉⣀⣀⣀⣘⣀⣀⣀⣀⣁⣀⣈⣛⣁⣘⣛⣁⣀⣼⣁
⣿⣿⠋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⣹⠗⠛⠉⠁⠐⠈⠉⠛⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠈⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠈⣽⣿⣿⣦⣤⡤⠤⡦⠦⣴⢦⣴⠶⠶⠚⣛⣿⣿⣷⣾⡯⣭⡙⠲⡄⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣿⠟⠛⣿⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠋⠁⠀⠠⢶⣾⣥⡈⠀⠠⣄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣇⠀⢰⣼⣿⡿⠻⢆⠀⠐⠒⢄⡀⠀⠀⠀⠀⠀⡞⠁⣤⠈⣥⠙⣦⠄⢸⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⡴⠋⢴⣩⣭⢤⣶⣶⣿⢠⣤⡀⠀⣴⣦⠀⠁⠀⢁⣀⡀⠀⠛⠀⠉⠸⠏⣀⠈⠆⠈⠀⠀⠤⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠐⢷⣤⣾⣷⣶⣿⣿⣿⠛⠻⢿⠃⠀⠉⠀⠤⠀⠀⠈⠛⢏⣦⣀⡀⠒⠀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⢛⡛⠛⠉⠁⠀⠀⠀⠀⢀⣄⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣴⠟⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⡀⢀⣶⡾⢛⣫⣴⠖⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣝⣶⣀⠀⢀⡀⠀⢀⣂⠐⠂⣀⣉⣩⣤⠾⢿⡿⠿⠿⠛⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⠉⠉⠛⠿⠿⠿⣿⡿⠟⠛⠁⠀⠀⠀⠸⣶⣤⡴
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⣀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣦⣤⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠹⣤⣤⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠘⠦⠀⠀⠉⠀⠰⢦⢀⠴⠤⢀⠀⠀⠀⣸⣉⡛⠛⠒⠀⠀⠈⠲⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢈⠹⡙⠿⡿⢷⣄⠀⠀⢀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⡀⠀⣀⣤⣶⣭⣉⡈⠑⢠⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠨⡇⠀⠿⠿⡿⣿⣿⣷⣤⣤⣿⣷⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⣴⠀⠀⠀⠀⢰⣾⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⢠⠔⠀⠀⠀⡀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⢁⠀⠀⠀⠀⠸⣄⠂⢤⣦⠆⠀⠀⢠⡀⠈⠀⣩⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡄⠠⠄⠀⠤⠟⠧⠄⠀⠀⣈⠳⣄⠈⢦⠀⠀⠀⠈⠲⢾⡿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠃⠀⡈⠀⡀⠀⠀⠠⡀⢀⠀⠌⡱⢔⠀⢧⠘⠀⠀⠐⠿⠒⡂⡆⠀⡠⠄⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢤⠄⠲⠀⠁⡠⢀⠀⠀⠈⠐⠁⠄⠺⡀⠀⠀⠀⠀⠀⣠⠔⠁⠈⢧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⢁⠀⠀⠀⠤⠤⡬⠓⠀⠙⣤⡀⡦⠤⣼⠃⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠄⣸⣠⠀⠀⠀⡀⠀⠄⠀⠀⣈⠋⣔⢤⡆⠻⠔⠄⠀⠈⡄⢀⠀⠀⠀⠑⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣍⠞⡁⠉⠳⠄⠀⠀⡠⠆⠁⠀⠐⠀⠂⠀⠀⠀⠀⠄⠀⠋⠀⠀⠀⠲⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⡀⠀⡐⣻⠂⠘⣷⠈⢢⡌⠃⠁⠤⠴⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢿⣏⣷⡀⣻⣧⡀⠈⢢⠅⡀⠀⠐⠀⠀⠐⠀⠀⠀⠢⠀⠐⠠⠀⠀⠂⠀⠀⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠋⡁⠀⡈⢿⣵⠄⠀⠑⠀⠌⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠂⢼⣆⠀⠀⡁⠰⢀⡌⠻⡷⢵⠜⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠐⠀⠀⠠⠀⠀⠀⢐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠐⣤⡿⡊⠋⠈⠀⠀⠈⠄⠀⠈⠀⠒⠖⠀⠀⠠⠀⠙⠒⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⠀⠀⠀⢤⡌⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠡⠀⠀⠀⠈⠀⠀⣀⠀⣀⣀⠀⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣱⠊⠙⡂⢀⠀⠀⠀⠀⠄⠂⠀⠀⠁⣀⠠⠤⠀⠀⠀⠀⠂⡆⡔⢀⠒⠀⠔⠉⠢⠔⠑⠆⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠀⠠⠀⠀⠀⠁⠀⠁⢀⠀⠀⠄⠀⠄⠡⠀⠀⠠⠔⢻⠉⠉⠀⠀⢠⢄⠀⠀⣠⠈⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐⠂⠀⠠⠀⢀⡤⣄⠂⠐⠀⠀⠐⢠⢔⠁⠁⠀⠒⠒⢄⠥⠀⠶⠎⢈⠀⡀⢀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⢈⡈⠀⠀⠀⠘⠦⠞⠠⠀⠀⠀⠀⣠⠞⠀⣀⠤⠨⠂⠀⠶⢀⠆⢀⡀⠋⢁⠏⠀⠈⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠄⠀⠒⠑⡄⠀⠈⠆⡀⠀⠋⢁⡔⢢⠘⢠⠄⠐⠢⣀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠁⠌⡀⠀⠀⡀⠂⠠⠄⠁⠀⡌⡀⠀⣠⡋⠁⠈⢡⡀⠑⡊⠈⠦⠀⣔⠂⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢣⡌⠀⠀⠈⠨⠃⠈⠀⠛⠈⠁⢠⠤⣀⠧⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢂⡀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠠⠂⠉⠑⠂⠀⠜⠒⠁⢃⢀⠎⠣⣀⠂⠀⠀⠀⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠀⠐⠊⠉⠀⠀⠀⠀⠀⠃⠒⡆⠀⡀⠘⠁⠀⠀⢀⣀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠢⠔⠑⠦⠊⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣿⣶⣖⣰⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣜⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣎⢣⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠺⢛⣿⣯⡝⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡓⠤⣀⣀⣀⣀⣀⠀⣀⡠
⠀⠀⢀⡀⠄⣨⣴⣾⠓⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⢀⠄⠈⠁
⠀⠀⠀⢈⣾⣿⣿⣿⣦⣥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⣿⣶⣮⣤⣁⡾⠁
⠀⠘⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣠⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠘⣿⠏⠁⣿⠟⠁
⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠁⠀⠀⠉⠀⠞⠁
⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡟⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣏⢸⣿⡟⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠸⣿⣷⢿⣿⡿⠿⢸⠃⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⡆⢸⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣮⢀⣹⡤⠐⠒⢸⠇⠈
⠀⠀⠀⠀⠀⣠⣠⡶⠛⠉⡏⠀⠀⠀⢘
⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠈⠉⠁⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠁⠀⠀⢀⠼⠁⠀⠈⠑⡄⠈⢀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠞⢀⡄⠀⢶⠀⡺⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂
⠀⠀⠀⠀⠀⠈⢘⠉⠉⠙⠌⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠴⠒⢾⠀⠀⠈⠀⠀⠀⡔⠂⠉⠉⠑⢢
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢦⣀⠜⠀⠀⠀⠃⠀⠀⠀⠀⡌
⠀⠀⢠⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠁⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡌
⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇
⠀⠀⠀⠀⢀⠈⠒⠀⠀⠀⠀⠀⠀⠠⡶⠒⠒⠒⠆⠀⠀⠀⠐⠦⠀⡠⠀⠀⠀⠀⠀⢐⠀⠘⠿⠀⠀⠚⠷⠄
⠀⠀⠀⠁⠈⠀⡀⢠⠀⠀⠀⠀⠀⡄⡀⠀⠀⣿⡁⠀⠒⠛⠓⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠩⠟⠡⢲⡖⠒⠒⠒⠋⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇⡀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢸⣄⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠣⣾⠆⠃⡡
⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⢸⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠳⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣠⣤⡜⠥⠄
⠀⠀⠀⢀⣤⡄⠀⡄⢾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⢀⡹⣀⠀⣀
⠀⠀⠀⢠⣯⣤⡄⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡈⠃⠠⣄⠉
⠀⠀⣀⡈⠉⠉⠁⢠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢈⠀⠉⠙⠂
⠀⠀⣛⡁⠀⠻⣣⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢀⣃⣴⣦
⠀⢀⠈⠋⠁⠂⠻⢟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠿⠿⠈⠉
⠀⠈⠑⠀⣱⡄⢀⠞⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣟⣛⣲⠶⢦
⠀⣴⡆⠀⠿⢏⣨⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢉⡉⠙⢻
⠀⣨⣤⣠⠾⠛⠋⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢠⣾⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆⠿⠟⣠⣬
⠀⠉⢱⠋⠰⠛⠷⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠋⠀⢸⡇⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠁⠀⠀⠈⡛⠋
⠀⠈⡈⠢⡀⣘⣠⢇⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢿⠀⠀⠘⡇⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⢐⢧
⠀⠀⣠⣤⠀⠍⠰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠃⠀⠀⣷⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⣀⡀
⠀⠀⠙⠡⠘⠀⣀⣨⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⣀⣿⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡇⣠⣘⡟⠃
⠀⠀⠀⠀⢀⠀⡘⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢛⡁⠉⠉⠋
⠀⠀⠀⠀⠀⠀⢁⣤⢀⡀⢶⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢀⣀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠟⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣅⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠙⢩⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠘⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁