Shocking Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠛⠻⢿⢷⣦⣤⣴⣶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠈⠙⢆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡏⠁⠀⠀⠀⠀⠀⠳⣝⢿⣿⣶⠤⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⣰⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡀
⠀⠀⠀⠀⣠⣴⡿⡿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⣌⠙⠛⠶⣄⠀⢈⠙⢷⣄⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣴⣿⠀⠃⠁⠹⣇⠀⠐⣄⠳⣤⡳⣄⠢⣀⢄⡀⠀⠠⣀⠙⢷⣤⣽⣾⣿⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢠⣿⠀⠀⠀⠀⠦⢬⣿⣶⣬⣽⠿⠿⣿⣿⣿⣿⣿⣷⣶⣮⣿⣦⡙⢿⣿⡟⠿⣦⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⢠⣿⣦⡀⠀⢀⣨⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠙⠳⡀⠈⠻⣧⡴⠖⠚⠦⣀⠀⠀⠀⣀⠤⣀⣀⣀⣠⣴⠞⠁
⠀⠀⣿⣿⡛⠿⠷⢶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⡀⠀⠀⡸⣿⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠉⠉
⠀⠀⣿⡃⠁⠀⠀⢨⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⠀⢰⣿⡿
⠀⢠⣿⣷⣄⣀⣰⣿⣿⠴⠛⠉⠛⠶⢶⣤⡄⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⢹⣿⠀⣾⣿⣿⣄
⠀⠀⢿⣎⠙⢻⡿⣿⡏⠀⠀⠀⢀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠉⠺⣿⠀⡿⢸⣿⣿⣦
⠀⠀⢸⡟⠷⣶⠞⣿⠁⠻⣿⠿⠛⣛⡓⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣤⣤⠀⣿⣠⠁⢋⡿⣿⣿⡄
⠀⠀⠈⣿⣄⣙⡆⢸⠀⠀⠈⠓⠾⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⢦⣗⣆⣨⠟⠋⠀⣿⠉⣆⠞⡽⢱⣿⡇
⠀⠀⠀⠈⠻⣿⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠃⡜⠁⠈⣰⡿⣿⠃
⠀⠀⠀⠀⠀⣿⠟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠇⠐⢛⣩⣾⠋
⠀⠀⠀⠀⣸⣿⢿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠘⣶⣶⠿⣻⣿⣇
⠀⠀⠀⠀⣿⡏⠀⠀⢷⡀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠛⠉⣠⢞⡿⢿⣿
⠀⠀⠀⠀⠙⣷⡀⠘⡘⠃⠀⠀⠂⠄⠰⠡⣤⣶⣶⣦⣄⡀⡀⠀⠀⠀⠀⣰⣯⣀⡀⠈⠀⠀⢠⣾⡿
⠀⠀⠀⠀⠀⣼⡏⠛⠁⠀⠀⡘⠁⠀⠀⠀⡀⠉⠉⠉⢀⠀⠀⠀⠀⠀⣰⣟⢿⣿⣷⡤⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⢹⣷⣔⠀⠀⢨⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣾⢯⡻⣮⡛⠿⠿⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⡾⠘⡀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣿⣷⡿⠶⡅⠀⠀⠽⣫⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠀⠉⠒⠒⠀⠒⠊⠁⠀⠀⠀⣿⢿⣿⣗⣒⣠⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⣍⠛⠛⢋⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣂⣀⣨⣽⠟
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⡛⠁
⠀⠀⣀⠤⠔⠒⠉⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⡀
⣾⣿⣤⣄⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣶⣦⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣠⣿⣿⣤⣿⣄⣾⣆⣀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⣴⣦⣴⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠳⣭⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣶⠀⢀
⠀⠀⠀⠀⢀⣠⣬⣽⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⡆
⠀⠀⠀⢄⣨⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠙⣿⣿⣿⣥⡄
⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⣠⣴⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⠉⠛⢿⣿⣦⡀⠀⠘⣿⣿⣧⣄
⠀⠀⢀⣾⣿⣿⠏⠀⣠⣾⣿⡿⠋⠁⠀⠀⠉⠂⠄⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⢹⣿⣿⣧
⠀⠠⣶⣿⣿⡟⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃
⠀⢘⣿⣿⣿⠁⠀⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣴⠞⠛⠛⠳⣦⡀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⣹⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠻⣦⡀⠀⣰⡟⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢿⣿⣿⠏
⠀⣺⣿⣿⠁⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠈⣇⠀⣿⠀⠀⠀⣠⡀⠀⠀⠈⣿⣤⡀⠀⢸⣿⣿
⠀⢺⣿⡟⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠠⣶⠀⠀⠀⡟⠀⢿⣀⠀⠀⠙⠁⠀⠀⢠⣿⠿⠷⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠠⣾⡾⢿⣇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⢿⣷⣄⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⣿⣿
⠀⣿⣿⠁⠀⠀⠀⠘⠋⠀⠀⠻⣧⣄⠀⠀⠀⢀⣠⣿⠃⠀⠀⠀⠙⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⡇
⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⢸⡇⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⢸⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢯⠉⢳⡄⠀⠀⠀⠀⠀⠸⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣷⠀⠀⠀⠀⠀⠀⠈⣧⡾⠃⠀⠀⠀⠀⠈⢀⣿⣿⡇
⢸⣿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠉⣁⡀⠀⠀⠀⢀⣼⣿⣀⡀⡀⣄⡖⢮⣝⣴⣽⣿⣿
⢸⣿⡧⠄⠀⠀⠀⠄⠠⠀⠀⠁⠀⠈⠀⠀⠀⠈⠈⢻⣶⢯⣭⢴⣦⣴⣯⢏⣅⣍⠟⠮⢯⡾⠋⠙⢿⡾⣿⣿⡆
⢸⣿⡇⠀⠀⠀⠂⠀⠁⣠⡾⠟⠻⢶⣄⡀⠀⣀⣠⠤⢄⡈⣥⠀⠊⣦⢞⡩⢁⣩⠱⣚⠏⠠⡔⠀⢸⣇⢹⣿⣧
⢸⣿⣧⠀⠀⠀⢀⠀⢠⠟⠤⠒⢀⡠⠻⣿⠟⢋⡀⠂⢄⠈⠛⢶⠋⣉⣏⠠⠤⡇⠰⣾⠒⢚⡇⠀⣾⠇⠈⣿⣿
⠈⣿⣿⠀⠀⠀⠀⠀⠸⣄⢏⠀⢘⡗⢂⣟⣐⡸⢗⢈⡽⢍⣩⣝⡁⠤⠋⠀⠊⠙⣾⣭⡓⠁⠈⣩⡟⠀⠀⢹⣿
⠀⢻⣿⡆⠀⢀⠀⡀⠄⠻⣦⣌⣀⣬⣿⠟⠻⣦⣀⣁⡴⠋⠀⠈⠙⢦⣀⡀⣠⡾⠃⠀⠙⠶⠶⠋⠈⠀⢀⢸⣿
⠀⠈⣿⣷⠀⠂⡀⠂⡀⠀⠈⠉⠉⡉⠁⠀⠀⠀⠉⠩⠀⢀⠀⠀⠴⠦⣭⡉⠅⠀⠀⠀⠀⠀⡀⠑⠀⠐⠀⣾⣿
⠀⠀⠘⣿⣧⡀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠨⢻⣆⠀⠀⠀⠀⠀⠀⠀⠄⣠⣾⣿⡿
⠀⠀⠀⠈⠻⣷⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠀⢘⣷⣀⣀⣤⣤⣤⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⠿⣶⣤⣤⣄⣀⣠⣠⣤⣤⣦⣶⣴⣶⣶⣿⣾⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡖⠀⣠⢴⡶⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣡⠞⣡⠿⢊⣵⣫⠥⣤⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⡿⠃⠘⠁⠞⣫⠵⢒⣋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠃⠘⠀⠀⠀⠐⢛⣫⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠠⠊⠁⠠⠆⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡸⠇⠀⠀⢀⠆⡀⠱⡀⡴⠒⠂⢄⠀⡠⠐⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣺⡧⠄⠀⠀⠀⠀⠀⢷⠈⢧⠀⠀⠀⠙⠀⣤⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⡲⠖⠂⠀⠀⠀⠀⠀⠀⠑⡌⠠⡀⠀⠀⣀⠀⢀⣞⣀⣀⠤⠴⠒⠚⢉⡽⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣚⣥⠔⣀⠄⠀⢀⠀⠀⢀⡠⢤⡖⠀⠀⠀⠈⠀⠉⢠⣌⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣱⠷⣻⣫⠴⢺⠏⠀⠀⣏⠐⣉⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⠟⠁⠀⡟⣶⢀⠀⠀⠉⠁⠀⠀⠀⢠⢐⠛⠋⡶⠲⠆⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⣷⢿⢸⢦⠀⠢⡀⠀⠀⠀⢃⣈⡉⠘⠀⣠⠞⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠹⠀⠓⠄⠀⡀⠀⠀⠀⠀⠀⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⣸⠁⠀⠒⠲⢾⡀⢱⠺⠦⠔⣶⣃⣀⣀⣀⣀⣀⣀⡀⢀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣠⣼⢸⠘⠶⠒⠒⢒⠆⠀⠀⡗⠲⢴⡳⠒⠒⠒⠒⠒⠒⢦⠬⡑⣟⠛⠃⠀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠴⢣⠒⢭⠆⠀⠀⡞⠀⠀⢲⠁⠀⠀⠠⠀⠀⠂⠐⠀⠀⠀⠀⠈⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢖⠀⢁⡀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢨⡇⢸⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⣰⠅⣺⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣀⣀⣮⠤⣽⠒⢲⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠿⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣀⡏⢷⠏⣧⢚⠆⢠⡖⠛⢢⢠⡧⠘⠃⠀⠀⠀⠀⠘⠓⢼⡄⠔⠛⢲⡀⠰⡓⣼⠙⣾⢹⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠹⡌⠷⠞⠳⢃⣎⡀⣸⠷⡆⢸⠀⢀⡠⠄⠀⠀⠀⠀⠠⢄⡀⠀⡆⢠⠾⣇⢀⣱⡘⠖⠳⠾⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠐⠈⡡⠟⠻⣄⣿⠘⢄⣀⢀⡤⠈⠁⠈⠁⢤⡈⣀⡴⠃⣿⣠⠟⠛⢌⠉⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠒⢺⠀⠀⠀⠀⣽⠀⠀⠀⠀⠉⠑⠢⠔⠊⠉⠀⠀⠀⠀⣿⠁⠀⠀⠀⡗⠒⠒⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣄⣀⣠⣤⣏⠀⠀⠀⢠⣶⣶⣤⣤⣶⣶⡄⠀⠀⠀⣹⣤⣄⣀⣠⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠛⢦⡀⠀⢻⣿⣿⣟⣻⣿⣿⡟⠀⠀⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠦⣤⣈⡁⠀⠀⢈⣁⣤⠶⠋⠀⠀⠰⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣛⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⣛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢤⣄⣀⣀⠀⠀⠐⢸⡇⠀⠀⠀⣀⣀⣠⡤⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⢹⡏⠁⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠛⠓⠒⠒⢺⡗⠒⠒⠛⠛⠛⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣽

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡿⢿⣿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣼⣭⣽⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠙⠻⠶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⣾⠁⠀⠀⠀⠀⠸⠁⢄⠙⣦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⠊⠁⠠⡏⠀⠀⠀⠀⠀⠀⡇⠘⠀⠘⠀⠈⢁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢰⡇⠀⠀⠀⢛⡀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⢘⠀⢿⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣷⠀⢸⡇⠀⠀⠠⠈⣇⣨⡄⠀⠀⠀⠀⢸⠀⠀⢀⠀⢸⢀⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡀⠸⣧⢰⣿⣦⡾⠋⢉⣡⣄⠀⠀⣠⠆⠀⠾⢋⣴⣃⣀⠀⣰⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡄⢸⣯⡳⠌⠋⠀⢹⡀⢰⠋⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠛⠁⠘⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠘⢧⡉⠉⠀⠀⠀⠀⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⠀⠀⠀⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢈⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠞⠋⠙⠻⣿⡄⠀⠀⠀⢀⣿⠿⠛⠃⠐⠤⠀⠀⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠤⢒⣀⣀⠀⠁⠀⠀⠀⠈⠁⣀⣈⣙⠃⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⠘⠉⠉⠉⠳⣀⡀⠀⠀⢤⠛⠉⠉⠉⠳⡄⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⠀⠈⠀⠀⡶⠀⠀⡧⣾⠀⢰⡆⠀⠴⠆⠀⠀⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠳⣮⡇⢰⡀⠀⠀⠀⠀⣴⡿⠀⠸⣷⡀⠀⠀⠀⣠⡁⠀⣸⠀⡤⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⣤⣄⣼⠁⠀⣽⣒⣀⠐⠊⠜⠳⠀⠀⠘⢟⠒⠒⠊⠁⠉⠀⠹⡏⡠⠤⠄⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⣸⡏⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡶⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⣧⠀⠀⠀⠀⠀⠴⠃⢈⡀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⢀⡟⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⢸⠀⢰⣄⠉⠀⠀⣠⣶⡆⠘⠀⠀⠀⠀⢸⣧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢸⣏⣉⣉⣉⡛⣛⣛⣒⣉⣉⣉⣉⣉⣩⡏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢨⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣦⡀⠀⣤⣤⣤⣤⣤⡄⢀⣴⣶⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠂⠤⠶⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠟⠀⠀⠀⠀⠀⠀⠿⢀⡴⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠈⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠙⠲⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⡿⠙⣿⠛⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣏⡀⠛⡟⢠⣿⡿⢹⣿⣿⠃
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠁⠘⠻⢣⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠔⠒⠒⠄⠀⠀⠠⠖⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⡉⣧⠀⠠⠾⠯⠀⠀⠀⠀⠚⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⣿⣿⣿⣶⡷⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣇
⠀⠁⠈⠀⠀⠀⢠⣤⣼⡁⣻⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢛⣧⣀⡀⠀⠀⠀⢠⣿⣶⣶⣾⠁⢰⡋⠁⠀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠛⠧⢤⡀⠀⠘⣏⠀⠈⡟⠠⠛⠀⠀⠀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠁⠐⣄⡙⠦⠴⠧⠀⠂⠀⠀⠀⠀⢐⡡
⠀⠀⠀⢀⣤⠾⠁⠀⢠⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢥⣀⣀⣤⠃⠀⠀⠀⢀⣴⠋
⠀⠀⣴⠋⠀⠀⠀⠀⠈⢷⣿⣿⡿⣿⡿⢿⣦⣤⡀⠀⠀⡠⠀⠙⠃⠀⠀⢀⡄⠉⠙⢧⡀
⣠⠞⠉⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠘⢧⡞⠀⠀⠀⠀⠜⠀⠀⠀⢠⠀⠀⠀⢡⠀⠀⠀⢳⡀
⠻⡄⠀⡾⠉⠀⠀⠀⠀⠉⢆⠀⠀⠀⡸⠁⠀⠀⠀⢠⡀⠀⠀⠀⠈⡇⠀⠀⠈⢇⠀⠀⢀⡗
⠀⠙⣆⢻⡀⠀⠀⠀⠀⠀⠘⡀⠀⠠⠁⠀⠀⠀⢠⠃⠱⡀⠀⠀⠀⣿⠀⠀⠀⠈⢆⠀⡼⣧
⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⢁⡠⠁⠀⠀⠀⢀⡆⠀⠀⠘⣄⠀⢀⡟⡄⠀⠀⠀⠀⢳⡃⢹⡀
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡜⠀⠀⠀⣀⠘⣆⡜⢀⡇⠀⠀⠀⠀⠀⠳⡄⠃
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠐⠒⠚⢻⠀⠸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠹⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣣⠀⠀⠀⢸⣂⣀⣀
⠀⣀⠤⠤⠀⢶⡧⡈⣻⣵⠞⠙⠉⠀⠀⣀⣭⣵⣦⣀
⢸⡱⠉⠀⠀⢹⡿⡞⡏⠀⡀⣄⠀⢤⣀⡈⠉⠉⠉⠛⠷⣦
⠀⠙⣆⠀⢀⡞⣁⣻⡷⠶⠿⠿⠾⢦⣬⣭⣥⣤⣄⡀⠀⠈⢳⡀
⠀⠀⠈⢻⡟⢤⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⢦⠀⠀⡇
⠀⠀⠀⢼⡌⢾⡏⣠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⠀⡟
⠀⠀⠀⠘⢞⣻⢀⣀⣀⣀⠉⠃⠀⠀⠐⠚⠋⠉⠙⢺⣿⣧⡞⠁
⠀⠀⠀⠀⠘⢹⠈⠛⢍⡿⠁⠀⠀⠀⠀⢐⣟⢻⡶⠀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⠀⠉⠀⠀⠀⠀⣴⠟⠋⠉⠉⠓⠦
⠀⠀⠀⠀⠐⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢆⠀⢠⡴⠒⠚⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠲⣠⠉⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠠⠙⠛⢋⠀⠈⢢⠀⠐⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⣼⣟⣿⡇⢄⠀⠀⠀⠀⠠⡄⠘⠀⠀⡀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⣾⠸⠘⡿⣇⠀⠁⠒⠀⠒⠃⠉⠀⠀⠀⠃⠀⠀⠉⠈⠉⠉⠢⢤⣀⣀⠤⠒⠤⠤⠴⠶⠛⠁
⠀⠀⠀⠀⣿⡀⣀⠈⠚⢧⡀
⠀⠀⠀⠀⡈⢿⠂⠙⠳⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠠⠐⠂⠁⡀⠈⣷⡄⠀⣲⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠌⠂⠂⠄
⢀⠀⠀⠂⠂⢹⠟⣡⡾⠯⣀⣀⡀⠀⠀⠄⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠄
⠨⠌⠀⠐⠀⠘⠦⡽⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠁⠠⠀⠀⠈⠀⠀⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢂⠀⠀⠀⣀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢠⢸⠌⣶⢁⣀⢀⡼⢦⡹⠀⠤⠀⠀⠀⣀⣀⡀⠀⠤⢤⣤⣄⡀
⠀⠀⠀⠀⡤⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠛⣇⢀⠏⠙⣆⣀⠜⠓⠒⠋⠩⠌⠀⠀⠀⢀⡈⣤⠀⠀⠃
⠀⠀⠀⠀⠐⠙⠀⠀⠄⠉⠉⠉⠒⠂⠛⠦⠰⢲⣤⣄⣀⣌⣰⡆⣠⠶⠞⠛⠙⠉⢀⣀⠤⡀⢀⠐⠶⠬⠏⠘⡀⢋⠂
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠉⠐⠊⠉⠑⠂⠠⣄⡂⣹⠈⠛⠙⢘⠻⠀⠐⣈⠂⠈⠡⠍⡠⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⠜⢉⠀⡇⠀⠀⠀⠀⡀⠀⢀⡨⠁⢀⠃⠠⠀⣀⠀⠠⠀⠐⠂⣨⠄⠀⣀⡇⠘
⠀⠀⠀⠀⠀⠘⠀⠀⠢⠀⠀⠠⢁⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠃⠀⠄⠀⠈⠀⣒⠒⠀⠃⠸⠨⢃⡀⠊⡀⣴⠀⡭⠅⣄
⠀⠀⠀⠀⠀⠀⢃⣩⠀⠀⠀⠈⡒⠂⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⡔⠡⠔⠅⠀⠐⢀⠀⠀⢠⠼⠆⢷⡀⠩⠏⠀⠗⠒⠀⡅
⠀⠀⠀⠀⠀⡄⠤⡜⠀⡀⠀⠀⠁⠀⢀⠀⠀⢠⠀⢀⠄⠀⠀⠀⠀⠅⠀⠀⠰⠘⠌⠂⠣⠁⢑⡠⠤⠀⠊⢉⠄⢜⡉⠰
⠀⠀⠀⠀⠀⢡⣰⠇⠀⠉⠁⠓⠂⠦⠤⡈⢀⠀⠀⠀⢁⠂⠀⠀⠣⣀⣁⡨⠈⣉⠀⢐⡒⠁⠐⢀⠈⠀⠀⣐⠀⢸⠔
⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠤⠀⠈⠀⠀⠀⠈⠉⠁⠲⠤⡀⠀⠀⠠⠤⠄⡀⣩⠉⠈⠁⠊⠑⣠⣿⣼⣿⣿⣽⠃⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⡀⠀⠀⠄⣸⠁⢈⢀⣙⣉⣉⣉⣉⣉⣉⣀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠑⠂⠲⠤⠄⠀⣀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠩⠥⠂⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠐⠂⠀⠀⠠⠀⠀⡀⠤⠒⠀⠀⠠⠀⠀⠀⠈⣁⣀⣈⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⠀⠀⠀⠤⠈⠄⠀⠀⠀⠀⠀⡄⠀⠥⠂⠤⠀⢀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⢀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠂⠀⠄⠈⠑⢒⠤⠄⠊⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠉⠉⠉⠉⠙⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⡀⠸⢦⡖⣆⢤⠀⢀⡤⠧⡀⣔⣒⠦⠀⠀⠀⠀⠴⢒⣢⢀⡼⢤⡀⠀⡤⣰⢲⡴⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣍⢷⡼⠧⠏⡞⠀⣸⢤⠀⡇⠉⢀⡀⠀⠀⠀⠀⢀⡀⠉⢠⠀⡤⣇⠀⢡⠹⠼⢧⡾⣩⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠚⣫⠟⢧⣸⡇⢣⡀⣉⣀⠐⠀⠀⠀⣀⣉⢀⡼⢰⣇⡼⠺⣝⠓⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠶⢾⠁⠀⠀⠉⡇⠀⠀⠀⠙⠓⠆⠰⠚⠋⠀⠀⠀⢸⠉⠀⠀⠈⡷⠶⠖⠾⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣤⣤⣤⣼⡇⠀⠀⢀⣴⣶⣤⣤⣶⣦⡀⠀⠀⢸⣧⣤⣤⣤⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡔⠳⣄⠀⠘⣿⣿⡟⢻⣿⣿⠇⠀⣠⠞⢆⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⠀⠀⠀⣀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣤⠴⠚⠁⠀⠀⣀⠀⠀⢀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡍⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢩⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠢⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⠀⠦⢸⡇⠀⠀⠀⠀⠀⠀⣀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠉⠒⠒⠲⠶⠶⠼⠧⠶⠶⠶⠒⠒⠉⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢢⡖⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠒⠒⠒⠲⢾⡷⠖⠒⠒⠒⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣀⣀⣄⣼⣧⣀⣀⣀⣠⣄⣨⡇

⣀⣄⣀⣀⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣛⣟⣉⡛⣻⡛⣻⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌



⡀
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣤⣀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡫⣴⣾⡿⠿⠛⠛⠉⠉⠉⠉⠙⠛⠻⢿⣿⣷⣟⢳⣦⠀⣀⠔⠋
⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣩⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠛⠓⠒⠨⢝⡀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⢻⣿⣿⢹⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠦⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⠁⠀⣾⠟⠳⡆⣹⠛⣿⠋⢁⣤⣤⣌⠉⠓⣶⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡜⠂⠀⠀⠌⣿⣿⣿⡿⣿⣧⣀⠀⠀⠀⢀⡴⠃⠀⠸⡄⠈⠛⠀⠛⠀⠀⡾⢻⣿⣿⣿⣿⣆⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢌⢸⣿⣿⣿⡇⣿⠀⠉⠙⠛⠛⠉⢀⠀⢀⠀⠙⠦⣤⣤⣤⡤⠚⠀⢸⣿⣿⣿⢿⣯⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⠎⢘⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⢸⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣹⣿⢧⣾⡇⣠⠀⠀⠀⠀⣠⡶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣸⡇⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠉⠀⠙⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢰⠆⠘⠓⣿⣿⢠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣶⣿⣿⣿⣿⠀⠀⠀⣤⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠻⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡿⣿⡼⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢻⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣽⣿⡙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣿⠿⢣⣾⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣾⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⡿⢹⣿⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣷⠇⣾⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⡿⠁⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿
⣴⣴⣴⣶⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣼⣿⣿⣷⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣩⣟⣻⣹⣿⣥⣉⣻⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣯⣭⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠂⠀⣴⣶⣿⣯⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠌⠛⠛⢁⣶⣦⠘⠿⠿⠃⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢢⠀⠀⠀⠀⠘⠟⠛⠀⠀⠀⠀⢤⡄⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠉⠙⠶⠶⢀
⠀⠘⢄⠀⠀⠀⠀⠀⠢⠀⠀⠀⠘⠧⠜⠂⠔⣢⣤⠈⡂⠂⢰⠀⠀⠀⠂⢄⣲⠤⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦
⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⣶⣾⠦⡴⠔⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢳
⡆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⡋⠕⠾⢟⡢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣴⡄
⠆⠀⠀⠀⠀⠀⠣⢄⡀⠀⠀⠀⡠⠀⠤⠤⠔⡂⠬⠛⠉⠁⠀⠀⠈⠙⠛⠅⣚⠢⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠁
⠀⠑⠄⡀⠐⢂⠀⠀⠁⠒⠀⠀⠙⠓⢲⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠤⠀⠀⢀
⠀⠀⠀⠀⠘⠤⠓⠀⠀⠠⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠉⢢⣤⣠⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠱⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠘⢆⠀⠐⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⣀⣤⣀⣀⠱⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠁⠂⠀⠲⡀⠀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠣⡄⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢦⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢁⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⡄⠄⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣈⠉⠉⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠲⢎⣁⣁⡀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠁⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⣤⣀⡀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⣉⠛⠛⠿⣿⣿⣶⣾⣿⣿⢯⣌⠙⠳⣄⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣟⣡⠞⣡⢞⡭⠌⠙⠻⣿⣿⣿⣿⣭⣥⣄⡀⠈⢷⠀⠈⢳⡄⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡥⢞⡵⠋⣠⡶⠟⠛⠛⠉⠛⠛⠻⠿⢿⣿⣄⠈⢧⡀⠀⠙⣦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⣠⡿⠛⠋⢁⡤⠋⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠈⢳⡄⠢⡈⢷⡀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⣼⠋⠀⢠⠰⠋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣽⣿⣆⠹⡌⣷⣔⣁⣀⡤⢴⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⢸⡇⢸⣆⡇⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢻⣿⣿⣄⣿⣿⣿⠀⠀⠀⠀⠉⠒⠶⠤⠤⠶⠊⠉⠛⠲⠶⠾⠛⠋⠁
⠀⠀⢸⡇⠸⣿⣷⣿⡟⢣⠞⠛⠲⠶⢦⣤⡀⠀⠀⠀⠀⣤⠶⠞⠋⠉⠉⠓⠀⣿⣿⣿⣿⠏⢸⡇
⠀⠀⠀⠻⣦⡙⢿⣿⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⣿⣿⣿⠋⡀⢸⡇
⠀⠀⠀⠀⢻⣿⣾⣿⣧⠘⢿⣿⠋⣿⢭⠀⠀⠀⠀⠀⠀⠀⠨⣹⣏⣉⡿⠋⢠⣿⣿⢁⣮⢀⡞
⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⣿⣿⣿⣧⡟
⠀⠀⠀⣴⣏⡿⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⣸⣿⠟⣴⢏⡼⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⣿⡇
⠀⠀⣿⣿⠟⢡⣾⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⡿
⠀⠀⢻⣿⣆⠘⢿⣿⣿⡿⡴⠂⠀⠀⠀⠀⠀⠊⣁⣤⣈⠁⠀⠀⠀⠀⠀⢠⣿⣿⡿⢸⢿⡇
⠀⠀⠀⠳⣝⡷⣬⡻⣿⡗⠀⠀⠀⠔⠈⠀⢀⠙⠻⠿⠛⠉⠀⠀⠀⠀⢠⣾⣿⡿⠁⠟⣼⠃
⠀⠀⠀⠀⠈⠙⢿⣿⣿⡇⠀⠀⣴⠀⢀⠀⠀⠉⠀⠤⠀⠀⠀⠀⠀⣠⣿⣿⣿⡁⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠃⠀⢰⡦⠂⠀⠀⠀⠀⠀⢀⣠⠞⣽⣇⣿⣿⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⠟⠀⣾⠖⠤⠤⠴⠒⠉⠁⠀⠸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣴⣥⡾⠇⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠄⠀⠀⢠⣿⡿⢋⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣿⣿⣿⣯⠉⡆
⠀⠀⠀⠀⣾⣿⣜⠸⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢆⣿
⠀⠀⢀⡀⣿⣿⢀⢸⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢹⣻⣿⣧⢫⠄⡀
⠲⠟⠛⠦⣜⢿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣛⣥⢺⣯⣿⡟⣸⡠⠞⠛⠓⠶⣦⡤⢄
⢄⠀⠀⠀⠈⠳⣍⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣝⣉⡴⠋⠀⠀⠀⢀⡾⠉⠀⠀⠈⠐⢄
⠘⣇⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⢰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠟⠉⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⢆
⠀⢻⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⢊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣼⢇⡴⣪⣯⢄⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣾⠋⠴⢋⠴⣛⠭⠟⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡼⠰⠃⠀⠀⠴⣛⡷⠾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠃⠀⠀⢀⢶⠉⠀⠔⠀⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⢶⠛⠀⠀⠰⠅⢈⠣⣴⠉⠑⠦⣠⠖⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠁⣀⣭⢟⣓⠀⠀⠀⠀⠈⠣⡘⡄⠀⡀⠽⠘⠇⢰⠃⠀⠀⢀⣀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡉⠁⠀⠀⠀⠀⠀⠀⣑⠈⠛⠤⡼⠂⠀⠛⠒⠚⠉⠉⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠞⢺⡯⡶⣋⠤⡖⠀⠠⡊⠥⢚⡀⠀⠀⠀⠀⠈⠉⠁⠀⢸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠉⢰⠟⠁⣸⣵⢀⠀⠉⠉⠁⠸⠀⣠⡲⢲⢲⠤⠄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣸⢆⢰⢦⡀⠀⢀⣏⣉⣫⠏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠛⠀⡬⣘⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⣀⣀⢀⡇⢊⣠⠔⣉⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠛⣆⣀⡤⣬⠓⠘⣭⣁⢩⣫⣤⣤⣤⣶⣶⡒⠼⣭⢵⠆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡿⡥⢗⡄⠀⢀⠇⠀⢠⠇⠀⠙⠁⠀⠄⠀⠀⠀⠉⠙⠚⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡅⠀⡄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢐⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⣰⢁⣾⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠿⠯⠭⠛⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠿⠿⠿⠿⠿⠿⠷⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⠀⣠⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢠⠞⠉⠙⠓⠶⠶⢦⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣤⣶⠃⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⣸⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠄⠂⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⠃⠀⠀⠀⠂⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠉⣿⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⣿⣄⢀⣻⠏⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣀⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠀⠀⢸⠀⠀⠀⣠⢞⡋⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⠁⠀⠀⠀⠁⠀⠀⠀⠐⠠⠤⠤⠤⠤⠚⠁⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠊⠙⠏⠁⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⢓⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⣾⣻⣦⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⣻⡿⠛⠛⠛⠛⠛⠛⠉⠁⠈⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⣾⣿⣽⠿
⣤⣤⣄⠀⠀⠀⠀⢀⡀⠀⠈⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠁⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠙⠛⠁⠀⣤⣤⣼⣿⣙⠳⢦⣾⡛⢿⣟⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⢿⣟⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠿⠿
⠀⠀⠀⠀⠙⠛⠷⣮⣉⠋⠀⠙⠃⠀⠹⣦⣼⠏⠈⠙⠛⢿⣄⢀⣀⠀⠀⣰⠶⠶⠶⠚⠛⠛⠋⠉⠀⠀⠀⠀⣿⣀⣠⣴⠶⠟⠛⢋⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡶⠶⠶⠶⠾⣿⣤⡀⠈⢳⠄⠉⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⢹⡟⠉⠀⠀⠀⠾⠋⢀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢹⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿⠿⠶⠶⠶⣤⣤⣬⣩⣥⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠇⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠛⠿⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣤⣀⣀⣸⣧⣤⣤⣼⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣯⣤⣤⣤⣬⣭⡽⣯⣤⣤⣤⣤⣶⣶⡾⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠛⠛⠛⠛⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠐⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⢦⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⣄⠈⠙⠳⣤⡀
⠀⠀⠀⠀⢀⣴⠟⠁⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⢳⣄
⠀⠀⠀⣠⡟⠁⢀⡴⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⢻⡑⣆⠀⠀⢻⡆
⠀⠀⣰⡟⠀⢠⡟⠁⣴⠃⠀⠀⠀⢀⠶⠶⠶⠶⠶⣶⣶⣶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⡇⠘⣧⠀⠀⢿⡀
⠀⢠⡿⠀⢀⡟⢀⡞⣿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣷⠀⠘⣇⠀⠸⡇
⠀⣼⡇⠀⢸⠀⡾⠀⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠋⠙⠃⠀⠀⠀⠀⠀⠀⠚⠛⠆⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣿⠀⠀⢻⠀⠀⣷
⠀⣿⠁⠀⠀⢰⡇⠀⡇⠀⠀⢠⡇⠀⠀⠀⠀⢀⡤⠶⠒⠒⠶⣄⠀⠀⠀⢀⡤⠖⠒⠲⢦⡀⠀⠀⠀⠀⢻⠀⠀⠀⡧⠀⠀⢸⡆⠀⣿
⠀⣿⠀⠀⠀⢸⠀⠀⢿⠀⠀⣸⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠘⡆⠀⡴⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⢸⠁⠀⣿
⠀⣿⡂⠀⠀⠈⠀⠀⠘⡆⠀⡟⠀⠀⠀⠘⠀⠀⣠⣤⣤⠄⠀⠀⠃⠘⠁⢀⣴⣶⡶⢄⠀⠈⠀⠀⠀⠀⠘⡇⠀⣸⠁⠀⠀⢸⠀⠀⣿
⠀⢻⣇⠀⠀⠀⠀⠀⢀⣹⣄⡇⠀⠀⠀⠀⠀⢸⣿⠟⠳⣴⡆⠀⠀⠀⠀⢸⡿⠋⢳⣾⠀⠀⠀⠀⠀⠀⠀⣇⣠⣇⠀⠀⠀⠈⠀⠀⡿
⠀⠘⣿⡄⠀⠀⠀⢠⠏⠁⢸⡇⠀⠀⠀⢂⠀⠀⠻⠦⠴⠟⢀⣀⣀⠀⠄⠈⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⢷⠀⠀⠀⠀⢠⡇
⠀⠀⠹⣿⡀⠀⠀⣿⠀⠉⢿⠁⠀⠀⠀⠀⠁⢄⣀⣀⣀⣴⡾⠁⠀⠉⠂⠐⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠓⡼⠀⠀⠀⠀⣼⠁
⠀⠀⠀⢹⣷⠀⠀⠸⣦⡀⢸⠀⠀⠀⠀⠀⠀⡔⡉⡁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠔⠐⠐⠀⠀⠀⠀⠀⠀⠀⣿⢀⠔⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢻⣧⠀⠀⠈⠉⢹⡄⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣿⡄⠀⠀⣄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⠀⠀⠀⣿
⢀⣴⠂⠀⠀⣾⠁⠀⠀⢸⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⡇⠀⠸⣇⠀⠀⢿⣆
⢸⣧⣀⣠⡼⠃⣠⠀⠀⣿⠃⠀⢸⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠀⢸⣧⠀⠀⠻⣷⣄⣈⠻⣷⣶⠞
⠘⢿⣿⣥⣴⣾⠏⠀⣼⠏⠀⢀⣞⡴⠁⠈⠳⣄⠀⠀⠀⠀⠀⣀⠳⠞⠁⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⢻⣧⡀⢿⣦⣀⠀⠈⠙⠛⢛⡟⠁
⢤⣤⣶⣾⣟⣁⣤⠞⢃⣀⣴⠟⠋⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠈⠓⠂⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠙⠻⠶⠽⠿⠿⠿⠶⠛⠉
⣀⣈⣁⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣶⣶⣶⣶⣟⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣿⣷⡄⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⠀⠸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣄⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡃⠀⠐⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣶⠀⠀⠀⠀⢠⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⡿⢿⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⡿⠃⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣱⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⣸⣿⣿⣷⣇⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠐⣿⣿⣿⣿⣿⣤⣀⡀⢠⣿⡿⣿⠁⠀⠀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⣠⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣳⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣉⣋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⡀⠀⠀⢀⣤⣴⣤⣀⡀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣫⣿⣿⣷⣤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⣥⢨⣿⣿⣿⣿⣿⣷⣿⡏⠉⣠⣿⣿⣶⡶⠀⠘⢿⠿⢿⣿⣿⣿⣿⣯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣉⣻⣿⣿⣿⣶⣾⣿⣿⢿⣿⣿⣆⣠⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠻⠿⠿⣿⠉⠀⠈

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣭⣶⣷⠿⠿⠟⠛⠛⠻⠿⢿⣿⣿⣷⢦⡀⠀⠀⠔⠁
⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣉⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇⢿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢁⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡜⣷⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⢠⣿⣿⣿⣿⡏⠉⣉⣄⡚⣤⣀⣀⠶⠶⠶⠶⢄⡀⢸⣿⣧⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⢁⠀⠀⠀⣼⣿⣿⣿⣿⠀⠘⠛⠉⢃⡞⠉⡏⠀⠾⠛⠦⠀⢹⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⣀⡀⢠⣿⣿⣿⣿⡏⠓⠲⠤⠐⠋⠀⠀⠘⢄⣀⣀⣀⡠⠊⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠁⣿⣿⡞⣿⠁⠀⠀⠀⠀⠈⠁⠙⠀⠀⠈⠉⠁⠀⠀⢸⣿⣿⡏⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⢠⠀⠀⠀⢠⣶⠶⣦⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠀⠈⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠇⠈⢙⣿⣗⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⣾⣿⣿⣿⡇⠀⠀⠻⠀⠀⢿⣿⣿⣿⠃⠀⠀⢶⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⢿⡯⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣿⣿⡏
⢀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢡⣿⣿⣿⣿⣷⣶
⠀⡅⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⣾⣿⣿⣿⣿⣿⣿
⠐⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣵⣣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿
⠀⠇⠀⠀⠀⢈⣿⣿⣿⣿⣿⢿⣿⣿⣷⡸⡏⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⣿
⠠⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⢠⡿⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣿⣿⡻⣿⢻⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠛⠛⠉⠛⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠉⠙⠛⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣀⣠⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠘⠃⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠈⠙⠿⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠠⣤⣾⠏⠀⠀⠀⢀⠤⠄⠠⠤⣀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢀⠤⠄⠠⠤⣀⠀⠀⠀⠘⢿⡖⠃
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⡔⠁⢀⣤⣤⠀⠀⠱⡀⠀⢻⡆⠀⠀⠀⠀⠀⣿⠁⠀⡔⠁⢀⣤⣤⠄⠀⠱⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⢰⠀⠠⣿⣿⣧⣀⡀⠀⡇⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⢰⠀⠀⣿⣿⣧⣀⡀⠀⡃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢆⠀⠻⢿⣿⠿⠁⢠⠃⠀⣾⠇⠀⠀⠀⠀⠀⣿⡄⠀⢆⠀⠙⠿⠿⠟⠁⢠⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠑⠤⠄⠀⠤⠒⠁⢀⣼⠏⠀⢀⡀⢄⡀⠀⠘⢷⣄⠀⠑⠤⠄⠀⠤⠒⠁⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⣈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠚⠷⢦⠴⠾⠛⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⣉⣀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⠉⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⠑⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠉⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡄⢀⣠⠆⠀⠙⠁⠆⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠞⣤⠗⠐⠒⠀⣀⠀⠀⣀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠓⠓⢏⠀⠋⠿⣦⡀⠀⢃⡀⠀⠈⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⣾⣿⠀⣈⡁⠂⠄⠆⢀⠶⠋⠀⠀⠁
⠀⠀⠀⠀⠐⠈⠀⣀⣉⣈⡇⣸⡀⠀⡀⠐⠻⣿⢃⡀⣀⣤⠤⠀⠀⠐⠷⢶⣦⡀⠀⠀⠀⡀⠀⠀⡠⠃
⠀⠀⠀⢀⣠⣴⣾⣿⣿⢿⣧⣾⣇⣠⣿⣯⣠⣽⣿⣿⣿⡇⠀⠀⣤⣄⣀⢈⡀⡷⠤⣤⣄⠀⠀⠀⠀⡀⣶
⠀⠀⠀⣀⣼⡿⣛⣿⣥⣭⣽⣿⣿⣯⣹⣿⢿⣿⣿⣟⠆⠀⢶⣾⣿⣦⣿⣏⣴⣾⣦⣾⣧⣾⡃⢴⣄⣀⡀⠓⠂
⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠶⣶⣬⣴⣿⠿⣿⣿⡻⣿⣿⣽⣿⣻⣿⣿⣿⣿⣦⣶⡄
⠀⠀⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣽⣻⣷⣞⡉⠿⡽⠿⠿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⢰⡿⠿⠿⠛⠛⢛⣿⡿⢿⣿⣿⡟⠋⠙⠿⠿⣿⡿⠿⣿⣿⡋⠙⠛⠟⠛⠿⡿⠶⣶⣶⣮⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣡⣴⠶⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢶⣌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢈⣠⡤⠴⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⢤⣤⣈⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡴⣋⠕⠊⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠉⠒⢭⡳⣄⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣼⠁⢀⠎⡴⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠑⡌⢦⠀⢹⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠊⢰⠁⠀⠀⡀⢐⣶⣄⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⢀⠀⣶⣦⠀⠀⠀⢱⠀⠂⠀⣇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⢿⣿⣿⡟⠀⠀⡀⡀⠀⠀⠀⠠⠀⠀⠹⣿⣿⡿⠃⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠧⡀⠀⠀⠈⠁⢀⡠⠊⡠⠁⠀⠀⠀⢣⠑⠄⡀⠈⠉⠀⠀⠀⣠⠟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⠢⣌⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⡡⠂⠀⠀⠀⡟
⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠐⠢⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⠈⠥⠐⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⣶⣦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⢸⠟⠉⠁⠀⠉⠙⠿⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠂⠉⠉⠁⠂⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣤⣄⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⠏⢹⣿⣿⡻⠿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⢻⣿⣿⣄⠈⢿⠿⠃⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣅⠈⣻⣿⡟⠀⠼⢰⡶⠾⠿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⡄
⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠳⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣟⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣾⣭⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡤⣤⣀⠀⠀⠀⠀⠀⣀⣤⠤⢤⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣀⡉⠣⠀⠀⠀⠈⢉⣀⣀⠀⠙⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠋⠙⠋⠁⠀⠀⠀⠀⠉⠾⡟⠷⠀⠀⠀⣿⢡⡙⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣶⣾⣿⣿⣿⡏
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⣾⠁⠀⠀⠚⠛⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣾⡆⠀⠀⣶⣶⡶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣍⡠⢸⣷⡶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡖⠀⠈⢉⠄⠉⠻⣧⠀⠀⢿⣥⣤⣤⣬⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣿⣿⣷⣾⣷⣿⣿⣷⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠘⠁⠀⠈⠁⢻⡆⠀⢸⣿⠟⠛⠛⢿⡇⠀⠀⠀⠀⠀⢀⣷⣾⣿⡷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⡔⠀⡀⠦⠀⠀⠙⠆⢸⣿⠀⠀⢀⣾⠇⠀⠀⢀⣴⠖⠷⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⠆⠀⠀⠀⠀⠀⠀⠀⢔⠈⡸⢿⣤⣤⣾⠟⠀⣰⠁⠈⣧⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠈⢲⡅⠀⠉⠁⠀⠾⠋⠙⠀⠀⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⡤⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠯⣹⡇⠀⠀⠀⠘⠛⢶⣤⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠑⣄⠀⠀⠀⠀⠀⠺⠁⠀⠘⣄⠀⠀⠀⠀⣀⣀⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠁⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⡟⠃⠀⠀⠀⢀⠄⠀⠀⠀⠘⢧⠀⠀⠈⠉⠉⠁⠹⡆⢀⣿⠏⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢻⡾⠋⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠖⠶⢦⣄⡀⠀⠀⠈⢻
⠀⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⣠⠋⢱⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢧⠀⣴⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣰⠃⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⢀⡾⠃⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⢻⡀⢠⡟⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠀⢳⡾⠀⢰⣶⣄⣀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⢸⡟⠉⠉⠉⠑⠒⠊⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢰⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇⠀⠀⠀⠀⣤⡀⢄
⡇⠀⠀⠀⠀⠸⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⠅
⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠇
⡇⠀⠀⣤⠶⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠶⢷
⡇⠀⢀⠉⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠓⠂⠒⠛
⡇⠀⠀⠀⠀⢀⣤⡀⢠⣤⠀⣴⣥⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣕⠆⢀⣸⡆
⡇⠀⠀⠀⠐⠈⠛⡷⠻⣟⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡟⠟⠃⠘⣿⠧
⡇⠀⠀⠀⢀⣄⣤⠀⣠⣈⡉⠀⡿⠃⠀⠀⠀⠀⠀⠀⡀⢿⡤⣤⣀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠠⠻⠏⢸⠁⠉⠠⣄⠰⠞⠂⠀⠀⠀⠀⢀⡹⣤⣤⠀⠿⠆
⡇⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⢨⣄⣄⠀⠀⠀⠀⠀⠀⠹⣿⠋⠘⣾⡶⠆⠀⠀⠀⠀⠘
⡇⠀⠀⢀⣄⣴⣄⢽⠇⠀⣤⠨⣯⣤⢠⡀⠀⠀⠀⠀⠀⢨⠀⢀⣿⣿⠖
⡇⠀⠀⠀⠹⠋⠁⠀⠀⠀⠙⠀⡿⢡⠘⠃⠀⠀⠀⠀⠀⠘⣆⠈⠻⣿⡀⠃
⡇⠀⠀⠀⠀⠀⣀⠀⣠⣭⡀⠀⣠⡄⡀⠈⠀⠀⠀⠀⠀⠀⣹⣧⠀⢸⡇
⡇⠀⠀⠀⠉⠛⠺⠷⠹⠾⠗⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣷⠈⢻
⡇⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣷⡴
⡇⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠧⢘⡗⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠒⠀⠉⠀⠁⠀⢐⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠂⢠⡔⠒⠀⠀⠀⡀⠀⠈⣙⣠⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠼⢿⢧⣶⡀⢾⣿⡏⢉⡿⠿⠿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡆⢤⣄⡀⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⢿⡉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⡂⡶⠉⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⢲⡄⠀⠀⠀⠀⢠⡿⡿⣿⡟⠀⠀⠈⣿⢿⣿⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠁⠿⣀⠀⠀⠀⠀⠈⡇⠈⣹⣇⠀⠀⣸⣿⡆⠸⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡄⠀⠈⠀⠀⠀⠀⠀⠸⣧⣾⣿⣧⣾⣿⣷⣾⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⠿⠷⠟⠉
⡇
⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠦⣀⡀⣀⠀⠤⢶⠶⣖⣶⣶⣷⣶⡶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠖⣿⡿⣫⣿⠟⠋⣠⢐⣨⣵⣾⣿⣿⣿⣟⣭⣶⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⡾⢛⡟⢡⣾⣯⣾⡟⣡⡨⣶⣵⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢿⣿⣿⣿⣿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣾⣿⠀⣾⢁⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠟⢋⣴⣿⠿⣿⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣤⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠿⠻⠟⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣄⣠⣤⣄⣀⣠⣄⡀⠀⠠⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠀⠇⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡇⢠⣾⣿⠟⠋⠉⠉⠉⢉⣭⣍⡉⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠉⠉⠙⠻⣿⣿⡆⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⣾⣿⣎⡸⢏⠀⢀⣤⣴⣶⣷⣿⣿⣿⣿⣶⣦⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⠀⠙⣧⠀⣿⣿⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡾⣍⣿⡏⠁⠿⣉⣽⢻⡟⢩⣽⣭⡙⢿⣿⡿⠿⠃⠀⠠⣿⡟⣹⣿⡿⠛⣩⣭⡉⠻⣿⣿⣧⠀⠀⠀⢿⣷⠟⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣽⠿⡇⢸⠀⠉⠳⣾⠇⣼⣽⣯⣥⣤⣿⠆⠀⠀⠀⠀⣿⠘⠙⠿⢠⣜⣛⢻⠃⠀⣿⡿⠛⠃⣤⠀⡼⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢇⠀⠀⠈⠀⠀⠀⠙⠾⢷⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣉⣡⣤⠾⠏⠀⠀⠀⠘⡶⢈⡆⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⢲⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣘⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡅⠘⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡀⠀⠀⠀⢠⡀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠔⢸⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢻⡟⢿⢿⣦⣤⣼⠿⣿⣼⣿⣿⠀⠀⠀⠀⠀⡀⠃⡜⠀⣽⣛⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣹⡿⣿⡿⣿⣿⣟⢿⣏⠀⠀⠀⠀⠠⠎⠀⠀⡼⠀⣤⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⡆⠀⠀⠀⠀⢠⣾⣷⢞⣇⢼⣴⠆⣜⡷⢾⣦⡀⠀⠀⠀⠀⢿⡶⠁⣔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⢷⡄⠀⠀⣰⣿⣾⢷⣾⣿⠷⠿⢾⣿⣿⡾⣿⣷⣆⠀⠀⢊⠼⣿⢘⡐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠸⢧⡿⣶⣾⣷⣾⣿⣿⣿⣷⣤⣶⣶⣾⣿⣿⣿⣧⣺⣷⡶⣾⣾⣟⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠛⠿⣿⣿⣿⡟⠁⠹⡿⠿⢿⣿⣿⡿⠉⢻⡿⣿⣿⠿⣻⡏⠂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢠⣽⣿⣿⣿⡄⠀⠈⠁⠉⠈⠁⠀⢀⣾⠁⠰⠂⣰⠋⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣾⣿⣿⣿⡏⠛⠦⣄⣤⣤⣤⡤⠖⠟⣁⠔⠀⠌⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⣀⣂⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡖⠲⣯⣍⣉⣩⣭⣩⣉⣨⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠙⠢⡀⠈⠻⣷⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⡿⡽⢾⣷⣄⠈⠳⣄⠈⠻⣿⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⣧⣠⣦⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡟⢫⡳⡿⣧⣑⣜⣦⣳⣽⡕⣄⠈⢣⣀⡈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠈⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⢶⣖⣛⣻⣿⣶⣽⣦⣷⣿⠶⠶⡶⠶⠶⠶⠶⢾⠟⢹⠋⢉⣿⠿⣿⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡞⠳⣬⣇⠀⠀⠀⣞⣷⡶⠾⣛⣭⠵⠖⣛⣋⣩⣭⣥⠤⠶⣾⣷⣧⣧⣇⣀⣀⠀⠀⠀⠀⢠⠃⢠⠇⢠⣾⠋⠘⢛⣣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⣴⢶⣷⣿⣿⠿⣛⡭⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⠿⣿⣤⣋⣠⡿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣋⣬⢟⣫⠶⠋⠁⠰⣦⣀⣠⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⣭⢞⣫⠷⣋⠁⠀⠀⠀⠀⠹⡍⢉⣤⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣋⣥⠞⣋⡴⠛⠁⢰⣿⡀⠀⠀⠀⠀⠀⠛⠋⠈⠳⣼⠁
⠀⠀⢀⣀⡤⠶⠚⣋⣡⡴⠞⣉⡴⠞⠉⠀⠀⢀⣟⣈⠙⠛⣶⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢩⣥⠴⠞⢛⣩⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⣽⠁⠀⡟
⠀⠀⠀⠰⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠈⠀⠒⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠶⠶⠶⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣀⡤⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⢤⡀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠚⠁⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠈⠳⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡠⠊⣀⣴⡿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣷⣦⣄⠑⢄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢆⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⣤⣤⣾⣤⣴⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣦⣤⣾⣤⣤⡀⢀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢲⡶⠋⠁⠀⠀⠀⠀⠉⠛⢧⣀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣰⡟⠀⠀⠀⢀⣠⡤⠀⠀⠀⠈⢏⢳⠀⠀⠀⠀⡔⡹⠁⠀⠀⣠⣤⠄⠀⠀⠀⠀⢻⣆⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⢿⡇⠀⠀⠀⢾⡿⣧⣤⡧⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢼⡿⣧⣀⣴⠀⠀⠀⢸⡿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠈⣇⠀⠀⠀⠈⠳⠿⠟⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘⠷⠿⠟⠃⠀⠀⠀⣸⠁⠀⠀⢸⣇⣤⡀
⠀⠀⠀⠀⠀⡜⠁⠀⢿⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⡠⠎⠀⢀⡀⠀⠀⠀⠀⠠⡱⢄⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢸⡇⠀⠱⡀
⠀⠀⠀⠀⠀⡇⠛⣧⣸⠀⠀⠀⠀⠀⠠⢌⣑⠒⠒⠒⠒⠉⠀⠀⡴⠋⠀⠀⠀⠈⠑⢦⠈⠢⣍⣒⠒⠒⠒⢊⣁⠤⠀⠀⠀⠀⢸⣴⡏⠃⡇
⠀⠀⠀⠀⠀⢧⠀⠇⠸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢧⣀⢦⣀⣀⠴⢀⠞⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⣸⠀⠇⢰⠃
⠀⠀⠀⠀⠀⠈⠳⠤⠤⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠦⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⣿⣷⣶⣿⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⠴⠤⡤⠟⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⢠⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠶⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠀⠓⢲⣶⣦⡤⠀⠀⠈⠀⠀⢈⢩⡀⠤⣇⠀⢂⡀⣤⣦⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣠⡼⠉⠉⠸⣴⡆⠀⣈⣷⣞⡿⠗⠘⠙⠂⠀⠀⠀⠀⠑⣶⣾⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠈⠉⠙⠻⠇⠈⠙⢿⡟⠹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡽⠿⠟⠉⠀⠁⠀⠀⢠⣴⣄⠀⠀⢓⣄
⣀⣄⠀⢠⠦⢄⣀⡀⢤⣀⠀⠀⡀⡀⠀⣛⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠾⣦⣤⣄⣴⣿⣿⠖⠚⢃⠀⢉⠿⡇⠹⡿
⣬⣝⡿⣧⣤⢀⣹⡗⠰⣿⣀⠐⠈⡅⠀⠐⣿⢠⣸⠆⠀⠀⠤⣄⣴⡆⠀⠀⠀⠀⠀⠀⠶⡄⠐⠊⣻⡟⠉⢻⣿⡿⠀⠀⠀⠑⠓⢺⣿⣷⣄
⡿⢋⠉⢈⠉⢩⠛⠋⠛⠉⠙⣷⡦⠀⢠⢣⠿⠮⠿⣆⡀⠀⠀⠈⡽⣷⠀⠀⠀⠀⠀⠀⢠⡹⠀⣠⣯⣙⣿⡦⠛⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿
⢶⣄⣴⠶⢶⣄⡀⠀⣀⠂⠀⠙⠂⢤⣠⣿⡃⠀⡐⠨⣿⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⠘⣯⣷⣿⣧⣿⡵⠃⠀⠀⠀⠀⠀⢸⣷⠿⢿⡿⣻
⠛⢿⣿⣿⡾⠿⢛⠛⠻⢦⣀⣀⠀⠀⠀⠈⠀⠀⣿⣿⡇⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠈⢳⣿⣏⣿⣿⡟⠀⠀⠀⠀⢠⡶⢠⡿⢿⣷⣄⠀⠙
⣠⣾⣿⣷⣶⠶⠉⠉⠻⣶⣌⢿⣄⡀⠀⣀⠆⠀⣍⠰⣿⠀⠀⣾⡏⢤⣤⣤⣤⣤⣤⣴⠿⣿⣯⣀⠹⠁⠀⠀⠀⠀⠘⠀⠃⠙⡿⣿⣿⠀⣠
⠿⣿⣿⣿⣿⣶⣶⣶⣿⣼⣿⢮⣿⣷⣤⡇⢀⣸⣿⣿⣧⣤⣠⣿⡇⠀⠈⠉⢿⣿⡟⣿⣿⣿⠋⠙⠀⠀⠀⠀⠀⠐⠢⣴⣾⣿⣷⣿⣿⣿⣿
⠀⠀⠉⢹⣝⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣤⣷⡔⣲⢻⣿⡏⠙⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠢⠌⠻⣿⣿⣿⣿⣿⣿
⠂⡀⠀⠙⠋⠉⣿⣿⣿⢿⣿⣻⣿⡻⣛⡻⣿⣷⣿⣿⣼⠛⣿⡿⠋⠉⠁⠩⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣤⡀⠀⢴⡽⣿⣿⣿⣿⣿
⠙⠛⣷⣦⣤⣿⣿⣿⣿⣿⣿⣻⣿⠖⠉⣷⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣷⠹⣿⣿⠋⢉
⢦⣟⡀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣶⠔⢈⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠛⢿⣿⢛⣦⡔⠄⠀⠀⠀⣼⣿⡟⠀⠀⢀⣿⡈⣿⣠⢰⣿
⠀⣭⠀⠀⠀⢼⣯⣿⣿⣿⡿⠉⠡⠞⢫⡞⢀⠀⠀⣡⣧⣶⣀⣤⣶⠞⠁⠀⣀⣤⡰⢿⣯⡿⢉⡄⠀⢀⣼⣇⣼⣧⠀⠀⠈⡼⣇⢿⣿⡿⢿
⢠⣟⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠘⠷⢜⣶⣾⣿⡿⠃⠈⣿⠃⠀⣀⣾⣿⠿⠛⠀⢻⣶⣯⣍⣻⣿⣿⣿⣿⣇⠀⠀⢀⠀⠉⠌⡿⠽⢾
⡿⠿⡧⢀⠀⠀⢻⣿⡿⠇⠀⠀⠀⠀⠰⣄⣰⣿⣿⣿⣿⣐⣾⣿⣷⣾⢿⣿⣿⠿⣦⠀⠘⠿⠿⢿⡿⡿⠿⠿⢿⣿⣦⣀⡈⠀⠀⠀⠁
⣶⣶⢳⡾⡗⠀⣨⡟⣀⠀⠂⠀⠤⠤⠄⠘⣿⣿⡿⠋⠈⠻⣿⣿⣿⢧⣿⣿⣿⣴⡾⢷⣄⢛⣾⣿⣷⣷⣤⣤⣬⣿⠛⠻⠿⣦⡀⠀⣦⣀
⣿⡾⢾⡃⠀⢰⣿⣷⣯⠀⣀⣀⣀⣠⣤⠤⣛⡘⠇⠀⠀⢰⣿⣿⣿⣾⣿⣿⣿⣿⣟⣀⣹⣿⣟⠋⠻⠿⠷⠤⡷⠁⠀⠀⠀⠀⠀⢀⢿⣿⣿
⠀⠀⠀⢰⡀⣼⣿⣿⣿⣿⣿⡿⠛⠋⣠⣾⢻⠏⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠙⣛⣿⣧⡀⠀⠀⠀⠀⠀⢲⣶⣜⣆⠀⠘⣷⡟⠁
⠐⠚⠛⠛⡆⣿⣿⡏⠀⠀⠈⠁⠀⠀⠻⠁⢸⠆⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣯⣯⣿⣿⣶⣀⠀⣠⣿⣯⣽⣿⣿⣇⠀⣾⣷⣦
⠶⠖⠀⠀⠉⢻⡏⠉⢙⣒⣶⡾⠿⡿⠃⠀⠀⠀⣾⠏⢹⣿⣿⣿⡟⣿⣿⣷⣿⣿⣾⣿⣿⡿⣤⣿⣉⣿⣿⣄⣐⢿⣍⣉⣉⣉⠉⠀⡙⠿⣄
⠀⠀⠀⠀⠀⠸⣷⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏⢀⣿⣿⣿⣿⣻⣜⣿⣾⣿⣿⣿⡋⠛⠛⠳⠿⠿⠯⠍⣿⣿⣿⣿⣿⣯⣩⣹⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡰⢟⣀⣀⣴⣿⣵⠾⠷⠟⠛⠛⠛⣿⣿⣿⣿⣿⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢷⣏⠛⠣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣸⡿⠫⠁⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠄⡀⠀⣆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠛⣀⣭⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠻⢿⢫⡅⣾⣦
⠀⠀⠀⠀⠀⠀⠀⡜⠁⡠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⢀⠀⣰⣄⡀⢀⣤⡄⠃⠀⢠⢿⣿
⠀⠀⠀⠀⠀⠀⠀⡇⣞⠀⠆⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⣸⡷⠟⠳⡟⢸⡟⠀⠀⠀⠲⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠀⠈⠁⠀⠁⠀⠠⡿⠇⣤⠠⡐⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⡀⠀⠀⣠⣶⣴⣾⡆⠀⢘⠁⠂⠐⣿⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⢀⡈⠀⠀⠀⠀⠀⠀⠂⠀⠈⢻⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣐⢈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠉⠁⠀⠀⡀⠀⠀⠠⣶⣄⠀⠀⣾⠀⠀⠀⠸⠿⠿⠿⠟⠀⠀⢸⣦⣮⣫⣾⣄
⠀⠀⠀⠀⠀⣀⣄⣠⣻⣟⡀⠤⠼⠤⠅⠚⠗⠂⠒⢺⣿⡟⠀⣠⣿⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⡛⣿⣿⣻⣿⣞
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣘⠽⡇⢀⣹⣿⡶⠄⠀⠀⠀⠠⣬⠀⢀⠈⠣⠈⡙⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⠘⣛⣿⣿⠀⠀⠀⠄⣈⣿⣷⡐⠶⢄⣀⠠⢾⢿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣄⠀⠀⠐⢻⣿⣿⣿⡀⡔⠗⠀⢸⣈⣛
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⡍⣿⣿⢻⣦⢻⣿⣿⣷⣄⢠⣼⣿⣿⣿⣿⣷⣎⠫⣼⣿⣿⡿
⠀⠀⠀⠛⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠾⡿⢿⣶⣿⣄⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⠀⠀⠀⢀⣠⣿⣿⠿⣿⠿⠋⢉⡡⡠⣏⣈⣁⣀⣤⣤⣀⣉⣉⣩⣴⣿⣿⣿⣿⢡⡖⢠⣽⣿⣿⣿⠽⣿⣿⣿⣿
⠀⣠⣾⡿⣫⠽⠛⠛⠋⣴⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣯⣿⣿⣿⢟⡰⠟⣿⣿⣿
⣾⣿⢟⣣⣶⣾⣿⡿⢿⣛⣯⣾⣻⣿⣿⢿⣿⣿⡿⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⡔⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣭⣵⣶⡿⢿⣭⣿⣿⣿⣟⣿⣿⣿⡇⠲⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣾⡦⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣾⠀⣠⠔⡿⢋⣀⣠⡅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣧⠞⢡⡾⢛⣥⣾⠥⢶⣦⠤⠀⠁
⠀⠀⠀⠀⠀⠐⠀⢠⡀⢰⠃⣾⠋⠀⠋⠰⣛⡭⠖⣛⣉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⣼⣧⡟⠰⠃⠀⠀⠀⠚⣛⡭⠿⠛⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠂⠀⢻⠘⠇⠀⠀⠀⣠⡖⠋⠁⣠⠀⠀⠐⠀⠈⠲⡄⠄
⠀⠀⠈⠀⠐⠶⣤⠬⣧⠀⠀⠀⣜⠁⠙⣄⢠⡔⠲⢤⡀⠀⣠⠔⠒⢦⠀⠁
⠀⠀⠠⠀⠚⠿⢭⣇⣀⠀⠀⡄⠁⠈⢰⡌⠻⡄⠀⠀⠈⢾⢁⣤⠀⢸⡇⢈⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠴⠾⢭⣥⠤⠀⠀⠀⠀⠀⠀⠑⣄⠱⣀⡠⠔⠚⡇⠉⠀⡼⠀⠀⣂⣀⡤⠤⠖⢒⡆⠠
⠀⠐⠀⢀⡴⢚⣩⠄⠀⠀⠀⠀⠀⠀⠀⢀⣈⡄⠈⠓⠶⣺⠋⠒⢚⠛⠋⠉⠉⠀⠀⣀⡴⠛⠀⠂
⠠⠀⡰⠿⢺⣟⢵⡞⢁⡤⣶⠂⠀⣰⠊⡅⠶⣀⠀⠀⠀⠁⠀⠀⠉⠁⠒⠒⠒⡺⠋⠁⠀⠀⠂
⠀⠀⠂⠀⠟⢁⣾⠞⠉⣰⢃⠀⠀⠘⠲⠶⠚⠙⡄⠀⢀⣠⡤⡄⣀⣀⡀⠀⡴⠁
⠀⠀⠀⠒⠀⠌⢁⠀⠀⡏⣿⠀⡆⠀⢀⠀⠀⠀⠁⢀⡯⡾⢴⢥⠏⠈⣡⠞⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣼⡟⣆⢸⠳⢄⡀⠀⠸⠴⠦⠧⡏⣠⠞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠈⠁⠈⠛⠀⡶⢭⡇⠀⠀⠀⡠⠞⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⣀⣐⡀⠈⠀⡟⢸⠀⣠⠔⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⠿⡇⠀⠉⠉⠛⢧⠀⢟⠻⠛⢛⠿⠥⠄⠀⠀⠀⢀⣤⠤⣲⣓⣢⣤⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠢⣖⣶⠾⠇⣀⠓⠚⠉⠉⡟⠀⠀⢸⠉⠒⢼⡟⠉⠉⠉⠉⠉⠉⠳⠴⢭⣻⠉⠍
⠀⠀⠀⠀⠀⠀⠯⢶⢫⠒⢢⠕⠀⠀⢸⠁⠀⠐⣏⠁⠀⠀⠀⠈⠐⠁⠐⠀⠁⠈⠀⠀⠁⢈⡃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⠀⡏⠀⠀⠀⠸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠳⢴⡚⠋⢁⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣇⠀⣹⠄⣻⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢽⠠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠏⠁⢨⣗⣐⣯⠤⣄⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣃⣽⣿⣉⡭⠗⠒⠚⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⢷⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⢸⡇⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡾⣦⠀⢀⣀⣀⡀⠀⣴⢷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠇⠀⠀⠀⠀⠀⠀⡟⢰⠿⠏⠉⠁⠈⠉⠹⠿⡄⢻⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠐⢂⣴⣶⣦⠀⠀⠀⠀⢀⡐⢢⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠃⠘⣩⣴⣦⣝⠃⠘⣳⣄⠀⠀⠸⡇⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣶⣦⣤⣤⣤⣤⡟⠻⠿⣿⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⣤⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⣻⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⢿⠀⢸⠀⠸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⣀⣼⣿⣿⠁⠀⠀⠀⣸⣤⡄⠀⠀⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣿⣾⡇⠀⠀⡇⠀⠀⠀⠀⠟⠀⠀⠀⢀⣄⠀⠀⠰⣦⠀⠈⢻⡿
⣿⣿⣟⠛⠷⣄⣀⡉⠉⠛⠻⠿⢿⡯⠙⠛⠁⠀⠀⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣷⣴⣆⠈⢷⡀⢀⣧
⣧⠈⠙⠓⠦⣤⣈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠙⠃⠀⢠⠇⠀⠀⠀⠀⠠⣁⣛⣩⣥⣶⣾⣟⣻⣿⣄⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠤⠭⣭⣙⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⡂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣤⢧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣀⡸⠲⢀⣤⣄⡲⡀⢢⠠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡏⠀⣴⣿⠟⠛⠻⢾⣾⣾⣏⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗⢠⣿⡇⠒⠀⢀⢄⠙⠿⣽⡿⠗⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠾⢿⠃⠀⠈⠈⢳⠀⣠⠤⡍⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢰⣦⣠⣿⣷⡈⠈⠁⢠⠒⢢⠈⣈⡃⢀⠇⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⢏⠃⣠⣄⠀⠀⠀⠈⠨⢀⡵⠊⢀⠜⠁⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢋⡕⠉⠑⢉⡭⠗⠤⢩⣤⣴⢮⢄⡀⠈⠀⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⣴⣿⣿⣶⣿⣿⣄⣀⠐⢒⡛⢡⡶⢾⣀⡅⠀⠤⠄⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⠻⢿⣿⣿⣿⠃⢀⠄⠉⠁⠘⠱⡀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⢈⠙⠋⠀⠐⠀⠀⢡⠐⢤⡇⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⠛⠀⠈⠀⠀⠀⠋⠀⠀⠰⣖⠠⠙⠋⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠤⠔⠂⠁⠀⠀⠀⠀⠀⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⣾⠉⣷⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⢰⡏⠀⢻⡆⠀⠀⠀⣠⡾⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡀⢾⠁⠀⠘⣷⠀⣠⡾⠋⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣤⣀⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⡿⠋⠀⠀⢸⡏⠀⠀⠀⠀⣀⣀⣤⣴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡙⠛⠳⠶⡆⠻⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣴⠶⠞⠛⢋⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠹⣿⡯⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠐⠻⠿⢿⣭⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣭⡿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⡴⠶⠟⠛⠉⢉⡿⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢿⡍⠉⠛⠳⠶⢦⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡄⢸⣷⠀⠀⠀⣼⡇⣤⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣴⠟⠁⢸⣿⡄⠀⢠⣿⡇⠈⠻⣦⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⠟⠁⠀⠀⢸⣿⣧⠀⣾⣿⡇⠀⠀⠈⠛⠊⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢸⣿⣿⣤⣿⣿⡇⢠⣾⣿⣿⣷⣆⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡿⠿⠇⠿⠟⠛⠛⠛⠛⢀⠛⡛⢛⠛⠛⠻⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣶⣿⠆⣠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠆⠀⢴⣶⣶⣶⣶⡦⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣀⠉⢥⣾⣷⣌⠛⠿⠿⠛⣡⡄⠻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣷⣾⣿⣿⣿⣦⣌⣉⣉⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⠾⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⠀⠀⣀⣤⣶⠾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠈⢿⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠈⠻⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⢠⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⢸⣿⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⠿⣧
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⣼⠿⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠘⣷⡀⢠⡾⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠷⠶⠶⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣀⠴⢾⡿
⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠰⣄⡀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠉⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢀⣀⠀⣾⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢠⣾⠿⠛⠻⣿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⡏
⣿⡇⠀⣠⣤⡽⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠶⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣼⣿⣦
⠻⣧⣀⣠⡾⠁⠀⠘⣁⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠛⠀⠀⠀⣿⠀⠀⠀⣴⢛⣡⡄⠀⠙
⠀⠈⣻⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠉⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⢻⠁⠀⠀⣰
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣴⣾⠟
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠁⠉⠀⠉⠉⠛⠳⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠁
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⣤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⡴⠟⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠃⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⡶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⠙⠛⠿⠶⣶⡆⠀⠀⠀⠀⠀⠀⣾⣤⣤⣤⣤⡶⠶⠾⠛⠛⠉⠉⠁⠉⠉⠛⠻⠷⣶⣤⡀
⠀⠀⠀⣀⣴⡿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠞⠿⣦⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢷⣦⣀
⠀⠀⣴⠟⠉⠀⠈⠻⣦⠀⢀⣀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢠⡾⠋⠀⠙⠻⣧⡀
⠀⢸⡟⠀⠀⠐⠶⢶⣿⡿⠛⠛⠉⠉⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠛⠛⠿⠶⣿⣧⣴⠦⠀⠀⢹⣷
⠀⠸⢷⣦⣄⣀⣀⣠⣽⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠠⣿⣁⡀⠀⢀⣀⣼⡿
⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠶⠶⠾⠛⠛⠛⠛⠛⠲⠶⠶⠶⠶⠶⠶⢤⣤⣤⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢠⣿⠟⠛⠛⠛⠿⠿⠿⠿⠷⠶⣶⣄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠋⣀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠘⠿⣶⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣻⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⢩⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣴⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣯⣍⠛⠛⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⢿⣿⣿⣿⣿⣿⣦⠀⢹⣗⣭⠹⠟⣉⢹⣿⣿⣷⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢫⠔⣹⡞⣿⠂⣽⣿⢿⡷⢿⠀⠃⠸⡿⣾⠄⠻⠻⡧⠐⡛⢻⣯⠳⡆⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⠰⣿⡇⡶⢛⣠⣰⡍⣴⣿⣿⡀⢤⣶⣿⣧⡉⣄⡁⠘⢱⠼⣯⡇⣻⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠉⠀⢡⣿⣧⣟⣷⣿⣿⣿⡁⠶⢿⣿⣿⣾⣿⣿⣞⣎⠂⠉⠀⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⣱⣿⣙⣿⣯⣻⢯⣿⣿⡁⠔⡿⢽⡯⢿⣿⣿⣿⣿⣇⡀⢠⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⡿⢋⠵⢾⣝⢻⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⡀⢠⣿⣿⣿⣿⣿⣛⣴⣿⠄⠸⣿⣷⣟⣻⣿⣿⣿⣿⡁⢤⢾⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⡁⣾⠻⣿⠉⠿⢿⣿⣿⡏⣠⣼⡻⣿⣿⣿⣿⠏⣿⣿⣛⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠂⠈⠤⢈⠠⣿⣿⡧⢀⡤⠀⠀⣦⣱⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⣀⣀⠀⢀⠀⠻⠿⠏⠈⣅⣠⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⠉⣿⢟⡿⠷⢀⡀⠀⢠⡂⣾⣸⣿⡟⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠾⣷⡾⢹⣷⣾⣷⣾⣿⣿⣿⣿⣏⢹⣯⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣧⡃⠅⣸⡇⢨⣿⣿⣿⣿⡛⣿⢁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⣟⣿⣻⣇⣼⣧⣾⠛⢣⣨⣯⣷⡿⣎⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⢠⢀⢈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡀⠒⡄⠉⠀⠈⠁⠉⢹⣧⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢠⡄⠀⠀⠰⠀⠀⠀⠸⡛⢉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⠠⠒⠚⠋⠁⠀⠀⠀⠀⠈⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠆⠀⠰⡀
⠀⠀⠀⣆⠀⠀⠀⠀⠀⡇⢀⡄⠀⠀⠀⠀⢀⡤⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠢⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⢀
⠀⠀⠀⢸⡄⣀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⣾⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⢠⠀⠀⠀⠀⢣⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡠⠀⠀⠀⠈⠀⠠⠊
⠀⠀⠀⠀⢷⣿⡀⠀⠀⡿⢹⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠀⠀⠀⠀⢀⠈⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊
⠀⠀⠀⠀⠈⠁⢳⠀⠀⠀⠘⠀⠀⠀⡼⠉⠁⢀⣤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠓⠑⣄⠄⡠⠊⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢁⡠⠚⣽⡧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠔⠏⠈⢀⠴⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠈⠁⠀⢀⠠⠔⣊⠷⠔⠒⠁⠀⠀⢺⡄⢀⡀⠀⠀⠀⡘⠃⠀⠐⠁⠰⢧⣆⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠐⠀⠀⠀⡀⠀⠀⠒⢆⠁⠀⠀⠀⠀⠀⡐⠒⠤⠐⠄⢳⠈⠙⠢⠤⠔⢁⡆⠁⠀⠀⡀⡀⠛⣄
⠀⠀⠀⠀⡆⠀⠀⠀⢠⣄⣠⡄⠉⢹⠀⠚⠀⠂⠈⠃⠀⠉⣉⣀⢸⡇⠸⡀⣀⠜⢦⡀⠡⡀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠘⡈⢆
⠀⠀⠀⠀⡇⠀⠰⠂⠓⠋⠈⠁⡄⠀⠓⠛⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠛⠓⠑⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠒⠒⠢⠦⢤⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠇
⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠘⡄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠘⠛⠛⠲⠦⢤⣄⣀⠀⠸⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢹⡄⣀⠀⠀⠀⢭⣽⣶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢠⠀⢀⣀⣀⣤⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⡀⠀⢳⣹⡄⠀⠀⠀⠀⠉⠙⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠨⠠⠐⣦⣴⡿⠟⠛⠋⢉⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢧⠀⠀⠻⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⣾⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⣀⡄⠀⠀⠙⡄⠀⠀⢀⣠⡤⠤⠤⠤⢄⣀⠀⠀⠀⠀⣼⣿⠿⠁⠀⠀⠀⢀⣾⣿⠏⣁⣠⠤⠐⠂⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⢷⡀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠒⠭⣒⠦⣼⣿⠃⠀⠀⠀⠀⣠⣼⡿⠟⣋⠥⠒⠈⠁⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⢀⠀⢀⡈⠉⠂⢽⡀⠀⠀⠀⠀⡹⣫⠔⠉⠀⠀⣀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠊⠁⠀⠀⠀⢸⡟⢁⠀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣴⣶⣶⣶⣶⠶⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⡿⢿⣿⣿⣶⣦⣤⣼⣿⣶⣶⣽⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠁⠉⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⢠⡿⠛⣿⣿⣷⠆⠀⠀⠀⠀⠀⠹⢿⣿⠟⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⡟⠀⠀⠀⠈⠳⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣶⣴⣿⡿⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⡟⠁⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣆⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡅⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⡄⠀⠀⢿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠘⣿⡇⢹⡇⠀⠀⠈⠃
⠀⠀⠀⣀⣀⣀⣀⣠⣤⡀⠤⢠⡶⠏⠐⠶⣾⣤⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⡰⡄⢰⣶⣶⣦⣤
⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠤⡤⣴⣮⣁⠀⠀⢀⣠⡶⠟⠇⠀⠀⠀⠀⠀⠊⠇⠀⠀⠀⠀⠀⣸⣷⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢢⣿⣯⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⡠⣥⣶⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣞⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣦⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⡄⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⠀⠀⢿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡟⠀⠀⠠⣤⡄⢿
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⡀⠀⣸
⠀⠀⠀⠀⠀⣾⡟⠀⣴⠶⣦⡄⠈⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢿⣧⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠉⠉⢹⡟⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢻⡆⠀⠘⣷⠀⠀⢿⣧⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠹⠇⠀⠈⠁⠀⢸⣿⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠿⢿⣶⣤⣤⣄⣀⣀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠈⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣷⡀⠀⠀⠀⠀⢻⣿⠀⢀⣠⣴⡿⠟⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⢿⣧⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⣿⣦⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠹⢷⡄⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡆
⢀⣴⣶⣶⣶⣶⣶⣶⣶⠿⠿⠋⠀⠀⠀⠀⠀⣠⣾⠟⠋⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⠀⣀⣠⣾⠋
⠀⠙⣿⡿⠿⠿⠿⠿⣿⣿⣆⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡟⠉
⠀⠀⠹⣿⣦⣠⣤⣶⠿⠛⢿⣧⠀⠀⠀⣸⣿⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠻⢿⣿⠿⠟⠃⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣿⠇⣿⣿⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⢙⣿⡆⢸⣿⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠚⢿⡏⠙⣿⣶⣿⣷⣾⣷⣿⣿⠀⢘⣿⣷⣿⣶⣾⣷⣾⠟⢉⣾⠗⢲⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⣽⡷⣠⣿⣦⡾⠁⠀⠀⠀⠀⢹⣿⠀⢸⣿⠀⠀⠀⠀⠀⠹⣦⣼⣷⣤⣾⡿⠛⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣁⣀⣀⣀⣨⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣀⣀⣀⣀⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇⣿⣯⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⠿⠿⢿⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠤⠀⠀⠀⣄⡤⠀⠘⠉⠉⠁⠀⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡀
⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠤⠴⠦⢤⣄⡀⠀⢸⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢬⣿⠿⠒⠲⣾⠄⠈⠀⢙⣆⠀⠀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎⠐⠂⠈⠉⠀⠀⠀⠠⢠⣤⣦⣠⠁⣾⢋⠀⠀⠀⠈⠀⠀⠀⣘⣿⠇⠀⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⡠⠤⠀⠀⠀⠄⠀⣻⢟⠛⢿⡿⢿⣄⣀⡀⢀⣀⣀⣴⣿⣧⣤⣦⣴⠶⣶
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⢶⣶⣽⡟⠄⣀⣘⠟⠹⣷⣿⡿⠟⠋⠹⠿⢿⣿⡿⠏⠐⠁
⠀⠀⣻⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣴⣏⣙⠀⣤⢋⣿⢸⣿⣿⣶⣾⣿⠟⠀⣀⣀⠀⣓⡚⣿⣷⣀⣀⣀
⠀⠤⠤⠒⠀⠀⠴⠀⢒⡀⠒⠀⠒⠂⠁⠛⠛⠻⠿⠏⠉⣿⣻⣼⡀⠈⣏⣵⣿⣿⣿⣶⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⣎⢉⡼⠿⠟⠛⢿⣥⣹⣿⣿⣿⡟⢿⣈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠂⠁⠁⠀⠀⠠⣴⣶⣾⣿⡟⠀⢠⣼⣤⣤⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣤
⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠁⠈⠙⣳⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣷
⠤⠀⠄⠤⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠉⠘⠋⠙⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⢿
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠻⣿⣿⣿⣿⣿⣿⠃⠈⠁⠈⠛⠙⠿⠟⠃⢸
⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠖⠲⠆⠀⠠⠰⢷⡀⢛⡛⠛⢿⣿⣿⣤⡶⢤⡄⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣠⣤⣤⠤⣤⡴⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⣨⣥⡈⠉⣿⣿⣿⠾⠿⠿⠆⠐⠆⠒⠈⠙
⠠⠀⠀⣀⡀⠽⠿⠛⡛⢋⣭⡁⠀⠂⠀⠀⠀⢠⣤⣼⣿⣀⠀⠠⠤⠾⠿⣿⣿⡏⢀⣿⣿⣿⣶⣦⣀⣼⣿⣦⡀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠠⠀⠀⠛⢟⣉⡁⣉⠙⠲⠦⢀⣸⣿⣿⠁⠘⣿⢏⢿⣿⣿⣿⠛⠛⠉⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠙⠿⠿⠛⠋⠀⠀⠙⣯⢽⣿⣿⠛⡗⢦⣤⠖⢹⣿⡿⢤⣄⠷⢶⣿⠆⣽⠃⣴⡆⡀⠀⡼⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡒⠀⠀⠀⠀⠈⠋⠙⣿⠶⠛⠉⠔⢠⣾⡇⠀⠀⢹⡇⠠⣿⣿⢿⡇⠘⠃⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠁⡶⣶⢛⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⠇⢸⣿⡏⣸⡇⢨⡄⠀⠦⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠗⠈⠚⠓⠒⠶⠐⢲⡆⠀⠀⠀⢰⡆⣨⣿⠁⢉⣟⠚⠓⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⣰⣮⣙⣒⠀⣀⠺⣿⡿⢿⡿⠸⠃
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢀⣠⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣣⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⢸⣿⡟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠉
⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣠⣿⣿⣿⣿⠋
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣴⣾⣿⣷⣶⣄
⠀⠀⠀⠙⠻⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⠁⠈⠻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠈⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋


⣿⠿⠿⡿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠊⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡔⠉⠉⠙⢦⠀⠀⠀⠀⠀⢀⠖⠉⠉⠓⣄⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⢀⣴⣦⡄⣧⠀⠀⠀⠀⡏⣠⣤⣄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣼⠀⠀⠀⢸⣷⣿⣿⣿⡇⠀⡧⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⣋⡝⠁⠀⠀⠀⠀⠙⣝⠛⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢻⡿⠛⠿⠿⣿⣿⡿⠿⠿⣿⡟⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠋⠉⠁

⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠸⣧⠻⠈⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠐⠀⠀⠐⠀⣨⣅⡀⠀⠀⡼⠇⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⢐⣸⣶⣿⣿⣿⠇⠀⣶⠀⠀⠀⣀⡀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣏⠯⠉⠀⠀⠀⠀⠀⡀⠠⣴⣤⣤⣴⣤⣰⣶⣖⣘⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣋⣚⢠⢯⠈⠁⣰⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠸⡀
⡿⠿⣿⣿⠿⠿⠶⣰⡿⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⡿⣿⣿⣿⣿⡝⣿⣿⣿⣿⡏⠀⠘⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣁⠾⣿⣿⠀⠀⣰⣏⣴⠀⠀⣸⣄⡀⣸⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣶⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠆⠀⠀⢀⠀⠀⣀⣾⣷⣀⣤⠀⢸⠐⣶⡄
⣿⣆⣹⣿⣿⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢻⣿⣿⣿⡟⠀⡈⠉⠙⢿⣿⣿⣄⣿⣿⣏⣆⣴⣦⣴⣳⡄⠀⣈⣋⣿⣿⣿⣿⣇⣹⣶⡦⢀⣹⣿
⢨⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⠀⠄⠾⣿⣿⣹⣿⣿⣯⣿⣿⣶⣿⠇⠁⠸⣿⣿⣼⣿⣿⣧⣿⡿⣿⣷⣸⣻⣿
⣾⣿⡝⠿⠛⢋⣿⡟⠻⣿⣿⣿⣿⡏⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣶⣶⡖⠿⣿⣿⣷⣿⣿⣿⣿⣿⡏⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⡙⢱⡆⢸⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠟⢶⣿⣿⣿⣿⣿⣿⣿⡿⠧⠰⣾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠀⠉⠻⣿⣿⣾⣿⡄⢀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡶⠴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣟⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣧⣶⣴⣶⣧⣹⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⡿⢿
⣿⣿⣿⣿⣿⣿⡇⢨⣽⣩⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣾⠏⣰⣿⣿⣿⣿⣿⣿⡏⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⢀⣾
⣿⡿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿
⣿⣷⣿⣿⣿⣿⣇⢻⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣯⣿⣿⠟⠳⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⡿⠿⣥⣶⣛⣿⢖⣿⠋⣿⣿⣶⢿⣿⣿⣽⣿⡿⠿⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⢠⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠦⡀⠠⠀⠀⠀⠀⠒⠤⠌⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⢘⠀⠀⠂⠈⠄⠄⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠰⠀⠀⠰⢦⡀⠀⠠⠀⠀⠑⠤⢠⠁⡀⠃⠀⠘⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠈⢦
⠀⠀⠀⠀⠂⠀⠀⠀⢘⠀⠀⠈⠒⠀⠂⠀⠉⠀⠀⠑⢄⡀
⠾⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢠⠬⠲⣤⠢⠦⢂⣤⣄⠀⠀⠀⠈⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡟⠿⠃⠀⠀⠠⠏⠀⠀⠈⠛⠃⠈⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢃⠀⠀⠸⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠢⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡐⠢⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣊⣂⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀
⣿⣿⡟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⣏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣮⣨⠀⠀⠀⠀⢸⣗⣀⣀⣀⡀
⠀⠀⢀⣀⣤⠤⠄⣶⠧⡀⠙⣷⣨⡶⠞⠝⠋⠁⠀⠀⢀⣈⣩⣶⣤⡀
⢀⡞⣡⠖⠀⠀⠭⢘⣷⣽⡔⡟⠙⠁⠀⠀⠀⡀⠀⠒⠒⠒⠿⠿⠿⢿⣷⣤⡀
⠘⢧⡃⠀⠀⠀⠀⢹⡟⢹⣠⡀⠀⢤⡀⣧⢀⠈⠲⠤⠤⠤⠄⠀⠀⠀⠀⠙⢿⢦
⠀⠀⠙⣆⡀⠀⣰⠋⣄⣌⣳⠿⠻⠷⠿⠿⠿⠷⠶⢤⠴⣶⣶⣶⣤⣄⠀⠀⠀⠈⢧
⠀⠀⠀⠙⠛⣾⠛⣄⣈⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣮⡙⣆⠀⠀⠸⡆
⠀⠀⠀⠀⢰⡏⢢⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⡴⠀⡀⡇
⠀⠀⠀⠀⢸⡳⣄⣹⠇⠴⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡀⣇⣾⡟⠀⣰⠃
⠀⠀⠀⠀⠈⠳⣍⣿⠀⣀⣀⣀⣀⡀⠈⠁⠀⠀⠀⠘⠋⠉⠀⠀⠀⠑⢿⣿⡇⡼⠃
⠀⠀⠀⠀⠀⠀⡏⢹⠀⠛⢟⠋⣽⡇⠀⠀⠀⠀⠀⠀⠀⣛⡿⢶⣶⡆⢸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠁⠀⢸⢙⠿⠄⠀⠀⠀⠀⠀⢀⣴⡶⠶⠿⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠑⢀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠐⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⡆⠀⢀⣴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢒⠀⡎⠉⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠰⠶⣿⣷⠦⠀⠐⢣⠀⠀⠋⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞
⠀⠀⠀⠀⠀⠀⠀⢠⢷⣿⣦⠀⠀⠀⠑⠀⠀⠠⠔⠀⠀⠀⣆⠀⠀⡀⠀⠀⠀⠀⠀⢱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⢏⡟⣼⣿⠑⢄⡀⠀⠀⠀⠀⠀⠔⣄⠀⠘⠀⠀⡇⠀⠀⠀⠀⡠⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⢠⡏⢸⠀⣇⢿⠀⠀⠈⠒⠀⠀⠠⠲⠂⠙⠀⠀⠀⠀⡇⠀⠀⠀⠚⠒⠒⠛⠉⠓⢤⣀⡀⠀⢀⣀⠔⠦⣤⣀⣤⣤⣶⠾⠋
⠀⠀⠀⠀⠀⢼⡅⠈⠂⠘⠢⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠸⣷⣄⠲⢄⣀⡀⢙⣶⡀
⠀⠀⠀⠀⠀⣀⠸⢯⠉⠀⠉⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀
⡀⠄⠄⠂⠁⠀⠀⠈⣷⡄⡀⠀⢰⣼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠐⠂⠠⢀⡀
⠀⠅⠂⠀⣀⢈⠐⢲⣿⠟⢁⣴⡼⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣋⠩⠀⠂⠄⠌⠁⠂⠨⢁⠀⠠
⢐⠀⡈⠀⠀⠄⠈⢼⠁⢰⣿⠯⠛⡒⠒⠒⠒⡒⣀⠀⠁⠀⠀⠀⠀⠀⢀⠁⡘⠐⢀⠀⠌⠐⡀⡂⢂⠀⠠⢢
⠠⠠⢐⠀⠈⠡⠠⠌⡳⠦⠧⠂⠠⠠⠀⠀⠠⠐⡀⠂⠠⠀⠀⠀⠀⠀⠀⠲⠠⠈⠄⣐⠀⠄⠄⠀⠠⠈⠄⡀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⣩⠖⢂⣀⣤⡴⠶⠶⠾⠟⠛⠛⠛⠛⠿⠷⠶⠶⠦⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠚⠑⣚⣯⠽⠶⠒⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠙⠆⠀⠋⠉⠰⠶⠒⣛⠛⠓⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⠴⠒⠃⠀⠀⠀⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⡾⢁⠆⠀⠀⠀⢠⣄⠰⢶⣭⣝⣛⠲⠶⠦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠀⢠⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⡿⢁⠞⢰⠃⣿⡆⣸⡿⣷⣦⣍⠛⠿⣿⣷⣶⢤⣤⣀⣉⠉⠉⠀⠀⠀⠀⣀⡤⠚⠁⢠⠟⢠⡿⠁⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣴⡟⣱⠋⢀⡏⣼⣹⢡⡟⠀⠈⠙⠻⢿⣶⣦⣌⡉⠛⠲⠯⣭⣝⣛⣛⣛⣛⣉⣁⣀⡤⠖⢃⡴⠏⠀⠀⢸⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⢃⣾⠏⡼⠁⢠⡟⣼⣷⣧⡟⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣶⣶⣤⣤⣄⣉⣉⣉⣉⣩⣤⡴⠞⠋⠀⠀⠀⠀⠀⣿⠘⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣾⠏⣼⠁⢠⡟⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⠖⠿⣦⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢰⠛⢷⣄⠀⠀⠀⣿⡇⢿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡏⢸⠇⠀⡾⢰⣏⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⠃⡿⣼⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣇⠀⣿⢰⡇⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⡀⢿⠀⠁⢸⣷⡇⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⢸⣿⢹⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⣿⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⣼⣿⢸⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠸⡿⣆⢿⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⢻⣼⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣥⣌⣂⣻⣆⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⠘⢀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣿⣿⢀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠙⠳⠦⣤⣀⠀⠐⢦⣍⠋⠁⠀⠀⠀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣇⠀⠀⠀⠀⠀⠀⠉⠙⣿⡶⠶⠶⠶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⢰⣿⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⠷⣦⣤⣤⣤⣿⠃⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣽⡿⠿⣧⣀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣼⡟⠀⠀⠈⠛⢷⣄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣰⡿⠀⠀⠀⠀⠀⠀⠙⠳⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠲⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢠⢆⡴⣄⣤⠀⢀⣸⣁⢀⢔⣤⠀⠀⠀⠀⣴⡢⡀⣈⣇⡀⠀⣄⣠⢦⡴⡄
⠀⠀⠀⠀⠀⠀⢯⢻⡸⠧⠏⡜⠀⣯⡄⢸⠈⠁⣀⠀⠀⠀⠀⣀⠈⠁⡇⣠⣷⠀⢣⠻⡼⣧⡟⡽
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠚⡩⠞⣇⣻⠸⣄⣉⣁⠐⠂⠐⠀⣈⣉⣠⠃⣟⣸⠲⢝⠓⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⢺⠀⠀⠈⣹⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⡏⠀⠀⠀⡗⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠦⠤⠤⢾⠀⠀⠀⣶⣿⣶⣶⣿⣦⠀⠀⢀⡷⠤⠤⠴⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢰⠃⠳⣄⡀⠻⠿⠛⠛⠿⠟⢀⣠⠎⠱⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⡆⠀⠀⠀⠉⠓⠲⠶⠶⠖⠚⠉⠀⠀⠀⢠⠤⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠔⠤⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠄⢬⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢔⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⢸⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⠓⠒⠶⠶⠤⠼⠦⠤⠶⠶⠒⠚⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⡀⠀⢸⡇⠀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿⠿⣿⣷⣦⣀⣠⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠁⠀⠀⠉⠓⢄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡟⠋⠀⠀⠀⠀⠀⠳⣝⢿⣿⣯⣍⡀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⣀⣤⣶⣾⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠻⠷⣮⣄⠀⠈⠛⠿⣦⡀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⠀⢀⣾⡟⠻⠘⠋⣿⡀⠀⢀⠘⢦⡀⢤⡀⢄⠀⠀⠉⠃⠀⠀⠉⢷⣄⡐⢦⣬⣿⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏
⠀⠀⠀⣼⡟⠁⠀⠀⢀⡘⠷⣤⣈⠓⢦⣽⣶⣿⣮⣷⣮⣷⣤⣄⣑⡲⣤⡙⢿⣿⣿⣿⣷⡀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⢭⣽⣿⣿⡿⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣦⡙⢿⣇⠈⠻⣷⣤⠈⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⣰⣿⢿⣦⣄⣐⣒⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠃⠀⠈⠻⣿⡍⠀⠈⠑⠦⢤⣤⠤⠔⠉⠳⠶⠶⠶⠟⠋⠁
⠀⠀⣿⡟⢧⠉⠛⢛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⣆⠀⠀⣢⣻⡷
⠀⠀⣿⣏⠀⠀⠀⢀⣾⣿⠃⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢀⣿⣿⡃
⠀⠀⣿⣿⣷⣤⣤⣿⣿⡷⠚⠁⠀⠉⠛⠻⢶⣦⠀⠀⠀⠀⠀⢀⣤⣤⣤⠴⠶⠶⣦⢸⣿⡇⢸⡿⣿⣷⡄
⠀⠀⢻⣷⡈⠉⠽⢿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⣿⡇⣿⢡⣿⣿⣿⡆
⠀⠀⠀⣟⠻⢷⡞⠻⡟⠀⠻⣿⠟⠛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⢶⣶⣶⣤⠀⣿⣇⡏⠘⣸⣻⣿⣿
⠀⠀⠀⢿⣦⣈⣳⠀⡇⠀⠀⠈⠳⠾⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣗⣆⣨⠟⠋⠀⢹⠉⣗⡰⢣⠏⣾⣿
⠀⠀⠀⠈⠻⣿⣿⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠏⢰⠋⠀⢀⣼⢿⡿
⠀⠀⠀⠀⠀⣸⡿⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡏⠤⠞⢋⣵⡿⠃
⠀⠀⠀⠀⢠⣿⣷⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢧⣴⣾⠿⣿⣷⡀
⠀⠀⠀⠀⢸⣿⠃⠙⠸⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⠛⠉⣠⢾⣿⣿⣇
⠀⠀⠀⠀⠸⣿⡄⠀⠆⣿⠃⠈⠀⠄⠀⢀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠊⠁⠋⢠⣿⡏
⠀⠀⠀⠀⠀⢈⣿⠦⡖⠀⠀⢠⢰⠂⠁⠈⠈⠙⠻⠿⠿⠛⠃⠘⠀⠀⠀⠀⢠⡾⣿⣿⣶⡀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⢸⣿⡀⡆⠀⠀⢰⡆⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣷⡝⢿⣿⣯⣵⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠸⠀⠀⣦⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⣝⣮⣛⠦⠈⠉⠴⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡟⠁⢤⣀⡀⠀⢀⣀⡤⠖⠋⠀⢸⣿⣿⣿⣛⣛⡂⠀⢚⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣏⠻⢿⣿⣶⣶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⠦⠀⠀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣅⣠⣴⣾⠟⠁
⠀⠂⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣍⡀
⠀⣀⣀⠤⠔⠊⠉⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⡀
⣿⣿⣦⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣶⣦⣤⣀⣀

⠀⠀⠀⠱⡄⠀⡀⢠⡀
⠀⠀⠀⠀⠓⠆⠱⠖⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣠⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠒⠚
⠻⡿⢿⣿⣧⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠦⠄⠄
⠀⠉⣸⣇⡛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⡶⠀⠀⠀⠀⠀⠀⣍⠉⠨⠀⠚⠅⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠐⢺⣦⣄⡀⠀⠀⠀⠀⠀⡰⢃⠀⠄⠀⠀⠀⠀⢀⡜⠏⠀⠐⠐⠀⣠⣦⣌⠀⠐⠂
⠀⢀⣠⣘⣠⡄⡘⢓⢱⡼⠒⢶⣦⣶⣿⣦⡠⠀⠀⠀⠈⠄⠀⠼⠀⠀⠀⣈⣀⠀⢬⡳⣛⡗⠀⠘⠃⡀
⣢⣾⣴⣿⠉⠴⠉⣿⣬⢁⠀⠼⠉⡫⣤⠉⠂⠀⣤⣤⣆⠀⠀⠀⡀⠂⣀⠏⠛⠢⠄⠉⠉⣤⣤⡀
⣿⡿⠛⠉⣈⣿⣷⣾⣟⣴⣤⣠⣾⣿⣿⡀⣁⣴⣿⣿⠋⠣⢁⢷⡷⠄⠁⠀⣠⠔⠃⠀⠈⠛⢿⣾⢽⣦⡤
⠛⢃⣼⡗⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣆⠐⡼⠾⢿⣷⣶⡆⢰⣶⣖⡖⣀⠀⣤⠈⠁
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣿⣥⣾⣇⠉⢿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣶⣿⣿⣿⢉⡀⠈⠎⢦⣄
⣿⣿⣿⣿⡿⢟⣛⠻⣿⣿⣿⣿⣿⣿⣧⣦⣛⣉⣛⡻⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣖⣿⣷⡀
⢩⣭⣭⣷⣼⣯⣶⣄⠈⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣶⣰⣶⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⡰⠢⠂
⣍⠹⢿⣿⣿⣿⡟⣋⣂⡉⣘⢿⠙⠻⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀
⡿⣖⣳⣎⣹⣧⣾⣿⣿⣯⡈⠋⠀⠀⠘⢿⡔⣘⣻⠿⠿⣏⠻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀⠀⠉⠛⠁⠀⠀⠈⠰⣄⡸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠑
⠿⠿⣿⣿⣿⣿⡿⠿⢿⣯⣿⣿⣿⣿⣿⣦⣤⣦⣶⣶⣶⣶⣦⠠⣟⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠉⠙⠋⠀⠀⠀⠙⢿⣿⣟⠛⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠻⠿⠿⠟⠋⠉⠉⠛⠛⢿⣿⣭⣉⣁⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠊⠉⠉⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⢀⣄⡟⣶⢳⢴⠄⢠⠚⢢⢰⠭⠓⠀⠀⠀⠐⠣⢵⢠⠛⢢⠀⢴⢼⢳⡞⣇⣄
⠀⠀⠀⠀⠀⠈⢣⠓⠛⢋⡬⣀⡞⢲⢸⠀⠤⠆⢀⠀⠀⠀⠦⠀⢸⢰⠚⣄⡨⣌⠋⠓⢣⠃
⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⡔⠁⠑⢾⠀⠑⠒⠲⣄⣀⡀⠴⠒⠒⠁⣸⠖⠁⠑⣄⣀⣀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⣀⣀⣸⠀⠀⠀⣠⣤⣀⣢⣤⡀⠀⠀⢸⣀⣀⣀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠉⠁⡜⢦⡀⠀⣿⣿⡟⣿⣿⠇⠀⣠⠞⡌⠉⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⣀⣀⡠⠀⠀⠙⠲⠤⣄⣀⣀⡤⠴⠚⠁⠀⢀⣀⣀⣀⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠒⠢⠤⠤⠤⠼⠤⠤⠤⠤⠒⠊⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠐⢲⠒⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠉⢹⠉⠁⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠰⡂⠀⡠⣲⠀⠉⠀⢀⠄
⠀⠀⠀⠀⠀⠀⡄⠈⠓⠀⠈⠀⠀⠀⢀⣦⣸⡖
⠀⠀⠀⠀⠀⠘⠑⠂⠀⠀⠀⣀⣠⡜⠈⠻⢗⠂
⠀⠀⠀⠀⠀⢀⣢⡄⠀⠀⠘⠷⠞⠁⠀⠀⡀⠐⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡴⢋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡀⠀⠀⣀⡀⠀⡄⢦⢌⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣤⣚⣯⣭⣵⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⢄⣾⠀⠀⠛⠁⠀⠙⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠿⠿⠾⠋⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦⠴⠖⠻⠟⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⢀⡈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣦⡄⠀⠀⠀⠀⢀⡀⣤⢲⣌⡐⡆⠀⢠⡿⠀⠀⠙⠋⣰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠉⠉⠻⣿⣿⠟⠀⣤⣿⠁⠀⠀⠀⣀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠳⠶⠀⠀⠀⠀⠘⡧⠒⠙⢿⠏⠀⠎⠰⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠀⢘⣿⣿⣦⣤⢤⡤⠄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢀⠁⠂⠀⠀⣷⣆⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠀⠀⠀⢀⡁⢿⣿⠟⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠸⠂⢘⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠰⣿⣿⡇⢀⢀⡀⠀⠠⠀⠀⠀⠀⠀⢄⣵⠇⠐⠀⠘⠡⢈⠀⠘⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⢾⣤⡶⠶⠶⠾⠳⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⢀⣠⣤⡤⠿⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⡀
⠀⠀⢀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⡴⠛⠲⠄⡀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠰⠖⠂⠠⡄⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢾⡆⠸⡂⠀⠀⠀⣸⡏
⢱⠀⠀⠀⠀⠀⠀⠀⣠⢧⡀⠙⠁⢀⠄⠀⠀⠀⠀⠀⠦⠀⠀⠀⢀⠀⠛⡄⠀⣠⡟
⠘⣇⠀⠀⠀⠀⢰⡞⠁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠠⣴⠋
⠀⠹⡄⠀⡀⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⣤⡄⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠘⢦⡉⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠃⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠙⢦⠶⢿⡆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣄⣀⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣨⣍⢑⡆⠀⣿⠁⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⠧⠤⠿⠉⠀⠸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠄⣀⣀⠀⠀⠀⠀⢀⣤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠐⠉⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠃⠐⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠐⠂⠠⠤⠤⠤⣀⣤⠤⠤⠤⠤⠤⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿⣷⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠈⢿⡄⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⡇⠀⠈⣿⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠷⠒⣶⠀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣴⠀⠀⠀⠀⠀⣯⠁⡸⠇⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠃⢹⣏⣀⣀⣀⠀⠀⠘⣇⠀⣀⠀⢀⠀⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠂⠀⠀⠀⠀⠀⠙⡄⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣤⣄⣤⡀⠀⠴⠇
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠉⠉⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠳⡖⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⣰⠟⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠾⠛⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⡘⢦⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⠃⣠⡿⠀⠀⠀⠀⡜⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠘⡇⠈⢷⠀⠀⣷
⠀⠀⠀⠀⠀⢸⡏⠀⢰⠃⣰⢃⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⣇⠀⠘⣇⠀⢸⡆
⠀⠀⠀⠀⠀⣿⠃⠀⠌⢠⡏⢸⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⣉⣁⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡿⠀⠀⣿⠀⠘⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠸⡇⠀⠀⣼⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠳⡄⠀⠀⡠⠚⠉⠉⠉⠙⣄⠀⠀⠀⠀⢹⠀⠀⢀⡇⠀⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢷⠀⠀⡇⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢹⠀⡜⠁⠀⣀⣀⠀⠀⠘⡀⠀⠀⠀⢸⡄⠀⢸⠃⠀⠀⢾⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⠀⠀⠘⣆⢸⠇⠀⠀⠠⠀⠀⣰⣿⣿⡛⣄⠀⠀⠀⠁⢠⣾⣿⣏⣡⡀⠀⠁⠀⠀⠀⠘⡇⢀⡟⠀⠀⠀⡌⠀⢀⡇
⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⢀⡴⠚⢮⠀⠀⠀⢀⠀⠀⢻⣏⠀⣹⠏⠀⠄⠀⠀⠘⢿⣀⣨⡿⠀⠀⠀⠀⠀⠀⠀⡗⠚⠳⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣾⠠⢤⣸⠀⠀⠀⠀⠢⡀⠀⠉⠉⠁⣠⡖⠒⠤⢐⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⡄⣿⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢿⡀⠀⢻⠀⠀⠀⠀⠀⠈⡰⠶⠒⠋⣿⠀⠀⠀⠀⠀⠀⢉⠍⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠃⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠳⠦⢾⠀⠀⠀⠀⠀⠔⠐⠐⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⡄⠀⠀⣿⠁⠀⠀⣿⡆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡄⠀⢸⡀⠀⠸⣷
⠀⠀⠀⠀⢰⡏⠀⠀⣰⠏⠀⠀⢀⣿⠀⠀⣼⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⢸⡇⠀⠘⣷⣄⠀⠻⣷⣤⣠⡖
⠀⠀⠀⠀⢹⣿⣷⣛⣁⣴⡏⠀⣼⠏⠀⢀⡟⡰⠉⠳⣄⠀⠀⠀⠀⠀⠀⢣⣠⠞⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢿⣄⠘⣿⣄⠀⠈⠛⠿⢶⢾⡟⠉
⠀⠀⠀⠀⣀⣉⣩⣽⡿⠋⣀⡾⠋⠀⣠⡿⠟⠁⠀⠀⠈⠳⢤⣀⠀⠀⠘⠦⠄⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠈⠻⣶⣌⣻⣷⣦⣤⣤⠶⠋
⠀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠉⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣤⣤⣴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⢤⢀⡀⠀⠀⣰⡃⠀⡠⢤⣄⠀⠀⠀⠀⣠⡤⢄⠀⢸⣆⠀⠀⢀⡀⡤⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡖⢾⣀⣟⣸⢋⡏⠀⣟⡀⢸⠐⠓⠉⠀⠀⠀⠀⠀⠀⠉⠚⠂⡇⢀⣻⠀⢹⡹⣇⣻⢀⡷⢲
⠀⠀⠀⠀⠀⠀⠀⠙⡎⠉⠉⣉⡾⢤⣴⡋⣽⠸⡀⠐⠜⠃⠠⠤⠤⠀⠘⠳⠂⢀⠇⣯⢹⣦⡤⢧⣉⠉⠉⢱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⡔⠉⠀⠳⢾⡀⠙⠒⠒⠶⢄⡀⢀⡠⠷⠒⠒⠋⢈⡷⠞⠀⠉⢢⣀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⠀⠀⠀⣸⠀⠀⠀⠀⣀⣀⠈⢀⣠⣀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠛⠛⠛⣻⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡟⠛⠛⠛⠛⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢰⠃⠘⠦⣄⠈⠛⠛⠋⠙⠛⠛⢁⣠⡴⠃⠘⡄⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠦⠤⠤⠤⡆⠀⠀⠀⠈⠙⠓⠶⠦⠶⠶⠚⠉⠁⠀⠀⠀⢱⠤⠤⠤⠴⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣄⣀⠀⠀⠀⠀⠓⢸⡄⠀⠀⠀⠀⠀⣀⡠⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠉⠙⠛⠒⠒⠚⠓⠒⠒⠛⠋⠉⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠛⠛⠛⠒⠒⢺⡗⠒⠒⠛⠛⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⡷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⠈⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣎⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠚⡓⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⠤⠜⠒⠒⠒⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⠤⠤⠒⠒⠉⠉⠉⠙⠲⣄⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⠊⠁⠀⠀⠀⢠⠖⠒⠒⠦⣄⠈⢣⠀⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⠀⠀⡰⠚⠲⡄⠸⡀⠀⠀⠀⠈⡇⠀⡇⠀⢀⡜⠀⠀⠀⠀⢀⡖⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⢰⠁⠀⠀⢰⠀⠈⠓⠤⠄⠴⠁⣰⠃⠀⠘⡆⠀⠀⠀⠀⠀⣇⠘⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠘⡄⠀⢹⡀⠀⢀⡌⠰⠀⠉⠁⢀⣈⡞⠁⠀⠀⢰⠇⠀⢀⡤⠖⠛⠁⣀⣂⠗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠘⢦⡀⠉⢊⠉⠀⠀⡠⠴⠉⢡⡈⢻⣆⠀⢀⣾⠴⢊⢁⠂⡊⠌⠂⡤⠚⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢆⠀⠉⠓⠲⠤⡔⢊⠁⠸⢁⠐⣮⠟⣨⡇⠤⡐⠀⠁⠓⢈⡠⠴⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠘⣄⠠⢒⣾⠭⠲⣉⠬⡱⠐⠉⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣓⠶⠶⠈⠉⠩⠐⢧⠀⢋⣀⡠⠖⠀⠙⣄
⠀⠀⠀⠀⠀⣰⠲⣄⡀⠀⢀⣀⡠⠴⠒⢋⣁⠐⡄⠠⠁⠈⢀⡤⡐⠧⠀⢣⡄⠲⢃⠀⠈⣆
⠀⠀⠀⠀⠘⣄⠐⢊⢙⠓⠋⡀⢄⡈⠡⠂⠂⣈⡡⠴⢆⠀⢁⡄⠀⣘⣇⠀⢶⠈⡀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠉⠢⣱⢨⠀⠐⠊⢀⡠⠔⠋⠁⠀⠀⠘⡄⠀⠰⠌⢀⠉⢦⡪⠚⠀⠀⢈⢄⠈⠢⢄⣀⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠉⡤⠖⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠁⢀⠀⠀⠀⡠⠀⠢⠀⢀⠐⠢⡨⣉⠓⠲⠋⠠⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢨⠐⠒⠄⠀⠀⠀⡀⢀⣀⣀⣀⣀⠀⠐⠢⢆⠂⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡀⠌⡐⠁⠀⡠⠖⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠁⠢⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠂⠐⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠃⠨⠐⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣠⡄⠠⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠇⠀⠀⢹⠀⠀⠀⠀⠀⢀⠔⠚⠓⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⢸⣿⠀⠀⠀⠀⢠⣇⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⣆⠀⢀⠞⠀⠀⠀⠀⢸⠿⠃⠀⠀⡸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⠊⠉⠑⠀⠀⠘⢤⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠛⢿⠛⠉⠉⠙⢿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢰⠉⠣⠤⢤⣀⣈⣙⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⢄⡀⢀⡠⠤⠤⠤⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡀⠈⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠉⠉⠓⠲⢤⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣀⣀⣀⣀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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