Rosé Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣙⣶⣴⣾⣿⣿⣿⣿⣯⣿⣯⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣅⢸⣿⠀⠀⠀⣠⣾⣿⢟⡿⠟⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⣠⣿⣿⣷⣿⡵⠿⠟⠉⠻⣅⣉⣴⢸⣿⣿⢹⠏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠛⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣆⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⠿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡷⣄⢀⣠⣴⣾⣿⢿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠐⠒⢦⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢼⠁⠀⡀⠀⠀⢀⡠⠂⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢰⠀⢷⠀⠀⢀⡎⠀⠒⢋⡡⠔⠂⠓⠀⠀⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⠀⡆⡼⣠⡏⠀⠀⠈⠀⢀⡀⠁⡀⣀⡀⠀⠀⠀⠢⠳⢄⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⣿⡦⠀⢰⠂⢸⡀⠀⠊⣳⡀⠈⠴⢆⠤⣀⠀⠈⠉⠀⡣⠠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠀⢹⠀⢳⡷⡡⠈⢆⡸⢷⡀⢣⣿⢣⡀⠐⠒⠲⡄⢡⠀⠀⡆⠘⣀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣿⣿⠻⡀⠀⢿⠹⣆⠈⢷⣤⣥⡈⣿⣶⡙⣶⣗⠀⠈⠉⠀⠀⠁⠀⠈⠙⢢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⢙⣿⣶⠀⠀⠈⠓⠿⣦⡈⢯⡛⠭⠛⠻⢿⣾⠾⢷⣼⣠⣇⡀⣀⣀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡴⣻⠁⢻⣦⣄⠀⠀⠀⠀⠙⠮⣧⣶⣤⣦⢀⣉⣁⣂⢀⠈⣭⣽⣿⡏⠀⠀⠸⠀⠀⢸⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣾⠀⠀⣿⣯⣿⢦⣕⣒⣄⠀⠉⠻⢷⣄⡀⠢⢤⣄⠈⢈⠈⢉⣁⣠⣴⣿⠄⠀⢀⡿⠁⠉⠉⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⢿⣿⡀⠀⠘⣿⣿⡇⠈⣁⣽⢷⣤⣤⣤⣈⠉⠛⠦⣄⣀⠀⢏⣿⣿⣿⣻⠋⠀⠀⠊⠁⠀⠀⠉⠀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢈⣿⠏⢸⡿⣇⠀⠀⠈⠻⣗⣀⣿⣿⣤⡀⠈⠙⡟⠛⠒⠲⡾⣯⣟⣿⡿⠿⠛⠁⠀⠀⡀⠀⠀⠀⣸⡦⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡟⣏⡔⠀⣾⣿⣷⣄⣀⠀⠈⠻⣟⣋⣹⣛⠻⠶⠾⠿⠤⠧⠿⠽⠿⠞⠛⠛⠁⠀⠀⠈⣥⠀⠀⢰⣧⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡏⠙⢻⣷⣔⡝⠹⣻⠛⡿⣿⣿⣶⣄⡉⠻⢯⣍⠒⠤⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⢴⣶⣶⠏⣱⠚⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⡇⠀⠈⢻⣿⣿⣦⣻⣔⣏⡿⣿⣿⣿⣿⣿⣷⠎⡇⠀⢹⣶⣤⢏⣿⣿⣿⣿⣿⡷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣶⣶⡀⠻⡏⠉⠍⣹⢿⣏⣿⣿⣿⣿⣿⢿⠀⣷⠀⠠⣸⣏⣾⡿⠿⠛⠋⡉⠈⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⡄⠀⠴⠊⣿⣿⣿⡟⣵⣷⣿⣆⠸⣤⡶⠛⣩⡶⠶⠖⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣷⠙⡆⠀⢠⣿⣿⣟⢟⣻⣧⡿⠿⠤⢟⣒⡉⠁⠀⢀⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣼⣶⣤⣘⣿⣿⡶⠚⠉⠀⠀⢠⣶⣟⣿⣿⣶⣾⣿⠯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠈⢏⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠠⠶⢶⣶⡶⠶⠿⣿⣿⡿⡿⠿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣀⣸⡷⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⣀⣀⣠⣾⣿⠿⠋⣽⠏⠙⣿⠟⠻⠿⣿⣿⣿⣧⣽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⣼⠏⠁⡸⠃⠀⠀⠀⠀⠀⠀⠈⢻⡍⢿⠸⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⣿⢸⠇⠔⣽⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡓⢄⠀⢹⣿⠋⣀⢸⣿⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⢟⣫⠴⠶⠶⢷⣍⠈⢷⣀⢡⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⢁⣤⡤⡒⡠⣟⢦⡀⠈⡎⠹⣏⡀
⠀⠀⠀⠀⢠⣤⢞⡵⢇⣧⡘⢩⣿⠀⡇⣁⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠘⢿⠁⠀⠀⣌⠃⢺⠏⡸⢁⠿⢺⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠈⣵⢤⣊⡉⠉⣀⡴⢃⡎⢠⡟⢀⠊⡣⠀⡀
⠀⠀⠀⠀⠀⠐⡇⠀⠀⣹⡟⠛⠉⣉⣤⠟⠉⢉⡼⣡⢾⣿⡄
⠀⠀⠀⢀⣴⣣⡱⣄⠀⠈⠉⢉⠟⠀⠀⢀⣀⡿⢰⢃⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠿⠾⠵⠒⣂⠓⣒⣦⠥⠤⠤⠅⠇⢠⣿⣿⡏⡠⢤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣧⠙⠿⣻⣾⠿⠿⠶⢌⣻⡟⠀⢴⣿⡿⠁
⠀⢀⣠⣤⠴⠶⠤⠤⣄⠁⢿⣯⠤⡼⠯⣤⣀⠀⠀⠀⠈⠉⢹⠚⠋
⠀⠀⠙⣿⣿⣿⣷⣦⣠⢠⡟⠁⠀⣠⠦⠤⢌⣙⣶⡖⠦⣄⠀⠙⢦⡀⠀⢀⠴⣲⣿⡇
⠀⠀⠀⠀⠙⠿⢿⣿⣿⣽⣧⠖⡿⢁⡴⣾⡛⣝⢯⣿⣄⠈⢳⡤⢤⡷⠐⢃⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡠⠋⣸⡇⢸⡇⣯⡾⣿⢿⣿⣾⠏⡟⠀⠀⣿⠈⢿⠀⢼⡿⠟⠁⠀⠀⠀⠀⢀⡴⢦⢤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⢳⣴⡗⣸⡿⠵⢋⣼⢋⡴⣧⣀⡴⡿⠀⢸⡄⣀⡀⢤⣀⡀⣀⣀⠤⠾⢦⣖⣚⣪⠅
⠀⠀⠀⠀⠀⠀⢸⣆⠀⢸⡀⠈⢷⣀⣈⠿⠉⣰⠟⢀⡿⠀⣰⠃⠀⣼⢁⣴⣶⣿⡿⣱⠯⣧⠤⠴⢶⣤⣬⢯⠶⠆⠠⢄⣠⣤
⠀⠀⢀⣤⣖⣈⣜⣧⠀⠀⠙⢦⣤⠬⠤⠶⠛⢁⣠⠞⣡⠞⠁⣠⣾⡟⠾⠿⣟⡋⢰⣿⡶⢯⡼⣀⡾⢕⣢⠌⣷⢠⣶⣿⠟⠃
⠀⠀⠀⠙⠻⢿⣿⣮⠳⡀⠀⠘⠳⣶⣶⣶⡾⠿⠗⠋⠁⠀⢀⣿⣿⣤⡤⣄⠈⠙⢦⡉⠑⠺⡛⠓⠺⡉⢀⣛⣁⡉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⣠⠞⣀⣤⣴⡀⠒⣏⠀⠀⠙⢻⡷⠶⠴⠶⢒⣽⡜⣿⣿⣿⣿⣿⣦⣄⠹⣆⠈⢿⣿⣶⣜⢎⢿⣿⣿⣿⣷⣦⣽⣄
⠀⠀⠀⠀⣴⣡⣾⣿⣿⠟⡇⣾⣾⠲⢤⣤⡿⠀⠀⢠⢱⣿⡿⠁⠈⠻⢿⣿⣿⣿⣿⣷⣼⣇⠀⠙⠻⠿⠿⠄⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠱⡿⠋⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠐⠒⢄⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠠⡍⠀⠀⠀⠀⠁⢀⡠⠂⠀⢀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⡇⠐⣇⠉⠀⢀⡊⠐⠒⢊⣉⠵⠤⠒⡀⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⢠⢀⡇⣸⠏⠀⠀⠈⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⢌⠣⡈⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡾⢻⣿⣄⠀⣤⠀⣆⠈⢰⠚⣧⠉⠉⢰⡆⢀⠀⠀⠈⠓⠀⢸⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠘⡇⠸⣽⣌⠀⠹⡀⡼⣦⠸⢀⣿⣇⠀⠠⠤⠤⡈⢀⠀⠀⡄⠐⠆⠀⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣹⣷⡷⡇⠀⠸⣞⢷⡀⠹⣧⣘⣃⢸⣿⣌⠳⣤⡦⠀⠑⠚⠀⠀⠁⠀⠘⠒⢦⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠛⢿⣷⡌⠀⠀⠙⠮⣷⣀⠹⡟⠿⡛⠿⢿⣧⣳⣽⣦⣰⠂⡄⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⢀⡴⡟⠻⣧⣀⠀⠀⠀⠈⠙⢦⡹⣇⣤⣀⣀⠙⠛⠂⠭⠭⠙⠛⢳⣾⣟⠀⠀⠘⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⣾⣄⡇⠀⢹⣿⣳⣦⣀⠤⣄⡀⠉⠻⣿⣯⠉⠈⢉⡙⠓⠘⠒⠛⠛⠛⠁⢀⣤⡄⠃⠀⣼⡇⠐⠲⠶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣿⡇⠀⠈⢿⣿⣷⡋⠛⠚⣷⣄⡀⣀⡉⠛⠷⣤⣈⠉⠉⠐⡦⣶⣾⣿⡿⡿⠁⠀⠠⠟⠀⠀⠠⠊⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⢿⣿⠋⣿⣷⠀⠀⠈⢿⣿⢁⢰⣺⣯⠙⠛⠛⢷⡶⡤⢀⣈⣹⣷⢦⣽⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⣤⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⣿⠏⡀⢛⣿⣧⡀⠀⠀⠙⢷⣾⡿⠿⠿⣦⣴⣀⣧⣤⢀⣌⣷⢿⣿⣛⣿⡤⠅⠀⠀⠀⠖⠀⠀⠀⣼⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠿⣾⣾⡀⡸⡿⣿⣿⢶⣦⣤⣄⣈⠲⢶⣿⡲⢤⣉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣄⣿⠇⣠⣤⣟⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠑⠀⠀⢿⣿⣾⣥⠡⡏⢸⣏⣿⣿⣿⣷⣤⣬⣙⢳⡄⠉⣟⣛⠒⡶⣤⣤⣤⣶⣶⢖⣫⣾⡟⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣄⣀⠀⢻⣿⠿⠶⠿⣾⣾⢹⣿⣿⣿⣿⣿⣿⠸⣃⠀⠘⣷⡿⣱⣿⣿⣿⣿⠿⠿⠽⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣧⣄⡛⡀⠐⠐⢊⣿⣾⣿⣿⣿⣻⣏⣿⠀⢿⠀⠰⣾⠷⠟⣛⣉⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⣄⠀⠉⢸⣿⣿⣿⣽⣿⡿⣿⣧⠈⣾⢋⡡⠾⠝⠛⣩⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⣿⣿⡇⡙⡀⠀⣼⣿⣿⢏⣧⠽⠓⠛⠋⢁⣭⣶⣄⠀⣀⣴⡿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣰⣿⣿⣶⡼⢿⡿⠋⠀⠀⠀⠀⣴⣿⣭⣿⣾⣿⣿⡿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠈⡆⠀⣴⡀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠛⠛⠿⠟⣛⣛⠻⠾⠟⠻⠛⠋⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⠿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣠⣤⣴⣾⠿⠟⠋⣰⣟⠀⢸⠟⠉⠛⠛⠿⠿⠿⣶⣼⣿⡿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⢰⡟⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⡌⢷⠸⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⣧⣻⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⣞⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⠒⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢀⡀⠒⠂⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⢀⣴⡆⢀⣴⠋⠁⣤⣬⣹⣿⣄⡄⢠⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢇⠀⠍⢱⣬⡵⢾⠟⠛⢿⣿⣿⣇⢻⣾⠟⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢈⠈⢭⠓⠂⠀⠴⣿⣿⣴⣿⢛⣥⢾⣿⡆⠀⠒⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⡀⢠⣿⡆⠀⠀⠀⠀⣂⡈⣓⠺⣧⣀⣠⣦⣬⣭⣍⣽⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣤⣄⡀⠀⠈⢳⣽⣿⣤⣤⣬⣉⣛⠻⢿⣿⣿⣿⠟⠁⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⢉⡙⠻⣿⣧⡀⠀⣀⣙⡛⢿⣿⣿⣿⣋⣿⣿⣿⣿⣵⣶⣿⠛⣿⣟⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣿⠿⣿⢿⣿⡿⠋⢉⣿⣿⢿⣿⣿⣿⣿⣿⡏⠉⠻⣼⡁⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⣀⡡⠉⠉⠀⠀⠀⠀⠛⠋⠁⠈⠿⣿⣷⣷⡀⠀⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣉⠀⠄⠀⠀⠀⠀⠀⢀⣠⣾⢿⣦⣾⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡻⣿⣦⠀⠀⠀⠀⢐⢋⣶⣿⣺⣿⣿⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠹⡟⠛⠉⡻⣧⣀⣀⠈⢨⣿⡍⣿⡿⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣬⣛⣶⣬⣿⣿⣿⣦⠈⣿⡏⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⢁⠋⠀⢱⣤⠇⠀⠀⣀⣴⡆⠀⠀⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠃⠀⢀⣾⣿⡿⠿⢤⣾⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡔⠀⣴⣿⣿⣿⠋⢸⣠⡿⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣾⣿⣿⣿⢀⣁⣸⣿⣧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡹⠿⣿⠿⣿⣿⣿⣿⡦⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠠⣴⣿⡷⢶⣮⠭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⡴⢚⣉⣁⡀⠁⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⠴⠃⣠⠞⢁⡞⠋⠀⢀⡔⢋⠉⠀⠠⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢣⠀⢸⡆⠀⠀⡸⢠⡎⠉⠢⠀⠈⢣⡄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⣠⠏⢀⣾⡇⢆⡇⢡⠘⢌⢂⣰⢱⢀⠀⡥⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣼⡏⢀⡞⠁⠘⢦⠱⣀⠀⣠⣤⣥⡖⣚⣐⣡⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⡎⠀⠀⠀⠈⢆⣀⣉⠢⡀⠤⠒⠋⠉⠁⢀⡞⠁⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠢⢄⠀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠳⣌⠢⢄⡉⠐⢲⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠙⠄⠀⠀⠉⢻⡇⠀⠀⠀⠀⠛⣀⡠⠤⠶⠶⠤⢄⡠⢀⣨⠷⠖⠒⠛⠉⠀⢰⠖⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⡀⠀⠈⡄⠀⢀⡼⢷⡀⠀⢠⡖⠛⠓⠤⣀⢀⣠⣤⡀⠈⠋⢁⣀⡀⠀⣿⠛⠒⠋⠀⢨
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠢⣰⠀⣸⠁⡜⠁⠀⠀⣙⡷⣾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠑⠢⠞⣹⠟⠊⠁⠀⢀⡶⢤⠎
⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⡇⣸⢁⡠⠖⠋⢁⡞⢉⣷⣤⣄⣀⣀⡀⠀⠀⣀⣀⡤⢞⣁⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠉⠁⠒⠠⠈⠟⣁⣁⣀⣀⡼⠉⡴⠋⠁⢡⠉⠉⠉⠉⠛⠿⣟⡶⠾⠛⠉⠉⠑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⣀⣤⢸⠀⠀⣠⠟⣠⠊⠀⣀⠤⢼⡴⠂⠤⠤⢤⣀⠀⠙⢄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠈⣇⢀⠔⢡⠼⠁⠀⡼⠁⠀⠈⠀⠀⠀⠀⢠⠟⠀⠀⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⡴⠃⠀⢀⡼⢁⣠⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⣓⣒⣀⡛⠻⢭⡐⠢⢄⣀⣠⠔⠛⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠖⠉⠀⠀⠈⠙⢦⠀⠈⠢⡀⠈⠳⡒⠤⠄⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡄⠀⢳⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠷⠦⠤⠤⠤⠶⠒⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⢠⢊⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡇⢸⠃⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢢⣼⡡⠞⡰⠖⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⡀⡜⠁⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⢤⣀⠀⡁⠀⠈⠁⡇⠀⠀⠀⢳⠀⣀⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢒⡶⠋⠀⠀⠀⠀⠈⠉⠢⡀⠈⠳⣇⠀⢰⠂⠀⠀⠀⢀⡮⠞⢋⠨⠵⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠀⠤⠤⣄⡀⠀⣠⠊⠁⠀⡤⠒⠋⢐⣲⡤⠤⠤⠄⡀⠀⠀⠘⡆⠀⠘⡧⣌⡙⠓⠒⠚⠉⠀⠚⢥
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠸⠀⢠⠊⠀⢀⠤⠠⢤⠀⠘⠦⡀⠀⠸⠀⠀⠘⣄⣜⠉⠉⠉⠉⠓⢦⡀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠒⠦⣄⣨⢧⠀⠀⠀⠰⠀⣼⢆⠠⣡⠖⠀⠒⣿⠀⠀⣸⠀⠀⡇⠀⠀⢁⠈⠉⠲⣄⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⣠⠖⠋⠁⠘⡆⠀⠀⠀⠱⠝⣄⠙⠢⠤⠖⠊⣛⡤⠊⡌⢀⡴⠁⠀⠀⢸⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢑⠞⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠆⠈⠢⡀⠀⠠⠀⠉⠀⠀⣧⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠹⡀⢀⡴⠊⠉⠉⠙⢆⠀⠀⡎⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠲⢄⣀⡀⠀⠀⣳⠋⠀⠀⠀⠀⠀⠀⠑⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⢊⠝⠋⠁⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⣧⠤⢤⡀⠀⠀⠀⡴⠿⠶⣤⡈⠉⠀⠒⠠⠶⠶⠒⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡤⠂⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⢀⣀⣀⣀⠠⣤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠙⠳⢦⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠒⠒⠒⠒⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠚⢻⠤⠤⣤⡤⠤⠴⠶⠒⠈⠿⠄⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣀⣀⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠢⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠶⠋⠉⠀⡴⠛⡏⠉⠓⠲⡖⠒⠒⣶⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⠞⠁⠀⢰⡄⠀⠀⠁⠀⠀⣿⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠙⠲⢤⣤⣀⣀⣀⠤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠊⠀⠀⠀⢸⠛⠦⣄⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠉⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠤⢶⠤⣄⡀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠠⠀⣬⣤⣄⣉⣵⣦⣾⣿⣿⣿⣿⣿⣿⣿⣭⣯⣧⣄⠙⣿⣿⣿⣿⣿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⣾⣿⣿⣷⣶⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣯⢻⣯⠂⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣰⣿⠟⠟⠋⠉⠁⠀⣠⣿⣿⣿⣿⣟⡿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣦⣿⡆⢸⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⢟⣽⡾⠋⣹⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⡇⢸⣿⣿⢣⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⣾⣿⣿⢯⣿⣿⣤⣾⡿⠟⠋⠙⢿⣑⣉⢁⣼⢠⣿⣿⣿⢸⣧⠉⣾⣿⣿⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿⠀⠀⠀⣾⠙⠿⠻⢿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣼⣿⣿⣿⣸⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢸⡀⠀⣼⣿⣧⡀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⣵⣿⣿⣫⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣠⣤⡞⣿⣿⣿⣦⣧⣰⣿⣿⣿⣿⣆⡀⠀⠘⢿⣷⣦⣄⣀⡀⠀⠀⠀⢠⣄⣀⣴⠞⢻⣿⢟⣽⠟⠙⠻⠿⢋⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠀⢿⢿⣿⣿⣿⣴⣶⣿⣿⣿⢏⣴⣿⠟⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠘⢻⠿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣳⡾⠛⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⡻⣿⣿⣿⣷⣦⣀⣭⣩⣻⣿⣿⣿⡋⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋⣤⡿⠟⠋⠛⠛⠛⠛⠿⢿⣾⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡽⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣈⣻⣡⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠀⠉⠉⠉⠉⠙⠻⣿⣄⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣾⣿⣿⠿⠿⠟⠻⠟⣛⣂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣉⣉⣀⣭⣹⣿⣿⣟⣫⣯⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣭⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⣿⣯⣷⣿⣿⡿⠛⠛⢦⣴⣾⣿⣿⣿⣟⣻⣿⣭⣭⣭⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⡼⠟⠛⠉⠉⠛⠻⠿⠿⢿⠿⠿⠿⠛⠉⠀⠀⠀⣼⣿⣿⣿⣿⣟⣯⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣾⣿⣿⣿⠿⣟⣻⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠛⠛⠛⠛⠟⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢬⣾⠿⠟⠁⠀⠀⠈⠙⠿⠿⠿⣿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⢀⡴⢠⡀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠀⠀⠀⠏⠀⠀⠉⢠⠀⡀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⡃⢿⡀⠀⠀⠀⡄⠀⠀⠀⡄⢡⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠐⠤⢄⣀⠁⠌⠁⠀⠀⠀⠓⠂⠀⠁⠙⠚⠟⠒⠀⣀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⡀⢸⡀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠔⠀⠀⢀⡠⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠙⠛⠀⢀⡜⠊⠀⠀⠀⠀⠀⠠⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠠⠐⠈⢱⠄⠀⠀⠀⠈⠀⠀⢀⣀⣈⣲⡒⠀⠶⠓⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢀⠟⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⠄⠀⠀⠀⠀⠐⠉⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠛⠁⠀⠀⠀⠀⠀⠓⠒⠛⠓⠲⠶⡒⡟⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠛⠒⠒⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠻⡀⠎⠀⠀⠀⠀⠀⠉⠉⠓⠐⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣶⠶⣦⡀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⠀⠀⠴⠟⣉⠉⠉⠃⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠈⠳⡶⢶⣤⣤⠅⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⢳⣤⣤⣤⣤⠄⠀⠈⢀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣙⣷⣿⠁⣠⡴⠶⠋⠉⣉⣯⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠉⠻⣅⣾⣥⡴⠂⠀⢉⣉⣤⣤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⡘⣿⡏⠀⠐⡛⠉⠁⠀⢠⣶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⢄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠀⠀⢠⡟⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡖⣠⠞⠀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣈⠻⣦⣤⣤⣦⣴⣤⡶⠋⠀⣸⣟⣁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣯⣭⣤⣴⣦⣀⣠⣾⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣲⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣿⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢣⣿⢵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠈⠱⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡔⠁⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠏⠀⠀⣠⢰⣿⣏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡻⠀⢀⣼⢣⣿⡿⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣗⣅⣠⣿⣟⣿⣿⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣄⠀⢈⠻⣶⡀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣿⣿⣟⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠛⠳⢄⠀⠀⠀⠈⡇⠀⠀⠀⠘⢻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⡇⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣐⠀⣀⠀⠀⠀⠀⠀⠀⠘⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠛⢿⣿⣦⣿⣤⣤⣀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣆⠈⠉⠙⠻⢿⣿⣿⣷⡄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣭⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⣥⣄⣤⣀⠀⠀⠀⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⠚⠛⠂⠼⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣀⣼⠁⢠⡀⠢⠶⣠⡁⠀⡀⣤⣀⣶⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠙⢿⠀⢸⡇⠀⠀⠁⡈⡀⠑⢛⣿⣿⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣧⡒⠂⠛⠢⣀⠀⠀⠀⠣⠀⡍⢩⠟⡀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠠⡺⡄⠸⡄⠀⠹⣿⣷⡀⠈⠉⠀⠀⠀⠀⠠⣀⣀⠀⠁⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣽⣦⡀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⢀⣼⠿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠄⠈⠙⠻⣽⡟⢿⣾⣷⣦⠀⠀⠈⠀⠀⣀⡤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⣀⠀⠉⠻⣿⣯⣄⡀⠀⠀⠤⠾⣿⡟⠀⣠⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠢⣄⠈⠙⣿⢿⣶⣦⣤⣾⠋⠴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀⠀⠘⢿⠿⠛⠁⠚⠛⠉⠉⠁⠀⣔⡴⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠚⠂⠃⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠨⠐⠢⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣷⡄⠀⠀⣠⡆⠀⣀⡴⠛⠁⣀⣈⠙⣶⣶⠀⡀⠈⣥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠀⢘⠟⢣⠐⠛⣣⣶⣶⡿⢿⣷⣾⣿⠛⣷⣄⣿⡟⢁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠇⠸⠿⣟⣉⠛⠁⠀⣸⣿⡿⠻⣧⣼⡿⢋⣴⣏⠀⠁⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠈⠂⢠⡀⠰⣎⠉⠉⠉⠛⢿⣿⣷⣿⣿⣡⣶⢏⣿⠿⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣤⣀⣀⣿⣿⡆⠀⠀⠀⠀⢪⣀⠈⣉⡛⠿⣦⣤⣤⣶⣶⣶⣦⣤⣿⣿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠉⢳⣜⣿⣦⣀⣤⣍⣉⣙⠻⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡉⠛⠿⣿⣿⣷⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣟⠿⢻⣿⣿⣿⣿⣋⣥⣼⡶⠳⣾⣿⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢻⣶⣶⣿⣿⣷⣶⣶⣿⡿⠷⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣟⢷⠀⠻⠿⣿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠙⠿⠉⠿⠩⣿⡿⠋⠀⠀⠛⢿⣿⣽⠿⠛⢿⣿⣿⡟⣇⠀⠈⠙⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠔⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⢿⣿⣿⣦⡀⠀⠸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠀⠀⢀⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣷⣤⣼⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⢷⣶⣤⡄⠀⠀⠀⠀⠀⢰⠞⣉⣿⢸⣿⣿⣿⣭⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣽⣿⠧⣤⡄⠀⠀⠀⢆⢰⣿⡿⣶⣿⣿⣿⣥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⠀⠈⢯⣁⡀⠐⢜⣿⣦⣴⡆⠀⢸⣿⡇⣿⣿⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣮⣽⣷⣶⣿⣿⢿⣿⢆⠈⡿⡇⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠉⠉⡿⠃⡸⠁⠈⢻⣤⠗⠀⠀⠀⢀⣴⣶⠀⠀⢀⡶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡀⠄⠀⠐⠁⠀⠀⣾⠏⠀⠀⢀⣾⣿⣿⣿⡄⣰⣿⠷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡈⠁⣠⣴⣶⣿⣿⠟⢰⠄⣴⣿⡟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣰⣿⣿⣿⡟⠳⠄⢸⣶⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠨⣿⣿⣿⣿⣇⣴⣴⣾⣿⡟⠚⠓⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⠟⠛⠿⠿⠿⣿⣿⣿⣿⡻⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⡤⢠⣾⣿⣿⠿⣶⣦⢭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣏⣻⠿⠿⡁⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣠⠼⢛⠋⠉⠀⠒⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⠴⠃⡤⠊⡱⠋⠁⣡⠒⣉⠀⠠⡀⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡧⠀⣧⠀⠀⡏⡾⠁⠐⡀⠈⠶⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⡼⠁⡼⠻⣝⢇⠀⠀⠀⠞⣘⡤⠼⡱⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠸⡇⡜⠀⠀⠈⡄⠑⠨⡉⠉⠵⠖⠚⠁⡴⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠂⠄⡀⠀⠀⣀⣀⡇⠀⠀⠀⣿⠁⠀⠀⠀⠈⠉⠓⢌⠢⢀⡀⢂⡼⠃⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢆⠀⠀⠹⡇⠀⠀⠀⣉⡤⠴⠶⠒⠒⠦⣄⣤⠛⠒⢚⣉⠀⣸⠓⠋
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠌⣆⠠⠀⢰⠀⡠⠚⠻⢤⣀⡎⠉⠉⠐⠤⠴⠒⠠⡀⣠⢦⣤⡸⠏⠉⣁⢀⡆
⠀⠀⠀⠀⡤⠚⠉⠀⠀⠀⠀⠐⠇⡎⡸⠁⣠⠴⢂⡽⢧⣀⡀⠀⠀⠀⠀⠀⢀⡡⠊⠁⠀⠀⢠⠏⠉
⠀⠀⠀⠀⠀⠢⡀⠀⠐⠂⠀⠀⠈⠗⣁⢉⢀⣰⢋⡴⠋⢉⠙⠛⠛⠲⢾⣿⠭⡖⠛⠓⠢⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⣤⡈⠀⢀⠞⡱⠋⢀⠤⢸⡜⠒⠠⠤⣄⠈⠳⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡧⡴⢡⠞⠀⢠⠋⠀⣀⠀⠀⠀⣠⠋⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠰⠁⠀⠴⣧⠶⠉⠀⠀⢀⡴⠅⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠴⠒⠈⠛⠲⣄⠉⠢⡈⠙⠯⠄⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠔⠁⠀⠀⠀⠀⠀⠸⡀⠀⠐⠄⠈⡆⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡟⠒⠒⠒⠒⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⢠⢊⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡇⢸⠃⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢢⣼⡡⠞⡰⠖⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⡀⡜⠁⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⢤⣀⠀⡁⠀⠈⠁⡇⠀⠀⠀⢳⠀⣀⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢒⡶⠋⠀⠀⠀⠀⠈⠉⠢⡀⠈⠳⣇⠀⢰⠂⠀⠀⠀⢀⡮⠞⢋⠨⠵⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠀⠤⠤⣄⡀⠀⣠⠊⠁⠀⡤⠒⠋⢐⣲⡤⠤⠤⠄⡀⠀⠀⠘⡆⠀⠘⡧⣌⡙⠓⠒⠚⠉⠀⠚⢥
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠸⠀⢠⠊⠀⢀⠤⠠⢤⠀⠘⠦⡀⠀⠸⠀⠀⠘⣄⣜⠉⠉⠉⠉⠓⢦⡀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠒⠦⣄⣨⢧⠀⠀⠀⠰⠀⣼⢆⠠⣡⠖⠀⠒⣿⠀⠀⣸⠀⠀⡇⠀⠀⢁⠈⠉⠲⣄⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⣠⠖⠋⠁⠘⡆⠀⠀⠀⠱⠝⣄⠙⠢⠤⠖⠊⣛⡤⠊⡌⢀⡴⠁⠀⠀⢸⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢑⠞⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠆⠈⠢⡀⠀⠠⠀⠉⠀⠀⣧⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠹⡀⢀⡴⠊⠉⠉⠙⢆⠀⠀⡎⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠲⢄⣀⡀⠀⠀⣳⠋⠀⠀⠀⠀⠀⠀⠑⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⢊⠝⠋⠁⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⣧⠤⢤⡀⠀⠀⠀⡴⠿⠶⣤⡈⠉⠀⠒⠠⠶⠶⠒⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡤⠂⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⢀⣀⣀⣀⠠⣤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠙⠳⢦⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠒⠒⠒⠒⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠚⢻⠤⠤⣤⡤⠤⠴⠶⠒⠈⠿⠄⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣀⣀⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠢⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠶⠋⠉⠀⡴⠛⡏⠉⠓⠲⡖⠒⠒⣶⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⠞⠁⠀⢰⡄⠀⠀⠁⠀⠀⣿⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠙⠲⢤⣤⣀⣀⣀⠤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠊⠀⠀⠀⢸⠛⠦⣄⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠉⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠖⣶⣦⡄⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⣀⠀⡖⠂⡇⣰⠛⣄⣣⠋⢹⣄⠈⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⣳⣷⣇⠀⣿⠹⠀⠈⣻⡾⢋⣸⠀⠀⠀⠁⢠⡄⣠⠔⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣠⠼⢦⡑⣾⣯⠭⠭⠿⠿⠏⡸⠀⢀⢰⠀⠀⣿⢁⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⡇⢸⡞⣏⣽⣶⣷⣼⠈⣶⣤⡖⠒⠖⡡⠚⠁⠈⢷⠰⣿⣾⣧⡾⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢠⠏⠣⣸⣇⣈⣣⣾⢼⡇⣠⡇⠈⢿⢶⣰⠇⢀⡖⢀⢇⣨⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠻⣬⣁⣀⣀⣼⠞⠁⢸⠀⣼⣾⡏⣷⣿⣶⣿⣮⣥⣤⣄
⠀⠀⠀⠀⠐⡶⠦⣔⣢⢄⢸⠀⠙⠲⢤⣤⣽⣟⡋⠁⠀⣠⠏⢠⣧⡶⣿⠀⠙⠳⣤⡙⠋⠀⠈
⠀⠀⠀⠀⠀⣨⠷⠞⠺⣿⣼⡷⢦⣀⠀⠀⠈⠉⠉⢩⣿⣷⡶⠞⠀⠳⡜⢦⣈⡒⢽⡵⡀⠀⠀⢀
⠀⠀⠀⠀⠂⡰⢀⣤⢸⣳⠈⠛⣆⢈⢓⣦⣄⣠⣴⣧⠘⢿⣿⣀⢀⠘⢮⡄⠈⠉⠂⢳⡙⠦⠬⠴⠇⠄⠂
⠀⠀⢀⣠⣎⢤⠞⠁⠈⢯⡇⣸⢁⣼⠟⢻⠋⠙⢿⠀⢇⠀⠀⠉⠋⠉⠛⢧⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣱⡿⠁⠀⢹⣆⡄⠸⡄⣾⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠉⠛⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠉⢉⡽⠋⡿⢿⣷⡆⠀⠀⣠⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⠀⢠⡔⠒⠘⡀⢠⡟⢳⡀⢃⡴⠃⢹⣦⠀⠈⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠠⣭⣳⣄⡇⠀⢠⣧⠏⡇⠀⠙⢾⣤⣴⠞⠈⣧⠀⠀⠀⠀⠇⠀⠀⠀⠀⣀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣴⠶⠿⣿⠧⢄⡀⣿⣤⣥⣤⣤⣤⣟⣡⡤⠴⡏⠀⠀⠀⠀⠀⠀⢽⣦⡾⣏⠈⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡎⠀⣠⡤⠾⠳⣄⠹⡿⣷⠶⠶⠖⠒⠚⠛⠃⢠⠇⠀⠀⡠⢷⠀⠀⢸⣿⠀⣻⠆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢒⡏⠀⣧⡼⣿⢛⣷⣤⣺⣆⣇⠈⢳⣤⣠⣤⡤⠤⣤⠟⣠⠖⠋⠀⠸⣦⠀⣾⣿⣼⣿⣀⣾⠿⠿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡾⣇⠠⣿⡇⠻⣿⠋⣽⠙⣿⡇⠀⢸⠟⠻⣶⣤⡀⠀⣴⠁⠀⢀⡄⢀⡞⠀⣼⣿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢀⡞⠀⠈⢦⣿⣧⣤⣬⡿⠿⠛⣽⢀⡴⠻⡄⠀⢸⡏⢿⡄⡇⠀⣠⠟⢀⡸⢳⣤⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⡇⠀⠀⠙⢷⣤⣀⣀⠀⠀⣰⣷⡟⠁⠀⡇⠀⢸⣿⣼⡇⢹⣾⣿⢶⣫⣴⣯⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣀⠀⢸⠉⠙⠷⣤⣀⣀⣉⣛⣿⡿⠟⠋⠁⠀⠀⣰⠇⠀⣿⣉⣭⣷⠋⠰⠾⣏⣁⠈⠳⠿⠛⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠧⣍⠉⣓⠲⢭⡷⠸⣄⠀⠀⠀⢈⠟⡛⠻⠷⠶⢤⣤⣤⣤⣖⣋⣀⣸⡟⢻⡉⢹⣄⠀⠠⡀⢹⡿⣔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠮⠿⠉⠉⣽⡿⣶⣟⡛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⡿⠛⠋⠀⢈⠹⣆⠻⢦⣤⡈⠢⣽⡘⣆⠈⠢⡀⠀⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠁⢠⠞⠐⣄⢰⡏⣧⠈⠛⢷⡄⠀⠙⢶⣄⣀⠀⢀⣴⣿⡁⠹⣿⣧⣇⠀⢀⠀⠙⣎⣆⠀⠉⠉⠓⢬⢻⡌⠦⣄⣈⣒⣼⠇⠠⠴⠁
⠀⠀⠀⠀⠀⡀⡰⠁⣠⡷⠋⠈⢷⠻⡄⠈⣾⠃⢸⣷⣾⢟⡿⠿⢿⣿⠉⢹⡄⠀⠙⠛⠻⡾⠷⠦⣬⣿⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠁
⠀⠀⠀⠠⠴⠞⠒⠚⠋⠀⠀⠀⠈⣧⣇⣼⠏⣰⣿⠟⠁⣾⠀⠀⠀⢹⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣠⣾⠟⠁⠀⠀⢹⣾⣰⠀⠘⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣻⠋⠀⠀⠀⠀⠀⠉⠻⢧⡀⡇⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠰⠟⣉⠉⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠛⠛⠶⠖⠀⠄⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠳⣄⣀⡀⣀⠀⠐⠋⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢈⣻⣿⠁⣠⠴⠚⢉⣻⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠙⢧⣾⡶⠂⣀⡠⠤⠤⠐⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠈⠂⣿⡀⠀⠁⠀⠀⢸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡖⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⣆⠀⠀⠀⠀⠀⢠⠟⢀⣆⡼⢁⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣬⡷⠶⠚⠒⠚⢋⣀⣾⣧⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣿⣶⣿⡟⠛⠛⠋⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡟⠀⠀⠀⠀⠀⠀⣰⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠙⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠔⠋⣱⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠇⢀⡸⣹⡿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⠀⠀⠹⣦⡀⠀⠀⠀⠀⢷⠀⠀⣿⣤⣾⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣬⣿⡄⠀⠀⠀⢼⠀⠀⠘⣿⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣸⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡀⠀⠀⠀⠀⠀⠀⠘⢄⢿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣬⣠⡄⣀⠀⠀⠀⠘⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡈⠻⠿⢿⣿⣷⣄⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠉⠙⠻⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣦⣤⣀⣀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠙⢻

⠀⠀⠀⠀⢀⣰⢶⠀⠀⠀⠀⠀⠀⡠⢾⡱⣤⠀⠀⠀⠀⠀⠀⡰⢺⣯⠀⢄⡀⠀⠀⠀⢀⡄⣖⠟⢿⣦⣀
⠀⠀⠀⣜⠋⠀⢸⠀⠀⠀⠀⠀⠀⡻⠀⠙⡌⡄⠀⠀⠀⠀⠸⣤⠳⣜⡯⠞⠁⠀⠀⠀⢻⠙⠫⢍⡻⠁⡇
⠀⠀⠀⠘⠢⠴⠋⠀⠀⠀⠀⠀⠀⠱⠤⣤⠵⠁⠀⠀⠀⠀⠀⠘⢅⣈⡠⠊⠀⠀⠀⠀⠈⠢⢄⡀⠁⠔⠁

⠀⠀⣀⠤⠀⣤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠤⡄⢢⡀⠀⠀⠀⢀⢤⣞⣑⡲⢤⠀⠀⠀⠀⠀⣠⠤⣔⡢⡀
⠀⠀⢧⡀⣟⢉⣧⡘⡄⠀⠀⠀⡀⡯⡞⠽⢣⣼⢸⠀⠀⢰⠋⣧⣾⣻⣫⢙⠦⡀⠀⠀⡎⢠⡾⠟⢳⣜⢢
⠀⠀⢧⡑⠄⠛⠾⡥⠚⠀⠀⠘⢤⡓⣚⣛⡫⢏⠎⠀⠀⠈⠢⡓⢅⣨⠶⣎⠴⠃⠀⠀⠉⡳⣥⠴⠆⠚⡎
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠚⠁⠈⠁⠀⠀⠀⠀⠀⠙⠲⠴⠚⠉⠀⠀⠀⠀⠀⠑⠒⠚⠑⠛⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠞⣽⣛⠤⣽⡀⠀⠀⠀⣰⢋⣿⣿⢵⢤⠀⠀⠀⢀⡤⠢⣮⣭⣷⠤⣄⠀⠀⠀⡠⡯⢯⡼⢻⣦⡀
⠀⢠⠋⣿⣸⣰⢵⡿⢸⠀⠀⢠⠃⠈⠉⠃⠜⡄⣇⠀⠀⠘⢆⡟⡝⠢⣿⣿⢸⡄⠀⢠⡷⢱⢭⣹⢿⠱⣘⠆
⠀⠈⠦⣝⠚⠯⠟⡳⠋⠀⠀⠐⣍⠣⣝⣋⠤⢁⡜⠀⠀⠀⢫⡙⠚⣲⠈⣉⠽⠀⠀⠈⢻⠢⡹⢾⣭⠼⡗
⠀⠀⠀⠀⠙⠒⠊⠀⠀⠀⠀⠀⠈⠉⠉⠁⠚⠉⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠀⠈⠓⠛⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⢀⣠⠃⠀⠈⠿⠛⠓⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣀⣠⣤⣼⠏⠀⢠⡆⠒⠲⢾⣠⣌⡀⠀⡀⢴⡆⣠⣾⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠻⣿⠀⠀⣾⡇⠀⠀⠀⠋⠀⠁⠀⢡⠬⠟⣿⣿⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢿⡄⣈⣇⣀⣿⣇⠀⢀⡀⠀⠜⠲⡂⠀⠠⡷⠿⣿⡇⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣤⣄⡀⠈⠉⣡⣄⠀⠄⠀⠀⠉⠀⠒⠒⠒⡏⢰⠆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢢⣙⢷⠀⠸⣇⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⡀⠀⠋⠀⠀⠀⢠⣶⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠆⠀⢹⣦⡀⠀⠻⣿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⡿⠗⠀⠀⠀⣠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠛⣻⣿⣶⠤⣽⣿⣯⣛⣦⣄⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⢀⣴⠞⠛⠁⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠀⠀⠀⠙⢳⣿⣌⣙⣿⣷⣿⠷⠆⠀⠀⠀⠀⠀⢀⣤⣾⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠐⠦⡀⠀⠀⠉⠻⣿⣿⣤⣄⣄⠀⠀⠀⠤⠞⢿⣿⡿⠁⠀⣠⣴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠳⡦⣀⠀⠈⠙⢻⣿⣿⣶⣤⣄⣀⣠⣾⠟⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠈⢨⣷⣦⣤⣤⢛⢈⣿⣿⠿⠿⠿⠛⠈⢉⡁⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠘⠻⠋⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡟⠾⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠆



⣿⣿⠿⠿⣿⢻⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣿⣟⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡶⠚⢙⡉⡉⢹⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⠀⣼⢹⠓⢶⡏⢖⣹⠇⡻⢿⡆⠀⣎⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣏⠀⠐⢿⣞⣆⡀⢻⣈⣭⢎⣵⣿⣶⣤⠼⠋⡸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠲⢬⣦⡀⣿⡟⢀⣽⣷⣻⠕⠉⣼⢋⠤⠄⣤⡜⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠓⠲⣼⣿⣾⣿⡞⢩⡉⠁⠤⢚⠝⠁⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣀⣤⣤⣄⣀⡴⠉⠁⠀⠀⣠⣿⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠋⠁⠀⠛⡻⣿⣧⣤⣆⣀⣴⠟⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠙⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣄⡀⠀⠀⠀⠀⠁⠀⠀⠹⡧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡘⢦⢄⠀⠀⠀⠀⠀⢠⡄⢀⠄⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢻⡦⡀⠀⠀⠀⠀⠁⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢤⠀⠀⡀⠁⣧⠀⣾⠀⠁⠀⡔⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠁⣀⡟⠀⡇⠀⢀⠀⡀⠀⠠⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠘⠅⠀⠁⣀⠯⠄⢀⣤⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢦⣽⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣶⠒⠐⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠚⠋⠐⠄⠀⠘⣄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠴⠄⠘⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠃⠈⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢾



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡏⢱⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡌⡇⠀⣠⣶
⠀⠀⠀⠀⠀⢰⣤⣄⠀⠸⣼⣧⠇⢊⣾⡿
⠀⠀⠀⠀⠀⠘⣿⣷⣑⣤⣛⡧⠒⢮⠛⠔⣒⣶⣶
⠀⠀⠀⠀⠀⠀⣱⢋⣁⡠⠌⣹⢆⡈⠑⡜⢿⡛⠁
⠀⠀⠀⠀⣀⡴⣫⢏⣏⠚⢻⡎⢱⢁⠀⡇⠀⢹⡆
⠀⠀⠀⠀⢻⡏⠁⠀⣝⢃⠾⢃⠇⡼⠾⠁⠀⣸⠃
⠀⠀⠀⠀⠀⣹⠶⣌⣉⣁⣠⣞⡸⢠⣟⣠⢊⡇⣠⡀
⠀⠀⠀⠀⢀⢇⠀⠀⢽⣏⣉⡡⠴⠚⠁⣠⢎⡜⣿⣧
⠀⠀⠀⣴⣿⣾⣢⣄⣀⢀⣜⣁⠀⠠⠴⠏⡜⢸⣿⣿
⠀⠀⠀⠀⠉⠉⠉⠉⣠⣶⡰⣾⣯⣉⣭⣧⣁⢸⣿⡟⢀⣽⣿⠇
⠀⠀⢀⣀⣀⣀⣀⡀⠑⣿⣇⣈⣿⠋⠉⠀⠉⠙⠓⠶⡾⠿⠃
⠀⠘⢿⣷⣶⣶⣄⣉⢠⡟⠉⢉⡤⠉⡙⠲⣤⡤⣄⠀⠱⢄⠀⠀⠀⡠⣴⡖
⠀⠀⠀⠙⠻⢿⣿⣿⣾⡧⢔⠏⣠⣴⡾⡟⢿⣷⡈⠳⣤⢄⣷⠰⢃⣾⣿⠇
⠀⠀⠀⠀⠀⠀⡠⠊⣼⡁⢸⢸⡿⣿⢿⣿⣾⢹⠇⠀⢹⠀⢻⠀⠾⠿⠋⠀⠀⠀⠀⢀⠴⠤⡤⡀
⠀⠀⠀⠀⠀⢠⡇⠀⢿⠳⣼⠢⡿⣗⣋⡼⣡⢾⡦⠤⢺⠀⢸⡄⠤⠤⣤⣤⢠⣠⠄⠛⠶⠎⣽⡕
⠀⠀⠀⠀⣀⠸⡷⠀⠸⣀⠈⠣⠤⠟⣁⡾⠃⣸⠇⣠⠃⢀⣾⣰⣾⣿⡿⣣⡏⣷⢒⠚⢳⠶⠚⣛⠓⢀⣠⣶⡖
⠀⠀⠲⣿⣶⣶⣽⡄⠀⠈⣷⣖⣂⣉⣉⣤⣞⡥⠞⠁⢰⣿⠏⠛⠛⠧⣀⠿⢿⣱⣿⣖⡋⠵⢳⡼⠱⣿⡛⠋
⠀⠀⠀⠀⠉⣛⠟⠉⣂⠀⣠⠟⠛⠻⣿⣍⣁⣀⣀⣤⡞⣷⣿⣯⣶⣤⡈⠳⣄⠈⣦⣤⣐⢄⢶⣶⣶⣤⣬⡓⣄
⠀⠀⠀⢀⣜⣵⣾⣿⡿⢀⣾⣧⣀⣀⣸⠉⠉⢉⣠⣿⡇⠘⢿⣿⣿⣿⣿⣦⣽⣆⠙⠿⣿⣷⣎⠛⠿⠿⠿⠿⠟⠃
⠀⠀⠀⠸⠿⠟⠛⠉⠀⢾⡿⠃⠀⠉⠁⠀⠀⢸⡿⠋⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣋⣭⡠⣜⣦⣄⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⢼⣿⡈⢷⣓⣥⣪⣿⣄⡷⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣄⠸⡏⣬⣷⡯⠈⣽⠉⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠛⠛⠀⠂⡠⠄⠃⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠊⠙⠻⣿⣥⣄⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⣤⡀⠀⠀⠀⢠⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⡄⢀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⢀⡇⢘⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣠⠷⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠀⢠⠈⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠚⠋⠀⠈⣄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⠂⠈⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⡜


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣦⠟⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢬⣚⡷⡖⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠰⣯⡦⢘⠲⢤⠀⠀⠀⠀⠀⠀⣰⡉⣯⣖⠉⢙⣷⣧⣶
⠀⠀⠀⠀⢠⢏⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠙⣆⢳⡀⠀⠀⠀⠀⠀⠀⢸⣀⣈⠧⡔⢚⡭⢴⠋⠀⠀⠀⠀⠀⠚⡯⠙⠳⣕⡉⢽⡟⠁⣧
⠀⠀⠀⠀⠘⢮⡀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠜⣸⠃⠀⠀⠀⠀⠀⠀⠀⠸⡝⠤⠘⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠺⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀
⠀⠀⢀⡴⠚⢉⣩⣥⣭⡓⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⣍⣿⠀⢸⠦⡄⠀⠀⠀⠀⣰⢫⠿⣒⣒⣲⡤⣉⣆⠀⠀⠀⠀⠀⠀⣠⢾⠉⣹⣷⣮⠳⣄
⠀⠀⢠⠷⡄⠂⣏⠁⢸⣷⡀⢣⡀⠀⠀⠀⠀⢀⡜⡕⢿⠡⠞⠹⣠⣯⢰⡇⠀⠀⠀⡞⠁⣻⢼⢿⣉⣏⣷⠈⣿⢳⡀⠀⠀⠀⣞⢁⠸⡞⠯⡒⠃⡷⡎⢳⡀
⠀⠀⠘⣇⠙⢄⡈⠩⢭⣴⣃⣠⠗⠀⠀⠀⠠⣏⠘⠷⠶⠷⠾⠖⣋⠟⣸⠁⠀⠀⠀⠙⣄⡱⢌⡓⠌⢋⣴⡵⢃⣠⠇⠀⠀⠀⠈⢞⢧⠙⢀⣒⣮⢡⠷⡼⠃
⠀⠀⠀⠈⠳⠄⠁⢀⣀⡬⠟⠁⠀⠀⠀⠀⠀⠈⠛⢦⣑⣲⣖⣛⡥⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⠙⠚⠉⣨⣧⠏⠀⠀⠀⠀⠀⠀⠘⣎⣙⣉⣩⣁⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⢀⡤⠤⣤⡖⠒⢶⡀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣴⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠖⠒⣦⣀
⠀⠀⠀⢀⡞⣠⢾⣭⣍⡛⢶⡷⣄⠀⠀⠀⠀⢠⠿⢠⣿⡿⣯⠳⡏⢳⡀⠀⠀⠀⠀⣠⠞⠉⣹⣴⣞⣓⢮⣗⠓⡆⠀⠀⠀⠀⢠⠞⠶⢒⣚⢫⡉⣯⠷⣄
⠀⠀⢰⠃⣹⣇⢺⣀⣢⢹⣾⠇⢸⠄⠀⠀⠀⡟⠀⠊⠈⠙⠃⡴⢣⡀⣳⠀⠀⠀⠀⠻⡄⣾⢻⠙⠦⠬⣾⢿⠇⢻⡀⠀⠀⢀⣿⡞⠹⣏⣀⣙⡷⣌⢲⡈⣷
⠀⠀⠸⡄⠹⣌⣻⡶⠶⣚⣽⡤⠞⠀⠀⠀⠀⡷⠴⣌⠲⢤⠤⠄⣘⠁⢹⠆⠀⠀⠀⠀⡟⠻⢬⣳⣄⣊⠥⠞⠶⣞⠁⠀⠀⠘⢾⣧⡘⢲⣭⣭⠶⠋⣸⢿⠁
⠀⠀⠀⠙⠚⢦⡀⠈⠉⢁⡼⠁⠀⠀⠀⠀⠀⠹⣤⣈⣳⣦⡶⠚⣁⣤⠟⠀⠀⠀⠀⠀⠘⢦⣀⣀⡬⢦⣀⡴⠚⠁⠀⠀⠀⠀⠀⢧⠙⠢⠙⣳⣒⣚⢋⡞
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡗⠐⠋⣠⠀⣀⣤⣤⣤⣌⠙⠻⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⣠⣶⡿⢡⣾⣿⣿⣿⠿⢿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⣼⣿⡿⢀⣿⡿⢋⣥⡶⠶⣶⠆⠙⠇⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⣿⣿⣷⢸⣿⠁⣾⡟⠐⠺⢯⣳⡄⢠⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣷⡈⢿⣿⣆⢻⠀⣿⡇⢹⣿⡈⣳⠇⠘⣿⣿⣿⣿⡟⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⢿⣿⣆⠙⢿⣦⠰⣿⣿⣦⣬⡍⠁⣤⡀⢹⣿⣿⠋⡀⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣌⠻⣿⡇⠰⣭⣀⣉⣉⣉⣡⣴⣾⣿⣷⠀⠻⢃⣾⡇⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠘⢃⣀⡈⠻⠿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣿⡿⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢰⣿⣿⣿⣿⣶⣦⣭⣍⣉⣉⣡⣴⣾⣿⡿⠁⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣀⣤⣤⣤⣬⣭⡛⠻⠿⠿⠿⠿⠿⠋⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠛⠿⣦⡐⢶⣶⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⠿⠟⣋⣤⡈⠀⢠⣬⣭⣝⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⢉⣴⣦⣿⣿⡇⣿⣷⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⢁⣶⣼⣿⣿⣿⣿⡇⢿⣿⣿⣿⣦⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠏⢠⣻⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣿⣿⣧⡘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠛⠿⢿⣬⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣴⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡴⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⠙⣿⡾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣷⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣇⣼⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣎⣿⣿⣨⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣋⠘⣻⠇⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⡏⠀⠀⠀⠀⠀⠀⠀⠰⡀⢀⠄⠈⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⢀⣀⣀⣠⣹⡿⡆
⠀⣀⣀⣤⣤⣀⡀⠡⣀⠁⠀⠲⢽⡀⠀⠀⠀⠀⢀⣶⠞⠀⠀⢠⡟⠙⠛⢿⣡⣴⣷⣶⣤⣤⡄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⢷⣄⢀⣵⣖⠀⠀⠀⣾⠋⠀⢀⣴⠟⠀⣤⣶⣼⠟⢱⣧⣘⣿⣯⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⡏⠀⠀⠸⠹⠀⠀⠘⡇⠀⢠⡿⠉⠀⠀⠀⢹⡿⠸⣿⣦⣷
⠀⠀⠀⠘⠒⢄⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⢸⡟⠀⣾⣴⠿⡀⠘⣧⠀⠀⠀⠠⠚⡶⣀⣹⣿⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⣴⢷⣮⣤⡆⠀⠈⣇⣸⠟⠁⠀⣿⠀⠸⣷⠀⢀⡠⠞⠛⠛⠙⢿⣏⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⢀⣀⣹⠏⠐⠀⣶⣷⡏⠀⠀⢀⣿⣷⢀⣧⠞⠋⠀⡀⠀⠀⢀⣤⣹⣶⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠀⣿⣿⠂⠀⢀⣾⣉⠉⠉⠀⣠⡴⠞⠿⠲⠛⣿⣋⣴⡙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⠀⠀⠀⣀⡀⠀⣧⣿⡀⢀⠌⠉⠘⠛⠟⠋⠉⠀⠀⠘⠓⢀⣿⡟⢉⠖⠁
⠀⠀⠀⠀⢠⠄⢰⠏⠀⠀⠀⠀⣔⣨⠉⠻⠻⠿⢿⣧⣿⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠈⠐⠊
⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢸⣿⣡⣶⠒⠂⠀⢲⡏⠹⣾⣦⣠⠄⣀⣀⣠⣤⠴⠟⠉
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠘⠛⠟⠛⠀⢠⡟⠁⠀⠹⣿⣿⢿⡟⠿⠟⢻⡆
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠠⢀⣿⣇⠀⠀⠀⣱⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠾⠛⠃⠉⠙⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠒⠀⠀⣀⡀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡤⠤⠔⠒⠂⢣⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠂⠀⢀⠊⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠃⠀⠰⠁⠀⠀⠀⠀⠒⠂⠀⠒⢄⠘⡄⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢨⠀⠀⠁⢨⠀⠀⠀⠀⠀⠌⡐⠀⠀⠁⠡⠀⠀⠀⢱⠀⠀⡀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡶⠃⠄⢠⣄⣄⠀⠀⡆⠀⠀⠀⡸⠀⠀⠰
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⢄⠀⠀⣀⡶⠀⠙⠀⠀⠀⠀⠐⠃⠀⡼⠀⠀⠀⠰⠁⠀⢠⠃
⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡷⠀⠀⠀⠀⠀⠔⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠑⢀⠀⠰⡀⠀⠀⢸⠀⠀⢉⣗⠀⠠⠤⠀⠒⠀⠕⢒⡉⠀⣠⠗⠂⠁⠀⠀⢀
⠀⠀⠀⠠⣀⠀⠀⠁⠀⢈⡲⣄⠀⠑⠄⣀⠛⠀⠈⣉⡀⠀⠀⠈⠩⠐⠊⡙⠀⠀⠀⠀⠀⢸⣀⡠
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠡⡈⠢⡀⠀⠀⠈⠈⠁⠠⠀⠀⠀⡀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⣀⠠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠲⣄⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⡠⠖⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠢⠤⢤⡤⠄⠀⠈⠁⠒⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⣀⡀⠀⠊⠀⠀⠀⠠⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡤⣤⠤⢤⣤⣀⠀⢀⣠⡤⣤⣤⣤⣄⡀
⠀⡀⡀⢠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠋⠁⠈⠉⠋⠙⠳⢦⣄⣰⠋⣀⠔⠁⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠁⠉⠀⠔⠀⠀⣠⠶⠋⠁⠀⠘⢌⠛⠀⠀⠀⠀⠄⠀⠀⠀⠈⢁⡔⠁⠀⠀⠀⠈⠱⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠹⡶⠳⡶⣤
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⢀⣀⣼⠤⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡀⠛⠠⢾⣏
⠀⠀⢠⠟⠁⢀⣰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣭⢰⡖⠎⠀⢻⡆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠹⢷⡄
⠀⠀⣿⠀⠀⠀⡏⠀⠀⠰⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⢀⣤⡦⢼⠀⠈⠑⠀⠈⠁⠃⢀⡉⠂⠀⠹⡄⠀⠘⠧⢠⠴⢤⠀⠈⡆⠈⣷
⠀⠀⢸⡀⠀⠀⠧⠀⢠⠀⠀⠀⠀⠙⠂⠠⠀⠐⠀⠠⠀⠀⠈⠡⡀⠃⠀⠀⢠⣄⠀⣤⢠⣤⡄⢸⡏⠂⠀⠀⢹⡄⣀⠰⠆⢠⠀⠀⠦⣁⠀⣿
⠀⠀⠀⣳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡄⠁⢶⣄⠀⢀⣿⠀⣧⣄⣨⡴⠆⢻⡷⠀⠀⠀⡱⠁⠀⠀⠀⠀⠀⡀⠘⠀⡿
⠀⠀⣼⠁⠐⠆⠀⠀⠀⠀⣀⣀⣀⣈⣃⠀⡀⠀⠀⠀⠀⠈⠁⠆⠸⢿⡇⡘⡽⠇⠠⡗⢸⠁⠀⠀⣼⠷⠚⢧⠚⠄⣀⠑⠀⠀⢀⠊⢀⣀⣼⢃⡀
⠀⠀⡏⠁⠀⠀⠀⢠⠄⠁⠀⠁⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⡘⠀⢦⠤⠛⠃⠀⠀⠻⠩⠂⣀⡖⠉⢀⡶⢻⡄⠀⠀⠀⢀⢴⡀⠀⠀⣿⠁⠐
⠀⠀⢻⠂⠒⠀⢙⠁⠀⠚⠀⠀⢈⣁⠈⠀⠉⠀⡀⠑⢶⠖⡄⠃⠀⠀⢀⠆⠀⠲⣀⢶⠞⠀⡀⠀⠀⣾⠃⢈⣥⠐⠤⠤⠀⠛⠁⠈⢉⡏
⠀⠀⠈⢷⡀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠙⠻⠀⢰⠁⠀⠀⠈⢹⡣⢀⡄⠊⠀⠀⠀⠀⢁⠀⠀⣴⢠⣴⣩⡄⠈⠘⢦⠀⠀⠀⠴⠄⢀⡾⠁
⠀⠀⠀⠀⠙⢦⣌⣀⠄⡐⠤⠀⠀⠀⠘⠂⠄⠀⢐⣤⠄⠀⠨⡜⡼⠠⠄⡀⠠⣤⡤⣤⡀⠀⡷⠀⠀⠈⠙⣃⠳⠈⡄⠀⠑⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠘⠀⠁⠡⡀⢀⠀⠘⠠⠀⠀⠀⠊⠁⣠⠔⢢⠚⠁⠀⠀⠀⠀⢹⠀⠀⠀⠉⠘⠯⣄⡀⠒⡂⠉⠀⠐⢀⡴⠴⠞⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢙⠂⢄⣀⠀⠠⢆⡀⠀⣈⡵⠂⣵⠆⡀⠈⠀⠀⠀⡸⠄⠀⠀⢀⡨⠓⠤⠷⠤⠤⠴⠒⠺⠥⢄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⡍⠈⠉⠈⠉⣉⣍⢀⡴⠃⠈⠉⠐⠒⠂⠀⠀⠐⠒⡊⠁⠡⡀⢴⣄⡀⠸⠇⠀⠀⡤⠴
⠀⠀⠀⠀⠀⠀⣇⠀⣀⣅⢀⠀⠃⠀⠀⠲⠛⠉⠁⠾⠡⠤⠤⠤⠦⠤⠤⢤⠤⠆⡘⣉⡀⠀⠹⠀⣀⣉⣡⠬⠼⠓⡶⠖⠚⠒⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠏⠀⠘⠛⠂⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠟⠂⠀⡟⠉⢱⡤⠞⠋⠉⠀⠀⠀⠀⠈⠀⠀⠒⡄⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠠⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣏⠀⢸⠀⣀⣤⠀⠀⢀⡀⠀⠐⠀⢒⠂
⠀⠀⠀⠶⠦⣤⣴⡄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⣏⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡏⠀⠈⡄⠀⠀⣦⣤⣄⣀⡀⠀⡀⠠⠄⣄⠀⠄⣀⣀⡇⠀⣀⣤⡷⠞⠉⠀⢀⣠⣄⠘⡁⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⣇⣀⢀⣃⡀⠀⡀⠀⠈⠙⠋⠈⠋⠃⣊⡀⠀⠀⠉⠏⡴⠛⠁⠀⠀⠀⠀⠒⠀⠁⢈⡁⠋⠈⠹⣗⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⡾⠁⠀⠀⢀⠀⠀⡠⠚⡁⠀⠀⠀⠀⠁⠠⠉⣤⠦⡀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢐⠂⠀⠀⠘⡏⠉⠉⠉⠉⢉⠉⢋⡾⠁⠀⠀⠀⠘⡀⡘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⢀⠀⢡⠜⠉
⠀⠀⠀⠀⠀⠀⢸⣄⣄⣀⡀⣨⠀⢀⣀⡀⡃⠀⠀⠀⠀⠀⠂⡞⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⢆⡴⠋
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⠀⡈⠊⠰⠇⠀⠀⣧⠀⠀⣸⠁⠀⢀⡀⠀⢠⠀⠘⠀⠉⠀⢄⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣀⢰⠈⡄⠀⣀⣀⡀⠀⢐⠁⠀⠀⠀⠀⠀⠨⡦⠤⣾⠀⣀⡀⡀⠀⢸⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡠⠖⠀⣀⡶⢋⠄
⠰⠞⠋⠉⠉⠀⣸⠋⠀⢀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠈⠐⠀⠦⠀⡙⠀⡄⠀⠀⠁⠀⠀⣀⠴⠋⠀⠀⠀⠃⠈⠀⢀⡴⡞⠉⢰⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡘⠀⠀⣠⠀⠑⢚⡦⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢮⣅⣠⠀⣀⣴⠋⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⡇⢀⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠘⠡⠶⠴⠇⠤⠄⠹⠶⠒⠒⠾⠀⠀⢀⡠⠔⠑⠢⢄⣀⠀⠀⠀⠉⡀⢁⠀⠋⠀⠀⠀⠀⠀⠀⣴⢯⠀⢰⠀⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠊⠁⠰⠂⠀⠀⠀⠭⠦⢀⣀⣀⠀⠀⠓⢦⡀⠀⠀⠀⠀⣸⡇⠘⠀⢨⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠙⠲⢄⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣆⠀⠀⢠⡏⢀⠈⡤⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠛⠀⠸⠆⠁⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠊⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠛⢃⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣏⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣽⢛⣿⠀⠀⠠⠆⠀⠀⢀⠀⠈⡀⢀⠀⠀⠘⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⣥⠀⣄⡖⠃⠀⠀⠁⠀⠀⠀⣾⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢾⠖⢠⡆⠀⢰⡾⠁⠀⣼⠀⣠⡷⢠⢤⣤⣤⡤⠀⣤⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢦⡘⢿⠀⣸⠙⢤⣿⣷⣮⣿⢋⣼⣿⣷⣧⣾⣿⡟⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠻⠟⠿⢿⣿⣿⣌⢷⣴⣤⣾⣿⡿⠟⠁⢉⣿⣿⡟⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠄⣀⣀⣀⣈⣰⣤⣤⣤⣤⣼⣿⣿⣿⡆⢿⣽⠃⠀⠀⠀⣠⠊⠁⠈⠛⠋⠳⣶⠊⠀⠛⢲⡞
⠀⠀⠀⠀⠀⣈⠉⠉⢉⣽⠟⠛⠙⠏⠉⣿⠟⡻⣦⡰⠿⠋⣹⠾⠛⢻⣶⣤⣤⣄⣀⠀⠈⣷⠀⠀⠀⡻⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠔⠁⠀⠐⠇⠀⠀⠉⠀⣴⡶⠾⢉⣀⡌⣩⣽⡿⠛⢿⣦⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⣀⣶⠀⢸⠛⢁⡴⢛⣼⣽⣶⣿⢦⡴⠀⠀⢻⢿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠂⢠⡄⠒⢦⡄⣻⡞⠉⢳⡀⣿⣄⣼⢷⢸⣭⣿⡏⢻⡏⠐⠓⢻⠟⠀⢻⢿⡆⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠺⠛⢛⣶⣷⣿⠂⠀⠈⢿⣿⢻⡏⢾⣼⣽⡿⢅⣏⠛⠁⠀⠃⠀⠀⣷⠸⣿⡄⠀⣀⡞⡠
⠀⠀⠀⠀⠀⢘⣦⣀⣞⠀⢀⣤⣤⡼⠇⠈⠉⣆⠀⠀⢸⡣⡘⢷⠒⠭⠾⠓⢀⣁⠀⠀⣸⠄⠀⡐⠁⠀⠻⣿⢶⣿⣿⠁
⠀⠀⠀⠀⠀⠁⢺⣿⣿⠀⣿⣾⠋⠀⠀⢠⠞⠛⠁⠀⢸⡇⠈⢦⣧⣀⣀⡀⣿⡟⠁⠁⠀⠀⢰⠇⠀⠀⣼⡿⣿⣿⣷⠶⢶⣤⠀⡾
⠀⠀⠀⠐⢉⠛⠉⣡⣬⢷⣿⠉⠁⢂⡀⠈⠛⠲⣤⠀⠻⢷⣄⠀⣶⠈⠙⠛⠳⣤⡀⠀⠀⢠⣿⠀⣴⣼⣿⡽⠋⠀⠀⠀⠀⠘⡟⠁
⠀⢀⡀⠂⠀⠠⢞⡿⢳⠀⠉⠳⡄⠀⠀⠀⠀⠀⠈⢧⡀⠀⠹⣶⣬⠿⠿⠿⠛⠉⠛⠷⣤⣼⡟⢀⣿⣿⣿⡷⠄⠰⣴⣶⠶⠚⠁⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠰⢿⠃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡤⠠⡤⠄
⠀⠀⠀⠀⠀⠀⣆⠀⣆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⠶⣶⣦⣴⣶⣾⣶⣶⠾⣿⡿⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣠⡘⣧⡤
⠀⠀⠀⠀⠀⠀⣿⡟⠋⣀⣀⡀⢠⣤⣤⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠉⠛⠁⠙⠿⣶⣶⣌⠀⠀⣀⢀⣠⡴⠋⠀⠀⠀⢀⡀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠠⠜⡛⠄⠂⣉⣤⣬⣹⣿⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⠙⠛⠳⢶⣶⠮⣉⠡⢶⣶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠴⢾⣶⢆⣿⣿⠯⢺⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠙⢆⠈⠃⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠉⠉⣽⡶⣛⣻⣿⣿⣷⠠⠤⢴⡀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠁⠀⢁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠐⠢⣀⠀⠠⣤⡘⣦⣀⣿⣿⣿⣿⣿⠙⣿⡄⠀⠀⠙⠳⣄⠀⠀⣀⡄⢁⡀⠀⠀⣀⡤⢘⡩⢉⠛⠀⡀⠀⠀⠀⠀⠀⠣⡈⣧⡀
⠀⠀⠀⠀⠀⢀⣠⠒⠺⠋⠀⡴⠎⠉⡉⣹⣿⣿⣿⠸⣧⣿⣿⣦⠀⠀⠀⠀⠈⣴⠟⠁⣼⣿⡷⣾⣿⠞⠛⣯⠙⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣠⠋⡌⢀⣤⠀⠖⠀⠀⢲⣿⣿⣿⣿⠿⠖⠻⢿⡿⠀⢀⣁⣡⠤⢶⣧⣄⡀⢱⣿⣿⣯⠛⢧⡉⠉⠀⠉⠁⡀⡴⢆⣀⣴⣦⣤⣤⣀
⠀⠀⠀⣾⠃⠚⠁⠉⠀⠀⠀⠀⠀⣿⣿⣿⠟⢻⡦⠀⠀⠈⠳⣦⣉⣽⠄⢀⡼⢿⣿⣁⠞⢻⡇⠀⢳⡄⠙⢦⡀⣠⣾⣶⣴⠟⠋⢉⡁⠉⠀⠀⢱
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⡏⠠⠿⠃⣀⠀⠀⠀⠉⠀⠀⠀⢸⡇⠈⢻⣿⠀⠞⣿⣄⠈⠀⠀⠈⠻⡈⠙⠻⠷⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠁⠀⢰⡏⠢⢄⣀⡀⠀⠀⠀⢮⠙⠄⠀⠉⠀⠀⠈⠏⢻⡆⠀⠀⠀⢹⣆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠰⣤⣄⣙⠋⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠲⢰⣼⠇⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡿⣉⣩⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠚⣓⣀⣉⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⠞⠁⠀⠈⠀⣲⠶⠖⠒⠛⠉⠉⠁⠘⣆⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠀⠒⠂⠈⡵⠁⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠤⢀⡀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢳⡄⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡜⠀⡀⠀⠀⠀⢀⠠⠉⠩⡁⠀⠀⠉⠳⢄⠀⢻⡀⠀⠀⠀⠙⢦⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠸⠀⢐⠁⠀⢀⠔⠁⠄⠀⢀⣈⠑⠢⣄⠀⢠⡇⠀⡇⠀⠀⠀⠀⠈⣇⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠐⠈⡇⠀⠀⢀⠈⣠⠀⢈⠉⠝⠀⡈⡆⢸⠇⢀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⡁⢃⠀⣸⠻⠃⠘⠀⠀⠴⣧⣷⡠⢀⠀⣸⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡅⠀⠀⠀⠀⠠⡀⠈⠀⠀⠆⠀⣼⡀⠀⠙⠧⠀⠣⠀⠀⠀⠀⠴⠞⠁⠀⢠⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠏⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣦⠀⢀⢸⣼⠇⠱⡄⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⠄⡠⢻⠀⠀⠀⠀⠀⠊⠀⠀⠀⣠⠎⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠜⢇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⡘⠄⠀⠈⠠⡀⠀⠀⠀⠀⠀⢤⡔⡡⠞⢀⡿⠊⠀⢀⠔⠁⠀⢀⠤⠞⠉⢳⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠂⠀⠈⠳⡀⠀⠀⠹⡄⠀⠀⠀⠀⠸⡇⠀⠀⠠⠙⡾⠥⠀⢀⣈⣙⣒⠒⠒⠒⢊⣩⠴⠖⠉⣀⠠⢂⣧⠤⠐⠊⠁⠀⠀⠀⢀⠇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀⠀⠈⠢⡀⠀⠀⠀⢳⡀⠀⠀⠱⣿⠖⢀⣀⣠⠄⠀⠀⢀⣀⠀⢠⡤⠖⠉⣀⠴⢺⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠈⠑⠠⠤⡈⢳⣄⠀⠀⠙⠲⢤⣀⣈⠓⠀⠀⣀⣀⣀⠀⠀⢀⠀⠂⠐⢋⠛⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢦⡀⠀⠀⠀⠀⠈⠉⠉⠙⠄⣀⠀⠀⠈⠁⠀⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠂⠀⢀⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⣀⡀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠲⢄⡂⠀⠈⠉⠉⠉⠋⠉⠈⠁⠀⠀⠀⠀⢀⣀⡤⠴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠉⠁⠐⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⠏⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⡠⠖⠉⢠⠈⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⣶⠶⠖⠂⠀⠁⠀⠀⠉⠉⠀⠀⠀⢀⠟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⢀⡀⠜⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠋⠁⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠌⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⢰⠃⡞⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠟⠈⡱⠋⠀⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠘⠰⠁⠀⠀⢸⡇⠁⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⠔⠊⠉⠉⠉⠙⢭⡉⠑⢦⡇⠀⢀⠀⠀⠀⠀⢠⣃⠴⠓⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⡠⠚⠉⢀⡀⠴⠥⢄⣀⣀⡀⠀⠀⠀⠙⡄⠀⠹⣄⠘⠶⠤⠤⠰⠋⠤⣖⠉
⠀⠀⠀⠀⠀⠰⡎⠉⠀⠀⠀⠀⠀⠀⠉⢢⠞⠁⠀⢠⠋⠀⠔⠀⠉⡀⠀⡀⠈⠤⡀⠀⠘⡄⠀⠱⣉⡶⠒⠒⠒⠲⢤⡀⠃
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠐⠢⢤⣀⣹⡄⠀⠀⠈⠀⣠⢆⢀⢪⠄⠀⢈⡆⠀⠘⠆⠀⡇⠀⠀⠏⠉⠒⢤⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⣠⠔⠋⠀⢡⠀⠀⠀⠰⡏⢆⠙⠤⠤⠖⢈⣃⠄⢈⠀⣠⠃⠀⠀⢰⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⢑⡞⠁⠀⠀⠀⠀⡆⠀⠀⢀⠆⠈⠢⡀⢀⠀⠈⠁⠀⢸⡜⠁⠀⠀⠀⡎⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⡄⢠⠖⠉⠀⠀⠙⣄⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡃⠀⣀⢠⡌⠀⠀⠀⠀⠀⢰⣆⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠦⢤⣄⣀⣀⣱⠁⠀⠀⠀⠀⠀⢈⠳⣬⡄⠀⠀⠀⠡⠀⠀⠀⢀⡠⠖⢋⠔⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠧⠒⠢⡀⠀⠀⠰⠛⠓⠲⣄⠀⠀⠈⠁⠓⠂⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣼⣡⣔⠈⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣀⣀⣃⠀⠀⠀⠀⠀⠀⠈⠻⢔⡂⠤⠤⢀⣲⡞⠉⠀⠀⠀⠀⠀⣀⡤⡶⠋⠀⠀⠈⠙⢦⣠⠞
⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⢈⠟⠈⠒⠒⠒⠛⠉⠁⣴⠛⠒⠄⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡀⢀⡤⠔⠒⢺⣷⠤⢄⣀⣀⣀⣀⣀⠠⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠋⠀⠀⡴⠃⠈⡄⠀⠀⠋⠀⠀⢸⠓⠦⢤⣀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠓⢤⣀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠜⠁⠀⠀⣿⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣰⠇⠀⠉⠓⠶⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠙⠀⠀⠀⠛⠛⠛⠓⠲⠢⠠⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠐⢤⣀⠈⠙⠻⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡟⠀⠀⠀⠀⢠⣏⢠⠆⠂⢀⠒⠀⠉⠀⠁⠀⣘⣮⠛⣭⠉⠙⠲⢄⠀⠀⠀⢑⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠻⠹⠀⠀⠀⠀⠀⢨⠃⢻⣤⣾⣦⣤⣴⡀⠀⠃⠀⠙⢻⡆⠉⢲⣄⡀⠀⠁⠠⡀⠀⠆⠀⠐⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⢰⠀⣄⠀⠀⢸⡀⠈⡙⠻⢿⢯⣬⡙⠳⠀⣡⣹⣆⣷⠀⣸⡿⠃⠀⠀⠀⡵⠀⠀⢀⣤⣬⡀⣄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⡆⠀⣿⣧⠀⠈⠀⠀⠀⠈⠛⠶⣿⡿⡏⠘⠋⠸⣿⣧⠀⠀⠀⠘⢇⠀⠀⣻⢿⣿⣿⣯⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⡟⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠄⠀⢿⣿⡷⠀⠀⢀⣞⡃⢠⡿⠒⠃⠘⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠄⡉⠙⠲⣶⠖⠈⡠⠀⠀⣾⠻⢣⣿⡇⠀⠀⠀⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠃⠄⠐⠀⠙⣿⣿⣿⣶⣤⢤⣤⣤⣤⡤⠄⠀⢀⣴⡊⣠⡔⠋⠀⢀⣿⡟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠉⠉⠛⠛⠚⠛⠋⠁⠀⠀⠀⠀⠈⢠⡟⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⢀⡀⠀⠀⢀⣀⣴⡿⠀⠀⢠⣿⠟⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣷⣤⡶⠟⠁⠀⢠⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠈⢣⣀⡀⠀⢀⣤⣤⣤⣤⣤⠤⡤⠤⠤⠖⠒⠐⠉⠁⠀⠀⠀⠀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡟⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⢄⡀⠀⠀⠀⣀⢀⣀⣠⣤⣤⣔⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡖⠉⠀⣦⠉⠁⠈⠑⢾⠝⡛⠋⢉⣵⠶⠾⠿⠿⢿⣛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠁⠀⣼⠀⠀⠀⢹⣷⠀⠀⠀⢈⡿⠚⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⢪⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⠒⣿⠀⢀⢾⣿⠃⠀⠀⣴⢿⠤⢂⣶⡶⢿⣏⣦⡀⠀⠀⠀⠀⠀⠀⢁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⡰⠁⠀⢻⣧⢸⣿⡻⢃⢾⡷⢃⡼⢦⣻⣿⣿⣷⣿⣿⡙⣶⣾⠯⣴⣤⣀⠀⢋⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⡄⠀⠀⠀⢻⠈⣿⢹⡇⠈⠻⣟⠁⠀⢿⣿⣼⣯⡏⣼⣷⢸⡇⠀⠀⠉⠀⠑⡼⣿⠤⠤⠄⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠀⠸⢰⣟⠀⢿⣦⠀⠈⢷⡀⠀⠈⢳⣹⡀⣷⡏⣼⠃⠀⠀⠀⠀⣼⢻⠁⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⢿⡀⠀⠰⣿⠀⠀⠀⠀⢿⣿⣄⠀⠹⣆⠀⢸⣧⣤⠤⠾⠁⣇⣿⣿⣥⣤⠀⢀⣶⡶⣣⡞⠀⠀⠀⢀⡴⠊⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⢷⣄⠀⠻⢦⣀⣀⣀⡈⠻⢿⣿⡆⠈⠓⠒⠛⠛⠿⠚⠉⠉⠁⠈⣀⠸⠀⣸⣿⣿⣿⡇⠀⠀⣴⠋⠁⠀⢰⠋
⠀⠀⠀⠀⠀⢀⣀⠷⠶⠄⠀⠀⣀⣠⣿⠦⠄⣄⡀⠈⢻⡏⢳⣄⠙⢿⣄⣀⣀⣀⡀⢀⠠⢔⣬⡶⣶⣶⠶⣿⡿⠿⠛⠋⠀⠀⣰⠇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⣞⡁⠀⠀⢀⢀⣠⣽⣦⣼⣿⣤⣿⣦⣸⣿⡿⠛⠛⠛⠷⠿⠟⢡⣶⠟⣱⠟⠋⠀⠀⠀⢀⣤⡾⠋⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⠉⢳⣆⠀⠀⠀⠀⠈⣏⣁⣀⣈⡙⠛⠯⠀⠀⠀⠀⠀⠀⢀⣾⢏⠼⠃⠀⢀⣠⣴⡾⠟⠁⠀⣀⣠⠶⠛⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠘⢿⣷⣶⣤⡀⠀⠀⠀⠙⠣⣀⡀⠀⠀⢲⣌⣙⣶⣾⣿⣟⣫⣴⠶⣿⣿⣯⡶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢀⣸⠿⠿⠿⣦⡀⠀⠀⠀⠀⠉⠻⠶⢶⣬⣤⣤⣭⣶⣄⣀⠀⠈⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠻⣆⠀⣰⠿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠈⣽⡿⠛⠉⠉⠉⠻⢦⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠃⠀⠀⠈⠻⣿⣶⣦⣤⣤⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣠⣤⣤⣀⣀⠀⠀⢀⣀⣽⠿⠋⠉⠉⠉⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⡶⣋⣙⠲⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢀⡠⡶⣫⠞⠛⠳⣶⣤⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢶⡟⠀⣠⣿⣸⠟⢉⣉⡛⣆⢸⡌⣿⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⣧⠀⡇⠸⣯⣰⣧⣚⡷⢋⡼⣱⢻⡇⢠⠷⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢸⠏⠻⣧⠀⠙⠿⣽⡿⢚⡭⠞⣁⣼⣵⡏⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠦⢼⡇⠀⠈⠳⢾⡛⠛⠛⣿⠛⠋⠉⠁⣸⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⠀⠈⢳⣄⠀⠀⠀⠙⣆⣀⣯⡀⠀⠀⣠⡿⠖⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠳⣤⡀⠀⣿⠁⠈⠉⢛⣻⠏⠀⢀⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣄⣀⣉⣻⡿⠶⠶⣾⣏⣥⣤⠶⠋⢁⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣄⣀⠉⠉⠁⢀⣶⡀⠘⣇⠀⠀⣰⠋⣧⠚⢓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢄⡸⡟⣄⢀⡜⣯⢷⠀⣿⠀⣾⠁⢦⡇⢁⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣊⢳⡅⢹⡿⢣⡟⢺⢀⡿⠀⣟⠜⢋⣤⣟⣥⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣳⣸⣧⡏⣠⠋⣼⡷⠚⢻⣟⣶⣿⣶⠷⠶⢞⣻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣤⣄⠙⢿⡯⠞⠁⣰⠟⠀⢰⠃⢿⡍⢳⡉⠙⠚⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡞⢷⣭⠾⡽⠃⠀⠀⢷⢀⣼⠋⠀⠀⠘⣧⠼⣯⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠥⠗⠋⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠈⢻⣩⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠙⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⢀⠂⠀⠒⠁⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠓⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠁⠫⠀⠸⠀⣦⠀⢀⡥⠀⠈⠀⠀⠀⠀⡀⠀⠀⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡖⠀⠘⡔⠄⠸⣄⣁⣸⣧⡑⣤⠀⠀⠂⠀⠀⠀⠒⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣹⢷⠀⠀⠈⠚⢦⡹⡝⠉⠛⠳⢆⠳⠶⢴⣄⣠⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣮⣣⠈⢿⠦⣄⠀⣀⠉⠳⣶⡒⠂⠀⠐⠀⠰⠶⠟⠁⣠⡀⠀⢠⡆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣯⢿⡇⠀⠸⣇⣦⠙⠉⠧⣄⣀⠉⠓⠤⢉⡀⠀⢲⣾⡟⠚⠀⠀⠋⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⡏⠨⢻⡄⠀⠘⢷⣀⣴⣠⣀⡀⠉⠃⠀⠰⣻⡿⢿⢛⠁⠀⠀⠀⠀⠀⡴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢧⡄⠀⠸⠿⡶⣤⣤⣉⠣⢴⡋⠉⠉⠛⠚⠈⠈⠉⠉⠁⠀⣀⣀⠦⣀⢸⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠹⣷⣄⣀⡀⢇⢿⣿⣷⣶⣮⢳⠀⢠⢈⡐⢲⣶⣶⣶⣮⠾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣶⣆⠸⠏⠉⠙⢿⣰⣿⡿⢿⢿⠀⡆⠈⣼⡰⠿⠛⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⣟⣿⣿⡻⣄⠀⢸⣿⣿⠡⡿⢿⣆⢱⡞⠡⠔⠊⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⠇⡈⣀⢸⣿⣧⠖⠋⠉⢁⡴⣿⢦⣤⢾⠯⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣷⣭⣿⣇⠹⠀⢀⠀⠀⣿⢟⢻⣿⡿⠃
⠀⠀⠚⠛⠁⠁⠉⠛⠚⠓⠉⢁⣾⣿⢿⡿⣿⣿⣿⡲⣦⣾⠛⣿⣿⣷⡿⠛⠁
⠀⠀⠀⠀⠀⢤⣶⠶⠴⠖⠚⠋⠉⢀⡾⠀⡜⠁⠈⠉⠉⠛⠻⡟⣏⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠌⠀⠀⠀⠀⠀⠀⠀⠙⣼⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠖⣶⣦⡄⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⣀⠀⡖⠂⡃⣰⠛⣄⣣⠋⢹⣄⠈⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⣳⣷⣇⠀⣿⠹⠀⠈⣻⡾⢋⣸⠀⠀⠀⠁⢠⡄⣠⠔⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣠⠼⢦⡑⣾⣯⠭⠭⠿⠿⠏⡸⠀⠀⢰⠀⠀⣿⢁⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡇⢸⡞⣏⣽⣶⣷⣼⠈⣦⣤⡖⠒⠒⣡⠒⠁⠈⢷⠰⣿⣾⣧⡾⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢠⠏⠣⣸⣇⣈⣣⣾⢼⡇⣠⣇⠈⢿⢶⣰⠇⢀⡖⢀⢇⣨⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠻⣤⣁⣀⣀⣼⠞⠁⢸⠀⣼⣾⡏⣷⣿⣶⣿⣮⣥⣤⣄
⠀⠀⠀⠀⠐⡶⠦⣐⣢⢤⢸⠀⠙⠲⢤⣤⣽⣟⡋⠁⠀⣠⠏⢠⣧⡶⣿⠀⠙⠳⣤⡙⠋⠀⠈
⠀⠀⠀⠀⠀⣨⠷⠞⠺⣿⣼⡷⢤⣀⠀⠀⠉⠉⠉⢩⣿⣷⡶⠞⠀⠳⡜⢦⣀⠒⢽⡵⡀⠀⠀⢀
⠀⠀⠀⠀⠂⡰⢀⣤⢸⢳⠈⠛⣆⢈⢓⣦⣄⣠⣴⣯⠘⢿⣿⣀⢀⠘⢮⡄⠈⠉⠂⢳⡙⠦⠬⠶⠇⠄⠂
⠀⠀⢀⣠⣌⢤⠞⠁⠈⢏⡇⣸⢁⣼⠟⢻⠋⠙⢿⠐⢇⠀⠀⠉⠋⠉⠛⢧⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣹⡿⠁⠀⢸⣆⡄⠸⡄⣼⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡟⠀⠀⠀⠀⠉⠛⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠒⠤⠄⠀⠀⠀⠀⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠒⠂⠀⣤⣀⠤⠭⠕⢢⡀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⠀⠐⢂⠞⠁⢀⡤⠊⠁⠀⠀⠀⠀⠀⠳⣄⠀⣀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠃⠀⢠⠋⠀⠀⠀⠀⠤⠤⠀⠤⡀⠘⡆⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡸⠀⠀⠁⡀⠀⠀⠀⠁⠀⡐⠠⡀⠈⡆⢸⠀⠀⠀⠘⡇⠀⠄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢡⠀⢀⠀⢡⡀⠀⣄⡆⡠⠉⠃⣈⠀⠇⢸⠀⠀⠀⠀⡇⠀⠈⠄
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⣄⠀⠴⠋⠄⠀⠈⢙⡿⠂⢀⠏⠀⠀⠀⡰⠁⠀⢠⠇⢄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣘⣾⠙⠄⠀⠀⠂⠀⠀⠀⠠⠀⢾⡀⠀⠀⠐⠁⠀⣠⡇⠀⢠
⠀⠀⠀⠀⠈⢣⡀⠀⠰⡀⠀⠀⠀⡏⠀⠸⢦⣤⠀⠐⠠⢄⣀⡀⠾⣀⡡⠛⠀⢠⣂⠠⠐⠋⠀⢱⠀⠈⠂
⠀⠀⠀⢀⠀⠀⠀⠄⡀⠑⢄⡀⠀⠱⡀⠀⠹⡷⠤⡩⠉⠁⠀⠀⠉⡤⠖⣀⠴⡏⠀⠀⠀⠀⠀⢸⠀⠀⠄
⠀⠀⠀⠀⠲⡄⠀⠀⠈⠀⢢⠹⢆⠀⠈⠐⠦⠬⠤⡤⠤⠄⠀⠄⠈⠘⠙⠁⡴⠀⠀⠀⠀⠀⠀⢸⠴⠊
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠱⡀⠑⢄⠀⠀⠀⠀⠀⠁⠀⠀⠒⠊⠀⣠⠐⡁⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠑⠤⠤⣄⣀⠀⠱⣄⠀⠀⠁⠐⠀⠐⠲⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⡤⠔⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⠤⠊⠙⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠉⠒⠒⢲⠖⠒⠀⠁⠈⠉⠉⠀⠀⡘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠠⠤⠀⠁⠄⠀⠠⠄⠒⠒⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⡴⠞⠉⠙⠳⢦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢉⣠⠞⣡⣴⠞⣫⣽⣟⢶⡄⠉⢻⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡏⡏⣾⢁⣿⡼⣡⣖⣻⣾⠟⢦⣀⣇⠀⠹⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢫⠷⡌⢳⣧⠙⣾⡛⠻⢿⣭⣀⣿⡥⠊⣿⠉⡧⢀⡿⢀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠏⢀⣸⡀⠻⣤⣻⣷⣸⡏⠙⢒⣀⣨⣽⠷⠛⣡⠞⠁⣼⠟⠁⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠠⢌⣻⣶⣄⠙⠻⢿⣿⣛⣋⣉⣥⡤⠖⢻⡏⣠⢾⡏⣀⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⠒⠿⣿⣮⣳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠟⠁⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⠛⠛⠻⠷⣦⣀⣠⣤⣶⣫⡥⠶⠒⠛⠻⢤⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠲⣤⣀⠀⠀⠉⠛⠛⠛⠒⠂⠀⠀⢀⣠⠟⠀⠀⢀⣤⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠿⣷⠶⣤⣄⣀⣀⣤⣤⠶⠋⢡⣀⣤⠾⠋⢉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⢀⡀⠀⠀⠀⠳⣄⣀⣨⡴⣟⠹⠈⡟⢧⠟⠓⣦⠟⠋⣅⠀⣀⡞⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢍⡛⠛⡻⠶⣤⣦⡀⠀⠀⠙⠀⢹⡆⢰⠇⠈⣠⠞⠉⢀⠀⢹⣠⠟⣀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠙⢦⣷⠘⡌⢫⠙⢶⡀⠀⠀⠀⡇⡿⠀⣸⠃⠀⡆⠸⡄⣸⠟⠋⠁⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣉⣉⣳⣷⡘⡆⠂⢷⠀⠀⠀⣿⡇⠀⡏⢠⠀⢳⠀⣿⣥⠴⠒⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⣈⣀⡽⠷⣿⣾⣀⣀⠀⣿⡇⠀⣷⠀⣇⢨⡟⢁⣀⡤⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠤⠔⢺⣿⢭⣍⡓⢿⡇⠀⠘⣆⣸⠟⠋⠉⠁⠀⢘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣄⣬⠵⠃⠀⠀⠹⣮⡇⢀⣠⣾⡛⠛⠛⠉⢁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠋⠹⣍⡫⣉⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⡀⠀⣀⠀⠀⢀⣮⣾⣫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⡇⠀⣿⣽⡆⢸⣿⡏⣁⣀⠀⠀⠀⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⡾⠁⠀⣿⣿⠃⣾⣿⡿⢋⡟⠀⠀⠀⠀⢠⣇⣈⣡
⠀⠀⠀⠀⠀⢀⠀⢀⠈⢿⠿⠋⠐⣀⢙⠋⠒⠉⠁⠈⠀⢈⠢⡀⠀⣴⡨⠶⠖
⠀⠀⠀⠀⠀⠸⡟⠩⣹⡇⠀⠀⣠⡟⣸⣡⣶⠶⢀⠶⢦⡀⠁⣰⡄⠿⠶⠂
⠀⠀⠀⠀⠀⠀⢷⣄⣸⠀⢠⣾⠟⠁⡟⠀⣯⢙⡚⣷⠀⡿⢀⣿⢿⣞⡉
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣿⡇⠀⠀⣿⣄⠙⠛⢃⣩⠁⠠⠾⣏⣩⡭⠁
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⢿⣷⣄⣶⣟⣠⣾⣿⣿⡿⠟⠀⣀⣸⡿⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢙⡿⠛⠿⠿⠿⠁⠀⠀⣿⡏⣐⠿⠗⢀⡾⢃⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠙⣇⠀⠀⠀⠀⢀⡀⠸⣧⢸⠿⠃⢠⣏⠀⡸⣁⢈⣉⣀
⠀⠀⠀⠀⠀⠀⠶⠊⠋⠒⠒⢼⣿⢸⢷⡷⢸⣿⡗⢤⣽⣄⢄⠁⣼⣿⣿⡵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⡌⣿⡾⠛⣷⣾⣶⣷⠾⣿⣟⠀⢰⣿⠟⠉⢀⣠⡤⠤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣤⣽⣯⣾⣇⣿⣃⣼⣿⡋⢻⣿⣿⣿⣄⠀⣴⢏⣴⣶⣾⡇⡏
⠀⠀⠀⠀⠀⣀⣄⣸⣿⡿⢿⣿⣿⣿⣟⡀⠻⡿⠿⠒⠟⠛⠻⣿⣿⣇⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⡿⣾⣿⠿⠇⢠⣤⡄⠰⡶⢶⡄⠹⣿⣿⣿⣿⣿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⡞⠁⣴⠏⣼⣡⠶⣶⠀⠘⠛⠀⠛⢿⣿⣿⣿⣿⣦⣱⡀
⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⢳⠀⢸⡏⠀⠉⢻⣿⣾⣧⢰⣦⡀⠀⢐⡙⠿⣿⣿⣿⡿⢋⣠
⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⠀⢸⣧⣘⡀⠀⢳⡜⠋⢉⣡⠼⠟⠃⣠⠀⠀⡄⢀⣥⡾⠥⣟⡉⠛
⠀⠀⠀⠀⠀⠀⠉⡻⠿⣿⠀⠀⣿⣿⣧⡀⢀⣤⡶⠋⠁⠀⣠⣿⣿⠀⠠⣿⠿⣯⡛⠦⠌⠉⠁⢀⡠⠒⠒⠒⠒⠆
⠀⠀⠀⢀⣀⠸⣦⢻⣦⢹⣦⠀⠘⣿⣿⣿⣾⣿⣶⣶⣶⣿⣿⡟⠁⢀⣴⣷⣿⣿⣿⣶⣶⣾⣁⣯⠤⠀⠀⣠⠊
⠀⠀⠈⠉⠛⣿⡿⠿⠿⠿⠛⣷⣤⣀⣽⣿⡿⢿⡿⠿⠛⠉⠉⠁⢀⣀⡉⣿⡿⠿⣿⣿⠿⠉⠁⠈⠉⠓
⠀⠀⠀⢠⣾⡿⣟⠛⠁⠀⠀⢿⣿⡿⠟⢉⠿⣄⠀⠀⠀⣀⣤⡀⣸⡿⠿⠣⢶⣤⡄⠀⠀⠀⠀⠈⠂⠀⠀⢂
⠀⠀⠀⠈⠉⠉⠛⠛⢁⣀⡀⠀⢀⣤⣾⣿⣿⣽⣿⣿⡿⠋⢉⣵⡋⠀⠴⠚⠉⢛⣛⣀⣤⡀⠈⠃⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⣷⠄⠐⠾⢁⣟⣷⡌⣧⠉⢆
⠀⠀⠀⠀⠀⣰⣿⣿⣷⡾⢻⣿⣿⣿⣿⢡⣿⡿⢯⣬⣦⠀⠉⣿⣿⡀⠀⠈⠻⣿⣿⢻⡥⠀⣈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⠉⠁⣠⠀⠚⢿⣿⣿⣏⢰⣿⡟⢺⣿⣿⡁⢤⣔⡙⣷⣶⣾⣶⣬⢛⣍⡄⣨⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣮⠞⠋⡜⢻⡀⣿⣿⠟⠠⢀⣿⣾⡛⣣⡀⠉⠉⠉⠁⢀⢬⣿⠆⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠇⠀⠙⢾⡇⣀⡀⠙⢻⡟⠛⣍⢿⡁⠀⠀⠀⠁⠈⠋⠀⠈⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠠⣾⣿⠶⢾⣦⠙⢦⡀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠸⣯⡉⠁⠈⢣⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠣⠀⠀⠀⠃⠀⠈⠳⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠀⠀⠉⠙⠻⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠀⢀⣠⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠋⠁⢨⣿⣁⣴⣿⢿⣿⣿⠿⠟⠛⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⣠⣿⡿⠟⠉⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄
⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣴⡿⠁⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⣼⣿⠁⠀⢀⣴⡿⠟⠉⢉⣀⣀⣹⣿⣷⣌⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⣾⠏⠀⢀⣾⠿⠏⢤⣍⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⣿⡄⠀⠀⠀⢸⣇⠀⢸⣿⠀⠀⢸⡿⠻⢷⣄⢹⡇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏
⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⠘⢿⣦⡀⠀⠀⢻⣆⠸⣿⠀⠀⢻⣇⠀⠀⢿⣾⠇⢠⣿⣇⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣿⣦
⠀⠀⠀⣾⣿⠀⠈⠛⢿⣦⡀⠀⠀⠻⣿⣆⠀⠀⠻⣿⡟⠀⠀⠘⢿⣶⣤⣤⣥⣶⣿⣿⣿⡄⠀⠀⠀⢀⣴⣿⣿⠃⠀⠹⣿⣷⡀
⠀⠀⠀⢿⣿⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⢿⣷⣤⡀⢹⣷⠀⠀⠀⠀⢀⣀⣼⣿⠟⠁⠘⣿⣷⠀⠀⢀⣾⠟⢹⡟⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⢻⣧⡀⠀⠈⣿⡏⠙⠻⠿⢿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⢸⣿⣧⣠⣿⠋⠀⣼⡇⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣄⣀⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⢠⣿⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠙⠛⠻⠿⣶⣤⣄⣀⡀⠀⠀⠀⣀⣠⣴⣿⡿⠋⠀⠀⢀⣾⡇⠀⠀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⢠⣾⡿⠁⠀⠀⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠹⣿⣶⣾⣿⣿⠿⠿⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡷⠶⣶⣶⣶⣿⡿⠟⠋⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣤⣄⣤⣤⣤⣶⣶⣶⣤⡀⠘⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠟⠛⠉⠉⠁⣀⠀⠀⢀⣩⣭⣿⢿⣷⣿⣿⣿⡷⣶⣤⣤⣤⣤⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⢿⡏⠁⠀⠘⣿⡟⠛⢶⣤⡄⠀⠀⠀⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠠⠤⢤⣴⡿⠋⠀⠈⣧⠀⠀⠀⣿⠀⠀⠐⠈⠙⣷⣄⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢷⠀⠀⠀⠉⠀⠀⠀⣿⡄⠀⠀⠀⠀⠃⠙⣦⡤⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠉⠉⢳⣿⡟⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠤⠤⣴⣿⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣦⡀⠀⠀⠀⠀⠉⢿⣦⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣾⡿⢻⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠙⠻⣿⣷⣦⣄⣀⠀⠀⠹⢷⡀⠸⣿⣧
⠀⠀⠀⠀⣼⣿⠁⠀⠀⢩⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣤⣽⣦⣽⣿⠇
⠀⠀⠀⢠⣿⡟⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠁
⠀⠀⢰⣿⡟⢁⣠⡾⠋⠀⢀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠸⢿⣿⣿⣿⣶⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡐⡀⠠
⠀⠀⠀⠀⠀⣀⠀⡄⢰⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢀⠀⠥⠂⠐⢈⠀⡀
⠀⠀⠀⠠⠆⠰⣤⠷⣧⡠⢶⠉⠀⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠂⠂⣉⡣⡄⡖⢘⢩⠄⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⣤⣀
⠀⠈⠙⠂⣐⣲⣼⣿⣵⣼⣖⡛⠉⠁⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠈⠢⢤⣧⠕⢤⠙⠢⡀⠂⠀⠀⣤⣾⣿⣿⣿⣿⣿⠛⠉
⠀⡤⠚⣧⣿⠟⠋⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠃⠀⠀⠀⢀⠀⠀⣼⠁⠀⠁⠀⠁⠀⢠⣾⢟⣵⣿⣿⣿⠏⠉⠁
⠀⠠⠖⣹⠃⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢀⣴⣷⣀⠈⣏⠀⠀⠀⠀⡾⣦⣰⠃⠀⠀⠀⠀⢀⣼⡟⣵⣿⣿⡏⠉⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣿⣿⣿⡇⠹⣄⠀⠀⠠⣿⢈⣿⣶⣦⠀⠀⢀⣿⡟⣼⡿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⣿⡟⣿⡇⠀⠑⠄⠀⠀⠈⣿⡇⠻⣿⣷⠀⢿⡿⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣾⣿⣷⢻⣷⡄⠀⠀⠀⠠⡀⣾⢹⣧⣹⣿⣧⣾⣳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣷⣦⣄⡀⠀⠈⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣷⠄⣿⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣌⣹⡿⢿⣿⣿⣿⣿⣿⣷⣿⡄⣿⣿⣿⣿⣿⠿⠛⠁⠿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠛⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠾⣿⢿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⢄⣤⣴⣾⠿⢿⠟⠙⢿⠉⠛⠿⠿⢿⣿⣿⣿⠿⠿⢷⣶⣾⣽⣷⣶⣤⣾⣿⢹⣧⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⣧⣾⡿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠃⠀⠀⠀⠙⠛⠻⣿⣿⣧⣼⣤⠻⣷⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡾⠒⠳⣽⡿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⢀⡠⠚⣡⡴⠚⠉⠀⠀⠈⠙⢶⣄⠀⠀⣀⣠⠤⠤⠤⠤⣤⣄⣀⠀⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣅⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣬⣳⠐⠀⠂⠒⠢⣄
⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠚⠓⠒⠒⠒⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⡜⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠙
⠀⠀⡜⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠉⠙⠒⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢰⠁⠀⠀⣠⠔⢠⡏⠀⠀⠀⠀⣸⠃⠀⠀⢀⠠⠀⠒⠒⠂⡸⠋⡠⢀⣀⣀⡀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠃⣀⠴⠊⠁⠀⡾⠀⠀⠀⠀⢠⡏⠀⠀⡔⠁⠀⠀⠀⢀⡞⢁⠊⠀⠀⠀⠉⠉⠉⠉⠲⣄⠀⠀⣷⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠞⠋⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠁⠀⠘⠀⠀⠀⠀⢀⡎⠀⠎⠀⠀⠐⡲⠖⢒⡒⠄⠢⡈⠆⠀⠘⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⡜⠀⠀⠅⢀⠀⠌⢠⠊⠁⡈⢲⡀⢱⣄⢀⡇⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡀⢸⡄⠀⢀⡈⠀⡨⠧⠚⠻⢉⡼⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⡀⠀⢹⡆⠀⠀⠀⠈⡆⠀⡆⠘⣇⠀⠈⠀⠀⠈⣟⠫⡑⠀⠉⠀⠀⠀⠀⣀⠜⡞⠁⠀⢸⠀⢸⠿⡄⠀⠀⠀⠀⠀⡼⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠔⠀⠀⠀⢷⡀⠀⠀⠀⠱⠀⠀⠀⠘⠓⠒⢤⡀⠀⡞⠣⠈⠳⡤⠤⠀⠀⢁⠄⠀⠀⠀⠀⡌⠀⡜⠀⣷⣨⠀⠀⠀⣰⠁⠀⣠⠞⠁
⠀⠀⢀⠂⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠹⠀⠀⠀⠁⠀⠀⠈⠉⠓⠦⢄⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⣸⠃⠀⠀⡼⢹⣠⠞⠁
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢇⠀⠀⢜⢦⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠠⢠⡏⡴⠁⣠⡾⠁⠀⣠⠎⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠈⢧⡀⢾⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⣠⡾⠋⠀⣠⠞⠁⢀⡼⠃⣰
⢠⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠈⠂⢀⠀⠹⡼⠆⠀⠀⠀⠉⠒⠢⠤⣀⣀⣠⡤⠤⠔⢊⡡⢒⠝⠉⠀⡠⢾⠏⢀⣴⠏⠀⠀⢸
⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠁⡀⢷⠀⠢⢄⣀⣀⣀⣀⣀⠀⢀⡠⠴⠚⠉⡠⠐⢁⡠⠔⢉⠔⡡⢔⠋⠈⠀⠀⠀⢸
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢮⡛⠳⣶⠶⠦⠤⠤⠒⠚⠉⠀⠀⢐⡠⠤⠒⠉⠀⠔⡡⠊⠀⠘⠐⠀⠀⠀⠀⡎
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⢦⡈⢣⣤⣤⢄⣢⠤⠖⠊⠉⠀⠀⠀⡠⠂⡠⠞⠀⠀⠀⠠⠀⠀⠀⠀⡼⠀⠀⡀
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠈⠛⠿⣥⣀⠀⠀⠀⠀⣀⠤⠒⡉⠄⠊⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠃⣠⠜⠁
⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⠀⣀⣡⡤⠶⠖⣂⠀⠀⣀⣀⠤⠤⠒⠛⠉⠉⢉⠈⣀⡦⠗⠊⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠓⠦⢄⡀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⠉⠐⠂⠶⠦⠤⠴⠶⡖⠊⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠲⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠈⠉⠓⠦⠤⣤⡤⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⣤⣤⣤⠤⠖⠋
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠓⠶⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠤⠖⠛⠉
⠀⡁⠈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣐⡂⡀⢀⢐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠤⠒⠀⠃⠁⠈⢠⠁⠈⡀⠁⠉⠘⠀⠒⠠⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡀⠂⢁⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠰⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠈⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢑⡐
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠆⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠰
⠀⠀⠀⢀⠐⠠⡁⠀⠀⡀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⢈⡔⠂
⠀⠀⠀⣈⠀⠀⠄⠐⠀⠀⠀⠀⠀⢈⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⡁⠀⠀⠀⠀⠀⠂⠠⠀⠀⡁
⠀⠀⠀⠀⠰⠐⡂⠄⠀⠁⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⢐⠂⠆
⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⡜⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠤⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠤⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⢀⠐⠠⠂⡀⢀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐⠀⠂⣀⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠉⠐⠆⠆⠠⠈⡀⣀⠁⡈⣀⢀⡁⠄⠰⠠⠂⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠁⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⣀⠾⡦⠀⠀⠀⠀⠀⢠⠶⣝⣦⠄⠀⠀⠀⠀⢀⠔⢻⣯⡠⢄⠀⠀⠀⠀⣔⣲⡟⢻⣷⣤
⠀⠀⠀⡞⠁⠀⡇⠀⠀⠀⠀⠀⢸⠁⠈⠃⡆⠀⠀⠀⠀⠸⣤⠳⡬⠗⡋⠀⠀⠀⠘⡏⠙⠫⣹⠃⡣
⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠈⠲⠤⠖⠁⠀⠀⠀⠀⠀⠘⠦⠤⠔⠁⠀⠀⠀⠀⠙⠢⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡴⠂⣠⣴⠢⡄⠀⠀⠀⠀⢀⢔⣒⣆⢙⢄⠀⠀⠀⡰⡾⣧⣬⣙⣂⠀⠀⠀⠀⡠⠒⣶⣽⢦⡀
⠀⠠⡳⡈⠧⡼⣳⠑⡄⠀⠀⡠⢶⣹⣘⣹⢾⢸⠀⠀⠺⡀⡻⣿⠿⢇⡼⢱⠀⠀⠸⣀⠯⠓⡁⢳⣹
⠀⠀⠑⠌⠂⠈⠽⠋⠀⠀⠀⠙⠢⣗⣤⣒⠥⠃⠀⠀⠀⠙⢍⡒⠚⣹⠔⠁⠀⠀⠀⢸⣓⣒⣋⣁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⡠⢤⣄⠲⡄⠀⠀⠀⠀⣠⢤⣴⢤⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀⠀⠀⠀⠀⠀⣠⠤⠔⣤⡀
⠀⢀⠜⡴⡗⢒⢝⡟⡆⠀⠀⡰⠁⠻⠿⢹⡈⣆⠀⠀⢰⣉⣼⢿⣛⣿⡍⣆⠀⠀⢰⡹⡽⠿⣬⢏⠲⡀
⠀⠸⡀⣯⣻⣿⣾⡥⠋⠀⠀⡷⢤⡢⠤⢀⠃⣹⠀⠀⠀⡟⠯⠦⡐⠽⠣⡞⠀⠀⠻⣄⠻⣭⠵⢣⣷⠁
⠀⠀⠈⠑⠦⠤⠔⠁⠀⠀⠀⠈⠒⠛⠛⠥⠖⠁⠀⠀⠀⠈⠲⠒⠓⠖⠉⠀⠀⠀⠀⠣⠭⠝⠛⠯⠎

⠀⠀⠀⢰⣿⠿⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⢸⣿⠀⠀⠙⣷⣄⠀⠀⠀⠈⠻⣷⡀⠀⠀⢀⣤⣤⣶⡾⢿⣦⡀
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠙⣷⣄⣴⣶⣶⠿⠿⠶⢾⣿⣯⣥⣤⣤⣄⣹⣿⣤⣤⣄⣤⣶⡾⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠈⢻⣧⡀⠀⢀⣼⡿⠋⠀⠀⢀⣀⣴⣿⠛⠉⠁⠀⠈⠙⢿⣿⠉⠉⠉⠛⠿⣦⣤⡦⠀⣿⡇
⠀⠀⣀⣀⣀⣤⣹⣿⣦⣾⠋⢀⣤⣶⠿⠛⠛⣛⣿⣿⣦⣤⣀⣀⠀⠀⢻⣧⡀⠀⠀⠀⢹⡏⠀⢠⣿⠁
⣾⡿⠛⠋⠉⠉⠉⠛⣿⠇⣴⡿⠋⠀⣠⣶⠿⠛⠉⠉⠉⠉⠙⠛⢿⣦⡀⠙⣿⣄⠀⠀⢸⣷⣠⣿⠃
⢿⣇⠀⠠⣶⣤⣠⣾⣿⣼⡟⠀⠀⢰⡿⠁⠀⣠⣶⠿⠟⠻⠿⣶⣄⠘⣿⡄⠈⠻⣷⡄⠀⢿⣿⠁
⠘⣿⣄⠀⠀⢙⣿⠇⠻⣿⡇⠀⠀⣿⡇⠀⢰⣿⠁⣀⣠⣀⡀⠈⢻⣧⣿⡿⣦⡀⣸⡷⠀⠈⣿⡀
⠀⠈⢿⣦⡀⣾⡟⠀⠀⣿⡇⠀⠀⣼⣿⣄⠸⣿⣾⡟⠉⠙⣿⡄⠀⢿⣿⠁⢹⣿⣟⠁⠀⢀⣿⡇
⠀⠀⠀⠙⢿⣿⣧⡀⠀⣿⡇⠀⣼⡟⢸⣿⠿⣿⣿⣧⣀⣠⣿⠃⠀⣸⡇⠀⢸⣿⠻⣷⣀⣾⠿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⡇⠀⣿⠁⠈⢿⣆⠀⠀⠉⠙⠉⠀⠀⣠⣿⠃⠀⣸⡿⠀⣿⡿⠋⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢻⣇⠀⢿⣇⠀⠈⠻⢷⣦⣤⣤⣴⣶⠿⠛⠁⠀⣰⡿⠁⢠⣿⠃⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡈⢿⣦⡈⢿⣦⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⣾⠟⠁⢀⣿⠇⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠙⠻⢿⣿⠿⢷⣶⣤⣤⣤⣤⣴⣶⠿⠛⠁⠀⠀⣸⣿⡿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡄⠀⠘⢿⣆⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⡿⠁⢠⣿
⠀⠀⠀⠀⠀⠀⢴⠟⠁⠀⠹⣷⣄⠀⠀⠙⠻⠿⠿⠿⠿⠿⣶⣶⣶⣶⣾⣿⣯⣤⣴⣾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢶⣶⣦⣤⣴⣾⠟⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠉⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠴⠶⠶⣤⡎⠈⠋⠀⠀⠀⠓⠂⠈⣀⡤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⠔⡖⠙⣄⠀⠀⠀⠀⠀⠀⣠⠗⣢⣠⣄⠀⠈⠱⣍⠢
⠀⠀⠀⠀⠀⢰⡡⠖⠁⠀⢰⣫⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⣙⠆⠀⠈⠑⢼⡀
⠀⠀⠀⠀⢀⡏⠁⠀⢠⠚⢦⡈⠓⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⢀⡴⢲⡀⠈⣧
⠀⠀⠀⠀⠘⡀⠀⠘⡀⠀⠀⠧⠛⢴⣄⡀⠀⠀⠀⠐⠀⡀⠀⢀⣀⣤⣴⠎⠙⣾⠀⠀⢹⣀⡏
⠀⠀⠀⠀⠐⡃⠲⣏⠉⠀⠀⠀⠀⢸⣠⢌⡤⠀⠐⠲⡝⠄⠃⠰⢛⣄⡸⠀⠀⠀⠀⠀⢀⣹⣀⢀
⠀⠀⠀⠰⡖⠴⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠈⣿⡋⠀⠀⠀⠀⠰⠛⠁⠀⢸⣀
⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰⠀⠀⠓⢀⣀⣠⡇⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠑⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⠛⠉⠉⠢⢀⡤⠄⠈⠉⠉⣳⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠌
⠀⠀⠀⠀⢹⠁⠀⢀⣴⠆⠈⢀⠀⠀⠀⢄⠀⠀⠀⠰⡇⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠰⢦⡄⠀⢖⠚
⠀⠀⠀⠀⠀⣶⠚⣏⡀⠀⠀⠀⠀⢰⠱⣄⠡⣆⣀⠜⢳⠖⣀⠤⣮⠟⡧⠀⠀⠀⠀⠀⣀⣱⠠⠤⠄
⠀⠀⠀⠀⠀⡇⠀⢼⣁⠀⣀⡿⣤⠞⠁⠉⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠹⡦⢾⠂⠀⠀⣿⠍⣇
⠀⠀⠀⠀⠀⠧⠀⠀⠹⠶⠃⣰⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⡈⠙⣥⠎⠁⠀⡏
⠀⠀⠀⠀⠀⠈⢄⠒⢄⡀⠘⢧⡀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣹⠆⠀⠀⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠑⠦⠑⢆⠀⠈⠉⣻⡴⠚⠁⠀⠀⠀⠀⠀⠙⢦⡴⠉⠋⠀⠀⣀⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠤⠤⠦⠀⠀⠀⠀⠠⢄⡸⠒⠲⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠣⣀⣀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⢤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠻⣿⣧⣞⣶⡴⣀⠈⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡛⣃⣴⣾⣈⠻⡥⠔⣻⠀⡆⠀⠘⢷⡄⠀⠐⢦⣄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣧⣽⣿⣿⡿⢿⠷⣦⣤⠉⢠⣷⠀⢱⡀⢹⢀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠽⣿⣿⣿⠏⠀⠀⢶⡾⠁⠀⠚⣿⣥⠀⢳⣼⣷⡟⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠈⠻⡿⠀⠀⠀⠟⠀⠀⡴⠁⠞⣿⣅⠈⣿⡟⠁⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣶⣿⣏⣿⡄⠀⠀⠄⠀⠄⠀⠀⠴⠀⠊⢀⣻⣷⡄⠻⠀⢠⣟⡀⠠⡀
⠀⠀⠀⠀⠀⠲⢿⣿⣷⣜⠃⠙⠿⣿⣿⣿⡦⠀⢨⣤⢴⡪⠃⠀⠀⠀⢠⣽⣿⡗⢀⣠⣿⣿⣿⡄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡷⡀⠀⢹⣿⣿⡇⠀⠀⢻⣆⠰⣄⡀⣄⢀⣼⣿⡿⢡⣯⣾⣿⣿⡿⠟⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣯⢣⣤⣶⠴⠾⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢋⣦⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡿⠿⠛⠛⣿⣟⣿⣶⣬⣤⣀⡀⡀⠀⠐⢤⢟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣯⣿⡿⠋⠉⢻⣿⣿⠏⠀⠀⣿⡈⠱⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣻⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠑⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠚⠋⢉⠛⢱⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠑⣿⣫⡶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡂⠐⠒⢀⡀⠀⠈⡇⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⠃⠚⢶⣄⠀⡙⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠄⠀⡀
⠀⠀⠘⢮⢳⡔⠢⡀
⠀⠀⠀⠈⠱⢿⣆⠀⢳⣄
⠀⠀⠀⠀⠀⢀⠙⢄⡀⣻⡆
⠀⠀⠀⠀⠀⠀⢳⣴⣿⡿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⠇⠀⢰⣾⢶⣄⣼⠧⠀⠖⡆⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢿⣇⠀⠀⣸⡇⢀⣻⣏⠀⢀⣄⠳⡆⠀⠀⣠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠶⠞⠃⠀⠀⢽⣆⠐⣿⠇⠀⠀⠉⢙⣿⣿⡆⠘⣆⣆⡟⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⣽⣿⣿⣿⣧⣠⡴⠟⠛⠿⢿⣿⠀⢹⣿⣥⠾⠷⠾⣶⠀⣽⠂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⢄⡽⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠻⣄⢾⣿⡁⠀⠀⠀⣿⠸⡟⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢴⡾⠁⠀⠀⠀⣠⣷⣤⡤⣶⡢⣴⣆⠀⠈⠻⣿⣿⡄⠀⠀⢳⡄⢻⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡟⠀⠈⠁⣹⣟⠿⣿⠏⡿⠂⠃⠁⠃⠈⠈⠻⣤⣀⡙⢿⣿⣷⠀⢻⡇⡞⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢤⣜⠯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡟⠛⠸⣿⡇⢘⠉⢗⡼⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⢉⡍
⠀⠀⠀⠀⠀⠴⠂⠒⠒⠛⠓⠈⠃⠶⢦⣤⣶⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⣉⣩⣷⣤⡀⠀⡀⢀⠀⠀⠀⣀⠤⠖
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠄⠆⠈⡼⠛⠀⠙⣿⣏⣹⣿⣷⣄
⠀⠀⣠⣷⣾⡶⠶⠶⠶⠦⣤⣀⣰⢁⣠⣶⣆⠁⠀⠀⠀⠀⢿⣿⠀⠙⠿⣿⡄
⠠⠄⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⢿⣏⣿⠂⠀⠀⠀⠀⠸⣿⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⢉⡿⢤⠤⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⢠⣤⠿⠿⢠⠂⣀⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⡄⠀⢸⢠⠄⣀⢀⣀⡀⠀⠀⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣟⣏⣶⢟⠝⠚⠲⠒⠀⢑⡠⢶⣥⣿⣴⢶⡶⠦⢸⣿⣿⣿⣿⣿⣿⣿⢙⡿⡫⠗⠢⠔⠀⠙⡛⣿⡇⢿⣿⠟⣿⣿⣿
⠀⠀⠀⠀⠀⣀⡞⢩⡵⢁⢈⣿⢿⣷⡌⣺⠓⡒⠿⡉⠀⣠⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢩⠜⡀⣹⡷⣾⣦⢑⠛⣖⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⡾⠿⠓⢻⠞⣅⣫⣝⣶⢾⢀⣾⢉⣖⡽⢶⣩⠯⢼⠀⠀⢸⣿⣿⣿⡿⠗⢓⡷⠻⣐⣭⣳⡶⡁⣴⡉⣔⡹⢶⣉⠧⢼⣿⣿⣿
⠀⠘⠋⠉⠉⣵⠛⣆⠀⢷⣬⣬⠟⣋⣉⠴⠋⢐⠞⢷⡒⠁⠀⠀⢸⣿⣿⣿⣿⣿⡟⠳⡄⠸⣦⣤⡽⢋⣁⠤⠋⢀⡞⢳⡶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢳⣌⣓⣲⠂⢙⠛⠿⠋⢺⣚⠭⠖⠛⠿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣦⣍⣩⡇⠈⡛⠛⠏⢸⣯⣭⣴⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣾⡫⠽⣿⡻⠲⠶⣶⡶⠛⠽⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣥⣾⣮⣿⣷⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠒⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣠⠀⠀⠉⢛⡀⠀⠚⠶⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠰⣂⠫⣀⠀⠸⠢⠁⡄⠀⠀⠀⠀⡀⠀⠙⠋⠀⠀⣶⢯⣤⡤⠤⡀⠈⣤
⠀⠀⠀⠀⠀⠀⠰⢇⢪⡏⠀⣀⡄⠾⠛⡯⢱⠀⡸⢀⠀⠀⠀⠀⠙⣿⣦⣄⡾⠀⢀⢴⡎⠁⠳⣔⠏⢠⠸
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⣦⡌⣆⠳⠔⣡⡎⠀⠁⢀⠻⠀⠀⠀⢀⠈⢡⣾⠇⢰⣿⡀⠓⢀⢀⣼⠃⠸⠇⣠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠦⠙⢃⠤⠼⠭⠐⠋⠀⣠⣎⠄⠀⠀⢀⡴⠞⠋⢝⢌⡐⠻⠳⠒⣻⠗⠁⢀⣔⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠈⠉⠑⠠⡄⠹⣦⡀⡠⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠍⠢⠛⠉⠁⠐⠀⠀⠨⠁
⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣤⣈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠀⡦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢐⣠⡍⠁⠚⠉⠁
⠀⠀⠀⠚⠋⠁⠘⠛⢂⡠⠌⠙⠛⠆⠀⠀⠀⠃⠯⠊⠛⠛⠛⠚⠛⡟⠛⠁⠀⠀⣰⡟⠁⠀⠉⣉⣻⣾⠀⡀⠤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣶⣯⣤⡖⠶⣤⡀⠀⠀⠀⠀⢠⢖⣅⢔⣀⡄⣀⡀⠀⠀⠀⠀⡍⠀⣠⣞⡑⡟⠓⣒⡦⣌⠃⠹⣾⣄
⠀⠀⠀⠀⣠⠊⠂⣡⣞⠉⠑⠮⣛⠀⣦⠀⠀⠀⠀⠘⠣⣜⡁⠋⠃⠋⠀⠀⠀⠀⢿⢰⠈⢋⡞⠁⠀⠨⠃⣹⣿⠀⡞⡳⡀
⠀⠀⠀⢸⣿⠀⣴⡆⠙⠀⡀⢠⡿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠸⡇⠈⠻⣶⣰⣦⡶⠼⠟⢊⡴⡱⠁
⠀⠀⠀⠈⣏⠂⠘⣿⠤⠶⣻⠏⠀⠀⠀⠀⢀⠄⡀⠘⠣⠄⠀⠄⠀⠀⢀⣀⠀⠀⠙⠦⢰⣦⢀⠀⠉⠓⠶⠶⢖⠞⠰⠁
⠀⠀⠀⠈⠛⠕⡒⢄⠶⠚⠁⠀⠀⠀⠀⠐⢀⡘⠋⣀⣠⠂⣄⠀⠁⠻⠋⠀⠀⠀⠀⠀⠙⠉⢀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⢄⠈⠆⢸⢹⠛⡯⣀⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣷⡤⠀⢀⣤⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣤⠴⣧⣠⠀⠀⠼⠌⡒⢪⠝⣠⠀⣇⠜⠃⡀⠀⠀⠀⠀⣠⡴⠶⠙⣿⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠹⣂⠞⢃⡴⠁⢰⣿⠁⠀⠀⠀⠐⠉⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠁⠐⠚⢃⠀⠐⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠖⠛⠛⠉⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠿⠴⠶⠶⠦⠤⠤⠬⣭⣙⣺⢄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⡀
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⣠⠞⣁⢔⡢⢬⠽⠿⠿⠶⣴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢦⡀
⠀⠀⠀⠀⣿⠁⠀⠀⠀⣠⠖⠚⣇⠀⠀⠀⢠⡿⣡⠞⡱⣫⠞⠁⠀⠀⠀⠀⠈⠑⢄⠁⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠙⢦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠹⣄⠀⠀⣼⡷⠁⡼⢰⠃⠂⡀⠠⢀⣂⠀⠒⠒⠈⢣⠀⢱⠈⠙⢦⡀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⠙⣆⠀⣿⠇⢀⡇⡟⢰⠋⣠⡖⣋⠉⠁⠘⠟⡓⠚⠢⢤⡇⠀⠀⠱⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠘⣆⢻⠀⠀⡇⠇⢨⠀⡧⣪⣥⢍⠓⢄⠀⠻⢀⠀⠃⠈⢆⠀⠀⠘⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⢎⢧⡀⣿⠀⠈⢆⠈⠛⠄⠈⠀⢠⡄⢀⡜⡀⠀⠀⠈⡄⠀⠀⠸⡄⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⠀⠀⠱⡕⢿⠀⠀⠈⠑⠢⠤⠐⠂⢁⠄⡪⠊⢡⠀⠀⣸⠀⠀⠀⠀⢷⠀⢀⡏⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠱⡹⣄⠀⠀⠀⠀⠘⢆⠑⢤⡀⠀⣀⣠⠤⠖⠑⠈⠀⢀⠌⣠⠞⠁⠀⠀⠀⠀⢸⡄⣸⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠱⠘⢦⠀⠀⠀⠀⠀⠑⠤⢈⠣⢀⠀⠀⢀⣀⣤⡴⠿⠋⠁⡐⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢡⡀⠙⠛⠛⠓⠒⠒⠶⠤⠬⠭⠽⠛⠋⠉⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢷⡢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠳⢤⡉⠉⠛⠒⠶⠶⠤⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⣀⣀⣀⣤⣤⡤⠶⠒⠛⠋⠉⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⣀⡤⠤⠴⠶⠾⠯⣥⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠒⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡧⣤⣤⣤⡆⡀
⠀⠀⠀⠀⠀⢀⢡⡄⣄⡠⣦⣾⡎⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⣠⡿⢋⠷⢿⣯⠟⡀
⠀⠀⠀⠀⠰⢾⡏⠰⢾⣿⣷⣴⢰⡄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⡄⠀⠀⠤⣤⠞⠃
⠀⠀⠊⠀⠀⡼⣄⢻⣏⣟⣽⣥⠚⠛⣤⡤⢀⠆⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣿⢇⡤⠂⠈⠁⠀⠀⠸
⠀⡀⠀⠀⠀⢧⠀⠀⠀⠁⡠⠦⢦⡿⠋⢀⡌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡿⠊⠀⠀⣠⠄⠠⠤⡀
⠀⢀⡀⠀⠀⠀⠀⠙⠶⣜⠀⠀⣈⣠⠄⠛⢣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠔⠒⠒⣈⡿⠀⠀⢠⣴⣍⡛⡟⠓⠂⠁
⠀⠀⠑⣀⡀⠀⢀⠀⠒⠚⠋⠛⠋⠀⠀⢠⡴⠁⠰⠂⠀⠀⠀⢀⠄⡄⠀⣆⡼⣉⠇⠀⠀⠀⢸⠋⠀⠃⢀⡄
⠀⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⠀⣀⠀⣀⠈⠀⢀⠁⠀⠀⠀⠀⠈⢸⡧⠾⠃⣤⠏⠀⠀⡀⡐⠁⢀⠤⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠐⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⡾⠋⢛⣒⠚⠁⠀⠀⡀⠂⠀⠀⣁⣆⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠀⡞⣀⣶⣋⣡⣤⣡⡴⢺⠕⠀⠀⣶⡿⠿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠋⠉⠛⠹⠭⠥⠍⠛⡝⠀⠀⡀⠛⠷⠶⠧⣤⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⠀⡀⠀⠀⠀⠀⠘⢂⡀⠀⠀⠀⠀⠀⢸⡤⠞⢩⣷⣄⡀⠀⠀⢸⣿⣿⠃⢀⠐⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⠃⢀⡐⢲⣬⣶⣾⠋⢉⣭⣽⣿⡆⡁⠀⠀⠀⢠⡶⠃⠀⠀⣸⣿⡦⠑⣄⠀⠈⠻⢻⡿⣯⣤⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠧⢐⣶⠿⣿⠟⢹⡇⠋⢠⣬⡿⠻⠉⢻⠙⡆⠀⢰⡞⠀⠀⠀⠀⢰⡿⣧⣀⠘⠆⠀⠀⠉⠓⠟⠒⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠐⠛⠒⠈⠀⠀⣾⢹⠇⠀⢀⡞⠆⠰⡀⢻⠁⠀⠀⠀⠀⠀⠳⡟⢤⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⡛⣛⠉⣅⢲⣮⡸⠀⣀⡜⠀⠀⠐⣵⠋⠀⠀⣀⡒⣘⢂⣲⢚⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣙⠓⠻⢿⣿⡷⠾⣉⡀⠀⡇⢀⡇⢀⣠⣰⣿⣴⣿⣾⡏⢛⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⠿⠲⡄⠉⢶⢱⣎⠟⠁⣴⣿⠉⢢⠉⠻⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⣶⣶⡆⠹⣟⣿⣏⠐⠀⢸⡀⠀⢹⠇⠀⢸⠾⡷⠀⠀⠃⢀⣶⣿⢟⡓⢠⡀
⠀⠀⠀⠀⠀⠀⢀⢊⣀⣉⡽⠻⠟⢉⠀⢛⣿⢉⠙⠀⠠⡇⠀⣴⠀⠀⠈⢴⠻⣦⠀⠇⠈⠙⢹⠛⣦⣀⠹⡀
⠀⠀⠀⠀⠀⠀⠄⢀⡴⠟⠀⠀⢠⠜⠀⠈⠛⢿⣝⠀⡴⠁⢸⡏⢃⠀⠀⠀⢱⣴⠆⠀⠀⠑⠼⡀⣙⣛⣄⣧
⠀⠀⠀⠀⠀⠚⠒⠘⠒⠒⠓⠉⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⣸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠄⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡆⠀⢠⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⢸⠃⠰⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠀⢾⠀⠀⢰⡆⠀⠻⢦⣴⡀⢠⠄⠀⣧⡜⠀⢀⠀⣼⢀⠀⠈⢳⡀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡀⠄⠀⢹⡀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠉⢷⠾⣿⣷⣿⠀⠀⢸⡷⠟⠉⠀⠀⠀⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠉⠻⣶⣤⡳⣄⠠⠷⢀⣾⠀⠀⢀⠀⠀⠀⠀⣹⢿⠛⢷⣤⡈⠀⠀⠀⠀⠀⠀⢸⠷⠖⠒⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡢⡀⠀⠘⣿⠶⠶⠦⣄⠀⠀⣙⠾⢿⠁⠀⠀⠀⣿⣈⣧⠀⠹⢇⢀⣤⣄⠀⠀⠀⣈⡠⠄⠒⠊⠈⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢷⡈⠲⢶⣿⡄⠀⠀⣈⠻⣶⠇⠀⠸⣄⡀⣸⣾⣿⣿⣿⡁⣠⠊⡿⠋⠀⠀⠀⢀⣯⣀⣀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠙⢦⡀⠙⢷⣤⠞⠁⠀⢸⠀⠀⠀⠜⢧⠙⠿⣿⣿⣿⠟⠁⢀⡁⢀⠠⠒⠉⠀⠀⠀⠈⠉⠙⠂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢽⣶⣤⠾⢿⣦⠞⡇⠀⠀⠀⠈⣇⠀⠀⠀⢻⠀⠀⠙⢿⡃⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⡠⠴⠤⢴⡞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠖⠉⠁⠀⣠⠴⠋⠀⠀⠊⠀⠀⠘⠀⠀⠀⠀⠈⣷⣿⠀⠸⣇⠀⢀⣈⠋⠉⠙⠻⣧⡀⠀⠀⠀⠴⠿⡀⢀⣴⠏⠀⠀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡥⠴⠒⠒⠒⠤⣤⣀⣀⣠⣶⣤⠴⢾⣿⣧⣠⠞⢿⡷⢻⣿⡇⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠠⣍⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠰⠖⠛⠁⠀⠀⡀⠀⣀⣀⣨⠿⠿⡿⠉⠀⠀⠀⠀⠈⣿⠀⠀⣣⣼⠟⠀⡀⠄⠀⣦⠀⠹⡤⠴⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣵⣤⡄⠀⠠⣤⢤⣇⣠⣾⠷⢤⣤⣾⣦⣄⡠⠇⠀⠀⠱⣤⣤⣤⣤⣥⣤⡤⠤⠴⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣰⠃⡈⠁⠸⡇⠀⠀⠸⠋⠀⠈⠳⣄⡀⠀⠀⠈⠦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠲⣤⣼⠗⠀⠀⠀⣠⣿⡀⢀⣶⣄⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠉⠉⠙⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⢀⣀⣠⠖⠛⠛⠳⢼⠀⠉⠛⠶⢤⣄⡁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⢸⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠑⠂⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣿⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢋⡟⢻⢽⣶⡄⠀⠀⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⢰⠒⠊⡇⣰⡟⢧⡘⡴⠃⢹⣄⠀⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⢯⣵⣼⠀⠀⣷⢳⠇⠀⠙⢷⡶⠟⠘⡇⠀⠀⠀⠃⠀⡀⠀⣠⠴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠋⠛⣏⠓⢦⣿⣖⠒⢒⣶⣿⣶⡖⢻⡅⠀⠀⣀⠀⠀⢿⡞⢹⡄⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⣿⣠⣾⢯⣉⢱⡄⣏⠻⡍⠉⠉⠉⠉⢁⡜⢀⡠⠔⢹⡀⠀⣿⡇⣼⠃⣸⣷⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣾⠀⣿⡇⢧⣾⠟⡟⢿⡟⠀⢹⠿⣯⣍⠉⠉⡰⠋⠀⠀⠈⡽⠀⣿⣿⣿⣾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡟⠈⢣⣽⣧⣀⣹⡾⠷⢻⠃⣠⢯⠀⠈⣯⢻⣴⡇⢀⣼⠃⣸⢧⣠⠟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠈⠳⣤⣀⣀⣀⣠⣿⠞⠁⢸⡇⢀⣿⣼⡇⢳⣾⡷⣾⣵⣯⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠠⡤⣤⣐⠒⢤⡀⢸⠀⠙⠶⢤⣀⣈⣻⡿⠟⠋⠁⠀⢀⡼⠀⣸⣭⣭⣿⠁⠒⠻⣥⣀⠙⠛⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠑⠦⣬⣭⡱⢾⣘⣦⣀⠀⠀⠊⠉⠛⠛⠛⠒⢲⣶⣯⣥⣤⡟⠉⣧⠹⣤⠀⠢⣈⢿⢮⠀⢄
⠀⠀⠀⠀⠀⡠⠊⡩⠁⠀⣼⡟⠻⣶⣌⠙⠦⣄⠀⠀⠀⠀⣠⠞⢿⣿⣯⠀⠀⠐⢬⡳⡈⠻⠷⢬⡙⣮⢣⡀⠑⢄⢲⡄⠀⣠
⠀⠀⠀⠀⠀⢀⠎⢀⡼⠆⢿⣽⡀⢠⣽⠀⣦⣬⣿⣶⣶⣾⡿⢳⡀⠙⠿⠷⣤⣦⣀⣱⣇⠀⠀⠀⠈⢺⡇⠉⠒⠒⠋⠁⠉⠁
⠀⠀⠀⠠⠴⠧⠶⠟⠁⠀⠈⢧⡇⣸⢇⣴⡿⠋⣸⠁⠀⠙⡇⠘⢇⠀⠀⠀⠈⠀⠀⠉⠻⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⣡⣿⠋⠀⠀⢹⣦⠀⠀⢻⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠁⠀⠀⠀⠀⠉⠻⢦⣸⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠀⠀⠁⢃⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠊⠀⠉⠁⠀⠼⠃⠒⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⢀⠔⠈⠒⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠀⡄⠀⡆⠀⠀⠀⡐⢀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡌⠀⠀⠀⢃⠀⠁⠀⠀⠈⠀⠀⠀⣀⠀⠁⠐⠀⠀⡀
⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠢⣀⠀⠸⠑⠈⡀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⢣
⠀⠀⢀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣬⣧⡈⠣⢀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣿⣹⣿⣿⣿⣷⣶⣦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠉⠂⠄⠀⢀⡤⠤⠤⠀⠀⠀⠀⠀⡸
⠀⠀⠈⢿⣿⣿⣿⣛⣿⣿⣟⢻⣿⣷⠤⢴⣄⡀⠀⠀⢀⣼⠋⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠙⢦⣀⣾⠃⠀⡿⠁⠈⠂⠀⠄⠀⠀⠀⠀⡀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣿⢀⡶⠛⠻⣷⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠁⠀⠀⠀⠀⠆⠢⠀⠀⠄⡀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠐⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠂⠀⠸⣧⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣿⣍⣿⣿⣯⣼⣿⣿⡇
⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢻⣷⣴⡀⠀⢀⡾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠁⠰⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⣠⣤⠤⠀⠙⢿⣷⣄⣼⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁
⠀⠀⠐⠀⢠⡀⡀⠀⠀⠀⠀⠀⠆⠂⠀⠁⢀⣿⣧⠀⠀⢀⣀⣙⣿⣿⣦⡀
⠀⠀⡰⠂⠈⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢠⢾⣿⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣷⡀
⠀⠰⠁⢀⠤⠀⠤⠤⡄⠐⠈⠀⢀⠤⠒⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⡀⠀⠀⠈⠢⠀⠀⠀⡀
⠀⠐⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⠂⠀⠁⠀⠀⢦⠁⠠⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠃⠀⠀⠑⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣏⡟⢀⣴⣶⣤⡄⠀⠰⣴⠀⢀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣇⠿⣿⣿⠟⠁⠀⠀⡿⠀⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡈⢸⠿⠁⠀⢀⡄⠀⢇⡜⠀⣀⣀⣁⣸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠿⠽⠛⠛⠔⠄⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⡀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⡀⠀⠀⠸⡄⠛⠀⠂⠀⠐⣦⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠚⠋⠙⠓⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢿⣶⡀⠀⠀⠀⠀⠀⠐⢸⣧⣴⣄⠀⠛⢿⣿⢷⢤⠀⢠⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢛⡀⠀⢀⣾⡿⢟⣛⣿⡈⠛⢿⡿⣧⣄⡀⠘⠒⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠿⣿⡗⠚⠉⡾⣟⣿⣿⣄⡀⠀⠀⢈⡃⠀⢃⠀⠖⠚⠓⠋
⠀⠀⠀⢠⣤⣶⡀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠙⠙⣩⣿⢿⡟⠀⢀⣠⣴⡆⠀⢸⠀⢠⣄⡀
⠀⠀⠀⠀⠙⠷⣽⣇⠀⠀⠀⠀⠀⢀⣠⡀⠘⠐⣻⡟⢻⣥⣾⣿⣥⠌⠁⢀⠞⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⡔⢁⡼⠃⠀⠚⠉⢆⣹⠁⠀⠛⢹⣷⣆⢡⣀⣲⡖⠿⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠤⠦⠟⠉⠁⠀⠈⠉⠉⠀⠀⢀⢙⣾⡮⡟⠀⠀⠀⠘⢿⡏⠀⠉⠻⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠀⣴⣼⣯⡋⢱⣇⠀⣤⣤⣤⣠⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣠⣶⣤⡀⠀⠀⡹⣿⣿⡟⢿⣿⡻⡇⡿⢿⡌⢊⠘⣿⡿⠀⢸⠟⠟⣡⣤⣶⣶⣦⡦⣄
⠀⠀⠀⠚⠋⠉⠛⠛⠩⠿⠿⠛⠛⣻⣗⡤⠭⣇⠠⣇⠘⣿⡴⠀⣩⣤⣦⣭⣭⣄⠈⠙⠻⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠖⠀⠀⠙⢸⠀⠈⡧⢊⣀⣨⣞⡿⡿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠲⡆⡸⠁⠈⠛⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢋⣁⣀⣀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⠛⠋⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣉⠳⢦⣄⡀⠀⠀⠀⠘⣷⡀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⣀⣭⠥⣄⣬⣥⣄⣉⠻⣦⠀⠀⠀⢸⡇⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⣤⡿⠋⠀⢠⠞⣁⣐⣛⣛⠛⠻⠟⠿⣿⣿⣧⢦⠀⠀⣷⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣾⡟⠁⠀⢠⢃⣾⣿⢟⣵⣿⢾⢿⣶⢠⡘⣿⣿⣼⡇⠀⡏⢠⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⣼⡟⠀⠀⢠⡿⠘⡿⣱⣿⠃⢿⣤⣤⡿⣹⡇⣿⠏⣿⠇⢰⡇⣸⣧⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⣰⠃⠈⢧⠀⠉⠉⠁⠀⣠⣿⣧⠀⢰⣿⣿⠀⠀⠙⠿⣿⣿⢣⠏⣠⠏⠀⣼⣷⣿⣿⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢨⡃⠀⠀⠀⢿⣿⣿⣿⣆⠀⢻⣿⣆⣀⣠⣤⣶⠗⢃⡼⠃⢠⣾⣿⣿⣿⣿⠁⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⢸⠀⠀⠸⣷⡀⠀⠀⠸⣿⣿⣿⣿⣆⠈⣿⣿⣿⡿⠛⢁⣴⡿⢁⣴⠿⠛⠛⢻⣿⠏⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣷⡀⠀⠀⢯⡙⠿⢿⣿⡶⠟⢋⣡⣤⣾⣿⠿⠛⠉⠀⠀⢠⣴⡿⠁⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣿⣿⣦⡀⠀⠻⣶⣶⣦⣤⣉⡉⠉⠉⠉⠀⠀⠀⠀⣰⠶⠓⠁⠀⢀⣴⣿⣿⡿
⠀⠀⠀⠀⠘⣿⣄⠀⠀⠉⠛⢿⣿⣿⣶⡀⠀⠙⠻⠿⢿⣿⣷⣶⡶⠞⢋⣁⠀⠁⢀⣀⣤⣾⣿⠟⣹⡟⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⠀⠙⣿⣿⣷⣶⣶⣦⣤⠤⠤⠤⠤⠶⠾⠿⠿⣿⣿⣿⣿⣿⡟⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣤⣭⣭⡭⠶⠞⠛⠛⠛⠻⠶⠶⠶⢤⣤⣤⣤⣶⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠠⡀
⠀⢀⠢⠀⠀⠀⠀⠀⢀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢈⣩⠿⠿⢿⣅⠁⠀⠀⠈⠀⠀⠀⣿⠈⠀⠀⣀⠂⡠⠀⠂
⠀⠀⠀⠈⠦⠀⠀⠀⠈⢂⣈⡄⠀⠀⠀⠀⠀⠀⡿⠁⠀⡀⢖⡀⡀⠀⠐⣄⠀⠀⢀⢸⠇⣤⠐⠋⠁
⠀⠀⠀⠀⠀⢉⢠⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠸⠋⠉⣿⠅⠈⡾⣄⣸⠆⠀⢸⠉⢀⢑⡆
⠀⠀⠀⠀⠈⠀⠎⠁⠀⡀⠀⠀⠀⣀⣠⠄⠀⠃⠀⠀⡁⠘⠶⠤⡾⠱⠋⣹⠆⢀⡦⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀⣴⣿⣿⠀⠀⠀⠘⢷⡟⢶⣶⡾⠁⣰⣾⠏⠀⠏⠀⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠐⠁⠂⠀⠠⠄⠀⠀⢾⡿⢛⠙⠓⢀⣄⠀⠀⠙⢦⣈⡁⣀⣉⣁⡤⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠶⠟⠡⠎⠈⠀⠀⡄⢠⣄⣀⣀⣨⠀⠘⠿⣥⡤⠠⢲⡀⠀⠀⠀⠀⢱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠰⠀⠀⠉⠉⠈⠙⢳⡀⠀⠀⠀⠂⢈⠁⠦⡄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀