Rose Emojis & Symbols

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

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

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

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

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


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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃

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

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





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

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

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

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

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

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

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

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

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



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

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



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

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

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


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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢲⣤⡀⠀⢾⢩⣤⠟⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⣦⣉⣛⣢⣀⣬⣽⠎⣿⠃⣼⣿⣶⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢀⣤⣿⣿⣿⣷⣿⣦⠀⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣠⣶⣤⣄⢈⣽⣿⣭⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣶⣄⣿⣿⣿⣿⢾⣿⣿⣿⣿⡿⢃⡰⣾⣻⣽⣿⣿⣿⣿⣿⣟⢻⣿⣿⡟⠿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⢛⢿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣽⡻⠿⠿⠿⢿⣀⠉⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣶⣿⣿⣷⣿⣿⡟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣷⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⠟⠋⠀⠀⣿⢿⣿⣿⣿⣿⣿⡇⠘⢿⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣟⣿⠿⠃⠀⠀⠈⠀⠀⠀⢀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠸⣷⢸⡇
⠀⠀⠀⢀⣼⡿⣿⣿⣿⣿⣿⢇⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⣱⣿⣤⣶⣆
⠀⠀⠀⢸⣿⣿⣹⣾⣿⣿⡷⢿⣿⣿⣷⣿⣿⣿⣶⡄⠀⠀⢢⣄⠀⣱⣄⠀⣰⡃⠀⠀⠀⣼⣿⣦⢠⣤⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣄⠀⣀⠘⢿⡄⣿⣿⠀⣿⢣⣴⣶⣶⣌⣻⣟⣽⣿⣿⡟⠢⠋⣿⣿⣿⣾⣿⣿⣷
⠀⠐⠒⠶⣿⠿⠗⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⠁⠀⠈⢿⣿⡣⣸⢳⡾⡇⠈⠛⠿⠛⣿⣿⣿⢿⣿⣿⣇⡁⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢣⣜⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠣⡹⡌⣱⣀⣀⠀⠀⠀⠈⠉⢁⡶⢈⣟⣿⣿⣿⡿⢩⣿⣿⣭⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠿⢟⣭⣿⣿⡏⣸⣿⣿⡃⠀⠀⠀⠀⢴⣶⣶⣿⣿⡿⣿⣿⣿⠗⠀⠀⢀⠟⢃⣵⣦⡍⠉⢏⡀⠸⣿⣿⣿⣷
⠀⠀⠀⠠⠾⠟⠁⣀⡤⠈⠉⠀⠉⣿⣿⡆⢿⣿⣷⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠻⣴⣽⡿⠀⠘⢿⡆⠹⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠰⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣴⡿⣿⢿⠿⣿⡿⣿⠿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣥⣤⣤⣤⣿⢣⣤⣤⣤⣤⣴⣿⣬⣤⣄⣀⣤⣧⣤⣤⣤⣿⣿⣿⣿⣿⣿⣧⢻⣧⣿⣼⣷⣹⣿⣿⣛⡿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⣿⣟⢹⣟⡻⣿⢛⠟⣻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⠿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⠟⠛⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣿⠇⠀⢰⠏⠀⢀⣴⠃⣠⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣋⡀⣠⠏⠀⠀⠿⠿⠀⠉⠉⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠚⠿⡟⢁⣐⠿⠿⠿⠚⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢉⡽⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠔⠁
⠀⠀⠀⠀⠀⠀⢐⡆⠉
⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠨⠁⠡⠭⢤⡾⢰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡒⠤⠠⡴⣶⠤⡤⠈
⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⣶⣶⠖⣋⣡⣴⠄
⠀⠀⠀⠀⠀⠠⣄⣀⠛⠛⠙⢿⢛⣿⣿⣩⣤⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠒
⠀⠀⢸⣶⣶⣶⣶⣤⣤⣍⣛⣿⣟⠛⠛⠛⠉
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣴⣶⣤⡀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣽⡯⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠁⠛⠃
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣿⣟⣛⣟⣛⣻⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

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

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


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

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



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

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

⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠋⠉⠁⠀⠈⠁⠀⠀⢀⣴⣿⡆⠀⠉⠀⠀⠀⠀⠙⢋⣁⠿⣿⡆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣈⣦⣀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⣀⡀⠀⠂⠂⠈⠁⠶⣿⠇
⠀⠀⠀⣿⠀⠛⢦⣄⠀⠀⠀⠀⠀⠠⣿⣤⣤⣴⣶⣤⣾⣿⣿⣿⡄⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⠿⣾⣿⣿⣄⣤⣤⡀⠀⢰⣿⡆
⠀⠀⠀⣿⠀⠀⠀⠈⠻⢦⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠙⣿⣿⡅⢠⣾⣅⠚⠛⢿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢙⠿⢛⣛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⢷⡇⠀⢸⠀⠀⠀⢀⠀⠀⣀⣴⣿⣤⣀⣠⡄⠀⢫⠉⠁⠉⠉⠀⢰⣿⡆⠁
⠀⠀⠀⣿⠀⠀⠀⠀⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠀⢸⠀⠀⠀⢻⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠋⣰⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⠀⡇⠀⣸⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠄⠀⠀⠀⠀⢀⣷⣿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠗⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠄⠀⡐⠐⠿⢿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣏⠉⠘⢏⢿⡿⢿⣿⢿⣎⡇⠀⢻⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⠞⠛⠀⠀⠁⠀⠀⠀⠆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⢀⠀⠘⡀⢷⣠⢻⣦⠛⡇⠀⢸⠀⠀⠙⠛⠛⠛⠛⠻⠿⣿⣿⡿⠿⠿⠿⠀⢀⡤⠀⠀⠀⢹⣾⡇
⠀⠀⠀⣿⣀⣀⣀⡀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⢀⣘⣛⣿⣟⣀⡇⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⣴⣿⣦⣄⣹⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⠟⠛⠒⠒⠋⢉⣻⣍⣿⣿⣌⡯⢙⣿⣿⣿⣿⡖⠖⠚⠓⠒⠓⢀⠀⢸⣿⣿⣿⣷⣶⡆⠀⠈⣙⣁⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣦⡀
⠀⠀⠀⣤⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣦⣿⣿⣿⢏⣏⡀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡟⢹⣿⣿⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⢿⡇
⠀⠀⠀⣿⣶⡖⠊⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⡄⢠⡴⠒⢻⠀⢸⣿⣿⣷⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⢋⣾⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⠀⢸⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠄⠀⠀⠀⡇
⠀⠀⠀⣿⠼⣿⣿⣿⣿⣿⠁⢰⣾⡿⠉⣀⠉⠛⠛⠛⢻⡛⢛⡉⠉⣀⠀⣸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣻⠀⠛⣻⣿⣿⠇⠀⣾⣿⠃⠀⣿⠇⠐⣇⠀⢿⡇⣾⡇⠈⠋⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣿⠀⠘⣻⢿⠋⠀⠸⠿⢛⠀⢰⣿⠀⢀⣿⡄⠈⢠⣿⡇⠀⠀⠒⢾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣷
⠀⠀⠀⣀⠀⣀⣼⣾⣿⣷⣦⣤⣾⣆⠈⠛⠀⣼⣿⣷⠀⢸⣿⡷⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⠆⠸⣤⣄⣀⠾⠃⡄
⠀⠀⠀⣿⣿⠟⠛⢿⡻⠿⢛⣿⣿⣿⣷⣶⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣋⣯⣿⣿⣿⣿⣷⣾⣿⡶⣾⠀⠈⠙⠀⠀⡇
⠀⠀⠀⣿⡉⠤⣶⣏⡤⢶⠿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⡃
⠀⠀⠀⣿⠄⠐⠉⠁⠀⠀⠀⠀⠀⢀⣽⡍⣋⣫⣟⣻⣿⣿⣛⣿⣿⣽⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠖⠚⠃
⠀⠀⠀⠘⠓⠚⠚⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡟⠙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠖⠑⠀⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠉⠀⠟⠀⠃⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠋⣤⠄⡆⠀⠀⢀⠀⠓⠠⠀⠛⢱⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣉⠀⣳⠂⠃⠀⣄⠐⠁⣀⠙⢦⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⠻⠟⡀⠛⠀⠀⠀⠉⠀⠀⢉⡶⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠴⢾⡷⠃⠀⡀⡀⠀⠃⣴⠐⠀⠁⠀⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡷⠁⠀⡤⠀⢠⡀⠁⠈⠀⠄⠁⠠⡦⣾⢧⡆⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡴⣧⣄⢠⣶⠄⠀⣿⢀⠀⠀⢀⠀⢤⡄⠀⠀⢾⠇⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡈⠉⡌⠁⠀⠀⢀⠈⢞⠗⢁⣀⠀⡀⢀⡄⠀⠀⠀⠀⢆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠛⠋⠁⠀⠀⠆⠠⠶⡜⢀⡀⢰⠎⠛⠂⠉⠀⡀⠀⢀⠈⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⢸⡆⠁⠀⠀⡠⠞⠒⠘⠳⠶⠾⣀⡀⠘⠈⠀⠠⡌⠓⠢⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠂⢀⠊⣠⣾⠏⠶⢸⣦⠐⣮⣀⠈⣾⠆⡈⠠⠴⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠂⠠⠄⠲⣿⠰⠈⣥⣰⣀⡌⠁⠖⠉⠁⠀⠀⠻⠃⡐⢃⡄⡀⠂⡀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠡⣶⠂⢫⡶⠀⠙⣆⢀⠀⠟⡡⣴⡶⠁⣼⠇⣀⡻⠟⠱⠿⣯⣂⡐⠓⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⠆⠴⢫⡍⡑⠂⢈⡉⢈⡑⢤⣎⠴⠚⠓⣿⡐⠓⠻⠤⢴⠐⠃⢬⠍⠁⡳⠂⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣌⠁⠀⠀⠀⢰⣄⠀⠀⠘⣃⡘⠿⠇⠉⠀⠙⡃⣠⣦⠸⠇⠀⣦⡈⢳⠂⢐⠋⢢⣄⠈⣠⣭⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠘⣷⠀⠈⡉⠁⢀⣘⣿⠇⠐⠚⡛⠃⠛⠂⠘⠤⠄⠀⠆⠛⣵⡎⢡⡾⢠⡍⣀⡀⠹⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠀⣠⡌⠈⠡⠦⠀⣩⣄⠙⣠⣤⠀⠠⣦⣄⢢⣛⡤⠀⢀⣈⠀⠀⠀⢀⠈⠟⠣⠤⠄⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⠇⣛⠋⠈⣿⠀⠀⠈⠉⠁⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢿⡛⠃⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠄⠈⣡⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠞⠱⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠲⠀⠀⠀⠂⠂⠂⠂⠀⠀⠂⠀⠂⠐⠐⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠃⠘

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

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

⠀⠀⣠⣤⣤⣴⣶⣶⣶⣾⣆⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣶⣿⣶⣴⣾⣷⣦⣀⡀⠀⠀⠀⠠⣴⣶⣶⣶⣶⣶⣄⡀
⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⣦⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⡛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠜⢻⢿⡏⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⠛⠁⠀⠀⠀⡠⠊⠀⠁⠈⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⣶⡄⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠘⡇⠀⢷⣦⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣷⣦⣄⠀⠀⠀⢀⣀⣲⣶⣶⣿⣿⣶⣤⠀⠀⠀⠀⢠⣶⣿⣷⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠉⡙⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⢾⣾⣿⣿⣶⣤⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣠⣤⡞⢹⠀⠀⠀⠙⠻⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣹⣿⣿⣿⣿⡥⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⠇⠸⣇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠉⡿⡟⠙⠓⠀⠀⠀⠀⠀⠙⠿⢿⡿⠟⠛⠉⠁
⠀⢸⣿⣿⣿⠏⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠿⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣤⣀⣀⠀⠀⠀⢦⣀⠘⣧⣠⣶⣎⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠭⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⣿⣿⣿⠿⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣿⣿⣧⣤⣤⣤
⣿⣏⣙⣿⣿⣹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠓⠪⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠑⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⣾⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⢰⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⡟⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣄⠀⠀⠸⣿⣇⢠⡟⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣼⣿⣿⣿⣦⠀⠀⢹⣿⡏⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⣿⣿⣿⣿⣿⣦⣀⣼⢿⣷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡀⢾⣇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠐⠁⠀⠘⣿⣆⣠⣤⣤⣤⣌⡁⠀⠙⡄⠀⢀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⡿⠉⢻⣿⠿⢿⠟⠲⠄⠀⠀⢀⣾⣿⡋⠉⢀⠀⠉⠙⠣⡀⠀⠀⠈⡀⠀⠃⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠀⣠⣾⣿⣿⣾⣇⡀⣿⡀⠀⡾⠀⡴⠋⠀⢹⣷⣠⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡁⡇⢸⡇⠀⠀⠀⢿⣇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡐⣈⢷⣀⠀⠀⠈⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠂⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠁⠉⠀⠸⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⡷⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠐⢿⣿⠿⢿⣿⢿⣿⠿⣟⠛⠛⠻⣄⡀⠈⠀⠀⠀⠀⠀⠠⣷⣦⠆⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⣀⠁⠀⠀⢸⠀⠀⠀⠌⢷⣦⣄⣈⡙⠒⠂⢀⣀⣤⣴⣶⢿⣷⡀⠖⣷⠀⠀⢀⢠⠀⠀⠘⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣛⣉⠡⠼⣿⠁⠘⢇⠀⠀⠀⠀⢰⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⢎⣠⣤⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠈⠳⣤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⢰⣿⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⡀⠀⢀⡼⠀⠀⠀⠀⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢷⣄⢫⡉⠉⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡑⠙⠒⣒⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⡾⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠼⢿⣦
⠀⠀⠀⠉⠳⢤⣆⣰⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣠⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠃⠓⠀⣸⠏
⠀⠀⠀⠀⠀⢀⠽⠋⡱⠛⣻⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⠿⣿⠛⠈
⠀⠀⠀⠀⠀⠀⠤⠀⢰⣲⣶⡦⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡭⣞⠿⠁⠀⣇
⠀⠀⠀⠀⠀⠀⡠⠻⢋⡵⣿⢦⡀⠀⠀⠀⠠⠈⠰⠀⡠⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⡞⢡⢤⡀⠀⠀⠀⠀⢰⠚⠳⡄
⠀⠀⠀⠀⠀⢺⣏⠙⣁⠤⠋⣲⣇⠀⠀⠀⠀⠈⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡼⡆⠀⣀⡇⠀⠀⠀⠀⢈⡀⣠⠁
⠀⠀⠀⠐⡻⢓⢊⡏⡉⠎⠛⠏⠁⠀⠀⠀⠘⡜⠁⠀⢢⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⢯⢯⣰⡿⣦⣶⣲⡥⠚⡇
⠀⠀⢀⣰⠧⠱⠪⢆⡀⠄⣍⢶⡅⠀⠀⠀⠀⠇⠀⠒⠀⠀⠀⠐⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢰⢮⣋⢦⡏⢐⢢⣧⡐⠁
⠀⠀⡊⠃⢚⡐⠳⠈⢱⠤⠣⢭⣁⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠈⠁⠈⠀⢄⠠⠀⠒⠀⠀⠈⠙⠤⠜⠛⡹⣝⡫⣿⢟⡷
⠀⠀⢫⠫⠇⡀⣋⠘⢈⠃⠇⡘⢁⠀⠀⠀⠀⠘⡀⠘⡖⠀⠄⡱⠀⠐⠋⠁⠀⢀⡄⠀⠀⠀⢀⣠⣄⡀⠘⠋⣿⣻⣛⣿⡆
⠀⠀⡞⠒⢂⠉⡅⢤⢈⠧⢸⠀⠃⠁⠀⠀⠀⠀⠑⢀⠓⢦⢐⡀⣢⠀⠀⠀⠉⠉⠀⠀⠁⠀⡟⠀⠀⣷⠖⠲⠟⣹⡳⠋⠁⡀
⠀⠐⠙⡧⠬⠂⡑⣄⡼⠐⠞⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⢈⠁⠉⢂⠀⠀⠀⠁⠁⢈⠂⠀⠀⢳⣀⠀⠘⠦⡤⢔⡵⣟⠁⡰
⠀⠀⠀⠇⢠⣠⣁⠎⡙⠃⡇⠃⠀⠀⠀⠀⠀⠀⠀⢁⠠⠈⠠⢄⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠋⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠁⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⠀⡀⢀⠀⠀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⣿⣿⢛⠿⢛⠛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡖⠂⠈⢉⡀⣾⣤⣶⣿⡶⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣴⣿⠯⠍⠩⢤⢐⣮⡟⣉⣛⣿⣿⣿⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢀⡠⢿⣦⣌⠉⢻⡿⣦⠙⠣⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡀⡀⠀⢀⡠⠞⠉⣴⠏⠙⣿⣧⠈⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡜⣁⠔⠋⣀⡴⠞⠁⠀⠀⢹⣿⡆⢧⠀⢠⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠗⠚⠉⠁⠀⠀⠀⠀⠀⢈⣿⡇⡘⠀⠀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⣟⠿⣦⠀⠀⢀⣤⣤⣄⣀⣸⠻⣧⣷⡄⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⠉⠁⠀⣸⡟⠙⠿⢓⠄⢀⣿⣿⣿⡆⢿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢿⣿⣻⡟⡇⢸⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡙⣧⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⣸⣿⣽⣷⠣⢸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡘⢷⡈⢆⠒⠍⠍⢀⠀⠀⠀⠒⠉⠁⠘⣼⣿⠀⣸⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣆⠻⡎⠆⠀⠣⠔⠊⠉⠀⠀⠀⣠⡼⣿⢏⡇⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣭⡻⠆⠘⠀⠀⠀⠀⠀⢀⣶⣿⣵⢞⣁⣾⣷⡏⣿⢼⡟⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣭⡛⠃⠀⠀⠸⣿⠀⠀⠸⣿⣿⡿⢫⡾⣿⣿⢣⠿⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⡍⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⣷⣾⢟⣼⣿⠃⠈⠸⢸⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⡶⠞⠉⠀⠀⠀⠀⠀⠀⢸⣯⣥⡾⠛⠁⠀⠀⢀⢸⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡄⠀⠀⡀⠀⠀⠀⠀⣸⣿⣏⠁⠀⠀⡰⡠⡘⣸⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣘⠿⣷⣶⣶⣶⣿⣿⣧⢀⣷⢇⣇⡇⣷⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠉⠙⠛⠛⢸⡿⠸⣿⡇⠹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠊⠀⠑⡀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠔⠀⠤⢀⠒⠀⠒⡄⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⠄⠈⢀⡆⠔⡅⠶⠻⣚⣦⣵⢦⡔⡃⠢⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡄⢡⡆⠝⠒⠀⠭⠀⣈⡝⣠⠘⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠘⠂⠁⠱⠌⣀⣄⡀⢠⡤⠆⡠⠋⠀⡀⡡⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠈⢢⡀⠹⠀⠈⠀⠤⣌⠀⠀⢄⡤⠞⠀⠴⡞⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⡀⠀⠐⢄⠁⠀⠀⠀⠀⠑⠂⡁⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⢠⡀⡀⠀⠁⠓⠠⠀⠀⠀⠀⠈⢢⡠⠔⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠓⠀⠈⠶⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠁⠒⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣇⠀⠀⢠⡤⢐⡶⢂⠄⠐
⠀⠀⠀⠀⢄⢀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⣼⠋⡣⡞⣡⢋⠔⠃⢚⠃
⠀⠀⠀⠀⠀⣵⣜⠈⢃⢴⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠐⢠⡈⠐⢄⠀⠀⢀⡀⢟⡠⣇⠣⣟⠛⠀⣈⠍
⠀⠀⠀⠀⠀⠘⢦⡚⢬⣰⣼⢀⡀⠤⣀⠀⠀⠀⠀⠉⠳⢠⠔⠒⠀⠀⠀⠢⡠⠒⠉⢻⠠⠙⠮⡀⠈⣭⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⢿⠙⣆⡑⠦⠛⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠛⠂⠊⠑⠛
⠀⠀⠀⠀⠀⠀⣒⣄⡙⢙⡖⢦⠤⢌⠣⣖⣠⠗⠀⠄⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⡾⢾⢱⠂⡎⡇⠈⡇⠎⡀⠒⠁⠉⠢⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⢸⣁⡂⡘⢀⠃⡸⢠⠇⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⣘⢙⠇⠀⣡⠴⠑⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠈⠀⠙⠨⠀⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣤⣄⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣰⢂⡇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠛⢇⠈⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣈⣆⠀⢠⠀⠁⠀⠠⡆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡑⢀⣫⡽⢿⠶⠂⠀⠀⢀⡇⠐⠂⠚⠃⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣛⡥⣀⡀⠈⠀⣤⠀⠀⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⢧⡀⠀⠙⠒⢶⠊⠐⠄⡀⠀⠂⠠⠤⣀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⠀⠀⠙⢦⡄⠀⠀⠑⢦⠀⠁⠀⠀⠀⠀⠸⠇⠀⠀⠀⢠⠋⠀⠀⠴⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠆⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠉⡄⠀⢀⠂⣀⡀⠀⠁⠀⠀⢀⡣⡌⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠔⠁⠀⠀⠀⠐⢒⠐⠀⠈⣄⠀⠀⠀⠀⠈⠀⠃⣴⠀⡀⢀⠀⠓⠒⠀⠀⢀⠀⠁⠀⢲⣀
⠀⠀⠀⠀⠀⠀⠄⠀⣀⠄⠀⠐⠀⢀⠀⠄⠀⠀⠀⠀⢹⡂⠀⠁⠀⠀⠀⠇⠈⠛⡇⠈⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⠀⣚⣚⢉⣠⡜⠂⠀⠀⠀⠀⢁⠀⠀⠀⠄⠀⠁⠀⠀⠘⠑⢀⣘⡃⣄⣠⠀⠁⠈⠉⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⣉⡡⡬⠐⠙⡀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⢈⡿⢄
⠀⠀⠀⠀⠀⠀⠈⡄⠐⡗⠉⡉⠉⠀⣁⡤⠔⠒⠒⠒⠛⢣⡀⠀⠀⠀⠐⡖⣦⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠚⠉⠀⠀⠀⣤⠀⠀⠀⠉⠉⢀⠤⠀⠘⠃⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠁⠀⠀⠀⢀⠄⢰⠁⠋⢳⡀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠐⢶⠆⠛⣶⠑⠂⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠋⡀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠇⠐⠑⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠓⠾⡏⠐⠂⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠒⠹⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠢⡜⠁⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠠⠀⢄⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⠠⠦⠤⠶⢄⣀⠀⠀⠀⠀⠀⡠⢰⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠗⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣷⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣾⡆⢰⠏⠀⠉⠉⠻⡏⠀⠀⢁⣈⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠘⣇⡏⠀⠀⠀⠀⠀⢻⣠⣾⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⢿⡿⢿⣿⠿⠛⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠖⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡜⠁⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠋⠙⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢀⣀⣠⣤⣤⣤⠶⠶⠶⠶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⣖⣚⠋⠉⣉⣈⣀⣠⣤⣤⣤⣤⣤⠾⠧⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠾⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣬⣤⣷⣶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠤⢐⣀⣤⡴⠶⠛⢻⡿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣊⡭⠶⢟⣋⠁⠀⠀⠀⠀⠀⢡⡿⠟⠋⠁
⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⡤⣒⡭⠖⠋⠁⠲⠶⣶⠪⠉⠀⢀⣰⣄
⠀⠀⣠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠷⣪⣵⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣀⡤⠔⣡⣾⣏⣴⣿⡋⢦⣉
⠀⠀⠀⠀⠉⠻⢿⣶⣦⣭⣭⣷⣾⣿⣿⢿⠟⢻⣿⢷⣤⣀⣼⠆⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠸⢦⠀⠹⣧⡀⣍⣁⣰⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣆⠈⠻⢶⣭⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⡉⢀⡀⠨⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⠋⠀⠀⠘⣿⣮⣧⣀⠀⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡿⢹⡿⠈⣷⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢚⣫⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡇



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

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

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⠶⠖⠀⠀⠀⠶⠒⠒⠻⠷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡾⠁⠀⢠⡶⢋⡅⠀⠀⠀⢌⡙⢳⣦⠀⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠃⡤⠀⣿⣇⠸⣇⠻⢥⣤⣼⠇⠀⣿⢀⣈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠈⢸⣧⠀⢨⣻⣶⣤⣥⣤⣤⡤⠖⢰⠇⠜⣽⣷⠈⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⡄⠀⠛⢷⣦⣙⠛⢰⢰⢰⠠⠀⠠⠋⠀⣚⣿⠏⠀⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡛⠄⠀⢻⣿⣿⣷⣌⠀⠈⠀⠀⣠⠴⠚⠉⠀⢀⣼⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣗⣀⣀⡀⠉⠋⠻⢷⠀⣴⣾⡿⠗⢀⣠⠶⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠛⣛⣛⡛⠛⡉⠙⢒⠂⠉⣠⢔⣚⠉⡀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣽⣾⠆⢡⣾⣿⣿⣿⣿⡴⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡩⣁⡀⠀⢈⣉⣉⡉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠒⠺⢿⡄⠛⠯⠉⣉⡭⠴⣶⣾⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⡗⠚⠛⠛⠛⠒⠦⡀⠈⡇⠀⠠⠊⠥⠒⢉⣡⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣯⣶⣢⡤⢀⣤⠄⡀⠀⡇⠀⠁⢀⣤⠶⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⢿⣾⣯⡵⠾⠿⣧⡇⠀⡴⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⣄⢀⣤⢦⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⠆⡀⠈⣧⡀⠀⢀⣄⢀⠀⠄⠻⡿⣶⣇⠇⢭⠇⣳⡾⡽⠃⢠⠀⠀⣇⠀⠈⢠⡎⠀⣀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⣠⠘⠓⠨⡀⠀⠈⢃⠤⣍⠁⠀⣴⣷⡿⠀⣲⠠⣷⣶⡄⠀⢉⡅⠠⠈⠀⠀⣈⠓⠚⠀⣄⠄⠈⠉
⠀⠀⠀⠀⠀⡔⠓⠚⠂⠈⠉⠀⢹⣶⣾⣇⠀⠀⠘⠲⠀⢇⠀⣀⣋⠂⠶⡵⠆⢊⣓⣀⢀⡇⠰⠚⠁⠀⠀⣽⣶⣿⠁⡈⠉⠁⠘⠒⠓⣂
⠀⠀⠀⠠⠂⠀⢀⠀⠀⠀⢀⡄⠉⣀⣁⣉⣁⣙⣲⣦⣁⣈⣳⣉⣽⣷⣾⣹⣷⣼⣏⣹⣋⣀⣡⣴⣖⣁⣈⣁⣉⡈⡉⣀⡀⠀⠀⠀⠀⠀⠠
⡤⠠⠀⠀⠀⠠⠀⠄⠀⠀⠀⠤⠀⠠⠀⠀⠄⠠⠀⠀⠀⠄⠀⠠⠠⠠⠄⠀⠀⠀⠠⠠⠄⠄⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠄⠤⠀⠀⠀⠄⠀⠄⠀⠠
⡇
⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣈⡄⢢⢠⢢⢇⢀⢠⢎⢀⡀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠀⠀⠏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡟⣠⢀⡄⣠⢀⡄⣠⢀⠄⡄⣠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠐⠃⠘⣰⠃⠊⡼⠁⠊⠘⢱⠇
⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠰⠃⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⡇
⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠒⠖⠒⠒⠒⠲⠲⢒⣶⠶⠒⠒⣶⠒⣶⢶⣶⢲⡶⣶⠖⢲⡒⠒⠲⣶⡒⠶⠲⠒⠒⠒⠂⠖⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠑⡂⣀⣀⠀⠀⠀⠊⣹⣾⣷⠟⠈⠁⢀⢠⠁⡾⠙⢛⠻⠁⣝⢯⣄⠹⡛⠋⠹⡄⢁⢀⠈⠁⠙⣷⣿⣮⠑⠀⠄⠀⣀⣀⡀⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠘⠜⠦⢉⣁⡘⠃⠀⠀⠙⠠⠞⠁⠀⣬⣿⡦⢰⡢⢠⣾⣥⠆⠈⠑⠠⠜⠀⠀⠀⠻⢀⡉⠱⠏⠈⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣀⠰⠊⠀⡿⠀⠀⠘⡆⠀⠹⠁⣠⢦⣾⠃⡼⠄⡈⣷⣧⣦⡀⠉⠂⠐⠟⠀⠀⠺⡆⠉⠂⣠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠈⠁⠐⠀⠀⠁⠀⠀⠀⠛⠉⠸⣵⠗⠰⢷⡅⠈⠙⠃⠀⠀⠀⠀⠀⠐⠀⠉⠐⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⢀⡀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⢹⡟⣋⣴⡾⠿⠿⣷⠌⠛⠳⣶⡘⢋⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⣰⣿⢋⣴⡿⢓⡀⠾⠿⣷⡄⢤⣌⠻⣿⡟
⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠻⣿⡀⠟⣡⡸⣿⢰⡿⢡⠾⢷⣌⢻⡈⣿⡆⠉
⠀⠀⠀⠀⢹⣿⣿⡷⣠⡶⠶⢆⣭⣭⡁⢤⣬⠁⢰⣿⣷⠹⣌⢁⡀⠞⡦⢹⢸⡇⣿⡇⣴⣶⣶⡶⢂⣀⣀⣀
⠀⠀⣀⣀⣀⠙⠏⣾⢋⣾⢫⡄⣵⠶⣍⢣⠹⣧⢸⣿⣿⡄⢤⡘⢿⣉⡥⢋⣼⠇⠻⢡⠿⠛⢩⣤⣬⡍⠛⢿⡆
⠀⠙⠛⠿⣿⣿⣆⠟⣠⡻⣌⠇⣁⣻⢆⡎⡧⠙⠈⠻⣿⣿⡌⠛⢶⣦⣄⡉⢡⡞⢰⠃⡞⢡⡆⢩⠉⣅⠸⡈⡷
⠀⠀⠀⠀⠀⠉⠛⢣⡜⣿⣆⠡⣜⣓⣉⣘⠁⣧⠀⠀⠻⢿⡇⠻⣷⣤⣴⡶⠿⠇⣸⠀⠃⣌⠁⠶⠖⠛⠠⢣⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⣮⣝⢷⡄⢦⣭⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⡇⢹⣧⠠⣍⠻⠾⢋⣴⡶⠘⢿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣬⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠉⠓⠦⠙⠻⢟⣫⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠈⠈⠁⠐⣄⠀⢰⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠂⢀⠀⣀⣀⣴⣀⠀⠀⠀⠈⠁⠀⠉⢴⣿⣇⣸⡿⠲⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣵⣿⣿⣿⣿⣷⡶⠒⠂⠉⢷⡀⠀⠉⠛⠉⠛⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⡄⢙⠤⠤⠀⢼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡅⠈⠂
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⡀⠀⢃⡄⢠⣿⡄⠀⠀⠈⣻⢿⣿⣿⡿⠟⠓⠦⣄⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀⠔⠁⠀⠈⠈⢇⠀⠀⢀⢘⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡄⠀⠀⠀⡌⢦⣴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣮⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘