Lepidoptera Emojis & Symbols

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠄⢠⣤⣤⡤⣀⡀
⠀⠀⣴⡿⠃⢹⣿⣇⢀⠛⠂⠉⠉⣙⣒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣋⡉⠁⠐⠀⠀⠈⠿⣿⣁⠙⣿⡆
⠀⠀⢿⣿⡂⠿⠥⠄⠀⠀⠀⠀⣤⡿⠏⠉⠓⠪⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠙⠈⠉⠘⠿⣶⣆⠀⠀⠀⠐⢒⡸⠇⣼⣿⠃
⠀⠀⠈⠫⢷⣾⡍⢀⣶⡀⠀⠀⠀⠀⢦⣤⣠⣶⠾⣿⡊⣳⢄⠀⠀⠀⠀⠀⣠⢞⠝⣻⠿⠻⣷⣤⣴⠊⠄⣀⣀⡀⢭⣏⢐⡾⢿⡷⠁
⠀⠀⠀⠀⠉⠲⣛⣿⡷⢐⣛⡅⠀⢀⡻⣿⣇⠚⠒⠶⢤⣈⡓⢷⡔⠆⣆⣴⢿⣳⡬⠔⠒⠛⢐⣿⡿⢃⣀⠀⢬⣉⠐⠾⣯⠝⠋
⠀⠀⠀⠀⠀⠀⠉⠶⣛⣷⡄⠒⣩⡅⠰⢿⣟⣛⠛⠁⠰⠭⡿⠟⣿⣧⣿⡟⠋⣩⠤⠌⠉⠩⢙⣿⠿⠂⢬⡉⠒⣶⣎⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⢿⢾⣥⣔⠊⠭⠠⠐⠒⠉⠁⠀⢁⠔⣡⢻⠧⠑⢄⠀⡀⠁⠠⠔⠂⠠⢍⠵⣶⣿⠻⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠧⠍⢠⠆⠐⠀⠀⡠⠀⠀⡰⠛⠨⠐⡀⡀⡑⠢⡁⠀⠀⠀⠢⠈⠐⠿⣍⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣔⡦⠔⢣⠀⡠⠔⠊⠀⠄⡰⠁⠀⠘⠀⢡⠐⡘⡄⠈⡂⠠⡌⢠⡃⠲⢥⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣾⣡⢄⡔⠁⢠⠀⢀⠁⡘⢠⠃⠀⠀⠈⠀⠀⠂⠠⠘⡄⠁⠀⠰⡀⠙⢄⠢⣸⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣳⡋⣰⢃⠇⡄⢸⢠⠃⠆⡌⠀⠀⠀⠀⠀⠀⠄⠂⢱⠘⡄⣆⢳⠹⡆⣻⡟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣿⢳⣾⣰⣃⣇⣾⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣧⣧⣸⡤⢿⠛⣧⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠿⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠛⠚⠉

⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢰⡿⠛⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⣹⣤⣼⡇
⠀⠀⠀⠀⢹⣷⣴⣿⣿⠟⠁⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠊⣤⡀⠀⠀⠀⠚⣿⣯⣽⠇
⠀⠀⠀⠀⠸⣿⣤⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠐⣪⣬⣭⣿
⠀⠀⠀⠀⠀⠻⣿⣽⣯⣅⣀⠀⠀⠀⠀⠀⠓⢴⣶⣤⣤⣾⣿⣁⡤⠴⠂⠀⠀⠀⠈⠙⢙⣋⠏
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠖⠛⠛⠒⠒⠒⠒⠲⣿⣿⣿⣿⣿⣿⡷⠤⠤⠀⠀⠀⠀⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣴⣧⡴⠋⠀⠀⠀⠀⢰⡿⣷⣿⢿⢻⣿⢻⠘⠿⣿⡀⠀⠀⠀⠀⠀⠈⢑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣧⡦⡘⠀⠐⠋⢀⡵⠋⠀⠸⠟⠀⠀⠀⠉⠀⠀⠀⠀⣈⠲⢦⣬⣿⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡃⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣠⣄⣠⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣦⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣯⠛⠁⠀⠀⠈⠀⠦⡽⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⢸⣿⣶⡄⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⣠⠒⠉⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⣼⣟⡻⠟⠀⠀⠀⠀⠀⠀⠘⣿⣯⡉⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⠖⠀⠀⠘⠉⠉⠉⣡⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⢽⡷⢌⡛⢷⡀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣝⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠳⣭⣬⣿⣦⣀⢀⣿⣿⣿⣣⣀⠀⠀⠐⠀⠀⠀⠀⠀⢴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣛⡛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⣀⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠀⠀⣠⣀⣠⣤⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢶⣦⣤⣀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁⠀⠀⠈⠁⣨⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠠⣌⢱⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢠⠀⠋⠉⠁⠀⠀⠀⠀⣩⣿⣿⣿⡟⠂⠀⠀⠉⠉⠉⠉⠀⠀⠀⢸⣾⣄⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⢀⣀⡀⠀⠀⠀⠀⠠⠂⢀⠄⠀⠀⠀⣿⡇⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠘⠿⠟⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⣿⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣤⣄⡁⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠛⠋⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠘⠿⢂⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣚⣻⣿⠷⢿⣿⠿⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣼⣿⣿⣤⡤⠶⠖⠛⠛⠛⠙⠛⠛⠻⢿⣿⠾⢿⣿⣛⣲⣦⣤⣀⡀
⠀⠀⢀⣠⢶⣿⠿⠟⡫⠀⠉⡁⠴⢒⣿⡁⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⣤⣿⣿⠘⣧⠀⠀⠂⠀⠀⣀⠀⣀⣀⡀⠀⣻⣗⠢⢄⡉⠁⠬⡛⠿⢿⡷⢦⡀
⠀⢠⣾⣁⡟⠁⠀⠀⢀⠔⠉⡠⠞⠉⠀⢀⠔⠋⠀⢀⠌⠀⠀⠀⠀⣰⣿⣿⣿⠀⢹⣷⡀⠀⠀⠀⠐⠄⠀⠈⠲⣄⠀⠈⠓⢄⠈⠐⢄⠀⠀⡀⠹⣏⣹⣦
⠀⢿⣹⣅⣻⣎⢀⡔⠁⢀⡄⠀⠀⣠⠞⠁⠀⠀⡠⠂⠀⠀⢀⣴⣾⡿⠁⣿⣿⠃⡀⢻⣿⣦⣄⠀⠀⠈⠢⡀⠀⠀⠑⢄⠀⠀⠑⣄⠀⠱⡀⢸⣾⣋⣿⣺
⠀⠈⠷⢿⣷⣾⡏⡿⢤⣏⣹⣟⣻⣇⠀⠀⡠⠊⠀⠀⢀⣴⣿⠟⢁⠂⠀⠹⣿⠀⠁⠀⠈⠙⢿⣷⣄⠀⠀⠈⢦⡀⠀⢀⣿⣛⣿⣉⣧⠿⡩⣟⣶⣯⠾⠋
⠀⠀⠀⠀⠉⠉⠉⠙⠛⠳⠿⣿⣦⣿⣻⣿⡁⠀⢀⣾⣿⠟⠁⡠⠘⠀⠀⢰⣿⢀⠀⠀⠈⠠⡀⠙⢿⣷⣄⠀⠀⣿⣿⣻⣦⣿⡿⠗⠛⠋⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣇⣼⢛⣶⣿⠟⠁⠂⠂⠀⢰⠀⠀⣾⣿⠀⡇⠀⣶⠀⠀⠂⠂⠙⢿⣷⡞⢿⣨⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⣽⢯⠉⠁⠠⠀⠀⠀⠀⠸⠀⠀⢹⣿⠀⠇⠀⠙⠀⠀⠀⠀⢀⠀⠉⠭⣯⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣟⣠⡠⡆⠀⠀⡇⠀⠀⣀⠀⢸⠛⡋⠀⢀⡀⠀⠀⠀⠀⢀⡄⣤⢘⣭⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣾⣹⡯⢽⡯⣟⣲⣞⣫⣿⣿⠀⢻⣿⣿⣛⣶⣚⡯⣿⢭⣟⢹⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠓⠿⠻⠗⠟⠛⠋⠀⠘⠛⠻⠷⠿⠿⠓⠛⠈⠉

⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠲⣤⣀⣄⣠⡴⠒⠦⠠⣤
⠀⠀⠹⣯⠿⣱⣆⣀⣠⣮⣽⣮⡟⠀⢰⡔⣠⣄⡀⠀⢀⣠⣄⢲⡆⠀⠙⠲⣄⡀⠈⢉⣿⠉⠀⣀⡴⠚⠁⠀⢶⡶⢢⣤⣤⣠⣠⣤⡄⠲⠆
⠀⠀⠀⢉⣟⣿⡽⣿⢻⣽⣫⡍⠀⠀⠀⠻⠟⣿⣿⣿⣿⣿⠻⠟⠀⠀⠀⠀⠈⢿⣶⡾⠙⣶⣶⡏⠀⠀⠀⠀⠈⠠⣻⣿⣋⢻⣋⣻⣟⡦⠉
⠀⠀⠀⠘⣿⣿⠇⠛⠰⣯⣿⠃⠀⠀⠀⠀⢢⣌⣙⠙⣋⣠⡴⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠈⠙⠄⠀⠀⠀⠀⠀⠀⠙⠿⠍⠀⠨⠽⠛⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⢀⣀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⢰⣶⣶⡶⠤⢀⡀⠴⢶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠂⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⣀⠀⠘⠿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣽⣿⠿⠃⠀⠀⠹⢿⣧⠀⢸⡇⠀⣜⡿⠋
⠀⠀⠀⠀⠀⠀⠜⠿⠇⠀⠀⠀⠀⢠⣶⣿⣼⣿⣿⣿⣿⣿⣾⣿⣦⡀⠀⠈⢹⡟⢛⠛⣟⠛⡿⠁⠀⠀⠀⠀⠀⠀⠘⣷⣶⡎⣴⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠛⠻⠿⠾⠿⠶⠿⠋⠙⠁⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠁⠈⠉⠣

⠀⠀⢠⠀⠤⠀⡀⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⡟
⠀⠀⠈⠓⠀⠀⢻⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢷⣨⣿⣿⣰⠏⠀⠈
⠀⠀⠀⠀⠘⠙⠀⠙⠁⠀⠀⠈⠗⢠⣄⠺⠁⠀⠀⠘⠃⠀⠋⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠈⠿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠷⣄⠛⢢⢤⣤⣠⠴⠲⢃⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠀⠀⠀⠀⠀⠐⠋⣼⠁
⠀⠀⠙⢷⡄⠸⢻⠙⠄⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠀⠀⠀⠀⠧⠀⡀⠀⢐⠀⠀⢀⠀⠝
⠀⠀⠀⠈⢧⣄⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠈⢈⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠂⠈⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⢀⣤⠜
⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠙⢷⣟⠛⠉⠂⠀⢀⠀⠐⠋⠙⢻⣷⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢷⣀⣠⣤⠴⢿⠶⣤⣤⣀⣸⠃⠀⠑⢄⠀⠀⠀⢰⡄⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢸⠀⠀⠈⢷⡄⠀⠀⠀⠀⠃⡀⠀⢸⠇⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠘⣄⣀⣠⡜⠀⠀⠀⠀⠀⠀⠐⠤⠔⠦⠴⠃
⠀⢶⣶⠒⠤⠀⠀⠀⠀⠠⠔⢲⣶⠂⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢻⣆⠀⠀⠀⡄⠀⠀⢀⣾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠫⣖⣤⡀⠀⠀⣠⣴⡾⢫⣿
⠀⠀⠈⢩⠀⠀⠀⠇⠀⠀⢈⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⠿⣦⡈⠹⢞⣾⡞⠾⢁⣠⡿⠇
⠀⠀⠀⠸⣆⣠⠀⠀⣄⣀⡾⠀⠀⠀⠀⠳⣤⠀⠀⠠⠀⠀⢠⡤⠇⠀⠀⠀⢰⣿⠀⢸⠸⢸⠀⣸⡇
⠀⠀⠀⢀⠏⠉⠀⠀⠈⠉⢇⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠻⣷⡎⠀⠀⣶⡿⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⢀⠁⠀⢀⠀⠀⠀⡀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢀⣴⣶⡖⣴⣶⣤⣦⣶⢶⡶⣦⣦⡀⠀⠀⣿⠒⠀⠂⠂⠀⢠
⠀⠀⠀⠀⠂⠀⠀⣁⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣌⢹⡟⣡⣶⣼⠟⠋⠁⠀⠀⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⢀⡅⡀⠀⠁⠀⠀⠀⠀⠀⠈⢯⣟⡿⢻⣛⡽⠃⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢻⡇⠀⠀⠀⡾⣿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠃⠀⡻⠀⠀⠀⠀⡅⠀⠀⠈⢿⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⣸⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣠⠴⠋⠁⠻⡆⠀⢣⢱⠀⠀⠀⠴⠛⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⢀⠔⠊⢉⠟⢦⡄⠀⠀⣰⠏⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⢀⣶⣄⢀⣤⡈⠙⠛⠋⢰⡀⠀⠀⡰⠒⠋⠉⠉
⠀⠀⠀⠀⣴⡿⠄⠀⡼⠂⠀⠀⡀⠉⠁⠀⠀⠀⠀⠉⠙⠓⠀⠠⢠⣄⣼⠃⠀⠀⣾⡟⢹⡿⠟⣷⡀⠀⠀⠀⠙⠲⠚⠁
⠀⠀⠀⠸⠿⠶⠴⠄⢣⣀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⢱⡟⠱⠀⠘⣻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠟⠛⠳⢦⡀⠀⠀⠀⠀⢹⣸⠀⠀⣠⠞⠁⠛⢷⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⠃⠀⠀⡀⠀⠀⠀⠙⠲⢤⡀⠀⠀⢿⣤⡎⠉⡀⠀⠀⣰⡇⠀⢠⡿⠋⠻⠋⠣
⠀⠀⣀⣤⠤⠀⢀⠀⠀⢀⠔⠁⠈⣿⠃⠀⠸⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠁⠀⠀⠀⠒⠋⠀⢀⡾⠁
⠀⠀⠙⣿⡀⠀⠈⠑⢤⡏⠀⠀⠠⡿⠀⠀⣼⠁⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⢰⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠘⢷⡤⠄⠀⢸⡇⠀⠈⠉⠳⡄⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠩⠞⣣⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠀⢞⠀⠀⠀⠀⠁⢀⠀⠀⣼⠃⠀⠈⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣼⡇⠀⢼⣿⣧⡀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠰⠋⠁
⠀⠀⠀⠀⠈⠷⣤⣠⠇⠀⠈⠓⠚⠃⡀⠀⠀⠀⡿⠁⢰⠟⠁⠀⠀⠀⠀⢸⣿⠀⣠⠀⣿⣿⣷⣦⣄⡀⠀⠙⠓
⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡞⠁⠀⠀⣤⠀⡀⠀⠀⠀⠀⠛⠇⠀⠘⣩⠉⠙⠛⢡⡞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣄⠀⠀⣦⣥⣀⣤⡦⣦⣼⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠹⣄⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⢀⣤⣠⣶⡄
⠀⠀⠀⠀⠀⠀⣰⣛⣿⢶⣿⡄⠀⠀⠛⠦⠌⠀⠀⢠⠶⠟⠂⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⣿⢻⡇
⠀⠀⠀⠀⠀⢰⣯⣽⣙⡓⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢀⣀⡾⠁
⠀⠀⠀⠀⠀⢸⣴⣥⣌⠃⠀⢿⣿⣤⠀⠀⠀⠀⠀⠀⢴⣿⡃⠀⠀⠀⠀⠙⠆⠀⠀⠰⠟⠓⠂⠀⢀⣴⣿⠽⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢻⣿⠃⠀⠀⠀⢀⣠⡧
⠀⠀⠀⠀⠀⠀⠾⠿⢿⠂⠰⠦⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⡿⠀⠀⠀⠀⠀⠠⠤⠾⢷⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⣶⣦⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⣶⡶⠄⠀⠀⠀⠀⣀⡴⣶⡆⠀⠀⠀⣠⡶⣶⡀
⠈⣿⣭⣷⣄⠀⠀⠀⠘⣈⠑⠶⠀⠼⡤⠠⢟⣀⠃⠀⠀⠸⣇⠀⠐⣶⣶⡞⠋⣁⡿⠁⠀⠀⠰⣅⢰⡹⣧
⠀⣽⠿⣿⣿⣆⠀⠀⠀⠻⠶⠂⠀⠀⠀⠐⠺⠟⠁⠀⠀⠀⢾⣿⣆⣿⡏⠹⠜⣫⠇⠀⠀⠸⣷⡈⣷⢻⣧⡀
⠀⠹⣄⠈⠙⣿⣦⠲⡷⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠁⠀⠈⠁⠀⢸⢿⣧⣼⣿⣿⡇⣻⣷
⠀⠀⠈⠁⡼⣽⣧⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⡄⠐⣶⠦⠤⠄⠀⣀⠀⠲⡄⠙⣼⣿⣶⣿⣿⣟⠟⢠⠿⠃
⠀⠀⠀⣾⣾⠟⠋⣁⠬⠻⣿⣿⡿⢲⣦⡀⠀⠀⠀⠀⠏⠀⠀⠀⠸⣦⣄⢢⣯⣟⠻⣿⡿⠿⠈⠛⠂
⠀⠀⠀⡉⠀⠀⠄⡍⠓⠲⠾⠛⠛⠛⠛⠋⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠉⠉⠉⠻⣷⣶⣶⠾⠃
⠀⠰⢩⠀⠀⠛⡰⠁⠀⢀⣀⠀⢿⡇⠒⢤⡀⠀⠉⠉⠍⠉⠉⠀⢀⡤⣒⣼⡷⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠘⠷⠿⠂⠀⠀⡰⣿⣿⡆⠈⢿⣷⢊⡻⠦⡀⢀⠀⠔⢀⠴⢷⠛⢲⣿⠁⢸⣿⣿⡄⠀⠀⠀⢀⡰⠉
⠀⠀⠀⡀⠀⠀⠀⣸⣿⣧⣿⣧⡀⠐⢻⣧⣅⡈⠝⡆⢸⣶⣌⡂⢌⣼⣿⠇⠀⣸⡿⢹⣿⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⢴⣖⠠⠀⢀⡟⢻⡿⠁⢀⡀⢠⡦⠀⠀⣻⠗⣿⣿⡇⠀⠀⡤⢀
⠀⠰⣶⣄⡀⠀⣸⡛⠏⠉⠁⡐⡄⠀⠈⢻⣆⡿⡁⠈⠛⠉⠄⢯⡱⡟⠁⠀⠰⣿⠂⣿⣿⣿⠀⠀⠀⠈⠁
⠀⠀⠘⢿⣿⣆⠸⣟⣾⠀⠀⠁⡗⠰⠀⢠⣿⠙⠀⠀⠀⠀⠈⠻⣿⡀⠀⠠⢽⣿⣸⣿⠟⠁⠀⠀⠳⣿⣆
⠀⠀⣀⣤⠀⠀⠀⠈⠙⠿⠶⠤⠅⢀⠠⠊⠁⠀⠀⢀⣤⡀⠀⠀⠉⠱⣄⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢻⣿⣿⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠺⢿⣿⣦⣄⡀⠀⠀⢠⣾⣶⣆⣀⠀⠀⠀⠀⣤⣛⣿⣿
⠀⠀⣼⣿⣿⣿⣿⡄⣀⣠⣶⣷⣿⣿⠿⠂⠀⠀⠀⠒⠤⢤⣤⡈⠹⣷⠀⠀⣿⢙⣿⣿⣷⣄⣤⣾⣿⣿⣣⣿⠂
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠋⠀⠀⠙⣻⢪⣿⣿⣿⣿⢿⣿⣿⢿⣧
⠀⠀⢿⣿⣿⣿⡟⣿⢻⣿⣿⣿⣿⠉⠀⣀⡀⠀⠀⠑⠐⠂⠒⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠛⠹⢿⣷⣿⡿
⠀⠀⠀⠙⠛⠉⠀⠁⠘⢿⣿⡿⠏⠀⠀⡿⢣⣶⣄⡀⠀⠀⠀⠀⣀⢠⣤⠀⠀⠉⠛⠿⠏⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⡀⠀⠀⠠⣀⠈⠁⠀⣀⡀⠀⢨⣷⢯⣯⣵⣶⣦⣘⣞⣿⣋⡟⠀⢰⣶⣀⡀⠐⠆⠀⠐⠂
⠀⠀⠀⠀⢘⣦⣴⠿⠛⠋⠀⣠⣿⣿⡄⠀⠛⠿⠿⠙⣾⠏⣿⣿⣿⡗⢀⣠⣿⣿⣿⠿
⠀⠀⢠⡶⠂⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣾⣿⠿⡍⢾⡏⠀⠶⠀⠀⠀⡔⣷⣷
⠀⠨⠊⠀⢀⣠⡶⣤⠀⠀⠀⢘⡿⣿⣿⣿⣄⣀⠀⠀⠀⠀⢀⣴⣶⡾⢻⣵⣾⣷⣿⠁⢀⠖⠄⠀⠀⠄⠹⣿⡀
⠀⠀⢰⣦⣻⣿⠟⠉⠀⠀⠀⢸⣷⣄⣿⣿⣿⣿⡇⠀⠀⢰⣿⡿⢡⡌⣻⢿⣿⣸⡇⠀⠉⠀⠀⠀⢠⣵⣤⣿
⠀⠀⠘⠿⠏⠁⠀⠀⠀⠀⣰⣿⣿⣿⠿⢿⣿⣿⠇⠀⠀⢸⣯⣴⣿⠿⠟⠙⢟⣋⣤⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⡀⢤⣶⡶⣦⣟⣿⣿⣿⡗⠏⢧⡀⠀⠁⠀⠀⡠⢤⣤⣀⣀⡀⠀⠛⠉⡿⣿⣭⣛⡶⠦⣤⣄⡀⠈⠁
⠀⠀⠐⢽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣠⠔⣓⣦⣴⠞⠛⠋⠉⣠⣴⣿⣏⠙⡿⠿⠟⣛⣳⣬⣥⣾⡗
⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣯⣿⣿⠟⢁⣼⣿⡿⠋⠉⠉⠀⠀⠀⠀⢯⣥⣴⣮⣴⣶⠟⠻⠿⠿⠛⠛⠻⠧⠄

⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⢢⡶⠀⠀⠀⠀⠀⠀⠰⣆⠶⠀⣶⠒⠂⢀⠀⠀⠀⠠⡐⢰⡶
⠀⠀⠀⠈⢧⣀⡀⢰⡆⢀⣀⡼⠁⠀⠀⢰⡇⡶⢡⢀⢠⡱⡆⣷⠀⠀⠀⠈⡷⠀⠀⢀⡀⠀⠀⢸⡇⠀⠀⠘⡆⠀⠀⢥⣤⠄⠀⠀⣾⠁
⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⡆⠀⠀⠀⠈⣡⡇⠻⣼⣼⠃⣧⡉⠀⠀⠀⠀⢀⡄⠀⠈⡇⠀⠀⣄⠀⠀⠀⠀⠙⡶⢠⡴⡿⣦⡐⢶⠃
⠀⠀⠀⠀⠘⢷⣤⡤⢤⣤⡾⠃⠀⠀⠀⠀⠹⣿⡄⠸⠁⣼⡿⠃⠀⠀⠀⠀⠙⢷⣤⣄⢁⣤⣼⠟⠀⠀⠀⠀⠘⢧⡛⡧⠁⣜⢃⡼
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠉⠧⠀⠀⠀⠀⠀⡀⠈⠛⠁⠀⠉⠋⠀⢀
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⣠⠠⡄⡀⠀⠀⠀⣀⠤⠄⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠘⣇⠀⠀⠀⢠⡀⠀⠀⠀⡼⠁⠀⠙⣆⠦⠏⠶⣤⠞⠻⠶⣴⠃⠀⠸⡇⠀⠀⠀⣀⠀⠀⠀⢠⡗⠀⠀⠈⣷⢦⠀⣤⠠⢾⡾
⠀⠀⠀⠙⣷⠀⠀⢸⠇⠀⠠⡾⠃⠀⠀⠀⢻⢤⡀⠦⡿⠞⢀⠴⡟⠀⠀⠀⢷⡄⠀⠀⢿⠀⠀⢀⡼⠃⠀⠀⢠⠀⠀⠀⠟⠀⠀⢠⡀
⠀⠀⠀⠀⠹⣷⣄⡈⢠⣰⣾⠇⠀⠀⠀⠀⠈⠳⣙⡆⠀⢒⣫⠞⠁⠀⠀⠀⠀⠳⣀⡀⠈⢀⣀⡼⠁⠀⠀⠀⠈⢧⣀⡀⠀⣀⣠⡞
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠉⠁⠀⠈⠉
⠀⠀⠘⣧⠐⡢⠀⠀⠀⠠⠔⢂⡼⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠈⢧⡀⠀⢸⡆⠀⢠⠞⠁⠀⠀⢰⣆⠀⠀⠘⣿⠁⠀⠀⣰⡆⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠴⣬⣿⣱⠆
⠀⠀⠀⠀⢺⣄⣀⠸⢁⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠁⠀⣰⠃⠀⠀⠀⢠⣘⠷⠶⢢⠴⢾⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠈⠛⠒⠂⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐⠒⠛⠀⠀⠈⠧⠀⠀⠼⠁⠀⠀⠀⠀⠿⠆⠽⠵⠿⠮⠏⠸⠗
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢿⠃⣼⡗⠀⠀⠀⠀⢻⡆⠹⡟⠀⠸⡟⠳⠗⣦⣀⣠⣔⠻⠛⡿⠀⠀⢿⠛⠓⢄⠀⠀⠚⠛⣿⠃⠀⠛⣿⠂⠀⠀⠀⠀⠀⢺⡿⠋
⠀⠀⠈⠀⢸⣆⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⢻⡀⣰⡆⢸⠁⢼⡀⣰⠇⠀⠀⢸⡁⠀⠀⣶⠃⠀⠀⡿⠀⠀⠀⠹⣇⡀⠀⣿⠀⢀⡼⠃
⠀⠀⠀⠀⣄⠙⠶⠜⠷⠾⢋⡄⠀⠀⠀⠀⠀⣧⠈⠀⠈⠀⠈⢀⡇⠀⠀⠀⠀⡏⠉⠀⠹⠀⠈⢉⡇⠀⠀⠀⠀⢼⡃⢀⣧⡀⢸⡇
⠀⠀⠀⠀⠘⠿⠶⠀⠐⠶⠟⠁⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠛⠻⠁⠀⠀⠀⠀⠹⢾⠃⠀⠀⢷⠞⠁⠀⠀⠀⠀⠈⠻⠞⠈⠷⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣾⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣨⠟⣩⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⡿⢻⡿⢛⡿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣿⣤⣿⣴⣾⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⠟⣹⠋⠁⢀⡿⣾⣻⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣘⣰⠃⣠⠔⠋⠀⣸⣿⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠉⡷⠊⠁⢀⡴⠚⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢸⣿⠇⠀⢰⢃⣠⠖⠉⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⡟⠀⠀⡾⠉⠀⠀⢀⣴⣿⡿⠋⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠻⣿⢿⡛⢦⣿⠿⢭⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢰⠃⠀⢀⣴⣿⣿⣿⠿⠛⠙⢻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠻⣟⣾⣿⠲⢶⣿⠿⠝⡛⣿⣿⣷⣦⣄⡓⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⢠⠇⢀⣴⣿⣿⡿⠋⢁⡠⠖⠊⢁⣀⡬⠷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣿⣿⡉⠉⠒⠺⣇⠈⠉⠛⠿⢿⣷⣦⣄⠀⠀⡀⠀⡀⠀⡟⠀⣾⣶⡿⢟⣡⠿⣴⣊⣁⣤⠖⠊⠉⣀⣀⠠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⡶⠖⠒⠚⠛⠲⢦⣄⣀⡀⠉⠛⠿⢶⣄⣹⣿⣿⣷⠿⠛⣉⠴⠋⠀⠀⠀⠀⢀⣈⠽⠿⣉⡀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⠖⠒⠚⠉⠁⠀⠈⠉⠙⠛⣛⣿⣿⣿⣿⡻⣷⣿⠷⠒⠒⠒⠒⠒⠛⠭⢄⣀⠀⠀⠉⠙⡺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣤⣴⣶⣾⣿⡿⠟⣉⠴⣻⣿⣾⣿⣝⡓⠦⢤⣀⡀⠀⠀⠀⠈⠙⠲⣤⣴⡷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠿⠿⢯⣥⠖⠊⠁⢠⠃⢙⢿⢿⣷⣭⣒⢤⡀⠉⠙⠒⠦⢤⣀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡤⠊⢹⡄⠀⢀⡏⠀⢸⠈⢆⢻⣷⡀⠉⠙⠳⢤⣀⣀⣠⣾⣯⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣠⠟⢣⣀⡾⡄⠀⠘⡇⠘⡆⣿⣿⣄⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⡉⢆⠘⣄⠀⢱⠀⠘⣿⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣬⣧⣈⣣⡀⣃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣻⣿⣫⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣿⣿⣯⣿⣽⣯⣿⣿

⣶⣾⣿⣿⠲⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢒⣿⣿⣿⡿⢶
⢿⣸⣿⣿⣿⠳⠆⢹⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⣿⣷⠀⢘⣿⣿⣿⣧⡿
⠈⢳⣼⣿⣿⣷⣄⢾⣿⡇⠈⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠀⣿⡿⢴⣺⣿⣿⣧⡟⠁
⠀⠀⢳⣹⣿⣿⣤⣀⠺⠧⠀⢸⣿⡟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢹⣿⣿⣄⡤⠘⠛⢻⣿⣿⣯⡾⠁
⠀⠀⠀⢻⣙⣿⣿⡙⠣⠀⣀⠘⣿⡏⠀⣸⣿⣿⣦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⢿⣿⡁⢊⣤⣼⣿⣿⣿⣼⠇
⠀⠀⠀⠀⢿⣸⣿⣿⡟⠆⠀⠀⢹⣧⠀⣿⣿⡟⠙⢿⣦⣄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⣠⡾⠋⠉⢿⣿⡄⢠⠞⠉⠀⠤⢌⣽⣿⣿⣥⡟
⠀⠀⠀⠀⠘⣏⢹⣿⣿⣦⠶⣬⠉⠉⠑⢿⣿⠁⠀⢰⣿⣿⣦⡘⠢⢌⠢⡀⠀⠀⡠⠞⣁⠔⣢⣾⣿⣶⠀⠀⠈⣿⡏⠀⠀⠀⡐⠶⣿⣿⣿⣇⣾⠁
⠀⠀⠀⠀⠀⠹⣞⠻⣿⣿⣇⣤⣒⣒⠈⣾⠗⠐⠀⣿⣿⣿⠙⣿⣦⡈⡆⢰⣿⣿⣄⡰⣡⣾⠟⢛⣿⣿⡂⠄⡀⡝⠁⠀⠀⢀⣠⣴⣿⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠻⣦⠿⣿⣿⣍⣉⠀⠀⠊⠁⠀⠀⣻⣿⠇⢐⣨⣿⣿⣮⣪⣽⣯⣿⣿⣿⣗⠀⠀⢹⣿⣇⠀⠈⠁⠀⣀⡐⢈⣹⣿⣿⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⣿⣿⣿⠟⣃⠀⠤⠄⣰⣿⠟⠀⢀⡘⠿⢿⣿⣿⣿⣿⣽⣿⡛⠢⣤⣦⡾⠻⢿⣦⣤⣀⡀⢘⣻⣿⠿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠓⣒⣂⠈⠀⢀⢹⣧⠐⠂⢻⠿⣿⣿⣿⣿⣿⠃⠀⢸⣿⠇⢀⡀⢸⣷⣤⡉⠉⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠠⠒⠃⠀⢻⡄⠀⡀⢠⢙⣿⣿⡿⠏⠂⠀⢸⡇⠀⠈⡝⠶⣿⣅⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢛⣿⣏⡀⠀⢠⠀⠀⠈⣓⢀⠀⡆⣿⢿⣿⠐⣷⠈⠄⢸⠃⠀⠀⣴⠤⣾⣿⢿⡃⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⡔⠉⢧⠀⠀⢾⠃⠀⠁⡇⣼⣿⠏⡙⡆⠀⣞⠀⠀⣠⡟⠐⢿⡇⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⣿⣿⣧⣶⡀⠠⠠⠀⢸⡇⢰⠀⡇⠹⡿⠀⡷⡄⠀⡇⠀⠺⠋⢤⣄⣼⡷⣾⠇⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣴⣿⣿⣿⣿⢀⣤⡀⡀⢸⡇⠸⠂⡆⠀⠀⢠⠟⡇⣸⡁⠀⣇⡐⠈⢹⡟⣴⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⢹⣿⣿⣿⡿⠁⡀⢈⣇⠰⢓⠃⠀⠀⠘⢀⠁⣿⣧⡀⠈⢹⣿⣿⣧⠏⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⣿⢻⣷⡿⢿⡿⢿⡿⣛⡃⠀⠀⢘⣛⣰⣿⣿⣿⣶⣟⣵⢾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⢳⣟⣁⣾⣇⣰⣿⠉⠁⠀⠀⠈⢹⠋⡹⣿⠇⠸⣿⣠⣴⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⣿⡿⠛⠻⡟⣋⣿⠀⠀⠀⠀⠀⠸⣿⡻⣿⠟⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢽⣿⣶⣦⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇

⠀⠀⣀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠈⠏⠀⠑⠀⢀⠀⠔⠁⠀⠟⠀⠀⠘⣇⢾⣶⢀⠀⠀⢠⢰⣾⢸⡏⠀⠀⠨⣯⢥⠆⠀⢀⠀⠠⣮⣹⠅
⠀⠀⠲⠦⠤⠤⣽⡧⠤⠤⠴⠃⠀⠀⠀⠘⢦⡜⠛⢲⣷⠚⠳⣴⠟⠀⠀⠀⠀⠸⡮⠂⢒⣿⡖⠐⢳⠏
⠀⠀⠀⠀⠠⠀⠿⠇⠠⠄⡀⠀⠀⠀⠀⠀⣿⣇⠓⠏⠛⠗⢢⣿⠇⠀⠀⠀⠀⡖⣾⠣⠀⠘⠀⠜⢿⡶
⠀⠀⠀⠨⠤⠀⠀⠀⠠⠤⡁⠀⠀⠀⠀⠀⢩⠿⠛⠁⠀⠙⠿⢏⠀⠀⠀⠀⠀⠤⠵⠎⠀⠀⠀⠸⠮⠠⡀
⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣡⣤⡤⠀⢀⠀⢨⣀⡀⠀⠀⠀⣀⡌⠀⢠
⠀⢹⣯⠁⠑⢄⠀⢀⠔⠁⠩⣿⠁⠀⠀⢳⣦⠁⠈⣲⣶⠈⠀⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢿⡤⠬⠤⣿⡧⠤⠥⢼⡏⠀⠀⠀⠀⢹⠋⠩⠸⡿⠍⠙⣿⠁⠀⠀⠈⠲⡀⠀⠀⠀⣿⡇⢀⠀⠀⠖
⠀⠀⢽⣀⠀⠂⠾⠇⠒⠀⣸⡇⠀⠀⠀⠀⠈⢧⣤⠆⠀⢦⣴⠃⠀⠀⠀⠀⠀⠀⠊⠀⠀⣛⠀⠀⠉
⠀⠀⠈⠛⠛⠂⠀⠀⠚⠛⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⡀⠀⢀⡄⠀⠀⡿⣖⣤⠀⠀⠀⠀⠀⢤⣲⢿
⠀⣇⡈⠒⠒⠀⢸⠆⠐⠒⠊⣀⡵⠀⠘⢀⣀⣀⡈⣰⣷⡈⣀⣀⣀⠈⠀⠀⢻⠉⠈⠈⠣⣀⠜⠁⠁⠉⡝
⠀⠈⠒⠀⠊⠁⢸⡀⠉⠒⠐⠚⠀⠀⠀⠠⠊⢀⠀⣸⣿⡀⢀⠈⠂⠀⠀⠀⠀⡜⠉⠋⠙⣿⠋⠙⠉⢳⡀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⢧⣀⣀⠘⠙⠁⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⠉⠉⠀⠀⠀⠈⠉⢀⣀
⠰⡇⠈⠢⡀⠀⠀⠀⠀⡠⠊⠁⡿⠀⠀⣿⡏⠈⠀⠀⠀⠀⠈⠘⣿⠇⠀⠀⢿⣿⢯⡦⡀⠀⢀⠴⡽⢿⡿
⠀⠘⠂⠀⠈⠀⢠⠀⠊⠀⠀⠒⠀⠀⠀⠘⢷⠤⠀⢰⣶⠀⠠⢴⠏⠀⠀⠀⠈⢿⣦⠹⢿⣶⡿⡏⣵⡿⠃
⠀⠀⠀⡠⠂⠀⢾⡗⠀⠰⠀⠀⠀⠀⠀⠠⡇⠀⠀⡘⠏⡀⠀⢀⡇⠀⠀⠀⠀⠀⣿⣄⣰⢿⣧⣠⣿
⠀⠀⠈⠇⣀⠀⠘⠁⠀⡀⠘⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⢙⠿⠓⠀⠚⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠐⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠤⠠⠴⢃⡞⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⣀⢒⢲⠌⠃⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⡀⠀⢀⠀⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠁⠈⠀⣁⣀⣤⣤⣤⣤⣤⣶⣶⣾⡟⠁⠹⣷⣶⣶⣦⣤⣤⣤⣤⣄⣀⡖⠚⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣀⣶⣟⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⣯⣿⣿⣟⢿⣻⣶⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣼⣿⡿⣟⣻⣯⢿⢿⡿⣿⣷⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⡿⢿⣽⣟⣿⣿⣿⣧⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣫⣪⣾⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣷⣗⣝⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣿⣿⣿⡿⠛⠉⠛⣿⣿⣿⡿⠋⠉⠙⣿⣿⣿⣷⣿⣿⣿⠿⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⢀⣠⣠⠉⠉⠩⠹⣿⣿⣇⠀⠑⠀⣽⣿⣿⣇⠀⠁⠀⣽⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⢀⡰⠶⢓⡤⠀⠀⠈⠛⢿⣷⣶⣾⣿⡟⠉⠙⢷⣶⡿⠟⠋⠀⠀⡩⣍⡛⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊⠆⡉⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣤⣤⣄⡀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣦⢄⠀⠀⡠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡤
⠈⠳⣝⠿⣦⣀⣠⣾⢟⡿⠁⠘⣿⣣⣄⡀⣀⡴⢎⡿⠃⠘⡏⢠⢧⡼⠆⢸⠃⠐⢦⣤⣀⠀⢀⣠⣤⠆⠀⠹⠧⢾⠦⠟
⠀⠀⠙⠳⣌⢻⠟⣷⠛⠀⡀⠀⠈⢣⠿⠿⠿⡟⡏⠀⠀⠀⠰⠀⠈⠁⠀⠠⠀⠀⠈⠂⠉⡿⠉⠀⠃⠀⠀⠀⢀⠀⠀⢀⡀
⠘⣓⣦⣄⡈⠁⢈⣡⣶⢫⠋⠀⠀⠘⣢⠀⢠⣸⠁⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⡀⠀⠚⠉⢓⡀⠀⠀⠁⠴⢺⠓⠐
⠀⠈⠳⣍⣹⣶⢿⣉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢻⡓⣤⠞⡿⠁⢀⣀⡀⠀⠀⠀⢀⣀⡀
⠀⣠⣄⠘⠛⠈⠘⢋⣀⡄⠀⠰⠿⣍⡀⡗⢈⣱⠶⠀⠻⡏⢿⣶⣿⢏⠟⠁⠀⠀⠀⣿⡏⣾⠃⠀⠀⠙⠿⠗⡶⠾⡟⠉
⠀⠙⡾⢷⡄⠀⣰⡾⣶⠁⠀⠀⣀⠈⠉⠈⠋⣁⠀⠀⠀⠘⢦⡍⣥⠏⠀⠀⠀⣀⣀⠊⠀⠁⠀⠀⢀⠀⠀⠀⠛
⠀⠀⠉⢀⠻⣿⠟⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢨⠀⣠⣤⡀⠃⠀⠀⡃⠤⣤⠀⢱⣣⠖⢀⣄⢲⡸⡿⠁⣀⠀⠀⡆⠀⢀⡀
⠀⠀⠀⢿⣷⠘⠾⠟⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠘⡇⠀⠑⣀⠈⠀⠀⡏⠀⠀⠈⣄⡀⢄⣀⡉⠁⠀⠀⠁⠀⠀⠀⠁
⠀⢠⡤⠂⠀⠀⠀⠃⢤⠀⠀⠀⠀⠛⠀⠈⠋⠀⠀⠀⢑⠀⠀⣻⡀⠀⢈⠀⠀⠀⠀⠑⠁⠈⠛⠁⠀⠀⠀⢃⢤⣀⣆⠇
⠀⠀⠃⠈⠀⠀⠀⠁⠈⠀⠀⠈⢳⣄⣀⣀⣤⣤⡔⠁⠈⠣⠠⠋⠣⠤⠋⠀⠀⢠⣤⣤⡀⠀⠀⢀⣤⣴⡄⠀⡦⠳⡶
⠀⠀⠐⠒⢰⣶⠀⠒⠀⠀⠀⠀⠀⠉⠁⢻⠀⠉⠀⠀⠀⢾⠃⠀⠀⠀⠀⠘⢿⠆⢻⣿⡈⢢⡴⠁⢼⡿⠁
⠀⠀⠀⠀⠃⠀⠃⠀⠀⠛⢿⣽⣷⣦⡀⠀⣠⣴⢖⣻⠿⠪⠄⠀⠰⠂⠀⢠⠃⠀⠀⢹⡃⠘⠃⠐⡍⢁⣤⣶⣶⣶⣦⣄
⠀⠀⠠⡆⠀⠤⠀⡲⠀⠀⠀⠈⠛⡙⠳⡶⠟⢛⠛⠁⠀⠀⢀⡀⠀⢠⣀⠇⠀⠀⠀⠈⠻⠇⠹⠟⠁⠈⠉⠻⠏⠹⠟⠛⠓
⠀⠀⠀⠀⠢⠀⠚⠀⠀⠀⠀⠀⠘⠮⠦⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⠶⠶⣶⣶

⠀⠀⠀⣤⣶⢖⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠶⣦⡀
⠀⠀⢸⣿⣯⡈⠉⢿⣽⣿⣟⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠸⣿⣿⣿⢿⡟⢡⣿⣿
⠀⠀⠈⣿⣿⡥⠀⠺⠿⠹⣷⣦⡐⠿⣿⣦⠀⠀⣶⣤⣀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⣠⣴⡖⠀⣸⣿⣷⡄⣠⣿⢟⣿⡷⠀⢴⣿⡏
⠀⠀⠀⢫⣿⣷⡀⠀⠘⠿⣿⣿⣷⣦⡙⢡⡄⠀⢻⣿⣿⣷⣦⣄⣰⣿⣷⣀⣠⣴⣾⣿⣿⣿⠁⠀⠻⠿⣉⣾⣿⣿⣾⡟⠁⢀⣿⣿⠁
⠀⠀⠀⠈⢷⣿⡿⣀⠀⠀⠈⣿⣾⣿⣿⡈⠁⠀⠀⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠛⣁⣾⣿⣿⡿⠏⠉⠀⣀⣿⣿⠇
⠀⠀⠀⠀⠀⠱⢾⣿⡇⠀⠈⠻⣿⣏⣿⣿⠄⠙⠦⠀⠈⠋⠘⠊⢻⣿⣿⡁⠘⠋⠻⢥⣀⣴⠆⢰⣿⣏⣿⣿⠇⠀⠀⣤⣝⡻⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠔⠛⢻⣦⠁⠀⠀⠠⡦⠀⠀⠁⠀⣿⣿⣿⣇⠀⠈⠀⠀⢠⡍⠁⠛⠻⠿⣿⣷⣀⣀⣼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣾⡧⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⣿⣿⣰⡄⠀⠀⠈⠁⠀⠀⠀⡚⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠉⢿⡧⣿⢟⣿⣶⣶⣿⠿⣿⣿⣿⣿⣿⣤⣴⣴⣶⣤⣦⣤⡝⠃⠈⠉⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣶⠀⠀⠛⠀⠀⠀⠈⠛⠻⣿⣿⠇⢹⣿⣿⡇⢟⣿⡝⡿⠿⠉⠈⠉⠱⠇⠀⠀⣬⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⣠⣀⠀⣀⡀⣀⣤⣄⡻⠀⠘⣟⣿⠃⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠈⠁⠀⠀⠙⠿⢿⣿⣶⣶⣴⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⣶⣄⠀⠀⣠⣶⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⡀⠀⠀⠀⠀⡠⣤⠀⠀⣤⣀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⢿⠻⣶⣴⠛⡿⠀⠀⠀⠸⡏⣉⢢⣤⡞⡉⣻⠁⠀⠈⣿⣭⣦⣀⣠⣮⣽⡞⠀⠀⢻⣿⣷⣄⣀⣾⣿⣿
⠀⠀⠀⠀⣾⠠⠚⠓⠄⣷⠀⠀⠀⠀⣾⢿⡻⠻⣿⠿⣆⠀⠀⠀⢠⣾⣯⢽⢏⣿⣦⠀⠀⠀⠀⣿⣏⡻⠿⣡⣿⡆
⠀⠀⠀⠀⠛⠃⠀⠀⠘⠛⠀⠀⠀⠀⠉⠋⠁⠀⠈⠛⠁⠀⠀⠀⠈⠛⠃⠀⠀⠛⠋⠀⠀⠀⠀⠙⠛⠁⠀⠙⠛⠁

⠀⠀⠀⣤⣄⡀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢄⡀⠀⠀⣀⠤⣦
⠀⠀⠀⠸⣾⣽⣦⣴⣯⣿⠇⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠷⣀⢀⣶⣆⢀⡰⠏⠀⠀⡔⠈⠛⢲⣖⠖⠂⢠⡀
⠀⠀⠀⠠⣿⣿⠙⠋⣿⣿⠀⠀⠀⠀⠰⠂⠀⠯⠀⠐⠀⠀⠀⠀⢺⣍⣼⠿⢿⣆⣽⠂⠀⠀⠈⠻⣟⡻⢟⠳⡷⠋
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⡀⢀
⠀⠀⠀⠹⡅⠙⣷⣾⠋⣨⠏⠀⠀⠑⠢⣀⠙⣿⠉⣀⠔⠉⠀⠀⠀⠀⠀⢲⠆⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⣻⣿⠄
⠀⠀⠀⠀⠫⠿⠙⠉⠯⠏⠀⠀⠀⠀⠀⠹⠟⠈⠿⡃⠀⠀⠀⠀⠀⠀⠶⠀⠰⠆⠀⠀⠀⠀⠀⠸⣷⡽⢿⣵⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣄⠀⢀⣞⣴⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣾⣯⣼⢦⡀⢤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣯⠹⣦⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⡜⣳⢻⣿⢿⡇
⠀⠀⠀⢐⣿⣯⡤⠤⠽⢯⡈⠙⣧⠀⠇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠳⡉⢿⡛⣆⠀⣄⠀⠀⠀⠀⠀⠀⢸⣟⠋⣿⣫⡟⣹⣿⣧
⠀⠀⠀⢯⡎⠁⡄⠀⠀⠀⠀⠄⠘⣧⢸⠀⠀⠀⠀⣤⠀⡇⠀⢀⠀⣀⣿⣯⡙⢆⠃⣎⠃⣿⠀⡅⢰⠀⠀⠀⠀⠀⢸⡇⢰⣿⡿⢾⣟⣹⣯⣧
⠀⠀⠀⠘⣟⠄⡀⠀⠀⠢⠀⠀⢀⡇⢿⡤⠀⠀⠀⠃⠀⠀⠀⠈⢹⣿⣿⡿⣍⠠⣀⣿⢀⡿⠀⢁⠀⠀⠀⠀⠰⠀⢸⣿⣸⡟⢁⡜⢉⠴⢛⡏
⠀⠀⠀⠀⠈⠳⣈⡀⠀⠀⣄⠀⠐⣇⢸⡟⠀⢀⡤⠊⠀⠀⠀⠀⠈⠻⠦⠝⣈⡳⣿⣽⣼⢃⡔⠃⠀⠀⠀⠀⠀⠐⠆⢿⣿⣧⡞⣴⣧⣶⡭⠴⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣉⠳⣤⣄⡀⠀⠈⣤⣷⠚⠋⠀⠀⠀⠀⢀⡤⣶⣾⢛⡛⠛⠛⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋⠁⣠⣖⡩⣿⣯⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠉⡻⣩⠗⡟⠁⠀⠀⠀⠀⠀⣰⡿⢰⣿⣿⣿⡿⢖⣿⠟⠋⠁⣸⢷⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⡷⢷⣿⣯⣉⠀⣽⣯⡗
⠀⠀⠀⠀⠀⠐⢀⣈⡡⠴⠚⠁⠀⠀⠃⠀⠀⠀⠀⠀⢠⣿⠗⠐⠛⡋⢻⣶⠋⠈⠀⠀⣸⠉⢧⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣭⣝⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⠀⣼⣷⣿⣾⣯⣡⠞⠁⠀⠀⠀⣰⠃⠀⠉⢻⢩⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠉⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢡⣖⠈⠁⢄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⡏⠀⠐⠐⠀⣻⠉⢡⠀⠀⠀⠀⡖⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⡀⠁⠈⠉⢑⣮⣱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠒⠠⢸⣷⡿⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣦⡇⡘⢀⠐⠁⡀⠸⠎⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⢻⡇⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⠻⡷⣦⢊⠀⠀⢸⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠳⠤⠀⣀⠈⣷⣄⡰⣟⠁⠀⠀⣒⣶⠋⣿⣟⣻⣿⣟⠁⣴⣶
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠎⠀⠀⠀⠁⣼⠤⠤⢀⣼⣁⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡶⠋⠉⣫⠽⣟⡿⣦⣤⣴⣾⠿⠷⢋⠉⠛⣉⠉⠛⠉⣹⠁
⠀⢠⡀⠰⠆⠀⠀⠈⢶⣤⣄⡠⠀⠀⢹⣗⣠⡶⠋⠀⠀⠳⡀⣙⠗⠀⠀⠀⠀⠀⣄⠀⠄⠘⠻⠖⠛⠀⡰⠌⢠⣼⠿⡄⢀⠐⠀⠀⠁⢀⡀⠑⢂⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⣴⣚⠏⠋⢁⣠⠞⠂⠐⠢⠙⡷⠀⠀⠀⢀⡤⠞⠙⠂⠀⠀⡄⠄⠀⠈⠁⠀⠸⣇⢀⣿⠀⡵⢬⣀⣠⣤⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡈⠋⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠉⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣀⡀⣀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠘⣿⣿⣿⡿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⢸⣿⣿⣿⣷⠀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⣦⣈⠻⣽⡆
⠀⠀⠀⠀⠹⣿⣿⣿⠷⣦⡄⠚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠁⠀⠀⣐⡯⣌⡻⡏
⠀⠀⠀⠀⠀⣹⣿⣿⣶⣘⠂⠀⢜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⢿⣾⣯⠺⢧⠓⣻⣯⠃
⠀⠀⣀⡴⣾⣿⣿⣍⢳⣾⣿⣦⣽⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧⠀⠀⠐⡀⠑⠂⣈⠉⡃⠸⡇
⠀⣼⢻⣿⣿⣿⠉⠐⠛⠹⣿⣿⢇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡋⠋⠲⠌⠉⡗⠀⣤⠀⣻⠭⡇
⠀⣋⠻⣿⣿⣿⡶⢀⣠⣤⣬⣽⣿⣿⡿⢯⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠁⢀⠀⠡⢄⣀⡩⠦⠀⣟⣲⠃
⠀⠈⠀⠙⠋⠛⠃⠛⠛⠟⠛⠩⠎⠉⠁⠚⠀⠀⠀⠀⠀⠀⢶⡞⣼⡇⢉⣴⣦⡈⠒⢂⡻⠄⣾⡳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠘⠓⠺⠃⠀⠀⠐⠂⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠉⠹⣿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣏⣻
⠀⠀⠀⠀⠀⠀⣰⣿⠛⠀⠀⠀⠀⣿⡄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⡋⣼⣗⣺
⠀⠀⠀⠀⢀⢰⣿⡯⠀⠀⠀⠀⠀⢻⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣃⣿⡧⡟
⠀⣠⠶⠿⠋⠈⠑⠠⡀⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣓⡏⠺⣿⢿⡇
⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⠸⣿⢿⣿⣿⣼⡏⢳⣤⣤⡤⠤
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣬⣽⠘⣹⣿⣿⣯⣼⠅
⠀⠐⢦⡄⠀⠀⠀⢀⠀⠀⣰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠉⠒⠂⠀⠀⠹⠛⠛⡙⠀⠀⠀⠀⠀⠀⠀⠀⡭⠿⣿⣿⢿⣿⣿⣿⣶⣤⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠄⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠒⠉⠡⠀⠂⠀⠨⠩⠍⠓⠶⣦⣤⣿⣿⣤⡴⠖⠋⠩⠡⠀⠀⠂⠠⠉⠑⠂⠀⠀⠀⣴⣤
⠀⠀⠀⠀⠀⣴⣿⣿⣷⠀⡀⠐⠁⠀⠀⠀⢀⣠⠄⠀⠐⠋⡩⢿⣿⣿⣿⣿⠯⡉⠓⡀⠀⢤⡀⠀⠀⠂⠈⠑⠠⡀⢰⣿⣿⣷⡄
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⠊⠀⠄⢲⣥⡄⠀⠔⢁⠄⢊⢔⣽⣿⣿⣿⣿⣕⢌⠢⢄⠐⠄⠀⣤⣵⠂⢄⠈⠂⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠈⠋⠀⠀⢀⣁⢔⣡⠋⢾⣿⣿⣿⣿⠎⢣⣕⢄⣁⠀⠀⠈⠋⠀⠀⠀⢠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⢀⠀⡠⠈⢀⠿⠋⡾⠁⠈⡜⣿⣿⣿⡟⡌⠄⠹⡆⠻⢇⠀⠠⠀⢀⠀⢰⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡁⠈⠀⡀⠁⢀⡞⠀⠘⢀⠁⣿⣿⣻⡇⢁⠐⠀⠘⣆⠀⠁⡀⠈⠀⣸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣌⣠⠔⢱⢃⠴⠃⠘⠂⢿⣿⣿⠇⠚⠀⠳⢄⢱⠑⢤⣈⣦⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⢠⠟⠁⠀⠀⠀⠈⡸⣿⡿⡘⠀⠀⠀⠀⠙⢷⡀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⢠⠁⠀⠀⠃⠀⠀⠀⠁⡻⡃⠃⠀⠀⠀⠃⠀⠀⢡⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢇⠀⠀⡄⠀⠀⠀⠀⣸⠁⢹⡀⠀⠀⠀⠀⡄⠀⢀⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠊⠁⠀⠀⠉⠒⠒⠒⠒⠛⠉⠁

⠀⣠⡤⣤⣄⣀⡀
⠀⣧⣿⡿⣷⣶⣤⡉⠳⠶⣠
⠀⠻⣷⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣦⣀⡀
⠀⠀⠸⣿⣤⣿⣿⣏⣉⣻⣾⠿⠿⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⢽⣿⣽⣙⣷⠤⠼⣿⠀⠀⣠⣾⣿⢯⣷⣄⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⣏⣉⣿⣗⠒⠛⣣⣀⠿⡿⠉⠀⣩⣮⣳⣄⡀
⠀⠀⠀⠀⠈⣻⣏⣛⣿⣏⠁⢈⣉⣓⣦⣀⠺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤
⠀⠀⠀⠀⠀⢈⢫⣩⣽⣿⣁⠀⠀⠉⣁⣿⣿⣶⣭⡃⠈⢿⣿⡄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠫⣿⣭⣼⣏⣀⠀⢀⣉⣹⣿⣿⣇⠈⠱⢦⣻⣿⡀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⢀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣾⡧⠥⠿⣤⣤⡤⠤⠤⠤⠬⠍⢙⣓⡻⢿⣿⣿⣿⣶⣿⣿⣠⣤⣤⢴⠶⠾⠿⠿⣿⣿⣿⣟⣛⣓⠲⠾⢭⣽⣛⠲⢦⣄
⠀⠀⠀⠀⠀⡿⣧⣬⡷⠒⢻⠋⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⢿⣾⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⡀⢰⣿⣿⠀⠸⣿⣽⠉⠙⢶⣮⣭⣟⣾⣟⡿⢷⣄⡀
⠀⠀⠀⠀⠀⣿⣏⣱⣿⠆⢙⣦⣀⡀⠀⣀⣤⠞⠋⠁⢀⡠⣺⣿⣛⣿⣿⡷⠪⠙⠳⢄⡀⠀⣠⣿⣿⣿⡦⣄⣻⡟⠁⠀⣀⡼⠣⣄⣹⣿⣻⣿⣿⣟⠹
⠀⠀⠀⠀⠘⣿⡟⣍⣿⣶⠁⢠⠏⠙⢋⡻⠋⠀⠀⣰⠟⣰⣿⣳⣾⠏⠈⢰⡄⠀⠑⠦⡉⠻⣿⣿⡿⠋⠙⠁⠉⠋⠉⠛⣭⣑⣦⣾⠿⣍⣙⢿⣆⡿⠟
⠀⠀⠀⠀⢶⣟⢛⣋⣿⣿⣾⣿⣀⣄⣭⡀⠀⣠⣾⠋⣰⣿⣿⡿⢃⡼⠀⠀⣧⠀⠀⠀⠹⣷⢄⣹⣷⣬⣦⡀⢰⣤⣤⣶⡿⢯⡝⣹⣧⣼⠟⠛⠚
⠀⠀⠀⠀⢀⣿⣿⠻⡉⣫⣿⠿⣿⣿⣛⣿⡶⣥⠃⢰⣿⡿⠟⢠⠞⠁⠀⢈⡟⢧⡀⠀⢀⠿⣆⣹⣾⣿⢿⣿⣿⣭⣿⣼⣿⡟⠛⠏
⠀⠀⠀⠀⣼⢃⠐⠀⢼⡻⠛⢺⣿⠙⠛⡟⣭⠋⠀⠛⠋⢀⢐⡿⢶⣤⠀⢸⠃⢸⠋⠒⠘⣆⣹⣽⣼⣿⠀⠈⠉⠈⠁⠀⠈
⠀⠀⢀⣼⡖⠁⠀⠀⠀⠀⠀⠘⠛⠀⠀⠉⠁⠀⠀⠀⠀⣴⠹⣿⢇⣿⣇⣜⠀⣸⣄⣸⣶⡟⠿⣤⣿⡇
⠀⠀⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣤⣾⣿⣿⣿⣶⣿⡿⣿⡍⢻⣶⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣃⣿⠿⣿⣯⣿⣥⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡛⣶⣿⣿⣿⠿⣿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⣰⣿⠿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⢿⣿⣆
⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⡿⢿⣟⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣻⡿⢿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠙⣿⣟⣿⣿⠉⣹⣷⣾⡿⢏⣙⣿⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣿⣋⡹⢿⣷⣾⣏⠉⣻⣿⣻⣿⠋
⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠉⠙⠛⠶⡟⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⢻⠷⠛⠋⠉⢻⣿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠖⠒⠢⠤⠷⣄⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣠⠾⠤⠔⠒⠲⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⣀⣈⣑⣦⣀⠀⠀⠙⢷⣄⠀⢀⡀⠀⣠⡾⠋⠀⠀⣀⣴⣊⣁⣀⣀⣀⣀⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠙⢦⣾⣷⡴⠋⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠈⠙⣲⣿⣿⣖⠋⠁⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡿⠿⠿⠛⠻⢿⣛⡻⡿⠿⠿⣿⣿⣿⣿⠻⠿⢿⣟⣛⡿⠟⠛⠿⠿⢿⣯⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⠤⠴⠒⢒⡲⠋⠀⠀⢀⡠⠚⣹⣿⣿⣏⠓⢤⡀⠀⠀⠙⢶⡒⠒⠦⠤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢋⣀⠤⠔⢺⠏⠀⠀⣀⠔⠉⢀⠜⡸⣿⣿⢏⠣⡀⠉⠢⣀⠀⠀⠹⡗⠢⠤⣀⡙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠉⢀⡠⠖⢻⠖⠒⣹⠃⠀⣠⠋⡰⠡⣿⣿⠈⢆⠙⣄⠀⠘⣏⠒⠲⡟⠲⢄⡀⠉⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢶⡋⠀⢠⠋⠀⢰⠃⠀⡼⠁⣰⠃⠀⣿⣿⠀⠘⡆⠈⢧⠀⠘⡆⠀⠙⡄⠀⢙⡶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢶⡇⠀⣠⠃⠀⡜⠀⢠⡇⠀⠀⢻⡟⠀⠀⢸⡄⠀⢣⡀⠘⣄⠀⢸⡶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣦⢾⣀⣠⠟⠀⠀⠀⠘⠃⠀⠀⠀⠻⣄⣀⡷⣴⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⢻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⢸⠟⠻⡟⠙⢿⠻⣏⣵⣼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠻⡉⢻⠙⣿⣦⣿⡇⠀⡇⠀⠎⢀⢿⣧⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠓⢄⠀⣈⡃⠡⢸⣿⠁⠀⠁⢀⠶⠚⣻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠲⢦⣝⡇⠙⠦⣼⣿⠀⠀⡴⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠓⠦⣌⠻⣄⠀⢿⡇⠀⠘⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠑⢈⣳⣼⣇⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠶⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⣠⠔⣨⠞⢿⡏⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠤⠒⢋⣥⡞⠁⢀⣿⡇⠀⢠⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠴⠚⢋⢴⣀⡴⠋⢿⣇⠀⠀⠳⡀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠚⢁⠌⢰⠀⡆⣼⣿⠀⠀⠀⠘⠲⣤⡝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣤⣯⣼⠿⠋⣿⠀⢸⠀⠀⡆⢰⣾⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⣦⣾⣦⣴⣷⣾⡉⡏⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣷⣧⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⣴⠲⡉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⡂⠔⠡⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣕⡒⡄⠈⠳⡄⠀⡀⢻⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠪⠤⠏⠌⠀⠁⢐⣨⡎⡇⠀⠘⠇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠉⠓⠢⠀⠀⠀⠀⠈⠄⠥⢢⢹⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠏⣮⠍⢳⠱⠀⠀⠀⠀⠀⠐⠈⢁⡸⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢺⠀⠑⠒⠫⠈⠀⠀⠀⠀⠠⡀⢀⠁⢃⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠳⣄⠀⠀⣟⣻⢰⡍⢣⠀⠀⠀⠠⠄⢀⣴⣶⣾⡿⠟⠛⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡅⣴⣾⣾⡟⢦⠀⢻⣬⡆⠐⠁⠀⣀⠤⠒⣽⡿⠟⠁⠀⠀⠀⠀⢠⢾⡍⠋⣹⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣞⣳⠗⢌⣧⡱⣹⣾⣇⠀⠙⠛⠒⠚⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⣟⢳⣾⡊⣀⡼⣧
⠀⠀⠀⠀⠀⠀⢀⣾⣏⢰⣶⣾⣿⠙⣏⠘⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣧⡼⢯⡀⠘⣟⣧
⠀⠀⠀⠀⠀⠀⣼⣟⡾⢈⣻⣦⠙⣧⠸⣶⣷⢹⠀⢰⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣽⣿⡔⣩⣧⠐⣩⢾⢧
⠀⠀⠀⠀⠀⠀⠸⣿⡃⣤⣿⣿⡂⠀⢳⣿⡿⣏⡇⠀⠁⠀⠀⠏⠀⠀⠀⣀⠀⠀⠀⡶⣶⣛⢢⢹⢎⡁⠼⣏⣠⠎⣹⡆
⠀⠀⠀⠀⣀⣀⣀⣈⡓⢿⣿⠁⠠⠀⠀⠻⣇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢡⡥⢲⡹⣼⣋⡤⠒⠛⣥⠀⢰⠧⣄
⠀⠀⡴⢿⡿⣿⣌⢙⠯⠙⣿⢷⣤⣶⣤⡀⢠⡜⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⡸⣿⣯⡴⠖⠚⣁⣔⣀⠀⠚⢲⡄
⠀⢸⣓⡟⢠⣬⣍⣴⠛⠫⠉⣛⠧⣿⣷⢝⣮⣻⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠰⠐⠁⠋⣹⢦⠖⠋⠐⢛⣧⣤⠤⠾⠧⡄
⠀⠸⡷⢻⡀⠶⢂⣜⢛⠶⢶⣖⣻⣿⡿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⡀⠀⠙⣮⡳⢯⠁⠀⠘⣷⠀⠀⠒⠛⢀⣀⣀
⠀⠀⠘⠳⢽⣤⡿⠭⠟⠛⠉⠁⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡦⢤⣬⣻⣭⢧⣀⣀⣽⣏⠁⢴⢲⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠉⠙⠳⢦⣼⡉⢿⣚⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁

⣿⠿⢿⠿⣿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⣿⣿⡿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⠄⠀⠈⠙⠀⠉⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠴⠉⠑⡆⠀⣤⠀⠀⠠⠛⠉⢳⡄⠀⠀⠀⠀⠀⢸⣄⠀⡀⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣌⠑⠆⠠⠴⠃⠀⠈⢷⣄⡀⠀⠀⠈⡧⠀⠀⣾⣦⣴⣦⠈⠉⠈⢦⣀⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⡰⡁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢸⡏⡼⠏⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣠⡄⠰⠚⠲⢤⡀⠀⠀⠈⣴⠀⢀⡴⠋⠛⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢰⠃⠀⠀⡀⠀⠀⠙⠲⣄⠀⠘⠶⠉⠀⠀⢀⡟⠀⣰⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢄⡠⠂⠀⢸⡇⠀⡼⠀⠀⠀⠷⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣷⠀⠐⠛⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡽⢆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⢠⡀⣠⠇⠀⠀⢀⡄⠀⣤⠀⠀⠀⠀⣼⠃⠸⣿⣇⠀⠀⠀⢹⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠀⠀⠉⠁⠂⢀⣀⡞⠀⠙⠀⠀⠀⠀⠘⣷⡐⠢⠿⠿⣿⠖⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠈⠁⠁⠀⠀⢀⡀⠀⢠⣊⣀⣤⣬⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠹⡄⠈⠉⠋⠁⠀⠀⠀⠀⢠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⣿⢻⡆⠀⠈⠓⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡺⠈⣿⣤⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠳⡄⠀⢠⡷⠤⠀⠀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⢻⣆⠀⠀⠀⠀⠈⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠐⠒⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠒⠚⠳

⢼⣶⠆⡀⠀⠀⠀⠀⣀⠰⣾⡧⠀⢸⡿⢖⣀⠀⠀⠀⠀⠀⢀⡴⢶⣶⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⣷⣦⡀⠀⠀⢀⢴⣾⣿
⢸⠿⣛⣛⣥⡀⢀⣬⣉⣛⠻⡇⠀⠈⣿⠛⠻⢷⡄⠀⢀⡴⠿⠟⢾⡏⠀⠘⣭⠚⣱⣿⣶⣄⣴⣤⣴⣾⣌⠓⡽⠀⠀⢹⣿⡇⠈⣦⣠⠀⠀⣿⡟
⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠡⢀⠄⠀⠙⣶⠞⠀⠀⠀⠨⠁⠀⠀⠀⢨⠛⠿⠛⣻⣿⣿⠛⠿⢛⠄⠀⠀⠀⠀⣸⠿⠋⠹⠛⠉⠻⣧
⠀⠉⢿⣿⠏⠸⠇⠹⣿⣿⠁⠀⠀⠀⢰⠁⠀⠀⠀⢻⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⠟⠀⠠⠁⠀⠀⠀⠀⠀⠻⣦⣀⡄⠀⣄⣠⡿
⠀⠀⠀⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠘⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡇
⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡿⠛⠉⠀⣀⠀⠀⣀⠀⠉⠉⠻⡄⠀⠸⣿⡗⣦⡀⠀⠀⠀⠀⣠⢾⠛⡟⠁⠀⠀⠀⠈⢢⠀⠀⢀⠀⠀⠀⠀⠀⣸⠿⠛⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠁⢠⣾⣏⠁⢠⡀⠀⣹⣿⡦⠀⠀⠀⠀⢳⣷⣻⣿⣦⠀⢀⣼⡿⠁⣷⠃⠀⠀⠀⠀⠀⣤⣗⣄⣦⡄⠀⠀⠀⠀⠉⢀⣤⣶⠊⠀⡀⠈⢳⣶⣆
⢠⢾⣿⣟⢀⣼⣧⡀⢹⣿⡇⡆⠀⠀⠀⢈⡝⠋⠈⢿⢿⢿⠎⠉⠜⣌⠀⠀⠀⠀⢠⡟⢿⠟⠟⣿⠻⣦⠀⠀⠀⠀⣼⣿⣿⠂⣨⣇⡀⢺⣿⣷⢀
⠈⠀⠙⠻⠿⠉⠋⢻⡿⠋⠀⠁⠀⠀⠀⠀⢢⢈⣱⡦⠈⠠⣴⡍⢁⠊⠀⠀⠀⠀⠘⢷⡆⠀⠀⢰⣶⠏⠀⠀⠀⠀⠂⠙⢿⣿⠏⠏⢿⡾⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡾⣻⣴⠦⠀⠀⠀⠀⠀⠠⠶⣮⣝⠇⠀⠉⠰⣄⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⢶⡴⣤⡀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣟⠒⢀⠀⠀⠀⠀⠀⠀⠀⠐⢚
⣿⠋⢀⣠⣤⣠⣠⣠⣠⣤⣀⡀⢙⡇⠀⢀⣀⣿⣷⡀⠀⠀⣠⣾⣗⣀⡀⠀⠸⣿⡙⢯⣆⠀⢀⣴⡽⢫⣿⠃⠀⠹⣮⢿⣷⣄⠀⠀⢀⣴⣿⢦⡾
⠘⢓⢛⡿⡝⣯⣿⣏⡿⣽⣿⢛⡛⠁⠀⠸⣿⣁⣹⣿⣤⣴⣿⣁⣹⡿⠁⠀⠀⠙⣣⠘⢻⣿⣾⠛⢠⡛⠁⠀⠀⠀⠻⡇⢙⣿⣦⣤⣾⡟⠡⡿⠃
⠀⢾⣼⣿⣿⣿⢸⠹⣷⣿⡿⣼⠇⠀⠀⠀⣴⣿⣿⡿⣿⡿⣿⣿⢷⡄⠀⠀⠀⠐⣿⡄⠞⠸⠘⣇⣬⡗⠀⠀⠀⠀⠀⣶⣿⠛⠛⡏⠙⡟⣶
⠀⠈⠛⠾⠟⠁⠈⠀⠈⠒⠛⠋⠀⠀⠀⠀⢿⣦⠿⠀⢩⠁⠸⢷⡾⠇⠀⠀⠀⠠⠙⠇⠀⠀⠀⠈⠟⢢⠀⠀⠀⠀⠀⠈⠻⠃⠀⠃⠘⠿⠉
⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠁⠈⠱⠗⣄⠀⠀⣠⠐⠆⠃⠂⠀⠀⠘⣿⠿⠶⡄⠀⠀⠠⠾⠿⡿⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⢿⣿⢟⣥⠄⠀⠀⠀⢠⣔⢻⣿
⠀⠀⠀⣀⠀⣿⣿⡄⣀⠀⠀⠀⠀⠀⠀⣯⡦⠀⣀⣰⣆⣄⠀⠀⡱⠀⠀⠀⠄⠀⠀⠀⢰⡖⠀⠀⠀⠀⠃⠀⠀⠈⢿⣸⣁⣀⡠⣿⢀⣀⣹⢣⡟
⠀⠀⠔⠈⠀⢹⡏⠁⠛⠦⠂⠀⠀⠀⠀⢠⣼⠛⢙⢻⡟⡏⠛⣷⡄⠀⠀⠀⢀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⠀⡏⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠞⠉⠉⢳⡤⠛⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⢤⡄⠀⠁⠠⣤⠴⠃

⣴⠉⡟⢓⣶⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣖⠛⡏⢱
⣿⣿⡻⣿⣿⢿⣍⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣋⣽⢿⣿⡿⣻⣿
⠹⣿⣬⣿⣿⡿⣏⠉⠉⠁⣈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡀⠉⠉⣉⣿⣿⣿⣯⣼⡿
⠀⠸⣿⣿⠿⣃⠐⢫⣿⣿⠛⣿⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣿⡟⢻⣿⣯⠓⢀⣻⢿⣿⡿
⠀⠀⠹⣿⡤⠾⣿⣿⣿⠟⠛⢿⠋⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢻⠟⠛⢿⣿⣿⡿⠦⣼⡿⠁
⠀⠀⠀⢻⣿⣼⡟⠉⠀⠀⠀⠀⠑⢄⠀⠙⢿⣷⣄⠀⠀⠀⢀⣴⣿⠟⠁⢀⠐⠁⠀⠀⠀⠈⠙⣿⣼⣿⠃
⠀⠀⠀⠘⣟⢻⡽⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣿⣦⣶⣦⣾⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠺⣽⢛⡟
⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣈⣿⣿⣿⣏⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠈⠛⠿⢿⣿⢿⡿⠿⠿⠿⢿⠿⠛⠉⠁⠀⣿⡇⠀⠉⠙⠻⢿⠿⠿⠿⠿⣿⢿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠠⢿⠇⠊⠈⠀⠀⠶⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠱⠆⠀⠈⠈⠒⢿⠧
⠀⠀⠀⠀⠀⠀⣾⠙⡧⠀⠀⠀⠠⠟⠒⠂⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠒⠚⠧⠀⠀⠀⠠⡝⢹⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣙⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠉⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣹⣇⣀⡀⣂⣀⡤⠂⠀⠀⠀⠀⠀⠀⠢⣄⣀⡂⣀⣀⣿⡩⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⡿⠷⢦⣄⠀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡇⠀⠂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠈⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢷⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠿⠻⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⡈⣿⣶⣀⣾⠃⢦⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⡾⣟⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢀⣾⣿⣿⣿⡟⡗⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⡏
⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣼⣿⣿⣿⣿⣿⣆⠙⢿⣿⣆⡙⠦⣄⠀⢈⣿⣿⣿⣷⡄
⠀⢸⣿⢿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣿⡄⠀⠙⠫⣑⠦⣌⠙⣿⣿⣿⣿⣿⣿⡀
⠀⢸⡏⠀⢱⡟⠉⠙⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡇⠀⠀⠀⠁⠀⠀⠀⠈⠓⠯⢻⣿⣿⣿⣿⣿⣿⠇
⠀⢸⡇⠀⢸⠇⠀⠀⡇⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⣿⣀⣠⣤⣼⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁
⠀⠘⣷⣦⣾⣶⣤⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠛⠛⠛⠛⠿⠛⠛⠛⠋⠉⠁⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢱⣇⣀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣥⡀⠀⠐⠟⢛⣿⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠙⠳⢤⣤⣽⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⠄⠀⠀⠀⠈⣙⣛⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠷⢣⠀⠀⢠⠞⠋⠀⠙⢛⠟⠃⠲⣷⠀⠀⠿⠇⢹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⢁⡴⠋⠀⠀⢦⣴⣻⡄⠀⠀⠀⠀⠨⣦⠉⣟⡉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⠾⠀⠀⠀⣀⡿⢟⣏⠁⠀⢰⣄⣰⣦⣍⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⣿⡀⠀⠀⣶⠈⠀⠀⠉⠒⠚⠻⣿⣿⣭⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣿⡿⢃⠞⠃⠰⢦⣤⠄⣀⣀⠀⠀⠈⢛⣻⣃⣙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣈⢁⣿⣧⠞⠁⠀⠀⠤⠶⠾⡶⠄⠀⠀⢠⣬⣭⣋⡀⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡆⠒⠒⠀⠀⠀⠒⠒⠀⠀⠐⢸⣯⣟⣡⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠻⣦⠀⠂⢄⡀⠀⠀⠀⠀⣷⣾⣝⠋⣹⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠒⢤⣀⣴⣿⣟⣻⣷⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠻⠟⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠖⠀⠀⠄⠴⠶⣾⣿⣿⣿⣷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠺⡄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡗⠘⠇⠀⠀⠀⢠⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣟⣍⡁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⠻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢹⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⡷⠆⠇⠰⣿⠟⠀⠀⠀⠀⠀⠈⠳⠞⣣⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢠⣤⡄⠀⠀⢀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠹⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠳⡤⣠⡼⡧⣤⡠⡞⠉⠀⠀⠀⠀⠀⠻⠿⠿⢷⡾⠿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣾⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⠠⠀⡀⠈⡃
⠀⠀⠀⠀⠀⠷⡶⠂⠑⢶⡾⠃⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡗⠄⠀⠆⠀⠀⠀⠀⠀⢀⣨⠟⠃⠃⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣰⠖⠀⠀⠀⠻⣟⢷⣦⣀⠀⠀⣀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢀⡄⠀⣴⠏⠀⠀⠀⠀⠀⠘⢷⡝⠻⢷⡶⠟⢫⡾⠃⠀⠀⠈⢿⠊⠻⣷⠄⡀⢴⡿⠋⢚⡟⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣇⠀⠹⠏⠀⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣄⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⣡⣴⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠘⣟⡾⠀⠀⠸⢗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠞⠁⠐
⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠈⠹⣿⣿⣷⡄⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣴⣶⣶⠂⠀⠀⠀⠀⣀⠂⡀
⠀⠀⠀⠀⠙⡟⢻⣿⡿⣟⢻⠛⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠇⠈⢠⡄⠀⠀⠀⠀⠀⠙⠳⣦⣶⣟⢇
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠘

⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀
⠀⢾⡿⢍⠳⠈⠛⠙⢶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⠋⠟⠡⠞⡩⢿⡇
⠀⠸⣗⠄⡱⣚⠭⠭⠶⢷⣬⣟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣛⣥⡾⠶⠭⠭⣓⣎⠠⣻⠃
⠀⠀⠹⡗⢽⣱⢊⣭⠤⠬⢜⣛⣿⢷⣽⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣯⣾⣽⣋⡡⠥⠬⣭⡑⣾⡇⣺⠏
⠀⠀⠀⠹⡆⢿⢺⠀⢲⡖⠐⠠⠭⡝⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⢿⢫⠭⠄⠂⢲⡖⢀⡇⡿⢰⠏
⠀⠀⠀⠀⢹⡄⢦⠑⢤⣙⡢⢄⣀⠀⠁⠂⠝⣺⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣝⡫⠒⠍⠀⣀⡠⢔⣃⡤⠋⡼⣠⠏
⠀⠀⠀⠀⠀⣷⠈⡷⣄⡤⠉⣑⠒⠡⠕⣴⣄⡈⠚⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⡝⠓⠁⣀⣦⠪⠘⠒⣈⠉⢄⣠⣾⠡⡾
⠀⠀⠀⠀⠀⢸⡅⢻⣦⣉⢉⠈⠳⠥⠤⠶⡉⡙⠷⣠⡛⣽⢟⣷⡀⠀⠀⠀⠀⠀⠀⢀⣞⡿⣫⢋⣤⠖⢋⢉⠖⠤⠭⠞⠡⡉⣉⣴⡟⢨⡇
⠀⠀⠀⠀⠀⠸⣇⢸⠟⣩⡥⠤⡤⠤⣀⡀⠙⠢⠄⢂⠙⠿⣿⡿⣿⡄⠀⢀⡀⠀⢠⣟⢯⣿⠟⠋⡐⠠⠔⠋⢀⣀⠤⠤⠤⢬⣍⠻⡇⣺⠇
⠀⠀⠀⠀⠀⠀⢿⡼⣜⢧⣠⣰⣰⣀⣸⣈⣹⡐⢠⢈⡳⢅⠨⠻⣼⣿⡔⣿⣿⢢⣿⣳⠟⠅⡸⢞⠀⡄⢒⣏⣀⣅⣀⣇⣆⣄⡼⣣⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠮⣓⣤⣀⡉⠀⠀⢀⣀⠈⠉⠓⠺⠶⣄⡀⠘⢿⣷⣿⣿⣾⡿⠁⢀⣠⠶⠓⠊⠉⠁⣀⣀⠀⠀⢉⣀⣴⣛⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢲⣴⣶⢢⣤⣤⣩⣵⣄⣀⣩⣷⡾⣿⣧⣾⡿⢷⣾⣍⣀⣠⣮⣁⣥⣥⡔⣶⣦⡖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡉⢱⢁⡛⠀⡇⢻⠙⠉⢹⣿⣿⣮⡿⣿⣿⢿⣤⣿⣿⡏⠉⠋⡟⢹⠀⢛⡈⡌⣉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠠⢇⠀⡇⢼⡐⠂⠀⠸⠛⣿⡇⣿⣇⢸⣿⠛⠇⠀⠐⢂⡇⢸⠀⡼⠄⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⢣⠈⣻⡀⠹⡀⢹⡀⠂⠀⠀⢹⠀⣿⣿⠈⡏⠀⠀⠒⢀⡏⢀⠏⢀⣟⠀⡜⣄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⢀⡒⡀⠐⢣⡀⠙⣄⠉⠱⣄⣡⠇⠀⣿⣿⠀⠸⣌⣠⠊⠉⡠⠋⢀⡜⠢⢀⢒⡀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⢘⡒⡄⠉⠷⣄⠀⠙⠲⢼⠏⠀⠀⢻⡗⠀⠀⠹⡦⠖⠋⢀⣠⠾⠉⡠⢐⡁⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠤⠦⣀⠁⠟⢲⡾⠁⠀⠀⠀⠈⠁⠀⠀⠀⠘⢷⡖⠻⠈⡠⠴⠥⠀⢸⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣜⢂⣭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣭⡐⣣⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠶⠖⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢶⣶⣼⣆⠀⠀⠀⢘⣧⣤⡶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣠⠶⠛⠉⣩⡽⠛⠋⠉⠉⠛⠻⣭⡉⠙⠳⢦⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟⠁⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⢷⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠹⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⣧⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡤⠶⠿⢦⡦⡼⠗⢦⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠛⣲⣦⣀⣟⠀⣠⢼⠷⠲⣄
⠀⠀⠀⠀⢰⣋⣀⣀⣾⠻⣣⠖⠻⣼⣁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⡝⢦⣰⠃⠧⠟⠹⠿⢻⡀⠀⠀⢿⡀
⠀⠀⠀⣾⠉⠁⣸⡽⠿⣤⡇⠀⠀⠸⣏⣠⣴⡒⠻⢦⣀⣀⣀⣀⣀⠀⢀⠀⢰⡓⠟⠀⠉⠀⠘⣿⣀⣀⣀⡀⠀⣠⣙⣦⢴⡞⠓⠲⢤
⠀⠀⣀⣼⣦⣞⣡⡤⠤⠤⣧⠀⡶⢶⠇⠉⠀⢹⠆⡴⠃⠀⢰⡏⠀⠙⢹⣷⣏⠀⣀⣀⢸⡳⣤⢻⣞⠁⠈⠉⠳⣿⠈⠀⠀⣿⠀⠀⣀
⢤⣬⡿⠉⠸⡅⠀⠀⠀⠀⢾⠳⠟⠀⠀⠀⢀⣼⡿⣥⣀⣀⣾⣅⡀⠀⠀⠁⣿⡶⠿⠈⠉⠁⠘⣿⡿⣄⡀⠀⠀⢸⠀⠀⣠⡾⠷⠯⣅
⠀⠈⢉⣙⣿⡳⣄⡀⠀⠀⠈⣳⣄⠀⢀⡤⠬⠗⠀⣸⠋⠉⠉⠛⢦⡀⠀⢠⡟⠀⠀⠀⠀⢀⣀⢸⡀⠀⠉⠿⣖⠚⠶⡏⠁⠀⠀⠀⢈
⠀⠀⠈⠙⠻⠶⢶⠭⠭⠿⠿⠏⠈⠓⢮⣽⣄⣠⠾⣅⠀⠀⣀⡤⣾⣥⠴⠾⠳⠶⣄⡴⣆⡞⠙⠞⠓⠒⠚⠏⠻⠛⠲⠿⠶⠤⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠭⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠧⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡞⠛⠛⠣⣼⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⣿⡤⠛⠛⠛⣾⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣯⠉⠉⠛⣿⠃⠀⣠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⢻⡟⠉⠉⢩⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣉⣉⣙⣇⣸⣿⡿⢉⣿⣷⡀⠀⠃⠀⠀⠃⠀⣰⣿⣏⠹⣿⣿⣀⣟⣉⣉⣉⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠉⣀⣀⣍⣿⣿⡀⢸⣿⣿⢿⡄⢡⡀⡠⠁⣼⢿⣿⣿⠀⣸⣿⣯⣅⣀⡀⢹⣟⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣀⣀⣀⣤⠿⠿⢿⣿⣧⣈⣿⣘⣿⣟⣸⣏⣠⢿⣿⠿⠿⢷⣤⣀⣀⣰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣇⣠⠤⠤⠶⠒⢾⣿⠦⠬⣭⣿⠁⢹⣯⡭⠴⢾⣿⠗⠒⠦⠤⠤⣀⣿⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣦⡤⠴⠶⠒⠚⢻⣶⣶⢾⣿⠁⢸⣿⢶⣶⣾⠛⠒⠒⠶⠦⣤⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⠴⢒⠞⠉⣿⠃⢀⡾⣿⣗⣿⡿⣆⠀⢻⡏⠙⢖⠲⠤⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣼⣃⣤⡏⠀⠀⣿⢠⡞⢰⠏⣗⡏⢷⠘⣦⣸⡇⠀⠈⣧⣄⣻⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⠻⡅⣸⣇⣀⣠⣿⣻⢀⡞⠀⠻⠃⠘⣆⢸⣽⣧⣀⣀⣿⡀⡽⢻⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⢾⣾⣷⠁⡜⠉⡏⠈⣿⣽⠃⠀⠀⠀⠀⢻⣭⡏⠈⡏⠙⡄⢹⣿⣿⠿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣿⣼⣿⠷⣴⡷⢾⣷⣿⠀⠀⠀⠀⠀⢸⣷⣿⠶⣧⡴⢿⣿⣼⣿⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⢹⣿⣿⣲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣯⣿⣷⣿⣿⣿⢡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣶⣽⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⣿⣵⡾⣿⠿⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢿⡟⠈⠳⣄⠀⠀⠀⠀⡤⠊⠁⣻⠗⠀⠀⠀⣿⡇⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⡆⣿⡇⠀⠀⠘⢻⡷⡦⣄⠀⠀⠀⠀⠀⣠⣴⡾⣿⠓
⠀⠀⠀⡉⠁⠀⠈⠁⣴⡄⠊⠀⠀⠈⣩⠀⠀⠀⠀⠸⣷⡙⠻⣤⣇⢀⣄⢀⣧⡼⠛⣱⡿⠀⠀⠀⠀⠫⢿⡹⡟⠀⣀⣸⣀⡠⠘⡟⣽⠯⠃
⠀⠀⠀⠛⣳⠖⠶⠖⣿⡗⠲⠖⠲⡛⠋⠀⠀⠀⠀⠀⠙⣷⡾⠉⠉⣹⣿⡉⠉⢹⣾⡟⠁⠀⠀⠀⠀⠀⠻⣿⣛⡈⣹⣿⣏⠁⣘⣿⡟⠁
⠀⠀⠀⠘⡀⢠⠔⠀⣿⡇⠑⢤⠀⣈⠀⠀⠀⠀⠀⠀⠸⣿⣷⠘⠻⠏⠏⠿⠛⢸⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⠁⢸⠈⢠⣟⣿⣿⣆
⠀⠀⠀⠀⢳⣀⣀⠂⠀⠀⠂⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡞⠂⠀⠛⣾⣿⡟⠃⠀⠀⠀⠀⠀⠸⣨⣻⣴⠇⠀⠀⠀⠘⣧⣝⣉⡇
⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱
⠀⢿⣿⣶⣦⢀⠀⠀⠀⠀⢀⠀⡠⣴⣾⣿⡇⠀⠰⣄⣀⣶⣶⢤⡀⠀⠀⠀⣠⢴⣶⣆⣀⡶
⠀⠈⣿⡯⠨⠈⠳⣄⠀⠀⡠⠋⠩⠁⣿⡏⠀⠀⠀⠘⢷⣮⡁⠀⠈⣶⣷⡎⠀⠀⣩⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢸⣿⣀⣈⣀⣈⣶⣞⣁⣊⣀⣰⣿⠃⠀⠀⠀⠀⠈⢿⡿⠛⣋⣹⣿⣉⡛⠻⣿⠏⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⢺⣿⡗⠂⠀⠀⠀⡰⡾
⠀⠀⠀⣿⠁⠈⣉⠉⣿⣏⢉⡉⠀⠹⣯⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⡉⠃⣉⠁⢠⡿⠀⠀⠀⠀⠀⠀⠈⠀⡤⡖⠉⠘⣿⡇⠈⢐⣤⡄⠋
⠀⠀⠀⢿⣥⣀⡀⠘⠙⠙⡀⣁⣡⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠲⠚⠁⠀⠙⠲⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠿⠄⠀⠀⠄
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣾⣷⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿
⠀⠴⠀⠶⣤⢀⠀⠠⢴⡤⠀⢀⡀⡴⠖⠰⣄⠀⠀⡏⠁⠂⠀⠉⠢⣠⣦⡠⠚⠁⠀⠂⠉⡇⠀⠀⠹⡶⠻⠹⠊⠶⡄⠀⢀⡶⠂⠏⠝⠳⡏
⠀⠻⣷⡀⠀⢀⣠⠔⢻⡃⢤⣄⡀⠀⡐⡾⠋⠀⠀⠑⠒⣶⠶⠦⠤⣾⣿⡦⠤⠴⢶⠒⠒⠁⠀⠀⠀⠷⣀⣀⣀⣀⣸⣶⣏⣀⣀⣀⣀⠸⠃
⠀⠀⠈⢃⠈⠉⠀⠀⣼⡄⠀⠈⠉⠀⠛⠁⠀⠀⠀⠀⠘⠁⢀⠄⢀⡿⡿⣇⠀⢤⠀⠙⠀⠀⠀⠀⠀⢰⡏⠀⠈⡀⠘⣿⡧⠀⡉⠀⢘⣦
⠀⠀⠀⠈⠢⢀⠠⠜⠁⠈⠢⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡦⠀⠠⠃⠀⠀⠈⠣⠀⠠⣆⡀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠋⠹⠙⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠛⠁
⢀⣤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣄⠀⠀⢰⣿⣿⠳⢄⠀⠀⠀⠀⢀⠴⢻⣿⣷⠀⠀⠀⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷
⠀⢿⠂⠀⠙⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⢘⠟⠀⠀⠘⣿⡏⠂⠀⠐⠀⠀⠀⠀⠀⠊⣿⡟⠀⠀⠀⠘⣿⣿⠷⣟⣳⣄⠀⢠⣖⣻⡾⣻⣿⡏
⠀⠀⡛⢐⠢⠀⠈⠀⢰⡄⠔⠁⠠⠐⠘⠋⠀⠀⠀⠀⠹⢿⡥⠄⠐⢶⣷⠖⠀⠤⣽⠟⠁⠀⠀⠀⠀⠘⣿⣷⡉⣿⣿⣿⣿⣿⣉⣴⣿⠏
⠀⠀⠈⠂⢠⡤⠀⢠⣾⣧⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠾⡟⠆⠀⠂⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣧⡀⢸⣿⡅
⠀⠀⠀⢰⠏⠀⠀⠀⢿⡇⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠀⠁⠸⣦⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠉⢹⣿⣿⡿⠃
⠀⠀⠀⠈⠃⠼⠄⠀⠀⠀⠀⠤⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⢸⣣⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠡⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆
⠀⠀⡴⠀⠀⠀⠀⠠⢻⠐
⠀⠀⠂⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⡶⣶⡦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢺⣏⢹⡇⣩⣿⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣋⠈⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⣀⣠⣴⣿⣿⡔⠋⢀⣼⣿⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣗⠙⢷⠆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⣿⢿⠇⠀⢠⣾⣿⡷⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⣌⣀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣿⣿⣟⢿⣿⣌⠂⠀⢠⢸⣿⣘⠇
⠀⠀⠀⠀⢀⣠⢺⣿⣿⣿⡄⣷⣿⣿⣧⡽⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣆⡹⠟⠛⠻⠈⠃⢿⣿⡧⠀⣠⣿⣿⠧⠃
⠀⠀⠀⢠⣜⣿⣿⣿⡟⠁⠘⠋⠹⣿⣿⢇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⠿⠦⢉⣁⣀⣠⣀⠠⠄⢀⣉⣟⠞⢻⣿⡟⣺⡀
⠀⠀⠀⢘⡉⢿⣿⣿⣷⡶⢀⣠⣤⣬⣽⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⡶⡿⢿⢿⣿⣟⢿⣿⣿⣿⣿⣦⡀⠀⠗⠉⠀⠓⠄
⠀⠀⠀⠀⠁⠈⠛⠉⠟⠃⠻⠿⠿⠟⠫⠌⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠷⠛⠛⠉⠉⠁⠈⠋⠖⠋⠽⣉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣬⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢿⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⠾⠁⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠉⠁⢑⣶⠄⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣶⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢋⡀⢁⡂⠀⠀⢀⠀⠀⣠⡀⠀⠒⣀⠘⢛⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠥⢠⣶⣿⡃⠀⠀⢥⣄⢺⠭⠞⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⡷
⠀⠀⣾⣿⡟⢶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⢀⠀⠱⠀⠵⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠟⣡⣿⠐⡟
⠀⠀⠙⣿⣿⣴⠿⠿⠟⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⠇⣾⣿⣹⠇
⠀⠀⠀⠘⣿⣷⠒⠒⠂⠀⠄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣭⡛⢲⡿⣧⣼
⠀⠀⠀⠀⠘⣿⡏⠉⣁⣠⣤⣤⣤⣀⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣷⣶⣷⣤⣿⡈⣿⢤⣄
⠀⠀⠀⠀⠀⣿⡛⠻⠟⠉⠍⠉⣡⣾⣿⣿⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣈⠿⢹⢿⣿⣿⣷⣤⡟⣿⠟⠛⠋
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠞⠀⣾⣿⡿⠁⢿⡆⠀⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⠀⢶⣿⣿⣿⣗⣿
⠀⠀⠀⠀⠀⠀⠹⠿⣷⡶⣾⡟⠁⣀⠂⢸⡇⠀⠁⢀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠈⠁⠐⢿⡇⢰⠀⢾⠘⣽⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⢿⣿⡿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣦⣼⣷⣾⣦⣾⣾⣯⡍⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠻⢿⣿⠟

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⢹⠆⠀⠀⢀⣤⣠⡏⠉⠃⠀⠈⡗⠒⠀⠐
⠀⠀⠀⠒⠶⡶⢼⡶⣶⣦⡀⠀⠀⠀⠂⠀⠀⠀⠂⢤⠤⣘⣤⡟⠲⡁⠠⠒⠱⠋⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⢅
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡌⢿⠄⠈⠀⠀⠀⠀⠀⠀⡸⢐⠛⠀⠀⢀⣄⠀⠀⣤⠐⠉⠁⠀⢠⣾⢻⣻⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣣⠀⡇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠏⠈⠲⠒⠊⠉⠙⠋⠁⠀⠀⠀⠈
⠈⠺⡄⠀⠀⠀⠜⡿⠾⡟⠦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠄⠀⠀⠉
⠀⠀⠈⢩⠖⠀⠀⡅⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠀⠀⠀⠋⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠤⢰⡤⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠶⠀⠃⠆⠀⠇⠶⠘⠰⠆⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⢠⡴⠶⣶⠉⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄
⢀⠔⠚⠂⠀⠈⠀⠀⠜⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣤⣾⡛⠛⠯⣃⢄
⢸⠄⠀⠀⠀⢀⣤⣤⡄⠀⠐⠋⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣀⣴⡜⠛⠦⠀⠙⠦⡈⢳⣃
⢀⠀⠀⢀⣨⣿⣭⣷⠁⠀⠀⠠⢄⠀⠀⠂⠐⢀⡀⠉⠀⠀⠀⠀⠆⠠⢤⣿⣤⣔⠉⠀⠇⠀⠀⠑⠄⠀⠱⠄⣿
⠈⠟⠉⠁⠀⠈⠉⠀⠀⠀⢀⣀⠈⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢡⠈⢇⠀⠀⠀⠀⠀⠈⠆⠀⣧⡟
⠀⠀⡀⢀⠄⠀⠀⢠⠀⠀⠀⠁⣠⠎⠀⠀⠀⠠⠀⠀⠀⠀⠢⣀⡀⢈⠀⠀⡰⢀⣿⠄⠀⠐⠀⠀⠀⢸⡴⠋
⣤⣤⣥⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣤⣽⣶⣶⣿⣬⣥⣤⣵⣤⣤⣵⣦⣥⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢰⣶⡶⠖⠛⠛⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠒⠛⠓⠶⣶⣶
⣿⡋⡉⠀⠀⠀⠀⠔⠂⠀⠀⠈⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠒⠄⠀⠀⠀⠈⡉⣻
⢻⣀⡀⠠⠄⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠤⠀⢀⣸
⠀⠛⢦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⢠⣴⣤⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠞⠃
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣀⠠⠀⠀⠉⠐⠀⠤⢀⣀⣙⣷⣴⣿⣷⣴⣟⣁⣀⠠⠄⠀⠈⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⢶⡖⠒⠉⠁⠀⠀⠀⠀⢀⣠⡤⠖⠚⠛⠛⠻⣻⣿⣿⠛⠏⠛⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠉⠑⠒⣶⠎
⠀⠀⠀⠀⠀⠀⠳⣦⣀⠀⠀⢀⣠⡶⠋⠁⡀⠄⠤⠀⠀⢀⡞⣿⡟⣆⠀⠀⠠⠄⠄⠀⠉⠳⣦⣀⠀⠀⢀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠉⠀⠀⠀⠀⠄⠀⠀⢀⣾⠐⣿⡇⢸⣆⠀⠀⠀⠄⠀⠀⠀⠀⠙⢿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠃⠀⠠⠂⠀⠀⠀⠄⢸⣿⠀⢿⠇⢸⣿⠁⠄⠀⠀⠀⠢⠀⠀⠱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⡠⠁⢀⠀⠀⠀⠀⠀⢻⠀⠘⠀⢸⠇⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡐⠀⢀⠂⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢣⠀⠐⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⠆⠀⠀⠀⡆⠀⢀⠀⣃⠀⢀⡇⠀⠀⠀⠆⠀⠀⠀⢂⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡜⠀⠰⠀⠀⠆⠀⢸⣠⡏⠀⠈⣧⣸⠀⠀⠂⠀⠘⡀⠈⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡇⠀⢠⠀⢀⣼⠋⠀⠀⠀⠈⢻⣄⠀⢰⠀⠀⢇⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⢾⡿⠛⠛⠀⠀⠀⠀⠀⠘⠛⠻⣿⠾⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢻⡛⠦⣀⣀⡴⠛⡿⠀⠀⡤⢀⠄⠀⠀⠀⠠⣄⢠⡄⠀⢸⣷⣄⠀⠀⢀⣴⣿⠀⠀⠀⣶⣶⣦⡀⠀⢀⣴⣶⣶⠀⠀⢻⣶⣄⠀⠀⠀⠀⡠⣶⡟
⠀⠀⠀⠈⠃⠀⠸⢇⠀⢐⠃⠀⠀⠱⠁⠀⠀⣴⡀⠀⠀⠛⠁⠀⠀⣿⢻⣧⣠⣿⣳⡇⠀⠀⠀⢾⣟⣹⣿⣴⣿⣏⣻⡗⠀⠀⠈⣷⣿⣷⣄⣠⣾⣿⣾⠁
⠀⠀⠀⠀⢹⣤⠂⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⢿⣯⣏⠀⠀⠀⠀⠠⣿⣬⡿⠿⣿⣭⣿⠀⠀⠀⠀⠈⣽⣿⠟⠻⣿⣯⠁
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠹⡟⠀⠀⠀⠀⠀⠙⠛⠇⠀⠸⠛⠋⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⢠⣴⡆⠀⣤⠤⢄⠀⠀⠀⠀⢀⠤⢤⡄⠀⣶⣤⡀⠀⠀⠀⢀⣴⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⣿⣿⢗⣤⣴⣦⣤⡲⢿⣿⠀⠀⢫⣴⣾⣤⣾⣶⣌⠇⠀⠀⣀⠀⠹⣄⣀⡶⠁⠀⡀⠀⠀⠘⣿⢿⣆⣀⣰⡿⣿⠇⠀⠀⢸⡿⢷⢀⠀⠀⣀⡾⢿⡇
⠀⠀⠈⢷⣸⣿⣿⣿⣿⣟⡼⠃⠀⠀⠈⢉⣿⢿⢿⡏⠉⠀⠀⠀⢀⠐⠀⢈⣏⠀⠐⢀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⢉⢊⣉⣿⣿⣃⡙⠈
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢦⠀⡞⠹⡄⢠⠆⠀⠀⠀⠀⣿⣿⠉⠀⠉⣿⣿⠀⠀⠀⠀⢸⡸⠿⠁⠀⠿⠇⡆
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠉⠉⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉
⠀⠘⣇⠉⠀⠄⠀⠀⢀⠔⠉⢠⠇⣶⣦⣄⠀⠀⠀⢠⣴⣶⠄⠸⡟⡷⢀⠀⠀⢀⢸⡟⡿⠀⠰⡾⠂⠀⠀⠀⢀⠠⠐⣿⠄⠀⣤⠄⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠈⢦⣴⣾⣦⣰⣿⣶⡴⠋⠀⢸⡟⢹⣷⡤⣼⣿⠙⣿⠀⠀⠃⠀⡜⢱⣶⠙⡄⠀⠁⠀⠀⠅⠀⠒⠃⣴⠘⠓⠀⠨⠀⠀⠁⢠⠀⠀⢰⡆⠀⠀⡄⠘
⠀⠀⠀⢀⣼⣿⡿⢿⣿⣧⡄⠀⠀⠀⢴⠈⠿⠻⠻⠇⢰⠀⠀⠀⠠⡀⠀⠈⠏⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠈⡿⠞⠁⠀⠁⢺⠅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⣤⡀⠀⠀⠀⠀⣠⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⢤⢤⣄⠀⠀⠀⠀⣠⡤⣤
⠀⠀⠘⣿⣋⣴⣄⢠⣴⣝⣿⡇⠀⠘⣿⢚⣦⣀⣠⡟⣽⡇⠀⠀⡇⣧⠀⠀⠀⠀⢠⡇⡇⠈⢻⡿⣷⣄⠀⠀⠀⣠⣾⢿⡟⠀⠘⡍⠈⢳⡄⢠⣾⠁⢉⠇
⠀⠀⠀⢻⡟⠛⠻⡿⠛⠻⣿⠀⠀⠀⣡⣾⣿⢿⣿⣿⣬⠀⠀⠀⠁⠸⡿⢷⣷⡿⡿⠀⠁⠀⠀⠻⠌⣻⣷⢶⣾⣟⠡⠟⠀⠀⠀⠘⣡⣿⣿⣿⣷⣌⠃
⠀⠀⠀⠘⠷⣤⠂⠐⣤⡾⠃⠀⠀⠀⢹⢉⡛⠀⠘⣃⣻⠀⠀⠀⠐⣄⠃⠁⠂⠀⢃⡔⠀⠀⠀⠀⢾⣅⡉⠚⢉⣩⡷⠀⠀⠀⠀⠈⠢⠝⠀⠀⠫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⢀⣤⡤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⡤⣤⡀
⠀⠀⠘⣿⡇⣿⣿⢸⣏⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠰⡍⡇⢹⣿⡧⣿⠇
⠀⠀⠀⠹⣯⣾⣷⣀⣹⠤⣃⣀⡾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠑⢷⣄⣈⢤⣇⣁⣾⣿⣼⡟
⠀⠀⠀⠀⠹⣧⣾⣿⡤⠔⠚⢻⣤⣤⣾⣿⡟⢦⡀⠀⠀⠀⠀⢀⣴⢟⣿⣷⣤⣠⡟⠛⠒⢤⣽⣟⣾⠏
⠀⠀⠀⠀⠀⠙⣿⢻⣷⠖⠉⢁⣀⠹⠿⣿⣿⣿⣿⣦⣴⣶⣠⣿⣷⣿⣿⠿⠯⣀⡈⠉⠓⢶⡿⣾⠟
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠞⠉⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠓⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⣠⣤⡤⠶⠒⡛⠛⠻⣿⣿⡿⢿⣿⣿⡟⠛⢛⠒⠶⢦⣤⣄⡐⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢻⣯⠀⡀⠴⠁⢀⣴⡟⠙⡿⢺⠏⢹⣦⡀⠀⠦⢀⠀⣿⡟⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⡟⣷⠚⣿⡁⠐⠣⠔⡋⢸⠀⠀⡇⢸⠀⢀⡇⠉⠲⠔⠂⣌⣿⠓⣾⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⡶⢿⣅⡀⡆⠀⡇⡞⢀⠀⢧⢸⠀⠠⢧⢘⠀⠐⣀⣸⡿⢷⠏⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣼⠛⢿⣷⣸⣄⣧⡈⠀⠈⠀⠀⢀⣼⣨⣆⣶⣿⠛⣧⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣛⣿⣦⣄⣋⣻⣩⣧⠀⠀⠀⠀⣼⣏⣛⣉⣠⣼⢿⣻⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣝⣻⣝⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⠂⣄⠀⠀⠰⠀⠀⠀⡄⢀⠀⢠⡀⠀⠀⠀⠄⢠⠄⠀⢀
⠀⡮⠷⠀⣠⠈⠀⠀⢀⡀⠀⠙⢆⠀⠈⠁⠀⡛⢌⡀⠀⠤⠀⠀⢻⡁⢲⠀⠈⠱⠀⢁⡁⠀⠺⠛⠁⢀⠖⠀⠘⠀⠀⠫⢠⣫⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⠺⠀⠠⠀⠀⣴⠼⠧⢹⠀⣁⠁⡀⠐⠆⠀⠂⠀⠀⠉⠐⠀⠀⠀⡀⡂
⠀⡐⢖⠩⢀⠀⠀⢀⠴⠒⠈⠉⠉⠓⠂⠀⠆⠀⣄⣀⣠⡄⠀⣈⠉⠉⠁⠀⣤⠀⠃⡀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣠⣀⠈⢉⡆
⠀⣚⣅⠤⠑⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢾⣿⠄⠀⠀⠄⠀⠀⠘⠀⠀⠇⠸⠀⡀⠉⠀⠄⠀⠠⡀⢉⠁⠀⠁
⠀⠠⡈⠁⡐⠀⡉⠀⠉⠉⠁⢻⠂⠉⠉⢁⣍⡁⠘⠒⠊⠀⢀⠁⠀⠤⠄⠀⡐⠂⣂⠀⠂⠁⠀⠀⠈⡀⡋⠁⠈⠏⣈⣁⠄⢶⢀
⠀⠠⣈⡁⠀⠀⢹⠃⠉⠀⠀⢸⠀⢤⠀⠨⢱⠀⠀⢰⢈⣄⠊⠀⠀⠀⠀⠀⠂⠀⠉⣉⠰⢢⡄⠀⢀⠁⠁⠀⠈⠱⠛⠓⠀⢠
⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡇⠀⠀⠀⠀⢈⠀⠀⢀⠀⢀⠄⣴⡀⠀⡀⡀⠀⡀⠘⠛⠃⠀⠀⡀⠠⣀⠂⠄
⠀⠠⠁⠀⡄⠂⠁⠀⢀⡀⢴⡸⠀⣀⠀⠠⠈⡇⠀⠁⠀⠀⠘⠀⠤⠚⠃⢀⣸⠁⡱⠀⢠⣴⠀⠹⢄⠀⠀⢀⠀⠀⠠⠐⠐⡀
⠀⢐⡂⠀⠈⠈⠀⠀⡉⠀⠀⡀⠘⠀⠄⠀⠠⠐⠄⠄⡀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣤⣌⡄⠀⠒⠋⠀⢀⣄⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠁⠐⠀⠺⠗⢀⢀⠁⠀⢀⠀⠠⠂⠀⢈⠂⠡⠀⠀⠀⠀⢠⠄⠀⢶⣦⣤⡄⠀⠀⠁⠀⢀⣶⡤⠐⢀⣉⢓⠄⠀⢀⠄
⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⠈⠂⠀⠁⠐⠀⠤⠐⠂⠀⠠⠀⠢⠄⠀⡈⠀⠀⠉⠀⢰⡇⠀⣄⢻⣺⣟⣃⣞⣿⣯⡄⢀⡀
⠀⠀⠀⠀⢂⡁⡀⠀⢦⠀⠀⠢⠘⠀⠀⡅⠀⠀⠂⠀⢈⠁⠀⢀⠢⠀⢐⡀⠂⠀⠀⠀⠀⠈⠁⠘⠉⠃⠈⡏⡍⠋⠈⠁⠑⠀⠁
⠀⢌⠤⠀⠈⣄⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢜⠀⠈⠀⠀⠀⠑⠀⡀⠂⠀⠀⡀⠀⣤⣄⡄⠀⠀⠃⠀⠀⠠⠀⠀⠦
⠀⠠⠎⡄⠀⠘⠀⠀⠒⠋⢀⠀⠃⠉⠘⠀⠃⠉⠐⠁⡀⠈⠁⠀⠀⠀⠀⡀⠈⢴⡥⠀⠀⠃⠀⠁⢛⠃⠀⠀⠀⠀⠂⡀⢠
⠀⢁⢚⡠⢡⠀⠀⠀⢀⠀⠉⢀⡁⠀⠁⠉⠁⢈⡁⠈⠁⣠⠘⠠⣀⣀⠶⠃⡀⣈⠈⠁⠀⠀⠀⡀⠘⠶⡄⠓⠃⠠⠀⠉⠠⠠⠆
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣀⠀⠀⠀⢠⠅⡊⠁⠀⠀⠀⠀⢉⡁⢁⠁⠀⠂⠀⠄⠠⣌⡀⠂
⠀⡎⠀⠀⠀⠆⠀⠰⣶⡴⣧⡄⠩⠤⠀⠀⠐⠋⢱⠀⠀⠈⢐⠃⠀⣀⠀⠐⠒⠁⠀⠒⠂⢠⠀⠀⢂⡊⠒⠀⠀⠀⡐⠀⠉⣀⡀
⠀⠀⠘⠈⠣⠀⠀⠀⠋⡏⠉⠇⠀⠀⠁⠄⠀⠀⢊⢄⠀⠁⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠇⠐⡁⠀⢠⠀⠀⠀⠩⠐
⠀⠀⠦⠀⠄⠀⠲⣒⠚⢁⣐⡇⠀⠀⠤⠀⠀⠄⠀⠽⠇⠀⠠⠄⠁⢀⠀⢀⡂⠈⡆⠙⠂⠁⢰⠘⠀⢩⢨⠅⠀⠒⠀⠀⠀⠀⠅
⠀⠀⣀⢠⠀⠀⢠⡌⠉⠉⠉⠁⠀⠄⣷⠲⠀⣠⢶⣖⠤⣄⠀⠲⠆⠀⠀⠶⢄⠀⠀⠀⠀⢤⠖⣆⠀⠒⠰⠂⠀⠀⠀⠐⠔⠁
⠀⠀⢘⠬⠆⠀⢈⠉⠢⠀⢀⠈⠀⠀⠀⠀⢨⣶⠋⠉⠙⢶⠆⠀⠄⢀⠘⠈⠁⠀⠀⠀⠀⢊⡗⢤⠀⠀⠂⠀⠤⣥⢀⢤⠀⠀⢄
⠀⠀⠈⠓⡯⠂⠈⠠⢀⠀⠀⠉⠀⠗⠀⠀⠈⢭⣷⣠⣶⡿⠂⠀⠂⢁⠀⢀⠀⠘⠉⠀⠀⠼⠧⣐⠀⠂⠀⢤⠀⠁⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣾⠀⢀⡏⡹⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢾⡿⢖⠂⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠀⠃⠲⡛⠿⣦⣤⠄⠀⠀⠀⠀⠀⠀⢀⠴⠻⣶⠾⠳⢽⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⣲⠀⠀⠀⠙⣆⠀⠙⢷⡀⠀⠀⠀⢀⠔⠁⢀⠼⠓⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣃⠈⢀⣀⣉⣕⣦⣄⡙⢦⣶⡷⠃⣀⣒⣉⣀⣀⣀⢀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢛⢻⠿⠟⢉⡙⠫⡭⣿⣿⣷⣯⣋⡉⠉⠛⠿⣿⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣉⠀⠀⡐⠊⡠⠂⠐⠸⣿⠘⠂⠠⡈⠲⠀⠀⠘⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠁⠒⠀⡐⠀⢀⣿⠀⠠⠠⠈⠒⢤⠀⠀⢐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⡄⡀⠀⠀⠠⠀⠄⠈⣿⠀⢀⠂⠡⠀⢂⠁⣈⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢇⣞⣦⣷⡾⠀⠀⠁⠀⠀⠺⢦⣷⣾⣿⠿⠋

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⣠⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⢶⢢⡤⠀⠀⠀⠀⠀⠀⠠⣦⢰⠆⢰⣶⠒⠠⡀⠀⠀⠀⡀⠄⢒⣶⠄
⠀⠀⠀⠈⢧⡀⠀⠀⣤⠀⠀⢀⡼⠁⠀⠀⢠⡟⣠⢒⡀⠀⡐⢦⠸⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⡄⠀⠈⣢⣠⡊⠀⠀⢠⠏
⠀⠀⠀⠀⢀⡍⠉⠀⣿⠀⠈⢩⡀⠀⠀⠀⠘⠃⡇⢸⣸⣇⡗⢸⡘⠃⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⢀⠉⠀⠀⠀⠘⢧⣤⢀⣨⣿⣄⢠⣤⠞
⠀⠀⠀⠀⠘⣧⣀⣀⣙⣀⣀⣼⠇⠀⠀⠀⠀⢻⣿⡄⠙⡟⢀⣼⡾⠀⠀⠀⠀⠀⢾⣧⡀⠀⠃⠀⣠⣾⠇⠀⠀⠀⠀⢸⡁⡿⡃⠃⡹⡗⢸⠆
⠀⠀⠀⠀⠀⣸⠋⠉⠉⠉⠙⣇⠀⠀⠀⠀⠀⠀⠙⠾⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⢉⡟⠛⠀⠛⢟⠁⠀⠀⠀⠀⠀⠀⠙⡶⠇⠀⠻⣴⠋
⠀⠀⠀⡀⠘⠋⠀⠀⠀⠀⠀⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⢼⡈⣋⣶⢄⠀⢀⢴⡎⡉⣨⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢳⣀⡀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⢱⣄⠀⠀⠀⣷⠀⠀⠀⣠⡏⠀⠀⠀⣷⠙⠉⣈⢿⠏⡈⠉⢱⡇⠀⠀⠘⡇⠀⠀⠀⢰⠄⠀⠀⠀⣿⠀⠀⠀⠘⠗⠛⠀⣿⠀⠛⠿
⠀⠀⠀⠀⢹⣇⠀⠀⠟⠀⠀⣸⡏⠀⠀⠀⠀⢸⡙⢆⡈⠺⠊⣁⡼⣹⠁⠀⠀⠀⠛⡆⠀⠀⢸⠁⠀⠀⡶⠃⠀⠀⠀⢺⠀⠀⠀⠋⠀⠀⢀⠆
⠀⠀⠀⠀⠈⠻⠷⠦⠀⠶⠾⠟⠁⠀⠀⠀⠀⠀⠙⢦⡭⠀⠨⣭⠞⠁⠀⠀⠀⠀⠀⠙⠦⡤⠀⠀⡤⠴⠃⠀⠀⠀⠀⠈⠷⣦⡄⠀⢠⣴⠟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢿⡀⠡⠂⠀⠀⠀⠲⠝⢠⡟⠀⠀⠀⠀⠀⠀⠠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⡰⠀⠀⠠⡠⡄⠠⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠻⡄⠀⠀⣿⠀⠀⠰⠏⠀⠀⠀⠰⣇⠀⠀⠀⢻⠃⠀⠀⢀⣽⠀⠀⠀⠀⠀⡧⠀⢰⣷⠀⠠⡇⠀⠀⠀⠀⠀⠀⠶⣬⢿⣤⠆
⠀⠀⠀⠀⠘⣆⡀⡀⠟⢀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠓⠀⢂⠛⠀⠀⠀⠀⣠⣻⠷⢶⣶⡶⢾⣷⡄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠉⠁⠀⠘⠓⠒⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠒⠛⠀⠀⠈⢷⠀⠀⢐⠛⠀⠀⠀⠀⠘⠟⠋⣿⣷⣿⣿⡯⢹⡿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢿⠟⢡⣶⠆⠀⠀⠀⠰⣶⡍⢻⡗⠀⠰⡿⢧⡶⢤⡀⠀⣠⠴⣎⢿⡷⠀⠀⣿⠿⠗⠄⠀⠀⡠⠺⢻⡟⠀⠐⢻⣗⠄⠀⠀⠀⠀⠀⠄⣾⠟⠂
⠀⠀⠘⡀⠸⣇⠀⠀⣶⠀⠀⣸⠃⠸⠁⠀⠀⢻⠀⢠⣍⠙⡟⢉⡥⠀⣸⠃⠀⠀⢹⠀⠀⠈⢦⡜⠀⠀⢸⡇⠀⠀⠀⢿⡀⠀⠀⣶⠀⠀⢸⡟
⠀⠀⠀⠀⢀⠻⣦⣀⣿⣀⣴⠋⡀⠁⠀⠀⠀⠈⣓⠘⠇⠀⠃⠈⠟⢐⡋⠀⠀⠀⠘⡶⠒⠀⢸⠃⠐⠲⢞⠀⠀⠀⠀⠈⣿⠂⠀⡿⠀⢸⡏
⠀⠀⠀⠀⠸⣷⣌⡉⠀⢉⣡⣾⠃⠀⠀⠀⠀⠀⠹⣦⣤⠀⠀⢠⣤⡾⠁⠀⠀⠀⠀⢧⣠⡖⠈⠀⢦⣠⡟⠀⠀⠀⠀⠀⠹⣦⣼⠹⣆⣴⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈

⠀⠀⠀⢰⣦⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡤⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣑⣴⣞⣁⠹⠃⠀⠈⠾⣬⣢⣤⣴⣧⠿⠃⠀⠘⣿⣿⣦⣀⣼⣿⡿
⠀⠀⠀⠰⣏⡖⠙⠑⣊⡇⠀⠀⠀⢸⣟⣻⠛⢿⣛⡷⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⡜⠛⣣⣿⡇
⠀⠀⠀⠐⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⠈⣿⣟⣿⣟⣿⡏⠀⠀⠀⠀⣀⠀⢿⠀⢀⠀⠀⠀⠀⣁⠤⢸⣿⡇⠠⣌⠀⠀⠰⣄⣀⣭⣿⣍⣀⣠⠆
⠀⠀⠀⠈⢿⠟⠈⠘⢿⠟⠀⠀⠀⠀⠁⠀⠘⠀⠀⠁⠀⠀⠀⠹⣦⠟⠉⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠉


⠀⠀⠀⢾⠒⢦⣤⣤⠆⢺⠆⠀⠰⢖⠋⠲⣴⠶⠊⢒⠶⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣴⣦⡈
⠀⠀⠀⠈⣷⡤⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⢦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡀⠀⠀⠀⠀⠸⣿⣛⣿⣋⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢐⣾⣻⣻⣿⠖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⣿⣟⣟⣶⡂
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⢰⣟⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣻⡆⠀⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣶⣛⣻⣍⠙⠛⢷⡄⠀⠀⠀⠀⢠⡾⠛⠋⣩⣟⣛⣶⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣉⣠⡤⠬⠷⠦⣄⡹⣆⢀⡀⣰⢏⣠⠴⠾⠥⢤⣄⣉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⣁⣀⣠⣤⣤⣤⣤⡭⢻⣿⣿⡟⢭⣤⣤⣤⣤⣤⣀⣈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣍⠻⡿⠛⢋⡝⢿⡿⢫⡙⠛⢿⠟⣩⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣏⠽⢗⡚⢀⣴⠋⠀⢨⡅⠀⠙⣦⡀⢓⡚⠯⣹⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠴⢫⠏⡽⠁⠈⠀⢨⠅⠀⠠⠈⢯⠹⡝⠦⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⠋⣼⠁⢌⠄⠀⠈⠁⠀⢠⡡⠈⣧⠙⣦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⣾⡞⠀⠀⠀⠀⠀⠀⢳⣷⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠸⢿⣄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠱⡁⠀⢻⡇⠀⢡⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠘⡄⠀⠃⠀⣻⠃⠀⢈⡟⠀⠀⠀⠀⣠⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢀⣴⡿⠗⠠⠀⠀⡀⠴⠁⠀⠀⠈⢷⡀⠢⣠⡞⢹⡇⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠂⠀⠠⣠⠟⠁⠀⢠⡖⠀⢨⠀⠈⢄⠀⠀⠀⠀⡇⠀⠻⢇⠀⠹⡆⠀⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠋⠀⠀⠀⠚⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⢨⠗⠀⢠⠎⢃⠀⠀⠀⢃⠀⠈⠢⠀⢿⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⠀⠐⠁⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣠⡟⠀⢈⡀⠀⠀⠀⠀⠀⠀⠁⠀⠡⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⠀⠀⢰⡄⠀⠀⠒⠒⠶⠤⠤⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠒⠒⠂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣺⣿⣷⣂⠐⣿⣗⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣃⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⣿⣿⣿⡅⣸⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠂⠤⡀⠀⢀⣽⣿⣿⣧⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⣻⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⢴⣿⣿⣿⡷⠦⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡛⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠒⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠀⠀⢠⣀⠠⣿⣿⠀⠀⢨⣶⣦⣀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢶⡿⠀⠀⢘⢿⣷⣿⣯⣶⣶⠀⠛⢿⣯⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠘⣾⡷⠂⠀⠛⣻⡿⣿⣿⣯⡀⠰⢶⣿⠿⣇⣴⣤⡦⠹⣿⠇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⠚
⠀⠀⠀⡀⠀⠀⣠⣾⠀⠈⠀⠘⠃⢩⣤⣤⣴⡄⠀⠉⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠃⠀⢢⠇⠀⢀⠄⠀⢀
⠀⠀⠀⣿⣧⣰⣿⠃⠀⠀⠀⣤⣾⣿⣿⣿⠟⢀⣴⣾⣯⡀⢰⣿⣧⠀⠀⠀⠠⡀⢰⠁⠈⠣⣀⡼⠒⠋⠁⡠⠏⠁
⠀⠠⣤⣼⣿⣿⣷⣶⡷⠂⠀⠛⠛⠟⠛⠉⢠⣿⣿⣿⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠘⠢⣀⡀⢸⡇⣀⠤⠯⣤⠤⠤⠄
⠀⠀⠀⠀⠉⠻⣯⡀⠀⠀⢼⣿⣦⣶⣿⠀⠀⠉⠙⠻⠿⠛⣀⣧⣀⠄⠀⠀⠀⠀⠉⠙⠉⠙⣾⡿⠁
⠀⠀⠀⠀⣠⣤⣄⡁⠀⢀⣼⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⠀⣺⣷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣆⠈⠛⣿⣿⠟⠉⠀⠀⠀⠀⢿⡿⠀⢺⣿⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⡉⠉⠉⠉⠀⠀⠙⠁⢰⣤⣄⠀⠀⣤⣬⣶⣆⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠾⠟⠣⣦⡿⢿⣠⣤⡤⠀⣾⣿⣿⡇⢸⣿⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠛⠋⠀⠀⠁

⠛⣁⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⡋⠀⠈⠑⠓⠄⠀⠀⠀⠀⠰
⠈⠋⠉⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡔⠀⡄⠀⠀⠀⠣⠄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠳⠀⠀⠐⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠐⣆⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁⠠⠤⠄⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣵⣤⢄⠐⠂
⠀⠀⠁⠀⠀⢐⣀⣠⡀⠐⠲⠶⣶⡶⠀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⠆⠀⠀⠀⢘⠀⠀⠀⢠⣤⣴
⠀⠐⠁⠀⠀⠀⠉⠁⣀⠀⠀⡄⠁⢐⡆⠀⠀⠀⠀⠀⠐⠈⠆⠶⣄⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⠑⠦⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⣴⢀⠀⢰⠁
⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠧⠠⠀⠃⠀⠀⠠⢄⡂⠐⢦⠘⠱⡀⢧⠇⢀⡠⠤
⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡓⠦⢙⣦⣁⣆⢀⡡⠀⡨
⠀⠀⠈⢀⠀⠠⡄⠁⠈⠀⠀⠀⠀⠀⡘⠖⠉⣠⡼⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠛⠙⠻⢿⣿⣿⡶⠒⠛⠁
⠀⠀⠀⠈⠷⠢⣤⠀⡀⠀⠀⠀⢀⠐⢁⣦⠟⡉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⢰⣥⠴⡺⠋⢁⠞⡿⢹⢟⢣⣀⠀⠁⠁⠀⠐
⠀⠀⠀⠀⠤⠒⠄⠁⠀⠀⠀⠀⠀⣴⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠤⠂⠁⠐⠀⣰⠈⣥⠜⢆⠉⠁
⢄⠀⡄⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⢠⡄
⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⠀⠀⠴⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠃⠀⠈⠸⠀⣴⡃⡀⠄⡠⠀⠀⠀⠀⠐⣡⠾⠀⠀⠀⠀⠐⠀⠂⡨⠿⢧⡀
⠠⠄⠀⠀⡀⠀⡐⠀⠀⠃⠀⠈⠁⠀⠊⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢸⠀⠀⠁⠈⠁⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⢀
⠅⠊⡀⠌⠀⠀⠠⠄⢀⠠⣈⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠁⣀⣒⠒⠂⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣈⠄⡤⠈⠓⠒⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠊⠉⠄⠘⠉⠉⠐⡄⠀⠀⠀⠤⢀⡐⠠⠀⠠⣄⠉⣠
⠀⠀⠒⠀⠂⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⢄⡙⣳⣄⡀⠁⠘⠛⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠱⣤⠉⠛⠶⣶⣸⠀⠋⠃⡀
⣉⣯⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⢒⡀⠙⢛⢃⣀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢣⠀⠀⢀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠸⠀⢈⠀⡔⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⢢⠀⠀⣀⡄⠻⡲⣕⣾⡰⠧⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢸⢠⠋⠀⠀⠀⠈⡩⠯⡖⠉⠁⠉⠑⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠐⠒⢤⠙⣤⣀⠴⢁⡤⠊⣀⠠⠬⢕⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠠⠷⣜⠀⡰⠻⠛⠭⡑⠄⠀⢀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠐⠳⠀⣸⠊⠀⠸⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⣆⠀⢀⡐⢤⣴⠗⠉⢉⠇⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⠢⣗⡔⠁⡄⡸⠋⢰⣌⢡⠊⠉⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⢄⣀⣱⠾⣧⡀⠃⠃⢠⣜⢼⡶⠤⡴⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣍⣿⡟⠰⠀⡇⠘⣄⡥⢎⠀⢀⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠉⡟⠲⡄⠡⣀⡿⢀⠄⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⢒⡩⠤⣀⢱⠀⣹⡗⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣀⡀⠴⣋⠻⡀⠈⠉⡩⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠆⠙⢄⠀⡁⢘⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠉⠑⠪⣢⡄⣴⣭⣛⣺⣾⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣒⣂⣉⠤⣏⠁⠀⡠⠤⠤⢬⠖⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠁⠰⠁⠱⠀⣇⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠊⠀⠀⠈⢢⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣰⣿⡿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⣷
⡀⣸⠆⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⣠⣾⡟⠁⢰⣿⡇⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⡀⢀⡁
⣇⣿⠈⣰⠄⢀⢻⣧⠀⠐⠀⠐⠃⠀⢿⡟⣀⣴⣿⣏⠀⠀⠀⠹⠀⠀⠀⠀⢠⣷⠀⠞⠁⣠⠜⠛⠟⡛
⢾⣿⠀⢻⡐⡗⢀⠹⣷⣆⠀⠀⠀⠀⠀⠙⠿⠟⠿⠛⢿⡦⠀⡀⠀⢀⣔⠀⠀⠀⢀⠀⠉⢀⡆⠀⢰⡇⡄⣼⢴
⣿⣿⡀⣸⣿⣇⢺⠀⠀⢠⢼⣄⢆⠀⢀⠀⠀⢀⣠⣀⠀⢀⠀⠃⠀⢀⣀⣐⣢⣇⣾⣶⣶⣼⠇⣿⣾⣿⣷⣿⢼
⠈⠉⠉⠙⠻⠿⣾⣶⠿⠻⠛⠛⠋⠀⠘⠃⠀⠈⠙⠛⠛⠛⠛⡃⠀⠙⠿⠿⣿⣯⠿⠿⢿⣿⡴⠿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢉⣀⣲⣶⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠠⢄⣠⣤⣤⣤⣄⣀⣀⢀⣀⣈⣁⣠⣴⣶⣦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠈⠉⠉⠉⠉⠹⠟⠋⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠂⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣄⡀⢈⣿⣶⣤⣤⣾⣿⣤⣤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃
⠀⠀⠀⣠⣼⣷⣤⣽⣿⣿⣿⣿⠏⠉⠛⢿⣿⣿⠉⠉⠤⠀⠤⣤⣶⣤⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⢘⣀⡠⠤⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠊⠀⢀⢤⡤⠆⢁⠠⢄⣰⡭⡄⣤⡤⣌⢑⡄⠀⢠⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣸⠉⠈⣖⠁⢹⢊⠇⢸⢪⡀⠀⣇⠀⢰⡏⠀⠘⠁⠘⠆⠉⡶⠂⢻⠤⢖⢃⠠
⠀⠀⠀⠀⠀⠀⠘⡤⠶⠀⢿⣧⠀⣽⠀⣜⢸⠀⡏⠁⠇⢠⠇⡇⢸⢹⠀⡴⠀⢀⡆⠀⡟⡄⢠⡄⠸⠂
⠀⠀⠀⠀⠀⠉⢨⠸⠸⠀⢸⡏⠀⣿⠀⣇⣾⠀⢧⠀⡇⢸⠀⡇⢸⢸⠀⣧⠃⠸⡟⠀⢷⠃⢸⠃⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠊⠓⠤⠣⡀⢀⡀⠈⣿⠀⠈⠲⡇⠀⠉⠀⠈⡎⠀⢹⡀⢀⡷⠤⠺⢤⠎⢉⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠉⠙⠈⠢⠤⠔⢉⠒⠊⠒⠊⠑⠒⠁⠍⠉⠂⠀⠀⠀⡐
⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠰⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠂⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡵⠀⠀⠀⠀⢀⣼⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⠞⠀⠀⠀⠀⠀⣾⡏⢸⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⢸⣿⢠⠃⣰⡟⡸⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢠⠜⣿⡇⡠⣾⡧⠀⠀⠀⢸⣿⠏⢠⣿⣳⠃⠀⠀⡤⣤⡠⠊⠀⣠⠔⠊⢉⡴⠋⡾
⠰⡿⡢⠖⣄⡀⠀⠀⢿⠟⣰⣿⢃⣴⢦⠀⢸⣿⠀⢸⣿⠁⠀⢸⠃⢩⣿⠃⠀⢰⠃⢀⡴⠋⠀⢐⡇
⠰⣉⡘⠢⣁⢾⠖⢦⠀⠀⣿⡏⢸⣯⠜⢠⠏⠘⠛⢹⣿⠀⣠⠋⠑⠚⠋⠀⢀⡤⠛⢯⣀⣀⡤⠎
⠀⠺⠄⡤⠈⠷⣄⣚⠆⠀⠻⠧⠜⠷⠔⠁⠀⠀⠀⠘⠿⠚⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠴⠂⢤
⠀⠀⠘⠦⡤⠛⠃⠉⠲⠄⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⠠⠀⢀⣀⠤⣤⡤⢲⣦⠀⠘⢄⣀⡤⣿⡆
⠀⠀⣠⡤⡀⠀⠀⠀⡠⠒⠒⠛⠒⠶⢶⣿⡷⠴⠴⠶⠚⠋⠁⠀⠀⣿⡏⠀⣿⠃⣼⡟
⢀⣾⠋⣠⣿⠀⠀⣀⡀⠀⢀⣀⠀⠀⢸⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⠁⠀⠛⠀⣿⡇⠀⣸⣷⠴⠲⣦
⢸⣯⠔⣿⡏⠀⣰⣿⠃⢀⣾⣯⠀⢀⣾⣿⠀⣰⣿⠀⢠⣿⡇⠀⡸⠁⠀⠀⠀⠀⣿⡇⠀⣿⡏⠀⢀⣿
⠀⠀⠀⣿⣇⡴⢻⣏⡠⢛⣿⡇⢀⠞⠀⠙⠋⠘⣿⣀⢼⣿⠀⣰⠃⠀⠀⠀⠀⠀⢽⡇⢠⣿⠇⠀⣾⡟
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠘⣿⣧⠏⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠈⠀⠀⠘⠂⡀⠀⠀⠀⠀⠀⠀⠙⠂⢀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⡀⢀⣠⡇⠀⢠⢀⡄⣠⠀⠀⣀⣦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⢀⣿⣼⣿⣿⣿⣾⣿⡧⣿⣿⣼⣿⣿⣷⣿⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠣⣼⠤
⠸⡿⢿⢿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠤⢽⣖⡃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣒⢻⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⣤⣀⠤⢾⣆⠠
⠀⠀⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣾⡀⢤⡥⠽⣿⠷⢒
⠠⣸⣿⣧⣶⣷⣾⣷⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡂⣨⣿⠤⠀⠙⠶⢾⡟⣋
⠀⣿⣿⣿⣿⣿⣿⣉⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⢂⠀⣑⣲⣿⣊⡁⠈⢳⣾⣟⣋
⠀⢿⣿⣿⣿⡿⠟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣼⣧⡄⠠⠽⣿⠆⠆⠤⣻⡿⣿⣋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⣄⣁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣵⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣱⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⢀⡴⠛⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠘⠋⠀⠀⠴⠚⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠄⢀⣰⣆⣼⣿⣿⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣤⠤⢴⣶⠾⠟⠛⠋⠉⠉⠁⠈⠉⠙⠛⠛⠛⣛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣏
⠀⠀⠀⣴⡾⢛⠩⠀⠲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡿
⠀⠀⠰⣿⣖⠃⣴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠃
⠀⠀⠀⠹⢿⣿⣧⣤⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡿⠛⢻⣿⣿⣿⣿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿
⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⠻⣷⡀⠈⠙⠢⠀⠀⠀⠀⠀⠀⢈⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣤⣤⣴⠇⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠹⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢥⣄⣠⣾⡴⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⡇⠀⣼⠀⠀⢠⠀⠀⠀⠀⢠⡀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣦⣤⣾⣇⣀⣦⣤⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⡶⢶⣶⠶⢶⡶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠴⠿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⡀
⠀⠀⠀⠀⠰⢦⣤⣤⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣯⡀⣺⣼⡗⠂
⠀⠀⢀⣤⡀⣤⣉⣙⡿⢾⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠒⣻⣿⣿⣿⢾⠶⠄
⠀⠀⠀⠙⠿⣮⡿⢯⣧⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢦⣀⡄⠀⠀⠀⠀⢆⡀⠛⣿⢿⣿⣿⣷⣀
⠀⠀⠀⣤⡄⢠⣄⣸⣯⣿⣿⣿⠋⠀⡠⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠙⠓⠀⢀⣈⣿⣑⣛⣿⣆⣿⣿⣿⡉⠉
⠀⠀⢀⡙⠛⠿⠟⣫⣿⣻⣿⣤⡤⠁⢠⠀⡄⠖⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣼⣿⣅⣚⣿⣿⢿⣿⣿⠷⠆
⠀⠰⣿⣿⡤⡄⢀⣻⠨⣿⣽⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠒⠚⠓⠛⠛⠿⢿⣿⣭⣿⣍⡝⣯⣿⣛⣿⣿⣿⣀⡀
⠀⠀⠠⠴⠿⢟⣢⣿⡘⠛⠛⠿⠗⠛⠶⣶⣤⣤⣶⣯⢤⣶⡶⣶⡿⠟⠉⠉⠉⠉⣸⠙⠛⠹⠉⠉⡇⣒⠂⠀⠁
⠀⠀⠀⢤⣤⢬⣍⣽⠉⠶⢤⣤⣤⣤⡀⠀⠈⠀⠀⠁⠠⣴⣤⣀⣀⡀⠄⠐⠒⠂⠙⠛⠛⠓⠓⠙⠛⠛⠛⠋
⠀⠠⢶⣶⣾⡷⠀⢼⡆⡂⠀⣿⣷⣶⣤⣤⡄⠀⠀⠀⠀⠀⡉⠉⠁⣀⣀⡀
⠀⠀⠀⠈⠉⠀⠀⢸⡇⠤⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠂⠘⠿⠿⠋⠁⠀⠀⣀⣀⣤⣤⡤⠀⢻⣩⣁⣠⣀⡀
⠀⠀⠀⢀⣀⣴⢶⡾⠇⢀⡀⢀⣀⣤⢠⣄⢀⡀⡄⢀⡀⡀⠀⠹⣿⠿⠟⠋⣉⣉⣡⠄⠁⠀⠈⠁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠉⠙⠻⠿⣿⡇⡟⠃⠻⠶⠿⠖⠀⠀⢀⣉⡉⣀⣀⣠⣤⣤⡤⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠌⠛⠒⠀⠀⠀⠀⠉⠁⠀⠒⠒⠒⠂⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠓⢄⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠉⣐⠀⠈⠘⡄⡴⠊⠗⡙⢉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠂⢄⠉⠰⠃⡰⢧⢇⡁⢸⠆⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡕⠒⠒⠪⢕⠤⡀⠀⢿⡟⡇⠀⠀⠀⠈⠫⣍⠉⡴⠊⢨⠄⠀⡵⠂⠸⠥⢲⡒⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡎⠙⠻⣶⡀⠀⠉⠪⡳⢌⢯⣿⠀⠀⣀⡤⠴⠞⡗⢳⡒⠛⠚⠳⠠⠆⣀⣤⣊⠀⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡇⡁⠀⠀⠘⣵⠀⠀⠀⠈⠳⣽⣝⣷⠋⠁⠀⡠⠊⠁⠘⡀⠁⣬⣀⠃⠠⠀⡶⢭⣀⣐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠱⡳⣄⣀⢴⡝⠀⠀⠀⠀⠀⠈⣯⠞⣆⠀⠀⣅⠄⠈⠐⢙⠀⢧⢸⡀⢒⠀⠈⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣝⣛⡟⣆⠀⠈⢆⣰⡀⠚⢢⣈⠎⢦⠮⣡⣹⠁
⡰⠋⠑⠂⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠫⡏⣀⠹⠊⢧⡀⠀⠁⠙⠢⠇
⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣤⣴⠾⣾⣷⢦⣤⠿⠛⠷⠻⠿⣦⣤⣤⣤⣤⣀
⠘⢦⣀⣀⡤⠞⠁⠀⠀⠀⢀⡴⣛⡉⢢⡀⠄⢡⢬⡸⣌⣛⡿⠀⠁⠔⡠⣒⡪⡔⠘⡆⢉⢰⠋⢨⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡏⣿⣷⠄⡇⣰⠿⢀⠅⣂⢀⢀⡈⢿⡜⣇⠳⠟⢣⣴⠣⠘⣾⡀⠻⡿⢃⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢄⠑⠬⠵⠚⣰⠯⡡⢀⡈⠄⠀⠃⠀⢸⡇⡈⠙⠋⠉⡲⠓⠓⢾⡝⠲⠒⠋⠂⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠂⡬⠀⡀⣾⡟⢢⠐⠀⡠⠚⠉⢉⢉⢺⡇⢀⢄⠰⠶⢇⠿⣿⠀⣷⡠⠖⢛⠓⣅⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠋⢅⣁⡤⢴⡀⣿⠿⠠⠀⠀⡇⢴⣫⢯⢣⢸⡇⠁⠣⡠⠄⡀⢝⠩⡀⣿⠡⢸⣟⡿⢸⢆⢻
⠀⠀⠀⠀⠀⠀⠀⢻⠇⡔⠁⣴⠲⡌⣿⠦⠴⣥⠤⡱⣤⣉⣩⢼⢸⣇⠔⠋⡉⠑⣔⣘⠀⢈⣿⠀⠘⠲⡖⠁⠜⢻⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧⠀⡳⢭⠖⣿⣤⣦⡄⢱⠈⠂⢠⣴⡅⣿⡇⠀⡎⣟⡇⣸⣀⣪⣦⣿⡢⠂⡻⠋⢋⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢙⠲⠤⠤⢿⣜⣚⣃⠜⢀⠄⢀⢠⠡⣺⠇⡁⡑⣢⢒⡏⣡⣤⣨⡏⣴⣕⠐⢈⠚⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠖⡡⢌⡘⡇⢩⠝⡋⠉⠑⢦⡌⡄⣿⢀⠂⠐⠙⠉⢣⣙⣛⣼⠏⣤⣌⠑⣬⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣴⣶⣁⣹⢏⡀⡔⡭⣷⢈⡗⡈⠃⡸⣋⡙⢦⡕⣠⠀⡸⠁⡧⣝⣝⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢤⣧⣉⣡⣞⣀⣤⡾⢧⣿⣿⣀⣏⣥⡶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⠞⢻⣭⠭⢽⡓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⡯⠭⣭⡟⠳⡄
⠀⠀⠀⠀⣿⠀⠻⠿⠁⣀⣈⠑⢄⠙⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠿⠋⡠⠊⣁⣀⠀⠿⠟⠀⣿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠻⠟⠁⠀⠑⣄⠈⠢⡑⢄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⡠⢊⠔⠁⣠⠊⠀⠈⠻⠟⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠹⡄⠀⣤⣤⠀⠀⠔⠋⠀⢱⣄⠈⢆⡑⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣠⢊⡴⠁⣠⡎⠁⠉⠢⡀⠀⣤⣤⠀⢀⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠛⠛⠀⡌⠀⣀⣠⠃⠈⠳⣜⠛⢌⠳⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠜⡡⠛⣣⠞⢁⠘⣄⣀⠀⢡⠀⠙⠛⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣤⡅⠘⠿⠟⠀⠋⠀⠈⢳⣄⠱⣝⢄⠀⠀⠱⡀⠀⠀⠀⠀⢀⠎⠀⠀⡠⣋⠎⢠⡞⠁⠀⠙⠀⠹⠿⠃⢈⣤⣦⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠙⠋⠁⢀⣤⣤⠀⠀⠀⡰⢅⣈⠳⣌⠁⢧⡀⠀⠱⠀⢀⡀⠀⠎⠀⢀⡼⠛⣩⠞⣁⡈⠆⠀⠀⠀⣠⣤⡀⠸⠙⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡘⡈⠛⠛⡀⠀⠀⡇⠀⠋⠙⠪⣑⠦⣙⢦⡀⣨⣿⣿⣅⢀⡴⣋⠴⣊⠔⠊⠙⠁⢸⠀⠀⢀⠛⠛⢃⢂⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⡀⠀⠡⣾⣿⠧⣀⣉⠉⣁⡲⣵⣬⣓⢿⣿⢻⡟⣿⡿⣞⣥⣮⣴⣊⡉⣉⣀⠸⣿⣷⡌⠀⢀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡈⠄⠀⢣⣠⠤⠷⢒⠒⡉⠩⣿⣭⣍⣛⣿⣿⣿⣿⣛⣩⣭⡿⠍⢉⠐⡒⠾⠤⣤⡜⠀⠠⢃⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠟⠋⠁⣀⣠⣤⣈⡑⠾⢦⠶⢾⣿⣻⣿⣿⣿⣿⣿⣿⡷⢶⡴⠷⠊⣁⣤⣄⣀⠈⠙⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠊⠍⣙⡽⢃⠠⢀⣶⢶⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡶⢦⡀⠄⡘⢯⣋⠩⠙⢦⡀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣺⢟⣪⠴⠛⠉⢀⣠⣶⣫⣽⠿⣻⡿⠃⣸⣿⣿⣇⠈⢿⣯⠻⣼⣝⡶⣄⡀⠉⠛⠦⣕⡻⣗⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⢉⠁⠀⠀⡀⠘⠋⢉⠔⠁⡼⢻⠁⣠⢿⣿⣿⡿⣆⠈⡛⢷⠈⠢⡉⠙⠓⢄⠀⠁⠈⡉⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠔⠁⠀⢀⢸⣿⠀⣐⠁⢠⠟⠄⡄⢠⠇⢸⣽⣯⡇⠸⡄⢡⠠⠻⡄⠈⣂⠀⣿⡇⠀⠀⠈⠢⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠁⢸⡏⣸⡿⠀⣟⡜⡐⢀⡎⠀⢸⢾⡷⡇⠀⠱⡀⢂⢳⣳⠀⢿⣧⢹⡇⠈⠄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠂⠀⠈⢰⡿⠁⠀⠟⡰⠁⡸⠀⠀⠘⣿⣿⠇⠀⠀⢧⠈⢆⠻⠀⠈⢿⡆⠁⠀⠘⣀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⠆⠀⠀⠀⡰⢁⣶⠇⠀⠀⠀⠛⠛⠀⠀⠀⠘⣶⡈⢆⠀⠀⠀⠐⠀⢀⡴⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⠴⡀⠀⣀⣠⡷⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢾⣄⣀⠀⢀⡦⠞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠙⠊⠉⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠉⠑⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⢀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⡄⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⣻⡇⢸⠠⡇⠀⢀⣧⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⡇⢠⠀⢠⣄⣿⣽⣿⠀⠀⠀⠀⠀⠀⢰⡆⢸⡇⢠⠀⠀⠀⢤⣿⣼⣷⣾⣿⣷⣶⢫⣿⣰⣿⣾⣽⡏⢷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⣿⠨⡀⢼⣷⣿⣿⣿⡇⠀⠀⠈⣵⣶⣾⣧⣾⣷⣾⠆⠐⠒⠞⢿⡿⠋⠉⢻⣿⣿⢨⡍⣷⡿⣷⡾⢣⡎⢻⣇
⠀⠀⠀⠀⠀⠀⠀⡀⢧⣴⣿⣿⣿⣿⣦⡆⠸⣿⣿⣿⠻⠁⠀⠀⠀⢹⠛⣿⣿⣿⣿⠷⠀⣀⣀⡀⣰⠃⠀⠀⠀⢹⡶⢞⣿⣧⣬⣿⠇⣵⣦⠘⣻⠄
⠀⠀⠀⠀⡄⣠⣤⣿⣿⣿⣿⣿⣿⠯⣾⠁⠀⢹⣿⡏⠈⢢⠇⡀⣀⡞⠀⠸⣿⣿⠃⠀⠀⢩⡉⠙⢿⢀⠠⠤⡄⠉⢹⣾⠋⣷⣈⣷⣾⣛⡿⡃⠛
⠀⠀⠀⢰⣿⣿⣿⣽⣿⣿⣿⢟⣿⣰⡟⠀⠀⠀⣿⠂⠁⢸⡟⢿⣟⠀⠀⠁⢿⣿⣦⣀⣀⣄⢀⡖⠉⠀⠀⠀⠈⠀⠻⣿⣄⡿⣿⡯⠘⣿⡄⣍⠃
⠀⠀⢠⣿⣿⣿⠿⠟⠛⠉⠉⠁⠈⠉⠀⠀⠀⠠⠏⠐⠤⠄⢿⢾⠁⠐⠂⢈⡀⠙⠉⠉⠙⠟⠿⠄⠀⠀⠶⢾⡷⠶⣾⣉⣿⢿⣞⠡⠘⢻⡉⠙⡄
⠀⠀⠛⠋⠁⠠⡶⢀⠀⠀⠔⢺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠄⠐⠞⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠓⠚⠓⠂⠚⠻⠷⢴⠄⠐⢓⣒⠾⣒⣶⡀⠵⢤⡀⠀⠀⠤⣀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠠⢤⡀⠐⠢⢤⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠃⠒⠒⠛⠛⠷⠖⠒⠾⠧⠀⢀⣠⣀⣀⢉⡛⣋⣉⣳⡔⠈⢙⣆⣀⣈⣷⠤
⠀⠠⠀⠰⠆⠀⣀⣤⣤⠤⠀⠀⢠⣀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠈⠉⠛⠻⢻⢾⣿⣷⣼⣿⣠⣀⠸⣿⡄⣠⢠⣞⣆⣦⢀⢹⣇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣦⣼⣿⣿⣯⣿⣾⣿⣼⣽⣹⣆⣿⡆⠀⠀⢀⡀⠀⠀⠀⣿⣾⡄⢡⢸⣆⠀⠀⠀⢘⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠛⢿⣿⣥⣤⣼⣿⣿⢿⡇⠀⢰⠸⣿⢷⣴⡄⣿⣿⣇⠈⡏⣿⠀⠀⠀⡇⣟⡄⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠿⠇⠉⢭⣍⠙⢭⡀⠔⠀⣋⣿⣿⣿⣿⣿⣿⡤⠷⠛⠀⣀⠀⣿⣻⣿⣄⣽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠒⠂⠀⠀⠀⠀⢳⣶⠶⡒⢬⡿⠿⠶⠶⣶⣿⠁⠀⠛⢛⣿⣤⣤⠤⠿⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠀⠀⠁⠀⠀⠈⠐⠛⠛⠛⠛⠛⠛⠞⠙⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣈⠧⢵⣶⣤⣠⢄⡀⠀⣀⡀⢀⣤⣴⣾⣶⣄⠀⠀⠤⠤⠶⠤⢤⡤⠤⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠈⣈⣛⠋⠉⢱⣼⣿⣿⣿⣟⣻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢄⡹⠿⣿⠿⢿⠿⠟⡛⡉⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠲⠦⠶⣤⡝⠃⠲⢀⣛⣸⣣⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠁⠀⠀⠀⠉⠹⡇⡚⠤⠤⣿⠿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠰⣄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡷⠘⠇⠀⠀⠀⢀⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣿⣍⡁⠀⡠⠖⠉⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠙⣧⡈⢻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢻⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⣷⠆⠇⠴⣿⡟⠀⠀⠀⠀⠀⠈⠷⠞⣃⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⣑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃
⠀⠀⢠⣤⡄⠀⠀⠀⡀⠀⠀⠠⣤⡄⠀⠀⠀⠸⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠻⡤⣠⡼⣧⣤⡠⡞⠋⠀⠀⠀⠀⠀⠻⡿⠿⢷⡶⠿⠿⠿⠀⠀⠀⠀⠀⠀⢹⣿⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⢠⠀⡀⢈⡃
⠀⠀⠀⠀⠀⠷⡶⠆⠑⢶⡾⠇⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡟⠄⠀⠆⠀⠀⠀⠀⠀⠀⣨⠿⠃⠃⠛⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠻⣿⢷⣦⣀⠀⠀⢀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡦⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢠⡄⠀⣰⠏⠀⠀⠀⠀⠀⠙⢷⡝⠿⢶⡶⠿⢫⡾⠋⠀⠀⠘⢿⠊⠻⣷⡄⠀⢰⡿⠋⢘⡟⠁⠀⠀⠀⠄⠂⠐
⠀⠀⠀⠀⠰⣇⠀⠙⡟⠁⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣅⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⡡⣤⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠘⣟⡿⠁⠀⠸⣗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠾⠅⠐
⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠈⠹⣿⣿⣷⡄⢀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣶⣴⣶⣶⠆⠀⠀⠀⠀⣀⠂⡀⠁⠄
⠀⠀⠀⠀⠙⡟⢻⣿⣿⣟⢻⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠘⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠏⠈⢠⡄⠀⠀⠀⠀⠀⠹⠷⣆⣶⣗⢇
⠀⠀⠀⠀⠀⠹⠤⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠖⠃⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡄⢲⡾⣧⡠⢀⣀⠐⣀
⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠢⢤⣁⡀⢂⣴⣂⣄⣇⢦⣯⣷⣿⡗⣣⡍⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢤⡄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⢿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣿⣾⣶⡿⣶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠡⠀⠀⠀⠀⠀⠀⠂⠀⡒⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢠⡒⠶⣮⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠡
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⣄⡀⠀⠀⠈⠀⠀⡾⠻⠝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⢰⡟⠉⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢾⡯⣿⣿⣿⣿⣿⢿⠿⣿⠋⣽⣾⣿⣿⢿⣿⣿⣿⣿⠻⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠷⢿⠿⣟⡿⠿⣿⣿⣿⣿⣿⣍⡬⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠄⠱⠏⠉⠀⠂⠀⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⡤⢤⣴⣶⣷⣿⣿⣶⣶⣿⣶⣖⣶⣶⣶⣾⣶⣶⣶⣤⣦⣤⣦⣄⣀⡀⠀⠀⠀⡀⣿⣿⡇
⠀⠀⠀⠀⢤⣠⣦⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣟⣋⣇
⢀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀
⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⢄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠂⠈⠀⠑⢦⣀
⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣩⣟⢠⠄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠺⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠉⣩⢏⣍⣀⡀⠘⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠍⡀⠉⠃⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⢫⡥⢲⣾⣧⣾⣏⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠁⢀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠹⠟⠛⣿⣧⠿⠿⠉⠃⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠊⠀⠈⠁⠁⡗⠀⠀⠀⠀⠀⠰⡄⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠛⠂⠰⠂⠐⠂⠒⠒⠚⠿⠿⠶⠖⠒⠠⠆⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠦⢤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠚⠂⠉⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠘⠓⠦⢤⣤⣄⣤⣤⣀⣀⣀⣀⣀⡤⠀⠀⠀⠈⠛⠧⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠁⠈⠁⠀⠀⠀⠀⠘⠢⣄⠉⠁⡄
⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⠿⠿⢷⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠶⠀⠀⠀⠈⠉⠓⠺⠶⣦⣴⣶⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠙⠋⠉⠃⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣄⣠⣄⣀⣀⣀⠀⠈⠁⠉⠉⠉⠋⠉⠙⠛⠛⠉⠂
⠀⠀⠀⠀⠀⢤⠄⣤⠆⠀⠀⠈⠂⠐⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠙⠟⠋⠀⡀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢿⣏⣠⡤⠶⢿⣿⣟⣒⠒⠶⣶⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠄⠈⠙⠺⠧⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼⣿⣥⣤⡀⠈⠻⣿⣿⣷⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢐⠀⠀⠀⢹⡀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠘⢿⣆⢀⡎⠀⠈⠻⣿⣿⡄⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠵⢀⠀⠀⠀⠀⠂
⠀⠀⠀⢶⣤⣄⠀⠙⡿⠀⠀⣀⣤⣤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠥⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢻⣿⣇⠀⢡⢠⡼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⢛⡁⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠉⠉⠙⠻⡏⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⠀⠀⠘⠡⠂
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡘⢄⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡀⢢⠸⡅⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣻⠀⠀⠀⠀⠀⠀⠐⠪⠅⠳⡗⡨⠊⡁⠀⠀⠀⠀⠀⠹⣦⡄⠸⡇⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣦⠀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢅⠀⠶⡗⢐⠄⠄⠀⠀⠀⠀⠀⠀⠘⢿⡄⣇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡆⢀⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠑⢤⡷⠥⡐⢥⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡇⡼⠋⢀⣀⣀⣀⡀⠀⠀⠀⠀⢈⢢⡀⢐⣠⡧⠊⠀⢐⡀⠀⠀⠀⠀⠘⣿⡆⠀⢹⡇⠀⣠⣴
⠀⠀⠀⠀⠀⠀⡾⢆⠀⠀⠹⣾⣞⡥⠚⠉⠀⣠⠜⠁⠀⠀⠀⠀⠈⠂⠀⠠⣄⣧⣐⠈⠄⠊⠀⠀⠀⠀⠀⠈⠻⣄⢸⡇⢠⡿⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠳⡄⢠⠟⠛⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣬⣧⠐⠀⠈⠩⠀⠀⠀⠀⠀⡀⠀⠘⢾⣇⡞⠁
⠀⠀⠀⠀⠀⠀⢧⡀⠀⣷⠏⣀⡠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠐⠠⣀⡇⠄⠀⠀⠰⠀⠀⠀⠀⠀⣿⣦⠀⢸⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⣚⣁⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠊⠉⠠⣁⠈⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⣦⢸⠃⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠙⡟⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣾⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⡟⠃⠠⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⢀⡀⠀⠀⠒⠒⠒⡒⠒⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠤⠐⢀⠒⠒⠒⠀⠀⢄⡀
⠀⠀⢿⣾⢲⢤⡀⠠⢏⠁⠘⣻⠁⡶⢦⠀⠀⢀⠀⣤⡤⠀⡀⠀⠀⡴⢶⠈⢟⡃⠈⡹⠄⢀⡤⣖⣷⡿
⠀⠀⠀⠉⠻⣦⡙⢦⡀⠙⠚⠓⢲⠓⣿⠂⠀⠾⣷⣿⣸⣾⠧⠀⠀⡷⠛⡖⠚⠓⠋⢀⡴⢋⣴⠟⠉
⠀⠀⠀⠀⠀⠉⠻⢶⣕⠲⣄⠀⠀⠙⠋⠀⠀⠉⢻⡯⢽⡟⠉⠀⠀⠙⠋⠀⠀⣠⠖⣨⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⡵⠔⠁⠀⠀⠀⠀⡏⡿⢿⢹⠀⠀⠀⠀⠈⠢⢮⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣙⣆⠀⠀⠀⠀⠀⢀⠁⢷⡿⠈⡀⠀⠀⠀⠀⠀⣰⣋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡚⢻⢶⡄⡆⢰⣖⠆⠀⠘⠃⢀⠰⣲⡆⢰⣠⡶⡟⢚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡙⢧⠼⣄⠊⠁⠀⠀⠈⠐⣀⠯⢸⣉⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⢄
⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢹⠀⡀⣀⠀⠀⠀⠀⠆⣊⠑⣢⢉⢛⠐⢺
⠀⠀⠀⠀⠀⠀⠈⢳⣿⡒⠂⠀⠁⠀⠀⠀⠀⠀⣄⣀⡈⠢⢄⣿⣷⠲⠋⠀⠀⠀⠈⠸⠬⣱⣇⠸⢸⣂⠉
⠀⠀⠀⠀⠀⠀⠠⠊⠃⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣡⡦⠤⣀⣄⡄⠀⠀⠘⠒⠋⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠖⠀⣄⣬⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠘⡳⠤⣤⡀⠪⠑⠂⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠢⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⣨⠆⠁⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠈⠑⣃⠴⢁⠂⠐⣢
⠀⠀⠀⠀⣐⠀⠀⠑⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡛⣫⣕⣶⡆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣞⣀⣣⡊⠑
⠀⠀⠀⢐⣀⡀⠠⠑⠖⢨⠁⠀⠀⠀⠀⠀⢀⣀⢉⡚⢬⣭⡼⢿⣜⣇⠀⠀⠀⠀⡠⡀⠓⣤⢵⣿⡿⢇
⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⢴⣿⠟⡁⡏⢩⡟⠈⠀⠀⠀⠀⠀⠜⠐⢋⣱⠗⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠩⠀⠖⡀⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⡶⢀⠀⠀⢀⠐⡆⠀⠀⠛⣴⠂⠀⠀⠀⠀⠀⣲⠘⠀⢻⠉⠀⢄⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠘⡢⠄⢸⡇⠠⠔⠃⠀⠀⠸⡧⡇⡖⡔⡆⡣⢽⠀⠀⠀⠘⠀⠀⠠⡆⠀⠀⠛⠀⠀⠈⣇⠀⠀⢲⡇⠀⢀⡟
⠀⠀⠀⠐⣇⠀⠘⠃⠀⣸⠂⠀⠀⠀⢾⣇⠙⡿⢁⣾⡆⠀⠀⠀⠠⣦⡀⠀⠃⠀⣰⡆⠀⠀⠀⢨⠋⣾⠹⠹⡮⢹
⠀⠀⠀⠀⣸⠛⠉⠉⠛⣇⠀⠀⠀⠀⠈⠻⠄⠁⠸⠋⠀⠀⠀⠀⠀⠈⡿⠓⠘⠻⡋⠀⠀⠀⠀⠀⠳⡼⠁⠸⢶⠋
⠀⠀⣀⡀⠁⠀⠀⠀⠀⠈⢀⣀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣆⠀⠀⠀⠀⠀⠀⡶
⠀⠀⢻⡀⠀⠀⢀⡀⠀⠀⢀⠏⠀⠸⡄⡼⠷⣄⡤⠻⠤⣴⠃⠀⢿⠀⠀⠀⣀⠀⠀⠀⣼⠀⠀⠸⣶⡄⢠⠀⣴⣾⠁
⠀⠀⠀⢳⡄⠀⢸⠃⠀⢰⡟⠀⠀⠀⢳⢤⠐⢼⠵⢀⡄⡏⠀⠀⠸⣄⠀⠀⢿⠀⠀⣠⠇⠀⠀⢠⠁⠀⠸⠀⠀⢁
⠀⠀⠀⠈⠿⣦⡄⢠⡴⠟⠀⠀⠀⠀⠈⠻⣙⠀⢐⣫⠎⠀⠀⠀⠀⠘⢤⡀⠀⢀⡤⠃⠀⠀⠀⠈⢧⣤⠀⢠⣤⠞
⠀⠀⢠⠀⡀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⢦⠑⠁⢠⡀⠘⢊⡼⠁⠀⢀⡀⠀⠀⣾⡗⠀⠀⢀⡀⠀⠀⠀⡖⠐⢀⡀⠂⡆⠀⠀⠀⠀⠀⡀⣾⡇⡀
⠀⠀⠀⠨⡇⠀⢸⠇⠀⢨⠀⠀⠀⠘⠂⠀⠀⠸⠁⠀⠀⠚⠁⠀⠀⠀⡍⠀⠸⠃⠀⡡⠀⠀⠀⠀⣤⣙⣊⣛⣡⡄
⠀⠀⠀⠀⠙⠒⠀⠐⠖⠋⠀⠶⠤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠤⠆⠀⠘⣆⠀⠀⡴⠁⠀⠀⠀⣼⠓⣮⣵⣯⡔⢻⡆
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠘⡿⢡⡶⠀⠀⠀⠐⣷⠈⣿⠀⠸⡟⠳⢢⣄⣀⣤⠲⠛⡗⠀⢸⡟⠓⢀⠀⠠⠚⢻⡇⠀⠛⣿⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠈⣧⠀⢸⡇⢀⡾⠀⠀⠀⠀⢻⡀⣾⠈⡇⢸⡆⡸⠃⠀⠀⣇⠀⠀⣶⠀⠀⣸⠃⠀⠀⠹⣇⠀⢸⠇⢀⡼⠃
⠀⠀⠀⠰⣌⠓⠚⠓⢛⣠⠀⠀⠀⠀⠀⣦⣀⠀⠀⢀⣠⡆⠀⠀⠀⢸⠁⡀⠙⢀⡀⣽⠀⠀⠀⠀⢿⡀⡼⣄⣨⡇
⠀⠀⠀⠀⠉⠛⠀⠈⠛⠉⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠙⠀⠀⠀⠀⠈⠛⠁⠀⠀⠛⠁⠀⠀⠀⠀⠈⠉⠁⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿