Clip Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣍⠛⣛⣭⣶⣾⣿⣿⣷⣶⣭⣛⠛⣩⣾⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢸⣿⣿⡿⣋⣴⢰⣮⡻⢿⣿⣿⣿⣿⡿⢟⣵⡆⣦⣙⢿⣿⣿⡇⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠸⢟⣡⣾⣿⣿⢸⣿⣿⣦⣙⢿⡿⣋⣴⣿⣿⡇⣿⣿⣷⣌⡻⠇⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⡄⢴⣶⣶⣶⣦⠰⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⠆⣴⣶⣶⣶⡆⢠⣶⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠙⣿⣿⣿⣇⢿⣿⣿⣿⠇⠸⣿⣿⣿⡿⣸⣿⣿⣿⠋⢠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡜⣎⢻⣿⣿⡘⣿⣿⣿⢸⡇⣿⣿⣿⢣⣿⣿⡟⣱⢣⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡜⣷⡙⣿⣧⢹⣿⡟⣸⣇⢸⣿⡏⣾⣿⢋⣾⢣⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⣿⣎⢻⡆⢿⡇⣿⣿⢸⡿⢰⡟⣱⣿⠃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡙⠸⢡⣿⣿⡌⠃⢋⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢸⣿⣿⡇⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⣿⣿⢱⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠸⠇⠞⠁





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠸⡈⠢⢄⣀⣀⣀⣠⠤⠒⠋⠉⠉⠀⠀⠀⠈⠉⠙⠒⠦⢄⣀⣀⣀⣀⠴⠊⡸
⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠁⠀⠀⠈⠀⢀⣀⣀⣀⣀⠀⠀⠀⢐⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⣠⠖⠉⠀⠀⠀⠈⠑⢄⠀⠄⡠⠊⠁⠀⠀⠀⠈⠑⢦⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⠁⠀⠀⣠⠤⠤⣤⡀⠀⢣⡼⠁⠀⢀⣠⠤⠤⣄⠀⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃⠀⠀⡾⢡⣶⣶⣦⠹⡄⠈⡇⠀⢠⡏⣰⣶⣶⣌⢳⠀⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⡄⠀⠀⢧⠸⣿⣿⡾⢠⢇⠤⠥⡀⠸⣆⠻⣿⣷⠟⣸⠀⠀⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⡀⠀⠈⠓⠦⠤⠖⠋⣯⣄⣠⢼⠀⠈⠲⠤⠴⠞⠁⠀⡰⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠞⢦⣰⠟⢤⣀⠀⠀⠀⢀⡠⠞⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠋⠀⠀⠈⠉⠉⠉⠁⠀⢀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⢀⡜⠁⠀⢀⣠⠄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣀⡀⠀⠙⣆
⠀⠀⢀⡼⢿⣁⠀⠼⣥⠄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢤⡽⠆⢀⡹⠿⡄
⠀⠀⠾⣴⠞⡉⠀⠀⠓⡶⠀⡼⡸⠀⠀⠀⠸⡀⢀⠀⠀⠀⠀⠠⣀⣀⠞⠀⠀⠘⡜⢄⠙⡖⠃⠀⠨⡛⣶⠿
⠀⠀⣰⠃⣸⣶⠞⠁⢀⢓⡟⢠⠃⠀⠀⠀⠀⠈⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡈⢻⢋⡀⠙⢶⣞⠈⣇
⠀⠀⠿⠚⢱⠇⡅⣠⢾⡞⣰⠇⢀⠀⠀⠣⠤⠂⠀⠘⠦⠔⠁⠀⠀⠢⣄⠜⠀⠀⡰⢹⣄⣻⢧⣄⡇⢯⠙⠛
⠀⠀⠀⠀⢸⣤⠟⣽⠈⢋⣿⢠⢸⢆⠀⠀⠀⠀⣄⣠⠀⠀⠰⣀⣠⠀⠀⠀⣠⡌⢇⢸⣿⣍⠈⣏⠳⡾
⠀⠀⠀⠀⠀⠀⠀⢹⡴⠋⠸⣌⡽⠉⠑⠦⣄⡀⠀⠀⣄⣀⠄⠀⠁⣀⡤⠚⠁⠈⢯⣁⡟⠘⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣇⡪⠛⠒⠒⠒⠒⠒⠻⣕⢼⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⢉⡀⣉⠑⡄⠀⠀⠀⠰⢋⡉⣈⣁⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠟⠉⠊⠀⠀⠀⠀⠘⠚⠈⠞⠉⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⢺⣿⡆⠀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠉⠉⠀⠌⣛⠁⢰⣿⡿⠋⠀⠀⣀⡀⢀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⢶⣦⡀⠀⠱⣄⠁⠀⠀⠀⠰⠟⠁⣾⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠰⣷⡀⠀⠀⠀⠙⠡⣀⠀⢹⡆⣀⣤⠶⢏⡉⠉⠀⣴⣤⡀⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⢧⣸⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⠀⠀⣼⣷⠀⠀⠀⣸⡿⠁⢰⠿⠃⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢿⡿⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⠰⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡷⠀⠤⠒⢚⡛⠛⠛⠷⣦⣤⡀⠀⢸⣿⠀⠀⠀⠀⣠⣧⡤⠤⠤⢀⡀⢠⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢾⠇⠀⠀⣠⠞⠛⢻⣦⣸⣿⡄⢀⣴⠟⠉⠀⠀⠀⢿⣶⣄⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢠⣤⣴⠤⠤⢴⠁⠀⠀⠀⠙⣿⣿⣷⣿⠷⠚⠛⢟⠒⠢⠈⠙⠛⠀⠐⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢴⣦⡀⠀⠀⢹⣿⣿⡏⠀⣀⡀⠀⠀⠀⢠⣦⠻⠷⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⠁⠀⠀⢸⣿⣿⡇⠈⠉⢩⣦⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣹⡛⣻⢟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠒⣒⣀⠀⠀⠀⠀⣐⡒⠂⠤⣀⠀⠀⠀⠀⠀⢠⠠⠠⠀⠀⠒⢳⡈⠒⣴⡄⠀⠀⠐⠒⠂⠠⠄⡀
⠀⠀⠀⠀⡀⠄⢒⡈⠅⠐⠂⢈⣁⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⣁⠤⠳⠂⠀⠀⠠⠀⠐⠒⠀⠉⠁⠀⠙⠶⠀⠀⠀⠀⠀⠀⠉⠐⠂⢄⠑
⠀⡠⢒⡡⠒⠈⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⠄⠂⣁⠤⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⡰
⡌⡔⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⠅⢊⡠⠒⠉⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⠄⠊⡠⣊
⢣⢁⠢⠠⠄⢀⣀⣀⣀⣀⠀⠤⠀⠠⠀⢒⣨⠃⡐⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⡀⠤⠒⢈⠠⠐⠉⠀⢹
⠈⡄⢠⡌⠐⠒⣂⠒⠒⠒⢲⡀⠉⠁⠀⠀⠘⣄⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⢀⣀⠠⠄⠀⠒⣉⡠⠄⢒⣈⠀⠀⠀⠀⠀⠌
⠀⠘⣞⡣⢀⢀⠯⠀⠀⠀⠸⠄⠀⠀⠀⠀⣈⠝⠁⠀⠀⠀⠀⢀⣘⡒⠒⠒⢂⣀⣈⠉⡁⠀⠤⠀⠒⠒⠈⣥⠀⠀⠀⠈⡯⠀⡀⠀⠐⠀⠂
⠀⠀⠈⢄⠡⡐⠀⠢⠀⠀⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⡄⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⢀⠋⠀⡀⠀⠰⠁⠠⡁⠀⠀⢨⡘
⠀⠀⠀⠀⠑⠵⣇⠀⠑⢄⠸⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠨⠃⠀⠀⠀⠀⠈⢆⠀⢠⠀⠀⠄⠀⡐⠀⠠⡀⠀⠀⡇⠀⠑⢄⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣑⣇⡀⠀⠀⡀⠀⠀⠀⠀⠤⠀⢊⠀⠁⠈⢆⠈⠀⠈⠆⠈⢂⠀⠀⠀⠀⠀⠃⠀⠀⠐⢄⠀⠀⠀⠀⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠠⢙⠳⣆⡀⠀⠠⢀⠀⠀⠀⠑⢄⠣⢐⠀⠈⢢⠀⠀⢀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠳⣦⣈⠢⡙⢦⡠⠀⠀⠀⠀⠀⠀⠁⠺⢆⠀⠀⠑⢄⠈⡀⠀⠀⠈⠂⢄⠀⡅⠀⠀⠀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠛⠷⣌⠢⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⠑⢧⣀⣀⣀⣀⠀⠅⠶⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢧⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇⠀⢀⡤⠒⢫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡇⢰⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣⠀⠀⠀⢀⣀⠙⣟⠢⣑⣴⢁⠾⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⡆⡴⠋⠉⢸⠀⠀⠉⢉⣿⣡⠔⠊⠉⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠐⢾⠀⡁⠀⢀⡜⠀⢀⠔⠁⠈⠑⠦⣀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠉⠉⠉⠑⡄⢳⡧⠔⠋⢠⣖⣁⣠⡴⠒⠉⠉⠢⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠀⠤⠛⢮⡇⢀⠔⢛⠛⠒⢦⡙⠢⠤⠤⠤⠬⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠞⢣⠀⠀⡷⠃⠀⠸⡄⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⢦⠀⠀⠀⠈⢆⢈⢀⣾⠔⠒⠒⡶⠈⠒⠶⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⡇⢀⡴⢣⠀⢻⡿⢇⣀⡠⠞⢁⡤⠤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠤⣉⠲⡇⡏⠀⢸⠀⡎⠀⢀⠷⣄⠰⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣀⣈⡷⠼⣷⡀⢸⢰⠁⢠⢦⠳⣿⡷⠤⣴⣊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠳⣿⡷⠃⢸⠀⡇⠈⢣⢸⣠⡞⠁⠀⠀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠛⠿⣿⣤⣸⠀⢇⠀⢸⣼⠁⠉⣒⣒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣠⠎⠀⠘⡄⠈⢦⣾⢇⡔⠉⠀⠈⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⠄⠂⠤⣀⢳⠀⣸⣿⣋⠀⠀⢀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⡀⣀⣀⠜⡋⠻⡁⠀⠈⠉⢩⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡜⠹⡄⠙⢄⠀⢠⠃⠈⡆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⡀⢇⠀⢱⠀⡠⢵⣌⡣⣀⣷⠋⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣎⠁⠀⠀⠈⣳⣕⣿⣸⡷⠮⠥⠽⠾⢏⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣀⠴⣏⠀⠀⠀⡠⠶⠒⠤⢬⠟⠓⠲⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢈⡍⠀⡼⠉⠱⡄⢸⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠋⠀⠀⠣⡀⠀⡇⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢶⠇

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

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⢄⠖⢟⡹⠦⠄⠀⠀⠔⠉⢐⡂⠀⠀⠀⠀⢀⠄⠲⡿⠁⢤⠠⠀⡀⢀⠠⠌⠀⠀⠀⠠⠁⠀⠀⠀⠐⠀⠘⢹⠀⠀⠃⠹⠀⠀⠐⠁
⠀⢉⠓⠉⠡⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⠀⠀⠀⡨⠇⠀⠒⠈⠈⠁⢀⠀⠀⠀⠍⠀⡀⠀⠂⠀⡀⠘⠀⠀⡀⢨⠀⠁⠀⠈⠂
⠀⠨⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡠⠀⢀⠑⠀⠄⠀⠄⠀⢀⠀⡀⠀⢰⠠⡖⠈⠀⠐⠈⠁⠖⠘⠁⠀⠈⠀⠀⠠⠂⠑⠈⠈⠀⠀⠄
⠀⠀⠠⠀⠀⠀⠀⡀⠄⠀⠀⠀⣰⠏⠁⠀⠈⠒⠐⣂⠀⠀⠉⠈⠌⠃⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⡠⡔⢢⡀⠀⢀
⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⡐⠳⠃⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⢄⠄⠰⠀⠂⠀⠀⠈⠀⠀⠰⠭⠌⠀⠈⠀⣤⢌⣬
⠀⠀⠠⣄⣄⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠁⠀⠀⢤⠰⣋⣥⡠⡀⠀⠀⢀⡄⠈⠐⠀⠀⠀⠀⢀⡀⠈⠢⣱
⠀⠀⢰⡿⣮⣵⡕⠀⠀⠀⠠⣏⡤⠤⡀⠀⠀⠀⡀⠀⠀⠀⠘⠽⠓⡠⠀⠀⡘⠀⠀⠑⠀⡀⠀⠂⠋⠀⠀⠀⠀⢠⠄⠀⠀⠀⡉⠒
⠀⠀⠘⢵⣭⣻⢤⡁⠀⡠⠺⣧⡽⠢⠀⠀⡠⠊⡀⠄⠀⠀⠘⠖⠋⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠂⠐⠀⠀⠀⠀⠔⡁⢀⠠⢀⠀⡀
⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠈⠁⠉⠁⠀⠪⢄⡘⠄⣄⠀⠀⠀⠀⡤⠴⠀⠀⡀⢀⠀⠀⠀⠀⢆⠀⠀⡒⡊⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⠀⠀⠀⠉⠀⠈⢀⠂⠀⠧⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠚⠤⠤⠀⠤⠖⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠠⠀⠀⠀⠈⠰⢿⠱⠀⠀⣠⡖⠒⠦⠤⢀⠀⠀⢀⡀⠀⠀⠀⠀⢴⢻⠞⠁⠀⠀⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠐⠂⠀⠀⠀⢁⣠⠋⠀⠈⠃⠀⠄⠀⠀⠠⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢂⠄⢠
⠀⠀⠀⠀⠀⢂⡀⠐⡀⠁⠀⢠⠘⡂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠂⠂⠁⠀⠈⢁⠀⠔⡄
⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠇⣂⠀⠀⢰⠀⠀⠁⠈⠀⠀⠀⠂⠀⠀⠀⢸⡏⠀⠂⠀⠀⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠶⡵⢄⠀⠀⠑⣧⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⡜⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠟⡱⠦⠙⠀⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠆⠀⠀⠀⠀⠀⡉⠀⠐⢸⠅
⠀⠀⢀⡄⠐⠊⠉⡙⠧⡁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠶⠶⠶⢬⣠⣤⣤⣄⣁⡞⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠐⠀⠠⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠐⠛⠦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠠⣀⠄⣑⠄⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣄⣠⣊⣄⠐⠃
⠀⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠘⣄⡄⠀⠀⠀⠀⠀⠀⠠⠆⡐⠳⣸⠆⠉⠾⣀⠁⠒⠀⠀⠀⠀⠀⠀⠀⣴⠖⠉⡀⠁⠈⠀⠉⠲⡕⠂
⠀⠀⠀⠀⣠⠴⠒⠃⠀⠠⠀⠀⠀⠀⠲⡶⠦⢄⠀⠀⠀⠀⠀⠀⢀⣉⡤⠻⢀⢀⣈⠙⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠰⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠈⠠⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⣹⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⢟⠉⠀⠀⠀⠀⡰⠁⣀⣀⡀⠀⠀⢀⣀⢀⠀⢳⠀⠰⠶⠻⠿⢻⡧⠤⠤⡦⠤⠤⠤⠤⡴⠤⠴⢟
⠀⠀⠀⠀⢀⡇⠀⠀⣠⣄⠀⠀⠀⣤⡄⠀⠸⡀⠀⠀⠀⢠⠻⣾⡿⢟⣡⣆⣠⣿⠟⣩⣶⠧⣇⠀⠀⠀⠀⡜⠀⢠⡼⠗⢄⠀⢤⣴⠟⣤⠤⢸⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⡐⠀⠈⠲⣿⠟⠁⠀⠱⣾⡿⠁⠀⢁⠀⠀⠀⢠⠀⠀⠀⠔⠺⡇⠀⢀⠴⠺⢏⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠁⠈⠈⠳⣄⣀⠄⠢⢄⠀⣠⣒⠦⠤⠁⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠰⠶⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⢀⠐⠋⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⠔⠋⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⠐⠏⣠⠄
⠀⠀⠀⠀⠀⢀⣀⠀⢣⠐⡆⢰⢃⡄⠤⢤⠀⠀⠀⠀⠀⠀⢀⣀⠈⣆⠱⠆⠸⠊⡄⠀⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣆⠱⠆⠸⢂⡄⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠠⠐⢀⣱⡄⣤⣀⠔⠢⡀⠀⠀⠀⠀⠀⠀⠈⢁⠴⢌⢰⡀⣦⠊⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠶⢌⢰⡀⣥⠊⠰⠎
⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠈⠙⢇⠒⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠈⠉⠲⣖⠧⠀⠀⠀⠀⠀⠀⠀⢠⡵⠖⠋⠀⠀⠈⠉⠲⣖⠧
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢣⠀⠀⠀⠀⣜⣠⣤⡤⢄⣄⣀⣠⣤⠤⣤⣄⣡⠀⠀⠀⠀⠀⣎⣴⣶⠖⢀⢄⢀⣶⡾⠃⡠⣢⣧
⠀⠀⠀⢀⠁⠀⣀⠼⠿⢤⣀⡠⠼⠯⢄⡀⠘⠆⠀⠀⠰⠉⠽⠏⠤⣾⡿⠟⢿⡁⠴⠿⠿⠻⠄⠀⠀⠀⠘⠹⠟⢁⢔⣵⡿⠛⠟⢁⢔⣼⣿⠻⠆
⠀⠀⠀⢘⡠⠊⢀⡀⢀⣀⡽⣀⣀⠀⣀⠈⢢⡆⠀⠀⠘⠀⠀⡠⠊⠉⠙⣶⠉⠉⠱⣄⠀⠀⡄⠀⠀⠀⠎⠀⠀⠃⠛⠉⠀⠀⠀⠁⠛⠛⠁⠀⡄
⠀⠀⠀⢸⡷⡶⠋⠗⠙⠁⠤⠀⠉⠑⠏⠳⡶⡇⠀⠀⢸⠀⠻⢤⣀⡠⠔⣉⠦⢀⣀⠬⠛⠀⠆⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠺⡃⠀⠠⠄⠀⢀⣀⡀⠀⠠⠄⠀⢘⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠰⡁⣠⠊⠉⠖⢠⠤⢤⢀⣀⣠⡤⠤⠄⠒⡁⠁⡀⢰
⠀⠀⠀⠀⠀⠀⠓⠠⠤⠄⠀⡀⠤⠄⠚⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⢀⣀⣀⡠⠔⠉⠀⠀⠀⠀⠒⠀⡎⢀⡄⠀⣄⠀⣄⠀⣆⠀⠷⢄⡑⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈⠚⠉⠐⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⢿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠶⠶⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠓⠒⠲⠶⠶⠦⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠈⢿⠉⠙⠛⠛⠒⠒⠲⠶⠶⠤⣤⣤⠤⠤⠴⠶⠖⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠀⢠⠀⣿⡆
⠀⠀⠀⢀⣤⣾⣧⣀⣀⣀⣀⡀⠀⠀⠀⠤⣂⣿⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠾⢶⡟
⠀⠀⠀⠀⣿⠈⠉⠉⠓⠲⣾⠛⠛⠛⠛⠛⠛⠓⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⣿⡀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⣒⣒⣚⣩⡇
⠀⠀⠀⠀⠈⠙⣷⠒⠦⢤⣽⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠶⠶⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠁⠀⢸⣇
⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠈⢉⡙⢻⡏⠰⠒⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣷
⠀⢶⡾⣯⣭⣥⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠍⣿⠀⠀⠀⠀⢀⡠⠀⢀⣀⣀⣤⠤⠤⠶⠒⠚⠋⢉⣠⣿⣀
⠀⠈⡷⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠶⣤⣤⣿⣤⡤⠶⣾⣛⡿⠛⠋⠁⠀⠀⠀⠀⣀⡠⢔⣚⣭⠤⠖⠛⢿⡄
⠐⢿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠈⠀⠀⣄⣀⠠⡌⣷⠀⠀⢀⣀⣤⠶⠟⢛⣋⡩⠄⠂⠀⠀⠀⠈⣿
⠀⠘⣷⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠯⣭⣿⣛⣓⣒⣺⣿⡶⣿⠴⠚⣋⠥⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠁
⠀⣀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠭⠥⢖⣒⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠁⢸⡇
⠀⠉⠛⢻⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠒⡉⠭⢝⣒⣺⡇⠀⠀⠀⢀⣀⣤⠶⢚⡭⠟⠁⠀⠀⠀⢀⣼⣧⣄⣀⣀
⠀⠀⠀⠈⢹⣯⠉⠙⠛⠛⠛⠛⠻⠷⠾⢶⣶⣶⣮⣭⣒⣿⣀⣤⠴⠚⠋⠁⣠⠶⠋⠀⠀⠀⠀⢀⣰⠋⠀⠀⠈⣉⡽⠟⣷
⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⡉⠛⠛⠿⢿⣇⠀⡀⢇⠀⠀⣠⠞⠁⢀⣠⠶⠋⠁⠀⠀⢸
⣠⣴⠚⠋⢩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠠⠔⢒⣈⣈⣿⡄⣧⢸⣠⠞⣡⡴⠚⠉⠀⠀⠀⠀⠀⣀⣼
⠈⣿⠙⠛⠛⠿⢷⣶⣶⡦⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⡴⢒⣡⣾⠥⣶⣿⡇⣿⣾⠗⠋⠁⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣍⣉⡉⠛⠛⠓⠶⠶⠦⢶⣶⣶⣿⣯⣿⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠁
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣀⣠⡴⠞⠉⠉⠁⠀⠀⠀⠀⠀⣠⢴⣫⡿⠛⠁
⠈⠛⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⢖⣩⢽⢛⣿⡀⠀⠀⠀⠀⠀⠀⣠⢔⣫⡾⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⠀⠀⠐⠀⠀⠂⠈⢔⣋⠯⢾⣇⠀⠀⠀⡠⢔⣫⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣀⣀⡀⠠⢀⣊⠽⣿⠀⢀⣨⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣷⣶⣽⣧⡶⠟⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠂⠐⠲⡄
⠀⠀⠀⠀⠀⠈⡏⡒⠤⣀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣠⠔⠩⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠸⡀⠐⠄⠉⠒⠒⠉⠁⠀⠀⠀⠉⠉⠋⠀⠀⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢇⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡌⠀⠙⠀⠀⠀⠀⠀⠀⡎⠈⠃⠀⠀⠀⢸⣀⣀⣀⣀⣀⡀⠀⠸⡀⠀⠀⠸⡀
⠀⠐⠒⠒⢒⣒⣒⡇⠄⠀⠈⠂⠊⠀⠀⡄⢠⠄⠀⠑⠀⠁⠀⠀⠈⢽⠇⠀⠀⠤⠄⣀⠀⠀⢣⠀⠀⠀⠱⡀
⠀⠐⠉⢉⣀⡤⠤⢧⠁⠀⠀⠀⠀⢀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠀⠈⣹⠉⠐⠒⠤⠀⠀⠀⠀⠈⢧⠀⠀⠀⠱⡄
⠀⠀⠀⠁⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠑⠈⠈⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⢸⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠘⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢰⠂⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢦⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡔⠀⣀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡘⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢱⢦⡀⠀⡇⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠈⠑⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⣠⠃⠀⠀⠀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡌⠀⢠⡎⡝⠀⠀⠀⠀⢰⡤⢤⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠇⠀⠈⢳⠁⠀⠀⠀⢠⠇⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡜⠀⠀⣠⠃⠀⠀⠀⢀⠞⠀⣼⠐⡀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣌⡠⠜⠀⠀⢰⣁⠂⠄⠀⣠⠎⠀⠀⠈⠓⠂⠒⠒⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠉⠁

⠀⠀⠀⠀⠀⢀⠄⢂⣀⣈⣀⣀⡀⠀⠂⡤⢀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢀⡀⢤⠀⠀⢀⣀⣀⣁⣀⣐⠤⡀
⠀⠀⠀⠀⠀⣏⠉⠀⣀⡀⠀⠤⢀⡩⠺⠝⠥⠙⠷⢦⣄⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⣀⡴⠾⠋⠬⠫⠗⢅⡠⠤⠀⣀⣀⠀⠉⣸
⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠠⠄⣼⢱⠇⡈⠀⠡⠀⡀⠈⠙⢤⡀⠀⠑⡀⠀⠀⠀⠀⠀⠊⠀⢀⠤⠋⠡⢀⠀⠈⠀⢀⠸⡆⣧⠠⠄⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢤⠆⡄⠘⠂⠤⣀⢂⠐⡈⢀⠂⠈⠢⡀⠀⡀⠀⠀⢀⠀⢀⠔⡁⠐⠀⠁⠂⡐⢀⠤⠐⢣⢠⠰⡤⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡎⠒⡂⢰⠤⠤⠀⠼⠷⢴⡄⠢⠠⠠⠱⡀⠘⢤⡄⠃⢀⠎⠄⠀⠀⢠⡤⠾⠧⠀⠠⠤⡆⢐⠒⢸⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠐⣈⡁⣇⢈⠅⡞⠀⠈⠉⠉⠉⠀⠘⠢⡑⠈⢆⠱⡀⢻⡟⢀⠎⡰⠀⢂⠔⠃⠀⠉⠉⠉⠁⠀⢳⠨⠁⢸⢈⣁⠒⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠡⠔⠲⡇⢩⠄⢹⠬⠥⠀⣀⣀⣈⣉⣉⣙⠓⢤⣧⣾⣿⣿⣿⣼⡤⠚⠋⣉⣉⣁⣀⣀⠠⠬⠩⡟⠠⡍⢹⠖⠢⠄⣽
⠀⠀⠀⠀⠀⠀⠀⣧⠤⠖⠒⡇⢠⠌⠘⣖⡂⠀⡉⢉⡀⠉⠉⣑⣛⡙⠿⠿⣿⣿⠿⠛⠛⣛⣋⠉⠉⠁⡉⢉⠀⣐⣲⠇⠩⡄⢸⠒⠲⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠖⠛⢒⡾⠛⠋⠙⡏⠉⢉⣉⣉⠉⠓⠲⢮⣭⣒⣿⣿⣒⣭⡴⠖⠚⠉⡉⣉⡉⠉⢹⠋⠙⠛⢾⡒⠛⠒⠶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢳⠀⣴⣦⡙⢅⠀⡀⠠⠀⠒⠂⠉⠝⣻⣿⣿⣟⠋⠉⠐⠒⠠⠄⣀⠀⡩⠛⢶⣿⡆⡞⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢣⡀⠸⡄⠛⠿⠃⠀⢇⣀⠔⠀⠀⡠⠔⣹⣿⣿⣿⣿⣮⠲⢄⠀⠀⠢⣀⡹⠀⠀⠉⠉⢡⠇⠀⡜⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠨⠑⣄⠈⡄⠀⢠⣦⣌⠑⠦⣤⢊⠔⠪⡝⠘⣿⣿⠃⢫⢇⠢⡑⢤⠴⠚⠡⣾⣷⠀⢠⠁⢠⠊⡅⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠌⣆⠳⢄⡘⠛⠇⠀⠀⠘⢅⡴⢠⠁⢀⣿⣿⡀⠀⡄⢦⡨⠃⢀⠀⠈⠉⢉⡠⠞⣰⠁⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠢⡀⠘⣆⠀⢀⣶⣦⠀⠈⠏⡠⢣⠾⠿⡜⢄⠹⠁⠀⢺⣿⡇⠀⣰⠃⢀⠔⢑⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⢙⡦⡈⠢⣄⠛⠛⠁⢠⣾⡵⠃⠀⠀⠘⢮⣷⡄⠀⠈⠉⣠⠔⢁⣴⡏⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⢆⠀⢳⠀⠀⣾⡿⠁⠀⠀⠀⠀⠈⢿⣷⠀⠀⡞⠀⣠⣯⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠳⣴⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣦⠞⢡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣂⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣰⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠴⠶⠖⠒⠂⠀⠀⠀⠀⠀⠐⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠩⢑⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠌⣑⠢⠍⠛⠶⢦⣄⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠋⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠬⢐⠪⢕⡂⠉⠒⠠⠀⠀⠈⠻⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠉⠓⢯⣑⠢⠅⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢶⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠉⠉⠉⠙⠳⠦⣤⣀⣀⣀⣠⡾⣁⣀⣤⡤⠶⠞⠛⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⡿⣟⢿⣛⣛⣛⣛⣋⣉⣉⣉⣭⣭⣭⠿⠿⠟⠛⠛⠉⠉⠉⠉⣉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠁⠹⣆⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠈⢳⡀
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⢁⣀⣤⣤⣼⣿⣶⣶⣶⣶⣛⣛⣛⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⢀⣤⠶⠛⠋⠉⠀⠠⣿⠟⠉⠀⠀⠀⠀⠀⠲⠬⠭⠭⠭⠭⠭⢉⣉⣛⣛⣛⣛⣓⠒⠒⠒⠲⠶⠶⣶⠿⠂
⣰⠟⠁⠀⢄⣀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡉⠉⠉⠉⠁⠀⠐⢒⣒⣒⣂⡀⠀⠀⠀⢰⠉⠓⠦⣄⡀
⡟⠀⠀⠀⠀⠀⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠠⠬⠭⠭⠭⡭⠁⠒⠒⠒⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⣳⣦
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠯⣭⣭⣭⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⠤⠀⠀⠀⠀⠀⠀⣀⠀⠈⢲⡶⠚⠛⢹⠋⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⡀⠀⠀⠈⠉⣉⣩⡭⠭⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⡾
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⣀⣀⡤⠤⠀⢀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡘⢿⡂⠄⠀⠀⠀⠠⠔⠒⢒⣒⣛⣫⣭⠭⠶⠶⠒⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠸⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠄⠠⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣤⡤⢤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⠓⠒⠒⠀⠀⠀⠀⠀⠲⠒⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠀⠀⠀⡴⠉⠢⠄⠚⠑⠢⠤⠤⠒⠉⠳⠄⢀⠜⠓⠤⠀⡤⠛⠤⠤⠚⠣⠤⠖⠙⠒⠚⢦⡀
⠀⠀⢀⣸⠉⠉⠚⠁⠀⠀⣵⢤⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠑⢄
⠀⣰⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⣷⠾⢅⣀⡤⠢⣄⡀⠀⣠⠗⠤⡀⠤⠚⢦⣀⣀⠤⠳⣄⣀⠤⠛⠤⣀⠠⠔⠙⠢⠤⠖⠉⠢⠤⠞⠳⡄
⠀⣸⡄⠀⠀⢀⡎⠈⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⢸⡁⠀⠀⢀⣧⠀⠀⠀⠀⢺⡀⠀⢀⢤⡀⠀⢀⠶⣄⣀⣠⠶⣄⣀⣀⠜⢦⡀⢀⡠⢦⣀⠀⢀⡠⢧⣀⣀⣀⡴⢧⡀⠀⢀⣴⡀⠀⠀⠀⡼⠁
⢠⠟⠀⠀⠱⠀⠀⡄⠀⠀⠀⠉⠚⠳⡄⡏⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉⠀⢀⣀⠉⠀⠀⠀⠉⠉⠉⡇⠉⠒⠒⠉
⢇⠀⠀⠀⠀⠀⠈⠓⢶⠀⠀⠀⠀⣴⠃⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣄⣀⠀⠀⠀⢠⢾⠉⡍⣹⢆⠀⠀⠀⠀⢀⠃
⠀⢩⠛⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡟⠀⡇⠀⠀⡎⠀⠀⠟⠀⠀⡇⠀⠀⡿⠀⠀⡟⠀⠀⠀⠧⠤⠿⠿⠷⠾⠂⠀⠀⠀⢸
⠀⠈⠢⣤⡄⠀⣠⣤⡤⢤⣤⣰⠇⠀⠀⡇⠀⠀⡇⠀⠀⢴⠤⠴⡗⠒⠒⡷⠀⠀⡇⠀⠀⢀⡶⠐⠚⠓⠛⠚⣆⠀⠀⠀⢸
⠀⠀⠀⠏⠉⡻⠁⢸⡀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢇⠀⠀⠞⠀⠀⡇⠀⠀⢠⠀⢠⡇⠀⠀⢰⠀⡖⠂⠉⢹⠀⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠉⠛⠒⠒⠛⠂⠒⠛⠋⠋⠀⠀⠀⠐⠀⡇⠀⠀⡎⠀⡇⠀⠀⠀⢸
⠀⠀⠀⣼⠀⣇⠀⠀⡇⠸⡀⠀⠀⠀⠀⡇⠀⠀⣀⣠⢄⣀⣀⣀⠤⣤⠤⣤⠶⣤⢤⠀⠀⠀⠀⠉⠛⠛⠃⠀⡇⠀⠀⣀⣸⣄⡀
⠀⠀⠸⠭⠭⠭⠽⢇⠇⠀⢧⠀⠀⠀⡤⠿⠑⠏⠉⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠸⠑⢀⠇⢜⠙⠃⠃⠰⠛⡆
⠀⢀⠀⠀⢀⣦⣀⣼⣀⣀⣈⣧⣀⣀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢸⠀⠀⠀⠀⠀⢸⠀⠸⣁⡀⠀⠀⡈⠉⣆⣀⣀⣀⣰⠳⣄⣀⣀
⠀⠈⠉⠉⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠛⠒⠚⠳⠤⠛⠤⠔⠣⠄⠳⠤⠴⠒⠚⠉⢹⠛⠛⠛⠛⠛⠛⢿⡒⠚⠓⠓⠤⠛⠚⠉⡉⠉⠉⣹⠀⡏⠉⠉
⠀⠀⠀⠀⡇⢸⢦⣀⠀⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⢸⠛⡤⢊⣽⠀⡇
⠀⠀⠀⠀⡇⡸⢦⡈⢻⠁⢸⠀⠀⠀⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⡷⢀⡧⠊⠸⠤⠇
⠀⠀⠀⠀⠉⠁⠀⠈⠻⠀⢸⠑⠢⣼⠀⢸⠀⠀⠀⡜⢳⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠑⡖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⠙⠒⢾⠀⣏⠉⠛⢺⠃⢸⣀⡀⠀⠀⡇⢘⠀⠀⠀⠀⡇⢹⡀⠀⠀⣀⡇⢸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠀⠀⢸⠀⡏⠉⠛⠺⡀⢸⣄⣉⣉⢛⡇⢸⡓⠒⠈⣉⡇⢸⣏⡩⠭⠽⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢧⣼⠀⠀⠀⠉⡇⢈⡏⠉⠉⠀⢧⢘⡄⠀⠀⠀⢧⣸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⢿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠗⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠺⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠃⠀⠀⠀⠀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣤⠀⢀⣤⡄⠀⣤⡄⠀⠀⠀⣿⡇⠀⠀⠹⣿⡆⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⢠⣿⠟⠉⠉⠙⢿⣷⠀⠀⠀⢸⣿⠇⠀⠀⠀⠉⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⣾⡿⠋⠉⠉⠻⣿⡄
⠀⠀⠀⢺⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡗
⠀⠀⠀⢘⣿⣷⣤⣀⣤⣾⣿⠀⠀⠀⢸⣿⡄⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣷⣤⣀⣤⣾⣿⡃
⠀⠀⣰⣿⠟⠉⠛⠛⠋⠉⢻⣷⡄⠀⢸⣿⣿⡿⠋⠸⣿⣇⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⣿⡇⠀⢠⣾⡟⠉⠙⠛⠛⠉⠻⣿⣆
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⠿⠋⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣈⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣯⠿⠿⣿⣿⡿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣺⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢐⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⢲
⢰⠀⠀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠑⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡞
⠈⢆⠀⠀⠈⢦⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⠛⠛⠁
⠀⠀⠑⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬



⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡧⠤⡧⢤⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⢳
⠀⠀⡀⢴⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣡⠤⠧⢤⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠒⠚⠦⢊
⠀⠀⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤
⠀⠀⠀⠀⣠⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣄⠀⠀⢀
⠀⠀⠀⠀⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠁
⠀⢀⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠀⠀⠣⣀⠜
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠙⠄⠀⠖⠉⠱
⠰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠿⠿⠟⠋⠀⠀⠁⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣅⡋⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢸⠗⠀⠀⠀⣀⠤⠶⡾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⣿⣿⡟⠉⠉⠓⠒⠒⠢⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⢙⣿⡿⠁⡀⠁⠀⠀⠀⠀⣠⣴⣿⣿⣦⣄⠀⠀⠀⠀⠌⠀⠀⠀⢸⡇⢀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣴⡿⠁⡀⠀⠀⠀⠀⣠⣾⡿⢻⣿⣿⣿⣿⣿⣦⣀⡼⠀⠀⠀⠄⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠟⠉⠉⠉⠉⠉⠉⠙⠛⠻⣿⣿⠃⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠐⠀⠀⠀⠀⢀⠀⠰⢁⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢶⣄⣀⠀⠋⣠⠂⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⣷⣻⣀⠈⡅⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⣿⣶⣆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⠲⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡅⢎⡇
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠛⠀⠒⠒⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢊⠴⠁⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠸⠃⠀⠈⡆⡔
⠀⠠⠀⠀⠀⠀⣰⣁⡍⢀⡴⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠓⠒⠒⠒⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠀⠀⠀⠀⠀⡠⠂⠉⠉⡇⠢⡀⠀⠀⠀⠀⠀⡇⡤
⠀⠀⠀⠙⠔⠉⠉⠉⠉⠁⡜⢣⠈⠉⠉⠉⠉⠑⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢘⠀⠀⢀⡴⢆⠀⢸⠀⠀⠀⠀⢀⠈⡀
⠀⠀⢠⠖⠉⠉⢹⠙⠢⡀⠑⠊⠀⢀⠔⠋⠉⠉⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⢦⡀⠀⠈⢹⠈⠁⠀⠀⠸⠛⠀⠀⢀⠔⠁⠀⢈
⠀⢀⠁⠀⠀⢀⠾⡀⠀⢡⠀⠀⢀⠃⠀⠀⢀⠼⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⠦⣠⡈⢆⡀⠀⣀⠞⢸⡤⠔⠁⠀⢀⠴⠁
⠀⠀⠙⠂⠉⠁⠀⠈⢙⠈⠀⠀⠈⠛⡆⠈⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠉⠈⠉⠀⠁⠀⠀⢀⠔⠁
⠀⠀⠀⢆⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡔⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⡠⠒⠛⠂⠘⠓⠢⡀⠀⠀⠀⡤⠖⠛⠃⠘⠋⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠊⠙⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢣⠀⡴⣔⢉⢩⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡔⠒⢄⠀⠈⠁⠒⢄
⠀⠀⠰⠢⢄⠀⠀⡰⠛⢤⡣⠄⠃⠈⢣⠀⢀⠀⢀⡆⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠢⡊⠗⢄⠀⠀⠈
⠀⠀⢐⠀⠠⠃⠀⠑⠀⠲⡀⠁⡛⠀⠘⠀⠀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠙⠦⠴⠃⡀⠜
⢀⠄⣈⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠑⡲⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡀⠑⠄⣀⡠⠎⢠⠒⠄
⠣⠠⠆⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢦⠀⠀⠐⠒⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢬⣊⠀⠀⠀⠀⠀⠀⢈⡓⠅⢠⣄⡀
⠀⢠⠄⠤⡀⠀⠀⠠⣁⣀⡠⠚⠤⣀⡇⠀⠀⠀⡠⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢠⠀⠑⢄⠀⠀⠀⡰⠋⠀⠀⢠⠀⠉⢆
⠀⠸⡀⠀⠉⠢⡀⠀⢘⡀⠀⠀⠀⡇⠀⠀⡠⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⠴⠋⠢⣀⣈⠀⠀⠀⣇⣀⣀⠤⠊⠢⢀⣈
⠀⠀⠈⠢⡀⠀⠈⠒⠤⠵⠦⠤⠾⠤⠐⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⢨⠈
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⣀⣠⠃⠀⠀⠀⠀⡇⠑⣄⣀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠗⠉⠀⠀⠀⠀⠉⠲⡀
⣀⣀⣀⣀⣀⣀⣀⣘⣤⣄⣀⣤⣤⣤⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣤⣤⣤⣤⣤⣤⣤⣃⣀⣈⣀⣀⣀⣠⣄⣤⣤⣤⣃
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣾⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠸⣇⠀⢀⡟⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢹⡆
⣸⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⡆⣾⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⢀⡾⢿⡛⠛⣻⠟⢿⡟⠛⣻⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⡙⢋⣿⠟⢿⡙⠛⣻⠿⣆
⠀⠀⠀⠀⢠⣿⣥⣤⣿⣾⣯⣤⣤⣽⣶⣯⣤⣬⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣤⣬⣷⣾⣥⣤⣬⣿⣾⣧⣤⣽⣧
⠀⠀⠀⠀⠀⠙⣦⡀⠀⢿⡀⠀⠀⢰⡏⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠈⣷⠀⠀⠀⣸⠇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣆⠘⣧⠀⢀⡿⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠸⣇⠀⢠⡟⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣆⣼⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣄⣾⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠁
⢻⣏⠉⢩⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⡉⠉⣹⠟⢿⡉⠉⣹⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣯⠉⢉⣿
⣤⣽⣷⣿⣤⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣬⣿⣾⣥⣤⣤⣽⣾⣯⣤⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣤⣼⣷⣿⣥
⠀⢠⡟⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢷⠀⠀⠀⢸⠇⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠘⣧
⠀⣾⢁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠘⣧⠀⢠⡟⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢹⡆
⣸⣧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣆⣾⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣿
⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⢠⡾⢿⡍⠉⣹⠟⢿⣍⠉⣹⠟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢿⡉⢉⣽⠛⢿⡉⠉⣽⠿⣆
⠀⠀⠀⠀⢰⣿⣤⣤⣿⣾⣧⣤⡤⣽⣷⣯⣤⣬⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣤⣬⣷⡾⠥⠤⢤⣿⣾⣧⣤⣼⣷
⠀⠀⠀⠀⠀⠙⢦⡀⠀⢻⡀⠀⠀⢰⡏⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠈⣷⠀⠀⠀⣸⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⣧⠀⢀⡿⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠸⣇⠀⢰⡏⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣇⣼⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣄⣿⡴⠋
⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠻⣍⠉⣩⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢿⡉⢉⣽⠟⢿⣍⠉⣹⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣯⡉⢉⡽
⠤⠼⣷⠿⠤⢤⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠤⠤⢿⣾⠧⠤⠤⢿⣾⠧⠤⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠤⠼⣷⡿⠤
⣀⣠⣏⣀⣠⣾⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⣀⣀⣿⣀⣀⣀⣸⣇⣀⣠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣦⣀⣈⣧⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣷⠆⠀⠀⣠⣶⠿⠛⠋⠉⠉⠉⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠀⠻⠋⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢀⣴⡿⠿⠿⣶⡄⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⠻⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠸⣷⣤⣀⣤⣾⠏⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠉⣿⠏⠁⠀⠀⠀⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣤⣶⣶⠶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠈⠉⠛⠻⠿⠾⠿⠿⠛⠋⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣴⡿⠋⠁⠀⠀⠈⠙⠃⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣤⣼⣿⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢀⣤⣿⣯⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠙⢿⣦⣤⣀⣀⣤⣶⠆⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⢀⣠⡾⠋⠀⠀⣠⣦⠀⣀⣠⣴⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⣀⣀⣠⣤⣶⠿⠋⠀⠀⠰⢿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢠⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⣴⣦⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣦⡈⢿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⡿⢁⣼⣿⣿⣦
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠻⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⠟⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⠸⣿⣿⣿⣿⠇⣸⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⢻⣿⣿⡟⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢿⡿⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⠀⢀⡠
⠀⠀⠀⠀⠀⠀⢠⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠟⠻⣆⠈
⠀⠀⠀⠀⠀⡴⠁⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠘⢄⠀⠐⠂⠤⠄
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⢢
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⢻⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡺⠃
⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⡆⠀⠀⡜⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢰⠀⢠⠃⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⡆⡜⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡟⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠛⠛⠭⠟⠁⠘⢿⠋⠛⠛⠛⠒⠶⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⣠⣼⣿⣿⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠷⣟⣻⡿⠿⠛⠛⠛⠛⠺⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⣀⠤⠐⠊⠉⠁⠠⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⢿⡏⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠛⠂⡟⠻⣝⠻⣦⡀
⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⢠⠇⠀⠀⠀⠀⠹⣶⡆⠀⠠⢄⣀⣀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣾⣿⣿⣦⣍⣀⡀⠃⠀⠈⠁⠸⡝⢦⡀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⢉⣩⣽⣿⣾⣿⣿⣿⡛⣛⠉⣿⣿⠿⣟⠟⠝⠛⠛⣿⣷⠆⠀⠀⠀⠸⡄⠙⣦
⠀⠀⠀⢸⠁⣨⡄⠔⠉⠀⠄⠠⡇⠀⠀⠀⠀⠀⠀⠀⠙⠆⣀⡤⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡾⠃⠀⠀⠂⠀⠀⠀⠀⠙⠉⠄⠀⠑⠤⣼⡇⣿
⠀⠀⠀⠘⣟⠀⠀⠀⠀⠌⠀⢘⡇⠀⠀⠀⠀⠀⠀⣠⠴⠻⠛⠄⠀⠰⠿⠿⠛⠛⡏⠉⢹⣿⣿⣿⣷⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠹⠆⠀⡐⠃⣽⡏
⠀⠀⠀⠀⠈⠳⣅⢠⡁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣼⡇⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠆⠀⠀⠙⣦⣴⡼⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⠀⠀⡿⢠⣾⣿⠿⠿⣿⣿⣭⣶⡻⣿⣿⣶⣄⣠⠀⣐⣻⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣦⣀⣀⠀⠀⠀⣠⣀⡀⠀⠀⠈⢻⣦⣠⢶⣿⣟⠉⠐⠈⠉⠘⣈⣯⣹⣧⣭⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠋⢿⣿⣿⢿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣽⣷⣿⣯⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡱⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠣⡈⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡀⠈⠈⡙⢯⡈⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⢿⣿⣿⣿⣿⣿⣏⣻⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠟⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⢻⡆⠀⠀⠀⠀⣾⠃⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠘⣿⠀⠀⠀⢸⡟⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢹⡇⠀⠀⣿⠁⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⣿⡀⣸⡏⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⠋⠉⠈⠓⢄⣀⣀⡤⠶⠚⠉⠁⠀⠉⠙⠒⠦⣤⣀⣀⠴⠋⠈⠉⠓⠲⠬⣷⣤⡀
⠀⠀⠀⠀⢀⣠⠞⣯⠀⠀⠀⠀⠀⢀⣠⠴⢺⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢻⡒⢤⣀⠀⠀⠀⠀⠀⢈⡟⢦⣄
⠀⠀⣀⢴⡿⠃⠀⢻⠀⢀⣠⠴⠚⠉⠀⢠⠏⠀⠀⠈⠙⠦⣀⠀⠀⢀⡠⠞⠉⠀⠀⠀⢧⠀⠈⠙⠲⢤⣀⠀⢸⠃⠀⠹⣷⢄⡀
⠀⢾⡷⣿⠶⠶⠶⢾⣾⠿⠶⠦⠴⠶⢶⣿⡶⠶⠶⠦⠶⠶⠾⣷⣶⡿⠶⠶⠶⠶⠶⠶⣾⣷⠶⠶⠤⠶⠾⢿⣾⠶⠶⠶⢾⡷⣿⠆
⠀⠀⠙⢮⡳⣄⠀⠀⠈⢷⣄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⡴⣫⠞⠁
⠀⠀⠀⠀⠉⠢⣕⢦⡀⠀⠹⣷⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣰⡿⠃⠀⣀⢔⡫⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠈⢯⡳⡄⠀⠀⠘⡆⠀⠀⠀⠀⡾⠸⡆⠀⠀⠀⠀⡼⠁⠀⠀⡠⢪⠟⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡢⣄⠱⣌⠢⡀⠀⠹⡄⠀⠀⠀⡇⠀⣇⠀⠀⠀⡼⠁⠀⣠⠞⡴⢃⡠⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣷⣌⢦⡙⢦⡀⠹⡄⠀⢸⠃⠀⢹⠀⠀⣸⠃⣠⠞⢡⢞⣴⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣷⣄⠙⢦⣳⡀⣼⠀⠀⠸⡆⣰⣣⠞⠁⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠙⢷⡇⠀⠀⠀⣷⠟⠁⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⢧⠀⠀⢠⠏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣧⢠⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠉⠉⠉⠉⢉⣿⠋⠉⠉⠉⠉⠉⠙⢿⣏⠉⠉⠉⠉⠉⠉⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣷⡀
⠀⠀⠀⠀⠀⠈⠻⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠈⣿⡄⠀⠀⠀⠀⣿⠇⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⢸⣷⠀⠀⠀⣸⡟⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⢿⣇⠀⢠⣿⢁⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⡄⣾⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣶⡶⣶⡶⠶⠶⠶⠶⠶⣶⣶⡶⢶⣶⣶⠶⠶⠶⠶⠶⢶⣶⢶⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠉⠁⠀⠈⠙⢦⣠⡴⠖⠛⠉⠀⠀⠀⠀⠉⠛⠲⢦⣄⡴⠋⠁⠀⠈⠉⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠀⠀⠀⠀⣠⡴⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡟⢦⣄⠀⠀⠀⠀⣯⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⠀⢀⣤⠞⠁⠀⢸⡇⠀⠈⠳⣤⡀⠀⠀⢀⣠⠞⠁⠀⢸⡇⠀⠈⠳⣤⡀⠀⣟⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣏⣀⣀⣀⣽⣶⣏⣀⣀⣀⣀⣼⣄⣀⣀⣀⣈⣹⣦⣴⣏⣁⣀⣀⣀⣠⣧⣀⣀⣀⣀⣹⣶⣧⣀⣀⣀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢠⣾⠁⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⣿⣦⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣴⣿⠃⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⣯⠳⣄⠀⠀⠈⣧⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⣼⠁⠀⠀⣠⠞⣽⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⣇⠙⢦⡀⠀⠸⡆⠀⠀⢸⠃⠘⡇⠀⠀⢰⠇⠀⢀⡴⠋⣸⠃⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⣆⠈⠳⣄⠀⢻⡀⠀⣾⠀⠀⣷⠀⢀⡟⠀⣠⠞⠁⣰⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣆⠀⠙⢦⡘⣧⠀⡟⠀⠀⢻⠀⣼⢃⡴⠋⠀⣰⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠈⠳⣽⣼⡇⠀⠀⢸⣧⣧⠞⠁⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢿⠀⠀⠀⠀⡿⠃⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⣇⠀⠀⣸⠃⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢹⡄⢠⡏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣷⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⡤⣀⢤⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⢛⣛⣛⠛⠛⠛⣛⣛⡛⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⡹⡿⣫⣾⣿⣷⣝⢿⣏⣾⣷⣄⠀⠀⠀⠀⣿⣿⣿⡿⢋⣴⣧⠈⠟⢁⣴⣿⣦⡈⠻⠃⣰⣦⡙⢿⣿⣿
⠀⠀⠀⠈⢿⣿⣿⣧⣸⣿⣿⣿⣿⣿⡧⣼⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣄⠠⣤⣤⣄⠀⣤⣤⣤⣤⣤⠀⣠⣤⣤⠄⣰⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣧⢿⣿⣿⣿⣿⣽⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣌⢿⣿⡆⠹⣿⣿⣿⡏⢠⣿⡿⢡⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣿⣿⣿⣳⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢿⡄⢻⣿⡟⢀⡿⢋⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡑⠀⠿⠁⠚⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⠟⠙⡄⠀⢀⠔⠉⠢⡀⠀⢀⠏⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡴⢻⣏⠉⣩⡿⠛⢿⣍⠉⣹⡿⢷⡀
⣿⣿⣿⣿⠁⠀⠀⢵⡴⠁⠀⠀⠀⠈⢦⡮⠠⠀⠈⣿⣿⣿⣿⠀⠀⠀⣴⣯⣤⣤⣿⣿⣯⣤⣤⣤⣽⣿⣿⣧⣤⣽⣦
⣿⣿⣿⣿⣦⡀⠀⠀⢣⠀⠀⠀⠀⠀⡜⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠈⠳⣄⠀⠈⣿⡄⠀⠀⠀⢀⣿⠃⠀⣠⠟⠁
⣿⣿⣿⣿⣿⣿⣦⠀⠀⢃⠀⠀⠀⠰⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢷⡄⠘⣷⡀⠀⠀⣾⠇⢠⡾⠃
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠆⠀⠠⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣧⠀⣼⢏⡴⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢀⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠓⠶⣤⡀⠀⠀⠀⢀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣸⢃⣠⠖⠶⠶⠶⠖⠛⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠙⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠈⠙⢻⣿⠉⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠛⠛⠚⠛⠛⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡄⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣸⠇⠀⠀⣿⠀⠀⢸⡇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠃⠀⠀⣿⠀⠀⢸⣇⣀⡟
⠀⠄⠀⠀⠀⠀⠈⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣿⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠿⠤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣶⣶⣾⣿⠛⠛⠛⠛⠛⠋⠉⠁⠈⠉⠉⢿⣶⣲⢤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣀⡚⠉⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⠄⣀⣴⠖⠀⠀⣨⣿⠀⠷⠶⣭⣙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⡾⠁⠉⢀⣴⣿⡓⣶⠀⠀⢼⣭⣭⣭⣛⣛⢛⡁⣚⠻⠥⠄⠀⠲⡶⠲⣶⢒⣝⡳⣿⣿⣈⣷⠤⡀
⠀⠀⠀⠀⠀⣠⣶⢃⣾⢃⣤⣾⡟⣽⢻⣇⢿⠀⠀⠀⠹⢟⣿⠟⣡⠎⠘⢎⡢⡀⣀⣤⣤⣴⠆⠨⣼⣿⣯⠪⢝⢿⡋⢱⡈⠒⢄
⠀⠀⠀⠀⡞⡏⣑⡽⢟⡿⠟⠋⠀⠈⢸⡇⠀⠀⠀⠀⣴⡛⣣⣪⣵⠂⠀⠈⠳⣌⢎⢿⣿⣷⣦⢼⡏⠈⢧⠀⢰⡗⠨⡚⢿⣶⣌⣷
⠀⠀⠀⠀⠰⠞⣡⣶⠛⠀⠀⢀⢀⠀⢸⡇⠄⣾⣁⡠⣪⣺⣾⣿⣿⡟⠁⠀⠀⠀⢱⣕⢝⠟⠁⣾⣿⣿⣶⠄⠀⠀⠀⣸⣶⣍⠻⡏
⠀⠀⠀⠀⠀⠫⣉⣛⠂⠠⠤⠼⢻⣿⣦⠓⣴⡻⢋⣼⣿⢿⣿⡿⠋⣴⡀⠀⣤⡀⠀⠙⠳⡕⢄⣿⠿⠋⣀⣀⣠⠴⠒⠛⣛⣉⠟
⠀⠀⠀⠀⠀⠀⠈⠳⢌⡉⠑⡶⢦⢤⣌⣉⣉⣱⣃⣉⣀⣀⣀⣁⣐⣉⣁⣂⣈⣉⣀⣀⣐⣘⡊⢻⣿⠿⢭⠵⢒⣾⣿⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣜⡄⡠⢋⣭⣿⣄⢫⠉⠙⣲⣤⠄⠀⣹⣿⣿⣿⣟⡛⠋⢉⠝⣡⣿⣷⣔⠢⢞⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡻⠿⣿⣿⣆⠣⠸⣟⠁⠀⠀⡏⣿⣿⣿⣿⣿⢃⠎⣰⡿⠻⠁⢀⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠉⢧⠱⡹⣿⣦⣀⡇⢸⣿⠿⡻⢡⣶⣶⠇⡠⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⢳⣵⡘⣿⣿⡇⠈⠁⡴⣡⠿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣽⣷⡘⢿⣇⠀⡜⠐⣡⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡌⢿⠜⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢶⣶⣶⡶⠶⠶⠶⢶⣶⠶⠶⣶⡶⠶⠶⠶⠶⣶⣶⡶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠛⠉⠁⠀⠀⣙⣦⣔⠊⠁⠀⠀⠀⠀⠉⠑⢢⣤⣊⠀⠀⠀⠉⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⡻⠃⡇⠀⢀⡠⠴⠒⠉⣰⠁⠈⠑⠦⡀⠀⠀⢀⡤⠖⠉⠀⢧⠉⠒⠦⢄⡀⠀⠘⠘⢟⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠸⢿⡓⠻⡟⠛⠻⣟⠛⠛⠛⠛⠛⢿⠛⠛⠛⠓⠛⠻⠟⠛⠛⠛⠛⠛⢻⠟⠛⠛⠛⠛⣿⠛⠛⣻⠟⢚⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣌⠢⡄⠈⢷⣄⠀⠀⠀⠈⡄⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⠏⠀⠀⠀⣠⡞⠁⣠⠞⣡⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠢⡀⠻⡳⣄⠀⠀⠘⡄⠀⠀⠀⡇⢸⠀⠀⠀⢀⠎⠀⠀⣠⢊⠏⣠⢞⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣢⡘⢎⠳⡀⠀⠹⡀⠀⢰⡇⢸⡆⠀⠀⡞⠀⢠⠞⡱⢃⢖⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣮⣣⡈⠢⡀⢱⡀⢰⠀⠀⡆⠀⡜⢀⠔⢁⢞⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠘⢦⣣⣸⠀⠀⡇⣸⡴⠁⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢏⠀⠀⡹⠋⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣜⡆⢰⣣⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁







⡿⢿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠟⠛⠛⠛⠛⠻⠿⢷⣾⣿⣿⠛⠛⠛⠛⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⣠⣄⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢀⣼⣿⣿⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⢸⣿⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣿⡇⢀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣴⣦⣴⣶⣶⣦⣴⣤⣾⣿⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⣿⣷⣿⠏⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠻⠟⠁⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣄⣀⣀⣉⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁⠉⠉⠙⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢲⡄⢦⣴⢢⡶⠶⢼⡷⢶⡆⢶⣲⡄⣶⠶⣦⣰⠖⣶⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣭⠅⡾⠻⡜⢧⡴⠾⡇⠸⡗⢿⡽⡇⡿⠀⡿⠻⣤⣿⠙⢯⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋




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

⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠆⡀
⠉⠈⠀⠀⣤⣤⠤⠤⠤⠤⠠⠠⢄⣄⣀⡀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⢴⢦⡈
⠀⠀⠀⠀⡟⡌⠑⠢⢄⡀⠀⠀⢀⡴⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⢟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⣀⢏⣀⠽⣦⡀
⠀⠀⠀⠀⡇⠘⡄⠀⠀⠈⢑⣶⣏⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢟⡺⢗⡺⣗⡟⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⢸⠀⢠⠟⢧⡀⢰⠁⣙⣆
⣖⣲⠀⠀⡇⠀⠘⡄⢀⡴⠋⠈⡆⠈⠑⢺⠅⢐⠊⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⢠⡀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⢸⢠⠏⠀⣀⡽⢿⡋⠁⡆
⠈⠁⠀⠀⡇⠀⢀⡼⡯⠤⢄⣀⢸⣀⠔⠁⠐⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣖⣋⣁⣀⣀⣙⣦⠃
⠀⠀⠀⠀⣇⡴⠋⠀⠘⡄⠀⢀⠝⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠒⠒⠒⠤⠾⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⢀⠴⠦⡀⠀⠀⠀⠀⠀⢠⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣯⠟⠗⠪⣦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢁⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢧⡟⣟⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡏⠳⢄⡀
⠀⠀⡀⢆⡀⠀⠀⠀⠀⠀⡰⠛⡆⡸⠙⡄⡸⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡇⠀⢀⣉⣦⠀⠀⠀⡴
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⡗⠒⢺⠓⠒⢺⠗⠒⡺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⡠⠴⡷⢍⡁⠀⠰⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢇⠀⡎⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⣴⡟⠒⠋⠉⠀⠀⠀⡇⠀⠉⠓⣴
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠈⠺⣶⠞⠁⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠓⠲⠤⢄⣀⣇⡤⠖⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡠⠚⢏⠉⠒⠒⠒⠤⣤⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⡏⠐⠲⠤⣬⠄⡐⠂
⠀⢰⡶⣒⢒⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠈⢦⠀⠀⣠⠞⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡇⢀⡠⠞⠁⢠⡉⠁
⠀⢸⢱⣴⢻⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡠⠊⢻⠉⠙⠒⠲⠬⣧⠞⠁⠀⠀⡇⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠙⠗⠉⠀⠀⠀⠀⠁
⠀⠸⠯⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⠀⢠⣎⠀⠀⠈⡇⠀⠀⣠⠞⠉⢆⠀⠀⢀⡇⠀⠀⠀⠙⠊
⠀⠀⠀⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡀⠉⠒⢤⣸⣠⠞⠁⠀⠀⠈⢧⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠞⠉⠒⠤⣀⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠔⠀⠀⠀⠀⢰⡷⠾⣑⡷⡆
⢠⠶⡄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢛⣠⠞⠁⠀⠀⠀⠀⠈⠉⠒⠤⣈⢦⡇⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢸⣏⣶⣛⣯⠇
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠒⠒⠒⠒⠒⠚⠛⠃⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠛⠸⠞⢁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣖⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠔⡹⠙⡝⢦⡀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⢠⡏⢦⣀⣠⠴⠚⡽⡇⠀⠀⠀⠈⠁⠀⠀⠀⢤⠦⠆⠀⠀⠀⠀⠀⠈⠠⠈⠀⠀⠀⢀⠔⠁⢠⠇⠀⢱⠀⠙⢦⡀
⠀⣤⠀⢸⡤⠒⡟⢢⡀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣯⠟⣽⠳⡀⠀⠀⠀⠀⠀⠀⠰⡇⠤⠤⣾⠠⠤⢰⣷⠠⠄⣿
⠀⠐⢣⠀⠙⢾⡤⠒⡿⢧⡀⡇⠀⠀⢈⡁⡋⠀⠀⠀⠈⢧⡹⡁⣏⡽⠃⠀⠀⠀⠀⠀⠀⠀⠙⢆⡸⠀⢣⣀⠎⠘⣄⡔⠁⠀⠀⠀⢰⢱⠄
⠀⠀⠀⠀⠀⠀⠙⠾⠥⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣼⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⢸⣿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⣿⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣤⡄⠀⠀⣿⡿⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⠀⠍⢻⣧⠀⠀⣤⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠙⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡽⠟⠛⠙⣇⣀⡤⠔⠛⠉⠉⠛⠻⢭⣍⣹⠋⠛⠻⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⡏⠉⠀⠀⠀⣀⢴⠏⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠹⣦⣀⠀⠀⠀⠉⢹⣦⡀
⠀⠀⠀⠀⣠⣾⠏⠀⢣⠀⢀⡤⠚⢡⠋⠀⠀⠈⠳⣄⠀⠀⣠⠞⠁⠀⠀⠘⣿⣷⣤⡀⠀⣼⣿⣿⣷⣄
⠀⠀⣴⣯⣿⡥⠤⠤⢼⡴⣭⠤⣴⣧⣤⣤⣤⣤⣤⣬⣷⡾⠥⠤⠤⠤⠤⠤⢬⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠈⠳⣌⠳⡀⠀⠀⢳⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣰⠁⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⢿⢳⡀⠈⢧⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⡸⠁⢠⠞⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣽⣄⠈⢧⠙⢦⠈⢧⠀⠀⠀⢸⠁⠘⡆⠀⠀⠀⣰⢁⡴⠃⣸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡌⣧⠈⠳⣌⢧⠀⠀⡿⠀⠀⢧⠀⠀⣰⣣⠎⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣇⠀⠘⢮⣧⢰⡇⠀⠀⢸⡀⣰⡿⠁⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠻⣿⠀⠀⠀⠀⣷⠋⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⡆⠀⠀⣰⠃⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⡄⢠⠃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢸⡇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⣸⠉⠩⣿⠍⠈⠇
⠀⠀⠀⠀⠀⡻⠴⣄⠛⡤⠤⠖
⠀⠀⠀⠀⠀⠧⠤⠬⠭⠥⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡀⡀⢀⢀⡀⣀⣀⢀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣾⣿⣿⣿⣷⣶⣷⣷⣿⣿⣿⣶⣶⣶
⣿⣿⣼⣮⣷⣦⣴⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⠋⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢠⣿⣿⣿⡿⠋⣠⠀⣽⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣯⣤⣾⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⢿⣿⣿⣷⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣤⣄⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠓⠒⠒⠦⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡤⠴⠖⠒⠚⠉⠉⠙⢦⡀
⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠻⡗⠲⠦⠤⣤⣀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⣀⣀⣠⠤⠴⠖⢺
⠀⠙⣆⠀⠀⠀⠀⠈⠉⠉⠓⢿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡿⠚⠉⠉⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠸⡄⠀⠀⠀⠀⢠⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢳⠀⠀⠀⠀⡞⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣇⠀⠀⣸⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡄⢠⣇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠏

⠀⠀⠀⠀⠠⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠑⠂⠰⠀⠐⠒⠉⢀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⣀⣀⣄⣀⣠⣀⠀⠐⠂⠂⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀⠀⠀⢈⠔⠒⠃⠈
⠀⠀⠀⠀⢀⠁⠀⡰⠀⠀⠀⣠⡆⣀⣒⢀⠄⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⡀⠠⡐⠀⠀⠀⠈⠄⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠂⠀⢈⢠⠟⠀⠀⠉⠉⠓⠺⡄⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠔⠅⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠼⠀⢀⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠐⠀⡼⠴⠀⠠⢬⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠀⠉⠀⠀⠈⠉⠁⡤⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠴⠦⠆⠀⠔⠋⠁⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠠⠄⠀⡆⠠⢸⡀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⢄⡀⠀⠀⡈⠀⡠⠂⢀⡀⠀⠀⠀⠀⠀⠙⢄⡁⠂⠀⣀⡄⢁⠀⡀⠳⣄⠈⠀⠁⡠⡞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠢⢄⣀⢥⠚⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠀⠀⠀⠆⠙⠒⠊⣩⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣁⠀⠁⠂⣤⠐⠈⢀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣤⠒⠓⢤⡀⠀⡠⠓⣥⠤⣇⠸
⠀⠀⠀⠀⠀⡄⠒⠉⠀⠀⠀⠙⠒⠚⠑⠙⠒⠉⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠁⠂⠤⠤⠅⠀⠈⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⡇⠀⠒⠀⢰⠀⠀⡖⡆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀⡠⠂⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠁⠊⠈⠀⠁

⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⠿⣶⣶⣤⣴⣶⡾⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠛⠻⠿⠿⠿⠿⣷⣶⣶⣦⣤⣄⠀⣿⣯⠀⣠⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣄⡀⠈⠉⠉⠀⣿⣿⠀⠉⢉⣁⣀⣠⣤⣤⣤⣴⣶⣶⣶⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣈⣉⠉⠉⠙⠁⠀⠀⠀⠀⣿⣿⠀⠻⠿⠛⠛⠋⠉⠉⣉⣁⣀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⣿⡇⠀⠛⠛⠛⠛⠛⠿⠿⠿⢷⣶⣶⣦⠀⣿⣿⠀⣤⣶⣶⡾⠿⠿⠿⠛⠛⠛⠛⠋⠀⠘⠛
⠀⠀⠀⠀⣿⡇⠀⠾⠆⠠⣶⠀⢠⣦⠀⢠⡄⠀⠀⠀⣿⡿⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⣿⡇⠀⣤⣤⣤⣤⣀⣀⣀⣀⠈⠁⠀⠀⠀⣽⣷⠀⠙⠛⠋⠉⣀⣀⣀⣀⣤⣤⣤⣤⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⢷⡶⠀⣿⣿⠀⢶⡾⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠻⣿⣿⣿⡿⢷⠆⠀⠀⠀⠀⠀⠀⣿⣿⠀⣠⣤⣤⣶⣶⣶⡾⠿⠗⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣴⣿⣁⣿⣷⡀⠀⠀⣤⣶⣦⡄⠀⣿⣿⠀⠉⠉⠉⠀⣀⡀⠀⣤⡄⠠⣦⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠙⠉⠉⠛⠉⠁⠀⠸⣿⣅⣽⡿⠀⣿⣿⠀⠀⠘⠛⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠛⠋⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣶⣶⣶⣤⣄⣿⣯⣤⣤⣶⣶⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉



⣿⡫⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⢠⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢥⡬⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢡⠀⠀⠀⢠⠃⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⡄⠀⠀⡌⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢱⠀⢰⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠆⠆⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⠫⠀⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⠤⠔⠚⣉⣩⡦⣄⠀⠀⠀⠀⢊⡔⠛⠒⠀⠀⠄⠀⢀⡀⡀⢕⡣⠼⠂
⠀⠀⠐⠀⠙⠺⠯⣅⣤⣴⡖⢟⠛⠇⠂⠀⠈⠑⢦⣀⠔⠉⠀⠀⠀⠀⠀⡀⢄⣢⢕⠞⠁⠀⢘⠁
⠀⠀⠀⠉⠀⠀⠈⢻⡯⡀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢀⠠⢐⡥⠐⠉⠀⠀⠀⠀⠀⢨⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠅⠂⠤⡠⠦⢅⡂⠄⢀⣁⠠⢐⡬⢔⠬⠆⡤⢠⣠⣤⣠⣤⣤⣴⣿⣤⣤⡤⠁
⠀⠀⠘⠢⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⣶⠊⠁⠀⢸⣂⡒⣐⣘⡛⣙⣻⠛⣛⣻⡟⠛
⠀⠀⠀⠀⠀⠀⠑⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠀⠀⠀⠀⠉⠈⣠⠵⠋⠉⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⢀⠀⠀⠀⡚⠀⠁⢀⣠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⢄⣂⣕⡤⠞⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠀⠀⠉⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈⠍⠉⠭⠉⠭⠉⠅⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡋⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢙⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣷⡀⠐⠒⠒⠒⠒⠀⠀⠀⢀⣾⠟⣿⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⢈⣿⣦⡀⢀⣴⣿⡁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣦⣀⠀⠀⠀⠀⢠⣴⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⢀⣴⠟⠁⠈⠻⠟⠁⠈⠻⣦⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢈⣿⣦⡄⣠⣶⣿⡁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣦⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⠁⠈⠻⠟⠁⠈⠻⣦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣅⣤⣤⣤⣄⣤⣤⣤⣤⣌⣿⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠀⣠⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢈⡷⣄⣠⢾⡁⠀⠀⡇⢾⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠈⠻⣦⡀⠀⠀⢀⣴⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⢸⣀⡴⠋⠀⠈⠁⠀⠙⢦⣀⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⡾⠻⣦⣴⠟⢷⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣙⣉⣉⣉⣉⣉⣉⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣠⡾⠋⠀⠀⠈⠁⠀⠀⠙⢷⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠴⠶⠒⠚⢻⡿⢍⠉⠉⠉⠉⠷⣄⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠉⡠⢺⠳⠀⠀⠀⠀⢀⠆⢻⠀⠱⣄⠀⠀⢁⠈⠳⣄⠀⠀⡴⠋
⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡆⠀⢠⠊⠀⡏⠀⢣⠀⠀⢀⠎⠀⠘⡇⠀⠈⠳⣄⠘⠀⠀⠈⠳⣄
⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⣠⠞⠁⠰⢀⠔⠁⠀⢸⠃⠀⠈⡄⠀⠌⠀⠀⠀⢿⠀⠀⠀⢈⣢⣦⡤⠶⠒⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡼⠁⠀⢀⡷⠁⠀⠀⢀⡟⠀⢀⣀⣰⣜⣀⣤⣤⠤⢼⡶⠚⠛⠉⡹⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡛⠛⠛⠻⡛⠉⠉⠙⢯⠉⠉⠉⠉⢃⠀⠀⠀⠀⣸⠀⠀⠀⠠⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠑⢄⠀⠀⠈⢧⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⢠⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠱⡄⠀⠈⢧⠀⠀⠀⡆⠀⠀⢰⠇⠀⢠⠃⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⠢⡀⠈⢧⠀⠀⢁⠀⠀⣼⠀⢀⠂⣰⠋⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⡐⢄⠈⢧⠀⠘⠀⢀⡏⢀⢎⡼⠁⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⠌⢧⠀⠆⢸⠃⣬⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣷⣀⣾⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠓⠶⣄⡀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⣠⣀⣀⣀⣠⠴⠚⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡤⠖⠛⠛⠲⣼⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠻⢿⣷⡖⠋⠉⠙⠳⣄
⠀⠀⣾⠁⠀⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢸⡆
⠀⠀⢿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⢤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠞⠁
⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⢠⠄
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⢠⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⠀⠀⢸
⠳⣤⣾⠀⠀⢸⠀⠀⠀⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⡇⠀⠀⢸⠀⠀⢸⡦⠴
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠹⣄⠀⢸⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣼⣀⣀⡼⠁
⣶⣶⠶⠾⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠉⠉⣉⣉⣛⣛⣛⠛⠛⠛⠛⠛⠛⢛⣛⣛⡛⣛⣛⠛⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⢦⡀⠸⣿⡛⠛⠛⣻⣿⡿⢃⡴⢦⣄⠙⣿⣟⠛⠛⢛⣿⡿⢃⡴⣮⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⡾⠃⠈⠻⣆⠈⢷⣴⡾⢟⣡⡶⠋⠀⠀⠙⢷⣤⡙⢷⣤⣾⠏⣰⡟⠁⠈⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⣴⣿⣥⣤⣤⣤⣽⣷⡄⠉⣴⣿⣯⣤⣤⣤⣤⣤⣤⣽⣿⣦⠉⢁⣾⣯⣤⣤⣤⣤⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢰⣏⠀⣉⣉⣉⣉⣉⣉⣉⣩⡀⠀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⠀⢀⣉⣉⣉⣉⣉⣉⣩⣥⡈⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⣧⡉⠉⠉⠉⠉⠙⣷⠀⢻⡍⠉⠉⠁⠀⠈⠉⠉⠉⢩⡿⠀⣼⠁⠈⠉⠉⠉⢉⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣦⡀⠀⠀⠀⢹⣧⠈⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣰⠇⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⢷⣄⠀⠀⠈⣿⡆⢸⣷⠀⠀⠀⠀⠀⢀⣿⠏⢠⡟⠀⠀⠀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⢷⣄⠀⠸⣿⡄⢿⣧⠀⠀⠀⠀⣾⡟⢀⣿⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⠻⣦⡀⢻⣷⠸⣿⡆⠀⠀⣼⡿⢁⣾⠇⣠⣾⢿⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⢿⣾⣿⣧⢹⣿⡄⢰⣿⠃⣾⣟⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡻⣿⣿⡆⢻⣷⣿⡏⣸⣿⡿⣫⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⠈⢿⡿⠀⠿⣫⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟

⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⢸⠟⠛⠛⠛⠛⢻⡇⠀⠀⠀⣠⠴⣖⣷⠦⣀⠀⠀⠀⠀⠀⢤⠀⢀⣀⣀
⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⢻⢫⠝⡟⢹⠀⠀⠀⠀⠀⢿⠀⢀⣿⣽⡗
⠀⠀⠀⣧⣤⣤⣼⡇⠀⠀⠀⠘⠛⢛⣿⣿⡛⠛⠃⠀⠀⠀⠈⠛⢼⡤⠗⠊⠀⠀⠀⠀⠀⠉⠀⠀⠈⠗
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⣠⣾⣫⣟⣷⣄⠀⠀⠀⠀⠤⢒⣉⣉⡒⠤⠀⠀⠀⠀⠀⢘⣧⡴⢒⣆⠀⠀⠀⢰⠒⠒⡒⠒⣶⣶⡆
⠀⠀⡧⡧⠴⡧⢾⢾⠂⠀⠀⠀⠀⠡⢒⣒⠌⠁⠀⠀⠀⠀⢰⣫⣤⣿⣿⠏⠀⠀⠀⢸⠹⡇⡇⢦⣬⠍⡇
⠀⠀⠙⢿⣾⣷⣻⠟⠀⠀⠀⠀⠀⠀⢱⡦⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⡀⠀⠀⠀⠸⠤⠤⠥⠥⠶⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠠⢲⢶⣀⣶⡲⡄⠀⠀⢠⠒⠉⠀⠉⠉⠐⡄
⠀⠀⠀⣾⣿⣿⣷⡄⠀⠀⠀⢠⢀⠵⠤⠤⢎⠙⠀⠀⠀⢰⣟⠋⣾⣿⡦⢏⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡏⣿⣿⡿⠁⠀⠀⠀⠈⠛⠒⠒⠒⠒⠛⠀⠀⠀⠈⠹⡶⠾⠿⠷⡾⠀⠀⠀⠀⠉⠒⢦⠔⠀⠉
⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⡀⢀⢄
⠀⡔⠀⣲⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⢸⠄⢠⠀⠀⠀⠀⣦⣼⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠑⠠⠿⢁⠔⡠⠤⣄⠀⠀⠀⡄⠀⠉⠉⠀⢸⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠮⠥
⠀⠀⠀⠀⠃⠚⢇⡀⠿⠀⠀⠀⡇⠀⠀⠀⢠⠞⠀⠀⠀⠀⣼⣛⣿⣟⣟⡿⠀⠀⠀⠀⠀⢰⢲⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠘⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢹⣧⠀⠀⠀⣠⡾⠋⠀⠈⠻⣦⡀⠀⠀⢀⣾⠏⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢿⡆⣠⡾⠋⠀⠀⠀⠀⠀⠈⠻⣦⡀⣼⡏⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠶⠶⠶⠶⠾⣿⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⡿⠶⠶⠶⠶⢶⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠘⣷⡄⠀⠀⠀⠀⣰⡟⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡘⣿⡄⠀⠀⣴⡟⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⡄⣼⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣴⣿⣿⢋⣀⣀⡙⣿⣿⣦⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢻⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠺⡇⠀⠀⠀⠺⣿⣿⣿⠟⣿⣿⣿⣿⠻⣿⣿⣿⠗⠀⠀⠀⢸⠗⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⣧⡀⠀⠀⠀⠈⠛⠁⠀⣿⣿⣿⣿⠀⠈⠛⠁⠀⠀⠀⢀⣼⣿⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢀⣴⣿⡿⠛⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⢿⣿⣦⣴⣿⡿⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣠⣾⣿⠿⠁⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⡟⠛⡿⠛⠛⢻⠟⠛⠻⣟⠛⢿⡛⢻⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡧⠸⡇⠸⡷⢶⠀⢿⠀⣸⠀⡄⠁⣸⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣾⣷⣶⣶⣷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠃⠉⠁⢈⣦⢔⠂⠁⠀⠀⠉⠐⢢⣴⡁⠈⠉⠙⠛⢦⣄
⠀⠀⠀⠀⠀⣠⣖⣫⣋⣰⣀⣤⣒⣉⣠⣂⣀⣁⣢⣀⣀⣄⣊⣁⣈⣄⣉⣒⣤⣀⣇⣙⣝⣲⣄
⠀⠀⠀⠀⠀⠙⠧⣍⠢⡈⠳⣄⠀⠀⠈⠅⠀⠀⠀⢈⡁⠀⠀⠀⢠⠋⠀⠀⣠⠟⢁⠔⣩⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢦⡙⠷⡄⠀⠘⡄⠀⠀⡈⢁⠀⠀⢀⠂⠀⣠⡾⢋⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⢪⠢⡀⠘⡀⠀⡇⢸⠀⢀⠎⢀⠔⡕⣡⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⡈⠢⡱⠀⠄⠀⠀⣌⠔⢁⣾⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡈⢷⠀⠀⡾⢁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⣸⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢠⡇⠀⠀⠀⣀⡇⠀⠀⢀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣤⣤⣾⣧⣤⣤⣤⣿⣧⣤⣤⣧⣿⣿⣄⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢺⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟⡟⢻⠟⣿⠻⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⢀⡴⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⣿⣧⢠⡌⢸⢃⣃⢹⡇⠿⢿⠸⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣴⠀⠀⠀⠐⣿⠀⠀⢀⡅⠀⢠⡇⢰⣶⣄⡄⠠⣼⣿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣉⣵⡆⠀⠀⠴⣿⠀⠀⣾⡇⠀⢸⡇⣾⣿⣿⣷⣏⡹⣿⠀⠈⠘⣿⡇⠀⠿⢿⣿⣿⠒⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠂⢀⣴⠀⡿⣿⡃⠀⠀⠀⢺⣷⣴⣿⡇⠀⣞⣿⣿⣿⣿⣿⢏⡼⢻⡀⠀⢀⣻⣇⠠⠄⢸⣿⣿⡧⡤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢾⠈⣉⢠⣶⣿⡃⠀⠀⠀⢸⣿⣯⣀⣀⢀⠸⣵⢛⡿⣿⢏⡾⣡⠏⡼⠃⠀⣽⣿⠚⠛⢻⣿⣿⠀⠀⠀⢸⣿⠀⣀⠠⣤⡴
⠀⠀⠀⠀⢀⠀⣴⠈⣿⠀⣿⣿⣷⣄⠀⠘⢾⣿⣿⣿⢱⢏⣾⢃⡞⣰⢋⡾⣱⢏⣾⠁⠀⠀⢿⡇⠀⣐⣤⣾⡏⠄⠰⣿⡿⠛⠉⡁⡠⠤⠔
⠀⠀⠀⠀⠙⠀⢹⠀⢸⠀⣿⣿⣿⣿⢣⢶⣾⢣⢿⢧⠏⡜⣸⣏⡼⢁⠞⣰⢏⣾⣻⠀⢠⣶⣶⠃⣶⣿⣟⣭⣥⣾⣷⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⣿⣿⢿⠇⢏⠞⣼⢘⢈⡔⠘⢠⣿⠟⣰⢃⡴⣡⣾⡿⠋⢐⣻⡩⠥⠰⠸⠿⠟⠁⠀⠀⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⣿⣿⡎⠈⣎⣾⡇⡏⢸⣡⢧⣾⣃⠘⣡⠞⡴⠋⠺⠁⠁⠀⠉⠁⠀⢀⡀⡤⠄⠀⠐⠒⠐
⠀⠀⠀⠀⠰⠀⠀⠀⠚⠈⣿⣾⡃⠘⡸⠀⠀⠷⠟⢧⠋⢘⣀⣀⢀⠾⠤⠴⠒⠒⠚⠁⠁⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠘⠴⠁⠶⣖⣒⣛⣉⣉⣡⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⣞⣿⠿⠸⢩⣯⡄⠀⠉⠉⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢨⣿⣿⣿⠿⢿⣿⠏⠉⣿⡎⠉⢽⣿⠉⠀⢸⣿⠁⠀⠀⢸⣿⠆⠀⠀⠀⣻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠀⠐⣿⠄⠀⢻⡧⠀⢘⣿⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢈⡁⡐⢄
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠁⠘
⠠⠀⡶⠉⢫⠑⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠛⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⢼⣉⠀⠀⢖
⡄⢻⡤⠔⠚⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠴⠊
⠘⢦⣈⣓⣂⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⣜⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠠



⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠄
⠀⠀⢸⣄⣬⡀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠒⡂⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⡆
⠀⠀⠸⣿⣇⠇⠀⠀⠀⠀⠀⠀⢧⣀⣈⣉⡁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠳⡅⠀⠜⢀
⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠘⠛⣿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠄



⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡍⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡘⢢⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠄⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢔⠂⢹
⠀⠀⠧⠤⠭⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣒⣒⣒⣲⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣞⠡⠨⠤⢌⣳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⣤⡴⠾⠛⠉⠁⠈⠛⢶⣄⣀⣤⡴⠾⠛⠉⠁⠈⠉⠛⠳⢦⣤⣀⣠⡴⠛⠁⠈⠉⠛⠷⢦⣤⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⣀⣤⡴⣾⡿⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠻⣷⠶⣤⣀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⣀⡴⠟⢹⡇⠀⠀⠀⣀⣤⡴⠞⠛⠉⢡⡾⠋⠀⠀⠀⠙⠷⣄⡀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠙⢷⣄⠉⠛⠳⢶⣤⣀⡀⠀⠀⢸⡏⠛⢦⣄
⠀⠀⠀⣠⣾⣯⣤⣤⣬⣷⣴⣾⣿⣭⣤⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣬⣿⣦⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣽⣦⣤⣤⣤⣤⣭⣿⣷⣦⣼⣧⣤⣤⣽⣷⣄
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢷⡝⢷⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⡏⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⢫⡾⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢻⣄⠙⢷⣄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⠇⠘⣧⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⡾⠋⣠⡟⢁⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣆⠀⠙⢷⡀⠀⠈⢿⡄⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢀⡿⠁⠀⢀⡴⠋⠀⣰⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠙⣦⡀⠈⢿⡀⠀⠀⢰⡏⠀⠀⢹⡇⠀⠀⢀⡾⠁⢀⣴⠟⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣦⡈⢷⡀⠀⣸⠇⠀⠀⠸⣇⠀⢀⣾⢁⣴⠟⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣾⣷⠀⣿⠀⠀⠀⠀⣿⠀⣼⣷⠟⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣷⡏⠀⠀⠀⠀⢹⣾⠟⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠘⣧⠀⠀⠀⠀⣼⠇⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠹⣧⠀⠀⣼⠏⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣆⣰⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠉

⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣻⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡽⠋
⠀⠀⠀⠀⢸⣿⡟⠻⣿⣼⠟⠻⣿⡇⠀⠀⠀⠀⢀⣀⡀⠀⠸⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠞⠀⢀⣀⣀
⠀⠀⠀⠀⠈⢿⣇⣀⣀⣀⣀⣀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣼⣿⣿⡇⠀⠀⠀⠀⡇⠈⠳⠤⠤⠤⠏⠀⢹
⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠼


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠊
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠃⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠣⠤⠤⠴⠁⠀⡇⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠠⠃

⠀⠀⢠⣴⣞⣷⣦⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣶⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠄
⠀⠀⠶⢼⠴⠆⡧⢾⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⠀⠀⠀⠀⣿⢀⠴⠤⠞⠁⠀⠀⠀⠀⣿⢸⠳⠧⠊⠏
⠀⠀⠘⠿⢿⣿⠟⠃⠀⠀⠀⠀⠨⠧⠀⠀⠼⠅⠀⠀⠀⠀⠛⠛⠛⠛⠙⠛⠀⠀⠀⠀⢿⣠⣤⣤⣤⡄⠀⠀⠀⠀⠈⠲⠤⠴⠛⠃


⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⣄⠀⠀⠀⠀⠀⠀⣠⠤⠦⣄⠀⠀⠀⠀⠀⠰⢡⣭⣬⡌⡆⠀⠀⠀⠀⢀⣴⢖⡷⣦⡀
⠀⠀⠀⣿⡗⠒⠒⠒⠀⠀⠀⠀⠀⡇⢾⡷⢸⠀⠀⠀⠀⠀⠰⡇⠶⠶⢸⠀⠀⠀⠀⠀⢨⢐⣀⡂⡆⡇⠀⠀⠀⠀⢸⠻⢯⡀⠈⡇
⠀⠀⠒⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠨⣐⣒⣒⣃⠇⠀⠀⠀⠀⠈⠓⠦⡽⠚⠁


⠀⠀⣰⠖⠖⢶⣴⡇⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⢄⠀⠀⠀⠀⡔⠒⠒⠄⡀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⡄
⠀⠀⢸⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀⠸⡀⢀⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷⢀⡨⠀⠀⠀⠀⠷⠺⠗⠋⠉⢶⠀⠀⠀⠀⢺⣿⣶⣶⡾⣧
⠀⠀⢸⣤⣤⣼⠋⠇⠀⠀⠀⠀⠀⠀⠱⠎⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠈⠁⠀⠀⠀⠀⠦⠐⠔⠒⠖⠋⠀⠀⠀⠀⠈⠿⣿⣿⡿⠏


⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡴⠒⣶⣦⡖⢶⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⢸⠰⣯⣻⠆⡁⠀⠀⠀⢸⠀⠀⠀⠚⠘⠂⡇⠀⠀⠀⠀⡏⠉⠉⢹⠀⠀⠀⠀⠀⣯⣉⣿⣿⣏⣹⠀⠀⠀⠀⢀⠬⡒⢒⠥⡀
⠀⠀⠈⠁⠉⠉⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠳⠒⠺⠇⠖⠂⠀⠀⠀⠀⠉⠀⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⠖⠚⠛⠋⠉⣹⡟⢍⠀⠀⠀⠀⢹⠳⣄⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠉⠁⢀⠔⡿⢱⠀⠀⠀⠀⠀⡰⠁⣷⠀⠑⢄⠀⠀⠈⡀⠈⠳⣄⠀⠀⡴⠞⠁
⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡌⠀⠀⡴⠃⢰⡇⠀⢆⠀⠀⠀⠰⠁⠀⢸⡄⠀⠀⠱⣄⠀⢃⠀⠀⠈⠳⣄
⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⠀⡠⠊⠀⠀⣾⠀⠀⠘⡄⠀⢠⠃⠀⠀⠀⣧⠀⠀⠀⠈⠳⣼⣀⣀⣤⠴⢾⠗
⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⢀⡼⠃⠀⠀⣇⠜⠁⠀⠀⢠⡇⠀⠀⠀⢱⢠⠃⠀⠀⠀⣀⣹⣤⣤⠴⠶⠛⡻⠉⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣤⣤⣼⣧⠤⠤⠤⠤⣾⠤⠶⠶⠖⠒⠟⠛⠛⠋⠉⠉⢹⠁⠀⠀⠀⡰⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠐⢄⠀⠀⠀⠈⢧⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠰⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠑⣄⠀⠀⠈⢧⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠀⢠⠃⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡀⠀⠈⢧⠀⠀⠀⢃⠀⠀⠀⣸⠀⠀⢠⠃⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢦⣄⠘⢆⠀⠈⢷⡀⠀⠘⡀⠀⠀⡟⠀⢀⠃⣠⠟⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⢄⠈⢷⡀⠀⡇⠀⢸⠇⢀⠎⣴⠋⠀⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡣⡈⢷⡀⢰⠀⣼⢀⢎⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⣦⢳⡈⣀⡏⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠈⠀⠉⠀⠀⠈⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠉⠀⠀⠈⠁⠘



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣦⠀⠀⢀⣾⣆⠀⠀⢀⣾⣄⠀⠀⢠⣶⡄⠀⠀⣠⣷⡀⠀⠀⣰⣧⡀⠀⠀⣴⣦⠀⠀⢀⣼⣆⠀⠀⢀⣾⣄⠀⠀⢠⣶⡄⠀⠀⣠⣷⡀⠀⠀⣰⣧⡀
⣿⣷⣤⣾⣿⣿⣧⣠⣿⣿⣿⣦⣴⣿⣿⣿⣆⣴⣿⣿⣿⣄⣼⣿⣿⣿⣤⣾⣿⣿⣷⣤⣾⣿⣿⣧⣠⣿⣿⣿⣧⣰⣿⣿⣿⣦⣴⣿⣿⣿⣄⣼⣿⣿⣿⣤⣾
⣿⠏⠀⠻⣿⣿⠏⠈⢻⣿⡿⠃⠈⢿⣿⡿⠁⠘⢿⣿⡟⠁⠙⣿⣿⠟⠀⠹⣿⣿⠏⠀⠻⣿⣿⠋⠈⢻⣿⡿⠃⠈⢿⣿⡿⠁⠘⢿⣿⡟⠁⠙⣿⣿⠟⠀⠹
⡃⠀⠀⠀⢙⠁⠀⠀⠀⢙⠁⠀⠀⠀⣛⠀⠀⠀⠈⡋⠀⠀⠀⠈⡋⠀⠀⠀⢘⡃⠀⠀⠀⢙⠁⠀⠀⠀⢛⠁⠀⠀⠀⣛⠀⠀⠀⠈⡋⠀⠀⠀⠈⡋
⣷⡄⠀⣠⣿⣷⡀⠀⣰⣿⣧⡀⠀⣴⣿⣦⠀⢀⣼⣿⣆⠀⢀⣾⣿⣄⠀⢠⣾⣷⡄⠀⣰⣿⣷⡀⠀⣰⣿⣧⡀⠀⣴⣿⣦⠀⢀⣼⣿⣆⠀⢀⣾⣿⣄⠀⢠
⣿⣿⠶⣿⣿⣿⡿⠺⣿⣿⣿⡷⢾⣿⣿⣿⡗⢾⣿⣿⣿⠗⢿⣿⣿⣿⠖⣿⣿⣿⣿⠶⣿⣿⣿⡿⠺⣿⣿⣿⡷⢺⣿⣿⣿⡷⢾⣿⣿⣿⠗⢿⣿⣿⣿⠶⣿
⡿⠃⠀⠘⣿⡟⠁⠀⠙⣿⡟⠀⠀⠹⣿⠟⠀⠀⠻⣿⠋⠀⠈⢿⡿⠃⠀⠈⢿⡿⠁⠀⠘⢿⡟⠁⠀⠙⣿⠟⠀⠀⠻⣿⠏⠀⠀⢻⣿⠋⠀⠈⢻⣿⠃⠀⠈
⣄⠀⠀⠀⣸⡄⠀⠀⠀⣼⡀⠀⠀⢀⣤⡀⠀⠀⢀⣧⠀⠀⠀⢠⣇⠀⠀⠀⣠⣄⠀⠀⠀⣸⡄⠀⠀⠀⣼⡀⠀⠀⢀⣤⡀⠀⠀⢀⣧⠀⠀⠀⢠⣇
⣿⣦⣀⣼⣿⣿⣆⢀⣾⣿⣿⣄⣠⣾⣿⣷⡄⣠⣿⣿⣷⡀⣰⣿⣿⣧⡀⣴⣿⣿⣦⣀⣼⣿⣿⣆⢀⣾⣿⣿⣄⣠⣾⣿⣷⣄⣠⣿⣿⣷⡀⣰⣿⣿⣧⣀⣴
⣿⡟⠉⢿⣿⣿⡟⠙⢿⣿⣿⠏⠙⣿⣿⣿⠋⠹⣿⣿⡿⠋⠻⣿⣿⡿⠉⢿⣿⣿⡟⠉⢿⣿⣿⠟⠙⢿⣿⣿⠏⠙⣿⣿⣿⠋⠹⣿⣿⡿⠋⢻⣿⣿⡿⠉⢻
⠏⠀⠀⠀⠻⠋⠀⠀⠈⠻⠃⠀⠀⠘⠿⠁⠀⠀⠘⠟⠁⠀⠀⠙⠟⠀⠀⠀⠹⠏⠀⠀⠈⠻⠋⠀⠀⠈⠻⠃⠀⠀⠈⠿⠃⠀⠀⠘⠟⠁⠀⠀⠙⠟
⣧⡀⠀⢀⣾⣦⠀⠀⣠⣾⣆⠀⠀⣠⣿⣄⠀⠀⣰⣷⡄⠀⠀⣴⣷⡀⠀⢀⣼⣧⡀⠀⢀⣾⣦⠀⠀⢠⣾⣆⠀⠀⣠⣿⣄⠀⠀⣰⣷⡄⠀⠀⣼⣷⡀⠀⢀
⣿⣷⣤⣿⣿⣿⣷⢴⣿⣿⣿⣧⣴⣿⣿⣿⡦⣼⣿⣿⣿⡦⣾⣿⣿⣿⣤⣾⣿⣿⣷⣤⣿⣿⣿⣷⢴⣿⣿⣿⣧⣴⣿⣿⣿⡦⣼⣿⣿⣿⡦⣾⣿⣿⣿⣤⣾
⣿⠋⠀⠹⣿⡿⠃⠀⠻⣿⡿⠁⠈⢻⣿⡟⠁⠈⢿⣿⠟⠀⠘⢿⣿⠏⠀⠙⣿⣿⠋⠀⠹⣿⣿⠃⠀⠻⣿⡿⠁⠈⢿⣿⡟⠁⠈⢿⣿⠟⠀⠘⢿⣿⠏⠀⠙
⡁⠀⠀⠀⢹⡁⠀⠀⠀⣹⠀⠀⠀⠀⣉⠀⠀⠀⠀⣏⠀⠀⠀⢈⡇⠀⠀⠀⢈⡁⠀⠀⠀⢸⡁⠀⠀⠀⣹⠀⠀⠀⠀⣉⠀⠀⠀⠀⣏⠀⠀⠀⢈⡇
⣿⣆⠀⣰⣿⣷⡄⠀⣴⣿⣷⡀⢀⣼⣿⣧⡀⢀⣾⣿⣦⠀⢠⣾⣿⣆⠀⣠⣿⣿⣄⠀⣰⣿⣷⡄⠀⣴⣿⣷⡀⢀⣼⣿⣧⡀⢀⣾⣿⣦⠀⢠⣾⣿⣆⠀⣰
⣿⡿⠛⣿⣿⣿⡿⠺⣿⣿⣿⡟⠻⣿⣿⣿⠗⢻⣿⣿⣿⠗⢿⣿⣿⣿⠛⢿⣿⣿⡿⠛⣿⣿⣿⡿⠺⣿⣿⣿⡟⠺⣿⣿⣿⠟⢻⣿⣿⣿⠗⢿⣿⣿⣿⠛⢿
⡟⠁⠀⠈⢿⡟⠀⠀⠘⢿⠏⠀⠀⠙⣿⠋⠀⠀⠹⡿⠃⠀⠀⠻⡿⠁⠀⠈⢻⡟⠁⠀⠘⢿⠟⠀⠀⠘⢿⠏⠀⠀⠙⣿⠋⠀⠀⠹⡿⠃⠀⠀⢻⡿⠁⠀⠈
⣆⠀⠀⠀⣴⣄⠀⠀⢀⣴⡄⠀⠀⢀⣶⡀⠀⠀⢠⣦⡀⠀⠀⣠⣦⠀⠀⠀⣰⣆⠀⠀⠀⣴⣄⠀⠀⢀⣴⡄⠀⠀⢀⣶⡄⠀⠀⢠⣦⡀⠀⠀⣠⣦
⣿⣧⣀⣾⣿⣿⣦⣠⣾⣿⣿⣆⣠⣿⣿⣿⣄⣰⣿⣿⣷⣄⣴⣿⣿⣷⣀⣼⣿⣿⣧⣀⣾⣿⣿⣦⣠⣾⣿⣿⣆⣠⣿⣿⣿⣄⣰⣿⣿⣿⣄⣼⣿⣿⣷⣀⣼
⣿⠟⠉⢻⣿⣿⠏⠈⢿⣿⣿⠋⠙⢿⣿⣿⠋⠙⣿⣿⡿⠁⠹⣿⣿⡟⠁⠻⣿⣿⠟⠉⢻⣿⣿⠏⠈⢿⣿⣿⠋⠙⢿⣿⡿⠋⠙⣿⣿⡿⠁⠹⣿⣿⡟⠉⠻
⠋⠀⠀⠀⢹⠃⠀⠀⠀⢻⠁⠀⠀⠈⠛⠁⠀⠀⠈⡟⠀⠀⠀⠘⡏⠀⠀⠀⠙⠋⠀⠀⠀⢹⠃⠀⠀⠀⢻⠁⠀⠀⠈⠛⠁⠀⠀⠈⡟⠀⠀⠀⠘⡏
⣷⡀⠀⢠⣾⣧⡀⠀⣠⣿⣧⠀⠀⣰⣿⣦⠀⠀⣴⣿⣄⠀⢀⣾⣷⡄⠀⢀⣾⣷⡀⠀⢠⣾⣷⡀⠀⣠⣿⣦⡀⠀⣰⣿⣆⠀⠀⣴⣿⣄⠀⢀⣼⣿⡄⠀⢀
⣿⣿⠶⣿⣿⣿⣷⢴⣿⣿⣿⡷⢾⣿⣿⣿⡧⢾⣿⣿⣿⡦⣾⣿⣿⣿⠦⣿⣿⣿⣿⠶⣿⣿⣿⣷⢴⣿⣿⣿⡷⢼⣿⣿⣿⡷⢾⣿⣿⣿⡦⣾⣿⣿⣿⠶⣿
⡿⠃⠀⠙⣿⡿⠁⠀⠹⣿⡟⠁⠀⠻⣿⠟⠀⠈⢻⣿⠏⠀⠈⢿⣿⠋⠀⠘⢿⡿⠃⠀⠹⣿⡿⠁⠀⠹⣿⡟⠁⠀⠻⣿⡟⠀⠈⢻⣿⠏⠀⠈⢿⣿⠋⠀⠘
⡅⠀⠀⠀⣨⡀⠀⠀⠀⣨⡀⠀⠀⢀⣭⠀⠀⠀⢀⣅⠀⠀⠀⢀⣅⠀⠀⠀⢨⡅⠀⠀⠀⣨⡀⠀⠀⠀⣨⡀⠀⠀⠀⣭⡀⠀⠀⢀⣅⠀⠀⠀⢈⣅
⣿⣆⠀⣴⣿⣿⣆⢀⣼⣿⣷⡄⢀⣾⣿⣷⡀⢠⣾⣿⣧⡀⣠⣿⣿⣧⠀⣰⣿⣿⣆⠀⣼⣿⣿⣄⢀⣼⣿⣷⡄⢀⣾⣿⣷⡀⢠⣾⣿⣧⡀⣠⣿⣿⣦⠀⣰
⣿⡿⠛⢿⣿⣿⡟⠙⣿⣿⣿⠟⠻⣿⣿⣿⠏⠻⣿⣿⣿⠋⢻⣿⣿⡿⠋⢿⣿⣿⡿⠛⢿⣿⣿⡟⠙⣿⣿⣿⠟⠹⣿⣿⣿⠟⠻⣿⣿⣿⠋⢻⣿⣿⡿⠛⢿
⠟⠀⠀⠈⢻⠏⠀⠀⠈⢿⠋⠀⠀⠘⠿⠃⠀⠀⠙⡿⠁⠀⠀⠻⡟⠁⠀⠀⠻⠟⠀⠀⠈⢻⠟⠀⠀⠈⢿⠋⠀⠀⠘⠿⠃⠀⠀⠙⡿⠁⠀⠀⠹⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿
⠀⠀⠀⢠⣴⣦⣤⣤⣦⣄⠀⠤⣤⣤⣤⣤⡤⠀⣠⣴⣤⣤⣤⣶⡄⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠻⢿⣟⡛⠛⠛⠛⢛⣿⡿⠛⠛⠛⠛⠛⠻⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡇⣿⢀⠛⢸⠀⡂⢽⢡⣶⠘⡆⠁⣾⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠘⡗⠿⠧⢿⣾⣿⣗⣾⠛⣿⢜⣷⡏⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣧⣾⣼⣧⣼⣤⣥⣾⣦⣭⣾⣥⣦⣽⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠐⠂⠒⠐⠚⠙⠛⠋⠙⠛⠛⠘⠋⠓⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⢖⣒⡿⠛⠻⣿⡷⠶⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠻⠉⠉⠐⠀⠀⠀⠀⠈⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠂⢩⣽⣟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣤⣶⣿⣿⣿⣿⣿⣮⣟⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡤⠴⠖⠛⢉⣹⣴⠛⠋⠉⠁⠀⠀⠀⠈⠉⢉⣷⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣯⣿⠁⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠚⠉⠀⠀⠀⠀⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⢀⣠⡴⣟⢿⣗⢛⡳⣄
⠀⠀⠀⢀⣤⡾⠛⠋⠛⣿⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⡅⠉⢸⡌⠛⢏⡛⣷⣄
⠀⢀⡴⠋⠄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠺⣿⣇⠀⠀⠤⠄⣀⣀⣄⣀⡀⠀⢤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣶⣴⣤⣀⡘⡇⠀⠀⠀⠈⢮⠳⣄
⣴⠋⠀⠀⠀⠀⠀⠀⡶⡏⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢀⣩⣽⣿⣿⣿⣿⣿⣟⠛⣋⠍⣿⣿⠿⣛⡹⠵⠛⠋⢽⢟⡷⠄⠀⠀⠀⢈⢧⠈⢳
⡇⢀⣡⡠⠐⠉⠀⡐⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⠾⠓⠀⠌⡔⠀⠀⠀⠀⠁⡇⠡⡀⠀⠑⠢⣬⣷⢸
⣿⠋⠁⠀⠀⠀⠌⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⣧⠀⠀⢼⣿⡿⠿⠛⡟⠋⢙⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡄⠀⠠⠜⢉⣿
⠈⠳⣌⠂⣀⠂⠀⠀⠀⢿⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⢴⡧⠀⣸⣿⣿⣿⣿⣿⣿⣷⣦⣀⠁⠀⠀⠀⢠⡅⠀⠀⠾⣆⣡⣠⡾⠋
⠀⠀⠈⠳⣼⡗⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⢶⣖⠂⠀⠂⣻⠑⣹⣿⣿⣿⣿⣿⡿⣗⣉⢿⣿⣷⣤⡀⠀⢘⠀⢠⠦⣄⣫⡿⠋
⠀⠀⠀⠀⠈⠻⣿⣶⣦⣬⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣏⣼⣿⡿⠉⣈⠼⠿⢻⢫⠟⢮⢟⠻⣿⣿⣷⣦⣴⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⣿⣷⣶⣦⣤⣄⣀⣚⣒⡒⠀⠠⠀⠄⠙⢿⣞⣽⣿⠿⠄⠥⠤⣤⠤⣀⢷⣾⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⡻⣯⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣺⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡘⣎⠻⣟⢻⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠳⡀⠰⣵⡿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣌⡀⠀⠑⠉⠻⣶⣨⣿⢿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⡿⣋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠠⠘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠛⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣬⣩⣤⣭⣽⣭⣼⣏⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡌⠛⠓⠀⢸⣿⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠠⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⡀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⣇⠆⣔⣻⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⡇⠘⠐⠛⠉⠃⠘⠁⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⡄⢸⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣿⣿⣿⣿⡇⠀⡀⠀⡄⠀⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠀⠀⠀⢸⣄⣧⣇⣸⣂⣜⣀⣞⣰⣶⣀⣸⣀⣐⣇⣧⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡅⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣻⣿⣿⠁⠸⡇⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣩⣉⣄⣤⣿⣿⡿⠀⠀⠇⠁⠙⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⢿⠿⠀⢸⣿⣧⠀⠀⡇⠀⠃⠀⡤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠊⠁⠀⢛⡧⣼⣿⣿⠀⠀⣇⠀⠀⠀⠒⢃⡤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⣀⣠⠄⠀⣔⣯⡄⣾⣿⣿⡀⠐⣿⠀⠀⣠⣾⠟⢒⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢉⣞⢃⣼⣻⡟⢻⣿⣿⣷⢠⠀⣿⡾⣹⡿⠛⠂⠄⠉⠙⢷⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢴⠸⡋⣾⣷⣿⣽⣷⣿⣿⣿⡆⠀⣿⣿⣿⡀⢛⣷⣤⡌⣠⠀⠈⠠⡀⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣄⣶⣿⡿⠛⢫⣙⣿⣿⣿⣿⡃⠀⣽⣿⣿⣥⣬⡼⠋⣀⡋⠁⠂⠀⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠹⡿⠡⣆⠐⡀⢨⣿⣿⠟⠛⠓⢀⣼⣿⠿⠛⠉⠉⠁⠀⡐⠠⢤⠈⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠉⠑⡧⢨⣿⡇⠀⠀⠀⠨⢾⣧⢞⣩⠄⠀⠀⠀⡌⠰⠤⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠶⠒⣓⣶⣦⣴⣦⠘⣿⠀⠀⠀⠆⠀⠚⢟⣋⣠⡴⠂⠀⠀⠘⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠥⠶⠒⠋⣀⠙⡇⢀⠀⠀⠀⠀⠈⠿⠷⠞⣋⣠⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠍⠁⠀⠀⠀⠀⠀⠀⠈⠉⠷⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠻⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣄⠙⠿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣠⣼⠟⠃⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠟⢃⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⣿⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡆⠈⣁⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠄⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⣀⡀⣀⠀⢀⡀⢀⢀⠀⢀⠀⣀⠀⣀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠸⡤⠇⠽⠸⣿⠇⢧⡼⠨⠯⠀⠸⠸⣤⠸⣥⠗⠟⠾

⠀⠀⠀⠀⠀⢀⣀⣤⣠⣀⣠⣀⡀⠀⠀⠀⣰⡖⡶⡖⢲⢶⢲⣆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⡯⠽⣾⠥⠬⣶⠧⢵⠄⠀⠰⡗⠛⠓⢺⡗⢺⠟⢺⠆⠀⢠⡞⢩⣦⣮⣽⣤⢤⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⠇⡴⠃⠀⠀⠀⠘⢦⠀⢸⠇⡜⡴⠃⠀⠀⠀⠙⢦⡈⡆⢰⠃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣧⣾⠊⠀⠀⠀⠀⠀⠀⠀⠳⡀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠑⢿⣾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣞⣧⣏⣣⣀⣀⣼⣳⡀⠀⠀⣠⠶⡒⡶⢶⢒⠶⣄⠀⠀⠀⣠⣞⣁⣀⣙⣮⣳⣄
⠀⠀⠀⠀⠈⢣⡘⡇⢸⡅⠸⢣⡞⠀⠀⠘⢿⡋⠉⠉⠉⠉⢉⡿⠁⠀⠀⠹⣽⡏⢸⡇⢨⣫⠋
⠀⠀⠀⠀⠀⠀⠙⣼⣸⣇⣰⠋⠀⠀⠀⠀⠀⠙⢦⠀⠀⡰⠋⠀⠀⠀⠀⠀⠈⢿⠸⡇⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠽⣦⠤⠤⣼⢽⡦⠀⠀⢀⣞⣹⣄⣀⣀⣠⣏⣳⡀⠀⠀⣒⣁⣸⣋⣙⣏⠲⣄
⠀⠀⠀⠀⠀⠈⢢⡹⡀⢠⠳⠦⣤⠀⠀⠀⠑⢄⢳⠀⠀⡎⡠⠊⠀⠀⠀⠹⣍⠹⡉⢉⡏⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⣼⠞⠁⠀⠀⠀⠀⠀⠈⠳⣧⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣀⣤⣶⡿⠸⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⣐⣒⣒⣒⣒⡂⠤⣄⠀⠀⠀⠀⠀⢀⣤⢴⣿⣿⡟⣛⢻⣿⣿⡧⣠⡀
⠀⠀⠀⠀⢠⣝⢋⣵⣾⣷⣮⣝⢫⣵⠀⠀⠀⠀⠀⣔⣁⡈⢆⣀⠔⠉⠑⢄⢀⠞⢀⣑⡄⠀⠀⠀⢻⣛⣳⡙⢛⠾⠿⠷⡝⢋⣾⣟⡟
⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠈⠢⡀⠉⠩⠀⠉⠉⢹⠉⠉⡡⠊⠀⠀⠀⠀⠀⠙⢿⣿⡽⣿⣿⣿⢯⣿⡿⠋
⠀⠀⠀⠀⠸⣫⣜⡻⢿⡿⠟⣫⣜⡻⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢇⠀⢀⠇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹⣿⣏⡿⠋
⠀⠀⠀⠀⠀⠉⠛⢿⣷⢰⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣄⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠇⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠇⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠉⠒⠀⡠⡤⠄⠐⢒⣒⠒⠀⠤⣤⡀⠐⠊⠀⠀⠀⠉⠂⠀⣠⣠⣶⣶⡖⡒⣶⣶⣦⣀⡀⠒⠁⠀⣠⣶⣾⣻⣿⣿⣿⣿⣻⣿⣶⣄
⠀⠀⠀⢮⠄⢈⣦⣠⠊⣈⢢⣠⠌⡀⠸⠆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⢋⣾⣿⣯⢛⣿⣻⠏⠀⠀⠀⠹⣿⡟⣿⣿⣿⣿⣿⡟⣻⣿⠟
⠀⠀⠀⠀⠑⢄⠀⢣⠀⠀⢠⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠑⠄⠄⢀⢆⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠘⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠃⠀⠀⢀⡖
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠈⣀⣀⣀⣀⣀⣀⡈⠀⠀⠀⢀
⠀⠀⠉⠀⠀⠚⠠⠄⠀⠀⠀⠤⠐⠃⠀⠀⠉⠀⠀⠈⠁⢀⣴⣾⣽⣿⣿⣿⣿⣿⣿⣶⣄⠈⠁
⠀⠀⠀⠙⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣽⡛⢿⣿⣿⣿⡿⡷⢿⣻⡿
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣿⣿⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠈⠂⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠙⠛⠿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⢀⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡛⠁⠀⠀⠀⠀⠀⠛⣿⣟⠋
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠐⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆



⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣦⡀
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢣⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣧
⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣭⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⠎⣀⣀⣀⠤⠤⠶⣚⡉⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠛⠛⠉⠽⣶⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠋⢁⣀⣀⣀⣀⣀⣀⣀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢼⣿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⢸⡿⠿⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⢀⣤⡀⣠⣤⣠⣤⡤⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢸⡿⠛⣿⣽⢧⣽⠇⠸⠇⢀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡷⣾⣷⠀⢀⣀⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠘⠃⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠉⠛⠿⣿⣿⣧⡶⠶⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡏⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⡾⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇⣠⢤⣴⡶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣾⣿⣷⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣿⢿⠿⠿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⠩⠀⠠⠑⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣾⣷⡆⠀⠀⠀⠀⠀⢠⣤⠶⡶⢶⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⠂⡒⠲
⠀⠀⠀⠀⡐⡄⣦⡄⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⡇⠀⠀⠀⠀⠀⠈⢩⣿⠩⡯⣻⣎⠉⢱⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⠀⢸
⠀⠀⠀⠀⠡⠁⠈⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢀⡇⠀⠀⠀⠀⠀⠀⠿⠿⠷⠾⠿⠿⠖⠃⠀⠀⠀⠀⠀⠀⡸⠅⠤⠤⠼⣀⠌
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣶⣾⣿⢶⣤⢀⠀⠀⠀⠀⠀⠀⢰⠶⡐⠂⠒⢂⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⢿⣿⣭⣿⣽⣿⠃⢱⠀⠀⠀⠀⠀⢸⠀⠈⠲⠞⠁⣠⣾⣎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⣀⣭⣯⣄
⠀⠀⠀⠀⠀⠿⠟⠫⣡⠒⠁⠀⠀⠀⠀⠀⠘⠏⠀⠠⢀⡸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡸⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠆⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃



⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⡄⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠠⠐⠒⣦⡀⠀⠀⠀⠀⠀⠀⡖⠂⠒⣀⠂⠒⢲
⠀⠀⠀⠀⣿⣿⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣘⣟⣁⠀⢃⣙⣟⣁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⣽⡇⠀⠀⠀⠀⠀⢀⡥⡄⠠⠿⠄⠀⢸
⠀⠀⠀⠀⣍⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠺⠿⠿⠿⠂⠀⠀⠀⠀⠀⠿⠷⠶⢤⡤⠤⢼⠅⠀⠀⠀⠀⠀⠸⣿⠟⡿⢿⠿⠟⠛



⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠰⡶⠀⠼⠧⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⡛⢍⠉⠉⣉⠝⡇
⠀⠀⠀⠈⠉⠀⣈⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡘⡐⢛⡘⢰⠀⠀⠀⠀⠀⠀⠀⠃⡀⠑⠚⢡⢖⡲⡄
⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣭⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠀⠂⡛⠛⣰⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠂⢣⣛⡓⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠛⡲⠀⠋⢭⡬⠉⠰⢦⠴⠈⠡⣬⠍⠃⠴⡚⢻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠃⣔⠡⠀⠿⠀⠀⢱⢄⢰⢀⠴⠀⠀⠸⠃⠠⢑⡄⠁⠹⢦⡀
⠀⠀⠀⠀⠀⠀⣞⠁⠨⢐⠐⠃⡀⠀⠀⢡⣤⣂⠄⡛⡃⢄⣢⣠⠁⠀⠀⡀⠓⠐⠠⠀⢉⡆
⠀⠀⠀⠀⠀⠀⠙⢷⡲⣿⠄⣣⣉⢤⡀⠐⠛⢄⡀⠀⠀⣀⠜⠓⠀⣀⣈⣡⡃⢼⡧⣲⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⡀⠀⠈⢯⠉⠉⠉⠉⢹⠉⠉⠉⠉⢩⠏⠀⠀⡰⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣦⡀⠀⢣⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⣠⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠳⡀⠀⢸⠀⠀⡰⠃⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡱⡀⢸⠀⡰⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣼⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡇⣠⣿⣀⣶⡟⢡⣾⠋⠁⣾⡿⢀⣴⣾⡆⢠⡾⠆⢰⡆⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠟⠋⠈⠛⠋⠉⠉⠉⠀⠈⠃⠀⠀⠉⠛⠛⠛⠈⠳⠚⠛⠛⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠖⠶⢀⡀⣀⣤⠀⣠⣤⠀⣼⣇⡀⠀⣀⣀⡀⠀⢀⣀⠀⠀⣉⣛⠛⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣀⢀⣼⠿⣯⡀⢸⣇⣀⣴⣿⠟⣧⣸⣏⣽⣇⣰⡟⠹⣆⣾⣏⣽⡇⢸⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠀⠀⠈⠉⠀⠉⠉⠀⠁⠀⠈⠁⠉⠁⠈⠁⠀⠀⠈⠉⠈⠀⣷⠀⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠷⠶⠿⠶⠶⠶⠶⠶⢤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⢀⣄⠘⢿⣆
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⡦⠀⣿⡇⠀⣤⣄⢀⣴⡿⠋⠀⢸⣿⠀⢴⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠛⠿⠋⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿
⠀⠀⠀⠀⣿⡇⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⡀⠀⠀⠀⠀⢀⣤⣾⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠙⢿⣶⣤⣤⣶⡿⠋⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣧⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣼⣿
⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠀⠀⠀⠀⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⠶⠶⠶⢾⣿⠀⠀⠀⠀⣿⡷⠶⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣀⣀⣀⣀⣿⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⢸⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⡇⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣁⣀⣀⣀⣠⣀⣿⣧⣀⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢀⣀⣸⣿⣀⣄⣤⣄⣀⣀⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣦⣤⣴⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠿⠿⠟⠋⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣅⠋⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢸⡶⠀⠀⠀⢀⢠⠴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣿⣿⡟⠉⠑⠒⠒⠒⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢹⣿⡿⠀⡀⠁⠀⠀⠀⠀⢀⣴⣿⣿⣦⣀⠀⠀⠀⠀⡈⠀⠀⠀⢸⡇⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣼⡿⢁⡀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣷⣤⡀⣰⠀⠀⢀⠀⢠⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠈⠀⠐⠾⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠋⠀⠁⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠰⠀⠀⣀⠀⠀⠀⠠⠁⡀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⣦⡂⡠⠀⠞⣀⠄⢊⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠘⣧⣷⠄⠘⡋⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⣿⣥⡔⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄
⠀⣰⣿⣿⣿⣆⠀⠀⣰⣿⣿⣿⣆⠀⠀⣰⣿⣿⣿⣆⠀⠀⣰⣿⣿⣿⣆⠀⠀⣰⣿⣿⣿⣆⠀⠀⣰⣿⣿⣿⣆
⢼⣿⣿⣿⣿⣿⡧⢼⣿⣿⣿⣿⣿⡧⢼⣿⣿⣿⣿⣿⡧⢼⣿⣿⣿⣿⣿⡧⢼⣿⣿⣿⣿⣿⡧⢼⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⡟
⠀⠀⠹⣿⠏⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⠹⣿⠏
⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⡀
⠀⢠⣾⣿⣷⡄⠀⠀⢠⣾⣿⣷⡄⠀⠀⢠⣾⣿⣷⡄⠀⠀⢠⣾⣿⣷⡄⠀⠀⢠⣾⣿⣷⡄⠀⠀⢠⣾⣿⣷⡄
⣰⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⠃⠘⢿⣿⣿⣿⣿⠋⠘⣿⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣿⠃⠙⣿⣿⣿⣿⣿⠋⠘⣿⣿⣿⣿⡿
⠀⠈⢻⣿⡟⠁⠀⠀⠈⢻⣿⡿⠁⠀⠀⠈⢿⣿⡟⠁⠀⠀⠈⢻⣿⡟⠁⠀⠀⠈⢿⣿⡿⠁⠀⠀⠈⢻⣿⡟⠁
⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⠀⣋
⠀⢀⣼⣿⣧⡀⠀⠀⢀⣼⣿⣧⡀⠀⠀⢀⣼⣿⣧⡀⠀⠀⢀⣼⣿⣧⡀⠀⠀⢀⣼⣿⣧⡀⠀⠀⢀⣼⣿⣧⡀
⢠⣾⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣷
⠻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿
⠀⠙⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⠋
⠀⠀⠈⠿⠁⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠈⠿⠁
⠀⠀⣰⣿⣆⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⣰⣿⣆
⢀⣼⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣧
⢾⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⠟
⠀⠀⠙⣿⠋⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠙⣿⠋
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣟⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⠿⢷⣶⣄⡀
⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡾⠿⠟⠛⠋⠉⣡⡴⠛⠁⠀⠀⠈⠙⠻⢿⣶⣤⡀
⣤⣶⡶⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣷⣦⣄⡀
⢹⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠀⠀⠀⠀⣀⣀⣠⡤⠴⠶⠒⠛⠉⣩⣿⢿⡟⠙⠻⢷⣦⣄⡀
⠈⣿⡄⠉⠻⣷⣦⡀⠀⣠⣖⣋⣠⣤⠤⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⢀⣴⡿⠋⠀⣼⠁⠀⠀⠀⠈⠙⠻⢷⣦⣄⡀
⠀⢹⣧⠀⠀⠀⠙⠿⣿⣏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄
⠀⠘⣿⡀⠀⠀⠀⠀⣿⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣦⣄
⠀⠀⢻⣇⠀⠀⠀⠀⣿⠀⠀⠈⠛⢿⣦⣄⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣹⡿⠉⣇⠈⠛⢿⣦⣀
⠀⠀⠸⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠻⣷⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⢰⣿⠁⠀⣿⠀⠀⠀⠈⠛⢷⣦⣀
⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⠋⠻⢷⣦⣄⠀⠀⠀⠀⢀⡟⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢠⣿⠃⠀⠀⢹⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⢸⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠛⠿⣶⣄⡀⣼⢁⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠈⣿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⢸⣷
⠀⠀⠀⠀⢻⣇⠀⠀⠈⡇⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠉⠻⢿⣦⣄⡀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⠃⠀⠘⣿
⠀⠀⠀⠀⠘⣿⡀⠀⠀⣇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣰⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠃⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠈⠉⠛⠻⢿⣶⣦⣄⣀⠀⣧⣰⠃⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⡀⠀⠀⣼⡇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠁⠀⠈⠙⠛⠿⣷⣦⣤⣀⣻
⠀⠀⠀⠀⠀⠀⠘⣿⡄⢸⡇⠀⠀⣿⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⡇⠀⢸⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⣸⡇⠀⠀⢠⡞⠀⠀⠀⠀⣠⣴⡟⠋⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣇⠀⣿⠇⠀⢀⡞⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⣀⣠⣴⣶⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⢸⣿⠀⢠⡟⠀⠀⣠⣾⠟⠁⠀⠀⣀⡤⠖⠋⠁⠀⣀⣠⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⡏⢀⡞⢀⣠⡾⠟⠁⢀⣤⠶⠋⣁⣠⣤⣶⡾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢇⣞⣴⡿⢋⣠⣴⣞⣭⣴⡾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣶⣿⠿⠟⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣟⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⣻⢿⠛⡻⢻⠟⢛⣿⢟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡾⠿⠿⠿⠿⠿⠿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⣼⡟⠁⠀⠀⢰⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣶⣄
⠀⠀⣼⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣷⣄
⠀⢠⣿⠇⠀⠀⠀⠀⠀⢈⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣋⠀⣋⣉⣉⣉⣉⣉⣉⣉⣉⣭⠀⠀⢠⣿⣿⣿⣿⡿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠋⠉⢹⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠸⣿⡀⠀⠀⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⡟
⢀⣀⣿⣷⣶⣶⡆⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⠃
⠹⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠓⠛⠛⠿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠀⠀⠀⢠⣿⠏
⠀⠈⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⠿⠟⠛⠉