Barber Emojis & Symbols

⠀⢂⡰⠀⠀⠀⠀⢸⣇⠀⠀⣩⢞⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠁⠀⠀⠘⣾⡿⠀⠀⠙⠋
⠀⠈⠁⠂⠀⠀⠰⣼⣿⠀⠀⢴⣯⠇⠀⠀⠀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠾⣷⠄⠀⠀⠀⠙⡇⠀⠀⢀⣿
⠀⡴⣶⡄⠀⠀⠀⠻⡇⠀⠀⠀⣀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣾⡇⠀⠀⢊⡴⡃⠀⠀⠀⠀⠃⠀⠀⢠⣿
⠀⢞⣵⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⡠⠁⡀⠀⠀⠀⢸⣇⠀⠀⣩⢞⡅⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣫⢾⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠈⠨⠮⡈⠀⠀⢠⣸⣿⠀⠀⢴⣯⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⣵⣻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⢿⡟⠀⠀⢀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⡆
⠀⠈⠉⠀⠀⠀⠀⠆⠀⠀⠀⠈⣉⡀⠀⠀⢋⠿⡃⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡐⠁⠀⠀⠀⠀⢹⡇
⠀⢸⣿⠀⠀⠀⢠⠃⠀⠀⠀⠀⢿⡇⠀⠀⡡⢚⡅⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠊⠩⢎⡁⠀⠀⢠⣸⣧
⠀⢸⣿⠀⠀⡐⢓⡜⠂⠀⠀⠀⢸⣷⠀⠀⠔⣫⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠃⠀⠀⠸⣼⣿⠀⠀⠺⠷⠃⠀⠀⠀⡄⠀⠀⠀⠈⣉⡀⠀⠀⢚⡿⠂⠀⠀⠀⠈⡇
⠀⠈⠋⠀⠀⠀⠴⣷⠄⠀⠀⠀⠹⡟⠀⠀⠀⣤⠀⠀⠀⢀⠆⠀⠀⠀⠀⣿⡇⠀⠀⣩⢞⡁
⢀⠀⣿⡇⠀⠀⢚⡵⠂⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⠬⡠⠄⠀⠀⠀⢸⣇⠀⠀⠴⣫⡄
⠀⡀⢿⡇⠀⠀⣩⢞⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠑⠄⠀⠀⠸⣼⣿⠀⠀⠺⡷⠃⠀⠀⠀⡄
⠀⢠⣸⡇⠀⠀⢴⣯⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣠⣦⡀⠀⠀⠀⠻⡇⠀⠀⠀⣤⠀⠀⠀⠀⠆
⠀⠈⢿⡇⠀⠀⠀⣁⠀⠀⠀⠐⠂⠀⠀⠀⠀⣤⡄⠀⠀⡴⣫⡄⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⢌⠠⠄
⠀⠀⠈⠇⠀⠀⠀⣿⠀⠀⠀⠘⠁⠀⠀⠐⠀⢻⣇⠀⠀⢞⡵⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠐⠑⠄
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠔⢣⡜⠂⠀⠀⢀⢸⣿⠀⠀⣫⣞⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠇⠀⠀⠈⣾⣿⠀⠀⠈⠋⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⡄⠀⠀⡵⣫⡅
⠀⠀⠄⠀⠀⠀⠈⣉⡀⠀⠀⠾⣿⠆⠀⠀⠀⠘⡇⠀⠀⠀⣿⠀⠀⠀⢠⠃⠀⠀⠀⠀⢻⡇⠀⠀⢞⡵⠆
⠀⠰⠂⠀⠀⠀⠀⣿⡇⠀⠀⢚⡵⡇⠀⠀⠀⠀⠁⠀⠀⢠⣿⠀⠀⠔⠓⡜⠂⠀⠀⠂⢸⣧⠀⠀⣫⣞⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠛⠉⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⢁⣀⣀⡀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠞⠂⠈⢁⡤⠀⠘⣿⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠚⣰⠀⢀⠀⢀⠠⡉⠐⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢓⡶⢽⡲⡶⠑⠘⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣴⣶⣶⣤⣤⡀⠀⠘⢦⡓⠀⠚⢁⠀⠀⠀⠀⠀⢀⡷⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠀⠀⠉⠙⠛⠻⣷⣦⡀⠙⢦⡁⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠴⠆⠀⠀⠤⣄⠀⠀⢿⣿⣿⢀⡤⠟⠲⢤⣤⠴⠚⠁⠀⠀⠀⠀⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢴⢀⠀⠀⣄⠈⠀⠀⠸⣿⣿⢯⡤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣓⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠾⣡⢤⠀⠁⠀⠀⠀⠀⠙⠙⣷⢍⣻⠅⡉⠉⠒⠲⠤⣄⣀⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠘⠿⣖⣩⠿⠂⠀⠀⠀⣼⡛⠛⠁⠉⠓⠶⠔⠲⣞⠒⠶⢴⡇⠈⠉⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⢋⠲⣦⣤⡴⠒⠒⠻⢤⣉⡽⠃⠀⠀⠀⢠⠔⠚⣦⡀⠈⠉⠛⠒⠲⠦⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⡀⠙⠒⠀⠒⠈⣀⠄⠀⠪⠭⣓⢦⡄⠀⠉⠀⠈⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠉⠒⠢⠤⠤
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠱⡐⠒⠢⠤⠤⠤⠤⠶⠒⠋⠁⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠺⢧⣄⡀⠀⠀⠈⠑⠦⢤⣀⡀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠈⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣠⣤⡀⠀⢤⣤⣤⠄⠠⣤⣤⣄⠀⢀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠘⣿⣛⣷⠀⢸⣯⣽⣧⠀⢸⡷⠆⠀⢸⣿⣶⡟⠀⢿⣭⡉⠀⣿⣃⣀⣿⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡶⢿⣦⠀⠀⣼⣿⣧⠀⠀⣿⠉⣿⡀⢸⣷⣶⠿⠁⠸⠷⠶⠇⠸⠇⠸⠷⠀⢶⣼⠟⢀⣿⠙⢻⡇⢰⡟⠁⢹⡇⢀⣿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣻⡇⠀⠿⠉⠙⠃⠀⠉⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡁⠀⠙⠁⠈⠻⠶⠟⠁⣸⡟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⣀⣠⠤⠴⠖⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⠦⢤⣀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⡀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣿⣿⡟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠁⠀⠀⠑⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠀⠈⠁⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠫⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠝⠁⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠨⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⠢⠄⠈⢠⠀⠀⡠⠗⠁⠀⠀⠀⢐⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠕⠀⠠⠪⠂⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣀⡀⣀⡠⠬⠭⣥⡄⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠠⠼⠓⡉⢠⡆⠀⠀⠀⠙⣴⠟⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⣀⣄⣦⠸⡧⠈⣻⠂⠀⠀⢀⣇⢐⠆⠈⠀⢠⣴⠘⢧⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠾⠟⠁⢀⡠⡄⠀⣿⣝⢿⠀⠛⠁⣠⡶⠶⠶⠟⠋⠀⣀⢰⡸⡇⠹⡄⠘⠁⠀⣠⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠠⣿⡘⣗⢷⠀⠋⢉⡤⠐⣫⡾⠋⠀⠀⠀⠀⠀⠐⣇⡈⠳⠛⠀⢀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠸⠃⠉⢀⣠⠔⣉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠠⢄⠉⠢⣑⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⢴⣾⠟⢋⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡙⠳⣿⡷⢉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⣈⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢟⣥⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣓⣧⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⣠⣤⠀⠸⣿⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠭⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡏⠋⠀⠓⠤⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⣈⡶⠁⠀⠀⠀⠀⠀⠀⡠⠊⢁⡫⢹⣿⣧⣢⠤⠀⠀⠀⠀⣸⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠓⠀⡇⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⣴⠂⢾⣿⣯⠁⠈⠀⣀⡾⢁⠏⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠠⢀⡀⠀⠋⠀⠀⠀⠀⠀⠀⣻⠀⠉⢻⠿⣷⡶⣞⡋⠀⢀⠀⠁⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⣴⡶⢿⠿⣿⣿⣶⡀⢀⣴⠃⢀⡀⠈⠀⠈⠟⠹⡇⠰⠃⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠻⠿⢿⠿⠿⠿⠛⣿⡋⠁⠀⠈⣹⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠃⢐⡆⠄⠀⢴⡀⠂⠈⣏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣨⣄⢀⡀⠤⠀⠀⠀⠀⠀⠀⢸⡾⣇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⠀⠠⣤⠔⠀⠀⢸⡝⢩⣟⠂⠁⠀⠀⠀⠀⠀⠀⠈⢷⢙⡀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡌⠀⢶⠂⠒⠚⢀⣿⣿⣎⣻⡇⠀⠀⣇⠀⠀⠀⠀⠀⢈⣟⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⣀⣀⣀⣴⠋⣿⣿⣿⣽⢿⣤⣀⠀⠉⠉⠁⠐⠒⠚⠫⠴⠶⠶⢦⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⡻⠿⠟⠋⠁⣠⣿⢿⢻⣿⡸⣿⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣇⠹⣯⠁⣀⠠⢥⡟⡟⠈⢸⡟⠻⢿⣿⡧⢸⢛⢻⣷⣦⣤⣀⠘⠚⠶⢆⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⡟⠹⡇⢻⡄⠹⡆⢠⡴⠋⡜⠁⠀⢸⢿⠀⠀⠛⠿⣾⣿⣿⡞⢻⢿⠋⠙⠓⠲⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠃⠆⢸⠇⠀⣧⠈⢷⠀⠙⠀⠀⠈⢠⠆⢠⠇⢸⠀⠀⠀⠀⠀⠙⢿⣗⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⡄⠀⠘⠀⠈⠀⠀⢀⣠⠶⠁⢠⠎⠀⠸⠀⠂⠀⠀⠀⠀⠀⠙⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣧⠀⠠⣄⡀⠀⠺⠛⢁⠠⠊⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠉⠀⠀⠋⠁⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠊⠁⠠⠞⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠄⠤⠀⠀⠤⠀⢖⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠐⠁⣤⠶⠦⠀⠀⠀⠀⠀⣤⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⢀⠂⢹⡠⠀⠀⠂⠐⠄⠀⠀⠀⠠⠄⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⡀⢰⡇⠙⠁⠀⢠⣾⣿⡆⠀⢠⢠⣴⣶⣼⠀⠀⠀⠀⢠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠀⡄⠀⠀⠀⠀⠉⠁⠀⠀⡈⢳⠉⠉⡁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⡼⠁⠄⠀⠀⠀⠀⢠⡀⠀⡉⠉⠀⡰⠀⠀⠀⠀⢠⣬⠍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠘⠀⠀⠈⠢⡀⠀⠀⠀⠀⠙⠁⢀⠜⠀⠀⠀⠀⠀⢩⠖⣒⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡄⠀⢠⠀⠀⠀⠻⠐⡤⠤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠈⠯⣥⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡣⠖⠀⠲⡀⢁⠀⢀⣑⡒⣲⣡⣄⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡱⠁⠀⠀⠀⢱⠀⠞⠁⠀⠉⠁⠀⡏⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⡈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠃⠀⠀⠀⠀⠸⠀⠀⢁⠀⠀⠀⠀⠇⠀⠀⠀⠉⢢⠄⣤⠤⠀⠀⣔⡡⠿⠠⠧⠼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢆⠀⠀⡀⠀⠀⠀⠀⠠⠂⣰⠃⠰⣀⡙⢤⣡⠷⢛⣡⡌⡁⢘⠛⠳⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁⠈⠀⠳⢄⠀⠐⢁⣴⠇⠀⠀⣢⢴⡶⠋⢔⠉⡍⣿⣿⠊⢗⢄⠑⠻⣷⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢀⡩⠖⠉⠀⠀⣀⣐⠖⣿⢡⠜⣡⠎⠀⣿⡝⠀⠈⠳⣄⠢⢨⠇⢂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡀⠀⢀⠔⠀⢀⠤⢇⠀⣀⡠⠔⠋⠁⠀⠀⠀⡠⠊⠀⠀⢸⣷⡷⠚⠥⠆⠀⣿⠇⡇⠀⠀⠾⠹⠂
⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠐⡄⠀⡠⠊⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠠⣇⣇⠀⣴⣿⠆⠆⠀⡇⣼⣿⠗⠀⠀⣶⡴⡆
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⢈⠞⠑⢦⡀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠈⣈⣿⠀⠉⠉⠄⢀⠄⠀⠈⠉⠀⠀⠀⡟⡄⠃
⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⢀⠔⠁⠀⠀⠀⠙⠲⠤⡤⠴⠚⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣆⠀⠀⠀⠈⣀⠄⠀⠀⠀⢀⡜⠻⣜⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡟⡏⠑⣠⣀⣀⠀⠀⣀⡀⠰⣁⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡴⣿⠋⣼⠆⠙⠛⠻⢤⣤⡼⠁⠀⠹⠓⣀⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠣⡌⢂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣴⣶⠀⠀⠀⠙⠉⠀⣠⣤⠀⠈⢦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⡀⠃⠈⠄⠀⠀⠀⠀⠀⠀⠔⢠⣀⠈⠈⠀⢼⣶⠀⠀⠀⠙⠛⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣡⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣁⣀⣀⣀⣈⡀⠀⠀⠀⠀⠜⠀⠹⠛⠀⠀⠀⠈⠀⠀⢤⣶⠆⠀⠀⠈⠛⠃⠃

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢠⣤⣄⠀⠀⢀⢀⡀⢀⡤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠄
⠀⠀⠀⢰⠟⢋⣩⠀⠀⡇⠀⡱⢮⠀⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢋⣡
⠀⠀⠀⢰⡾⠟⢛⠀⠀⠀⢀⠀⠀⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⢋
⠀⠀⠀⢨⣴⡾⢿⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⠢⠀⠀⠀⠌⠀⠀⠀⢠⠁⠈⠀⠀⠀⣚⣿⠀⠀⢸⣴⡾⠟
⠀⠀⠀⢘⣡⣴⠿⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠊⠉⠱⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⣒⣾⠀⠀⢘⣡⣴⠿
⠀⠀⠀⠸⣋⣥⣾⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠤⣾⠀⠀⠸⢋⣥⣶
⠀⠀⠀⠸⠛⣉⣴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢰⠁⠀⠀⠀⠀⠠⠭⣽⠀⠀⠸⠟⣉⣴
⠀⠀⠀⠁⠈⠉⠀⠁⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⣀⣀⣀⣀⣐⣂⣩⠭⠀⠀⠀⠀⠀⠉⠭⠀⠀⠁⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⢀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⢰⡾⠀⠀⠀⠀⠀⢷⠀⠄⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⢠⠀⣦⠀⠀⠀⠀⠀⠀⠀⣾⡘⠀⠀⠀⠀⠀⢢⡞⠀⠀⠀⠀⠀⢀⠔⢋⣉⡙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠆⠀⠀⠈⢼⣷⠄⠀⠀⠀⠄⣿⠇⠁⠀⠀⠀⠀⣠⠀⣾⣉⡷⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢶⣄⠀⣤⠎⠡⠀⠀⠀⠀⠶⠁⠘⠦⡈⡉⢡⠴⠁⠨⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠂⠒⠶⠶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡿⢹⣿⣿⣦⢀⣀⣠⣤⣶⣦⣤⣶⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⢸⣿⣿⢽⡿⢀⣈⡻⣿⣿⣿⣿⢿⡛⠻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠿⠀⢸⣿⣧⣀⣙⣻⣛⢳⡎⠙⣿⡏⠀⢠⣴⣾⣿⣿⣿⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠧⠀⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠙⣴⣿⠃⠒⠋⠨⣽⣻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⡿⠋⠠⠀⢲⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠘⠛⠀⡠⠔⠁⣴⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⡿⠀⠀⠀⡠⠊⠁⠀⠀⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⢀⠔⠁⠀⠀⣀⣠⣶⣿⣿⣿⣿⣷⡄⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠊⠀⢀⣴⣿⣿⢿⣿⣿⣿⣿⡜⠿⣿⣦⡀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⣴⠃⢀⣴⠿⠋⠡⣾⠘⣧⣿⣿⣿⣿⡄⣈⠙⢳⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⠉⢿⡿⠁⠀⠖⣴⣿⣦⣝⣿⢻⣿⣏⣿⡏⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⣸⣷⣄⣠⣾⣿⣿⣿⣿⣿⣷⣽⣿⣿⠀⣿⣿⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⠀⢀⣧⣼⣿⠀⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⡆⣼⠀⠀⠀⣰⠞⣿⣿⠛⠟⠃⠸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⠀⢀⠀⠀⠸⠋⡿⠀⢀⣷⢶⣶⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣤⢸⡇⠀⠀⠀⣠⣶⣿⠇⢾⡀⣔⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣧⠀⠀⠘⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡈⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢐⠂⢈⡠⣌⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢅⠘⠿⠿⣦⣕⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⣬⡐⠤⣀⠈⠻⢶⢿⡖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢸⣿⣄⠀⠁⠐⠠⠠⠔⠹⣟⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠑⠲⣽⢷⣦⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢀⡀⠤⢐⣢⣍⣤⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⣀⣠⡤⠵⠚⠛⠛⠠⣭⣤⣶⣾⣿⣿⠿⠛⠋⠉⠉⠋⠙⠖⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉⠀⠀⢀⣠⣉⣠⣤⣼⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣤⡾⠶⠶⠶⠿⠛⠛⠛⢫⡀⠀⣺⣿⣿⠆⠀⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡼⠉⠁⠀⠀⣼⠏⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⣸⣿⣠⠊⠀⠀⠀⣠⣴⡿⢳⡄⣼⡿⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣼⢁⠀⠀⢀⣤⡤⢼⣿⠀⣴⣿⢁⣿⡏⠀⣿⣿⠟⢉⣿⠀⢰⣿⠟⣠⠞⠀⡿⠷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠞⠋⢻⣇⢠⣿⡏⠀⣿⣿⠀⣸⠿⢻⣿⠁⢀⣿⡿⣦⣼⡏⢀⣿⣿⠋⠁⣠⠞⠀⢰⣿⠇⡠
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣠⡿⠁⢸⣿⡇⢠⣿⡏⡠⠁⠀⣾⣿⣠⠚⣿⣇⡼⠋⠀⠈⠿⣿⠤⠞⠁⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠞⣸⠃⠀⠸⣿⠷⠋⠿⠋⠀⠀⠀⠙⠋⠁⠀⠉⠁⢀⣀⠀⠀⠀⢀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠁⠀⣴⣿⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⣸⣿⣯⠔⠁⠀⠀⣴⣾⠷⣆⠀⢠⣿⡖⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⣀⠴⣿⣿⠅⣴⡦⠀⣸⣿⡇⠀⣿⠀⣼⣿⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡅⢸⣿⡟⢸⣿⠁⣠⣿⣟⢷⣠⡧⠈⣿⡟⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⣿⡇⣼⣿⠇⣾⣿⠜⠁⠻⢿⡶⠟⠀⢸⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⣼⡿⠃⠻⠟⠀⠀⠁⠀⠀⠀⠀⠀⠐⠊⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⣟⡙⠿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣿⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣤⣦⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢀⠁⣸⣿⣿⠇⠀⢀⣶⣿⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠨⣿⠿⠃⢀⣰⣿⡻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⣀⣀⠀⠐⠄⣠⣶⡟⡭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣣⠾⢿⣯⣎⢰⡏⠉⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠛⣄⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⡀⠀⠀⠀⠀⠀⢀⡄⠚⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠉⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⡀⣠⣟⡿⠶⠶⣤⣀⣀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⡤⠀⠰⡿⣿⣿⠆⠀⠀⠀⠀⠀⣾⣴⣿⣿⣿⣓⣀⣨⣍⣛⢿⣗⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣦⡀⠸⢿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠘⢿⡋⠙⣿⣿⣆⢻⣿⣿⣶⡀⠀⠀⠀⠀⠀⢰⠀⢨⣿⢿⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⢛⣿⣿⣿⣿⣿⡻⡄⠀⠀⠀⠀⠈⠀⠘⠻⣪⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⢸⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⡇⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⢠⣜⣻⣿⣿⠀⠀⠀⠀⠉⠐⣥⣀⡀⠆⠀⣹⣯⠙⣿⡿⢋⣿⣟⣽⣧⣿⡿⠀⠀⠀⠀⣃⠀⢠⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢸⣿⣷⣆⠘⠀⠀⠀⠀⠀⠠⠜⠁⠁⠀⠀⠘⢿⣦⠈⢿⢸⠌⣿⣼⢃⣿⠀⠀⠀⠀⠀⣷⡀⢸⣿⣿⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⢀⠒⣀⠀⠀⠀⠀⠀⠘⣳⠀⠀⠀⡼⢿⣿⣾⠟⠀⠀⠀⠀⠀⣿⡇⠈⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⢻⣿⣿⠀⠀⠀⠀⢺⣗⠚⢧⣄⠀⢀⣠⣼⡉⠀⠘⣿⣧⣞⢋⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣶⣿⡟⢻⠀⠀⠀⠀⢘⡻⣿⠿⠟⠀⢾⣟⠟⠃⠀⢸⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⡧⠀⢠⣿⣿⡟⢹
⠀⠀⠀⠀⠀⠀⠀⢈⠈⠁⠀⢻⣿⣿⣿⡇⠀⠀⠀⢀⡛⠁⠀⠀⣾⡿⠗⠀⠀⢀⣼⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉⢹⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⡿⠁⠀⠀⠀⠈⢧⣶⠀⣤⣭⢴⣦⣶⣿⠿⢿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠘⠂⠒⠲⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠀⢰⣿⣿⣷⣤⣤⣶⣤⣀⠀⠀⠀⠀⠀⠀⠼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠁⠀⠸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣤⣀⡀⢀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣦⡀⠀⠀⠀⠀⣀⣤⣴⣆⠈⠀⠠⣤⣶⣤⣤⡿⠟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣜⢿⣿⣼⡇⢠⣴⣶⣿⣿⣿⣿⣿⣷⣮⣤⣈⣹⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣾⢟⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠉⠀⠙⢿⠗⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠹⢟⣵⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣆
⠀⠀⠀⠀⠀⠘⣿⡧⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⡾⠋⣴⣶⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢴⣶⡘⢷⣄⠀⠀⠀⠀⢀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠰⡽⠇⣼⡟⢠⣿⡇⠀⢠⣶⠄⣤⠀⣤⡄⢤⣤⠀⠀⣾⣧⠸⡦⡈⢿⡷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠾⠿⠀⠀⢸⡇⢰⣟⠀⢽⡇⠀⣷⠀⠀⢹⡿⠆⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⠥⠵⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⣘⢤⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠘⠛⠁⠀⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠁⢂⣠⡔⠀⠀⠻⣀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⡿⢷⡤⢀⣀⡴⠂⠀⠉⠓⠠⢄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⢵⣶⣿⠥⠤⠀⠀⢄⠀⠀⠈⠉⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣽⠉⠀⠀⠺⠂⠆⡄⠈⠀⢁⠀⠀⠀⠐⣀⢀⠐⠁⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢉⠐⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠈⠢⠄⠀⠀⠙⢄⠀⠀⣴⢳⣀
⠀⠀⠀⠀⠀⢠⠖⡙⠀⠤⢀⠀⠐⡳⠀⢧⠀⠀⠀⠀⢀⡀⠈⠢⡀⠀⠉⠲⡤⡄⢩⣆
⠀⢀⣀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠉⠛⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠀⢃⠘⠄⢻⡆
⠀⠈⡿⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠖⣮⠐⣤⠼⡧
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠚⢻⡟⠁⠀⠁⡼⠁
⠀⢸⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⡄⠀⠀⠀⢠⠟⠀⡀⡠⠂
⠀⣾⠀⡥⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⢄⡀⠀⢰⠃⣠⠖⡹⣧
⢀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠱⠤⠁⠀⡀⢘⠃⢹⣆⡀
⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠄⠁⠀⠀⢛⡀⠘⠳⡈⠁⠀⠈⡁⠈⠉⠙⢦
⣼⡇⠰⠀⡆⣠⠤⠤⠤⠤⠄⠀⠀⡀⠤⠴⠖⢩⠀⠀⣀⣀⠴⠛⢧⣀⡰⠚⠀⠉⠉⠀⠀⠀⠀⠀⠳⣦⡀
⠀⢅⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⠉⠁⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡀
⠀⠀⠸⠋⢲⡷⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⢟⡰⢰⣻⣿⣿⣿⣿⣿⠏⣴⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠹⣟⣿⣧⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⡟⢲⢠⣤⣄⡀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣏⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣶⣶⣯⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⡏⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⢳⡆⠛⠛⠛⠛⠋⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⢸⣿⡇⢀⡾⢧⣄⠀⠀⠀⠀⠀⠀⠀⠈⠃⡆⠀⠀⠀⠀⠀⣀⣀⣀⣿⡏⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢸⣿⡇⠸⠧⠒⠛⠓⠒⣶⣶⣶⣶⣶⣶⣄⣻⣲⠖⠿⢯⣿⣟⣿⣛⣿⠀⠀⠙⢿⣿⣿⣷⣀⡴⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⢩⢿⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⡿⠆
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠉⢀⣠⠖
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢑⠂⠉⠉⠉⠹⣃⣹⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠈⣿⠿⠛⠉⣱⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⠿⠟⠛⣉⡠⢿⣶⣶⣠⣤⠚⠁⡄⢀⣼⣿⠿⠏
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⣿⣇⡠⡄⠒⠈⠋⠘⠄⠒⠈⠀⠍⢀⠰⡟⠉⠉⠁⡌⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣶⣞⣿⠀⠀⠀⠀⠀⢐⢸⢇⡐⠈⠆⠂⠈⢀⡠⠀⢀⣀⣤⣾⡷⢇⣒⣂⠠⠚
⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⡠⠽⠟⠛⠟⠀⠀⠀⠀⠀⠀⢂⣁⣌⣹⡟⣓⣦⡀⠀⢀⠠⠄⠀⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠁⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠁⠈⠉⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣄⣈⡉⠃⠀⠀⠀⠀⠐⠂⠀⠀⠈⠉⢀⣀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⢿⣿⣷⣶⣾⣿⣿⣿⡿⠿⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡙⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠤⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠚⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠁⠀⠀⣈⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢿⣿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⡤⣦⡀
⠀⠀⠛⠁⠀⠈⢷⡀⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠈⢷⣶⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⢀⣿⣷⣦⣄⡀
⠀⠀⢀⣴⣧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⡀
⠀⣴⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠙⣦⣀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣂⠒⠁
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠘⠿⠇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣩⣶⣿⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠉⠀⠰⠾⠿⣿⡿⠉⡁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢹⣿⡀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠃
⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣤⠶⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⣠⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⢀⣴⣿⣿⣿⣿⠟⠀⠀⠀⡐⠄⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⠈⢂⠀⠀⣠⣾⡟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⣾⣧⠈⠻⣿⣿⠟⠀⠀⠀⠀⠀⢰⡃⠀⠀⢣⣼⣿⡟⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⢀⣴⣿⣿⣿⣿⣧⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣇⢀⣴⣿⣿⢏⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠗⠄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠟⠁⠈⠑⢄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠠⣤⣀⠀⠀⠀⣾⣿⣿⡿⣇⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣜⢿⠟⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠉⠛⢳⠀⠀⠀⠈⠳⣄
⠀⠀⢠⡞⠁⠀⠀⠀⠀⢸⣿⣀⣨⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⣥⣿⣷⣦⣀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠙⠃⠈⠻⠿⠿⠿⠷⣦⣄⡀⠀⠈⠙⠒⠲⠤⠼⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⣠⠞⠋⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠉⠻⣦⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡾⠁⠀⠀⢀⣼⡇⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣷⣶⣦⣀⠀⠀⠀⢿⣦⡀⠀⠀⠈⣷⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣯⡀⣀⣴⣿⠟⠀⡤⢴⣾⣿⣿⣿⡿⡿⢿⢻⡿⣿⣿⣿⣷⣶⢦⡄⠙⠿⣶⣤⣴⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⠋⠀⠀⠀⡇⢸⠈⡇⢿⢸⠀⡇⢸⠘⡇⡇⢸⠀⡇⢻⢸⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠃⠘⠀⠇⠠⠸⠀⠇⢸⠀⠇⡇⠸⠀⠇⠐⠘⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣴⣤⣶⢶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠗⠓⠛⠿⠿⠟⠋⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠃⢠⣄⡀
⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⢅⠀⣀⣀⣀⣙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⣠⣴⡶⠞⠛⠃⠄
⠀⠀⠀⠀⠀⠀⣾⠻⠻⣿⠛⠛⢻⡾⣿⠏⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠒⠛⠫⢹⠷⠀⡀
⠀⠀⠀⠀⠀⠀⠹⣎⢁⢸⡆⠀⠀⠉⠡⣤⡜⠀⠀⠀⠀⠀⠀⠀⢀⣶⢸⠂⠀⠀⡀⢀⢀⡀⣾⡀⠀⣀⡤⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⣤⣤⡶⢷⣟⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⠆⡾⢹⡇⠿⣿⢰⡿⡼⢰⡟⠊⠘⣿⡁
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠾⢿⣯⣫⡽⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠍⠀⠓⠙⣁⣀⠋⢈⠍⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⡋⠀⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢷⡀⢰⡿⡈⢠⡶⡄⢰⠆⡄
⠀⠀⢚⢀⣴⣿⣇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣽⢿⡇⢾⣧⠇⣿⠔⠁
⠀⠀⢸⣿⣿⣿⣿⠀⠂⠠⠀⣼⣿⣿⣿⣿⣿⣿⡷⠀⠀⣤⠁⠀⠀⠀⠀⠀⠠⣋⡴⠏⠛⠈⠀⠀⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠲⠷⠿⣿⣿⣿⣿⣿⠇⠀⠸⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠢⡀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⢠⡄⠀⠈⠂⠰⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⣤⠃⠠⠉⡇⠸⢱⠀⡎⣠⠀⡮⠈⡐⢉⠂⡔⠐⠆⠁⠰⠋⡃⢠⠒⠂⢀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠤⠀⠁⠂⠸⠤⠁⠐⠘⠒⠉⠈⠂⠊⠀⠐⠊⠡⠤⠄⠐⠀⠸⠴⠇⠼⣥⠃⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⣠⣾⠾⠟⠿⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣧⣤⣀⣾
⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠉⣰⣿⡿⠛⠛⠉⠉⠛⠛⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⡆⢸⠇⡿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⢹⡿⠷⠦⠄⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⡇⠈⠀⠘⢹⣿⣿⡟
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠙⠞⡇⠀⢰⣿⣶⣤⣀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢿⣿⣶⣶⣴⣿⠏
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠙⠀⠘⣿⣿⣿⠿⣿⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠛⠛⠁
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⡁⠀⠹⣿⣷⠀⠀⠙⠻⣦⣀⣼⡿⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⡄⠀⠹⣿⣦⣀⠀⣸⣯⣿⣿⠁⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠈⢢⣀⢈⣿⣿⣿⣿⡿⠋⠙⢷⡀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠹⣿⣄⠀⠀⠀⠀⣱⣤⣾⡿⣿⣍⠀⠀⢀⡈⢻⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠶⠾⢿⡶⠶⠿⠿⠛⠛⠳⣤⣈⣿⣷⣀⢋⣾⡾⢟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⣀⣈⣿⣿⣿⣿⣿⡿⣷⡿⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠟⠻⣿⡿⠻⢷⡹⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠑⢦⢀⢂⢀⢀⢀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠈⠃⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠊⠀⠘⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⣾⣿⣷⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⢀⡾⣟⣽⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡼⠡⠔⢁⠎⡀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣴⢶⣾⡟⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠠⠜⠀⠀⠜⠊⠰⠡⠠⠡⠃⠎⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠋⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠬⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠀⠀⠙⡆
⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠉⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠼⠦
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⡠⣀⠀⣠⠞⠉
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⡀⠀⠀⠀⢀⡴⠛⠃⠀⡠⠚⠉⠀⠀⠀⠀⢰⡏
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣿⣶⠖⠛⠉⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣀⣀⠀⣠⡴⠶⢄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠼⠷⣄⠀⠀⠀⢀⣠⠜⠁
⠀⠀⠀⠀⠀⠈⣻⢶⣀⠉⢫⣿⠛⠉⠀⠀⠀⠈⠢⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠽⠶⠖⠛⠉
⠀⠀⠀⠀⠀⡔⠁⠀⠻⣿⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠱⣀⠀⠀⢩⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⢸⣿⠇⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢦⣆⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣙⢿⡏⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠏⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠟⠘⢠⣶⣜⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠛⢖⣥⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣩⡟⠁⠀⠀⠀⠙⢿⣿⣯⣻⣿⣿⣿⣷⡀⠀⢀⡠⢊⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠰⣷⣀⣄⠈⠛⢿⣿⣿⣿⣿⣿⣷⡉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣾⣫⣻⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⣿⡘⢿⣿⣿⣿⣿⡿⢋⣵⡿⠋
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⣟⠿⣿⣿⡿⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣯⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠂⠀⠘⠇⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣯⣨⣿⣿⣅⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⣰⠊⠁⠈⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣾⣿⣿⣿⣿⡿⢫⣾⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡠⠤⣀⡼⠉⢑⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣛⡻⠟⢱⣷⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢣⣀⡽⢸⡶⠊⠀⣀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣧⡻⠿⣸⡎⣩⣾⡿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀⠈⢳⠘⡇⠀⢀⣿⣿⣷⣶⠂⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⢹⡇⣿⣿⠇⠀⠀⠉⢩⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠃⠀⠀⣿⣿⣿⣿⠀⠘⣳⡇⢠⣿⣿⣿⣿⣿⠀⠈⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣿⣿⡇⠀⠀⠀⢸⣿⡧⠃⣿⠏⠀⠀⠀⠀⢸⣿⣦⣾⣿⣿⣿⣿
⠀⠀⠀⢀⣤⠀⠀⢸⢿⣽⣿⡆⠀⣿⡇⢸⣿⣿⣿⣿⡟⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⣿⠀⠐⠀⠈⣿⡇⠀⣿⠀⠀⠀⠀⠀⣼⡟⢻⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣥⠴⠆⠘⣮⡛⣿⣷⠀⣿⡇⢸⣿⣿⣿⡟⠐⠦⢤⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢻⡟⢛⠋⠛⠓⠀⠻⡗⢸⣿⢧⠀⢀⡆⣾⣿⣿⣿⢿⣿⣿⣿⣿
⠀⢀⣀⣿⣆⠀⠀⠀⢸⡿⣿⣿⡄⣿⠇⣾⣿⣿⣿⠀⠀⠀⢀⣿⣅⡀⠀⠀⠀⣿⣿⣿⡿⠗⠀⢻⣿⣿⣛⠛⡛⠂⠘⡟⠘⣿⠂⠀⡰⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠒⠯⣀⠘⣿⣠⡤⠄⠘⡿⣎⣿⣇⢹⠀⣿⣿⣿⠃⠤⠤⣤⣻⡏⢀⡨⠗⠀⠀⣿⣿⣅⡺⢿⡆⠘⠛⣛⣿⡏⠙⠃⠀⣿⢸⡇⠁⠀⢁⣿⣛⡛⠛⠁⣿⠿⣋⣽⣿
⠀⠀⡎⣀⡽⠟⠂⠀⠀⠓⠛⠉⠁⠈⠀⠙⠛⠉⠀⠀⠀⠚⠿⣄⠸⡀⠀⠀⠀⣿⣿⣿⡿⣼⠟⣀⣼⣿⣿⣧⣤⣴⣶⣿⣾⣷⣤⣴⣿⣿⣿⣯⣄⡘⢿⣼⣿⣿⣿
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣶⡾⣡⣶⣶⣦⣍⡙⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣇⠀⠀⠀⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⣽⡿⣿⣿⢷⠘⠻⢿⣧⠻⠇⠾⣛⣿⢿⡋⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣀⡠⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠙⣟⠉⡟⠁⠀⠀⠀⢹⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⢠⠏⠀⠹⣄⠀⠀⢀⡼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣎⠙⠂⠈⠁⠀⠀⠀⠈⠁⠉⠉⣼⣿⡇⠀⠀⠀⠀⢀⣤⣄⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢳⡀⠀⠀⢀⣿⣿⣄⢀⣀⣴⣾⣶⣷⣦⣄⣀⣼⣿⣿⡷⠁⠀⠀⢠⣿⡟⠀⠈⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢷⡀⠀⠀⣿⣿⣿⣿⡿⠛⠛⠉⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⠏⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⠶⢦⣬⣿⡀⠀⢸⣿⣿⣿⣿⣆⣵⣶⣧⣴⣿⣿⣿⣿⣿⡄⠀⣰⣿⠏⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠉⢻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⠋⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠓⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠇⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠉⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠒⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡟⠁⠀⠀⠀⠳⠀⠀⡠⠒⠉⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⡐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⡀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠒⣴⣾⣿⡷⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⣀⣀⠤⠒⠁
⠀⠀⠀⠀⢠⡈⠉⠁⠀⠠⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠈⣿⡠⢀⣾⣡⠆
⠀⠀⠀⠀⠈⢧⣀⠀⠀⣀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠓⠛⠇⠚⣁⣴⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣿⢁⠘⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡼⠁⣸⠆
⠀⠀⠀⠀⠀⠺⠘⢿⡀⠋⢀⣼⣿⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠺⣧⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠁⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠀⠀⠀⠰⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡿⢛⣤⣍⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⣻⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⣼⣿⣿⣿⡄⡤⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠁⣀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⣶⣿⣿⠀⠀⠀⠀⠀⢤⣖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠻⠟⢻⠄⠀⠀⠀⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡸⠛⠚⠋⣡⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⡠⠀⣽⣄⣀⣾⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣁⠀⠀⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢍⠉⢉⣹⠟⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⢀⠔⠁⠀⠁⠀⠓⢄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⡿⣫⣾⣿⣾⣿⣬⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡿⠿⣿⡇⠹⣴⠀⣶⣄⣠⣦⠊⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣀⣀⡀⢹⣟⠛⣿⠛⠻⠟⠛⣽⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣾⣀⣿⣿⣿⣿⠻⡆⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣷⢸⣿⡇⠿⠀⠀⠀⠀⣤⢹⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣠⡟⠀⠀⠀⣿⣿⣿⣿⣿⠠⣿⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⠟⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠈⠉⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣾
⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠊⠚⠒⠀⠀⠀⠀⠊⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⢶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣵⣖⠚⠉⠛⠻⣿⣟⡻⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⣿⢵⣧⠤⠞⠙⠛⠻⢿⣟⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠉⠙⠳⣦⣄⢤⡙⢿⣦⠙⢹⡄⠀⠀⠀⠀⠀⠀⡟⠈⠛⠻⠿⣶⣤⡀⢄⠙⢿⣎⠳⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢁⣀⠀⠀⠀⣼⠆⠙⢿⣿⡌⣿⣧⠀⡇⠀⠀⠀⠀⠀⢸⢀⣀⠀⠀⢠⣿⣊⣙⢾⣷⡈⣿⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⡘⠸⠇⠀⠀⠀⢸⣿⠿⠿⣿⣿⣹⣿⢠⡇⠀⠀⠀⠀⠀⡘⠹⠅⠀⠀⠀⣏⣩⡽⠿⣿⣷⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠘⠁⠞⣹⠟⣿⣿⡿⡼⠀⠀⠀⠀⠀⡔⠀⠀⠀⢀⠀⣼⡟⠡⠞⣹⢿⣿⣿⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⢩⡖⠶⢾⣿⣷⣸⣷⣄⠈⣇⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⠀⠈⠙⣖⠋⠁⠀⠀⠀⠀⠀⠀⣸⠟⢿⡷⣿⣿⣿⢿⡟⠀⠉⢳⡖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠒⠲⡖⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠘⠁⣛⣉⣵⠟⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⢒⣒⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⢒⣒⣲⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣵⣖⣚⠉⠙⠛⢿⣿⡛⢿⡷⣄⠀⠀⠀⠀⠀⠀⢸⣷⣷⣖⣒⠉⠉⠛⠿⣯⣟⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⠉⢻⣶⣄⢦⡙⢿⣧⡙⠹⡆⠀⠀⠀⠀⠀⡸⠁⠀⠈⠉⠻⣷⣤⡠⣌⢻⣷⡌⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⡀⠀⠀⣼⣿⣿⣿⣿⡌⣿⣧⠀⡇⠀⠀⠀⠀⠀⣇⣀⣀⠀⠀⢴⣿⣿⣿⣿⣦⢻⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠸⠇⠀⠀⠀⢸⣿⠿⡛⣿⣿⣹⣿⢠⡇⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⢸⣿⠿⣛⢿⣿⣼⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠈⠁⢚⣱⣿⣿⣿⣿⡼⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠾⠁⠘⣣⣿⣿⣿⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡷⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢵⣤⣀⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⠆⠀⠈⠉⢟⠉⠁⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⡏⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢞⠉⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡆⠀⠀⠀⠶⡄⠄⠈⠉⠙⠗⢲
⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⣿⡷⠀⠀⣾⣿⣿⠀⠀⠨⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣴⠀⠀⢀⣿⣷⣗⠀⠀⣹⣿⣿⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⡻⠀⣄⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⠼⣿⣿⣟⠀⠈⣿⣿⣿⡂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⣯⠀⠀⣹⣿⣿⡅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠏⠀⠀⢾⣿⣯⠁⠀⠀⡇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⢸⣿⣿⡏⠀⣀⣺⣿⣿⡂⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢸⣿⡿⡇⠀⠀⢸⣿⣿⠀⠀⠀⢿⡄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠠⠺⣷⠶⠺⠛⢹⡟⡿⠚⠋⠛⣿⣿⡃⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣺⠚⠈⡷⠶⡶⡶⡯⡉⣵⠀⠀⠈⠁⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠶⢭⣀⣀⣀⣀⠀⡀⠀⡀⠀⡀⢀⣀⣀⣀⢤⠵⠂⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠂⠂⠀⠐⠂⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤
⠀⠀⠀⣠⣀⠀⠀⠀⠁⠀⠀⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡃⠜⢛⣉⡉⠉⢁⣀⣠⠤⠤⠤⢼⠄
⠀⢰⣖⠛⢛⣼⣷⠀⡷⠈⡄⠈⡇⢰⡀⣼⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠃⠀⠈⠁⠀⢀⡀⢀⠀⠀⠀⠀⠀⡀⠀⡆
⠀⠀⠹⡇⠿⠟⠁⠀⡇⢀⡇⠀⡇⠀⠀⢠⡇⠀⠀⠀⢀⠈⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣤⠾⣣⣮⣿⡅⠀⢀⡀⡇⠀⠃
⠀⠀⠀⠰⠀⠀⠀⠀⣿⠈⠀⠀⡇⠀⠀⠀⡇⠀⠀⠆⢠⣀⡀⠀⠦⠠⣁⣀⣰⣦⣤⣄⣤⣴⣿⣿⣿⣤⣶⡤⣇⠸⠟⢸⣿⠇⠀⠀⠀⡇⠀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⣿⢀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠁⠠⠠⠶⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣼⡑⢂⣼⣯⠀⠀⠀⢾⡇⠀⡇
⠀⠀⠀⠘⡇⠀⠀⠀⣿⠘⠀⠠⡇⠀⠀⢸⡯⣄⠚⠟⠻⣦⣀⡄⠀⠀⠕⠉⠉⡭⠉⠭⢉⠁⣽⣿⣿⣿⣿⣴⡯⢰⣿⣿⣿⣷⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠐⠇⠀⠀⠀⣿⠀⠀⠀⡇⠀⢀⣘⡇⠀⠀⠀⢰⠂⠙⠁⠀⠐⡇⠀⠤⠁⢄⠀⢸⡅⣿⣾⣿⣿⣷⣤⣵⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⣂⣱⣮⣿⣿⣿⡆⠀⢀⡐⢠⠈⠀⠀⠀⠀⣀⣤⢀⠀⠠⣾⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⣸⠀⠀⡇
⠀⠀⠛⠻⠿⠿⠿⢿⡏⣫⡽⠾⣾⣋⣫⣿⣿⠁⢈⡬⠀⢉⢀⣀⣒⣴⣶⣿⣷⡄⠛⠀⠀⠈⠛⠡⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⢸⢃⡿⢻⢹⣿⡇⣁⣳⢀⠀⠈⠱⣿⣿⣿⡟⠁⠀⠀⠀⠈⠀⠁⠀⠿⣿⠿⣿⣿⣿⣿⣿⢇⠘⠀⢰⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⢸⣇⠰⣾⣿⣇⣷⡇⢠⠙⣢⢐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠸⠿⣿⡿⠟⠋⢀⣀⠀⢰⣶⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠈⣿⡆⢸⣿⣷⣿⣸⣿⣿⣿⡈⣿⣿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡇⠀⢼⣷⡟⠓⠒⠋⠀⠚⠿⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣷⠀⣿⣿⡿⠈⣏⣿⣿⣿⣷⣿⡏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠐⣿⣿⡥⠬⠤⠤⠤⠶⠤⠥⣤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡰⠀⡇⠞⢿⣽⡇⠠⠹⠟⣟⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⢻⣿⡧⠀⠀⠀⠓⠀⠇⢰⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠉⢀⣯⢴⣟⣽⣇⠀⣲⠫⠝⣻⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠛⠛⠛⢻⣿⣶⣄⡤⣄⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠀⠈⢇⣨⣿⣿⣿⣿⢯⡴⣂⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠖⠐⠀⢀⡀⠸⢻⣷⢰⡆⣑⠀⣧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⡿⠿⠟⠻⠉⠉⢀⡴⠃⠐⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⣠⣾⣻⣿⣦⡀⠉⠀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠸⠟⠉⠓⠛⠁⠀⢀⡠⠋⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⢀⣠⣾⣷⡿⢿⣿⣿⢀⠀⢈⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠰⣆⣄⣼⢿⣦⣤⣤⡀⠀⠋⠀⠀⢀⣴⣾⣯⣻⣿⠃⣾⣿⣷⣰⣿⣿⣷⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣾⣿⢸⡿⠟⣿⣿⣿⣿⣿⡟⣿⣿⣽⣿⣿⡥⣾⣿⢿⣿⣿⣿⣿⡗⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⢺⡟⡃⣿⣿⣏⣱⣿⣿⡋⣿⣿⡿⢀⣼⣿⣿⣷⡟⠻⢿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠀⠀⢀⣸⠞⢁⣿⠀⠘⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⡿⠟⢑⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⠞⠋⠉⠀⠉⢿⢽⡶⠿⣿⣿⠿⠟⠛⢉⢁⠐⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢁⠟⣦
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣀⡄⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠘⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡆⢨⣿⣶⣷⢊⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⣀⠟⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢃⣿⣿⠝⠹⡍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⣸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⢰⣿⣿⣑⣀⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢴⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢠⠏
⠀⠀⠀⠀⠀⣤⠉⠛⠛⠛⠛⡋⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣏⠀⠀⠀⢸⣄⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⡏
⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡛⠉⠑⠚⠋⠉⠩⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢐⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠙⢂⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⢸⠁⠈⢿⣿⡿⠏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠋⢦⣤⡉⠓⠁⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠉⠁⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⣬⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠰⠶⠶⠤⠤⠤⢤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢠⣴⣶⠀⠀⠀⠀⠀⢠⣿⣶⣦⣶⣶⣶⣴⣶⣶⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣭⣿⠎⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢠⡀⡀⢠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡷⠠⠀⡠⠀⠀⠀⠀⠀⠉⠛⠛⠛⣛⡛⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣧⡶⠂⢁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡴⠆⡀
⠀⠀⠀⠀⠀⠀⢼⣏⣯⣭⢍⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠶⠀⠉⠀⠰⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤⣶⠾⠿⢿⣿⣛⠓⠲⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣛⡛⠛⠶⠦⣄⡉⢳⡄⢀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣿⢻⣿⡛⠿⢭⣉⠒⢦⡈⢳⡄⢿⡌⡇⢻⡽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡟⣆⠙⢿⣕⡲⢬⡻⣆⣷⣹⣷⣿⣿⣿⣾⣷⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣳⣜⢮⣙⢦⣜⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⡋⠁⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠉⠙⠛⠛⠋⠭⠒⠁⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠰⣿⣿⣿⣶⣤⣠⡾⣦⣤⣴⣾⣿⣿⡷⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠻⠿⠿⢿⡿⠟⣤⡜⠿⣿⠿⠿⠿⠃⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⣀⠀⠀⠀⣸⣿⣿⡀⠀⠀⢀⡀⠀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣧⠀⠀⠉⠁⠉⠁⠀⢰⡿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⡒⠒⠒⠲⠲⠒⠒⣺⢳⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠘⢯⣭⣤⡀⣠⣬⡽⠟⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⣿⣹⣿⣿⣿⣿⣻⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣽⣿⣿⣿⣿⣿⣿⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁

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

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠉⠓⠒⠒⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢿⡂⠀⠀⠀⢠⣾⣷⣦⣤⣄⣀⣀⣀⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⡟⢹⣶⡀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⢰⡇⣀⣛⠚⡋⣀⣀⣀⣀⣀⣀⡀⣀⡀⡇⠀⠀⠀⠀⡇⣀⣀⠀⡀⢀⣀⣀⣀⣀⣀⡀⣀⡀⣷
⠀⠀⠀⢸⡇⣿⣿⢰⡇⣿⣿⣿⣿⣿⣿⡇⣿⡇⡇⠀⠀⠀⠀⡇⣿⣿⢠⡇⣾⣿⣿⣿⣿⣿⡇⣿⡇⣿
⠀⠀⠀⠀⡇⣿⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⣇⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⡏
⠀⠀⠀⠀⢻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⠀⢻⢸⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠸⡎⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⡇⡾⠀⠀⠀⠀⠀⠘⡆⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾
⠀⠀⠀⠀⠀⢷⢸⣷⢹⣿⣿⣿⣿⣿⣿⣿⢰⠇⠀⠀⠀⠀⠀⠀⢳⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢡⡇
⠀⠀⠀⠀⠀⢸⡌⣿⣿⣿⣿⣻⣿⣿⣿⡏⣾⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⣿⣿⣿⣻⣿⣿⣿⡟⣸
⠀⠀⠀⠀⠀⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢸⠇⠻⠿⣿⣿⣿⣿⡿⠿⠁⢷⠀⠀⠀⠀⠀⠀⠀⢰⠇⠙⠿⣿⣿⣿⣿⡿⠿⠃⢻
⠀⠀⠀⠀⠀⢿⣀⣀⡐⠒⠒⠒⠒⠒⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⢺⣄⣀⡐⠒⠒⠒⠒⠒⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠠⣄⢤⡰⣄⢦⡰⣄⠠⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣐⣰⣦⣀⣒⠦⣄⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⢿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⡟⠛⠂
⠀⠀⠀⠀⠀⠀⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠛⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠋⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⡦⠤⣀⡤⠄⠀⢠
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣭⡻⠿⠗
⠀⠀⠀⠀⠀⠀⠹⡿⠋⠁⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⠿⠟⠛⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠉⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣷⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⣄⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣶⣾⣿⣶⣶⣼⣿⣷⢶⣶⡎
⠀⠀⠀⠀⠀⠀⢿⣿⠟⠉⠉⠙⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⣿⣿⡿⠛⠉⠋⠀⠀⠀⠀⠀⢸⡿⠟⠁⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣄⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣾⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣛⣻⣿⣟⣛⣛⣓⠾⢭⣅⡙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⢯⣭⣭⣭⣭⣭⣟⣻⢶⣬⡙⢶⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣬⣭⣙⠻⢿⣷⣌⠛⢦⡙⢦⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠂⠀⠀⠉⠛⠿⣿⣦⣹⣿⣯⢦⡉⡀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⣷⣌⠻⣿⣿⣿⡎⣷⡹⡄⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠘⣿⣿⡇⣿⣧⢹⣽⡜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⡆⢿⣿⢃⣿⣿⢸⣿⡇⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡟⣼⣿⡿⣼⣿⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣾⣿⡟⣽⡿⢃⣼⢏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢫⣾⠟⢠⠞⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣵⡿⣵⠃⣴⢣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠰⣿⢹⣿⢸⣿⠘⠀⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠠⣟⠌⣿⣿⣿⡀⢄⣒⣞⣵⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢻⣆⠻⣷⣌⡻⢿⣷⣤⣺⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢷⣝⠣⠈⡛⢿⣦⡙⣿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⣸⡿⣷⣆⠠⣷⣎⠳⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣩⣾⣿⡿⠀⠑⣣⣷⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠐⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣲⠳⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⠄⠀⠀⠀⢀⡴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠥⠖⠎⠵⠻⠧⠿⠎⠮⠸⣷⠃⠀⠎⠿⠴⠿⠱⠿⠇⠀⠰⡧⠎⠯⢦⠇⠿⠇⠮⠾⠿⠾⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡶⣶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⣶⣶⣶⠶⡶⢶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⣿⣾⣿⡇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠇⣿⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣿⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣿⣿⣿⣿⣿⣷⠀⢀⣼⠟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⣿⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠻⣿⠻⣿⣿⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢠⣄⣈⡿⣿⣿⣿⣿⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⠀⣶⣦⣤⣼⣿⠁⠀⠉⠙⣿⡿⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠻⡿⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠖⠶⠶⣾⣅⠒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢈⣦⣭⣒⠤⣀⣀⣼⢀⣦⠈⣿⣷⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⠟⠉⠻⣦⣌⠉⠙⠛⠴⣿⣿⠆⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠐⣦⢤⣤⣤⠄⢈⣉⣿⡆⢠⣶⠎⣿⣄⣠⡟
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠿⠀⠀⠙⠁⣀⣨⡝⠛⠙⣿⣴⡿⠛⠋⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣤⣤⣶⣶⣿⣿⣿⣷⣝⢓⣤⠟⠛⠀⢠⠁⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣴⣿⡿⠟⠻⣧⣽⣏⠻⣿⣅⠉⠀⠀⠀⣠⠈⣷⡄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⢿⣿⣿⣧⠘⣿⡇⢀⠀⠸⣿⣷⣌⠇⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⠠⣾⣿⣿⣿⡄⣿⠇⠠⢀⣼⣿⣿⠋⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢀⠂⢸⣿⣿⣿⡿⢠⣿⢀⡄⠈⠸⣿⣿⡄⠀⠀⠀⠀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⣷⣤⡀⠀⠹⠟⢋⣤⣿⢣⣿⠁⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⣶⣾⠿⠛⣁⡼⠋⢧⠀⠀⠀⠈⢿⣿⣧⡘⣿⣦⡀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣥⣤⠖⠛⠁⠀⠀⠈⢧⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢾⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀⠇⠀⠀⠀⠐⠶⡒⢯⡞⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠀⠀⠀⠈⠢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⢀⠀⠀⠳⣄⡀⠀⠘⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠀⠀⠀⠀⠀⡄⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠈⠀⠀⠀⠀⠠⢌⠹⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢌⠄⠀⢻⣄⠜⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⡀⠀⠀⠀⠀⠢⡕⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠳⡀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠨⠥⠌⠘



⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⠴⣼⣿⣿⣿⡷⢶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⣿⣿⣿⣟⠁⠀⠈⠙⠛⠻⠋⠉⠑⠛⠓⠒⠒⠶⠶⠆⠀⠀⣠
⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⢤⡄⣀⣒⠒⠶⠆⣿⣿⣿⣿⠁⠀⣀⣠⣶⣄⠀⠀⠀⠀⠀⠀⣀⠀⡼⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠚⠛⣯⡄⠀⠀⡀⠀⢈⢳⡇⠀⠀⡀⠀⠀⣻⣿⣿⡿⢀⣈⣿⣿⣿⠿⠷⢦⣄⡀⠀⣧⣿⢠⡇⠀⠀⡘
⠀⠀⠀⣾⡆⣶⣼⣿⣿⠠⠄⠀⠁⠀⠰⠆⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⠿⠿⣿⡶⣤⣹⣿⣦⡛⣿⣿⣄⠄⢠⢁⣆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣼⠆⠀⠠⠤⠀⠀⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⣰⠟⢻⣿⠃⡋⢻⣿⣿⣦⣧⣼⡿
⠀⠀⠀⣿⣿⣿⡟⢿⢻⢀⠠⣶⣿⣿⠉⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⡿⣻⡄⠀⠀⣼⣿⢴⡿⡟⠀⣲⡏⠘⣿⣿⣿⣿⣷
⠀⠀⠀⢿⣿⣿⣧⢾⣿⣿⣷⣿⣿⢿⢿⠉⠒⠲⠒⠒⠐⣿⣾⠋⢻⣧⣻⣯⣤⣾⣻⣿⣾⡟⠁⢀⣞⠉⢠⠋⠛⠛⠻⢿⠇
⠀⠀⠀⠀⣿⣿⣿⣾⣾⣿⣟⣛⣛⡥⡀⢸⠀⠀⠒⠲⢴⣿⡿⣧⣾⡿⣿⣿⣿⣿⠿⠿⠿⠃⠀⣾⠉⠀⠀⠀⠈
⠀⠀⠀⣤⣿⣿⣿⣿⡟⢻⣿⣿⣿⠛⠿⠀⠀⢀⣀⡀⢸⣿⡋⢻⣿⣾⣾⣿⣿⣿⣷⣂⣷⡇⣼⣹⠀⠀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⠀⣤⣸⣇⣿⣿⣷⣼⣿⡿⠺⠿⡿⢻⡿⠿⠿⠿⠿⢇⣼⣁⣿⡄⠀⠃⠀⢀⡀
⠀⠀⠀⢿⡿⠿⣿⣿⠟⠉⠉⠛⢿⡆⠀⠈⠙⠛⠿⢿⣿⣷⣿⣿⣷⣯⣀⠇⠀⠀⠀⠀⠀⠉⠛⠿⠿⠦⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣤⡶⠶⢶⣶⣶⣶⠶⠦⣄⣄⣀⣀⣀⠄⠒⠐⠂⣄
⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠿⠿⣯⡴⠿⠿⠿⠷⢶⣤⡈⠙⣷⣆⠀⢻⣷⣸⣄⣀⣀⣠⣴⣿⣧⣀⡀
⢠⣴⣿⡿⠟⠛⠉⠁⣀⠀⠰⠚⠁⢴⣄⠐⣦⡀⣠⡙⣿⣆⠘⣿⡆⠿⢿⣿⣿⠠⠤⠧⢼⣿⣿⠻⣿⣷⣤
⢸⣿⡇⠀⠀⠀⠀⠀⠁⠐⢩⠾⣦⢐⣹⣦⡘⣿⣿⣧⡘⣿⠰⣿⠇⣠⣾⣿⣿⠀⣶⣶⢸⣿⡇⠀⠀⣿⣿
⢸⣿⡇⡠⠀⠀⢠⠂⠀⢂⠀⢼⣿⣦⡈⠉⠙⠻⢿⡧⠷⠋⠐⠙⠛⢭⣿⣧⣏⠀⠛⠋⠈⠸⠀⠀⠀⣿⣿
⠸⣿⡇⠁⠀⢀⠃⠱⢰⠃⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⠃⠀⣀⣤⢠⣾⡇⠀⠀⣿⡿
⠀⣿⡇⠀⠀⠙⡄⠀⣾⠀⠀⢸⣿⠃⠶⠶⠒⣲⡀⠀⠀⠔⠶⠶⠶⡌⢿⣿⣼⡇⣿⣿⢸⠏⠁⠀⢀⢿⡇
⠀⣿⢸⠀⠀⢀⡜⡶⢻⠀⠀⢸⡏⠀⡠⢶⡗⠯⠃⠀⠀⠰⢶⡽⢎⠛⠀⣿⠟⠃⠉⠀⠀⣇⡀⠀⢸⢸⡇
⠀⢹⡏⠀⠀⠈⢤⡜⠸⡀⠈⣿⠇⠀⠀⠈⠁⠀⠀⠄⠀⠀⠀⠉⠁⠀⢀⢦⣞⠡⣴⣶⣾⣿⡇⠀⡸⣾⠁
⠀⠸⣧⠀⠀⠀⠸⡇⠀⡇⠀⠱⣇⠀⠀⠀⢀⣀⣤⣤⣤⣴⣀⠀⠀⠀⠀⡟⠁⡾⠿⠿⠛⡇⠀⠀⣧⡿
⠀⠀⢿⣷⠀⠀⠀⡇⠠⠃⠀⠈⢿⣷⣤⢖⣩⣭⣥⢶⣾⣭⣬⣙⠦⣠⣼⡟⠀⠀⠀⠀⣀⣧⡆⢸⣿⠇
⠀⠀⠸⣿⣇⠀⠃⢧⠀⢠⠀⠐⣾⣿⣾⣿⣿⡉⢹⣶⣿⡉⣹⣿⣿⣿⣟⣿⣀⢰⣿⣿⣿⡟⣧⣿⡿
⠀⠀⠀⢿⣿⡄⠈⠃⢦⢸⠀⠀⢼⣧⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡇⣷⠾⠭⡥⢤⣷⣾⣼⠇
⠀⠀⠀⠈⢿⣳⠀⠀⠀⣨⡄⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣤⠤⢧⣼⣿⣿⡟
⠀⠀⠀⠀⠘⣿⣧⠀⠀⢹⠀⡂⠨⡏⠀⠈⣷⠀⡂⢸⠂⢐⠀⡇⢐⡦⣖⠀⡂⢸⡀⠀⢈⢛⡝
⠀⠀⠀⠀⠀⠘⢿⣳⡀⠻⠤⠴⠖⡴⠾⠤⠶⠤⠷⢶⠤⠶⢴⡷⠶⠦⡶⠶⠦⠼⠃⣰⣳⠟
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⡧⠄⠘⡇⠠⠄⢸⠀⠿⢀⡇⠨⡤⠆⠀⠀⢀⣴⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠛⠒⠛⠛⠚⣷⣾⣿⣶⠛⠓⠛⠃⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣄⣀⣀⠀⠛⠋⢁⣀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⡿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠠⣦⣤⣀⡀⠀⠀⠀⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢁⣴⣾⣿⣿⡄⠀⠀⠰⠶⣤⣍⠛⢶⣄⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⢤⣄⡉⠻⣦⠙⣧⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣦⠘⣷⠘⣧⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢻⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠻⠀⢸⡇⢿⡀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠈⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣶⣿⣿⣶⣦⣄⡀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠟⠛⠛⠋⠉



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠳⠎⠁⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣵⣶⣶⣭⣵⣿⣷⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⡻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⢤⡏⡇⠀⡟⠉⠙⢦⣄⡤⠋⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⡛⢰⢸⣿⢰⣶⣦⣙⠿⢟⣵⡆⣡⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡇⢠⠀⡄⠀⠀⢠⠘⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣧⣭⣭⣛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⣀⡇⠐⠀⡇⠀⠀⠐⢸⠋⠙⡆⢹⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡸⡿⢸⣿⣿⣿⣿⣿⣿⡏⣶⣶⢹⡎⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⠀⠀⡇⠀⠀⠐⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠠⠀⡇⠀⠀⢘⢸⣄⡤⠇⣸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⢟⣸⢇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⠀⠰⠀⡇⠀⠀⢘⢰⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣭⣵⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠈⠀⠈⠀⠁⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣛⣛⣛⣛⣛⣛⣛⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛








⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠊⣁⡀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠔⢉⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⢸⣿⡿⠀⠀⠀⠀⠀⢡⠀⠀⡈⠀⠀⢀⠅⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠹⣷⣄⢀⣤⡀⠀⢠⠀⠀⠇⠀⠈⢀⠢⠀⡀⠄⠀⠀⡄⠀⠀⠀⠀⠙⣷⣄⡀⣤⡀⠀⠀⠀⠀⠀⢄⠢⡀⡠⢀
⠀⠀⠀⠀⢂⠀⠀⠈⠛⠿⡿⠟⢀⠂⠀⠀⠐⡀⠀⠀⠁⠀⠀⠠⠃⡰⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠤⠒⠁⠀⠀⠀⠀⠈⠒⠤⠀⠀⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠐⠉⠝⠻⠛⠛⠛⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡱⠁⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⡀⠠⡀⢀⠐⢄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⢡⠃⡞⢰⠀⠀⠁⠀⡌⠈⠀⣰⠻⡄⠱⣌⠀⠈⢢⠀⠈⠇⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠃⣸⡀⠀⣼⣧⣦⠞⠁⠀⠱⡔⣌⠑⠀⠀⠀⠀⠀⠈⡞⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣿⠿⠚⠛⠉⠁⠀⠀⠀⠀⠘⢮⡢⡀⠀⠀⠀⠀⠀⢧⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⣆⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⡄⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⡜⠀⡀⠀⢀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣷⠐⢤⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣄⣼⣿⣴⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⠺⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠲⠓⡔⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠉⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⣤⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣷⣤⣤⣤⣾⣷⣶⣶⣦⡀⠀⠀⠀⢠⣾⣿⣿⠁⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣦⡤⠤⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⢿⠿⣿⣶⣶⣶⣶⣾⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠙⠻⠛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠒⠂⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢀⣄⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣶⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠁⠀⠀⠀⠉⣻⣦⡄⠀⠀⠀⠀⢠⣴⣶⣿⣿⣧⣀⣀⣀⣼⣿⣿⣶⣦⡀⠀⢀⣴⣶⣾⣿⣧⡀⠀⠀⣠⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀⠀⣀⣴⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠛⠋⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠃⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⠳⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⡀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢴⠄⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠈⠛⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣷⣤⣀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠒⠛⠛⠛⠃⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠟⠻⠛⠛⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠈⠛⠿⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⡿⠿⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⣀⣠⣾⣿⡄⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣄⣀⣀⣀⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠉⠀⠀⠘⡀
⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⢸⡟⠉⠉⠉⠉⠉⢻⡗⠀⢸⣿⠟⠛⠛⠛⠛⢿⣿⠀⠀⣸⣦⣤⣤⣴⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⣯⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠟⠉⠉⠉⠉⠙⢻⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀⠀⠀⠀⠀⠐⣿⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⣶⣤⣤⣤⣤⣴⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣆⠀⠀⠀⠀⠀⣸⡏⠀⢸⣿⣤⣀⣀⣀⣠⣼⣿⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣶⣤⣤⣤⣤⣴⣾⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣦⣤⣤⣠⣤⣴⡇
⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⢿⣿⣿⣿⣿⣿⡿⠃⠀⠸⢿⣿⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣿⣿⠇

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣬⣍⣿⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣿⣿⣿⣧⣤⣬⣽⣿

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⣀⡀
⠀⠀⠐⠁⠉⢄⠀⠀⢰⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣤⣿⣭⠁⠀⠀⠀⣀⣡
⠀⠀⠘⠦⠠⠓⠀⠀⠺⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠁⠀⠀⡄⠀⠀⠀⠀⢹⣝⠋⠀⠀⠀⠀⠉⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠈⠉⢱⣶⡾⠁⠀⠀⠀⠀⢢⣉⠀⠀⠀⠀⠀⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⡷⠆⠰⢾⡄⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠄⢳⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢻⣥⠒⠒⣬⡞⠀⠀⠀⠀⢠⠭⡄⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣷⡆⠸⢛⠀⠀⠀⠀⠀⣴⣶⢠⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣧⡄⠰⢞⠀⠀⠀⠀⠀⠋⣿⣏⠀⠀⠀⠀⠀⠐⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⢀⣿⣿⣿⡟⢛⡆⠀⠀⠀⠀⣇⡄⢰⠾⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡏⡅⢠⣾⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⡴⠏⠁⢨⠴⢦⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠇⠀⠀⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣞⠻⣿⣿⡏⡀⠀⠀⠀⠁⡇⠀⠀⢸⠈⠀⠀⠀⠀⠸⠆⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⣷⣦⣄⠀⠈⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⠀⠉⠻⢿⣦⡀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠻⣷⣦⡀⠀⠹⣿⣆⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠈⢿⣧⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡧⠀⠈⣿⡆⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⢁⡤⠤⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠄⡀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠊⠉⣀⠘⣢⠲⣐⠀⠀⠈⠀⠀⢀⡇⠈⠀⠉⡇⠳⠤⣀⠔⢺⠉⠡⠀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠗⠒⠒⠲⡟⠀⠀⠀⠀⠀⢸⡇⢠⠀⠀⠇⠀⠀⠀⠀⢸⡄⡄⡞⠉⠉⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠯⣝⢉⣁⣹⠀⠠⠀⠠⠄⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡇
⠀⠀⠀⠀⠀⣀⠀⠀⠙⡂⠀⠇⡄⣀⠀⠀⠀⠀⢠⠇⡇⠀⢀⣤⡀⠆⠙⠀⠀⠁⠀⢱⠤
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠰⡓⢬⣀⡀⠀⠰⣊⣰⠁⠀⠈⡈⢳⡄⠀⠀⠠⠄⣱⠈⡱⠢⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠭⢭⣭⠏⠜⠀⠀⠀⡏⢶⢶⠶⠶⢚⡋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠁⠢⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠁⠉⠉⠉⠑⠀⠐⠒⠲⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⠴⠒⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡶⠧⠤⢤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠀⠀⠂⠰⠆⠄⠄⠀⠠⣀⡀⠤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡀⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⡦⠀⠀⠁⢰⡆⣀
⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠴⠶⠶⠖⢢⡍⠁⢰⠁⠀⠀⠀⠀⠀⠀⢀⡤⣿⠐⣸⢁⣄⠀⠀⠀⢀⠀⡇⠶⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠀⠉⠈⠉⠹⡧⠀⠀⠀⣇⠒⠂⠈⠀⢸⠃⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⡇⠀⠀⠀⠀⡶⠉⠀⢀⠀⠀⠀⠀⠀⠘⢠⠄⠀⠀⣽⣦⣄⣀⠀⣠⠃⠀⠀⠀⠀⠀⠘⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡇⠀⠀⠀⠀⠀⣠⠆⠙⠓⠂⠉⠯⣤⡀⠹⠂⡀⠀⠶⣜⣁⠀⢦⣸⠆⠀⠀⡀
⠀⠀⡠⠋⠀⠀⢀⠾⠊⠋⠈⠣⡄⠀⠀⢸⠀⠀⣇⠀⠀⠀⠤⠰⠁⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠉⢦⡆⠈⠳⡎⠰⠅⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠊⠄⢠⠋⠀⠀⠀⠀⠀⠰⠀⠀⠘⡇⠀⣿⠀⠀⠀⠦⣼⠀⣀⠀⠀⠤⠀⣀⣀⢬⡹⠀⠸⢌⢫⡄⡾⢠⠓⠀⠤⠀⡀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠴
⠀⠀⠆⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠀⢣⠀⠀⠀⠀⠡⠀⢳⣤⠀⠀⠲⢶⠏⡘⠀⠀⠀⠈⢦⡙⣤⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡬⠀⢀⡆
⠀⠀⠀⠀⣦⣼⡄⠀⠀⠀⠀⠀⡸⠃⠀⠀⡇⠀⣺⠀⠀⠀⠀⠀⠙⠢⡄⠐⠂⠂⡠⠖⠀⠀⠀⠀⢀⡌⡁⢬⡳⠖⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠙
⠀⠀⠀⠀⠁⠀⠉⠠⡀⠀⣀⡴⠁⠀⠀⠀⡑⣿⣫⣄⠀⠀⠀⠀⠀⡀⠏⠀⠀⠘⢦⡀⠀⠀⠀⢸⠋⢘⡿⠢⣴⡜⠁⠀⠉⠙⠛⠶⠤⣀⣠⠊⠉⠁⠐
⠀⠀⠀⠀⡈⠁⠈⡀⡏⠉⠁⢠⠀⠀⠀⠀⣧⡀⢩⡄⣰⢄⣴⠋⠉⠃⢀⣄⡰⠀⠀⠉⠉⢃⡀⢈⡟⠉⠡⣠⣼⢓⡤⢄⡀⠀⠀⠀⠀⠀⡁⠀⠉⠀⠐⠆
⣀⡐⠀⠁⣀⠀⣀⠔⠓⠰⠆⠉⠉⠑⠶⡄⣙⠙⠡⢶⣅⠛⢷⣶⡄⠀⠀⠅⠠⠀⠀⠀⠀⠁⠸⠋⠀⠀⡜⠁⠀⠀⠀⠀⠀⠋⠰⠂⡄⠈⠣⣤⠲⠶⠀⠐
⣉⣈⣁⣀⡀⣀⣡⠤⠤⠖⠘⠓⠒⠒⠒⠢⡙⢄⡀⠈⠘⡣⣀⣩⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡷⠊⠀⠻⡑⠉
⠀⠀⠀⠈⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠻⢯⡄⢀⠸⢇⠀⠀⠀⠀⠀⠀⠀⣸⢣⣤⢠⡴⠁⠀⠀⠀⠁⠴⠀⠀⠀⠀⠀⡮⠀⠀⠀⠀⢐⢹⡷
⣀⣀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠤⠤⠤⠤⢾⠀⠀⠀⠀⠀⠀⠀⡇⢺⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠠⣇⡀⠀⠀⠀⠠⠘⠁
⠀⠀⡌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡯⠄⠀⠀⠀⣺⠀⠀⠀⠘⠀⠀⠀⡃⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠈⠀⠀⣰⠆
⣀⠀⣐⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡆⢳⠒⠒⠀⠉⢹⠂⠀⠤⠤⠤⠀⠤⠁⠀⠀⠈⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠘⠁⠈⢠⠤⠚⠁⠀⠘⠃
⠀⠠⡴⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠤⠀⣀⢀⠀⡈⠠⠉⠉⠈⠁⠂⢉⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢠⣄⠀⣀⠀⠀⠀⠀⠀⠒⠁
⣀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠈⡏⠀⠠⣀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⣡⣈⡐⠇⡀
⠉⠀⠀⠙⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠤⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠔
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠹⡄⣀⣀⣀⢀⡀⣀⠠⠤⠤⣤⠖⠂⠁⠠⠄⠀⢻⠀⠀⠀⢸⣷⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄⠂⠁
⠀⠁⠀⠀⠀⠁⠀⠀⢩⠙⢤⣀⡀⠀⣠⠞⠁⡇⠀⢀⣀⠀⠀⠾⠀⠀⠀⢰⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⣄⠀⠀⢸⠀⢀⣀⣀⡏⠀⢀⣀⡠⢤⡇⠀⠀⠀⢺⠀⡇⠀⠀⠀⢛⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠞⠻⠀⠈⠁⠉⡟⠛⠈⠁⠀⢀⡇⠀⠀⠀⢸⠀⢰⠀⠀⠀⢸⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣤⠤⠤⢶⠒⠒⠚⢉⠭⡀⠀⠀⠀⣇⣠⠋⠁⠂⡄⠀⠙⠀⠀⠀⠀⣏⠀⠸⡆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠠⠀⠁
⠈⠀⠀⠀⠀⠀⠑⠄⠀⣏⠀⠘⠀⠁⠀⠁⠁⠀⠀⢀⠇⠀⣿⢀⣀⣠⣰⡇⠀⠀⢿⡀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣈⣉⣀⣀⠤⠖⢁⣤⠎⠀⠀⠀⠀⢸⡇⠀⢠⡞⠉⠁⠀⠈⣳⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠁⠀⠸⠶⠒⢤⠒⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣂⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠋⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣛⣛⣟⣻⣻⣿⣿⠛⣿⣟⠛⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⣤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠄⠀⠤⠀⠉⢤⣬⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣍⠠⠤⠂⠘⠘⣦
⠀⠀⠀⠀⠀⣠⣾⣥⣶⠆⠀⠀⠀⠀⠛⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣿⡑⣶⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢀⣴⣿⢿⣷⠀⠀⠀⠰⢄⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⠀⠀⠀⢀⡴⠖⢃
⠀⠀⢀⣾⡇⢙⠀⠀⠀⠀⠉⠁⠀⢀⡤⣁⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⡛⡭⠑⣆⠀⠉⠁⠈
⠀⠀⣿⡄⣴⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠾⠛⢻⣶⣿⣿⠇⠈⠀⣛⣄⠀⠠⠀⠂
⠀⢰⣿⣿⣿⠷⠆⢄⠀⠀⢲⣄⡲⢀⣤⠉⢀⣆⡀⠀⠀⠀⠀⠀⣇⠞⠁⠄⠀⢿⣷⣦⠆⠈⠁⠀⠂⠀⡆
⠀⠀⠹⠟⠟⠃⠀⠀⠑⠄⡀⠈⣡⡟⡟⠳⢴⠆⢸⠀⠀⠀⠀⠘⣿⣠⠀⠀⣀⣀⢻⣷⣀⠆⠀⣚⠁⠰
⠀⠀⠐⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⠒⠀⠈⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣷⣦⣬⣥⣴⣾⣿⣿
⠀⠀⠀⠀⠦⠄⠀⠀⠼⠁⠈⡝⠛⠛⣁⠔⠁⣀⠄⠢⠀⠀⠀⠀⠀⢸⠔⢀⡠⠆⠉⠛⠿⠿⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⠀⠀⡠⠊⠀⠀⠀⡡⠄⠂⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣭⣴⣶⣶⣶⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣛⡶⠤⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣭⡶⠶⠶⠶⠶⢶⣶⣤⣍⣙⠳⢦⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣛⠿⠿⠿⣿⣿⣶⣶⣮⣽⡻⢷⣦⡉⠳⣦⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣦⣭⣙⠻⢿⣿⣦⡈⡛⢦⡈⢳⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠲⠄⠀⠀⠉⠛⠿⣿⣿⣦⡹⣿⣷⡹⣆⢉⠂⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⠀⠀⢰⣌⠙⢿⣷⣿⣿⣷⢹⣧⠳⡄⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠹⣿⣿⣿⡌⣿⣇⢹⡜⡌⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣿⡀⢿⣿⣿⠁⣿⣿⠀⣷⣿⡈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠧⢸⣿⡿⢸⣿⣿⠀⣿⣿⡇⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⢡⣿⣿⡿⣸⣿⡟⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⣿⣿⡿⣱⣿⠟⢡⣿⢏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢋⣾⡿⠃⣰⠟⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣱⣿⢫⡆⢈⣵⢢⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣼⣿⢣⣿⢀⣾⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⠀⢿⡏⢸⣿⣸⣿⠀⠁⠀⠛⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣮⡛⠘⣿⣿⣿⣇⠐⢄⣙⣚⣵⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢻⣷⡘⣿⣦⣌⠻⣿⣿⣦⣔⡲⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡙⠷⡈⠙⠿⣷⣦⡙⢿⡟⠿⢿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⡛⢀⣜⣿⣷⣄⠈⢓⣮⡙⢿⡌⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⣤⣬⡾⢏⣿⣿⣷⠉⠿⣹⢢⡑⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠁⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⠀⠈⠴⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⣏⠁⠀⠀⠀⠀⠀⠀⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⠞⣀⢁⡤⣀⣤⡄⣠⣀⠄⡶⢣⣄⡄⠀⠀⣠⣤⢀⣄⡤⣠⣤⠞⠀⠀⣠⢋⣤⡤⠀⣤⢠⣞⡅⣠⢃⣤⣄⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠙⠂⠙⠘⠊⠛⠛⠘⠃⠙⡿⠃⠀⠈⠃⠛⠙⠙⠃⠙⠙⠂⠀⢸⡻⠉⠊⠓⠛⠋⠉⠙⠉⠓⠙⠊⠙⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⡇⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐⣿⣛⣛⠛⠛⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢶⣄
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⢸⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⠖⠒⠀⠀⠀⠀⢶⣤⡀⠀⠀⠸⢻⡄
⠀⠀⠀⢸⠀⠈⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠁⠀⣿⣿⠀⠈⢹⠿⠷⢶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢹⡀
⠀⠀⠀⠀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⡄⠀⠀⢸⡇
⠀⠀⠀⠀⣷⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⠛⠿⠁⠙⠟⠙⠥⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡇⠀⠀⠘⡇
⠀⠀⠀⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣭⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣄⣀⣄⣀⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡛⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⢸
⠀⠀⠀⠀⠁⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣸
⠀⠀⠀⠀⣶⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠘⣫⠙⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣈
⠀⠀⠀⠀⣿⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢢⠟⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⢀⡏
⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢐⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠇⡀⠀⠘⡇
⠀⠀⠀⠀⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠁⡀⣾⠃
⠀⠀⠀⠀⠛⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⣸⣿⠰⣶⣶⣶⣏⣁⣠⠖⠀⠀⠀⠀⣀⡜⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⡀⣿⡿⠟⠋⠁⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣏⣿⡇⣿⠃⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⡿⣿⣻⣇⣿⣤⣠⣤⠞⠋
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⢼⣦⣿⣿⣿⢀⠟⠁
⠀⠀⠀⠀⢸⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⣀⣠⣿⣿⣿⣿⠈
⠀⠀⠀⢀⣌⠿⣿⣿⣧⣔⣀⣀⠠⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣤⣄⣱⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠙⠻⠶⣭⣝⠛⠿⢿⣿⣿⣶⣾⣿⣿⣷⣦⢠⣦⣤⣴⣦⣤⣴⣿⣤⣦⣼⣿⠿⠟⢛⣩⣶⣿⣿⠁
⠀⠀⠀⠀⢶⣤⠀⠀⠈⠉⠛⣶⣦⣤⣭⣍⣉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⣿⡧
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠉⢁⣀⣀⠠⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⣶⠀⢰⣦⡆⠐⡶⠀⢰⠀⠀⣶⠂⢰⣦⣶⠀⣶⠀⢰⣶⠄⠐⠀⢴⡆
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠙⠛⢀⣛⣂⡈⠉⠁⢀⣋⣀⣘⠓⠀⠙⢃⣈⣉⣙⡀⠛⠂⣘⣙⣁⣀⡀⢚⣃⣀⣀⡀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⢨⣿⣿⣧⠀⠀⢸⣿⡿⣿⣿⡆⠀⢸⣿⠟⠻⣿⡆⠀⣿⡿⠛⠻⠃⢸⣿⡿⠿⢿⣧
⠀⠀⠀⠀⠀⢸⣿⠁⠈⣿⡇⠀⢸⣿⢿⣿⠀⠀⢸⣿⠀⠀⣿⡷⠀⢸⣿⣦⣶⣿⡃⠀⣿⣷⣶⡆⠀⢸⣿⣇⣠⣼⡿
⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⡁⠀⣾⣿⢸⣿⡇⠀⢸⣿⣷⣿⡿⠃⠀⢸⣿⠋⠙⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡟⢻⣿⡁
⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⣇⠀⣿⣿⣾⣿⣇⠀⢸⣿⠋⢿⣿⡄⠀⢸⣿⣦⣶⣿⠏⠀⣿⣿⣿⡿⠇⠸⠿⠇⠀⠿⣷⠄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡿⢸⣿⡟⠛⣿⣿⠀⢸⣿⠆⠈⠿⠟⠀⢛⣋⣉⠉⢀⣴⣶⣶⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⢸⣿⣦⣶⣿⠃⣸⣿⠅⠀⠘⠛⣁⣀⣀⢠⢤⡆⣴⡟⠋⠉⣻⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⠿⠟⠁⢀⣀⣀⣠⣤⣤⣭⣭⣭⣭⣥⣭⣥⣬⡥⠶⠞⣋⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⣠⡴⣾⠛⢻⣿⡆⢠⡆⠀⠀⢀⣤⡄⢠⣶⠛⣿⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠹⠦⠾⠟⠀⣿⢷⣷⣴⡏⣸⡿⣾⡇⣸⠟⠀⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⣶⡄⢸⡟⣼⠏⣿⣥⡟⢱⡿⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⣿⣿⣶⣿⡿⠿⣿⠃⣾⠃⠿⠃⠈⢀⣀⣉⣥⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⣠⠏⠀⣋⡤⠴⠞⣛⣉⠉⠁⢀⣽⡿⠁⣺⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⡇⠀⢀⡴⠃⠀⠁⠀⠶⠶⢶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠸⣿⣷⠞⠋⠀⠀⢀⣠⣤⠶⢞⣛⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣫⣥⣒⡛⠋⣁⣠⣤⣤⣾⣿⣿⣿⣿⣯⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠂⠟⢲
⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⠶⠶⣦⠁⡠⣾⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⣻⣄⠋
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣀⣼⠋⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡼⣧⣀⣠⣀⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢁⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣸⣿⣿⣿⣿⡟⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣇⢹⠁⠀⠀⠙⠦⠬⣭⣍⣉⣉⣉⣉⣉⣙⣛⣛⣛⠛⠛⠛⡻⢋⣴⣿⣿⡿⠟⠉⡇
⠀⠀⠀⠀⠀⠀⢠⣆⡽⢮⣡⠴⣄⢠⠀⠀⠀⣠⣾⣵⣧⣤⣴⣿⣽⣁⣉⣉⣙⣟⡛⠐⠾⣿⠻⠛⠁⠙⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠸⡏⣽⡿⠉⣿⠟⢸⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⢸⢾⣀⣿⣐⡇⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢀⡇⠀⢈⡬⣉⣩⢭⡭⣩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⢸⠀⠀⠹⠤⠻⠟⠘⠇⠨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠾⣉⡛⠿⠿⢿⡿⠃⣸⠤⠤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠉⠉⠉⢉⠛⠛⠛⠛⠿⠿⠷⣿⡁⠊⠀⣿⡆⠐⠐⣈⣃⡒⠁⠀⠀⠀⠀⠀⠉⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⡀⠉⠁⠀⠀⣿⡇⠀⠀⠉⢻⣿⣶⣦⣄⢲⡄⠀⠀⢀⣠⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⢶⣶⣿⣯⣤⣤⣤⣭⣭⣭⣭⣥⣴⡶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠶⠶⠶⠶⠤⢤⣄⣠⣿⣀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣀⣤⡴⢶⣴⠛⠉⠁⠀⣀⠀⠀⣀⣠⡴⠦⢤⣤⣿⠯⣽⣏⣀⣀⠤⣤⡾⠋
⠰⠶⡶⠶⣞⠛⠉⠁⠀⠀⣿⡆⠀⠀⠻⠿⠟⢛⣋⣥⡤⠤⠀⢰⣿⣤⣤⣿⡻⣻⣿⡟⣷
⠀⠀⠀⠀⣿⡄⠀⠀⣀⠀⠸⣧⣾⣄⣀⠀⠐⠛⠉⠀⠀⠀⢀⣿⣇⣿⢻⣿⡿⠋⠀⠔⠃⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣿⡇⠀⠀⣿⣻⣆⡿⠀⠈⠙⠛⠳⢶⣤⣀⡀⣰⣾⣿⠙⣿⡿⠟⢰⡄⠀⠀⠀⠀⢠⣶⣾⠿⡏⠉⣉⣹⣋⡻⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⣨⣥⣤⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣿⣯⡿⢛⠀⠀⢾⣿⣷⣦⣴⣿⠿⢋⣡⡾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠙⠛⢿⣶⣄
⠀⠀⢰⠟⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠐⣿⣇⠀⠈⣉⣿⣿⠟⢫⣴⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣾⣿⡿⢷⣆⠻⣿⢦⡀⠛⠛⢋⣠⣾⣿⣴⡟⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⣀⠀⢠⣤⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣻⡿⠟⠋⠀⣀⣼⣿⡆⠈⠳⢿⣿⣾⠛⠋⣨⣾⣿⣾⡾⢡⣆⣴⢀⣴⣆⣼⣿⣧⣾⣶⣿⣿⣸⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠏⠀⠀⢀⡛⠁⣹⢿⣧⠦⣷⣶⣾⣷⣾⠟⢻⡿⠙⣟⡀⣾⣿⣿⡿⠿⠙⠋⠉⠙⣿⣿⣿⢟⣿⡀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⠁⢾⣿⡾⢹⡄⠘⠛⠋⠟⠁⠠⢏⡄⢠⡟⠀⠛⣸⠿⠃⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠘⠛⡋⢹⣷⣠⣤⣤⣤⣀⣴⣞⠁⣽⠎⠀⠀⠛⠀⠀⠀⠸⣶⣾⣿⣯⠙⠻⠿⠿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⠷⠟⠀⣴⣝⣛⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⠄⢰⡇⣀⣹⡿⠂⠀⠀⠐⠶⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠛⢷⣄⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣟⣿⣤⣤⣾⢃⣼⡿⢲⣾⣴⣟⣾⠃⠀⠰⣿⣿⠃
⠀⠀⠀⣀⣀⣠⡴⠒⢻⣏⠀⠀⠀⠀⢹⡇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢈⡙⠛⢿⣛⣛⣿⣿⣏⣴⣿⣿⠟⠋⠁⠀⠀⢠⡏⣿
⠀⠀⠀⠉⠉⠁⠀⠀⠀⣿⣄⠀⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠘⠻⢧⣄⣉⠙⢯⡁⠀⠉⠉⠀⠀⠀⢀⠀⢠⡶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠾⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⣀⣀⣀⣀⠀⠀⠈⠻⣧⢬⣷⠟⠳⣄⠀⠀⠀⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⠉⠉⠉⠉⠉⠛⢛⣳⣆⣼⣿⣯⣀⠀⠙⠷⣤⠶
⠀⠀⠀⠀⠀⠀⢀⣠⡖⠹⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⢀⣈⣩⣟
⠀⠀⠀⢠⣶⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠰⠶⠶⣶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠒⠶⢭⣉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠶⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠺⢶⣄⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠶⣤⡀⠙⢷⡄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠈⢿⡄⠈⣿⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣾⠃⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⡀⠀⠀⠀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⡀⢈⣀⠉⡰⠀⠀⠀⠀⠀⢂⠤⠤⠤⠠⠦⠴⠀⠀⠀⠀⡀⠠⠌⠄⠙⢷⣄
⠀⠀⠘⠖⠖⠒⠲⠒⠢⠀⠀⠀⡀⠁⠀⠀⠀⢀⠀⠀⠀⡤⡉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸⡅⠀⠀⠁⠀⠫⠌
⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠰⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣀⣀⣀⣠⣤⢀⠂⠀⠀⠀⢀⡀⢉⡅⡉⡱⠀⠀⠀⠀⢀⡆⠀⠀⢸⣿⣧
⠀⠀⣾⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⡏⠀⠀⠀⠈⠐⠀⠀⠀⠀⠻⠋⠉⠉⠉⠉⡆⠀⠀⠀⢸⣤⠄⠤⠦⠂⠏
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⢠⠖⢉⣭⠉⠯⣭⣖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣧⡈⠀⠁⠀⣽⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⣀⣀⣀⣀⠀⠀⣿⣿⣧⠀⣠⣷⡞⠓⠉⠉⠱⣶⣿⢱⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠘⠧⡅⢹⠀⡏⣿⠀⠀⣿⣿⣿⣶⡷⢟⣿⣉⣩⣭⣭⣯⣩⣚⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠛⠃⠘⠀⠛⠋⠀⠀⣿⣿⡟⠀⠙⣿⢟⣻⣿⣿⡟⠛⠻⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⢸⣿⠟⠋⠀⢰⣾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠈⢀⣠⣾⡇⠘⠛⢸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣄⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠲⠶⠿⠿⠿⠿⠿⠷⠶⠞⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⣾⣿⠀⢸⣿⣶⡄⢰⣶⣶⡄⣶⡶⠶⢰⣶⣶⡆⢠⣶⢶⡆⢰⣶⣾⡗⢠⣿⢿⡆⢸⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠀⣿⣿⡇⢸⣯⣿⠇⢸⣯⣿⠇⣿⣧⡀⢸⣿⣼⡇⠘⢿⣎⠋⢸⣿⣽⡇⢸⣿⢸⡇⢸⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⢀⣿⣽⡇⢸⡟⣿⡇⢸⡟⣿⡇⣿⡏⠁⢸⣿⢹⣗⢀⣌⢿⣧⢸⣿⣻⣇⢸⣿⢸⡇⢸⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⢸⡿⢹⡇⢸⠗⠿⠇⠸⠿⠿⠃⠿⠿⠷⠸⠿⠸⠿⠈⠿⠿⠏⠠⠿⠿⠇⠘⢿⣾⠇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⣀⣀⣀⣤⣤⡤⠤⠤⣶⣶⡶⠶⠶⢶⠶⠶⢶⣶⡶⢶⠶⢶⠦⠤⠤⠤⣤⣤⣄⣀⣀⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⢠⣴⣿⡿⠃⠀⣠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⠸⠟⠁⣠⡄⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⡰⣿⣷⣶⣿⣿⣧⣼⣾⣿⣦⠀⠀⠀⣤⢠⢤⡀⢤⡄⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣷⣶⣯⣭⣉⣉⡩⡭⣭⣤⣾⠇⠀⠀⣿⢘⣺⠇⣼⠁⣟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠘⣟⡷⠤⠤⠤⠼⢿⣿⡞⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⡟⣿⣿⠀⠀⢄⣀⢙⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠈⠺⢽⣗⣄⣉⡭⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠈⠙⢿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠉⠉⠛⢿⣶⡀⠀⠀⠀⢘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠿⠿⣷⣤⡀⠀⠀⠀⠀⠹⣿⡄⠀⠀⣼⡿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣆⠀⠀⠀⠀⣿⡇
⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⣰⡿⠁
⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠁
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢸⣿⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢾⣿⠛⠋⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣿⡋⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣤⣤⣤⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠤⠽⠀⠀⠀⡀⠀⠀⠀⠀⢀⢠⠉⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠒⠄⠐⠂⠀⡀⠀⢀⡐⠁⠀⢂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⡴⠤⠔⠿⠃⠀⡀⠈⠱⢤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠐⠁⠀⠀⡜⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⡐⠀⠱⡂⠉⠁⠀⠀⠐⠊⠉⠑⣼⠀⠀⠀⠡⠠⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠘⠦⠎⠀⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⠃⡠⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠘⡀⠈⠉⢩⠀⠀⠀⠀⠢⠇⠀⢸⣮⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⣇⣀⣀⡘⠀⠀⠀⠀⠀⡰⡀⣺⣛⣓⣤⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠏⠉⠉⠁⠉⠓⢄⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⣤⣤⣤⡦⠬⠶⠤⡀⡇
⠀⠀⠀⠀⠀⢧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⢘⠃⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠏⠳⣄⠢
⠀⠀⠀⠀⠠⡟⠒⠻⠦⣤⠀⠀⠀⠀⢀⠠⠤⠀⠂⠺⣀⡤⠔⠀⠤⢄⡘⢄⡀⠀⣀⠼⠶⠶⠟⠛⠃
⠀⠀⠀⠀⠀⠁⠉⠙⠒⠒⠁⠀⠀⠀⠘⠀⠄⢀⡀⢀⣀⣀⢀⣀⣀⡀⠜⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⣠⡶⠾⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⣤⣶⣶⠖⠛⠻⣧⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡞⣿⣟⣿⣿⣶⣿⣿⣿⣿⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠊⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠟⠋⠁⠀⠹⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠀⢘⣄⠀⠀⠀⡠⠒⠒⠐⠒⠤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢖⡦⠀⠀⠈⠶⠆⠀⠀⠀⠀⠀⡄⢿⣯⠛⠙⠓⠴⣾⣉⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣷⣤⣀⡀⠀⠀⠈⠙⠢⣀⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠙⠶⣉⣉⣉⡿⠲⠖⣤⣄⣀⣿⡛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠰⠀⠀⠀⣀⢾⡿⠀⠀⠀⠀⠀⠉⠒⠒⠛⠋⠉⠁⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠑⢄⠀⠀⢀⡠⠚⠕⣯⢶⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠉⡉⢁⡠⠔⠊⠀⡌⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⢀⡠⠔⠊⡡⠂⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡠⠔⠊⠁⣀⠔⠋⠀⠀⠀⠀⠀⢠⠁⠀⠀⡄⠀⠀⠀⠀⠈⠑⢄
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄
⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀
⣿⡿⠿⠿⠻⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣶⡒⡶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡇⣼⣇
⠀⠀⠀⠀⠀⠀⣠⢟⠁⣿⣷⡙⢿⣄
⠀⠀⠀⠀⠀⡼⢡⠁⠈⣿⣟⢱⠈⢻⣦
⠀⠀⠀⠀⠀⡇⢸⠀⣷⣿⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠉⠉⠉⠙⠧⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠀⠀⠈⣀
⠀⠀⠀⠀⢸⡧⠀⠀⠀⠠⠀⠀⠀⠖⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⣿⣄⣀⡀
⠀⠀⠀⠀⢸⠁⠀⠈⠁⠀⠀⠈⠀⣤⢹⡇⠀⠀⠀⠀⠀⣿⠀⣶⡖⣲⣶⠀⣶⣶⣿⠿⠛⠙⢹⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠀⠀⠀⠉⢾⡇⠀⠀⠀⠀⠀⣿⠀⣿⠁⠸⣿⢠⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠔⠂⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⣿⠀⠃⠀⠀⠀⠸⣿⣯⣿⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢅⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣉⣽⠇⠀⠀⠀⠀⠀⣷⠀⠀⠆⠀⣁⢰⣤⢿⣿⠿⠇
⠀⠀⠀⠀⠀⡏⠀⠀⣶⣤⣤⣴⡆⣸⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠺⢺⣽⣿⣿
⠀⠀⠀⠀⠀⣧⣤⢀⢿⣿⣿⣾⣧⣿⡿⠀⠀⠀⠀⠀⣰⡿⠛⠓⠒⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠛⠛⠛⠛⠋⠉⠁

⠀⠀⢠⣤⡀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⡀⠀⡄⣀⠀⠀⠀⠀⢀⠔⠠⠀⢠⢀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⣿⣿⠷⠀⠀⠢⡑⠀⠀⠀⠀⣿⣿⠿⠀⠤⡢⡑⡀⠀⠀⢀⠀⠀⠅⠤⢐⢝⢆⠀⠀⣿⣿⠗⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠸⣿⣆⠀⠀⢡⠐⠐⡀⠀⠀⠘⣿⣧⠀⠀⠀⠠⡅⠀⠀⠈⢆⠀⠄⠀⠈⠨⠐⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣷⣤⣦⡀⠀⠁⠀⠀⠀⠈⢿⣷⣤⣦⡀⠀⠀⠀⠀⠀⠢⡀⠒⠂⢂⠀⠀⠀⠀⠘⢿⣷⣤⣦⡀⠀⠀⢿⣿⣿⣿⣄⡉⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠙⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠃⠀⠀⠀⠀⠀⠉⠛⠿⠓⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠛⠛⠛⠛⠛⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠞⠋⠉⠉⠀⠀⠈⠉⠙⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡾⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣹⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⢻⡄⢠⣤⣄⣀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⢹⡟⢰⡿⠉⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣿⠃⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠇⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⢰⡏⣼⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣸⠷⢿⣅⣀⣀⣀⣤⣤⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣦⠀⠀⠀⠹⢦⣄⣀⣀⣀⡴⠋⠀⠀⢀⡼⠃⠀⠀⠀⠉⠉⠉⠀⢀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢛⣟⠛⠶⢦⣤⣤⣤⣴⠶⠛⢻⠟⠳⠶⠶⠶⠶⠶⠶⠞⠛⢻⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠶⠾⠿⠿⠷⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⠈⠙⢿⣷⠶⢶⣾⠃⠀⣠⡟
⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⣀⡴⢾⡏⣸⡟⠀⠀⠀⠀⠹⢦⣾⠛⢿⣴⣏⣛⣦⣄⣀⣿⠛⣿
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⡾⢠⣿⠁⠀⠀⠀⢠⣤⣤⣽⣦⣬⣭⣭⣭⣭⣭⣭⣥⣤⣿⣤⣤⡄
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⣾⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⢿
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⣿⣤⣤⣤⣤⣾⡇⠀⠀⠀⣠⣾⡿⣿⣿⣷⣟⣿⣷⣆⠀⠀⠀⢸⡇
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⠀⣾⠁⠀⠀⣰⣿⣻⣿⠟⠉⠉⠛⢿⣾⣿⣧⠀⠀⠈⣷
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⣄⠀⢀⡿⠀⠀⠀⣿⣟⣿⡇⠀⠀⠀⠀⢸⡿⠞⣿⠀⠀⠀⢻
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⢾⡇⠀⠀⠀⢻⣿⣻⣷⣄⡀⢀⣠⣾⠁⢀⡿⠀⠀⠀⠸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠻⣿⣿⢿⡿⣯⠉⢻⡟⢿⡅
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠿⠋
⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⢻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡅⣦⣖⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⢀⡴⠚⠓⠶⠋⢳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡸⣿⣿⣿⣿⢫⣵⣬⣭⣶⣎⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠘⣆⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣧⠹⣿⢋⣶⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠀⠳⣴⣦⢰⠒⠶⣄⠴⢲⠞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⡇⣿⣜⠋⢹⡏⣭⣝⠻⣫⡍⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⢸⠀⠀⢸⣿⢸⠰⠀⠠⠀⢨⣿⡳⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⡇⣿⣿⣿⣿⡷⢚⢭⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⢸⠀⠀⣾⠙⠋⠸⠀⠐⠀⢸⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣧⣵⣿⣿⣿⣿⡇⣿⢸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⢸⠀⠀⢿⠀⠀⢀⠀⠀⠀⠘⣶⣫⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⢉⠜⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⢿⠠⠄⠸⠄⠐⠄⢸⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠀⠀⠘⠒⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣭⣭⣭⣭⣭⣥⣿⣿⣧⣭⣭⣭⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠄⢢⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⢀⠼⡋⠉⠳⢹⢰⠀⠀⠀⠀⠀⡠⠚⢉⠄⠀⡀⢀⠢⡀
⠀⢰⡉⠉⠁⡔⠀⠀⠀⠀⠀⣀⠀⠀⢠⢯⠏⠀⠀⠀⠀⠯⠀⠀⠀⠀⣸⠁⡴⠁⠔⠚⡁⠀⢧⢱
⠀⢸⡁⠰⣂⡼⠀⠃⠀⠂⠀⡡⠃⠀⠸⡀⠐⠈⠁⠀⠠⠐⠆⠀⠀⠀⡇⢰⠁⠄⠀⠀⠀⠈⢸⠈⡇
⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠁⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢊⠜

⠀⠀⢀⠤⣤⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠠⠠⠦
⠀⠀⡟⠚⠋⠤⣴⠖⠊⠀⠀⠀⠀⢀⡠⠤⠖⠋⢁⡔⡡⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠐
⠀⠀⠈⠂⠉⠋⠁⠀⠤⠠⠀⠀⠐⠁⠀⣀⣤⠴⠋⣰⠃⠄⠀⠆⢠⡀⠀⠀⠀⠀⣀⠀⠐⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠰⠉⠀⢀⣀⠴⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⡄⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁⠀⠡⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⢀⠀⡀⠀⢀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡀⢆
⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠈⠂⠠⠄⠠⠌⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⡇⢨⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⢷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⠻⡅⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢻⡄⢘⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔⣬⢐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠻⠿⣦⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠰⣅⠂⢄⡙⠻⠿⠖⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢿⣧⠀⠀⠑⠲⠊⠘⠯⠁⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠠⠟⣛⣿⣭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣀⠀⣈⣢⡰⠿⠗⢀⣂⣭⣤⣶⣿⣿⠿⠛⠛⠗⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠀⢉⡉⢁⣀⣀⣀⣤⣿⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⠟⠚⠛⠋⠉⢩⡄⠀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⢀⡴⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⠜⠀⠀⠀⣠⡤⢄⢠⣴⢠⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣰⠃⠀⠀⣠⣤⣴⡦⢠⣶⢂⣾⠇⢸⣿⠞⢺⡆⠀⣾⡟⣡⠎⢸⡿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞⠋⣿⡇⣼⡟⠀⣿⡇⢀⠿⢻⣿⠀⣸⡟⢦⣾⠃⣸⣿⠊⢁⡔⠁⠀⣿⣃⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⢴⡟⠀⣿⣇⣠⣿⡧⠊⠀⢺⣯⠔⢻⡧⠞⠁⠀⠘⠻⠖⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠊⡼⠀⠀⠙⠋⠀⠉⠀⠀⠀⠀⠀⠀⣀⣤⠴⠦⠀⠀⣠⡖⢙⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⣼⣿⡠⠊⠀⢀⣤⣤⡀⠀⣠⣄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣀⢼⣿⡏⣤⡄⠀⣾⡏⠀⡇⢀⣿⠇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡅⣼⣿⢠⣿⢁⢼⣿⠻⣰⠗⢸⣿⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣿⡇⣿⡏⠸⠿⠉⠈⠛⠓⠋⣀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣠⣾⠟⠀⠙⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣦⣤⣤⣴⣦⣶⣴⣦⣦⣴⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣴⣤⣶⣶⣴⣦⣴⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣋⣤⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠿⣿⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠻⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡽⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄⠀⡤⠦⠀⠸⠟⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣐⣒⡛⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣀⡀⠀⠀⠀⠂⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡐⠼⠀⠀⠀⠀⠀⠀⢀⡔⠈⠰⠐⡀⢿⣿⡔⣒⠀⠀⠀⢀⠼⡗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⣾⠁⢀⣿⣷⣀⠀⣀⡴⠋⠀⠁⠟⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢂⣀⣡⣤⣤⣀⠀⠀⠀⡼⠀⠀⠸⠍⠻⣏⢽⡂⠀⡄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣠⣾⣿⣿⣯⣹⣿⣿⣧⣠⠞⠁⠐⢤⠀⠀⠀⠁⠘⣇⠈⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢰⣿⡄⠉⠙⠛⠋⠉⠁⢿⣷⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⢸⡿⢁⣀⡀⠀⠀⣀⡀⠙⡏⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠺⠿⠂⠈⠛⠖⠀⡗⡆⠀⣈⠇⠀⠀⠀⠀⠀⠀⢸⢻⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠷⠟⡔⡂⠈⠀⠀⠀⠀⠀⠀⠘⣈⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢤⣉⣡⠤⠀⣸⣧⡄⠗⡆⠀⠀⡄⠀⠀⠀⠀⠀⠹⡶⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠁⠀⢀⡖⣿⣿⣷⡞⣷⡀⠀⠙⠒⠀⠤⠤⠀⠸⣟⣁⣤⣄⣀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⡿⣿⢶⠾⠛⠀⣿⢻⢿⣿⣸⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠘⣿⠒⠒⠒⡂⣼⢿⠘⠀⣿⠷⣿⣿⡇⢹⠻⢷⣦⣄⣀⠀⠠⠴⣤⣀⠀⣝⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠛⢿⠸⣇⠘⣇⠉⣡⠞⠡⠃⠀⢠⢿⠀⠈⠻⢷⣴⣼⠶⡘⢿⣿⠛⠒⠦⠤⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠁⠃⣿⠀⢸⡄⢻⡀⠘⠂⠀⠀⠀⡄⠀⡌⢸⠀⠀⠀⠀⠈⠛⢿⣤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣯⠀⠀⠃⠀⠁⠀⠀⢀⡴⠊⠀⡜⠀⠨⠀⠀⠀⠀⠀⠀⠀⠹⣶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢹⡄⠀⢄⡀⠀⠠⠞⠋⠠⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⠁⠀⠈⠉⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⡀⠀⠀⠠⠂⠈⠀⠀⡄⣤⣥⡀⠀⣀⢀⣀⡁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⣼⣿⣿⡇⠀⣾⣾⣿⣿⡆⠀⢷⣿⣿⡇⠀⣿⣿⣿⡇⠀⣀⠆⠈⠀⢸⡠⡀
⠀⠀⠀⣼⣷⣿⣿⡇⠀⢿⣿⣿⠃⠀⢻⣿⣿⣿⠇⠀⢸⣿⣿⠁⠀⢹⣿⣿⠃⠀⣰⢸⣶⣿⣾
⠀⠀⠀⠻⣿⣿⣿⠇⠀⠸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠹⡏⠀⠀⣿⣼⣿⣿⣿⡄⢀⠆
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠿⠿⠀⠀⠀⢿⣿⡇⠀⠀⠀⠉⢋⠀⠀⠀⠘⡀⠀⠀⠉⠛⠛⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠉⠰⠖⠚⠉⠑⠲⠒⠒⢤⢄⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⢀⡤⣄⠀⠀⠀⠀⠀⢠⠤⠖⠀⠒⠒⠓⠒⠊⢳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡼⢥⠈⢁⠴⢾⡃⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⡄⠀⡀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠁⠀⠀⠘⠀⠘⣆⠀⠀⠌⠁⡀⡇⢠⠀⠀⠸⠀⠀⠀⢀⢡⣼⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡏⠀⠀⠀⠀⠀⠀⣼⠀⢀⠀⠀⠀⠃⢸⠀⠀⠐⠀⡀⠀⠈⢸⠐⠀⠒⠒⠀⠈⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣯⠀⢤⡀⢀⡀⢀⣿⠀⡎⠀⠀⠀⣀⢸⠀⠀⠀⡀⣇⠀⠠⢼⣀⡤⠞⠛⠛⠒⢄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠁⡇⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⠇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⢀⠀⠀⠀⠀⢻⡴⠀⠀⠀⢰⠀⢠⠀⠀⠀⡆⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡇⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠃⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⢰⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡇⠀⢸⠀⡄⠀⢸⡃⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⢸⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⢀⡅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡼⠀⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡁⡏⠓⠲⠤⠀⠊⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⡇⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⣿⣀⠤⠤⣄⣢⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⡘⠀⡅⠀⠀⡇⢰⠀⠀⠀⠀⢀⠀⠇⠀⠀⢸⠀⢇⠀⠀⢻⡴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡈⡀⠁⠀⠈⠂⠚⠁⠈⢦⣀⠀⠀⠰⠀⠈⠂⠀⠈⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠶⢭⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠉⠉⠓⠒⡂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⠁⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠤⣤⣥⣄⣤⣤⣤⡤⠤⠶⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠰⣶⣶⠀⢰⣶⠀⠂⠀⠰⣶⣶⣶⣶⡆⢤⡐⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣖⣺⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣤⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣻⠿⢛⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣶⣭⣭⣿⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣿⣿⣿⣿⡄⢠⣤⣾⣿⣿⣿⣿⣿⣧⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⢾⢿⣿⡿⡻⢿⣝⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡄⠁⢫⣿⣿⣦⣤⣿⣞⣿⣿⣷⡈⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⢡⣿⣿⣿⣷⣶⣟⣻⡾⠛⣻⣿⣿⣾⠿⣿⣧⢹⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢻⣷⣿⣿⠋⠉⢻⣿⣿⣯⣴⢟⣫⣼⠿⢿⣧⣿⣿⡆⢻⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⣠⣾⣿⡿⠃⠀⠀⣠⣿⣿⣿⣿⣿⣯⡵⠋⣸⣿⣿⣿⣿⣾⣿⡿⢋⡾⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⣾⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡼⣿⣿⣧⣄⣰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠻⢿⣿⣿⣿⡏⢉⣉⣋⣩⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣫⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣿⣯⢷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣹⣿⠿⣋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣥⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣛⣷⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣶⣿⣿⣿⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡀⢻⣿⠋⠛⠁⠹⣿⣿⣿⣿⡟⢫⡛⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣕⣺⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣤⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⠿⡛⣛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣶⣭⣍⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣛⣿⣿⣿⣿⡄⢠⣤⣾⣿⣿⣿⣿⣿⣧⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⢶⢿⣿⡿⠻⣿⣝⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡄⠠⢫⣽⣿⣦⣤⣿⣞⣿⣿⣷⡘⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠟⠁⠿⠿⠿⠷⠶⠟⠻⠾⠛⠻⠿⠿⠞⠻⠿⠇⠹⠿⠆⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣲⣽⣾⣿⣏⠁⠀⠀⠀⠀⣉⠉⢙⡛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣪⡵⠛⠙⡛⠣⣿⠛⠀⠀⠀⠸⣿⣶⣿⣷⣿⣷⣶⣍⡻⣷⣦⡀
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⡟⠀⡐⢀⠻⣄⠻⢰⠀⠀⠀⠀⠈⠙⢿⣿⣟⠻⣿⡝⠻⣮⣿⣿⣦⡀
⠀⠀⠀⣠⢟⡽⠛⣩⣿⣿⣿⣿⣿⡁⠀⢃⢿⡀⠈⠳⢄⣧⡀⠀⠀⠀⠀⠀⠙⣿⣧⠘⢿⡄⠈⠻⣿⣿⣷⡄
⠀⠀⠀⠃⡾⢁⣾⠟⠙⠉⣩⣾⣿⣇⢀⠀⠘⢷⣤⣇⢠⠈⠙⠷⣦⡐⣄⢢⡀⠈⢿⣧⠀⠻⡀⠀⠙⣿⣿⣿⣆
⠀⠀⠀⠀⡇⢸⣧⢠⣴⠟⠁⠸⣟⣿⣦⣷⡀⠀⠙⠻⣿⣦⡘⣶⣄⠙⣾⣆⢳⡄⠘⣿⡇⠀⠀⠀⢀⠸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠈⠻⣏⠻⣿⣶⣄⡀⠀⠉⠻⢮⣿⣷⣌⢿⡎⣿⡀⢸⣿⠀⢧⡀⠸⣆⢹⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⣿⣿⣶⣦⣄⡈⠙⢿⣾⣿⣼⣧⠀⣿⡇⢸⣧⠀⣿⡌⣷⣿⣷⡙⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⡄⠀⠀⠀⠠⠶⠛⣋⣉⣁⡀⠀⢉⠙⠿⣦⡀⠹⣿⣿⣿⠀⢸⣧⢸⣿⡄⢹⣧⣿⢸⣿⣷⡡
⠀⠀⠀⠀⠀⠀⠀⠰⠞⢳⣦⡀⠀⠀⠀⠀⠟⠹⣿⡟⡿⠟⠋⠀⠀⠘⣷⡄⢹⣿⣿⠆⢸⣿⣼⣿⡇⣸⢿⣿⢸⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢘⣿⣿⠀⢸⡟⣿⠿⣷⡿⠘⣿⣸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⢸⣿⡟⠀⣼⠃⡿⠀⣿⠇⠀⠃⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣸⣿⣾⣿⠇⢰⡟⠀⠀⠀⠟⢸⠇⣼⣿⣿⣿⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣷⣿⢿⣿⡟⢀⣿⠃⡀⠀⡄⢀⣿⣰⢟⣿⣿⡏⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣼⠁⣼⠙⢏⣿⣿⠁⣼⡏⢠⠇⢰⡇⣼⣿⢋⣾⣿⣿⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠃⠀⠀⢠⡏⠀⣿⠀⣼⣿⡇⣼⡿⢠⡟⢠⣿⣿⠟⣡⡾⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣿⢀⣿⡟⣸⣿⢣⣿⣱⣿⡿⢋⣴⠟⢡⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⢸⣿⣧⣿⣣⣿⣿⠟⠋⣴⠟⠁⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠰⢸⣿⣿⣿⣿⡿⠟⠁⠀⠈⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢧⣿⣿⠟⠋⠀⠀⠀⠀⡠⢂⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢿⡄⡜⣿⡿⠀⣠⠆⠀⣠⠞⣡⡾⣱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⡼⣷⡸⣽⣷⣾⣧⢎⡾⢃⣴⠏⣴⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⣷⣽⣿⣿⡿⠋⣴⠟⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⠻⣿⣿⣷⠞⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⢱⣠⢈⣿⣿⣦⡾⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣾⣿⣿⢠⣿⣿⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⣿⣿⣷⣾⣿⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⢿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⠀⠀⠀⠀⠀⠀⢠⠀⡄⢠⠀⠄⠀⠀⠄⠀⠠⠀⠀⠀⠀⠠⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣛⣩⣥⡄⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣮⣭⣳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢞⣭⣶⣿⣿⣿⣿⠧⣼⡿⠟⠻⠛⠿⠿⠿⠛⠁⢿⣿⣿⣿⣷⣮⣗⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⣭⣭⣿⣿⢇⡀⠑⢻⣦⣤⣤⣤⣤⡤⠀⠀⣠⣌⣋⠁⠀⣀⣉⣁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣿⠇⢠⣾⠿⣻⣽⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⡀⢠⣿⣮⣝⡻⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠠⣭⣤⣬⠲⣿⣿⣿⠟⠃⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠛⢿⣿⣿⣷⣶⣿⣯⣵⠇
⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⠀⠘⠿⠿⠶⠛⠉⠀⠀⠀⠀⠿⢫⠷⣦⠰⠛⡦⣩⡂⢄⠀⠈⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠯⣿⣷⣶⣖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠼⠛⢆⡴⠃⠀⠑⠲⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⡍⠀⠀⠀⠀⣠⡦⢠⣤⡀⣾⠁⠀⠀⠀⠀⠈⣷⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣰⣿⠁⠙⣀⡁⣧⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⡿⠁⠀⢠⣿⠃⠀⡰⣯⠙⣈⡳⠦⢤⣤⠶⡂⠣⠀⢀⣿⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣿⡿⠋⠀⠀⢀⡏⠋⠀⣰⣿⣦⡸⠧⠍⣴⠛⠒⢾⡉⢀⣀⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠠⣾⣿⡟⠋⠀⠀⠀⠀⡾⠀⠀⢴⡿⠋⠀⠙⠷⠶⣮⣥⣤⡶⠾⠛⠁⠈⠻⢿⡇⢻⡄
⠀⠀⠀⠀⠀⣜⣿⠿⠁⠀⠀⠀⠀⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣜⣷
⠀⠀⠀⠀⣬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠰⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠁
⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣯⣿⣾⣾⣿⣶⣤⣄⣠⡀
⠀⠀⠈⣷⡼⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⢷⡶⣠
⠀⠀⠀⠸⣿⣬⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣮⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠻⣿⣷⣭⣅⣢⢄⠤⢤⣀⣒⣦⣶⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠻⠿⠿⠿⠛⠛⠉⠁

⣀⠀⠀⠀⠀⠀⠈⠇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣽⣆⠀⠀⢻⣆
⣿⣷⡶⠀⠀⠀⠀⠘⢀⣿⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⡊⠈⢢⡴⠊⠓⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣤⣤⣿⣧⠀⠀⠀⠀⢀⣰
⣾⠋⣡⠀⠀⠀⠀⠀⠆⢿⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠑⢶⠃⢱⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣮⡀⠸⣿⣧⠀⠀⠀⠈⠛
⠃⣴⡿⡄⠀⠀⠀⠀⢰⣼⡀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠸⡄⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣹⣿⣇
⣼⠏⢠⣧⠀⠀⠀⠀⢰⠌⡇⠀⠀⠀⠀⣸⡏⣿⣿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣝⢿⡄
⠃⣰⡿⢻⡄⠀⠀⠀⠈⡅⠁⠀⠀⠀⠀⡟⠙⣿⣿⡇⠀⠀⠀⠠⡖⠀⠀⠀⣹⡇⠀⠋⢁⣭⣿⣿⠗⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣕
⣸⠏⢠⣾⣇⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⠇⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⡾⠛⢉⣠⡄⢠⣶⡆⠀⠀⠀⠀⠀⠀⠙⠻⢯⣷
⠈⣰⣟⣁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⢁⣠⣶⠿⢿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠚⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⣠⣴⣿⣿⠋⢀⠔⠃⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⡶⠿⠛⣹⠟⣁⠔⠁⠀⠀⠀⠀⠻⣷⣶⣾⣷⣶⣤⣄⡀
⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⣠⣴⣿⣿⠞⠁⠀⠀⠀⢺⣿⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿
⢿⣿⣿⣿⣦⣀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦⠀⠀⠀⠀⠶⣶⣿⣋⣁⡿⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠙
⠀⠈⠉⠉⠉⠉⠁⠀⠀⣀⣀⣤⣤⣶⢶⣾⣟⣿⣽⣧⣿⣿⣿⡆⠀⠀⠀⠀⠻⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠰⣾⢿⣛⣯⣿⣼⠷⠿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠀⠀⠀⠘⣿⣇⠀⠀⠀⣴⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢻⠛⠋⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⢉⣁⣀⣀⣤⣤⣦⡀⠀⠛⠛⠀⢰⣶⣿⣿⠿⠿⢿⣿
⢀⣿⡗⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣷⣾⣿⣿⠿⠿⠿⠟⠛⠋⠀⠀⢀⣠⣄⠀⢸⠛⠿⣷⣤⡀⠙
⢸⣿⠇⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⣀⣀⣠⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⢸⣦⣄⠈⠻⣿⣦
⣾⣿⠀⠀⠀⠀⠀⠈⢻⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣾⣶⣤⣄⠀⠀⠀⠒⢆⠀⠀⠀⠀⠒⠂⠹⣿⣿⣿⣿⣿⣷⣄⡈⠙
⣿⣯⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣾⠟⠀⠀⠀⠈⠳⡀⠀⠙⣿⣿⣧⡈⠙⠻⣿⣦
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⢦⠀⠹⣿⣿⣿⣶⣄⠈⠻
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⣄⡼⣿⡉⠛⢿⣿⣦
⣿⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠳⢄⠀⠚⣄⣀⠖⠠⠄⠀⠀⣴⣾⣿⣶⡄⠀⠀⠂⠀⠙⢧⡀⠀⠀⠀⠀⠘⢷⣼⣿⣦⡀⠈⠻
⠿⠇⠀⠀⣧⣀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⢹⠋⠙⡆⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣦⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠹⡿⠿⣿⣦⣀
⣤⡄⢀⠞⠉⠉⠹⣆⣾⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣿⣄⣠⣽⣿
⠀⠀⠀⣧⡀⠀⣠⠏⠙⢦⣀⣠⠞⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣦⣤⠟⠀⠀⠻⣿⣿⣿⣿⣿⣦⠐⡀⠀⠈⢳⡄⠀⠀⠀⠙⠙⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠛⢿⠀⠀⢸⡏⠀⠀⠀⠀⠙⠾⠿⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣼⡄⠀⠀⢻⣄⠀⠀⠀⠀⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢄⠀⣄⡀⢀⣿⣿⣿⠛⠉⠉⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠸⣿⣿⠋⠠⠤⠴⠤⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⡆
⠀⠀⠔⠁⠀⠀⣠⠼⠋⠀⢰⠛⣏⠀⠀⠙⠋⠀⠀⠉⠛⢣⠀⠀⠐⠐⠀⠓⠒⠒⠒⠚⠒⠒⠓⠒⠓⠒⠊
⠀⠀⠀⠀⠄⢘⣅⠀⠠⠤⠼⡀⢻⣄⠀⠀⠀⠀⡄⣠⡀⢈⠀⠀⠀⢀⣀⣀⣄⢀⣀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠐⠀⠀⢇⠘⣆⠀⠀⠀⠈⣾⣿⣿⣾⡏⠉⣉⣀⢿⡟⠀⠀⠀⠘⠛⠛⠛⠛⠛⠂⠂⠐⠂⠐⠚⠛⠂⠀⣀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⡄⢸⡀⠀⣀⠄⠉⠛⢿⣿⣷⣦⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢊⣂⠀⢈⡉⠉⠀⡗⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣾⠗⠊⠀⠀⠀⠀⠀⠀⠉⠙⠛⢉⠷⢄⠀⠀⠀⠀⠀⠆⠴⠠⠸⠠⠄⠷⠀⠆⠶⠀⠀⠀⠀⠀⣶⡄⠰
⠒⠒⢲⢲⢲⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠄⠉⠢⣄⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢠⣶⣾⣏⠀⢠⣿⣷⣆
⠴⠤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣅⠀⠀⢄⡠⠀⢀⡀⠠⡤⠠⡄⠘⠿⠟⠀⠒⠄⠈⠉⠿⠓
⠻⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠆⠀⠈⠀⠀⡄⠠⡀⠀⠘
⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⡀⣀⡀⠀⣇⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠘
⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡈⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⣀⠀⠀⣀⡀⠀⠈⠁⠉⠉⠉⠉⠉⣉⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠏⠈⠻⠏
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣤⣄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠟⡃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠦⡄
⡀⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⡀⠀⠀⠀⠑⠢⢄
⣥⠐⠊⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠚⠃⠀⠀⠀⠠⠀⠀⠱⠄⢀
⢹⠀⠀⠔⣠⠼⠒⠁⠒⠒⠒⠤⠤⠤⢄⣀⣀⣀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⣔⠠⠂⣿⣉⣛⣒⠒⠒⠦⠤⠤⢤⣀⣀⣀⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣾⠀⠀⠉⡆⢧⠈⠉⠉⠉⠉⠀⠒⢖⠀⠤⠍⣩⣉⣙⡓⠒⠒⠲⠤⠄⠁⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠐⠀⠠⠄
⠀⠀⠀⠀⢷⠸⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠀⠠⠀⡀⠀⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠘⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣿⣿⡇⠀⠀⠀⢸⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣷⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠉⠀⠀⠀⠀⠈⠉⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⣠⣶⣾⠿⠿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢁⡀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠘⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⢷⡒⠂⠀⠀⠀⠀⠀⠒⢚⡃⣀⡀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠉⠙⢻⠇
⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠈⢉⢙⣿⣿⡗⠋⠹⡷⡀⠀⠀⢸⣷⣶⠀⠀⠀⢐⠀⡒⠖⣾⣷⣶⣄
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣷⡇⠀⠀⢸⣿⣿⠛⠞⠉⠞⢳⡿⢻⣿⡇⠀⠹⠆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡃⢸⣿⡇⠀⢸
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⣾⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡃⢰⣿⡇⠀⣼
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡾⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢰⡇⢰⣿⣧⢴⡏
⠀⠀⠀⠀⠀⢻⣧⣧⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣷⡆⠀⡄⢰⡿⢧⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⠂⠀⠀⢐⣚⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣂⠐⠒⠖⣶⣾⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢺⡄⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⣷⣖⣤⠀⠀⠘⢿⣆⠀⠸⣄⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡄⣈⣿⣷⣶⠹⣄⣀⡀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠀⢹⡟⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⢰⡟⠀⠉⠻⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠸⣿⠃⡀⠀⠀⠀⣽⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢿⡀⡇⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠘⣿⠁⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠦⡀⢰⡿⠷⠶⣄⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢙⣿⠁⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣼⢏⡿⣄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠛⣼⡇⠈⠳⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠄⠀⠘⣷⣶⣄⠘⢄⠀⢹⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠋⠙⠳⣄⡀⢹⣿⡵⢀⠈⠲⣼⠏⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣸⣆⡀⠀⠈⠙⢿⣿⣿⠟⡐⠀⠘⠃⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣞⠁⠀⠙⠳⣤⡀⢈⣿⣿⠀⠹⣦⣄⣀⣀⣀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡅⡿⢶⣤⣀⠀⢘⣿⣿⡇⣴⠂⣸⣿⣿⣯⣭⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠶⠿⢿⣿⣿⣿⣿⢟⡼⢋⡴⠉⠈⢻⣟⠮⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠛⠉⣿⣿⣷⠟⠁⠞⠀⠀⠀⠀⠉⠁⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠈⠢⣤⣄⣀⣀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⠚⢶⣶⡦⠈⠉⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⣿⡀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣰⠾⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠉⡈⠹⠋⠉⣄⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⠈⠣⢦⠳⢧⡐⠀⠛⢀⢀⠀⢀⡀⢀
⠀⠀⠀⠀⡠⠂⠁⠀⠊⠁⠀⠀⠀⢀⡀⠁⠈⠐⠘⡆⡇⠂⢣⠐⡅
⠀⠀⠀⠰⢀⡵⠂⠄⠐⠈⠁⠁⠀⣠⠄⠁⠋⠀⠐⠁⠃⠀⠈⠀⠳⢦
⠀⠀⣰⠎⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⢳
⠀⡸⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⢃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢰⠃⠀⠀⠀⠀⠀⠠⡰⠀⠀⠀⠀⠀⢀⠐⠀⡐⠀⠀⠀⠀⢀⣀⠀⠀⠀⢣
⡾⠀⠀⡀⠀⠀⠀⠀⠇⢀⠀⡇⠀⠀⣿⠀⡖⠀⠀⠀⡠⠊⠉⠉⠉⠓⠀⡸
⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠃⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⣇
⡇⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠳⢦⣦⠄⠀⠈⢄
⢃⠀⠠⠃⣰⠀⠸⠰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠴⠂
⠸⠀⠀⠄⠀⢠⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⡇⠀⢸⠀⠘⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡲⠂
⠀⢻⠀⠘⠀⠀⠇⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡴
⠀⢸⠄⠀⡆⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠤⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠠⠄⡀
⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠸⠀⠀⠀⠠⣄⣀⠀⠀⠀⢀⠴⠊⠁⢠⡠
⠀⢠⣁⣇⡖⠶⠤⡤⠦⡤⡄⢀⣀⢀⠈⢠⡀⠀⠀⢰⠀⠀⠉⡠⠋⠀⠀⣠⠄⠈
⠀⠀⠩⣯⡅⠘⠁⠛⠀⠛⠘⠃⠒⠒⠻⠉⠬⠭⠓⣶⢆⡐⠚⠄⣲⠬⠛⠒⡤⡀⣀⠀⠤⠀⠤⠐⠂⠁
⠀⢠⠘⣿⠁⢴⠀⠁⠀⡀⠀⠀⠀⡀⠘⠀⠀⠀⠠⢁⠙⠋⢔⡾⡁⢀⣰⠀⠸⢈⠀⠐⠁⣤⣀⠀⣀⣀⠀⢀⠠⠚⠁⠐⠦
⠀⢸⡌⣳⠀⡄⠠⠀⢠⠁⠀⢀⠀⠇⠠⡀⠆⠀⢀⠀⠀⢁⠂⠈⡹⢍⠉⠐⠢⠁⡠⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠚⠘⠃⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⢾⠀⠀⠈⠒⠚⠀⢨⠀⢀⡇⢈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡄⢠⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡄⢿⣇⠀⠘⡇⢸⠄⠸⡇⢸⠃⠀⣸⡷⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠸⣷⡘⠿⠘⠉⠀⠀⠀⢠⡄⡀⠀⠀⠀⠀⠑⠃⠿⢠⢾⠇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⠻⣦⡀⠀⠀⠀⠀⠀⠉⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⢀⡇⣧⣿⣧⠀⠀⠀⠀⠀⠀⣄⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⣸⢁⡎⡼⢠⡏⣿⣿⣷⠀⠀⠀⠀⠀⣽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⣇⡞⣸⢁⡼⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣽⣿⡿⠿⣿⡀⠀⠀⠀⠀⣻⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠈⠙⠟⠋⠀⠀⣽⣷⠀⠀⠀⠀⠈⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢐⠋⠉⣁⣀⡀⠀⢶⠂⠀⣀⡈⠉⠙⠓⢤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢸⣯⠖⠢⡀⠀⠀⣴⣿⣿⣿⣿⣷⠈⣰⣿⣿⣿⣿⣷⡄⣻⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡰⠻⡀⢀⠇⠀⠀⣿⣿⣿⣿⡿⠋⣸⡝⣿⣿⣿⣿⣿⡷⢀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠈⠁⠀⠀⠀⣈⡛⠿⢋⠀⣴⡿⣷⡌⠙⠻⢛⣛⣡⠖⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣥⣤⣬⣤⣛⣧⡛⣧⣽⣤⣤⣬⣥⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠁⢀⣨⣿⣿⡻⡿⠛⣿⠛⢿⠿⣿⠿⠛⠁⢀⣀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣾⣇⣷⣶⣿⣿⣿⣿⣝⣷⣶⣿⣶⣾⣯⣥⣶⣶⣿⣿⣿⣟⣶⣴⣦⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠛⠛⠙⠛⠛⠛⠛⠋⠀⠉⠛⠋⠉⠙⠛⠉⠋⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠰⠸⡾⠿⠧⠸⠹⠤⠇⠏⣰⢦⢤⣀⡀⠀⠰⣭⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠺⠀⠀⢘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠯⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟

⠀⠀⠇⡇⡇⣸⠇⠀⡿⠀⣼⢡⡿⢱⣿⡿⢋⢔⣡⠔⡠⠔⠁
⠀⠀⡆⢲⡇⢹⠀⠀⡁⠀⡏⣾⢑⣿⡟⠁⣵⠟⠡⠊
⠀⠀⡧⠈⡇⣸⠀⠀⠃⠰⣿⡏⢠⠏⢀⡞⠁⠂
⠀⠀⢰⠀⣇⢸⠀⢠⠀⢸⣿⣇⡟⠀⡜
⠀⠀⠀⡇⢻⠘⡇⢸⡄⠀⣿⣿⠑⠰⠁
⠀⠀⠀⢹⡜⣇⢣⠈⣷⠀⠘⡏⠀⠈
⠀⠀⠀⠀⢳⡹⡆⠀⠸⣧⠀⠃
⠀⠀⠀⠀⠈⢧⠹⡄⠀⢹⣆
⠀⠀⠀⠀⠀⠈⢷⣻⡌⠄⣿⡂
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣸⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣹⡯⢿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠒⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡙
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠘⠌⡏⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣉⣠⣤⣶⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠛
⠀⠀⣰⠆⣴⡴⠊⠀⠀⠀⠈⡦⠀⠠⠀⣀⠀⠠⢐⠀⢀⠵⠖⠛⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣀⣀⢠⣀⡄⢀⠀⡄
⠀⠀⣿⠞⢻⠆⠀⠀⠀⠀⠀⠅⠐⠈⠀⣀⡀⠤⠭⠶⠭⢤⣠⡀⢴⣿⣿⣿⣿⡿⠿⠿⠟⠋⠀⢀⣤⡾⠟⠛⢛⠈⠀⠁⠀⠀⠄
⠀⠀⢏⠀⢸⡷⡤⠖⠀⠒⡶⢒⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠞⢡⣤⡿⠋⣡⠄⣄⢀⣤⡶⠟
⠀⠀⠈⠲⣄⠛⢦⣤⣶⣚⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠢⣿⣿⣥⣿⣏⣠⡿⠟⠉
⠀⠀⠀⠀⠈⠙⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣶⣾⣷⣤⣿⣿⣶⣿⣿⣾⣿⣷⣶⣿⣿⣶⣿⣦⣤⣶⣷⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣉⣩⣤⣤⣤⣬⣭⣛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⠿⢿⣿⣧⡙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠋⠁⠀⠀⣀⣤⡶⢶⣦⣀⠈⠛⢷⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣾⣿⠟⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⠟⢁⡴⠺⢿⡝⢧⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⡀⠈⠀⠀⠹⣿⣿⠛⠻⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣘⠛⠻⣆⢻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠀⠀⠀⠀⠈⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣷⢀⡌⢸⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⣡⠾⢡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⢀⣴⢟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⣀⣤⡄⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⣴⣶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠛⠛⠛⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠤⠴⠖⠛⢿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⡴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠀⠀⠀⢸⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⢿⠙⠿⠟⢙⡟⠛⣟⠟⢻⡿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣔⡾⣟⠛⣛⢛⣛⠛⡿⢷⢢⠀⠀⠀⠀⠀⠀⢀⣴⣿⢅⠉⠙⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⣠⠔⠔⠚⠛⠯⠉⠓⠦⣄⡀
⠀⢀⣾⣿⣿⣿⣾⡗⡖⠀⣆⠀⠀⢀⣣⠀⠀⠀⠀⠀⢸⢿⣏⡧⠀⠀⠀⠀⣀⡠⠷⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⢀⣀⠤⢤⡀⠙⢢⡀
⠀⢠⣿⣿⣋⣿⡟⠃⡃⠀⠁⠀⣀⡿⠿⠀⠀⢠⣾⣿⣿⢻⣿⣷⣼⣶⣿⡍⣀⠲⣼⠀⢠⡇⠀⠀⠀⠀⠀⠀⢡⠴⠃⠀⠀⠉⠑⣄⡇
⠀⣸⣿⣿⣿⣿⢿⢷⡖⠚⠛⠉⠁⠀⠀⡇⠀⣿⣿⠀⠈⠨⣿⢻⣿⢸⣿⡅⢹⠀⣿⠀⢘⠀⠀⠀⠀⢡⠄⢠⡎⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢿⣿⣿⣿⣿⢸⢸⡇⠀⠀⠀⠠⢠⣴⡇⠀⣿⣿⠀⠀⠀⣿⢸⣿⢸⣿⡇⢸⠀⣿⠀⠹⡄⠀⠀⠀⠀⣴⢚⣤⣤⣤⣤⣄⣀⠀⠀⡇
⠀⠸⣿⣿⣾⣿⣿⣍⣄⣀⣀⡤⠴⠚⢋⠁⠀⢹⣿⡀⠀⢠⣿⢸⣿⢸⣿⡇⢸⠀⢿⠀⠀⢰⡀⠀⢀⠟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣆⡇
⠀⠀⣿⣿⣿⣿⣿⡿⡇⢀⢀⠀⠀⣀⡾⠀⠀⠈⠻⣿⣶⢬⣛⣻⡿⠌⠿⠇⣋⢠⢰⠀⠀⠀⢹⠀⢸⠀⢹⣼⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠈⢿⣯⣿⣟⠉⠁⠈⠉⣀⣽⠟⠁⠀⠀⠀⠀⠈⠻⢨⣿⢹⣿⢹⣿⡇⢻⠀⢿⠀⠀⠀⠈⡦⣨⠂⢸⣯⣿⣿⣿⣿⣿⣿⡟⡏
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣚⣻⣃⣫⣴⠾⠀⠀⠀⠀⢱⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢻
⠀⠀⠀⠀⢀⣀⡤⠴⠲⢶⡒⠚⠳⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠈⠁⠀⣀⣀⢀⡤⣀⠘⡄⠀⠀⢻⣿⣿⣿⣿⣿⡟⡎
⠀⠀⡀⣐⣭⣩⡑⢢⣅⠠⠈⠳⡀⠀⠈⢮⢻⣦⠀⢀⠄⢒⣀⡐⠒⠠⢄⣠⢖⣭⣶⣾⡛⠃⡆⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣷⠇
⠀⣴⣽⠋⠀⠀⠙⢣⡸⢣⠀⠀⢘⡄⣶⣾⣧⣿⡇⠀⠱⡝⠿⣿⣿⣶⣤⣿⣾⣿⣟⠋⠁⡰⠁⠀⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⣾⡇⠀⠀⠀⠀⠀⢳⠼⣧⣻⣿⣿⢹⣿⣿⣿⡇⠀⣤⢘⢶⣟⣿⣿⣿⣿⣿⣿⣶⣤⠞⢁⠀⠀⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿
⠀⡿⣇⢀⡀⣠⣀⠀⠘⠖⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣏⣻⣹⣿⣿⣹⣿⣾⣯⣻⣿⣧⠈⠀⠀⡏⡇⠀⢰⣿⣿⣿⣿⣿⡿⡄
⠀⠸⡽⣄⠃⣛⡃⠀⣰⣳⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⡾⣽⣯⣹⣧⡿⠶⣽⣋⣻⣟⣿⡆⠀⢠⢷⣇⠀⠙⣿⣿⣿⣿⣇⣧⡇
⠀⠀⢈⣮⣜⢿⣥⣶⣵⣿⣿⣿⢱⣟⣉⣭⢽⣮⡄⠀⠙⠷⣿⠾⠟⠻⣷⡾⣭⣿⣏⣻⣿⠃⠀⢸⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠈⠙⠛⠋⠉⠉⠉⠛⢿⣿⣦⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⣶⣻⡾⠋⠀⠀⠈⠪⣟⡋⠉⠉⡉⠉⠉⣋⡭⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⡀
⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⢠⣘⠛⠉⢉⡠⠷⠄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠉⠙⠋⠉⠉⠈⠁⠉⠀⡀⠄⠐⠉⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠑⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣰⢃⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢃⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⡇⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣾⠁⠀⠀⠀⠳⣮⡱⡦⠔⠂⠀⠄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢰⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢡⠀⠀⠀⠀⠤⠄⠀⠀⢀⣀⢤⣤⢀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠖⠋⠁⢀⡀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡌⣄⠀⠀⠀⠀⠀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣄⡉⠛⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⢸⠛⠻⢶⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⣠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣿⣿⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠸⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⢳⣤⡤⠀⠀⠀⢸⡿⣧⠀⠀⠀⣼⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠄⠀⠀⢸⡤⠠⠀⠀⠀⠘⠛⠋⠀⠀⠀⠘⠷⠂⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⣤⣤⣴⣤⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣾⣿⣥⣤⣤⣄⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠟⠋⠈⠻⢿⣷⠆⢀⣴⣿⣿⣿⠛⠻⠿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠁⢀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠀⠀⠀⠀⢠⣿⡿⠋⠻⣿⣦⠀⠀⠀⠘⣿⣏⠉⣇⠀⠀⠓⠀⠀⢺⠀⡶⠄⠠⢶⠀⣿⠂
⠀⠀⢀⣴⣄⠈⠀⠀⠐⢄⠀⠀⠀⠀⠘⢧⣄⣇⠀⠀⠒⠛⠋⠀⠀⠀⠈⠛⠳⠂⠀⠀⠹⠏⢰⣿⣤⣀⣤⣤⠀⢸⣦⣀⣄⣀⣀⣴⣯
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣇⠀⢼⣿⣿⣩⣝⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⠀⠀⠈⢧⠀⠀⠀⣠⣾⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠘⠻⢿⠃⠀⠈⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠄⠀⠸⠀⠀⠀⠈⠧⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋