Drupe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠒⠉⣉⣹⠇⠀⡿⠉⠋⠑⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⠀⠠⠙⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠀⠁⠀⠀⠻⡄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢂⠀⠀⠀⠀⢡⠀⢀⢻⡄
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠄⠈⠀⣷⡀
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠐⠀⠀⠀⢠⠀⠀⠸⣧
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠰⠀⠀⠁⠀⠆⠀⠄⠀⠀⠀⠀⣿
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⢟
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠘⠀⠃⠀⠀⢸
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢠⢰⢸
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠇⠀⠇⢠⠀⢸⠸
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢨⠀⢸⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡇⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⢼⠸
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⡇⠘⠀⡈⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⡆⡀⠀⡇⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠂⠀⠀⢀⠀⠀⢤⡇⣸⡇⢣
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢸⡀⠀⡀⠀⡀⠀⠀⢀⢀⠀⠀⢸⣠⠿⡆⣼
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠁⠈⢁⠀⣷⠀⠀⠘⠘⠂⡄⠈⡟⣼⢁⣿
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠸⠀⡆⢸⡜⠀⡴⢠⢹⡴⢡⡈⣸⡟
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠀⢂⠀⡀⢠⠁⡄⣵⠛⡅⣎⣦⢃⢨⣣⣿⠁
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⠀⡄⠀⢨⠀⠀⡸⠄⢠⡉⡾⠀⣽⠇⣼⡄⣼⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠘⠀⢠⢳⠀⢦⣿⢧⢠⠏⣼⣷⣼⠏
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣀⢀⠀⡶⠀⠁⠀⠀⣴⠏⡌⠌⢲⡏⠳⠝⣾⣃⣿⠃
⠀⠀⠀⠀⠈⢷⡀⢀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⢀⠀⠉⠘⠀⠃⠀⠈⠀⣠⠏⡘⢈⣲⠾⠇⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠠⡈⠀⠇⠀⠀⣴⡟⠙⠀⣠⢿⠖⣵⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠁⠁⠰⠰⠆⠀⢰⡀⢋⠀⠂⢠⠁⠀⠂⣠⡞⢩⠇⢷⠐⠿⣠⣞⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠃⠨⠀⠀⠀⠀⣠⣾⣫⡴⠂⢀⣈⣥⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣤⣀⣀⣀⣀⣀⣤⣶⢟⣋⣀⣤⠴⠾⠛⠉⠁

⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠌⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢂⠀⠐⢦
⠀⠀⡀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠁⢀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠲⠛⠻⠖
⡀⠈⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⢀⠴⠃⣠⠀⠀⠀⠀⠀⡸⠁⠔⢰
⠀⠀⠀⠀⠀⠀⠰⢾⡂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠀⠀⠀⠀⠀⠀⠁⠐⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⡷⡄⠈⠀⠀⠀⡔⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡀⠃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠃⠀⠁⢀⣈⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠈⡌⠓⠄⠢
⠙⢧⡀⠀⠀⠀⠀⠀⠰⡃⠀⠀⠀⠀⢄⠀⠀⠀⠉⠙⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡤⢄⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⢀⡈⠥⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣶⡊⠑⠠⠀⠀⠲
⠀⠀⠀⣀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢩⠋⠉⠁⠹⡀⠀⠁⠂⡀
⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠐⠂⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⣧⠀⠀⠀⡇
⠈⠀⠀⠈⠁⠀⢠⡇⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⡶⡔⠚⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢸⡀⠃⠀⠀⠀⠀⡞⠀⠀⠰
⠀⠀⠉⠤⠴⡞⠉⢀⡤⠊⡰⠁⠀⠀⠀⢠⠖⢡⠀⠈⠌⢢⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠰⡀⠀⠀⠀⠃⠀⠀⠂
⠂⠀⠠⠤⠶⠴⠚⠉⠀⡴⠁⠀⠀⠀⡰⠁⠀⠈⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠠⠴⠦⠄⠊
⠀⠀⠂⠀⠠⠀⠀⠒⠉⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠘⠳⠶⠄⠉⠑⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣎⣀⡀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⡔⠉⠀⣀⣂⠀⢤⣔⠀⠀⠀⠀⠀⠀⠔⠉⠀⢰⠁⠀⠙⢢⠀⠀⠐⡀⠀⠀⠀⠀⡠⠀⢠⣄⡠⠖⠂⠀⠀⢀
⡜⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢸⠀⠀⠀⠁⠀⠀⡰⠊⠀⠀⠴⠿⠆⠀⠀⠀⠸⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠙⠳⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠃
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠈⠳⢤⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠘⠄⢀⣀⠀⠀⣀⡰⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡬⠉⠓⠐⠀⠂⠀⠀⠀⠀⠀⠘⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠀⠉⡉⠉⠩⠥⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠⠄⠂⡁⠤⠔⠒⠚⠉⢉⡁⠀⠈⠱⢄
⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣡⡀⠤⠀⢀⡀⠭⠅⠒⠒⠂⠉⠉⡃
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⣁⠤⠒⠉⠀⠀⠀⡀⠀⠀⠐⠒⣉⣱⣀⠤⠤⠤⣄⣀⡀
⠀⢠⠊⠀⠀⠀⡀⠀⠀⣀⡠⠀⡠⠔⠉⠀⠀⢀⠀⠀⠀⠀⢀⣠⡴⠒⠏⠉⢀⣀⣠⣄⣀⣀⠀⠉⠑⠢⣄
⢠⠁⡀⠀⠔⠋⠀⡠⠘⢁⠴⠊⠀⠀⢀⡤⠚⠁⡀⢀⡤⠊⠁⢈⣿⣠⢞⢊⢍⡔⠒⠊⡠⠌⡏⡓⠦⡀⠀⠱⡄
⡆⠀⢀⡮⠒⠁⠈⢀⠐⠋⠀⣠⣶⠞⠁⡀⠐⠊⡠⠋⢀⡴⡿⠟⠿⢰⠟⠢⡸⡄⢀⡀⠀⠀⠉⠈⠓⠌⠢⡀⠘⡄
⡇⠀⠀⠀⠀⠀⠔⠁⠀⢀⡌⠁⠀⡠⠊⠀⢀⡼⠁⠠⠟⠒⠂⠉⠑⠈⢀⠀⠀⠙⢢⡘⠀⢀⠄⡜⠉⠉⢣⡱⡀⠘⡄
⠇⠀⠀⠠⢠⠊⡠⣲⠋⠀⠀⠀⢀⠠⣴⠞⢡⠃⢀⠀⠀⠀⠀⢀⠇⢀⠆⠀⠀⠀⠀⠉⠉⡅⠀⠁⠀⠄⠘⢣⡡⠀⢱
⠸⡠⠀⡔⠁⢠⡟⡁⣀⠔⠒⠉⠠⠊⢑⣗⣸⠀⢸⡀⡀⠀⠨⣄⡤⢾⠆⠀⢆⠀⠀⠈⢰⠁⠐⠒⠀⠀⠀⣰⡴⡀⠈
⠀⡷⡾⠀⠀⢾⡵⠋⠀⠀⢀⡠⠁⠠⠜⡦⢾⠀⠸⡝⠋⠠⠀⠔⠉⣉⠤⢄⠄⠀⠀⠀⡮⠁⢀⠀⡄⠀⠉⠳⡀⡇
⠀⣽⣧⣾⣭⠫⠂⠒⠂⠴⠯⠤⠶⠺⡿⢵⡜⡆⠀⢇⢢⠀⠀⠀⠊⠈⠀⠀⢣⠀⠀⠀⢙⠲⣟⠀⠀⠣⠀⠰⢃⡇
⠀⠉⠀⠉⠢⢍⠒⠒⠶⠤⠤⠤⠴⣾⣏⢩⣿⡵⡈⠀⢻⣶⡆⠀⠘⣄⠀⠀⠘⠢⡀⠀⠀⠣⢹⠲⢲⠖⠀⠀⢨⠇⢀
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠤⠤⠤⠤⠬⠴⠖⠒⠱⡀⠈⢧⣷⠀⢠⠄⠀⠀⠀⠀⡀⢤⡀⢀⠸⡁⠸⠀⢄⣀⡼⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠙⢗⢷⢀⡀⠀⠐⠊⠈⢣⣑⣆⠀⢱⠃⠀⣰⡳⠃⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠤⠙⠳⢤⡀⠀⡀⠀⠀⠀⠈⣹⡚⢧⡵⡳⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⢉⣉⣉⠈⠙⠛⠛⠙⠚⠒⠺⠅⡜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣑⣒⣒⣦⣤⣔⣁⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢯⠀⠀⠈⡥⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢁⠄⠀⠀⠣⠀⠈⢠⣠⠀⠀⠐⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠄⠐⠒⠀⠈⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⠔⠁⠀⠀⠀⢀⠀⠀⡠⠋⠀⠀⠑⠦⢀⡀⠈⠒⢄⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢃⠃⠀⠀⠀⠀⠀⠈⠅⢰⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢼⡀⡀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢢⣧
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠠⠈⢼⣃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡂⠈⡀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠹⣄⠀⢀⠀⠉⠀⠀⠀⠀⠀⠁⢀⡈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢼⡀⣯⣉⠑⠠⠄⠀⢰⣀⠀⠀⠀⢈⠀⣶⡀⠀⠀⠀⡄⡰⠁⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣾⠀⠑⠀⠀⠀⢸⠉⠳⢤⡀⣚⠀⠀⢣⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠰⠀⢀⢸⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⡰⠁⠀⡀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⡠⠙⣷⠀⠀⠄⠐⢄⠀⢘⢔⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠁⠀⠀⠉⠀⠀⠀⠡⠈⢿⣿⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠢⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣶⡆⠘⣆⠀⡀⠀⢸⠏⡐⠁⠀⠀⠀⠀⠀⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⠆⠀⠀⡈⠵⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠠⡀⠀⠀⠄⡀⠀⠀⠢⠀⠀⠉⢧⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣦⣄⠀⠈⠁⠀⠓⢀⣠⠄⠃⠀⠀⠂⠉⠐⠀⢀⣠⡴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉⠁⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠒⠈⠉⠉⠙⣧⡤⠞⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀⠉⠤⡀⠤⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠈⠉⡞⠈⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠔⠈⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣷⡄⠀⠀⠀⠷
⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣼⢁⡀⠀⠀⢠⠀⠀⠈⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠
⠀⠀⠀⠀⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡼⠁⠿⠃⣤⠀⣾⠀⠀⠀⠀⣹⢷⣄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸
⠀⠀⠰⣄⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡼⢣⡄⠄⠾⢁⣼⡇⠀⠀⠀⠀⠸⣾⢿⣆⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⣠
⠀⠀⠀⣹⣿⣿⣿⣄⠀⠠⠀⠀⠀⠘⣿⡀⠀⡜⠀⠀⣟⠈⣴⡟⣤⡁⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⣠⡀⠀⣯⠀⡼⠀⢠⡾⠋⢼⣿⣇⠟⣥⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠋⣿⣿⣧⣼⣧⠃⠀⠟⢸⡡⠐⣩⠀⠀⠘⢋⣙⡀⢹⠆⠀⠀⠀⢠⣧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠀⠀⣸⣯⣵⣿⡇⠀⠀⠈⢻⣿⠃⣸⡂⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⠳⢿⠀⠀⠀⠀⠀⠋⣤⠟⠁⣠⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠃⠀⠀⠀⠀⠈⢁⣠⣾⣟⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⡠⢸⡁
⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⢰⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⡇⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⢀⡨⠀⢘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣿⠶⢄⠀⠀⠀⠀⠀⠀⠐⡆⠀⢀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠈⠀⠀⣷⡀⠂⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⣾⣿⣍⠑⠂⠂⢀⠀⠀⢸⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠹⢿⣧⠀⠁⢈⣂⠀⠸⡀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢻⡗⠀⠀⢹⣆⠀⠣⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣾⣷⠀⠀⠙⣿⡆
⠀⠀⣴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢸⣇
⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠰⣶⣿⠃
⢼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣿⣧⢀⣿⣿
⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡿⢻⢿⣿⣿⣿⡿⠳⠚⠀⠶⣦⣄
⣿⠿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠻⣿⣿⡟⠁⠀⠀⠠⠀⠀⠈⠛⢿⣆
⠘⠾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠈⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣡⣿⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⣿⡆
⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡉⡎⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⠦⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠏⡻⢬⡇⠀⠀⠀⠀⠀⠀⠀⡁⠠⣼⣦⡂⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣴⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣆⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⣭⣝⠶⣄⠀⠀⠀⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢋⠀⠀⠙⢆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⣅⠈⠓⢹⣆⢠⡾⠛⠻⣟⣧
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⡀⠀⠀⢸⡾⠥⢴⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠞⣿⣿⠀⠀⢠⣾⣇
⠀⠀⠀⠛⠃⠀⠀⠁⠀⠀⣳⡀⣀⠏⠀⠀⢼⣥⣸⡯⣿⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⢠⢾⣿⣧⢄⡀⠀⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣯⣇⠀⠀⠀⢀⣀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⢠⠟⠈⠉⠙⠀⠛⠲⠆
⠀⠀⣷⠈⠀⠉⠱⢿⠂⠀⣾⢿⠛⠛⠛⠛⠛⣿⡿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠠⡖⢱⡄⠀⣀⣅⠀⣠⣼⡧⠀⠀⠙⠃⣠⣂⣿⣀⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢝⡀
⠀⢾⠀⠀⢀⠈⠉⢉⣉⠙⢧⣄⣠⡾⠿⠻⠛⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠰
⡠⠈⢡⣤⠌⠦⣄⠈⠁⣀⠀⣼⠿⢧⣤⣀⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡎⠇⠀⠀⠀⠀⠀⠀⠋
⠁⢠⡎⠀⠀⠀⠈⣹⣏⠀⠀⠀⢠⡄⢹⣿⣿⢿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡀⠁⠀⣤⡔⠋⠉⠉⠉⢣⣤⣤⣶⣼⣿⣿⡶⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠈⢃⠀⠀⣼⣅⢀⠀⣋⣴⠏⠉⠀⠀⣙⢻⣧⡘⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⡞
⠀⠉⠉⠋⠀⠀⠉⠙⢻⣿⣀⣀⡀⠀⣠⡜⠛⠿⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⣰⡿⠋
⠀⠀⠘⠌⢻⣧⣤⡀⠉⠁⣠⣄⠈⢻⡇⢀⣀⣠⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠆⠠⣤⡾⠿⣀⣼⠿⠋
⠀⠀⠀⠓⠈⠀⠀⣳⡤⠤⡤⢶⣴⣾⣟⠋⠉⠃⡄
⠀⠀⢿⣄⣀⡀⠀⠁⠀⡤⠦⡘⣫⣿⢿⣧⣤⡤⠛⠃
⠀⠀⠀⠀⠀⠀⢸⠄⠀⢀⡘⠉⠁⠈⣽⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠨⠀⣤⣿⠗⠀⠀⢺⡿⣄⢠⡷
⠀⠀⠀⠀⠀⠀⠘⠂⠈⠈⠀⢀⣀⡼⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⡤⢈⡿⠉⢳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⡼⣃⣠⠶⠟⣗⠂⠚⠳⠤⠸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣁⣀⠄⠿⠱⠁⠀⠀⢀⡇⠀⠀⣺⠀⠀⠙⠻⠓⠺⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣸⣏⠔⠉⠀⠀⠀⢰⡐⠀⠀⠘⠷⠮⠀⣿⣆⡀⠀⠀⢀⠀⠀⠈⠢⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⡔⠋⠁⠀⠀⢠⠀⠀⠀⣮⡀⡇⠀⢀⠀⢠⢆⡁⠙⠛⠀⠐⠪⣦⠀⡄⠀⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⠟⠀⠀⣄⠢⡠⠃⣦⢠⠀⠀⠈⠉⠀⠀⠈⢳⣾⠀⡃⠀⠀⡀⠀⠀⠉⠙⠃⣴⡅⢄⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡷⠒⡌⢣⣿⣦⠀⠀⢿⡄⠂⠀⠀⠀⡜⢠⠀⠈⠛⠔⠛⢆⣠⡇⠀⠀⠀⢀⠀⠈⠓⠘⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢿⠀⢯⡈⣼⣏⠻⢤⣀⢈⢄⡀⠀⠀⢀⢳⠘⡆⠀⠀⠀⠀⠈⢿⡥⠀⢰⣄⣨⠂⠀⠀⠀⠀⠀⣦⣾⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⢆⢾⣇⣼⣿⣴⣦⣽⣦⢰⣆⠰⠀⠘⠿⠘⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠹⣏⡥⠀⡀⠀⣀⠀⠈⠻⠜⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠃⣸⣧⣿⣿⣿⣏⢿⡟⣾⣜⣿⠀⠆⠁⠀⠀⢠⠀⠹⣧⡀⠄⠀⠀⠀⣤⠀⠀⠀⠀⠉⣴⡿⡆⠀⠀⠀⣘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣒⡜⣿⣷⣿⣿⣿⣿⠿⡁⢀⣽⡿⣺⠠⠀⢠⢠⡏⢣⠀⠘⠷⠃⠀⠀⣶⡇⠀⠀⠀⠀⠀⠻⣄⡄⠀⠀⠀⢿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡟⣷⣿⣿⣿⣿⣿⣿⣎⣓⠻⣿⡁⣰⢠⠆⣸⢾⡿⢀⠄⠀⢰⠀⠀⠀⠘⠓⠂⠀⢀⡀⠀⠀⠀⠀⡄⠀⡄⠀⢸⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⢻⣿⣿⣿⣿⣿⣿⣿⡟⣴⠾⣿⠉⣼⠀⠋⡌⠛⠉⡄⢠⣎⠀⠀⠀⠀⢀⠐⣀⡎⠁⠀⠀⠀⠀⠁⢸⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⣤⣘⠟⣻⣿⣿⣷⢙⣿⣿⣿⣷⣿⣿⣸⣿⢁⡿⣠⠀⣥⡀⠀⠃⠈⢿⣃⡄⠘⠀⠀⠀⢹⡇⡀⠀⠀⠀⠀⠘⣿⡠⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢛⣿⠃⢻⡼⢸⡀⠀⡀⠀⠀⣄⡀⢠⠞⠀⠀⠀⠉⠀⠀⠀⢀⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡀⠘⢿⣁⠇⠀⡄⠰⠀⠈⣿⡯⠀⠀⠀⢀⠀⠀⠀⣤⠎⢰⠀⠀⢰⣛⡹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣻⠀⠀⣠⣡⣄⡀⡏⢠⠀⠀⠛⠳⠂⠀⢀⣸⠀⠀⠀⠻⢧⠜⠀⡀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣧⣀⡐⢻⣿⣿⡁⢀⠠⠐⠀⠀⡀⣻⡾⠇⡀⠀⢀⠐⠀⠀⡇⣀⡾
⠀⠀⠀⠀⠀⠀⣀⠀⠼⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣦⢩⣿⠤⡊⢠⢀⡆⠀⠇⢹⠷⠆⠁⠠⠈⢰⡆⠀⣾⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⢯⢃⣿⣛⣟⣿⠈⣇⣼⠏⣀⠳⣧⠈⡀⢀⡈⠈⣠⠉⠈⢀⠝⠙⠃⠪⢤⡀
⣀⣀⣀⣀⣤⠴⠒⠛⣩⣿⣿⣿⣿⡷⢿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣮⣼⣿⣿⣿⢿⢀⣹⣟⣀⠋⡷⠈⣠⡟⣬⠣⠐⡇⠀⣠⢏⣠⣴⢶⣦⣤⣙⣂
⠉⠉⠉⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣯⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⡟⢸⣦⣉⣟⢾⣄⠿⣾⡏⢸⠈⣲⡶⢿⣾⣿⠿⣿⡟⠀⠈⠙⠻⠷
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠾⠋⣿⣿⣿⣿⣿⣿⣿⣯⣍⡛⣽⣹⣿⣿⣿⣿⣿⡟⡛⠋⢻⠦⢘⣺⣯⣴⡦⠛⠀⠉⠀⠈⢿⣆⢀⡀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠀⠜⠉⠁⠿⠻⢿⣿⣿⣿⣿⣿⣾⣟⣿⣟⣿⣨⣶⣾⣶⠾⠿⠿⠻⠾⠅⠀⠀⠀⠀⠀⠀⠻⡀⠀⠐⠄⠢
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡻⠋⠉⠉⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⡀⠱⡶⠶⠶⠲⠶
⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⢀⡄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢃
⠀⠀⠀⠀⠀⠰⠶⠖⠶⠶⠶⠒⠖⠀⠀⡴⠂⠶⠲⠖⡚⠙⠁⠈⣿⡁⠀⠀⠀⢠⣿⠀⡀⠛⢦⣤⣀⣀⡀⠈⠂⠀⠀⠀⡀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣐⡶⡹⠚⣹⠢⡀⠀⠀⠙⠈⠫⠙⢟⠲⡶⢦⣤⣀⠀⠀⢸⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢳⡵⠃⡋⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠏⠻⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣹⣷⠀⠀⠹⣇⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠖⠚⠛⠛⠛⠛⠛⠓⠒⠒⠒⠀⠛⠛⠚⠃⠀⠓⠲⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⡀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢳⠀⢈⣠⣧⢤⣿⣀⠀⡇⢰⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠙⢄⣨⢟⣿⢹⢾⢸⢺⣿⣿⡷⣎⣸⠁⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡘⢦⡈⠢⣀⣞⣿⢻⢿⢸⢸⣼⣽⣟⢩⢛⠁⠟⣦⡼⡰⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢦⡙⢢⣾⣹⢹⢰⢸⢹⢸⠞⣿⢿⢸⠠⠀⠦⡇⡟⣦⠰⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⣉⠓⢄⣙⡞⣿⢹⢸⢸⠸⣘⣈⣼⡿⣴⣘⣸⠠⠆⠇⠀⠏⢽⢄⠋⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠬⣉⣲⡟⡣⠸⢸⢠⣼⣿⠳⢸⢹⡇⡃⣎⠙⢦⡄⠀⠀⠀⢸⢸⢷⡄⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣿⡃⣶⢸⢸⣾⢟⠋⡇⡿⣿⡇⣧⢸⠸⡄⢳⡄⡤⠀⢼⢸⢰⣷⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠦⢤⣿⡇⣿⢸⢸⡏⠈⠀⢱⡧⡟⠁⠃⢸⠀⡇⣾⡇⣷⠀⢸⢸⢸⣿⣗⣋⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠦⢼⣇⣷⢸⢸⢸⡇⡇⠀⢸⢸⡇⠀⠀⠈⠀⡇⣿⡇⣾⢠⠀⢸⢸⣇⡇⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠑⠲⠾⡿⣽⢸⢸⠸⡇⠁⠀⢸⠸⠇⠀⠀⠀⠃⠁⢸⡇⣿⢸⠠⢸⢸⣧⠔⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣉⠚⣿⢸⢸⢸⡔⣿⡀⠀⠈⡄⡆⠀⠀⠀⠀⠀⢸⣷⣿⢸⢘⢸⢈⣿⠶⠒⢋⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⣿⢸⢸⢸⡇⡟⣷⡀⠀⠀⣷⠀⠀⠀⠀⠀⡞⣥⣾⢸⢸⢰⣼⣇⣚⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⣸⢸⡚⡇⡇⡿⣧⠀⢀⢸⠀⠀⠀⠀⡸⣷⠷⣿⢸⢸⠸⣿⣯⠭⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣸⣿⢸⣿⡇⡇⣇⡟⣷⡘⡄⠇⠀⠀⣠⡇⣿⡆⣽⢸⢸⣼⡧⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣧⡷⡇⡇⡇⡟⣷⣇⢹⠀⢠⣏⠇⣿⡗⢺⢸⣸⡿⠖⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⣉⡹⢷⡇⡇⣏⣇⡇⡏⣿⠀⢠⣏⡏⡶⣿⣷⢹⣼⡿⠳⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣁⠤⠂⣹⣿⡇⡇⣿⡇⡿⣿⡏⠉⣦⡛⣿⣹⣾⠛⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡴⢋⡽⢻⡷⠇⡗⡁⡇⡏⡇⡏⣿⣿⣹⡿⣍⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡴⢊⡟⢳⣇⣷⢅⡇⡇⡏⣿⣼⢿⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠾⢀⡞⣻⢧⣿⣇⣧⣵⢾⠳⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡼⠃⣰⠏⢸⠃⣿⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣐⣯⣤⣬⣴⣶⣶⣶⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣶⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣶⣶⣷⣿⠿⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠀⠠⠐⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⡠⠊⠀⣰⣆⠀⠁⠢⡂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⣴⡏⠉⠳⣄⠀⠉⠙⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⡼⠀⠀⣸⣿⠁⠀⠀⠘⣆⠀⠀⠘⣖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⠀⠀⢰⣿⠁⠀⠀⠀⢘⣼⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣿⠇⠀⠀⠀⠀⠀⣯⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⢻⣇⣄⣀⣴⣤⣿⡿⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⢆⠀⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠀⠈⠿⣿⡿⠛⠇⠀⠀⡴⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⢣⡀⠀⠀⠀⠘⠀⠀⡜⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡇⠀⠀⢀⡤⠤⣤⣤⣀⡀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⡇⠀⠀⢸⠿⠿⠿⠿⠚⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣀⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣆⠌⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢠⠀⢀⠏⠀⠀⢀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⠀⡎⡤⠖⠊⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⠀⠀⠀⢀⣸⠧⠖⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⡇⢠⠃⠀⣠⠔⠁⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠒⠒⠾⠧⠤⣤⣀⣿⣼⠖⠋⠁⣠⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠉⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣀⢐⡾⠃⠀⠀⠀⡞⠀⠀⢠⠂⠀⢀⠾⠊⠉⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠀⢠⠃⠀⢀⣣⠔⠚⠓⠒⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣈⣀⣀⣧⣤⣐⣀⣤⠧⠖⠚⠫⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢐⠠⠀⠄⢀⣠⠶⠞⠋⠉⠁⠀⠀⠤⠀⠍⡉⠛⠳⠶⣤⣄⣀⠀⠀⠉⠀⠀⠀⠀⠀⣰⠃
⠀⣠⠞⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠛⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⢀⡞⠁
⢿⣀⣀⠀⠴⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠙⢦⡤⠞⠉
⠀⠉⠉⠉⢿⡮⣕⡢⠀⡀⠀⠈⠀⠀⠈⠉⠀⢻⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠈⠑⠫⢿⣒⣦⡤⠭⢥⣤⣭⣤⣤⣿⣧⡈⢆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠻⣷⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣈⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣤⣀⠢⠄⠈⠓⠠⠄⣀⣀⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⢶⣤⣤⣤⣀⣀⣡⣤⡴⠖⠋⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡄⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡀⠀⠊⠁⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂⡀⡤⠁⠀⠀⠀⠀⠁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⢄⠀⠀⠆⢀⠊⠀⠀⠀⠰⠀⠀⣠⢀⡀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠐⠀⢰⠂⠀⠀⠁⠀⠐⠀⠀⠀⠀⠁⠀⠀⢀⠊⠀⢤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠠⡀⠀⠘⡀⡀⠀⠀⠀⡆⢰⠀⡠⠀⠀⡇⢀⡏⠐⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡧⠀⠀⡄⢰⠀⠀⡀⠀⠀⠀⢁⠎⠠⢷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⢰⠆⠀⠄⢡⠀⠀⢠⠏⠀⠘⠁⠀⠀⣠⡎⠐⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠀⠙⢶⣿⣀⣸⠂⢸⡀⢀⡎⠀⡄⠀⠀⠀⢠⠏⠀⠀⢖⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠢⠦⠾⠿⠛⠉⠀⢸⢁⠎⢁⠈⠀⠀⠀⣴⠋⠀⠀⡠⠊
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⡏⢀⠞⠀⠀⢠⣞⠁⠀⠀⡜
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠐⣆⠀⠀⢸⢡⣏⡠⠴⣎⣼⣿⣷⠶⠞⠠⢄
⢃⠀⠀⠀⠀⠀⠒⠀⠰⠀⠒⠀⠒⠚⠓⠒⠒⠛⠒⠶⠶⠦⢼⣦⡳⠎⣞⣁⠴⡲⠟⠋⠛⠿⠦⠤⠄⠊
⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠉⢰⣋⡴⠚⠁
⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⢠⡎⢬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢱⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢠⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠜⠀⠀⡀⠔⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣤⣒⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⣛⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⢒⣈⠁⠀⠀⠈⣉⣳⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⢹⠝⠒⠶⢍⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⠎⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣇⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗⠐⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⢧⣼⡀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⣤⡴⠾⠓⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢄⡀⠀⠀⠈⠛⠻⠶⠖⠚⠛⠉⠛⠒⠒⠤⠤⣴⠶⠛⠉⠀⠀⠀⠀⡀⢄⣢⠔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠭⢴⣖⣒⣀⣠⣤⠤⠤⠤⠤⣤⣀⣀⣒⣒⣤⠭⠴⠖⠚⠉⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢾⣠⣤⠤⣤⣄⠄⠤⣆⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢛⡿⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⢴⠁⠀⣿⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠀⠰⣦⣛⠀⢰⣏⠀⠀⠀⠀⠉⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡀⢂⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠱⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⠀⡄⠁⠀⠰⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠰⠀⠀⠀⠂⠀⢠⠸⣇
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡄⢻⣆
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠈⠄⠀⡀⠀⠁⠀⡄⠀⢰⠘⣿⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠸⠀⣻⣇
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡄⡀⢸⣿
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⢠⠀⡇⡇⢸⣿⡀
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡈⢀⠃⠇⢸⣿⡇
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠇⠀⢹⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⣿⠀⠀⡆⢸⡇
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠁⣿⠀⡄⢗⢸⡇
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢘⠀⡄⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⢸⡀⡅⣻⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠛⢸⠀⡟⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠇⡇⢹⣼⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⢠⡇⢸⣇⠈⣿⠇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⢨⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⠀⣿⢁⣾⢈⢰⣿
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡇⢠⡀⠇⠀⠘⠀⠀⢰⢀⡀⠀⠀⣇⣼⢻⣼⣿⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⢠⠀⠈⡇⠀⠀⡇⠀⠀⢸⠈⠇⢀⠠⢸⡏⣿⢀⣿⠇
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡇⠀⠀⠀⠳⡅⢀⠇⢀⠸⠀⣰⠀⡌⣇⡎⢱⠀⣸⡟
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢡⠁⡆⠘⠀⠀⡼⠀⠘⣠⠷⡏⢄⢱⡸⡀⣦⢀⣿⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡀⠀⡈⠠⠐⡆⠀⠀⡇⠈⠐⣯⣠⠁⣘⣷⢃⣧⠘⣿⠇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠃⠂⢰⡕⡀⣰⣯⢀⠹⣠⣏⠂⣹⢇⣾⠏⣰⡟
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡸⡀⠀⡏⠀⠀⠃⣰⠏⠄⡈⢣⡿⣜⢰⢇⣼⠟⣾⠟
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠄⡆⢠⠁⠀⣠⠀⠌⣲⠏⠠⠀⠘⣿⡇⠘⠃⣾⣷⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠄⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⠀⠀⠅⡀⣰⡏⣨⠃⠠⣿⢻⡃⢤⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠘⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⡄⠘⡀⡘⢀⠀⠸⠃⠀⢀⣼⡿⡘⠃⢀⡾⡿⢋⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⡀⠀⠘⠰⠄⢶⠀⣈⢤⡀⢋⠀⢡⠀⡌⠀⠸⠂⣠⡞⢡⡖⢚⡤⠸⢇⣠⣛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠈⠀⠁⢀⣠⣾⣫⡔⠆⠀⣊⣏⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⠀⡃⠀⠀⣀⣤⡶⠟⠋⣁⣉⣤⣴⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣌⡿⠀⠀⠀⢀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⠀⠈⣿⣿⠀⢀⣴⣿⣿⣷⣶⡖⣶⣄⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡘⣿⣠⣾⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠒⠀⠈⠁⠈⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠆
⠀⠀⢠⠀⢀⡀⣰⣶⣶⣄⣀⡀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣴⣿⡏
⠀⠀⣌⣷⡿⠟⠋⠉⠉⠙⠻⠿⣤⣄⠀⠀⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠻⣿⣿⠖
⠀⠀⠟⠉⠀⠀⢀⣀⣀⢀⡀⢤⡈⠛⠷⣦⣄⣹⣿⣿⠖⡀⠀⢠⣀⣀⣤⣀⡀⢀⣴⣀⣀⣀⣀⡀⠈⠁
⠀⠀⣠⣀⠀⠀⢴⡿⢿⣿⣿⡦⠐⠀⠀⠀⢸⡏⠋⣹⣛⣿⣶⣿⣿⣿⣷⣯⣥⣈⣋⣉⣭⣿⣿⣿⠿⠓⠂
⠀⠘⣿⡟⠃⠀⠠⣿⣯⣿⣿⣿⣿⡏⠸⡆⢘⣼⠏⣸⠿⠟⠛⣉⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⢶⢟⣈⠁⠌⠁⣀⣠⣾⣿⣿⣿⠟⣻⣟⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⣵⣶⠀⢀⣜⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣄⢹⡅⠀⢸⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣶⠄⢀
⠀⠀⢀⣾⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⣿⡀⢹⣿⣆⣨⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢀⣀⣰⣶⡍
⠀⠀⢸⣿⣆⣠⣿⣿⠟⠀⠈⠉⠛⠛⠃⠾⠿⣀⠀⢸⣿⡧⠈⠻⠿⠿⣿⣿⣿⡧⠀⢐⣤⢻⣾⣿⢛⣿⡀
⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠡⣤⣿⣷⠉⠀⠀⠀⠀⠀⠒⠉⠛⠁⠁⠈⠐⠐⠻⢿⣿⠛⢻⣣
⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠈⠳⡀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣈⣤⣴⣿⣷⣿⡛⠋⠉⣽⣿⣿⣶⡄⠀⠀⠀⠘⣿⣇⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠠⣾⠉⣿⣿⡿⠛⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠛⠿⠿⠻⣿⣿⣿⡿⢳⣿⣿⣿⣿⣿⣟⣶⠿⣾⠲⣈⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣹⣇⠴⣴⣿⣿⣿⣿⣿⠋⡜⠁⠀⠙⠻⣿⣿⣿⡿
⠀⠀⠀⣀⣠⠀⠀⠉⠀⠒⠂⠐⠒⠀⠐⠆⠰⠴⠾⣿⣤⣦⣴⡿⠿⢻⣯⣭⣅⣿⣚⡵⠶⣄⠀⠈⣿⣿⡇
⠀⠀⣸⠟⢁⣀⣀⣀⣤⡀⡰⣶⣀⢀⡀⢠⡄⠄⠀⠸⣿⣿⣿⣀⣰⣏⠀⢨⣿⣧⣿⡁⢀⣿⠇⠀⠸⡿
⠀⢐⣧⠚⠛⠉⢠⣴⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢀⡴⠛⠙⣿⠉⡿⠷⠿⠟⣿⠘⠻⣿⠉
⠀⠈⠁⠀⠀⠀⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠙⠷⠺⣷⡆⠀⠸⣶⣶⡿
⠀⠀⠀⠀⠀⢸⡟⣱⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣠⣇⣸⡿⠻⢶⡟⠓⣶⡀⠘⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡰⠾⠛⠛⠛⠻⣿⣤⣤⣿⣿⣿⣿⠗⠀⢣
⠀⠀⠀⠀⠀⠈⠿⣿⣇⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠀⣾⣿⣽⣻⣿⣿⣿⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠈⠁⠀⢀⡀⢀⣸⣷⣾⣿⣿⣿⡟⠹⣿⠛⠋⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣴⠿⠿⢯⣿⣿⣿⣿⣿⣿⠃⠀⢻⣧⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠹⣷⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠈⢿⣦⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠈⠻⣯⣿⡐⢶⣿⣿⡟⠀⠀⠀⠙⢷⣦⣀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⢿⣿⣿⣦⠀⠀⠀⠈⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣁⣀⣀⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣄⣉⠑⠢⢄⠀⠈⠉⠙⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣄⠀⠉⠂⠀⠀⢀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠙⢷⡽⢅⢀⠀⠢⠤⡀⡑⠂⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠿⠩⠓⢄⠀⠀⠀⠙⠷⣴⣄⠀⠀⠀⠉⠢⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣾⡇⣟⠀⠣⠀⠀⠑⣄⠀⠀⠀⠈⠛⢿⣲⢀⣀⠑⠀⣠⢐⡺⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⠀⠂⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣧⢽⡆⣧⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠊⠉⠉⠉⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣗⠘⡃⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⣀⣀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠻⣄⠻⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠔⠉⠄⢀⡔⠊⠀⠀⠤⢚⣉⠴⣆⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢻⢄⣭⢄⠀⠀⠀⡂⠀⠀⠀⣆⠄⡜⠀⠋⠀⠀⠠⠒⠊⣉⡡⣪⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣧⣋⠇⠀⠀⣠⠇⠀⠀⠀⠘⣾⣢⠀⠀⠀⣀⣤⠶⢟⣽⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡷⠤⠒⠁⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣻⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⡾⢠⡇⠀⡄⡄⡀⡀⠀⢠⡀⡀⢀⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⠘⠂⠈⠃⠃⠓⠣⠌⠘⠀⠳⠘⠒⠃

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⠀⠀⠀⢰⡀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠆⠀⠀⠀⠀⠄⢠⠀⡀⠀⡄⢸⢀⢏⣾⢇⢻⣼⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⢠⣼⣧⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⢂⠀⠘⠸⢹⠇⡀⠚⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣄⠀⠸⣿⣯⢆⠙⠹⣄⠀⢀⠀⢀⠀⠀⠀⠀⢰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢀⠀⠏⠃⠁⠀⠀⠀⠁⠀⠀⢰⣿⠿⠶⠄⠴⠖⣶⠀⠀⢀⠃⠀⠀⣴
⣿⠐⠆⡹⣿⣾⣇⢣⠸⣂⣄⡿⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣦⠀⠀⠀⠀⠀⢤⣶⣦⣄⣧⠀⣀⡀⣀⠞⠁⠀⠀⠈⢧⡠⣼⣿
⣿⡆⠣⡄⠙⣿⣿⡞⣧⡘⣌⠴⢖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠀⠀⠀⠀⠀⠀⣿⠄⠀⣹⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢳⣸⣿
⣿⣿⣦⡈⢦⡈⢿⣿⣦⡄⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣏⠀⢀⣱⣿⡴⢀⡴⣊⠀⠀⠀⡌⠀⢀⡿⠀⠀⠀⠀⣄⠀⠀⢀⡆⠀⠀⠙⣿
⣿⣿⣿⣷⣎⢿⣷⣿⡷⢾⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠆⠈⠁⠃⠀⠀⠀⢸⣥⠞⠋⠀⠀⠈⠁⠶⠟⠉⠀⠘⠛⠏⠁⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⣤⡶⠤⢼⣆⠖⠀⠾⡍
⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⡅⣾⣣⠂⣀⢠⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠒⠻⢆⠠⠙⠛
⠸⣯⡻⣿⣿⣿⣿⡻⢿⣿⣟⡁⢳⡝⠂⠽⢿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣦⣤⣤⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠛⠀⢀⠀⠀⠀⠀⢀⡀
⠜⠘⢿⣮⣻⣿⣽⡿⣴⠊⢿⣷⢿⡏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠹⡿⠉⣿⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⢙⣿⣿⣿⣁⡈⠆⠘⡿⢘⣷⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⡰⢇⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠠⠿
⠂⠀⠐⠉⠀⠘⢿⣧⡙⣿⢿⢆⣼⣿⠇⢠⡟⠁⠀⠀⠀⠀⠠⠄⢸⣟⣿⡋⠒⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣷⠀⠀⠠
⠀⠀⠀⠴⣣⠀⠀⠙⢻⣦⢳⡚⣶⣿⣿⣁⡴⢞⠉⠀⠀⠀⠀⢠⢋⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⠻⣿⣿⣯⠞⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣀⠶⡀⡀⣄⣀⠀⠙⢷⡝⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⡴⠀⠀⣿⣦⡀⠀⠀⠠⠖⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣄⡠⠄
⠀⠀⠀⠈⣿⣷⡄⠺⠋⠉⠀⠀⠀⠻⠉⠀⠈⠇⣴⣄⡆⣠⣶⠞⠀⠀⢸⠿⠟⢁⠠⠆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡏⠀⣀⠀⢠
⠀⠀⠀⠀⢻⣷⡘⢿⣆⠀⠀⠈⢀⣀⠀⢠⠴⢗⣿⣾⡿⢡⣿⣤⡀⢀⣼⡤⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢨⣿⣡⡠⢟⣀⡤⠤⠤⠆
⠀⢠⣤⠀⠘⠿⠆⠀⠘⠳⠀⠰⣯⣿⣿⣿⣿⣯⣷⡜⠃⣀⣄⣼⡟⠚⠁⣡⠤⣄⡙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠘⢿⣿⠯⡽⡆⠀⡆
⢀⡘⠙⠀⠀⠀⠀⠀⣀⣴⣦⣼⣿⣿⣿⡏⣹⡏⢸⣧⣸⡿⣷⣤⡽⠶⢾⡱⠷⣄⡁⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⠀⢈⣶⣤⣷⡄
⢺⣿⠗⠀⠀⠀⡀⢀⡹⣿⣿⢿⣾⣿⣧⠠⣾⣷⣯⣽⣿⣳⣿⣿⣧⣾⣿⣷⡶⡟⠇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠸⣆⡞⠛⠏⠰⣷
⠀⠈⠀⠀⠀⠀⠉⢰⡾⠛⠳⠿⣏⣿⣥⡔⠛⣿⣦⣾⡛⣷⠂⣿⣿⣿⣿⠯⣷⡀⢠⡃⠀⠸⣶⠴⠂⠀⠰⠷⠐⠃⠁⠐⠃⠆⠀⠀⠁⠀⠀⢣⡅⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣘⢿⣯⠳⣾⣍⣭⣤⣿⣿⣷⢬⣙⠟⢻⣽⣿⣁⠀⡿⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠀⣴⣿
⠀⢀⠀⠄⠀⠀⠰⠤⣤⣀⣀⠀⠉⠀⠻⣄⢉⣹⣿⡟⣻⣛⣋⣤⣙⣦⡀⠙⠋⠈⠀⠀⠀⠀⠀⠀⣠⣴⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣯⡀⠙⠋⠁
⠀⠀⠀⠀⠀⠄⠀⢀⡀⠉⠍⠻⡓⠈⣠⠼⣟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀⢀⣤⣤⣦⠘⠙⠻⡾⠋⠀⠀⠀⠀⠘⠶⣦⣶⣾⣶⣤⡀⣿⠀⠀⣂⡖
⡠⡇⠀⠠⢀⡄⠀⠀⠀⢀⣰⡿⠋⠀⣡⠞⠉⠀⡴⢿⠟⠉⠉⠉⠉⠉⠈⠂⠀⢀⡐⣿⣿⣿⣿⣇⠀⠀⠀⣦⣤⡤⠄⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⡀⠀⡇
⠀⠀⠀⠀⠚⠐⠀⠀⣠⣿⠟⠀⠀⠐⠁⠀⠀⠞⠁⠉⠀⣔⠀⠀⠀⠀⠀⠠⠀⠀⣁⣸⣿⡟⣿⡟⠀⠀⣼⣿⣭⣤⣄⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⢦⠁
⠀⠨⠀⠂⠀⠀⢀⣰⠟⣱⡇⠀⠀⠀⠀⡀⠀⢄⣀⡀⡰⠏⠀⠀⣁⠀⠀⠀⠀⠀⠉⠻⠁⢸⡏⠁⠀⡿⡀⠀⠉⠉⠉⠉⠉⠉⠒⠀⠀⠀⠘⢏⠁⠱⣼
⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢍⡹⠁⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡌⠀⠀⠀⢷⣌⡱⠀⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⢂⠀⢹⣄
⠀⠀⠀⠀⠀⣤⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠀⢠⣾⡔⢠⣾⢻⡌⢷⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠠⢲⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣯⣷⡄⢠⡩⠻⠃⠀⠀⠀⣠⠔⠚⠉⠀⠀⠙⠬⠱⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠿⢥⣆⡀⠀⠀⢀⢴⣞⠉⢠⣐⡀⠀⣿⠉⢺⣤⠏⣀⠀⢀⡠⠋
⠀⠀⠀⠀⠈⡳⠉⠀⣢⡄⠀⠀⠸⡀⠀⡈⠀⡇⢷⠳⡄⣰⠿⠟⠅⢀⣄⡙⠙⣶⣿⡠⣾⠏⠘⠁⠀⠀⠁⠀⠤⠀⠲⠲⡽⠈
⠀⠀⠀⠀⠀⠙⠁⠀⡉⢉⢢⠀⠀⢣⠀⣧⠀⡇⢸⠀⢸⣿⡀⣀⠤⢴⡛⢿⣷⣿⣿⣿⣿⠴⢃⣠⠊⠀⠀⠀⠀⢰⠢⠦⡶⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⣹⡃⠀⡈⣧⣼⣀⠧⣾⠄⣯⡟⠓⠋⠹⠭⣭⣭⣨⣿⣿⣿⣇⡀⠈⠀⠀⠀⠀⠀⢈⠼⠷⣿⣻⣿⡿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⣨⣍⢶⣬⣾⣯⠟⠲⢿⡏⠋⠀⡄⠐⣀⠀⠲⣶⢾⠿⣿⣿⢻⣓⣋⠩⠂⠀⠀⠘⠋⢍⡿⠋⠉⠀⠀⠈⠂⣶⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⣽⣽⠋⠙⢳⡀⢸⣷⢸⡆⢣⠀⠘⠁⠐⢹⡯⢶⡟⠋⠙⢉⠉⣠⠀⠀⠀⠀⡆⡸⡇⠁⢀⣤⢊⠠⠎⡍⡽⢀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣘⠿⠶⡒⠻⣿⣿⣽⣿⡔⢻⣦⡀⣀⠀⠀⠱⣸⢷⣄⣶⡏⠐⣁⠀⠃⠌⢀⣼⣰⣿⣤⠞⠛⣍⡠⠞⣼⠃⠈⢾⡇
⠀⠀⠀⠀⠀⠀⡶⡦⢀⣠⣄⣾⡃⢀⠶⠶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠌⣭⠎⣹⣼⢿⣷⣿⣎⢚⡡⠂⠀⠀⠀⠀⠙⢯⣠⣤⣼⣯⢶⡿⠃⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⣤⠴⠻⠛⠻⠉⠀⠀⡱⢒⣫⠿⣿⣿⢧⣀⡀⠀⠠⠦⣄⣠⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⢀⣠⣾⠿⣡⠭⠄⠚⠟⠀⠀⢀⣀⠀⠀⠀⣌⠃
⠀⠀⠀⠀⠀⢀⡟⠱⠂⠀⠀⠰⢤⣰⡛⠙⠋⠁⠚⠫⢨⠜⠁⠀⠀⠀⠀⠒⠭⣙⡿⣻⡿⠿⠃⠤⣤⣶⣶⢻⢿⡆⠀⠠⠖⠀⠀⠀⠂⠀⠸⠋⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠐⠀⢀⡅⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠁⠀⠁⣀⡘⠁⠁⠙⠀⠀⠀⠀⠙⢷⠀⢤⢳⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣁⠀⠦⣀⣀⠀⠦⠀⠀⡀⠀⠀⠀⠀⡔⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠈⠀⠐⠀⠀⠂⠀⠀⠦⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠉⠡⠀⣀⠨⢧⣜⣿⣄⣀⠀⠀⠀⠤⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠲⠄⠘⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢉⠓⢂⣈⣉⣼⣿⣿⣿⣿⢵⡤⠠⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⣑⠦⣀⠀⠀⠀⠘⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢄⠿⣏⠈⠙⢛⡿⣿⣿⡿⣿⣆⡅⠈⠁⠀⠀⠀⠐⠀⠀⠂⢤⣄⣤⢴⣾⣧⣤⡴⠾⠥⠈⣆⣀⠑⠢⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡱⠀⠀⠀⠈⠰⣾⣷⡯⠏⣝⢀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠘⠰⠈⠉⠺⡿⣿⡿⠙⠋⠁⠀⠀⠙⣌⠑⠲⠤⣬⠭⢄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⠌⠀⢈⡍⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠙⠚⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡀⠈⣷⣀⡀⠀⡈⠐⢲⠖⠒⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡀⡼⠛⢏⣿⣾⡇⠈⡿⠈⠀⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡮⢞⠵⠋⠀⠀⠈⢻⣿⡇⢠⠇⠀⡴⠛⢀⠠⡀⠀⠀⠀⠀⢀⠔⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⢹⠀⣾⣀⡼⣣⣤⡤⠰⠆⠀⠂⠠⠐⠉⠀⠦⢶⠑⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡅⣫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⠀⠀⢀⣀⣾⡿⣿⣾⢿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣶⣼⣿⣿⣿⣿⣧⣶⣀⠀⠀⠀⠀⠀⣀⣠⣿⠿⣷⣿⢿⣷⣀⡀
⠀⠀⢸⣿⡟⠛⣰⢦⡴⣆⠛⠛⣿⡇⠀⠀⠀⢤⣿⡟⢋⣤⣴⣤⣬⡙⣻⣿⡤⠀⠀⠀⢸⣿⠛⡛⣰⢦⡴⡆⣛⠛⣿⡇
⠀⢀⣼⡿⢃⣹⢍⡵⢶⡭⣿⡘⢿⣷⡄⠀⢘⣿⣿⠠⣾⢫⡶⢦⡙⣷⠀⣿⣿⡀⠀⣠⣾⠿⢃⣿⢭⡵⢯⣫⣏⡘⢿⣧⡄
⠀⠈⢻⣷⡌⣻⣚⡳⠾⣃⣿⢡⣾⡿⠃⠀⢨⣿⣿⠀⢿⣜⠷⠞⣡⡿⠀⣿⣿⠁⠀⠙⢿⣶⡌⣿⣚⡳⢞⣜⣏⢡⣾⡟⠃
⠀⠀⢸⣿⣧⣬⠹⠞⠳⠏⣤⣤⣿⡇⠀⠀⠀⠚⣿⣧⣌⠛⠻⠛⢛⣡⣽⣿⠓⠀⠀⠀⢸⣿⣤⣥⠹⠞⠳⠇⣭⣤⣿⡇
⠀⠀⠀⠈⠉⢿⣷⣿⣿⣾⡿⠋⠉⠀⠀⠀⠀⠀⠉⠿⢻⣿⣿⣿⣿⡟⠿⠉⠀⠀⠀⠀⠈⠉⠙⣿⣶⡿⣷⣾⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⣰⣆⣠⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⣄⣰⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⣤⣼⡟⠿⠙⢏⠿⢻⣧⣤⠄⠀⠀⠀⠰⣦⣼⡟⢿⡹⢏⡿⢻⣧⣴⠆⠀⠀⠀⢀⣴⣿⡿⠟⠛⠛⠻⢿⣿⣦
⠀⠀⣶⡿⠇⢡⣷⠿⠿⣾⡬⠸⢿⣶⠄⠀⠰⣶⡿⢦⢯⣡⡷⣦⣎⠝⡴⢷⡶⠆⠀⠀⣼⣿⠋⣠⡾⣛⣛⢷⣄⠹⣿⣧
⠀⠰⣾⣟⠠⣿⡣⣏⢹⡎⣿⠅⣛⣷⡦⠀⠴⣾⣛⡯⢽⡏⡎⣱⢹⡯⢝⣛⣷⠦⠀⢰⣿⡇⢰⡏⢼⢵⣯⡇⣿⠀⣿⣿
⠀⠠⣾⣯⡤⠹⣷⣭⣭⣾⠯⢡⣽⣷⠄⠀⢠⣾⣯⡭⡝⠻⣾⡶⠟⢭⢯⣽⣷⡄⠀⠀⣿⣿⡀⠻⣮⣛⣋⣵⠟⢠⣿⡿
⠀⠀⠀⠿⢷⣧⣥⢉⡍⣬⣸⡿⠿⠄⠀⠀⠀⢠⠿⢶⣏⣷⢣⡔⣮⣹⡶⢷⡄⠀⠀⠀⠘⢿⣿⣦⣌⣉⣉⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠘⠋⠻⠟⠻⡟⠙⠃⠀⠀⠀⠀⠀⠀⠀⠸⠋⢹⠏⢻⡏⠙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡀⠀⠀⢀⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠈⠑⠀⠁⠀⠀⠘⠁⠈⠀⠛⢩⠋⠉⠆⠀⠀⡜⡿⠐⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠖⠀⠀⠐⠀⠀⠁⠈⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠰⢦⠍⠀⠀⠰⠶⢶⠆
⠀⠀⠀⢀⠀⠀⠠⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠃⠀⠂⠀⠀⢰⡈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⣾⠆⠀⠀⠄⠀⠀⠈⡀⠛⠀⠀⠄
⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⠄⠘⠃⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠃⠀⠠⢀⠀⠀⠀⠀⠀⠀⠛⠀⡆⠀⠀⠀⠁⠀⠀⣰⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⡀⠀⢰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜⠩⣰⢠⡄⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠃⢀⠈⠀⣶
⠀⠀⣀⠀⠀⠀⠀⠀⡀⣀⢀⣀⠀⢀⡀⢀⣍⠀⠀⠀⠀⠀⠈⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠈⠀⡄
⠀⠀⠈⠙⠒⠀⢰⠀⢹⡇⢸⣇⠀⡾⢷⠀⣶⠁⠀⠀⡀⠀⠀⠰⠈⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠈⠀⠐⠂⠀⠐⠒⠙⢂⠀⠀⠀⢀
⠀⠀⠀⢰⡆⠀⠏⠀⠀⠀⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢂⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠉
⠀⠸⢀⡈⠀⠀⠀⠀⠑⠲⠤⢴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠
⠀⠀⠈⠁⠀⠀⠐⠒⠒⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣄⡀⡠⠀⠉⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡆⠀⠀⡄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⡀⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⢓⠐⢀⡀⡀⠀⠀⠠⡜⠤⠀⢠⠀⠀⡦⠀⠃⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⡀⠘
⠀⠀⡅⢀⠀⢀⣀⣰⢀⣀⡅⠀⢠⠁⠀⠀⠨⠀⠀⡤⠐⠀⠒⠂⠀⠠⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠁⠀⠀⠒⠒⠂⠈⠭⠭⠃⠀⠀⢦⡼⠀⠀⠈⠦⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑
⠀⢀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠄⠐⠦⣀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠰⠀⠰⢆⡀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡘⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠁⠀⠀⢀⠀⠀⠀⠘⠃⠈⠉⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠈⠙⠳⡄
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠉⠦⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡎⠀⠰⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠇⢠⠁⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠒⠀⠀⠀⡄⠀⠀⠀⡠⡋⠀⢠⣁⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣠⠋⠀⠀⠀⡀⠀⠀⠀⢠⣮⡄⠛⣀⠀⢠⣷⠞⠁⠈⠪⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣦⣄⣈⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⣀⠀⣀⠠⠚⠟⠁⠀⠋⠉⠛⠉⠛⠿⠦⠌⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡐⠁⢸⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⣥⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠀⠀⣼⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢿⣻⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⢰⡏⠀⢠⡇⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡀⠀⢸⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠇⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠈⣦⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠙⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠠⣸⠃⠀⠀⢀⢀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⡄⠀⣿⢦⠀⠀⠀⠀⠀⠀⠀⠈⢇⠜⠁⠀⠀⠀⢀⡌⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢹⡜⠳⣀⡀⢀⡠⠀⠀⠘⠁⠀⠀⠀⠀⠀⢿⡿⠫⢔⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡴⡸⣼⠃⠀⣇⣴⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⢆⠗⣎⢀⣄⣿⡉⡁⠈⠧⠜⣀⠀⠀⢀⣤⣠⡶⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢮⠔⢹⣟⣟⢁⠈⠈⢋⣑⠟⣁⠽⠭⠩⠤⠿⠾⠻⠙⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇⡄⠞⢻⠀⠃⠀⠀⠈⠁⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠁⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣙⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⡿⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠑⠒⠶⠤⠤⣄⢠⡖⠉⣉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣀⡤⣬⡇⡞⠁⣀⣀⣠⠞⢷⣀⡾⠉⠓⠦⣄⣼⣾⠉⠉⠉⠑⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⢀⡿⠳⠚⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡴⢋⡤⠴⠒⠒⠲⢤⣀⢀⡴⠚⠉⠉⠉⠉⠓⠢⣄⡈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡾⢥⡏⠀⠀⢠⠖⠒⠲⣄⠀⢠⠟⠫⣷⠀⢀⡤⠖⠲⢤⡀⠀⠈⣇⣠⠽⣖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢩⣟⣹⠾⠯⠷⠶⠶⠶⢶⠖⠚⠲⣼⢦⡤⠿⠤⠬⠤⠤⠤⠤⠧⠤⠶⠿⠴⠶⣾⣷⡒⠲⠆⢀⡠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⡤⠬⢿⠀⠀⠀⡿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡞⡴⠒⠲⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⠋⠀⢀⣀⡤⠤⡖⠒⠒⢛⡗⢒⡞⠉⠉⠙⠓⠒⠒⠒⠤⠤⢤⣀⣀⣀⠀⠀⠀⠉⠙⠒⠲⢧⣇⠳⣀⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡤⣖⠉⠡⡄⠀⠈⠲⣄⡞⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠉⢉⠛⠒⣦⢤⣀⡀⠀⣧⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠋⠀⠈⠳⠤⠞⠀⠀⠀⡾⠀⢀⡷⠤⠤⠤⢤⡤⠤⠴⠖⠚⠉⠀⠀⠀⢰⡃⢀⠜⠁⠀⠀⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠶⠆⠀⠀⠀⠀⠀⠈⠳⣇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠒⠢⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠔⠚⠉⠁⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉





⣿⠿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣛⣿⣿⣿⣿⣿⣿⣟⣿⣿

⠀⠀⡇⠘⣦⠈⡇⠀⠀⣿⠀⢀⡄⡇⠀⣶⠛⣿⠀⠀⢸⠀⠛⢣⣿⠣⡆⢸⠀⠀⡶⣾⡏⢻⡇⣼⠃⣸⡏⠀⠠⡗⠀⠀⠀⣿⡾⠈⢿
⠀⠠⣇⠀⢘⢧⢻⠛⠛⣟⢛⡛⠛⣟⠛⣛⣛⡿⢛⢛⢻⠟⠛⠛⡇⢸⠀⠸⠀⠀⡇⢸⠀⣼⢱⢏⠀⣿⡗⠒⠺⡿⠒⠒⢲⡗⠒⠒⣾
⠀⠀⣿⣀⣾⢾⢿⡇⠀⣿⠙⠃⠀⠁⠀⢀⠀⠀⠀⠀⠈⠓⢆⠀⡇⢸⡀⠀⢰⡄⠇⢸⠀⣿⡿⢸⠀⣏⣇⣰⠷⡇⠀⠀⠀⡇⠸⡿⢹
⠀⠀⣿⠻⠃⢸⣈⣃⣀⣿⣠⠃⢀⣈⡓⠀⠀⠀⠀⠀⡄⢀⢈⣆⡇⢸⣅⣤⠟⢿⡇⢘⠀⣿⠁⢸⡆⡇⡏⣛⣀⣇⣴⣶⣾⣷⣶⣦⣼
⠀⠀⣿⠀⢀⢸⢤⠀⠀⣿⢸⠽⠛⣓⠛⠀⠀⠀⠀⠀⠀⠉⢸⠁⡆⢸⠉⢟⣀⡾⠃⢸⠀⠁⣠⣼⡷⠆⣧⡀⠀⣿⡏⠛⠿⠛⠙⣿⣿
⠀⠀⣿⣿⣿⣿⡄⢁⡀⣿⠀⢄⠠⠇⠐⢚⣳⠦⠄⠀⢀⣀⣼⣦⡇⠈⠀⠈⠻⠃⠀⢘⠀⡀⠛⠛⠂⠀⡇⠘⠀⠻⣧⡀⠀⣀⠈⣿⢿
⠀⠀⣿⣿⣿⡿⢀⢂⢉⣿⡄⠆⠀⠀⠀⠈⠉⠁⠀⠀⠛⢲⣛⣻⣿⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⡀⠧⠀⠠⠀⠈⡆⠠⠀⠀⣉⢸
⠀⠀⣿⢗⡓⣦⠒⡼⢘⣿⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠄⠈⢫⠀⣀⠔⢹⣿
⠀⠀⣿⠀⠀⠉⠛⠷⣾⡟⠁⠀⢀⠀⠀⠀⠀⣀⣀⠀⣰⡋⠄⣼⣿⠿⡟⣵⣿⣿⣿⣿⢾⣯⣽⣭⡻⣿⣿⡄⢠⠄⠸⢾⣩⣄⠀⣾⣿
⡀⣀⣟⣀⣤⣤⣶⣿⣿⡀⠀⢢⠘⣷⣄⠀⠀⠀⠁⡼⡅⠀⢸⣿⣿⣾⣿⣿⡟⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣇⡀⡴⣆⠟⣸⡇⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠾⣿⣿⡿⠟⣯⡐⢃⠀⢸⣿⡟⡿⠋⠁⠀⠠⠤⣄⡀⠀⠀⠈⠉⣿⣿⠇⠀⠉⡹⢲⠟⢷⣾⣿⣿
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣥⣄⠀⣿⣿⣦⢨⣈⠿⣷⡅⠀⠀⠀⠦⢥⡀⢁⠀⣠⠴⢶⡟⢁⠀⠀⡼⢡⡇⠀⠈⢻⣿⣿
⣎⠂⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡴⠋⢹⣿⠙⠧⣿⣿⣿⠿⠟⢳⠏⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⢳⡇⠈⠀⡼⠁⠸⡇⠀⠀⠀⠹⣿
⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⡿⠖⠒⣩⣽⣟⣦⡀⠀⠛⡄⠻⣄⠀⠀⠠⣤⣴⠃⡄⢸⠀⢿⡄⡼⠁⠀⠀⠙⠐⣄⠀⠀⠘
⣎⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡜⠉⠀⠀⠉⠀⢀⣀⣉⡛⠀⠀⠘⠱⢹⣶⣤⣀⣀⠏⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⢠⣴⣿⣷⣄⡀
⡙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⣠⠊⠀⠀⠀⠐⠀⢈⣿⠿⣶⣄⡀⠈⠘⠙⠹⡟⠀⠀⠀⠀⠁⠀⠙⡘⡄⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⡔⠁⠀⠀⠀⠀⢀⡀⢸⣯⣿⢬⣿⣿⣿⡗⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡞⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣦⣸⣿⠿⠿⣿⣟⣿⣿⡟⠀⣼⠀⠀⠀⢀⡴⠊⣷⡞⣻⣿⣿⣾⡿⣾⣿⣷⣾⣷⢶⢺⣵⡦⣄⣠⣴⣾⠁⣠⠄⢿⣿⣿⣿⣿⣿⣿
⣵⣿⣷⣶⣴⣿⣿⣿⣿⣿⡇⠀⢻⣤⡖⠉⠁⠀⢰⣿⣿⣏⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠂⠀⠀⠀⠀⢠⣄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣤⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣴⣾⠋⠇⠳⢠⠏⢭⢿⣄⠄⠒⣀⠀⠦⠀⠀⢀⠀⠀⡀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⠜⠛⠻⢒⡖⠲⠻⢷⣀⠒
⠀⠀⠀⢠⡐⢄⣶⠉⠙⠷⣼⣜⡅⠀⠈⠙⡦⣌⡠⠖⢫⡡⠀⠁⠔⠀⣀⠀⢸⢴⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠛⠶⣼⣜⠄⠀⠀⢠⣉⠅
⠀⠀⠀⡀⢹⣷⣈⢆⠀⠀⠈⣙⣣⣀⠄⢘⡱⠉⠀⢰⣾⣁⠠⡀⠁⡀⣥⡀⢨⢰⣿⠁⠠⠀⠀⠁⠄⠀⡘⢷⣞⡙⣄⠀⠀⠀⣩⣶⣤⣒⢨⢎⡄
⠀⠀⠀⠠⠀⢿⣿⣿⣓⡁⣞⠭⠼⢛⣳⠎⠁⠙⠲⣜⣝⣦⣶⢷⠀⠰⣿⡇⠈⣼⣿⠀⠀⠀⠀⠀⣀⡤⢓⠈⣿⣷⣮⢓⣃⣾⠫⠔⢛⣽⠃
⠀⠀⠀⢢⡄⠘⡼⠔⠋⢻⣷⣄⡠⣪⠃⠀⠀⠀⠀⡘⠩⢒⣲⣼⣧⠀⢻⠀⠀⣿⠋⣰⣶⣶⠂⠘⡁⠐⢤⡂⠸⡉⠀⠝⢻⣷⣤⡐⠹⠁
⠀⠀⠀⢴⣿⣄⠸⢌⣠⣔⡽⣿⣿⣷⣄⡀⠀⠀⢀⣁⢉⣀⠉⣼⣿⡆⠀⠀⠀⠁⠐⢋⡩⠽⠗⠿⠿⣤⣬⣿⣄⡡⣔⣀⣄⡙⣿⣿⡷⣤⡄
⠀⠀⠀⢠⡟⢷⣀⡨⠍⢁⡈⠬⢿⢀⠈⠃⠀⡍⢈⢉⣯⣭⣛⣍⠻⣷⠀⠈⠁⠹⢆⡞⠛⢦⣄⠀⠀⠀⢈⡿⢷⣀⣈⠏⢀⠀⠬⢿⢅⢀⣂
⠀⠀⠀⠘⠀⠂⠁⠀⠈⠀⢀⠀⢰⠀⠁⡀⠀⠃⠘⠙⣻⣿⣿⣿⡷⠈⠁⠀⢢⠠⢀⣬⣀⣀⣬⠟⣠⢀⠼⠁⠘⠉⠀⠈⠀⢀⠀⠠⠀⠁⡀⠀⡇
⠀⠀⠀⢀⠀⡐⢀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢠⠀⠟⠛⠛⠛⠻⠛⠁⠀⠀⠓⢈⡴⡯⠼⡏⠉⠀⢁⡈⣵⡄⠂⠀⠂⠀⠀⠀⠁⠀⠀⠃⠀⢠⠠
⠀⠀⠀⠘⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠤⠤⠄⠀⠠⠀⡀⠀⠔⠧⠄⠠⠀⢈⣦⣊⣥⠞⢋⠞⠑⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠰⢰⠀⠁⡠⠁⠀⡠⠡⠊⣀⠀⠂⠀⠐⢦⡰⠿⠿⢿⡧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⢈⠀⢀⠠⠀⢀⠔⣤⢇⣔⠠⣄⣀⢠⢬⢏⠒⠦⣄⡊⠀⠈⢃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠂⠀⠀⢻
⠀⠀⠀⠐⣄⡤⢀⠀⠀⠐⢀⠀⠀⠈⢆⢻⠸⠈⠰⠄⢁⠄⡈⠸⣿⡆⠀⠙⡆⠀⠀⢀⡀⠀⠁⠀⠀⠀⠑⢄⡤⠀⠀⠀⠀⢀⠀⠀⠈⢄⢸⠸
⠀⠀⠀⢸⡟⠘⢦⡀⠀⠐⠁⠀⠐⠀⢘⢻⡇⠀⣶⢀⠂⢰⣶⣦⣝⡧⠤⠚⠋⠲⣴⡶⢶⣤⣀⠐⠀⣠⣶⡿⠰⢧⡀⠔⠀⠀⠀⠀⠄⠸⢻⣷
⠀⠀⠀⢘⠁⠀⠀⡈⠒⠄⣀⠀⠐⠀⢸⡌⣇⠀⣿⠇⢀⣶⣮⠍⠉⢁⠀⠀⠀⠀⠘⡏⠀⠙⣤⣷⠞⣿⢟⠃⠀⠀⣈⠒⠄⣀⠀⠐⠀⢰⡄⣿
⠀⠀⠀⠀⣠⣠⡞⠀⢻⣶⣏⠩⠙⠛⠠⢄⣿⠀⠏⠀⣼⣧⣈⠋⠁⠚⠀⠀⠀⠀⢀⣸⣴⣾⠟⠈⠁⢀⠃⣠⣠⡞⠁⢺⣶⣞⠋⠉⠛⠀⢤⣿
⠀⠀⠀⢰⣿⣿⣿⡟⢻⣒⣫⣧⡢⢎⢠⠖⠈⠀⠀⢰⣿⣏⣛⣭⡭⠉⠃⢃⠀⠈⠉⠉⡿⠑⠲⠶⡤⠃⢰⣿⣿⣿⡿⢻⣄⣫⣧⡂⢞⣀⠞
⠀⠀⠀⣾⡿⠛⠀⢷⢈⢂⠀⠐⠚⣠⡑⢄⣠⠀⠓⣾⠏⣴⣿⣟⣛⠛⠓⠀⠀⠀⠀⠁⠙⠒⠀⠠⠒⠦⣾⣿⠿⠁⢻⠰⣂⠀⠒⠚⣢⡁⢤⠠⠄
⠀⠀⠀⠟⠀⠅⠀⡈⢈⢽⡋⠓⡭⣉⣹⣦⡑⠴⠃⠀⠘⠻⠿⠿⠷⠶⢾⠈⡄⠐⠁⢀⠀⠀⠄⠀⠀⣼⠟⠁⠄⠀⠈⢃⠽⡏⠓⡭⢍⣍⡦⡙⠔
⠀⠀⠀⢀⠀⠐⠀⣜⠷⣔⠺⣄⠀⢀⢀⣀⣩⣄⠐⡀⠀⠄⠈⢀⣉⡀⢀⠀⠗⠃⠀⠀⢀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣔⢿⣗⡻⢦⠀⠀⣀⣠⣬⠦
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡴⢶⣶⡄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠾⠿⠷⡄⠀⠀⠀⠠⠀⠀⡀⠀⠀⢰⣷⣶
⠀⡄⢀⡄⠀⠀⠀⠀⠀⠠⣶⣎⡉⡇⡓⢒⠷⣄⠐⢀⢤⣆⠐⠱⠀⡀⠀⣠⢀⡴⠀⠀⠀⠀⠀⠀⠰⣿⣭⡄⣫⡍⠻⠻⢦⡀⡡⢴⣣⠀⢀⠂⣠⢸⣿⣿
⢈⢱⡏⠀⠀⠀⠀⠀⣄⡠⠇⠨⠛⠿⠃⠀⢁⢄⠙⠁⣼⠃⢀⠐⠈⣅⠀⢣⣿⠀⠀⠀⠀⠀⠰⣤⠼⡁⠀⠙⠛⢃⢀⠀⡢⠋⠀⣼⠃⢠⠀⠀⣬⢸⣿⣿
⠈⣾⡇⠀⠀⠀⠀⡰⠘⣷⣌⡤⠀⡴⢚⡷⡤⠃⠲⢄⣫⣢⣼⡄⢰⣿⠀⢸⣧⠀⠀⠀⠀⣠⠇⢸⣷⣴⠤⢠⠞⠫⠗⠜⠁⠒⠤⣽⣶⡾⣇⠀⣿⢸⣿⣿
⠀⡿⢁⣦⡆⠐⠉⢄⡀⠩⠛⠱⣷⣅⠀⡼⠃⠀⠀⠌⢉⠨⡱⣷⠀⠿⠀⣿⠃⣴⣶⠒⠉⠠⣄⠀⢝⠭⠺⣷⣅⡀⡞⠁⠀⠀⢠⡍⢒⣞⣿⡄⠹⠸⣿⣿
⠀⡠⠚⡻⠷⠶⢧⣤⣷⡀⢠⠀⡈⢿⣷⣦⡀⠀⠀⢘⡁⣋⢢⣿⡇⠀⠀⡀⠘⡉⠽⠲⠿⢦⣬⣧⠀⠄⣀⡜⢿⣿⣦⡀⠀⢀⢀⣉⣩⡀⣿⣧⠀⢰⣿⣿
⠀⠣⣘⠛⢦⡀⠆⠈⡿⢧⣀⠛⢁⠀⢿⠅⠉⠀⠄⢈⣙⣙⣭⡙⢷⠀⠀⠘⢦⠋⠳⣄⢈⠀⢨⠿⣄⡈⠋⠀⠈⢿⠀⠁⡀⠅⣈⣽⣯⣍⣍⠻⡀⢸⣿⣿
⢀⠀⣰⣀⣤⡞⢑⠤⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⠀⢉⣉⣿⣿⣿⠈⢁⠀⠔⡠⣇⣤⠴⠃⡢⠘⠀⠉⠀⠈⢀⠀⠀⠈⢀⠀⠁⠏⣉⣽⣿⣿⠂⢉⣸⣿⣿
⠀⠚⠓⢇⠀⠀⢈⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠀⠉⠉⠉⠉⠁⠀⠈⠁⠼⠳⠺⡀⢀⡤⣼⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠀⠋⠉⠉⠉⠁⠀⠀⢹⣿⣿
⠐⠂⠀⣠⣦⡴⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠀⢀⣶⣤⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢺⣿⣿
⠀⢨⣞⡛⠛⠗⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠁⠀⠄⠃⠀⠀⠀⠀⣶⡛⠛⠛⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠅⢸⣿⣿
⠐⠚⠀⠉⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⡀⠠⠀⠚⢾⡉⠲⡤⠒⢁⠉⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢠⠂⠞⢶⡅⠒⣼⣿⣿
⠤⡄⣀⣂⠀⠀⠀⢀⣴⢪⠀⠀⠀⢂⠀⠀⢦⣇⠀⡃⠐⢀⣀⡺⡇⢀⡴⢤⢀⡂⠀⠀⠀⠀⣀⡶⢁⠀⠀⠀⠀⠀⠀⢤⣇⠀⡋⠠⢀⢀⠘⢇⠀⣸⣿⣿
⠀⠘⡷⠉⠟⣤⣤⣿⠏⠀⠑⠄⠀⠀⠀⠀⡀⣿⢸⣷⠁⣸⠻⠛⠎⠁⠀⠈⢿⠌⢻⢂⣄⣴⣿⠁⠈⠂⢁⠀⠀⠀⠀⡈⣿⢸⣷⠁⣘⣛⠿⠶⠉⢸⣿⣿
⠀⠀⢨⣠⣾⠋⠒⠱⢀⢀⡞⢠⣤⡲⠶⠦⠉⢸⠸⠏⢰⣏⠿⠆⠤⠀⠀⠀⠈⣄⣴⡿⠣⠊⠇⠀⣠⠖⢤⣐⢦⠤⢄⠃⣹⠘⡏⢠⡟⠷⠤⠠⠀⢸⣿⣿
⠀⠘⠋⣿⠣⢤⡴⠀⣼⣿⣷⠾⣛⣳⡂⡄⢠⠋⠀⠀⣾⡟⢂⠰⠲⠀⠀⠠⠞⢻⡟⠠⣄⠈⢠⣿⣿⣶⢿⢛⣦⢀⠄⣨⠛⠀⠀⣼⡿⢶⡴⠶⠂⢸⣿⣿
⠀⠀⠋⠐⠀⠀⠐⢴⣿⠿⠹⡐⡉⠀⠥⣈⠡⡀⠀⢰⡟⣹⣿⣷⠶⠆⠀⠀⠐⠉⠂⠀⠈⢤⣼⣿⡏⢷⠘⠉⠨⠥⠈⢋⠀⠀⢤⡿⢫⣿⣶⡶⠦⢸⣿⣿
⡀⠂⠀⠂⠀⠀⢀⡾⠁⠀⠀⢁⠽⠘⠪⠉⡵⡈⠰⠂⠈⠻⠿⠿⠶⠆⠀⠀⠀⠀⠀⠄⠀⢰⡟⠁⠀⠈⢊⢗⠒⢙⣛⣦⠁⠴⠊⠀⠿⡿⠷⠶⡄⢸⣿⣿
⢉⠁⠀⠀⠀⢀⠞⠀⠀⠀⢰⡻⢤⠳⠀⠀⠠⠮⢄⠀⠀⠀⠀⢬⠄⠀⢈⠅⠀⠀⠀⠀⣠⠏⠀⠀⠀⢔⢷⡂⢦⠀⠉⣊⣅⡄⠂⠀⠀⠀⢀⡁⠐⢘⣿⣿
⠘⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠻⠌⠳⠾⠆⠔⠂⠀⠄⠀⠐⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠈⢧⠙⢦⣶⡄⠤⠄⠌⠄⠀⠰⠀⠀⢀⠀⠸⣿⠿

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⢤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠹⢿⣿⣿⢿⣭⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⠉⠙⠛⠻⡿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⠛⠛⠉⡛⠛⠛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⣶⣤⣤⡀⠀⠀⠀⢼⣿⣿⣟⠛⠛⠻⣿⣿⣿⡁⠈⠻⣿⡷⢬⡛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡗⠁⠤⣨⣿⣿⣿⠄⠀⢩⣝⠿⣶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⠿⠛⣻⠿⠿⠿⠿⢿⢹⣿⣿⣿⣿⣯⠀⠀⣸⣿⣿⣿⡃⠀⠀⣉⣧⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣤⣴⣿⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⡅⠀⠀⠀⣩⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣶⣿⣿⣿⣿⡿⢻⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢽⣿⣿⣿⡇⠀⠀⠀⢀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⠛⠿⠿⠋⣠⣾⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠘⣿⣿⣿⡇⠀⠀⠀⢠⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣶⣾⠿⠛⠁⢀⣴⣿⣿⣿⣿⣿⡿⢊⣿⣿⣿⠶⠦⢻⣿⣿⡇⠀⠀⠀⢸⣿⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⡟⠉⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡛⠛⢤⣿⣿⡟⠀⠀⢿⣿⣿⠅⠀⠀⠀⢸⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣻⣹⣰⣿⡇⠀⣹⠆⠀⣸⣿⡟⠀⠀⠀⠀⠐⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠠⠀⠀⣿⣿⠃⠀⠀⠀⠀⠨⣿⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣐⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢲⣶⣾⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⢿⢿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⡑⠀⠀⠀⠀⠀⣀⣴⡾⠟⢻⣿⣿⣿⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡀⠀⠀⢰⡾⠋⠀⠀⠀⠘⢻⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣶⣄⠘⠇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣄⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠋⡀⠀⠀⠀⢀⢠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⢀⣤⣶⡿⡛⢛⣩⡄⠀⠀⣀⡀⠀⠀⣾⣿⡿⢟⠻
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣆⠀⠀⠻⠋⢩⣽⡟⣱⣿⣿⠇⠀⢠⣻⣿⣤⣾⣿⡿⠃
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⡽⢿⣿⣿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣿⣛⣫⠬⠉⠉⢛⠀⠙⠻⠛⠛⠋⠁⠙
⠀⠀⢸⣍⣁⣾⣿⣿⣿⣞⣣⣴⣾⡿⠋⠀⠐⢿⣿⣿⣿⣿⠟⠛⠁⠉⠀⠀⠒⠈⠝⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢸⣿⣿⡿⣫⣿⣿⣿⡿⠟⠋⠀⠀⠀⢰⣾⣿⠟⠉⠃⠀⠀⣀⡤⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉
⠀⠀⣸⣿⣿⣼⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⣠⣤⣶⠾⠋⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛
⠀⠀⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠟⠛⠋⠉⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡘⠻⡆⠀⠀⠀⢥⡀
⠀⠀⠻⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⢀⣀⠀⠉⠙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⣤⣶⣶⣿⣟⣶⡀⣰⣿⣿⣿⣶⣦⣤⡀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⢁⣤⣤⣤⡈⢿⣿⣯⣿⡿⣿⣧⣿⣿⣿⢿⣿⣯⣿⠇⣠⣤⣀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⣠⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣷⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢰⣿⣿⣮⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⢸⣯⣿⣿⣿⢣⣾⣿⡿⣿⣿⣿⣿⣧⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠈⠿⣿⣿⣿⣟⣿⣿⣿⣧⡹⣿⣿⣿⢸⣿⣿⣿⢣⣿⣾⢿⣿⣿⣿⣽⡿⢋⣀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⣶⣿⣿⣶⣤⣙⠻⢿⣿⣽⣿⣿⣷⡜⣿⣿⢸⣿⣿⣣⣿⣿⣿⡿⢟⣻⣭⣶⣿⣿⣿⡇⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣸⣿⣛⣿⣷⣿⡿⢿⣷⣮⣭⣟⣿⣿⣿⣎⠿⠟⠿⢳⣿⠿⣻⣵⣾⣿⣻⣿⣿⣿⣿⣿⣷⡀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠀⠀⠀⠈⢽⣿⣿⣿⣻⣿⣿⢿⣷⣿⣿⣿⣿⣷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢻⣿⣿⡿⢿⣿⣿⣷⣿⣿⡿⠾⢛⣩⣥⣶⢀⣀⢀⣀⢶⣿⣿⣯⣭⣟⣛⣿⣿⣿⣿⣿⣿⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠛⠿⠿⠿⠿⣛⣋⣭⣤⣶⣿⣿⣿⣿⢣⣿⣿⡿⣿⣷⡻⣿⣿⣿⢿⣯⣿⣿⣿⣯⣭⡉⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣯⣾⠃⣾⣿⣿⣿⢿⣿⣿⣮⡻⣿⣿⣿⣿⣿⢿⣿⣿⣿⠄⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⡾⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⠏⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠈⢿⣿⣿⣻⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⡿⠋⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣌⠻⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣾⣿⡾⣿⣿⣿⣿⣿⣿⣷⡈⠉⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠙⠛⠛⠁⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡿⣣⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠘⠿⣿⣿⣿⣾⣿⣿⣿⡿⠃⠈⠛⠛⠛⣉⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣦⣤⣌⣉⣉⣉⣉⣀⣀⣠⣤⣴⣶⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰⠶⠤⢀⣀⡀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠐
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⠀⡠⠶⠖⠀⠄⠀⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠻⡄⠘⠟⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠈⠇⠈⠉⢿⣿⣿⠃
⠀⠐⠚⠿⢛⠻⣤⣀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⠢⡀⠀⠀⠀⠀⠀⠈⠀⠀⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣾⡇⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⣿⡄⠘⣆⠀⠀⠀⢀⠄⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢛⣿⣏⠄⠘⡄⠀⠀⠈⢄⠀⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣤⣠⣴⣴⡶⠿⠟⠓⠤⠀⠀⡇⢠⣭⣿⡷⠂⠀⡇⠀⠀⠀⠀⠀⢈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠿⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠠⠬⣿⣟⣁⢀⠇⢀⠀⠀⢠⣆⣀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡯⢀⠎⠀⠈⠻⣶⡋⠀⠀⣽⣿⣿⠋⡨
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠈⠻⣶⣾⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠳⣍⠒⠌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⢍⡑⠲⣟⠋⠠⠠⠄⠆⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠳⣄⠑⠢⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠈⠉⠒⢄⡈⠳⢄⠙⢇⠒⠒⠃⠀⢂⠐⡦⢀⡀⢀⠠⢆⠙⢆⠈⠓⣤⠟
⠀⠀⠀⠀⢀⠞⣀⠄⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈⢁⣀⣀⣀⣙⣉⣀⣃⠀⣄⣈⣠⣄⠵⠚⠁
⠀⠀⠀⠀⡞⠈⡀⠔⢉⡤⠋⠀⠀⠀⠂⠄⠀⠀⠀⢀⠀⣠⡄⠭⠭⠐⠒⠒⠀⠠⠤⠄⡉⠃⠀⠀⢀⡔⠁⡰⠂⠖⢰⢀⠏⢠⠖⠂
⠀⠀⠀⠀⢸⡀⢀⡠⠊⠀⡴⠃⠀⠀⠀⠀⠀⢀⠀⢈⡆⠄⠒⣊⠉⠉⠉⠑⠒⠢⠤⣀⠀⠉⠆⠐⠎⠀⡸⠁⡜⠀⡆⢸⢀⡇
⠀⠀⠀⠀⠀⠙⢎⣀⠀⠊⢀⠔⠁⡰⠀⡶⠀⣋⡠⠚⠔⣈⠥⠖⠒⠒⠤⢤⡉⠒⠠⡀⠁⢠⠀⠀⠀⠲⠁⣠⠃⢰⠁⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⠴⠤⠴⠓⠊⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡐⠂⢤⠀⣄⠀⡀⠀⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⡰⠚⡡⠋⢉⡬⠛⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡆⠸⡀⠘⡄⠈⢆⠀⠈⠂⠀⠀⠀⠆⠐⠀⣉⠤⢚⠏⢀⠜⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠱⠀⡇⠀⢸⠀⠈⢆⠀⠠⠁⠀⠀⠀⠀⠈⢀⢴⠏⢀⠊⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠠⠀⠠⠀⠀⢂⡀⠀⠉⠀⠀⠀⠀⠰⠄⠀⡠⠊⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁






⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢀⡠⠴⢂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢆⠀⣴⡀⠁⠀⢠⡄⢀⠀⠉⢩⠀⠈⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⣉⠈⠀⠀⡇⠐⠤⠀⠀⠑⠉⠉⠁⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⣁⣉⠀⠀⠀⡀⣀⡠⠠⠖⠀⠀⠀⢀⠁⢀⠐⠉⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠑⠆⠀⡴⣀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠃⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣆⠀⠀⠛⠨⠁⠀⠀⠀⡘⠂⠄⠀⠀⠙⠶⢞⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⡠⣁⠶⠂⠀⠉⠀⠠⠂⠀⠀⢄⡠⣔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠀⢙⡗⠒⢲⠶⠚⠛⠛⡖⠒⠓⣿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠚⠃⢠⡞⠀⠀⣽⠀⠳⢀⣠⢙⠤⠔⠃⠑⠂⡴⢌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣀⢏⠀⠀⡠⠘⠃⠂⢡⠀⡖⠈⠉⠀⠤⠠⡄⠠⡀⠀⠀⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⠇⡀⠱⠞⠀⣤⢀⡠⠟⠠⠉⡀⠼⠀⡀⢀⢷⠀⢨⠉⠘⠣⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠟⠢⡀⡘⠀⠀⠀⠈⢠⠁⠸⣀⠀⠀⠀⢄⠀⢀⣄⠈⠠⠄⢠⡇⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⡏⠀⠀⠚⠁⠀⢀⠉⠂⢁⠀⠠⠉⠁⡈⠀⢀⠁⠀⢨⠀⢀⠀⠁⠈⡃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡞⠁⠀⠀⡐⠀⠀⠤⣀⢠⠊⠀⡧⠒⠋⠁⠀⠀⠒⠒⢻⠀⠈⠒⠂⢠⡇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⢰⠀⠠⠴⡎⠀⠀⢸⠀⢀⡌⠀⠀⠉⠂⢀⠄⠀⠀⠆⠀⠊⠀⠀⡀⠒⠁⢸⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡼⢆⠀⡰⠁⠀⡀⠀⠈⠉⠀⠀⠀⠀⠂⠉⠀⠀⠸⡀⢀⠾⠀⠀⢑⠦⠀⣼⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡞⠀⠄⠚⠁⠀⠀⠧⠀⠤⠛⠀⠀⠜⠒⠀⡠⠀⠀⢠⠀⠁⢀⠆⠀⢨⠀⠋⠀⡆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⢳⡀⠀⡠⠀⠀⠀⡄⠀⠀⡄⠀⢘⠀⠐⠊⠑⠀⠀⠘⠂⠒⠡⠀⠀⠀⠃⠒⢂⣯⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠉⠉⠛⠲⠦⣤⣄⣄⣀⣀⠀⠀⠀⢸⠢⠄⠀⢀⠂⠀⢀⡀⠀⢀⡀⢀⢀⣃⣠⠮⠜⠂⠀⠡⠀⠡⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⡇⠀⠀⠉⠹⠉⠛⠛⠛⠒⢓⠚⠛⠛⠛⠋⠉⠉⠉⡍⠀⠀⠀⡀⠀⢀⠀⠀⠀⠆⠀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⠀⠀⡇⠀⠀⢘⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢤⠀⣄⢠⣀⣀⣀⣀⣆⣄⠀⠀⠀⠀⣄⢀⣀⠀⠀⠀⠸⠀⠆⠀⠀⠀⢀⣄⣠⠦⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈⠀⠀⠈⠀⠁⠈⠛⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠏⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠯⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠋⠻⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣔⢀⠓⠈⣤⣀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣰⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣅⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⠦⡈⡀⣿⡗⢰⣼⡀⢰⣦⣶⣶⡀⢉⣡⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⢳⣿⣿⣿⠿⡇⠐⢻⢟⡛⠁⠹⣿⣁⡀
⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⡇⠐⠃⠘⣻⣿⣿⣿⣿⡟⢡⣽⠁⢀⡘⠀⠀⢀⢧⠀⠚⠂⠀⠰⡎⠃⢀⣤⣀⣀⣠⡄
⠀⡀⢀⢀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣳⠁⡐⠛⠀⠀⠀⢾⣿⣿⣿⣿⡏⢀⣸⣿⣄⡉⠄⢸⡆⡈⢰⡀⢿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⠈⢳⡀⠀⠀⠹⣿⣿⣿⠁⢸⣿⣿⣿⣿⣶⣿⣿⣵⣿⠀⠈⡄⢀⣀⣵⣞⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣀⠀⠀⠘⢷⣤⠀⠐⠿⢿⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠇⠸⢻⣿⡖⡘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⠀⠰⣏⢀⣤⣀⡘⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡆⢹⣿⡟⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠂⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢭⠃⠀⠀⠀⠀⢱⣐⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠽⠿⠿⠿⠛⠋⠉⠠⠞⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡞
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡄⠴⠞⠀⠀⠀⡰⠏⠀⠀⠀⠀⣦⠐⢯⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣥⣄⠀⠀⠀⠀⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡍⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠟⠟⢋⠉⠉⠀⠀⠀⠻⣄⠀⠉⠉⠉⠉⣏⣙⣇⠀⠂⠀⠀⠀⠀⠀⠀⢺⣯⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠠⠄⠀⠉⠻⣀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠈⠛⠛⠓⠢⠄⢀⡴⠟⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠤⠤⠀⠀⠒⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠤⠴⠖⠒⠒⠒⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣤⣶⣴⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣩⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⣀⣴⣶⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠿⢤⣄⣚⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣿⣿⣿⣿⡁⣦⣤⠉⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓
⠀⠀⠀⠀⠐⠤⣄⣀⠀⠀⢀⣴⠟⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣏⡁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠙⢿⣦⡀⠀⠀⠀⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⣹⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣀⣰⣿⡏⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢿⣧⣀⣴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠛⠛⢿⣯⠄⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⡀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⡀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⣾⣇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣿⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠸⣿⣿⠻⢿⣿⣷⠀⣤⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢠⡄⢠⣿⡿⠟⢻⣿⣿⠁
⠀⠀⠀⠀⠰⣦⣿⣿⠀⠀⠙⣿⣿⣿⣆⣰⣶⣿⣠⣸⣧⣶⣿⣶⣄⣼⣿⣿⠏⠀⠀⣸⣿⣧⡶
⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⢀⡀⣿⣿
⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠉⠁⢀⣤⠉⢿⣿⣿⣿⣿⣿⣿⠟⣭⡀⠀⠈⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢠⣤⣿⣿⠀⠀⠀⢸⣿⡇⠀⢻⣿⣿⣿⣿⠏⢰⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣤⠄
⠀⠀⠀⠀⠀⣀⣽⣿⣿⣧⡀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⠀⠸⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣶⣤⣟⣀⣀⣰⣿⣿⣿⣿⣀⣀⣛⣡⣤⣾⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠒⠚⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠚⠉⠉⢀⠴⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢤⡈⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣾⠿⢿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣶⣿⠃⠀⠀⠀⠀⠀⢤⣶⣶⣤⣿⣷⣿⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣷⣀⠀⠉⠉⠀⣠⣾⣿⣿⣿⣿⣿⣴⡶⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣽⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⠄⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⠀⠀⠉⠁⠉⠀⣸⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡿⡟⠙⠙⡿⣿⣿⣿⣿⣝⠻⠿⠿⠿⢿⣿⣿⣿⠿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⣠⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⡠⠞⢉⣤⣴⣶⣾⣿⣶⣬⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢀⡀
⠀⣼⣯⣾⣯⣹⡿⡿⣿⣿⣿⣿⣿⣝⡆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠟⠸⡣⠔⠀⠀⠀⠀⠤⠉⢷⡀
⠀⢸⣿⣿⣿⣾⣶⣿⣾⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⢴⡿⠷⠶⠀⠘⠀⠀⠀⠀⠀⣰⠀⡀⣴⣧
⠀⢸⣿⣿⣿⡿⢿⣿⣿⢫⢾⣿⣿⣿⡟⠀⠀⢀⡴⢩⡞⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣦⡀
⠀⠀⠹⣯⡻⢿⣿⣿⣿⣾⣿⡿⠟⠿⠃⠀⣴⠃⠈⣸⠧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠶⠖⠀⠉⠀⠉⢇⡀⠔
⠀⠀⠀⠈⠛⠖⢒⠛⣻⣭⠥⠐⠁⠀⢀⠚⢁⣷⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣅⣀⣴⠃⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⠿⠏⠛⠛⠋⠀⡉⠉⢩⣀⡀⠀⢀⡀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁⠀⠰⠂⠀⠒⠀⠙⠓⠀⠉⠉⠀⠠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⢶⣿⡇
⠠⣠⡄⢀⠀⠸⠟⠁⠀⠀⠀⠀⠀⢀⣠⣦⣾⠋⠀⠀⠀⠀⠀⠀⠙⢢⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠸⡿⣥
⠀⡵⣕⠘⠄⠀⠀⠀⠀⠀⠀⢀⠸⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⠃⣿⡆
⠀⠉⡄⠁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣿⡛⠿⣧⠀⠰⢻⢸
⠀⠢⣑⠀⠀⠀⠀⠀⠀⠀⡇⣠⠜⠂⠀⠀⣀⣀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣧⡀⠀⠀⡠⠋⢷⡀⠈⠇⠀⠨⠀⠄
⠀⠐⡄⠀⢀⡀⠀⠀⠁⠀⣷⠇⠠⠁⠀⠀⡏⡯⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠉⠀⠀⠀⠀⠈⠻⡄⢀⠀⠀⠣⣸⡄
⠀⠀⠉⣖⣒⡀⠁⠀⠀⠴⠁⠀⢀⠈⣄⠀⠐⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠙⠋⢁⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠠⠀⠠⢄⡈⣷⣤⣀⣀⣀⣿⡏
⠀⠀⠀⠒⢒⡿⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣿⡟⠛⠛⣿⣛⣋⡀⠂⡀
⠀⠀⠀⠀⠀⠃⠤⠄⠀⠶⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠿⠻⠛⠉⠃⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⡀⠀⠀⠘⢳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠓⠒⠒⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠂⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠞⠀⠶⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⢣⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠰⠀⠀⠇⠀⠠⠘⠒⠒⠂⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡔⠀⠀⢀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠀⢀⡄⢚⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⡀⠀⠀⠀⠀⣼⠊⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⡇⠈⡀⢉⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠐⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠦⠐⢀
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡁⠀⠁⠘⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⡀⠀⠆⡀⠆⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⢀⡀⠀⠀⠉⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡤⢀⣀⡀⣀⣈⡄⠰⠆⠀⠀⠓⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⢁⠈⠁⢃⠐⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠄⠠⠀⠘⠄⠘⡆⠀⠀⢀⡀⠀⠶⠀⠀⣑⡤⠀⠤⠄⡀⠀⠀⠀⢀⠠⠜⣶⣠⠀⠠⠆⠦⠠⡖⡠⠃⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡐⠀⠐⠀⠒⡀⡇⢀⠀⢀⡀⠀⢀⡤⠊⠀⡤⠀⠄⠀⡈⠑⢄⡰⡫⠊⢹⠛⠲⣎⠱⣞⢀⡊⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣀⠉⣄⢡⡽⢌⡁⣀⡠⠔⠉⡅⠚⡀⡠⠀⠆⢠⡄⠀⣼⠭⣀⠁⢀⡡⣄⠀⠓⣌⣏⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠄⠆⠺⡤⠧⠩⠄⠚⡀⠴⠈⡁⠠⠠⠄⣄⠀⠘⠉⡐⠊⢠⠌⠐⠮⠕⠢⣈⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠚⣇⣹⣆⣂⢙⡀⠴⠘⣃⠥⠔⠒⠰⢀⡈⠀⠄⢀⣀⢉⠜⢁⢂⣜⡵⠋⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⠱⣿⣶⠄⠲⠀⢃⢠⠴⠚⠓⠃⠦⢀⠚⠀⠖⡰⢊⢬⡥⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢯⣃⠩⡄⠆⢋⣽⣍⡚⠠⠂⣄⣉⠘⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠺⠼⠿⠾⠄⠡⠶⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠬⡗⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣾⡿⠾⠼⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⡀⠀⠀⠐⢆⡀⠁⣀⡐⣹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢯⡓⣿⡄⠀⠀⠀⠀⠈⠊⢥⣿⡏⡉⠀⠙⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⢾⣿⣷⣠⣏⢠⣀⡀⡀⠀⢀⣿⠿⣿⣷⠋⠙⢷⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡖⠘⠛⠋⢸⡟⢤⣹⠀⠻⠈⠀⠘⠛⢿⠀⠀⣿⡏⠋⠱⢿⡄⣿⡄⠀⠀⠀⠀⠀⢆⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠓⠀⠀⡀⢰⠖⠻⠿⠚⠏⢈⡈⣿⡤⠀⠀⡀⠀⠸⠁⠀⠀⢀⣭⣤⣬⣽⣿
⠀⢀⣀⣴⡶⢚⣁⠀⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠂⠒⠤⠠⡠⠐⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉
⢀⡩⠤⣞⠟⡉⠀⠄⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠠⢦⡀⠻⠁⢀⡀⢠⠔⠀⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⣠⣼⣿⢤⣤⣤⣴
⠨⡁⠀⡷⠰⡅⠀⡨⠄⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠄⡘⠢⡿⠃⠀⠀⠀⠀⠀⣀⡐⡀⢀⠀⠆⠀⠀⢸⡇
⠀⢳⣰⢵⡀⠨⠁⠺⣿⠄⠀⠀⠀⠀⠈⠃⠀⠤⡆⢠⠀⡾⠠⠴⠄⠑⢤⠎⠀⠀⠀⠀⡀⡴⢚⡾⢿⠗⠶⡌⠀⠀⠀⡾
⢀⣹⡋⠛⠓⠂⣀⣴⢻⣇⡀⠀⠀⣤⠈⠛⠠⠏⠻⠈⠋⠀⠣⠀⡴⠂⢸⡀⠀⠀⠀⠹⠇⣠⠟⠁⠁⠀⠀⣨⣵⠙⣺⡓⠦⢴⡷⣴⡦
⠠⣟⡷⢈⠓⠖⠛⠛⠷⠼⠃⠀⠉⠁⢠⣎⠐⠀⠸⣼⡄⠀⠀⠀⠀⠀⠀⠧⠤⠶⠤⠤⠬⠴⠾⠆⠀⠠⠞⢿⣿⠂⠙⠓⠒⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢩⠇⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠠⠂⠈⢼⠀⠠⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢄⡀⠀⣸⡰⠁⠀⠙⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠈⠑⢿⠣⣠⡹⢑⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡂⠂⠁⡿⢀⠤⣌⡡⢻⢦⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠒⡒⣒⠊⡉⠐⠒⢉⠢⡀⠀⠀⠀⠀⠀⡃⠄⢀⡠⠀⢾⢚⢰⠙⡡⣳⠁⠀⠀⠀⣸⠟⠢⢂⠄⢐⣒⠰⢒⠋⠁
⠀⠀⠀⠀⠀⣌⡷⡦⣄⠀⠈⢆⠈⠉⠧⡐⣌⠠⠇⠄⡎⠀⠀⣯⠚⡡⠆⡴⣩⣀⡔⣃⠂⡃⠘⢀⠜⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⠒⠀⠀⣀⠈⠉⢷⠀⢠⢬⣨⡦⡾⡟⠔⣡⠈⠉⠓⢷⢀⡇⣀⡂⠷⠀⠒⠒⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⣗⠦⠠⠀⠄⠠⠐⠉⠓⢢⣈⣇⠸⠃⡎⢼⠁⣟⠴⠁⡆⠀⠀⣸⠝⠁⣭⡄⠉⠀⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⠀⠐⢤⠀⠀⠔⢀⡀⠀⣻⡬⡽⠳⢄⠱⣘⣆⢳⠂⠀⠀⢠⢚⢧⡂⢀⠐⠂⢀⠖⡾⢢⡤⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣈⠁⡌⠀⠘⢷⢒⠆⠳⢤⣈⠟⠀⣠⡞⠉⠁⠈⢿⡸⠆⠯⠷⠞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣱⣞⡠⣤⠄⡿⠷⡖⠷⡲⢿⡶⠶⡍⠂⡤⠆⢀⣄⠻⢆⣀⣤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡡⠖⢺⡟⢸⠀⠆⠀⠈⢈⢠⢆⣡⠞⠀⠀⠈⠲⣀⣠⠊⣉⣀⢨⡟⢭⣱⡚⠵⠦⠄
⠀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠢⠬⠤⢌⣑⠚⠂⠀⣝⡠⠛⠁⠀⢀⠀⠀⠀⠈⢂⣩⠵⠎⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡛⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠦⠤⠾⠋⢹⡆⠀⠀⢀⣠⠶⢻⡟⠀⠈⠉⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠲⠦⣄⣹⡎⠙⠶⣤⣀⣤⣤⣴⠶⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠁⠀⣾⠁⠀⠀⣠⡟⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣀⣠⣿⠾⠛⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠉⠛⠛⠋⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⣷⠀⠀⠀⣾⣀⣤⠾⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣸⠷⠶⢿⡶⠚⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⢻⣄⠀⠀⠀⣠⡏⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠙⣶⡀⠀⠟⠀⠀⠀⢨⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣇⣠⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣤⣤⣿⠀⠀⠀⠀⠈⢷⣤⣀⣀⣀⣀⣠⣤⣤⠤⠶⠋⠀⠀⢸⡇⠀⠀⠉⠉⠉⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡟⠛⠋⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠄⣸⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠉⠐⢿⣤⡀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⣿⡀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠙⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠿⠆⠀⠰⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠔⠊⠉⠙⠓⢄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠻⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⡴⠋⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⢠⠗⢄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠈⠓⠶⠤⠶⠋⠀⢈⡇
⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⢀⡼⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠘⢧⡀⢀⡴⠋⠀⠀⠀⠀⠀⢱⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⡛⠀⠀⠀⠀⠀⢺⣄⡈⠻⠿⣟⠉⠈⢷⢦⣀⣀⡤⠚⢁⡴⡃⠢⣄⠀⠀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⢧⠀⠙⠻⢧⣛⡜⠦⣤⠏⢦⣭⢥⣖⡾⠿⠋⠀⠀⠈⠙⠒⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣬⠿⠶⣄⠀⠈⣙⢷⡀⡤⣶⣟⣉⣠⣴⣶⣦⣤⣀⣀⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⡷⡀⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡗⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢙⡌⠈⣢⡈⣛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠹⠤⠏⠉⢯⠟⠙⠪⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠤⠤⣄⡀⠀⢰⡃⠡⠀⠀⠀⠀⠐⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠐⠑⠁⠈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠚⡄⠀⠈⢀⠆⠀⠀⠀⠅⠂⠀⠦⡀⠀⠀⠠⠐⠀⠀⡀⠴⠳⣱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞⣁⠀⠈⠁⠀⣠⠆⠀⠀⠀⡀⠐⣒⠖⢲⢫⠀⠀⠀⢀⡱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠈⠃⠉⡀⠙⠐⠒⠒⠉⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠤⠤⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⢃⡀
⠀⠀⠀⠀⠀⠰⠂⠐⠎⠁⠀⠀⢸⣀⣠⢀⠅⠀⠀⠀⠀⠀⠉⠛⡛⠐⠒⠔⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠜⠀⠀⠀⡄⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⡇⢸⡀⠀⠀⠀⢂⠖⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀⢠⡦⠂⠀⠊
⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣛⣟⣜⢳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡞⠋⣩⠉⠙⢿⣧⣽⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⠻⣦⡀⠠⠀⠀⠈⠡⢘⡁⠄⠙⠻⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⡀⢀⡔⠒⠰⠂⠀⡠⢾⣿⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠟⠿⣿⣿⡋⠀⡀⢴⣼⠿⠛⠋⠉⠹⣿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡆⢈⠟⠈⠀⢀⠻⣤⠃⠀⢀⠀⣄⢘⠁⠆⡜⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⡺⠀⢸⠛⣄⠸⣏⢸⣎⢺⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠠⡄⢿⠑⢿⡕⠬⣿⣽⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠈⢀⡘⠳⡄⣻⣄⣻⣮⣽⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠴⡶⠹⣦⡀⠻⣿⣏⣺⣿⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣄⣠⣴⣷⣄⣿⢻⣶⣿⠙⣿⣻⢟⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡍⣿⡿⠿⣥⡾⠹⣷⣴⣿⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⣷⠟⠛⢾⣼⠷⣎⠻⢽⣿⣾⣼⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣼⢟⣄⣀⣾⢻⠛⠿⢿⣵⣶⣭⣻⣿⣟⠻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢹⡟⠛⠠⢄⠀⠉⠛⢿⣿⣷⣬⣵⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣶⣂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡼⠛⣿⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢢⣧⢸⣿⣇⣿⣏⣿⢻⣿⡗⠯⡂⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠡⢹⡿⠋⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠐⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀
⠀⠀⠈⢀⠠⡄⠴⠠⠀⠀⠀⢀⠤⣀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⡄⠉⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠈⠈⠀⡀⠀⣀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠄
⠀⠀⠀⠀⠀⠀⡶⠛⢯⠛⣢⠀⠀⠠⠁⠀⠀⠀⣀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠈⠀⠀⠀⠀⡐⢀⠀⠀⠄⠀⠀⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣇⣀⠀⠀⠠⣾⠇⠀⠈⠈⠉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠛⠉⠑⠀⠀⠈
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠴⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠁⣄⠀⠀⠁⠀⡆⠀⠀⠀⠀⠸⠀⢀⠀⠀⠦⠄⠀⠀⠀⠢⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⡀⠀⠈⠋
⠀⠀⠀⠀⡰⠉⠉⠀⠀⠀⠁⢄⣀⣤⠰⠊⠀⠄⠀⠸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⠉⠀⠛⣉⠄
⠀⠀⠀⠀⠀⠐⠄⠀⢖⡀⠀⠀⠀⠀⠀⠤⠈⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢸⠃⠀⠒⠀⠀⠠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢠⠀⠆⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⡀⠁⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⣇⡼⠀⠀⠀⢀⢄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠃⠀⠀⠀⠀⠀⢠⡄⠀⢀⡠⠤⠐⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠀⠀⠀⠆⠘⠈⠴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⡂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠄⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⡴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠠⢀⡀
⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢚⣄⠀⢨⡆⠘⠊⠀⠠⠁⠀⢀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡄⠀⠀⠀⠁⠵⡋⠀⠀⠀⠳⢄⠀⠀⠀⢀⡠⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣾⡯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣀⡁⠀⠀⠀⠂⠐⠀⠀⠂⡀⠀⠀⠀⠁⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀
⠀⠀⠀⠀⠀⠌⢄⠀⠀⠀⠀⢩⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠠⠀⠃⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠂⢀⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠈⠀⠑⠴⠃⢛⠆⠤⠌⡀⡀⡀
⠀⠀⢀⢄⣀⠀⠀⡀⢀⠤⠀⢤⠄⡄⠀⠀⠠⣤⡊⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠐⡐⡉⣆⣀⠀⠀⠀⠋⠀⠄⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢜⢀⠁⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠁
⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠐⠀⠀⠀⢀⡀⠆⠀⠠⠘⠃⢀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⢠⠀⠀⠠⠀⠉⠀⠰⠀⡄
⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠂⠠⠄⠐⠀⠀⠀⠈⠀⢰⠀⠠⠈⢀⠀⠁⠀⠀⠂⠐⠄⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠣⠀⠀⢀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣤⠀⢀⣤⢀⠀⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣦⣰⣿⣿⣿⣧⣾⣿⣿⣷⣧⣷⣾⣧⣆⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⠏⡿⣿⣿⢿⣿⣿⡿⠻⠟⠇⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⡀⠄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⢛⢉⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠙⢦⡀⠀⣙⠃⠉⠳⠆
⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠢⡀⠀⢙⡂⠉⠻⠦
⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢮⣄⠈⠛⠶⠄⠻⢶⡤⣮⡀
⠀⠀⠀⠘⣿⠟⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠈⠛⠦⠶⢦⡄⢶⣄⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⣤⣀⠴⣤⠰⣇⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡄⠀⠀⠐⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⢳⡄⠀⢹⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣿⢤⣾
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢳⡆⠀⠘⣿⠁
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣤⣤⣄⣀⡀⠀⢤⣤⣶⣶⣶⣶⣶⣶⣤⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠙⠻⢿⣿⣿⣷⣦⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠂⠀⠰⠀⠀⠈⠃⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠆⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⣆⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⡀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣴⣿⠂⠀⠀⠀⠀⠂⠀⢀⡈⠀⡉⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣫⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠉⠁⠀⠀⠀⢈⣙⣻⢶⣤⣀⠀⣀⡀⠀⡘⣹⠏⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⢈⣀⣀⣴⣄⣀⣄⣹⢾⣾⣿⣿⣿⣿⣷⣦⣀⣰⣿⣏⣀⣬⣴⣶⣶⡾⠿⠿⠿⠿⠷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⢠⣾⡟⠡⠀⠈⠉⠉⣉⣠⣤⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣦⡀
⠀⠀⠀⠀⣠⡿⠯⠀⠀⢀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⡄
⠀⠀⠀⣼⣿⠵⠀⣁⡤⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⠏⣿⣿⠟⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⣸⣿⣉⠐⠉⢁⣤⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⡿⢸⡿⣸⣿⠇⠠⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⢠⣿⡏⢀⣤⠶⢿⣽⣿⣿⣿⣿⣿⣿⡵⢸⡿⣹⣿⡿⡡⢁⣿⢣⣿⡟⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠃⠀⠀⢀⠀⢀⠀⠀⠀⠀⢹⣿⡀
⠀⣼⡟⠀⢫⣡⣴⣿⣯⣾⣿⣿⣿⡟⠻⢡⠏⢀⣾⡿⠁⢀⣾⠏⣾⣿⡇⡜⡰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⡀⠀⠒⠘⡄⢡⠀⠀⠀⠀⠀⣿⣧
⢀⣿⠇⠀⠈⣿⣿⡋⣻⣿⣿⡟⠈⠀⢠⠏⠀⠐⡿⠁⣠⣾⢏⣼⠟⣿⠑⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠄⠰⠀⠠⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢸⣿⣆⣀⣼⣿⡿⣸⠿⠋⡿⠀⠀⢠⠏⠀⠀⣀⣤⣾⠟⣡⣾⣏⡌⣍⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠠⣾⣾⠑⣦⡚⢰⠀⠀⠀⠀⢸⣿
⢸⣿⣿⣿⠏⡿⡵⠁⠀⠼⠁⣀⣠⣭⣴⣿⠿⣛⣭⣵⣾⣿⢿⡟⢸⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣷⣿⢳⡏⡗⠀⠀⠀⠀⠀⢸⣿
⠸⣿⡁⠉⠸⠁⠀⣀⣴⡶⠿⢛⣛⣭⣥⣶⣿⣿⣿⣿⡟⣋⡟⢸⡼⠀⣠⢀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⢹⣿⣾⣧⣧⠀⡀⠀⠀⠀⢸⣿
⠀⣿⣇⠒⣠⣴⣟⣯⣴⣿⣿⣿⣿⣿⣿⢟⣿⣿⣡⣿⢡⡆⡟⢸⣇⠈⢸⣸⠀⠀⠐⢆⡀⠈⡇⠀⠀⠄⠀⢀⣿⡇⢸⣿⣿⣧⣿⢿⢈⠳⠀⠀⢀⣼⡟
⠀⣿⣿⡿⢻⣿⡟⢿⣿⣿⣿⣿⢻⡟⣱⠿⢿⣿⣿⡟⢸⡇⣧⣸⣿⣆⣺⢃⡄⡆⠀⡤⠁⡆⠀⣴⠀⠀⠀⠸⣿⡇⣾⣿⣿⣿⣟⣾⡁⡾⠂⠀⣼⣿⠃
⢀⣿⠋⠀⢸⣿⡇⠀⢿⠀⢸⡟⠈⠟⢾⢸⡦⣿⣿⡇⢸⡇⣿⢿⣻⠙⢿⣼⡇⠀⡀⢀⠧⠃⠀⠇⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣸⣇⠀⣰⣿⡏
⠈⠁⠀⠀⠘⣿⡇⠃⠈⠀⠈⠁⠠⣀⠸⠈⣧⡏⡿⣇⡈⣷⣿⣿⣿⣷⣾⣿⣗⢰⡇⡘⢠⢦⢇⡇⠈⠂⠀⣸⣿⢹⣿⣿⣿⢋⣿⣿⣿⠿⣠⣿⡟
⠀⠀⠀⠀⠀⢿⣷⠀⠈⠀⠐⡀⠁⠿⣄⠘⣟⢿⣇⣼⠇⣽⣟⣿⣿⣏⠘⣿⣿⡼⢳⣠⡟⢡⣜⣶⠊⠀⢰⣿⣿⣿⣿⡿⣾⣿⡡⡿⢃⣴⣿⡟
⠀⠀⠀⠀⠀⠸⣿⣧⠀⡀⠄⢹⢀⠘⢢⡀⣜⢿⣯⣻⣗⠻⣿⣌⢯⡸⣿⣿⣿⣿⣠⣿⢧⣾⡿⣡⡇⠀⣾⢷⣿⡿⢣⣼⣿⣎⠄⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⢠⠘⢦⣙⢤⣽⣮⣷⣕⣛⠿⣷⣾⡿⣷⣄⠻⣿⣟⣸⣿⢻⣿⣿⣡⠋⠀⣰⠟⢀⣿⣽⣿⣿⠟⢁⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠈⠳⣍⡳⣟⡻⢿⣿⣿⣿⣷⣯⣙⡲⣭⣓⢬⣿⣿⡹⣾⣿⣯⣯⠂⣼⢟⣠⣿⣿⣟⡥⣠⣴⣿⠿⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣴⣾⡿⣿⣿⣾⣯⣽⣻⢿⡿⣿⣿⣿⣿⣿⣶⣿⣷⠘⣿⣿⢃⣾⣿⣾⣿⠿⣿⣵⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣝⡛⠿⢿⣿⡿⠿⢾⠿⢿⣿⣿⣿⣿⣿⣷⡟⣹⣿⣽⣿⣿⣵⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣷⣾⣿⣿⣿⣶⣦⣬⣉⣻⢿⣿⣿⣴⣯⣾⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠋⠛⠛⠻⢿⣷⣿⣿⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢄⠀⢊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣠⣶⣿⣿
⠀⠀⠀⠀⠄⠀⡀⠀⢠⠠⠈⢠⡷⠐⠱⠀⠀⡀⠀⠀⠀⠀⣠⣤⣤⣯⣾⣿⣿⣿⣿⣿⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠈⠢⣀⠑⢜⡡⠐⠊⡄⠂⠀⠒⠁⠐⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠁
⠀⠀⠀⠀⠡⡀⠈⢢⢎⢀⠀⠀⠘⠉⠀⣰⠄⠂⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣉⢂⡀⠀⠺⠁⢳⡷⠒⠲⠃⠠⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠡⡈⣡⡐⢄⣀⠈⠐⡘⢠⡔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠁⢰⣜⡁⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⣷⣯⣼⣝⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⡳⢻⠛⠟⡻⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⡀⣘⠀⣁⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠏⢉⠀⡈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠂⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢇⠳⣀⢦⡤⡎⠑⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣠⢋⡀⠀⠀⠈⠦⢎⣹⠒⠁⠀⠀⠀⣀⣨⣦⣤⣀
⠀⠀⠀⠀⠀⡇⠀⠈⠂⠀⠀⠀⣸⠙⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⣷⠀⠀⣿⣿⣿⠿⣋⣌⠻⡏⢹⣧⣀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀⢠⢋⠋⡾⣪⠞⡩⡇⠀⠈⢁⠛⣍⠉⠓⠒⢦
⠀⠀⠀⠀⢰⡧⠖⠒⢤⡇⠀⠀⢸⠀⢸⠀⢸⢸⠀⠀⠀⢜⡾⠃⣠⠃⡸⠀⠟⠤⣷⣯⣿⠗⢄
⠀⠀⠀⠀⠸⠤⠒⠒⠢⣵⢀⣀⣸⠀⢸⣤⡼⡍⠀⡴⠒⠉⠈⡏⣉⣦⠁⣤⡄⠀⠀⠈⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⠀⢸⠈⠀⠐⠺⣄⢸⠃⣷⡇⠀⡇⠀⠀⠀⠘⠏⢻⢶⠏⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⡇⠀⡀⠀⠀⠀⡜⠉⡆⠀⠠⠄⠀⠈⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⢳⠀⣱⡀⠀⢰⠇⠀⣧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱
⠀⠀⢀⣀⣰⡇⡃⢀⡁⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⢸⢠⠇⠙⡄⡼⠀⢀⣿⡄⠀⠀⠀⠀⠀⣴⠒⣛⡓⠺⡆
⠀⠀⠀⣈⣭⠋⢀⠈⡟⠛⠓⠒⠓⠒⠲⠶⣇⠀⠀⢸⢻⣀⣀⣸⢃⡤⠾⢌⣁⣀⣠⠤⠴⠒⠋⠉⠉⠉⢣⢹
⠀⠀⠰⠿⠓⠊⢩⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣯⠏⢠⠞⠁⢼⣿⡆⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡤⠾⠯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠒⠒⠋⠙⠂⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣠⢠⣾⢀⡄
⠀⠀⠀⠀⠀⢠⡦⠀⡀⠀⡜⠛⠀⠀⠀⢰⡇⢿⣇⡞⢀
⠀⠀⠀⠀⠀⠋⢤⠀⠛⣾⡟⠆⠀⠀⠀⢸⣃⣇⢸⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⡧⠀⠀⠀⠀⠘⡋⠉⠻⣣⣾⣀⡀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡇⠀⠀⠀⠀⠀⠁⠀⢠⠈⠹⠿⠃⠀⠀⠀⠀⡠⠊⠁⣀⠴⠂
⠀⠀⠀⡤⢀⡀⣿⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⢀⣼⠋
⠀⠀⠀⠀⣀⠙⡷⣴⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣤⡐⠀⠀⢠⣼⠉
⠀⠀⠀⢱⠋⣼⣿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠝⠛⠙⠀⠀⠈⠊⢅⣀⣀⣠⠤⠐⠀⠀⠂
⠀⠀⠀⠘⣰⡟⢻⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⡵⠂⠀⠀⠀⢤⣤⣤⣬⣿⣿⣧⣀⠀⠀⠀⠈
⠀⠀⠀⢰⡏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣏⣹⠛⢿⠷⠤⠄⠀⠀⢀⠠
⠀⠀⠀⢸⢷⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⡠⠐⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡇⠀⡜⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠢⣀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⡃⠀⡃⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⣽⠾⠧⠇⠀⠀⠀⠀⠀⠀⣶⣥⡒⠂⡐⢾⣶⢄⣀
⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠛⠛⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢸⠀⠀⠛⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠉⣴⣯⡆⠀⠀⠀⠀⠀⠰⣀⠿⣿⣦⡟⡂⢴⠈⠖
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠂⠋⠈⠁⠀⠄⠱⠈⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠤⡀⠈⠁⠀⠀⠀⣠⠱⢦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠁⠀⠀⠀⠀⠀⠸⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣷⣶⣿⣯⣽⣛⣛⣓⣖⣲⢤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⣤⠖⠈⠉⠉⠉⠉⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡞⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⠏⠀⠀⢸⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⢄⡀⠀⢀⣠⣀⣀⣀⠞⣱⠋⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⣤⠀⠀⣠⣾⡿⠟⠛⠛⢑⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡡⠂⢀⣤⢨⣬⠀⣸⣿⣫⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⢷⠁⠀⢾⣿⠸⣷⣾⡿⠛⠉⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⡏⡇⠀⠀⠀⠈⠻⢿⡛⠳⠀⢀⠀⠀⣿⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢧⡇⠀⠀⠀⠀⠀⠘⣿⣄⣤⠛⠁⣼⡏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡰⠷⠀⠀⠀⠀⠀⠰⠞⠿⠃⠀⢀⣿⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⣥⠞⠀⠀⠀⣿⡄⠀⠀⠈⠉⢉⣉⡙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠲⠾⠟⠃⠰⣻⠁⠀⠀⢀⣐⡻⣧⢀⡤⣲⠽⠋⠉⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⣥⣤⢀⡴⠀⢀⣀⣀⣀⣿⣤⣶⣿⠿⢿⠿⣿⠷⡟⣠⡄⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡀⠀⠀⢀⣹⣿⣿⣻⣿⡏⠉⠙⣿⠋⢹⠧⢂⣴⢿⣿⡴⣟⠼⣝⢦⡀⠀⠀⠀⢠⣆⢹⡄
⠀⠀⠀⠀⠀⢠⣲⢏⣴⡟⠀⠀⠀⠀⠙⡾⠟⠋⠽⠁⠀⠀⣿⠀⣞⣼⡿⢃⡾⠁⢱⣝⠀⠈⠙⠳⠀⠀⠀⡠⣿⢸⡇
⠀⠀⠀⠀⢀⣿⠃⢸⡿⠀⠀⠀⠀⠀⠀⠤⣤⠤⡞⠀⠈⠀⢹⡀⣿⣿⠀⣸⠁⠀⠈⡟⡄⠀⠀⠀⠀⠀⢀⣷⣯⣾⠇
⠀⠀⠀⠀⢸⡏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⠀⠀⣿⢸⡇⢻⣿⡘⠁⠀⠀⠀⢳⡇⠀⠀⠀⠀⢈⣾⡿⣹⡟
⠀⠀⠀⠀⢸⣷⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣧⠀⠛⠃⠀⠀⠀⠀⠀⠃⠀⣠⣶⢫⣾⢏⣴⡟
⠀⠀⠀⠀⠈⣿⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡆⠛⠉⠀⠀⠀⠈⠂⠠⠤⣴⡶⣿⣿⠷⣫⣴⡿⠏
⠀⠀⠀⠀⠀⠘⣽⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⣻⠷⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢻⣎⠀⠀⠀⠀⠀⠀⣤⠾⢛⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤

⠀⠀⠀⠀⠀⣀⡴⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣦⣤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠋⠉⠈⠀⢀⠀⠀⠉⠉⠁⠉⠉⠁⠀⠀⠀⠉⠀⠈⠉⡁
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣀⣤⣤⣭⣽⣷⣿⣿⡄⠀⣰⣧⣶⣖⣛⣁⣀⡄⠀⢤
⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠤⣉⣻⣿⣿⣟⣹⣿⣿⠀⣿⣟⢻⣿⣿⣟⣉⠔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣈⣉⠙⠛⢉⠉⢹⠟⠀⠘⢯⠙⡛⠋⣉⣁⣤⣴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⣿⣶⣿⡀⠀⠀⣾⣤⡀⣀⣿⣾⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠋⣨⣿⣿⣯⣉⣉⣿⣿⣧⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡛⠻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⡿⢻⣿⣿⣿⣷⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠠⠤⢰⣯⡟⣻⠟⢉⠿⠁⠈⢹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣼⠃⣠⠎⠀⠀⠀⠘⠃⣧⢸⣿⣿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠀⠀⠀⠀⠠⢶⠺⢿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠻⣌⢯⣿⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣾⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢿⣿⠇⠀⠀⡀⠀⠀⠀⠀⠀⣤⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣯⠟⠈⠀⠀⠀⠰⡄⠀⠀⠀⠠⢾⣿⠀⢀⣾⠀⠀⠀⣤⠀⢀⣿⣿⠃⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣲⡿⢷⣷⠐⢦⣾⡟⠀⣼⡏⠈⠀⢸⡏⠀⢸⣿⠃⠀⠀⣠⣏⣠
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣰⡟⠀⠀⢻⡟⣿⣿⡇⢰⣿⡝⠀⣠⣿⠁⢠⣿⣿⣆⣰⣾⢟⠽⣿⠤⠤
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠘⣷⣆⠀⢺⣿⣿⣿⠇⣼⣿⠁⢤⢹⡏⢠⣿⣿⣿⣏⣿⡏⠉⢺⣷
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⣸⣿⣿⠀⣸⣿⣿⣿⢀⣿⡇⢰⣼⡿⢡⣾⣿⣿⣻⣿⣿⠄⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⠀⠀⠀⠒⠘⣿⣼⣿⣿⣿⣿⢸⣿⠀⣾⣿⢃⣾⣿⡟⣯⣻⣎⣿⠀⢹⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣆⡀⠀⢀⠘⢻⣿⣿⣿⣿⡇⣿⡇⢰⣿⡏⣼⣿⣧⢳⡈⢡⢹⣿⣤⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣤⣷⢺⣿⣿⣿⣿⢃⣿⡇⣸⡿⣸⣿⢿⠹⣆⣿⠃⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣿⣿⣿⣿⢸⣿⣷⣿⢱⡿⣿⢸⢀⡿⢹⣦⢾⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⣿⣿⣿⠃⢸⣿⣿⠃⣾⣯⣿⢰⣏⣿⣼⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⣦⣬⣿⣉⠀⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠼⠷⢶⣶⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣴⣼⡿⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠔⠁⡀⠙⢢⠀⠀⠀⠀⠀⢠⠃⣀⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇
⠀⠀⢨⠀⠠⠋⠓⠀⢣⠤⡄⢠⠒⣼⠘⠋⣤⡀⠀⢹⠀⠀⢀⡀⠤⢤⠐⠒⠒⣦⠀⠠⢠⣀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⡠⠀⠀⠀⠈
⠀⠀⢈⠀⢀⡾⠓⠀⢸⠀⣿⢨⠄⡟⠀⠠⣋⡉⠀⣼⠀⠀⡌⠀⡄⠀⠈⣦⠀⠀⠁⢄⠀⠀⡤⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⡀⠀⣰⢦⡀⢸⠀⡇⠀⠇⡇⠀⠴⣫⡓⠀⣿⠀⠀⢰⠀⠈⢢⠂⠀⠑⡄⠁⠀⢣⠊⠈⢴⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⡡⠶⠄⢸⡞⠀⠀⠈⣇⢀⣘⠥⢥⣀⣹⠀⠀⠀⠐⡄⠈⠑⣤⠊⠈⢢⡄⠈⠁⡠⡎⠀⠀⠰⠶⠦⠤⢤⣄⣀⡀⠀⠀⠀⠆
⠀⠀⢰⡗⢚⠃⠉⠉⠙⡇⠀⠀⠀⠸⡅⣠⢠⢠⡆⣸⠀⠀⠀⠃⠈⣦⠂⠀⢡⡀⠀⠈⢂⠈⠑⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠼⠤⡄
⠀⠀⠀⢿⣾⣼⣾⣇⣧⠇⠀⠀⠀⠀⠣⠽⠧⠼⠾⠟⠀⢀⣤⣧⡀⠀⠑⡤⠀⠉⢢⠄⠈⢣⣠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣩⣀⣸⢧⣀⣀⣀⣀⣀⣀⠀⢠⣾⠉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⠀⠀⢀⠀⠀⠀⠀⢽⠒⢻⡵⠊⠁⠀⠀⠉⠉⠉⠉⠛⣌⡿⠽⡇⠀⠀⠀⣴⣂⡤⢄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⣜⣛⣉⣉⣉⣉⣛⣛⣒⣒⣒⡒⠒⠾⠷⠴⡇⠀⠀⣸⠇⣏⠑⡞⠉⣴⡂⢀⡀
⠀⠀⠀⢀⠐⠷⠶⠶⢤⣤⣤⣤⣤⣀⣤⠞⢀⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⡏⠀⠀⣿⢠⢎⣩⠓⢠⠧⣸⠁⠲⢇⡴⢠⡄
⠀⠀⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠈⢆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠟⠲⠤⣍⠸⠁⠶⢥⣝⣉⠖⢀⡟
⠀⠀⢆⡀⠛⠛⠛⠛⠓⠒⠶⠤⠤⠄⠠⣶⣦⡄⠼⡄⠀⢻⢻⡟⠉⠁⠀⠀⠀⠀⠒⠒⠒⠶⢲⠋⠀⢰⡏⠘⠢⣤⣀⠛⢱⠆⣼⠈⡏⢘⡏
⠀⠀⠀⠈⠁⠒⠈⠉⠁⠀⠀⠀⠀⠀⠠⠤⠤⠀⠠⠔⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢀⡴⠋⣤⠋⠰⢠⡍⢉⠓⠲⠤⣤⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣟⡶⠒⠂⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢤⣈⠑⠂⠠⠊⡨⠓⠦⢦⢨⠏
⠀⠀⠀⠀⡠⣶⣶⠯⠷⣻⣿⡿⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⢔⢢⠆⠐⠒⠬⡈⠓⠒⠤⠧⣏⡐⠀⡌
⠀⠀⠠⠊⠙⢯⣿⣾⣻⣯⠟⠁⠀⠤⢀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠌⡀⠴⠋⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠙⠛
⠀⠐⠀⠀⠀⣀⠀⠉⠁⡠⢀⡾⡻⣷⣦⣄⣀⠀⠙⠺⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠠⠀⠀⣶⡟⣽⣷⡀⠈⠀⠈⠳⣕⣦⡟⠁⠈⠁⠉⠉⠁⠊⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠱⡀⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⣀⠀⠀⡰⠃⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢄
⠀⠀⠑⣯⠉⠁⠀⠀⢧⠀⢦⡀⠀⠀⠀⠈⣉⠽⠪⣍⣀⠴⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢌⠀⠀⠈⠻⠀⠀⠀⠈⢂
⠀⠀⠀⠙⠀⠀⠀⠀⠈⢧⠀⣈⠥⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠂⠀⠀⠀⠀⠐⢤⠔⠁⠠⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠄⠀⠀⣀⡀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠈⢆⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠶⠤⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠉⠙⠶⣄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⡤⠴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⡠⠤⠔⠁⠀⠀⠀⠀⣀⣀⣀⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⢀⣀⠛⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⢷⡈⠉⠙⢄⣀⡀⠀⣀⣀⣠⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣼⠃⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⢀⣠⣬⣙⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠙⣷⣤⡀⠀⠀⠀⠀⠀⣸⠃⠙⠲⠶⠛⠉⣷⣀⣀⣤⠖⢫⡏⠀⠀⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠲⢾⣄⠙⠓⠒⠒⠛⠛⣿⣠⡄⠀⠀⠀⠀⣿⡏⠁⠀⠀⣾⠀⠀⣠⠏⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠓⠶⠶⠖⠒⠛⣿⠁⠀⠀⠀⠀⢰⡇⣷⠀⠀⢰⠇⣀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣾⠶⢾⡶⠶⣾⠋⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⣼⠃⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⠀⠙⠆⠀⠃⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⡤⠟⠀⠙⡟⠙⠛⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡶⠛⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⢹⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣼⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠸⢷⡄⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⠀⠰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠑⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡉⠀⣸⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠑⠕⠙⣬⣇⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢛⣷⣄⠀⠘⣞⡟⠀⡴⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣇⣄⣑⣒⣒⣒⣒⣒⣶⣥⣬⡵⠢⣾⣯⣽⣆⡇⠀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠅⠘⠒⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠌⠚⠥⠤⠤⠤⠑⠚⠤⠵⡄
⠀⠀⠀⠀⠀⠀⠀⢧⠀⡠⠠⠤⠠⠄⠀⠠⠤⠄⠤⠤⠤⠀⡀⠠⠠⠤⠤⠤⠤⠤⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⢀⣀⡁⠀⡀⠀⢀⠀⡀⣀⠀⠀⣀⠀⠀⣀⢀⠀⢀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠢⢸⢒⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇⠀⠀⠰⠒⢢⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠉⠀⠀⠀⠀⠀⢣⢱⠀⠀⠀⣧⡀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠀⠀⠀⠀⢀⡴⠃⣜⡔⠲⠀⡗⠷⠂⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠀⠤⠀⡔⠁⠀⠀⠻⠀⠰⡀⡇⠈⠁⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⢸⠀⠚⠀⢇⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠤⠜⢸⠀⠀⣠⣊⣑⣖⣉⣑⣖⣉⣢⡇⠀⢀⠐⠄⠚⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⠉⠉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣰⣾⡷
⠀⠀⠀⠀⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣴⣶⠖⠉⠉
⠀⠀⠀⠀⠜⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⣦⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢈⢆⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡆⠀⠠⡀
⠀⠀⠀⠀⠈⠓⡁⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⢺⡇⠀⠀⠀⠀⠈⢿⠋⠹⠿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡄⠀⡀⢀⣴⣾⡷⢷⣶⡟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠐⠀⠸⢡⠋⠣⢸⣿⣿⣿⣿⣷⣾⣷⣂⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣴⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣾⡇⠻⢿⢿⣿⣿⣿⣿⡿⠇⢀⣦⢠⡆⢀⡀⣿⡇⣿⣿⣿⣿⡿⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠛⠛⠉⠀⠀⠐⠃⠉⠞⠁⠩⠙⠹⠀⠋⠀⠻⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣸⣤⡾⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢀⣴⣏⡾⠁⠀⡀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⠶⠛⠉⠘⠷⣤⣤⡤⠖⠋⣡⣏⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣤⡀⠙⢦⣄⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢾⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠛⠻⣾⣧⣀⣀⣀⣠⣶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣿⠀⠀⠀⠙⣦⡉⠉⢩⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿⡀⠀⠀⠀⣼⣇⣰⡟⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⣿⣏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⣧⣤⠤⠤⠴⠶⢶⣶⡶⠶⠶⢼⡇
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣧⡾⠉⢿⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⡿⠁⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡟⠀⠀⠀⠻⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣾⣿⠟⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠁⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣄⣠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣩⠟⢿⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⢟⣡⡾⠟⠁⠀⠀⠹⣷⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣾⣯⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠙⣷⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠻⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⡄⠉⠀⠀⠀⠀⠀⣠⣤⣬⣿⡀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓



⠀⠀⣀⡀⠀⠀⢀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡇⡤⠤⠀⠀⠀⠒⠒⠂⠀⠠⠄⣀⡀
⠘⢄⡒⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠀⠤⠄⢀⣀⠀⠀⠀⠠⡀
⠀⠈⠙⢇⠤⣀⡠⠇⠈⠉⠁⠹⠁⠀⠀⠀⡙⠉⠁⠙⠒⠒⠂⢠⠭⠅⢒⣤⣄⠀⠀⠠⠄⠀⠀⠈⠻⢓⣈⡦⣶⠒⠀⠀⠣
⠀⠀⠀⠀⠈⠐⠩⠍⣒⡒⠠⠬⠄⠤⠤⠀⢣⣀⣀⣠⣄⠀⡀⣠⣀⣀⡤⢽⣽⠛⠋⠈⠀⠀⠀⡠⠒⢣⠀⡰⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠐⠒⠐⠒⠀⠀⠀⠐⠂⠂⠀⠉⠁⡠⠀⠀⠀⢀⡄⠉⠙⡆⡾⡪⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠳⠤⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⢢⠠⡴⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⣀⢀⣡⡲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⡀⠀⢀⡧⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠠⢔⠒⠉⠻⡀⠀⢀⣋⢝⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⡀⠀⠈⠄⠀⣀⡉⢔⡫⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠚⠓⠀⠁


⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠉⠉⠉⠀⠀⠀⠐⠒⠒⠂⠀⠢⠤⠄⠀⠀⠠⠤⠤⠤⢆⠀⠀⢀⡀⠀⠀⠀⡰⠄
⠀⠀⠠⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠺⡷⠛⠋⠉
⠀⠀⠀⠀⠉⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠄⠀⠀⠤⠤⠤⠤⠤⠀⠐⠒⠈⡿⠔⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⠀⠀⠀⠀⡤⢀⣀⡀
⠀⠈⣈⣤⣤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣨⡝⢆⢀⡀⠀⠀⢠⡆⠀⠀⢈⣄⡀
⠀⠀⠉⠀⠰⠷⠄⠀⠀⠀⠈⠙⡏⢀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡈⠩⢓⡏⡈⠀⠀⠀⢠⡀⠀⠕
⠀⠀⠀⢈⣵⡆⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠀⠀⠀⠀⠡⠀⡀⠀⠈⠐⢩⢠⣶⠀⠉⠁⠀⠀⠀⠘⠃⠂⠒
⠀⠀⢈⡧⠄⣠⡔⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⡎⡔⠀⠀⣁⣤⠄⢅⠉⠁⠀⠀⠀⠀⠰⢢⠀⡀⠙⠷
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⡀⠀⡿⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠈⣽⣶⠃⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨
⠀⠀⢀⠱⢟⣛⠀⠀⠀⠀⠈⣱⡀⠀⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⢈⣻⡩⢊⠁⠄⠀⠀⠀⠠⡀⠠⠒
⠀⠀⠈⣇⠀⠉⡤⠀⢀⣶⣿⡿⠅⠀⠀⠉⠉⢀⠀⠰⠀⠆⡂⠀⠀⡰⠀⠾⢿⡿⠀⠀⠀⠀⠀⠉⠂⠀⢀⠈
⠀⠀⠀⢹⣶⡟⠁⠀⠘⢛⣿⣿⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳⠀⠀⠀⢰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣌⡤⢀
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⡄⠀⠀⠀⠀⠀⢱⡁⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠱⣦⣄⡀⠀⢠⣄⣿⣿⣏⣠⠄⠀⢀⣠⣶⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣴⡄⢻⣿⣿⣿⠏⣦⣰⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣽⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠻⠛⠉⠈⠙⠟⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠟⠋

⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠠⠀⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿
⠀⣿⣿⣿⡿⠻⠟⠛⠃⡚⣻⣿⣿⣧⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣽⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉
⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠋⠉⠉⠉⠉⠉
⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⡀⣀⣀⡤⠤⠤⠤⠤⠤⠴⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠹⡀⠀⠀⠀⠀⠀⠀⣔⠙⡀⠀⡘⡅⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⢀⡤⠟⠒⠈⠉⠁⠒⠲⡄⠂⠐⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⢍⠑⠂⠤⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠀⠄⡀⢀⠙⢄⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡰⠁⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠈⢣⠀⠀⠀⠠⠈⠳⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⣱⡄⠀⠈⢄⣁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠒⠒⢄⠀⠸⠛⠒⠀⣠⡾⠃⠈⡗⠓⠊⠁⠸⠦⡄⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠣⡀⢀⠜⠀⠀⠀⣠⡾⠋⠀⠀⢰⠀⠀⠀⠀⠀⣀⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠁⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⣠⠗⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠊⠉⠀⠀⠀⠀⣀⡤⠖⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣠⡴⠚⣩⡿⣿⠉⠣⠤⣀⣀⣀⣀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⢸⣇⣤⠞⡿⠁⣿⡇⠀⠦⠄⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⣀⡠⠔⠚⣇
⠀⠀⠀⠀⠀⠀⠉⠀⢸⡇⣰⢿⡇⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠉⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⢸⡷⠀⠉⠁⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠇⢣⡀⠀⠙⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⣄⠠⣠⠀⠈⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠙⠣⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠰⠖⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣖⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⡶⠖⠀⢠⡤⠀⠐⠖⡖⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠱⡄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡌⠀⠑⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⠀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡈⠧⡏⢇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠢⠤⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠺⣀⠘⠍⣡⠀⣆⣤⠃⠈⢈⠙⡌⣟⠉⠉⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠐⣈⠙⡊⢩⠒⠲⣌⡄⢨⡷⡐⠀⠹⡶⠒⠥⠠⠁⠀⣆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠡⡎⠉⡾⢋⣫⠂⠐⢼⡊⠀⢀⣱⣼⡚⠑⢲⢁⣀⣹⠤⠼⠀⢆⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠀⢀⠈⡡⢼⠁⠘⢳⠦⢤⣡⣚⠍⠙⡀⢑⣓⡶⣫⠛⢷⡠⠤⠢⠠⡔⠀⡂
⠀⠀⠀⠀⠀⠀⠀⢘⡤⢈⡌⣹⢧⡧⠈⠑⡘⢣⠀⠈⠃⡈⠐⢊⡗⠁⠋⣧⡨⢦⣀⢟⠀⠈⡀⠠⡀⠃⡀
⠀⠀⠀⠀⠀⠀⠨⡀⢢⠙⢁⣽⡔⠉⢫⠖⠉⢲⡖⠓⠮⠻⣽⠝⠓⡔⠚⠛⡄⠘⠅⠉⠳⢄⡤⢃⠊⡀⢾
⠀⠀⠀⠀⠀⠀⠀⠘⠊⠋⠸⠉⠒⠺⣿⡃⠆⢶⣄⡤⢇⣀⢾⡗⠀⣙⢾⡗⠉⢹⡎⠉⡇⠈⠉⢻⠾⢅⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠸⠀⢠⠈⠂⢈⡋⡐⢐⣩⠖⠀⢹⠃⢙⠃⠀⢨⠀⢐⡇⠀⠀⣺⢈⣜
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡀⠃⠀⠀⢸⠀⡆⢸⠐⣶⠋⢘⠀⠀⢸⢅⢵⠀⠀⢸⢀⠵⠀⠀⠀⡷⠊⠼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠈⠐⠀⠀⡄⠃⢨⠀⣗⠄⢵⠀⠀⢘⠁⡼⠀⠀⢒⠀⡺⠀⠀⠀⠇⢅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢅⠀⡀⡇⠀⡇⠀⠠⠀⣕⠅⢽⠀⠀⢸⠂⣭⠀⠀⡍⠀⡛⠀⠀⢸⡃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⡀⢁⠀⡅⠸⠀⠀⡗⠀⡹⠀⠀⠽⡨⣪⠀⠀⡧⡪⡃⠀⠀⠨⠨⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠇⠁⢸⠀⠇⠚⠀⠀⡯⡂⣺⠀⠀⡪⠂⡆⠀⠀⡫⣪⡇⠀⠀⣎⡬⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢵⢘⡸⠀⢨⠀⠀⡁⣿⠂⢼⠀⠀⣖⠐⠅⠀⢨⢗⡏⠁⠀⣈⣉⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⡯⡇⢸⣺⠀⡅⣗⢐⢽⠀⡀⢟⠁⡅⠀⢸⢐⢷⠀⠄⢠⠆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡆⣯⡃⢨⣿⠀⡇⣵⠐⡽⠀⠇⡭⠊⡇⡨⢸⠔⢹⠀⡄⢸⠀⢱⡂⠀⣰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢸⢦⢸⡺⠀⠅⡯⡪⣾⢀⠀⡯⡪⡇⡀⣸⠁⡿⠀⠀⣷⠀⣽⢓⣁⣈⣁⣈⡉⠃⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠸⣿⡈⣬⡀⡅⣿⠀⣿⠐⠁⡏⢨⠁⠀⣿⠀⡇⠠⠀⡏⣞⣟⣀⣀⣀⣀⣀⣀⣀⣀⣐⣂⣂⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⡞⣇⢹⡅⣷⠰⡃⡇⢘⡀⣂⡯⢮⠦⠐⢒⣛⣋⡋⢀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠵⢷⢴⣖⣛⣓⣫⣉⣀⣀⣀⠀⠤⠯⠃⢀⡀⠄⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠢⡄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡀⣀⡀⠀⠀⡠⠒⠂⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⠎⡄⠩⣑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡠⠋⠀⠀⠀⠈⢠⠔⠢⠤⣈⠀⠀⢀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⠘⢰⠁⠀⠀⠀⠀⠀⠰⠀⠀⡠⠂⡠⠊⠀⠀⢠⠀⠀⠑⠆⠀⠀⠀⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⣠⠔⠒⠒⠚⢦⠀⠀⠀⠀⠀⠀⢀⣼⢀⡜⠀⠀⠀⠀⡇⣠⠀⠀⠸⠇⠀⠘⣱⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠖⡠⠚⠁⢀⣀⣠⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⢀⠜⠁⠀⠈⠀⠀⠀⣀⠀⣶⠁⠀⠀⣸⠋⠀⠀⢣
⠀⠀⠀⠀⢀⠖⢁⠔⠉⠀⠀⡜⡩⠋⠀⢄⣀⣠⠤⠤⠐⠁⢀⡓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢠⡏⠀⠀⠀⣿⢈⡀⢨⠀⠘
⠀⠀⠀⠀⡆⠀⣼⣦⡤⠚⡁⠐⠁⠀⠀⠀⠀⠀⣀⣠⣗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠧⠄⠀⡾⠁⡀⣠⢲⡿⠈⠄⠀⠂
⠈⠀⡄⠀⠐⠀⠻⠽⠐⠠⠄⠀⠀⢁⣈⣩⣽⣛⡋⠍⠁⠀⠀⣓⣂⠀⠀⠀⠒⠈⠈⠉⢡⠀⠀⠀⠀⠀⣰⠃⡼⢋⡵⠏
⠀⠀⠄⠀⣀⣀⡀⠀⠀⣀⡀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢂⡀⠀⣠⠔⠰⠤⢼⡤⠤⠲⢖⣪⣥⣾⣿⣋⣀⣀⣀⣀
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠫⠊⠀⠀⣀⣠⡀⡼⠀⠀⠀⢐⠀⠀⠘⠋⠉⠉⠉⠙⠛⠿⣟⡲⢤⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠤⠴⠛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣀⠠⢄⡽⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢹⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣌⣉⣉⣉⣀⣡⣴⣾⣿⣿⣿⣿⡿⠋⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⡀⠀⢉⣿⣿⠋⠉⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁