Pigeon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠉⠙⠋⢻⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢻⠟⠻⣿⣼⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠸⡿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⠀⢀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡯⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣋⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣻⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣇⡐⠀⣴⠚⠂⢀⠁⠀⠀⡄⠄⢀⢀⣠⣼⡿⠁⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠀⡠⢽⣧⣌⠁⠀⠸⠀⠆⠀⡤⡠⢚⣥⡿⢛⣇⣴⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠟⠑⠃⠀⠀⠛⠩⠍⢀⡠⣀⣤⣤⣾⡿⠿⠛⠋⣸⣿⠟⠁
⠀⠀⠀⠀⠀⣠⢴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣗⣦⠀⢼⠟⠁
⠀⠀⠀⢀⣶⣃⣭⣯⣤⣤⡤⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣆⣠
⠀⣠⣴⣾⣿⠽⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡍
⠈⠈⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠊⠿⠭⢩⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠉⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⠀⠀⣠⡶⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣭⣰⡩⢁⣴⠠⣶⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠻⣿⣿⣿⡛⠻⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣻⠟⠟⠀⠀⢺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠄⠀⠀⠀⢛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣽⡁⠒⢀⠄⠀⠀⢈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡁⡘⠋⢄⣠⡠⠀⢀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠏⠚⠙⠀⠚⠀⠀⠀⠂⠈⠀⠄⠄⠓⢄⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡿⠋⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢠⡼⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡟⠔⠋⠰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡇⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣟⡃⠺⠤⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⡔⢳⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡾⠿⠿⠖⠷⠖⠀⠐⢮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢎⡄⠉⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⢿⠟⠛⠉⠀⢦⡰⠛⠛⠋⠙⠻⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢢⡴⠋⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡮⠙⠁⠈⠛⢻⣯⣭⣶⣄⠀⠀⠷⠶⠆⠂⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⠔⠁⠀⠀⠀⢠⠋
⠀⠀⠀⠀⢀⣠⡴⣒⣿⢿⣿⠟⠛⠓⠂⠂⠀⠀⠀⠈⠙⢮⣭⣤⡄⠀⠀⠲⠖⠒⠂⠠⣀⣙⠛⢀⢀⡀⠀⣀⡴⠟⠁⠀⠀⣀⡴⠚⠁
⠀⠀⣠⠾⢿⣿⢿⠿⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠄⣀⣀⣀⢠⣶⣾⣶⡷⠞⠛⠛⠛⠉⠁⠀⣀⡴⠖⠋⠁
⠀⠀⠘⠛⠟⣿⣿⣿⢉⡉⣉⢀⣠⡤⢒⠢⠤⠴⠶⠶⠶⠒⠒⠻⠿⢿⣿⣿⣿⡟⢿⣩⢀⠀⠀⠀⠀⠀⣀⡔
⠀⢀⣠⣴⣟⣻⣷⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠂⠴⣆⠁⠀⠀⠘⠁
⠺⠿⠛⢿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠒⠶⠶⠶⠤⣤⣀⡀⣀⣈⢳⣄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⢀⡤⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣰⠁⠀⠀⠀⠀⠀⢀⡴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⡰⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⡴⠕⠒⡄⢀⡤⠞⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠤⠂⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠤⠤⠄⡄⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢀⡴⠛⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰⢀⡠⠤⠒⠉⠀⠀⠒⠀⠀⢀⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠁⠆⡴⢁⡀⠀⡀⠀⠀⠢⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡾⡠⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⢌⡁
⠀⠀⠀⠀⠀⠀⠣⣸⢩⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢿⠋⡰⠋⡀⠀⠀⠉⠂⢄⠀⠀⠀⠀⡘⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⢸⣜⣁⠈⠀⠀⠀⠀⠀⠀⠑⠢⠀⣀⣁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠂⠀⠀⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⢀⣈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠢⠤⡀⠀⠀⠀⠀⠀⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⡀⠈⢁⠒⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡄⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢤⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⠁⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⠉⠉⠐⢄⠀⠀⢀⠀⣈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠠⢁⢨⣭⠬⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡽⠞⠉⠠⠇⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣁⣑⣓⣀⡀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣰⣶⣿⠿⢚⠋⠉⠁⠈⠉⠙⠲⡄⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣪⣶⣿⡿⢫⠐⠤⠪⡄⠀⠒⠄⠀⠀⠀⢹⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⣟⣩⠗⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢻⣿⣷⣤⠈⣀⠈⠉⠙⠛⠱⠲⠚⠶⠚⣂⣾⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⣿⣿⣿⣿⣿⡂⠛⢿⣿⣿⣿⣶⣦⣶⣮⣤⣆⣴⣤⣾⡿⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣟⣯⣆⣀⡉⠛⠿⠿⣿⣭⣭⣽⣽⠿⠟⢉⣤⠞⠁
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠖⠚⠋⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠻⠿⠵⣿⣷⡟⢓⣾⣓⢁⣤⠀⡐⠁
⠀⠀⠀⠰⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⡍⣯⣠⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣛⣤⢀⠰⣿⡿⠽⠛⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠯⣿⣭⣤⣤⣀⡰⠾⣶⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡯⣤⣮⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢟⣷⣭⣭⣼⣟⡷⢤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⢿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣷⣦⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠻⣾⣩⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣳⣮⣛⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠻⠿⣟⣿⣿⣿⣟⣋⢿⣿⣿⡿⠿⠉⠁⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠋⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠁⠀⣸⣟⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠚⠁⣸⠁⠀⠀⢽⣿⣏⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠚⠁⠀⠀⠀⠀⠀⢀⢙⣲⣄⠀⠈⢻⣿⡄⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⢀⣤⠴⠋⠁
⠀⠀⠀⣠⠴⠘⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠻⣤⡀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⣁⣤⠴⠚⠉
⠀⠀⠀⠈⠉⠉⢉⣉⠤⠿⠶⠿⠿⠟⠶⠶⢶⠶⠶⠶⠦⠤⠤⣭⣷⣾⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⠚⠉⠁⢀⡴⠞⠉
⠀⠀⢀⣠⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡠⠤⠀⠂⠉⠁⠀⠀⠉⠉⠛⠛⠻⢿⡛⠋⠉⠉⠁⠀⠀⢀⣴⡀⢠⡟
⠀⣾⣿⣿⣷⣯⣴⡠⠀⠀⠀⠈⡀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⡄⠀⢀⠔⠋⠙⢷⣼⡇
⠀⠈⠛⢿⣿⣿⣿⣶⣿⠥⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡎⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⠸⡟⢧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡵⠛⠍⣟⣛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠉⡑⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢈⣏⡇⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢰⠀⠈⠉⠉⠁⣈⣫⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢢⡄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠳⣍⠳⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠈⠂⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣩⠅⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠉⠀⠈⠉⠉⠉⠙⠀⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠉⠢⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⠋⠀⢀⡞⠀⣠⠆⣠⠆⡠⠆⠀⠀⠀⣄⣀⠜⠁⠀⠀⠴⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠀⡠⠒⠛⠉⠀⠋⡠⠞⠁⠉⣀⡤⠞⠴⠊⠱⠄⢀⡈⠁⠤⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠴⠋⠁⠀⠀⠀⢤⣆⠀⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⢀⣁⠀⠠⠆⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡡⠞⠁⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⣴⠞⠁⠐⠆⠀⠲⢢⠄⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢠⡀⠉⠁⡆⠀⡆⠠⠃⠄⠰⢀⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⢀⠲⠤⠀⠲⠦⠀⠐⣀⣀⣀⣤⡠⠤⠔⠂⠀⠀⠀⣠⠉⠁⠀⠃⠀⠔⡃⢰⢆⡴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣋⠀⢈⠛⠒⠁⣌⡙⢦⡔⠚⡇⢠⠄⠀⢀⠈⠙⠃⠀⠸⢅⣀⠀⠀⠀⠀⠋⠁⣥⢞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⠎⠁⢠⠈⠳⠤⠤⠤⠖⠋⣠⢞⡇⠻⢀⡴⠋⠀⠀⠀⠀⠯⠀⠀⠀⠀⣄⡤⠞⠋⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠞⡟⠀⠀⠈⠁⠀⠀⠀⠀⠐⣊⠵⠋⢳⣀⠛⠒⠀⠀⠀⢀⣀⠀⢼⣁⠤⠒⠀⠀⢀⡤⠋
⠀⠀⠀⠀⢀⡤⢊⡴⠋⠓⠉⠑⢂⠠⠒⠁⠀⠀⠐⣈⡩⠴⠒⠋⠉⠈⣉⡭⢿⣏⠉⠁⣀⠴⠂⠀⠀⠠⠄⠒⠉
⠀⠀⠀⠐⠁⣠⠟⠳⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠒⠒⠚⠿⡇⢘⠇⠀⠀⠀⠀⠀⢠⡀⠀⠻⣄⣀
⠀⢀⣠⠔⠋⠀⠀⠀⠒⠶⠖⠒⠀⡀⢀⡰⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢇⣼⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠷⠶⣍⠩⠯⣭⠀⠉
⢶⣉⣉⣋⣉⡉⠀⠀⠠⠴⢋⣠⠞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⠤⠤⠀⣀⡠⠄⠀⠰⢦⡤⠖⠁⠈⠙⠒⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠤⠤⠖⠚⠩⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⢦⣐⣛⢱⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠒⠒

⠀⠀⠀⣠⡴⠚⠛⠉⠉⠛⠲⣤⡀
⠀⠀⣴⠋⡀⢀⢪⣤⣡⠀⠀⠈⠻⣄
⢀⣾⡧⠤⠂⠀⠑⠂⠁⠀⠀⠀⠀⢻⣆
⠸⠟⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⢨⡇⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢹⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⢂⠀⠆⡀⠀⢄⡀⠦⠐⠆⠀⠀⡠⡀⠀⠀⠀⢠⠆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠐⠈⠀⠀⡀⢀⢄⠀⢀⠀⠢⠀⠓⠀⠀⠀⢀⠆⢁⠄⠀⠀⠀⠀⢙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⡰⠀⠈⡁⠔⠁⠀⠀⠀⢀⡘⢡⠁⠘⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⡔⠀⠘⢈⡁⠄⠒⠁⠀⠀⠀⠀⠀⢀⡀⠁⣎⠁⠀⠃⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⣀⠀⠀⠀⠀⠀⠹⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⡷⠄⠀⠀⠀⠀⠀⠀⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠒⣀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣴⣤⣤⣠⣴⠋⠀⣠⣶⡄⠀⠀⠀⢀⡶⠛⠷⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠫⣭⣭⣅⣠⣭⠍⢀⣠⣤⣭⡭⠃⠀⢀⣾⠋⠁⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠶⠤⣤⣤⣤⣤⡀⠨⠃⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠑⠒⣫⡭⢄⣀⡾⠁⠀⣴⣋⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⢀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢯⣻⣛⣉⣨⣭⠅⢀⣤⣬⣭⣭⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣡⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢶⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠸⣌⠂
⠀⠀⠀⠀⠀⠀⡀⢯⡳⠄⣐⣬⣰⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣌⡘⠳⢄⢈⠦⠌⣶
⠀⠀⠀⠀⠀⠀⠻⣓⠛⠓⠀⠙⣻⣿⣷⡢⢟⣳⣤⡢⡀⠀⢐⠚⠒⠤⠈⡁⡸⠃⢀⡠⠔⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠐⠞⢛⣉⣉⡭⠔⢓⣻⣿⣧⠭⢌⡙⢪⡳⢶⡀⠄⠀⢀⣸⢃⠔⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣖⣉⣥⣾⣿⣷⣾⣽⠒⣦⠙⣶⣍⠛⠲⠤⠟⠁⠀⠀⠀⠀⢀⣤⠴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠟⣋⣵⢿⣖⠪⣈⠽⢧⣘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢭⡼⡻⢫⣿⠼⠇⣬⢧⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣫⡿⣿⣥⠘⠾⣧⡋⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢟⡼⢳⣾⡟⠀⠀⠀⠀⠀⠀⠐⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢳⡿⠃⠀⠀⠒⢲⣤⡀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠠⡀⠀⠰⠿⣿⡿⠻⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠳⣦⣶⣷⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠱⠉⡎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣸⣴⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣼⣧⣦⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣾⣹⢧⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⣿⣵⣻⡰⣧⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣛⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡷⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣯⢻⡃⠀⢀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢧⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣗⠻⡆⠀⠀⠀⢀⣴⣿⣿⣿⡿⢏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠈⠳⣤⣤⣴⣾⣿⠿⠟⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠄⠀⠘⠿⠛⠉⠉⠣⠄⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠐⠲⢬⡳⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢧⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⢳⢠⡟⣤⣀⢠⣿⣯⡻⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣽⣼⣿⣧⡹⣿⣿⣝⢿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣿⢹⣿⣿⣯⣻⣿⣿⣿⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠻⠛⢿⡿⠿⠛⠏⠙⠃




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⣉⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣼⡽⢘⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠸⡀⠀⠀⠀⠔⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢜⡲⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠑⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠵⠂⢠⠤⣤⠤⡀⠀⢀⢠⣤⣄⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠊⠀⣠⠀⣀⠀⣠⢀⡄⠀⠀⢀⠀⡰⠋⠀⢀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠀⡠⠒⠚⠁⠊⡡⠚⠑⢁⡠⠶⠴⠫⠍⢀⠐⠀⠄⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡠⠚⠉⠀⠀⢀⣶⠀⠉⠀⠀⠉⠁⡀⠀⠀⢀⠀⠀⡅⠀⠖⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⠉⠀⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⢀⠀⠃⣠⠞⠁⠀⠃⡀⠋⠆⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡂⢀⣀⠀⠀⠃⠀⠀⠀⢀⣀⠀⠐⠋⠘⠦⠀⠸⠀⢃⡌⢀⠀⣣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠁⠦⠤⢀⠐⢤⡀⢴⡟⢈⠉⠉⠑⠦⠄⠠⡞⠀⠀⠀⠀⠴⠂⢊⢞⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠞⠁⡄⠣⢤⡀⠡⠜⢁⢼⡇⠏⣀⠞⠀⠀⠀⠴⠈⠉⠀⢀⣀⠴⠚⢡⠎
⠀⠀⠀⠀⠀⠀⠀⣠⠖⡟⠀⠀⠁⠀⠀⠀⠀⣚⠵⠋⣧⣘⠓⠂⣀⣀⡀⠀⠰⠥⠔⠊⠀⢀⠴⠁
⠀⠀⠀⠠⠔⣠⡊⠉⠁⣉⠡⠐⠁⠀⠀⠀⠥⠒⠊⢉⣀⣠⠴⣻⠧⠀⠀⠔⠁⠀⠀⡒⠈⠁
⠀⠀⠀⡡⠞⠉⢑⣈⣉⡀⠀⠀⠀⣀⠠⠴⠚⠋⠀⠉⠈⢹⢀⡇⠀⠀⠀⠀⠘⠦⠤⣽⣲⠤⢄⠀⠀⠠
⡠⠖⠯⠤⠄⠀⠀⣀⠴⢀⡴⣢⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣀⠀⠀⣀⠀⢀⣀⣩⠅⠑⠬⠉⠃⠤
⠈⠉⠉⠉⠀⠀⠠⠤⢒⡩⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠐⢆⣀⡒⣭⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣛⣉⡙⠿⣿⠿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣷⣶⣿⣶⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣦⣽⣿⣿⠟⠉⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠉⣉⠙⢥⣤
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠈⠙⠶⠾⢿⣿⣿⠝⠉⠙⠳⠦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠛⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿
⠀⠀⠀⢰⣿⣿⣿⡿⣏⠹⣦⠈⠉⠙⣿⣷⣦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠉⠈⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣟⡿⣅⣀⣀⢰⣛⣿⠟⣻⣷⣤⡸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⣇⣼⣿⣿⣷⣾⠿⠿⡿⢷⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢠⠴⠂⠀⠄⠀⠐⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣡⣼⢿⡤⡆⠠⣌⡆⡂⠸⣨⣏⠵⢻⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⡞⢠⠋⡁⠐⢣⣾⡥⣬⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⢠⡗⠚⣁⡟⠚⡋⢶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠼⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⡟⢻⡿⠴⢀⣸⣿⡆⣉⣙⣃⣠⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠤⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⠇⠐⢏⣧⡸⣿⣿⣿⠃⣰⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣯⠿⣿⣿⢽⡿⠿⠛⠛⣿⠿⠟⠓⠂⠀⠁⠀⢘⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠇⠁⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⣴⣶⡄
⢠⣄⠀⢸⣿⣿⡀
⠸⣿⣷⣠⡏⠼⣧⠀⣷⠖
⢀⡤⠉⣿⠓⡄⢹⡖⢥⡄
⠀⠀⠀⡁⢀⣤⣽⣷⡆⢀⡆⠀⠀⢀⣀
⠀⠀⢠⠇⣿⡵⠃⠘⢷⣜⣇⠄⣰⣿⣿⣷⡄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣠⣴⣶⡾
⠀⠀⣈⡧⠍⣠⣀⠄⢀⡹⢎⠱⠈⠉⠉⠀⠁⠀⠀⠀⣠⣿⣿⣿⣿⠀⢠⣿⣿⡿⢓⠀⢰⣦⣤⡀
⠀⠉⠁⣿⠊⠁⠀⠀⢹⣿⣽⣟⠒⠀⢠⣶⠀⣠⣾⣧⡿⠟⠛⣿⡏⢀⣼⣿⠟⠙⠻⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠁⠀⠂⢀⠔⠀⠙⠀⠹⣦⠆⣄⢀⣠⣬⣿⣿⣷⡆⢰⣿⣿⣿⣿⣿⠀⠀⣠⣿⠎⠻⣿⣿⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣌⠻⣾⣾⣿⣿⣿⢹⣿⡇⢼⣿⣿⣿⣿⡏⠀⣰⣿⣿⢀⣴⡿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣶⣿⣑⢿⣿⣿⣿⣿⣵⣯⣇⡸⣿⣿⣿⣯⢀⣰⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣭⠇⢴⣿⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡵⠃⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣵⣟⣿⡛⣻⣧⠟⣻⣿⣿⣽⢷⣛⠛⢧⡴⠬⠝⣡⡶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣷⣿⣿⣿⢿⣿⣿⣇⣴⣤⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡛⠿⠿⣿⣿⣋⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⡛⠳⢾⣋⣠⣭⣭⡥⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠸⠿⣀⣤⣰⠀⠚⠟⢛⢿⣶⠒⡏⠓⣺⣿⡿⠿⣿⣟⣁⡁⠨⠉⣯⣤⠌⢠⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠘⠻⠀⠈⣫⡬⡝⢟⣭⣷⢾⡟⠳⠹⣶⣾⣿⢿⣻⣿⣿⣷⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠘⢿⣿⣷⠄⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢆⠀⠀⣸⢿⡄⠀⢀⣺⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⡦⡀⠀⠀⡸⠇⠻⣆⣰⠏⠈⢿⣀⡻⠁⣷⠀⠀⠀⣴⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠻⣄⣠⡟⠀⠀⠹⡟⠀⠀⠈⢟⡀⠀⠸⣇⣠⡾⠋⠘⠃
⠀⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⢸⠀⠀⠀⠉⣿⠁⠀⢠⡟⠀⠀⠀⠀⠈⢗⡀⠀⢻⡏⠀⠀⠀⣿⠀⠀⠀⢀⣤⣶⡄
⠀⠀⠀⠀⠀⡿⠈⠙⠷⢦⣄⡿⠀⠀⠀⢰⠃⠀⢀⡟⠁⠀⠀⠀⠀⠀⠈⣧⠀⠈⣧⠀⠀⠀⢏⡀⣴⠾⠋⠁⢸⡇
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠉⣇⠀⠀⠀⣿⠀⠀⣮⠁⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠸⡄⠀⠀⢸⠋⠀⠀⠀⠀⠸⡧
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡃⠀⠀⣸⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡇⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠸⡆⠀⢀⣧⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡅⠀⢀⡛⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠈⣷⠀⠀⣽⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢰⠇⠀⣼⠁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⣧⠀⢸⡅⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡟⠀⣸⠏⠀⠀⠀⠀⢀⢴⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠹⣦⠀⠿⡞⠦⣀⠊⠢⠊⠡⡌⠁⡀⠘⡇⣬⠃⣰⠟⠀⠀⠀⠀⣠⡺⠃
⠀⠀⠀⠀⠀⠀⢀⣠⡽⠵⡦⡀⠀⢀⠉⠁⠸⠁⠀⠂⠠⠁⠀⠀⠀⡄⠁⠀⠸⠚⠀⢉⠀⠀⢀⣠⡮⣮⣄⡀
⠀⠀⢀⡠⣴⠮⠛⠁⠀⠀⠈⠙⠷⣆⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⢀⣆⠾⠛⠁⠀⠀⠈⠘⠳⢦⣤⢀
⠀⠾⣞⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠄⠀⠀⠀⠀⠄⠄⠐⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠃
⠀⠀⠀⠉⠛⢖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣤⣤⡾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠶⠦⣤⣠⣤⡤⣤⢤⣤⠴⠞⠓⠁⠀⠈⠛⠶⢤⣤⡤⢀⣀⡀⣤⣤⡤⠶⠛⠋⠁



⣿⣿⣿⣿⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣻⣿⣛⣛⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⠤⠀⠰⠴⠒⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠐⢂⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠋⠀⠀⢠⠀⠀⠀⠀⠈⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡰⠊⠁⠀⠰⠆⠀⢆⠀⠨⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣀⣀⣤⣦⡤⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠦⠀⡀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠓⠠⡌⠀⠀⠀⠀⡰⠀⡀⠀⠀⠀⠀⠐⢉⣉⣹⣿⡿⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠃⠀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠲⡆⠀⢧⠊⠠⠀⠀⠠⢃⠈⠥⡥⢦⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⠀⠀⡘⠃⠄
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠰⠀⡁⠰⠀⢨⡧⠒⠄⠀⠀⢀⠀⠀⠀⠟⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠰⠀⠀⢄⠀⠠⠖⠋⣠⠋⡠⠊
⠀⠀⠀⠀⠀⠸⣤⣆⣸⣷⠞⠁⠀⠳⡄⠀⢸⠀⠁⢀⣮⠉⣿⣿⣰⣄⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⢰⠁⠀⠀⢀⣟⠃⠀⣠⠎⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠈⢫⣿⢳⣦⠠⠀⢠⡿⠀⣠⠀⣶⠛⠛⣿⡏⣽⡁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡄⠈⠀⠄⠘⠷⣲⣶⢻⠮⣐⡀⠈⢚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠁⠀⣁⠈⠠⢘⣫⡄⠃⣀⠀⡜⢁⣬⣽⠇⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠃⠁⣿⣰⠛⢉⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢼⡻⣊⣣⣤⡄⣼⠷⠛⡆⢟⠿⡧⡼⠿⣵⠋⠀⠀⠀⠀⠀⠀⠀⠶⣶⠤⢄⡶⠦⣄⠁⠀⠂⠄⣀⣰⡟⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢋⢾⠛⢾⣋⣀⣿⢢⣿⢮⣉⣼⠀⠀⢈⠆⠀⠠⠛⠀⠀⠀⠀⠀⠋⠘⠲⣤⣀⠀⠐⠚⡒⠠⢤⣼⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡑⠭⣧⠠⢼⠽⠟⢛⣉⡉⠦⠴⠇⠀⠀⢸⣁⠀⠐⠀⠀⠠⠀⡀⠀⠐⣌⠁⠒⠂⠨⠛⠯⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠀⠑⠄⠠⠀⠀⠀⠈⠀⠄⢀⢀⣰⡤⠂⠀⠀⠉⠙⠒⠶⠄⣀⣺⠾⢛⣿⣷⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠓⢒⠊⣀⡀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠑⠦⣀⠀⣠⡶⠞⠛⢉⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠉⠲⠦⣄⡀⣀⠀⠀⣀⡤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣠⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡔⣸⡋⣓⡄
⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢱⡟⣿⡑⣜⠄⢆
⠀⠀⢀⠁⣌⡙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⢠⢯⢱⢦⠑⡘⠷⠀⡀
⠀⠀⠀⡢⠄⡈⠉⠐⠒⠶⠭⣥⣶⢶⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡈⡆⣌⡛⢀⡟⠄⢣⡸⡿⢀⠇
⠀⠀⠀⠀⡠⠤⠀⣀⡀⠀⠐⠒⢿⠺⢤⣀⡉⠙⢟⡷⣤⡀⠀⠀⠀⡀⢰⣄⠱⣞⠣⡀⢤⡏⠃⡨
⠀⠀⠀⠀⠀⠔⠄⠀⠀⠀⠀⠈⢹⣍⡠⠽⡦⠄⠀⢿⡽⣿⣄⠠⠀⢄⠼⢄⢳⡉⢢⡰⣶⠑⢠⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠚⢦⡶⠛⣟⣈⡩⢷⣒⣻⣧⠀⠲⠸⢄⠧⡘⣦⡿⠈⢀⠆⠀⠀⠀⠀⠀⠀⠘⠃⣀⡴⠤⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠋⢁⡀⠉⢉⠉⠉⠩⠽⣏⣉⢯⠴⠚⣖⡒⠛⣷⣤⠄⠀⣁⠸⠮⠃⣀⡾⠄⠀⠀⠀⣀⠀⠀⣾⡜⢋⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠀⠀⠐⠒⢒⡿⢥⡴⢻⣋⣹⢶⣉⡥⢟⣿⣥⡀⠁⠠⠴⠋⠀⠀⠀⠀⠀⢀⣀⠖⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠠⡐⠒⠛⣻⣏⣸⣥⢊⣹⢖⣈⠴⢚⣿⠷⠒⠂⠀⠀⠀⠀⠀⢸⢥⣈⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡴⠒⣊⠵⣻⣿⣾⣋⣥⢾⣙⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⣉⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠚⠁⠊⠎⠝⠟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠸⣶⠖⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠠⠈⠃⠀⣠⢶⣚⢂⡀⢠⠒⣿⠦⠀⣀⡰⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠒⠁⠀⠀⠀⢈⡇⡹⢆⡉⡿⣾⠽⠹⠋⢏⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⡄⠀⠀⠀⠐⠫⣿⢷⡾⠋⠁⠐⠕⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠆⠰⣖⠿⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠎⠁⣀⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠨⡀⠀⠛⠁⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⢀⠰⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠈⠉⠀⠈⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⢹⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣿⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡷⢶⣤⣀⣀⣸⣿⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢷⡀⢀⣠⠎⠈⠁⠈⠉⠉⠉⠁⠙⢦⣀⠉⠙⠛⠻⢤⣀⡀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠈⠉⠛⠛⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠬⠅⠐⠰⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⡄⠁⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠩⡭⠭⠭⠬⠼⡜⡜⡚⡎⠈⡘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠩⢩⠭⠭⠭⠥⠵⠰⠰⠐⠐⢐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠰⠒⡒⣂⡂⡀⡃⣃⢋⢩⢅⠥⠥⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠐⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⣀⣴⣄⣀⡀⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⠉⠀⢸⠄⣀⠀⠐⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣀⣀⡾⠦⠦⠀⠀⠀⠀⠀⢠⠤⡇⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠃⠀⢯⠁⠠⠤⠴⠞⠀⢀⣀⣤⣤⣴⠆⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⣀⣠⣼⣾⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠠⠆⠵⢾⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⡄⢀⣀⣤⣻⣾⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣴⠾⠟⠁⠈⠛⠋⠛⡀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠔⠀⢀⢠⠞⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠄⠀⢀⠤⠂⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⠀⠤⠀⠠⠤⠉⠉⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢲⣠⢲⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠑⢷⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠑⢧⡀⠱⡀⠀⠱⣄⠀⠀⠀⠀⠀⣠⠒⡇⢀⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠠⢧⠀⠳⡀⠘⢄⠀⠈⠣⡀⠀⢠⢶⡇⠀⡇⢸⠁⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠸⡀⢣⡀⠙⣄⠈⡳⡀⠀⠘⢦⡇⢸⠀⠀⡇⢸⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⡎⠳⡀⠱⡄⠈⢦⡇⠈⢦⡀⠀⠑⣼⡄⠀⡇⢸⣴⠉⡇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠱⡀⠙⣄⠘⢦⡐⠛⣄⠀⠱⡄⠀⠈⢣⡀⣷⠋⡟⠀⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢨⠙⣄⠈⠣⡀⠹⣄⠈⢦⠀⠘⢆⠀⠀⠳⡏⠀⡇⠀⢸⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⣷⡈⠳⣄⠈⠲⡊⢦⡀⠳⡄⠈⢧⠀⠀⢳⡀⢻⠀⢸⣀⠴⠊⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠙⢦⡈⠳⢄⠳⡀⠙⢄⠈⢶⠙⢣⡀⠀⢣⢸⠀⡜⠁⠀⠀⠀⠀⠀⢰⡶⣄⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠠⠓⢄⠉⠢⣀⢫⠉⠢⣄⢱⠦⠷⣄⢳⡀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠠⡇⠿⣹⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⠢⣌⠑⣷⢤⡈⠓⣵⣦⣌⠀⠳⡀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠉⢉⣀⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠤⣍⡓⢤⣈⣛⢷⣦⠄⠀⠀⠱⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⣀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠲⠤⠬⣧⣤⠤⠽⢖⣏⡴⡼⢀⠀⠀⠀⠀⠀⠀⠒⠦⣤⠔⠒⢣⡫⡽⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣖⣒⣚⣲⠾⣩⠽⠛⢁⠎⠀⠓⠦⠴⠤⠂⠀⠀⡇⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠪⣉⠙⠓⠒⠢⠤⣖⡒⠒⠚⠉⠀⣀⣀⣀⢀⠘⠤⠲⣆⡠⡶⠀⣰⣀⡼
⠀⠀⠀⠀⠮⢉⣉⣉⣉⡩⠭⢕⡢⢜⣒⠀⠀⠀⠀⠀⢠⢵⡄⠠⠤⠤⠀⠙⣪⠔⠉
⠀⠀⠀⠀⢠⠖⢋⣁⡠⠔⢊⡩⢽⣭⡵⣂⠤⠦⢤⣔⡿⣺⣿⣶⣤⣶⣶⠟⠁
⠀⠀⠀⠀⠀⡝⢋⣁⡤⠊⣁⠔⢋⠼⠋⠀⠀⠀⠀⠉⠋⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠈⠡⠥⢴⣎⠥⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣀⢸⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⢀⠎⠀⣰⠂⡠⠁⢀⠜⣼⣿⢸⣿⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡌⠀⠀⠈⠀⠀⡔⢠⠃⡀⠀⠎⠀⣤⢃⡾⡡⢁⡞⣼⣿⣯⠸⣿⣷⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣾⣠⣀⣌⣠⣀⣼⣡⣁⣼⣠⣎⣠⣼⣁⣿⣴⣤⣎⡼⠛⠛⠿⠈⠟⠛⠳⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡡⣽⣿⠀⠀⡴⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣝⠿⢿⣷⠀⠗⢲⠞⠑⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣹⣟⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠠⢦⢤⡤⣤⠤⠤⠤⠤⠴⠶⠶⣶⡦⢤⠤⣿⣬⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠠⠠⠁⡁⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣁⣱⡄⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⢸⣷⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⣤⡠⢼⡇⣦⣰⡏⠏⡍⣉⣻⡥⣿⠰⠥⢼⣿⡧⠦⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠛⠋⠀⢹⠉⠉⠉⠉⢀⣙⠃⠀⢸⣹⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠐⠂⣀⣨⣤⣤⣼⣤⣤⣤⣤⣤⠤⢤⣤⣼⣿⡇⠐⢠⠀⠸⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣉⣉⡈⠛⠻⠿⠿⠿⢿⢿⣿⣿⣿⣿⠿⠿⠿⠊⠙⠃⡤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⣿⣿⣯⣉⣛⡒⡒⢴⠦⠤⠴⡤⠀⠐⢒⠀⠀⣈⣁⣤⣔⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠳⠀⢼⣿⣿⣿⣿⣷⠏⠽⢻⢙⡉⠉⡙⡍⠉⠉⢛⣇⣠⡌⢱⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢠⣿⠆⠀⢀⣸⣿⣿⢟⢻⣗⢳⡶⢧⣀⠠⠀⢁⡀⠀⠐⢺⡄⠬⣴⡶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠛⠶⠵⣬⣿⣿⣿⣟⣻⣿⣸⠟⢺⣇⢐⣌⠜⠢⠤⠴⣼⠃⠠⠌⢸⣿⣤⡀⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢮⠿⠛⠻⠿⠟⠵⠏⠲⣤⣽⢿⣯⣯⣄⣦⠒⠀⠈⠴⠈⠩⠶⠋⠉⠉⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⡠⠶⠛⡛⠶⢄⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣩⣭⣬⣸⠏⣵⣾⢋⡙⢳⣮⠙⣇⣤⣭⣌⡛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣞⣴⣟⢡⡄⢹⡿⣆⡻⢧⣌⣡⡼⢟⣠⢿⡏⢠⠌⣻⣆⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢋⣡⣴⣶⣦⢹⡿⠶⢤⠟⣠⢞⡳⠶⢮⡥⠶⢞⠷⣄⠻⠤⠶⢿⡏⣠⣶⣦⣌⡙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢃⣾⠀⡦⢙⡟⢸⡗⠗⠒⣻⣅⣄⣁⡵⠚⠓⢮⣈⣠⣨⣟⠒⠺⢺⡇⢹⡏⢤⠄⣷⡈⡇
⠀⠀⠀⠀⠀⢀⣠⢾⡘⢿⡷⠶⠞⣡⠟⢘⣁⡼⠁⢃⡀⢰⡆⠴⠦⠠⡆⢀⡐⠈⢧⡈⡃⠻⣌⠳⠶⣾⡿⠇⡷⡀⡀
⠀⠀⠀⣤⣶⢋⣴⢾⣷⡶⢶⠾⣛⢁⡟⢍⠀⠰⢆⣫⠓⣶⢹⣏⣹⢏⣶⠚⣝⡰⠆⠀⡩⠻⡍⣛⠷⡶⢶⣾⡿⣦⡙⣶⣤
⠀⠀⠀⢸⡅⣾⠁⠦⠘⡇⢹⠁⢅⡸⢀⡀⣯⢛⢷⡹⠶⠗⠯⢋⡑⠝⠪⠶⢏⠶⡛⣝⢀⡀⢧⣈⠘⡏⢸⠃⠶⠈⣷⢸⡇
⠀⠀⠀⠀⣡⣻⣷⡶⠛⣡⠟⣶⠥⣀⡬⣹⣽⡳⠕⣥⣥⣄⡰⢫⡝⢆⣠⣤⣬⠪⢜⣯⣏⢥⣀⠬⣷⠻⣌⠛⢶⣾⣟⣀
⠀⠀⠀⡠⢏⣤⣤⡹⢾⡣⠄⢹⢀⣈⣹⣤⢼⠇⠁⢿⠰⣦⡿⡼⢷⢿⡴⠆⡿⠈⠸⡧⣤⣏⣁⡀⡏⠠⠌⣷⢋⣥⣬⡹⢄
⠀⢀⣼⢃⡾⢉⡉⢷⡘⣇⣰⠋⢀⡅⡷⢮⣣⢊⡴⣋⣻⡯⡺⠊⠓⢗⢽⣟⣑⢦⡐⢸⡴⢾⣩⡁⠙⣎⣸⢋⡾⢉⡛⢷⠘⣧⡀
⠀⠈⢻⡌⢷⣬⣁⡾⣡⡏⡹⣍⢉⣃⡷⢞⡗⠌⠳⢍⣽⣗⢵⣤⡠⡿⣸⣯⣩⠞⡡⢪⡳⢾⢘⠉⢩⡏⢹⡌⢷⣈⣁⡾⢡⡟⠁
⠀⠀⠀⠑⣎⡛⢛⣡⢾⡐⠂⣸⠈⢉⣹⠛⢪⡆⠀⣾⠰⠎⣷⢷⡾⣾⠳⠆⣷⢀⢰⡕⠛⣏⡉⠁⣇⢐⢊⡷⣎⠛⢛⣱⠊
⠀⠀⠀⠀⡍⣽⡿⠷⣄⡙⣦⣿⡒⠊⢓⡹⣫⡵⡢⡛⡛⠋⠱⣜⣣⠎⠙⡛⢛⢔⢾⣝⢏⡘⠁⢒⣿⣴⢋⣤⠾⢿⣯⠉
⠀⠀⠀⢸⡇⣿⡀⠶⢠⡇⣸⡀⡉⢲⠉⠁⣟⢬⡾⣵⠶⡦⣖⢌⣁⣰⢔⠶⣎⢷⣥⣻⠈⠁⡖⢉⢀⣇⢸⡆⠲⢀⡿⢘⡇
⠀⠀⠀⠛⠿⣌⠻⣾⡿⠷⠾⠶⣭⣘⣦⠊⠀⢰⠏⢝⡤⢿⣰⣏⣹⢎⡿⢤⣛⠱⠆⠀⠑⣴⢃⣭⡶⠷⠾⣿⡷⠟⣡⠿⠛
⠀⠀⠀⠀⠀⠈⠉⠾⢰⣿⡿⠲⢦⡙⣧⢩⡉⢣⡀⡜⠁⠸⠂⠲⠎⠸⠇⠈⢡⢀⡜⢉⡍⣼⢋⡴⠶⢿⣷⡌⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡈⢿⠀⠓⣸⣇⢹⡧⡦⠤⣽⡓⠋⡉⠲⢤⡤⢖⢉⠙⢛⣯⠤⢴⢼⡇⣼⣅⠚⠀⡿⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⣙⠻⠿⢋⣼⣷⠶⠒⣦⠙⢾⡵⠶⢚⡓⢶⢬⡴⠋⣴⠒⠶⣾⣇⠻⠿⠟⣋⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢫⠹⣯⡐⠃⣸⣷⠋⣵⡞⢋⡙⢳⣦⠹⣾⣇⠘⢃⣽⠟⡹⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣬⣙⣛⠛⢹⣄⡻⢧⣌⣡⡿⢟⣰⣏⠛⣛⣋⣥⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠑⠶⣬⣥⠶⠂⠀⠀⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠀⠀⠌⢿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢠⠄⣠⣿⣿⣿⣿⣿⣿⠟
⣿⠟⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠁
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⠛⠀⠈⢻⣿⣿⠟⠃⠀⠀⠉⠉⡿⣿⣿⡿⠋⠹⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠈⠋⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠻⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠁⠀⠀⠀⠐⠀⠠
⠀⠀⠄⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠈⠙⠛⠛⠿⠻⠛⠛⠉⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡄⠀⠀⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠆⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠋⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣷⡄⢀⡀⠀⢀⣶⣿⣿⣿⣷⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠘⠻⠿⠦⣻⣇⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠰⠿⠟⣡⣼⡷⠤⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠉⠑⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢠⠀⠀⠠⠆⠀⢴⠀⠀⠘⡆⠀⠀⣀⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠸⡵⡄⡟⡄⢀⢠⡄⠀⠀⠀⠀⢀⠔⠊⠀⠀⠸⠀⠀⠀⠈⠀⠠⠦⠐⣄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢷⢥⠈⠳⡙⢄⠀⠛⢤⡀⠀⠘⠌⠀⠰⠂⠀⠆⢀⠀⠀⠀⢀⡜⠀⣸⣸⡰⢹⢠
⠀⠀⠀⠀⢀⠀⠀⡴⣌⠣⡉⠂⠈⡄⠀⡞⠀⠀⠀⠀⣡⡀⠀⠂⠀⠀⢀⣏⠉⠉⠉⢣⠀⢤⠋⣠⢗⡿⢀⢶⠀⢀
⠀⠀⠀⠀⠘⡗⢤⣳⣝⠻⢥⣀⢸⠻⣄⡇⣰⠫⣧⠊⠀⡈⡐⠠⠖⠛⠉⢉⡵⠀⢀⡼⣷⠀⠉⣀⣛⡞⠥⠯⢒⠟
⠀⠀⠀⠀⠠⣌⣢⣈⣉⠉⢹⣶⢌⣣⡈⠳⢽⣆⠙⢦⣀⣷⣌⡳⢤⡈⠛⠓⠖⠚⣋⡴⢋⣀⡤⡾⢿⠀⠐⢒⡳⠎
⠀⠀⠀⠀⠀⠙⠒⠤⢀⠀⠘⣎⠳⢍⡛⠢⠤⠀⠉⠂⠈⠉⠉⠉⠀⠑⠀⠀⠈⠉⠉⠉⣉⡵⣾⣓⢁⣢⡬⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠛⠳⣲⣥⣭⣿⢶⣾⣒⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠲⢤⣭⣛⣛⣿⣿⣟⡓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢒⣻⣮⣍⣉⡀⠀⣀⣀⠹⢦⡀⠀⠲⠤⣜⣦⣬⣍⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠛⠒⠛⠉⠉⠉⠀⠀⠀⠉⠛⠛⠋⠁






⣿⣿⣿⣿⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣿⣟⣻⣛⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⢿⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡽⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣙⢎⢳⡀⠀⠀⣰⣟⣧⡀⠀⠀⣰⢫⢎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢈⡇⣳⢴⡛⠁⡏⡇⠙⣶⢼⠣⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⢀⡴⣊⢴⡷⢊⠀⠀⡇⡇⠀⢉⠪⣳⣌⠢⣀⢀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⣩⠞⠑⠉⠰⣁⠰⠞⠁⠙⠖⢀⡵⠈⠊⠛⢮⡉⠀⠂⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠲⡤⠟⢁⠤⠒⠒⢦⡅⠙⠈⠀⠀⠘⠁⣥⠒⠒⠢⣄⠙⢦⡴⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠂⠀⠀⠡⣄⣀⣀⢸⡀⠀⣠⠀⢠⡀⠀⡸⢀⣀⣀⡄⠉⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠔⠒⠀⠀⠈⠹⣙⠻⡏⠉⠀⠀⠈⠈⢉⡿⢋⡹⠉⠀⠀⠐⠒⠔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡖⠲⣄⠀⠀⡀⠀⠀⠀⠤⢄⠀⢀⠤⠄⠀⠀⠀⡀⠀⢀⡴⠒⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠄⠀⢱⢀⠔⠋⠉⠲⣕⡕⠊⠉⠓⢄⡰⠀⠀⣾⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠚⢀⠂⠀⠃⢀⡄⠀⠐⢸⠓⠀⠀⡆⠈⠇⠀⢄⠘⠦⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡊⠁⡔⠒⢄⢸⠃⢨⣆⣙⣱⣯⠀⣷⢀⠖⠲⡄⠉⣢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠷⠀⠈⣾⠀⣼⣉⠀⢈⣹⠄⣿⡎⠀⠰⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠾⠀⠸⠉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣟⠻⠢⠟⢻⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡄⠀⠀⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⠀⠈⣼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⢿⠿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠦⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣠⠖⢻⠓⠦⣄⢢
⣀⣀⣰⣶⣶⣦⣶⣿⣶⣄⣀⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠁⢸⠀⠀⠀⡰⡏⠉⠁
⠿⠿⠿⠿⠿⠿⢿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣇⣼⣀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⠃⠀⠀⠀⠇




⠀⠀⠀⠀⠀⠀⣠⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⣆⠻⠃
⠀⠀⠀⠀⠀⣀⡬⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢀⠖⠀⠘⠉⠉⠓⢀
⠀⠀⠀⣠⡉⠉⠐⢈⣣⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣛⡻⣿⣿⣿⣿⣟⣛⢣
⠀⠀⢰⣿⣷⣤⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠋⠉⠉⠉⠉⠙⠿⠋
⠀⠀⠈⢿⣿⣿⣿⡄⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⠿⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿




⠀⠀⢀⣤⣶⠶⠶⠶⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖
⠀⣴⣿⡿⠁⠀⣠⡀⠀⠉⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣡⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠘⣿⠟
⣼⣿⡿⠟⣦⣴⣿⣧⣄⣰⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦
⣿⡇⠀⠀⣹⣿⣿⣿⣿⡅⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣀⣸⣿⣿⣷⣄
⢹⡄⠀⠘⠛⠛⣿⠟⠙⠓⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⡟⠛⠛⣿⣿⡇⠙⠁
⠀⠻⣦⣤⣤⣼⣷⣤⣀⣤⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠒⢂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇
⣀⣀⣈⣙⣛⣿⣿⣿⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣶⣶⣿⣿⣷⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⠓⡴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⢠⠧⡀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢠⡆⢀⣀⣀⣀⡀⣀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠰⠖⠀⠄⠠⠤⠀⠀⠉⠉⠐⠾⠀⠀⠀⠀⠀⠀⢠⢪⣿⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠐⠦⡄⠘⢍⣉⣉⢉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠊⣙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡂⠸⡓⠂⠘⢧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠀⠒⠀⠉⠉⠢⠄⠀⠀⠀⠀⠂⠀⢤⡄⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢏⣱⠀⢡⠫⣀⠙⠓⣄⣚⡀⡀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⣠⠀⠀⡐
⠀⠀⠀⠀⠠⢤⢠⡄⠀⠀⠀⠀⡀⠨⣝⢧⡬⠩⠥⠈⠀⠒⠀⠀⡀⠀⡂⠁⢠⠄⣀⠐⠒⢑⡄⣀⡀
⠀⠀⠀⠀⠸⣍⡁⠀⠀⠉⠟⠁⠁⠈⠀⢀⠰⠤⢀⠉⣲⢆⡤⠀⢀⡥⠂⢂⡀⠀⠀⣴⢓⠀⠀⠳⡄
⢠⣴⣶⣶⣶⣻⣯⡿⠧⢴⡼⢢⢄⣀⣁⣶⣖⣉⣍⣂⡀⢠⡀⠍⢋⡴⠀⠈⠅⠀⠀⠀⠁⠐⠁⠀⠂
⠈⠉⠉⠀⠀⠩⣄⠦⠢⠀⠘⠊⠁⢭⠌⡉⠉⠉⠛⣼⣯⡟⠾⡷⡒⢡⠅⠴⡢⣀⣄⣐⡄⠐⢠⣠⣴⣒⣠⣤⠆⡀
⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢈⠋⡩⠘⠂⠄⠀⠬⠉⢻⣾⣌⡁⠀⠈⠁⠛⠓⠻⣯⣷⣞⣿⣥⣄⣀⡀⡑⠤⠬⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠕⠙⠻⣷⡦⠄⠀⠰⡮⢠⡝⠂⠉⠙⠻⢷⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠣⣀⢹⡀⠀⠀⠀⠀⠈⠻⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣾⣿⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣯⣍⣉⣭⣥⣉⣍⣥⣤⣭⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⣾⡟⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠨⣿⠇⠀⠀⠈⠢⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢛⡆⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣤⣀⡛⠛⠛⠛⠒⠒⠀⠛⠃⢀⣀⡄⠀⠀⢸⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⠀⠀⠀⠀⢾⣧⠃⠀⠀⠀⡀⠦⣤⣿⣿⣿⣿⡇⠀⠀⠈⠀⠿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢧⠓⠀⢸⡴⠀⠀⠀⣼⣯⠇⠀⠀⠀⢛⡼⡛⣿⣿⣿⣿⡇⠀⠀⠀⣧⠀⠀⣾⣠⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣶⣦⣼⣿⡵⠖⠂⣿⡇⠀⠀⠀⠀⣼⣿⣻⣿⣿⣿⣿⣿⣶⣶⣿⣿⣦⣤⣿⣩⣄⡀
⠀⠀⠀⠀⠀⠠⠴⢤⣤⣞⣿⡾⠛⠉⠀⠀⠀⢘⡳⠤⠀⠀⠀⠻⠿⢽⣿⡿⠿⠿⠟⠛⠉⢁⣠⠿⠿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠸⠿⢻⣿⣥⣬⣥⣤⣤⣤⣬⣤⣥⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣄⣀⣤⣤⣬⣿⡿⠿⠋⠁

⠀⠀⠀⠀⡜⠉⠒⠒⠤⢄⣀⣀⣀
⠀⠀⠀⣸⡀⠊⡉⠀⠀⠀⠀⠀⠀⢉⣉⡉⠉⠉⠁⠀⢒⠖⢒⢲⣶⣄
⠀⠀⢰⠁⠛⠿⠽⠓⠲⠒⠖⠦⣬⣉⣀⣍⡀⠀⠀⠀⣄⠀⠀⣏⡿⣿⣗⣦⡀
⠀⢀⢧⣤⣄⣀⣀⡀⠀⡀⠘⠊⠁⠈⠉⢀⠭⠉⠛⠟⠛⠟⢿⢸⣷⣟⣟⣿⣾⣷⣤⡀
⢀⠎⠀⠀⠉⠉⠙⠋⠟⠓⠖⠶⠦⠤⢶⣤⣀⣀⢀⣄⠀⠀⡏⣿⣏⢯⠊⢋⠉⠉⠛⠉
⠿⠵⣖⣦⡴⢦⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠩⠉⠋⠙⣹⣹⣿⠃⢄⣴⡀
⠀⠀⠀⢹⣿⡙⣻⡟⠛⠛⠿⠷⠶⣶⣤⣤⣞⣦⣾⣍⡽⡳⠁⣿⢠⣾⡧⡇
⠀⠀⢀⣼⣿⣾⣷⣧⣴⣄⣠⣄⣀⣀⣀⠀⠀⠀⠈⠉⠉⠀⠀⢹⡄⣶⠥⡇
⠀⠀⠸⣾⣧⣤⣸⣿⣡⢻⢫⢯⣾⡵⠚⣟⡿⢷⢲⠶⠤⠤⣠⣸⡆⢀⢄⣇
⠀⠀⠀⣾⣿⣿⣿⡿⠳⠿⠼⣿⣿⣷⣾⢸⣧⡯⣿⣤⡆⣠⣠⠀⣷⢳⢩⠿⢤⣄⣀⡤⢄
⠀⠀⠀⣵⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⣿⡟⠉⠙⠛⠉⠉⠛⠛⠃⡙⣼⣿⡟⠓⠲⢿⢦⣮⡇
⠀⠀⠀⣿⡏⣽⡟⣧⡤⣤⣤⡤⠤⠴⣿⡧⠤⠤⣤⣄⣀⣀⣀⡀⡷⣼⣿⡇⠀⠀⠸⢸⠇
⠀⣠⠔⣿⡇⣈⣀⣷⣤⣤⣿⡿⣶⣞⣿⣷⡖⠒⠚⣷⠤⠤⢭⡇⣟⣟⣟⣧⡀⠀⠇⡿
⢰⡃⠀⠘⠛⣻⡿⣯⢻⣯⣿⣹⣿⠷⡇⣿⣯⣴⣄⣷⠀⠀⠀⡇⠙⣿⣏⣏⢳⣸⢠⡇
⣾⣿⡋⠉⠁⠈⠻⢿⣿⣻⣭⣷⢗⣞⡇⣿⣿⡴⣦⣌⠉⣶⣴⣷⣅⣸⣿⣿⣻⡇⣾
⢸⡇⠑⢄⣀⡠⠒⠉⠀⠉⠉⠛⢻⣿⠷⠿⠿⠿⡿⠟⠋⠉⠑⠮⡙⠛⠂⣽⣧⢃⡏
⠘⢇⠀⠀⣿⠓⠒⠢⠤⣄⣀⣰⡿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡬⢿⡟⢹⠿⠞⠃⠦⠀⢀
⠀⠈⣷⣀⣿⠀⠀⠀⠀⠀⢸⣿⠛⠒⠒⡒⠒⠲⡟⢒⣒⣋⣭⡝⣰⣽⣄⣨⠤⠂⠃⠃⢶⣼⢉⡄
⠀⠀⢹⠻⣿⣦⣀⣀⠀⠀⢸⡟⠀⠀⠀⡿⡪⡊⡇⠸⡫⣺⣟⣿⣿⣿⣾
⠀⠀⢸⣦⣀⠀⠙⣿⠝⢷⠞⣷⡦⡤⡤⣭⣮⡶⣧⢾⢾⢟⣿⣎⢎⣿⡇
⠀⠀⠘⡄⠉⠛⠶⣿⣦⣄⣀⢈⡏⠈⠨⣂⢔⡟⢕⡕⣵⣡⣿⣷⣿⢿⣧⠃⠆⣆⣇⠄⡰⣴⢀⣾⡤⡄⡀
⢸⢜⢂⣿⣦⣀⠀⠸⠀⠉⠙⠛⡟⠛⢻⣷⣷⡟⡿⡿⡿⡻⣿⡺⣱⢟⠜⡈⢶⡉⣿⢰⢳⡗⢫⡏⣍⣄⠱⠱⠠⢠⣤⣠⢀
⠈⠂⡏⣿⣘⡟⢻⡿⢦⣤⣀⣨⣇⣀⠘⢯⢴⣿⣜⣟⣞⣼⣷⡟⣿⡿⢺⡷⢎⡗⡍⣠⢸⣇⣼⣴⠹⡗⢳⢃⢀⢿⣸⠸⢡⢃⢷⣱⡄⠀⢠⢀⠀⢀⠀⡀
⠀⠀⠀⠙⠛⠿⣜⡡⠋⣹⢋⡅⣩⡉⢻⠻⣯⢫⠯⢿⡧⡾⡿⣻⡇⢡⡘⡇⣸⢾⢹⢏⢠⣠⣨⡎⡈⡞⣌⣌⣈⠸⠛⣝⠄⡧⡤⢆⡹⡠⠋⠏⣉⡾⢾⠓⡀
⠀⠀⠀⠀⠀⠀⠘⠋⢻⠛⠿⡧⠯⡧⢼⣞⣱⣿⣵⢿⣧⡿⣷⡟⣦⣉⢷⠓⣇⡄⢿⢁⢏⢻⢉⡤⡛⢇⡥⢈⡄⡠⣧⢹⡇⡔⢠⣆⠧⡗⠃⠙⠚⠐⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠱⠱⠹⠈⠛⠐⠙⠁⠉⠫⠪⠏⠁⠰⠘⠡⠚⠈⡇⠷⢣⠀⠛⠉⠈⠁

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢢⣝⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣋⠔
⠀⠀⠀⠀⠀⠀⠀⢦⣝⠻⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠞⣡⡶
⠀⠀⠀⠀⠀⠀⠀⢈⡻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣴⣶⣤⢀⣾⣿⣿⣿⣿⣿⣿⣶⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣯⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⢿⣿⣿⣿⣛⣛⣛⣛⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣟⡛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠵⠿⢿⣿⣿⣿⣿⣿⣿⣿⠳⠿⠷⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⣀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⣯⡿⢦⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⡄⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣿⠟⢼⣿⡏⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣡⣾⣿⣿⣿⣿⡿⣡⣶⣮⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣛⣯⣿⣿⣿⡿⢛⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⣤⣴⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⡾⠛⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⣴⠟⠉⠀⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⡶⣯⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢠⡾⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠉⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⡏⢿⡈⢰⣿⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⣵⣿⠟⣽⠁⡸⠁⠸⣿⠀⠙⢫⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠾⠟⠛⠛⠛⠋⠉⠉⠁⣚⣩⣶⣿⡿⠟⠁⣼⠏⠞⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠶⠶⠿⠿⠿⠿⠿⢿⣿⠷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢭⠈⠉⠀⠀⠀⠠⠄⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⡛⠛⠛⠛⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣾⣷⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⡟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⣠⡴⣶⣶⢦⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⡀⢘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⢻⣿⣿⣷⢼⡎⢷⣽⢻⡼⣯⣷⢸⡇⣗⢿⢨⢸⡟⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣟⣸⡟⢿⣟⣰⣏⣿⢸⢦⡇⢿⣼⣸⠗⡿⣼⢩⢂⣷⣿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢻⡇⠈⠉⠉⠛⠛⠛⠛⠿⣿⡿⠿⠾⠷⠿⠿⠿⠋⠈⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⡏⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⢃⠀⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣾⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢈⣷⣤⡞⠂⣿⣾⠆⣿
⠀⠀⠀⠀⠀⣿⠿⠿⠿⣿⣿⣿⣏⣿⠇⣷⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⡤⠞⠛⣿⠋⠓⠢⣿⣿⡗⣿
⠀⠀⠀⠀⠀⣼⠀⠀⠀⢺⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⢿⣄⠀⠀⣞⣀⣤⢴⠿⡶⢶⣦⣼⣿⡇⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⣾⣿⣷⣿⣦⣀⣠⣤⣤⣤⣬⣿⣷⣴⣏⣽⣸⣧⢸⣷⢰⣿⣿⢻⣿⣿⡇
⢿⡶⠶⠶⠾⠿⠀⠀⠀⣀⣴⣿⡏⣦⣿⡟⠉⠉⠀⣿⠉⠉⠉⠽⣿⢿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⠛⠷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⣴⡿⠉⢸⣿⡇⠸⣿⣧⣶⣤⣤⣿⣷⣶⣶⣾⣿⡀⡏⢉⡏⠉⡏⢹⡏⣯⣿⣿⣿⣷⠋⠉⠹⣷⡄
⠀⠀⠀⠀⠀⠀⣾⡟⠛⠷⠺⠿⠧⠾⢿⣿⠿⠿⠿⠿⢿⢿⣿⣿⣿⡇⠀⠘⠇⢸⠇⢼⠀⣿⣿⡿⠿⠻⢦⣤⣄⣹⣿
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢴⠿⠀⠰⠒⠢⢤⣋⣼⣇⡴⢋⣻⠿⣶⣶⣾⢶⠾⠿⠿⣧⠀⠀⠀⠀⠘⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢻⣤⣀⣤⣀⡀⣿⡀⠀⠀⠀⠀⠈⠉⣿⠉⠀⠀⠁⠀⠀⢻⠀⠀⠀⠀⠀⢹⠀⠀⠀⣀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣻⣿⣿⣿⣿⣤⣤⣤⣀⣀⣀⣠⣟⣀⣀⡀⠀⢀⣀⣸⣧⣀⣠⣤⣶⣾⣦⣾⣿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⢿⣷⣤⣤⣙⣻⣿⡟⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠻⢿⣿⣟⡛⣻⣽⣿⣗⣈⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠋⠛⣿⣿⣛⠛⠛⠿⢶⣶⣾⡿⠿⠿⠷⣶⣶⣶⣶⣾⣿⣯⣥⣤⣶⠟⠛⣉⣙⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡆⠸⣿⡷⠟⠛⠛⠿⣭⣅⣈⠰⣾⣿⣶⣶⣶⣶⣲⣾⣿⣯⠄⢠⣤⣄⣾⣿⣷⣤⣶⣶⣮⣿⣿⡟
⠀⢰⢸⡀⠀⠀⠁⢰⣿⣧⣤⣄⣍⣔⣂⣿⣿⠿⠟⠡⡺⠿⣿⣿⡿⠿⠿⠛⠶⠶⣿⡿⠛⢉⠛⢻⣿⣿⠏⣁⣼⠇⠀⠀⢀⠀⠀⠀⢀⡶
⠘⣌⠚⣇⠀⠀⡀⣼⣿⡟⠛⢻⣿⡿⠿⣿⣿⠛⠛⠛⣡⣤⣾⣿⣗⣒⠒⠂⢴⣾⣿⠿⠿⢯⣽⣿⣿⣷⠿⠿⢿⣄⠀⠀⡾⠀⠀⢀⠎
⠀⠈⠳⠿⣤⣾⣷⣿⣿⣷⣾⣿⣟⣀⡀⠤⠉⢛⣿⣷⣶⡾⠿⣿⣶⣶⣿⣾⣿⠿⣿⣿⣿⣿⣿⢟⠩⢀⣀⣀⣾⣯⣼⣼⣷⣄⢀⠊⠐⣰⠆
⠐⠂⠐⠂⠀⠀⠀⠀⠙⠛⠻⢿⡿⠿⠿⣿⣿⣾⣿⣿⣥⡤⠤⠄⠀⣠⣿⣿⣿⣛⣛⣩⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⣉⡙⠩⣾⡿⠾⠱⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⠿⠿⠟⠛⠛⠛⠿⠿⢿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠭⠭⠥⠄⠀⠀⠐⠛⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠳⡴⠋⠁⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠦⡏⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⢀⣠⣴⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠶⠦⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣀⣀⣀⡀⠀⠀⠄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠋⠁⠀⠀⠉⢢⠀⠠
⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠚⠂⠀⠀⠑
⠀⠈⠙⣲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠰
⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⣶⡆⠀⣿⣦
⠀⠀⠘⠳⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠻⠟⠁⢠⠈⠛
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⡿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⢋⣥⡄⡀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⡿⠁⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠖⢾⣦⣤⡤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⣴⡶⠂⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠞⠋⠁
⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉
⠀⢠⣾⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂
⠀⠀⠉⠙⠛⣻⡈⠁⠀⣀⠴⣆⣀⣀⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣠⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⢀⡶⣻⣯⡴⠞⣻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⡶⣤⣼⡇⢹⠏⠰⠋⠁⢀⡾⠓⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠆⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠠⠄⠒⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣠⠞⠁⣠⣴⣶⣶⣤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⣤⣶⣶⣦⣄⠈⠳⡄⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠇⢠⣾⣿⣿⣿⣏⠀⠹⡆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣰⣿⣿⣿⣿⣯⠈⣡⠀⠙⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⣿⣿⣶⣾⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡇⠀⠀⠀⠀⢹
⠀⠀⠀⣿⡀⡇⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⡆⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡇⠀⠀⠀⣀⣸
⠀⠀⠀⢹⡏⠓⠀⠀⠀⠀⠀⢸⡀⢹⣿⣿⣿⣿⣿⣿⣿⡏⢰⠀⠀⢀⣴⠿⠛⠛⢷⣄⠀⠀⠳⡘⢿⣿⣿⣿⣿⡿⠋⣠⡟⠀⠀⠒⠀⠈⠙⠷⣤⣀
⠀⠀⠀⠀⠻⣄⠀⠀⠉⠓⠂⠀⠱⣄⠙⢿⣿⣿⣿⡿⢋⣤⠃⠀⣠⠞⠁⠀⠀⠀⠀⣙⢷⡀⠀⠈⠲⢬⣍⠉⣩⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢤⣤⡿⠋
⠀⠀⠠⣶⠚⠛⠓⠀⠀⠀⠀⠀⠀⠉⠳⣦⣤⣠⣤⡴⠟⠁⠀⡴⠋⠀⠓⠀⠀⠀⠀⠉⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣦⡄
⠀⠀⠀⠈⠛⢷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠿⡿⢿⠶⣦⣄⣀⣤⢶⡟⣻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢿⣉⠉
⠀⠀⠀⠛⠿⢧⣥⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡰⣄⠙⠛⢡⢞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⡛⠛⠛⠛
⠀⠀⠀⠀⠀⢠⠶⠿⠷⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣵⣊⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⣟⠋⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠻⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡤⠴⠚⢻⠏⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠂⠉⠛⢦⡀⠈⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⣿⣡⠆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣾⣣⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⢀⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⣀⣤⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣛⡩⠶⣾⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠏⠙⠛⠻⣿⣛⠛⠛⠛⠛⠋⠉⠉⣠⣤⠶⠞⠁⠀⠀⠀⠙⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀⢠⡞⠉⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄⣙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣠⣴⠂⠀⠀⢰⡀⠀⠹⣦⣴⠟⠀⠀⠈⠛⣿⠁⠀⣠⣿⠀⠀⢀⣧⣄⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠦⣤⡴⠛⠻⣦⣀⡿⠀⠀⠀⠀⠀⠀⠙⠶⠞⠃⠙⠶⠶⠛⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠲⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⣀⣰⠒⠲⡖⢲⠒⡶⠒⠒⠒⠲⣄⣀⣸⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠹⠤⠼⠧⠼⠤⡧⠤⠤⠤⠤⠋⠉⢹⠀⣿⠉⠹⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⣠⠴⠖⠓⠶⢤⡀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢸⢁⣀⣀⣀⣀⣀⠹⡄⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠘⠚⡇⠀⠀⠀⣼⠛⠁⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⣀⣀⣀⣀⣀⣁⣀⣀⣀⣁⣀⣀⣀⣀⣸⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡏⠀⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⢙⡏⠉⠉⠉⠉⢹⠋⠉⠉⠉⢻⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡗⠒⣶⠒⠚⠓⠒⢲⡖⠒⠚⠒⠒⡖⠒⢺⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠧⠤⠿⠤⠤⠤⠤⠼⠧⠤⠤⠤⠤⠧⠤⠼⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠘⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣠⡞⠁⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠠⠒⣉⣠⠽⠶⠒⠋⠉⢁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠤⠖⠚⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢀⡀⠀⠀⡠⠚⠉⠉⠓⢤⡀⠀⠀⡞⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠋
⠀⠀⠀⠀⠀⠶⠀⠒⠄⢀⡇⠈⠑⠀⢸⠁⠶⠀⠀⠀⠀⠙⣄⢰⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣠⢂⡸⠋⡘⣿⣀⣸⢄⠀⠀⢀⠀⠀⠀⠘⣾⠃⣸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠔⠋⠈⠇⠺⣉⠉⢹⠀⠀⠀⠀⠘⢦⡟⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⢤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠦⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⢀⡀⠐⠲⢤⣈⠉⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡈⣳⢦⣀⣈⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢠⣶⠆⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⡀⠀⠀⠀⠀⣮⠿⣣⠀⠀⣾⠋⣾⡄⠀⣼⠟⣶⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠛⢗⢄⠀⠀⢰⡿⠀⠹⣷⣜⠇⠀⠘⡵⣾⠋⠀⢿⡄⠀⢀⣔⡗⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠙⢷⢄⢿⠁⠀⠀⣼⡎⠀⠀⠀⠘⣿⡀⠀⠘⣿⡤⡻⠋⠀⢸⣧
⠀⠀⠀⠀⠀⢰⣷⣢⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⡇⠀⠀⣸⡟⠀⠀⠀⠀⠀⠘⣵⡀⠀⢸⣯⠀⠀⠀⠘⣽⠀⠀⠀⢀⡠⣶⣷
⠀⠀⠀⠀⠀⢸⡟⠈⠙⠻⢶⣤⣸⠙⠀⠀⠀⢰⡟⠀⠀⡰⡟⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢿⡆⠀⠀⠀⣿⣄⣴⡾⠓⠉⠀⣟⡀
⠀⠀⠀⠀⠀⣮⠇⠀⠀⠀⠀⠉⢛⡇⠀⠀⠀⣼⡃⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣧⠀⠀⠀⢹⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣯⠁⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⣽⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣸⠀⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⣿⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⠀⠀⡜⠇⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠱⣧⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢫⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡏⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⢮⠃
⠀⠀⠀⠀⠀⠀⠙⣵⡄⠀⠀⠀⠀⠀⠸⣧⠀⠈⣷⠘⣿⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⢀⣿⢀⣿⠃⢠⢿⠃⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠪⣢⡀⠀⠀⠀⠀⠹⣧⡀⢳⣷⠙⠇⡠⠉⢢⠊⠈⢶⠉⢆⠠⠚⡇⣸⡏⢠⣾⠃⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠮⣢⣄⠀⠀⢀⠉⠑⠠⠏⠀⢠⠁⡠⠃⠀⠀⠀⢣⠈⡆⠀⢸⠛⠀⠉⡁⠀⠀⢀⡠⣺⣿⢅⣀
⠀⠀⠀⠀⣀⢤⡶⠟⠋⠁⠀⠈⠑⠿⣦⡌⠀⠀⠀⢠⠀⢘⢠⠁⠀⠀⠀⠀⠀⡆⠀⠀⡈⠀⠀⠀⢡⣤⡶⠟⠋⠀⠀⠉⠛⠿⣶⣤⣀
⠀⣴⣦⡛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠈⢆⠘⡸⡀⠀⠀⠀⠀⢀⠃⠆⡠⠁⠀⠀⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣾⡷
⠀⠉⠑⠻⠷⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠁⢅⣵⣀⠀⠀⣀⣌⡬⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡲⠝⠋
⠀⠀⠀⠀⠀⠈⠑⠫⢖⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣝⠿⠋⠻⢟⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣔⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠻⠿⠥⠤⠤⠽⠟⠓⠋⠉⠀⠀⠀⠀⠀⠉⠙⠛⠿⠴⠶⠒⠶⠶⠽⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠁⠀⠀⠀⠈⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠢⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⡾⠐⠲⠄⢄⢤⠤⢀⣠⣀⠀⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⠯⠁⠰⠀⢠⠴⠒⠂⠀⠈⠀⠈⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣿⣷⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⢄⣆⠀⢾⡋⠉⠉⠉⠉⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠉⠉⠀⠌⠓⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡠⡄⠹⡦⣄⡈⠹⣖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠑⣄⠈⠀⠈⠭⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⣀⡐⠀⠈⠁⠀⠀⠀⠙⠒⠀⠁⠀⠀⠀⠀⠁⠐⠐⠶⠆⠐⠊⠁⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠲⠤⣄⣀⣄⠀⢧⡉⣣⡀⢱⡸⣥⡉⢻⢳⢦⣠⡋⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⢀⣠⠶⢛⣄⡤⠤⢴⡃⢀⣠⠤
⠀⠀⠀⠠⠠⣄⣀⣈⣫⣍⠠⠶⢴⣦⢀⠟⣍⣻⣿⣿⣻⣿⣿⣛⡙⠻⣿⣶⡦⡼⣄⣠⣾⣿⡗⣺⣋⡭⢿⣽⣼⢴⣿⣿⣿⡥⠔⠒⠂⠐
⠀⠀⠀⠀⠉⢩⡭⠻⡿⣻⣷⠶⣶⣾⣿⣿⡿⣾⣿⣿⢻⣿⠭⣃⣾⣵⣀⣌⣹⣮⣿⣿⣿⣿⣽⣶⣿⣧⣾⣯⣶⣯⣿⣿⣻⣙⣓⠶
⠀⠀⠀⢀⣀⣤⣷⣴⣧⣸⣿⣷⣟⣿⣿⣟⣿⢯⣾⢷⢾⣿⣿⣿⣷⣿⣿⣿⣿⣧⣽⣿⣛⣻⣭⣾⣏⣽⣿⣿⣿⣿⣾⣽⣟⣯⠆
⢰⣶⣾⣿⣿⣿⣿⣿⣭⣿⡿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣷⣞⣯⣿⣷⣟⣿⣿⣿⣿⡛⣻⣿⡟⡷⠖⠛⠋⠙⠃
⠘⠉⠉⠁⠀⠀⠘⣭⣙⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⢿⡙⢯⣟⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠀⠣⣔⣀⣤⠖⠂⣐⣰⣆
⠀⠀⠀⠀⠀⠀⠐⢻⢻⠋⠈⠁⠟⣻⣻⣿⢿⡿⢿⢿⣿⣿⡿⣥⣻⣿⣿⣶⣾⡿⣿⡿⣿⡿⠿⢟⡿⣿⣿⣟⣻⣯⣿⣿⣛⠉⠁⠉⠉⠙⢇⡀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠢⠤⠋⠀⠋⠉⢻⡂⠫⠥⠼⢿⢟⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⠔⠫⢍⡓⠺⢿⣿⣿⣗⠲⠰⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠛⢿⣟⡉⠉⠉⠉⡿⠂⠶⣌⠁⠀⠀⠀⠉⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠹⢄⡀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢒⣒⣒⣒⣂⣋⣹⢹⡹⡍⣏⢭⢩⢭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠤⠧⢦⠰⠰⠒⡖⠖⢒⢒⣘⡒⣒⣒⣚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⢓⢛⣘⡋⣉⣉⣉⣩⡌⡥⠥⠥⠴⠴⠴⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠦⠀⣸⡭⡥⢥⠤⠤⠄⠆⠲⠰⠒⡒⡖⢂⢛⢙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠀⠁⠁⠈⠈⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢨⠀⠀⠀⠀⣀⣾⠀⡀⡀⠀⠀⠀⡀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠒⠀⠘⠛⠛⠙⣹⠉⠉⠁⠈⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⠐⡆⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣼⠀⠀⠀⡇⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡹⣇⣀⣸⠿⠶⠷⠂⠄⠀⠐⢀⣀⣠⣄⣁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠠⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡠⣤⠀⠀⡀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⢸⠀⠘⣿⠉⠀⠀⣠⡶⠟⠀⠀⠀⠀⠀⣀⢴⡆⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⡀⢴⣸⣿⣷⠀⠀⠁⠀⠈⠀⠀⠐⠀⢀⣀⠂⣄⣠⠏⣷⣾⠀⠁⠉⠁⠀⠀⠀⠀⠉⠙⠒⠋⠋⠀⠀⠀⠀⠀⢀⣀⢝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⡷⠆⠛⠿⠿⠿⠿⠀⠀⠀⠀⠀⠘⠂⠀⠀⡄⠀⢀⡄⠁⠡⣀⣴⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠑⠚⠞⠋
⠀⠀⠀⠀⠀⠀⠦⠊⠛⠋⠉⠀⡀⠀⠂⠀⠈⢑⠀⠈⠁⠀⠤⠂⠀⠀⠀⠀⠘⠃⢀⠐⠔⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠨⠐⠀⠂⠀⣀⠠⠀⠒⠁⠀⠐⠚⢀⣁⣤⠹⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⠀⢀⡄⠐⠒⠂⠀⠲⢖⡐⠸⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⢰⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡏⠹⣿⠿⣿⡿⡄⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢸⠀⠀⠀⠀⠈⢃⡰⠙⡀⣀⡀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢃⠀⠀⢁⣓⣽⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⠛⣿⣜⣿⣾⡿⢿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢈⠛⢉⣻⣿⣷⣯⣟⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡄⣰⣶⣿⣧⠾⢿⣿⣶⡾⠏⠂⣴⢢⣬⣀⠤⣄⣀⢠⣀⡠⢊⡠⠊⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⠈⣭⣿⡿⢋⣀⣡⣽⣿⣍⡄⠅⠀⠀⠈⣹⣿⣿⣽⣟⢿⣿⡿⠛⠲⢤⣄⣀⡀⣀⠀⠀⠹⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣿⣿⠗⠚⢭⣭⣭⣭⠴⠖⢂⣠⣬⣙⣛⠿⠿⢿⣿⢟⡡⢄⣰⡄⢁⠀⠀⠀⠀⠈⠳⢬⣉⣀⣀⠈⠻⢿⠍⠉⠋
⠀⠀⠀⠀⠀⢀⡤⠤⠚⣩⠕⠴⣿⢏⡲⢤⣒⣲⣚⣉⣉⣥⠤⢤⣭⣭⣥⣭⣭⣴⣾⣟⣻⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢳⣾⣤⣿⣿⣿⠟⠛⠛⣷⠤⣭⣿⣿⣿⣿⣿⣷⣞⣛⣛⣿⣭⣵⣶⣿⣽⣭⣿⣿⣻⠓⠶⣤⣤⣤⡴⠖⠂⠒⠒⠒
⠀⠀⠀⠘⠿⠛⠛⠉⠀⠀⠀⠀⠘⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠛⠛⠁⠀⠀⠀⠈⠙⠓⠶⠤⣄⡀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠯⣤⣀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠶⠶⠶⣤⣀⣴⡇⢸⣦⣀⣤⠶⠶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠶⢭⣷⣆⠰⢦⣍⣸⡃⢸⣇⣩⡴⠆⣰⣾⡭⠶⠶⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢦⣄⠒⡌⠉⠑⠒⢦⡉⠃⢸⡇⠙⣇⣸⠋⢸⡇⠘⢉⡴⠒⠂⠉⢡⠒⣀⡴⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⢹⡆⠘⠀⠀⢀⡏⠀⢀⣘⣓⣦⡌⢡⣴⣚⣃⡀⠀⢹⡀⠀⠀⠃⢰⠏⠀⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⢧⣸⠇⠠⠀⠀⠸⠗⢋⣩⡭⠭⢭⣭⣭⡭⠭⢭⣭⡙⠺⠇⠀⠀⠄⠸⣇⡼⠃⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⢀⡀⠁⠀⠀⠀⢀⣀⣰⣯⠀⠀⢀⡾⠁⠈⢷⡀⠀⠀⣽⣄⣀⡀⠀⠀⠀⠈⢀⡀⠀⣀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣡⠞⣻⠁⢀⣠⠶⣚⣩⣭⠤⠀⠀⠀⠺⡅⠀⠀⢨⠗⠀⠀⠀⠤⣭⣍⣓⠶⣄⡀⠈⣟⠳⣌⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⣱⣆⢸⡴⢋⡴⠚⢩⠟⠁⠀⠀⠀⠀⠀⢹⡀⢀⡏⠀⠀⠀⠀⠀⠈⠻⡍⠓⢦⡙⢦⡏⣰⣎⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣼⠃⢹⡌⢡⡟⠀⠀⡏⠀⢠⣤⣤⣄⡀⠀⢈⡇⢸⡁⠀⢀⣠⣤⣤⡄⠀⢹⠀⠀⢻⡌⢡⡏⠘⣧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠻⡟⠀⠀⠀⣿⠀⠀⠷⣌⠻⣷⣄⠀⠃⠘⠀⣠⣾⠟⣡⠾⠀⠀⣿⠀⠀⠀⢻⠟⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣀⠤⠤⣤⠀⠀⠀⡀⠘⢧⠀⠉⠒⠲⡌⣿⠆⠀⠀⠸⣿⢡⠖⠒⠉⠀⡼⠃⢀⠀⠀⠀⣤⠤⠤⣀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣥⢶⠀⡟⢰⡤⠤⠟⠀⢸⡆⠀⠀⠀⢰⠏⠀⠀⠀⠀⠹⡆⠀⠀⠀⢰⡇⠀⠻⠤⢤⡆⢹⠀⡶⣬⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡆⣇⠈⣇⠀⠀⠀⠘⢧⡀⢣⠀⣸⣀⣠⣄⣀⣠⣀⣇⠀⡼⠀⡼⠃⠀⠀⠀⣸⠁⣼⢰⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡌⣇⠸⡀⠈⠢⣄⣀⡀⠈⠳⣤⠇⢣⡁⠹⣄⣠⠏⢀⡜⠸⣤⠞⠁⢀⣀⣠⠔⠁⢀⠇⣼⢡⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣾⣆⠳⣀⠤⢤⠀⠀⠀⠀⣾⠪⣒⠀⠀⢸⡇⠀⠀⣒⠑⣿⠀⠀⠀⠀⡤⢤⣀⠎⢰⣷⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⣠⢥⠀⠘⣆⢀⠀⠀⠙⢶⣶⣶⠶⠋⠙⠶⣶⣶⡶⠋⠀⠀⡀⣠⠃⠀⡬⣄⡉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡰⢋⣤⢸⡇⠀⠘⢶⠀⠀⠀⢸⣷⠂⠀⠀⠀⠀⠐⣾⡇⠀⠀⠀⡶⠃⠀⢰⡇⣤⡙⢆⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡏⢸⢸⡇⠀⠀⠀⠀⠠⡄⠈⢿⣶⣄⣠⣀⣠⣶⡿⠁⢠⠄⠀⠀⠀⠀⢸⡇⡇⢹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⡞⣼⠁⣠⡴⢶⡆⢸⣁⣀⠀⠟⠻⣿⣿⠟⠳⠀⣀⣈⡇⢰⡶⢦⣄⠈⣧⢳⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⣏⢸⡏⠀⢸⡇⣨⡅⢸⠀⠀⠀⠘⠃⠀⠀⠀⡇⢠⣅⢸⡇⠀⢹⡇⣹⠎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⢿⡇⠀⠘⣿⠁⣿⠘⡆⠀⠀⠀⠀⠀⠀⢰⠃⣿⠈⣿⠃⠀⢸⡿⣫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠹⠀⠸⣇⠙⠇⠀⠀⠀⠀⠸⠋⣰⠇⠀⠟⠀⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⣆⠀⡴⠋⠙⢦⠀⣰⠏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⠀⠀⣼⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣿⣣⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠟⣿⠀⠀⠀⣀⣠⣶⣶⣿⡿⣿⠿⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⢻⣿⡿⢋⣴⣶⣶⠟⠀⣀⣼⣿⠻⣿⠋⣿⡠⠿⢶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢄⣿⣇⣿⣿⣿⠟⢠⣼⡿⠿⢿⣆⣽⣖⣻⣦⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⡀⠀⠀⠀⣴⠿⣿⣂⠳⢦⡹⣿⣫⠟⢁⣴⣿⡏⡶⠛⢷⡻⠟⠛⡻⣯⡁⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡟⢹⣿⣿⣿⣷⣄⠀⢠⡟⢋⡉⠻⣿⣆⠹⣿⠃⣠⡿⠿⣿⣧⡻⠶⣻⠃⠀⠀⣷⢹⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⡇⢿⣤⣼⡟⣿⠀⢻⢠⡟⢰⣤⣿⡃⣩⡭⢀⣠⡶⣰⢏⡾⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢶⣤⣾⣿⣿⢠⡄⢸⡇⣠⠼⠾⠻⢟⣛⢿⠵⠞⢋⣺⣞⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣫⣭⣭⣭⣙⠻⣶⣝⠻⣿⣿⠘⣷⢸⢁⣶⣿⣿⢿⢿⣍⠳⣾⣻⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣹⣯⡙⢻⣏⠑⣄⡹⠷⣜⢿⣇⢻⡌⣿⠿⠟⠋⠀⠈⠋⣷⢨⣿⣝⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣡⣶⡶⠿⠾⢯⡑⢯⣾⣿⣿⣆⠻⡌⢷⡡⣤⣀⣠⣤⣴⡾⢃⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣄⣴⣾⣶⣝⣾⣿⡏⠹⣿⡀⠙⠈⢷⣬⣉⣛⣋⣩⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠛⠛⣿⣿⣯⣬⣿⣿⣧⣰⠟⣻⣿⡦⠈⠙⣿⣿⣻⣮⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⢿⣿⣿⣻⠿⠦⣄⠁⣰⡿⠛⠓⠂⠀⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡠⣌⣩⣭⣶⡶⠊⠱⣏⣠⡈⢻⣷⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣯⣟⣻⠷⣿⣷⣥⣙⠿⠶⠶⣿⣷⣶⣤⣈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣷⣶⣭⣛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⡉⣟⡿⣿⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⢿⣿⣿⣿⣦⡙⠻⠶⣶⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⡞⣿⣝⢿⣮⣙⠶⣬⣭⣍⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⢿⣧⡝⢿⣷⣬⡉⠛⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠉⠛⠛⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⢛⣩⣥⣴⣶⣶⣶⣶⣦⣬⣍⡛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢋⣴⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢣⣾⣿⣿⣿⣏⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣰⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢰⣿⣿⡃⠦⢹⣿⣿⣿⣿⣏⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢃⣿⣿⣿⣿⣶⣿⣿⡟⢁⢻⣿⣿⣿⣿⣿⢋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⢿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣴⣶⣬⣉⣛⡛⠛⠛⢛⣛⣋⣭⣴⣦⣬⣙⣛⡛⠛⠛⢛⣛⣉⣥⣶⣦⡄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡌⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢁⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠇⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠹⠿⠟⣡⣶⣌⡛⠿⠿⠟⣋⣴⣦⣙⠻⠿⠿⢛⣡⣶⣌⠻⠿⠏⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣌⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣄⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣬⣉⣛⠛⠿⠿⠿⠿⠛⣛⣉⣥⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⠉








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠘⠀⠀⠀⠐⠐⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠢⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠒⠚⠉⠈⠀⠀⠁⠀⠈⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠟⢋⡉⡉⠉⢻⡄⠀⠀⠀⠀⠀⣠⣶⣶⣶⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢁⠖⢉⡤⢬⣷⡀⠇⠀⠀⠀⢀⠞⠉⣀⡀⠈⠙⢿⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣄⠀⢸⡑⣄⠀⠀⠀⠀⠀⠀⢸⠀⡏⢰⣿⣦⣼⣿⡇⠀⠀⠀⠀⠈⣴⡯⣥⣄⠙⢦⠈⡇⢀⠶⢀⢞⠅⠀⢀⡄
⠀⠀⠀⠀⠈⢆⠑⠤⣣⡈⠳⣄⠀⠀⠀⠀⠸⡈⢇⠘⣿⣿⣿⠟⠀⠒⠐⢦⠀⢸⣿⣤⣼⣿⡇⢸⢄⠗⢁⡧⢃⣎⡠⠚⢡⠃
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉⠀⠀⠑⢄⠀⠀⠀⢱⡀⠉⠉⠉⠁⢢⡀⠀⠀⠀⢀⢹⣿⣿⣿⠿⠁⡸⣸⠠⠋⠀⠉⠁⢀⡴⠃
⠀⠀⠀⠀⠀⢏⠁⠺⠁⠀⠀⠀⠀⠀⠙⠢⡀⠀⠑⢄⠀⠀⠀⠈⡇⠀⢀⡴⠃⠀⠉⠋⠒⠒⠚⡵⠁⠀⠀⠀⠀⠀⠩⠓⠉⡙
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠑⢦⢀⠀⢧⣠⠎⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠼⠀⠀⠀⠁⠀⠀⢠⡔⣒⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣖⠀⠌⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠔⢀⣀⡠⠔⣊⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠁⠀⣈⠥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢈⡫⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣔⣊⡥⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠳⡀⢀⢠⠤⠤⠤⠤⠔⠺⣄⠀⠠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⢧⣀⡀⠀⠀⠀⠀⠈⢳⠁⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡀⠀⡄⠙⡄⠀⠀⠀⡔⠉⡀⠀⢀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡼⠣⣀⠏⠋⠁⠀⠀⠀⠑⠚⠳⣄⡸⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠾⣾⢶⡀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣄⣠⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⢀⣃⠠⠉⠁⢾⡧⣀⠐⢏⣍⠀⣀⡠⣀⡀⠀⠀⠀⣀⡀⢀⠀⣄⣯⣄⣠⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡷⠚⠛⠛⠛⠿⣿⠛⠛⣿⣷⠏⠚⣷⠋⠒⠈⠛⠋⢠⠆⠀⠀⡙⠀⠉⠈⠛⠒⣟⠚⠛⠲⣦⡤
⠀⠀⠀⢫⡁⠀⠠⡀⡀⢹⣯⠀⢰⣶⡆⠀⢸⠀⠀⣿⣿⡃⠀⣯⠀⢰⣿⣷⠀⠀⣼⠀⠀⣷⣦⡄⠀⢰⣶⣿⣧⡀⠀⠿⠁⢠⣆⠀⣂⣠⣤⣄
⠀⠀⠀⠠⡝⣟⢿⣿⣿⣿⣿⠀⢈⣉⡀⢀⣴⡀⢐⣿⣿⡃⠀⣿⠀⢀⣀⠀⢰⣶⣾⡀⠀⣿⣿⡇⠀⣼⣿⣿⣿⣿⡀⠀⣠⣿⣿⣎⡹⣿⣧⠌⠁
⠀⠀⠀⠘⢻⣿⠙⠛⠀⠹⣿⠀⢸⣍⣾⣿⣿⣇⠀⠛⠛⠁⢠⣿⠀⢸⣿⣷⡀⠹⣿⡄⠀⡏⣽⣿⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⠿⠿⠷⠾⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⣾⣿⣾⣿⢟⣿⣿⣶⣶⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣷⣿⣵⣽⢏⣲⣾⠿⠏⠻⡋⣱⣶⣾⣯⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠙⠛⡄⠀⠹⠏⢻⣿⣿⣿⣿⣿⣯⣿⢿⠍⠈⠋⠉⠹⠛⠛⠮⠑⠈⠀⠀⠀⠀⣻⣻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣯⣭⣿⣿⣿⣷⠄⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠙⠛⡯⢟⠀⠈⠀⠀⠀⠀⢙⠷⣤⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠞⠁⠀⠀⠀⠀⠀⠸⢷⣶⣯⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣟⢟⣉⡛⢻⡛⣹⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⢲
⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⢦⣄⠀⢯⣦⠟⡁
⠀⠀⠀⠀⢸⡏⠀⠀⠉⠉⠛⠛⠛⠛⠓⠲⠶⠦⣤⣄⠀⠀⢀⡞⠁⠀⢠⡄⠈⠳⣤⡟⠿⠟
⠀⠀⠀⠀⠀⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⠃⠀⠀⠀⠀⠀⡾⢸⠷⠿⠂
⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⣰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠘⢳⠖⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⠄⠀⠀⣠⠞⠁⠈⠙⠓⠶⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠚⠁⢀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣠⠞⣀⡀⠀⣠⡤⢄⠀⢀⡴⠒⠆⡞⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢁⡞⣩⠗⢰⡏⢀⣼⣀⣸⣇⣀⡤⠿⠥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠻⠥⠖⠋⠙⠋⠁⠉⠁⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠠⣾⡧⣾⡶⠄⠀⠀⠀⢭⣼⣦⠄⠀⠀⠀⢀⣿⠚⡤⠀⠀⠀⠒⢸⡇⣚⠀⠀⠀⣿⢰⡇⣾⡄
⠀⠀⠐⠿⠓⠻⠟⠀⠀⠀⠘⠀⠘⠇⠀⠀⠀⠀⠐⠟⠉⠀⠀⠀⠀⠈⠸⠃⠐⠀⠀⠀⠟⠸⠃⠿

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡀⢰⡆⣀⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣷⠀⣷⠀⠀⠀⢰⢫⣤⠟⡄
⠀⠀⠀⠂⢼⠇⠒⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠿⠀⠿⠀⠀⠀⠈⠫⠭⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⠁⠈⡇⠀⠀⠀⠀⡏⠉⣤⡀⠀⠀⠀⠀⠊⠂⠀⠀⠀⠀⣾⣿⣽⣷⠄⠀⠀⠀⣄⣤⣤⣀
⠀⠀⠀⠸⡶⢶⠇⠀⠀⠀⠀⡧⠄⠀⠀⠀⠀⠠⠧⠀⠤⠧⠀⠀⠀⠀⢮⠷⠏⠀⠀⠀⠀⡧⠿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠸⡯⠤⡟⠀⠀⠀⠀⣿⣽⣽⡇⠀⠀⠀⢿⣷⣻⠟⠀⠀⠀⢸⣿⣼⠿⠃
⠀⠀⠀⡿⠇⠸⢿⠀⠀⠀⢰⠟⠛⠷⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⢺⣿⣿⠂⠀⠀⠀⠸⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣦⠈⡢⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠀⠤⠤⠞⣡⣆⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣴⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣛⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣿⣿⠋⠀⠀⠀⢙⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠻⢿⣿⡿⠀⡐⠉⣦⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠚⠹⢧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⢤⠤⠊⠀⠀⠈⠷⣄⣈⡉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠈⠢⡄⠀⠐⢃⣀⢤⣤⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢦⣤⣀⡉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠉⠓⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀⠤⠴⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠘⠳⠛⠛⠉⠉⠉⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢳⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣠⠄⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⠳⡀⠨⠄⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠰⣇⠀⠀⠀⠀⠙⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡙⢮⡃⠈⠓⠋⠀⠋⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠇⣸⣆⢳⡭⠗⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⠒⠒⠒⠠⢤⡈⠾⠀⠀⠀⠀⠀⣀⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢣⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠓⠦⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⣹⠟⢷⣄⠀⠀⠀⠀⠀⣸⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⢠⡶⠛⠁⠀⠀⠉⠳⢤⣄⣤⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠹⢆⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠘⢆⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⠀⢀⡠⠔⠊⢁⠄⢀⠀⣀⣤⣤⣀⣀⡿⠻⠂⠀⠀⠀⣴⣿⡌⠉⣉⡀⢀⠀⠀⢈⠉⠉⠉⠁⠤⠤⠤⢼⡿⠷
⠀⠀⣀⣴⣦⠀⢀⣀⣤⡴⠞⢋⡴⠋⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠁⠀⠀⠀⠀⠰⣄⠙⠲⠀⠀⠀⠀⠀⢸⣿⣶
⠀⠀⠛⠙⣯⣜⠋⠉⠀⢀⠴⠋⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢉⣿⡟⠁⠉
⠀⠀⠀⢴⡿⢿⣇⡤⣾⣁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⢼⡿⣿⠆
⠀⠀⠀⠈⠀⠀⠀⠰⡿⠿⣧⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄
⠀⠀⠀⠀⠀⣴⠶⠶⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⢀⣬⣿⣿⡧⡤
⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠉⠉⠛⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⠉⠻⣷⣽⡿⠊⠁
⠀⠀⠀⠀⠀⢰⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠀⠀⣰⠃⠀⠀⠀⠀⠙⠋⠀⢀⣿⠿⡇
⠀⠀⠀⠀⠀⠈⢻⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠃
⠀⠀⠀⠀⠀⠀⣼⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣻⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⢀⣤⣤⣤⣤⣤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠴⠋
⠀⠈⠙⢷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣹⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠻⣦⣤⣀⣀⣄⠀⠀⠀⠀⢀⠤⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠹⣯⣀⣠⡤⠴⠊⠁⠀⣾⣁⣴⠟⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣶⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠠⢤⣤⠉⠁⠀⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠐⠂⢄⠈⠀⠁⠐⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠐⠀⠰⠀⡄⠀⠘⠀⠃⠠⠄⢀⡀⢈⠀⢀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣉⠀⠀⠈⢘⡀⠀⡀⠀⠉⡀⠂⠶⢠⡀⡄⢀⠀⡁⠈⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠄⠀⠀⠀⠀⠀⠰⠂⠀⡀⠀⠐⠀⠀⠄⠁⢈⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠠⢤⣤⣴⣥⣤⠶⠶⠶⠾⠋⠁⠐⢊⣤⣔⣠⣤⡀⠀⠥⣀⣰⠀⢀⣐⡦⠔
⠀⠀⠀⠀⠀⠈⠀⢁⣤⡶⠶⠶⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⣿⣿⣿⠟⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠘⣁⣴⡾⠟⢋⣠⡤⢄⣤⠤⠂⠀⠀⠘⠉⠉⠙⠉⠉⠛⢉⣿⣏⣤⣄⣠
⠀⠀⠠⠞⠋⠉⠀⠚⠉⠥⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠻⠿
⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⠄⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠁⠀⠈⠀⠈⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡁⠈⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⣿⠇⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢦⡀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠘⣿⣇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⢦⣄⡀⢯⡀⠀⠀⠀⢠⣶⣶⣦⣄⣀⠉⠓⠦⣄⣀⠀⠐⠾⣿⣿⣿⣿⠃⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠛⠆⠘⢿⣿⠓⠧⣤⣀⣤⣼⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠲⣄⠀⣤⣤⣄⣱⡀⣾⣿⡟⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣼⡿⠛⠒⠑⢹⣿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠈⢧⠈⠻⠿⠿⠿⣿⠋⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠘⢿⣷⣤⣘⠓⠘⣿⡶⠂⢀⣀⣀⣀⠀⠀⠉⠻⣿⣿⡄⠀⢸⡇⢀⣀⣀⣀⠈⢦⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⣾⣏⠀⢠⡤⠄⢹⡿⠂⠈⠉⠉⢀⠀⠀⠀⠀⢹⣿⡇⠀⣸⠁⠙⢿⣿⣿⣿⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⢼⡁⠀⠘⠻⣿⠶⢂⣀⢸⣧⠀⠘⠿⠛⠉⠁⠀⠀⠀⢸⡿⠀⡰⠃⠀⢀⣠⣬⣍⣉⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠼⠵⡞⠉⠉⢢⡹⣄⣀⠀⢿⣄⣙⢉⠀⢹⡿⠂⣤⣶⠖⠂⠀⠀⠀⣼⢃⠞⠀⣠⡞⠁⠀⠀⣀⣀⢩⡒⣾⡆
⠀⠀⠀⠀⠀⠀⠀⣎⣿⣀⠀⠠⣌⣦⣹⣾⣷⠀⢏⡀⠀⠉⢻⣏⠠⠸⣿⣤⣌⠁⣀⣀⠀⠀⢠⣿⠏⣠⠞⣽⢃⠀⢠⣾⣯⣻⣿⡟⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⠙⠻⢿⡿⢯⣼⠧⢄⣉⣹⠃⠈⠻⢷⣶⠠⢼⣇⣀⠉⣀⡀⠀⢸⡿⡞⠉⢤⠀⣾⠀⣿⢟⡟⢹⡿⠀⠀⠀⢇
⠀⠀⠀⠀⠀⡴⣻⠶⠒⠒⠲⢶⣾⣿⣧⡼⠇⠀⣶⠟⠋⣷⠶⠶⡎⢻⣧⡐⠙⣿⣬⠁⠴⠀⢸⣌⠲⢄⠈⠦⠤⡄⠱⠚⠆⢺⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠸⣹⡇⠀⠀⠀⠀⣽⣿⣿⣜⣧⠀⢰⡟⠲⢡⣅⠲⡄⠳⣄⠹⣧⣝⣁⡻⢷⣶⠀⣸⠿⣘⠡⠆⡤⠀⠈⠛⠒⠶⡞
⠀⠀⠀⠀⠀⠛⠿⠶⠶⠿⠛⠛⠛⠛⠛⠛⠳⢾⣇⠞⣃⠉⠳⠀⣶⡟⢛⡲⠲⢿⣷⣶⣟⠛⡋⢞⠀⢹⡻⠅⢀⡾⠀⠄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢷⡀⣴⡿⠛⣈⡄⠛⠛⠛⠋⠁⠀⣾⣎⣴⠆⢉⠙⢟⣀⠉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠁⢻⣇⢸⡹⣿⣷⣶⠶⠒⠊⠀⢿⣻⢥⢠⡾⠀⠀⢨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⠇⢙⣶⠄⣀⣠⣤⣤⣴⠖⠈⢮⣙⡚⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡈⠻⣦⣉⠛⠛⠉⣠⣤⣤⠄⣠⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠭⠿⠷⠶⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡠⠀⠱⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡙⢀⡤⠀⠀⠀⣀⣠⡴⠞⣩⠖⠁⠀⠀⠈⠫⣙⠦⣄⡀⠀⠀⠀⠀⣦⡀⠋⡹⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣿⢦⡀⠀⠀⠀⠀⠀⠀⠉⢉⣡⡴⠖⡋⠕⢈⡤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⢬⡙⠿⣶⡤⢄⣈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡴⣯
⠀⠀⠀⠀⠀⠀⠀⣿⣆⢳⡀⠀⠀⠀⢀⡤⠚⢉⣡⠖⠉⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡙⠳⣬⡙⠒⢤⣀⠀⠀⠀⢀⡞⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⡇⠀⡠⠚⠁⢠⡴⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠙⢷⣄⠈⠓⢄⡀⢸⠟⠛⠁
⠀⠀⠀⠀⢀⡴⠒⠀⠒⢲⡧⠊⠀⢀⡴⠋⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢷⣄⠀⠑⢼⡖⠊⠉⠓⠢⡄
⠀⠀⠀⠀⣿⠀⡀⠀⠀⡞⠁⠀⢠⡞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠙⣦⠀⠈⢧⠀⠀⢀⠀⣿
⠀⠀⠀⠀⠈⠉⠁⠀⡜⠀⠀⢠⠏⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢧⠀⠀⢣⠀⠀⠉⠁
⠀⠀⢸⣗⢦⡀⠀⡼⠀⠀⢠⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢇⠀⠀⢇⠀⣠⣖⣾⠇
⠀⠀⠀⢷⣬⣿⢠⣇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⣴⣿⣠⡾
⠀⠀⠀⠀⠙⠻⣿⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⣿⡟⠋
⠀⠀⠀⠀⠀⠸⠘⡄⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠃⢣
⠀⠀⠀⠀⠀⡇⠀⡇⢸⢀⡤⠖⢒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠲⢦⡀⡇⣸⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢩⣷⣿⣄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣹⣷⡆⠀⢸
⠀⠀⠀⠀⠀⣇⠀⠈⢻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠃⠀⣸
⠀⠀⠀⠀⠀⢸⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡇
⠀⠀⠀⠀⠀⠈⣧⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠄⣠⣤⣤⣙⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠃⠀⠀⠁⠈⠀⠀⠀⡠⠊⠀⣠⣋⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠳⢦⡀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣤⣌⣻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡜⠁⠀⠀⠀⠀⢀⣀⣠⣤⣖⣊⣥⣴⣾⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡊⢁⡈⠙⢦⠀⠀⠀⣀⠈⢉⣙⠲⢤⡀⠀⠀⢱⡜⠀⠀⣀⣤⡶⢿⣛⣛⣛⣉⡉⢉⣿⠛⢡⡀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⢣⠔⣩⠔⠂⠉⠉⠛⠲⣌⢳⡄⠈⡇⣠⡾⣛⠕⠋⠉⠉⠑⠦⣄⠙⢻⡇⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠀⡠⢃⠞⠁⠀⠀⠀⠀⠀⠀⠈⠣⠹⣆⣿⢟⡜⠁⠀⠀⡀⠀⠀⠀⠈⢧⡘⣇⠀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⡩⠔⠁⠀⠀⠀⠀⠐⢩⣽⠀⣀⣤⣤⣻⣯⣮⣤⣀⠀⣯⡍⢂⠀⠀⠀⠀⠙⠬⣉⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣾⡿⠋⠙⢿⡿⠋⠛⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣴⣏⡀⢺⣌⣶⡄
⠀⠀⠀⣴⠵⣶⣿⣿⣜⢉⣹⣷⡀
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣧⢽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⢀⣿⡿⠛⣧
⠀⠀⠀⠀⠀⢸⠋⠄
⠀⠀⠀⠀⠀⢻⣿⠃⡆
⠀⠀⠀⠀⠀⢸⣟⡆⡦⠀⡀⠰⠔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⣟⣻⡌⠦⠀⠄⠀⠄⠈⠂⠂⠀⠀⠀⠀⠀⠀⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠘⢛⢋⣄⠲⠼⣦⠰⠂⠴⠄⠆⠄⢀⠃⢀⣠⣿⣿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⣿⣿⣿⣿⣶⣦⣴⣦⣶⣷⣿⠿⣟⣻⣯⣿⣾⠿⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢩⣹⡏⠛⠻⢯⣷⣿⣶⣿⢷⣾⣿⣿⣋⣠⠐⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢆⡀⠘⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢧⣬⣟⣀⠀⠀⢀⠑⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠘⣿⠿⣛⠉⠉⠁⠉⠉⠙⠉⠋⠛⠛⠻⣿⣿⣿⣦⣜⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣠⣄⡀⠀⠏⠀⢩⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠘⠉⣉⡈⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡖⠛⠈⠋⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⠠⠀⢀⠀⠀⢠⡤⠄⢠⡔⢂⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⡥⣾⡧⢶⣿⠦⢴⠿⠶⡶⠾⢳⠶⢛⡿⠛⣡⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢢⡴⠗⡴⠞⢲⡴⠋⣲⠾⠓⡶⠟⢱⠟⢉⣾⡇⢸⣯⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠗⡶⠟⢲⠞⠓⣶⠟⠒⡴⠗⢢⠞⠂⡶⠃⢰⣿⣟⡇⢸⣿⣇⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣰⡦⢦⡤⠤⣴⠥⢤⣴⠥⣤⣤⢄⣤⠤⣠⡌⣤⣴⣯⣭⣭⠃⠈⣭⣭⠔⡜⣿⡆
⠀⠀⠀⠀⢀⠔⡃⠀⡊⠀⢔⠁⠀⠛⠁⠠⠚⠀⠔⠁⡀⠉⢀⡴⠿⠘⠛⡇⠂⢰⠛⠓⠘⠓⢊⢻⣄
⠀⠀⠀⠀⠘⠋⠘⠋⠙⢿⡯⣳⡿⢻⣦⣾⠛⠟⠿⠶⠿⠷⠿⠿⠿⠿⡍⢿⡃⠈⡟⡸⠟⠻⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⡇⢸⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⣈⠉⠁⠀⠀⠊⢉⠉⠉⡁⠉⠀⠈⠁⣿⡃⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⢿⡀⠀⢨⣹⣆⠈⠈⢂⡇⣀⣠⣰⡀⣿⡭⢩⠏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠙⠋⠉⠉⠉⠛⠉⠉⠏⠉⠉⠉⠋⠋⡇⠸⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⠀⣠⣀⠀⠀⠀⡂⠀⠀⠀⠀⠠⡆⠀⠀⠀⠘⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠛⢺⣿⠁⠊⠉⢉⣽⣡⣍⣥⡌⣠⠈⢀⡉⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠔⢻⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠀⡆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣶⠸⣿⣤⣄⣤⣼⣏⣫⢉⠉⠉⣉⠉⠤⣽⣰⠀⣥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠿⢿⣙⡟⠒⢶⠶⣿⡾⣿⡴⠤⢤⡶⠴⠶⣿⣾⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡼⣄⡍⠙⠓⠶⠤⣷⠠⡯⠤⣤⡤⠦⠤⠴⣿⣿⠀⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣯⠉⠷⣦⣄⢀⣷⣴⠇⠀⣺⠀⠀⢠⣠⣿⣿⠤⣿⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣆⣰⣀⠈⠈⢩⢀⡁⢈⣥⡁⣠⣿⣽⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠠⡀⠀⢳⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠
⠀⠀⠀⠀⠀⢀⠀⠙⣄⠈⣧⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢆⢳⡀⠀⢦
⠀⠀⠀⠀⠀⠀⠳⡀⠈⢆⠘⣧⠘⣆⠀⠀⠀⠀⠀⠀⡘⡘⣦⠱⣄⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠳⡈⢧⡘⣆⠀⠀⠀⠀⠀⠀⠐⡌⠣⡈⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⢦⡘⢦⡱⣌⢦⡀⠀⠀⠀⠀⡑⡌⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⠒⢆⠘⠳⡉⠂⢀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡴⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⡉⠂⠈⠢⣬⣦⡀⠙⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣠⣿⣵⡖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⠌⠓⠲⣾⣿⣧⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣈⣁⡘⣻⣿⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⣄⡤⡞⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⢛⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢹⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡈⠛⠦⣀⣀⠀⠀⠀⠀⠀⠀⡴⢠⣧⣿⣫⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠚⠉⣫⣾⣤⣤⣦⠀⠀⠀⢀⡇⠈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡡⠞⠟⠛⠉⠀⠀⠀⢀⡼⠁⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡄⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⣀⣀⣰⡋⠹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣶⣶⠖⠋⠉⠟⣉⣟⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢊⣴⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡫⢋⠼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢦⡀
⠀⠀⠀⠀⠀⢀⡴⢋⡴⠒⢄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡠⠒⢦⡙⢦⡀
⠀⠀⠀⠀⢀⡾⢡⠎⠀⠀⠀⠓⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠚⠀⠀⠀⠱⡌⢷⡀
⠀⠀⠀⠀⣸⠇⠸⡀⠀⠀⠀⠀⠀⠀⡸⢆⣤⠶⣖⣛⣛⣛⡛⣷⣾⢛⣛⣛⣛⣲⢶⣤⡰⢇⠀⠀⠀⠀⠀⠀⢀⡇⠸⣇
⠀⠀⠀⠀⣿⠀⠀⠱⣀⠀⠀⠀⠀⣪⡶⣫⡵⠋⠉⠉⢀⢈⡇⡟⢻⢸⠁⡀⠉⠉⠙⢮⣝⢶⣅⠀⠀⠀⠀⣀⠎⠀⠀⣿
⠀⠀⠀⠀⠹⢧⣄⠀⠙⠀⢀⣠⠾⣫⠞⣡⠔⠉⢋⡽⠃⢸⢹⠇⠸⡏⡇⠈⢯⡛⠙⠢⣌⠳⣝⠷⣤⡀⠀⠋⠀⣠⡼⠏
⠀⠀⠀⠀⠀⠀⠻⣆⣀⣴⢟⡵⢛⡥⠊⠁⠀⡠⠊⠀⢀⡏⣾⠀⠀⣷⢹⡀⠀⠑⢄⠀⠈⠓⢬⡛⢮⡻⣦⣀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣫⠵⣋⠔⠋⠀⠀⠀⠔⠀⠀⠀⠊⠀⡇⠀⠀⢸⠀⠑⠀⠀⠈⠢⠀⠀⠀⠙⠢⣙⠦⣝⠟
⠀⠀⠀⠀⠀⠀⠀⢸⢡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡌⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡜⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⠀⢹⠀⠀⡏⠀⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣤⣤⣤⣤⣉⠢⣴⠋⠇⠘⠀⠀⠃⠸⠙⣦⠔⣉⣤⣤⣤⣤⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⣠⣦⠀⠸⣄⠈⠙⠛⢿⣯⠀⠀⠀⠀⠀⠀⠁⠀⣽⡿⠛⠋⠁⣠⠇⠀⣴⣄⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⡀⠈⠛⠒⠋⠀⢻⠂⠀⠀⠀⠀⠀⠀⠐⡟⠀⠙⠒⠛⠁⣀⣴⠏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠻⠶⠶⢶⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⡶⠶⠶⠞⠋⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢢⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⡄⠀⠀⠀⠀⡜⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢣⡀⢀⢀⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡀⡀⢀⡜⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡑⠎⠀⣼⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⣧⠀⠱⢊⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⢸⡖⠲⢦⣄⣠⡴⠖⢲⡇⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠳⣄⡀⢀⣠⠞⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⣀⣤⡤⠖⠲⠤⣤⣀⣀⣤⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣄⣀⣀⣀⣀⣀⣤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠋⣿⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⡉⠀⢸
⠀⠀⠀⠀⠈⣟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡇⠈⠘⠛⠂⢸
⠀⠀⠀⠀⢀⣈⣯⡲⠉⠙⠲⢤⣄⡀⠀⠀⠀⢀⣄⣸⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡀
⠀⠀⠀⠀⠈⠳⣌⠙⠆⠘⠯⠀⠀⠉⠙⠲⠤⣌⣇⠉⠃⢠⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡗⢠⣿⣯⣾⠛⠋
⠀⠀⠀⠀⠀⠰⡞⠷⢤⡀⠀⠀⠀⠀⠀⢀⣤⡈⠙⠦⡀⠈⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢸⣿⣵⣋⡛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠈⣳⣤⣀⠸⠍⠀⠀⠀⠈⠃⠀⠀⠀⠈⢦⡀⠀⠀⠟⠈⣇⠀⠀⠀⣀⣀⣀⡀⠀⢸⣿⣣⠟⠛⠻⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠘⣆⣠⠾⠁⣀⡀⢹⢦⢘⡿⠯⠭⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡛⠓⠂⠀⠠⡖⠄⠀⠀⠀⠀⠀⠙⢦⣀⠀⣀⡼⠃⠀⠀⠉⠁⢿⣿⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠬⠍⠁⠀⠀⠀⠀⠀⣠⠞⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣟⡓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⠃⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢭⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠈⣳⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⡴⣴⠃
⠀⠀⠀⠀⠀⠰⣗⢦⡘⣎⠳⣄⡀⠀⠀⠀⢀⡞⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⣤⣌⣳⣌⡛⠷⠀⣭⠓⠲⢶⡞⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠑⠾⣏⣉⡙⠀⠀⠀⠀⠀⠉⣠⢤⠖⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡴⢲⡟⠋⠁⣃⡀⠀⣄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠉⢙⣻⠿⢛⣉⣤⠄⠈⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⣫⠽⡯⢅⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⡉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠿⣛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⠛⠛⠉⢹⡷⠶⠶⠶⠶⠶⡦⣀⣀⣤⣤⣤⣴⣶⣿⡾⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡄⠀⠀⠀⣸⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣿⣿⡇⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡿⠉⠘⠇⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣻⣘⣿⣀⠀⠀⣀⡀⠀⠀⣺⣿⣿⣿⣿⣿⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⠃⠁⠻⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡀⠀⠀⣿⣿⣿⣶⣶⣶⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣇⠀⠙⢿⣿⣿⡭⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢿⣿⣾⣶⣦⣤⣤⣾⣿⣿⣶⣶⣶⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁