Spongebob Emojis & Symbols

⠀⢀⡠⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣀⣀⣀⣀
⠀⡎⠑⡎⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠄⠠⠤⢤⣀
⠀⠣⢬⡋⠀⡎⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡰⠦⢠⡆⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠲⠤⢤⡀
⠀⠀⠀⠈⢳⡰⡀⠀⠀⠀⠀⠀⠸⠀⠀⠔⠁⠀⠀⠀⠈⠛⡀⠀⠘⠂⠼⠃⣠⠀⠀⠀⠀⠀⠀⢀⠄⠊⠻
⠀⠀⠀⠀⠀⢳⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⡇⠀⠀⠋⠀⠠⡀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⠀⠢⣄⠀⠈⠀⠀⠄⢆⠀⠀⠀⡀⢀⣀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠶⠋⠀⠀⠀⠀⠀⠀⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⢺⠀⠀⠀⠣⣄⡉⠓⠒⠀⠀⠀⠙⠒⠘⢀⣀⠀⢡⠀⢀⡇⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠⣋⠉⠖⡖⠒⡲⠒⠈⠉⡠⠃⠀⠈⢀⠜⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⡀⠀⠐⠀⣀⢸⣋⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⡜⠉⠀⢁⢀⣁⡠⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⡸⠅⣒⡦⠠⠐⣀⠤⠔⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣔⣁⣀⣡⠔⠊⠀⠀⠀⠀⢠⠂⠀⡖⠁⠀⠀⠷⣶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠑⠲⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⠻⠹⢶⠤⣤⡤⢄⣀⠀⢀⠀⠀⠀⣀⣀⠴⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠶⠦⠉⢥⣴⡉⢳⣑⡉⠀⠉⠉⣉⡀⣟⣁⠤⠒⡊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠄⠀⢄⢀⠀⡠⠉⠉⠁⠐⠲⠶⠀⢹⠀⠶⠛⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⢄⠀⢀⡞⠉⠉⠉⠑⠒⠒⠒⠒⠦⣤⠷⠒⢈⡟⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠴⡯⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠈⠉⠐⠲⠭⣅⣒⢶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⣠⡶⠶⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣰⠟⣇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠲⣤⣀⣀⣀⣀
⠀⠀⠀⢀⣰⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠉⠉⠓⠶⠤⠤⠤⢤⣀⡀
⠀⠀⢠⡟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠙⠓⠦⣇⠀⠀⠀⢰⡀⣾⠀⢈⠙⠛⠓⠒⠲⣄
⠀⢠⠟⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⢢⠀⡔⠊⠁⠈⠁⠻⡀⠀⠀⠀⠀⠈⣇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡄⠀⠀⢂⣤⣍⢢⠀⠀⠛⠀⢀⠀⠀⣄⠀⠈⠆⠀⠀⠀⢠⡇
⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣃⠀⠠⡘⠿⠟⠠⠀⠀⢸⠀⡎⢰⣶⡎⠃⠀⠈⡀⠀⠀⠀⢳
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡠⠪⠅⡀⠝⣦⠉⠒⠂⠀⠀⠀⣘⠀⠡⡈⠛⡡⢁⣠⠖⠓⢲⡄⠀⢸⡇
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡁⠀⠠⣥⠀⢦⡀⠀⠀⠀⠀⡰⠉⢄⠀⠀⣀⠴⠋⠀⠀⠀⣸⠧⡀⢸⠃
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⠂⠀⢸⡲⣄⠈⠑⠒⠒⠉⠀⠀⠠⠗⠊⠁⠀⢀⣀⣴⠞⠁⡀⡈⢾⡄
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢇⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠐⠒⠛⠉⠁⢀⣠⡟⠂⢀⠇⣷
⠀⠀⠀⠀⢻⠀⡖⠓⠶⣤⡀⠀⠳⠀⣠⣴⠒⢻⣄⠀⠀⠀⠈⣿⠓⠶⢦⣤⣤⣤⢤⡶⠞⠋⢁⠃⠀⠁⢠⡏
⠀⠀⠀⠀⠸⡇⢃⠀⠀⠀⠙⢦⢀⠀⣇⠊⠀⠈⢉⣧⣀⣀⣀⠿⢤⣀⣸⠀⣗⠀⠀⡇⠀⠀⡘⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢻⠈⡆⢠⡞⢧⣸⢿⠀⠈⣳⠀⢀⣀⣴⣿⣿⣿⠀⢠⣶⣮⠀⠉⠙⠛⠃⠀⢰⠃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢈⡇⠙⠦⠽⣄⠻⣌⣧⠞⢁⡴⠋⠁⠈⢿⣿⣿⣦⣼⣿⣿⡇⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠢⣈⣡⠔⠋⠀⠀⠀⠀⠈⢿⡛⠻⢿⡿⠿⣅⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠈⠙⣆⡴⠋⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡠⠞⠛⠲⠒⠒⠶⣤⣄⣀⣀⣀⡀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⣇⣠⠶⠊⠀⠀⢀⠀⠀⠀⠀⠀⠉⠻⣤⡀⢙⣿⣶⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢀⠤⠂⠋⠈⣀⣉⡐⠒⠀⠤⠀⣙⡋⠀⢹⡦⣤⠞⠳⣭⣽⠿⠿⠷⣤⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠤⢊⣥⣶⠇⠀⠀⠙⠛⠛⠿⠷⠀⣶⣦⣤⣭⠟⠀⢸⡦⠤⠀⣀⡀⠀⠀⠈⠉⢹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠋⢀⣠⠶⠠⠤⣀⣀⡀⠀⠀⠀⠀⠉⢳⡄⠀⣠⠿⠿⣶⣠⣤⣭⣍⣒⠶⠾⠦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠢⠤⠽⣞⣁⣀⡴⠛⢱⡴⢛⣩⠴⠒⣶⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⠾⢉⡧⢤⣀⡿⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⢀⡞⠛⠲⠶⠦⣤⣤⣀⣀⣀⠀⠀⠀⢤⠤⠶⠞⣋⡤⠞⢩⡇⡸⠀⣠⣤⣤
⠀⠀⠀⠀⠀⣰⣶⣶⠀⠀⢻⣦⣀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠴⠚⠉⠀⠀⣜⣠⡃⢰⣿⣥⢿
⠀⠀⣠⣶⣿⣿⠛⠿⠀⣰⠋⡴⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⢀⡼
⠀⠀⣿⣧⡟⢐⡦⡷⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢟⣦⠔⠋
⠀⠀⠈⠉⠀⠀⢆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠄⠀⡠⠤⠠⠤⠤⠔⠒⠂⠐⠒⠈⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⠉⠁⠀⡀⢀⣄⢀⡀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⡰⠁⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⡠⠋⠁⠀⠈⠑⢤⠖⠉⠀⠀⠉⠢⡀⠀⠀⠀⡃⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⢀⢠⡄⠀⡇⠀⠀⢠⡄⠀⠀⢱⠀⠀⢰⠃⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠒⠢⣄⠀⠀⠀⢇⠀⠈⠂⠀⠀⠀⠼⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⢄⡀⠙⠢⠔⠉⠑⠤⠀⠀⢄⣠⠄⠰⠀⡼⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠮⣬⣉⣉⣁⣀⣀⣤⠴⠒⠉⠂⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢧⠀⠀⠀⠀⠰⠤⠤⠿⠄⠀⠄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡜
⠀⠀⡂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠁⢒⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⢸⠀⠀⠠⠀⠈⠁⣠⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠃⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠀⣀⠀⠠⠠⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⠢⠤⠒⢢⡤⠤⡤⠤⢄⣀⣀⣀⠄⣀⣰⠠⠤⠤⢒⡎⠄⢉⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣠⣄⣀⠀⣈⣀⠔⠢⡄⠂⠀⠀⠀⠀⠀⠀⣀⠀⢠⠊⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠉⠉⠡⠀⠉⠙⠁⠀⠛⠛⠂⠀⠀⠘⠛⠀⣀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃⠀⠒⠒⠲⠒⠀⠤⠆⠲⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠈⠀⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠷⣦⣾⣶⣷⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠿⠛⠀⠀⠀⣾⡛⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⣾⠙⡞⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠲⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠣⣽⠛⢡⠎⠀⠀⠀⠀⠀⠀⠀⣠⠃⠿⠂⠀⠀⠀⠉⠢⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⣆⠀⠀⠀⠀⠀⢠⠎⠤⢀⡤⠾⠦⢼⡀⡀⠀⠀⠀⠀⠉⠉⠉⠓⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡄⠀⠀⠀⠀⡼⠀⡴⠁⠀⢀⣀⡀⠈⣇⡠⠼⠧⣴⡆⠀⠀⠀⣀⣄⠀⠈⠓⠲⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣱⡀⠀⠀⡞⠀⣰⢧⣀⠀⢟⣿⣹⡖⠁⢀⣤⣄⠀⠙⣏⠀⠀⠻⠿⠃⢠⠞⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢣⠀⢠⠇⠀⢣⠀⠈⠣⡀⠉⢸⡁⠀⠸⣿⣯⠃⠀⢸⠀⠀⠀⡠⠔⠃⣼⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠗⡏⠀⠠⣶⠓⠦⣀⡈⠒⠚⢣⡀⠀⢀⣤⣀⣠⠏⠀⠀⡸⠁⠀⠀⠈⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⢀⡀⠀⢹⠶⢤⣈⣀⠀⠀⣉⣒⣣⣄⠀⠙⡄⠀⡎⠀⠀⠘⠇⢀⠞⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠁⠀⠀⠀⢈⡷⠞⠿⣍⣽⠏⠉⢉⡴⠃⠀⠚⢠⠞⣴⡆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠊⡍⢻⠼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠿⠀⡀⢾⣀⣠⠞⠻⠖⢛⡶⠋⢀⣤⡀⠀⡇⠀⠈⣁⣼⠥⣄⢀⣀⡠⠤⠴⣒⣋⡥⣄⣿⡛⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣀⣀⡙⠦⠬⢝⣒⠒⣚⠍⠀⠀⠘⠛⢁⠜⠁⡴⠋⠁⠀⣾⣯⠭⠒⠒⠋⠉⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠙⢟⣲⣤⣈⡉⠀⠀⠀⠐⠆⠀⢸⠰⡦⠙⠲⡦⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⠿⢻⣶⣾⠻⣽⣟⠓⠲⠦⠤⣀⣼⡠⠤⠖⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⢶⣤⣌⣿⣀⡿⠿⠿⢽⣶⣶⢤⣯⣴⣶⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⢲⡄⢀⡜⠉⠉⠙⠓⠲⠦⣬⣉⣀⣿⣈⣡⣤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡥⠚⠿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣉⣡⢾⣓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠛⠿⣗⠲⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣿⣹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠤⠄⠤⠔⠒⠤⠤⠒⠒⠒⠒⠒⠉⠉⢳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⠀⢀⠀⢠⡀⢀⠀⠀⢀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠎⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠜⠋⠉⠈⠉⠲⣄⠔⠉⠉⠈⠉⠢⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⡎⠀⠀⠀⣂⡂⢀⠇⠀⠠⢂⡐⠄⠀⠸⡀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⠧⠤⣀⠐⠍⠅⠈⡆⠀⠐⠬⠡⠂⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢦⣀⠈⠑⠦⣀⡠⠛⢦⣀⠀⠀⡈⢀⡀⠁⡄⢀⡇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣨⠛⠒⠢⠤⠄⠀⠀⠈⣉⡭⠔⠛⠁⠈⠀⢸⠀⠀⠀⠀⠀⡎
⢀⠤⠂⠄⠈⠐⠀⠤⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠉⡏⠉⢱⢲⠂⠉⠋⠀⠀⠠⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄
⢈⢂⢦⠀⠌⠁⠈⠀⠀⠂⠀⠬⣉⠂⠀⠙⡆⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⡁⣀⡠⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⣸⠁⡀
⠡⢀⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠰⡁⠀⠀⠀⠀⠀⢢⠐⠁⠐⠁⡀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠘⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠑⠒⡤⠤⡬⠘⢉⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠉⠙⠫⢉⠝⡒⠲⢖⠒⡲⠤⠤⠴⠒⠲⠴⠗⠒⠒⡪⠙⠒⣁⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠶⠤⠄⢠⣤⣴⠃⠱⣒⣁⡀⠀⣀⣀⡀⠀⠤⠀⣀⡎⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⣀⣀⣀⣀⣀⠁⠀⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠉⠑⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠉⢉⠉⠉⠉⠁⢐⠒⠒⠒⠒⠒⠎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡁⠀⠀⠀⠀⠀⠀⠁⠲⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣶⣼⣦⠀⠀⠀⠀⠀⠀⠀⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡿⠿⣿⠿⠀⠀⠀⣴⡶⣦⣾⣷⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠸⠆⠐⠃⠀⣠⠄⠀⣤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠁⠀⠀⠀⠀⠀⠁⢀⠀⠘⠁⠈⠁⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠘⠛⠃⠀⠀⠀⢹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣇
⠀⠀⢀⠀⠔⠂⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⠀⢀⡀⠔⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⡠
⠀⠀⠶⢊⠅⠀⠀⠀⢀⢑⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠦⣄⣀⡈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠃⠒⠉⠉⠉⠀⠀⠈⠁⠂⠈⠀⠂⢄⠀⠀⣀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡀⠁⠁⠀⠀⠀⢀⣀⣤⣾⡟⠂⠀⠀⠀⠀⠀⠀⠛⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⠃⠀⠁⠀⠀⠀⠀⠀⠀⣇⠀⢸⣿⠉⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠄⠀⠀⠀⠀⠀⢨⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⢿⡋⠀⠀⠉⠉⠉⣉⠟⠀⠀⠀⠀⠀⠀⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⣭⣥⡔⠀⣀⣀⡜⠹⣀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⡇⢀⣀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠉⠛⡀⢀⠵⠾⢧⠀⣠⣀⣀⠀⣤⣀⣀⠑⢸⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠓⠲⠶⡬⢥⣀⣀⢀⠀⠀⠉⠉⠁⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢲⠖⠁⠀⠀⠀⢉⡏⠙⠛⠒⢾⠿⠿⠿⠿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠒⠠⠲⠊⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢃⠀⠀⠁⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⠂⠈⠃⠠⡘⢁⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⡀⢀⣀⣤⣄⣀⣀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⠴⠦⣤⣄⣀⣀⣀⣀⣄⡀
⠀⠀⠀⡾⠋⠉⠉⠉⠉⠁⠀⠀⠙⣯⣉⠉⣉⣼⠋⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠉⠀⠀⢀⣤⠶⠯⣭⡉⠀⠈⢻
⠀⠀⠀⣷⠀⢀⡶⠋⠉⠙⢦⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠹⡆⠀⣾
⠀⠀⠀⢸⡆⠈⠳⢤⣤⡤⠟⠀⡀⠀⠀⠀⡆⠀⠀⣠⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⣠⠘⢦⣀⠀⢀⣰⠇⢸⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⣼⣧⣄⣠⡏⠀⠀⠀⠀⠹⣆⣠⣼⣧⣤⣠⡏⠀⠀⠉⠉⠉⠁⠀⢸⡆
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠉⠻⣦⡀⠀⣠⠞⠋⠁⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⢀⡴⢾⡇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠁⠀⠀⢀⣤⠶⠦⣄⡀⠈⢷⣼⠃⠀⢀⣤⠴⠦⣤⡀⠀⠀⢻⡄⠀⢰⡏⠀⣼⠁
⠀⠀⠀⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⢀⡟⢠⣶⣶⡌⢷⠀⢸⡇⠀⠀⡾⢡⣶⣶⡌⢷⠀⠀⠈⣧⠀⠸⣇⢰⡇
⠀⠀⠀⠀⣸⣧⣤⡀⠀⠘⣇⠀⠀⠀⢷⡘⠿⠟⣣⡟⣠⠼⠷⢤⡀⢷⡘⠿⠿⢃⡾⠀⠀⢰⡇⠀⠀⠈⢻
⠀⠀⠀⠀⣿⠀⠀⠹⣆⠀⠹⣦⠀⠀⠀⠙⠛⠛⠉⢰⡇⠀⠀⠈⡇⠀⠉⠛⠛⠉⠀⠀⣠⠟⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢹⡄⠀⢀⡟⣠⡶⠎⠛⠶⣤⣤⣤⣤⠶⠛⠃⠀⠀⣸⠛⠶⢤⣤⣤⣤⠴⠞⠁⠐⣶⡄⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢿⡴⠟⠁⠋⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠛⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⢀⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠲⠶⣶⣶⠶⠶⢶⡟⠋⠁⠀⠀⠀⢀⣀⡀⠀⠀⣰⠋⢷⡀
⠀⠀⠀⡟⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣿⣿⣀⣀⣸⡇⠀⠀⠀⠀⣴⠋⠉⠉⢳⡄⢹⡄⠀⢻⡄
⠀⠀⠸⣇⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣥⣉⣩⣤⣬⣥⣁⣩⡴⠞⠁⠀⠀⢧⡀⠀⠀⣠⠇⢸⣇⣀⣀⡷
⠀⠀⠀⢸⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢸⣿⡏⣿
⠀⠀⠀⢸⠀⣿⠻⣤⣤⣤⣀⣀⣀⣤⠴⣶⡶⠦⣤⣤⣤⡶⠖⢻⡶⠶⣤⣄⣠⣤⣤⣤⣤⣤⡤⣤⣤⠟⢸⡇⣿
⠀⠀⠀⣾⠀⡿⠀⢻⠀⠀⠉⠉⠉⠀⠀⠈⠙⠶⣤⡴⠛⣷⣴⡏⠙⣦⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⢿
⠀⠀⠀⣿⠀⣧⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡟⠀⢿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⢾⡇⠀⣸⠇⢸⡀
⠀⠀⣰⡃⢀⣾⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⡿⣆⠈⣷
⠀⠀⣿⣷⣸⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢈⣷⣇⣸⢿⡇
⠀⠀⠻⣌⣻⣿⡿⠀⠙⠒⠒⢲⡖⠒⠒⠒⠒⢲⡖⠒⠒⠒⠒⠒⠒⢶⠖⠒⠒⠒⠒⢶⠖⠒⠚⠃⠀⢸⣿⣿⣉⡾⠁
⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠘⠷⢦⣤⣤⡴⠞⠃⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠟⠛⠾⠃⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠶⠋⠷⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⠴⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠳⢦⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⣠⠖⠛⠋⠓⠦⠤⠒⠚⠙⡷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠤⣤⣤⠴⠖⠉⠁⠉⠙⠲⠖⠚⠉⠁⠀⠈⠓⠒⠚⠉⠀⠀⠀⠈⠙⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⢠⠇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣸⠀⠀⠀⠀⣰⠋⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡞⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠀⠈⠧⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⡼⠀⢻⠀⣀⣀⣯⣀⣀⣀⣠⠏⢀⡤⠖⣚⣩⢭⣝⣓⠲⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡀⠀⠀⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠓⠚⠁⣠⠞⣫⠟⠛⠓⠲⣄⠉⢙⡶⠋⣰⠋⠁⠀⠀⠀⠈⠳⡄⠈⠳⣤⠞⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⣧⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⠎⢹⣄⡞⠁⢸⠁⣠⣤⣶⡄⢘⣦⠏⠀⠰⡇⢀⣴⣿⣿⣿⠀⠀⡟⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠁⢰⠇⠀⡟⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⡼⣿⠀⠀⠘⢦⣿⠿⠛⣡⠞⡟⠀⠀⠀⠳⣌⠛⠛⠛⠁⢀⡼⠁⠀⠀⠀⢻⠀⠀⠀⠀⣼⠁⠀⡟⢀⡴⠃⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠀⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⡇⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠈⠓⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠲⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠤⠄⣾⠁⠀⠉⠙⠲⣄⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠈⠑⠤⠀⠀⠀⣿⠀⠀⠀⠀⠐⣇⣀⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠲⠤⣄⣠⣴⠛⢦⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠈⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢠⠖⣦⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⡟⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⣸⠃⢀⡏⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⢀⠠⢤⣀⠀⣀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠞⠁⣏⣠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡀⠀⠀⢀⠊⢁⠔⠉⠀⠀⣨⡀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡤⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠈⡶⠁⠠⠃⠀⠀⡠⠊⠀⢈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⢸⡄⠀⠀⠀⠠⡏⢀⡏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠙⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡼⠀⠀⡼⠀⠀⠀⠀⣠⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⢀⣨⢷⠀⠨⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⢸⠁⠀⠀⢀⡾⠁⠀⠀⢳⡀
⠀⠀⠀⠀⡤⠞⠉⠀⢸⠇⠀⢣⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⡆⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢀⡞⠀⣤⣀⠀⢸⠀⡠⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⢸⡆⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣼⢀⠔⠁⠈⢣⡼⠊⠀⢀⣬⡤⠤⣄⣀⠀⢀⣠⠴⠶⠤⣤⣀⣀⢀⣀⣠⠤⣄⣀⠀⢀⣀⣤⣄⡀⠀⣸⠃⠀⡏⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠸⠃⠀⠀⡠⠊⠀⢀⡴⠁⢠⣀⣀⡤⠬⠉⠉⠀⠀⢶⢦⡤⠤⠭⢭⣥⣄⣀⣀⣉⡭⠍⠁⠀⠀⣍⣛⣉⣙⣋⣻⣄⣐⠋⠉⢱⡤⠋
⠀⠰⠁⠀⠀⠀⠀⡠⠂⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠶⠸⡀⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠙⠻⠀⠀⢀⠁
⠀⠠⠀⠀⠠⠐⠈⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠰⠋⢠⢡⡅⢡⢁⠐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠢⡰⠡⠊⠀⢸⢡⡑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠤⠤⠀⠀⣤⡤⠶⠀⠀⢤⡤⠶⠖⠀⠂⠠⠶⠶⠒⠒⠀⠴⠶⠖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠐⠦⡀⠀⠀⡄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠒⠀⠰⣆⡀⠿⠀⢰⡇⠀⠀⠈⡷⠀⠼⠄⣠⡖⠈⠠⠀⠀⠂⠀⢀⠃⠠⠄⠉⢲⡄
⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠁⡴⠉⠀⠀⠀⠀⠀⠑⠄⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠈⠢⡌⢳⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠀⠀⠀⡔⣭⣅⠆⠀⠀⣴⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⣸⠆
⠀⠀⠀⠀⢠⡟⢐⡧⠐⢄⠀⠀⠀⠀⠈⠇⠀⠀⢀⠀⠀⠀⠂⠻⠯⠂⠀⡀⠉⠛⠃⠀⠀⡀⡀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⢁⡀⢈⠷⠆⢘⠀⠀⠀⠀⢀⡄⠀⠀⣄⠀⠀⠀⠠⢀⣀⣤⠊⠉⠂⢀⢀⡔⠋⠁⠀⠙⠂⠀⠀⠀⠅⠀⢈⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠳⠌⣀⠠⠋⠀⠀⠀⠀⠈⣧⠀⠀⠈⠙⠓⠤⢤⠤⠤⠀⠀⠀⠀⠀⠀⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠤⡈⠢⠂⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠀⠹⠀⢀⣀⠀⠀⠚⢳⠖⠀⣤⣤⠀⠀⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠌⠇⠀⡅⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀⠀⢀⠀⢆⠀⠐⠀⠀⠘⠀⠠⣿⣿⣤⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠐⠀⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠳⠤⠾⡉⠻⠆⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⡿⠟⠛⡟⠀⢀⡀⠀⠀⠀⠂⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⢶⠃⠀⣈⠀⠀⠀⠆⠀⠀⠀⠀⠘⠿⢥⣤⡤⠤⠶⠊⠁⡠⠀⠁⠀⠀⠀⠀⠖⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣄⢀⠀⠀⠀⠀⠀⡀⠐⠒⠂⠒⠒⡒⠚⠉⠀⠀⠀⠂⠀⠀⠀⣀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠉⠀⠉⠉⠫⠉⠉⠛⣉⡸⠋⠍⣉⠩⠝⠋⠉⠉⠉⠙⠁⠀⠈⢲⠐⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⠀⣤⣤⣼⠃⠘⣦⣤⣤⠀⢠⣤⣤⣤⠀⠚⠠⡶⠿⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣛⠛⠛⠛⢳⠖⠒⠐⠒⠒⢶⠖⠲⠖⠲⠖⢾⠋⡝⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠉⠁⠀⠀⠀⠀⠀⠈⠑⠀⣶⠴⠖⠉⠀⠥⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠘⠀⠀⠀⠀⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣧⠀⠀⠀⠀⠀⠀⠀⢀⣆⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠉⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠠⣀⢠⡀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠈⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢐⡭⠄⡷⢑⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡒⠈⠤⠚⠂⠢⡀⡄⠈⡤⡌⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡱⣍⠀⠠⡀⡈⠃⠀⠄⠜⣠⠅⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠀⠱⣌⠰⣤⣤⣥⠀⣶⣭⡀⠰⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢝⠠⣬⡢⡈⠻⣿⠿⠿⠛⠇⠘⠿⠘
⠀⠀⠀⠀⠀⠀⠶⠖⠀⠶⠆⠶⠆⠰⠆⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⠑⠈⢄⠡⡾⢂⠁⢒⣚⣥⢶⣾⣥⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠈⠁⠀⠛⠠⠘⠐⣚⣻⣷⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⣀⠻⢿⣿⣿⠟⠋⣉⡀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⢼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⢆⡨⠏⠉⠀⢸⡏⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠻⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣴⣶⣶⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣉⠛⢉⡉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡛⣠⣌⣵⣿⣿⠀⠀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⣾⠁
⠀⠀⠀⠀⠀⣘⣶⣧⡀⠀⢿⣿⣿⣿⣿⡿⢿⢻⣿⣿⠡⠴⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡽⠋
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠳⠎⢻⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⠛⣛⣻⣿⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠻⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⡏⠁⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡀⠀⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢰⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀⡠⠤⠤⠤⠤⠒⠒⠀⠒⠒⠐⠒⠒⠉⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠁⠀⠀⣀⣀⣄⣀⠀⠀⢠⣀⣠⣀⡄⠀⠀⠀⠀⢠⠃⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢀⡔⠉⠀⠀⠀⠑⡴⠋⠀⠀⠀⠉⢢⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢱⡌⢰⠁⠀⠈⣤⢑⠀⠀⡇⠀⠀⡎⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣎⠉⠒⢄⡀⠈⠈⣆⠀⠀⠀⠀⠄⠐⠇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠓⣤⣀⣉⠒⠊⠀⠑⠢⠤⢔⡠⠖⠀⠁⢰⠃⠀⠀⠀⢀⠎
⠀⢀⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠓⠤⠤⢬⢤⠤⠤⡖⠊⠁⠐⠀⠀⠀⢸⠀⠀⠀⠀⠘
⠐⢅⣀⠀⠔⠀⠀⠀⠁⠀⠐⠐⡌⠐⢳⠀⠀⠀⠀⠓⠖⠚⠘⠀⠐⠃⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡜
⢠⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⢼⠀⠀⠀⠀⠀⢀⠀⠂⠰⠊⠀⠘⠀⠀⠀⠀⠀⡇⠀⠠⠂⠈⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⢠⡄⢰⠠⠒⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠑⠊⢉⠑⡒⡲⠒⠒⠤⠤⠤⠔⠢⠤⠗⠒⠒⠊⠛⠂⡡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⠦⠠⠤⣴⠁⢱⣬⣀⠀⢀⣀⣀⠀⠠⠀⣠⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⡤⢀⣀⣑⣀⣀⣀⡀⠈⠉⠉⠀⠀⠀⢉⣁⡠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⡀⠈⠀⠀⠀⠈⢍⠉⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⡇⠀⠀⢀⣠⣄⣠⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠉⠁⠀⠀⢸⣿⣽⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⣀⡀⠤⣤⣄⣀⡀⠠⠤⣤⣀⣀⠀⢀⣀⣀⣀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⡀⢀⠹⡄
⠀⠀⠀⣠⠔⠁⣀⠀⡄⠀⠀⡂⠀⠀⡽⢠⡄⠀⢰⡆⠀⡶⠀⠀⠀⢴⡀⠀⣶⠀⢠⡄⠀⠄⠈⢠⡇
⠀⠀⣰⠃⠀⠀⠀⠀⠘⡄⠀⠈⡠⡁⠀⡠⠛⠉⠉⠉⠉⠙⢦⡀⡠⠊⠉⠁⠉⠀⠛⠀⠀⠀⠀⠸
⠀⡞⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠠⠄⠠⡀⢹⠀⢀⠄⠠⡀⠀⠀⠈⠆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡽
⠀⢳⡄⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⠇⢠⠀⡅⢿⡿⢈⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⢀⣎⣴⡋
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⠢⠐⠢⣄⠈⠐⠂⡠⠲⣀⠈⠑⠂⢁⡀⠀⠐⠃⡀⠀⢸⠀⠀⠀⠀⠀⡜⢁⢈⡷⠒⠓
⠀⠀⠘⢧⠀⢀⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⢤⠀⠀⠗⠐⠉⠀⠀⠀⠓⠒⠈⠀⢀⣀⡤⠞⠁⠀⢸⠆⠀⠀⠀⠀⠣⡀⠈⠱⢂⠜
⠀⠀⠀⠀⢱⠀⠉⢠⠋⠑⡄⠀⠀⠀⠀⠀⢸⣷⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⣫⣍⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡏⡴⠒⠁
⠀⠀⠀⠀⠸⡀⠀⠈⡄⠠⠁⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠉⠉⣿⡏⠁⠈⡇⠀⠀⡠⠀⠠⠀⠇⠀⠀⠀⠀⢀⡞⣰⠁
⠀⠀⠀⠀⠀⠈⡆⠀⠈⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠅⠀⠐⠀⣄⡠⢄⠀⢀⠞⣰⠃
⠀⠀⠀⠀⠀⠀⢹⠤⣄⠂⠀⠈⡄⠠⠖⠀⠈⢯⡉⠉⠛⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠸⠁⢰⣚⣚⣩⠼⠁
⠀⠀⠀⠀⠀⢀⡇⠀⠈⠁⠀⠀⠇⢀⠂⠁⠆⠠⣌⣙⣓⣒⡒⢚⣉⡀⠀⠀⠀⠀⠘⠒⠁⠀⣠⢤⣬⠝⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⡷⠤⠀⢄⣀⠤⠥⣄⣀⡠⠤⠤⢤⣀⣁⣀⣠⠤⠤⣄⡀⠤⠤⠤⣴⠋
⠀⠀⠀⠀⠀⠀⠈⡏⢯⢀⠀⣀⢀⡀⠀⠀⠀⠉⠒⠲⠠⠂⢉⡦⢞⣈⠒⠖⠉⢀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠘⠛⠇⠈⠁⠰⠶⠶⠶⠀⠰⠶⠶⢾⠀⢈⠷⠶⠶⠀⠶⠶⠶⠆⡇
⠀⠀⠀⠀⠀⠀⠀⡁⠘⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⢀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠸⡄⢹⡉⠉⠉⠙⠉⢹⠏⠉⠉⠉⠉⠻⢍⣉⣉⡉⠽⠁⠀⠈
⠀⠀⠀⠀⠀⠀⢸⣠⠘⡃⠉⠀⠈⢹⢳⡖⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣸⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣦⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡉⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣢⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⠃⡠⠤⣕⠒⢄⡀⠀⠀⠀⠀⢣⠋⠉⠮⣒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠰⠁⡀⠄⠳⠀⠹⡆⠀⠀⠀⠘⡎⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠻⢄⣀⡠⠓⠚⠃⡄⠀⠀⠰⢸⠁⡰⠉⣑⠦⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣶⣤⣤⣤⣤⣶⠟⠁⡀⠀⡄⠏⢞⡡⠒⠉⠘⢥⢂⣰⢀⡍⠉⠙⢒⣒⠢⠤⢄⠀⠀⠀⠀⢀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢿⡿⠿⠿⠛⢒⡞⢹⣠⢽⢋⢎⠀⢰⣶⣆⠈⢁⡀⠀⠘⡇⠀⠧⠔⡠⣂⠹⡄⠀⠀⠀⡸⠘⠊⠔⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠀⠀⠀⠀⠑⠲⠶⠒⠁⠀⠘⣧⡞⠸⣄⠀⢄⣁⡅⠀⠿⠿⠀⡠⠁⠀⡔⠉⠰⠇⠇⣧⠠⠀⠨⠑⠊⠀⢛⠚
⠀⠀⠀⠀⠠⠤⠀⠀⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⡀⢫⢕⣒⡀⠑⠠⠤⣀⠘⡅⡠⠊⢐⣋⡠⢔⠋⠀⠂
⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠃⠃⢸⣶⣯⣉⣿⣿⡿⠃⢀⠜⢀⡔⠉⠯⢶⠁⠈
⠈⠳⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢰⣿⠟⠛⠛⣻⢟⡀⢀⢡⠒⠘⢢⠴⠒⠁
⠀⠀⠀⠀⠀⠈⠉⢹⠁⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢑⡈⠥⠭⠭⠀⠦⢀⠏⢨⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣄⠠⢬⣈⡽⡙⠓⠒⠒⠲⠼⠂⠄⢠⠃
⠀⠀⠀⠀⠀⢠⠛⢋⡒⠀⠀⠀⠢⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠾⡤⠉⣤⣛⡃⠘⠓⠂⡇⠶⠚⡙
⠀⢠⠂⠀⠒⠚⡄⠀⡈⠁⠀⠀⠀⠀⠁⠀⠠⣖⠀⢀⡴⠖⠛⢚⠉⠙⣠⢷⣀⣠⡏⠉⢉⣿⠈⠁⢻⠉⠁⢀
⠀⠈⠢⣀⠀⠀⠘⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⣈⣥⠾⠃⠀⠈⠱⡕⢤⣾⣿⣷⣯⢣⠀⣼⣿⣿
⠀⠀⠀⠈⠙⠲⠦⠤⠵⠦⠤⠖⢛⡶⠤⠤⣄⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣿⣿⠃⠱⠽⠚⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠈⠙⣲⣶⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣤⣤⡴⠞⠋

⠀⠀⠀⠀⠀⢀⡤⢤⣀⣠⡤⠶⠶⠦⣤⣤⠤⠴⠶⠦⣄⣀⣀⣀⣤⣤⣀⠀⠀⢀⣤⢤⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠙⠛⠁⠀⠀⠈⠙⠋⠉⠉⣧
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣩⡕⢆⠀⠂⢀⠖⣀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡤⠤⠤⡀⠀⠀⠀⠣⠌⠥⠂⡠⠀⠘⢄⣛⡡⠁⠀⠀⠀⣠⣀⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⠀⠰⡀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⠆⢧
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠄⠀⠀⠀⠀⠀⠁⠂⠠⠄⡀⢀⣀⣀⣀⡀⡤⠄⠐⠈⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠆⠘⢄⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⡃⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣽⡋⠉⠉⠉⠛⠉⠙⠦⣌⣙⢖⢒⣏⣉⡶⠖⠒⠒⠋⠓⠒⢾⣡⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡇⢀⣐⣒⡒⠒⣒⣒⣒⠲⡎⠙⡆⣥⣤⣤⠤⢤⣤⣤⠤⡞⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠈⠋⠉⠁⠈⠙⠛⠛⠙⢄⡴⠋⠉⠉⠉⠀⠉⠉⠙⢁⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣻⡖⠒⢶⡦⠤⠤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠼⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⢳⣇⠀⠀⠉⢹⠉⡏⠀⠀⠀⠀⢀⡏⣹⠉⠁⠀⣸⡄⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣫⡻⠁⠀⠀⠈⡧⢽⠀⠀⠀⠀⢸⠒⡇⠀⠀⠀⣗⠝⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⡇⠸⡆⠀⠀⠀⢸⠀⡇⠀⢀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⣿⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠿⠿⠂⠀⠀⠀⠈⠛⠋⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠠⠤⢀⣀⣀⣤⠤⠄⠀⣀⣀⡤⠴⠦⠀⠤⠤⠤⠤⠶⠦⠤⠄⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄⠀⠀⠀⢀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠠⠤⠀⢠⡀⠀⢸⡆⠀⢠⡆⠀⠀⠀⢶⡄⠀⣾⠀⠀⣠⠄⠻⡀⠀⠀⡇⠀⠀⠸⠀⢀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⢀⠿⠂⠈⠁⠀⠙⠢⠄⠀⡠⠚⠉⠀⠉⠁⠘⠫⡀⠀⠁⠀⠀⠀⠀⢠⠃⠀⠈⠑⠀⠀⢃
⠀⠀⠀⠀⢞⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡟⠀⣀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⣆
⠀⠀⠀⠀⠈⠳⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠰⢱⣶⣮⠃⠀⠁⢸⣷⣶⡄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⡆⠀⠀⠀⠊⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣰⠏⣘⡷⠐⠢⡄⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⡀⠀⠀⠘⠬⠻⠥⠃⠀⣃⠀⠝⠋⠄⠀⠀⣀⣀⣀⡈⠀⠀⠀⠀⡜⠁⠀⠀⡀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⢇⠀⠈⡷⠴⠀⡓⠀⠀⠀⠀⠀⡌⠀⠀⢸⡀⠀⠀⠁⠠⠄⣀⣀⣠⠎⠀⠑⠄⣀⢀⡔⠋⠀⠀⠀⠳⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⢦⡉⢀⠀⡔⠁⠀⠀⠀⠀⠀⢷⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠑⠤⠂⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢱⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠠⠦⣅⠀⠀⣀⣀⠀⠀⢀⣤⣤⣴⣾⣿⡇⠀⠀⠀⠀⠀⡀⡆⠀⢘⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀⠀⠀⠀⠀⢀⠁⢀⠀⠐⢠⠀⠀⠀⣯⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡁⠀⠀⠸⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢻⣄⠀⢀⣤⣼⣄⠈⠂⢀⡤⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⣓⠛⢶⠀⠙⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠋⠉⢉⡿⠀⠀⠶⡀⠀⠀⠀⡈⢀⣀⢤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣁⣀⣀⡆⠀⠐⠤⠃⠀⠀⠀⠀⠀⠈⠛⠢⠶⠶⠖⠚⠛⣉⠀⢠⠒⠀⡀⠀⠀⠀⠀⢛⠁⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⣀⣀⡀⠀⠀⠀⣀⢀⡀⠈⠉⠃⠈⢉⢛⡉⡛⠁⠀⠀⠐⠐⢃⠀⠀⠀⢀⡌⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠉⠉⠛⠍⠉⠝⠛⣉⣠⠟⠉⢉⡉⠩⠝⠛⠉⠉⠉⠉⡋⠁⠀⠈⠑⡆⢴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⣀⣀⣀⡀⢀⣀⣀⣰⠏⠙⣦⣀⣈⣁⠀⢀⣀⣀⣀⡀⠀⡷⢀⣴⣶⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠁⠈⠉⠉⠛⢄⣠⠞⠛⠛⠋⠀⠈⠛⠛⠛⠋⠀⠂⠀⠁⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⢶⠟⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣤⢠⡤⠋⠀⠀⠀⠈⠈⠹⣅⡈⠉⠉⠉⣁⡽⢀⠞⢀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⢻⠀⠀⠀⠈⠻⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣼⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀⣤⠴⠶⢦⣄⣀⣀⣤⡤⠶⠦⣤⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠈⠙⠲⠶⠚⠉⠀⠈⠙⠲⠖⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⣭⠑⡄⠀⠂⠀⡔⢋⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣀⢤⣤⡀⠀⠀⠀⠀⠣⣈⣛⡠⠃⡠⠤⡀⢇⠘⠛⣠⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠞⠀⢀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠊⠈⠉⠱⡄⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⠌⠁⠰⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⡤⢤⠤⠤⢰⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠠⠃⠐⠦⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢲⠤⠤⠶⠲⠦⠤⠴⢶⣚⠛⠲⢤⣄⣠⡴⠶⢤⣄⣀⣀⣠⠤⠤⣄⣀⣠⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠊⡳⢴⡟⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⣼⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡏⢉⣭⣭⣭⠉⠉⣭⣭⣭⣭⢹⠃⠀⢯⣹⣿⣿⣿⠛⣻⣿⣭⣭⠙⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠀⠉⠉⠉⠀⠀⠉⠉⠉⠁⠙⢦⡴⠋⠀⠀⠈⠀⠀⠈⠉⠉⠉⢸⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢙⣟⠓⠲⢶⠶⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⣿⠀⠀⠈⠉⢻⡏⢿⠉⠀⠀⠀⠀⠀⢹⠋⣹⠛⠉⠀⠀⣇⠂⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⢾⢻⡗⠀⠀⠀⠀⣇⢘⡆⠀⠀⠀⠀⠀⣯⣠⡇⠀⠀⠀⢼⡑⡶⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠛⠁⠀⠀⠀⠀⡏⠁⢷⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠀⠘⠾⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣇⠀⢸⠀⠀⠀⠀⢠⡇⣸⣧⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠻⠿⠛⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠉⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⡁⠠⠂⠀⠀⠙⢤⣀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢊⡡⠖⠒⠓⠲⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠞⡱⠋⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡠⢊⠞⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⣄⣠⠃⠀⣀⡀⢀⡠⠤⠤⢴⣁⡤⠤⠤⣄⠀⠀⠀⠈⠀⠈⠑⠆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⣠⡤⠷⠤⢤⡤⠒⠋⠉⠉⡉⠛⠀⠈⠁⢄⡰⠴⠀⠀⠀⠠⠐⠈⣧⠀⠀⠀⠀⠀⡀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⣞⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠁⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠏⠑⠠⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣶⠄⠀⠀⠀⠛⠦⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠄⠙⡀⠀⠐⠁⠀⠀⠤⠤⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⡠⠀⠀⢀⠆⠀⠀⠀⠈⠀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠂⠈⠲⢄⡀⠀⠀⠁⡄⠃⢹⠀⠀⠀⠀⠀⠁⠒⠈⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⢹⣀⠔⠁
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠀⠀⠄⠈⠢⠀⠐⠆⠒⠋⠀⠀⣈⣀⣀⣀⣀⣠⡤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠈⠛⠲⠦⡀⠁⠊⠀⠀⠀⠀⠀⠆⠀⠈⠄⠀⠀⠀⠀⠀⠉⠀⠈⡄⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⣠⠶⠚⠋⠈⠀⠀⢁⡀⠲⠆⠘⠛⢈⠂⡈⢆⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⢰⠁⠀⠀⠀⠀⠀⡴⠋⠀⠐⠂⠀⠀⠀⠑⢦⠀⢡⠀⠘⢿⣿⣷⣄⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡿
⠀⠸⠀⠀⠀⠑⢠⠌⠀⠤⠌⠁⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢷
⠀⠀⢣⠀⠀⠀⠺⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠙⢇⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠑⢄⡠⠈⡀⠂⠄⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠘⠆⠁⠔⠀⠀⠑⠢⣄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠦⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⢛⣋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢰⠈⠑⠀⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠒⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠐⠀⠀⢀⠝⠒⣈⠓⠤⣀⢠⠀⠀⡈⠠⠄⠐⠂⠀⠢⢀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠉⠒⠠⢈⡉⠠⠀⠀⠀⠀⠀⠈⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣀⣠⠤⠔⢚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⠢⣄⣀⣀⣠⠤⠴⠒⠋⠉⢁⣴⣦⠀⠈⢐⠄⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⣿⠀⠀⢄⠀⠀⠀⠉⠀⠄⠀⠀⠀⢀⣴⡟⠛⣍⡀⠠⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡀⡅⠀⠀⠀⠓⡶⠀⠀⠚⠀⠀⠀⠀⠘⠿⠃⠀⠰⠽⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠉⠤⠊

⠀⠀⠀⠀⠀⠀⣴⠖⠲⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣼⠋⡆⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠦⣤⣤⣤⣀⣀
⠀⠀⠀⣠⠞⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⠀⡀⠈⠙⠒⠶⠖⠒⠤⣄⣀⡀
⠀⠀⣴⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠓⢇⠀⠀⠀⣶⠀⣇⢀⡄⠉⠉⠉⠛⠲⡄
⠀⡴⠃⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠳⣠⠊⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⣿
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢠⠀⢠⢁⣶⣦⠱⠀⠀⢃⠀⠠⢂⡐⢤⠀⠘⡀⠀⠀⠀⣿
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠄⠴⢤⡈⢄⠛⠋⠔⠀⠀⢸⠀⠀⢿⣿⠀⠀⠀⣠⣀⠀⠀⠸⡆
⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢳⠀⡴⠁⠃⠤⠁⡹⠀⠀⠀⠀⠀⢀⢦⠀⠐⠠⠄⢈⡴⠋⠀⠈⡇⠀⢰⡇
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠃⢧⣀⠀⢻⣄⠙⠢⢄⣀⣀⠴⠊⠀⠣⣀⡠⠞⠁⠀⠀⣀⡴⠋⠲⣼⡇
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⣇⠑⠦⣀⠀⠀⠀⠀⠀⠈⠀⣀⣠⡤⠶⠚⠋⢠⡔⠐⣈⢷
⠀⠀⠀⠈⣧⠀⣠⣄⣀⠀⠀⢳⡀⠀⢀⣠⣼⡀⠀⠈⠙⠲⣤⣄⣀⡀⠀⠀⢀⣀⣀⡤⠖⡛⠀⠔⠃⣼
⠀⠀⠀⠀⢻⠸⠁⠀⠉⠳⣄⠀⠁⢸⠹⠂⠈⠛⣆⠀⠀⠀⣟⡀⠈⢿⢙⡏⠉⢹⠁⠀⠀⠆⠀⠀⢰⡏
⠀⠀⠀⠀⠘⣇⢣⠀⣠⢴⡈⣷⡀⠈⢦⡀⠀⠀⢩⣷⣿⣷⠈⢉⣙⡛⠈⠳⠦⠼⠀⠀⡼⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢹⠈⢦⣙⣆⠹⣅⢃⣠⠞⢁⡴⠋⠙⣿⣿⣿⣄⣸⣿⣿⡄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⡈⠋⣡⠔⠋⠀⠀⠀⠘⢿⠿⢿⣿⣿⣿⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠀⠀⠙⢦⣀⡴⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢀⡴⠾⠦⠶⠶⢦⣤⣀⣀⣀⣀⠀⠉⠛⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⣇⡠⠔⠋⠀⢀⡀⠀⠀⠀⠈⠉⠻⣍⠉⢙⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⡀⠔⢘⠉⢁⣐⡂⠀⠀⠤⠈⣙⡋⠀⢳⣤⣴⠛⢯⣹⣿⠿⠷⣦⣀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⡧⠔⣩⣴⡾⢨⠀⠘⠛⠛⠿⠷⠀⣶⣦⣤⡽⠋⠀⢻⡤⠄⢀⣀⠀⠀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠘⠋⠁⣠⠼⠢⠤⠄⣀⣀⠀⠀⠀⠀⠈⢳⡀⢀⡼⠿⠿⣆⡴⣮⣭⣍⠷⠾⠓⢄
⠀⠀⠀⠀⠀⠀⢸⡇⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠤⠽⣯⣄⣠⠞⠁⡶⢚⣩⠴⠒⢺⡆⣼
⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⢶⡴⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠙⢋⡽⠦⣤⣼⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡋⠀⠀⠀⢀⡞⠉⠙⠛⠒⠶⠶⢤⣤⣄⣀⣀⠀⠶⠒⠛⣩⡴⠚⠁⡏⣸⠁⣠⡶⣦
⠀⠀⠀⢀⣀⣾⣿⣇⠀⢈⡿⢦⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠋⠁⠀⠀⢰⣥⣯⣸⣿⠷⠻
⠀⢀⣾⠿⡿⢿⢉⠃⣠⠏⡴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⣠⠞
⠀⠈⢿⡾⠃⠸⠓⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠃⣽⠊
⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠂⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣁⣤⣿⡿⠟⢿⠿⣷⣶⣆⣀⣀⣰⣦⣶⢦⣾⣤⡄⡀⠀⡆⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣿⡛⣤⣴⣶⣷⣾⣿⣿⣿⠿⢛⣉⣤⣴⡀⠈⢽⣿⣷⡀⠻⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠥⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⡀⠐⣿⣿⣧⠀⡁⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⡗⠛⡿⢿⣿⣿⣿⡿⣻⡟⠀⢿⣿⣿⣿⣻⣿⠃⢠⣿⣿⣿⢠⡋⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢹⡶⣴⣻⣻⣏⣿⣿⣿⣷⣄⣴⣿⢻⠟⠛⠁⣤⣾⣿⣿⡏⠀⠿⠀⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣠⡿⣹⡿⣿⣿⡿⠟⣿⣿⣿⣿⣷⣴⣤⠚⠋⠙⠉⠛⡀⠀⠀⢠⣿⣿⣿⣗⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣋⡽⠿⠳⣿⠴⣿⠺⠇⠀⠼⣿⣿⣿⣿⣿⣷⢀⣠⡄⠀⢀⡄⠀⣠⡾⣿⣿⣿⢹⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠛⢌⠉⠛⣉⣥⣶⣿⡟⠀⠰⠋⠀⣼⣧⣟⣿⣿⣃⣸⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠐⣢⣤⠀⠐⣿⣿⣷⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣻⡍⢿⠞⠛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣇⠚⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⠇⣠⣤⡀⠀⣰⣿⡴⠳⣾⡿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠻⠿⡿⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠋⠃⠈⢻⣿⣿⣯⣿⢿⣇⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⣶⡄⠡⢾⣿⣿⣿⣿⢿⣿⡿⠿⢋⣻⡿⠋⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⢟⣻⠈⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⣸⣿⣿⠏⠀⠀⡿⢿⣿⣷⣿⣿⣴⣷⡾⠋⠀⠀⢠⣿⣿⣿⡆⠀⣠⣿⣿⣿⠃⠀⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣇⣀⣼⣟⢁⡀⠹⢿⣦⣄⣈⡉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡿⡋⠓⢼⣿⣿⣿⡇⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠙⢟⠿⢿⣿⡿⢶⣾⣿⣿⣿⣟⡿⢶⠖⠒⠀⠀⠀⠀⢻⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣉⣼⣏⡹⡿⠻⠻⣿⣿⣿⠿⣏⠙⣿⣷⣦⣤⣾⣿⣦⣀⡀⣸⣿⣿⣿⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣧⣤⣌⣉⣋⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣏⢉⣿⠏⢸⡟⠻⣿⣿⣿⣿⢿⣿⣿⠉⢛⣿⣿⣷⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⢿⡷⣾⣧⣤⣹⣿⣿⠛⣮⠀⠀⠀⠀⠉⠉⠛⠻⠟⠇⠐⣿⣿⣽⣿⣿⣿⣿⣿⣿⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡇⠘⢻⢸⠃⢐⠿⣿⣟⠭⠿⣿⣷⣶⣶⣴⣄⣀⠀⡤⠁⠀⠀⢾⣿⢹⣿⣭⣿⣿⣿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⠇⢩⡀⠀⢋⣿⣿⠛⠉⠛⣿⣻⠛⢿⣷⣶⡶⢿⣾⣿⣿⢿⣿⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⡇⠐⣦⣄⠀⠟⣴⠉⢹⢁⠇⠘⣻⣏⠀⠚⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⢀⣿⠀⠀⠀⠹⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠤⠤⠄⠤⠔⠒⠤⠐⠒⠒⠒⠒⠂⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠉⠀⠀⢀⣀⣄⣀⡀⠀⠠⣀⣠⣀⡀⠀⠀⠀⠀⢠⠃⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠋⠀⠀⠀⠉⡢⠊⠀⠀⠀⠈⠢⡀⠀⠀⢨⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠁⠀⠀⠠⡆⠀⡃⠀⠀⢴⢄⠀⠀⡇⠀⠀⡎⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⡉⠑⠢⣀⠀⠀⣣⡀⠀⠀⠀⠄⠐⠣⡀⠀⡁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⣲⠤⣀⣉⣊⠀⠉⠒⠒⢒⡠⠖⠀⠀⢰⠁⠀⠀⠀⢠⠃
⠀⠀⢀⡔⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢲⠒⠢⢤⠄⠐⡖⠉⠁⠐⠀⠀⠀⢸⠀⠀⠀⠀⢈
⠀⠀⡒⠤⡄⡐⠀⠀⠀⠀⠈⠀⢀⡃⠈⠘⠀⠀⠀⠀⠈⠒⠘⠉⠀⠀⠃⠀⡐⠀⠀⠀⠀⡜⠀⠀⠀⠀⣎
⠀⠀⠄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀⠀⣀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁⣰⠄⠨⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠠⠈⡉⡙⠋⠉⠑⠒⠒⠂⠁⠒⠋⠉⠉⠁⠉⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠛⠛⠀⠒⠶⠅⢈⠶⠦⠀⠠⣤⣤⠀⠐⠀⡴⡇⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠖⠒⠂⠠⠥⠤⠤⠤⠀⣀⠀⣀⣀⣀⡤⠤⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⡀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣶⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠟⠿⠟⠀⠀⢠⣶⢶⣴⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡤⠤⠰⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠖⠋⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢃⠃⠀⠀⠀⠀⢀⡤⠴⠖⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠙⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⡆⠀⡀⢀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⢹⡆⠘⠀⠁⠀⠀⢀⡴⠀⡀⠀⠀⢀⠤⠛⠦⣄⣀⠀⠀⠀⠀⠁⠊⠀⠀⢀⡇⠀⠀⠀⢁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠀⠀⠀⠀⠀⠀⢠⡇⠈⢒⣁⣠⠶⠋⠀⠀⠀⠑⡖⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡋⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⡄⠀⣁⠄⠰⠁⠀⠀⢀⠀⡰⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠸⣧⠀⢼⣁⣀⣤⣤⣤⣤⣶⠿⠖⠒⠒⠛⠛⠛⠻⣿⡿⢻⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⢀⣽⠄⣈⡏⠀⠀⠀⢦⣙⣃⠾⡀⠀⠀⠀⠀⠀⠑⠤⠔⡫⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡤⠄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣀⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⡹⢄⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠆⠰⠀⣸⠇
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠳⢤⡀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠈⠑⠂⠴⠊⠁⠀⠉⠒⠒⠒⠚⠁⠀⠀⠀⠀⢀⠁⠠⠈⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠠⠚⠢⠠⢍⠲⣄⠀⠀⢸⡇⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠃⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⠀⡀⢀⠀⠱⣸⠃⠀⠀⢿⠀⠀⠀⠀⠈⠉⠛⢓⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢁⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⢀⡤⠴⢧⡀⠀⠈⠀⢈⡀⠀⠘⡀⢀⡍⠀⠀⠀⡈⠀⠀⠀⠀⠶⢶⠓⠧⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠂⠄⠂⠀⠀⠀⢀⠃
⠀⢸⡧⠦⢴⡇⠀⡆⠐⠂⣵⡀⣀⣴⠏⠀⠀⡶⠈⠃⡀⠀⢀⡤⡦⠈⠀⠠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢸⠆
⠀⢿⣀⡄⢤⠃⠀⡇⠀⠀⠈⠙⠉⡟⠀⠀⠀⢣⡀⠀⠀⠀⠁⠀⢘⠀⠀⠀⢸⠶⡀⠀⠀⠘⠛⠂⠀⠀⠀⢀⣠⡴⠖⠒⠲⣄⠀⠀⠐⠔⠀⡼
⠀⠸⣅⣤⠴⠃⠀⣅⠒⠉⠁⠒⢤⡇⠀⠀⠀⠀⡇⢠⢳⠀⠀⠀⣌⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸⠃
⠀⠀⠉⡇⠀⠀⠀⠸⡀⠐⠀⠀⠀⢱⠀⠀⠀⢰⡇⠘⠋⣼⠖⠋⢻⡀⠀⠀⠐⣍⠙⠲⣄⠀⠀⠀⠀⢸⣀⡶⣄⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⢀⠄⠑⢤⣀⠀⢀⣸⠀⠀⠀⠛⠷⣶⠞⠁⠀⠀⠀⠙⠛⠲⣄⠈⠢⣀⠀⠀⠀⠀⣀⡼⠋⣠⠼⠂⢀⡜⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠉⠉⠙⡍⠲⢄⡤⠦⠀⢸⡷⠶⠶⣤⣤⡴⠶⣦⢬⣷⣄⡈⠳⢖⡲⠟⢁⡤⠞⠙⠢⠴⠛⠛⠛⠒⠊⠙⠛⢿
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢈⡏⠲⢄⡤⠞⠧⢼⣇⣀⡀⠀⠉⠒⠖⠁⠒⢮⠙⠿⢦⡀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⢴⣤⣤⡈⢩⣍⣽⠀⠈⣷⡒⠒⠘⠂⠀⠠⠤⠤⠤⠠⣤⠄⠀⣒⣀⣨⣭⠁⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠈⠉⠛⢆⢠⠛⠛⠛⠀⠀⠿⠿⠶⠶⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⢶⡶⠶⢶⣤⣧⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⡻⠛⠛⠛⠶⠿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠃⣤⠀⢰⠇⠀⠀⠀⠀⢰⡁⢠⣄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠰⠷⠶⠋⠀⠀⠀⠀⠀⠀⢹⠏⢠⣟⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⡶⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⡋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠚⠱⡀⠀⠀⠀⠀⠀⠀⠀⢦⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣷⡀⣨⣿⣆⠀⠀⠀⠀⠀⠈⢷⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣤⣀⣼⣿⣶⣿⣿⡆
⠀⠀⠀⠂⠐⠂⠀⠀⡌⣙⣃⣎⣁⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⠿⠻⠽⠟⠋⠀⢰⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣶⠾⣿⡟⣿⣹⣩⣥⣷⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠉⠉⠉
⠀⠀⠀⠉⠛⠛⠛⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⢀⠘⠂⠘⠀⢤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠂
⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⠀⠈⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠂
⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠤⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑⡢⠤⣄⡀⢀⣀⣤⣤⣾⡏⠀⠀⠀⣀⡀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢑⣤⣿⣤⣤⣿⣿⣿⡟⠀⠀⠀⠀⠻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⢿⠉⠉⠛⠉⡙⠋⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣀⠀⠀⢀⠥⠀⠀⠐⠀⠀⠀⠀⠀⠰⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣉⠀⠙⠋⠀⠱⠶⠄⢠⣄⡀⣠⣀⣘⢨⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣉⡲⠒⠢⠤⢤⣀⣀⣀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠨⠄⠀⡼⠉⠉⠉⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⣠⠖⠛⠋⠓⠦⠤⠒⠚⠙⡷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠤⣤⣤⠴⠖⠉⠁⠉⠙⠲⠖⠚⠉⠁⠀⠈⠓⠒⠚⠉⠀⠀⠀⠈⠙⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⢠⠇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣸⠀⠀⠀⠀⣰⠋⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡞⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠀⠈⠧⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⡼⠀⢻⠀⣀⣀⣯⣀⣀⣀⣠⠏⢀⡤⠖⣚⣩⢭⣝⣓⠲⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡀⠀⠀⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠓⠚⠁⣠⠞⣫⠟⠛⠓⠲⣄⠉⢙⡶⠋⣰⠋⠁⠀⠀⠀⠈⠳⡄⠈⠳⣤⠞⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⣧⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⠎⢹⣄⡞⠁⢸⠁⣠⣤⣶⡄⢘⣦⠏⠀⠰⡇⢀⣴⣿⣿⣿⠀⠀⡟⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠁⢰⠇⠀⡟⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⡼⣿⠀⠀⠘⢦⣿⠿⠛⣡⠞⡟⠀⠀⠀⠳⣌⠛⠛⠛⠁⢀⡼⠁⠀⠀⠀⢻⠀⠀⠀⠀⣼⠁⠀⡟⢀⡴⠃⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠀⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⡇⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠈⠓⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠲⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠤⠄⣾⠁⠀⠉⠙⠲⣄⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠈⠑⠤⠀⠀⠀⣿⠀⠀⠀⠀⠐⣇⣀⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠲⠤⣄⣠⣴⠛⢦⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠈⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢠⠖⣦⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⡟⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⣸⠃⢀⡏⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⢀⠠⢤⣀⠀⣀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠞⠁⣏⣠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡀⠀⠀⢀⠊⢁⠔⠉⠀⠀⣨⡀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡤⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠈⡶⠁⠠⠃⠀⠀⡠⠊⠀⢈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⢸⡄⠀⠀⠀⠠⡏⢀⡏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠙⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡼⠀⠀⡼⠀⠀⠀⠀⣠⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⢀⣨⢷⠀⠨⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⢸⠁⠀⠀⢀⡾⠁⠀⠀⢳⡀
⠀⠀⠀⠀⡤⠞⠉⠀⢸⠇⠀⢣⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⡆⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢀⡞⠀⣤⣀⠀⢸⠀⡠⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⢸⡆⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣼⢀⠔⠁⠈⢣⡼⠊⠀⢀⣬⡤⠤⣄⣀⠀⢀⣠⠴⠶⠤⣤⣀⣀⢀⣀⣠⠤⣄⣀⠀⢀⣀⣤⣄⡀⠀⣸⠃⠀⡏⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠸⠃⠀⠀⡠⠊⠀⢀⡴⠁⢠⣀⣀⡤⠬⠉⠉⠀⠀⢶⢦⡤⠤⠭⢭⣥⣄⣀⣀⣉⡭⠍⠁⠀⠀⣍⣛⣉⣙⣋⣻⣄⣐⠋⠉⢱⡤⠋
⠀⠰⠁⠀⠀⠀⠀⡠⠂⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠶⠸⡀⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠙⠻⠀⠀⢀⠁
⠀⠠⠀⠀⠠⠐⠈⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠰⠋⢠⢡⡅⢡⢁⠐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠢⡰⠡⠊⠀⢸⢡⡑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇

⠀⢠⢒⣦⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⠤⠤⢠⣀
⠀⠂⣿⠀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⢀⠀⠈⠉⠉⠁⠀⠚⠒⠤⠀⠀⢀⡀
⠀⠈⠑⢆⢀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠉⠉⠰⠆⠀⠶⢀⡄⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠈⢎⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠊⠀⠀⠀⠀⠋⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠈⢯⢆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠈⢫⢂⡀⠀⠀⡑⠢⢄⣀⠀⠈⠠⣀⠠⠀⠒⠄⠀⠰⠂⠀⠀⠀⡐⠋⠀⠀⠀⠀⠀⠴⠖⢂
⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠈⢱⠂⠤⡤⠤⠤⠀⠐⡘⠂⠘⢀⠞⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠐⡌⠘
⠀⠀⠀⠀⠀⠀⠀⠘⢶⠀⠀⠀⢀⠃⠀⢁⢈⡀⢀⠜⠀⠀⠀⠁⠀⢀⡸⠁⣢⠀⢀⡀⠤⠒⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠦⢠⠤⠔⠀⠀⠀⠀⠰⠀⢰⡁⠀⠀⡲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣤⡄⢀⣈⠚⡟⠝⠓⠒⠒⠀⠴⢂⠩⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠠⢈⣀⡘⠛⠃⠒⠶⠆⢹⠠⠖⢃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠕⡆⢀⠞⠁⠈⠉⠉⠁⠐⠒⠶⡓⢉⠾⣀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡕⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠒⢮⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋

⠀⠀⠀⠀⢀⡴⠒⠒⠒⠂⠚⠓⠒⠂⠀⠚⠒⠲⠦⠀⠒⠒⠦⠄⠒⠒⠢⠄⠀⠠⡀
⠀⠀⠀⣀⠞⠀⢠⠀⠀⠐⠉⠁⡆⣀⠀⢠⠀⢀⡀⠀⠀⣀⠀⢠⠀⠀⡀⢀⠀⠂⡇
⠀⠀⡘⠁⠄⠁⠈⢂⠀⠈⠀⠈⠀⠹⠒⠈⠁⠘⠢⡀⡠⠘⠀⠈⠀⠺⠁⠀⠀⠀⠃
⢠⡏⠀⠀⢄⠀⠀⠀⡀⠀⠁⠀⠎⠀⠀⠀⠠⣀⣄⠘⠀⡠⣀⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⡩
⠀⠳⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠆⠀⠀⠀⠘⠿⠟⢠⠀⢜⣿⡣⠀⠀⢀⠁⠀⠀⠇⠀⠀⠀⠀⡠⢠⠧⣮⡀
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠒⡄⡀⠔⠉⠂⣀⠀⠄⠂⠀⠀⡰⠀⠀⡄⠀⠀⠀⢸⠐⠤⣋⠀⡅
⠀⠀⠈⢣⠀⠒⢡⠀⢀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠂⠶⠒⠒⠉⠀⠀⢰⠇⠀⠀⠀⠀⡱⢠⠤⠊
⠀⠀⠀⠰⡄⠀⢰⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠂⠀⣶⡖⠀⢺⠉⠀⡠⠠⠀⠘⠀⠀⠀⠀⡰⢡⠃
⠀⠀⠀⠀⠈⡆⠀⠉⠀⢠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠅⠀⠂⣰⡠⢄⠀⡰⢡⠇
⠀⠀⠀⠀⠀⡹⠢⣌⠀⠀⠄⠐⠂⠀⠱⢄⣈⣉⠉⣛⣿⠇⠀⠀⠀⢀⠀⡆⠀⠃⠐⣪⠭⠔⠃
⠀⠀⠀⠀⢠⠃⠀⢠⠀⠀⠃⠠⠀⠀⠀⠲⠠⠍⠩⠭⠤⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⠂
⠀⠀⠀⠀⠈⠢⠤⡜⠉⠀⠙⠃⠉⠙⠒⠮⣉⡉⠓⢖⡐⠻⢉⠹⠂⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⡇⡏⠷⠦⠘⠀⣤⣤⣤⠀⢠⣤⣴⠃⠘⣦⣤⠄⢠⣤⡤⠜⠃
⠀⠀⠀⠀⠀⠀⡇⢣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⢘⠀⢀⢣⠸⢍⣉⠉⢉⡹⠋⠉⠉⠉⠙⢭⢭⠍⠨⠃
⠀⠀⠀⠀⠀⠸⢦⣨⠀⠀⠀⡏⠹⠁⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡎⠀⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣡⠀⠀⠀⠀⠀⠀⠀⣼⣬⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣶⣦⠀⠀⠀⠈⣿⣿⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠐⢪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠣⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠴⠒⢡⡵⢄⠀⠀⠀⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⢂⣩⡁⡐⠉⠉⠐⠄⠊⢢⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠠⠄⠀⠋⠀⠀⡌⢢⠙⠀⡜⢉⠂⠰⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣶⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣤⡑⢤⡀⡱⠂⠄⠀⡠⠐⠚⢀⡗⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⡀⠙⢄⠙⢶⣶⣶⣆⣸⣷⣶⠀⢘⡂⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢅⠰⣦⠣⡀⠙⢿⠟⠛⠋⢙⠃⠈⠛⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠶⠆⠰⠖⠀⠖⠐⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡄⠓⠈⢄⠈⡞⠃⡈⠐⢒⣫⡴⢾⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡐⠀⠁⠉⠀⠀⠻⠠⠘⠠⠖⣚⣿⣶⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣤⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠘⠀⠀⠀⠀⠀⠀⢿⣿⣶⢿⣿⠿⠛⡉⠘⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⡀⠈⡿⠚⠃⠀⣼⡟⠦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠈⠻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠋⠀⠀⠀⠀⠙⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣤⣴⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⡙⠛⣁⡈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⡘⠛⣠⣙⣵⣿⣿⡇⠀⢰⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣴⣏
⠀⠀⠀⠀⠀⠀⢲⣴⡇⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⡇⣠⠾⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠻⠟⠛⠳⢦⡜⢿⣿⣿⣿⣿⣷⣿⣾⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⠿⠟⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣥⣤⣶⣶⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠏⠁⠈⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢿⣿⡿⠛⠛⢿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⡀⠀⢾⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠃⠄⠀⡄⡄⢀⠁⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡄
⠀⠀⠀⠀⠁⡀⢀⠤⠀⠀⠀⠀⠀⠹⢄⠀⠀⢀⣤⣣⡄⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠔⠀⠐⠁⠀⠀⠀⠀⠀⠀⢠⣈⠐⠀⠁⠘⠡⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠸⠀⣀⠀⠀⠀⠀⠀⠅⢰⠀⠀⢈⠉⣲⠖⢲⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁
⠀⠀⠀⢰⠀⠀⠀⠉⠁⠉⢀⡘⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠁⠂⠐⠠⠠⡀⠊⠄⠴⠀⠀⢰⡿⠿⠿⠿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡑⢀⠀⠀⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠀⠈⠀⠜⠑⡄⠀⠀⣀⡀⠀⢀⠀⡌⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢤⡔⠀⣀⠂⠈⠀⠀⠀⠁⠀⠀⠤⡔⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⣀⣀⠈⠙⠃⠶⢦⡄⠀⠠⠶⠇⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⣀⠝⠐⠒⠠⠄⣀⣀⣀⡠⠀⠃⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠄⣀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣶⣶⣦⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠛⠋⠀⣴⣶⣤⣶⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠟⠃

⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣠⣤⡤⢤⣤⣀⣀⠀⠀⠀⣀⣀⣠⠴⠶⠦⣤⣀⣀⣀⣤⣄⡀
⠀⠀⢠⡏⠁⠀⢉⣉⣁⠀⠀⠙⢯⣉⣉⣤⠞⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⢀⡴⠖⠶⢦⣄⠀⠀⣷
⠀⠀⠈⣇⠀⢴⠋⠁⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⡆⢠⡏
⠀⠀⠀⢹⠀⠈⠛⠲⠒⠋⠀⣦⠀⠀⢸⠇⠀⢠⠆⠀⠀⠀⢤⠀⠀⢸⠀⠀⢠⠆⠙⠦⣤⣤⠼⠃⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠶⠒⠛⠓⠶⢿⡀⠀⠀⠀⣨⡷⠖⠛⠓⠲⢿⣄⠀⠀⠀⠀⠀⢀⣸⠆
⠀⠀⠀⠘⢧⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⡀⠀⠙⢦⢀⡞⠁⠀⢀⣀⣀⠀⠀⠈⢷⡀⠀⢀⡴⠋⣽
⠀⠀⠀⠀⢸⠇⠀⠀⠀⡟⠀⠀⢀⡾⢋⣭⣉⢳⡀⠘⣿⠀⠀⣴⢋⣭⣍⠳⡄⠀⠀⣷⠀⢸⡇⢠⡏
⠀⠀⠀⠀⣾⣀⡀⠀⠀⣇⠀⠀⠘⣇⠻⣿⡿⣸⠇⣠⣿⣀⠀⣧⠸⣿⡿⢠⡇⠀⠀⡿⠀⠀⠙⣾
⠀⠀⠀⠀⡏⠈⠙⣦⠀⠹⣆⠀⠀⠈⠓⠶⠚⠋⡾⠁⠀⠈⡇⠈⠓⠶⠖⠋⠀⢀⡼⠃⠀⠀⠀⢹
⠀⠀⠀⠀⢧⠀⠀⣼⢠⣴⠎⠳⠦⣤⣀⣠⡤⠶⠇⠀⠀⣰⠟⠦⣤⣀⣀⣤⠴⠋⠁⣶⣄⠀⠀⠘⡇
⠀⠀⠀⠀⠘⣧⠞⠃⠛⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠛⠀⠀⠀⡟
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⣴⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠛⢶⢶⠖⠚⢻⡏⠁⠀⠀⠀⢀⣠⣤⡀⠀⣼⠉⢳⡄
⠀⠀⢸⠇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠿⠤⠤⠾⠸⠦⠤⠼⠂⣠⠀⠀⢰⠋⠀⠀⠙⡆⢸⡆⠀⢻⡀
⠀⠀⠘⣶⢤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠒⠒⠲⠶⠶⠋⠁⠀⠀⠘⢦⣄⣠⡴⠃⢸⣧⠤⡼⠃
⠀⠀⠀⣿⢸⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⡇
⠀⠀⠀⣿⢸⡇⢹⡟⠛⠓⠒⠒⠋⠉⠻⢯⣉⢉⡿⢯⣀⡼⢿⡉⢙⣻⠿⠋⠙⠋⠉⠉⠉⣿⠁⢸⠀⣷
⠀⠀⠀⡏⢸⡃⠈⣧⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣤⣼⠋⢷⣤⣽⣯⣤⣤⣤⣤⣤⣤⣤⣤⡏⠀⢸⡆⣿
⠀⠀⣰⠃⢨⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⡀⠹⡄
⠀⠀⡿⣇⣻⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢘⣷⡇⣼⣿
⠀⠀⢷⣙⣿⣿⠃⠘⠷⠒⢲⡖⠲⠶⠲⠒⣶⠖⠖⠒⠒⠖⠖⢶⠖⠶⠒⠲⠲⡶⠒⠶⠋⠀⢸⣿⣿⣡⠟
⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠘⠳⠶⡤⢴⠶⠛⠀⠀⠀⠀⠀⠀⠘⠲⣦⢤⡴⠞⠃⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⣸⠷⡄⠀⠀⠀⠀⠀⠀⢀⡶⣿⣸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠁⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠈⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⣠⠾⠷⠞⠁⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⣄⣀⣀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠶⢤⡀⠀⠤⣀⡀⢀⣀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⣆⠰⡆⣠⠀⠀⡀⠀⡄⠀⠈⠉⠁⠀⠀⠌⠁⠀⠀⢹⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠁⣀⠄⠋⠈⠁⣴⠂⠀⠀⠂⠀⠀⠀⠀⢀⠌⠀⠈⠓⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠠⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⡄⢠⠄⠀⠴⠒⢄⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⡀⠀⠐⢠⣿⡦⣴⣦⢠⠀⠀⠐⠲⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⣰⠄⠀⢠⠜⠓⠈⠁⡀⠀⠀⠀⠀⠀⠇⠀⡀⠙⠂⠄⠀⠉⠀⠙⢃⣄⡀⠆⠀⠠⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⢰⠁⠀⠁⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⡘⠀⠈⠑⠲⠤⢤⣀⣀⣀⠀⠀⢀⣀⣤⣾⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⡗⠂⢂⣤⡀⠀⠀⠀⣁⠀⠀⠰⣆⠀⡇⠀⠀⠀⢠⣀⠀⣼⡏⠈⢙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠈⠉⢁⠀⠉⠀⠀⣹⠀⡅⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⠤⣀⡀⠀⠐⠀⠀⠀⠐⢂⡾⠀⠰⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⡀⢲⠈⠉⠀⠂⠒⠇⢈⠁⠀⣼⣿⠟⠛⠛⠻⠟⠛⠛⡟⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠉⠋⠒⠄⣀⠀⠃⠀⢿⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⣠⡏⠀⠐⢄⠠⠝⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠁⠒⢀⠈⢏⠈⠓⠀⠀⣤⣄⣀⠀⢀⣇⣀⣸⠀⠀⠀⠀⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠶⣶⣄⣠⣀⠎⠈⡄⠑⠂⠈⠁⠀⠀⠀⠀⠉⠀⠀⠠⢄⣤⣤⠔⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠛⠀⠀⢰⣶⣦⣄⢀⣀⠀⠀⠀⣀⠀⠀⠀⢀⡇⢸⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⠤⢌⣀⠁⠀⠀⠁⠈⠛⠻⠷⠆⠀⠀⠐⠟⠛⡇⡘⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢹⠋⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⡀⠁⢻⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢻⠁⠀⠀⠀⠀⠈⠁⠉⠓⠒⠚⢻⠙⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠓⠤⠤⢀⡤⢜⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⡀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣸⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⢰⡇⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠿⠟⠻⠿⠿⠁⠀⣠⣴⢦⣤⣴⣶⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠈⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠶⠖⠚⠉⠙⠛⠋⠀⠈⡏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡤⠴⠖⠓⠒⠚⠉⠉⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠉⠑⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠄⢀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠈⡇⢀⡠⠀⣀⠔⠁⠀⢀⡀⠊⠈⠑⠢⠤⢤⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⢠⠃⠀⠲⠋⠁⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠰⠃⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠘⣇⠀⣏⣀⡀⣤⣤⣤⠷⠀⠒⠒⠒⠒⢶⡶⣾⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠁⠀⠀⠀⠀⢠⠾⠠⢽⡀⠀⠘⠬⠥⠛⡀⠀⠀⠀⠈⠐⢂⠇⠀⠀⢀⠇⠀⠀⠀⠀⠂⠀⢀⡞
⠀⠀⠀⠀⠀⢀⠴⠒⠾⣀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠐⠤⣀⢀⡠⠛⠢⢀⣀⡀⠴⠊⠀⠀⠀⠌⠀⠄⠀⠀⠀⠀⠀⡞
⠀⠀⠀⢀⠔⠁⠀⢀⠤⠌⡑⢤⡀⠀⠀⡏⠳⢦⣄⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡼⠀⠀⠀⢐⠀⠀⠀⠁⡽⠀⠀⠷⠀⠀⠀⠉⠙⠓⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⣠⠒⠓⡄⠀⠀⠠⡄⠀⠀⡠⠂⠀⣀⡄⠀⠀⠀⡚⠋⠛⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡟⠉⢙⠆⢸⠀⠁⠳⠴⣾⠁⠀⠸⠀⠀⠀⠀⠂⠃⠀⠀⢸⣀⠀⠀⠠⠤⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⠀⡀⢀⡇
⠀⢿⣁⣬⠀⢘⠠⠒⠂⠄⡇⠀⠀⠀⢣⠀⠄⠀⠀⡀⠀⠀⠈⣸⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⠃⠀⠀⠀⡞
⠀⠈⢻⠀⠀⠀⢇⠐⠀⠄⢰⠀⠀⢀⡇⠘⢣⠖⠋⢣⡀⠀⠀⢍⠓⠦⠀⠀⠀⠸⣄⠦⡀⠀⠀⡜⠁⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠐⠈⠲⠤⢤⡼⡀⠀⢈⠙⢿⡁⢀⠀⠀⢉⡙⠲⣌⠳⣄⣀⣀⣤⠞⣁⣴⠋⣠⣮⣀⣀⣤⣀⡼⠁
⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⡷⢌⡐⣉⣄⣸⠋⠉⠛⠿⣉⠝⣋⡿⢷⣌⠑⢋⡠⠞⠁⠀⠉⠁⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⡇⠀⠉⠁⠀⢸⠋⣭⣤⡐⣀⣲⠀⠸⡄⠬⠱⠉⠀⠀⣀⡀⢀⡀⠀⢀⣀⣂⠀⡇
⠀⠀⠀⠀⠀⠀⠙⠲⠴⠊⠀⠀⠀⠀⠀⢸⣀⣈⡉⠀⠉⠉⠃⡰⠛⠛⠀⠐⠛⠲⠶⠀⠀⠀⠀⠛⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡻⠛⠛⠒⠳⡶⠶⠦⣤⣤⣤⣄⣀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⢀⠀⢸⠃⠀⠀⠀⡔⠁⡀⠈⠉⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠾⠥⠎⠀⠀⠀⠀⠘⡞⢩⣂⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡰⣆⠀⠀⠀⠀⠀⠀⠘⠀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠉⠠⣄⠀⠀⠀⠀⠘⢦⠽⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣾⣷⣾⣿⡇⠀⠀⣀⡀⢈⣦⣤⣷⡄
⠀⠀⠀⠀⠄⠀⢔⣒⣢⣂⣀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⠿⠿⠟⠃⠀⣾⣟⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣞⣿⣹⡽⢽⠷⠾⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠉⠉⠁
⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⢀⣴⣤⣤⣴⣄⣀⣀⠀⠀⢀⣀⣀⢀⣄⠀⠀⠈⢁⠙⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢹⣶⣟⢛⣉⣬⣉⣽⣿⣿⣶⡶⠞⠛⡻⠙⠛⣿⣶⡀⢯⡄⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣿⡙⣾⣿⣿⣿⣿⣿⣿⡿⢉⣴⣿⣿⣿⡆⠈⢹⣿⣷⠀⠫⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠯⢼⣿⣿⣿⣿⣿⣷⣿⠁⣾⣿⣿⣿⣻⣿⠀⣰⣿⣿⠄⠜⠀⢸⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢳⣬⡴⠿⣿⣻⣿⣾⣿⣀⣨⣿⣿⠿⠟⢁⣠⣿⣟⣿⠀⢷⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡏⣠⠟⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣤⡤⠚⠛⠋⠻⠃⠀⠀⢀⣼⣿⣿⡷⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣋⡿⠿⢾⡯⢾⡿⠟⠀⠨⣿⣿⣿⣿⣿⡧⢀⣤⠀⠀⡤⠀⢀⡼⣿⣿⡿⢻⡀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣀⠀⠀⠀⠀⠀⠀⠚⢎⠉⢛⣉⣥⣾⣿⠇⠀⠞⠁⢰⣿⣾⣻⣿⣃⣼⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢐⣢⣤⠀⢺⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⡿⣏⢿⡊⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⠿⢣⣴⣦⠀⣠⣿⣖⣛⣾⣟⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠏⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠟⠉⠀⢙⣿⣿⣿⣿⢻⣧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⢀⣾⣿⡆⠐⢻⣿⣿⣿⣛⣿⠿⡛⣣⣼⠟⠁⠀⣠⣤⣄⠀⠀⢨⣿⣿⡯⠽⡀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⠟⠁⣤⣰⠛⠛⠿⣿⡿⠿⠟⠛⠁⠀⠀⣼⣿⣿⢿⡀⣠⣿⣿⡿⠁⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⣿⣧⣤⣦⣜⣛⣷⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠘⣿⠛⠈⠈⣿⣿⣿⡇⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠁⠭⢹⡿⣯⣿⣿⣿⣿⣿⣿⣽⠧⣤⣄⣀⣀⣠⣏⠀⠀⠀⣿⣿⣿⡇⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⠿⣾⣦⣤⣼⣿⣿⡋⠙⠶⠾⠛⠛⠛⠛⠛⠻⠶⣶⣿⣿⣿⢷⣦⣤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡟⠛⣿⡏⣿⠿⣿⣿⣿⣿⣿⣿⣷⠖⠶⣦⣤⣤⣤⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣾⣿⣤⣿⣀⣘⣿⣿⡿⢯⠋⠉⠀⠀⠛⠛⠿⣿⢿⠏⢽⣿⣿⣿⣿⣿⣿⣿⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⢿⢹⠇⢸⣿⣿⣻⠻⢶⣿⣤⣤⣤⣀⠀⠀⡄⠂⠀⠠⣾⡟⣿⣟⣿⣿⣿⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠈⢾⠃⣇⠀⠘⣹⣿⠻⠋⠿⣿⢿⠷⣶⣦⣤⣾⣷⣿⣿⣿⣿⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⡛⠐⢤⣄⠀⠟⣴⠉⡟⠹⠀⢻⣟⠉⠘⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⢠⡇⠀⠀⠈⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣻⡜⢣⠀⠀⠀⠀⠀⠀⡠⠒⢄⣀⣀
⠀⠀⠀⠀⠘⠺⡉⡎⠀⠀⠀⠀⢀⡠⠃⠋⡀⢀⠀⠑⠒⠢⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠘⡼⡀⠀⠀⠀⡎⢈⠔⠉⠉⠙⢶⢀⣠⣀⡀⠀⠀⠉⠑⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⡜⢁⡮⡀⠰⣿⣷⠞⢁⣤⡈⠑⡆⠀⠺⠟⢀⠔⠒⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢇⣠⠃⠈⣆⠈⠢⣀⣸⠀⠘⠿⠏⠀⡇⠀⢀⠔⠋⠸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⢹⠀⠈⠣⣍⡒⠀⠀⠑⠤⣔⡓⠺⡀⢠⠊⠀⠤⠀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠈⠀⢈⡶⠿⢏⡽⠋⢉⡽⠁⠐⡡⢣⡄⢀⡔⠊⠀⠀⠀⠀⢀⠞⣟⡭⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠠⡘⠤⣞⣉⣋⠽⠋⢠⡦⢀⠇⣀⠥⢛⣲⠤⢄⣒⠢⠭⠑⠢⠯⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠒⢬⣍⡐⠒⠂⠀⠀⠀⠀⠃⡜⠥⣀⣈⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠿⠺⣷⡟⣿⣗⡒⠠⠤⣠⡧⠤⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡛⠒⢶⠧⢾⣛⣛⠿⠷⢺⠶⠿⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠥⡿⠔⠁⠀⠀⠀⠈⠉⠓⢾⡒⣻⡯⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠛⢷⣲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⡠⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠁⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠶⢈⣙⡤⢀⠀⠀⠀⠀⢐⠆⢃⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠆⠀⠐⠆⠱⡄⠀⠀⠘⣔⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⠢⠤⠊⠈⣡⠄⠀⠘⡞⡠⠉⣉⣒⠒⠤⠤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⣷⣶⣾⡿⢉⡰⡀⣮⡍⠔⢁⣀⠈⠇⠘⠐⢦⠀⡝⠉⢉⢰⠀⠀⠀⢰⢠⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠣⠤⠤⠊⠀⢿⡝⢮⠁⢈⢛⠃⠰⣷⠀⡘⠀⡠⠂⠐⠂⣇⠀⠀⠢⠔⠰⠖
⠀⠀⠀⠠⠄⠀⠀⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⡐⡭⣆⣀⠁⠤⣠⢸⢀⠘⢑⣃⠄⠂
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⢁⣷⣿⣾⣿⡿⠁⠔⡁⡔⠁⣓⠇
⠀⠉⠑⠒⠒⠤⡄⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠜⢋⠠⠕⠋⡒⡴⠘⠄⠨⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣍⣘⣖⠢⠄⠠⢤⠧⠌⡼
⠀⠀⠀⠀⣰⠉⢔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣈⡼⡤⠩⢌⣁⣘⡓⣸⢐⣊⠇
⠀⢄⠀⠈⠙⣀⠄⠀⠀⠀⠀⠀⠀⠙⢀⠐⠋⠉⠤⢀⡴⠛⠤⣾⠀⣸⣧⣀⡝⠀⣠⣤
⠀⠀⠑⠦⢤⣈⣢⣀⢀⠤⣤⣀⣀⠀⠀⠁⠂⣠⠖⠋⠀⠀⠀⠙⠾⢻⣿⡿⠻⣲⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠈⠑⢢⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⠤⣤⣀⣀⣀⣀⡤⢤⣄⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠈⠙⠲⠖⠊⠁⠀⠙⠒⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡁⠀⠀⢤⣤⡤⠀⠘⠲⠃⠀⢤⣤⡄⠀⠀⣐⡀⠀⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣦⡀⠄⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢻⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⡟⠀⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⣾⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠀⠀⠉⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⣞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠣⣄⣀⡤⠤⣄⣀⣤⣤⠴⠤⣄⣀⣀⡤⣄⣀⠀⠀⣀⣀⣀⡀⢀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡒⢧⠀⠀⠀⠀⠀⠀⠈⠑⠦⠞⡯⢽⠣⠴⠛⠉⠉⠁⠀⠀⠉⢹⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⠈⣭⣭⣭⠉⢩⣭⣭⣭⣹⠁⠘⡧⣾⣿⣿⠉⣿⣿⣯⡍⡟⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⢹⠉⠉⠻⣽⣓⣲⡶⠒⠒⠒⠒⠲⣶⣶⣶⠶⠒⢒⠛⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣀⡞⡄⠀⠀⠀⢰⠘⡀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⡰⣆⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠮⠁⠀⠀⠀⢸⠒⠣⠀⠀⠀⠀⠸⠑⡇⠀⠀⠀⢫⣎⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⢸⠀⠀⠀⠀⣀⠀⣇⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠛⠋⠀⠀⠀⠀⠈⠉⠁⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠙⠓⠒⠚⠋⠉⠀⠈⠉⠙⠛⠛⠉⠉⠉⠈⠉⠙⠳⠦⠤⠴⠖⠛⠛⠲⢤⣀⣀⣠⠶⠛⠙⠓⢦⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠀⠀⠀⠀⠀⠀⠀⢦⣀⡠⠎⠀⠀⠀⠀⠀⠈⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠘⠉⣿⣿⡿⠉⠁⠉⠉⢉⠈⠁⢻⣿⣿⠃⠂⠐⢠⣬⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠂⠀⠁⠀⠐⠀⠄⠀⠀⠂⠙⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠸⣿⣷⣍⡐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠂⠠⠤⢄⣴⣶⣿⡇⠀⠈⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⣤⡀⣀⡀⠀⢀⣀⢀⣤⣤⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠁⠀⠀⠙⠁⠀⠈⠉⠉⢉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢶⡀⠀⠀⠀⠀⠉⠀⠀⠀⠤⡀⠁⠚⠀⠀⠐⠀⠀⠘⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠈⠁⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⣄⣀⣀⣀⣠⣤⣀⠀⣀⣠⡤⠤⠤⣄⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣤⡏⠉⠁⠀⠀⠈⠉⠉⠈⠙⠶⣄⣀⡽⣟⢛⣿⣄⣈⣽⠗⠒⠒⠛⠉⠉⠉⠓⠒⣿⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⣤⢭⣤⡎⠉⣧⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⢼⣿⣿⠿⠀⠀⠾⣿⣷⣶⡆⣼⠀⠀⣸⠴⠿⠿⠿⠇⠀⢴⢶⣶⣶⡆⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⡉⡍⠛⠛⢲⡒⠶⠶⠤⢤⣤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⡤⠤⢤⠶⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣀⠐⣄⡇⠀⠀⠀⠉⠛⣟⠛⡏⠁⠀⠀⠀⠀⠀⠈⡹⠋⡟⠛⠉⠀⠀⢸⡠⠀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢦⡼⣙⠆⠀⠀⠀⠀⢹⠀⢱⠀⠀⠀⠀⠀⠀⢠⡃⢐⠃⠀⠀⠀⢀⢎⠿⡜⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡽⠜⠀⠀⠀⠀⠀⢸⡗⠙⡆⠀⠀⠀⠀⠀⢸⠉⢹⠀⠀⠀⠀⠀⢧⣎⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⣾⣦⣤⣇⠀⠀⠀⠀⠀⣾⣦⣾⣷⣶⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⠿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠂⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡇⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠀⠀⠈⠓⢄⣀⠀⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⡠⠚⣡⠤⠖⠒⠢⢌⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⣠⠞⣠⠞⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠌⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠠⠄⣀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⣠⣦⣾⣥⣤⡠⠤⣤⡴⠞⠛⠛⠛⠳⠶⠛⠛⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⡈⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣄⣤⡴⠖⠛⠓⠒⠶⠊⠉⠀⠀⡀⢠⠈⠁⠀⠀⠀⠰⡌⠒⠃⠀⠀⠀⠐⠈⠁⠹⣆⠀⠀⠀⠀⠀⢄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⠀⠉⠁⢀⠂⠀⠂⡀⠀⠀⠀⠘⠂⠁⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠂⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠢⠤⣀⠀⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠂⢰⣦⠀⠀⠀⠠⠚⠶⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⠈⠳⡀⠀⠁⠚⠀⠀⠠⠄⣄⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⣰⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡀⠑⢤⡀⠀⠀⠀⠐⠆⠀⠎⠑⡄⠀⠀⠀⠀⠀⠂⠠⠄⠊⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⢱⡄⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠰⠀⠀⠉⠓⢄⠀⠀⣀⣁⣀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊
⠀⠀⠀⠀⠀⠀⠸⣦⣀⡀⠀⢤⠀⠠⠀⠈⠈⡀⠀⢃⠀⠀⢱⠀⠀⠀⠀⠀⠶⠲⠤⠔⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⣀⣀⣀⡉⠉⢧⠀⡈⠀⠀⢀⣠⢃⣀⠘⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠼⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢠⠞⠋⠉⠁⠀⠀⠀⠀⡠⠄⠛⠃⠈⠉⠠⢌⠠⠈⠦⡀⠀⢢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠒⠀⠀⠈⠀⠀⠱⡆⠀⠱⠀⠀⠹⣿⣿⣷⣤⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠓⢠⡘⠀⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠙⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⡀⠀⠀⠀⢼⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠠⠒⠈⠻⡀⠀⠀⠀⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠱⣄⠀⡄⠰⠀⢀⣈⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⣆⠐⡀⠨⠀⠈⠢⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠑⢧⡀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⠈⠄⠈⢀⠐⠂⠀⠀⠙⠲⢤⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢙⢢⣄⡁⠒⠀⠄⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠓⠀⠀⠀⠀⣀⠀⠠⠄⠀⠐⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠶⠀⠀⠀⠀⢀⡀⠀⣀⠋⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⠀⠈⠀⠀⣀⠜⠙⢃⡌⠉⠒⠤⢀⡄⠀⠠⠄⠐⠒⠈⠉⠀⠈⠒⢤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠴⠄⠂⠉⠀⠀⠀⠀⠉⠒⠠⢄⣉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⢀⣀⣤⣤⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠈⠑⠣⠄⡀⠀⢀⣀⠀⠤⠄⠒⠂⠀⠁⠀⣀⣀⣤⠤⠒⠒⠉⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⠛⠀⠀⠀⢀⣀⡤⠴⠖⠚⢋⠉⠀⠰⣀⠀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⣶⣦⠀⠀⢀⠀⠀⠉⠶⣴⠴⠶⠚⠋⠁⠀⠀⠀⣠⣾⣿⡗⠀⠀⡠⠁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠛⠻⠻⡟⠁⠀⠱⣄⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⣿⣏⠉⢱⢤⣀⠔⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡄⠀⠀⢀⠊⢹⠖⠀⠀⠊⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠳⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⠃⠈⣠⠔⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⣥⣤⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠽⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⢀⣠⣤⡶⠾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠃⣿⣿
⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⠿⢀⣀⣀⣤⣶⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠃⠀⣿⣿
⣯⡘⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠇⠀⠀⣿⣿
⣿⢳⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⡟⠀⡄⢸⣿⣿
⣿⠀⣜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⡇⣸⣿⣿
⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡿⠀⣿⣿⣿
⣿⣿⢿⢻⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣻⣟⢁⣺⠃⠀⣿⣿⣿
⣿⡿⠘⣇⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⣿⣿⡿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠋⣾⡏⢀⣠⣿⣿⣿
⣿⣷⡆⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣵⣶⣿⣿⡿⠁⠁⠀⠈⠿⣿⣿⣟⣻⣿⣿⣿⡿⢸⡟⠀⣼⣽⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣬⣿⣯⠀⠀⠩⢵⣶⠏⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃⣾⠁⢠⡇⣿⣿⣿⣿
⣿⣿⠿⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⢀⣺⠇⠀⠀⢠⣾⠟⠛⠛⠟⢛⣩⣵⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⢸⠇⠀⣾⢱⣿⢹⣼⣿
⣿⣿⣷⠺⠿⣿⣿⣧⠀⠀⠀⢀⣴⡿⠿⠿⠿⠛⠘⠛⠛⠀⠀⠀⣿⣽⡀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠃⣿⠀⢸⣿⢸⡏⢰⣿⣿
⣿⡿⠁⠀⠀⠀⠙⠿⠇⠀⠀⠈⠿⠿⠿⠿⠿⠿⠧⢻⡯⠀⠀⠐⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⣿⠆⠸⣿⣈⣠⣾⣿⣿
⣿⣷⠀⢀⣀⢤⠄⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⣿⣿⡀⠀⠘⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠐⣿⣷⡀⠻⣿⣿⣿⣿⣿
⣿⣷⡄⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⠦⣤⠤⠤⠶⢾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡆⣿⣿⣟⣶⣤⣴⣿⣿⣿
⣿⣿⣿⣶⣄⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢛⡉⠁⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠿⠿⠓⠀⠀⠀⢀⣛⣫⣭⣽⣶⣇⢻⣿⣯⠡⠀⢉⢻⣿⣿
⣿⣿⣿⣿⣿⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣤⣴⣶⣆⠀⠀⠀⠀⠙⣿⣿⣯⣽⣿⣿⡈⣿⣿⣅⠀⠀⢈⣿⣿
⣿⣿⣿⣿⣿⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣷⡘⢛⣏⣴⣿⣿⣿⣿
⣿⣿⣿⠿⠛⠾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡋⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣾⡿⣿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⡿⠿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠋⠾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢾⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠏⠉⠙⠛⠉⠀⢀⡀⠀⠀⠀⠀⠀⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠠⠄⠒⠊⠃⠀⠀⢀⣤⣤⡄⢠⣩⠌⠁⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣾⣿⣿⣷⣲⣦⡄
⠀⠀⢨⣦⢀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⠿⠒⣷⡀
⠀⠀⣿⣽⣷⣽⣦⠀⠀⢀⣴⣿⣿⣿⣿⠆⠹⣿⣿⣿⣿⣿⣿⡆⠀⠩⣭⣄
⠀⠸⣿⣿⣿⣻⣾⣿⣳⣾⣿⣿⣿⣿⣿⡎⡄⣿⣿⣿⣿⣿⣿⡷⠀⠀⠘⠩
⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢆
⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⣿⡄
⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣆⠠⠀⠀⠉
⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⣀⡔⣃⣠⣀⢀
⠀⠀⠀⠀⠀⠀⠁⠉⠙⠻⠿⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢶⣴⣴⣿⣿⣷⡧⢭⠤⢿⠒⡁⢰⡀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⣽⢿⣽⣿⣳⢞⣂⡙⢟⣿⣾⣿⣽⣷⣿⣿⣁⣨⣷⡀⠙⢻⡄⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠹⠛⠉⠉⠮⠗⣹⢏⡼⣻⠿⣿⣿⣿⣿⣿⣿⣿⣦⡼⡓⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠈⠉⠈⠃⠊⠈⢽⣿⣿⣿⡟⠻⠇⠜⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠒⠲⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠭⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠐⠒⠶⠚⠁⠀⠲⠒⠈⠐⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣦⡀⠤⠀⠀⠀⠎⠹⠃⠘⠛⢁⡴⣤⠀⠀⢶⡶⠈⢙⡒⠄⢠⣀⠀⠀⠀⠀⠀⠀⡞⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠓⠦⢀⡫⠗⠀⠀⣠⢄⠀⠀⠀⠠⠦⠀⠀⡀⠘⠋⠀⠀⡠⡉⠒⠤⣀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⣔⢂⠈⠉⠲⡖⣌⠉⠀⢴⠶⠀⡴⢦⠈⠛⣀⠤⡀⠀⠉⢠⠖⢲⠌⠓⠶⠤⢤⣀⡀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠃⠈⠁⠀⠀⡀⠀⠀⠉⠒⠤⣄⡀⠉⠁⠀⠀⠓⠚⡁⠀⢀⡈⡙⠉⢠⣶⠆⠀⠀⠈⠙⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⣏⠆⠀⠘⠬⠀⠀⠰⠵⠀⠀⣬⡑⠢⣤⠠⢄⡘⠊⠀⠈⠉⠀⠀⢀⢤⡀⠐⠛⢃⡴⢹
⠀⠀⠀⠀⠀⠀⣀⣠⢤⡄⢀⡤⡄⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠀⣈⣀⠀⠀⠉⠒⠓⠄⡀⠀⠀⣔⠄⠈⠛⠁⣠⠴⢋⡄⣼
⠀⠀⢀⢠⠖⠋⠁⠀⠀⢧⣀⠓⠃⠀⠀⢰⢢⠀⠘⠶⠚⠀⠀⠀⣇⠀⡇⠀⡀⠀⠀⡤⢬⡑⠤⣤⣠⡤⠔⠊⢁⣠⠀⡅⣸
⠀⠀⠏⣯⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⡀⠀⠁⢀⡀⠀⠀⠨⠇⠀⠈⠉⠁⠀⠉⠀⠀⠓⠶⠋⠀⠀⡔⠢⠀⠸⠆⠀⠈⠒⢻⡄⠀⠀⠀⣀⣀⠀⠀⡀
⠀⠀⠀⠈⠓⠶⠶⢤⡀⠀⠀⠀⠀⠀⠛⢄⡀⠘⠚⠀⢀⣀⠀⠀⠀⠀⢰⣓⠀⠀⠀⠛⠃⠀⠀⠀⡇⠰⠳⠀⠈⢁⠐⠂⠘⡟⠉⠉⠉⠉⠉⠙⢳⡀
⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡘⠚⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢠⢶⠀⠀⡀⠀⠣⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⡤⡄⠀⠀⠉⢀⡀⠀⠈⠋⠀⠀⠽⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠴⠞⠃⢤⡀⠀⠘⠞⢠⡀⡄⠀⡀⠔⠉⠀⠀⠀⠀⠀⢀⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠶⠖⠒⠒⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠽⠵⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣤⣶⣶⣶⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣴⣿⣿⣿⣯⣭⣭⣭⣉⠛⢿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣧⣀⣠⡾⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⡄⠹⣷
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢰⣾⣝⡆⢹⣿⠀⣿⡅
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣧⠸⣿⣭⣵⡿⠏⣰⡿
⠀⠀⠀⣄⡀⡐⠈⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠭⠭⢴⣾⡿⠥⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠛⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣷⣶⣮⡍⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠓⠛⠛⠋⠛⠛⠋⠛⠙⠛⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⢸⡿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡆
⠀⠀⠀⠀⣠⣿⣧⣿⡿⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⣾⣿⡟
⠀⠀⠀⣴⣿⣿⣿⣿⢣⣾⣿⣿⣷⣿⣿⣿⣶⣶⠦⣬⣶⣾⣿⣿⣿⣿⣿⣦⣤⣀⠀⣿⡟⣠⡄
⠀⠀⣼⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⠻⣿⣏⢻⣷⣿⡟⠉
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠉⠹⣏⠹⣿⡿⠿⠯⠄⠀⠀⢸⣿⡟⠇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠿⠿⣟⣿⣿⠃⠀⠀⠹⣄⠈⠛⠷⠄⠀⠀⣀⣼⣿⡇
⠀⢸⣿⣿⣿⣿⡿⠘⣿⣿⣦⣤⣶⣷⣾⣿⣿⡄⠀⠀⠀⠻⣷⡤⠤⠀⠤⠤⣿⢿⣿⠒
⠀⢸⣿⣿⣿⣿⠃⠀⠸⣿⣿⡟⢁⣼⣿⣿⣶⣤⣤⣄⣠⣄⡿⣿⣿⣿⣿⣟⠃⢸⡷
⠀⢸⣿⣿⣿⣿⡆⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠉⢿⣿⡗⠀⠀⣼⠁
⠀⢸⣿⣿⡾⢿⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣄⢿⣿⡃⣰⠏
⠀⢸⣿⣿⠤⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠛⠛⠊⠟⣸⡿⡀
⠀⢸⣿⣿⣽⣿⣿⡿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⣠⡀⠀⠰⣿⠇⢽⡆

⠀⠀⢘⣆⢠⣾⠆⠛⠋⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⣾⣆⣀⣀⠀⠀⠀⠀⠸⠿⠃
⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⡞⣷⠀⠀⠀⢀⡤⡞⠿⠗⠀⠀⢀⡾⠿⠂⡼⠿⠆⠀⠀⣾⠁⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡴⣦⠀⠰⣞⡇⠀⠀⣵⠏⠀⠀⠀⠈⠙⠁⣤⠀⠀⠀⡜⠁⠀⡼⠁⠀⠀⠀⠠⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣹
⠀⠸⣿⠞⠚⠁⠀⠈⠃⠁⢀⡞⣽⠶⢶⡄⠀⢀⣤⣴⠃⠀⠀⠀⠉⠙⠚⠁⣀⠀⠀⠀⠀⠀⠀⡤⢄⣰⣩⠆⠀⠀⢠⣶⣦⠀⢰⣿
⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠸⣆⠧⢁⣸⠇⠀⠈⠙⠃⠀⡠⠤⡀⠀⠀⢀⣴⣏⠀⠀⢀⡤⣄⠀⠙⠊⠉⠀⠀⠀⣠⠏⠈⠁⠀⠈⠁
⠀⠀⠀⠯⠵⠫⠖⠃⠀⠀⠀⠈⣙⠛⠁⠀⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠻⣴⠋⠀⠀⣸⣼⠃⠀⢀⣶⠀⠀⠀⣀⠀⢀⣴⣄⠀⢠⣖⡦
⡀⠀⠀⣀⠀⣀⡴⠛⢦⡀⠀⠀⠉⠋⠀⢠⠏⠉⢹⠃⠀⠸⠀⠀⢀⣀⠞⠁⠀⣰⢞⣽⣄⡀⠀⢘⣧⠀⠀⣼⠻⠃⡼⠉⠁⠀⠸⡇
⠃⠀⠀⠻⠟⢡⣤⣠⠜⠻⣄⠀⠀⠀⣀⡼⢀⣄⡟⠀⠀⠀⣠⣄⠻⡟⠀⠀⠰⡇⠏⠀⢨⡇⠀⠘⠀⠀⠰⢿⣗⣺⠃⠀⣼⠃⠀⠃⠠
⠃⠀⠀⠀⠀⠈⠛⡁⠀⣠⠞⠁⠀⠘⠿⠃⠈⠛⠁⠀⣴⡆⠻⣅⠀⣹⣆⠀⠀⢙⠲⠶⠛⠁⠀⡤⣤⠀⠀⢠⣄⠀⠀⣸⣧⠀⠀⠀⢰
⠀⣠⣖⠁⠀⠀⠘⠿⠋⢁⡀⢠⢞⡆⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⢾⡥⠞⠁⠀⠙⠓⠁⠀⡔⢠⡟⠁⠀⠀⢸⡸⠃⠀⠈⠉
⠈⠁⠋⣀⣀⠀⠀⠀⠀⠸⠿⠋⠉⠀⠀⠀⣠⢾⡅⠀⠀⠈⠯⠖⠋⠀⠀⠀⠀⢀⠀⠀⠀⠈⣉⠀⠀⠀⠰⣉⠇⠀⢠⠏⠙⢲⠆
⢀⡀⠈⠓⢮⣇⠀⠀⠀⠀⢀⣠⣴⣦⠀⠀⠀⠉⠀⢠⡤⠤⣤⠀⠀⠀⣀⣤⡞⠉⢳⡀⠀⠸⡯⠭⢽⠀⠀⢀⣤⣴⠋⣀⣠⠏
⣻⠏⠀⠀⠸⡿⠃⠀⠀⠐⠋⠀⠈⠉⢠⣶⡄⠀⠀⢸⠋⠉⣿⠀⠀⢺⡁⠀⣳⡀⢀⣷⡄⠀⣷⣦⢸⡇⠀⠀⠉⠁⠈⠛⠋⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⢠⣶⡆⢸⠉⠀⢀⣤⡿⠰⣿⠇⠀⠀⠀⢳⡐⠿⠃⠈⠛⠁⠀⢀⠀⠀⠿⠗⠀⠀⠀⠀⡞⣇⠀⠀⠉⠋
⠀⠀⡀⠀⠀⠀⠀⠘⡷⢄⠀⢸⡥⠤⣾⠀⠀⠀⠉⠁⠀⠀⣤⣆⠄⠀⠿⠗⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣤⡀⢈⠽⡄
⠀⣷⣿⠄⠀⠀⠀⠀⠛⠃⠀⠈⠛⠉⠉⠀⠀⠀⢀⣀⠀⠘⠱⠋⠀⠀⣤⡄⠀⠺⣝⣦⠀⢠⣶⡇⠀⢠⣶⡄⢸⠋⠁⠈⠊⠁⠀⣄
⠀⠉⠈⠀⠀⠀⢠⡒⡄⠀⠀⠀⢠⠖⣛⣛⡶⠾⡥⠾⠃⠀⠀⢠⣦⠀⡟⠁⠀⠀⠀⣿⡆⠀⠉⠀⠀⢸⣉⣤⣿⠀⠀⠀⠀⠀⣿⠋
⠀⠀⢀⡞⠀⠀⢸⡇⠀⠀⢀⣀⢿⠈⠁⢛⣷⠀⠀⠀⡄⠀⠀⢸⡁⠀⢻⠀⠀⠀⠀⠈⠀⠀⣤⣄⠀⠘⠒⠒⠋⠀⠀⠀⠀⠟⠙
⠐⣿⡟⠀⠀⠀⠘⠃⠀⠀⠈⠫⠘⠛⠲⠛⠁⠀⠀⣼⣥⡀⠀⠘⣧⠴⠞⠀⠀⣀⡀⠀⠀⠀⣿⣉⠀⠀⠀⢀⡄⠀⠀⢠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠛⠒⡆⠀⠀⠀⠀⠀⠀⠀⠸⢧⡞⠀⢠⣦⡀⠀⠀⠀⡴⠛⠛⠀⠀⠀⠸⠜⠀⠀⣰⡟⠁⠀⠀⣾⠀⠀⡇
⢠⣶⡄⠀⠀⠀⢰⠇⣀⣸⠃⠀⠀⢀⣀⠸⣿⠃⠀⠞⠀⠀⣀⡯⠇⠀⠀⠘⠁⠀⠀⠰⣖⢦⠀⠀⠀⠸⠉⠃⠀⠀⠀⢿⣶⠀⣇
⠋⠉⠁⠀⠀⠿⠟⠀⠻⠛⠀⣠⣤⠸⣟⠀⠘⣦⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢀
⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠙⣏⠀⢈⣶⣚⡭⠇⠀⢠⠤⣄⡴⣻⠆⠀⢰⠯⣟⣷⠀⠈⠛⡁⠀⠀⢸⡭⠃⠀⠀⢀⡞⠓⢦⣤⣀⠈
⠀⢀⡤⠖⢿⠉⠈⢧⠀⠀⠀⠀⠈⢿⣭⠞⠉⠀⣀⠀⠀⠉⠁⠉⠁⢀⣀⡏⣠⣤⡏⠀⠀⣿⣿⠀⠀⠸⡇⠀⢠⣄⡾⢀⣄⡾⠀⢉⡟
⣀⣈⣧⣀⣈⣧⣀⣨⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼⣻⣇⣀⣀⣀⣀⣀⣻⣟⣀⣈⣉⣀⣀⣀⣘⣀⣀⣀⣀⣁⣀⣈⣛⣁⣘⣛⣁⣀⣼⣁
⣿⣿⠋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣶⣦⡄⠀⠀⠀⠀⠀⠀⢰⣦⣦⣶⣴⣤⣴⣴⣤⣀⠀⢦⡠⠀⠀⣤⣰⣶⣦⣴⣶⣶⣶⣦⠀⡀⠀⣠⡆
⠘⢿⣿⣄⡀⢀⠀⢴⢖⣴⣿⣿⠿⣿⣿⣿⣿⣿⣿⣽⣷⡘⠷⠀⠀⢻⣿⣿⠿⠛⠙⡿⢿⣿⣿⡆⠀⣵⣧⣤⡄
⠀⠋⠀⠉⠉⠈⠁⠀⠀⠀⠈⠁⠀⠙⠀⠁⠻⠿⣯⣿⣟⠻⠆⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠊⢻⣿⢭⠽⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠘⡄⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠏⠀⠀⠀⠀⠀⠀⢉⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠐⣀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠉⣍⣻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣶⡄⠀⠀⠀⠀⣾⣷⣦⠀⠀⠀⠀⠀⣼⣿⣿⠟⢀⣰⢟⣿⣿⣿⣿⠇
⠀⠀⠀⢀⠄⠢⣄⢼⢿⣿⣿⢿⣤⡀⣠⣼⣟⠉⠙⠛⠲⢶⣴⣶⣿⣿⣿⠀⢲⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣏⣽⢿⣿⣽⣷⣂⣀⣀⡀⠀⣬⣿⣿⣿⣿⣇⡩⢿⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣾⡠⢹⠛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣴⣿⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠙⠛⠻⣿⣿⣿⠿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⣷⡶⠛⠉⠀⢈⣩⣻⡿⠙⣿⠟⢇⠀⠀⢀⠀⢀⣸⡟⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣤⣍⡉⠛⠿⠟⢻⣾⣿⣤⣼⣦⣀⣤⣞⣻⣷⣷⣴⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠙⠛⠉⠙⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠇⢸⠀⠀⢀⣤⣚⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣗⣌⣀⣠⣟⣉⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠲⠒⠛⠉⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⠀⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡁⡱⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⢦⣀⣰⣄⣀⡤⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠤⣀⣀⣇⣠⡞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠑⡀⠀⠀⠀⠀⠈⣉⡥⠖⠒⠒⠒⠲⢤⣀⠀⢀⣠⠤⠤⠤⠤⣄⡈⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠃⠠⢄⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠀⠀⠀⠀⠀⠀⠉⢢⡀⡊⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠊⢠⠋⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⢹⡀⠀⢀⣀⣀⡀⠀⠀⢱⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡞⠀⠀⠀⠀⠀⣼⣿⣿⣟⠁⠈⣧⠀⡇⣴⣿⣿⡟⠉⢣⠀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣿⢠⡟⣿⣿⣿⣷⣶⣾⠀⢰⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⢄⠸⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠁⡼⠀⠙⠿⣿⣿⠿⠋⢀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠒⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠢⢤⣀⡀⠀⣀⡴⠋⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠙⠓⠒⠶⠒⠚⠉⠀⢠⡀⠀⠀⠀⠉⣏⠁⢀⣀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⢠⠉⠒⠦⠤⠖⠃⠀⠀⠀⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢇⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠘⠦⣽⡒⠶⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⠖⡇⣠⠜⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡤⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⡸⠁⢧⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠀⠈⠻⢶⣒⠤⠤⠤⣀⣄⣀⣀⣀⣀⣠⣀⡤⠤⠤⠄⣲⠞⠁⠀⠀⠣⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⡖⠒⠒⡶⡖⠒⠒⡶⡖⠒⠒⠻⢉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠀⢀⣠⠞⠀⠀⠳⢄⡀⠀⠀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣄⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⣤⠄⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠽⠀⠠⠀⠀⠀⠀⠠⠄⠂⠀⠠⠠⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠈⠁⠀⠀⠁⠰⠚⠋⠁⠀⠠⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠠⠂⠈⢁⡀⠀⠀⠠⠄⠀⠀⠐⠂⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠐⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠇
⠀⠀⠀⠀⢀⡤⠀⠀⠁⣤⡌⠁⠀⠀⠀⠁⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠒⠒⠀⠀⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠉⠀⠈⢦⠃⠉⠀⠀⢡⡎⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⢀⠀⣀⠀⠀⠀⠀⠈⠀⠒⠂⠀⠀⠐⠀⠀⠀⠀⢂⠄⠀⠠⣀⡠
⠀⠀⠀⠀⠀⠄⠀⠊⠀⠀⠀⠒⢢⡔⡂⠀⠀⠈⠀⠀⠐⠀⠀⠀⡅⠀⠈⠠⠀⠀⠀⡠⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⡀⠉⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠄⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⡀⡀⠃⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣠⠄⠠⠄⠀⠰⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠔⠈⠀⠄⠀⠀⠂⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠠⠠⠂⠆⠀⢠⠎⠁⠀⠀⠁⠀⠀⠀⢀⠄⠀⠐
⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠠⠄⠢⠀⠤⢄⠀⠀⠀⠀⢀⠀⠘






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠇⠀⠀⣼⣇⠀⠰⠀⠖⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢑⠚⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⣠⣠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠘⠃⢀⠀⠀⠰⣴⣶⣼⣷⣷⣿⡻⣿⣯⠀⠂⠶⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⡀⣴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠻⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠟⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⢠⣤⣶⣦⣼⡅⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡏
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁⢸⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣄⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡴⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⣿⣿⡿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠀⠛⣌⢻⣯⠤⠖⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⢸⣿⣿⣿⣿⡏⠉⣩⣿⣿⣿⣿⣿⣿⢻⣿⡏⠠⠤⠈⢿⣷⣤⠀⠂⠀⠀⢙⣿⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⣿⣿⣿⣿⠒⠐⣿⣿⣿⣿⣿⠟⠑⠛⠉⢿⣄⠀⠶⠊⢻⣿⣷⠀⢠⡄⢺⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⢋⣹⣿⣿⡇
⠀⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⠟⣡⡆⠀⠀⠈⠁⠹⣿⣶⣶⣾⣿⣿⣶⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣷⣿⣿⣼⣿⣿⣿
⠀⢿⣿⣿⣿⣿⡁⠀⣸⣿⣣⣾⠟⠑⢪⣶⣤⠀⠀⠙⢿⣿⠃⠈⠻⣡⣿⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣷⣶⣿⣿⣿⣿⣧⡐⢿⣷⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣆⠘⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣦⣔⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣦⣽⣶⠬⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡟
⠀⢸⣿⣿⢿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣷⣄⡑⠀⢌⡹⣿⣿⣿⡿⠛⠛⠛⡻⠋⠀⠈⡀⠆⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⢸⣟⠛⠿⢿⣿⠿⡇⡄⠀⠀⢻⣿⣿⣿⣿⣿⣶⣤⣄⣿⣿⣿⣿⣶⠖⣸⠃⠀⠀⢠⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇
⠀⢸⣿⣿⣦⣾⣿⣶⡂⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣄⣀⣴⣿⣧⠀⠀⠀⠀⢹⣿⣿⢿⣿⣿⣿⣿⣿⠇
⠀⢸⡿⠿⣿⣿⣻⣉⠁⢻⣷⡀⢻⣏⠙⣿⡇⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣇⡀
⠀⠸⣿⣂⠈⠻⣏⣡⣤⣤⢿⣿⣾⣿⡴⠋⠀⠀⠀⢀⣴⣿⡿⠉⠉⢩⠃⠘⢧⣴⠛⢉⣛⣿⡀⠀⠀⠀⣠⣿⣷⣿⣶⣚⣉⣉⡁
⠀⢸⣿⣯⢀⣾⣿⣿⡿⠃⢸⠉⠻⣿⡀⠀⠀⠀⢺⣆⣿⣿⣿⣄⣶⣮⣧⣀⣤⣌⣡⠾⠿⢿⣷⣠⣶⣿⣯⡈⢠⣧⢹⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣾⣧⣄⡻⠿⢶⡀⠀⢻⣿⣿⢟⣿⣿⡿⠴⠷⠿⣻⡟⠁⠀⠀⠀⠹⣿⠀⠈⣿⣿⣿⣧⣴⣿⣿⣿⡟
⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡦⢬⣥⣤⣬⢥⡶⠛⠛⠻⢷⣤⣤⣾⡏⠀⠀⠀⠀⠀⢠⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠙⣿⠛⠛⣿⣋⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⡆⠀⠀⠀⢀⣼⣿⣧⣾⣿⢿⣿⣿⣿⠿⠿⠿⠇
⠀⠀⠀⠀⠛⠿⠿⠿⠟⠛⠛⠿⣿⡇⠀⢀⡰⣦⠤⠀⠀⠀⣤⣾⠛⠥⠉⣦⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣬⣴⣼⣶⣤⡀⣬⣽⣿⣶⣶⣮⡘⢻⣿⡛⡟⠛⠋⠉⠉⠉⠛⠻⢿⣿⣶⣶⡿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⠿⠿⠛⠁
⠀⠀⡶⣦⡴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠿⠛⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠤⠤⠤⠤⠄⠿⡿⠏⣿⠆

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠈⠀⠈⠠⠀⠄⠠⠀⠀⠀⠀⢀⣤⡀⡀⠠⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⢢⡀⠈⠁⡀⠀⠈⠀⠠⡌⡙⢿⡛⢿⡀⢙⣷⠀⢰⣦⡼⢷⣀
⠀⠀⠐⡆⠀⠀⢨⠁⠀⠀⠀⣦⣦⣄⡀⠀⠀⠂⢥⠰⠌⡛⣁⠀⠼⠏⣾⡿⠛⠉⠀⠞
⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠰⠫⢻⢻⠛⢦⡣⠀⠀⠀⢡⠁⠀⠀⠀⢆⠋⠀⡀⠔⢐⣶⣤⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⡄⠎⠁⠀⡀⠸⠦⠀⠀⡄⠈⢃⠀⠂⢁⢣⠂⠁⠂⠀⣀
⠀⠀⠀⠂⣈⠀⠂⠀⠀⠀⠀⠀⠀⠢⠀⠘⠀⡀⠄⠋⠢⢠⠸⡦⠜⠀⠀⠀⠐⠃⠄⠀⠀⠈⣡⠆⢔⠀⠀⠂
⠀⠀⠀⡾⠁⠀⣴⡏⠐⠂⢤⣤⣀⣂⡙⠀⠴⣤⡈⠠⢖⠚⡠⠅⢂⠄⠀⠂⠨⠄⠄⣠⠔⢾⡇⢴⠂⠐
⠀⠀⠀⠀⢶⣤⣿⡇⠀⠀⠈⠛⢻⠋⠀⠄⠀⡀⠈⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠒⢺⠇
⠀⠀⠀⢀⣰⣿⡏⠀⡓⠊⠐⢀⣈⠀⠠⠎⠀⠀⠨⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠐⠀⠄⣁⣴⡿
⠀⠀⠀⠈⡿⠋⠀⠁⠀⠀⠀⢀⠉⢠⡄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠙⠂⠰⢿⣽⠇
⠀⠀⠀⢷⠔⠀⢀⣤⣶⡎⣤⠜⠁⠀⢀⠄⣀⡂⣀⠀⠀⠒⠀⠀⠀⡀⠀⢀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠨⠄⠀⢸⣏⣌⣁⠙⢶⠀⠀⢸⠀⢇⠀⠀⠀⣠⠧⠀⠀⠐⢃⠀⠘⠠⣁⡀
⠀⠀⠐⠁⠀⠀⡀⠉⣱⠏⠀⠰⠀⠀⠈⡇⠈⠃⠌⠁⣀⠀⠀⠀⠐⣠⢦⡤⠚⠻⢟⡀⠖⡤⠀⠀⡠
⠀⠀⠀⠀⠐⢾⣶⣴⣿⠁⠀⠀⠀⣤⣴⣷⣄⡀⠀⠀⠅⠀⢂⣠⠶⢹⣥⣂⢐⡘⠃⠁⠾⠷⢂⣠⡀
⠀⠀⠀⠶⠀⠀⠻⣿⣃⣀⣀⣀⠈⢨⠟⠉⠉⠍⠈⠀⠸⢂⠯⠀⠩⠀⡟⠟⠅⠈⢢⠲⢟⠛⠋⠉⠀⣠⠀⡀
⠀⠀⠐⠀⢰⠀⠀⠈⡿⠏⠛⠉⠀⢀⡀⠀⡘⢆⠛⠠⠠⢹⣥⢤⠴⣎⠁⠈⢃⡔⠁⠁⡀⣘⡂⣴⡞⠛
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⣰⣾⣿⣗⠀⠄⠈⠦⠤⠀⣸⢕⠥⡊⠀⠑⡤⠋⣀⣤⠅⣬⣭⠃⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⡻⠷⠠⣤⣤⣤⣾⡃⠁⢀⠄⠠⡀⡏⠀⠀⠋⠀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠛⠛⠉⠢⠁⡡⠠⢴⣶⣶⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠈⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠄
⠀⠀⠀⠀⠈⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠀⠀⠈⠵⠿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠴⠢⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣠⠄⠀⠀⠄⢁⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠁⡀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡁⠀⠀⠁⠀⠀⡀⠀⠀⠙⠔⢫⠂
⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠆⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⡸⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠎⠀⢠⣀⠀⢀⡀⠄⠊⠀⠸⠀⠀⠀⠁⠀⠀⠂⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⡈⠁⠠⡀⠀⠀⠁⠀⠀⡠⠊⠀⠘⠅⢀⡀⠚⠀⠠⠂⠀⠀⢄⠀⠀⠈⠀⠀⠀⠀⢀⡬⠃
⠀⠀⠀⠀⠈⠃⠄⠀⠀⡀⡁⠰⣀⠀⠉⠀⠀⠀⠀⢀⠁⠚⠀⠀⡀⠀⠀⠀⠀⠁⡦⢀⣀⡀⠠⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠔⠈⠈⠀⠑⠆⠀⠀⠀⠀⠸⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠤⣀⢺⣀⡀⠀⠀⠀⠀⡄⠀⡐⣂⠀⡠⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠄⠀⠀⠀⠠⠀⠀⠀⠀⠈⠈⠀⠨⠉⠀⠀⠀⠀⠀⠀⠠⣄⠀⣀⠌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠂⠘⠂⠈⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡠⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠘⠀⠂⠀⠂


⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣟⣛⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣥⣥⡙⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣏⣽⣯⠀⢀⠀⠀⠀⠀⠄⠂⠉⢤⣤⣀⢨⣑⢢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣰⣄⣀⣀⣀⠀⠀⠈⢿⣷⡏⠀⢡⣀⣄⣀⡚⣿⣶⣶⣾⣿⠷⠿⠿⠷⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣤⠞⠑⠛⠛⠻⢿⣿⣶⣤⣼⣿⣿⡀⠐⠩⠿⣯⣛⣿⣿⡿⠉⢐⣮⣶⣷⣶⣮⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠴⠃⠌⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣇⡀⠈⠊⣿⣿⡟⠐⣛⣻⣿⡟⢉⡍⢹⠧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣌⢻⣷⢤⣿⣿⠁⠀⠨⣿⣿⡅⠠⠿⠏⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣿⣿⣿⣿⡄⠠⣿⣻⣿⣿⣶⣶⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⣿⣿⣷⡀⠈⠵⠞⣽⢿⡿⣩⠟
⠀⠀⠀⠀⠀⠀⢠⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡺⢿⣿⣿⣷⣤⣤⡤⠶⠛⠁
⠀⠀⠀⠐⠒⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠛⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠀⠈⡆⠀⠀⠀⠐⠀⢀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠆⠈⢀⠈⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢃⢠⠜⢻⠆⠠⢀⠀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠡⠀⠀⠀⢄⡄⢠⡎⡃⢀⢆⢀⣀⡉⠆
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠊⠓⠀⠀⠁⢁⢀⠀⠀⠀⠀⠐⣢⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⢃⠛⠁⠁⢠⠀⠰⠈⠉⠀⠄
⠀⠀⠀⠠⠀⠀⠀⣀⡀⠀⢀⠀⠐⠀⠠⡀⠀⠀⢀⡀⢀⡈⠀⠀⠈⠌⠉⠀⠀⠉⠑⡑⢦⢴⠬⡰⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣶⠀⠃⠀⠠⠂⣀⠐⡯⢙⠁⠀⠀⠁⠁⠁⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠁⠀⠉⠁⢑⡄⠛⠋⠇⠀⠀⠀⠀⠀⠁⠐⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠒⠌⡄⠀⠀⢈⠀⠀⠀⠸⠰⠀⠸⠁⠊⠀⠀⠀⠄⠀⠀⠀⠀⢀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡄⠀⠀⢀⠠⠢⠇⠀⠀⠡⠉⠉⠉⠍⠀⠀⠀⡇⠀⠀⠀⠀⣐⠃⠘⡼⠀⠘
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠘⠞⠫⠠⠐⠂⠀⠆⠀⠀⠀⠀⠂⠀⣎⣡⠠⠁⢠⣠⢼⣀⣀⣠⠂⠉⠀⢀⡠
⠀⠀⠀⠠⡀⠙⡔⠀⠀⠂⠐⠒⠋⢴⠒⠠⢢⡀⠀⠀⠀⠀⠀⠀⠝⠉⠀⠀⠀⠀⠈⠎⠈⠘⠋⠉⠉⠁
⠠⠠⠀⠠⠈⠊⠀⠠⠠⠀⠀⣠⢤⡀⡃⢸⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠠⠛⠏⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⡀⢀⠄⠀⠈⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⢀⡀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⣄⠀⣀⣈⡙⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⡀⠈⡖⣁⡀⠙⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡄⠈⢹⢩⡄⠈⠑⡇⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⣸⣎⠁⠀⣠⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣁⣉⠉⠀⠈⠓⠊⠁⠀⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠉⠓⠒⠲⠒⠒⠋⠁⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⡑⢄⡀⠀⠀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢟⠢⣍⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡄⠀⡏⠒⠬⣍⣒⠒⠤⠤⠤⠤⣤⡤⠤⠤⠤⠖⣒⣋⠥⠂⢳⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠙⡆⠓⠶⢶⠄⠀⠉⢉⣑⠒⢒⡖⠒⠒⠂⠉⠉⡴⠋⢱⣰⠁⢙⡦⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⣀⠀⠀⢸⠆⠉⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠲⢤⣀⡀⠀⠈⢹⠒⠒⠒⣄⠀⠀⠀⠀⠀⢯⡀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢉⡽⠛⠛⠀⠀⠀⠘⠦⠤⣤⠤⠤⠖⠛⢉⠏⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣠⠴⠋⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠉⢹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⡻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠋⠀⠀⣠⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⡌⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⢀⣀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣯⣠⣶⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡁⢈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⣿⣿⣿⠟⠁
⠀⠀⠀⢀⣠⣤⣤⣤⣤⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣷⣴⣿⡿⠋
⠀⢀⣾⣿⡿⠿⠟⠿⢿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⣠⣾⣿⣿⣧⣀⣼⣿⡿⠋
⠀⠸⣿⣿⣄⡀⠀⠀⣀⣼⣿⡟⠀⢀⣴⣿⡿⠿⠿⠿⣿⣿⣿⡟⠁⢙⣿⣿⡿⠋
⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁⢠⣿⣿⠋⠀⠀⣠⣾⣿⠟⢿⣿⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠁⣀⣠⣤⣴⣿⡿⠃⢀⣠⣾⣿⡟⠁⢀⣴⣿⣿⣿⡀⠀⠀⣴⣶⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠟⠛⠉⠀⣴⣿⡿⠛⢿⣿⣶⣿⡿⠋⢸⣿⣷⠀⠀⣿⣿⡏⠉⢉⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⡇
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⣠⣿⡿⠋⠀⠀⣸⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⣿⣿⡇
⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠟⠁⣀⣤⣾⣿⠟⠀⠀⠀⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⡏⠀⠀⠀⠀⠰⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠘⣿⣷⠀⠀⠀⠀⠀⠈⠻⣿⣶⡄⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣿⣿⡇
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⡇⠀⠀⠀⢀⣾⣿⡿⠿⠿⢿⣿⣿⡇
⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣄⣀⣀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢺⣿⣯⡁⠀⠀⣉⣿⣿⠇⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣾⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠰⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⢀⣤⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⣠⡟⠉⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠈⠉⠉⠀⠀⣇
⣴⣶⣦⡿⠀⠀⠀⠀⠀⠉⠑⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⣯
⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⢀⣴⣶⣴⣾⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠘⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⠟⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⡿⠃⠀⠀⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣈⠄⠀⠀⠀⠀⠘⠛⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠚⠲⠄⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠆⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢀⠤⣀⠴⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⠟⠉⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡄⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡼⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⠁⠀⠀⠀⠀⣼⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠉⠉⠁⠀⠻⠇⠀⢠⡿⠀⠀⠀⢀⡼⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⡥⢤⡴⠞⠁⢀⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⡀⠀⠈⢷⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠙⠛⠶⣦⣤⣤⣤⣤⣴⣶⠶⠞⠛⠁⠀⠘⣷⡀⣨⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣵⣤⣤⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⠋⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢹⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⡀⢸⡀⠀⠀⠀⠸⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠶⠿⢿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⡼⠏⠉⠛⠀⠀⠀⠀⠀⠈⣿⡉⠉⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡆⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣤⣤⣭⣬⣯⣬⣥⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠈⡏⠀⠀⢹⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⢾⡇⠀⠀⢸⡷⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣾⡇⠀⠀⢸⣷⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⠒⡶⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⢀⡴⡋⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⢬⠍⢩⠍⠉⠀⠀⠂⠀⠆⠀⡀⠆⠉⠓⢦⡀
⠀⠀⠀⢀⡞⡀⠋⠀⠀⠈⠀⠄⠀⠀⠋⠀⠀⠰⠀⠠⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢀⡀⠀⠁⠀⠹⡄
⠀⠀⠀⢸⠃⠁⠀⠈⢀⠀⠀⣀⠀⡀⠀⠁⠀⠀⡀⠀⠀⠰⠆⠀⠐⠀⠸⠆⠀⠄⠀⠀⠠⠀⠁⡀⢻
⠀⠀⠀⢸⡀⠉⠀⠀⠈⠠⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠄⠀⠖⠀⠀⠀⠤⢠⡄⢸
⠀⠀⠀⢸⢳⡀⠀⠀⠐⠗⠀⠀⠀⠂⠀⠀⠠⠀⠴⠀⠀⡠⠆⠀⠀⡀⠀⢀⡀⠀⠀⠂⠀⠀⡀⠀⣾
⠀⠀⢀⣼⡀⡝⢦⣀⠈⠀⠈⠃⠀⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡒⠀⠰⠆⠀⠀⠀⠀⠤⠀⢀⣾⠇
⠀⠀⡏⠈⣧⠀⢀⠈⢹⡗⠒⠶⠶⠶⡒⠒⠟⠉⠉⡁⠐⠀⠀⢨⠉⠙⠓⠲⠤⠤⠤⠤⠴⠚⠁⡞
⠀⠀⢧⠀⠈⠳⣄⠠⠀⠤⠈⠀⠄⠀⠅⢀⡀⠀⢀⠠⡦⠀⠄⢀⡀⠀⠀⠁⠀⠂⡀⠰⠄⣀⡞⢁⣤⣄
⠀⠀⠈⠳⣄⡀⠈⠙⠲⠦⠤⣤⣤⣤⠤⠴⠖⠒⠚⠒⠒⠶⠶⠬⠥⠤⠥⠤⠭⠤⠤⠴⢚⡟⠀⠛⠒⠚
⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠙⠒⠦⢤⣀⠀⠀⠀⢀⣀⡤⠖⠒⠛⠛⠒⠒⠦⠤⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠰⣏⣉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⠿⠿⠿⠿⠿⠿⠿⣿⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠁⣀⣤⠤⠖⠒⠒⠒⠒⠒⠲⢖⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⣠⠶⠋⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⣠⠊⠹⠀⠀⢂⠀⠐⣄⠀⠀⠀⠀⠀⡆⡀⠀⠄⠀⠀⡠⠂⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⣰⣿⠏⠀⠀⣰⡇⠀⠀⢀⠀⢀⢢⣳⣽⣧⡶⠶⢷⣦⣧⣄⣞⡒⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣰⣿⠏⠀⠀⠰⠋⠳⣄⠀⠘⢿⡶⠛⠉⠘⠁⠀⠀⠀⠀⢘⠙⠷⣥⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣤
⠀⠀⢀⣿⡟⠀⠀⠀⡇⠀⠐⢌⡻⣶⠏⠀⠀⠀⠰⡀⠀⠀⠀⠐⠀⠀⠔⠊⢻⡞⡀⡐⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠁
⠀⠀⣸⣿⠃⠀⠀⢰⠀⠀⠀⠀⣹⠃⠀⠰⡤⠿⠛⠉⠟⢛⣍⣀⡄⠀⠀⠀⠀⢿⣿⢁⠄⠀⠀⡀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣿⣷⠰
⠀⠀⣿⣿⠀⠀⠀⢸⣁⣀⣲⣶⣿⠀⢠⣾⠁⢠⡞⠲⣶⡀⠈⢻⡤⠀⠀⠀⠀⠤⣟⣡⠎⠀⠀⠀⠀⠀⢀⣠⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡀
⠀⠀⣿⣿⠀⠀⠀⠈⡥⡂⠔⢻⣿⡀⠈⢿⡀⠺⠆⠀⢈⡃⠀⢘⣇⠀⠀⠀⡀⠉⣻⣋⠀⠀⠀⣰⠄⣲⣍⠷⢋⣩⣭⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠻⢰
⠀⠀⢻⣿⡀⠀⠀⠀⢹⢀⠀⠀⠻⣿⡄⡀⢙⠶⢤⠴⠟⠁⢒⣿⠀⠉⠉⠉⠀⣉⣿⣿⣻⣝⣫⠔⢛⣩⣴⣿⢿⣻⣭⡏⡶⢦⠤⣤⣤⢤⡆⠀⢿⢀⡼
⠀⠀⠘⣿⣇⠀⠀⠀⠀⢧⣮⠀⠀⠀⠹⢧⣯⣄⣄⣀⣤⡶⡟⠃⠀⠀⠀⠀⢈⣩⣿⣿⣿⡩⣫⡾⢿⣝⠽⠌⣑⠼⣙⠲⢍⣳⡾⢛⠻⣿⣁⢈⣰⣿
⠀⠀⠀⢻⣿⡄⠀⠀⠀⠈⢿⣏⢀⡀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢈⠐⠻⠿⠿⣿⣿⣿⣿⣿⣿⣼⣽⣋⣗⡚⡏⣰⢎⡑⠦⣵⠺⡉⡷⣏⣿⢟⢽⢣⣢⢷⡀
⠀⠀⠀⠀⢻⣿⡄⠀⢀⡀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢙⣺⣿⣿⣶⣿⣿⣻⢹⡟⣻⠻⠿⢟⠿⢿⣿⣿⣿⣯⣖⣥⡛⡼⣢⣮⡓⣱⢲⣾⣯⣇
⠀⢀⣀⣤⣤⠟⡛⠉⠝⠐⠂⠙⡙⢿⣿⣷⣾⣄⠀⣦⣻⣬⣦⣳⣬⣾⣿⣿⠿⠛⠯⠯⠿⠏⡭⠫⠝⠻⢲⢤⣦⢤⣄⣅⣩⣽⣙⣻⣾⣷⣿⣿⣣⡿⢿⣥⠋⠉⠙
⠃⠀⠂⠀⠀⠠⠤⢤⣤⣤⠤⠤⠤⠬⢭⡙⠛⠛⠻⠿⠿⠟⠿⠛⠛⣋⣁⣠⡤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⣁⠀⡉⣉⠛⠛⠋⢃⣹⣄⠄⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠾⠿⠿⠿⠿⠷⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠙⠃⠀⠀⠰⢶⠶⠶⠶⠶⠶⠦⣤⣄⣉⠙⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣠⡤⠀⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠻⠶⢦⣈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⠞⢉⠁⠀⠀⠀⠘⠀⠘⠁⣠⠄⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⠟⢁⣴⠇⠈⠀⠀⠀⠀⣀⣀⠀⠀⡠⠀⠁⠀⠙⠠⡖⠀⠀⠐⠃⠀⠀⣠⡀⠠⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣠⡾⢁⣴⠟⣡⡆⠀⠠⠀⠀⠐⣿⣿⠇⠀⠀⢀⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠘⣿⡿⠀⢁⡀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣰⡟⢀⡾⢃⣼⠟⠁⠘⣄⠀⠀⠄⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⢀⠇⠀⠀⠀⠀⢀⡀⠀⢠⡈⢿⡄⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡿⢀⡿⢁⣾⠃⡄⠀⠀⢈⡳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠸⠃⣠⠚⣷⠈⢿⡄⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣿⠃⣼⠇⣼⠇⣼⠃⠀⠀⠀⠑⠢⣄⣀⠀⠀⠀⠀⠀⣀⣠⣶⠂⠀⠀⠀⢀⣾⡆⠀⢀⢹⣇⠸⣇⠘⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡟⢀⡿⢠⡿⢰⡏⠀⠀⠆⠆⠀⠰⣁⣀⣿⡋⠉⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠛⠁⡀⢿⡄⣿⠀⣿⠀⣿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡇⢸⡇⢸⡇⢸⡇⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠆⠀⠀⠀⠰⠆⠀⣿⢸⡇⣿⡆⣿⠀⢹⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠸⣇⢸⣇⢸⣿⢁⠀⠀⠁⠀⠀⠻⢥⣀⣐⣉⡥⠞⠁⠀⡀⠀⠀⠀⠀⣀⠀⢸⡟⢸⡇⣿⠇⣿⠀⣼⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⣷⠀⣿⠀⣿⡘⣿⢲⡇⠀⠀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡞⠉⢦⣾⠇⣾⢀⣿⢀⣿⠀⣿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣿⡆⢹⣇⠸⣧⠹⣦⣷⣶⣦⣤⣤⣀⣻⣿⠋⠀⠀⠂⠀⠀⠀⣀⠀⢼⠀⠀⢸⠏⣼⠇⣼⠇⣼⠇⣸⡿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⣿⡄⢻⡆⠻⣦⡹⠻⢯⣯⣿⣛⢿⣿⣿⣿⣷⡖⣦⣤⣤⣀⣬⣤⣤⣿⢺⣏⣼⠋⣼⠏⣰⠟⢠⣿⠃⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠹⣷⡄⠻⣦⠹⣇⠤⠾⣌⡻⢿⣿⣿⠿⠿⣾⣯⣭⣿⣻⣿⣿⣿⣿⣿⢸⠟⣡⡾⢃⣴⠏⣠⣿⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⢿⣆⠙⢷⣄⠒⢼⣍⡛⠶⡇⣛⡛⠷⠶⠾⠿⣿⢿⣟⣛⣭⡿⠋⠀⡾⠋⣠⡾⢁⣴⡿⠃⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⣷⣄⠙⠷⣤⣉⠻⢶⡇⢹⣙⡛⠛⠒⠒⢻⣼⣋⣩⣴⠶⠀⠀⣴⠞⢋⣰⣾⠏⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡈⠻⢿⣦⣌⣙⠳⣦⣶⣸⣍⡛⠛⠛⠛⢻⠘⣋⣩⣤⡶⠖⢒⣡⣴⡿⠋⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠉⢻⣿⣿⣿⣿⣿⣿⠛⣛⣛⣻⣿⣀⣯⣉⣤⣴⣾⠿⠛⢉⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣿⣟⣛⠙⠛⠻⢿⣿⣽⣿⣿⣿⡿⠛⠋⣉⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⢶⣿⣿⣿⣶⠶⠶⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠶⠒⠒⠛⠛⠛⠉⠉⠛⠛⠲⠦⡤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⢀⡖⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣀⣀⡀
⠀⠀⠀⠀⠈⡷⢤⣀⡀⠈⠉⠉⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣆
⠀⠀⠀⠀⢀⡇⢀⣄⠉⠉⠒⠲⢤⣀⠀⠀⠀⠈⠙⠒⠤⠤⣀⠀⠀⢀⣠⣀⣠⠤⠤⠤⠒⠒⠒⠒⠉⠋⠉⠁⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠁⣠⡀⠀⢀⠀⢀⠉⠙⠒⠦⢤⣀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠚⠋⠉⢹⡆
⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠙⠃⠀⡦⠀⠀⠈⠙⠲⠤⣄⣠⣤⠤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠴⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠺⠂⠰⠆⠀⠂⠀⠀⠀⠀⠀⠁⠰⠆⠀⡇⠀⠀⠀⠀⠀⠘⠛⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣠⠤⢇⠀⠰⠆⠠⠐⠀⠀⠀⠀⡀⠀⠐⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠄⣠⡀⠰⠷⠀⠀⠔⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⠾⣭⠿
⡴⠊⠁⠀⠀⠀⠑⠤⣀⠀⠀⠛⠃⢀⡄⠀⠀⠀⠀⠀⠐⠂⠀⠀⣇⠀⠰⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠓⠲⢄
⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡶⠀⠀⣠⡈⠀⠀⠀⠣⠃⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠉⠓⠶⠤⠤⠤⠤⢤⣄⣀⠀⠀⠈⠉⠓⠦⣄⣀⠀⠈⠀⠀⠀⠛⠀⢀⡀⠀⠀⠀⠀⠉⠀⢀⣀⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣤⠖⠒⢦⡄⠀⠀⠀⠀⠉⣳⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠈⠁⣀⣠⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠒⠚⣁⣀⣀
⠀⠉⠛⠛⠋⠁⠀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⣥⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠤⠤⠴⠖⣖⡒⠶⠒⠲⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⣷
⠀⠀⠀⠀⠀⠠⣤⠴⠶⢚⡋⣉⡉⠛⢁⡀⢘⣋⠀⢰⡮⠀⠛⠀⣤⡀⢶⠄⠙⠓⠦⢤⣀⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⡤⠞⠰⠶⠀⠀⠓⠚⠒⠮⠥⢈⡉⠀⠀⠀⠀⠀⡤⡄⠀⢠⠒⡄⠀⠰⠭⠆⠉⠙⠶⠦⣄
⠀⠀⠀⠀⢸⠃⢰⠒⡄⢠⠤⡀⠀⠀⢠⡚⡆⠀⠈⠻⣉⡹⠄⣈⡀⠶⠀⠉⠀⣖⡀⣤⣠⠔⠒⠂⠉⢹⡆
⠀⠀⠀⠀⢸⡄⠈⠉⠁⠘⠒⠁⣤⢄⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠈⢱⠂⠈⠉⠀⠀⠀⠀⠀⡤⡀⠁⠀⣷
⠀⠀⠀⠀⢸⡇⠀⢠⢤⠀⠀⣀⢌⠁⢀⣀⠀⠛⠁⡤⡀⠀⣠⡀⠀⠸⠀⠐⠝⠀⡴⢆⠀⠈⠒⢁⣀⠀⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠉⠀⠀⠧⠴⠃⠘⠆⠃⠀⠀⠉⠁⠀⠓⠃⢀⣇⠀⢀⡀⠈⠓⠊⠀⠀⣀⠀⠛⢸⡇
⠀⠀⠀⠀⠀⠳⣤⣛⣀⢰⢒⡄⠀⢠⢤⠀⠀⢀⡀⠀⢴⠄⠀⠀⠰⠎⠀⠈⠁⠀⠀⡠⢄⠘⠿⠃⠀⣾⠥⢤⡀⠀⠀⣠⠶⠒⠒⠶⡄
⠀⠀⠀⡴⠊⠉⠀⠁⠘⠮⣍⡀⠀⠳⠔⠁⠀⠣⠜⠀⠀⢀⣀⠀⢠⡇⠀⢀⡞⢲⠀⠓⠊⠀⠠⢄⠀⢸⠀⠸⣄⠀⠀⠓⠶⠖⠒⠚⠁
⠀⠀⠀⠳⢤⣄⣀⣀⣀⠀⠀⠉⠓⠖⢢⡀⠀⠀⣠⡀⠀⠐⠚⠀⣸⠀⠿⠀⠉⠁⠀⠸⠧⠀⠈⠁⢀⣸⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣳⠄⠀⠀⠀⠈⠑⠲⠬⣠⢄⠀⠀⠈⠛⠀⠀⠐⠆⠀⣀⣀⠠⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠦⠤⠔⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠴⠒⠉

⠀⠐⢄⠙⠀⠀⢀⠢⠀⠀⠁⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠀⠌⠠⠃⠈⠀⠀⠜⠀⢀⠈⡠⢊⡠
⠠⡘⠂⠀⢀⠀⠀⠠⡀⠀⠀⠀⠃⠈⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⢀⠀⠂⠀⠈⠀⢁⠈⠜⡠⢣⠊⠔⠁⠈⡴⠋
⠑⠄⠐⢄⠦⡑⠌⠂⠀⠈⠀⠀⣦⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⠀⠀⠀⡰⢣⠔⠑⠀⠀⣠⠔
⠤⠢⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⢠⠀⢀⠁⢀⠔⠡⠚⠁⠊
⠢⠀⠈⠁⠀⠠⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠄⠑⠀⠂⠀⠀⡠⢂⠁⡈⣀
⢅⡀⠁⣀⣴⣶⣤⣤⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠠⠂⠀⠀⠀⠀⠀⠉⠊⠅
⠄⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠊⠀⠁⠀⠐⣁⠀⢁
⠠⠄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⡈⠁
⠒⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣯⣭⣛⠽⠿⢽⣷⣤⣤⣤⣤⣄⣈⣉⣀⡀⠐
⡀⠀⠓⠆⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡷⠆⠘⠛⠛⠉⠉⠙⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⢶⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠿⠧⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠒⡀⠄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉
⠂⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⣄⣀⠀⠀⢀⣤⣤⣷⠤⠀⠈⠀⠑
⢂⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠛⢷⣄⢠⣿⣿⣿⡯⠀⠂⠀⢀
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⡄⠀⠀⠙⣿⣿⣿⣿⠫
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⠃⠁⠀⠀⠈⠛⠛⠁⠁⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠈⠂⠀⣁⢈⠀⢄⡀⢑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠉⠈⠉⠀⠀⠀⠀⠂⢀⠂⠀⠀⠠⡁⠀⠢⡍⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡄⠀⠠⣄⠀⠀⠀⠁⠀⠑⠄⠈⠀⡀⠠⣅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⣷⣶⣾⣇⣀⣤⣴⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀
⠀⠀⠀⢠⣾⠟⢉⣠⣴⣶⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄
⠀⠀⠀⣿⣥⣶⣿⣿⣿⣿⣿⣿⡿⠁⣀⣤⣶⣶⡿⠿⠿⠿⢿⣶⣶⣤⣀⠀⠀⠙⢷⣦
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠋⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠉⣹⡟⠉⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠈⢿⡄
⢀⣀⡏⠂⠀⢰⡟⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠈⣿⡄
⠿⠿⠃⠀⠀⣾⠃⠀⠀⢀⣿⡇⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠸⣿⡆⠀⠀⢸⣧⣴⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣧⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣿⡇⠀⠀⢸⣿⡿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣶⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⣾⠏⠀⣿⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⢻⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢹⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠀⢠⠇⠀⠀⢀⢜⣥
⠀⠀⠀⠀⠀⠘⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣾⡾⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢸⣇⣴⠋⠀⠀⠀⠘⢌⣡
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⠻⢿⣿⣿⣿⣿⠀⠀⠙⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢋⣴⠿⣿⠁⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⣰⡟⠁⠀⣹⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠀⢀⣾⡿⣿⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠋⢹⣇⠀⠘⣿⠀⢹⡀⠀⠀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⢠⡄⠀⠀⢿⣄⠀⠈⠁⠸⣇⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠙⠿⢶⣦⣤⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢾⢳⡄⠀⠀⠀⠀⣠⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠋⠀⠀⠀⠀⢰⣿⠿⠟⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⣿⣇⣀⠀⠀⣰⡿⠀⠀⠀⠘⢿⣆⢀⣀⠠⠿⠧⢀⣀⠀⢠⡿⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡠⠟⠋⠉⠀⠀⠀⠀⠈⠙⠻⢄⠀⠀⠀⢀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢇
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⣉⡑⢢⡀⢰⡇⠀⠀⠀⡠⢊⣩⣍⡙⢦⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⠆⠃⠸⡇⠀⠀⠀⡇⢸⣿⣿⡷⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢆⡙⠛⢉⡠⠃⠀⢳⠀⠀⠀⠑⢄⡉⢉⣀⠔⠀⠀⠀⠀⢀⣠⣠⣇⡀
⠀⠀⠀⠳⣄⡴⠋⠉⠑⠒⠤⣄⠀⠉⠀⠀⠀⢀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠦⠀⠉⡓⢦
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣴⠊⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠲⠀⠉
⠀⠀⠀⠀⠀⠘⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠉⠃⠀⢶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡶⠶⣤⣤⣤⣤⣄⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⣶⠚⠛⠉⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠉⠉⠉⡏⠉⣯⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣧⠀⢿⣀⣀⣀⣀⣽⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⢀⣀⣀⣀⠀⢠⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡤⠖⠒⠚⠒⢲⠶⠛⠉⠉⠉⠉⣻⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣰⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⢤⣤⣤⣤⣤⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠉⠀⠁
⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠉⠉⠛⠒⠚⠛⠉⠉⠉⠛⠓⠶⠚⢿⡉⠉⠉⠉⣻⢶⠶⠶⢶⡿⣏⠉⠉⠛⠛⣶⠶⠶⠶⠿⠛⠉⠉⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠞⠁⠀⢣⠤⢾⠀⠈⠷⣠⠴⠋⠁
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡞⠀⠈⢧
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⣴⠃⠀⠀⠈⢦⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠹⣄⠀⠀⢀⠜⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⡿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⣁⠀⢹⣧⣿⣿⣿⣿⣿⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠼⣿⢷⣿⣸⡟⣿⣧⣻⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠰⣿⣾⣿⣿⣧⢹⣿⣿⣿⣿⣿⣏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢹⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢠⣀⢲⣶⣶⡓⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣎⢿⣆⠿⠛⠁⠁⣤⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣷⡄
⠀⠀⢀⡀⠀⠄⠀⠀⠀⠠⠷⠿⠛⠛⠋⠉⠟⠛⠛⢦⠀⠀⠀⠀⠀⢻⣿⣻⢹⣿⣾⣿⣿⣻⢿⣿⣿⣆⣿⣿⣿⠇
⠀⠀⠀⠀⠈⠀⢲⠀⠙⠢⡀⠀⠀⠀⠀⠀⠈⢣⠀⢻⣥⡄⠀⠀⠀⣼⣿⣿⣾⠿⠛⠉⠁⠙⡏⢢⣿⡻⣿⣼⣿⡀
⠀⠀⠀⠀⠀⢠⡊⠀⢀⡀⠑⠆⠀⠀⠀⠀⠀⠐⡗⠀⢸⡇⠀⠀⣨⣵⣿⣿⠋⠀⠀⠀⠀⠀⠃⠀⠙⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⡇⢠⣿⣿⢟⡿⠉⠀⢠⡤⠴⠛⠀⠀⠀⠀⢻⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣏⡵⠋⠀⢠⣀⠀⠀⠀⠀⢀⣜⣥⠠⣯⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⣷⠘⠋⠀⠀⠀⠀⠙⣿⣶⣤⡀⣼⢿⠁⣼⠸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠷⢤⣾⣿⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠏⠙⠈⡡⢂⣘⣿⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⣀⣠⣶⡛⣿⠿⠛⡛⠋⠀⣀⡴⢡⣾⣿⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠛⠉⠙⣿⣿⣿⣷⣷⣻⣆⣀⠙⣶⣿⣟⣹⣿⠁⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣈⣿⣿⣿⡙⠛⡋⠁⠛⠿⢾⣿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠋⠉⠉⢱⣿⣿⣳⣶⣬⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠾⠿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣠⣤⣠⡄⠘⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⠠⢄⣀⣀⣨⣿⣿⡏⠉⠉⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣶⡛⠋⠙⢛⢿⡛⠛⠓⠒⠒⠒⠒⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣾⣿⣶⣻⡶⠀⠀⠀⢠⣤⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢉⣉⣭⡌⣇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠛⠉⠀⣀⣾⠂⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠈⠓⠀⠀⠀⠀⠲⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢶⠒⣚⣟⢉⠍⠩⠹⡗⢄⠤⡆⠀⠀⠀⢀⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢫⡹⠥⢧⣄⢠⠴⣺⠭⡉⠒⣅⠀⠀⠀⢸⡗⢄⠙⢦⡀⠀⠠⠂⠉⠓⢲⣄⡀
⠀⠀⠀⠀⡠⣤⠄⢄⠀⠀⠀⡇⠀⠀⠈⠀⠀⣿⣼⠃⡀⣿⣺⠇⠀⢸⠀⠀⠀⢸⡇⠈⠢⡀⣹⢀⠁⠀⠀⠀⠀⠀⢳
⠀⠀⢠⡚⠂⠀⠀⠀⢳⠀⠀⡇⠀⠀⠀⠀⠀⠈⢩⡄⠑⢄⣀⣀⡠⠞⠀⠀⠀⢸⠇⠂⠀⠈⡏⢸⠀⠀⠀⠀⠀⠀⡾
⠀⠐⡅⠁⠀⠀⠀⠀⢸⡇⠀⡇⠤⣦⠑⣦⣴⡄⠀⢀⣄⣀⣀⣀⣴⠋⠔⢲⡄⣾⠂⠸⠆⢸⠃⠘⣶⣶⣦⡀⠀⣰⠃
⠀⠀⠘⡆⠀⣠⣴⣿⡟⠀⢸⠃⢤⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠢⣾⠇⣿⠀⠀⠀⣼⣀⣤⠞⠉⠻⢿⡟⠃
⠀⠀⠀⠈⠻⣿⠛⡡⠉⠲⣼⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠀⠀⠀⠀⣿⠁⠢⣀⡏⠁⠀⢂⠀⢀⡞
⠀⠀⠀⠀⠀⠘⡎⠀⠀⠀⠜⠀⠀⠀⠀⢻⣿⡿⠋⠉⠳⠀⠈⠙⠁⠀⠀⠀⢀⡷⣤⠞⠉⠘⡄⠀⠀⠙⡾⠁
⠀⠀⠀⠀⠀⠀⠹⣄⢀⠌⠀⠀⠀⠀⠀⠀⠻⠧⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⣸⠟⠁⢁⠀⠀⠈⢦⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠜⠁⠀⠀⠀⢢⡀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢰⠋⢻⡆⠠⠄⣍⢉⣉⣩⠄⠄⠰⡟⠉⣷⠀⠀⠀⠀⠀⠀⣹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠌⣿⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⡏⠉⢹⣇⢠⣴⢒⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⠛⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠧⠤⠤⠇⠀⣈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠙⠙⠛⢻⣧⣤⣤⣾⡿⠛⠟⠟⠛⠛⠛⠛⢹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠶⠶⡶⣶⠶⠞⠒⠲⠶⠶⠶⠶⢷⠿⡛⢿⡙⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣈⣢⣵⣿⣀⣀⣠⣤⣤⣤⣤⣤⣀⣙⣾⣦⠳⡘⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠺⠀⠈⠉⠙⠛⠒⠶⠶⠶⠶⠶⠶⠒⠛⡛⠉⠉⠉⠉⠙⢛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢠⡞⣡⡄⠀⠁⢀⡀⠀⠐⠂⠀⢀⡀⠀⠈⠁⠀⠀⠿⠂⠘⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠉⠁⠀⡈⠙⢦⡀
⠀⠀⠀⠀⢠⡏⡀⠈⠁⠀⠀⠈⠁⠠⠀⠀⠀⠈⢁⠀⠀⠘⠃⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⢀⡄⠀⠀⠁⡀⠀⢷⡀
⠀⠀⠀⠀⢸⠇⠁⠀⠀⠁⢀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠⠆⠀⠀⠐⠀⠰⠷⠀⠀⡀⠀⠀⠀⣀⠀⠋⠀⠈⣇
⠀⠀⠀⠀⣼⠀⠰⠂⠀⠀⠈⠁⡀⠐⠿⠀⠁⠀⠀⣤⠀⠀⠈⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⣀⠀⠁⠀⣿
⠀⠀⠀⠀⣿⣇⠀⠀⠒⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠉⠘⠛⠀⣿
⠀⠀⠀⠀⣿⠙⢦⡀⠀⠀⠀⡉⠀⣀⡀⠀⠁⠀⠀⠀⠉⠀⠘⠃⠀⠀⠄⠋⠀⠀⠀⠄⠀⠀⠰⠄⠀⠀⠈⠀⠀⠀⠆⠀⣰⡇
⠀⠀⠀⣠⢿⡀⠶⠙⢦⣀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠐⢀⣀⣀⣤⣤⣤⣄⣀⡛⠀⠐⠿⠀⠀⠤⠀⠀⠰⠆⠀⢀⡼⡿
⠀⠀⢸⠃⠘⣧⠀⠀⣀⠉⢙⡓⠲⠶⠶⠶⠶⠶⠶⠒⡛⠋⠉⢉⠀⠰⠀⠀⠀⣈⠉⠛⠓⠶⠦⣤⣤⣤⣤⣤⠴⠚⠉⢰⠇
⠀⠀⢸⡀⠀⠘⢧⡀⠀⢀⠈⢁⠀⠒⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⢁⡀⠀⣀⠀⠁⠀⠆⠀⠚⠂⠀⠄⠀⠀⣀⠀⠉⣠⠟
⠀⠀⠈⢳⡄⠀⠀⠙⠶⣬⣀⠈⠁⠀⠀⠁⠀⠈⠀⠘⣃⣀⣀⣆⣈⣁⣀⡀⠀⠲⠂⠀⠆⠀⠀⡤⠀⠐⠀⢁⣠⣾⠁⢰⣋⣉⣳
⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣉⣙⣛⣒⠒⠒⠒⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⢉⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⣉⡵⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠉⠉⠛⠛⠲⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠠⣞⣋⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢢⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢤⢺⠀⠀⠀⠀⠀⠀⠀⠀⢹⣨⠔⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⣎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⠀⠀⠀⠀⠀⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢂⠀⠀⠀⠀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⡀⠀⠀⡠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠀⠒⠢⡀⠀⠀⢣⠀⠀⠉⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⣀⠤⠤⠤⡀⠀⠀⠀⠈⢢⠀⢸⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡔⠋⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠈⡆⠀⠈⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠑⠤⠤⠔⠊⠀⠀⢠⠃⠀⠀⢀⠇⠀⠀⠈⠿⠶⢶⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡉⢡⠎⠀⠀⠀⠀⠈⠒⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⣀⠄⠊⡀⠒⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⡀⠤⠄⠀⠐⠒⠒⠒⠚⠂⠤⠤⠶⠦⠭⠖⠐⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠓⠤⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠉⠉⠒⠤⠤⠒⠉⠉⠉⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣀⣠⠞⠓⠤⣉⢒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡋⠀⢠⠾⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠱⠤⠞⢁⡤⢄⣀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠑⠴⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⡹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠜
⠀⠰⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡰⠁⡜⠉⢢⡀
⠑⢮⠀⠀⣎⢉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⣴⣶⣶⣤⡀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣱⢦⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠙⢿⣿⣿⣻⠗⠚⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⣤⠖⠛⢤⡙⢦
⠀⠀⠣⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠁⠸⣄⣠⣶⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠤⡄⢀⣹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁⠁⠀⠀⠀⠀⠀⠒⠀⠀⠈⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢴⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣹⠤⠖⠙⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠹⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡄⠀⠀⠀⠼⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢠⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠂⠄⣠⠁⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⣿⡏⠛⢧⡀⠀⠀⠀⠀⠀⠀⢹⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⡀⣀⠀⢸⣷⣄⠀⠈⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠠⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠷⠄⣀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⣿⠿⠟⠋⠉⠂⠈⠓⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡤⠄⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠶⠤⠶⠋⠀⠶⠶⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣆⡀⢤⠄⠀⠀⠶⠭⠖⠐⠟⢃⡤⢤⠀⠀⢴⣺⠉⠓⡒⠄⢀⣀⠀⠀⠀⠀⠀⠀⢰⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠒⢤⣀⡶⠶⠀⠀⢀⣀⡈⠉⠁⢠⣤⠀⠀⠀⠘⠛⠀⠀⣀⡁⠲⢤⣀⠀⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠠⢄⠈⠑⠢⣤⢌⠉⠀⣤⣠⠀⡠⢤⠀⠛⠃⣀⡀⠀⠑⢁⡤⠒⡌⠓⠤⢤⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠫⠃⠈⠋⠀⠀⠀⠈⠈⠑⠒⠤⣀⠀⠉⠉⠀⠀⠻⠔⠃⠀⠀⢈⡓⠚⢁⣤⡦⠀⠀⠈⠙⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡞⡆⠀⠀⠌⠂⠀⠠⢲⠀⠀⢉⡒⠠⣤⠤⢀⡀⠟⠀⠀⠓⠁⠀⠀⡉⡀⠀⠶⠆⢠⠿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⣠⡀⠈⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢈⡁⠀⠈⠁⠲⠷⢄⠀⠀⠀⣠⣄⠀⠓⠃⠀⣠⠖⠁⣰⡇
⠀⠀⠀⢀⡤⠚⠉⠁⠀⢇⠀⠳⠃⠀⠀⢠⢤⠀⠐⠧⠼⠀⠀⠀⣎⠈⢳⠀⠀⠀⠀⢀⣌⡒⢤⣈⣀⣀⡠⠔⠋⡀⡀⢉⣸⡇
⠀⠀⡶⣿⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⡀⠈⠈⠀⠀⠀⠀⠰⡣⠀⠈⠓⠋⠀⠘⠀⠀⠹⢤⠽⠀⠈⢉⠍⠀⠠⣦⠉⠁⠣⠾⡇
⠀⠀⠀⠙⠶⢤⣤⣄⠀⠀⠀⠀⠀⠈⠳⢄⠀⠸⠵⠀⠀⡀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠸⠆⠀⠀⠀⢸⠀⣔⡄⠀⠒⠀⠤⠀⣷⠒⠒⠒⠛⠛⠛⠲⡌
⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠘⠽⠀⠀⡠⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⠵⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠁⠀⢀⣄⠀⠀⠛⠁⠀⠀⠈⢲⠃⠀⢟⠄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣠⣴⢎⣄⡀⠀⠀⠿⠆⡀⢸⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⣀⡤⠖⠚⠁
⠀⠀⠀⠀⠈⠓⠦⠤⣤⣤⣤⡤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣘⣏⡼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠴⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠉⠙⠓⠒⠒⠲⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠠⠀⠠⠀⠀⠀⣀⠀⠆⠀⡀⠀⢀⠴⠂⠀⠀⠀⣄⢀⠒⣀⣀⣀⡀⢀⣀⡐⠦⠀⢀⣈⣉⣹⣛⣛
⡴⠟⠛⡆⠀⠐⠟⣉⡟⠓⠒⠀⠀⠀⠀⠈⣿⢎⠉⣷⠖⠛⠙⠁⢀⠛⠛⠛⠂⠀⠀⠀⠀⠐⠉⠟⠌⡏⠉
⠀⠀⠁⠀⠀⠀⠇⠀⠲⠶⠶⠀⠀⠀⠀⠀⠗⠀⠒⢛⣷⣦⣢⠄⢻⡀
⠀⠀⠀⠀⣀⣠⡀⠀⢀⠀⡤⠀⠠⠀⠀⠶⠎⢀⠀⢰⣾⣿⣧⢇⡀⠀⠀⠀⠹⠀⣠⠄⠀⠀⠀⠀⠀⡀
⣿⡾⠿⢾⣛⣙⣍⣧⣤⣤⣀⠀⠀⠀⠀⠈⠟⡿⠁⠀⠙⠙⠛⠁⠀⠀⠀⠀⢐⣃⠟⠛⠙⡷⠍⠋⠭⠭⠭
⠙⢿⣿⣿⢾⡟⠞⠋⠁⠁⠀⣤⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠘⠚⠶⠶⠒⣽⣿⡿⢪⡍⠛⠀⠉⠁⠀⠲
⠀⠀⣉⠁⠘⠀⠀⢠⣀⣒⣠⣽⢿⠛⠃⣠⣠⣤⠀⠀⠀⠰⢷⡆⠿⣿⣿⢿⣿⣿⣷⡄⡁⣀⡀⣤⣄⣀⣉
⣀⢞⢛⣄⣀⠠⠖⠻⣿⣿⣼⣿⣳⣆⠀⠋⣭⣿⡀⣤⣤⠀⠈⠐⢿⡏⠀⠉⠉⠉⠉⢩⣭⣩⠁⡿⠄⠀⠤
⠉⢙⣛⣿⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣦⣅⡙⠻⠆⠀⠀⠀⠈⢃⣀⡀⠀⠘⠛⠊⠉⠙⠆⢧⡀⠐⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠤⣌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢰⠁⣘⠄⣀⠛⠄⡀⠂⠌⠀⢀⣀⣀⣀⠀⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠌⡘⢀⡏⠔⠂⠚⠂⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⡰⠤⠌⠴⠃⣘⠴⡄⠀⡤⣤⠒⣶⣒⢆⣜⣡⣌⡹⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠐⢠⠁⡊⠀⠀⠀⠀⠀⣯⣱⡇⠀⠁⢉⣉⣉⢉⡁⢤⢄⠀⢤⠐⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠂⠌⣑⠦⠄⠀⠒⠚⢶⢯⡇⠀⣭⡿⣼⣛⠾⣽⢃⠎⣐⠢⠌⡁⠀⠉
⠀⠀⠀⠀⠀⠈⡐⠠⡎⠁⠀⣀⡤⣴⡖⣶⣸⢿⡇⠀⣿⣽⣳⣯⣿⢣⣏⡲⢠⠋⠴⠅⠀⡦⢀
⠀⠀⠀⠀⠀⠀⢀⠂⠴⠀⠀⠯⠓⣋⣩⣭⢯⣿⡇⠀⣿⣿⣟⡾⣭⣛⡾⣱⠃⡌⣑⠇⠀⡵
⠀⠀⠀⠀⠀⡀⠂⠌⡰⢇⠀⢰⢏⡟⣼⣟⡿⣽⡇⠀⣿⣿⣿⣽⢧⣟⡳⢧⣝⢰⣁⠄⠀⣇⠂
⠀⠀⠀⠀⠀⢀⠀⠠⢁⠺⡀⠀⢿⡽⠗⠛⠛⠋⠁⠀⣿⣟⡿⣯⣟⡶⠋⠁⠀⠀⠀⠀⠀⡏⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠂⡘⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡾⣹⠿⣼⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠠⠀⠐⠠⢙⡀⠀⡆⠀⠀⠀⠀⠀⢀⡟⡳⢯⡟⠰⢦⡀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣱⠀⠸⡤⢤⣀⡠⢴⠛⠤⢁⠒⡬⢁⠆⡌⠃⠎⡐⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠀⠀⠀⢇⠂⠬⣑⠂⡌⠑⠎⡜⠠⢌⡐⠠⠉⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⢸⡌⠠⢀⡘⠠⢁⠒⠠⠁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠉

⣧⣷⠠⠀⠀⠀⣀⣐⡊⠈⠌⠀⠀⠈⢀⠀⠀⠀⠀⢸⡀⠀⣉⡀⠀⡀⢀⠀⠀⠀⢈⡩⠀⢀⡀⠀⠀⠀⠘
⠿⠁⠀⠀⠁⠀⠀⠁⠀⠂⠙⠃⠀⠀⠘⠿⢒⠙⠁⢀⣀⠉⢁⡀⠉⢒⠡⠀⠀⠠⢤⡀⠁⠀⠄⠓⠂⠀⠈
⠀⠀⠀⢀⣷⠒⠂⡀⠀⠀⠒⡄⠀⠀⠀⠀⠒⠐⠀⠈⠁⠀⢈⠅⠸⠡⠤⢤⡄⠀⠀⡸⠀⠀⠰⢀⡀
⠀⠀⠀⠈⣋⡂⠀⠺⡹⣄⡠⠸⠐⣀⢈⠸⠄⠀⠐⢦⠄⠀⡀⢠⠀⠀⠀⣴⣋⠨⣢⣇⢀⣩⡌⣖⡇⣐
⡀⠀⠀⠈⠀⠹⠈⠐⣀⣌⣁⣨⢖⢁⣈⠀⠀⠀⣠⠀⠀⢘⠀⠉⡈⢉⠡⠘⡛⢹⠁⢸⠃⢈⣗⣀⠀⡀
⠁⢸⠀⠀⠀⠂⠀⠀⠿⢿⠛⠟⠷⠗⠗⣧⣤⣀⢀⠀⠀⠌⠻⠭⠙⣩⡋⠀⠸⣿⠀⢸⠀⡼⠀⡼⠐⠄⢄
⠀⡦⢰⠁⠀⠀⠚⠉⠀⠀⠀⡀⠀⠀⠘⠙⠛⠁⠠⣞⢷⠄⢀⣀⢀⡕⢚⣛⠷⣼⡄⢸⠀⡇⢰⠃⠸⠀⢀
⣦⡶⠁⢈⠂⠠⠬⠃⠠⣤⡤⠄⠀⠀⠀⠂⠠⠀⠄⡁⢰⡄⣉⠤⢋⣴⢿⡿⠛⠺⣅⠘⠀⠁⠘⣆⣀⢂
⠘⣃⠑⢜⣛⠷⢚⠰⠉⣇⢰⠾⢛⠁⢀⠀⠀⠀⠀⠐⣠⠞⣡⣴⠛⢁⣾⣀⠀⠀⠈⠳⡄⠀⠀⢻⡿⢺⣿
⠉⠰⠀⠀⠀⠀⠉⢀⠌⠛⠙⣢⠈⢀⢀⡶⢾⡿⠻⣯⣥⠿⣻⣦⣶⣶⣿⣏⣢⠴⢶⣦⡈⠀⠀⠈⢷⣀⠼
⠀⠀⢁⡀⡀⠀⠂⠪⡷⣶⠄⢉⠄⠀⢘⡇⠀⣀⡴⠋⠀⣼⠟⠉⠀⠀⠈⠻⣿⣌⣎⠁⡉⢒⠶⠶⢤⡀
⠀⠣⠁⠀⡁⠀⠀⡄⢁⡙⢠⣤⣂⡤⠊⣠⠞⠉⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢸⣿⣯⢢⡍⠀⠀⡀⢠⣹⣦
⠀⠰⠋⠂⣀⠀⢀⠈⢠⣴⠟⠛⢉⠵⢛⣧⡶⠿⠿⣇⠀⢀⡀⢻⡀⠀⠀⠠⠱⠃⠻⣿⡶⡏⠫⠅⠘⣯⡿
⢄⠒⠒⠒⡈⡅⠜⢦⠘⣷⣤⡤⠀⢀⣿⠋⠀⠀⠀⢈⣻⣾⠏⠸⣇⠐⠊⣀⣴⡆⠀⣸⣷⡾⠾⣡⡾⠋⢀
⣋⡐⢠⠄⠛⠳⠦⢶⡄⠀⠙⠿⣦⣘⣿⢀⠀⠀⠀⣿⡟⢲⠒⠚⣉⠤⡎⠙⢿⣿⠟⠁⡞⠋⠀⠈⠣⠀⡀
⣄⠐⠡⣄⣠⠀⡀⠀⠲⢄⡀⣤⠈⣿⡝⣿⢇⣀⣀⣈⢕⣣⠔⠚⣅⠀⢙⣶⣿⢏⣠⠞⠁⠀⠀⠢⢠⡠⠘
⠉⣲⠸⣁⡀⣹⠁⠄⠠⠼⠁⠔⠈⠙⠿⣿⡑⠮⣍⡙⡍⠀⣳⡤⠊⣹⣿⠿⣣⠏⠂⠐⠂⠀⠀⠀⠀⠙⣿
⠀⠈⡀⠈⡉⢁⠄⠘⡳⡄⠀⢀⠀⠨⡃⠻⢷⣤⣨⡀⠈⢫⠀⠀⢒⣩⠵⠺⠋⠀⡀⠀⢀⠱⠀⠀⠀⠀⢨
⠄⠂⡑⣢⠔⣦⣊⡷⠻⣄⢸⠖⢲⠀⣷⠂⡈⢹⣧⣍⣳⣶⣴⠚⠅⠀⠀⠠⡄⠚⠄⠀⠂⠀⠑⡀⠀⢀⠎
⠂⠼⢗⠥⡑⢧⡬⣇⠐⠉⠋⠀⠀⣦⢽⢉⡖⣰⣈⣿⡄⠀⠤⡀⠁⢰⠀⠀⠘⠄⠀⢀⠀⠈⠀⠀⡠⠋

⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠳⣄⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⣷⡄⠀⠀⠐⠶⠀⠈⢏⠛⢦⡀⢸⣧⣀⠀⠀⠀⢰⡀⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⣿⡆⢀⣀⠀⠤⠤⠼⠿⠶⣇⢸⣎⠻⣆⠀⠀⢸⢷⡸⡿⢦⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⠀⡀⠤⠄⠒⠒⠘⡖⠚⠺⡿⢿⣿⠀⡀⢸⠀⢻⢃⠀⠃⢸⢿⣄⢀⡀⢀⡀
⠶⠦⣶⣶⠞⠛⠛⠓⠢⢀⡴⠊⢸⣿⣿⡉⢀⠤⠾⠂⠉⣁⣩⡅⠈⣇⠀⢻⢽⣿⣿⠀⠚⠈⣏⠉⢹⣀⢹⡆⠀⠛⢸⡆
⠀⠀⠀⠈⠉⠓⠢⠤⣠⣋⠀⡠⢺⣿⣿⠛⢧⣴⣶⣾⣥⣈⠿⠁⠒⡧⠠⠉⡐⠄⣺⡐⢨⣾⡷⠀⢺⠂⠘⣥⣐⠛⣻⠴⣆
⠀⠀⠀⠀⢶⠆⠀⢰⢣⣿⣿⣇⠸⣿⣇⢀⣿⡟⢧⡞⠙⢻⡆⠸⠿⠷⠀⠀⠀⢁⣼⠀⠉⡩⢐⣬⣽⢴⣶⣍⣿⠛⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⣤⣇⠀⢻⠿⠟⡼⠙⢿⣧⡙⡿⠥⠈⠲⣼⠃⠐⢾⡿⠀⠀⠘⠛⠋⠐⠍⡀⠿⠿⠋⠀⠉⠁⢠⡄⠠⣦⣤⠖⠁⢴
⠀⠀⠀⠀⠀⢸⣿⣿⠏⣻⠶⢤⣇⣀⢸⠉⠻⠷⠖⠒⠋⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠜⢵⣶⠎⠈⢀
⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⠀⠀⡇⠉⢙⠓⠶⣤⣀⠀⣶⣷⣀⠟⠀⠀⠀⢀⡀⣀⢀⡀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⡞⢉⡟
⠀⠀⠀⠀⠀⣿⣿⡏⠀⢸⢀⡴⣷⣶⣼⡀⠰⣿⣿⡆⠀⠉⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣧⠉⡄
⠀⠀⠀⠀⢠⣿⣿⣧⠀⠈⢿⣴⣶⡀⠙⣷⠀⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣸⣿⢿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢀⡀
⠀⠀⠀⠀⢸⣿⣿⠘⡆⠀⠘⡄⠀⢱⡀⠘⢆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣶⣶⣞⢲⡖⠀⠀⠀⠀⠀⢠⡆⢀⣀⡿⣶⡆⣾⡏
⠀⠀⠀⠀⠈⢉⡉⠙⠛⣖⠒⠻⡦⠤⠷⣤⣌⣢⠀⠸⣤⡀⣀⠀⠀⠀⠀⢸⡇⢿⡿⣿⢩⠿⣧⠀⠀⠀⠀⠀⠈⠁⡘⠻⢿⣤⠁⠉
⠀⠀⠀⠀⠀⠛⠃⢀⣀⡈⢶⣦⠘⣆⠀⢿⣿⡷⠑⣔⠿⠳⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠌⠲⡄⠠⡤⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠨⠿⠶⠈⠻⣃⡠⠷⡌⢉⡱⣶⣾⡧⡀⠈⣢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠖⠙⣦⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠢⣀⡼⠫⡀⢈⣻⣁⠈⣿⢋⣉⠫⡉⠀⠀⠀⣴⠇⠀⢰⠗⣼⠇⠜⣿⡠⠀⣨⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣿⣧⠖⠉⢢⡠⠚⠻⣿⠿⠓⢷⠾⠛⢄⠀⠑⢄⠀⠀⡄⠀⠀⢢⠜⣄⡠⠊⢣⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣼⠟⢁⣤⡊⠁⠈⠢⡀⢈⡷⣶⣾⣷⢤⡀⠑⠢⣠⣷⢆⡘⡤⢊⠔⠱⡈⢣⣾⡗⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⢺⣧⠹⣷⡄⣀⠴⠊⠓⢄⠈⠙⠯⡀⠈⠢⣀⠹⠫⡀⢉⢘⣅⣠⡾⠋⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⢻⣧⡜⣿⣄⠀⠀⠀⠀⣙⡦⡖⣿⣿⣷⡌⠑⢧⣈⢔⣴⡿⠋⠀⠀⠰⣤⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⢿⣦⣠⠔⠊⢁⣀⠈⠛⢍⣩⠗⢆⡘⣷⡿⠋⠀⠀⠘⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠚⠉⠀⠀⣤⣈⠙⠋⢠⣾⠛⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠶⠤⠔⠒⠛⠛⠓⠶⠤⠔⠂⠉⠙⠓⠶⠐⠂⠙⠛⠒⠶⠶⠒⠉⠉⠓⠶⠤⠴⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⡆⠀⠀⣀⠀⠀⠀⣤⠀⠀⢰⡂⠀⠀⣀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠗⠒⠈⠁⠒⠺⠁⠀⠀⠀⠸⠓⠀⠉⠁⠂⠾⡁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣂⣠⣾⣿⣦⠀⠀⠀⡇⠀⡌⢀⣶⣷⣦⠈⣂⠀⢀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠤⠚⠛⠚⠒⢤⡐⠛⠊⠉⠉⡽⠿⢌⠉⠉⠉⠉⠉⡭⠛⠛⠛⠓⠢⢄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡁⠀⠰⡒⠀⠀⣠⠇⠀⠀⢀⡼⠁⠀⢘⣄⠀⠀⠀⠸⡁⠀⠀⣒⠂⠀⢈⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠂⠀⠈⠢⣄⠉⠒⠓⠈⠁⠀⠀⠀⠊⠀⠉⠀⠒⠊⠁⢀⠔⠁⠀⠐⠉⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⣤⠤⢀⣀⣀⣀⣠⡤⠴⠖⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢈⣿⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠰⢅⣀⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠙⡦⠒⠒⠒⠢⠴⠲⢦⡤⠤⠖⠒⣤⠰⢲⡖⠠⠤⠴⡲⠖⠦⠖⠒⠒⠶⡖⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠘⠦⠎⠈⠢⠐⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡇⠈⣠⣤⣤⣥⡈⠈⢡⣭⣭⣭⠍⠀⠈⣭⣬⣭⠉⠉⣩⣬⣭⣤⡍⠉⡇⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⡄⠀⡇⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠢⣀⠠⠋⠉⠉⠀⠀⠈⠉⠉⠉⠀⠀⠃⠀⡔⠀⠑⢄
⠀⠀⠀⠀⠀⠖⣁⢀⠀⡤⣉⠄⠧⠤⠤⠤⡤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⢤⡤⠤⠤⠼⠀⡒⢁⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠘⠥⠐⣀⠇⠀⠀⠀⠀⠀⠀⠦⢤⣀⣀⡤⠌⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⣀⠼⠇⠀⠀⠀⠀⠈⠀⡀⠃⢌⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢳⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠈⠙⢢⡀
⠀⠀⠀⠀⠀⢌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠋⢹⣦⡀
⠀⠀⠀⢌⡳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⣅⣽
⠀⠀⠀⠀⠀⠀⠙⠦⣀⠘⢦⣠⡤⢀⣀⣀⡀⣀⣀⣸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⡖⠁
⠀⠀⠀⠀⠀⢤⡤⠤⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣀⣀⡀⠠⠄⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠣⠴⠒⠓⠚⠛⠓⠦⣄⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⡠⠴⠛⠓⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣤⡤⠴⠤⠤⢤⣀⣀⣀⣠⠤⠖⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢄⡀⢀⣠⠤⠶⠤⣀⢀⣠⠴⠒⠒⢤⣠⠔⠋⠉⠈⠙⠚⠉⠁⣹⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠑⠒⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡠⠒⡄⠀⠀⠀⣰⠃⠈⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠞⠉⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⠄⠐⣧⠜⠁⠀⠀⢰⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⢠⠃⢲⢀⣀⣼⣀⣀⣀⡴⢀⡠⢖⣚⠿⢗⣒⠶⣅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡀⠀⠹⣀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⣈⡛⠁⡠⢞⠝⠋⠉⠓⢆⢈⡽⠋⡴⠉⢀⣀⣀⠈⢱⡀⠙⣤⠊⠀⠀⠀⠀⢸⠀⣸⠀⡇⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⣹⡜⠁⢸⢠⣾⣿⡆⣸⡞⠀⠀⣇⠰⣿⣿⠿⠀⣰⠁⠀⠘⡆⠀⠀⠀⢠⠏⢠⠇⢀⠇⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠘⠖⢹⡇⠀⠀⠙⠻⠵⠚⢩⡇⠀⠀⠈⠳⠤⣤⠤⠞⠁⠀⠀⠀⡿⠀⠀⠀⡏⠀⠸⠴⠊⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⡴⢄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠉⠙⠢⣄⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠈⠑⢄⠀⠀⡷⠀⠀⠀⠘⣇⡸⠀⡠⠃
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⠒⠦⠴⠎⠓⢤⣀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠁⠀⡀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⢹⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢰⠁⢸⠁⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠀⠀⠀⢀⠠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡰⠃⣏⡠⠃⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⢀⠄⠡⠂⠁⠀⠠⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠁⠀⠀⢀⡤⢤⠀⡎
⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠸⠁⠐⠁⠀⡀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⡆⠀⢱⠀⠀⠀⠸⣀⠜⢠⠃
⠀⠀⠀⠀⠀⠀⡏⠀⠀⡁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠃⠀⡜⠀⠀⠀⠀⣀⢀⠏
⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠋⠀⡸⠁⠀⠀⡴⠋⠈⢻⡀
⠀⠀⠀⣠⠖⠋⠀⡇⠀⠂⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢲⠀⠀⢇⠀⠀⡼⠁⠀⠀⠀⢱⡀
⠀⠀⡼⠁⡤⣄⠀⡇⠐⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠊⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠈⡇
⠀⠐⣧⠊⠀⢈⠷⠉⢀⠔⠓⠒⠒⠦⠤⠴⠚⠉⠑⠒⠤⠤⠴⠒⠒⠦⢤⡤⠖⠒⠤⣀⠾⣀⣼⡀⢀⠀⠀⡀⡸⠁
⠀⠀⠁⠀⠀⠁⢀⠔⡏⠀⠘⠛⠋⠉⠀⠀⣠⣌⢹⢉⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠙⠛⢲⠛⠒⠿⢾⠀⠀⡏
⠀⢇⠀⡀⠄⠊⠀⠀⢹⠀⠀⠀⠀⠀⠀⠰⠁⢀⡈⡌⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⠀⢰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠤⠦⠎⠀⠙⢌⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣮⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⢄⠀⠀⠀⠀⠀⠀⡰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠳⣄⠀⠀⢀⡜⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⠉⠉⢅⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣩⠃⠀⠀⢠⠆⠀⠀⠀⢠⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠞⠋⠙⠒⢤⡔⠁⠀⠀⣠⠔⠁⠀⠀⠀⡛⢆⠀⠀⠀⠀⠀⢀⢼⣃⠄⠀⠀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣟⣛⣦⡀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⢀⡜⠀⠈⠳⡄⠀⢀⡴⠋⢻⡟⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢸⣅⡀⣷⠚⠉⠁⠀⠈⣧⠀⠀⠀⣀⡴⠋⠀⠀⠀⣠⢋⡽⠋⠀⠀⣽⠃⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢓⠉⠢⣰⡇⠀⠀⠀⠀⠀⠸⣦⠶⠛⠁⠀⠀⣀⡴⢛⡵⠋⠀⢀⢈⡴⠏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢷⣤⣤⠏⠀⠑⢤⡀⠀⠀⠀⡇⠀⠀⣠⢖⣫⠵⠚⠋⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢿⡜⠀⠐⡄⠀⠀⠀⠑⡄⠀⢰⡧⠶⣫⠵⠋⠀⠀⠀⠀⢀⣤⢞⠕⠁⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠀⠀⠀⠹⣦⡀⠇⠀⠀⠀⠀⢸⣠⡾⠖⠛⠁⠀⢂⣀⣀⣀⡴⡋⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠠⠶⠿⠿⠶⠶⠿⠷⠶⠶⠶⠴⠶⠶⠿⠷⠦⣴⣶⣶⣟⡛⠮⠭⠭⠽⠿⠯⠩⠭⠥⠤⠤⠤⠤⠤⠤⠼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠒⢦⡀⠈⢁⡔⢁⢍⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢨⣀⡠⠶⠖⠚⣛⣛⣉⣉⣉⢭⡽⠃
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⣇⠐⡩⢦⡘⠒⣡⡈⠢⡀⡰⣡⠔⣒⣒⢠⠃⠀⠀⠀⠀⠀⠰⠯⣥⠶⡖⠉⠙⢉⠁⠀⠈⢸⡄⠀⡇
⠀⠀⠀⠀⣶⡋⢻⡆⠙⠲⠤⢤⠔⡡⣊⡴⣛⣳⣄⠉⢶⠄⠈⠳⡇⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠠⠈⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⢎⡴⣫⣾⢟⣵⣿⣦⡀⠀⠀⡤⠜⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠠⠄⣿⠀⡇⠀⠀⢸⠃⠀⠀⠀⠃⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢔⣹⠿⣋⣴⡷⡄⠀⠘⢆⠀⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⣀⣀⣰⣦⠦⠤⠚⠛⠉⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⠻⡥⣪⢟⣭⡾⢟⣦⠀⠀⢳⣀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣉⣉⣉⠥⠤⠤⠒⠒⠚⠋⠻⣧⣤⣤⣤
⠀⠀⠀⡠⠂⠀⠀⠐⠄⠄⠀⠾⠿⠀⠀⠀⠘⢷⠟⡫⣴⡿⡫⣣⡀⠀⠉⠀⢱⣀⡀⠀⠤⠠⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⢀⢀⠠⠇⠀⠀⠀⠀⠀⣀⠤⠤⠒⠒⠈⠉⡂⠀⠻⣊⢕⡪⣞⣭⣷⣂⠀⠀⠀⢷⢓⠲⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿
⡎⠀⠀⠀⠀⠀⠀⠀⠸⣴⡀⠀⠀⠀⠀⢠⠇⠤⠤⢽⣯⡪⢟⣫⣶⣷⠂⠠⣶⢸⠀⠀⠀⢔⣢⠒⣼⡂⣀⠀⠀⢀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠈⠀⠀⢒⢀⡀⠀⠀⠀⠈⠙⢶⣤⡀⠤⡼⢦⠤⣤⣃⠘⣾⣟⠟⣋⢼⡧⠤⠒⠉⠀⢰⠒⣤⠿⣋⡡⠄⠈⢷⣾⣷⣄⠈⠉⠏⠀⠙⢯⡁
⠀⠀⠀⠈⠁⠙⠦⣄⣀⠀⣰⡪⠛⢧⢠⠇⠈⠲⠃⠈⠉⢙⣶⣿⣿⡉⠀⠀⢀⡤⠒⠉⠱⡜⢧⠀⠐⠂⢀⡼⠈⢿⣿⣆⠎⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡹⠒⠒⠒⠢⣤⠀⣾⣿⣿⠋⣡⠴⠊⠁⠀⠀⠀⢀⣵⢈⡧⢴⠊⡿⣦⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠘⠂⠤⠼⠁⠀⠀⠀⠀⢹⠀⢻⡿⠗⠉⠀⠀⠀⣀⠴⠒⠉⠉⠈⢋⠀⠛⠃⠈⠁⠀⠀⡟⣠⡆⠀⠀⠀⠀⠀⡟⠫⠯⠃
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠒⠉⠀⠀⢀⡤⠖⠛⠁⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠰⣟⠄⠃⠀⠀⠀⠀⠀⠃⠀⢀⣤
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⢰⠃⠀⠀⣠⠴⠚⠉⠓⠦⡄⡀⠀⠀⢰⣿⢋⠽⢻⣾⣧⡀⠀⣀⠀⠄⠀⠈⠀⠀⠀⠀⢸⣶⣤⡀⠉
⠀⠀⠀⠀⡄⠀⣀⡀⠀⣬⠀⠀⠹⡆⠀⠀⠀⠈⠳⣍⣉⠀⠀⠀⠀⠀⢄⠈⠳⠀⠀⠸⣷⣝⠊⣠⣿⡴⠋⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷
⠀⠀⠀⠀⣷⠈⣿⣇⠀⠙⠧⣄⠼⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣶⣶⣬⣉⠀⠀⠃⠀⠀⠈⠓⠶⠿⠿⠅⠀⠰⠆⣉⠢⣄⠀⠀⠀⠀⢠⡿⠿⠟⠁
⠀⠀⠀⠀⢸⡆⢹⣜⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⢱⣶⣿⣿⣿⣿⣿⠟⠉⠛⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠳⢄⠀⠀⡜
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⢀⣿⠿⠿⠻⣿⣿⣄⣀⣀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠒⠒⠾⢷⣈⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠉⣀⡤⠔⠊⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⡶⠖⠉⠉⠀⠁⠢⣀⠀⠀⠠⡖⠒⠢⣝⢆⠀⠀⢱⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀⠀⠀⠰⠋⠈⠀⠙⢦⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⣉⣀⣀⠤⠤⠀⢠⣤⣈⡑⢦⡔⠋⠀⠀⠀⠀⢣⠀⠀⠀⠠⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⢣⠀⠀⠀⠀⡀⡇⠀⠘⢿⣿⣿⠿⠋⠀⠀⠹⡄⠀⡰⠁⠀⢸⡿⠋⠁⠀⡍⠓⠢⠤⠤⠴⠋⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠑⠤⠤⠤⠜⠁⠀⠀⠈⢟⠁⣀⠤⠤⠤⣄⠘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠠⡄⠀⠀⠀⢀⠏⠒⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⡠⠤⡄⠀⠀⠈⢎⠃⠒⠒⠒⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠓⠤⠂⠀⣀⣠⣼⠀⠾⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣴⣾⡿⠿⠿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣹⣛⣩⣙⣙⣟⣩⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⣤⢄⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠼⠃⠘⣷⡈⠷⠀⠷⡤⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣺⠋⡝⢻⢶⡴⠟⠻⠿⠯⢡⡙⢆⡁⣼⢹⠲⣄⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠔⠢⣽⣆⢿⠁⠛⠀⠸⢡⣄⢁⣈⡜⣂⠖⠀⣼⠸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠏⠠⢖⡠⠌⡳⠾⠧⣦⣘⣂⠓⠎⢘⠋⡳⠤⠠⠶⣿⡄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⡙⠀⠀⠉⣠⠔⠀⣀⠀⠁⢀⡹⢳⣯⢱⠂⠓⢌⠀⠂⠘⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⡄⢀⠚⠃⢘⢄⠲⣭⠀⠀⢹⡇⠠⣋⠀⠀⠀⢈⠙⢀⡶⠉⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠖⠊⡀⠘⠱⢢⡐⠈⠰⠲⠤⣴⡶⠿⠲⣆⠠⢤⠖⠞⠀⠀⢡⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣤⡀⠁⠘⠋⠀⢀⡀⢴⡀⠀⢰⣞⡀⢤⠹⣦⠀⡄⠰⣮⣤⣶⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠠⠀⢰⡖⠀⡿⠏⢀⠠⣌⠳⡖⢿⣿⣶⠑⠁⠐⠸⢠⣿⣼⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣐⢀⠀⡼⠂⠆⠛⢁⡀⠠⣶⡍⢛⢷⡄⠀⣻⣌⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣉⠀⠸⠃⠅⠾⢀⣻⣿⣭⣀⡶⡬⠋⠛⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠯⠽⠧⠞⠓⠶⠋⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⠿⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡀⣸⠿⠿⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠚⢡⣿⣷⣦⡤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢨⣿⡧⢸⣿⣿⣿⣄⣀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢾⣿⡅⢸⣿⣿⣿⡁⡀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⢸⣿⣿⣿⣥⡀⢸⣿⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⣤⣷⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠁⠀⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⣿⣿⣿⡿⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣝⢿⣦⠘⢿⣷⣦⣄⣀⣠⣤⣶⣶⣾⣿⠿⠟⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣌⠃⠸⣿⣿⣿⣿⣿⡿⠿⣯⡥⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣤⣈⡉⠀⠀⠀⠒⠒⠛⠲⢤⣁⡈⠈⠉⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⢿⣿⣶⣤⣤⣶⣶⣤⣶⣾⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡦⣄⡉⠉⠉⠉⠙⠛⠛⠛⠷⢦⡶⠶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢸⣿⣿⡛⠛⠛⠻⣯⠈⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣿⣿⣿⣿⠶⣦⠀⣽⠂⠀⠈⠁⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣠⣤⣀⣀⣴⣦⣀⣼⣿⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣯⠙⣯⣝⣿⢷⡤⠟⣛⠯⠙⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⡿⢿⠿⠳⠓⠈⠋⠛⠒⠒⢊⠉⠙⢢⣄⣈⠛⠻⠻⢷⡆⠀⠀⠀⠀⢠⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣶⠤⠂⡄⠀⠀⠐⠒⠉⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠂⣶⣾⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣄⠀⠀⠁
⠀⠀⠈⠀⠐⠒⠒⠒⠠⠀⢸⣿⠟⠻⠷⣶⣿⣿⣿⣿⠟⠁⢀⡀⣰⡞⣿⡿⣿⣆⣿⣿⣀⠀⡀⠰⢲⣦⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢻⣿⣿⡟⠛⠋⠶⣿⡷⣾⡷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣒⡊⠉⢩⣇⣸⣷⡆⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⢷⡀⠀⢸⣿⣿⡇⠀⠀⢤⣾⣧⣾⣧⣾⣧⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡩⠤⠶⢾⡿⠛⢹⣇⣤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⢿⣿⣿⡀⠀⠠⣽⣧⣼⣧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣛⡏⢤⣤⣴⣶⡧⠀⠀⠈⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠉⠁⠉⠉⠉⠛⠟⠻⠿⠟⠛⠿⠉⠁⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣡⡼⠟⠛⠛⣷⣶⣀⣤⠶⠶⠰⢧⣀⡀⣆⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠋⢰⣾⣿⣷⣻⣿⢋⣴⣶⣾⡄⠀⣿⣧⠈⠆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠑⢿⣿⣿⣿⣿⠇⢸⣿⣿⣿⡿⠀⣾⣿⠀⠃⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⠗⣬⣭⣽⣿⣿⣧⣤⡯⠛⠉⣠⣼⢿⡟⠀⠃⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣳⡾⣵⣯⡿⡿⠉⢻⣿⣿⣿⣏⠀⣀⠀⢀⠀⢀⢾⣿⡿⣅⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠊⣉⣛⣭⣷⣿⠃⠐⠃⢰⣿⣺⣿⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣴⣦⠨⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⢻⣈⣇⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢸⡟⠃⠸⣿⣶⣻⢿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣴⣶⠀⢺⣿⣿⡿⣿⠿⢋⣩⠟⠁⣀⣤⡀⠀⢀⣿⣿⠿⣈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠋⢠⣤⡉⠛⠿⠿⠟⠛⠁⠀⢰⣿⣿⠣⣠⣾⣿⠏⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⡿⢾⣶⣮⣿⣿⣶⣶⣶⣖⠀⠀⠀⢹⠁⠀⢸⣿⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣾⣽⣯⣉⣿⣿⠟⠯⣽⠿⠶⠾⠿⠦⣤⣼⣿⣿⣄⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠻⣿⢺⡿⣿⣿⣿⣿⣶⡖⠲⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⣿⠾⣧⣬⣿⣟⣣⠁⠀⠀⠉⠉⠻⠛⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠉⠀⢻⠿⠁⠹⢿⣿⡿⢷⣦⣴⣤⣀⣘⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠈⠇⢠⣄⠹⢆⠘⡟⡋⠙⣟⠉⠛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⡇⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢒⣋⣥⣶⠀⣿⡟⠉⠀⠀⢻⡁⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⣭⣥⣶⣿⠊⣿⡟⢹⠀⣿⡇⢀⡀⠀⢸⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣻⢸⠏⢸⠀⣿⠀⢸⠀⣿⠇⣿⡇⠀⢸⠀⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⡆⢸⠀⣿⠀⢸⠀⣿⠀⠉⠀⠀⢸⠀⣶⢿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⢸⠃⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣾⠀⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⣿⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⣿⠀⣿⣿⠀⢸⠀⣿⠀⢸⠀⣿⠀⢸⡇⠀⢸⠀⣿⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⠀⣿⣿⡄⢸⠀⣿⠀⢸⠀⣿⠀⠘⠃⠀⢸⠀⣿⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⡀⠿⣿⠁⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⣟⣠
⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡿⢁⣤⠀⠀⡀⠉⢙⡿⠿⢧⣿⠀⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⠀⣿⣀
⡇⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠋⠀⣿⠏⢀⣾⠏⢀⣿⡁⠀⣾⢹⡄⢸⠀⣿⡆⢸⠀⣿⠀⣶⡆⠀⢸⡀⣧
⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠋⣰⣾⣿⣷⣾⢿⣼⠁⢸⠀⣿⠁⢸⠀⣿⠀⠛⠃⠀⢸⡇⣿
⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣄⠀⢸⣿⣿⣿⣿⠁⢾⣾⠀⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⡇⣿
⡇⣼⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢹⣿⣿⣿⣷⣾⣿⡿⠋⣿⠀⠇⣿⡄⢸⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⢸⠁⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠟⠋⠀⠀⣿⠀⣄⣿⠇⢸⠀⣿⠀⢸⠀⣿⠀⣿⡇⠀⢸⠀⣧⠒
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣀⡿⣿⠀⢸⠀⣿⠀⢸⠀⣿⠀⠻⠇⠀⢸⡀⡟⠤
⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣦⣤⣤⣤⣾⣭⣯⣿⣶⡾⠀⣿⣀⢸⠀⣿⠀⠀⠀⠀⢸⡅⡇
⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣟⠉⠈⠝⣏⡉⠙⣟⢻⣿⣿⠀⣿⣶⣤⣤⣀⣸⠇⡟⠛
⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⣿⣦⣿⣏⣿⣿⣷⣯⣄⣻⢸⠈⣿⠛⣿⣯⣽⣻⡆⣩⣭
⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠷⠿⠛⢻⠻⠿⣿⣿⣿⣿⡄⣿⠀⠿⣿⠀⢹⡇⣿⣿
⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣦⣀⣀⣨⠟⢚⠛⠛⠛⢻⡇⣿⡀⠀⠀⠀⢸⡇⣿⣿