Cute adorable sweetheart Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠈⠉⠉⠉⡙⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢵⡠⠎⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠠⠀⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠏⠀⠀⠈⠀⠠⠄⢸⢄⠀⠀⠀⢂⡤⢒⠭⠀⠈⠉⠀⠀⠀⠐⠄⠰⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠂⢸⡌⠀⡶⡠⢋⠔⠁⠀⠀⠀⢀⣆⠀⠀⠀⠀⣀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⢀⣰⣿⣄⣰⣵⡁⣀⡀⠀⢸⡀⢀⠀⠑⠀⠈⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣡⠔⠚⣁⡥⠔⠶⠤⠬⠛⠋⡉⠀⠀⠈⠀⡙⠻⢧⡈⠀⠀⠠⡄⠀⠠⠉⠂
⠀⠀⠀⠀⠀⠀⡠⠊⢁⠴⢋⠁⠀⠀⢀⠄⢀⡴⠀⢈⠢⡀⠑⠢⣀⠐⠀⠙⢦⡀⠀⠀⠐
⠀⠀⠀⠠⠀⠔⠀⠔⠁⠀⠀⠀⡠⢐⠁⢠⡿⠃⠀⠀⠢⠈⠁⠀⠈⠳⡀⠀⠀⠙⠈
⠀⠀⠀⠀⡉⠠⠀⠀⢀⡤⢖⡫⠒⠰⡛⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⢠⡰⠀⠀⠐⠥⠒⠁⠀⠀⠀⠀⠀⠁⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⠰⠈
⡂⠀⢀⡞⠃⢀⠄⠁⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠙⠒⡠⠀⠀⠀⠐⠀⠀⠀⠀⠙⠂⠐
⠀⠀⠈⠗⡀⠅⠀⠀⠀⠀⠐⢿⣿⠆⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠐⡄⠀⠀⠀⢰
⠀⠀⠀⠠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠉⡅
⠀⠀⠀⠀⠀⡈⠦⡀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⡆
⠀⠀⠀⠀⠘⠄⠠⠿⢁⡀⠨⠵⠦⣤⢀⣀⡀⠀⠀⠀⣀⣀⠀⠊⠉⠀⠀⠛⠧⠠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠈⠠⢀⣀⡀⠀⠀⠀⠀⠐⠀⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨⡆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠔⠀⠭⠤⠶⠶⠒⠀⠉⠉⠑⠀⣰⠁⠃⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡃⡀⠀⠄⢀⠀⠀⠄⠀⠀⠐⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠑⢄⠀⠀⠈⠀⠉⠀⠀⡀⡀⠂⠀⠘⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠂⠄⣀⢀⡀⠌⠊⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⡀⢰⠄⠀⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⡈⠶⠀⠀⠀⠍⣀⣤⣂⠠⠷
⠀⠀⠀⠀⠀⠀⠀⠔⠃⠰⠄⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠂⡠⠔⠚⡉⠉⠁⠀⠀⠀⡀⠘⡀⠿⢴⠿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢠⠗⠀⠘⠴⢀⣤⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠆⠀⠀⠀⠀⠀⠀⠀⠙⢘⠇⠀⠀⠀⡴⠷⠖⠓⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠈⡅⢀⠀⠀⠀⠀⠀⠀⢀⢄⡌⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⢟⠁⠐⠤⠀⠀⠄⡄⠀⢈⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣂⣀⣀⣘⣀⣄⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⣀⣤⡀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠘⢿⣿⣿⠟⠁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⠁⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢿⣿⣿⠃⠀⠀⠘⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣿⣷⣶⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣶⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠠⣤⡄⠀⠀⢤⣤⠀⠈⠙⠛⠿⢿⣧⡐⠀⣿⡷⠀⠀⠀⠀⢾⣿⠀⠀⣼⡿⠿⠛⠋⠁⠀⣤⡤⠀⠀⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠈⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⣦⣄⠀⠀⠀⣀⢤⡶⠐⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠂⣰⠄⢀⡗⢠⠾⠁⡄⠀⠆⠘⣧⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣠⢼⣀⣿⡟⡟⣖⣷⠾⣸⣯⣉⣿⣟⣦⣇⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠰⡺⣽⣿⡿⡿⢩⣭⣿⣴⣶⣶⡤⠉⣉⢽⠉⠙⠻⢆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⣠⠬⠚⠁⠀⠆⢸⡗⠽⡛⢻⢶⠃⣸⠎⡋⠀⠀⠀⠀⢣⠀⠀⠀⠈⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠊⠁⠀⣠⠔⠉⠀⠀⡀⠤⢊⡠⠶⣄⢏⢩⠀⢸⡄⢻⡞⠁⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠸⡔⠊⠁⠀⠀⠈⠓⢠⣴⣿⡉⠢⠑⡄⠀⠀⠀⢀⢤⡄⣈⢲⣤⣄⡀⡤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣶⣺⣷⡟⣻⡿⣺⣇⣌⣀⣠⣔⣵⢿⢛⡟⣂⠜⢉⢃⡇⠘⡄⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⢀⡀⢠⣎⣀⣰⣿⡷⠿⠞⣿⠋⠁⢘⣯⠉⢻⠛⠭⣉⠝⠊⠀⠀⠚⠉⠀⠀⢀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⣊⣁⢀⣤⡶⣖⠋⠀⠹⣯⠽⣧⣶⣾⣿⣿⣿⣿⣿⣯⣥⠞⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢎⡁⠘⣿⠙⡹⠟⠢⠶⠯⠿⠔⠃⢀⣿⣿⣿⣿⣿⣿⡏⠈⠢⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⢀⡀⠜⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣷⣭⣭⣽⣭⣧⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣁⠀⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠊⠉⠀⢀⣠⠔⢒⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠼⡀⠈⢀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⢌⡢⡉⠀⠰⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢷⣬⠦⡀⢠⠀⢨⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⢿⡋⠑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⣀⣽⣦⡀⠀⠀⡀⠉⣿⠛⡉⠉⠳⠀⣤⠈⠁⣀⠘⠃⢀⡀⠗⠀⢠⡉⠀⢉⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠉⠊⢝⣳⣬⠁⣀⣀⣀⠹⣔⠪⢿⠉⠑⢶⡭⣤⣄⣈⣃⣀⣀⠠⠤⢖⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⢀⠔⠢⡉⠐⠂⠤⢀⣸⣿⣧⡈⠉⠁⠐⠉⠐⠊⠱⡀⠀⢓⠂⠓⠴⠚⠠⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣤⠉⠒⠒⠋⠐⡆⠂⠀⠀⠀⢀⠉⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠆⠀⠄⠀⠀⠰⠗⠒⢲⣶⠀⡌⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⣀⣀⠀⡠⠋⠀⣷⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠈⢲⣷
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⢻⣯
⠀⠀⠀⠀⠀⠻⠽⣄⠐⠒⠄⢀⠀⡦⠺⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠣⣿⣿⡇⠐⢤⣆⣉⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡼⠏⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋

⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢛⡹⢿⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⠚⠛⠿⠛⠉⠸⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠿⠆⠴⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣶⢀⠘⠿⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠟⠋⠀⠀⢀⣤⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡿⠛⠋⠀⠀⠀⢀⣴⣿⣿⣧⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣆⠀⠀⡀⢠⣴⣿⣿⣿⣿⣿⣇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣭⣈⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⡿⠛⣭⠁⠀⢸⣿⣿⣿⣯⣿⣿⣿⣧⡄⠀⢀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⢠⠞⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢷⡏⠀⡀⠂⠀⢴⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣷⣿⣥⣶⡌⢀⣽⣦⠀⠛⠿⣿⣿⣿⣿⠿⠛⢩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡾⠃⠀⣿⡇⢄⣙⣩⡁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣟⢂⣴⡿⠀⣏⠱⣼⣿⣿⣀⠀⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠼⢿⣳⣤⠛⣴⣿⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠀⡠⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣦⣬⢿⡄⠀⢠⠁⠀⡿⠥⣴⣤⠠⠄⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⠀⣀⡀⣾⡅⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠲⢄⡀⠀⠀⢘⠀⠀⠀⢀⠥⠒⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⢰⡒⢄⠀⠙⣄⠠⢿⠧⢀⡔⠁⢀⠔⣲⠀⠀⠈⢻⡀
⠀⠀⠀⡠⠀⠐⠠⠀⠀⠀⠀⠀⠛⠉⢻⢦⣀⠀⠀⢈⡹⠁⠁⢸⠀⠀⠀⢸⠀⠁⠹⣈⠀⠀⢀⣠⢾⠋⠙⠃⠀⠀⠀⠀⠠⠀⠀⠠⡀
⠀⠀⠈⠀⡀⠀⠀⡀⠀⠀⠈⠐⠤⣀⠋⠀⠀⠉⠉⢉⠀⢱⠀⡜⠀⠀⠀⠸⡄⣸⠀⢈⠉⠉⠉⠀⠈⢃⡠⠔⠈⠀⠀⠀⡠⠀⠀⡀
⠀⠀⠈⠀⠁⠂⣀⠜⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣈⣠⠿⠚⠀⠀⠀⠀⠀⠘⠾⣦⣈⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠘⢄⡀⠂⠁⠘

⠀⠀⠀⢀⡤⠤⢤⣴⣁⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡤⠤⣤⣎⠁⠀⠀⠀⠀⢀⡤⠤⣴⣎
⠀⠀⠀⡟⢠⡄⣼⢁⣈⣀⣀⢀⣀⡀⠸⠀⡀⠀⢠⡏⢤⣠⡏⣸⢀⡀⣴⠀⢠⡏⢤⣰⢇⣸⠃⣀⠀⣀⢀⢠⣆⡛⣀⣀⢀⢀⡀⣀⡀
⠀⠀⠀⢓⠚⢱⢷⢃⣟⢠⣏⣎⣼⡁⠀⣜⣧⠀⠈⡓⠚⡿⠒⢫⡇⣺⣣⠀⢈⡓⢚⡟⠀⣷⣼⣡⣳⣃⣏⣞⣼⣸⣡⣏⣞⣼⣹⢕⡇
⠀⠀⠀⠙⠖⠃⠈⠉⠉⠈⠉⠉⠉⠀⠀⠉⠁⠀⠈⠳⠚⠀⠀⠈⠉⠉⠁⠀⠘⠓⠊⠓⠒⠃⠉⠁⠈⠉⠉⠉⠉⢉⡟⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠤⡁⠁⠀⠀⠙⡠⠄⠀⠠⠄⡀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠒⡁⠀⣀⣀⡀⠀⠈⡄⠀⠀⡈⠀⠀⣀⢀⡀⠀⡁⠂⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣾⠉⠀⢀⢬⠆⢀⡃⠀⠀⣃⠀⢮⢀⠀⠈⢹⡦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣈⣁⠤⠊⠀⠀⠀⠀⠂⢄⢉⣀⡤⠞

⠀⠀⠀⠀⠐⠲⠶⠶⠂⠀⣀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣠⠒⢦⠀⠀⠀⠆⢂⠄
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⣿⣷⣿⢯⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⣳⣾⣤⣯⣤⣄⠀⠈⠁⠀⠀⠀⢠⢄
⠀⠀⠀⠀⣀⣸⡀⠀⠀⠀⠘⣿⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠟⢿⣿⢿⡧⢤⣸⠀⠀⠀⠃⠲⣤⠁⠘
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠓⠔⢻⣿⣀⡗⠀⠀⠀⠀⠀⠑⠐⠛⡈
⠀⠀⠠⠀⠀⣠⣄⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠷⠦⢸⠩⠾⠷⠟⠁⠀⠀⠈⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠘⣃⣉⠖⠈⢆⠂⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣯⠉⢉⡉⠉⣇⣇⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣆⡰⢠⠶⠄⢳⠀⣰⠀⠀⠀⠀⡘⢿⣿⣿⣿⣿⠧⠴⠿⠁⠀⢠⠀⡀⠀⡀⠀⠀⣺⡃⠘⠋⢠⣿⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠹⢦⠜⠘⠒⠋⠀⠀⢀⣾⣁⠀⠹⣿⡿⠁⠀⠀⠀⠀⠀⠸⣻⡿⣶⠃⠀⠀⠻⣧⣤⣤⡼⠛⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠃⠀⠀⠀⠀⣀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢃⡪⠋
⠀⠀⠰⣳⣿⣷⡤⠤⢀⠀⠀⠀⠈⣏⠻⠎⡿⠕⠀⠀⠀⠀⠀⠀⡴⠶⢒⠤⢄⠀⠀⠀⠀⠀⠀⣠⣆⣄
⠀⠀⠀⠛⠛⢿⣾⣿⣦⣆⠀⠀⠀⠘⣦⠚⠁⠀⠀⠀⠀⠀⠤⣏⣳⡾⠮⠧⣾⠦⡀⠀⠀⢰⡉⠛⣿⡾⢻⣄
⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⢟⠄⠀⠀⠀⠀⠀⠈⠓⡀⢰⠿⣿⣌⣃⡀⠀⢸⣿⢾⣖⡿⠔⠐⣀⡭⢿⡙⣌⣇⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⠀⠀⠀⠀⠀⠀⢦⡀⠀⠘⣴⣿⠺⠻⡿⣁⡟⢾⣀⠹⣚⡆⣷⣯⠁⡇⣿⣻⠙⠁⣠⠇
⠀⠀⠀⠀⡴⠦⣄⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢈⣿⡞⣳⠋⣿⣜⣹⣀⡮⠐⠟⣑⣙⠋⠇⡚⢿⣷⠃⠀⠀⢠⠄
⠀⠀⡠⠀⠙⢦⣼⣯⣤⠞⠀⢀⠀⠀⢀⡀⠀⠀⠙⠂⠀⠀⢠⠴⢽⠣⢨⠿⣷⣽⣟⣳⣴⠟⠹⣿⣬⣯⡜⡄⠀⠀⠚⠃
⠀⠀⠀⠀⢘⠉⢹⡿⠉⢹⠀⠀⠀⠈⠻⠃⠀⠀⠑⢄⡀⠀⠀⢲⠽⣶⠼⣰⠀⡟⢫⢍⣨⠼⡟⠊⡷⢧⠎⠀⠀⡀⠔⠁
⠀⠀⠀⠀⢙⠙⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⡶⣿⢙⠻⠯⣾⣁⡠⣿⣧⡿⠛⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠉⠀⠙⠂⠐⠁⠀⠀⠀⣤⠀⣀⡀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠛⠽⣎⢳⣌⢸⡧⣼⡏⠃⠀⡀⣀⣀⣀⡀⣀⣀⡀
⠀⠀⠀⢀⣤⣴⣾⣶⣄⠀⠀⠀⠰⣿⣟⠁⠀⣶⢠⡒⠀⢏⠉⠀⠀⠀⠀⠀⠘⠮⡜⣿⣿⠙⠃⠀⠀⠋⠣⠀⢀⠀⢀⠌⢹
⠀⠀⢀⣾⣟⣛⣩⣭⣽⡇⠀⠀⢀⡇⠙⠳⠄⠿⢀⡽⠂⢤⠟⠀⠀⢀⢀⡠⡀⠀⠇⠜⠀⠀⣤⡄⠀⡆⠀⠀⠙⠛⠁⠀⢸
⠀⠀⠀⠻⠿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠤⠔⣁⡀⠄⠀⠀⠀⠈⠀⠀⠓⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⠄⠀⠀⢸⡤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠎⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠤⢈⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠈⠀⠘⠀⣀⠂⠤⣀⠀⠀⢨⠁⠀⠎⠀⡆⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠠⢇⠀⠀⠀⡆⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠑⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢠⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣄⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⢉⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠴⠒⢤⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠀⢠⠀⡠⡵⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⢠⠂
⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠊⠀⣠⠂⠀⠀⣶⠙⠋⠁⠀⠀⠀⠀⢀⢀⠀⠈⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠃⠀⠀⠀⣿⡇⢀⣩⠄⣆⠀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠄⠀⠤⠀⠈⠀⠀⠀⠀⡀⣄⠀⠀⠀⣇⣣⠀⠀⠈⠁⠀⠈⠉⠉⢈⠀⠀⡠⠂⢉⡉⠐⢄⠀⠀⠤⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣽⣬⣽⡆⠀⠀⢀⠶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠑⠁⢀⡠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠂⠀⠀⠶⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠈⠛⠟

⠀⠀⠀⠀⠀⢀⡠⢤⠶⣶⠶⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢂⡒⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠶⣶⠶⡤⢄⡀
⠀⠀⠀⠀⡰⣏⣷⠾⣿⣿⡿⡷⣾⣉⢦⠀⠀⠀⠀⢠⣾⡝⣩⢩⢮⡵⡍⣌⢫⣷⡀⠀⠀⠀⠀⣴⣉⣷⣾⣛⣯⣛⣷⣾⣹⣆
⠀⠀⠀⢰⢦⣞⢶⢿⣿⣿⣿⡿⣷⢻⡴⡆⠀⠀⠀⣌⢏⣶⣴⣫⣾⣷⣝⣦⣶⡹⣣⠀⠀⠀⢰⢦⠿⡿⢿⣿⠽⣿⡿⢿⢷⡴⡆
⠀⠀⠀⢸⡟⣠⡶⢦⠘⣿⠃⣴⠶⣄⢻⡇⠀⠀⠀⣿⠏⣠⣤⡉⢿⡿⢁⣤⣄⠹⣿⠀⠀⠀⢸⡟⢠⣶⣆⠸⣿⠄⣴⣦⡄⢻⡇
⠀⠀⠀⠘⣧⠘⠶⠞⢡⠿⡄⠳⠶⠋⣼⠃⠀⠀⠀⢻⣆⠙⠛⢁⡾⢷⡈⠛⠋⣰⡟⠀⠀⠀⠘⣯⣄⠉⣁⣰⠿⣆⣈⠉⣀⣽⠃
⠀⠀⠀⠀⠈⢻⣾⣾⣿⣶⣿⣷⣷⡟⠁⠀⠀⠀⠀⠀⠙⣯⣟⣿⣷⣾⣿⣻⣽⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⣀⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠻⠻⠟⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⡟⠿⠻⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠻⢿⣷⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣶⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⠷⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣖⣯⣇⣿⣸⣽⣲⣄⡀⠀⠀⠀⠀⠀⣀⣴⣺⠽⣸⣇⢯⣗⣦⡀⠀⠀⠀⠀⠀⠀⡠⣖⣻⣽⣿⣹⣟⣲⢄
⠀⠀⠀⠀⡾⡿⢻⠿⣿⣿⣿⡿⡿⢻⢷⡀⠀⠀⠀⠰⣿⢻⠿⣿⣿⣿⣿⠿⡟⡿⠆⠀⠀⠀⠀⠚⣶⣿⣿⣧⢿⣼⣿⣿⣶⢃
⠀⠀⠀⢸⣿⠻⠋⠻⢦⣿⡴⠟⠙⠟⢿⡇⠀⠀⠀⣿⡟⠛⠙⠷⣿⡻⠾⠛⠛⢻⣷⠀⠀⠀⢸⣽⠟⠛⠻⢿⣿⡿⠟⠛⠻⣯⡇
⠀⠀⠀⢸⡉⣰⠉⡆⠘⣿⠃⢰⠋⣷⢈⡇⠀⠀⠀⣏⠁⣾⣷⠄⢻⡗⠠⣾⣷⠈⣹⠀⠀⠀⢸⡇⢼⡋⣳⠀⣿⠀⣟⢙⡧⢹⡇
⠀⠀⠀⠈⠡⣌⢉⣁⡾⠛⢿⣈⡉⣡⡌⠁⠀⠀⠀⠙⢤⡈⣁⣰⡟⢻⣄⣈⢁⡤⠋⠀⠀⠀⠈⠳⣌⣛⣉⣼⠛⣦⣙⣛⣡⠞⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣍⣯⣩⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣯⣏⣏⣉⣹⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣦⣩⣙⣛⣫⣵⡎⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣏⣉⣉⣹⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠯⠿⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠿⠿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠟⠻⠛⠁


⣰⣶⣶⣶⡆⢠⣶⣦⣶⢠⣴⣤⣦⣦⢰⣶⣦⣴⣶⢠⣶⣶⡄⣴⡶⢴

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠙⠋⠉⠋⠉⢻⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣏⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣦⣤⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢹⠈
⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡼⣿⣿⡿⠻⣿⣿⣿⣿⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠
⡇⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⡯⢦⣽⠋⠀⣠⣾⣿⣿⣿⣟⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠚
⣷⢸⡄⠀⠀⠀⠀⠀⠀⠨⣹⣧⣶⣿⣧⣴⣿⣿⣿⣿⣿⣿⢻⡆⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡋
⣿⣸⣃⣀⣀⣀⣀⣀⣀⣀⣙⣋⣉⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣀⣀⣈⣒⣀⣀⣀⣀⣺⣓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣷⠞⢻⣶⣇⠀⣀⢀⣀⢰⡧⢀⠀⣀⢀⣀⣀⠀⣀⠀⣀⠀⡀⣀⡀⡂⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⢳⣿⣄⣸⢿⣿⣯⣽⢸⢿⢸⣇⣿⣿⣯⣹⣿⣽⢸⣿⢸⢹⣿⣿⣿⠋⣷⡟⠁
⠀⠀⠀⠀⠀⠀⢿⣍⠙⠿⠉⣿⠈⠁⠘⠟⠛⠟⠚⠚⠚⠛⠟⠛⠞⠙⠚⠛⠚⠺⠺⢿⠷⠛⠛⠀⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠄⠋
⠀⠀⠀⠀⠀⠰⣦⣴⣇⡴⢷⡀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣿⠀⢸⡇⣦⣴⢶⡶⢦⠶⢶⢶⢶⢠⢺⣴⡳⢀⠀⢸⣧⠞⢡⠦
⠀⠀⢀⡞⠛⢷⣦⠺⣿⠻⠏⠁⣿⣇⣼⡇⢸⣀⢾⣽⣸⢸⣼⣯⡹⢾⡀⢼⡗⠀⠘⣇
⠈⠀⠀⠻⢶⣄⣁⠀⠋⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⡸⠀⠀⠀⠿⣻⣷⣶⠀⣻⠀⠀⠰⡄⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⠿⠛⢐⡽⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⡟⠀⣠⡚⠙⠂⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠈⠈⠴⢟⠀⢀⣎⣁⡄⢠⣿⡟⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠉⢦⣈⣿⡽⠃⠀⢈⡤⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡄⠀⢰⡄⢹⡇⠀⠀⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡄⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⢀⣀⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣀⡀⣀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣀
⠀⠀⡃⠀⠠⡉⠠⠀⠘⠁⠀⠀⠀⠁⠀⣠⠉⠄⠂⢹⡄⠀⠀⡌⠀⢀⣈⢀⡀⠀⡆⠀⠀⡎⢀⠤⢭⡠⠤⡈⣕
⠀⠀⠱⡀⠠⠀⡀⢀⡼⠃⠀⠀⠀⠣⡀⠨⢬⠀⢀⡾⠁⠀⠀⠹⣤⠜⠋⠓⢃⢴⠇⠀⠀⠑⢜⠓⠖⠛⢲⣵⠋
⠀⠀⠀⠈⠑⠤⠾⠋⠀⠀⠀⠀⠀⠀⠙⢦⣄⡺⠋⠀⠀⠀⠀⠀⠑⠵⣢⡔⠕⠁⠀⠀⠀⠀⠀⠑⠤⠶⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠤⡠⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠔⠒⠢⠄⠒⠒⣄⠀⠀⠀⡄⠀⠲⣰⠂⡆⢰⠀⠀⠀⡔⠉⠉⠓⠊⠉⠹⢂⠀⢠⠊⠀⠉⣎⡅⠈⢳⡀
⠀⠀⠸⡀⠺⠸⢱⠰⠀⣸⠀⠀⠀⠳⡆⡁⠉⢀⢕⠟⠀⠀⠀⢣⠠⠨⡙⠞⠇⣠⠎⠀⠈⢆⠀⠀⠉⠀⢀⣼⠁
⠀⠀⠀⠑⢤⡛⢿⣤⡾⠃⠀⠀⠀⠀⠈⠊⠾⠑⠁⠀⠀⠀⠀⠀⠑⠤⣀⣠⠾⠋⠀⠀⠀⠀⠳⣤⡠⣼⠟⠁
⠀⠀⠀⠀⠀⠙⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⣀⣀⠀⠀⠀⠀⢀⠔⠂⢄⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀
⠀⠀⠀⠃⢀⢈⠣⠤⢄⡀⠀⠀⢰⠁⠀⣬⡃⠀⠀⢡⠀⠀⠀⢘⣰⠂⠄⠂⠀⠢⠀⠀⠀⡃⠀⢣⠌⣒⠒⢄
⠀⠀⠠⡄⣠⡉⠰⡒⠀⡅⠀⠀⠘⣆⡰⢷⣷⠀⡠⡟⠀⠀⠀⢸⡀⠐⠰⠂⠁⣰⠃⠀⠀⢧⠀⣤⡘⠃⠀⣸
⠀⠀⠀⢿⣀⠏⠠⢄⡪⠃⠀⠀⠀⠈⠫⣢⣄⠫⠊⠀⠀⠀⠀⠈⢷⣐⣒⠪⠕⠊⠀⠀⠀⠘⣦⠀⢒⡒⠝⠊
⠀⠀⠀⠈⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⢀⡠⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠹⠿⠃⣀⣄⠘⠿⠟⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⣀⠤⠀⠂⠠⢄⣀⡠⠄⠀⠀⠤⣀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⣀⠤⠄⠀⠤⢄⣀⡠⠄⠀⠂⠤⣀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⢠⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠉⠒⠤⠤⠒⠁⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⡠⠤⡀⠀⠀⡤⢤⠀⠀⠀⠀⠘
⠸⡀⠀⠀⠀⠈⠀⠈⢤⣤⡄⠁⠀⠁⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠠⠄⠔⠀⠀⠀⠀⠀⠀⢀
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣠⠤⠒⠒⠒⠢⢄⡠⠔⠒⠒⠒⠤⣀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⡜⠀⠀⠀⠀⣠⢤⡀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠇⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠒⠉⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠙⠟⢣⡀⣠⠌⠻⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⠲⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⡠⠴⠒⠒⠲⠤⣀⠤⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⡠⠴⠒⠒⠒⠤⣀⠤⠖⠒⠒⠦⢄
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⢠⠁⠀⠀⠀⠀⡠⠤⡀⠀⢀⡀⢄⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⠤⢤⠀⠀⠀⣤⣦⠀⠀⠀⠀⠈
⠘⡀⠀⠀⠀⠀⠀⠀⠰⡤⠆⠀⠀⠀⠀⠀⠀⢨⠃⡠⠔⠒⠂⠒⠒⠤⠤⠒⠂⠐⠒⠢⢄⠘⡃⠀⠀⠀⠀⠀⠀⠰⠶⠆⠙⠋⠀⠀⠀⠀⢀
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡌⠀⠀⠀⠀⣠⣲⡄⠀⠀⢠⣔⣆⠀⠀⠀⠀⠇⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢡⠀⠀⠀⠀⠈⠋⠁⠶⠶⠀⠙⠁⠀⠀⠀⠀⡆⠀⠀⠈⠲⢄⡀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⠊⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⠑⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁

⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⣼⣿⣿⣷⣾⣿⣿⡆⠀⠉⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠋⠉⠳⠞⠉⢳
⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀⠠⡀⠀⠀⠂⠀⢠⠀⠀⠀⠈⢇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠁
⠀⣤⣤⡄⠙⢿⡟⢁⠤⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠞⠁⢰⠚⡱
⠀⠘⠏⠀⠀⠀⣀⠀⠓⠊⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⢴⣴⡦⠀⠀⠀⣀⡉⠁⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄
⠀⠀⠀⢀⠒⠴⠁⡇⠀⡾⠃⢦⠞⠉⢻⠄⠤⡄⠀⠀⠀⠀⣈⠛⠃⠿⠂⠀⠽⣷⣿⡄⠀⣠⣄⢸⣿⣀⡉⡉
⠀⠀⠀⠈⠑⠦⣀⡇⠈⢷⠀⠀⠀⢀⠟⠈⠀⠘⠀⠠⠀⠀⠉⠁⢿⠗⠀⠀⠈⠨⠋⠀⠀⠙⢿⣿⣿⡏⣿⠋
⠀⠀⠀⠐⠾⠂⠀⠀⠀⠈⢲⣄⡴⠋⠀⠀⠀⠐⠂⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢁⣠⡀
⠀⠀⠀⣠⠤⢤⢠⡏⠙⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⡁⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠢⣼⣿⡷
⠀⠀⠀⢻⡀⠘⠁⠉⡼⠁⠀⠀⠀⠂⠀⠀⠀⠤⠀⠈⠢⡠⠈⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⠇
⠀⠁⠀⠀⠙⠲⢤⡼⠁⠤⠀⠂⠀⠀⠀⠀⠀⣤⣠⣤⡀⢀⣄⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡈⠉
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⣀⠀⠀⢀⡀⠀⠙⢿⠟⠀⠈⠛⠸⠣⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁
⠀⠀⠀⠉⠁⠀⣠⣄⠀⡅⠙⠀⡅⢠⠒⡞⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣠⣤⣄⡀⢴⣯⣿⠀⠰⠀⢠⠁⠈⠳⠵⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⣴⣶⣶⡄
⠀⠘⢿⣟⣿⡘⣿⡇⠀⠀⢇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠈⠛⠃⠈⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡰⠁⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢆⠰⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠈⡇⠀⠀⠀⠰⠁⠀⠀⠈⠲⢤⡅⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠸⡄⠑⠀⠀⡅⠈⠁⠀⡀⠀⠀⠀⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠭⢍⠑⢦⡠⠊⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠀⠤⣠⠇⠀⠀⠀⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢀⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠠⣆⠀⠀⡇⠀⠀⠀⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡠⠐⡏⠀⠈⠢⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠸⡄⠀⢱⡀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⡠⠃⠀⠀⠐⠈⠀⠀⣇⠀⠀⠀⢃⠀⠡⡐⡀⠀⠀⠀⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣦⠔⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⢀⠀⠀⠀⡄⠘⣦⡀⠀⡸⠀⠀⠑⢄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡤⠔⢊⠄⢀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠄⣀⠂⠈⡙⠶⠁⠀⠀⡀⠀⠑⠒⠒⠋⠀⠀⠠⡄
⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⢄⠀⠐⠋⠀⠁⠀⠀⠀⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠁⠀⡄⠀⠐
⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠐⠀⠀⠀⠀⣠⠤⠤⣀⠀⣠⠖⠉⠀⠙⡆⠈⠀⡴⠁
⠀⠀⠀⠀⠀⠉⠓⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠈⢰⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⢹⠀⠀⠑⢄⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⢀⠴⠒⠒⠒⠒⠒⠂⢠⢦⡀⠀⠀⠀⠂⠀⠀⠀⢀⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⠀⠀⠀⠳⡄⠀⠂⠖⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡀⢀⠀⠀⣠⠃⠀⢟⠲⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠣⡱⡀⠀⠀⠀⠀⠀⢂⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⠃⠄⠀⡰⠁⠀⠀⠘⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠀⠀⠀⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⡜⠁⠀⢀⡠⠔⠂⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠸⣀⠞⠀⠀⠈⠁⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢄⠀⠎⠀⠈⡀⠀⠀⠀⠀⠀⠀⠄⠖⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡤⠤⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⡠⠋⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠑⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢀⠆⢀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠊⠀⠀⠀⢠⠒⠀⠪⣧⡠⠒
⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢀⠀⠠⠊⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢆
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢦⡀⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡔⠂⠐⠒⠘⠶⠀⠀⠀⠈⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠀⠀⢇
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡢⢄⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠆⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⣴⠉⠙⢢⡴⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣐⣤⠤⠷⠶⠲⠾⠦⠬⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⢄⡈⠑⢄⠀⠀⢀⠠⠤⠤⣈⠟⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠢⠄⣉⡈⠤⠐⠒⢢⠏⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠓⠉⠀⠈⠑⠢⡀⠀⠀⠀⠀⣀⠄⠀⢀⡎⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡫⠤⠀⠠⠤⠄⣀⠀⠈⠑⠒⠂⢉⠠⠠⠄⢼⠃⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢀⡴⠖⠺⣛⠛⠟⠛⠒⠒⠲⠦⠤⣀⡀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⣸⠀⠀⠀⢀⣀⠀⠀⠀⠸⡄⣀⠤⡄
⠀⠀⠘⢇⣉⢁⡂⠅⣀⣀⠈⠀⣉⠀⠐⠂⠭⣟⡠⠂⢉⣁⡉⠁⠐⠤⢀⠀⠀⠀⠀⡠⠒⡩⠤⣿⠀⠀⠐⠉⠈⠓⠀⠀⠀⡟⠡⢾⡁
⠀⠀⠀⠀⠉⠒⠮⢥⣀⣒⣒⡀⠄⣈⣀⠠⠤⣯⠊⠁⠀⠀⠀⠈⠁⠒⠤⠈⣁⣀⠡⠔⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣉⣀⠠⠀⣠⠖⢁⢽⡀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠊⡉⢹⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣠⡫⠒⡡⠄⠀⠀⠊⡡⢘⡥⠖⠳⡔⢁⠠⠤⠤⢈⠑⠂⠤⠤⠄⠂⢁⠔⠁⠀⠈⢣⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠐⣏⡠⢊⠔⡨⠍⣉⠵⠚⠉⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠐⠒⠂⠒⠊⠁⠀⠀⠀⠀⡨⢷⡀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠙⠲⠯⠾⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⣀⠤⠤⠤⠀⣀⣀⠠⠞⡠⠊⠙⢦⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠮⣠⡐⠈⠀⠐⠒⠐⠒⠈⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⡆⠉⠟⠙⠒⡲⠒⠻⢋⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⣇⣀⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡀⠀⠀⠠⢁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⢸⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠌⠁⠉⠀⠈⠁⠉⢄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠁⠘⠃⢄⠀⠀⠀⠀⢀⠘⠁⠱⣿⡂⠀⠁⠢⠀⠀⠀⠀⠀⢀⠔⠋⠁⠁⠁⠐⠂⠶⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⡆⠀⠀⠈⠀⠀⠀⠈⠑⠂⠂⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⡀⠀⠀⠄⠉⠀⠀⡀⠀⠀⠀⠀⠣⢀⠀⠀⠐⡁⠀⣀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠣⠓⠙⠿⣿⣿⡿⠋⠺⠆⠀⠀⠀⠀⠀⠉⠃⠂⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣤⠀⠀⠈⠀⠈⠁⠀⠀⣠⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠡⡆
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠐⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠷⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⢄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠄⠀⢠⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠂⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠄⠐⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⢄⠀⠈⠀⠀⠆⢀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠑⢆⠀⠖⢀⠉⠌⢡
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠘⢦⡰⠃⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠰⡎⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⠐⠔⠁⠀⠀⠀⠀⠀⡐⢁⠠⠐⠖⠀⢄⠐⢄⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠠⠊⠀⠁⠀⠀⠀⠀⠀⠑⠀⠡⡀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠘⠀⠀⠀⠓⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠢⡀⠀⠄⠀⡀⠊⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠁⠈⠐
⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠀⠀⢸⠀⠀⡀⠀⠀⢨⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠀⠀⠰⠀⠀⠦⠀⠠⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠘⠀⠀⠁⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⡠⠐⠀⠀⠀⠀⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⡐⠁⠀⠀⣀⠄⠀⡀⠀⣀⠀⠀⡀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⣀⠈⠀⠊⠀⠉⠠⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠇⡅⠀⡠⠂⠀⠠⠀⠀⠀⠀⠁⠀⠀⠈⠊⠀⠸
⠀⠀⠀⠀⢈⠁⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠐⠀⠐⠂⠀⠐⠀⠀⠃⠃⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠈⠉⠉⠉⠉⠉⠙⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⣀⡀⠤⠀⠐⠂⠒⠒⠒⠂⠤⢄⣀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡤⠒⠉⠀⠀⢀⡀⠤⠤⠤⠤⠤⠀⣀⠀⠀⠈⠐⠤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠞⠁⠀⠀⠀⠈⠀⠀⢀⣀⡀⠀⢀⣀⣀⡀⠀⠉⠒⠤⡀⠀⠑⢄⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⠊⠀⡠⠂⠁⠀⠀⠐⠈⠀⢀⣀⡀⠀⢀⣀⣀⠉⠉⠒⠤⡀⠈⠑⢀⠀⠉⢦⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡔⠁⡠⠊⢀⠤⠊⢀⡠⠔⠊⠉⠁⠀⣀⣀⣀⠀⠀⠉⠑⠂⢄⡀⠑⢄⡀⠑⢄⠀⠱⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⡔⠁⡠⠁⣀⠔⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠀⠀⠈⠢⡀⠑⢄⠀⠳⡀⠱⡀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⠼⠤⠴⣀⡜⢀⣎⣀⡔⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⠀⠣⠀⠱⡀⢱⠀⢰
⠀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠈⠖⠋⠁⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢱⣀⠷⠤⠷⡀⣦⠚⠁⠒⠒⠒⠐⠢⡀
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⡠⠒⠠⠔⠚⠁
⠀⠀⠈⠒⠢⠤⠒⠉⠑⠤⠀⣀⣀⣀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣀⣠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠘⣆⠀⠀⢀⣠⣤⣷⣤⣄⡀⠀⢹⣧
⠀⠀⠀⠀⠀⢰⣿⣠⡾⠟⠛⠛⠿⣶⣄⣤⣤⣼⣧⣤⣀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣤⣾⠟⠉⠁⠀⠈⠙⠻⣦⡘⣿
⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠈⠛⠉⠁⠰⠶⢭⣙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣠⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣤⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣭⣋⣠⣤⣶⣧⡀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠻⠷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠉⠙⢦⠀⠀⠀⢀⡔⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢨⠀⠀⠀⠸⡀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⣏⠀⠀⠀⠀⡹⠦⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠉⠓⠲⢄⡀⠀⠀⠀⠀⠘⣆⠀⠀⡰⠁⠀⠀⠀⠀⢀⡤⠖⠒⠉⠉⠉⠉⠉⠉⠒⠲⢄⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⣀⣀⡠⠤⢄⣀⡀⠀⠈⠢⡄⠀⠀⠀⠸⡀⢠⠃⠀⠀⠀⢠⠔⠁⠀⢀⣀⣠⠤⢄⣀⡀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⡰⠃⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠉⠓⢤⡀⠘⢦⠀⠀⠀⡇⠸⠀⠀⠀⡴⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠘⢆
⠀⠀⠀⣰⠁⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⢣⡤⠒⠛⠛⠲⢤⡼⠁⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠈⡆
⠀⠀⠀⡇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠋⠀⠀⠀⠀⠀⠀⠙⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⡤⣤⠀⠦⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⢧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡸
⠀⠀⠀⠘⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠘⢄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠉⠓⢲⠆⠀⠀⠀⠀⠀⠀⠀⢱⢄⣀⣀⡀⠀⢀⣀⣀⣀⠤⡇⠀⠀⠀⠀⠀⠀⠀⠰⣖⠚⠉⠀⢀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢄⣀⣀⣀⣀⣀⣀⡤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣧⢤⣀⣀⣀⣀⡤⣼⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠢⣀⠀⠀⠀⢀⣀⠴⠊⠁⢠⠎⠹⡄⠀⠀⠀⠀⢠⠏⠱⡄⠈⠑⠦⣀⡀⠀⠀⠀⣀⠴⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣠⠞⠁⠀⠀⢳⡤⠤⠤⢤⡞⠀⠀⠈⠲⣄⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠱⣄⣠⠎⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⣀⣀⣀⠤⠚⠁

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠤⠤⠐⠒⠂⠉⠉⠉⠉⠐⠒⠒⠤⢄⣀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠃
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠒⡖⠉⢢⠄⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢇⠀⡸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠐⠒⠒⠒⠀⠒⠒⠒⢿⣿⣿⣿⣿⡿⠂⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠤⠇
⠀⠀⠀⠀⠙⢶⢤⡀⠀⠀⢀⠀⠀⠀⠶⣤⠼⣴⠏⡀⠀⠀⡀⠔⠈⠀⡀⠐⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠑⢮⡓⠄⣨⠝⠿⠶⣶⡀⠀⠈⢓⣛⠤⠥⠤⣀⠴⠏⡀⠀⠑⠊⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢦⡈⣱⠖⡻⠛⢌⠁⠈⠁⠀⢀⣠⠄⠸⡆⠀⠀⠀⣠⠴⠒⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⡞⠁⠘⠇⠀⠀⠁⠀⠀⠈⠉⠀⠠⡤⢤⡶⡶⠋⠉⠢⢀⣀⡄
⠀⠀⠀⠀⢀⠀⠀⠁⢀⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠣⡂⠀⠀⠈⠼⠐⠂
⠀⠀⠀⠀⠘⠭⠤⠴⠋⠀⠀⢀⠄⠀⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀⠈⠲⢤⡶⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠸⢿⡾⠂⠀⠀⠀⠀⠄⠀⠀⢄⢀⠉⡓⢤⠀⠹⡌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠈⢎⡆⠀⠀⠱⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣹⠀⠀⠀⠀⠀⠈⠇⠀⠀⣀⠘⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢹⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠣⣀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠀⣸⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡜⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣶⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠉⢠⣤⠀⠀⠀⢰⣿⠄⠀⠀⢀⣤⡀⠈⠙⠻⣿⣿⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⣾⣿⡿⠋⢁⡀⠀⠀⠈⠋⠀⠀⢀⣀⣀⣀⠀⠀⠈⠛⠁⠀⠀⣀⠈⠙⣿⣿⣧⡀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠻⠟⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠘⠿⠃⠀⠈⠻⣿⣿⣄⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⡟⢁⣤⡀⠀⠀⣠⠞⠉⠀⣀⣤⣶⣶⣿⣿⣶⣶⣦⣄⡀⠈⠳⣦⡀⠀⠀⣤⡄⠹⣿⣿⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⡏⠀⠀⠛⠁⢠⡞⠁⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀⠈⠳⣄⠀⠛⠁⠀⠸⣿⣿⡄⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⣤⡄⠀⣠⠏⠀⢠⣾⡟⠁⠀⣀⣤⠶⠞⠳⠶⢦⣄⠀⠀⠙⣿⣆⠀⠹⣆⠀⣠⣤⠀⢹⣿⣿⡀⠀⢀⡀
⠀⠀⠀⠻⠀⠀⢸⣿⣿⠁⠀⠙⠁⢠⡏⠀⢠⣿⠏⠀⢀⡼⠋⠀⠀⠀⢀⡀⠀⠙⢷⡄⠀⠘⣿⣇⠀⢹⡄⠘⠋⠀⠈⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⠀⠀⣾⠀⠀⣿⡏⠀⠀⣾⠁⠀⠀⢺⣷⣿⡗⠀⠀⠀⢻⡄⠀⢸⣿⡀⠀⢷⠀⢀⣀⠀⢹⣿⣿
⠀⠀⠰⠖⠀⢀⣿⣿⡇⠘⠛⠃⢠⡇⠀⢸⣿⠁⠀⢸⡇⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⡄⠘⠟⠀⢸⣿⣿⡀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠁⠀⠘⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠛⠛






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠉⠐⢄⡀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡘⠀⢀⣀⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣀⠘
⠀⠀⠀⠀⣀⡷⠛⠋⠉⠙⢠⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡠⠊⠉⠙⠛⢷⣀
⠀⡰⠖⠛⠉⠉⠀⠀⢀⣄⡐⠋⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢂⣤⡀⠀⠀⠉⠉⠛⠲⢆
⠀⠁⠀⠀⠀⠀⢠⡞⠉⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⣳⠄⠀⠂⠀⠀⠈
⠀⠀⢳⡄⠀⠀⠀⢻⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣠⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠷⣤⣤⣤⣤⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠳⣤⣤⣤⣤⠾




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⢠⣾⡏⣹⡟⣻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣿⣶⣾⣷⣿⣷⣿⣿⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠿⠿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠚⠉⠉⠉⠛⠓⠲⢦⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢷⣀⣠⣶⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣛⣻⡿⠀⠀⠀⠀⣾⣿⠿⢿⣿⣿⣆⠀⠀⢸⡆⠀⠙⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣼⠈⠛⠿⠛⠁⢤⣤⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⢸⠇⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣠⣤⣤⣾⠀⠀⠀⠀⠀⣿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠥⠠⢤⠈⠱⡙⢧⡜⡀⠀⠀⠀⠀⠠⣄⡰⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⢂⡁⣠⢃⠞⠑⢦⡀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡏⠩⣕⠂⠉⠉⢉⡁⠁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⠔⠀⠈⠄⡀⠀⠀⢂⢻⣻⣷⠆⠀⠀⠈⠁⠁⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠸⣦⠠⠔⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠴⢤⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢑⡲⠊⠀⠀⠀⢹⠂⠀⠀⠀⠀⠠⠤⠒⠩⡒⠀⡸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠈⠓⠤⠤⢤⣐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠄⣀⡀⠤⠒⠉⠀⠀⠀⠀⠉⠢⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠐⠢⣀
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡠⠔⣈⣀⠤⠠⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠑⢄⠀⠱⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠈⠛⢶⣤⣄⣒⡩⠔⡫⠚⢁⠄⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢳⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢀⡔⠁⡠⠂⠸⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢠⠆⠀⠀⠀⡜⡄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠎⢀⡤⠊⢣⠀⠀⠀⢘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠑⢄⠀⠀⠀⢡⠘⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠃⡠⠊⡠⠊⠀⢄⠀⠀⢸⠉⡒⠒⠐⠂⠑⠄⠀⠀⠀⠀⡆⠈⢆⠈⢧⣀⠀⠔⢣⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⡰⢁⠜⢁⠔⡡⣞⠀⢀⠆⢠⣁⣠⡆⠀⠀⡨⡄⠀⠀⠀⡗⢤⠈⡆⠈⡬⠒⠲⡞⠂⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠈⠑⡎⢀⢊⡐⠁⠣⡩⠏⠀⠘⠒⠊⢀⡀⣜⠀⠸⣈⠉⠀⣰⠜⠒⠢⡌⠀⠀⢀⠌⠐⢄⠼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡍⠀⠀⠉⠳⡄⠀⠀⠀⣀⢠⠊⠀⠀⠀⢡⠖⠉⠉⠉⢣⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⢠⠊⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠇⠀⠀⡜⠀⠘⠤⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢧⡀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠠⠤⠤⠀⠀⠒⠒⠒⠒⠊⠁⠀⠀⠀⠉⠉⠁⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠸⠀⠀⢸⠀⢀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠂⢀⡠⠅⠰⠒⠀⠐⠆⠤⣈⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠓⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠁⣀⡔⠊⠑⠢⠤⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢆⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡁⠀⠀⠏⠙⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢱⠒⡛⠤⣀⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠒⠾⢄⡉
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡀⣈⢆⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⢫⠳⡀⢀⡜⠁⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⢊⡄⣨⠟⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠈⢣⠀⡀⠄⣀
⠀⠀⠀⠀⠈⠒⠲⣀⢀⡤⠤⠊⠉⣰⡏⠀⠀⡰⠋⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⣄⠀⠀⠈⢆⠀⠀⠀⢏⠀⠀⠈⠓⠒⠖⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡸⠁⠀⢀⠞⠁⣀⡠⢤⠤⠤⢄⠀⠈⠳⡀⠀⠹⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢠⠃⠀⡶⠋⠀⠀⠀⠀⠀⠑⡄⠀⠱⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠌⠀⠀⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠠⠀⠀⡀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠢⠴⠣⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠧⣀⡰⢇⣀⡠⠛⠒⠊⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠘⠄⠀⠃⠀⠂⠠⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⠔⠂⠈⠀⠀⠀⠈⠀⠢⡈⠠⠆⠀⡠⠠⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠠⡀⡹⠀⠀⠀⠀⠉⠀⢑
⠀⠀⠀⠀⠠⠤⣀⠁⢠⠀⢀⣄⡀⠀⠀⠀⠀⠀⠉⠈⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⢣⡀⢄⠀⢀⣀⠜⠉
⠀⠀⠀⠀⠐⠤⠤⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠠⠤⣀⠂⠉⠁
⠀⠀⠀⠀⢀⣀⠤⠭⠤⣣⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢀⠅⠀⠀⠀⠀⡸⠑⢠⠞⠀⠀⡠⠔⠊⠉⠉⠉⠉⠒⠤⡀⠀⠈⢢
⠀⠀⠀⠘⠤⡄⠀⣀⡠⠒⢡⠋⠀⢠⠊⠀⢀⡠⠤⠒⠦⠤⡀⠀⠈⣦⠀⠀⢱⠊⠉⠢⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⠃⠀⠰⠁⠀⡔⢁⣠⠤⠄⠤⣀⠈⠢⡀⠘⣇⠀⠀⡆⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⡌⠀⡞⠁⠀⠀⠀⠀⢣⠀⢡⠀⠸⡀⠀⢰⠀⠀⠀⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡨⢄⣀⣇⡰⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀⢀⡀⠀⡼⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢦
⠀⠀⠀⠀⠀⠠⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢀⠏⡀⠀⢀⡀⠀⠀⠀⠀⢀⣀⡠⠤
⠀⠀⠀⢀⠩⠶⡄⠀⠀⠉⠓⢦⡀⠀⢀⠴⠋⠀⠀⠉⠀⠤⠖⢉⠁⠀⣠⠴⠋⠉⠀⠀⣠⠮⢅⠀⠀⡄
⠀⢸⡀⠀⠀⢀⣘⣆⠀⠀⠀⠀⠹⠃⠁⠀⠀⠀⠀⠀⠲⡲⠦⢤⣙⡾⠁⠀⠀⠀⠀⣜⣁⡀⠀⠀⢰⠃
⠀⠀⢳⡀⠀⠁⠀⠈⢆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠐⠢⡘⡄⠀⣀⣀⠀⠀⠀⠀⡜⠁⠀⠙⠀⢠⠏
⠀⠀⠀⠱⣄⠀⠀⠀⣞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢚⡕⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠓⣤⠀⠀⠀⠀⣠⡞⠋⠙⢦⡀⠀⠀⠀⠀⠀⣠⠖⠉⠙⣦⡀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠘⠲⢂⢀⠀⢰⣿⣧⣀⣀⣠⣷⡀⠀⠀⠀⢰⣿⣄⣀⣠⣿⣿⡀⢠⢀⢲⠘
⠀⠀⠀⠀⠀⠀⠀⠁⠙⡆⢸⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⠇⣸⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⢯⡣⣀⣀⣿⡿⠀⠀⠀⠀⠘⣿⣏⣀⡠⣫⠞⠀⢻
⠀⠀⠀⠀⠀⢀⣀⣀⣼⡀⠀⠀⠉⠙⠋⠉⠀⠀⣠⠲⡄⠀⠀⠉⠙⠋⠁⠀⠀⢈⣄⣀⣀
⠀⠀⡠⠶⠯⠭⠤⣀⠀⠉⠁⠒⠂⠤⠤⢤⡤⠀⠀⠀⠀⠠⢤⠤⠤⠄⠒⠂⠈⠁⢀⡠⠤⠭⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⢀⠤⠄⠀⠤⢄⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠁⠀⠀⠀⠀⠀⠉⠒⠚⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠲⢄⡠⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠈⣦⠔⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠑⣤⠋⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠦⡤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣟⣁⣀⠀⠀⠀⠀⣠⠞⠋⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠒⢶⠦⣤⣀⣠⡟⣾⠟⠈⢿⣹⡉⠀⠀⣠⠟⠁⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣸⠀⠀⠈⢻⠀⢿⠰⣄⠀⠙⠻⢦⣞⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠙⢀⠇⠀⠀⠀⠸⡆⠈⢦⡈⠙⠒⠤⣀⠈⠻⣦⠞⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠙⢦⡀⠈⠲⠤⠀⢈⣑⣴⣧⠤⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⣞⣹⣷⡄⠉⠓⠒⠶⠖⠿⡫⠅⠒⠂⣀⡽⣠⠎
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣠⠋⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⣌⣭⣭⣶⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⡏⢻⡹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⡿⡿⠋⡰⠁⢸⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢲⠖⠶⠶⠖⠒⠛⣿⠋⡰⢋⠎⢀⡔⢁⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠀⠀⠀⠀⢰⡇⢸⢁⠃⢀⢎⡴⣫⠟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⢧⠘⣌⣆⢹⡘⣇⢇⣀⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠈⠳⣮⣿⣷⣿⣾⣿⣿⡿⠉⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⠳⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⠽⠛⠂⠀⠀⠀⠀⠹⣆⣀⣤⡶⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣏⡉⠓⢄⠀⠀⠹⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⣼⡃⠀⠀⠀⠤⣿⢶⠟⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢆⠙⢢⡀⠳⣄⠀⠹⣄⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣼⠁⠙⠲⢤⣤⣴⠋⠸⣇⠀⠀⢳⡄⠀⠀⠰⡄⠀⠀⠀⣰⠋⢧⡈⠣⡀⠙⢦⣈⠓⠤⣈⣙⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⢠⡏⠀⠀⠙⣆⡀⣠⡽⠛⠛⠛⠛⠓⠶⠚⠁⠀⠈⠳⣄⡉⠢⢄⣉⣘⣛⣉⡽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢦⣴⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠶⠶⠶⠤⢤⣤⡤⠴⠒⠊⠉⠉⠉⠉⠙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣧⠀⠀⠀⠀⢻
⠀⠀⠀⠀⡇⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⡀⠀⠀⢀⣴⣾⣿⣂⣠⡤⠤⠤⠴⠤⠤⠤⢄⣀⣀⣈⠙⠛⠷⠄⠀⣰⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠑⠒⠊⠋⣁⣠⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠭⣍⡒⠒⠤⢈⡀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠈⢸⣇⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡎⠉⠺⡄⠀⠀⢰⡏⠀⠀⠀⢀⣤⣤⣄⡀⣷⠀⢠⡏⠀⠀⠀⣠⣶⣶⣶⣦⣀⣷⠀⠀⠀⠀⣼⠁⠀⡷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠻⣄⡀⢣⠀⠀⢸⡇⠀⠀⢰⣿⣿⠿⠉⣱⣾⠀⢸⡇⠀⠀⢸⣿⣿⡿⣏⠀⣹⣿⠀⠀⠀⢰⡿⠴⠚⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⡏⠉⣧⠀⠀⠻⣄⠀⠸⣿⣿⣿⣿⣿⠃⠀⠈⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⣧⡀⠀⠈⠛⠶⠾⠿⠟⠋⣠⠄⠀⠀⠈⠳⣦⣄⣙⣻⣿⣿⠟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢄⡀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠈⠻⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣉⣉⣁⣀⣠⣤⡤⠶⠚⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣲
⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠈⠉⡏⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⠀⣠⠃⠈⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠒⠐⠋⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠀⠀⠀⠀⠀⠀⢸⠦⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠉⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠠⢀⠀⠀⠀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⠄⠊⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢃⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠒⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⠀⠀⠀⠈⠂⠀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⡀⠠⠊⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠘⢋⠹⠉⠉⠉⠻⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⡇⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠩⣍⠉⠀⠀⣀⣵⣄⠀⠀⢀⠜⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⢀⠀⠭⠕⠒⠉⠀⠈⠛⠮⣁⣀⣀⡠⠞⠁
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣠⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⢀⡀⠤⠐⠒⠒⠒⠒⠒⠂⠒⠒⠂⠤⢄⣀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠊⠀⠀⠀⠀⢀⡠⠤⠒⠂⠈⠉⠉⠉⠉⠉⠀⠀⠐⠒⠠⠄⡀⠀⠀⠈⠓⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⠔⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⡀⠤⠄⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠀⡐⠁⠀⠀⠀⠘⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠀⠀⠀⠀⣱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⡔⠀⠀⠀⠐⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡤⠖⠁
⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠇⠀⠀⠀⠀⠀⣤⣀⣄⣀⡀⠀⠀⡔⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠢⣀⠔⠂⠁⠀⠀⠀⠀⠀⠈⢓⣬⠀⠄⣀⡀
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡗⠀⠀⠀⠈⠳⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⠁
⠀⠀⠈⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠢⢀⡀⠀⢀⣂⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⡠⠤⠚⠀⠙⠢⢤⣀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣼⠻⣿⣿⢿⣻⣿⣿⡅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠉⠉⠙⠛⠛⠛⢿⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣦⢀⣤⣶⣶⣤⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣽⣿⣿⣧⣤⣿⣿⣿⣿⣿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡙⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⣿⣿⣿⣿⠿⠿⢿⣿⣿⡆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⣭⠩⠍⠀⠀⠀⠀⠀⠀⢰⣿⣬⣅⣲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣄⡀⠀⢀⡾⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣶⣾⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠇⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢠⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⣾⠁⣙⠻⢶⣶⠂⢹⣿⠃⠒⣶⡶⠟⣉⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡮⢄⣤⡝⠀⠈⠿⠀⠈⣥⣄⡠⢴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣄⡀⠉⣠⣄⠀⠀⠀⠀⢀⣤⡀⠁⢀⣬⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢃⢉⠇⠀⠀⠀⠈⣉⠄⠀⠀⠀⠀⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠙⣛⠉⠡⢀⡀⠰⠀⠀⠀⠀⠀⡄⢀⠠⠬⠙⡛⠛⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⢀⠊⠀⢀⠀⠀⠈⢳⣶⣤⣤⣤⣶⠏⠀⠀⠀⠀⠈⠳⠰⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡄⠀⠀⠑⡀⠀⠀⠉⠛⣟⠛⠁⠀⠀⠠⠁⠀⠀⡸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢜⣄⠀⠀⠑⢄⡀⠀⠴⠉⠢⠤⠤⠒⠁⠀⢀⣔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⣘⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⠤⠤⠤⠤⢐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠈⠙⠿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⢀⡀⠀⢀⡌⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢺⠃⠀⠀⡾⠀⠂⠀⠂⠀⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢸⣿⠀⠀⡄⠀⠀⠾⠀⠑⠀⢠⣿⠐⠂⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣀⡀⠀⠀⠀⣽⣌⠻⠀⠸⠇⠀⠀⠀⢀⠁⢀⠄⢹⣷⠆⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠤⠟⠉⠀⢀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⢤⡀⢀⠁⠀⠀⠀⢠⣼⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⠀⠀⢰⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣧⣀⣀⣀⣴⡋⢀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠐⢚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡿⡕⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠻⠒⠀⠐⠚⣿⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡟⣌⢁⣠⡿⢠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⢀⠀⠈⣹⠃⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠣⠉⢡⠴⢿⣏⠦
⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⢀⡼⠷⠄⣀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⠟⢁⣀⣀⠀⠀⠙⠿⡆⠠
⠀⠀⠀⠀⠀⠀⢿⢀⡤⠋⠀⠑⣠⠴⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣼⣿⢃⣶⣛⠛⠲⣌⠠⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠆⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣿⣜⣿⣿⡠⠔⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣭⣀⣀⣉⣠⠋⠔⠀⠀⢀⡌⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠹⡆⠀⠀⠀⠀⢸⠋⠉⠉⠉⠛⠻⠿⢿⡠⠴⠤⠀⠠⡟⠊⢁⣌
⠀⠠⡄⢸⠿⠇⢀⠁⡀⠁⠀⠀⠀⠀⠀⠠⡤⠤⠄⠾⠷⠄⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁
⠀⠀⠐⠀⡂⠞⡀⠴⠀⠁⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⢢⡀⢀⠀⠠⠀⢐⠀⢼⠷⢀⠈
⠀⠀⠀⢀⡄⠀⠁⠀⠀⢄⡀⠀⠀⠀⠀⢰⣀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⣀⠀⠀⠀⠈⠀⠊⠀⠀⠀⡇⢰⡄⠀⡁⠘⠂⢠
⠀⠀⠀⠀⠠⠄⠂⡀⠂⣀⠀⠀⠀⣰⠄⠀⠉⣤⠀⠀⠆⢠⡀⠃⠀⠀⣡⣤⠉⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⢹⠀⠀⠀⠘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣀⠀⠀⠀⠀⡌⠀⠐⠀⠀⠈⠀⠟⠀⠐⠀⠉⡀⠀⠀⠂⠷⠄⠀⠀⠊⠀⠀⠚⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠛⠀⠘⠀⠀⠙⠀⠀⠈⠀⡀⠀⠂⠔⠛⠂⠀⠀⢀⠠⢄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⣛⣛⣛⣛⣳⠶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⢞⣭⢞⣫⡭⠷⠶⠶⠾⣭⣟⡷⣭⡳⣤
⠀⠀⠀⠀⣠⢟⣵⢫⡶⣫⡵⠞⠛⠉⠉⠛⠳⢮⣟⢮⡻⣮⢳⡄
⠀⠀⠀⣰⣏⡾⣱⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣞⢷⢻⡄
⠀⠀⢀⣟⣼⢱⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⡞⣧⣿
⠀⠀⠘⠋⠀⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠀⠙⠃⡀
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣄
⠀⠂⠄⠠⠤⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠤⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⡄⠠⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⣗⢮⣟⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⡄⠈⢳⡝⣮⢳⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠐⡲⠂⠒⠐⠂⠒⠐⠀⠲⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠛⠛⠁⠀⠀⢿⣸⡏⣿⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣛⣘⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠈⠀⠀⠀⠀⠁⠀⠑⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣄⣀⣤⣀⣠⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠠⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠇⠘⢸⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⡄⡖⠀⠀⢀⡴⠾⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⢸⡇⡸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠠⠋⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⠀⠀⠀⠀⣤⣴⣾⠇⣼⠀⠀⣼⡇⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣀⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡟⠀⠀⣿⡇⡅⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢀⣤⣾⠟⠛⠉⢋⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡇⠁⠀⠀⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡇⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⡆⢀⢻⣿⠀⡇⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠘⣼⡿⢠⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣆⠀⠀⣿⡇⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣷⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡇⠘⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢇⡏⠀⢹⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠃⠀⠀⠀⣄⠀⠀⠀⣏⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠐⢸⡆⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡄⢰⢻⣇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⡇⣿⣿⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⡀⠀⠀⠆⠀⠀⠁⢸⢸⢸⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠁⢀⠀⠀⢀⠀⠘⡼⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⡇⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠇⡀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⣧⢿⢹⣿⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢠⡄⢠⡆⣿⢠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⣷⢸⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⡟⢸⠀⢸⠁⣿⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⠁⡼⠀⢸⠀⣿⢸
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢘⣿⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡆⢿⠘
⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢸⡏⣿⡿⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⣸⠀⢠⢸⡇⣟⠇
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢸⣏⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⣸⠁⢬⠂⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠆⡇⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⢤⣇⠀⠀⢀⠇⠀⠀⣿⣘⠈⢳⣬⣿⣽⣖⣶⣦⣤⣀⡀
⣀⣤⣤⣶⣶⣶⣤⣴⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⠰⠀⣿⣿⣿⣷⣦⣭⣽⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠀⠹⠆⠀⠀⠀⢰⠁⠀⠀⡟⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣶⢰⠀⠀⠀⠁⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠛⠛⠛⠛⢿⣿⣿⣋⠉⢉⣽⠔⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣿⣿⠀⡇⠀⢸⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⡇⠀⢸⢸⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣾⣿⣿⣿⣿⡿⣿⣦⣄⣀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⢰⡇⠀⠀⣼⠀⠀⣼⣿⣿⣿⣿⣿⡟⣿⣿⣻⣿⡏⣿⣾⣿⣿⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠛⠛⠛⠛⢹⣿⣿⣿⣿⣿⢸⠁⠀⠀⡇⡀⠀⢸⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠻⠿⠛⠛⠛⠛⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠇

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠡⠀⡀⠄⠀⠀⠀⣀⠀⠤⠤⠤⢀⡀⠀⠀⠀⠀⡀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⣀⠀⠡⡶⠤⠭⢀⠀⠀⠉⠉⠃⢔⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠉⢆⡀⠀⠋⠀⠀⠀⠀⠀⠀⠐⡀⠀⢁⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⡘⠀⠀⠙⣆⠀⠀⡈⠀⠀⢰⠖⠰⡆⠁⠀⠁⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠰⢡⠀⠀⠈⠢⠀⠀⠀⠀⠀⡨⠀⠀⠁⠀⠀⠸⢸⠀⠁⠀⠠⣄⣤⡤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⡆⠀⠀⠆⢰⠏⢢⡄⠀⠘⡆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠒⠀⠀⢹⠀⠀⢀⠌⠀⠀⠜⠀⠰⠀⠘⠁⠀⢀⡆⢁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⡀⢂⠀⢀⣸⠀⠔⣀⣀⠀⠈⠀⡐⠁⠀⠀⠀⠀⡼⠔⠙⡖⠈
⠀⠀⠀⠀⠀⢀⠀⠠⠈⡀⡐⡄⢀⠴⠊⠁⣀⠠⠑⠎⠁⠀⠀⡐⢀⡞⢆⠀⠀⢠⠁⠀⡰⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣐⡾⠊⢉⠃⢀⠔⠊⠀⠀⠀⠀⢀⣶⠀⠀⠀⡇⠈⠓⢦⡬⠉⡎⠉⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠐⠀⠈⣡⣀⠂⠀⠁⣀⠀⢀⣀⡠⢔⡕⠃⢡⡀⠀⠄⢀⠟⠉⢱⠊⠙⠆⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠈⢀⠁⢠⠖⠁⠉⠈⡹⠁⠀⠀⠁⠀⠐⠀⠩⡀⠀⠈⢀⠴⡋⠠⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⡀⠁⠠⠀⠅⠂⠀⠁⠀⠀⠀⠀⠀⠈⠂⠎⠀⠀⠐⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠎⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢡⠀⠎⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⣾⠞⠀⢀⡠⠔⠒⠒⢂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠈⣄⠔⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠴⠖⠒⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠤⠒⠊⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠤⣄⡀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠑⣄⠠⠊⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡐⣠⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⢀⠔⠀⠄⠀⢀⡈⠄⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠣⢄⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠵⠆⠙⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠓⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⡠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣭⣥⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⡄⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⢀⠄⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠗⣼⠂⠁⣀⠀⢀⡈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠳⡬⠊⠁⣀⠤⢀⡈⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣲⡴⡉⠖⠊⢀⣀⢴⠟⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣣⣔⣩⠔⠋⣀⣀⢴⠟⢋⣷⡀
⠀⠀⠀⠀⠀⠀⣤⡄⠀⣾⣪⠄⠀⠤⠴⠊⠁⠀⠢⣤⢾⠃⢰⡀⠀⠀⠀⠀⠀⠀⢀⠦⠄⠀⣠⣫⠄⠠⠤⠔⠊⠀⠀⠣⣤⢿⠃⢡
⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⠗⠀⠀⠀⠔⠒⠆⠀⠜⡡⠊⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢘⠏⠀⠀⢠⠒⠒⠆⢀⢞⡵⠋⠀⣸⡃
⠀⠀⠀⠀⢀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠎⢀⠜⡠⢃⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⠎⢀⠎⡰⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣠⢀⣀⡐⣮⡼⡰⢁⠎⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠣⢄⣀⣤⢀⣀⠐⣮⣜⡔⢡⠞⡠⡎⡇
⠀⠀⠀⠀⠀⠐⡖⢙⠤⠀⠀⠀⡠⠚⠀⠰⣐⢡⢠⡡⡞⢀⠃⠇⠀⠀⠀⠀⠀⠀⠘⡖⢳⠤⠀⠀⠀⡠⠊⠀⠰⣐⠹⣰⡡⡞⢠⠃⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠀⠌⠀⠀⠀⠰⡁⢸⡿⢐⡡⣊⠎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠎⠀⠀⠀⠐⡑⣻⡿⢚⠵⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢕⠩⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠓⠭⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢠⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡀⠀⠀⠐⡄⠀⠀⠠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠡⠀⠀⠀⠁⠀⠀⠡⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢐⠀⠁⠀⠠⠊
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂
⠠⡀⠀⠀⡀⠀⠀⠁⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠄⠀⠀⠀⢀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠘⠀⠀⣀⠠⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⢂⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡂⠰⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠊⠡⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠒⠐⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠠⡄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡐⠁⠂⢂
⠀⠀⢀⠐⠂⢉⠁⠀⠀⠀⠀⠀⡠⠀⠀⠁⢄⠀⠀⠐⡀⠀⠀⠐⠣⡕⡤⠐⠒⠯⠆⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡈⠢⡀⠀⡐⡄⠈⠁⠈
⡔⠈⠀⠅⠀⠈⠐⠄⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠀⢀⢃⡐⢀⠀⠀⠰⣀⣀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠸⡄⠑⠆⠁⠂⠔⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠤⠤⠐⠓⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣻⣡⣻⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣽⣽⣿⣭⣯⣽⣯⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⢀⠀⣀⠄⠘⢀⠀⡠⢄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⢀⡠⠔⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠤⠀⠀⠸⣼⡿⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠡⠀⠀⠀⠀⠀⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠀⠐⠀⠀⣠⠀⠀⠀⠎⠀⠜⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠂⢀⡀⠀⠈⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢇⠀⠀⠁⠠⠂⠝⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠑⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢢⠀⢦⠀⠁⢀⠠⠊⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⠠⠠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠆⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠚⠀⠈⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠐⠈⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠈⠐⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠉⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠔⠉⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡠⠊⠉⠉⠒⢄⠀⠈⠄⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⢀⡤⠤⠤⣀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠈⢂⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠡⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠥⠐⠁⠀⠀⠈⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣴⠠⠀⠐⠀⠀⠒⠒⠒⠊
⠀⠀⢀⠠⠔⠒⠈⠁⠉⠉⠉⠑⠲⣄⡀⠀⠀⠀⠀⠀⢀⠔⠝⠁⠀⠀⠀⠀⠀⠀⠈⠃⠈⠢
⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⡠⠁⠀⣀⡤⠀⠀⠀⠀⠀⠠⠲⢤⡀⠀⠀⠣⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠇⠀⠀⡐⠁⠀⠘⠁⣀⠤⠒⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⠠⠠⠤⢄⠀⠀⠀⢀⠎⠀⠀⢠⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⠅⠀⠒⢄⠀⠀⠀⠸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⠀⠀⡰⠁⠀⠀⠀⢠⠀⠀⡰⠁⠀⠑⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠑⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⠀⠀⢀⠔⠀⠘⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠁⠀⠀⠠⠃⠀⠀⠀⠑⣌⡀⠀⠀⠀⠄⣀⠤⠒⠤⠤⠤⠖⠀⠀⠀⠀⣠⠃⢀⡀⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⠛⠤⣀⠀⠀⠀⠀⠀⠐⠤⠀⠜⠀⣀⠤⠋⠑⢮⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠒⠂⠀⠉⠀⠀⠀⠀⠀⠉⠐⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⠇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠳⣄⠀⠀⠀⢠⠖⠉⠉⠉⠉⠲⡄⠀⠀⠀⠀⡔⠉⠀⠀⠀⠈⠙⣄⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⡀⠌⠓⠤⣀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠃⠀⠠⠤⠤⠤⠶⠒⠓⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣿⣟⣿⣿⣟⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⢀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⣤⠠⠤⠤⣄⣀⣀⠈⠉⠲⢤⡀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⠠⡤⠄⣀⣀⠈⠉⠒⠤⣀⠈⠓⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡠⠊⠀⡠⠊⠁⣠⠔⠊⠉⠀⣀⣀⣀⣀⣀⠀⠉⠑⠢⣀⠈⠑⢄⠀⠑⣄⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⠁⣠⠎⠀⡠⠊⠀⡠⠔⠊⠉⢀⣀⣀⣀⠀⠉⠑⠢⣄⠈⠑⢄⠀⠱⡄⠈⢦⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣜⡀⣰⠃⢀⠞⠀⡠⠊⠀⡠⠖⠋⠁⢀⣀⡀⠈⠙⠲⣄⠀⠑⣄⠈⠣⡀⠘⣄⠀⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⠉⠉⠉⠉⠓⢮⡀⡼⠁⢠⠎⠀⡠⠚⠉⠁⠀⠈⠉⠲⢄⠀⠳⡀⠈⢆⠀⡱⠖⠋⠉⠉⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⢀⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⡀⣈⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⠣⣄⣀⡤⠤⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡴⢤⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣠⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠈⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠞⠋⠀⠀⠀⣀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⡀⠀⠈⠙⠶⣄⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠴⠋⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠈⠛⢦⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢁⡴⠃⠀⠀⣠⠞⠉⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀⠀⠀⠙⠷⣄⠀⠀⠙⢷⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢠⠞⢀⠀⣰⠋⠀⠀⣠⠞⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠈⢷⣄⠀⠀⠙⣦⡀⠀⠙⣧
⠀⠀⠀⠀⢠⡏⠀⢀⡼⠁⠀⢀⡼⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠙⢦⡀⠀⠈⢻⡄⠀⠘⣧
⠀⠀⠀⠀⡞⠀⢀⡞⠁⠀⢠⠞⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠻⣆⠀⠘⣧
⠀⠀⠀⣸⠁⢀⡾⠀⠀⣰⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠹⣆⠀⠀⢹⡆⠀⠹⡆
⠀⠀⢀⡏⠀⣼⠁⠀⡴⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣦⠀⠀⢻⡄⠀⢿⡀
⠀⠀⢸⠃⣰⣇⣀⣼⠁⢠⠏⢀⣤⠖⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣷⡀⠘⣧⢀⡬⠷⠒⠺⢧⣄
⠀⠀⣸⠋⠉⠀⠀⠉⠓⢯⡴⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠳⢤⡼⠋⠀⠀⠚⠉⠀⠙⣆
⢠⡴⠟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⠲⠶⠞⢻⡄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢰
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣰⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣀⣀⣴⣤⣀⡀⣀⣀⡴⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣷⣶⣶
⣿⣿⣇⣤⣍⣤⣮⣬⣧⣥⣾⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣶⣄⣤⣤⣀⣶⣄⣰⣶⣿⣿⣷⣄⣀⠀⣰⣾⣷⣶⣿⣿⣶⣶⣶⣦⣴⡆⣿⣧
⠀⠀⣶⣶⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡦
⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⢀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠸⣯⣻⣿⣿⣿⣿⡿⠿⢿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⡄
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⢸⣿⣻⣧⣬⣯⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠊⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢛⡟⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⡤⠀⠀⠀⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠈⠙⠋⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠤⢭⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⡿⠑⠙⠓⠒⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⢏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡌⠉⢈⠀⠀⠀⠀⠀⠀⠠⠴⠶⠦⢤⣄⠀⠀⠀⠀⠀⣨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣁⢧⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⢀⣴⡯⢤⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠈⠉⠛⠠⠄⠀⠀⠀⢾⢋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠹⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠺⢿⡇⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢰⡤⠟⠱⠃⣄⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠒⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⣦⣀⠀⠀⠀⠈⠘⠓⢲⢟⡁
⠀⠀⠀⣀⡤⠶⠛⠛⠧⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⢀⣈⣠⣴⠃⠀⡅⠐⢦⣤⣄⣀
⠀⠠⠊⠁⠀⠀⠀⠀⠀⠈⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢸⣿⣿⡟⣴⢠⠇⠀⠀⠈⠛⠙⢿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣰⢇⡎⠀⠀⠀⠀⠀⠀⣈⣿⣧⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠁⡻⢾⡇⠀⠀⠀⢀⣠⣾⣿⣿⣿⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢃⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠛⣀⢴⣧⠈⣿⣢⡶⠺⠟⣻⣿⣿⡿⠿⠟⣿⡟
⠀⠀⠀⠀⠐⠚⣧⡠⢊⠞⠉⠓⠀⢄⡀⠈⠑⠒⠀⠀⢀⣀⣌⣉⣉⠄⠒⣉⣁⣤⠄⣳⣿⡇⠁⠀⠀⣿⡏⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢛⣴⡞⠀⠀⠀⠈⠒⠀⠈⠉⠉⢀⣘⣉⣭⣿⣿⠗⠚⠛⠛⠉⠁⢰⣿⣿⡇⠀⠀⠐⠿⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠟⠉⠉⠉⠑⠒⠀⠀⠀⠀⠠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠾⠿⠻⣿⣶⣤⡀⢀⣠⣤⡴⠶⠶⠶⠶⣦⣤⣀⠀⣠⣤⣾⣿⠟⠻⠷⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠀⠀⠀⠀⠈⠑⠈⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠁⠋⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⣀⣤⣶⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⣶⣦⣄⠀⠀⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⠉⣩⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⣿⣯⡉⠃⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣼⣿⣿⣿⡟⠀⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠦⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡆⠀⢹⣿⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⢰⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠹⣿⣿⠀⠀⠀⣻⣿⣷⠀⡰⢻⣿⣿⣆⠀⣐⣻⣿⡆⠀⠀⠘⣿⣿⠏⣀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣌⣻⠀⠀⠀⠙⠛⠉⢀⡇⢸⣿⣿⣿⡄⠘⠛⠛⠁⠀⠀⢸⣟⣡⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡆⠀⠀⠀⠀⠀⠀⢷⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠷⠶⠦⠤⠄⠀⠀⠀⠀⠀⠴⠶⠚⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠐⠒⠒⠶⢤⣜⣆⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⡓⢦⣄⡀⠀⠀⠀⠀⠀⣀⡿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢦⡈⠛⠳⠶⣤⣴⡶⠟⠁⣿⣠⠶⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⣠⠶⢶⢶⣄⠀⠀⢀⣴⣿⡇⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⢶⣶⣶⣶⣾⣿⣿⣶⣤⣀⣇⣀⣁⣀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⡶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡤⠖⠛⠉⠉⣾⠁⠀⠀⠈⣷⠚⠉⠛⣦
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣸⡃⠀⠀⠀⣼
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡶⠛⢶⡾⠋⠉⠙⣦⣠⡴⠋
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠸⣇⠀⠀⠀⣼⠉⠉⠳⣄
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠈⢷⣄⣀⣤⡟⠻⠶⠟⠁⠀⠀⠀⢹⠄
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⢷⣄⡀⠀⠀⠀⠀⠈⠉⣽⠀⠀⠀⠀⢸⣆⢀⣠⠟⠓⢤⣀
⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠙⠻⠷⣶⣤⣀⢀⠀⠘⣦⣀⣀⣀⣼⠋⠉⠁⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠳⠶⣶⡾⠋⠀⠀⠀⢀⡤⠶⠒⠛⠿⣿⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⣰⠏⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡿⠳⡶⢵⡄⠀⠀⣴⣯⣴⣶⣲⠶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⢠⡾⠁⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣾⠇⣠⠿⠀⠘⢧⣀⠻⣿⣿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⢰⡟⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣉⣛⣩⡴⠛⠃⠀⠲⢦⠀⠉⠳⠦⢭⣥⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠈⢷⣄⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⣠⡟⠉⠌⠀⠋⠀⠀⠁⠀⠀⠐⠶⠞⠀⠀⠀⠀⠀⠁⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⢷⠀⠀⠀⠀⠳⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡾⠀⠀⠀⠀⢀⠇⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⣠⠇⠀⠀⠀⠀⠀⢀⡼⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣠⡞⠁⠀⠀⠀⢠⠞⠀⠀⠀⠀⠘⢯⡻⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⡴⠋⠀⠘⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣿
⠀⣼⠋⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⠻⠶⣦⣤⣀⣀⣀⣀⣀⣤⣴⠾⠛⠁⠀⠀⠀⠴⡆⠀⠹⠂⠄⠂⠀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⣠⣿⠏
⣸⡇⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢨⠏⢉⠿⡏⢙⠁⠀⠀⠀⠀⣀⠔⣪⠦⠝⠦⢄⠈⡐⠃⠀⡠⠊⠁⠀⠀⠀⣀⣀⣤⣾⠿⠋
⣿⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡤⠖⢒⣫⣼⠃⠀⠹⣼⣓⣒⣒⣈⡥⠴⠊⠁⠀⠀⠀⠈⠀⠀⠀⡜⠀⠀⢀⣴⡾⠿⠛⠛⠉
⢿⣆⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠈⢡⠏⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠁
⠈⠻⣷⣤⣀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠈⠢⣰⠒⡄⢠⠏⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠹⣦
⠀⠀⠀⠈⠙⢷⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢠⠋⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠘⣇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⠞⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⠔⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣆⡀⠀⠀⠀⠀⢶⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡷⠂⠀⡰⢁⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣤⣄⡈⠉⠒⠒⡤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠖⠚⠁⠀⠀⠀⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⡇⠀⠀⠀⠀⢸⠁⠀⠉⠁⢹⡀⣀⣀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡏⠉⠉⠉⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴⣤⡙⠲⢤⣤⣀⣀⣼⣧⣄⣀⣠⣤⠾⠿⠴⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⣀⣁⠠⠤⠤⠈⠛⠉⠈⠉⠂⠩⠤⠒⣒⣊⣁⡨

⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠶⣄⠀⣀⣤⠶⠖⠛⠛⠛⠛⠛⠓⠶⢦⣄⡀⢀⣴⠞⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⣼⠃⣠⠶⠲⢦⡀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣴⠖⠶⣤⠀⢻⡄
⠀⠀⠀⠀⠀⡏⢰⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⣇⠀⣷
⠀⠀⠀⠀⠀⣷⠘⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠇⢠⡏
⠀⠀⠀⠀⠀⠘⢷⡈⠁⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠁⣠⠟
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠉⠀⠀⠈⠙⢦⡀⠀⣠⠞⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⡏⠀⠀⠀⢀⣀⡀⠈⣷⢰⡇⠀⣀⣀⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠘⣇⠀⠀⠀⢿⣿⡗⢀⡿⠸⣇⠀⢿⣿⠇⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⡟⢦⡀
⠀⠀⢀⡾⢁⡟⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⣀⣠⠞⠁⠀⠙⢦⣀⡀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⣷⡈⢳⡀
⠀⢠⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢻⡀
⠀⡾⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢷
⢸⠇⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠈⣷⠸
⣿⠐⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡟
⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⢿⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀
⠸⡇⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠛⠉⣇⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⣸
⠀⢻⡀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣠⡿⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀⢠⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣽⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠈⢳⣄⡤⠶⠚⠓⠲⠶⣤⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠒⠶⣦⣠⡟⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠀⠀⣀⣀⣀⠀⠀⣀⠀⠀⣠⣤⣄⠀⢸⣗⠀⠀⠀⠀⣿⡁⠀⢀⣀⣀⠀⠀⣀⠀⠀⣀⣤⣀⡀⢸⡇
⠀⠀⠘⣧⡾⠉⠀⢉⡿⠋⠉⠻⣟⠁⠀⠉⣷⣼⠛⠛⠛⠛⠛⠛⣧⣰⠋⠀⠈⣿⠋⠉⠙⢾⠉⠀⠈⣿⣼⠃
⠀⠀⠀⠈⠛⠶⢤⣼⣧⣤⣤⣤⣿⣤⡴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣿⣤⣤⣤⣾⣦⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⢉⡠⠄⠒⠒⠀⣀⡀⠐⠒⠀⠤⢈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⠔⠊⡠⠔⠂⣉⡉⠤⠤⠤⠈⠁⡁⠂⠤⡈⠒⢄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠔⢁⠄⢊⡡⠄⢒⣂⣀⣀⢒⠂⠄⢁⠂⢄⠑⢄⠑⢄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⢁⠔⢡⠞⡡⢊⠥⢒⠩⠄⠐⠒⠒⠀⠬⢁⠢⢁⠢⡈⠀⠐⠄⠑⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡐⢀⠊⡰⢁⢎⠔⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡑⠌⢀⠁⡀⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣰⣁⡎⣐⢠⣃⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠉⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠉⢂
⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠑⠤⠄⠀⢄⡀⠀⠀⠀⢀⡠⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠠⡀⠀⠀⠀⠀⢀⠄⠀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠀⢶⠁⣖⢒⣄⣀⠀⡠⠒⢩⠀⢀⡴⠁⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢧⡀⠤⢒⠉⠉⡱⢶⣩⣶⡴⣤⠾⣯⣹⢦⠁⡀⠫⠀⣠⠾⠖⠛⠀⠀⠀⣰⠃⣠⠔⠒⠒⠒⠒⠦⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⠤⢍⣰⠧⣸⢏⡜⠰⠻⣦⢶⡼⢰⠉⢱⠞⠉⣥⣠⠴⠦⠤⢤⣞⡡⠊⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⢠⠊⠼⠓⣌⣹⣤⡜⠢⣜⣉⠔⢁⣴⢮⠤⠴⣃⠄⢀⣀⠴⠊⠁⠀⠄⣀⣂⠀⠛⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⡖⠚⢙⣟⠘⢈⠓⠤⢀⡨⢳⢫⠹⠦⠀⠤⡽⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢄⣀⣀⠀⢀⡨⢻⣄⠈⠤⠁⠀⠀⠀⠀⠸⣈⢠⠀⢀⠶⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⣠⠤⠤⠶⠒⠉⠁⠀⠀⡀⠀⠀⡀⠀⠀⠈⠘⢣⠦⡀⠀⠀⠀⠀⠀⠀⠁⢠⠃⢀⠤⠀⠀⠀⢰⠏
⠀⠀⠸⣇⠀⠀⠀⠠⠄⠲⠀⠊⠃⠐⠒⠁⠀⠀⠀⠤⢀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡎⠠⣿⣻⣾⡤⠀⢸⡄
⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣆⠐⣰⣿⣷⡄⢃⠀⠀⠀⠀⠀⢠⠃⠀⠛⠛⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⣤⠤⠖⠋⠁⠀⠈⢳⡉⠛⠋⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⠀⠀⠀⠀⠀⢮⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠹⡀⣰⢃⡀⢀⣀⡀⠠⠤⠘⠦⡀⠁⢢⠀⠀⡸⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢹⠷⣁⠀⠀⠀⠀⠀⢀⣴⠀⢸⠀⠀⡇⢠⠃⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣏⢰⠘⠷⠆⠀⠀⠀⠙⠁⠀⢸⠀⢀⡗⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⣸⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⢧⡘⠒⠒⠋⢉⣉⣉⣩⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠐⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢊⠝⣠⡿⠒⠒⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠉⢀⠔⠁⠸⠃⢐⣀⡔⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢸⠀⠎⠀⠀⠀⡀⠉⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠥⠒⠁⡠⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⠀⢠⠞⠁⢀⠀⡅⠀⠀⠀⠈⠑⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⣸⠃⠀⠀⡴⣫⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠢⠤⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠎⠁⡀⠀⢊⠔⠁⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠙⢍⠉⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⡆⠀⢷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠂⡜⠀⠀⠀⠀⠈⡄⢰⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⠀⠸⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠀⠀⠀⠀⠀⠀⠇⡼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⠃⠈⢧⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⣼⠀⠀⡎⠀⣦⠀⠙⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡤⢄⠀⠀⠀⢠⠄⠒⠊⠁⠱⡀⠀⣏⠄⠀⡇⢀⡿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡂⠀⢣⠀⠀⡈⠀⠀⠀⠀⠀⢇⠀⣿⠀⢸⢀⣾⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠈⡆⠀⡇⠀⠀⠀⠀⠀⠘⡆⣿⠀⡆⣼⠃⠀⡰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⡅⠀⠀⠀⠀⠀⢀⡇⣿⢀⠃⠇⠀⣸⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⠀⠀⢃⠀⡇⠀⠀⠀⠀⠀⠸⠼⡇⢸⠀⠀⠀⠻⡈⠒⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⢠⠇⡼⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⠀⠘⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⡺⠀⠀⢠⠇⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢖⢠⣠⣤⣄⣀⣀⣠⣄⡣⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⣿⣿⣿⣿⠿⣿⢿⣿⠷⣐⣄⣠⠀⠀⠀⠀⠈⢧⣀⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣷⢶⣿⢿⡿⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡖⢲⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢫⣿⣿⣳⣿⣿⣆⢹⣿⣿⣶⣅⣀⣀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⣿⣻⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠞⠁⠈⠹⠿⣿⠻⡇⠙⠉⠛⠛⠒⠀⠀⠀⠀⠀⠉⢺⣿⣿⣿⣿⣿⠋⢉⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡣⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢉⣠⣿⡿⠿⠿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⢠⣴⢦⣾⣿⣿⣍⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡒⠀⠀⠀⠀⠀⠀⢀⠀⠴⢟⣫⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠦⣤⣤⣤⣄⠀⣀⣠⣶⣯⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⢹⢣⠱⠀⠛⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⡀⠀⠀⠲⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣦⢠⡆⢠⣶⡆⢶⡶⠆⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⢻⡇⢸⣟⣷⢸⡇⠀⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠸⠇⠾⠋⠿⠸⠇⠀⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⣠⡄⣤⣠⡆⢰⡶⠂⣿⢻⡆⢻⣴⡇⣼⢻⡆⢰⣦⡆⢴⡤⠀⠀⠰⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢶⠀⠈⢿⠆⢸⣿⡇⢸⡟⠀⣿⢾⡃⠘⣿⠀⣿⢘⡇⣸⣿⡇⣿⠃⠀⠸⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⡷⠀⠘⠦⠀⠿⠇⠸⠷⠆⠛⠘⠃⠀⠛⠀⠙⠛⠃⠿⠛⠑⠟⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠂⠀⠀⠈⠁⠈⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠉⠑⠀⠼⠀⣀⣀⣀⣤⠀⣠⣀⠤⠀⠂⠉⠀⠀⡀⢠⣀⠖⠙⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⢺⠀⠀⠇⠀⠀⠈⠑⠀⢀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡠⠂⠀⠀⠀⠆⠀⠀⠐⠄⠀⠠⠘⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢔⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠡⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⢆⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠒⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣁⣄⣀⣀⣀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠡⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢧⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⠜⠋⠉⢁⣠⣬⣅⡉⠙⠳⡄⠀⠀⠆⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠠⠀⡴⠋⠀⠀⠀⠙⡄⠀⡘⠀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠐⠁⠀⡠⠀⠀⠀⢁⡠⠁⠀⠀⠀⠁⠀⠀⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⠀⠀⠀⣠⠖⠈⠉⠀⠀⢦⡀⠀⠀⠀⠘⠧⣄⣀⡤⢂⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢈⡤⠀⢄⠀⠈⠁⢀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠀⠀⠀⠞⠁⠀⠀⠈⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠤⠞⠀⠀⠀⢀⠀⠠⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠔⠁⠀⣀⠔⡠⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠁⠀⢀⣠⠜⡐⠀⠀⠀⠀⠀⠂⠈⠒⠀⠀⠀⠇⠀⠀⠀⠀⠁⠀⠀⠈⠀⢰⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣖⠋⠁⢠⡞⠀⠀⠀⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠸⠀⠐⠈⡀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠀⠀⢸⠁⠀⠀⡎⠀⠀⠀⢸⡀⠀⠀⠠⡀⠀⠘⣆⠀⠐⠲⠆⠀⠀⡄⡀⠀⠐⢀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢦⣔⡀⠜⠀⠠⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠁⡀⠀⠀⠱⡄⠀⢹⡀⢀⠞⠀⢀⠔⠁⠳⠐⠅⠚⠀⠉⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⡇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠀⠘⡇⠀⠀⠈⢀⠤⠤⠄⢤⡄⠄⢐⢸⡥⠖⠶⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠈⡃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠱⡀⠀⠀⠀⠠⠆⠀⡼⢠⡀⠀⢀⠀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠀⢄⣀⠶⠃⠀⡃⠘⠘⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⠎⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠌⠀⠀⣴⣾⣷⣄⠀⠀⠀⠀⠀⣰⣾⡷⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣼⣿⡟⠀⢹⠀⠀⠀⠀⢠⣿⣿⡀⢸⡆⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⢿⣿⣶⡿⠀⠀⠀⠀⠘⡿⣿⣷⣾⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢮⡿⠟⠁⠀⠀⠀⠀⠀⠘⠦⠿⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⣀⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠷⣤⣀
⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠉⠻⢶⣄
⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⣀⣀⣈
⢠⣯⣤⣤⣀⠀⠉⠑⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠟
⠈⢿⣝⠛⠻⣷⡀⠀⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢂⠀⠀⠀⣼⡟⠀⠀⢀⠖
⠀⠀⠙⢧⠀⢹⣧⠀⠀⢀⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢦⠀⠀⢻⣇⠀⠀⡏
⠀⠀⠀⡼⢀⣼⠇⠀⢀⡞⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢣⡀⠀⠛⢦⡀⠇
⠀⢀⡞⠰⠋⠁⠀⡠⠋⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠉⢸
⠀⠘⣧⡀⠀⠀⠈⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣀⣠⠞
⠀⠀⠈⠙⠳⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣏⠛⠟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠞⠋⣼⠋
⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠉⢛⣿⠟⠛⠶⣤⡀⠀⠀⠀⠀⣠⣶⠶⢶⣤⣀⣀⣀⣀⡼⠛⣷⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⣇⡀⠀⠀⠀⣙⣦⣄⣀⣴⠋⠛⠚⠻⣿⣌⣉⠉⠉⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠒⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣶⣾⣯⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⣿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⢀⣀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠌⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡎⠲⢐⠀⠀⠻⣿⣿⣿⣿⠃⠄⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠉⠛⠁⠀⠢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⠀⠀⠀⣾⣿⣿⠟⠀⠀⣤⡄⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢹⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣶⣜⣿⣿⣿⣿⣷⣄⠀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠘⠿⣿⣿⣿⡿⠘⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⠄⠀⢀⡙⠻⠟⣿⣿⣿⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠋⠓⢠⣞⠳⣄⣙⣧⣼⣾⣷⠿⢿⣷⣶⣗⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⢀⠰⡅⢠⣶⡟⣦⣛⡻⣿⣧⡄⡘⣿⣟⣻⣿⣿⡏⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢂⣠⠄⠀⠀⠐⢄⠀⠀⠐⢷⠸⠟⣫⡾⢟⡿⠥⢈⣉⢻⡵⠶⠞⡿⣿⠻⠀⠀⠈⠓⡀
⠀⠀⠀⠀⠀⠀⣤⢺⣯⡶⢋⡁⢀⡥⠊⡀⠀⢛⣤⡀⠈⠣⡐⢛⡤⣈⣴⣾⣿⣿⣦⢑⠀⢶⣟⠂⠀⠎⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⣿⠼⣿⣷⠋⢄⡻⠿⠋⣀⠾⢟⣠⡟⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣷⣤⠈⠐⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠹⣦⣽⣶⣼⠀⢀⣶⣿⣥⡶⣾⣿⣷⣐⣤⣄⣠⡾⠟⠉⠁⠀⠀⠀⠀⠉⠙⠻⣤⠈⢀⡀⢀⡀⢱⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠟⡀⣷⣤⣍⣸⣿⣛⡝⣠⣶⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡝⣆⠸⡅⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⢿⣿⣿⣾⣯⡾⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⡄⢡⠀⣏⣹⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣷⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣤⡏⣿⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⣾⢻⡾⣹⣿⡟⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠛⠴⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⣿⣿⣿⣷⣾⣿⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⠇⠉⠓⠤⣀⠀⠀⠀⠀⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠟⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠈⠐⠠⠄⡀⠀⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠰⡶⠀⠤⠶⠖⠒⠐⠛⠋⠁⣹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠹⠿⣷⣴⣿⡿⢉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠛⠁⠀⢸⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠃⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⣴⣶⣶⣶⠶⡶⠿⣆⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣟⣿⣾⣿⣯⣿⢶⣿⣺⣿⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠿⠟⢿⣿⡿⠻⡿⢋⣿⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣿⣿⣿⠶⣀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣮⣽⣿⠿⣛⣿⣷⣶⡽⢲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠀⢿⣿⣿⣠⣼⣿⠿⣿⣶⣮⡟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢻⣿⣿⣿⣷⡀⠀⠈⢿⣿⣿⣿⣻⣶⢧⣶⠋⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣈⣭⡿⣤⣟⣷⠀⠀⠈⠻⣿⣿⣧⣼⡟⠁⠀⢀⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⣿⣿⣿⣶⣷⣾⣿⣷⡄⠀⠀⠹⣿⣿⠏⠀⠀⣠⣾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠙⣩⣿⣇⣉⠘⡐⢻⣿⣆⠀⠀⠘⣿⡀⢠⣾⠻⠇⣰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⣿⣤⠏⡠⡈⢻⣿⣇⠀⠀⣀⣸⣿⣿⣿⡷⢀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣾⣿⣿⣶⣦⣿⣿⣿⢁⣴⣆⣸⣿⣧⡽⢻⣶⣿⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⣿⣿⠏⢹⣿⠟⢿⣿⢿⡟⢻⣝⠛⣿⣿⠀⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢿⡷⠀⠁⣤⣾⣿⣿⣿⣾⣿⣟⣿⡧⣠⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠈⠙⠢⠜⠛⠛⠛⠻⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣀⡀⠀⠀⢀⡤⣄⠀⠀⠀⣀⣀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⣿⡿⠀⠀⢸⠀⢸⡆⠀⠘⢿⡿⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠓⢤⠀⠀⠀⠀⠀⠈⠲⠚⠀⠀⠀⠀⠀⢠⠔⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣠⣤⡀⢀⣤⣤⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡁⣿⣻⣿⢸⣟⣿⡇⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠉⠉⢉⣀⣀⣀⣀⣀⡉⠉⠉⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⢁⣠⣤⠶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣤⣄⡀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣀⡴⠞⠋⠁⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀⡈⠙⠳⢦⣄⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠞⠉⢀⣤⠶⠛⠉⣀⣠⣤⠴⠶⠶⠶⠛⠶⠶⠶⠶⣤⣄⣀⠉⠙⠳⣦⣀⠈⠻⢦⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣴⠟⠁⣠⡾⠋⢀⣠⡶⠛⠉⢁⣀⣤⣤⠴⠶⠶⠶⠦⣤⣤⣀⡈⠉⠛⠶⣤⡀⠙⠳⣄⡀⠙⢦⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⣠⡟⠁⣠⠟⠁⣠⡾⠃⢀⡴⠛⠁⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠈⠙⢶⣄⠈⠻⣄⠀⠻⣆⠀⠹⣆
⠀⠀⠀⠀⠀⣰⠏⠀⣴⠏⠀⣴⠋⢀⣴⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢷⡀⠘⢷⡀⠘⣧⡀⠹⣦
⠀⠀⠀⠀⢠⡟⠀⣸⠇⢀⡾⠁⢠⡾⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢻⣄⠈⢷⡀⠘⣷⠀⠹⣆
⠀⠀⠀⠀⣿⠀⢰⡏⠀⣼⠃⢀⡿⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄⠈⣷⠀⠸⣇⠀⢻⡄
⠀⠀⠀⢸⡇⠀⣾⠀⢰⡏⠀⣼⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⠀⠸⣇⠀⢿⡀⠘⣇
⠀⠀⠀⣼⠁⢠⣯⣤⣼⣁⣀⣟⣀⣼⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣧⣤⣿⣤⣼⡇⠀⣿
⠀⣠⣤⠿⣶⠋⠁⠀⠀⠉⠛⠟⠉⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠛⠛⠛⠋⠁⠀⠀⠀⠈⠙⢷⣿
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄
⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠈⠙⠛⢷⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡷⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠞
⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⣤⠾⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣤⡶⠶⠋⠛⠲⠶⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠂⠀⣀⣀
⠲⠿⢠⠤⡰⠊⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢈⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢟⣻⠇⢸⠀⠈
⠀⠀⠱⢄⡀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⢀⡭⠥⣬⡉⠁⠆⠀⠀⠀⠀⠀⠀⠈⠀⠔⠻⣦⢸⠀⢀
⢠⠴⢳⠀⠀⣀⠀⡔⠔⠢⠀⠀⠀⠀⠀⢨⢠⣱⠹⡀⠀⣸⡿⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠚⠒⠋
⠈⠒⠊⠀⠈⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠢⠀⠀⠓⠬⠭⠿⢵⡒⠟⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⡀⠔


⠀⢔⠖⡲⢇⠶⠖⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠰⠆
⠀⢻⢸⣍⠢⠌⢽⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠀⠉⠂⣤
⠀⠀⠁⠓⠲⠜⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠥⠈⠉⠩⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣈⣀⣉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠠⠠⢰⠁
⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⡠⠃


⠀⠀⣀⡀⠰⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠠⣄⣀⡀
⠀⡎⠀⠈⢻⠘⠁⠀⢑⠀⠀⠀⠀⠀⠀⠀⡎⠐⠒⠒⠒⠊⠉⡣⣵⠀⠀⠀⠀⠀⠈⠉⠉⠑⢒⢒⡒⠀⢄
⠀⡠⠀⢀⢀⡇⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡡⡀⠈⠛⠁⠀⣠⠷⡃⠀⠀⠀⠀⠀⠘⠀⠑⡪⢋⣨⢻⢳⠈
⠎⠀⠐⠁⠈⢀⠢⠄⠘⡦⠀⠀⠀⠀⠀⢎⠀⠹⠵⠶⠴⠮⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⠠⡐⣈⣉⣼⠏
⠀⠀⠂⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈