Ribbon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠁⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⣇⡀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢤⢀⣸⠒⠈⠀⠀⠀⡆
⠀⠐⠂⢀⠀⠐⢯⠄⠄⢄⡂⢀⠙⠤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠋⡀⢔⡪⠤⠠⡽⠂⠀⡀⠒⠂
⠀⠀⠐⠚⠂⠀⠋⠀⠀⠀⠉⠒⠬⠂⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠐⠥⠒⠉⠀⠀⠀⠙⠀⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠒⠒⠒⠒⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⣑⡾⠟⠉⠉⠉⠉⠻⣷⣊⣀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠸⡒⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⢒⠗
⠀⠀⠀⠀⠀⠀⠀⣨⠗⠀⠈⠦⢴⣾⡿⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⢿⣶⡦⠴⠁⠀⠺⣁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉⠉⠗⢶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⢾⡉⠉⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣃⣸⠀⠀⠉⠙⠓⠒⠦⠤⠤⠤⠒⠚⠋⠉⠀⠀⣇⢘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⠤⠤⠤⠤⠔⠐⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠀⠁⠒⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⢰⠒⠲⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠖⠒⡆
⠀⠀⠀⣤⣒⠂⢻⠀⠀⢱⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠢⠤⢄⣀⠀⠀⡞⠀⠀⡟⠐⣒⣤
⠀⠀⠀⠀⡼⠁⠈⢷⣶⣦⣓⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣚⣴⣶⡾⠁⠈⢧
⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠙⠃


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

⣶⣶⠶⠾⠟⠛⠛⠛⠛⠳⣝⣿⣼⢸⠇⣿⠀⣿⠀⣿⠁⣿⠇⣿
⣦⣤⣤⣶⣶⠿⠿⠿⠻⠷⣜⡇⡇⣾⢰⡏⣸⡇⢸⡏⢰⡟⢠⡟
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢷⢣⡇⣾⢁⡿⢀⣿⢀⣿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⢡⡏⣸⠇⣼⠇⣸⡏⣸⡏⠀⠀⠀⢀⣀⠤⣄⠲⣮⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⢸⠇⣿⢠⡿⢠⣿⠀⡿⢥⣶⣽⡪⡕⣎⢳⡌⢷⡈⢿⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡸⡸⣇⢿⡘⣧⣸⢿⣚⠭⢿⣛⣻⣿⡼⡜⡆⢿⡘⣷⠘⣷⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠽⠿⠿⣟⡫⠵⣚⡭⢖⣫⡭⢖⣒⣻⠵⢷⢹⡘⣧⠹⣧⠸⣧⠘⣷⡀⠀⠀⢀⣀⣀⠤⣤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⡭⠭⠵⣚⣩⠵⢚⣩⠴⢚⣩⡵⠖⠛⢻⢿⣧⡙⢧⡙⢷⣌⠳⣌⡻⢔⣪⠽⠶⠮⡝⡌⢧⢳⡜⢮⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣒⣛⣋⣭⠴⢚⣩⡴⠞⠋⠁⠀⠀⠀⠈⣿⡼⡼⡶⢋⣗⠾⣛⠵⢚⣭⠶⠞⠛⠓⢾⢹⢸⡆⢿⠈⣧⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣇⣿⡭⠗⣋⡵⠞⣋⣤⡶⠿⠛⠛⢾⢸⡈⣇⢸⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣸⡖⣋⣩⡴⠞⠋⣁⣤⣶⠾⠿⠷⣼⡇⣿⠘⣧⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣉⣥⣴⠶⠟⠋⣁⣠⣤⣶⣦⣼⡇⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣴⡶⠿⠛⠋⠉⠀⢨⢹⢇⢸⡇⢻⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⡈⣷⠘⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣛⢌⢧⣘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠚⣛⣩⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠛⠋⢁⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣾⠿⠛⠁

⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠰⣶⣿⢿⣶⠆⠀⠀⠀⠀⣶⣶⡿⢿⣴⣶⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⣄⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⣼⣯⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣼⣅
⠀⠀⠠⡶⣀⡀⠀⢀⣤⠴⠖⠒⠲⠶⠶⣮⣭⣳⣀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⣈⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⢀⣠
⠀⠖⠔⠁⠠⠁⣰⡯⠖⠒⠒⠒⠶⢤⣄⣀⠀⠉⡿⠛⠻⠶⠶⠶⠾⠛⠋⠀⣠⣿⣧⣶⣿⠃⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⣰⣿⠛⢿⣟
⠼⠚⠀⢀⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⢦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣥⣤⠴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⢻⣶⠞⠿⠃
⠀⠠⠀⠈⡀⢂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⢀⡀⠁⠀⠀⠀⠀⢠⠚⠉⠉⠁⠉⠙⢿⣆⠉⠉⠙⣛⠛⣿⠲⠶⠶⠶⠾⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣆⠀⣤⣿⣛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣠⡾⠋⠉⠓⠀⠙⢋⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠠⠤⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠢⡴⠓⠶⠉⠲⠚⢦⠔⢆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠓⢃⠀⠡⠀⢠⠀⠀⠀⡆⠀⠀⠀⡌⠀⡘⠚⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠺⡀⠈⢆⠀⢂⠀⠀⠀⠀⢐⢀⡀⢀⠁⠐⠀⠐⠀⡠⠁⢀⠗⢦
⠀⠀⠀⠀⠀⢰⠚⠣⠀⠈⠂⠀⠂⣀⠄⠚⠀⠉⠀⠀⠀⠈⠉⠑⠲⢄⡐⠀⠐⠁⡠⠞⠓⡆
⠀⠀⠀⠀⣚⠉⠑⠄⡀⠑⢀⠐⠊⠀⡠⠄⠒⠉⠁⠀⠀⠉⠐⠂⠄⡀⠈⠓⢄⠈⠀⠠⠊⠉⣓
⠀⠀⠀⣺⠁⠁⠂⠄⠈⠠⠊⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⡁⠠⠐⠈⠈⣕
⠀⠀⢸⡁⠈⠑⠂⠀⡨⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠱⡄⠐⠊⠁⢈⡇
⠀⠀⣏⠈⠁⠀⠐⢠⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⠀⠈⠁⣹
⠀⠰⡉⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠁⢉⠆
⠀⠰⡋⠉⠉⣁⠀⢩⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⣉⠉⠉⢙⠆
⠀⠀⡏⠉⢀⡀⠀⠴⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⠈⢹
⠀⠀⢸⠉⢀⣀⠀⠀⢳⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠤⣀⡀⠉⡇
⠀⠀⠀⣝⠁⣀⠤⠂⠁⠱⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠐⠤⣀⠈⣫
⠀⠀⠀⠀⢽⣀⡠⠐⠁⡠⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢄⠈⠂⢄⣀⡫
⠀⠀⠀⠀⢠⠿⣀⡠⠊⢀⠔⠀⠈⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠋⠀⠢⡀⠑⢄⡀⡍⢣
⠀⠀⠀⡰⢃⠊⠀⠣⢤⠃⢀⠌⠀⠌⠀⠂⠀⠁⢸⠈⠁⠈⡀⠠⠀⢡⠀⠡⡀⠘⡦⠜⠀⠈⠂⠱⡀
⠀⠀⡜⢠⠂⠀⠀⠀⠈⠉⠻⡀⡜⠀⡰⠀⠸⠀⠀⠀⡇⠀⠁⠀⠇⠀⢣⢀⡜⠉⠁⠀⠀⠀⠀⠡⠘⠄
⠀⡈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠱⠤⠣⣀⠦⣀⡤⢀⡔⠤⠎⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⡀
⢰⠁⠄⠀⠀⢀⣀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠄⢀⠜⠁⠘⢆⠈⢀⠀⠀⠀⠀⠀⢠⠤⠤⣄⣀⠀⠀⠀⠂⠐
⣌⣠⠤⠒⠋⠁⠀⠀⠀⠈⡇⠀⠀⠀⢀⠂⢠⠋⠀⠀⠀⠀⢣⡀⢂⠀⠀⠀⠀⡟⠀⠀⠀⠀⠉⠑⠒⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠌⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠂⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡞

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣄⣠⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡫⣠⣾⡟⠀⠀⢻⣷⣄⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⠿⢿⣿⣿⣿⣛⣛⣻⣭⣷⢾⣫⣾⣿⠏⠀⠀⠀⠀⠹⣿⣷⣝⡷⣾⣭⣟⣛⣛⣿⣿⣿⡿⠿⢿⡄
⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⡿⠿⣟⣫⣭⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣭⣝⣻⠿⢿⣿⣿⣿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠛⠛⠛⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⠒⠶⠦⣄⡀
⠀⠀⠀⠀⢠⣾⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⢀⡴⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⣀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⢀⣠⡤⠶⠖⠚⠛⠛⠉⠉⠛⠛⠛⠿⢤⡀
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠙⣷⠴⠶⠶⢿⣁⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⣿⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠁⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⢻⠁
⠀⠀⢸⠀⠀⠈⠙⠛⠳⠶⠦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠛⠛⠉⠀⠀⣿
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣇⠀⠀⠀⠀⢀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣄⠀⠀⠀⣸⣷⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠖⠛⠉⣡⠞⡿⠀⠈⠉⠉⠉⠁⢸⡆⠀⠙⣟⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠞⠛⢉⡿⠁⠀⢀⡴⠋⢰⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢹⡄⠀⠀⢻⡝⠛⠷⢶⣤⣄⣀⣀⡀⠀⠀⣀⣠⡴⠋
⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⣠⠟⠀⠀⣠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣷⠀⠀⠀⢳⡀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣴⢿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⣿⡇⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡾⠃⡿⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⣠⡟⠁⣸⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⣧⠀⠀⠀⠘⣧
⠀⠀⠀⠲⣶⣶⡶⠒⠛⠋⠉⠀⠀⠀⠀⢀⣼⠏⠀⣠⠏⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⣧⢻⡆⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢻⡟⠀⢀⣴⠟⠁⢀⣴⠋⢀⣀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡌⢿⡄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢋⣠⡴⠟⢁⣠⡴⢛⣡⡾⢛⡟⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢷⡈⢿⡄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣠⣴⣶⡿⠷⠞⠛⠉⠀⠈⠛⠛⠛⠋⠁⢀⡾⢁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡌⢻⣄⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠙⢦⡙⢧⡀⠀⠘⢶⣤⣤⣤⣤⡽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣀⣀⣀⣹⡿⠛⢷⣄⡈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣿⠙⠉⠁⠀⠀⠀⠉⠛⠷⢶⣤⣭⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠘⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⡬⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠒⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠐
⠀⠀⠀⠀⠤⠂⠈⡞⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠾⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⠋⢂⠀⠂⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢌⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠂⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠠⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⡉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠉⠐⠒⠒⠤⠤⢀⣀⠀⠀⠀⠀⣟⢠⣧⣴⣇⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣴⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡫⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡥⠴⠶⠶⡟⠛⡟⠉⠉⠉⠉⠉⠁⠐⠒⠒⠒⠂⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠉⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠒⠒⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠒⠂⡠⠤⠤⠶⠿⠂⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠠⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠗⠀⢀⣀⠀⠠⠤⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠦⡴⠓⢶⠋⢳⠖⠳⡤⠶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠒⠺⡁⠈⡄⠀⢁⠀⠈⠀⢸⠀⠀⠀⠀⠎⠀⡱⠒⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠉⠙⢆⠀⠡⠀⠘⠀⠈⠀⢠⠀⠸⠀⠸⠀⠘⠀⠰⠁⢀⠎⠁⢹⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠴⢅⠀⠑⣄⠀⢢⠀⢁⣀⠤⠄⠒⠘⠒⠚⠀⠓⠠⠅⣠⠁⠠⠂⢀⠔⠁⢀⠷⢤⡀
⠀⠀⠀⠀⢀⡤⠷⣄⠀⠑⢄⠈⠢⣠⠖⠉⠀⢀⡀⠤⠄⠀⠀⠠⠤⢀⡀⠀⠉⠣⢤⠂⢀⠔⠁⢀⡴⠧⣄
⠀⠀⠀⢠⡴⠧⢀⠀⠑⠠⡀⡱⠊⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠑⢄⡠⠐⠁⢀⠠⠷⣄
⠀⠀⢀⡸⠦⢀⠀⠉⠒⢄⡜⠁⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠣⠐⠊⠁⣀⠠⠮⣀
⠀⠀⢈⡦⣀⣀⠈⠁⠀⡜⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢳⠀⠉⢀⣀⡠⣏
⠀⠀⢫⣀⣀⠀⠀⠁⢰⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⣀⣀⣸⠃
⠀⠐⢏⠀⠀⠀⠈⠉⡉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠀⠀⠀⢈⠗
⠀⠠⡏⠉⠁⢀⡀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣀⠀⠈⢉⡦
⠀⠀⣜⠉⠁⠀⢀⠀⠸⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⠀⠉⢹⡄
⠀⠀⢈⠗⠈⠉⠀⡀⠄⢣⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⡀⠈⠉⠐⣏
⠀⠀⠈⢱⠖⠉⠁⣀⠠⠊⢣⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⢄⡀⠉⠑⢖⠉
⠀⠀⠀⠈⠳⡖⠉⠀⡠⠔⠁⡱⢄⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠑⠠⡀⠈⠑⡶⠋
⠀⠀⠀⠀⠈⢳⡶⠉⠀⡠⠊⢀⠔⠑⠤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠄⠈⠢⡀⠈⠳⠶⡋
⠀⠀⠀⠀⢠⠎⡹⠲⡊⠀⡠⠊⢀⠜⠀⡘⠉⡒⠢⠤⢄⠀⣀⠠⡤⠔⡆⠙⡀⠐⢄⠈⠢⡀⠈⠶⠚⢣⠙⣄
⠀⠀⠀⡰⢁⠌⠀⠀⠉⢹⣀⣠⠎⠀⡐⠀⠰⠁⢀⠀⠰⠀⢰⠀⢰⠀⢠⠀⠰⡀⠈⢆⣀⡸⠉⠁⠀⠀⠑⡈⢦
⠀⠀⡜⢀⠊⠀⠀⠀⠀⠀⠀⠘⠤⠰⡁⢀⠃⠀⡈⠀⢀⠀⢸⠀⠀⠀⠀⢆⠀⡱⠠⠎⠀⠀⠀⠀⠀⠀⠀⠐⡀⢣
⠀⡘⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠒⠳⡤⠒⣤⣴⠢⣴⠓⠲⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢣
⢰⠁⡌⠀⠀⠀⣀⣠⡤⠤⠴⡄⠀⠀⠀⠀⠀⢀⠊⢀⠞⠁⠀⠳⡀⠑⡀⠀⠀⠀⠀⠀⢀⡦⠤⠤⣄⣀⠀⠀⠀⢡
⣘⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠂⣠⠋⠀⠀⠀⠀⠘⣄⠘⠄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⠃⡰⠁⠀⠀⠀⠀⠀⠀⠈⢆⠈⠄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃

⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠀⠀⢀⣀⣤⣶⣶⣿⣿⣷⡆⠀⢀⣀⡀
⠀⠈⠉⣽⠿⠿⢻⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⢿⣿⠿⠿⣿⡿⠿⢿⣯⡉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⠟⠋⠉⠹⣿⣿⣿⡿⠿⠛⠉⠀⠀⢿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡄⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠠⠶⠿⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣥⣄⡀⠀⠀⠀⢠⣤⣤⣿⣿⠿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣤⣤⡄
⠀⠀⠀⠀⢀⣴⡿⠟⠛⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠹⠿⠿⠟⠛⠉⠀⠀⣠⣴⡶⠟⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠙⢷⣶⣶⣄⡄⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣯⣤⠀⠀⠀⠀⠀⠈⢿⣶⣤⣼⣿⣿⣿⣷⣦⣤⣀⠀⠀⣠⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠐⠶⣶⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠃⠀⠀⠈⠙⠻⢿⣿⣿⣿⡟⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣀⣠⣤⣤⣤⣤⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠯⠟⠛⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣯⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢦⣄⠀⣠⡤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠘⠟⠁⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⡶⠛⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣄⣹⣷⠞⠛⠻⣯⡉⣉⣉⣉⣉⣉⣹⣧⣴⠾⠟⠛⠛⣷⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠉⣿⠃⢀⡀⠀⠈⢿⡛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢀⣼⣧⣤⣄⡴⠚⠛⠻⣏⢹⡆⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⡏⠀⠀⣠⣾⡁⠀⠀⠀⣽⠋⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯
⠀⠀⠀⠀⠀⢻⡀⠀⠿⡼⢷⣤⣤⠶⠋⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⣿⣦⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣤⣤⣄
⠀⠀⠘⠛⠛⢻⡟⠛⠂⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣠⣼⣷⡤⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⢲⣿⠷⠦⠄⢀⣴⠶⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠹⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣾⡁⠀⠀⣴⠏⠀⠀⠀⣀⢸⡇
⠀⠀⠀⠀⢠⡴⠞⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠈⠙⠳⠤⣟⠀⢀⣀⣴⢏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣋⠁⠀⠀⠀⠀⣠⡶⣫⣤⣍⣭⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣤⡾⢋⡟⠉⠉⣿⠉⠉⠉⠉⠉⠁⣿⠀⠀⢹⣆⢙⣷⠶⠦⣤⡾⣫⡾⠋
⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠈⢛⡿⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⢹⣿⠁⠀⠀⠘⡿⠋⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣠⡴⢦⣤⠶⢦⡄⠀⠀⠀⣾⠁⠀⠀⠀⣰⠇⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⢦⣄⣠⡴⠋⠀⠀⢀⣸⡛⣻⣇⡀
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣾⠁⠀⠀⠀⠀⠈⠻⣄⡀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⡶⠛⠉⠙⠉⠉⣙⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⣧⡴⠞⠛⠳⠾⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠞⠛⣻⡟⠁⠀⠘⢻⡾⠻⠛⠛⠛⠛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⠀⠀⣀⣽⣇⣀⣀⣀⣀⣠⣤⡾⠏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠩⠭⠩⣉⣉⣉⣉⠀⢀⣀⣀⣀⡄⠄⠤⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠷⣄⠀⠀⠀⣤⣦⠀⠀⠀⠜⠉
⠀⣴⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠰⠺⠶⠆⠈⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⢰⢋⠉
⠰⠇⣠⣴⣿⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠀⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠷⠀⠀⠆⢀⠞⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡰⠛⠙⠻⡄⠀⠀⠀⠈⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡿⠿
⠀⠀⠀⣠⣤⣤⣧⠀⠀⢀⡇⠀⣀⣀⠀⠃⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠈
⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠘⠉⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠖⢦⠀⠀⠂⠀⠀⢀⡘⠉⠀⠙⢷⣄⣰⠀⠀⣸⣤⠞⠛⠻
⠒⠆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠹⣧⡀⠀⢀⣿⠋⠁⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠖⢶⣦⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠁⠀⠼⠿⠶⠀⠀⠀⠀⠸⠷⠶⠄
⠀⠀⣠⣤⣄⢸⡄⠀⣰⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣤⡀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠉⠙⠻⣶⣄⠀⢀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠈⠻⣷⣀⣴⡾⠛⠉⠁⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠉⠉⠉⢉⣿⠁⠀⠀⠀⢀⣀⣀⣈⣿⣯⣤⣄⡀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⣟⠋⣽⡟⠋⠉⠈⠉⠻⣷⣶⠶⠶⠶⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⠻⣷⣿⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣠⣬⣿⣆⠀⠀⠀⠀⢀⣼⡟⠙⣿⡄⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠻⠶⠶⣶⡟⠛⠛⠛⠋⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣠⣴⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠸⣿
⠀⣀⣀⣀⣠⣤⣼⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣿⣤⣤⣀⣀⣀⡀
⠘⠛⠛⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣴⡶⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠰⣶⣤⣤⣿⠁
⠀⠀⠀⠠⣶⠾⠟⢿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣽⡟⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠶⠶⠶⠶⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⡐⠀⠄⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⠄⠀⠆
⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠈⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠐⠠⠀⠀⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠁⡄⠀⠀⡀⠠
⠀⠈⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠂⠐⠢⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⡀⠁
⠀⠈⠀⠀⠀⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠂⠀⢀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠐⠁⡠⢄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠅
⠠⠄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠁⠠⠀⠄⠠⠂⠀⠀⠀⢀⠐⠂⠀⠀⡀⠀⠀⠉⠀⠂⠐⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠈⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠠⠰⠀⠁
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⢀⠲⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠄⠂⠀⠀⠀⠨⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠂⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⠠⠀⠀⠀⠏⠀⠀⠉⢩⠗⡆⠀⢀⣴⣒⣒⣦⡀⠀⠀⢶⠊
⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠄⠠⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠤⠈⠀⡁⠀⣍⠿⠿⠿⠿⣿⠀⠀⠈⢧
⠀⠘⠀⠠⠀⠨⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠂⠂⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⡀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠰⠃⡰⠀⠀⢆⠘⠆
⠀⠀⠀⠀⠀⠐⠁⢠⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠁⠀⠀⠊⢀⠰⠀⠀⡀⠰⠂⠄⢀⠀⠐⠀⠀⠠⠀⠀⠀⠐⠄
⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⠌⠀⠀⠀⢀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠀⠠
⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⠀⠀⠠⠄⡀⠀⠀⠀⠠
⠀⠈⠂⠀⠄⠀⠁⠈⠁⠈⠄⠀⠀⠂⠔⠂⠐⠢⠐⠀⠠⠁⠀⠀⠀⠀⠀⠀⠄⠀⠁⢀⡀⠉⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠒⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠔⠈⠉⢁⠀⠖⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⡀⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢐⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠢⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠢⠤⢤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⣿⡿⣿⣶⣤⣤⣀⣀⠀⠀⢀⠀⠀⠈⠉⠛⠛⣿⣆⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠸⣿⣷⣿⡿⢿⣿⡿⣿⣷⣆⣈⣄⠀⠀⠀⠀⣰⠿⣿⡆⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣾⠿⠃⠀⠉⠓⢦⡀⣼⠃⢀⡿⠈⠢⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣠⡾⠛⢿⡆⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣼⣿⣿⣶⣿⣿⠇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠘⣿⣿⡀⠀⡾⠁⠙⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠘⢰⡟⠋⠀⠈⠻⣿⣶⣇⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢀⠀⠑⠂⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡿⢦⣤⣶⣶⣾⣿⣿⣷⣄
⠀⠀⠀⠠⠁⠀⢀⠀⣀⡀⠀⠀⠊⠀⣀⠔⠡⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣽⣿⣿⠂⠀⠃⠀⢤⡀⠀⡤⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⠀⠀⢿⣿⣷⣤⣀⣤⣶⣾⣾⣿⣆⠉⢠⣖⣺⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠿⣿⣷⠒⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣶⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣴⣿⠟⠀⠀⠀⢰⣿⠻⣿⣿⣿⣿⣿⣷⠀⠸⣡⣤⡈⢉⡉⢻⡿⣾⣿⣿⡟⡉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⠿⠿⠿⣦⠀⠈⠁⠀⠻⣿⣿⣿⣿⣿⡆⢠⣙⢛⣁⠻⡿⢚⠃⢿⡿⢹⣏⣁⣌⠁
⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣶⣋⣤⡀⢰⣶⣾⣷⣿⣿⡿⠒⠈⠀⠀⠉⠉⠙⠈⢿⣯⣽⣶⣶⣿⣿⣿⣷⣾⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⡿⠉⣐⣤⣽⣿⠙⠉⣡⣤⣀⡠⠟⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⠿⠈⠙⠻⢿⣧⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣟⡙⠹⢀⣻⣿⣾⡟⠁⠀⠀⠀⠀⠀⠒⠀⠀⠦⣀⣤⣿⣶⣶⣶⣶⣦⠈⠁⠀⢳⣾⣿⠋⠙⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢜⣛⣥⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡿⢿⡿⠿⢿⢿⡿⠿⠀⠀⡄⣾⡿⠟⢤⠀⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣷⣿⠛⠁⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣐⠰⡶⢲⣶⣾⣿⣦⣿⡿⠀⠀⠉⡀⠎
⠀⠀⠀⠀⠀⠀⣿⡿⠟⢿⣿⣿⡿⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣴⣦⣄⠀⠀⠐⠂⠈⠉⠈⠟⡟⠙⠻⠟⢻⣿⡌⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⣿⠁⢀⣴⣶⣿⣿⡿⢇⡀⢸⡿⠋⠉⠙⢶⣦⣀⣠⣤⣤⣤⣸⡑⠂⠀⠲⢸⠋⠻⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠈⢀⣸⣿⣿⣿⡇⡀⠨⣍⣹⢀⡀⠀⣄⠸⣿⡟⠛⠿⣿⣿⣿⣷⣾⣽⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⣿⣿⣷⠀⠀⠠⣶⡶⣤⡴⣦⣤⣴⣿⡇⠀⠰⢿⣿⣿⡿⠉⠙⢹⡀⠀⠀⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠶⠶⠶⠾⠿⠿⠟⣽⣿⣷⣤⣀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣷⠒⠒⠋⠠⣤⠄⠉⠉⢛⣿⣧⣄⣠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⠀⠀⢀⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡷⢿⣿⣿⣷⣶⣶⣦⡿⠏⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⢾⣫⢻⡇⠸⡿⡿⠿⠻⡆⠈⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣡⣶⣶⠶⣬⣿⣿⣄⣄⠘⠛⠟⠁⢀⣼⣿⣿⣷⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡭⠙⢻⣿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣍⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡀⠀⠘⠻⣿⣿⣿⣿⣿⡟⣿⣮⣹⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⢃⠘⠙⣿⣿⣿⣤⣤⣤⣤⡈⢉⣩⣽⣿⢸⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠿⠗⠀⠠⠄⠛⢋⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣯⡽⣯⣿⣿⣛⣵⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠃⢰⣿⣿⣿⣿⣿⡯⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢸⠁⢀⣴⠟⠃⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢠⠚⢿⣿⣄⣈⣙⣿⣏⠎⠀⠀⠀⠀⠀⠈⠐⠻⢷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⡀⠀⠀⠂⠀⠐⠀⠀⠀⠀⡎⢠⣿⣿⣿⡘⠿⠿⣻⣤⣓⣶⣦⣄⡀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⣷⡆⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠷⣿⠟⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣅⡄⣹⠿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣯⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣶⡌⠁⠀⠀⠧⢀⠀⠀⡀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣁⣤⣴⠖⢢⣤⣤⠀⣀⠀⠀⢤⣅⡰⢟⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣅⣀⠀⠀⠀⠀⣩⡏⢁⡀⠀⢠⡟⣿⣿⣿⣷⡀⠅⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⢷⣦⠄⠀⠈⢈⣷⣄⣽⣿⣿⣿⣿⣿⣷⡀⢦⡀⠀⠀⠀⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⣀⡀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣎⣛⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠐⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢲⣤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞
⠀⠀⠀⠀⠀⢀⡞⣥⢶⣤⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⣸⣽⠃⣿⣿⣿⣷⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣢⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠻⣿⣿⡿⠿⠷⣵⣄⢀⣠⣤⣤⣤⣤⣤⣴⣾⢟⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⣿⢸⣇⠀⠈⠁⠀⠀⣤⠈⠁⠀⠀⠀⠀⠒⢼⣛⠛⠃⠾⣿⣿⡿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⡏⠻⡤⣶⣶⣶⡾⠁⢀⣀⣠⡤⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⠺⣿⣧⣴⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢸⣿⠇⠀⠀⠈⢛⣩⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢹⠛⠿⢿⣷⣶⣶⣤⣤⣄
⠀⠀⠀⠀⣿⣿⣄⣠⣴⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⡀⠀⠀⠈⠉⠛⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⡴⠚⠷⣦⡀⠀⠀⠀⠀⠀⠀⡀⠲⡦⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⣴⣿⣿⣿⣿⣟⠉⠉⠁⠀⠀⠀⠳⣄⣁⣽⣿⡄⠀⠀⠀⠀⣠⣡⡼⠁⠀⣷⠘⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⡀⠀⠀⠀⠀⢹⣆
⠀⣠⣾⣿⣿⣿⣿⣿⣿⠛⢦⣀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⠀⠀⠀⠹⡀⠀⠀⠀⢻⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠈⢦⡀⠀⠀⠀⢿
⢠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠳⠶⣤⣄⡀⠀⠘⠛⠛⠓⣠⠤⠤⠤⠀⣀⣀⣀⢸⠃⠉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢻⣄⠀⠀⠘
⢸⣿⣿⣿⣿⣿⠟⠋⠀⠤⠔⠒⠒⣒⣲⣖⣞⣛⣻⣿⡿⠈⠓⣶⣀⠂⢸⣭⡿⢢⣌⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⣾⢻⡿⣿⣿⡟⠀⣸⡦⠒⠊⠉⠥⣰⣿⣿⠻⣿⣿⣻⣶⢒⣢⣼⣍⣰⣾⠿⢑⢢⣟⠉⢺⣄⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣄
⠃⠸⠁⣿⡿⠀⠘⣿⣇⠀⡠⠐⡈⠙⢿⣿⣶⣯⣉⠛⠟⠋⠀⠀⢈⡍⠀⠐⢤⣿⣧⡙⣿⣇⠑⢼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⣿⣿⣿
⠀⠀⠀⣿⠇⣠⣾⣿⣿⣿⣿⠂⠀⠀⠈⢿⣿⣿⣿⣿⣶⣦⣤⣾⠟⠀⠀⠀⠈⣿⣿⡀⠈⢹⠀⢸⣿⣿⠀⣦⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿
⠀⠀⠀⢿⣾⣿⡟⣿⣿⣿⣿⡀⣠⣿⣤⡀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⢀⣄⣹⣿⣇⠀⠈⠀⣼⣿⣟⣠⣿⣷⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿
⣀⣀⣀⣈⣉⣉⣛⣛⣛⣻⣟⣛⣛⣛⣛⣉⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⣛⣉⣛⣛⣓⣀⣀⣛⣛⣛⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣿⣿⣿
⣿⣻⣛⣛⣟⣝⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿

⠀⠀⠀⠀⢠⠖⠊⠉⠙⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠉⠑⠲⡀
⠀⠀⠀⠀⡾⠀⢀⣠⣤⣤⣄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⣤⣶⣤⣄⣀⢠⣷
⠀⠀⠀⢸⠁⢠⣾⣿⣿⣿⣿⣿⣆⠀⢢⡀⠀⠀⠀⣀⣀⣠⣤⣤⣬⣝⢻⣟⣛⣥⣤⣤⣤⣀⣀⡀⠀⠀⢀⡴⠁⣴⣿⣿⣿⣿⣿⣷⡄⠘⡇
⠀⠀⠀⢸⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠓⠻⠃⢉⣤⣴⣶⠦⠤⣬⡭⢭⣥⠤⠴⣶⣦⣬⡉⠻⠟⡻⠏⠀⣸⣿⣿⣿⣿⣿⣿⣿⡃⠀⡇
⠀⠀⠀⠀⠡⡸⣿⣿⣿⣿⣿⣟⠙⠙⢀⠴⠋⢀⠔⠋⣉⣠⣤⣴⡶⠶⡖⢲⠶⠶⠦⣤⣄⣉⠙⠦⡀⠙⠦⡀⠋⠋⣽⣿⣿⣿⣿⣿⢇⠌
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡋⠁⢠⠐⢠⠄⠀⠀⣠⠾⠿⠋⠉⢀⣠⠄⠰⣧⣦⣄⡀⠈⠛⠿⢷⣄⠉⠀⠠⡄⠢⡄⠈⢙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣽⣿⠿⠟⢁⡔⠁⣰⠋⠀⢀⠼⠁⣠⡴⠖⢂⣉⣁⡀⠇⠆⣶⣌⣉⡐⠲⣦⣄⠈⠧⡀⠀⠹⣆⠈⢦⡘⠻⠿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⣾⡁⠀⣴⡟⠁⢰⡇⠀⠀⠀⠀⠜⠁⡄⠀⠉⣸⠏⡤⡀⢠⠸⠹⣏⠙⠀⣦⠙⠣⠀⠁⠀⠀⢹⡆⠈⢿⣦⠀⢈⣷
⠀⠀⠀⠀⠀⠀⢹⠏⢸⡟⠁⢰⣿⣧⠀⣠⣀⣤⡄⢸⡇⠀⢰⡷⠀⠇⠇⠈⠃⠐⠞⡆⠀⢽⠇⣠⣤⣀⣄⠀⣾⣿⡆⠈⢿⡆⠹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣤⠘⠛⣯⠀⠉⠉⣉⣙⠀⠻⡄⠀⠀⠚⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⣋⣉⠉⠉⠁⣿⠛⠃⣧⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⣿⠀⢠⣿⠷⢶⣿⢿⣿⣻⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⣿⠶⠺⣿⡀⠀⣿⠀⢿⣷
⠀⠀⠀⠀⠀⡆⢸⣿⡇⠀⣿⠀⢺⠻⢷⡄⠻⢮⣍⣥⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣬⣩⡵⠋⣠⡾⠛⡇⠀⣿⠀⢸⣿⡆⢰
⠀⠀⠀⠀⡐⠀⣾⣿⡇⠀⣹⠀⢸⡄⢀⡙⠶⠦⠄⠀⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢿⠀⠠⠶⠾⢋⡀⢠⡇⠀⡏⠀⢸⣿⣷⠀⢄
⠀⠀⠀⠀⠁⣠⣿⣿⠃⠀⢻⠀⡘⢿⣄⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠛⠋⣠⡿⢀⠀⡟⠀⠸⣿⣿⣄⠈
⠀⠀⣠⠀⠀⣿⣿⣿⠀⠀⣸⡂⡇⢀⡹⠶⡣⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣔⠜⠶⢏⡀⢸⢘⡇⠀⢀⣿⣿⣿⠀⠀⣄
⠀⢐⠁⠀⠀⣻⣿⣯⡄⠀⣿⣧⢰⣜⢿⡴⠃⢀⡔⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑⠒⠬⣞⢦⡿⣣⡆⣼⣿⠀⢨⣿⣿⣟⠀⠀⠈⡀
⠀⣾⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⡏⠻⠄⠀⣠⠏⡴⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠠⣄⠀⢠⠟⢸⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⣷
⠈⣏⠆⠀⠀⠀⢿⣿⣿⡄⠈⠿⣧⠀⠰⣼⡏⢀⡤⠀⠀⢠⣄⣀⣀⣀⠀⠀⣀⣀⣀⣸⣿⢷⠀⢤⡀⢹⣧⠇⢀⣾⡿⠁⣠⣾⣿⡟⠀⠀⠀⠐⣹
⠐⢿⣏⠀⠀⠀⠸⢿⣿⣿⣤⣀⠙⢷⣄⠙⢳⣿⡃⠐⠀⠘⣯⣤⣀⠉⠙⠋⠉⣀⣤⡽⠻⠚⠓⠚⢿⣾⣿⣶⡾⢋⣤⣶⣿⣿⣿⠇⠀⠀⣠⣿⣿
⠀⠙⡿⠂⠀⠀⠀⠉⠙⣿⣿⣿⣶⣄⠙⠧⣀⡙⠛⠛⠓⠤⠈⠛⢿⣷⠀⠀⣾⡿⠛⠃⠴⠖⠒⠒⠊⠉⠾⠋⠴⣿⣿⣿⣿⠟⠙⠀⠀⠀⣿⣿⠟
⠀⠀⠐⣶⣦⡀⠀⠀⠀⠀⠈⠁⠸⣿⣿⣶⣿⡏⠛⠛⠲⠶⠤⠄⠀⠉⢻⡏⠁⠀⠠⠰⠖⠖⠛⠛⢻⣿⣾⣿⣿⠟⠉⠉⠉⠀⠉⠀⢠⣿⣿⠋
⠀⠀⠀⠙⢿⣷⡆⢀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣛⠐⠂⠃⠁⠀⢀⣤⣾⣷⣄⡀⠀⠈⠘⢐⡂⣛⣿⣿⡿⠿⢁⡄⠀⠀⠀⠀⡀⢰⣾⡿⠃
⠀⠀⠀⠀⠀⠙⠗⣼⣧⣠⣀⡆⠀⠀⠀⠈⠉⢹⣿⣿⣿⣶⡖⠺⠋⠉⢻⠏⠈⢙⠗⢶⣶⣿⣿⣿⡿⠛⠁⣶⠾⠃⢰⣀⣠⣴⣧⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣧⣤⠀⢀⣴⣀⢈⣙⣿⣿⣿⣇⢀⣟⣶⣶⣶⣶⣻⡀⣸⣿⣿⣿⣿⣿⣼⣶⣄⠀⣤⣼⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠋⠙⠛⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠏⠙⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣛⡿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣛⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣼⡁⠘⠉⠃⠁⠚⠚⠉⠃⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⠀⡀⠀⠀⣀⠀⡈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠳⠞⠟⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⣆⢶⢰⣦⣤⣠⣤⣤⢠⡴⠄⣆⣤⣤⠄⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣿⢸⣾⢹⣗⡀⣿⣏⢠⣙⡦⣿⠀⡇⢀⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣀⣀⣀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠁⠀⠀⠺⣿⣿⣿⡗
⠀⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⢾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⠟⠁⠀⠀⠀⠈⠮⠁⠀⠀⣠⣿⣆
⠀⠀⢀⠄⠂⠀⠁⢠⣶⣿⣶⡄⠀⠀⠉⠀⠀⠀⢠⣶⠶⣶⡀⠀⠀⠀⠀⣿⡟⠛⠂⠀⠀⠀⢠⡶⠳⣦⠀⠀⠀⠀⣾⡏⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣻⠇⠀⣠⣴⣦⡀⠀⠘⠓⠐⠚⠃⠀⣠⣴⣤⡘⢦⣠⡄⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⢀⠉⠁⠀⠈⠉
⠀⠀⢠⣶⣶⣦⠀⠀⠈⠋⠀⠀⠀⠟⠋⠻⠇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠇⠀⢉⣀⣀⠀⠀⠀⠑⠒⠁⠀⠀⠀⣸⡿⠛⠓⠀⢀⣀⣤⣤⡀
⠀⠀⠹⣱⣤⡟⠁⠀⣠⣶⣶⣦⠀⠘⠿⠛⢀⣴⣷⣿⣶⡀⠀⢸⣿⡄⠀⠀⣾⡿⠛⠻⣿⡄⠉⢠⡾⠿⢦⠀⢰⣿⡇⠀⠀⠀⠉⠙⣿⡟⠁
⠀⠀⣾⠃⠉⠀⠀⠀⠙⠖⠰⠎⠀⠀⢀⠀⠘⠿⠉⠉⠿⠃⠀⠘⠿⠃⠀⠀⠻⣇⠀⢀⡿⠃⠀⠈⣛⣜⣋⠀⠸⢿⠇⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡶⠳⢦⡀⠀⠀⣠⠶⠳⣦⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢠⠖⠒⣄⠀⠀⡠⠒⠲⡄
⠀⣧⠀⠀⢈⣶⣎⠁⠀⢰⡇⠀⠀⠀⠀⣸⠇⠈⠳⣀⡰⠋⠀⢿⡀⠀⠀⠀⠀⣟⠀⠀⠈⠂⣤⠐⠁⠀⠀⣻⠀⠀⠀⠀⢻⣀⣀⣈⣦⣴⡁⣀⣀⠇
⠀⠙⠛⠋⣱⠃⢻⡉⠛⠛⠁⠀⠀⠀⠀⠻⣤⡤⠖⡿⡗⠦⢤⡼⠃⠀⠀⠀⠀⠈⠁⣢⡤⠞⠉⠳⢤⣔⠈⠁⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠑⣄
⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣸⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠁⠀⠀⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠋⠀⠀⠀⠈⠃
⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⣀⣤⣶⡄⠀⠀⠀⠀⠀⢠⣶⠒⢄⠀⢀⠔⢳⣦⠀⠀⠀⠀⠀⣴⣔⡠⢄⡀⣀⡠⠄⣢⣦
⠀⢹⣿⣶⣤⣶⣶⣤⣶⣿⡇⠀⠀⠀⠀⢿⣿⣿⣽⣶⣾⣫⣿⣿⡟⠀⠀⠀⠀⠀⠸⢿⣷⣶⣶⣶⣶⣿⠿⠀⠀⠀⠀⠀⢿⣿⣿⠿⡿⢿⠻⣿⣿⣿
⠀⠸⠿⠿⢫⡿⢿⡝⠿⠿⠃⠀⠀⠀⠀⠸⠿⠛⢡⣿⣿⡉⠛⠿⠃⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠱⣤⣀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣾⡇⠸⣷⡀⠈⠁
⠀⠀⠀⠰⠿⡇⢸⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⠘⠻⢿⠇⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣤⣀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⢀⣴⠲⣄⠀⢀⡴⢲⣄⠀⠀⠀⠀⠀⠀⢀⣴⠖⠻⡆⣰⠛⠲⣦
⠀⠀⣏⡀⠹⡆⢰⠋⢀⣻⠀⠀⠀⠀⢠⣿⣽⣷⣼⡆⣼⣴⣿⣽⣧⠀⠀⠀⠀⢀⣤⠿⣶⢄⢻⣇⡴⡶⠿⣤⡀⠀⠀⢰⡉⠉⠓⢄⠀⠀⡠⠒⠉⠉⡇
⠀⢰⠋⠛⠓⣷⡶⠚⠛⠙⡆⠀⠀⠀⠙⠦⣝⣻⣿⣷⣿⣿⣛⡥⠞⠀⠀⠀⠀⢿⣇⣀⣀⡁⣿⣿⣈⣀⣀⣸⡇⠀⠀⣠⠛⠛⠓⢒⠷⠶⡒⠒⠛⠛⢦
⠀⠘⠓⠒⢉⡟⢳⡑⠒⠚⠃⠀⠀⠀⠀⠀⣀⡴⠚⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⡇⢳⠀⠉⠉⠉⠀⠀⠀⠈⠒⠒⡾⠋⠀⠀⠈⢷⡒⠒⠋
⠀⠀⠀⠠⠟⠀⠀⠷⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠙⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⡠⠠⠀⡠⠢⡀⠀⠀⠀⠀⠀⠀⢀⣴⢄⠀⠀⠀⡀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⣄
⠀⠀⠀⢣⠀⢀⠀⣰⠁⠀⠀⠀⠀⠀⢀⣼⣿⣆⢳⠀⡴⢡⣿⣿⡄⠀⠀⠀⠀⠀⢀⡞⠙⠓⢦⠀⠠⠚⠙⠳⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠃⣘⡐⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣳⣶⣗⣻⣿⣿⣿⠀⠀⠀⠀⠀⠘⢧⡀⠀⣠⣷⣆⡀⢀⣠⠇⠀⠀⠀⢠⣾⣿⡷⡶⣶⢾⣿⣧
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢉⣼⡞⣷⡉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⣩⠜⠙⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣿⣄
⠀⠀⠀⠀⠀⢦⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⣿⣿⠆⠀⠀⠀⣤⣄⣤⠖⠒⢛⠋⢁⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⠿
⠀⠀⠀⠀⠀⠈⠳⠮⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀
⠀⠀⣾⣶⣄⣀⣤⣶⣶⠀⠀⠀⠀⣤⣤⣀⣀⣤⣤⠀⠀⠀⠀⢰⣦⣀⣀⣀⣴⡆⠀⠀⠀⠀⠐⠄⢀⣀⢀⡔⠂⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⡇
⠀⠀⠿⠿⠋⠉⠛⠿⠿⠀⠀⠀⠀⠛⠛⠋⠙⠛⠛⠀⠀⠀⠀⠸⠿⠛⠉⠛⠿⠇⠀⠀⠀⠀⠉⠔⠈⠉⠐⠦⠁⠀⠀⠀⠀⢾⠛⠉⠉⠉⠛⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡿⠀⢠⣿⡟⢀⣴⡶⢲⡆⣾⡶⠛⣿⡇⣿⠏⣀⡿⠃⠀⣼⣷⠀⠀⣴⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢱⣿⠇⢠⣿⣿⢃⣿⡟⢀⣾⢳⣿⣵⠞⠉⢠⣿⣿⠉⠀⠀⢸⣿⠃⣠⢾⣿⠇
⠀⠀⠀⢠⣤⠀⢀⡾⠁⣾⡿⢠⡏⣿⡏⠘⣿⡛⣋⡴⣻⡟⢿⡀⠀⢸⡿⣿⠀⠀⢸⡎⠛⠛⠃⣾⡟
⠀⠀⠀⠸⣯⡠⠟⠀⠀⢿⣷⠏⢸⣿⠃⠀⡈⠉⠉⠀⣿⡇⠘⣇⠀⠺⠇⠘⢦⣤⡼⢣⡤⠀⣼⡿⢡⣎⡗
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⠿⣤⠾⠁⠀⠀⠀⠉⠁⠀⠘⠳⠤⠾⠀⠀⠀⠀⢿⣀⣼⡿⠁⣞⡷⣞⠄
⠀⠀⠀⠀⢀⡴⢻⣿⠀⠀⣿⡇⠀⢀⣠⣴⠖⠛⣷⠰⣿⡇⢀⣴⠞⠓⣦⡀⠀⣶⡆⢀⣭⣭⣤⣤⣤⣤⣶⣶⡦
⠀⠀⠀⢰⠟⠀⢸⣿⠠⠾⠻⣤⣶⠋⣿⣿⠀⣠⡿⢡⣤⠀⣿⡏⠀⠀⠛⠃⠀⣿⣇⡤⣤⡀⠀⠀⣿⡇
⠀⠀⠀⣿⠀⠀⢸⣿⠀⣠⠞⠙⣿⡄⣿⡷⡞⠁⠀⢸⣿⠀⣿⡇⠠⠶⣶⡶⠂⣿⡏⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠈⠀⠀⢸⣿⣰⠏⠀⢀⣿⠇⣿⡇⢻⡄⠀⠸⠿⠀⠻⣧⣀⣰⣿⠇⠀⣿⡇⠀⣿⠃⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢻⣀⣀⣼⠟⠀⣿⡇⠀⠻⣤⣀⣠⠆⠀⠈⡇⠘⠿⠂⠀⣿⡇⠘⣿⣠⡷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠦⠠⠁⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠓⡄⠀⠀⠀⠀⠀⠀⢀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠖⠀⠀⠀⠀⠀⠀⠀⢘⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⡸⢣⢇⢔⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⠀⠈⠀⢀⠴⠙⢻⣶⠖⠀⠀⠀⠀⠐⠀⢀⠀⠀⢉⢶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠀⠀⠀⠀⢠⢡⣛⠻⠿⣧⠀⠀⠀⠀⠸⠋⠘⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢀⠐⠿⣳⡆⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣢⠇⢰⡄⠀⠀⢩⠶⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠌⠀⠀⠀⣠⠀⡌⠣⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡴⣰⢰⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠈⠀⠠⢦⣄⠉⠀⠂⠀⠁⣊⢞⢔⣭⣠⠄
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠒⠲⢿⡢⠀⠀⠀⠜⠁⠄⡽⠷⠭⠤⠀⠄
⠀⠀⠰⠄⠀⠈⡹⢦⠀⠀⠀⢀⠀⠄⠀⠋⠸⣄⡄⠂⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠨⠙⢒⣨⣍⡙⠃
⠀⠀⠀⣤⢀⠀⢨⠷⠠⠀⠀⠐⠻⠀⠀⠀⠁⡤⢿⣥⠀⠀⠀⠨⠀⠀⠠⠄⢀⠀⢀⠀⠀⠲⡤⡙⢾⣛⠅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠶⡶⠀⠄⠀⠀⠠⠂⢴⡧⡎⠀⠸⠀⠁⠀⢘⡛⠓⠭⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠓⠁⠃⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⣶⠀⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⡠⠀⠠⠀⠀⠀⠀⠀⣎⡁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠑⢄⡀⢀⠔⠀⠀⠀⠑⢄⠀⡀⠄⠩⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡅⢀
⠀⠐⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠠⠧⢄⠀⠊
⠀⠀⠀⠀⠠⠊⠀⠀⡴⠀⠀⠀⠀⠀⢀⠀⠀⡅⠀⠀⡇⠀⢀⠀⠀⠇⠀⢀⠔⠀⠀⠀⠢⡀⠀⠀⠀⠀⣄⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠊⠐⢒⠆⠀⠀⠀⠀⠁⠀⠈⠁⠉⠀⠀⠈⠊⢀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂
⠀⠀⠌⠀⠀⠀⠁⢘⡤⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢄⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⣀⠠⠬⠉⠡⠠⣄⡀⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠀⠀⣀⣀⠀⡀⠄⠀⠄⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠶⠊⠀⡵⣄⠀⢀⢴⠁⠈⠂⠤⢄⠀⠀⠀⠀⡆
⠀⠀⢠⠊⠀⠀⡌⠀⠀⠀⠀⠘⠁⠀⠀⠣⠀⠀⠀⠀⠀⠀⡀⡡⠂⠀⠀⠀⠈⢠⠒⡄⠁⠀⡀⠀⠈⠢⣱⡀⠀⠀⠈
⠀⠀⠸⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠊⡇⠀⠀⠉⠀⠀⠀⠉⢢⡀⠀⠈⢣
⠀⠀⠀⠀⠀⠘⠉⠢⠀⠀⠀⠊⠙⢆⠀⠀⠈⢆⠀⠀⡔⠉⡇⠀⠀⠁⠠⠓⠒⢀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡌⠀⡀
⠘⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⡆⠀⡇⠀⠇⣀⠀⣸⠁⠀⠀⠀⠑⢄⠀⠀⠀⢸⠀⠀⡸⠃⠀⡅
⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡁⠀⡇⠀⠄⠸⠡⠃⠀⠀⣠⠀⠀⠈⠢⡀⠀⠀⠁⡎⠀⡇⠀⡇
⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⡄⠀⠀⢀⠀⠀⠀⣰⠀⠑⢄⠀⠀⡜⠀⠀⠀⡇⠀⡇⠀⡇
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⡧⠤⢤⠂⠀⠀⡰⢭⠀⠀⢸⠅⠬⠤⠤⠤⠤⣧⠤⠤⠤⡇
⠀⠀⠀⠀⠑⠢⢄⠀⢀⣀⡀⡀⠄⠂⠁⠀⠀⠀⠀⠀⡇⠀⠰⣀⢀⡴⠁⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⢸⡁⠀⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⣧⠀⢀⡠⠇
⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⡀⣀⠀⠀⠸⡀⡸⠀⠀⠀⠘⢄⣀⠜⠀⠀⠀⠀⠀⠀⠣⣀⡼⠀⠀⡤
⠀⠀⠄⠂⠄⠈⢆⠀⠀⠀⠀⡰⠃⠀⠀⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠧⢤
⠀⠀⠄⠀⠀⠀⠀⠱⡀⢀⠜⠀⠀⠀⠀⠈⠢⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠰⠧⠄⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⡔⠉⢳⡀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠚



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡽⢠⡤⠀⡄⢠⠖⢾⢀⡔⢢⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣸⣇⣀⣇⣘⣦⣺⣈⣣⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⣷⣦⣄⢀⣴⣾⣿⡿⠟⠋⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠙⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣾⣿⠃⠀⠀⠀⠀⣀⣀⠀⢹⣿⣄⣀⣀⠀⠀⠀⣀⣨⣿⣿⣤⣀
⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣾⣿⣿⣿⠿⠿⠛⠛⠋⣿⡟⠀⠀⠀⢠⣾⠿⢿⣿⡿⠟⠛⠛⠿⣷⣾⡿⠛⠛⠉⠉⠙⢿⣧
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣿⡀⣾⡟⠀⠀⠀⠀⠀⠈⣿⣷⣤⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡟⢙⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⣀⣀⣀⣤⣿⣿⣦⣀⣀⣀⣠⣾⡿⢿⡿⠟⠁⠀⢠⣿⠏
⠀⠀⠀⠀⠀⢿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠋⠁⠀⠉⠛⠛⠛⠛⢿⣦⣀⠀⠀⢀⣠⣾⣿⣦
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠿⠟⠉⢻⣿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⢿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⢀⣤⣴⣾⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣀⣀
⠈⠋⠉⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡿⠛⠿⠿⣿⣶
⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣟
⠀⠀⠀⠀⠾⠿⠛⠉⠻⣿⣧⣀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⠻⠿⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠛⠿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⠛⠉⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⣿⡏⠁⠀⠻⣿⣦⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⡟⠉⠁⣴⣿⠟⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠙⣿⣷⡀⠀⠀⠈⢻⣿⣧⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⠙⣿⣿⣄⣾⣿⣯⣤⣤⣀⡀⠙⢿⣷⣤⣀⣀⣀⣀⣤⣾⡿⠋⠀⢀⣀⣤⣤⣼⣿⣷⣄⣀⣤⣴⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠿⠿⠿⣿⣷⣤⠉⠛⠛⠿⠿⠛⠛⠉⠀⣠⣾⣿⠿⠿⠿⠿⠿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣤⣤⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣶⣦⣤⣴⣶⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡏⠀⠀⠀⠉⣿⣷⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⣀⣴⣿⠏⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⣴⡿⠛⢢⣿⣿⠀⠀⣀⣤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠚⠋⠉⠉⠀⢰⡦⠐⢻⡆⠀⣨⡄⠀⠀⢀⣿⡟⠀⠀⠈⣿⡟⠀⣴⡟⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠁⢰⣿⡇⠀⠀⢸⣿⠁⠀⠀⠀⣿⠇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢸⣿⡁⠀⠀⠘⢿⡦⠤⠂⠀⣿⠀⠀⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡆⠙⡖⠐⠤⠐⠒⠀⢒⠂⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠁⠁⠀⠀⠙⠃⠀⠉⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡠⠀⠃⠤⠒⢤⡄⡀⣀⠠⠔⠢⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠔⠸⠁⠀⠀⠀⢢⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⡐⠲⠂⠀⠐⠖⢰⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⡁⠀⠀⡐⠀⠀⡆⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠁⠀⡀⠀⠀⠎⠀⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⢤⡀⠠⠒⠀⠀⠀⠀⠀⠰⡄⢀⠀⢬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠑⢆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⢹⠀⠀⢠⠂⠀⠀⠀⠈⠁⠒⠒⠒⠀⠁⠀⠀⠀⠰⡄⠀⠈⣋⣉⠩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠘⠒⠈⠐⠀⠠⠼⠀⠀⢀⠀⠀⠀⣀⠀⠀⣦⡀⢀⠝⠉⠉⣅⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⡄⠀⠀⣶⠀⠠⠄⠊⠱⢄⠀⠉⠀⠐⠀⠀⢩⠀⠀⣀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠐⠀⡎⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⠤⠁⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡐⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢣⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠰⢧⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣀⠔⠁⠄⠠⠀⠀⢀⠂⠀⡀⠴⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⢄⠉⢤⡀⠘⢆
⠀⠀⣀⠠⠴⠊⢁⡴⠋⠀⠀⠀⢠⠀⠤⠊⠀⡀⠀⠌⠘⡀⠀⠀⡄⠈⢆⠀⠶⠒⠤⢄⠱⠀⠈⠓⢄⠑⠒⠤⠤⣤⣤
⣴⢟⣯⡁⢠⠶⠊⠀⠀⠀⠀⢀⡧⠀⠀⠀⢀⠁⡸⠀⠀⠃⠀⠀⠇⠀⠀⠳⡀⣥⠀⠀⠁⠷⠀⠀⠀⠙⠠⣐⢃⠘⠷
⠀⠈⣡⠎⠁⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠸⢀⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⣾⠀⠀⠀⠀⠀⠠⣀⠀⠀⠙⢌⠁
⠀⣴⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⠀⠀⠸⠆⠸⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠓⢒⠒⠈⣁
⢠⡇⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⡄
⢸⠁⠀⠀⣠⠁⠈⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⠀⢀⣀⠤⠀⠀⠀⠀⠀⣸⠇
⠘⢧⠤⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍
⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠀⠠⠂⠑⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡴⠦⡄⣀⣀⠀⣀⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢄⣀⠀⢀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣋⣀⡠⠜⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⡖⠒⠂⠔⠒⠂⠈⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠆⠀⢠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠈⠀⠀⠀⠀⠇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠻⣦⣤⣴⠶⠟⠛⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⠿⢶⣦⣤⣤⡴⠶⠶⣿⠃⠀⠀⣀⡈⣿⡀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢾⣉⡟⠋⠉⠛⣶⠛⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣽⡄⠀⠀⢀⡿⢳⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠓⠶⣟⠉⠉⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠛⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢴⠶⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣤⣀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⣀⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡅⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢩⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠻⠶⣦⣀⠀⠀⠀⠀⠀⠀⠛⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⣡⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠳⢶⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣀⣀⣤⣤⣤⣤⣤⣶⣶⣿⠿⠋⢁⣠⠴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡌⠳⣤⣀⣤⣦⡀⠀⠀⠀⣸⡿⠉⣽⠋⠁⠀⠀⠉⠙⠁⢸⣷⡚⠉⠀⠀⢸⣿⡀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣴⡟⠁⠉⠻⣶⠶⠟⠋⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⠉⠉⠉⣿⡏⠁⢾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣦⣤⡴⢋⡀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⢀⣼⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⢤⣅⡀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⡞⠋⠳⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡏⠻⣦⡉⠀⠀⠀⢸⣿⣾⠆⠀⢀⣀⠀⠈⣧⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⠀⠈⠙⠳⠶⢦⣄⠋⠁⠀⠀⠸⣿⡿⠃⢹⡀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡘⢷⡀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣅⣀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣽⣦⣀⠀⠀⠀⠀⠀⠀⢠⡿⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⠤⠤⠤⠶⠋

⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⠀⠀⠀⠀⢰⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⣶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠹⠀⠀⠀⠸⣿⣿⣷⠀⠀⢼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠋⠀⠀⠀⠙
⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠁⠀⠀⣿⡆⠀⠀⠀⠠
⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢠⣿⠇⠀⠀⠀⠀⣾⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⢠⣿⠃
⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡟⡉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⡀⠀⠀⠀⢸⣿⡟⠉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠉⠀⠀⠠⠸⢿⣿⣷⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠘⡏⠉⠄⠀⠠⠹
⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠁⣿⡆⠀⠀⠀⠠
⡟⡋⠛⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠⣾⡟⠋⠙⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠
⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍


⣀⣤⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⢠⡟⠉⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠈⢷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡴⠶⠶⠶⠶⢶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣀⣀⣀⣀⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣠⡤⣶⠟⠉⠀⢰⠏⠀⠀⠈⢳⡄⠉⠙⠓⢶⣤⣄⣀⡀⠀⠀⠀⢠⡏
⠀⠀⠀⠈⠳⣤⡤⠶⠖⠛⠉⢁⡼⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠻⣄⠉⠙⠛⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠷⠶⢺⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢸⠟⠲⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⢉⣩⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⢀⣤⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⢀⣴⡿⠛⠉⠀⠀⠀⠀⣀⣠⣤⣤⠶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⣠⠟⠁⠀⠀⠀⣠⡴⠞⠋⠉⠁⢀⣠⠞⠋⢀⣤⣾⣿⣿⡿⢿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⣰⠋⠀⠀⣠⣴⠟⠉⠀⠀⢀⡠⠖⢋⣠⣴⣾⣿⢟⣩⣾⠟⠀⠘⣿⣿⣎⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢰⠃⠀⣠⣾⡟⠁⢀⣠⣔⣮⣵⣶⣿⣿⡿⢟⣫⣴⡿⠛⠁⠀⠀⠀⣿⣿⣹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠃⢀⣼⣿⣯⣶⣾⣿⣿⣿⣿⣟⣻⣭⣷⣾⠿⠛⠉⠀⣴⠶⠖⠢⠀⣿⣿⡏⢸⡇
⠀⠀⠀⣀⣀⡀⠀⣿⡇⠀⠀⣾⣿⣿⣿⣿⡟⠙⠛⠛⣛⡛⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⣿⣿⡇⠘⠀⡀
⠀⡰⢋⣀⡀⠉⠀⠸⣇⠀⢰⣿⣿⣿⣿⣿⡏⠳⡶⠛⡿⣿⣷⡄⠀⠀⠀⠀⠀⢠⡾⣿⣿⠻⣶⣿⣿⠇⠀⢠⠇
⠀⠀⡊⠀⠁⠀⠀⠀⠹⡄⢸⣿⢿⣿⣿⣿⡇⠀⠙⠄⣳⣟⠋⠀⠀⠀⠀⠀⠀⠈⢒⣿⡛⠐⢹⣿⣿⠀⢀⡾⠀⠀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣿⡌⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢀⡾⠁⠀⢸⡀⣀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⠺⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣼⣿⠏⡰⢫⠇⠀⠀⠘⠛⠃⠀⠀⢸
⠀⠀⢀⠴⠊⠁⢀⣀⡀⠀⠀⠢⡙⣆⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠈⣀⡈⠁⠀⠀⣠⣾⡿⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⢰⣏⠀⠀⠀⠀⠀⠉⠓⢄⠀⠘⠜⠄⠀⢸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⣀⣴⣾⡿⠋⠀⠀⣠⠏⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠈⠁⣠⠤⠒⠀⠀⠀⠀⠀⢳⠀⠐⠀⠀⣼⣿⡇⣿⣿⡿⠀⠈⠉⠛⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⢀⡀⠀⠢⢄⣀⣀⡠
⠀⣠⠎⢁⡴⠚⠁⠀⡀⠀⠀⠀⠃⠀⠀⢠⣿⣿⡇⣿⣿⠃⠀⠀⠀⢸⡟⢸⣿⠁⠀⠀⠀⠀⣤⡀⡴⢻⣇⣀⠀⠀⠀⠁
⢰⠃⠀⣾⠁⠀⠀⠚⠃⠀⠀⠀⠀⠀⢠⣾⣿⡿⢰⡿⠁⠀⠀⠀⠀⢻⣇⠀⠙⢦⠀⠀⠀⠀⠣⢘⡀⢋⡉⠉⠳⣄
⡟⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⣾⠁⠀⠈⠂⠀⠀⠘⢿⡄⠀⠀⠀⠀⣠⢒⣡⢚⠛⢄⠲⢤⡤⠞⠃
⣇⠀⠀⠀⠙⠻⢶⣶⣶⣶⣾⣿⣿⠿⠛⠁⠀⢠⡇⠀⠀⠀⢰⠀⠀⠀⠀⠻⣦⠀⠀⠀⠉⣽⠁⠉⢸⡄⠀⠀⢷
⠘⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀⣠⠞⠙⢦⣀⠸
⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⠟⠁⠀⠀⠀⠈⠓⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⢧⡀
⣠⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣉⣢⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⣧⢸⣸⡸⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⣀⣈⣤⠀⢀⠀⠀⠀⢬⣓⣬⣾⣿⣿⣟⣥⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡆
⠀⠐⠀⠀⠁⢡⣙⠃⠒⠤⠀⠀⠀⡦⠶⣿⣿⣿⣿⣿⣿⡭⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠠⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠐⢛⡩⢻⢿⢿⢟⢮⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠈⠐⠻⠸⠸⠘⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⡈⣐⡚⣼⣄⣤⠁⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠄⠪
⠀⠀⠀⠀⠀⠀⠀⠂⡩⠙⣿⣿⡁⠖⠀⠠⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⡡⠢⢓⠉⠀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣄⠀⣿⡼⠃⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡱⣄⠟⠉⠃⠃⠀⠰⠋⠋⠀⣰⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠈⠀⠀⣀⠀⠀⠀⠀⠀⠞⠉⠉⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⣾⡔⠁⠈⢳⡄⠀⠀⠀⠀⠀⠈⠔⠚⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠖⠂⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠳⢶⠏⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢠⣧⠀⠀⠀⣼⢇⠀⠀⠀⠘⠃⠀⢀⢀⡟⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡏⠢⠤⠴⠋⠀⢸⠇⢠⡏⠀⣼⠃⢸⡗⠁⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⢼⡇⠐⢿⠀⢿⠀⠀⣾⠀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣃⣀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠀⠘⠆⠀⠙⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣦⠀⠀⠀⣼⣿⣿⡄⠈⢿⣿⡆⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠈⣿⣿⡇⠀⣸⣿⡟⣿⣷⠀⠈⢿⣿⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣿⣿⡇⢠⣿⣿⣀⣿⣿⡆⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⠟⠀⣾⣿⠛⠛⠻⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠙⠛⠁⠀⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⠢⠀⠀⠈⠙⠻⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠙⠋⠉⠁⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢴⠦⠀⠀⠀⢠⣄⣀⢈⠩⠿⣷⢿⣿⣿⣿⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠩⠉⠒⠀⠀⡁⠈⢹⣿⣿⣶⣿⠈⠉⠹⠛⣿⣿⣿⣿⣿⠟⢙⠛⠁⠀⠀⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⠐⠀⠀⠀⠤⠲⠶⠿⠻⣿⣿⣠⣤⣶⣷⣿⣟⡟⠿⣷⣿⣶⣠⣀⠁⠈⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣖⡄⠀⠀⢀⡀⢠⣤⣴⣿⣿⠿⠿⠿⠿⠿⠿⢿⣓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⡶⠾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢦⣤⣤⣤⣀⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣝⣭⣍⣽⣭⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⠀⢴⣾⣿⣿⠀⠘⠈⠙⠓⠀⠀⠒⠀⠀⠀⠐⠁⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⡿⠀⡀
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⠀⠀⠀⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠄⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾
⢀⠔⠈⠁⠈⠁⣀⠀⠀⠀⠀⢠⣖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢀⣾⣏
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤⠀⡴⠊⠉⠉⠐⢄⠀⠀⠀⠁⢄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣀⡀⢀⣤⣿⣿⣟⡡
⠁⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠦⣄⡠⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⡀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡻⣿⣿⣷
⠙⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠴⠊⠁⠀⠀⢀⣿⡟⠃⠀⠃⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢱⣄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠈⢆⠀⠉⠁⠀⢄⠵⠶⣦⠀⠀⠀⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⣾⠇⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⣀⢀⡀⠉⠉⢻⣿⣿⣧⢠⣿⣷⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⠁⠀⠠⡄
⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠃⠀⠁⠈
⠀⠐⢄⢿⡄⡀⠀⠀⠀⠀⠕⠀⠄⠀⠀⠀⠀⠀⠀⠒⢂⣩⡴⠋⡉⠀⠙⢷⡀⠈⠀⠀⠐⠒⠒⠄⠠⠄⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠙⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠅⡔⠁⠀⠋⠀⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣴⣶⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠖⠀⠀⠀⠀⠀⠀⠁⠰⣀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⠀⠀⠀⠈⠙⠙⠓⠚⠠⢄⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠉⠉⠒⠆⠒⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⢠⠀⢀⣴⣿
⠀⠀⠀⠀⠇⠑⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢺⣧⣠⣿⣿⣿⣿⠏
⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠸⠁⠀⠀⢀⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⣀⠀⠀⠀⠈⢻⣿⣷⣀⢠⠀⠀⣤⣿⣿⠋⢀⠀⠠⠠⠀⠠⠄⠀⡸⠉⠐⠙⠧⣐⠀⠤⠤
⠲⢀⠈⠁⠀⠁⠀⠀⠠⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠈⠻⣿⣿⠛⠃⢸⣿⣿⡡⠊⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠒⠒
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣶⣦⣉⡀⠃⢌⣿⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠐⠚⠉⠉⠉⠻⠛⠛⠛⢻⡿⢿⠁⣠⡆⢫⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣴⠂⠀⠀⠀⠠⠀⢀⡀⠀⠂⣀⣼⡇⣀⡖⠃⣼⠛⠻⣶⣬⡛⠒⠀⠀⠻⠄⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠈⣿⢶⢫⠟⢈⡡⠶⠀⠀⠀⠀⣠⠐⣼⡟⣿⣿⣿⣿⣶⢾⡾⡛⠀⠐⠻⣿⣏⠐⠀⢀⠠⠉⠂⠀⣈
⠀⠀⠀⠀⠀⠀⡀⠈⠀⠚⣼⣦⣿⠾⢻⣷⠶⢀⠀⠀⠠⠚⢀⣸⣿⣿⠋⣿⣿⣿⣿⠦⠤⠄⠠⣄⣻⣿⡇⢠⠴⠣⣰⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠐⠳⠔⣦⣿⣿⣵⠈⠐⠋⠀⡔⠓⣾⣴⣾⡿⢧⠃⣸⣿⣿⡏⣠⠀⠐⢂⠀⠀⠀⠈⢿⣧⣖⠁⠀⢠⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡕⢦⣘⣿⡿⣿⠞⠅⠛⠠⡼⠓⢿⣿⣿⣿⠀⣼⣿⢫⣅⣴⣾⣟⣿⣻⣿⣲⣆⠐⢾⣿⣯⣵⠀⠘⢀⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⡙⣋⣿⡷⠀⠀⢀⠘⢨⣿⣿⣿⣿⠧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⠀⠀⣾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢐⠙⣾⣷⣿⣿⡇⠀⠐⠁⢠⣿⣿⣿⣿⣧⣾⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣩⣿⣷⣆⢠⣏
⠀⠀⠀⠀⠀⠀⠐⠺⣽⡟⣿⣿⣿⡏⠀⠐⠲⣾⣿⣿⠵⣿⣿⣿⣯⣁⣾⡿⠛⣟⣿⣿⣿⣿⣿⣟⣳⣿⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⠙⢿⡜⢠⣤⣾⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣩⣿⣿⣿⣿⣛⣿⣻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣾⣿⣾⡧⠈⣹⣿⡿⠎⠸⣿⣿⣿⣿⣿⠿⢍⣉⣉⡹⠿⢾⣷⣿⣿⣿⠂⠀⠋⡇⣨⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⣾⣿⣿⣾⠟⢿⣷⠃⠐⠀⣿⣿⣿⣿⣿⡧⣄⠈⠛⣉⠠⠀⠄⠀⡀⠀⠀⢠⢈⡏⢠⣿⠷
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⣿⣿⣿⣟⡀⠘⣫⡴⠊⠁⢸⣿⣿⣿⣿⣷⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣘⣿⣿⠋⡷
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠹⣿⣿⡿⢦⡞⣉⠀⢀⣵⣿⣿⣿⣿⣿⡍⠛⠖⠀⠀⠀⠀⠀⡀⠀⢐⠟⢰⣾⠟⡏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⣿⡞⠀⠂⢠⡆⢋⣹⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⢩⡴⣻⢯⠜⡋⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠐⣥⡾⠀⠄⠀⠰⠛⣉⣲⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⠀⢀⣠⢷⣾⣿⡟⢁⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢱⣃⡄⢸⡂⠀⣌⣹⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⡼⣯⡻⢿⣿⣿⣻⠟⠀⠁⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠻⠉⢤⠉⠁⠀⠉⣷⣽⣿⣿⣿⣼⣦⡀⣀⠀⠠⠈⠐⣦⠲⠿⡀⠁⠀⠄⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⡀⢠⠄⣨⣿⣿⣿⣿⣿⣿⣷⣼⣦⣷⢀⣶⣿⡀⠀⠰⡦⠀⠀⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠞⠀⠀⠐⠂⢀⠀⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⡀⠀⠀⠄⠲⠖⠋⠉⢀⣙⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠂⠁⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⣀⠀⠀⢀⣄⠰⠄⠀⠀⠘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⡀⠈⠁⠠⠀⠀⠀⠀⡀⣄⣰⣾⣿⣿⣿⡟⣻⣿⣧⢋⠶⣀⠘⣿⣿⣿⡠⠄⠀⠀⠀⣰⡾⠓⠀⠀⠐
⠀⠀⠀⠨⣶⣮⣄⠃⠀⠀⠀⠀⣀⣌⣶⣿⠟⠿⣙⣿⣿⣿⣿⡿⠟⣛⠠⠞⠀⠙⠉⣿⣟⣠⠀⠀⣠⣴⢏⠗⠀⢠
⠀⠀⠀⣻⣿⣿⣿⣽⣿⣶⣶⣬⣯⣥⣯⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠒⠆⠀⠀⢤⣾⠿⠧⢀⣾⠛⡁⠀⠀⢀
⠀⠀⠀⣽⠋⠉⠻⠿⠿⢿⢿⢿⣿⡿⠟⣉⠉⢈⣹⣧⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⣾⢿⠏⠀⠀⠀⠠⠉
⠀⠀⠐⢿⣿⣿⣿⣷⣄⢤⣦⠰⡿⠣⠶⣧⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠐⠀⣼⠿⠶⣽⠇⠀⠘⠀⠐⠃
⠀⠀⠀⠈⠀⣰⣿⢿⣿⣷⣶⣾⣿⣶⣾⣿⡿⢿⡟⠋⠛⢥⡀⠀⠀⠀⠀⠀⠀⢾⡷⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠀⠈⣤⣿⣿⣿⣿⣿⡿⠛⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡿⠀⠀⠈⠁⠂⠀⠄⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡗⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠈⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⢀⠀⠈⠐⠀⠒⠆⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠈⠀⠸⣆⠀⠀⠀⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠻⠷⣶⣤⣄⣠⣶⠟⠋⠉⠙⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⣹⠟⠁⠀⠀⠀⠀⠀⠹⣷⡶⢶⣶⣶⣶⣶⣤⣤⣾⠿⠛⠋⠉⠁⠀⠙⣿⡇
⠀⠀⠀⠀⠀⢀⣼⣧⣤⣀⡀⠀⣠⣴⠶⠿⣶⣶⠟⢷⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⢠⡿⠋⠉⠉⠉⠙⣿⠟⠁⠀⠀⠀⠹⣧⣼⠇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡞⢿⡀⠀⠀⠀⠀⢀⣿⣅⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠇
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠻⣦⣼⣷⣤⣀⣀⣤⡾⠋⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣻⣧⣀⠀⠀⢀⣠⣴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⢸⣿⠉⠛⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠿⠿⠿⠿⣿⡿⠶⣶⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣀⣀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡆⠀⠀⠀⠀⠛⠛⣻⡿⠛⠛⠛⠛⠂
⠀⣤⣶⣶⣾⣿⠿⠆⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⢀⣀⣀⣿⠇
⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⠉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠷⠶⡦
⠀⠀⠀⢀⣀⣼⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣼⡟
⠀⠀⠰⠛⠋⠁⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠳⣤⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⣧⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣿⠋⠀⠀⠀⠈⢻⣇⡈
⠀⠀⠀⠀⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣅⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢂
⠀⠀⠀⠀⠀⣠⠋⠉⠉⠉⠙⠓⠒⠀⠀⠀⢘⣿⣿⠆⠠⠀⠀⠀⢿⣿⣟⠀⠀⠀⠀⠒⠛⠉⠉⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠠⠸⣿⡿⠫⠃⠀⠀⠀⠀⠀⠀⠯⠻⣿⡿⠢⠀⠀⠀⠀⠈⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢨⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠀⠱⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠶⠶⠶⠟⠛⠛⣉⣙⠳⢜⣿⣼⢸⢃⡟⢰⡏⢸⡇⢸⡇⣸⠇
⢶⣶⣶⡶⠿⠟⠛⠛⠛⢦⡇⡇⡟⣸⠃⣾⢁⣿⢁⣿⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⠇⡿⢸⡇⣸⠇⣼⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⡇⣿⢠⡟⢠⡟⢰⡟⠀⢀⡠⣐⢤⡒⢮⡙⢦⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠠⡇⢸⡇⣾⢇⣘⡵⣿⣶⣿⢮⢧⢹⡌⢷⡈⣷⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡮⡮⣣⣿⡬⣗⡮⢗⡪⠭⣓⣚⣷⢏⡏⣇⢷⠘⣧⠸⣧⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯⠯⣝⣚⡭⢗⣫⠵⢚⣫⠵⣒⣫⠭⢯⣽⡜⢧⡙⣧⡙⢧⡙⢧⣀⢤⣒⣒⡺⣝⢯⢢⡐⣄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠶⣚⣩⠴⢚⣭⠶⠛⠉⠀⠀⢸⢷⢧⢮⡽⠢⢽⡲⣝⡬⢚⣩⡥⠶⢭⡞⡎⣇⢻⡘⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣩⡭⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠻⣼⣸⣖⣺⠵⣊⡵⠞⣋⣤⡶⠶⠶⡅⡇⢿⠘⣇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⡯⠖⣛⣡⡴⠟⢋⣡⣴⡶⠶⣆⣿⢸⡀⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⣭⣥⣴⠾⠛⣉⣤⣤⣤⣤⣿⢸⡇⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⠶⠶⠿⠛⠋⠉⠉⣿⣿⡼⣷⢸⣇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡏⣇⢻⡌⢿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡯⣳⣙⠬⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⣭⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⣁⣤⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠋⢁⣠

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

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢠⡐⠂⢰⠐⠄⢠⠀⡆⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣐⠀⡀⠀⢱⣎⣈⠐⠡⣀⡨⡅⠀⠉⠠⡀⢀⠴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠠⡆⠀⡂⠙⣏⡥⢀⠛⢿⢏⠀⠃⣤⡀⣿⡏⡄⠧⢀⢀⠁⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢠⠀⣜⣠⢾⠛⡏⢫⠿⣦⣼⠒⡿⣠⡁⠀⠷⣷⠂⠜⡠⠁⠖⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣠⢉⣽⡈⢛⣶⣬⣏⠘⢁⣍⠿⢻⣿⡴⠛⢻⣿⡅⡲⢎⣽⣇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢘⡟⢃⣞⣱⣧⣿⣵⣾⣷⣞⣿⣿⣽⡤⣿⣬⣤⣤⠜⢃⡈⡛⠂⠊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠚⢆⠈⣋⣀⡍⢫⣯⣽⡍⠥⣿⣿⣿⣿⣿⣷⣿⣞⣷⣾⣿⢂⣻⣶⣎⡹⡇⢀⢦⡆⠁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠹⠀⢠⣿⠈⡙⠘⣬⣿⣷⣶⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⢻⣏⣻⡓⢻⠮⣨⣁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⢗⣁⣈⢓⣻⣿⣿⣿⣯⠿⣾⣷⣾⣯⣈⣿⣿⡶⣟⣻⡿⣿⠛⢫⣶⡄⢞⠣⢙⠁⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡈⢠⡏⠉⣴⣡⣽⣯⣷⣮⣿⣴⣯⣿⣿⣿⣿⣿⣟⣛⣿⣿⠟⡿⣋⣿⣵⣦⢎⠟⣈⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⡴⢣⡍⢟⣲⠼⣿⠿⣿⣯⣾⣿⣿⣿⣟⣺⣿⣿⣇⡟⠸⣧⡟⢬⠉⢁⡀⠤⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⢊⠋⠉⠷⣬⣿⢶⣸⣻⡿⣿⣿⠻⣿⣿⢛⣽⣿⣛⣿⡅⠿⣞⢃⠁⣸⣻⠃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢂⢃⡀⢽⣯⣀⢾⣽⢮⣤⡤⣿⣿⡟⣿⢹⣿⡷⣼⣿⣟⠻⠟⢟⡰⠅⠱⠒⠊⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌⡙⠳⠆⡸⠚⠫⠙⢻⣾⢗⣾⠟⣟⠱⢦⡽⢻⢷⣬⡸⢋⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠠⠓⠃⠒⠉⣼⣠⣥⡴⢦⠐⣀⣼⢿⡐⢻⣯⡴⣤⠐⠴⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⠠⠒⡀⠉⢻⠳⠛⠊⢁⡱⠥⠚⠙⠂⡁⠀⠀⢀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠋⠁⡀⠁⡀⠈⠴⢆⢉⡆⠹⠄⠋⠒⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠤⠄⠂⠐⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀



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

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⣄⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⠙⠻⢷⣦⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠈⢻⡇
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⢻⣇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⢀
⠶⠻⠟⢻⣿⠛⠒⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠐⠛⢻⣿⠛⠛⠛
⠀⠀⠀⢘⣿⣄⣀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣠⣼⣿⣀⡀
⠀⠀⠛⠛⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠙⠁
⠀⠀⠀⠀⣀⣽⣿⣿⡋⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠈⣿⣿⣷⣤⡀
⠀⠀⠀⠟⠋⠁⠀⠙⣿⡿⠋⠉⠀⠀⠉⠙⢷⡄⠀⠀⠀⠀⢠⡿⠋⠉⠉⠉⠉⠻⢷⣿⠋⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣀⣠⣤⣀⣤⣾⠏⠀⠀⠀⠀⠹⢷⣤⣤⣤⣀⡀⢀⣴⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠛⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠛⠉⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡀⠘⢶⡞⠲⠖⢦⠊⣠⠆⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣀⣀⣀⣀⡀⠀⠀⠉⠑⢲⡇⠀⠀⢸⠉⠁⠀⠀⠀⣀⣀⣀⣀⣄⢹⡄
⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠶⠶⠤⣿⠸⣟⠋⠀⠀⠉⠉⠉⠀⣈⣹⠁⣼⢀⣿⣉⡁⠁⠀⠀⠀⠀⠀⠈⠹⠃⡧
⢠⣤⣶⣒⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣥⡤⠤⠶⢖⣺⠟⢡⡟⠙⠻⡻⢄⠻⡉⠻⣗⠒⠶⣤⣤⠤⠤⠖⠃
⠀⠀⠈⠉⠉⠉⣻⠆⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣤⠴⠞⠋⠀⡔⣼⠀⠀⠀⠘⣆⠳⣝⣄⠈⠳⢄⡀⠉⠓⠒⠶⠤⠤⢤⣤⣤⠤⢤⡖
⠀⠀⠀⠀⠀⣾⠁⣀⣠⣤⠤⠴⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠰⠀⡇⠀⠀⠀⠀⠈⢇⠈⢮⡳⣄⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⢰⠇⠀⠀⠀⠀⠀⠘⣆⠀⠱⡌⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⢸⠀⠀⠀⠀⠀⠀⠀⠹⡄⢱⡙⣆⠀⠈⠙⠲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢷⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠌⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢹⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣧⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⡆⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢻⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠂⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⠞⣇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⠞⠁⠀⢸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⡀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠛⠳⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡿⠀⠀⠈⠙⢦⣄⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡇⠀⠀⠀⠀⠀⠈⠓⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢣⠀⢠⠀⢠⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠂⢸⠀⠂⢀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⢉⣀⡀⠀⠀⠐⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣷⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⡀⡼⣿⣦⣤⣝⠂⠐⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠔⠈⡀⠐⠁⡉⠀⠑⢀⠁⠈⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠄⠀⠀⠁⠠⠀⠡⠀⠀⠀⠑⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⢠⠀⠀⠀⠈⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⠀⠂⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣿⣿⣷⣤⡠
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⢶⡦⢀⠁⠀⠀⠈⠁⠉⠊⠢⠻⢿⣿⣭⣤⣴⣄⡢⣤⣤⣀⢠⣦⠀⣀⡀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣠⣤⣶
⣶⣴⣦⣶⣿⣿⣿⣶⣭⣉⢴⣤⣀⣨⣤⣿⣦⣿⣤⣦⣤⣤⣤⣶⣶⣤⣤⣔⣶⡬⠻⣿⣿⣿⣿⢧⣞⣷⣳⣷⣿⣷⣦⣷⣾⣿⣷⣿⣿⣾⣾⣿⣿⣿⣾⣯⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣿⣿⣿⣿⣯⣿⣿⣿⣿⣇⣿⣿⣿⣟⣿⣿⣿⣿⣾⣿⣿⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣉⣸⣿⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣿⠿⢿⡿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣹⣿⣿⣍⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⠛⢶⣄⣀⣤⣤⣤⣤⣤⣤⣤⣶⠟⠛⠛⣷⣤⡶⠞⠛⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣴⠟⠁⢀⣀⣄⣹⣇⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣴⡟⢻⡿⠿⠿⢦⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠠⢻⣿⣿⢠⡄⢀⡀⠹⣷⣶⠶⠿⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣿⠟⣀⠁⠻⠟⣸⡟⢻⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣍⣱⣿⣿⡿⣷⡾⠏⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢿⣇⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⠻⣷⣶⣾⣿⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠛⣿⠉⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⣘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠔⠃⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⢨⡿⠉⠉⠓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠳⢤⣀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣞⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡶⠾⠟⠛⢁⣿⠃⠀⠈⢿⡿⠏⠉⠉⠉⠉⠉⢿⡿⠁⠀⠘⣷⡝⠻⠶⣤⣄⣀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⢿⣤⢀⠀⣿⠇⠀⠀⠀⠈⠳⣤⡄⠀⠀⣀⣤⠞⠁⠀⠀⠀⢹⣷⠁⢀⠐⣿⡛⠙⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢛⣷⣿⣿⠏⠀⢀⡴⠶⢤⠀⠈⠉⠛⠋⠉⠀⠀⢀⣠⣤⡀⠀⢿⣤⣿⣿⡏⠁⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢘⣋⣿⠏⠀⠀⠸⣄⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣹⠀⠘⣿⣿⠃⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⡐⠁⣸⠏⠀⣠⡴⠾⠿⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣎⠁⣼⠃⢠⡞⠁⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠟⠻⢻⣿⣷⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢿⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡠⠊⣿⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⠀⢠⣶⡀⠀⠀⣀⢀⣼⣿⢀⣤⣶⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣿⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣄⡾⠿⢻⣷⣾⠿⠿⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⣿⣇⡄⠀⢀⠁⠀⠀⠀⠀⢀⣿⡟⠃⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⢐⠎⢻⣿⣒⡞⢀⠀⢠⢀⣠⡾⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⠻⠷⣾⣶⠾⠿⠋⠀⠀⠈⠛⠳⠶⠶⠶⠶⠶⠛⠛⠋⠁

⣄⣀⣠⠀⢀⡀⠠⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠘⠋⠋⠙⠀⠀⡀⠀⠀⠁⠀⠄⢢⠈⠀⣤⡀⠈⠀⢁⡄⠠⠑⠈⠁⠀⠀⠀⡈⠀⠀⢹⠂
⠀⠀⠀⢠⠯⣀⣀⠈⡆⠀⠀⣴⠋⠉⠾⠿⣿⣧⢳⡄⠀⠀⢀⠟⠛⠓⠢⡀⠀⠀⠀⠀⡜⠒⠑⢳⡀⠀⠈⠀⠀⡀⠀⠀⠳⠂⠀⠀⠀⢁⠈⠀⣀⠵⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠇⠀⢀⠃⢠⠀⠃⠀⠉⠐⢈⡄⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠰⠀⠀⣷⠚⠂⠒⢺⣌⣉⣉⣙⡎⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢰⠀⠀⢠⠀⠃⡀⠀⠐⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠰⠰⠂⠀⠙⢄⠰⠂⠈⠦⠤⠤⠤⠥⡀⠒
⠀⠄⠀⠀⢐⣦⣤⡆⠀⠀⠰⡀⠀⡰⠀⠀⢹⡀⠀⢨⠄⠀⠀⢈⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⡌⠂⠀⠀⠀⠀⠀⢠⡀⣼⡋⠂⠀⠀⠀⠒⠓⠡⠐⠀⠀⠈⠉⠈⠁⠀⣠⣄⢀⡉⠀⠀⡀⠀⠁⣴⠶⠦⡀⠀⢟⠢⡶⠓⡦⣤⠔⠠
⠀⠀⢃⠀⣀⠀⠀⠀⢀⠂⠁⠈⠊⡇⠀⠀⠀⣀⠑⠐⠂⠀⠀⠀⠀⠀⠀⠠⠀⠁⠐⠋⠄⠀⠀⠀⢸⡅⠘⠀⢻⡈⠀⠀⠀⢠⠉⠉⠓⠚⡇⠀⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠘⡉⢉⡉⢉⠃⠀⠀⠀⣹⡆⠀⠀⢰⠆⠂⠀⠀⠀⠇⠀⣀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠠⠉⠀⠀⠀⠀⠀⠀⠁⠨⠉⠉⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢁⠀⠀⠀⠀⠀⢸⢢⠀⠠⣞⠀⠀⠀⠀⠀⠰⠀⠀⠆
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠥⣁⡨⠅⠀⠀⠀⠀⠸⠃⠀⢀⠳⠄⠀⠀⠀⠀⠁⣀⣀⠘⠀⡀
⠓⡶⠛⠻⠝⠓⠈⠉⡄⠀⠀⠀⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⡲⣒⠳⣤⠀⠀⠀⠀⢠⣏⣀⠀⠙⡄⠀⠀⠀⠀⢀⠂⡖⠂⠀⠀⠀⠀⠀⠰⠆⡀
⠀⠃⠀⠰⠖⠒⠐⢂⠇⠀⠀⠀⠀⠀⠈⠀⠀⠈⠰⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⢰⠀⠈⠀⠀⠏⠂⡑⠍⠁⠀⠀⠁⢀⢂⠆⡀⠀⢨⡁⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠐⠂⡀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠐⠂⠰⡄⠀⠄⠀⡟⠁⠄⠀⠀⠠⠴⡦⠠⠃
⠀⠀⠀⠀⡈⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰
⡤⡤⠀⠀⠠⠐⠂⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡀⠈⠐⠀⠂⠁⢀⠄⣀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠚⠘⠽⠄⠀⠀⠀⣀⠸⢅⠀⠀⠀⠀⠀⠀⠘⢀⠁⠀⠀⠀⠂⠀⠀⠀⢠⣀⠀⠸⡓⠀⠀⠀⠀⢀⣾⠋⠙⣶⡄⠀⠀⠀⠀⠜⠁⠉⡸⠆⠀⠊⠀⢰⡿
⠀⠀⢸⠁⠀⠀⠀⢾⠀⠀⠀⢘⡂⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⣹⠿⠤⠴⢿⡄⠀⠀⠀⢘⣗⣇⣀⡟⡗⠀⠂⠒⠂⢸⠁⠀⠀⢸⡀⠀⠀⠈⡇
⠁⠀⠁⠀⠀⠀⠀⠈⣄⠰⢀⡤⠀⠀⠀⠀⠀⠣⠄⠐⠠⠏⠀⠀⠀⠀⡎⢄⠐⢀⡼⠀⠀⠀⠀⢸⡀⢀⣀⠀⣡⠀⠀⠀⠀⠘⠀⠨⠆⠘⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠖⠀⠀⠀⠀⢨⢏⠀⠀⢂⣉⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠁⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠁⠀⠀⠉⠀⠀⣴⠰⢄⡅⠀⠀⠐⠀⠀⢀⡀⠀⠀⠈⠉⠉⠀⢀⡴⠶⠖⠂
⠇⠀⠀⠀⠌⠁⠀⠈⠁⠀⠀⢀⡰⠅⠁⠁⠜⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡀⠀⢀⢰⠃⠀⠀⢱⠐⡖⠀⠀⢐⣀⠀⢸⠓⣒⣒⣒⣶⡩⠒⠸⠦⠤
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠈⠓⡆⠀⡀⠀⠰⠀⠀⠀⠀⠀⢇⢀⣀⢠⠇⠀⠀⠀⠀⠘⡄⢀⠀⡘⠀⠁⠀⠀⣼⠿⠄⠴⢷⠀⠀⠀⠙⢾⡄⠠⠀⢠
⠀⠀⠀⠀⠈⣦⠒⣠⣿⠀⠀⠀⠀⠀⠈⠋⠁⠁⠀⠀⠀⠀⠀⢀⡀⠁⣀⠀⠀⠀⠀⠀⠀⠳⠈⠐⠁⠀⠀⠀⠀⡏⡀⠐⠀⣼⠀⠀⠀⠀⠀⠑⠀⠀⠈
⠀⠀⠀⡀⠃⠀⡀⠙⠙⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠨⠜⠀⠀⠀⠀⠀⠀⠃⢀⡀⠁⠀⠀⠀⠀⠓⠆⠀⠘⡗⠒⠀⠐⠀⠶⠆
⠀⠀⡐⢄⠀⠢⢌⠀⠜⠀⠀⠂⠀⡀⠀⠀⠀⠀⠔⠁⢤⣄⡀⠀⠀⠀⠀⠀⠏⠀⠀⠉⠀⠐⠉⠑⠀⠔⢈⢹⢶⠀⠐⢀⠂⠀⢀⡤
⠀⠀⠂⡀⣁⠘⠛⠫⢢⠃⠀⠀⢉⠁⠀⠀⠀⠃⠀⠀⠉⠙⣷⠀⠀⠀⠀⡧⠀⠀⠀⢀⡄⠀⠀⠀⡬⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⠓⢀⣀⡨⠍⠈⠄⠐
⠀⡀⠀⠴⠉⠀⠀⠀⠘⠧⠴⠦⠞⠈⠀⠀⠀⢁⡄⢀⡀⢀⠏⠀⠀⠀⠀⢠⡀⠤⠀⣸⠀⠀⠀⠀⠈⠀⠀⠄⠀⠁⠀⠀⠀⠰⠇⠠⠀⠀⠏⠀⠈⠀⠙
⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⡍⠀⠂⠀⠀⠀⢡⠌⠁⣶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡿⣿⣿⡂⠀⠀⠀⢻⠔⠞⠷⢆⠸⠷⣾⠷⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠂⠀⠀⠀⠛⠳⠶⠲⠾⠶⠂⠿⠶⠲⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⡐⠂⣠⣴⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠿⠽⢯⣹⣿⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⠀⠀⢺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣷⣶⡀⢸⡿⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣤⣤⡄⠈⠹⣄⠀⢠⣀⠀⠉
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⠻⠿⡿⠛⠁⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣠⣤⣤⣦⣠⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠻⡿⠄
⠀⠀⠀⠀⣿⣿⣏⢿⠁⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢤⣿⢨⠁⢀⠆
⠀⠀⠀⠀⠈⢻⣿⣦⣷⣿⣿⣾⣿⣿⣿⣿⣿⡟⢩⣿⣿⡿⣿⡏⣥⣺⡽⣿⣼⣥⣄⡈⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⢸⣏⣉⣉⣍⣉⣹⣿⣿⣿⠿⣿⡄⡘⠾⠝⣽⡍⠲⠉⢿⡿⠛⡛⣾⠃⣥⣄⣈⣋⣉⣠⣿⣿⣤⣤⣀⣈⣹⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠀⠀⠈⠀⠂⠄⠸⠀⠈⠉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⢰⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢽⣦⠄⠀⠘⢉⣿⣖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢢⣌⠈⠀⢁⠝⠳⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠂⣸⢰⣾⢏⡞⣼⣷⠀⡠⠀⠖⠀⠀⠀⠀⢉⢿⣭⡅⠀⡀⠀⡀⢠⢠⢠⡆⡀⠀⢀⣉⠋⠁⠀⠀⠐⠿⣝⠿⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡙⢦⠡⣔⠈⡏⡾⠐⡿⣫⠞⣠⠾⡃⣷⡟⠰⠀⠈⢷⠿⠷⢤⡈⠃⠳⠈⠋⣘⢿⢔⣅⣤⡄⢆⣠⠀⡀⠀⢦⣛⢿⡃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⠌⢀⠁⠘⠀⠃⠀⣠⠖⡡⠎⣲⡿⢷⣛⡯⠀⢰⠁⠎⠀⠒⠾⢿⠎⠀⠀⠐⢁⠤⠿⠿⢾⢵⠟⠇⠌⠃⣀⠘⢏⠛
⠀⠀⠀⠀⠀⠐⠛⠛⢺⣿⡢⠶⠁⠀⠀⠀⠔⠁⠀⢴⣩⣵⣾⣯⣶⣤⣤⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠐⠉⢹⣥⣭⣉⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠈⠉⢀⠀⠉⠀⠀⠀⢐⣚⣢⣬⣤⠤⠶⠶⠶⠶⠤⠀⠀⠀⠀⡀⢚⣤⡆⢠⡀⠀⠙⢦⣍⢾⣕
⠀⠀⠀⠀⢀⣩⠴⠒⠂⢀⡠⠄⠀⠀⠈⠀⠀⠀⢈⠄⠀⠤⣽⡿⢶⣦⣤⡀⠀⠀⠀⠈⠐⡿⡻⣠⠈⠇⢀⠀⠸⣌⠛⠂
⠀⠀⠀⠀⠀⠔⠪⠀⠀⠜⡴⡀⣢⡄⠄⣀⠀⠀⠀⠑⢧⣤⡉⢙⣯⣓⠶⠄⠀⠀⠀⢠⠀⡇⣥⡟⣦⣶⣿⢿⡷⠈⡀
⠀⠀⠀⠀⠀⠠⢒⡥⢆⣴⡾⣣⣾⠃⠀⢿⡄⠘⠀⠀⢀⢰⡾⣷⢭⡛⠗⠀⠙⢦⣄⠲⡙⡆⢸⠛⣽⢃⣿⡿⣠⠞⢁⣤
⠀⠀⠀⠃⠀⠀⢉⠔⠹⣿⡟⣹⠏⢠⠀⠉⡇⠀⡐⠀⠀⢳⣧⡀⠑⢽⣲⢦⣐⠢⠙⠧⠙⡆⢸⠀⠁⠐⢋⡼⣫⢖⣫⣤⣀⣠⠤
⠀⠀⠀⠀⠠⠀⠀⠀⠔⠙⠰⡝⠰⢀⠇⠀⠅⠠⣧⠂⢈⣆⠉⢳⣀⣤⣄⣙⣶⡕⠠⠦⡀⠀⠈⠀⢀⠼⠋⠜⣉⠵⢚⣫⡭⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠆⠄⠀⡆⡆⣴⣿⣄⠘⡜⠃⠀⠉⠰⠾⠻⠿⣍⠺⠃⢀⡀⠀⠐⠋⠀⢀⠚⣶⠾⠿⠿⠿⠿⠶⠶
⠀⠀⠠⡀⡀⠶⢲⣧⡀⠀⡀⠈⠳⣅⢘⠏⡏⠏⣽⣣⢊⡤⠀⢀⣀⡩⠤⠀⠀⠀⠀⠤⠀⠀⠐⠈⠀⠨⣍⡽⠶⠶⣖⣚⠛⠛⠛⠻⠆⠀⢠
⠠⠭⣧⡄⠀⠀⠚⣉⣿⣞⣛⢳⡄⢈⠀⠃⠁⢠⠖⠕⡹⢾⡶⢯⡤⠖⡛⠋⢉⡠⠄⠀⠀⠀⠁⠀⠀⠀⢀⠠⡀⠰⢶⣽⠻⠷⣶⣤⡄
⠀⠴⠀⠀⠀⠀⠈⠛⢪⣭⣛⠛⠿⠃⠠⠀⠀⠁⢠⣓⡚⣛⣛⣳⣖⠩⢒⠀⡴⡠⠂⢘⣔⠠⠂⡆⠀⠀⠀⠙⢮⣦⣄⠩⣻⢭⣓⢶⣄⢀
⠀⡀⣺⣴⠂⡆⠀⠙⣾⣿⡿⠂⢀⠀⠀⠀⠀⠀⠙⠈⠩⣵⢶⣤⣩⢖⣥⠖⣠⣶⢏⣼⡿⠀⠀⣷⠀⠘⠆⠀⢀⠨⣪⣷⣮⣝⠿⡿⠋⡛⢦⣆⡀
⠀⠀⠋⠃⠀⠀⣰⠠⡙⠊⠃⠰⢶⡀⣦⠀⣄⠀⡀⠙⢶⣌⡹⣿⡓⠙⡡⢊⣿⣵⢏⡿⠁⠀⠀⢻⡇⠀⠀⡀⠀⠱⣽⡈⠛⢿⡳⠆⠈⢠⣞⡿⣷
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠊⢴⣿⢺⠃⠀⢻⠀⠀⠀⢸⣏⠻⡪⠁⠈⠀⡠⠫⢃⢮⢃⠆⢣⠀⠈⡇⠀⣇⠇⠀⣦⠙⠻⣏⡀⢀⠀⠀⠀⣄⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠎⠂⡇⠀⠀⣿⠀⣦⠙⢆⠀⠀⡀⠀⠁⠀⠈⢎⢊⢀⠊⢠⠀⠁⣰⣿⠀⠈⡞⡧⠐⠻⣿⡟⠐⡇⠀⠨⡟⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⡘⠀⢸⢸⠀⠹⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠇⠸⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤⣤⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⡍⠁⠋⠀⠀⠀⠀⠉⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⡿⢿⡿⣿⣭⣷⣶⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠙⠈⠀⠛⠛⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣄⣀⣠⣿⣿⣿⢿⠃⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⢰⣾⣾⣿⣿⣿⣿⡛⢻⣿⣻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠋⢻⣿⣾⣥⣾⣇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣹⣿⣿⣿⣿⣿⠃⢀⣽⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣶⣶⣿⣿⣿⣛⣿⣿⢻⠟⠉⢻⣿⣿⣿⣿⡿⠟⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢿⢿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⢿⣿⣿⣤⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⡽⠀⠀⠉⠀⠀⠀⠙⡛⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠰⢣⠀⢀⠀⢀⢀⡇⢹⣀⡠⢤⣄⡀⣃⢸⣂⣀⠤⣄⠠⡞⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡼⢋⣉⣙⣷⣷⣈⣃⢸⣛⡷⣯⡋⢙⣥⠤⠻⠥⢤⡟⠉⣫⣤⣏⣀⣸⣃⣹⡶⠟⣫⠝⢷⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠑⠲⢠⣮⣀⣱⡞⢟⡀⣏⣙⣯⣭⣶⢲⣤⣮⣭⣿⣉⣹⡛⣧⣼⣁⣹⣥⠚⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣮⢤⡿⠾⣿⣀⣿⢛⣛⣿⡀⣹⠈⣅⣠⡌⢩⡝⢻⣆⣸⡷⠟⣻⣿⢳⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠛⠓⠒⢢⢯⣀⣽⡞⠳⠤⠌⣽⠉⢹⡥⠞⠛⠛⣾⣅⡸⣧⠚⠀⠀⠙⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⡏⣰⠋⢤⣙⡆⠀⣼⠉⡟⣏⡑⣆⠀⢸⢀⠎⠳⣌⡱⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⣴⠃⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠁⠀⠿⠞⠀⠀⠉⠳⠀⠚⠋⠀⠀⠀⠉⠀⠀⠀⠀⠈⢷⡴⠋
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠠⢤⣤⣤⣼⣇⣀⠀⠀⠀⠀⠀⢠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⠀⠀⠀⠀⠀⢀⣀⣧⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠸⡏⠉⠁⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠈⠉⢹⡏
⠀⠀⠀⣠⡤⠶⢿⡖⠒⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠐⠒⣾⠷⢦⣄
⠀⠀⠈⠁⠀⠀⠈⢷⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠏⠀⠀⠀⠁
⠀⠀⠀⢀⣠⡴⠶⠛⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠳⠶⣤⡀
⠀⠀⠀⠋⠁⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠈⠻⣿⡗⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⢞⣿⡟⠋⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠸⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⡟⠀⣠⣶⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠙⠿⣷⣄⠘⠾⠿⠟⠛⠻⢶⣦⣀⣤⣶⡿⠛⠛⠿⠿⠟⢀⣼⡿⠛⠉⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠈⢻⣦⠤⠖⠚⠋⠉⠉⠉⠛⠉⠉⡉⠙⠙⠲⢦⢤⣿⠋⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⣣⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣼⣿⣨⢤⡀⠄⢡⣇⡽⣶⡾⣭⣧⠀⠀⣠⡭⣸⣿⡀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣀⣠⣾⡷⠟⠛⠻⣿⣮⣿⣿⣶⣤⣴⣾⣿⣿⣾⡟⠛⠿⢷⣿⣦⣀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⠛⠁⠀⠀⠀⠈⠄⠁⠀⠀⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠨⠙⢻⣿⣥⣄⡀
⠀⠀⠀⠀⠀⢀⣴⠿⣶⣶⣄⠈⢦⣐⣀⣠⠤⠖⠒⠒⠒⢦⣀⠀⢀⡤⠔⠒⠒⠲⠦⢤⣄⣀⣰⠏⢠⣶⣶⣿⣶⣄
⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣦⣀⣉⣁⣤⣴⣾⣿⣭⡛⢦⡈⠙⠋⣠⢞⣩⣽⣿⣶⣤⣄⣉⣀⣠⣿⣿⣿⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡾⠾⠛⠋⠉⠀⠀⠈⠙⢷⣽⣒⣻⣵⠟⠁⠀⠀⠈⠉⠛⠿⠿⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣾⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⢀⠀⢄⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠂⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠀⠈⠀⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⡒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⠀⡀⠁⠈⢈⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠄⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠄⡃⠰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⠄⢳⡀⡿⠣⢀⣗⠅⡀
⠀⠀⠀⠀⠂⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢒⡙⠦⠤⠅⠀⠐⡡⠴⠃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢋⠛⠇⠀⢀⢩⣐⢒⡖⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡟⣤⠊⡠⢸⣀⣈⣳⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢁⡜⢣⢘⠁⣯⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠢⣯⠰⠁⠶⠠⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣏⣱⡄⡇⠀⠀⠀⠠⠿⠿⠿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣗⡏⢉⡀⢿⣀⣀⠀⢀⣀⡴⠊⣿⡷⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠈⠉⠀⠀⢀⠸⠙⢛⠋⣰⣿⣭⣍⢱⣦⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⣤⠀⠀⠀⢥⣿⡛⢉⡻⣿⠛⣼⣿⠀⢀⣅⣂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠑⢀⡘⠻⢧⡁⠶⠾⠛⠛⠆⢠⣤⣭⣁⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡤⠀⠀⠀⠀⠀⠀⢆⢸⠇⠀⣼⠁⠀⠀⠀⠄⠐⢦⣉⡠⣍⡂⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠒⠀⠀⠀⠀⠀⠃⡞⠈⠀⠀⠙⠀⢲⡀⠁⠄⠀⠀⠈⢿⣌⡻⠀⠈⣤⠷⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⣤⣤⣤⡀⡆⠀⠀⠀⣸⡆⢰⠀⢸⡅⠀⠀⠀⠰⣄⠀⠹⠙⢶⡈⠟⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠛⠿⢟⣡⠀⠀⢸⡿⢧⠀⠀⣿⢀⠀⠀⠀⠀⠈⠇⠀⠀⢸⣆⣶⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣶⣾⠁⠀⠀⠈⠁⠀⠀⢰⠿⣆⠑⢄⣀⣀⠀⠀⠀⢿⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠀⠀⢠⠃⠀⠀⠀⡀⠣⠘⠂⡈⠙⠟⠀⠀⠀⠹⢆⣄⠉⠀⠂⠀⢸⣄⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡼⠀⣢⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠀⠀⠀⣿⣆⣰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠘⢸⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⢻⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠘⡄⠀⢠⡁⠄⠀⠀⠀⠀⠀⠀⠄⠳⠀⠀⠀⠀⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⢑⠰⡇⣷⣾⣄⢀⠀⠀⠀⠀⢠⣰⣾⡖⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⢀⠀⠀⠀⠀⠈⣇⢿⣿⠛⢿⣿⣧⠀⠠⢸⣧⠛⢁⡇⠀⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢤⡀⢰⣷⡎⠉⠀⠀⠿⣿⣿⣄⠈⠀⠀⢸⡇⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠛⠘⠋⡄⠀⠀⠀⠀⠈⢿⣿⠆⠀⠀⢸⠁⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠰⠆⠀⡾⠛⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⢰⡇⠃⠀⠀⢘⠀⣀⣀⣀⣀⣀⣰⣶⣷⣤⣄⡠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⣤⣄⣤⣾⡟⠀⠀⢀⡀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠊⠂⠤⣴⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡀⠀⠀⢁⠀⠀⠀⢤⠀⠏⠀⢀⠀⠠
⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠁⡄⠈⠁⣾⠁⠀⠀⠒⢾⣷⠀⡀⡆⠀⣄⣠⣗
⠂⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠧⢵⣶⠶⠾⠿⠋⢀⡀⠀⠀⠈⠘⠋⠉⠛⠉⠉⠁
⢠⠄⠀⠁⠆⡀
⢄⠉⠦⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠃⠠⠤⠘⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢤⢶⡆⡀⠐⠠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠛⡛⠣⢛⡈⢎⡂⠋⠁⢠⣻⣧⢮⡔⣄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⢹⣶⣤⡔⣾⢠⡶⣼⣳⣤⡃⠀⠌⠪⠥⠞⣱⣸⡇⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⢠⢾⣷⣌⡞⣿⡿⣹⣿⣶⢿⣮⡻⣿⣿⣷⡀⠀⠀⠀⣽⡟⠉⠀⢀⡀⠀⠁⠳⣀
⠀⠀⠀⠀⠀⡴⢣⢷⣙⢿⡆⡿⣱⣿⣿⣿⣏⢿⣿⣮⡳⣿⡇⠀⠀⠀⠏⠻⢻⠿⢳⠷⠀⠀⠀⠈⢦
⠀⠀⠀⠀⣼⡷⢽⢼⣿⡷⡙⡤⣽⣍⡹⠶⡶⣴⣿⣛⠷⢾⠀⠀⠀⢄⣀⠀⠻⢮⣥⠴⠂⢀⠀⠀⠘⣧
⠀⠀⠀⣸⣷⣶⣇⣮⣻⣿⡏⣿⣮⣟⣿⡾⣰⣿⡿⠿⠿⠿⢳⠀⠀⠺⡽⢟⣀⣶⡀⠀⠀⠀⠀⡘⢠⣽⣇
⠀⠀⢀⣏⢿⢹⡿⠻⣿⢷⡋⣽⡿⢿⣷⣶⣶⣤⣟⣿⣿⡥⠏⠀⠀⠀⠀⠘⠯⡿⠆⠀⠀⠀⠀⣠⣷⣹⣿⡀
⠀⠀⢸⠁⠻⢓⣥⣴⣾⢟⣾⣷⣭⠖⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢰⣠⣤⠀⠀⢀⣠⢴⣮⣝⣛⡿⢸⡇
⠀⠀⢸⣤⣶⣾⢮⣟⠳⣛⣫⡽⠁⠀⣠⠀⡄⢀⢔⣤⣉⠦⢈⣠⠈⠀⠘⡋⠀⠀⣴⣿⢯⣿⣿⠿⣫⡇⣼⡇
⠀⠀⢸⠝⢉⣾⣿⢿⣾⣿⣶⣧⠀⠀⠀⢴⣒⢺⣼⠿⣧⠎⠃⠈⠀⢸⣿⢳⡞⢸⢿⠻⣟⣯⠒⣫⡾⢰⣿⡇
⠀⠀⠈⡇⠿⡟⢯⣿⣻⣯⣽⣾⠀⠀⠀⢶⣒⠃⠾⢴⠖⣶⡶⠀⢀⠈⡁⠅⣠⢿⣾⣳⣝⢿⣷⣾⢣⣿⣿⠁
⠀⠀⠀⢹⣿⠂⣜⢿⢟⠻⢍⣽⠀⠀⠀⠀⠀⣱⢶⣭⣞⡟⠛⠴⠨⣥⣶⡿⣿⣾⢣⣿⣿⢯⣿⠏⣛⣭⡏
⠀⠀⠀⠀⢫⢸⢹⣦⣠⡤⠛⠁⢀⣀⣤⠀⠀⠹⠸⣿⡿⡈⠀⠂⢸⣿⣿⣧⣿⢧⣿⣿⠟⣪⣵⡾⣶⡝
⠀⠀⠀⠀⠀⠳⣿⣿⣮⡀⠀⠠⠛⣡⣿⢀⠀⡀⢑⠚⠉⠀⠐⠀⠸⣟⣛⡧⠛⠞⠯⣶⣿⣤⣽⣞⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣟⠂⢀⣶⠟⠙⠁⢎⢁⡑⠈⠀⢀⡀⠀⠀⠀⠙⢯⣾⢱⣎⢿⣶⢬⣍⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠘⠙⠓⠈⠠⠀⠄⠽⠀⣀⣛⠋⣺⣷⡀⠀⠈⢻⣸⡿⡎⢿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⡛⢺⡵⠜⣥⣽⡁⠙⠉⠀⠀⠀⠀⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠐⠉⠀⠀⠀⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠔⢄
⠀⠀⢠⠋⡱⢤⡴⢦⠀⠀⠀⠀⠀⡃⢾⡉⣷⡸⠀⠀⣀⣄⡀⠀⣀⣠⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠘⠮⠧⢴⠃⡘⠀⠀⠀⣠⣤⣌⣒⣁⣀⣀⣤⡞⠁⢀⡙⣟⡉⠀⢈⣧⠀⠀⠀⡞⢉⣹⡤⣤⠔⠲⡄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⡇⠀⠀⠈⠉⠉⠀⢸⡇⠀⢯⡟⠉⠙⣿⡉⠙⣆⠀⠀⣇⠈⣺⣀⣸⠷⢀⡇
⠀⢀⣀⡀⢀⡴⠲⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠓⠶⠚⠳⠤⣴⠓⠃⣠⡇⠀⠀⠈⠉⠁⠈⠉⠒⠋
⠀⢸⠀⣿⠉⢹⠆⣸⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢹⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠦⡬⠋⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⣹⣇⡀⠀⠀⠀⠀⠰⢒⡤⢮⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣟⠃⠀⠰⡿⠀⠀⠀⣠⢤⡀⠀⠀⠙⠁⠀⢀⣸⣯⣷⣶⣶⣤⣄⠰⣈⡷⠚⠒⠁
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣿⣏⣀⠀⢀⣀⣀⡀⠉⠋⠁⢀⡴⠶⠶⢦⣼⣿⠿⠛⠛⠛⠻⢿⣷⣄
⠀⠀⠀⢠⣾⣿⠟⠋⠉⠉⠉⠙⠛⠿⡶⠋⠉⠉⠙⣦⣤⣤⣿⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣤⣤⡿⠿⠛⠛⠷⢾⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠈⣿⣧⠀⠀⠀⠀⣾⣿⠇
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⡿⠃⠀⠀⠀⢀⣿⣿
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠉⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣧⣄⣀⣀⣀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠙⠛⠻⠿⠿⠛⠋⠉⠉⠛⠿⠿⢿⣿⠿⠟⠋⠀⢀⣀
⠀⢀⣀⠀⠀⠙⢿⣷⣦⣄⣀⣀⣤⣶⣿⡿⠋⠀⠀⠀⢀⠎⢉⣲⣄⣠⠴⢤⠀⠀⠀⠀⠀⡔⢒⡖⢪⡄⢣
⢠⡏⣠⡵⢤⡴⠢⡙⠻⠿⠿⠿⢿⡛⠁⡠⢤⠀⠀⠀⠸⡀⠘⣏⠀⣸⠆⢠⠇⠀⠀⠀⠀⠡⣈⡳⠐⠓⠃
⠀⠳⠼⠦⢴⠋⣠⠁⠀⠀⠀⠀⠉⢸⡋⢱⢀⠃⠀⠀⠀⠉⠋⠉⠉⠑⠖⠋⢀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠲⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠘⠈⠈⠉⠀⠀⠘⠈⠠⠀⠃⠀⠀⠈

⠀⠰⠲⠂⠀⡴⡄⠀⠀⠒⠂⠀⠀⡤⢤⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡒⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠐⠂⠀⡔⠆
⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠁⠈⠁⠀⠈⠀⠀⠀⣴⠀⠠⣤⡆⠀⢋⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠱⡆⠀⠈⠀⠀⠀⠛⠓⠀⢶⡶⠀⢠⡆
⠀⠘⠇⠀⠀⠀⠀⠀⣈⣃⣃⠀⠀⠄⠠⠀⠀⠀⣰⣆⠀⠈⠁⠀⠉⠀⢀⣈⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠾⠷
⠀⠀⠀⠀⠀⠻⠗⠀⠻⠋⠿⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⢹⠀⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⢀⣬⠀⠃⠀⢠⣄⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠁⠈⢀⣤⠈⠁⢡⣤⡀⠀⠀⣀⣅⠈⠁⣠⡀⠀⢀⡈⠉⠁⣀⡀⠀⠀⠀⠀⠀⢀⡐⠀⢀⣀⣐
⠈⠁⠀⠀⣠⣄⣤⡀⠀⠀⠙⠀⠀⣠⡀⠃⠀⢀⡀⠀⠀⠀⠀⠀⠈⠦⠃⠀⠰⠃⠀⠆⠀⠀⠹⠀⣘⣀⡀⠀⣥⠀⠀⣀⡀⠀⠀⠀⠀⠀⠛⠉⠉
⠀⠤⡄⠀⣿⣿⣿⣧⠄⢀⣀⣀⠀⠙⠁⠀⠀⣤⣤⠀⢘⡆⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠛⠓⠀⠙⠿⠁⠀⠿⠂⠸⠿⠿⠀⠀⢤⡄⠀⠀⠐
⠀⠰⠃⠀⢙⡅⠉⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠿⠀⢸⡟⡇⠀⢸⣾⣶⡆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩
⠀⠠⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠠⠄⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠏⠙⠉⠀⠀⠀⠈⢋⡀⠀⠀⠀⠀⠸⡿⠛⠻⠗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠛⠋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢐⣞⣟⣿⣶⡄⠀⠀⠀⠃⠀⠀⠀⠀⠘⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⡿⢙⣿⡀⢿⠆⠀⠀⠀⠀⢐⡀⠉⢀⠈⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠡⡞⢹⡗⠈⠀⠀⠀⠀⠀⢸⡷⠄⠀⢳⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⣻⠋⠐⣰⠀⣠⡼⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠉⠀⠁⢀⠘⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡷⠀⠀⠀⠀⠀⢸⠝⣿⡆
⠀⠀⠀⠀⢰⣄⠈⣿⣿⠀⠀⠀⠀⢼⣆⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⢁⣴⣢⡶⠂⣀⠀⣴⣷⡄⠀⠐⣧⣀⣀⡤⣤⣄⡈⠀⠏⠸⡀
⠀⠀⠀⠀⠀⡇⣼⣿⣿⣀⡀⠀⠀⠀⠹⢷⠆⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⣃⣤⣾⡿⠙⣿⣤⠔⠛⣿⠿⠛⠓⠛⠿⢿⣟⠀⠁⠈⢂⡶⠀⠀⠁
⠀⠀⠀⠀⠀⢁⠸⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠋⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣀⠈⣷⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠙⡿⢿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⠀⢾⣿⣿⣿⡀
⠀⠀⠀⠀⢀⠀⠦⠚⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣇⠪⢿⣿⣿⣿⡇
⠀⠰⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠉⠀⠸⣿⣿⣿⡾
⠀⠰⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⡇⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⢀⡀⠀⠀⠂⢸⣿⣿⡇
⠀⢀⣆⠰⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣼⣆⠠⠑⠂⠀⠀⡰⠋⠀⠉⠉⠻⠻⣷⢶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣴⣾⣿⣿⣿⣿⣥⣦⣀⣀⣠⣿⣿⣿⡄
⠀⠀⠙⠳⠄⣀⠀⠀⠀⠀⠀⢀⡄⠀⠺⠇⡉⠀⡀⠀⠀⠈⠁⠀⢀⣤⠶⢴⡶⠷⢢⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣭⣁⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⣼⣟⣧⠀⣾⠿⣤⡁⠀⠀⠀⣤⣴⣿⣶⣾⣿⣿⣶⣧⣌⠑⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣻⣟⣿⣿⣷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠏⠉⠀⠀⢩⣄⣠⡟⠀⠀⠀⠈⠉⢻⠟⠸⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠊⢢⣼⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⡁⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⢹⢿⡿⣿⢿⡟⠋⣰⢠⣿⣿⣿⣯⣿⠃
⠀⠀⠀⠀⣷⠄⡀⠀⠀⢣⣀⣀⣤⣶⡇⠸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⣇⣸⡿⣿⡿⠟⠁
⠀⠀⠀⠀⠙⠷⣿⣦⣤⣄⡿⠉⣿⣿⣷⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣧⠴⣿⣿⣿⠃⣿⣟⣧⠐⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣶⣤⣀⣴⣾⡛⢁⠘⠀⠀⠀⠀⠀⠀⢀⣶⡾⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠘⢋⠉⠠⣤⣽⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣟⢻⣿⣏⠖⠀⠀⠀⠀⠀⠀⠀⣍⢽⣿⡿⢜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠐⠛⠛⠛⠉⢩⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⡉⠓⠀⠄⠀⠘⠃⠀⠒⢸⣿⣾⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠂⠀⠀⠀⠐⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢤⣮⡉⠀⠀⣠⣧⠀⠀⠀⠈⠀⠀⠀⠈⣮⣛⣛⡳⣾⣿⣽⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡽⠊⠁⠀⠀⠀⠀⠈⠀⠀⠈⠙⢿⠿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⣀⠰⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠁⢀⠋⠉⠉⠀⠀⢺⣏⠀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣐⣫⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣠⣾⣿⣟⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠁⠈⠛⠳⢶⣶⣶⣶⣶⣿⣿⡿⣿⣷⣧⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢤⠀⠀⠀⠀⠀⠀⣼⣉⣿⣿⡿⣿⠷⠶⣤⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡞⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⢻⣴⡴⣳⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠒⠒⢤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠒⠚⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣠⡇⠀⠀⠀⠀⠀⣄⠀⢀⠀⣀⡠⠤⠖⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⣰⠚⠉⠉⠁⠀⡇⠀⣀⣀⣤⠴⠛⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠙⠒⠦⢤⣀⡀⠀⠀⢸⠃
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠑⠾⠭⠖⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⠷⠒⠒⠲⠦⣄⣀⠉⠙⠒⢾⡀
⠀⠀⠀⢸⣇⣧⣀⣀⣀⣀⣀⣀⡠⠞⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠭⢭⣥⠄⠀⠉⠣⢄⣰⣆⣀⠀⠀⡏⠉⠓⠂⠋
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠒⢒⣲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣀⣀⣀⣀⣀⠀⠀⠈⠉⠑⣷
⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠉⠉⠉⠓⠲⢤⡈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡯⠴⠒⠉⠉⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠤⠤⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠤⢄⣀
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⣄⣀⡀
⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⢐⡷⠤⠤⢄⣀
⠀⠀⠀⠀⠀⡧⠀⢀⣠⠤⠖⠚⠉⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠤⠤⣀⢠⠇⠀⠀⠀⠈⢱⠄
⠀⠀⠀⠀⠀⣿⣋⣁⣀⣤⡴⠒⠛⠉⠉⠛⢻⣤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠉⠓⠚⠋⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠈⠉⠉⠁⢰⢃⣀⡤⠤⠤⠖⠚⠁⠀⠀⠲⠶⣒⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠲⠤⠤⠤⠤⠤⠶⠦⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⣀⣀⣀⡠⠤⠤⠤⠤⠤⣀⡈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠭⢍⣥⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠉⠉⠉⠙⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⠀⠀⠀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣭⣭⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠙⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣸⣿⣿⣿⣿⣿⢿⣿⡏⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⣿⣿⣿⣿⠃⠸⡿⣅⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⢸⣿⣿⣿⣿⠋⠰⠁⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⣀⣤⠄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⣿⠛⢿⣿⣿⣿⣿⣥⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠈⠃⠀⠀⠉⠉⠻⢿⣿⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠖
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣶⠄
⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣾⣿⣿⠷
⣷⣶⣶⣾⣿⣿⣦⣤⣤⣴⣯⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢍⠁⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠃⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡶⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡤⠠⣄⡜⠋⠹⡀⠀⠀⢠⡆⢀⠦⣄⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢇⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⠷⡄⠀⠀⢀⡇⠀⢳⡀⠀⣰⠃⢸⡀⠀⠀⠀⣀⠀⠀⠀⢀⡖⠲⡆
⢀⡠⠊⠁⠀⠀⠀⠀⠁⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⢦⡀⡼⠀⠀⠀⠻⡴⠃⠀⠈⡇⠀⣠⠞⡻⠰⡖⠂⠋⠀⠀⠻⢠⣤
⠉⠒⠠⣤⠀⠀⢀⢀⣀⡀⠠⠖⠋⠀⠀⠀⠀⠀⣟⠒⠦⣄⡀⢸⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⡇⠀⢈⠆⠀⠀⠀⠂⣾
⠀⠀⠀⢸⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣄⣀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣸⣤⣴⡷⠤⡤⠟
⠀⠀⠀⠀⣧⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠃⠀⢈⠻⡀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⣹⠛⢦⡀⠀⠀⠀⠘⠛⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡴⠤⣄⠀⠀⠀⢰⡖⠒⠛⠳⡆⢠⡤⠐⠋⠀⠀⡠⢶⣉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⢄⠀⠀⠀⠀⣴⣃
⠀⠀⠀⠀⠀⡜⠀⠀⠽⠦⢤⣤⡀⠙⠢⣄⠀⠛⠚⠁⠀⠀⠀⡜⠁⠀⠈⠉⠒⠤⣤⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠉⠒⠒⢤⣤
⠀⠀⢶⡐⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣈⣳⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⡦⠀⠀⢀⡀⠀⠀⠸⣞⠉⠉⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⡸⠁⠰⣎⠁⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⠓⣻
⠀⠀⠀⠀⣇⣀⡠⠞⠉⠉⠘⠚⠉⠑⢤⡀⠀⠀⠀⢀⠇⠒⠀⠀⠤⠤⠀⣀⠀⠀⠀⣃⠀⠠⠔⠊⠁⠀⠀⠀⠀⠰⠁⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⠛⠢⡄⢀⣀⣨
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠶⠒⠒⠋⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣀⣉⡶⠀⠀⠀⠀⣧⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⢛⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠋⠀⣠⠔⠉⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⡰⢻⣄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡞⠉⠳⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⠉⠓⢄⠑⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡶⠦⠿⢦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⣀⣀⠀⠉⠂⢵⣼⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⣄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠙⡄⠀⣸⣠⡟⠲⠛⠁⠀⠀⠀⠀⡴⠋⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠁⢈⠉⠉⠉⠁⠀⢠⣦⠀⠀⠀⠀⠀⠀⠑⡄⠀⣷⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⢍⡁⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠉⣇⠀⠀⢀⡴⠋⠸⡆⠀⠀⢀⣶⡀⠀⠈⢦⣿⣮⣀⠀⠀⠀⢸⡟⠒⠦⢤⣀⠹⡄⢀⢀⠀⠀⠀⠀⠀⠀⢸⣀⡶⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⠏⠀⠀⠀⢳⡀⢀⡞⠀⢳⡀⠀⣼⠋⠀⠈⠛⠲⢤⣘⡆⠀⠀⠀⠈⠙⢋⠏⠈⢳⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠠⠤⠄⠚⠀⠀⠀⠛⠒⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢠⣀⠀⢁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠊⠀⠀⠀⠀⠀⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⣀⡔⠁⠉⠳⠾⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠟⠒⠤⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠛⠿⣷⣶⣶⠿⠛⠉⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠛⠿⢿⣷⣶⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢻⣧⣀⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣼⡿⠁⠀⢀⣾⡿⢿⡿⠛⠛⠛⠻⢶⣶⡶⠾⠿⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣤⣾⠀⠀⠀⠀⠀⠈⣿⣄⡀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⢀⡟⢹⣷⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠶⠟⠛⠻⢷⣶⣶⣶⠿⠿⠿⠋⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⠛⠛⣿⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣤⣤⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠚⠛⠛⠋⠙⢿⡏⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠈⢻⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣿⠃⢀⣠⣶⣿⠿⠿⠿⢶⣤⡀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠻⠷⣦⡀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠉⠛⢿⣿⣿⣯⣥⣀⠀⠀⠀⠉⢻⣦⠀⢀⣴⠟⠉⠀⠀⠀⠀⢀⣤⡾⠿⢾⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢠⣾⡿⠋⠉⠉⠙⢿⡄⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣴⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠻⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠛⠉⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⣷⣄⠀⢀⣴⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠈⠻⣷⡿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠿⣆⠀⠀⠀⠀⡼⠿⡆⠿⠛⠛⠛⠀⠀⠀⢰⠛⠋⡷⠀⠀⠀⠀⣼⠛⠛⣿⠄⠀⠀⠀⠀⣼⡟⢻⣦⠀⠀⠀⠀⣸⠿⢿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠠⠀⢰⣿⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⢠⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠂⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⢤⠄
⠀⠀⠀⠀⠚⠙⠛⢰⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠋⠋⠉⠁⢰⡏⠀⠙⣧⠀⠀⠀⠀⢠⣾⠋⢻⡆⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⣿⠀⠀⠀⠀⢸⣿⡆⢼⣷⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡧⠄⠀⠀⠀⠀⠀⢶⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠉⠀⠀⠀⠀⠀⠹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡴⢿⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠐⢭⡢⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣣
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣵⣄⡀⢀⣀⣠⣾⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈⢿⡆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣷⠋⠙⠳⣿⣿⣿⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⡇⠀⠀⢽⣿⣿⣿⣄⡤⠴⠂⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠒⠚⠛⣋⣹⣿⣿⡿⡧⠀⠀⣾⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠘⣸⣷⠀⠀⠀⠀⠀⠀⠀⢉⣼⣿⣿⠛⡇⠀⠀⣠⣿⡿⣿⣿⣍⡉⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁
⠀⠀⠀⠀⡿⣿⣷⡄⠀⠀⠀⠀⣠⣾⡿⣿⣽⣿⣿⣶⣿⠿⣽⣾⣷⣿⣿⣿⣷⣤⣀⣀⣠⣴⣿⣿⣿⣿
⠀⠀⠀⠀⢱⣿⣿⣿⣦⣤⣶⣿⡿⣽⣿⣿⣿⠟⡿⣿⡇⠀⢿⠛⠿⡻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢿⠿⣿⢿⡿⠛⢉⣴⣿⣿⣿⠃⠘⠁⣿⠀⠀⢸⠀⠀⠈⠈⢻⣿⣦⠈⠙⠻⢿⣿⠏⡼
⠀⠀⠀⠀⠀⠈⠦⠚⠁⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⢿⠀⠀⠘⡄⠀⠀⠀⠀⢹⣿⡳⡀⠀⠀⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⣇⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠻⣿⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⢾⡻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣆⠀⠀⠀⡇⠀⠀⠀⠸⡀⣠⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢝⣦⡀⠀⢇⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆

⠨⣕⠢⠁⠀⠀⠀⠀⠀⠀⠀⣀⠨⣑⠬⠁⠀⠀⠀⠀⠀⠀⠀⡀⢭⡓⠌⠀⠀⠀⠀⠀⠀⠀⢀⡀⢍⡢⠍
⠍⠀⠀⠀⠀⠀⠀⠀⢀⠠⣕⠢⠅⠀⠀⠀⠀⠀⠀⠀⣀⠨⣑⠬⠑⠀⠀⠀⠀⠀⠀⠀⡀⠬⡒⠌
⠀⠀⠀⠀⠀⢀⡀⢄⡲⠍⠂⠀⠁⠀⠀⠀⠀⢀⠠⢄⠢⠑⠂⠀⠀⠀⠀⠀⠀⢀⠠⣐⠮⠑⠀⠀⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⡀⠤⡒⠬⡒⠀⠁⠀⠀⠀⠀⠀⠀⢄⡲⠍⡒⠀⠁⠀⠀⠀⠀⢀⠠⢔⠢⢑⠂⠈⠀⠀⠀⠀⠀⢀⠠⣐⠮⢑
⠀⠤⣐⠪⠑⠊⠁⠀⠀⠀⠀⠀⠀⠄⡐⠬⡒⠈⠀⠀⠀⠀⠀⠀⠠⢄⡲⠍⠂⠁⠀⠀⠀⠀⠀⠀⠤⢐⠢⢕⠂⠁
⠢⢕⠂⠁⠀⠀⠀⠀⠀⠀⠀⣐⠪⡑⠈⠁⠀⠀⠀⠀⠀⠀⠄⡐⠬⡒⠈⠀⠀⠀⠀⠀⠀⠀⢀⡒⢌⠂⠉
⠭⠀⠀⠀⠀⠀⠀⠀⢒⠢⢕⠂⠥⠀⠀⠀⠀⠀⠀⠀⣂⠨⣑⠨⠅⠀⠀⠀⠀⠀⠀⠀⡂⠬⡓⠈⠄
⠀⠀⠀⠀⠀⢀⡀⢌⡲⠍⠂⠀⠀⠀⠀⠀⠀⢀⠠⢍⠢⠁⠂⠀⠀⠀⢀⡀⢀⣀⠠⣑⠮⠁⠀⠀⣀⠀⣀⡀⣀⣀⢬
⠀⠀⠀⡀⠤⡐⠬⠐⠂⠀⠀⠀⠀⠀⢀⡀⢄⡲⠍⠒⠀⠀⠀⠀⠀⠀⣇⠈⣍⠠⠽⠾⠿⠿⠿⣿⣿⣿⣿⠯⣕⠮⣷
⠀⠬⣐⠪⠑⠈⠀⠀⠀⠀⠀⠀⠀⠬⡐⠬⠒⠈⠀⠀⠀⠀⠀⡀⠠⢅⡒⠌⠒⠚⠒⠐⠒⠒⠒⡛⠻⢝⠺⠝⠚⠛⠋
⠢⠝⠂⠁⠀⠀⠀⠀⠀⠀⠠⣐⠪⠑⠀⠁⠀⠀⠀⠀⠀⠀⠠⡐⠬⠓⠈⠀⠀⠀⠀⠀⠀⠀⢄⡒⠍⠂⠈
⠉⠀⠀⠀⠀⠀⠀⠀⢄⠢⢝⠂⠁⠀⠀⠀⠀⠀⠀⠀⣐⠢⣑⠈⠁⠀⠀⠀⠀⠀⠀⠀⡐⠬⡓⠈
⠄⠀⠀⠀⠀⢀⡒⢌⣒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠢⢝⡂⠁⠀⠀⠀⠀⠀⠀⠀⣐⠪⣑⡊⠁⠀⠀⠀⠀⠀⠀⠀⣐⠬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠿⠙⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣾⣿⠟⠙⠉⠀⠀⡀
⠀⠀⠀⠀⢀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣼⣿⠏⠁⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠛⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡀⡀
⠀⠀⠀⠀⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⠻⣿⣿⠇
⠀⠀⢠⣾⣿⣿⣿⣿⣦⡂⠀⠀⡀⢀⣀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠸⠋
⠀⠀⠘⡿⢿⣿⣿⣿⡿⠿⠾⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠙⣆⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⡁
⠀⠀⠀⠀⠘⡎⠇⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐
⠀⠀⠀⠀⠀⠑⢄⣀⣂⣀⣠⣤⣶⣾⠋⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣠⣀⠠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢝⠿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠩⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⣠⣴⣿⣿⠇⠀⠀⠀⠀⢠⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠙⠿⣿⣿⣷⣄⣤⢶⣿⠟⠙⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠁⠀⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣲⢻⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⢳⡰⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠸⢀⣯⡿⣟⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⡿⣯⣇⠸⢀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⡡⣢⡟⣦⡽⠻⣉⣉⡷⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠠⠴⣏⣉⡽⠿⣥⡟⣧⠲⡁
⠀⠀⠀⠀⠀⠀⠀⢧⠘⣿⣟⣭⡿⠂⠀⠀⠀⠀⢀⠠⢀⣤⡶⠟⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⣦⣄⠀⢀⠀⠀⠀⠀⠀⢺⣯⣝⣿⡏⢠⠇
⠀⠀⠀⠀⠰⣄⣼⢆⣹⠟⠡⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠄⣀⣠⣦⠶⠶⠶⠶⠶⣦⣤⣀⡀⠌⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⠤⠝⢿⣁⢾⡀⡰
⠀⠀⠀⠀⢸⡁⢿⣺⢿⣽⣟⣀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣴⠞⢋⠡⠀⠀⠈⠀⠀⠀⠐⠀⢉⠛⢶⣄⠀⠀⠀⠀⠐⡄⠀⠀⣀⣘⣿⣽⢿⣺⠇⣱
⠀⠀⠀⠀⢠⡙⢸⣿⢋⠭⠟⠈⠀⠀⢀⣦⠀⠀⢀⣴⠟⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡉⢷⣄⠀⠀⣠⡇⠀⠀⠈⠘⠯⠍⢻⣿⠘⣡
⠀⠀⠈⢳⡸⣏⣾⡗⣲⢆⣀⠀⠀⠀⣼⠇⠈⢠⡿⢡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠹⣧⠈⠀⢿⡄⠀⠀⢀⣀⣶⡒⣿⣎⡿⣰⠋
⠀⠀⠀⠹⣄⢱⣿⡝⣋⡽⠀⠀⢀⠼⠟⠀⢠⡿⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠹⣧⠀⠘⠿⢀⠀⠀⠸⣍⡛⣽⡶⢃⡼⠁
⠀⠀⠀⠐⣦⣌⣿⣡⣴⠂⡀⠀⠂⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠆⠀⡀⢲⡤⣹⣏⣤⡖
⠀⠀⠉⣲⠹⣆⣿⣰⠟⣻⠁⠀⡆⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⡆⠀⢹⡓⢷⣺⣇⡾⢳⡊
⠀⠀⠀⠈⠲⠌⢿⡇⣊⡅⢀⠀⠃⠀⠀⠀⢸⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠂⢀⠀⣍⡂⣿⠏⠴⠊
⠀⠀⠀⣀⠘⣶⣺⣿⢹⡗⣯⠀⠀⠰⣶⠀⠘⢿⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣸⠟⠀⢰⡶⠀⠀⢨⡗⣿⢹⣿⣲⡞⢀⡀
⠀⠀⠀⠈⢼⣞⠓⢽⣾⡰⣫⠀⣀⠀⢻⣆⢀⠘⢷⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣰⠟⠄⢀⣾⠃⢀⡀⢠⡳⢸⣾⠕⢋⣺⠌
⠀⠀⠀⠀⠀⠈⣅⣨⣹⣾⣹⡖⣧⠀⠀⠟⠀⠀⠈⠻⣦⡑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣡⡾⠋⠀⠀⠘⡇⠀⢠⡗⣾⣹⣾⣩⣀⡉
⠀⠀⠀⠀⠀⢠⠬⡻⠶⣹⣾⡠⢋⡄⡰⠧⡀⠀⠀⠀⠈⠛⢶⣤⣁⠂⠠⠄⠀⠀⠤⠀⢂⣩⣴⠞⠋⠀⠀⠀⠀⡠⢷⡀⣄⢃⣸⣾⡱⠞⣥⠤
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⣛⣷⣎⢿⠏⡆⠈⢢⡀⠀⠀⣠⠊⠈⠙⠛⠛⠳⠶⠶⠛⠛⠛⠉⠀⢢⡀⠀⠀⣠⠊⠀⡏⢽⢟⣶⣟⠓⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⢶⣙⣿⣦⢁⣷⣼⠀⠁⠉⠙⠻⢶⣴⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠛⠉⠀⠁⢸⣴⣇⢡⣾⣟⣱⢾⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠶⠶⢊⣩⠿⣦⣻⠀⠀⠀⠀⠀⠀⠀⠐⠠⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⡾⢯⣉⠲⠶⠞⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢹⡛⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠚⡻⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠚⠓⣶⡼⢿⣾⣷⣾⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⠏⠀⠀⠀⡰⣿⠃⢋⣴⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⣠⠋⠀⠀⢺⡂⠁⠀⠐⠛⠛⠛⠿⠛⠶⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢽⠀⠀⡁⠀⠠⢔⣾⡅⠀⢀⣻⣛⣻⡟⡟⢛⡟⠉⠉⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⡾⠏⠀⡇⠀⢀⡼⣻⢸⣷⣦⣽⣏⢙⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣇⠐⠡⣰⡇⠻⠛⣧⡈⣻⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⢀⣠⣤⣆⣀⣨⣿⣿⣧⠶⢻⣿⣿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠲⢶⡿⠟⠛⢉⣽⠟⠉⠁⢈⣿⡿⠛⣧⣠⣼⡿⠿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠋⠌⣿⠂⢤⣾⡟⠊⠁⢉⣿⢻⡗⢂⡾⣻⡟⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⢀⣁⣈⣆⠔⠋⠀⠀⢠⣿⣿⣿⣴⠪⣭⣬⡙⢦⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢚⣿⣿⣏⣀⠀⣠⣟⣯⡿⠋⠁⢚⣃⣨⣤⣤⣤⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣥⣽⣿⣿⣿⡿⠿⠿⠿⠿⠿⠻⠛⠛⠋⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡷⢋⠙⠉⠀⢀⡬⠁⠈⠋⠽⡛⡲⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⢁⣠⠤⠂⠀⠈⠑⠒⠀⠀⠀⠐⠬⣩⣽⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⡄⡘⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⢱⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣠⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣣⠋⠀⠀⠄⠀⠀⠀⠀⠀⢰⠀⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢋⡆⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢧⣿⣇⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⡿⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡴⢾⣿⡿⠿⠛⣉⢁⣼⣵⣴⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⡗⣸⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⠀⢀⣼⠃⣽⢋⠇⠀⠰⡏⣸⣿⡟⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⢿⣿⡟⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⡿⣿⣿⣟⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠜⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣷⣿⣷⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣎⢿⣿⣿⣿⡿⠿⣿⣟⠻⣿⣧⣶⡄⠀⠀⠀⠀⢾⢟⣫⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠈⠸⢿⣿⣿⣿⣿⣹⢿⣿⣿⣿⣿⣿⡛⠛⠋⠥⣤⡤⣀⠀⠰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡝⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣁⡛⠋⠠⠬⠐⣣⡐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⢘⣓⣀⡈⠱⠶⠀⠶⢿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⢈⡀⡱⢿⣿⣿⣿⣇⣻⣿⡿⣝⣿⡿⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠋⠉⠛⠻⠿⠿⠿⠶⠖⠀⢀⣀⣈⣤⣥⣴⣼⣿⣿⡿⢿⡾⡿⢽⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⢿⣿⣿⡷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠺⢿⡓⠲⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⠀⠀⠀⠀⠀⠀⠉⠻⣝⠲⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠶⠦⣤⣸⠃⠀⠈⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⢄⡴⠋⠀⠀⠀⠀⠀⠈⣧⠠⣤⣤⣤⠤⠤⠴⠖⢲⠿⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢰⡏⠀⠀⠀⠀⠀⠀⢲⣴⣠⡼⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠎⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢳⣄⡀⠀⢀⣀⣠⡴⠋⠁⠀⢀⣴⠟⠛⠳⠶⣤⣀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⣉⡽⠟⠋⠉⠷⣄⣀⣠⡾⣅⠀⠀⠀⠀⠀⠉⠳⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠈⠉⣻⠀⠈⠑⠄⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣠⠶⠛⠉⢹⡀
⠀⠀⠀⠀⠀⢴⠶⠿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⠶⠶⢚⣁⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⡴⠛⠉⠉⢯⠉⠉⠁
⠀⠀⣀⣠⣤⣼⢶⣿⣦⡤⠤⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⢾⣦
⠈⢉⣁⡤⠤⠴⠒⠛⢿⣉⣉⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⢷⠖
⠀⠀⠀⢀⣀⡤⠶⠒⠋⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋
⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣈⣹⠶⢯⡉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡳⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠛⠳⣄⡀⠉⠳⢤⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⣀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠖⢶⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢻⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣰⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⡴⣰⠋⠏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠻⣆⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣰⠋⡿⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠛⠳⢦⣄⠀⠀⠀⣀⣠⢾⣥⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⢀⣴⠿⣤⠤⠴⠖⢒⡛⠉⠉⡀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢾⠀⠀⢸⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣄⠘⡇⠀⢸⠀⠀⠸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿
⠀⠀⠀⠀⠀⡔⠒⣄⣀⠀⠀⢸⡄⠀⢹⡇⣠⠞⠛⠓⠶⠞⠛⠓⢦⠀⣿⠀⠀⠀⠀⠀⢠⠚⢲⣀⣀
⠀⠀⢀⡞⢻⡇⠀⡏⠉⡇⠀⠀⣧⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠀⣸⠂⣿⠀⠀⠀⢰⠋⢻⠀⢸⡇⢸⡆
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡟⠛⡆⢸⡄⠀⠀⠈⠳⣄⠀⠀⠀⣀⡴⠃⠀⡿⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡏⢻
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡇⠀⣧⠀⢳⡀⠀⠀⠀⠈⠳⣤⠞⠉⠀⠀⢠⡇⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡇⢸
⣞⠳⣄⡇⠘⠃⠀⠃⠀⠇⠀⣿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⡟⢳⣼⠀⠘⠀⠘⠁⠸⠃⠸
⢹⠀⢹⡇⢀⡤⢤⣠⠤⣄⠀⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣧⠀⣿⠀⣠⠤⣤⡤⢤⡄
⠈⡇⠈⠁⢿⡀⠀⠀⠀⣸⠂⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠈⠘⣇⠀⠀⠀⢀⡿⢀
⠀⢻⡀⠀⠈⠛⢦⣠⠞⠁⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠈⠳⣄⡴⠋⠀⢸
⠀⠀⠳⣄⠀⠀⠀⠁⠀⠀⢰⠇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⣶⣶⠶⠶⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣾⣷

⢀⡀⠀⣴⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣆⠀⢀
⢨⡇⠀⣿⡄⢀⡀⠀⣿⡇⠀⠀⠀⣶⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⣶⠀⠀⠀⢸⣿⠀⢀⡀⢠⣿⠀⢸
⢸⡇⠀⣿⡇⢀⠁⠀⣿⡇⣤⡄⠀⠺⠀⣽⣇⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣸⣯⠀⠟⠀⢠⣤⢘⣿⠀⠈⡀⢸⣿⠀⢸
⠀⡃⠀⣿⡇⠀⠀⢠⣿⠁⣿⡇⠀⢽⠀⠛⠛⠙⠋⠁⠀⠀⠀⠀⠈⠙⠋⠛⠛⢀⡧⠀⢸⣿⠈⣿⡆⠀⠀⢸⣿⠀⢘
⠀⢄⠀⣿⡇⠀⠀⢸⣿⠀⣿⡇⠀⠊⠉⠑⠈⠋⠋⠉⠀⠁⠀⠀⠙⠙⠋⠁⠋⠋⠘⠂⢸⣿⠀⣿⡇⠀⠀⢸⣿⠀⠠
⢠⡈⠀⣿⡇⠀⠀⢸⣿⠀⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣾⣿⠀⣿⡇⠀⠀⢸⣿⠀⢁
⠀⡇⢀⣿⡇⢠⡄⢸⣿⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣦⠀⠀⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣿⡇⢠⡄⢸⣿⡀⢸
⠸⡅⢸⣿⠄⣿⣷⣈⡉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣁⣼⣿⠐⣿⡇⢨
⠀⡅⢸⣿⡇⡛⠛⠛⢉⣀⣀⣀⣀⣀⣀⣀⣁⣈⣁⠀⠀⠀⠀⠀⠀⣈⣁⣈⣀⣀⣀⣀⣀⣀⣀⣉⠛⡛⢛⢰⣿⡇⢸
⢀⡇⠸⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠇⢸
⠀⠑⠆⠒⠲⠴⠢⠴⠒⠒⠦⠈⠑⠀⠂⠒⠶⠶⠶⠲⠆⠀⠀⠰⠖⠶⠶⠶⠒⠐⠀⠊⠁⠴⠒⠒⠶⠶⠢⠒⠒⠰⠊
⠀⡠⠆⠤⠤⠲⠖⠲⠤⠤⠖⢀⡠⠀⠀⠠⠶⠶⠶⠴⠆⠀⠀⠰⠦⠶⠶⠶⠤⠠⠀⢄⡀⠲⠤⠤⠖⠢⠖⠦⠤⠰⢆
⠈⡅⢰⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⡆⢨
⠀⡃⢸⣿⡏⣥⣤⣤⣈⠉⠉⠉⠉⠉⠉⠉⡉⢉⡉⠀⠀⠀⠀⠀⠀⣉⡉⢉⠉⠉⠉⠉⠉⠉⠉⣁⣤⣤⣬⠨⣿⡇⢘
⢐⡃⢸⣿⠂⣿⡟⢉⣁⣀⣀⣀⣀⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⣀⣀⣀⣀⣀⣉⡉⢻⡿⠐⣿⡇⢈
⠀⡇⠈⣿⡇⠘⠃⢸⣿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⠀⠀⠛⠿⠿⠿⠻⠟⠛⠛⠛⠛⠛⠻⣿⡇⠈⠃⢸⣿⠁⢸
⠘⢁⠀⣿⡇⠀⠀⢸⣿⠀⣿⡿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⢿⣿⠀⣿⡇⠀⠀⢸⣿⠀⡈
⠀⠊⠀⣿⡇⠀⠂⢸⣿⠀⣿⡇⠠⢄⣠⡀⢀⣄⣤⡄⠀⠀⠀⠀⣀⣤⣠⡀⣀⣄⡠⠄⢸⣿⠀⣿⡇⠀⠀⢸⣿⠀⠐
⠀⡄⠀⣿⡇⠀⠀⠘⣿⡀⣿⡇⠀⠻⠀⣤⣤⣠⣄⡀⠀⠀⠀⠀⢀⣠⣄⣤⣤⠀⡗⠀⢸⣿⢀⣿⠃⠀⠀⢸⣿⠀⢨
⢸⡇⠀⣿⡇⢈⡀⠀⣿⡃⠛⠃⠀⣴⠀⣻⡏⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⢹⣟⠀⣦⠀⠘⠛⢨⣿⠀⢀⠁⢸⣿⠀⢸
⢘⡇⠀⣿⠃⠈⠁⠀⣿⡇⠀⠀⠀⠿⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠿⠀⠀⠀⢸⣿⠀⠈⠁⠘⣿⠀⢸
⠈⠁⠀⠻⠀⠀⠀⠀⠛⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠟⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠓⠲⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣄⡀
⠀⠀⣀⣤⠶⠚⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀
⣠⠞⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠛⠶⠶⠤⣄⠀⠀⠸⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⡇⠀⢀⣀⡤⠖⠋⣹
⠀⠀⠀⣰⠏⠀⠀⠀⠉⠛⠿⣍⡉⠉⠉⢻⠓⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠋⠁⠀⢀⡼⠃
⠀⢠⡞⠁⠀⠀⢀⣀⣠⣤⣤⣤⣽⣷⣦⣼⠀⠀⠀⠀⠀⠉⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠟
⣰⠏⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣧⣄⣀⣀
⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⣤⣤⣤⣤⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢀⣠⡴⠞⠉⠀⠀⠀⣀⣠⡴⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣿⣵⣶⣶⣶⣶⣟⣋⣉⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁