Rain Emojis & Symbols

⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢀
⢹⠄⡄⠀⠛⠀⠀⢻⡄⠀⢸⡇⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠸⡇⠀⠙⠁⠀⠀⢸⠀⠀⠀⠀⠰⠇⠀⢀⠀⢿⠀⠀⠀⣯
⠀⠰⡽⠀⠀⢰⠀⠈⠀⠀⠀⠁⠀⠀⠀⡷⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢘⡄⠈⠀⠀⢰⡄⠀⠀⠀⢮⡆⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢲⠇⠀⠀⠀⠀⠀⢀⡀⠀⠸⡂⠀⠀⣵
⢸⡀⠀⢰⡄⠀⠀⠀⠀⠘⠁⠀⠀⠸⡄⠀⢸⡆⠀⠀⠀⠀⢴⠀⠨⡇⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⡔⡄⠘⠆⠀⠘⠃⠀⠀⣀
⠈⠀⠀⠘⠃⠀⢠⣆⠀⠀⢰⡀⠀⠘⠃⠀⠀⠀⠀⣀⣀⣀⣿⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠐⣆⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⣠⠀⢀⡄⠀⠋⠀⠀⢈⣀⠤⣠⢶⡶⢒⠩⣀⠦⠅⠒⠈⢋⢩⠅⡒⠒⠶⠦⣤⣄⣀⣀⡋⠀⠀⠀⠀⠀⠀⢸⢣⠀⠸⠆
⠀⠀⢷⡇⠘⠃⠀⣀⡤⠾⢁⣰⡪⢃⠡⡲⢐⡩⠔⠊⠀⠀⠀⠋⣂⢥⡐⠠⠄⠀⠀⠈⠑⠾⣬⡉⠒⠢⠤⣀⠀⠈⠛⠀⠘⠃
⢰⡀⠀⠀⢀⠔⣪⠅⠁⢠⢊⠕⡪⢂⠥⣊⠅⣊⠁⠀⠀⠀⠀⠀⢨⡈⡡⠐⠂⠭⡄⠀⠀⠈⠈⠙⣔⠡⠂⠤⠉⠲⢄⡀⠀⢸⡄
⠘⠃⢠⠜⠥⢂⠂⠀⢠⢃⢔⡡⣊⠕⡪⢐⠩⠀⠀⠀⠀⠀⠀⠀⠀⡆⠅⢂⠡⠄⠐⣀⠀⠀⠀⠀⠈⢫⢔⡨⢐⡀⠀⠙⢆⠈⠁
⠀⡴⡳⣄⠬⠀⠀⠀⣎⢔⠡⠪⡰⢝⠨⢐⠬⢐⠀⠀⠀⠀⠀⠀⠀⠳⠞⡀⠌⢑⣀⡀⠀⠀⠀⠀⠈⠄⢳⡪⠐⡠⠄⣀⠢⡳⡀
⣼⠚⠃⠉⠚⠒⠤⣀⠇⡡⣠⠮⠴⠆⠚⠓⠚⠐⠖⠴⢤⣄⡀⠀⠀⢈⢵⡀⢡⣐⣒⣮⣍⣙⣀⣂⣀⠤⠎⢗⣡⡴⠷⠒⠓⠓⠷
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠳⢤⣸⡵⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⡖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⢠⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⣉⣁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠠⠄⢂⠔⡠⢂⠄⣊⠔⡠⠐⡠⢒⠄⡠⢂⠄⡠⢂⠔⡠⢂⢔⠠⡠⢀⠄⡀⢄⠄⡠⢀⠄⡀⡀⢀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁⠈⠐⠁⠋⠐⠁⠊⠖⠑⠋⠊⠐⠁⠊⠐⠁⠊⠒⠕⠡⠪⠂⠕⠡⠊⠔⠡⠊⠞⡕⠰⢢⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠓⢦⡤⠶⢤⣀⡀⠀⠀⠀⣠⠴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠀⡴⠋⠉⠉⠛⣦⣰⣏⠐⠀⠀⠀⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠀⠀⠀⣠⠤⢼⠁⠀⠀⠀⠘⠁⠀⠈⠉⠀⠂⠀⠀⠀⣼⠶⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⡞⠁⠀⠀⣀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⠞⠉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠋⠁⠹⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣂⣁⠀⠀⠀⠀⠠⠀⠀⢀⡼⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠐⠲⠤⠴⠒⠀⠀⠀⠲⠀⠀⠀⣠⠋⠉⠓⠤⠄⠀⠀⠀⠐⠒⣉⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⠀⠈⠑⠶⠖⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠖⠋⠡⡀⠀⠀⠀⠀⢠⠀⠀⢀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠲⣦⡀⠀⣀⡼⠻⣤⣙⠢⣌⣀⡥⠆⠀⠤⣁⢀⣀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⣉⢠⢂⠀⠉⠉⠉⠙⠦⣤⡤⠞⠉⠉⠹⣄⠀⠀⠀⠀⠀⣀⣀⣠⠏⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⡟⢰⠇⡎⡞⠀⠀⣶⡇⠀⢀⡄⢠⠄⣾⡇⠀⠉⠳⠦⠤⠴⠚⠁⠈⢁⠀⠂⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⢁⡟⡘⠸⢀⠃⢰⡟⠀⠀⣼⢁⡟⣸⡾⠀⠁⣠⡄⠀⢀⡤⢰⡇⡜⡞⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠇⣼⢡⢁⠃⠌⠀⣽⠁⠀⢰⠇⣼⢡⢷⠃⠄⠠⣿⠁⠀⣼⠃⡞⢰⢱⠁⠄⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡟⢰⠃⡎⡎⡘⠀⣰⡟⠀⢀⡟⢰⡇⣾⡟⠀⠀⢰⡇⠀⢰⡏⣸⠃⡇⡆⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡾⢁⡏⡰⢸⢡⠃⢠⣿⠁⠀⣼⠁⡞⣸⣽⢁⠃⢰⣿⠁⠀⡾⢀⡏⡸⡸⢀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠇⡼⢠⢃⠇⠆⠀⣾⡇⠀⢰⡇⣸⢁⣿⡏⠄⠀⣼⠇⠀⣸⠇⣼⢠⢇⠇⠌⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⡏⢰⠃⡄⡘⠀⠀⡸⡟⠀⢀⡿⢀⠏⣸⡿⠰⠀⢰⡿⠀⢀⡟⢠⠇⡎⡼⠠⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⢁⡏⠸⢠⠁⠀⢠⣻⠁⠀⣼⠃⡜⢠⣻⠃⠀⢀⢿⠃⠀⣼⠁⡜⠐⢱⠃⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠇⡼⢠⢃⠇⡀⠀⢾⠇⠀⢰⡏⢰⠃⣞⡟⠀⠀⡜⡎⠀⢰⡏⢠⠁⠄⡎⠀⠀⡘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡎⢐⠃⠎⡌⠀⠀⢈⡾⠀⠀⣾⢀⡇⡸⣼⠁⠀⠰⡽⠀⠀⡾⠀⠇⠰⢰⠁⠀⢀⠱⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⠀⡎⠸⠠⠀⠀⠀⠾⠃⠀⢸⠃⡼⢠⢣⠇⠀⠀⢣⠇⠀⢸⠇⠸⠀⠀⠇⠀⠀⠀⠃



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

⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢀⡄⠀⠀⠀⠀⠀⠲⠁⢸⠀⠀⠀⢸⠈⢃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠀⡀⠀⠀⠀⢁⡀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠓⠤⠈⠉⠈⠁⠂⣀⠠⠄⠀⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢰⠀⠀⠀⠀⠠⠅⠉⠈⠉⠉⢈⠝⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⠀⢈⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡐⢩⠀⠀⠀⠀⠈⡁⠀⠄⠀⠀⠐⠈⠁⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢠⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠁⠐⠒⠈⠀⠄⠀⠉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠠⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠀⠩⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠁⡖⢁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠒⠆⠚⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠚⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⡄⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠘⠀⠤⠀⠒⢀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⡎⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂
⣡⣤⣀⣀⣀⣠⣀⣀⣀⣀⣀⣠⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠁⠙⠀⠀⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⣦⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣽⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣤⣀⠀⣀⣄⣀⣀⣰⣶⣶⣶⣾⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠉⠙⣷⡀⠀⣀⣀⣀⣀⡀⢘⣭⣿⣿⣯
⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣷⣤⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠀⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠙⠛⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⣤⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣰⠟⠁⠀⠀⠀⠀⠙⣦⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠳⣤⠶⠛⠛⠛⠶⣄⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⣷⠶⠶⠶⣤⣸⡇
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⠛⠛⠛⠛⠛⠛⠛⢻⡛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⣠⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠈⣻⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⣾⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢁⣼⡄
⠀⠀⠀⠀⠀⠻⣦⣤⠾⠁⠀⠀⠀⠀⢠⡟⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡆⠀⠀⣠⡶⠟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠸⣧⣀⣠⡟⠀⠀⠀⠀⡀⠀⢀⣴⠛⠁⢀⡇⠀⢰⡏⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢹⡇⠀⠈⠉⠁⠀⠀⢀⣠⡼⢿⡀⠸⣧⣀⣀⣼⠃⠀⠀⠛⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⠟⠉⠀⣸⠁⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⠁⠀⠀⠀⠀⠀⠀⠹⣆⣀⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠋⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠚⠓⢦⣀⣼⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⠤⠤⠦⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⠶⠶⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠙⠲⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⡽
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠠⢾⡁
⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡋⠀⠀⠀⠀⠀⡀⠹⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠐⠐⢀⣀⣀⡴⠃
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠳⡤⠖⠁
⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡱⢦⣄⠈⠦⠂⠂⠀⣀⡴⠋⠳⣄⣈⠘⠁⠀⠀⠈⣀⣤⠞⠙⠶⠶⠞⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠈⠙⡛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠃⠀⠀⢰⡄⠀⠀⢸⠀⠀⠀⠀⠀⢲⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡆⠀⠀⠀⠀⠘⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡆⠀⠀⠀⢠⡄⠀⠸⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣦⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⢛⡛⠛⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠶⣤⣄⣠⡶⢋⣥⣶⠿⠿⠿⠿⣿⣿⣶⣤⡉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣩⣴⣶⣿⢿⣿⣿⣶⣦⡌⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠈⢻⣿⣤⣍⣉⡛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣄⡙⠛⠻⠿⣿⣷⣦⡈⠳⣦⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣠⡴⠟⢀⣠⣴⣾⠿⠿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠈⠙⢿⣿⣶⣶⣮⣭⣍⡛⠶⣤⡀
⠀⠀⢀⣤⠞⣫⣵⠾⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣌⠻⣦
⠀⢠⡞⡡⠚⠉⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡈⢷
⢠⡟⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸
⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠶⠶⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢦⣄⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣿⡇⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⢰⠏⠀⠀⣸⣷⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⢀⡟⠁⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠴⢞⣿⠇⠀⣠⡞⠁⣿⡀⠀⠀⠀⠀⠸⣇⡠⠾⣻⡟⠀⢀⡼⠋⢸⡇⠀⠀⠀⠀⠈⢷⣀⠴⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠉⠙⠉⠁⠀⣼⠋⠀⠀⣿⡇⠀⠀⠀⣠⣦⠈⠙⠋⠉⠀⢠⡟⠀⠀⢸⣿⠀⠀⠀⢀⣴⡀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣷⠀⠀⠀⠀⠀⢻⣄⠤⠾⣻⠇⠀⢀⡾⠋⢿⡄⠀⠀⠀⠀⠸⣇⠠⠴⢿⡿⠀⠀⣴⠏⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⡆⠀⠀⠀⣠⡄⠉⠛⠛⠉⠀⣰⠟⠀⠀⣸⣇⠀⠀⠀⢀⣤⠈⠛⠛⠋⠀⢀⡾⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣤⡾⣿⠇⠀⣠⡾⠋⣿⠀⠀⠀⠀⠀⢻⡄⢠⡴⢿⡟⠀⢀⣴⠏⢻⡆⠀⠀⠀⠀⠸⣇⠀⣤⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠛⠓⠛⠁⠀⣰⠏⠀⠀⣿⡇⠀⠀⠀⢀⡄⠙⠓⠚⠋⠀⢠⡞⠁⠀⢸⣧⠀⠀⠀⢀⣤⠈⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠹⣇⠀⠀⠀⠀⠀⢿⡀⣀⡴⣿⡇⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⢸⡇⢀⣤⢿⡿⠀⠀⣠⠟⢻⡆
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣿⡀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⣠⠟⠁⠀⣹⡇⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⢀⡾⠃⠀⢸⣷
⠀⠀⠀⠀⠀⠸⣇⠀⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⡿⠻⣽⣿⣦⡁⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣂⣽⣿⣿⣿⣿⡿⢫⣤⡤⠶⠾⣿⣿⣦⠉⠑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⣀⣾⣿⣿⣿⣿⡿⠁⠀⠀⢚⣽⣿⣿⣿⣿⣦⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⣾⣿⣿⣿⣿⣿⡟⡀⠀⠀⠒⢛⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⠟⠀⠀⠈⠉⠉⠉⠉⠹⣿⢿⣿⣿⣟⡀⠀⠀⠀⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣭⣾⣿⣿⣿⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣤⣤⣤⣄⣀⣈⢃
⠀⠀⠀⠀⠀⠀⢠⢶⢿⢿⣿⣿⠟⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠈⠀⠋⠀⠛⠟⠿⠿⡇⠅⠹⢼⡿⠽⢿⣿⠃⠛⣿⣿⢻⣿⢸⣿⣿⣿⣿⢿⣿⡗⣿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠈⡏⢹⠋⠁⠀⠀⠈⠘⠁⡇⡄⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠇⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠸⠀⠀⠀⠀⠇⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡖⠖⠀⠀⠀⣾⠀⠀⠀⠃⠀⠀⠀⠀⡃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢀⠀⣸⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠎⠛⠅⠈⠑⠔⠒⢄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠄⢠⠄⠀⠀⠀⠀⠀⣄⠈⡵⠤⠴⠒⠊⠀⠀⠖⠐⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣀⡴⠚⠄⠀⠀⠈⠀⠀⠀⠀⢀⡔⡲⠚⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⠚⠁⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⢳⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⠤⣀⠤⡤⠤⢄⠀⠀⠀⠀⠀⢰⡟⢡⣄⡀⠐⠁⠀⢀⡀⠀⠀⠀⠺⠀⠀⢈⠁⠀⠀⠀⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠟⠚⠁⠀⠀⠀⠀⠀⠐⢳⡠⣋⠑⡖⠀⠀⠁⠈⠙⠔⠢⡤⡢⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⡂⡄
⠀⠀⠀⠀⠀⠀⡠⠤⢖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠭⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄
⠀⠀⠀⢀⣠⣼⡅⠀⠘⠀⠀⠀⠀⡠⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⠿⢗⠂⣀⡀⢀⣀⢀⣀⣀⣀⣘⣳⣶⣶⣦⣠⣄⣀⣀⣀⣀⣀⡀⠂⢱
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣅⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣉⢁⣉⣀⣈⣉⢀⣙⣛⡯⠛⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉⠉⠋⠉⠁
⠀⠀⠀⠈⠒⠢⠤⠶⠘⠳⠶⠖⠒⠛⠛⠛⠛⠛⠛⠉⠉⠛⠙⠛⠋⠉⠛⠋⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠀⠀⢀⡏⠀⠀⡼
⠀⠀⠀⠀⠀⠠⡆⠀⠀⣼⠀⠀⡏⠀⢀⡇⠀⠀⠰⠀⠀⠀⠀⡾⠀⠀⠀⢠⠆⠀⠀⠀⠺⠂⠀⢠⡇⠀⠀⣼⠀⠀⡀⠀⠀⣸⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠇⠀⢸⠁⠀⢀⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠚⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⡞⠀⢀⡏⠀⠀⠘⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠀⠀⢸⠁⠀⠀⠀⣀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣸⠁⠀⣸⠀⠀⢀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠀⠀⡟⠀⢀⠀⠀⠉⠀⠀⡟⠀⡀⠀⢸⠁⠀⠀⠀⢸⠃⢰⡄⠀⠀⠀⠋⠀⢠⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠁⢰⠇⠀⠏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⣰⣟⣩⣶⣶⣶⣦⡉⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣫⣽⣛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⣿⠿⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⡿⣿⣿⣷⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣿⣿⣿⢿⣛⣉⣭⣉⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣭⡛⣿⣦
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⡜⣿⡇
⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⠃
⠀⠀⠀⠀⣿⡜⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠘⣷⣜⢿⣦⣽⣿⣿⣭⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⣽⡿⠟⠉
⠀⠀⠀⠀⠀⠈⠻⢷⣯⣿⣿⣿⣿⡿⠟⠙⠻⢿⣿⣿⣿⣿⣿⠿⠻⠿⠿⣿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢢⡀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⡀⠀⠠⠀⠀⠀⠀⠀⠰⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⢦⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⠉⢉⡩⠟⠒⠲⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠙⡄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠱⣄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠒⣤⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡰⠋⠀⠈⠳⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣠⠏⠉⠉⡗⠒⠤⢄⡀⠀⡇⢀⣀⣀⣀⣀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡠⠞⢹⠀⠀⢠⠃⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⢀⠆
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⡘⠓⢂⢾⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠎
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠭⢍⠥⡊⠀⡠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢇⠀⠀⠙⠓⠊⠑⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠣⣄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡠⡄⠉⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⢲⢄⣀⠀⠀⠺⠊⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡠⠔⠊⠉⢻⣿⠟⠉⢳⣶⣖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡤⠴⠃⠀⠀⢠⠿⠟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠣⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣠⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠛⠿⣿⣷⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣦⠀⠀⠈⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣀⡀⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡞⣽⣿⣿⣶⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠈⢷⣄⠁⠙⠻⣿⠀⣤⠀⠀⠰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⣀⡀⠀⠠⠤⠌⠐⢒⣀⣐⣐⣒⣒⡉⣆⢨⣸⠁⣀⠠⠤⡬⠁⠀⠀⣀⡀⢠⣀⣀⡀⢀⡀
⠀⠀⣀⠤⠖⣒⠭⠋⠉⠉⠀⡀⣠⡴⠶⠓⢛⣉⣉⠥⠤⠒⣀⡀⠀⢰⠇⢠⠷⠤⠬⣭⣉⣉⡉⠛⠒⠢⣤⣀⠀⠀⠉⠑⠐⠌⢁⡒⠒⠠⣄⡀
⠐⠉⠀⣠⠎⠀⠀⠀⠀⢔⠈⣞⠁⠀⢰⣾⠋⠁⠀⠀⢎⠀⠀⠐⠂⠁⠀⣀⣘⠢⡄⣀⠀⠬⡙⢿⢮⡅⠈⠛⢷⣤⡢⠀⠀⠀⠀⠘⣲⣄⠀⠈⠑⠦⣀
⠀⠀⠀⢯⡠⠀⠀⠀⠀⢕⡨⣷⠀⠀⠐⠽⣆⠀⡂⠀⠀⠁⠢⢤⣀⡀⣀⣈⣉⣑⡊⠎⠠⠔⠁⣼⠯⣻⠀⠀⠈⡍⣋⠀⠀⠀⢀⠢⡒⢽
⠀⠀⠀⠈⠲⣡⢂⢔⢄⠀⠈⠉⢶⡔⢄⠀⠈⠉⠒⠢⠦⣎⣦⣴⣮⣥⡤⢶⣲⣶⣆⣴⡶⣐⣑⠥⠚⠁⣠⢶⠕⣅⠎⠀⠀⢌⠢⠑⡬⠎
⠀⠀⠀⡀⠀⠀⠉⠉⠈⠊⢎⣆⡄⡈⠚⠊⠊⠃⠂⠠⣰⣒⡤⠤⢬⣭⣉⣊⣭⠉⡉⠉⡀⠠⠴⣶⣊⡪⠨⠖⠊⢁⢀⢊⣄⠦⠒⠉
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠉⠉⠙⠓⠲⠦⠤⠄⣄⣄⡉⣉⣉⣹⣻⣬⣭⠝⠻⢇⢙⢉⣉⣤⣤⠠⠤⠆⠛⠚⠈⠉⢀⡀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠀⠀⠀⠀⠠⠤⠄⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠄⠀⠀⠒⠒⠀⣉⡉⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣡⠀⠀⠀⢸⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⢤⣶⣶⣦⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠔⠃⡀⠘⠆⢸⢿⣿⣿⢿⠋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡠⠒⠂⡟⠂⢄⣟⡘⣙⠘⢻⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣇⣀⣀⣇⢀⠀⠀⡄⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⡀⠀⠀⠀⠈⢋⣭⡉⠉⠉⠁⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡙⠢⣤⡤⠴⠋⡍⠒⠀⠀⠀⠀⠆⢪⣥⣌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠷⠊⠁⣄⢀⠀⠁⠀⠸⠀⠀⠀⠀⣀⣸⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠋⠙⠃⠀⠠⡏⢹⠀⠀⠀⢠⠀⠀⠸⠀⣶⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡅⠀⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⡀⠀⣥⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡄⠀⢸⠃⢀⠀⡼⠀⠀⠠⠀⢀⠃⠀⠀⠀⡟⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠇⠀⠰⠆⢁⡼⠁⠀⠀⡀⠀⠸⠄⠀⠀⠀⡇⣄⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠺⠷⡶⠶⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢸⠇⢸⣀⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣇⣀⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⢨⣅⡾⠀⠋⢀⢠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠀⠀⠀⡏⢸⠀⠑⠛⠲⣶⡄⣀⠠⠀⠀⠀⣼⠁⠀⠀⡼⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡿⠺⣇⠀⠀⠀⠚⠑⠫⡄⠀⠀⡜⠳⡧⠀⠀⠷⠀⢠⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⢻⣆⠀⠀⠛⠀⠀⠀⣠⢾⠇⣾⠆⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⢰⠋⠀⡾⠋⡷⣄⣀⣀⣠⠞⢁⡎⣠⠁⠣⡉⢀⠙⡀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠈⢯⣸⠃⠁⡗⠛⡁⡸⠣⣤⡞⡰⠋⢠⠀⣧⣰⣦⢧⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⣸⠀⠀⡧⢀⡟⣁⢠⣿⠃⠀⠀⢸⠀⡟⠁⠙⠚⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⢧⣄⡘⡇⣰⢂⡇⠀⣼⠀⠀⣀⠋⠀⣋⣠⠴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠈⣧⠉⡱⠃⠸⢱⡀⠘⠳⠲⠟⠊⠉⠁⣤⢼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠒⠒⣶⠒⣿⣤⣌⣳⡀⢚⣠⡗⠀⠀⠀⠃⠀⠀⠀⢹⣹⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠴⠤⢤⣌⠭⠭⠥⠝⢙⠿⠭⠿⠶⠶⠶⠶⠂⠠⠴⠶⠤⢷⠤⠤⠤⠤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠤⠭⢤⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠂⠀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠙⠛⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠃
⡏
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠰⠿⠟⣻⣿⣿⣿⣶⡇⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⢹⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⣹⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⠁⠀⠀⣰⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣄⢀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⠋⠀⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠰⢿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣰⣿⣿⣿⣿⠋⠀⣿⣿⣿⠇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⠋⠀⢻⣿⣿⣠⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠰⣀⣤⣀⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢦⣰⣤⣀⡆⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣄⢠⣀⣠⡄⢀
⠀⠀⣄⣹⣷⣿⣿⣿⣿⣶⣿⠄⠀⠀⠀⠀⠀⢠⣌⣿⣾⣿⣿⣿⣷⣾⡥⢀⠀⠀⠀⠀⢀⣘⣿⣾⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣶⣠⡄
⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡷⠂
⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⣺⣿⣿⣿⡿⠛⠉⠉⠀⠈⢑⠀⠀⠀⠠⣿⣿⣿⣿⡿⠟⠉⠉⠁⠩⠳⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠟⠁
⠐⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠈⢩⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠺⠿⣿⣿⣿⣿⠻⡍⠁⠀⠀⠀⠀⠀⠀⠐⠻⢻⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⡦⣤⣴⠂⡄
⠀⠀⠀⠀⠀⠉⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠠⠡⠀⠀⠀⠀⠄

⠀⢀⣀⠀⢀⠠⠐⠒⠠⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠠⠁⠀⠌⠄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⣶⣟⣿⢿⣶⡠⡀⠀⠀⠀⠀⠀⠄⠒⠒⠂⢀
⠀⠀⠀⡠⣢⣾⣻⡿⣶⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⡻⣶⡀⡀⠀⠀⠀⠀⢀⣸⣶⡿⢱⣿⡟⢸⣿⡆⢿⣿⡜⡄⠀⠀⡐⠁⠀⠀⢀⠔⡴⠁⢄⣀
⠀⠀⡜⣼⣿⠃⣿⣧⢹⣿⡌⡆⠀⠀⠀⠀⠀⢀⣂⣾⣿⢰⣿⡇⢻⣿⣘⡄⠀⠀⠤⣿⣿⣿⣿⣿⣿⣇⣸⡿⠇⣸⠟⠛⠛⠀⠀⢡⠀⠐⠈⠡⠈⠀⠀⠈⠀⠀⡄
⠀⠀⠉⠙⠻⠔⠛⠛⠸⠟⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠻⠘⠛⠓⠼⠋⠉⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠐⠂⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠙⠛⠆⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠇⠀⠀⠀⠀⠀⢀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⡠⠔⠤⡐⠛⠀⠀⣰⠭⠏⡀⢀⢞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠉⠓⡄⠀⠀⠉⠀⠀⠱⠴⠖⠀⡠⠖⣋⠀⢀⠤⣈⢹⣗⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣠⡗⠁⠀⢀⡔⠒⣢⣀⡠⠔⢫⠒⠛⡾⠃⣞⡶⡿⠀⠉⠰⠉⠱⡄⠀⣎⣱⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠁⠀⡔⠁⣨⡷⠛⡇⠀⠀⠱⢤⡾⠃⣴⡌⠁⠀⣠⠔⠃⡤⠤⡘⣆⠌⢥⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢃⢌⣀⡳⠾⠃⡤⠒⣤⣤⡀⠀⢠⢄⠀⡞⠀⡠⠚⠣⣴⠃⠈⢦⣐⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢒⢦⣠⠴⠊⠁⠀⠳⠞⠉⡕⠀⡠⠗⠒⣿⠉⢀⡀⠈⠛⠀⡇⢨⡀⠀⡔⡐⠀⠀⠀⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠚⢇⠀⡀⡰⠘⡘⠸⣰⠀⠀⣅⢀⣴⡟⠀⢧⠯⠀⠀⠀⠘⡄⠉⠀⠉⠀⠀⠀⢠⣄⠱⣤⡄⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠒⠋⢰⢡⢁⢣⢁⠗⢣⠀⠀⠈⠁⠉⢠⠶⣽⠂⠀⠀⢆⡆⢨⢀⡄⠀⠀⣔⣢⠀⢡⠠⡟⠀⣠⠼⣄⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢃⢁⢃⠆⡌⡐⡜⠛⠋⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡠⠖⠶⡁⠘⠶⠀⠀⠉⠁⠂⢡⠐⢡⠀⢇⣠⢀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⢢⠀⠈⡘⡜⡸⢠⢱⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⢄⣼⢂⠀⠀⠀⢀⠀⡂⡄⠈⠀⣸⠀⠀⠉⠠⣎⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⡇⠀⠡⢂⠱⢁⢃⠇⡌⡜⡠⠀⠀⠀⠀⠀⣀⡀⠀⢠⣇⠀⢔⠌⠁⠿⠀⢀⢀⠰⠟⠁⠀⣶⠀⡼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⡄⠙⢢⡀⠱⣂⠘⡘⢠⢡⢠⠃⠀⠀⠀⠀⠮⣀⡼⠀⡆⠈⠉⠉⠀⢀⠀⠀⠐⠈⠀⠀⠀⣀⠘⠤⠃⡉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⠘⣷⡀⠀⠱⡈⠡⡀⠁⡎⡈⡌⠀⡠⢊⡹⣄⠴⡌⢀⡴⠁⠀⠀⢀⠰⠘⣀⢤⡀⡎⠉⢧⡀⡧⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠘⠤⡨⠇⠀⠙⡇⠀⠀⠳⡀⠀⠀⠀⠁⠁⠇⡇⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⣨⠔⠋⠀⢰⠁⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢇⠆⠠⡀⠘⣄⢀⠴⢦⡈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⡇⠀⣦⠂
⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⣁⡀⠘⠊⠣⡑⡀⠈⠁⠀⠀⠓⠔⠋⠀⢀⠄⢂⡠⠖⡆⠰⡇⠀⠀⠀⠀⠀⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢌⠂⠀⠀⠙⢌⠠⠀⠀⠀⠀⢀⠄⢂⡤⠚⠉⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠑⠢⡄⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢸
⠀⠀⢀⡠⢄⣠⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⡴⠒⣢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠎⠤⠌⠽⣃⣃⣘⢤⠀⢉⣒⣒⣀⣩⣯⡑⣤⣤⠔⢒⣈⠉⢑⣲⣤⠤⠌⠉⣭⠥⠤⠤⠔⠋⠀⢙⠦⠤⠤⢤⢄⠀⣄⠈⠂⢒⣚⠂⠀⠀⡤⠠⡖⠒⣄
⠀⠀⠀⠀⣆⡀⣀⣀⡠⠤⠴⡖⠒⠒⠒⢲⣒⣒⣒⡒⠀⢘⣋⣀⣠⡼⠧⣄⣀⣀⣀⣀⣀⣈⠉⠀⠉⠉⠀⢀⠀⠵⣎⣷⢮⡭⡥⢤⣬⡌⣓⡌⣁⡚⠉⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠄⠒⠒⣲⡶⢤⣀⢱⠞⠣⢀⣀⣬⠿⢍⣁⡚⠛⣮⠔⠛⠛⠛⢮⡘⠃⢘⠉⠙⠮⡛⠓⡎⠀⠀⠉⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠦⠤⣄⠀⢀⠤⠒⠊⠉⠉⠉⠙⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣠⠊⠁⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠔⠒⠒⠒⠤⣄⡀
⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡌⢱⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡜⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢀⡬⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠉⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⡀
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⣀⣀⣀⣀⣤⡀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⣇
⠈⠲⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠞
⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁
⠀⠀⠙⠒⠶⢶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢠⣄⠀⠀⠙⠢⢤⣀⣀⣀⣀⣠⠤⠖⠊⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠓⠶⠤⠤⠤⠤⠴⠒⠋⠀⡀
⠀⠀⠀⢿⡾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠙⠒⠒⠤⠤⠤⠐⠒⠋⠁⠀⠀⠀⢀⣄⠀⠀⠀⢰⢳⡀⠀⡟⢦
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⣼⢹⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠸⠸⡄⠀⠀⠸⣤⠇⠀⠙⠋
⠀⠀⠀⠀⠀⡏⡇⠀⠀⠳⠞⠀⠀⠀⢀⣄⠀⠘⠚⠀⠀⠀⠀⢰⠛⡄⠀⠀⠀⠀⢿⢸⠀⣀⠀⠸⣤⠇⢠⠻⡄
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢠⡄⠀⠀⡎⢸⠀⠀⠀⠀⢀⣄⠀⠘⠦⠇⠀⢀⣶⡀⠈⠉⠀⡟⡆⠀⠀⠀⠸⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣳⠀⠀⠣⠼⠀⠀⠀⠀⢸⠘⡆⠀⠀⠀⠀⢸⠀⢧⠀⠀⠀⠳⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣤⣤⡤⣀⣤⣤⣠⣶⣶⣶⣶⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣣⣶⣾⣻⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠐⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣏⢩⣤⣤⣤⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⣿⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⡿⠀⠙⢿⣿⣿⣿⣿⣿⣶⡟⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⠋⠉⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢆⣄⣠⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣧⡼⣿⡽⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⣿⡿⠙⠙⣹⣿⣿⣿⣿⡿⢿⣿⣿⠀⣸⡿⣿⠿⠛⣷⡻⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠀⠀⠀⢠⣶⣿⣿⣿⣿⣧⡀⠹⠿⠀⡛⠡⠄⣴⣿⣞⡛⢿⣿⡆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⣿⣿⣿⣿⣧⣴⣖⣁⣀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣯⣦⣀⡀⢀⣀⣀⣤⣤⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠙⠢⡄⢀⡤⠔⠒⠚⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⡰⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⢀⣀
⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠓⢤
⠀⠀⠀⣀⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠢⡀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣄
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⢲
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⠽⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠈⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠢⣄⣀⡀⠀⠀⠀⣀⣠⠞⠁⠙⠲⢤⣤⣀⣀⣀⡤⠴⠊⠁⠀⠈⠉⠙⠛⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⡸⢳⠀⠀⡀
⠀⠀⠀⠀⢀⣴⡀⠀⠀⢯⣸⠇⠀⠀⠀⠀⠀⠀⡏⠸⡆⠀⠀⠀⠀⠀⣇⢸⡆⠀⠀⠀⡀⠀⠀⢇⣸⠇⢰⠻⡄
⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠁⠀⠀⠀⢰⢧⠀⠀⠳⠼⠁⠀⠀⣠⡀⠀⠘⠛⠀⠀⠀⢰⠻⡄⠀⠈⠉⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠙⠋⠀⠀⢠⡄⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⢠⡇⢧⠀⠀⠀⠀⣤⠀⢸⡀⡇⠀⢀⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠙⠚⠀⠀⣠⡀⠀⠀⠘⢇⡼⠀⠀⠀⢸⠀⡇⠀⠉⠁⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⢠⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠏⠀⠀⠀⠀⠘⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⢦⡤⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠀⠀⠀⠀⠀⠀⢿⠖⠋⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠤⡄
⠀⠀⠀⠀⣀⡤⠤⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡤⠶⠶⠦⣄
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢳⡀
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀
⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢳⡀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢦⡀
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⢀⡿
⠀⠈⠳⣤⣀⣀⡶⠒⠛⣲⣞⣂⣀⣀⣀⣀⣀⣀⣈⣻⡉⠉⠉⠙⣅⣁⣀⣀⣀⣀⣀⣀⣀⣀⣲⡶⠓⠒⣲⣋⣀⣀⣈⣛⣏⠉⠉⢧⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⢠⡟⠀⠀⢰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠿⢤⡄⠀⠀⠀⢈⡗⢀⡴⠋⠀⠈
⠀⠀⠀⢠⣯⣤⡤⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢴⡶⠚⠃⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⢀⡴⠋⠀⠀⠀⠼⢥⡄⢈⡽⠂
⠀⠀⠀⠀⢠⠞⢀⡴⠋⠀⠀⠀⢀⡞⣇⠀⠀⠀⠀⠙⢢⡀⠀⢶⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⡼⣁⡴⠋⠀⠀⠀⠀⠀⣠⣏⡴⠋
⠀⠀⠀⣠⢏⡴⠋⠀⠀⠀⠀⢠⣯⣄⠈⣹⠇⠀⠀⠀⠀⠙⢦⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠀⢀⣞⠓⡆⠀⠘⠛⠁
⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⣰⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⢷⡇
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠉⠉⠉⠑⠢⣄⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠉⠀⠀⠀⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠒⠒⢤⡀
⠀⠀⠀⠀⠀⢀⡤⠖⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢹⠴⠶⠤⣄⡀
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⣀⠼⠗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⣄⡀
⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠙
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠱⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠙⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⠞⠁
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠓⠒⠚⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠦⣀⣀⣀⣤⡀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠲⢤⣀⣀⣀⣠⢤⡀⠀⠀⢀⡴⠓⠒⠚⣉⠀⠀⠀⠀⠀⠀⢠⡆⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⣏⡼⠀⠀⢸⢧⡀⠘⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣶⠀⠀⠀⠀⢠⡏⢣⠀⠀⠀⠈⠀⠀⠀⠸⣄⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡾⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠀⠀⠈⠳⠞⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⠀⡀⠀⠀⠈⠶⠃⠀⠀⣄⠀⠀⠀⠀⠀⢰⠉⡆⠀⠀⠀⠀⠀⣰⢻⡀
⠀⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⢀⡴⢻⠀⠀⠀⠀⠀⠀⢠⠋⡄⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⢇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡼⠁⠀⠀⠀⠀⠀⠘⠖⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠾⡄⠀⠀⠀⠀⠀⠀⢠⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡞⢱⠀⠀⠀⠀⠀⠸⣤⠇⠀⠀⠀⣴⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⡜⠹⡄⠀⠀⠀⠀⠀⠈⢧⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⡄⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⣄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠙⠴⠃⠀⠀⠀⠀⠀⢸⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⢰⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣆⠀⠀⠀⠀⠀⠸⣀⡼⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡄⠀⠀⠀⠈⣇⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⡝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⢀⡀⠀⡀⠀⠠⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠐⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠂⠐⣀⡀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠉⠄⡄⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⢄⡀⡀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠰⠠⠀⢈⠀⠁⠐⠄⢔⠀⠉⠛⠲⠒⠺⠁⠀⠀⠑⢔⠀⠁⢅⠔⣐⡀⠁⠈⠁⠀⠈⠮⠤⡀⠀⠀⠉⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠞⠉⠱⠒⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣄⡴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡉⠣⠀⠅⠈⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁
⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣄⡤⠀⠠⣊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠀⡄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠋⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠐⠀⠈⠉⠀⠀⢀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠤⠀⠠⠄⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠁⠀⠀⡀⢀⢀
⠀⠀⠀⠸⠔⠀⠀⠆⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢈⡀⠀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⢥⠀⠀⠀⠀⣀⠀⠀⡄⠀⠚⠀⠀⠁⠈⡁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠃⠀⠉⠀⠀⠌⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠿⠛⠿⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣠⣶⠿⠟⠻⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⡀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⣠⣶⠟⠛⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠛⠛⠻⢷⣤⡀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠉⠁⠀⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⠶⠶⢶⣦⣄⢸⣷
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢿⣿
⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⡄
⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠈⢻
⠀⠙⠿⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⣿⠟⠉⠉⠉⢩⣿⠛⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⣰⣿⣥⣤⣼⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣀⣀⣀⣀⡀⠀⠀⣠⡿⠃⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⣿⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⣴⣿⣷⡶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣤⣤⣤⣤⡤⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠛⠛⠋⠛⠛⠻⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠙⠻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀
⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣀
⠀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣀
⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠈⠻⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠁
⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⣴⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⠙⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠽⠿⠿⠛⠿⠟⠿⠿⣿⠿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠄
⠘⠛⠛⠋⠘⠿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠁
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣿⠂⣰⣶⣏
⣀⠀⠀⠀⠀⠀⠋⠙⠉⠈⢿⣿⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣠⣤⣶⣶⣤⣿⣿⣷⣿
⣯⡙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡤⠀⡟⠉⠉⠙⢉⡛⠉⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠇⢠⣬⣤⣥⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣿⣛⡛⢀⡩⠀⠀⢀⠀⠀⠀⠀⠀⠄⣠⣠⣦⣤⣆⠀⠀⠀⣴⣾⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣻⣤⣄⣶⣆⣂⣴⣿⣿⣿⣿⣧⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⢀⡖⢚⠀⣀⣀
⠚⠲⢤⣀⣀⣀⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⡆⢒⠀⠀⢀⡀⠀⠀⢸⡈⣁⠀⠀⢀⡘⡦⢶⢤⢾⡇⠿⠯⠋⠁⠁
⠀⠀⠀⠈⠀⠚⠠⠍⣅⡐⠒⠀⠀⠀⠀⢀⡶⢺⡗⣤⣀⣀⣀⣴⠀⠚⠗⢺⡩⠉⠩⢹⡅⠀⢘⠯⣬⢸⠛⠻⣇⠁⢠⠰⢸⣷⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⠀⣿⡇⢤⠚⠏⠀⠀⢠⣉⡣⠀⠀⠉⠛⢿⡀⢰⠿⡄⠈⢀⡽⡏⠀⣠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢈⣇⠄⠀⠀⢀⡀⠀⠀⣠⠂⠀⠀⠈⠀⠀⠀⠉⠉⡄⠘⡀⣸⠀⢧⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠓⣾⣿⠛⠀⠀⠀⠐⠀⠀⠀⡀⠃⠀⢹⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠖⠸⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠭⣀⠀⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠄⡅
⠀⠀⠀⠀⠀⠀⠀⢐⠁⣰⠒⡄⢱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠠⠜⠉⠁⠀⠉⠙⢇⡇⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠘⢌⡑⠒⠲⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡦⠴
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠂⡈⠀⠀⠃⠒⠂⠀⠚⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣀⡀⠄⠀⠀⠀⠄⠀⠴⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢔⡗
⠀⠀⠠⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⣿⣿⣯⣦⡀⢀⣀⣤⣤⠄⠀⠀⠀⠀⠀⣀⣴⣆⣤⣜⣿⣏⠁⠆⠀⠀⠀⠀⣸⣦⣤⣀⣴⣴⡶
⠀⠀⠀⠈⠛⠋⠁⢨⣓⠿⠿⠿⢛⢦⣴⣶⣶⣿⣿⣿⣿⡿⢘⣿⣿⣶⣿⣦⣤⣤⣼⣿⠾⠿⠋⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣿⣿⣟⡿⣿⣿⣿⡿⠛⠁⣿⠿⠿⠿⠋⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠂⠀⠈⢧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠉⠀⠢⣷⣴⣄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⣤⣴⠤⠴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣶⣤⣦⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠻⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⢶⣄⡀⠀⠀⠀⠀⠀⢻⣷⠶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠴⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⢷⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠙⠷⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣀⣀⣠⣾⠃
⠀⠀⠀⠀⢀⣘⣷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⣰⡟⠉⠉⠙⠻⣦⡀
⠀⠀⣠⡾⠛⠉⠉⠀⠀⠉⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣀⠀⠀⠘⣷
⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠿⠶⣶⣄⠀⠈⠛⠛⠋⠀⠀⠀⢹
⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⢀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠀⠀⠀⢻⣦⣀⣀⣠⣴⠟⠁
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢠⡿⠀⠀⠀⠀⣿⠉⠉⠉
⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠙⠳⣦⣄⣀⣀⣀⣠⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣤⣤⣤⡶⠟⠉⠀⠀⠙⠳⣦⣄⣀⠀⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⣀⡤⢤⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠙⢋⡀⡙⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣩⣻⡆⠀⠀⣀⣀⣠⠤⠷⣄⡘⢧⣐⣛⣦⣼⡵⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢇⡬⠖⠚⠉⠉⠀⠀⠀⠈⢻⣙⡞⠃⢹⠞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣦⠽⡶⠒⠒⠚⢛⡽⣿⠀⠀⠉⠀⠉⠉⣇⠀⠀⠰⡏⢭⡉⠉⠉⠉⢹⡛⠾⠟⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠊⢻⣦⠘⡇⠀⡔⠲⠋⢠⠇⠀⠀⠀⠀⡠⣄⢻⠀⠀⠀⢻⡀⠹⣄⠀⢀⣼⠇⠀⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⣿⠀⣧⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠓⠊⢸⠀⠀⠀⠀⢷⠀⠘⡆⣏⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡿⡏⠀⡏⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⣷⢹⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⣿⠇⠰⣇⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⢯⡽⠀⡇⠀⠀⠀⠀⠸⡄⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⣄⣀⣀⣀⣀⣤⣤⠴⠶⠶⡶⠶⠶⠶⡶⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡄⠀⠀⠘⡇⡴⢡⠜⠛⠛⠛⢻⠀⠀⢰⠋⠉⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⠀⢰⣧⡄⠀⢸⠃⡇⠈⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠘⠿⠁⠀⠸⣴⠃⠀⡟⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⡼⠒⠒⠛⠛⠃⠘⠛⠛⠛⡟⠀⠀⠀⣠⠋⠉⠉⠹⣄⣀⠀⠀⠈⢯⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣭⣝⣛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⣀⣠⠖⠒⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠙⠲⣄⣠⠤⠒⠒⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠶⠤⢄⡔⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⢄⣀
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⢀⡤⠖⠤⡀⠀⠀⠀⠀⠀⢠⠚⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠹⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢤
⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⡄⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⢀⡴⠲⠤⣀⣀⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠒⠋⠀⠀⠉⠛⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⡰⡆
⠀⠀⠀⠀⠀⣠⡄⠀⠀⣇⡇⠀⠀⠀⠀⠀⡎⢹⠀⠀⠀⠀⢸⡀⡇⠀⠀⢀⠀⠀⢇⣸⠀⠟⡄
⠀⠀⠀⠀⠀⢇⣸⠀⠀⠀⠀⠀⠀⡜⡆⠀⠑⠊⠀⠀⣠⡄⠀⠉⠁⠀⠀⡜⢧⠀⠀⠀⠘⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠐⣆⡗⠀⠀⠀⠀⠀⡇⢱⠀⠀⢀⠷⡀⠳⠜⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠇⠀⠀⠀⠀⠀⡞⡆⠀⠀⠉⠁⠀⠀⢸⣀⡇⠀⠀⠀⠰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⠛⠓⢲⠞⠉⠀⠀⠀⠀⠀⠉⠳⣴⠒⠛⠛⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⡴⠋⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠳⡄
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠈⢳⣤⣀⣀⠀⣀⠀⠈⠓⠦⠤⠤⣤⠤⠖⠚⢹⠗⠦⣄⣀⣀⣀⣀⡤⠖⢿⠙⠒⠦⢤⡤⠤⠤⠖⠋⠀⢀⡀⢀⣀⣠⣴⠋
⠀⠀⠀⠀⠀⢠⠎⠀⠈⣹⢿⡉⠀⠀⠀⢠⡀⢠⠏⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⢧⠀⣠⠀⠀⠀⠈⣹⢯⡁⠀⠈⢧
⠀⠀⠀⠀⠀⠿⢶⠆⠘⢓⡖⠙⠲⠦⠤⠶⢋⡏⠀⠀⠀⡾⠚⠧⢤⣄⣀⣀⣀⣀⣤⠤⠟⠺⣆⠀⠀⠘⣏⠳⠦⠤⠶⠚⠑⣖⠛⠀⢶⠾⠇
⠀⠀⠀⠀⠀⡴⠃⢀⡔⠋⠀⠀⠀⣀⠀⠀⡼⠀⠀⠀⣼⡥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣽⡄⠀⠀⠸⡄⠀⢀⠀⠀⠀⠈⠳⣄⠀⠳⡀
⠀⠀⠀⢀⡼⢁⡴⠋⠀⠀⠀⠀⣰⠻⡆⠸⠗⢺⠂⠀⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠀⢺⠒⠿⢀⡞⢷⠀⠀⠀⠀⠈⠳⣄⠹⣄
⠀⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⢿⣀⡇⠀⢀⡏⠀⢀⡞⠁⡼⢧⠀⠀⠀⠀⠀⠀⠀⣰⢳⡀⠙⣆⠀⠈⣇⠀⠸⣄⣸⠂⠀⠀⠀⠀⠀⠈⠳⣜⣆
⠀⠠⠿⠋⠀⠀⠀⠀⠀⣰⡄⠀⠀⠉⠀⠀⣼⠀⣰⠋⠀⠰⡇⢈⡇⠀⠀⠀⠀⠀⠀⡇⢈⡇⠀⠈⢷⡀⢸⡄⠀⠈⠁⠀⢀⣦⠀⠀⠀⠀⠀⠈⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡀⠀⠀⠀⢰⢃⡜⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠹⣄⢷⠀⠀⠀⠀⡾⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠞⠀⠀⠀⢀⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢿⡇⠀⠀⠀⠹⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢑⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡠⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠀⠔⠒⠤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠉⠀⠀⠀⠓⠐⠤⠤⠤⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⡠⠂⢊⠄⡐⠡⠂⠄⠠⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠀⢀⠔⠀⡀⠊⢔⠑⡡⠊⠀⠀⡡⢊⠔⠀⢀⠔⡀⡁⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠂⠀⠀⠀⠀⠊⠀⠁⠀⠈⠀⠁⠁⠈⠀⠀⠀⠈⠐⠁⠀⠐⠡⠊⠀⠠⠒⠆⢀
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡄⠀⢀⡄⠀⣠⠀⠀⡀⠀⠈⢀⠋⠉⣭⠶⢀⠔⠀⠀⡀⠀⠀⠐⠂⠀⠀⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠼⠁⠬⠁⠈⣠⠀⢈⠀⣀⠁⠀⠜⣠⠀⡰⠃⠀⠐⡡⠂⠀⣀⣀⠈⠀⣀⠀⠀⠞⠐⢃⡔
⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡄⠀⠁⠀⠁⠀⠁⢀⠀⠐⢁⠜⣀⣀⣀⣈⡉⠁⠀⢈⠒⡊⠀⢁⠀⠀⠞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠊⠀⢠⠆⢠⠎⠀⠐⠋⠀⠀⠈⢀⡀⠀⠠⠊⠀⠀⠀⡨⠊⠀⠀⠁⠀⠀⠐⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠚⠀⠀⡘⠀⠀⣠⠀⠐⠃⠀⡄⠀⢠⠀⠈⢀⠔⠀⠀⠀⡠⠊⠀⠀⠀⢠⠆⠀⠀⠖⢀⡄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠆⠀⠁⡴⠀⡤⠀⠀⠀⠋⠀⠔⠁⠀⠀⠐⠀⠀⠞⠁⡄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠊⠀⡠⠂⠀⢀⠔⠁⠀⣠⠀⠀⠀⠀⡠⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠚⠀⠀⠜⣀⠊⠀⢀⠀⠀⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⠤⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠁⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠁⠀⠀⠎⠀⠀⠀⠀⡔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠐⠠⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄
⠀⠀⢀⡀⠀⠐⠀⠀⠀⠄⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠄⠀⠀⠈⠁⠠⠀⠀⠐⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠆⠐⠂⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠁⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⡈⠀⠀⡀⠀⠀⠄⠀⠀⠁
⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⡀⢈⣠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣪⣴⣶⣾⣶⣿⡋⠁⠀⠀⠠
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⢊⣼⣿⣿⣿⣿⡇⠀⠀⣀⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⠿⠗⠁⠀⠀⠀⠈
⠀⠀⣀⠀⠀⠀⠀⠈⠡⠡⢞⣿⣿⣿⣿⣿⡗⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢳⠶⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⠀⢏⠻⣁⠀⠐⣨⢋⣠⣤⣤⡀⢂⠀⠀⠀⠈⠀⠀⠂⠈
⠀⠀⠀⠈⠀⠀⠀⠁⢈⣴⣿⣿⣿⣿⣿⣿⣿⣄⢀⣑⣘⣟⣤⣦⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠈⠀⠀⠀⠀⠐⢻⣿⣯⣭⣽⣾⣿⣿⣿⣿⠧⠤⠴⠿⠛⠛⠋⠁⢻⣿⣿⣿⣿⠈⢄⠀⠀⠀⠄⠀⠠⠄
⠀⠐⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⣄⡀⠀⡀⠄⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠈⢿⣦⣙⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠚
⠀⠈⠀⠠⠀⠀⠀⠂⠀⠄⠙⠿⣳⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣟⢏⢱⢃
⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠈⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⣧⠀⠉⠸⠀⠀⠈⠡
⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠠⠀⠈⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡔⠁⠀⠀⠀⠀⠀⠀⢲⣆⣮⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢮⣤⡝⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣟⣛⣟⣛⣻⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠛⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⡤⠤⢤⣀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣶⢛⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⢦⡀⠀⠀⠀⠸⣧⣀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠂⢀⡞
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠘⠻⣄
⠀⠀⠀⠀⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⢶⣋⠀⠀⠀⠀⠀⠐⣀⠈⡇
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠊⠊⣀⣀⣀⡴⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⢦⠴⠞⠁⠈
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠐⣣⢦⣀⠀⠡⠄⠠⠀⠀⢀⡴⠛⠦⣄⠀⠁⠋⠀⠀⠀⠀⢀⣀⡴⠛⠦⠤⠤⠞⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠋⠁⠀⠉⠓⠶⠶⠶⠖⠚⠉⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⢠⠀⠀⡀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠃⠀⠀⣄⠀⠀⠉⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⠀⠀⡆⠀⠀⠀⢸⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⠀⠀⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡆⠀⠘⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢰⡆⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠓⠦⡄⢀⣠⠤⠖⠒⠛⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣠⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣠⠚⠉⠁⠀⠈⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠲⢄⡀
⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⣄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣉⣀⣀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠈⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠳⢤⣄⣀⣀⣀⣀⣀⣠⠴⠋⠀⠀⠉⠙⠒⠒⠒⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡏⢸⡆⠀⠀⠀⠀⠀⠀⢀⠏⢳⠀⠀⠀⠀⠀⠀⣼⠈⣇⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⡴⣆
⠀⠀⠀⠀⠀⡞⢹⡀⠀⠀⠙⠚⠁⠀⠀⠀⣤⠀⠀⢸⡄⣸⠀⠀⠀⠀⠀⠀⠸⣤⠟⠀⠀⠀⢠⣦⠀⠀⠙⠶⠃⢠⡇⢹
⠀⠀⠀⠀⠀⢧⣤⠇⠀⠀⠀⠀⠀⠀⠀⣸⠉⡆⠀⠀⠉⠁⠀⠀⠀⡼⣇⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠀⠳⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⢿⣀⡗⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠀⡼⢳⠀⠸⣤⠇⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠉⠀⠀⢠⢶⡀⠀⠀⠀⠳⠞⠀⠀⠀⢠⡇⠘⡇⠀⠀⠀⠀⢸⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣾⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠁⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠻⠶⣦⣀
⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣠⣴⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⢸⣇⣀⣀⢀⡾⠋⠀⠀⠀⠀⠀⠙⢷⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣠⡾⠛⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠛⢷⣄⣠⣤⠶⠶⠶⣤⣄⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠙⣷⡀⣀⣀⣀⠀⠈⣷⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠛⢷⣼⡇
⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣤
⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹
⠀⠈⠙⠻⠶⠶⠶⠶⢶⣶⠶⠶⠶⢶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣠⣿⣁⣘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾
⠀⠀⠀⠀⠀⠀⣰⣟⣁⣀⣀⣈⡉⠉⢉⣿⠋⠙⠿⠶⠶⠶⠶⠶⠶⠶⣶⡶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⡿⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠠⠾⠿⠶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠶⠶⠶⣶⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠉⠕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⠈⡄⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠜⠒⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠑⠒⠒⠢⡤⠒⠚⠀⢀⠂⠄⠔⡠⡠⢃⢊⠎⠀⠀⠀⠀⠀⠀⡄⢣
⠀⠀⠀⡠⠄⠠⢼⠀⠀⠀⢀⢀⠄⡠⢀⢀⢀⠄⢄⣄⣐⣆⣐⣀⣀⡀⣠⣠⡥⠚⠘⠺⡴⠋⠁⠳⡎⠀⠀⠀⠀⠀⠀⠀⠄⠸
⠀⠀⡜⠀⢀⢤⢀⢄⠔⡀⠡⢂⠜⡴⠥⠆⠚⠈⣩⠜⢋⢩⠉⠉⠙⠩⢍⣉⠒⠲⢤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠑⠤⠤⠤⠤⠀⠂⣒⠶⠂⠁⠀⠀⢀⡤⠊⠀⠀⠀⠂⢣⠀⠀⠈⠐⠀⢙⠢⣕⠀⡨⢉⠐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠈⡆⢁⠄⠀⠀⠂⠠⠈⠓⢄⠑⡡⢂⠄⢉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠋⠐⠄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡐⢍⡀⠀⠀⠈⠒⠤⠀⠑⢄⠕⡨⠐⡨⢐⣌⣲⣄⠀⠀⠀⠀⠀⠀⠓⠢⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢀⠜⠀⠁⠀⠀⢀⣀⣀⣀⣀⣀⠠⠀⠇⠀⡂⠤⠄⠒⠒⠒⠀⠠⢈⣢⣀⠕⠊⢁⠀⠄⠈⢀⠂⠄⡀⠠⠀⠀⠀⡅
⠀⠀⠀⠉⠉⠉⠁⠒⠠⢁⡬⠔⠒⠈⢉⠄⠍⠀⠀⠀⠀⢿⠁⠁⠚⠁⠀⠀⠀⢠⠀⠀⡠⢀⠀⠌⡙⡰⠡⠂⠌⡰⢠⠂⠎⡐⠡⢂⢂⠂⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⣀⣀⣻⣏⣐⣁⣊⡐⠀⠁⠂⠈⠀⠀⣁⣊⣈⣀⣀⣁⣈⣀⣁⣁⣈⣐⣀⣁⣀⣈⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡤⠀⣠⠀⠀⠴⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠄⠀⢀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣜⠇⢀⡀⢸⡃⠀⠀⠸⠁⢰⡌⠀⠰⠊⠀⠀⣢⠆⠀⢰⡁⠀⠀⠗⠀⠀⠗⢠⠃⠰⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢀⡀⠁⢰⡥⠀⠸⢀⠀⢠⠚⠀⠀⠀⠰⠂⡜⠁⠀⢀⠀⠀⢀⠴⠀⣀⡒⠀⢀⡶⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡀⠀⠀⢈⡸⠀⠘⠃⠀⠀⠸⠊⠀⠀⠀⢀⡭⠀⠀⠘⠃⠀⠉⡀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⢸⢻⡀⢀⡀⢀⠴⠀⠀⣀⠀⢀⠄⢀⣈⠁⢀⠀⠀⠼⠃⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⡀⠂⠈⠁⠀⢰⠄⠀⠛⠀⠈⠁⢀⡪⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⡀⠀⠠⢀⠀⡀⠀⢀⠀⡀⠀⠀⢀⠀⠀⢀⠀⡠⠀⠀⡀⢀⠀⡠⠀⡀⠀⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠉⠂⠁⠊⠔⠨⠊⠔⠄⠈⠔⠡⠊⠔⡡⢂⠅⢊⠔⠡⢊⠄⡥⢊⠔⠨⠔⡡⡪⢂⠁⢊⠔⡡⢊⢔⠡⢊⠔⡥⢊⠂⠕⠊⠠⢊⠄⠔⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣷⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢟⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠙⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣶⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠻⠿⣿⣿⣿⣿⠿⠋⠉⠻⢿⣿⣿⣿⣿⣿⡿⠟⢱⠿⣭⣭⣭⣭⣶⣿⣿⣿⠟⠛⠛⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣾⠉⠉⠁⠀⠀⢠⡟⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⣤⣶⣤⡀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣶⣶⡄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠹⢿⡿⠃
⠀⠀⢀⡿⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢾⣿⡷⠀⠀⠀⠀⢿⡿⠂⠀⠀⠀⠀⣤
⠀⠀⣾⠁⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠏
⠀⣼⠃⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡟
⣸⠏⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡿
⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠉⠙⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠲⠶⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣠⠴⠖⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀
⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡟
⢿
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠙⠶⣄⣀⣀⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⣀⡴⠶⣄⡀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⢀⠀⠈⠉⠉⠁⠀⠀⠉⠛⠓⠒⢛⡋⠁⠀⢰⠏⠉⠛⠒⠚⠛⠉⣼⠉⠙⠲⠦⠤⠤⠶⠞⠋⠀⠉⠙⠛⠛⠋⠉
⠀⠀⢠⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣆
⠀⠀⠈⠛⠁⠀⠀⠀⠀⢀⡾⡆⠀⠀⠀⠙⠋⠀⣸⠃⠀⠀⠀⠀⠀⠀⣼⣀⣀⣀⡀⠀⠀⣸⢻⡄⠀⠀⠀⠀⠀⠀⠈⠷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠋⠀⠀⠀⠀⠀⢠⣯⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡞⢀⡀⠀⠀⣰⢧⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡿⠀⠀⠀⠀⠀⠀⣿⣤⣤⡀⠀⠀⠈⠉⣹⠏⠀⠀⠻⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⢸⣿⣧⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣽⣿⣇⠀⠀⠀⣰⣿⣷⣶⣼⣿⣿⣤⣤⣤⣶⣶⣆⠀⠀⠀⢀⣿⣿⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⣿⣆⡀⠀⣿⣿⠋⠛⢿⣿⣿⠟⠛⠛⢻⣿⣿⠀⢀⣠⣾⣿⣿⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠺⡿⠿⠿⠟⠛⠻⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣾⣿⡿⠟⠋⠉⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣶⣤⣿⣿⣀⣠⣴⣾⣿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠙⠻⣿⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠛⠁⣿⣿⡇⠈⠙⠻⢿⣿⣿⣿⣇⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⡄⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠁⠀⢸⣿⣷⣶⣶⣿⣿⣿⣶⣦⣤⣰⣿⡏⠀⠈⢿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⣿⣿⠃⠀⠀⠀⠙⠛⠛⠛⢻⣿⡟⠙⠛⠿⣿⣿⠇⠀⠀⠈⣿⣿⡍⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⡀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠛⠛⠻⢿⣿⣿⡿⢫⠵⠶⠶⢦⡌⠙⢿⣿⣦⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⣡⡶⠆⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣧⣤⣀⣠⣶⣿⣿⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠐⠇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠻⣿⣿⡿⣫⠖⠛⠳⢮⡙⢿⣿⣿⡄
⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢸⡿⠀⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠉⠻⡆⠀⠀⠀⡶⠀⠀⢠⡀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⣼⣿⡿⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⡾⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇
⣿⣿⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⡀
⠹⣿⣿⣶⣤⣴⣶⠶⠦⠄⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠈⠛⣿⡟⣩⠴⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⢸⣿
⠀⠀⢰⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡐⢛⣡⣿⣿
⠀⠀⢸⣿⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠋
⠀⠀⠀⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠘⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣷⣶⣾⣿⠟⢿⣿⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣶⣶⣾⣿⣿⠿⠋⠀⠀⠈⠉⠀⠀⠈⢿⣿⣮⡓⢦⣄⣀⣀⠀⠀⣀⣠⣶⣿⣿⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⣴⠀⠀⠀⠀⠀⡀⠀⠙⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⠟⠁⠀⣸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣰⠏⢆⠀⠀⠀⢰⡇⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠉⠀⠀⠀⢰⠃⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧⠀⠀⠀⠀⠸⣧⣠⡼⠀⠀⣰⠏⠳⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣴⠀⠀⠘⠲⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⡟⠀⠀⠀⠀⢠⠟⢹⡄⠀⠀⢠⠏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡄⠀⠀⢿⡀⣠⡇⠀⠠⡏⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⢇⠀⠀⠀⠉⠉⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⠆⠀⠀⣼⡀⠀⠀⠀⣰⠃⠘⡆⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⠞⠁⢷⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⢠⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠈⠳⠖⠒⢶⡄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠢⠟⠒⠲⠦⣄
⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣼⡎⡀⠀⠀⠀⢸⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠭⠒⠀⢠⣄⡤⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇
⠀⠀⠀⠀⣇⠀⢁⠠⡆⠀⠐⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⡁⠀⠀⠀⢢⣈⠀⡆⢊⣼⠇
⠀⠀⠀⠀⠹⣦⠸⢲⡄⠉⠐⢀⠒⢭⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠠⠃⡆⠒⣆⡈⣨⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠈⠛⠶⣤⣭⣥⣤⠴⠋⢧⠰⢀⢇⠀⠀⡀⡀⣀⠀⣘⠀⠏⣬⡀⠇⠗⠂⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢈⡷⢙⣜⣛⠚⣃⣋⣥⠞⠋⠙⣛⡁⠉⠛⠚⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣧⠀⣾⠀⢈⡏⠉⠉⠉⠉⡴⣄⠀⠀⡇⢳⡄⠀⢸⡏⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠟⠀⠙⠷⠞⠁⠀⠀⠀⢸⠃⠸⡄⠀⠳⠞⠁⠀⠘⢧⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡤⠤⠦⢤⣀⠀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠈⢹⠃⠀⠀⢠⠶⠛⠉⠉⠙⠓⢶⡞⠉⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠔⠒⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠉⢠⠋⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⣆⠀⠀⠀⠀⣠⠖⠤⠀⠀⠀⠀⣀⠀⠈⠣⢰⠋⠁⢀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⡰⠋⠀⠀⠀⠀⢰⠃⠀⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣰⠁⠀⠀⠀⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⠦⠢⠄⠀⠀⠀⠀⠠⢈⠛⠀⢰⠛⢁⡀⠀⠀⠅⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡈⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠈⠳⣞⠛⠀⠈⢞⠑⠒⠀⢄⣀⡴⠁
⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⢱⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢤⣀⡰⠓⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠈⠳⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣀⣄⣠⣄⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠡⠴⠃⠀⠀⠀⠰⠀⠀⠈⠙⣆⠀⠀⠀⣀⣀⣀⡴⠋⠀⢰⠃⢾⠓⢎⡀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⠀⠀⠀⠀⠈⠓⠦⣄⣀⣈⣇⠀⠀⠀⠘⢆⡃⢃⠀⠉⠣⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⢨⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠣⣄⡀⠀⠀⢹⠈⠆⠀⠐⢄⡉⠒⠤⡀⠀⠀⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠰⠁⡆⠀⠀⠀⠀⠀⠀⠠⢫⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠉⠉⠈⡇⠘⠀⠀⠀⠙⠦⣀⠀⠁⠒⠁⠀⠀⠀⠘⣦
⠀⠀⢀⠀⠀⡁⢀⡇⠀⠀⠀⠀⠀⠠⠁⢸⠀⠀⠀⠠⠜⠀⠀⢀⠀⠀⠀⢈⠀⢷⠀⠀⠀⠀⠀⠀⠚⠉⠉⠙⠂⠀⠀⠀⠀⡼
⠀⠀⢁⠀⠀⠉⠉⠀⠀⠀⣠⡄⠀⠠⣠⠞⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⡀⡸⠀⢸⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⠑⢆
⠀⢀⠌⠀⠀⣠⠀⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⢠⢖⠀⠀⠀⣸⠀⠀⠈⢀⡜⠁⠀⠀⠔⠋⠉⠉⠉⠙⠓⢦⡀⠀⠀⣀⠀⠀⢈
⠀⠀⠀⠀⡐⢠⠀⠀⠐⠀⢸⠃⠀⠀⣀⠀⠀⠠⠁⣸⠀⠀⠉⠁⢀⡄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠱⣄⠞
⠀⠀⠀⢀⠀⢸⠀⠀⠘⠦⠞⠀⠀⠀⢠⠀⠀⡁⠀⡟⠀⠀⠀⢀⠊⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠠⣀⡼⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠙⠷⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⢀⣠⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢾⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣾⣿⣿⠏⠙⣛⣿⣷⣄⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠑⣼⣿⣿⣿⣿⡿⠑⢂⡺⠭⢿⣿⣿⣧⡀⠈⠡⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠴⣿⠿⣿⣿⣿⣷⠀⠀⠀⢙⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠂⠠⠄⠲⠶⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣻⣿⣿⣿⣏⣀⣠⣤⣴⣶⣦⣤⣼⣿⣽⣿⣿⣿⠀⢀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠈⡏⠙⠉⠉⠛⠂⠛⠁⠿⠿⣿⣿⠙⢹⣿⡿⡟⣛⣿⠃⡿⣿⣿⢿⡇⣿⣿⣿⣿⢿⣿⣧⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⡀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠁⠉⠘⠁⡟⡏⠉⢀⠈⠉⠃⠃⡄⠸⡇⢰
⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⡎⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⣸⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣤⠤⣤⠤⠴⠖⠒⠛⠓⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠉⠛⢲⡉⠋⠀⠻⣔⣀⡤⠤⣴⣒⣓⣲⡚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⣀⣈⣡⠴⠚⠉⠁⠀⠈⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⢰⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠮⣭⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⢀⣀⣀
⠀⠀⠀⢰⣒⡦⠀⣀⣤⣤⣄⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⣀⣴⣶⠿⠚⠀⠻⠶⠟
⠀⠀⠀⠀⠉⢀⣀⣓⣶⡤⠾⠃⠀⠀⢳⣤⣀⠀⠀⢀⠀⠀⢀⡴⠋⠉⣀⣤⡘⠮⠶⠭⡖⠃⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⢰⠋⠉⠁⠈⠙⠲⠤⠤⢤⣀⣈⠛⠛⠛⠛⠛⢫⠟⠒⠒⠚⠁⢰⠃⠀⢾⡭⠽⣀⣠⣤⡀⠘⠓⠒⠋
⠀⠀⠀⠀⠈⠳⣕⠤⣀⣀⡀⠀⣀⣤⣤⣭⡿⠀⠀⠀⠀⠘⠷⠶⢦⣄⣠⢿⡖⠛⠛⠒⠛⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠋⠁⢶⣛⣒⣶⠿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⠗⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣾⣿⡿⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⢰⣿⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⠀⠸⣿⣷⣄⠀⠈⣿⣿⠀⠀⣠⣾⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⡀⠀⠈⠻⣿⣷⣄⣿⣿⣠⣾⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⢿⣿⣦⡀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⢀⣴⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠙⢿⣿⣦⡀⠀⠈⣿⣿⠁⠀⢀⣴⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣶⣦⡀⠀⠙⢿⣿⣧⡀⠀⠀⠙⢿⣿⣦⡀⣿⣿⢀⣴⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⣿⣿⣤⡀⠀⠙⢻⣿⣦⣀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⡿⣿⣿⢿⣿⣦⡀⠀⠈⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠛⠋⠀⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⡿⠋⠀⣿⣿⠀⠙⢿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⢀⣴⣿⡿⠋⠀⠀⣠⣿⣿⣄⠀⠀⠙⢿⣿⣦⠀⢸⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣴⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠙⢿⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⠀⠀⣠⣾⣿⠟⠉⣿⣿⠉⢻⣿⣷⣄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢻⣿⣿⠀⠸⣿⠟⠁⠀⢀⣿⣿⡀⠀⠈⠻⣿⠆⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠸⢿⠟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⣿⣿⠻⣿⣿⠄⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⠀⠈⠁⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣾⣿⣿⡿⠟⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣴⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣾⣷⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣠⡤⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⡆⠀⠀⠀⠀⠀⠀⠉⠀⢼⣿⣿⣿⣶⣶⣶⣦⣼⢿⣏⣷⠸⣿⣯⣿⣿⣿⣿⡷⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠊⠀⠀⠀⢀⡠⣀⡔⡀⠀⠀⠀⣿⢿⣿⢿⡿⢻⠧⢸⢸⠟⣿⡄⢻⣿⣷⣿⢻⣿⣧
⠀⠀⠀⠈⠄⠀⠋⠀⠀⠀⠀⠀⠀⢸⠱⠊⠝⠃⠀⡀⠐⠁⠀⡾⠃⠸⣁⣼⡇⢘⢨⢀⣽⠃⡈⣿⡟⡵⢀⢼⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠚⠁⠀⠚⠂⢣⡆⡄⠀⠀⠀⠂⠀⠀⠠⢸⣿⠛⠀⢈⢸⢻⠇⣸⣇⢹⣿⣷⣯⢸⡏⠀⠀⢳⣦⠄⢀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⢀⠀⠀⠀⠀⠘⢳⠀⠄⢚⢰⠿⢸⣿⣿⢀⣿⣟⣉⣼⣯⡸⢲⠀⡆⡄⢠⠘⣙⣦⣄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠢⠀⠀⠀⠀⠀⠘⠨⠘⢸⣿⣿⠀⢠⣌⣉⠙⠛⠓⠾⡀⢃⡗⠁⠀⠁⢿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠀⢁⣿⣧⢾⠀⣼⣷⣯⢸⣿⣷⠂⣸⣏⠀⠐⢠⠠⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰⣿⢼⡟⢸⠀⣼⡿⣿⣽⡿⣿⣀⠛⠷⡀⠀⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿⡿⢾⠃⡜⠠⠋⣸⠿⠃⢸⣿⠀⠘⠆⣰⣠⠄
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢙⠟⢩⡇⠁⠀⣀⡥⠀⠠⠘⡥⠀⠀⠀⠻⠁
⠀⠀⠸⠉⡇⡏⠀⠈⢀⢤⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⡡⢀⢠⠀⢀⠎⡏⠹⠀⠀⠀⠏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡇⠀⠀⠘⠀⢸⡿⣿⣿⣿⣏⣷⣿⣶⠶⢀⣤⡴⠀⠁⠀⢈⠁⢁⡺⠁⠀⠉⠈⢀⠄⣈⡔⠀⠀⣠⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⢀⠀⠈⡇⣿⢿⢟⢥⣿⣿⢣⠘⠄⢋⡀⠀⣠⠔⢉⠔⠁⠀⠀⠀⠢⠐⡎⢠⣌⠛⣶⡟⠸⣄⣠⣔⠀⠠⠎
⠀⠀⠀⠀⡧⠀⠀⠀⠀⠔⣩⢷⡿⣇⢸⣿⣿⠈⣀⢖⢹⡇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⣿⡏⣷⣎⠙⣏⣿⢘⣵⣶
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⢈⡡⣿⣸⢿⢸⠊⠀⠸⠀⠃⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣏⡿⠻⣷⠘⠻⣿⣟⣹⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⠀⠐⠀⠀⢨⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠠⠀⠀⢚⡁⠈⠀⢾⣣⠘⢾⣿⣿⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢠⠀⠎⢛⡇⠸⣿⠻⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠂⠀⠿⡀⡉⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠅⠀⡇⠃⠀⠀⠀⣀⠖⢠⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡂⠀⠀⠀⡆⠀⣏⣥⠴⠚⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠒⠶⣄⡀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡀
⠀⠀⠀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠞⠁
⠈⠳⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠴⠛⠁⢀⡴⠟⠓⠶⠤⠴⠞⠋⠀⠀⢸⡇
⠀⠀⠈⠉⠉⡍⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠳⠦⣤⣤⠴⠛⠉⠛⠒⠒⠒⠛⠉⢠⡄⠀⠀⠀⠀⢸⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⡇⠀⠀⠉⠓⠲⠶⠶⠖⠛⠁⣄⠀⠀⠀⠀⢰⡆⠀⠀⢰⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⢠⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⡄⠀⠀⢨⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠋⠀⠀⠀⠀⢘⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠛⢦⡀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠚⠛⠓⠶⢤⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⡶⣶⣶⣶⣶⡞⢉⣿
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⣠⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡉⠱⣯⠀⠀⠀⢹⡿⢷⣄
⠀⠀⠘⠳⢤⣤⣀⣀⣠⣤⠤⠶⠚⠉⠀⠈⠛⠒⠶⠶⢺⡿⣅⠀⠘⠛⣷⢶⡦⢤⣤⣤⠶⡞⢷⠞⣴⠛⣛⡀⠀⠀⣼⢃⡤⡿⢀⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣓⠘⢓⣒⣒⡛⠂⢛⠒⠛⠘⠳⠿⠂⠘⣓⣚⠋⣙⣓⡚⢁⣛⣛⣛⣛⡁⣛⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣿⡴⠋⣩⠽⢏⡼⠋⠉⢻⣞⣩⡟⣴⣎⢿⣉⣷⠿⠉⠙⣎⢻⣉⡁⠈⠳⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣼⡆⠀⠀⠸⣯⠍⢸⣇⣼⢀⢨⡿⠀⠀⠀⣸⠇⢩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠳⠶⠶⠶⢋⡾⠋⠁⠉⠛⣧⠹⠶⠶⠴⠻⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⠉⣹⢃⣌⢷⡀⠀⠀⣰⢋⣦⡸⣟⢳⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⢣⠟⣽⠈⢹⣿⡏⠁⣿⠀⢳⡘⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⢀⡹⣆⠈⠛⠋⠈⠳⠟⠋⠀⢠⡏⡐⢿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠏⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠢⢶⣤⢀⢄⡀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠑⣇⣚⢡⡞⡥⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⢢⠃⠙⠙⢇⡇⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣸⠀⠀⠠⢀⡷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠉⠉⠁⠓⠀⠁⠸⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠁⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⡱⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠇⢠⠁⠀⠀⠀⣨⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣄⡁⠀⣀⡤⠄⠗⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠉⠀⠂⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣨⠀⠀⠀⠈⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠐⠠⠰⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠂⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣧⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⡘⢀⠢⠃⠀⠀⢀⠄⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠉⠉⠛⠀⠀⢀⡇⠀⠀⠀⠀⡠⠈⠀⢼⣄⣀⢀⠔⠁⠰⠀⡸⡊⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠀⠀⠀⢃⠀⢀⠊⠀⠙⠊⠀⢀⡶⢂⢫⡑⢄
⠀⠀⠀⠀⠀⠈⠒⠀⠀⡀⡀⠀⢀⣦⡴⠋⠠⢔⣶⣶⠒⣲⠗⠀⠀⠀⠀⣀⣀⠴⢏⣠⣈⣄⠝⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡁⢤⣤⡤⢎⣉⣀⠿⠉⠓⠲⡦⢀⠀⠀⠀⠀⠀⠻⣭⣹⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠼⠿⠇⠼⢿⣏⣉⣶⡆⠐⡏⠀⠙⠛⠛⠛⠙⠻⠿⠀⠿⠧⠼⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠄⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠒⢛⡉⠛⠒⢦⣀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠔⡡⣫⡟⢀⡤⠛⢦⡀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⣾⠫⠞⣵⣹⡏⢰⣿⣆⡇⠀⢰⠀⢷⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⡞⠁⠀⠣⣭⠽⠳⢤⣭⠞⠁⠀⢸⠀⢸⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⣰⠏⣠⠴⠒⠚⠋⠉⠉⠛⢲⡄⠀⠀⢸⠀⠈⣇⢸⣤⠖⠒⠒⠲⢤⣀⠀⠀⠈
⡏⠀⢧⣀⠀⠀⠀⢀⣀⣤⠾⠁⠀⠀⢸⠀⠀⢻⠘⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠐
⠻⡄⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠙⢦⣄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣏⠛⢦⣄⠀⠈⠢⠄⣤⠘⣆⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⡟⠀⠀⢸⡟⠶⣤⣀⣠⣴⠏⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠸⡄
⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠈⠁⣯⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡀⠀⠒⢮⡁⢚⠄⢣
⠀⠀⠀⠳⠶⠚⠁⠀⠀⠀⠀⠀⠘⣾⢦⣤⠴⠞⠁⢀⡠⠖⠋⠉⠉⣧⡤⠤⢷⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠻⡄⡖⠒⠚⠉⠀⠀⢀⣀⣼⠁⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢤⠇⡇⠀⠀⠀⠀⡞⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⠃⡇⠀⠀⠀⠀⠙⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡗⢀⡇⠀⢀⣀⣀⠀⠀⠉⠓⢤⡀⠈⢦⡀⠀⡐⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠘⠣⡀⣇⠀⢌⠟⠉⠉⢁⣒⣛⡂⠒⠛⠢⠈⠓⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣇⣀⡇⠀⠀⡇⠈⠑⢾⣀⡄⣞⠀⣫⠈⠉⠉⠙⠓⠒⠦⠾⠀⠳⣌⡑⠒⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠿⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠿⢷⣦⣴⡿⠉⢀⣠⣤⡀⠀⠀⠙⢿⣶⣶⡶⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⣀⣤⡀⠀⠈⠉⠀⢠⡿⠋⠉⠀⠀⠀⠀⠈⠁⠀⣀⣀⠀⠉⠻⣧⡀
⠀⠀⠀⢀⣠⣤⣼⡟⠀⢠⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣆⠀⠹⣷⣤⣄⡀
⠀⣠⣾⠟⠋⠉⠉⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠙⠻⣷⡀
⣰⡿⠁⢀⣴⡾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣦⠀⠘⣿
⣿⡇⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢹
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠈⢿⣦⡀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠙⠻⢷⣶⣶⣶⡾⠟⢻⣧⡀⠈⠛⠿⠷⠀⠀⠀⣠⣤⡀⠀⠀⠰⠾⠿⠋⠀⣰⡿⢿⣶⣶⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣠⣤⣾⠟⠛⢿⣦⣄⣀⣀⣠⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠹⣷⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣼⡟⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⣹⡇⠀⢀⣼⡿⣷⡀⠀⠀⢸⣿⡀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠻⠷⠾⠟⠁⠀⣾⠏⠀⠘⣷⠀⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣴⡿⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢸⣿⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠉⠁⠀⠀⢀⣾⠟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡾⠋⠀⠀⠀⠀⣴⡿⢻⣦⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⢹⡇⠀⠀⠀⠀⠀⠈⠻⠷⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠶⠚⠳⠶⢦⡴⠚⠉⠁⠀⠀⠀⠈⠙⢳⣦⡴⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⢶⣟⠋⠀⢀⣿⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⠿⠶⠖⠒⠒⠀⠀⠀⠀⢀⡤⠶⠒⠲⢾⣅⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠐⠉⠉⠳⠄⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⢿⡇⠀⠀⠀⠀⣀⣴⣏
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡾⠛⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠻⣆⠀⠈⠀⠀⠀⠀⢨⣁⠀⣹
⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠓⠀⠀⠀⠀⠀⠀⣾⠁⠀⢨⣿⣿⣿⣶⣾⠇⠀⠀⠀⣷⣶⣿⣿⣿⣇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠹⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠻⠿⢟⡿⠋⠀⠀⠀⠀⠈⢿⡛⠷⠿⠋⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠛⠓⢶⣶⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⢷⣲⡶⠖⠛⠋⠀⠀⠀⠀⠀⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠙⠳⠶⣤⣤⣤⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣤⣴⣶⠟⠉
⠀⠀⠀⠀⠀⣠⠴⠻⣇⣀⠀⠀⠀⠀⣰⠇⠀⠙⠦⣤⣀⣀⡀⠀⠀⣀⣰⣦⣤⣄⣀⣀⣀⣀⣀⣠⣤⡶⠟⣧⠀⠀⠀⢸⣧⣤⠤⣦
⠀⠀⠀⠀⠛⣻⠟⠀⣀⠭⠛⠀⠀⣴⠃⠀⠀⠀⢴⣏⣉⡉⠛⠛⠛⠛⠉⢸⡆⠈⠉⠉⣿⠉⠉⠉⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢀⡴⣚⡵⠖⠋⠁⠀⠀⢀⡾⠁⢀⣀⠀⠀⠀⠀⠉⣩⠗⠀⠀⠀⠀⢸⡇⠀⠀⢸⡷⠶⠛⣿⠀⠀⠀⠀⠸⣦⣤⢾⡆⠀⢸⡇
⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠛⠋⠉⢩⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⣄⠀⠀⠈⠀⠈⣧⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣁⣤⠴⡶⠀⠀⡾⠀⠀⠀⡟⠶⠖⡶⠀⠀⢹⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⡴⠋⠀⠀⠀⠀⢀⡴⢿⣀⡀⠀⠈⠉⠀⠀⣧⠀⢸⠃⠀⠀⠠⠧⡆⡼⠁⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠞⠉⠀⠀⠀⠀⠀⢠⡾⢴⢀⡼⠁⠀⠀⠀⠀⠀⣿⢀⡏⠀⠀⠀⠀⢰⣷⠃⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣣⠎⠀⠀⠀⠀⠀⠀⠀⣿⢸⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠛⠉⠙⢦⠀⠙⢶⠦⣄⡀
⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⣆⠀⠙⠲⣄
⢣⠀⠀⠀⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠓⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⡆⠀⠀⠈⢳⡀
⢻⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⠀⠀⠘⣆⠀⢹⡀⠀⠀⠀⢻⡀
⢸⠀⠀⢀⢠⢶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⣽⡀⠀⢧⠀⠀⠀⠀⣇
⢸⡀⠀⠨⢸⠰⡏⠅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡷⢤⣀⠀⣿
⢸⡇⠀⠨⢸⠀⡇⡃⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠒⠒⠒⠲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⠈⠳⣇
⢸⡇⠀⠶⠺⡄⡗⠶⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠒⢦⣀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣄⣀⣀⣰⡒⠢⢼⣀⠤⣼⠴⢦⠀⢸⡆
⠈⡇⠀⠀⠥⡇⡇⠅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡇⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠄⠀⠁⠀⠈⠁⠀⠀⠀⠛⠉⡿
⠀⡇⠀⠀⠄⡇⡇⠁⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢷⣀⡀⠀⢸⢸⡆⠀⠀⠀⠀⠀⠀⠛⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆
⠀⡇⠀⠚⢋⡇⣇⣉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⣿⣁⣤⠏⠘⠃⠀⠀⠀⠀⠀⠀⠰⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧
⠀⢿⠀⠀⠄⣇⢿⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⡀⠀⠀⠘⣇⠠⣄⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⢸⠀⠀⠀⣿⢸⠀⡰⠄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡞⣇⡇⡇⢠⠶⢮⡳⠀⠀⠀⠀⣼⣯⠏⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⢸⠀⠘⢋⢹⢸⢨⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⠳⠻⠇⠁⠀⠀⠈⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢻⠀⢀⡀⠀⣄⠀⢸⠻⣅
⠀⢸⡆⠀⢐⢸⣸⠐⠀⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣜⣋⠛⠦⠟⠀⠀⠀⣀⣤⠴⠶⠶⠦⣄⠀⠀⠀⠈⠓⠋⠣⠤⠏⢹⠏⠀⡻⣄
⠀⠸⡇⢠⣴⢸⣾⠐⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣀⠀⠀⠀⠈⠳⣀⣠⠴⠖⢻⡁⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡇⣸
⠀⠀⡇⠀⢀⢺⣿⠀⡂⠀⠸⡇⠀⠀⠀⣀⡤⠖⠛⠋⠉⠁⠀⠀⠀⠀⠙⠲⢖⡶⠒⣲⠖⠲⢤⡀⣽⠀⠀⠀⠐⠛⣿⡟⠀⠀⠀⠀⠀⢀⡴⠁⠀⢠⡟⢀⡟
⠀⠀⡇⠀⠀⠈⣿⡆⠂⠰⠰⡇⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠙⠲⣄⠀⠙⠳⣄⡀⠀⠀⠀⣿⠇⠀⠀⠀⢀⡴⠋⠀⠀⢠⡟⠀⡼⠁
⠀⠀⣿⠀⣤⠄⣿⡗⠚⠁⠀⣿⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⡿⠀⠀⠀⠀⠉⠓⠒⠚⠁⠀⠀⣀⡴⠋⠀⠀⠀⣠⠏⢀⡾⠁
⠀⠀⣿⠀⠀⠀⡿⣇⡀⠀⠀⢹⠀⠀⠈⠣⣤⣀⡀⠀⠀⠀⠀⠀⣴⡆⠀⣾⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠸⠃⣠⠏
⠀⠀⢸⠀⠀⣰⠃⣀⣽⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧⢀⣼⣦⢠⣤⠇⢧⡿⣸⠀⠀⠀⢀⡞⠻⠦⠤⠤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⢸⠀⠀⠘⠿⠶⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⢸⠁⢺⢸⣿⠀⠘⠑⠟⠀⠀⠀⠈⢳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢦⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠘⡇⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⡇⠰⡇⣹⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣇⢸⠀⠀⠀⠀⡇⠀⠷⢣⣏⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⢦⡑⠿⢸⠀⠀⠀⠀⣇⡴⠲⢤⠞⠲⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡤⠾⡄⣀⣀⡔⠻⡇⠀⠸⡄⠀⠘⢦⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⡴⠛⢾⠁⠀⣿⠁⢸⡀⠀⢳⠀⠀⠹⡄⠀⠈⠳⢶⡛⠋⠉⠙⠻⢄⠀⠀⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠷⣸⠃⠀⡏⠀⠀⡇⠀⢸⢧⠀⠀⢧⠀⠀⠈⢦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠘⢯⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⡽⠋⣹⠀⠀⡇⠀⠀⢻⠀⠘⡎⢧⡀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⣿⡀⠀⢻⡀⠀⠈⢇⠀⠘⢆⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⡍⠲⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⢏⢧⠀⠀⠱⣄⠀⠈⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⢧⢀⡘⢿⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡳⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⠀⢸⣸⡏⢳⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠚⢧⠜⠁⢹⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢀⡉⠀⠀⠀⠀⣧⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠉⠙⠒⢲⠒⠒⠋⠁⠀⠀⠀⠘⡟⡟⠉⠉⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠓⢋⣀⣠⣤⣀⡀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠎⢁⡠⠤⠤⢤⡴⠋⠁⠀⠀⠀⠀⠉⠳⣄⠀⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⢠⠔⠋⠁⣀⣠⣾⣁⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣶⣶⡦⢤⣀⠀⠘⣆
⠀⠀⠀⠀⢰⠃⢀⠔⠊⠁⣀⣀⣤⣹⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⠿⣿⡷⠀⠈⢳⡀⠹⠦⢄
⠀⠀⣠⠔⠋⣠⠧⠀⠀⠸⠟⣻⠛⠻⣿⣆⠀⠀⣀⠀⠀⣠⣿⣏⠀⠙⢧⠀⠈⠁⡤⠂⠉⠉⠑⢦⡀⢳⡄
⠀⡼⠁⢠⠎⠀⠀⠀⠀⠀⢀⣿⠀⠘⢷⣿⣷⠾⠙⠷⣾⠿⣭⡿⠃⠀⣸⡆⠀⠸⣄⡶⠀⠀⠀⠀⢳⠀⣷
⢰⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠋⠓⠦⢤⠶⠋⠀⠀⠀⠘⢷⠦⢤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼
⠈⢧⡀⠣⣀⠀⢀⣠⠴⠒⣵⠆⠀⣠⡴⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⠇
⠀⠀⠙⠲⡌⠉⢏⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠻⣶⣤⣼⢷⡀⠀⣰⠀⠀⠘⢉⡗⠲⠖⠒⢉⡴⠋
⠀⠀⠀⠀⢧⠀⠀⠑⠤⣄⣀⣀⣀⣀⣁⣱⢦⣀⠀⠀⠀⠀⢀⣸⠥⠚⠣⠤⠤⠒⠋⢀⣀⡼⠋⠉
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠉⠉⠉⣩⣄⣀⠈⣹⠋⠉⠉⣹⠤⢤⣚⣩⡍⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠖⠒⠋⠁⠀⠉⢹⠇⠀⠀⠀⠛⠋⠉⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⡤⠤⢶⡄⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⡇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠛⠻⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠉⠛⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⠛⠛⠿⣶⣄⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡿⠋⠉⠀⠀⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣶⣶⣶⣦⣄⡀⢿⡆
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⢠⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠈⠻⣧
⠀⠀⠀⠘⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⢛⣿⠟⠛⠛⠛⢛⣿⠿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⣰⣿⣃⣀⣻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠈⠛⠛⠛⢻⣿⠋⠛⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⢻⣿⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣾⣿⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣀⣀⣀⣀⣈⠉⠉⠉⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⣻⡏⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⢛⣛⣛⡛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣚⣛⣛⡒⠶⢤⣀⡴⢋⣵⡾⠿⠿⠿⠿⠿⣿⣶⣤⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⡾⠿⠿⠿⠿⢿⣷⡦⠈⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡹⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠈⢿⣷⣶⣤⣍⡙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠰⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣦⡉⠉⠙⠻⢿⣷⣄⣙⡶⠶⠦⣤⣀
⠀⠀⠀⢀⣠⠶⣛⣯⣠⣶⠿⠛⠋⠉⠉⠉⠉⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠙⠛⠿⠿⢿⣷⣦⣍⡛⢦⡀
⠀⢀⡴⢋⡴⠛⢋⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠹⣆
⢀⡾⠁⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠸
⣼⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⣀⣠⡤⠞⠛⠒⠶⠶⠚⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠳⠦⣤⣀⣀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠒⠚⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⣿⠀⠀⢀⡼⢿⡄⠀⠀⠀⠀⢾⡀⢀⣠⣿⡇⠀⢀⡴⢻⡆⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠳⠯⠷⠋⠀⣴⠏⠀⢸⣇⠀⠀⠀⢀⡈⠳⠯⠷⠋⠀⣠⠟⠁⢸⣿⠀⠀⠀⠀⣀⠛⠾⠽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣧⠀⠀⠀⠀⠸⣇⢀⣠⣾⣿⠀⠀⣠⠞⣷⠀⠀⠀⠀⠀⣯⠀⣀⣼⣿⠀⠀⣠⡞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡀⠀⠀⠀⣀⠙⠳⠷⠞⠁⢀⡾⠃⠀⣿⡆⠀⠀⠀⢀⡈⠳⠷⠞⠋⠀⣴⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⣴⣿⠇⠀⢠⡾⢻⡆⠀⠀⠀⠀⢸⡅⢀⣤⢿⡇⠀⢀⡴⠛⣇⠀⠀⠀⠀⠸⣇⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⠲⠞⠋⠀⣴⠋⠀⢸⣷⠀⠀⠀⢀⣀⠙⠲⠖⠋⠀⣠⠟⠀⠀⣿⡀⠀⠀⠀⣀⠙⠳⠖⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣷⠀⠀⠀⠀⠀⣧⠀⣠⣾⣿⠀⠀⣰⠟⢻⡀⠀⠀⠀⠀⢿⡀⣠⡼⣿⠇⠀⣠⠞⢻⡆
⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡇⠀⠀⠀⠀⠈⠛⠒⠛⠁⢀⡾⠁⠀⢸⣇⠀⠀⠀⠀⠈⠙⠓⠛⠁⠀⣴⠋⠀⢸⣷
⠀⠀⠀⠀⠀⢸⣄⢠⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣴⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣤⢾⡿

⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠲⣢⣾⣧⡲⠃⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣷⣴⠂⠀⠀⠀⠀⠀⣴⣿⠁
⠀⠲⠾⣿⣿⣿⡿⠶⠂⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠒⠢⡀⠀⠀⠀⢀⠈⠉⠿⠿⢟⠉⠀⠀⠀⠠⠀⠹⠿⣄
⠀⠀⠼⠊⢻⡏⠳⠆⠀⠀⠀⠈⠿⣿⣷⣤⣀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠁⡱⠀⠀⠀⠀⠀⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠠⣄⣿⣠⠄⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠄⣲⣶⠂⢄
⠀⠀⡀⠆⣿⣿⣿⠒⠀⠀⠀⠀⠠⠘⣿⡄⠀⠀⠀⠀⠀⡔⠀⠐⠤⢄⠀⠀⠀⠀⠀⣠⣿⣆⠀⢿⠗⠀⠀⢐⠁⢰⣿⣿⣧⠀⢁
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠂⠀⠀⠀⠘⠓⠂⠀⠀⠎⠀⠀⠀⠀⠀⠓⢢⠀⠀⢰⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠉⠉⠙⠉
⠀⠈⡄⡀⡄⡀⡄⠀⠀⠀⠀⢀⠀⢠⢀⢠⠁⠀⠀⠀⠈⢁⠀⢀⡀⠀⣀⠁⠀⠀⠈⠮⣿⠿⠃⠀⠀⠀⠀⠀⠀⠠⣤⠆
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢈⣀⠀⠀⠀⠀⠀⠈⠘⠈⠀⠃⠁
⠀⠀⠀⠐⣦⣿⣴⠂⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⡀⠐⠂⠒⠄⣀
⠀⠀⠀⠃⠻⠿⢿⡉⠀⠀⠀⠀⠐⠚⠿⢆⡀⠀⠀⠀⢀⠌⠁⠈⠂⠠⡀⠀⠀⠀⠀⢀⣿⣏⡄⠀⠀⠀⡠⠁⠀⠑⠒⢄⠀⠀⠓
⠀⢈⠀⠀⠀⠀⠀⠁⠀⠀⠀⡁⠀⠀⠀⠈⠩⠁⠀⠀⢇⡀⠀⠀⠀⠀⠉⡱⠀⠀⠀⠀⢀⠟⠁⠀⠀⠘⣀⠀⠀⠀⠀⠈⢈⠆⠒
⠀⠀⠈⠃⠘⠃⠀⠀⠀⠀⠀⠀⠘⠀⠛⠀⠀⠀⠀⠀⠀⠀⢻⠅⠹⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣘⣷⣿⣾⣁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢠⣄⣈⣿⣇⣠⣄⠀⠀⣠⠤⠤⣤⣠⠤⠤⣤
⠀⢀⠀⠁⠙⠻⠿⡌⠀⠀⠀⡠⠀⠈⠛⢦⣀⡀⠀⠀⡠⠊⠀⠀⠁⠐⣄⡀⠀⠀⠘⢹⣓⣬⣞⡋⠋⠀⠀⠒⣚⣛⡒⠖⣚⣓⡒
⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⠈⠀⠀⠀⠣⠀⢀⠀⠀⡀⢀⠜⠀⠀⠸⠿⠫⣾⡜⠻⠿⠀⠀⢩⠥⠤⢭⣭⠥⠦⢭
⠀⠀⠰⠀⠂⠰⠀⠀⠀⠀⠀⠀⠆⠐⠀⠆⠀⠀⠀⠀⠀⢠⡆⠠⠄⢰⡄⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⣰⡆⠀⣴⠂⢀⣶⠀⠀⠀⠀⣤⠀⢼⣿⡯⠀⠀⠀⠀⠀⠀⢘⣶⣷⡃
⠀⣶⣶⣶⡦⠤⠄⠁⠀⠀⠘⠛⣓⠚⢛⡓⠛⢛⠂⠀⠀⠀⣿⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠈⠀⠃⠁⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣾⣇⣠⣿⣀⣴⣿⡀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠂⠀⠀⠡⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠄⠀⠀⠀⠤⠀⢠⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠤⠰⠄⠂⠀⡄⠀⠀⣠⣀⣀⡀⠉⠙⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠐⠒⠂⢼⢛⠉⠉⠈⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠃⠀⠛⠁⢼⠀⠀⠀⠀⠀⠀⠐⠄⠐
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⡘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⡠⠳⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⡈⠢⠁⠀⠤⠀⠀⠤⠄⡄⠀⠐⠀⠀⠎⠰⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⠘⠛⠿⠤⢰⡖⢲⠇⠀⠚⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠒⠀⠀⠠⡄⠀⠀⡀⡀⠀⠐⢀⠀⠁⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠁⠀⠡⢒⡄⣁⣛⠄⠁⠀⠃⠂⠈⢄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⡀⠀⠀⠀⠩⠁⠀⡫⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠉⠉⠃⠈⣋⠁⠈⠉⠉⠘⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠀⠀⠉⠁⡀⠤⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⢐⡒⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⣛⣛⣛⡛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣚⣛⣛⣛⡓⠶⢤⡴⣫⡴⠿⠛⠛⠛⠻⠿⣿⣶⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡶⠟⠛⠛⠛⠛⠿⠟⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡘⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠿⠿⠿⣶⣦⣄⠹⢿⣿⣶⣦⣍⠛⢦⡀
⠀⠀⠀⠀⠀⣀⣠⡏⢀⣠⣴⣶⠶⠶⢶⣶⣤⣀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠈⠙⠿⣿⣦⣭⣭⣛⡓⠦⣄
⠀⠀⢀⡴⣋⣽⢾⣶⠟⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠉⠉⠛⠻⢿⣷⣌⠻⣄
⠀⣴⠋⠞⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡘⣧
⣸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⣀⣠⡴⠞⠓⠒⠖⠒⠛⠳⣄⣀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠶⣤⣄⣀⣀⣀⣤⠴⠶⠶⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⡼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠴⣿⠇⠀⣠⠞⢹⡇⠀⠀⠀⠀⢧⡀⠴⣿⠇⠀⣠⠞⢹⡆⠀⠀⠀⠀⢧⡀⠴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠉⠋⠉⠀⣼⠃⠀⢸⣷⠀⠀⢀⣴⡄⠉⠋⠁⠀⣼⠃⠀⢸⣷⠀⠀⢀⣴⡄⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⣧⠀⠀⠀⠀⠹⣄⣒⣻⠟⠀⣠⠟⠈⣧⠀⠀⠀⠀⠻⣄⣒⣻⠏⠀⣰⠟⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⣿⠀⠀⢀⡴⣆⠀⠉⠀⠀⢸⠃⠀⢠⣿⠀⠀⢀⡴⣆⠀⠉⠀⠀⢸⠃⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⡽⠟⠀⣰⠏⠀⣿⠀⠀⠀⠀⠘⠷⣼⡽⠟⠀⣰⠏⠀⣿⠀⠀⠀⠀⠘⠷⣼⡽⠟
⠀⠀⠀⠀⠀⠀⢀⡼⢿⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇⠀⢀⡾⣿⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇⠀⢀⡾⣷
⠀⠀⠀⠀⠀⣰⠋⠀⢸⡇⠀⠀⠀⠀⠙⠾⠷⠋⠀⣰⠋⠀⢸⡇⠀⠀⠀⠀⠙⠾⠷⠋⠀⣴⠋⠀⢸⡇
⠀⠀⠀⠀⠀⣧⢀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣤⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⡠⠘⠃⡴⡀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⢱⠯⠀⠐⢿⠲⠀⠀⠀⠀⠀⠀⠀⢠⣼⠷⠇⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢰⠲⠤⠀⠀⣾⠀⠀⠀⠀⠘⠰⣤⠄⠀⠀⠀⠀⠀⢠⠀⠀⠋⢉⠈⣏⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣆⠀⠀⠀⠀⠀⠟⠮⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉⠀⠈⠳⣤⣏⣠⡀
⠀⠀⠀⠀⠀⠀⣡⡞⠀⡀⢠⣄⡤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠀⠀⠀⠀⠿⣿⢿
⠀⠀⠀⠀⠀⠴⠏⠙⠀⠻⣾⣿⡇⠈⠇⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣂⣄⣠⣿⡀
⠀⠀⠀⠀⠃⠀⠀⠚⠦⠀⠈⠋⡇⠀⣀⠀⠁⠈⠀⠀⠀⠀⠒⢷⡀⠀⠃⠤⠀⠀⠀⠀⠀⢉⡉⡀⠀⠀⢀⡷⠉⠉⠸⣟⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⡀⣀⢷⡀⠸⣶⠠⡀⠀⠤⠀⠀⠘⣿⣧⣠⡤⣤⣤⠄⠀⠀⠀⣈⠻⣿⣶⣿⠉⠀⠀⠈⠀⠼⠃
⠀⠀⠀⠈⠲⣷⠗⠀⠀⠣⠁⠀⢸⣿⣦⡈⠋⣑⣀⣀⡀⣀⣠⡜⠋⠙⠿⣋⣥⠦⠀⠀⠀⠘⠛⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠈⢶⣔⣲⡄⠀⡠⢿⣿⡞⢷⡶⣿⠿⣬⣙⠛⢯⡁⠀⠠⠀⣤⢤⠀⠀⢀⠀⠀⡆⠠⣄⣄⢀⡃⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠈⢷⡀⢛⣆⡾⠃⢻⡀⠹⢿⡿⠛⢠⡀⢠⡐⠘⠈⠇⠀⠈⠂⠀⠸⠀⠙⠀⠈⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠛⣆⠀⠀⠈⠇⠀⠀⢆⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⠈⠁⠀⠄⠘⠀⠀⠘⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣾⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣄⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⠀⣠⣶⡿⣟⣛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⣵⣮⣿⣇⣠⣴⣾⣿⣿⡿⢋⣍⠙⠋⠉⠀⡀
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣾⣿⣿⣿⣿⣿⣿⡝⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡯⠴⠟⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢢⡀⠓⢢⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⣿⠛⠻⢿⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠓⢾⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⣠⣿⣷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⢿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠙⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠉⠙⠛⠛⠿⠿⠟⠛⠛⠉⠁⠀⠠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⡄⠀⠀⢠⣧⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠟⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠿⣿⣿⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿
⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⠁
⣿⣿⡇
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⢻⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⣀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⠷⣦⣄⡀⠀⣰⡿⠋⠀⠀⠀⠀⠈⠙⢷⣄⠀⣀⣤⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠉⠛⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠁⠀⠀⠀⠙⢿⣦⡶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⣴⡿⠋⠁⠀⣀⣉⣀⣀⠀⠀⠀⢀⣴⠿⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣄⡀
⠀⠀⢸⡟⠀⠀⢠⡾⠛⠉⠉⠙⠛⢦⣴⠟⠁⠀⣀⣀⣀⠈⠳⣤⠶⠛⠛⠛⢷⣆⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷
⠀⠀⣿⡇⠀⢠⡟⠁⣠⡶⠖⠒⠶⠀⠉⠀⠀⠀⠀⠀⠈⠓⢄⡠⠔⠚⠛⠒⠀⠛⠁⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⡇⠀⣼⠇⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⡿⠿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⡀⢀⣾⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠿⣿⡿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠃⠈⠻⠿⠿⠿⠋⢿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠟⠁⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡧⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃⠀⠀⠀⠘⠿⠟

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⠶⣦⣤⣴⡶⠿⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢀⣠⣤⣴⣶⠶⣶⣤⣤⣀⣠⣴⠶⠿⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⣽⡟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢀⣾⠏⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠶⢶⣼⣇
⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢿⣦
⠹⣧⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠙⢷⣄⡀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠉⠛⠻⠿⠿⠛⠋⠻⢶⣤⣄⣀⣀⣀⣤⣴⠾⢻⣧⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢭⣉⡍⣩⠁⡀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣸⠀⠀⢹⡟⠁⠀⣿⡤⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣠⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠙⢦⡀⢸⡇⢀⡴⠋⠉⠉⣀⠀⠀⠙⠛⠷⠶⠶⠶⠶⠿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠻⠶⠶⠶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣀⣀⣙⣶⣷⣏⣀⣀⣠⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠟⠛⠛⢛⣿⣿⡿⠟⠛⠻⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⡴⢛⡟⢦⡀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⢀⡴⠋⢸⡇⠙⢦⡀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⠋⠀⢸⡇⠀⠙⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⢿⠀⠀⢸⣇⠀⠀⡿⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⣠⠾⡷⣄⠀⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶⠻⠏⠳⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠈⢻⡷⠃⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⠻⣄⢸⡇⣠⠞⠛⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⠤⠬⣿⣿⠧⠤⠴⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣠⠞⢹⡏⠳⣄⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣼⣧⡀⢸⠛
⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣷⣶⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠾⡿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣶⣤⣴⣶⣶
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠟⠁⢈⣽⣿⣿⣿⠿⠛⠿⠟⠛⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠟⠉⠉⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠛⢋⣡⣤⣤⣤⣶⣶⣶⣾⣷⣶⣶⣄⡀⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡾⠛⠉⠋⠀⠀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡟⢉⡻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣿⣿⣸⣿⢿⣿⣏⣽⣿⣿⣿⣿⣿⣧⣼⣿⡈⠉
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣠⣤⣶⣶⣦⡀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣶⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠛⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⢤⣼⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠉⠙⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿
⠀⠀⠀⠀⢻⡏⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣽⡟
⠀⠀⠀⠀⠈⢿⣄⢅⡂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⡠⢐⠠⢐⣼⠟
⠀⠀⠀⠀⠀⠈⠻⣷⣬⣄⡂⠀⠀⠄⣀⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢤⣄⣅⣂⣌⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠑⢦⣥⣅⣐⡐⡀⠀⢂⠄⢅⣐⣐⡽⢿⣦⣄⠄⡀⡀⡀⠀⠀⠄⣄⡶⠟⠁⠀⠈⠉⠉⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠛⠷⠾⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢤
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣰⡟⠁⢰⡄⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⣾⠋⠀⢱⡀⠀⠀⠀⢿⡄⠀⣸⠇⠀⠀⠀⠀⠀⢰⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⢀
⠀⠀⠀⢿⣄⣀⡼⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⠀⠀⠘⢧⣀⣠⠟⠀⠀⢀⣴⠞⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡞⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠉⠁⠀⢀⣼⠟⠁⠀⠀⠀⠙⠷⠴⠟⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠋⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣄⠀⠀⠀⠀⣿⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⡾⠁⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠙⢦⡴⠟
⠀⠀⠀⠀⠀⢠⡾⠋⡀⠀⠀⠀⠀⠀⠹⢦⡴⠟⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠙⠶⠾⠋
⠀⠀⠀⠀⠀⣿⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠻⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠐⣄⠀⠀⠀⠀⠀⠀⢼⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠷⠤⠾⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠙⠳⣤⣤⡤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⡤⠶⠲⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡞⠀⠻⡴⠶⠤⠶⠦⠤⠶⣴⠋⠈⢷⡶⠦⠴⠶⠤⠶⢦⡾⠁⠹⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣏⠀⠀⢘⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⠀⠀⠙⠓⠶⠛⠀⠀⠀⠀⠀⠀⠀⠛⠲⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠈⢷⡀⠀⠀⠀⠀⠀⣰⠃⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣏⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋




⠀⢀⣀⢀⣀⡀⣀⣀⠀⣀⡀⢀⣀⡀⣀⣀⠀⣀⡀⢀⣀⠀⣀⣀⢀⣀⠀⣀⣀⢀⣀⡀⢀⣀⠀⣀⡀⢀⣀⠀⣀⣀⠀⣀⡀⢀⣀⠀⣀⣀⢀
⣿⣏⢭⣟⡛⣛⣛⠛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⣿⣏⠙⢿⣷⡄⠀⠀⠀⠀⠀⢸⣿⠙⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣠⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣀⣨⣿⡗⠀⠀⠀⠀⠀⠸⣿⣆⣀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⡶⠟⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⣀⣿⣦⣤⣤⣾⠋⠀⠀⠀⠀⠀⠈⢻⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢠⡾⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢻⣦⡶⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢻⣦⣤⠶⣤⣤⡈⣿
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣿
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠙⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⢀⣴⠾⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣙⡳⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⠁
⢠⡟⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠈⢿⣤⣤⡾⠋⠀⠀⠀⠀⠀⣰⡟⠉⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⠀⠀⠀⣠⡶⠟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣆⡀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁⣿⠃⠀⢸⡏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⢀⣤⡾⠛⣿⠀⠀⠉⠛⠋⠁⠀⠀⠀⣀⣼⣷⠀⢸⣏⠀⠀⢠⡿⠀⠀⠘⢷⣤⣴⠿⠁
⠀⠀⠀⠀⢰⡟⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠾⠋⠁⣿⠀⠀⠙⠷⠾⠛⠁
⠀⠀⠀⠀⠘⣧⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⢠⡿