Christmas text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⡀⠘⠑⠉⡍⠩⠀⠀⠀⠀⠀⠀⠀⡠⢢⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⠰⠈⠻⠉⠀⠡
⠀⠀⠀⢸⠁⣇⣤⣴⡧⢠⠴⠇⠀⠀⠀⠀⠐⠁⠂⠨⠈⡟⠈⠙⠉⠈⠂⠀⠀⠀⠀⡇⠶⠀⡄⣬⠤⡕⠆
⠀⠀⠀⠀⠁⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣄⢀⢀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠆⢀⠤⠖⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⢰⣴⣀⣀⣀⣀
⠀⠀⠀⡠⢀⠁⠘⠈⣈⠀⣠⠇⠀⠀⠀⠀⢠⠇⢡⣏⢀⣀⣄⣎⣀⣠⣠⠀⠀⠀⠀⡧⣄⣈⢡⣡⠁⡿⡀⡄
⠀⠀⠸⠁⠷⠠⠀⠸⠁⠰⠐⠂⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⢋⠄⠈⠀⠚⠁⠀⠀⠀⠓⠉⠋⠘⠉⠉⠏⠉⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⡇⢀⡀⢀⠠⡄⠄⣄⠠⢤⠀⠄⢠⡎⠉⣦⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠇⢀⣇⠘⢇⠀⠀⡇⠀⣧⠀⠘⡆⠠⡮⠀⠀⠨⡦⠀⢀⠎⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡄⢤⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠚⢲⣖⣒⡖⠚⠂⠌⣄⣠⠡
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⠀⣆⢰⡄⠂⡆⢠⡀⠐⡇⢰⠄⢢⠀⣦⠠⠀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠼⠀⠿⠸⠇⠀⠇⠠⠹⠀⠇⠸⠄⠸⠀⠿⠰⠁⠧⠠⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢢⠀⠃⢠⢦⢍⠆⠈⡽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠔⠑⣥⠀⣖⠄⠈⢬⠀⠇⣇⠀⠀⣀⠀⠀⠠⢀⠄⠠⣀⠀⡀⠀⠤⡀⠠⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢹⠀⠷⠀⢠⢰⠀⠞⢁⠀⡠⡄⠋⢠⣤⡴⣂⢢⠀⡤⢤⡒⢆⠀⠤⠀⢠⢦⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢸⣾⡸⠀⢸⠸⠀⠀⣎⠆⣱⡄⠀⡾⢣⠏⠉⠉⡴⢓⠌⠀⠀⣰⠅⠀⠈⡄⡃⠈⡗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠘⣼⡼⠀⢸⠄⠀⠀⣿⣔⠟⠀⢰⡇⡘⡆⡀⠂⠀⢸⢨⠀⠀⣾⠀⠀⠀⠇⡅⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢈⠁⠀⠹⡝⠀⢸⡇⠀⢠⠻⣶⡀⢠⡾⠀⡃⠁⠀⠂⠀⠺⡘⠀⠀⠹⡦⢀⡈⠦⠁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠖⠈⢀⠀⠢⠂⠀⠀⠫⠴⠋⠀⠈⠛⠛⠀⢀⠓⠀⢀⠀⠀⠘⠁⠀⠁⠄⠉⠉⠀⠨⡃⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⢤⡠⣀⠈⠀⠉⢀⣀⡤⡀⠀⠀⠄⠈⠠⠀⠀⠁⠂⠀⠐⡀⡀⠀⠀⠀⠀⠁⡠⣄⡀⠀⣷⠀⠀⢠⠁
⠀⠀⠀⠀⡐⡡⠂⠀⠘⠉⡀⠀⠀⢧⠀⢨⠇⠀⠀⠐⠁⠂⠀⢦⣹⠆⠀⠀⠀⢄⠀⠘⡃⠀⠰⠏⠈⠋⣰⠅⠀⠄⡆
⠀⠀⠀⢠⠀⠇⠀⠀⠈⠡⡀⠂⠀⣘⣰⣟⣀⡀⢀⣀⣠⡠⢄⣠⢤⠀⠀⡦⣌⠀⠠⢺⡴⠛⠈⠙⠓⠺⠋⠀⠈⠉⠂⠀⣀⠀⣀⠀⢀⡀⠒⢤⣀
⠀⠀⠀⠸⠈⡄⠀⠀⠀⠀⠀⠀⠀⡏⣿⠟⠉⡇⢸⠁⡍⠀⠀⢠⠱⠀⢠⡏⠓⡑⡀⠘⢂⠀⠀⡤⣵⣴⢿⢦⡎⣗⠠⡻⠁⠝⡋⠀⠈⡿⢕⢄⠘⠷⡄
⠀⠀⠀⠀⠱⡑⢄⠀⠀⠀⠀⣀⡾⢻⡃⠀⠈⠁⡘⢠⠁⠀⠀⢘⢇⣠⡟⣀⡀⣓⢁⡮⡼⣀⣸⠁⡼⠏⠸⢟⠀⢛⠈⠢⡀⣐⢂⠀⣴⠇⠀⢱⠆⢸⢐
⠀⠀⠀⠱⢄⠈⠒⠡⠐⠆⠙⠃⡀⠘⠂⠀⠐⠈⠀⠰⠁⡠⣄⠀⠘⠉⣀⠙⠢⠏⠋⡀⠐⠚⠁⠀⠃⠁⠈⠊⠀⠂⠈⠑⠘⠓⠚⢋⠡⣀⣰⠊⡠⢌⡉⠠⡀
⠀⠀⠀⠀⠈⠳⢶⡤⠠⠠⢐⡡⠷⢤⣀⠝⠧⡊⠷⠖⡈⠔⠉⠛⠫⠕⠚⠙⠶⠦⠅⠛⠲⢒⡪⠷⣄⣒⠷⢄⡲⢤⣒⠦⣄⣲⠀⡆⡋⢀⣼⠟⢉⡉⠻⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠪⠉⠈⠀⡻⠋⠢⢄⣂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠭⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢰⡿⠀⠠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠀⠀⣾⡇⠠⢰⣿⠁⠀⠀⣀⣀⠀⣾⠋⠀⠀⠸⣇⣠⣤⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⡈⣿⠁⠀⣾⡏⠀⣠⡾⠋⠈⠀⠻⢾⣶⠀⠀⠀⣿⡏⠀⠀⣼⡏⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢀⠜⠀⣿⡀⠀⣿⡇⢠⣿⠁⠀⠊⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣀⠤⠂⠀⠀⢿⠇⠀⢹⣧⠀⢿⡀⠀⢀⠐⠁⢸⣇⢀⠀⠀⣿⣀⠄⠀⣿⣀⠄⡿⠀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠬⠍⠁⢀⣀⠀⠀⠈⠀⠀⠀⠻⣆⠀⠉⠉⠁⢠⣤⠀⣉⠁⠀⠀⣈⠁⠀⠀⠈⢁⡼⠃⠀⠀⠉⢻⣦⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠸⡿⠀⣿⠇⠀⢀⣀⠀⠀⠀⠀⠈⠓⠂⢠⠀⠀⠉⣸⡟⠀⠐⠿⠁⠀⠀⠀⠠⠊⠁⠀⠀⣀⣤⠾⠃⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢸⡟⠀⠀⣾⠀⠀⠀⠀⠠⣿⠆⢀⡀⠀⠀⢀⣿⠁⢀⡈⠀⠀⠀⠒⠒⠒⢒⣒⢊⣉⠉⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢀⣿⠒⢻⡆⠛⢺⡿⠀⠀⣴⡆⠀⢸⡄⠀⠀⣼⠇⠀⣿⠇⢳⡆⢹⣇⠀⣰⡟⠁⣸⠏⢼⠁⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⢀⢾⠃⠀⣸⡇⠀⣿⠇⠀⣰⡿⠀⠀⠈⢻⡄⢸⡿⠀⣸⠇⠀⡿⠀⣼⡇⠀⣿⠁⠀⣿⠀⠘⣷⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⠎⡞⠀⢀⣿⠁⠀⢿⣄⠄⣿⠇⠀⡤⠀⣸⠇⣼⠇⢠⡿⠀⢸⠇⢠⡿⠀⠘⣿⣀⠘⣿⡠⠀⠘⣷⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣠⠴⠁⠀⠀⠀⢸⣏⡀⠀⠀⠀⠀⣿⣀⠄⠈⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⣄⣀⣴⠟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⢀⣷⣧⣹⡆⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡇⣶⢸⢰⡓⣞⠀⡇⣸⡖⣆⣤⠁⣷⢰⠀⡆⣜⡆
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢡⠵⣾⢸⠁⢸⠀⣿⡆⡇⢹⢿⠀⢸⣬⢰⢷⡽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣾⠃⠀⢠⡖⢠⠀⣾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣾⡟⢀⡟⠀⣀⡘⢷⣘⡀⠻⣦⣀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣠⡟⣼⢣⠃⢸⡇⣾⠃⠂⠠⣿⠃⠠⣰⡏⣰⠇⣾⢣⡶⠂⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢂⡾⢇⠣⠠⠾⠣⡼⠀⠸⣇⠿⠤⠀⡀⠧⠔⠁⢻⡂⠛⢸⡏⠈⠁⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠘⠃⣪⠄⠄⠀⣴⢿⠀⠀⠈⠁⢀⣤⠀⠀⢠⠃⣰⠏⢀⡿⠀⢰⡏⠁⢱⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠙⠄⣼⠇⠀⣼⡁⠉⠁⢠⡄⠀⠀⢸⡟⠀⠀⠚⠋⠁⠔⠋⠀⠀⠀⢉⠀⢠
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⡏⢀⡆⠘⢳⡶⢠⣶⢰⣿⠀⣾⠃⣰⡇⢰⡖⣰⡆⣴⠋⣾⠀⣿⢀⠆
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣾⠃⣼⢃⠀⣿⠁⣼⡇⠀⣿⡆⣿⢀⣿⢁⣿⢡⡿⢸⡇⢸⣇⠀⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠉⠀⢉⡥⠀⠉⠀⠈⠁⠎⢸⡇⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠐⠉⠀⠀⠀⠀⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠁








⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⣞⣢⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠈⠀⠀⠀⡀⠐⠄⠈⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠥⠄⠀⠀⠀⠀⠪⡩⠇⠀⠀⢤⠤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⣋⣁⣈⡀⠙⠚⠁⠀⠀⠁⢠⡤⠆⠡⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠀⠈⠉⠉⠙⠓⠲⠦⢤⣄⣀⡉⠁⠀⠀⠀⠈⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢸⣷⡀⢰⣶⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⠆⣿⡇⠈⣿⠀⣿⠂⡶⠂⢆⠀⣶⠂⡄⣰⡆⢠⣦⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⢻⣿⡄⠹⠄⢻⠀⢿⣀⠄⠘⠇⠀⠀⠿⠀⠘⠧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⢀⡀⣿⣿⠀⠈⠛⠁⠀⡠⠖⠒⠶⠤⣄⡀⣰⣶⠀⠀⠠⡄⠈⠀⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠀⢸⣿⢀⣀⡀⠀⠀⠁⠘⢠⠀⢀⡀⠈⣿⡇⢀⡀⠈⠀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠘⣿⠀⣿⠉⠄⣸⡏⠠⣿⠃⠘⣿⡀⣿⡇⣿⠃⣿⢸⡿⢱⡿⠃⣶⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠄⠀⠘⠂⠹⠄⠀⠹⠆⠀⠻⠄⡀⢸⡇⠹⡇⠛⠀⠓⢸⠁⠜⠣⠘⠧⢀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠄⠄⠠⠀⠀⠀⠄⠠⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⢋⣉⡤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⢤⣉⡙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠻⣄
⠀⠀⠀⠀⠀⠀⣴⠋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠘⢧⡀
⠀⠀⠀⠀⠀⣼⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⢷⡀
⠀⠀⠀⠀⣼⠃⠚⠀⠀⠀⠀⠺⠃⠀⢀⡀⢻⠁⡶⠆⠀⢰⣶⣄⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢳⡈⢷
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡫⡽⠤⣤⠀⠀⢿⡛⣷⡄⣸⡟⢹⡇⠀⢀⣠⣀⠀⠀⠀⢠⣦⠀⢸⣇⠀⠀⠉⠀⢀⢂⣂⡀⠀⠈⢧⠘⣧
⠀⠀⠀⡿⠀⠀⠀⢀⠀⠀⠀⢐⢖⡀⠀⠛⠀⠞⠂⠁⠀⠀⢸⣇⠈⢿⡿⠁⢸⡇⠰⣾⠟⠋⢀⣤⣤⣾⡏⠀⢸⣿⠀⣤⢴⡀⠀⠃⠂⠀⠀⠀⠘⡆⢹⡄
⠀⠀⢸⡇⠀⠀⠀⢸⡄⠀⠀⠀⢈⣀⣠⣤⣤⣄⣀⠀⠙⠃⠈⣿⠀⠀⠀⠀⣘⡛⠀⣿⡀⣿⡟⠉⠁⠹⣷⣤⡾⢿⡆⠾⢴⠋⠀⢴⡆⠀⠀⠀⠀⢳⠘⣇
⠀⠀⣼⠀⠀⠀⠀⠈⣷⣀⣴⡾⠛⠉⠉⠀⠀⠉⠙⢷⡄⣷⠀⣿⡇⠀⣠⡟⠛⣿⠀⣿⠁⢹⡇⠀⠀⠀⠀⣀⣤⣼⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⣿⠀⡀⠀⠀⠀⣽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⠀⣿⠇⠀⣿⠒⠞⠁⣸⡟⠀⠘⠃⠀⢀⣴⡿⠛⠉⢹⣿⠀⢀⠈⠙⠻⣶⣄⠀⠀⠀⠸⠀⣿
⠀⠀⣿⠀⡇⠀⠀⣼⠏⠹⣿⣶⣄⣀⠀⠀⢀⣠⣴⣿⠁⣿⢠⣿⠀⠀⠙⠿⠶⠿⠋⣀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢸⣿⠀⠊⠀⣀⣀⠈⠛⠆⠀⠀⠀⠀⣿
⠀⠀⢸⡄⣧⠀⢰⣿⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋⠁⢸⡟⣸⡟⠀⠀⠀⠀⠀⠀⠈⠛⢷⡀⠀⢸⣿⠀⠀⠀⢀⣾⡏⠀⠀⢸⠋⠿⣁⣀⠾⠁⠀⠀⠀⡟
⠀⠀⠘⣇⢸⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣉⠁⠀⠀⠀⠿⠇⠀⠀⠀⠘⣧⠀⠘⣿⣧⣤⣤⣾⠟⠀⣠⠤⡌⠓⠚⠙⣿⡇⠀⡀⠀⢸⠇
⠀⠀⠀⢻⡀⣧⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣼⡟⠋⢻⡇⣀⣴⠿⠷⢀⣤⢶⡄⣀⣿⣀⠀⠈⠉⢛⣉⣁⠀⣼⠃⢠⣦⠀⠀⣠⣿⠇⠈⠁⠀⡿
⠀⠀⠀⠈⣧⠘⣆⠘⢿⣄⠀⠀⠀⠀⠀⢀⣼⡟⣼⡟⠀⢀⣿⠃⣿⡇⢰⡇⠘⢷⣬⡉⠛⣿⠁⢠⣾⠷⣿⡏⠹⣷⣿⣀⣰⡿⠿⠿⠟⠁⠀⢀⠀⣼⠃
⠀⠀⠀⠀⠘⣧⠘⣄⠀⠙⠿⣶⣶⣶⣶⡿⢋⣾⠏⠀⠀⣼⡏⠀⣿⠀⣼⡇⣠⡀⠈⣿⣤⣿⣀⠘⣿⠀⢹⣧⠀⠻⡏⠛⠛⠁⠀⠀⠀⠀⢠⠏⣰⠏
⠀⠀⠀⠀⠀⠘⢧⡘⢦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢷⣾⠟⠀⠻⡇⠙⠷⠶⠟⠁⠻⠿⠇⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣴⠋
⠀⠀⠀⠀⠀⠀⠈⢳⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⢋⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣌⣙⠒⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠖⢋⣩⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣤⣤⣀⣀⣀⣉⣉⣉⣩⣥⡤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⢨⣿⠔⢸⢆⣤⡄⠴⠂⢀⠄⠈⠂⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⣿⡃⢀⡿⢪⡾⣷⡞⠀⠈⠳⢦⠸⣧⡀⣸⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⢣⡟⠀⠻⡐⢀⡴⠚⢁⡴⢀⠃⠓⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠐⠃⣠⢄⠀⠀⣾⠀⠀⠀⢩⠄⠁⠁⠈⠒⠊⣠⠞⠀⢀
⠀⠀⠀⠀⠀⢀⡴⠒⠘⢀⣾⢁⠜⢰⡂⠘⠀⠀⠀⠒⠀⠀⠀⠀⠐⠊⠁⠀⠨⢆⠇
⠀⠀⠀⠀⢠⡿⠁⠊⠀⣼⢃⠤⣦⠈⠛⢶⠠⠒⡖⢒⠒⠒⠒⣶⠿⢥⡀⢀⠐⣁⠀⢀⣀⠀⣠⠖⡄⡀
⠀⠀⠀⠀⣼⡇⢤⠐⠀⣿⠋⢠⠏⡴⠊⡁⣰⡾⠀⢿⡂⠀⣰⠏⢠⣿⠃⡾⢋⡞⢰⡏⣐⠀⢿⡉⠠⠃
⠀⠀⠀⠀⢻⡇⠀⡀⠀⠏⠀⠏⠀⠉⠈⠁⡟⢀⢀⡈⢿⡎⡟⢠⠈⠃⠈⠃⡟⠄⠘⠣⣇⠖⢈⢻⡎⢢
⠀⠀⠀⠀⠀⠑⠈⠀⢀⠴⡄⠂⠀⣈⠕⠁⠁⠁⠘⠀⠚⣀⡡⠄⠒⠀⠀⠀⠀⣠⣒⠀⠀⠸⠀⠴⠃⡜
⠀⠀⠀⠀⠈⠐⠒⠊⠁⠀⠙⢦⣄⣀⠀⣀⣀⡠⠴⠒⠉⠀⠀⠀⠀⢎⠗⡠⠀⠙⢄⡀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡴⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⡇⠀⠸⣆⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⢀⠉⡲⠤⠀⢉⣤⠀⢸⡖⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠁⠀⠁⡿⢸⢡⡇⣴⠁⢠⡟⠀⢸⠃⢸⢸⡇⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⡆⠀⠀⢀⠅⠀⢸⡁⠉⠀⠀⠃⠀⠈⠃⠂⢸⠇⢸⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠘⠂⠀⢠⡟⢀⣀⠀⢀⡀⢴⠇⢁⢠⡆⠀⠠⠎⠀⠋⠀⣼⢣⠄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠀⠀⣸⠁⣾⠀⠆⠉⠀⢸⡆⠀⣿⠁⠀⠀⠀⠀⡠⠜⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡏⠀⠀⣿⢀⠻⣴⣀⠀⠄⠀⢻⡄⣿⠀⣄⠀⠀⠀⢠⢄⡀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠿⢸⠀⢰⡟⢸⠃⠀⠀⢻⡉⠀⣿⣲⢰⠀⠸⠸⡇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠓⠈⠁⢀⡀⠸⣧⠈⠃⠉⣿⠀⠒⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢸⡇⢀⡿⠀⡐⠀⢇⠀⠀⣸⠆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠞⢁⡼⠁⠀⠇⠀⠀⠀⢰⠏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⣀⠤⠚⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣹⣶⢶⣄⠀⡠⢶⣄⡔⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣿⠀⣿⡞⠀⠈⣿⠀⠀⣿⠀⠀⠀⠀⠀⢀⡤⡀⠀⡀⢠⡞⠂⣠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠟⠀⣿⡇⠀⠀⣿⠀⠀⣿⠀⠀⢰⡏⠀⠸⣧⣀⣾⠁⠘⠖⣾⠏⠀⢰⡿⠁⣠⡦
⠀⠀⠀⠀⠀⠀⣠⡤⢄⠀⠀⣠⣄⠀⠀⢸⡇⠀⠀⣿⡆⠀⣿⠀⠀⢻⡇⠀⡠⠃⣸⠃⡀⠀⢸⡏⡠⢀⣿⣡⢎⣿⠃⠀⠀⡄
⠀⠀⠀⠀⠀⣼⡏⠀⠈⡇⠀⣿⡀⡆⠀⢸⡇⠀⠀⠛⠃⠀⠹⣄⣀⠌⠉⢉⣀⣀⣈⣉⡤⠀⢈⣉⠄⠀⠉⢀⣾⣃⣀⣠⡾⠃
⠀⠀⠀⠀⢀⣿⡇⢦⡴⠁⠀⢻⣇⠃⠀⠈⠁⠀⣀⠀⢠⡆⠀⠠⡤⠀⢠⡖⡂⠀⠉⣿⠛⠋⠉⢠⠒⢁⣠⠟⠁
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢼⠉⣇⢿⡇⠀⢰⡆⠀⢸⣇⠀⠀⢸⡏⠀⢠⡀⣈⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠸⣷⡀⠉⢷⡜⠷⡏⢸⡇⠀⣾⡇⠀⠌⢿⣆⠠⣿⠀⠀⣾⠃⣸⠂⣸⠂⢠⡾⠁⣿⠃⢸⡧⠀⠀⣆
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⣧⠀⠀⠘⢧⠄⢹⣧⢌⡠⠞⣿⡀⣿⣀⢼⡏⠀⡿⠀⡟⠀⣿⠃⣸⡏⠀⠘⣿⣀⡴⠃
⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢸⣿⡄⠀⢻⣤⠇⠀⠀⠀⣠⠔⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠁⠈⠓⠊⠛⠊⠘⢓⡡⠄⣿⡏
⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⡼⠘⠃⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⣇⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡿⠃⢀⣿⣿⠁⢸⣷⡴⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⣿⠇⠀⣾⡟⠀⣸⡿⣰⡿⢻⡆⢾⡷⡄⠀⣾⡇⣄⢸⡿⠀⢸⡇
⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⣿⡿⠀⢰⣿⠃⢠⣿⢃⣿⣤⠎⣠⡟⢸⠇⢠⡿⢡⡏⠸⣷⠔⣹⣇⣀
⠀⠀⣠⣾⣿⠟⠉⠀⠈⢹⣷⠀⠸⣟⣃⡀⠸⠿⠀⠸⠿⠞⠿⣤⠶⠋⠀⠸⣶⠟⠁⠸⠧⣠⠖⠁⣿⠇⡀⠉⣦
⠀⣰⣿⡿⠁⠀⠀⠀⣴⣿⠟⣠⣿⠋⢀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣾⣇⣀⣀⡀⠀⢰⠇⠀⣼⡟⠐⠉⠁⠞⠀⠀⠀⣶⡏⢹
⢰⣿⣿⠁⠀⠀⠀⠀⠈⠁⢰⣿⠣⠴⠛⠁⠀⠀⠠⠾⠃⠈⡡⢤⡀⢸⣿⠉⠉⡉⠁⠀⠘⠷⠿⠛⠀⠀⢀⣤⡶⠶⡄⠀⢿⣧
⣼⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⡟⢻⡆⢰⣷⣀⡀⢠⣿⠀⣾⡅⢾⠇⣼⡏⠀⢸⣿⡞⢻⣷⣤⠲⣷⠀⣠⣿⠋⠀⠰⠃⠀⠘⣿⣧
⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⠇⢸⡟⣹⠃⢸⡇⠀⢹⣷⡀⢀⣿⠃⠀⣼⣿⠀⢸⣿⠃⢰⣿⢠⣿⠃⠀⣰⠏⣴⠟⣷⡘⣿
⢸⣿⣷⠀⠀⠀⠀⠀⠀⣿⡏⢸⣿⣠⠟⠀⣿⣀⣾⣧⢰⡶⢿⣧⢸⣿⠀⣼⣿⡇⠀⣿⡏⠀⣼⡇⣼⣿⢀⣴⡏⠀⣿⡀⠟⢀⣿
⠀⢻⣿⣷⣀⠀⠀⠀⠀⠉⠀⠈⠉⣁⡴⠃⠈⠁⠀⠁⠈⠷⣾⡿⠸⣿⡼⠙⠟⠀⠈⠛⠃⠀⠻⠛⠉⠛⠛⠉⠛⠒⠛⠻⠶⠛⠋
⠀⠀⠙⠿⣿⣷⣶⣤⣤⣤⣴⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡤⡄⢤⢠
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠁⠃⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠲⠖⠒⢲⠆⠂⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣀⡀⠀⢀⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⣾⠀⠀⠈⠉⢻⡇⠀⠸⣷⠀⢸⡇⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⡇⠀⢠⠖⠀⠙⠚⣿⠀⠀⠘⣧⠀⠀⢻⣄⠈⡇⠀⠀⠘⣷⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢸⣇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠸⡆⢀⠀⠹⠶⠀⠀⠈⢰⠇⠀⠀⣠⠟⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⡀⠈⢿⡄⠻⣇⣀⡠⠀⣀⠙⣁⠀⢠⡖⠀⠀⠀⠁⠠⠐⢫⡄⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢠⠀⠈⢿⠀⠈⠻⣆⡈⠁⠀⠀⠙⠁⣿⠀⠀⠀⠀⢀⡀⠀⣼⠇⢹⡇⠳⣄⡀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⣿⠀⢶⡖⢶⠀⣿⠀⢻⡆⠸⣇⠀⠈⢻⡆⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⣤⠀⣿⠀⠀⡔⠀⠀⠀⠘⡓⠀⣄⠀⠀⣿⠀⢸⠀⢸⡄⢻⡆⠘⠷⠄⠉⠉⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠉⠀⣿⠀⣀⠷⢴⣶⠀⢸⡇⠀⠈⢻⣆⢹⡄⢸⠄⠘⠃⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⠊⢹⡆⠘⣿⠀⢸⣇⠀⢔⣠⠟⠸⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡲⣆⠛
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢿⠀⠈⣷⠀⠙⠷⠀⢻⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⢠⠘⠃⠀⢿⣀⠀⠀⠀⠀⠁⠀⠀⢰⢰⢰⠰⢤⡦⡴⠀⡄⣶⢠⣀⡄⢠⠢⠀⡄⢴
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡬⣼⠉⠁⠁⠀⣷⣿⠉⣿⠇⠈⣙⢠⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠀⢀⣾⠏⠘⣷⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠈⢳⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣥⠀⠀⠀⡇⢀⢙⠀⠌⠀⡇⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⣿⡿⠃⠀⠀⠀⡇⠀⢸⡀⠀⢰⡇⠀⠀⠀⠀⠶⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠍⠁⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⣾⢠⡆⠘⡄⠘⣄⢰⡠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣀⠴⠒⠐⣆⢀⠤⠀⠀⠛⠀⠀⠀⠀⢻⣀⣉⡀⠗⠁⠓⠈⡡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠃⠀⠀⢀⣿⠇⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢀⡇⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠈⢸⠀⠌⠀⡀⠀⠈⠁⠀⠀⣠⠀⠀⠈⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⠺⠁⣿⠂⢤⠀⡧⣀⢈⡁⣾⠀⣿⠀⣶⢠⡄⣷⢠⡆⣀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⡴⠹⠇⣼⡐⠀⣯⠘⠇⡘⡿⢿⠜⠿⠸⠁⣧⠈⠋⢻⡄⠐⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣄⠀⣰⠂⠆⠄⣤⠀⠠⢠⡄⢀⡄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⠇⠀⢿⡀⠀⢰⡇⠀⠀⣼⠁⠨⢇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡠⠀⢸⠀⠀⠀⢀⠀⢸⡀⠀⠀⣏⠀⠀⠀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠀⠼⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢸⠠⠀⢰⢠⠻⡀⡄⢰⢠⡰⠠⢰⢢⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠸⠀⠀⠀⠀⠃⠈⠈⠀⠁⠀⠈⠀⠇⢀⡀⠔⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⠊⠉⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢠⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⣻⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣾⡆⢀⣿⣿⡇⠀⢀⣀⣀⠀⢠⣾⠿⣷⡀⢀⠀⠀⠠⣶⡄⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣼⡿⣿⡇⢀⣿⣋⣿⡇⢸⣿⣰⣿⠁⣿⣅⣴⠆⢻⣷⣠⡿⠋⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠇⠀⠀⣿⣿⢻⣿⡇⢿⣷⠸⣿⡛⢉⡀⢸⣿⣿⡃⠀⠉⣿⡏⠀⠈⣿⡟⠁⠀⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⡇⠈⠛⠀⢸⣿⡀⠛⠿⠿⠟⢸⡯⠹⣷⡄⠀⢿⣷⠗⢠⣿⠃⠀⠒⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⡀⠀⠀⠈⠛⠃⢀⣀⡀⠘⠛⠁⠀⣠⣤⣄⠘⠃⠀⠘⠛⠀⠀⠀⠀⠘⠛⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠿⢂⡴⣶⠀⠀⣿⠛⣿⡆⢀⡀⣾⣿⠉⠿⠀⠀⣶⠄⣰⣆⠀⢠⣿⣷⠀⠀⠀⠀⣾⡏⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣸⣿⡃⠀⢸⣿⣠⡿⠃⣛⠁⢿⣿⣄⠀⣠⣼⣿⡄⣿⣿⣀⣾⢿⡟⢰⡟⣿⠇⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠠⡶⠟⣿⢿⣿⠀⢸⣿⡏⠀⢸⡿⠀⠀⠹⣿⣆⠉⣿⠏⢰⣿⢹⣿⡏⣸⡇⢿⣿⢿⣧⠀⣨⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠛⢸⣟⡀⣿⡟⣿⣄⠺⡷⣇⡀⠀⢹⣿⡆⣿⣴⢸⣿⠈⠛⠀⣿⡇⠀⠀⠀⢡⣾⠋⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢀⣴⣿⠈⠛⠁⠿⠃⠘⢿⡆⠀⣿⣇⣀⣼⣿⠃⠈⠁⢸⡿⠀⠀⠀⠛⠃⠀⠁⠀⠸⣷⣀⣴⣿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠁⠀⠀⠀⠀⠀⠘⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀⣀⠀⠀⠀⡠⠀⠠⢀⠤⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⡀⡐⣀⠢⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⢠⠠⡴⠀⡢⠀⡂⢀⠀⠈⠀⠤⠁⠈⠀⠀⠈⠁⠀⡀⢠⢀⠤⠀⠀⠠⡀⠄
⠀⠀⠀⠄⡑⠡⡀⣀⠀⠒⡔⠀⠀⠀⠀⠐⠆⠁⢸⠀⡀⢠⠀⣇⢠⡀⠰⡀⢀⠀⢎⠀⠀⡄⠀⠀⠀⠀⠀⡲⠀⠀⡈⠈⠁⢀⡀
⠀⠀⠰⣑⢀⢊⠰⠄⢂⢁⠀⠁⠀⠀⠐⠐⠀⠀⠈⠀⠇⠀⠀⠀⠂⠁⠀⠂⠀⠑⠀⠁⠀⠃⠀⠀⠀⠀⠃⠀⢢⠉⡄⢑⠐⢑⣁
⠀⠀⠀⠂⡁⠐⠁⠊⠀⣄⢂⠁⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠡⢌⠁⠒⠄⠊⡈⠨⠄
⠀⠀⠀⠀⠁⠡⠒⠄⠐⠂⠀⠀⠀⠁⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠈⠄⢠⠰⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀
⠀⠀⠀⡰⠀⢀⠀⠀⠀⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠈⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠙⡄⡀⣂⠀⠀⠀⠀⠐⡀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠁⠀⠉⠂⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡉⠀⠀⢀⠠⠐⠄⠀⢿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠈⡀⠌
⠀⠀⠀⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⢀⡂⠓⠀⠀⠀⢺⡍⠀⠀⠰⠈⠰⠂
⠀⠀⠶⢮⣹⠴⠄⠀⠀⠐⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠄
⠀⠀⠀⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢸⠀⠀⠠⡊⣠⠀⠀⢸⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁
⠀⠄⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠐⡀⠀⢸⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠒⠒⠎⠀⠀⠀⠉⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⢸⠠⠄⠒⠲⠄⠀⠀⠸⠒⡒⠀⠀⠀⠰⡀⠡
⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠠⣀⠁⠀⠀⢀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠀⠀⠈⡃⢀⠀⠀⠀⠀⠐⣰⠈⢐⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠰⠀⠈⠀⢀
⠀⢀⠤⠀⠀⠈⠃⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠨⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠈⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠐⠀⠘
⠀⠀⢀⠀⢀⠀⠀⢀⠄⠀⠀⠆⠘⠀⠃⠘⠀⣀⠐⠏⢹⠀⠀⠠⡄⠀⠀⠀⡦⠠⠀⡀⠀⠄⠀⠂⠀⠀⡀⠀⠀⠀⡀
⠀⡐⢀⠐⠄⢑⠀⠂⠀⠂⠀⡆⢀⢀⡀⠨⠀⠒⠀⡄⢸⠀⠑⠚⠁⠁⠀⠉⠁⠀⠡⠀⡀⢰⠀⢐⠆⠐⠄⠐⠒⠎⠀⠀⣀⢸⣄⠖
⠀⠠⣀⠀⢁⠌⠀⠀⠀⠀⠀⠠⠼⠀⠄⢨⢀⠆⠈⢣⣸⠑⠚⢀⠄⠀⠀⠀⠀⢻⠀⠠⠇⠘⡀⠂⠠⠀⣊⠓⠒⠀⠀⠀⠀⡜⢺⠙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣀⣉⣁⣉⣁⣈⣉⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣴⠋⠀⠀⠀⣀⠀⠈⢲⡀⠈⣧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⠀⠀⡈⠉⠛⠻⡿⣶⣿⣌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣸⡄⠀⠳⣄⠀⣸⠇⢸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣦⡼⣿⣯⣴⣟⣡⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⡆⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣉⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣛⣿⣿⣿⣾⣦⣶⣶⣾⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⠟⠋⠉⢿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠸⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡆⠀⠈⣿⡿⠻⢿⣿⠟⠛⠛⠛⢻⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠉⠛⠛⠉⢹⣿⡏⣠⣾⡿⠃⠀⠀⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⠀⠻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣇⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⣿⠀⠀⠘⣿⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⢿⣄⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⠿⠆⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⣿⠀⠀⢠⣿⠃⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⣿⡟⣋⣹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣏⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⢋⡇⣿⣿⠿⡿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠿⡇⣿⣿⣰⣄⣧⣙⣸⣀⣄⣿⣀⣿⣰⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣡⣴⡇⣿⣿⣿⡟⢛⢿⢟⠻⡟⢻⡟⢛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⣡⡇⣿⣿⣿⣏⣰⣶⣌⣡⣇⣙⣇⣐⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⢋⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⡀⠀⢀⣸⣆⣳
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠀⠀⠀⠰⠀⠀⠀⠀⢏⡀⠀⠀⠀⠀⠠⡆⡂⠀⣿⡇⠀⢀⣼⣿⠏⣩⢷⡄
⠀⠀⠀⠀⠀⠀⢈⡇⡆⠀⠀⠀⠀⠀⢠⣭⡄⠀⠀⠀⠐⣆⡄⠀⠀⠼⠃⢈⣅⠀⠀⠀⢰⡏⣵⠀⠈⠠⠀⣁⣾⣿⠿⠁⠈⣉⠄
⠀⠀⠀⠀⠀⢀⣴⡏⠃⠀⠀⠀⠀⢠⠟⠛⠀⠀⣀⠀⢐⣍⣡⡄⢀⢸⠇⠈⠋⠠⡆⠀⣀⡗⢻⣀⠀⠁⢰⢹⣿⠁⣀⡤⠞⠻⣇⠀⣖
⠀⠀⠀⠔⢠⣿⣯⠦⠄⠀⠾⠂⠀⣤⣶⠀⠀⢠⣙⡂⢸⣇⣼⠃⢿⠀⠀⣰⣦⣀⡽⠚⠉⠉⠈⠉⢑⣦⡔⠈⣤⡾⡉⠀⠀⡀⠃⠀⠞⢆
⠀⠀⡌⢠⣿⠟⢏⡔⠒⢠⠋⠳⣀⠹⠍⣴⣤⠚⠿⠀⡾⠉⢹⡆⠀⠀⡿⢻⡇⣹⠛⠛⠛⠛⠛⠋⠉⣩⣤⡈⢇⢸⣥⠔⠊⠁⠀⡾⠃⠙⠧
⠀⠀⢳⡌⣷⢆⢹⡅⠢⠆⡌⠘⢘⠁⠀⠉⠉⠁⠀⠘⠁⠀⠀⢿⠄⠀⠁⠀⠀⢿⣿⢳⡖⢲⣶⣋⢾⣽⣿⠃⠀⠻⠃⡠⠎⠀⠀⡖⠀⠒⢳⡀
⠀⠀⠈⠣⣿⣿⣧⡜⠒⠢⢞⡳⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢨⣧⠆⠀⠀⠀⠈⢿⣛⣛⣛⣛⣉⣈⣭⠇⠀⠀⠀⠙⠃⠀⠀⣴⠷⠒⠒⠚⢷⡄
⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠈⠀⠀⠀⣤⣾⣿⣷⡶⠶⠀⠀⠀⢠⠇⠐⠤⠤⠔⠁⠀⠈⠛⠍⠭⠄⠚⠁⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⢿⣿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠻⣇⠀⢧⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣧⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⡖⢀⠀⢀⡀⣀⠀⠀⠀⢀⠀⠀⣀⡀⢀⠀⠀⠄⡀⠀⡀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠡⠁⠇⠸⠁⠟⠀⢄⡃⠀⢈⠀⠐⠁⠐⠁⠈⠀⠇⠀⠏⠃⠃⠄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠀⠀⠀⠤⠂⠁⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠸⠿⠃⠀⢁⠀⠀⡀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⡀⠐⠒⠀⡀⠀⠄⠸⣳⡆⠠⠥⠀⠈⠁⡤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠧
⠀⠀⠀⠀⣀⠀⠉⠉⠁⠀⠆⠀⠂⠀⠀⠀⢀⠀⠠⠀⡀⠁⠈⠃⠀⠀⣼⠀⠀⠘⠀⠀⠀⠂⠈⠋
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠠⠀⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠘⣄⡀⠀⠀⢀⡀⠀⠀⡀⠐⠀⠈⠁⠀⠀⠀⠀⠂⠀⢲⠀⠀⠆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠤⠘⠃⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡁⠀⠀⠀⡄
⠀⠀⠀⣶⠀⠀⠀⠀⠀⠰⠀⠠⣁⠀⠀⠄⠁⠧⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⡀⠀⡈⠀⠀⡀⠁
⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠈⠠⠔⠀⢠⠂⠀⡀⠀⠀⠀⠇⣄⣀⣀⠀⢠⠀⠀⠂⠈⠃⠈⠀⢂⡄⠀⠀⠄
⠀⠀⠀⠐⠀⠄⠈⡄⠠⠄⠀⠂⠄⠀⠜⠀⠀⠁⠀⠈⢀⠀⠉⠁⠀⠹⠀⠀⢀⠀⠂⠩⠄⠀⣠⠄⠀⠂
⠀⠀⠀⠀⢀⠀⠂⠐⡄⠄⡀⠀⡈⠈⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠈⠓⠦⠄⠰⠚⠉
⠀⠀⠀⠀⠈⠃⠀⢁⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠄⢤⡀⠀⠀⠀⡀⠀⠀⣀⡀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠠⠀⠄⢉⠀⠐⠎⠉⠋⠀⡀⡌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡀⠠⠄⠠⠀⠀⢀⠀⠁⠀⠈⠀⠀⠀⡀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⣠⣀⠀⠠⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠠⠐⠋⠉⠉⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠰⠀⠂⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣤⣀⣤⣤⣤⣄⣀⣀
⠀⢀⣀⣤⣤⣤⣤⠶⠶⠶⠶⢶⣶⡶⠿⠛⠛⠋⠉⠛⢻⣿⣿⠿⣿⣿⣋⣉⣉⣹⣿⣭⡿⠟⢋⣩⠿⣷⣶⢾⣿⣿⣿⣷⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⣿⣿⣿⣟⠿⠿⢷⣤⣤⣤⣾⣯⣀⣀⣀⣀⣀⣤⡴⣾⣧⣤⣶⣿⣿⣿⣭⣭⠷⣾⣿⣶⠾⠉⠁⢀⣸⣷⠿⠛⠉⢸⣿⣶⠟⢻⡿⠁⠀⠀⠀⠉⢻⣷⣦⣄
⠀⣿⡟⣉⠛⠿⣾⣷⣌⣁⣽⣿⡏⠉⠉⠉⠉⠉⠀⠀⠈⣿⠁⠀⢀⣀⠉⠉⢀⣲⠄⣹⣿⣶⡶⠾⠛⠋⠁⠀⠀⠀⢸⣿⡁⠀⠘⣧⠘⠀⠀⠀⢠⡾⠃⠀⠈⠳⣄
⠀⣿⠠⠉⠀⠀⠀⠀⠉⠉⠙⠛⠻⠷⠶⣶⣶⣶⣤⣤⣼⣷⣤⣤⣬⣵⠶⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢵⢀⣠⣿⣷⣤⣄⣤⡟⠁⠀⠀⠀⠀⢹
⢰⣿⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣤⠔⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⠀⢸⣿⡷⠛⠉⠀⠀⠀⠈⢻⡁⣄
⢸⡏⠈⠀⣴⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠞⠁⠀⠀⠀⣤⣄⡀⠀⢄⠀⡈⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠛⠒⠚⠻
⢸⡇⠀⠀⠋⠈⠁⠀⠀⠐⣿⡅⠀⠀⠀⢀⠏⢁⣤⣾⣿⠀⣿⣿⠚⣦⠐⣿⣷⢤⣀⣤⠀⠈⠉⠛⢪⣿⣦⡂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⡐⠁⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⢷⡀⡜⠀⣿⢁⣸⣿⠀⢻⡏⠻⠟⠁⣿⡇⢸⡇⢸⠀⠀⠀⠀⢡⠉⢿⠉⠿⣧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀⡀⢀⣾
⢸⡇⠀⢀⣀⡀⠀⠀⠰⠆⠀⡿⠇⠈⠿⠇⠀⠉⠉⣹⣿⠀⠿⠿⠀⠀⠀⠿⠧⠘⠃⠘⠀⠀⠀⠠⢧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠗⠎⠉⠙⠻⣿⠇
⢸⡇⣰⡿⠋⢻⡄⠀⠀⡀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⡎⠉⢳⠄⣿⡇⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⠟
⢸⡇⠘⠳⠶⠟⠀⠘⣿⡇⠀⠀⢨⡋⠻⠛⠀⣴⣶⣀⠀⣼⣿⠧⠀⢀⣴⢦⠄⠀⣾⣧⠴⢶⡄⠀⠀⠘⠷⠖⠋⠀⣿⠁⠀⠀⠀⠀⠀⣰⠿⣦⡀⠀⠀⣰⠏
⢸⡇⣤⠀⠀⠀⠀⠀⢻⣧⢀⡄⢸⠀⣿⡟⠀⣾⡿⢹⠇⣿⣇⡴⡄⣾⡟⠉⢠⠀⣿⡏⣶⡤⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠏⠀⠀⠙⢷⣴⠏
⣸⡇⠀⠀⠀⠀⠀⠀⠈⣿⡏⠹⣾⡀⣿⡏⠀⣹⡟⢸⡀⢿⣇⣃⠇⠸⠿⠾⠃⠀⣿⡇⠀⠀⠀⠀⠐⣶⣧⠄⠀⠀⣿⠀⠀⠀⣠⣾⠡⠀⠀⠀⢀⣼⠏
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠀⠙⠉⠈⠃⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⢀⣠⣀⠀⠀⠀⠹⠄⠀⠀⣿⠀⢀⡼⠋⠙⠷⣤⣀⣠⠞⠁
⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⣠⠀⣶⠄⣴⠞⠙⢳⣴⡶⢀⣴⠻⡆⣼⡏⢠⣽⠇⠀⠀⠀⠀⠀⠀⣿⣴⡟⠀⠀⠀⠀⢨⡿⠃
⢻⡇⠀⠀⠠⣤⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⡏⢠⣤⡄⣿⣆⠓⠋⢹⡇⢸⣿⠞⡁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣌⠀⠀⢀⣴⠋
⢸⡇⠀⠀⠀⠈⣃⠀⠀⠀⠀⠈⣿⣀⢿⡅⢸⠀⠀⣿⠀⠈⢿⣧⠀⣿⣧⣄⠛⠛⣁⡀⢹⣿⠀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠉⣷⣤⠞⠁
⢸⡇⠀⠀⠀⢠⣴⣞⠀⠠⣤⣤⣿⡏⠀⢻⣧⠀⢀⣿⡌⢿⣤⡿⠀⣿⡇⠈⡇⠀⠹⠶⠾⠃⡀⠀⠀⠀⠀⠀⠀⢸⣯⠀⣠⡾⠋
⢸⡇⢤⢿⠒⠃⠉⢻⡧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠛⠋⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋
⢸⣷⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢀⡶⠛⠛⢆⠀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⣿⡄⠂⠀⠀⠀⠀⠟⢉⡀⠀⠀⠀⠸⣧⣤⣴⠏⠀⠀⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⢀⣼⣿⠁
⠀⠙⣿⣄⡋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠞⣁⣴⣾⣿⠃
⠀⠀⠈⠻⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠻⢿⡿
⠀⠀⠀⠀⠈⢻⣯⡟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣉⣉⣅⢀⣀⣀⣸⣵⣿⠇
⠀⠀⠀⠀⠀⠘⠻⠿⠿⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠾⠶⠿⠟⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣾⡀⣀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢿⡏⠓⢿⣀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⣾⠛⠻⠿⣟⢆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣁⡴⠶⠦⢭⣿⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠈⢦⣿⡿⡄⠉⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡆⠀⠀⢯⣷⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡇⠀⠀⢰⡏⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⠀⠀⠀⠀⠀⠀⠀⢈⣾⣧⡤⣠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⢿⣦⣀⡀⠀⠀⢠⣺⡾⢋⣩⡾⠟⠋⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣵⣶⣌⣉⣙⣓⣪⡴⣫⣶⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣀⣤⣤⣤⣴⣶⣶⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠐⠟⢨⣿⣿⣿⣧⣿⢗⣤⣀⢀⢀⣄⣠⣤⣶⣿⣿⣿⡿⠿⢛⣻⣿⣿⣿⣿⠏⠁⠂⠐⠲⠝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠛⣟⢛⣏⣸⣿⣈⠉⠛⠛⠿⠻⢿⡟⣿⠟⠙⠉⠘⡃⠸⣿⣿⣿⣿⣿⣷⡄⠀⠀⢰⣌⢸⡿⢂⣀
⠀⠀⠀⢠⡄⡀⢀⠀⠀⠀⠀⠀⠐⠒⠒⠒⡻⡻⠻⠟⢻⣿⣿⣿⣿⣶⣤⣤⠇⠀⠀⠀⣧⢀⠀⠀⣥⣾⣿⣿⣿⣿⣿⣿⣷⣔⢧⣾⣿⣿⡷⠿⠿⠿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⡀⣠⣴⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣿⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⠿⠛⠉⠋⣧⡤⠆⠀⠰⣦⠀⠋⣹⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠁⠀⠀⠀⠀⢶⣤⠿⠟⠛⠛⠋⢻⣿⣿⡿⣿⣿⠟⠛⠛⠛⠛⣿⣿⡆⠀⢻⣿⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠴⠦⠤⣤⣤⣤⣤⣄⠀⠈⠂⣠⠸⡧⠤⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡏⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠉⠀⢹⠿⣦⣤⡶⣾⡑⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⡇⠀⢀⠀⠄⠀⠀⢸⣿⠃⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠰⣄⣷⡄⠀⢀⣀⠀⠀⢀⡏⠀⣀⣼⠑⠿⣇⠀⠀⠀⠀⠀⢃⡠⠠⣤⣬⣳⠟⢿⣿⡇⢸⡃⣼⣴⣷⣶⠧⠂⢸⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠠⢸⠟⠉⠙⠛⠺⢲⣿⣿⡿⣿⡿⠛⠳⣦⣨⠀⠀⠀⠛⠞⣷⣥⣾⣿⣿⣿⣤⣸⣿⢠⣼⠛⠉⠀⠀⠀⠀⠀⢻⠁⠀⠀⢀⣟⠠⠄⠀⢠⠄
⠀⠀⠀⠀⢠⠆⡇⠀⠀⠀⠀⠀⠌⠀⣿⡇⠈⠁⠀⠈⠀⠀⠄⣐⣥⣟⣆⣻⣿⠿⠛⠋⠉⠉⠈⣉⠀⢸⠀⠀⠀⢀⣀⣀⠀⣼⣤⣶⣶⠜⣿⢶⣶⣶⡆
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⠇⠀⠸⡇⢲⠐⣄⡤⣀⣀⣤⠘⠫⠙⠉⠁⠀⠀⠀⠀⠀⠀⣀⢻⠀⠀⣄⣀⣤⡾⣿⣥⣍⣵⣿⣿⣯⣍⣹⡿⠟⠋
⠀⠀⠀⢀⡃⡀⠀⣀⣤⣤⣄⠀⠰⢤⣤⠳⣼⣿⠿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠶⠿⠛⠓⠲⢯⣏⣉⣁⣀⣩⠟⠂⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠈⠀⠐⠂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⡔⠀⠀⢀⠀⠰⠀⠀⠐⠻⠿⠟⠋⠋⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠱⣿⣄⣤⣀⡀⡀⠀⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠚⠛⠛⠻⠿⣿⣿⣦⣦⣤⣠⣶⣶⣄⣀⣠⣄⣀⡛⢮⣀⡀⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⡀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡿⠯⠟⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠁⠈⠋⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡄⠀⠀⠀⣄⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢋⡈⠶⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡆⠈⠨⠳⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠈⠙⠛⠛⢓⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡄⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠄⠀⠀⠀⡿⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠑⣃⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠉⡀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣺⢡⠄⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⡔⢒⣠⡀⠆⠀⠀⠀⠀⣗⠀⠀⣠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅
⠀⠀⠀⡀⠈⠀⣹⣄⡴⡤⣀⣈⡁⠂⠰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠆⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⣃⢀⠀⡁⠨⠿⢇⠠⣼⠃⠀⠀⠆⠨⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⢀⡠
⠀⠀⠀⢯⡤⠞⢅⢔⠒⠂⠀⠀⠀⢠⠀⠠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠁⠀⣀⡀
⠀⠀⠀⠰⡀⠀⣨⡜⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⢠⠍⠵⢄⡁⠁⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⣤⠎⢈⡁⣰⣆⠀⠜⠠⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠀⠀⠀⠀⠀⠀⢰⢀⠜⢂⠀⠄⠀⠐⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠘⣿⠋⠁⠁⡀⠈⠀⡠⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣯⡇⠀⠀⠀⠀⠀⠀⠈⣄⠈⠡⡔⠃⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⢀⡞⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠐⠈⢠⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⠃⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢦⣤⠴⢮⣷⡝⠁⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠰⠚⠛⠚⢦⠔⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⠠⠐⠀⢤⣼⡇⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⢰⠛⠶⢦⠀⠀⠀⠀⠀⠀⠀⠰⢟⡏⠀⠀⠀⠀⠀⠈⠛⠂⠀⡀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀⠀⠀⠀⠀⢈⠳⠴⠛⠀⠀⣀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡄⠀⠀⠁⠂⠀⠀⠀⠁⢀⡆⠀⣰⠟⠡⠀⡀⠀⠀⠀⠀⠀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⢀⡀⢀⣀⠀⠀⢷⡀⢀⠀⢀⣠⠀⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⠤⠀⢀⢠⠈⠄⠀⠄⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠑⡀⠀⠀⠀⠠⠊⠁⠀⢂⠀⠀⠀⠀⠀⣠⡀
⠀⢀⠠⠄⠚⠈⣁⠠⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠐⠤⠂⢀⠀⠀⠀⠀⠀⠉⠁
⠀⠡⡠⠀⠈⢃⠈⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠊⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢞⡛⠠⣄
⠀⠀⠀⠀⡀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⢒⠈⠦⠀⠀⠀⠀⠸⠅⢎⢎⠆⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠺⠤⡁⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⡀⡈⠀⠀⠂⠀⠀⠈⠃⢀⠄⠈⢃⠀⡠⡀⠑⡀⠄⠠⠂⠠
⠀⠀⣀⠲⠦⠤⡀⠀⠀⠀⠀⠀⠀⡀⠰⠀⣀⠀⡆⠘⠀⠘⠁⠈⠊⠀⡘⠀⠓⠁⠠⠇⠈⠁⡠⠁⠀⠀⡀⡀⡠⠆
⠀⢸⠇⡖⡙⠆⣱⠂⠀⠀⠀⠀⠀⠃⠀⠀⠋⠀⠁⠰⠄⠰⢤⠰⠄⠈⢣⠀⠆⠀⠑⠄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠠
⠀⠐⢲⡌⢩⣡⠆⠀⠀⠀⠀⠈⠈⠀⠁⠈⠈⠀⠃⠀⠀⠀⠘⠀⠀⠁⠊⠀⠀⠈⠐⠀⠒⠒⠀⠀⠀⠀⠂⠒⠀⡈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠤⠄⢴⠀⠂⠀⠂⠐⠒⠀⠂⢤⡂⠐⡀⠀⠀⣀⠀⠀⠀⠤⠠⡀⢀⠁⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠊⠀⠄⠀⣀⠡⠐⠒⠀⠀⠀⢈⡠⠀⠀⠀⠀⠄⢀⡴⠂⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢁⠀⠀⠄⠀⠰⠁⢀⢀⡀⠃
⠀⠀⠘⡀⠀⠄⠀⠖⢄⠐⠐⠀⠀⠀⢀⠀⢰⡁⠀⡦⠀⣄⠈⠀⠀⠀⠀⠀⠀⣆⠘⠁⣰⠀⠋⠀⠈⠁⠀⢈⣢⠀⢀⠈⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠒⠂⠀⠒⠒⠀⠈⠠⠀⡑⠰⠀⠀⠀⠀⠀⢀⠀⠄⢀⣀⠈⣀⣀⠁⡀⣠⠄⠀⠀⠆⠠⠅⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠐⠰⠀⠀⠀⠀⠀⢀⠔⠂⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠁⠀⠂⢀⡄⢠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠔⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡄⠀⠝⠐⠢⠀⡀
⠀⠀⠀⠃⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠁⠀⠀⠀⠀⠀⣠⠈⢞⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⣀
⠀⠰⢈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢪⡀⡑⠰⠇⠀⠀⠀⠀⠀⠐⠠⠀⡐⠀⠀⠀⠐
⠀⠀⠀⠠⠊⠀⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠶⢈⠦⠓⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠐⠉⠑⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠀⠀⣀⣀⡄⡈⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⣀⠄⠖⢃⣃⣈⡦⣬⣭⣍⠂⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡡⠲⠶⠋⠉⠉⠀⡀⣴⢸⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⡀⢀⢠⢰⡖⡄⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⣍⣁⣩⣥⡞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠶⡿⠾⠟⡇
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢴⠏⠷⢼⣰⡇
⠀⠀⡠⠦⡔⠉⠁⠈⠉⠲⠤⠖⠒⢢⡤⠤⠤⣀⣠⠛⠛⠺⣞⣋⡿⠗⠤⣀⡠⠤⠢⠤⣀⢀⡠⠖⠒⠤⠤⠒⠒⢦⣀
⢀⡞⢀⠀⠀⠶⠙⣣⣄⠠⡤⠄⠀⠁⢀⢀⢀⠈⠀⠀⢀⡄⣠⠄⡀⢠⠠⠄⠀⣀⡀⠀⠘⠉⡀⡄⠀⠀⢀⡄⢠⢠⢠⢙⡆
⢏⢀⣣⡼⠓⠛⠋⠁⠙⠛⠓⠲⠹⢦⢭⢭⢥⠶⠤⠶⠤⢥⢴⠚⠙⠳⠶⠶⣬⡴⠦⢅⣁⣡⠴⠛⠲⠶⢦⢤⠶⢤⢦⣤⡞
⠀⠀⢸⠀⢲⠒⡄⣖⡖⣠⠄⢄⢠⠄⢄⢤⣠⣄⡀⣠⢠⠄⡄⣤⢤⠀⠀⢠⠄⢤⡀⢠⢄⠀⡄⣀⠀⢀⡀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⠀⠸⢸⡷⣯⠃⡏⣿⡆⢸⡏⡊⡝⠉⠀⣯⠈⢹⠒⣇⡟⠸⠀⠀⢸⠡⠗⣳⡗⢶⠁⣷⢼⠀⠀⡿⢸⠙⠃⠈⢷⡇
⠀⠀⢸⠀⢨⡅⡙⡆⡄⡇⠿⠀⢘⡯⠻⣧⡀⠀⣧⠀⢸⡁⡇⢳⡀⠀⠀⢸⠀⠊⢸⡂⣼⠠⢿⢻⠀⠀⢹⢸⡯⠀⠠⣟⡇
⠀⠀⢼⠦⢭⠉⠉⠉⠁⠈⠐⠊⠈⠓⠃⠉⠛⠘⠓⠃⠘⠒⠓⠚⠿⠀⠀⠺⠴⠆⠈⠧⡩⠃⠾⣙⣄⡇⣼⣸⡤⡆⠀⣿⣧
⠀⠀⠈⢣⡈⢛⣛⣛⠛⣻⠋⠉⠉⠉⠉⠉⠉⠙⠛⢻⣛⣿⠷⢲⡶⣶⠶⠶⠶⠦⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣈⣁⣠⣿⣿
⠀⠀⠀⠀⠁⢸⠀⠈⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⣈⠽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡟⠋⠀⠀⢹⠀⡴⢏
⠀⠀⠀⠀⠈⡜⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡴⠟⢹⢠⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⡇⡇⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣾⣾⠼⢋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠀⠘⣽⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⡦⠄⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⣶⠶⡢⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠩⠭⠭⣤⢤⡄⠀⠀⡟⠉⠁⠐⢛⣴⡇⠀⠦⠄⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠒⠈⠉⠁⠐⠒⠒⠉⠉⠀⠀⠀⠀⠀⣧⣤⣤⠶⡋⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⣌⣡⡷⣫⠅⠀⠀⠀⠰⠶⠶⠶⠭⠭⠭⠍⠉⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣉⡿⠃⠾⣵⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⣀⡀⣀⡴⠋⠁⠀⠀⠀⠈⠀⠉⣦⠤⢄⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠔⠊⠋⠀⣀⢄⣡⡤⠞⠁⠀⠀⠀⠀⢤⡐⣔⣄⢌⠠⡠⡄⠼⢂⠤⡤⠖⠤⣤⠔⠢⠞⣉⡑⡀
⠀⠀⠀⠐⠋⠭⠀⠈⠋⠀⠀⠀⠈⠀⠈⠁⠀⠀⢀⢤⡦⡙⢯⢢⡱⢮⡴⠚⠒⠳⣅⡸⠞⠛⠉⠛⢾⣉⣉⠛⠙⠻⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠏⠀⠀⠀⢀⢄⢄⠈⠀⠀⠀⡀⢄⢀⢀⠠⡑⢼⣼⡌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠰⢁⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⢰⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠂⣀
⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁⠉⠉
⠁⠒⠂⠁⠀⠃⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣂⠥⣌⠂⠀⠤
⠀⠀⠀⠐⠀⠀⠊⠐⠄⣁⢀⠀⠀⠀⠒⠁⠀⠀⠀⢀⠔⠂⢀⠀⠀⣀⠤⠄⣀⡀⠤⠔⠊⠀⠀⠈⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠆⠀⠀⠈⠈⠣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢇⠀⠀⡤⠀⡀⠀⠀⣆⠀⠉⠉⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⡇⠁⠘⠳⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣀⠀⠀⣄⠀⠸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡶⠁⠀⠀⡌⠀⠀⠀⠀⠀⠘⡳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠁⠸⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡄⠣⡀⠀⢠⠔⠋⠉⠀⠉⠑⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢃⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠢⣀⠀⠀⢠⠁⠀⣸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠈⢳⠒⢁⠀⠀⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡄⠀⠀⢠⠀⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢁⠀⠀⢸⠀⢸⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢸⡄⠀⠈⠀⢸⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡧⠀⠀⠆⣀⠆⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃⠀⠁⠘⣅⣰⠀⠈⠁⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣶⡭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠄⠀⣶⡆⠀⡯⡆⠀⡦⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠈⠷⠀⠁⠀⠀⠀⠀⠀⠁⠀⣠⠏⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠀⠀⣠⠞⠙⠳⠀⠀⠀⠀⣀⣴⠟⠋⠉⠀⠀⠀⠉⠀⠀⠀⠀⢠⡖⠀⢰⡏⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⢀⣠⠴⠋⣹⠃⢀⡄⠀⣠⠀⢀⡀⠀⣠⠞⣹⡿⠀⢀⡞⣧⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⢦⠀⠀⢠⠀⠀⠀⠀⢀⣠⣴⠀⣀⣀⠙⠓⠒⢛⣉⠀⠀⣰⠃⠀⡾⢀⡼⡿⢠⠟⡇⢠⣏⡴⠋⡇⣠⠞⢀⣸⡦⠞⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢸⠃⢠⡿⠸⣧⣤⠖⠋⢠⡏⡴⢡⡏⠀⠄⢠⡏⠩⠇⢠⡏⠀⣼⢃⡞⢰⣣⠏⠀⣇⠀⣉⣀⣀⡉⠁⢰⡏⠁⣿
⠀⠀⠀⠀⠀⣸⠃⠀⠀⢠⠏⢠⣿⠇⢀⣴⡄⠀⠀⡞⡾⣡⠏⠀⡾⠀⣸⡀⠀⣠⢿⠀⣰⢻⡞⠀⠘⠋⣀⡴⠾⣏⠁⠀⠀⠙⡆⠈⠳⠶⠋
⠀⠀⠀⠀⢀⡇⠀⠀⠰⠃⢀⡟⡾⢠⠟⣸⠁⠀⣸⣿⠋⢷⣀⡼⣇⣰⠋⣧⡴⠃⠘⠚⠁⠀⠀⢀⡴⠚⠁⠀⠀⠈⠳⠦⠤⠞⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡼⢁⣇⡟⠀⡟⠀⢠⣿⡏⠀⠀⠉⠀⠉⣠⠞⣿⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠁⠈⠟⠀⠀⣇⢠⠟⠿⠁⠀⣰⠛⠁⠀⣇⣠⠇⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠖⠛⠅
⠀⠀⠀⠀⠸⡄⠀⢀⡼⠁⠀⠀⣀⠀⠀⠉⠉⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠉⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣿⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⡼⠃⠤⣤⣙⠉⠀⡴⠆⠀⠀⠀⠀⢠⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡴⠛⣀⠀⠀⠨⣥⡀⣆⠛⠀⠀⠀⢶⣦⢸⣇⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⡷⢛⡁⠀⠀⠁⠲⣄⣧⢚⣥⠄⠀⢢⡝⠞⣥⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣝⣷⠋⢐⣷⠘⣶⣤⠘⡇⣚⠅⢀⠸⣦⠙⣏⢉⣥⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⠉⠙⠳⠾⣇⡠⣤⣹⣴⡟⣡⠀⣾⠀⡀⢠⠷⠿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣧⡘⠖⠈⢛⣶⣭⣽⣦⣁⠀⢿⡄⢹⡿⠖⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡄⢩⣟⠛⣩⢅⡟⠁⢶⣭⣝⣿⣷⣾⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣼⠿⠃⠾⠋⠸⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣶⠿⡿⢀⡿⢛⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⢾⢟⣿⡛⢿⣿⡿⣿⢻⣶⣶⢶⠿⣻⢿⠇⣾⡽⠿⣾⣷⠿⠶⢿⣿⡟
⠀⠀⣴⣾⣿⣿⣟⣓⣛⠻⢭⡿⢿⡦⣧⣿⠧⠾⢛⣡⠾⣶⠏⡼⢡⢖⣛⢲⢬⣙⣛⣛⣿⠃
⠀⠸⠋⠉⢸⡿⢉⡵⣛⡓⢦⡹⣯⣿⠾⢷⣔⡛⠛⠒⣋⣵⣚⣷⡐⢜⡽⢢⡇⡌⣭⣿⠃
⠀⠀⠀⠀⢸⡿⡏⠸⡩⠿⢢⠇⣿⣿⠻⣳⣴⣶⡦⣤⣤⣔⠿⣿⡷⣔⢶⡟⣇⣿⣼⡇
⠀⠀⠀⠀⠘⣇⡇⢸⣬⢍⣭⣾⣿⣿⣿⣿⣼⣿⣿⡌⣧⡙⣷⣬⣿⢾⣇⣦⣿⣿⣿⣅
⠀⠀⠀⠀⢰⣿⢃⣇⣹⣶⣿⣿⣿⠃⠉⠙⠻⠿⠿⠿⠿⠿⠿⠛⢿⣿⣼⣿⣿⢿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠈⠉⠛⠛⢿⣿⡇
⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⡿⠃⠸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⢸⡟⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⣿⠃⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣶⡿⠃
⢸⣿⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠉
⠸⣿⡆⠀⠀⠀⠀⠀⠹⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⣀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣀⣼⡖⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡿⣯⣏⣽⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⡘⢑⡙⠎⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠠⡤⠄⠀⠀⢀⡀⠀⣀⣀⣀⣀⣠⢀⣀⣤⣭⡍⠛⠊⠻⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⢹⠄⠉⡀⢉⡖⠶⡈⠈⣃⢰⣿⠂⢹⠠⣿⣺⣇⣽⣿⣷⣤⣤⣴⣿⣿
⠀⠀⠀⠀⣾⢛⡁⠈⠀⠀⢂⠀⢆⠓⢠⡀⠠⠰⠀⢙⡯⢼⡛⠉⣗⡑⠘⠿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢸⣯⠘⣷⠀⠄⢀⠀⠀⠈⠃⠐⠃⠘⠃⢀⠉⠀⡉⠉⠀⠀⠃⢷⡀⠈⢻⣟⣿⡟
⠀⠀⠀⢸⡏⢠⠈⢷⡄⠀⠀⠀⠂⣸⣟⠂⠰⣯⣤⣍⣻⣧⣾⣶⣸⣷⣴⣷⡔⣻⣿⡿
⠀⠀⠀⠈⠓⠉⠀⠁⠈⠆⠀⢠⡿⠛⣿⣿⣾⡛⣷⡞⠓⢽⣿⣯⣷⠛⢳⣏⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⡴⢃⠀⢠⢒⠎⠀⠀⠉⠉⠛⠛⠓⠒⠒⠒⠛⠛⠙⣦⢻⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠂⡀⣠⠀⠐⢫⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠿⡆⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⣈⡼⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣧⢳⠀⠀⠀⠠⠖⠂⠀⠀⣰⠖
⠀⠀⠀⠐⢠⠃⠀⠀⠀⠀⠓⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠈⠁⠀⠉⠀⠀⠀⠀⣅⡈
⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡖⠐⠐⠋⠀⠉
⠀⠀⠠⠖⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠿⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠇⠀⠜⠃⠀⠀⠀⠀⠀⠘⠲⠓⠉⠁⠀⠀⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢟⡻⡿⢿⣿⢿⣻⣿⡿⠿⣻⠿⣟⢿⢟⡻⢿⣿⡿⣿⡿⡿⢛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣠⣙⣣⣿⣿⣿⣜⣻⣏⣇⣜⣛⣤⣛⣻⣜⣣⣞⣿⣩⣼⣇⣿⣘⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡯⣿⣟⡩⣟⡯⣫⣿⢻⣿⡟⢿⠛⡿⢻⣟⢻⢻⣛⣿⠛⢻⠟⣿⢻⡿⣿⣿⡟⣟⠛⣿⣿⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣵⣦⣧⣼⣧⣽⣼⣤⣶⣦⣵⣦⣧⣿⣽⣧⣭⣾⣤⣦⣿⣧⣿⣿⣿⣿⣧⣿⣿⣯⣿⣿⣿
⢸⣿⣿⣛⣩⣭⣶⠀⠀⠐⠒⠒⣶⡶⢭⣭⣛⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠛⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠈⠛⠛⠋⠉⠛⠛⠓⠚⠓⠒⠖⠛⠛⠛⠋⠉⡟⠛⡛⠛⠛⠃⠀⠀⠙⠛⠛⠛⢛⡛⠋⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⠠⠀⠀⠀⠀⢀⠇⠀⠯⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢿⠿⠛⠁
⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠲⠶⠚⠛⠛⡋
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠶⠂⢀⣶⡶⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⢀⠐⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⠤⠼⠿⠖⠘⠋⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠈
⠀⠀⠀⠀⣠⡄⢶⠀⠀⢁⣀⣸⠿⠛⠀⡄⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⣀⠌⠀⣤⠀⣀⡀
⠀⠀⠀⠀⠉⠙⠛⠁⠈⠉⠁⠀⠀⠀⠀⢻⠀⣀⣤⢔⣐⣶⣤⠉⠙⢯⣭⣭⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠛⠉⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠃⠀⠀⢠⣪⣵⣦⣀⣤⣀⣹⣿⣶⣶⣾⣿⣿⠿⠀⠀⠀⣀⠀⠀⠀⠀⢀⠸⣧⠁⠀⠈⠹⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠄⠀⠖⢀⣀⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣁⣀⣴⠀⠀⠈⠁⠀⠢⠀⠀⠘⠓⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀⠀⣾⣿⠟⢷⣤⣤⣤⣤⣴⣶⣶⣶⣿⠿⠟⠋⢉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣧⠀⠁⠉⠉⠉⠉⠉⣉⣁⣀⣠⣤⣴⡆⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠿⠿⠿⠿⠿⠿⠿⠛⠛⢉⡁⣴⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣤⣤⣶⣶⣶⣶⣿⣿⠿⠇⠛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⢋⣉⣉⣉⣉⣁⣤⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⢿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣷⢀⠹⡿⢸⣿⢁⣤⣌⢻⣿⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⣿⣏⣸⣧⣄⣸⣿⠘⣿⡿⢠⣿⠰⣶⠈⣿⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⡿⠛⠛⢿⣿⣿⣷⣤⣴⣿⣇⣴⣆⠰⣿⣷⢀⣈⣿⠿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⡇⢸⡷⠆⢹⠏⣡⣄⠙⣿⣿⣿⣿⣶⣿⣿⣠⣿⡟⠀⠿⠿⠉⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⢠⣶⣶⣿⠘⣿⣿⡇⣼⡇⢸⣿⣿⣿⣿⣿⣿⣧⣴⣷⡶⢘⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⣿⣿⣾⣿⣿⣿⣷⣤⣭⣴⣿⡇⢸⣿⣿⡗⠠⣮⣭⣿⣿⣿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠁⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣶⣤⣿⡇⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣏⠀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠙⠻⠿⠋⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣤⣤⣤⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⡉⠉⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠉⠙⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣄⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠈⠙⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⠛⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠓⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⡀⠀⣀⣀⣿⣷⣤⣀⡀⠀⢻⣇⣀⣀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠋⠉⠛⠙⠛⠛⠿⣷
⣿⠛⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂
⣷⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⡗⠀⠀⠀⠀⠸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⣿⠀⠀⠀⠀⠀⠀⠠⠀⠈⠛⠛⠛⠛⠛⠛⠛⠀⢠⡄⠀⠀⠀⠀⠀⠃⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠄⠀⠀⠀⠀⠀⢈⡇
⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢸⡇
⣹⣷⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣤⣤⣸⣄⣴⣄⣄⣿⣌⣴⣾⣩⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠟⡗⢸⠀⡇⢀⠠⣄⡄⣦⠄⡤⣀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢠⠤⡖⣴⣤⢤
⠀⢀⡖⠀⢴⠀⡇⠸⠃⠇⠸⠀⣘⣀⠘⠘⣣⠇⡰⠀⠀⠀⡠⠂⢰⡃⠀⠀⠚⢉⢉⢛⡗⠚⠂
⠀⢸⡏⠁⠸⡆⣀⣆⣾⢠⠐⡇⢸⢁⣀⢒⢁⢀⢀⠀⠀⢸⠇⠀⢸⡇⣧⠪⣼⢸⢸⡼⡇⠏⠇⠇⡏⡏⣎⣀⠆
⠀⠘⣧⠀⠀⢳⠸⡄⠐⠘⠄⢻⠙⠘⠘⠎⠮⠾⢸⡆⠁⠸⣇⠀⠈⠇⠙⠀⠈⠀⠀⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⠧⠄⠈⠀⠀⠀⢠⣠⠞⠀⠀⠀⠀⠀⢄⡴⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⢠⣤⢠
⠀⠀⢀⡀⢠⡎⠀⠀⡠⠤⠬⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡄⠀⠀⠀⡴⢶⢢⣄⣄⣀⡄
⠀⢠⡏⠀⢸⡇⡄⣠⣰⢰⢰⢰⡇⡄⡆⡆⡔⡖⡄⠀⡀⢸⡀⢠⡇⠀⠀⠀⢁⠂⠤⢭⣙⡘⠁⠀⠀⢀⢠⣆⠂
⠀⢸⡄⠀⠨⡇⢻⠈⠻⠈⠘⣯⠁⠁⠙⠂⠉⠁⣷⠘⠁⠈⠓⠃⡇⢱⠰⡾⢸⠀⣄⢨⠀⡆⡆⡇⣾⠸⠄⠙
⠀⠀⠳⠄⠀⠁⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠤⠋⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠂⠚⠈⠈⠁⠁⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢿⡟⣶⣀⠔⢻⣦⠃⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⢸⡏⠀⠈⣿⠀⢸⡇⠀⠀⣠⡀⢰⡋⢀⡤⢠⣏⣠⡖⠀⢠⡦⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⢸⣷⠀⠀⣿⠀⢸⡇⠀⢸⡧⠀⢨⠛⣾⠁⠀⢁⡿⢀⢰⡿⢁⢴⡟
⠀⠀⠀⠀⢀⣾⠋⠙⡄⢠⣿⢡⠀⢸⣿⠀⠀⡿⠀⠸⣇⠀⡸⠷⠖⠁⠀⠳⢊⠀⠘⠓⡁⠘⠓⢡⡟⠀⢀⣰⠇
⠀⠀⠀⠀⣸⡏⢤⣰⠃⠀⣿⣸⠀⠘⠋⠀⠀⠀⣠⡄⠈⣩⠀⢠⡮⠍⠙⢻⡿⠖⠚⢉⠄⢂⣰⠟⠉⠉⠉⠁
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⠙⣤⣿⠀⢠⣤⠀⢸⡇⠀⠀⣾⠁⢀⡀⣘⠚⠋⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⢿⣆⠈⢻⡜⠷⡇⣿⠀⢸⣿⠀⠌⢿⣄⢴⡇⠀⣸⠋⣸⠊⣿⠀⣴⠋⣼⠇⢸⡧⠀⢰⡄
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠘⣿⡀⠈⣷⠀⡇⠹⠦⠘⣿⣎⠴⠚⣿⠸⣧⠔⠟⠀⡟⢰⡇⢰⡏⣠⡟⢀⠘⣿⡠⠞
⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⡿⣧⠀⠹⠶⠁⠀⠀⣠⠊⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⡩⠔⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣰⠁⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡏⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣀⡼⡴⢃⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣛⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣠⠏⠀⣏⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡤⠤⢤⣤⡼⠛⢩⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣶⣶⣶⣶⣶⣖⣒⣒⣒⣖⣾⣵⣾⣿⣶⣶⣬⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠁⠈⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⣀⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⢳⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠦⣀⣿⣠⠔⠃⠀⠀⠀⠀⠀⡗⠋⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠶⠒⣺⣿⣗⠒⠶⠀⠀⠀⠀⠀⣇⣀⡤⠏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁⣿⠈⠧⠀⠀⠀⠀⠀⠀⣇⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡤⠖⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠦⣤⣈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠁⣴⠋⠀⠀⠀⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣠⠏⠀⠀⡈⠙⡆⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⢄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⣡⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠉⠓⠲⠦⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠊⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⡤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠘⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢠⠃⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⡞⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠷⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣷⠀⠇⡁⠀⠈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢰⠱⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⣴⢃⠀⠸⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⡠⢘⠀⠀⠜⣶⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢄⠘⡿⡄⠀⠙⢆⢦⡀⠀⠀⠀⠀⠀⠜⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⡼⡰⠃⢀⣾⣶⠃⡰
⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠤⠀⠑⢤⡌⠰⠄⠀⢠⡙⠆⠀⠀⠀⠀⠄⢧⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⢀⠀⠴⢋⠔⠀⣴⢟⣿⣿⡎
⠀⠀⠀⣀⠀⠀⡀⠀⢀⠀⠀⣀⠀⠀⡀⠙⢢⡴⢒⣒⠛⠓⠦⠌⠐⣤⣸⠀⠂⠀⠀⠀⠀⠠⠀⣃⣤⠂⢡⠴⠛⠛⢂⣲⣾⣿⣯⣾⣿⣄
⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠈⣌⣂⣀⡀⠢⣄⠈⢑⣦⠀⠀⠀⢀⣆⡈⢁⣠⠔⢀⣀⣂⣡⢰⣻⣿⣿⣿⣿⣯⣿⣆
⠀⠀⠀⠓⠀⠀⠃⠀⠘⠀⠀⠚⠀⠀⠃⠀⠐⠂⠀⠒⠠⠀⠀⠉⠳⠠⡙⡀⡀⢡⠀⣀⡄⠀⢀⠉⠠⠞⠉⠀⢀⡿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢁⡜⢅⠀⠼⢠⡅⠦⢀⡀⢃⠌⠀⠀⢀⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢑⡉⠀⠁⠀⠀⢰⠀⠁⣊⣦⠐⢀⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠳⣐⠆⠚⠓⠰⣀⠞⢠⠂⢀⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⢃⠀⠀⠌⠹⠀⡏⠀⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠆⠈⠛⠛⠂⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡆⠘⠃⠀⠀⠶⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠜⢂⠠⠴⠦⠄⠺⠣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠑⠐⠂⢊⠀⡠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠭⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠛⠠⣀⣀⠄⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⣒⣒⣒⣒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠠⠬⠭⠭⠭⠭⠭⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠸⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣥⡀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠓⠒⠒⣆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢁⣀⣀⣀⣈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣫⡧⠤⠴⠖⠒⠚⠋⠉⠉⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⣉⣉⣉⣭⡤⣤⣄⣀⣀⣤⣄⠀⠀⠀⢀⡠⠶⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⣴⠛⠒⠶⠖⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⠒⠋⠀⠀⠀⠙⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠦⡤⠞⣷⣶⣶⡆⢀⠀⢀⢀⣤⣸⣿⣀⠀⢻⣿⣿⣆⣤⣈⣿⢠⣤⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡟⣿⣻⣿⣿⡀⣼⣿⡋⢿⣿⣿⣿⢿⣿⡇⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠛⠛⠉⠛⠋⠛⠁⠙⠉⠉⠉⠁⠉⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠋⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⠋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣤⣴⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠶⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠉⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⠉⣤
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⢀⠿
⠀⠀⠀⠀⠇⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠆⠒⢸⡀⠀⡀⠤⢄
⠀⠀⠀⠀⠐⢄⡡⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣁⡠⠆
⠀⠀⠀⠄⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⠞⠁⠀⠉⠉
⠀⠀⠦⠀⠤⠄⠁⠈⠢⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣋⡀⠓⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠈⢀⠶⡈⠑⠆⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣉⡤⠚⠁⠈⠶⣄⠀⢀⡙
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠈⠉⠒⠒⠀⠈⠉⠉⠀⠀⠤⣄⠀⠀⠀⠀⠄⠀⢀⠐⢄⠀⠀⡤⠒⠀⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠞⠁⠀⠀⠀⠀⠈⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⢀⠀⠀⡠⠄⠀⠀⠀⠀⢀⡀⠒⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣤⡀⠁⠀⣾⠆⠀⠀⠈⠥⠄⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠇⠀⠀⠀⢠⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢠⠀⠀⠀⢆⠀⠀⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠀⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠠⠴⡿⠦⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣻⢢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⣀⡤⠄⠠⠦⡄⡀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⠣⡀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⠏⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⣄⡀⠀⠀⢠⠁⠀⠀⣸⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠛⠦⠒⢛⠀⠀⠀⠻⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢰⠀⢸⠀⠀⢰⠀⢡⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⠀⢸⠀⠀⢸⠃⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢢⠸⠀⠀⠈⠀⠈⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣄⠀⠀⠀⠀⠀⣦⠀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠘⠀⠀⢀⡇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⠀⡿⠀⣤⡄⢠⡠⠚⢁⠖⠀⠤⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⡇⠀⠀⠀⠀⢣⣀⡎⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠘⢷⣄⣀⣀⣀⣼⠟⠙⠢⠤⠤⠴⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣙⣿⠛⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡶
⠀⠀⠀⠀⠀⡀⠂⣀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢁⢹⡀
⠀⠀⠀⠀⠸⢷⣤⠀⠉⠟⢡⣤⠻⡇⠀⠀⢠⣬⣆⠿⠒⠒⠂⢀⣰⢠⡄
⠀⠀⣠⠒⠐⡆⠀⠑⠻⠏⠙⠉⠘⠇⠀⠀⠘⡟⠙⠓⠂⠀⠐⠚⢣⠀⠀⠀⠀⠀⠀⣄⠀⠐⢄⠉⢀⡀
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠉⠉⠁
⠀⠀⠈⠓⠦⠴⣆⣀⣀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣯⣗⠶⠂⠀⠀⠀⣀⣀⢀⠈⠂⣉⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡛⠻⢄⣀⠟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠝⠈⠁⠀⠀⠀⠀⠉⠈⠀⠉⠁⡁⠈⠁⠀⠀⠀⠀⠀⢀⣀⠙⠣⠤⠶⠶⠬⠴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠀⠄⣤⡤⣾⠋⠘⡆⠀⠀⠀⠘⠁⢱⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⡀⠀⠄⡂⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠃⣿⠀⠀⡇⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⣿⡑⣦⡍⢉⡅⣠⣾⡇⠀⠀⠀⠀⢸⣇⠀⢀⢨⠀⣿⡤⠀⠀⠀⠀⠀⠈⢀⣘⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠋⣽⣩⠄⠀⠀⠀⠈⠻⣦⣬⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠤⠀⠀⠸⠾
⠀⠀⠀⠀⠀⠈⠓⠄⠠⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠸⡥⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣐⣺⡛
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠓⠚⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠋⢀⣠⣄⠁⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⡀⠀⣿⠀⠀⣾⠡⠈⠑⠂⣿⠀⠀⠚⢀⣷⠀⢰⡇⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢸⡇⢸⡏⠀⠀⢿⣀⢀⠄⢰⡟⠀⠀⠆⣸⠇⠀⠀⢧⡠⠂⣿⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢂⠈⠁⢼⠀⢀⠆⠀⠉⡰⠀⢸⡇⠀⠌⠀⣿⠀⢀⠂⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠦⠂⠀⠀⢠⡇⠀⠘⠷⠊⠀⠀⠘⠖⠁⠀⠀⢀⠌⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⢸⡇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠃⢸⠀⡆⠀⢸⠀⡎⢻⠀⢸⠀⡞⢠⢰⠇⠰⢸⠛⡆⠀⠀⠈⠀⠀⢸⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠂⠘⠁⡇⠀⢫⠀⠉⠈⡇⠈⠂⠙⠈⢸⠀⠀⠘⠂⢹⠀⠀⠁⢀⡤⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡤⠔⠛⣁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⢤⣤⣤⠤⠤⠤⠶⠒⠚⠋⠉


⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣯⣼⣷⣦⣶⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⡜⠁⡏⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠸⡈⠳⡀⢀⠎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠲⠁⠸⡇⠀⡜⠁⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠳⡀⠀⡇⠀⠳⠋⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠞⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠓⠚⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠓⢄⡀⠀⠹⡦⢄⣀⣰⣄⡄⠀⠀⢀⡴⠃⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠓⢤⡀⠀⠙⣄⠤⠷⣄⠀⠈⠉⡿⠤⣤⡏⠀⢀⠴⠊⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠋⠉⠁⠀⡀⣉⠑⠢⣌⡶⠋⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠉⢶⣡⠔⠊⡉⣀⠀⠈⠉⠙⠒⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠁⠀⠉⠙⠂⡞⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢳⡐⠛⠉⠀⠈⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠴⠚⢹⠁⠔⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠣⠀⡏⠓⠦⣄⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣿⣛⣷⡀⠀⠀⠀⠀⠀⣾⣿⣹⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡻⠟⡢⠁⠀⣀⡀⠀⠀⢿⠿⢟⡜⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡈⠉⠀⣠⣤⣶⣶⢦⣄⠀⠉⢁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣨⣇⡀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠦⢤⣀⣑⣊⣀⡠⠴⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠏⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⢦⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⣧⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡇⠀⠀⣇⣀⣀⣸⠀⠀⢸⣷⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠃⠀⠀⠈⠿⣶⠿⠁

⠀⠻⡙⠒⠢⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠚⡹⠃
⠀⠀⠱⡀⢳⡚⠿⠿⣿⣿⡙⠒⠲⣶⣤⣤⡤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⣤⣤⣴⡖⠒⠚⢻⣿⡿⠷⠖⣲⠃⡰⠁
⠀⠀⠀⢻⣶⣷⠀⠀⠀⠀⠉⠉⠑⠛⠛⠻⠿⠦⠤⠤⣿⣿⣿⣿⣄⣀⣘⣿⣿⡿⠧⠤⠤⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠈⡿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⢀⣄⠀⢠⢄⡀⢀⢄⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⢳⣀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⢀⣃⣙⣛⣀⣛⣙⣀⣘⣙⣃⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⢰⠃
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣀⣀⠀⠀⣉⣍⠉⠉⠀⠀⢀⡤⠤⠤⣄⡀⣠⠈⠉⠉⣩⢥⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⠿⢿⡇⠀⢀⣾⠫⣖⣸⠂⣸⢇⡜⠀⠀⠀⠀⢘⠒⢃⡀⠀⢨⡟⠒⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿
⠀⠀⠀⠀⢸⠀⢀⠇⠀⢸⠃⠀⠈⠀⢀⡿⠛⡆⠘⢦⡿⠃⣾⠀⣻⣏⠀⡟⠀⣼⢒⡖⡶⢀⡶⢲⠆⢰⡶⠀⠀⠀⣇⠀⢸
⠀⠀⠀⠀⣿⣶⡾⠀⠀⠘⠦⠤⠴⠚⠙⠃⠈⠓⠁⠘⠓⠁⠛⠊⠑⠞⠘⠓⠂⠃⠘⠀⠓⠘⠒⠛⠒⠋⣿⠋⠁⠀⠸⣷⣾⡇
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⣤⣤⣤⡤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⢀⠟⣻⢃⣀⣠⡤⠔⢶⣶⣿⣍⣉⣙⣿⣿⡿⠦⠤⠽⠿⠿⠷⠤⠤⠽⠿⠿⠿⣄⣀⣘⣿⣿⣿⡟⠒⠲⣤⣤⣀⣀⢻⡛⢇
⠀⢀⠎⠀⣉⣿⡿⠿⠗⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠚⠿⠿⣿⣉⠁⠈⢆
⠀⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠉⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠰⠂⠑⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠂⠠⠤⡀⠀⢘⠀⢸⠀⡐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠃⠠⠇⠀⠀⢀⠀⠀⠈⠀⠈⠀⠈⢠⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⣄⡀⣀⠀⠈⠆⠀⣸⠏⣔⠀⢀⣸⠆⢠⠁⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣜⢋⠁⡀⠂⠁⠈⢲⡁⠄⠤⢍⠐⠍⡆⠈⠼⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⡉⠀⠀⠹⠦⠀⢤⠀⢨⡀⠀⠀⠁⠀⠱⠾⢦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠄⠐⠐⠆⢊⡀⡔⢁⡘⠀⠀⢨⠒⣄⡴⠂⠸⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⡄⢀⠀⠀⠠⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠠⠈⠀⠂⠠⢂⠄⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⠁⠱⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡊⠴⠂⡅⠀⠒⢌⡒⢀⠀⠁⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠆⠂⠀⠀⠀⠇⠍⠀⠀⠀⠂⠋⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣌⠳⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠾⢷⡿⢿⣿⣷⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⢁⡾⢿⣿⣾⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣅⢙⢴⣿⡿⠞⣩⠗⣷⡾⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠛⢟⡿⠟⣨⣽⣍⡉⣛⣤⣶⣖⣡⠃⢀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠟⢖⠉⣀⣰⣿⣿⣤⣩⣵⣦⣤⣻⡿⣿⠿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡴⢂⣠⣼⣷⣿⣿⣾⣿⣿⠄⠼⢯⣹⡻⢿⠷⡾⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠻⣿⡿⠟⢫⡿⢿⡽⠿⠷⣶⣦⣄⣸⡃⡀⢉⣭⣬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠷⠀⠰⡌⠉⣠⣤⠿⢓⠾⣿⣒⠒⠊⢿⣭⡈⠛⠻⠿⠥⠷⢀⣠⡄
⠀⠀⠀⡰⣰⣶⣤⠀⠻⠴⢿⡦⣰⣿⠺⢋⣠⣶⢽⣦⠈⠻⣿⡀⠀⡜⢻⠿⣶⣼⣶⠟⠋⠉⠁
⠀⠀⠀⢻⠿⣱⠃⣀⣀⠀⢈⣿⠟⢁⣀⣽⣷⣟⣹⣿⣀⠀⠸⢿⣷⣬⣭⣄⠈⠛⠤⣀⠀⢀⣴⣄⣿
⠀⠀⠀⠏⢠⢳⣎⢿⣿⡗⠋⢁⣴⣦⢿⣿⣧⣤⣠⣿⣿⣶⡦⢰⣬⡟⠺⡁⠿⠛⠶⣦⣭⣽⣿⠛⡿⠤
⠀⠀⠀⣇⢺⣀⢿⡜⠟⠛⣘⣟⣩⣬⣿⣿⣿⡟⠉⠀⠀⢹⡇⣿⣿⣇⣞⣥⣦⣄⠀⡏⡞⣻⠇⢠⠛⠁
⠀⢀⣴⣿⠀⢳⣾⣴⣾⠛⢻⣾⣿⡏⠀⠸⣻⣇⡼⠛⠻⡖⠤⠤⣽⣿⣿⠁⠀⢻⣦⠧⢛⣫⣮⢏⣀
⠀⠀⠺⠟⠣⣼⣻⠟⠋⡀⢰⣿⣿⣄⢀⢰⡇⢽⣇⠠⢸⣆⡀⠐⢿⣿⠙⡀⢃⠛⣿⣯⡽⠛⠳⣦⢤⠐
⠀⠀⠀⣰⢲⠙⢟⠻⢿⣥⠏⣩⣏⠈⠑⠚⠁⣸⣱⣤⡴⠷⣠⡖⢾⣿⣷⣦⣅⢖⠁⠙⢂⠧⠄
⠀⠀⠀⡧⢈⢤⣼⣶⣤⢰⢬⣉⠛⠳⢦⣴⣶⣿⣿⣿⣿⣴⠅⣴⠾⠿⠟⠛⠉⠀⠀⠀⣸⣷⠄⢠
⠀⠀⢠⢻⡇⠸⡻⠏⠁⢸⣸⣿⢠⣀⠀⡀⠀⠉⢡⠰⢰⠀⠀⠀⢀⢠⣄⣠⡄⣤⢢⢀⡿⢡⠄⠊
⠀⠀⢸⠋⢳⣰⠑⠦⢤⣀⡈⠉⠃⠸⠀⠇⠯⡇⠸⠀⠸⠽⠼⠸⠏⠞⠒⠛⠋⢉⡀⢼⢀⡞
⠀⠀⠸⣆⡿⠁⠀⠀⠀⠀⠈⠉⠙⠒⠤⣀⢤⣀⣀⣀⣀⣀⡀⠤⠴⠤⠐⠊⠉⠀⠀⠀⠉
⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⣀⡠⣶⣿⡟⣠⣿⠇⠀⠀⠀⢀⣾⡶⠀⢠⣾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⢁⣼⡟⣼⡿⣻⡟⢀⣴⣶⡆⢘⣿⣤⡀⢺⣿⣄⠀⣰⣷⠀⣴⡆⠀⠐⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠙⢡⣿⡇⣾⡯⠞⣡⢏⣾⡟⣠⢯⣿⠏⣰⣿⢃⣼⡿⠁⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⢿⡌⠿⡿⣰⡄⠘⣿⠇⠻⠶⠛⠁⠘⠿⠖⠁⠘⣿⣛⣙⣛⣫⣿⣁⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⢀⣾⠇⠀⣰⡿⠃⠀⣴⣷⠆⠀⠀⣾⠆⠀⠀⢰⣿⢡⣷⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠘⠿⠋⢀⣼⣿⣡⣤⠘⣿⣧⡀⠀⣠⡄⢠⣶⢿⡷⢹⣿⠟⣹⣄⣤⣶⡠⣴⡄⣠⣶⣶⣴⡆⢰⣿⠟⢁⣿⠃⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⡴⣿⣿⠋⣽⡟⣰⢳⣿⢃⣴⡿⣡⢿⡇⢞⣵⣿⢃⣼⣿⠋⣼⡟⣰⡟⣰⣿⢁⣾⡟⣠⠿⣿⡘⠛⠃⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠻⣿⣶⡴⠞⠋⠀⢿⠇⠘⢿⠞⠁⠿⠷⠋⠿⠿⠑⢿⡽⠇⠸⠿⠋⠿⠇⠐⠿⠀⠿⠟⠙⠿⠋⠙⠗⠁⣴⠮⢿⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣶⣾⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠁⠉⠉⠉⠛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡀⢀⡀⠀⠀⠀⠒⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡿⠃⢰⠣⢶⡆⣈⠁⢰⣄⠀⣨⠄⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠇⠀⡟⣱⠟⣿⠃⠀⢀⣩⠟⠈⢳⠆⡏⡴
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠘⠀⠀⢰⠏⠀⠈⠦⠐⠋⠄⢰⣉⠔⠀⡼⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠇⢀⡴⢋⡆⣀⠸⡀⠀⠀⣀⠀⠀⠀⠀⢀⠤⠊⠀⢀⢢
⠀⠀⠀⠀⢀⡾⢡⠄⠀⣿⠓⣉⠘⢷⣤⡀⣀⠡⠤⠤⢄⣀⣀⣴⠀⠀⠀⠨⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣾⠇⡀⠄⢰⣧⠊⣸⢃⡤⠈⢁⣤⠃⣴⡀⠀⢠⡟⢡⣶⠄⡷⢀⡗⣰⠏⠅⢸⡇⠂⡔
⠀⠀⠀⠀⣿⠀⠁⠀⢸⠇⢰⠃⠘⠀⠊⣼⠃⠀⠘⣷⡔⡟⢀⠸⠇⠸⢣⠏⡀⠿⣸⣠⠈⢻⣌⢦
⠀⠀⠀⠀⠙⠦⠀⠀⢀⣄⠈⠀⠀⢣⠆⠃⠈⠰⠅⠼⠁⣣⡢⠀⠀⠀⠀⠉⡠⠄⠈⠁⡊⣁⠟⢸
⠀⠀⠀⠀⠐⠀⠴⠒⠁⠈⠦⣀⠀⠀⠀⠀⣀⡠⠔⠊⠉⠀⠀⠀⠒⠆⡠⠀⢏⡁⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁




⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠓⠀⠔⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⠀⠀⠀⠀⣏⠁⠀⠀⠳⡤⢰⠄⣼⠀⠀⠑⠂⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⡟⢰⡇⠀⡴⢒⠀⠨⢩⡟⠀⡀⠀⡟⢀⣏⠀⠀⠀⡎⠀⡸⠋⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⡤⠁⠀⢠⡇⢸⠀⠰⣗⠉⡰⠁⠘⠧⠀⠀⠀⠈⠐⡆⠀⠀⠀⠉⣩⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢷⣋⢁⡠⠂⠘⠇⠉⠃⠀⠈⢉⡀⠀⢸⠇⠀⠂⠒⠒⠛⠁⢀⡤⠀⠀⣿⠃⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡽⢣⠀⠀⠀⠀⠀⠀⠤⠀⢸⡄⠀⣿⠀⢠⡔⢰⠂⡽⢠⡟⢠⡇⡠⢻⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢞⢅⠀⢸⡇⠈⠀⠸⣁⡠⡦⢠⡆⠀⢸⣧⢘⡇⢀⡟⢀⡏⠸⣇⠈⠓⠈⠁⡰⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠨⠞⠀⢸⡇⢀⡗⠀⠌⣼⠃⢾⡁⢰⠃⣿⠈⠃⠈⠁⡤⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠠⠂⠀⠸⣇⠀⠀⡠⢿⡇⠸⠇⠊⠀⠉⠀⠀⠀⠘⠶⠋⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⢼⠃⡀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠉⠃⠉⠀⠀⠀⢠⠔⠊⠁⠀⠀⠀⠀⠀⡀⠀⡀⣴⠂⣿⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠄⠀⣼⠁⡄⢰⡇⣼⢰⣇⠰⠇⠀⠀⠀⠀⢠⡎⠠⡌⠐⣄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⠀⠀⢀⣈⠑⠈⠀⠀⠳⠔⡃⠘⠁⠈⠁⠀⠂⠀⢢⡀⠀⠀⠈⠓⠐⠃⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢀⡶⢉⡀⠉⠂⠀⠀⣀⡜⢡⡆⠀⠀⠀⠀⠀⢀⢸⡇⢲⣄⡇⢸⡇⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢸⡁⢯⡀⠀⠂⢠⠎⢀⠃⣾⠀⡼⠉⡅⣼⠁⣸⣸⠃⣸⠻⡇⣼⠁⣀⠞⠁⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⢷⡀⠀⠀⠀⠈⢁⠈⢸⡇⠘⠇⠰⠇⣿⠐⠃⣿⠈⠁⠀⠀⡟⣊⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⠀⠀⠙⠒⠤⠤⠒⣁⠀⠀⠁⠀⠀⠀⠠⡇⠀⠀⠏⠀⢀⠐⠊⠰⣏⣀⣤⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⠀⣠⠶⡳⠄⠀⠀⠸⣇⣀⡄⠀⠀⠀⠀⣠⠀⡄⣴⠛⢴⠃⣰⠀⠀⠂⣰⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠈⠳⠐⢠⡟⢠⡟⠀⣠⡄⢠⠀⣦⠀⠀⠀⠀⠀⠀⢠⡏⣸⠇⣏⠀⠛⠆⠛⠐⣁⣀⣬⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢾⡇⣼⠁⠀⠸⡄⠿⠀⠀⠀⠀⠀⠀⣨⡥⣿⠶⠤⠤⢤⣤⣔⡋⠁⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠁⠙⢒⣁⣀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠔⠁⣀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣀⠀⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠦⢄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⢶⣀⠐⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠈⠀⠀⠀⠀⠀⠀⠐⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢋⠃⠀⠀⠀⠀⠀⢠⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⢀⢔⡗⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡤⠆⣀⠀⠀⠀⢀⣲⠿⠛⠁⠀⣀⡠⢤⢎⣼⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⣀⣴⠀⠉⠙⠛⠓⠛⠛⠛⢿⣷⣄⢀⣷⣐⠥⢆⢀⡾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣛⢿⣿⣿⣿⣋⢵⣿⡟
⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠦⣽⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡆⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠘⢃⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡶⠿⠿⣿⣰⡿⢿⠃
⠀⠀⠀⠀⠀⣾⣿⣡⣴⠀⠤⠄⠐⠰⠤⡁⠀⠰⠶⢦⣀⣀⠀⠀⠀⠀⠀⠋⠹⠉⠁⠀⠀⠈⠛⠙⠋
⠀⠀⠀⢀⢸⣿⣿⠟⡽⣶⣮⣰⠷⠶⠶⠾⠀⠀⣰⣋⣩⣿⣆
⠀⠀⠀⠊⣼⡿⢁⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⣽⡏⠁⠀⠀⠉⠢⠄⠀⠀⠀⢀
⠀⠀⠀⡟⡟⢰⣋⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⡂
⠀⠀⠀⢹⡇⠀⢶⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢺⡄
⠀⠀⠀⢺⡇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠼⣧
⠀⠀⠀⠸⣇⢼⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⢶⣿⠿⠀⢸⡻⠀⠀⠀⢰⡇⠀⠀⣸⣧⠀⠀⠀⠀⣄⣠⠀⠀⢸⡆
⠀⠀⠐⠿⠟⠀⠀⠸⣿⣷⡀⠀⠈⠉⠂⠰⢿⣿⠜⠓⠒⠂⠁⠀⠀⠀⣾⣿⢆⡀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠶⠿⠗⠀⠀⠀⠘⠻⡷⠶⠂⠀⠀⠀⢠⣐⠠⣶⣩⣤⡥⠀⢈⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⣱⡱⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢻⣀⣹⡣⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠔⠂⠢⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡼⠢⣿⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠘⠧⠔⠻⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢠⡆⢠⠲⡶⠀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠀⣿⢠⣾⠀⢋⢴⡄⠐⢻⠇⠐⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢛⣀⣀⣀⡁⢿⠀⢀⠞⢀⡐⡏⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⡀⠉⣤⠤⢨⢙⠢⡀⠀⣆⠘⣷⣣⡤⠆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠀⢠⢞⣇⣴⣜⡀⢸⠘⡧⡡⢀⡟⣈⡙⠶⣅⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⢊⠴⠃⠘⠁⣟⡏⠁⣸⠀⡇⠀⣸⠀⣹⠏⠙⢓⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⠙⢷⠀⣸⠁⠀⠇⡦⠄⠟⠠⠃⣰⢃⣖⠈⠳⣄⠛⠁⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⢠⡏⢰⢷⡖⡍⢵⣤⣦⡍⣡⠊⠉⠳⣤⠈⠁⠐⠛⢿⠇⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠻⣄⣀⡘⡽⢑⡏⣸⡟⠁⠀⢸⡇⠀⠻⠖⢛⡆⠀⣰⢰⣦⢶⢠⣰⣠⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠃⠰⠆⠀⠀⠸⠁⠘⣇⣣⠹⠤⠤⣼⣤⡄⠠⠴⠋⠀⠀⡟⠽⢿⠎⠈⡿⠿⠃⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠂⢒⠚⢀⡀⢤⠀⣀⢤⡀⠀⠠⣤⡀⠀⢀⣠⠤⠄⡀⠀⢀⠀⠀⡀⠀⢄⡀⡆⠒⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠉⠀⠀⠉⠀⠀⠰⠈⠀⢨⠅⠀⠀⠈⠀⠀⠈⠑⠃⠀⠀⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠉⠲⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⡤⠼⡄⠀⠀⠀⢋⠀⠀⢀⣹⣴⡊⠉⠉⠙⣆⣀⣀⡀
⠀⢀⣤⠒⣉⣁⣠⣤⠤⡴⠳⣀⢀⣠⣎⣀⡔⠉⠀⠀⠹⡄⠀⠀⣵⡤⠤⣉⣉⡉⠉⠒⠒⢤⡀
⠀⢸⠈⠉⠓⠒⠾⠤⠤⠧⠤⠬⢧⣀⣀⣀⣱⣄⡀⠠⠤⠿⠭⠭⠤⠷⠴⠒⠒⠛⠛⠉⠉⠉⡇⠀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⠀⠀⠈⠙⠢⣄
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⠒⠦⡀⠀⠀⠀⠱⡀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡇⠀⠙⢦⣧⠎⠀⠀⢳⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⢧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⣼⠀⠀⠀⡇⠀⠀⠀⣵⠾⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠑⢄⠀⡇⢀⡴⠊⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⣤⣄⡬⢶⠤⠤⠤⠤⢵⣷⠯⠤⠤⠤⢄⣴⣊⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠸⠀⠀⠀⠀⠀⠀⠀⠉⢀⡔⠁⠀⠀⢀⠔⠁⡇⠑⢄⠀⠀⠀⠘⢦⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠞⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣴⠋⠀⠀⡇⠀⠈⠳⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠊⠉⠀⠀⠀⠀⣠⠃
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⢸⠀⠀⣰⣇⠀⠀⠀⡏⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡠⠞⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠠⠊⣸⡀⠳⡄⠀⠃⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠒⠒⠒⠊⠉
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠚⢷⣠⠞⠁⣸⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⢉⣁⡀⠈⠙⢦⡀⠀⠈⠁⠀⠀⣿⣠⠴⠚⣿⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣷⠀⠀⢀⡞⠉⠀⠀⣠⠴⣛⡩⠤⠒⠚⠛⠉⠉⠛⢲⡄⠀⠀⠉⠀⠀⢰⣇⣠⠴⠞⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠉⠉⠀⢠⠏⠀⠀⣠⡾⠟⠋⠁⠀⢀⡤⡄⠀⠀⡴⠤⢄⣳⡄⠀⠀⠀⠀⠛⠉⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⡟⠀⠀⡴⠃⠀⠀⠀⢠⠚⠉⣀⡿⠒⠒⠓⣤⡤⣸⣿⣄⠀⠀⠀⠀⠀⠀⠾⠥⠤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡼⠁⠀⠀⣠⣴⠿⠐⢉⣿⣢⡤⠔⠾⣷⣒⠬⠷⢬⣳⡀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠰⣶⡶⠶⠶⠶⠶⠶⠶⠖⠀⠀⡟⠀⣸⠁⢀⡴⠛⠁⡼⠒⠒⣞⣭⣿⣭⡀⠀⠀⢙⡖⠊⠉⣉⣉⠓⢦⡀⠀⠀⠈⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⣠⠞⠛⠛⢧⣴⣋⠀⠀⣸⡧⠚⠉⢁⡀⠀⠀⠉⠓⣒⠋⠀⢠⠞⠁⡈⢳⡄⢳⡀⠀⠀⠀⠒⠛⢉⡽⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢰⡃⠀⠀⠀⠀⣻⠁⠀⠼⡟⠀⣰⠋⣉⠉⠳⡄⢀⡼⠋⠳⣄⠸⡀⠈⠳⠞⠁⡼⠻⡆⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢧⣀⠀⣀⣠⠏⠀⠀⠀⣇⠀⠻⣤⡼⠀⢀⣷⣿⣷⣾⣿⠉⠙⠛⠓⠒⠒⠋⢁⠀⣿⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠰⢶⣟⡉⠁⠀⠀⢸⠉⠉⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠴⠋⠀⢫⡈⢉⡿⠀⠀⠀⠀⠠⡀⠀⠈⢷⠟⢦⡀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠁⠀⠀⣻⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⣠⠞⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⠙⣆
⠀⠀⠀⠀⠈⠉⠉⠓⠀⠀⠀⣠⠞⠙⣇⠀⠀⢠⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠤⠞⠁⠀⠀⢸⣇⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢷⣄⢸⡇⠀⠀⠉⠳⠦⠤⡤⠄⠘⣆⠀⠀⠀⠀⠀⣠⠄⠀⠀⢹⠀⢠⠟⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣤⣄⡲⣤⠌⠙⣇⢀⣠⣤⡖⣏⠑⣤⠞⢩⢟⣷⣦⡤⠴⠚⠁⠀⠀⠀⣸⡶⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢙⡏⠀⠀⣸⣯⠀⢠⢿⡙⢦⣌⡴⢋⡹⡄⠀⡹⠛⠒⠲⠶⣶⡞⠉⠉⠙⠲⢤⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⠶⠚⠛⢛⣳⠖⠋⠙⠒⣿⡾⢶⣉⡲⢿⣶⣉⡻⠗⠿⠥⣤⣠⠶⣿⠛⠷⠴⠶⢤⡀⠀⠙⣆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠟⠀⢀⡤⢶⡿⠤⢤⣤⣶⣛⠁⠀⣀⡤⠖⠛⠛⠲⠶⢤⣤⠶⠋⣿⢀⣘⣷⣤⠆⠀⠀⠉⠀⠀⢹⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⠏⢠⣴⠇⠀⠀⣿⠈⠉⠙⣿⠛⠶⠤⣤⣄⣠⠶⠋⢹⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠀⠘⢿⣇⡀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⣀⣼⡇⠀⠀⠀⠀⠀⣠⠞⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⣦⠀⠀⠈⢻⡓⠺⢧⣤⣄⣿⠀⠀⠀⠀⠀⣷⠀⢀⣸⠟⠉⢸⡟⠦⣤⣤⣖⣋⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣄⠀⣸⠃⠀⠸⡇⠀⠉⣿⠛⠲⠶⢤⣿⡴⠋⢹⡀⠀⢸⣇⣠⠞⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣄⣀⠀⣧⠀⠀⢿⠀⠀⠀⠀⣇⠀⠀⢸⡇⣠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢤⣼⣀⡀⠀⠀⣿⠀⣀⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠿⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⣵⣦⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣷⢶⡀⠀⠰⠿⠁⠀⡠⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢇⡀⣐⣤⠐⣿⠉⠉⠧⠀⠀⢸⣞⡁⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢇⣱⠤⢄⣖⠰⠆⢴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⢷⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⣶⡛⣠⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠙⣿⣿⡿
⠀⠀⠀⠀⢀⣤⣶⣾⣯⣻⣵⣾⠩⢉⡁⠊⠸⣿⣿⣴⣾⣯⣉⣻⣚⣇⠜⢶⣟⣉⣟⡛⢹⣏⣽⣿⡃⠀⠠
⠀⠀⢀⠐⣾⠃⠞⣿⣿⠀⠀⠁⠀⠀⠀⠛⣶⢞⣿⡿⠟⣛⠘⠃⠿⠿⡟⣠⣤⡿⢿⣿⠛⣹⡾⢻⣿
⠀⠀⠻⢸⣿⠠⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⢰⠘⣷⣻⡟⠈⠙⠀⠂⠀⠘⠛⠻⣧⠿⣿⣽⢿⡛⣿⣿⠄⠀⠀⣠⣤⡆
⠀⠀⠀⢟⣿⡀⡀⢸⡟⠀⠀⠀⠀⠈⠉⠀⢀⠽⣏⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢛⣀⠠⣛⣵⣟⣠⠐⣾⣿⡟
⠀⠀⠀⠈⢻⣇⠡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣩⣿⠀⠀⠀⠀⠀⠀⠀⣰⣦⡾⠩⠄⢺⣏⣻⠿⣿⡟⡹⠋
⠀⠀⠀⠀⠀⣿⡄⠉⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⡽⠟⠀⠀⠀⠉⠉⠏⠀⠙⡟⠁
⠀⠀⠀⠀⠀⠸⣿⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠁⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠠⠄⠀⠀⠀⠀⠒⠒⢷
⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣀
⠀⠀⠀⠀⠀⠀⣤⡀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣄⣼⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⡄⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⠁
⠀⠀⠀⠀⠀⠛⠀⡀⠒⠬⠀⠄⠢⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣶⡴⣽⣲⣤
⠀⠀⠀⠀⠀⠐⡛⠲⠶⠤⠦⠴⠶⠚⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠶⠶⠒⠛⢣⠀⢀⠀⠀⠀⠀⠀⡠⣼⠈⠀⠉⢹⠹⠅⢘
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡶⠣⢀⣀⡀⠀⠀⠀⣿⣰⣧⡀⠀⠀⠀⠐⠄⢸⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⣠⠎⠁⠀⠆⠀⠀⠀⠀⠀⢀⡿⠀⢰⡿⠀⠉⣿⠛⠛⣿⠁⠄⠀⠀⠀⠀⠑⠺⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠘⠶⣶⣾⣿⣿⠿⠿⠿⠖⠚⠁⠀⠀⣷⠐⠐⣶⠉⠳⢄⣸⣇⣀⣀⣿⣀⣤⡟⠔⠁⠀⠀⠀⠀⠒⠿⠷⠶⠤⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠿⠒⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠸⡗⠀⠀⢀⠀⠀⢈⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣥⠐⠂⠉⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢘⠛⠛⠛⠛⠛⠛⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡁⠀⠀⠂⠈⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⣶⣶⣾⠷⢶
⠀⠀⠀⠀⡌⠀⠟⠉⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠉⠉⠁⠀⢰⣄⠠⠀⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢻⣄⠀⠀⠀⣐⣴⡀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠂⠀⢈⡀⠠⠀⠄⠠⠡⡈⠀⡡⠀⠀⠀⠀⠀⠀⠀⡇⠱⣄⠀⠀⠀⠀⢸⡸⣦⠀⠤
⠀⠀⠀⠀⠀⠙⢣⡀⠀⠘⠉⠂⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⣆⠉⠀⠀⠈⢠⠿⠎⡀⠀⠀⠀⠀⠀⠀⠂⢹⠀⠀⠉⠐⠒⠒⠚⠛⡹⠄⠂⡤
⠀⠀⠀⠀⠀⠀⢈⣏⡓⠒⠒⠓⣻⠃⠀⠶⠀⠀⠀⠀⢠⣥⣀⡐⠨⠷⠦⠤⠶⠋⢀⣀⠬⠀⠀⠀⠀⠀⣈⣄⠈⠢⣀⡀⠀⠀⠀⣀⣠⣁⣀⡎
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⠋⠉⠉⠛⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⡖⢀⡤⠀⡀⣤⠀⢀⣆⡀⡤⣠⠂⢼⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⣰⢣⡇⢸⠁⡾⢗⢼⠏⠜⡏⠼⢡⠇⠀⢀⡠⠊⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡸⠀⣰⠃⠸⠇⢸⠀⠁⠊⠈⠈⠀⠡⠒⠞⠒⠋⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⠔⠁⠀⣠⢄⠀⠀⠀⠀⠀⠀⣴⣀⠤⠶⠒⠂⠀⡀⠀⣶⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⠒⠀⡆⣴⡡⣫⠀⠀⠞⡶⠈⣽⠁⣴⢔⡦⣲⢠⠏⣼⢡⠝⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠼⣱⣿⢫⠆⣝⡖⡼⣡⠿⡅⢇⠸⠏⠾⠁⠇⠉⠊⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⠺⠏⠊⠈⠘⠊⠁⠉⠀⠀⡠⠀⠀⠀⠀⠀⢀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⢢⡀⠀⠀⠄⡀⠀⠀⠀⠈⠑⠀⠀⠀⠠⠐⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠁⠀⠀⠀⠂⠀⠃⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠦⠤⠤⠶⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠠⠠⢀⠀⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡔⠄⠀⡀⠀⠀⠎⠑⠀⠀⠀⡆⠀⠀⠆⠈⠀⠀⠃⠀⠀⠉⣑⠀⠄⡀⠉⠀⠠⢀⠀⢋⠑⢀⠌⢀⠂⠀⠀⠀⣀⢀⠇⠀⠀⠀⠶⡌⢏⡠
⠀⠀⠠⡊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠘⠃⢠⠀⠀⠈⠉⠘⠃⠀⠁⠀⣠⠀⠈⠀⢀⠶⡀⠉⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢣⠚⠦
⠀⠀⠀⠈⠤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⡀⠀⠎⠀⢸⠀⠂⠘⠣⣀⠇⡀⠙⣀⡸⠀⠈⢢⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠈⠀⠁⠈⠀⠉⠋⠀⠀⠀⠐⠁⠀⠈⠐⠁⠀⠀⠁⠊⠐⠂⠂⠀⠀⠀⠀⠤⣀⢄⠀⢀⡀
⠀⠀⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⡀⠀⠀⠀⠀⠀⢠⠘⠀⢀⡔⠀⢂⠘⠈⣆⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠊⢀⠀⡈⠠⡀⠀⠀⠐⠤⠔⠀⠀⠀⠀⠦⢼⢲⣉⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠢⠀⠀⠀⠐⠄⢀⠜⠀⢡⢌⠉⢠⠂
⠀⠀⠀⠀⢠⠀⠂⣀⠔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢹⠀⠁⠀⠀⠀⠁⠀⠀⠀⠃⠀⢄⡎⠀⠀⠀⢌⠁⠀⠃⠘⠃⡀⠀⠰⠂⠤⠐⢉⠂
⠀⠀⠀⠀⠀⠑⠄⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠁⢃⠚⠃⢈⠁⠴⢄⠤⡄⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⠂⠄⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⢀⢀⢤⠀⢆⠠⠀⠀⠀⠰⡀⠊⢁⠤⠍⢤⠐⠎⠀⠐⠈
⠀⠀⠐⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠈⠑⡀⠤⠄⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠀⠤⠊⡹⠤⢄⠈⢉⡀⠀⠀⠢⠤⢄⡁⢠⠂⣀⠀⠀⠁
⠀⠀⠀⠀⢀⠤⠀⠠⠁⠀⠡⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⠀⢃⡘⣠⢆⢑⣢⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠑
⠀⠀⠀⢈⠁⠐⠤⢒⡈⠈⡒⢀⠐⠈⢀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠃⠧⠀⢊⢁⢄⠘⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠄⠤⢀
⠀⠀⠀⠀⠂⡲⠀⡈⢁⠈⠊⣀⠰⠂⠌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠂⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠄⠠⡀⢡
⠀⠀⠀⡒⠠⠕⠈⠁⡈⢂⡀⠉⠠⠠⠀⠄⠀⠀⢎⡠⠀⠀⠀⠀⡀⠀⠀⠔⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢃⠀⠂⠀⠁⡰
⠀⠀⠀⢅⡀⢰⠑⠌⡁⢈⠨⠔⠂⢀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⠀⠀⠑⠀⠀⠊
⠀⠀⠀⠀⠀⠊⢠⠂⡁⢈⠂⡄⠁⠂⠀⠀⡀⠀⠀⢀⠄⠂⠁⠄⠐⠁⠒⠀⠀⠀⠐⢆⠀⠠⢀⠀⠀⠀⠀⠀⠀⠈⡍⠁⢐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠄⢲⠜⠁⠀⠀⠀⠀⠀⠀⠲⢆⢄⠀⠐⠂⠀⠀⠀⠀⠀⠃⠒⠌⠀⠀⠀⠀⣀⠠⠔⢂
⠀⠀⡋⠈⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠂⣀⣀⡀⠀⠀⠀⠈⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠘⠂
⠀⠀⠈⠈⠀⠀⠀⠀⠸⠈⠂⡤⠰⣊⣀⣀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⠀⠘⠂⠂⠤
⠀⠀⠀⠀⠀⠀⡆⠒⠈⠀⠈⡉⠀⠁⠀⠀⠀⠀⢘⠀⡸⢀⡀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⢀⡆⣲⣈⣀⣀⣀
⠀⠀⢠⡄⠀⠀⢧⠄⠀⠀⠀⠗⠀⢺⠀⠀⠉⠉⠃⠀⡇⠀⠀⠀⠉⠉⠀⠀⠀⠂⠀⠀⠐⠒⡗⠢⡀⠀⢀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠀⠰⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢈⣀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢉⠀⠀⠀⠀⠛
⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⢀⣈⡀⢠⠅⡤⠤⣤⠀⢀⡈⠤⠬⣄⢀⡀⠀⠀⡀⠀⢀⡂⣀⠜⠄⠎⠀⠀⢀⡀⠀⠀⢐⠀⢸⠀⠀⠀⠸
⠀⢀⠀⠀⠐⢀⠆⢈⠋⠁⣀⠉⠣⠘⠄⠄⠀⠀⠀⠄⠀⢣⠀⠛⢉⡉⠘⣏⡉⠉⠉⣉⠇⠀⠆⢠⠂⠀⠂⠠⠁⠀⠩⠉⠝⠉⠉⠙⡧
⠀⠙⠤⠀⢀⢘⠀⠆⠀⡊⠀⢁⡂⢁⠄⡄⠀⡀⠀⠂⠀⡐⠀⣄⠈⠈⠛⠄⠀⠀⠀⢸⠀⠀⠀⠆⢀⠀⢰⠁⠠⠥⠀⠘⠀⠈⠈⠛⡀
⠀⠀⠀⠋⠀⠀⠀⠐⢀⠈⠀⠁⡨⠹⠀⠀⢀⡄⢐⢆⠀⢳⣀⡛⠉⠙⠀⠄⠀⠀⠀⢸⠀⠘⡀⠀⠸⠀⠈⠠⠀⠀⠄⠈⡞⠁⠐⠀⡐⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠉⠀⠂⠁⠀⠈⠂⠊⠘⠂⠃⠐⠐⠁⠃⠚⠁⠀⠀⠈⠈⠉⠂⠐⠈⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡀⣆⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠜⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂
⠀⠀⠀⢐⠀⠀⠈⡈⠉⠈⡀
⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⡁⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢈
⠀⠀⠀⢸⡥⠤⠤⡿⢶⣏⡇⢠⢴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣸⡀⢀⡦⣤⡀⢀⣯⠒⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡠⢖⡥⠁
⠀⠀⢠⠤⡬⡬⠴⠰⡠⡇⢸⠉⠀⠀⡍⡇⠀⠀⠀⠀⠀⢀⡠⠔⠈⡅⠐⠙⠿⠿⠯⠿⠛⠀⢀⡠⠥
⠀⠀⠠⢠⡜⠀⠪⠀⠄⡜⢼⠀⠂⠀⡃⠁⠀⠀⣀⠔⠊⠁⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⢠⣨⣟⢄⣩⣨⣠⣌⣸⣀⣀⣀⣆⣇⠔⠊⠠⠇⡄⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠒⡆⠂⠀⠀⠀⠀⠙⡆⠀⠈⢤⡀⠀⠀⠁
⠀⠀⠆⠀⠀⠊⠁⠀⠀⠀⠐⠒⠀⠓⠂⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⣭⡶⠾⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣼⠟⠁⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠀⠀⠀⠀⢸⣇⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣄⠈⠢⣤⣤⡴⠿⠋⠉⠀⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣷⡘⢷⣄⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⡙⢷⣄⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠻⣶⡿⣧⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠚⠉⠙⢿⣎⠻⣯⣿⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡟⠁⠀⠀⠀⠀⠀⢿⡄⠈⢻⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⣷⣄⡀⠀⠀⠀⠀⠘⣇⠘⣦⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣿⣿⣿⣷⠶⠖⢀⣈⠀⠸⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠶⣛⣛⣛⡻⣦⢹⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠻⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠾⣇⡀⠀⠀⠀⣿⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠁⠀⠀⢠⡿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣤⣄⡀⠀⣼⠃⠐⠀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠑⠒⠀⠛⠀⠀⠈⣠⡤⠶⣦⣬⣙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣤⣤⣤⣤⣀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⢷⡌⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠸⣷⡀⢿⠉⠀⠈⠉⠉⠓⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⣿⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣽⠟⠉⠁⠀⡛⢷⣦⣀⡀⠀⠸⣧⣄⣀⣀⡀⠀⠀⣹⡇⠀⠀⢠⣿⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⡇⠀⠀⠀⠀⣿⠘⢮⣍⣛⠻⠶⣤⣭⣉⡉⠶⠾⠛⠋⠀⠀⣠⠾⣫⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣤⡀⠀⠀⢹⡄⠀⠈⠙⠛⠷⢶⣮⣭⣝⣓⠦⠀⠀⠠⢊⣵⡾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⢶⣄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣦⡀⠰⠋⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣡⠔⠀⠀⠀⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣉⠙⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠉⠛⢦⡈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣷⡀⠀⠀⠀⠀⠀⢠⡀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⡟⠁⢢⠀⠀⠀⠘⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠻⢶⣤⣀⠀⠀⠀⠻⢦⣄⣈⠉⠛⠛⠿⠿⠟⠛⠋⠁⢀⣠⠟⠀⠀⠀⣰⡟⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣬⣙⡛⠷⣶⣦⣤⣌⣙⠛⠿⠶⢶⣶⣶⠶⠾⠟⠋⠁⠀⠀⢀⣴⠟⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⡷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠿⣿⣶⣄⠀⠀⠀⡼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠄⠀⢰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢤⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢱⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠁⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡛⠒⠦⠤⠖⢚⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣛⣛⣛⣻⣤⠤⠤⠶⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣭⢉⡍⠉⠉⢉⠉⣯⠉⣅⠀⠀⠒⠀⠈⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠹⡗⠈⠔⠘⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⢸⣇⠌⢐⢒⠀⡆⠞⠋⠀⠠⠀⠀⠁⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣈⣈⣡⣼⡧⠤⠤⣴⣶⠶⠶⠶⡖⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣧⣤⣤⡤⠤⠶⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⠀⠀⢀⠀⢀⢠⠀⣄⢠⣍⠓⠲⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠰⠉⠀⠃⠀⠀⠜⠸⠨⠄⠄⠸⠊⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠤⠤⠤⣤⣤⣤⣤⣤⣶⠒⠒⠀⠤⠼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡼⠤⠤⠤⠤⠴⠦⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢡⠁⠀⠀⢀⢠⠦⠀⠂⡄⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⠀⣤⠈⠁⣀⠁⢈⠈⢁⢀⡀⡀⢀⠤⢀⡠⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣥⣈⡘⠉⠃⠉⠀⠘⠉⠑⠊⠚⠀⠻⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⡾⠿⠿⠿⠿⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⠀⢀⣇⠀⠀⠀⢀⣴⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⡀⠀⢨⣉⠩⢍⢩⠉⡡⠀⣌⠙⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⡀⢉⠐⣄⠘⡀⠃⠀⠉⠀⠀⠀⢀⡩⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢁⣈⣃⣉⣀⣁⣂⣀⡀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡟⠛⠛⠛⠛⠛⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡆⠠⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠵⠒⠺⠴⠒⠒⠢⠜⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡆⢠⣿⠃⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⣠⡴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣦⣀⠀⢸⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠻⣷⣼⡇⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⢿⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠌⢿⣶⣶⣤⣤⣀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢀⣀⣴⣶⣿⣿⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠛⠻⠿⢾⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣆⠀⠀⠀⠀⢐⣼⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⢰⣞⠋⢹⣇⠀⠠⠊⠛⣿⣁⡀⠴⠶⠆⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣮⡿⠏⠁⠈⠉⠀⠈⢠⣿⡟⢡⣴⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠈⢿⡟⠁⠀⠀⠀⣄⣠⣄⠀⠘⠋⢀⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠐⠛⠛⠛⠁⠀⠀⠚⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣈⣿⣿⣿⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣭⣄⣀⣀⡀⠀⠀⣀⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠻⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡏⠀⢻⣿⣷⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⡋⠀⢙⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⣻⡯⠀⠀⠈⣿⣿⣿⠿⣻⣿⠃⣾⣿⡻⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡋⠀⠘⠿⠀⠀⠀⢿⣿⣥⣖⣺⣿⣵⣿⣿⣷⣮⣿⣇⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⠈⡓⠀⠀⠀⠚⢻⣿⣿⣿⠟⢳⣿⣿⣿⡿⢻⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣁⡀⣀⣹⣿⢰⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣿⠇⠈⡟⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⡟⣿⢻⣿⣿⡿⠀⢟⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⣿⣿⡿⠸⢿⠁⠀⠁⠀⠈⠁⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣛⣿⣿⠿⠰⢷⣶⣦⣤⡀⠀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣷⣶⣾⣮⣿⣿⣿⣶⣿⣿⣷⣶⣯⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣾⣝⣛⡛⠿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠟⣆⢀⣀⣀⣼⣻⠏⠉⠉⠙⠷⣠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠞⠉⢻⣀⡤⣧⣬⠶⢛⠉⠛⢀⢀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣀⡁⠄⠚⠑⠀⠀⠀⢰⣼⢅⣀⠀⠸⣀⠘⣠⡷⠄⠠⠾⠉⣟⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⠐⡆⠀⠀⠐⡄⠱⣦⡀⠐⠁⠘⠶⢴⣦⣀⡈⠢⠚⠁⠀⣈⣳⣄⡋⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⡇⠀⠀⢀⠏⢢⠰⡁⢠⠐⠉⠉⠉⠀⠀⢷⠘⣀⠀⢦⠁⠉⠉⠠⡁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡾⠈⣀⣴⠎⠀⠀⠈⡇⡹⠸⡆⠂⠀⠀⠀⠐⠘⡇⠃⠈⠾⣇⠠⠀⠀⠈⠀⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠲⣴⠳⣄⠀⠀⠊⠰⡧⠀⢻⡀⠀⠀⠀⠀⠀⢷⢷⠀⢠⠏⠀⣁⣴⡿⠖⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⡶⠶⠤⣄⣸⠃⠀⠀⠘⣗⣨⢭⣁⡒⠶⠘⠆⣀⣳⡄⢠⠤⠶⣤⣀⡶⠶⣻⡼⣿⠉⠀⡎⢂⢰⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢞⡽⠛⢩⠽⠿⠯⢭⡓⠀⣽⠀⠀⠀⠀⠈⠁⠀⠀⢹⡶⣤⡤⢦⡁⠀⣡⠋⠛⠉⠁⠙⠞⠋⠀⢸⣷⣼⠁⠈⡏⢸⡇
⠀⠀⠀⠀⠀⠀⣰⠃⢀⡴⠖⠚⠛⠛⠓⠦⣅⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠈⣿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠀⠀⣧⣿⡇
⠀⠀⠀⠀⠀⢠⡏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠘⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡇
⠀⠀⠀⠀⠀⢸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠘⣇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠐⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢹⡄⠈⠳⣄⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠞⠓⠚⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠈⠉⠙⠛⠒⠒⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠂⠠⢀⣄⣁⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠶⠛⠓⠋⠉⠉⠄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⠤⠴⡶⢶⡴⠶⠦⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠳⣤⣴⢿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢧⠃⠂⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⢹⡷⡆⠄⣀⣀⠀⠀⢀⡻⠎⢀⠈
⠀⠀⠀⠠⢆⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠰⠻⠁⠀⠀⠘⠛⠻⠺⢙
⠀⠀⠀⠀⠈⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣄⣀⣀⣀⣀⣲⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⢈⠛⠀⢀⣤⣤⢀⣀⣀⣠⣄⣴⡆⠀⠀⣀⣶⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠶⣬⣽⠿⠀⢻⣿⣿⣿⣿⢿⣿⣿⣷⢀⡄⡹⣿⣿⣿⡼⢿⣿⠋
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠘⠙⡿⠁⠈⠀⡀
⠀⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⢢⣄⠀⠀⠀⢄⠆⣀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠲⣈⣤⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡄⠀⣀⣦
⠀⠀⠀⢀⡀⠳⠀⢴⠟⠙⠀⠀⢸⡏⠁
⠀⠀⠀⠈⠁⠀⠀⠘⣇⠀⢠⠀⢸⡇⠀⢀⠀⢀⣤⠀⣶⠀⠄⠀⡴⠌⠲⡄⠤⠐⢢⡄⠠⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠻⠀⣿⠀⠈⣓⡄⠈⠁⢸⡧⡖⠋⠀⠀⠀⠇⢀⣰⠇⠀⠀⢿⠀⠀⣿⠈⠀⠐⣏⠂⢠⣤
⠀⠀⠀⢀⠀⠀⣿⠀⠀⢰⡇⠀⢸⡏⠀⠀⠀⢰⡦⢇⡀⠀⠀⠀⡟⠈⢱⠀⠈⠀⣼⠄⢺⡁⠀⠀⡀⠙⣰⠋
⠀⠀⠀⠈⠋⠀⣿⠀⠀⣼⠀⠀⠘⠇⡀⠀⢀⣈⣃⣀⣻⡰⣤⣤⣱⠦⣬⡷⢀⣠⣙⣆⠀⢧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣯⠀⣀⡿⣀⣠⡦⠴⠟⠈⠉⠉⠉⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠰⠶⢤⣱
⠀⠀⠀⠀⠀⣀⣈⣽⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠞⠛⠃
⠀⠀⠀⠙⠚⠋⠉⠀⠀⠀⠀⣠⠶⠛⠉⢽⣓⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⠉⢰⡇⠀⢠⣤⠐⣦⠀⢠⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⢠⡶⣄⣷⣀⠀⠀⣤⠀⠀⡄⠀⠀⡤⠀⠀⢸⡇⠀⢰⠢⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣩⡄⢸⡇⠀⢨⣅⠰⡏⠀⢸⡇⠀⠳⣄⠈⠀⠀⣿⠉⠀⠀⢿⠀⠀⡇⠀⢀⠸⡇⠀⠈⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿⠀⢸⣇⣄⣼⡇⠀⣧⠀⢸⡇⢀⡀⠈⢦⠀⠀⣿⠀⠀⡆⠀⡤⢀⡇⠀⣼⠀⣧⠀⢠⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢀⣀⡿⠴⠾⠃⠛⡿⠃⠒⠻⠲⠼⡇⡈⠂⢀⣾⠀⠀⡏⠀⠀⡏⢠⡇⢸⡇⠀⡶⠂⢸⡀⣈⣁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠐⠦⠷⠀⠤⠇⠼⠠⠼⠧⠶⠇⠐⠚⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⢸⣠⠏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⢰⠃⠘⣄⠀⢠⠇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢻⡀⠀⢠⡏⠀⣀⠈⢶⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣾⠛⠋⠁⠀⢸⡆⠀⢀⣼⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢶⠦⣝⠷⣴⠀⢀⣼⠷⣶⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠷⡼⠳⠞⠛⢀⢑⢋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠋⠈⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢧⣀⡀⢀⣀⣀⣾⡯
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠷⠿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡄⠀⠙⡖⠤⠤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣾⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠰⣤⡀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡹⣿⡟⣇⣾⢳⡀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣿⠀⢻⣷⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠸⠇⢻⣧⣿⣿⡈⢃⡀⠀⠀⣷⣠⠀⠀⠀⢸⡟⢸⣿⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠈⣧⠀⢸⣧⠟⠄⠀⢠⢟⣠⣿⢿⣿⣇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⣸⣭⣤⣤⣶⡾⣿⣿⣷⣮⣿⣿⣧⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢻⡇⢿⡇⡰⠉⠉⠉⠁⠀⠀⠈⠻⣿⣿⣿⣧⡙⠻⣷⣤⡈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡻⣦⠀⠙⠫⣼⣟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢨⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡨⠍⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠤⠆⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠃⡰⠲⠀⡋⠐⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠅⠀⠀⡀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠐⠉⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠒⠀⣉⢀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀⠀⠀⠀⢀⡤⠤⠠⠤⢄⣠⠄⡰⠈⠉⠈⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⡔
⢀⣀⣀⠤⢔⠉⠉⠑⠉⠉⠑⠎⠁⠉⡐⠡⠂⠀⠀⣀⢄⠀⣠⣄⢀⣀⠤⠒⠻⡀⢰⠚⠓⣄⠀⠀⡴
⠀⠠⠔⠈⣉⠀⢀⡶⡂⠀⣠⣄⢠⠊⠇⡔⠢⡀⠼⠁⠀⠑⠁⠀⠀⠀⠀⠀⠀⢇⡘⠀⠀⠘⣄⡜⠉⡄⣶⠀⠘
⢡⠀⠐⢻⠈⡍⣁⠜⠀⠀⠀⠘⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣀⡈⣀⣀⠀⠀⠀⠀⠀⠡⠁⡄⡃
⠀⡅⢰⠸⡄⠆⠀⠀⠀⠀⠀⠴⠢⣤⡶⠠⢲⠲⡲⢼⠑⠛⡗⡾⠹⠌⡉⠋⡇⣣⢜⢸⠀⠀⠀⠀⠀⠀⠀⢱⠁
⠀⠇⢸⠀⡇⢰⠀⠀⠀⠀⠀⠘⡟⠪⣹⢧⡸⣀⣇⢼⣀⡿⣜⡧⠠⠧⠧⠀⠧⠵⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠲⡸⢠⠇⠌⠀⠀⠀⠀⠀⠙⠈⠀⠉⠀⠈⠉⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⡾⡖⣤⠚⠏⢫⢢⢹⢸⠀⠀⢱⢹⠾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣝⠒⠙⢄⣧⣼⠜⠸⠬⠶⠟⠺⠜⠒⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠀⠤⠤⠒⠂⢉⠁⠠⣀
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⠐⠒⠒⠂⠒⠈⠁⠉⢰⠚⣇⢀⠒⠴⠊⢂⠀⡌⠉⠙
⠀⠀⠳⡚⠓⠂⠒⢂⠉⠉⠉⠉⡠⠝⠉⠉⠂⠉⠢⠴⠉⠈⠀⠐⠙⠁⠀⠈⠁⠀⠀⠀⢂⢠⠇⠀⠀⠇⢰
⠀⠀⠀⡈⠘⠆⢐⢣⠁⢤⡸⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡌⢀⡂⠀⠀⠀⠀⠀⠀⠸⣸⠀⠀⠀⢰⠊
⠀⠀⠀⢁⠆⢠⢰⢨⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠁⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠘⠂⠀⠀⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠒⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⢠⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⢇⠂⠀⠀⠀⡀⢇⡀⠁⠢⢄⠀⠀⠀⠀⢀
⠀⠀⢀⡀⠤⠤⠖⠀⠒⠒⠒⠒⠒⢒⡓⠁⠀⠀⠀⢀⡓⠠⠖⠉⠀⠀⠉⠒⠤⢀⣉⣀⠈⢁⣀⡀⣉⠑⠂
⠀⣾⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡄⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⣀⣀⠀⢀⠔⠉⠀⢁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠄⠰⠄⠀⢸⡠⢇⡀⡸⠷⢒⡠⠂⠁⠀⣀
⠀⠀⠀⠚⠀⠀⠀⠀⠀⢠⠂⠐⢢⣀⣀⠚⠐⠣⡀⠠⠃⢦⠀⣸⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠒⠚⠒⠒⠑⠀⠠⠦⠶⠀⠤⠤⢈⡐⣇⣈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠤⠀⠤⡀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⢐⡄⠀⠀⠀⠀⠀⠀⠀⢸⡔⠂⠲⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠐⠛⣥⣰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢲⢦⣁⠉⢀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠌⠀⠄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡰⠀⠁⠒⣛⠋⠄⠀⠀⠀⠀⡜⠁⠈⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠓⠒⢲⣲⠒⠀⠉⠀⠀⠀⡜⢁⣉⡀⡠⣐⠀⠀⠐⡦⢀⠠⠀⠄
⠀⠀⠀⢚⡚⣦⠀⢀⠠⠒⠠⡀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⢶⣀⢁⣀⠌⠁⠈⠍⠈⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠊⠉⠛⠉⠕⠛⠂⠄⣀⡘⠉⢽⣖⠋⠠⢬⣋⡀⠂⢈⠉⠉⠀⠈⠉⠋⠉⠙⠚⠉⠁⢀⠙
⠀⠀⠀⠠⠀⠀⠤⣀⡂⣤⡠⢅⡠⠍⠠⣅⣄⡀⣀⠁⢀⠀⠀⠠⠍⠍⠀⠐⢖⠂⢠⣠⣄⣐⣡⡄⠀⠁
⠀⠀⠀⠭⠨⠙⠁⠀⠊⠀⠀⠈⠃⠐⠀⠀⠀⠈⠉⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠑⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠘⠂⠋⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠔⠨
⠀⠀⠀⠀⡀⠀⢀⠔⠉⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢐⡾⣚⡀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⢀⡀⠀⡈⠠⢀⢄⣨⠆⠀⡀⢠⠊⡀⠠⠊⠑⢄⠈⠂⠑⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠨⡀⠈
⠀⠀⡐⠀⠘⢤⣅⠀⠀⠂⠒⠠⢄⠀⢸⠀⠐⠀⠀⠀⢘⠀⠀⠀⠄⠀⡠⠊⠀⠑⠤⠔⠀⠀⠈
⠀⠀⠨⢡⡉⢸⡀⢀⠀⣀⠀⠁⠀⣠⡈⣦⡀⠀⠀⢀⡌⠀⠀⠀⠀⠈⠒⠤⣔⠀⢐⠤⠐⠤⠄⠒
⠀⠀⠧⠤⣠⡃⠀⡀⠽⠒⠚⠁⡉⢉⡀⠀⣹⣛⠛⢩⡧⠤⠤⠤⠴⠄⠀⠢⡀⠉⠅⠀⢀⠀⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⡔⠛⣁⢀⡩⣠⡤⠖⣤⡄⢰⡝⢖⡦⣂⢸⡇⠀⢸⠀⡀⠐⠢⢤⣀⣀⠴
⠀⠀⠀⠀⠊⢳⢛⡓⠀⠀⠣⣀⣋⣛⣉⡈⠡⣤⣤⣤⣤⡄⠄⠀⠖⠒⠒⠊⠁⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢿⠀⡠⠂⣇⠀⠀⡠⠊⠉⠑⠒⠐⠢⠤⠀⠤⠊⠉
⠀⠀⠊⠁⠀⠈⡉⠒⠰⠶⠀⠀⠀⠒⠂⠐⠒⢺⡉⢀⡔⢹⡤⢯⡄⢀⡀⠐⠊⠓⠒
⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠁⠀⡸⣧⠉⠀⠀⢠⠈⠀⠁⠀⠀⠒⠨⠤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⢳⠐⠊⠁⣯⠈⠢⠠⠀⠁⠀⠀⠁⠑⠠⢀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠘⡦⠔⠋⢸⠦⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈
⠀⠀⠄⠂⠀⠀⠐⠒⠈⠁⠄⠀⠈⠀⠀⠀⠦⠴⠀⡧⠤⠔⠉⣇⣀⣀⣁⣀⠇⠻⠿⠇⠀⠂⠁⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⣂⡄⠀⠀⠀⡄⢹⡀⠠⠊⢡⠨⠥⠬⠥⠀⢠⣤⡀⠐⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠠⣀⣀⠨⡇⢀⡠⠚⡄⠀⠀⠀⠀⠀⠂⠈⠉⠐⠂
⠀⠀⠀⠀⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢏⠀⢀⡴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢈⣑⢀⣀⡀⠀⠀⠀⠀⠀⢀⢸⠉⠁⢀⢾⠀⠐
⠀⠀⠲⠖⢶⣤⠤⣀⣀⠈⠀⠂⠀⠀⠁⠀⠈⠀⠀⠀⠀⡇⢈⣀⠨⠦⠔⠒⠒⠒⠒⠀⠄⠀⠀⠀⡀
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠠⠉⠀⠒⠂⠀⠀⠖⣲⣶⡶⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⢀⡠⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⠀⠀⠀⠼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠⠊⠀⠀⢠⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠀⡀⠀⣰⣮⢖⣆⠆⠀⠐⠄⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠁⢀⣰⣿⠛⠉⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣬⡀⠀⠐⠂⠀⣸⡿⠁⡀⠀⠀⢀⠀⠰⠊⠁⠠⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⠓⠶⠶⣿⣿⣄⣘⣆⢨⣠⣤⣀⣀⠀⠀⠁⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⣿⣿⣿⣍⠙⠷⣄⣷⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⢿⣿⣶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠦⠂⠀⠩⢽⣷⣄⠈⠻⣁⠖
⠀⠀⠀⠀⠀⠀⢠⡶⢿⣿⣿⣿⡷⢿⢟⣿⣿⣯⣿⠋⡉⠛⠿⠟⡿⢿⠛⠛⠓⠒⠒⠶⣤⣄⡀⠠⠞⠀⠀⠀⠀⠀⠀⣀⡈⣻⡷⢀
⠀⠀⠀⠀⠀⢰⡟⣰⣟⣿⡿⢿⠐⠀⡀⠰⢻⣿⠟⠀⠀⠀⠀⠀⠀⠹⠓⡀⠀⠀⠈⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣵⣾⠁⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣷⠘⣆⠈⣧⠀⠈⢹⣯⣃⣀⠀⠀⠀⠀⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⠘⠀⠙⣷⢀⣀⣀⣉⠉⠑⠀⠀⠀⠙⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢿⣖⡷⢰⣅⡂⢉⣿⣿⣷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠠⠀⠀⢁⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣉⠘⣿⣧⠀⢈⡿⠛⠲⠤⣌⡉⠉⠛⠛⣻⣿⣶⣷⣤⣦⣤⣴⣾⣇⢀⣄⡠⠶⠛⠁
⠀⠀⠀⠀⠀⢀⠐⢋⣤⠟⠁⡠⣳⢿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢙⣿⣿⠛⠋⠁⠀⠀⠁
⠀⠀⠀⠀⡼⢋⡴⠋⠀⢀⣺⠏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⣿⢻⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠇⢸⣿⡇
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢻⡇
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⣧
⠀⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠸⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠛⠛⠒⠀⠀⠀⠀⠀⠘⠛⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⢤⣀⠛⠻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⡀⠀⠀⢁⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⣿⡿⠛⠣⠾⣿⠍
⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⠛⠙⠛⠿⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣷⣶⡄
⠀⠀⣿⣾⣿⣿⣿⡙⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⠇
⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠆⣠⣿⣦⡌⣽⠍⠿⣿⣿⣿⣧
⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣷⡾⠋⠀⣰⣿⣿⣿⡿⠁
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢗⣾⣿⣷⣾⣿⣿⣿⡟⣀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⢻⡶⠜⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⡰⣤⡀⠲⣬⡻⣦⡳⣌⢧⡘⣦⡀⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣶⢿⡷⢻⡿⣻⢗⡿⢛⣿⢛⡿⣻⡿⢺⣿⣶⡷⣽⣦⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠉⠀⠀⠈⣀⠈⠁⠈⣘⡯⡿⣿⠹⠁⠈⠁⠚⠋⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠀⠀⠀⠀⣾⢻⡄⣠⣴⠀⠘⠟⠁⠀⠈⠈⣀⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠓⠀⠀⠀⢸⣿⢸⡇⡿⢻⡇⢀⣴⡴⣶⡀⠈⢷⣇⡀⠀⠀⢯⣗⣀⠀⠀⣤⠀⣀⠀⠀⠽⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣾⠇⢸⡿⠃⢸⡇⢸⣏⣠⠟⠀⣰⠋⣽⠇⠀⣠⠞⢩⡿⢀⡴⣿⣰⣿⡀
⠀⠀⠀⠀⠠⣼⡶⠀⠀⠀⢀⡀⠀⠻⣤⣴⠃⠀⠀⠀⢠⢸⡇⠸⣿⣤⣤⡾⠁⠀⠻⠶⠚⠁⠀⠈⠛⠋⠀⠈⢸⡿⣠⣶
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠻⢥⣤⠤⠴⠖⠚⠛⠛⠲⡜⢸⡇⠀⠈⠉⠈⢠⣴⣠⠀⠠⠖⠒⠒⠲⠤⠤⠴⠃⣾⠿⠋⣘⠀⠀⠀⠀⠠⣾⡦
⠀⠀⠀⠀⠀⢠⣿⠟⣿⠆⠀⠀⣠⡞⢳⠀⠀⣠⣦⠀⠁⠈⠁⠀⣀⠀⠀⠙⡽⠍⠁⢀⠀⠀⠀⠗⠀⠀⣾⢻⡏⠀⢰⣿⡆
⠀⠀⠀⠀⠀⣾⡇⢀⡿⠀⠓⢠⡟⢀⡞⠀⠀⢈⣁⠀⠀⢀⠀⠸⣿⠆⠐⠃⠀⢀⣀⣾⠀⠀⣀⡄⠀⠀⠳⠞⠀⠀⠀⣀⣀⠀⠀⠈⣠⣄
⠀⠀⠀⠀⠀⣿⠀⢀⣄⠀⠀⢸⣷⣋⠀⠀⠀⣯⡿⢀⣤⠈⠀⢠⡄⠠⡞⣻⠀⣫⢼⡏⠉⠉⠉⡶⠚⣷⢚⡇⠀⢠⡞⢁⣿⠀⠀⢀⣧⡞
⠀⠀⠀⠀⠀⣿⡄⠘⠉⢀⡴⣿⠏⣿⠀⠀⣠⠞⠑⣿⠇⠀⣠⣿⢀⡴⣻⢷⡋⠁⠸⣇⣀⣀⣴⡇⠀⣿⢸⣇⣀⡼⠶⠟⠻⠴⠚⣉⡀⢳⡄
⠀⠀⠀⠀⠀⠘⠻⠶⠖⠋⠀⣿⠀⠻⠤⠞⠋⢀⡀⠻⠶⠊⠁⣉⣉⣀⣙⣚⣁⣀⣀⣈⣉⣁⣈⣁⠀⠁⠀⠉⣁⣤⠀⢤⣶⣠⠄⢧⣽⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⠤⠴⠖⠒⠦⢀⠛⢋⡀⠀⡀⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠻⡿⣿⣉⠛⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠰⠀⠀⠀⣀⣴⢯⣴⣿⣶⣿⣷⠾⢷⡶⣤⣤⣴⣶⠛⣁⣤⠴⢂⣠⡞⢁⡴⠂⣠⡶⢀⣤⠀⣁⠅⣀⢀⣄⡁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⡴⠖⠋⠁⠀⠀⠙⠀⠙⠉⠻⠻⡟⢶⣾⣆⣭⠙⠛⠙⢿⡓⠻⣷⡶⢿⡥⢾⣿⡴⣿⡇⠚⢿⡞⠛⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠛⢷⢶⣤⠉⠀⠈⠻⠆⠙⠂⠈⠙⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠓⠂⠀⠈⠓⠤⣀⠀⠠⠐⢰⠀⠰
⠀⠀⠀⢂⣬⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⠤⡑⣆⡣⢆⡊⠐⠄
⠀⠀⠀⠀⠅⠘⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⣠⡀⠀⠀⠢⠀⠀⠀⢀⠈⠳⢉⢏⠐⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠒⠛⠁⠀⣾⠇⠀⠀⠀⠀⠈⠖⢬⡐⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⠒⠒⢲⠂⠒⠀⡀⠀⠀⠀⠀⠀⡑⠂⠂⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠂⠀⠘⠁⠉⠀⠀⢠⠀⠀⠀⠀⠤⠀⠐⠀⢀⠠⠐⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠘⠀⠀⠀⠀⡁⣴⢦⡀⠀⠀⠀⠀⠀⠀⠠⢞⣿⡆⠀⠀⠀⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠈⠀⠀⢀⡀⠙⠻⢟⠀⢠⣗⣶⣀⣈⣈⣄⠸⠛
⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢴⡤⣦⣴⠾⠶⠶⢛⠀⠀⢤⠀⠀⠉⠛⠚⡿⠽⠫⠟⠀⠀⠿⣦⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠀⠀⠀⠈⠀⠠⣤⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⣀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡄⠀⠀⠀⠀⡧⠥⠗⠛⢃⠠⠀⠀⠀⠈⢷⣄⡀
⠀⠀⢠⠀⠀⠀⢀⢧⣸⢨⠀⠀⠃⡅⡇⡰⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⢠⡀⣀⣀⣠⡬⣆⠐⣄⠀⢰⠟⢿⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠈⡜⠁⠀⠻⡀⡿⡀⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣯⡭⡭⣷⠼⢋⠑⠈⡀
⠀⠀⠀⣀⢀⠀⡘⢀⠘⢛⢂⡂⢃⠓⣃⠑⠀⡃⠀⠀⠀⢀⡀⠀⢐⠀⠀⣠⡀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⠋⠈⢹⠀⡇⡆⢘⢸⢸⠈⠂⠹⠀⡿⣠⡇⠀⣾⠀⢨⠈⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡆⠀⠀⢸⠒⡇⡷⡊⢸⠀⢢⠀⡄⠀⡇⠁⠃⢸⡠⡇⠈⢢⠀⠀⠀⠀⠀⠛⠂
⠀⠱⣄⡼⠸⠀⠳⡇⠱⡸⠳⣀⠇⠇⠀⠇⠀⢾⡇⠀⢸⠳⣀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⣁⣠⠐⠂⠲⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀⠰⢦⠃⠸⢀⠉⢿⣇⡀⠀⠀⠀⣿⡿⠿⢷⣶⣤⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⡀⠀⡏⠅⠂⠘⠀⠂⢠⣹⠿⠷⢤⣤⣌⠠⢠⠄⢼⠁⠂⠄
⠀⠀⠀⠀⢣⠈⠂⠠⡀⢰⣧⠒⠁⡠⢷⠦⠘⠄⠂⠀⠀⠀⠀⠀⠁⠀⢿⣤⠀⢻
⠀⠀⠀⠀⠀⠑⢤⣆⢀⣿⣀⡀⠋⠠⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢻⣦⣠⣤⣀⠀⠂
⠀⠀⢀⠄⢈⣃⣤⡬⣿⣿⣿⣧⢿⣗⣨⢭⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡈⠹⢿⣷⣄
⠀⢀⠄⣉⠀⢤⡠⠒⢩⢻⣿⡗⠢⠄⠸⡉⠄⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡲⠩⠏⠁⠆
⠀⠈⠀⢀⣀⣾⠒⡺⢋⠀⢻⠂⠏⠻⠀⠀⠀⠀⠀⠀⠎⠊⠲⠶⠓⠖⢶⠄⠀⠀⢸⡟⡂⠄⠂⠘⠰⢅
⠀⠀⠄⠈⣑⣠⠰⠁⢠⢆⢸⠠⠠⠀⠈⠁⢰⠉⣺⣄⣄⣀⣴⢢⣄⣠⣩⠀⠀⠀⠈⠅⠠⠥⡁⣑⡀
⠀⠀⠀⠂⠈⠹⡇⢲⣾⡲⠿⠳⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⢀⠄⠀⠒⠤⠄⠠⠈⣧
⠀⠀⠀⠀⠀⢵⢂⠊⣉⡙⢓⣘⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠈⢢⠨⣽⣗⠑⢄⠰⡜
⠀⠀⠀⠀⠀⠈⢿⡗⠇⢪⣭⣽⢌⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣅⠐⠪⢬⠋⣓⠃⣉⠀⠚
⠀⠀⠀⠀⠀⠲⢦⣤⣼⣷⣾⣛⣾⣿⣿⣿⣿⣦⣤⣀⣀⣠⣤⣶⡄⠀⢿⡿⠀⣒⠐⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠁⠈⢀⠀⣈⣿⡿⡿⠛⣿⣿⠟⢙⠧⠠⡗⣠⡆⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣤⣴⣾⣇⡈⠿⢀⣲⠀⣹⠃⠀⣸⡶⠀⢠⣿⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⣴⣤⡄⠀⠉⢀⡿⠿⠋⠀⠠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣹⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡷⠁⡿⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢹⡴⠁⠀⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠀⠠⢷⠒⠒⠒⠶⢤⠀⠀⠀⡰⢻⣸⠁⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠉⣍⡷⠒⠚⢛⢢⠀⡠⠞⠓⠒⠒⢧⣸⠃
⠀⠀⠀⠀⠀⠀⢠⡶⠛⢋⠹⡄⠀⠀⠀⡇⠀⠀⠈⢸⣴⡇⠀⠀⠀⠐⢻⡟⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠘⢬⣓⠶⠤⣭⣙⣛⣩⣓⡒⠂⠤⠾⢋⣓⣒⣈⣚⡭⠭⠗⣚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠓⠒⠶⠦⠬⠭⠭⢭⠭⠭⠭⠭⠥⠶⠖⠒⠚⠉⠉⣇⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⠀⠪⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡇⠀⠀⠀⠱⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⣿⣹⠿⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢴⡶⢾⣿⣗⠚⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⣠⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢲⢏⣿⡈⠿⠂⠀⠀⠀⠀⠀⣀⢸⡏⠉⠉⠉⢀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠚⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢂⢀
⠀⠀⠘⢯⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠰⠇⡀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⢘⠘⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢠⠤⠤⠤⡀⠀⠴⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣁⠈
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠁⠀⠂⠈⠁⢠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⠀⠉⠉⠁⠀⠀⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠒⠀⠀⠀⡀⠀⠐⠆⠀⠀⠀⠀⡠⠔⠁⠂⠀⠀⠀⠀⠋⡘⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⠏⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠙⠋⠠⠀⠀⠀⠀⠒⡄⠀⣭⣭⣥⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠐⠀⠀⠈⠉⠁⠁
⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡆⢸⡨⠅⢸⣈⠀⢻⣉⠀⢱⠈⠀⠀⠀⠈⠀⠀⠀⢼⣿⡇
⠀⠀⠐⢋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠉⠈⡉⠉⠈⠁⠁⠈⠈⢁⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⢰⣶⡆⠀⠐⢟⢦⠖⠲
⠀⠀⠐⢁⣠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠐⠂⢸⢠⡁⠀⣇⠂⠀⠀⠀⠢⠃⠘⢧⠀⢸⠠⢠⡀⣰⠑⣂⠀⡐⠍⠀⠀⠀⢰⣾⣿⠇⠀⠀⠀⢹⡏
⠀⠀⠐⣋⠴⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠒⠀⠘⠀⠉⠀⠉⠙⠀⠉⠈⠑⠃⠀⠈⠁⠈⠁⠈⠁⢉⠁⠈⠁⠈⠉⠀⠀⠈⠑⠃⠐⠂⠀⠀⠀⢸⡇
⠀⠀⠘⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠤⠀⠀⢛⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠀⡂⠉⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⢲⢲⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠉⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠐⠄⠀⠀⠀⠠⠈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⡀⣠⢀⠀⠀⠀⡜⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠘⠀⡁⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠘⠁⠀⠀⠀⠀⠇⢀⠈⠆⠂⠐⠒⠀⠀⠀⠀⠈⠉⣂⠀⠀⠸⠇⠀⠀⠀⠘⠋⠀⠀⠀⠑⠀⠀⢀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣷⣶⣶⣦⣾⣷⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤
⠀⠀⠀⠀⣧⣾⣤⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⢼⣢⣆⡤⠄
⠀⠠⣤⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⢸⣿⣿⣿⣦⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣶⣦⣶⣶⣤⡄
⠀⠀⢠⡞⠛⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣄⠀⡀⢰⡄⠀⠀⠀⠀⠀⢸⣯⡛⠛⠻⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⢳⡀⠀⠀⠀⠈⠻⢿⣿⣿⠀⠀⠀⠀⠈⠻⢟⣺⣁⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⠀⠀⠀⠘⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢰⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⢹⡏⠉⠉⠹⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⣧⢾⣰⣦⠤⠂⠀⠀⠀⠀⠀⠈⢦⠸⡇⠀⠀⠀⢸⡗⠘⢷
⠀⠀⠀⠀⠀⠐⢶⣾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⠃⠀⠀⠘⠀⠀⠀⣿⡴⢉⡀
⠀⠀⢀⠀⢸⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣿⣿⡍⠉⠒⠒⠁
⠀⠀⡟⠙⡿⢿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠃
⠀⠸⡇⠀⠙⠆⠈⠉⠉⠉⢹⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣾⣿⣿⣿⡁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⡀⠀⠀⠀⠀⠒⢛⡭⠝⠛⠉⠉⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠀⠀⠀⠀⠁