Cherry Blossom Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠶⢾⣄⣼⣤⣴⡀⠀⢀
⠀⠀⠀⠀⠀⣨⡁⠛⠉⢁⣤⡀⠀⠀⠀⠐⠈⣄⠀⠀⠀⢠⣈⣷⣎⣉⠁⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⢶⠤⣤⡄⠻⠿⠗⡀⠀⠀⠈⠁⠀⠑⢄⠀⠘⠌⠀⢻⡍⠙⠒⠀⣠⣄⠀⠀⠀⡀⠀⠀⠀⣰⣄⠒⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⢠⠿⣷⠒⠒⠒⠤⣤⣤⣱⣄⣀⣀⣀⣀⣀⣽⣤⣈⣁⣴⣄⣀⢹⡄⢀⠀⠛⠁⠂⢢⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠰⠾⠐⠓⠚⢛⠶⠒⠛⠉⠁⠀⠉⠁⠀⠀⠇⠈⠋⠉⠉⢡⣉⣉⣻⣿⡯⠿⠶⠤⣜⡉⠁
⠀⠀⡀⠤⠤⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠈⠛⠢⣄⣀⠀⢻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠘⣷⣶⡄⠀⠀⠀⠘⠃⠀⠀⠱⠃⠀⠀⠀⢰⣦⣌⢋⣀⠀⢄⣠⡤⠖⠚⠛⠛⢛⣩⣈⣁⠙⠶⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⣀⠹⡀⠀⠀⠀⢡⣬⠈⠉⢉⠁⠉⢉⡷⠆⢰⡍⠉⠀⣩⠴⠋⠀⠀⣀⣤⡖⠒⠉⠁⠀⠉⠙⠲⣤⡀⠀⢘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠬⠜⠓⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠈⠁⠈⠁⠐⠂⠉⣠⣦⠴⠊⠁⡀⡌⠀⠀⠀⠀⠀⢀⣠⠾⠛⠛⠳⢤⣈⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣤⡀⠈⠉⠂⠀⠀⠀⣀⠒⠻⢁⣀⠀⠀⠀⠀⠈⠳⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠙⠯⠉⢰⣦⡄⠈⠀⠀⢴⣄⠊⠙⠀⠀⠀⠀⢀⣠⡾⢿⠀⠠⣿⢾⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⡈⢃⠀⢦⡿⠃⠖⠂⢸⡉⠙⠀⠀⠀⠠⠈⠀⠀⢠⣦⠤⣲⠟⠋⣰⡆⢻⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠂⠀⠈⠁⠀⠀⡉⣤⠀⠀⠀⠀⠀⠀⣀⠤⠖⢙⡿⠞⠁⠀⠀⠀⠀⠚⠸⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠊⠀⢀⠐⠈⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠠⠊⠀⠠⠄⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣈⣍⠁⠀⠀⠀⠀⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛


⠀⠄
⠀⡃
⠀⡁

⠀⠄
⠀⠆
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡧⠀⠈⢷⣖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣤⡴⣷⣠⣿⣿⠿⠀⠀⠀⢀⠀⠀⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣭⣵⣋⠙⠋⢼⣿⠶⣤⣞⣙⣿⣏⠛⠽⠟⠀⠀⠀⠀⣠⡀⠀⠀⢀⣆⣀⣰⣆
⠀⠀⠀⠀⠀⠘⣿⣩⣿⠈⣀⣠⣦⠈⠀⠰⡋⠈⡉⠁⠀⠀⠀⣀⡀⠰⣶⠋⣻⣶⣿⣏⣽⣹⣧⢾⠅
⠀⢀⣤⣄⠀⠀⠉⢹⡏⣠⣿⡷⠿⠶⠶⣞⢻⡶⠟⢀⡀⠀⣴⣽⠏⠉⠻⠋⢻⣏⣿⡮⠈⠁⠁
⢀⣼⢿⣿⣠⣶⣄⢸⣷⡿⠻⣷⡆⠀⠈⠛⠻⣧⣤⡼⢿⣦⠉⠉⠀⠀⢠⣄⠀⠋⠀⠀⣀⣐⡠
⠈⠻⣦⣿⣿⣼⣿⡿⣿⣷⡴⣿⡧⠂⠀⠀⠀⠈⣽⣧⣴⣿⠶⠶⠶⠶⠾⠽⣶⠆⠠⠏⠁⠀⠙
⠀⠀⠈⠛⠀⢠⠏⠀⣈⠉⠈⠉⠁⣀⠀⠀⠀⠀⠈⠁⠀⣁⠾⣤⠀⢀⣀⣰⢦⡀⢐⡿⣆⡀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠒⠶⠶⠟⠁⠀⠀⠄⠀⠀⠀⠽⠖⢿⣤⠺⣮⡷⠺⠇⠙⠎⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠙⠟⠋⠀⠐⠜⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣸⣟⣹⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠋⠙⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷

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

⠀⠀⠀⠀⠠⣤⠏⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠅
⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⣄⢤⡀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠐⣿⠘⠛⠀⠀⠀⠿⠟⠛⠃⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⡀⠢⡀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢀⠀⠀⠀⣀⣈⡙⢦⣱⣰⡇⠀⠀⠀⠀⠀⢲⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠊⠀⣄⠀⠙⡛⠛⠤⠀⠀⠉⠉⠉⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⣠⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⣀⣴⠀⠀⠀⠲⠋⠀⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⣶⡿⠂⢤⡠⠀⢠⡿⠋⢰⣦⡀⠀⡀⢠⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢿⣿⣆⠱⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠻⢦⡸⡆⢲⠼⠗⠀⠀⣀⣤⠀⠀⠙⠻⣷⣾⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠠⠽⣿⣄⠀⠀⠀⠀⠈⢉⡴⠀⠉⠉⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠚⠋⠉⠀⣴⡿⢂⠀⠀⠁⣠⣬⠀⠘⠛⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⣦⣦⡀⠨⠉⠄⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠈⠙⠻⣦⣇⠸⡄⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠈⢀⣀⠒⠒⣛⣛⠿⠿⠿⣤⣄⣀⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣀⠈⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⠤⠴⠒⠲⡄⢠⠖⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⢳⡀⠀⠀⢀⡐⣀⣀⠀⠀⢸⠀⠀⠀⢀⢘⣧⠀⠀⠀⠈⡇
⠀⢠⣐⣒⣒⠦⠤⣄⣀⠘⡄⠀⠀⠀⠀⣻⠿⣥⣶⠏⠁⠀⠀⠉⠢⢘⣄⣤⣤⣤⣿⡿⣿⣤⣤⠾⠥⡀
⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣾⡷⠶⠶⡿⢿⣿⣿⠷⣄⠀⠀⠀⠀⣾⠁⠀⠀⠨⠛⢿⣷⣿⣯⡁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⠀⢨⡇⠙⠀⠈⠑⡄⠀⠊⣼⠀⠀⠀⠀⣀⡾⠁⠙⠛⢧⡀⠀⢀⡇⠀⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢰⣄⣀⡈⠑⢲⠤⠚⢙⠀⠀⠀⠀⠀⡏⠑⣭⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊⠀⠢⠤⢀⣀⡠⠁⠀⠈⢫⣉⣟⣒⡒⠾⠦⣄⠀⢠⠾⠤⣼⣿⡒⠀⠈⠉⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⡦⣌⠁⠀⠘⢍⠁⠀⠀⠀⠈⠣⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⡇⠀⠀⠀⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠒⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡀
⠀⠀⠀⠀⠐⠉⠈⠁⠲⡀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠤⠄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠂⠀⠀⠀⠱⡄⠀⢀⣴⢁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠁⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣨⠂⠋⠀⠀⠐⠒⠤⢤⡀⠊⠀⠀⠀⠀⠀⡄⠀⢀⠤⠂⠀⠀⠀⣀⠀⣄⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠎⠀⠀⠀⠀⠈⠄⠀⠠⣠⠀⠀⠀⢀⢃⠀⠀⠀⠀⠀⠉⠑⠊⡗⢠⠆⡁⠀⣤⠘⠃⠀⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠰⠀⠀⠀⠠⢄⡐⠦⡀⠀⠁⠀⠂⠀⠀⠈⠀⠐⢄⠀⠀⢈⠅⠂⠙⣻⠾⠂⠀⠐⠂⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠁⣀⣹⡇⠀⠀⠘⠁⠀⠀⠀⠀⠸⠖⢒⠔⣠⠋⠈⠁⢊⡀⠀⡀⠀⠢⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢉⠀⢈⠁⠀⠢⢤⡀⠀⠀⠀⠠⠰⠋⠀⠀⠑⠂⠀⠸⣦⢫⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⣀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⡠⠒⡰⠃⠣⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠠⡀⠙⠓⠆
⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⡁⠈⠃⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠄⠀⠀⡾
⠀⠀⠀⠂⢐⣃⠀⠄⠰⠆⡄⠀⠑⠀⠀⠦⠄⢑⠀⠀⠀⢰⠄⠂⢰⣿⡆⠀⠀⠂⡀⠁⠃
⠀⠀⠐⠀⠻⠿⠃⡀⠀⠁⠀⠀⠀⠀⠀⠘⠂⠈⠀⠀⠀⡞⠣⠀⠐⠀⠤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠚⠀⡁⠰⠤⠤⡀⣀
⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⢀⣀⠈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢠⣤⡄⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡷⠀⢠⠀⠀⠀⣀⠘⠛⢁⡀⠀⠀⠀⠠⣴⣤⠀⠀⠀⠀⠀⠀⠸⣀⠔⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠰⠀⠀⠀⠈⠛⠃⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⡀⣰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠉

⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣭⣿⣧⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠐⢦⣠⠀⠀⠴⠊⠉⠀⠈⠓⢦⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⢄⠀⠀⠀⠀⠀⢀⠄⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠓⢤⡀⠀⠀⠀⠸⡝⠄⠀⠀⠈⠑⠄⠀⠀⠀⡀⠀⠀⠈⠂⠀⠀⣀⡀⢿⣿⣿⡄⠀⠀⠁⠀⠀⡠⠔⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠙⠢⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠉⠀⢀⣾⠙⢿⡇⠀⠀⣀⠤⠀⠈⠙⠻⠧⣤⣀⠔
⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠔⠒⠦⣀⠀⠐⡀⠀⠀⠀⠉⠓⢦⡀⠒⠊⠁⠀⠀⠀⠀⡰⢉⠵⠃⠀⠀⠁⠐⠉
⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠝⠢⠄⣀⢀⠀⠀⠹⠆⢀⣀⣀⣀⡤⠚⠉⢀⡤⠖⠋⠉⡆
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠟⠉⠀⠠⠀⢀⡄⢿⠃⠀⠀⣠⠖⠉⠀⠀⠀⠀⢻⣶⣄
⠀⠀⠀⠀⠀⠉⢦⣐⡆⠀⠀⢳⠀⠀⠀⠀⣿⣷⣦⣄⡀⠀⠀⣀⣀⣉⣹⡇⠈⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠐⠒⢒⠊⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠁⢀⠄⠈⠣⠀⠀⠀⢿⣿⡇⠉⠉⠛⠁⠀⠀⠀⠈⠻⡄⢠⡏⣼⣶⣦⠀⠈⠑⠠⣤⡄⠙⢿⣄⠀⠀⠀⠈⢆⣀
⠀⠀⠀⠀⠀⠒⢁⡤⠖⠋⠀⠀⠀⠀⠀⠘⠢⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠹⢿⣿⠿⠟⠛⠛⠁⠀⠀⠀⠉⠑⠀⠀⠹
⠀⠀⠀⠈⢦⡀⢮⡀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠉⠓⠙⠒⠂⠀⢀⡨⠕⠊⠉⠉⠁⠰⣆⠀⠀⠀⠀⠀⠀⣀⠀⠊⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠠⠋⠀⢠⠆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⡁⣀⣠⣾⠆⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⣿⣿⣿⣿⣋⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠤⠆⠀⣹⣿⣿⣿⣿⠏⠀⠀⢄⣀⣀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⠀⠀⣨⠟⠉⣤⠁⠈⠙⢻⣧⠉⠰⠄⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠊⠀⠐⠃⠲⢰⠆⢂⠐⠂⠀⠀⠀⠂⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠀⠀⠀⠀⠀⢸⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠲⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠄⠀⠀⠀⢀⡴⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⡇⠀⢀⡴⠋⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠀⠀⠀⡜⠀⡇⢀⣎⢎⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠈⣇⠀⠀⢇⣠⢇⣾⣷⠯⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⠀⡇⠀⠸⡄⠀⢸⣿⣾⣃⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢸⡀⠀⠀⠀⢹⠠⠀⡇⠀⡸⠃⢀⣀⠤⡔⢲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⠀⠀⠀⠈⣶⣦⠇⣰⡥⠚⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢇⠀⠀⠀⠸⣟⡴⢋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠑⢤⡀⠀⠀⠀⠀⢣⠀⠀⢸⠀⠀⠀⢠⣿⣟⠥⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠙⠢⣄⠀⠀⠀⢳⡸⣼⡇⠀⣰⠟⠁⠀⠀⣀⡠⠤⠤⠄⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠦⠀⠈⠳⡄⠀⠀⠙⣿⣇⡼⠃⣀⠴⠚⠉⠁⠀⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠦⣀⠘⢦⡀⠙⣄⠀⠀⢈⣿⣡⣞⠁⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠤⣀⠀⠈⠓⠦⣍⡳⣼⡄⠀⣼⣿⢋⣁⣀⣠⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠉⠲⢤⡀⠀⠉⠻⢿⣾⠛⠉⠉⠀⠀⣀⣀⣠⡤⠤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢄⠀⠀⢸⠃⠀⣀⡴⠒⠋⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠬⣷⣷⣄⣏⣴⣋⣥⠄⠒⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡰⡿⢃⣠⠞⠉
⠀⠀⠀⢀⡠⠤⠴⠶⠦⠬⢽⡃⢸⠃
⠀⠀⠔⠁⠀⠀⠀⠀⢠⣶⠗⣉⣛⣰⣾⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠤⢾⣿⣷⣤⡀⣼⣿⣿⣿⣟⣿⣟⡿⣿⣟⣤⡀⠀⠀⣦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢿⣶⡙⣧⣙⣿⣿⣿⣿⣿⣿⣿⣇⣛⣿⣿⡆⠀⣝⡴⠂⡈⠿⢷⢰⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⢿⣿⣾⣞⢆⣿⣯⣿⣋⢀⣠⣌⢳⣿⣿⣀⡸⠉⠉⠁⠉⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣾⣿⣪⡻⣿⣿⣿⡾⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⣥⠟⣡⣤⡀⠀⠀⠀⢴⣦⣿⡿⠿⢿⣶⡄⢷⠄⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣿⣾⡿⠇⠀⠈⠁⢰⣿⣿⣿⣿⣿⢛⣻⢟⣿⣿⣿⣿⣿⣷⡆⠻⡿⠀⠀⢀⣼⣿⣿⢿⣷⣶⣿⢆⠔⢋⣛⠃⠀⢜⢡⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣾⣿⢒⣲⣿⣿⣿⣿⣟⣾⣿⣿⡿⠿⣛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⣿⣿⢿⣿⣿⠋⠴⠚⠛⠒⠲⢤⡻⠃⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣫⣾⣿⡟⡮⣯⡉⠁⣿⣿⣿⢿⣿⣏⣿⡿⣿⣿⡄⠀⣀⠀⠠⢦⡄⠈⠉⣠⢡⣾⣶⣾⣶⣆⡀⠀⠀⠉⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡿⠛⣿⣿⣸⣿⠀⣴⣿⣿⣿⣿⣿⣿⣾⢩⣍⠀⠘⣋⣠⣤⣜⣃⠤⠊⢵⣷⣿⣻⣿⢃⢿⣟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⡁⠀⠀⠹⣿⣿⠏⠀⠉⢛⡟⣭⡤⡙⠛⣹⣮⣿⡇⢱⡶⠏⠉⠡⡀⣴⣶⠌⣽⣿⣿⣿⣴⣿⡛⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⣾⣷⠿⠁⡇⠀⠈⢛⡟⢱⡿⢋⡟⠂⠀⣷⣬⠁⠀⠉⠉⢻⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⣀⡠⢖⢀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠸⣯⠁⣼⣟⣛⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⡄⠀⢠⣦⡀⠀⣠⠖⡋⢸⠇⠀⠀⠈⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣞⣹⠇⠀⢨⣟⡇⢀⡷⠭⠴⠋⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢸⠉⠁⠀⠀⠀⢻⣀⡟⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡾⠛⠶⠞⠛⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠸⣿⢸⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣤⣀⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⠈⠓⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡙⣆⠀⠀⢻⡏⠀⢠⠖⠖⢒⠒⣺⠏⡴⢲⠞⠉⠀⠈⠻⣦⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣻⡏⠀⠀⠈⡇⢀⣿⣾⣛⣋⣤⠟⠀⣿⡼⠁⠀⠀⠀⠀⢸⣇⣼⡏⠀⠀⠀⠀⢀⣾⣿⣃⡀
⠀⠀⠀⠀⠀⠀⣴⣶⠖⠛⠲⢆⢸⠀⠀⠀⣰⠖⠋⠀⠀⢉⣉⠀⠀⠘⠋⡴⠟⠀⡀⠀⠀⠘⣿⣿⠀⠀⠀⢀⣴⣿⠋⠀⠀⠈⡟⣷⡀
⠀⠀⠀⠀⠀⢸⠋⠥⠃⠀⠀⠀⠻⣄⠀⢰⡇⠀⠀⢀⡾⢿⡒⠽⣆⠀⣴⠥⢮⣉⡝⠀⠀⠀⢸⢿⠀⢀⣴⡿⠟⣥⠀⠀⠀⠀⠳⣈⣙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⠀⠀⠀⠀⠀⠀⢹⡎⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣿⠰⢊⡵⠋⢀⡴⢻⡆⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⣾⠏⣿⠀⠀⠀⠀⣰⢇⡼⠋⢠⠀⣿⢁⣼⣥⣴⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠃⢀⣿⣋⡴⠃⠀⢀⣠⢔⣥⡾⣥⣾⣿⠀⣷⠞⢉⣩⡥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧⠎⠉⣿⡄⠀⡴⢫⡶⠛⠉⢹⡏⡿⢸⣿⣯⣤⣟⡛
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣦⣛⣎⣀⠀⢻⣆⣀⣠⡤⣄⠀⠀⢸⠀⠀⠘⢿⡊⢠⡏⠀⠀⠀⠘⢧⣧⢾⠀⠀⣠⣼⣯⠽⠟⠛⣛⣡⣲⠂
⠀⠀⠀⠀⠀⠀⠀⣿⠖⠲⠤⠊⠁⠉⠙⢿⣿⣦⣉⠙⠛⣷⠀⢸⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣹⣎⠴⠚⠙⠦⣤⣤⣤⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣌⠛⠉⠉⠱⣼⣆⠀⠀⢸⡇⠈⣇⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠘⢿⣧⠀⠀⣿⠀⠘⣄⢴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠘⡏⢧⡀⠸⡆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣭⣛⠀⠉⠙⠓⢤⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠹⡇⠀⢀⡄⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠘⣃⣼⣭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⢀⣟⣀⡤⠤⢤⣀⢛⣋⣛⣳⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣸⡶⣫⠟⠁⠀⠀⠀⠉⠱⢌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣿⡼⠁⠀⠀⠀⠀⠀⠈⠒⠈⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢀⣤
⢸⢛⠀⠀⠀⠲⣀⠀⢀⠀⠀⠀⠀⠀⣐⠀⠀⢰⠆⠤⢦⣤⣤⣄⣀⣀
⢸⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⣀⡆⠸⠃⠀⢀⠙⠚⡻⢯⡙⠲⠨⣧⠈⣠⡂⠀⠀⠀⠀⠀⢠⡆
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⣿⡇⠸⠇⠀⠀⡤⢤⠁⢸⡟⠙⠙⠿⣷⠊⠁⠀⠀⠀⠀⠀⣼⡁⢀⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠁⡹⡇⢰⠀⠀⢀⠀⠀⠀⢿⢿⠀⠒⢰⡘⢷⠀⠀⠀⠀⣶⣷⡿⠀⣩⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣠⣠⣤⣿⡇⢸⡇⠀⠷⠄⠀⠀⣾⣿⠷⡄⠠⣉⣻⣆⣤⡰⣆⣿⣿⠁⠀⣿⣇
⢸⣿⣦⣄⠀⠀⠀⠀⢨⡄⠀⠀⠈⠙⢛⣾⡇⢸⡁⠀⢐⣶⡄⠀⢹⣿⠠⠆⠀⠉⢹⣿⣿⠷⣿⡿⡟⡇⠀⢼⣤
⢸⣿⡿⣿⠨⠀⠄⠀⣼⢇⠀⠀⠀⠀⢠⢿⡧⢸⠆⢠⠤⠹⠇⠀⣾⣿⠃⣤⡀⠀⢸⣯⣟⡿⣛⠀⠷⠁⣴⣿⣿
⢸⣿⠀⢈⡁⠀⠀⢠⣃⡘⡀⡀⠀⠀⠀⠈⣇⢸⣷⣟⣾⣶⢀⠀⢿⣿⣶⣿⣿⣿⣿⣏⣿⡇⠉⠀⢐⣻⣿⣽⣿
⢸⣿⣴⣬⣿⡀⠀⠾⠟⠽⢷⡇⠀⠀⠀⠀⣿⢸⡿⣿⣿⡁⠀⣲⢾⣯⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⡽⣿⣿⣿⣿
⢸⣿⣿⣿⡃⢀⣦⣀⣀⣀⣼⡇⡄⣤⣴⡴⡿⢸⡇⠐⣇⣟⠀⠉⣿⡏⠙⠛⠋⠛⢹⡟⠙⣸⠟⠛⠿⡿⣿⣿⣿
⢸⣿⡿⣛⣿⣿⣇⠀⠄⠀⢻⡇⠰⣮⠔⣯⡇⢸⡇⢀⣿⣿⠦⠀⢿⠓⠂⠀⠀⠀⢸⡆⠀⢸⠄⠀⠀⠀⠼⢿⣿
⢸⣿⣿⣥⣾⣿⠛⠀⠀⠈⢻⣿⠷⣴⣾⣿⡿⢸⣿⣗⣯⣉⣁⡤⠯⠥⠤⠤⠤⠄⠘⠗⠒⠒⠒⠛⠓⠀⠈⠉⠁
⠘⠿⠿⠿⠿⠛⠂⠒⠒⠒⠛⠛⠋⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⢀⣤⣶⣆⣤⠶⠂⠀⠐⠂⡒⠀⢀⣠⠤⠆⠤⠤
⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⣪⡷⢾⢿⣥⣿⣦⠹⣿⣦⢀⠀⠃⠀⠰⢿⡀⡀⠄⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣤⣤⣤⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣻⠿⣻⣧⣶⣿⣿⣿⣿⣷⠒⠀⠌⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠉⢹⣋⣙
⠀⠀⠀⠀⢸⣿⣿⣟⣣⡿⢿⣿⡏⠉⠐⠘⡟⠛⠟⠁⠉⠻⠷⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣻⢟⡿⣶⡆⣀⣉⡉⠉⠋⠠⠀⠀⠊⠒⡖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣯⣼⣦⣽⣿⣿⣢⠌⠀⢀⣄⠀⠀⢘⡁⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢸⣿⣿⠀⢝⣯⣶⣬⣿⡿⣿⣶⣶⣿⣿⣿⣷⣌⣟⠻⢿⡀⠀⢠⣄⣄⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢀⡅⠀⠻⠤⠨
⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⣄⡸⠿⣿⠟⢻⡌⠛⠁⡈⢘⢿⠏⣄⠀⠈⠉⠩⠭⠉⠁⠀⠀⠀⠀⠀⠀⢀⡷⣆⢈⡉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣻⣟⣽⣷⡤⠀⣎⣁⡀⣀⣄⠀⠀⠈⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣛⡘⡇
⠀⠀⠀⠀⢸⣿⣿⡛⣿⣿⣿⣿⣿⣼⠉⡡⣇⡤⢁⠀⠛⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢰⣠⣿⣿⣿⡆⢘⠿⠟⠾⢿⣧⣶⣶⣰⣖
⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⠟⢷⠓⡶⠏⠀⠃⢠⠄⠀⠀⠂⢀⣶⣦⣽⣷⣶⣶⣤⣤⣽⣿⣉⣀⠀⠁⣿⣀⠀⢴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠻⣿⡿⠿⠽⢶⣄⠈⠤⠀⣀⣶⣤⣯⣿⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣬⣿⣾⣼⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣠⣿⣿⣴⡖⠀⣠⠁⢀⣠⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡛⣿⣿⡛⠛⠛⢻⡟⠛⢛⣛⣛
⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣯⣄⣷⣷⣶⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⡿⢿⣟⣿⠟⠛⠻⣿⢿⣽⡿⠛⠛⠛⠛⠛⠛⢹⡟⢉⣉⣉⢉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣉⣉⣙⣛⡛⣋⣀⣀⣀⣉⡉⢁⣀⢀⡇⠀⠉⠁⠀⠀⠀⣾⠠⣿⢣⡀⠀⠀⠐⠂⠀⢸⡧⠽⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠿⠋⠉⣻⡟⢻⢿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣠⡶⣦⣤⣤⣼⣧⣤⣤⣤⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣡⣴⡶⠟⠋⣉⣵⡦⠻⠿⠿⠛⠛⠉⠙⠻⢻⣿⣿⡿⣟⡛⢻⠛⣻⣿⣾⡛⣟⠛⠛⣿⣿⣿⣷⣿⣿⣭⣿
⢀⣀⣀⣀⣸⣿⣿⠿⢿⣿⣯⣥⣤⣴⣾⣿⣿⣿⣿⣯⣆⣀⣀⣠⣤⣴⣿⣿⣋⡙⠫⣝⣳⣿⡻⢿⠿⠁⢧⠈⠹⠿⠿⠏⠛⠛⡻⠿⠟
⠀⠉⠻⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠏⠒⠉⠓⠀⠁⠉⠉⠫⠖⡿⠿⠾⠟⠋⠈⠀⠐⠋⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠈⠻⢿⣿⠋⠉⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠷⣄⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠈⠁⠢⡀
⠀⡠⠂⠁⠀⠀⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠈⡐⠠⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠐⡀⠀⠉⠐⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⣶⣶⣶⣶⣶⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⢤⣄⠠⢤⣀⣀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠈⠁⠀⠀⠀⠀⠀⠀⣀⠤⠝⠒⠛⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⢉⣉⠀⠒⠒⠒⠀⠀⠒⠚⠤⡀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⢀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡠⠊⠁⠀⠉⠒⠂⠠⠤⠤⠤⢄⡀⠘⣦⢀⣀⡤⠊⠁⠀⠀⠀⠀⠀⢀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢉⡏⠉⠀⡠⠚⠉⠒⠠⠤⠤⠤⠤⢀⡀⠈⢢⡝⢢⡀⠈⠑⠢⡀⠀⠀⠀⢀⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⠎⢹⠊⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⡄⢀⡇⠀⠳⠤⢄⡀⠈⢦⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡤⠒⠚⠀⢠⢧⠀⢀⠀⢰⠀⢸⠀⢀⠃⠀⠀⠀⣀⡜⠉⠂⠤⣀⠀⠙⢄⠈⣖⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⣠⠤⠔⠉⢄⠣⡈⢢⠈⠀⠈⠀⠘⠀⡴⠁⣠⠏⠀⡀⠀⠀⠈⠢⣄⠀⡹⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣰⠀⠀⡇⠀⢀⡀⠢⡑⠌⢲⠣⣰⠿⠚⠓⠶⢤⠞⢁⡠⠊⠀⠀⠀⠀⢀⢆⡜⠇⢸
⠀⠀⠀⠀⠀⠀⢀⠤⣄⠚⠓⠂⢷⠤⢄⣈⡒⠌⠐⠟⡞⢰⡿⠖⣶⡆⠼⣇⣡⠔⠀⠀⠀⠀⣠⠞⢏⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⢱⠀⢸⠀⠀⠐⠨⢭⣚⡷⢧⡰⢧⣴⡾⢁⡷⢟⠲⠾⠿⠶⠒⠉⠀⠀⢸⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠇⠀⡼⠀⠀⠀⠈⠭⢐⠁⢼⡑⠢⡠⣶⠋⠁⡈⠷⡶⣌⠍⠉⠉⢀⠔⠋⠀⡸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣇⠀⠀⠀⠤⠒⠥⢊⠎⡆⢀⢡⠈⡀⢱⠈⢆⠈⢢⣍⣁⠶⠇⠀⡰⠊⠀⣠⠃
⠀⠀⠀⠀⠀⠀⢀⡼⠣⡈⠢⡀⠈⠑⣄⠀⠀⢀⡴⠃⠰⠁⢸⠘⠂⠇⠀⡆⠈⠀⠀⠹⡁⢀⡤⠔⢁⡴⠊⠁
⠀⠀⠀⠀⠀⠰⢣⠀⠀⠘⠢⣈⠢⡀⠈⣑⡶⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣊⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⡠⠋⠉⠉⠀⡇⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡜⠁⠀⠀⠀⠀⠱⣒⡊⠁⠀⠙⠒⠀⠒⠒⠲⠒⠉⠉⢁⣀⠴⠃
⠀⠀⠀⠀⠀⠠⣥⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⡎⠀⠀⠀⠀⠀⠀⠀⣠⠓⠊
⠀⠀⠀⠀⠀⠀⠳⠸⠀⠀⢀⠀⡤⣄⠞⠊⠁
⠀⠀⠀⠀⠀⠀⢶⡇⢀⠶⠊⠋
⠀⠀⠀⠀⠀⠀⠘⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠝⠊⠁⠹⠊⠀⠒⠂⠀⠀⠀⢀⡟⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠲⠔⠦⠶⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠗⠀⠀⠊⠙⠉⠁⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠀⠀⠀⠴⢊⡤⠄⠤⠴⠀⠀⠀⢀⣀⣀⡀⡰⡀⠈
⠈⠁⠀⠀⠈⠉⠋⠉⠀⠀⢀⠰⠒⠉⠉⠒⠒⠤⣀⡀⣀⡀⡀⠀⠴⠿⣷⡄⢀⣠⣴⡶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠉⠉⠀⠙⣅⡀⣠⠖⢗⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠁⢀⠛⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠚⢄⢠⠔⠤⠀⠊
⠀⠀⠀⠀⠀⣀⡴⢧⡶⠒⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠑⠀⠀⠀⠁
⠀⠀⠴⠂⠉⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠤⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠢⢄
⠀⠀⠀⡰⠁⠀⡀⠀⠀⢀⠀⠙⡆⠀⠀⠀⠀⠀⠀⣴⣥⣤⣤⣤⣤⣤⣤⡵⡄⠀⠀⠀⠀⠀⠀⡞⠁⢀⠀⠀⠀⡀⠀⠱⡀
⠀⠀⠀⡇⠀⠈⠁⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢰⠁⠛⠿⠟⠁⠛⠿⠟⠃⣷⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⢇⠀⠀⣄⣀⣀⡠⠀⠀⡜⠀⠀⠀⠀⠀⠈⣆⠀⠠⣀⣀⣀⡠⠀⢀⡏⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⣤⣤⠀⠀⢀⠇
⠀⠀⠀⠈⠣⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠑⢄
⠀⠀⠀⡎⠀⠀⠆⠀⠀⠰⠀⠀⢣⠀⠀⠀⠀⠀⢀⠇⠠⠖⠦⠀⠠⠖⠦⠀⢇⠀⠀⠀⠀⠀⢰⠃⠀⢠⠀⠀⠀⡤⠀⠈⡆
⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠸⡀⢀⣀⣀⣀⣀⣀⡀⠀⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠱⡄⠑⢤⣀⣀⠴⠃⣠⠃⠀⠀⠀⠀⠀⠀⠳⡀⠳⢤⣀⣠⠴⠃⡰⠃⠀⠀⠀⠀⠀⠀⢣⡀⠐⠉⠉⠉⠃⠀⡴⠁
⠀⠀⠀⠀⠈⠓⠦⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠖⠋


⠀⠀⠀⠀⢀⠴⠒⠚⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠚⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⢄
⠀⠀⠀⡰⠁⡠⠀⠀⠀⠠⣄⠘⣆⠀⠀⠀⠀⠀⠀⡜⠁⣠⡀⠀⠀⣠⡀⠙⡄⠀⠀⠀⠀⠀⢀⡞⢀⡤⠀⠀⠀⠤⡀⠱⡀
⠀⠀⠀⡇⠀⠈⠃⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⢰⠁⠈⠁⠉⠀⠀⠁⠉⠀⢱⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⢇⠀⠀⡤⠴⠦⢄⠀⠀⡜⠀⠀⠀⠀⠀⠈⣆⠀⠠⣄⣀⣀⡤⠀⢀⡎⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⠤⢤⠀⠀⢀⠇
⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠃⠀⢠⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠐⡀⠀⠀⠀⢠⠘⠀⠀⢸⠀⠀⢸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢤⣇⠀⠹⡄⠀⠀⡏⢘⢂⠀⠸⡀⢣⣼⠀⠐⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⢹⡀⠀⡇⠀⠀⡂⠀⠑⣼⣃⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢪⣇⠄⢸⡇⠀⠑⣄⠀⡅⢀⢜⡁⠤⠐⠒⠒⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠐⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠄⡟⠀⡸⠀⠀⠀⣸⣮⡞⢁⠋⠀⣀⣀⣀⣤⠔⠂⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠤⠤⠤⢬⣳⣄⢸⡧⣶⣵⣾⣿⡟⠛⠻⣍⠙⠍⣋⠁⠀⢀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⡇⠀⠀⢠⠎⠀⠀⠀⠀⣀⣬⣷⡧⠶⡯⣍⠉⠉⠀⠉⠛⢿⢽⣑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡀⠀⣿⠀⠀⡇⠀⣀⣿⣀⣰⢥⣿⡾⠿⠯⠿⣇⠀⢣⣨⠧⠤⣄⡀⢆⠀⠁⠨⠻⣤⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⢠⡟⣠⠞⠋⠉⠀⠉⠻⣯⡝⠁⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠉⢾⢢⡀⠀⠀⠈⠓⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⡟⠁⠀⠀⠀⣀⣤⡀⠈⢷⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⡇⠈⠒⠤⢄⣀⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣇⠀⠀⠀⢸⠁⢂⡇⠀⢸⠠⣤⣤⡀⠀⢹⡀⡀⠀⢀⡴⠢⡄⣰⠇⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡣⠁⠹⣆⠀⠀⠀⠛⠉⠀⣰⠏⠓⠯⠭⠤⠶⠋⠑⢬⣦⣜⣧⣿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡕⣀⣤⣔⢚⠛⢶⡦⠴⢖⠊⠙⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡜⠋⠁⠀⠀⠉⠙⠦⣤⣕⠲⡤⣀⣀⣀⣭⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠀⠁⠈⠉⠀⠀⠀⠀⠀⠂
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡟⠀⢄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢞⠟⠁⠀⠐⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠
⢠⠀⠁⠀⠀⡀⠀⠀⠀⣤⡒⠂⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⢁⡄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠈⢂⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣴⣤⣄⣴⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⠀⠁⠁⠀⠀⠀⢀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣷⣶
⠓⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠄⠂⠀⠀⢹⡿⠃⠙⠉
⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠘⡁⠀⠂⠀⡐⢤⣄⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠈⠉⣺⣿⣿⣠⣿⣶⣾⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⠛⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⣰⠁⠀⠶
⠀⠁⢰⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠤⠀⣲⠞⠛⠻⣇⠐⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⢠⠋⠁⠊⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠶⢦⣤⡄
⠀⠁⠀⠀⡀⠀⠀⠀⠠⠤⣀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠉⢘⡄⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠆⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹⣄⣸⣦⣶⣾⠋
⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠋⠀⠀⣠⣖⠀⠀⠀⠀⠀⠀⢈⣿⣿⡛⠉
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⢄⡀⠀⠸⣿⣷⣤⡆⢠⣾⡿⠋⠄⠀⠀⠀⠐⠀⠈⠁⠀⠙⠦⣀⡒
⠁⠀⠀⠀⠀⠀⠀⢠⠀⠠⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⣙⠇⠀⡸⣿⠗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠔⠒⠊⠩⠛⠛⠛⡿⡿⢉⣤⢚⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠠⢄⣀⢀
⠀⠀⠀⠀⠀⠀⢠⡖⠦⡀⠀⠀⠀⠀⠀⢰⠏⢀⣴⢱⡿⢛⡎⣑⢒⣳⣶⣾⣦⣴⢯⡠⡄
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⢶⡀⠀⠀⠀⠰⢬⢣⡄⠈⠹⢮⠑⣮⣿⣿⣿⣿⣿⣿⣦⡷⣿⠄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣾⣇⠀⠀⠀⢠⣡⢻⠙⢉⢳⣼⣀⠸⠉⠉⣿⣿⡟⠉⠻⢧⢿⣆⡴⣠⡄
⠀⠀⠀⠀⠀⠀⠠⣳⣶⣛⣿⠃⠀⠀⣀⡏⠙⠳⣄⣹⡆⠧⠬⣉⠙⠲⠣⢽⣿⣵⣶⡛⠛⣿⠃⣸⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠶⡄⠠⠀⠃⠈⣟⠻⠉⠛⣧⣰⠂⠈⠓⠀⠀⠀⠛⡻⠭⣤⣤⣿⣝⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣓⡛⣆⠉⢽⣿⣿⣧⣼⣏⣛⡉⡉⠈⠙⡷⣾⣻⣯⣽⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡀⢱⠀⠋⢿⡡⢩⡗⠂⠤⠄⠤⠋⢹⣿⣏⠛⢙⣿⣿⣿⢯⣠⠾⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⣦⣶⡵⣿⡾⡫⠊⠐⠀⡤⠰⠒⠺⠛⠪⡟⡛⢿⣮⣍⣙⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⢌⣻⣵⣿⡭⠴⠂⢀⣶⠆⠀⠀⡆⠀⠀⢠⠤⠶⠯⢁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣷⡖⣦⣈⣿⠁⢀⠆⢰⣿⡔⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣆⡝⠀⠘⢁⣠⣴⡎⣩⠂⠀⠀⢢⠀⡀⠀⠀⢠⡞⣹⣋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢁⣀⣀⢹⣄⡇⣾⠿⠿⠛⢻⣀⣠⠘⣦⡰⠀⡠⣰⣿⣟⣫⠏⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠚⠻⠿⣗⠷⢦⣧⣀⢀⠀⠀⠘⢧⡅⠀⠀⠀⣿⣏⣇⠀⣼⡇⢰⠟⠋⢰⡍⢀⣰⣢⣤⣴⣾⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢶⣿⢷⣌⣄⠀⠀⠣⡀⠀⠀⡆⢿⡟⠀⣹⠠⠞⣶⣯⣾⣾⣫⠭⠥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡭⠷⠿⢿⣾⣴⣤⣈⡐⢤⡇⠘⡇⠔⠁⣠⣞⠋⣙⣻⣉⣴⣟⢂⣄⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⡤⠟⠊⠉⠉⠉⠉⠙⠻⢷⣛⣿⣛⠻⠛⠷⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⠉⢐⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⣴⠋⢀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣸⠃⠀⠉⢿⠞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡷⠺⠏⠀⠀⠀⢀⠟⠀⠀⢀⢠⣧⠻⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡷⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣾⣿⠀⠀⠘⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣤⣶⠀⣼⡀⠀⡀⠸⠿⣟⠀⠀⠀⠘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⣠⡶⣿⡿⠋⠀⠙⠁⠀⠈⠶⣄⠿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠟⠀⠀⠀⠀⠀⠀⡀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡆⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠀⠆⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣤⣶⣵⠊⢿⣶⣄⣄⠀⣀⠀⢀⣠⣤⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⠘⢷⡌⠉⠛⠛⠈⢿⡿⣿⡿⠙⠃⣩⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡜⠀⠀⠀⠙⣦⡀⠀⠀⣀⣽⠟⢛⣤⣈⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣀⠀⢀⡉⠉⢉⠹⠠⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢻⡇⢼⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣿⠇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣿⣿⠃⠀⣠⡴⠁⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠟⠀⠚⠻⠃⢰⡟⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠐⣾⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠙⠛⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠈⣡⠆⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡶⠶⠿⠿⠿⣿⢿⣿⣯⡴⠞⠁⣤⠀⠈⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠔⣸⣿⠀⠄⢠⠇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⣼⠟⠁⠀⠐⠛⢋⣁⣤⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣠⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺


⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆⠀⠀⠀⠀⠀⢀⠀⡈⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠛⡀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠤⣤⡁⠠⠊⠀⠀⠀⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦⣀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠓⠀⢢⢀⢐⠠⠀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠐⠂⢠⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡤⠈⢕⣣⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠈⠲⣄⠀⢀⡠⠀⠐⠀⢀⡀⠀⣠⣤⠵⣧⡔⠋⠉⢉⡓⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠈⠊⠁⢹⣿⣶⡗⠠⡀⠀⠀⠀⠐⠏⡀⢲⠀⠀⠁⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢩⡀⢀⣾⣿⠿⠁⠀⠈⠒⣄⠀⠠⠔⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠃⠀⠀⠀⠀⠘⡧⠈⠈⠀⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠛⠙⠀⣤⣞⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠐⠀⠀⠀⠒⠉⣀⣀⣠⠞⠁⡉⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣮⠇⢀⠈⢠⠀⢠⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠆⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠈⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⢆⠀⠀⠀⢦⠀⠠⠀⠀⠀⠀⣄⠀⠈⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢃⠐⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠉⢷⡛⣷⣦⠀⠀⠀⠀⠊⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠰⠀⠋⠀⠀⠀⡰⠻⢿⣿⠛⠉⠉⢀⠀⢀⡠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⡘⢠⠚⠂⠠⠀⣰⡾⠇⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⢀⠹⠆⠘⠁⠘⢆⠀⠀⢠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠣⡀⠀⠠⠀⠀⡌⠄⠀⠀⡷⠀⢀⣑⣶⠻⣦⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠤⢄⠀⢙⣄⣶⣠⠈⠀⠀⡠⠎⠀⠀⠈⠉⠙⣿⡅⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠀⠄⠄⠀⠙⣿⡋⠅⣽⡧⠒⠉⠐⠂⠠⢶⠀⠀⠐⠈⠇⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠘⠂⠀⠳⢐⣻⠤⠤⠀⠐⢿⣿⣾⠟⢿⡀⠂⠀⠀⠀⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⠈⠁⡌⢽⡀⢀⡠⠀⠀⡟⠈⢀⠀⠙⢄⠐⠂⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢠⠴⠾⡃⡠⠂⡆⠀⠸⠀⠦⠀⠈⢃⡀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠂⠀⠉⢀⡞⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠏⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⣄⠀⠀⠀⢀⡤⠤⠀⠢⢄⡀⠀⠀⠀⠹⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⡿⡄⠀⠈⠛⠦⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⢸⣿⣿⣆⠀⠈⠢⠀⠀⠀⢀⢴⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢦⡀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⢀⡿⢿⣿⠀⠀⠨⠀⠐⠊⠵⢶⣎⣀⠀⡠
⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠉⠑⠒⠦⣄⠀⠄⠔⠊⠉⠀⠀⠀⡰⢐⡿⠃⠀⠙⠀⠔⠊⠁⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢧⠀⠘⢦⡀⠀⠀⠀⠈⢳⣄⡀⠀⠀⢀⣠⠜⠁⠉⣠⠴⠒⢢
⠀⠀⠀⢸⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠽⠖⠀⢸⣿⠟⡋⣿⠏⠉⠀⢀⠔⠋⠀⠀⠀⠸⣦⣄
⠀⠀⠀⠀⠓⣄⠀⡆⠀⠀⡆⠀⠀⠀⢸⣷⣤⣀⠀⠀⠀⢀⣀⣑⢹⡇⠘⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠒⠂⢀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠘⢄⠀⠀⠸⣿⣿⠉⠛⠳⠊⠁⠀⠈⠉⠻⡄⢠⡟⣴⣶⡄⠉⠑⠢⢄⣠⠘⢿⣧⠀⠀⠀⠈⠧⢀⠄
⠀⠀⠀⠀⠒⢀⡠⠖⠃⠀⠀⠀⠀⠀⠲⢄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠻⣿⣿⡿⠛⠶⠋⠁⠀⠀⠉⠑⠀⠀⠸⠀⠁
⠀⠀⠀⢧⡀⢎⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠤⠤⠤⣄
⠀⠀⠀⠀⠉⠛⠛⠒⠀⠀⢀⡬⠖⠋⠉⠉⠀⢧⠀⠀⠀⠀⠀⠀⣀⠐⠊⠁⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⡀⠀⠠⠋⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠁⠀⢠⣾⢆⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣦⣶⣷⣷⣯⠍⠀⠤⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⣀⠛⢀⣨⢿⣿⡿⡏⠀⠀⠀⠢⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⢠⠟⠁⠴⠆⡀⠀⠐⠷⠀⢘⠂⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡎⠀⠀⠁⠘⢰⠃⠡⠈⠁⠀⠀⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠳⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣽⡝⡆⠀⠀⠀⢀⠠⠄⢤⡀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀
⠀⠀⠀⣠⠰⣈⣏⡖⢂⡀⠀⠛⠿⠿⠁⠀⠀⠠⠍⠀⠀⠀⢘⡆⠀⠀⠀⠀⣏⠀⠀⠀⣿
⠀⠀⢐⠮⡿⠉⠈⠹⡧⠣⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⠲⠤⠖⠃
⠀⠀⠐⣊⠻⣤⣠⣼⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠈⠑⠣⠧⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⣾⠛⠙⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠈⣿⣄⣀⣼⠟
⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣾⡟⠉⠙⣿⡄⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⢿⣷⣤⣴⣿⠃⠀⠀⠀⣴⢯⣽⣾⣭⢷⡄⠀⠀⣤⣿⠟⠛⢿⣧⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢿⡸⣿⣿⡿⣹⠇⠀⠀⢾⣿⣄⣀⣸⣿⡆⠀⠀⠀⢀⣤⢶⣤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠾⠞⠋⠀⠀⠀⠀⠻⠻⡿⠛⠃⠀⠀⠀⠀⠸⣧⣀⣿⠃
⠀⠀⠀⡶⠏⠋⠹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠘⣇⠀⠀⢀⣿⠀⠀⠀⣠⡶⢦⡀⠀⠀⠀⠀⣠⣶⣶⣶⣄
⠀⠀⠀⠉⠳⠗⠚⠀⠀⠀⠀⠿⣤⣼⠇⠀⠀⠀⢠⣿⡟⠁⢹⣿⡇⠀⠀⠀⠀⢀⡴⣶⣶⢦⡄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⡿⠃⠀⠀⠀⠀⣿⣽⠉⠉⢳⢹⡄
⠀⠀⠀⠀⣿⣿⠆⠀⢀⣠⣠⣄⡀⠀⠀⠀⣤⣦⣤⡀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠻⣝⡶⢶⣫⡾
⠀⠀⠀⠀⠀⠁⠀⠀⣾⡏⠉⢹⣖⠀⠀⠘⣿⣿⣿⠇⠀⠀⢠⡿⠿⣶⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⢶⡾⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⢷⣶⠟

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠐⠂⠄⡀⠀⠀⠐⠂⠄
⡿⠓⢠⡀⠀⠰⢀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡊
⢩⠀⠀⢷⣄⡀⠈⠁⣠⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀
⠀⢈⣠⠌⠙⠛⠻⠦⠄⡀⠚⠀⠀⠀⣤⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠉⠁
⠆⠠⠀⠀⠀⠀⠁⠀⣀⣅⠀⠈⠃⠀⠀⡤⠀⠙⠲⠄⠀⢀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠁⢰⡆⠀⠀⠰⠏⢻⠿⠄⠀⠺⣄⠀⠀⠀⡀⠘⠃⠛⠶⠆⠀⠰⠎⠛⠂⠘⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢃⠀⠛⢀⣨⠡⠄⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠐⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡄⠀⠀⣀⡤⠉⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠒⠛⠁⠀⠀⠀⠹⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⢀⡇⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⡄⠀⠀⠀⠀⠀⠈⠉⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠛⠉⠉⠋⠙⠛⠛⠉⠙⠛⠻⠟⠛⢛⠛⠛⠛⠛⠛⠿⠟⠻⢿⡿⠿⣿⣛⠙⠛⠿⠟⠋⠉⠙⠛⠿⠿⠿⠿⠛⢛⠛⣿⣻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠐⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⣿
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠰⠆⠈⠀⠀⣾⣿
⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠎⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⠐⠀⠀⠐⠈⠀⠀⣿⣿
⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠚⠀⠀⠀⠀⠁⠈
⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠤⠁⣈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠰
⣿⠇⠀⠀⠀⠀⠈⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢂⠻⡀⠐⠒⠞⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡪
⣿⣁⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠁
⣿⡿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⠀⠀⠀⠀⠀⠐⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠤⠀⠀⠀⠀⠀⢰
⣿⠄⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⣸
⣿⡆⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣆⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣤⣤⣶⣶⡄⣀⣴⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠢⠤⠤⠒⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⢣⠀⠀⠀⣀⡠⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢦⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣇⠔⠊⠁⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷
⠀⠀⠀⠀⢠⠛⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⡀⣆⢩⣸⣖⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠇
⠀⠀⠀⢠⠃⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢈⣻⣿⡿⣿⣾⡏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡄
⠀⠀⠀⠸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣿⣿⢿⣿⢻⡷⢾⡧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡆
⠀⠀⠀⠀⠙⢄⠑⢦⡀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠻⡏⡁⠛⣛⣋⠐⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⢀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠑⠤⣈⣒⣤⠤⠒⠚⠉⠁⠀⠀⠀⠀⠁⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⣠⠇⠙⢄⡀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠤⠤⠴⠚⠁⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⢢⠁⢉⠁
⠀⠀⠬⡕⡀⠀⠔⣱
⠀⠀⠠⢅⡂⢸⠀⠀⢀⠰⡀⠠⠕⡀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢺⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠇⠘⠎⠀⠌⠣⣀⠔⠈⠁⠂⡄⠠⠗⠀⢀⠀⠀⠀⢀⠃⠁⢢⡤
⠀⡴⠀⠁⠥⠁⠀⠘⡇⢀⢀⡀⠈⠁⢀⣀⠏⢂⠐⠀⠄⠁⠀⠠⠡
⠀⠈⡁⡞⠃⣰⣧⣾⠿⡋⠛⠷⣴⠞⠉⠉⠱⠄⠄⡠⠒⠂⠠⠀⢠⠉⣉⠀⠀⠀⠀⣠⣀
⠀⠀⠉⢣⣼⠏⠁⠀⠀⠀⢐⡍⢹⠀⠀⠰⣤⠓⢲⠃⠀⠀⣤⠲⡆⠈⠀⠀⠀⢰⠒⢌⣴⠂⡄⠀⠀⡀
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⢀⡈⠢⢛⠈⢴⢂⡴⠛⠛⠓⠶⡥⣤⢬⡀⢐⠰⡀⠈⠗⠈⠊⠉⢀⠈⠀⣘⠂
⠀⠀⠀⢀⣿⣷⣶⣶⣦⣴⣏⣀⡀⠈⢉⣠⣾⣥⡴⠶⠶⠶⠾⣤⣆⣈⣠⡴⠒⠋⣒⠂⠐⠀⣈⢈⣒
⣠⣤⣾⣿⣿⣋⣉⣉⡉⠉⠙⠛⠛⡻⠿⢯⣍⡀⠀⠀⠀⠀⠰⠂⠄⠀⠈⠉⢩⡫⠈⠑⠠⠍⡀⠀⠐⡀
⣿⠿⠟⠁⠀⠉⠉⠈⠉⠲⢤⠀⠈⢈⠀⡆⠀⠉⡓⡲⠤⠄⠀⠌⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠃⠄⠄⠊⠀⠀⠀⠈⠁⠀⠀⠒⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠦⠤⠖⠋⠙⢦⣀⠆⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣄⠈⠀⠀⠀⠀⠀⠀⠀⢀⡔⠩⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⠲⣦⡀⠀⠀⠀⣰⠏⠀⠀⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⣠⠞⢳⡝⠲⣤⣼⠃⠀⠀⠀⠠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠚⠒⠂⠘⠁⠀⠀⠙⠛⠛⢻⡀⠀⠀⠀⠀⠈⠛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⢠⡀⠀⢀⡴⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡤⠤⠤⣤⣤⣼⠳⣖⠋⠀⠀⠀⢠⠞⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⠀⠈⢹⡟⠛⠳⣤⣀⠀⠘⣷⠶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠛⣏⠁⠰⣞⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⢰⣏⠀⠀⠀⠀⣀⠀⣾⣄⠀⠈⠙⠚⠦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣤⡞⢻⣄⠀⡼⢻⣉⠛⠀⠸⣄⣠⡄
⠀⠀⠀⠀⣀⠀⣰⠏⠉⣿⢣⠾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣰⠀⡜⣼⠛⠡⠚⣻⡗⣾⡓⠀⠀⠑
⠀⠀⠀⢀⠋⠉⠁⠀⢠⣿⡆⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⣼⡉⠀⠀⠀⡙⠀⠈⠙⢆⠀⠤⣄⣀
⠀⠀⣀⣈⣣⡀⠀⠀⣺⣿⣥⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠝⠀⠀⠙⣇⣀⢄⠁⠀⠀⠀⠀⢻⡤⠞⠁
⢀⡴⠋⠀⠉⠻⢦⡾⢻⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠒⢲⡶⠚⠑⡟
⠈⠻⣄⠀⠀⢠⡟⢁⡾⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡤⠀⠀⠀⠐
⠀⣠⠟⠀⣴⢋⡴⠛⡁⢺⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡑⢾⣷⠂⢈⡁⠐
⠰⡏⠀⠀⣻⣸⡇⠈⠀⢈⡇⠀⣠⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⡀⣀⡹⡄⠈⠂⠈⠃
⠀⠙⢦⠄⠹⠏⠀⣀⣀⠀⣇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⠤⠼⠀⠉⠻⣏⠛⢻⣄⡀
⠀⠀⠀⢀⡠⠖⠚⠁⠀⣬⠁⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠛⠛⢧
⠀⠀⠐⢋⠀⠀⠀⠀⢀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠀⠀⠀⢀⣻⠆⠀⠀⢀⠠⠬⣄
⠀⣟⠉⠁⠐⣀⠀⢀⣼⠀⠀⣠⣎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡁⠀⠀⠈⠉⠛⡞⢻⣶⡶⠋⠀⠀⣠⡿
⢀⡞⠁⠀⠀⠈⣳⣮⡟⠀⠘⡇⠈⠀⢀⡴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⣸⠋⠈⢷⣄⠀⠘⣯
⠈⠳⠳⣄⡀⠛⠙⠏⠀⠀⣠⠇⠀⢀⣜⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⠜⡌⠀⠀⠀⠛⢦⠄⠚⠃
⠀⠀⠐⠈⣷⡐⠠⣦⣤⣞⢙⡆⠀⠀⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢦⣤⠴⢦⣄⣼⠃
⠀⠀⠀⠀⠀⣀⡀⠀⡼⠀⠈⠑⠀⠀⠚⠉⢻⣄⠀⢀⣀⡀
⠀⠶⡤⠀⢀⡟⠈⠉⠁⠀⠀⠀⢀⡴⠒⠢⠼⠋⢱⠎⠀⠘⢧
⠀⠈⠐⠐⡺⣁⣀⡀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⣨⠁⠀⠀⠀⠉⢱⠆
⠀⠀⠀⣼⠁⠀⠀⠉⠋⠰⢾⣅⠀⠀⠈⠑⢦⣠⣿⣀⣀⣀⣠⣤⣞⣀⢀⣠⡀⣦⠢
⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⣇⡞⠀⠀⠀⠀⠰⠿⣾⡋⠉⠉⠁⠀⠈⠙⡆
⠀⢀⠀⠀⠀⡟⠀⠀⠀⠛⠻⠤⣄⠀⠀⠈⠀⠀⠸⡇⠀⠀⠀⠀⢀⣼⠁
⠀⠈⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢳⡀⢀⣴⠟⠉⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠘⠦⣤⠖⠢⢬⡷⠛⠓⢦⡴⠋⠉⠛⠁
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠁⠤⡤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⢘⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣦⠀⠈⠛⠃⠀⠉⠁⠸⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡒⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠄⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠄⠀⢀⣀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⢰⡆
⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠙⠀⠀⠀⠀⠀⠻⠀⠀⡀⠀⠀⠀⠀⠈⠋⠀⢀⠀⠊⠁
⠀⠁⠀⢄⡀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢂⣠⡀⠁
⠀⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


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

⣠⣄⡀⣀⣠⡄⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠛⠿⠋⠻⠟⠃⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠁⠰⠊⠂⡂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⠀⠀⠐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⠀⠀⠀⠀⠀⠄

⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠑⠂⠐⠊⠁⠀⠀⠀⠀⡂⠀⢐⠀⠀⠀⠀⢀⡠⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀⣀⠲
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠠⠀⠘⠊⠀⠈⠀⠀⠀⢀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠶⠂⢀⠀⠀⠀⢀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠
⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠤⠄⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⠀⢈⠊⠁⠀⠙
⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣄⣀⣔
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠀⠀⠀⣀⣆⣿⣿⠃⡠⢀⣤⣾⡩⠴⢴⠊⠈⡱⠤⣈⣱⣄⢀⡾⢑⠤⠤⢦⣤⠤⠞⠁⠀⠓⠄
⣖⣛⣛⣭⣥⣼⣿⣿⣿⣿⡿⠿⣶⣶⣴⣇⣀⠀⠀⠀⣣⣠⣤⠟⠓⠶⣒⠒⠛⢄⠀⢀⡠⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣟⠉⠉⠉⠉⢩⡟⢉⣉⡹⡈⠉⢿⡿⢷⣾⡛⠹⣄⣠⠖⠛⠒⠛⠶⠖⠛⠛⠗⠒⠒⠛⠊⠓⠄
⠋⠙⢦⣏⠻⢷⣾⣶⣄⣾⣠⣴⠶⠚⣟⠛⠲⣤⠶⠒⠛⢿⣙⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⠠⠀⠀⠀⠂⠈
⠀⠔⠡⠈⠉⢉⣽⡿⠟⡟⠛⠻⣷⢶⣿⡀⠀⢀⣀⣄⣀⡠⢹⠓⠶⢦⡤⠦⢤⣴⣮⡥⠤⠬⠄⠄⠐⠒
⣤⣤⣴⠶⠟⠋⠁⢇⣸⠃⠀⡰⢩⠛⠚⣟⠛⢿⣅⣀⣤⣤⣤⣥⣀⡀⢹⠄⠀⠀⢀⠌⠑⢄⣀
⣿⣿⣧⠀⠜⠉⠀⠈⣟⠀⠀⠹⡌⠢⡀⠀⠱⡀⠙⢧⡄⠀⢳⠄⠙⠛⢾⠦⣼⡁⠀⠀⠀⢀⡀⢁⡠
⠈⠛⢿⣿⣤⣤⣀⡞⠸⠗⠦⠮⣧⡀⠀⠀⠀⠀⣀⣤⠇⠀⠯⣄⣀⠀⢸⡤⢄⡉⡑⠉⠀⠈⠁
⠀⡎⠀⢹⣿⣗⠪⠀⠀⠀⠀⠀⠈⡟⠐⠀⢠⠜⠱⣏⡀⠀⠀⠀⠈⠳⣄⡇
⠆⠀⢠⡞⠛⠻⠷⣤⣑⢀⡤⠴⢤⢤⡤⣶⡃⠀⠀⠀⠹⠉⠁⠀⠀⣠⠟⢱⠤⠤⠒
⣇⣀⠀⢳⠀⠀⠀⢈⡟⠛⠓⠶⠶⠶⣤⣀⡉⠀⠀⢀⠠⠠⠄⠀⢀⠓⢄⠈⠂⢀⠀⠀⠠⠄⠀⠀⠀⡀⡀
⠀⢹⡀⠺⠤⡀⠀⠈⣇⣀⠀⠀⠀⠀⠎⠻⣯⠝⠒⠦⠤⠔⣋⠉⠙⠀⠀⠀⠀⠈
⠀⠟⠀⠀⠀⠀⠂⠀⠀⠙⣦⡀⠠⠀⠀⠀⠘⢷⣤⣀⡘
⠀⠘⠀⠀⠀⠀⣠⠤⡤⠞⡃⠉⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣤⡆⠀⠰⣿⣿⣿⣿⣿⣶⣶⣶⣶⠂⠠⣤⣤⣄⣀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⡀⣥⠄⢿⣃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣉⣁⣸⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡋⠃⣥⡀⢈⣭⠀⠀⡀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣟⠳⣤⠜⠀⠸⣿⠀⠠⣤⣴⣿⣿⡟⠋⠁⠈⣨⣿⣿⡿⣾⣿⡆⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣵⠀⠀⠀⠀⢀⣿⠀⢠⠜⠋⠉⠻⡟⠀⣠⣴⣿⠛⣿⡟⠻⢿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣸⣟⡳⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣶⣟⠻⠟⠁⠀⠁⢀⡈⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠻⠇⠀⠀⣤⠀⠀⠀⢨⣿⠀⠀⣀⣀⣠⣤⣿⡟⠿⣏⡗⠀⣀⠀⠀⠛⢹⡀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣤⣤⡀⠀⠀⠀⢺⣿⠀⠈⣉⣽⣿⠋⠉⣡⣾⣿⣧⡅⠉⡀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠋⠛⠋⠂⠀⠀⣿⣿⠇⠈⣋⣘⡉⠠⠀⠙⣻⠉⠈⠀⠚⠅⢤⠇⠀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⡜⠂⠀⠀⠀⠀⠀⣿⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣴⣾⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣹⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠉⢩⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠘⠿⠿⢏⡙⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⢄⠀⢠⣾⣿⣿⣿⠋⢁⣤⣤⣾⣿⣿⣿⣿⣷⣶⣔⠄⣤⣦⣶⣿⣮⡑⠦⣼⢇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣌⣿⡇⠃⠘⠛⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣀⣿⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⣿⣷⣄⣤⡄⢠⣶⣶⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣵
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠊⠱⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⡿⠟⡋⠁⠀⢀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡀⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⡉⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠄⠰⢿⡇⠠⡀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⡈⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⠠⠀⢀⢝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠌⠉⠁⠀⠀⠂⠀⠀⠀⠀⠙⠿⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣾⣿⠄⠀⠀⠐⠀⠀⢀⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⢴⣥⠀⠁⠠⠀⣤
⠀⠀⠀⢀⣄⠀⢦⠀⡀⠀⠈
⠀⠀⠀⠀⠘⠂⠈⠒⠠⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⣀⣠⡆⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⠿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠉⢻⣿⣧⠀⠀⠀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣴⣾⣿⠿⠿⠿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⠿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⣼⣿⣿⠇⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠟⠛⠛⠛⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⢻⣿⠿⠓⠛⠿⣿⣠⣤⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⡇⠀⠀⠀⠀⠀⠀⢨⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⡀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠈⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠟⠋⠉⣿⣷⣶⠶⣾⣿⣷⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣤⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⢰⣿⣿⡏⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣷⣶⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣾⣿⣿⠿⠋⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⢀⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⣠⠞⠛⠛⠛⠛⠷⠶⣦⣄⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣄⠀⠀⠈⢻⣆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⢿⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⡇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⢻⡆⠀⢀⣠⣶⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⣿⡿
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢠⣆⠀⠀⣾⣿⡆⠀⠘⠁⠀⠀⠀⢀⣤⡶⠚⠂⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠈⠷⠀⠈⢿⣷⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠂⠐⢿⣷⣾⣿⣿⣿⣿⣀⣤⣶⡷⠀⠀⢠⣄⡀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⣭⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠉⠻⣦⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣶⣤⣤⣤⣤⡤⢀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⣡⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣨⡆⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⣷⡀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢻⣷⡀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢋⣿⡏⠀⠀⢻⣷⡄⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣸⣿⠁⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢠⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣀⣴⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣸⣿⣧⣴⣶⣶⣿⠆⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠛⠉⠀⠀⠀⢠⣶⣦⠀⠀⠀⣰⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠑⢆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠎⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⠂⡎⠀⢑⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠒⠊⢠⠤⠴⠃⠀⠀⢀⡀⠐⠃⢀⠔⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⢄⣀⡰⠀⠀⠀⣀⠠⠤⢀⣐⡦⣎⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢧⠈⢦⣀⣀⡤⠶⣁
⠀⠀⠀⠀⡰⠋⠀⠁⠀⠈⠑⡄⠀⢰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢐⡝⢦⠈⣦⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢇⠀⠀⠄⠀⠁⠀⠼⠀⢸⣀⠔⠒⠂⠀⠀⠀⠈⠒⠤⠤⠖⠋⠀⠈⠱⢴⠢⠤⠤⠤⠊
⠀⠀⠀⠀⢘⣄⠀⠀⠠⠀⠀⢠⠟⢹⠃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡠⠃
⠀⠀⠀⡔⠉⠈⠓⢄⣀⣀⡔⠁⢠⠟⠩⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠑⠂⠊⠁
⠀⠀⠀⢣⠀⠀⠀⠀⢀⡞⠀⣰⡏⢀⠀⠀⠀⡀⠀⠠⠉⡄
⠀⠀⠀⠀⠑⠒⠬⠔⢾⣠⡞⠑⠘⢆⡀⠀⠀⠀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢧⠀⠀⠀⠈⠙⡖⠓⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠿⠿⠀⠀⠄
⠀⠀⠀⢀⡴⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⢁⠀⠀⡀⠀⠐⡈⠒⣄⠉⠷⢤
⢀⠀⠀⠞⠁⢈⢀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠓⠀⠐
⠎⠀⡁⠀⠄⠈⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠐⠠⡀⠂
⠀⠀⠁⠁⠀⠀⠒⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣴⣾⡖⠁
⠀⠀⠀⠀⠀⠀⠐⠲⠇⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⠠⠄⠀⠠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠘⢉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠁⠀⠉⠂
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠉⠀⠀⣀⠈⠀⡀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⡃⡈⠠⠀⠐⡷
⠀⠀⠀⠉⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠈⠈⠈⢀⠀⠙⠻⢁⡆⠀⡀⠄⠀⠀⠈⠀⢳⠀⠻⡆⠀⠀⠀⠀⠀⠀⣸⡁⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⢀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠀⠃⡉⠁⠘⠛⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⡍
⠀⠀⠀⠘⣦⠀⠳⠀⠁⠀⣴⣶⡌⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣶⠀⠀⠐⠈⠀⠀⠀⠀⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠋⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⠀⠀⠀⠈⠄⠔⠂
⠀⠀⠀⠀⠀⠀⢲⣶⡾⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢄⠁⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢢⣳⠀⠀⠀⡼⠁⠀⠀⢀⣠⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡝⠀⢠⣞⣠⣤⣤⣼⠕⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣀⡴⠛⠉⠀⠀⠀⠀⠉⠓⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠟⠉⢀⠤⠴⠒⠒⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣕⣡⠤⠶⣗⡒⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣚⠡⠐⠊⠉⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣩⠖⣋⡁⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⡡⠖⠉⠉⠉⠉⠩⣉⠃⠒⠀⠑⠀⠀⠀⣰⠟⠚⠉⠈⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣁⣐⣉⣀⣀⣀⠀⠄⠠⣤⠄⠉⢉⣁⣀⣤⡤⠎⢥⣭⣘⣲⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢀⣨⠤⠖⠒⠚⠛⠛⢾⡛⠉⠁⠀⠈⠛⠻⢥⡀⠀⢄⡀⠀⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⡠⠞⠉⠀⠀⠀⠀⢀⡀⠀⠀⠙⢦⠤⣄⣀⡀⠀⠀⢌⠓⠦⣈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢀⡴⠋⠀⠀⠆⢀⢀⠀⣰⠞⣀⡀⠀⠀⠈⢷⠠⡀⠀⠀⠀⠀⠑⠤⣈⠑
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⠔⠉⠀⠀⠀⠀⢀⣾⡴⠾⠟⠳⠟⠉⠙⠢⠀⠀⢱⠘⡄
⠐⠒⠒⠒⠋⠉⠉⠀⠀⠀⠔⠁⠀⢀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠉⠑⠒⠂
⠀⠀⠀⢀⣀⡤⠤⠴⠆⠴⠶⠒⠶⠦⠭⠥⢤⣀⣠⣤⣄⣀⣀⡀⠀⣀⣀⣀⡀⣠⠖⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢀⠈⠀⠀⠀⠈⠉⠂⠀⠄⣒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢄⡀⠀⠀⠀⠠⡀⠈⠑⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⡆⠀⠀⠀⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠐⠿⢛⠻⠓⣛⣠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⡿⠃⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠁⠒⠆⢀⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢫⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠉⣡⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⠂⠀⠛⣿⠟⠋⠍⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣄⢀⡿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠓⠈⠻⡿⠀⣠⡌⠉⣼⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⢀⠀⡈⠁⠀⠀⠀⠞⠻⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣛⠛⠹⢄⠀⠀⠀⠆⢹⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠊⠁⣤⣶⣶⣦⣤⣴⣟⠀⢹⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⠀⣛⢷⡄⠀⠀⠀⠐⢶⡜⠷
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⣿⠀⠀⢀⠙⣿⣿⣿⣯⢽⠿⠁⠛⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣿⡿⠁⠈⠓⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠻⣀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠖⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠐⠆⠠⠀⠀⠀⡄⠀⠀⠀⠀⡠⡁⠡⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠁⠐⠂⢃⠰⠆⢠⠂⠋⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡁⠀⠎⡀⠠⠆⠀⣀⠀⠀⠀⠀⠀⠄⡀⠄⠀⠈⠄⠀⠃
⠀⠀⠀⠀⠀⠁⢀⢀⠀⠀⠀⠀⠀⠈⠁⢦⡀⠓⠸⡀⠤⠔⠁⠀⠉⣁⠀⢀⠀⠀⠀⠀⠋⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⠀⠙⢶⠀⠁⠂⡴⠒⢋⠀⠀⣀⠠⠀⠀⠀⢀⡠⠠⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠁⠀⡀⠀⠀⡀⠀⠀⢁⠠⠄
⠀⠀⠀⠀⠀⠐⠿⠄⠀⡀⠀⠀⠀⠂⠀⠀⠈⠀⠈⠀⠒⠀⠈⠁⠀⠀⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠐⠲⠀⢈⣊⣉⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠉⠃⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⡏⡀⡀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⢀⡀⠀⢤⠆
⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⢅⠢⠌⠻⡖⠀⡦⠮⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠈⠑⠢⡌⠉⠐⢲⠮⡶⣄
⠀⠀⠀⠀⠀⠈⠀⠁⢐⡄⠀⠄⠀⠀⠀⠀⠐⠃⠀⠑⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢣⠀⠀⠄⢆⠈⠊⢁⠠⣄
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⣀⠹⡄⠀⠀⠙⠋
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠆⠀⢠⡀⠈⢀⠀⠀⠀⠀⢀⡀
⠀⡴⢉⣌⠱⣄⣀⣀⣀⣀⣀⣰⣉⣦⣄⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⣀⠀⢄⠘⠂⠐⠂⣢⡅⠱⡀
⠀⢳⣌⠛⢿⡇⢰⢦⢹⡇⣴⣸⠀⡇⢠⢦⢸⠃⣴⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠒⠃
⠀⢯⡙⠛⣠⡇⢘⢊⣸⣃⡇⢸⣀⣇⣸⣸⢸⣆⣙⡁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠉⠉⠁⣇⣸⠉⠀⠉⠀⠀⠉⠈⠁⠈⠉⢧⣙⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠔⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡑⠶⢄⡀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡛⣷⠀⠀⠀⠈⢳⡤⡀⠀⠀⠀⠀⢉⡶⠶⠿⢢⣀⣀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⡀⠀⠀⠀⢧⠈⢧⠀⠀⠰⠋⠝⠀⢒⣁⡁⠙⠾⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠇⠀⠀⠀⠀⠙⠺⠧⠀⠀⠀⣆⠤⣀⠉⡉⠉⠲⢤⡞⠉⢀⠄⣰⠶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⣀⡀⡀⠀⠀⠀⢐⡚⠙⠳⡆⡠⠓⠲⣄⠀⠈⠀⣤⠄⢡⡴⠳⠚⠁⠀⠀⠀⠀⢀⠤⠔⠂⡋⢹⢾
⠀⠀⠀⠀⠀⠀⣘⣷⠺⠃⠀⠈⣇⡹⠉⢏⡁⠢⠠⠙⠳⢄⡻⢄⡀⠀⢈⠳⠔⠊⠁⣀⣠⣅⣠⠴⠖⠀⠀⡤⠚⠁⣀⠐⠈⡀⠁⢠
⠀⠀⢠⡖⡶⠘⠿⠟⠀⠀⠀⠀⠀⠀⡀⠀⠙⡄⠠⢰⠘⡁⠀⠀⠀⣤⣖⣒⣓⡠⡀⠈⡋⠈⣡⡔⢒⡶⠛⠁⠄⠄⠀⠀⠈⠠⠁⠠
⠀⠀⠈⠛⢻⠙⣆⠀⠀⠀⠀⠈⣄⣾⣋⡧⠀⠁⣴⠆⠐⣱⠁⢀⣘⠉⣉⡉⠉⢧⣉⡤⠦⠾⡀⠀⠀⠀⠢⠀⢀⡠⠂⡠⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⢨⡄⠀⠊⠄⣠⠞⢁⠀⡸⡸⡖⠿⠓⣳⢺⠹⠅⠁⠒⠤⠑⠀⣆⡠⠖⠉⠀⠘⢀⠠⠞⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢆⠀⠀⣆⠀⠰⣆⢰⠀⡈⠁⠀⠀⠈⠡⣈⣑⢚⡼⠉⠸⡇⠀⠉⠀⠀⠀⡆⡙⢂⣀⠉⠀⠐⠎⣀
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣨⡓⣀⢸⡁⡀⠻⣼⡃⠑⢄⠱⡈⢆⠀⢁⠀⡠⢀⢗⠄⠁⣸⢠⠆⢼⠸⠻⠓⠲⠤⣀⠀⠀⢀⠀⠈⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⢀⣱⣤⠈⠀⢥⠀⠂⢹⡆⠸⣝⡁⠠⠔⠠⣆⡰⢟⠍⠁⠀⠘⠠⠀⠁⠄⢀⠀⠈⠑⠦⣈⠀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠮⠋⠁⠁⡨⠕⣦⠶⣦⢀⢧⠡⠐⠌⠓⠤⡴⣋⢉⣀⣃⡄⣀⡀⢀⠀⠀⠐⠂⡀⠑⠈⠀⡀⡀⠑⠌⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠈⠀⠠⠀⠉⡠⣳⣥⠦⠤⠔⠈⠁⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⢀⣈⢀⠀⠐⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠝⠀⢠⡴⠠⠀⣀⢴⠗⡀⢁⡙⡆⠐⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠀⠊⢀⠻⠐⢋⠀⠸⠊⢀⠘⠀⡇⠀⠊⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠝⣇⠀⠀⠀⠒⠀⠀⢀⡤⢺⡄⠠⡀⢳⠀⢀⠆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠒⠊⠁⠀⠀⡆⠀⠀⠈⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀⠀⠂⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠰⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢡⡃
⠀⠀⠀⠀⠰⣿⡏⢛⣿⠏⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⡐⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠿⠟⠿⢿⠀⠀⠀⠀⠀⡺⠀⢀⠘⠀⠀⢠⡆⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠠⠀⠈⠐⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠈⠁⠀⠀⣼⠗⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢧
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⢰⣳⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣆⠄⠀⠐⠃⠀⠀⠀⠀⠀⡄⠁⠁⠠⠀⠀⠈⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠇⠀⠀⠀⠘⠁
⠀⠀⠀⠓⠞⠂⠀⠀⠀⠀⠀⠀⠄⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⣤⠀⠐⠀⠘⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡀⣤⠄⠀⠀⠀⠀⠚⠄⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉
⠀⠀⣠⡄⠀⠁⡀⠰⠆⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣠⣆⠀⠀⠀⠀⢀⡄⠀⠀⠂⠀⠀⠀⠀⠘⠡⡀⢠⠀⢀⡀
⠀⠶⠈⠘⠳⠆⠀⢴⢄⢰⠆⠀⠀⠀⠠⠀⡆⢀⠀⠀⠀⠐⠛⡟⠉⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠴⠀⠀⠈⡆⡀⠂⠁
⠀⠀⢤⠑⢂⠀⡁⠀⣝⢁⠰⠆⠀⠈⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠆⣠⠁⠀⣀
⠀⠀⠀⠀⠐⠆⠡⡀⠡⠀⠦⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⣠⠏⠁⠀⠀⠖⡀⠀⠠⡁⠄⠂⠉
⠀⠀⣘⠃⠛⠐⠖⠀⡀⠴⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠢⣘⠀⠀⠀⠀⡸
⠀⠀⠈⠀⣤⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⣘⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠⠁⠀⠀⠀⢹⣋⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⢀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⣿⠛⣻⣇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠾⠀⠀⠀⠁⠀⠀⠀⠄⢯⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⡞⠋⠁⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⢀⡀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⡆⠊⠤⠶⠂⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣈⠀⠛⠋⣱⠉⢶⡄⠀⢀⣠⡿⣀⡿⢛⣷⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣌⠷⢺⣷⠀⠄⠀⠀⠀⠀⠀⠈⠻⢿⠳⠀⠀⠋⠀⣀⡤⠖⠚⠷⢶⢿⣏⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣝⢐⡛⠀⠀⡠⠔⠈⠉⠉⠒⣄⠀⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠺⡾⠛⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣄⠀⠿⠀⠼⠁⠀⠀⠀⠀⠀⠸⡆⢠⣠⡞⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠤⠭⣶⣤⠞⠀⠀⠀⠃⢀⠀⢸⡇⣼⠏⣿⣿⠏⣀⣀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠤⠤⣤⡤⠤⣀⡀⢠⠟⠛⠒⠁⠼⠋⠀⠀⠀⠀⠀⠁⠀⡾⣰⢃⣤⠾⠛⠉⠉⠉⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⡴⠋⠀⠀⠀⠀⠹⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⡼⣱⡿⠋⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢳⠄
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⠁⠀⠀⠀⢠⠀⠀⠀⠈⢳⡀⠀⠀⢀⣤⠀⠀⠈⣠⣯⡾⢋⠀⡀⠀⠀⠀⠐⡤⢤⡶⣦⣀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⣄⠀⣸⣄⠀⠀⠀⠀⠀⠀⡠⠀⠀⢳⠀⠀⢸⣿⠇⣠⣾⡿⠋⠸⣿⡿⠃⠀⠀⠀⢠⣶⠾⢧⣽⠋⣹⣿⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣈⡃⠉⠾⠶⠆⠀⠀⠤⠚⠁⠀⠀⢸⠀⠀⠘⣡⣾⠿⠻⡉⠻⠁⠀⢄⠀⠀⠀⠀⢀⢻⣿⣋⣏⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣼⠁⠻⡆⠀⠀⠀⠀⢀⣄⠀⠀⡸⢀⣴⡾⠋⠁⠀⠰⢻⠤⣍⠁⠀⢡⡄⠀⠀⠀⠜⠿⠋⠙⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⠔⠂⠐⠢⡀⢸⣿⡗⣰⣷⡿⣋⣤⠴⠶⠒⠒⠾⢄⠀⠀⠀⢐⡷⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⢹⠘⢛⡿⣫⡾⠛⠉⠀⠀⢀⢀⠀⠀⠀⠘⣂⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⣴⢋⡀⠀⠀⠀⠀⠀⠻⠛⠿⠲⠗⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣼⢃⡀⢀⣀⢀⡀⠀⠀⠀⠀⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠲⠦⣌⣷⡿⣦⣄⠀⠀⠀⠀⠀⣾⣿⠙⠿⠃⠛⠓⠿⣥⣖⡀⠁⠀⣀⠀⠔⠁
⠀⠀⠀⠀⣀⣛⣻⢿⠏⠋⠀⠀⠈⠻⣄⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠃⣿⣭⡄
⠀⠀⠀⠀⢼⣿⡙⠃⠀⠀⠀⠀⠀⠀⠹⡼⣷⣿⣿⠁⢸⣞⡤⠀⠀⠀⠀⠈⣿⠶
⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⡟⠀⠀⠁⠁⠀⠀⠀⠀⢀⡾⠷
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠒⠀⠀⠀⠀⠀⡇⢸⣿⠃⣀⣠⣤⠀⠀⠀⠀⠀⢠⡿⠆
⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠠⠀⠀⠀⢰⠃⣿⡏⠾⣿⡿⠃⠀⠀⠀⠠⠀⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡏⣰⣿⠔⠒⠓⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠂⢀⡞⣰⠟⡁⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠞⣰⠋⠀⠁⠰⠊⣁⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠜⠁⠀⠀⠀⠀⠀⠉⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠂⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠐⠠⡀⠀⠀⠀⠀⠀⠐
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠠⠂⠀⠀⠐⠣
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⡀⠀⢹⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠀⠀⠀⠀⠀⢁
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠈⣆⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠐⢀
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠀⠀⢀⠂
⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣂⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡄⠁⠀⠀⠀⠀⠀⠀⡄⠀⠃⣠⣆⡰⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⡆⠀⠀⠀⠀⠀⢀⠴⠖⡛⢄⠂⠈⠙⣤⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠸⡀⢤⠎⢈⡏⢳⠐⡁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⠶⢄⡀⠀⡴⠒⢄⠈⠒⠲⠶⣷⣋⣰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠤⠀⢠⠀⡔⠀⠀⠀⡈⠆⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⢼⠠⡆⡇⢈⠇⣸⢃⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠐⣂⣀⠀⠐⠦⣿⣷⣷⠞⢊⣠⡺⠋⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡀⠔⡈⠘⣋⣿⡗⠟⠛⣁⡀⠀⠄⡠⢁⠀⠀⠀⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠂⠀⠾⣣⡞⠉⢼⠙⠐⠆⢀⠀⠀⣸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠐⡑⠠⠇⠸⡆⠡⡀⠑⠀⢀⡍⠰⠀⠄⠀⠠⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠟⠒⠨⡛⣁⠈⠁⡄⣸⠔⠐⠁⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠂⠄⠊⠀⠂⠠⠄⢀⣳⡎⣰⢃⣤⡾⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠒⡀⢀⣿⣿⣯⣴⠁⠂⠓⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠒⠖⠠⠀⠀⠀⢄⠀⠀⠤⠄⠀⣋⣲⠵⢿⢻⡦⢎⢍⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣷⣀⣀⣿⢦⣷⣤⣀⠤⠿⠗⠿⣫⠟⠉⢁⠎⠀⡄⡱⣀⡑⡑⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠙⣶⢏⠅⠀⠀⠀⡀⡠⢂⠂⠀⠀⠀⠀⠰⠁⢿⡌⠑⠉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠽⠃⠀⠀⣀⣬⡄⠀⠀⠤⡀⠀⠀⠀⠀⠀⣨⠙⢦⠠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠿⡄⠀⠀⠀⠀⠀⠁⠂⠐⠊⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡱

⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⣸⡐⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⠀⠀⠀⠈⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠂⡀
⡀⠀⠀⠠⠃⠓⠀⠀⠀⠀⠀⣄⠀⠀⡄⠐⠀⠀⠰⠠
⠀⠀⠀⠀⡄⠀⠀⡄⠀⠐⠄⢠⠄⠀⠀⡀⠀⠀⠠⠀⠀⠴
⠈⠀⠀⠀⠁⢠⠚⠀⢀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣶⣀⣀⣀⣀⣀⣀⣴⡶⣦⣄⠢⠀⠀⠀⠀⠘
⣤⣄⣀⣀⣠⠿⠶⠒⠒⠊⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠘⠛⠷⢶⣴⣶⣾⠗⠲⢷⣤⣀
⠀⠉⠉⠉⠑⠒⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠶⣶⣄⣀⡉⠹⣷⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡷⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⢻⠾⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠁⣼⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣷⣾⣿⡧⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡿⠛⠋⠉⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢹⣦⣦⣀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣟⣛⢫⡉⠂⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⣾⣿⣿⠘⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⣰⣿⣿⢿⡄⠀⠘⢷⣄⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⣴⣿⣿⡏⢸⣧⠀⠀⠘⣿⣆⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⢹⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠇⠸⢿⠄⠀⢀⡤⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⣶⣿⠉⢹⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠀⠘⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⢻⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⠀⠀⠀⠈⣿⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⠀⠀⠀⠻⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⢀⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢼⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠿⠿⠿⣷⣦⣄⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡋⠀⠀⠀⣴⣿⠿⠿⣿⣦⣤⣤⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⢸⣿⡇⠀⠀⠈⠛⠛⠋⠉⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠟⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⢀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠿⣿⣦⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⣿⣿⠿⠿⠿⠛⠛⠉⠀⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠈⠙⠢⡀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠙⣆⠀⢠⠇⡀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠘⢦⡀⠘⡆⡼⢰⠃⡀⠂⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠙⢦⣹⣇⣮⠜⠁⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠴⠶⠦⠭⠿⣶⠋⠀⠙⢶⠿⠛⠒⠛⠛⠓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠰⠖⠒⠒⠛⠋⣹⣄⠀⢀⣜⠛⢿⣛⠛⠒⠒⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠏⢈⣏⠉⣎⠢⣀⠈⠙⠂⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣠⠤⠖⠋⢁⡞⡽⠀⢸⠹⡄⠸⡄⠈⠓⢤⣀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠸⠀⠀⠀⢳⠀⠀⠀⠈⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢻⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠲⣄⠀⠀⠀⢀⡇⠀⠀⠀⠳⣄⡀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠙⠲⣌⠳⡄⠀⢸⠁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠑⢾⣆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⡤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠚⣁⡤⠴⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣞⡤⠚⠁⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣋⣠⠤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇