Watermelon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢆⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢣⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⡶⠀⠀⠱⡄⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⢎⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠣⡈⠊⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠇⠀⠀⢀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⣄⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠈⢦⠃⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠳⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢶⠒⠒⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⡼⠓⠒⢒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⣠⠴⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⣀⣤⠶⠋⠁⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠉⣁⣀⡤⠖⠛⠉

⠀⡀⠀⠀⠀⠀⠀⠀⠈⠢⢝⡂⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢣⣙⠂⢀⠀⠀⠉⠳⣌⡒⠦⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠄⠀⠈⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⡀⢐⠈⡉⠀⠀⠀⠢⣕⢦⠀⠀⠀⢤⡀⠠⠆⠦⠳⠳⠈⠁⢀⡔⠀⠀⠀⠀⠀⢀⣴⢋⠴
⠀⠀⠀⠈⠀⠘⠀⡁⠏⠼⣠⠀⠈⢦⢱⡀⠈⠳⣬⣑⡰⠤⠤⠤⠔⣚⠡⠊⠀⠀⠀⠀⢠⡷⣁⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⡀⠠⡆⣧⠀⠀⠀⠘⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⢣⠇⢐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠆⢈⡇⣿⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⠀⠀⠀⠀⢻⢸⠀⠠⠖⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣸⡝⠀⠀⠀⡀⡀⠀⠈⠉⠉⠙⠒⢨⣙⢶⣄⠀⠘⡌⢇⠀⠚⣡⢀
⠂⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠋⠀⠀⠀⠀⡄⠀⢠⡰⡆⢶⢰⢢⢄⡉⠢⠻⣃⠀⠐⠌⠀⠀⠀⠉
⠒⠈⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡘⠢⠃⠀⠀⠀⠈⠈⠠⠀⢣⢹⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣼⢰⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⢰⣿⢨⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰
⢀⡐⠆⡀⠀⠀⢿⡘⡀⠈⠵⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡆⠇⠘⣠⢀
⠃⠁⠰⠁⠀⠀⠈⢣⡱⣄⠀⠉⠰⠃⠇⠶⠘⡂⠊⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⢾⣌⢦⠀⠋⠞⠰⠆⡇
⣿⡿⠷⠷⠶⠶⢶⣶⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣾⣿⣷⣷⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣲⣦⣶⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⣩⡵⠶⣺⡽⣫⡟⣻⢻⡻⢿⡛⠭⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⢀⣴⠏⢀⣤⠞⢁⣶⠏⠰⣇⠀⢷⣀⠙⢦⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢀⡿⠋⠀⣠⡾⠋⠀⣰⡿⠀⠀⡏⠀⠈⣳⠀⠀⢳⡄⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠃⠀⣶⠿⠁⠀⣴⡟⠋⠀⢀⡿⠀⠀⠘⣧⠀⠀⢹⣆⠀⠀⢹⡀⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣸⠏⠀⠀⣿⡟⠀⠀⠀⣼⣇⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠈⣿⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣰⡿⠀⠀⠀⣿⠋⠀⠀⠀⣾⡏⠀⠀⢀⣾⡄⠀⠈⢿⡄⠀⠀⢿⡇⠀⠈⣯
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⡿⠀⠀⢠⣾⡷⠀⠀⠀⢠⣿⠁⠀⠀⠈⣿⠇⠀⠀⢸⣦⠄⠀⢺⣧⠀⠰⣿⣤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢸⡷⠀⠀⣼⣿⠃⠀⠀⠀⣿⣧⠀⠀⠀⢀⣿⠆⠀⠀⢸⣷⡀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⡇⠀⠀⢻⣿⠁⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢾⡆⠀⠀⢾⡿⠀⠀⠀⠀⣾⣷⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢸⣷⠀⠀⣸⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣿⡀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠀⠀⠿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣦⣤⣀⣀⣠⣤⣤⣤⣶⣶⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣞⢀⣷⡦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣿⡷⢿⣿⣿⣿⡿⢹⡛⠛⠲⢦⣌⣙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⡟⠉⣰⣿⠋⢸⣿⡇⢸⣧⠀⠀⠀⢈⠻⣷⣮⡳⣄
⠀⠀⠀⠀⠀⠀⣰⢋⣴⣿⠋⠀⣾⣿⠃⠀⣸⡿⠁⢻⣿⡄⠀⠀⠀⠀⠈⠻⣧⡈⢳⡀
⠀⠀⠀⠀⠀⣰⠃⣾⣿⠃⢠⣴⡿⠋⣀⣴⣿⡇⠀⠸⣿⣧⠀⠀⠀⠀⠀⠁⠹⣿⡀⠹⡄
⠀⠀⠀⠀⢠⠇⣴⣿⠇⢰⣿⣿⡇⠀⢹⣿⣿⠀⠀⠀⣿⣿⠈⠁⠀⠀⠀⠀⠀⢹⣷⣀⠹⡀
⠀⠀⠀⠀⣼⠀⣿⡟⠀⢸⣿⣿⠆⠀⢸⣿⣿⡀⠀⠀⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢧
⠀⠀⠀⠀⡇⣰⣿⡇⠀⢸⣿⡿⠀⠀⢘⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⡄
⠀⠀⠀⠀⡇⢹⣿⡇⠀⢸⣿⣇⠀⠀⣸⣿⡿⠀⠀⠀⣿⣿⡇⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣄
⠀⠀⠀⠀⡇⢸⣿⡇⠀⣻⣿⡏⠀⠀⢿⣿⡟⠀⠀⠀⢻⣿⡇⠉⠀⠀⠀⠀⠀⠀⡀⢿⣿⡀⡇⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⢷⠈⣿⡇⠀⣿⣿⡇⠀⠲⢾⣿⣇⠀⠀⠀⣸⣿⡇⡀⠀⠙⠀⠀⠀⠀⡃⣸⠿⠶⠗⠒⠉⠉⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠘⡆⢺⣿⠃⠈⣿⣿⠀⠀⢹⣿⣿⠀⠀⠴⢿⣿⡁⣁⠀⠤⠀⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡜⣿⡀⢀⣿⣿⡁⠀⢼⣿⣿⠀⠀⠀⡎⠉⠁⠀⠀⠀⠀⠀⡀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢁⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⣿⣿⡇⠀⢺⣿⣿⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⢠⡀⠀⠀⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⣿⡇⠀⠀⣿⡇⠀⠀⢾⣿⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣷⣄⠀⣿⡇⠀⢠⣿⡿⠙⢿⣦⣀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠷⠤⠴⠿⠧⠶⠒⠛⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢷⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠸⣇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⡆⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠸⣇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢹⡆⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⢷⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣧⠀⠀⢀⢞⣷
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⢫⡞⢹⡆
⠀⠀⠀⠀⠀⣼⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⠏⣰⠏
⠀⠁⠀⠀⢰⡏⠳⣮⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣥⠞⠹⣶⠋
⠀⠀⠀⠀⠀⠙⢦⣄⠙⠳⢮⣝⡒⠢⠤⢄⣀⣀⢀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠖⣚⣩⡴⠞⠋⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣈⡉⠛⠲⠶⠶⠶⠭⠭⠭⣭⣭⣭⡥⠴⠶⠖⠛⠋⣉⣠⡴⠖⠛⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠦⠤⠤⠤⠤⠤⠤⠶⠶⠶⠚⠛⠋⠉
⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠖⠂⠈⠉⠉⠉⠉⠙⠶⢶⣲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⢿⠛⠛⡟⠟⢱⢢⣦⣀⠀⠀⢀⠀⠈⠛⣷⣄⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠚⠷⢧⣲⣀⠄⠘⢻⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢀⣠⡤⢊⠀⠢⠀⣡⣢⠠⡀⠤⡀⢀⠄⠀⠀⠀⠉⠙⠀⣄⠈⠻⡄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⠉⠀⠀⠁⠁⠀⠀⠀⠀⠃⡦⠺⠿⢾⢶⣵⣄⣠⡀⠀⠀⠑⠂⠡⠀⠈⣷
⢀⡟⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⣀⠠⠀⣠⣀⢀⡀⢠⡀⣀⠀⡀⠀⠀⠀⠀⠈⠁⠙⠶⢶⣤⣄⡑⢿⡼⢈
⢸⠃⠀⠀⠀⠈⠉⠉⠑⠢⠤⢄⣸⠉⠁⠈⠉⠀⠙⠉⠉⠉⠁⠋⠃⠋⠋⠉⠁⠢⠀⠲⠀⠠⠀⠀⠀⠀⠤⠈⣻⣷⢿
⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠑⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡤⡐⠴⠤⢒⠘⢹⣽⣿
⣿⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⠠⠠⢔⡤⣶⣲⠿⠎⠝⠊⠙⠀⠀⢀⠄⠃⢀⡿⣼⣷
⢻⡀⠀⠀⠀⠐⠀⠀⠈⢀⠀⢀⠀⢀⠀⠂⠀⡄⠀⠀⢠⠟⢾⠆⠓⠀⠐⠀⠀⠀⠀⠀⣀⣠⡤⠾⠋⠀⣤⣾⢇⡇⠏
⠈⢧⡀⢀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⢀⢀⡏⣰⢸⠀⠀⢀⣀⣠⣠⣶⢶⠞⠋⠁⠀⠀⠀⣼⠟⠠⢸⠋
⠀⠈⠣⡈⠢⡀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⡠⢡⠞⡴⣿⣸⣶⣰⠶⠞⠚⠛⠀⠀⠀⠀⠀⣠⣴⡿⣛⡰⠙⠁
⠀⠀⠀⠙⢦⣈⠂⠀⡀⠀⠀⠀⠀⠀⢀⠄⢀⣴⣾⣾⣷⣟⢁⠀⠀⡠⡀⠀⢀⢀⠀⢀⣰⣿⣟⠿⠓⠉
⠀⠀⠀⠀⠀⠙⠻⢶⣤⣬⣁⣈⣈⣥⣤⡾⠿⠛⠋⠁⠀⠈⠉⠛⠚⠚⠒⠺⠒⠓⠛⠋⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁⠀⣴⣠⢆⣶⣦⣴⣶⣤⠤⣤⣤⣤⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⣴⣤⣤⣾⠟⠛⠋⠉⠀⠀⠀⠁⠀⠀⠉⠉⠘⢧⣄⣿⣷⡄⣀⡠⠆
⠀⠀⠀⠀⠀⠀⢀⡏⢀⣼⡿⠛⠁⠈⠀⠀⣀⣀⣠⣤⣾⣷⣶⡿⢭⠴⠾⣶⣿⣭⣵⣾⡁
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⣰⣷⣤⣿⡿⣿⠋⠙⠀⠀⠀⠀⠀⢠⣴⠏⣿⢿⡻⣷
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⢠⣴⣼⡿⠛⠻⠁⠀⠀⠀⠀⠀⣄⣀⣠⣶⠇⠁⢰⡧⢸⡃⣿⡀
⠀⠀⠀⠀⠀⠀⣯⣀⣸⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠇⠀⣙⣿⡗⢾⣿⢹⠇
⠀⠀⠀⠀⠀⠀⢻⣾⠏⠈⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⣿⡿⠟⠏⠀⠰⣶⣿⣿⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡀⠀⢠⣤⣷⣾⣿⣿⠋⠁⠀⠀⢠⣤⣾⣿⡿⣽⣽⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⣠⣿⣷⣿⠻⠋⠀⠀⠁⢀⠂⣶⣴⣿⡿⠟⣙⠳⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠉⢉⠀⠀⠀⠀⣶⣤⣼⣿⣿⣟⡋⠡⠌⠿⠿⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣼⣶⣾⣿⣿⡿⠿⣧⡀⣒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠭⣿⣴⣤⣴⡏⡆⢹⡄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣀⠂⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢼⡀⠧⠀⠀⢠⡾⢀⡄⢀⠂⠀⠃⠐⠀⣌⠁⣤⡀⠙⠃⡈⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣷⡐⢦⡀⠀⠀⠟⢡⡿⠀⣾⡄⢸⡆⢹⡇⠙⠃⠀⣰⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣌⠻⣆⢀⠀⠈⠁⠀⠙⠁⠘⠃⠀⠀⠀⢀⠔⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣈⣉⡘⠛⠙⢀⣁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⢰⠀⠐⠀⠠⠄⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠀⠀⢀⣴⡆⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠛⠁⣀⡀⠀⠻⠃⠀⠀⠀⢀⣶⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⡄
⠀⠀⠀⢸⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠰⣿⠃⠀⠀⠀⣀⠀⠀⠈⠿⠁⠀⠘⢿⠇⢠⣦⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⣿⣆⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣴⠀⠀⢀⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣶⡄⠀⡀⠈⠻⠃⠀⠀⠀⠠⠁⢠⠇
⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠻⠋⠀⠀⣿⠇⠀⠀⠀⠉⠀⣴⡄⠀⠀⠛⠁⢸⣿⠀⠀⠀⠀⠀⡠⠀⢠⠏
⠀⠀⠀⠀⠀⢻⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠻⠇⢠⣶⡀⠀⠀⠉⠀⠀⠀⠀⠈⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠛⠛⠛⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⠀⠀⣰⠊⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠀⠀⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⣤⠴⠶⣶⣶⣲⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠲⣶⠒⡒⠒⠒⠒⠒⢶⣶⣶⣒⠦⢤⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠉⠻⣖⢤⡉⠓⢤⡀
⠀⠀⠀⠀⠀⢀⡤⠖⣋⠍⠉⡠⢊⠄⠀⡀⠈⡆⠈⠀⠄⠀⠀⠀⢱⡀⠉⠙⢶⣌⠙⢢⣄⠀⠀⠀⢳⠀⠀⠀⣠⡄⠀⠱⡈⠢⡀⠙⢦
⠀⠀⠀⢠⠞⠁⡰⠁⠀⢀⠎⠀⠘⠀⠀⠇⠀⢘⠀⠀⠀⠁⠀⠀⠀⢣⢀⣤⠀⢣⠱⣌⢋⢣⡀⠀⠈⡇⠀⠀⠉⢀⡠⡄⠈⢆⠙⡄⠀⢳⡀
⠀⠀⡴⠁⢀⠎⠀⠀⠊⠁⠀⢠⠂⠀⢀⠆⠀⠀⢇⠀⠀⠀⠑⠀⠀⠈⢏⠁⠀⠀⢣⠘⡆⢣⠹⡄⠀⢹⠀⠀⠀⠈⠉⠀⠀⠀⢢⠘⡄⠀⢳
⠀⡜⠁⠀⠁⠀⢐⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⢆⠀⠀⠀⠃⠀⠀⠘⡆⠛⠃⠈⡆⠸⡄⢆⢱⠀⠘⡆⠀⠶⠂⠀⠴⠴⠀⠀⠆⢰⠀⠘
⠸⠁⠀⠌⠀⠀⠎⠀⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠘⡄⠀⠀⠀⠄⠀⠀⢹⠀⡠⡀⢰⠀⢧⠸⠀⡇⠀⣇⠀⠒⠒⠀⠀⣀⡀⠀⢸⠀⡆
⡇⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠈⠄⠀⠀⠀⠀⢣⠀⠀⠀⢀⠀⠀⠀⡇⠈⠁⠀⡀⢸⠀⢆⡇⠀⢸⠀⢀⣀⡀⠘⠂⠁⠀⢸⢀⠃⢠
⡇⠀⠀⡁⠀⠀⡅⠀⠀⠀⢀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠰⡀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠇⢸⡆⠈⡇⠀⢸⡄⠀⠀⠀⠠⡴⠀⠀⡄⡘⢀⡞
⡇⠀⠀⠡⠀⠀⢁⠀⠀⠀⠀⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⡃⠀⠀⠀⢱⠀⠀⢸⡄⠙⠃⡀⢸⠀⢠⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⣱⣡⠞
⢹⠀⠀⡘⢄⠀⠘⠀⠀⠀⠀⢣⠀⠀⠀⢀⠀⠀⠀⠀⠀⡕⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠇⡸⠀⡼⠀⠀⠀⡇⠀⠀⠈⠣⠂⣠⣿⠟⠁
⠈⣇⠀⠀⠈⠀⠀⠰⠀⠀⠀⠸⡀⠀⠀⠈⡆⠀⠀⠀⠀⢣⠀⠀⠀⡨⠀⠀⠀⡇⠘⢁⢠⠃⡸⠁⠀⠀⠀⡇⠀⠀⠀⣀⡴⠟⠁
⠀⠘⡄⠀⠀⢢⠀⠀⠇⠀⠀⠀⢃⠀⠀⠀⢃⠀⠀⠀⠀⢆⠀⠀⠀⡇⠀⠀⠀⡇⠀⢂⢎⡜⠁⠀⠀⠀⠀⢧⣤⠶⠛⠉
⠀⠀⠘⢆⠀⠀⢢⠀⠸⠄⠀⠀⠈⢆⠀⠀⠘⡄⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⣇⣼⡿⠋⢀⠀⠀⢸⠓⢄
⠀⠀⠀⠀⠳⣄⠀⠣⣀⠐⠄⠀⠀⠘⡀⠀⠀⢡⠀⠀⢀⠃⠀⢀⠃⠀⠀⠀⢠⡿⠋⠀⠀⢈⠟⡆⠸⣄⡼
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡣⡘⡄⠀⠀⠐⢄⠀⠘⠀⠀⢐⠁⡀⠁⠀⣀⡤⠚⠉⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠦⣤⣤⣤⣱⣤⣤⣤⣶⠴⠖⠚⠉⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡋⠉⠉⠉⠉⠙⠒⠲⢤⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡴⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠔⠀⠔⠈⠀⠀⢀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢺⢷⣾⡀
⢀⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡐⢁⠀⠀⠀⡀⠐⠀⡀⠀⠂⠀⡀⠀⠂⡠⠀⡁⠠⠀⠙⣿
⡼⢰⠃⠀⠀⠈⠉⠉⠓⠒⠲⠤⢤⣀⡀⠀⠀⡞⠀⠠⠀⠀⡀⠊⠀⠀⠁⠀⠠⠐⠀⡀⠐⠀⠠⠊⠠⠁⠀⠄⡇
⡇⣦⠀⠀⠷⠂⠀⠰⠟⠀⠀⠀⠀⠀⠉⠉⠚⠳⠤⣅⣀⠐⠀⠈⠀⡀⠀⠁⠀⠄⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⠇
⡇⢋⠀⠀⢀⣠⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⣝⡳⢤⣈⠀⠀⠊⠀⠀⡠⠀⠀⡀⠀⠀⡐⠀⠀⠀⡄
⢱⠘⠄⠀⠈⠉⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢰⡄⠈⠁⠀⠈⡷⡄⠀⠄⠀⢀⠄⠈⠀⠀⠄⢀⠀⠀⡜⡸
⠈⢧⠩⣄⠀⠀⠾⠇⠀⢠⡆⠀⠀⠀⠻⠂⠀⠀⢠⣄⠀⠀⠀⠀⡸⣸⠁⡀⠄⠀⠀⠀⠀⠐⢁⠐⠁⢠⠞⡴⠁
⠀⠈⠳⡑⢦⡀⠀⠀⠀⠈⠀⠀⣦⠀⠀⠀⣦⠀⠀⠉⠀⠀⢀⡴⣱⠋⠀⠀⠀⠀⠄⠊⠀⠂⠀⠀⠒⣠⠞
⠀⠀⠀⠙⠦⡙⠴⣄⡀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⣀⡴⢋⡔⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⠥⠊⠁
⠀⠀⠀⠀⠀⠈⠓⠬⣁⡁⠤⠤⣠⠤⠀⢤⡀⠤⠖⣋⡥⠖⠉⠛⠺⠦⠤⠤⠤⠤⠴⠶⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣶⣶⣶⣶⣶⣶⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⡿⠿⣿
⣿⡇⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣿
⢻⣇⠀⢿⢹⠀⠀⠀⠀⠀⠀⢠⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⢸⢹⠇⢀⣿
⠸⣿⡀⢸⡾⡇⠀⠀⠀⠀⠀⠈⠋⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀⡟⡾⠀⣸⡿
⠀⢿⣇⠀⢷⢻⡀⠀⠀⠀⠀⠀⠀⠛⠛⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠃⢠⣿⠇
⠀⠘⣿⡄⠘⣧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⢀⣾⣧⠀⠀⠀⣿⣧⠀⠀⠈⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠏⢀⣾⡏
⠀⠀⠸⣿⡄⠘⢧⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠋⢀⣾⠟
⠀⠀⠀⠘⣿⣄⠈⢳⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠁⣠⣿⠏
⠀⠀⠀⠀⠈⢿⣦⡀⠙⢮⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⡴⠋⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠳⣝⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣚⡽⠞⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠙⠳⢯⣝⣲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢶⣚⡭⠷⠛⠉⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣀⠉⠙⠓⠲⠾⠯⠭⠭⠭⠭⠽⠷⠖⠚⠛⠉⢁⣀⣤⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⢀⣀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡀⢴⡀⠲⣶⢀⠉⠻⢷⣄⣠⠙⠳⢦⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⡁⠸⣿⡀⠈⢻⣧⡀⠀⠛⠷⣦⣀⠀⠙⢧⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢸⣿⠀⠀⠻⣿⡀⠀⠹⣧⡀⠀⠀⠘⢿⣧⠀⢠⠻⣄⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠀⣼⣿⠀⠀⠀⢻⡏⡀⠀⠈⣷⡦⠀⠀⠀⢿⣦⠀⠀⠈⢳⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⣿⠀⠤⣼⣿⡄⠀⠈⢏⠻⡏⠀⠀⠉⣷⣄⡀⠀⠈⢿⣇⠀⠀⠈⢧⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⣿⠀⠘⠉⣹⣷⠆⠀⠠⡜⢻⣦⡀⠀⠈⢻⡀⠀⠀⠀⠘⣦⠀⠀⢸⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣷⡀⠀⠀⠰⢿⣖⡀⠀⠈⠠⣷⣅⠀⠀⢨⣿⠀⠀⠀⠀⢹⡷⠀⠈⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⢿⣷⣤⠀⣰⠿⣿⡇⠀⠀⠸⣮⢿⡇⠀⠉⠻⣷⡆⣀⠀⢹⡇⠀⠀⡏⠸⠀⠀⠀⠀⠀⠀⢀⣤⡀⢘⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⣿⣏⡀⠃⠀⠉⢻⣶⡄⠀⠘⠂⢿⡄⠀⠐⢻⣿⠃⠀⠸⠇⢀⡠⠄⠂⠁⠀⠀⠀⠀⢤⡄⣈⡁⠈⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢹⣿⡇⠀⠀⡶⠟⣹⣧⡄⠀⠀⠸⢿⠆⠀⠘⠟⣀⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢙⣷⡀⠀⠀⠀⢀⣿⣧⣤⡘⠀⠈⢃⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠘⠷⠀⠛⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠛⢦⣀⠀⠀⠋⠙⣿⣆⡀⠀⠌⣦⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠷⠀⠀⡼⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠙⠛⢷⣦⣄⡀⠙⠿⣿⣈⢊⢧⡀⠀⠀⠀⠀⠀⣷⠀⠰⠆⠘⠇⠀⠹⠆⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠜⡛⠛⠒⠚⠉⠀⠁⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠓⠤⠤⣄⠀⠀⡀⠀⠤⠔⡋⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠲⣦⠀⢤⡄⠀⡷⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡇⣸⣷⣠⠇⢚⢹⣧⢘⣿⠀⣶⡩⠗⢸⡗⠛⢸⡗⢻⡗⣿⡆⣴⡋⠗⢸⡟⢰⡏⢹⡆⢹⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠻⠟⠀⢿⠼⣿⠐⣿⠀⠻⣦⠄⠸⡇⠀⢸⠇⢸⠇⢻⠇⠻⢧⡀⠸⡇⠘⢧⡼⠃⢸⠇⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⣠⡞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢦⡀
⢀⡼⠁⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠏⠳⣄
⢻⡀⠀⠀⠀⠙⠦⣌⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣠⠞⠁⠀⠀⢹
⠀⠙⢦⡀⠀⠀⠀⠈⠓⠦⣌⡙⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⢋⣡⠴⠋⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠉⠓⠶⢤⣌⣉⣉⠛⠛⠓⠒⠒⠛⠛⣋⣉⣩⡤⠶⠚⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠖⠶⣦⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣥⣶⠶⠾⢷⣛⣿⣮⣝⣎⡼⢱⠦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⢩⣶⣶⠶⢻⡟⠉⠉⢭⡟⠻⠧⠝⢋⣻⠆
⠀⠀⠀⠀⠀⠀⠞⣡⠾⠋⣠⡤⠶⡟⣁⣴⡿⠟⢁⡜⢹⣇⣆⢻⣿⣧
⠀⠀⠀⠀⠀⢸⠟⣷⡞⠉⠋⣀⣴⡾⠟⠋⢠⣾⡿⣤⡾⢸⠙⡏⢿⣻⡀
⠀⠀⠀⠀⠀⢨⣾⠛⠁⣀⣼⡿⠋⠀⢀⣴⣿⠋⢀⣿⠃⣸⡀⣿⠈⣯⠁
⠀⠀⠀⠀⠀⢸⠃⢠⣼⣿⠋⠀⢀⣴⣿⠋⠀⢀⣼⠇⠀⡏⢈⡟⢠⣿⠀⠀⠀⠀⢀⣀⡠⠤⠤⠲
⠀⠀⠀⠀⠀⠀⢦⡟⠛⠛⢦⣤⣾⡟⠁⠀⣰⣿⠏⣀⣰⣿⣸⡧⠯⠇⠂⠒⠈⠉⠁⢀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢨⣿⡟⠁⢠⣴⡿⡹⣦⠀⠀⠀⠀⠴⣠⣤⣀⡀⣀⣄⢤⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢿⡟⠀⢀⣴⠞⠻⣧⣿⡀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠂⠙⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠐⠩⠭⠭⠥⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⡉⠀⠀⠀⠤⠠⠄⠀⠉⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢀⠠⠐⠁⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠁⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠈⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⢼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠊⠀⠀⠠⠐⠀⠀⠀⠁⠈⠉⠁⠀⠀⠉⠈⠐⢠⣹⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠐⢈⠀⠀⠀⠀⠀⢀⡀⢀⢀⠠⠀⠀⠀⠔⠀⠀⠐⠀⠀⠈⡗⢢⡇⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢐⡬⠀⠁⠄⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⡷⠸⣳⢖⡽⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⡶⣄⣠⣷⠀⣷⢄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⡇⢀⡨⠥⠤⠶⠞⠁⠀⠘⡆
⠀⠀⠀⠀⠀⣶⠞⠁⠠⠀⠸⡄⠈⠂⠈⠐⠤⠀⡀⠀⠀⠀⢰⠞⠲⠦⠶⠶⠴⠖⠒⡒⠦⠒⠛⠙⠉⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠙⠒⡌⠱⡀⢻⡀⠀⠀⠠⢀⣀⡀⠀⠀⢨⡏⢸⢰⠀⢀⠀⠠⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⢀⠀⡇⡇
⠀⠀⠀⢴⠒⠒⠒⠚⠁⢀⠠⠄⠳⣄⠀⠀⢀⡀⠀⠑⠀⡾⠁⠘⠈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠠⡎⠀⠀⠠⠊⢀⢈⣀⣀⠀⠈⠳⢤⣄⡀⠑⠀⢰⠃⠀⠀⢁⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡸
⠀⠀⠀⢸⠀⠀⠁⠀⢠⠋⠀⠈⣧⠀⢰⠀⠐⢍⠉⠓⠺⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣰⠃
⠀⠀⠠⠯⠤⡤⠖⠦⠟⠀⠀⢠⣏⠀⠀⡆⢀⢰⠉⠉⢦⣹⣆⠀⠀⠀⠁⡀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡠⢔⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣃⡤⠽⠇⠀⠀⠀⠈⠙⠦⣤⣀⣈⠒⠄⣀⠐⠂⠀⢀⣀⣲⡬⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡊⠉⣍⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠉⠀⠀⠀⠀⠙⡳⢄
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⣄
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡠⢀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡠⠦⠁⢀⠄⠀⠀⠀⠀⠀⢰
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠈⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡜
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠤⠐⠀⠈⡈⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⡂⢀⠀⠀⠀⠀⠄⠄⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠘⣆⠀⠘⡀⠀⢔⠈⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠈⢦⡀⢷⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠙⢾⣧⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣈⣙⣲⣦⣤⣤⣤⣴⣿⣿⣛⣋⣛⣛⣛⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠘⠟⠻⠿⠛⠿⠶⠚⣶⡿⢶⣄⡀⢉⡀⠢⣄⡀
⠀⠀⠀⠀⠀⢀⠠⠚⠀⢀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣤⡀⢈⠙⢱⣦⡀
⠀⠀⠀⠀⣐⣥⡶⠖⠳⠿⠷⠾⠿⠿⠿⠿⠿⣷⣿⣤⣦⣀⠀⢀⠀⠀⠈⠙⢻⡄⠀⠙⢏⠂
⠀⠀⠀⡰⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠐⠛⠶⢖⣤⣄⡀⠉⢲⣆⠈⣡⠣
⠀⠀⢀⡏⢠⣤⣴⣶⡾⣤⢦⡠⡄⢀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠈⠙⠳⣤⡌⢆⢨⡇
⠀⠀⢘⠷⠟⠁⠀⠀⠉⠉⠉⢶⠈⠁⠊⠛⠋⠉⠉⠀⠚⠋⠑⠒⠚⠛⠛⠂⠤⣀⠀⠙⢆⠆⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣷⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂
⠀⠀⠀⢿⣄⣀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣀⡠⠶⠒⠋⠾⡥⠉⠐⠒⠂⠀⠀⠀⠀⢀⡨⠟⣁⠸⠀⠀⠀⠀⠀⠰⢀⠈⠀⠘⠂
⠀⠀⠀⠀⢎⠙⠿⠛⠿⣷⣾⣳⣶⢾⣶⣋⣡⣀⣀⣀⣀⣀⣀⣀⢤⣤⣤⣤⣤⡤⠞⢋⠴⠑⢸⠇⠀⠀⠀⠀⠀⠀⠁⢠⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠳⣄⠀⢀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠀⠋⠁⠁⣠⠴⠞⢁⠐⢠⠂⠀⠀⢀⡐⠀⢠⠀⡤⠨⠁⠀⠈⠿⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠙⠿⡻⠶⣤⡄⣀⣀⣀⣀⣦⣀⣀⣀⣀⣀⣀⣤⣤⠴⠞⠋⠁⠀⠜⢃⡔⠀⠀⠀⢀⡀⠀⠐⠧⣀⠃⠀⠁⠀⠀⠀⣀⡤⠚⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡈⠀⠀⠈⠈⠛⠋⠙⠃⠉⠁⠀⠀⠀⣀⡤⠆⠋⡠⠔⠁⠀⠀⠀⠀⠀⠈⠓⠢⠤⢀⣈⣁⢀⣉⣉⡉⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠦⠤⢄⣠⣤⣀⣤⣀⣂⡉⠥⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⠛⠛⠛⠛⠿⠿⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⠁⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣰⣷⣤⣬⡿⠷⠜⠳⡶⠛⠛⢷⣿⢦⢀⡈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣼⣷⣶⠿⡟⠋⠉⠁⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠈⠳⣦⣽⣿⠧⣀⡦⠝⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣼⣿⠋⠁⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠷⣿⠇⠤⠒⠛⣶⣿⣶⣴⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⢠⣾⣶⣼⣿⡿⣿⠉⠉⠃⠀⠀⠀⠀⠀⢠⣴⠏⣹⠿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣤⣤⣿⠿⠛⢿⠀⠀⠀⠀⠀⠀⢤⡀⠀⣰⣶⠊⠀⠐⣿⠀⡟⢸⣷
⠀⠀⠀⠀⠀⠀⢸⡇⡀⢰⣶⡮⠍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠉⠀⠑⣿⡿⢤⣿⠞⣿
⠀⠀⠀⠀⠀⠀⠘⣷⣽⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣾⣿⣿⣿⠋⠀⢠⣀⣿⣿⡁⣲⣿⣥⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⠀⠀⠀⢠⣄⣰⣿⣿⡿⠟⠛⠀⠀⠀⠀⣼⣿⣿⢿⢱⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣳⣤⣠⣿⣿⡿⠛⠛⠿⠀⠀⢀⠀⣠⣽⣿⡿⣿⣃⢻⣿⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⡿⢿⡿⠃⠉⠀⠀⠀⠀⠐⣌⣼⣿⣿⣿⠋⠣⣔⣪⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⢀⠀⣀⣠⣿⣶⣾⣿⠿⢟⠉⠀⠒⠀⠛⠛⠛⠻⠁⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⣶⣿⣿⣿⣿⠿⠟⠛⣯⡆⢸⡥⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠤⣧⣤⣤⣴⣿⢰⠈⣧⠀⠀⣴⠆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⣄⠐⠀⣸⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⠸⠄⠀⠀⢠⡶⠀⡤⠀⡒⠀⠰⠀⠐⠀⣌⠁⢢⡀⠈⠻⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣹⡄⠲⣤⠀⡈⠁⠾⠃⣼⠃⢠⣆⠀⣴⡀⢻⡇⠘⠟⠀⠀⡜⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣹⣆⠘⢷⡀⡀⠀⠀⠋⠀⠘⠟⠀⠻⠃⠀⠁⠀⠀⠀⠜⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠙⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣈⠙⠓⠢⠄⣤⣤⡤⠀⠄⠀⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⠤⠤⠤⠒⠊⠁



⣿⠿⠿⡿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⡤⡂⠄⠰⠛⠚⠒⠶⠶⣤⡑⢦⡀
⠀⠀⠀⠀⠀⢦⠀⠀⠈⠑⠀⠁⠀⢁⣴⣾⠇⠀⠀⠀⢀⣎⠠⠤⠤⠶⠶⠶⠶⠶⢦⣤⡙⣜⡟⡆
⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⣀⣒⣾⠿⠗⠁⠀⠀⠀⠀⢸⠁⠀⠤⣴⠦⣴⠶⠶⠶⠦⠴⠒⠄⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⠉⠉⢀⣀⣀⣠⣤⡴⣾⣵⣧⡟
⠀⠀⠀⠀⠀⣀⣤⣖⣾⣿⡶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣯⣭⣍⣩⣽⣭⣶⣾⣿⡿⠋
⠀⠀⠀⠀⣼⣿⣿⣿⣯⣤⣤⣤⣄⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⢰⣿⣿⣿⡟⠿⢿⣇⣄⣡⣤⣤⢥⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠒
⠀⠀⠀⠈⣿⣿⣿⠁⡀⠸⣭⣴⡶⢟⣿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⢿⣿⣷⣶⣴⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿

⡏⠉⣟⠉⠉⡏⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠠⠤⠤⠤⡤⠤⡤⠤⢄
⡇⠀⢹⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⡾
⢻⠀⠸⡄⠀⢅⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠠⣿⡟⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⣿⣧⠀⠀⢻⣿⡄⢠⣶⡄⠀⠀⢀⡄⢰⠃⢀⡇
⠸⡇⠀⢣⠀⠀⠈⢙⠄⠀⠀⠀⠉⠁⢀⣀⠀⠀⠁⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡀⠉⠀⠀⠻⡿⠊⠰⣎⠀⡎⠀⣸⠁
⠀⢿⡄⠈⢇⠀⠐⠡⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⡇⠀⣶⡦⠊⢸⣿⠀⠈⠛⣄⢠⡏
⠀⠸⣿⡀⠈⢦⠀⠈⢰⠃⠀⠀⠀⠀⢀⣠⡀⢠⣶⡆⠀⢠⣶⡀⠀⠀⠈⠋⠀⢰⣦⠀⠀⠈⠁⡠⢋⣤⠀⠈⠁⠀⠀⠀⠈⠻⣅
⠀⠀⠹⣿⣄⠈⠳⡀⠀⠀⡅⠀⠀⠀⢾⡿⠁⠸⠟⠁⠀⠸⠿⢀⡀⠀⠀⠀⠀⠘⠿⠀⢸⡿⠊⠀⠸⠿⠀⠀⠀⢰⣶⡀⠀⠀⠈⢣⣄
⠀⠀⠀⠹⣿⣦⡀⠘⢦⡀⠉⠑⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣎⠀⣰⣦⠀⢠⣤⠀⠀⠀⠛⠁⢠⣦⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠹⣿⣿⣦⡀⠉⠢⣄⠀⠙⠢⠔⠩⡀⢄⠀⠀⣀⠀⠈⠁⢀⡀⠀⠀⡠⠊⢾⠟⠀⠛⠃⠀⠸⠟⣠⡀⠀⠀⠀⠘⠿⠀⢾⣧⠀⠈⠷⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⠈⠙⠢⢄⡀⠀⠀⠀⠙⠉⠀⠑⠠⠒⠁⠑⣤⠚⠣⣀⠀⠀⣠⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠸⠣⠤⠊⠀⡨⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣄⣀⠈⠙⠒⠲⠤⢤⣄⣀⣀⣀⣠⣎⠉⠲⢄⡀⠑⠊⠰⠒⢄⡠⠔⣄⠀⣀⠦⡀⠀⡰⠢⠴⠀⠀⣀⠴⠋⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣘⣿⣿⣷⣦⣀⠉⠓⠦⢄⣀⣀⠀⠀⠀⠉⠀⠀⠈⢈⣀⣠⠤⠖⠋⢁⣠⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡉⠉⠉⠙⠛⠛⠉⠉⠉⣁⣠⣤⣴⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⣠⠀⢀⠀⠑⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠒⢀⡀⢁⣌⠃⠜⠢⠀⡠⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠨⣧⡅⠠⡄⠀⠀⣀⠀⡈⠃⡄⠀⡩⢎⠰⠵⣢⢈⡾⢃⢈⣄⢓⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⢉⡅⡁⠤⠀⠂⠀⠉⣆⢲⣬⣥⡼⢸⢗⢍⣾⡵⠐⢤⢬⡬⡄⠀⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣛⡠⠶⡆⠚⠘⠉⢵⢆⢩⡵⣾⡎⠾⢮⣎⣵⣬⣻⠰⣘⠠⠋⠑⣦⢁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⡴⣷⡜⢇⣲⣜⣧⣅⡳⢳⣞⣷⣷⣿⣰⣽⣯⣧⣭⢧⠂⡤⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣳⣿⣎⣥⠎⡎⢳⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⢺⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⣯⣿⣷⣿⣷⣿⣧⢹⣩⣿⣿⣿⣻⣿⣿⣿⣿⡿⠋⠀⠀⣀⠠⣄⣤⣲⣮⠱⢀⠜⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⡫⢿⡻⣻⠙⣝⣵⣰⣿⣸⠿⠟⢋⡁⠔⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢷⠨⠹⡆⠀⠉⠑⠣⠽⠟⣹⣭⠏⠽⠥⠀⠂⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣠⠖⠋⢉⡀⢢
⠀⠀⠀⣴⠋⠁⠀⠀⠈⠛⠀⢢⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢠⠀⠀⠀⠀⣠⠖⠒⠒⠒⢦
⠀⢀⡾⠁⠀⣀⠀⠐⠆⠀⠀⠀⢣⢰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠔⠊⠁⠀⠈⠁⠀⡏
⠀⡾⠀⡀⠀⠉⠀⠀⣠⠀⠀⠀⠀⢣⢧⠀⠈⠁⠀⠀⠠⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣄⠀⠀⢰⠇
⠰⡇⠀⠉⠀⠀⠀⠀⠀⢀⠀⠘⠂⠀⢻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠓⠂⠤⠬⢁⣀⡀⠀⠉⠃⠀⠀⠀⠀⢣⠳⣄⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⢠⡄⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠀⢤⠀⠧⠈⠳⣄⠀⠀⠀⠀⠚⠀⡀⠀⠛⠀⠀⠀⠀⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣠⠔⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠚⠋⠁⠠⠐⠂
⠀⠀⠀⠀⠀⡀⣴⠾⢋⣥⠊⣠⠊⠹⡜⢬⠻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⢀⣈⠤
⠀⠀⠀⢠⢊⣼⠋⣰⡿⠃⢘⣿⡄⢰⣿⢸⡇⢸⡇⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢆⠀⠀⠈
⠀⠀⢰⣵⡿⠃⣸⡿⠁⠀⣿⡏⠀⣼⡏⣾⠇⢀⣿⡀⢹⣷⡀⠀⠀⠀⠀⠀⠒⠦⢤⠀⢆⠀⠀⠀⢀⠀⣀
⠀⢀⢻⣿⠀⢀⣿⡆⠀⣾⣟⠁⣼⣿⠃⣿⡇⠀⢹⣷⠸⣿⣧⠀⠀⠀⡀⢀⢠⠀⠀⠳⠬⠄⠀⡀⡠⠊⠀⠑
⠀⠘⢸⡇⢀⣸⣿⠀⢸⣿⡟⠀⣹⣿⠀⣽⣟⠀⢨⣿⠃⢻⣿⠀⠀⢘⠀⠀⡈⡐⡀⠀⠀⢀⠀⠀⠀⠠⠤⠖⡀
⠀⢸⢻⡇⢸⣿⡁⢀⣼⣿⠂⢰⣿⣏⠀⢻⣿⠂⢼⣿⠀⢸⣿⠀⠀⢠⠓⠀⠈⠀⡌⢲⠀⡌⡠⢀⢤⠤⠤⢎
⠀⠈⡾⣷⠈⣿⡇⠘⣿⡧⠀⢰⣿⣿⠇⢸⣿⠀⢨⣿⠇⣾⡏⠀⠀⠀⠉⠐⣢⡄⠈⠞⢰⢁⠔⠁⠀⠀⢠⠚
⠀⠀⠘⣿⡀⢿⣧⠀⢻⡇⠀⠀⣿⡏⠀⢸⣿⡀⢀⣿⠀⡟⠀⠀⠀⢀⠊⠁⠀⠀⠀⣀⡇⠀⠀⠤⣒⡂⠤⠁
⠀⠀⠀⠈⢷⡀⠻⣄⠈⣧⠀⠀⣿⡇⠀⣼⠿⢡⡾⣣⠎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡜⠈⠣⣄⠀⠀⠨⠂
⠀⠀⠀⠀⠀⠈⠲⢌⣣⣌⠻⣼⣿⣠⡾⢟⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠁⠒⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⣰⣧⣆⣾⠷⠶⠿⡶⠶⠶⣶⣶⢀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠁⣰⣷⣶⠾⠏⠉⠉⠀⠀⠀⠀⡀⠀⣀⣀⠀⢈⠳⣦⣿⠷⣀⠤⠚⠃
⠀⠀⠀⠀⠀⠀⣼⣁⣴⠿⠏⠀⠀⢀⠀⢠⣤⣴⣶⣿⡿⠻⠟⠐⠋⠛⠿⣿⣶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⣿⠿⠁⠀⠀⠀⣴⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⣀⡰⠟⢡⡏⢻⢹⣧
⠀⠀⠀⠀⠀⢸⡏⠀⣀⣤⣿⡟⠛⠁⠈⠃⠀⠀⠀⠀⢀⣷⣴⣼⡟⠁⢤⣼⣇⣸⣤⣿
⠀⠀⠀⠀⠀⠘⣇⣶⡿⠏⠉⠀⠀⠀⠀⠀⢀⠀⣀⣴⣿⣿⡿⠋⢁⣀⣾⣿⢩⣿⣇⣿
⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⢠⣀⣾⣿⡿⠿⠛⠉⠁⠀⣨⣿⣿⡿⣾⣿⣻⠇
⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⢸⣦⣤⣿⡿⠟⠛⠻⠀⡀⣀⣀⣬⣿⡿⢿⣕⢿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠻⠟⠁⠀⠀⢀⡀⢀⣤⣿⣿⡿⠏⠑⣶⣽⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣂⣤⣠⣤⣾⣿⣿⣟⠛⢓⠂⠈⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣟⣻⣋⣍⣀⣿⡃⢸⡀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢻⣹⡈⣇⠀⠉⢀⣤⠀⡀⢠⠀⢠⠀⠀⢀⠸⢀⠀⠙⠆⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⣧⠠⣄⠀⠘⠁⡾⢡⡆⠀⣆⠀⣤⠘⣷⠘⠟⠀⠀⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⡈⠷⡄⠀⠀⠘⠁⠈⠟⠀⠿⠀⠉⠀⠀⢀⠞⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡙⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣈⣉⠃⠚⠚⠒⠂⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡔⣶⡿⣷⡶⢿⣷⣤⡶⣦⣾⣯⣭⠉⠑⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠙⠻⡷⣿⢷⣶⣞⡁⠀⠘⠻⢆⣄
⠀⠀⠀⠀⠀⡠⢚⣩⣠⣤⣴⣭⣤⣴⣤⣴⣧⣤⣤⣄⣴⡀⢀⠀⠈⠂⠀⠈⠉⠻⢶⣶⡀⠀⠻⣷⢄
⠀⠀⠀⠀⡰⡖⠛⠋⠁⠈⠉⠉⠉⠙⠋⠉⠈⠉⠙⠟⠛⠻⣿⣶⡆⣤⣆⣀⣀⠀⠀⠈⠿⣄⠀⠈⢦⠱⡀
⠀⠀⠀⢸⠅⠀⠀⠀⢀⣠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠫⣿⠶⣦⣀⠈⠻⠄⠀⢿⡑⡀
⠀⠀⠀⡿⢀⣾⣶⠿⣿⣟⣶⣳⡴⠶⣦⢤⣄⢠⣄⣀⣀⡀⢀⣀⣴⠀⠀⣀⣠⣀⠀⠀⠙⠳⢶⡘⢆⢸⡁⠂
⠀⠀⠀⡟⡟⠉⠠⠀⠀⠀⠈⠉⠹⡇⠉⠈⠈⠉⠁⠀⠁⠈⠈⠙⠉⠙⠛⠉⠙⠙⠓⠒⠤⣀⠀⠙⣜⢌⣇⣾⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⢆
⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣘⣞⢊⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠌⠁
⠀⠀⠀⢸⣧⣀⡀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡶⠒⠿⠽⣯⡞⠉⠶⠖⠂⠀⠀⠀⠀⠀⣀⡽⠿⣁⡸⠀⠀⠀⠀⠀⠀⠴⢀⠉⠀⠘⠃
⠀⠀⠀⠀⢱⡛⠻⡶⠿⢿⣷⣶⣶⣴⣶⣷⡶⠛⣉⡀⠀⡀⠀⡀⢈⠀⢀⣤⣀⣀⣀⣠⣄⡴⠖⢫⡜⡃⢹⠇⠀⠀⠀⠠⠈⠀⠐⠃⢠⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠱⣔⠐⠀⠀⠘⠋⠉⠉⠁⠉⠉⠉⠘⠙⠛⠻⠿⡿⠿⠿⠓⠉⠟⠉⠋⠉⣡⣴⠚⠁⠜⢀⠌⠀⠀⠀⠠⠂⠄⡐⠀⡀⢘⠃⠀⠀⣿⡆⠀⣆
⠀⠀⠀⠀⠀⠀⠘⢳⣦⣬⣤⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠁⢀⡶⠃⡤⠊⠀⠀⠀⠀⠃⠂⣴⡇⢼⠃⢠⠂⠀⠀⠀⠀⢀⣨⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣉⡛⠣⠖⠚⠛⠟⠿⣿⠾⠶⡏⠶⠶⠚⠛⠛⠙⠁⢀⡀⡴⠂⢀⡰⠋⠀⠀⠀⠀⠀⠳⢤⣄⠈⠙⠒⠠⠄⠤⠤⠴⠶⠞⠋⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⡤⠰⠚⢋⣁⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠐⠒⠒⠂⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠖⠲⠶⠷⠘⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢀⡤⢂⠀⢤⠶⠶⠶⠶⣤⣤⡀⠲⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠦⠄⠠⠄⠐⠂⢂⣠⣿⠁⠀⠀⠀⠀⣠⠋⠀⢁⣀⣤⣤⣤⣤⣀⣀⡀⠙⢧⡙⣷⣄
⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⣀⣠⣶⢟⡿⠃⠀⠀⠀⠀⢀⡗⠋⠉⠉⢁⡈⢉⣀⣀⣉⣉⠉⣙⣂⠑⣃⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠭⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⡇⠒⠂⢻⣯⡝⠛⠛⠛⠉⠛⠋⢉⣉⡅⡞⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠦⣄⣀⣀⣀⣤⣠⣤⡶⢶⢛⣿⣾⣷⡿
⠀⠀⠀⠀⠀⢀⣠⣶⣿⣽⣿⣿⠷⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣥⣤⣬⣭⣴⣧⣶⡿⣿⣿⡿⠋
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣥⣤⣤⣤⣀⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⣿⣛⣉⣈⣉⣩⣭⣽⡄⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄
⠀⠀⠀⠀⢻⣿⣿⣟⡷⠀⠈⣿⣛⣩⣭⣿⢾⣾⠈⠀⠀⠀⠀⠀⢸⠆⠀⠀⢀⠀⠄⠄⠀⠀⠀⠀⠀⠂⠀⠀⡆
⠀⠀⠀⠀⠈⢿⣿⣿⣦⣍⡀⡹⠿⣿⣽⣴⡿⠃⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠐⠀⠀⠁⠒⠠⠄⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠟⢙⣛⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢦⣤⣤⣤⣤⠴⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣩⣛⣟⣫⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠉⢍⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠙⠒⠘⠃⠀⠀⠀⠈⢿⠦⣀
⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠳⡄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠄⡀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡠⠴⠉⠀⡠⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⡈⠁⠁⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⡼
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠠⠄⠒⠈⠃⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠙⠅⠀⠀⢀⠀⢀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠹⡄⠀⠀⡆⠀⠀⢀⠠⠒⠉⠀⠀⠀⠐⠤⠦⣐⣐⠨⠤⠥⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠹⣄⠀⢰⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡤⠚⠁
⠀⠀⠀⠘⢦⡈⣇⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣶⣦⣤⣴⣾⣛⣛⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡇⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣤⣿⣟⣒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⣽⡾⢋⣽⠟⢹⣿⢠⣇⠀⠈⠙⢶⣮⣕⢄
⠀⠀⠀⠀⠀⢀⠞⣵⡿⠋⣰⣿⠏⠀⣼⡟⢸⣿⡀⠀⠀⠐⠈⢿⣇⠱⣄
⠀⠀⠀⠀⢠⠏⣾⡿⠁⣠⣿⠟⣀⣴⣿⠀⠀⣿⣇⠀⠀⠀⠀⠁⢻⣷⠘⢆
⠀⠀⠀⠀⡎⣴⣿⠁⣾⣿⡏⠀⢹⣿⡏⠀⠀⣿⣿⠈⠀⠀⠀⠀⠀⢹⣦⡈⣆
⠀⠀⠀⢸⠃⣿⡏⠀⣿⣿⠇⠀⢸⣿⡧⠀⠀⢻⣿⡠⠄⠀⠀⠀⠀⠀⣿⣧⢸⡀
⠀⠀⠀⢸⢸⣿⡇⠀⣿⣿⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⢀⡀⠀⠀⢠⢸⣿⡄⡇
⠀⠀⠀⢸⢨⣿⡇⠠⣿⣿⠀⠀⣾⣿⡇⠀⠀⢾⣿⡇⠄⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠚⢹⡀
⠀⠀⠀⢸⡈⣿⡇⠠⣿⣿⠀⢠⣼⣿⡇⠀⠀⢸⣿⠇⠀⠠⠄⠀⠀⠀⠀⣿⣇⠧⠤⠖⠒⠉⠉⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣇⢸⣷⠂⢻⣿⡀⠀⢸⣿⣧⠀⠠⣼⣿⠈⡁⠀⠄⠀⠐⠀⠁⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⣞⣿⠀⢸⣿⡇⠀⢸⣿⡇⠀⠀⣞⠉⠁⠀⠀⠀⠀⡀⠈⠠⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠈⢿⣦⠨⣿⡇⠀⢸⣿⡇⠀⠀⣿⡀⠄⠀⠀⠀⠀⠁⠀⢀⠀⠀⠰⠄⠀⠘⠂⠀⠈⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⣧⠀⢀⣿⡄⠀⢹⣿⣿⣌⠢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢬⣿⣄⣀⣿⣟⣠⣻⣷⣦⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠙⠛⠶⠦⠤⠤⠤⠤⠤⠤⠤⠖⠒⠉⠁
⣶⣶⣶⣶⡶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⢶⣶⣶⢶⡶⣶⢶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⣤⢸⣭⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠄⠀⠲⣣⣏⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠐⢻⣷⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡈⠟⡃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢰⣄⠀⣀⣀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠐⠸⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⡠⠈⠁⠋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⢠⢴⠀⠠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠼⣀⢸⠘⠀⠠⠧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠢⢀⡏⠈⠁⠀⠈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⢆⡀⠀⠁⠰⠊⠀⠀⠀⠀⠀⠘⡐⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠹⠈⣀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠛⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⣶⡽⣟⣷⡂⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠄⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠍⠉⠉⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⣀⣀⣀⣀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢰⠃⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⠳⠶⠶⢶⡛⣛⣛⣛⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣾⡄⠀⠀⠀⠀⢸⠋⠉⠉⠉⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢻⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠛⠉⠉⠉⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⣶⢦⡀⠀⠀⠀⠀⠀⢀⣴⡶⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣿⣤⣿⡇⠀⠀⠀⠀⠀⣾⣤⣾⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⣤⣤⣤⣤⡄⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⠛⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢀⡞⠁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⢠⡞⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⢠⡿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡤⠤⠤⠒⠒⠛⣦
⠀⠈⠳⣦⡙⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣉⡼⠗⠒⠛⣉⣭⠟⠉
⠀⠀⠀⠀⠙⠳⣦⣍⡓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⣋⣡⠴⠚⠉⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣭⣍⣙⡒⠒⠒⠶⠶⠶⠶⠒⠒⠒⢚⣋⣉⣭⡤⠴⠒⢋⣉⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠭⠭⠭⠭⠴⠖⠒⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⢛⣛⣋⣉⣉⡙⢿⣍⠷⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⣥⣾⡿⠿⠛⠛⣟⣛⣻⣿⡶⣌⣻⣄⡿⢸⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⣷⣦⣤⣴⠶⣿⡛⠋⠉⢩⣭⡽⠿⣿⣇⣹⢟⡺⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢁⣤⡾⠟⠋⢉⣁⣴⡿⠃⢀⣤⣴⣾⠃⢀⡶⢺⡇⢄⢹⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣋⣶⡟⣉⣀⣤⡾⠛⠉⠿⣢⣶⣿⡿⠛⣧⣤⡞⠀⣸⢿⣼⣦⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠟⣹⣾⠟⠁⠉⢁⣠⣾⣿⠿⠋⠉⢀⣶⣿⡿⢶⣾⡟⠸⡇⢹⡆⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⣉⣴⡿⠟⠀⠀⣰⣿⣿⠛⠁⠀⠀⣠⣾⡿⠟⠀⣼⣿⠀⢠⡇⢸⣷⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⢠⣾⡿⠟⠁⠀⠀⣴⣾⡿⠛⠁⠀⢠⣿⠃⠠⣿⠃⢺⣿⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣤⣿⣿⣿⡅⠀⠀⢠⣾⣿⡿⠀⠀⢀⣤⣿⠟⠀⢀⣿⠀⣸⠇⣠⣿⠇⠀⠀⢀⣀⣠⠤⠴⠖⠚⠋⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠉⠉⠙⠻⣦⣤⣾⣿⡋⠀⠀⢠⣾⣿⡏⣀⣀⣸⣿⣧⠿⠤⠿⠚⠒⠋⠉⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣸⣿⡿⠋⠁⢀⣤⣿⡟⣿⣶⡄⠀⠀⠀⠀⢀⣴⢄⣀⡀⠀⠀⠀⠀⡀⣤⡀⠛⠃⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣴⣿⣿⠃⠀⠀⢉⣹⣿⣸⣹⣿⡃⠀⠀⠀⠀⠀⠁⠘⠙⠻⠛⠗⠘⠇⠛⠈⠁⠀⠀⠀⠀⢀⢯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢥⣀⣀⣴⣿⠋⠀⠹⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠙⣿⡟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⣿⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣭⣒⣒⠦⠤⠤⠄⢂⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢱⠀⠀⣠⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢦⡈⢣⣼⠀⣼⣁⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡖⠊⠁⠀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⢷⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠒⠚⠉⠉⠀⠀⢳⠀⠀⠀⠁⡇
⠀⠀⢠⢤⠤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⠶⠖⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉⣟⠀⣠⣆⠀⣸⢆⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠈⠃⠀⠀⠀⢠⠀⠀⠀⡀⡇
⠀⠀⢸⢰⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠢⠼⠀⠰⠠⡀⠀⠀⠄⠀⠀⠀⢃⡇
⠀⠀⢸⡀⡄⠀⠀⠐⠀⠀⠀⠀⠀⣖⠃⠀⠀⡠⡄⠀⠀⢀⡄⠀⠀⠀⠂⡀⠀⠀⢆⡱⠀⠀⠀⠀⠀⠀⠑⠃⠀⡐⠀⠀⠀⠈⣸
⠀⠀⠀⢧⢁⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⠣⠃⠀⠀⠠⡼⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠈⡑⠆⠀⠀⠀⠀⡐⠀⠀⠀⢀⢣⠇
⠀⠀⠀⠈⣆⢆⠀⠀⠀⠱⡀⠀⠀⢎⡅⠀⠀⠀⢀⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠉⠁⠀⠀⢀⠜⠀⠀⠀⠀⢄⡏
⠀⠀⠀⠀⠘⣎⢢⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⢸⢱⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⢊⡞
⠀⠀⠀⠀⠀⠘⢦⡱⡀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠱⣌⠢⡀⠀⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⠀⠀⠀⢀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣩⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣑⡢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⣋⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠭⣭⣁⣐⠒⠂⠀⠀⠀⠒⠒⣂⣉⣩⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⡠⠐⠈⠉⠉⠑⠢⡀⠀⢀⠄⠒⠈⠁⠒⢤⡈⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⢖⠁⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⡠⠒⡟⠉⣹⠉⠉⠉⠉⠉⠉⠉⠉⠉⢡⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠁⠀⠀⡤⣤⠀⠀⠀⠀⠓⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⢲
⠘⠀⢰⡇⠀⡟⠀⠀⠀⢠⣶⡖⠀⠀⠀⠈⡄⠀⠀⠈⠛⠁⠀⠀⠀⡘⠀⠀⠀⠙⠋⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⢸⡆⠈
⡃⠀⢸⡇⠀⡇⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡠⠊⠙⢄⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⢸⡇
⡇⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠐⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⢸⠀⢠
⡇⠀⠸⡇⠀⢿⠀⠀⠀⠘⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣼⠀⢸
⡅⠀⠀⣇⠀⢸⡀⠀⠀⠀⢂⠀⠀⠀⠈⠑⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡇⠀⡼
⢠⠀⠀⢹⡀⠀⢧⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⠀⠻⠿⠗⠀⡼⠀⢠⠇
⠀⡆⠀⠈⣧⠀⠘⣆⠀⠀⠀⣀⠀⠈⠐⠀⠤⠀⠀⠀⠀⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡞
⠀⠘⡄⠀⠘⣆⠀⠘⢆⠰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡆⠀⠻⠿⠷⠀⠀⡴⠁⠀⡜
⠀⠀⠘⠄⠀⠘⢦⠀⠈⠳⡀⠀⠀⣴⡿⠂⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠐⣿⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⠎⠀⢀⠞
⠀⠀⠀⠈⠢⡀⠈⠳⣄⠀⠈⠲⣄⠉⠀⠀⠀⣰⣿⠀⠘⠟⠁⠀⣀⠀⠀⣠⡀⠉⠀⣶⣦⠀⠈⠻⠿⠀⢀⡠⠊⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠢⢀⠈⠳⣄⠀⠀⠙⠒⠤⣀⡈⠁⠀⠀⠀⠀⢸⣿⠀⠀⠻⣿⠀⠀⠈⠋⠀⢀⡀⠄⠒⠁⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣙⠲⢤⣀⠀⠀⠈⠉⠑⠒⠒⠠⠤⠥⠄⠀⠤⠤⠀⠒⠒⠈⠉⠀⠀⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠛⠷⠶⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡴⠒⠒⠚⠉⠉⠉⠉⠙⠛⠷⣶⣶⠲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⣷⢦⣮⢆⡠⣤⢀⢀⠀⠀⠀⠀⠈⠛⠿⣷⣽⡉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠿⠚⠕⠈⠐⠇⠙⠒⠻⠔⠻⡿⡆⢁⡄⣦⢴⣄⢀⠀⠘⠿⢷⣽⢄⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠚⠳⡮⣧⡤⡄⠀⠉⣿⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡀⢀⣀⡴⠛⠄⠲⡤⠊⢩⠴⡀⢤⣀⢠⡀⠀⢀⣀⠀⠀⠀⠀⠙⠋⠙⠉⣆⡀⠘⠿⣦⠀⠏⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢗⡷⠾⡟⠛⠀⠉⠱⠔⠈⠈⠉⠉⠉⠰⡧⣤⣨⣷⣿⣬⣦⣠⢦⡄⠀⠀⠀⠀⠈⠙⢵⢦⠙⠆⠰⡘⣿⡄
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠈⠉⠈⠓⠛⠿⠿⣶⢏⣦⡀⣀⠀⠀⠀⢰⣉⣆⢠⣸⢿
⠀⣿⠋⠉⠓⠲⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⢸⢠⣀⠄⢀⢆⡀⠲⡀⣴⣄⣠⣠⣄⢠⣦⡀⣠⡄⣀⣀⠀⢀⠀⢀⡀⠀⠀⠀⠈⠛⠻⣟⠿⡦⢄⡈⢿⡿⢃⣼
⢸⡟⢀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠦⠤⢄⡀⢸⠈⠘⠀⠈⠁⠓⠀⠙⠋⠙⠉⠁⠐⠚⠛⠆⠋⠛⠉⠉⠁⠚⠄⠀⠳⣀⡒⢤⣂⠢⠄⠠⣀⣠⣄⠘⣻⣷⡿⡟
⣾⡇⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠠⠀⠀⠈⠛⠒⠲⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣠⣀⣴⠤⡶⢻⣻⣿⣿
⣿⠁⢰⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠤⢤⣤⠀⠀⠀⠀⡀⢀⡀⢀⡠⣀⣶⣤⢶⠶⣿⠩⠖⠊⠉⠁⡴⠊⠁⣼⢃⣿⢻
⣿⡄⠘⡀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠎⣼⢻⠐⠷⠞⣻⣽⠣⠿⠯⠟⠛⠓⠋⠉⠉⠉⠀⠀⣀⣴⠊⠁⠠⣶⡏⣼⣿⡿
⢹⣇⠀⠁⠀⠀⠀⠛⠀⠀⠀⠉⢀⡀⠀⣀⠀⢀⡀⠐⠂⠀⢠⠀⠀⠀⠀⣼⠿⣾⡷⠚⠓⠁⠈⠒⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⡾⠟⠁⠀⢤⣶⣿⠇⡟⡸⠁
⠈⢿⡄⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠉⠀⠈⠀⠀⢠⡀⠀⠀⠀⠀⣸⡏⣤⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣼⡿⠛⠋⠁⠀⠀⢀⣸⣿⡯⠱⢸⡷⠁
⠀⠈⢿⡄⠸⡄⠀⠀⠀⠀⠉⠀⠚⠠⠠⡄⠀⢠⠆⠀⠀⠀⠀⢀⠞⡰⡝⣰⣾⢸⣀⣀⢀⣚⣰⣖⣿⣿⠛⠛⠞⠁⠀⠀⠀⠀⠀⢠⣾⣿⠃⡦⣧⠏
⠀⠀⠀⠹⣄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⢜⡟⣸⢇⡿⣮⡿⠧⡿⢙⠞⠁⡀⠉⠀⡀⡀⢠⢀⢄⣀⣾⣾⣿⠏⣜⡼⠋⠁
⠀⠀⠀⠀⠈⢷⣤⡈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⣰⣯⣯⣾⣿⣾⢟⠅⡠⢂⠔⣡⢎⢌⢔⡔⡔⡴⡠⢃⣎⣾⣿⣟⡿⠞⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣌⣉⡉⠛⠀⠓⠒⢛⣉⣡⣴⣾⣿⡿⠟⠋⠁⠈⠙⠛⠲⠧⠾⢵⣧⣮⣮⣮⡼⠴⠷⠟⠛⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣻⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⢠⣾⣿⣿⡟⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⣿⡿⢿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⣴⡿⠉⠙⣷⡄⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠈⢻⣿⣤
⠀⠀⣠⣿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⣠⣿⣿⣷⡀
⠀⣴⣿⡟⠉⢿⣿⣦⡀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠙⠿⠟⠋⢀⣾⣿⠟⠙⣿⣷⡄
⣼⣿⡏⠀⠀⠀⠙⣿⣷⣄⠛⠋⠁⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋⠀⠀⠈⣿⣿
⠈⢿⣿⡄⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣿⡄⠀⠀⠸⣿⣿⣿⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⢿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠈⠉⠁⢀⣤⣾⣿⠿⠋⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠛⠿⠋⠀⠀⣀⣠⣤⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣾⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡒⠬⢙⡡⡹⢛⠟⢹⢻⢿⣄⠠⢀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⡡⠐⠉⡠⠒⡡⠊⢠⢁⠆⠀⠆⢣⠑⣝⠦⡉⠒⢄⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠴⠋⠀⡠⠊⢀⠜⠀⠠⠃⡘⠀⠀⢸⠀⢣⠈⢢⠈⢢⡀⠉⠢⡀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡰⠋⠀⢠⠎⠀⢠⠃⠀⢠⠃⢀⠁⠀⠀⠈⡀⠀⢣⠀⠱⡀⠑⡄⠀⠈⢦⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡜⠀⠀⡰⠁⠀⢠⠁⠀⠀⡌⠀⢨⠀⠀⠀⠀⠃⠀⠈⡆⠀⠐⡀⠈⢆⠀⠀⠱⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡞⠀⠀⠰⠁⠀⢠⠃⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠐⡀⠈⢆⠀⠀⠘⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡸⠀⠀⢠⠃⠀⠀⡆⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠈⡄⠀⠀⢃⠀⠈⡄⠀⠀⢡⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢀⠃⠀⠀⠄⠀⠀⠀⠁⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁⠀⠀⠈⠀⠀⠰⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠂⠀⠀⡀⠀⠀⢠
⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⡞⠀⡝⠑⠢⢄⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⡀⠀⠀⡆⠀⠀⢸
⢸⠁⢰⠃⠀⢀⣠⣈⠑⠢⢄⣀⠀⠀⡄⠀⠄⠀⠀⠀⡃⠀⠀⠸⠀⠀⠀⢰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⡄
⡎⠀⡸⠀⠀⠘⠤⠜⠃⢀⣀⣈⠙⠲⢧⣀⠰⠀⠀⠀⢡⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⠸⠀⠀⡘⠀⠀⡘⠀⠀⢠⠁
⡇⠀⡇⠀⠀⠀⠀⠀⠀⠺⠤⠜⠁⠀⠀⠈⠉⠓⠤⣀⠈⠆⠀⠀⢃⠀⠀⠘⡀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⢀⠃⠀⠀⠁⠀⠀⠆⠀⠀⡸
⡇⠀⢱⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠤⣀⠈⠆⠀⠀⢃⠀⠀⢰⠀⠀⠀⠀⢠⠀⠀⢰⠀⢀⠎⠀⢠⠃⠀⢀⠎⠀⠀⡰⠁
⢱⠀⠸⠄⠀⠘⠤⠔⠁⠀⠀⢧⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡈⡄⠀⠸⠀⠀⠀⠀⡘⠀⠀⡌⢀⠎⠀⡰⠁⠀⣠⠋⠀⠀⡴⠁
⠀⡄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠢⢤⣇⠀⠀⢀⠃⠀⡀⡠⠀⢀⠎⠀⢀⠜⠁⠀⡠⠊
⠀⠱⡀⠈⢧⠀⠀⠀⡠⠒⡶⠀⠀⠐⢧⠔⠁⠀⣠⢤⠀⠀⠀⡤⡀⠀⢸⡈⣳⠀⢀⣀⠈⠉⠒⠼⣀⣰⠖⢁⠔⢁⡠⠚⠁⢀⡤⠊
⠀⠀⠱⡀⠈⢣⡀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠐⢇⡼⠀⠀⠸⣄⡽⠀⠀⠉⠁⠀⠸⣄⡱⠀⠀⢠⠎⢉⣖⡡⠐⢉⡠⠤⠊⠁
⠀⠀⠀⠙⢆⠀⠑⢄⠀⠀⠀⠀⠀⢀⡤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢄⠀⠀⠀⠀⠀⠀⡰⠃⢀⠾⠁⠒⠈⠁
⠀⠀⠀⠀⠀⠳⣄⠀⠑⢤⡀⠀⠀⠘⠤⠎⠀⠀⠀⠀⡰⠲⡀⠀⠀⠈⠳⠞⠀⠀⠀⢀⡤⠊⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠑⠖⠁⠀⠀⠀⠀⠀⣀⠤⠚⠁⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠉⠐⠒⠆⠤⠤⠤⠤⠤⠄⠒⠒⠂⠉⠀⣀⠤⠚⠁
⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣑⠒⠢⣤⣤⣀⣀⣀⣀⣠⣤⡄⠒⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡔⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠈⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢞⠛⠛⠛⠯⣭⣓⠲⢤⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⡉⠻⠹⠈⢃⠀⠀⡀⠀⠀⠹⡛⠓⠮⣍⡒⢤⡀⠀⠀⠘⡆⠀⠀⢀⡈⠐⠕⢦⡈⠳⡄
⠀⠀⠀⡠⠊⠡⠀⠀⡠⠂⠀⠁⠀⠀⠀⡂⠀⠀⠀⠀⠀⢱⡀⣀⠘⡝⢆⠙⢦⡀⠀⢹⠀⠀⠉⠁⢀⠀⠢⠑⡄⠈⢆
⠀⢀⠞⠀⠄⠀⢀⠊⠀⠀⠃⠀⢠⠀⠀⠱⡀⠀⠀⠂⠀⠀⢫⠉⠀⠘⡌⢣⠡⠱⡀⠈⡇⠀⠀⠈⠉⠀⠀⠡⠈⡄⠈
⢀⠏⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⢣⠀⠀⠈⠀⠀⠈⡆⠋⠀⠰⠈⡆⠢⢱⠀⢳⠀⠚⠁⠐⠂⠂⠀⢃⢰
⡌⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠐⠀⠀⠸⡐⠶⠀⡄⢸⠘⠈⡆⢸⠀⠈⠉⠀⣤⠤⠀⢨
⡇⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⡇⠀⠀⠠⢸⡄⢳⡇⠀⡇⠐⠒⠀⣀⡀⠀⠘⠸⢀
⡇⠀⠐⠀⠀⠃⠀⠀⠀⢣⠀⠀⠀⡄⠀⠀⠀⠈⠂⠀⠀⠠⠀⠀⢹⠐⠖⠀⢸⠃⢰⠀⠀⢃⠀⠀⠀⠈⠁⢀⢃⣢⠞
⢣⠀⠀⢂⠀⠸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠰⠀⠀⢸⡀⠀⠀⢸⠀⡎⠀⠀⢸⠀⠀⠐⠶⢀⣼⠟⠁
⠘⡆⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢠⠀⠀⢸⡇⠁⢂⠆⡼⠀⠀⠀⢸⠀⠀⢀⣤⠞⠁
⠀⠘⡄⠀⠐⠀⠈⠀⠀⠀⠐⠀⠀⠈⡀⠀⠀⠀⡇⠀⠀⡈⠀⠀⠘⡇⣀⣮⠞⠀⠀⣀⡀⠸⠶⠛⠉
⠀⠀⠈⢦⡀⠐⡄⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠇⠀⢠⠀⠀⠀⢠⣾⠟⠁⠠⣤⠀⢇⠙⡄
⠀⠀⠀⠀⠙⠢⣌⠐⡈⠄⠀⠀⢃⠀⠀⠇⠀⠠⠂⠀⠁⠀⢀⡤⠚⠁⠀⠀⠐⠵⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠾⠦⣀⣀⣀⣄⣅⣀⣬⠴⠥⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄
⠀⠀⠀⢸⡷⠃⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠉⣿⠁
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⣯⠀⠀⠀⠀⠀⣴⣿⣿⣿⡷⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠶⢄⠀⠈⠻⣦⡀⠀⠀⣼⠃
⠀⠀⠀⢿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣄⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⣀⣸⣧⠀⠀⠘⢿⣦⡾⠁
⠀⠀⠀⠘⢧⡀⣰⡿⠉⢯⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣄⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣿⠏⠀⠀⠈⠛⠿⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⣠⡿⠃⠀⠀⠀⢠⣶⣶⣶⣦⡀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⡿⣷⡀
⠀⢀⣼⢿⣄⡀⠀⠀⠀⠙⠿⣿⡿⠟⠁⠀⠈⢿⣆⠀⠀⠀⣠⣿⠃⠀⠀⠻⠿⣿⠿⠟⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⢻
⣠⡾⠃⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⣠⡾
⠻⣧⣀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⠀⣠⡾⠋
⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠿⠛⠋⠉⠀⠀⠀⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠈⠙⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⣿⠛⠻⡟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣠⡴⠃
⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢤⢦⡀⢀⠀⠀⣇
⠀⠀⠀⢀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡠⠛⠁⠘⠃⠀⢱⠀⠀⠀⠀⠠⡀
⠀⠀⠙⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⣄⠀⠁⠙⠄⢀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠐⢄⠀⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠶⢤⣀⣀⣀⣄⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠲⣄⡈⠂⠠⣄⣀⣀⠀⠀⠠⣀⠀⠀⠈⠲⢠⣀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠤⠼⠮⠑⠛⠛⠋⠙⠲⠤⣤⣦⣈⣁⡉⠀⠀⠙⠋⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠛⠒⠙⢉⠉⠙⠉⠙⠋⠹⠗⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢃⢀⣤⢦⠶⠶⠷⠞⠾⠲⠾⠲⢶⢦⣤⣤⡉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠞⢋⡉⠃⢀⠀⠀⠀⠀⢀⠀⢀⠀⢄⠀⢀⡉⠉⠳⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣤⠰⠟⠻⠛⠻⠚⠿⠛⠻⠋⠹⠟⠛⠙⡿⠛⠛⢶⢧⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⣤⢀⣀⠀⡄⠀⢀⠀⠀⠀⠀⣄⠀⠀⠉⠀⠠⣄⣨⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⣷⣀⢀⠉⠙⡿⠶⠛⢿⡶⢶⣶⢾⠟⢻⡷⡿⢻⣻⡟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢳⣽⠻⢾⣄⣠⡀⡀⢤⡀⠀⢀⠀⠀⠈⢀⣠⣴⣷⣾⣿⠏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠙⢷⣶⣄⣜⡉⢟⠛⠓⠞⡶⠛⠞⠋⡻⢻⣿⣿⠿⠋
⠀⠀⠀⠀⠑⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠁⠛⠿⠷⣿⡷⢾⡶⢶⡿⣶⣻⠟⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⡼
⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣖⠒⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣦⣤⣀⡀⠀⠀⣀⣀⣀⠀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠷⠾⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⣀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⣶⡄⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⢠⡀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢠⡀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⣀⠀⠀⠁⢠⡀⠀⠀⠀⢸⣶⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⡐
⢆⠁⠀⠑⢄⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠈⠀⢀⠔
⠀⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⢄⠀⠀⠀⠂⠄⡀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠉⠠⠐⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠁⠐⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠂⠈⠀⠀⢀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⢸
⠀⢸⠀⠀⠀⢀⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠣⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡠⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠑⢄⠑⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡉⠐⠂⠀⠤⠤⠤⠄⠐⠒⠈⡀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣿⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣽⣿⣽⣿⣿⣿⣭⣿