Pumpkin Spice Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⣿⡆⠀⠀⣀⠀⠀⣤⠀⢹⡇⢀⡆⠀⡄⠀⢲⡄⢀⣿⠔⡡⢠⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⠀⠀⢀⡿⢰⣇⠀⣿⡇⢀⣿⠀⢸⠇⣼⠃⣰⣿⠀⢸⡧⢸⣟⣼⡴⠛⠁⢰⡟⢀⣾⢠⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠁⠉⠀⠈⣿⣠⠻⣇⡌⠻⠀⠀⠀⠙⠖⢹⣿⠸⠟⠁⠈⠿⠹⣆⢀⠔⢻⢁⢾⡿⢁⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠐⣦⠀⠀⠈⠁⠠⠦⠀⠀⢀⣀⠀⠀⠀⠈⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠸⠧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠉⢠⡀⢀⡞⣷⡄⣠⣶⠀⣰⡿⠉⠛⠀⣠⣤⡄⠈⠛⠀⠀⠀⠀⡀⢀⠀⠠⢤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣠⠟⣿⣸⣤⣿⠛⠉⠛⠒⢻⣇⠀⢀⡴⣿⡒⢁⡴⠂⠀⠀⠀⢰⠷⡘⠳⡇⣇⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢻⣿⠋⠁⠀⠀⠀⠀⠀⠉⠙⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠀⠉⢉⡉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⢡⡀⠈⣿⡀⠀⠀⠈⠉⠒⠠⠀⠙⠋⠀⠠⠀⠒⠉⠀⠀⠀⠀⢦⠄⠀⢸⣧⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠁⠀⠙⠁⠀⢰⡒⠀⠀⢀⣀⣀⠀⢀⡀⢀⣤⡀⠀⡛⠀⠀⡀⠀⢀⠸⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢤⡤⠆⠀⠀⢸⣷⠘⢷⣀⣠⣿⢁⡾⠀⣿⣧⠃⣿⠁⢸⡿⠀⣼⣇⠎⣽⡇⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠘⣿⠀⢸⠀⠘⣿⠁⠀⡜⢻⡇⠐⣿⢀⢿⡇⡰⣿⡏⢰⡿⢀⣼⠏⠀⡠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⢠⠃⠙⢦⠄⣀⣀⠉⢓⣥⠀⠈⠁⠀⠙⠁⠈⠋⠀⠙⠀⠘⠧⠊⢿⡠⠚⣁⣿⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⣀⠴⠃⡀⢀⡀⢰⠋⣿⡀⠀⣉⠀⠀⣼⡟⢳⠄⠀⣤⣤⡀⠐⠶⠀⢀⠴⠚⠉⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⠖⠋⠁⢸⣿⣾⢠⣿⠀⣸⣿⠀⣸⣿⠀⠀⠀⣸⣿⠾⠁⡼⠀⢰⠃⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠘⢿⠇⢸⣿⣰⠇⠙⠛⠙⣿⣄⢀⣰⠏⠻⠶⠚⠁⠀⠘⠂⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡿⠀⢀⡿⠀⠀⠀⠀⠀⠀⢰⠄⣀⠀⣾⠀⡀⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠴⢻⠇⣴⠀⣧⢶⣦⣤⣼⡞⢩⣷⣷⠞⢁⡖⣸⡶⢻⠀⠀⠀⠀⠀⣤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡟⠀⠀⠸⠿⠙⠼⠏⠸⠃⣾⡿⠓⠊⠸⠛⠦⣜⣟⡿⠁⠻⠀⠀⠀⠀⣀⠛⠀⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡆⠀⠀⣦⢀⡆⠀⠀⠀⠀⠀⠀⠀⡄⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣞⣠⡄⠐⠀⢀⠀⢀⡛⠀⠀⣼⡿⠁⠒⢻⡏⣻⠛⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠺⣕⢹⣿⢁⡾⣿⣴⠋⣱⡿⢟⡀⢀⡟⢠⣶⡖⣾⢀⡟⣰⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠲⠚⣸⠏⠉⠀⠉⠈⠉⠀⠙⠉⠀⠀⠷⠛⠋⠙⢿⠼⣧⠟⠛⠁⠀⠀⣠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠁⠀⠀⠀⠀⠐⢠⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢪⡟⠀⠀⠀⠀⠀⠀⠀⣴⣦⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣾⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡦⣤⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⢻⣿⣿⣿⡟⢻⣿⣿⠙⠃⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢸⣿⣿⣿⣴⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠛⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣿⣿⣿⣿⢟⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣧⣿⣿⣿⣿⣫⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣥⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡦⣤⣤⣄⣀⣀⣀⠀⠀⣀⣀⣠⣿⣿⣷⣿⣿⣿⡌⣅⠿⢶⡶⢦⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣷⡆⠈⠛⢿⣿⣿⣿⣿⢡⣜⠋⣡⣾⣿⣿⣿⣿⣿⣯⠈⣿⠛⣁⣿⣿⣿⣿⣿⣿⣷⠈⠉⠙⠾⢶⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣷⡤⠀⠀⠙⣿⣿⡼⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣼⣿⣼⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⠟⠛⠃⠀⠀⠀⠈⠈⠥⠚⠻⠿⣿⣿⣿⣿⣿⣿⣛⣴⣦⠈⠿⠿⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣄⢀⣻⡑⢋⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⢰⠋⢠⠞⢠⠎⠁⢹⡀⢳⡀⠹⡆⠀⠀⠀⠀⣀⣀⡠⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠭⠤⠤⠤⠤⢴⣶⣶⣷⡖⠒⠋⣿⠀⣾⠀⣾⠀⠀⠀⡇⠈⡇⠀⣿⠓⠒⣶⣶⣦⣤⢤⣀⣀⣈⣉⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣩⠞⣡⠏⠀⠀⠀⠸⡄⢹⡄⢻⠀⠀⢠⡇⢠⡇⣰⠇⠀⠀⠈⢮⡙⢍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣩⡿⠟⠁⠀⣐⠥⠚⠁⠀⠀⠀⠀⠀⠈⠂⠷⠬⣧⣀⡾⠠⠾⠐⠁⠀⠀⠀⠀⠀⠓⢬⣣⠀⠈⠲⣶⣒⠦⣄⡀
⠀⠀⠀⠀⠀⢠⠞⢁⡴⣫⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠻⡷⣄⠙⢦
⠀⠀⠀⠀⢠⣃⠴⠋⡜⠁⠀⠀⠀⠀⠀⣠⢠⠊⠹⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠣⣀⠳⡀
⠀⠀⠀⠀⠛⠁⠀⣸⠤⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⡇⠀⠀⣀⠀⣄⡾⠉⣇⡴⡆⢠⡴⢢⢀⣏⡤⣶⠀⠂⢀⠀⡠⣶⠀⠀⠀⠀⠀⠀⢘⡆⠈⠓⢧
⠀⠀⠀⠀⠀⢀⠎⠁⠚⠁⠀⠀⠀⠀⠀⣿⡇⢀⡼⢡⡄⣰⣿⢰⣿⠇⠀⡟⢰⡇⣿⠁⣸⢸⣿⡞⠁⣸⠀⣾⡞⢠⡏⠀⠀⠀⠀⠀⠘⠭⠛⢄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣤⠇⠻⠜⢹⠀⠰⠇⠘⠧⢿⠙⠃⠸⠃⠑⠐⠛⠚⠹⠁⣿⢀⠎⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡀⢀⢴⣄⠖⢲⢀⠁⢀⡞⠑⢀⣴⠄⠀⠀⢠⠔⣲⡟⢠⣦⢔⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣷⠃⢸⡟⠀⢸⢻⣀⢾⡁⢀⣿⢁⡔⠀⠀⢿⡴⢹⢃⣾⠃⣼⠃⣼⣹⢻⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡼⢹⠆⢸⡇⠒⠃⠀⠀⠈⠓⠋⠈⠉⠀⡀⠀⣀⠀⠈⠉⠀⠀⠙⠚⠉⠁⠸⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠼⠀⠀⡇⠀⠀⠀⠀⠈⠃⠤⠤⠤⣼⠓⢛⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢀⡀⣹⠀⣾⢀⡆⣰⡇⣰⡇⠀⣸⣡⡀⠀⣠⠁⣰⡠⢲⠄⢀⡄⢀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⡼⣧⢠⠃⡟⢡⠇⢰⡇⣸⠓⢁⡟⢹⠁⣰⣿⠁⡇⢠⣇⣰⡟⠁⣾⢀⣾⡰⢻⡇⠀⡠⠋
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠧⠜⠁⢹⡾⠀⠙⠉⠀⠀⠛⠁⢠⣾⠃⠈⠛⠁⠁⠀⠉⠁⠈⠘⠃⠀⠈⠁⢀⠀⣼⠒⠉
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣄⢀⠔⣦⠘⠋⠀⠀⣠⢤⡀⠀⢀⠀⠀⠀⠀⠀⡴⠊⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢧⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣇⠎⢠⡇⠀⣠⠀⣰⠃⠀⠀⣸⠛⠀⡀⠀⠀⡜⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡀⠀⡴⠁
⠀⠀⠀⠀⢠⡀⠀⠙⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡟⠀⢸⡇⣰⢧⠜⢹⡀⢀⡴⠛⠦⠜⠁⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠫⣵⠚
⠀⠀⠀⠀⠈⢏⠓⢄⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠓⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠔⡞
⠀⠀⠀⠀⠀⠈⠣⡀⠑⢮⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢲⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢔⡵⠊⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣝⣻⣦⣄⠀⠙⣕⠦⣄⠀⠀⠀⢠⠖⢉⡬⠓⡶⠻⡖⠲⡍⠑⢦⠀⠀⠀⠀⢀⡤⢖⠟⠁⠀⣠⣶⢟⣋⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣌⡲⣌⢣⡀⠀⡿⠀⣾⠀⡼⠀⠀⢸⡀⢹⡀⠘⡇⠀⠀⡴⢋⡔⣋⡤⠖⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣖⠒⠒⠒⠒⠒⠻⠿⡿⠗⠤⣧⠀⣇⠀⡇⠀⠀⢸⠇⢸⡇⢠⠧⠔⠺⢿⠿⠿⠷⠒⠒⠶⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠚⠉⠀⠀⠀⠘⢦⡸⣄⢳⡀⠀⡸⢀⡼⣠⠏⠀⠀⠀⠀⠉⠒⠒⠶⠶⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠘⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢠⡄⠀⢠⢾⢀⣇⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣼⠃⠀⠀⣀⡴⠀⠀⠀⠀⠘⠂⡀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇⢀⠋⠆⠸⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣦⡀⠀⠀⠀⢰⢿⢤⢊⢃⠀⠀⠀⠠⢁⠀⠀⠀⠀⠠⠠⠆⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⠁⢠⡽⠖⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢣⠙⢀⠀⠀⠂⠘⢘⡜⠨⢠⣾⣶⣤⣿⡗⢀⣀⣤⠖⠛⠀⠰⢄⢀⢀⠀⠀⣀⣀⠀⠀⠀⡀⣠⣷⡯⢔⡿⠋
⠀⠀⠀⣤⡀⠀⢀⠀⠀⠀⠀⠘⡄⠈⢆⠀⠀⠃⣸⣴⠂⣀⡉⣿⣿⣿⣞⣧⠀⠿⠇⠈⠰⠀⢬⣀⣈⢒⡒⣊⣐⢒⣒⣢⢀⣿⣥⠔⣋⠀⣀
⠀⠀⠀⠉⠱⡄⠘⢧⠀⢠⠀⠀⡥⠀⢘⠜⠚⠊⠉⠉⠉⠂⠄⣸⣿⣇⠬⠞⠋⠀⠉⠁⢂⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⡀⠤⠄⡀⠐
⠀⠀⠀⠀⠻⣇⢠⢈⠆⠈⣀⠔⠛⠁⠉⡠⠽⠻⠿⠿⣶⠶⢶⣾⣿⣷⡦⠶⣶⠿⠿⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢦⢄⣘⡏⠀⡴⠁⠀⠀⡔⠈⠀⠀⠀⠀⠞⠀⠀⠀⠀⠉⠀⠀⠀⠀⠱⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠣⣀⣻⣄⠁⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀
⠀⠀⠀⠀⠀⣀⣀⡉⠙⢀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⢀⠈
⠀⠀⠀⠀⠀⠈⠙⠆⢈⣧⠀⠀⢁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠶⣶⠚⢆⠀⠘⣆⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣀⡠⠭⠒⠲⠖
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠵⠊⢑⣄⡘⢦⡀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡴⠶⠿⠦⣀⡀⢀⢠⣟⠛⠛⠦⢤⣄⣀⡈⠳⣤⣀⠀⣠⣠⢾⣁⣀⠤⣤⠴⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠠⣄⢰⡄⡀
⠀⠀⠀⠀⠘⢳⣤⣀⠀⠀⠬⣿⣿⢧⣤⣄⣀⠀⠀⠀⠉⢻⣯⠉⠛⠉⠉⠈⠉⡄⢀⡆⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠇⠀⠤⢾⣿⣿⡥⠄
⠀⠀⠀⠀⢰⣇⠁⠉⠙⠓⠺⣿⣥⡄⠙⠀⠙⠲⠬⣶⣶⣿⡽⣟⡆⠐⠐⠲⢶⣿⣿⣧⠦⠊⠀⠀⢴⣾⠀⠀⢿⠇⢸⡀⠀⠀⣾⡗⠀⠀⠋⠹⠋⠒
⠀⠀⠀⠀⠀⠈⠉⠒⠠⢄⣰⣻⠀⠉⠛⠷⠴⣦⣾⣯⣽⣻⠉⠉⠀⠀⡠⠔⠻⣿⣿⡿⠧⠤⠤⢠⠞⠀⠀⠀⢼⠀⠀⢿⡧⠀⠈⢀⡀⢀⣠⡀⢠⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠒⠦⢄⡀⠀⠀⣩⡿⣿⣅⠀⠀⠀⠀⠁⠀⢰⠉⠈⠣⡀⠀⠀⡀⢀⢀⡀⢠⡀⠀⢰⣖⠀⣾⣳⢸⡇⣿⣉⣤⢸⣯⡭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣶⣧⡞⠀⠀⠈⠉⠓⠻⠿⠽⠞⠀⠀⠀⢀⠀⢠⣨⡄⠀⡶⣦⢸⣿⠃⢸⡎⣿⣼⡇⠀⠠⡬⠇⠿⠀⠀⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡿⢏⠁⠀⢀⣶⣶⡂⠀⠀⣾⣳⠎⣧⣸⡆⣿⠛⢻⡄⠿⠁⠈⠟⠙⠈⠃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠛⠀⠀⠀⠹⠁⠀⠙⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠔⡟⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⣕⡡⠞⢀⠀⠙⠫⢝⣛⡷⠄⢼⣭⡷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⠘⣝⠄⡀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠉⢰⢿⢤⡤⡤⣤⢤⢤⡤⡖⣶⢻⠀⠀⠀⢜⢯⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡄⠀⡀⠈⢻⠶⠷⠷⠾⠾⠾⠶⠓⢛⢯⡀⠀⠀⣂⠎⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢢⡸⣤⣷⠆⠁⢰⣫⠁⠔⠒⠉⠉⠉⠉⠒⠒⢷⣷⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣾⠀⠀⢿⣦⣤⣬⣤⣤⣤⣤⣤⣤⠶⠶⢿⠀⢐⣹⡶⣂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⢹⢹⠳⡾⡗⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠉⠒⠁⡀⠀⠤⠀⣤
⠀⠀⠀⠀⣴⡿⢷⣄⠐⠀⠘⠟⠀⢳⢱⠀⣼⢰⠖⠤⠐⠒⠐⡗⠗⠐⠛⠂⢸⡀⢠⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⢤⡀⠙⢗⣄⠀⠲⠀⠈⣇⠇⢺⠐⣠⠀⣤⡀⡀⢁⠄⢠⣦⠀⢸⡇⠀⢠⠊⡥⣩⠏⣙⡆
⠀⠀⠀⠀⠀⢀⠈⠓⢄⡉⠻⣦⡀⠀⠘⠚⢸⠀⠩⠇⡗⠃⠃⠘⠒⠈⠒⠂⢸⡇⠀⡍⠀⠌⠐⠔⣡⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⠢⣄⠀⢸⣀⡀⠀⠃⠀⠀⠀⠀⢀⣀⣀⣸⡇⠀⠃⠤⠮⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠑⠪⠆⢸⣿⡛⠛⠛⠛⢛⣛⣋⣉⣉⡽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠛⠛⠛⠛⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠀⡀
⠀⠀⢀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠂
⠀⠀⠀⠑⠈⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⢀⡔⠐⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⢀
⠀⠀⠀⣀⠸⣷⠎⢠⢀⠀⠒⠈⠉⠉⠉⠉⠉⠉⠉⠭⢒⡄⠀⡀⡀⠀⠂⠀⠄⡿⠁⠄
⠀⠀⠀⠀⠑⢌⣦⠆⢸⠍⣉⣀⣀⡐⠒⠒⢂⣀⣁⣀⢠⠇⢀⠁⣽⠀⠀⠀⣾⠡⠀⠄⠀⢀⡀⢠
⠀⠀⠀⠀⢀⢀⠛⢶⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠈⠀⠄⠀⠀⠟⠃⠈⢀⠔⠉⠀⠠⠂
⠀⠀⠀⠀⠀⠐⠈⠲⣶⠦⠄⣀⣀⣀⣀⣀⣀⣀⡤⠄⠚⠒⣆⢰⡗⡱⠾⠴⠤⠤⣼⣈⣠⠚⠁⠀⡰
⠀⠀⠀⠀⠸⠀⠂⠄⠀⠀⠀⠀⠀⠀⠠⢀⠄⣚⡓⠀⠀⠀⠘⢸⠀⠐⠒⠉⠉⠙⠛⠷⡒⠒⠀⠉
⠀⠀⠀⠀⠀⠣⠀⠀⠘⡆⠀⠀⠀⠀⢠⡥⠚⠉⠉⠁⠀⠀⡌⣀⠔⠀⠀⠀⠀⠒⢤⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠑⠠⠀⢳⠦⢄⣀⣤⡞⠀⠀⠀⡠⠐⠀⡀⠀⠀⠀⣀⡀⠈⠐⣄⠀⠹⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⠀⠀⢀⠞⠁⠀⣸⠁⠀⠀⠀⠀⠙⣆⠀⠈⡆⠀⢳⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⠸⡆⢀⡎⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⠸⡆⠀⡿⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⡷⠞⠛⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⢀⡇⢰⣃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠙⢦⣈⢀⣧⡀⠀⠀⠀⠈⣑⣾⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠒⠒⠒⠊⠉

⠃⠀⠀⠀⠀⣄⣤⣄⡄⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣶⣦⡀
⢠⠀⢠⣄⡀⣯⣻⣷⣟⣺⢣⣤⣀⠀⠀⢰⣠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣦⣄
⢸⠀⠚⠉⢳⢛⣽⣫⣸⣟⣼⠛⠛⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠸⠀⠀⠀⠘⠛⠋⠘⠙⠚⠓⠀⠈⡿⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠘⠛⠛⠀⠙⠿⣿⣿⣿⠿⢿⣯⡄⠻⢽⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣀⣼⡇⠀⢻⣄⠀⠀⠀⠀⠿⠟⠂⠘⠿⣿⣿⣿⡿⢿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠙⠛⠛⠀⠠⣿⠿⠃⠀⠀⠀⠀⠀⠀⣀⣠⡟⠀⢹⣦⡀⠉⠁
⣾⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠛⠿⠇⠀⣼⡿⠗
⢠⣿⣯⠀⢻⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢈⡟⠛⢿⡁⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠰⣶⣿⠇⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠴⣤⡀⠛⠉⠀⠀⠄⠀⢤⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⢼⣟⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⢀⢀⣤⢠⡅⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣹⠋⠻⣏⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢐⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠀⠔⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⢳⡅⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡄⠀⢘⡀⡠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣄⡔⢁⠀⢀⡀⠤⠤⠤⠤⠲⠲⠲⠿⠶⠾⢦⢀⡀⠀⠀⠀⠀⠀⡀⠀⡄⢾⠟⠑⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡙⢿⠀⡘⢰⡇⠤⠀⢀⣀⣀⣀⣀⣀⡀⠀⠬⠉⠐⠃⠀⠔⠢⡄⠀⠐⠀⢢⡾⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⡪⣿⠁⡸⡓⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠐⢒⢺⠁⠀⠀⢰⠁⠀⢠⣀⡯⡀⠁⠘⢀⡠⠄⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡉⢻⠀⠂⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣸⠀⠀⠀⠐⠀⠀⢠⠋⠁⠀⠈⡶⠁⠄⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠷⢶⠓⠢⠤⠄⣀⣀⣀⣀⣀⡀⣤⠶⠒⠉⠑⢶⢸⣿⢋⠵⠓⣒⠒⠶⢴⣗⣡⡴⠈⠁⠀⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡤⠐⣛⠃⠀⠀⠀⠈⠸⡇⠀⠐⠚⠋⠉⠙⠛⠻⣆⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⡀⠑⡆⠀⠀⠀⠀⠄⢠⣊⠴⠛⠋⠑⠀⠀⠀⣈⠀⢉⠆⠀⠀⠀⠀⠠⢄⡁⠂⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢦⣄⡀⠀⠀⢁⡼⠁⠀⠀⠀⣀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠐⢤⡀⠠⠙⣆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡄⠈⠉⠉⣿⠃⠀⠀⢀⠔⠀⠀⣰⠇⠀⠀⠀⠀⠓⢄⠀⠀⠙⡄⠀⠘⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⢹⠀⠔⢠⠋⠀⠀⠀⡏⠀⠀⠀⠀⠀⠠⠈⢷⡀⠀⢸⠀⠀⣧⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣳⣘⣧⣠⡇⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢄⠘⡇⠀⣾⠀⢠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢹⠟⡋⠉⢛⣧⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⢠⠿⣰⠇⢰⣏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠄⠖⠀⠘⠳⣆⡄⢀⣧⡀⠀⠀⠀⠀⢈⣌⣾⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠈⠀⠀⠀⠈⠉⠀⠙⠒⠶⠶⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⡀⠀⠀⢠⡶⠋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⣀⠀⠀⣠⡄⣀⡀⠀⠈⣹⡿⠉⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⠀⢰⣆⣤⡞⣿⠀⢰⢻⡿⢹⣷⣀⣴⡿⢲⡄⠀⢀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣿⡆⢸⡇⢿⡇⣿⢀⠇⣸⡇⣸⣿⢡⣿⣲⡾⠃⢠⣿⡇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣀⡀⣿⣇⠀⣿⣇⡾⣷⠸⠇⣿⡜⢠⣿⡇⠙⠁⣾⠃⣼⠇⠀⣾⡿⣀⢴⣿⣏⣤
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠉⢻⡏⣿⣴⠈⠉⠀⠁⠀⠀⠿⠁⡂⣿⠁⠀⠀⠉⣰⡏⢠⠎⠛⠛⣡⡿⢋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠸⡻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏⠀⢀⠀⠀⠻⠗⠃⠀⠀⠀⠉⢠⡞⠁⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣰⣿⠛⠀⠀⢀⠀⠀⠀⠀⠰⠿⠃⠀⢀⡀⠀⠀⣴⡶⠀⠈⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣷⠀⠀⠀⢹⣿⡤⠒⢉⣿⣇⣄⡀⢀⣴⣷⠀⣰⣿⠉⠂⢸⣿⡞⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠿⠀⢀⠔⢩⣿⡆⠀⣸⣿⠁⢸⡟⠁⣿⡇⣰⢻⣷⠀⠀⡸⢿⣧⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠢⠾⠛⠀⡼⣹⡏⢠⣽⠇⠀⢿⠶⠁⠈⠻⠷⠚⠁⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢠⣆⢀⡀⠀⡸⢁⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢀⡀⣀⣀⠄⢦⡆⠯⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠊⠛⠀⣇⡼⠃⠀⣾⠁⢦⠆⢿⠀⠹⢾⠈⠋⠀⠓⠘⠙⠛⠀⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣧⣀⠀⠀⢀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⣤⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⡏⠁⠀⡔⢹⣇⢴⣶⠀⠀⠀⣙⠁⠀⢠⣶⠒⠀⢰⣿⡧⠃⠀⡀⠀⠹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢸⣿⠀⠀⣰⣿⠀⢠⣿⣏⠀⠀⣸⣿⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⢸⣿⠀⡰⠹⣿⠔⠁⠻⠿⠶⠊⠀⠻⠷⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡧⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⣏⢢⠞⡆⠀⠀⢹⣿⡆⠀⢠⣤⢀⢆⠌⡇⡠⠊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⢿⣸⡜⡐⠻⠀⠘⣿⣧⠰⣦⠏⠁⢸⠀⡟⠁⡰⠀⠀⠀⢠⠞⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠤⠽⢄⡧⡷⢩⠀⢹⣿⣆⣌⣀⣠⡼⣼⣁⠔⠁⢀⢀⠎⢡⠦⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡑⣄⣀⡫⠭⡫⢵⠷⠛⠒⡾⠋⠉⠙⢆⠈⢳⡀⠉⢦⣰⠁⢙⡴⠃⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢦⡀⠱⠼⣴⠃⠀⠀⢰⠁⠀⠀⠀⠈⣇⠀⢣⠀⠀⣧⠴⣋⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠍⠢⢄⣹⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⢸⠆⠀⡾⠉⠀⠀⠉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⠤⠄⣨⣆⡀⠀⠈⣇⠀⠀⠀⠀⢸⠀⡼⢀⡼⠁⠙⠢⡤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠀⠤⠤⠚⣍⣉⠛⠓⠚⠒⠒⠒⠒⠚⠛⠛⣉⣹⢆⡀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁⡝⠀⠉⠒⠠⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠲⡴⠒⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢧⠀⢀⡜⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⠀⠀⠑⠚⠀⠀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠧⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠴⠀⠀⠀⠰⠀⠀⠰⠀⠀⠐⠀⠀⠐⠀⠀⠀⢿⡟⡡⠔⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢸⠙⡏⠳⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢀⠔⠁⣰⡇⠀⢸⠀⠈⢳⠤⠤⡀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠎⠀⠀⠀⠀⠀⢀⡀⡆⡀⡀⣠⠀⡄
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠎⡔⠁⠀⢠⠃⠁⠀⢸⠀⠀⢸⠀⠀⣧⡴⠖⠲⠦⡀⠀⢸⡠⡊⢠⠀⡄⡆⡴⡔⢁⢳⢯⡠⠇⠿⠀⠁
⠀⠀⠀⠀⠀⢿⠀⡀⠀⠀⠇⠀⠀⡇⠀⡀⠀⠈⠀⢀⠌⡠⠊⣧⠚⠉⠙⢦⢻⠀⠠⠀⡇⠫⡘⠃⠁⢸⠁⡁
⠀⠀⠀⠀⠀⢸⠳⢥⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠖⠈⠀⠀⡆⠀⠀⠀⡬⢰⠂⠀⠀⠀⣎⠘⠀⡂⠚⠠⢰⠋⡔⡙
⠀⠀⠀⠀⠀⠈⡄⠀⠉⠉⠀⠂⠈⠉⠉⠉⡠⠤⢄⠐⠤⠀⠀⣿⠀⢀⡴⣡⠏⠀⠀⠀⠀⢈⠢⢠⡇⠔⢡⠺⠐⢧⠜
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⢰⠒⢦⡀⠎⠀⠀⢨⠀⡀⠀⠀⢸⠴⣫⠔⠃⠀⠀⠀⠀⠀⠣⠔⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⡄⠀⠙⠀⠀⢠⠋⠐⠀⠀⠀⢸⠊⠁⠀⠰⠀⠀⠀⠀⡠⠦⡀⠀⠀⢀⠀⠀⠀⠂⠠⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠄⠈⠢⣀⢀⡴⠁⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠐⠀⠀⢀⠁⠀⢁⠀⠀⡐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠐⠀⠈⠋⠀⠀⠀⣀⠤⢊⠜⠀⠀⢀⠀⠀⠀⠀⠀⢇⢀⡀⡰⠀⠰⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⢀⡀⣀⣀⣠⣄⣒⠭⠔⢊⡁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣈⢳⡀⠀⠀⠀⠀⡊⢀⠑⢆⠀⠀⠀⠄⠊⠂⢀⠐⠤⡄
⠀⠀⠀⠀⠀⡄⠠⠁⠇⠀⠀⠀⡄⠀⢀⠄⠀⠀⠀⠠⠀⠈⢆⡇⠀⠀⡠⠊⡠⠂⠸⠀⠉⠓⠢⡀⠀⠀⠀⠑⢄⠉⢀⡀
⠀⠀⠀⠀⠀⣇⠃⠜⠀⠀⢀⢀⠁⢺⣾⠖⡶⣮⢸⠁⠑⠠⠰⠃⠀⡘⢰⠰⠁⠀⢆⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠑⢄⠑⠄
⠀⠀⠀⠀⠀⡗⠊⣰⢸⢾⠿⢨⠖⠃⠃⠈⠀⠀⠘⠀⠀⠀⢀⠀⠂⠑⢄⣈⣀⠀⠈⠂⢀⠖⠊⠀⠀⠀⢀⣀⢀⠀⠨⠆⢡
⠀⠀⠀⠀⠸⡇⠒⠙⢈⣤⠀⠸⢀⠔⢢⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⣉⣉⠉⠤⠄⠀⠒⠈⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⢀⠊⢸⢠⠀⡆⠀⠀⠀⠀⠀⠀⠛⠐⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡆⠂⠴⠃⠈⠀⠜⠁⢠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢀⡀⠀⠀⠠⠄⠀⠀⠐⠂⠇
⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠁⠐⢄⡠⠊⠀⠀⠀⠀⠀⡆⠒⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⣠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠂⠀⠀⠀⠐⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁


⡶⣶⢶⢶⢶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⢣⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⡄⠒⣢⠴⢞⣋⣀⣀⣉⣿⣖⡒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠀⠀⠡⡄⠁⢀⡜⠁⠀⠉⠙⠄⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣦⣀⡀⠀⠀⠀⣖⡁⠀⠀⠀⠀⠀⣰⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡆⡞⠻⢿⣿⣷⠄⢤⠸⠮⠻⠍⠻⠟⠉⠉⠛⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡿⡿⢿⡻⠿⠀⠢⠋⠉⠂⠀⢀⡆⠉⠀⢀⠀⠀⠀⢺⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠋⠀⠀⠀⠀⠠⠀⠊⠉⠀⠀⠀⠀⠈⠖⠀⠆⠢⠐⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠃⠀⠄⠘⡦⠀⠀⠀⠠⢤⣾⠀⠀⠀⠀⡁⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠹⠖⠐⠤⠄⠋⠡⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⢁⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠀⠀⣽⣆⠀⠀⠀⠀⢀⡞⠀⠀⢀⡼⢠⢁⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⢀⠀⠀⠠⣀⠀⠓⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠁⠉⠈⠉⠁⠑⠲⠶⠞⠋⠉⠀⠀⠀⠉⠙⠻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⢀⡀⡀⠀⡀⠀⣀⡀⠀⠀⠀⣀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⣀⠿⢱⠤⢼⠘⡷⠳⠏⠃⠈⡎⠿⠛⢯⣸⡚⠀⡇⢳⢻⠺⠏⢳⣇⣽⠖⡼⠟⠹⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢄⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠠⢞⡶⠦⢙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠅⣸⢇⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠈⠓⠒⠒⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠊⣼⠁⢊⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢶⠒⠶⠶⠶⠶⠶⠶⠖⢲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣁⣉⣀⣘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠴⠟⢖⠠⠀⡀⠂⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⣯⣷⣶⣶⣶⣶⣶⣶⣭⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⡄⠃⠛⠻⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠛⠛⠋⠉⠉⠁⠀⡧⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⢅⣀⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣤⣴⣥⢤⡀⠀⢠⠗⠉⣳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠁⢤⣄⡭⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠁⣿⢸⡌⣧⠀⢸⣀⢔⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠺⠙⠉⢊⢢⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠻⠧⣿⣾⡿⠋⢀⡯⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠠⠀⡄⢐⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠥⠿⠭⠭⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀
⠀⠀⠀⢺⠞⢹⢾⡇⢸⢸⡄⣼⣾⡖⢙⡶⣇⡜⢸⡏⣿⣸⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁⡀⡏⠳⣤
⠀⠀⠀⢸⠒⠉⠸⣇⡼⢿⢻⢻⢿⠗⠋⠀⡿⣄⢸⣇⡏⢻⠀⠀⠀⠀⠀⢠⠎⡡⠒⠩⣲⢗⣡⡦⢫⠛⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣄⢠⡄⣀⢤⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠧⠤⠴⠥⠬⠯⠤⠷⠲⡇
⠀⠀⠀⠀⠀⠀⠘⢧⣀⣿⣁⡼⢸⣧⡇⠈⣸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⣄⣠⡀⠀⢸⣛⡓⢦
⠀⠀⠀⠀⠀⠀⠀⠓⠛⠙⠀⠀⠘⠃⠓⠞⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⢺⠋⠛⠗⢄⠀⡞⠀⢸⢸⠇
⠀⠀⠀⠀⠀⣤⠀⠀⣠⣤⡤⡀⢠⡀⣄⡤⠤⢠⡤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡄⢂⠸⠀⠸⢸⠀⡷⠒⣡⠎
⠀⠀⠀⠀⠀⣿⠀⢸⣇⣿⣱⣸⠘⣷⢻⡏⠁⢸⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠚⠒⠓⠓⠁⢀⠏⠉
⠀⠀⠀⠀⠀⠉⠛⠀⠉⠙⠋⠁⠀⠉⠀⠙⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠤⠤⠤⠔⠊

⣮⣭⣶⠶⣥⡾⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⣿⣇⢸⡽⠷⢊⡿⠁⠀⠀⣿⠿⠷⠾⠋⠀⠀⠀⠀⠀⣁⠇⠀⠀⠀⡟⠁
⠁⠀⢎⣳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⣂⠀⣻⣿⠓⠶⠶⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣴⡆⠰⠁
⠙⠶⠶⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠲⠏⠉⠳⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡓⠤⣄⣠⣶⣄⠀⠀⠀⠹⣄⡁
⣀⣤⣀⣀⠀⠀⠀⠀⠀⢀⣿⣿⣁⠀⢁⡎⢥⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠀⠈⠁⢈⡟⠁⠀⠀⠀⠙⢳⡄⠂⢀
⠤⣈⣹⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⢩⣵⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠉⠀⠀⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀⠀⠈⠑⢟⡝
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⢠⠚⡠⠊⠉⠛⠈⠀⠀⠀⠀⣀⡤⢶⠀⠉⠁⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⡆⠀⠁⠀⠀⣼⠼⠛⣳⠄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠉⠂⠀⠀⣀⣐⡇⢠⠞⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠆⠸⠳⢤⣀⣀⡀⠀⠿⠀⣼⠀⠀⠀⢚⡇⠀⠀⠀⠀⠌⣁⡛⢦⡀
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣺⣿⠊⠉⠙⢦⡤⠦⣄⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠄⣸⣦⡀⠈⠙⠁⣶⠃⠀⢫⡀⢀⣠⠟⠁⠀⠀⠀⠈⣄⣞⢛⣹⠇⢰⠟
⣾⠇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⣠⠂⣾⡶⠀⠀⣿⠃⠀⢸⣷⣀⠀⠀⠀⠀⠀⠑⠢⠤⢾⢿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢰⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣄⠏⣰⠋⠀⠀⣴⣽⠿⢠⡿⣿⠁⠉⣷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⢧⣤⣴⣫⡾⠃⢀⠾⣷⠟⠁⢠⣿⡆⠀⠀⠀⠀⠀⠈⠓⠒⠲⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⡟⢻⡛⡹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠳⠷⣾⡾⢿⣤⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢠
⠑⣀⠁⠀⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠘⠛⠓⠤⡀⠀⠀⠀⠀⢿
⣗⠧⣙⣲⡟⠁⢀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⢄⡵⠞⠁⠀⠀⠀⠀⢄⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠄⠀⠀⠀⠘
⠙⠛⠛⠁⠀⣴⣏⡔⢊⠂⠀⠉⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⢙⢯⡟⠀⠀⠀⠀⠘⠛⠑⠦⣱⣄⠀⠘⢦⡀
⠀⠀⠀⠀⠀⣿⡿⣿⢸⠆⡀⣠⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⢸⣃⡀⠀⠀⣈⣻⣷⣄⡀⡹⣶⣦⡒⢤⡀⢀⡏
⢻⣛⠷⠦⢄⠘⢿⣾⣗⣿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣶⣄⠈⠉⠙⠛⠀⣿⣻⣿⣿⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠊⠉⠀⢄⣨⢆⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⢀⢾⡵⢋⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣛⢛⣉⡙⢎⣛⣛⢛⣛⡛⠙⢃⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠁⠠⠄⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠡⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣛⢻⣿⣿⡟⠻⣍⠙⠻⢬⡙⠷⣀⠀⠀⠀⠀⠈⢿⣿
⣧⡀⢀⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠚⡁⠊⠄⣠⠞⠁⢠⡤⢶⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⢻⢻⣦⡀⠣⡐⠠⣝⣷⣌⡙⢦⣀⠀⠀⠈⠻
⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡡⡋⠀⡠⠚⠁⠀⡴⣿⠃⡼⠀⠀⠀⠀⠀⠸⡿⠛⠿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣽⠿⠿⢷⣄⣻⣿⡿⣷⣿⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⠄⠋⢀⡤⠊⠀⠀⢀⠞⣠⠋⡸⠁⠀⠀⠀⠀⠀⣸⣧⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠠⣌⠻⣿⣟⣯⣽⢿⣏
⠀⠀⠀⠀⠀⠀⣀⠔⣩⠞⠁⢀⡴⠋⠀⠀⠀⢀⠎⣰⢃⢀⠅⠀⠀⠀⠀⢀⠜⡋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣾⣿⡿⠿⣟⣽⣾⣧
⠀⠀⠀⠀⠀⠠⣿⣾⣷⣄⡴⠋⠀⠀⠀⠀⢠⢫⣰⠃⢠⠎⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠉⠻⠟⠁
⡀⠀⠀⠀⠀⠀⠙⠛⠋⠋⠀⠀⠀⠀⠀⣰⠃⣴⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⡶⢦⣄
⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡼⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢭⣿⣿⣷⣁⢸⣿⡆⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠁⠀⠀⠀⢠⠄⣣⡼⠂⠀⠀⠀⠀⣾⣶⣾⡁⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣇⣴⢉⡈⠙⠿⣯⣽⡇⠀⢸⣏⡈⠘⣧⠀⠀⠀⠀⠀⢰⡒⠖⠀⠠⠒⢁⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠆⡔⡰⠑⡐⡄⢢⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠒⠞⠟⠀⠸⠐⡂⡇⠀⡇⡀⠸⠁⠘⡳⠒⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣂⠶⠋⠠⠆⠊⠀⠀⠀⠁⠓⠲⠐⠐⠓⠁⠀⠀⠉⠠⠄⠑⢶⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠊⠁⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠙⡢⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⡇⣀⢃⢠⡆⣶⢠⡖⣧⠆⢦⣧⠇⠄⣦⢰⠂⠀⠀⠀⠠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⠂⠃⠙⠘⠀⠺⠈⠈⠉⠈⠉⠃⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠠⡄⢠⠀⢠⠀⠠⠀⠀⠀⡴⢠⢠⠄⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠐⡇⠌⠁⠹⠔⠃⠀⠀⠃⠑⠋⠸⠜⠊⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⢀⢀⠀⢀⡐⡞⢸⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⢦⡐⠖⠄⢈⡘⢨⢿⡁⡟⢁⠼⢰⠃⠇⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⡀⠀⡄⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⡿⠀⠇⣄⢰⠁⢠⡎⠠⠀⠀⠀⠊⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠝⢢⣄⠀⠆⢄⠀⠀⡠⢀⠄⠼⡙⡄⢄⠀⠀⢀⠀⠄⠀⣠⠞⡉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢉⡦⢤⣥⣀⡃⡆⡌⠀⠠⢸⠀⡆⣠⣥⡤⠂⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠡⢡⠀⡄⠜⠜⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⠀⡀⠄⠅⡀⠀⠀⠈⠀⣠⠒⣀⠰⡗⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠃⡤⠐⠁⠀⠈⢛⠁⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠠⠤⠀⠀⠆⠀⠀⠀⠀⣃⠠⠂⠠⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣀⡠⣤⠆⠀⠀⠐⢄
⠀⠐⣀⠀⠀⠀⢀⡤⠀⠂⠀⠀⠀⠀⠢⠄⠀⠀⠋⠀⡠⠂⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠐⡄
⠀⠀⠀⢠⠂⣀⠀⠀⠀⠀⢄⠀⠀⠀⢀⡴⠀⢐⠀⣀⡀⠸⠀⠀⢀⠀⠋⢆⠀⠄⠀⢀⢁⣀⠈⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠉
⠀⠘⠰⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠄⠁⠀⠀⠠⠐⡀⠠⠀⠁⢠⠀⠞⠁⠘⠀⠁⠀⠀⠐⠀⠀⣀⠀⠀⢮⠆⠀⠈⠀⢀⠀⢀
⠀⢈⠀⠁⠀⠈⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢢⣀⠀⠁⠀⠀⠀⠀⠀⠊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⡀⠰⡄⠈⠁
⠀⡈⠀⠆⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⡘⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠤⠀⠘⠀⠀⠀⠀⠂
⡈⠀⠀⠀⠀⠃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠊⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠲
⠁⡀⠀⠀⠀⠄⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⡤⠞⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⣀
⠀⠐⠂⠀⢂⠀⡀⠃⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢀⣠⣀⠀⠀⠦⡴⠀⠐⣂⠤⠍⡉⠁⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢰⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠙⠣⠔⠀⠉⢂⠀⠈⠢⡀⠀⠘⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⡁⠀⠄⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⡀⠀⠀⠐⠄⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠔
⠀⢀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠤⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⡠⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠆⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠢⢀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠐⠁⢠⣦⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠀⡶
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⢀⣄⠀⠀⠊⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠉⢀⢀⠁⠀⠑
⠉⡵⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⣀⠋⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣐⢂⡔⠂⠀⠀⠀⠀⠐⠀⠀⠀⢠
⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠠⠄⠀⢀⠀⢀⠀⣀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠
⠈⠁⢀⣀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠔⠁⠰⢀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣐⠁⠀⠀⠒⠠⠠⠀⠀⠀⠀⡀
⠀⠀⠈⠀⠀⠀⠰⡀⠀⠀⠀⠀⣴⡂⠀⢀⡀⠀⠈⠀⠀⠀⠊⠁⢀⠋⠁⣀⠄⠲⠀⠀⣀⢀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠄⠀⠀⡤⠈⠘⡄⢘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠈⠀⠀⠒⠁⠀⠀⠀⠜⠁⠀⠀⠎⠀⠀⠁⠀⡀⠀⠀⡀⠀⠀⠰⢂⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⢠⠀⢀⡀⠀⠀⢠⠀⠢⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢙⣢⠃⠀⢹⡄⠚⠁⡀⠀⠈⠢⡀⠀⠈⠀⠈⠀⠀⢡⡐⠀⠠⢀⠠⠆⢀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠎⠁⠀⠀⢀⠤⠖
⠁⠉⠒⠉⠀⠈⡄⠀⠀⠢⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠂⠀⠀⠘⠀⠀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠒⠊⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠶⠖⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢶⣶⣼⣆⠀⠀⠀⢘⣧⣤⡶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣠⠶⠛⠉⣩⡽⠛⠋⠉⠉⠛⠻⣭⡉⠙⠳⢦⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟⠁⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⢷⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠹⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⣧⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡤⠶⠿⢦⡦⡼⠗⢦⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠛⣲⣦⣀⣟⠀⣠⢼⠷⠲⣄
⠀⠀⠀⠀⢰⣋⣀⣀⣾⠻⣣⠖⠻⣼⣁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⡝⢦⣰⠃⠧⠟⠹⠿⢻⡀⠀⠀⢿⡀
⠀⠀⠀⣾⠉⠁⣸⡽⠿⣤⡇⠀⠀⠸⣏⣠⣴⡒⠻⢦⣀⣀⣀⣀⣀⠀⢀⠀⢰⡓⠟⠀⠉⠀⠘⣿⣀⣀⣀⡀⠀⣠⣙⣦⢴⡞⠓⠲⢤
⠀⠀⣀⣼⣦⣞⣡⡤⠤⠤⣧⠀⡶⢶⠇⠉⠀⢹⠆⡴⠃⠀⢰⡏⠀⠙⢹⣷⣏⠀⣀⣀⢸⡳⣤⢻⣞⠁⠈⠉⠳⣿⠈⠀⠀⣿⠀⠀⣀
⢤⣬⡿⠉⠸⡅⠀⠀⠀⠀⢾⠳⠟⠀⠀⠀⢀⣼⡿⣥⣀⣀⣾⣅⡀⠀⠀⠁⣿⡶⠿⠈⠉⠁⠘⣿⡿⣄⡀⠀⠀⢸⠀⠀⣠⡾⠷⠯⣅
⠀⠈⢉⣙⣿⡳⣄⡀⠀⠀⠈⣳⣄⠀⢀⡤⠬⠗⠀⣸⠋⠉⠉⠛⢦⡀⠀⢠⡟⠀⠀⠀⠀⢀⣀⢸⡀⠀⠉⠿⣖⠚⠶⡏⠁⠀⠀⠀⢈
⠀⠀⠈⠙⠻⠶⢶⠭⠭⠿⠿⠏⠈⠓⢮⣽⣄⣠⠾⣅⠀⠀⣀⡤⣾⣥⠴⠾⠳⠶⣄⡴⣆⡞⠙⠞⠓⠒⠚⠏⠻⠛⠲⠿⠶⠤⠤⠖⠋

⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⢸⣣⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠡⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆
⠀⠀⡴⠀⠀⠀⠀⠠⢻⠐
⠀⠀⠂⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢒⣛⣭⣭⣥⣶⣶⣶⣶⣶⣾⣿⣭⣽⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣋⣥⣶⣿⣿⣿⣿⡏⠉⠉⠀⣸⡿⠟⠿⣿⣿⣿⣿⣿⠿⣿⣾⣭⣓⢤⡀
⠀⠀⠀⠀⠀⠀⡰⠋⣤⣾⣿⡿⠟⣽⣿⣿⡟⠛⠓⠶⢴⡏⠀⠀⢀⣿⠇⠙⣦⠉⠳⣦⠉⠻⣿⣷⣮⡣⣤⠤⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⡼⢡⣾⣿⣿⠋⢠⡾⠃⡿⠈⠻⣤⣀⡀⠀⠀⠀⣠⠞⠋⠀⠀⣸⠀⠀⢹⡇⠀⠈⢿⣿⣷⡹⡄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢰⡇⣾⣿⣿⠃⠀⣾⠁⠀⣿⡀⠀⠀⠉⠉⠉⠛⠺⠁⠀⢀⣠⠴⠋⠀⠀⣸⠇⠀⠀⢸⣿⣿⡇⣷⠖⣶⠒⠀⠀⡇
⠀⠀⠀⠀⠘⡇⢻⣿⣿⠀⠀⢻⣆⠀⠈⠛⠶⣶⣤⣤⣤⣤⣤⣀⢰⡟⠁⠀⠀⢀⣴⠏⠀⠀⠀⣼⣿⣿⠃⡏⢠⠏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣿⡄⠻⣿⣦⡀⠀⠙⠷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠀⣀⣤⡶⠛⠁⠀⠀⣠⣾⣿⡿⢃⡼⡷⠃⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢸⡘⢦⡈⠛⢿⣶⣤⣀⣀⠀⠉⠉⠉⠛⠛⠛⠒⠶⠶⠶⠛⠁⠀⢀⣠⣴⣿⡿⠟⢉⡤⠊⢰⠇⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠈⣇⠀⠈⠓⠆⠈⠙⠛⠿⠿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣶⣶⣶⡿⠿⠛⠋⠁⠀⠀⠉⠀⠀⣸⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⢹⠆⠀⠀⢀⣤⣠⡏⠉⠃⠀⠈⡗⠒⠀⠐
⠀⠀⠀⠒⠶⡶⢼⡶⣶⣦⡀⠀⠀⠀⠂⠀⠀⠀⠂⢤⠤⣘⣤⡟⠲⡁⠠⠒⠱⠋⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⢅
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡌⢿⠄⠈⠀⠀⠀⠀⠀⠀⡸⢐⠛⠀⠀⢀⣄⠀⠀⣤⠐⠉⠁⠀⢠⣾⢻⣻⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣣⠀⡇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠏⠈⠲⠒⠊⠉⠙⠋⠁⠀⠀⠀⠈
⠈⠺⡄⠀⠀⠀⠜⡿⠾⡟⠦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠄⠀⠀⠉
⠀⠀⠈⢩⠖⠀⠀⡅⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠀⠀⠀⠋⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠤⢰⡤⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠶⠀⠃⠆⠀⠇⠶⠘⠰⠆⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⢠⡴⠶⣶⠉⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄
⢀⠔⠚⠂⠀⠈⠀⠀⠜⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣤⣾⡛⠛⠯⣃⢄
⢸⠄⠀⠀⠀⢀⣤⣤⡄⠀⠐⠋⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣀⣴⡜⠛⠦⠀⠙⠦⡈⢳⣃
⢀⠀⠀⢀⣨⣿⣭⣷⠁⠀⠀⠠⢄⠀⠀⠂⠐⢀⡀⠉⠀⠀⠀⠀⠆⠠⢤⣿⣤⣔⠉⠀⠇⠀⠀⠑⠄⠀⠱⠄⣿
⠈⠟⠉⠁⠀⠈⠉⠀⠀⠀⢀⣀⠈⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢡⠈⢇⠀⠀⠀⠀⠀⠈⠆⠀⣧⡟
⠀⠀⡀⢀⠄⠀⠀⢠⠀⠀⠀⠁⣠⠎⠀⠀⠀⠠⠀⠀⠀⠀⠢⣀⡀⢈⠀⠀⡰⢀⣿⠄⠀⠐⠀⠀⠀⢸⡴⠋
⣤⣤⣥⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣤⣽⣶⣶⣿⣬⣥⣤⣵⣤⣤⣵⣦⣥⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⣤⣤⣤⣤⣤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣮⣽⣶⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣗⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⣾⣿⡿⢫⠖⣠⣴⠶⠶⠶⣽⣿⢟⡉⠠⢄⣐⡲⢬⣑⢮⡻⣷⣮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡅⣿⣿⢺⡇⢿⡘⢿⣧⣀⡀⠀⠀⠙⠁⠀⠄⠀⣹⣿⡦⣹⡆⣿⣿⣿⣷⢹
⠀⠀⠀⠀⠀⠀⠀⢰⣾⡉⠉⠉⢛⢻⣮⡛⢦⣕⣈⠙⠲⠬⢭⣽⣛⣓⠀⣠⡴⠶⠿⠛⠩⢒⣩⣾⣿⣿⠟⣡⡿⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⠿⣿⣾⢿⣿⣷⣮⣝⣛⠿⠿⣷⣶⣶⣿⣅⣿⣶⣶⣿⣿⡿⠿⢿⣛⣭⣶⣿⣿⡇⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡞⠙⣿⢿⣷⣄⠈⣹⣮⢿⢿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⠉⣾⣆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢸⢵⠀⠈⠳⣝⡻⣿⣷⣾⣘⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠋⠁⠀⠀⡼⠙⣿⣇⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⡸⡒⠦⢼⣿⣿⣶⣮⣭⣍⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⠞⠁⠀⣿⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⢷⡱⡀⠀⠀⠹⡀⠉⠉⠙⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⣀⣤⣾⠁⠇⠀⣰⡿⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⠳⣌⡢⢀⠀⠙⠦⣀⠀⠀⠢⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠴⠋⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣅⡂⠀⠀⠉⠀⠀⠈⠒⠩⢛⣻⠿⠿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣇⠈⡇⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⠚⢻⣿⣿⣿⠿⠶⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⢻⡜⡄⠀⢠⠀⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠚⣡⡾⠉⠉⡡⠄⢀⣈⢩⣶⣾⢣⡀⠀⠀⠀⠀⠀⠀⠀⣦⡆⢧⠈⢿⣜⠀⢐⡄⢀⠈⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⠹⣦⠟⣿⣿⣷⠀⠀⠀⠀⢠⣶⣼⣿⣧⠈⢇⠈⢿⡂⠀⠀⣀⣠⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠚⣡⣿⣿⣿⣿⠀⠀⡀⠀⠈⠿⢿⣿⣿⣿⣎⠢⣀⠛⠲⣶⣝⣿⣦⣿⠇
⠀⠀⠀⠀⢀⣎⡀⠠⠃⠀⠀⠀⠀⠠⠐⢁⣴⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⣀⣿⣯⣿⣿⣷⣬⠑⢄⡙⠿⣿⣿⡿
⠀⠀⠀⠀⢠⠟⡄⠁⠀⠀⠀⠐⢀⣴⣀⣨⣿⡿⠛⠃⠀⠀⠀⠾⡿⣿⣟⣻⡿⠛⠙⣿⡿⢹⣿⣿⣦⣬⣑⡢⣝⡗
⠀⠀⠀⠀⠀⣆⠀⢀⣀⢤⣔⠠⢚⣽⣿⡿⠋⠀⣠⠎⠀⠀⠁⣰⠟⠉⠉⠙⢿⣤⣴⡿⢁⣾⡿⠿⠿⠛⠛⠛⠺⠃
⠀⠀⠀⠀⠀⠘⠢⢽⣞⠯⣖⣤⣿⣿⣿⣷⢴⡶⠋⣀⣀⣤⣾⠏⠀⠀⣀⣤⡾⠃⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⣸⡀⠊⠀⠉⢙⣥⣄⡠⠴⠋⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣍⣙⣒⣒⢒⣁⣀⣠⣤⠖⠋⠁⢓⣿⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣻⡟⠁⠀⠉⠀⣰⣯⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣷⣍⣀⣠⠀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⠂⣄⠀⠀⠰⠀⠀⠀⡄⢀⠀⢠⡀⠀⠀⠀⠄⢠⠄⠀⢀
⠀⡮⠷⠀⣠⠈⠀⠀⢀⡀⠀⠙⢆⠀⠈⠁⠀⡛⢌⡀⠀⠤⠀⠀⢻⡁⢲⠀⠈⠱⠀⢁⡁⠀⠺⠛⠁⢀⠖⠀⠘⠀⠀⠫⢠⣫⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⠺⠀⠠⠀⠀⣴⠼⠧⢹⠀⣁⠁⡀⠐⠆⠀⠂⠀⠀⠉⠐⠀⠀⠀⡀⡂
⠀⡐⢖⠩⢀⠀⠀⢀⠴⠒⠈⠉⠉⠓⠂⠀⠆⠀⣄⣀⣠⡄⠀⣈⠉⠉⠁⠀⣤⠀⠃⡀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣠⣀⠈⢉⡆
⠀⣚⣅⠤⠑⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢾⣿⠄⠀⠀⠄⠀⠀⠘⠀⠀⠇⠸⠀⡀⠉⠀⠄⠀⠠⡀⢉⠁⠀⠁
⠀⠠⡈⠁⡐⠀⡉⠀⠉⠉⠁⢻⠂⠉⠉⢁⣍⡁⠘⠒⠊⠀⢀⠁⠀⠤⠄⠀⡐⠂⣂⠀⠂⠁⠀⠀⠈⡀⡋⠁⠈⠏⣈⣁⠄⢶⢀
⠀⠠⣈⡁⠀⠀⢹⠃⠉⠀⠀⢸⠀⢤⠀⠨⢱⠀⠀⢰⢈⣄⠊⠀⠀⠀⠀⠀⠂⠀⠉⣉⠰⢢⡄⠀⢀⠁⠁⠀⠈⠱⠛⠓⠀⢠
⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡇⠀⠀⠀⠀⢈⠀⠀⢀⠀⢀⠄⣴⡀⠀⡀⡀⠀⡀⠘⠛⠃⠀⠀⡀⠠⣀⠂⠄
⠀⠠⠁⠀⡄⠂⠁⠀⢀⡀⢴⡸⠀⣀⠀⠠⠈⡇⠀⠁⠀⠀⠘⠀⠤⠚⠃⢀⣸⠁⡱⠀⢠⣴⠀⠹⢄⠀⠀⢀⠀⠀⠠⠐⠐⡀
⠀⢐⡂⠀⠈⠈⠀⠀⡉⠀⠀⡀⠘⠀⠄⠀⠠⠐⠄⠄⡀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣤⣌⡄⠀⠒⠋⠀⢀⣄⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠁⠐⠀⠺⠗⢀⢀⠁⠀⢀⠀⠠⠂⠀⢈⠂⠡⠀⠀⠀⠀⢠⠄⠀⢶⣦⣤⡄⠀⠀⠁⠀⢀⣶⡤⠐⢀⣉⢓⠄⠀⢀⠄
⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⠈⠂⠀⠁⠐⠀⠤⠐⠂⠀⠠⠀⠢⠄⠀⡈⠀⠀⠉⠀⢰⡇⠀⣄⢻⣺⣟⣃⣞⣿⣯⡄⢀⡀
⠀⠀⠀⠀⢂⡁⡀⠀⢦⠀⠀⠢⠘⠀⠀⡅⠀⠀⠂⠀⢈⠁⠀⢀⠢⠀⢐⡀⠂⠀⠀⠀⠀⠈⠁⠘⠉⠃⠈⡏⡍⠋⠈⠁⠑⠀⠁
⠀⢌⠤⠀⠈⣄⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢜⠀⠈⠀⠀⠀⠑⠀⡀⠂⠀⠀⡀⠀⣤⣄⡄⠀⠀⠃⠀⠀⠠⠀⠀⠦
⠀⠠⠎⡄⠀⠘⠀⠀⠒⠋⢀⠀⠃⠉⠘⠀⠃⠉⠐⠁⡀⠈⠁⠀⠀⠀⠀⡀⠈⢴⡥⠀⠀⠃⠀⠁⢛⠃⠀⠀⠀⠀⠂⡀⢠
⠀⢁⢚⡠⢡⠀⠀⠀⢀⠀⠉⢀⡁⠀⠁⠉⠁⢈⡁⠈⠁⣠⠘⠠⣀⣀⠶⠃⡀⣈⠈⠁⠀⠀⠀⡀⠘⠶⡄⠓⠃⠠⠀⠉⠠⠠⠆
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣀⠀⠀⠀⢠⠅⡊⠁⠀⠀⠀⠀⢉⡁⢁⠁⠀⠂⠀⠄⠠⣌⡀⠂
⠀⡎⠀⠀⠀⠆⠀⠰⣶⡴⣧⡄⠩⠤⠀⠀⠐⠋⢱⠀⠀⠈⢐⠃⠀⣀⠀⠐⠒⠁⠀⠒⠂⢠⠀⠀⢂⡊⠒⠀⠀⠀⡐⠀⠉⣀⡀
⠀⠀⠘⠈⠣⠀⠀⠀⠋⡏⠉⠇⠀⠀⠁⠄⠀⠀⢊⢄⠀⠁⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠇⠐⡁⠀⢠⠀⠀⠀⠩⠐
⠀⠀⠦⠀⠄⠀⠲⣒⠚⢁⣐⡇⠀⠀⠤⠀⠀⠄⠀⠽⠇⠀⠠⠄⠁⢀⠀⢀⡂⠈⡆⠙⠂⠁⢰⠘⠀⢩⢨⠅⠀⠒⠀⠀⠀⠀⠅
⠀⠀⣀⢠⠀⠀⢠⡌⠉⠉⠉⠁⠀⠄⣷⠲⠀⣠⢶⣖⠤⣄⠀⠲⠆⠀⠀⠶⢄⠀⠀⠀⠀⢤⠖⣆⠀⠒⠰⠂⠀⠀⠀⠐⠔⠁
⠀⠀⢘⠬⠆⠀⢈⠉⠢⠀⢀⠈⠀⠀⠀⠀⢨⣶⠋⠉⠙⢶⠆⠀⠄⢀⠘⠈⠁⠀⠀⠀⠀⢊⡗⢤⠀⠀⠂⠀⠤⣥⢀⢤⠀⠀⢄
⠀⠀⠈⠓⡯⠂⠈⠠⢀⠀⠀⠉⠀⠗⠀⠀⠈⢭⣷⣠⣶⡿⠂⠀⠂⢁⠀⢀⠀⠘⠉⠀⠀⠼⠧⣐⠀⠂⠀⢤⠀⠁⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠀⠀⢠⣀⠠⣿⣿⠀⠀⢨⣶⣦⣀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢶⡿⠀⠀⢘⢿⣷⣿⣯⣶⣶⠀⠛⢿⣯⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠘⣾⡷⠂⠀⠛⣻⡿⣿⣿⣯⡀⠰⢶⣿⠿⣇⣴⣤⡦⠹⣿⠇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⠚
⠀⠀⠀⡀⠀⠀⣠⣾⠀⠈⠀⠘⠃⢩⣤⣤⣴⡄⠀⠉⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠃⠀⢢⠇⠀⢀⠄⠀⢀
⠀⠀⠀⣿⣧⣰⣿⠃⠀⠀⠀⣤⣾⣿⣿⣿⠟⢀⣴⣾⣯⡀⢰⣿⣧⠀⠀⠀⠠⡀⢰⠁⠈⠣⣀⡼⠒⠋⠁⡠⠏⠁
⠀⠠⣤⣼⣿⣿⣷⣶⡷⠂⠀⠛⠛⠟⠛⠉⢠⣿⣿⣿⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠘⠢⣀⡀⢸⡇⣀⠤⠯⣤⠤⠤⠄
⠀⠀⠀⠀⠉⠻⣯⡀⠀⠀⢼⣿⣦⣶⣿⠀⠀⠉⠙⠻⠿⠛⣀⣧⣀⠄⠀⠀⠀⠀⠉⠙⠉⠙⣾⡿⠁
⠀⠀⠀⠀⣠⣤⣄⡁⠀⢀⣼⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⠀⣺⣷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣆⠈⠛⣿⣿⠟⠉⠀⠀⠀⠀⢿⡿⠀⢺⣿⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⡉⠉⠉⠉⠀⠀⠙⠁⢰⣤⣄⠀⠀⣤⣬⣶⣆⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠾⠟⠣⣦⡿⢿⣠⣤⡤⠀⣾⣿⣿⡇⢸⣿⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠛⠋⠀⠀⠁

⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣘⠃
⠈⠀⠀⠘⠄⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠔
⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⡆⠀⣂⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠗⠀⠀⠈⠓
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⢃⠀⠁⠀⠻⣤⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠰⣄⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠉⠁⠀⠀⠀⠀⠉⠳⢄⣀⡀⠀⠀⠀⠒⠂⠀⠀⠈⠽⠠⠄
⢀⡔⠢⠄⢤⣀⠀⠀⠀⠙⠁⣀⡤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂
⠋⠀⠀⠀⢀⣿⠆⠀⡴⠚⠉⠀⠀⢠⠏⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠄⠀⠀⠈
⢷⣤⣤⣤⠾⠋⢀⡎⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⠀⠀⡐⠀⠄
⠀⠀⠀⢀⣤⠖⠛⠁⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⢠⠶⠛⠛⠒⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⢰⠋⠁⠀⠀⠀⠀⠐⠀⡸⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠸⣄⡠⠄⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⢼⠁⠀⠀⠀⠀⠄⣀⡀⠔⠁⠀⠀⠀⠂⠀⠀⠌⠁⠀⠈⠀⡀⠈⠂
⠤⠄⠀⠀⠀⢈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠀⠀⠀⠀⠀⠁⠀⢂⠄⠀⣢⡷⠀⠐⠏⠀⢀⣠⢄⠔⠀⠀⠀⠀⠀⠠⠔⠂⠀⠈⠀⠀⠀⠠⠄⠀⠀⢰⡇⠈⠙⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠖⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⣀⠔⠋⠈⢷⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠙⢦⡀⢀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡁
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠳⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⢁⡀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠂⠠⠍⠁⠀⠚⠛⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊
⠀⠈⣆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠶⠶⢿⣟⣶⣿⣿⡿⠿⠿⠶⠶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉⠀⢀⠀⣀⣤⣄⣀⣨⣿⢋⣥⣶⣦⡄⠀⠀⠀⠈⠙⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠠⠈⢠⡶⠉⡿⠋⠉⠙⠿⠁⠀⠹⡏⠑⡄⠀⠠⠀⠀⠀⢻⣿⠻⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠛⣿⠁⠀⠀⡆⢠⣯⠀⠐⢷⡀⠀⠀⠀⠀⠀⣰⠃⠀⣽⠀⢀⠀⠀⠀⠀⣿⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣠⣽⡀⠀⠀⢇⠀⠙⢦⡀⠀⠁⠐⠶⠄⢠⠖⠀⣀⠤⠁⠀⡜⠀⠀⠀⣰⣿⣿⡇⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠳⣄⠀⠉⠛⠶⢦⣤⣀⠀⠴⠋⠀⠀⠐⠈⠀⠀⣀⣴⣿⣿⣿⣿⠟⢀⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠛⠿⣷⣦⣤⣈⣉⠓⠒⠀⠤⠤⠈⠁⠐⢈⠀⢀⣠⣤⣶⣿⣿⣿⡧⠾⠛⠁⢀⠟⠁⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠛⠛⠿⠿⠿⠴⠾⠷⠦⣀⡴⠾⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⡇⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠐⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⠎⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠧⠤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣿⣦⡤⠄⠐⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠈⣀⠤⠤⠀⠀⠀⠈⠉⠉⠂⢠⣄⣀⣀⣀⣠⣤⡶⠛⠻⠏⠁⠁⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠄⠀⠉⠀⠀⢀⣠⡤⠀⢨⣤⣤⡀⠤⠀⠀⠤⠀⠀⠀⠒⠉⠙⠛⠛⠛⠃⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⢀⡂⠀⠀⣀⠠⠒⠉⠓⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠂⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢩⠥⢖⠲⣄⡈⠉⠉⠉⣀⣀⡈⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠈⢢⣄⠀⠈⢻⠳⢢⢌⠁⠶⡿⣽⡲⣄⠀⠻⣦⡠⠀⠐⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢼⡒⡻⡆⠈⠂⣉⣓⣂⣀⠀⢺⢃⣦⣎⣷⡽⡜⡆⠀⣿⣄⠤⢒⣊⣉⣙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣌⠻⡽⣍⡀⠀⠀⡏⠉⠉⠳⢯⡺⠞⡨⢜⣵⠟⢀⣰⣿⡥⠚⠁⠀⡼⠈⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠙⠳⢮⣖⣩⠑⠲⢤⣤⣤⣥⣴⣷⠾⠞⣋⣡⡴⠞⠋⡼⢤⣀⣠⠞⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠈⣇⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠶⠶⠞⠛⠛⠉⠁⠀⠀⢰⢃⡤⠊⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢉⣠⡾⠟⠁⠙⢆
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡴⠂⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣴⠟⢫⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡌⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⢣⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣤⣄⣀⣀⣤⣤⣴⠾⠋⠁⠀⠀⠀⠀⡠⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⢘⣀⡠⠤⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠊⠀⢀⢤⡤⠆⢁⠠⢄⣰⡭⡄⣤⡤⣌⢑⡄⠀⢠⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣸⠉⠈⣖⠁⢹⢊⠇⢸⢪⡀⠀⣇⠀⢰⡏⠀⠘⠁⠘⠆⠉⡶⠂⢻⠤⢖⢃⠠
⠀⠀⠀⠀⠀⠀⠘⡤⠶⠀⢿⣧⠀⣽⠀⣜⢸⠀⡏⠁⠇⢠⠇⡇⢸⢹⠀⡴⠀⢀⡆⠀⡟⡄⢠⡄⠸⠂
⠀⠀⠀⠀⠀⠉⢨⠸⠸⠀⢸⡏⠀⣿⠀⣇⣾⠀⢧⠀⡇⢸⠀⡇⢸⢸⠀⣧⠃⠸⡟⠀⢷⠃⢸⠃⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠊⠓⠤⠣⡀⢀⡀⠈⣿⠀⠈⠲⡇⠀⠉⠀⠈⡎⠀⢹⡀⢀⡷⠤⠺⢤⠎⢉⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠉⠙⠈⠢⠤⠔⢉⠒⠊⠒⠊⠑⠒⠁⠍⠉⠂⠀⠀⠀⡐
⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠰⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠂⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡵⠀⠀⠀⠀⢀⣼⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⠞⠀⠀⠀⠀⠀⣾⡏⢸⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⢸⣿⢠⠃⣰⡟⡸⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢠⠜⣿⡇⡠⣾⡧⠀⠀⠀⢸⣿⠏⢠⣿⣳⠃⠀⠀⡤⣤⡠⠊⠀⣠⠔⠊⢉⡴⠋⡾
⠰⡿⡢⠖⣄⡀⠀⠀⢿⠟⣰⣿⢃⣴⢦⠀⢸⣿⠀⢸⣿⠁⠀⢸⠃⢩⣿⠃⠀⢰⠃⢀⡴⠋⠀⢐⡇
⠰⣉⡘⠢⣁⢾⠖⢦⠀⠀⣿⡏⢸⣯⠜⢠⠏⠘⠛⢹⣿⠀⣠⠋⠑⠚⠋⠀⢀⡤⠛⢯⣀⣀⡤⠎
⠀⠺⠄⡤⠈⠷⣄⣚⠆⠀⠻⠧⠜⠷⠔⠁⠀⠀⠀⠘⠿⠚⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠴⠂⢤
⠀⠀⠘⠦⡤⠛⠃⠉⠲⠄⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⠠⠀⢀⣀⠤⣤⡤⢲⣦⠀⠘⢄⣀⡤⣿⡆
⠀⠀⣠⡤⡀⠀⠀⠀⡠⠒⠒⠛⠒⠶⢶⣿⡷⠴⠴⠶⠚⠋⠁⠀⠀⣿⡏⠀⣿⠃⣼⡟
⢀⣾⠋⣠⣿⠀⠀⣀⡀⠀⢀⣀⠀⠀⢸⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⠁⠀⠛⠀⣿⡇⠀⣸⣷⠴⠲⣦
⢸⣯⠔⣿⡏⠀⣰⣿⠃⢀⣾⣯⠀⢀⣾⣿⠀⣰⣿⠀⢠⣿⡇⠀⡸⠁⠀⠀⠀⠀⣿⡇⠀⣿⡏⠀⢀⣿
⠀⠀⠀⣿⣇⡴⢻⣏⡠⢛⣿⡇⢀⠞⠀⠙⠋⠘⣿⣀⢼⣿⠀⣰⠃⠀⠀⠀⠀⠀⢽⡇⢠⣿⠇⠀⣾⡟
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠘⣿⣧⠏⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡤⠒⠂⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠛⢦⠱⣄⠀⣀⡄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣀⠀⣸⠀⠀⠈⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠁⠚⠃⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣈⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠛⠉⠛⠛⠛⠻⠿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠃⠀⣠⠤⠔⠒⠊⢁⠉⠉⠭⠭⠥⠡⠄⠉⠉⠉⠉⠑⢲⠄⠀⠀⠉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣕⢀⣀⠀⠑⠦⢄⣀⣀⣁⣐⠂⠀⠤⠬⠭⠭⠤⠖⣒⣒⡫⠅⠂⠀⠀⠀⠐⢠⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠛⠻⠿⣶⣦⣤⣤⣤⣀⣉⣉⠉⠉⠉⠉⠉⣉⣉⣁⡠⠄⠀⠀⣀⣰⡤⠖⡿⠉⠙⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⠁⠀⠚⠉⠉⠉⠙⠛⠙⠉⠈⠙⠓⠀⠀⠉⠉⠁⠀⠀⢾⠇⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡇⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡽⠁⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⣀⣤⠴⣶⡒⠊⠡⠸⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⠾⠛⠿⢷⣶⣶⣿⣋⣄⣀
⠀⠀⠀⣀⣴⠯⠓⠋⠉⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣪⣴⣿⣶⡶⢿⣿⡿⠁⠈⠉⠙⠛⠿⣦⡀
⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣦⣤⣄⠀⠀⠤⠐⠚⠋⠁⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷
⠀⠀⠀⠈⠙⠿⡷⢶⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠿⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠋⠯⠽⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣕⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⢀⣠⣤⠀⠀⢤⡀⠀⠀⠀⠀⠴⠒⠀⡄⡁⠀⠀⠀⠤⠤⠤⠀⣀⡀⢰⡗⠢⣿⡜⢻⡤⠔⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⣾⠀⠈⢷⡀⠀⠀⠀⠁⠀⠈⠀⣄⠺⢑⡇⢸⢃⡇⠀⠀⢠⡞⠁⠈⡞⠅⠨⠿⠷⠚⠛⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡤⠄⠘⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⣉⢀⡀⠀⠀⡾⠀⡀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢚⢷⠀⠈⢻⠴⣤⡄⣀⣀⣀⣀⣀⣈⣉⣒⣀⣀⡠⠤⠤⡇⠀⠀⡟⠀⠀⢰⠀⠀⠀⡆⠀⠀⡇
⠀⡀⠀⠀⠀⠀⠰⠀⠀⡀⠈⡆⠰⠃⠘⣇⣀⣸⡆⣀⡀⠆⠀⢰⠈⢹⡏⠁⠀⡆⠀⠀⠀⢸⣧⣐⣸⢡⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠀⠄⠀⣿⢶⣼⣧⣤⣤⣤⣴⢸⠆⢸⡇⠰⠆⠎⡷⠤⣤⣼⡴⢦⡟⢼⠦⠶⠾⠶⡶⠶⠷⠶⠾⠧⠶
⠀⠄⠀⠀⠀⠀⢠⠐⠀⠀⠐⡤⠃⠂⢰⡇⠀⠀⣿⠀⣿⠀⢸⠀⠀⢸⠀⠀⠀⢸⠇⠀⣼⠀⡇⠀⣇
⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⢠⠂⣸⠁⠀⠀⡇⠀⣿⠀⢸⣇⣤⣼⣧⣀⡀⣸⠀⠀⡟⠀⣧⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠊⠀⠛⠐⠐⢸⡇⠒⠛⠒⠀⣿⡙⠛⠋⠉⠉⠿⠀⠈⠁⠀⢿⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⢠⣾⠀⠀⠀⠀⠀⠘⢀⣐⣒⣒⣛⣛⣒⣀⣀⣀⡀⠀⠀⠀⠀⢒⣚⣓⣒⡒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠓⢄⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠉⣐⠀⠈⠘⡄⡴⠊⠗⡙⢉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠂⢄⠉⠰⠃⡰⢧⢇⡁⢸⠆⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡕⠒⠒⠪⢕⠤⡀⠀⢿⡟⡇⠀⠀⠀⠈⠫⣍⠉⡴⠊⢨⠄⠀⡵⠂⠸⠥⢲⡒⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡎⠙⠻⣶⡀⠀⠉⠪⡳⢌⢯⣿⠀⠀⣀⡤⠴⠞⡗⢳⡒⠛⠚⠳⠠⠆⣀⣤⣊⠀⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡇⡁⠀⠀⠘⣵⠀⠀⠀⠈⠳⣽⣝⣷⠋⠁⠀⡠⠊⠁⠘⡀⠁⣬⣀⠃⠠⠀⡶⢭⣀⣐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠱⡳⣄⣀⢴⡝⠀⠀⠀⠀⠀⠈⣯⠞⣆⠀⠀⣅⠄⠈⠐⢙⠀⢧⢸⡀⢒⠀⠈⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣝⣛⡟⣆⠀⠈⢆⣰⡀⠚⢢⣈⠎⢦⠮⣡⣹⠁
⡰⠋⠑⠂⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠫⡏⣀⠹⠊⢧⡀⠀⠁⠙⠢⠇
⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣤⣴⠾⣾⣷⢦⣤⠿⠛⠷⠻⠿⣦⣤⣤⣤⣤⣀
⠘⢦⣀⣀⡤⠞⠁⠀⠀⠀⢀⡴⣛⡉⢢⡀⠄⢡⢬⡸⣌⣛⡿⠀⠁⠔⡠⣒⡪⡔⠘⡆⢉⢰⠋⢨⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡏⣿⣷⠄⡇⣰⠿⢀⠅⣂⢀⢀⡈⢿⡜⣇⠳⠟⢣⣴⠣⠘⣾⡀⠻⡿⢃⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢄⠑⠬⠵⠚⣰⠯⡡⢀⡈⠄⠀⠃⠀⢸⡇⡈⠙⠋⠉⡲⠓⠓⢾⡝⠲⠒⠋⠂⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠂⡬⠀⡀⣾⡟⢢⠐⠀⡠⠚⠉⢉⢉⢺⡇⢀⢄⠰⠶⢇⠿⣿⠀⣷⡠⠖⢛⠓⣅⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠋⢅⣁⡤⢴⡀⣿⠿⠠⠀⠀⡇⢴⣫⢯⢣⢸⡇⠁⠣⡠⠄⡀⢝⠩⡀⣿⠡⢸⣟⡿⢸⢆⢻
⠀⠀⠀⠀⠀⠀⠀⢻⠇⡔⠁⣴⠲⡌⣿⠦⠴⣥⠤⡱⣤⣉⣩⢼⢸⣇⠔⠋⡉⠑⣔⣘⠀⢈⣿⠀⠘⠲⡖⠁⠜⢻⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧⠀⡳⢭⠖⣿⣤⣦⡄⢱⠈⠂⢠⣴⡅⣿⡇⠀⡎⣟⡇⣸⣀⣪⣦⣿⡢⠂⡻⠋⢋⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢙⠲⠤⠤⢿⣜⣚⣃⠜⢀⠄⢀⢠⠡⣺⠇⡁⡑⣢⢒⡏⣡⣤⣨⡏⣴⣕⠐⢈⠚⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠖⡡⢌⡘⡇⢩⠝⡋⠉⠑⢦⡌⡄⣿⢀⠂⠐⠙⠉⢣⣙⣛⣼⠏⣤⣌⠑⣬⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣴⣶⣁⣹⢏⡀⡔⡭⣷⢈⡗⡈⠃⡸⣋⡙⢦⡕⣠⠀⡸⠁⡧⣝⣝⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢤⣧⣉⣡⣞⣀⣤⡾⢧⣿⣿⣀⣏⣥⡶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢻⣟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢷⣽⣷⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣦⣤⣄⡀⠀⠀⠆⠀⠀⠀⠈⢻⠀⠀⠸⢧⠀⠀⠀⢀⣴⣾⢿⠿⠟⠉⠉⠋⠛⠛⢻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠒⠶⣤⣀⣈⠀⠀⠀⣈⡀⠀⠔⠙⠉⢀⣤⣄⣦⣴⣶⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣿⣿⣿⣄⠀⠀⠀⣻⡿⣿⣦⣾⣿⣿⣷⢰⣶⣿⠾⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠙⠀⣸⣼⣿⣿⣿⣿⣿⣁⣀⠄
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⢿⠂⠀⠀⣰⣈⢠⣿⠿⠟⠛⠋⠁⠈⠁
⠀⣠⣴⣿⣿⣿⣿⣶⣦⠌⠿⢿⡆⠀⠀⠀⠀⣄⡴⠖⠓⠲⠋⠀⠀⠀⢄⣀⠀⠀⠢
⠠⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠉⠑⢢⣄⠀⠀⢳⠠⣠⣤⣤⣤⣶⣶⣦⣤⣄⣤⣤⣤⡤
⠀⠀⠀⠀⠀⣀⣀⣄⣠⣤⣴⣂⡀⠀⣰⠏⠋⠡⣀⣠⣽⣷⣶⣾⠟⠋⠉⠉⠛⠿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠖⠛⠋⠉⠁⠀⠀⠀⠀⠨⣡⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡹⣏⠉⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣁⡀⠤⠚⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠀⡀⠀⠀⠀⠀⠀⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣤⣀⣠⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⣿⡟⠻⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⢠⣶⠖⢲⡦⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠘⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⣿⡇⠀⠀⠀⠀⢳⠛⠀⢀⠀⠪⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⣀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠠⣿⠃⠀⠀⠀⠀⠈⢣⣤⠞⠀⠀⠺⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⡀
⠀⠀⢠⣶⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⢸⣿⣍⠁⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⡰⠆⠁⣠⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⣆
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⡏⠀⠐⢼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠂⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠈⠛⠆⠉⣿⠿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣆⣰⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣿⣿⣿⡟⠀⠀⠒⠀⡀⢰
⠀⠀⠀⠀⢀⣤⠶⣿⡿⠿⣿⣿⣿⡇⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⣳⠂⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⠀⣘⣿⣿⣏⠁⡌⠀⠀⠀⠐⢸⠃
⠀⠀⠀⡴⠛⣁⣀⣄⣈⣉⠿⠋⠁⠰⠶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣠⣤⣿⣿⣿⣿⣿⡷⠿⠄⠀⠀⠀⢸
⠀⠀⠈⠙⠳⠯⠽⠟⠉⠁⠐⠒⠀⠀⠀⠀⠁⠚⢦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣻⣿⣿⡿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠄⡽⢹⠟⠲⠙⢷⠑⠀⠀⠀⠀⡀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠠⣄⠀⣤⠀⠀⠀⠁⠀⠀⢐⠀⠀⠐⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡲⠤⠀⠀⠀⠠⠄⠀⠐⠒⠁⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣤⣤⣀⣉⡉⠤⠶⠚⠉⠁
⠀⠀⠠⣤⣤⣚⡛⠋⠉⠛⠛⠻⠿⣦⣀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠙⠻⣷⣤⡀⠈⢉⣙⠛⠿⣟⠪⣿⣦⣴⢘⣉⡋⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⣿⣿⣿⡷⡻⢯⣿⣿⣦⣤⣄⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠻⢿⣿⠟⠂⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⢠⡏⠀⢀⡀⠀⠀⠀⠀⣶⣤⣼⣿⣿⡅⡂⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢶⣿⣿⡿⠏⠋⢻⣿⣿⣧⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⢿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⣿⣧⣄⣀⣼⣿⣿⡗⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⠇⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⠁⠻⢛⣿⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣤⡀⣀⠀⠀⠀⠀⢀⣀⣀⢰⣶⣩⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣄⣀⠀⠀⠀⣀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣊⣉⣁⣭⠤⠤⠀⠀⠤⠤⠤⠭⣭⡉⠓⠒⠦⢤⣀⡀
⠀⠀⠀⢀⡤⢒⡩⠥⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣓⢤⡀
⠀⢀⡔⡩⠚⠁⠀⠀⠀⣀⡤⢤⣖⢲⣿⣯⡙⣿⣯⣍⠉⠉⠉⠛⠒⠲⠦⠤⣀⡀⠀⠈⠳⡝⢆
⠀⡏⡌⠀⠀⣠⠴⣚⣭⣤⣤⣿⣿⣷⣬⣿⣿⣦⡹⣿⣷⣄⠰⣶⣶⡄⠀⠀⠀⠈⠑⢦⡀⡱⢸⡇
⠀⣧⢣⡀⠞⠁⣠⣿⣿⣿⣯⣽⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣷⣜⣿⣿⡄⠀⠀⠀⠀⢀⡷⢃⢼⡃
⠀⡏⠳⣝⠦⣄⡙⠻⠿⠿⠿⢛⣋⣭⣶⣾⣿⣿⣿⠿⠟⢛⣛⣿⣿⣿⣿⣦⡠⠔⠊⣩⠔⣉⣼⣧⣒⡒⠒⠤⣄
⠀⢳⠀⠀⠙⠲⠬⣉⡛⠛⠿⠿⠿⣿⣿⣿⣛⣉⣀⣾⠿⠿⠿⠛⠛⠉⢉⣀⠤⠒⠋⠀⡾⠟⢻⠛⠓⠪⣕⣄⠀⠱⡄
⠀⠘⡄⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠶⠶⠦⠤⠤⠤⠤⠴⠖⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡞⠂⠀⢹
⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣿⠄⠀⡼
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠻⣀⠀⠀⠀⣀⣴⡝⠀⣠⠃
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀⢉⣉⣭⡫⠊⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠙⠛⠻⠿⠅⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⣑⣒⣒⣀⠤⠤⠤⠤⠤⣤⣤⣒⣒⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡄⢲⡾⣧⡠⢀⣀⠐⣀
⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠢⢤⣁⡀⢂⣴⣂⣄⣇⢦⣯⣷⣿⡗⣣⡍⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢤⡄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⢿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣿⣾⣶⡿⣶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠡⠀⠀⠀⠀⠀⠀⠂⠀⡒⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢠⡒⠶⣮⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠡
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⣄⡀⠀⠀⠈⠀⠀⡾⠻⠝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⢰⡟⠉⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢾⡯⣿⣿⣿⣿⣿⢿⠿⣿⠋⣽⣾⣿⣿⢿⣿⣿⣿⣿⠻⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠷⢿⠿⣟⡿⠿⣿⣿⣿⣿⣿⣍⡬⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠄⠱⠏⠉⠀⠂⠀⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⡤⢤⣴⣶⣷⣿⣿⣶⣶⣿⣶⣖⣶⣶⣶⣾⣶⣶⣶⣤⣦⣤⣦⣄⣀⡀⠀⠀⠀⡀⣿⣿⡇
⠀⠀⠀⠀⢤⣠⣦⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣟⣋⣇
⢀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀
⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⠧⢨⠟⡺⠋⣁⣤⡀⠮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣖⢢⡖⣾⢣⡟⢸⣟⡼⢻⠋⠁⢠⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡭⣹⠏⡾⠙⠁⠈⠀⢈⣿⢀⢻⡇⠃⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢿⡆⢠⡟⠀⠀⠀⠀⠀⠀⢿⡇⢼⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣫⡾⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢹⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠠⠒⠉⣑⣦⣹⡀
⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣀⠔⡁⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡠⣚⠉⠀⠀⠠⣌⠉⠢⡀
⠀⠐⠄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡠⠊⠁⡬⢴⠁⠀⣠⠟⠢⠀⠀⠀⢀⠄⠀⡞⠀⠰⠆⠀⠰⡶⠀⠀⠀⠸⡀
⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠘⡍⠛⠋⡽⠜⡠⠔⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢘⣦⣎⠀⠀⠀⠀⠀⠀⠀⠸⡄⠡⣄⣀⣀⣀⡠⠆⠀⠀⢠⠇
⠀⠐⠄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠪⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡈⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀⠤⠒⠉⠀⠀⠀⠐⠛⠓⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⡠⠒⠒⢶⣤⣞⡀⠀⠀⠀⠀⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣀⡠⡴⠁⠀⠀⡜⠃⠀⠀⠀⠉⠉⠉⠉⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡴⠁⠀⠀⣼⠒⠖⠒⠒⠒⠒⡶⠴⠊⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⡿⠁⠀⠀⣼⠏⠉⠁⠀⠀⠂⠚⢳⠂⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⠼⠈⢉⣑⠲⣤⣄⠴⠒⠉⠁⠀⡼⠁⠀⢀⣼⢧⡤⠀⠀⠀⣀⣀⠔⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢶⢖⠛⠛⠛⠛⢳⡞⠀⠀⢀⣾⠧⠼⠦⠶⠶⠶⢧⠄⠀⣰⠏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣣⠀⠀⠀⡜⠀⠀⢀⣾⠃⠀⠀⠀⢀⣀⠠⠃⢀⣼⠃
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠤⢄⣀⡀⠒⢧⠂⠀⡼⠀⠀⠀⣮⣫⣝⣉⣿⣀⣰⣁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡞⠉⠉⠛⠓⠒⠛⠻⠷⠶⠬⠻⠀⠀⠀⣜⠂⠀⠀⠀⠀⢀⡠⠃⣠⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣀⣀⡀⢀⡴⠓⢲⠒⠤⣤⡄⢀⣀⣀⠀⠀⠀⠀⠀⣘⣯⠭⣉⣉⣙⢓⣒⠀⣴⠋⢠⡀
⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠒⠀⠀⢀⠴⠃⠀⢀⠎⠀⣰⡟⠀⠠⠄⠀⡝⢉⣿⡄⠀⢸⣇⠀⢀⠀⠀⠀⢣⠀⢻⡆⠤⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡔⠁⣠⣐⢶⠏⠀⣰⠏⠀⠀⠀⠀⡜⢀⡾⠃⢣⠀⠀⢿⡄⠀⠐⠀⠀⠈⡆⠈⢿⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠸⣶⣨⡄⠀⠈⠀⡜⠀⣼⠏⠀⠀⠀⠠⢌⡀⣺⠁⠀⠘⡄⠀⠸⣧⠀⠀⠀⠀⠀⠸⡀⠘⣧⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠀⠀⠀⢜⣀⡜⠋⠀⠀⠀⣀⠀⠻⠿⠏⠀⠀⠀⢣⠀⠀⢟⡄⠉⠁⠐⠂⠀⣡⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⢧⠀⠘⠀⠂⠀⠀⠘⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣤⣼⣉⣀⡀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠿⢿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠋⠁⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠈⠛⠛⠉⠻⠿⠟⠉
⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⣶⣤⣼⣿⣿⣄⠙⠷⠤⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⠻⠛⠻⣿⡿⠿⠛⠛⠋⠀⠀⠤⠤⣤⣤⣤⣤⣴⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠤⢤⣤⣤⣿⣏⣉⣉⣉⣉⣉⠁⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠰⠤⠄
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀
⣿⣿⣿⡿⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠙⠿⠿⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⣀⣤⣤⣤⣀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣾⣿⣾⣏⣿⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⢠⣟⣿⡿⣾⣿⣿⣿⣿⣷⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢆⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁
⠀⠀⠀⠀⣰⣿⣷⣽⣿⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠈⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠈⠀⢧⣿⣿⣿⣭⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⣠⢯⣀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠠⡀
⠀⠀⠀⠀⢿⢿⣿⡿⣛⡿⣻⣦⣶⣿⣷⣿⣯⣽⣟⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⢀⠃⠀⠆⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⢀
⠀⠀⠀⠀⠘⢏⢻⣿⣾⣻⣿⡏⣿⣿⣯⣿⣿⣷⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠣⡼⣯⣿⣿⣷⣿⣿⣿⣿⣷⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠁⠀⠀⠀⢀⣠⣤⣶⡶⣀⣀⣸⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣤⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⣀⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡃⠀⠀⠙⠿⠟⠸⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠛⠶⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠉⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠤⠒⣀⣠⣤⣤⣄⣤⣤⣈⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢵⠋⡝⣷⠊⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⣿⣿⣟⣵⣾⣿⣿⣿⣿⣿⡄⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠋⠁⢀⠀⠀⢒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢛⣯⣿⣿⣿⣿⣼⣿⣿⣿⡿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⢚⡖⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⠟⠛⡛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠔⢀⣿⣯⣿⡋⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣥⣴⣾⣿⣿⣿⢿⣿⠟⢋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣟⣮⣼⡟⣻⣫⣛⠀⠀⠂⠀⠀⠀⠀⠀⢻⡍⠀⣀⣠⣾⣿⣿⣿⣿⠇⢹⣿⣿⠞⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⢾⠓⣟⣿⠏⡵⠏⠀⡀⠀⠀⠀⠀⠀⠈⢄⠙⠛⠻⢯⣭⣤⣤⡶⠿⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠏⠘⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣠⣄⣀⣀⣀⣠⠐⡂⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢿⡿⡦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠮⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⢄
⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢹⠀⡀⣀⠀⠀⠀⠀⠆⣊⠑⣢⢉⢛⠐⢺
⠀⠀⠀⠀⠀⠀⠈⢳⣿⡒⠂⠀⠁⠀⠀⠀⠀⠀⣄⣀⡈⠢⢄⣿⣷⠲⠋⠀⠀⠀⠈⠸⠬⣱⣇⠸⢸⣂⠉
⠀⠀⠀⠀⠀⠀⠠⠊⠃⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣡⡦⠤⣀⣄⡄⠀⠀⠘⠒⠋⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠖⠀⣄⣬⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠘⡳⠤⣤⡀⠪⠑⠂⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠢⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⣨⠆⠁⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠈⠑⣃⠴⢁⠂⠐⣢
⠀⠀⠀⠀⣐⠀⠀⠑⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡛⣫⣕⣶⡆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣞⣀⣣⡊⠑
⠀⠀⠀⢐⣀⡀⠠⠑⠖⢨⠁⠀⠀⠀⠀⠀⢀⣀⢉⡚⢬⣭⡼⢿⣜⣇⠀⠀⠀⠀⡠⡀⠓⣤⢵⣿⡿⢇
⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⢴⣿⠟⡁⡏⢩⡟⠈⠀⠀⠀⠀⠀⠜⠐⢋⣱⠗⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠩⠀⠖⡀⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡀⠈⠀⣀⣠⣶⡄⠀⠀⢀⡴⠊⠀⠀⠂⡀⢀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠛⣾⢿⣤⡄⠙⠐⠤⣿⣿⣿⣷⣄⡀⢠⠀⠀⠀⠀⠀⢹⡦⢑⢦⣶⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠢⠀⠀⠀⠈⣷⣾⣿⡇⠀⠀⠀⡄⠀⢹⠏⠈⠀⢸⢀⠀⠀⠀⠀⠀⠙⠚⠀⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⡈⠹⡅⠀⣠⠤⡿⠀⠀⠀⣠⡟⣸⣿⠽⠟⠛⢷⣦⣄⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢉⡷⢞⡻⠁⠀⠀⠀⢀⣼⡟⠁⠘⠋⠀⠀⠀⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⣀⣔⣁⠀⠈⢹⣷⣶⣤⣀⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣿⡄
⠀⠀⠀⢀⡔⢎⠩⡯⠥⣴⣀⠀⠀⠀⠀⠒⠛⠛⠛⠉⠉⠁⡈⢻⡙⢾⣿⠑⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣯⠿⡇
⠀⠀⣄⡠⠶⠶⠛⠛⠛⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢁⣸⡿⢦⠈⢳⣿⣾⡿⠷⠄⠀⠀⠀⠀⢀⣿⣿⣶⠇
⠠⠞⠁⠀⠀⠀⠀⠀⠠⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠁⢰⢏⣠⠏⢸⣾⣧⠈⠻⣿⠀⠀⠀⠀⠀⣀⢾⣾⣿⣽⠋
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣰⡄⠀⠀⠀⠀⠀⠀⢠⢰⣫⡞⠁⠀⠀⢹⣼⠀⠀⠉⠠⢤⣈⣁⣉⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⢀⡫⠿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣞⠨⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣤⣶⣶⣿⣿⡿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣛⣿⣩⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠒⠋⠉⠉⠉⠙⠛⠉⠉⠓⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠢⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⡀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣠⣄⣀⡀⢀⣠⣤⣀⣠⣶⡇⠸⠊⠁⣀⡀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⠋⠀⠈⢣⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⡌⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡇⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠀⡌⠀⢸⠀⠀⠀⡰⠁⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠸⡀⠴⠊⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢣⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⣆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠶⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠓⠤⢤⣀⣀⣀⣀⣠⠤⠔⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣨⠈⡇⢹⠀⡏⢰⡏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠈⠁⠈⠁⠉⠀⠁⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣽⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠾⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⠀⠀⠀⠰⢞⣛⣛⣛⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⠀⠈⠭⢵⣒⣒⠀⠀⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣀⠈⠹⡍⢹⡀⢀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⡴⢦⠹⣼⡇⢿⡆⣄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣡⡈⢧⠙⣇⢸⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠻⡌⢷⡈⠘⡇⢿⢷⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠿⡄⠹⡄⢳⡀⣧⢸⡈⣇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢃⣦⠙⣆⠹⣆⢳⡝⠘⡇⢻⠘⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⣡⢏⡈⢧⠘⣆⠙⣆⠻⡄⣧⢸⡄⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⢁⠞⢳⡈⢧⠘⢧⠘⣆⠹⣿⠈⡇⢻⠃⢻⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡆⢋⡼⣆⠻⡌⢳⡈⢧⠈⢧⠙⠆⢷⢸⡆⣌⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠘⣠⡘⣦⠹⡄⢳⡈⢷⡈⢧⡀⢸⡈⡇⢸⠸⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠘⠋⢳⡘⢧⠹⣄⠻⡄⢳⡈⢷⡸⡇⢿⢸⡆⢳⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⡇⡀⢲⡄⢳⡈⢧⠙⣆⠹⡄⢻⡄⢳⡅⢸⡀⣇⢸⡇⢻⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣼⢠⡇⠀⠻⡄⢳⡈⢧⠘⣆⠹⡄⠹⡄⢳⡌⡇⢿⠈⡇⠈⣧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡇⣼⢀⡘⣆⠹⡄⢻⡌⢧⡘⣆⠹⣆⠹⣆⠹⣧⢸⡀⣷⠸⡿⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼⢠⡇⣸⠁⠘⣦⠹⡄⠻⡌⢷⡈⢧⠘⣆⠘⣆⠙⠈⡇⢸⡀⣇⢻⠈⣧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠇⣼⢀⡏⢀⢰⡘⣧⠹⣄⠹⡄⢳⡈⢧⠘⣦⠘⢦⠀⣧⠸⡇⢹⠀⣇⠸⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⢠⠇⣸⠁⡾⠀⢳⡈⢧⠹⣆⠹⡄⢳⡈⢧⡘⢧⠈⢧⠘⠀⣇⢸⡆⢿⠀⢻⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡼⢠⡏⢸⠃⡄⢀⢳⡈⢧⠘⣆⠹⡄⢻⡌⢳⡈⢧⠈⢷⡀⢿⠈⡇⢸⡄⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢰⠇⣼⠁⡟⢰⠇⠸⡄⢳⡈⢧⠘⣆⠹⣆⠹⡄⢳⡈⢷⡀⢳⡸⠄⣿⠘⡇⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠘⠃⠚⠀⠊⠻⡄⢳⡌⢧⡘⣆⠘⣆⠹⡄⢳⡀⢳⡀⠳⡄⠀⠀⠓⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠳⠘⣦⠘⣆⠹⣄⠻⡄⢳⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠆⠙⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⠔⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⢀⠀⠀⢀⠂⢠⡎⣰⣾⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠻⣷⣲⡦⣤⣿⢉⡻⣿⠏⣁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠤⣥⣿⠑⢶⡿⣸⠷⡋⡉⢐⣤⣆⠁
⠀⠀⠀⠀⢀⣀⢠⠾⣍⣄⣿⣺⣠⡳⣿⣧⣿⡾⠿⠓⠈⣀⣀⣀
⠀⠀⠀⢴⣎⢿⣯⣠⡀⢿⣿⢟⢷⣗⣽⣛⢿⣣⢖⣶⠟⠁⠀⠈
⠀⢀⣴⣷⣿⣿⣿⣿⠖⠂⢹⡗⢌⢻⣿⣿⢛⠻⡅⣃
⠀⠈⠁⣻⣿⣿⣿⢉⡈⠙⠃⠳⣾⣷⢼⡿⣿⡴⢛⠳⠔⠂
⠀⠀⠀⢭⣯⣝⣿⣵⠄⠀⠀⢲⢱⣹⣿⣷⢲⣾⣿⢀⡀
⠀⠀⠐⣾⣼⣿⣿⢟⡁⠀⠀⠙⣬⣿⣏⠹⣿⣿⣿⡉⠏
⠀⢀⣼⣿⣿⣿⣿⣿⣇⠄⠴⣏⣾⡻⣿⡽⣿⢟⣻⡟
⠀⠛⠉⠛⠛⠛⠟⠛⠙⣁⢠⣠⢿⣿⣿⣧⠻⢩⢰⣷⢖⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣽⢻⣿⢻⣍⠟⡆⢹⣆⣿⡈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⢾⢏⢸⠿⣰⣧⣘⣿⣿⣷⣷⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢁⣻⣟⣿⡿⣷⡐⣿⣿⣿⣿⣿⣿⣇⣿⣧
⠀⠀⠰⣵⠞⢈⠭⡻⢿⣿⢿⢿⣷⢿⣿⡞⣿⣿⣿⣿⣾⣿⣿⣯⡤⢤⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣷⠃⡎⠀⢠⡏⣆⡆⣿⠙⢿⣷⣾⣯⣺⣿⣿⣿⡿⢁⠄⠠⠈⠉⡟⡍⠛⣆⠀⠀⠀⢀⠀⢠⠊⠁
⠀⠀⠐⠀⡙⣽⡅⣴⢿⣛⠋⠛⠑⢶⣾⣬⣿⡿⣿⣿⣿⡿⣷⣸⡤⡇⣀⣼⣡⣇⣷⣿⣰⣷⠶⣗⡘⠾⠂
⠀⠀⠀⠰⣟⡿⠋⡙⠋⠀⢲⡈⣦⣿⣍⣛⡉⡑⢘⠿⢫⣵⠚⠉⠦⣿⠉⣴⣿⡿⣿⣧⣤⣌⠑⠾⠃
⠀⠀⠀⠀⠀⢁⢡⣹⡘⢦⡤⢿⣙⣷⣤⣤⠾⠵⠿⠛⠚⠉⠀⠀⠀⠈⠉⠁⠩⢭⡍

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀⡀⠀⠀⡀⠀⠀⣀⡀⢀⠀⢀⣀⢀⣀⡀⣀⣀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⡠⠁⠀⠀⠑⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⣈⠢⡀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠌⠀⠀⠈⠓⠠⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠅⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡁⣸⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠒⠒⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠙⠉⠉⠙⠉⠋

⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣧
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛
⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⢹⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⡀⣀⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠈⠙⢿⠿⠋⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⠖⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣰⠞⠀⠓⢀⠀⠀⠄⠀⠀⠀⡖⠀⡄⠀⣴⡏⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠈⠀⠸⠄⠣⠄⠚⠀⠀⠀⠘⠀⠠⠄⠈⠁⠀⠠⠆⠀⠶⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⠀⠈⢸⡇⠀⢉⠀⠀⡅⠀⢸⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡇⠀⠀⠀⠀⡇⠀⠀⠸⢺⡇⠀⢠⠀⠀⠇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⢇⡀⠀⠀⢸⡇⠀⢘⠀⠀⡁⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢁⣤⡾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢋⣠⡶⣟⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡜⠋⠀⣶⣟⣭⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠀⠀⢰⣦⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⣤⣹⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢤⣘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢰⣦⣘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣸⡏⠀⡀⠀⠀⠀⠀⠀⢀⣿⠁⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡇⢠⣇⠀⠀⠀⠀⠀⣼⠇⢸⣏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⠀⢸⣿⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⢠⡿⠀⣿⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣉⡁⠀⠀⢸⡇⠀⠀⣿⡇⠀⢻⣇⠀⢀⠀⣼⠇⣸⡟⣿⠁
⠀⠀⠀⠀⠀⣀⡴⠞⠛⢉⠀⠀⠀⠛⠀⠀⠀⣿⠁⠀⢸⣿⠀⠸⣇⠀⠀⠛⣿⡏
⠀⠀⠀⢀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣸⠏⠀⠀⡿⠀⠹⣆⠛
⠀⣠⣾⣿⠟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠃⠀⠀⡿⠐⣦⡀
⢸⣿⡿⢁⣴⡟⢁⡀⠀⣠⣴⠞⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠘⢿⣷⣿⣏⣴⠏⣰⣾⠟⣡⠀⢀⣠⣶⠿⠋⠀⠀⢀⣴⠞⠀⠀⢀⡴⠀⢠⡀⣠⡿
⢢⡄⠙⠿⣿⣿⣾⣿⣣⣾⢇⣴⣿⠟⣡⡴⢃⣴⡾⠛⣡⠖⣠⣴⣿⣡⣾⡿⠟⠋⢀⡄
⠈⣿⠀⣤⡀⠉⠙⠛⠿⠿⢿⣿⣿⣾⣿⣵⣿⣿⣵⣿⣿⠾⠿⠿⠛⠋⠁⢠⣤⢀⣿⠁
⠀⢻⡇⢹⣷⠀⣷⡆⢀⣤⡀⠀⣀⠀⠀⠀⡀⠀⠀⣀⠀⢀⣤⡄⠀⣾⠆⣿⡇⢸⡏
⠀⠘⣿⠀⣿⡆⢻⣧⠀⣿⡇⠀⢻⡇⠀⠸⡏⠀⢸⡿⠀⢸⣿⠁⢸⡿⢠⣿⠁⣿⣧⣤⣶⣶⣶⣦⣤⣀
⠀⠀⣿⡀⣿⡇⢸⣿⠀⢻⡇⠀⢸⠃⠀⠀⠁⠀⢸⠇⠀⢸⡟⠀⣼⡇⢸⡟⢠⣿⣉⣀⣠⣤⣀⡀⠈⠻⣦
⠀⠀⢹⡇⢻⣿⠀⣿⠀⢸⡇⠀⠘⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⣿⡇⣾⡇⢸⣿⣿⣿⣿⣯⣝⡻⣆⠀⢹⣧
⠀⠀⢸⡇⢸⣿⠀⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡇⣿⡇⢸⡟⠉⠁⠀⠀⠙⢷⡍⠀⠀⣿⡄
⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⡇⣿⡇⢸⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡇
⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⣸⡇
⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⢸⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠃
⠀⠀⢸⡇⢸⣿⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣿⡇⢻⡇⢸⡇⠀⠀⠀⠀⣰⡿⠀⣰⢀⣿
⠀⠀⣾⡇⣾⣿⣿⣿⡇⢸⣿⠀⠐⣷⠀⢸⡇⠀⣿⡇⢸⣿⡄⣿⣿⣇⣼⡇⢸⡇⠀⢀⣤⡾⠋⠀⣴⠏⣼⠇
⠀⠀⣿⠇⣿⣿⣿⣿⡇⢸⣿⠀⠀⣿⠀⢸⡇⢸⣿⣇⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⠟⠛⠁⣀⣴⠾⢋⣼⠏
⠀⠀⢿⡇⢻⣿⣿⣿⡇⢸⣿⠀⠀⣿⠀⢸⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣴⣾⠿⢛⣡⡶⠟⠁
⠀⠀⢸⣇⠸⣿⣿⣿⣷⠸⣿⠀⠀⣿⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣯⣥⡶⠟⠛⠁
⠀⠀⠀⢿⡆⠻⣿⡿⣿⡆⢻⠀⠈⣿⠀⢸⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⠏⣰⡟⠁
⠀⠀⠀⠈⢻⣆⠙⢿⣮⡛⢦⡀⠘⣿⠀⢸⣿⣿⡿⠿⠛⣡⠞⣩⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠙⢷⣄⡉⠻⢦⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠛⢁⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⠻⠿⠿⠛⠛⠋⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠙⠻⠶⠶⠶⠶⠞⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠙⠻⠶⠶⠶⠿⠛⢁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⣤⣤⣤⣤⣶⣿⣏⢰⣶⣤⣄
⠀⠀⠀⠀⢀⣤⢚⣤⠄⠀⠀⣿⠀⠇⢈⠉⣿⠉⣿⡿⣿⢸⣿⣿⡻⣿⣦⡀
⠀⠀⠀⢠⡿⠁⣾⠁⡾⠁⠀⢿⠀⠀⢨⠀⣿⡆⣿⡇⠿⢀⣿⡟⣿⣆⠹⣿⡆
⠀⠀⠀⢻⣇⠀⠻⠄⠙⠂⠀⠀⠀⠀⠀⠀⠙⠁⣉⣁⣤⣾⠟⢁⣾⡿⢀⣿⡟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣉⣩⣤⣾⠿⢋⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣀⣀⣀⠀⠒⠛⠛⠛⢛⣛⣉⣥⣴⣾⡿⠟⠋

⠉⢻⣿⣿⠛⠛⠛⠋⠉⠁
⠀⢸⣿⣿⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠛⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⡄⠀⠀⡄⠀⠀⡄⠀⠀⡄⠀⢰⣶⣶⣶⣶⣶⡆⢴⣶⣶⣶⠀⡇
⣤⣤⣤⣤⣤⣄⠀⠀⠀⢸⠀⠄⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⠀⡇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⣉⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⣸⣿⣿⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⠀⡇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣼⠀⠀⠀⠀⢠⠈⢿⣿⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⢀⠐⠂⢀⠐⠂⢀⠐⠂⢀⠐⠂⠀⠀⢢⣤⣤⣤⣤⣤⣾⣧⡀⠻⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠁⠈
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⣿⠏⠠⣾⣿⠟
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡈⠉⠀⡰⠦⠀⠀⠤⠀⢸⡇⠀⠀⠀⢰⣿⡇⠀⠀⢸⠀⠀⢀⣀⣀⣤⠀⠀⠙⢋⣤⣶⣤⣴⣶⡄
⠛⠟⠛⠛⠛⠃⠀⠀⠀⠀⡇⠀⠀⡇⠀⡀⠀⠀⠀⣀⣠⡄⠀⣀⡈⠙⠃⠀⠀⠘⠀⠀⢸⣿⣿⣿⠀⠀⣤⣝⠋⠁⢈⣉⣉⠰⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠊⠀⣭⣤⡄⠀⡧⠿⠃⠀⠀⢘⣻⡿⠇⠈⠙⠛⠛⠀⠀⣹⣿⠷⠀⠙⠿⠿⠃