Happy xmas text face Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠉⠉⠉⠛⠛⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣦⡀
⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠙⣦⡀
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠀⠀⠠⠬⠷⣄
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠻⢷⣶⣶⣾⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⣼⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⡁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⢿⣦⡀
⢀⣴⠶⠋⠀⠀⠀⠀⠲⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢉⡴⠋⠉⠉⠳⣄⡴⠋⠉⠉⠙⢦⠀⣀⣀⣤⣽⣷
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠠⠀⠀⠀⠀⣠⠟⠁⠀⣾⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣧⠘⠻⠿⢿⣥⡀
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢶⡇⠀⠀⣴⠏⠀⠀⠀⢿⠀⠀⣴⣷⡄⠀⠀⠠⣾⣷⠀⠀⣿⠀⠀⠀⠀⠙⢿⣦
⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⢦⣴⣷⣶⠀⠀⠀⠘⣇⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⢰⠇⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠘⢧⣀⠀⠀⠀⣀⡴⠛⠉⠀⣾⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⣰⢆⠀⠀⠀⣰⠋⠀⠀⠀⠤⠀⠻⢿⣿⣿
⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⢀⣈⣿⡷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠙⠒⠛⠁⠈⠛⠒⠋⠁⠀⠀⢀⣴⠃⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠁⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣤⣀⣀⣀⣀⣀⣀⣤⣶⣿⡿⠃⠀⠀⠀⠀⠀⢤⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⡿⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⣀⡠⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⡿⠃
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⢿⣿⣛⡉⠉⠁⠀⠀⠀⢻⣍⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣟⠁⠀⠀⠈⠙⠿⣶⣄⡀
⠀⣠⣤⣤⣴⣾⠿⠋⠀⠀⠀⠀⠘⠃⡶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢶⠜⠓⠀⠀⠀⠀⠀⠀⢉⣿⣿⡆
⠀⠘⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⠀⣰⣆⢰⢦⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡤⡆⢠⣆⠀⠈⡆⠀⠀⠀⠀⠀⠀⣠⣤⣼⠿⠁
⠀⠀⠀⠈⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⢣⡴⠃⠈⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠁⠈⢢⡼⠁⠀⠀⠀⠀⠀⠈⢿⣇
⠀⢠⣶⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⣿
⠀⢠⣿⣋⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠉
⠀⠈⠛⠛⠛⠛⠛⠛⠛⢿⣶⠆⢀⣠⣤⣤⣶⠶⠶⠶⣶⣤⣀⣀⣀⡀⠀⢀⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⡶⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠛⠉⠉⠛⠁⠀⠀⣀⣽⠉⠉⠉⠙⠿⣦⣿⡿⣿⠿⠃⠀⠀⠈⠻⣷⣶⡟⠋⠙⠛⠃⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠓⠒⠒⠚⠃⠛⠒⠒⠚⠛⠛⠛⠛⠛⠛⠁

⣷⡾⠀⠺⣶⠀⠀⠀⠀⠀⠀⠀⠀⠤⣈⣠⣡⣄⠉⣿⡟⠻⠛⠀⣠⠃⣨⠀⣉⠀⠘⠛⠛⠄⠐⠀⡆
⢿⣷⣤⣴⠿⠀⠀⠀⢀⣀⣀⠠⠄⢾⡏⠀⠈⣿⠆⠀⠐⠀⠀⠀⠉⠆⠀⠖⠌⠈⠀⠀⠀⠀⠀⠀⢤⠶⠀⠶⡄
⠀⠀⠄⠀⠀⠀⠀⣼⣿⡿⢿⡇⢠⠸⣧⣄⣴⡿⠁⢠⠶⠶⢦⠀⡐⢀⠀⣀⠀⠰⠆⠌⠈⡀⠄⢠⡌⢦⣤⡶⠁
⠀⠀⠀⠀⠀⣀⠀⠹⠂⠀⠂⠇⠀⠀⠉⠉⠀⠀⠀⡄⠶⠰⠦⡆⠁⠈⠁⠉⠀⠀⢲⡿⠋⠄⣷⠀⠀⠈⠉⠁⡀
⠀⣀⣭⣅⣀⠉⠀⠤⠠⠤⢄⠀⠀⠀⠀⠤⠀⠀⣀⠘⢢⡄⢈⡏⠀⠀⠀⠀⠉⠀⡸⠀⣤⡄⠋
⠘⠉⠂⠘⠉⠠⠀⠀⠀⠀⠀⠀⢀⣦⣀⢀⣀⡄⠉⢀⣏⠉⠈⣧⠒⣰⣟⠋⣿⣏⠁⠀⠁⠉⢀⠀⣠⣴⣶⣦⣀
⠰⢠⣤⣤⡀⠀⡄⠀⢀⣈⣀⠀⢀⣷⡍⠍⣩⣿⠁⠀⠁⠀⠀⠀⠀⣿⣏⠀⢩⡿⠀⠀⠀⠀⠀⠀⣏⢩⠉⣀⠉
⠂⠀⠀⠀⠉⠀⠀⠸⠟⠋⠙⢿⠐⠙⠋⠀⠙⠋⠀⠀⠐⠀⠂⠀⠐⠀⠚⠛⠛⠀⠀⣠⠄⠰⣄⣀⠀⣆⡀⠀⠰
⠀⣠⣤⣀⠀⠀⢀⡁⢠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠄⠶⡷⠀⠀⠀⠀⠀⠀⢐⣯⣤⢤⣼⡏⠀⠛⠉⠉⠉
⣎⠹⠠⠌⣡⠁⠈⠀⠀⠀⠀⠀⠀⠴⠞⠻⠦⠰⠇⣿⣿⠂⢾⣇⠃⣞⣉⣉⣢⠠⠌⠿⠀⠄⠼⠿⠂⠀⠠
⢸⣄⢠⣀⣾⠀⠀⠀⠀⠀⠀⢀⠀⢄⠂⠐⠂⠆⠀⠀⠀⠀⠀⠉⠐⡏⠀⠈⠹⠀⠀⠀⠀⠁⠀⠀⣰⠞⠓⢦⠠
⠈⠙⠀⠘⠁⠀⠀⠀⠀⠀⠀⠜⠃⠘⢦⡤⠞⠀⠀⠀⠀⠐⠀⡀⠐⠀⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠠⢸
⠀⠀⠀⠄⠀⠀⠀⠀⣌⠀⡐⠂⡀⠀⠀⠀⠀⠀⢠⡚⠄⠡⣀⡁⠀⠉⠐⠛⠊⢰⣤⡠⠥⣀⡀⠰⠄⢠⠤⡀⡁
⠀⢀⣴⣦⣄⠀⣠⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⣼⡗⠂⠐⣿⠆⠀⠐⠂⠂⠀⠐⣏⠲⠀⠒⡡⡀⠀⠉⠀⠉⠁
⠀⠾⡿⠿⡿⡇⠀⠀⠀⠀⠄⠀⠒⣠⣿⣦⣄⠦⣿⣿⡦⢶⣿⠀⠀⠀⠀⠀⠀⣤⠈⠿⠿⡞⠉⠀⠀⢀⣀⣀
⡤⠘⢤⣀⡴⠁⠁⠀⠀⠀⠠⠀⠰⣿⠯⠭⢻⡄⠉⠁⠀⠀⠀⠀⢰⢤⠀⣠⢵⠀⠐⠏⠁⠁⠀⠀⢰⣭⡍⠉⣃
⠀⠀⠛⠉⠓⠀⢀⣤⣶⣦⡄⢀⠀⢁⣤⣤⡌⠀⢀⠀⠀⣀⡀⠀⣀⠉⠠⠀⠘⠀⠀⣀⣀⠀⢀⠀⠘⠇⠀⠀⠟
⠁⠀⠀⠀⠀⠀⠘⠒⠀⠀⠻⠀⠈⢉⠉⠉⠉⠁⠀⣼⡿⢿⣿⡆⠉⣄⠈⠠⠀⢀⣚⡓⢚⣓⠘⠃⠀⠀⠈
⢀⣴⠶⢦⡀⠀⣤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠈⠛⠃⠀⠀⠀⠀⠀⠘⠏⠁⠈⠙⠀⠂
⣾⣶⣶⣶⢶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠮⢠⠇⠀⠀⠀⣤⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣥⡎⢸⠋⠀⠀⠀⡇⠿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣤⣤⡀⠠⠶⡶⠏⠐⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢻⡿⠿⢿⢷⣶⡿⣟⣻⣿⡲⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⠉⢁⣶⠓⡿⣛⣫⣽⠟⠾⡛⣿⣿⠴⠶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⡑⢸⣿⣷⣶⣿⣿⣿⣭⣾⣿⡭⢉⣀⣀⣚⣿⣁⣠⠖⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡶⣻⣷⡿⠿⡿⣫⣿⠃⢰⠟⠵⣿⢻⣿⣿⣿⣿⡿⢱⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠸⣽⡇⠠⠐⠀⠀⠋⠀⠈⢂⡀⣠⠿⢟⣾⣿⣿⣷⢿⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡟⡰⣭⣿⣷⣤⣴⣯⣧⣀⣰⣁⣧⣤⠿⠟⣯⠹⣿⣿⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣷⠁⠨⠷⢤⣴⣼⢿⣿⣿⠟⠉⠉⠐⡽⠓⠂⣉⠙⢧⡀⢺⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣻⣿⣦⣁⣍⣽⣷⣾⣿⣷⣾⣥⣵⣽⠗⡶⠏⠀⡄⠀⠙⢶⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣫⣽⡛⠻⠟⠋⠉⣻⠟⢹⣿⣿⠘⠆⠙⠟⣦⠄⠈⠀⠁⠀⠀⠀⢱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠋⠈⣤⠔⠀⠀⠉⡡⢴⠷⢊⣙⢂⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠋⠀⠄⠀⣠⣦⠔⢀⠘⠋⠅⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠿⢸⠀⡄⠀⠟⠰⢋⡄⠚⡀⠀⣬⠁⠀⠀⠀⠀⠀⠀⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠈⠇⠃⣘⠇⠂⢢⣼⠀⠈⠀⠠⠛⠀⡀⠀⠀⢀⡔⠀⠀⠀⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠁⡂⠄⢌⠁⠉⠀⠀⠀⠘⠏⠀⠀⠒⠀⠀⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠐⠀⠀⣀⣀⠀⠁⠀⠙⣀⡾⠥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠄⠀⠀⠈⠁⠀⡠⠙⠒⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠓⠋⠉

⠀⠀⠠⠶⠛⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠳⠦
⠀⠀⠀⢸⣦⠙⠛⠃⠀⠀⠀⠀⠀⢀⣴⣿⣯⣿⣡⣽⣶⠋⠀⣽⠛⣻⣷⣦⡀⠀⠀⠀⠀⠀⠛⠛⢡⣾
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⣿⣧⣏⢹⣽⡿⠿⠾⢿⣟⣅⠈⠙⡙⣧⢄⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠫⠉⣿⣿⢿⣻⠟⠥⢤⠀⣀⡀⠹⣿⣷⠀⢠⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡾⠿⠁⣸⡄⢤⣒⠀⠀⢀⠀⠆⡹⢿⡇⢰⢡⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠫⢷⡦⠮⢠⡀⠢⣬⣖⣁⡀⠢⣼⠀⠿⠒⣺⣿⠚⠠⡀
⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⢸⣇⢸⠁⠀⣄⠡⠭⠋⢀⠀⣾⣀⡰⠿⣉⣽⡶⢶
⠀⠀⠀⠐⠂⢀⠀⠐⠀⠀⣶⠶⣾⠛⣿⣦⠣⡀⠈⠀⠀⠀⠋⣠⠉⢁⣀⠀⠛⠛⣦⡞⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⢶⡿⠀⢹⣤⣷⣮⣷⣤⣤⣶⣿⡗⢻⡟⢻⣥⣄⣰⠟⠁⠐⠀⠀⠀⠀⠐
⠀⠀⠀⢰⣦⠀⠀⠀⠀⠑⠀⠀⠳⣾⣋⣹⠄⠀⠀⠉⠉⠉⠁⠀⢸⣷⡀⣉⡽⠋⠀⠁⠀⠈⠀⠀⢠⣶
⠀⠀⠀⠺⠏⣤⣶⠆⠀⠀⠀⠈⠀⠀⠙⠻⠷⠆⠀⢰⣷⡀⠀⢲⣿⠋⠙⠉⠀⠀⠀⠁⠀⠀⢶⣦⡌⠿⠂
⠀⠀⠈⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠊⠉⠉⠉⢻⣿⣿⣿⠩⣿⣿⣿⣿⣇⣇⣏⣙⢿⡏⣯⣟⣿⣿⣿⣿⣿⠉⣿⣿⣿⡧⠤⠤⠄
⠀⠀⠀⣆⠀⠀⠀⢸⣿⡿⠃⠀⠹⣿⢫⣽⣛⠟⡿⡟⢿⣻⡛⣻⡟⢟⢻⣿⠃⠀⠹⣿⣿⠇⠀⠀⢀
⠀⠀⠀⠘⢧⡀⠀⠘⣿⡇⠀⠀⠀⣿⣷⣾⣿⣿⣿⠷⣾⣾⣿⣿⣶⣿⣾⡇⠀⠀⠀⣿⣿⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠙⠦⣨⣿⣁⣀⢀⣀⣸⣿⣿⣿⣿⡀⠀⠸⠿⠿⣿⣿⣿⣿⣅⣀⠀⣀⣸⣿⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣸⣿⣿⣿⣿⣿⠟⠋⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣠⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡆⢀⡀⠙⢻⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣀⣼⣿⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⠄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣀⠀⣧⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡌⣇⢿⣼⠋⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⡄⡍⢠⡦⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠙⠧⢺⡄⣿⠶⣶⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠛⠀⠻⠶⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠇⡀⣠⣀⣀⢀⡀⠀⠀⢀⣀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡿⠧⠈⠿⢺⡁⠀⠀⢸⣏⣷⣀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢰⡅⢠⡏⠀⡟⣿⢹⡗⣷⣰⡳⠰⢶⠀⠾⡇⣾⢰⣧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠋⠀⠀⠉⠿⠸⠃⠷⠻⠶⠃⠘⠂⠀⠓⠙⠛⣿⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡷⢀⣀⠀⠀⠀⠀⠀⣠⣤⠤⠤⣄⣐⣶⡀⠀⢠⡞⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⡿⠁⠀⢀⣾⣃⣀⠀⢀⣀⡀⠉⢰⠂⢠⣶⠈⣿⠋⠀⠈⠓⠋⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⡇⠀⢀⣼⠋⢹⡟⠀⠌⢻⡇⠀⣿⠇⡸⣇⡐⣿⠀⣶⣶⢶⣦⡾⣦⠀⣿⡇⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠚⠁⠿⠀⠘⠷⠊⠀⠈⠧⠄⠻⠊⢐⣿⠆⠸⡆⠿⠘⠘⠋⠛⠉⢉⠬⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠟



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

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣄
⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⣰⣿⣿⣇⡄⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⢀⣾⣿⣿⡿⠉⠀⠀⠈⠹⣿⣿⣷⡄
⠀⣾⣿⣿⣿⣿⠁⡀⢀⢸⣿⠿⣿⣿⣷⠀⢰⣿⣿⣿⣬⠇⢀⠀⡀⢺⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⣇⠀⠀⠀⢀⣴⣽⣅⣹⣷
⠀⣿⣿⣿⣿⠃⠈⠁⠈⠈⢻⣿⣿⣿⣿⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠀⠸⣿⣿⣿⠃⠀⠀⠈⠀⠀⠈⣿⣿⣿⠇⠀⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠁⠀⠀⠙⢿⣿⡗⠀⠀⠀⠀⠀⠰⣿⡿⠋⠀⠀⠈⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢀⣾⠋⢷⡀⠀⣠⡄⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠈⠳⡀⠀⢀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡶⠀⠀⣾⠀⢨⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡾⠟⠋⠀⠀⠀⣿⠀⢸⠀⢰⠇⡀⡄⠠⡈⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠠⠄⢄⢀⠀⠀⠸⠀⠈⠀⠸⡈⠃⠸⠄⠺⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠏⠀⠀⣸⡇⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⠀⣸⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣄⢸⡀⠀⢀⠀⠈⡁⡀⢰⠀⡀⠈⢁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠁⣸⡇⣳⠈⣰⢰⡆⢣⣼⣠⡇⡷⣸⠰⡧⡆⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠊⠀⠁⠉⠀⠙⠀⠀⠚⠈⠁⠁⠀⠉⠀⠀⠙⠀⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠢⣄⢀⡤⠖⠚⠋⠉⠙⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠾⠄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡤⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⡀⠀⠀⣀⠼⣄⣀⠀⠀⠀⠀⢀⣼⡏⣹⡅⠈⢹⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠉⠁⠀⠀⠉⠉⣭⡟⢦⣬⣽⠝⢯⡿⢯⣿⠛⣾⡭⠶⠤⠞⠵⠯⠴⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⠞⣹⢟⡴⠋⢳⣞⢟⣴⡻⣽⡾⠉⢧⢯⣉⠙⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢧⣀⣨⢗⠼⠒⠷⡼⣅⣀⣼⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢻⢧⡼⣄⣀⡰⣣⣔⣖⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠫⡟⠧⠼⢻⡤⠗⢘⡎⢳⡶

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

⠀⠀⣤⡀⢻⢀⡤⠄⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⢀⣩⢝⠯⣤⡀⠀⠀⠀⢀⠐⠳⠄⠀⠀⠀⠁⠀⠀⠀⠀⠙⠇⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠉⠁⢼⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠂⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡍⠀⠀⡀⣀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⡇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠐⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⣃⣁⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡈⠃⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⡤⢤⢤⡀⠀⠀⠁⠐⠃⠀⠁⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠒⢂⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⢀⡡⣆⣾⣶⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢈⠊⠀⠀⠀⠀⣠⢀⡄⠀⠀⠀⠰⢂⠚⢛⢂⡄⠀⠀⠀⡘⡈⠀⠐⠀⣀⠀⠃
⠀⠀⠝⠽⣿⡛⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⡛⠤⠀⡃⠆⠀⠀⠘⠀⠀⠀⠠⠂⢀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠔⣪⠿⠋⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣉⡼⢋
⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠠⠚⠁⠈⡙⠀⠀⠀⢀⡤⠔⠊⠡⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢰⡆⠀⠀⠀⢼⡇⢨⣡⣶⣮⠈⠒
⢠⣾⠴⣻⠇⣸⠀⠀⠀⠀⠚⣍⡄⢦⠀⠀⠀⠄⣦⠐⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣧⠀⠀⣠⣿⣿⣈⣋⡼⠟⢶⠶⣶⢀⣆
⣿⡿⣊⢃⣲⣼⣇⣤⡶⠚⢈⠉⢰⢌⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⡆⠀⠀⣫⣜⠅⠀⡜⢛⡎⢉⣻⣀⣤⠈⢃⡀⠙⢿⣀
⣿⠞⣹⣈⡽⢌⣿⣿⡷⠂⠀⠈⡃⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠂⠘⣁⡙⢶⡀⠟⠁⡴⣄⡘⣿⡏⠳⡌⠙⠷⣾⣿
⠿⠓⣅⡟⢘⣦⣹⡿⠗⠚⠶⠖⠉⠛⠧⣌⠳⣦⣦⣴⣀⣴⣠⡠⢼⡿⢄⣀⣰⣄⣦⣦⣾⣷⣶⣏⢜⡁⢸⠞⢉⡅⢸⡡⠒⠉⠻⡀⠻⣌⣗⣦⣤⣀⠈⠻⣿
⣰⡎⠀⣿⢺⣏⣠⡤⢾⣀⣤⠾⢶⢸⡆⠘⠷⣿⣿⣿⣿⣿⣿⡗⡹⡟⢺⣿⣿⣿⡟⢹⣿⣿⣿⡥⢟⠙⠓⠛⣩⢸⢛⣀⠀⠂⣧⠘⣤⣼⣿⣇⠀⠙⠷⢴⣿
⠴⠳⣀⣿⣶⠟⠉⣀⢀⣉⣇⠀⢨⡽⡟⢦⣀⠸⣿⡟⡟⡿⡿⣉⣠⠉⢈⢻⣿⣿⡴⢊⣻⣿⠋⡠⠴⠗⠶⣦⣽⣇⣼⠡⠤⠖⠛⢿⡀⠘⢯⠉⠁⣄⠀⠀⢹
⢀⣶⡟⣹⣷⡞⠋⢀⣬⠋⠀⡖⠈⠀⢀⡀⠙⠳⣾⣿⡏⣿⠯⠎⣀⢧⡼⠨⢿⡵⡁⠊⢉⡟⢋⠀⣠⢤⠦⣀⢹⣿⣅⠀⣠⡀⠀⢹⣉⠉⠺⣆⡀⠈⠂⢤⣀
⣾⣁⣼⣿⡯⠀⠚⢻⣁⣠⡞⠀⢠⡀⠘⢳⡄⣀⠈⡿⢿⡅⠀⠈⡇⢸⠀⠀⠠⡾⠁⠲⢎⠁⣣⣤⡇⢀⡷⣄⣉⣿⣿⠜⠛⣧⠀⢠⡏⠶⣄⡘⢧⣠⠂⠀⢻
⠀⠀⡽⠃⠀⠀⣀⡤⠞⠉⠀⠀⠀⠛⣆⢨⡗⠛⠓⠇⠘⠓⠐⠋⠙⠛⠒⠀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠁⠀⠘⠛⣁⠆⠀⢈⠉⠓⠃⠀⠀⠀⠙⠻⣯⠁⢀⢈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠀⠀⠀⠙⠻⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠠⠾⠴⣄⡀⠀⢠⣀⣣⡀⠈⣻⠿⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⢘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡆
⠀⠞⡞⢻⡇⠰⣾⣷⢖⡶⡖⣀⣤⣤⡌⢓⣂⣄⢘⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⠯⢿⠓⠒⣦⣠⣤⡔⢂⣤⣼⣰⣇⢰⡆
⠀⣛⣥⠘⠉⢛⠿⡟⢙⡄⠁⡩⢨⣗⢩⡍⢹⡟⢊⣩⣬⠇⣀⠀⠀⢀⣤⠀⠀⣀⣀⣀⠾⢠⡮⢳⠈⣼⠨⣯⣳⡍⢿⣿⠯⠀⠛⡚⢇⠤⢳⠼⣧
⠀⡯⠘⢶⣸⢓⡖⢹⣅⣷⠚⡳⢘⣵⠈⣓⡭⠶⣤⠒⣶⡂⢿⣿⢻⡏⠛⢿⣿⣯⣿⡿⣺⣙⢈⢫⠀⣶⡠⢿⢧⠱⠶⣿⣆⠩⢠⡈⢻⠒⠸⢱⡼
⠀⠈⢀⣯⡜⠸⣆⡠⠿⣠⠋⣡⡬⡀⢛⡿⢖⡱⢉⣞⠉⡍⠺⣻⡤⠁⠡⠈⢿⢁⡹⡂⡩⠌⢹⡏⣹⠁⢩⡘⢄⠱⠦⣬⡁⠲⡆⠓⠘⣥⡋⡜⠳
⠀⠀⠀⠙⠀⠺⠤⡘⠀⡀⠀⠉⠐⠉⠛⢡⣄⢱⣏⠀⢢⣸⠓⠈⠁⠐⠒⠀⠈⠀⠀⠈⠁⠉⢚⡙⢉⠑⠏⠉⠒⢇⣠⡁⠉⠠⠆⠨⠂⡌⠔⢠⡉
⠀⠀⠀⠃⠐⠁⠄⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⢈⠧⠀⠘⡟⠠⠩⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡠⡆⠀⢀⠛⠃⠀⠀⠀⠐⡀⠂⢄⠈⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠉⠀⣠⣤⣤⡄⠀⠀⠀⠡⠄⠤⡔⠀⠀⠀⣀⠹⢼⣦⡔⣤⡌⠳⣌⡇⠈⠁⠒⢼⣆⡿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣆⢰⣾⣿⣿⣿⣷⣄⡀⢀⠀⠠⠀⠀⠀⠀⠀⠙⡀⠶⠦⠿⣾⣿⠆⠈⠻⡄⠀⠛⠿⣿⡇⠈⢣⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠲⢞⣫⠉⠃⠤⣄⠀⢰⣿⠟⠁⠈⢳⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⡀⢈⠙⣿⣿⡄⢣⡀⠀⣿⡇⡀⠀⢅
⠀⠀⠀⠀⠀⠀⣀⣴⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠉⠓⠀⢀⠀⠀⢅⠠⠦⢀⡭⠙⠒⠲⢼⣿⣇⠀⣿⡀⣘⣧⡅⢠⡏
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠶⢄⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡷⠿⣧⠀⢿⡆⣸⣇⡠
⠀⠀⠀⠠⣼⣿⣿⣿⡿⠛⡻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠚⠶⠒⠲⢦⣄⣀⣀⡀⣠⣴⢶⡞⢻⣿⣿⠄⠈⣷⣾⣿⣿⡟⣀
⠀⠀⠀⠀⣻⣿⠟⠋⠀⠀⠉⠙⢻⣷⡆⠈⠙⣿⣿⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡶⣆⢀⣠⠜⠉⣹⡿⠛⠛⠻⠿⠷⣾⣿⣿⡀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣾⠃⠀⣀⡀⠀⠀⠀⣧⣿⣿⣦⠀⣷⣿⠿⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⣔⠒⣚⡙⢀⠀⢀⣄⠀⠀⠀⣿⢿⣷⠈⢸⣿⡿⠁
⠀⠀⠀⠘⠷⠶⠛⣷⣯⣴⣿⣿⣿⣿⡿⠟⠠⠛⢟⡄⠁⢹⣻⣿⠛⢿⡿⠿⢿⠿⠟⠛⠛⠻⠊⠒⠾⠓⠐⠂⠒⢿⣋⠘⢷⣿⡾⢿⠀⡷⠈⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣦⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⣸⣽⣷⣿⣟⡇⠀⢿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢙⡹⠟⠏⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢰⣴⣶⣶⣶⣾⣿⣿⡿⠋⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⠿⢿⡷⠶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣦⣤⣤⣤⣶⣬⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⠟⠉⣉⡥⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢠⣿⠀⠀⠀⣠⠤⡀⠀⣤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣼⡇⠀⠀⢸⣿⠀⡇⠀⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣶⡀⣸⡟⡏⠀⣿⠁⣠⡤⠄⠙⢳⣥⡄⠈⡿⣤⡄⢠⡆⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⢤⣿⣡⡿⢸⠁⢰⣿⢰⣿⠐⠁⡀⣾⡟⠀⡔⣸⡟⢠⡿⢡⣿⢡⣾⠋⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣰⠟⡅⠣⢀⡴⠟⢧⡯⠀⠈⣿⡸⠧⠠⠒⣀⠻⠤⠊⠀⣻⡇⠘⠃⣾⡇⠈⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠻⠤⣋⡤⡀⠀⢀⡴⡗⠀⠀⠈⠛⠂⠀⣨⡁⠀⠀⢠⠃⢀⣿⠀⢰⡿⠀⢠⣾⠋⠙⢦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢲⡀⠀⣼⠏⠀⢠⡖⠚⠷⠃⠀⠀⠀⠀⠀⢰⣿⠀⢀⣀⣸⡴⠛⢁⣠⠟⠀⠀⠈⠻⠄⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠈⣼⡟⠀⠀⢸⣷⠀⡀⠀⣘⠃⣠⡄⠀⣾⡇⠀⣀⠀⢀⡈⣀⡉⠀⣀⡄⣠⠀⣴⡆⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠄⢸⡇⢀⢉⣿⠃⣰⡿⠀⣿⡇⢠⣿⠁⢸⡿⠁⣾⠏⣸⡏⣴⡟⢰⡿⠀⢿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢸⡟⠀⣿⢁⠄⣾⡇⢠⣿⡇⠀⣻⣿⢸⣿⢀⣿⠃⢸⡟⢰⣿⠰⣿⡀⢿⣇⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠘⠁⠀⠉⣡⠀⠈⠁⠀⠈⠁⡜⠀⣿⡆⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠀⠀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠃⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠛








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⡕⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠐⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠲⣧⡟⠛⠛⠾⠼⣵⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠁⢄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⣀⡀⠀⠦⠁⢣⡐⠿⣀⡀⢀⣭⢙⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠓⢲⡝⠀⠈⠭⠅⠚⠪⠥⠎⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠌⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⠏⠉⠠⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢑⠬⢖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⣸⠁⠰⡄⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢣⠈⠀⢀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⠐⠀⢁⠒⢪⠀⠈⠒⠲⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠦⠴⠛⠒⠲⠶⠶⢦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠀⠀⡉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡀⢀⡼⣿⣬⣀⠀⣤⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⣷⡟⠸⠋⢨⠉⠿⠈⠉⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢻⣤⣾⢋⡀⢡⡆⠁⠀⢀⠈⢀⡔⣰⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠊⠂⣬⠟⡇⢠⢊⠉⠀⡀⠀⢡⣭⡎⢳⣟⠀⠀⢷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣤⠞⢿⣏⠀⢹⣠⣖⡀⡢⢸⡼⢏⣿⡇⠾⣧⢤⣤⣼⠷⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡶⣾⢹⡆⣸⣇⣀⣸⡇⢻⣷⢃⣼⠁⣾⣿⣷⡶⠟⠻⠉⠛⢶⣏⣷⣰⡆
⠀⠀⠀⠀⠀⡰⠿⢸⢏⣤⠿⠿⠛⠿⠾⢷⣿⣷⡿⠙⣦⢿⣶⡿⠋⠁⠀⠠⠖⠃⠀⢀⠹⣮⣟⢳⡄
⠀⠀⢀⣠⣼⣅⣠⡾⠛⠰⠋⠀⠠⠄⠈⠑⠂⢄⠙⠻⣿⣯⣉⣀⠁⠘⠀⠀⠤⣄⡀⠀⠁⠬⠻⢦⣷⣄⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠁⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠈⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠄⢀⠠⡵⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣠⠴⠇⠀⠀⠀⢟⠎⠙⢆⣀⠔⠒⠒⠒⠲⢮⣀⢀⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢈⡲⣄⠀⠀⠀⢉⡹⢇⠀⠀⠠⠤⠤⠀⠤⠋⠀⠀⢀⠠⢀⠶⠒⠠⠔⣉⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠞⠁⠀⣈⠧⢤⡀⠚⢓⡶⠋⠀⠤⠪⠅⠐⠀⢶⡀⢀⡄⠀⠀⠀⠘⡀⠀⠰⣈⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠈⠀⠀⠀⠙⣯⡤⣶⠉⠀⠀⠤⢤⣄⣠⠀⠀⢠⡙⣺⢦⣀⣀⡠⢼⡂⠀⠠⠈⠳⢤⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢘⣯⠶⢃⣀⣀⢀⠂⠀⡠⠀⠊⠁⠐⠀⠤⠈⠄⢠⠄⠀⠀⠽⠿⡤⠤⠆⢶⠣⠴⠄⠨⠙⠷⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⡀⠂⠀⢀⣵⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠦
⠀⠀⠀⠀⠈⢁⠀⠀⠈⢇⠀⠀⠀⠀⠄⠐⠐⠇⢀⡈⠃⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠀⠀⠀⣿⠸⢀⢀⠆
⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠳⠂⠐⠒⠋⠉⠉⠀⠀⠁⠀⢀⠭⠐⠠⣄⠀⠀⠀⠀⡰⠆⠗⣇⠀⡀⡀⠀⠩⢅
⠀⠀⠀⡐⠀⢀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⢄⠨⣀⢘⠀⠀⡰⠃⠀⠀⠉⠂⠀⢄⠀⠀⠀⠡
⠀⠀⠀⠃⠐⠈⠰⠚⠂⡀⠀⣀⠀⠀⠀⠀⠀⠈⡅⠢⠎⢰⠤⠔⠂⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣀⣸⣀⣠⠴⠒⠊⠁⠀⠀⡀⠀⠰⠄⡀⠀⠐⣤⠀⠀⠺⠀⡀⠀⠀⠂
⠀⠀⢐⡒⠀⠀⠠⠤⠨⠓⠈⠁⠉⠀⠀⠀⠟⠦⠓⠂⠉⠀⠑⠊⠈⠀⠀⠀⠀⠀⠀⠒⠒⠒⠠⠸⠱⠈⠑⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⣿⠆⠀⠀⠀⣠⣴⣾⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡏⣇⠀⣸⣶⣝⣠⢴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣀⢠⠖⠈⠁⠀⠀⠲⣻⡶⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⡰⢧⠀⢠⡀⠀⣄
⠀⠀⠀⡀⠀⠀⠀⣦⡀⣀⠀⢞⠛⠋⡼⢡⠿⣞⣏⠌⢉⡅⠀⠀⠀⢀⣤⠆⠉⠁⠂⠀⢸⡧⠀⠀⣿⢉⣦⡄⠀⠀⠰⢿⠆⠀⠀⠀⣝⡄⠶⣷⡀⡶⣷⢴⣿
⢠⣦⣸⣷⠀⣶⣜⣍⣁⣿⣶⣯⠼⣷⢶⢿⡀⢈⠛⠁⠈⠀⠠⠔⠪⢿⠇⠀⠀⠀⠀⠀⣻⡟⠄⠘⣻⣾⢧⣀⠀⠀⠶⢻⣼⢠⡄⢸⣏⣹⢼⡀⢻⢧⣼⣌⣿
⢸⣿⣵⢾⣿⣯⠼⡯⣤⢿⣃⡞⠀⣿⠂⡸⣧⣰⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢤⡇⠿⠠⠶⣿⣌⡟⠀⠰⡶⣿⣄⠚⠄⠚⣿⣥⡾⠷⠾⣧⣏⢸⣹
⢸⣿⢿⡤⣿⣁⡠⢆⣦⣤⣿⣧⣾⣿⡿⢀⣾⣷⡀⢦⣠⣀⡆⠀⡀⡀⠀⠀⠀⠀⠐⣸⠟⣿⢼⣤⠚⢻⠉⠉⠀⠠⠖⠻⠎⢃⡄⠘⠻⣯⡴⣦⡀⢹⣽⢻⣿
⢸⣷⣿⣿⡀⣠⠀⣈⣧⣀⠙⣿⣿⣿⣽⣿⡏⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⠶⣾⣶⣋⢼⡴⢿⠶⣴⣦⣼⣤⣤⢺⣧⣤⡖⣲⠃⠑⣊⠻⣿⣾⣿⣿⣿⣷⣼⣿
⢸⣿⣿⡿⠉⢉⡶⠏⠈⢻⡟⢻⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢷⣷⣯⣿⣿⣿⡵⢚⣇⢘⠧⣜⣦⣿⡿⡄⣩⡐⢿⣋⠉⡇⢸⡅⢙⣻⣿⣿⣿⣿⣿⣿⣿
⢸⡿⣿⡿⠑⢺⡀⠈⡧⣀⣷⡖⠟⠘⠁⠹⡇⠁⠈⠋⠛⠁⠀⠀⠀⠉⠙⠛⢻⡡⠒⠻⠋⠀⠴⠗⠀⣿⠁⢯⠡⠅⠐⠵⡎⢁⣏⠙⠦⢭⢹⠟⠛⠉⠀⠙⠻
⠀⠀⡈⢛⠚⠉⡉⢁⣄⠀⠈⠿⠒⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠘⠃⠀⠚⠂⠉⠁⠀⠀⠀⠐⠈⠘⠃⠋⠸⠀⠆⠀⠦⠴
⠀⠀⠉⠉⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡽⠛⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠒⡿⠒⠂
⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠖⠁⠴⡏⠀⠀⠀⠀⢀⠀⠔⠠⠏⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⢸⣧⠀⡴⢏⣤⠒⢦⠄
⠀⣴⢠⣿⡿⢀⡀⠀⠀⠀⣠⡶⠂⣀⠀⠀⠀⢁⣀⠀⡐⠀⠀⣠⢤⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣸⣷⡄⢿⠛⢿⣣⣀⣀⡄⢀⡀
⣾⣿⣿⣿⣇⣾⠁⡀⢀⢠⠠⠶⢂⠈⠀⠀⠀⠁⢸⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⡀⠀⠀⠸⢻⡄⠀⢸⣿⠟⠷⣦⠒⠀⠈⣯⠉⢉⣸⡇
⢺⣿⠛⢨⣿⣿⣼⣷⣟⣠⠰⠀⡼⠁⠲⡴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⡀⢀⠞⠿⣁⠀⢙⡀⠚⡀⠲⣧⠔⢦⡘⢶⣤⡙⢻⣴
⢸⢿⣃⣤⢹⣿⣿⣿⠟⣡⡄⠀⡤⢀⡠⠀⢲⣶⣴⡄⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡬⢓⠇⢠⣠⡼⠆⠙⡧⣎⣀⠚⠙⢢⣻⠆⠀⠑⠂⠘⠿⣿⣿
⠠⡾⠋⢃⢸⣿⠟⠋⢁⠇⠈⣀⠀⠀⠀⠓⡀⣻⣿⣿⣿⣷⣶⣼⣴⣶⣠⣄⢀⣠⣴⣶⣼⣷⣶⣾⡶⠣⠤⣘⣇⡠⢢⣈⡶⠉⢀⡄⠀⠀⢻⡃⠀⠀⠠⣄⠀⢈⣿
⢀⣆⠀⠋⢘⣥⡴⠚⠛⠠⠖⠃⠀⠀⣀⠀⠉⢺⣿⢿⣿⢻⣟⣿⣻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⠂⢀⡀⠈⠡⣴⠀⢹⡴⠞⢉⡴⣦⠜⢶⡤⠀⠀⠀⠘⠛⠿⣿
⠸⠧⠆⢁⡞⠋⠀⠰⠂⡴⠦⠀⠀⡾⣯⠉⠢⣄⡛⣏⠍⣋⣽⣥⡿⠟⢁⡀⠀⠀⠀⠀⠈⠛⣿⡀⠄⠈⠉⠻⢷⣎⢢⡼⠷⠒⠉⠀⠘⠦⢄⡙⠀⠀⠐⣆⠀⠀⢈
⠀⠀⠀⠈⡽⠋⡀⣀⡔⠀⢀⠌⠛⢇⠘⡶⠀⠈⠉⠉⠉⠉⠏⢀⠤⢾⣧⣽⣷⣤⣀⣀⣠⣤⠌⡀⠀⠐⠂⡐⠦⣽⣿⣯⠔⡠⣆⠀⠀⢦⡄⠈⠛⣤⠀⠈⠁⠢⣌
⠀⠀⢀⡼⠓⠀⠁⠰⢤⡤⠟⠀⠀⢀⡓⠙⡇⢠⣄⢨⠀⠀⠀⠙⠺⠿⠛⠒⠓⠚⠛⠛⠚⠡⠀⠤⠐⠃⠠⠟⢦⣤⡹⠟⠊⠁⡼⡀⢠⠿⠟⠀⢠⢈⣦⣾⠀⠀⢻
⠀⠠⠞⠡⠀⣀⣤⠖⠾⡄⠀⠀⠀⠈⢳⣠⠝⢦⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀⡀⠙⠈⢢⠀⢄⠀⠻⣆⡀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠃⠐⠊⠉⠂⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣤⠄⠞⠉⠣⠠⡀⠀⢦⡨⠦⠀⢨⣿⢯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠰
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣽⣭⣿⣭⣯⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣶⣾⣿⣿⣶⣾⣶⣶⣶⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠁⠀⠀⠰⠄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⡤
⠀⢀⡄⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⡠⠀⠠⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠉⣄⠑⠀⠁⢀⠀⠀⠀⠀⢀⣿⠀⠐⠀⠀⠀⠺⠀⠀⠐⠀⠀⢢⠀⣰⡄⠊⠀⠠⠀⠈
⠀⠀⠀⠈⢀⢃⠈⠀⣠⣤⣤⣵⠀⠀⠖⠢⠂⠒⠆⠀⡌⣂⠀⣐⠩⠁⢀⢠⣆⠰⢃⠱⡀⠤⣼⡇
⠠⣾⡀⠀⠐⠐⠰⠛⠛⠛⠃⠌⠶⠒⠀⠓⠐⠃⠘⠘⡖⠿⠀⠿⠀⠗⠀⣤⠈⠻⠫⠛⢋⠈⢀⠃⣠⣤⡀
⠈⣾⡅⣠⠨⠺⠀⠰⠂⠗⠀⡂⡄⠚⢀⠄⠄⠄⠘⠃⡇⠀⣏⡅⠀⠀⣶⠀⣶⠀⠿⠿⠀⢠⡄⢘⢁⣤⠉
⠐⠛⠂⢸⠐⠾⠀⠐⠂⠂⢸⠽⠃⠀⠀⠂⡀⠂⠀⠰⡇⠰⠃⢧⠈⠘⠛⠀⠛⠂⠿⠽⡄⠘⠃⢸⠀⠅⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⢛⣛⣛⡉⣉⠙⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢩⣖⣦⣶⣆⢸⣿⠃⢹⡇⠸⢷⣿⠀⣿⠉⠉⠉⠛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣿⢸⡟⠁⠟⢻⠈⠋⠳⠈⠁⠒⢚⣁⣀⣯⣀⣀⣀⣘⠛⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⡶⠀⠀⣻⣄⣡⣤⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠙⠋⠀⣀⡴⠃⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠠⠀⡇⢨⡄⠀⣼⣡⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⠀⠀⠀⣹⣶⢶⡖⢲⢶⡶⡾⢯⣹⡇⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⢸⡇⣇⢸⡀⠀⠉⠁⠀⢠⣤⡤⢤⠤⣤⢲⣶⢿⡁⢹⣌⣿⠀⠀⠀⠿⠋⠈⢷⠇⠈⠻⠃⠀⠙⠃⢸⡇⣿⡇⢠⣤⡄
⠀⠀⣴⢒⠊⠉⠙⠋⠛⠙⢓⠒⢦⡀⠀⢸⣿⡇⢸⣧⣽⠸⣿⠾⡇⠀⠋⠈⠀⠀⠀⠀⢸⡇⠀⢰⣢⠀⠀⣴⣦⠀⢸⣧⠻⠇⠈⠛⠉
⠀⠀⡧⢀⣀⢉⣭⡉⣩⣅⢠⣤⡀⢻⠀⠈⠈⠀⠈⠀⡁⠀⠁⠀⠐⣦⣀⢿⣠⢿⠀⢰⢟⣧⠀⣰⠿⡀⠀⢸⣻⣦⠈⠿⠀⢠⣦⣀⡀⠻⠃
⠀⠀⢷⡟⢻⣿⣸⣇⣟⣻⡿⢹⡇⡿⠀⠀⠀⠀⣶⣾⡿⣰⠀⠀⠀⠹⡉⣂⡡⠼⠀⣯⣵⡿⠀⣿⠃⢷⡀⣾⣭⣼⠇⠀⠺⣼⢿⣻⠅
⠀⠀⣸⣗⠀⣤⠙⠿⣃⠉⢠⣌⣻⠧⣄⢠⡖⠒⢻⣿⡏⢉⣳⡄⠀⡶⣄⢠⢺⠂⠀⢀⡀⣀⠀⢙⡓⠛⠁⠀⠀⠀⠀⢀⣀⡙⠋⠁⣀⢀
⠀⢸⠁⠈⠉⠓⠒⠚⣉⠉⠉⠉⠀⠀⠘⡇⢳⠚⠹⣿⡏⠉⣹⠁⣤⣷⣿⣿⣾⣧⠀⡸⠖⢶⣉⡳⣆⡵⠀⡶⠉⢲⣤⠟⠁⢸⡆⠀⠻⠟
⠀⢸⣴⢶⣄⡞⣷⣼⢻⡆⣾⢻⢠⡟⣦⣿⢸⡀⠀⣿⡇⠀⡟⠀⢸⣏⠋⠋⣭⡏⠀⠁⠈⠁⢀⣉⡉⠀⠀⣷⡀⠀⠉⠀⠀⣼⠃⣶⣤⡤
⠀⠀⣏⠈⠿⠃⠻⡿⠈⠷⣏⠈⢿⡃⣸⡅⠀⠣⢀⠛⠓⠚⠁⠀⠈⣿⣀⣴⣉⡇⠀⠀⠀⣰⠋⠀⠙⣦⠀⠈⠙⠲⢤⣠⡼⠃⠀⠻⠟⠁
⠀⠀⢿⠺⡧⢮⡥⣬⢤⡴⠶⢋⣛⣬⠾⠃⠀⣼⢁⢹⣠⡖⢒⡄⠀⠈⠉⠉⠉⠀⢀⡴⠒⣿⠀⠀⠀⣿⠞⠉⣶⠀⠀⣽⠁⠀⢀⡤⠖⠂⢤
⠀⣠⡀⠉⠓⠒⠒⠒⠒⠛⠉⠉⠀⢠⣤⡀⢠⡬⠽⡿⠻⣿⠏⣤⢰⣿⣤⣶⠀⣤⠞⠳⣄⢿⠀⠀⢀⣟⣠⠤⣿⡁⠀⠙⢦⠀⡞
⠲⡋⠹⡃⢤⢤⣶⣶⡾⣹⠀⡤⣄⢨⣿⡁⠸⡇⠀⣇⢠⡧⠀⢼⢻⣿⣿⡅⣸⠃⠀⠀⢹⣮⠧⣴⠻⡿⠁⠀⠈⣿⠀⠀⣼⠀⡇⠀⠀⠀⢠
⠘⠛⠉⠁⠘⠚⠉⢁⡀⠀⣠⢿⡅⠺⠾⠇⠀⣇⠀⣿⢸⠇⣀⣿⣸⣿⣸⠇⢻⡀⠀⢀⣾⡏⠀⢸⣿⡇⠀⠀⢀⡿⠀⠴⠃⠀⣸⠶⠴⠒⠋
⢸⠖⢦⠀⠀⣠⠚⣵⠿⠀⢑⣛⣁⡔⢰⠀⠀⠈⠉⠉⠉⠉⠁⣀⣀⠀⠀⠀⠀⠙⢶⠋⣿⡄⠀⣸⡿⠙⣦⡴⢛⣀⣀⡀⠀⢠⡇⠀⣸⣷⣶
⠉⠻⠁⠐⢊⣲⠗⠁⣴⠰⣿⣌⠿⠃⠘⢡⣾⠀⠀⠀⢀⡴⠺⣅⡽⢦⡀⠀⠀⠀⠀⠀⠈⢳⣤⠟⠠⠀⡄⡴⠋⠀⠀⠈⢢⠈⢇⠈⠛⡽⠋
⠘⠃⣠⡤⣤⣁⣀⣀⡈⠙⠋⠀⠀⢀⠴⢭⠭⠵⢦⠀⢯⢌⣓⣉⣫⣭⡽⠀⣔⠀⠀⠡⣠⠀⡅⢀⠃⠜⠐⡇⠀⠀⠀⠀⣸⠇⢸⡆⢠⣤
⠀⠀⣿⠀⠖⠀⢀⣠⡾⣷⣀⠀⠀⡾⢉⢚⣩⢉⡹⣄⢸⢸⣻⢹⢸⣿⠃⠀⣾⡆⠀⠀⠈⢳⡁⢀⠎⠀⠀⢻⣄⣀⣀⡴⠋⢀⡼⠀⠙⠛⠁
⠀⠀⢻⣆⣤⡾⠛⢋⣠⠾⣹⠃⠈⣶⣦⡭⡶⣤⡖⡟⠀⠉⠛⠛⠛⠁⡔⠀⠉⠙⠒⢄⡀⠀⣿⠀⠀⠀⢠⠞⠋⠁⠀⠀⣶⡄⠀⣶⣤⠄
⠀⠀⠀⠉⣷⣤⠴⢛⡵⠚⢡⣄⡄⠹⢾⣷⣷⣿⠼⠁⡠⣠⣶⣄⠀⢺⡄⠀⠀⠀⡀⣠⡗⠀⣿⡀⠀⠀⠸⡀⠠⣿⣖⠀⣀⣠⡆⠘⠁
⠀⠀⠀⠘⠧⠔⠚⠉⠀⠀⢮⢿⠗⠀⠀⠀⠀⠀⠀⠀⣱⢺⡟⡞⠁⠀⠘⡏⡏⣿⣏⣿⠃⠐⠁⠀⠀⠀⢀⡇⠀⠁⠀⣠⣯⡀⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣁⣀⣀⣀⣷⣿⣟⣛⣛⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣈⣀⣈⣃⣀⣀⣀⣀
⣿⣿⠛⡻⢛⡛⠛⣟⢛⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢘⣿⣻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡃⠀⡄⠀⢠⣯⠄⠀⠀⠀⠀⣸⠀⠀⢀⠀⠀⠀⠀⣨⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠠⣿⣿⠿⣿⣄⡀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢢⢠⣇⠀⣰⣿⡇⢰⠀⠀⣴⣿⡷⠀⢀⣆⢰⣿⣇⠀⣾⠀⠀⡀⠀⣼⡆⢀⠀⠀⢀⣼⣧
⠀⠢⢼⣿⣿⣶⣉⡶⢿⣤⠀⠀⣼⣿⣇⠀⢰⠀⠠⣿⠀⠨⠀⢠⣿⣾⣿⣤⣼⣿⣿⣿⠀⢴⣾⣿⡟⠂⢼⣿⣿⣿⣿⣿⣿⣦⣠⡆⠀⣼⣧⣾⡆⠀⢠⣿⣿⠄⢰
⢠⣾⣾⣿⡿⢿⠯⢹⣿⣿⣷⣾⣿⣿⣿⣶⣿⣶⣼⣿⣦⣾⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣀⣿⣿⣏⣼⣷⣿⣿⡿⠟⢟⡛⢿⣿⢿⣿⢈⣿⣿⣿⡇⠀⣼⣿⣿⣇⣾
⠘⢿⣿⣿⡿⣌⣴⣿⠿⠉⣿⡿⠿⠿⠟⠛⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⢿⠟⠓⠚⠛⣵⡎⢿⣾⣿⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠛⠻⠿⣤⣿⣿⢡⠤⡤⠠⠀⡦⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠉⠀⠂⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠛⠛⠿
⠀⢺⠙⠇⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⣀⣀⣠⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡄⠤⠀⠀⠦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠆⣀⡀
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⢤⢀⢬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡸⠄⡀
⠀⣠⡾⠟⠁⠀⠀⢀⠀⠐⣊⣠⢤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⠀⡾⠃⠠⣄⠒⠆
⠠⠿⠿⠿⠄⠀⠀⠀⠀⡀⠈⣤⠀⢀⠰⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠛⠂⣮⠅⣈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⢨⠀⡠⠀⠺⠇⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠵⠂⠨⡡
⡀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠉⠙⠒⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⢠⣅⣋⣭⡟⠒
⠈⠀⠀⠀⠀⠀⠀⢐⡤⠾⠀⠼⠀⢳⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠄⠿⢶⣶⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

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

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




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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⢂⡬⠴⠀⠞⠂⠀⢠⡒⠒⢐⡂⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠠⡄⠐⡠⠁⠀⠀⡢⣀⠀⡿⠦⣸⡀⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢑⡔⡅⠀⠀⠀⢑⣄⠤⠛⠊⡁⠄⠺⢐⠌⡑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠁⡐⠁⠀⣔⣈⢁⣸⠔⢂⣉⣀⠀⠀⠀⣙⠚⠴⣤⡇
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠠⠠⠎⣀⡀⠀⢨⠠⢤⢸⠈⠐⠐⠚⠀⢀⠀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣁⠀⠊⠁⠀⣈⣀⠐⠠⡀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀⠀⠀⠁⠉⠉⠚⠚⠴⠥⠀⣈⡂⢈⣈⣈⣀⣀⣁⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠋⢀⠔⠈⠀⠀⠀⠀⠈⠘⢦⠀⠈⠀⠀⠀⡧⠄⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠈⠰⠁⢀⣄⣈⠠⣤⠖⢀⡑⣄⢃⠀⠀⣰⠡⢐⡂⠀⠀⠀⢀⠓⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⡟⠁⢠⣄⠀⠀⢠⣄⠸⡛⠀⡸⡡⢊⠄⠒⠀⠀⠀⣐⢐⠩⡄
⠀⠀⠀⠀⠀⠀⢳⡀⡀⠀⠈⠉⠀⠀⠈⠋⠀⠃⠀⡗⡐⡡⢚⠃⠂⠀⠀⠓⠢⠬⡇⠀⠀⠀⣀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠑⣔⢄⠀⠀⠁⠈⠀⣀⠔⠀⠀⠶⠐⠀⠈⠸⠇⠀⢀⣴⠂⠀⡇⠀⢀⠼⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡔⢀⡂⠒⠢⡉⠉⠓⢒⠎⠉⠀⠀⡀⠀⠘⡃⠀⠂⠀⢐⠒⠀⠈⠀⢰⠀⡠⠊⡀⠒⠂⠤⣀⢸⢏⣹
⠀⠀⠀⠀⠁⠀⠀⠉⠈⠉⡉⡏⡽⣀⠀⠀⠀⠀⠀⠀⠡⡀⠷⠤⣄⡈⢀⡤⠐⠁⢶⠀⠀⠲⡤⢉⠀⠀⡛
⠀⠀⠀⠀⠀⠀⡈⠀⢢⡀⡈⡉⡱⣿⠅⠀⠀⠀⠀⠀⠰⢩⠚⠒⠀⠤⠚⣄⢹⡀⢉⠦⢤⠑⠒⠡⠤⠤⡃⠀⠀⠄⠀⢈⠃
⠀⠀⠀⢀⡤⠠⠇⠒⠀⠀⢨⠋⡇⢆⠀⠀⠀⠀⠀⠀⣇⡆⠀⠀⠢⢴⠀⡈⣿⢿⠜⠂⠠⠤⠤⡴⠴⢤⠣⡠⠬⠷⠶⠚
⠀⠀⠀⣮⢅⡀⢀⠨⠒⠐⠛⢤⠁⠀⣣⡀⠀⠀⠀⠀⠉⠡⠀⠐⠚⠒⢀⠀⠀⡆⠀⠀⠐⠂⡰⣥⡇⠈⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠂⠀⠀⠀⠀⠀⠈⠃⠀⢈⠉⢻⠀⠀⠇⠀⠀⠐⠈⠁⠒⡧⣤⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣿⠁⢏⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉⢉⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠉⠈⠀⠀⠀⠐⠘⠃⠈⠁⠀⠈⠉⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠐⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⡩⠄⠀⠀⢀⡴⢏⡨⠁⠀⠀⠀⠊⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠀⠀⠀⠀⢠⡮⣕⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠋⠀⠀⠀⠀⠀⢰⠗⠥⠀⠀⠀⢈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣀⠀⠀⠀⠀⠀⢀⠢⢀⠄⠀⠀⠀⠀⠀⠐⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⠀⡀⢀⠀⠀⠀⠀⠀⢠⠀⢃⠀⠂⠀⠀⠈⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⠄⠀⡀⠀⠀⣔⢂⣨⠜⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠦⡀⠀⠈⠲⠐⠤⠊⠁⠀⡀⢀⠀⠀⠀⠀⠀⠴⢆⣄⠉⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠌⠀⠀⠔⠁⠀⢈⠦⡀⠚⠋⢄⠀⠀⠀⠄⠠⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠄⠄⠀⡠⠀⠀⡀⠐⠁⠀⢀⠰⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠈⠀⠀⠐⠈⠀⠄⠀⠈⠁
⠀⠀⠀⢠⠂⠔⡡⠀⡀⠄⡂⠠
⠀⠀⢠⣏⣀⡨⠔
⠀⠀⠚⠋⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⠐⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢚⣊⡤
⠀⠀⠀⣈⣙⣬⣁⠄⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣤⠖⠂
⠀⠀⠠⡌⣁⠼⣤⠤⠀⣠⠀⠀⠰⠀⢀⠀⠀⠀⠰⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀⡤⣵⣶⢦⣞⠳⢚⣃⠀⢀⠆
⠀⡀⣀⣉⣼⣧⣠⠴⠂⠀⡆⠀⠀⠀⠈⢠⠀⠀⢀⠀⢀⠀⠠⠀⠃⠀⠀⠘⠀⢈⣻⣭⢿⣟⣽⣟⣉⡁⠁⠈
⠈⠡⣬⣉⣠⠷⣦⣀⡴⠖⠉⠐⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣞⣷⣻⡶⣾⣧⣽⡆
⠀⣠⣬⣭⣡⣴⣇⣉⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣟⣽⠶⠒⢛⣿⠶⣤⠶
⠀⣄⣀⡩⢀⣠⣧⣉⠑⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠛⠛⠛⠳⠲⠖⠃
⠐⣧⠘⠓⠋⢠⣏⠉⢩⡧
⠀⠀⠈⠿⠲⠃⠛⠛⠛

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⣘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⢼⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡆
⠀⢾⣞⢻⡇⠱⣿⣶⣖⣶⣞⣃⣴⣤⡌⣗⣆⣄⢘⠏⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⢯⢿⠓⠂⣦⣠⣤⡜⢂⣤⣼⣰⣿⣰⡆
⠀⣻⣥⠚⡍⢛⠿⡟⢙⡄⠁⡭⢨⣗⢩⡍⢹⡟⢋⣩⣬⠇⣀⢀⡀⢀⣤⠀⠀⣀⣠⣀⠾⢠⠯⣳⠈⣼⠪⣯⣳⡍⢿⣿⠯⡁⠛⡚⢧⠤⢳⠾⣧
⠀⡯⠘⢶⣸⢛⣶⢹⣥⣷⠚⡳⢘⣵⠈⣗⡤⠶⣤⠒⣶⡃⢿⣿⢻⡏⠛⢿⣿⣯⣿⡿⣺⣛⢈⢫⠀⣶⡀⢾⢧⠑⠶⣿⣖⠩⢢⡈⢻⠒⡼⢷⡞
⠀⠈⣠⣯⡜⢸⣦⡸⠿⣬⠋⣥⡬⡀⢟⡿⢂⡱⢉⣾⠉⡍⠺⣿⡴⠋⠡⠈⢿⣣⡹⡋⡩⠎⢹⡯⣹⠀⢯⡐⢆⠱⠦⣬⡁⠰⡆⢓⠘⣥⡯⡜⠳
⠀⠀⠀⡙⠐⠺⠤⡘⢀⡀⠀⠉⠘⠉⠛⢡⣄⢱⣏⠀⢳⣸⡛⠂⠁⠒⠒⠀⠈⠀⠁⠉⠁⠉⢚⡙⢉⠑⠟⢉⠒⢯⣠⡃⠛⠠⠆⠨⠢⣬⠔⢠⣍
⠀⠀⠐⠇⠐⠁⠄⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡇⢈⠧⡀⡘⡟⠢⠩⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢠⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠀⢀⣀⡀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠘⣼⡇⠠⠀⡀⢸⣿⢆⣣⠀⠀⠀⡄⡧⠋⢀⠆⠀⠠⠀⠀⠀⣄⡇⢸⣧⠀⢸⢡⠇⢀⡇⢸⠀⢾⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡄⠡⡄⣿⠀⠂⠀⢸⣿⠈⠉⢀⡴⠔⠃⡧⠐⠁⠀⢀⠆⠀⠀⠀⠈⡆⢸⣏⣤⡏⠠⠓⠀⠇⢸⡇⠸⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⢸⡞⠁⠀⠀⣿⣆⠀⠆⠀⠀⢠⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠐⢼⡟⠻⠰⠁⠠⠀⠐⢾⡇⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡄⠀⢷⠀⠀⠀⣿⡿⠐⠀⡀⠀⠸⠴⠶⠚⡋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⣂⠀⠀⢘⡿⠂⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢾⡄⠀⠀⣿⡟⠤⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠐⡈⢋⣁⣤⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢰⣿⣇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣿⠀⡆⢀⢀⠀⠀⠁⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⣿⣯⣄⢀⣀⣥⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢹⠂⣇⣎⣁⡀⠀⠀⡀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣭⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣼⣄⡟⠻⠿⣷⡄⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣿⠃⠀⠀⠀⠀⠀⣀⣴⡾⠛⢿⣿⣿⣿⣿⣿⣿⡜⢱⣄⡀⠈⠀⠠⣿⠘⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⢸⣿⣿⠂⠀⠒⠀⣀⣴⠾⠛⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⡏⢸⣿⣿⣦⡀⠀⣿⠸⢃⡀⣴⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠹⣷⣾⣿⣿⢀⣠⡴⠟⢋⠥⠘⠀⠀⡀⠄⠀⢸⢠⢀⠉⠻⣿⡷⠇⣿⣿⣿⣿⣷⣿⣸⠀⠹⣧⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡃⠐⠀⢸⣿⣿⣼⠋⠀⠄⢼⣤⢤⣤⣴⣃⡴⠇⠈⠘⢽⡌⣆⣸⡷⢀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠡⠜⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠆⠈⣀⡴⠞⠉⣿⡇⢰⡇⢀⣧⡞⠁⠠⠤⡀⡄⠀⠀⠀⠀⠸⠀⣇⣿⣿⢷⠉⠻⣿⣿⣿⣿⣏⣋⣥⣶⡟⡋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠶⠛⠁⠀⠀⠇⣿⢃⡀⣥⡾⠁⠑⠎⠀⠀⡁⡇⠀⠀⠀⠀⠀⠀⢹⣿⣗⡈⠀⢀⣼⣿⣧⣼⡏⣻⣵⣾⣷⢹⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣴⠾⢛⠁⠀⠀⢲⡀⡆⠀⣿⣿⠙⡍⠁⠀⠀⠀⠀⠀⠃⠇⠐⠀⠀⠀⠀⠀⠘⣿⣟⠃⣰⣿⣿⣿⡿⣿⠃⢿⣿⡏⢻⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⠀⠐⠂⠺⠛⠉⢦⣿⣟⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢻⡏⢰⣿⣿⣿⣿⡇⣿⡄⢺⡻⡇⠈⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⢸⠀⠀⠀⣿⣿⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⣼⣿⢸⣿⣿⣿⣿⡇⣿⡆⣿⡇⣧⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⠀⠀⠀⠀⠀⣻⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⢀⣾⣿⡇⡄⣿⡿⣿⣿⡇⣿⡇⢿⡇⡿⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⡀⢤⣄⣸⠃⠀⠀⢰⠀⠀⠀⣿⣧⡔⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⣰⣿⣿⣿⣟⣥⢛⣿⣿⣿⣷⣿⠂⠸⡃⣷⡇⣿⠃
⠀⠀⣰⣦⣔⣃⣹⣷⣾⣿⣿⠀⠀⠀⠈⠀⡄⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⡏⠅⣸⣿⣿⣿⢿⣿⠀⡆⠁⣿⠇⡿⡇
⠀⢸⣿⣿⣿⣿⢿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠃⠀⣿⣿⢿⡅⠀⠀⠀⠀⠀⠀⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⢸⣿⠚⣿⠀⣿⠀⣿⡇
⠀⢸⣿⣿⣿⣓⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠏⠀⠀⠀⠀⠀⠀⠃⠠⠾⠿⣿⢿⠿⠿⠿⣿⣯⠴⢻⠿⣿⣿⠑⣿⣆⡿⡿⣯⣿⣿⠁
⠀⠀⠉⠉⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠧⢰⠀⠐⢠⢿⠿⠇⠁⠀⡃⠠⢀⡿⠿⠁⡀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢠⠀⠇⠀⠘⠇⠀⠀⠃⠀⢸⣽
⠀⠠⠠⢠⣄⣄⣤⠤⠄⠤⠤⠤⠴⢤⠴⠶⠖⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠴⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠂⠀⠀⡀⠀⠂⠀⠀⢄⡴⣤⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠦⠤⢄⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠠⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠐⠀⠐⠵⠶⢄⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠈⢀⡀⠛⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢔⡠⠆⡠⣀⢄⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠞⢁⡄⠏⢠⢄⢤⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⣠⢠⡀⣉⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⢰⠇⠀⠠⠸⠟⠽⣈⡀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣱⢀⡁⢍⣬⣙⢢
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠽⠡⠠⣤⡀⡀⠀⢀⢀⠀⠀⠑⡴⠊⠐⠔⠂⠀⣷⣭⡥⠄⡛⠚⠿⠻⠤⠐⠂⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⣀⣒⠓⠧⠗⠀⠾⠿⡇⠀⡧⣿⣏⣷⠁⠈⠃⠀⠿⠓⠚⣇⢀⠠⠀⠦⠔⠐⠒⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠸⠒⠀⠀⠐⠒⠸⠔⠒⠢⣼⠀⠐⡆⡠⠴⠊⠋⠉⠉⠐⠀⠀⠀⠓⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠺⣄⠤⢄⣀⣀⠀⠀⣀⣀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠟⠛⠋⠉⠉⠉⠙⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠛⠛⢲⣾⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠀⠀⠈⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿
⠀⠀⣿⣇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣾⠏
⠀⠀⠘⢿⣦⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠄⡀⠂⡀⢂⣥⡾⠋
⠀⠀⠀⠀⠙⢷⣦⣥⣈⣀⠄⠀⢀⣰⣤⡶⠏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠾⣤⣥⣀⣤⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠙⠲⣥⣬⣈⣠⣂⡄⣐⣀⢀⣅⣈⣤⡬⠿⢷⣬⣄⢄⠀⠄⠤⢀⢠⠠⣠⣴⠟⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠙⠛⠳⠿⠶⠶⠛⠛⠉⠀⠀⠀⡀⢀⠀⠀⢄⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣣⠆⠀⠪⠃⠊⠠⡆
⠀⠀⠀⠀⠀⠀⢈⣐⡸⠀⠙⠋⠈⢀⢩⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠁⢬⠳⠀⢀⠠⠐⠕⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⢂⡐⠀⠤⡀⣱⠩⡈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⢌⠂⠐⡀⠭⠌⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠮⠂⠄⠌⠔⠀⠙⠈⠃⠀⠀⠀⠀⠀⠀⢀⢐⠔⡎⠄⠒⠠⢑⢄⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠡⢰⠢⠀⠂⠖⠕⢀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠄⡬⠆⡠⡆⢌⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⡤⠀⠀⡞⡕⢂
⠀⠀⠀⠀⠀⠀⠈⠤⠁⠠⣦⠦⠀⢁⠅⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡨⢲⠁⢠⣤⠀⠰⡰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠂⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡏⠑⠂⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠊⠰⠐⠩⠒⠂⠀⠀⠀⠀⠀⡉⠠⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡆⠐⠭⠊⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠑⠨⠃⠀⠀⢼⠡⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⢀⢠⠀⡀⢄⢒⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠲⣁⠄⠄⠒⡕⠀⢁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣒⡄⠀⣡⢀⡒⠀⢀⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⠘⠠⠰⠂⠠⠩⡎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢂⠜⢀⣀⣄⠀⠐⣑⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣒⡆⠀⠤⡔⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⠢⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⢈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠟⣋⣥⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⡟⣿⡿⣹⡇
⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣇⣟⣼⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋⣾⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⠸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⣼⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⣿⣿⣿⣿⣿⣿⣿⡇⠛⢸⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢛⣾⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⡇⠘⣿⡿⢋⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣇⠀⠟⣴⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣅⣤⣤⣤⣤⠀⣾⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⡇⠀⣿⠿⠿⠟⠛⠛⠁
⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⡶⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢻⡀⠀⠳⢄⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢄⢸⡇⡄⢹⠑⡂⠀⣷⠀⢨⡏⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠀⠀⠀⠸⠁⠃⡟⢸⡁⠀⡟⠀⢸⡇⡸⢸⡇⢄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⢠⡞⠀⠀⠇⠀⠀⡠⠀⠀⡀⠁⠀⣸⠁⡼⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⡾⢀⡔⠀⠠⠔⢸⡇⠐⢰⡇⠀⠐⠁⠀⠀⢠⠟⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠆⠀⢠⡇⢸⡀⡀⠀⠀⠀⢷⡄⣾⠀⠀⠀⠀⠀⠊⠁⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⠀⠀⢸⡇⡎⠙⣷⠀⡄⠀⠘⢷⡻⠄⣷⣀⢠⠀⢸⢱⠂⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠁⠇⠀⠻⠐⠇⠀⠀⠘⣇⠀⠟⠾⣼⠀⣈⡈⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣿⠀⠀⠂⡏⠀⠀⢹⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠇⢠⠏⠀⡆⠀⠉⠀⢀⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠄⠀⠀⠈⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢀⡀⠠⠓⡀⠀⠀⠄⠀⠦⠊⠛⢲⠤⠀⢀⣀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡴⠛⠉⠋⠀⠄⠀⣐⠐⢀
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠟⠁⠓⠘⠇⠘⠋⢲⠞⠒⠁⠾⠁⠠⠈⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣸⠟⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠅⠀⠉⠒⠂⠀⠰⠀⠀⢠⠤⠀⠦⠀⠀⠀⠴⠂⢤⠄⠀⠚⠁⠘⠉⠉⠁⠀⢀⠀⠀⠁⠀⢸⢥
⠀⠀⠀⠀⠀⠐⠀⠀⠚⠠⡬⠑⠀⠸⠗⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠥
⠀⢀⣀⣤⣄⡤⠀⠂⠀⠈⠀⠀⠀⢀⠀⠀⠀⠉⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠫⡄⠀⠐⠂⠀⠲⠌⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠌⠀⠀⢄⠘⢁⠀⠀⠘⠁
⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡐⣒⠀⠀⠂⢀⡀⠀⡄⢸⡆⡀⠀⢄⠈⠉⠀⠀⢀⡴⠀⠨⠀⠀⠀⠀⠇⠀⠀⠀⣠⡄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⡀⠄⠀⡔⡷⠀⠯⠼⣧⢼⢦⠼⠷⠄⠀⠀⡖⠀⠀⠀⠀⠐⠀⠀⠚⠂⢠⠀⠈⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠀⠃⠞⠚⠀⠀⠂⡇⠀⠀⠀⠀⠀⡄⠀⠀⢠⡀⢠⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢖⡦⢀⢻⠀⢾⡘⠺⠈⢿⡚⠊⠓⡆⠀⠋⠀⠈⠀⠀⠀⠀⠀⠠⠈⠘
⠀⠀⡀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡀⠛⢀⡓⠀⣉⠀⠋⠁⢂⡑⠷⠀⠀⠆⠀⠂⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢨⠅⠀⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⡀⣠⠀⠀⠀⢠⡄⠀⠙⣓⠃⣼⠃⠠⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡾⠀⠦⡀⠀⠠⠄⠀⠀⢀⣀⣀⡀⠀⠀⠐⠊⠛⠀⠀⠀⠈⠀⠠⢀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠚⠋⠀⠀⠀⠀⠈⠀⠝⠲⢤⣉⣀⡀⠀⠉⠀⡀⠀⠄⠐⢊⠠⠸⢀⡀⠀⠀⠀⣀
⠀⠀⠀⣮⢧⢆⣄⠀⠀⠀⠀⠀⠀⠈⠫⠉⠁⠀⠐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⠁⠁⠀⠁⢐⢄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣼⡃⠠⠠⠀⠀⠀⠀⠀⠘⢞⡛⣭⡴⣄⣶⠀⠀⠄⠀⠨⠀⠀⡆⢸⠀⡆⡆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠳⣧⣾⣗⣻⡇⡮⠀⠄⠠⠸⠀⠀⠛⠘⠀⠃⠃
⠀⠀⠀⠠⠄⠐⠆⠠⠤⠀⠀⠢⣀⠀⠆⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠷⠍⠗⠀⢦⡤⢲⡀⠠⣆⠀⠀⠄⠲
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠙⡇⠀⠀⢤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⠀⡀⠀⠀⠀⠛⠀⠀⠲⠄⠀⠀⢀⡤⠘⣷⠀⠀⠀⢀⠀⠀⠠⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠟⠛⠿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠠⣾⣾⣿⣶⣄⠀⠀⠀⠀⠀⠘⢷⣌⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⢀⠸⢿⢙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣧⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢤⡟⢸⣃⣬⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡶⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡄⠀⠀⣉⣦⡆⣿⣾⠓⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣴⣶⣫⣅⣀⠀⢾⡇⣽⢾⣦⣻⢿⣞⣿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢛⣼⣋⢠⡀⢰⣛⣸⡇⣉⢋⣹⣻⣿⣍⣭⣦⡀
⠀⠀⠀⠀⠀⣄⠀⡀⠘⠖⣿⢠⡀⠐⠂⣀⡀⠀⠀⣀⡄⣂⡾⣻⢷⢋⣿⣿⣻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄
⠀⠀⠀⠀⠀⢬⡻⢤⠤⢼⠿⣏⡀⣤⡄⠀⠀⠐⠂⠉⢙⣋⡶⣉⡄⠙⣿⣿⡟⠿⢟⣫⡿⢟⡿⣿⣿⣿⣿⣋⣥⢼⣇⣶⣄
⠀⠀⠀⠀⠀⠀⠠⠈⣤⣤⡤⣿⣧⡄⠳⢄⣤⣤⣀⠲⣾⣿⣴⠏⢠⠟⠹⣿⣤⣦⣟⣉⣷⢟⣿⡟⣿⣷⣾⣿⢻⣿⡿⠿⡝⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣄⠐⠂⠞⢻⣧⣀⢀⣍⠛⢋⣴⣿⣛⣥⡆⠀⣠⣾⠛⢻⣟⣿⣿⣷⢬⣿⣼⣿⣿⣿⢿⡼⣿⡇⣶⣷⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢄⣠⠼⢿⣿⡿⢃⣥⣿⣁⡿⢧⣿⣀⡾⢻⣇⣵⠟⢉⣽⣿⢿⡿⣿⣿⣿⣾⢛⣼⣇⣻⣿⣿⣧⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣳⣶⣊⣿⠿⣿⣾⣯⣿⣟⣷⢿⣯⢥⣿⡟⣻⣆⢸⣯⣴⣎⣾⣯⣿⣻⡿⠿⣿⡛⣿⣣⣼⣽⣷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣿⠟⣽⣾⡟⣻⡿⠿⢿⣣⡾⣻⡾⢻⣿⡿⣿⣼⣯⡿⢿⣿⠏⣹⡿⣷⠿⣿⡿⢿⣿⣿⡿⠻⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣾⣋⣷⣿⣍⣛⠻⣻⣿⣿⢛⣿⣿⣧⣴⣋⣿⣏⣴⢦⢶⣾⣻⣶⣏⣤⣾⣵⣶⣿⣶⣶⣾⣿⣿⣿⣯⡛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣟⣻⢶⣿⣿⣹⣷⣾⣏⢛⣿⣿⣩⣿⣿⣻⣿⣽⣯⣶⣿⠛⡿⡟⣿⣿⡿⢿⣿⢿⣏⢉⣿⣽⣿⣿⣿⣿⣽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣯⡽⣿⣿⣯⠵⣿⣿⣽⣿⣿⣏⣴⣿⣿⣿⣿⣏⣴⣤⣧⡆⢩⣼⣀⠀⣼⢛⢿⠻⢿⡛⠛⣍⢿⣿⣷⡿⣯⠛⠩⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠶⢻⣷⡺⣿⡋⢷⣅⣭⣿⣿⣿⣿⣿⣿⣿⠛⢿⡛⠿⣿⡟⣿⣿⡾⢿⣿⣴⣿⣤⣿⣿⣿⣼⣿⣿⣷⣄⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣾⣿⣮⣿⣽⣿⣿⠿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣎⣻⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣯⣟⣹⣷⣿⣷⣶⣛⣿⡼⢿⣵⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣯⡢⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⣯⣍⣬⣯⣙⣿⣿⣋⣶⠾⢿⣿⠟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣭⣿⣟⣿⣾⣷⣤⠶⠶⢿⡾⢫⡜⢻⣿⣿⣯⡀⠙⠻⢿⡿⠿⣿⣿⣷⣿⡿⡏⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡿⠋⠙⢿⣯⣷⣶⠞⣻⡅⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⢇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⣾⣿⡟⠀⠀⠈⢀⣀⣀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⢻⡏⠙⠃⠀⠀⠀⣼⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣻⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡀⢀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠠⢠⣤⠀⣀⡀⠀⣠⠴⠀⠀⡉⠻⣀⠯⠤⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠃⠀⠘⠤⠧⠽⠀⠀⡁⠣⡀⠀⡁⠜⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠀⠀⢰⡀⠀⠀⠀⠖⠒⠒⡀⠀⢀⡐⠀⠈⠑⢂⠂⠁⣸⠷⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠠⠄⡀⠢⠅⠀⠀⠀⢀⠤⠀⠘⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠚⠁⠀⠑⠬⢀⡀⠀⠀⢠⠃⠀⣀⣤⣒⡉⠥⠀⠐⠸⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠋⠙⡗⠛⠥⣌⠀⠄⣸⠃⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⠠⠀⠀⠑⠢⡉⠢⣄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠴⠟⠂⠀⠈⠑⠠⠈⣈⠁⠉⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⡀⠄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⡄⠠
⠀⠀⠀⠀⠀⠦⠲⠴⠂
⠀⠀⠀⠀⢘⣀⡄⠈⠉
⠀⠀⠀⡀⠈⠉⠁⠃⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠦
⠀⠀⠀⠉⢒⠀⢠⣤⡦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣉⣁
⠀⠀⠈⠘⠃⠀⢀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣅⣠⣬
⠀⠀⠐⠀⡴⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣅⠀⢤
⠀⢀⠀⠈⠀⠀⢢⡄⠛⠦⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢈⣀⡠
⠀⠈⠁⢨⠄⠀⠂⠐⠢⣆⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢴⣲⠊⣀⠀⠥
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢲⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣶⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⣧⡀⠀⠀⠀⢠⣤⢲⡴⣲⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠂
⠀⠀⠀⠢⢡⠐⢤⠀⠀⠘⣿⡾⠞⠁⠀⠀⢀⣀⣀⣀⣀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀⠀⠀⠈⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆
⠀⠀⠑⢄⠘⠆⠀⠀⢀⡔⢩⠀⠀⠀⠀⠐⠛⢢⡤⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠰⢃⠀⠀⠀⣴⣾⠀⣾⡿
⠀⠀⡀⠈⠁⠀⢀⡴⠣⡈⣿⠀⠀⠀⠀⠀⠚⠃⠒⠒⠀⠤⠅⢀⣤⠀⠉⠁⠀⠒⠠⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠒⢾⣏⣩⠟⠃⠀⠙⠁
⠀⠀⠀⠀⢀⡴⣋⠐⢄⠘⣿⠀⠀⢀⣀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠢⠀⠀⠈⠲⣄⠀⠀⠟⠁⠉⠛⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⡀
⠀⠀⢀⡴⠋⠠⣌⠱⣄⢳⡏⠀⠀⢙⣞⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⣤⠌⣢⡀⠀⠀⠀⠀⡀⠀⢤⣞⠓⠀⠈⡿⠇⠠⠅
⠀⢰⡟⠒⠚⠦⣌⣆⠘⣎⡇⠀⠀⢸⠹⣆⣰⠋⣿⠀⠀⠀⣞⡦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡄⠈⠓⠀⢀⡤⠀⢠⠜⠉⠻⣀⣀⣠⠇
⠀⠀⠙⠦⣄⣀⠀⠉⠳⣿⠇⠀⠀⢸⠀⠙⠃⠀⣿⠴⠚⣹⠋⠀⢴⣏⠩⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡤⠖⠉⠄⠀⠀⢀⣀⢀⣀⣬⠁⠐⢄⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⣿⠭⠭⢭⣛⠲⢤⣠⠏⠀⠀⠀⠾⠋⡜⠑⢩⡟⢛⢶⠲⡶⢶⡶⡖⡻⣏⢹⠙⣄⢰⠺⠆⠀⠈⠒⠚⠲⠀⠀⠀⢰⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⣖⣶⣬⡙⢶⠋⢀⡤⠤⣄⠀⠀⠙⠚⠁⣷⠃⢸⣠⣀⡌⢧⠀⡇⠈⠺⠀⠈⠛⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠸⢆⠄
⠀⠀⠀⢴⠶⠒⠒⠒⢒⡶⠖⢦⠀⠀⠉⠒⠾⠭⠿⠃⢠⠏⡴⠶⣌⢳⠀⠀⠀⣀⣤⣄⡈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠐⡧⠀⣤⣀
⠀⠀⠀⠈⠳⣄⠀⠀⣾⡩⠽⠾⠦⣄⠀⠀⠀⢀⣀⠀⠸⡜⡇⠀⠈⢧⡇⢀⣾⠟⠒⢆⢻⠀⠀⠀⢰⣆⠀⠀⠀⢸⠁⠟⠁⠀⢠⠖⢉⡠⢪⠞⢀⠉⠛
⠀⠀⠀⠀⠀⠈⠳⣄⡿⢤⡠⠔⠒⠚⠻⢦⡀⠈⠻⣍⠲⢵⡹⣄⠰⡘⣷⣾⡣⠂⢀⠌⡼⠀⠠⣠⠤⠙⠀⠀⣀⣠⡤⠤⠄⠀⠈⠀⠉⡜⢁⡤⠃
⠀⠀⡋⢋⠢⡀⠀⡈⠓⠴⠛⢦⣀⠤⠤⠤⢽⣖⠺⠿⣅⣀⡉⠻⣧⣧⣿⡟⠁⣀⣴⡾⠥⣤⠆⠀⠀⣴⡙⠒⠻⣄⠀⠀⢀⠀⠀⠀⠀⢈⡉⠤⠤⢀
⠀⢠⠛⢶⣌⠁⠀⣍⢦⠀⠀⠀⠻⡄⣀⡤⠶⢻⡄⠀⡤⠬⠭⠷⢾⠧⠀⣹⣿⣭⣤⢤⠬⠑⣦⠀⢸⡇⠈⠉⢉⠃⠀⠀⢸⠀⠀⠀⡴⠅⠐⠂⠂⠀⠑⡄
⠀⠀⠶⡒⢆⠀⠀⣈⣟⡀⠀⠀⠀⠻⣥⠴⡖⠋⠀⠀⢷⡀⠀⠀⡸⠀⠀⡀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⢠⠏⢧⣀⢀⡼⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠈⠁⠀⠀⡏⢨⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠉⠉⠉⡇⠀⢀⠋⠉⠉⡏⠁⠀⠀⠀⠀⠘⢦⠴⠃⠀⠀⠈⢩⡄⠀⠀⡇⠀⠀⠂⡀⠀⠀⠀⡘
⠀⠀⠀⢀⡤⠶⠶⡇⣼⠠⠤⣀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⡇⠀⡘⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠎⠀⢀⠠⠀⠀⡴⠁
⠀⠀⠀⢸⠓⠲⠤⠽⠥⠤⠴⢚⠃⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⢀⣠⣿⡤⠄⠀⣆⣠⣁⣤⠶⠊
⠀⠀⠀⢸⣤⠋⠢⠚⣆⡰⠓⡼⠀⠀⢀⡷⢼⣷⡆⠀⠸⠤⠤⠤⠧⢼⣄⣀⣀⡇⠀⠀⠀⠀⢀⣀⡈⠁⠀⣀⣀⡀⠈⠁⠀⠀⠐⢏⡇
⠀⠀⣠⠼⣇⠀⠀⠀⠈⠁⢠⠇⣀⠀⠈⠿⣤⡼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⢻⠋⠉⢉⣩⣭⣓⠊⠈⢩⣑⢂⠀⠠⠀⠀⠀⠀⢀⣄
⠀⠀⠳⢤⣈⣓⠶⠤⠤⢖⣋⣠⠼⠂⢀⡼⠉⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⡰⢹⢋⣭⣭⠳⡄⣿⣼⡛⢠⠁⠀⠀⠀⠀⣸⠀⠙⣻⠷
⠀⠀⠀⠀⠈⠳⣭⣭⡭⠟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⠀⢇⠘⢆⠠⠀⠢⡀⠀⠀⣇⢧⠀⠱⣼⡜⠿⠿⣣⠇⠀⢠⠁⡆⠀⠀⠀⣴⠉⠉⠳⡞⠁
⠀⠀⠀⠀⠀⣠⣴⣖⠲⣄⠀⠀⠀⠀⢀⡀⠀⢘⠱⡄⢄⠈⠢⡀⠑⣄⠑⠳⠀⣘⣶⡦⠙⢾⣦⣀⠈⠉⠓⠚⠁⠀⢠⠃⢀⠀⠀⢀⠾⡈⠑⠦⢤⡞
⠀⠀⠀⠀⡞⢁⠄⠈⣷⢸⣤⡄⠤⠒⢯⢹⡆⠈⠣⡈⠢⢡⡀⠐⣴⣄⠱⣄⠻⠿⠀⠐⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠁⠀⢸⠀⠀⢸⡓⢌⡑⣒⠞
⠀⠀⠀⠀⢧⠈⠳⠴⠛⠁⠀⠀⣀⡤⠞⠋⠀⠀⠀⠈⠢⡀⠶⣿⠋⠙⡀⠈⠑⠂⠄⠊⠀⠀⠀⠀⢠⡀⢸⠙⡆⠀⠀⠀⠸⠀⢴⠋⠝⡲⠚⠁
⠀⠀⠀⠀⠀⠙⠒⠒⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠔⠁⠀⠀⠀⢀⡀⣀⡀⣹⢆⣀⠷⣄⢑⡗⠐⠀⠀⠀⠀⠈⠳⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⢈⣐⢆⠐⠄⢿⡿⠿⠟⠛⠛⠛⠉⠀⠛⠿⣿⣶⣤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠆⡷⣿⢄⢡⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣡⣤⡂⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢉⡑⠊⢬⢋⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢉⠛⣯⡙⢳⡌⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⣿⡿⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⠉⡷⢤⣕⣶⢦⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢿⡗⠃⠉⠁⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⠀⡑⢟⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⢠⠆⠀⢀⠒⢽⡏⠀⠀⠀⠀⠀⠼⢻⣦⠞⢻⡴⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡆
⠀⠀⠀⠀⢠⣾⣖⡀⡄⠾⡅⠀⠀⠀⠀⠀⠀⣸⡏⠀⣾⠃⢰⡏⢠⡖⡦⢰⣶⡆⢰⣶⡆⣰⠆⣴⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠻⣿⠿⠀⠌⠨⢃⡶⠀⠀⠀⠀⠀⡿⠁⠠⡿⠀⠸⣧⠾⣯⡵⠿⠃⠛⢿⠃⠙⢿⣴⣿⡴⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂
⠀⠀⠀⠀⠀⠘⠢⠒⠂⠰⠆⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠂⡀⠀⢅⣀⡈⢋
⠀⠀⠀⠀⠀⢀⣃⠚⡉⠐⠂⠌⠅⠀⠀⠀⣠⠤⡄⣰⡦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠛⠛⠁⠀⠐⢀⠼⡁⣠⠦⡬⢆⡀⢂
⠀⠀⠀⠀⠀⠀⣿⣿⣤⡏⠸⠰⠇⠀⠀⣼⠡⠴⠃⣿⣥⢠⣤⢀⡍⢀⡔⣾⠓⣤⣤⡤⣠⢤⠀⣠⠀⢠⠛⣀⡟⠸⣻⣗⡀⠰⠀⡁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠻⣤⡤⠞⠋⠳⠚⠋⠹⠗⠫⠗⠻⠖⠟⠟⠷⠷⠻⠞⠽⠒⠀⠀⠢⡈⠙⢀⡞⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⢉⠀⠅⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣄⢀⡀⠠⣦⠀⡀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡄⢣⡰⣷⡎⠢⠀⠄⠀⠀⠀⠀⠀⢎⣽⣧⡧⡌⣱⠙⢃⠄⠀⠀⢠⣤⠴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠬⠋⡽⢀⠅⣴⣄⠀⠀⠀⠀⠠⠼⣫⡾⢃⣠⣴⣷⡤⠔⢈⠀⠡⢘⠡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠺⢿⣿⣿⣷⣿⣷⣶⣿⢟⡶⠁⢥⡶⠛⠄⠰⢂⠈⢠⠈⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠘⠛⠛⢏⠉⠙⢉⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢀⠄⠀⠀⠀⠀⠘⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢠⠊⠀⠀⠀⡔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠒⠂⣄⠀⠴⠊⠁⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠔⠒⠀⠒⠚⠤⡒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢰⡀⢰⠊⠀⠀⠀⠀⠈⠂⠀⢠⠔⠒⠀⠑⠒⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⢸⢀⡄⠈⠡
⠀⠀⠀⣀⠠⠄⠒⠒⠀⢼⠀⠀⠀⠉⠑⠒⠠⠤⠄⢀⡀⣈⡀⡁⠀⠀⠀⠀⠀⠀⡁⢀⣤⣀⡀⠠⠤⠄⠒⠋⠁⠀⠀⠀⠇
⠀⣠⠊⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢰⠁⠀⠀⠀⠀⡠⠄⠀⠤⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⢡⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⣆⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢸⠀⠀⢀⠄⠀⠄⠄⡠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⢦⡀⠀⠀⠀⠳⣄⠀⠀⠀⢸⠀⢠⠑⣀⠂⢐⡀⠀⣌⠀⠀⢀⣀⠀⢠⠂⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠑⢄⡀⠀⠀⠀⠙⠦⣄⣸⠀⠀⡕⡁⠀⡉⠀⠠⠊⡠⠊⡔⠀⠇⡇⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⡹⠀⠹⠭⢀⠔⠡⠀⠑⢂⢅⠀⠓⡀⠫⡀⠘⢂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣠⠇⠎⠁⠈⠉⠀⠀⠉⠈⣡⣬⡁⠉⠀⠀⠉⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⠔⡨⠂⠅⠠⠀⠀⠀⠀⠀⢀⣀⠀⢀⢠⠠⡀⢀⠀⡀⠄⠰⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠠⠃⡐⠏⠈⠔⡡⢂⠏⠨⠠⢊⠲⠤⠗⢡⠏⡀⡰⢁⢊⠄⢠⣡⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡆⠀⡇⠀⢀⠜⠀⡩⣀⢷⠁⠀⢀⢮⠀⢒⠥⠙⣄⣨⠷⡤⠬⡁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⠱⠤⠤⠴⠒⢕⠒⠚⠀⠒⠛⠈⠉⠬⠭⠉⠀⠀⠒⠒⠀⣀⣨⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠲⠶⠶⠦⠤⠤⠤⠤⠤⠶⠶⠖⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⠟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣧⠞⣶⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢠⠇⠀⣿⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠒⠲⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣰⡇⢸⠏⠀⠀⢿⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣤⣄⠀⠁⣟⣁⠀⠈⠉⠓⡄⠀⠀⢰⠃⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠋⠁⠀⠰⢼⠋⠉⠉⢨⢳⠀⡴⠋⠉⠉⠉⡙⣆⣟⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡛⠋⠭⠸⣆⠀⠀⢀⣸⠀⠀⠀⠀⢸⠼⡇⠀⠀⠀⠀⠃⣿⡉⠙⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠳⣌⡓⠲⠤⢭⣍⣙⣉⣘⣓⡒⠀⠒⠚⣋⣙⣒⣉⣉⣭⠭⠷⢒⣋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠙⠓⠲⠶⠦⠬⠭⣭⣭⣭⣭⣭⣭⡭⠭⠤⠶⠶⠒⠛⠉⢹⣂⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠩⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢸⠉⠉⠉⠉⠳⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠢⡦⢶⣴⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣦⣧⣏⣴⡦⠀⠀⠀⠀⠀⠀⠃⢸⠆⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⣉⡝⡟⢢⣀⡁⠀⠀⠀⠀⠀⠀⠀⢸⡦⠤⠤⠤⠖⠃⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠷⠌⠉⠀⠀⠀⠀⠀⠀⠀⡆⢸⣄⣒⣐⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠶⠶⠒⠒⠚⠛⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⡄⢣⢠⠁⠀⠀⠀⠀⠀⠠⢬⡄⣰⣾⠁⠀⠀⠀⠀⠀⠀⡄⠀⡨
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠋⠀⠠⠀⠀⠀⠀⡂⢤⡄⢄⡦⢄⠀⠀⠀⠀⠈⠀⠘⣔⣅⠤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠬⠭⠕⢘⢛⢻⠅⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢃⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠂⠴⢶⡋⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⡠⠌⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠔⢏⠀⠀⠈⡼⠑⡜⠀⢀⡠⠊⠁⠀⠀⠀⠀⠁⠀⠱⠚⠒⠎⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠢⠀⠀⠐⠀⠀⠠⢀⡡⠀⠈⡇⠀⠉⠐⠉⠀⣴⠊⠁⠀⠁⠀⢄⣀⢀⢀⡂⠐⠶⠚⠲
⠀⠀⠀⠀⠀⢴⣤⣨⡦⠐⠶⠜⠶⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣈⣉⢁⣉⡑⠶⠶⠴⣴⡄
⠀⠀⠀⠀⠠⣖⢤⠤⣴⠲⠶⠻⠔⠴⠄⠀⠐⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠈⢉⠉⠉⣶⣄⢠⣤⣄⠴
⠀⠀⠀⠀⢐⣠⣀⣤⣬⢖⢰⣠⢤⠠⣄⠐⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠐⡋⠉⠉⠉⠙⠮⣌⠠⡀⢈⠁⠀⠀⠄
⠀⠀⠀⠀⢄⣠⡠⣄⣬⢅⡀⢀⠀⡀⣀⡠⠀⠀⠈⠂⢄⠈⠁⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠛⠓⠓⠘⠓⠓⠦⣿⡆
⠀⠀⠀⠄⠄⢀⣀⢀⠍⡉⠛⠙⠛⠉⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⡆⠀⠀⠀⡾⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠠⣇⠀⠈⠠⠁⢺⡆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠠⠀⠀⡁⠀⠀⠀⠀⡌⠉
⠀⠀⠀⠀⠀⠠⣁⠀⠀⠀⠤⠆⡗⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠬⠀⠀⠀⠀⠉⠤
⠀⠀⠀⠀⠀⠀⠉⠓⠶⠀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠁⠛⠀⠀⠀⠐⠀⠠⠀⠀⠈⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⣒⡓⡆⠀⠀⠀⠀⢠⠖⠒⢦⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡁⣔⠈⠉⠐⢷⡹⡄⠀⠀⠀⣾⡠⠒⢲⡇⢸⠋⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠑⡜⠦⠄⢒⡉⣥⢳⠤⠴⠶⣿⡠⠤⢼⣧⡿⠊⠉⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⡄⢏⠂⠉⢹⡎⣇⠀⠀⢙⡠⠄⢸⢹⠗⠉⠉⢹⠷⣤⣠⠴⣒⡛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢧⡘⡌⢒⣪⡭⠲⣸⡤⠤⡏⢀⠔⠚⠛⠖⠂⠐⡎⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠀⢳⡘⣜⣄⣤⣊⠁⠀⠀⢘⢒⠀⠀⠀⢸⣒⣺⠓⣄⠀⠀⢸⣶⠾⠛⢻⡗⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢦⡢⣸⠉⠉⣌⠀⠈⢆⢀⡤⠊⢸⠊⠉⠉⢺⠀⠀⠀⢸⡠⣠⢿⡇⠀⠀⢀⡿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠙⠪⢕⣢⠤⣉⣑⠛⠉⠀⠀⠘⠒⠐⢒⣉⠠⢄⣲⠽⠞⢉⢸⡇⠀⢀⣼⢃⠎⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠑⠒⠚⠫⠯⠭⠭⠿⠓⠒⠚⠉⠁⠀⠀⠀⢸⣸⣃⣴⠟⡡⠋⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠟⠋⠁⠊⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⡾⠃⠠⠄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠻⣯⡓⠤⣀⡒⠀⠤⠄⠀⠀⢀⣀⡠⠔⣫⡾⠁⠀⠀⠀⠀⠀⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⢀⣀⠀⠀⠀⠈⠛⠲⠦⠭⣭⣭⣭⣭⣭⣭⠤⠶⠞⠉⠀⠀⠀⠀⣀⣀⠤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠐⠒⠒⠂⠀⠐⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⢸⡏⢠⠁⣿⠀⣿⠁⠀⢾⠋⢷⡄⣿⠙⣦⢻⣆⠀⢠⠂
⠀⠀⠀⢀⡄⡀⠀⡇⢸⣧⡌⠀⣿⠀⣿⡀⠀⣿⣆⡾⠃⣿⣠⠟⠀⢻⣤⠃
⠀⠀⢰⡿⠀⣹⢠⠀⠀⠿⠇⢸⣿⠀⣿⠀⠀⣿⡉⣷⠀⣿⠙⣦⠀⢰⣿⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠘⣷⠀⠋⡜⠀⠀⠀⠀⠉⠉⠙⠛⠳⠶⣮⣄⡘⠧⠈⠀⠘⠦⠈⠿⠀⣴⡟⠀⣀⠀⢹⣦
⠀⠀⠀⠈⠑⠈⣠⡴⠞⠋⠲⡀⠀⠀⢀⣀⡀⠀⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⢿⡄⠀⣿⠇⢸⣿⠀⣀⠀⡀
⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⢀⠇⣠⡞⠉⢀⣽⡗⠒⠒⠒⠒⠒⠶⣿⣤⣀⣀⠀⠉⠉⢁⣠⡿⠃⣾⢁⠀⠈⡆
⠀⠀⠀⢀⣾⠇⢠⠒⢢⡠⠊⣼⠏⠀⢰⣡⡾⠃⠀⠀⠀⡀⠀⢰⣿⠀⠀⢉⡉⠉⠉⠉⠁⠀⠀⢻⡜⠂⠂⢁⣾
⠀⠀⠀⣼⣿⠀⠀⠈⠉⠇⢸⡟⠀⠀⢠⡀⠀⠀⠀⠒⢸⣇⠇⢸⡇⠀⢠⢿⣿⣠⣦⠀⣠⠀⢰⠎⢿⣦⠀⢸⡏
⣴⠏⠀⣿⣿⠀⠀⠀⡐⠀⣾⠃⠀⣀⡀⠉⢹⡿⢠⡿⢸⣿⡀⣼⡇⣦⡌⢸⣿⠁⣿⠀⡏⠀⢻⠀⢀⢿⣧⠸⡇
⠻⣆⡀⢻⣿⣀⡤⠂⠀⠀⣿⢀⠎⢰⡟⢠⣿⠁⠸⠧⠂⣹⡇⣾⡄⢿⠃⠘⠃⠈⣇⠀⠑⢀⡈⠓⠂⢘⣿⠠⡆
⠀⠀⠉⠉⣿⣇⠀⠀⠀⠀⢿⡏⠀⣾⡇⢸⡏⢐⡦⠀⠜⢸⡇⢹⡇⠀⠀⢀⣀⣠⣤⣄⡀⠈⠳⠄⠠⠞⠃
⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⣠⠀⠹⡄⠀⣉⣉⣁⣀⣑⠋⠀⠈⣿⣶⡾⠛⠉⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠋⠁⠀⠀⡴⠋⠉⠉⠉⠉⠉⣻⣷⣾⣏⢉⠲⢤⣀⣀⢀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣠⣤⡶⠟⠋⣁⠀⢻⣧⠙⠲⠤⣤⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢹⡄⣿⠀⠑⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣉⡴⠃

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠠⡅⠰⠉⠂⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠘⠁⠈⠉⠉⠃⠀⡤⠀⠘⡄⢀⠤⡀⠹⠉⠂⠀⠋⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡄
⠀⠀⠀⠔⢄⠀⢢⢐⣁⢠⠐⢂⠔⠀⠀⠀⠀⠀⢠⠀⠞⠀⡄⠀⡆⠘⠐⠙⠇⠀⠁⠁⢀⠃⠈⠂⠁⡠⠄⠈⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠈⡰
⠀⠀⠂⣈⠀⣑⠃⣄⡌⢠⠂⠨⠑⠀⠀⠀⠀⠀⢸⠀⠀⢠⠃⠀⡇⠰⠖⠰⢇⠀⢆⠀⠛⡄⠰⡆⠀⠣⠈⠀⠀⠁⠀⠀⠀⡔⠒⢢⠀⠀⠀⠀⠀⠧⠀⠄⣰
⠀⠀⠐⠔⠈⢀⠑⠠⠤⡉⠂⡀⠲⠀⠀⠀⠐⠂⠂⠘⠒⠂⠐⠒⠧⠤⠤⠤⠴⠉⠀⠑⠂⠋⠉⠀⠑⠐⠀⠤⠤⠀⠀⠀⠀⠑⠄⠊
⠀⠀⠀⠐⠀⠖⣠⠀⠀⡇⠒⠤⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠐⠀⠑⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⡎⠑⠀⠠⠠⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠸⣅⡴⠆
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠠⠃⠈⠂⠘⠀⠓⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠁⠐⠀⠃⠘⠠⠂⠀⠰⠀⠀⡀⠀⠀⠀⠉⣹⢤⠓⠶
⠀⠀⣤⣈⠧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠤⠄⠀⠐⠐⠢⡀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠂⠒⠂⠠⠤⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃
⠀⠀⢀⡴⢳⡍⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠔⠠⢄⠀⠁⢀⠀⠀⠀⠀⠀⠉⠀⠀⠂⢸⠀⡀⠄⢢⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠁⠓⠘⠂⠂⠀⠀⠀⠀⠀⠀⠂⠘⠊⠀⠀⠌⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠈⠍⠀⠀⠀⠸⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⡀⠀⠀⠀⠠⢄⠀⠀⠀⠐⡀⠁⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠐⠃⠀⠀⣀⣰⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠤⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠊⠀⠀⠀⠰⠀⠄⡌
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⡈⢁⢘⢁⢺⣀⠀⠀⠀⠀⠀⠠⠂⠀⡔⠀⠀⠢⠀⠈⠂⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠅⢺⠠⠌⡕⠨⠣⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⡇⢀⠴⠘⡅⢨⡁⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡀⣀⠀⠀⠀⠀⠸⠆⠀⠀⠐⠲⣉⠎⠁⣉⠔⠂⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠠⠀⠀⡠⠂⠀⠀⠀⠀⡂⠭⢤⣉⠓⡘⣉⡤⠼⠀⠀⠀⠀⢀
⠀⠨⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡇⢮⠚⣉⡖⠱⣌⡑⢸⠀⠀⠀⠌⠀⢑
⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠐⠐⠂⡇⢘⡆⠃⢰⠀⠀⠀⠀⠀⡇⠈⠑⠠⣋⢈⡄⠒⠉⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⢔⡐⠀⠈⡠⠂⢰⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⣀⠜⠣⠀⠁⠈⠁⡜⠃⣄⠠⠆⢀⠀⡇⠀⠀⠀⠀⠁
⠀⠀⠀⡐⠱⠀⣀⠵⠀⠃⡐⠤⠃⠀⠐⢄⠀⠀⠀⠀⠀⠀⠐⠠⠤⠴⡀⠨⠀⠀⠀⠀⠇⢀⠴⠠⠤⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡒⣀⢱⣀⡀
⠀⠀⢥⠀⠀⠑⠀⠺⠀⠘⠂⣀⡐⡍⠀⢈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠁⠈⠁⠀⠀⠀⠀⠀⠇⠀⠀⠸⠂⠀⠀⠀⢔⠠⠄⡀⠐⡄⡨⠐⢁⢤
⠀⠀⠂⠐⠉⡇⠰⠆⠘⠌⠀⠑⠁⠢⠀⢀⠀⠀⠀⠀⠀⠑⠄⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠠⡁⢋⠁⠳⠰⠁⠆⢠
⠀⠀⠀⡒⠂⠜⠀⡀⠼⠀⠘⢃⡐⠒⠀⡤⠅⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠓⣈⡉⠜⠉⠢⢙⡄
⠀⠀⠀⢸⢁⡀⠨⠉⠀⡢⠈⠁⠤⡈⠒⠁⠀⢀⢄⠀⠀⠀⢀⠜⠀⠓⡄⠀⠀⠀⠀⠀⠀⢀⠜⠁⠣⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⠠⣋⠴⠘⠀⡀⡀⣅⢐⠄
⠀⠀⠀⠀⠀⠐⠒⠀⠌⠠⣄⡐⠒⠁⠀⠀⠀⠐⠄⠁⠀⠀⠐⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠘⠄⠠⠀⠂⠀⠀⠀⠠⠄⠔⠀⠀⠀⠀⠀⠐⠂⠀⠔⠑⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣀⠀⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⢄⠀⠀⠀⠀⢀⠔⠁⠈⠘⠢⡀⣀⡀⠀⠀⠀⠄⠈⢣⠀⠖⠀⠀⠐⡆⠀⠀⠀⣀⡃⠀⠆⠠⠀⠀⠂⠠⠃⠈⢡⠀⠔⠀⠀⠀⡄⠀⠀⠀⠀⠨⠤⠃
⠀⢀⡠⠂⠀⠉⠩⠀⠀⡄⠀⡊⠀⢑⡂⠁⡀⡀⠀⠀⠈⠒⠁⡘⠀⣀⠘⠊⠛⡅⠈⠀⢸⢸⠀⠀⠈⡆⢀⠀⢰⠁⢠⠣⠀⢣⠀⠘⠉⠲⡀
⠀⠀⠁⠄⠀⣀⣸⠀⠀⠐⡀⠈⠀⠉⢨⣆⠀⢀⣀⡀⢰⣄⠈⢳⢀⡛⠋⠑⠀⡀⠀⠀⠸⢸⠀⠸⡀⠀⡸⠀⠀⢀⠤⠤⡄⠈⠞⠣⠴⠀⡐⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠀⠁⠘⠀⠁⠀⠀⠈⠀⠀⠂⠈⠘⠀⠂⠑⠒⠀⠂⠚⠁⠀⠀⠘⠀⠁⠐⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢸⠆⠀⠀⣀⣀⣀⣀⣀⣼⣯⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣠⠋⠀⠀⠀⠀⣀⡀⠉⢩⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢁⠖⣻⡆⠀⠘⠿⢽⡶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡏⢀⣿⠃⣼⡟⠀⢀⡇⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣼⠏⢀⢿⣧⣠⠞⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢰⡟⢀⡜⠀⢈⠀⠀⠀⢻⣆⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠊⠈⡆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣦⣆⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⣀⡸⠤⠔⢲⠖⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣖⢲⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⠝⢆⠀⠈⠃⠀⡰⢏⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠐⠉⣉⠉⠑⠤⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣤⣀⠀⠀⣀⣀⡀⠀⠀⣤⡦⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⣽⡇⢀⣘⠻⢾⣺⣿⡟⠉⠁⣠⣤⡝⠓⢷⢲⣾⠟⠉⣁⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠈⠉⢠⣿⠏⠀⢸⢿⣿⠀⠀⣰⢻⡟⠀⠀⡟⣿⡏⠀⡼⣿⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⠴⠋⠿⣧⡴⠋⠘⠿⣦⠴⠃⠘⢿⣤⠜⠁⠹⢷⡼⠁⠻⣤⠎

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⡰⠾⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢬⢺⣁⠀⠀⣰⠀⠀⠀⣂⢠⣭⢀⣶⣠
⣤⣤⢧⢰⣆⡋⣼⣶⠦⢶⡶⢧⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠺⣾⢅⡀⠀⢺⡦⢀⢐⣏⡷⡎⢻⢼⣞
⣿⣿⠛⡿⠊⡓⠚⣧⡇⣼⣡⠚⣶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣣⣇⡃⢺⡿⠬⠁⠘⣻⡧⠑⢈⣿⠞⡓⠛⡿⣴
⣿⣥⣷⠓⠋⢸⡏⠙⣿⣿⣧⣾⣿⣦⣿⣷⣷⣴⣶⣦⢤⣤⠒⣧⠯⢝⣄⡀⣀⢠⣌⡠⢥⠘⢄⢴⣯⣿⣦⣿⣈
⢸⣿⣟⠉⡱⢋⠙⣟⢻⡿⡿⣿⢻⢿⣿⣿⠿⠿⢶⣿⣿⡯⠔⣣⠘⢦⠷⣿⢇⡨⡚⣧⢉⠄⣍⢸⣿⣿⣿⠿⢿
⠘⠹⢏⡨⠦⠈⠓⠛⣍⡁⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠩⠃⠁⠭⠀⠉⠠⠓⠐⠀⠀⠠⡇⠘⠀⠓⢊⣃
⠀⠐⠒⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠂⠂⠠⠤⠤⠤⠤⠀⠄⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣶⣤⠠⠄
⠀⠀⠀⠀⠀⣀⣰⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠈⠡⠔⠂⠀⡴⠆⢞⠿⡿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠤⠤⠤⠤⠷⠾⠳⠲⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⠴⠶⠛⠡⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿