Big brother Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠈⢻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⡀⠀⣄⠀⠈⠠⠀⠐⠀⠸⣿⣿⣿⣷⡙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠂⠀⠀⠀⠦⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⡈⠀⠀⠀⡄⠀⢀⣼⣿⣿⣿⡇⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢡⡿⢿⣿⣿⡆⠀⠃⠀⠀⢠⣤⣶⣿⣿⣿⡿⠿⠃⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⢰⣿⠁⠀⠈⠻⣧⡀⠠⠀⢠⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢺⡇⣸⡆⠀⠀⠀⠙⠒⠐⠿⠿⠛⠛⠁⠀⠀⠀⠀⢳⡀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢿⣿⠀⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣿⡆⣾⣿⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⣸⣿⡟⢡⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣤⣤⣤⣴⡶⠦⢼⣿⣿⣿⣶⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠹⠛⠟⢉⣿⠆⠀⠀⠲⣯⣉⠫⡻⠏⠐⠂⠈⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡘⣿⡟⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣸⡇⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣡⣶⣦⣄⠀⣤⣶⣤⡀⠀⠀⠀⢼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⡀⠀⠀⠀⠛⠋⠉⠉⠉⠉⡉⠉⠉⠀⠀⠀⡜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡘⢷⡀⠀⠀⠀⠀⣼⣿⠿⢿⣧⠀⠀⠀⣠⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢢⠒⡖⢂⣀⡄⠀⠂⡐⣤⠀⡐⠤⠂⢀⠲⡆⢀⡖⠂⠖⣶⢀⣶⢂⡐⠀⢠⠐⡆⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠨⡀⠇⠘⠂⠀⠀⠀⠂⠸⢀⡄⢧⠈⢀⠀⠃⠀⠇⠐⢆⣧⠐⢿⠠⠄⡄⠸⠀⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣴⢀⡆⢰⡆⠲⡶⢀⡾⠃⣴⠀⣦⢰⡅⣶⠠⡆⣰⠟⠆⠀⠸⡆⣴⢠⡖⢶⠀⡆⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⣼⢁⡞⣷⠈⡇⢸⡇⠀⣸⠒⣧⢸⡇⣿⢼⡇⣿⠠⣤⠀⠀⢹⡇⢸⡇⢸⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠿⠰⠏⠹⠆⠇⠈⠷⠄⠻⠀⠟⠸⠇⠿⠸⠇⠹⠦⠏⠀⠀⠸⠇⠘⠧⠾⠀⠧⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡴⠛⡆⣉⠀⠀⠀⢠⠖⢢⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢠⡇⣿⠀⠀⣠⡟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠋⠀⠙⠲⠚⠉⠳⠞⢹⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡁
⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⣰⣄⣢⣈⣳⣀⣆⣠⣀⣠⣀⣀⣀⣀⣀⣠⣏⣸⣇⣠⣤⣀⣠⣤⣀⣀⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢼⣉⡽⠽⠋⠉⠏⠙⠉⠙⠉⠉⠉⠀⢉⡟⠉⣹⠉⠉⠛⠉⠉⠋⠉⠉⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⣄⠀⠀⢠⣤⣴⣦⣶⣤⣤⡀⠉⠁⠀⠀⣀⣤⣰⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠅⢾⣿⣿⣿⠿⠟⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⡆⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⢻⣿⣿⣿⣦⣠⣾⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣷⣿⡿⣾⣿⠇⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⠿⠛⠀⢸⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠙⠻⣿⣿⣿⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⢀⡤⢦⡄⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⡞⢀⣾⠇⠀⣀⣴⣦⠀⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⡞⠠⠾⢛⡷⣮⢸⣿⡟⢠⣿⣿⢋⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠇⠀⡴⠋⠀⣿⠈⠛⠛⠁⠉⠛⠉⣼⣿⠀⠀⠀⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢸⡇⢀⣴⠋⣠⡶⠞⣛⡛⠛⢳⣿⣿⣤⣤⣴⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠀⣘⠏⠀⣼⣿⢁⣴⡿⠋⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⣀⡀
⢀⣀⡀⠀⠀⢀⡀⠀⠀⡿⠳⠶⢶⣤⣄⠀⠀⠀⠀⠉⠓⣺⣿⡟⠋⢁⣴⡾⢷⡄⠀⠀⠀⠀⠀⢻⡏⠉⠉⣿⣷
⣾⣿⡇⠀⣼⠉⣷⠀⢰⠇⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣰⣿⣿⠀⢠⣿⡟⠀⣼⠃⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⡏
⣿⣿⣷⢠⡇⣰⠿⢤⡏⠀⠀⢠⣿⡿⠁⢀⣴⣶⣶⠊⣿⣿⡇⠀⣿⣿⡡⠞⠁⠀⢠⣾⠛⣷⠄⣸⡇⢠⣿⡟
⠹⣿⣿⢸⡇⠀⢀⡏⢿⡀⠀⣾⣿⠁⠀⣸⣿⡏⡟⢠⣿⣿⠁⠰⣿⣿⣠⢺⡗⠀⣿⡧⠴⠋⣰⠟⠀⣾⣿⠁
⠀⠹⢿⣿⡇⠀⡾⠀⣼⠀⢰⣿⡇⠀⣰⠏⠛⣛⣀⡈⣿⣿⠀⣠⠟⠿⠁⢿⣇⡴⠛⠳⠶⠚⠁⣀⣤⣿⣿⠛⠋⠙⣷
⠀⠀⠀⠈⠀⠀⠣⠜⠁⠀⠀⠻⠧⠞⠃⢠⣿⣿⣿⠃⠈⠛⠚⠁⠀⠀⠀⠀⠉⠀⠀⣀⣤⣶⠿⠛⠉⠘⠻⢷⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⡀⠀⠀⣀⣀⣀⣤⣤⣶⠾⠟⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣒⠒⠒⠒⠒⠒⠒⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠖⢢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⡉⢍⠉⠀⠒⠒⡒⠒⡲⠂⢐⣺⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢀⡀⣱⠴⠊⠉⠉⣷⠙⣘⠀⠀⢀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠄⠐⠀⠀⠈⣾⠁⠀⢀⡀⡠⠃⠀⠳⠒⡂⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡀⠀⠀⠀⠈⠖⠊⢉⠉⠁⠠⡸⠀⠈⠠⣄⠀⠀⠀⠉⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢁⡩⣭⢉⡇⢱⢄⡀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⠀⠚⠀⡠⠂⠤⠤⣶⠟⠚⢧⡀⠈⠁⠒⠤⢀⣀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠐⠊⣧⠀⢀⠌⠀⠀⢀⣀⣏⠁⠀⡴⡇⠉⠉⡟⠀⢠⠎⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠁⠀⠄⢀⠀⠀⣏⠉⠓⠉⠙⣄⠀⣀⡜⠀⢀⣮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠀⠰⠈⡆⠀⠀⠸⡇⠀⠀⠀⠉⣁⡀⠀⠀⠾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢁⣀⣴⠖⠀⠒⡿⠟⠓⣀⠀⡠⠚⠠⣀⠀⠀⠡⠀⠀⠀⠀⡜⠀⢠⠄⠋⠓
⠀⠀⠀⢸⠅⡀⠀⠀⠀⠀⠀⠀⢉⠁⢀⠌⠀⠁⠀⠀⢨⠁⠀⠀⠀⣀⠦⠀⠂⠀⠀⠘⠁⠀⠁
⠀⠀⠀⠈⠚⠓⠊⠀⠀⠀⠀⠀⠒⡸⠃⠀⠀⠀⠀⠀⠀⢉⡽⢂⣴⠿⣁⠀⢀⣀⠀⠀⢀⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣹⣶⢤⣤⠀⢠⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢹⢻⠒⠲⠤⠤⢤⡼⠀⠀⠀⠀⢺⠏⠘⠒⡹⠒⠁⠣⠔⠃⢀
⠀⠀⠀⢀⠦⢾⣶⡀⢀⡤⠊⠀⠀⢠⠃⠏⠀⠀⠀⠀⠸⠀⠀⠀⢀⡴⠁⠀⠀⠀⠢⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠨⠥⠭⡍⡏⠁⠀⠀⠀⠀⠝⠉⢶⠀⠀⠀⡀⠆⠀⠀⠀⡼⠓⢠⢤⣀⣀⢘⡶⣖⠂
⠀⠀⠀⢸⣀⡘⡃⠃⠀⠀⢀⠔⠁⠀⠀⠈⢀⢀⡂⠸⡟⣓⠄⠀⠀⠀⠀⡞⠀⠀⢈⢀⡯⢤
⠀⠀⠀⠘⡆⢲⡗⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⢹⡂⠬⣿⡇⠀⠀⢀⡝⢻⠃⠀⠀⠹⣤⣬⣓
⠀⠀⠀⠀⠉⠙⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢽⡿⠀⣠⣴⠟⠁⠈⢦⡀⠀⠀⠀⠀⣸⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠿⠷⠟⠋⠁⠀⠀⠀⠀⠈⠁⢲⠒⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡴⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠊⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣰⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠐⠀⢰⡇⠀⠀⢀⠞⢸⠁⠀⠀⠀⠠⠀⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣤⠀⠀⠘⠧⠠⠔⠁⠀⡞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠇⠀⠀⠖⠋⠁⠉⠲⣄⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⡔⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠀⠀⢿⠀⠏⠑⢦⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⠀⠀⠀⢆⠀⠀⠃⠀⠀⣠⠤⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠀⠀⠀⡧⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡆⠀⠣⠈⣆⠀⠀⠄⠒⠂⠐⣦
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢸⠇⠀⠀⣼⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⡾⠠⠐⡿⠂⠉⣸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠤⠤⢤⡀⠀⠀⠀⠀⢠⢺⠇⠀⢸⠇⠀⡴⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠔⠀⣦⠈⠓⠒⠊⠉⠀⠀⠀⢸⡇⠀⢀⡠⠐⠁⣸⠀⠀⣿⠤⠊⠀⠀⠀⢀⣀⡀⠀⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡟⠀⠀⠀⡟⠀⢰⡏⠀⠀⠀⠀⢀⡟⢠⠇⡘⠀⠀⢀⡾⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠃⠀⠀⡜⠀⢀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢸⣇⠀⠀⢰⡇⠀⢸⡇⠠⢤⠀⠀⡜⠧⡀⠔⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠇⢀⣴⠏⠀⠀⠀⠙⢦⠀⠀⠀⢠⡏⠀⠀⠇⠀⠀⠀⢸⡇⠀⠘⣷⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡼⢀⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣾⠀⠀⡜⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⢀⡠⠒⠉⠀⠈⡇⠀⡇⠀⠈⠱⡄⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⢠⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⡴⠋⠀⠀⠀⠀⠀⢿⢰⠀⠀⠀⢀⡟⠀⠀⠀⠀⣸⠃⠀⢸⡅⢀⠎⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠
⡼⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠈⠀⠀⠀⠀⣰⠃⠀⠀⠈⠣⠊⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢠⠎
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⡠⠋
⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠉
⣀⣈⣐⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣄⡉⠉⠉⠉⠉⠉⠙⠛⠒⠲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠥⠤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠖⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⣤⠄⠀⢤⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⢲⡄⢑⣠⡤⠤⢤⣀⢢⠀⣰⠃⠀⠀⠲⣟⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡤⣠⡿⠋⠁⠀⠀⠀⣿⠀⢰⡇⠀⣀⣠⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠶⢤⡞⠳⠤⠤⠼⢿⡏⠀⠀⠀⣠⢀⡼⠃⢀⢞⡿⢟⣛⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠉⠀⠀⠀⠀⠈⢷⠴⠖⠛⠛⠛⠀⢠⢿⡟⠀⠻⢍⡁⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⢠⡯⠿⠒⠒⠲⣄⠿⡓⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠐⠾⠽⢓⡠⠏⡠⠞⡓⠦⣀⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢀⡴⢚⠏⠀⣠⠞⠛⠒⠒⢚⡿⠛⠉⠓⣦⠁⠀⠀⢉⠑⠒⠤⣄⡀⠀⠀⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠔⠚⢻⣠⠏⢀⡞⠁⠀⠀⠀⠀⢸⡈⠀⠀⢠⣾⡋⠉⠉⢹⠛⠀⢀⡔⠁⠀⠀⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠋⠁⢀⡞⠀⠀⠀⢰⡏⠙⠻⣍⠒⠒⡏⠈⠀⠀⢠⠏⠀⠀⡼⢡⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡞⣽⣽⠃⠀⠀⠳⣄⣀⠀⠀⠀⠹⠦⠒⠒⠃⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣤⠀⠀⠀⠀⠀⠀⠀⣴⣏⣻⠀⣀⡠⠜⠋⢕⡿⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⢘⣛⣉⠓⢦
⠀⠀⠀⠀⢀⣀⡤⠤⠴⠚⠁⢾⣁⣀⣀⣶⡖⠒⠒⠒⡿⡿⠹⢋⣥⡀⣀⡔⠋⠳⢤⡀⠀⠀⠸⡄⠀⠀⠀⠀⢀⠏⠀⢀⡤⣌⣓⠛⣉⡼
⠀⠀⠀⠰⣏⠥⢂⡄⢀⠖⠒⠤⠤⣈⣉⢹⡇⠀⢀⡞⠁⠓⠚⠉⠀⢙⡟⢀⠀⠀⠀⠉⢳⣦⠀⠹⡄⠀⠀⢀⠞⠀⢠⠋⠀⠀⠉⠉⠉
⠀⠀⠀⠐⢧⣰⣏⡴⠋⠀⠀⠀⠀⠀⢸⣹⣤⣶⠏⠀⠀⠀⠀⠀⠀⠘⠧⠬⣶⡀⢀⣼⣿⠧⢄⡀⠹⡄⠀⠉⠀⢀⠷⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠈⠾⠛⠉⠲⢤⣉⡶⢷⠀⠀⣀⣶⣚⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⣿⢹⢶⡊⢁⣯⣀⡽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⡝⢹⠓⠲⠦⠤⢤⢤⣤⡿⠀⠀⠀⠀⠀⢺⡞⠁⠻⠖⣩⠟⠋⠈⢣⣤⠺⠧⣀
⠀⠀⠀⠀⣠⣖⣶⣦⡀⠀⠀⢀⡴⠋⠀⠀⠀⡰⢡⡏⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠠⣏⣰⠁⠀⡠⠀⠑⠒⠋
⠀⠀⠀⢀⡟⠰⠼⠟⣽⡴⠚⠉⠀⠀⠀⠀⢰⣧⣾⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠀⠀⢰⣇⣀⣀⡅
⠀⠀⠀⢸⡏⠉⠉⣃⢿⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⣯⠁⠀⠀⡠⢤⣬⡀⠀⠀⢀⡜⠁⠈⣹⢛⡶⠶⠴⢤⡟⢻⡽⠇
⠀⠀⠀⠘⣏⣉⣉⣉⡸⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠈⢦⡀⣼⡃⠺⣿⢻⡳⠖⠉⠀⠀⢰⠇⡼⠀⠀⠀⢀⡇⣸⠶⢶
⠀⠀⠀⠀⢷⠠⠤⣿⠃⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠬⣉⣿⣼⠀⠀⠀⠀⢉⡞⢶⠧⠀⠀⠀⠸⣄⢀⣈⠳
⠀⠀⠀⠀⠘⠶⢾⣃⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣐⠲⣿⡏⠀⠀⣀⢔⡿⠁⠘⣆⠀⠀⠀⠀⠈⠉⠛⠒⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠪⣽⡿⣀⣴⣪⠵⠋⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⣀⡾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⢹⣳⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡴⠋⣿⠀⠀⣨⣍⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⠁⠾⣳⢶⣹⣿⡏⣰⣿⣏⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⡜⠁⢸⠇⠙⢋⣀⣉⠉⣸⡟⠀⠀⢺⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢇⡤⠋⣰⠞⢫⣿⠉⣹⡿⠓⠶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⣀⠀⠀⠀⠀⠰⢭⣠⣿⡧⠾⢋⣠⣄⠀⠀⠀⠀⠻⣶⠤⠴⣤⡄
⠀⠀⠀⠀⠀⠀⣾⣿⠀⣠⢲⡄⠀⡟⠀⠉⣹⣿⠆⠀⠀⠀⢀⣿⣿⠀⣰⣿⠃⣿⠀⠀⠀⠀⠀⢿⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⠀⡇⣸⢧⣼⠁⠀⢠⣿⠏⠀⣤⣤⡔⢺⣿⡇⢰⣿⣇⠔⠁⠀⣴⠖⣦⠀⣾⠀⣾⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣴⡇⠀⡰⢹⡆⢀⣿⡏⠀⣸⣿⣡⠃⣿⣿⠀⢸⣿⡥⢺⡇⢸⣿⠐⢋⡼⠃⢸⣿⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⢰⡇⣸⠃⠸⣿⠀⣰⠋⣩⣥⣤⢻⣿⣀⠞⠛⠁⠻⠤⠋⠙⠛⢉⣠⣴⠾⣿⡉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋⠁⠸⣿⣿⡇⠀⠈⠁⠀⠀⠀⢀⣀⣤⣴⠾⠛⠉⠀⠀⠉⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⠶⠶⠾⠛⠛⠉⠁

⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠛⢶⣦⡀⢀⣿⣿⡄⠀⣠⣾⣿⠛⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⢹⣿⢸⣿⣿⠁⢸⣿⣿⠃⠀⠀⠘⠇⠀⠀⠀⠀⠀⢠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣾⠟⢸⣿⣿⠀⣿⣿⣿⠰⠶⠶⢶⣄⣀⣠⣤⣤⣤⡤⢼⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠲⣜⢦⣻⣄⣀⣠⣤⣤⡤⠤⢾⣿⣿⠶⣾⣯⡁⠀⢸⣿⣿⠀⣿⣿⣧⠀⠀⠀⢸⡏⠀⠀⢀⡀⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣴⣫⡞⢹⠫⣶⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠙⣿⡆⠈⣿⣿⠀⢿⣿⣿⠀⠀⠀⣼⡇⠠⠀⠙⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⠀⠀⠀⠀⠘⣿⣿⡄⢀⣴⠟⠁⠀⣿⣿⠄⣼⢿⣿⣇⠀⣠⡿⠁⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠉⠋⣼⠃⠀⠉⠛⣛⣭⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⢀⣴⣶⠶⡆⠀⠀⠙⠷⣤⣀⠀⣰⠞⣋⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⢹⡇⠀⢀⣠⣄⡀
⠀⠀⠀⠀⣰⣿⡿⠃⢠⡇⠀⠀⠀⠀⠀⠉⠙⣿⠋⠉⠀⠀⠀⣀⣤⠞⣱⣶⡄⠀⢠⣿⡿⠀⠀⠀⠀⠀⢀⣼⠇⣰⣿⠁⠀⠹⡆
⠀⠀⠀⣸⣿⣿⠁⣠⠟⠀⠀⣠⣤⡄⠀⠀⠀⠈⠳⠶⠶⠖⢛⣉⣀⣀⣿⣿⡇⠀⣾⣿⠇⠀⠀⢀⣠⣴⠟⠁⠀⣿⡇⠀⠀⢀⣿⡴⣶⣶⡄
⠀⠀⢀⣿⣿⣧⡾⠃⠀⠀⢰⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⢹⣿⣿⠛⢻⣿⣿⠶⠾⠛⢛⣉⠀⠀⠀⠀⠙⠻⠾⠛⢋⡏⢠⣿⣿⠃
⠀⠀⢸⣿⣿⠁⠀⣠⣤⡀⢸⣿⣸⠇⢀⣀⡀⠀⠀⢰⡿⠋⢳⡄⠀⣸⣿⡇⠀⢸⣿⣿⠀⣠⠾⣿⣿⠀⠀⣠⣶⡿⠛⣷⠀⣸⠇⣾⣿⡏
⠀⠀⣿⣿⣿⢀⡞⠉⣿⣿⠀⣻⠿⠞⣻⣿⡇⠀⣴⣿⣇⠀⠀⣧⠀⣿⣿⠃⠀⠘⣿⣿⣼⠋⣼⣿⡟⠀⢰⣿⣿⣁⣼⠏⢀⡟⢰⣿⣿⠀⠀⡤
⠀⠀⢹⣿⣷⡾⠀⢰⣿⣿⠟⠁⠀⢀⣿⣿⠀⠀⣿⣿⠿⣄⣀⣿⡾⣿⣿⠀⠀⠀⢻⣿⠃⠀⣿⣿⠁⠀⣼⣿⡏⠉⠀⢀⣾⠁⢸⣿⡇⠀⣸⠇
⠀⠀⠘⣿⣿⢃⣠⣾⣿⡟⠀⠀⠀⢸⣿⡏⠀⠀⣿⣿⡀⠈⣹⠇⠀⣿⣿⠀⠀⠀⢀⠉⠀⠘⣿⣿⠀⣰⠿⣿⣇⠀⢀⡾⠃⠀⢸⣿⡇⣠⡟
⠀⠀⠀⠈⠻⣟⣱⣿⠟⠀⠀⠀⠀⢸⣿⡇⠀⢠⡟⢿⣧⣴⠟⠀⠀⠸⣿⡄⠀⢀⡿⠀⠀⠀⠹⠿⠶⠋⠀⠙⠻⠶⠛⠁⠀⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠞⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⢲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢉⡉⠒⠒⠒⠒⠒⠒⠒⠢⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⣆⡤⠖⠒⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠹⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠄⠀⠁⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣤⣤⣄⡙⣶⠄⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⠦⣀⠇⣨⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠦⠤⠶⡺⠗⠚⠧⡈⠀⠈⢉⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠤⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠀⠀⣠⣿⠒⠁⠙⡟⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣾⠉⠻⢍⠒⠲⡇⠉⠀⢀⡜⠀⠀⣼⣡⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠄⠀⠀⠀⠙⠒⠒⠛⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣲⠄⠀⠀⠀⠀⠀⢠⣾⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⡖⠀⠀⠀⡭⣍⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⢤⣾⡏⠉⠉⠹⠋⠁⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠜⠒⠀⠉
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⢀⣼⡷⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠁⠀⠀⠈⣰⣤⢀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠙⡷⣦⢤⣄⣀⣀⣀⣀⡏⠀⠀⠀⠀⠠⣾⠏⢻⡬⢿⠦⠞⠹⣉⣩⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⣀⡔⠃⠀⠀⡸⢰⠇⠀⠀⠀⠀⢈⡏⠁⠀⠀⠀⢀⡴⠁⠀⠀⢠⡏⠠⠀⠀⠉⠑⠤⠚
⠀⠀⠀⠀⠀⡶⠤⠤⢨⣧⠄⠀⠁⠀⠀⠀⠤⠃⡞⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠠⡗⠒⡒⡆⣷⠀⠀⠀⠀⠀⡠⠂⠀⠰⡄⠀⠀⠀⢤⣀⡀⠀⠀⠀⠊⠁⠀⠀⡶⠦⠤⠄⠈⣷⠝
⠀⠀⠀⠀⠀⣯⠄⠉⠃⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢆⠀⢀⡒⠉⢨⡴⠂⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡼⢒⠆
⠀⠀⠀⠀⠀⢀⠀⢀⡴⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠤⣄⡈⠀⠀⠀⢀⣭⠀⡓⠠⠀⠀⠀⢀⣀⡉⠂
⠀⠀⠀⠀⠀⠈⠑⠻⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠬⢝⣿⡇⠀⣠⢔⡽⠃⠀⠳⡀⠀⠀⠀⠀⠈⠉⣽⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣶⣿⣴⡮⠗⠉⠀⠀⠀⠀⠈⠓⠢⢤⡤⣤⡾⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⣠⣄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⡞⠁⣿⡇⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢠⡟⢀⣼⡿⠁⢀⣤⣄⠀⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⠑⠛⠛⢦⣀⣼⣿⡟⠀⣾⣿⡟⣡⣷⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢡⡇⠀⣠⠔⣻⠇⠸⣿⡇⠀⠻⣿⠞⣹⠃⠀⢀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢠⠞⠁⣰⠏⠀⠀⠈⠉⠔⠋⣉⠽⠛⠛⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⠀⢤⣘⠒⠋⢡⡖⠀⠀⠀⢠⡄⠈⣠⣶⡶⣄⠀⢶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢰⠃⣾⠀⢸⢛⣿⡄⠘⠿⠶⠶⢶⣿⠗⣾⣿⠟⢓⡿⠂⠀⢹⡇⢈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡟⢠⡟⢀⡟⢸⣿⠃⢠⣾⣷⡠⣾⣿⢠⣿⣿⡴⢛⣥⣤⡄⢸⡇⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠺⢥⡼⠁⣾⡿⠀⣿⣿⣹⢠⣿⡏⢸⣿⡇⠀⣿⣟⡼⠃⡾⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⡸⢳⠀⢿⣇⠞⠙⠿⠏⢸⣿⡇⠘⢿⠋⠒⠻⣧⣠⠾⠁⢸⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠃⢸⠀⠀⠁⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢲⠃⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠤⠾⣟⡁⠀⠀⠰⡦⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢻⣆⠀⣾⡇⢀⣾⡿⠹⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣿⡏⠐⡄⠀⣸⣿⢰⣿⠇⣾⣿⠁⢸⣿⡀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠋⠀⠁⣠⣿⠏⠈⣿⣇⣿⣿⣠⠏⣿⡇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀⣀⣤⣴⠿⠋⠀⠀⠈⠉⠀⣩⠵⠒⣿⡏⠀⠰⣿⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⢶⡄⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠿⠇⠀⠀⣿⣱⣿⠟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣇⡏⠀⢀⣾⠇⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⢠⣶⠚⠧⣠⡾⠛⢳⠀⠴⡷⣻⣵⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠠⠶⢿⣉⠀⠀⣀⠀⠀⠉⠀⣀⡊⠉⠉⣿⡟⠒⣺⣿⠓⠒⠁⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⢹⣧⠘⣿⣄⡀⠀⢸⣡⡙⡄⢸⣿⡇⠀⣿⣟⡴⢋⣿⡆⢀⣾⡏⡹⠀⣿⣄⣀⠀⢀
⠀⠀⠀⠀⠀⢠⠖⢿⣿⠉⢢⠀⢠⣿⡇⢠⣿⡟⢀⣾⡿⠀⡿⢺⣿⠀⢀⣿⣿⠁⢸⣿⠇⢸⣿⠋⠀⢠⣇⣿⡿⠀⡞
⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⠈⢀⣾⡿⠀⢾⣟⣠⠞⢻⣇⣠⠇⠘⢿⣆⡼⢻⣧⠀⢸⣿⣀⡾⣿⣄⣠⠞⢸⣟⣀⠼
⠀⠀⠀⠀⠀⠹⣦⣄⣀⣠⣴⠿⠋⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢰⣶⢀⡸⣦⡀⠀⠀⠀⢀⣰⣫⡭⠿⠶⠶⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣁⠀⠠⣠⣶⣌⡛⠛⠛⢒⣛⢛⣿⡿⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⠸⠓⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⠶⢶⡄⢙⠁⠀⠀⠀⢠⡴⢦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠏⠀⢸⡇⣿⠀⠀⠀⣠⡟⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣠⡟⠀⢿⣄⣀⡴⢻⡇⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠉⠉⢸⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⢉⣄⣲⣦⣐⣄⣈⣣⣀⣦⣀⣆⣀⣆⣀⣀⣀⣀⣀⣀⣰⣃⣸⣇⣀⣠⣤⣀⣠⣦⣄⣀⣐⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣔⣋⣹⣯⠽⠋⠉⠿⠉⠏⠉⠏⠉⠉⠉⠉⠉⢹⡏⠉⢹⡏⠉⠛⠛⠉⠉⠛⠋⠉⠉⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀⢀⠀⠀⠘⠷⠞⠁⠀⠀⠀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⣿⣿⣯⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⣰⣾⣷⣿⣿⣿⣿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠛⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠰⣿⣿⣿⣿⡿⣿⣿⣷⣽⣿⠂⢾⣿⣿⣿⣿⠛⠛⠙⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣷⣟⣯⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⡽⠋⠀⢛⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣷⣿⢿⣷⣿⣯⡗⠀⣿⣿⣿⣿⢿⣿⣿⣿⣆⠀⠀⠈⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣯⡿⣿⣾⣿⡿⠀⢀⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⠛⣯⣿⣿⣿⣿⣿⣿⡗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠐⠿⠿⠿⠿⠇⠙⠿⠿⠿⠟⠀⠀⠀⠀⠀⠉⠙⠊⠛⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢛⣛⣩⣭⣤⣶⣶⣶⣶⣭⣭⣭⣟⡛⠷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣡⣾⣿⠿⠋⠁⢀⣀⣋⣉⣉⣛⣛⣻⣿⣿⣅⡀⢉⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣴⣿⣿⣿⣦⣶⣾⣿⠿⠿⠟⠛⣛⣋⣛⣿⣿⣿⣿⣿⣷⣦⣍⣙⡛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣼⣿⣿⣿⡿⠟⠢⢄⣀⣠⣤⣴⣶⣶⣶⠶⠾⠿⣿⣿⣿⣿⣿⣿⣍⠠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣴⢟⣡⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣩⣥⣤⡶⣂⡉⠀⠀⠀⠹⣿⣿⣿⣦⡹⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⠟⠁⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⠿⠷⠞⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣹⣿⣯⢠⣤⡿⠃
⠀⠀⠀⠀⠀⢰⡟⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣼⠇⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣼⡇
⠀⠀⠀⠀⣰⡏⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣿⣇⢸⡇
⠀⠀⠀⠀⣽⠗⢸⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠆⠹⣿⣿⢣⣼⡟
⠀⠀⠀⠀⢻⣆⢸⣿⣿⣿⠇⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣀⣠⣤⣤⣸⡿⠤⢍⠻⣆
⠀⠀⠀⠀⣾⡋⢸⣿⣿⣏⣈⣉⣉⣛⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⣿⣿⣿⣿⡿⣿⠣⠀⢀⢠⡿
⠀⠀⠀⠀⢸⡇⡄⠀⡿⣿⣿⣿⣿⣿⣿⠟⣛⣿⠷⢲⣤⣄⠀⣴⣾⣿⣿⡿⠁⣼⣿⣿⣿⣿⢣⣿⢀⣠⢣⡾⠃
⠀⠀⠀⠀⠸⣧⡳⣄⢤⣿⣿⣿⣿⣿⣵⣿⠟⢁⣴⣿⣿⣿⠟⠿⢿⣿⣿⠃⣼⣿⣿⣿⡿⣣⣿⣿⠚⢡⡿⠁
⠀⠀⠀⠀⠀⠈⢳⣎⢷⠹⣿⠟⣽⣿⠟⢁⣴⣿⣿⣿⣿⠇⠀⠀⠈⠻⢷⣴⣿⣿⣿⣿⠿⠛⠉⠘⣠⢻⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣜⠦⠙⡿⠿⠤⣶⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠃⠀⠀⠀⠀⢀⡴⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⢄⠀⠀⠀⠀⠀⠀⠌⠀⡆⠀⢀⡤⢂⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⢗⣩⣶⠦⣄⠀⠀⠀⠀⣁⠴⣩⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣵⣾⣿⣿⣿⠀⠈⠋⢽⡇⠀⢹⣶⣭⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⣿⣿⣿⠀⢴⣿⡟⠀⠀⣼⣿⣿⣿⣷⣌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣱⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠃⠀⠀⢈⠙⣿⣿⣿⣿⡎⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⢐⠢⢀⣠⣿⣿⣿⣿⣿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⣿⣿⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠰⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢮⣭⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣜⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣣⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣭⣭⣛⣛⣛⡟⠻⠿⠿⢿⣛⣛⣛⣭⣭⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⡠⡪⠐⣀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⣠⣾⢂⢎⡾⢋⠔⢊⡤⢐⡀⠄⠀⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢮⠐⢄⡢⢄⢄⡀
⠀⠀⠀⣀⣰⣿⢡⢎⣿⠕⣡⡾⠟⠋⠁⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠠⠀⠐⡄⠀⠱⡀⠳⡀⠱⡄⠙⢄⠑⣌⢢⡀
⠀⠀⣾⠛⣿⢏⠎⡾⢃⡴⠉⠀⠀⠀⠀⠀⠀⠀⣀⡸⠁⠀⠀⠀⢰⣥⡀⠀⠙⣆⠀⢱⠀⠱⡀⠘⢄⠈⢧⠈⣆⢣
⠀⢰⡗⣀⣿⢀⠜⢁⡾⠀⠀⣀⣸⣿⠀⠀⠀⠾⡷⠦⠀⠀⠀⠀⢁⣀⡀⠀⠀⠈⢷⡀⡇⠀⠱⡀⠈⠣⡈⠆⠸⢸
⠀⢨⡯⡿⠿⠈⠈⠡⠁⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⡿⡗⠄⠀⠘⠦⡀⠘⢠⠀⡆
⠀⠈⢧⡇⠘⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢸⠰⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡀⢰⠀⠈⠐⣤⡤⢴⠦⡄
⠀⠀⠀⠙⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⣈⣁⣠⡀⢠⠀⡇⠘⠀⣷⠀⠀⠀⠀⠀⠀⢹⣄⠈⠡⠃⠈⠒⠦⠐⠀⠀⡛⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣒⣴⠆⠈⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⡀⠀⠀⠄⣧⡆⢎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⡤⠒⠀⠀⠀⠀⡇⠀⣼⠃⠀⡜⢀⣿⡇⢸⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢡⢰⡿⢀⡜⢀⢎⣾⠁⡸⠀⠇
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢾⡵⠋⡠⢫⠎⠈⠀⠃⡘
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠜⠐⠁⠤⣀⠒⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠄⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠤⢤⠀⢠⠄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⡆⢠⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⢣⠐⠀⠂⡀⢠⠁⠀⠀⠀⠀⠃⢠⡆⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠉⢱⠁⠀⠀⠀⠀⠀⠂⠀⠃⠘⡇⠀⠀⠀⠠⠐
⠲⠰⠀⠀⠀⠀⠠⢬⣀⡀⢦⡀⠈⠀⠀⣆⣠⠀⠀⢀⠀⠀⠚⠀⠀⠠⠀⠄⠀⢱⣾⠴⢤⡏⠀⢠⠎
⠀⠀⡅⠀⠠⡁⠀⠀⢠⠀⠀⠙⢮⠀⠂⡩⢉⣀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠀⡀⠠⠀⣠⣄⣤⠔⠁⠀⠀⠀⠀⠄⠐⠦
⠀⠀⠀⠀⠀⠀⠂⢀⠐⠀⠀⢀⡂⠁⠀⠀⢀⡀⠩⠠⠀⠀⡛⠀⠀⢀⠤⠞⠑⠲⠶⢋⣉⠤⠐⠒⠒⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠀⠀⠀⡐⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⣄⡀⠀⠀⠀⢠⡧⠊⡁⢠⣤⡤⣤⣄⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣻⢯⡻⡾⢶⠀⣸⡁⠘⠁⢺⢿⣧⣧⣽⡂
⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⠀⢥⠁⢸⠀⠀⠀⠙⢾⣼⠁⡇⠀⠀⢸⣼⡇⣟⣉⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠈⠀⢸⡆⠀⠀⠀⢸⠿⣤⠇⠀⠀⢸⢸⣇⣧⣦⡅⠀⠀⠀⠠⣤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠸⠀⠀⠂⠀⢸⠀⢹⠆⠀⠀⠸⠜⠃⢧⠟⠇⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢀⡄⣶⢐⢙⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠐⠀⡀⠀⣀⠁⠂⢠⠐⠾⢿⠿⠾⡿⠦⣵⣏⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢠⠂⢀⡔⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡴⠁⢀⠎⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠁⢀⠎⠀⠀⠀⠐⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠎⠀⢀⠎⠀⠀⣠⠊⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡠⠃⠀⢀⡔⠁⠀⣠⠏⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⠞⠀⠀⢠⠊⠀⠀⢠⠋⠀⠀⠈⠉⠁⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠠⡶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠁⠀⢀⡴⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⢤⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠞⠀⠀⠒⠉⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠘⠡⠧⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠬⠶⣤⠤
⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⡀⠀⠛⢀⡔⣀⡀⠀⣀⣠⠾⠃
⠀⠀⠀⠀⢀⠹⡄⠀⠻⣦⠙⢦⠀⢸⡏⠁⢹⡆
⠀⠀⠠⡀⠀⠳⣄⠄⠀⠘⣧⠈⠳⣼⡧⠀⠀⠃
⠀⠀⢀⠑⠄⠀⠙⠶⣄⡀⠙⢦⡀⠘⣷⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢤
⠀⠀⠈⠀⠐⣄⠀⠀⠈⠻⣄⠀⠹⠀⠘⣧⠀⠀⠀⠉⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠳⡀⠈⢧⣄⡀⠀⠙⠆⠀⠁⠀⢸⠳⣄⠀⠀⠀⣷
⠀⠀⠀⠀⠙⢆⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠰⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠓⠆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⡌⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠙⠓⠤⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠙⠲⢤⣄⣀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⢰⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣀⣀⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⡏⢁⣈⣉⣀⣴⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⣿⣿⣿⣿⣿⠿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣿⣿⣿⡏⢉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⢿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠠⣄⢠⢠⠤⠄⡤⣤⢠⣠⢠⡤⡄⢤⠄⣤⢠⠤⣄⣤⡀⡄⠀⡄⡠⠤⢠⠤⣄⢠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠐⠋⠻⠙⠶⠂⠏⠣⠀⠇⠘⠋⠁⠸⠀⠛⠙⠶⠋⠊⠙⠇⠀⠇⠳⠴⠘⠦⠚⠸⠙⠇


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣠⡀⠉⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣾⠟⠛⢿⣶⣾⠛⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠻⣿⡀⠀⣠⣿⣿⣄⣀⣤⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠙⣿⣿⣿⡿⠟⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣴⣾⡿⠿⣿⡀⠀⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢀⣠⣾⣿⠟⠋⠀⠀⠙⢿⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣀⣴⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢾⣿⣿⠻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⣀⡀⠀⣀⠀⣀⠀⢀⠀⣀⡀⣠⡀⡄⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡄⠏⠹⠸⣭⠸⠏⢸⡞⢸⣧⡿⢸⠄⠇⢯⡼⠺⠏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡼⠃⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢉⡷⢤⠀⢀⣤⣄⠀⢸⡇⠀⠀⠀⢀⡼⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⠀⠘⢧⡼⠀⢸⡇⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣇⣠⣸⣇⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣹⠀⠀⠀⠀⠀⢀⡼⠞⠋⠉⠀⣀⣀⠀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⡴⠋⠀⠀⢀⣶⠟⠛⠙⠻⣶⡀⠀⠀⠙⢦⡀⣀⣀⣀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⡾⠁⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⢿⠉⠉⠙⠦⠞⠀⢀⡶⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⣠⣿⣤⣤⣤⣤⣤⣤⣿⣄⠀⠀⠀⠘⣧⠤⠤⠤⠤⠖⠛⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⠴⠶⠶⠶⢾⡄⠀⠀⠀⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠻⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⡿⠉⠀⢠⡤⣄⠀⠀⢳⡀⠀⠀⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠀⠀⢀⣾⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠦⠞⠉⠉⠉⠹⣄⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣠⠟⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣀⡀⠀⠀⢀⣀⣤⠴⡏⠁⠀⠀⠀⠀⠀⢸⡋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢹⡏⠉⢹⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢸⡇⠀⣼⢧⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡴⠋⠀⠀⠀⣸⣇⠈⠧⠴⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠃⠀⠀⠀⠸⣇⡼⠃⠀⠀⠀⠀⠧⢴⡋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠽⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠔⠉⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢳⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⣇⠀⠀⠀⢠⠇⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢀⡄⢀⠈⢦⠀⠀⢸⡀⠀⠀⠉⠀⢀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠉⠓⢌⣇⠀⢀⠷⠒⣒⣒⢲⣯⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠻⣈⣋⣀⣤⠞⠑⠚⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢵⠀⠀⠀⠚⠁⠠⡄⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⡸⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠱⠚⠒⡀⠀⠀⠀⠀⠀⢙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠢⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠑⠦⢄⣂⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡜⠉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⣰⠁⠀⣾⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⢀⢇⡴⠚⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⡦⢧⣀⠀⠀⠈⠀⠀⠀⢻⣀⡄⠀⡌⡞⠠⣾⠟⢶⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠬⣉⡒⠢⠾⡓⠲⡞⢇⢸⠈⠛⢹⡄⠀⠀⣎⣉⡉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡙⢷⣤⣸⡀⠟⠙⢾⣆⠀⡼⠙⠦⣀⣯⣀⡈⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠉⠳⣌⠓⢯⣑⢄⢩⢻⡷⠣⡀⠥⣼⣴⡒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠑⢦⡈⠙⠛⠁⢀⡔⢉⡶⢥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠙⠦⣤⣴⣉⠹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡛⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠒⠶⠤⢤⣀⣀⡀⠀⠀⠀⢠⣧⣀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡴⢋⠜⠉⡩⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣀⣤⣴⣫⡔⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣜⠁⠀⠀⠀⢀⠔⢁⣁⣰⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠥⠤⠼⠿⠂⠙⠛⠉⠉⠉⠉⠛⠒⠻⠥⠬⠉⡑⠆

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⣦⣄⣀⣀⡀⢸⡇⣇⠀⠀⣇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢻⣄⠰⠒⠒⢦
⢳⡀⠉⠁⠀⣿⠷⢹⡄⠀⢻⡄⠀⠀⠱⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢰⠉⠓⠦⡀
⠸⡇⠀⠀⠀⣿⢀⠀⢳⡄⠀⣿⠀⠀⠀⠋⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠏⠀⠀⣿⠀⠀⣠⠆
⠀⢙⠄⠀⢠⡟⠈⢧⠘⣧⠀⢹⡆⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣸⠀⠀⢹⠀⠀⣇⠀⣀⣀
⠀⠈⣆⠀⢸⡇⠀⠸⣇⠘⢧⡀⢻⣄⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⠀⠀⢸⠀⠀⠈⡆⢁⣍⡽⠋⠉⠁
⠀⠀⠹⣤⡼⠃⠀⠀⣿⠀⣼⠁⢸⡏⠀⢿⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡆⠀⠀⢇⣽⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠸⣇⠀⢸⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡇⡀⠘⠦⠀⠘⠄⠘⠆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠤⠿⠄⠀⢠⣇⠀⠀⠣⡀
⠀⠀⠀⠀⣀⣠⠴⣻⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠲⢸⠄
⠀⠀⠀⡖⠀⢀⣠⠏⠠⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠉⠑⠒⠦⣄⣀⣀⣤⡀⠄⢺
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠙⠛⠮⣟⠋⠛⠉⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⢤⠔⠉⠁⠀⠀⠀⠈⢧⡀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢀⠀⠀⣀⡠⠴⠽⣦⡀⢀⣀⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⣀⠠⠤⠤⢀⡀
⠀⠀⣠⡇⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⠩⠀⠒⠈⠉⠉⠲⠈⡆⠀⠀⠀⠀⠀⠠⢐⣀⢀⠀⠀⠀⣀⣀⡄⠄⠤⠀⠀⠐⠒⠀⠈⠉⢩⢃
⠀⠀⢀⠙⠢⣤⣄⠀⠀⠀⡀⠀⠀⡀⠀⡀⠷⡄⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⢸⠣⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠘
⠀⠀⠀⠀⠀⠈⠙⢿⣭⡙⠋⣩⠍⠋⠉⠀⠀⠇⠀⠀⠀⠀⠐⢉⣤⣬⡙⢦⢀⠠⠂⡨⠅⡀⠐⠁⠀⠀⠸⠀⠈⠒⢄⡀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠠⠐⠉⠉⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠙⢭⢨⣥⠐⠉⠀⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⣈⠓⠦⠤⠊⠓⠤⣀
⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠀⠀⠀⢠⡚⣐⡿⠶⠶⠾⠀⣧⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⡆⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠊⠘⠂⠠⠄⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠳⡜⠀⠀⠀⠀⡆⠂⠀⣠⣄⡀⠩⡭⠁⠀⠀⠀⠉⠠⠀⠀⣀⣀⡰⢠⡄⠁⠀⠀⠀⠀⠐⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠈⠉⠁⠀⠀⠀⢠⠀⠀⠘⣿⣾⠇⢐⣁⡆
⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣟⠽⡄⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⠛⠛⠛⠃⠴⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠀⠐⠟⠛⠛⠛⠛⠛⠛⣁⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣤⣤⣤⣤⣤⣤⣤⡾⠟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣷⠶⠞⣿⣻⡇⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡄⠠⠐⠘⢋⣉⡄⢤⠸⡆⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣻⣭⣴⣶⡿⣿⡉⢟⣫⣿⣴⡶⠾⢿⣛⣼⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠄⠒⠛⢉⢁⠀⠰⡤⠆⠣⠘⠁⣉⣠⠠⠗⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣟⣷⣿⣭⠶⠿⣟⣛⣩⣭⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠐⠈⠁⠐⣋⣁⠠⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣯⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣷⣶⣄⣀⣠⣴⣶⣾⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⡇⠀⠀⢸⣿⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠰⠿⠿⠿⠿⠛⠛⠛⢻⣿⡇⠀⠀⢸⣿⠋⠛⠛⠛⠛⠻⠿⠿⠿⠷⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣄⣀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣾⣿⡇⠀⠀⢸⣿⣶⣶⣶⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣿⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⠛⠉⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣶⣶⣶⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⢱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⢹⢸⣌⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢁⠀⢐⣒⠒⠒⠒⡶⢸⠀⣶⠰⣜⣀⣀⣀⠔⠉⠑⡀⠀⠰⠁⠀⠀⠑⠀⠀⢀⠚⠉⠉
⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠈⠂⠐⠀⠀⠀⠀⠀⠀⢸⠀⠇⢠⡿⠠⠌⠀⠑⠠⠐⠀⠀⠔⡡⠢⠔⠁⢀⡴⠂
⠀⠀⠀⠀⠀⡂⣀⠀⡑⠲⠦⠄⠭⠭⠭⠭⠥⠈⠉⠁⠹⢘⠀⡀⢸⠀⣡⣤⣤⣤⣤⣤⣔⠅⠈⠀⠀⣀⡼⠉
⠀⠀⠀⠀⠀⠑⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⠀⡇⠱⢠⣤⡤⡤⡤⠤⠄⠀⢀⠬⣊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠀⠀⠈⠉⠁⠤⠤⠄⠸⢐⠀⡿⠀⡇⢀⣳⣤⣤⣤⣄⣀⣀⠀⣀⣂⠁⡀⢘
⠀⠀⠀⠀⠀⠀⡠⡮⠊⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡇⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐
⠀⠀⠀⠠⠚⠀⠰⡀⠀⠀⠀⢎⠀⡀⠙⠒⠀⠀⠀⠒⠚⠀⡇⣿⠀⡧⠀⠸⢦⡴⠴⠶⠶⠤⠐⠂⢐⢄
⠀⠀⠀⠡⡀⠒⡠⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠺⠀⢸⠀⠋⢭⣀⣀⣀⣀⡔⠒⠢⠀⠑⠿⡦⣀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⡔⠀⠀⠂⣀⣀⣀⡀⠀⢀⣀⣀⣠⠀⡇⠰⠀⠀⠈⢛⠉⠉⠉⠉⠈⠐⠁⠖⠀⠀⠀⡌⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⡝⠒⣤⣤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠈⠢⠅⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⡤⠤⠤⢼⠀⡇⠈⠀⡟⡇⠀⣦⣁⡠⠤⢌⠺⢦⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢞⠁⡀⠂⠢⣀⣀⠀⠀⢠⠀⡇⢀⠀⣓⣇⠀⡯⠋⠑⠴⠄⠀⠀⡋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢂⠌⠈⢦⣀⠔⠉⠉⠉⠉⠉⠀⡇⠈⠀⡇⡇⠀⣧⡦⠤⠄⠄⠤⣠⡈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠃⠀⣀⣁⣁⡀⠋⠥⢀⠀⠀⠀⠈⠻⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡡⠀⠐⠉⠁⠀⠁⠈⠈⠉⠒⠢⣌⡐⠤⡀⠀⢠⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡠⠋⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠙⢢⡈⠢⡀⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡼⠁⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠔⠠⠊⠀⠱⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⠁⠀⡀⠔⠡⠂⠀⠀⠀⢀⠀⠀⠈⠀⠈⠐⠡⠀⠀⢡⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠔⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠢⢄⠀⠀⠀⠀⠀⠀⡌⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢧⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡐⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠢⡀⠀⠀⠀⠘⣄⠀⠀⠀⢀⣰⠂⠀⠀⢀⠴⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⣀⡀⠈⠛⠓⠋⠋⢁⣀⠤⠖⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠭⠉⣉⣁⣀⣈⡉⠤⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠄⠀⠄⢀⠠⠀⡀⠀⢀⠠⢀⠠⠀⢀⠠⠀⠠⠀⡀⠀⢂⠠⢀⠀⠐⡀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠀⠈⠀⠈⠁⠀⠈⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⢸⠿⠻⠛⠿⠄⠀⢀⡀⢀⡼⠈⣥⣠⢄⣦⣴⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⡞⡿⢪⡅⢻⡻⡋⡉⣿⢭⢻⣄⣾⣶⠂⢂⠀⠀⠀⠀⠀⠀⠚⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⡀⣠⢖⣿⢉⡄⠉⣀⣤⣴⣶⣶⣾⣷⣬⣾⡗⢿⡿⡽⢦⣞⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣩⢱⠞⢋⣷⣿⣻⡿⣛⢿⠉⣿⢻⡙⠿⢿⣿⣤⡲⡯⠝⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⡿⠟⢇⣾⣿⠋⢭⡔⢡⣤⡟⡷⢲⠏⢲⡆⠻⣿⣿⡄⢠⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣭⣥⣶⣃⣼⣷⠿⡴⠬⣱⠆⠿⠓⠗⢛⠞⠑⠞⠓⢿⣿⣧⢤⡴⠷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣯⡯⠃⣿⣿⣤⣦⣼⣥⣴⣤⣴⣤⣦⣤⣦⣤⣧⣼⣿⣷⠀⠒⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡌⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⡟⣿⣿⣽⡇⣿⢻⣿⠏⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⠹⣿⣻⡇⣿⠏⣿⣸⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⡅⣿⢸⡇⣿⡐⣿⠻⣿⢿⣿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢺⡿⣿⣿⣿⣿⣧⣿⢸⡄⣻⢂⣿⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠦⠀⠀⢸⣿⣿⣷⣿⣿⣏⣿⡜⣷⣸⣿⣿⡯⢿⣿⣿⣿⣿⠂⠀⠀⠀⠂⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠛⠋⠉⠉⠉⠙⠋⠉⠉⠉⠛⠛⠋⠋⠉⠛⠉⠛⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡶⠀⢠⠀⣶⡆⠀⡖⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡏⠀⣿⠀⣿⠁⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⢠⢸⡇⣇⡀⢻⡀⢹⢠⡀⣇⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⢉⠀⡈⠁⠈⡀⠀⢉⠀⢈⠀⡀⠀⠀⠸⢷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢹⠈⡿⠃⢸⠇⡇⢽⠄⢸⠀⡇⠀⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣄⠀⢽⠀⡿⠀⢸⠀⡇⢰⠀⢻⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠂⠸⠀⠓⠐⠘⠂⠁⠺⠒⠸⠈⠃

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣾⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡀⠀⠀⠸⣿⣤⣿⠇⢸⣿⠿⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠛⠿⠀⠀⠀⠈⠉⠁⠀⢸⣿⣦⡄⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⣿⡇⠀⢀⠀⣴⡿⣷⡄⠙⠋⠀⠀⣀⣴⣶⣤⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⣿⡇⠀⣿⣇⣿⡇⠿⠃⣀⠀⢠⣾⠟⢉⣤⣿⠃⠀⠀⠀⠀⢸⣿⠛⠛⠻⠷⠀⣼⡇
⠀⠀⠀⠀⣿⡇⠀⠘⠛⠋⣠⣴⡿⠿⣷⡈⠻⠿⠟⢋⣤⣾⣷⡄⠀⠀⢸⣿⠿⢷⣶⠄⢠⣿⠁
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣿⠙⠟⠀⠙⠁⠀⠠⣾⠟⢻⣧⣾⠏⠀⠀⢸⣿⣶⣤⣄⠀⣼⡏
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⠃⢀⣴⣾⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠁⢠⣿⠃
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣏⣄⠐⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣄⣼⡟
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢉⣠⣶⣿⢻⣷⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠛⠿⣷
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣽⡿⠿⠋⣠⣄⠀⠀⠀⠀⢸⣿⠀⣾⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣴⣿⡟⢻⣦⠀⠀⠀⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠙⠃⠀⠉⣤⡀⠀⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⣽⣿⣄⠀⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠈⠋⠀⠀⠀⢿⡇⠀⣿
⠀⠀⠀⠀⣻⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣾⠟⠿⣷⡀⠀⠀⠀⣿⠀⠀⠀⢀⣶⠿⠻⣷⡄⠀⢸⣿⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⡏⠀⠀⢹⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⢹⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢹⣷⡀⢀⣿⠇⠀⠀⠀⣿⠀⠀⠀⠸⣿⣀⢀⣼⡟⠀⠘⣿⣄⣀⣀⣀⣀⣀⣀⣈⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠛⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⡿⠿⣶⡀⠀⠀⢀⣶⠿⢿⣦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣴⡾⠟⠋⠉⢀⣀⣀⠈⠉⠛⢿⣦⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⢹⣷⠀⠀⣾⡏⠀⠀⢻⡇⠀⠀⠀⠀⠀⣿
⠀⣰⣿⠋⠀⠀⠀⣼⡟⠛⠻⣷⡄⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⡀⢀⣼⡟⠀⠀⢹⣷⡀⢀⣾⡇⠀⠀⠀⠀⠀⣿
⢰⣿⠁⠀⠀⠀⠀⢿⣧⣀⣠⣿⠇⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⢀⣾⠟⠻⣷⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⣟⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣄⣀⣾⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⣿⡿⣶⣶⣶⣶⣶⠾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠛⣿⡟⠛⠛⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣼⡿⠂⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣷⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠂⠀⠀⠀⠀⠂⠐⠀⠀⠀⠂⠂⠀⠀⠀⠀⠃⠐⠸⠀⠀⠀⠀⠀⠐

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣠⣀⣀⡀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣤⣄⣠⣄⣤⡀⣠⣄⣀⣀⣀⣀⣀⡀⣀⣀⣄⣀⣀⣄
⠀⣽⠏⠁⠼⠂⢹⣿⣿⠀⠘⠀⠀⢠⡐⢠⡤⠄⠀⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢠⣷⠀⠀⣿⣿⡀⠀⠀⠘⣿⠀⠀⣽⠟⠛⣿⣿⣿⡤⣈⣹⣿⣿⣿⣿
⠀⢸⠔⠂⠀⠀⠘⠛⠋⡈⠀⠀⠀⠀⠋⠈⠀⠀⠃⠀⠂⠀⠀⠀⠀⢰⡏⠀⣀⠀⣀⣨⣄⠀⠀⠂⠀⢿⣿⡟⠐⠚⠀⣿⠀⠀⠉⠀⠀⣿⣿⣿⡿⢿⡏⠉⠉⠙⣿
⠀⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⠓⠻⢿⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢸⣿⣿⣃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣯⡄⠉⠙⣦
⠀⢸⠀⠀⠀⠀⠀⠀⢸⠋⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣄⣿⡚⣿⣇⢸⣷⡰⠇
⠀⢸⠀⠀⠀⠀⠀⠀⠊⠁⣽⣤⣉⠐⠀⠠⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⠀⠀⢂⣻⠁⣿⣿⣿⣿⣷⣦⣶⣤⣴⣶
⠀⢸⣠⠄⠀⠀⠀⠀⢠⠀⠰⠿⠾⠃⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠑⠀⠀⢸⣧⡀⠀⠀⠀⠈⠁⢀⣿⣏⣿⡠⢿⣿⣿⣿⣿⣿
⠀⢸⠁⠀⠘⠂⠀⠀⠈⣠⣞⠂⠀⠀⠀⠀⠀⠀⢘⠄⠀⣤⡜⠃⠉⠀⣄⢠⣤⡾⠟⠛⠳⠻⣆⠀⠠⡇⢀⠀⣰⡍⠳⣶⠀⢀⠐⠀⠉⣻⣿⡃⣀⢸⡟⣿⡖⠻⣿
⠀⢸⡄⠀⠀⠁⠠⡄⠀⠀⠙⠁⠐⢦⠀⠀⠀⠀⠈⠀⣸⣿⠗⠀⠤⠐⣤⣎⠉⠓⠲⢦⢀⣠⣬⣦⠀⡇⠈⠀⣿⡇⠀⢿⠀⠈⡀⠀⠀⣿⣿⠁⣿⣷⣏⠛⡉⠙⣦
⠀⣾⣿⡂⢀⠀⠘⠃⠀⣿⣰⠞⣀⡠⠀⠀⠀⠀⠀⣰⣿⡟⠶⠐⠶⠄⣿⢋⡂⠀⡆⠀⠈⠀⢺⣯⡀⡇⠀⠀⢹⡿⣤⣼⣴⣿⠑⠂⠀⣿⠉⠀⣹⣧⣹⣼⣿⣷⣦
⠀⣹⠋⠉⠉⠀⢰⡇⠀⣮⡥⠀⢟⠳⠀⠀⠀⠀⣸⣿⢸⣷⡾⠆⠀⢸⣿⣆⠁⡤⠱⣦⣶⠀⠌⢉⡥⣿⠟⠃⠙⠛⠟⢻⠛⠿⣴⠆⠀⢿⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⠀⠀⢸⡇⠀⣤⠀⢲⣌⡴⢀⣠⣴⣾⣟⣿⣾⡟⠓⠂⠀⢿⣿⣏⣠⣦⠼⣟⣿⣀⣼⡿⢹⡷⠀⠀⠀⠀⠀⠛⠳⣀⣿⣄⡀⠘⢇⠛⠻⣉⣰⣿⣿⣿⣿
⠀⢻⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⢋⣿⣫⠟⠛⢋⣠⡼⠷⠶⣶⢎⣽⣿⣿⣿⣿⣿⣿⡟⠛⢋⠤⠼⠃⠀⡀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣦⠌⠀⠰⣿⣿⣿⣿⣭⣿
⠀⢸⠀⠀⠀⠀⢸⡁⢀⡹⠿⠛⠋⣼⣿⣯⡴⠊⢁⣀⠀⠶⢞⣛⣻⣿⣿⣿⣿⣿⣿⢿⣯⣤⣤⣴⠗⠀⠀⠈⠲⣀⠀⠀⣠⠶⡄⠀⠑⢤⠀⠒⠚⢶⣿⣿⣿⣽⣿
⠀⢸⣦⡀⠔⠀⢸⣿⠟⠓⠖⢨⣾⣿⣯⣥⣶⠾⠿⣿⡿⠉⠉⠻⠿⠻⣿⣿⣿⠿⢿⣮⢹⣿⣿⣯⣆⠈⠲⡄⠀⠈⠠⠐⠟⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⢻⣟⠛⣿
⠀⢸⡧⠀⣀⣶⠸⠁⠀⠈⣰⢿⣿⣛⡿⢿⣿⠀⢰⡿⢁⣶⣤⡀⠀⠒⠛⢿⠿⠶⢆⠙⢾⣧⡀⠀⠛⠣⢀⠈⠁⠀⡀⠐⠐⠀⠂⠀⡀⠀⠙⠉⠉⠉⣿⡿⠛⢳⣏
⠀⢸⣿⡛⢋⣑⠚⠂⠀⢠⡿⢸⣿⡏⠑⠃⠻⣿⣿⡷⠛⣹⣿⣿⣿⣦⣤⣀⠀⠀⠈⠁⠈⣿⣧⡶⣠⡀⠈⢳⣄⠀⡀⠀⠠⣤⡿⠟⠀⠀⠐⣤⣤⣶⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣦⡆⢀⣿⠇⢸⣿⣷⡄⠀⠀⠀⠉⣱⠆⠙⠿⠛⠿⣿⣿⠿⣿⡶⣶⣤⣼⣿⣿⡐⠟⣷⣴⣾⠿⢷⣦⣰⣤⣠⡴⠛⠀⠀⠐⠛⠩⠌⠙⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡏⠀⠇⣼⡿⠀⢸⢿⣯⣼⣿⣿⣦⣤⣀⣤⣀⣶⣦⣤⠸⣿⠃⠹⣷⣿⣿⣿⣿⣹⠇⠀⣿⠛⣧⡀⠀⠻⣿⣁⣤⣤⠿⠠⠀⠀⠀⠰⣤⣼⣿⣯⣏⣿
⠀⢸⣿⣿⣿⣇⡀⢾⣿⣷⠀⠈⣸⣿⣿⠿⡿⢆⣉⡙⠻⠿⡿⠋⠉⡀⣛⢀⠀⠉⢿⣿⣿⣷⡿⠀⠀⠉⢠⣿⣿⣶⣤⣌⠁⢠⡉⠢⣀⠀⠀⢉⢲⣶⡾⣿⣿⣿⣿
⠀⢸⣾⣿⣿⡿⢿⣿⣿⡇⠀⠀⣧⡌⠀⠐⠀⠀⣿⠋⢸⠾⠋⢈⣉⡑⣿⣿⠀⢠⣾⣿⣿⣿⠃⠀⠀⠀⢸⡟⠁⠀⣠⡏⠹⠆⠹⠆⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣷⣶⣦⡇⠸⣿⣿⡇⠀⠀⣿⣷⣦⡀⠀⢠⣿⠀⠀⠀⠀⠈⠁⠁⢿⣯⠀⢺⣿⣿⣭⣤⣤⡤⣤⡀⢸⣿⠛⠙⢨⡗⠀⠀⠀⠐⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡇⢸⣿⣿⡟⠀⢰⣿⣿⣿⣿⡗⣿⣷⣶⠿⠃⠉⠀⠀⠘⣾⡟⠀⢹⣿⣿⣿⣿⡿⢣⣼⡈⠻⢿⣷⡄⢸⡟⠀⠀⠀⠀⠙⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡁⣿⣿⣿⣿⠀⢸⣿⣿⣿⠹⡇⣿⡏⢹⠂⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣻⡇⢸⡇⠀⠀⠀⠀⠀⠁⢠⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢨⣿⣿⠿⡇⠘⢻⣿⣿⡆⠸⣿⣿⣿⡇⠀⣿⠇⡾⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣿⡇⢸⡇⠀⠀⡜⠃⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⡟⣀⡇⠀⠀⢻⢿⣇⢀⣿⣿⣿⣿⣿⣿⣶⣶⣶⠛⠛⠛⠛⣲⣾⣿⠀⡿⣿⣿⣿⣿⣷⡈⠳⠁⠘⠏⠛⠀⠘⠋⠀⠀⠁⠀⠀⠀⡆⠀⢸⣿⠿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠇⠀⠀⣾⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣾⠇⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠿⠿⠾⠟⠋⣿
⠀⠀⣿⣿⣿⣧⣠⢷⡀⠉⠛⠟⠁⠀⠻⣿⣿⣿⣿⣿⣧⠀⠀⢠⡟⢻⣿⠉⢻⡀⠘⣿⣿⣿⣟⣿⣿⣦⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣡⡄⣷⣿
⠀⠀⣿⣿⣿⣿⢿⣿⡷⠀⠀⠠⣢⡄⠤⣀⠠⠹⣿⣿⣿⣦⡀⠘⡇⢸⡏⠀⡼⠃⠀⠻⣿⣿⣿⣿⣽⣿⣷⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿
⠀⠀⣿⣿⣿⣿⣾⣿⣤⣿⠶⠿⠛⠛⠒⠋⠀⠀⢹⣿⡿⣿⣧⠀⠈⣾⣿⢤⣀⠀⠀⠀⢻⣿⣿⣇⣨⠛⢿⣿⢦⡐⠀⠀⠈⡀⠀⠀⠼⠂⠀⠀⢱⠀⠠⡏⠽⠟⣿
⠀⠀⣿⣿⣿⣿⣿⡿⣿⣷⣶⠖⠀⠀⠀⠀⠀⠀⠚⣿⣷⣿⣿⠀⠀⢸⣧⠈⣉⣽⣟⠳⠌⢻⣿⢻⣯⢰⣿⠁⠀⠉⠀⣤⣄⠙⠂⠀⠀⠀⠀⠀⠘⣧⠀⢹⡄⠤⠻
⠀⠀⣿⣿⣿⣿⣛⠻⠿⠛⠁⢠⠄⢘⣀⠀⠰⠦⠀⣿⡏⢹⣿⡆⠀⠈⣿⣿⣿⣧⠿⠶⠀⢸⣿⣿⣿⢾⣿⠀⢰⠀⠀⢸⣿⣿⣦⣄⠃⠄⠀⠀⠀⡿⠀⠘⣀
⠀⠀⣿⠙⠛⡛⠡⠤⡤⢀⣠⣶⡤⠀⣁⣤⠄⠄⠀⢾⣷⠈⣿⡇⠀⢸⣿⠻⠛⣋⣰⣦⣾⣿⣿⣸⣿⣿⡏⠀⠸⡆⠀⠀⠋⠹⣿⣿⣷⠀⣀⠀⠀⠟⢸⣆⠈⣆
⠀⠀⣷⣼⡛⠿⠀⠀⠀⠈⠉⠃⣤⣾⠛⢻⠱⠶⠀⠀⣿⡀⢹⡇⠀⢸⣿⣿⣿⣯⣥⣽⣿⣷⣶⣿⣿⣿⣷⣾⣿⡷⠶⠶⡟⠚⣻⣿⣿⡀⠹⠃⠀⢀⡈⢿⣧⡈⠳
⠀⠀⣿⠽⢿⣿⣦⣴⣶⠖⠛⠻⠿⢏⣵⣿⣷⣶⣆⣴⣿⣧⣾⣇⠀⠚⣿⢿⠟⢛⣿⣿⢿⣿⣯⡿⣿⣿⣿⡟⢿⣧⣾⡾⠻⢿⣿⣿⣿⣇⠀⠛⠀⠀⢷⡀⠻⣷⣤
⠀⠀⣷⠀⠀⠿⠟⠁⠀⢠⣶⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣟⠐⣛⣿⡿⣿⣿⣷⣶⣾⣿⣶⣿⣿⡿⠟⣀⣈⣥⣾⣶⣿⣶⠟⢻⣿⣿⣧⡀⠀⣦⡌⠻⣆⢉⣻
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣛⠉⣉⣬⣿⣿⡯⠤⢯⠀⠀⠀⠀⠀⣉⣽⣿⣛⣉⣁⣀⣠⣭⣩⠆⠈⠙⠛⠐⠒⠋⠀⠈⠉⠙⠛⠓⠤⠤⠤⠭⠿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠦⠤⠚⠀⣀⡤⠖⠀⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣿⠂⠀⠀⠀⠀⠠⠤⠤⢤⣤⣶⡶⣀⡀⠀⠀⠠⠤⢶⠦⢤⣤⡴⠾⠥⠠⠤⠤⠤⠄⠤⠀⣠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣄⠀⣀⣰⡄⠀⠀⣠⣤⣴
⠀⠀⣿⠠⣄⡀⠀⣀⣤⣤⣼⡿⢉⠉⠁⠈⠀⠀⠀⠀⢀⡴⠶⠎⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠉⠁⣀⣀⣀⣀⡀⠀⠀⠰⠌⠙
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠻⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⢻⡀⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⣦⣄⣀⣀⡀⢸⡇⣇⠀⠀⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣧⡀⠶⠒⠲⡄
⢻⡀⠉⠁⠀⣿⣷⢹⡄⠀⢻⡄⠀⠀⠳⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡎⠙⠒⢦
⠘⡇⠀⠀⠀⣿⢀⠀⢻⡆⠈⣿⠀⠀⠀⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⡇⠀⠀⡇⠀⢀⡼
⠀⠙⠄⠀⢠⡏⠈⣧⠘⣧⠀⢹⡆⠀⠀⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⡷⠀⢸⡄⢀⣀⡀
⠀⠀⣇⠀⢸⡇⠀⠸⣇⠘⣧⡀⢻⡄⠀⣿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡇⠀⠀⠇⠀⠀⢙⠊⣨⣭⠏⠉⠉
⠀⠀⠹⣦⡼⠃⠀⠀⣿⠀⣾⠁⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀⠀⢸⠀⠀⠸⣨⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠀⠸⣇⠀⣿⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⢸⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠘⠢⠀⠸⠀⠘⠄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠜⠧⠀⠠⢼⣀⠀⠘⡄⡀
⠀⠀⠀⠀⢀⣠⠾⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠇⡷
⠀⠀⠀⡾⠀⠀⡠⠃⠢⡄⠀⣅⠀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠉⠙⠲⠦⣤⣀⣤⣤⠤⠀⡇
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠛⠾⣝⠉⠉⠉⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡤⡤⠊⠁⠀⠀⠀⠀⠹⣆⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠦⣤⣤⣤⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠐⠾⠛⠠⣴⣶⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⢀⡀⠀⠀⠀⠀⠲⠶⠄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠸⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠻⠀⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⠀⠀⠀⢾⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡃⠀⠀⢀⡈⠀⠀⠻⣄⠀⠀⠂⠤⠀⣀⣀⣀⣀⠀⠠⠤⠘⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⣤⡜⠃⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⡠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⣤⣤⣄⣀⣠⣄⠰⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⠤⠤⠤⠶⠄⠛⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠑⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠆⠀⠀⠀⠀⡆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠉⠉⠲⠶⠆⣀⣠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠁⠀⠀⠀⠀⠀⠁⢸⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⠔⠃⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡧⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⡀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠸⡇⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢛⡀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠘⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⡆⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⢻⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⢣
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠼
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⢠⣧⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣌⠉⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⠙
⣉⣤⣤⣤⣤⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⢀⠤⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⣀⣁⣀⣤⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⣶⣿⡿⠛⠁⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡴⠶⠶⢶⣤⡄⠀⠀⠀⠀⠀⣠⣴⠶⠾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠫⠘⠿⠃⠴⠀⠆⠀⠀⠰⠆⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠖⢄⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠞⠀⠀⠀⠀⢠⠀⠀⠠⠀⠄⠀⠘⢆⠀⠈⢂⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠀⠀⠀⠠⡤⠀⠁⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⡾⠀⠤⠀⣾⣿⣿⣿⣿⣿⡦⠄⠘⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠈⠻⠶⠶⠾⠋⠁⠀⠀⠘⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠃⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣄⠀⠀⠀⣀⡀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠀⢸⡟⢻⣿⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠿⠇⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠸⠿⠿⠟⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⣴⣾⡆⠀⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣧⡀⠀⠀⠀⠀⠀⣭⣿⣧⡀⣿⣧⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢀⣤⣤⣄⠀⠈⣩⡉⠀⢀⣤⣤⡀⠀⠉⠉⠉⠀⢈⣭⣭⡁⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣿⡇⠀⠀⢸⣿⢹⣿⠀⠻⣿⡇⠀⢺⣟⢻⣿⠀⠀⠀⠀⠀⣿⡟⣻⣿⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠉⠀⠀⠀⠘⠿⠿⠟⠀⠺⠿⠿⠂⠘⠿⠿⠟⠀⠀⠀⠀⠀⠻⠿⠿⠏⠀⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⢷⣦⣄⠀⠀⠀⠀⢰⣾⢿⣷⠀⠀⠀⠀⠀⢰⣿⢿⣦⠀⣴⣾⡆⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⢸⣿⣼⣿⠀⠀⠀⠀⠀⢸⣷⣼⣿⠀⣬⣿⣧⠀⠀⠀⠀⠀⠀⣽⣿⣤
⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⢰⣿
⠀⠀⠀⣾⡟⠀⠀⠀⠀⣴⣾⠟⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠘⠿
⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⣶
⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣄⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠙⠿⣷⣶⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⡿⠛⠛⠛⠛⠛⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠂⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣤⣤⣀⣠⣤⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⣰⣿⣿⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣷⣄⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠻⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⠟⢁⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡶⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢪⠊⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⡄⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⣒⡒⢴⡉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠭⢤⡴⠊⠀⠁⠀⢀⡀⠀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⣙⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠑⠢⢄⣸⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠔⡆⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣀⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠒⠾⡐⢞⣃⢀⠀⠁⡀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⣙⠶⣷⣌⠈⣿⣄⣌⠀⠂⡔⣂⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠑⢌⠑⠦⠶⠋⣈⠂⣽⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⠤⣠⣄⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠉⠒⢲⠄⡤⠤⡤⠞⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣀⣀⣔⡡⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣎⡀⠀⢀⣠⡋⣁⣔⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠛⠈⠉⠉⠀⠀⠉⠀⠙⠒⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⠀⣿⣿⡿⠿⠿⣿⠿⢿⣿⣿⠿⠿⣿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⡇⠺⠂⣀⠐⢿⣿⣇⠺⠂⣀⠐⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⢡⣤⡉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⣛⡛⢿⠀⣿⣿⠀⣾⣿⡇⢰⣿⡆⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⣿⣿⣄⣿⣿⣧⣾⣿⠃⣼⣿⠂⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠂⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠑⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡶⠛⠛⢦⡀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢹⡆⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣨⣧⣤⣤⣤⣼⣇⠀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⣿⣿⣿⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣸⣿⣿⡇⠀⠀⠀⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢸⣿⣿⣿⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠐⠀⠂


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠶⠦⠤⣄⣲⣦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠽⠿⠒⠒⠀⠉⠃⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⠛⢻⡖⠒⠦⢀⠀⠀⠙⣛⠓⢢⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡎⠀⢠⡄⠉⣏⠙⠃⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠀⣀⣐⠀⠀⢸⠀⠀⡸⢡⠖⠠⠏⠑⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⠿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⢩⡯⠀⠈⢳⡀⡌⠀⢰⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠤⢺⠀⠀⠀⠀⢿⠁⠀⣾⣻⠁⠀⠀⠀⢀⡴⠒⠒⠢⢄⠀⠀⣀⣀⢈⡀⡰⠛⢦⡀⠀⠘⢒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢸⠀⢠⣟⡧⠔⡒⢢⡀⠈⠦⣀⣀⣠⡼⠓⠉⠀⢀⡴⠋⠀⢀⠞⠉⠁⠀⠙⠻⣍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⢁⠣⣀⡀⣠⠎⠀⠘⠋⠔⠋⢁⠼⠓⠒⠠⠤⠴⡏⠀⢀⣠⠔⠋⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠘⡄
⠀⣀⠠⠤⠐⠒⠒⠉⠉⠁⠀⠀⢀⠼⡇⠀⠈⠉⠀⠀⠀⢀⡖⠒⠛⠓⠦⠤⠤⠤⠤⡄⠉⠉⠉⠀⠀⠀⠀⠷⢖⣒⠶⢄⠀⠀⠀⠀⢀⠇
⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⢸⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠬⡭⣭⠵⠋⠀⠀⠀⠀⡜
⠑⠤⣀⣀⣀⣀⠤⠔⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢠⣄⣨⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡷⢌⠳⡸⡄⠀⠀⠀⠀⢸⡀⠀⠀⢠⡞⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⢄⠱⠁⠱⣦⣤⡀⠀⠨⡍⠓⠊⠽⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⢡⣏⣶⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⢄⠀⠀⠀⢸⠤⢒⡒⢲⡄⠀⠀⠀⠀⠀⠀⢸⠀⡤⠘⠳⡉⠀⠘⡖⢹⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠲⣾⠀⠀⠀⢸⡠⠞⣡⠋⠀⠀⠀⠀⠀⠀⠀⡜⢸⠃⠀⢀⡼⢆⢀⡵⠋⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡇⠀⠀⠀⢀⣠⠔⠋⠀⣀⠝⠀⠀⠀⠀⠀⠀⠀⢠⠃⡏⠀⠀⢺⡴⣴⠻⣄⣠⠏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⢶⣧⡤⣖⠊⠉⠀⠀⡠⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⡎⣸⡡⠔⠊⢁⠂⢀⠀⠈⠁⠀⠈⢲⣌⠳⣄⠀⠀⠀⢠⠶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣠⡋⠀⠸⡆⢀⠔⠉⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢸⠋⣋⠤⠀⠀⠉⣆⠘⠆⠀⠀⠀⠀⠈⢏⠳⣌⠳⣄⠀⢸⠀⠇⡎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠚⠙⠁⠀⠀⠙⠁⠀⡟⠀⠀⠇⠛⡒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⡄⠈⠳⣌⡧⣼⢰⠞⣰⣃⠔
⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⣤⠼⠈⠈⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢘⡇⣁⠀⢀⣨⠴⠊
⠀⠀⠀⠀⠀⠀⠙⡶⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⣯⠤⠖⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠲⠶⠶⢶⣶⣶⡾⢡⣖⣩⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢯⠙⡟⠓⠒⠒⠛⢋⡉⣹⢠⡇⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈⠉⠁⡀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⣧⣸⡀⠀⠀⠀⠀⣀⠤⠊⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠑⣶⣖⠒⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣸⣀⣀⠈⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⣀⣈⣎⢆⠘⣌⢆
⠀⠀⠀⠀⠮⣅⣀⠤⠽⠓⠋⠉⠉⠙⠒⠢⠶⠶⠶⣦⣒⣶⠞⠓⠒⠲⢄⠀⠀⠀⠀⠈⠂⣤⠒⠒⠒⠛⠛⠛⠺⣗⣚⡈⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⢀⣶⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⢿⣟⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠹⣆⠀⠀⠀⢈⡿⠿⠃⠀⣀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⢸⣿⣿⠇⣰⣶⣶⣄⠹⣆⠀⢠⡿⢁⣶⣦⠰⣿⣿⡗⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣉⣁⣴⣿⣿⣿⣿⠂⣽⣶⣿⠀⣿⣿⣿⣦⣌⣩⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡂⣠⣀⡀⢀⢀⣀⣀⣀⡤⣀⣠⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠁⠉⠑⠈⠀⠃⠛⠋⠁⠉⠑⠁⠁⠁

⣏⣈⣯⣭⣟⣯⣿⣹⣽⣽⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠒⠈⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠒⢄⠀⠀⠀⠀⠀⢠⠊⠀⠀⢀⠀⠀⢠⡀⠀⣠⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣦⣵⡀⠀⠀⢀⠂⠀⠀⠀⠈⠳⠰⠀⠉⠲⠃⠃⠀⠀⠀⢠⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠦⢂⡔⠁⠀⠻⣇⠀⠀⢸⠀⠀⠀⠀⠐⠛⢂⣀⠀⠀⣀⡘⠆⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⢻⡇⠀⠏⢀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢀⠘⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡆⠀⠀⠅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠘⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠇⡤⠂⠁⠀⢸⠀⠀⠷⢤⡀⠀⢠⡙⠀⠀⠀⠀⢀⠠⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⢀⡀⠔⠁⡌⠀⠀⠀⠀⠀⡄⠀⠀⠀⢉⠁⠀⠰⠤⠤⠀⠂⠁⠀⡇
⠀⠀⠀⠀⠀⠄⠀⡄⢀⡠⢄⠀⣀⠹⡍⠉⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠦⠊⠀⣠⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⠰⢿⡉⡓⠾⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⢀⠁⠀⢀⠻⡆⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢣⠀⠀⠉⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⢠⢀⡠⠂⠀⠀⠘⠀⢀⠘⠄⢹⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⡤⢤⢷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢠⠀⡘⠀⠀⠀⠀⡈⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢰⠀⣦
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⢀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠂⠀⠉⠉⡇
⠀⠉⠲⠀⠠⠤⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⡼⠦⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠌⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤
⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣈⣀⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿