Calligraph Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠰⢁⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡏⠀⠀⠀⡐⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡶⠀⣿⠃⠀⢀⠊⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⣿⠀⠐⡁⢀⣿⠀⢀⡴⠄⠀⠀⠀⡄⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠀⠸⣿⠀⢠⡞⢸⡇⢠⡿⠁⠀⠀⠀⣼⡇⠠⠀⢸⡄⢿⡄
⢀⡴⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣿⡀⣸⡇⣾⡇⣼⡇⠀⢀⠀⠀⠻⡀⡅⠀⢸⠇⢸⡇⠀⠀⠀⠀⣀⠄
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠋⠣⣿⡇⠸⣇⠀⠌⠀⠀⠀⠀⠡⠀⠀⢀⠜⠁⠀⢀⣴⠊⠁
⡇⠀⠀⠀⢀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠠
⢃⠀⠀⣰⠏⠀⠸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⣗⢀⠀⠀⠀⠀⣰⡶⠀⠀⠀⠀⠀⠀⣰⡟
⠈⢂⢀⡿⠀⠀⡀⠀⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⢹⡇⠀⡐⠀⠘⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡀⢸⡇⡐⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⡟⠸⠁⠀⠀⠀⠀⢸⡇
⠀⠅⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⣸⡇⠀⣸⠄⢸⡇⠀⣴⠃⣰⠆⠀⣿⠀⠀⠀⠀⠀⠰⣏⢲⡄
⠀⠀⢸⣇⠀⢤⡀⣴⠋⢰⡏⢱⡟⢠⡟⢰⡟⠀⣿⠃⢠⣿⠀⣿⡇⢸⡟⢀⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⣿⠀⣸⡏⣿⢀⢿⣁⠺⣇⠜⢇⠸⡇⠐⣿⠀⠸⢧⠀⣿⡇⠈⠣⠀⠻⡰⠁⣿⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠡⠞⠁⠈⠁⠀⠁⠀⠈⠀⠀⠀⠈⠁⠹⣇⠆⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡼⠁⠂⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⢇⡀⢀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⢸⡇⠀⠀⢀⠀⠀⢀⣶⠀⣀⠀⢀⠔⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣧⠀⢹⡇⠀⣼⠃⣵⡆⢸⡇⠀⣿⡄⠁⠀⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⢸⡇⢠⣿⢀⣿⠀⠜⢧⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡿⠀⠀⠳⠂⠙⠃⠘⠞⠀⠀⠠⢻⡇⠀⠀⡠⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⠠⠄⠀⠀⠀⠀⠠⠀⣾⡆⠀⢀⡂⣼⠃⢀⠌⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠡⠞⡉⠀⢀⠀⢰⡆⠀⢠⡅⢠⣿⠀⢀⡂⠙⠁⢀⢋⡤⢠
⠀⠀⠀⠀⠀⠀⠀⣿⢇⣀⡀⢅⡄⠈⡄⠈⢷⡄⣿⠃⢸⡏⠀⣾⠃⣼⠃⢢⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠢⠐⣿⠇⠸⣷⢺⡇⠀⠇⢠⠚⡇⢹⣄⢿⡇⠀⣿⣠⢿⡌⢸⡇⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣞⡏⠈⠓⠊⠀⠘⠘⠁⠀⠁⠸⡇⢸⠀⠁⠈⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠈⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠘⠁⠸⠁⡰⠂⣀⡀
⠀⣤⠀⠀⠠⠀⡶⣰⠀⢀⡀⢠⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⣾⣷⣶⣶⠞⣻⢻⣆⣤⣤⡦⣤⡀
⠀⣿⠀⣰⢳⣴⡇⣿⠈⣿⠀⣿⣸⢹⢰⣇⣗⣆⡖⣰⢰⠂⠀⠀⠀⠀⡇⢸⣿⠋⡎⣿⢠⡇⣾⡝⢰⣿⠁⡇⡝
⠀⠸⡄⢻⠼⡿⠇⠏⡧⢿⢠⠏⠏⠿⡼⠸⠹⠹⠁⠏⠾⠀⠀⠀⠀⠀⣇⢸⢿⣀⣇⣻⣸⡁⡆⣇⢸⡟⣸⣡⣇
⠀⠀⠀⠀⠀⢠⠴⠴⢖⣢⢀⡀⠀⣔⣒⣲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⠇⡇⣹⢹⠋⡟⢸⢈⡏⠁⠈
⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢇⡇⣄⢰⣇⣾⣨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⢭⣍⣉⣫⣩⣵⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠘⠊⠙⠈
⠀⠀⢀⣄⠀⠀⢀⢀⠀⢀⡀⢀⡀
⠀⠀⢸⡿⠀⢀⡴⣪⠀⣾⠁⣾⢀⢄⣶⠢⢸⡇⣳⢠⡄⠀⠀⠀⠀⠀⢰⠀⣠⡀⡴⡔⢀⡄⣤⣄⠀⣄⡀⢀⢀
⠀⠀⢸⡇⠀⢸⡇⣿⢠⡟⢸⡷⡆⢸⡇⠀⣾⠃⡿⢸⠇⠀⠀⠀⠀⠀⢸⠀⠇⠷⠧⠷⠸⠠⠧⠻⠻⠻⠿⠟⠞
⠀⠀⠈⠃⠀⠈⠁⣬⢠⡍⣘⢃⣋⢈⡇⢴⠋⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡿⢸⢇⡿⣾⡇⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⣷⣟⣧⣸⢡⢷⢿⣼⣿⣶⢲⢶
⠀⠀⠀⠀⠀⠀⠘⠃⠚⠘⠃⠛⠀⠙⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠶⠀⣼⣿⠉⠉⠀⠀⠀⠀⠾⠀⣾⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣶⠀⣿⣿⠂⣴⣏⠆⠀⠀⣾⠀⡹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡤⠀⢿⡤⠿⡿⠀⠿⣇⡀⠀⠀⠿⠜⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⢀⣀⡀⠈⣿⡇⠶⣶⠶⠆⣠⣄⠀⣿⡏⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⡆⣾⡯⠎⣠⣿⡇⠀⣿⠀⢸⡯⠞⣰⣿⣷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢧⠴⠃⠙⠷⠞⠁⠿⠇⠀⠛⠀⠈⠛⠚⠁⠿⠏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⡖⣶⣶⠒⣶⡖⢶⣶⣶⣶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⡋⠃⣾⣿⡇⢹⠟⡿⣸⡟⣿⡷⠀⣾⠇⢾⠛⣿⣏⠋⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣷⣨⣶⣴⣿⣇⣛⣴⣄⣻⣆⣼⠀⣾⣿⣾⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠶⠀⠈⠉⠉⢩⣍⠉⠉⠉⠉⢉⡉⠉⡉⣩⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠤⠀⢸⡏⣷⡆⢈⡁⠀⣠⡤⡀⣿⣧⢸⡇⣿⡇⢸⡆⣾⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣷⣟⠃⢸⡇⢰⣿⠛⣡⣿⡟⣿⡇⣿⡇⣸⠇⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠘⠃⠙⠂⠈⠷⠋⠈⠉⠁⠙⠃⠉⠀⠻⠟⠋⠀⠲⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⣠⣤⣤⣄⣀⣀⣰⡄
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⣾⠇⠀⠀⠀⠀⠙⡁⢉⣉⠉⠛⣿⠟⠛⠁
⠀⠀⣠⣶⡿⠛⠉⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣿⢁⡤⣤⢰⣿⠀⢠⣾⠋⣿⣾⠃⢸⡟⠀⢸⡿⠰⣦
⠀⢰⣿⡟⠀⢀⣴⠄⣼⡿⠀⣠⡀⣠⣄⠀⣴⠖⡆⢀⣾⠋⣸⣿⠏⢸⣿⣋⣴⠟⢸⣿⣆⢿⡇⢘⣿⡏⣠⠊⣿⡶⣿⡇⢀⣿
⠀⢸⣿⠀⣺⣾⣿⢰⣿⣇⡀⢸⣿⢹⣿⢸⣿⡴⠃⣼⡏⠈⣻⣿⢀⣼⡏⣿⣇⠀⢸⣿⢸⢈⡓⠊⠈⠋⢡⠞⣿⡇⠈⠓⠛⠁
⠀⠀⠛⠲⣿⣽⣿⣄⠀⢻⣿⣼⣿⠘⠛⠚⣿⣀⡼⠉⠓⠚⢁⣙⣋⣘⡃⠘⢿⣄⠀⠻⠞⢸⣿⠀⠀⠀⢿⣴⠿⠁
⠀⠀⢠⣾⠏⢸⣿⣹⡇⢸⣿⡏⢿⡄⠀⠀⠀⣀⣠⣴⣶⠿⠟⠛⠛⢛⣿⠀⠀⠙⠓⠲⠖⠛⠁
⠀⠀⠸⣿⡄⠸⠏⠉⢀⣿⡟⠀⢷⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠈⠛⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⢙⣿⣷⣤⣤⣤⣤⣤⣤⣤⣼⣿⣶⡿⠁⣴⡿⢷⣄⠀⠀⣰⣿⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⣠⣾⠟⢻⣿⠋⠉⣉⣉⠉⠙⢛⣿⡏⠁⠀⠀⣿⡁⠀⣿⠀⠀⣿⣿⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢿⠁⠀⣼⠏⠀⢸⣿⢻⡆⠀⣼⣿⠀⢀⣴⢶⡙⢷⣤⣿⡀⠀⢿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢀⣠⡾⠋⢶⠆⢸⣿⣼⠁⢠⣿⡏⠀⣾⢇⡞⠀⠀⣼⢫⡿⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⣶⠀⠀⢻⣿⡀⢸⣿⠃⢠⣿⠛⠀⠀⡼⣳⠟⠀⢀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢸⡿⠀⢀⡞⢿⣷⢸⣿⣠⠏⢿⣄⣤⠞⢡⡟⢀⣤⠟⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡴⢻⡇⢠⠎⠀⢸⣿⡇⠛⠋⠀⠀⠈⠀⠀⠀⠙⠋⠀⠀⠀⣿⣿⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠘⠷⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣤⣴⣿⣿⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⣷⠀⠀⢀⠀⠀⣸⡿⠁⠀⣠⣴⣿⣿⠿⠟⠛⠛⠛⠛⠛⣻⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢻⣿⠀⠀⠘⠶⠾⠛⠁⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⠿⠿⠟⠋⠁






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

⠀⠀⠀⠀⠀⣀⣰⡶⠲⠒⢀⡀⠀⣀⣀⠀⢀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⣀⡘⠃⣀⣠⡀⠀⢰⡄
⠀⠀⠀⠀⢀⣿⣿⣃⢡⣤⠻⠿⠂⣽⣿⣀⣈⡛⠿⠿⠋⢀⢸⡇⢀⣤⡀⠀⡙⣿⡇⣸⣿⡇⣰⣿⣦⣿⣿⡄⠐⠉⠉⠛⢻⣿⣿⠆⢹⣿⣿⠀⣽⣿⡇⠐⢸⣿
⠀⠀⣠⣴⣞⣉⣁⡟⣈⠭⠒⠊⢩⡿⠃⣠⡴⠚⢓⡉⢹⣿⡇⣇⠻⢿⣿⡿⢁⠟⠀⣿⣿⡇⠛⠀⢈⣿⣿⣧⣤⣤⣀⣀⣸⡀⠀⢀⡌⢹⡟⠰⣿⣿⠁⠀⠘⠿
⠀⠀⠈⠉⠙⠻⣿⠿⣿⣶⣶⡶⣋⡀⢸⠃⠀⣠⣿⡇⢸⣿⡇⡏⠀⠦⠤⠖⠃⠀⣠⣼⣿⣇⣀⠰⠟⢿⣿⠟⠿⠿⠿⣿⣿⣿⡿⠿⠤⣈⣄⠀⢻⣿⣀⣶
⠀⠀⠸⠃⠀⣾⣿⣀⣀⣈⠁⠘⠿⠟⠀⣳⢘⢸⣿⡇⣸⣿⡇⡇⠀⠀⠀⣀⣰⠞⠛⢿⣿⣿⣿⣦⣀⣿⠟⢀⣄⠀⣴⡏⢸⠁⣀⡀⠘⠉⠻⣧⣿⡛⠻⣿
⠀⠀⢀⡀⢀⠼⠛⠛⠿⣿⣿⣷⣶⣦⠴⣁⣼⢸⣿⡇⢻⣿⠇⣷⡿⡿⣿⣿⢋⣤⡀⢸⣿⡟⢿⢿⠛⠁⢰⣿⡇⣼⣿⡇⢸⠚⢿⡟⠀⠠⠾⠿⣿⣿⣿⣿
⠀⠀⢸⡇⡀⠀⠀⠀⣴⣿⠀⠈⠉⠀⠈⠻⢻⢸⣿⡇⣸⠏⢀⡇⠀⠀⣾⡇⠙⣿⡏⢸⣿⡇⠘⠿⢶⣦⣾⣿⠃⣿⣿⡇⢸⠀⢿⣿⠂⠀⠀⣠⣿⡟⢉⣷
⠀⠀⢸⡇⣠⣤⠄⠀⢹⣿⣧⠀⢀⣠⣧⣀⣸⣼⣿⣿⡁⠐⢿⡿⠂⠸⣿⣿⠘⢿⡿⢸⡿⢀⣄⠀⠀⢸⣿⣿⡇⢸⡿⠁⣼⣄⠀⠁⠀⢀⣾⣿⣿⣿⠿⣿
⠀⠀⣸⡃⠛⢻⡾⢿⣷⣿⣿⣶⠛⠻⠇⣴⣿⣧⡙⢿⣿⣦⣤⣧⠄⠀⣿⣿⠀⠀⠐⠋⠀⣾⣿⣷⠦⠉⢹⣿⣿⣯⡀⠻⣿⡿⢂⠆⢀⣼⣿⠛⣿⣷⣶⣿
⠀⠀⢿⣿⡿⠏⣠⣤⡈⢿⣿⣿⡄⠀⠀⠁⠀⣹⣧⣤⣬⣛⠻⡏⢀⡀⣿⣿⡶⢾⠶⡄⢀⣸⣿⠟⢛⣿⠛⠛⢿⣿⣿⣿⣿⣷⣏⣠⣾⣿⠏⠀⣿⣷⠈⠋
⠀⠀⠀⠀⢀⣀⣙⠛⠁⠀⠹⣿⣿⣀⡀⣀⠊⠉⠉⠙⠿⢿⣿⣷⣄⣠⠟⢻⠁⠈⡀⠳⣤⣾⣥⣴⣾⣿⣤⣤⣠⣼⠋⠙⢻⡏⠙⢿⣿⣧⣄⠀⣿⡇⣰⣟
⠀⠀⢰⠟⠙⠻⣿⣷⣤⠘⠋⣹⣿⡍⠉⠙⡶⠀⠂⢀⡤⠀⠈⠛⠛⠋⠀⠀⢀⣴⡄⠀⢀⣽⣏⣸⠿⠿⠿⠿⣿⡃⠀⢶⣿⡷⠄⠀⠀⠉⣿⡴⢛⡟⢻⣿
⠀⠀⣾⣆⠀⠒⣉⣙⡻⠟⠋⡿⢋⣄⠀⣠⠷⣶⣶⣿⣧⡀⠀⢰⣾⣦⠀⡀⣾⣿⡃⠀⠸⣿⣿⡇⢠⣴⣶⡄⠛⠿⢷⣦⣿⣧⠈⣶⣤⠚⠉⠀⢸⣶⣿⣿
⠀⠀⠈⣿⣠⠞⠛⢿⣿⣷⡀⣧⣾⣿⣿⣧⣤⣀⢹⣿⣿⣿⣶⣤⣉⠀⠀⡄⢻⣿⣤⣾⣦⢿⣿⣇⠀⢉⣉⣠⣤⠀⢠⡟⢿⡟⠛⠻⣿⣷⡀⠀⢻⡍⠉⣹
⠀⠀⠘⣿⣿⣦⡀⠀⠹⣿⣷⣿⠀⢹⣿⠏⠙⡿⢺⣿⣿⡿⠛⠻⢿⣿⣦⠀⢸⣿⢄⣿⣧⢸⣿⡿⢛⣉⡀⣿⣿⣇⠁⠀⣿⣷⡄⠀⢹⣿⣷⡞⢸⡇⣾⣿
⠀⠀⣴⣏⣿⣿⣿⡇⠀⣿⣿⣇⣠⣎⣡⣤⡄⠀⣼⣿⡟⢰⣾⣷⠀⡿⠋⠄⢸⣿⡄⠙⠋⣀⣉⠐⠿⣿⣇⠼⣿⣿⣇⣀⡻⣿⣿⣆⠀⣿⣿⡇⢸⡅⣿⣿
⠀⠀⢹⡟⠀⠀⣿⠃⠈⣿⣿⡟⠛⠻⣿⣿⣅⣴⣿⣟⣀⣀⣭⠴⠊⠀⢠⣦⣽⣿⠇⡰⠾⢿⣿⣷⣦⡞⠁⠀⢹⣿⡿⠋⠁⠈⣿⣿⡆⢻⣿⠀⢸⡇⢸⣿
⠀⠀⢸⠁⣠⣌⡁⢀⣠⠿⢿⣿⠆⠀⣿⣿⡿⠛⣿⠛⢻⡿⣿⣷⣤⣀⠙⣿⣿⣿⡆⢧⣀⣀⠿⠿⣿⣿⣿⣦⡼⢿⠃⠀⠀⠀⢸⠟⠀⣿⡟⢠⣾⣧⣸⣿
⠀⠀⢸⡔⠻⣿⣿⣿⣿⣿⣾⣿⣏⠉⢹⣿⠟⣳⣆⡀⠸⢀⣈⢙⠿⣿⣷⠏⠘⢿⣿⡶⠋⢁⣤⣄⠀⠙⠛⢋⠀⣾⣴⣆⣠⡔⠉⢀⣴⣯⣤⣈⣻⠏⣸⡿
⠀⠀⢸⠁⢰⠋⣡⣦⣬⡛⠻⣿⣿⣷⣾⠟⠉⢹⣿⡇⣸⣿⣿⡿⣷⣄⢴⣿⡦⣸⡿⠁⠀⠈⠛⠋⢀⣴⣾⣿⢠⡿⣿⣿⡅⢀⠴⠋⣉⠛⠿⣿⣿⡷⠉
⠀⠀⣸⠀⠈⣿⣿⠟⠉⠁⣴⣿⡎⠉⢀⣴⡇⢸⣿⣇⣿⢻⣿⣷⡈⣿⣧⣿⡄⢸⡇⣴⣷⣄⠀⢠⣾⠃⣿⣿⡟⣧⠘⣿⣿⡄⠀⠻⡿⠗⠀⣀⣽⣅
⠀⠀⣽⢀⣼⣿⠏⠀⠀⠀⣨⣿⡄⠀⢸⣿⡇⢸⣿⣿⢹⠀⢻⣿⣿⠁⠈⠟⠀⢸⡟⠙⢿⣿⡇⢸⣿⠀⣿⣿⠁⣿⠀⠈⣿⣿⡄⣠⣤⣶⣦⣽⣿⣛⣷⣿
⠀⠀⣾⣾⣿⠏⣠⡶⢾⣷⣿⣿⣁⣴⣿⣿⡇⠘⣿⡏⢠⠀⠀⣿⣿⠀⢀⣀⡀⢸⡇⠀⠼⠋⠀⢸⣿⣧⣿⣧⣤⣿⣄⠀⢸⣿⡿⠛⠛⠿⢿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣥⣾⣿⣧⠀⠈⠹⣿⣿⠀⢻⣿⣿⡼⠋⢀⣾⣆⠀⣿⡟⢠⣿⣿⠟⢿⣷⣾⣦⣄⡀⣨⣿⣿⣏⠉⠙⣿⣿⣷⣾⡿⠁⠀⠀⠀⠀⠀⢈⣽⠋
⠀⠀⠿⠿⢿⣿⢻⣿⣇⠀⠀⣿⣿⠀⢠⣿⣿⣷⣤⡈⢿⠟⣱⠏⢠⣿⣿⠁⠀⢸⡏⢻⣿⣧⡉⠉⣽⣿⣿⣷⣦⣿⣈⣿⣿⣿⣦⣀⣴⣦⣤⣴⣾⣵⡶⠂
⠀⠀⠀⢰⣿⡇⢾⣿⣿⡿⠀⣿⣿⣠⠞⠁⠙⢿⣿⣿⣿⡟⢁⣠⣿⣿⠃⠀⢀⣾⣧⡀⠹⣿⣿⣄⢠⣿⣯⠛⠿⣿⢋⣥⣬⡛⠿⠿⢿⡿⠿⠿⢿⡿⠁⢉
⠀⠀⣤⣾⣿⡷⠟⠁⣠⣤⣶⣿⣿⣷⣶⣶⣆⣤⡈⣉⣿⣍⠻⢿⣿⣷⣷⣶⣬⣿⡟⠉⠀⠙⣿⣿⣦⣙⠋⠠⣴⣿⣯⠀⠉⢻⡄⠀⠀⢠⣶⣦⠸⠇⠠⣿⠄
⠀⠀⠋⢹⣿⣇⡴⠋⢉⡿⠋⣿⣿⡇⠀⠉⠙⠟⠋⠙⣿⡟⠁⠎⢀⡀⣨⣟⠻⢿⣿⠶⣷⣶⣾⣿⡿⠋⢠⣴⣬⣿⡅⠀⠀⣠⣿⣷⣦⣤⣉⡁
⠀⠀⠀⢸⣿⣿⠀⣰⠏⠀⢰⡿⣿⣷⣄⣀⡀⠠⠀⠺⣿⣿⠂⠚⢿⠿⠻⠿⢱⣿⣤⣀⡀⠙⣿⣿⠀⠀⣿⣿⠙⣟⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤
⠀⠀⠀⢸⣿⡏⣴⣿⠀⠀⠀⣠⠼⠿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣷⣶⣿⣶⣾⣿⠻⠿⣿⣷⢸⣿⣦⡀⣿⣿⠋⢩⣿⠀⠏⠁⠠⣿⠟⠉⠻⠙⢻⠿⣿⣿
⠀⠀⣤⣾⣿⣿⣮⡻⣦⣀⣼⣧⣀⡀⠈⠉⠙⣿⣿⡆⠈⠀⢉⣽⡟⠁⠈⢉⣿⠃⠀⣀⡸⠋⣸⣿⣿⡀⣿⣿⠀⢻⣿⣾⡄⣠⣄⠙⢂⣤⣤⣴⣿⡀⠈⢻⠇
⠀⠀⣩⣾⣿⣿⣿⣁⠀⠉⠛⣿⣿⣿⣿⣦⡀⢸⣿⣧⠀⠀⢸⣿⡏⠀⠀⣼⣿⠀⠈⠉⣡⣴⣿⠁⠀⠀⣿⣿⠀⠈⢿⣿⡇⠿⣿⣿⣦⠛⠋⢻⣿⣷⣄
⠀⠀⠉⠉⠉⠻⡿⢿⣿⣷⠾⢋⠀⠈⠹⣿⠧⣾⣿⣿⣠⣶⣿⣿⣿⣾⣿⣿⣿⠀⠀⠘⠛⠛⠻⣿⣿⠟⣿⣿⣀⣀⢘⣿⡇⣀⢈⣯⣤⣤⣤⡀⠙⣿⣿⡆
⠀⠀⠀⡀⠀⣾⣷⠾⢷⣦⣾⣿⠷⢀⣴⣿⣆⣸⡿⢋⡛⠉⢻⣿⡟⠉⠀⣻⣿⢀⡴⢶⣿⣦⣀⣠⠶⠚⣿⡿⠉⠉⠙⣿⡷⣿⣿⣿⣟⠛⢿⡇⠀⢸⣿⠇⢰⣶
⠀⠀⣼⡁⠀⣼⠟⠀⠀⠈⠛⠳⠒⠛⠁⠈⠛⠛⢡⣾⣷⡄⢸⣿⣇⠀⠀⢸⣿⣿⣀⣀⣬⡿⣿⣷⣤⣤⢿⣵⣶⣦⣴⣿⣀⡋⠈⢿⣿⣦⡀⠁⣀⠜⠁⢀⣾⡃
⠀⠀⠙⢿⣷⣿⣄⣠⣤⣤⣤⣤⡄⠀⠀⣤⣤⣄⣶⣽⡟⠁⣼⣿⣿⡄⠠⠼⠿⠿⠿⠿⠥⠀⠈⠙⢋⣥⣤⡀⠉⠛⢿⣿⣿⠇⢠⣴⣿⣿⣿⣿⠁⣠⡴⢿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣠⠏⠀⠀⠀⠀⠀⠀⢰⣾⡏⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⠞⠁⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡜⠀⢀⣴⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣸⠃⢀⣾⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⣿⣿⣰⠃⠀⣾⣿⢠⠏⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⣀⣤⠴⠖⢛⣽⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⣿⣿⢀⡔⣹⣿⡟⠀⠀⠀⠀⠀⣿⣿⠇⠀⢰⣿⣧⠏⠀⠀⢠⠀⣞⣻⣷⡞⠁⠀⠀⣰⠊⠁⠀⢀⡴⠛⠁⢸⡇
⠀⣞⢝⢣⣞⢳⠀⡀⠀⠀⠀⢻⣿⠏⢠⣿⣿⠁⣰⡶⢦⡀⠀⣻⣿⡀⠀⣸⣿⠋⠀⠀⠀⣿⠀⠀⣿⣿⠃⠀⠀⢸⠋⡀⢀⡴⠋⠁⠀⠀⣾
⢠⡜⠪⠱⣬⡘⠩⢸⣂⣤⣀⠀⠀⠀⣾⣿⠇⢸⣿⢃⡼⠁⣰⠋⠹⠧⠶⣿⣿⠀⠀⠀⡼⠹⢄⣰⡿⠃⠀⠀⠀⢈⡷⢷⠋⠀⠀⠀⣀⡴⠃
⠈⠓⡖⡒⢄⠱⢶⡘⠋⠀⣸⠂⠀⠀⣿⣿⠀⢸⣿⠏⢀⡴⠃⠀⠀⠀⠀⢿⣿⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠈⠓⠶⠶⠖⠋⠁
⠀⠈⠓⠂⡲⠆⠠⠝⢲⣄⣩⠗⠀⠀⠙⠿⠖⠛⠻⠷⠋⠀⢀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡶⠺⠁⠐⣄
⠀⠀⠀⠸⣇⣀⣠⠿⠼⠃⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⣤⣀⣠⠤⣤⡄⠀⠘⢇⡀⠀⢠⣹⠟⣧
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣀⣿⣿⡇⠀⠀⢀⣀⣠⣤⠴⠖⠈⠀⠀⣰⣶⠞⠁⢸⣿⠁⢰⣿⡟⠀⠀⠀⠉⠉⠉⠉⠛⠃
⠀⠀⣠⣶⠞⠲⣄⠀⠀⠀⠀⠰⠋⠁⠀⠀⠈⠉⠉⠙⢻⣿⡟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣾⡿⠀⣼⣿⠇
⠀⣼⣿⠋⠀⣸⣿⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠻⠃⠀⣿⣿⠀⠀⢠⣿⣷⡴⠖⢲⣦⡀
⢰⣿⡇⣠⢾⣿⡏⠀⠀⣰⣿⡇⠀⠀⣰⣿⡏⠀⠀⢀⣼⣿⡁⠀⢀⣿⡿⠀⠀⣰⣷⡄⠀⠀⣰⠏⠁⠀⠀⠀⠀⠸⣿⣿⠀⠀⢸⣿⡏⠀⠀⠠⣿⡇
⠈⠛⠛⠁⣼⣿⠃⠀⣰⣿⣿⠁⠀⣴⣟⣿⠇⠀⢀⡾⠙⣿⣇⡴⢿⣿⡇⠀⠀⣿⣿⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠇⠀⠀⣾⣿⠁
⠀⠀⠀⠀⢿⣿⢀⡼⠃⢿⣯⣤⠞⢡⣿⣿⠀⢠⡞⠀⠀⠈⠉⠀⠀⢿⣇⣠⠾⣿⣿⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣠⠿⡿⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠉⠀⠀⠸⣿⣿⣠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠹⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠾⠿⠿⠷⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⢉⣠⣤⣴⣶⣶⣶⣶⣤⣬⣙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⣠⣾⡿⠟⣋⣩⣭⣤⣤⣭⣭⣙⠛⢷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢁⣾⡿⢫⣶⡿⠟⣛⣉⣉⣉⣉⣙⠻⢿⣦⡈⢷⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣼⡟⣰⡿⣫⣶⠟⢛⣉⣉⡉⠙⠻⣿⣦⠹⣷⠀⢷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣿⢁⣿⢱⠏⠔⣛⣉⣙⠛⢿⣷⡄⠘⣿⠀⣿⡆⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⢸⡇⢊⣴⣿⡿⠟⠻⢿⣦⠹⣷⠀⣿⠀⣿⡇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⡤⠤⣤⡀⠀⣀⣠⣄⠀⠀⠀⠀⠀⢻⠀⢿⠸⡇⣾⣿⠃⠀⠀⠀⠀⣿⡆⣿⢠⡟⢀⣿⠀⣼⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⠄⠈⠑⢤⠁⣠⠤⣄⠙⠖⢉⡀⡉⢳⠀⠀⠀⠀⠈⣆⠸⣇⠃⣿⡇⠀⠀⠀⠀⠀⣿⢡⠇⡾⠁⣼⠃⢀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣧⣀⡤⠤⠤⠤⣏⡀⠜⢀⠎⠹⡆⠈⠈⠂⠀⠀⠀⠀⠈⢆⠹⣆⢹⣇⠀⠀⠀⠀⠸⢁⠎⡼⠁⡼⠃⠀⡜⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠋⠛⢶⡄⠀⠙⠓⢚⣡⣴⠶⠾⠿⠟⠿⠿⠿⠷⣶⣦⣤⣱⣜⣦⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠘⠷⣶⣿⣃⣀⣀⡴⠋⠁⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠛⠉⠉⠉⠉⢹⠉⠐⠀⠀⠉⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⢫⠀⡰⢾⣽⣟⠓⢀⡟⠀⠤⠄⣈⡁⢂⣴⡿⠋⢀⣤⣄⠉⠛⠲⠶⢤⣤⣄⣀⠀⠹⢿⡄
⠀⠀⠀⠀⢠⡞⠡⠀⠘⡀⠀⠈⠉⠁⣠⡾⠧⡀⠒⠤⡄⡹⢸⣿⠁⠀⠀⠀⢈⣷⠘⠒⢂⡴⢒⢀⣈⢉⠲⢌⣿⡄
⠀⠀⠀⠀⠀⠈⠀⠀⢒⠗⠲⠶⠿⠟⡛⠀⠠⣌⠑⢦⠈⠀⢸⣿⠀⠀⠀⠌⢠⡟⢡⠀⠀⣻⣅⣼⠤⢊⡮⢤⠙⢇
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡀⢱⡀⢢⡈⠁⠀⠀⠀⠈⢿⣧⡀⠀⠈⠉⣠⡎⢠⠈⠁⣥⠿⣏⡈⢁⡴⢠⠄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣧⠈⠁⠈⠁⠠⠀⠁⠄⠀⠈⡿⢿⢶⡶⠞⠋⡀⢡⠤⠀⢾⡠⠌⠙⢷⡀⠭⢾⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠔⢒⠢⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠣⣕⠢⣜⣒⢱⠠⠋⠊⢏⠀⠀⠀⠃⣆⢢⠈⠄
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠀⠱⣁⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⣌⠓⢦⣍⣛⠳⠷⣶⣤⣤⣄⣒⣚⠣⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⠔⠉⠱⡌⢷⣄⠀⠂⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⣦⣈⡙⠻⠶⣶⣤⣭⣍⣙⣛⠛⠛⠛⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⣿⠀⠙⢷⣄⠂⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣙⠛⠷⣶⣤⣤⣍⣉⣛⠛⠛⠛⠛⠋⣹⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠀⠙⠻⢶⣤⣤⣄⣀⣀⣄⣤⣤⣬⣿⢿⢶⣦⣤⣍⣉⣛⣛⣻⠟⠛⠛⠉⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠉⠋⡉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠑⠒⣤⠄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠶⠞⠛⠉⣠⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢄⡈⢩⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠞⢆⠁⠀⠁⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠸⠀⠏⠀⣀⠇⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡋⣁⢀⠤⠒⢬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠞⢰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠫⣆⣶⠄⡠⢤⠀⠀⠀⠀⠀⢀⢈⣁⣄⡀⠀⠀⠀⠀⠀⠀⣨⠷⠖⠛⡛⠃⠈⠁
⠀⠀⠀⠀⠀⣦⠘⢉⣉⡉⠑⠄⢠⠀⠀⠀⠀⠈⠁⠄⠬⠍⡁⠀⠀⠀⠀⠀⢤⡶⡴⣿⢄⣦⣼⣤
⠀⠀⠀⠀⠀⠉⡇⢰⣷⢰⣯⢹⠉⠀⠀⠀⠀⠏⠛⢫⡛⠍⠚⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⢠
⠀⠀⠀⠀⠀⠀⢉⠉⠡⠌⠉⠈⠀⠀⠀⠀⠀⠀⠰⠴⠶⠁⠀⡀⠀⠀⠀⠀⠶⢠⣄⣴⢠⠈⠚⠃
⠀⠀⠀⠀⠀⡦⢘⣶⡼⢫⣴⠀⣤⠀⠀⠀⠀⠱⠛⠂⠛⠓⠶⠉⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠈⠀⠋
⠀⠀⠀⠀⠄⢲⣀⢀⢺⡓⣠⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⢂⡰⢦⢰
⠀⠀⠀⠀⢀⡾⢓⣋⣈⠛⢺⠀⠀⠀⠀⢹⡔⣶⣞⠁⢀⢑⣨⡇⡸⠃⠀⢀⣴⠄⣠⠀⠘⢀⠰⣶⡄
⠀⠀⠀⠀⠀⣁⣐⣦⣆⣲⣀⠀⠀⠀⠀⠀⠙⠛⠱⠽⠏⠼⠆⡉⡀⣀⠀⠐⢿⡄⢳⡛⠛⡝⠀⠿⠃
⠀⠀⠀⢠⣾⣿⡿⢿⡿⠿⢿⣷⡆⠀⠀⠀⠒⣞⠈⠦⡇⠆⢱⢧⠽⠁⠀⠀⠀⠀⠎⢠⣮⣤⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⠯⢇⡀⡀⠀⠀⠀⠀⠀⡔⢉⡠⠤⣄⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⣼⡏⢰⡏⠀⠈⠀⠀⠀⠀⠘⠀⠀⢹⠀⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠠⠄⡀⠀⠀⠀⣶⠀⢠⣿⠀⠘⢧⣄⣀⠠⠊⠀⠀⠐⣄⣑⣩⠞⠡⠄⠠⢼⡃
⠀⠀⠀⠀⠀⢠⡏⠀⠈⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⡇⡰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣍⢰⡄⠀⠀⢠⠏⠘⡆
⠀⠀⠀⠀⠀⠸⣧⣀⣀⣠⣢⠴⠪⡀⠀⣿⠇⢠⣿⠔⣡⠤⠀⣰⠄⢰⢤⡏⢀⡟⢰⠇⣾⠁⠀⠴⠋⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢉⡏⠉⠀⠀⢀⣃⣸⣿⠐⣺⡏⢰⡇⢰⡆⡿⢂⠟⣽⠉⠚⠁⠈⢩⡟⠀⠀⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡴⠛⠁⠅⣾⡇⠀⣿⠃⠀⠉⠀⢸⣇⣀⢠⡿⠀⠀⠀⠠⣼⠧⠴⠒⠋⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⢰⣿⠁⢸⣿⠀⠀⢀⡴⢿⠁⠀⠸⢇⣀⣀⣀⣰⠏⠀⠀⣀⡴⠚⠋⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠁⠀⠀⣾⠏⠀⠸⣧⠀⠀⣿⡇⠀⠀⠀⠀⠉⠀⠈⣹⢿⣄⠤⠊⠁⠀⢠⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠠⠚⠁⠀⠀⠀⢿⡀⠀⠹⣿⣄⠀⠀⠀⠢⣤⠴⠅⠚⡇⠀⠀⠀⠀⠀⠒⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠙⠒⠒⠉⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⣀⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣶⡀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣿⡇⣠⢿⡇⠀⠀⠀⣤⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⣵⢏⡟⠀⠀⢀⣾⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⣼⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠏⢸⠃⣀⠀⣸⠇⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⠀⠘⠞⢹⠀⣿⠞⠁⢀⡴⢂⠀⠀⣠⠖⢃⣿⠇⣠⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣿⠀⠀⢀⣼⠛⢿⠀⢰⣟⣰⣿⠀⡰⣇⣠⠞⢿⡼⢷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠛⢀⡞⢡⡏⠀⠈⠁⠈⠉⠁⣙⣚⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣀⡾⠁⢠⣾⡇⣼⣱⢡⣏⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⡀⠚⠉⠈⠁⠁⠘⠋⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠈⡆⠀⣾⠇⠀⠀⠀⠀⢠⡗⠀⣀⣴⠋⡼⠁⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⡾⣿⡆⠀⡇⢸⡟⠀⠀⠀⠀⠀⠀⠈⠛⢻⣟⡿⠁⠀⣰⠟⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡟⢠⣿⠃⢠⡇⣿⡇⢀⣴⣿⠀⠀⣼⠃⠀⣿⡟⠀⠀⢰⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢸⣿⠀⡾⠀⢿⣇⣾⢻⡏⢀⣴⢿⣀⡴⠛⠧⢤⠴⠚⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠻⠾⠁⠀⠈⠛⠃⠈⠓⠚⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⣠⠖⠂⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢤⣾⡏⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⡀⢀⠀⠀⢸⣿⠀⣰⠛⣷⠀⣾⣆⣴⣿⢂⣾⠛⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠛⠟⠇⠀⠀⣾⡇⢸⡟⢤⡿⣼⣿⠞⠀⠃⣾⠇⢀⣿⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠁⠘⠷⠞⠁⢿⠇⠀⠀⠘⢿⠴⠻⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠟⠉⠒⠲⠦⠤⠤⢤⢤⠴⠶⠶⠶⠶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡇⢢⠀⡷⡷⡞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢹⡇⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⣧⣼⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠚⠉⣿⠋⣭⠉⣠⡀⣠⢄⢠⡄⣠⣄⠀⣠⡬⡛⢩⣿⢡⡿⢠⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡞⠈⣿⡄⢸⡏⢰⣿⠎⠛⣼⠷⠋⣾⠏⣿⠃⣼⡟⣰⡷⣼⠇⣾⡗⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⡿⠃⠺⠴⠻⠃⠀⠀⠻⠶⠚⠟⠀⠿⠎⠻⠄⣿⢣⡿⠀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠈⠣⠴⠂⠀⠻⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⢿⠀⣤⣦⡤⣄⠀⠀⠀⡄⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠁⠁⠁⠉⠀⠀⠀⠹⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⢶⠀⣰⡄⠀⠀⢀⡀⠀⠀⠀⢠⣶⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠿⢠⣿⠁⠀⠀⠰⠇⠀⡀⠀⣴⡆⠀⢀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢿⣆⠀⣾⣧⢾⡟⢰⡿⢀⣾⣩⢠⡿⠀⣼⠋⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⢠⣿⠁⣿⣡⣾⣃⢾⣏⣠⣾⣇⢼⣏⣰⣿⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠁⠈⠃⠀⠈⠁⠈⠁⠀⠉⠁⠈⠉⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⣦⣰⡾⠷⠲⢲⠀⣸⠪⢻⢐⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣧⡄⠀⠀⠀⠀⠀⠻⣶⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⡁⠠⠽⠟⠃⣄⡐⠰⠶⠀⠉⢠⡀⠀⢀⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡁⢋⡳⠀⢀⡤⠀⠈⠠⢦⣤⣲⡖⠀⠀⠘⢿⠯⢚⡽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠂⠘⣷⣤⣜⠁⠘⠋⠀⠩⣳⣹⡿⡶⠓⡤⡄⢈⢻⣧⡶
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢾⡆⠹⢏⣿⣷⠂⠀⢀⣀⢸⡿⣿⠏⠘⠛⠻⢻⡟⣳⣄⠢⠐⣀
⠀⠀⠀⠀⠀⠀⢀⣿⡗⠦⣷⠬⣅⡶⠎⠻⢯⡄⠂⠻⠿⠸⢿⠿⠀⣀⠀⠀⠀⢰⣿⣅⣤⠖⡭⠅
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⢢⣴⣿⠶⠼⠾⠀⢀⣀⠠⢀⣰⣤⣾⣿⣧⣤⣀⠙⣏⢀⣀⡰⢶⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣈⠉⠀⠀⠐⠂⠀⠈⠁⣠⠀⠊⠋⡉⠉⠙⣄⠈⠀⢀⡀⠈⠃⠄⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠠⠞⠉⠙⠻⣿⣶⡷⢤⣤⣌⣀⠀⠀⠀⠵⠀⠘⠉⠉⢘⣿⡟⠂⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠐⠀⠀⠀⠀⠙⠴⠛⠧⣾⣻⣾⠃⠐⢒⡀⠀⢐⡛⠘⣿⣁⣀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⢝⡷⢸⡀⠈⢀⠺⢻⡿⠁⣒⠠⣴⣮⠤⠀⣉⣡⠀⠈⢹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣷⣾⣧⣼⣠⣴⢫⠀⠸⠟⢳⠎⢡⣾⣿⠉⠉⠀⣰⠚⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣟⢊⢸⣿⡒⠀⡀⢀⠍⢶⣦⡉⠹⠷⢘⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣼⣀⡐⠻⠞⠃⠀⠀⠀⢀⣀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⢛⣿⣿⣿⣿⣿⣿⣯⠻⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣷⣮⣭⣭⣭⣭⣭⣴⣾⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠭⠯⠭⠯⠏⠛⠛⠉

⠀⡠⠀⣶⣶⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠾⠋⠀⣀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠸⢿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⣆⠀⠀⠀⠈⣷⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣯⣤⣤⣄⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣼⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢰⡖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⡐⠒⢾⣿⣷⣼⣷⣶⣶⣦⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⣿⣶⣀⠤⠀⠀⠀⢶⣽⣿⠇⠀⠀⠀⠨⠿⢭⣙⣋⣻⣿⣦⢶⡀
⠀⠀⠀⠀⠀⠀⠹⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣏⢻⡿⠻⢿⣿⡿⠟⢛⢿⣿⡿⠛⠛⠻⣿⣏⠀⠉⣷⣔⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣎⢦⣰⣿⠱⣯⣤⢸⣿⡄⢦⡤⠀⣾⣿⣮⣴⡿⠿⡋⠁⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠈⢹⡿⣿⡿⣿⣷⣷⣷⣿⡿⣿⣾⣶⡾⣿⡿⠿⠻⣄⠀⣱⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⣯⣶⣿⣷⣄⣀⢸⣏⣽⡋⠁⠀⠀⣽⡁⢀⣸⣇⣀⡀⣿⣿⣿⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⢿⢿⣿⣿⣿⣿⣷⣾⣾⠿⠿⠿⠿⠿⠿⠛⠻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⢀⣀⣀⣒⣒⢂⣀⣀⣠⣀⣀⣤⣤⣤⣤⠤⠄⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⠇⣠⣾⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣯⡌⠁⠠⠄⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⢋⣵⣾⣿⣿⣿⣿⡍⠻⠗⠚⠟⠻⠋⠉⠸⠋⠙⠉⣀⠀⠀⠀⠀⠈⠿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡌⠹⠿⠟⢿⢿⡀⠸⣿⣿⣿⣿⡏⠀⠀⠠⠴⠆⠀⢤⠄⠀⠀⠀⣴⣿⣿⣷⣤⣶⣦⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣠⡶⠾⣷⣦⡘⣷⣄⠙⠿⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠹⣿⣿⣷⣿⠇⠈⣻⡷⠀⢨⣿⣾⣿⣿⣿⣿⣿⢻⣿⣶⣦⠀⠀⠀⠀⡈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢻⡟⠉⠁⠀⠘⠛⣣⣴⠀⡍⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⠀⠀⠀⠈⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠃⣤⡄⢀⣴⣿⣿⠿⢤⠇⠀⣿⣿⣿⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠏⢿⣿⡟⣭⣤⣤⣤⣾⣿⣿⣩⣯⣉⣘⣻⣿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠆⠀⠹⣽⣿⠟⠉⣁⠀⠠⢬⠻⠉⠉⠙⠻⣿⣷⣶⣤⡀⠀⠀⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢾⠁⢠⡇⢀⣿⡏⠀⠩⠠⣤⡀⡀⠀⠀⠀⠐⢂⡄⣉⠛⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⣆⢘⣳⡿⠋⠀⠢⠀⠀⠀⠀⡠⠀⠁⠀⠀⠈⠀⠻⠓⡦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣉⣣⣴⠇⡔⠀⠨⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢀⣂⠚⠁⠀⢀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⡇⠁⢠⣄⣀⠀⠀⠑⠴⠀⠀⠀⠀⠒⠀⠀⠄⠀⠉⠀⠀⢀⠀⣖⣾⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡍⣹⣯⠀⠸⣿⣿⠦⡀⠀⠀⠠⠱⢶⣄⡀⠀⣀⣀⣀⣴⣦⡀⠈⠀⠹⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣽⣿⠀⠀⣿⣿⢠⡈⠀⠀⣀⠀⠀⠈⠙⠛⡋⠁⠈⣿⣷⢻⡄⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⣿⣿⠇⠻⢴⣦⣴⡦⣄⠀⠀⠀⠂⢹⡿⢿⣿⡆⠀⢠⠋⡄⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣶⣿⣿⣿⣷⣾⣿⣧⡀⣘⣿⡷⢶⣿⣿⣇⣴⣿⣷⠇⡁⢼⡇⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣟⣸⣽⡏⢿⣿⣿⣿⣿⣾⣯⣶⣮⣤⣤⣜⣛⣿⣿⣿⣿⢻⡆⢩⠤⠃⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠉⠛⠛⠟⠛⠉⠁⣿⣏⢟⣿⣋⡁⠆⢀⣽⣿⣻⣿⣿⡿⢻⡇⠀⠌⠩⠽⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠰⣶⠶⣶⡆⢀⣏⠀⡲⣅⠠⠀⠀⠀⠉⠉⠉⠙⠛⠃⠸⡧⠐⣤⣀⣉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠛⠛⠉⢁⠜⠛⠢⠙⠓⠀⠀⠛⠛⢲⡄⠀⠀⠐⠀⠀⠐⣻⠎⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣤⡶⠀⠈⡄⠀⠀⠀⠀⠀⠀⡀⠀⢾⣥⣄⣀⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠠⠼⢶⣽⣿⠿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠃⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⢰⣶⣶⡄⠀⣦⢲⠶⠀⢀⣴⣺⣷⠄⠀⣼⣷⣰⠀⠀⠒⠀⣾⠆⠀⠀⢤⠀⠀⠐⠛⠴⠋⠰⠠⠟⠠⣤⢰⣼⣇⠘⣦⠠⣽⡧⣿
⠀⠀⢈⡑⠟⣨⠀⢸⣼⣷⠀⠘⠳⣼⡟⠡⠆⠙⢇⣿⣿⡀⠀⠀⠀⠁⠀⠆⠀⠀⠙⠆⣆⠘⠁⡠⠖⠒⢦⣬⣭⠵⠃⠄⡀⢰⢣⣾⣿
⠀⠀⢠⠟⠀⢿⡦⠸⠇⢀⣠⣶⡀⢠⣤⣰⡆⠘⢮⣯⠟⠁⠀⢰⡾⠀⠀⠀⣠⡆⢠⡘⠛⡛⠀⣤⠸⣍⠆⢹⣧⡀⠀⠂⣁⠀⡦⠸⣷
⠀⠀⠀⢰⣿⠈⠁⡐⠃⣼⡟⢿⣥⡄⢈⠉⠁⠀⠲⡿⠀⢀⡀⠈⠀⠠⠆⠀⠘⠻⠈⢠⡄⠁⡀⣿⣠⣦⠀⢸⣿⡇⢈⡠⣿⣦⣄⡀⡄
⠀⠀⢀⣤⡙⣇⣼⠋⣀⢈⣥⠀⣀⠀⣿⣾⢠⣄⡀⢰⠂⠀⠁⠀⣤⠀⠀⢤⡄⠀⠠⠊⢹⡄⠛⢷⣿⢃⠒⢸⣿⡇⠘⣿⣿⣿⣟⠁⢳
⠀⠀⠙⠛⠿⠾⣧⠞⣋⣤⠁⠰⣿⣼⢸⣣⡿⠟⠀⡎⠉⠀⠦⠀⠀⠀⠶⠀⠀⠀⠀⠴⢿⢱⠁⠶⣿⠟⣁⠘⠛⢁⣄⣉⡳⠄⡀⣼⡆
⠀⠀⢺⣄⡛⠛⠻⠋⠉⡭⠤⠐⠛⠻⣼⠏⠀⠶⠾⠟⠋⠀⠀⠠⢤⡄⠀⠤⠄⠀⠠⢶⣿⠰⢤⡁⠤⠀⢩⠀⠛⠀⢬⠍⢡⣴⣷⣯⡾⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠘⠈⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠂⢄⠀⠀⡍⠂⣈⠀⠐⠁⠀⠐⣆⠀⡀⠤⠐⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠓⠀⣋⣀⣈⣀⣈⣈⣀⣈⣁⠈⠂⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣗⠐⢉⣃⢀⣠⠂⣸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠁⠀⠼⠿⠿⠿⠿⠿⠿⠿⠦⠈⢳⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠠⠏⠓⠲⠸⠸⠄⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⡟⠠⢉⡅⠂⡀⣀⢄⠴⣡⠂⢀⡆⠸⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠰⠆⠒⠒⠐⠂⠲⠒⠂⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠃⠀⠤⠌⠁⠁⠀⠊⠀⠀⠠⠢⠉⠀⠙⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡦⢎⣡⢰⢹⢼⠙⡶⣂⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠛⠻⠘⠀⠸⠉⠠⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠄⠰⡄⠤⠂⣿⠀⡀⠀⠀⠀⢀⣔⠄⠀⡀⠀⡤
⠀⠀⠀⠀⠀⠀⣀⠠⠦⠄⠀⠀⠀⠙⠉⠆⠨⡍⠁⡰⢀⠈⡏⠐⢄⠀⠀⠀⠀⠀⠀⢸⡇⠈⠩⠭⣭⣥⠀⠃⡤⠤⠃⠊⣉⡉⢩⣀⠀⣈⢀⣀⠂⡀
⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠉⠀⢨⠤⡊⡡⡄⢘⢑⠯⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠑⡚⢻⠀⢠⡇⢀⡙⠙⠙⠧⠟⠪⠜⠓⠙⠚⠖⠁
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠰⠒⠃⡈⠁⠘⢈⠃⡐⠃⠒⢁⠀⠀⠀⠀⠀⠀⠀⢒⣀⣀⡀⠠⣸⡄⠃⠈⡁⠀⠰⠦⠀⠀⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢩⠁⢀⡔⢻⠀⠰⠶⠀⠈⠁⡛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠈⠀⠺⠀⠀⠀⡇⢠⢶⡤⢂⡐⢶⠓⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⢸⠀⢾⠗⠺⡔⠻⣋⠴⢊⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠘⠀⠀⠀⣅⡠⠥⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣀⡀⠀⠠⠀⣄⢄⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠦⠀⠤⡅⡴⠣⡖⠓⢞⠈⢢⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⣶⠀⠂⢠⢀⡄⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠄⠀⠉⠃⠂⠁⠀⠀⠈⠂⠣⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡏⠀⠃⠘⣾⢁⣟⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠂⢁⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⣙⠉⠁⠀⡀⢀⠉⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠐⢸⠀⣿⢸⣹⠆⣇⡾⢸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⠀⠀⡁⠌⠉⠀⠐⡂⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠄⢸⠀⠷⠤⠅⠀⠘⠃⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠄⣀⠀⡀⠠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡀⢰⣛⡆⠶⢳⡄⣇⡼⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢸⡋⣳⠰⣿⡇⡏⢧⢸⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠹⢀⡠⣤⠤⠤⠤⢢⡀⠶⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⠁⠈⠉⠁⠀⠈⠁⠁⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠓⠲⢤⣀⠀⢀⡴⠋⠛⢲⣄⠀⠀⣀⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⠳⠞⠀⠀⠀⠀⣿⡷⠚⠁⠀⢀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣬⣇⠀⠀⣄⡀⠀⣰⣷⣄⡀⢀⡴⠃⣠⣾⣿⠋⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⢸⡇⠀⠀⠀⣿⠀⠀⢿⣿⠷⣿⡿⠉⠛⢿⠃⣴⣿⡟⠁⢀⡴⠚⠉⠀⠀⠈⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⢈⣿⣾⠃⠀⠀⢰⣿⣅⣀⣈⣙⡶⠖⠶⢤⣀⠸⣶⣿⡟⠀⣰⠋⠀⠀⠀⢀⣴⣾⠄⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⢠⣾⣿⡭⠟⠛⣿⠁⢀⠀⠀⢈⣷⠬⠿⢇⣼⠃⠀⠀⠀⣴⣿⡿⣿⠀⠀⢰⣿⣧⡀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠂⠀⠀⣠⣿⠋⠀⢀⣴⣿⣿⡅⠀⠀⣼⣿⣦⣿⠀⠀⠈⢁⠀⠀⣼⠃⠀⠀⢀⣾⣿⠟⠀⣏⣀⢀⣴⣿⡿⠃⠀⢀⡾⠳⣦⡀
⠀⠀⠀⠀⡼⠀⠀⠀⣰⣿⠀⠀⠀⠟⠁⠀⠴⠛⠋⠉⠉⠀⠀⠀⣾⣿⡽⠋⠀⠀⢠⣿⠀⢰⡇⠀⠀⠀⠸⠻⠿⠦⠤⢬⣛⡿⠿⠟⠀⢀⡰⠋⠀⣸⣿⡇
⠀⠀⠀⠀⡇⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⣀⠀⠀⠉⣉⣴⠀⠀⣰⣿⣿⡀⠈⠀⠀⠀⢀⡀⠀⢰⣶⡄⠀⠈⣿⣆⣠⠴⠋⠀⠀⣴⣿⡟
⠀⠀⠀⠀⢧⠀⢠⣿⡿⡇⠀⠀⠀⣴⣾⣿⡟⠀⠀⠀⣰⠿⢿⣿⣿⠿⠿⠷⠶⠿⠿⠦⠷⠶⠀⠀⠀⢸⣷⣦⣀⡉⠁⠀⠀⠉⠉⠀⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠘⣦⣿⡿⠁⡇⠀⠀⠀⢹⣿⣸⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢨⣿⣿⣽⠏⠀⠀⣰⣶⣶⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠈⠻⠃⠀⣿⠀⠀⠀⠀⢿⣿⣄⣀⣤⣾⠏⠀⠀⢀⣀⣤⣤⣶⠾⢿⣻⣿⣿⣿⢷⡀⠀⠀⣿⠟⠃⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⣿⡌⠛⠻⣯⣤⣶⣿⣿⠿⢋⣩⣴⣾⣿⠿⠛⠉⠁⠀⠻⣤⡀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⣿⣿⠀⠀⠉⠛⠋⠻⣷⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰⣴⣶⣤⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠘⣿⠀⢀⣀⣀⡈⢻⣿⠀⢿⣿⡆⠀⣌⣉⡳⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⢰⠟⠀⢻⣿⡿⠋⣠⡟⠁⢀⣿⣿⠀⣀⠀⠀⠈⠉⢦⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠙⠁⠀⠻⣿⢠⣾⣿⣿⣿⣿⠋⢸⣷⣤⣀⡀⠈⠐⡀⠈⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⢀⣿⠁⢾⣿⣿⣦⠀⠈⠛⢿⣧⠁⠙⡆⠀⠹⣿⣿⣿⡷⠂⠩⠄⠈⠉⢳⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠋⠛⠃⠀⢸⣿⣤⣶⡄⠈⠁⢀⣶⠀⢸⣿⠃⠀⠁⠀⠀⣿⣿⣿⣷⣤⣤⠀⠀⠀⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⠘⠢⡀⠀⠀⠀⠘⠛⠻⠋⢵⣦⣠⣾⣿⣷⣌⠁⠀⡆⠀⠀⠀⠛⠁⠙⠛⠛⠉⢀⠀⠺⢗⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣠⡄⠀⠀⢀⣤⡤⠴⠏⠉⠙⠛⠉⠙⠳⢦⣴⣶⣤⠄⠀⠀⡀⢀⡀⢀⣠⣶⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠸⠿⠁⢠⣾⣿⣶⡀⠀⡇⠀⢠⣿⡟⠋⠀⠀⠀⢀⠋⠈⣿⣿⡿⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⠀⠀⠀⣤⠀⠸⣿⡟⠿⠿⠾⢻⡆⠈⣩⣥⡀⠘⠃⢀⣤⠀⠸⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡄⠀⠻⣷⠖⠀⠀⢸⡇⠀⠘⢿⣿⡄⠈⠻⣿⠀⠀⣿⣿⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣍⣹⠇⠀⠀⠀⠴⠁⠀⠀⠀⢸⣿⣄⡀⠀⠀⣀⡴⠚⠃⠀⠰⢂⣿⡇⠀⠀⢨⡗⢤⠀⠀⢤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠻⣷⡔⢀⠀⣾⠀⠒⠀⠀⢸⣿⡿⠿⠛⠛⢿⡄⢠⠀⠀⢰⣿⡿⠀⠀⠀⠀⢱⣤⠴⠛⢳⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡏⠀⠈⠀⠟⠀⠀⠀⣠⣿⡟⠁⠀⠀⣀⡄⠀⢀⣴⣠⡞⠁⠀⠀⠀⢠⡄⠿⠁⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠇⡜⠀⠀⠀⢰⣶⣿⣿⢿⣇⠀⣠⡾⠟⠁⢀⡾⢻⡟⠀⠀⠀⠀⢁⡘⠇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⢷⣷⡄⠀⠐⣿⣿⣿⢏⡼⠃⢸⣿⣷⣄⠀⠙⡇⢸⡧⠀⠀⠀⠀⠀⠀⠛⣶⣤⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⠉⠀⠀⠈⣿⣧⠂⠠⠐⠊⠉⠁⠛⠂⠀⠈⡌⠳⠆⣤⡄⢀⠀⣤⣤⣿⣿⠀⢀⣀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢶⡀⠙⠿⡧⣠⠄⣤⠀⠈⢉⢵⣶⣶⣤⣤⠀⠀⠀⠀⣤⡿⠀⣤⣵⣶⣿⣿⡿⠋⠉⠉⠀⠀⣿⣿⣿⡶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠸⣿⣤⡀⠀⠀⡀⣿⠀⠀⢠⠀⠹⣿⣿⣿⠀⠀⠀⠰⠀⠀⣀⣀⠉⢿⣿⡁⠰⣿⣿⡆⢀⡖⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⢄⠀⠙⣅⠀⠀⠀⠀⠀⢻⣿⣿⠗⠀⠀⠀⠐⣿⡿⢿⣧⠘⠿⠷⠀⠘⠋⢠⡎⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡼⠀⠀⠀⠑⢄⠿⠑⢤⡀⠀⠀⢈⢿⣥⡶⠒⠀⠀⢴⠏⢀⠀⠛⠀⠂⠀⠀⠀⣤⡈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠆⠀⠋⠀⠀⣴⣾⣿⠁⠀⢈⣃⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠶⠀⠀⠀⣀⣀⠀⠀⠀⠀⠻⣿⠛⣿⠃⠀⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢰⣿⠙⢮⣯⠐⣆⡰⢶⠶⠛⠛⠁⠀⠀⠀⠀⢈⣤⡿⠃⠀⠀⠀⠀⢴⡏⠀⠘⠇⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠛⣤⠍⠁⠀⠀⢀⣆⠀⠀⣀⡀⠀⠈⠻⣇⠀⢠⣾⡆⠀⠘⠁⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⠒⢦⠀⠀⢸⡟⠀⣼⣿⣿⠀⣤⣾⠟⡠⣿⣀⠀⠀⠀⠀⢠⡉⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢛⡃⠀⡼⢃⣴⣧⠈⠉⠄⣴⣆⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡀⠀⠀⠐⣤⣤⠀⠀⠀⠓⡈⠉⠳⠄⣶⣶⡯⠈⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠀⠀⠀⠈⠁⢠⣦⡀⠀⠱⠆⠀⢸⠟⢫⣴⣿⠟⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⣿⣶⡖⠀⠀⢴⣤⣦⣠⡄⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⣯⠀⠈⣿⡇⠀⠀⣴⠃⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⢹⠄⠀⣯⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢦⠀⠀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⡼⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⢀⡾⠁⢠⠇⠀⣶⣟⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠃⣸⠃⢀⠞⠀⠀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⡰⠃⠀⣿⡠⠊⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⣿⡇⠀⡠⢶⠀⢠⡞⡡⠃⢸⡏⠀⠀⢸⡏⠀⠀⣰⠇⡖⢲⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⣿⡇⡰⠁⣾⠀⣾⠋⠀⠀⡼⡇⠀⢀⣾⡇⠀⢀⣿⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⣿⠃⠀⣿⢀⢿⡄⢀⠜⠀⠻⣄⠞⠘⢧⡠⠋⢿⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠻⠋⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠔⠀⡄⢀⣾⣏⣿⡄⠀⢠⠞⠘⡆⠀⣠⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠐⠢⢀⠀⢠⡏⠀⡴⠁⠀⠀⠀⠀⠀⢠⡟⠀⡼⢁⡾⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠀⢩⡀⠛⠘⠁⣾⢠⠞⠀⠀⠀⠀⠀⠀⠀⣾⡃⠞⠀⣼⠇⠀⡰⠃⠀⠀⠒⢠
⠀⠀⠀⠀⠀⠀⠀⢴⠆⣈⠁⠀⠀⢠⡿⠁⠀⠀⢠⡏⢡⡄⠀⠀⣿⠁⠀⢰⣿⠔⠊⠀⠀⠆⠦⢐⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⢾⡇⠀⣀⠴⣿⠁⣸⡇⠀⡼⣿⠀⠀⢸⡏⠀⠀⠀⣰⠀⠀⢈⡄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡟⡅⠀⠀⣿⣠⠛⡇⢰⠃⢻⡄⠀⡾⣿⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⣼⠀⠀⠈⠁⠀⠛⠃⠀⠈⠳⠞⠀⠻⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡤⠄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣦⢀⡶
⠀⠀⠀⠀⠀⡀⢀⠀⢸⡇⠀⠀⡘⠇⠐⠥⢠⡟⠀⠀⠀⠀⠉⠼⠶⠂
⠀⠀⠀⠀⠀⠙⣊⢃⢸⣧⡀⠀⠀⠀⣠⡄⢸⣇⠀⢨⡅⢀⡤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⢿⣆⠈⣷⣀⣿⠀⠸⣇⠀⢸⡇⢿⡂⠀⣿⠀⠸⣠⡶⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠁⠉⠉⠀⠙⠂⠀⠁⠈⠁⠀⠸⡧⠀⢿⡁⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠠⠤⠶⠀⠀⠀⠴⠋⠀⠀⠀⠀⠦⠞⠣⠄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢢⡉⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠻⠀⣀⡀⠀⣦⠀⢀⡀⠀⠀⠀⠰⡀⠀⢠⠠⠀⠀⠀⣾⠀⣠⠄⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢹⡆⣼⠦⢤⠀⣷⠀⢠⡇⠻⣦⣠⡾⠀⣿⢰⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠳⠀⠘⠃⠻⠂⢸⡅⠀⠈⠃⠳⠄⢻⣸⣧
⠀⠀⠀⠀⠀⣤⠍⣁⠀⠀⠀⠀⣼⠃⠠⢀⣀⠀⣠⠄⣀⠀⠀⠀⠀⣀⠐⡀⠈⢧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠶⠞⠁⠀⡶⡍⠁⠀⢱⠇⠙⠃⠀⠀⠀⢫⡌⠳⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⣀⡀⡀⢔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠋⠀⠀⠀⡀⠀⠀⠀⠈⣀⠀⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣦⠀⠈⣧⠘⣧⢠⡏⠀⣼⠁⣰⣾⠁⠀⠙⣳⠆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⢸⡇⠀⢿⣀⠘⡇⠀⠀⢰⡏⠀⠘⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣿⠌⠓⠀⠈⠋⠀⠀⠀⢲⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠘⣇⠀⠀⣾⠀⠀⠀⠀⠀⠴⠋⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠃⠄⠹⣆⠀⣿⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢄⢹⡆⣿⠀⢰⡆⡠⢸⡇⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠀⢺⣆⡇⢻⠀⢾⡁⠂⢸⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠈⠀⠉⠞⠀⠈⠋⠀⠁⠀⢸⠇⢀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⠀⠀⢀⠀⠀⠠⡇⠀⠀⠀⠀⡀⠀⠈⣀⢀⡇⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⡏⢰⠃⡆⠑⣶⠀⢰⠄⡇⣴⠀⣿⢸⡇⡇⢸⡄⠂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠃⠘⠀⢇⠀⣿⠀⠘⢠⡇⠛⠀⠉⠈⠃⠀⠘⣇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏




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

⠀⠀⠀⠀⠀⠀⠐⢿⠀⡀⠀⢀⠠⠠⠠⢀⠀⠀⠀⠀⠀⠀⠠⡶⡀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄
⠀⠀⠀⠀⠀⢀⣤⣼⣦⣧⠄⠱⣀⣤⣴⣄⡄⠀⠀⠀⠀⠀⠀⢨⠷⡻⡽⠶⡙⠓⠀⠀⠀⠀⠀⠀⠀⢀⠄⣁⣀⣄⡀⡀
⠀⠀⠀⠀⠀⠈⢇⠀⣧⠣⣎⡿⠐⢶⢀⣎⢇⠀⠀⠀⠀⠠⡿⡐⠀⣶⠒⣀⢈⡀⡇⠀⠀⠀⠀⠀⠀⠘⠋⢉⡉⣍⡛⠁
⠀⠀⠀⠀⠀⣴⣌⣓⣁⣤⠀⣴⣤⣰⡥⡄⡾⠋⠀⠀⠀⠀⠂⣇⣸⢿⠈⣿⠀⡇⠃⠀⠀⠀⠀⠀⠀⡖⠦⡦⠲⠴⠐⢺⠆
⠀⠀⠀⠀⠀⠈⡍⢍⡉⠈⠀⠐⡐⠐⣒⠂⠒⣤⠀⠀⠀⠀⠀⢀⠀⢐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠟⠂⡁
⠀⠀⠀⠀⠀⠈⣟⣘⣳⣶⣛⣶⣿⣿⣭⣧⣤⣷⠀⠀⠀⠀⡇⢘⣶⣥⣛⣴⡆⢠⣆⠀⠀⠀⠀⠀⢠⡀⣀⡋⠛⣋⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠈⠁⠘⠉⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠄⣇⢘⡟⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣧⣶⣿⢧⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠤
⠀⠀⠀⠀⠀⣠⡄⠀⢈⡁⠲⠦⠈⢠⣄⣄⡀⠀⠀⠀⠀⠴⠂⡶⠒⠁⠈⠈⢩⠀⠀⠀⠀⠀⠀⠀⢻⠦⠐⠘⠟⠲⠧⠆
⠀⠀⠀⠀⢐⣿⡏⠰⣟⢡⠄⣤⣾⠉⢙⣿⡇⠀⠀⠀⠀⠀⠸⠥⠼⣾⠾⠚⠞⠀⠀⠀⠀⠀⠀⠐⠒⣂⣐⣒⠀⡂⠀⠒
⠀⠀⠀⠀⠈⠻⡿⠀⡹⡍⠉⣉⠎⠁⠘⠏⠁⠀⠀⠀⠀⠀⣠⠀⠉⣉⢉⠛⢁⡀⠀⠀⠀⠀⠀⠀⠈⡩⣏⣍⠩⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⣰⢧⣦⡀⠀⠀⠀⠀⠀⠀⠻⠐⣁⡼⡟⣗⢸⠇⢸⡆⣩⠀⠀⠀⠀⠀⣶⡀⡍⣉⡀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠚⠻⠋⠙⠥⠂⠀⠀⠀⠀⠀⠀⠰⣌⠐⠐⠐⠒⢒⡰⠂⠀⠀⠀⠀⠀⠀⣹⣓⠓⠃⠿⣛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣶⡀⠀⣸⡇⠀⠀⠀⢰⢿⡄⠀⠀⢀⡴⠶⢦⠀⠀⠹⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⢳⣰⠇⣿⠀⠀⠀⣾⠴⣧⠀⠀⣾⠀⠀⠈⠀⠀⠀⡆⠀⠀⢰⡄⠀⠀⡼⠀⠀⢸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡿⠀⠋⠀⢸⡄⠀⢰⠇⠀⢹⠄⠀⢿⠀⠒⣲⠆⠀⢰⡇⠀⠀⡾⠹⡄⢰⠃⠀⠀⢸⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣠⣴⠶⢦⠀⠀⠠⣄⡀⠀⠀⢠⡀⠈⠓⠒⠋⠀⠀⢸⠁⠀⢠⡇⠀⢻⡟⠀⠀⠀⢸⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣶⣿⣷⣦⣿⣶⣤⣀⡉⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠁⠀⢤⣾⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⢿⣿⣿⣶⣶⣦⣤⣤⣴⣿⠷⠖⠒⠁⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠆⠀⠀⠀⣿⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⢀⣼⠟⠁⣠⣤⠀⠀⢸⡟⠀⠀⠀⣰⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⣤⠀⠀⣾⠇⠀⠀⡠⠸⡇⠀⢰⣿⠏⠀⠀⣾⠇⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⣹⠏⠀⠀⢻⠀⠠⠀⠀⢀⠀⠀⣼⠏⠀⡀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠔⠁⠀⠀⢠⡏⠀⠂⠀⠀⠀⠀⠀⠒⠀⠠⠀⣿⠀⠈⠀⠀⢹⡄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⣀⣈⠐⠐⠀⠀⣀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⢀⡗⠀⠀⢰⡏⠙⠗⠀⠀⣿⠉⠉⢻⡄⠀⠀⣿⠀⠀⠀⡟⠉⠛⣦⠀⠀⠀⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣷⡀⢸⡇⠀⠀⠈⠙⢦⡀⠀⠀⣿⣀⣠⡾⠁⠀⠀⣿⠀⠀⠀⡇⠀⢀⡿⠀⠀⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠈⢷⣸⠁⠀⠀⣀⠀⠀⣷⠀⠀⣿⠉⠁⠀⠀⠀⠀⣿⠀⠀⢸⣷⣖⠋⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠿⠀⠈⠿⠀⠀⠀⠛⠶⠞⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠇⠉⠳⣦⡀⠀⠀⠷⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⣀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⣴⠋⠆⠀⠀⠈⠙⠓⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⠀⢀⢒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⣠⣶⡦⠀⠀⠀⣿⠀⠀⠀⠀⠒⠊⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡏⠀⠀⠀⠀⢠⡿⠋⢁⣤⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢀⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⡿⠁⠀⢸⡿⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢿⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠘⢷⣄⠠⠈

⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡆⠉⢡⣤⣭⣿⣶⠟⠣⡄
⠀⠀⠀⠀⠀⣺⡇⠄⠀⠀⠠⣤⣤⠎⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠲⢶⣿⣦⣀⣴⣷⣤⢨⠿⣶⢟⠉⣇
⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⣄⣀⠀⠀⠀⣴⣶⡄⠠⣼⣍⠐⣿⣙⣿⣿⠾⡛⢯⡜⠡⣿
⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⡄⣿⣿⠀⣟⣛⣻⣿⢸⡟⠛⢓⣲⣿⣦
⠀⠀⠀⢴⣿⣿⡇⠀⠀⡄⣴⣶⡄⠙⢛⠇⠀⣠⡆⠀⠀⢀⠆⠀⠀⣿⣿⢻⣿⣾⣿⠀⣷⣿⣿⣶⣤⡀⠰⡎⢠⣿⣿⣀
⠀⠀⢤⣾⣿⣿⡇⠀⠀⡼⢫⣿⢷⣤⣼⡄⠈⠸⡇⠀⢰⣷⡄⠀⠀⣿⣿⠈⢿⣿⣿⠀⣿⣟⣛⠛⠿⢛⡶⣣⣼⣿⣿⡏
⠀⢠⣽⣿⣿⣿⡇⠀⠀⣃⣸⢿⣦⣏⢩⠁⣼⣶⡄⠀⢸⣴⡇⠀⠐⠋⡉⠀⠀⠻⠿⣸⣿⣿⡿⣿⣆⢸⡀⡉⠐⣿⣿⣷⡀
⣀⣀⣹⣿⣿⣿⡇⠀⠀⣿⣿⠃⢿⣿⣿⠀⢹⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⢸⣷⣿⣿⢨⣵⠖⠚⣿⣿⣿⠋
⠉⣹⣿⣿⣿⣿⡇⠀⠰⠛⠛⠂⠀⠙⠻⠂⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡘⢛⣿⣿⢀⣟⠀⠀⣿⣿⣿⡭
⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠋⠉⠉⠀⠀⣿⣿⣿⣿⡂⢀
⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⠁
⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡦
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⣤⡀⢰⣴⣶⡄⣠⡶⠶⣦⣄⠀⠀⠀⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⠋⠉⠀⠀⠀⣀⡤⠦⡀⠀⠀⠀⠀⠀⠀⢺⣷⠿⣷⣜⣿⣿⣷⣾⣿⣿⣳⣿⣗⣆⠀⣿⣿⣿⣿⣷⢦
⣿⣿⣿⣿⣿⣿⡇⠀⢈⣽⣄⠀⠀⡄⣰⡿⠀⣩⣥⣤⣤⣴⠂⠀⠀⢾⣽⣆⣹⣹⣿⣿⣿⣿⣻⣿⣷⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣷⣰⣟⢿⣷⣼⣽⣶⡚⢻⣿⡆⠀⠀⣾⣧⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⢠⣭⡿⣏⢿⣷⣍⣿⣷⣿⣾⠉⢀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣿⣿⣧⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⢈⣻⣷⣏⠀⣿⣿⣿⣏⢿⣿⣶⣌⣿⣿⡷⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠘⢸⣿⡟⠀⠛⠻⠿⢿⣼⡿⠿⠿⠿⠟⠁⠀⠠⣿⣿⣿⣿⡏⣿⣿⣿⣻⣿⣿⡟⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠸⣨⠟⠁⠠⣀⠀⠈⠉⠈⠀⠀⢠⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣴⣿⠇⠀⠀⠀⠀⣽⣿⢿⣿⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣦⣤⣄⠀⠀⢀⣤⣀⢠⠖⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⣇⢹⣷⡴⠁⠈⣿⠏⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡟⠈⣿⡇⠀⠀⣿⡇⠀⢸⡇⠀⠀⢀⡤⠄⠀⡟⡐⢀⣴⠂⢼⣡⣠⡿⠁⠀⣰⡶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⠀⣿⡇⠀⢸⡇⠀⠀⣿⣇⠂⠀⡹⠓⣿⠃⠀⠈⢡⡿⠁⠠⢺⡿⠁⡰⣿⠇
⠀⠀⠀⠀⠀⠀⣠⡶⠛⢳⡀⠀⢰⡖⢆⠀⠀⣿⡇⠀⠀⢹⡇⠀⢸⡇⠀⠀⢻⣧⣠⠔⠁⠸⣏⡠⠊⠀⠸⡧⠔⠀⢿⡥⠊⣼⠏⠀⠀⢀⡷
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡇⠀⢻⣇⢸⠀⠀⣿⡇⠀⠀⠉⠁⠀⠀⠻⠦⠴⠃⠀⠠⠤⠤⣤⣤⣴⣆⣀⣠⡤⠂⠀⠀⢀⣼⠯⠤⠤⠶⠟⠁
⠀⠀⠀⠀⠀⢸⣿⠈⠷⠞⠁⠀⠸⣿⡸⠀⠀⠀⠀⢀⣀⡀⢠⣾⠀⠀⠰⠆⠀⢰⡏⡁⠀⠀⣸⡟⠉⠉⠀⢠⠊⣀⣤⠞⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣾⠁⣇⢼⣿⠀⠀⣶⡆⠀⢹⣯⠀⠀⢀⣿⠁⠀⣠⠀⣈⠉⢉⠁⠀⠀⢀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⣿⣆⠐⠙⣷⡘⠷⣟⢸⣿⠀⠀⣿⠀⠀⠌⢿⣇⠀⢼⡇⠀⢀⣿⠁⣸⠆⢸⡇⠀⣴⠏⢠⣿⠁⢸⣇⠆⠀⢦⡀
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢸⣇⠀⢸⠈⣿⣀⠜⣿⣆⠌⣀⠼⣿⡄⢺⡇⣠⢾⡇⠀⡿⠀⣾⠁⢸⡿⠀⣼⡇⠀⠸⣿⡀⢀⡾
⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⡀⡔⠀⠀⠀⠀⢈⠽⠊⠁⠀⣿⡇⠈⠉⠀⠈⠀⠈⠃⠀⢿⠔⠻⠷⠊⠻⠤⢊⡀⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⡏⢿⠇⠀⠈⠋⠁⠀⠀⠀⡴⠁⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⡀⣰⣷⢠⣦⢰⣿⠀⠀⢀⡶⣳⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠀⠀⣾⣿⣷⢿⣿⠈⠿⢾⣿⠤⠄⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⡏⢹⡿⢸⣿⢠⡞⢹⠏⠀⠀⠀⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢶⣦⠀⠀⠀⠀⠀⠈⠉⠁⢾⣠⣿⣀⡠⠤⠴⠒⠒⠒⣾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣴⡆⣠⢛⣶⠀⣠⣶⠀⣴⢦⣶⠀⣿⠃⢠⣶⡄⢠⡤⡀⣸⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠯⢞⣿⠏⠁⣾⠏⢀⣿⢋⣼⣯⣾⡏⢸⡏⣠⣿⢋⣠⢻⣷⠊⣿⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡟⠀⠀⠛⠒⠉⠉⠁⠀⠀⢿⡠⠋⠉⠁⠈⠉⢰⢉⣿⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢪⡾⢻⠀⣰⡟⡇⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠇⢠⣿⡰⢡⡤⠀⣴⠶⢸⣿⠉⣠⡍⣤⢀⣄⠀⣤⠦⣾⡆⣴⠲
⠀⠀⠀⠀⠀⠀⠀⠦⢴⣿⢥⣄⣼⡟⢁⣿⠟⡠⣿⡆⠈⣿⡖⣿⢠⣿⢻⡿⢸⣏⢜⣿⢋⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠼⣿⠈⠓⠋⠙⠊⣴⢹⠇⡼⢻⡇⠙⠁⠉⢸⡧⢃⡔⢹⡏⠸⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⣀⠀⠀⢀⠀⢈⠁⠀⠳⠛⠀⠀⠀⠀⠀⢀⢘⣒⣋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⢠⡟⠙⡇⣰⠟⡇⣿⠀⠀⣿⠀⠀⠀⣿⣆⢰⣿⢸⡏⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠠⠴⠒⢂⢸⡇⠀⣄⣿⢶⡇⣿⠀⠀⣿⠀⠀⠀⣿⠻⠟⣿⢸⡗⠒⠀⢐⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠈⠷⡾⠋⠿⠀⠇⠿⠤⠄⠿⠤⠄⠀⠿⠀⠀⠿⠸⠷⠶⠄⠈⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⡀⠀⠀⢴⡞⠲⡄⢠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣷⢾⣧⢨⣿⠂⡶⢺⣿⢟⣿⡔⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡏⣾⡇⡼⣟⣠⠃⢸⡿⢸⣿⢰⡿⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢿⡼⠁⠈⠀⠀⠀⠀⠀⠀⠘⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣸⣿⡀⢠⣤⣿⣟⣿⠁⢠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠀⢹⣿⣿⢿⣧⠈⣹⡿⠉⣿⠀⣾⠏⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣟⢻⣷⠸⠿⠈⠈⠛⠀⠉⠁⠈⠛⠸⠿⣶⢄⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⠈⠻⠿⠋⠀⠀⣤⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠻⠷⢄⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣿⠃⡾⠀⠀⡤⠤⣼⡿⢄⣀⣤⡤⠞⠋⣠⣤⠀⠀⠀⠀⠀⠦⠹⣯⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡷⠀⢀⣼⡿⠁⢀⣤⡶⣦⠀⢰⣿⡧⠒⢲⡄⠀⢠⣶⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢉⣿⡦⠊⣹⣿⠁⢠⣾⠿⠚⢁⣴⣿⡟⣀⣠⣿⠧⠚⠹⣿⡀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⣠⠖⠁⣿⡇⠀⣿⣃⡴⢻⣏⣀⡴⢋⣿⢿⣎⣽⠟⠁⣠⠖⠒⣿⡷⠲⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣀⣠⠿⠁⠀⠉⠁⠀⠀⠉⠁⢀⣾⡏⠀⠀⠀⠀⠀⢿⣀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣀⢀⣀⣀⠀⢀⣀⣀⠀⣀⣾⣋⣀⡀⠀⣀⣀⣀⣀⠀⠀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⢿⠀⢻⣿⠀⢸⣿⡏⠀⣿⣿⠛⠛⠃⠀⣿⡟⠙⢻⣿⡀⣿⣿⠀⠀⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣤⠀⠀⢸⣿⡇⣸⣿⠁⠀⣿⣿⠾⠃⠀⠀⣿⣷⣶⣾⠟⠀⢸⣿⣄⣸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠋⠀⠀⠀⣿⣧⣿⡟⠀⠀⣿⣿⠀⣀⣠⠀⣿⡏⠉⣿⣆⠀⠀⠙⠛⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⣴⠀⠀⢻⣿⣿⡇⠀⠀⠿⢿⡿⠿⠿⠀⢿⡇⠀⣿⣿⠀⠀⣿⡇⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠀⠀⠈⠁⠀⠀⣠⣶⣿⡿⢿⣿⣶⣄⠀⠀⠀⠈⠙⠃⠀⠻⣿⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⣉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠈⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢿⡄⢰⡆⠀⣶⣦⣄⡘⠛⠃⠀⠀⠀⠀⠀⢸⣿⡄⠀⣾⣿⠀⢰⠆⣸⣟⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⠽⠆⠁⣼⣿⠟⢻⣿⣧⠀⣰⣶⣶⣶⣷⠀⣿⣷⠀⣸⣿⣇⠈⠺⢯⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣼⣿⡏⠀⢸⣿⡿⢀⣿⣿⣀⣿⣿⡄⠘⢿⣿⡿⣿⣿⡄⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣤⣴⣿⡿⠁⣾⣿⠟⠛⠻⣿⣷⠀⠀⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⣼⣿⡿⠀⠀⠀⣿⣿⣧⠀⠻⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣤⣤⣶⢶⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⢾⡏⣾⣯⣿⣇⢿⣧⣻⣿⣾⢿⣝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣫⠟⢳⣝⣧⣟⣻⡷⢶⣿⣭⣻⣿⣹⣟⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠁⠀⠀⠉⠛⠛⠛⠻⣷⡽⣿⣧⣿⣯⢿⣮⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠀⠀⠀⠀⠉⠉⠑⠂⠘⣷⡻⢿⣮⣟⡻⣮⣟⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀⣀⠄⡸⠀⢤⠀⠀⠀⢀⡄⠹⣟⡻⣮⡻⣿⣮⢿⣯⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠃⠀⠀⠙⠒⠚⠉⠀⠀⠁⠀⢸⣷⣿⣿⡾⣿⡏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡁⠀⠀⠀⠀⠀⣴⡄⠀⢀⣀⣤⣿⡟⣿⣿⣧⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠉⠉⠁⠀⠀⠀⠉⠁⠀⣸⣿⣯⣽⣾⡿⣻⣾⡟⣼⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠷⠶⢿⣷⣿⣿⣯⣾⣟⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⡀⠀⣴⣿⣻⡇⣰⣾⠏⢸⣿⢹⡿⢛⠛⡛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣩⣿⣿⣷⣿⠇⣿⠏⣴⢸⡇⢈⣴⡟⠸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡾⣫⣴⢶⡌⢿⣰⡏⣴⣶⢸⢃⡌⢿⡇⣾⣟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡟⣰⢯⣾⣇⣿⡼⠟⠻⢿⡟⢻⣾⡿⣾⣤⣍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⠁⣿⣿⣿⣿⠟⣰⣿⡟⣰⡟⣠⠄⣰⠟⣩⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣯⣒⣁⣿⡄⢿⣾⡾⢋⠰⡿⠟⢠⡟⣰⢋⣾⡏⣼⠏⣴⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡅⢹⣾⡿⠿⣯⣿⡶⣤⣶⣿⡷⣶⣷⣤⣾⡇⣾⡿⠇⢡⡾⢋⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣧⠘⠋⣠⣾⡟⢁⣴⣄⠹⣯⡞⢻⣷⢻⣿⣷⣬⣴⣟⣶⣾⣟⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⡿⠀⣾⢷⣿⠀⣿⣿⡿⢀⣿⠁⣾⣿⣼⡇⢸⡏⢈⣉⠛⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣇⣿⣇⣸⣿⡸⣯⠀⣿⡿⠃⣼⡏⢰⣿⣳⣿⠀⣿⠃⠸⠿⠇⢸⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣮⣛⣿⡿⠿⣿⣦⣄⣤⠾⣻⣧⠘⠿⠿⠃⣼⡟⢠⡄⢰⣾⣟⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣷⣭⣟⣿⢰⣷⣼⡟⣩⣍⣻⡿⣿⣷⣶⣶⣾⣵⣇⣸⣿⡀⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣽⣿⣿⣎⢻⣿⠃⠻⢿⣿⢰⣿⣹⡟⢰⣤⣽⣿⡟⣿⣷⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠻⠟⣸⣿⢸⣿⣿⡇⣼⡏⣿⠃⣙⣿⣯⣭⡾⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣧⣌⣛⣿⠁⠿⢿⡿⢸⣿⣿⣿⣽⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣾⣷⠾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣇⠀⠀⠀⠆⢢⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠸⣿⣿⡄⠀⠂⠁⣨⡕⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⣿⣷⡀⢀⠐⠋⠐⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢸⣷⣶⣎⠘⠂⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⣈⢛⢹⠿⠶⢱⣤⡢⢜⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⣌⢠⡄⢡⠃⠿⣤⠚⠁⣀⢹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣭⣾⣷⣶⣾⣤⡬⣠⣵⢦⣿⣧⣯⣴⣤⣹⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⠧⠠⣾⠟⡺⠜⠆⠁⠈⠁⠐⣼⣺⣿⣿⣏⠁⢴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡟⠒⠁⠀⠀⠀⠀⠀⢀⡠⠙⢻⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠂⠝⠃⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡚⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⢀⣇⣀⠀⠀⣀⢀⡀⢀⣀⡀⢀⠀⡀⠀⠀⢀⠀⡀⢀⠀⢀⣄⢀⣀⣀⢾⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⠀⣿⡈⠀⠀⡟⢸⡇⣟⢹⣇⣼⢀⡇⢀⠀⢸⠀⡇⢸⢰⠋⣶⢸⡏⢹⢸⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⣷⠀⠀⠙⢻⡗⠙⠛⠉⠙⠋⠙⠁⠀⠘⠛⠙⠋⠈⠛⠛⠛⠁⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⠀⠀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⢀⣀⠀⠀⢤⡄⠀⢠⡄⠀⢀⣀⣀⢀⣀⣀⣀⡀⣤⡄⠀⣀⡀⣀⡀⢀⣤⠀⢀⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠈⠀⣟⠈⢷⠀⢸⣧⠀⢸⣇⠀⡏⠉⠙⠈⠁⣿⠀⠁⢸⠀⠀⢽⠀⢸⠁⢸⣷⡀⢀⡇⢀⡞⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢰⡏⠳⢼⡤⢼⠹⣆⡏⢿⠀⡇⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⢸⠀⢸⡏⣧⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⠘⡇⠀⣸⠀⢸⠀⠿⠁⢸⠀⡷⠆⠀⠀⠀⣿⠀⠀⢸⡶⠶⢿⠀⢸⡀⢸⡇⠸⣾⠀⢻⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣡⡼⠀⠙⠶⠋⠀⠸⠆⠀⠀⠘⠃⠷⠤⠗⠀⠀⠿⠄⠀⠸⠧⠀⠾⠆⢸⡇⠸⠇⠀⠻⠀⠈⠳⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠖⣗⣤⠀⣠⣄⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣀⡟⢸⣇⣷⠏⣸⠁⣇⣠⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⣼⣇⠠⣴⡤⠀⣠⡶⢦⡀⠀⠚⠛⡟⠙⠛⢶⣄⠀⠛⣿⠋⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⣿⠀⣿⠀⠀⣿⠀⠀⢻⡄⠀⠀⡇⠀⠀⠀⣿⠀⠀⣿⠀⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢻⡀⣿⠀⢰⡟⢧⣄⣸⡇⠀⣠⡧⠀⣠⡾⠃⠀⠀⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣼⠃⢸⣷⡇⠀⢸⡇⠀⠉⠛⡿⠛⠉⣿⠛⣿⠀⠀⠀⠀⣿⠉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠀⠘⣿⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠘⣧⠀⠀⠀⣿⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⢿⣄⣠⡾⠁⠀⠀⣿⠀⠀⠘⠷⡤⠀⣿⠀⠀⠈⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠉⠀⠀⢀⠀⠉⠉⠀⠀⠀⠺⠿⠂⠀⢀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠳⣼⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢸⡟⢳⡿⣷⢸⢯⡇⠀⠀⡇⢸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡌⠷⠟⠋⠘⠷⠃⠀⠳⠛⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠠⠀⣎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⡀⣿⠀⣟⢶⢰⣶⣶⣶⡆
⠀⠀⠀⠀⠄⣠⢄⣤⣀⣨⣌⣡⣀⣤⠄⠠⠀⠀⠀⠀⣤⠈⣥⢀⣠⡀⣉⢩⡝⡈⣠⠄⣘⣡⡀⠀⠀⠈⠋⣤⠭⣤⢭⠬⠬⢭⡅⠩⢁⣴⡀
⠀⠀⠀⠀⠀⢙⡦⡟⠻⢿⡸⢻⠗⢿⡄⠀⠀⠀⠀⠀⣿⠀⣿⢸⡇⡐⢻⣸⣇⡇⣿⠀⣿⣞⠁⠀⠀⢠⡯⣹⢓⡟⣸⣇⡟⠛⢱⢷⣯⢉⡅
⠀⠀⠀⢤⣦⡄⣦⣀⢦⡶⣤⠶⣴⠶⢄⣰⡀⠀⠀⠀⠉⠀⠉⢁⠌⠀⣌⢡⡍⠀⣭⠁⢉⡈⠁⠀⠀⠘⠓⢛⣞⣲⠛⠃⠛⠀⢙⡻⡙⣛⡂
⠀⠀⠀⣈⢋⢁⣉⢉⣈⣋⢈⢃⣙⠈⡈⢛⢁⠀⠀⠀⢰⣿⡆⣿⢰⡄⡇⢸⣷⡀⣿⠀⢾⡷⠀⠀⠀⠈⡏⡽⠆⡄⢩⡉⢁⣤⢤⠰⠹⡸⡃
⠀⠀⠀⠟⠸⠆⠿⠸⠿⠘⢾⠸⡸⠻⠲⠻⡾⠀⠀⠀⠀⠀⠀⠈⠉⠠⠥⠌⠈⠡⠍⣠⣤⠀⠀⠀⠀⠘⠓⠻⠒⡂⠀⡀⠀⡀⠐⠐⠛⠒⠛
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⡀⢰⣷⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠛⠛⠀⠀⠀⠀⠀⠺⠿⠸⠳⠹⠿⠨⠗⠚⣾⠸⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⠀⡤
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢧⠸⡇⣿⢠⡇⣰⠃⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⠠⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢤⡳⣌⣧⢳⣿⣸⣱⢣⢞⡡⠆⠀⠀⠀⠀⣄⡀⢺⣠⡇⡀⣠⡄⣿⡀⠀⢠⡀
⠀⠀⠘⣧⠘⡇⠀⡞⠀⢻⢸⡃⣟⠰⡏⣿⠀⠀⠀⠀⢠⢀⢩⣈⢬⣨⢌⣠⢁⣥⡉⣠⠄⠀⠀⢀⡤⣟⢁⠸⠈⠃⠃⢻⡇⡋⠷⠀⢾⣿⢇
⠀⠀⠀⡜⣧⣁⢰⡆⡀⠀⢀⡦⢸⣆⣠⠌⠁⠀⠀⠀⠸⠼⠤⠻⠤⠻⠯⠹⠼⠷⠃⣬⠗⠀⠀⠈⠳⣆⣞⣴⣆⣴⣎⣴⡾⣵⣾⢸⣆⣶⣯⡆
⠀⠀⠀⣙⢿⣃⠘⢂⣓⡁⠀⣃⠘⣑⠛⣀⣀⡀⠀⠀⢀⡤⣾⢩⠀⢢⡤⣃⡤⣱⢺⣼⠆⠀⠀⠙⠚⠉⠉⡉⠉⠁⡉⠉⠉⠉⠉⠈⠉⢉⠁⠉
⠀⠀⠘⣿⠋⣿⢶⣿⠉⣿⣼⣿⣆⣿⢸⣿⣉⠁⠀⠀⠘⠒⠓⠛⠊⡿⠘⠙⠛⢨⡆⠛⠂⠀⠀⠀⠀⠀⠘⠛⢐⡭⠒⠋⠉⠙⢪⠢⠤⠜
⠀⠀⠀⣿⣋⣿⠜⣿⣀⣿⠑⣿⠹⣿⠈⣿⣉⡀⠀⠀⠀⠀⠀⢰⠒⢷⣲⢶⡶⡆⠀⢠⡦⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠠⠠⠜
⠀⠀⠀⠁⠈⠁⠀⠀⠉⠀⠀⠁⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⡇⠀⢀⠄
⠀⠀⠀⣀⠀⣾⡇⣲⡀⢀⠁⣀⠀⢃⡀⢱⣆⡀⠀⠀⢠⡌⠟⢿⢱⣄⢠⢀⣤⣄⣦⣬⡋⠀⠀⠀⠀⠀⠄⣀⠢⠁⠀⠀⠀⠂⠔⣀⠤
⠀⠀⠸⣏⣱⠏⣼⠉⣻⣾⢟⡿⣰⡿⢋⠎⡾⣡⠀⠀⣤⡀⠀⠀⢸⡏⢹⠻⣗⡁⣿⢾⠀⣤⠀⠀⠀⢀⣀⢠⣉⣀⡀⢒⡀⢂⢁⠠⣀⡀
⠀⠀⠀⠟⠙⠋⠛⠚⠁⣛⠈⠛⠙⣳⠋⡀⠛⠁⠀⠀⠇⣿⡆⢛⡴⢦⣰⢄⡦⣠⢶⡶⣸⠏⠀⠀⠀⣸⣟⢸⣿⣟⡇⡏⢿⢹⣾⣑⡯⡟
⠀⠀⢠⣰⣆⡥⣾⢱⡆⣷⢘⣷⡆⣿⠠⣀⣆⡤⠀⠀⠀⣿⣰⠻⠧⠞⢿⣾⠵⠿⠺⠷⠿⠎⠀⠀⠀⠙⠛⠙⠛⠛⠋⠛⠛⠛⠘⠋⠓⠛
⠀⠀⠐⠛⠛⠂⢙⡿⠃⠿⠸⠻⠇⠛⠀⡛⠛⠃⠀⠐⡓⠈⡁⣀⠀⡂⠺⡋⠀⣀⢀⡀⢐⡃⠀⠀⠀⡇⣴⢎⡱⣧⢼⠀⠘⢇⡙⣼⣿
⠀⠀⠀⠀⠄⠐⠀⠀⠉⠉⠀⠀⣀⠀⣺⣿⠇⠀⠀⢰⣧⣿⣿⡏⣽⣧⣿⣿⣿⡏⠹⣏⠻⣍⠀⠀⠀⠀⣴⣤⢠⠤⣬⣤⢤⣤⠠⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠃⠙⠉⠁⠉⠁⠁⠛⠈⠋⠈⠋⠀⠀⠀⠀⠉⠁⠘⠂⠋⠙⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⢀⣾⣿⠏⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⢠⣿⣿⠏⢀⣴⣿⠿⣿⡇⢀⣶⣿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⢠⣿⣿⠏⣰⣿⣿⢣⣾⡿⢣⣿⣿⠋⣠⡾⠁⣠⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣷⡄⠀⠀⠀⠀⠀⣿⣿⠏⢰⣿⣿⠃⠘⠿⠇⣿⣿⡧⠾⠋⠀⢀⣿⡿
⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⣠⣿⣿⢃⣴⣶⣦⡀⠀⣿⣿⡀⠘⣿⣿⣄⣀⣤⠞⠻⣿⣄⠀⢀⣠⣾⠟⠁
⠀⠀⠀⣼⣿⣿⡿⠁⢠⣾⣿⡟⠁⣼⣿⡅⣸⠇⠀⠈⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⣀⣀⡀
⠀⠀⣸⣿⣿⡿⠁⠀⠸⣿⡏⠀⠀⠘⢿⣿⣿⣤⣤⠀⢀⣤⣶⣿⣿⣦⠀⢀⣴⣾⣿⠿⣆⣾⣿⠆⢀⣿⣿⡟⡴⢿⣿⠇⣴⢟⣿⣷
⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣹⣿⡟⢀⣾⣿⡟⠁⣼⠏⢀⣾⣿⠟⠁⢰⣿⣿⠏⠀⣼⣿⣿⡟⣱⣿⢏⡾⢁⣾⣿⠃
⠀⠸⣿⣿⡏⠀⠀⠀⣸⣷⠀⠀⣠⣾⡿⣱⣿⡿⠁⢸⣿⣿⡴⠞⠋⢀⣾⣿⡏⠀⣠⣿⣿⠏⠀⣼⣿⣿⠏⢰⣿⣿⡟⢀⣾⣿⠃
⠀⠀⢿⣿⣇⠀⠀⣠⣿⡿⠐⠿⠿⠛⠀⣿⣿⣁⣴⠟⣿⣧⣀⣠⡴⠛⢿⣿⣷⡾⢻⣿⣯⣴⠞⣿⣿⠏⠀⣿⣿⡟⠀⣾⣿⠃
⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠉⢉⣥⡀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⢀⣉⣀⣤⣬⣽⣶⣾⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⢻⣿⠁⠈⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣼⡇⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠃⣀⠀⠀⠀⠀⠰⠋⠁⠀⡀⢸⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⠀⣬⠀⣤⠀⣤⡄⢀⡀⠀⣤⢸⣿⠀⢀⣤⢀⣤⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⠀⣿⣼⢹⣷⢛⣗⢸⡿⢸⣿⠀⣿⠌⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⠀⢰⠿⠌⠻⠇⠸⠟⢸⡇⣸⠷⠻⣿⠀⣿⣤⠞⠓⠺⣿⠀⡼
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠧⠂⠀⠀⠀⠀⠀⠀⢸⣧⠃⣠⠀⠻⠞⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣿⠀⡀⠀⡀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢋⡀⠀⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⡤⢼⡇⢠⡆⠀⣿⠀⣴⡄⣶⠒⢦⣰⣷⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠁⣿⡇⢸⡇⢸⡇⢰⣿⠀⣿⠀⣾⡉⢹⠸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡴⠻⠧⢿⡇⢸⣧⠞⣿⠀⣻⠞⠈⠑⠁⠀⠉⠀⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠀⠀⢿⣆⠇⠀⠀⠀⠀⠀⠀⠘⣿⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠤⠀⠀⠀⡂⠤⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⢀⣀⡀⠀⠀⣀⡤⣪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢩⠃⣀⣴⣷⣾⣿⣿⠿⠟⠛⠙⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢠⣣⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣰⣿⣿⣿⣿⡿⢿⡍⠐⡒⠂⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⡏⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⣱⣿⣿⡿⣛⠠⡲⠋⠀⠀⠀⠀⣰⣇⣠⣴⣿⣿⣽⣆⣡⡔⠀⢢
⠀⠀⠀⠀⠀⢠⠜⠀⢰⣿⣿⣿⣋⠤⠰⠁⠀⠀⠀⢀⣿⠿⣿⠁⣼⣿⣿⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡉⠠⣸⣾⣿⣿⣿⠁⠀⡂⠀⠀⠀⠀⢿⣇⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣶⣴⡾⠁
⠀⠀⠀⠀⠀⠡⣀⣿⣿⣿⣿⡧⠀⢀⡿⠀⠀⠀⠀⠸⠃⠀⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣷⡶⠛⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠙⠛⠛⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣷⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣸⣇⡠⠤⠤⠀⠀⠈⠥⠴⠾⣟⣛⣛⠲⠦⣤⣤⡥⠴⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠋⠉⠉⠉⠹⣿⣿⡷⢠⡾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣁⣠⣤⡀⠀⠀⣀⣰⣿⣿⢧⣿⠁⢀⡞⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⡾⠿⠿⣿⡿⠀⠀⠙⠛⠋⠁⣾⡏⢀⡾⠁⠀⢿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠞⠁⠀⠀⠀⠉⠁⠀⢀⣴⡞⠀⢠⣿⣣⠞⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⢀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⣾⣿⣦⣀⣼⣿⠋⢀⣀⠀⢸⣷⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⡼⢁⣠⡀⢤⢨⠁⠓⠁⠁⠀⠙⠿⣿⠛⢻⣿⠀⠈⣿⠀⠀⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⡼⠃⠀⠃⠀⠀⠀⠀⠀⣀⣀⣴⡦⠀⣿⡇⢸⣿⠀⠐⣿⡄⣸⣿⣧⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⣿⣿⡾⠁⠀⠀⣠⣤⡄⠐⣿⡼⣿⡟⢸⡇⠀⣿⡇⠈⢿⣷⡄⠙⠛⢁⣿⣿⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣠⣿⡿⠀⠀⢀⣾⠏⢀⣥⠀⣿⠃⣿⡇⢸⣷⡄⠻⠿⠂⠀⠀⠀⠀⢠⠟⣿⡇⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⣉⣿⣇⡀⣀⣼⣿⠀⢸⣿⠀⣿⡇⠙⠗⠀⠈⠀⢀⢠⡀⢐⠂⠀⢠⡟⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠛⢧⠘⣿⣦⠏⠛⠋⠀⠁⠀⠀⠀⠀⠡⠌⠘⠋⢈⡄⠀⣼⠀⢨⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⡇⠈⠁⠀⠀⠀⠀⠀⠀⢠⣾⣇⣀⣀⣤⡶⠋⡠⠀⡇⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣿⠀⣤⣾⣿⡿⠿⠀⠀⠸⢿⣿⠿⠟⢁⣠⠞⠀⠀⠓⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⠇⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣤⡶⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣠⣤⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣞⡳⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⠙⠫⠹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠐⠁
⠀⠀⠀⠀⠀⢀⣴⠞⣿⡟⣀⣀⠀⠀⣠⣤⢄⡀⠀⣾⣆⡤⣤⡄⢰⣆⠤⣦⡄⢰⣦⠀⣾⡆⠀⣠
⠀⠀⠀⠀⢰⡿⠁⢰⣿⠋⣼⡿⠀⣰⡟⣡⣾⠇⣠⣿⢃⠄⣾⠏⣽⣇⢤⣿⠃⣿⣃⢼⣿⢁⣴⠏
⠀⠀⠀⠀⠈⠃⠀⠘⠃⠰⣿⣁⠔⠉⠉⠘⠯⠊⣾⠏⠘⠛⠉⢰⡿⠈⠋⠁⠀⢉⣡⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣾⠃⠀⠀⢀⠔⢉⣾⠋
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⣦⠤⢄⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠘⠤⠞⡁
⠀⠀⠀⠀⠀⠀⠀⣸⡄⣀⢧⠑⠦⡍⢆⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⢀⣠⠤⠒⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢬⣳⢄⣉⣾⠄⡜⢁⣹⡒⢢⡌⠳⡄⡀⢋⣀⠴⣋⠜⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⢉⣥⣲⠃⢸⡀⡁⢾⣫⡤⠓⡤⠁⢸⠛⢒⣈⣁⡀⠆⢀⠘⠛⠓
⠀⠀⠀⠀⠰⠾⠖⢀⠀⠀⠐⠛⠓⣫⡆⠀⠉⡍⠓⠚⠁⡠⠅⠀⢞⣶⡈⣿⢉⠉⠀⠘⠲
⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⢀⣴⠏⠺⠙⠦⡀⠉⠙⠂⠚⠁⡠⠊⠀⠑⠂⠻⠈⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠈⠁⠉

⠀⠀⠀⠀⢀⡀⠀⢀⡀⢀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢀⡀⣀⠀⢀⡀⡀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡘⢧⠀⢸⡇⢺⡀⢾⠀⠀⠁⣸⠀⢸⡇⢸⠶⠈⠀⣿⣴⠉⢼⠁⠀⣈⠀⠀⢀⠀⠀⡔⠀⡄⠄⠰⢀⡄⣽⠀⡄⠆⢰⡇⠠⢀⠆
⠀⠀⠀⠐⠀⠚⠃⠀⠓⠚⠁⠈⠒⠚⠁⠛⠂⠉⠀⠘⠂⠚⠀⠘⠂⠀⠈⠁⠐⠃⠀⠀⠘⠘⠂⠃⠀⠁⠘⠒⠀⠁⠘⠀⠑⠂⠘⠃⢐⢲⡄

⠀⠀⠀⠀⣯⠀⡟⠀⢸⠀⠀⣾⠀⢰⣥⡊⠁⢠⡇⠀⠀⠚⢧⡀⢻⠁⠐⠓⣌⡇⠀⠀⠠⢠⠀⢨⠀⡉⢀⣀⠄⠀⡃⠀⡤⢤⢤⠀⠠⢠⡀
⠀⠀⠀⠀⠧⠀⠷⠀⠸⠄⠂⠟⠠⠸⠄⠱⠄⠀⠆⠴⠂⠤⠈⠁⠸⠆⠀⠀⠸⠇⠀⠀⠠⠀⠄⠈⠀⡇⠘⠍⠦⠀⠇⠠⠄⠸⠸⠄⠠⠔⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢠⠂⠐⣦⠀⠒⢀⠄⣠⠀⠀⡄⠀⡆⢐⡆⠠⣀⠲⠀⠀⡂⠒⠀⡆⠀⠆⠀⠀⠀⢀⠀⢀⣀⠀⢀⣀⠀⢀⣀⡀⢀⡀⢠⡀
⠀⠀⠀⠈⠄⠀⠟⠀⣻⠀⠀⠙⠀⢀⠇⠀⣄⠘⡄⢠⡀⡳⠀⠀⣇⠀⠈⣇⣀⠄⠀⠀⠀⢸⠀⣃⣨⠇⢀⣠⡄⢸⡀⢀⣱⠄⢰⡀⢢⣰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠀⡠⠀⢠⡄⢠⡄⢠⠀⠠⡀⠄⠀⢠⠀⡠⢀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠈⡶⠀⠀⠀⢳⠎⢱⠃⠀⠀⠛⡄⠀⠀⣺⠁⠀⠠⠂⢀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⢲⠜⡦⠁⠘⡇⠀⢱⡌⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠁⠀⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠠⠜⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⡄⠀⠀⢤⡋⠀⠀⡄⡀⠀⠀⠀⡟⠀⠀⢃⡴⠀⠠⡀⢲⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠇⠘⠀⠀⢠⣄⠀⠀⢾⣤⠀⠀⣀⠛⠀⠀⠒⡷⠀⢀⣀⠸⠀⠀⢇⡽⠀⠀⢰⠁⠀⠀⣀⡽⠀⢀⡱⠋⠀⠀⠆⠉

⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠐⠸⠃⠀⡇⠀⣀⣆⣀⠀⠀⠀⠀⢰⡜⢀⠀⢀⠊⡠⢤⠑⡀⠘⢿⡓⠀⢲⡗⡠⠃⠀⠀⢰⢷⠂⠘⡆
⠀⠀⠀⠀⠘⡇⠀⢤⠀⢠⠀⠀⠆⠀⠀⠆⠀⠀⠇⠀⠈⠉⠁⠸⠤⠽⠧⠄⠸⡐⠷⠯⠜⡀⠠⣼⠟⠀⠀⡔⠁⠺⡗⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢻⡰⢹⠁⣷⡇⠀⣧⡀⠀⠀⡟⠰⡇⢹⣿⠀⠀⢺⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠁⠁⠀⠁⠈⠀⠀⣁⣀⠁⠁⠉⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⠴⣄⠀⠀⠀⡔⢲⠀⠀⠳⣄⡎⠀⠀⠀⢠⡖⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠁⣿⠀⣿⠀⠀⣼⡝⣲⠗⠒⠊⠉⠉⡇⠀⠀⣾⠉⠉⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⡏⠀⡼⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⡜⠘⣧⣀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⣇⡄⢽⣷⠈⡇⠈⢧⠘⡖⠘⣾⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⠀⠋⠓⠈⠋⠀⠃⠀⠘⠁⠈⠈⠈⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢢⠀⠀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢾⠓⠒⢦⡀⠀⠀⠀⠀⢸⠁⠀⡸⠀⡼⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⠢⡄⠀⠀⣸⠔⠊⠀⠀⡧⢔⡪⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⢧⡜⢣⣀⠔⢹⠀⠀⠀⡜⢳⢾⠊⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡰⠃⠀⠀⠀⠀⠀⠘⣇⠀⡜⠀⠀⠀⠑⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣾⡇⢲⣠⠀⣶⡆⢰⢸⡇⠀⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠛⠃⠚⠙⠀⠛⠇⠙⠘⠃⠀⠘⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡆⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⢸⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⢠⣶⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⣾⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⠀⢠⣿⣿⣷⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⠀⢸⣿⣿⣿⡆⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⠀⣼⣿⣿⣿⡇⠀⢛⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣇⣿⡿⢿⣿⡇⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢸⣿⡟⣹⣿⣿⣼⡆⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⠠⣽⣿⡿⢟⣵⣿⣿⢿⣿⢿⣿⡇⠀⠀⠈⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⠀⣶⣶⠎⣽⡇⢀⡇⢸⡇⢸⣿⣷⠀⣠⣾⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠶⣦⣇⠀⣿⡏⠀⣿⠇⢸⠇⠼⠃⢸⣿⣿⣰⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⢹⠀⢹⣧⣄⣩⣦⣼⣷⣶⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣛⣛⣠⣾⣷⣴⣿⣿⡏⡀⣿⢻⣿⠇⣸⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢁⣿⣌⣩⣴⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⢛⡟⢻⠀⢸⣿⡿⣟⠛⣯⠉⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⢸⣿⠃⢸⡇⣿⠀⢼⣿⠀⣿⠀⣿⠀⣿⡯⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠸⢿⣄⢈⡀⢛⡀⠸⣫⣧⣽⣤⣿⣦⣩⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠛⠉⠉⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣋⣙⣏⣨⣉⣩⣝⣩⣿⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⠁⠀⠀⠀⡟⠐⢄⣀⠐⣿⠀⢀⣀⣀⣀⡀⠀⠀⠣⠤⠄⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⣧⢸⠀⠀⠀⢸⡇⡆⠘⣏⠀⣿⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⣿⢸⠒⠀⣴⢺⡇⡇⢀⡘⡇⣿⠀⡔⣲⢸⣧⣤⠀⡴⠂⣰⠶⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠈⠙⠃⠉⠈⠉⠁⠙⠁⠉⠉⠋⠁⠈⠋⠉⠋⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠒⠊⠁⠒⠊⠑⠒⠉⠐⠒⠉⠒⠊⠁⠂⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⢸⠳⡀⡏⠁⡏⠁⢹⠁⡇⠀⡇⡟⠁⣾⡄⡇⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠈⠛⠲⠤⠄⠀⠀⢸⢰⠃⡇⠀⡇⠀⢸⡀⣏⠀⡇⡇⠀⢿⢷⡇⠀⠀⠀⠒⠚⢋⣁⣀⣤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡤⠖⠂⠀⠀⢸⣣⠀⡗⠀⣟⠂⢸⡇⣿⣦⡇⣟⠂⢸⠘⣧⠀⠀⠀⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣀⢁⣠⡉⢀⣌⡁⣀⣄⠈⣨⣀⢈⣡⡀⢀⣄⡀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣀⠤⡀⠀⠀⣠⡀⢀⣤⣀⢠⡄⢀⣄⠀⣀⣠⠀⣠⣄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠙⢾⣤⠃⠀⠀⢿⢸⡌⡷⠊⣾⠀⢸⠸⢸⡏⢹⠸⡇⠉⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⢀⣤⣀⣀⠉⡀⣷⠄⢸⣸⡇⣿⡀⢿⡀⢸⠐⠿⡇⢸⠀⠹⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠶⠃⠘⠚⠇⠛⠀⠸⠞⠘⠇⠇⠸⠤⠸⠛⠀⠇⠸⠇⠦⠟⠀⠀⢈⢂⡡⢄⡂⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⣠⡀⣀⢀⢠⣄⠠⡖⠰⢢⠄⡂⠒⢒⠀⣿⠀⡀⢺⠆⠀⠀⠀⠭⢠⠁⡀⢀⡈⢒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡒⠦⠴⣒⠂⠀⠀⡇⡇⡻⣸⢸⡌⡆⢈⠛⠁⠀⠈⠒⠀⠀⣿⢀⡆⢸⡇⡀⢀⡀⠔⢀⠑⠤⡤⢒⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠬⣡⡩⠤⠅⠀⠀⠷⠇⠇⠹⠸⡷⠁⢸⠳⢠⢶⠆⡴⢲⠀⡇⢸⡇⢸⠁⠉⢹⠀⠀⠀⠠⠁⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣁⡒⢒⣉⡂⠀⠀⢖⠂⠼⠄⢂⠢⠀⠈⠀⠈⠒⠉⠉⠉⠃⠙⠉⠋⠈⠛⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡤⠤⠥⣄⡀⠀⠀⠀⠀⠀⠀⣶⡄⣶⠀⠀⠀⠀⠀⡆⠀⢀⡀⠀⣀⠀⣀⡙⡋⢀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⠀⡖⠀⠻⡄⠀⠀⠀⠀⠀⣿⢣⣿⠀⠀⠀⠀⢠⡇⠀⣏⢣⢸⠁⠇⢹⠀⡇⣾⢽⡆⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠀⠙⡆⠀⣷⣠⠄⣀⢤⠀⡟⢸⡏⢀⣤⡄⢠⢼⡇⠀⣿⢸⢸⠀⠀⢸⠀⡇⣷⢘⡇⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠳⠂⠦⠇⣠⠏⠣⠴⠳⠚⠆⠧⠞⠧⠞⠭⠔⠛⠾⡇⠀⠿⠺⠸⣤⠆⢸⠀⡇⢻⣼⠃⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠶⠒⠶⠶⠶⠶⠶⠖⠒⠲⠶⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠂⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣠⣤⡀⠀⣰⠃⠒⠋⠁⠀⠀⣀⠀⠀⠀⠀⣠⠀⠀⠈⠒⢦⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⢠⡞⡴⠂⠀⣷⢀⡆⠈⢀⠀⡴⢠⠏⢰⢄⡤⠀⢀⡞⢡⠀⡼⠀⣼⢃⡞⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠸⠀⠃⠀⢀⡏⣸⠀⣰⠋⡼⢁⡟⠰⢋⡞⠀⠀⠸⠁⡼⣰⠃⣰⠃⡼⠁⣼⠃⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠶⣴⡄⠀⠀⠀⠀⠀⡜⠀⡝⠀⡏⢰⠃⡾⠁⡄⢸⠁⠀⢀⠀⠀⠠⡏⠠⡏⣸⢃⡼⠁⠀⠁⠐⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠐⢆⡤⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢻⣄⠀⠀⠈⢐⡠⠀⠀⠀⢰⠇⠈⠀⠀⠀⠀⠀⠀⠀⢀⡰⠄
⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⡐⠀⢄⠀⠀⢰⡶⠀⠀⠀⠀⣷⠀⠀⠉⠉⣁⣀⣐⣓⣁⣀⣀⣉⣠⣤⣶⣿⠁⠀⢀⡀⡾⢬⠉
⠀⠀⠀⠀⠀⠀⠠⠀⣤⢀⣁⡉⠒⠂⠀⠀⢸⡇⠀⢠⣀⣴⠟⠢⡀⠀⣾⣏⠻⣏⠻⠉⡏⣻⡇⣿⣇⣛⣿⠟⢰⡌⠳⢒⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢅⢰⡾⠋⣭⢹⡧⠇⠀⢈⣥⡄⠀⠉⠁⠀⠀⣿⡆⢹⣿⡷⠿⠿⠿⠿⠟⠛⠋⢉⣉⣠⡤⢀⡁⢆⣾⡅⢠⢆⣓
⠀⠀⠀⠀⠈⣑⡄⠈⣌⠁⣀⢁⠊⠀⠀⢠⣿⣋⣄⠀⠀⣀⣠⣴⡟⠃⠘⠋⠁⠀⠀⢀⣀⣀⣡⣬⣵⡿⣋⡀⠚⡛⡛⠛⣷⣤⠌⠁
⠀⠀⠀⠀⠀⡁⠈⠡⣜⣃⠠⣎⢰⠀⠀⢸⣿⠉⠋⠁⠀⠀⢻⡉⠀⠀⢴⡶⡖⢛⣻⢻⢛⡏⢿⣿⡯⢉⣡⠔⠦⠢⡑⢀⠀⡉
⠀⠀⠀⠀⠀⠀⡘⠀⠐⠛⣹⡿⣄⡀⠀⢸⣿⠀⠀⠀⠀⢀⠠⣅⠱⠄⢸⣿⣏⣸⣿⣼⣶⣷⣾⡿⠀⠏⣀⡴⢂⡃⠙⠠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢙⠋⠄⠉⠓⢻⣗⢠⣄⣙⣀⣀⣸⣳⣾⣤⠀⢳⡌⠈⠻⠋⠙⢥⣀⡀⠀⠹⣷⠀⢀⢨⠁⢿⡇⢰⡔⠈⡤⠀⣠⣄⣠⣄
⠀⠀⠀⠀⠲⢶⣶⣸⡆⣠⣀⠑⣿⣿⢸⢯⠟⢛⣛⡛⠒⢿⠀⠉⢉⡀⠀⠀⠀⢠⣤⠭⠿⠒⣰⡎⢠⣀⠊⠀⠐⠥⢚⠲⢠⠖⢿⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⢛⣿⣾⣿⣿⣿⠇⠴⠛⢶⠀⣉⣸⠀⣶⢰⡆⣼⡇⣿⡆⣴⡏⠐⣾⡇⢰⣎⠀⠠⡉⠓⠛⠂⣒⢉⣤⠌⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡙⠛⢋⡡⢦⡄⢹⡦⢸⡄⢿⣿⠀⣿⢸⡇⣿⡇⣿⠇⣿⢇⠀⣿⡇⢸⣿⡁⣾⠀⡇⢰⠐⢏⢿⣥⠀⣾⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠞⠃⢸⡇⠘⣷⢸⣧⠘⣿⠀⠛⣸⡇⣿⡇⡈⢴⣿⢘⡂⢿⡗⢸⣿⡇⣿⠀⡇⢸⠀⢻⠀⣿⡆⠛⢿⣂
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⡇⣄⠉⢸⣿⡆⢹⠀⣿⣿⡇⢻⡇⣿⡀⡟⣿⡇⢸⡇⢸⣿⡇⣿⠠⡇⢸⠀⡘⠀⠛⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⣀⠈⠀⢄⠀⠀⢸⡇⣿⡄⢸⣈⣁⣼⣤⡿⠟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁⠺⣿⣅⣿⠀⠇⣸⠀⣇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠘⡇⠀⢸⣇⣽⡷⣿⣿⡿⠋⠉⠁⠀⢤⣶⣾⣿⣿⣿⣿⣷⠶⠆⠈⣿⣿⣿⣷⠶⣿⣄⣿⠀⠀⡏⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣃⠱⢿⡿⠉⠒⠀⡼⢧⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣧⠈⡆⠈⣽⠿⠒⢠⣥⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠤⢀⣙⣿⣦⣀⠀⢺⠆⡀⠀⠈⠳⢶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⣾⣛⠂⡀⡶⠂⣤⣴⣿⣏⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣾⡟⢢⠂⣤⠉⣄⠀⠀⠀⠈⠉⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢃⣼⠁⡁⠐⢲⠘⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠈⠁⠻⠃⠨⠄⠀⠀⠀⣠⡀⠀⣱⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠁⠸⠿⡃⢘⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⢀⠺⠿⢧⣶⣤⣤⣦⠀⠀⠀⠉⠉⠙⠳⣤⣤⣴⢁⠀⠀⠀⠀⣠⣤⣱⠶⡿⠿⣓⡲⣶⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢰⣶⠀⠀⠀⣰⡿⢷⡖⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠘⣿⣷⣾⣿⡆⠹⢿⣿⠟⣿⡇⠀⣿⠟⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⡀⢿⡏⠻⢹⣷⠀⢼⡟⠀⣿⡇⣸⣟⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠨⣿⣤⣿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⢴⣿⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⣲⢆⠈⠉⠁⠀⠀⢠⣶⠆⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠙⠛⠱⣖⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣾⠃⠸⠀⠀⠴⠒⢰⣿⠿⠆⠤⠶⠖⠛⠁⢠⣶⠆⠀⠀⠀⠀⠀⠇⠘⣷⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢀⣴⣿⠏⠀⢀⣴⠞⣷⠀⢠⣿⣿⠊⠉⣷⡀⠀⣠⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢉⣻⣷⠚⢁⣾⡟⠀⣠⣿⠷⠚⢁⣰⣿⡿⢁⣀⣼⡿⠒⠋⠹⣿⡀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣠⠖⠁⢸⣿⠀⢸⣿⣠⠞⢿⣇⣀⡴⠋⣼⡿⣗⣡⡾⠋⠀⣤⠖⠒⣿⣷⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣯⠀⢀⣾⠏⠀⠈⠉⠁⠀⠀⠉⠁⠀⣼⡿⠁⠈⠀⠀⠀⠐⣇⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⠀⢹⣿⡇⠀⣽⣿⡏⠀⣿⣿⠿⠿⠿⠀⢸⣿⠟⠻⣿⣦⠀⣿⣿⠁⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⠈⠀⠈⣿⣧⠀⣿⣿⠀⠀⣿⣿⣴⡆⠀⠀⢸⣿⣄⣠⣾⡿⠀⢻⣿⡆⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠿⠀⠀⠀⢿⣿⢠⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠟⢿⣿⡁⠀⠘⢿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⡀⠀⢸⣿⣿⣿⠃⠀⠀⣿⣿⣤⣶⣾⡂⢸⣿⠀⠈⣿⣧⠀⠀⣤⣤⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣴⣿⡀⠀⠈⠿⠿⠛⠀⠀⣀⣭⣭⣭⣭⣉⠀⠘⠛⠀⠀⠿⣿⡄⠀⣿⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢀⣀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣻⣇⠘⡇⠀⣸⣿⣶⣤⣈⠉⠁⠀⠀⠀⠀⠀⠀⣿⣷⠀⠘⣿⣿⠀⢸⠃⣸⣟⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠾⠓⠀⣰⣿⡟⠙⢿⣿⡆⠀⣼⣿⣿⣿⣿⡄⢸⣿⣇⠀⣿⣿⣇⠀⠚⠷⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣿⡿⠁⠀⣾⣿⡇⢠⣿⣿⣀⣹⣿⣇⠀⠻⢿⣿⠟⣿⣿⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣤⣾⣿⡟⢀⣾⣿⠿⠟⠻⣿⣿⡄⠀⢠⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠉⢀⣾⣿⡿⠀⠀⠀⢻⣿⣷⡀⠈⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉

⠀⢀⡠⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠶⠶⠒⠀⠀⠀⠀⡄⢴⡀⠀⠀⠀⢀⡀⣀⢄⡀
⠀⠫⠙⢉⣁⣄⡀⠀⠀⠀⠂⠨⠄⠀⠀⠀⠇⠓⠚⢛⠚⠃⠀⠀⠠⣿⡘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠄
⠀⠠⣄⣀⣀⣠⡄⠀⠀⠠⠠⠥⠤⡄⠀⠀⠸⠟⠘⠛⠚⠄⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⢀⡐⡶⠾⠄⠏⢜⠆
⠀⠀⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠘⠃⠀⠀⠀⠓⠒⠒⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠸⡶⢂⡀⣁⠀⠔⡧⠄⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⢠⠆⠀⠀⢀⡤⣸⡁⠀⠿⠈⠇⠆
⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠴⣐⣐⡈⠀⠀⡴⢾⡴⠚⠛⠑⠀⠀⠀⢺⢰⠘⣶⡂⠀⠈⠀⠀⠉⠒⠒⢋⠈⠁
⠀⠀⠀⠀⠈⠀⢀⠀⠀⡔⣆⣀⣀⣀⠄⠀⠄⡈⢁⢠⢀⡴⠀⠙⠀⠒⢰⠺⠴⠆⠀⢠⢠⣰⢚⣰⡄⠀⠀⠀⠄⠀⠄⠠⠁⠐⠂
⠀⠀⠠⠆⠠⡤⠀⠀⠀⠀⠁⣅⡑⠁⠀⠀⠈⡴⠄⢦⠎⠄⠀⠈⠈⠙⠋⣉⠙⠃⠀⠀⢂⢠⣰⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⢶⡀⢐⠖⢀⡔⠀⢢⡀⠐⡖⠀⠐⡆⠀⠀⢀⡔⠀⢰⠀⣠⠂⠒⣄⠀⢲⠂⠀⠲⠀⢰⠆⠀⠀⢰⡆⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⢸⠀⠀⢈⡇⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣹⠀⢸⠀⠀⠘⠀⢸⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠃⠤⠚⠁⠀⠓⠤⠔⠁⠀⠀⠈⠳⠤⠀⠀⠙⠤⠔⠋⠀⠘⠦⠤⠂⠀⠸⠂⠀⠎⠘⠇⠀⠚
⠀⠀⠀⠀⠀⠀⢤⡀⠀⣤⠀⠀⢠⡀⠀⢠⠄⢠⠄⠀⡄⠀⠄⠀⠀⠀⣠⠀⠀⠀⢠⡄⢠⡄⠠⠄⢠⠀⠠⠀⢤⠀⣤⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⠀⢠⠀⢧⠀⢸⡖⢆⠀⠀⡇⠶⠀⠀⠀⠠⠈⣇⠀⠀⠀⢧⡈⢧⡈⠀⢸⠀⠙⠲⢦⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠓⠈⠁⠚⠀⠒⠀⠘⠃⠘⠃⠈⠓⠀⠃⠀⠊⠀⠀⠃⠀⠘⠂⠀⠀⠘⠁⠘⠁⠀⠘⠀⠛⠀⠈⠀⠛⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠀⠀⣿⣿⣿⣿⣿⡇⠀⢐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⣀⠀⣀⠀⢀⡀⠀⠀⡀⠀⠀⠀⣀⠀⣀⠀⢀⡀⢀⡀⠀⣀⠀⠀⢀⠀⢀⡀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠘⢦⡐⠁⢸⠃⠀⠘⡇⠀⡇⠀⠀⡇⠀⠀⢸⠃⠀⠈⠀⡟⠀⠀⢻⠀⢸⠀⠀⢸⠀⢸⠄⠀⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢆⠀⡰⠃⠀⢧⣀⡠⠃⠀⠀⠘⢆⡀⠠⠀⠳⡀⢀⠞⠀⠸⣄⣀⠜⠀⢸⡅⢀⡴⢀⣇⠀⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢸⡇⠀⢀⢻⡄⠀⠈⡇⣀⠋⠁⠀⡏⢀⠙⠀⠀⠀⢹⠀⠛⠈⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⢸⡇⠀⠔⠀⢷⡀⠀⡇⠙⢦⠀⠀⡏⠙⢀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠁⠈⠁⠀⠈⠁⠈⠁⠀⠈⠁⠀⠉⠀⠉⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠠⣤⠀⠀⠀⠀⣤⠀⠀⠀⠠⣤⠄⠠⣤⡀⠀⣤⠄⠠⢤⡀⠀⢤⡄⠀⠤⣄⠀⢤⣄⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⠀⠀⡘⠹⣇⠀⠀⠀⣿⠀⠀⣸⠇⠀⣿⠀⠀⣸⡇⠀⢸⡇⣠⠄⠙⠀⢸⠙⢷⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⣿⠀⠀⠰⠧⠤⢿⡄⠀⠀⣿⠉⠉⠁⠀⠀⣿⠉⠉⠁⠀⠀⢸⡇⠙⠄⢠⠀⢸⠀⠀⠻⣆⡃
⠀⠀⠀⠀⠀⠀⠠⠿⠄⠀⠠⠿⠄⠠⠧⠀⠀⠠⠿⠄⠠⠿⠤⠀⠀⠀⠠⠿⠤⠀⠀⠀⠀⠼⠧⠀⠤⠿⠀⠼⠦⠀⠀⠘⠇

⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣴⠀⠀⢲⠂⠀⠀⠀⠀⠀⠀⠀⢡⡎⠀⠈⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣠⠔
⢀⣾⡇⠀⠀⣀⢀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠸⡿⠀⠀⢸⢦⣄⣤⠀⠀⢀⠤⢤⣼⡇⠀⠀⢠⡴⠁⠀⣰⣦⣀⢀⣴⡿⠁⠀⢀⣀
⢀⣹⡇⠀⠀⢳⣾⠇⠀⠀⣿⠀⠀⢰⣹⠀⠀⠀⣧⠀⠀⠀⠀⠈⣙⣷⠀⠀⢸⠛⢻⣿⠀⠀⠀⡿⠟⣟⡇⠀⠀⢸⡇⠀⠀⡿⠷⢶⠎⣼⠇⠀⠀⠸⢶⣳⣦⣦⠆
⠘⢿⡇⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⢸⣧⠆⠀⠀⢿⠀⠀⠀⠀⠐⠺⣿⠀⠀⠈⢰⢹⣿⠀⠀⠀⠀⡀⣿⡇⠀⠀⢸⡇⠀⠀⠁⠀⠀⠠⠸⣮⡢⣀⠀⠀⠈⠉⠣
⠴⣿⡇⠀⠀⣴⣒⣒⡽⣿⠇⠀⠀⢹⣷⠇⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢠⢰⣿⠀⠀⠀⡀⣤⣾⣇⠀⠀⢸⣇⠀⢀⡀⠀⠀⠀⠀⣠⠭⠷⣌⣒⣢⡀⠀⢠
⢠⣿⡇⠀⠀⠁⠀⠀⠀⢿⡰⠀⠀⠈⠛⠀⠀⢠⡷⠀⠀⠀⠂⠐⠚⢿⠀⠀⠀⢘⢸⡗⡀⠀⠀⡇⣉⣩⣈⠀⠀⢨⣃⠀⠘⢧⣴⠏⠙⢻⣿⠀⠀⠹⣿⡿⠃⠀⣸
⢠⣿⢇⣀⣀⡄⠀⠀⠀⠼⣮⠢⣀⠀⠀⣀⣠⢿⣶⡀⡀⠀⠀⠀⠀⣸⡀⠀⠀⠐⢾⡇⡇⠀⠀⡇⣭⣭⣥⠀⠀⢨⣥⣄⣀⡀⠀⠀⢀⣾⣿⣧⣄⠀⠀⠀⢀⣴⠋
⢠⣷⣷⣶⠊⠀⠀⠀⠀⠈⠘⠳⠶⢭⣭⡞⠡⠺⠷⠯⡤⠠⠫⣍⣭⣯⣭⣝⠉⠀⣁⣷⣭⣩⠉⠀⣦⣼⣌⣩⣨⣿⢦⣤⢨⣍⣁⣵⠟⠉⠙⠶⣬⣑⣐⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⣀⣈⡓⡷⣶⢴⠤⠴⠷⠻⣉⣡⡐⠒⠒⡲⠆
⠀⠀⠈⣑⠆⠀⣏⣥⣶⣵⣷⡌⣽⡍⢯⠇⡆⣿⣀⠨⠕⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⣉⠉⠁⠁⠏⢀⣛⣀⣩⣥⠬⠤⠒⠁⠀⣰⡃⠀⠀⠀⠀⠀⡜⢉⡗⠀⠀⡠⡄⠀⠀⠀⠀⣦⣤⣳⣀⡀
⠀⠀⠀⠀⠨⡓⠶⣿⠂⢈⢉⡉⣉⣩⣤⠤⣴⠶⣸⣎⠒⠀⠀⠀⠀⢹⣗⣋⠀⣀⣀⣧⠇⡄⠀⠐⠿⠛⢛⡛⠿⣧⡀
⠀⠀⠀⠀⠈⠀⠐⠧⠳⡼⠀⢧⣼⢁⣻⢚⢈⡯⠥⣸⠀⠀⠀⢶⣧⠈⢇⣈⡷⣧⣺⡏⣸⡇⣯⣇⢇⡽⢾⣛⡜⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡀⣿⣏⢈⣶⠈⡷⠈⢉⠁⠀⠀⠀⠘⠻⣷⣶⡿⠿⠙⠳⠈⣶⢠⡞⠲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡉⠈⠉⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠃⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡾⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⢃⣄⠀⠀⣀⢀⣠⣖⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣼⣷⠿⣷⠋⢾⣹⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⢻⠙⣾⢿⠈⣧⡴⢣⢟⢭⠶⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⠛⠀⠛⠃⠀⠈⢡⣤⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠈⠛⠁⠤⢔⡉⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠿⠃⡿⠀⠀⢀⠀⠀⠀⣿⡏⠶⡟⠀⠀⠀⠀⠀⠀⢀⣸⠀⣠⡖⣤⡄⣀⡎⡐⢨⣿
⠀⠀⠀⠀⠀⠀⢀⠔⣸⠇⣼⢿⡿⣾⣰⣧⣿⢛⡶⣇⡀⠀⠀⠀⠀⠀⣿⣘⣇⣿⣰⠻⡷⢧⠿⣻⠅⢿⠄
⠀⠀⠀⠀⠀⠀⠘⠶⠛⠚⠙⠋⠀⠛⠁⠁⠈⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠓⠢⠀⠐⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⢤⠀⠉⠉⢢⠔⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠂⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠖⢰⠂⠒⠰⠄⠀⢄
⠀⠶⢎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠒⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⠨⠄⠤⠰⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠘⢄⠤⠊⠀⠠⠊⠑⠃⡤⠀⠀⠄⠆⠀⠀⠀⠀⢘⠁⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠠⠁⢀⠀⠰⢄⠀⠀⡀⠴⠄⠀⠀⠀⠀⠀⠀⠁⡀⠶⢄⠋⠂⠊⠉⠐⠀⠈
⠀⠀⠀⠀⠀⡐⠈⢂⠠⠀⢠⠀⠁⠀⠀⠤⠀⠘⡀⠀⠀⠉⠈⠀⠀⠀⠀⠁⠀⠀⠜⠂⠤⠘⠀⠢⡀
⠀⠀⠀⠀⠀⠆⠀⠚⠀⠀⠘⠂⠁⢄⠀⠀⢀⡀⠈⠐⠀⢠⠄⠀⠞⠀⠀⡘⠢⢀
⠀⠀⠀⠀⠀⠘⢄⡀⠔⠢⣀⠀⠠⡆⠀⠀⢀⡀⠀⠀⡀⢆⠀⠀⣀⠠⢌⠀⠀⠀⡀⠀⠀⠀⠀⡠⠋⠠
⠀⠀⠀⠀⠀⠀⢰⠀⠠⡄⠈⠃⠀⢱⢄⠀⠀⠀⠈⠁⠀⠀⢢⡀⠀⠀⠀⠈⢢⠀⠉⠀⠀⠉⠀⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢄⢀⠗⠀⠐⠲⢅⠀⠈⠂⠐⠂⠐⠃⢀⢜⠀⠉⠈⠀⠀⢠⠄⠐⠂⠤⡂⢀⡌⠀⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠠⢀⡀⠔⠀⠰⠀⠀⠉⠀⠀⠑⠂⠠⠤⠐⡁⠀⠀⠀⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠢⠤⠤⢄⠀⠠⠀⡈⢀⠂⠀⢠⠀⠀⠄⠀⠀⢃⠀⠀⠀⠈⠃⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠈⢄⠀⡀⠀⢀⢄⠀⢀⠋⠀⠀⠔⠀⠐⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣼⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⡄⠀⠀⢀⡇⠀⠀⢀⡎⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠹⡆⠀⢸⡇⠀⠀⣾⠃⠀⢀⡾⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣀⠀⠈⠷⠀⣀⡥⠶⠖⠒⠒⠲⠶⣤⣀⠛⠁⠀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠗⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡈⠉⠀⠀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣤⠀⣼⠃⢠⡀⢠⠀⣠⣤⠀⣠⠀⠀⢠⠀⠀⣠⣤⣄⠈⢧⠀⠶⠖⠛⠉
⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠶⣾⢀⡷⠆⠀⡿⠀⠀⣿⠀⠰⡇⠀⣹⠀⢸⡆⢠⣀⣀⣀⣀
⠀⠀⠀⢀⣾⠟⠋⢉⣿⠇⠐⠒⠚⠛⠛⠸⠇⠀⠙⠀⠋⠘⠛⠓⠀⠛⠛⠀⠛⠛⠀⠙⠛⠁⠀⢸⡇
⠀⠀⠀⠘⣿⡄⠀⠋⢁⣶⢂⣴⠄⣰⣆⣴⡶⣠⣶⠀⣰⣆⣴⡶⣠⣶⠀⣴⡶⣦⢰⣿⣴⡆⠀⣼⠃⠛⠶⠦⠤
⠀⠀⢀⡔⠈⢿⣦⢠⣿⣣⣾⣋⣼⣿⢫⣿⢟⣿⣃⣼⣿⢫⣿⠟⣿⣃⣼⡿⠾⣣⠎⣼⠏⢀⡼⠃⣤⡀
⠀⠀⠈⠿⣶⡾⠟⠀⠛⠋⠙⠋⠙⠁⠀⠉⠈⠛⠋⠙⠁⠀⠉⠀⠛⠋⠈⠛⠛⠁⠀⠛⠚⠉⠀⠀⠈⠉⠓⠦






⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠏⠤⠤⠀⠠⡬⠁⠀⠀⠀⠀⠀⠀⠀⠇⢤⢌⣁⣤⣤⡑⠠⡀⠀⠀⠀⠈⢿⣭⢭⣍⠙⠏⢻⡦
⠀⠀⠀⠀⠀⢎⢵⣈⢀⣀⠀⣗⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣯⢳⠃⢂⣀⠀⠃⠀⠀⠀⠀⠉⠑⡿⠗⠂⡀⠉
⠀⠀⠀⠀⠀⠙⠆⢑⡛⠚⡗⢡⠃⠀⠀⠀⠀⠀⠀⣀⢉⠀⠛⠛⠓⣈⢀⣢⡄⠀⠀⠀⠀⠘⠞⣿⠾⠿⠯⣀
⠀⠀⠀⠀⠀⠀⢉⣞⣶⣣⣸⣿⠄⠀⠀⠀⠀⠀⠀⠉⠉⢰⠰⠻⠤⢶⡤⠀⠀⠀⠀⠀⠀⣛⠂⠿⠿⠛⠘⣡⡄
⠀⠀⠀⠀⠀⠈⠀⠙⡿⢿⠿⣏⠏⠀⠀⠀⠀⠀⠀⠀⠠⠘⢠⢢⣆⡡⡃⡀⠀⠀⠀⠀⠀⠙⣾⡛⠶⠶⣊⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢴⡂⢠⣀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⣼⡀⠠⣀⣠⣦⣡⠀⠀⠀⠀⣀⠠⠟⠝⠶⠺⠌⠃⡀
⠀⠀⢄⠀⠸⠆⣀⠜⠀⠠⠒⠀⠼⡀⣀⠔⠀⠀⠘⡆⢸⠘⢾⠿⠐⢆⠰⠹⠀⠀⠀⠀⢻⢤⠀⣿⡃⣥⠠⡔⠃
⠀⠀⠈⢃⢲⣤⠈⣶⣒⣂⣋⡒⠶⠆⡌⠀⠀⠀⢶⢬⣥⠴⠄⠶⠶⠶⠲⠲⠋⠀⠀⠀⠈⠸⠤⠛⠀⠿⠰⠇
⠀⠀⠀⠀⠻⠞⠛⠙⠉⠉⠉⠛⠛⠋⠀⠀⠀⠀⠰⡄⣆⣀⣀⣈⣌⣬⢭⠉⢽⠀⠀⠀⢰⠰⣀⡤⣥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠿⠓⠛⠚⠛⠛⠛⠛⠁⠀⠀⠘⠰⡿⠿⠔⠻⠇⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠍⢹⡆⢀⣀⡀⢀⡀⣀⡀⠀⠋⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⡼⢡⡏⢀⡇⣸⠟⣽⠃⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⢉⣀⢈⡓⢋⣀⣋⠀⡛⢀⣀⢀⢙⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣻⢹⣯⣿⣿⣿⣯⠿⡇⢸⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠙⠞⠹⠙⠛⠟⠇⠀⠷⠾⠛⠾⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⣤⡄⣠⣤⠀⣠⣤⣄⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⣿⢸⣿⣝⠛⠇⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⢸⣿⠀⣿⡇⣼⣿⢀⣙⢿⣷⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡿⠁⣿⣧⣿⣿⠸⣿⣶⣿⠇⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡿⢀⡤⢦⡀⠀⠀⠀⣼⠃⢴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡾⠁⣿⢀⡼⠃⠀⠀⣰⠏⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢀⣀⣠⣤⣤⡥⠤⠤⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⢛⡩⠝⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠛⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⣠⠴⠒⢦⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⡜
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢀⣾⠃⠀⠀⠉⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⡿⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠿⣦⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠿⠃⠀⢀⣾⡟⣀⠔⠁⠀⣀⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡤⠊⣹⣿⠆⢀⣶⠀⠀⢠⣿⡟⠊⠀⠀⣠⣾⠟⢁⡴⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⢀⣾⠇⡠⢊⣽⣣⠊⠀⣴⣿⠏⢀⣿⡟⠀⢀⣾⡟⠀⠀⠀⣼⡿⠧⠒⠉⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠘⣿⣿⠀⣼⡏⡜⠁⣾⡷⠁⠀⣼⡿⠃⠀⣸⡿⠀⢀⢾⣿⠃⠀⠀⣰⣿⡇⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⣿⡏⠀⣿⡟⠀⢸⡿⠁⠀⣼⡿⠁⠀⡔⠙⠷⠔⠁⢸⣿⠀⢀⡔⠁⠙⠓⠒⠋⠀⠀⣠⣶⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣀⡼⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠻⣧⡠⠊⢀⡴⢛⠂⠀⠘⠿⠗⠋⠠⠚⠛⠛⠛⠛⠲⣴⣿⡃⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⡁⣀⣀⠀⢤⡤⢤⠄⣠⢀⡤⣄⠀⠀⠀⣰⠟⡰⠃⠀⠀⠀⠀⣀⣀⡀⢀⣴⠖⠂⡂⣰⣿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠘⣧⠁⠀⡼⢀⡟⢲⣷⠟⠒⡋⠀⠀⣰⡿⢊⡴⠶⣦⡀⣠⡾⢋⠠⠂⣿⣧⠀⠘⢡⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠒⠋⠀⠀⠃⠘⠀⠙⠘⠲⠚⢁⡠⢶⣿⡵⠁⡀⠀⣿⢳⣿⠁⠀⢀⠀⠈⢿⣷⠀⣼⡏⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡠⠚⣿⡆⠀⢀⠴⣶⣄⠉⠁⠀⢸⣿⠁⢎⣀⠔⠃⠘⢿⣄⡴⠃⢄⣠⣾⠟⠀⠻⣧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⠞⠁⣼⡿⢁⠞⠁⣰⣿⢃⣤⣤⣄⡀⠁⢀⡴⢋⠝⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣤⢀⣴⡤⠚⠙⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣯⠊⠀⣰⣿⡱⠃⠀⣼⡿⠁⣉⡤⡀⠀⠉⣹⡟⣉⣥⣄⠀⣠⡶⠚⡂⢀⣼⡟⠁⢀⣾⢃⣾⠋⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣰⣿⡟⠁⢀⣾⡿⣡⡞⠁⠀⣼⠇⣰⡿⠊⠁⣠⢯⣾⢋⡠⠔⠁⣾⠏⠀⢀⣾⠃⣼⠇⠀⣠⣾⠟
⠀⠀⠀⠀⠀⢀⣿⠏⠀⢠⣿⡟⠀⠀⣾⡿⣱⡟⠀⠀⣼⠏⢠⣿⠷⣶⣉⠀⢸⣿⣀⣀⠔⢰⡏⠀⢀⢾⡏⢰⡏⠙⠛⠉
⠀⠀⠀⠀⠀⢸⡟⠀⠀⣾⡿⠁⠀⢸⣿⠃⢿⡅⢀⢼⡟⢀⣾⡇⠀⠈⢻⣧⣀⠈⠉⣀⡴⠈⠣⠴⠋⢈⡣⢼⡖⠒⠒⡆
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠃⠀⠀⠸⣿⡀⠈⠉⠁⠈⠉⠁⢸⡇⠀⠀⠀⠉⠛⠛⠛⠉⣀⣠⠴⠚⠉⠁⠀⠈⠳⠦⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠁⠀⠳⣄⣀⣀⣀⣀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠁

⠀⠀⠀⠀⠐⠲⡖⠂⣤⠀⢠⡆⣴⠒⠒⠀⠀⢦⠀⣶⡀⣰⢀⠔⠒⢦⠀⡖⠒⢦⠀⡆⠀⠀⡖⠒⢦
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠚⢺⡇⣿⠚⠓⠀⠀⠸⣼⠁⢧⡇⢸⡀⠀⣸⠀⡗⠒⣏⠀⡇⠀⠀⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠁⠉⠉⠉⠀⠀⠀⠉⠀⠈⠀⠀⠉⠉⠁⠀⠁⠀⠈⠀⠉⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠐⣶⠒⠲⣄⠀⢀⡔⠂⠒⢦⠀⢀⡴⠂⠒⢦⡀⠀⣶⠂⢀⠖⠂
⠀⠀⠀⠀⠀⠀⡸⠈⣧⠀⠀⠀⠀⠀⣿⠠⢴⣏⠀⣿⠀⠀⠀⢸⡇⣼⠃⠀⠀⠈⣷⠀⣿⣴⡁
⠀⠀⠀⠀⠀⣰⠉⠉⠙⣧⠀⠀⠀⠀⣿⠀⢀⣿⠀⠹⣄⠀⢀⡼⠃⠘⣇⠀⠀⣰⠏⠀⣿⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣀⢀⢀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⣴⣿⣿⣦⢠⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠀⠻⣿⡿⠏⠈⠉⠁⠁⠁⠉⠉⠉⠉⠉⠉⠉⠉⠈
⠀⠀⠀⠀⢀⣀⣀⢀⠀⡀⠀⣀⡀⠀⣀⡀⢀⣀⡀⠀⢀⡀⣀⠀⡀⣀⢀⡀⠀⣀⡀⠀⣠⢄⠀⡤⡄
⠀⠀⠀⠀⠈⣿⠉⢸⣤⣿⢸⡏⣿⠸⣯⡉⢸⣏⡁⠀⢸⡇⣿⣸⡇⣿⣸⡇⣼⠉⣷⠀⢿⡸⠘⢇⡿
⠀⠀⠀⠀⠀⣿⠀⢸⠁⣿⢸⣇⣿⢠⣌⣿⢸⣇⡀⠀⠈⣿⠙⣿⠀⣿⢸⡇⢻⣄⡿⠀⢧⣰⡏⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠃⠋⠐⠙
⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣀⣀⡀⠀⣶⠀⣶⣰⠀⢰⡀⠰⡄⠀⣶⠀⢰⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠘⠀⠀⠓⠀⠁⠀⠋⠀⠘
⠀⠀⠀⠀⢠⡴⠤⢄⠀⡤⠤⠆⠀⢠⣄⠀⢠⡤⠤⣄⠀⠀⢀⡴⠦⣄⠀⣤⠀⢠⡄⣤⠀⠀⣄⠀⣠
⠀⠀⠀⠀⢸⡗⢶⡋⢈⡗⠒⠂⢀⡯⢼⡆⢸⠀⠀⢸⠀⠀⢾⠀⠀⢸⠆⡏⢳⣸⡇⣿⠀⠀⠈⣶⠁
⠀⠀⠀⠀⠘⠁⠀⠙⠈⠓⠒⠒⠘⠁⠀⠙⠘⠓⠒⠋⠀⠀⠈⠓⠒⠋⠀⠃⠀⠙⠃⠛⠒⠂⠀⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⢠⡎⠉⠙⣦⠀⡿⣄⢸⡇⢸⡏⡉⠀⠀⡇⠀⣹⠀⠀⠈⢧⠀⠀⡾⠁⠀⠘⠀⠀⡇⠀⡈
⠀⠀⠀⠀⠸⣇⠀⢀⡟⠀⡇⠘⢾⡇⢸⡇⠁⠀⠀⡏⠈⠀⠀⡀⠀⠘⣆⠀⢷⡀⠀⢲⠂⠀⡇⠀⢁⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠀⠈⠁⠈⠉⠉⠁⠈⠉⠀⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠁⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⢆⣠⣄⢀
⠀⠀⠀⠀⢸⣇⠔⣿⣼⣀⡉⢳⣄⠀⠀⠺⣀⣺⡼⢶⣰⢙⡷⡀⠀⠀⠀⣰⣶⣶⢶⣷⣶⣷⣶⡆⠀⠀⢠⣤⣬⣭⣥⣼⣤⣶
⠀⠀⠀⠀⠀⢡⢴⡏⠃⣈⡉⠻⠏⠀⠀⢘⣁⡃⠈⠀⠈⣀⣃⠁⠀⠀⠀⡻⠟⠛⠛⠿⠛⣛⢛⠉⠀⠀⢸⣟⣿⣿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⢰⠏⡾⠀⠁⠄⠀⠀⠀⠀⠀⠫⠈⠛⠛⢈⠛⠂⠓⠀⠀⠀⠀⠳⠜⠺⠀⠞⢉⢎⠝⠀⠀⠀⠀⣤⠬⣐⣀⢛⠐⠂
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡴⠁⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠠⠶⠶⢆⡀⠀⠀⠀⠀⠳⠤⠒⠁⠱⢿⣋⡠⠀⠀⠀⠀⢣⠴⠶⢼⠦⠖⠶⠀⠀⠀⠀⢣⣡⡤⠠⠯⠦⢤⠄
⠀⠀⠀⠀⢀⣤⢤⣤⣼⣤⣬⣤⣤⡄⠀⠀⡠⢔⡄⣄⣅⡠⠘⢳⠀⠀⠀⢀⠈⣀⣆⣀⣄⣰⡖⠀⠀⠀⠠⠔⠀⢀⣠⣆⣤⣠⡀
⠀⠀⠀⠀⢸⣷⣿⣼⣯⣿⣿⣼⣿⡇⠀⠈⢓⢿⣉⡧⠂⠈⠉⠁⠀⠀⠀⢠⠂⠀⠋⢉⠌⠀⠅⠀⠀⠀⠀⠐⡩⠍⠥⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠢⡄⠀⡀⠀⠀⠀⠀⠀⢀⠔⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⢀⠁⡀⡀
⠀⠀⠀⠀⠀⠀⡞⠁⠀⢹⣄⣀⠀⠀⠀⠀⡎⠀⢀⣤⣅⡀⣠⠀⠀⠀⠀⠀⠈⠂⣀⠤⠦⢶⡀⠀⠀⠀⠀⡐⠈⠶⢋⣉⢁⠇⣀
⠀⠀⠀⠀⠀⠀⢧⡀⢐⣋⣠⣶⠰⠀⠀⠀⠙⢄⠃⡼⡁⡤⡟⢁⠇⠀⠀⠀⠀⠆⠈⣰⠀⢪⠂⡀⠀⠀⠀⠰⡉⡀⢌⣠⣤⢦⡀
⠀⠀⠀⠀⠀⠀⠄⡹⡇⠩⠥⠓⠂⠀⠀⠀⠀⠘⠅⠁⠙⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠃⠁⠈⠂⠀⠀⠀⠀⠀⢹⠃⣠⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣿⣂⠀⢠⣦⠀⣴⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢩⡿⢸⣿⠸⣿⣴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠀⠘⠛⠀⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡠⢴⡄⣴⠈⣿⢸⣷⣠⣶⣴⠋⣿⡆⢠⣶⢒⠆⣴⡶⢀⣄⡀⢀⣀⡀
⠀⠀⠀⠠⠆⠀⠈⠙⣿⣶⡆⣿⡏⣷⠸⣿⠟⢦⠏⣾⡿⠁⠻⠟⠀⣿⣧⠾⢿⡠⠞⢿⣧⣾⣿⡥⣿⣏⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣷⠹⠷⠟⠀⢀⡀⡀⠀⠉⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⢀⡠⢶⣿⡏⢞⣻⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡰⠁⢻⡿⠀⠀⠀⠀⣿⣇⣟⡀⣿⣅⣼⡟⠃⣿⣿⣆⣸⡇⢠⠏⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠇⠀⠀⠀⠀⢿⣇⣈⣿⢿⡇⢿⣏⣿⣿⢻⣿⢿⣿⠈⠂⠞⠋
⠀⠀⠀⠀⠀⠀⠘⡇⢀⠎⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⢉⠁⢉⡈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠹⣷⡄⠀⠀⠀⢸⣦⣿⣧⢹⣸⡞⡇⠀⠀⠀⢀⣴⢲⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢿⡇⠀⠀⣀⡈⠉⣉⠉⣀⡀⠀⠁⣀⠀⢠⣿⣷⣿⣾⠏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣤⣤⣴⡋⢸⣿⣼⣿⡞⢹⣿⣴⠟⣿⡇⣾⡟⢱⣿⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⣿⠀⣿⡇⠹⠃⢼⡟⠿⠞⠻⠷⢿⣧⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠟⣤⣤⣀⣤⣤⠀⣤⠄⢠⣤⡀⣠⢤⡌⠛⠲⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⠁⣿⠀⠀⣧⡀⢸⣇⡿⠹⢮⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢹⣷⢸⡄⠀⣿⣀⠘⣿⠀⢠⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠉⠉⠀⠁⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣶⢶⣆⡀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⣛⠃⢈⡃⠛⡋⢻⠏⢱⣹⣇⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣠⣬⣿⠀⠿⠁⢸⠇⢈⡀⢛⣽⣿⣀⠁⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣫⡭⠀⣹⣦⣶⣷⣾⣷⣿⡿⣿⣿⣯⣝⡿⠃⠀⣿⠶⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡁⣿⡟⠁⠔⣛⠉⠉⠙⣿⠟⠁⢰⡾⠱⢣⡞⣵⠀⢰⡶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣾⡷⠈⣴⣾⣿⡿⠀⠀⣠⣾⣇⠀⠹⣛⣤⠀⢸⣿⠀⢸⡟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⡆⢻⡿⠋⣀⣴⣿⣿⢿⣿⣷⣾⣿⣧⣧⣼⣿⠀⢸⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⣾⠟⠀⣴⣾⣿⣿⣿⣧⣤⣿⣿⣿⣿⣏⣹⣿⣿⣷⣤⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢽⣟⣻⠟⢻⣿⣿⢻⡿⣿⣿⠿⠹⢻⣿⡿⠋⣉⣥⣴⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠗⠀⣼⠋⣯⠀⠿⢻⡇⣼⠀⠙⠀⡄⢸⠏⣼⣿⠀⡿⢀⢈⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢿⣀⣫⡖⡄⣸⣆⣘⡀⠰⣄⣱⣤⣼⣿⣿⣤⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⣽⠿⠿⢿⣿⣿⡿⣵⠀⣿⣿⣿⣿⠛⢿⣿⣿⠟⠀⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠁⣠⣤⠀⠘⣿⣇⣃⣴⡿⢿⣿⣿⣶⣿⣿⣿⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣼⣛⣋⣠⣾⡿⣿⢿⣿⣿⣾⣿⣿⣿⣯⣿⣷⣶⣄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⡟⠀⢸⠇⢫⠁⠹⠟⠿⠋⠙⣿⡿⠛⡻⣦⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⣿⣿⣿⡇⠀⢰⡿⢸⠀⠀⣾⠀⣿⠀⠛⠀⢨⣿⡿⢋⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢿⣿⡟⣴⣄⡀⢃⣿⣇⣀⣻⣶⣿⣀⣴⣄⣘⣫⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠙⣼⠏⠙⠛⠛⠁⠙⠛⠋⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋


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

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⡼⠁⠀⠀⠀⠀⠀⠀⣠⣴⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⣸⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢠⠇⠀⣠⣿⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢀⡟⠀⢠⣿⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⣀⣤⣶⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⣿⠀⢀⣤⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⡞⠀⢀⣿⡿⢠⠇⠀⠀⠀⢀⣠⣄⡀⣠⡶⠋⠀⠀⣀⡴⠒⠋⠉⢀⡾⠛⢸⡇
⠀⢀⣀⡀⢀⣀⠀⠀⠀⠜⠁⠀⣿⣿⣠⠏⣠⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢸⣿⣷⠏⠀⠀⢠⡆⠘⠧⣿⣿⠁⠀⠀⢀⣾⠁⠀⠀⢀⡴⠋⠀⠀⣼
⠀⢯⠳⡝⠾⡈⣇⡠⡀⠀⠀⠀⠻⡿⠃⢰⣿⣿⠁⣴⣿⠛⣆⠀⢀⣿⣿⠀⠀⣼⣿⠇⠀⠀⠀⣼⡅⠀⢰⣿⡟⠀⠀⠀⢸⡁⠄⣠⠶⠋⠀⠀⠀⢸⡇
⢠⡎⠙⠌⠦⣇⠁⠄⣿⣤⠤⡄⠀⠀⠀⣿⣿⡇⢰⣿⡇⣰⠃⢀⡞⠁⠛⠷⠛⣿⣿⠀⠀⠀⣸⠃⠳⠤⠾⠟⠀⠀⠀⠀⣠⠽⢻⡇⠀⢀⠀⢀⣠⠏
⠀⠉⡟⠋⠂⠈⠳⣎⡙⠀⠀⣼⠀⠀⠀⣿⣿⠁⢸⣿⡟⠁⣠⠏⠀⠀⠀⠀⠀⢿⣿⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠙⠒⠒⠛⠋⠁
⠀⠀⠓⠂⢐⠶⠀⠬⠛⢦⣄⡩⠇⠀⠀⠘⠿⠖⠚⠻⠿⠚⠁⠀⢀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⠟⠋⠀⢲⡄
⠀⠀⠀⠐⢧⣀⢀⡼⢧⡽⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⣤⣄⠀⠀⢯⡀⠀⠀⢄⣱⢛⣧
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⣀⣀⣀⣀⠀⣰⣿⣿⠁⠀⠀⠀⢀⣀⣀⡤⠶⠂⠁⠀⢀⣴⣶⠋⠁⢻⣿⠁⢀⣿⣿⠀⠀⠀⠉⠉⠓⠉⠙⠺⠇
⠀⠀⢀⣤⣶⠶⣄⠀⠀⠀⠀⠀⢴⠛⠉⠉⠉⠉⠉⠛⠛⠻⣿⣿⡿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⣸⣿⡇
⠀⣠⣿⡟⠁⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠘⣿⠇⠀⣿⣿⠃⠀⠀⣼⣷⣄⣤⠤⣤⣄
⢠⣿⡟⠀⣠⣾⣿⠃⠀⠀⣰⣿⡇⠀⠀⢠⣾⡷⠀⠀⠀⢠⣿⣿⠀⠀⢠⣿⣿⠀⠀⢠⣤⡄⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⢀⣿⣿⠋⠀⠀⣨⣿⡆
⠘⣿⡷⠚⢹⣿⡿⠀⠀⣰⣿⣿⠁⠀⢠⣾⣿⡗⠀⠀⢠⡟⣿⣿⠀⣠⣾⣿⡇⠀⠀⣿⣿⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿
⠀⠀⠀⠀⢸⣿⡇⠀⣴⢻⣿⡏⢀⣴⢟⣷⣿⡅⠀⣠⠟⠀⠘⠿⠟⠉⢸⣿⡇⠀⣠⣿⣿⠁⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠀⠀⣾⣿⡇⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠘⢿⣧⠞⠁⠀⠻⠿⠛⠁⢸⣿⣿⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠻⠷⠞⠁⢿⣿⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠦⠴⠋⠋⠁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢹⠀⡇⢾⢸⡯⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⣿⢁⠞⠀⠀⠀⠘⠃⠃⠘⠸⣒⠀⢀⣾⣟⡽⠣⢧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⠸⣿⠃⢀⢠⣄⠢⣠⣴⠈⣇⡦⣩⡝⣿⣏⣵⢦⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡔⠻⣶⠁⢰⣟⣼⣏⢾⡜⣿⣿⡏⠼⣿⣹⣇⢀⢀⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠙⠃⣾⡟⠈⢡⡄⣠⢉⣀⢉⡀⡉⠀⠉⠀⢘⡛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠐⠀⠀⠻⠇⠛⠀⢹⠁⣿⣸⢿⣷⣇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣀⢠⢠⠀⡀⢠⡙⠃⠈⠁⠈⠁⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢆⠻⣴⡏⠘⠈⠀⠘⢿⣧⢡⡴⢤⡿⣶⡄⣿⠃⡄⣶⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⡇⠀⢸⣷⡀⠈⡿⣿⡇⡸⢠⣿⣡⣿⣾⣾⡁⠈⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢻⣇⠀⡟⢙⠿⠖⠁⣬⢻⡄⠸⠿⠃⠘⢛⣹⣷⡋⢩⢆⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠢⠌⠁⠀⠀⠁⠀⠀⡻⣮⣤⣤⣤⣴⠾⠛⠁⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⢨⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⢹⡇⢸⡇⢺⡈⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢔⣴⠁⢀⣿⢻⢡⡆⠀⠘⠃⠈⠁⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡎⢹⣇⣾⠏⠀⠀⠀⠀⣡⣴⢶⣿⠤⣾⠗⢛⣿⢅⠰⣶⣀⠢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁⠀⠸⣷⣼⣷⠉⢰⣿⢀⣿⣇⣾⡟⠉⣠⢏⣾⡇⠙⢁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣸⡿⠈⠻⢦⠃⠙⠋⠙⢟⡌⠛⠚⠁⢸⡿⢁⡴⠋⠞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠴⠞⢋⠄⠀⡄⢠⢄⣀⡀⣀⢠⠀⠀⠀⠑⠈⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢺⣯⠇⣿⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢀⡖⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⣄⠀⢀⣀⡀⠒⢶⣿⠷⣶⢶⠆⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⣿⡏⠀⣿⣿⣴⣿⡯⠿⣢⣿⡟⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣌⠛⠛⢋⣿⣿⠙⢿⡤⠞⠋⠻⣧⡴⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣿⡟⣀⠀⠀⠩⠀⠀⠀⠒⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣠⡾⠋⠜⠵⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡤⠀⠀⠄⣡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠘⠀⠀⠀⠀⠹⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣈⡀⠀⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠠⣿⣽⣷⠀⣾⣳⠆⣉⣬⡑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠙⢿⠛⣦⠂⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠺⠟⢀⣀⡉⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⢱⡶⠀⠀⣨⣇⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢪⠿⢃⣀⢀⠀⠀⣠⠀⠆⠀⠀⠀⠀⢰⡇⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⣞⣏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⢋⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⡀⠀⠀⠀⠠⠥⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⠘⢀⠀⠰⠀⠀⠀⢠⣶⠀⡀⠠⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⣜⡒⣆⣫⡴⠂⠙⠀⠈⠣⠀⠉⠉⠀⣀⡐⠀⣀⠤⠆⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡉⢉⣿⣱⣀⠄⠀⠀⠀⠀⠀⠀⠈⣡⡛⠟⠻⢷⠂⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢈⣡⣿⣤⠴⢾⣾⢄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⠖⠛⠈⠟⠀⠘⠉⢉⠆⠀⠐⠢⠀⠀⢤⠀⠀⠀⠀⠀⠁⠉⢫⠄⣀⡀⢈⣀⡜⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠶⢀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣻⣉⣹⠏⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⢸⠖⠂⠙⡆⠀⠀⠁⡀⠋⠀⣠⣤⣤⡤⢲⣶⠂⡀⠁⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠋⠙⠚⢧⡻⣿⣦⠛⠀⠀⠀⣍⠀⠚⠛⠛⢉⣀⣸⠀⣤⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣤⣶⡖⢂⡀⠀⠉⢀⣤⠀⢀⣿⡿⠀⠀⠀⠀⠈⠹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠈⠛⠁⠀⢮⣿⡷⢿⡿⠃⠀⠀⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠠⠈⢡⡄⡄⢰⣦⠛⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣆⢹⠘⠿⠛⠁⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣠⣶⡴⢻⠃⣠⡀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠉⠑⠃⣛⡈⠛⡉⠀⠛⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠎⠁⠯⠐⢄⠀⠀⠀⠀⢠⣀⣿⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠘⠀⠀⢀⡄⡆⣾⠿⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣲⡍⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⢀⠀⣀⣠⣾⠋
⠀⠀⠀⠀⠀⠄⠐⠓⠀⠉⠑⠒⣞⠋⠙⢯⡈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⡀⠀⠀⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢤⠀⠀⣠⠤
⠀⠀⠠⠀⢀⡔⠀⢀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠘⠂⡀⠀⠀⠈⠀⠀⠀⠀⠀⠆
⠀⠀⠁⡠⡌⠀⠀⠁⢠⡇⢸⢧⠃⠀⠀⠀⠀⠂⠀⠀⠠⠀⠜⠁⠒⠀⠈⠒⠚⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠀⠀⡇⠀⠙⠂⠀⠴⠀⠇⠘⠘⠄⠜⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀⠂⠀⢐⠈
⠀⠀⠀⠀⠰⠲⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⡀⠐⡶⠀⢸⢠⠂⢐⠄⠁⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢐⢠⠆⡄⡤⣰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠈⣧⠀⢸⡌⠣
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⢀⡀⣀⢀⠀⠀⠀⡀⠀⠀⠀⡀⣤⠣⠤⠃⠀⠚⠀⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠷⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⡀⣤⡔⠁⡎⠸⣴⡇⠀⡀⢀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⠀⠀⠀⠈⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠑⠚⠁⠥⠏⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠐⠈
⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⢀⡀⢀⡀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⣰⣿⠀⢸⣷⠀⠻⣿⡄⠀⠈⠁⠛⠨⣿⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⢻⣿⠀⢸⣿⠀⠀⠹⣿⣄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠐⠋⠀⠈⠛⠂⠚⠁⠀⠀⠀⠙⠋⠀⠀⠀⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠰⡆⣠⡖⠀⢶⡄⢰⣶⠀⠀⠀⠰⣶⣆⠀⠀⢴⢠⣶⡆⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⠀⠀⠀⠘⣿⣦⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀⢠⡆⠻⣇⠀⣼⠏⠘⢿⣄⠀⠀⠀⠀⠈⢿⡇⠀⠨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⢀⠀⣀⡀⠀⣀⡀⢀⣀⠀⣀⠀⠀⣀⣀⠀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⡇⠘⠀⣿⡇⢀⣿⡇⢸⣿⢀⡈⠀⠀⣿⣿⠀⢹⣷⠀⠸⣿⡀⠘⣿⣆⠀⢸⣧⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠈⣿⡇⢸⣿⠈⢁⡀⠀⢿⡿⠀⣸⡿⠀⠀⢿⣷⠀⢸⣿⠀⢀⠙⠛⢿⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠛⠁⠀⠛⠃⠘⠛⠀⠛⠁⠀⠙⠋⠀⠉⠀⠀⠀⠈⠛⠃⠘⠛⠀⠈⠃⠀⠉⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠀⣶⣖⠀⠀⣶⡄⠀⢰⣶⠀⡀⠀⠰⣶⡆⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣿⡇⠀⠀⢹⣿⡀⢸⣿⢾⣧⠀⢠⣿⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠿⠯⠀⠀⠈⠿⠧⠸⠿⠈⠿⠧⠰⠿⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡄⢠⠀⣤⡀⠀⣤⡀⢠⣄⠀⣄⠀⠀⣠⣄⠀⣄⠀⠀⢀⣄⠀⢠⣄⠀⠀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⠈⠀⣿⡇⢀⣿⡇⢸⣿⢠⡀⠀⠀⣾⣷⠀⢹⣷⠀⠸⣿⡄⠈⢿⣦⠀⢸⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⣿⡇⢸⣿⠈⢡⡀⠀⣿⣿⠀⣸⡿⠐⠀⢻⣷⡀⢸⣿⠀⢠⡉⠙⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠉⠁⠈⠉⠀⠉⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠁⠈⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠳⢠⣾⠃⠘⣷⡄⣿⡇⠀⠀⠀⠻⣿⣆⠀⠐⠇⢼⣿⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠘⣿⣆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠀⠾⠈⠻⠆⠰⠛⠁⠙⠷⠄⠀⠀⠀⠀⠘⠿⠀⠀⠾⠿⠀⠺⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠰⠀⠀⠀⠀⠄⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠈⠐⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠰⣀⣀⣀⡀⠆⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠈⣿⢟⠛⡛⣿⣿⣿⣿⣿⢻⣿⣿⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡿⢸⢡⢨⠇⡏⡄⡽⠘⣼⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠿⠷⠿⠾⠶⠶⠶⠷⠶⠿⠾⠿⢸⣿⣧⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣉⠉⠀⠀⠀⠐⠒⠐⠒⠒⠒⠒⠂⠀⠀⠈⠉⠉⠀⠀⠪⠤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢰⠀⢈⡇⢀⣀⠀⢀⡀⠀⠂⢠⠇⠀⠂⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠊⢰⡏⣸⣀⠊⢣⣠⡃⣸⠀⣸⠁⣸⠀⣼⣸⠧⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠈⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⢤⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠤⣀⠠⠃⠀⠀⠀⠀⠡⢀⡴⠒⢄⡐⠁⠀⠈⢣⡀⠀⣠⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣀⡈⢄⠀⡱⠀⠀⠀⠀⠈⠙⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⠹⢍⠀⠀⠀⠀⠀⠀⠀⡗⠂⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠳⢄⣀⣀⣀⢀⡠⠂



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣗⢂⠁⠀⠀⠀⠀⠀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠒⡻⡳⡶⣲⣤⡀⠀⠀⢀⣴⠟⠁⣡⠼⠄⠀⡰⠶⢶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠽⣧⣠⣼⣗⣵⣿⣿⣶⣾⡿⡤⣦⡀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⠾⠿⢿⣿⣷⣟⣵⣿⣿⣿⣿⡿⠀⠀⠀⠁⣿⣿⠏⠀⢡⠀⠄
⠀⠀⠀⠀⠀⣰⡾⠉⠁⠠⣬⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣧⠐⣿⠀⠀⣿⣿⣆⠸⠳
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢯⠳⢻⣿⠿⣍⠚⢿⣿⣿⣿⣿⡷⣤⡘⠀⠀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣟⢏⠂⠀⠈⠖⠟⠊⠂⠘⣻⣿⣿⣿⣧⡈⣷⠀⠀⣿⣿⣿⠇⠀⢩⠀⠀⠀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠹⡎⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠈⠱⡡⠀⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⢈⠠⠀⠀⠄
⠀⠀⠀⠀⢀⣾⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣦⣈⣀⣀⣴⣦⠀⡿⣷⣿⡿⣾⣹⡿⠂
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣿⣟⣛⣛⣛⣒⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣶⢰⣿⡍⠘⣿⠀⣠⡄⠀⣰⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣴⠟⣹⡇⢸⣿⠃⠀⣿⣴⣿⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⡴⠛⠁⠀⣿⠃⢸⣿⠤⢤⡟⢸⡏⣰⢫⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠛⠉⠀⠀⠀⢸⣿⠀⢸⡇⠀⣼⠁⢻⡿⠃⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠇⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣴⣶⣶⣶⣶⠶⢶⣶⣶⣶⣶⠶⠖⠲⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣾⣿⣿⣟⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠉⣀⣤⣤⣈⣿⢋⣠⡴⢒⣶⣤⠈⢿⣥⣤⣤⠀⢠⣤⣤⣤⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⠀⢸⣿⣿⡏⠀⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⣿⣿⣋⣉⣀⣤⠀⣽⠀⢸⣿⣿⡟⢀⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⠀⢿⣿⣿⡿⠟⢁⣾⣿⡄⠘⠟⠋⣠⣾⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠉⠉⠉⠉⢉⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⣰⠖⣶⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⢤⡿⠆⠀⣼⠇⠀⢀⡀⠀⢀⡉⠀⢿⣠⠇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡟⠁⡤⠀⠀⣸⠁⠀⡜⣿⠀⡠⢻⠃⢠⡾⠀⠀⡼⠻⣦⣴⠞⠉⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⡟⢀⠞⢰⡇⡴⠁⢿⡴⢻⣇⡴⠋⠀⣼⠋⢹⡆
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠀⠀⠀⠷⠊⠀⠈⠛⠀⠀⠈⠀⠀⠉⠀⠀⠀⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠴⠀⠀⣀⠀⠀⠀⠉⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⡇⠀⣰⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣰⡏⠀⢠⠞⠀⢰⠇⢀⡏⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣀⠔⠁⠀⠀⡿⢀⡞⢀⣿⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢼⡿⠁⣠⣤⡄⢰⣧⠎⠀⣸⡧⠚⠁⣴⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡇⠸⣿⠉⣀⠼⡇⠀⠀⣿⠀⠀⢠⠿⠧⠟⠀⣠⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⢤⣀⠘⠿⠂⢸⣧⠀⠈⠉⠁⠀⢻⡀⠀⠹⣆⡴⠋⠀⠀⠀⠰⣏⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠿⠄⠀⠀⠀⣤⡄⠉⠒⢂⣀⣀⣠⣶⣦⣀⡀⠙⠒⠒⢲⡟⠚⢳⣦
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣀⡤⠀⠀⢸⣧⠀⠳⠄⣀⣀⣀⣰⣿⠗⠒⠉⠉⠀⠰⡿⡼⠁⠀⠉⣷⠀⠀⣼⡇⢀⣾⡿
⠀⠀⠀⠀⠀⢻⡀⠀⠀⣼⡿⠁⠀⠀⢸⣿⠀⣀⣤⣤⠀⠀⣼⣿⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⣀⡄⠀⢰⡿⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠂⢼⣿⡇⠀⠀⠒⣿⡏⠀⣿⡇⠉⠀⣴⣿⡟⢀⣾⢻⡇⠀⣿⣧⡶⣦⣾⡿⠟⣱⡿⠁⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣼⡟⠀⠀⠻⣧⡴⠞⠉⣿⣇⠈⠿⠾⠁⠀⣿⡯⠴⠋⠻⣧⡴⠛⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣩⡴⠒⠐⢾⡶⣿⣆⠀⠀⠀⠀⠀⡯⡠⢤⣶⣼⣤⣿⣷⡟⣟⠛⠻⡿
⠀⠀⠀⠀⠀⠀⠀⡿⣏⢣⣿⠀⠀⠀⠀⢳⣟⠋⡆⠀⠀⠀⠀⢰⠐⠃⠉⢹⢾⢻⠹⡟⠛⠓⠤⠇
⠀⠀⠀⠀⠀⠀⠀⢻⢧⠘⣿⣆⠀⠀⠀⠘⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⢾⠅
⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⡛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣏⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡎⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⣿⣱
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⣱⣽⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣝⣿
⠀⠀⠀⠀⠀⠀⠸⡈⠀⣿⣧⣄⣠⡴⣣⡗⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣹⣟⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠑⡐⣽⡛⡷⣶⣶⣯⠧⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣻⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣾⣷⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡜⣿⢤⣬⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⢉⣱⣤⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⢶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣞⣽⢕⡰⠶⣲⠏⠥⢍⣳⡄⠀⠀⠀⠀⠘⣿⣷⡽⠖⢛⣛⣩⣭⡵⢛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡟⢡⣉⡱⠛⠉⠙⠫⣍⠁⢻⡀⠀⠀⠀⠀⢰⡏⣳⣯⡿⠋⠁⠀⠈⠣⣔⠹⣿⡀
⠀⠀⠀⠀⠀⠀⡿⣵⠲⡌⠀⠀⠀⠀⠀⠙⡓⠾⣇⠀⠀⠀⠀⠸⣇⠗⣿⡇⠀⠀⠀⠀⢠⡿⠯⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣈⠹⠃⠀⠀⠀⠀⠀⠀⢷⠥⢽⠀⠀⠀⠀⠀⠻⣦⣼⣷⣤⣀⡠⠴⢏⣐⣿⠋
⠀⠀⠀⠀⠀⠀⢿⣧⣛⡄⠀⠀⠀⠀⠀⠀⣼⣤⣽⠀⠀⠀⠀⠀⡟⣎⢿⣥⣆⣭⣤⣶⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⡀⠀⠀⠀⠀⢠⡿⣻⡏⠀⠀⠀⠀⠀⢿⡘⣀⠀⠀⠹⡜⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣾⡮⣿⣦⣤⣴⣷⣮⠷⣿⠁⠀⠀⠀⠀⠀⡟⠛⢤⡆⠀⠀⢷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢥⢦⣷⢾⡟⣦⡗⣤⠀⠀⠀⠀⠀⠀⣧⠀⢤⣧⠀⠀⢘⡽⢏⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠏⠾⠛⢻⣴⢏⠀⠀⠀⠀⠀⢠⡏⠴⣕⣈⡄⠀⠈⣿⠦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡽⠆⠀⠀⠀⠀⠰⠚⠓⠈⠋⠓⠀⠀⠻⠮⠿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠠⠑⣄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣷⣄⣀⣱⣤⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡂⠂⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣦⣴⡘⣿⡟⠛⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⠿⢿⣿⠿⠿⠛⠉⢿⣿⣷⡟⣿⠀⣴⡆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣷⠀⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⣿⠏⠻
⠀⠀⠀⠈⠉⠉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠙⠿⠛⠿⢟⠀⢠⡟
⠀⠀⠀⠠⠴⠶⠾⠿⢿⣿⣿⣿⣯⡏⢭⣭⣭⣭⣥⣥⣀⣤⣤⣴⣾⣿⠇⠸⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⠋⠀⢸⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣜⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣦⡤⠽⣿⣿⣿⣿⣿⠟⠁⠀⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⣰⡟⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢻⣿⣿⣿⣏⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢯⠈⠋⠉⣿⣿⣿⣿⣿⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⣄⣈⣉⠉⠉⠁⠀⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⡯⣿⣾⣻⣿⣯⣿⣶⣄⠀⡀⠞⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢷⠟⣿⣿⡉⠊⢳⣀⠱⡙⣿⣀⣀⡀⠈⢀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠂⣸⡇⣻⣿⣇⡋⢎⣧⣰⣳⣹⣇⢨⣿⣠⣬⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⡁⡏⣷⣿⣿⣿⡷⣶⣻⣏⣩⣼⣾⡿⡋⠄⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠷⣿⣻⣿⣽⣿⣶⣿⣿⢿⢯⣿⣿⢿⢻⣇⢡⢡⢠⢷⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠹⣿⣤⡛⣯⣿⣿⣿⣾⣿⢿⡋⠘⡎⣿⣀⣄⠆⠾⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡇⠈⡿⠿⠿⡟⠻⣿⣇⣠⣤⣧⣤⣷⡾⣿⣿⠓⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣀⣱⣤⣶⣷⠿⣿⡟⣿⣯⣭⣿⡿⢻⣿⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣿⣶⠾⡖⡋⢙⣹⠉⠉⠁⠀⠀⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⡆⠀⠉⠀⠀⣹⣿⣿⣿⣶⣦⣄⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⠀⠀⣾⣿⣿⣿⣟⡿⠉⠉⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠉⠛⠛⠁⠀⠀⢀⣾⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⠀⠀⠀⢀⣀⣴⣿⣿⡇⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠠⠤⡀⠀⢝⢤⡀
⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠴⡶⠴⠂⢀⣀⣂⡀⠀⠀⠈⠀⢀⠐⢁⡔⠐⠄⠀⠀⠀⠈⣏⢳
⠀⠀⠀⠀⠀⢂⠝⠁⢀⠜⠁⠀⠀⠀⠀⠀⢀⠀⡀⡠⠀⠀⢀⣖⢻⡓⢼⡽⠷⠆⠀⠀⣐⠀⡎⠀⠀⠀⡇⠀⡇⠀⢸⡈⡇
⠀⠀⠀⠀⢁⠀⠄⢴⡏⠀⢀⣀⣀⡀⡠⢀⠂⠐⠐⢁⡀⢠⣿⣭⡆⣏⣀⡈⠓⢀⠀⠀⢨⠀⢇⠀⠄⣀⠇⢈⡇⠀⢸⡤⡃
⠀⠀⠀⠈⠃⠠⠀⡘⠈⠉⠀⠀⠀⠈⠀⡈⠀⠀⠁⠉⢀⣿⡈⡿⢤⠋⡉⠲⣻⣷⣀⢄⠈⠧⡀⠉⠈⢁⣠⠎⠀⢠⡟⣸
⠀⠀⠀⢀⠀⡆⡇⡇⣀⣀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠀⣨⡷⠊⣤⠞⢿⡇⠀⣉⣹⠈⠂⣠⣄⣀⣉⠀⢉⣁⣠⡾⡏⠔⠁
⠀⠀⠀⢀⣇⢳⠁⠁⠀⠀⠀⠀⠀⠀⠀⢁⣨⠀⠇⠀⡹⠁⣾⡴⠒⠻⡿⠞⠻⡕⠀⠀⠈⠁⡬⠭⢍⡭⠏⠐⠂⠁
⠀⠀⠀⠀⠘⣌⠶⣔⡀⠀⠀⠀⠀⠀⠀⠰⠰⣆⢂⠀⠘⣿⣻⣾⣲⡂⢰⣾⠶⣇⣀⣀⣂⣤⡬⠀⠀⢠
⠀⠀⠀⠀⠀⠊⣺⣷⣷⣄⣀⠀⣀⡀⡀⢠⣣⡣⣊⣢⡀⠘⢿⣿⡿⡂⢯⡹⠂⣠⣤⣤⠀⠀⠙⢳⡖⠢⢁⣀⡰
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠀⠃⠉⠙⠋⠽⠉⠁⠻⡻⣻⡇⣼⣶⣞⣯⣭⣏⡙⢻⣻⠏⠛⠒⢭⣍⣉⠂⠐⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠈⣣⣌⡀⠙⠾⣟⠧⣍⣘⣥⠾⢛⠛⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠛⠉⠉⠙⠦⠤⠀⠀⠐⠘⠁⣰⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡈