Super Mario Bros. Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⢠⣾⣿⡿⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⣩⡽⠿⢷⣦⣿⣿⢃⣾⣤⡆⢹⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣾⣭⣉⡇⢸⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠰⠶⠞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⢀⡀⠀⠉⢹⣿⣷⡄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣉⣴⠾⠛⠛⠛⢿⡁⠀⠀⣾⡏⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡏⠀⠀⠀⠀⠀⠁⠀⠀⡿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠀⢾⣿⣿⣿⠋⠉⠈⠙⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣶⣤⣤⣶⣿⣿⣿⣿⣿⡿⠀⠀⠛⠛⠁⠀⢀⡴⠂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠘⣄⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡙⢿⣿⣿⠃⠀⠀⢀⣴⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠀⠈⣻⣿⣿⣷⣿⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⡄⠀⢤⡀⠹⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣀⣸⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠋⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣧⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢼⡧⣾⣾⣵⣦⣇⡴⠚⠇⣀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⢠⣛⠟⠁⢈⢠⣟⡋⢸⣏⣥⣤⢐⣿⡽⠃⠰⢀⠔⡆
⠀⠀⠀⣦⠀⠀⣴⣿⣇⣼⣦⣿⣷⠟⣿⠾⢫⡿⠳⠟⠉⠀⣴⣿⠊⠀⣷⠀⢀⢀
⠀⠀⠀⣆⠑⠤⡏⡁⢹⣿⠋⠘⣁⠀⣥⢀⡞⠀⠀⠀⣠⣞⣿⠃⠀⠀⠻⡶⠗⠚⠦⡄⢀⡠⠊⣸
⠀⠀⠀⠸⣦⡼⣿⣷⣷⢃⣤⠀⣿⣸⣿⣿⣿⣄⠐⠻⢛⡟⠻⣷⣄⣀⣶⠃⠀⢄⠀⣼⠉⠀⢴⡇
⠀⠀⠀⠀⠘⣇⢈⠻⣿⣸⣧⣼⢿⣿⣿⣿⣽⡿⠿⠛⠻⠧⡀⠈⠛⢿⠃⠆⠀⡾⠕⠁⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⣿⣷⠍⠳⢏⣁⣿⣿⡿⣹⡏⠀⠀⠀⠀⠀⡘⣆⢀⡎⠀⠀⠘⣴⠇⠀⠀⠀⢦⠋⣆⠀⡄
⠀⠀⠀⠀⠀⢸⢻⡿⠃⠀⠈⢻⡿⠶⠊⠛⠃⠀⢀⠀⠀⡠⠛⠛⠉⠀⠀⠀⠀⣧⠖⠂⣀⢠⠆⠀⣸⢿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⢀⡇⢀⣀⣀⠀⠀⣀⣴⠋⢠⣾⡿⠉⠀⣼⡿⠒⠗⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠘⡀⠀⢰⣔⣪⠄⠀⠀⠀⣠⣸⡏⠁⠀⣸⣧⡉⠁⢤⡀⠓⠿⠟⠻⢿⠀⢉⣵⣢⡿⢸⢂⣆⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠉⢿⠱⡟⣿⠶⠶⠰⡿⠈⠉⠁⣰⡞⠛⣿⠿⣧⣴⣿⡿⢿⣿⣿⠶⣶⣿⣿⣿⡗⣣⣿⣼⠋
⠀⠀⠀⠀⠀⢠⠒⢿⠁⠀⠀⣀⡀⠀⠀⢀⣠⡰⠟⠛⠀⠋⢱⣘⠯⠙⣅⠾⢿⣿⣶⣽⣿⡿⣫⣾⣿⡿⣿⢀
⠀⠀⠀⠀⢠⠣⠛⠀⡷⠶⠿⣿⠋⠛⠒⠒⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣨⣿⡿⠙⡏⣹⣿⣿⣇⡷⠒⠁
⠀⠀⠀⢠⠃⠀⠀⠈⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠸⢻⣿⠀⠀⠀⣿⡿⠀⡈⢧
⠀⠀⠀⠈⢂⣲⡶⠀⢀⡴⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⣼⡆⠀⠀⣿⣇⡘⠁⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠈⠃⠓⢤⣄⣠⢾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⣷⣾⣿⣧⠀⠀⣿⣿⣷⡀⢦⣤⢤⡬⠦
⠀⠀⠀⠀⠀⠀⢰⣿⡷⣽⣿⣿⣼⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠾⣿⡄⣰⣿⣿⣿⠖⢋⡀⠒
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢹⣿⣿⣦⠀⠄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠹⣿⡏⣹⡟⢄⠈
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⢸⣿⣿⣿⣶⡄⢀⠀⠀⠀⢀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠈⠛⣿⣿⣿⣦⡀⠀⠠⠴⣿⠘⠀⠀⠀⠀⠀⠀⠀⢀⡦⣿⣿⣇⠘⠃⠠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡒⠀⢁⣠⣼⣿⣿⣿⢻⡟⢿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠠⢿⣷⣿⣿⣿⣷⣦⣤⠄
⠀⠀⠀⠀⠀⠀⢀⡠⠘⢁⡁⠈⠅⠉⠿⢿⣿⡞⣷⠢⠙⠻⢿⣸⣂⠀⠀⠀⠀⠀⢔⣦⣿⣿⣻⡏⠯⠍⠒
⠀⠀⠀⠀⠀⢀⣈⡀⠠⢤⡀⡀⢀⣀⣀⣤⣼⡷⣿⠠⡦⠀⢸⠏⠛⠻⣦⣾⣿⣶⣾⣿⣻⡁⠀⣠⣠⣌⢀
⠀⠀⠀⠀⠀⠈⢈⢣⣴⣾⣿⠻⠿⠞⠛⠉⠙⠂⠁⠀⠀⠀⡠⠊⠉⠀⣤⠬⠩⠩⠆⠾⠛⣇⠀⠏⠻⠏⠩
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣈⠀⠀⢀⠀⣀⢠⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⣾⡏⡀⠀⢿⢻⣇⡀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠉⠙⠛⠦⠞⠋⠉⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠖⠶⠶⣏⡔⠉⠀⠈⠑⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⣄⠀⠀⠀⣀⡴⢾⡇⠀⠀⠀⠠⡈⠙⢦⣀⠀⠀⢸⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⢀⣴⠋⢻⡄⠀⠀⠹⣆⣤⠞⠉⠀⠸⡇⠀⢀⣀⡀⠈⢦⡀⠙⢧⣠⠎⠀⠀⠀⠸⣧
⠀⠀⠀⠀⣼⠋⢹⣤⠶⠛⠒⠒⠀⠹⣇⠀⠀⠀⠀⠻⣦⡟⢛⠻⠉⠉⣻⣶⣶⣽⢦⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⣠⠿⣆⠸⣇⠀⠀⠀⠀⠀⠀⢹⡄⠀⣀⣤⣤⣾⣜⣉⡇⠀⣠⠖⠺⣯⡙⠈⢷⡀⠀⠀⢸⡇⠹⣆
⠀⠀⠀⢻⣄⠙⠓⣾⠋⠹⠀⠀⠀⠀⠘⢻⡾⠁⠀⠀⠀⠙⢿⡅⢠⠇⢠⣲⡇⠉⠓⠚⢧⠀⠀⠀⣷⣄⢹⡆
⠀⠀⠀⠀⠉⠻⣞⠋⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠧⡽⠟⡀⢀⣠⡤⠾⡇⠀⠀⠇⠙⣧⣿
⠀⠀⠀⠀⠀⠀⠈⠛⢳⡖⠁⠀⣀⡴⠟⠉⣿⣦⣀⣀⢀⣀⣤⣾⣷⣶⣾⣿⣿⡾⠀⠀⣀⣿⣤⡀⠀⠀⣸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣍⠀⠀⠀⠸⣏⠿⠿⢿⣿⣿⠿⣿⡿⠋⠉⠘⠧⠴⠊⣡⠄⠀⢹⡶⠞⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⢷⣄⠀⠀⠹⣦⡀⠙⣯⡭⠭⢽⡇⠀⠀⠀⠀⠀⠾⠋⠀⠀⣸⠇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠙⢷⣀⣠⡴⢿⣄⠘⠢⠴⠊⠀⣀⣀⣀⣠⡤⣤⣤⣴⠞⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⣠⣴⠛⠁⣴⣋⣉⣳⣶⣶⠞⠋⡽⠛⠉⠙⠳⣦⡶⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠁⣹⢰⡯⠉⠉⠀⠠⣜⠋⠓⢾⠛⢶⣤⣄⡀⠀⠙⣦⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣱⡏⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣴⣇⣠⡿⢤⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⠨⠙⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⣀⣀⣰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⣄⠀⠀⠀⠘⠏⢥⣼⣶⣿⣷⣿⣿⣿⣿⣿⠿⠇⠀⢀⣠⣤⣶⣶⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣿⢿⣯⠁⠁⣴⡿⣿⣟⠻⣦⣶⣿⣟⣿⣏⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣤⠀⠀⣥⣦⡀⠉⣻⣿⠛⢷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠉⠛⠁⠀⠈⠉⣠⡈⠻⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣷⣄⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣦⣬⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣿⣿⣿⣿⣿⡀⢀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⡿⠿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠠⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣴⡿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣌⣥⣈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁
⠀⠀⠀⠀⠀⠀⡀⠙⠁⢀⣀⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣠⠋⠀⢀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠑⠠⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢀⣈⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠀⠉⢈⣉⣉⣩⣿⡷⠀⠀⠀⠊⠉⠉⠀⠀⠉⠉⠙⢛⡻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⠿⠛⠛⠛⠛⠛⠿⢿⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠻⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⢵⣷⣼⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣂⣀⣀⣷⣀⣀⣀⣂⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣛⠻⣿⣛⣻⣟⣿⣿⣫⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣺⠧⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⣀⣀⣠⢤⠒⠉⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⡀⢀⠴⠚⠅⠀⠀⢈⣖⣋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣰⠀⠀⠠⡀⡴⠀⠐⠺⢉⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢮⠀⠢⣀⡀⠀⠀⠀⠀⠈⢀⣁⠤⠞⢁⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠉⠑⠒⠢
⠀⠀⠀⠀⠀⠀⢀⠤⠶⠒⠒⠚⠋⠒⠒⠒⢢⡇⣠⣀⣧⡠⠤⠤⠤⠴⠟⢳⠋⠛⠉⠀⠀⠘⠓⠢⡄⠉⠓⠪⢂⣠⡮⠁⠀⠀⠀⠀⠀⠘⠒⡄
⠀⠀⠀⠀⠀⠀⣜⡀⠄⠀⠠⠤⠀⢀⣀⣠⠞⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⢲⡞⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠻⡤⢂⣤⡄⢀⡼⢋⡭⠟⠀⠀⠘⠀⠀⢀⡠⡤⠒⠚⠛⠛⠳⠷⠤⣤⠀⣦⣹⠋⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢀⡴⠛⠛⣜⠤⠏⣴⠋⠀⠀⠀⠀⠘⠤⣤⢴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⢀⠴⠟⠀⡠⠊⠈⠳⣤⠯⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠤⠔⠒⠉
⠀⠀⡰⠃⠀⠀⠰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣀
⠀⠀⢻⣀⠀⢀⣼⣤⡀⠀⠀⠁⠀⠀⢀⣠⢴⣀⠰⠞⠁⠀⠙⢷
⠀⠀⠀⠉⠛⠋⠁⠀⠈⠳⢦⠤⠶⠚⠉⠀⠀⠈⠳⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⣂⡀⣀⢀⢀⠀⣀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡼⠛⠋⠻⣆⠀⠀⠀⠀⠐⠆⠚⠞⠓⢃⣾⠄⢸⠀⣀⢠⣼⠐⢽⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠀⠉⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠚⠳⠖⠺⠛⠻⠻⠟⢻⡟⠛⠟⠛⠿⠛⠿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠛⠛⠛⠉⠀⠀⠀⠀⠠⢸⠀⠀⠐⢀⢈⠸⠀⠸⢸⡇⠀⠂⠁⡇⡇⠰⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣶⣶⣶⣾⣶⣾⣶⣾⡷⣶⣷⣶⣶⣶⣷⢶⣷⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⢁⣠⡤⣦⣴⢤⣄⡀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣴⠛⠁⠀⢀⠀⠀⠈⠙⢷⡀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⣠⣤⡿⠶⠟⠛⠛⠛⠿⠿⢶⣶⣄⣽⠃⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⡶⠟⣩⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⢀⣉⣙⠻⣦⣄⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏⠀⣾⣿⠿⢿⣿⡉⠉⠉⠉⠉⢙⣿⣿⣿⣿⣷⡌⠙⣷⡀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣇⣠⡾⠋⢠⡴⠶⣌⠃⠀⠀⠀⠀⢛⣩⣥⣈⠙⢿⣿⣄⠈⢿⡆⠀⠀⠘⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣛⣿⠁⢰⠏⠠⠔⣘⣧⠀⠀⠀⣴⠋⠀⠄⠙⣷⠀⠛⠻⣦⣸⣿⡀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⡿⣿⠀⣿⠀⣆⣼⣯⣿⣤⣀⣰⡇⠰⢀⣶⣷⣿⠄⠀⠀⠈⠛⠻⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⣈⣵⡟⠀⣻⡶⠋⠁⠀⠀⠀⠈⠙⢷⣆⢸⣷⣼⣿⠀⠀⠀⢀⣠⡾⢻⡄⢀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⣻⡿⠃⠀⣀⡀⣿⡁⠀⣸⠟⠛⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣁⣠⣴⣾⣿⣿⢼⣇⣸⢋⣠⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⢁⣾⡧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠸⡇⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⣰⡾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠉⠙⣿⠿⠼⠿⠿⠿⢿⡖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢁⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠻⣦⣄⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⣿⠟⠛⠛⠛⣻⠁⠀⠀⠀⠀⠀⣠⡾⠟⢿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢽⠟⠁⢠⣬⣿⣤⣶⠶⠶⠾⠿⠟⢻⣿⠿⢻⣷⡀⠀⠙⢦⣄⣠⠞⠁⠀⠀⢀⣠⣴⣾⣿⣷⠶⠟⠁
⠀⠀⠀⠀⣠⡶⠟⢻⡇⠀⠀⠀⠀⠈⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣾⠃⠙⢶⣤⣀⣈⣀⣀⣠⣴⡾⠟⠉⠀⣿⠉⠙⠻⢶⣤⣀
⠀⢀⣴⠟⠋⣀⡀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⢀⣾⠃⠀⠀⠀⠈⠉⣙⡛⣽⠟⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠛⢷⣤⡀
⢠⣾⣫⡶⠟⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣀⣤⣾⠷⠶⣄⠀⣸⣇⣠⣤⣤⣀⣀⣀⠀⣸⠏⠀⣀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⣸⡿⠃⣠⡴⠚⢿⡀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠛⣻⡟⢉⡿⠁⢸⡆⣿⢀⡿⠉⠉⠉⠉⠉⠉⠉⣻⣏⡴⠛⠉⠙⢦⡀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢹
⣿⣧⡾⠋⢀⣤⠞⠃⠀⠀⠀⠀⢀⣠⡿⠿⠶⠾⠟⠁⢸⣇⠀⠜⣡⠏⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⣴⠘⡇⣿⡀⠙⢷⣄⠀⠀⠀⠀⠀⡘⢸
⠈⠻⣷⣴⣿⠉⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⣼⣿⣳⢚⣫⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣦⡀⠐⣁⡞⣹⡟⢿⣤⣾⡟⠛⠀⠀⠀⠴⣱⡿
⠀⠀⠀⠈⠛⠷⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣉⣉⣡⡶⠋⠀⠈⢿⠛⣷⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢰⠀⣿⣦⡿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⢄⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠈⠉⠛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠛⠻⢶⣤⣀⠀⠀⠀⠀⣸⡟⠀⠀⣀⣤⣴⠶⠾⠛⠛⢻⡿⠿⢷⣬⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣿⣧⡴⠟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠉⠉⠛⠛⠛⠛⠛⠉⠉⣉⣩⣉⣀⣸⣿⠛⠳⠶⠦⣤⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠛⠿⠷⣦⣄⣀⣀⣀⠀⠀⠀⣀⣀⣀⣠⣴⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣶⣄⠀⠀⣼⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠛⢋⣴⠾⠿⢿⣷⣶⣿⣿⠃⣴⣿⣤⣶⠈⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣯⣘⠉⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠉⠁⠀⠉⠛⠿⣿⣿⣿⢟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣤⡤⠀⢀⣀⣀⣿⣷⣿⡇⠀⠀⠉⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⣠⣾⠟⠛⠉⠙⠛⢿⡇⠀⠀⢀⣿⣿⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⣶⣿⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⢀⣠⣶⣶⣾⣿⣿⣿⡇⠀⠙⣿⣿⡿⠋⠀⠀⠀⣀⡀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠈⠁⠀⠀⠀⢠⡾⠋⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢳⣤⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡙⢿⣿⣿⣿⠇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠈⠻⣿⣿⣿⣦⣝⣛⣋⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣄⠀⠀⢀⠀⠈⣷⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⡆⠀⠸⣷⣀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡠⢤⡀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣶⠳⢿⣆⡀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⣚⠻⠿⠿⣿⣿⢿⣶⣤⣄⣀⠀⠙⠟⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠴⢪⣷⣦⣀⠀⠘⣿⡏⡤⢸⠏⠙⠺⢟⡢⣄⡀⠀⠀⠈⣳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣆⠀⢸⡇⡜⠡⣀⠀⠘⢹⠀⠀⣿⡆⠀⠀⠈⠑⣭⡲⣤⡴⠋⠀⠈⢷
⠀⠀⠀⠀⠀⠀⢀⡴⠚⢅⡀⠀⠈⠳⣄⠹⣇⣀⣽⠷⠀⠘⡀⠀⠻⣿⠀⣀⢀⣼⣿⣿⣿⠃⠀⢾⠃⢸
⠀⠀⠀⠀⠀⣰⠟⣀⣀⡀⠙⣶⠴⠲⢬⡷⠋⠁⠀⠀⠀⠀⠑⢄⣡⠞⣠⣿⡾⠿⣿⣿⡟⠀⠀⠘⢀⣾⠶⠖⠛⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⡟⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠼⠷⢤⣀
⠀⠀⠀⠀⢸⡇⠀⠴⠒⢺⠀⠀⠀⣦⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢹⣆⡀
⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡀⠀⠀⣸⠿⣿⣦⣤⣤⣤⣾⣿⣿⡿⠛⡹⠀⡿⢆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢀⠴⠖⠋⠀⠀⢈⠙⢦⡀
⠀⠀⠀⠀⠀⠙⢦⠀⡀⠀⠙⣳⠛⢁⡜⠙⣿⢿⠉⠛⠛⠋⠀⢠⣞⣡⠞⠀⣼⢰⣧⠞⣇⠀⠀⠀⠀⠀⣠⡞⠉⣿⡀⠀⠀⠀⠀⢠⡄⢷⠈⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠸⣤⣙⣶⠞⠁⠴⠋⢀⡼⠃⠀⠳⢄⣀⣀⣲⣄⠈⠛⠦⠤⢋⣾⠁⠀⢸⡀⠀⠀⠀⠺⠃⢿⠀⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣤⣶⠋⠀⠀⠀⠀⢠⡏⠉⢹⡏⠛⠶⠶⠶⠋⢸⡆⠀⠀⢳⠀⠀⠀⢀⠀⢸⡇⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢸⡇⠀⠀⢧⠀⠀⠀⢀⡀⣼⡇⢀⠤⡈⢧⣀⣀⡜⠀⢸⡇⢠⡟⠁⠀⣤⠀⠀⠀⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣸⣇⢀⠤⢌⠳⡂⠀⠀⠀⢸⢡⡏⠀⣸⡼⡆⠀⠀⠀⢸⣇⣈⣧⣀⣴⡛⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡜⡀⢠⢱⠹⡆⠀⠀⢸⡆⢧⣤⡿⢁⡇⠀⠀⠀⢸⣏⣁⣀⢀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢿⣷⠚⠚⠳⠿⣄⡀⠀⠳⣤⣤⣤⠾⠁⠀⠀⢀⣾⣅⣀⠀⠀⠈⠓⢤⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣋⣉⡉⠛⠓⠶⢤⣈⠙⠂⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠉⢳⡄⠀⠀⠀⠙⣆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡀⠀⠈⣉⠒⠤⢀⠈⠓⢦⡀⠠⡀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠐⠀⢙⠢⣄⠙⣆⣿⠀⡼⠁⠀⣀⣠⣴⠿⠋⠀⠀⠀⢀⡤⠿⠤⠤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⠀⠀⠀⣠⠑⢌⠣⡈⣿⣾⣷⣟⣛⣛⣛⣛⡒⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠛⠷⠶⣇⡀⠀⢣⢱⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠉⠷⠾⠾⠧⠤⠄⠀⠊⠉⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢼⡧⣾⣾⣵⣦⣇⡴⠚⠇⣀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⢠⣛⠟⠁⢈⢠⣟⡋⢸⣏⣥⣤⢐⣿⡽⠃⠰⢀⠔⡆
⠀⠀⠀⣦⠀⠀⣴⣿⣇⣼⣦⣿⣷⠟⣿⠾⢫⡿⠳⠟⠉⠀⣴⣿⠊⠀⣷⠀⢀⢀
⠀⠀⠀⣆⠑⠤⡏⡁⢹⣿⠋⠘⣁⠀⣥⢀⡞⠀⠀⠀⣠⣞⣿⠃⠀⠀⠻⡶⠗⠚⠦⡄⢀⡠⠊⣸
⠀⠀⠀⠸⣦⡼⣿⣷⣷⢃⣤⠀⣿⣸⣿⣿⣿⣄⠐⠻⢛⡟⠻⣷⣄⣀⣶⠃⠀⢄⠀⣼⠉⠀⢴⡇
⠀⠀⠀⠀⠘⣇⢈⠻⣿⣸⣧⣼⢿⣿⣿⣿⣽⡿⠿⠛⠻⠧⡀⠈⠛⢿⠃⠆⠀⡾⠕⠁⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⣿⣷⠍⠳⢏⣁⣿⣿⡿⣹⡏⠀⠀⠀⠀⠀⡘⣆⢀⡎⠀⠀⠘⣴⠇⠀⠀⠀⢦⠋⣆⠀⡄
⠀⠀⠀⠀⠀⢸⢻⡿⠃⠀⠈⢻⡿⠶⠊⠛⠃⠀⢀⠀⠀⡠⠛⠛⠉⠀⠀⠀⠀⣧⠖⠂⣀⢠⠆⠀⣸⢿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⢀⡇⢀⣀⣀⠀⠀⣀⣴⠋⢠⣾⡿⠉⠀⣼⡿⠒⠗⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠘⡀⠀⢰⣔⣪⠄⠀⠀⠀⣠⣸⡏⠁⠀⣸⣧⡉⠁⢤⡀⠓⠿⠟⠻⢿⠀⢉⣵⣢⡿⢸⢂⣆⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠉⢿⠱⡟⣿⠶⠶⠰⡿⠈⠉⠁⣰⡞⠛⣿⠿⣧⣴⣿⡿⢿⣿⣿⠶⣶⣿⣿⣿⡗⣣⣿⣼⠋
⠀⠀⠀⠀⠀⢠⠒⢿⠁⠀⠀⣀⡀⠀⠀⢀⣠⡰⠟⠛⠀⠋⢱⣘⠯⠙⣅⠾⢿⣿⣶⣽⣿⡿⣫⣾⣿⡿⣿⢀
⠀⠀⠀⠀⢠⠣⠛⠀⡷⠶⠿⣿⠋⠛⠒⠒⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣨⣿⡿⠙⡏⣹⣿⣿⣇⡷⠒⠁
⠀⠀⠀⢠⠃⠀⠀⠈⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠸⢻⣿⠀⠀⠀⣿⡿⠀⡈⢧
⠀⠀⠀⠈⢂⣲⡶⠀⢀⡴⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⣼⡆⠀⠀⣿⣇⡘⠁⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠈⠃⠓⢤⣄⣠⢾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⣷⣾⣿⣧⠀⠀⣿⣿⣷⡀⢦⣤⢤⡬⠦
⠀⠀⠀⠀⠀⠀⢰⣿⡷⣽⣿⣿⣼⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠾⣿⡄⣰⣿⣿⣿⠖⢋⡀⠒
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢹⣿⣿⣦⠀⠄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠹⣿⡏⣹⡟⢄⠈
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⢸⣿⣿⣿⣶⡄⢀⠀⠀⠀⢀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠈⠛⣿⣿⣿⣦⡀⠀⠠⠴⣿⠘⠀⠀⠀⠀⠀⠀⠀⢀⡦⣿⣿⣇⠘⠃⠠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡒⠀⢁⣠⣼⣿⣿⣿⢻⡟⢿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠠⢿⣷⣿⣿⣿⣷⣦⣤⠄
⠀⠀⠀⠀⠀⠀⢀⡠⠘⢁⡁⠈⠅⠉⠿⢿⣿⡞⣷⠢⠙⠻⢿⣸⣂⠀⠀⠀⠀⠀⢔⣦⣿⣿⣻⡏⠯⠍⠒
⠀⠀⠀⠀⠀⢀⣈⡀⠠⢤⡀⡀⢀⣀⣀⣤⣼⡷⣿⠠⡦⠀⢸⠏⠛⠻⣦⣾⣿⣶⣾⣿⣻⡁⠀⣠⣠⣌⢀
⠀⠀⠀⠀⠀⠈⢈⢣⣴⣾⣿⠻⠿⠞⠛⠉⠙⠂⠁⠀⠀⠀⡠⠊⠉⠀⣤⠬⠩⠩⠆⠾⠛⣇⠀⠏⠻⠏⠩
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣈⠀⠀⢀⠀⣀⢠⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⣾⡏⡀⠀⢿⢻⣇⡀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠉⠙⠛⠦⠞⠋⠉⠙⠒

⠀⠀⠀⠀⠀⠀⠖⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢑⣄⡤⢠⡀⠀⠀⠀⠀⠆⠈⢰⣄⠑⠀⠀⢣⠀⠀⠀⠀⠀⠀⠐⠃⢀⠐⠀⠀⠀⠂⡀⠠
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠀⢠⠞⢀⡄⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠
⠀⠀⠀⡤⠀⠀⢀⠈⠀⠀⢈⠀⠀⠀⠠⠁⠀⠀⢀⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠤
⠀⠀⠀⠉⠀⠀⠀⠉⠈⠀⠀⡄⠀⠀⠀⢀⠤⢄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠞⠈⣀⡀⠄⠀⠀⠀⠀⢀⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠊⠉⠆⠀⠀⠀⠉⡎⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠄⠀⡀⠀⠀⠀⠀⠢⡀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠆⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠈⠠⡀⠊⢲⣀⣀⠴⠧⠤⠃⠀⠀⠀⠀⠀⠀⠈⡆⠠⠔⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠙⠂
⠀⠀⠀⢀⠤⠐⠒⠒⠀⢄⠀⠀⠀⠀⠀⠀⢀⠀⠰⠖⠒⠠⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⢀
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠤⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠘⠄
⠀⠀⠃⠀⠀⢠⠀⢠⠀⠀⠀⠃⠀⠀⠀⠁⢀⠀⠀⡀⢀⠀⢀⠀⠁⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠈⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠰⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡓⠀⢉⠀⠃⣀⢈⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠈⠲⡀⠀⠀⠀⠀⠠⠚⠂⠐⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⢿⠋⡙⡟⠉⡉⠻⠋⠻⠛⠃⠀⠀⠀⠀⠐⠀⠇⠀⠀⠘⠂⢀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠈⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣤⠄⠀⢀⡁⠈⠀⡁⢸⠀⣤⠀⠛⢀⡆⠀⠀⠀⢀⢀⡀⢤⠖⠀⠻⠑⠀⠀⠀⠀⢀⠀⡀⣤⡶⠐⠻
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠃⠀⠚⠛⠋⠘⠛⠛⠙⠛⠛⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠐⠄⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠚⠁
⠀⠀⠀⠀⠐
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢘⠀⠀⠛⠉⠉⠉⠉⠙⠀⠀⢉⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⣀⠄⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠁⠀⠀⡃⢘⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠀⠀⣁⠀⠀⠂⠀⣀⠀⠀⢈⠀⠀⢘⠀⠀⠀⠀⠁⡐⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠛
⠀⠀⣀⣠⣈⣡⣴⣆⣀⣀⣤⣀⠀⠀⠘⠄⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⢀⠔⠒⠒⢦⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⢀⡀⠀⠄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠔⠉⠁⢀⡀⢘⠀⠐⢄⠀⠀⠀⠑⠄⠀⠛⠘⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠈⠁⠈⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⢰⠁⠀⠁
⠀⠀⢐⣇⣀⣀⣀⣀⣀⣀⣘⡇⠀⠀⠣⣀⠀⠀⠀⠀⣀⣀⡠⠞⠀⠀⠀⠀⠘⠈⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠑⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡆⠰⣤⠀⠀⠀⣿⠀⠄⢸⠉⠲⠤⠤⠶⢊⡴⠋⠁⠀⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠙⠳⢶⡚⠁
⠀⠀⠀⠀⠧⠀⢤⢤⠤⢤⣥⡀⢀⠸⠀⠀⠀⠀⣰⠋⠀⠀⠀⣰⠋⠳⣄⣠⠞⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢤⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⢤⡾⠁⠀⠀⠀⢠⠇⣠⣄⠈⠁⣠⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠈⠉⠉⠉⠙⠲⠤⣤⣤⣤⠤⠖⠋⠀⢀⡞⠀⠀⠀⠀⠀⣟⣠⠏⠈⠳⠾⠁⠸⠦⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⠦⣤⣠⣤⠤⠶⢤⣤⣤⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣀⣬⠥⠶⠒⠚⠛⠛⠛⠛⠒⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡴⠚⠉⠁⣀⣤⠤⠴⠶⠶⠶⠶⠶⠤⢤⣄⣀⡀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⢀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠉⠛⠶⣤⣀⠙⢦⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡴⣿⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣷⡄⠀⢼⡉⠛⠾⣇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡤⠤⡖⠒⠲⣄⠀⠀⠀⢈⡟⢰⡏⣾⡟⢉⠝⢿⣿⡇⠀⠀⠀⡿⠿⢋⠔⠀⠢⡙⢿⠀⠀⠻⣄⠀⠈⠙⢦⣀⣸⣇⣤⣀⠀⡀
⠀⢀⡴⠛⠛⢋⠀⠀⠈⢂⠀⠘⡆⠀⢀⡾⠛⣿⠀⠋⢠⠁⢰⣶⡀⠀⠀⠀⠀⠀⠀⡌⢀⣾⣦⠰⠈⠀⠀⠀⢹⡆⢀⡼⠋⠉⡽⠁⠀⡨⠋⠉⠳⣤⣤⡀
⣰⠛⠢⡀⠀⠀⠑⡀⠀⣴⠛⠋⠉⠛⠻⣄⠀⡟⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠃⠀⠀⠀⠀⣇⣾⣥⠶⠚⠓⠶⢴⡁⠀⠀⡐⠀⠀⠙⢦
⡟⠀⠀⠐⠄⠀⠀⠐⠀⢸⡆⠀⠀⠀⠀⢸⣂⡇⠀⠀⠠⢸⣿⣯⠷⠶⠶⠶⢤⡀⠀⡄⣿⣿⣿⣷⣇⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⢨⠇⠀⡐⠀⠀⠀⠔⠉
⠻⣄⠀⠀⠈⣀⣠⠴⠓⠁⠙⠶⠖⠁⣠⠏⡿⠀⢠⣦⢘⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⢐⣹⡿⠟⠁⣿⠀⠀⠀⠀⠀⢹⡄⠀⢦⣀⡴⠛⠦⣴⡀⠀⠀⠊⠀⢀
⠀⢹⡉⠉⠉⠀⠀⠀⠀⠀⠈⢀⣠⠞⠁⢰⣇⠀⣼⠝⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠀⢘⣿⠀⣀⠀⠀⠀⠀⢹⣦⡀⠀⠐⠄⠀⠀⠈⠑⠒⠶⢲⡏
⠀⠀⠳⣤⡀⠀⠀⠀⠀⠐⠈⢹⡇⠀⠀⠈⣏⠙⢾⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⠟⠋⠁⠀⠀⠀⢀⡟⣀⣽⡗⠤⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⣇⠀⠀⢀⣀⣠⠤⠶⠺⢧⣀⡀⠀⠹⡄⠀⠻⣆⠻⢦⣀⡀⠀⢀⣀⣠⠞⠃⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡞⠛⣁⡼⢤⣄⣀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠙⠻⡏⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠓⠻⣄⠀⠈⠛⠶⡾⠿⠟⠛⠛⠳⠶⠶⠚⠋⡗⠀⠀⠀⠀⠀⠀⣠⠞⠛⠉⠁⠀⠀⠀⠉⠙⠓⠲⣶⠶⠃
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠹⠒⠲⠶⠶⠶⠒⠚⠙⠚⠁⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣷⢤⡀⠀⠀⠠⣄⣀⡤⠀⠀⠀⢠⠄⣀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⢦⢄⡀⠀⠀⣰⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠙⣦⣀⠀⠀⠀⠀⠀⣀⡴⠿⡟⠁⢰⡇⠀⠀⠀⢠⡦⠤⠶⠒⠛⠉⠁
⠀⠘⢆⠉⠓⠞⢁⣖⣒⣒⠒⠒⠉⣩⠛⠛⠓⠒⠲⡇⠀⢿⠀⠀⡇⠉⢙⣛⣛⣛⣋⣉⣀⣘⡇⠀⢸⡇⠀⣠⠴⠞⠓⠒⠲⢤⣄
⢀⡠⠚⠀⠀⠀⢿⡷⠞⠉⠀⠀⠀⠑⢤⡀⠀⠀⠀⡇⠀⢸⠀⣠⠿⠚⠋⠉⠉⠁⠀⠀⠉⠉⠛⢒⣼⣤⠞⠁⢀⠤⠤⣀⡀⠀⠈⢳⡀
⠯⠀⢰⠞⠓⢄⣘⣳⠶⢾⠀⣴⠗⢶⡆⠽⠂⠀⠀⣧⡤⢾⠟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢹⠀⡔⠁⠂⠄⡀⠙⢦⠀⠀⢳
⠀⢠⣋⣴⠞⠟⠁⣰⡒⠚⢟⠷⢤⡀⢹⡀⠀⠀⠀⣿⠀⠸⣄⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣴⠇⡼⠁⠒⠤⢀⠀⠑⠺⡆⠀⣸
⢀⡼⠁⢠⠟⠒⠚⠁⣅⠀⠀⡸⠂⠛⢮⡀⠀⠀⠀⢹⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠒⠠⢀⡀⠈⠐⢰⠃⢠⡟⠉⠉⠉⡏⠉⠉⠉⡋
⠟⠒⠒⣡⠤⢄⠀⢀⣀⣉⠉⠀⠀⠀⡞⠙⣆⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡏⠑⠢⢄⣀⠈⠑⠢⣞⡴⠋⠉⠉⠋⠉⠉⠉⠋⠉⠉
⢱⡄⢸⠁⠀⠈⣷⠋⠀⠈⢣⢴⠂⠐⠷⣂⣼⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢸⡃⠂⢄⡀⠈⠉⠒⣼⠋⠀⠀⠐⠒⠓⠒⠖⠒⠓⠒⠖
⠻⢤⣌⣦⣀⣴⣋⣦⣄⣤⣋⣦⣠⣤⠴⠞⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠳⣄⡀⠈⠁⢂⡴⠏⠠⡄⠀⠆⠀⡤⠀⠒⠀⠤⠀⠂
⠀⠀⠀⠀⣨⡏⠀⠙⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡬⠉⠛⠛⠉⠛⠛⠉⠀⠀⠀⣇⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣀⣶⡀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠏⠈⣀⣉⣼⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⣿⠿⢯⡀⢿⣿⠿⣿⠋⠀⠀⠀⠀⠀⠀⣌⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣡⠋⠁⠉⢣⠀⢀⣏⣀⠀⢹⣼⣷⣴⣿⣤⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⡇⠀⣰⣿⣿⡄⠀⣿⣿⣧⢠⡇⣿⣷⣶⣤⣄⠀⠀⠀⠀⢀⡀⢀⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⣇⠀⢻⣿⣿⠂⠀⢻⣿⠿⠚⠛⠛⠛⠿⣿⣿⣧⠀⢠⠀⣸⣿⡟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣿⣷⡄⠀⣀⡙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣠⡾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠤⣄⡀⠈⢿⣿⣿⣿⠿⠃⠀⣿⣿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠴⠿⣦⠀⠙⠛⠛⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣦⣄⣀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⢿⣿⠿⣿⡿⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣃⣤⣴⠾⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠿⠛⠉⠀⠀⠀⢀⡀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠⢤⠀⠀⠀⠈⠙⠻⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠈⠓⠂⠀⠀⠀⡀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⣠⣴⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠘⣷
⠀⠀⣠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡀⠀⠰⣆⠀⠀⠈⢧⡀⠀⣿
⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣶⣶⠀⠀⢿⠀⠀⠘⣧⡀⠀⢘⡿⠛⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣄⣀⣾⣷⣤⣤⡿⠛⠛⠛⠁
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⣄
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠛⠿⣿⣷⡀
⠀⠀⠀⠈⠉⠛⠛⠛⠻⢿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⢶⣭⣍⣛⣛⠛⠛⠛⢛⣛⣻⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢠⡧⢠⡀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⢀⠀⠀⠀⣇⢠⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠁⠀⠀⠀⣴⠈⠀⠀⣄⢀⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡸⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⠓⠀⠀⠂⣴⠈⠀⠈⠃⠠⡃⠀⠀⢧⡀⠀⠀⠀⠈⠁⠀⠁⢀⡤⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠄⠑⠀⠋⠁⠀⠠⣅⣠⡄⣀⣙⠶⠔⠢⡀⡀⠀⠠⡎⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠜⢀⠀⠀⠰⠀⠀⠀⣦⠀⡤⠐⠈⠸⣅⢀⡀⠤⠄⠀⡃⠀⠀⠴⣠⡭⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠓⠀⡣⠀⠀⢰⠘⣠⠀⠀⠀⠀⠈⠀⢹⠐⠂⡘⠀⢀⠀⡸⠁⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢈⠄⠙⠀⠀⠈⠧⣈⢢⡀⠀⠀⠀⠀⠊⠃⢼⠀⢀⣰⠂⠄⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠂⢐⡂⠀⠈⠉⠙⠒⠲⡄⠀⠁⠀⠀⠀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⡄⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⢳⡷⢄⡀⡤⡀⠀⠀⠀⠀⠀⠀⣆⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠁⢩⠔⠉⠀⠀⠌⣦⣀⢀⡀⢀⠴⠋⠀⠀⠀⠀⣠⠔⠀⠀⠋⠀⠅⠈⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠃⠀⠀⠀⣠⣼⣍⣤⠠⠔⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣠⠊⠙⠁⢠⠘⠖⠈⠑⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⢺⣿⣤⠆⡈⠉⢀⣀⡀⠀⠃⠀⣄⣰⠖⠂⠀⠀⠂⡀⠀⠀⢀⣀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⣉⠉⢸⣿⣶⠿⠉⠉⠢⠀⠀⠗⠚⠗⠲⣤⠄⣖⡿⢿⣿⣧⠖⠚⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠈⢣⡀⠨⠋⠀⠀⠐⢲⡀⠜⠀⠀⢀⠀⣾⢧⡞⢹⣿⣄⣴⠀⠀⠀⠺⢚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⠙⠳⣧⠀⠂⢉⠘⠀⠘⠂⢪⡔⠅⠌⢙⡛⠦⠤⠄⢉⡁⠀⢸⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⡸⢧⣤⡠⢒⡏⠀⠀⠀⠀⠀⡀⠉⢁⠀⠂⠂⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⠒⠢⢤⡤⠖⠚⠳⢄⠁⡄⠀⠀⠈⠀⠀⠐⠀⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢀⠠⢄⠉⠉⡇⢸⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠣⡰⠀⠠⢄⠁⠀⢀⠳⠄⢄⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠐⠲⢂⣊⡴⠊⠀⢺⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠗⠀⠠⣰⠗⠁⢈⣠⠀⣰⠓⣀⡀⠀⢆⠀⡦
⠀⠀⠐⠣⠀⢐⠒⡏⢸⣀⠂⠁⡈⠂⡤⢳⣄⡴⠐⣥⡤⠤⠚⠁⠀⠀⠀⢧⡐⠉⠁⠠⣞⠀⠘⢫⡅⠦⡀⢠⠁
⠀⠀⠀⠀⢱⠉⠃⡇⢸⡰⠀⠀⡧⠊⠀⢸⡴⢁⡆⠡⠣⠄⠒⡐⠂⢶⠛⠃⢇⠀⠃⠄⢨⠄⡀⠋⡀⠀⠐⠆
⠀⠀⠀⠀⠘⠀⠂⠁⠘⠃⠀⠀⠃⠀⠀⠘⠁⠘⠁⠀⠋⠀⠛⠘⠁⠘⠃⠀⠘⠀⠀⠘⠘⠘⠁⠀⠐⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⢶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡴⠛⡡⠔⠒⠢⢄⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠉⠙⠛⢷⣎⡀⠀⠀⠀⠀⢱⡀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠈⢻⣆⠀⠀⠀⢀⣠⡶⠿⣿⠀⠀⠀⠀⠀⠢⣀⠈⠻⢦⡀⠀⠀⠀⡇⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢻⣆⠀⠀⠀⠹⣧⣀⣴⠟⠉⠀⠀⣿⡀⠀⠀⣀⡀⠀⠈⢷⡀⠀⠙⢦⣀⡼⠁⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⢠⡾⠛⣿⣀⣤⠿⠶⠤⢄⠀⠹⣿⠁⠀⠀⠀⠀⠘⣷⡀⣾⠿⠿⣟⠛⠛⠻⣦⣤⣤⡻⣦⠀⠀⠀⠀⠀⠸⣿⣦⡀
⠀⠀⠀⠀⠀⣻⡇⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⣻⢃⠔⢲⡈⠀⠀⢚⣛⣻⡟⢿⠈⢷⡀⠀⠀⠀⠀⣿⡝⢷⡄
⠀⠀⠀⠀⣾⠋⢿⣄⡛⢧⣤⣤⡀⠀⠀⠀⠀⠀⣿⣄⣠⡴⠞⠛⠛⠿⣯⣴⣺⠁⠀⡴⠋⠀⢹⡟⢦⣀⡈⢷⡀⠀⠀⠀⢸⡇⠈⢿⡄
⠀⠀⠀⠀⠻⣦⡀⠉⢛⣿⠁⠈⠇⠀⠀⠀⠀⠀⠋⢹⡟⠀⠀⠀⠀⠀⠀⠙⢷⠀⢰⠃⢠⣏⣿⠃⠀⠉⠙⠛⣧⠀⠀⠀⢸⣷⣦⡈⣿⡀
⠀⠀⠀⠀⠀⠈⠙⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣼⡿⠋⠀⠀⣀⣤⡴⠻⣇⠀⠀⠘⠇⠈⢿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⡶⠖⠀⠀⠀⣠⣴⠟⠙⣿⣄⡀⠀⠀⠀⠀⢀⣰⣿⣶⣶⣶⣶⣿⡷⢸⡇⠀⠀⠀⣿⣀⠀⠀⠀⠀⢸⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣶⠟⠋⠀⠀⠀⢻⡿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠟⢣⣏⠀⣠⠖⠛⠉⠉⠛⣦⣀⣠⠞⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢷⣄⠀⠀⠀⠈⢿⡈⠙⠩⢽⣿⣿⣯⡭⠿⡏⠀⠀⠀⠀⠙⠋⠁⣴⣞⠉⠀⠀⢸⡏⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠙⢷⣄⠀⠀⠈⠻⣦⡀⠈⢷⡖⠒⠒⢻⠇⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⣠⡟⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠛⣧⣀⣠⡴⠞⢷⣄⠀⠓⠶⠶⠋⠀⣀⣀⣀⣀⣀⡴⢤⣤⣤⣶⠞⠉⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣀⣼⠟⠉⢀⡴⠋⠙⠳⣦⣤⣤⡶⠛⢉⡽⠛⠉⠛⠷⣦⣤⣴⠟⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡶⠟⠛⣷⢀⡴⠛⠛⠛⠉⠉⠉⢿⠳⢦⣠⡿⣤⣄⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⣢⢏⡾⠛⠁⠀⠀⠀⣈⡙⠀⠀⠀⠙⠆⠈⣿⠛⠛⠓⠀⠀⠀⠹⣧⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⡁⠀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⣀⣀⣀⣤⡞⢀⣼⣧⣤⣤⣄⣠⣤⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠻⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⢁⣤⠶⠶⠶⠶⣤⡀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢰⣏⣀⣀⣀⣀⣀⣀⠀⠀⠸⣇⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣀⣴⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⢶⣯⡀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣠⡾⢋⣴⣾⣿⣶⡶⠶⠶⠶⠶⣦⣤⣴⣶⣮⡙⢷⣄⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢰⠏⢀⣼⠟⢋⣉⡻⠇⠀⠀⠀⢀⡾⠟⠛⠻⢿⣿⡀⠙⣧⡀⠀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⢶⣿⠁⣰⠋⢁⠹⣦⠀⠀⠀⣠⠖⠛⠛⢦⡈⠻⢷⣄⢸⣷⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣿⣿⢠⡇⢠⢡⣾⣿⣀⠀⢠⡏⠠⢀⣤⣼⡇⠀⠀⠙⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢙⣳⡟⠈⣧⡾⠛⠉⠉⠉⠙⠻⢧⡀⢼⣯⣿⡇⠀⠀⠀⢀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⣿⣯⣀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣜⣿⡟⠁⠀⡀⢼⡋⠁⣸⠷⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣁⣤⣴⣿⣿⢸⡇⣰⢋⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⣿⣿⣿⣿⣦⣀⡀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠟⠀⠙⢁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡈⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠃⠀⠀⠀⠀⠸⡇⠀⢀⣴
⠀⠀⠀⠀⠀⢠⡿⠋⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠉⢻⣟⣚⣛⣛⣛⣻⠇⠈⠁⠀⠀⠀⠀⣀⣀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠷⣦⣴⠿⠿⣦⡀⠀⠀⢀⣀⣀⣀⣀⣹⣦⣄⠀⠀⢿⡏⠉⠉⢉⡟⠀⠀⠀⠀⢀⣠⡾⢋⣻⡟⠉⠁
⠀⠀⠀⠀⠀⣈⣿⣄⠀⠀⠀⠀⠿⠁⢀⣶⠾⠟⠛⠛⠋⠉⠉⢉⣽⠟⠉⣽⢷⣄⠀⠙⠶⠖⠋⠀⢀⣠⣴⠾⢻⡿⢿⣯⣉
⠀⠀⢀⣴⠞⠋⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⣼⠃⠀⠙⠻⠶⣶⣶⣶⣾⠟⠋⠀⠀⣼⠃⠀⠈⠙⠻⣦⣄
⠀⣴⢟⣡⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣠⣟⣁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠒⢢⡟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄
⢸⣿⠟⢁⣤⢾⡄⠀⠀⠀⠀⠀⠀⡀⠀⠻⡶⣶⠿⣿⠟⠁⡍⣷⢠⣿⠛⠛⠛⠛⠿⠶⢶⡞⣠⡴⠶⢦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣾⣃⣴⠋⠁⣠⠿⠀⠀⠀⠀⠀⢈⣿⣦⣤⣴⠟⢀⣿⠀⠰⢃⡟⣼⠇⠀⠀⠀⠀⠀⠀⣸⣷⠋⠀⠀⡄⢻⢸⡇⠘⣦⡀
⠙⢿⣇⣠⡟⠃⠀⠀⢀⣀⣤⡾⠋⠁⠀⠀⠀⠀⢠⣿⣦⠴⢋⣴⠏⠀⠀⠀⠀⠀⠀⠀⢹⡹⣆⠀⠰⢃⡞⣾⢻⣆⣨⣿⠶⠀⠀⠀⡄⣰
⠀⠀⠉⠙⠷⠶⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⡛⢛⣩⡾⠃⠀⠻⡟⣿⠀⠀⡀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⡇⣿⣦⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢧⣴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢸⡿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠲⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠸⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠟⠿⠷⢦⣤⡀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣀⣤⣴⠶⠶⢶⣶⣷⣦⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣦⣤⣿⣧⡴⢾⡿⠋⠀⠀⠀⠀⠀⠁⠀⠈⠙⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣈⣉⣉⠉⠉⠉⣉⣉⣉⣡⣤⣤⣼⣿⡙⠓⠶⠶⢤⣤⣤⣤⣴⣶⠶⠶⠿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁⠈⠉⠉⠙⠛⠻⢶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟

⠀⠀⡀
⠀⠀⠀⠐⠆⠀⠰⠀⠀⠄⢀⠀⠀⠀⠆⠰⡀⠐⢆⠀⠀⠀⠠⠠⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠈⠐⠂⠃⠀⠀⠂⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⡉⠙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⡶⠞⠛⠛⠖⠤⣄⡈⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠛⡛⠿⣦⡀⠀⠀⠀⠀⠀⠀⢸⠋⡠⠐⠀⠂⠒⠂⢄⠉⠓⢄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠠⠂⠁⠀⠁⠨⠻⡄⠀⠀⠀⠀⠀⠸⣆⡀⠀⣠⠀⠒⠲⠆⢙⡦⡀⠣⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢀⡠⠴⠒⠛⠛⠛⠓⠲⠦⣷⠀⠀⠀⠀⠀⠀⠀⠉⠲⡏⠠⠀⡀⠀⠊⠁⠹⣆⢡⠘⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⡇⣠⠞⣁⡤⢤⡞⠏⡁⡀⠀⠂⢄⠈⠻⣆⠀⠀⠀⠀⠀⢀⠼⣇⣼⣀⡀⣠⡆⠀⠀⠈⠚⠓⢤⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡰⠡⢈⠋⠀⠀⠐⠄⠀⠀⠘⢨⡄⠑⠀⢹⡆⠀⠀⠀⠀⠘⡞⠁⠀⠀⠉⠉⠀⠀⠀⠀⡴⠁⡸
⠀⠀⠀⠀⡴⠒⣆⢸⠋⡈⠙⠀⢸⠀⢸⣷⣰⡌⠀⣠⠌⡂⢱⣤⡶⠟⠀⠀⠀⠀⠀⠠⠛⠦⢄⡀⠄⠊⠈⡿⢀⣤⡤⠞⠁
⣰⠞⠲⣤⡇⠀⢸⢻⡀⠳⠠⠴⢚⡀⠈⠟⠉⠁⠉⠻⡴⠃⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣖⢛⠲⠖⠊⢠⢋⣈⡇
⢻⡀⠀⠘⣇⠀⢸⠤⣙⡖⠂⠀⠀⡄⠘⢄⠀⠀⠀⢠⡄⢴⠇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡤⢀⣤⡿⡻⠟⣦⣄⢀⣀
⠀⠙⣦⠤⠼⡷⠁⠀⠸⣏⣪⡤⠀⠐⠤⠤⡉⠁⢉⠁⠜⣱⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡞⠀⠨⠁⢧⡁⡄⠀⡘⠉⣩⡇
⠀⠀⡿⠒⠠⣱⡤⠴⢡⠋⡏⠉⠛⠒⣄⠑⠭⢟⣡⢶⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣴⠉⡶⠀⢀⡾⣄⠉⠀⠁⢿⠁
⠀⠀⠹⣤⡢⠾⠀⠀⣀⡼⠁⠀⠀⠀⠸⡀⠈⢢⠠⢆⠱⡝⢦⡀⠀⢀⣠⣤⣄⣀⡼⠃⣷⣚⠏⠈⠤⠤⠿⠰⡜⠦⠤⠖⢹⡆
⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⣹⠀⠀⡰⣇⡔⠘⠄⠀⢳⢈⡀⡳⡎⠑⢌⠀⠈⠏⢇⢸⠃⠀⠀⠀⠀⠀⠀⠛⣿⢦⣄⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠢⠞⠁⠸⣑⣰⠂⠀⠀⠲⡟⠀⠘⠲⢤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢨⡇⠀⡴⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⡼⠁⠀⠀⠀⠀⠈⠳⠴⠃⠀⠻⡆⠠⣀⠀⠀⠀⠀⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡴⠊⠁⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣇⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⡇⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢛⣁⠀⠀⠀⢰⣿⠀⠀⠀⠀⣘⣧⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠥⣀⠀⠀⡇⠀⠀⠀⢀⣘⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠈⠙⠲⢤⣿⣀⡤⠒⠉⠀⠀⠀⠹⡄⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠙⠺⡦⠤⠴⠚⠉⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⢻⡄⣀⠀⠀⢀⣀⣀⡧⢀⡀⠀⠀⠀⠀⠀⣀⣽
⠀⠀⠀⠀⠀⠀⠈⠻⠥⣤⣤⣬⠬⠽⠚⠁⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠛⠲⠶⠾⠛⠛⠉⠙⠲⠮⣭⣭⣤⠽⠿⠛⠉

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠖⢩⠭⡉⠲⡄⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢀⣥⠁⠀⠀⠀⠀⢰⡥⣚⣩⣭⣍⡒⣼⡆⠀⠀⠀⣴⡇⠐⡳⡄⠀⠀⠀⠀⠀⠀⡐⠊⠅⠀⠀⠀⢀⠉⣠⠐⡂⠠
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡼⢿⠉⣍⣀⣩⠉⡿⡇⠀⠀⢆⣀⣡⣿⠄⠈⠀⠌⠀⠀⠀⡀⠙⠒⠃⠀⠀⠀⠈⠀⠈⢳⣤⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⢶⣧⣀⣼⡖⡧⠃⠀⠀⠈⠉⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠲⣠⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠭⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢉⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠻⣄⣨⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠈⠐⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⠀⢐⡄⠀⠀⠀⠀⠀⡀⠀⢀⡴⠠⠄⠀⠀⠀⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠩⠶⠎⠈⢄⠀⠀⠀⠀⢀⡍⢩⠅⡉⡰
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠰⢧⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠄⠴⠀⠀⠀⠀⠀⠙⠚⠅⠀⢈⡅⢄⠀⠀⠀⠀⠀⠉⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠊⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡀⠀⠐⠄⠀⠀⠀⢀⠴⡋⠀⠴⣽⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠁⠀⠂⠀⠀⠀⠀⠀⡍⠤⠔⢀⠀⡀⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠃⠸⠀⠈⠡⠈⠀⠈⠡⡀⠀⠈⠁⠓⠁⢠
⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠄⠀⠀⠀⠀⠀⠐⢀⣀⠠⠀⠀⠀⠈⠀⠈⠠⠘⠂⠀⠊⠁⠄
⠀⠀⣠⠈⢧⠟⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⢀⠂⠀⠀⠀⠀⠀⢀⠆⠀⡠⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄
⠀⠘⢆⠀⠀⠐⠀⠒⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⡤⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑

⠀⠀⠀⢸⠀⠦⡂⠀⠀⡿⠀⠀⡎⠑⠲⠤⠖⢫⠔⠋⠀⢀⡄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠉⠓⠶⣏
⠀⠀⠀⠘⠆⠰⠶⠖⠢⠤⠤⠤⠅⠀⠀⠀⡴⠃⠀⠀⢀⡏⠘⢦⣠⠋⠈⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀
⠲⠤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣀⡴⠛⢲⡞⠀⠀⠀⠀⡾⢠⠶⣄⢁⡴⢧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣄
⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠋⠉⠀⠀⡞⠀⠀⠀⠀⠘⠷⢞⣀⣈⣋⣀⣈⣛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠙⠒⠒⠒⠛⠙⠓⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⣠⠴⠒⠋⠉⢉⣀⣀⣀⣀⣀⡈⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠋⢀⡤⠖⠊⠉⠉⠁⠀⠀⠀⠉⠉⠉⠛⠲⠦⣄⣈⠙⢦⡀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢠⣶⠁⣠⣤⣤⣄⠀⠀⠀⠀⢀⣤⣶⣿⣷⣦⡀⠀⣹⠛⠦⣷⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⣤⡤⠶⠦⡄⠀⠀⠀⣻⢃⡟⣾⡿⢛⠿⣿⣷⠀⠀⠀⣿⠿⢋⠁⠢⡙⢿⠀⠈⢳⡄⠀⠙⢦⣀⢠⣇⣀⡀
⠀⣠⠖⠒⠻⡁⠀⠈⢂⠀⢹⡄⠀⣰⠛⢻⠁⠋⠠⠁⣴⣆⠀⠀⠀⠀⠀⠀⠁⢰⣶⡌⠌⠀⠀⠀⢻⡀⣠⠞⠉⣹⠋⠀⡙⠋⠙⢦⣤⣀
⣰⠓⠠⠀⠀⠈⠂⠀⢴⠋⠉⠉⠙⢳⡀⣿⠀⠀⡆⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⢸⣷⣯⠖⠒⠛⠒⢶⡀⠀⢀⠂⠀⠈⢳
⣏⠀⠀⠐⠀⠀⠈⡄⡸⣆⠀⢀⠀⢀⣧⡟⠀⠀⢃⢸⡿⠞⠒⠛⠓⠲⣄⠀⠘⣿⣿⣿⢿⠀⠀⠀⠘⠛⡏⠀⠀⠀⠀⣸⠃⠠⠃⠀⠀⠔
⠙⣦⣄⣀⠤⠔⠚⠉⠀⠨⠙⠁⣠⠎⣼⠀⢰⢷⣸⠏⠀⠀⠀⠀⠀⠀⠈⢳⡤⠿⠛⢁⣸⡆⠀⠀⠀⠀⢳⡀⠐⠦⠾⠉⠑⠢⢄⣀⠈⢀⣠
⠀⠹⣄⠀⠀⠀⠀⠀⢀⠠⣴⠚⠁⠀⣿⢦⣸⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣠⣿⡥⠖⠀⠀⠀⢠⡟⠦⣄⡀⠀⠀⠀⠀⠈⠉⢩⠇
⠀⠀⢸⠇⠀⠀⠀⠀⣀⣀⣼⡂⠀⠀⢸⡄⠙⣧⡘⣆⡀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣤⠟⠋⠀⠀⠀⠀⢀⡾⠶⢻⡏⠈⠀⠀⠀⠀⠠⢴⠋
⠀⠀⠘⠷⣶⠖⠚⠉⠉⠀⠀⠉⠓⠲⠤⢷⡀⠈⠳⢤⣝⣶⣶⢶⠶⢯⣥⣤⠴⢺⠇⠀⠀⠀⠀⠀⢀⡾⠶⠚⠋⠉⠙⠒⠶⠤⣤⣀⡼
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⠶⠤⠤⠤⠤⠤⠖⠢⠞⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣦⣄⠀⠀⠠⣄⣀⡠⠀⠀⠀⡠⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠦⢄⡀⠀⢠⡆⠈⠓⠦⢤⣀⡀⠀⠀⠀⠀⡟⠀⡇⠈⢳⣄⡀⠀⠀⠀⢀⣠⠼⢿⠉⠀⡇⠀⠀⠀⢰⠤⠶⠒⠚⠉⠁
⠀⠘⡆⠈⠒⢁⣖⠴⣖⠒⠊⢁⡝⠉⠙⠛⠲⡇⠀⣧⠀⢸⠀⣉⣙⣛⣯⣭⣥⣀⣽⠀⢀⡇⢀⡤⠖⠛⠛⠓⠲⢤⡀
⣠⠖⠁⣀⠀⠘⣿⠋⣁⠀⢀⡀⠑⢤⡀⠀⠀⡇⠀⣿⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⣩⠾⣷⠋⢀⡤⠒⠂⢄⡀⠀⠹⡄
⠁⢈⡟⢁⣱⡤⢶⣛⣻⣠⡞⠉⢻⡀⠉⠀⠀⡷⠚⡛⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⡸⢠⢏⡈⠁⠂⠤⣙⡄⠀⢹
⠀⣾⠞⢻⣄⣀⠜⡆⠀⠁⢭⢳⣄⠇⠀⠀⠀⢿⠀⠘⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⡮⣀⠈⠁⠂⠄⡀⡇⠀⡾⠠⠤⢤⠤⠄⠤⡤
⣼⢁⡤⢊⡀⠀⠀⠑⠦⠔⠃⠀⢈⠷⣄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠥⣀⠈⠐⠢⠄⣨⢃⡼⠣⠤⠤⠴⠦⠤⠤⠦
⢢⠀⡔⠁⠈⢣⡔⠋⠑⣄⡠⠀⠼⡤⢸⡆⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⡇⠄⡀⠉⠒⠠⢀⡟⠉⠀⠠⠠⠄⠠⠤⠴⠄⡤
⠾⣀⣱⣀⣀⣞⣣⣀⣠⣋⣄⣀⣀⡬⠛⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠳⣀⠀⠀⠂⢀⡼⠁⣄⠀⠤⠀⡄⠠⠄⢠⠀⠤
⠀⠀⠉⢉⣽⠉⠉⢦⣹⡉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠙⠓⠛⠛⠒⠚⠉⠀⠀⣇⣀⣀⣀⣂⣀⣀⣐⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣱⡭⣄⢆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⡒⠚⠮⣀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣤⡔⠒⠿⠻⢟⡑⣄⠀⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⣰⠀⠀⣼⡆⢉⠝⢣⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣀⣐⣾⡤⠨⡤⢨⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⢶⡾⣿⠿⡏⠀⠀⠀⣈⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠷⢤⣈⠑⢀⣠⠴⡾⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⡠⠚⢿⠫⣵⠟⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⢶⠸⣁⠀⠀⠉⠀⠀⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠶⠞⠉⠉⢳⣦⣤⠴⠚⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢳⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠧⢄⣀⣸⠆⠀⣀⡤⠤⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⢹⠊⠛⠁⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡤⠤⣤⣄⣺⣤⣀⣀⣀⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠙⠚⠒⠒⠒⠒⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⠀⠂⣹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠿⢛⣻⣿⣶⣶⣿⣿⣿⣿⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡉⠉⡿⢿⣟⢦⣴⣾⣿⣿⣹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⣶⡄⠈⢿⠏⠻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣼⣿⣷⣦⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⢱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢹⡿⠿⠇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣄⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣬⣿⣿⣿⣿⣿⣿⣿⣦⣠⣠⣘⣋⣛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠤⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠨⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢹⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⢶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠧⠐⠚⠛⠻⢿⣿⠀⠀⠨⠿⠟⠉⠛⠿⠿⣿⣿⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠶⠶⠖⠒⠺⠿⡏⠀⠀⠐⠶⠶⠒⠒⠲⠶⣶⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠵⡦⠧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣤⣤⣧⣤⣤⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠶⠟⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⣤⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠖⠉⠈⠑⢌⣷⡶⠚⠋⠉⠙⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⢀⡴⠛⠁⣀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⢣⡴⠋⢀⡴⠊⢀⡀⠀⣠⡟⠙⠛⠶⣤⣀⠀⠀⠀⠀⢀⡴⠛⢹⡆
⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⢏⣀⣠⠾⠶⢲⠟⠻⢶⠏⠀⠀⠀⠀⣠⣭⣷⣦⡀⣴⠏⠀⠀⣼⡥⠖⠚⢶⡄
⠀⠀⠀⢰⡇⠀⠀⠀⡼⠃⡿⠋⣉⣁⠀⠀⡔⠒⢜⣇⠀⠀⠀⠀⣯⠀⠀⠙⣿⡃⠀⠐⠾⡋⢀⡤⠖⠛⢻⡄
⠀⠀⣴⠛⠀⠀⠀⣼⠛⠛⠃⢸⠁⠈⢣⠀⢻⣦⡼⠟⠒⠶⣄⠀⠈⢳⡄⠀⠀⠉⠣⠀⠀⠈⢯⣀⡴⠖⠛⣷
⠀⠀⣿⠀⠀⠀⢰⠿⡄⠀⠀⠸⣯⣧⠈⡇⠚⠃⠀⠀⠀⠀⠸⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡴⠋
⠀⠀⢸⣧⣄⣤⣿⡄⠉⠓⣆⠀⡈⠓⠚⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣟⠙⠆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⢸⡇⡟⢀⡤⣜⠦⣤⠏⢰⣿⣷⣦⣤⣶⣦⣤⣤⣤⣾⣿⠀⣴⠻⣦⡀⠀⠀⠀⣀⣀⣤⠾⠋
⠀⠀⢸⡄⢷⡀⠀⠚⠳⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢏⡞⠁⠀⠈⠛⢦⣤⣀⣼⣿
⠀⠀⢸⡇⠀⠛⢦⣄⣀⣤⢤⠀⠈⠛⢿⣟⣛⣓⣲⠎⢩⣷⠋⠀⠀⠀⠀⠀⣰⠏⠁⢀⡟
⠀⠀⠀⢷⠀⠀⠀⠀⢀⡗⠈⢳⡀⠀⠈⢇⠉⢉⡟⢀⡾⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠸⣤⣴⡤⢷⠀⠀⠈⠉⣉⣠⠾⣅⠀⠀⠀⠀⣴⠏⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣴⡞⠛⢷⡤⠤⠤⠥⠞⣆⠈⢷⡀⢀⡾⠁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠙⢾⡋⠙⢧⣽⡄⠀⠳⡄⠀⠀⠀⠙⡄⠀⠹⣿⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣸⠂⢻⡙⢷⠛⢲⣀⣀⣠⣼⣄⡶⢻⣦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣤⣼⠀⣸⠃⠀⣿⠭⠴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣷⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠛⠻⠿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⡟⠁⠐⢑⠀⢠⡉⠂⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢻⣯⠉⠩⣿⡛⠿⢿⣿⡆⠀⢀⠿⣿⡄⠀⡼⠓⠺⢇⠀⢸⡿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢰⠁⣾⣀⣠⣧⢈⠀⢸⣿⡇⠀⠸⡜⢾⣿⣶⣄⣀⣀⣴⣾⣿⣟⡠⠀⠠⠒⡶⣲⣆
⠀⠀⢀⡀⠀⡾⠛⣦⠀⠀⣰⢹⣿⣷⣦⣰⠋⠀⠀⢹⣤⣴⣼⣯⢍⡆⠀⠈⠛⢿⣿⡿⠟⠻⠿⢿⡿⡯⣄⠀⡇⠸⠐⣁⣼
⠀⣴⠟⠛⢿⡇⠀⣿⠀⠀⠘⢾⣿⠘⢿⣿⣿⣶⣾⣿⣿⠟⢠⡿⠋⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢰⠉⢃⠀⠑⠃⠀⠰⠃⣿
⠀⠹⣦⣀⠈⣷⣠⠟⠛⣦⠀⠀⠈⠳⢤⣀⠉⠉⠉⣁⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⣀⣠⣇⠀⢸⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠈⣿⣉⡹⣇⣀⡴⣹⣷⠀⢀⡴⣿⣿⠉⠉⠉⢻⣿⡟⢦⠀⠀⠀⠀⠀⠀⢠⣾⣿⠉⠉⠉⣿⣷⡜⣿⡶⠿⠶⢚⡟
⠀⠀⠸⣧⣠⣽⡏⠉⠀⣡⠿⣤⠎⡜⠉⣿⣿⣿⣿⣿⡇⠙⡄⢣⠀⠀⠀⠀⡰⡻⠛⣿⣶⣶⣶⣿⠻⣟⠟⠉⠙⢛⠋
⠀⠀⠀⠈⠛⠛⠶⢶⣞⡉⠀⠀⣸⣄⣴⣿⣿⣿⣿⣿⣷⣤⣷⣀⡇⠀⠀⢀⣡⣇⣠⣿⣿⣿⣿⣿⣄⣸⣄⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠛⠁⢢⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠌⠁⠀⠀⣠⠂⠄⢄⠘⠈⠃⠀⡏⠀⢀⠀⠀⠀⠀⠀⢀⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠦⠀⠠⠀⣇⠒⠀⠼⢁⡝⠀⠀⣇⠀⠀⠀⠀⠐⠀⠐⠀⣀⣼⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⡀⠃⠠⠒⠀⠀⣃⢀⣄⠈⠳⣤⠤⢀⠀⠀⠀⢔⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠃⠀⠀⠠⠀⠀⢠⡄⠠⠀⠀⠰⡇⢁⠀⠤⠌⠈⠀⠀⠸⣄⣭⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⠀⠓⢐⡇⠀⠀⡆⢃⠄⠀⠀⠀⠈⠈⢱⠐⢀⠚⠀⠀⢠⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⢀⠆⠉⠀⠀⠙⠦⣑⢄⠀⠀⠀⠀⡋⠃⡎⠀⠀⠖⠠⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠠⠼⠀⠀⠀⠉⠉⠑⢆⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠩⢋⠶⠐⠒⢄⠀⠀⠀⠀⢀⡧⠞⠁⠀⠀⠠⡀⠀⢠⠀⠠⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡠⠗⠒⢂⡠⠊⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⠴⠾⠛⠛⢏⡅⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢴⣧⣀⠀⠒⠓⠀⠀⠀⠸⠀⡀⢠⡄⠀⠀⢡⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠈⡛⠋⣴⣦⣴⡟⠛⠤⡀⠀⡭⠽⠦⢤⣠⢀⣼⠶⣶⣖⡭⠼⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠙⢆⠈⠹⠃⠀⠀⠐⡄⠰⠀⠀⢠⢀⡷⣠⠏⣿⣍⣩⡄⠀⠀⠺⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⠛⢶⠄⠀⠈⡙⠃⠘⠂⢪⠾⠡⠉⣛⠢⠤⡄⠀⡁⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠁⠀⠀⠀⠀⠀⠀⡀⠳⣤⠤⠒⠋⠀⠀⠀⠀⢀⠈⠡⠄⠂⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠃⠀⠉⠐⢒⡶⠖⠋⠙⠠⡀⠄⠀⠀⢀⡀⠀⠁⠈⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣄⢒⡄⢀⡝⠸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⡞⠀⠐⢢⣀⠀⡌⠃⠐⣀⡀⠀⠀⠄
⠀⠀⢠⡄⠈⢉⣨⠶⠁⠀⠙⠣⡀⢀⡄⠀⡀⡠⠀⠀⢀⡔⠋⠀⠐⡞⢀⠄⠴⢆⡸⢡⡤⠄⡀⠣⠀⠃
⠀⠀⠀⠡⡀⢦⢸⢰⠖⠀⠀⡄⡨⠋⠙⡺⢃⠑⣲⠉⢁⢀⡀⣀⣤⢵⠀⢀⠀⠙⠀⠀⣸⠃⠙⢄⡐
⠀⠀⠀⠀⡇⠀⠘⠰⡟⠀⠀⡏⠀⠀⠼⠁⡾⠀⢡⠉⢤⢢⠄⢩⠀⠀⠶⠁⠈⠌⠇⠔⠀⠂⡄⠠

⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⢀⡴⠊⡩⢍⠑⢦⡀⠀⠀⠀⠀⠀⠴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⣁⡁⠄⠀⠀⠀⠀⣞⡴⣒⣉⣉⣓⠦⣱⠀⠀⠀⠐⣴⡂⠰⠧⡀⠀⡀⠀⠀⠀⡀⡠⠐⠩⠀⠀⠀⠀⠀⢁⡬⢐⠀⢤
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⢿⡟⢉⣃⣘⡉⢻⡿⡄⠀⠀⣆⠈⣁⣾⡅⠈⠀⡀⠀⠀⠀⠀⠘⠦⠒⠀⠀⠀⠀⠡⠀⠙⣎⣸⡄⢺
⠀⠀⠀⠈⠀⠁⠀⠀⠄⠀⠘⣴⡧⣼⣁⢈⣧⣼⣦⠃⠀⠀⠘⠛⠛⠋⠀⠀⠀⠁⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠆⣀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠭⣉⣉⡭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣈⠠⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠆⠀⠓⣄⠁⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⢉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠜⠀⠀⠀⠂⠀⠀⠀⢬⡍⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⢄⣀⠞⢅⠀⠀⠀⠀⠀⠂⡤⠴⠏⠨⠑⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠉⠈⠀⠀⠑⡀⠀⠀⠀⠰⡧⣞⢁⡆⠪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⡤⠄⠀⠤⠤⠄⠀⠀⠀⠀⠀⠤⡁⠉⢙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠠⡀⠀⠉⡤⠤⠜⠒⢢⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⡀⠀⠑⠀⠀⠀⡠⠎⠡⠀⠐⠛⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡄⢀⠀⠀⡀⠀⡀⠀⢱⠐⠂⠀⣄⢠⡸⠍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⠄⠐⡀⢢⡀⠀⠀⣀⠁⠀⠇
⠀⠀⠀⠤⡀⢄⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⠀⠀⠀⠀⠀⠀⠈⠡⢤⠐⠀⠀⠀⠀⠀⠀⠀⠊⠉⠈⠈⠀⠑⠈
⠀⠀⢰⠀⠳⠊⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⢀⠇⠀⠀⠀⠀⠀⢀⠄⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠶
⠀⠈⢢⡀⠀⢈⡀⢚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣬⡵⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢍⢒⡠⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠴⠾⣍⣳⣸⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠒⢢⣄⣭⣶⢄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣰⠿⠏⠁⠛⢍⠻⢤⣱⣄⠀⠙⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⢤⣷⠀⠀⣾⡇⠀⡤⠋⣦⣀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⡀⣐⣾⣷⠀⢧⠔⣤⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣴⣾⣿⠿⣟⠁⠀⠀⠀⣁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣌⡀⠑⠩⠁⢀⣠⣴⢯⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠩⠀⠀⢈⣓⡶⢞⠫⣱⠞⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢣⣀⡀⡴⠁⠀⠙⠦⠛⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣙⣧⣳⢤⣀⠀⠀⠀⢀⡴⡳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠛⠁⠀⠀⠻⣿⣲⠟⠉⠙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⢷⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⡇⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢹⡀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠓⠶⣾⣁⣤⠶⠚⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⣛⣉⡭⠥⠭⣷⠤⠤⠤⠤⠤⠤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠨⠷⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⣠⡄⠤⢴⡊⢉⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⡀⠤⠔⠉⠣⠀⠀⢀⣿⣩⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡠⠆⠁⠘⠦⠴⠁⠀⢙⠠⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠘⢄⠈⠢⢤⠀⠀⠀⠀⠀⣡⡤⣒⣋⡤⠤⠴⣦⠀⠀⠀⣀⠀⠀⠀⠀⣠⠤⠞⠃⠀⠉⠉⣂
⠀⠀⠀⠀⠀⠀⣰⠚⡉⠉⠉⠉⠈⠉⠉⢉⡮⠤⠶⡾⠖⠒⠒⠒⠚⠉⢩⠁⠁⠀⠀⠀⠀⠉⠑⡄⠀⠉⠈⠤⢾⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠐⡧⠐⠀⠀⠐⠀⣀⡤⢤⡏⠀⠀⠎⠀⠀⠀⠀⢀⣀⣀⣠⡀⡀⠀⠀⠀⠀⣄⣹⠁⠀⠀⠀⠸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢙⣯⡔⣺⢀⡔⣫⠔⠋⠀⠀⠠⡀⠀⠀⡖⡾⠉⠁⠀⠀⠉⠙⠓⢻⣤⠷⠊⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⢀⡔⠋⢀⡹⢮⡋⢰⡇⠀⠀⠀⠀⠀⠈⠒⠚⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⠀⠀⠀⢀⡰⠞⠁
⠀⠀⢀⡔⠉⠀⢠⠊⠀⠀⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⣎⠀⠀⠀⡌⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⣀⠴⠋⠳⣄
⠀⠀⠘⠶⣤⠶⠛⠙⢦⣀⡀⣀⣠⡴⠞⠉⠓⢤⡁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠹⣦⠴⢤⡀⠀⠀⠀⠀⢀⠎⣤⣤⣤⢀⣖⠁⡆⠃⠃⢐⡂⣬⠃⢐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠒⠉⠀⠀⠀⡷⠀⠀⠀⠀⡀⡥⣄⡠⣤⠾⣿⣴⠷⣴⡶⣿⡷⣴⡶⣶⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠶⠶⠶⠤⠤⠞⠁⠀⠀⠀⠀⢰⢰⠈⠀⠀⠀⠀⠀⠄⣿⠀⠠⠐⢸⢰⢸⡐⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣨⣠⣤⣤⣤⣤⣤⣁⣿⣄⣤⣸⣸⣌⣼⣌⣼⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠉⡀⢠⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠰⠉⣁⣡⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢩⣿⣿⠻⣿⣿⣿⡿⠋⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠞⠙⢳⠀⢸⣃⠈⢳⣿⣭⣿⣀⠀⠀⠀⠀⠈⠻⣇
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡍⠀⣾⣿⡇⢸⣿⣷⢸⣹⣷⣶⣦⣄⠀⠀⠀⢀⢀⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢱⣄⣿⡿⠁⠈⠛⠛⠉⠉⠉⠙⢿⣿⡆⢰⣠⣿⠟
⠀⠀⠀⠀⠈⢿⣿⠟⣉⠈⠹⣿⣿⣿⣿⠇⢰⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠨⠽⢦⠘⠻⠟⠁⠀⠈⢻⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⣛⣿⠟⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣶⣶⣶⣶⠿⢻⡿⠟⠛⠉⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠤⠀⠀⠀⠙⠻⣄
⠀⠀⠀⠀⢀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⡉⠃⠀⠀⢠⡀⠀⠈⠳⡄
⠀⠀⣠⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⢀⠀⠈⢳⡀⠀⢻
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣦⡄⠀⢰⠀⠈⢣⡀⠀⢳⠶⠋
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄⣼⣷⣤⡼⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄
⠀⠈⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠾⢯⣟⣛⠿⠿⠿⠿⠿⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣯⣍⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⠟⠁⠰⡀⢀⠒⠍⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢿⡟⠙⣿⡿⠿⣿⣿⡄⠀⢸⢿⣇⠀⢸⠧⠼⡇⠀⣼⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢰⢩⣇⣀⣾⠈⠀⢸⣿⡇⠀⢢⠲⣿⣶⣇⣀⣀⣰⣶⣿⣆⡜⠀⠴⡶⢶⣄
⠀⠀⣀⡀⢠⠟⢷⡀⠀⢰⢻⣿⣶⣬⣼⠁⠀⢙⣤⣴⣾⣯⢹⠀⠀⠙⠻⣿⠿⠟⠻⠿⢿⣿⠭⣀⢸⠠⠃⢋⣼
⠀⣾⠋⠻⣿⠀⢸⡃⠀⠘⠾⣧⠙⠿⣿⣷⣾⣿⠿⠟⣠⠿⠋⠀⠀⠀⠀⠸⡄⠀⠀⠀⡸⠈⡆⠈⠋⠀⠀⠃⣸
⠀⠙⢦⣄⣸⣦⠞⠉⢳⡀⠀⠈⠓⣦⣄⣀⣀⣠⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⣹⣦⣤⣴⣇⠀⢡⣀⢀⠀⢀⣴⠃
⠀⠀⢸⠿⢤⣹⣤⠾⠹⣿⠀⣠⣺⢿⣏⣀⣀⣸⡿⢯⠳⡀⠀⠀⠀⠀⢀⣾⣿⡀⠀⣀⣿⣷⣜⣿⣟⣛⣩⠜
⠀⠀⠘⢶⣶⣟⣀⣀⡴⠛⠛⢡⠃⢨⣿⣿⣿⣿⣧⠀⣇⠱⡀⠀⠀⢠⢳⠉⣿⣿⣿⣿⣯⠙⣎⠁⠀⢠⠃
⠀⠀⠀⠀⠈⠉⠉⠻⠦⠤⠤⠾⠶⠿⠿⠿⠿⠿⠛⠛⠛⠒⠃⠀⠀⠲⠾⠶⠻⠛⠿⠿⠿⠶⠾⠒⠚⠁

⠀⠀⠁⠀⢤⠀⠀⡄⠠⢠⢀⢀⠀⠀⠀⠠⠐⡄⠀⠤⡀⠀⠀⠀⠠⢀⢀⠀⠀⡐
⠀⠀⠀⠀⠈⠂⠰⠐⠂⠀⠠⠌⠀⠀⠀⠂⠓⠈⠂⠀⠁⠀⠀⠀⠐⠠⠔⠀⠃⠤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢛⠛⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠯⣬⣀⡀⠈⡄⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢁⡀⠤⠤⢀⣈⠉⠓⢦⡀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⡠⠐⠀⠀⠌⠻⣦⠀⠀⠀⠀⠀⠀⠘⣇⠈⠀⠀⢀⢀⣀⣀⡉⢦⣄⠈⢢⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣥⣤⣤⣤⣄⣑⠘⣇⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡟⠀⠀⠀⠀⡐⠏⢱⡀⠱⠀⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⢀⡴⠚⠉⣉⣠⡤⠤⠄⣀⠉⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣐⠀⠂⠀⣀⠀⠀⠙⢆⣃⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠙⠀⠔⠁⣴⠖⠙⠚⠀⠰⠀⠠⣀⢌⠐⢄⠘⢷⡀⠀⠀⠀⠀⠀⢰⢹⠷⠛⠀⢤⡴⠏⠀⠀⠀⠈⡡⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⢤⣎⠐⢠⠁⠀⣀⢀⠑⡀⠀⠀⠈⠸⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⠀⣀⡀⠀⠰⠃⢠⠇
⠀⠀⠀⠀⣼⠋⠻⡄⡞⠠⡄⠍⠀⢘⠀⠐⣿⣤⣧⠁⢀⣶⢈⠄⢿⡶⠟⠋⠀⠀⠀⠀⠀⠀⢰⠉⠒⠤⡄⠒⠁⠀⡼⢁⡴⣶⠞⠋
⣴⠛⠛⢦⣇⠀⠀⡟⢧⡀⠓⠲⠜⢫⡄⠀⡙⠁⠀⠀⠉⢿⠞⢀⡸⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣎⢩⡓⠚⠉⢠⣎⣀⡸
⢻⡄⠀⠀⢻⡀⢀⡧⢤⣙⡖⢃⠀⠀⡄⠑⠣⡀⠀⠀⠀⣼⠀⢼⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢶⠶⢀⣠⠿⢛⠞⢳⣦⡀⣀⣀
⠀⠉⢳⡤⠤⢯⠎⠀⠀⢹⣙⢮⣤⠀⠐⠤⡤⡈⠉⠈⡉⠀⢜⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡞⠀⢨⠁⢣⡎⢠⠁⠀⠋⠁⣹⠇
⠀⠀⣼⠖⠠⠘⣄⣠⠞⢸⢻⡏⠛⠛⠲⣄⠐⠨⠽⢛⡴⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⣼⠓⡶⠁⠀⡸⣅⡈⠀⠈⠰⣟⠁
⠀⠀⠹⣄⠠⣬⠇⠀⠀⢀⡼⠁⠀⠀⠀⠘⡌⠁⠫⡁⣱⡈⢯⠳⣄⠀⠀⠀⣀⣀⣀⠀⣠⡞⢹⡧⢞⠏⠘⣀⣀⢾⠁⣜⢦⠤⠤⠔⢻
⠀⠀⠀⠈⠙⠒⠒⠷⠖⠛⠓⠀⢻⠀⠀⢀⣷⣠⠖⢧⠀⠐⡤⠱⠈⣧⡔⠢⣍⠊⠉⢻⢻⠀⣼⠉⠁⠀⠀⠀⠀⠀⠣⢿⣦⣀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣄⡴⠋⢸⡿⠄⣤⠀⠀⠘⢼⡶⠃⠹⣄⡀⠁⠀⠈⠀⠳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⣶⠀⢀⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣇⣀⣸⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣀⠤⠂⣴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⡇⠑⠲⡄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⡄⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⢀⣀⡀⠀⢠⣿⠁⠀⠀⢀⣀⡭⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠤⣄⡀⠀⡗⠀⠀⠀⢀⣠⠽⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠉⠓⠢⣿⣄⡤⠖⠉⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠉⠙⡧⠤⠴⠚⠉⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⡀⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠸⣧⢀⡀⠀⠀⢀⣀⣀⣧⢀⡀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠯⣥⣀⣐⣢⣬⡭⠗⠃⠈⠒⠻⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠿⠛⠋⠙⠲⠮⣭⣵⣶⣬⡽⠷⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⣤⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠖⠉⠈⠑⢌⣷⡶⠚⠋⠉⠙⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⢀⡴⠛⠁⣀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⢣⡴⠋⢀⡴⠊⢀⡀⠀⣠⡟⠙⠛⠶⣤⣀⠀⠀⠀⠀⢀⡴⠛⢹⡆
⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⢏⣀⣠⠾⠶⢲⠟⠻⢶⠏⠀⠀⠀⠀⣠⣭⣷⣦⡀⣴⠏⠀⠀⣼⡥⠖⠚⢶⡄
⠀⠀⠀⢰⡇⠀⠀⠀⡼⠃⡿⠋⣉⣁⠀⠀⡔⠒⢜⣇⠀⠀⠀⠀⣯⠀⠀⠙⣿⡃⠀⠐⠾⡋⢀⡤⠖⠛⢻⡄
⠀⠀⣴⠛⠀⠀⠀⣼⠛⠛⠃⢸⠁⠈⢣⠀⢻⣦⡼⠟⠒⠶⣄⠀⠈⢳⡄⠀⠀⠉⠣⠀⠀⠈⢯⣀⡴⠖⠛⣷
⠀⠀⣿⠀⠀⠀⢰⠿⡄⠀⠀⠸⣯⣧⠈⡇⠚⠃⠀⠀⠀⠀⠸⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡴⠋
⠀⠀⢸⣧⣄⣤⣿⡄⠉⠓⣆⠀⡈⠓⠚⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣟⠙⠆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⢸⡇⡟⢀⡤⣜⠦⣤⠏⢰⣿⣷⣦⣤⣶⣦⣤⣤⣤⣾⣿⠀⣴⠻⣦⡀⠀⠀⠀⣀⣀⣤⠾⠋
⠀⠀⢸⡄⢷⡀⠀⠚⠳⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢏⡞⠁⠀⠈⠛⢦⣤⣀⣼⣿
⠀⠀⢸⡇⠀⠛⢦⣄⣀⣤⢤⠀⠈⠛⢿⣟⣛⣓⣲⠎⢩⣷⠋⠀⠀⠀⠀⠀⣰⠏⠁⢀⡟
⠀⠀⠀⢷⠀⠀⠀⠀⢀⡗⠈⢳⡀⠀⠈⢇⠉⢉⡟⢀⡾⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠸⣤⣴⡤⢷⠀⠀⠈⠉⣉⣠⠾⣅⠀⠀⠀⠀⣴⠏⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣴⡞⠛⢷⡤⠤⠤⠥⠞⣆⠈⢷⡀⢀⡾⠁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠙⢾⡋⠙⢧⣽⡄⠀⠳⡄⠀⠀⠀⠙⡄⠀⠹⣿⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣸⠂⢻⡙⢷⠛⢲⣀⣀⣠⣼⣄⡶⢻⣦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣤⣼⠀⣸⠃⠀⣿⠭⠴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣥⠿⣆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢞⠻⠿⢶⣿⣿⣦⣄⣀⠈⠙⠞⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠂⣷⢶⡤⠂⠹⣟⠔⠺⡉⠑⠫⢖⣤⡀⠀⠈⣳⠤⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⡀⢿⡜⠐⢄⡀⠉⠀⠰⣿⡄⠀⠀⢨⣮⣷⡞⠁⣀⠘⡇
⠀⠀⠀⠀⢀⡾⠉⠐⠢⣄⣀⣙⢦⡷⠖⠋⠁⠀⢢⡀⢉⡇⣰⣴⣿⣿⣿⠃⠀⠫⢀⣅⣤⡤⠤⠤⢤⣄
⠀⠀⠀⢀⡏⠈⠛⠓⣶⠋⠀⢨⡏⠀⠀⠀⠀⠀⠀⣭⣭⣶⣿⠇⠈⠙⠉⠀⣀⡤⠋⠁⠀⠀⠀⠀⠀⣈⣹⣤⣀
⠀⠀⠀⢈⡇⠠⠔⢲⠃⠀⠀⣼⣇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠁⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠈⣧⡀
⠀⠀⠀⠈⣇⠀⠀⠈⢆⡀⣠⠟⣿⣷⣦⣴⣶⣿⠿⠟⢩⠃⡜⢣⢀⠀⣠⠏⠀⠀⠀⠀⢀⣠⡟⠀⠀⠴⠚⠁⢀⢠⡙⢦
⠀⠀⠀⠀⠈⢳⠠⣀⣀⠝⢁⠜⠁⡽⠻⡄⠉⠁⢀⠐⢧⣎⠀⣺⣸⠞⢹⡀⠀⠀⢀⡴⢿⠈⡷⠀⠀⠀⠀⠰⠘⠃⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠓⠾⢧⣀⣁⡠⠎⠀⠀⠈⢳⠶⢾⡷⣤⣈⣉⡵⢣⠀⠀⢧⠀⠀⠀⠁⢸⡄⣇⣄⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⠀⠀⣿⠀⠈⣇⠀⠈⠁⡀⣸⠀⡀⡈⢆⣀⣀⠇⠘⡇⢸⠛⠀⣀⠀⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣿⠀⠀⢌⢶⠂⠀⠀⣿⢸⠁⣸⡼⡅⠀⠀⠀⣇⣸⣄⣠⣟⠦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡄⢰⣣⢳⠀⠀⢹⡘⠦⠞⢡⡇⠀⠀⢸⡯⠤⠀⢀⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣶⣒⡛⠻⢍⠉⠉⠓⠄⡀⠙⠶⠖⠋⠀⠀⢀⣿⠲⢤⡀⠀⠈⠳⣄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⠒⠂⠤⢈⠉⠳⢤⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⣻⠀⠀⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡈⠀⠈⠁⠂⠈⠐⢤⡙⢦⢹⠀⡼⠀⠀⣀⣤⠾⠋⠀⠀⢀⣠⣧⣀⡤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⠀⠀⣠⠀⠝⢄⢻⡾⠷⠟⢛⣿⡛⠲⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠙⠛⠧⣄⡈⡊⣾⠃⠀⠀⣀⠀⠀⠀⢀⠀⠀⠤⠀⠠⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢤⠀⢀⡀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⡳⠦⣄⠀⠀⡴⢹⠞⠁⠀⣧⠎⡇⡠⠖⠛⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡠⠋⣀⣀⡼⠖⠊⢁⠀⠀⠀⠀⠀⢠⠟⠧⣄⣀⡑⠄⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠷⢤⠧⠔⠀⠀⠀⠀⠑⢦⣀⣠⡴⠋⠀⠀⠰⠴⣥⠴⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⡔⠋⠳⢄⣀⠀⠀⠀⠉⠁⠀⠀⡀⢀⡤⠶⣼⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡽⠀⢙⡶⢤⣀⠙⠉⠲⠀⠀⠠⠖⠩⠛⠁⣀⣠⠜⢯⠑⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⠃⠀⢸⠁⢸⣛⣿⣶⢴⣤⣠⣼⣤⢶⣶⣏⠁⣿⠀⢸⠀⠀⠱⣄
⠀⠀⠀⠀⠀⣰⠃⠀⢢⢈⡳⠤⣌⢆⣈⡻⠿⠧⣌⡀⠀⣈⣼⠿⣿⣃⢠⢃⠤⣼⠒⡆⠀⠘⡆
⠀⠀⠀⠀⢠⣇⠄⠀⢸⠏⠀⠀⠀⠙⠁⢀⣤⣤⡀⠈⠉⠀⣠⣤⡄⠈⠙⠁⠀⠈⢳⠃⠀⠀⢻
⠀⠀⠀⠀⢸⠃⠀⠀⢸⡀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠈⢺
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢳⡀⣒⠒⠂⣸⠛⢿⣷⠒⣢⡤⠤⠤⣀⣀⣀⣀⣀⣀⠤⣤⣤⣴⡾⢻⠀⠀⠄⠂⢀⠇
⠀⠀⠀⠀⠀⠈⠋⠛⢻⡏⠀⠀⠈⠛⠤⣘⣦⠚⠋⠓⢄⠜⠉⣓⣴⠷⠋⠁⠀⠈⢻⡿⠖⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠠⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣠⠂⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣤⣀⣀⣈⠛⢶⠶⠦⠤⠤⠴⢶⡖⠛⣡⣀⣠⣤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣎⡀⣸⠀⠀⣇⣈⠇⠀⠀⠀⠀⢸⣀⣌⠀⢈⡆⢈⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣥⣾⠟⠛⣻⡿⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡽⣣⡾⠋⠀⠀⠺⠵⣿⡟⣿⣆⡛⠻⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠖⢰⡟⠁⠀⣠⡴⠾⠿⢛⣻⣿⣿⣿⣷⣦⡙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⣾⡇⣠⣞⣩⣤⠶⠛⢿⣽⢦⡀⠀⣈⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⣄⠙⣿⣷⢀⣿⡷⣿⡇⠀⠀⢾⡇⠀⠀⢰⣿⣿⣟⠋⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣹⣽⣆⣿⢿⡟⢁⣤⠀⠛⠀⠀⠈⠀⢠⡾⠋⠉⠉⠻⣷⡘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣼⠟⠙⠛⠁⣿⠁⠏⠠⠀⠀⠀⢀⠀⠀⠸⣧⣀⠀⠀⣠⣿⠃⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣴⣋⣁⣀⠀⠀⠀⠹⣷⣄⣠⣴⣆⠀⠘⠀⢠⠀⣠⠹⠟⣻⡿⠃⣺⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⡟⠁⣴⣾⣿⣿⣿⠿⠿⠻⠿⣦⣤⣭⣭⠾⠿⣷⢶⡤⣤⣤⣥⣤⡾⠋⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⣠⡿⠋⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⣀⡿⠀⠃⠈⢿⣿⣟⣦⣀⣠⣤⣀⠻⣿⣿⣿
⠀⠀⢰⣿⢦⡾⠋⢈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⣿⡿⠀⠀⠀⠀⠈⡏⢹⠙⣿⠛⠙⢿⡇⢘⣿⣿
⠀⠀⠸⠟⠋⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠘⣿⡀⠀⠀⠀⡀⢀⡿⣯⣷⣿⣿⡙⢦⢡⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢀⣠⣴⡿⠛⠁⠀⣾⢛⡿⠶⢶⠞⣷⢿⢱⣀⣸⣿⡅⠑⠀⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⡾⠿⠛⠉⠀⠀⠀⠘⣷⡟⠀⠀⢺⣿⣿⠈⠑⠿⠛⢸⣷⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⡟⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⣆⠀⠀⠀⣠⣶⢾⣿⡿⠟⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣯⣽⣿⠿⠿⠛⢙⣿⠿⠷⢶⣦⡀⢀⣀⠳⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠉⠻⣿⣿⣶⣤⣴⣾⡿⠶⠶⢾⢿⣣⣼⣿⣿⡔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣴⣶⠿⠛⠉⠉⠉⠉⠀⠀⠈⠛⠉⠁⠀⠁⣼⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⠉⣉⠉⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⣵⣠⣦⠱⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦⡀⠀⠀⠀⣠⣴⠶⠾⠟⠛⠻⠾⠍⣁⠹⢆⠇⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣦⡀⠀⠻⢿⣿⣿⣶⣶⣤⣀⡀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠳⣄⠀⠀⠀⠉⢉⣿⣵⠈⠙⠳⢦⣄⣀⠀⠉⠢⡀⠀⠀⠈⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠂⠀⠀⠘⢷⣴⡾⠛⠛⠛⠿⡀⠀⢰⣿⠀⠉⠛⠛⠒⡿⢦⡀⠀⠈⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣰⠏⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢠⠖⠁⢈⠷⠄⠤⢄⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣦⣤⠤⠘⣷⡀⠀⠀⠀⠀⢀⣀⣤⠴⠊⣷⠀⠈⢦⡴⠋⢀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣿⣁⠀⠀⣀⡼⠻⣖⠒⠒⠊⠀⠀⠀⠀⡴⠏⠀⠀⠀⠀⠀⠇⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣄⠀⠈⠓⢶⣦⣤⣶⣤⢾⡃⠀⠀⠀⢀⣴⣶⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠈⠳⣝⢿⣀⣸⠇⠀⢀⣴⣿⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡶⡟⠛⠲⠶⠖⠚⠛⣧⠀⠈⠙⣳⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⢿⣷⣶⢏⣏⣀⣀⣠⠤⢤⠀⠀⠀⠈⢳⡴⠚⠉⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠀⠀⠀⠀⠹⣿⣾⣿⣿⣯⣝⣦⢈⡇⠀⠄⠀⠘⡷⠀⠀⠀⠀⢄⠲⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⡀⠀⠀⠀⢀⣾⠟⠥⡒⡄⠈⢻⣏⠀⠀⠀⠈⢸⠃⠀⡀⠀⠷⠈⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠡⠀⠀⠀⢸⡇⠀⠀⠈⠞⠆⠀⣿⠀⠀⠀⠀⠘⢦⣤⠿⠄⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢂⡀⠀⣸⡇⠀⠀⠀⠈⠘⠀⢸⠀⠀⢀⣀⣤⠞⢛⣷⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⡽⣿⣄⠁⠈⢉⣁⣠⡿⠿⠿⠿⠭⠖⠚⠉⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣿⢼⣷⡶⠟⠛⠋⠀⠀⠀⠀⠀⣀⡀⣼⠁⡾⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢷⡿⠀⠀⢍⠉⠉⠛⢛⢟⠉⠉⠉⢹⡇⠹⣄⣷⣄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣷⠀⡀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸⡇⠀⣿⣄⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣄⣐⠀⠀⠀⠀⠣⠤⠁⠀⠀⣸⡇⠀⣿⠋⠁⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠓⠒⠒⠖⠒⠒⠛⠉⠉⠀⠀⣿⣳⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢱⠀⢇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢧⢸⢀⣠⠈⠎⢦⡆⢘⡤⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢄⠘⠈⣿⠀⠀⠸⠃⠈⢰⣛⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣈⢀⡀⠀⢀⠀⠀⠀⠀⠘⣻⣯⣽⣯⣿⣷⣦⣀⠀⠀⠀⣠⣶⠾⠿⠿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡘⣇⣼⡆⣧⡄⡀⠀⠀⢡⣾⣯⣿⢷⣿⠛⠿⣿⣿⣷⣿⣥⣴⣶⣶⣄⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⡰⢀⠉⠈⠉⠙⢧⢇⠀⠠⢼⣿⣾⡿⣿⣿⣶⣤⣀⣠⣔⣫⣥⣤⣤⡌⠻⣷⣄⡙⠻
⠀⠐⠄⠀⠀⠀⠀⠀⠁⢊⡔⢳⡆⠁⠀⠀⠀⠀⢸⣫⠀⠀⢩⣿⣿⢿⣿⣧⣈⣉⣉⢟⣉⣥⣄⣀⡉⢿⣦⣈⠙⠻⠿
⠀⠀⠀⠠⠰⡂⠀⠀⠀⠛⠛⠋⠀⢠⣄⠀⠀⠀⡸⠒⠀⡠⠺⠾⣟⣿⣁⠙⠛⣻⣛⣩⣭⣉⣉⠙⣿⣦⡙⠛⠿⢿⠖
⠀⠀⠀⠂⢁⣁⣀⠤⡀⠀⠀⣀⣴⣶⠝⠀⠀⢸⣍⢀⣚⠻⠿⣶⣬⡙⠻⠿⢿⣋⣉⣉⣉⠛⢿⣧⡈⠙⠻⠿⠻⠂
⠀⠀⠀⠀⠸⢏⢰⡆⣽⣿⠛⠋⣿⠁⠀⢀⣠⣿⠂⣈⡹⠶⠶⣦⡙⠿⠶⠶⠋⢉⣈⣉⠙⢻⣦⡛⠿⣷⣶⡖⠁
⠀⠀⠀⠀⢀⠼⠻⠍⠈⠛⠀⠠⣧⠀⠀⡿⣟⠉⠤⣾⣿⣷⣶⣄⠛⠷⠶⡆⠀⠀⠀⠉⠹⠧⣈⠻⠶⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⢀⣿⣾⠉⠀⠚⠛⠛⠈⠙⠻⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠿⢿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⣴⣿⠟⠉⣀⣀⣀⠀⠀⠀⠈⠙⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⡿⠿⢿⣿⣷⣄⠀⠀⣼⣿⠋⡴⠋⣡⠀⠀⠙⠳⡄⠀⠀⠀⠀⠙⠻⣿⣶⡄
⠀⠀⠀⣠⣾⣿⠿⠛⠋⠉⣠⡶⠟⠛⠻⢿⣿⣶⣿⡇⡜⢀⣼⣿⣧⣴⣿⠀⢹⡄⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⣴⣿⡟⠁⠀⠀⠀⢸⣿⣶⠶⠶⠿⠿⠿⠻⠿⢷⣧⣼⣟⠹⠟⢹⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⣿⣿⡇⠀⠀⠀⠠⣿⣥⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢮⣍⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⣿⣿⡇⠀⠲⠶⠞⠛⠻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠈⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⡿⢁⡀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠙⢿⣿⣦⣀⣀⣀⠀⠀⠀⢀⣀⣠⣿⢱⣿⣿⠀⠀⠀⠈⠙⢳⣦⣤⣀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢹⣿⣄
⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⣠⣾⠿⠛⠛⠛⠛⠿⣿⡟⠀⠀⠀⠀⣰⣿⡇⠈⠙⠛⠶⠶⣤⣤⣤⣿⣦⠀⠀⠀⠀⠀⡿⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠘⢷⡀⠀⠀⠀⠁⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢘⣧⣀⣀⣀⡀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⣾⠋⠁⠀⠀⢀⡾⠋⠁⠀⠈⠙⢷⣄⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠾⠛⠉⢸⣿⠀⠀⠘⣿⡀⣀⣴⠟⠀⢀⣤⠶⠀⠀⠀⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⡶⣤⠤⠶⠾⠛⠁⠀⠀⠀⠀⠀⢀⣸⠏⠀⠀⠀⠈⠛⠋⠁⠀⢰⡟⠃⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⣷⣤⣤⣴⢶⣤⣤⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⡀⠀⢀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠙⢧⡙⢧⡎⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⣾⣭⣭⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣌⣻⣦⣙⠶⠦⠾⠃⠀⠀⠀⣀⣤⣾⡿⠟⠛⠛⠛⠛⠿⢿⣷⣶⣄⡀
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⣀⣿⣿⠟⣩⠟⠻⠶⢶⣶⠶⠛⠛⣿⠏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⣤⣀
⠀⢀⣠⣾⣿⡟⠉⠁⠀⠈⠉⠻⣿⣷⣾⣿⣿⡿⠁⢾⣧⣤⣀⣠⡟⠁⠀⠀⢀⡟⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⣠⣴⠾⠟⠛⠛⠻⢿⣷⡄
⢠⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⢸⡇⠀⠀⠀⢀⣬⠿⠶⢦⣄⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⣿⣷⡟⠋⠀⠀⠀⠀⠀⠀⠼⢿⣷⣤⡀
⢸⣿⣧⠸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⠃⠀⠀⢠⡟⠀⠀⠀⠀⢹⡄⠀⢻⣄⠀⠀⠀⠀⠀⠀⢿⣿⣠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣿⡄
⠸⣿⣿⡀⠹⡄⠀⠀⠀⠀⠀⠀⠘⣿⣧⡼⠋⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⡇⠀⠀⠙⠷⣤⣤⣤⣤⡴⢿⡟⠁⠀⠀⠀⠀⢠⣄⠀⢸⣷⡀⠘⣿⣿
⠀⢻⣿⣷⡀⢳⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⠳⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠘⣿⡆⠀⠙⠃⠀⣿⣿
⠀⠀⠹⣿⣷⡄⢳⡀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣆⠀⠐⢶⡀⠀⠀⠈⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠈⣿⣿⡄⢻⡄⠀⠀⠀⠀⠀⢨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣟⠉⠀⠈⠛⢿⣿⠻⠗⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠘⣿⣿⣄⣹⣦⣤⣤⣤⣾⣿⡿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢹⡆⠀⠀⠀⠀⠻⢷⣤⣤⣤⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠛⠛⠛⠁⠀⠀⠉⠻⢿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⣇⠀⠀⠀⠀⠀⠈⣇⠹⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⢸⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⣀⣀⣀⣠⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⢀⠄⠈⣠⣄⣨⡞⠀⢸⡆⠠⣾⠀⣀⠀⢢⠀⠀⢀⣶⠀⠀⣀⠐⢠⡀
⠀⠀⠀⠀⠀⢹⡿⠆⠀⠉⣺⡇⠀⠾⠃⠀⣿⠀⠛⠋⣸⠀⢘⣳⣿⡆⠀⠿⠋⢈⡇⠀⠀⡴⢩⣤⣾⠀⠀⠀⡰⢋⠹
⠀⠀⠀⠀⠘⣿⣶⣤⣴⣾⠟⣷⣤⣤⣤⢾⣇⠀⣶⣾⣿⣄⣨⣥⣤⣇⡀⢸⣦⣀⣽⣦⢰⣇⢠⣶⣶⡝⣆⡞⠰⠻⠆⠣⡀
⠀⠀⠀⠀⡰⠁⠀⢸⠏⠈⠉⠹⣧⡹⠋⠙⠛⢿⣿⡏⠉⠈⠉⠛⠻⢿⣿⠛⠛⣿⡿⠇⢸⣿⣶⣬⣭⣴⣿⣿⣿⣿⣷⣼⠃
⠀⠀⠀⢰⠁⠀⠀⠀⢀⠀⠀⠀⢏⠀⣠⢾⠀⠘⣿⡇⠀⠀⣷⡦⠀⠘⣭⠀⠀⢿⡠⠐⠚⠋⠛⠻⣿⠃⠉⠉⠉⠿⠿⠃
⠀⠀⢠⠃⠀⠸⣆⢀⣾⣷⡀⠀⠸⡌⠛⠺⠀⠀⢹⡇⠀⠀⠋⠀⠠⣶⣿⠀⠀⢸⡇⠀⢠⣶⣤⡀⠀⢹⡆
⠀⢀⠇⠀⠀⢸⣿⣿⣿⣷⡇⣀⣠⣷⣦⢤⡀⠀⠀⢣⠀⠀⣦⡀⠀⠈⣹⠀⠀⠀⣧⡀⠀⠛⠉⠀⠀⢸⠁
⠀⣾⣐⣶⣶⣾⣿⡟⡿⢻⣿⡸⣿⣯⣿⢿⣧⣶⡄⣼⣷⣾⣿⢹⣶⡟⣿⣦⣠⣤⣿⣿⣦⢤⣤⣶⡦⣺
⠀⠈⠻⠿⠿⠞⠿⠃⠀⠈⠻⠓⠉⠁⠀⠀⠷⠻⠃⠻⠀⠛⠋⠙⠧⠂⠿⠏⠸⠳⠟⠺⠯⠞⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠛⠛⣉⡙⠻⢿⣷⡀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⢀⠖⣯⢁⠽⡑⢦⣻⣷⡄⣠⣴⣿⣟⠛⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⡞⢠⡄⡈⣠⡘⢄⣛⣿⣿⣿⣿⣉⣙⣻⣦⠉⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠱⡘⣣⣤⣶⠿⠟⠛⠉⠉⠉⢉⣉⣙⣛⣿⡄⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠿⢷⣤⠴⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣠⡶⠟⢉⣌⢻⣿⠿⠛⠋⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡏⠀⠀⠀⢀⣼⠟⠁⠀⣀⣠⡴⣾⣏⠁⠀⠀⢸⣿⣯⣿⣶⣶⣦⣄⡐⠄⢰⣿⣿⠋
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠃⠀⠀⣰⣿⣿⡗⠛⠛⠋⠁⠀⢿⣿⡇⠀⠀⢈⡿⠋⠉⠉⠉⠙⢿⣿⣶⣾⣿⠏
⠀⠀⠀⠀⠀⣿⣿⠃⠀⢀⣀⣀⣼⣿⠁⠘⣷⣄⠀⠀⠀⠀⠘⢿⠇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⢻⣿⣤⣾⠟⠉⠉⠉⢿⣧⡀⠈⣹⣿⠄⢠⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠙⣦⡀⠙⢿⣶⣿⠏⠀⢸⣷⠉⠛⠻⠷⠶⢦⣄⣀⣀⢀⣀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢉⡿⠀⠀⠈⠀⠀⠀⠀⠻⣷⣦⠀⠀⠀⠀⠉⠙⠛⠋⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⡈⠉⢀⣀⣤⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣤⣤⣶⡶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣯⣿⣷⣄⠀⠀⠀⠀⠸⣧⠀⢻⣾⣿⣿⢋⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠛⠛⠋⠉⢻⣿⣶⣤⣄⣀⣙⣿⣿⣿⣿⣵⣿⠏⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣅⡀⠀⠀⣀⣤⣶⠟⠁⢸⣿⠉⠉⢻⣏⢁⣹⣿⡝⢿⣶⣦⣤⣾⣿⠟⠛⠛⠿⣿⣦⣀
⠀⠀⢀⣤⣿⡿⠦⠀⠀⠀⠉⠻⣶⣾⡏⠁⠀⠀⠀⢸⡿⠀⣤⡶⢿⣿⡉⠉⠀⣼⡏⢿⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣷
⠀⢰⣿⡟⠁⣤⠀⠀⠀⠀⠀⠲⣾⣿⡀⠀⠀⠀⣀⡾⠃⣾⡏⠀⠀⠈⣷⠀⠀⢻⣷⡈⣿⣧⠀⠀⠀⠀⠀⢠⠇⣿⣿
⠀⣿⣿⠀⣾⠏⢠⣾⠁⠀⠀⠀⢹⣿⠻⠷⠶⠟⠋⠀⠀⢻⣧⣀⣀⣠⡿⠀⠀⠀⠻⢿⣿⠃⠀⠀⠀⠀⠀⡞⢰⣿⡟
⠀⣿⣿⠀⠀⠀⠘⠋⠀⠀⣴⠆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⡼⣵⣿⡿⠁
⠀⠹⣿⣧⡀⠀⠀⠀⠀⣼⢿⣿⠟⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡃⠀⠀⠀⢀⡼⣽⣿⡟
⠀⠀⠘⠻⣿⣶⣦⣤⣤⣶⠿⠃⠀⠀⣴⠟⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣶⣤⣶⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠈⣿⣿⢹⠀⠀⠀⠀⠀⡟⠀⢸⣿⣶⣤⣤⣤⣤⣤⣤⣶⣾⠿⠛⠁⠀⠀⠉⠛⠛⠋⠛⠛⠋
⠀⠀⠀⠀⠀⢸⣿⠇⣿⠀⠀⠀⠀⠀⠇⠀⣼⣿⠉⠉⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⣿⣿⢰⡇⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⣿⣿⣼⣧⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣦⣄⣀⣀⣤⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠿⠿⠟⠻⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠛⠉⠀⠀⣠⠴⠒⢒⡦⣌⠹⣿⣧⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⢀⡞⢁⠓⢤⠎⠱⡈⠳⣼⣿⣧⣴⣾⣿⣿⣿⣤⣈⠻⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⠁⢸⠀⣄⡰⢦⠙⣀⣡⣿⣿⣿⣿⣯⣤⣤⣙⣿⣧⠀⠀⠈⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⣢⣤⣴⣾⠿⠛⠛⠉⠉⠁⠀⠀⣉⣉⣛⣻⣷⡀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠉⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣠⡄⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⢿⣿⣿⣿⣿⠿⠛⠁⠀⠈⠉⠁⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⣰⣿⣎⢿⣿⠁⠀⠀⠀⢀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡟⠀⠀⠀⠀⣠⣾⡟⠀⣀⣀⣤⣴⠾⠛⣿⣷⡄⠀⠀⠀⢹⣿⣿⣾⣿⣿⣿⣿⣷⣦⡉⠁⢩⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠃⠀⠀⢀⣼⣿⢿⣿⠛⠉⠉⠁⠀⠀⠀⢿⣿⣷⠀⠀⠀⢠⠟⠋⠀⠀⠀⠀⠈⠹⣿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⢀⣀⣀⣾⣿⠁⠀⢿⣧⡀⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⢿⣿⡇⢀⣴⡿⠛⠛⠉⠛⣿⣦⠀⠀⠙⢻⣷⡀⠀⣰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡏⠀⠀⠤⣄⡀⠘⢿⣷⣄⣀⣿⡟⠁⠀⣿⡟⠿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠼⢿⣆⠀⠙⠻⠿⠟⠁⠀⠀⢿⣷⡀⠀⠀⠉⠉⠉⠙⢷⣶⣶⣤⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⠀⠀⡀⠀⠀⠀⠉⠉⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⡀⠁⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣤⣾⣷⠶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⢿⣿⣿⣿⣯⣽⣿⣦⡀⠀⠀⠀⠀⠀⢸⣧⠀⠙⣧⣿⣿⣿⡿⢁⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠿⠿⠿⣿⣶⣄⣀⠀⠀⠀⠻⣶⣾⣿⣿⣿⣋⣴⣿⠏
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⡿⠿⠶⣶⡿⠟⠛⣿⣿⢿⣿⣇⣀⡀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⡿⠿⠟⠿⠿⢶⣤⣀⠀⢀⣤⡶⠿⠛⠉⠀⠀⣿⡇⠀⠀⠘⣷⣤⣤⣼⡿⠆⠙⣿⣿⣿⣾⣿⡿⠋⠁⠀⠈⠉⠻⣿⣷⣦⡀
⠀⠀⠀⣠⣾⣿⠿⠓⠂⠀⠀⠀⠀⠉⠻⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⠃⢀⣶⡿⠿⢿⣏⠀⠀⠀⢰⣿⠈⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⢀⣾⣿⠏⠀⣠⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⡀⠀⠀⠀⠀⢀⣼⠏⢠⣿⡏⠀⠀⠀⠹⣷⠀⠀⠸⣿⣆⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⣿
⠀⣸⣿⡟⠀⣼⡿⠀⣠⣾⠀⠀⠀⠀⠈⢿⣿⢿⣶⣶⣶⡾⠟⠁⠀⠘⣿⣇⠀⠀⠀⣰⡿⠀⠀⠀⠹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⠇⢰⣿⣿
⠀⣿⣿⡇⠀⠙⠁⠰⣿⠏⠀⠀⢀⡀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣿⠟⠁⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠀⠀⢀⡟⣠⣿⣿⠏
⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⣠⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⠋
⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠾⢛⣿⠟⠋⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣄⠀⠀⠀⠀⣠⠟⣼⣿⣿⠁
⠀⠀⠀⠙⠻⣿⣿⣶⣦⣤⣶⣶⠿⠋⠀⠀⠀⣰⡟⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⣿⣿⣷⣶⣶⣿⣿⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⣹⣿⡿⣹⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣦⣤⣤⣀⣀⣀⣀⣤⣤⣶⣿⡿⠟⠋⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⡏⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⣿⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣧⣄⣀⣀⣠⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⠶⠶⡤⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⢣⢀⣠⣤⣄⢀⣀⣊⡉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢌⣰⣾⣿⡿⣿⣿⣿⣛⣳⣄⣠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠈⢯⣻⣿⡇⠀⣿⣿⣟⡟⠛⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⡛⣹⡁⢰⣿⢿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣤⣶⡶⠟⣻⡶⣄⢀⡀⢠⣔⣮⣷⣿⣿⣷⣇
⠀⠀⠀⠀⠀⢀⣴⣿⣷⣷⣾⣿⣿⣿⣿⡿⠿⠋⣁⠈⠠⢀⣤⣿⣛⣻⣿⣻⣿⡆⣈⠁
⠀⠀⠀⠀⠀⠊⠁⠚⣻⣿⣿⣿⣿⣟⠋⠉⠁⠠⠀⠀⢠⡾⣿⣟⣿⣿⣦⣉⠙⢛⢿⣿⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⡇⣿⠿⠀⠀⠀⠀⣠⡀⠈⠑⣻⣿⣿⢻⣿⣿⠋⠀⢸⣿⣟⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠀⣤⣴⣾⣿⣿⣄⠈⠉⠉⡟⢸⠋⠀⢀⣴⣿⣿⣛⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠨⡑⠿⣿⣿⠿⠟⠁⣶⡆⠐⠁⠰⢾⣿⣿⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠘⠏⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⣾⡿⠀⠀⡰⠀⠀⠀⠘⠻⢿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡆⢀⡄⣰⢀⣿⣿⢁⣼⠁⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⢐⣷⣘⣿⡿⢸⣿⣯⣼⣏⡠⠀⠀⠀⠀⢳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣳⣾⡿⣾⣿⣿⠀⢀⣠⣤⣶⣾⣿⣿⣦⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⢶⣿⡿⢿⠟⢿⣿⣿⣿⣿⣿⣿⡷⢞⡿⠁⠉⠛⡇⠘⣏⠙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠶⠋⠉⡧⣼⠀⠰⢇⠈⢿⠈⣿⠙⠀⢺⠃⠀⡼⠶⠁⠈⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠙⠀⠀⠀⠤⠃⠁⠰⠀⠎⠀⠸⢠⡋⢃⠀⡄⠀⡴⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠁⠈⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠒⠀⠁⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠛⠛⠉⠻⣷⠶⡄⠀⠀⠀⣱⠄⠀⠳⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⢀⠀⢀⠦⢠⠒⢳⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣀⣀⡤⠴⠒⠉⢠⠴⠋⠀⡆⣠⠀⠷⠘⣴⣿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡰⡟⠀⢠⡷⠋⠀⢘⡴⢡⠉⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠺⢦⠾⡀⠀⠀⠀⢀⢻⠇⠀⢸⡂⠤⠂⠁⠀⠈⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⢃⣬⡂⣤⡠⠊⡝⠀⠀⢸⡇⠈⠱⠄⠤⡀⡜⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠀⠀⠀⠈⣲⠁⠀⠀⢻⠁⠀⠀⠀⠀⣇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠫⠤⠤⣀⡀⠀⠀⠀⣀⠴⠋⠁⠀⠀⡄⢸⡀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠉⠑⡦⠚⠁⠀⠀⢀⡴⠊⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⡀⠀⠀⠈⡄⡌
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣀⣀⣀⣀⠀⢠⠞⠀⠀⠀⠀⠀⠘⠣⠤⢞⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠘⡇⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⡼⠁⠁⠁⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣇
⠀⠀⢀⡠⠖⢲⠇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸
⠀⢀⠊⠀⠀⢸⠀⠀⡀⡄⣀⠀⠀⣀⣼⠁⠀⠀⠀⣠⠖⠋⠉⠉⠉⠁⠀⠀⠀⠘⠲⣄⠤⠒⠒⠲⣄⣀⢀⢀⡄⠀⠀⠀⠀⠀⠘⡄⠀⡆
⠀⢸⠀⠀⠀⢸⠂⠉⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠐⠀⠠⠴⠁⠀⡇
⠀⠈⢧⣀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠠⣖⣖⣹⠋⣏⢙⣦⣀⠀⠀⠀⢀⡤⠤⠷⠄⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠒⠒⠒⠒⠒⠋⠉⠉
⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠛⠒⠻⠠⢦⣆⣀⣀⡠⠴⠊⠉⠚⠀⠀⠈⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠿⠿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⢀⡤⠒⠀⠒⢌⢻⣦⣴⠶⠛⠛⠳⣆
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣼⠀⠀⠀⢀⣼⠟⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠸⣄⢀⡴⠋⠀⣠⠖⠁⠀⠀⢀⡾⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⡼⠋⠀⣠⣞⣁⣠⣶⣄⣠⡾⠁⠀⠀⠈⠙⠳⣦⣀⠀⠀⢀⡴⠋⠀⢠⡟⢀⣠⣄⡀
⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⡞⣥⣶⣾⣏⠉⠉⠛⢁⡉⢿⡀⠀⠀⠀⠀⣴⠟⠛⠿⣷⣤⡟⠁⢀⣀⣾⠟⠋⢁⣈⣿⣀
⠀⠀⠀⣠⡏⠀⠀⠀⢠⣏⣠⡟⢁⡤⠤⣄⠀⢰⣅⠈⢾⣇⣀⠀⠀⠀⠹⣆⠀⠀⠘⠿⣄⠀⠀⠙⢧⣠⠶⠋⠁⣀⣿⡀
⠀⠀⣸⠏⠁⠀⠀⢠⡟⠉⠉⠁⢸⢀⡀⠘⡆⠀⣿⡷⠛⠉⠉⠙⢶⡄⠀⠈⣷⠀⠀⠀⠀⠓⠀⠀⠀⠙⢦⡶⠛⠉⢉⡷
⠀⠀⢻⡀⠀⠀⠀⣾⢳⣄⠀⠀⠈⢿⣾⠀⣼⠀⠋⠀⠀⠀⠀⠀⠈⣿⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠈⣿⣦⣠⡼⢷⡀⠈⠛⣆⠀⣈⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢾⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⢰⡇⢸⠃⢠⣤⡙⢦⣤⠟⢰⣿⣷⣦⣤⣴⣶⣤⣀⣠⣤⣶⣿⠀⣠⡟⢷⣄⠀⠀⠀⠀⣀⣀⣠⡴⠛
⠀⠀⢸⡇⢸⡆⠀⠀⠛⢦⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣴⠋⠀⠀⠙⠷⣤⣀⣀⣸⣿⠁
⠀⠀⠘⣇⠀⠙⢦⣀⡀⠀⣀⣄⠀⠙⠻⢿⣿⠿⠿⠥⢤⠝⢛⣯⡞⠁⠀⠀⠀⠀⠀⣰⠟⠉⠁⣿
⠀⠀⠀⢿⡀⠀⠀⠈⠉⠙⡏⠙⢧⡀⠀⠀⢿⠛⠛⠻⡟⠀⣼⠋⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢸⡇
⠀⠀⠀⠘⣷⠀⠀⠀⠀⣼⠁⢀⡈⣧⠀⠀⠈⠳⠶⠚⢀⣼⠃⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠉⠛⢋⣩⣽⣇⡀⠀⠀⠰⢒⣿⡉⠳⣄⠀⠀⢀⡾⠃⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠈⢻⣄⣠⣤⣴⡟⢧⠀⠙⢯⡉⠙⠉⠉⠉⣧⠀⠙⢧⣰⠟⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢻⡾⣧⣤⣈⣳⣀⠀⠀⠀⠈⢧⠀⠈⣿⡄⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡼⠃⢸⡇⠙⡏⠉⢷⣤⣤⠶⠾⣆⣟⣩⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⣾⣁⣠⡏⠀⣸⠷⠶⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠲⠠⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⡀⠁⡀⠀⠀⠀⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⠐⠀⠂⡀⠀⠘⠂⠀⠀⠀⠀⠀⢀⠘⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠣⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠠⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠘⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⡀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢈⠉⠀⠤⠄⠀⠀⠀⠀⢤⡒⣠⠴⢖⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⣦⡀⠀⠉⡆⡄⢀⠉⠀⠀⠀⠉⠥⠀⠀⠂⠀⠀⠀⠀⡴⢀⡐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠖⢀⠀⠤⠀⠓⡀⠄⠈⠅⠀⠀⠁⢅⢂⢠⠄⠈⠄⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣉⡀⠤⠠⠀⠂⠩⢀⠀⠂⠀⢰⠦⠀⠲⠗⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⠓⠁⠂⠀⠠⠄⠉⣀⢰⢠⡄⢈⠡⠀⣈⠖⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⡆⠐⠂⠀⡇⠀⠀⠁⢠⠑⠀⢩⡶⣤⡇⢀⠀⠀⠀⢄⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠐⠀⠐⢀⠀⠉⠀⠀⡀⠘⡀⠀⠀⠐⠀⠀⠀⠉⠀⡀⠀⠀⠀⠂⠀⠀⠀⡤⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠌⠁⢠⢀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⡏⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠆⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠲⠂⠀⠆
⠀⠀⠀⠀⠀⢁⢀⠘⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠣⠄⡀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠠⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⢠⡀⠑⠈⠁⠈⠀⣀⣀⠀⠀⠀⠀⠀⠦⠰⠢⠠⠀⠀⠀⠀⠀⠠⠈⠁⠢⠄⠀⡀
⠀⠠⠀⠈⠀⠘⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠄⠀⠀⠂⠀⠐⠤⠀⠄
⠀⠀⢀⠀⠀⠀⠠⣀⡠⠀⠀⠀⡰⠀⠀⠀⠲⠇⠀⠀⠾⠀⠀⠀⠂⠀⠀⠱⠔⠀⠀⠘⠂⠀⠀⢨⠄⠀⢤⠇⠀⢀⣨⠁
⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠈⠓⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠢⠌⠀⠂⢤⠀⡼⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⢀⡀⢠⠠⠀⠶⡒⠇
⠀⠀⠐⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠀⠀⢢⣄⠀⠦⠀⠀⠀⡈⠀⠀⢁⠀⠀⠀⢠⠇
⠀⠀⠀⠈⠀⠀⠀⠑⠦⠤⠤⠞⠀⠀⠀⠀⠈⠃⠀⠠⠴⠀⠀⠀⠀⠀⠠⣸⢿⠀⠀⠀⠀⠀⠐⠄⠠⠜⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠃
⠀⠀⠀⠈⠐⠂⠀⠀⡀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠄⠄⣤⠄⠄⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠂⠂⢸⡇⠒⡄⠆
⠀⠀⠀⠀⠀⡀⡀⠀⠁⠰⠀⠂⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠜⢹⠓⠚⠩⣤⡆⠀⠀⠀⡀⠀⣺⣁⠔⢀⠀⠄
⠀⠀⠀⠈⠀⠙⠃⠉⠀⠀⠀⠀⠄⠀⠠⡴⠃⠀⠀⠀⠀⠙⠊⠀⠀⠘⠂⠀⠘⠶⠚⠐⠚⠀⠀⠀⠉⢀⣤⣽⠇⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠶⢖⠛⠛⠛⠒⠶⠦⣼⣍⡉⠉⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠙⠳⢶⣄⡑⠄⠀⠀⠀⠀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡁⡠⠀⠀⠀⠈⠹⡗⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠤⠄⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠛⠛⠛⠛⠓⠲⢦⣧⠀⠀⠀⢈⡉⣀⠤⠀⠚⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⡛⠒⢦⠀⠀⠀⢀⡤⠖⠿⠃⠀⡾⠛⠙⠙⠛⠛⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠃⠀⠀⣼⣷⠞⠛⠋⠉⠛⢛⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠉⠛⠷⣤⣸⣆⠀⢹⡛⣶⡄⠀⠀⡤⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣛⡫⠭⠤⠭⠶⢽⣷⣴⣇⣀⣀⣀⡀⠀⠀⠀⠀⠒⠠⠤⠠⠬⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠒⠉⠀⠀⠀⠀⠀⢀⢷⡿⠛⠉⠉⠉⠉⠙⠳⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠘⠟⠉⠈⠁⠀⠀⠀⠀⠀⢰⢡⡿⠤⡀⠀⠀⠀⠀⢀⢀⠤⠽⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢘⡆⠀⠀⠀⡼⠧⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠤⠤⡈⠀⠀⠀⠰⠁⢀⣬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠠⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠛⠉⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢏⡴⠒⣖⠲⢦⡀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⣴⣾⠿⣶⣶⣶⠶⣷⣦⡀⠀⢀⣀⣀⣀⣿⡇⡞⠀⣸⡿⠁⠀⠙⡄⠀⠀⠀⢹⣿⡄
⠀⠀⢀⣤⣴⣾⡟⠀⠀⠘⡿⠁⠀⠈⣿⣿⣿⠿⠿⠛⠛⠛⠿⢧⣴⣿⣷⣦⠀⢠⠇⠀⠀⠀⠀⢻⣿⡄
⠀⠀⢸⡏⠀⠙⢷⠀⠀⠀⡇⠀⠀⢰⡿⠿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠉⠻⢥⣴⠏⠀⠀⠀⠀⠀⠈⣿⣧
⢀⣴⠿⢷⡄⠀⠈⠃⠀⠀⠀⠀⣀⣿⠀⠀⣼⠟⠛⢻⣿⡿⠳⠶⣤⡀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⢹⣿⡄
⢸⣧⡀⠀⠙⠂⠀⠀⠀⠀⠐⠋⠁⠀⠀⢀⣿⣄⣠⣿⣿⣾⠇⠀⠀⠙⡳⣄⠀⠀⠙⢦⠀⠀⠀⠀⢸⣿⣷⣤⡀
⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠛⠻⢿⡿⠀⠀⠀⣼⡟⠈⠛⠶⣤⣈⣳⠀⠀⠀⠘⠃⠙⢿⣷⡀
⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡿⠁⠀⠀⢀⡀⠉⢹⣧⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣿⠖⠒⠒⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡟⠛⠛⠋⢹⡆⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⡴⠚⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢧⣀⣀⣤⡿⠋⠉⠛⢶⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡀⠘⣏⠉⠛⠛⠛⠒⠒⠒⠛⠋⠉⠉⢹⡆⠀⠀⠉⠉⢡⣶⠒⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠈⠳⠶⣤⡶⢦⣀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠹⣧⠸⡍⠛⢿⠿⠟⠋⠀⠀⢀⣤⣶⣄⣈⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠙⢧⡙⠶⠟⠀⠀⠀⠀⣴⠟⠁⠀⠈⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⠈⢿⡄⠀⠀⠀⠀⣼⣿⣶⣶⡶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣴⣾⠟⠛⢻⠟⢻⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢃⡞⠁⠀⣴⠋⠀⡾⣿⠉⠛⠻⢿⣶⣤⣀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣤⣶⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⡇⠘⠶⠤⠼⠁⠀⢸⠇⠙⣇⠀⠀⠀⠉⠛⠿⠿⣿⡿⠿⣿⡿⠿⠛⠋⠉⠴⠋⢀⡨⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣸⠀⠀⣠⠖⠋⠳⣆⢻⡀⠀⠘⢷⣄⡀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠐⠛⠃⠀⠐⠚⠁⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⠏⠀⠀⣇⠀⠀⠀⣸⠸⣇⠀⠀⠈⣿⣿⣷⣤⣀⣿⠀⠀⠀⠀⠀⠲⠶⠆⠀⠀⠰⠒⠋⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠘⠳⠤⠶⠋⠀⠈⠳⢤⣤⣿⣿⡏⠛⢿⣿⣄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠟⠻⣷⣄⠀⠀⠀⠰⣶⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣀⣀⠀⠀⠀⣀⣠⣴⡿⠋⠙⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠙⠛⠿⠿⠿⣿⠻⠛⠋⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⠂⠀⢀⣿⠷⠤⠶⠃⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢀⣾⢃⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣀⣠⣼⣷⣄⡀⠀⣀⣠⡶⠟⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣶⣶⣶⣿⣿⣿⣭⣭⣥⣶⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣋⣀⣂⣐⡀⠩⠙⠟⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠸⠭⡭⣭⡭⠽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⣴⡿⢋⣴⠓⠲⣦⠄⠀⠀⣠⠴⢀⢔⣉⣁⣔⣂⠓⠶⠀⠙⠄⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢀⡤⣶⣽⣎⣩⣴⣿⣯⣤⣌⢳⡀⠀⡐⢁⡤⠘⠹⡡⣐⣠⢊⠍⣒⢬⡒⡀⠘⠒⠄⠉⢟⡲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠴⢃⠴⠔⠊⡉⣠⣮⡭⠶⠶⣶⠬⠙⢠⣷⠇⠶⡡⣈⣿⣿⡿⠿⠿⠿⣾⣮⡄⢅⢌⡢⠄⠀⠀⠉⠉⠑⣦⠻⣷⣄
⠀⠀⠀⠀⠀⢀⠖⠦⠚⠓⢞⡽⢋⣵⡌⠙⣶⢡⢀⠡⠀⡎⢇⡌⣜⣼⣿⠟⢁⡤⠒⠒⠐⢤⡙⢻⣷⣆⠩⣢⡀⠀⠀⠀⠀⠈⠙⢨⣿⣦
⠀⠀⠀⠀⠀⢘⠒⠘⢋⣩⣵⣿⠍⠑⣡⢰⣧⣿⠟⡀⠟⡼⠎⢰⣾⡿⢁⡔⠁⠀⠀⠀⠀⠀⠘⢆⠙⣿⣶⠐⣤⣄⠀⠀⠀⠀⠀⢫⡨⠟⡇
⠀⠀⠀⠀⠀⠘⠛⡿⣻⡽⢊⡟⢠⠎⣡⠟⠁⠁⣮⠇⡶⡇⠱⣽⣿⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⣿⣇⡌⢲⠆⠀⠀⠀⠀⡆⢡⣖⡇
⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⠞⢠⠃⣼⠏⢐⠐⡇⢁⣜⠔⡀⣸⣿⠿⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⢿⣷⡄⣯⢏⠄⠒⢲⣣⣾⣿⠇
⠀⠀⠀⢀⢔⣲⣤⣄⠀⠀⢀⢴⠀⣿⡤⢀⢌⣀⣁⣥⣀⡴⠟⣡⣴⢦⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⣀⠻⣦⣬⣥⣴⡄⢸⡿⡫⠊
⠀⠀⠀⢘⣡⡞⣽⡿⢯⣯⣥⡼⢦⠘⢿⣿⣾⠀⠀⢀⣀⢴⣺⣿⣤⡴⢃⠸⢦⣦⡀⠀⣠⣤⣀⠀⣀⣤⣫⢟⠘⠑⠊⠋⢻⢇⡟⠁
⠀⠀⠀⠈⠀⠑⠃⠀⢹⣿⠀⠀⠀⠙⠀⠤⠭⠿⢿⡿⠿⢫⣖⢟⡵⠛⠛⠋⠁⠀⠁⠀⡿⢞⡿⢿⣞⡻⠞⣱⣴⢞⣷⣶⣯⠞⠙⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠠⠟⠟⠘⠑⠈⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣫⣤⣍⣽⣩⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⡇⠠⠀⠀⠀⠀⢸⡏⣠⣤⣤⣤⣼⣟⡓⠶⣿⡄⠀⠀⠀⠻⣌⠛⠋⠀⢰⡟⣸⣥⣾⣧⣶⣾⣝⣿⣄⠈⢷⡄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡯⠠⠬⠠⠌⠁⢹⣷⣿⣿⣿⡿⠛⣻⣿⠿⣿⣿⣦⡀⠀⠀⠈⠛⠷⣄⢸⣿⣿⣿⣿⣿⠟⡹⢏⠙⡝⢿⣦⣻⣾⣾⠀⠀⣰⡧⠌⠌⠡⠀⠈⠭⠁⢸⡇
⠀⢸⣧⠠⠄⠁⠀⠀⠀⠙⣿⣿⣿⡟⡆⣼⠿⠓⠈⠻⠈⠻⣦⡀⠀⠀⠀⢹⡇⠻⣿⣿⣿⢳⣁⡑⢂⣘⣵⣬⣹⣟⣿⡿⢀⣴⠟⠅⠤⠁⠄⠀⠠⢄⠀⢸⡇
⠀⠀⣿⠀⠀⠀⡀⠀⠀⢸⡏⠀⠀⠉⠳⣿⠞⠀⠀⠀⠀⢠⣿⠿⠒⢦⣤⣾⠃⠀⠘⠿⣿⣿⣿⡿⢿⣿⡿⢿⡿⢿⣿⣿⣟⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⢐⢒⠀⡂⢃⠀⠀⢻⣦⣀⣄⠀⠀⠰⢶⠟⠙⠀⠈⢡⠶⡇⠀⡟⠁⠀⠀⢀⣶⣼⣿⣌⡇⢸⢏⡇⡜⠀⣾⣏⡍⢻⣶⡿⢖⢦⡀⣱⠞⢲⡄⠀⢸⡇
⠀⠀⣿⢸⣿⡧⡟⡯⠆⣠⣟⡹⢿⣿⠿⡲⢊⠷⠂⠀⠀⠀⣉⠀⣠⣾⠁⠀⠀⠀⢸⣇⠉⠀⠈⣡⣴⣿⡿⠂⣰⠿⠋⠇⣸⣿⡗⡭⢩⣿⣇⠀⠄⣿⠃⢸⡇
⠀⠀⣿⠁⠈⡽⠉⢛⠸⡟⠛⠙⡦⣤⣀⣂⡝⠂⠀⢀⡀⠀⣿⡟⠋⠁⠀⠀⠀⠀⠈⢿⣭⣘⣋⢁⣌⡀⣡⢐⡤⢂⣾⣾⣿⠿⢶⣴⣴⣿⠥⠤⡼⣿⣇⢹⡇
⠀⠀⣿⡤⣿⠏⡿⢧⣾⠳⠋⠀⣀⣼⢿⣭⣥⣴⣾⣯⣙⢦⢹⣧⣤⣤⣀⠀⠀⠀⠀⠐⣿⡟⠚⠿⠧⠟⠿⢀⣴⣿⣿⣿⣇⡀⠀⠀⢨⠁⠀⣀⣴⠃⠱⢹⡇
⠀⠀⣿⢃⣠⣥⠙⠙⣯⣻⠽⣶⠏⢁⡾⣹⠟⠉⠀⠀⠙⣆⢧⢻⡄⠈⠙⢷⣄⣠⣴⣶⣿⣿⣮⣍⣐⣠⠜⠉⣹⣇⠹⣏⠙⠻⢶⣶⣻⡶⢦⣿⠿⡗⠚⢻⡇
⠀⠀⣿⢉⣿⣷⢤⣷⣰⡏⠀⢿⣴⠟⣰⣣⣶⣶⡀⠀⠀⢹⡈⣇⢻⣦⣄⢠⡟⠋⠁⠀⠀⢘⡏⠽⡍⠓⠦⣤⠃⠹⡆⠹⡆⠀⠀⠛⢷⣷⣔⡷⡆⠀⠀⢸⡇
⠀⠀⣿⡿⠋⡏⠀⠉⠀⣇⠀⢠⣯⣺⠟⠉⠀⠀⠙⣦⣆⡼⠁⠙⢶⣿⣿⠿⠦⠀⢸⣷⡄⢸⡇⣀⣥⣤⣤⡤⠤⠦⢿⠄⣿⣿⣄⢀⡴⠛⠙⢷⣿⣏⡉⢸⡇
⠀⠀⣿⠁⢠⠷⣶⡶⠦⡷⠀⣾⣯⣥⣤⡀⠀⣠⣤⣿⠏⠀⠀⠀⠀⠈⠹⡆⠀⠀⣨⣿⣿⣾⠡⡀⢈⠇⠀⠀⠀⠀⠈⠷⢿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⣿⠉⠀⠀⡟⠀⠀⣷⡾⠋⠁⠀⠈⠙⢷⣿⣿⣿⠞⢀⡀⠀⣠⠀⢠⣏⣤⢾⣿⣿⣿⡿⠀⠉⠁⠴⢖⣒⣒⣲⣭⣥⣭⣹⣿⣦⣄⠀⠀⠀⠀⠻⠿⣿⡇
⠀⠀⣿⠉⢀⣴⡧⣦⣾⠋⠀⠀⠀⠀⠀⣠⣾⣻⣿⣿⣷⣿⣥⣾⣧⣴⣿⣿⣕⣦⣼⡟⢓⠶⠉⠈⠉⣁⣀⣀⣀⣠⣤⡤⢤⡼⣿⡉⢿⣷⣴⠆⠀⠀⠀⢸⡇
⠀⠀⣿⡀⢈⡱⠞⣿⡇⠀⠀⠀⠀⣠⣾⣿⡧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣚⣛⣉⣉⣭⠝⠛⠳⠶⡖⠉⣀⡺⢿⡇⢸⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⢀⣴⠟⠋⠀⠀⠀⢠⣾⣿⣿⣳⣶⣶⣾⡟⢛⡻⢋⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⡒⠶⠶⢳⣶⣶⣶⠚⠁⠤⠋⠀⣻⣿⡼⣿⣀⢺⣧⣄⡀⢸⡇
⠀⠀⣿⠀⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⡉⢻⣿⣿⣿⣟⡥⢚⣡⠞⠉⠀⠀⢿⣿⣿⣿⣏⠀⢀⣥⣤⣤⣸⣿⣿⡿⠀⠶⠒⣛⣭⢟⣿⣿⠌⠛⠻⣿⣅⣀⣸⡇
⠀⠀⣿⣄⣹⡇⠀⠀⠀⠀⢀⣴⠄⣿⡇⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⠻⡛⠲⠶⠶⠤⢤⣤⠤⠶⠶⠟⠋⠁⣀⣬⠞⠻⣷⡀⠀⠈⠛⠛⢻⡇
⠀⠀⣿⠀⠀⢿⣃⠘⡆⠀⠙⣹⣿⢿⣇⠀⠀⡏⠋⣿⡟⣿⣿⡧⡀⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⢶⣾⣿⡉⠀⠀⠀⠘⣿⡀⠐⠂⠀⢸⡇
⠀⠀⣿⠀⠀⠈⠿⠷⠿⣶⣾⠋⠀⠀⢿⡄⠀⠇⢰⡿⠀⠈⠻⣷⣄⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢜⣿⠟⠁⠀⠈⣿⠿⢟⡻⠀⢰⡿⠀⠀⠀⠀⢸⡇
⠀⠀⢿⣤⣤⣤⣤⣤⣴⣶⡄⠀⠀⠀⠘⣷⠀⠀⢸⣧⡀⣠⣤⡈⠻⣇⠀⠀⠈⢻⣿⣿⣿⠄⠀⠀⠀⣴⡿⠋⠀⠀⠀⣸⡏⣠⠟⣀⣀⣾⠃⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡯⠍⠉⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢿⡷⠀⠀⠀⢠⣿⡀⠀⠀⠸⣿⡿⠿⡤⠤⣄⠀⣿⡇⠀⠀⠀⣠⣿⣤⢖⣟⠯⠟⠛⠛⠿⢶⣄⠀⢸⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣷⣀⣀⣠⣾⠁⠀⠀⠀⠈⢿⣄⣀⣀⣤⣿⣿⣥⣰⣿⣭⠷⣿⣇⢀⠀⢠⣏⣯⣿⠞⠁⠀⢀⣀⣠⣤⣤⣜⣷⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡏⢹⣦⡀⠀⠀⠀⠀⢹⠟⢻⠁⢄⡀⢀⡄⠠⣧⠈⠉⢻⡿⠿⢿⣿⣅⣤⢐⣴⣾⣿⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢶⣾⣿⣶⣬⣭⣛⣛⡛⠿⠿⠿⣻⣥⣤⣤⣤⣤⣿⡶⠈⠚⠋⠱⠞⠑⠋⠁⢈⢦⡾⣿⣶⣾⣿⣯⡳⢾⣿⣿⣿⣿⣿⣿⠿⢛⡅⢸⡇
⠀⠀⢸⡇⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡁⠛⠒⠛⠉⠉⠉⣉⠉⣁⠬⣰⠿⠿⣿⣿⣿⣿⣷⣮⣭⣅⣀⣠⣶⣿⠿⠃⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣾⡏⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠘⡷⠶⣶⢶⡶⠶⢶⠶⠶⠶⢶⣶⠶⠶⠶⢶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⡀⠢⠀⠀⠸⠀⠀⠉⠒⠐⢒⡵⠋⠀⣠⡀⠀⢀⢤⠀⠀⠀⠀⠉⠓⢮⡀
⡀⠀⠀⠁⠈⠉⠉⠚⠀⠀⢀⣀⣠⠊⠀⠀⢰⢃⡈⠶⢃⡈⢇⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠈⠉⠉⠙⠲⠤⠤⠤⠤⠒⠁⢰⠃⠀⠀⠀⣏⡜⠙⠶⠋⠱⠼⠆⠀⠀⠀⠀⠀⠀⠀⠹⡗⠦⠤⡤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡠⠴⠒⠚⢉⣉⣉⣉⡉⠙⠒⠲⠤⣀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠉⡠⠔⠊⠉⠉⠉⠀⠉⠉⠉⠙⠒⠦⢄⡙⢢⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⡏⣠⣶⣶⣦⡀⠀⠀⣠⣾⡿⠿⢷⡄⠰⣏⠓⠷⣀⠀⢈⡇
⠀⢀⡤⢤⠚⠙⠋⠉⢦⠀⠀⡼⢴⠳⠟⠀⢉⡛⠃⠀⠀⠛⠉⠀⣠⠀⠛⠀⠈⢧⠀⣨⠷⢾⠗⠒⡤⠤⣀
⡰⠋⠀⠀⠀⠀⢀⡖⠚⠒⠾⡅⣼⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢨⣿⣧⠀⠀⠀⢸⣴⣧⠤⠿⠤⡄⠀⠀⠉⠉⢳
⡇⠀⠀⠀⠀⢀⡀⢧⡀⠀⠀⣿⡏⢀⠀⣸⡿⠟⠒⠒⠲⢄⠀⢻⣿⡿⣇⠀⠀⠘⢻⡁⠀⠀⢀⡞
⠙⡶⠤⠐⠂⠁⠀⠀⠉⣠⠞⢸⠀⣼⢧⠏⠀⠀⠀⠀⠀⠈⢷⠚⠋⠠⣿⠀⠀⠀⠀⢣⡈⠓⠋⠈⠙⠢⠤⢀⣤
⠀⠙⣦⠀⠀⠀⠀⠀⢻⠀⠀⢸⡑⢿⠘⣆⠀⠀⠀⠀⠀⢀⡟⠀⢀⣺⠗⠋⠀⠀⠀⣞⣩⡖⠠⠀⠀⠀⠀⣠⠇
⠀⠀⠧⣤⠤⠔⠒⠋⠙⠲⠤⣄⣧⠀⠳⣌⣲⣤⣤⣤⣖⣋⣀⡴⡞⠁⠀⠀⠀⢀⣼⠥⠔⠓⠲⠤⣄⣀⣀⡇
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⠦⠤⠤⠤⠤⠒⠴⠁⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⢀⡼⠉
⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⡏⣷⢤⡀⠀⠢⠤⠄⠀⠀⣀⣠⢴⠋⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⢗⠢⢄⠜⡄⡀⠉⡳⠲⡤⠤⣄⣸⠃⢻⠀⢹⠢⠤⠤⠤⠴⠚⢹⠀⢸⠀⠀⣀⣿⣩⣉⡁
⢀⠔⠀⠀⢸⡿⠟⠀⠀⠘⢄⠀⠀⢸⠀⢸⣀⠼⠖⠚⠉⠉⠉⠉⠛⢢⣼⡴⠋⡀⠤⢀⠀⠙⢦
⠁⢰⠏⣑⡤⢕⣛⣇⡞⠓⣆⠋⠀⢸⡖⢺⠉⢢⠀⠀⠀⠀⠀⠀⠀⡁⢀⠇⡌⡁⠀⠀⢙⡄⠀⡇
⢀⠗⢛⠦⠤⠊⠀⠀⡫⠳⣜⠀⠀⠀⡇⠈⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⡸⠠⠀⠀⠀⠀⡇⢠⠇⠀⠠⠀⠀⠠
⠟⠒⡨⠠⡀⢀⠉⡈⠀⠀⡌⢳⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠃⠂⠀⡀⠀⢰⡵⠋⠀⠀⠈⠁⠀⠈
⣼⠀⡀⠀⡸⡁⠀⡰⡂⠀⢙⡶⠃⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠱⣄⠀⠸⡀⠀⠀⠀⢀⡏⠀⢀⡁⠀⢈⠁⠀⢈
⠀⠉⠉⣹⠋⠫⡙⡏⠉⠉⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⠒⠚⠓⠒⠒⠉⠀⢁⢀⡀⣁⠀⠀⣀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣇⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡇⢸⣼⡿⡉⢀⣠⣂⢌⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣸⣇⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣯⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢉⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡯⣿⣿⣿⣿⣿⣿⣟⠭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡙⢽⡿⣿⣿⣿⣿⣷⡿⣻⣿
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠻⡿⢣⣿⣿⣿⣿⣾⣿⠟⠁⠀⠙⣿⣗⣈⣯⣽⣿⣿⣿⣯⣥⡵⢿
⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢐⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣰⣿⡿⠥⡝⠟⣼⢿⢿⣿⣳⣳⣟
⠀⢸⣿⣿⣿⣿⣿⡏⠙⠉⠁⠀⠀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣴⣿⡟⠓⢲⣁⣧⣟⣞⣿⣿⣧⡼⠸
⠀⠈⠻⢿⣿⡿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⣟⠋⢹⣿⣧⡦⡷⡷⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣫⣽⣿⣿⣿⡿⠁⠀⠀⢀⣴⣿⣧⡈⠉⠛⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⠋⠀⠀⠀⣴⣿⣿⣭⡉⠛⠻⣶⣾⣟⣯⡯⣿⣿⣿⣿⣿⢿⣾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣤⣾⡗⡇⣷⣿⣿⣿⣿⣿⣿⢿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣿⣉⡇⣿⣹⣿⣿⣿⣿⣿⣿⣿⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠖⠒⠒⠒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣐⠦⡀⡠⠦⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠠⠉⠛⢝⠛⡀⢡⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⠳⢎⣀⣀⣀⣱⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠋⠀⠀⣠⣶⣿⣿⣅⠀⠀⠀⠀⠀⣠⣿⣿⣿⡷⢦⣀⠀⠰⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣀⡴⠛⠟⠉⠀⠈⠛⠆⠀⠀⠀⠘⠋⠀⠀⠈⠛⠀⠉⢷⡄⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣤⡜⠙⠀⠀⠀⠀⢀⣀⣄⡄⠀⠀⠀⣰⣠⣀⡀⠀⠀⠀⠀⠀⡉⢣⡴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢨⡇⢸⠀⠀⠀⠀⠸⣿⣿⠷⠤⠀⠤⢼⣿⣿⠇⠀⠀⠀⠀⠠⠀⢀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⡇⣈⠄⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⡀⠀⠰⡆⢸⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣷⠁⢠⣿⣷⣤⣤⠁⠀⠀⠀⠀⠀⠀⠀⢘⣤⣴⣾⣿⡆⠀⠐⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣿⠀⠈⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠃⠀⢠⣅⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⢿⣿⣿⣷⣦⣤⣤⣤⣴⣿⣿⣿⠿⠃⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠗⠦⣤⡀⠀⠀⠀⠀⠀⠤⠂⠀⣀⣤⠶⡏⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢰⠀⠀⠀⠹⠶⣄⣀⣀⣀⣀⡤⢾⠁⠀⠀⢡⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠈⠁⠈⠁⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠠⣄⠒⠐⠆⢸⠉⠛⠒⠛⠛⠛⠉⠙⢀⠐⠐⠢⣇⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣴⢋⠀⠀⣄⡱⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⠀⢠⠸⣷⡀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢀⣾⠁⠉⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠒⠁⠈⣷⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢏⠀⠉⠛⠒⠲⠶⠒⠚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⠶⠶⠶⠚⠋⠁⢸⠆
⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⠦⠤⠤⠴⠔⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠂⠀⠀⠀⠀⠀⣿⠦⠤⠤⠤⠤⠤⠒⢻⡄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣀⠀⠀⢀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠬⠀⠀⡇⠀⢸⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⢀⡇⠀⠀⡇⠀⠱⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠞⠳⣄⣨⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠐⠋⠀⠀⠀⠀⠀⢀⡇⠸⣄⣀⡴⠳⣄⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣤⠖⠋⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠓⠲⠤⠤⡤⣄⣀⣀⣀⣴⣟⠑⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠉⠳⣆⠤⢀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⠛⠦⠤⢶⣲⡶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⢠⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⠭⠅⡉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣴⠞⢷⡘⡆⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠉⠍⣉⠙⠳⢥⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⣤⡴⠒⢻⠿⢿⡏⠳⣄⠀⠈⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠉⣇⠀⠐⢙⣦⠉⠓⢛⣧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠛⠿⠀⢡⣸⡿⠀⢰⠋⢠⠗⠲⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣤⣤⣿⣿⠇⠘⠶⢣⡮⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⣾⡿⣿⠟⣻⠅⠀⠀⠀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣦⣀⠈⠩⠄⢀⣠⢤⡾⢥⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠁⠀⠀⢈⡉⣲⠆⠙⠍⠖⠁⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠄⠀⠀⡴⠁⠀⠘⠂⠼⠊⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠛⣀⣣⣄⡀⠀⠀⠀⠀⢀⡔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠾⠟⠀⠀⠀⢿⣶⡶⣶⠖⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠤⣄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣀⡀⠀⢘⡇⠀⠀⠀⣀⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⢻⡤⢶⠞⠋⠁⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣍⣉⣉⡭⠭⠭⢿⠲⡤⠤⠤⠤⠤⠤⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠚⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠄⠀⢠⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢴⠶⣚⠛⠂⢤⣶⠖⣿⡵⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠀⣀⡤⠄⠒⠂⠀⠐⠁⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠑⢦⣄⢀⡀
⠀⠀⠀⠀⠃⠀⢀⣰⠆⢐⡢⠠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⠁⠀⠁
⠀⠀⠀⢀⡠⠔⠋⠱⠚⣉⣀⣞⠁⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠉⠀⠀⢀⡀⠀⢉⢀⢈⠄⡀⣀⠀⢔⠀⣴⠃⢀⣀⣀⣀⣐⣦⡀⢠⣤⣄⣀⣈⠣⡤⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠛⠁⢠⣇⣀⣶⣿⣷⣿⣠⣾⣦⡟⠰⣿⣿⣿⣿⣿⣿⣿⣏⠙⢿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⠟⠁⠈⢿⣿⣿⠃⠀⣿⣿⣿⣿⡿⠟⠋⢈⣾⣿⣭⣿⢻⡁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠈⠻⣭⡀⠀⠈⠛⠛⠉⠀⠀⠀⣾⣿⣿⠀⠀⠀⢳⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⣶⢰⠶⣤⣶⣾⡤⠀⠀⠉⣁⣀⠀⠲⠄⠉⠉⠉⢰⣇⣀⡍⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠟⠀⠀⣼⠿⣿⣿⢿⣶⣿⣿⠄⠙⠒⠂⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣀⣶⣤⡄⢠⣿⣿⣿⡟⣾⣿⡆⢻⣿⡞⣿⣿⠄⠀⠀⣾⡇⠨⠨⠠⠤⢹⡿⠛⠿⠆⠐⠦⠤⠤⡄⠶⠒⠈⠁⠁
⠀⠀⠀⠀⠹⡏⠀⠈⠉⠁⠀⠈⢻⣿⡜⣿⣷⡄⢹⣿⡈⠻⡀⡀⠀⠁⠐⠀⠀⢀⠀⣾⢁⣿⣤⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣷⣿⣼⠷⠀⢢⡁⠀⠀⠀⠀⠀⠀⠀⢧⠸⣿⣏⣼⣤⣴⠂⣀⣤⣶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣾⣿⡻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣼⣶⡿⡟⠛⠛⠁⠾⠟⠿⠿⠋
⠀⠀⠀⠀⠀⠀⢰⡶⣾⣿⣷⣦⣍⠁⠉⠉⢋⡿⢶⣦⢄⣤⣤⣤⡾⣷⣾⠾⠿⠻⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣠⡴⠀⠀⠀⠀⠀⢲⠀⡀⠀⠀⠀⠀⢦⣄⣠⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⣟⣿⣿⣿⠿⠿⠓⠂⢀⣴⣾⣷⣾⣇⣧⠀⠀⠀⠐⠚⠿⠿⣿⣿⣿⣻⢿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⣤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⣿⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⣾⣿⣿⣟⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣹⣿⣿⡀⠋⣿⡟⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣻⣿⣿⣷⣬⡳⣄
⠀⠀⠀⠀⠀⢀⢜⣵⠟⣫⣿⣿⣏⣾⣿⠟⣡⣾⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣷⣄⠈⠳⡌⠃⠀⠀⠀⠀⠀⣸⣿⣿⣷⣌⠻⣿⣷⣹⣿⣿⣝⠻⣮⡣⡀
⠀⠀⠀⠀⢀⡵⢋⣤⣾⣿⣿⣿⡸⣋⣵⣿⣿⡿⣿⣿⣿⣄⠀⠀⠀⠀⠘⢻⣿⣿⣵⣤⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣿⣿⣮⣙⢇⣿⣿⣿⣷⣤⡙⢦⡀
⠀⠀⠀⣠⢋⣴⣿⣿⡿⣿⣿⣿⣽⣿⣿⡿⢫⣾⣿⣿⣿⣿⣦⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣴⣿⣿⣿⣿⣷⡝⢿⣿⣿⣯⣿⣿⣿⢿⣿⣿⣦⡙⣄
⠀⠀⡼⢫⣾⡿⠋⢁⣴⣿⣿⣿⣿⡿⠋⣰⣿⠟⣿⣿⣿⣿⣿⣷⣶⣿⠿⠙⢿⣿⣿⣿⣷⠹⢿⣶⣾⣿⣿⣿⣿⣿⠻⣿⣆⠙⢿⣿⣿⣿⣿⣦⡈⠛⢿⣷⡝⢧
⠀⠘⣱⣿⠟⢀⣴⠟⠉⠀⣠⣿⠟⠀⣰⡟⠁⣼⡟⣼⣿⣿⣿⣿⠿⠀⠀⣀⡼⣿⣽⣿⣿⠀⠀⠿⣿⣿⣿⣿⣧⢻⣧⠈⢻⣆⠀⠻⣿⣄⠀⠉⠻⢦⡀⠻⣿⣎⢃
⠀⣰⡿⠃⣠⠏⠀⠀⣀⡴⠟⠁⠀⢠⡿⠃⠀⢿⡇⢿⡇⠈⠻⠇⠀⡞⡟⠋⢳⣿⣿⣿⣿⣀⠀⠀⠘⠟⠁⢸⡟⢸⣿⠀⠘⢿⡄⠀⠈⠻⢦⣄⠀⠀⠹⣄⠘⢿⣆
⢠⣿⠁⢀⣁⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⡿⠏⢿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⣈⡀⠈⢿
⣾⠇⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠸
⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⢶⣄⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣿⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⣿⣰⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣰⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣻⣾⣧⡤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠒⠢⡄⠀⠀⠀⢀⣄⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⣿⠿⠛⠿⢿⣿⠗⣡⡠⡄⢀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣯⣀⣀⣀⣀⡷⠛⠓⢲⣤⠌⠣⢀⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡿⠿⠿⢿⣿⣷⠀⠀⠀⠹⣏⠣⡤⠁⠅⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠁⡇⠀⠀⠼⣿⣉⣧⠀⠀⠀⠹⡄⢁⠀⠰⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢂⢁⡏⠀⣇⠀⠀⠀⠈⢻⣿⣧⡀⠒⠉⠉⢳⠀⠃⣹⣇⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠢⡻⠀⠀⠀⠀⡘⠰⣿⡄⠀⠀⠀⠓⣅⠘⢉⠿⢿⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⣿⠃⠀⠀⠀⠀⢸⠀⠌⠀⠀⡿⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⢀⠀⠛⢮⣴⣌⣌⡇⠀⠘⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⡤⠄⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐
⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠁⠀⠀⠀⠀⢰⠀⠀⠠⣠⡶⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠉⠉⠀⠀⠠⠤⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠉⠉⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠠⠠⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠇⢨⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢎⣁⡀⢢⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⣂⡤⠀⠀⠢⠈⠇⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠃⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⡔⡀⠀⡠⡀⠀⠀⠀⠽⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠁⠀⠀⠉⡀⠘⠁⠱⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⡨⠀⠀⠠⠀⢀⡀⠀⠀⠄⠂⠀⠀⠀⢸⠀⢐⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠒⠒⠊⠉⠀⠀⠀⠂⣀⣀⣀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠂⢠
⠀⠀⠀⠀⠤⠦⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠢⠔⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠨⣳⠄

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

⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠈⠀⠔⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿
⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠂⢶⠒⡄⠀⠚⣅⠀⠐⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁⠀⣠⣴⠆⠈⠁⠀⠀⢀⠠⠐⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⢋⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠆⠀⡀⠐⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠘⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⠀⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣤⣄⡀⡀
⠀⠀⠀⢠⠶⠶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠻⣿⣿⣶⣦⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣯⣟⠿⡶⣤⡀⠀⠀⠀⠀⠀⣀⣨⣿⣯⠛⢿⡛⢿⣢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣴⣧⠧⠷⢦⠤⣴⣮⡽⠟⠻⣿⠿⡷⡄⠙⢦⣊⢻⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣯⣿⠏⠁⡴⢂⢲⠙⣿⣁⡰⠀⢰⠁⡠⢠⠋⠢⡀⣑⣜⣻⣿⡱⣦⡀
⠀⠀⠀⠀⠀⠰⣤⣼⢻⣝⢸⢁⣴⣠⣖⣿⣇⠀⣻⢿⡛⣶⣯⣤⣄⡀⡌⢠⣽⡝⣶⣤⢼⣗⡄⣍⢢⡀
⠀⠀⠀⠀⠀⣹⣿⣿⢘⡖⣛⣸⣿⠛⠏⠐⣘⣗⣋⣇⣷⠛⡟⣷⠄⠉⢳⣿⡯⢽⢮⣿⡇⠿⣷⣉⠁⢱⣄
⠀⠀⠀⠀⠀⡏⢹⣴⣿⡿⡟⡏⣽⣷⣼⣿⣷⢿⣩⣿⣿⡄⡕⠘⣖⠀⢸⢸⡇⠀⠉⠉⠀⠀⠀⠓⡔⠁⠉
⠀⠀⠀⠀⠠⣏⣯⣿⡽⠃⡰⣾⠏⡟⣸⣿⣿⣻⡿⣿⡿⣿⠳⣄⠈⠺⠿⢿⠇
⠀⢠⣸⢁⣠⢸⠿⢟⠀⢀⣻⣽⡄⠘⠲⠓⢺⣿⢟⠀⣿⣿⣅⡒⠛⠒⠚⠁
⠀⢽⡿⢟⣿⣵⣯⣞⠀⠘⣩⣯⣀⢀⣴⣾⣿⣿⠿⣿⠛⠋⠺⡿⠀⡀⠀⢤
⠐⣯⡿⣿⣿⣛⣾⣡⠀⠀⠿⠿⠃⢎⠀⠉⠙⠁⠈⠏⠀⠀⠀⠁
⠀⣸⣃⠿⢻⡾⠊⠂⠀⠀⢠⡌⠉⠀⠁⠐⠂⠠⠀⠂
⢸⠿⣿⠽⢿⣡⣏⣀⡄⠀⠀⠑⠒
⠨⢴⣻⡿⠻⡽⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⣋⣥⣤⣾⣿⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣯⡶⠾⠟⠛⠫⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣴⣿⣿⡭⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣭⣟⣛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣬⣼⣾⣿⣿⣿⣿⣷⣶⣾⣯⣽⣻⢿⣿⣿⣿⠟⠋⠉⠉⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠄
⠀⠀⠀⠀⢀⣠⣢⣦⣾⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⣿⠿⠿⠿⠿⠓⠒⠒⠂
⠀⠀⠀⢀⣾⣿⣿⠿⢿⣿⣷⣆⡠⢔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⠛⠉⠉⠉⠉
⠀⠀⠀⠺⠛⠉⠀⢀⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠛⠓⠒⠂⠀⠀⠀⢀⡤⠴⠖⠚⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿⡿⠟⠛⣻⣿⣿⣿⣿⣯⡻⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡏⠀⠀⢀⣿⣿⠟⢿⣿⣿⣿⣷⣭⣛⠿⣤⣶⣀⢀⡀⣀⢀⡀⣀⣀⣠⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠙⣧⠀⠀⠈⠻⣿⡀⠀⠈⠉⣹⣿⠉⠛⠻⠷⠶⠿⠿⠿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠞⠋⠠⠶⠾⠟⠀⠴⠶⠾⠛⠁⠀⠀⠴⡾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠋⠉⠉⠉⠉⢛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠰⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠉⠀⠀⠀⠀⠀⢀⣀⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⢢⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠀⠀⠎⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣄
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢆⡀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠁⠀⠀⠀⠀⠀⠘⢦
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠤⠐⠒⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⠈⢧
⠀⠀⡼⠁⡀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠈⢧
⠀⣸⢣⠊⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⠴⠁⠀⠘⡇
⢀⡏⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠳⢄⡀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠇
⢹⡀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢦⡀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⢦⣀⣀⣀⣀⣱⣦⠤⠤⠴⠟⠒⠒⡶⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⢻⠓⠒⠒⠦⠤⠾⢤⣠⣴⣂⣀⣀⡤⠊
⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⣞⣀⣀⣠⠞

⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⣰⣦⠶⣶⠈⢻⣿⣿⣿⣿⣿⠟⠁⣿⣿⡿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢶⣶⣶⠐⢿⣿⣿⣶⡝⢸⡆⢻⣿⣿⡿⠃⣸⢸⡿⠟⠁⣿⣿⣿⣿⣭⣥⣄
⠀⠀⠘⢻⣿⣿⣦⣀⣀⠘⢿⣿⣿⣿⠀⠀⠙⠿⣷⣼⠟⠟⠘⠛⠛⠋⠸⠏⠈⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠖
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⣃⣀
⢀⣀⣀⣉⣽⣿⣿⣿⣿⠟⠛⢿⢿⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣀⣀⣤⣤⣤
⣾⣿⣿⣿⣿⡿⠟⠀⠉⠀⠀⠀⠀⠹⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣤⣤⣶⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡆⠀⢀⣤⠤⠄⠀⠀⠀⠐⠛⠛⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⡿⠁⠀⢀⠀⠀⠀⣵⣆⠂⠀⣀⣷⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠀⢰⠇⠀⣘⣿⣿⣷⣾⣿⣿⣥⠀⠀⢲⡄⠀⠂⠀⢬⣙⠻⠿⣿⡿⣃⣼⣿⣿
⣿⣿⣿⠋⣿⣿⣯⣿⣿⣿⡿⠛⠁⠀⠀⠀⢾⠏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠑⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⡛
⣿⣿⣿⠄⢫⣭⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⢹⣿⣿⣿⣟⡅⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣬⠍⣠⣤⠖⠁⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠈⠀⡀⠀⠀⢀⡀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠈
⡟⠿⢛⣿⢟⣵⣾⠟⠁⠀⠀⢀⣴⠿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠒⠒⠛⠁
⠀⣴⠟⢁⣾⠋⠁⣀⡴⠂⠁⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠉⠓⠲
⡞⠡⣠⡟⠁⢀⣾⡟⠁⠀⢸⡿⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠈⠻⣿⣦⠈⢳⡀
⢠⡇⠟⠀⠀⣼⡟⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⢹⡾⢟⣛⣛⠁⠀⠀⠈⠛⠛⠿⣇⠀⠀⠀⠀⠀⠀⠈⠙⢷⠀⠁⠰⣄
⠸⠿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢛⠩⠭⠄⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡿⣠
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡷⠂⠀⠀⠀⠉⠉⢀⠀⠀⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢷⡀
⠀⢀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⣠⣴⣿⣷
⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣄⠀⠀⠺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣦⣠⣤⣿⣿⡿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣿⣤⣀⡘⢿⡛⠉
⣿⣿⣡⣭⣛⢿⣿⣿⣯⠿⠛⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡾⣷⠻⣿⣿⣛⣢
⠉⠉⠉⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣒⣖⢢⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠓⢛⠳⠼⢧⡁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣀⣠⠭⢶⡶⣿⠓⢄⠀⠘⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣏⢭⠀⠐⢒⡎⠑⢚⡧⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠛⠂⠠⣼⣇⠐⡏⡠⢛⠒⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣠⣶⣶⣿⠛⠀⠙⠁⠏⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⠋⠙⢥⡛⠁⠀⣠⡖⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠋⠙⢲⣤⣴⢾⣫⡽⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⣆⢀⢀⡞⠁⠙⢦⠷⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⣻⣜⣧⣄⡀⠀⠀⢀⡴⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠋⠀⠀⠸⢿⣷⠞⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⡆⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢻⡀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⠧⢤⣀⣈⠇⠀⣀⣠⠤⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⢹⠖⠙⠉⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠤⠤⠤⢤⣘⣦⣀⣀⠀⠀⢀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠙⠒⠓⠯⠭⠥⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿⢀⣠⡤⠶⢖⡒⣠⣖⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣼⡇⡔⢿⣏⢸⣧⡈⠉⣱⡏⢾⣽⣻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠔⣚⣉⣥⣽⣌⢿⣷⣿⣷⣔⢿⠀⠀⠈⠛⢿⣮⡻⣮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣛⣥⣶⣿⣯⣭⣉⡁⠬⢇⣿⣿⣿⣿⣷⡀⠀⠀⠐⢦⡉⢿⣮⣻⣟⣿⣆⢠
⠀⠀⠀⠀⠀⠀⢀⣤⣴⠦⠀⠋⢈⣩⣤⣤⣉⠉⠀⠈⢹⣿⣿⣿⣿⣿⣇⡹⣷⡀⠀⠀⠀⠙⣎⢻⣷⣻⣎⣿⡆⢷⣄⢠
⠀⠀⠀⠀⠀⠀⠈⠅⠙⡠⢀⣴⣿⡟⠻⢦⣈⠓⢦⡐⠾⡿⣿⣿⡿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠸⡎⣿⣿⢿⣾⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⣿⠟⢋⠉⠓⠂⠈⢉⡀⠈⠁⠀⣻⣿⡀⠀⠈⠻⣿⣿⣿⣷⣤⡀⠀⣿⢸⣿⢸⣷⣿⣇⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⡀⠘⠀⠀⠀⠼⠋⠀⠠⣤⣴⣿⣿⠅⠀⠀⠀⠀⠟⠛⠛⠛⠉⢀⡟⣼⣿⡇⣿⢻⣿⣿⣇⣿⡆
⠀⠀⠀⠀⠀⢀⡤⢸⣻⠷⣬⣭⣭⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣅⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⣿⣿⢠⣿⣿⣿⣿⢸⣿⣷
⠀⠀⠀⠀⢠⣾⣏⢸⡏⠀⡎⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣖⣯⣾⣿⣿⡏⣼⣿⣿⣿⣿⡆⠻⢹⡀
⠀⠀⠀⠀⠀⠀⣿⠈⡱⠘⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣽⣿⣿⣿⢿⣮⣿⣿⢟⣴⣿⢻⣿⢹⣿⣿⣶⣾⠁
⠀⠀⠀⠀⠀⠀⣿⡀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣵⣾⡿⢁⣾⠇⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⢀⡴⢟⣩⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣟⣥⣴⣾⠟⢰⢇⣿⣿⣿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡭⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣌⣹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⢿⣄⠀⠀⠀⠀⠀⠈⣰⣿⡿⠿⠛⠿⢻⣿⣿⣿⣿⣇⠀⢀⣤⣬⣿⣿⡿⢻⣿⣿⣟⡻⣶⠙⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢱⣼⣿⡀⠀⠀⠀⠀⢠⣿⣿⣶⣌⠀⠀⠢⢍⠿⣿⣿⣷⠈⢸⣿⣿⣿⣷⣶⣿⣿⠿⠿⠿⠟⠀⣿⢣⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⠀⠀⠑⠍⠙⠣⠂⠈⢉⣛⣿⣝⠷⣮⡍⠛⠳⠚⠋⣰⡟⡈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⣿⡀⣄⠀⠀⢦⢻⣿⣿⣿⣿⣿⣧⠈⢷⡄⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣶⣦⣠⣤⣾⡿⠹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠹⣦⣀⠈⢷⣽⣿⣿⣿⣿⣿⣧⡀⠁⠀⠀⢠⡞⣿⣶⣮⣍⣈⣛⣻⡽⠟⣩⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣌⡻⣿⣿⣿⣿⣿⣿⠙⣦⠀⢀⡀⠱⣌⢰⡿⣻⣿⣍⡁⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣽⣻⣿⣿⣿⣿⠏⣰⣿⣷⡀⣿⡄⣸⡆⡿⣳⣌⣛⣛⣭⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⣻⠏⠘⠻⠿⠿⡇⠿⣿⠉⠛⠃⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣴⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣯⣁⣹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠉⢉⡉⣀⣪⣱⡈⣄⡀⣀⠵⠩⠉⠙⠛⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀⣌⡀⣐⠀⠘⢿⡟⢩⢉⠙⣿⣦⣶⣿⣶⣤⣲⣦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢻⡟⠂⠀⠀⢻⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠶⡴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⡞⠀⠀⢠⠀⠀⢸⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢸⡼⢁⡄⢰⡿⠀⢠⣾⡴⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣾⣇⢸⣧⡇⣇⣦⣮⣼⡷⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⢻⠻⠸⠀⠟⠿⠉⠋⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡏⢋⠝⡍⠉⠉⠉⠉⠉⠉⠉⠉⢉⡝⠙⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠈⡆⠘⢦⡤⢤⢠⡤⢤⡄⢀⡾⠀⠀⠀⡇
⡇⠀⢹⡲⣌⢻⡜⣼⠀⢸⣢⡟⢁⣼⡃⠀⡇
⡇⠀⠀⢳⠹⠧⠛⢿⠄⣶⡏⠀⠚⠚⠡⠀⡇
⡇⠀⠀⠈⢲⠦⠬⠀⣶⠭⠭⠐⢒⣀⢸⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⠿⠿⣶⣦⣄⡀
⡇⠀⠀⠀⠈⣶⣶⡆⡼⠳⢜⠻⣿⣿⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⣰⡿⢋⡠⠄⠤⢀⠀⠀⠈⠙⠻⣷⣄⡀
⡇⠀⠀⠀⠀⢋⡿⡰⠁⠀⠀⠙⠦⣝⠷⢸⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⢋⣩⣽⣿⣷⣤⣰⣿⠡⣋⢔⡣⠐⠏⠱⠄⠀⠀⠀⠈⠻⣿⣆
⡇⠀⠀⠀⠀⠸⣠⠃⠀⠀⠀⠀⠀⠈⠓⢮⣇⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣿⣥⣴⠶⠾⠿⠿⢧⣿⣒⠈⠖⠃⠠⠀⠂⠀⠀⠀⠀⠀⠈⢻⣷⡀
⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠶⣄⣀⡈⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⣶⣤⣤⣄⣀⠀⠀⠀⠉⠉⠓⠶⢮⣤⠁⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠀⠈⠉⠙⠳⣤⣤⡀⠀⠀⢿⣷⠀⠙⠛⠋⠙⠻⣿⣿⣿⣿⣿⠷⢦⣄⡀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⢹⣷
⡇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠠⡄⠀⢿⠀⢷⣄⠀⠈⢿⣷⣀⠀⠀⠀⠀⠀⠈⠉⣿⢡⣶⠀⠉⠛⠶⣤⣀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢿⣇
⡇⠀⠀⡟⠳⣄⠀⢠⠟⠀⠀⢀⡤⠠⠄⢀⠀⠀⣄⠄⠂⠋⠚⠲⣄⢻⣿⡉⠁⢀⣴⠾⠟⠛⠷⢾⡿⠀⠀⠀⠀⣼⡟⠛⠶⢦⣤⣤⣤⣽⣄⠀⠀⠀⠘⠿⢷⣦
⡟⠳⢦⡇⠀⠈⠓⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠘⠈⠻⢿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢠⠏⠙⣆⠀⠀⠀⠀⠀⠙
⣧⡴⠠⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣠⠴⠋⠀⠀⣼⠶⠴⠦⣄⡀
⡦⠁⠀⠀⠈⢤⠀⠀⠀⢠⠈⠀⠀⠀⠐⠀⠁⠠⡁⣴⠲⣆⠘⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠞⢻⡄⠀⠻⡄⠀⣠⠞⠁⢀⡀⠀⠀⠻⣴
⡇⠀⠀⠀⠀⠀⠙⣗⠀⠀⠀⠰⠄⢄⠀⠈⠀⠀⠓⠠⢄⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⠴⠖⠋⠉⠉⠀⠀⢀⡼⠁⠀⠀⠙⠚⠁⠀⣰⠋⠀⠀⠀⠀⣿
⡇⠀⢀⠀⢀⠀⣠⠗⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣼⡟
⡇⠀⠈⠀⢀⠁⠽⡀⠀⠀⠀⠀⠠⢀⣀⡀⣻⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠙⢿⠲⢾⡛⠒⠛⣻⠀⠀⠀⠀⠀⠀⣠⡶⠦⣤⣤⣤⣶⡿⠋
⡇⠀⠀⠙⢇⠀⢆⡀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠈⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⠳⣄⡙⠦⣠⠟⠀⠀⠀⣀⣤⡾⠿⠿⠿⠿⢿⣯⣄⡀
⡇⠀⠀⠀⠌⢰⠋⠀⠉⠂⢀⠀⠀⠠⡌⢰⣄⣀⡀⢁⡋⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⡀⠀⠀⢈⣿⡿⣫⠟⠓⠶⡶⠖⠚⢻⠏⠻⣄⡀⠀⠀⠀⠀⠀⠙⠻⣷⣤
⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢠⢉⡞⠀⠀⠉⠉⠀⠀⣠⣴⣿⠟⠁⠀⠀⠈⠹⣿⣶⣿⢿⠋⠐⠓⠦⠤⠞⠁⠀⠀⣿⠀⠀⠀⠉⠓⢦⣀⢀⡤⠖⠛⠋⠉
⡇⠀⠀⠀⠀⠀⠘⡀⠀⡘⠀⠔⠀⠀⢮⣀⠀⠀⠀⠀⠀⠀⣿⡏⢿⠀⠀⠀⠀⠀⠀⢹⣿⠁⢸⠃⠀⠀⡰⠊⠉⠙⢦⠀⢹⡀⠀⠀⠀⠀⠘⣿⡏
⡇⠀⠀⠀⠀⠀⠀⢱⠂⠈⠀⣀⣀⣀⣀⡉⣳⡄⠀⠀⠀⠀⣿⣧⠘⡆⠀⠀⠀⠀⠀⢸⣧⣠⠏⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠙⢤⣀⣀⣀⡠⣾⠋⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠈⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠶⠤⠶⠋⠀⠀⠀⠀⠈⠁⠁⢠⡏⠀⠀⠀⠀⠀⢿
⡏⠉⠁⠂⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠘⡀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠑⣄⡀⢀⣀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠉⠀⠈⢻⣍⣁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⠿⠿⠛⠁⠈⠻⢿⣷⣦⣄⣀⡀⠀⠀⢀⣀⣀⣿⡅⠀⠃⠀⠀⠀⠈⠹⠛⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠛⠛⣿⡇⠀⠸⠀⠀⠀⠀⠀⡇⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠈⠀⠀⢃⠀⠀⠀⠁⠀⢀⣐⠘⠀⠠⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⢀⣀⣀⢸⡞⢀⣈⣀⣇⣤⣤⣀⣁⣀⠆⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢀⣾⣴
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠒⠉⠈⠉⠉⠁⢀⠉⠉⠉⠁⠀⠀⠀⠉⠉⡱⠞⠋⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⠿⠋⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⠀⠀⠀⢨⠀⠀⠀⠀⠀⠘⡄⠠⠀⠈⠆⠐⠀⠀⡇⠀⢸⡇⠀⠀⠀⠠⠄
⡇⠀⠀⠀⠀⠀⠀⠀⣒⡋⠀⡀⠀⢀⣠⣀⡋⠀⠀⠀⠀⡄⣀⠀⣠⠆⠀⠀⢀⠀⢀⣰⠄⡀⠀⣈⡔⠀⢀⡴⠀⠘⡇⠀⠀⣀⡼
⡇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠈⠈⠉⠉⠉⠁⠀⠈⠁⠀⠉⠉⠉⠉⠁⠀⠈⠈⠁⠀⠀⠁⠉⠈⠉⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠻⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢴⠊⢿⣿⣿⣿⣧⡈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⢁⠍⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣼⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢾⣅⡐⣿⣿⣿⣿⣯⡐⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡨⢉⣤⣿⠏⠙⣿⣿⣿⣿⣿⣇⠀⠀⠰⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⡾⢃⣾⣿⠤⠤⣾⣇⠉⠻⢿⣿⣿⣷⡀⠀⠐⠆⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠸⠇⠸⣿⣠⠀⠠⠋⠙⠃⠀⠀⠉⠻⣿⣷⣶⣾⣶⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣠⣬⣿⣄⣀⣤⡾⡿⢿⣾⠃⣀⣉⠐⢆⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⢻⣦⢉⣿⣿⠀⠀⠰⢾⡏⠀⠛⠉⠀⠀⠀⠀⣀⣄⠘⣿⣿⣿⣿⣷⣾⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣿⡷⣾⠋⠉⠶⠄⠀⡸⠰⡟⠀⠀⠀⢀⣦⣄⣤⠀⣄⠀⠟⠻⣿⣿⣿⣆⠀⣉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠘⡟⢀⣴⣤⣷⡴⣿⠈⢻⣶⣶⣄⣠⣿⣿⡶⠀⢸⡇⠀⠀⠉⢹⣿⣿⣿⡟⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠘⢷⣏⣙⣿⠋⠛⠷⣤⣤⣄⢿⣿⠛⠛⡿⢿⢷⡎⠀⠈⠰⣤⣷⣶⢿⣿⣿⣄⢀⠰⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠛⠻⠿⣤⣶⣤⠀⠈⠟⣠⣿⠇⣠⣿⠒⡿⠃⣀⣛⣿⠿⠿⠏⠀⢹⣿⡿⠿⢷⣴⠖⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠆⠀⠀⢀⡀⢀⣄⠀⣀⣤⠀⢺⡿⢿⣿⣿⣿⣧⡀⢰⣿⡟⡟⠃⠀⠐⠛⠿⣿⡇⢀⣾⡅⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⠀⣴⠞⣿⢧⣤⣶⣿⣏⡉⠻⣧⠽⣿⣿⣿⣿⣿⣿⣿⣽⢻⣤⢛⣼⣿⣷⠋⣠⣾⣿⣷⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣷⣤⣿⡄⠉⠐⠉⢿⣷⡿⠋⣀⣹⣶⣾⣿⣿⣽⠟⣭⣿⠏⠸⣿⣿⡝⠋⣹⣤⣽⡛⠛⣯⡀⠀⢈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⣿⣷⢆⣤⣥⣿⣿⣿⡀⢉⡀⢺⣿⣟⣩⣿⣿⣿⣿⣶⣿⣿⣶⠷⢎⡁⠀⠚⠉⠙⠛⢿⡿⠄⢁⣤⠺⣿⠆
⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠈⣿⣿⣿⣤⣤⣈⣀⣨⡉⢿⡿⠉⢻⡿⢿⣿⠟⠛⠿⢟⢻⡇⠻⠛⢠⣀⣿⠀⠀⠀⢺⡆⢼⣧⣄⡈⢉⣥⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣯⣥⠘⣷⣀⣼⠓⢂⣠⣶⠶⡶⠋⠈⠿⠀⠀⣟⠻⢻⣤⠄⠀⠀⠛⣮⣉⣾⣧⣤⣽⣿⡇
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠘⠙⢿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⡷⢏⣹⣿⣿⣧⣼⣇⠀⠀⠾⣧⣴⣿⡁⠀⠀⠀⠀⠉⠁⢩⣙⣿⠟⠉⠀⣡
⠀⠀⠀⠀⡀⢀⡇⣀⣼⣧⣷⣤⣿⣿⡿⠛⣿⣿⠉⣿⣿⡿⠛⢿⣤⣾⣿⣿⣿⣿⣿⡻⣿⣶⣾⡏⢁⣄⠙⢓⣤⣤⠄⣤⣴⠛⠛⠻⣶⣾⣷⡿
⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⡙⣻⣿⢁⣀⠁⠙⡟⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠟⢻⣧⣤⣶⣤⣉⣋⣛⣯⣤⣾⡇⢠⣿⣿⣿⣇
⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣉⣿⣿⠖⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣷⠂⣹⣿⢉⠽⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣷⣄
⠈⠿⠿⢻⣿⣿⣿⠛⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡿⠋⠙⣿⣶⣿⡁⢙⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟
⠀⠀⠀⠀⠉⠙⠃⠰⠿⠿⢿⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣾⠿⠿⣿⡟⣛⣀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠛⠿⠟⠿⠿⠛⠛⠛⠻⣿⣿⠷⠿⣿⣟⣿⠖⠋⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠏⠙⢻⡏⠉⣙⠛⢛⣏⠛⢹⣽⠟⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⣀⣀⠀⠀⢀⡤⠠⣄⠀⠀⠀⢀⠠⡄⠀⣀⡀⠀⢠⡤⣤⡀⠀⠀⠀⠀⣤⡀
⠀⢀⣼⣇⣀⣀⣿⡄⠀⡜⠈⣿⣿⣧⠈⠗⢺⡏⠀⠀⢀⠈⢉⠁⢴⣥⣷⠠⣿⣀⣸⠏⠀⣤⡀⠘⠿⠇
⠀⣼⣥⣽⣿⡿⠛⢋⢼⣻⣷⣭⠋⠁⠀⠑⠚⣡⠔⠈⠙⢷⣄⠀⠀⢸⠀⢤⡈⠉⠧⠀⢀⣁⡿⣆
⠀⠁⠟⡟⢹⢧⠀⠈⠛⠾⠃⢹⢒⣄⢀⢄⠘⢿⣤⣄⣀⡸⠿⢶⡀⠀⠒⠾⠋⠀⡋⢀⣲⡄⠠⠿⠆⢠⣄
⠀⠀⠸⡇⠉⡇⠀⠀⠈⠀⠀⢘⢿⠋⠛⢺⠆⠀⠘⠋⠟⠋⠁⠈⠁⠀⠀⢸⠀⠐⠃⠈⠉⠀⠀⠀⢴⣛⣿
⠀⠀⠀⡇⠀⡇⠀⠀⠀⢳⣦⡜⡌⠀⠀⢽⠀⠀⢄⡾⢀⠀⠀⢤⣄⠀⠰⡜⠀⠀⠀⠀⠀⠀⢰⡆⠈⠙⠋
⠀⠀⡀⠷⣶⠇⡄⣠⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠞⠙⠩⣷⣦⣼⠶⢓⣤⣔⠒⠒⢦⡀⠀⠀⢀⡆⢀⢨⡄
⠀⡞⢿⡀⠀⠀⠈⢉⡀⠀⠀⡀⠠⡰⣤⠉⠉⠀⢀⣀⠀⠀⢰⠀⠀⠻⣟⠛⠻⢶⣶⣿⣄⠚⠊⢀⣈⣧
⢀⡇⢸⣧⠀⠐⡲⠈⠁⠀⡸⡧⡑⣽⠻⡎⠀⢠⣿⣻⣷⡀⠘⡄⠀⠀⠀⠙⣺⠛⠛⠉⠁⣴⣶⡄⠉
⠘⠷⣾⠟⠃⠀⠀⠀⣤⠀⠈⢺⣿⢿⠨⠆⠀⢾⣾⣽⡿⠋⣤⣊⠉⣷⣦⠠⣽⠀⠀⠈⠻⢿⡶⠷
⠀⠀⠾⠀⠀⠀⠀⠀⠀⣴⠀⢴⡄⠘⡄⠀⠀⠀⠀⠈⡇⠀⠛⠻⣻⠟⠋⠀⣿⠀⢶⡷⠀⠈
⠀⠀⡄⠀⠀⠀⠈⠉⠀⠻⠿⠗⠃⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠁⠀⣆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠛⠿⠿⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣶⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⣿⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣸⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⡶⢒⠀⠈⢰⢠⣷⣄⠴⠖⣲⣶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⠫⣅⠢⣷⡓⠀⠀⠃⠠⣼⠟⢿⣿⣿⣿⠿⣍⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢝⣥⣏⡙⠛⣿⣧⣽⡧⢤⡤⢀⣽⣧⠀⣉⠁⡈⢰⣿⡿⡟⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣥⡾⣿⣦⣩⡿⢶⠏⣻⣷⣽⣿⣓⣚⠋⠻⣷⡟⢻⡇⠀⣗⠀⣼⣉⣳⣿⣦⡀
⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠜⡋⣹⣾⡟⣃⢌⣹⣽⠟⣿⠂⠿⣿⡟⢿⣿⢿⣿⣹⣬⡻⣄⣷⣤⣉⡄⠙⣿⣏⢅⠙⢿⣶⡄
⠀⠀⠀⠰⠟⠩⣍⣩⡿⢧⡡⣿⡿⢿⣼⠃⠀⣀⣨⠀⣿⡜⣿⣷⡷⣾⣿⣿⠿⣿⣿⣿⣮⣿⡟⠻⠿⣶⣎⢻⣎⡙⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠛⠀⠀⠀⠀⠙⠛⠋⢗⢈⣇⠸⣿⣷⡹⢻⣿⣶⣮⣿⡿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣩⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⢻⡓⠉⠹⢿⠿⣿⣿⣞⣷⣶⣌⠻⠿⠿⣿⡿⠯⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠨⠀⠀⢀⠘⠀⠛⠩⠻⢿⣏⡿⢷⣿⠓⠪⠱⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣷⣴⣤⣶⣤⣾⣵⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿