Sipping tea Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣷⡶⣾⣿⣿⣿⣿⣿⣿⡦⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣱⣿⣿⢿⣿⢟⣿⣿⣿⣿⣿⣿⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣽⠟⢻⢟⣿⡟⣡⣾⣿⣯⠟⠋⠙⠹⢛⡿⣖⣽⡿⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣏⣿⠏⢠⠏⣸⣿⣴⣿⠇⣹⣷⣀⢠⡄⠰⢉⣝⣫⣵⣶⣿⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢀⡾⢠⣿⣿⡽⢻⣾⣿⠟⠛⣢⠤⠛⠹⡿⠟⢫⢟⣉⢉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⣿⣿⡇⠸⠁⢸⡿⢋⠀⠈⠁⠀⠀⣀⣤⠖⠉⠀⠁⠀⠐⣻⣿⣿⢻⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣽⣿⣿⡹⡏⢿⠀⣰⣿⠈⠳⢿⣷⣾⣦⣄⡈⠉⠙⠛⠛⣿⣿⣷⣤⣴⣿⡿⠋⠓⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⠿⢷⣶⣿⡿⠋⠀⠀⠀⢭⣛⡻⢿⣷⣶⠆⠐⠂⠉⠉⠉⠙⠛⠋⠀⠄⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣷⣶⣶⣶⣶⠟⠀⠀⠀⠀⠀⠀⠙⣷⡆⠀⠀⣠⣴⠆⢴⡄⠀⢀⣤⣄⠀⠀⣀⢙⣭⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⣿⢿⣿⣿⣿⣿⣟⠀⠀⠀⢀⡀⠀⠀⠀⠈⠃⠐⠛⠃⠨⣤⡄⠁⠀⢨⣿⡟⣠⣾⢿⣿⣠⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠉⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢽⢦⣀⡛⠂⠙⣈⠉⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠻⣿⣷⢶⣿⣶⣤⣀⠀⠀⢠⠴⢶⣿⣯⣍⣅⡉⠃⠀⠀⣿⢿⢿⣿⣿⣦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠿⡋⢽⠏⣿⡇⠀⠠⠂⠁⠬⠿⠟⠋⠁⠀⠀⢀⡿⣉⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⢈⣄⠀⠀⠠⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⣀⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠖⠒⠛⠛⠋⠉⠙⢳⣎⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠻⡁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡄⣠⡀⢠⡴⣤⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠷⠚⠿⠀⠀⠈⠇⠈⠓⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡀⢠⣶⡶⠆⠀⠀⠘⣻⣶⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣾⠿⠞⠁
⠀⠀⠀⢰⠏⠁⠀⢀⠀⠀⠉⠛⠊⡀⢀⣀⣀⣀⡉⠉⠁⠀⢲⣼⣉⣀⡀⢀⣀⠀⠀⠀⠀⡴⠃⠄⠁
⠀⠀⠀⣼⠀⠀⠀⢨⣶⠆⣈⣩⣤⣥⣾⣿⡿⠋⠀⠀⠀⠀⠀⠚⠈⠉⠓⠀⠰⠶⢶⠄⠙
⠀⠀⠠⠇⠀⠀⠀⣼⣿⠰⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⣤⣶⣤⣤⣄⡀⠀⠀⢠⡆
⠀⣠⠄⠀⠀⢠⡼⣿⣿⣿⣿⣿⢻⣛⡋⠐⠂⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡈⠂⢀
⠀⠁⢀⣠⣾⡏⠀⠈⠋⢩⣽⣿⠟⠉⠉⠻⠿⣿⠟⠲⣶⣶⣶⣶⣒⣒⣀⣀⣀⣤⣶⣶⣿⣦⡀⠉⠙⠛⠛⠁⠹⢶⣤⣀⠉⠀⣦⡀
⠀⠀⢀⡟⠛⠀⠀⠀⠀⢈⡽⠃⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⠉⠉⠉⣉⣬⣉⣭⠍⠉⠀⢉⣦⣴⣶⠶⡆⠀⠈⠙⠣⠄⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢆⠀⡄⠀⠀⠀⠀⠀⠴⠤⠂⠀⠀⠀⠀⠉⠀⠠⣴⣤⣤⣉⡁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡦⠂⠕⡆⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠰⠏⠙⡿⠿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠦⠵⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠆⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠲⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣧⣄⠀⠨⣽⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠂⠻⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠙⣿⣿⣟⢣⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠉⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠖⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠶⠶⠤⠀⠈⣿⠟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠛⠋⠉⠙⠛⠿⣿⡆⠀⠀⠀⠾⠛⢛⣫⣴⣶⣤⡀⠀⠀⠋⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡘⢿⣾⠀⠀⢠⡞⢿⠟⠓⠦⠥⠀⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡧⠀⢿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠚⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣰⠰⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠉⠀⠀⠀⠀⢀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢀⠤⠀⠒⠀⠀⠀⠀⠐⠒⠤⣄⠤⠂⠈⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠴⠂⠉⠉⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣿⠏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠈⠀⠀⠀⢀⠀⠚⠳⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⢸⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⣀⠄⠂⠁⠀⠀⠠⣜⠁⢁⡀⠀⠀⠀⠀⠀⠀⢺⠅⠀⠀⢸⡇⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠷⡀⠀⠀⠁⠀⠀⠀⠔⠁⠀⠈⡓⢄⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠈⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣦⠀⠀⠀⠰⠂⠀⠀⠀⠔⠛⣏⣋⣠⣤⣤⣤⣤⣤⣄⣨⡇⠀⢠⡄⠀⠀⠀⢸⠇⠀⠀⠉⠙⠛⠛⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠇⠀⠀⠈⠉⢁⡀⠀⠀⠀⡠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⢃⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⢰⠏⠀⠀⠀⠀⠀⢀⠈⠁⡀⠀⠀⢀⣠⠖⠉⠀⠻⢿⣏⠉⠉⠁⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⢶⣾⢯⡁⠀⠀⠀⠀⠀⠈⠉⢑⣦⣖⣛⣥⡀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⡂⠀⠀⠀⠀⠀⠀⠀⠐⣨⠖⢫⡘⠿⣷⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⣿⣆⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠘⣧⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠈⢻⡦⣼⡻⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣆⠀⠂⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠿⣦⡀⠛⠀⢸⣿⣿⣿⣿⣧⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣷
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣽⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣟⣋⣝⣛⣻⠛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠿⢿⣿⣿⣿⢇⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠛⠛⠻⣿⣿⣿⠷⠶⠆⠈⡁⠻⣿⠿⢛⣃⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀⢛⡋⠀⢀⣴⣤⡀⠙⢷⣦⣀⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⣿⣿⣦⣄⠛⠿⣷⣌⠿⢋⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⠳⠿⢡⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⣿⣿⣿⣿⡿⢿⣿⡿⠿⠃⢸⣿⣿⣿⡿⠿⠿⠿⠛⢋⣤⣦⡀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⣿⣿⣿⣿⣿⣦⡀⠙⠻⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠚⠛⠷⢦⡄⠀⠀⠀⠀⠶⠞⠛⠓⠂⠀⠀⠈⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢠⣶⣦⡄⠀⠀⠀⠀⠀⠀⢤⣦⡤⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡆⠙⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣃⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢠⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡎⡄⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⡄⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⠿⣿⠘⠄⠀⠀⠀⠉⠻⠿⠟⠉⠀⠀⠀⠀⠀⣠⠞⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⢋⠤⠒⣠⣤⢀⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⢒⡂⠀⠖⠁⠀⠀⠀⠈⢩⣤⣄⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠂⠀⠀⠁⣀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢁⠀⠀⠀⠀⠀⢀⣠⣾⡿⢃⣶⣶⠈⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠈⠩⠁⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⣿⡿⢋⣴⣿⡿⠃⠀⢹⣦⡈⠻⣷
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠉⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢠⣴⣿⡟⢠⣾⣿⡟⠀⠀⣰⣿⣿⣿⣦
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⣄⠀⠀⠈⢀⣀⣀⣀⣀⣀⡀⠛⠀⠀⠀⢰⣿⣿⠟⢠⣿⣿⡟⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠤⠒⠉⠀⢺⣿⡀⣿⣿⣶⣦⣤⣭⣭⣉⣉⣉⣁⣠⣤⡀⢰⣿⣿⠇⠀⣾⣿⣿⠁⣴⣿⣿⡿⠿⠿⠿⠛⢀⣦
⠀⠀⢠⡟⠀⠀⠀⠀⢆⠀⣀⠀⠀⢸⣿⣧⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠉⠉⠀⡀⢿⣿⡇⠘⠿⠋⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⣸⠃⠀⠀⠀⠀⠘⡄⠹⣷⡄⠀⣿⣿⡄⣤⣤⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⣦⣍⠁⠀⢰⣦⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⢳⡀⠙⣿⡄⢿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣩⡁⠀⢀⣾⣿⡀⠀⠀⠀⢀⣾⠿⠋
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⡋⠉⠉⢠⣄⠀⠀⠸⣿⣿⠀⢸⣿⡿⠿⠀⠀⠀⠀⠀⠀⢠⡆
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⡀⠀⠀⢶⣄⠀⠀⠀⠀⣿⠀⠸⣧⠀⠀⣿⠀⠀⠀⠻⣧⡀⠀⠘⣿⡆⠀⠁⠀⣀⣀⣀⠀⢠⣤⡀⠻⣿⡀
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⣤⠹⣷⡀⠀⠀⣿⡆⠀⢻⡆⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠈⢁⣴⣶⣿⣿⣿⣿⡇⢸⣿⣿⣷⡝⠷
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⢿⣧⡙⠁⠀⠀⠘⣿⡄⠈⢿⠀⣿⠀⠀⠀⠀⠀⢹⡇⠀⣰⣿⠟⠋⠉⠉⠉⠉⠀⠘⢿⣿⣿⣿⠆
⢀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠁⠀⠀⣙⣛⣁⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦
⠻⣆⡀⠤⣀⣀⣀⠀⠠⠋⠐⠒⠉⢡⣴⣶⣶⣶⣶⠶⠰⠏⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠙⠻⢷⠆⠉⣴⣶⣾⣶⣤⠛⠒⠒⠒⠤⠤⠀⠴⠒⣂⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡆⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⡀⠀⠤⠤⠄⠐⠀⠀⠀⠚⠒⠒⠒⠒⠒⠒⠚⠉⠁⠀⠘⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠻⢿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠤⠀⠈⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠿⠋⢈⡙⠻⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⢀⠚⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡂⠐⠂⣀⡄⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠄⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠷⠶⡂⠀⠀⠀⠀⡀⢶⣤⣴⠶⠶⠾⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⡀⠀⠀⠀⠐⣀⠀⠀⠀⢀⠉⠁⠀⢹⣶⣶⣯⣉⠛⠻⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠈⠒⠂⠁⠀⣄⣀⣀⣈⡄⢃⣀⣼⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⠀⣌⠀⠀⣀⠀⠀⠀⠁⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⢰⣿⣆⠀⠀⠀⣴⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⣀⣉⣛⣛⡃⠀⢼⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⣿⣿⣟⣿⣿⣿⣿⣷⣦⡽⠟⠓⠻⣼⣿⣿⣿⣿⣿⠿⣷⠟⣽⣿⡏⣿⠳⣿⣿⣿⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣽⣿⠟⣾⢿⡿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣽⣿⠟⣻⠏⠀⢰⡏⢸⡟⣿⠀⢸⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⢏⣿⣿⣟⣻⣿⣿⣿⣿⣯⣵⣶⣶⣾⡟⢁⡴⠋⠀⣠⡟⠀⣾⠁⢿⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⣷⣾⡏⠀⠉⡿⠟⠛⠛⠘⠛⠓⠿⠿⠏⠠⠟⠁⠘⢠⡿⠀⢠⡟⠀⢸⡄⠀⣸⢇⣿⣿⣯⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⢛⣀⡀⠀⠀⠀⠀⠈⠉⠁⠀⣀⡠⠐⠠⣆⠀⠀⠀⣠⡴⡇⠀⠘⣷⠀⣿⠰⡏⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣥⣤⣀⣀⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⣠⠃⣠⢴⡏⠉⣇⡷⠀⢀⡇⠰⣏⠀⢿⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢡⣿⣿⣿⣯⣽⣿⣿⡟⠒⠲⠶⠦⢤⣤⣤⣴⠋⠁⠀⢰⡁⢻⡇⠀⢸⠃⠀⣿⠀⢸⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⢀⣼⣿⣿⣶⣿⡆⠀⠀⣾⣿⣾⣇⣀⣾⣡⣄⣿⣀⣾⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠟⠿⡿⠋⠙⠛⠛⢹⠋⠙⠛⠃⣀⡴⠛⠛⠛⠻⡏⠛⢃⠈⠘⠛⠛⠉⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⠇⠀⠀⠀⠀⡨⠀⡠⠰⠀⠉⠀⠀⠀⠀⠀⣇⠀⡌⡀⣰⡄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡜⠀⠀⠀⠀⠀⠀⠘⢳⣧⠄⠀⠀⠀⠀⠀⠀⣿⢀⣾⣡⣿⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⠈⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠓⠒⠶⢤⣄
⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⣴⢋⣥⣌⣐⡄⣀⣀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⠧⠴⣿⡀⠈⠃⠹⣻⠅⣴⠦⠌⣦
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢁⣠⣤⠶⢛⣫⣭⣶⡶⠶⠦⠙⠳⠶⡆⣀⣿
⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢠⣼⡿⠟⢁⣘⣿⡛⠃⠀⠀⢀⡀⠶⠿⣶⣿⣿⣷⡄
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠀⠰⠾⠏⠠⠶⢶⣝⠿⠛⠆⠀⠀⠀⠉⢽⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⠤⣄⠀⢀⣤⠤⡤⡤⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡶⠅⠀⠀⠰⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡀⠀⠀⠀⠀⡶⣄⠀⠀⠀⠀⠀⣀⡤⠶⠆⠀⠀⠀⠸⠄⠀⠀⠀⣀⣼⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢷⣄⠀⠀⠀⢡⣈⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣉⣭⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⡏⠙⠓⠀⠀⠀⠀⠀⠙⠻⠛⠀⠀⠀⠀⠻⠟⡉⠉⢸⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣩⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⣦⣀⣠⣴⠞⠁⠀⠀⠀⠀⣠⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⢣⠉⠛⠛⠁⠀⠀⠀⠀⣠⣼⠏⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣎⠉⠉⠀⠀⠀⠁⠀⢩⣾⣆⣀⣴⣾⡿⠋⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠠⣄⡉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠈⠂⠀⣈⠛⠷⠄⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⣴⡟⠂⢀⠀⠀⠀⠀⢀⣾⣤⣤⡬⠙⣆⠀⡄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢹⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⢁⣾⣿⣧⠁⠀⠀⠀⢀⣠⣤⣶⣶⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣧⣀⣠⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠴⠆⠆⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⡤⠘⠓⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠩⢉⠠⣴⣿⣿⣷⣟⡇
⠀⠀⠀⠀⠀⠀⠰⠀⠈⠙⠁⢀⡖⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠞⠉⠛⠛⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠀⠀⠀⠡⡄⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠳⠅⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡴⢉⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠂⠀⠁
⠀⠀⣸⡁⠀⢠⡉⡀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⡀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡟⠀⣀⡤⠄
⠀⢰⠟⠀⢄⠩⡇⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠼⠁
⠀⢺⠒⠁⠘⡮⡁⠐⢊⣀⠲⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠈⠇⠀⠐⠢⠄⡄⡜⡎⢠⠞
⠀⢸⠀⠀⠰⠑⠋⣾⡿⠙⡴⢄⠀⠀⠀⠀⠀⣀⢤⡤⣤⣀⡀⠀⠀⠠⠀⣴⣤⣼⠟⠀⠀⠀⠀⠀⠀⠃⡤⠄⠀⠀⠀⠠⢲⠀⣰⢡⠃⠀⣠
⠀⢸⠀⠀⣸⠴⢀⠀⢠⠾⢀⢀⣠⠄⠀⠀⢀⡩⠀⠀⠀⢀⣇⠀⠀⠀⠄⣩⡀⡑⠤⠄⠀⠀⣠⠠⠄⣀⠉⠉⠒⠒⠤⠤⣀⣠⡇⢨⠀⡞⠁
⠀⢈⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠐⠒⠒⠊⠉⢀⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠑⢄⠀⠀⠀⠀⡂⢹⡇⢺⡾⠁
⠀⡏⠒⠒⠀⠐⠂⠠⠜⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠎⠀⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠚⠷⢶⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢀⣷⠀⠀⠀⢀⡎⠀⠑⢦⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠈⢁⠋⠇⠀⠀⠀⢨⡇⠰⠀⠰⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠓⠮⣩⡽⢀⠀⠀⠀⠸⡇⠀⣀⡜⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠉⠁⠀⠀⠀⢤⠄⠈⠀⠀⠠⢂⣿⡿⠿⠋⣰⢿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⡿⠀⠀⢠⠐⠰⠂
⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠐⢸⡇⠀⠀⢸⣷⣾
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠴⢀⠀⢤⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠁⠸⣛⡛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⢃⠦⠀⠀⠀⠀⣬⠗⠁⠐⠂⠀⠀⢀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⣱⣲⢀⠀⢀⡀⠀⣀⡀⢀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⡀⠀⠠⠰⠉⠀⠉⠀⠀⠀⠀⢘⣿⣿⣏⡀⠀⠀⠠⠤⠴⠖⡋⠀⠈⠉⠉⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂⠀⠀⠚⠓⢀⡀⠀⠐⠀⠀⠀⠀⠉⠙⠋⠈⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣤⢩⡀⠀⠀⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢸⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⢶⠖⠶⣶⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠟⠁⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⢀⣤⣴⢠⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠋⠛⠛⠉⠹⣿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢠⣄⠀⣀⠀⠀⡈⠹⠁⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣄⢠⣷⣶⣿⡟⠳⠟⠱⢿⣧⣤⠀⠘⠀⠉⣧⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠋⠁⠁⠀⠀⠀⠀⠈⠛⠻⠃⠀⠀⠐⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣷⡄⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡰⠟⠛⠉⠁⠀⠸⣿⣾⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣉⡓⠀⠀⠀⠀⠠⠾⢒⡖⠀⠀⠛⠠⡁⢸⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⠥⠍⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢤⠴⠀⠀⠀⢠⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⡀⠈⠙⠒⠲⡤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⣉⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⠖⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⠘⡡⠀⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⢀⣠⠴⠛⠁⠂⠀⠀⠊⣄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣾⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⠃⠈⣿⠀⠀⠀⣖⣿⡆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣀⠠⣷⣾⣧⣄⣀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣶⡀⠠⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⠏⠫⢷⣦⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢹⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⠀⠀⠛⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣟⠃⠘⢻⡏⠀⠀⢻⣿⠀⠀⠀⠆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣟⡏⣩⡄⢠⣿⢿⣿⣶⠂⣐⠀⠈⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣻⣇⣿⡇⣸⡿⣿⣷⡾⣿⣿⠀⠀⠀⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣽⣿⣾⠇⢺⠽⢿⣿⣛⣷⣿⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣬⣭⣿⣿⣿⣷⣬⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⢠⣾⡿⠉⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠻⢟⣿⣾⣿⡓⢶⣦⠹⣿⣿⣿⣿⠏
⣿⡿⠀⠀⣴⣿⡟⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁⠙⢿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⢿⣇⣀⣽⢰⣿⣿⣿⡟
⢻⣿⠀⠀⣿⣿⡇⠀⡴⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣧⣤⣿⠿⠃⢸⣿⣿⣿⣿⣦⣄
⠀⠹⣷⡀⠘⢿⣿⣦⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠈⠻⢦⣀⠙⢿⣿⣦⣀⠘⢿⣿⣿⣿⣿⣿⡇⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠳⣤⡈⠙⠿⣿⣶⣍⡻⢿⣿⣿⣿⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⢠⠟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢀⣀⣉⡛⢿⣿⣿⣿⣿⣿⣶⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠖⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⢿⠄⢹⣿⣿⣿⣿⡟⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣤⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣿⠻⢿⡄⠀⠀⠀⠀⠀⠀⢤⣄⠀⡤⠀⠀⠀⠀⠀⠀⢠⡿⠒⠻⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡀⠿⡷⢰⣿⣄⠀⣸⣷⣿⠃⣤⣤⣠⣤⣄⠀⠀⠀⠀⣰⣿⠐⢿⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⣿⣿⣿⡿⠋⢠⣿⣶⣾⣿⣿⣶⣷⣶⣶⣶⣾⣿⣿⣿⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠋⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡾⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⢀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣸⠏⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⠋⠉⠉⠉⠉⠛⠲⢦⣤⣄⣀⡀⢠⡟⢠⣿⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠁⠀⠀⠀⠀⠤⠶⠶⠒⠶⢶⣦⣤⣄⣀⣙⡻⢿⢟⣴⠟⠉⢸⠛⠻⣷⡶⢤⣄⣀
⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠤⢤⣤⣤⣤⡀⠉⠻⣭⡽⠿⣷⣶⠟⠁⠀⠀⡾⠲⣾⡿⠂⣴⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⢶⣾⣿⣿⣿⡿⠉⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣈⠻⣷⣦⣹⣦⡄⠀⠀⠀⠀⢀⡼⠷⣴⡿⠳⣤⣾⣿⣿⣿⡿⠋⠿⣿⣿⣿⣶⣦
⠀⠀⣰⣿⢿⣿⣷⣦⢀⣴⣿⠀⠀⠀⠀⠀⠀⢀⡴⠿⣿⣄⡼⢿⡛⠛⠃⠈⠉⠀⠀⠀⠀⣠⠞⣡⣴⡿⠷⣤⣾⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⢿⣧
⠀⢀⣿⠇⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⣀⣠⣴⣿⣧⣤⠿⢿⣧⣠⠟⠢⣤⣀⡀⢀⣀⡠⠞⢧⣠⣿⡿⢧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢿
⠀⢸⣿⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣷⣄⡼⠛⢿⣦⣴⣇⣀⣹⣄⣀⣷⣤⣾⠿⠻⣄⣤⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸
⠀⠸⣿⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢰⡆⢀⣽⣿⣿⣿⣷⣤⣾⠉⠙⡿⠛⢿⡿⠻⣿⠉⢹⣦⣴⣿⣿⣿⣿⣍⠀⢀⣽⣿⣿⣿⡿⠁⠀⠀⠀⢸
⠀⠀⣿⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣤⣾⣦⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸
⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼
⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⡿⠛⠀⠈⠻⢿⣿⣟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣤⣀⡐⠲⠶⠶⠶⠶⠶⠶⠶⠶⢦⣀⣐⣠⣿⣿⣿⣶⣤⠀⠈⠉⠛⢶⣄⠀⠀⢰⡿
⠀⠀⠀⢿⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣙⣛⡛⠛⣛⣛⣿⡿⠟⠻⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⢷⡀⣼⡇
⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⡤⠔⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢻⣿⣯⡀⠀⣨⣿⣿⡿⠟⠙⢿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢹⣷⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣷⣄⢠⣶⣿⣿⣿⣷⣄⣠⣶⣿⣿⣿⣿⣷⣤⣈⡉⠚⠻⢶⣶⣶⠗⠀⠀⢻⡆
⠀⠀⠀⠀⠘⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢻⣿⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠘⣿⣧⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠟⠙⠿⣿⣿⣿⣿⣿⣿⠟⠉⢿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⡟⣾⡇⠀⠀⠀⠀⢸
⠀⢀⣀⡀⠀⡀⣻⣿⣾⣿⣀⣀⢀⣀⣀⣀⡀⢘⣿⣦⣀⣶⣿⣿⣿⣿⣿⣷⣦⣀⣴⣿⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⣿⣿⣿⣇⣻⣇⠀⡀⢀⠀⢘
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣤⣦⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡶⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⣻⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣧⡠⢀⣿⣿⣿⣿⣿⣿⡍⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠟⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡟⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠑⠈⠻⠿⠟⠁⠀⠀⠀⠈⠙⠶⠄⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⡅⠘
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠙⠟⠛⠛⠋⠛⠁⢹⣿⣿⡿⠟⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠉⢁⣀⠔⠀⠀⠀⢠⣏⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⡀⠀⠀⠀⠀⠒⠃⠙⠉⠉⠀⠀⠀⠀⢈⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⠢⠄⠂⠀⠀⠁⢄⡀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣷⠶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⢀⣤⡀⠀⠀⣤⣶⣤⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠿⠿⠃⠀⠀⠻⠿⠿⠃⠀⠀⠈⢢⡻⠗⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⢄⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠘⠿⠿⠃⠀⢰⣾⣷⡄⠀⣾⣷⡆⣰⣦⡀⠀⡀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡉⣴⣶⣄⠀⠀⠀⠀⣈⠛⠻⠃⠀⠻⠟⠁⠘⠿⠇⠀⠈⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷⠿⠟⠋⠐⠀⠁⠀⠉⠁⣰⠄⠀⠀⣠⣶⣦⠀⢀⡀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠴⣀⡾⠁⠀⠀⠀⠀⠀⠀⣸⣶⣄⠀⠻⠿⠏⢠⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠏⠀⣠⣶⣤⠀⠙⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠻⠿⠋⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⢀⣤⡶⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⣤⠀⠉⠁⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢸⣿⠃⢠⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣶⣿⣿⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡠⠤⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢹⠗⠒⠒⠒⠛⢿⡿⠻⠻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠠⢀⣠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣋⣁⡽⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢹⠿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠀⢠⠳⠖⠄⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠁⢎⣁⣤⣤⣤⣄⣈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⢸⠀⠉⡛⠟⠻⠿⠛⢋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠂⡀⠐⠒⠒⠄⠀⠀⠀⠐⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠤⣀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⠂⢄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠁⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠅⠀⠒⣻⣙⠻⣯⡻⣿⣿⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠉⠀⠀⠀⠁⢸⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣖⣈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⡜⠄⠀⠀⠀⠀⠀⢀⠊⠀⠆⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠋⠒⡠⠄⠀⠒⠀⢀⠠⠓⠠⡀⠀⠀⠀⠀⠀⠀⡘⠀⠁⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⡴⠬⠐⠒⠚⠱⡒⠒⠀⠀⠈⠠⠖⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠐⠒⠒⠒⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⢰⣿⣦⠀⣰⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠛⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠤⠤⠂⠀⠲⣟⠻⣿⡿⠿⣉⠐⠒⢦⣝⢿⣿⣿⣿⢸⣿⠇⠳⡄
⠀⠀⠀⠀⠀⠀⠒⢲⠠⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⡁⠉⠀⢨⣉⠉⠉⠙⠟⠿⠏⢛⢣⣤⣠⣿
⠀⠀⠀⠀⠀⣿⠀⠸⣄⡙⠟⠛⢿⣧⣄⢠⣄⣠⣼⠇⠈⠁⠀⠈⠳⢦⣤⢽⣔⡄⠈⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠻⠛⢋⠲⣌⠻⠿⢞⡉⠉⠀⠀⠀⠈⣿⠶⠖⠀⢸⣿⣷⠈⡽⣹⣿⠇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠌⠛⠛⢋⣠⣤⡀⠀⠀⠀⠈⢑⣠⡄⣼⣿⣿⡆⢸⣿⡟⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠘⣤⠲⣦⠀⠀⠀⠀⠀⠘⠛⠁⠈⠉⠀⠀⠀⠉⢉⠉⡰⠃⣽⣿⠇⠸⣿⣧⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠻⠞⠧⡴⢛⣿⠈⠳⣌⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢱⣿⠀⠀⠀⠀⠀⠁⣿⡿⠆⠀⠀⠀⠀⠀⡟⠁⣿⣾⠇⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡽⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠿⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⠆⠐⠆⠑⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣋
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⣀⣤⣤⣄⣀⣀⡤⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣧⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⠿⠿⠋⠀⠀⠀⢠⡔⠒⠉⠉⠉⠉⢉⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣹⠉⠙⠛⠛⠛⠋⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⠶⠶⣏⠘⠀⠀⠀⠀⠀⣀⠀⠀⠗⠚⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠈⢻⡅⣀⣙⠀⠏⣩⡟⣁⢀⡴⠋⠁⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡆⠀⣖⡚⠇⢹⣿⣇⠀⠁⣛⡟⢃⡴⢊⡴⢧⠀⢀⣠⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡾⠁⠀⠀⠙⣿⣾⣿⣿⡆⠘⣻⣶⣫⡴⢋⣤⡾⠶⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢀⡾⠁⣿⠀⠀⠀⠀⠀⢨⣿⣿⣭⠀⣀⠀⣻⣟⠶⠋⣡⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡾⠁⠾⣧⣀⡀⠀⠀⠀⠈⣟⣛⣋⠀⡈⢙⡛⡋⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠠⣬⣭⣿⡄⠀⠀⠈⣿⣿⠾⠿⠓⠾⢷⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠰⢤⣈⣹⠀⠀⠀⠙⠿⠶⠶⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⣀⣀⣈⠉⣳
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⡏⠀⢈⣥⠞⠋
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣴⠟⠀⠀⠈
⠀⠀⣴⢶⣯⠀⠀⠀⢶⡟⠁
⠀⠀⢰⡞⣻⣷⣀⠀⠘⠃⣶⡄
⠀⠀⠀⠉⣅⣻⡿⣿⢋⣼⣏⠁
⠀⠀⠀⠀⠙⠉⢠⣿⡆⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠈⠉⠉⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠛⠀⠀⠭⠷⠀⣾⠯⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢠⣄⣠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠈⠃⠐⡂⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠂⢈⡂⠠⢄⡀⣠⣴⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠁⠀⠀⠀⠀⠀⠀⠙⠂⢀⣩⡛⣿⣿⣿⠋⠁⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣿⠙⠘⣇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡀⠀⣿⣧⡀⠸⡄⢻⣦⣄⢹⡄
⠀⠀⠀⠀⠀⠀⢻⣸⠃⠀⠀⠀⠀⠀⠀⢧⢡⡀⠀⢣⡀⣿⣿⣷⣴⡇⢸⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣟⢃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⢸⡟⣿⣿⣿⣿⡃⢸⡿⠿⣟⡉⠀⢸⠂⠖⠘⠆⢘
⠀⠀⠀⠀⠀⠀⢀⣿⣌⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠿⠿⠿⠟⠛⠛⠳⠀⠀⠀⣍⠉⣴⢷⣶⣶⣴⡶⡚
⠀⠀⠀⠀⠀⠀⣼⠋⢻⣦⠀⣠⢂⣴⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⠀⣎⠘⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢹⣷⣕⠟⡿⣿⣿⢂⠀⠀⠀⡀⠀⢀⣀⠀⣦⣰⣶⣶⣶⣆⠉⠛⠹⢿⡿⣠⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠿⣷⣭⣸⣉⣬⣈⣥⣤⣶⣶⣶⣾⣦⡬⢿⡿⢋⠀⠈⠁⢠
⠀⠀⠀⠀⠀⠀⣷⡰⠃⠀⠀⠒⠺⠿⠿⢿⣿⣿⢿⣻⣿⠟⠀⠀⠠⠄⠀⠑⢋⡀⣂⢆⣄⡅
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠁⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠴⠶⠛⠻⠷⣶⢦⣰⣄⣨⣻⣷⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⡿⢿⠟⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠉⠉⠛⠿⠿⢿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⣤⠇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡏⠀⢀⡠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠓⠒⠤⠤⣤⣤⣄⣤⡮⠤⡼⠖⠚⠉⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠮⢟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⡶⣯⣭⣿⣿⣿⣯⣭⣽⣿⢿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣏⠀⣈⣿⠾⢯⣿⣉⣿⣿⡀⢀⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⢿⣿⢻⣤⣼⡟⠉⢹⣿⡟⢻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣦⣼⣿⣿⠁⠀⢹⡿⣿⣿⣹⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠭⣛⣛⣛⣛⣛⣛⡸⠽⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠉⠁⠀⠀⠈⠁⠒⠤⡀
⠀⠀⠀⢀⣀⡀⠀⡠⠊⣁⣀⣀⠀⠐⠒⠤⠤⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⡥⠄⡶⠉⠀⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢉⠄⠀⠀⠀⠈⠑⢍⠁⠒⠠⣀
⠀⠀⠀⠀⠰⢡⠀⠀⠀⠙⡆⠀⡗⠒⠠⠴⠤⠤⠤⠤⠽⠉⠐⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠖⠠⠃⠀⣴⠂⠀⠀⠀⠀⠑⡀⠀⠈⢳⣄⣀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣂⢀⡁⢀⡌⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⢯⠉⢆
⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠁⠀⢀⠖⠒⠒⠀⠓⠀⠉⡏⢑⡄⠀⠀⠀⠀⡍⠉⠀⠀⠀⠀⠈⠙⠃⠒⠀⢤⢀⣸⠀⠀⠀⠀⣼⠀⢨
⠀⠀⠀⠀⠈⠆⠀⠀⡜⠉⠱⠉⠀⠀⠀⠀⠀⠀⡀⢼⠀⠐⣆⠀⡤⠴⠾⣏⡁⠁⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠰⢄⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⣆⠬⠁⣰⡇⠙⠢⠴⡖⠁⠀⠀⠀⠘⠈⠀⡄⠀⠀⠀⠓⠀⠀⠀⠀⠘⠤⠀⢄⠀⠀⠀⡌⢰
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡩⠋⠉⡆⠀⠸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠜⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⡄⠀⠀⠲⡒⠉⡇⠀⢀⠜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⢄⡠⠐⠈⠉⢘⠅⠀⠀⠀⠀⠀⠀⠀⢈⠦⠻⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠀⢤⣿⡦⣤⠴⠋⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠎⠀⡠⠶⣶⢻⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠒⠢⠼⠛⠉⠱⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠈⡎⠉⣿⠁⠀⠀⣸⠦⡀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠁⠀⠀⠀⠀⠀⡸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⣇⠀⠘⠳⠶⠚⠋⠀⠈⢢⠀⠀⠀⠑⢄⡀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⠄⠀⠀⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⠀⠀⠀⠀⣀⣀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⣂⡀⢰⡀⣀⠤⠚⡅⠀⠀⡠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⠁⠀⠀⠀⠀⣀⠬⠦⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠋⠉⠘⠃⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠶⣐⣂⣙⢲⣖⣖⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠈⠀⠔⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠒⠀⢠⢠⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣉⣉⡉⠈⠉⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠸⠖⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⣀⢀⣀⣀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣈⢉⣉⣀⡀⠬⢥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⢆⡀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⠴⠃⠀⠀⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⡤⠤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣃⣛⣻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⡉⣿⠏⠉⢉⣡⠀⠰⢮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⡶⠀⠎⣀⠀⠀⣤⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠷⣦⡅⠀⠀⠿⠀⠀⢿⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠛⢘⠋⠀⢀⡀⠀⢀⣀⡷⠈⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⡀⠈⠙⠢⠤⠔⠀⢀⡇⠀⠀⠀⢏⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡼⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡳⠬⣙⣒⡺⣯⠤⠤⢄⣀⠈⣻⠤⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⡇⠙⢄⣰⠁⠱⣽⠘⢢⠀⠈⣿⡁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣲⠌⢫⠑⡴⠘⡔⢧⠘⣽⠶⣹⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠙⣄⠀⢻⠀⠘⡇⡞⡰⠃⠀⠘⢳⡀⠀⢀⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠀⠀⠀⠀⠙⣌⠣⡀⢧⣠⠿⣟⣅⠀⠀⢀⡴⣳⣎⣩⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠘⣆⢑⡞⠁⠀⠙⣮⣻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⣨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠚⠁⠀⠀⠀⢪⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢟⣫⣄⣴⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠕⠿⠿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢻⣿⠁⢴⣿⣿⣿⣿⣷⠀⠐⣾⣿⣿⣟⡒⢘⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣶⠀⠉⠋⠀⠀⠉⡇⠀⠙⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣹⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠧⢤⣤⠶⠂⠀⠀⠜⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠒⠳⠶⠤⢤⡆⠠⡾⠀⠀⠀⠀⢀⠄⡤⢛⡻⢥⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣠⠀⠀⠀⠀⠀⣇⠀⣿⠀⠀⠀⠀⠈⢀⣃⣤⣼⠈⠀⠀⠈⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠻⣿⣷⣄⠀⠀⠀⠘⣦⠙⣄⠀⠀⠀⢀⡄⣡⣿⡉⠙⠛⠛⠁⠰⣦⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣯⠘⢷⣙⣿⣿⠿⡿⠿⠟⠈⢷⢠⠀⠀⠀⠰⠇⠹⢿⣧⡤⠆⠐⠀⢰⡇⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠀⠻⣿⡀⠀⠙⢮⣗⠀⠀⠀⢀⠄⠺⠤⠧⠤⠤⠖⠀⠀⠈⡿⣷⠖⠒⠀⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠉⣳⣦⣶⡏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠛⠳⣶⡶⠀⠁⠈⠀⠀⢀⠷⡀
⠀⠀⢀⣤⠶⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣦⡀⢰⣿⣿⣿⣿⣆⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢲⡖⠂⡠⠊⠀⠈
⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⣿⣿⣿⡅⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠛
⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠟⣋⣹⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠛⠛⠻⠛⠛⠿⠿⠿⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣥⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⢀⣤⠶⠖⠂⠀⠈⠻⣿⣿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠛⣳⠀⠀⠰⠋⠙⠃⠀⠀⠘⠟⢡⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠳⠖⠂⠀⠠⢄⡀⠀⠀⠀⢰⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣦⡶⣶⡄⠖⠂⠀⠀⠀⠀⡼⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠶⠶⠆⠺⣋⣵⠞⠽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢀⠀⠀⠒⢆⠙⢦⡴⠞⢁⣠⣼⠋⠙⡀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠟⣧
⠀⠀⠀⢂⡤⠤⠝⣳⡦⠌⣈⣤⣶⣿⣿⠟⠀⠀⠈⡿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀
⠀⣠⢒⣥⣤⡀⢞⠁⣠⣾⣿⣿⣿⠁⠀⠀⠀⢀⠞⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸⠢⣄⡀
⠀⡇⣟⣽⣛⢿⡆⢿⣿⣿⣿⠟⠃⠀⠀⣀⡤⣾⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢠⠃⠀⠀⠉⠉⠓⠲⠆
⠀⠹⡝⠛⢫⣼⢇⣿⠟⠋⠀⠀⢀⠐⠏⠀⠀⠸⠀⠀⣡⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⣰⠃
⠀⠀⠘⠻⠷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠙⢦⠀⠀⠁⢷⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠃⠀⠀⠈⠳⠤⠈⠁

⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡁⠶⠂⠉⡑⡖⠒⠠⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠋⠈⢄⢣⡀⠇⡇⢀⡠⢊⠦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣀⣀⣀⣈⣧⠙⠠⠖⣩⠖⠁⠀⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠐⠒⠀⢠⡄⢀⡀⢈⡉⣀⣐⣒⣚⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⢤⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣰⡀⣀⣴⢾⠶⠋⣽⡌⠣⡀⠉⠉⠹⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠣⡉⠔⠀⠀⠀⣿⠈⠣⡹⢄⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠐⠀⠀⠄⣹⡀⡠⠜⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠶⢤⣤⣠⣤⠤⠶⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠦⣄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠀⠀⠀⠀⢀⡠⠔⠈⠉⠑⡉⠒⠢⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⣳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠐⠁⠀⣠⠴⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠃⠀⠈⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠐⣬⠒⠒⠒⠒⠒⠒⢦⡀⠀⠀⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠈⢆⢄⡀⠀⢀⡠⠔⢸⠀⠀⢠⠀⠀⠀⠀⠘⢆⠀⠀⠀⣼⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠈⠢⠤⠚⠉⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄⠀⠀⠀⠀⠀⠀⣠⠒⠢⢄⡘⢠⣀⠈⠀⠀⠀⠀⢀⢸⠀⠀⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠈⠙⠷⠄⠀⠀⠀⠀⠊⠜⠀⠀⢸⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⠀⠀⠀⠀⡐⠁⠀⡠⠉⠐⠢⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢃⠆⠀⠁⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢻⠀⠀⠀⠀⠀⠉⠂⠄⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠦⣈⠉⠙⠛⠛⠛⠛⠛⠋⢉⣁⠴⠖⠋⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠤⠤⠤⠤⠶⠖⠋⠁


⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣬⣭⣭⣉⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣦⣤⣿⣿⣿⣭⣿⣿⣽⣿⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⢷⣶⣶⣾⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⣠⠾⣿⠟⠟⢛⣻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⣧⣼⣟⣠⣪⣴⣶⣾⣷⣶⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠈⠛⠛⠛⠻⠟⠛⠉⠁⠈⢹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣲⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⢙⣿⣦⠀⠀⠚⠛⠛⠳⠦⠀⠀⢸⣿⠋⠐⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠉⠉⠀⠐⠀⠙⠛⠓⠀⠀⠀⠀⠀⣺⠀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠰⡄⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠻⢏
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠈⠆⠒⠆⠀⠀⠀⡤⠆⠁⡴⠀⠀⠀⡜⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡔⠉⠉⠀⠑⠢⣄⠀⠀⠀⢠⠀⠠⠄⣀⡀⠀⠀⠀⠀⣀⢀⠎⢀⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢀⡌⠀⠙⠂⠀⠀⠀⣉⢆⣴⣾⡇⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢀⣀⣀⣼⠁⠀⠀⠀⠀⠂⠀⠈⢸⣿⣿⣷⣤⣤⠀⢴⣶⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣠⣭⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠈⢻⡿⠛⠆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠀⣾⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⢀⠜⠀⣠⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⡴⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⡏⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢸⣧⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡿⠃⠀⠀⠀⢙⣧⣀⣤⣶⣶⠶⠶⠟⠛⠛⠛⠛⠿⠶⠶⣶⣶⣿⣁⣀⠀⠀⠀⢹⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠷⣾⣿⡿⠃⢀⣤⣴⠶⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢶⣤⡀⢹⣿⣿⣶⡶⢶⣤⣄
⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⣰⡟⠛⠛⣷⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠀⣸⣷⣤⣈⣙⢷⣦⡀
⠀⠀⠀⣠⣿⣥⣤⠶⠾⣿⣿⢿⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠻⢿⣭⣙⠳⠿⣿⡄
⠀⠀⢀⣿⢿⣯⣥⠶⠛⠋⠁⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠉⠙⠛⢻⡿⣿⡀
⠀⠀⢸⡇⠘⢿⡄⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢀⣴⠟⠀⢸⡇
⠀⠀⢸⡇⠀⠈⠻⣧⣀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⠿⠁⠀⠀⢸⡇
⠀⠀⠸⣧⠀⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⢶⣄⡀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⠀⠀⣿⠃
⠀⠀⠀⣿⡀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠉⠛⠻⠿⠶⠶⠟⠋⠛⠿⢦⣤⣤⣤⣤⣿⠟⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡇⢠⣿
⠀⠀⠀⢻⣇⢠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣴⠶⠆⠀⠀⠀⠰⠶⣦⡀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⣀⣀⣀⣀⣠⣶⠟⠁⣼⠏
⠀⠀⠀⠀⣿⡀⠙⣷⣦⣤⣤⣤⣤⡶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡄⠀⠀⠀⢀⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⢿⡍⢻⡆⢠⡿
⠀⠀⠀⠀⢸⣧⣰⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢻⣿⠇
⠀⠀⠀⠀⠀⣿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣿⡿
⠀⠀⠀⠀⠀⢸⡏⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸⡇
⠀⠀⠀⠀⢀⣿⠃⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⣰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣷
⣦⣤⣀⣴⡾⠋⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠙⢷⣤⣀⣤
⠈⢿⣏⠁⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢈⣹⡿
⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣀⣤⣽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠻⠶⠾⠿⠿⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣅⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠛⢷⣤⣀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣄⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠁⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣼⣿⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣄⣠⣤⣴⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⢻⣟⣉⣽⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠁⢠⡿⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠁⢹⣿⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣇⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⢰⡟⠀⠈⣿⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣾⣇⢀⣤⣿⠾⠟⠋⢻⣆⠀⠀⠀⠀⠀⣠⡿⠛⠷⣦⣤⣀⠀⣿⣧⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⢹⡿⠃⠀⠀⠀⠀⠈⠻⠶⠶⠶⢶⣴⠿⠁⠀⠀⠀⠈⠙⢿⡟⠁⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣧⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣦⣄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣿⠁⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠻⠷⣶⣤⣄⣀⠀⠀⠀⠰⣶⣦⣴⠟⠁⠀⠀⢀⣀⣠⣤⣾⠿⠛⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣤⣄⣠⣿⡁⢀⣤⣴⠶⠟⠋⠉⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⠟⠻⢿⠿⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠷⠶⠶⠶⠶⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠙⠛⠿⣦⣤⣤⣄⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠿⠛⠛⠉⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⣿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣈⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⡾⣿⠿⣦⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⡙⠻⠿⢶⣶⣶⡶⠾⠟⢛⣡⣴⠟⢷⣌⡛⠻⢷⣦⣤⣤⣤⣶⠿⢛⣫⣼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠛⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠃⠀⠈⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠉⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠂⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⡠⠐⠈⠳⡌⠂⠀⡀⢴⠧⠗⢄⡀⠀⠀⠀⠀⠀⣶⣶⣦⣨⣧⣤⡀⠀⠀⠀⠀⠀⠈⢡⠇
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⢸⡄⠈⢆⠀⠀⠀⠀⢿⠟⠑⠀⠉⠉⠀⠀⠀⠀⠀⢀⠔⡝⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠃⠀⠀⠀⢀⣄⢸⡄⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⠁⠀⡼⠀⠀⣤⣤⠀⠀⠀⠀⣠⢃⡴⠃⠀⠀⠀⠀⠀⠀⡈
⠀⠀⢀⠀⠀⠀⠀⣴⣿⡗⠈⣧⠀⠀⠀⠀⢹⡀⠘⡄⠀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢾⡁⠀⠀⠀⢀⠀⠀⡰⠁
⠀⢀⠚⢀⠀⠀⠜⢿⣏⢈⠂⢸⡄⠀⠀⠀⠸⣷⡆⡷⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⢀⡼⠁⠀⠀⡇
⠀⠈⢒⣡⣀⡀⡇⢸⣿⠀⠀⠘⡇⠀⠀⠀⠀⣯⠎⠀⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⣵⣴⣇⣰⠟⠁⠀⠀⠀⠇
⠀⢻⡿⡅⠀⠈⠃⢸⠣⠀⠀⠀⡇⠀⠀⠀⠀⢿⣶⣋⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⣠
⠀⠀⠈⠘⠄⠀⠀⣸⣦⡀⠀⠀⠗⠀⢀⣀⣴⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣤⣴⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣶⣴⣶⡏⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡛⢻⣿⣿⣿⣷⣦⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡧⠘⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡗⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠉⠁⠈⡉⢻⣟⡇⠀⠀⣴⣿⠟⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⢤⡐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠞⠿⠟⠛⠍⠃⠀⠘⣿⡟⠛⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠈⡄⠀⢀⡇⠀⠀⠀⠀⡶⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠶⣤⣤⠄⢀⣼⠁⠀⠀⠀⠀⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⣼⠃⠀⠀⠀⠀⠀⠈⢄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠖⠛⠛⠛⠛⠉⣼⠇⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⢸⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⣰⠏⠀⠀⠀⠀⠀⠀⠈⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣽⠇⠀⣽⠾⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⢇⠈⠷⡻⠎⠿⠻⢿⣷⣴⣦⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠑⢼⣇⠈⢈⠀⠀⠉⢹⠿⠿⠿⠿⠿⣿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠀⠀⠀⠀⠀⠀⠈⠳⢧⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣰⣿⣤⣥⣥⣢⣤⡀
⠀⠀⠀⠀⣀⣤⡼⠋⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⢸⡇⠉⠋⣭⠙⠛⠋⠙⢫⣭⠀⢃⠀⠂⠉⠑
⠀⠀⠴⠋⠉⠀⠀⠀⠀⠀⠄⠀⠀⣑⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⢸⠂⠀⠀⢸⡄⠀⠀⠀⢸⡇⠸⠓⠀⠀⠀⠀⠀⠀⢸⠀⢸⣷⣀⣤⡔⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡀⠀⠀⢀⣿⠁⠘⢷⡄⠸⣴⣾⣷⠀⠻⣦⡀⠀⢸⡇⠘⢁⡀⡄⠀⠀⠀⠀⢨⠂⠸⣿⠏⠀⣁⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⢹⡞⠛⠀⠹⣇⠀⠈⠻⢶⣼⡇⠸⠟⠡⠁⠀⠀⠀⠀⠘⠁⠸⢿⣿⠉⡏⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢼⡇⠀⠀⠀⠈⠀⠀⠀⠀⠉⣿⠠⠀⠀⠀⠀⠀⠀⠀⢠⡀⣄⡻⠋⠀⠓⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⣀⠀⠀⠀⠀⠀⢰⠀⣦⣀⣠⣦⡤⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⢺⠁⣿⡿⣿⠃⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣷⣀⣀⡀⠀⠀⠀⠈⣠⣿⡐⠤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⣿⣿⡿⣃⣴⠞⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⣤⣤⣤⣴⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⢀⢄⢀⠀⠀⠀⠀⠀⠀⡖⠈⣀⢀⢰⡆⠀⠀⠀⠈⠁⠈⠉⠙⡇
⠀⠀⠀⠀⠀⠀⣟⣛⡟⠚⣿⡇⠀⠀⠀⠀⠀⡀⠰⠀⠌⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⡃⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢾⠃⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠑⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠆⠈⣴⠟⠀⠀⠀⠀⠀⠀⠳⠄⣀⣠⠾⠀⠀⠀⠀⠐⠦⠀⠐⠶⠃⠀⠀⠀⠀⠀⠠⠐⣠⣴⠇⠀⠀⠀⠀⠀⠸⠦⠀⣀⣀⣀⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠰⣾⠀⠀⠨⢷⣩⡗⠀⠀⠀⠀⡋⠀⠀⠀⠁⠀⢹⠀⠀⠘⢆⠀⠀⠀⠀⣼⠃⠀⠀⢸⡛⠀⠒⠒⠒⠛⠻⠂
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠠⠋⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠀⠈⢢⠀⠀⡜⠁⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠰⠀⠀⢠⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⢃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⣿⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⣀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠐⠄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠘⠤⠄⠀⠐⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⡶⠊⠉⠉⣀⣨⣷⠀⠀⠀⠀⢠⣇⣤⣾⣧⣤⡄⠀⠀⠀⢠⠀⠀⠄⠀⣄⠀⠀⠀⠀⢰⠏⠉⠉⢭⣿⠀⠀⠀⠀⢠⣄⣒⣒⢒⢲⣦⡄
⠀⠀⠀⠀⠈⡇⠠⠆⠤⠖⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣁⠀⠀⠈⣿⠀⠀⠀⠀⢰⠂⣠⢿⡴⣣⢰⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠤⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣗⠀⠀⠀⡟⠀⠀⠀⠀⢸⠢⠔⠪⠃⡼⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⡀⠁⠀⢀⡅⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⢘⡀⠈⠉⠉⠁⣐⡀
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠃⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠃⠀⠀⠀⠀⠀⠂⠀⠐⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠚⠁⠀⠀⠀⠀⠈⠓⠂⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⣼⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⢸⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡏⢴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⢃⣽⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠪⠻⣿⣿⡿⠛⠁⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠤⠀⠈⠉⠀⠀⠀⠀⢀⣀⡊⠁⠊
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠿⠿⠟⠻⠛⢿⣿⣿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠋⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣀⣀⡋⠁⣀⠤⠀⠀⠀⢰⣹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠖⠚⠙⠉⠁⠀⠀⠀⠀⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠀⠀⠐⢀⣀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⠷⠶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠰⡓⠐⢶⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢀⣼⣿⠄⠀⢰⣿⣿⡆⠀⠀⠠⣠⣶⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⢀⣀⡀⠉⠉⠀⠀⠀⠀⠐⠌⠁⠐⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢿⣿⡷⠀⢀⣤⣤⡀⠀⣴⣤⠀⣠⡀⠠⡀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢟⣠⣄⡀⠀⠀⠀⠈⠻⢿⠗⠀⢿⡿⠀⢿⣷⠀⠈⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⡿⠿⠃⠐⠀⠀⠐⠃⢠⠄⠀⠀⣠⣦⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⢧⣠⡞⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⢿⡿⠃⢰⣿⠆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣾⡇⠀⠀⠀⠀⠀⠀⣿⡿⠏⠀⣤⣶⡄⠈⠛⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠻⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣽⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⢠⣶⠂⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⣶⡄⠀⢀⡀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠿⠁⢰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⠶⡶⢶⣶⡶⢶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⡀⠀⠀⠀⢀⣴⣿⠟⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣿⠿⢷⡾⠿⠿⠛⠋⠁⣿⣿⣿⣿⠿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡛⣦⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠠⠶⣦⡄⠠⠖⣋⣉⡁⠀⠀⠀⠸⠿⠋⡑⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠈⢹⠇⠀⠘⠁⠙⠉⠀⠀⠀⠀⠀⠈⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⢀⣸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢳⡤⠶⠘⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣈⡁⢀⣀⣀⣀⣰⣯⠤⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠽⠋⠀⠉⠉⠉⠉⢉⠛⠂⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⣶⡦⠀⠀⠀⠀⠀⠌⠀⢤⣤⣀⣴⡾⠏⠀⠀⡠⠂⠀⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣻⣷⠷⠦⠄⠀⠄⠀⠀⠀⠀⠺⣿⣄⣀⠤⠊⠀⠀⠀⠠⠂⠀⠀⠀⠈⠙⠓⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢛⣟⣿⡆⠀⠀⠀⠀⠀⢀⣠⠾⠃⣸⣿⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠩⠟⢫⠃⠀⢀⡴⠋⠉⠉⠁⠀⠾⣿⡿⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⣠⠏⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠱⠊⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠄⠰⠒⠀⠀⠀⠀⠀⢀⡐⠛⠃⠔⠀⢳⠄⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢤⠄⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡋⡸⢶⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⣡⣈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠰⠄⠀⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠘⢀⠀⡤⣤⣤⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢼⣿⣇⠀⠀⣰⠻⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⢠⣿⡿⣻⢟⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠻⠆⠒⠉⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠐⣸⡿⢟⠁⠙⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠠⣀⢿⣠⡀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⢿⣿⣷⣭⣬⣵⣿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⣻⣇⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⡟
⠀⠀⠀⠀⠀⢾⡂⠈⠉⠉⠉⠩⠅⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣧⣀⡀⢀⣀⣧⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⣿
⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⣤⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠈⠉⠉⠁⠀⢒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠑⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠹⣿⣿⣿⠏⠉⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠿⠻⣄⣀⠐⠒⠚⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠛⠁⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠓⠒⠀⣘⡃⠀⠀⠀⠀⠀⠀⣨⠀⠀⢀⣀⣤⣤⣀⣀⣀⣀⣀⣡
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⣚⠀⠀⠀⠀⠀⠀⢰⣿⣄⣀⣀⣠⣀⣀⣀⣀⣤⣤⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠿⣿⣣⠄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣷⠰⠀⠱⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣿⣁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠰⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠴⠾⣖⠛⠰⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⢿⢼⣧⣤⣠⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠂⠈⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛
⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣤⣤⣄⠀⠀⢠⣾⣿⣿⣠⡄
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣿⠋⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣤⣿⢁⣴⣶⣾⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠁⠈⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣤⣄⡀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣿⠀⠀⢠⣍⡀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⢸⣄⣷⣆⣰⣾⣧⣾⠀⣀⡀⣀⣽⣧⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣿⣿⠿⣿⠆
⠀⠀⠀⠀⠀⠉⠚⠿⠿⢿⣿⣓⠒⠻⢿⣼⣿⠏⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠏⠉⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⣶⣤⣤⣴⣿⡀⠀⠀⠀⠀⣿⣄⠀⣠⣄⠀⠀⠀⠀⣈⢛⣿⣿⡿⢿⣛⢯⣵⡤⣀⠸⠆
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⢝⣓⣊⣭⣶⣾⣿⣿⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢉⡭⠴⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⢀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣠⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⡀⠈⠁⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢘⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⣀⣨⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠸⡁⡈⠽⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣥⣈⠢⢄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡤⠚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠳⢶⣤⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⠏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠁⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⣠⠞⠁⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠄⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠉⠀⠀⠀⠠⢰
⠀⠀⠀⠀⠀⠀⢶⠐⠒⠒⠒⠠⢄⡀⢀⡝⢄⠢⢀⠀⠀⠀⠀⠀⠀⠉⠻⠦⢤⣀⣀⣀⡤⢊⣵⠟⠉⠀⠀⠀⠀⠀⢀⠔⡵⠃
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠒⠢⣀⡈⢪⡌⡆⠑⠢⣑⣢⢤⡤⣀⠀⠀⠀⠀⣠⠤⠞⢉⡴⠛⠁⠀⠀⠀⢀⡠⠔⣪⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⡓⢾⣿⣊⠉⣇⣨⡞⠿⢺⡙⠓⡖⣒⠒⠟⠿⠿⠭⠤⠀⡒⣒⡀⠭⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣽⣽⣻⠟⠿⡕⠞⡤⣫⢏⡅⣀⡊⠉⣵⣾⣺⣛⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡿⢿⠏⠸⠞⢙⠏⣏⠹⣋⣽⣿⠄⡟⡴⢿⣯⠞⣹⣷⢿⣄⡀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠁⠉⠆⠘⠋⢋⠕⣛⡦⢯⡽⢴⢿⡒⠤⣼⡟⠛⠋⠚⠛⠂⠂⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠁⠀⠸⢓⠒⠐⠮⡭⠝⠯⣨⠕⠀⡶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⣿⣿⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠤⢦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠠⠦⠴⡄⠀⠀⠀⠀⠀⢀⡤⠒⠀⡈⠳⢮⣧⣶⣾⢾⠇⠘⢆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠠⠒⠃⠀⠀⠀⠀⠀⢀⢈⣴⣾⣿⣿⣿⠂⠘⠟⠻⠿⠒⠶⡌⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣭⡏⠻⠀⠀⠀⠀⠀⠀⣆⢘⣁⣠⠤⠟⠛⠫⠿⣹⠿⠟⠋⠑⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣑⠷⠄⠀⠀⠀⠀⠀⠀⠈⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⠛⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠶⣦⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠈⠻⠒⠒⠶⢲⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⣄⠀⠀⠀⠀⠀⠰⡇⠀⠐⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢄⠀⠀⠑⠢⠤⠤⣀⣀⠁⣿⣿⠁⠀⠀⠀⠙⡉⠂⠄⠠⠤⠤⠀⠀⠀⢀⡔⢸⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠑⢄⡀⠀⠀⠀⢠⣞⢷⣽⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⡈⠣⡀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠼⠙⢷⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠲⢤⣠⡤⡇
⠀⠀⢀⠊⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠢⣑⠐⠢⠤⠔⠁
⠀⠠⠃⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⡀⠀⠀⠀⣀⣴⣭⠴⠄⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⡿⠛⠛⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣷⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢫⣭⣙⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⢁⣂⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⠶⣴⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡶⠛⠿⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⢣⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠰⢠⠅⠀⠀⠀⠐⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡄⡘⠀⠀⠀⠀⠀⠫⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠁⠀⠀⠀⠀⠀⠸⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠘
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠦⠤⠐⠒⠀⠐⠂⠤⠤⠒⢒⡠⠃⠀⠀⡇⠈⠢⠤⠤⠤⠤⠔⠂⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠚⠚⠀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠋⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⣠⣀⣤⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠛⠃
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡉⠹⠸
⠀⠀⣿⣻⠿⠿⠿⢿⣿⣿⡷⠀⠀⠀⠒⢶⠔
⠀⠀⢿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣀⠶⠤⠀⠀⢀⠀⠀⣄⢀⡀
⠀⠀⠈⢿⣿⣿⠀⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⢆⣀⠀⠀⢨⣁⠀⠀⠀⠀⠀⡄⠼⢦⣠⣷⠂
⠀⠀⠀⠈⠻⢿⣷⡎⠑⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠺⣋⣐⣶⣶⣶⡄⢠⠶⠾⠼⡿
⠀⠀⠀⠀⠀⠈⢿⠃⠀⠈⠳⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠪⡉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠁
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢸⡄⢀⣀⣀⣀⠤⠦⡀
⠀⠀⠀⠀⠀⡤⠊⠐⠀⠀⠀⠀⠀⠠⠏⡻⠀⠁
⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠣⡄⠀⠀⠀⠀⠀⠀⠘⠢⣀
⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣀⠀⠀⠀⠀⡌⢷⡀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⠢⣀⣀⢣⠘⣮⣳⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠱⠷⣌⡋

⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⠁⠀⣤⠼⠷⠚⢿⣿⣯⢪⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣴⡯⡀⠀⠀⠰⠿⠻⠆⠈⠙⠧⠉⢿⣿⣿⣷⣥⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡿⣹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠴⠚⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⣧⣿⣿⣿⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠛⠓⠋⠉⢯⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⣿⡿⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡤⠤⠄⠀⠐⠚⠒⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢎⣡⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⣀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠉⠓⠚⠻⣦⣱⣄⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡠⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠁⠐⠒⠀⢤⠤⠋⠘⠓⢲⠦⠀⠐⠚⠋⠀⠀⣀⠠⠚⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠙⠁⠀⠙⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⠈⣩⢍⣓⣐⡒⠶⠼⠧⡤⠤⣤⣀⠀⠀⠘⠢⠤⡤⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠠⠀⣀⡨⠋⠉⠣⢄⠀⠀⠀⠀⠣⣄⣀⠀⠉⠁⠀⠒⠚⠒⠀⠂⠀⠀⠈⠢⡀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠁⠀⠀⡠⠊⠉⠉⠉⠁⠀⠀⠉⠙⢅⠒⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖
⠀⠀⠀⠀⡠⠰⠳⠀⣁⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆
⠀⠀⢠⢨⣀⠀⠀⠀⠀⢉⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣤⣤⣤⡶⠆
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⣀⠤⠬⠭⡀⠀⠀⢐⠀⠈⢱
⠀⠀⠀⠀⠀⢀⣤⣄⡢⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⡿⡿⠟⡄⠠⡀⠀⠀⠀⠀⢼⣿⣷⡖⣰⣿⣿⣷⡌⢿⣶⣿⠀⠀⡠
⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠃⠀⠀⠀⢢⠘⣷⢿⡷⡘⠿⣿⠿⢃⠿⢿⡿⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢀⠐⠒⠂⠁⠀⠀⠀⠀⠀⠑⠘⢦⠀⠈⠀⠀⠈⠀⢀⠜⠓⠉
⠀⠀⠀⠸⠶⢤⢀⠀⢤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠈⠡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠶⠤⡀⠀⠴⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣻⣟⡻⡟⣻⣿⣿⣛⣿⣻⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⣿⢿⡧⡇⣿⣷⣿⣹⣿⣼⣿⣿⡿⠃⠀⠀⠀⡂⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠂⠤⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⢺⣿⣾⣿⣿⣧⡀⠀⠀⠀⠁⢀⠔⢁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⢯⣥⣧⣿⣼⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣾⠿⠿⠿⢾⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠎⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣁⠀⠀⠀⠀⠀⢀⡈⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠘⠓⠀⣩⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣭⣲⠀⠀⠀⠀⠀⢀⢰⠀⠀⠈⠉⠉⠉⠉⠉⠉⢩⡷⠚⠒⠐⢄
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⢹⠁⠑⠀⠀⠀⢸⠸⡀⢀⠀⡠⣢⣭⣭⡑⠄⠈⠁
⠀⠀⠀⢀⠁⠀⠀⢤⠀⠀⠀⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠸⡀⠉⡊⠸⠀⣿⣿⣿⣿⠀⠀⠄⠀⠠⢂⠊
⠀⠀⠀⠸⠀⠀⢾⣿⣷⠀⠀⠸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢠⠆⠔⠁⠀⠀⠀⠀⠑⢲⠀⠀⠑⠌⣛⣛⠡⠂⠀⠈⣁⠔⠁
⠀⠀⠀⠀⠂⠀⠀⠩⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⣦⡶⣤⡶⣤⡶⣶⠶⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠖⣚⣒⡒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣤⣯⣼⡴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠿⢿⣿⣟⣋⣽⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⣄⡀⠉⠋⣤⣿⢷⣄⡀⠀⢦⡀⠀⢎⠃⠀⡀⣀⣘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢰⡾⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⣠⣄⣬⡄⠘⣒⣹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⢩⡟⠛⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠚⠉⠉⠀⠀⠒⠲⠤⣀⣀⠤⠀⠀⠀⢀⠀⠀⠠⠋⠀⢠⢿⡏
⠀⠀⠀⠀⠀⠰⣡⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⢀⠀⠙⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠚⠳⢤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡁⠐⠚⠉⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⣥⣸⣧⠐⠀⡂⠀⠠⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠉⠁⠀⠈⡽⠳⢄⡀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⡀⡞⠁⠀⠀⠈⠓⠦⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠆⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠂⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⠴⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡀⠀⠀⠀⠀⠀⠀⣠⣠⠴⠶⠖⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣭⣥⣶⣖⣶⣶⣬⣵⠀⠀⢀⣀⣴⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⢿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⠁

⠀⠀⠀⠀⢰⡟⠁⣠⡾⠋⠁⢀⣀⣤⣴⣶⣿⡿⢷⣤⣀⣀⣉⣻⣿⣿⡑⢶⣿⣿⣿⠁
⠀⠀⠀⠀⢹⡇⠐⣿⡅⠠⢺⣿⣿⣿⣿⣿⠏⠀⠀⠙⠻⣿⣿⣿⣿⣭⡿⠋⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠙⢦⡙⢿⣦⡈⠻⣿⣿⣿⡏⠀⣀⡀⠀⠀⠀⠀⠉⢉⣁⡀⠀⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⠛⠷⣮⣿⣿⣿⣀⠀⠉⠳⠀⠀⠀⠘⠉⠁⢀⠀⣸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⠙⣿⣿⣿⠓⠖⠂⠀⠀⠀⠀⠒⠞⠋⠀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⠺⢎⣧⡀⡶⣶⢈⣁⣁⡀⠀⢀⣴⡱⠖⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋⡰⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢠⣾⣷⣄⣀⠀⠀⠀⠀⡄⣾⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠠⠤⠤⢤⣌⣉⣛⢶⢞⡼⠋⠗⢦⡤⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⣿⡿⠁⠀⠀⠀⠐⠒⠲⢤⣙⣶⡛⠛⠋⠀⣸⣹⣿⣑⣿⣿⣿⢶⣦⣤⣀
⠀⠀⠀⠀⠀⢠⡿⣿⣧⣀⣽⠁⠀⠀⢀⡴⢺⣯⠽⡛⠋⠉⠁⠀⢀⠔⣥⡿⢦⣿⣿⣿⣧⣠⣿⡿⢿⡀
⠀⠀⠀⠀⠀⢸⠃⠈⢿⣿⡟⠀⠀⢲⢿⣿⣎⣹⢷⣏⣔⢒⡔⢲⣉⡶⢏⣱⣾⣿⢿⣿⣿⣿⡿⠁⠸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠈⢿⣿⠀⠀⢰⣠⣿⣿⣷⣶⣍⣟⢛⡟⢻⣉⣷⣾⣿⣿⣧⣠⣿⣿⡿⠁⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠘⣿⣿⣯⣁⠀⢀⣀⣀⣀⣀⣀⣀⠀⢻⣯⣤⡉⠛⠧⣄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣴⣒⣒⣲⣶⠚⠛⠛⠛⠋⡉⠀⠀⠀⠱⣄⡿
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠀⢹⣿⡋⢙⣿⣿⠿⣿⣿⣿⠟⢿⣿⣯⣭⣤⡄⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⢸⣿⣷⣿⣿⣷⣤⣾⣿⣿⣦⣾⣿⣿⣿⣦⣬⣽⣿⣿⠃⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⠀⠀⠀⠀⢿⡁⣙⣿⣿⣿⣟⠁⣻⣿⣿⣿⡋⢙⣿⣿⣿⡏⣧⠀⠀⠈⡇
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣟⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣾⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣏⡟⠉⠑⢄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠛⠛⠛⠋⠙⣿⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣾⣿⣃⣀⣀⣀⣠⣤⣀⣰⡄⢸⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠁⠀⢠⣴⣶⣖⡤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠉⠚⠻⣧⣀⠀⢀⠀⡠⠊⡼⠀⠳⡤⡀
⠀⠀⠀⠀⠀⠈⣿⣿⡇⢿⠳⣌⠻⣿⣿⡁⢸⢷⡀⠀⠀⠀⠀⢀⢀⡴⠒⡜⢁⣼⡷⡠⠀⠀⠘⡷⣤⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣮⡑⣿⡁⠹⢿⠏⠀⠈⠀⠀⠀⠀⠀⠀⢁⠴⣶⠴⠛⠛⠛⠓⠀⢄⠀⠘⠎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠉⠛⠢⣄⡘⠃⠉⢰⣾⠂⠁⣤⣄⡈⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⢃⠀⠡⢽⣼⣶⣬⡛⣻⣷⣶⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⢻⣿⠟⢷⣤⣄⣀⣀⠀⢀⣠⣤⠤⠐⠃⠀⠀⠀⠀⠙⢶⣄⠀⠉⠙⠻⡈⠿⣷⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠉⠈⣿⡆⠀⠀⠉⠛⠛⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠀⠀⠘⠶⠋⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⢷⣠⠀⠸⣿⠀⠀⠀⠀⠀⡼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣵⡆⠀⠀⢇
⠀⠀⠀⠀⠀⢀⣠⠟⢆⠀⠀⠙⢷⣴⣿⣦⠀⠀⠀⣼⡁⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣷⣟⣠⠴⠛⡆
⠀⠀⠀⠠⠚⠉⠀⠀⠈⢣⡀⠀⠀⠈⠉⠛⠧⣄⣰⠃⠉⠆⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢰⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢰⣶⣆⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠠⣄⠀⠀⠀⢸⣻⢶⡠⡀⢹⠄⠀⠘⠇⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠐⠀⠠⡟⠀⣤⠂⠈⡇⠀⠀⠘⣿⡗⠋⠡⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣵⣄⣀⡀⠀⠀⡀⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢨⣍⣀⣀⡀⠀⠀⠀⢈⣻⣍⣏⣐⠞⠁⠀⠀⠀⣿⣇⠶⢦⠠⠈⠳⠈⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⠖⠂⣤⠄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⢸⣡⣍⠁⠿⢀⠀⠀⠈⠠⣿⠋⠁⠀⠀⠀⠀⠀⢺⣇⠳⣀⠶⠦⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⠁⠖⡔⠁
⠀⠀⠀⠀⠀⠀⠸⣿⢿⡷⠾⠽⠶⢶⠖⠈⣻⠀⠀⠀⠀⠀⠀⠀⣾⣄⢴⣟⡀⢠⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠈⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠓⠂⠀⢶⠀⢠⠋⡏⠀⠀⠀⠀⠀⠀⠀⡿⣟⣟⠋⠀⠻⠄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢸⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠟⠳⢴⡀⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⠸⡏⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣄⠀⠣⡖⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⠠⠃⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠄⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡛⠛⠓⠓⠛⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⢀⠠⠐⠀⠀⠡⠄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⠠⠠⠄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠛⠉⠀⠀⠈⢦⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣤⠀⠀⠠⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⠒⢀⡬⠷⣄⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡛⠳⠖⠉⠙⣣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⠛⠋⠉⠁⠿⠀⠀⠀⠀⠀⠀⣄⢦⢀⣠⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠯⢅⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠎⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣧⣄⡰⠂⠁⠈⠣⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⡀⡀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠹⡀⠶⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡀⠀⠈⢀⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠶⠄⠸⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⢿⠿⣿⣦
⣿⣿⣿⣿⡈⢁⡀⠙⠻⢿⣿⣿⣿⠶⢾⣧⣤⣶⣶⣶⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣾⣿⣷⣦⣄⣯⡿⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣤⣄⡀⠀⠀⠀⢠⠿⡿⣿⡿⢿⠿⢿⡿⠿⠿⠿⣿⢿⡿⠿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿
⣿⠙⠻⢿⣿⣿⣿⣿⣭⣽⠃⠀⢠⣤⡦⡉⠁⢀⡼⢥
⣿⣿⣷⣦⠬⢿⣿⣟⣛⣻⡄
⣿⣿⣿⣿⣿⣴⣤⣍⣿⣿⠃⠀⠀⠀⠀⠀⠠⠄
⣿⣿⣿⣿⣟⡿⣿⣯⠝⢿⡀⠀⠀⠀⠐⢶⣶⡶
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⣦⣄⡀⠀⠀⠉
⣿⢟⣿⣿⣿⣿⣿⣿⣿⣷⡄⠻⣿⣿⣷⣂⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣷⣄
⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⢿⠿⠟⠛⣛⣂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠰⠆⠤⣴⡛⠻⠿⠭⠿⠛⠂⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠐⠀⠐⠻⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠐
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣶⣮⣓⠀⠀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⠤
⣏⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⣼⠶⠀⠀⠠⠤⠄⠀⠘⠂
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣾⣿⣏⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⠋⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⢶⡟⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣿⠃⠀⠀⠀⠀⢀⣺⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣏⠀⠀⠀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⡄⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠑⠀⠁
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣟⣛⣿⣿⣟⣟⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⢯⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡻⠿⠿⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⢀⠀⠻⢿⠟⣻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣋⠀⢀⡀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡤⠀⠀⠀⠘⣧⡙⠛⠻⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠉⠅⠈⢄⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⢀⡈⣷⣼⣿⣷⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠠⢚⣿⡟⣾⠟⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⠀⠀⠉⡸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⡄⠄⠀⠐⠀⠀⢠⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠉⢉⡟⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⠁⠸⡀⠸⠀⢀⠱⡄
⠀⠀⠀⠀⠀⠀⣠⡾⡏⠀⠐⠄⠀⠸⣟⠀⠀⠀⠀⠠⠑⡄⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⡁⣘⠀⠀⠱⢠⠀⠀⠀⠘⢄
⠀⠀⠀⢀⡴⠛⠁⠀⢇⣀⣀⠈⠢⡄⣿⡇⠀⠊⠁⡴⠗⠉⢀⠴⠂⠀⠀⢑⠐⠂⠀⠠⠄⢧⣘⢄⠀⠀⠀⢢⡁⠀⠀⠈⣆
⠀⠀⢀⡞⠀⠀⠀⠠⣄⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⢡⠄⠾⠃⠈⠢⠖⠈⠘⠲⠶⣤⣄⡀⠀⠈⠻⠛⡷⢶⣄⢙⠖⣂⠀⠘⡀
⠀⠀⢸⠃⠀⠀⠈⠄⠈⠙⠦⣄⠀⠀⠀⡇⠀⠀⠋⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠈⠉⠛⠶⠦⠴⠃⣀⠗⠁⠀⠀⣁⡴⡀
⠀⠀⢸⠋⠉⠻⢯⢰⠀⠀⠀⠈⠛⢦⣰⠁⠀⠀⠈⠢⢽⣒⣒⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⣠⡴⠞⠁⠀⠘⢄
⠀⠀⣾⠛⢶⠄⠀⢸⢰⣄⠀⠀⠀⠀⡏⠀⡀⢀⣎⣉⠑⣶⠒⠉⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠀⣤⠶⢻⡍⢰⠀⠀⠀⠀⠈
⠀⠀⡯⠚⣁⣤⠤⣼⣧⡉⠀⠀⢀⡸⠀⠀⢇⠈⠉⠠⠀⠛⠀⢀⣀⠨⠤⠄⢀⡀⠀⠀⠀⠊⠀⠋⠋⠁⠀⣿⠁⢸⡄
⠀⠸⡆⠨⠖⠹⠛⠁⠀⠀⠠⣀⣁⠀⠀⢀⣒⠛⠘⢓⣚⡁⠰⡄⠉⣐⡖⠀⠀⠀⢠⠏⠀⠀⠒⠀⠤⠤⠀⣿⠀⠈⠁
⠀⠀⢿⡀⠀⠀⠀⣀⣠⣄⡄⠛⠥⣈⣉⡉⠁⠤⠉⠀⠠⠤⢔⣁⠰⠟⡀⠀⠀⠒⠉⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠂
⠠⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⢀⣾⣯⣬⡁⠐⡀⢀⢀⣤⣻⣧⡄⠀⠀⢀⠀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢹⡛⠁⡿⠿⠿⠿⠿⠉⠛⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣐⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⠄⠃⣾⡿⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠑⠂⠉⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠴⠒⠚⠂⠀⠀⠀⠀⢀⡀⠀⠘⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀
⠀⠀⠀⣠⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⡀⠀⢀⣠⣤⣤⣶⣶⣤⣄⡀⣼⣤⣤⣀⣀⣠⣤⣤⣤⣤⣠⣶⠖⠲⢶⣶⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠋⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢴⣿⡌⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⢸⡇⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢇⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⣼⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣉⣭⣫⣨⣉⣽⣉⣽⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠉⠛⠙⢿⣿⡿⠛⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⡿⡿⠛⠿⠻⠏⠀⠀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⣼⣿⣿⡟⠀⠀⠀⠠⣴⣤⣶⡾⠛⡿⠻⣷⣄⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿
⢠⡿⠋⠈⠀⠀⠀⣀⠀⢀⣅⡈⣠⣄⣰⣶⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣸⡇⠀⢀⣰⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣿⣄⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄⠀⠀⠚⢹⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣾⣧⠶⠛⠙⠶⣄
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠠⠞⠻⠿⠁⠀⠀⠀⣨⠟⠁⠀⢀⠔⢲⡌⠳⣄
⠀⠀⢻⣿⣿⣿⡿⠉⣉⣉⣉⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⡴⠁⢠⠞⠁⠀⣈⡓⢦⡀
⠀⠀⠀⠹⣿⣿⡇⠸⠋⠈⠙⣷⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠎⠀⣠⠆⠂⠉⠀⣀⡹⠆⢙⠻⣟⠒⠦⣄⡀
⠀⠀⠀⠀⠙⣿⣧⠀⠀⠐⠻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⡴⠃⠀⢠⠔⠋⠀⠀⣠⠿⡄⠈⠳⣄⡀⠙⠲⣄
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠁⠀⠀⠀⠐⠃⠀⠠⠖⠋⠀⣠⠃⠀⠀⠈⠙⢦⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣤⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⢮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⡀⠀⠀⠈⠉⠛⠿⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠙⠛⠶⣦⣄⡀⠀⠀⠀⠉⠙⢛⣿⣶⣶⣶⡶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⣄⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣰⠁⠘⣦
⠀⠀⠀⠀⠀⣴⠟⣁⣤⣤⣤⣀⠀⠀⠀⠉⠻⢶⣄⡀⢀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣦⣀⠀⢰⠏⠀⠀⠀⠀⢀⡴⠁⠀⠀⠘⣧
⠀⠀⠀⠀⣼⡿⠛⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣬⡿⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣿⣿⠇⠸⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢰⡟⢀⣠⠴⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠙⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⣿⣶⠟⠁⠀⣀⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧
⠀⠀⣸⡟⠁⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣷⡀
⠀⣴⠟⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⣤⣀⣙⣿⣦⣤⣀⣤⣼
⣼⡏⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣭⣽⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠁
⢿⡇⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠉⠉⠉⠉
⠘⢿⣄⢸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠻⣾⣿⣿⣿⣿⣷⣦⣤⣄⣠⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢈⡟⠀⠀⠀⠙⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⠴⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢁⣴⠋⠀⡎⠀⠇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⠁⢀⣼⣠⡴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡰⠀⠀⠀⠀⠐⠄⠐⠀⠒⢭⡀⠐⣿⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⢈⠛⠄⢄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡿⠀⠀⡶⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠈⠒⢠⣀⠀⠀⠀⢀⡞⠀⠘⢱⠿⠌⢀⠚⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⢀⡖⠋⠀⠀⠉⠃⠘⠊⠙⠁⠀⠈⠂⠀⠉⣡⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠄⠀⠀⠘⠀⢹⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣜⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠻⡄⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢰⣴⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⢈⣄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⣶⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣦⣀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡄⢨⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣼⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⢀⡴⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠀⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣄⣀⣀⣀⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠉⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢀⠞⠁⢠⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠄⠀⠠⠴⣊⠀⢶⡔⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢘⠓⠀⡄⠀⠀⠀⠀⠀⠀⡸⠀⣸⠃⠀⡤⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠘⠢⢤⡀⠀⠀⣠⠇⠀⡡⠟⣁⡀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢰⠋⠀⠀⠀⠁⠈⠁⠉⠀⠀⠁⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡷⡀⠘⠓⠒⠀⠀⠀⠀⠀⠀⠐⠒⠚⠃⢠⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⡃⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢱⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣲⣿⣿⣿⣷⣤⣄⣀⣠⣴⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⣸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⢀⠁⠀⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⢊⣉⣥⡬⠤⠴⠟⠛⠀⠀⠀⠈⠙⢿⣿⡀⠀⢐⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣡⡴⠖⠋⠉⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠤⣌⢾⣿⣄⠁⣄⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣴⠟⢁⣠⣴⣾⢟⡵⢫⣿⢿⣛⢿⣯⣝⣛⠶⣦⣄⠙⢧⠙⣦⣠⣀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⢃⣴⣿⠟⣩⣶⠟⣡⡟⠹⣧⣝⠿⣶⣮⣝⡛⢶⣝⢷⡈⢧⠘⣦⢈⠇⠀⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⡿⣋⣵⠿⣋⣴⡾⠋⠀⠀⠈⠻⠿⢶⣭⣟⣛⡻⢾⣿⣷⣸⡆⢹⡗⢦⣄⠉⠀⠈⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣞⣭⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⡉⠉⠙⠙⢿⡿⠳⡌⣷⠀⢹⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡄⡴⠛⢻⡏⠉⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⣰⣃⣿⠔⠁⣀⣠⠤⠚
⠀⠀⠀⠀⠀⠀⢳⠑⢄⡸⣇⠀⠐⠂⠤⠶⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⣔⠋⠉⠁⠀⠀⢠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠠⠤⠶⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠟⠀⠀⠀⠁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠞⣿⠂⠁⠹⣿⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢰⣆⠀⠈⠙⠶⣤⣀⣀⠀⠀⠀⣴⠋⣁⣉⣉⠁⢀⣀⣀⣨⠗⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣷⠀⠀⠀⠀⠀⢈⣉⡉⠿⠿⢧⡾⠥⠤⣀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢹⣷⣤⡀⠀⢸⣧⣴⣶⣶⣾⣿⣿⣶⡶⢾⣄⣀⡀⠀⠈⣳⣄⣀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠀⠈⠛⢷⡼⡇⢀⣀⢀⠈⠁⠀⠀⠀⢠⠖⡶⠛⠃⠉⡏⠈⠉⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠉⠰⢏⣤⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⣳⠄⠀⠀⠀⠀⢸⡀⣸⣤⢀⢠⡏⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠸⡇⠳⣄⠀⠀⠀⠀⢀⣀⣧⠖⠒⠋⠀⠀⠀⠀⠀⢈⡭⠐⠃⠀⠀⠈⠓⠶⣶⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢳⣦⣄⣤⣬⠿⠉⠣⣄⣀⣀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡍⠉⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠻⠇⠀⠀⠀⣿⠉⠉⠉⠉⢹⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣸⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠺⠃⠀⠀⠀⠈⠻⠶⠤⠞⠃⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⣤⣤⣀⣀⣀⣀⣇⠘⠃⠀⠀⠀⠀⠀⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠉⠙⢿⡉⠉⠉⠉⠉⠛⣿⠛⠉⠉⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣿⡆⠀⠀⠀⠀⣿⣦⣤⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣩⣯⣻⣿⡟⠈⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡟⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⢀⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⢠⡀⠀⠀⠀⠀⠐⠳⠻⠿⠟⣺⣿⡛⣫⣧⣬⣥⡎⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⣦⣤⣀⣀⣀⡀⠀⠀⠀⠈⠙⠙⠻⠿⠿⢿⠳⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠳⠀⠀⠀⠀⠀⠛⠷⣄⠀⠀⠀⠈⢣⣄
⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠓⠦⡀⢰⠙⢺⠈⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⢿⣷⠄⠀⢀⣀⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠒⠘⠁⠉⠉⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⣏⣀⣤⠤⠀⠀⢀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠢⢄⣀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⡆⠀⠉⠉⠁⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢸⠁⣠⠔⠊⠉⣉⡁⠒⢤⣠⢠⠊⠁⠀⠉⢉⡩⠕⠛⠒⠓⠒⠢⣄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡎⠀⡇⠀⠀⣀⣀⠉⠓⢄⠙⢾⡆⠀⠀⠀⠯⠤⠴⢲⡒⠖⠒⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢰⠃⢀⠇⠀⠀⣀⠈⠙⠢⣀⠉⢭⢞⠀⢀⠤⠐⠊⢉⣀⠤⣤⠤⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡼⠀⢸⠀⠀⠀⠤⢭⠕⠦⠤⠓⠚⠀⠳⠈⠉⣉⡉⠴⠒⠉⠀⣀⡠⠄⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢠⠇⠀⡎⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠒⠚⠭⠥⠀⠀⠤⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠸⠀⠠⡇⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢂⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⢢⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⣒⣯⣽⣵⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⣾⣿⣿⣿⣿⣿⣿⠿⠗⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠈⠉⠉⠻⡶⣶⣦⣤⣤⣤⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠑⡎⠩⣿⣿⣿⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠰⠖⠂⠀⠀⠀⢞⣁⣘⣿⣿⣿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠃⠀⠀⠈⠋⠀⠀⠀⢸⣽⡿⣛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⣠⣶⣅⠀⠀⠀⠀⣠⠏⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠂⠐⠂⡆⠀⠀⠀⠀⠀⡴⠚⠀⠐⠊⠁⠣⡰⠙⠃⡸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣬⠃⠀⣀⠀⠀⠃⠀⠀⣀⠴⠞⠁⠀⢀⠐⠢⠀⢠⠇⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢀⣹⣄⣈⣀⣵⠒⠔⠉⠀⠀⠀⠀⠀⠎⠀⢠⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠄⠀⠀⠀⠀⢙⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡉⢻⡏⣾⣿⡇⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠊⠀⣀⣤⠴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠉⣻⣿⣼⣿⣿⠁⠀⠀⢸⡄⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠁⢠⠎⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⢸⠁⠙⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⢢⠀⠈⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⡴⠁⠀⠀⠀⠀⣰⠏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⢀⠀⢧⠀⠀⢺⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣇⣠⣖⣁⣤⡜⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⢀⣧⡴⠖⠒⠒⠒⠢⠤⢀⡀⠀⢸
⠠⣄⣀⡀⠀⠀⠀⢀⣸⣦⣤⣤⡔⠒⠙⠛⠉⠉⠁⢸⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸
⠀⠀⠀⠉⠙⣢⠞⠁⠀⠀⠀⠀⠉⠙⠓⠦⡀⢀⣀⣋⣀⣀⣘⠀⠀⠀⣀⡤⠤⠂⠀⠀⠑⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠀⠀⠀⠳⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠞
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠳⢦⣤⣀⠀⡠⠤⠀⢸⣅⡧⠠⣤⣾⢿⣛⠛⠋⢉⡉⣉⢉⡟⠛⠛⠋⠉⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠛⠦⡀⣀⣠⠼⠒⠋⠁⠀⢀⣿⢠⣆⣼⣷⠿⣾⠃⢀⠂
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⢀⣀⠤⠶⡞⣹⠏⣾⣿⠻⠏⠀⠁⠀⢸
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣠⠋⠀⢀⡤⠖⠋⠉⠀⢲⡄⣷⠏⠀⠀⠁⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡿⠀⠀⡆⠀⠀⠀⠤⠤⠤⠄⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣠⣤⠴⠒⠋⠉⢁⣀⠤⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣄⣀⠀⠀⢀⣉⠉⠙⠳⢦⣄
⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⣶⡋⠁⠀⠀⠀⠀⠀⠀⢴⡄⠀⠠⠤⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠶⠶⠦⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠁⢀⣀⣀⣤⣴⠞⠋⡀
⠀⢠⣭⠿⣿⠷⠦⠤⢤⣤⣤⣤⣄⣠⣤⣄⠀⢀⣀⣀⣀⣀⣠⣀⣤⠤⠤⠤⠴⠖⠒⠚⠋⠉⠻⠋⠁
⠀⠀⢀⡆⠉⠙⠓⠒⠒⠠⠴⠶⠶⡤⠄⠀⠀⠴⠲⠐⠀⠀⠀⠀⠤⠖⠠⠀⠀⠀⠉⠀⠀⣀⣀⣤⡤⠴⡖⠉
⠀⠀⠈⠇⠐⠒⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡴⠶⠶⠞⠛⠋⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠃⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⠀⢸⠇
⠀⠀⠀⠀⢿⡔⠀⠁⠀⠀⢀⠤⠤⠤⠄⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁
⠀⠀⠀⠀⢹⡟⠦⢤⠀⢀⡎⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠉⠐⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⠀⠀⠀⣐⠶⠖⠷⠦⣤⢄⣀⣀⣀⣠⣤⣤⣤⣤⣤⡔⠚⠒⠉⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⡀⠈⠀⢀⡴⠋⠁⠀⠀⠤⡄⠀⠉⠉⠲⢄⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢻⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣧⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠰⠁⠀⢸⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠂⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠤⠐⠂⠉⣁⣤⠌⠒⠒⠲⠖⠛⠁⠀⠀⠀⠐⠀⠀⠄⡁⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⡀⠀⠘⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⣠⠟⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠐⢧⣄⣀⣐⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⠶⠶⠶⠖⠒⠒⠊⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠚⠛⠋⠉⠲⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡶⠈⢁⠸⠿⣶⣶⣀⣤⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⠟⣩⠀⡀⠖⠒⠚⣛⣉⣬⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠾⠃⢈⣡⡾⠟⠛⠓⠛⠻⠛⠉⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⡠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢁⡽⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⡎⣁⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⡇⢠⡇⠀⠀⣠⣴⠶⠛⠋⠀⠀⠀⠿⠢⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣏⠹⠇⣸⡇⠀⠈⠁⢠⣤⡤⠀⠀⠀⢶⣶⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣧⣰⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠈⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⣢⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⢿⣦⡶⢧⠀⠀⠀⠀⠀⠀⠀⢀⣦⣠⣄⡀⠰⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⢀⡴⠿⡉⠀⣰⠟⣧⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠹⣯⣽⠁⠀⢀⡴⠟⠧⠶⠀⠀⢀
⠀⠀⠀⢀⡴⠋⠀⠀⢠⡼⠃⠀⢿⣧⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⡐⠋⠀⠀⠀⠀⠀⢀⡠
⠀⠀⣠⠟⠀⠀⠀⠀⠈⠁⠀⠀⢸⡿⣆⠈⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠛⠙⠁
⠀⣴⠏⠀⠁⠀⠀⠀⠀⣤⠀⠀⠸⣇⠹⣧⡀⠈⠛⠿⣷⣶⣤⡀⠀⠀⠀⠀⠀⡉⠷⠶⠶⣤⡀⢄⣀⡀
⠈⠁⠀⠀⠀⣠⣴⠾⠋⠙⡆⠀⠀⢿⡄⠈⠻⣶⣤⡀⠀⠈⠙⣷⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⠙⢦⣤⡄⢀⠔⠈⠉⠲
⠠⠤⢤⣤⡾⠋⠁⠀⠀⠀⢠⠀⠀⠈⢿⡀⠀⠈⠙⠿⣦⡀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢏⠙⣿⠁
⠀⢀⡀⠈⠻⣦⡀⠀⠀⠀⠘⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡴⠎⢸⠇⠈⠁
⠀⠻⣿⣦⠀⠘⣷⡄⠀⠀⠀⠙⡀⠀⠀⢻⣆⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠻⣷⠀⠸⣿⠀⠀⠀⠀⢣⡀⠀⠀⣿⣧⡀⠀⣠⣿⡇⠁⠀⠀⠀⠀⠸⠃⠀⠀⠀⢸⡇⠀⣽⡇⠀⠀⠀⢀⠈
⠀⠀⠀⠀⢹⣇⠀⣿⡇⠀⠀⠀⠘⡇⠀⠀⢸⡟⢿⣶⣿⣿⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡞⠀⠀⣿⡏⠒⠒⠂
⠀⠀⠀⠀⠀⣿⡀⢸⣿⠀⠀⠀⠀⠇⠀⠀⠈⣿⠈⣻⣿⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣼⠁⣠⠾⠈⠇
⠀⠀⠀⠀⠀⢸⣧⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣾⡿⢉⢷⡄⠀⠀⠀⣠⠎⠑⠀⠀⠸⣇⠘⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠟⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠹⣦⠙⢆⠀⢰⡅⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⢀⠀⠀⠀⢾⣿⠀⠀⡇⠀⠀⣤⣼⡟⠀⠀⠀⠹⣧⡈⠳⣹⣇⠀⠀⣴⡾⠟⣿⠀⠀⠀⠀⠀⠸⣧
⠀⠀⣀⣀⣀⣀⣀⣀⣸⣿⡆⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠘⢿⣤⣿⢿⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠚⠛⠋⠉⠛⣉⣿⡿⢻⣇⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⣠⣾⣿⣏⣥⣶⠆⢻⡄⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⢰⣿⣿⡿⠛⣩⠋⠀⣸⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠄⢀⣾⡿⠁⠀⠀⣾⡇⠀⣀⣀⣀⣀⠀⠀⢻⡄
⠀⠀⣼⠿⡟⠁⡘⠁⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⣶⢆⣾⡟⠀⠀⠀⢠⣿⣤⠾⠛⠛⠛⠛⠛⠆⢸⡇
⠀⠀⡟⠀⣤⡄⠃⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡟⠲⢁⣾⡟⠀⠀⢀⣤⣾⠿⠷⠆⠀⠀⠀⠀⠀⠠⡀⢿
⠀⠐⠀⢰⣿⠛⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⢁⣾⡟⢀⣠⣴⠟⠉⠀⠠⣤⣀⣀⣀⠀⠀⠀⠀⠁⣿
⠀⠀⠀⣾⡿⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢠⣿
⡀⠀⡀⣿⠃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠁⠀⠁⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠛⠶⢤⣤⠀⠀⣠⣿⠇
⠀⠸⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢠⡀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⢀⠈⢦⠀⠀⠀⠀⢀⣀⣀⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⢸⠀⠀⢃⡀⣠⣾⠟⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⢹⡇⢁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⢀⣿⣦⣴⣯⣿⠏⠁
⠀⠀⠀⠀⠈⢿⣄⠣⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⣀⣴⠟⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⣀⣴⣿⢛⣁⣤⣤⣴⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣠⠒⢆⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢟⣭⡻⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣾⣤⣤⣤⣷⡄⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠛⠛⠛⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⢿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣠⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣳⡿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠟⣋⣽⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠞⠋⢁⣡⣴⣴⣿⣿⣿⣿⣷⠘⣷⡀
⠀⠀⠀⣠⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⢀⣴⠂⠀⣴⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⠃⠀⠠⣈⢛⣿⠂⠁⠀⢀⣀⠲⣾⣿⡟⣿⣶⠊⠉⢀⡀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠘⠛⠉⠙⠂⠀⡃⠀⠀⢀⣈⣯⡾⣿⣿⣿⠠⡾⠃
⠀⠀⠀⢹⣿⣿⣿⣿⠟⣛⠻⢿⣿⣷⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⡋⣡⣤⢀⣠⣶⡿⢿⣿⡿⠟⢠⣷⠁
⠀⠀⠀⠘⣿⣿⣿⣿⠘⠉⠓⠀⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⡟⠛⠋⠂⠀⠳⠈⠁⠀⠀⠙⢃⠀⠠
⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀⠚⠻⠀⠀⠀⠀⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠉⣥⠄⠀⠀⠠⠄⠀⣀⣀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⣶⡄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠉⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣟⠀⠀⠀⠙⠓⠶⣶⣶⣤⠔⣀⡀⠰⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠓⠒⠢⠤⠒⠋⠉⠀⠢⣤⣄⡀⠀⠀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠲⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠉⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠁⠆⡰⡄⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠒⠘⠸⠄⠀⠀⠀⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠄⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⠢⢆⣀⣠⣄⠀⣄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠂⠁⠁⢀⡜⠀⠠⡷⣜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⢠⡶⠒⡾⠿⠿⠃⢀⠀⠁⠸⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢀⠙⢆⣀⠀⠴⠤⢮⠐⠂⠓⠂⢸⠀⠁⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⠿⢃⠞⠉⠉⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⣀⠀⠉⠁⠃⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⠀⠀⠀⢈⠀⠀⠰⠒⠂⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⡤⠀⠀⠀⢋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠑⠒⠒⡆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⠌⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠿⠁⠀⠀⠀⠀⠀⠸
⣟⣛⣿⣻⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣛⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣩⣭⣽⡇⠀⠀⠀⠈⡁⢀⠈⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡾⠟⠉⠈⠏⠀⠀⠀⠀⢋⡬⠀⢰⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠠⠄⠈⠀⠀⠀⠀⠀⠉⣽⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⣤⡴⠐⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⢀⠀⠴⡀⠀⠀⠀⣀⣿⣿⣶⣯⡛⢿⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠃⣄⠀⠀⢀⡰⠁⠀⠀⢱⣿⡟⠙⣿⣿⡏⠸⠿⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⡀⠀⠀⠀⠛⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⢀⣤⣶⣿⣦⠬⠞⣆⠀⢀⡠⢖⡿⣿⡿⣿⢧⠀⠀⡠⠒⠦⣇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⠀⠴⢀⣾⡽⣿⣿⣿⣿⣀⣀⣶⢞⡽⠁⡼⢱⡟⣧⠸⡎⡇⠸⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⢀⣾⡏⢻⠿⠻⡟⠛⠿⠿⢷⠏⠄⠼⠡⣼⠀⣧⢀⡗⣾⠐⢣⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⢀⠈⠋⠣⠆⠀⠀⠀⠀⠀⠰⡈⡹⢂⣤⠾⣿⠀⢸⢺⡇⢻⡁⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡟⣿⣿⠟⡖⠒⠖⠲⠶⠤⣭⠟⠉⠈⣇⣿⠀⣿⠀⡷⢸⡇⠀⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣼⡿⠟⠁⢸⠇⢠⠀⡠⠎⠀⣷⠠⡀⠰⠤⢽⠿⠯⠭⠿⠭⠥⢤⡧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠘⣀⡐⠈⠀⠀⠀⢹⠀⡅⣴⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⢸⡞⠷⠛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⠞⣋⡙⠛⢉⠛⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣨⣤⣴⣎⢹⣖⢦⡈⠣⡈⢳⣄⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣶⣿⣿⣿⠀⢿⣷⣝⢦⠑⠈⢻⣷⡀⠑⢦⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣼⣿⣿⠟⠁⢻⣷⡈⠻⢿⣇⠁⠀⠀⠙⢿⣦⠀⠙⢦⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡆⣷⣿⠃⠀⠀⠘⣿⣦⣀⠀⠉⠓⢦⣀⡀⠀⠛⢷⣄⠈⣧⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡰⢱⣿⡟⠀⢀⣤⣶⣾⣿⣿⣮⡑⠂⠀⢈⣉⣁⣀⣀⣀⠙⣜⠂⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⠒⠀⡈⡁⣿⣧⠀⢹⢿⣿⣻⣿⡿⣿⣷⡖⢶⡖⢿⣿⣿⢿⣿⣌⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⢀⠄⢀⢸⣿⠇⠀⠀⠀⠉⠉⠁⢀⣿⣿⣿⡌⢿⡷⣬⣥⢤⣬⣉⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢺⡀⢧⣰⣿⠀⣀⣀⠀⠀⠀⢠⣾⣿⣿⡇⣇⠫⡻⣧⡻⡘⣿⣿⢱⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⣿⣸⣇⣩⣅⠀⠀⠀⢽⣿⣿⣿⣷⣈⠳⣍⡚⣿⣦⠈⠻⠧⣝⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⢿⣟⣩⡟⠃⠀⠀⢀⣼⣿⣿⣮⡳⡝⣿⡎⣿⣄⡀⠐⢦⠹⡝⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⢀⣀⣤⣾⣿⣿⡿⣿⣿⢧⣿⠃⣼⣿⣿⠛⣦⣷⣿⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠅⠖⠶⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⠻⣿⡟⠻⠋⠀⣿⣿⢸⣷⠀⢿⣿⣿⣷⣜⠺⣿⢘⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠐⠦⠤⣤⣈⠳⣇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⢹⣿⠀⠀⢰⣿⣿⡌⠻⢦⡈⠻⢿⣿⡿⣶⣽⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡒⠤⠤⣤⣬⡛⢿⡀⢀⡀⠀⠀⢰⣿⣿⣿⢿⣿⣿⣿⡧⣿⠀⠠⣿⣿⣿⡿⠶⢤⣼⣤⣤⣭⣽⣿⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⠶⢶⡦⢭⡟⣿⠛⡿⢿⣷⢿⣿⣼⢣⣿⣿⣿⣿⣿⠏⠀⣠⡿⠟⠁⠀⠀⠀⠀⢀⣠⠶⠛⢿⡇⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⣠⡾⠖⢻⡌⡇⢻⡿⣧⢻⣟⢸⣿⣿⣿⠟⣡⡶⠟⠉⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠻⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡇⠀⠀⢸⡇⣼⠃⡇⢷⢈⣿⣿⣷⣿⢸⢛⣯⠿⠛⠁⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⢀⡼⠁⣼⠁⠀⢀⣿⢧⢻⡀⠀⠘⣿⣿⣿⣿⣿⠞⠋⠁⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⡾⠀⢠⣿⡄⢀⡾⠉⠈⠾⣇⠀⢀⡿⢠⠿⠋⠀⠀⠀⠀⢀⣠⠶⠋⣁⣤⠆⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡼⠃⠀⣼⣿⣷⣯⠖⠀⠀⣶⠇⢀⣾⠕⠃⠀⠀⠀⠀⣠⠔⢋⣤⠶⠛⠉⠀⠀⠀⠀⢀⡠⠒⢩⠞⠁
⠀⠀⠀⣠⠎⠀⠀⢀⣿⠟⠋⠀⠀⠀⣼⠃⣠⠟⠁⠀⠀⠀⣠⠴⣋⡥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⣰⠋
⠀⠀⢠⡇⠀⠀⢀⡜⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣠⠔⠋⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣼⣃⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢓⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡭⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⣉⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠻⠥⣄⡀⣠⠔⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠠⠖⢒⣠⣄⣀⡀⢸⠁⣀⡀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣴⠯⡤⠀⠀⠀⣰⠃⠀⠀⠀⠉⠛⢮⣽⣿⠀⠀⠀⢠⠇⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⣲⣾⡏⠁⢀⣠⠴⢃⡠⠴⠒⠒⢦⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠉⢉⡒⢄⠀⠈⢧⡀⠀⠀⠀⠉⠁⡿⠚⠉⠀⠀⠈⠀⠀⢀⣠⠞⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠀⠀⠀⢙⣦⠤⠶⠒⠾⠁⠀⠀⠀⠀⠐⠒⠋⠉⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢠⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⠴⢻⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠟⢦⡀⢀⡠⠖⠛⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢻⡀⠐⠙⠓⠒⠉⢀⣠⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⡀⢻⡌⢦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠋⢩⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⡿⣍⠉⠉⠉⠁⠀⠉⠉⠙⣆⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⡇⠈⠳⣄⡴⣄⠂⠤⢄⡴⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠠⠷⡄⠀⠀⠀⢀⣜⡗⣧⠴⢾⡋⡟⠢⢝⡲⢼⣧⡞⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢦⢀⢼⣅⡀⠉⠙⠓⠲⠛⠧⠤⣀⠈⠙⠚⠻⠿⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢤⣤⣀⣀⣀⣈⠛⠁⠀⠉⢙⣶⠦⢤⠀⠀⠒⠾⡁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢹⢹⠉⠉⢯⠀⠀⢈⡦⠤⠴⠊⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠐⠲⠚⠾⠖⠂⣸⠀⠀⠀⠙⠲⠤⣄⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣀⣀⣀⣤⢤⡞⠢⣤⢿⠒⢦⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣗⡽⢮⣄⣀⣙⣉⣼⣴⣻⣴⣷⣺⣿⣶⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠋⠉⠉⠙⠲⢤⣀⠀⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⡜⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈⠓⢤⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠤⠤⠤⠤⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣀⡀
⣤⠒⣚⣉⣉⣉⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣮⣭⣭⣽⣖⣲⣤
⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿
⣿⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⡿
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⡟⠚⠉⠉⠉⠉⠓⠦⡀
⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣾⢁⡠⠴⠒⠲⢤⡀⠀⠘⢆
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠶⠶⠶⠶⠤⠶⠒⠒⠒⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⢹⡀⠀⠸
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢀⣀⠀⢀⣤⢀⣶⢀⣾⣩⡇⣴⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣸
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢰⣿⣹⣇⣸⡏⣸⠿⢾⣏⣩⡾⠃⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⡤⠖⠊⠁⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣿⣉⣽⠋⠹⠷⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠟⠒⠒⠚⠉⠉⠀⢀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣼⣿⣴⡶⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣃⣠⠤⠤⠤⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢀⣰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢄⠀⠀⠀⠀⣀⣶⣿⣿⣿⡿⣶⣶⣦⣄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠛⠛⠛⠸⢿⣿⣿⣯⢠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣷⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⢄⠀⠀⠈⡷⠶⣦⡀⠀⠚⣩⣤⡄⠀⢺⡿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠘⠁⠀⠀⠁⠈⠀⠀⠀⠐⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⢸⣆⠀⣀⣀⣤⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⣾⣿⣦⠀⠂⠄⠀⢀⡠⠊⠀⣿⣿⣿⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⢤⠠⠎⠠⠤⠬⠉⢹⢷⣦⣴⠊⠁⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣁⣀⣳⡀⠀⠀⠀⡐⠀⣀⡜⢃⠀⠀⠀⠀⠀⠈⠶⠠⠐⢒⠂⠈⠉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⠒⠊⠩⠃⠸⣖⣂⣤⣄⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣴⣶⣦⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⣴⣿⣿⣿⣿⣷⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⣿⣿⣿⣿⣄⣩⠐⠒⠒⠒⠒⠀⢈⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠻⣿⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⣈⡙⢿⣿⢃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡁⠈⠛⠋⠹⠟⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠙⠂⠈⣼⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣴⣿⣿⣿⣿⣍⣿⣁⢈⡻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠅⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠂⠀⠀⠀⠀⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡤⠞⠁⠈⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠻⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⢀⡀⠀⠰⠾⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣦⡐⠾⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⣀⣠⣶⡶⠀⠀⠀⠀⠰⢶⣶⣄⠲⣦⣠⣤⣤⣴⣶⣤⣶⡤⣠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣿⣿⣿⣿⣛⣿⣿⣿⣶⣯⣭⣭⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⠉⠿⣿⣿⣿⣿⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠷⣤⡙⣿⣿⣿⣿⡏⠛⢉⣩⣭⣿⣿⣿⣶⢤⡀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠛⠛⠓⠎⢳⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡟⠀⠀⠛⠋⠙⠿⣿⣋⣿⣷⠄⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⢷⣦⡀⠀⠀⣼⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠋⠀⠀⠉⠓⠊⠉⠁⠀⢠⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⣀⡤⡤⠀⠰⣶⣄⡀⣀⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠰⠯⠉⠀⣀⠀⠀⠈⢻⡿⠿⠋⠀⠈⡓⠄⡀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣘⣦⡤⠴⠶⠖⠒⠚⠛⠛⠛⠓⠒⠚⠛⠻⠫⠥⢬⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠚⠛⠛⠶⠶⡕⡴⠖⠖⠒⠻⠓⠛⠙⠛⠻⠛⠛⠷⠶⢶⠦⣦⣤⣈⣉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⢀⣀⣀⠤⠤⢤⣤⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠲⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠠⠴⠖⠚⠉⢉⣉⠽⠒⢲⣧⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠠⠚⣟⡵⠋⠁⠀⣀⣴⣯⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⠉⠀⢀⡴⠋⠁⠘⢿⣿⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠙⠻⣟⣍⠁⠒⠒⠚⠛⠒⠲⢶⣶⣦⣤⣀⣤⠞⠁
⠀⠀⠀⠀⠀⡰⣻⠃⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⠶⠤⠤⠼⠿⠿⠿⠛⠋
⠀⠀⠀⠀⣸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢰⢻⠀⢻⡀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⣠⣶⣿⣇⠀⢚⢳⡄⢀⠀⢀⣠⠔⠁
⣾⣿⣿⣿⣿⡣⠨⡀⠙⢯⣛⣿⡟
⢙⢿⣿⣿⠋⠳⠄⢂⠀⣀⠈⢲⠃
⠀⠈⠉⠛⠀⠀⠀⢨⠜⠵⡾⠃