Wake Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠿⠿⣋⡵⠋⠉⠉⣛⠛⣿⣿⣿⣷⣼⠒⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠁⠀⠈⣿⡟⠛⡉⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⡟⠀⢨⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠈⠂⣠⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⢸⡸⣿⡿⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡴⣿⣿⡇⠀⠀⢠⣚⣢⡀⠀⠀⢸⣷⣿⠃⠀⢠⣄⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣧⠀⠀⠸⡛⠡⠇⠀⠀⢸⠿⠉⠢⠤⢼⣿⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⣿⣿⣿⣷⣤⢤⣠⡤⠤⠤⢖⣞⠈⡄⠁⠄⢸⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⠿⠿⠋⢖⣠⣦⣴⣧⣨⣄⣠⣄⣒⠐⠎⡼⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠿⠶⠛⠛⢿⣤⡀⠀⣀⣀⣀⣈⣻⣿⠗⠧⡠⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢊⣡⣤⣤⣤⣶⣶⣿⣿⣷⣿⣿⣿⣶⣿⣽⣻⡷⣄⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⢛⣛⣛⣋⣙⠛⠿⠿⠿⠿⠶⠶⠶⠦⣤⣄⡈⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠙⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣆⡠⡀⠈⠓⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⠀⠠⠓
⠀⠀⠀⠀⠀⡔⡏⠂⠀⠂⠀⠀⢰⣿⣿⣿⡿⣿⡿⠉⠙⠋⠁⠹⣧⠀⠉⢀
⠀⠀⠀⠀⠐⠈⡲⠇⠀⠀⣀⠀⣿⣿⣟⠉⠐⠀⠀⠀⠀⠀⠀⠀⠑⠮⠄⠀⢠
⠀⠀⠀⠀⠀⠉⠠⣄⠀⡠⠀⠣⣹⣿⣿⡗⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠒⠀⠈⢻⣍⠋⠀⠀⠀⠀⠶⠾⠟⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡼⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠚⡄⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣣⡀⣀⡠⠀⠀⠙⠳⡖⠤⠤⣔⠂⠱⠃⠤⢇
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠛⣦⡄⠀⠀⠆⠠⠈⠦⠴⠁⠈⠣⣀⠔⠁⢀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢌⣻⣆⠀⠠⠂⠀⠀⠀⠈⠉⠑⣑⣄⣀⠁⠤⠤⠀⠒⠀⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⢻⡛⣻⣆⠀⣀⠄⢀⠤⠒⠈⠁⠀⢀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢱⠈⣻⣆⡡⠊⠁⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⢘⣾⡿⠋⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⠉⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣌⠻⡄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠙⣆⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⡾⠋⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡞⠁⠀⢀⡴⠟⠋
⠀⠀⠀⠀⠀⠘⠿⠿⠶⣦⣤⣀⠀⢀⠄⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⡠⠀⠠⣀⡀⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⠴⠋⠁⠀⡀⠀⠁⠀⡀⠀⠀⢄⠀⠈⠙⠢⡀⠀⢦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⡀⠀⠀⢐⡧⠒⠉⠉⡉⠉⠉⠉⠒⠬⣂⡄⠀⠈⠀⢸⠂⡿⠀⠀⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡆⠘⠀⠐⠀⢠⠔⠁⠀⢀⣀⠁⢠⣠⠀⠁⠀⠄⠈⠳⡄⠀⠀⠎⠐⠁⠠⢚⣥⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣵⠃⠀⢂⢀⠈⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠗⠦⠤⠤⠤⠤⠤⠀⡤
⠀⠀⠀⠀⠀⠐⠐⠘⡀⠠⡄⠀⠤⠐⠚⠇⠀⠁⠈⠉⠀⠑⢄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⡀⠀⠀⠀⢀⠄⠀⢀⠠
⠀⠀⠀⠀⠀⠦⢄⡠⠘⠀⢸⡆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠆⡆⠀⡇⠀⠀⡴⠁⠀⠀⠦⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠜⠁⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠃⠀⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⡀⠀⠀⠰⡀⠀⠀⠋⠀⡀⠈⠀⠀⠀⠀⡀⠀⠁⠈⢀⠎⠀⠀⠀⠀⢀⡠⠄⠀⣁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⣹⠀⠀⠀⠙⢄⠀⠀⠀⠃⠀⠐⠆⠀⠀⠃⠀⠀⡠⠊⠀⠀⠀⠀⢰⡏⠀⠈⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠘⠋⣡⡴⠁⡰⠃⠀⠀⠀⠀⡈⡑⠢⢄⣀⠀⠀⠀⠀⢁⡠⠴⢎⠡⠀⠀⠀⠀⠀⠀⠳⠈⠲⣤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠾⠏⠀⠈⠁⠀⠀⠉⢳⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠁⠁⠀⡴⠊⠁⠀⠀⠈⠀⠈⠙⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡖⠈⠀⡀⣉⠉⠳⡄⠀⣠⠐⢚⣉⡅⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⡆⠈⠂⣿⠀⠀⢠⣿⠀⡿⢀⠀⣤⠄⠜⡴⠿⠀⠉⢉⠁⠀⣠⠀⠀⣠⠁⢀⡀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢿⠀⣄⠀⠻⢸⠃⣙⡀⠘⠀⠾⢁⣿⠀⢚⠛⠀⠀⣿⠀⠀⣿⠀⣾⠀⢴⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⠀⣿⡄⢀⣏⡔⠘⣧⣀⡄⣶⡀⠻⠶⠶⠶⠆⠀⣿⠀⠀⡿⢀⡏⠀⣬⣤⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⠌⠿⠶⠚⠀⠀⠀⠿⠶⠛⠷⠶⠆⠀⠀⠀⠀⠙⠷⠶⠖⢸⣧⡠⠀⢠⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢯⡀⢻⡡⢤⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢿⠂⣇⣀⠀⠀⠀⠀⠀⠀⠀⠐⣫⠀⠀⠈⠉⠀⠀⠘⠻⡉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣸⠵⠉⠑⠤⣀⠀⠀⠀⠀⣼⠂⢀⣄⠞⣆⣠⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⠀⠈⠑⠦⣄⠀⢺⣍⢉⡁⢀⣀⠈⢳⣤⣀⡇⠀⠀⣀⠴⠒⠉⢥⢹⠀⠻⢟⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠑⢯⣿⢡⣆⢁⡄⠀⠀⠞⣽⡡⠖⠉⠀⠀⣀⡤⠜⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣸⡌⠒⠋⢀⣠⢏⡴⠋⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠘⣧⡟⢲⠖⢉⠏⡴⠃⠀⢀⡴⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⢀⣤⣋⡠⠞⢠⣶⠏⠀⣜⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⣀⠀⠀⠁⠀⠀⠠⡍⠁⠀⠀⠀⠉⡞⠀⠀⠀⠙⠲⣝⢦⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⠁⠀⠀⠈⠳⣴⢶⠂⠀⢠⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢠⡬⢷⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⢿⣀⠀⠀⢀⣶⡻⠆⣸⠇⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠴⠶⢶⡶⠛⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠒⠬⢀⡀⠀⠀⠀⡟⠈⠓⠤⣸⡟⢁⡴⠋⠀⢀⡤⠞⠹⡇
⠀⠀⢀⡴⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⣄⣉⡑⠢⢤⣇⡀⠀⠀⠀⠉⠉⢀⡤⠖⠉⠀⠀⠀⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢤⠁⠀⠀⠀⠉⠉⢢⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⣷
⠀⢰⡇⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢸⡇⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣀⡀⢸
⠀⢸⠇⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠴⠚⠁⠹⠞
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠖⠉
⠀⠈⠓⠒⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠤⠀⠀⠠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠟
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⣶⡄⣰⣦⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⡀⣰⣦⢠⣶⡄
⠀⠀⢸⣿⡇⣿⣿⠀⣿⡇⢲⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣦⢸⣿⡇⣿⣿⢸⣿⡇
⠀⠀⢀⣉⣤⣌⣁⣤⣉⣠⣿⠃⠀⠀⠀⠀⠀⠀⠿⢛⣉⣉⣉⣉⣉⣤⣶⣷⣤⣉⠛⠿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⣿⣄⣉⣤⣌⣡⣤⣉⡀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⢙⣉⣋⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⡉⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣥⣤⣬⣿⣿⣿⣿⣿⣿⣡⣤⣬⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⢛⣉⣉⡙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠘⠿⠿⠃⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠻⠿⠶⠶⠿⠿⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠟
⠀⠀⠀⣠⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠚⠻⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠟⠓⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡙⠻⠿⠿⠿⠿⠟⢋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⣠⣤⣍⡙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⣩⣤⣄⠀⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣶⣿⣿⣿⣿⣿⣷⡄
⢦⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣠
⠀⠈⠙⠻⠆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠰⠞⠋⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⣿⣿⣿⡿⠛⣋⣉⣉⣉⣉⣉⣉⣉⣁⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣈⣉⣉⣉⣉⣉⣉⣉⣙⠛⠿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⡿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⡇
⠀⠀⠀⠀⠈⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⢀⡀⢀⡀⢀⡀⢀⡀⠀⣀⠀⣀⢀⡀⣀⠀⣀⠀⢀⣀⡀⠀⢀⡀⢀⡀⢀⣀⡀⠀⢀⣀⣀⠀⣀⡀⠀⣀⣀⠀⣀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⣿⣼⣧⣼⢀⣟⣿⠀⣿⣾⡁⢸⡇⣿⢧⣿⢰⡏⢡⣅⠀⢸⡇⢸⡇⢹⣬⠿⠀⢸⡧⠄⢠⣟⣷⠀⣿⣼⡇⣿⠀⠈⢷⠟
⣤⣤⣤⣤⣤⣼⣧⣼⣧⣼⣭⣽⣧⣿⣬⣷⣼⣧⣿⣬⣿⣬⣿⣶⣯⣤⣬⣷⣾⣥⣽⣤⣤⣤⣼⣷⣶⣼⣭⣽⣦⣿⣬⣧⣿⣶⣤⣼⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢴⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢀⡄⠀⠀⠀⠀⠔⠀⠀⠀⠀⡀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣗⠀⠤⠙⠛⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⡀⠀⠘⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣧⣬⡓⠀⠀⠀⠀⠀⠀⠤⠂⠂⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠒⠂⠤⠤
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠧⢄⣠⡼⠋⠈⠀⠂⠀⠂⠀⠐⠅⠀⢠⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠄⠈
⠀⠀⠀⠀⠄⢨⠀⠀⠈⠉⠀⠀⠀⠘⠒⠀⠄⠀⠀⡰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠠⡀⠀⠀⠁⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡏⠙⠒⠒⠲⣄⣀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣨⠏⠀⣠⠀⠀⠀⠀⢠⠷⣄⡀⢴⡊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣸⢫⠟⡇⠀⠀⠀⠈⡳⢲⣏⣡⠤⢺⣀⠴⠃⢊⡙⠉⡿⣏⠀⠀⠀⠀⠀⠀⣖⡉⢯⢫⣻⡧
⠀⠀⠀⠀⠀⠀⠀⡟⠛⢷⠟⢨⠃⠀⠀⠀⠘⠳⣄⣴⠃⠰⠛⠓⠀⢀⡁⠉⠀⡷⡞⠃⠀⠀⠀⠀⠸⢏⠳⢾⡾⠛⢻
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⢧⣿⠀⠀⠀⠀⣀⠯⡀⠀⠀⣿⢇⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠚⣆⠀⠀⢠⡇⠀⡇⠀⢠⣏⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡈⠛⠋⢁⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⡤⠤⣴⢻⠈⠉⠛⠛⠉⢸⠉⢧⠴⠖⠶⢤⣄⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⢀⣠⠴⠚⠉⠀⠀⠀⢳⠸⢤⣀⠀⠀⢠⡏⠀⣾⠀⠀⠀⠀⠀⠉⠛⠒⣦⣀⣀⢹⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠓⠛⢿⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡼⢧⢀⡜⠉⠳⠾⠂⠀⠀⠀⠀⠀⠀⢠⡇⠈⠉⠉⠇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣄⣀⣀⡀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠴⠶⠞⠷⢤⣀⢄⡀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⠀⠠⣶⡿⠁⠀⠀⠀⠈⠉⠉⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⢿⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⣹⠁
⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠶⠒⠶⠶⢿⡀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⠰⣹⠓⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠒⠒⠒
⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠼⡟⠆⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⣯⠉⠙⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠁⢀⣠⡧⠴⠖⠚⠛⠛⠛⠉⠙⠛⠛⠛⠛⠛⠓⠿⣄⡀⠀⠀⠀⠈⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠲⠦⣄⡀⠉⠳⢤⣀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡴⠚⠉⠀⠀⢀⡤⠖⠚⠋⠉⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠳⢤⡀⠉⠓⠶⢤⣼⣧⣀⣀⣀⣀⣀⣀⣤⣀⣀
⠀⣀⣀⣀⣠⡤⠶⠚⠋⠁⠀⠀⢀⡠⠞⠉⠀⣠⡤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠤⣄⡀⠉⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡴⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⣴⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢠⡞⠁⠀⡀
⠀⠀⠀⠹⢦⣴⠧⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠈⠻⢿⣿⣷⡄⠀⠀⠀⠀⣸⣷⣦⠞⠁
⠀⠀⠀⠀⠈⢣⡀⠰⠀⠀⠀⠂⣸⣿⠏⠁⠀⠀⠈⠀⢸⣿⡗⠀⠀⡀⠰⠏
⠀⠀⠀⠀⠀⠈⢧⠀⢠⣶⣾⣦⣈⣿⡆⠀⣤⣤⠄⠀⣿⣿⡿⠓⢀⣤⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠸⡆⠸⣿⠿⠟⠛⠚⠹⠆⠀⠀⠀⢾⣏⠃⠀⠺⠿⠟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣴⡟⠁⢀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠙⣿⣿⣿⣿⣷
⠻⣷⣤⣾⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⢿⣿⣿⣿⣿
⠀⠈⢿⡁⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣼⠋⢉⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢷⡀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⢰⠏⠀⣾⣿⣿⢻⣿⣿⣿⣿
⠀⠀⠀⠘⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡾⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡇⢠⣿⣿⣿⣿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠘⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠁⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⣠⠶⠞⠛⣛⣛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣤⡴⠶⠶⠶⢮⣍⠛⠂⢀⣤⠶⠛⢛⣉⣉⣙⠛⠶⣄⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠳⢶⣤⡀⠀⢈⣁⡴⠚⠋⠉⠉⠙⠛⠷⣦⡀⠈⢷⡀
⠀⠀⠀⠀⢠⡾⣰⠏⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢻⣖⠋⠙⠻⣆⣀⣀⣀⠀⠀⠀⠈⢻⡄⠈⣷
⠀⠀⠀⠀⣾⢡⡟⢠⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢿⣷⣶⠞⣩⣭⣭⣉⡛⢶⣄⠀⠀⢻⠀⣿
⠀⠀⠀⠀⣿⢸⡃⣿⠀⣤⡤⠴⠶⢚⣩⣤⡀⠀⠀⠴⠾⠿⠶⠿⠿⠿⢿⣿⣦⡙⣧⠀⠘⠀⣿
⠀⠀⠀⠀⠻⠸⣇⠸⣦⠀⠀⠀⠘⣆⢻⣿⠷⡠⢂⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣭⣙⡻⢶⣤⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠙⢃⡸⠿⣦⣄⣀⣈⡤⢖⣫⠞⢋⡭⠶⠛⠉⢉⡉⣉⣉⠉⠛⠻⢿⣿⣷⣮⣙⢷⣄⠙⣦⡀
⠀⠀⠀⣀⠀⠀⠀⠉⠀⠀⠀⠈⠉⢁⠴⠯⢍⠝⠉⠠⡆⢠⡆⢸⡇⣿⣽⠀⠀⢠⡄⠈⠻⣿⣿⣷⡝⢷⡈⢷⡀
⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⡇⠸⢿⠸⣷⠖⠀⢸⡇⠀⢀⡈⠻⣮⢻⣆⢻⡄
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣰⠶⡆⠃⠀⠁⠀⣾⠀⣷⠀⠀⠘⠁⠀⠏⣿⠀⠙⣧⢻⣆⢻⡄
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡐⠀⠀⡇⢿⣀⡟⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠀⢀⣴⣧⡆⠀⠸⣇⢻⡄⣧
⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⡇⠀⠈⠁⠈⠛⠁⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⢶⡄⢿⠘⣧⢸
⠛⢠⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⢰⠛⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⢸⡆⣿⠘
⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠸⠶⡟⠀⠀⠀⠀⠀⠀⠀⢻⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⠇⣿
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡆⢀⡼⠁⠀⡀⠀⠀⠀⠀⠀⠘⣧⠅⠀⠀⠀⠀⠀⠀⣀⡌⠁⠀⢸⠀⡿
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣷⠀⠀⠀⡟⣻⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠏⡇⠀⠀⠆⢀⠇⠘
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢿⡄⠸⣧⠀⢠⡟⢳⠀⠀⣤⣤⣤⠀⠀⣠⠀⠀⢀⠶⠆⠘⠛⡟⠀⠀⠀⠘
⠀⠀⢀⠘⣯⣉⣉⣉⣉⣉⣉⡈⢿⣆⠹⣧⡈⠳⠞⠀⠀⠀⢰⠇⠀⣰⠃⠀⠀⠸⣆⠀⠀⠀⠃⡀
⠀⠀⠘⣧⠈⢻⣭⣭⣭⣭⣭⣥⣤⠻⣷⣌⢿⣦⡀⠀⠀⢀⡏⠀⠀⡏⢻⠀⢠⣤⠟⠀⢀⡠⠮⡭⠋
⠀⠀⠀⠈⠳⣄⠙⢷⣶⠶⠶⠚⠛⠶⣾⠿⢷⣯⣻⣶⣤⣈⠀⠀⠀⠻⠞⠀⠀⣀⣠⠖⣋⡴⢊⡕
⠀⠀⠀⠀⠀⠉⠳⠦⠉⠻⠃⠀⠀⠀⠘⣧⣀⣉⠛⠿⢿⣿⣿⣿⣷⣶⣾⣿⣿⠿⠞⣋⣥⠚⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣀⠤⠾⣷⣶⣒⣒⡂⠀⠀⠀⠉⣉⣉⣀⣤⠴⠖⠋⠉⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⠋⠉⠁⠀⠀⠀⠈⠉⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢃⣄⠀⣜⡇⠀⠰⠆⠀⠀⠀⠀⠀⠰⡄⠀⣿⡀⠖⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡽⠞⠋⠉⠭⢝⠢⡀⠀⣖⢲⡤⣄⡤⠒⠒⠛⢧⣞⣳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⡤⢒⡶⢋⣀⣈⣽⣖⣧⡀⠀⠀⠀⠀⠉⠛⢄⠰⠚
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⢺⢀⡤⣚⣩⠿⠛⠉⠉⠉⠉⠉⠙⠳⢤⣈⢳⣄⡀⠀⠀⢸⡌⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢋⡽⠋⣀⣴⠖⠛⠉⠉⢹⠛⠒⠤⡀⠈⠻⣟⠛⠲⢤⣀⣡⠇⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⠏⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢣⡀⢠⠙⣅⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⢳⠃⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢳⡀⢇⠸⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠇⡇⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣇⢸⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠂⠀⠀⠀⠀⠸⡊⢂⠀⠀⠀⠀⠀⠀⣀⣧⠀⢹⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡄⡇⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⡼⢸⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡸⡄⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⢇⡏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⣜⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣼⢞⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠓⢍⣒⠤⠀⠰⠀⠀⠀⣀⡴⠊⠁⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣲⢤⣈⠉⠛⠒⠛⠋⠉⢁⣀⡤⢞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⢱⣀⣤⠮⠀⠀⠤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠤⠀⠀⠴⣤⣀⡎⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠟⠉⠀⠀⠀⠀⠀⠈⠳⡀⠀⠨⢥⡬⠇⠀⢠⠞⠁⠀⠀⠀⠀⠀⠉⠛⢷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⣸⡇⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠠⣔⠩⠔⠐⠂⠉⠉⠁⠀⠀⠈⠉⠉⠐⠒⠤⠍⣲⠄⡀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⠄⢊⠗⠊⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⠑⠺⣑⠠⣀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠊⡠⠞⠁⠀⠀⢀⡠⠔⠂⠉⠀⠀⢀⠈⢁⡀⠀⠀⠉⠐⠢⢄⡀⠀⠀⠈⠳⢄⠁⠢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⠖⠁⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠈⠢⣄⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠳⡀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣼⠄⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠃⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⡀⠁⠀⠘⡄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡆⠀⠀⠘⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠒⠘⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠒⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠄⣀⠐⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡀⠰⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⢏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡹⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⣠⠞⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠓⢄⡠⠀⠀⠀⠀⠀⠀⠏⠰⠀⠀⠀⠀⠀⠀⢄⡠⠚⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠈⠑⠢⠄⣀⡀⠀⠠⠄⠀⣀⣀⠠⠄⠊⠁⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠢⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠔⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡔⠁⠈⠁⠒⠠⠤⠄⣀⣀⣀⡀⠠⠤⠄⠒⠈⠁⠈⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉


⣶⣶⣶⣶⣶⡾⣶⣶⣶⡶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⢷⠾⠷⠾⠷⣶⡶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢣⣰⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠞⣱⠃⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠈⢳⠦⡀⠀⠀⠻⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡆⣀⠀⠠⡧⠴⢤⠇⣠⣒⠛⢁⠎
⠀⠀⠀⠀⠀⠈⠫⣀⣨⠆⠀⠀⠀⠙⠃⠹⣸⠀⠀⠀⣠⣠⢄⠀⠀⠳⠛⠛⠀⠀⠀⠀⠀⠚⠉⠁⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢠⠔⠊⠙⠲⢍⠀⣴⣒⠃⠁⢈⣍⡷⠀⡠⠚⠉⠉⠉⢢⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡖⣄⠀⠀⡇⠀⠀⠀⠀⣨⠇⠈⠈⡇⠀⢸⠀⠀⠀⠧⣀⠀⠀⠀⠀⡇⠀⠘⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠧⠤⠴⡂⢫⡤⠴⠒⢲⡃⣠⣼⠋⣱⠖⣲⠏⢨⡓⠒⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⢀⠠⢀⣀⢀⠀⠀⠀⢀⠀⠀⣘⡆⠈⠉⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠄⠊⠁⠀⠀⠀⠈⡍⠁⠀⠀⠀⠀⠁⠀⢀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡔⠁⠀⠀⠓⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠀⠀⠀⢢⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠏⡢⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢣⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⠄⠀⢠⠀⢀⠂⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠑⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠉⠂⢄⣀⠀⠀⠀⠆⠀⠀⠀⢘⠁⠐⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡴⠤⠶⠤⣄⣉⣉⣉⣛⡤⠬⠥⠦⣄⡄⢖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢀⢀⣤⣤⣤⣤⣤⣄⣀⡁⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⢻⡄⠀⠀⣪⠒⠉⠉⠀⣄⠀⠉⠉⠙⠺⢕⢦⠀⠋⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣁⠀⣸⠇⠸⠀⠀⠀⠏⠀⠀⢰⠀⠀⠀⣧⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⣯⣅⠢⡀⠀⡶⢦⢄⣈⡤⣖⣒⣿⣦⣦⣶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⢠⢫⣾⣿⣿⣿⣿⣯⡵⠃⣀⣈⣷⣾⣇⠾⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢆⠻⣛⣽⣿⣽⣿⠿⠿⣿⣿⣿⣯⣭⣙⣳⣾⢿⣿⣿⣿⣿⡽⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⠈⢛⣽⠟⣫⣵⠞⠛⠋⠉⢹⠛⠛⢿⣟⠿⣷⣽⣿⣯⣟⡻⢃⠃⠀⠀⣀⣠⣤⠶⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠂⢠⡞⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⢻⣿⡝⣿⣿⡅⠀⠛⠉⠉
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⡟⣰⢳⠃⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣷⡈⣿⣿⡀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⣼⢡⠇⡇⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡇⢸⡇⡇⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⢸⠀⡇⠁⠀⠀⠀⠀⠸⡋⡀⠀⠀⠀⠀⠀⠀⡀⣿⢸⣿⢸⡇⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠖⠛⠉⠉⠀⠀⢻⠸⡆⣇⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⡿⢸⡏⢸⡇⡇⠀⠀⠉⠙⠛⠲⠦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣇⢳⡸⡄⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾⢃⣾⡟⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠘⣦⠳⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣼⢃⣾⠟⠀⠀⠀⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⣠⠄⠈⠳⣿⣷⣭⣒⠤⠀⠰⠀⠀⢀⣠⡴⢟⣥⣾⣷⠟⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣈⣿⢿⣯⣭⣽⣿⣿⣿⣿⣿⣿⢿⣟⠉⠀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠀⠀⡉⠉⠉⠉⠉⠉⠀⠀⠹⣻⡄⠀⠙⣆⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣰⠁⠀⠀⠀⣧⠀⠀⠀⠀⠈⠋⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠟⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⠶⠶⠦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣠⠴⠶⠚⠛⠳⠶⠶⣦⣄⡉⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡿⠲⠶⣦⡄⠀⡞⠉⡇⠀⣠⡶⠞⠛⠛⠷⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⠴⠞⠁⠀⠀⠀⢹⡆⣇⠀⡇⣼⠧⣤⣤⣀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⠛⠒⠳⠿⣤⣀⠀⠉⠛⠶⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣤⠾⣋⣤⠴⠶⠚⠛⠛⠛⠛⠻⢦⣄⠀⠈⢳⣄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡗⠚⠛⠋⣩⡶⢛⣩⠴⠖⠛⠛⠛⠛⠛⠶⣦⣄⠙⢷⣦⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⠟⢁⡴⠋⠁⠀⠀⢰⣉⡷⠀⠀⠀⠀⠉⠻⣦⡙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣾⠋⣰⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠃⡼⠁⠀⢠⣞⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣸⠃⠀⠀⠀⠈⠓⠦⣄⣙⣄⣀⠀⠀⠀⠀⠀⣀⣀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⣿⢠⡴⡄⠀⠀⠀⠀⠀⠻⣄⡼⣄⠀⠀⠀⠀⠳⠞⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢿⠀⢿⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢳⡈⢷⡀⠀⠀⠀⠀⢰⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⣇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡆⠀⠀⣠⠏⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⢆⠙⢦⣀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⠁⠀⢀⡼⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣀⠀⠙⠳⠶⣤⣤⣀⣀⣉⣉⣠⣤⣴⠞⠋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢻⡄⠀⠀⠀⠀⠉⠉⠉⠁⣀⣠⣤⡶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠋⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠳⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⢀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡤⠀⠀⠐⠒⠒⠒⠒⠒⠒⠲⠆⠀⢸⠀⠀⡇⡇⠀⠀⡅⢤⠤⠤⣤⣤⣤⣤⡄⠤⠤⠤⠤⠀⠠⢀⠀⠁⠀⠃
⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠅⠀⠘⠀⠀⡇⠃⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀
⠀⠀⠀⠘⠀⠀⠐⠐⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠁⡀⠸
⠀⠀⠀⠀⠀⠀⠘⡁⠀⠠⡀⠠⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠘⠂⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠆⠀⠜⠁⠀⠈⠈⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⢹⠀⠀⠀⠀⢀⠿⢜⡅⠀⠀⠀⠀⢀⠀⠇
⠀⠀⠀⠀⠐⠒⡲⠒⣒⢤⡁⢀⠨⠀⠂⠀⠈⠁⠒⠢⢄⠀⠀⣇⣽⣀⠀⠀⠀⠀⢾⢩⠀⠀⠀⠀⠀⠸⢠
⠀⠀⠀⠀⠀⢘⠀⠠⠔⢒⠟⡀⠈⠗⢤⡀⠀⠀⠀⠀⠀⠉⢶⡉⡀⠀⠘⠀⠀⠀⡿⠘⠀⠀⠀⠀⠀⡆⠘
⠀⠀⠀⠀⠀⠈⡰⠁⠀⠃⢰⠀⠰⠌⠀⠈⠓⢄⡀⠀⠀⠀⠀⢁⢹⢢⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⢀⠃⠈⠒⢄⠀⠀⠈⠐⠐⠀⠀⠘⣿⠀⡶⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⡠⠒⠀⡇⠀⡠⠊⠀⠀⠀⠀⠈⠈⠐⠒⠒⠒⢄⠀⠋⠐⢄⣀⣀⣀⡇⡀⠀⠀⠀⠀⠉⠀⠃
⠀⠀⠀⠀⠀⠃⢰⢒⣇⡈⠀⠀⣰⡆⠀⠀⡀⠀⠀⣴⡆⠀⠈⡤⣄⠀⢸⠀⠀⠀⠀⠈⠁⡈⡉⠈⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⠀⠀⢠⠦⠁⠩⠶
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⠜⠀⠆⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⣏⢑⡤⠤⣀⡁⠂⢤⣀⣀⣀⣀⡤⠔⣊⡉⣤⢤⡊⢰⡇⡖⠯⣁⠐⢂⡘⠖⢄
⠀⠀⠀⠀⠀⠀⢉⠍⡧⢀⡀⢀⠀⡌⠙⠒⠒⠋⢀⣀⣀⣀⣀⣨⠉⡅⠃⢳⠀⠹⠿⠟⡀⢀⡈⣦⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡤⠤⠤⠤⢼⠖⠀⠉⠉⠉⢹⠥⠴⠶⠂⠄⣀⡏⠉⠉⠁⠀⠉⢫⠲⡌⠀⠀⠀⠈⠀⠀⠀⡦⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⡸⠀⠐⠒⠒⠂⡡⠐⠐⠒⡂⠐⠠⢉⡐⠒⠒⠒⠐⠐⢶⡇⠀⠀⠀⠂⠀⠀⠠⠤⠤⢤
⠀⠀⠀⠀⠀⠐⠓⠘⠋⠹⢉⣬⠀⠀⡱⢒⣂⢆⡐⠀⠈⠉⠩⠉⡉⠑⠚⢷⠖⠒⠒⠒⠒⢲⡞⣀⣀⡀⡄
⠀⠀⠀⠀⢀⡎⠂⢜⡒⠀⡬⠖⡆⠀⠀⠈⠉⠁⠁⣶⠲⠦⠰⠀⠅⠂⣢⡈⣇⠀⠀⡀⠤⠤⠤⡀⠀⠀⠐⡀
⠀⠀⠀⠀⡼⠤⠁⠖⠃⠹⣀⡠⠉⠉⡑⢒⣒⣛⣈⣀⣂⣀⡉⠐⠒⠈⠀⠉⠘⢆⠈⢒⠴⠶⠂⠡⡀⠀⠀⠡⠀⠀⠂
⠀⠀⢠⠒⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠂⠈⠀⠐⠀⠐⠁⠀⠀⠀⠄⠀⠆
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⡀⡄
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠔⠀⠈⢐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⡈⢢⠔⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⠀⢐⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠛⠻⠿⠻⢻⣿⣷⡀⠀⠀⠀⠀⡐⠀⠈⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠑⠤⠠⠀⠉⠈⠂⠀⠀⡀⠀⠀⠀⢘⣿⣿⠋⠤⠀⠀⠀⠀⠄⠀⢻⣿⣄⠀⠀⠀⠔⠀⠀⠊⠀⠀⠁⠠⠤⠒⠁⠀⠔⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠂⡀⠀⠀⠐⠄⠐⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠑⠠⠌⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠌⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡀⠀⠀⠠⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⡰⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⠢⡀⠀⠑⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠁⠀⠀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠐⠿⣿⣿⣷⣄⣀⣀⣀
⡄⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠁⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛
⢁⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠
⠀⠈⢂⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⡀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠚⠉⠉⠉⠉⠀⠀⠉⠉⠉⠙⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⡷⠖⠚⠛⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠘⠳⠶⢤⡞⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢈⡦⠀⠀⡊⠉⡆⠀⠠⡊⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣀⠔⠊⢁⣀⣠⠠⠬⠯⠀⣀⣀⡈⠑⠢⣀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠤⠒⢫⠷⠒⠉⠁⣀⠀⣤⣤⢄⣤⢀⣀⠈⠉⠒⠴⣹⠂⢄⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⡠⠚⠁⣀⣔⠶⠙⠋⠉⠉⠁⣄⠉⠉⠘⠻⢷⣠⣀⠈⠓⢄⠈⠓⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡠⡪⠋⠁⢰⡆⠀⠀⠠⡆⠙⡦⠀⡄⠀⣤⠈⠙⢕⢄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⢮⠊⠀⠀⠀⢸⡇⢹⠀⠀⠃⠲⠆⡰⠀⢻⠀⠀⠀⠀⠑⣷⡀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⣯⠃⠰⢆⠀⡠⡈⠁⠈⠀⠀⠀⠀⢠⠁⠀⠉⠀⠀⠰⡄⣤⠘⣵⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣾⠃⠀⠀⢸⠸⣇⠇⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠮⠄⠀⠀⠘⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡏⠀⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣜⣀⣀⣀⣀⣀⣀⡀⠠⡄⠀⠀⢿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣇⠀⠋⠈⠞⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠛⠛⠛⠛⠛⠋⠈⠇⠛⠀⣸⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⢠⠠⠀⢰⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠱⣧⠀⣠⠸⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢀⡀⠀⣼⠏⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠹⣧⡀⠀⠀⠀⠀⣩⠁⠀⠀⢀⠀⠀⠀⢰⡂⠀⠀⠀⠀⢁⣼⠏⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠘⢝⢄⠀⠀⣤⠁⠀⠀⠀⡟⡦⠀⠀⠀⢋⣄⠀⠀⡠⡮⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠙⠯⣦⣄⡀⠀⠀⠀⠰⠆⠀⠀⠀⢀⣡⣴⠟⠊⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢢⢄⡀⠁⠚⠳⠶⠦⠶⠦⠴⠶⠚⠓⠉⠀⣠⡔⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢁⠔⠁⠀⠉⠑⠒⠤⠤⢀⣀⣀⡀⠤⠤⠒⠊⠉⠀⠑⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠐⠂⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠐⢀⠀⡰⠂⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⡂⠈⣀⠇⠀⠀⠀⡀⠚⠀⠁⢺⠟⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠈⠈⠁⠀⠀⣠⣎⠄⠊⠅⣂⣒⣀⣰⣀⡀⠀⠀⠀⠀⠀⠀⢠⢲⠐⠤⣤⣶⣶⣶⣤⡡⣂⠄
⠀⠀⠀⠀⢀⡇⡴⣪⠟⡕⠡⣢⠞⠉⠀⠀⠀⠀⠀⠉⠲⣄⠈⢂⠀⠀⠀⢹⡆⠀⠀⠀⠈⠉⠉⢉⣷
⠀⠀⠰⠀⡈⢣⠜⠁⡜⠀⡼⠁⠐⠀⠀⢁⠀⠀⠀⠀⠀⠈⢧⠀⢣⠀⠁⠀⠉⢆⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢰⠃⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⡏⠈⠀⠀⠀⠀⠀⠑⠠⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⡀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢷⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⢀⡼⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠳⢄⠀⠀⠈⠀⠀⠀⢀⡠⠞⢈⠔⠋⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠉⠓⠲⣶⣶⠾⠟⣃⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠓⠖⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠂⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣇⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⢿⣿⠟⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣛⣿⣿⡇⣾⡷⢰⣿⣟⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣎⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠈⠿⣿⣿⣿⡟⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠈⠙⠛⠷⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⣄⡀⠀⢸⣿⣿⣟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⣿⣄⠀⣿⡜⣿⣦⠻⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣿⣿⣦⠘⣿⣎⢿⣿⠿⠿⢛⣣⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢿⣿⡆⠈⢿⣷⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⣀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠙⠻⢷⣦⣀⣀⣤⣤⣤⣤⣀⣀⣠⣾⠟⠋⠉⠉⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠛⠉⠉⠉⠉⠛⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢹⣷⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠈⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠘⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣴⣶⣶⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣦⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠙⠻⢿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶⡿⠟⠋⠉⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡽⠒⠚⠉⠉⠉⠉⠉⠒⢿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣞⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡵⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡝⠶⠛⠻⠿⣷⣶⣄⠀⣤⣤⣀⡠⣴⡬⠾⠟⠚⠳⠾⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⣀⣤⡶⠾⢿⣿⠊⠛⣿⠿⢿⠿⠷⣦⣤⣀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣾⣿⣿⣿⣏⢻⡀⣨⣟⣁⡀⣴⣿⠄⣈⣳⣄⣼⡿⢛⣿⣶⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⠛⡿⣿⣿⣦⣿⠿⠖⢀⣀⣁⣀⣀⡀⠐⠿⣿⣥⣿⣿⠋⠛⢻⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⡹⣫⣿⣋⡴⠞⠋⠉⠉⠀⠄⠉⠉⠙⠲⢦⣝⢻⡙⢯⠒⠺⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣩⡾⠋⠀⠀⠀⠀⠀⣰⠺⠀⠀⢠⡞⠂⠈⠳⣄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣴⠋⠀⠀⠀⠀⠆⡇⠀⠈⠉⠀⢠⠽⠇⠀⠀⠀⡈⢧⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠃⠀⠀⣾⣷⣀⡀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢸⡋⠑⠈⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡟⠀⡀⣀⠉⠁⠙⠦⠦⣀⣀⢠⡏⠀⠀⠀⠀⠀⢀⡀⣆⢹⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⢰⠂⡿⠀⠀⠀⠀⠀⠈⣷⣾⠀⠀⠀⠀⠀⠀⢈⡇⠛⢸⣷⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢿⣿⠞⠀⠀⣀⠀⠀⠀⠀⠠⠋⠈⠣⡀⠀⠀⠀⢀⡄⠀⠂⣼⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠙⢦⠠⠄⠿⠀⠀⠀⡰⠁⠀⠀⠀⠑⣄⡀⠠⠺⣧⣄⡖⠉⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠠⠃⠐⢆⠀⠈⡅⠀⠀⢠⡆⠀⠀⢨⣦⣀⣶⣿⠋⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣴⣦⡀⠼⣦⣤⣀⣀⣘⡋⢀⣠⣢⣾⡿⢟⠕⡊⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣮⣭⣓⣻⣿⣿⣛⣛⣩⣵⣾⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣹⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⣠⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠚⠒⠛⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠒⠒⠲⠶⠤⢄⡀
⢀⠞⢁⡀⠀⠤⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠤⠤⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⢸⠉⢀⠄⠀⠶⠒⠆⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠤⢄⡀⠈⠑⠀⠔⡋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠸⠀⠀⢪⢐⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣴⡿⠻⢿⡿⠻⣇⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⠀⠀⠘⠶⡁⠰⠆⠀⠀⠀⠀⠀⠀⠀⡻⠇⢀⠀⠀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠀⠀⠀⠀⢡⣠⠀⠁⠀⠀⠀⠀⠰⠀⠉⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠉⢀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢰⡖⠆⠠⠀⠄⠚⠀⠈⣁⠴⡀⠀⠀⠀⠀⠀⠀⡀⢠⠊⠀⠀⠈⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⡿⢷⠀⠀⡀⠀⠀⢀⡤⠧⡀⠀⠀⠉⠀⠀⠐⠘⡳⠄⠀⠀⠀⠀⣈⠄
⢰⠀⠀⠀⠀⢘⡣⠤⣀⠀⠁⠘⠀⠀⣇⠀⠀⠀⢨⡀⠀⠀⠀⣴⠀⢠⠄⡀⠳⢀⢀⣖⠀⠊
⢈⠠⠄⠀⠚⠁⠀⠀⠀⠉⠑⠒⠐⣷⠈⠀⠀⠀⠀⣡⠀⠀⠀⠚⠚⠉⠚⠓⠀⠤⣈⠁
⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢳⡀⠀⠀⢀⠖⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⠦⣀
⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡣⠀⡪⠀⠀⠀⠀⠂⠀⠁⡀⠀⠤⠴⠚⠛⠀⠂⢀⣉⠡⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠊⠁⠀⡎⠀⠀⠀⠂⠀⠀⠠⠋⠀⠀⣀⠤⠂⠁⠈⠀⠀⠀⠀⠀⡀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⢠⠀⠀⠈⠢⣄⠀⠀⠉⠉⢠⢊⠀⠄⠀⣸⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠓⠢⠤⣤⣄⣀⣀⣀⡀⠀⡠⢤⡄⢒⡩⠥⠒
⠈⠀⣠⠔⠀⠙⢄⠀⠀⠰⠃⠀⠀⠁⢀⠇⢀⠎⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⢛⠙⠁⣠⡔⠒
⠀⡐⠁⠀⠀⠀⠀⠉⢱⠁⠀⠀⠀⠀⢨⠀⡜⠀⠀⠀⠀⠀⢀⠴⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⠁⠀⡇
⢸⠇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠃⠀⠃⠀⠀⢀⣀⡔⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢸⠀⠐⢈⠀⠀⡇⡀
⠈⠁⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣰⠟⠙⢛⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠾⠰⠀⠀⠃
⠀⠂⠀⠀⠀⢠⠏⠀⠀⠀⠆⠀⡜⠀⠀⠀⠐⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠀⠐
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠒⠂⠈⠉⠐⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠠⠀⠀⠀⡎⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⡐⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘
⠈⡄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠
⠀⠈⠂⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢃⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣊⣀⣇⣀⣀⡰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢠⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢸⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡞⠀⠀⡴⠀⠀⠀⠀⠀⢀⡀⠸⣧⠀⣴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠀⠀⠷⣿⣠⠎⣀⣀⠀⢰⣿⣶⣒⣲⡆⠀⠁⠀⠉⠻⣿⣿⣥⡶⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣯⣙⡦⠈⣻⠋⠉⢡⠖⢛⣭⣽⣷⣧⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⢻⣿⣿⣿⣟⡽⢟⣛⠿⠿⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⢟⡭⠊⢡⠀⠀⠀⠘⠀⠀⠀⠍⠻⣯⣿⣿⠇⡇⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠒⣿⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⣸⣷⠃⠀⢹⡿⣄⠀⠀⠀⠀⠀⠀⢀⣤⠔⠛⠋⣿⡇⢄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⡏⣠⡀⠀⠀⠈⠓⢤⡤⠀⡴⠞⠉⠀⠀⢀⣀⢹⣧⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣇⠀⠀⠀⠀⠀⠀⠈⠈⡥⠀⠀⠀⠀⠀⠀⠀⣾⡏⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣧⢸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣹⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⠆⢻⣿⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣱⠏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⣿⣷⣦⣄⡀⠀⠸⠆⠀⢀⡀⢔⣨⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠾⠛⠻⠿⢿⣿⣿⡿⠶⠾⠛⠿⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠟⠛⠛⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣀⣠⠤⣴⣲⣽⠇⠀⠀⢀⡀⠀⠀⠀⠠⣤⠖⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⣠⠤⣒⣺⣭⣷⣚⣻⣭⣥⣤⣤⣤⣤⣟⣙⢻⡆⠀⠀⢠⣴⡶⠶⢦⣄⡉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠘⣯⠵⠞⢋⣩⡼⠟⠋⠉⠀⠀⣀⣀⣀⣀⠀⠈⠉⠙⠳⢦⣄⠈⢷⡱⡄⠀⠈⠛⣦⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⣠⠞⠋⠁⢀⡠⠴⣒⣯⣭⠭⠶⠦⣬⣭⣙⡒⠦⣀⠀⠈⠳⣦⡻⣜⣆⠀⠀⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠟⠁⢀⡠⣚⡥⠖⠋⠉⠀⠀⢠⡆⠀⠀⡤⢨⣝⠳⣬⡳⣄⠀⠈⢳⣿⣮⢦⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⡴⣫⠞⠉⠀⠀⠻⠂⠀⠀⠀⠀⠀⢈⡁⠶⡟⠀⠈⠻⣎⢣⡀⠀⠹⣏⢷⡳⡀⠀⣸⠀⡖
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⢏⡼⠃⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⠀⠀⠀⠀⣀⡘⢧⠹⡄⠀⢹⡎⢳⣝⣤⠏⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⢣⡞⠁⠲⠞⠋⠀⠀⠀⠀⠀⠀⠀⢰⣏⡾⠁⠀⠀⠀⠀⠉⠁⠈⣧⢹⡀⠀⣿⠀⠙⠁
⠀⠀⠀⠀⠀⠀⣸⠃⠀⡏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠠⡇⡇⢀⣠⠀⠀⠀⠀⢠⡾⠋⠛⣲⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢈⡇⡹⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⡇⣧⠀⠁⠀⠀⠀⠀⠀⠛⠶⠛⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⢇⡇⠀⣼⠁⡶
⠀⠀⠀⠀⠀⡀⠸⣇⠀⠸⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣀⠀⢠⡟⡼⠀⢠⡟⠀⠃
⠀⠀⠀⠀⠀⠹⠀⢻⡄⠀⢳⣻⡄⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⣰⡿⢣⡟⡼⠁⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠳⣽⣦⡀⠀⠀⣤⣶⠦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢉⣵⢫⠞⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡻⣄⠀⠈⠻⣿⢦⣀⠻⠽⠂⠀⠰⠇⠀⠀⠘⠃⣀⣠⠶⣋⠕⠁⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠐⣯⣀⣽⠟⠻⣦⡀⠈⠙⠯⣟⣓⠶⠶⠶⠦⠤⠶⠖⣛⡭⠔⠋⠁⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠷⣤⣀⡀⠈⠉⠉⠉⠛⠛⠋⠉⠀⣀⣠⡴⠞⠉⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠶⠶⠶⢺⣿⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠠⠀⠀⣀⠔⢊⠩⠔⠒⠃⠈⠘⠒⢄⡈⣧⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠈⠀⠰⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⡆⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢀⣠⣡⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⣷⡀⠀⠤⢠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠉⠁⠀⠀⠀⠈⠢⡀⠀⠀⢀⠤⢤⠞⠉⠁⠀⠀⠉⠲⢤⡌⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣼⣿⡇⠀⣀⣠⣤⢶⣶⣾⣿⡷⠀⠀⠀⠑⢲⡗⢤⣀⠀⠀⠀⠀⠀⠈⢑⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⣿⣆⢹⡘⣿⡽⠟⢶⢲⠲⠶⢶⣿⣶⣤⣬⣱⣦⣄⡀⠀⠀⣔⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⡿⢿⣛⡭⠖⠛⠋⠉⢉⡍⠛⠒⠯⣽⢿⣷⣿⣿⠛⠻⢿⡒⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠊⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣟⢻⣅⠀⠀⠀⠙⢦⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡴⠣⡄⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠐⠃⠈⢣⡙⣆⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⡧⠄⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠠⠄⢑⢻⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠅⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢸⢠⡄⠀⠀⠀⢀⣠⣴⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡇⣸⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠸⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢠⡇⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢷⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡖⣠⡎⡀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠴⢿⣷⣋⡄⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢳⣌⣒⣤⠼⣀⣀⣀⠠⠤⢤⠐⣐⣩⣶⠞⣋⣉⠁⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣤⣮⠟⠉⠛⠶⢿⣶⣾⣾⣿⣿⡻⠟⠛⠒⣰⠁⠿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⡄⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡈⣻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢀⣠⣴⣄⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣧⣴⣿⡆⠹⣿⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣿⡉⣷⣀⣿⣷⣶⣾⠿⠿⠿⠛⠛⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⣀⣤⡴⢶⡞⠻⡏⠉⣉⠉⠉⡿⠛⢻⣶⣄⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣶⣿⣋⠀⠀⠈⡇⠀⣿⠀⢻⠀⢸⡇⠀⢸⠇⠈⣳⣄⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣰⣿⠟⠁⠘⢿⣷⣆⠀⠁⠀⠀⠀⠈⠀⠈⠀⠀⠟⠀⢰⠏⠹⣦⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⢀⣾⡿⢧⣀⡀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢹⡆⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢠⣿⣿⡁⠀⠈⠉⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⡀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣾⣿⡋⠙⠓⠂⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⢸⣇⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⡟⠛⠲⠆⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣿⣷⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⡟⠛⠃⠀⢀⡀⠀⠀⠀⠀⡼⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠸⣧⣀⣤⠞⠋⠀⠀⠀⠀⢰⣣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠙⣿⣁⣤⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣄⠀⠘⢻⣿⠃⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠈⢿⣇⠀⡴⠀⠀⣼⡟⠀⠀⠀⠀⠀⡄⠀⠀⢳⡀⠰⣌⠛⣶⡾⠃⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠹⣿⣧⡀⢰⡟⠀⠀⢸⠀⢸⠀⣿⠀⠀⠀⣷⣤⣿⠿⠋⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡈⠉⠛⠻⢷⣤⣤⣿⣤⣤⣤⣿⠶⠾⠛⠋⠉⠀⣀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⣀⡀⠀⠉⠉⠉⠀⠀⠀⣀⣀⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠀⠀⠀⠀⠰⠲⠘⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠈⠁⠀⠀⠈⠠⠂⠀⠀⠋⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⢠⠰⠐⠆⠀⡘⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⡠⠀⠁⠀⠀⠈⢃⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣠⡃⠀⠀⠀⠀⠀⠄⠂⠠⠄⣀⡀⠀⡀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⡠⠉⠐⠄⠀⠀⠔⠁⢀⠀⠀⠀⠁⠀⠀⠀⠁⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡁⠒⠈⢪⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⣖⣀⡀⠀⠀⡠⠒⡁⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠒⠀⠉⠀⠀⠆⡀⢀⠱⢍⡤⠙⡆⠀⠀⠀⢀⡑⠁⠀⠠⠀⠑⡖⠉⣀⠔⡚⠁
⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠰⠀⠀⠀⠀⠰⠐⠈⡡⠁⠀⠀⠘⡎⠔⠘⠁⠀⡀⠁⠀⠀⠀⠰⠠⠗⠊⢰⣠
⠀⠖⠂⠀⠬⠭⠥⠀⠀⠁⢀⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⠂⡂⠀⠀⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠐⠖⠈⠀⠀⡠⢴⠀⠀⠀⣀⡇
⠐⠢⡤⠤⡤⠤⠄⢀⣀⣀⣀⡀⡆⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⣀⡠⠒⠉⠀⡸⠄⠠⠼⠀⠢⡀
⠀⠀⡇⢀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠎⠀⠈⠉⠉⢹⠉⢹⠉⠁⠀⠀⠀⠀⠑⢄⠀⠑⠂⠐⠁
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠴
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⠃⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠛⠻⣆⢸⡇⠉⠣⢠⠗⠀⠀⠀⠠⠠⠠⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢸⡇⠀⠀⠀⠁⠀⠀⠀⠂⠀⠉⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⢸⡇⣠⣄⠀⣠⣄⢀⡀⠀⠀⠀⠀⣀⣿⠀⣀⠀⣠⣄⠀⢀⡀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢸⣇⡟⢹⣦⡟⢹⣼⣷⢿⡆⣇⠀⡟⣿⣾⢻⣴⡏⢹⢰⠟⣿⣸⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⢸⣿⡿⠟⢻⡿⠟⢻⡏⢸⡇⢿⢠⡇⢿⡇⢸⣿⡿⠛⠉⣶⣼⢿⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⡇⢸⡏⣷⣼⠋⣷⣼⢻⣷⠟⠀⠸⣿⠃⢸⠀⢸⠹⣧⣼⠘⣇⣻⠈⢷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠁⠈⠁⠀⠈⢁⢸⡇⠀⠀⠀⣿⠀⠈⠀⠈⠀⠉⠁⠀⠙⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡨⠸⡇⠀⠀⢷⠇⠀⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠋⠀⠀⠀⠀⠄⡀⡀⠀⠀⠀⠀⠀⠁⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠐⠂⠂⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠐⠀⢃⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢅⠅⠀⠀⠀⠀⠀⣨⠀⣅
⠀⠀⠀⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠂⠀⠀⠀⠀⠀⠠⠥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⢩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠉⡇
⠀⠀⠠⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠒⠉⠁⠉⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡴⠁⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠂⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⣀⡤⠐⠤⠤⠊⠁⡜⠀⠀⠀⠀⣠⣞⣻
⠀⠀⠀⠀⠀⠀⠀⠌⠁⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⣀⣀⣡⠞⡇⠀⠀⠀⠀⠰⠁⠀⠺⣉⠉⠡⠀⠌⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠝⠊⠉⠉⣉⠉⠉⢓⣧⡀⠀⠀⢀⠇⠀⠀⠀⣨⠃⢀⠂⠀⣠⠒⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⢀⠟⠁⠀⡴⠊⠁⡈⠱⡞⢡⢌⢳⡀⠀⡸⠀⠀⠀⡰⠧⠒⠉⠱⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⢠⠋⠀⠀⠀⡇⠀⠈⠀⢀⠠⠄⠀⡼⡇⢠⡷⡄⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⣃⠔⢁⣷⡏⢰⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⡔⠂⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠴⠊⠉⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣠⡿⠋⠀⠀⠀⢠⡤⡀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠂⠀⠙⠒⠶⠖⠒⢉⡟⠀⠀⠀⠀⠀⠙⣇⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠊⠉⠉⢉⡞⠀⠀⠀⣀⣀⣠⡄⠀⠀⢈⡀⣒⣦⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠯⠑⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠂⡠⠋⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁⠄⠛⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠸⣍⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⣄⠀⢉⣉⠙⣀⠀⠀⠀⠀⠀⠐⢶⠛⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⣀⣀⣀⣐⠀⣀⣀⣤⣷⠚⠉⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⣍⠙⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢉⠿⡁⢀⡼⢻⣄⠀⠀⠀⠀⠀⠐⠀⡠⠒⠀⠀⠈⠁
⠀⠀⠐⠀⠀⠀⠀⠒⠀⢈⠁⠀⠀⠀⠀⠐⠿⣶⠿⠈⠙⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠀⠣⠄
⠀⠀⢀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣵⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⣦⠴⣶⡏⠉⠙⢦⡋⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢻⣿⢻⠋⣿⣿⡶⣿⣦⡀⢰⠿⡛⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢉⣽⣿⣿⣧⣄⠁⣰⣿⣿⡿⠿⣷⡾⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⠾⠟⣉⡿⣟⣯⠿⣿⠿⠛⢳⣶⠿⢷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢲⢀⡾⠉⠀⠀⠲⣿⣿⣧⣶⣤⡿⢿⣿⣿⣯⣵⡀⣴⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⡇⠌⢻⣤⣶⠋⢉⣙⣿⣿⡏⣽⣭⣷⣴⣿⣟⣩⣿⣾⣏⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⣷⣄⠙⢿⣿⡄⢤⡍⡽⢿⣄⣉⣁⣭⣩⡷⢤⣻⣟⠻⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠞⠀⠀⢻⡄⢀⠙⢿⣶⣼⣿⣾⡟⢉⣽⠛⢛⣷⡆⣽⣼⠛⠛⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⣖⣩⣿⣦⡁⢦⣘⣿⠿⣿⡛⣻⣿⣟⠛⢻⣿⣧⠉⠀⠡⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠋⠁⠈⢷⠀⠻⣯⠀⠈⡿⢿⣿⢧⣤⣾⠟⠉⠙⣁⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣿⣀⡇⠀⣾⣟⢀⣭⡷⣶⡄⣿⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠀⡀⠀⠈⠙⠻⣯⣁⠣⢹⠷⣦⠀⠀⣀⠻⣿⢷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣷⣆⠀⠀⢀⣹⣿⡷⠶⡥⠤⠲⢾⣷⣾⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⠿⠟⠋⢙⣿⣷⣼⣶⣦⠀⠀⠀⠀⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⠷⠀⣠⢔⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢚⣵⣖⢿⣿⢛⡵⢪⡟⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠀⢠⣷⡲⠦⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠚⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠁⠀⠀⠀⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠉⠛⠶⣄⠀⠀⠀⣴⡶⢦⡀⠀⣠⡴⠖⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⢠⣾⡟⠉⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠂⢀⣠⡴⣞⣩⡤⠶⠒⠚⠛⠛⠓⠒⠶⢤⣄⡈⠳⣤⡀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠶⠚⣩⡵⠛⣩⡤⠶⠚⠛⠉⠉⠉⠉⠙⠓⠲⢤⣍⠓⢦⣝⠲⣄⡈⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣌⠳⣄⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠹⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⢹⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⣠⣾⡿⠟⣿⠟⠀⠀⠀⠀⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢿⣷⣤⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡼⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⡀⠹⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⣄⠘⢮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⢦⣙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⢦⣌⡙⠲⠦⢤⣤⣤⣤⣤⠤⠴⠖⢋⣡⢴⣞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠛⠉⠉⠛⠒⠶⠶⠦⠴⠶⠶⠒⠛⠉⠀⠀⠈⠳⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠈⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⡇⢀⡀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⡇⠀⠳⡄⠀⠀⠃⠀⠀⠀⠋⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⡀
⠀⣇⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⣄⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠧⣠⢤⣤⡶⠞⠋⠉⠛⠲⣴⠒⠒⠲⢄⡀
⠀⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢢⣴⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢸⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⣴⣦⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣀⡶
⠀⠘⣿⣿⣿⡀⣴⣶⣀⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢦⣴⡇⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠢⣄
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⠀⠀⠀⠀⢴⠀⢸⠂⠑⠦⣀⣐⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⢻⠀⠀⢠⡤⣇⣠⠎⠀⠀⠀⠀⠀⠈⡇⠉⠉⠙⡏⢁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢹⡇⠀⠸⣆⡴⠋⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⢳⡤⢤⣀⡎⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⡰⠒⡆⠈⠧⠤⣽⣽⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠀⠀⡏
⠀⠀⠀⠀⠀⢸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⠀⠀⠀⠀⠀⠘⢦⣀⣤⣀⠀⠀⠘⠈⠓⢋⣀⡀⠀⠀⠀⠀⠀⠀⣄⡴⠧⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⠇⠀⠀⠀⠀⡴⠋⠁⠀⠈⠱⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣸⠳⣄⠀⠀⠀⠀⠈⠉⠉⠒⠲⠤⣀
⠀⠀⢀⡠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣸⣇⠀⠀⠀⠀⣠⠇⣠⣀⣀⡀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠑⠒⠛⠻⠞⠳⢤⣈⣁⣉⣀⣠⠤⠖⠛⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠢⣤⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⣤⣄⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠒⠒⠢⠤⣴⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠛⠒⠶⠶⠒⠋
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡿
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠾⢤⡀⠀⢰⠇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣒⠚⠉⠓⢤⣀⡀⠀⣠⠋⠀⠀⠙⢶⡏
⡼⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡠⠊⠉⠛⠁⠀⠀⠀⠀⠀⠉⠲⢤⣀
⠀⠀⠈⠙⠒⠒⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⢴⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠦⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠹⣆⠀⠀⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⠏⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡘⢧⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⡾⠃⠀⠀⠀⣠⣾⠿⠂
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢠⡟⠁⠀⠀⠴⠟⠋
⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠶⢦⣤⣀⠀⣠⠀⠀⠀⢀⣀⠴⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠦⣠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠴⠋⠁⠀⢀⠀⠊⠀⠒⠂⠀⠑⠄⡀⠀⠈⠑⠦⡀⠀⢣⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠁⠀⡀⠀⣲⠤⠒⠊⠉⠉⠉⠉⠑⠒⠬⣶⢤⠀⠀⠠⠀⢸⡇⢸⠃⠀⠀⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠑⠄⣇⠀⠃⠀⠄⢐⠉⡠⠊⢁⠀⠐⠈⠀⣀⢀⠀⠁⠂⠀⠈⠙⢆⠀⠊⠀⡼⠀⠏⠀⠠⠞⣁⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡄⠀⠀⠀⣆⠞⠀⠀⠀⠀⠋⠃⠀⠈⠁⠀⠀⠰⠀⠀⠀⠀⠳⣤⣈⣀⠀⠀⠀⠐⠉⠉
⠀⠀⠀⠀⠀⠀⣄⣀⢠⠀⠀⠀⠀⠀⠀⣀⣤⡏⠀⡠⠐⠶⠆⠢⡀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⢣⠀⠉⠉⠉⠉⠉⡉⠉⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠘⢆⠀⠻⡍⠉⠉⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠘⡀⠀⠀⠀⣠⠊⠀⠀⡂⠘⢄
⠀⠀⠀⠀⠀⠉⠐⢢⠎⠉⠀⠀⣿⠀⠀⠀⢸⠀⠘⠀⠘⠁⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠘⠀⡇⠀⠇⠀⠀⢰⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠈⡄⠀⠂⠀⣠⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢠⠀⠐⠀⢸⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⡀⠀⠀⠱⡄⠀⠀⠉⠀⢀⡀⠁⠀⠀⠀⠀⡀⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⠴⠒⢈⣁⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⢀⡇⠀⠀⠀⠘⢆⠀⠀⢀⠐⠀⠀⠰⠇⠀⠀⠙⡠⠀⠀⡴⠃⠀⠀⠀⠀⠀⣾⠁⠀⢈⣉⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠛⢉⣤⠊⢀⠞⠀⠀⠀⠀⠀⡠⢑⠦⢄⡀⠀⠁⠒⠀⠈⠀⢁⡠⠴⡛⠄⠀⠀⠀⠀⠀⠀⠙⢄⠐⢦⣀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠋⠀⠀⠀⠓⣆⠀⠒⠀⠀⠀⠉⠁⠒⠒⠒⠒⠈⠁⠀⠀⠈⠚⠀⠀⣠⠖⠒⠒⠂⠀⠐⠀⠙⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⠀⠐⠒⠦⡀⠀⠀⠀⣀⣤⠖⠒⠒⠒⠦⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⢰⡎⠁⠁⢸⡇⠀⣤⠂⠐⡀⠀⠙⡄⢀⣿⠀⠴⠶⠞⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣼⡇⠀⠀⢸⡇⢠⡏⣸⡀⠸⡏⠉⣹⠋⣽⠀⣀⣀⠄⠀⢰⡇⠈⠀⣾⠀⣦⡆⠀⠀⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠸⡇⢰⡄⠀⠃⣼⠀⢶⣆⠀⠃⠀⠃⢸⣿⠀⠨⠀⠀⠀⢸⡇⠀⠀⣿⠀⣿⠀⢸⡿⠀⢹⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢸⣷⡀⠰⣧⡄⠀⢿⣤⡴⠀⣧⠀⠻⠛⠛⠛⠋⠀⢸⣇⠀⠀⠿⢀⡟⠀⣤⡤⠴⣿⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⡤⠘⠷⠖⠋⠀⠀⠀⠸⠷⠖⠙⠷⠶⠃⠀⠀⠀⠀⠀⠛⠷⠶⠖⢹⣧⣤⠂⠀⣴⣁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⣠⣴⣇⣰⣶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣛⣿⠖⠛⠛⠰⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⠡⠹⠋⠈⠨⢆⠙⠎⠉⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠀⠸⢇⠀⠄⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢌⠀⠀⠀⠀⢨⠃⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⣷⣿⠉⢠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⠄⣴⠛⣧⠀⠀⠀⣰⠀⠀⠀⣾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⡀⠙⣿⡃⠀⠈⠓⣡⡖⠁⠀⠂⠀⠀⠀⢀⣀⠀⢸⠧⣰⡧⠨⠋⠀⠰⠤⠿⠦⠤⢤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⣄⠈⠃⠐⠀⠀⠹⣷⠉⠠⠀⠀⠀⠀⢿⣿⠗⠚⠒⠛⠛⠛⠃⠈⠍⡂⢀⡲⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠸⣏⠲⣀⠀⠀⢤⡀⠈⠣⠠⠴⠒⠂⠀⡈⠛⠃⠀⠀⠒⠒⠀⠀⢀⠀⠰⣾⣧⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⣸⣿⢿⡿⢸⠇⠀⠘⣄⠈⠦⣔⢑⡢⠈⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡇⠘⠿⢿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⡞⢧⣾⠁⠀⠀⠙⢦⡀⠉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⢿⣿⣿⢡⠁⠚⢂⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠅⢰⡿⠀⠀⠀⠀⠈⠃⠀⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠂⠀⢠⣿⡿⢞⡃⠀⠨⢁⣀⣾⠻⠛⠁⢀⠠⣦⣤⣄⡀
⠀⠀⠀⠀⣾⣿⡿⠃⠁⡅⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠉⠀⠀⠀⠀⢀⣠⣄⣀⢀⠀⠀⠉⠁⢠⣾⡟⠂⣶⣾⠀⠀⡀⠉⣻⣷⣤⠀⠘⠃⠨⡉⠝⢻⢶⡀
⠀⠀⠀⠀⣿⣿⡷⡔⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⣧⣶⣤⣶⡨⢭⣋⣿⡟⣙⣻⡟⠀⢠⣿⡟⠀⠀⠀⣰⡗⠈⣠⣀⡐⠶⡟⠑⢦⣈⣞
⠀⠀⠀⢰⣿⣿⡇⠘⠈⣢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⢿⣷⣄⠀⣿⣇⠀⢀⠅⠀⣸⣿⣾⡿⣿⢃⡀⠈⠋⠀⠀⠠⠾⠿⠀⠚⠿⠗⠃⢠⠀⠀⠀⢹⣿
⠀⠀⠀⣸⡟⢻⡧⠠⠀⠀⠉⡟⠃⠈⢿⠀⠀⠀⠀⠀⢿⣿⣶⡤⣿⣏⡀⠘⠂⠀⣿⣿⣾⣿⠟⣿⢿⣶⣤⣤⡀⣠⠃⣠⣤⠤⠤⠶⣶⣵⣿⣷⡀⠈⢹
⠀⠀⠀⣿⡇⢿⡁⠀⠀⠀⢀⠃⠀⠀⢸⠀⠀⠀⠠⣞⣻⣿⣿⠂⣿⣿⡁⠀⠀⠀⢻⣿⣿⣿⣾⣿⠈⢿⣯⣿⣆⡀⠀⡈⢧⣴⣿⡏⠀⠉⢿⣿⣇⠀⣼
⠀⠀⢘⣛⠷⢜⡟⢀⢀⣀⢸⢁⣀⣀⣸⣀⣀⣰⣶⣿⣿⣿⣿⣿⠉⢙⣠⠀⠐⡔⢸⣿⠠⡿⡻⢿⣷⡾⢿⣾⣻⣧⣿⡄⠀⠻⡿⠁⠀⠀⠈⠛⠻⠄⢾
⠀⠀⢼⣿⣿⣟⣛⣟⣼⣿⣿⣿⣿⣧⣤⠉⠉⠉⠉⠙⠛⠛⠉⠙⠛⠓⠀⠲⠋⠑⠛⠙⠃⠘⠛⠛⠻⣧⣾⡗⢰⣤⣿⣷⣄⠀⡠⣰⢟⡇⢠⣩⡾⠂⣈
⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠽⠧⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠉⠓⠲⡿⠾⠁⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⠲⢤⡀⠀⠀⣤⠤⣄⠀⢀⡤⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡥⠀⠀⠀⠀⣀⠼⠃⠀⢠⣿⠏⠁⠀⠘⣆⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢉⣀⡤⢖⡯⠵⢒⣛⣉⣉⣉⣉⣛⡒⠦⢌⡑⢦⡀⠀⢀⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⡥⢞⣡⠶⠚⠉⠁⠀⠀⠀⠀⠀⠉⠛⠲⣌⡳⢬⡓⢤⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠳⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⢹⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⠀⠀⠀⠀⠀⠸⣿⢿⣧⡀⠀⢀⣠⣾⠿⠋⠿⠃⠀⠀⠀⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡆⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢆⠈⠆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⣌⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡓⠮⣝⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⡡⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡹⠗⠦⢭⣉⣛⣛⣛⣛⣉⡭⠴⠚⠙⢦⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣄⣠⣄⣤⢤⣤⡤⢤⢤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡠⠀⠀⠀⣀⠂⡀⠀⠀⠀⣤⢲⠀⠀⠀⠀⠀⢀⠀⢠⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⢉⣹⠀⢒⣁⠛⣣⣤⡉⣀⣀⣇⡏⣀⡀⠸⠷⢀⣴⣦⡈⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⡀⠐⠊⣵⣰⡏⣉⣷⣟⣹⣿⣋⣭⣿⠙⣯⣽⣀⠀⣺⡏⢻⣷⣾⣿⣦⠃⢀⡠⠴⠒⡶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣶⣶⠏⣈⣻⣿⣬⣿⣏⣈⣛⠋⠙⠿⢟⡉⠛⠳⢼⡇⠘⠟⢦⣼⡿⠐⢋⢶⡲⢸⠴⠈⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡌⠛⢫⣵⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣌⠛⠘⣠⠈⢧⡀⢡⡾⠟⠁⡳⢫⣶⠷⠛⠺⢦⡘⣡⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⡋⠀⣠⣴⣦⣤⢠⠶⣴⣯⢙⠛⢿⡿⠿⠿⠟⡃⠀⠈⠙⠃⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⡖⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠉⢛⣍⠀⢩⡟⠛⠚⠉⠷⠿⠻⣼⢁⣶⣦⣼⣽⡀⢀⣠⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⡍⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣶⠌⠳⢾⡏⢠⣿⠇⠀⢀⢀⡀⣠⣄⠘⢋⡀⠈⠁⣩⢿⡏⢠⡄⠀⠀⢚⠀⠀⠀⠀⠀⠀⣠⢎⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣾⣟⠛⣷⢾⠉⢸⡱⣹⢻⡷⣋⣿⣦⣸⡇⠀⣾⠁⢈⣷⠈⠁⠀⠀⣆⣀⣀⣀⣠⣴⣚⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠻⢿⣿⡿⠈⠳⠛⠟⠉⢁⡧⠛⣛⡉⠉⢳⡄⠻⣷⣿⠏⠀⠀⠀⢸⡱⣴⠤⢦⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⣄⣾⣿⡇⣿⠆⠀⠐⢸⡿⠁⣹⣿⠰⣠⣿⣿⡿⣦⡘⠿⠀⢠⣇⠳⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠨⡏⣹⣶⣴⣿⣦⡿⣦⢻⣦⣿⡿⢰⣿⡏⣸⣷⠀⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠹⣿⠰⣽⢾⣽⣷⠿⡼⣶⡿⢧⣌⠻⣿⣿⡟⣠⠃⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠶⠌⠛⠿⡾⠿⠛⣁⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠚⠓⠚⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄
⠀⠀⡄⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡼⡟⠁⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛
⠀⠀⣇⣛⣛⣃⣙⣀⣀⣀⣀⣀⠀⠀⠀⣷⣙⣛⣃⣙⣀⣀⣀⣀⣀⡀⠀⠀⣧⣿⣟⣃⣀⣀⣀⣀⣀⣀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⠘⢿⢲⡆
⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠇⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡾⠘⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠄⠀⠀⠸⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠹⠄
⠀⠀⠀⡀⣠⡐⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⠋⠉⠙⣦
⠀⠀⠀⣇⣉⣙⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⣷⣙⣙⣃⣙⣀⣀⣀⣀⣀⠀⠀⠀⣤⣙⣃⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣇⣀⣀⣀⣤⣤⣙⣀⣀⣀
⠀⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠄⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠇⠀⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠰⠿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠸⠄⡀⣀
⠀⠀⠀⠀⠀⣀⣤⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣷⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⢸⡄⠀⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾⣾⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡷⠶⠶⢿⣿⡷⠶⠶⠶⣶⠀⠀⠀⡷⠶⠶⢿⣿⣷⠶⠶⠶⢾⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⢾⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠈⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠈⠁⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣠⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠈⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡤⠒⢚⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⠳⣄⡀⠀⠀⠈⣇⠀⢋⣭⡥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢰⣇⠼⠉⠉⠉⣭⡍⠁⠀⠀⠀⣤⣤⠉⠉⠙⢇⢸⠀⠈⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⣸⢦⣼⠹⢤⠀⠀⠀⠀⠀⡰⠒⠲⡄⠀⠀⠀⠀⣠⠞⢸⣇⡤⢮⡀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡈⠙⠺⢧⡀⠀⠀⠀⢷⠒⢒⡞⠀⠀⢀⣴⡧⠖⠋⢁⡠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄⠀⠉⠓⠦⣄⣈⣙⣉⣀⡤⠖⠋⠁⠀⢀⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠬⠷⣄⠀⠀⠓⠻⢶⠾⠗⠃⠀⠀⢠⠶⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠨⢸⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⠤⠼⠾⠖⠒⠒⠒⠺⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠤⢄⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢀⣀⡠⠴⠶⣋⠉⢀⡴⠃⠀⠠⡞⠲⢄⡈⠓⢄⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢹⠋⠁⠀⠀⠀⠈⠉⢉⡴⠲⢄⠀⠳⣄⠀⣱⠀⠀⠉⠓⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠁⡠⠚⠉⠙⡆⠀⠀⠘⢦⣤⠜⠀⠀⠈⠉⠁⠀⠀⠀⢰⠋⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠙⠒⠒⠋⣁⣀⣀⣀⡀⠀⠀⢀⡤⠖⠦⣤⣀⡀⠀⠘⢦⣀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢳⣄⡤⠴⠖⠋⠉⠁⠀⠀⠀⠉⠉⠒⠿⢤⣄⣀⣀⣀⣉⣧⣀⠀⠈⠉⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⠒⠦⠴⠋

⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠
⡜⠄⠍⡀⠀⠀⠀⠰⠓⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢰⣯
⠘⠀⠐⠀⢄⠀⢨⡀⣰⠽⠆⠀⠀⠀⠀⢀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⢦⠀⠁⠀⠀⠀⠠⠊⠉⠉⠉⠉⠒⡀⠇⠀⠘⢁⣀
⠈⠱⡐⢀⠀⠕⣲⠟⠀⠀⠀⠀⠀⠪⡘⢗⣄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡀⠀⠀⠀⠀⠀⢀⡱⢤⡄⠀⢋⠉
⠀⠀⠀⠀⠂⢲⠃⠀⠀⢀⣤⠄⠀⠋⢀⠈⣤⠔⠀⠀⠀⡀⠄⢰⠀⠀⠀⠀⠄⠃⠀⢜⡰⣢⡽⠒⣒⣊⣒⡒⠺⢽⢢⣱⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠁⠴⠂⠀⠀⠀⠀⠂⠈⡐⡒⠒⡀⠈⠄⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠈⢉⠏⡴⠋⠁⠐⢠⡌⠐⠄⢉⠁
⠀⠀⠀⠀⠀⠈⣌⠂⠀⡀⠀⠀⠠⠊⠄⡐⠀⠒⣢⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠠⠀⠀⡰⠂⠀⠠⢸
⠀⠀⠀⠀⠀⠃⠈⠓⢄⠀⠀⠀⣠⡆⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠐⠛⠀⠀⠀⢀⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢦⡙⣒⣒⣒⣊⣡⡞⠁⠈⡄
⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣧⣤⣤⣤⣤⣤⣴⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡓
⠀⠀⢀⡀⠁⠀⠁⠀⢀⡠⠤⠀⠀⠄⠀⠀⠠⠚⠁⢤⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⢻⡆⠀⠀⡎⠀⠀⠀⠀⠀⣨⠖⠲⡀⠀⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠒⢤⣀⢀⡀⠁
⠀⠀⠀⠀⠈⢀⡤⢥⠀⡠⠔⢒⣒⣘⡻⠆⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⣀⣐⣁⣤⡉⢢
⠀⣤⡾⠋⠀⠸⠁⣬⠊⡴⠋⠀⠀⣶⠈⠑⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠃⢀⡏⡡⠒⠉⢉⡛⢿⣞
⠀⠁⠀⠀⠀⠈⠊⡆⡘⠀⠀⠀⢠⠇⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠄⢢⠀⣠⠎⢸⠁⠀⠀⠈⠁⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⡇⢃⠀⠀⠀⡘⠁⠀⠀⢠⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⠀⠀⠀⠸⠀⠀⠁⢸⡆
⠀⠀⠀⢀⠀⠂⠀⠘⢌⠢⣀⠀⠁⠀⣀⠴⢃⣎⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢃⠘⣆⠀⢰⠇⠀⠀⢀⢀⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⣤⠬⠩⠥⠔⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣠⠈⠓⠤⠤⠤⢔⡫⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⣿⣀⣂⣉⣡⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠒⠨⠭⠄⢀⣒⠒⠀⠤⠤⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠫⠭⠭⢍⣒⡒⠠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⡤⠒⠢⣄⠠⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠉⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⢀⠀⡆⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡀⡸⠀⡆⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⢀⡀⢀⠦⣠⠁⠈⢧⡀⠀⠀⠀⠘⡦⢤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠒⠛⠁⠀⢇⠠⡀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⣄⠊⠓⠁⠀⠀⠀⡀⠈⢷⠀⠀⠀⠀⠉⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⢆⠷⠨⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠂⠀⠀⠰⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⢸
⠀⠀⠀⠀⠠⠔⠪⠕⢂⠿⡀⠀⠀⠀⠀⡤⠒⠂⡗⠀⢀⠆⠀⠀⠀⡇⡅⠀⢸⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⢸
⠀⠰⠪⠐⠈⠀⠀⠀⠀⢑⡛⠦⣀⡀⠀⠈⠒⣚⡤⠖⠉⢄⠀⠀⠀⣇⠀⢀⢸⠃⠒⠠⠬⢉⣒⠢⠤⢄⣀⡀⠀⠀⠀⠀⠀⠰⢰⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⡈⠉⠉⠉⠩⢉⠐⠀⠀⠀⠱⣄⢀⠀⠙⠉⠙⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠬⠭⣒⡒⠦⢤⡆⠇⠀⡆⣿
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠠⠀⡠⠄⠳⡀⠈⢢⡉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣰⠀⠀⠇⣿
⠀⠀⠀⠈⡄⠀⠀⠀⠈⠂⠀⡈⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠈⢀⠀⠙⠄⠀⠁⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠓⠁
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⡀⠀⠐⠀⠀⠀⡠⠐⠁⠑⠖⠈⠂⣀⠀⠀⠀⠀⠉⠁⠐⠀⠤⣀⡀
⠀⢀⢀⡀⡔⠀⠀⠀⠀⠀⡠⣄⡠⠊⠀⠑⡀⠀⠈⢢⠊⠀⠀⠀⠀⠈⠑⠛⠁⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠈⠁⠒⠠⠀⠀⣀
⠀⠈⢸⠀⠣⠀⠤⢤⡒⠉⢱⠊⠀⠀⠀⠀⢈⠦⡤⠚⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢢
⠀⠀⢸⠀⠀⠀⠀⠀⠈⢡⠃⠀⠀⠀⠀⢠⠋⠀⠈⠤⠴⠇⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢈⡇⠀⠀⠀⠀⠀⠀⣠⠔⠁⠈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡇⠈⠁⠐⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠈⠉⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠃
⠀⠀⠘⠒⠢⠤⢀⡀⠀⠇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⣠
⠀⠰⠴⠄⢀⣀⠀⠀⠉⠑⠲⠤⢀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⠔⠁⠀⠀⠀⠀⢀⡴⠋⣸
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⠀⠀⠉⠑⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⢀⠔⠉⡠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠁⠒⠢⠤⣀⡀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠔⢁⡴⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠙⢦⣅⣤⠒⢄⠀⠀⠈⠉⠒⠲⠤⢀⡀⠀⠈⠉⠒⠒⠤⢄⣀⠀⠀⠀⠀⠸⠀⡠⠊⢁⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⣀⡎⠀⠀⠑⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⢀⡀⠀⠀⠉⠑⠒⠤⡔⠋⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠂⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢄⣀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⠟⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠏⠀⠀⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢨⡅⠀⢠⡉⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠉⠉⠀⠀⠀⠈⠉⠻⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣷⣤⣀⣀⣤⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣤⣤⣾⣟⣛⡒⠶⣤⡀⣤⣀⣐⡄⣰⠞⠉⣁⣤⣶⣶⣿⣿⣿⣁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣷⠞⠃⠉⢻⡏⠁⠈⠓⠾⣿⣿⣿⣿⣿⣿⣿⣟⢦⠈⢳⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⣰⠃⣰⠃⣿⣿⣿⣿⣿⡿⢋⣠⡴⢶⣚⣻⣿⣿⣿⣿⣶⣦⣭⣿⡿⣿⣿⣿⣿⢸⡇⠘⡇⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⣿⠀⢿⣿⡿⢛⣿⠟⣫⣴⣾⠿⠟⠛⣛⠛⠛⠛⠿⣿⣿⣿⣷⣤⡉⠛⠿⣼⠇⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠹⣤⠞⠋⣠⠋⣡⣾⠿⢋⡀⠀⠀⠀⣿⠀⠀⠀⠠⠆⠉⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣾⡿⠁⠀⠈⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢈⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⡟⢠⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣾⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⣿⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠿⠇⢸⢿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣼⣿⡄⠉⠁⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡆⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⢃⣿⠇⢀⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻⡄⠘⣿⣿⣷⡜⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⣾⠏⢀⡞⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠻⣄⠈⢿⣿⣿⣦⣀⠀⣤⠀⠀⠀⣠⡀⠀⠀⠐⢂⣤⠞⣱⡿⠋⠀⠋⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⠿⣿⣿⣷⣦⣤⣀⣀⣘⣁⣠⡤⠶⣋⣵⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⣿⠿⢿⣿⣿⣿⣿⣿⣶⣾⠿⠟⠉⠹⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠈⠉⠉⠉⠀⠠⠤⠖


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

⠀⠀⠀⠀⣀⣤⣴⠶⠶⠖⠒⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠶⣦⣤⣄⡀
⠀⠀⣠⡾⠛⠉⠀⢀⣠⠤⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠤⣀⠀⠈⠙⠻⣷⣄
⠀⢸⡟⠀⠀⣠⠞⠉⠀⠀⢰⠟⠚⠉⠙⣿⣿⣿⣷⡄⠰⣿⣿⠿⠟⠀⠀⠀⢠⣶⣿⡉⠀⠀⠀⠁⠻⣇⠀⠀⠙⢶⣄⠀⠈⢻⡆
⠀⢻⠀⠀⣸⠏⠀⠀⠀⡰⠁⠀⢀⣤⣾⣿⣿⠟⠋⠀⠀⣀⣸⣇⣀⣀⣀⠀⠀⠙⠻⣿⣿⣶⣤⣀⠀⠘⣦⠀⠀⠀⠹⣆⠀⠀⣿
⠀⠈⠀⠀⣿⠀⠀⠀⢠⡇⠀⣠⣾⣿⡿⣋⢁⡠⠔⣚⣩⣥⣴⣶⣶⣶⣮⣭⣟⣶⣤⡀⢙⠿⣿⣿⣿⣾⣿⡇⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠘⠄⠀⠀⠘⣷⣾⡿⠟⠁⢈⠟⣩⣴⡿⠟⠋⠉⠁⣴⣤⠀⠉⠉⠛⠿⣿⣿⣿⣇⠈⠙⠿⣿⣿⡇⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⡰⢡⣾⡿⠋⠀⠳⠀⠀⠀⠙⠋⢀⣾⠀⠟⠀⠈⠻⣿⣿⣧⡀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⠋⡀⠀⠀⢢⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣀⡈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⣿⠇⠀⠙⠀⠀⠀⠑⢄⠀⠀⢠⣿⠀⠀⠀⠀⠀⠉⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣀⠘⣿⣿⡄⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣎⠀⡇⣿⣯⠸⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠛⠛⣀⣿⣿⡇⢸⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣸⢇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢆⠘⣿⣿⣧⠀⠴⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⡌⣬⣿⡏⢠⢍⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⡀⠀⠀⠻⠃⠀⠀⠀⢀⠀⠀⢀⢌⣼⣿⡟⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠘⠁⠀⠀⢰⣿⠀⠀⠀⢈⡡⢐⣵⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⣦⣤⣀⣀⣁⣀⣂⣨⣵⣾⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠉⠛⠻⠿⠿⢿⣿⠿⠿⠿⠛⠋⠁⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⢈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡀⠀⡀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔⠀⠀⠀⢲⠄⠂⠀⠀⣀⠀⠐⠠⢀⠀⠀⠀⠁⠐⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠄⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⢰⠂⣀⢀⠖⠝⠳⠀⠀⠀⠘⠣⡄⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠙⠀⠀⠀⠘⠛⡿⠌⠀⡀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣩⡀⠀⠀⢠⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠇⠀⠀⠀⢀⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢀⠀⠀⠀⣰⠀⠀⠀⠆⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠡⠚⡃⠿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢤⠀⠂⠘⢀⣀⣰⠀⠀⠈⣀⡤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠈⡀⠙⠒⡀⢧⣨⣤⡀⡀⡀⠀⠩⠤⢤⠴⠟⠐⠠⢀⡀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⣠⠴⠓⠋⠁⠃⠀⢠⠌⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠁⢢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠖⠂⠁⠀⠛⠒⠂⠀⠀⠀⠈⠁⠒⠒⠀⠤⠀⠀⠂⠀⠠⠈⡀⠃⠤⠂⠀⠀⡠⠦⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⢠⠀⡀⠁⠀⠀⠊⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡨⠶⣦⣴⠔⣀⠀⠄⠱⢤⡀⣀⠄⢀⠀⠀⢀⡆⡄
⠀⠀⠀⠀⠀⠀⠤⠄⠈⢁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⡇⠀⢀⢀⡄⠀⢆⡵⠛⣾⠈⠀⢠⢀⡹⣆⠀⢁⣤⠶⢛⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠄⢀⠀⠉⠑⠂⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠦⠤⠄⠀⠑⠤⠄⠠⠀⠀⠈⠉⠒⢧⠀⠹⠞⢉⠤⠶⠋⠐⠇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠑⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠰⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⡀⠀⠀⠀⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠆⣀⢀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠁⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⢠⡀⠀⣠⣤⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢀⣠⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣾⣿⣿⣽⣏⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢆⣀⣠⣴⣶⣶⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣡⣠⣶⣶⣦⡄⠀⠀⠈⣿⣷⠂⣸⣿⣿⣿⡴⠶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣹⣿⣾⣿⣿⡿⣧⣤⣤⣤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⡿⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠙⣻⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣿⣿⡿⠿⠿⣿⣿⣿⣯⣿⣿⣿⡟⢀⣿⣿⡿⠟⠿⣿⣍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣾⣿⣿⠋⣿⡿⣿⣷⢸⣿⣿⣇⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡟⠛⠛⣿⣿⡿⢹⣿⣿⣿⣿⡀⢿⣿⠿⠛⠁⢹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⠛⢿⣿⣿⣿⣧⠀⠹⣷⣾⣿⣿⣷⣾⠿⠻⡉⢻⣧⠸⡿⣦⣤⣶⡏⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠘⠁⠈⠁⠀⠁⠀⣿⣿⣿⣿⣿⣦⡀⠀⠉⢀⣹⣿⠃⠀⠀⠀⠀⢿⣷⣄⣈⣉⣹⣶⣿⣿⣿⣿⣿⣿⣿⣧⠈⠃⠀⠻⣧⡾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢸⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠋⣻⣿⣿⣿⣿⣿⡟⠉⠻⣧⠀⠀⠀⣿⡷⢘⣿⣄
⠀⠀⠀⣠⠇⠀⠀⢠⡟⠀⠀⢻⡇⠀⢹⣿⣿⠛⠉⠹⡏⠉⠙⠧⡀⠀⠀⠀⠀⣠⣿⡛⠛⠷⠀⠋⠁⠉⢿⣿⡿⠀⠀⠀⠙⠀⠀⠀⣿⣷⣿⣿⣿⡆
⠀⠀⣴⣿⣴⣶⣾⣿⡇⠀⠀⠀⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁
⠀⠘⢿⣿⣿⣿⣿⠙⢿⡄⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠂⠀⠀⠀⠒⠦⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋
⠀⠀⠈⠛⡟⠉⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⢿⣷⠀⢠⣶⠗⠒⠒⠲⢾⠤⠽⠟⠃⠀⠀⠀⠀⠤⣴⣿⢆⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣄⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠍⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⢚⣭⣶⡂⠉⠉⠁⠒⠬⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠢⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠞⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡞⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⢃⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣧⠀⠀⢸⠸⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠱⣄⠀⣇⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠻⣇⠀⡠⠋⢑⠼⣎⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣴⠧⣠⠈⠓⡟⠛⠛⠻⠿⠷⣶⣶⣾⡿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⣠⣴⣶⣿⣿⣿⣧⡀⠩⢃⠀⠀⠀⣸⠃⠀⠀⠀⠀⢠⣿⠟⠛⠃⠀⠈⠙⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣄⣀⣀⣀⣀⣀⣀⠀⠚⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡙⠻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢳⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⠉⠀⠀⠀⠉⠑⠦⡀⢔⠉⠉⣉⣩⠆⠀⣠⠖⠋⠁⠀⠀⠈⠙⠲⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂⠉⢹⠁⠀⠀⠸⣅⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣠⠴⠊⣁⣠⠤⠤⠼⠦⠤⠤⢤⣀⡉⠓⢤⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⡤⠖⣻⠿⠓⠉⠀⣀⣀⡤⠤⠤⠤⣀⣀⡀⠈⠑⠺⢿⡓⠢⣄⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⡤⠚⠁⣀⠤⠒⠉⠁⠀⠀⠀⡀⣀⠀⠀⠉⠑⠲⢄⡀⠉⠲⣄⠉⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⠞⠁⠀⠀⢀⣤⠀⠀⠀⣏⣹⠃⠀⠀⣀⠀⠀⠙⢦⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠞⠁⠀⠀⠀⠀⠠⣿⠀⠀⠀⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠙⢆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠎⠀⠀⣰⡔⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠀⠈⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡞⠀⠀⠀⠙⠳⠾⣀⢰⣦⣄⠀⠀⢰⠇⠀⠀⣀⣤⣶⠟⠻⠷⠀⠀⠘⡆⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⢀⡤⡄⠀⠀⠈⠉⠛⠿⣿⣦⣼⣤⣴⡾⠟⠉⠀⠀⠀⠀⢠⡀⠀⢳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠈⠓⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣘⠇⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢣⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣆⠀⠀⢠⠇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢧⠀⠀⠘⠛⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠳⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣴⡀⠀⠀⠀⢙⣳⠀⠀⠀⡰⠋⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠷⠏⠀⠀⠀⠈⠁⢀⡠⠊⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠈⠙⠲⠤⣀⣀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣹⠶⢤⣀⡀⠈⠉⠉⠉⠉⠉⠀⢀⣠⠤⠾⡉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡜⠁⠀⠀⠀⠈⠉⠉⠓⠒⠊⠉⠉⠁⠀⠀⠀⠙⣌⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢣⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⡀⠀⡸⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡗⠙⢦⣀⠀⣤⡟⠨⣿⠀⡚⠉⣄⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠲⠶⠶⢚⡅⠀⠀⢿⡄⢸⠁⠦⣿⡄⠠⣶⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⣆⠀⢸⡇⢠⡀⢸⣧⠀⣤⡀⠸⣇⣈⣥⠴⠦⢤⡶⠖⠊
⠀⠀⠀⠤⣤⣤⠤⢶⣆⠸⣧⢀⠻⡀⢸⡇⢘⣁⡀⢻⣄⠝⠿⠚⠋⠁⠀⠀⠀⠈⠳⠤⢤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠲⣽⣷⡘⠈⣧⡀⣸⣧⡜⠉⠛⠉⠁⠀⢴⡆⠁⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢿⠶⠛⠛⢁⠠⢠⡆⢻⡆⠚⠷⢨⣿⣠⠀⢠⠶⠶⠦⠼⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣀⣀⠀⠀⢻⣆⠈⣿⡈⣷⠀⣾⠻⢿⡷⠛⠻⠦
⠀⠀⠀⠀⡠⠶⠛⠚⠉⠉⠉⠉⠙⣦⠀⢿⣦⣭⡴⠻⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣤⣀⣘⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣋⡒
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣛⣻⡭⣯⢩⡭⠝⠻⣿⣟⣫⣽⣶⣶⣶⣤⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⢻⢡⡟⣃⣛⡈⠛⢷⣦⣬⣭⣙⡛⠻⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢳⣦⠠⠹⣇⠻⢻⢿⣿⣷⣦⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠂⠀⢸⣤⡾⣦⠹⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠙⢑⡀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡴⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⢦⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⣰⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡹⣄⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢈⡷⠟⠚⠋⠉⠓⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡖⠟⠋⠙⠒⡿⣾⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢫⠂⠁⠀⠀⠀⢀⣠⠤⠾⠂⣀⣀⣀⣀⣀⣀⠘⠧⢤⣄⡀⠀⠀⠀⠈⠀⠙⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠁⠀⠀⣀⣴⠚⣉⡤⠖⠚⣉⠩⠤⠄⠤⠤⠉⣉⠓⠲⢤⣉⠓⣦⡀⠀⠀⠀⠜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⢑⡴⠋⡡⠴⡈⠁⠀⠀⢰⠀⡀⠀⠀⠀⠀⢑⠢⢈⠛⢤⡋⠳⣄⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠞⠁⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⢆⠈⢣⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡞⢡⠚⠠⠀⠀⠀⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠷⡈⢧⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠃⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠆⡠⢄⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢡⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⡰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢠⠆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠹⡁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⠀⠀⡀⢀⡔⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡁⠢⣀⡐⠀⠀⠀⠀⠀⠙⠤⠁⠀⠀⠀⡀⠔⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢉⡷⢤⣉⡐⠀⠀⠠⠤⠤⠄⠀⠐⢂⣁⠤⢾⣁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣡⠎⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⠻⣦⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡀⠀⣠⣶⣾⠿⣦⠀⢠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⣿⠇⢤⠐⠆⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⡄⠀⠀⠀⣸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣤⣤⡀⣠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⣠⠔⠀⠈⠙⠛⠛⠉⠉⠉⠛⠃⠁⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠒⠒⠒⠲⠤⡀
⣼⡁⠤⠐⠒⠒⠋⠉⠉⠉⣉⠉⠁⠈⠀⠀⠐⠒⠂⠤⢀⡀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣧⡄⠔⠀⠉⠉⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠈⠙⠙⠉⡃
⡆⠀⢀⠤⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⣴⣶⣿⣿⣦⡀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⢀
⡄⠀⠈⣦⠗⢁⡀⠀⠀⠀⠀⠀⠀⢽⣯⠀⠉⠋⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⢱
⠀⠀⠀⠀⢛⠀⠁⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⢚⠈⡝⠃
⡇⠀⠀⠀⢸⡟⠀⠀⢀⢢⢤⠀⡀⢀⠸⠀⠘⠋⢰⠀⠀⠀⠀⠀⠀⡇⣀⠔⠀⠀⠛⢇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⡞⡆⠀⠀⠀⠀⠀⡤⢯⡀⠁⠈⠐⠒⠀⠒⣿⠀⠀⠀⠀⠀⣢
⡀⠀⠀⠀⢘⡢⠤⣀⠀⠁⠃⠀⢸⠀⠀⠈⠉⡀⠀⠀⠀⡄⢀⡄⢀⠻⢠⢀⣆⠠⠊
⣇⠤⠀⠐⠁⠀⠀⠀⠉⠁⠀⢻⡆⠀⠀⠀⠀⡤⠀⠀⠀⠛⠋⠑⠛⠀⠨⢌⡁
⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡟⣆⠀⠀⡠⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠼⢂⠕⠀⠀⡐⠀⠉⢀⡠⠐⠒⠒⠉⣁⡀⠈⠠⠄⠒⠶⢤⡀
⠀⠈⠢⣀⠀⢈⠠⠀⣀⡀⡠⠊⠀⠀⡎⠀⠀⠄⠀⠀⠀⠋⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄
⠄⠀⠀⡈⠳⠀⠀⠀⢀⠎⠀⠀⠀⢰⠀⠠⠂⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠢⠤⠎⣷⢯⠔⠊⣁
⠀⡐⠁⠀⠀⠑⠦⢤⠊⡄⠀⠀⠀⠃⢠⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠐⠻
⢸⠀⠀⠊⠀⠀⢀⠎⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⡁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⢀⡌⠀⢀⠀⠀⢀⠃⠀⠀⠀⢠⡞⠻⠇⠠⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠂⠘⠀⠄⠀⠀⢰⢸
⠠⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⠂⠀⠀⢠⠂⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠢⢸
⠀⠀⠀⠀⡜⠀⠀⠀⠃⢀⠎⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠄⠂⠀⠉⠙⠁⠀⠀⠀⠀⠀⢸⠀⡅⠀⠀⢸⠰
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠊⠀⠀⢀⡠⢠⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠁⠀⠀⠘
⠰⡀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⣀⣈⣒⣠⣤⣤⣤⣄⣤⣤⣤⣤⣤⣼⣸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣀⣄⣀⣀⣀⣀⣀⣬⣠⣇⣥⣤⣚⣁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿