Reaper and Trace Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣉⢂⠀⠀⢀⣀⣀⣤⣴⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⡴⠚⢛⣁⣤⣤⣤⠤⣴⣶⣶⣦⡀⢀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠐⢠⣿⣿⣿⣿⣿⣷⠖⠛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⠏⣿⣿⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⢣⡀⡘⡆⠀⢘⣿⣿⣿⣿⣿⣿⡿⠟⠿⢿⣯⡵⢿⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⡿⠿⣆⣀⣴⣋⡀⠈⠃⣾⣿⣿⣿⠿⠛⠉⣀⣀⣠⣤⡿⡶⣋⡉⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣴⡟⠛⢛⢻⡗⢢⣬⣙⣿⣿⣧⣄⠀⣾⠔⠛⡟⣖⣾⣶⡿⠇⣿⣷⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡤⠶⠄⠠⠾⡋⠻⣹⡟⠻⢿⣿⣿⣾⣽⣿⣿⣿⣿⣯⣧⣼⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣥⣿⣿⣦⣄⠱⠪⠎⠉⠀⢸⣷⣄⣀⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀ ⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣹⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠻⣿⠀⠀⠉⠁⢘⣷⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⡄⠀⠀⢸ ⡾⡻⠭⠚⣋⠁⠀⢉⠛⠻⣿⣿⣿⣿⣿⣟⣯⠦⢿⣿⣿⣿⣇⣤⡴⠋⢰⡿⣿⣿⣿⣿⠟⣸⣿⠆⢀⣴⣾⠟⠁⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡎⣧⠀⠀⠸ ⡋⠀⠊⠉⠙⠀⠀⠀⠀⠀⢻⣿⡿⣫⣿⢿⣷⣶⣾⣿⣿⣟⠻⢿⡀⢀⣾⣿⣿⡿⢿⣿⠞⢱⣷⣶⡿⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣤⢀⣔⡀⠀⠀⡂⡢⡛⠀⣨⣿⣿⣿⡏⣿⣿⣿⣿⡿⢿⣿⣿⣶⡑⣾⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⣿⣿⣷⣤⣀⣲⣬⢈⣍⣿⣿⣿⣿⣿⣼⣿⣿⠟⣏⣴⢿⣻⣿⡟⢳⢏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⢻⣿⣿⣿⣿⣿⣿⣶⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⠈⡎⢳⣿⣽⣿⣽⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡹⢛⣿⣿⣿⣿⣿⣿⣯⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀

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╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢀⣠⠷⠒⠉⠉⠉⠉⠉⠓⠒⠂⢉⡿⠃⠀⠀⠀⠀ ⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠛⠛⠓⠲⣶⠤⣤⣀⣀⠀⠀⠀⢠⠞⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣶⠋⠀⠀⠀⠀⠀⠀ ⠀⠻⡟⣩⣤⣽⡖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣧⠖⠚⢹⡷⠋⠁⠀⠈⣷⡉⠙⠒⠦⣄⣳⣴⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀ ⢀⡴⢻⣿⣿⣿⣿⡶⣤⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠲⠦⠤⠤⠖⠋⠀⢀⡔⠁⠀⠀⠀⠀⢀⣘⡏⠛⠶⣦⣄⠉⠻⢿⣿⠃⠴⠾⠛⠶⢄⡀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⣼⠁⢸⣿⠿⠋⠁⠀⠘⢦⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢀⠄⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⣼⣼⠀⠀⠈⠻⣝⢦⡀⠙⢷⡀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⢷⡀⢿⡁⠀⠀⠀⠀⠀⠈⢷⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠋⠀⠀⠁⠀⠀⠀⠀⣠⠎⣠⠞⠉⡏⡇⠀⠀⠀⠈⠑⣿⣤⡈⢿⡆⠀⠀⠀⠀⠀⠹⡄⠀⣀⡀⠀⠀⢧⠀⠀ ⠀⢷⡀⢳⡀⠀⠀⠀⠀⠀⠀⢷⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣠⠆⠀⠀⠀⢀⣴⡷⠚⠁⠀⠀⡇⡇⠀⠀⠀⡀⠀⡟⣿⡟⠋⢹⡄⠀⠀⠀⠀⠀⠃⠀⢹⡙⠳⢤⣸⠀⡀ ⠀⠀⢳⡄⠻⡄⠀⠀⣀⣤⣶⡶⢷⡄⠙⣆⠀⠀⠀⢀⡀⠀⣀⣯⠴⠊⠁⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣇⢸⣇⢯⡀⢀⣸⠛⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣹⣶⠁ ⠀⠀⠀⠹⣆⠘⣦⣿⠟⠉⠀⠀⠀⢻⣀⣘⣦⡀⠀⠀⠙⠫⢤⣤⡤⠤⠖⠛⣹⠟⠂⠀⠀⠀⠐⠒⠒⠢⢾⣧⡀⠀⠀⠸⣞⣿⣿⣿⣿⣿⠀⠿⣆⠀⠀⠀⠀⠀⠀⡇⣠⠞⢁⣩⣤ ⠀⠀⠀⠀⠙⢧⡈⢣⡴⣄⣠⣤⣾⣏⠉⠉⠉⠁⠀⠀⠀⠀⡼⢹⠀⠀⠀⢠⣧⣠⡄⠀⠀⠀⣦⣀⠀⠀⠀⢳⣬⠃⠀⠀⠹⡽⣿⣿⣿⡟⠀⡾⠸⡄⠀⠀⠀⠀⢠⡟⠁⠀⣸⣹⣿ ⠀⠀⠀⠀⠀⠀⠳⣼⡇⣿⠉⠉⡉⠉⠙⢲⡄⠀⠀⠀⢀⣼⣁⡴⣇⠀⠀⣼⠙⡟⣿⡇⠀⠈⠉⣿⡟⠦⣀⠸⣿⠳⢦⣀⠀⢻⠿⢿⣿⠃⢀⡇⠀⣿⠀⠀⠀⠀⣼⢀⣠⣶⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⢹⣥⠟⠋⠉⠻⣿⣿⣦⡻⡄⠀⠚⠋⠁⠀⠀⠹⡄⠀⣿⠀⡿⣿⠄⠀⠀⠠⣿⣧⠀⠼⠛⢿⠀⣀⣈⣽⢋⣄⢸⡏⠀⡾⠀⡸⢋⡇⠀⠀⢠⠇⠀⠉⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣿⣿⣷⡙⣆⠀⠀⣼⡇⠀⠀⠱⡄⣿⢰⠇⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⣿⡿⢱⠋⡸⣰⣇⣞⣤⠞⠁⣼⡇⠀⢠⡎⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠚⣆⣼⡿⠁⠀⠀⠀⠙⢾⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⣊⡴⠛⠁⠉⠀⠀⠀⣸⠏⡇⣰⠏⠢⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣴⣿⡏⠀⠀⠀⠀⣀⡀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⢰⠏⢀⡿⠃⠀⢰⡀⣠⣟⡿⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣿⣧⣶⣾⡿⠿⠟⠀⠀⠀⢰⡽⡆⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⠋⠀⣸⢁⣠⣾⣯⣭⣉⡉⠙⠲⠦⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⡆⠙⢲⡟⣻⣿⣿⣿⣿⣿⣿⣟⣽⣷⡄⠀⠀⢀⣠⠞⠁⠀⠔⠋⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⠤⣶⣋⠁⠀⠀⠀⠀⠀⣿⠿⣿⠿⠿⠛⠛⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣷⡀⠀⠀⢀⣠⠼⣷⣖⣫⣿⣾⣿⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠈⠛⢓⣦⣤⣐⣾⡁⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⢺⠙⢣⣭⡵⠾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣩⠟⠋⠉⢻⣿⣿⣷⣤⡀⠀⠉⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⢨⣶⣦⡀⠀⠀⠀⠀⣠⣿⠁⠳⣄⠀⠘⡿⠛⠿⣿⣷⠀⠀⠀⠈⠙⠢⣀ ⠆⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠀⠀⠙⠂⠐⢒⣾⣿⣿⣇⠀⢿⡄⠀⡇⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠈ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠙⣿⡿⣿⣿⣷⡀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠈⢧⡈⢧⡀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⡟⠀⠘⣿⣿⣷⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⣠⢾⠉⠳⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣰⡇⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡼⠁⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠟⣧⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣇⣠⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢸⣿⣦⠀⠀⠀⠀⢻⣿⣿⣧⣠⣤⣄⠀⠀⠀⠖⠀⠀⠈⣿⣿⡏⢹⠋⠙⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⣼⢻⣿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣩⣿⣶⡄⠀⠀⠀⣠⣿⣿⡟⠀⢸⡄⣼⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣾⠃⠀⣿⡄⠀⠀⠀⡆⠻⣿⣿⣿⣿⣿⣥⣽⣄⠀⣴⣯⣾⡟⠀⠀⠀⣿⠁⣸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⡟⠁⠀⠀⣿⣷⠀⠀⠀⡇⠀⠻⣿⣿⣿⣿⣿⣷⣿⢾⣵⣿⠟⠀⠀⠀⠀⣻⣿⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⠀⣀⣼⠟⠈⣧⠀⠀⠸⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⢻⡛⠉⠉⠈⠛⢿⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜🟧🟧🟧🟧⬜⬜⬜⬜🟧🟧🟧🟧⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬜🟧🟧⬜⬜⬜⬜⬜⬜⬜⬜🟧🟧⬜⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬜🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧⬜⬛⬛⬛⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜ ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛ ⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜ ⬜⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⢔⠒⠒⠖⣒⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⠀⠁⠀⠀⠀⠀⠀⠀⠙⠚⣕⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⣫⣶⠶⢶⣿⡿⠿⠯⢷⣦⡀⠀⠀⠀⠀⠳⣝⢄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⡯⠵⠛⠛⠾⠿⣾⣿⣹⣷⡀⠀⠀⠀⠀⠈⣏⣯⣿⣷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣟⠁⠀⠁⠀⠀⠀⢸⠆⠙⢿⣿⣇⠀⠀⠀⢠⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢹⠏⢦⢸⡀⠀⠀⠀⡜⠀⠀⢀⣹⣾⡄⠀⢧⢸⡟⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣾⢸⣷⣿⣷⣤⣤⣾⣤⣔⣾⣷⡖⣿⡇⠀⠘⣌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠾⠗⠀⠀⡼⡀⣾⣿⡀⠙⠛⢻⠀⠀⢠⠿⠿⠟⠛⢡⣿⣧⠀⠀⠘⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢱⣿⣿⣿⣷⡀⠘⡇⢀⣞⠀⢠⣶⣿⣽⣿⣺⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠆⢸⣿⣿⣿⢾⣷⠐⣿⣾⡏⢀⣿⣿⣿⣿⣯⣿⡆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢀⣤⣴⣶⣤⣄⢠⣟⠛⠁⠀⢸⣿⣿⣿⣦⣹⡆⣿⣿⠃⢸⡿⠻⣹⣿⣿⣼⣷⠀⠀⠀⠀⠐⡙⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠿⣛⡿⣿⣿⣿⢦⣄⣀⠀⣿⡿⠛⢻⣝⣇⠸⠿⢀⣸⣾⡽⡟⠙⣿⣿⣿⣧⠀⠀⠀⠀⠈⠊⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡿⣊⡐⠖⡾⢿⣿⠛⢯⣷⠿⣇⣹⣿⠀⠀⣿⡾⠢⣴⣿⡟⠁⢸⠁⠀⣿⣶⢉⣿⣇⣂⣤⢴⣶⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⠛⠚⠁⠀⠀⠀⠀⠉⠳⢽⡭⣿⣆⠨⡝⣻⡾⠋⠘⠁⢠⡇⠀⠀⣟⣏⣾⣿⠟⠉⢱⣾⠿⠋⡱⡄⣴⣀⠀⠀⠀ ⠀⠀⣠⣳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⣶⣏⣁⠱⡄⠀⠀⠘⢀⣀⣼⣿⣫⡞⣁⣤⡶⠋⠁⠀⠀⠙⡌⢿⣯⠄⠀⠀ ⣠⣾⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣝⡦⣄⠀⠀⢁⣼⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⡝⣄⠀⠀ ⠻⣷⡇⠀⠀⠀⠀⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⠿⣿⣿⣧⢶⣿⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⠮⠳⣄ ⠀⠀⣿⣦⣄⠀⡀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⠀⠀⠀⠙⢿⠛⠁⠀⢸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠠⣰⡿⠀⣰⣠⠞⠉ ⠀⠀⡿⣯⣏⡳⢽⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠸⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣰⣿⡇⠀⠀ ⠀⠀⣧⠘⢿⣾⣄⡙⣜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⡇⠀⠀⠀⢀⡇⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣏⣾⣿⢿⠃⠀⠀ ⠀⠀⠘⡇⠀⠙⢿⢇⡜⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢷⠀⠀⠀⠘⡇⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡞⢡⠏⠀⠀⠀ ⠀⠀⠀⡽⣄⠀⠈⠻⣵⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⢧⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⢀⣿⠏⢠⡏⠀⠀⠀⠀ ⠀⠀⠀⣧⠈⢦⡀⠀⠙⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠀⠀⠀⠀⢸⡀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣸⠃⢠⢿⠃⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠙⢦⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣻⠀⠀⠀⠀⢸⡇⠀⠀⣿⣁⡀⠀⣀⡬⠞⢸⠃⠀⢐⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⣀⠀⠁⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⢸⡇⠀⣈⣫⣥⠶⠋⠁⠀⣠⣏⡤⠤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⢳⡄⠀⠀⠀⠀⠀⠒⠤⠬⠦⠴⠶⢶⣺⡿⠿⠿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⣸⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢢⠢⡕⢣⠚⡔⢣⠎⡔⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⢣⠜⡌⣆⠳⣌⢣⡙⣌⢣⠚⡴⢡⢋⠖⡬⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣧⡈⢱⠪⢴⠌⠓⠈⠂⠀⠀⠙⠈⠒⠡⢞⡸⡰⢁⣴⣷⣄⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⠀⠀ ⠀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡆⢰⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⠀ ⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣼⣿⣿⡇⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⢸⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⡄⣠⣾⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⢠⣿⣿⣿⣿⡇ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⣈⠦⠒⠒⠒⠒⠲⠤⠐⣲⠏⠀⠀⠀ ⠀⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⣒⢒⡶⠦⣤⣀⡀⠀⠠⡎⠁⠚⠁⠀⠀⠀⠀⠀⠤⠤⣞⠁⠀⠀⠀⠀ ⠀⣹⣵⣶⣿⣉⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣀⠼⠋⢁⠝⠉⠀⠀⠸⣦⣈⡉⠒⠿⣿⣿⡶⠤⣤⣀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀ ⡸⠁⣿⡿⠟⠋⠹⡌⢣⡀⠀⠀⠀⠀⠀⠀⠘⢄⠉⢉⡁⢀⡔⠁⠀⠀⠀⡠⢲⣷⠀⠙⠻⣦⣌⠻⣧⠀⠀⠀⠉⠢⡀⠀⠀⠀⠈⢆⠀⠀ ⢧⠰⡏⠀⠀⠀⠀⠘⣄⠳⡀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠈⠀⠀⠀⢀⢜⡴⠛⢻⡆⠀⠀⠈⢛⣦⣈⣷⡀⠀⠀⠀⠘⠄⠀⣀⠀⠘⡄⠀ ⠀⢣⡘⣄⠀⠀⠀⠀⠘⣆⠙⡄⠀⠀⠀⠀⠀⢀⡇⣀⠔⠀⠀⢀⣴⠟⠋⠀⠀⢸⡇⠀⠀⡄⣸⢻⠏⠉⣷⡀⠀⠀⠀⠀⠀⡇⠙⠢⣇⡀ ⠀⠀⠳⡈⢦⣠⡶⠛⠋⠙⢇⠘⣆⠀⠀⠲⠶⣞⣉⣀⠤⠴⣾⠏⠀⠀⠀⠤⠤⢸⣇⠀⠀⢣⣹⣾⣦⣶⡇⢳⡀⠀⠀⠀⠀⡇⢀⡔⢻⣀ ⠀⠀⠀⠙⣄⠻⣴⣀⣠⣶⡞⠉⠙⠁⠀⠀⠀⡜⡇⠀⠀⣸⣥⡀⠀⠀⢄⣀⠀⠈⢯⡅⠀⠀⢻⣿⣿⣿⠃⢸⢳⠀⠀⠀⠀⡿⠋⠀⣿⣿ ⠀⠀⠀⠀⠈⢦⡇⣏⣉⣍⣉⣙⣆⠀⠀⣀⡼⠤⢾⠀⠀⡏⢻⣿⠀⠀⠉⣿⠓⢦⣸⡏⠲⢤⣈⠟⢻⡟⢀⡎⢠⣇⠀⠀⢠⠃⣴⣾⣿⠋ ⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⢿⣿⣿⢦⠀⠀⢠⡄⠀⢣⠀⡇⡜⠛⠀⠀⠀⠛⠃⠈⠀⠳⣴⣶⣿⢺⣸⣇⣜⣠⠋⣼⠀⢀⡎⠀⠀⡟⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢳⣠⡿⠁⠀⠀⠑⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣃⠜⠋⠋⠉⠀⣰⢿⣠⠞⠄⠀⢸⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣾⡿⠁⢀⣀⣠⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀⣾⣿⣟⠉⠁⠀⠀⠀⠀⢰⠃⣸⠃⢀⣦⣠⣿⡟⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠛⠉⠀⠀⠠⠛⠆⣠⢤⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⢀⠔⠁⢀⢧⣴⣿⣷⣶⣤⣬⣁⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⡆⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣦⣠⡖⠉⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⣠⡴⣷⣶⣽⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠉⢑⣲⣤⣴⣮⡀⠙⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣀⡇⠀⠒⠛⢿⣿⣿⣿⠟⣉⠀⠀⠀⠀⠀⣠⠾⡁⠀⢹⣿⣿⣶⡀⠀⠑⠢⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡗⠀⠀⠀⢸⠟⠉⠀⠀⠉⠑⠤⠠⢤⣾⣿⡄⢸⡄⢸⠁⠈⠙⠳⢄⡀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⡿⣿⣿⡄⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠙⣌⠣⢸⠀⠀⠀⠀⠀⠈⠓⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⠀⠈⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣀⠜⡏⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⢠⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⣿⣦⠀⠀⠀⢻⣿⣷⣀⣤⡀⠀⠀⠀⠀⢙⣿⡿⢻⠋⢳⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠟⣿⠀⠀⠀⠈⣽⣿⣿⣿⣿⣆⠀⠀⣰⣿⡿⠁⠸⣤⠿⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠋⠀⣿⡆⠀⠀⡁⠹⣿⣿⣿⣿⣿⣧⣼⣿⡿⠁⠀⠀⣷⣼⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⡟⠹⡄⠀⠁⠀⠈⢿⣿⣿⣿⣿⣿⣟⠒⠲⣖⠒⠋⠛⢶⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡄⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⢿⠋⠁⠀⠀⠀⠀⠙⠻⣿⣿⣷⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⡢⢄⡀⠀⣀⠀⠀⡈⠻⣿⣇⠀ ⣿⣿⣿⣿⣿⣿⢙⣷⣿⣮⡀⠀⠈⠑⢼⣿⣿⣧⠀⢻⣿⡀ ⢻⣿⣿⣿⣿⢃⢼⣿⣿⣿⡷⠆⠀⠐⣿⣿⣿⣿⠖⢸⣿⣇ ⠀⣿⣿⣿⠏⠀⠘⣿⣿⣿⡃⠀⠀⠀⢘⡿⠿⡇⠀⢸⣿⣿ ⠀⢸⣿⣿⣄⠀⠀⠁⠀⠀⠁⠰⠿⠆⠀⠀⠀⠀⣀⣾⣿⣿ ⠀⠈⠻⢿⣿⣿⣦⣴⣆⠀⡄⢀⠀⡀⣄⣸⣿⣾⣿⣿⠟⠉ ⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣷⣾⣾⣿⣿⡿⠿⠛⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠉⠑⠒⠒⠠⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢄⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⠑⠦⢄⣀⣙⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠉⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠐⠢⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣴⢺⣣⢄⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⡞⠀⠈⠉⠙⣿⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⡰⠋⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⡹⢀⡞⠀⠀⠀⠀⠀⠘⡄⠀⢱⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠖⢲⠎⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡤⠚⢁⣀⡤⢰⢃⡜⢀⣠⠴⢚⡽⠿⣄⠃⣠⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢀⣴⠁⠀⠀⠀⣠⣾⣟⣛⠭⣍⡀⢀⣮⠎⣉⣭⢔⣪⠥⠒⠢⣼⢠⠏⢠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⣀⡤⠚⠁⡇⠀⡰⣠⢾⡿⠛⡻⠻⣯⡝⠛⣿⠿⠏⢒⣿⣟⠛⠛⠿⣴⣿⣯⡗⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠔⠒⠉⠁⠀⠀⢠⠃⡴⣵⢣⠈⠳⣀⠹⣜⣻⠇⣸⠏⠀⠀⠾⣟⣻⠆⢀⡴⠳⡛⡟⡈⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣽⠹⣧⡱⣄⠈⠉⠀⠀⢀⣧⣴⢶⣢⣀⠀⠀⠈⠁⠀⡠⣻⢁⡅⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠈⠲⣝⡱⣌⠑⠦⠤⣺⠗⠉⠀⠀⠈⠑⢯⡢⢤⠤⢊⡔⢛⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢻⡏⠉⠉⠉⠻⣎⠑⠒⠚⠁⠀⠀⠑⡶⠋⠀⠀⠈⠲⠔⠋⡴⣁⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠤⠶⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢤⣀⠀⠠⠤⠄⠀⢀⡴⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠷⣒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⢿⣦⣤⣤⣶⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣄⠀⠑⠒⢦⡬⣷⣄⠀⠀⠀⠀⠈⢢⡇⠀⠀⠈⠛⠋⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⣤⣒⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⡷⣌⢦⣀⠀⠀⠉⠙⠈⢳⡄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⣾⡿⠛⣿⡶⣶⣦⣾⠟ ⠀⠀⠀⠀⠀⠀⣠⠼⠒⢆⠀⠀⠈⢻⢡⣤⣈⡉⠒⢲⣿⠇⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣾⣿⠀⠀⠉⠉⠙⢿⡏⢰ ⠀⠀⠄⠐⠒⠉⠀⠀⠀⠀⢣⠀⠀⠀⠉⣿⣿⣿⣿⡜⢏⠀⣴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢷⡇⠹⣬⠦⡤⣤⣤⣤⣼⣐⢋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣿⣿⣿⡏⠇⢸⣤⠇⠀⠉⠉⠒⠒⠲⠄⠀⠀⢀⡤⠒⠉⠁⠀⠘⢣⠀⣿⠀⠉⣿⣿⣿⣿⠺⠉ ⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⢧⠀⠀⣿⣿⣿⡇⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⡀⣿⣠⠀⣿⣿⣿⡇⠀⠀ ⠂⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠈⠀⡀⣿⣿⣿⡇⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⡀⣿⣿⣿⣰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⢱⣿⣿⡿⠋⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⢻⣇⢻⣿⡿⢁⣢⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣄⣀⡀⠐⢴⣿⠟⣁⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡙⢆⢿⡇⠞⢁⠔ ⠒⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡿⢑⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢣⡈⣿⡖⠓⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣨⡟⠙⠵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⣌⢿⡒⠲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣿⡿⠀⠀⠀⠀⠉⠒⠶⠤⣀⣀⣀⡀⠀⠀⢀⣠⠀⠀⣀⣀⣀⣀⣀⣀⠤⠴⠊⠁⠀⠀⠀⠘⣯⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿

⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⡿⣿⣿⠿⢿⣿⣿⠏⣡⣶⣄⣄⠄⡤⣀⡰⢋⣴⣶⡌⣯⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣀⣤⣴⣶⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⣄⣄⢸⠁⣾⣿⡿⠛⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠈⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣴⣾⣿⡙⠛⠿⠿⠿⠿⢋⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⣸⣿⣿⣦⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣂⣀⣀⣀⠤⢒⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⢹⣝⠛⠻⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠠⠤⠴⢞⡿⢸⣇⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣇⣸⣿⣦⡀⠀⠈⠙⠻⣿⣿⣿⣿⣶⣷⣶⣮⣌⣖ ⠀⠀⠈⢷⣄⠀⠀⠀⢰⡟⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡬⠝⠻⢿⣿⣿⣿⡧⠘⣇⣹⣿⣿⣿⣳⠤⣀⣀⡠⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠘⣟⣷⣄⣀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣤⣶⠀⢸⣿⣿⡏⣦⣠⣼⣿⣿⣿⣿⣟⢷⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠋⠻⣧⡀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⡿⢋⣤⣾⣿⣿⣷⣍⣽⣿⣿⣿⣿⣿⣿⣧⡙⢷⠀⠀⣀⡀⠀⠈⠻⣿⣿⣿ ⠀⠀⠀⢠⣤⣤⡠⠼⢿⣶⣶⣾⡿⢿⢿⣿⣿⡷⡄⠀⠀⠀⠀⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠚⠹⠷⢌⣩⣿⣿⣿ ⠀⠀⠀⣈⠝⠉⠀⢀⡀⢀⡸⣯⡀⠀⠘⣏⠁⠀⠃⠀⢀⠀⠀⠀⢙⠿⠉⢿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣟⡷⠂⠀⢀⣤⣴⣾⣿⣿⣿⣿ ⠀⢀⡞⠁⠀⠀⣀⠔⠛⢿⣦⣀⠉⠙⠒⠛⢤⡀⠘⠿⠏⣀⣀⠴⠀⠀⠀⣼⣣⠔⢁⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⠏⠀⠀⢠⡊⠁⣀⣴⣿⣿⣿⡇⠀⠀⢀⣼⣷⣦⣐⠛⢿⠇⠀⠀⢠⣾⠋⢁⣤⣾⣿⡏⢠⣏⣹⡿⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠀⠀⣠⠏⣱⣾⣿⣿⣿⡿⣱⠗⠶⢶⣿⣿⣥⠾⢛⣷⣦⣄⣤⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⡇⠀⣴⢧⣄⠘⣿⣿⣟⣡⡟⢁⣠⣴⣿⡿⠋⠀⢠⣋⣎⣼⣤⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣍⠀ ⣿⡾⠸⣿⣿⣇⠀⠀⠉⣡⣴⣿⣿⣿⡿⢁⣖⣹⣷⣾⣿⣙⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠘⣿⣄⠹⣿⡝⠀⠀⢴⣿⣏⣿⣿⡿⠀⢸⣿⣿⣟⣯⣿⣿⣿⡏⣿⡝⠏⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠶⠖⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⢀⣈⡟⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠁⠈⠉⠓⠚⡇⠀⠀⠀⠀⠀⠀⣼⢦⡀⢻⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⢧⣤⣄⣄⠀⢠⡏⠉⠀⠀⠀⠈⠙⠳⢤⣄⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢧⢠⢤⠾⢦⠀⢠⠇⠀⠈⠻⣷⡀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠘⢆⡎⠀⠀⠀⠀⠀⣀⣠⣀⠀⠈⠙⣲⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⢧⣾⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣅⣿⣷⣶⣿⣧⣤⣤⣸⡏⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠛⠦ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣭⠿⠛⠛⣷⢰⢀⡾⠒⠿⢿⣿⡿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢆⣼⠏⠈⣧⡄⠀⠀⠀ ⠀⠀⣀⣀⣠⡶⢻⣽⡾⠛⠛⠉⠀⠀⠀⠀⠀⣿⠈⢸⡇⠀⠀⠀⠀⠉⠛⠓⠽⣿⡶⣤⡀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⡛⠁⠘⠃⠀⠀⢿⡟⢻⡄⠀ ⠀⢺⣯⣾⣿⠁⡜⠁⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣤⣼⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢻⣿⡿⠆⣼⡇⠀⠀⠀⢀⣶⡛⠋⠀⠀⠀⠀⠀⠀⠘⠀⠘⠻⣆ ⠀⢈⣽⣿⡟⠀⣇⡀⣠⣤⠶⠚⠋⣥⢻⠟⠛⠛⢯⠳⡄⠀⠈⠙⠛⠒⠦⣤⣄⠀⢸⡇⢹⣟⠻⣟⠛⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠈⠀⢹⣧⡴⠚⠋⠁⠀⠀⠀⢠⣏⢿⠀⢀⡷⢨⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣾⠏⢳⣾⣦⠀⣀⠟⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⡿⣌⠷⣭⡤⠟⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠇⠙⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠛⠒⠒⢋⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠬⢿⣿⣟⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣆⠀⠀⠀⣿⢹⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⢧⣤⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⢹⡆⠀⠀⠀⠀⠀⣀⣤⣤⣀⠨⣿⠀⠈⠻⠶⣄⣴⠃⣿⣀⠀⠈⠹⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⣹⣿⠇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠉⣿⡟⠻⢷⣿⡀⠀⠀⠀⠈⠁⠠⣿⠙⠓⠶⠦⣄⣹⡛⠷⣤⣀⠀⠀⠀⠀⠀ ⠀⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⢽⣿⣶⣶⣿⠇⠀⠀⠀⠀⠀⠈⣿⡟⣿⡆⡆⣮⢹⣧⣀⢸⡏⠳⣦⣀⠀⠀ ⠀⠀⣿⠉⠉⠉⠉⠒⠲⣄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡤⠶⠦⠤⠤⢄⣀⣉⣉⡇⠀⠀⠀⠀⠀⠀⠀⡏⠇⢿⣿⣧⣿⢸⢶⣭⣽⣷⡢⣿⠉⢻⢦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧⢷⠀⠀⠀⠀⠀⠀⠀⣠⣎⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠉⠓⠲⠤⣄⣀⣀⡟⠒⣾⣿⡦⢭⣼⠮⢍⣿⡿⣻⣿⡀⠀⣟ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⢷⡀⠀⠀⠀⢀⡞⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⠉⡇⠀⠉⠩⢉⡺⢻⠀⠀⢸⡇⠉⣿⡇⣠⣷ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣷⠀⠀⠀⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠐⠒⢀⣾⣀⡤⣼⣷⣶⠿⣿⣯⣩ ⠀⢸⠋⠉⡉⠉⠉⠉⠉⢁⡥⢤⣞⣈⣗⣒⣺⣻⣓⣒⡒⠒⠒⠒⠒⠒⠲⠶⠶⠤⢤⣼⣇⣀⣀⠀⢄⣤⣀⣾⡦⠴⠶⠒⣋⣩⣽⡿⠿⠋⣉⡤⠾⠛⠉⠁ ⠀⣼⠀⢰⣗⣒⣒⣒⣒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣶⣶⣶⣶⠒⠀⠀⢸⣇⣼⣿⣟⣿⢋⡿⠀⢀⣠⣴⡾⠟⠋⠁⣀⡴⠊⠉⠀⠀⠀⠀⠀ ⠀⣿⠀⠉⠉⠉⠉⠉⠉⢻⡗⠲⠶⡶⢶⡶⣶⠶⠶⠶⢿⠙⠿⠿⠿⠟⠛⠛⠀⠀⠀⣼⡇⡸⡏⢯⡽⢿⣷⣶⠟⠋⠁⢀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⣀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣷⣸⢁⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣧⣧⣼⡷⠞⠁⠀⢀⡤⠚⠉⣀⣤⢤⣄⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⢹⡄⠈⠙⠛⠛⠓⠒⠚⠓⠒⠒⠓⠿⠛⠻⠤⠤⠴⠯⠤⠤⠤⠤⠤⠤⠤⠤⠴⡟⢸⣇⡽⠟⠃⠀⣀⡤⠞⠋⠀⠀⣿⠁⣣⣠⡿⠚⣦⡀⠀⠈⠙⠀⠀ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣀⡾⠋⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢿⣰⣯⣼⠀⠀⢿⡙⣆⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡿⢹⣧⣆⣼⣧⣙⣄⠀⠀⠀ ⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣼⡟⣿⠁⠀⠙⠛⠀⠀⠀ ⠀⠀⢀⣔⢻⣤⣤⣤⣤⣄⣀⣀⣿⣶⡬⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠙⠛⠹⢧⠀⠀⠀⠀⠀⠀ ⠀⣤⣭⣩⣽⡿⢻⣝⣛⣛⣛⣛⣻⠿⠿⠿⠿⢿⠿⣿⣷⣶⣶⣶⣾⣿⠃⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀ ⠘⢒⣶⣿⠋⣴⠿⠥⠤⠤⢤⣤⣤⣤⣭⣭⣍⣏⣛⣑⣻⣿⡟⣒⣲⡶⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣰⡆⠀⢸⠀⢸⡄⠀⠀⠀⠘⠙⣦⠀⠀⠀ ⢠⢟⡿⢁⡼⠓⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⢀⣀⣼⣿⣿⣉⣉⣹⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⣄⡾⢀⣼⠋⠉⠀⠀⠀⠀⡿⠀⣀⡄ ⢩⡟⢀⡾⠒⠒⠲⠶⠤⠤⠤⠴⠦⠤⣤⣤⣤⣤⣤⡟⢻⣧⣄⣀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡤⢿⣟⣲⣤⠤⢤⡤⠼⠧⢴⣿⠃ ⠀⢠⡏⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢸⣧⢸⡷⠶⠶⣾⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀ ⠀⡟⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⢾⠀⣸⡷⠶⠶⠾⠆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠄⠀⠀⠀⠀⠀⠀ ⠈⡉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠈⠈⠀⠀⠀⠈⢸⠀⢻⣇⠀⠀⠐⠻⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀ ⠈⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠘⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⡏⢓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⢹ ⠇⢰⠁⠂⢌⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⣠⠔⠊⡁⠔⠈⠁⢸ ⢸⠘⡀⠀⠀⠈⠒⢄⠙⡆⠀⠀⠀⠀⡎⡇⡠⡺⠃⠀⢠⠋⢠⠐⠉⠀⠀⠀⠆⡘ ⠸⡄⠇⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⢸⢰⠏⡜⠁⠀⠀⢸⠀⡆⠀⠀⠀⠀⠐⠀⡇ ⠀⢧⠸⡀⠀⠀⠀⢀⢆⡿⣠⠤⠤⠬⡌⠬⢤⡤⠤⣄⢸⡀⣅⠀⠀⠀⠀⡄⢸⠀ ⠀⠘⠒⠤⢭⣀⣊⡕⣫⠞⠁⠀⠀⠀⠈⠉⠀⢀⣴⠞⠳⣏⢲⣅⣀⣩⠤⠖⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⣤⣀⠲⡤⢄⣸⠀⠀⣠⣶⣿⣿⣿⣧⢰⠾⠛⠿⣶⣄⠀⠀⢧⣀⢤⡴⢀⣠⠆ ⠀⠘⣆⠉⠚⠦⠀⠀⢰⣿⣿⣿⣿⣿⡟⠸⣄⠹⠍⠘⣿⡆⠀⠀⠴⠓⠉⣡⠏⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠀⣻⡿⣿⠿⠯⠤⠤⠬⢿⣿⡿⠛⠁⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠙⠦⣄⣀⣰⣟⣸⣦⠃⠺⣵⣿⠿⠠⣿⣗⣀⣀⣀⣀⠤⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣟⢗⣦⢤⢤⢴⡲⠻⠍⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡿⠀⠈⠉⠉⠁⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢱⣣⢀⠀⠀⢀⡰⡟⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢾⢹⢤⢤⡏⢧⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣚⣒⣚⣒⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⣀⣤⣤⣤⣤⣤⣠⣤⣤⣤⠤⠚⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⣦⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⣿⠃⠀⠀⠀⠀⠀⠀⣀⣄⠠⠒⠋⠉⠉⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⠁⠀⠀⠀⠀⣠⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⣤⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢝⠒⠒⠤⠤⠤⠤⣤⣄⣤⠴⠋⠙⢦⣀⣏⣫⣁⣠⣷⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⠢⣜⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣀⣀⣀⣠⠶⠋⠀⠀⢀⡴⠞⣯⠉⠉⢉⡽⠋⠉⠙⢿⣷⡒⠒⠻⠷⣦⣀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣩⠶⠋⠀⠀⠀⠀⢠⣎⣀⣀⣘⣆⢰⣋⣰⣆⠀⠀⠀⢻⡻⣄⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠷⣄⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠗⡺⣻⠇⠀⠀⠀⠀⠀⢠⣾⠥⠐⠒⠒⠚⠻⢷⣖⢺⡄⠀⠀⠀⢳⠈⠳⡄⠀⠀⠀⠈⠻⢤⣄⠀⠀⠀⠈⠙⠓⠦⠤⠤⣤⠆ ⠀⠀⠀⢀⠾⣡⠟⣁⣼⡿⠃⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠈⣷⠀⡹⡆⠀⠀⠀⠀⠱⣄⠙⢷⡶⠤⠤⠴⠶⠟⠋⠁⠀ ⠀⠀⠀⠀⢴⡿⠊⢩⡟⠁⠀⠀⠀⠀⠀⢀⣼⣃⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣽⡀⠀⠱⡀⠀⢧⠀⢱⡀⠀⠀⠀⠀⠈⢧⡀⠑⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠻⣶⡶⣭⣀⣴⠋⠀⠀⠀⠀⢀⣠⡶⠟⠹⠭⣻⡄⠀⠀⠈⣟⣆⣀⡀⠈⢻⣇⠀⠀⠙⢦⡘⠆⠸⡇⠀⠀⠀⠀⠀⠈⢷⡄⠈⢳⡄⠀⠀⠀⠀⠀ ⣀⣠⣤⣛⣿⣦⠤⢤⣤⣤⠴⣺⣿⣁⣲⣦⠤⣤⡌⠃⠀⠀⠀⣽⠟⣿⡟⠛⢦⣿⣦⡀⠠⣤⡈⠓⢦⣅⡀⠀⠀⠀⠀⣤⣤⣳⡀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⣃⡴⡷⠀⠀⣼⣿⣟⢀⣟⣿⡇⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠟⠉⣇⠘⢿⣽⣿⢶⡆⠉⠛⠦⠀⠘⣸⠀⠙⢧⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠯⠟⠉⢰⡇⠀⠀⢠⣿⠉⠉⣿⡟⠁⠀⠀⠀⠀⠀⠸⠿⠿⠟⠂⠀⠀⡿⣴⣄⣹⣿⣸⠃⠀⠀⠀⠀⠈⡿⠀⠀⠈⣇⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⣸⠁⠀⢠⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢙⣮⡿⣿⠿⣆⠀⠀⠀⠀⣴⣿⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣾⠃⣀⠼⠋⣼⠁⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣿⡁⠀⠀⠀⠀⠀⣼⠛⣿⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠁⣴⡿⠞⠁⢀⡀⢛⣠⣧⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⡹⣿⠈⡇⠀⠀⠀⢀⡾⠁⢀⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⢀⡴⠋⣹⠏⢹⠏⠉⡗⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡟⣾⡁⣿⢀⣷⠀⠀⢀⡾⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢼⡇⠀⡾⠀⢠⠃⠈⣿⡄⠀⠀⠀⠀⠀⣠⣾⠋⠀⢸⠀⣾⣿⣾⣼⡟⢧⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠸⠀⢰⠇⠀⡾⠀⠀⣏⣇⠀⠀⣠⣴⣿⠟⠁⠀⠀⣾⡷⠃⠀⠉⠙⠇⠈⢧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠷⠶⣶⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡄⠀⠶⠤⠤⣤⡀⠈⠻⣿⣿⣿⣧⠀⡀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠤⠖⠒⠲⢾⣛⠛⠛⠻⣄⠀⠀⠀⠀⠙⢦⡀⠈⣿⣿⣿⠀⡇⢸⠀⣿⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⣬⢻⣶⣤⣤⣤⣬⣽⣿⣿⣿⣯⡀⠀⠀⣀⣿⣿⣧⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡏⠙⠒⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣿⣿⠿⡟⣿⣿⣛⢿⣿⣿⣾⡿⢿⣿⣿⠀⠀⠈⢷⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠙⠦⡀⠀⠀⡆⠀⠀⠀⢸⣿⠿⣶⣏⣱⣿⣿⣿⠀⠈⠉⠛⠛⠻⢿⣿⠀⠀⠁⠈⠳⡌⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⣄⡀⠀⠀⠀⠘⢧⠀⢹⠀⠀⠀⣿⠇⠀⠈⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡆⠘⣯⣝⠛⠛⠦⣄⠀⢸⡇⠀⢰⡿⠀⠀⠀⣾⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢀⣼⠀⠀⣀⣤⢤⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡥⠞⠁⠈⢙⣳⣄⣈⠑⣮⡇⠀⣿⠇⠀⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⡀⢀⡞⠁⠀⣸⠁⢀⡾⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⢀⣠⠶⠋⠉⠉⠉⠉⠳⣮⣧⣴⡟⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⢫⡀⠀⢰⡇⣠⠞⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⣯⣤⠤⠒⠛⣩⠟⠛⠛⠣⠤⣿⣷⠁⠀⠀⣿⢃⣾⠳⣦⣤⣄⣀⡀⠀⠀⠀⠀⠼⣷⠀⠀⠀⠐⢠⣾⠖⠃⢀⡤⢢⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡀⠠⣞⠉⣀⣀⡤⠴⠶⣸⣿⠃⠀⠀⢰⣿⡾⠏⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⢻⣄⠀⠀⠀⡼⣃⡴⠛⢁⣀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⣰⠿⠯⣉⣀⣠⢤⣰⣿⠏⠀⠀⢰⣼⡿⠱⠀⠀⠀⠀⠀⠀⠉⠻⢷⡄⠀⠀⠀⣿⣦⠀⠸⣇⠡⣶⠞⠉⠉⠉⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⠀⠀⣀⣴⡚⢲⣿⡿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠏⢷⣄⠈⢯⠁⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⢀⠔⡿⠋⢀⣼⡿⠁⠀⠀⠀⣘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡌⠳⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢻⢏⠞⠁⠀⣼⡿⠇⠀⠀⠀⠀⣤⣿⣿⡿⢿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣊⣿⡀⠈⠳⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢩⡏⠀⠀⣸⣟⠁⠀⠀⠀⠀⢠⣿⣿⣿⡇⡄⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠒⠚⢧⡀⢼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⣸⡿⡥⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⠀⣰⣿⡗⠀⠀⠀⠀⠀⣠⣿⣿⠏⠻⢿⣄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢛⣿⢶⣤⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡀⡟⣿⣧⡀⠀⠀⣰⣷⣿⣿⡏⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⣇⠈⣻⣧⡀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⡄⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠉⣿⣷⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⣿⡟⠀⢹⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣧⣄⠴⢴⣿⣤⣄⣸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠾⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣄⡀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⡀⠀⠀⠙⣆⠀⠀⠹⣆⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣿⣿⠆⠀⠀⠘⡆⠀⠀⠘⣆⠀ ⢀⡏⠀⠀⠀⠀⣠⠖⠒⠒⢄⠀⠀⠘⣇⠀⠈⠁⠀⠀⠀⣸⠃⠀⠀⠀⢹⡄ ⢸⠀⠀⠀⠀⢰⠃⢀⣤⡀⠈⡇⠀⠀⠘⠢⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⣇ ⣿⠀⠀⠀⠀⠘⢧⡘⠛⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⣿ ⢸⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠁⠀⢸⠃⠀⠀⠀⡇ ⠘⡇⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠛⠉⠁⠀⢀⣀⠴⠚⡻⠀⠀⠀⣸⠁ ⠀⠹⡄⠀⠀⠀⠸⣅⠀⠀⠀⢀⣀⣀⣠⠤⢶⠚⠉⠀⠀⡰⠃⠀⠀⣰⠃⠀ ⠀⠀⠙⣄⠀⠀⠀⠈⠻⣏⡏⠉⠉⡏⠀⠀⢸⡀⠀⣠⠞⠁⠀⠀⡴⠃⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⡇⠀⠀⢇⠀⠀⢈⡟⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⣇⠀⠀⠈⠀⠀⢸⠀⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢦⣀⠀⢀⣠⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠴⠤⠤⠠⠴⠤⠤⠦⠀⠂⠶⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⣀⡤⠤⠤⠔⠒⢂⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⢇⢀⣠⠖⠋⠁⠀⣀⣤⠶⠚⠋⠉⢧⡀⠉⠉⠒⠶⠦⣄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⣿⠃⠀⢀⣶⠟⠋⣁⡄⠀⢀⣤⠖⠛⠒⠦⣤⣄⣀⠀⠉⠛⠲⡄⢀⡾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠹⡀⠀⣸⡇⢀⡞⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⣤⡹⣟⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠸⡇⠀⢹⡴⣿⡇⢸⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⢄⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣷⣶⢞⡥⠛⢷⣿⣰⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢳⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⡄⢹⣦⠀⢆⢸⣿⣿⡀⠀⠀⣾⠀⠀⡤⠀⠀⠀⠀⡇⠀⣠⣧⠀⠀⠀⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡞⡇⠘⣎⣆⢸⣏⡇⣿⣧⣄⠀⣿⠀⣸⡷⢀⣀⠾⣿⣇⣰⣿⡿⣠⠆⢀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢹⣽⡀⣿⣿⢸⣽⣧⠻⣝⠻⣷⣾⣾⣿⣷⢽⣫⣼⠟⠛⠭⠟⠻⣧⣾⣟⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠈⢿⠛⠉⢸⠸⣿⣿⠀⢸⠀⣾⣴⣿⣿⣿⣷⣦⣤⠀⠀⠀⣠⣴⣟⣿⡷⢤⡈⠙⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠘⣧⡠⣾⡄⢸⡟⠀⢸⠠⠿⣯⣿⣿⢿⣿⡆⠀⠀⠀⢸⣿⣿⣿⡏⢿⡄⠉⠙⢦⡀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⣾⠀⠀⠹⣟⠫⠴⢯⡇⠀⡿⣤⣄⡺⠏⠉⠉⠉⠀⠀⠀⠀⠈⠉⠚⢿⣷⡎⢹⣤⠴⠊⣉⣉⠓⠚⠛⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⢸⠆⠀⣏⡄⠀⠀⢻⣄⣠⡼⠁⢀⡇⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⠟⠋⢁⡴⠋⠀⣀⣤⣌⣉⠉⠙⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⢰⣹⠁⠀⠀⣼⠿⣷⣄⣀⣼⠀⠀⣤⣴⣶⠟⠀⠀⠀⢰⣶⣴⣷⠂⢐⣿⣇⡀⠔⢉⣠⡶⠋⢁⣀⣀⠈⠉⠉⠓⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⡟⡟⠀⠀⣰⠃⠀⢹⡾⢿⣿⣆⠀⠙⠛⠁⠀⠀⠀⠀⣀⣭⣉⣤⢄⣾⠏⠹⠧⠴⡿⢧⡶⠋⠉⠀⠙⢧⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠁⠀⢠⡏⠀⠀⠀⢻⡀⢹⣿⣧⡀⠀⠀⠀⠈⠉⠩⣿⣿⡏⢡⡾⡇⠀⢰⡇⠀⣧⠀⠘⢦⡀⠀⠀⠀⡗⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠀⢹⡏⠀⠀⡞⠀⠀⠀⢠⠈⣷⡈⣿⣇⣙⣷⢦⣤⠤⠤⠤⣄⣀⣠⣿⡇⡀⠀⠀⣇⠀⢿⠀⠀⠘⣷⠀⠀⠀⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢠⡿⠀⠀⣸⠁⠀⠀⠀⢸⡆⢹⡿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠈⠉⡻⢿⣧⣇⠀⠀⠸⣄⠘⣧⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⢣⣿⠇⠀⢰⠇⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠇⠀⠀⠀⣴⣿⣛⣻⣦⡄⠐⢹⢿⣷⣤⡀⠘⣆⠘⣧⠀⠐⢲⣈⠙⢿⠓⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠞⢀⡾⡃⠀⠀⣾⠀⠀⠀⠀⠀⢸⠁⣼⣿⢳⡏⠀⠀⠀⠠⣝⠿⣇⣀⣿⠇⠀⠀⠀⢻⣿⣿⣅⢸⡦⢸⡇⠀⠐⠉⣹⢿⡇⠀⠀⠀⠀⠀⣿⡝⣳⡄⠀⠀⠀ ⠀⠀⡴⣿⠋⠀⣼⠁⡇⠀⢠⠇⠀⠀⠀⠀⢠⢇⣼⢫⠇⠀⢧⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠈⢻⣿⣿⣾⣦⣼⣗⠒⠀⣸⡗⢿⣷⣀⣀⣀⣀⣀⣹⠿⠘⡇⠀⠀⠀ ⠀⣼⣹⠃⠀⣰⠁⢸⡇⠀⣼⠀⠀⠀⠀⠀⢠⢿⠃⣼⠀⠀⢸⡿⡛⠛⠛⠲⢤⣤⡀⠀⠀⠀⠀⠀⢀⣸⡟⢯⠛⢿⣿⣿⣟⠓⠼⣇⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀ ⢰⢷⡇⠀⢠⠏⢀⣿⠀⠀⡿⠀⠀⠀⠀⠀⢯⠇⠀⣿⠀⠀⠀⢻⣷⠂⠠⠤⠤⣀⣉⠛⠲⠤⠴⠛⢋⣀⡤⠾⢧⣻⡟⢾⣽⣛⠶⣽⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠀⠀⠀ ⠸⣸⡇⠀⡿⠀⣸⢿⡇⠀⡇⠀⠀⠀⠀⠀⣾⠀⠀⢻⡀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠈⣹⠞⣀⡴⠊⢉⡀⠀⠀⠀⠻⣷⣞⠳⣽⣷⡈⠉⠳⣶⠶⠶⡞⠋⢩⡁⠘⣧⠀⠀⠀ ⠀⠙⣿⡀⡇⠀⣿⢸⡇⠀⡇⠀⠀⠀⡀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠘⢿⣆⡀⡀⠀⣾⢷⢾⡁⠀⠀⠀⠙⢦⡀⠀⠀⠈⠻⣷⣄⠄⠁⢄⠀⠈⢳⡄⢱⡀⠀⢳⡀⠸⣇⠀⠀ ⠀⠀⠀⠹⣿⠀⣿⠈⡇⣧⣿⠀⠀⠀⡇⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠛⢷⣤⣿⣸⡇⠘⢦⡀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠻⣷⣄⠘⣆⠀⠈⡇⠘⡇⠀⠈⢇⠀⢿⡀⠀ ⠀⠀⠀⠀⢻⣀⣧⢸⣧⠹⡹⡄⠀⠀⣇⠀⣧⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⣷⡦⠀⠉⠲⣄⠀⠀⠀⠙⠦⣀⠀⠀⠈⠿⣷⣿⠀⢀⣷⠀⣿⠀⠀⢸⡄⠈⣧⠀ ⠀⠀⠀⠀⠈⢻⣿⢸⠚⣇⠻⡽⣦⡀⠹⡀⢻⢣⡀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⡼⠁⠙⠻⢶⣄⠀⠈⠓⣄⠀⠀⠀⠈⠁⢠⣀⡀⠈⠙⠲⣼⡇⠀⢻⠀⠀⠘⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⡇⠘⢦⡹⣞⡻⣦⢳⡈⢣⡙⠦⣀⠀⠀⠻⣦⡀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠙⠳⣄⡀⠀⠙⠦⣄⡀⠀⠀⠀⠉⠓⢦⡀⠺⣷⣆⢸⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠙⢎⡙⠮⣷⣳⡀⠑⢄⣀⠙⠲⢤⣘⢿⣦⡀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠉⠙⠲⣄⠀⠀⠀⠱⡄⠈⠻⣿⣄⠀⢀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠑⣤⣌⢻⡻⢦⡀⠈⠀⠀⠀⠈⢻⣏⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣝⡦⣀⠀⠀⠈⢦⡀⠀⠀⠁⠀⠀⠈⠻⢷⣼⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠘⣦⠙⣧⡜⣏⢳⡀⠀⠀⠀⠀⢿⣾⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⡇⠈⠻⣤⠀⠀⠱⣄⠀⠀⠀⠲⣄⡀⠀⠙⢷⣠⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢱⠸⠎⢦⠙⠆⠀⠀⠀⠘⣿⡇⠀⠈⡿⣷⣤⣤⣀⡀⠀⠀⣿⡀⣿⠁⠀⠀⠙⣿⣕⡀⠘⠶⢴⡄⠀⠀⠉⠒⢄⠀⣙⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⡖⠿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⢀⠄⠒⠢⣄⡠⠞⠙⢚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⢸⣿⣷⣾⣄⣨⣃⣽⡇⠀⠀⢨⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡈⠷⢿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠸⠉⠀⠀ ⠀⠀⠀⠀⡴⠋⣠⠂⣀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⣀⡜⣠⣾⣿⣿⣿⣿⢿⣏⣹⣁⣿⣿⡿⡗⠒⢄⠀⠀ ⠀⠔⢹⣵⡿⣧⣲⣿⣿⢵⡏⢉⣉⡈⣿⣿⠧⢸⣂⡜⠀⠀ ⢸⠀⣸⣿⡏⠤⠤⠄⡇⠀⢧⣛⣀⡴⢿⠏⠐⠠⡝⢇⠀⠀ ⡇⠀⢸⣿⣿⣤⣤⠜⢁⣀⣀⡠⠋⢠⠃⠀⠀⡘⠀⠘⠢⡀ ⢣⢠⠸⢿⣿⣷⠀⠀⠷⣂⡘⠀⡠⡖⠓⣦⣶⠇⣠⣷⢦⣵ ⠈⢼⡀⠀⠹⣿⠗⢤⣄⣤⣡⣾⢀⠀⠀⢨⣁⡔⢟⣧⣾⡻ ⠀⠀⠙⠰⢄⣻⣰⡡⢒⠡⠀⠺⠈⣄⠀⡟⠁⠐⠄⣙⡟⠁ ⠀⠀⠀⠀⡠⢚⣇⡄⡗⠊⠉⢳⠓⣞⠛⡇⠀⠀⡠⠊⠀⠀ ⠀⢀⠤⠚⢄⡇⢼⣀⡿⠤⠔⣺⣀⣇⣀⣤⣤⠊⠀⠀⠀⠀ ⠀⠣⠤⠤⠚⣷⠞⣓⢽⠉⠉⣯⠋⣁⠙⣿⠏⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠻⢠⡇⡞⠀⠀⢸⠘⣿⣷⡌⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣾⡇⢳⣦⣼⡟⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⠛⠛⠦⠤⡄⠒⡖⠛⠉⢀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⠏⠁⡲⡖⠃⠀⠉⢎⠛⠄⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠦⢤⠊⠁⠀⠀⠀⠀⠇⠘⠁⠀⠀⠀⠀⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣉⣁⡀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣟⠹⠿⢯⣿⣳⡀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣏⢀⠀⠀⠸⠈⠻⣧⠀⡄⣾⣿⣿⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⡖⣸⢶⣾⡦⠴⣥⣴⣬⣿⠀⠡⣃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⢰⢶⣿⣦⡉⢇⢠⠋⣩⣥⣿⡆⠀⠙⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢀⣰⠃⢸⣿⣷⢷⢸⣿⢰⣿⣿⣷⣧⠀⠀⢘⢄⠀⠀⠀⠀⠀ ⠀⠀⣵⡿⢟⢿⣾⣦⣀⡘⣿⠟⣿⡘⠇⣸⡶⠟⢿⣿⣆⠀⠀⠘⣢⠀⠀⠀⠀ ⠀⠀⢿⣷⠬⠛⠋⠙⠫⣷⢿⡀⡻⣿⠟⠋⡸⠀⣸⣢⣿⠴⣺⡿⢋⢀⠀⠀⠀ ⠀⣠⠟⠁⠀⠀⠀⠀⠀⠈⠹⢷⣯⢕⠀⠀⠁⢴⣿⣟⠥⠞⠁⠀⠰⢹⡇⠀⠀ ⠺⣟⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⡏⠻⣿⣦⣶⠿⣿⠀⠀⠀⠀⠀⠀⡔⠹⢢⡀ ⠀⢸⣷⢄⡄⣿⠀⠀⠀⠀⠀⢸⣷⠀⠀⢹⠁⠀⣿⠀⠀⠀⠀⠀⣼⢃⣶⠉⠀ ⠀⢸⠙⢷⣝⣼⡄⠀⠀⠀⠀⠀⣿⡀⠀⢸⠀⠀⣿⡄⠀⠀⠀⠀⣿⡿⡟⠀⠀ ⠀⠀⣧⠈⠻⡟⣧⠀⠀⠀⠀⠀⣿⡇⠀⠈⡀⠀⣿⠇⠀⠀⠀⢸⠟⡰⠀⠀⠀ ⠀⠀⢃⠑⢄⠙⢿⡆⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⣿⠀⠀⢀⣀⠏⠐⡇⠀⠀⠀ ⠀⠀⠈⠢⢀⠀⠈⢃⠀⠀⠀⠀⠙⠇⠀⢀⣇⣀⣭⠔⠊⢁⠬⠄⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠐⠺⣆⡀⠀⠀⠉⠉⠉⠉⠏⠉⠁⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⣸⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⣴⡲⡳⡫⢜⠡⣻⡻⣆⠀⠀⠀ ⠀⣘⠉⢻⠘⠉⠁⠈⠉⠉⠉⡀⠀⠀ ⠀⠳⠾⠦⠇⣶⣯⡄⠀⠀⠀⡅⠀⠀ ⠰⣁⣠⣄⣼⡟⣧⠁⠀⠠⠔⠀⠀⠀ ⠀⣻⣿⣯⢿⢿⢿⠀⠀⠘⡀⠀⠀⠀ ⠀⣷⢿⢣⣿⠞⠃⢀⣠⣴⣷⣆⣀⠀ ⠀⠉⠛⢹⣷⣶⣾⣿⣿⣿⠿⠟⠛⠉ ⠀⠀⠀⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢣⠈⠂⢂⠀⠇⠀⠀⠀⠀⢸⢀⠄⡰⠁⣠⠆⠀⠀⠀⠀⠀⣀⣴ ⡇⠀⢠⠀⠀⠀⡈⠳⣄⣀⣧⣈⢦⣀⣀⣠⡿⠣⠮⠶⠿⣓⣈⣀⣀⡀⠀⠀⣠⣽ ⠈⠀⠈⠙⠂⠤⣶⡯⠛⠋⠁⠀⠉⠡⢀⡄⠠⠀⠀⠀⠀⠀⠙⢯⣅⣤⡤⣀⣚⣿ ⡂⠀⢀⠔⣆⣽⠋⠀⠀⠀⠀⠀⠀⣆⣆⠃⣦⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿ ⡟⣰⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠋⢹⠀⡇⠈⣀⡠⠄⠀⠀⠀⢸⠟⣿⣿⣿⣿ ⠊⢻⣿⢿⣿⡇⠀⠀⠀⠀⢈⣩⣭⣗⠀⠀⢠⣪⣴⡶⣾⡟⠒⡄⢸⡖⣿⣿⣿⣿ ⠀⠈⡇⡦⡙⡇⠀⢰⣜⠋⠹⠿⠓⢍⠀⠀⠀⠀⠏⠀⠉⠠⣾⢣⠛⡇⣿⣿⣿⣿ ⠀⠀⢸⢰⠈⡞⠀⣆⣗⡵⠄⠒⠀⢀⡴⠛⠛⠶⠤⠤⠀⠀⠓⢻⡞⣽⣿⣿⣿⣿ ⠀⠀⠈⠢⡑⠍⢧⣞⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠢⣀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡇⠀⠈⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡨⠻⡿⣦⡀⠐⠂⠴⠖⠒⠒⠠⠛⠉⠀⣴⠟⡀⠀⠀⠀⠹⣿⣿ ⠀⠀⠀⢀⡴⠊⠀⠀⢣⠈⢫⡳⣄⣀⡀⣂⠒⠊⣠⡶⢾⡏⠀⠫⡢⡀⠀⠀⠙⠛ ⠀⣠⣴⣿⠥⠄⠒⠂⢼⡆⠀⣯⠚⢏⡉⠊⠄⠀⣈⡔⠁⡇⠀⡀⠈⠙⠀⠀⠀⢠ ⢻⣿⣿⡏⠀⠀⠀⠀⢸⣷⡘⢻⡆⠀⠈⠻⣉⢡⠎⠀⢠⠃⠀⠡⠀⠀⠀⠀⠀⠀ ⣾⣿⠿⠁⠀⠀⠀⠀⠈⡏⠆⠀⢻⡄⠀⠀⠙⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠟⠋⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣴⣄⣦⢠⢀⣄⡀⠀⡴⠋⣡⣴⣦⡝⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞⠋⠀⠀⣀⣡⣼⣿⣷⣶⣶⣿⣿⡟⠁⣸⣿⣿⣿⣿⣯⠀⠁⠉⡿⠁⣰⣿⣿⣿⡷⣾⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣾⣷⣼⡇⢠⣿⣿⡿⠋⠀⠀⠈⠉⠛⠻⠷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡿⠿⣿⣤⣉⠉⠛⠛⠛⠛⠛⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣷⢸⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠂⠀⠀⠀⢀⣠⠤⠂⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡏⠈⣷⡙⠛⠛⠿⣿⣿⣷⣦⣠⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣴⣿⠇⣿⠉⣿⣿⣿⣭⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⡇⠀⣿⣿⣆⠀⠀⠈⠙⠻⣿⣟⣿⣿⣶⣵⣶⣤⣤⣤⣌⣑⠒⢤⣄ ⠀⠀⠀⢦⡀⠀⠀⠀⠈⠉⠉⢉⣴⣿⢠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠶⣿⣿⣿⣷⣤⣄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣿⠛⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡴⠶⠂⠉⠛⣿⣿⣿⣿⣿⠗⠀⢻⣤⣿⣿⣿⣿⣿⣝⡒⠦⠤⠤⠤⠆⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣯⣿⣦⣄⣀⣀⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣴⣴⣶⠄⠀⢿⣿⣿⣿⢸⣆⣀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣇⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠻⠟⢿⣯⠉⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠟⢀⣠⣼⣿⣿⣿⣎⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⣷⣦⡀⠀⢙⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠈⠛⠛⠛⠉⠴⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣄⢀⣐⣻⣦⣄⣀⣠⠬⢿⣿⣿⣿ ⠀⠀⠀⠀⢰⣷⣶⣶⠔⠚⠛⠿⠿⣿⣿⣿⠟⠻⠟⣿⣿⣿⠟⢻⠀⠀⠀⠀⠀⠀⢦⣤⣤⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠁⠀⠛⠓⢲⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⢻⣌⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠀⢿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡷⠂⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⣨⠿⢿⣿⣅⡀⠉⠛⠲⠶⠾⢿⣀⠀⠀⢷⣾⡟⠀⠀⠀⣠⠄⠀⠀⠀⣰⡿⢁⡴⠋⢩⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⠟⠀⠀⠀⢀⡴⠊⠁⠀⣀⣽⣿⣿⣦⡄⠀⠀⠀⠀⢹⣧⡀⠀⢀⣤⣶⣾⡟⠁⠀⠀⠀⣰⣿⠿⠋⠀⣰⣿⣿⡟⠛⣿⠿⢿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⠟⠀⠀⠀⢠⣯⡀⠀⣠⣾⣿⣿⣿⣿⢿⡇⠀⠀⢀⣴⣿⡿⠿⣷⣤⡀⠐⠿⠀⠀⠀⢀⣼⣿⠁⣀⣴⣿⣿⣿⣿⣁⣰⣇⣤⣾⣏⣴⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠀⠀⠀⣠⠟⢀⣹⣾⣿⣿⣿⣿⡿⣡⡾⠛⠶⠶⣿⣿⣿⣤⡾⠿⢛⣿⣿⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⡇⠀⠀⣴⣏⣀⠀⢻⣿⣿⣿⠟⣫⣿⠋⠀⣀⣴⣾⣿⡿⠛⠁⠀⢰⠋⡞⣠⣧⣀⠰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀ ⣿⣄⡼⣿⣼⣿⣧⠀⠉⠛⠛⠾⠿⢁⣠⣾⣿⣿⣿⡿⠁⣠⠤⣤⣬⣿⣿⠿⣿⣿⣦⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⡀ ⢻⣿⡅⠘⣿⣿⣿⡇⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⡟⠁⣼⣧⣶⣿⣿⣿⣿⣷⣬⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⢿⣿⡄⠘⢿⣷⠇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⢿⣿⣭⣿⣿⣿⣿⣿⣟⣿⣿⠘⠃⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿

⠀⠀⠀⠀⠀⢱⠢⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢄⡀⠀⢣⠀⠀⠀⠀⠈⠀⠐⠂⠠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠡⡀⠉⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠉⠉⠢⠀⠀⠀⠀⠀ ⡀⠐⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠴⣧⣀⠀⠱⠀⠀⠀⠀ ⠈⠄⡀⠀⠀⠀⡠⠀⠠⠀⠀⠀⠀⢀⡀⢔⢃⠎⠀⠀⠘⡀⢀⡇⠀⠀⠀ ⠀⠀⠈⠁⢂⠊⠀⢠⠁⠀⠀⣠⣦⠥⠒⣌⠮⣄⠢⣛⣢⢡⢈⠇⠀⠀⠀ ⠀⠀⢀⠔⢁⠄⠒⡇⢠⡴⡟⢻⢻⡟⢲⠛⢻⣿⠛⢲⣼⣿⢎⠀⠀⠀⠀ ⠀⠐⠋⠁⠀⠀⠀⠁⡟⡕⡉⠊⠓⢁⣡⣤⡈⠒⠁⠊⣹⢓⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢠⡾⠥⢧⡪⣑⠲⠋⢄⡠⠉⠣⣒⠠⡫⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠐⠁⠀⠃⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⣠⠎⠉⠁⠀⠈⠁⠀⢀ ⠀⠀⠘⢠⣄⡀⢀⠀⠀⠀⠀⠀⠋⠲⣤⣁⣤⠎⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⡀⢰⣣⡈⠐⠺⠶⡄⠀⠀⡳⠀⠈⠉⠁⠀⢀⠀⠀⢀⣤⣦⣁⣀⣤ ⡀⠜⠠⠈⠑⢧⣤⣐⣠⡞⢀⠎⠀⠀⠀⠀⠀⠀⠈⢂⠀⣾⠁⠘⠛⢻⢡ ⠀⠀⠀⠡⡀⠀⣿⣿⠋⢁⡞⠒⠠⠤⠄⠀⠀⠠⠀⠊⢣⢸⠁⢶⣶⡶⠖ ⠀⢀⠀⠀⠡⠀⣿⣿⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣧⢸⣿⡇⠀ ⠀⠀⠑⠂⠀⠐⣿⡿⣁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡻⡘⣿⢣⠄ ⠀⠈⠉⠐⢢⣼⢋⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⢻⡥⠊ ⠀⠀⠀⠀⡸⣵⠃⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠑⣿⡑ ⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⢿⣥ ⠀⠀⣰⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠔⢒⡖⢒⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠁⠐⠒⠒⡾⣷⠾⠯⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⣶⣾⣁⡀⠀⠀⠀⠀⠀⠀⣰⣿⣾⠃⢀⡿⠛⠓⣄⠀⢿⣆⠀⠀⠀⠀ ⠀⢀⢀⡴⠋⠀⠈⠙⢿⡷⠂⠀⠀⠀⡿⡿⠁⡔⠁⠀⠀⡆⠈⢣⡈⢾⡆⠀⠀⠀ ⠀⢸⠎⠀⠀⢀⡠⠤⠤⠽⣄⠀⠀⠀⠹⠇⠸⠀⠀⠀⠀⠉⠐⠊⠹⡌⢳⡀⠀⠀ ⠀⣿⠀⠀⢰⣋⡀⠀⠀⠀⠘⣗⡆⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢱⠈⣷⡄⠀ ⡇⡏⠀⠀⣇⣠⠟⠀⠀⠀⠀⢀⠇⠀⢀⣀⣀⣈⠢⣄⡀⠀⠀⠀⣠⠎⠀⢸⡱⡀ ⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠋⡠⠚⣅⠀⢸⢄⡩⠓⢭⣉⢉⣉⠁⠀⠀⠀⢃⡇ ⣿⠀⠀⠀⠈⠢⣀⣀⣠⠞⠁⡰⣧⡀⢸⡗⠂⠀⠀⠀⠀⠈⠉⠚⠳⡄⠀⠀⠸⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡇ ⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣀⣀⣠⠞⠉⠣⡀⢀⣀⡀⢸⠀⠀⡇ ⢣⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡼⠁⠀⠁⣀⠀⡔⠙⡞⠀⠙⣸⠀⠀⡇ ⠸⡘⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠁⠀⢀⡎⠉⢓⣡⠔⠓⠒⠚⠁⠀⠀⢹ ⠀⠱⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡔⠉⠙⢼⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞ ⠀⠀⢹⢦⠀⠀⠀⠀⢸⣁⠜⠉⠑⠼⢀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⠸⡄⠓⢤⡀⠀⠀⠈⠉⠉⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠀⠙⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠣⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠄⢧⠀⠀⠀⢀⠟⣿⣿⣿⠟⢸⣧⣼⣿⡿⣁⢸⡇⢻⢿⣿⣿⡟⠙⡀⢀⣄⡀⠀ ⡇⣸⡆⠀⠀⠈⡄⣻⣿⡯⠤⣄⡈⠏⠏⠀⢰⠖⢿⡞⠺⣿⣿⡹⢄⠃⣌⣲⠁⠀ ⠘⣿⣻⡄⠀⠀⠐⢬⣏⡇⠀⠢⠀⠀⠀⠀⠀⠈⠩⠀⠀⢟⣿⡪⠂⣴⣰⠂⠀⠀ ⢀⣽⣿⣿⣿⣿⡆⠀⠙⡀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠈⡸⠀⠀⡼⡐⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⠀⠀⡠⡓⡄⠀⢀⢈⡉⠁⠀⢰⠉⡆⢔⢑⣄⣚⠟⠁⠀⠀⠀⠀ ⠈⠉⠹⣿⣿⠷⠐⣸⠻⠀⡎⠢⡀⠒⠛⠁⠁⡌⢀⠇⡘⠀⠼⣿⣿⣿⣶⣤⣄⣀ ⣀⠤⠐⠉⢷⡄⠾⠏⠀⢀⠇⠰⡈⠂⠤⠤⠴⠀⡘⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⢀⡠⠄⢀⡀⠹⡜⢀⠀⠀⢲⠀⠁⠈⡄⢠⣅⢠⠁⠘⠴⡠⠁⠸⡏⣻⣿⣿⣿⣿ ⢈⠨⡪⢅⡹⡾⠀⠀⠰⠀⠀⠑⠠⡀⠘⠎⠀⡆⠀⢀⠆⠀⠀⡇⣿⣿⣿⣿⣿⣿ ⢦⡽⢦⠀⣹⠃⠀⠀⠀⢧⠀⠀⠀⢈⠎⢄⡀⢁⢔⠁⠀⠀⠀⡇⢼⣿⣿⣿⣿⣿ ⣷⡝⣄⣰⣌⢳⣤⡀⠀⡸⡡⡀⣴⠑⠁⠄⣈⣉⡛⠒⠠⢄⠀⠈⠙⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀⣰⢻⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⠀⢰⡏⣿⠁⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸⠀⡏⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⠀⠀⠀⠀⠀⢠⣿⢻⠀⠀⠀⠀⡏⠀⣧⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⢧⢻⣧⠀⠀⠀⠀⣼⡇⣿⠀⠀⠀⢀⣽⠀⢿⡆⠀⣸⣿⡟⠁⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠈⢣⣻⡄⠀⠀⣸⡟⢰⠇⢰⡤⢖⣿⣿⡷⠼⠟⣿⡿⡿⠁⠀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀ ⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢳⣻⡆⣸⡏⢀⣼⠞⠙⠺⣯⣅⡼⢧⣤⣾⣿⣿⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀ ⢀⡴⠟⣡⡞⠋⠉⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⡀⠀⠰⣷⣿⡟⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡜⢀⡞⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠀⠀⠀⠑⠀⠀ ⢸⠀⠀⣿⣧⡀⠀⠀⠀⠻⣄⡀⣤⡴⠞⠛⠛⣛⢛⣿⣟⠛⠁⠙⣄⠀⣼⡇⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢧⡾⠞⠋⠁⠉⠉⠛⠛⠛⣙⣛⣉⣉⣀⢄⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⣇⢹⣇⠀⠀⠀⠐⠛⠋⠉⠓⢦⣵⣤⣿⠿⠉⠉⠙⢲⡀⣸⣷⣿⠃⠀⠀⠀⠀⠀⠀⣀⣤⡵⠛⠳⡤⠤⢤⢸⡆⠀⠀⠀⠀⠀⣠⡴⠟⠉⠉⠉⠉⠙⢿⡤⠀⠀⠀⠀⠀⡆ ⠈⣿⡄⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⢠⡞⠋⣁⣘⡇⠀⠀⣿⣤⣤⣼⣦⣄⣀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⢀⡇ ⠀⣿⣧⣿⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡟⢿⣿⣇⢦⣷⠀⠰⠖⠛⠛⠈⠉⠁⠀⠉⠻⠟⠉⡀⢸⡟⠋⠉⢸⡇⠀⠀⠀⠀⠀⠀⢠⣼⠷⣄⡀⠀⣀⣼⡇ ⠀⣿⣿⣿⠀⠀⠘⠿⣦⣀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⢻⣿⡌⢿⡀⠀⠀⠸⡟⠿⣄⣀⡀⠀⢠⣤⣿⠇⢸⠇⠀⠀⠈⣧⠀⠀⠀⠀⠀⣠⡿⠁⣠⠴⠛⠉⠉⣹⠃ ⠀⣿⣿⣿⡆⠀⠀⠀⠈⠙⠛⠿⣿⡛⠛⠳⠾⣿⣦⡀⠀⢀⡴⠋⠙⠷⣼⣿⣿⡌⣿⣄⠀⠀⠹⣆⠠⠈⠉⠉⠉⣉⡜⣠⣿⣀⣀⡤⠞⠛⣷⡀⠀⠀⣰⡟⢁⠞⠁⠀⠀⠀⢠⣿⠀ ⠀⢻⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠈⠛⢿⡶⠛⢧⠀⠀⠀⠈⠻⣿⣧⢿⣿⣦⣀⠀⠈⠓⠦⣤⣤⠤⢿⣽⠃⣹⣿⠏⠀⠀⠀⠈⣷⣤⠾⣿⣷⡟⠀⠀⠀⠀⠀⣾⡟⠀ ⠀⠸⣷⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⢱⡀⠘⣧⠀⠀⠀⠀⠺⣿⣧⣙⢿⣿⣷⣦⣤⣀⣀⣠⣶⣿⣷⣶⠿⠓⠂⠀⠀⠀⠀⢿⡁⣼⡟⣿⠃⠀⠀⠀⢀⣾⣿⠃⠀ ⠀⠀⠹⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡒⠺⢷⣄⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣹⡿⠋⠁⠀⠀⠀⠀⠀⠠⣄⣽⣿⣟⣵⠏⠀⠀⣀⣤⣿⡿⠃⠀⠀ ⠀⠀⠀⠙⢿⣿⣷⣿⣶⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣤⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⣅⢀⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠿⣿⣧⣠⣜⡛⣿⣷⣻⣿⣿⡿⠿⠿⣷⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡙⠦⣤⡖⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⡛⠉⠁⠀⠀⠀⢻⣷⣄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡄⠀⠀⠀⠀⠀⠈⢿⣟⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⣦⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡄⠀⠀⠀⠀⠈⢿⣷⠶⢿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⢀⣴⣿⢧⣶⣤⣤⣠⣶⢾⡟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧⣤⠀⠀⠀⠀⠀⠻⣧⣸⣟⢿⣟⡿⣿⣶⣀⣀⣐⣺⣿⣿⣧⣤⣽⢭⣭⣍⣡⡞⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣆⠀⠀⠀⠀⠀⠉⢻⣆⠈⢻⣶⣄⣀⣡⡶⠞⠋⠉⠀⠈⢧⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⡀⠀⠀⠀⣿⡝⠛⢷⣌⣿⠋⠀⠀⠀⠀⠀⠀⣸⡆⠀⢠⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣻⠿⠿⠿⠻⣦⣀⡙⠻⣷⣀⣀⣀⣀⣠⡴⠟⢿⠛⠛⢹⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣃⠀⠀⠀⠀⠉⢿⣦⣼⡏⠉⠉⠉⠁⠀⠀⣸⣧⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣙⢿⣷⣦⣄⠀⣀⣼⣧⡈⢻⣤⣀⣀⣀⣤⡾⠛⣯⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣹⣷⣶⣾⣜⣿⠻⢿⣿⣿⡇⠈⠻⣦⣿⣯⣉⠉⡀⣀⣴⢿⢶⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⣳⣿⣿⠀⠀⠙⢿⣷⣤⣀⣀⡉⠛⢿⣟⣛⣉⣠⣾⢿⣇⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⢻⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⠛⣛⣿⣶⣴⣭⣛⣿⣯⡀⢘⣿⣿⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢈⡩⠿⠿⡴⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠚⠒⡦⠶⣉⠀⠀⠀⠙⡄⠀⢻⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⢀⣜⡀⠀⠀⠑⢦⡤⠚⢹⠑⢺⣠⡽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠉⢹⢺⡟⠛⠛⠛⠛⢿⣤⠜⡖⣾⠃⠀⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠈⡼⣷⡀⠀⠀⠀⠀⣻⢶⠽⣿⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣯⡛⠶⠶⣶⠛⠉⡝⠉⠉⢆⡟⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣤⡊⠁⠉⢲⠓⠒⠈⠙⣤⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣑⡬⣓⣤⣏⠠⠤⠔⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡏⠉⠙⡗⠒⡂⣴⡧⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢉⠏⡟⠒⢲⠗⠒⡏⡼⢆⠀⣠⠜⠓⣒⠤⠤⠤⠤ ⠀⠀⠀⣀⡠⠤⠄⢎⣁⢑⠴⡁⠀⡇⠀⣸⠀⠀⣇⣠⣔⠿⢤⠒⠋⠁⣠⠴⠒⠉ ⢠⠖⠉⠀⠙⠢⣄⣠⠞⠉⠉⢩⠟⠻⣲⣧⠾⠋⢹⠀⠀⠀⣀⡱⢔⠉⠀⠀⠀⠀ ⣎⡀⠀⠀⠀⢀⠞⠉⠉⠒⢢⡯⢀⣔⢼⢃⣢⣀⠨⡦⠒⠉⠀⠀⠈⠣⡀⠀⠀⠀ ⢣⠈⠑⠢⢄⣎⠀⠀⠀⠀⢸⠀⣯⣿⣿⣯⡷⠷⠀⢣⠀⠀⠀⣀⠤⠔⠛⡅⠀⠀ ⠈⠄⣀⣤⣾⣄⡉⠒⠢⢄⡇⠐⡟⡏⣿⡟⡟⢳⠀⣸⡤⠖⠉⠀⠀⢀⣤⣼⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠒⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⡔⠂⠉⠉⠀⢀⣀⣀⠀⢀⡀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀ ⠸⣀⠉⠢⡀⠀⠱⣤⣤⢴⣊⣹⣅⠽⠀⢠⠝⠂⠐⠢⡀⢈⡆⢀⡤⠊⠉⡵ ⠰⣁⡴⣙⡑⡰⠁⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢟⢼⠁⢈⡄⠄⢈⡱ ⠀⠈⠉⠁⢠⠁⠀⢀⡤⠶⠆⠐⠒⠂⠪⠱⢆⠀⠀⠀⠘⡀⠱⡈⠉⠉⠚⠁ ⠀⠀⠀⢀⡆⠀⡰⠋⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢇⠀⠱⡀⠀⠀⠀ ⢲⡒⠒⠉⠀⡜⠀⠶⠛⠁⠀⠀⠀⠀⣀⡀⠳⠦⠘⢦⡀⡘⡄⠀⠑⡄⠀⠀ ⠀⠈⠐⡞⢸⢀⢀⠆⠀⠀⠀⠈⢶⡉⢁⡅⠀⢠⡄⠀⠟⠛⠉⠀⠀⠘⠀⠀ ⠀⠀⢠⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡰⠀⠀ ⠀⠀⠈⢂⡧⡈⣗⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢺⢃⣎⢄⠔⠎⠀⠀⠀ ⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⢈⡩⠉⠉⠉⠀⢰⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⡱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⠀⠀⠢⣌⣷⣦⣤⣙⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣍⣉⣉⣉⣉⠤⠭⠽⣿⡿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣨⣿⡿⡫⠁⠀⣠⣴⣿⣿⣿⣿⣿⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣏⣜⠁⢀⣾⣿⡿⢯⠾⢟⣿⣿⣾⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣋⣽⡧⢭⣉⣉⣐⣲⣶⣶⣿⣿⣿⣵⡟⡟⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣏⠙⢯⡝⠕⠛⢛⣋⣉⢹⣇⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⢻⢯⠢⠉⠥⢄⣒⢿⣿⢿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⣖⡶⣿⢍⣳⡀⠈⠉⣁⣠⣀⠓⠵⣻⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⡔⢁⠞⢠⠙⣷⢸⡜⡇⠑⣄⠀⠣⢈⠟⢀⠴⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⣧⠈⡄⢸⠇⡾⢺⣧⠃⢀⠈⢻⠖⠐⠊⠁⢀⠙⡓⡀⠀⠀ ⠀⠀⠀⣸⣿⣿⣶⡾⢸⣇⠙⣿⣽⣿⡄⡡⠊⡆⢀⣀⠮⠄⣀⣒⣙⡄⠀ ⢀⢠⣤⡿⢿⣿⣿⠇⢸⢸⡴⣿⣿⣿⢿⣇⠄⣺⣿⣾⡟⠉⣧⠙⣄⠀⠀ ⠹⠖⣷⡁⠀⢏⣍⠀⢸⣿⡟⠉⣿⣏⢻⣿⣰⣿⣿⣿⢉⡁⡿⠯⠿⠆⠀ ⠀⠎⢎⣿⡢⡘⣿⣦⢻⣿⡇⠀⢸⣹⠎⠀⠈⠙⡿⣿⣾⣡⡗⣠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡴⠛⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⣰⠋⡰⠛⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠈⢳ ⠀⠀⠀⢀⡴⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠋⠑⠞ ⠀⠀⢠⠞⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⠃⠀⠀⠀ ⠀⣰⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⠃⠀⠀⠀⠀ ⣰⠃⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠏⢠⠇⠀⠀⠀⠀⠀ ⡇⢰⠚⠉⠉⠉⠉⠉⠉⠉⢣⣿⠛⠃⡞⠛⠛⠛⠛⠛⠛⠓⢲⠈⡇⠀⠀⠀⠀⠀ ⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⠀⠀⠀⠀⠀ ⠈⢆⠳⣄⠀⠀⠀⠀⢀⡼⣰⠇⠀⢳⡸⡀⠀⠀⠀⠀⠀⢀⡜⣸⠃⠀⠀⠀⠀⠀ ⠀⠈⠳⢬⣑⣒⣒⣒⣫⠶⠁⠀⠀⠀⠻⢮⣲⠤⣤⡤⠔⣫⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⡀⢀⢠⠀⠀⠀⠉⠙⡛⠛⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⢿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿ ⢸⡆⢹⡆⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡿⢠⡟ ⠘⣷⠘⣷⡀⠀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣼⠇⣼⠇ ⠀⠸⣧⠘⣷⡈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⣽⠏⣰⠏⠀ ⠀⠀⠙⣷⡈⢻⣄⠀⠀⣀⣀⣀⣀⣀⣀⣠⡾⢃⣴⠏⠀⠀ ⠀⠀⠀⠈⠻⣦⡙⢷⣄⡉⠉⠉⠉⣩⡿⠋⣠⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦⣀⠚⢉⣴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣄⠙⢷⣄⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⢉⣴⠟⠻⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⢁⣴⣟⣁⣀⣀⣈⠙⢷⣌⠻⣦⡀⠀⠀⠀ ⠀⠀⢠⡾⢁⣴⠟⠉⠉⠉⠉⠉⠉⠀⠀⠙⢷⡈⢻⣆⠀⠀ ⠀⢰⡟⢠⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⢻⣄⠹⣆⠀ ⢀⡿⢀⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢻⡄⢻⡆ ⢸⠇⣸⣇⣤⣤⣄⠀⣠⣤⣤⣀⣀⣀⣤⣤⣤⣄⠈⣷⠘⣧ ⣾⣤⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠳⢶⣾⠃⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⠟⠋⠉⠻⣦⣴⠶⠚⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠖⠀⢸⡗⠾⠀⠀⢸⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠸⣦⣀⠀⢀⣠⣾⣿⠶⠶⠶⠛⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠉⠙⠋⢩⣴⣿⠀⠀⢀⣶⠟⠛⣛⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠈⠻⠶⣾⢻⣷⡀⠀⠘⠛⢷⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⠆⠀⠀⠀⠙⢿⣇⣸⣆⠀⠀⠀⢻⡆⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢦⣤⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠘⠉⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⡤⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣆⠀⠀⠀⢿⡀⢀⣠⡾⣫⡿⠃⠀⠀⠀⢀⣠⣤⣤⠴⠶⠶⠒⠒⠚⠓⠒⠒⢶⣦⣄⠀ ⣾⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣤⣤⡀⢿⡄⠀⠀⠈⢿⡟⠉⣸⣿⣻⡖⠀⠀⢀⣾⡛⠛⠻⠷⠶⠶⠶⠶⠶⠒⠒⠛⠋⣡⣿⡄ ⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣶⣆⣀⣀⠀⡍⠉⣤⢰⣾⣿⣿⣧⠀⠀⠀⠈⣿⡶⣿⣿⣿⡷⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡷ ⠀⠀⠉⠉⠛⠛⠛⢛⡿⢿⠿⣻⡿⢻⡿⠛⠿⠻⠟⠉⠼⠟⣽⣿⠟⠻⢶⠿⠿⡿⢻⠟⣿⣀⣀⣶⣄⣽⡷⠛⠉⠀⠀⠀⢿⡿⢛⣿⠷⣶⢶⣶⣶⣶⣶⠶⠚⠛⠛⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣷⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣀⠉⣹⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⢀⡤⠒⠒⠒⠦⣄⠀⣠⡾⠋⠉⠛⠻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⣿⣿⣆⢠⡟⠀⠀⢠⢠⠞⠽⣿⡁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣾⣿⣦⣄⣇⣇⣤⣾⣿⡇⠀⠀⠀⠐⣤⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠜⡟⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣠⠖⠁⡀⢀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠘⣿⣿⣿⣿⣿⣿⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⢾⠏⢀⣾⣿⡿⠿⣿⣿⣿⣿⣿⠋⣿⣧⣤⣾⣥⣤⣝⣿⣿⣹⠓⣏⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⢀⡞⢁⡟⣰⣿⣿⣥⠤⢔⣛⣻⠿⣏⣱⣿⠟⠉⠉⠁⠀⠈⣿⣾⣿⣿⣀⠈⡟⠦⢀⡼⠀⠀⠀⠀ ⢀⡎⠀⢸⣿⣿⣟⡭⠶⠛⠛⠛⢻⣿⠋⠉⣿⠀⢰⡾⠛⠛⠂⣿⣿⣿⢅⠉⠙⠿⢴⣿⠀⠀⠀⠀⠀ ⣼⡆⠀⢸⣿⣿⣟⡇⣴⠶⠶⠶⠆⣿⠀⠀⠹⣧⣈⣁⣀⣤⡾⠟⣻⠃⠀⠙⠒⢢⠞⠙⡇⠀⠀⠀⠀ ⡿⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⣰⡟⠀⠀⠀⠈⠉⣩⠟⠉⢀⡔⠁⠀⠀⠀⢀⡎⠀⠀⣿⡀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⡻⠶⠶⠟⠉⣀⡤⠤⠴⢦⡾⠁⠀⠀⢮⠀⠀⠀⠀⠀⣸⠀⢠⠀⡇⠈⠢⡀⠀ ⣇⠀⡄⠘⣿⢿⣿⣽⣻⡆⠐⠀⠘⣧⡴⠒⠋⡟⠁⠀⢀⣤⠚⠳⢤⣤⣤⣾⡇⠀⣿⣼⣷⣶⣤⡹⡄ ⢹⡆⣧⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠈⠉⠉⡿⠀⢀⡴⠋⡼⠀⠀⠀⠻⡿⠻⠁⢠⣿⣿⡟⢉⣿⣿⡇ ⠀⠳⣿⡄⠀⠀⠀⠻⣿⣿⠏⠳⣦⣤⣤⣴⣧⣾⣿⡇⠀⡇⠀⠀⠀⢠⡇⢀⡴⠛⢮⣻⣷⣿⡟⣹⠁ ⠀⠀⠈⠻⣆⢧⠀⠀⢨⡏⢀⡞⢁⣠⠔⠋⠁⣀⣀⡏⠉⡇⠀⠀⢠⡿⠛⠁⠙⢄⠀⠙⠯⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠙⠓⠦⢤⣧⣾⠴⠋⣁⠄⠚⠉⠀⠀⠹⡀⢹⣦⣀⣸⠁⠀⠀⠀⠀⠑⠦⣤⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡇⡠⢊⣷⠒⠋⠉⠉⠹⡖⠻⣶⡟⠛⠻⡆⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⣸⠋⢙⡏⠁⡿⡄⠀⠀⠀⢀⡇⠀⣿⠑⠒⠒⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠴⠊⠉⠳⡀⡗⠒⠊⡇⢀⣧⠓⠶⠶⠎⢉⣷⣄⣸⡀⢀⣀⣿⣤⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡁⠀⣀⠀⣀⠽⢷⣤⡤⠯⣍⣋⠟⠒⠛⠛⣟⣩⠿⠋⠉⠹⣯⡻⣻⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠀⣼⣸⠀⣴⡆⢹⢿⠀⠀⢰⢿⡇⠀⣴⣶⣄⠈⢿⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠻⡏⠀⣿⡇⢸⢸⠀⠀⢸⠸⡇⠀⣿⣿⣿⣦⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⢸⣿⠀⢾⢰⡀⠀⣸⣶⡇⠀⢹⣿⣿⣿⣷⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠸⣼⣷⣜⣿⡿⠃⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⢿⣧⣤⣀⣀⣀⣀⣠⠤⣤⣴⠿⠟⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⣀⠀⠈⠉⠉⢻⠀⠀⠘⣇⠀⣀⣀⣠⠤⡶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣢⠌⠉⣛⣒⡖⠋⠀⠀⠀⠈⠹⡑⢒⣛⡀⢳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠁⠀⢱⠖⠃⠀⠀⠀⠀⠀⠀⠱⣤⡤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠀⠀⡴⠋⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠹⡄⠀ ⠀⢀⠎⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⣯⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣖⢦⡼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇ ⠀⢈⡷⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠛⠉⠀⠀⠈⠉⠙⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹ ⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠷⢦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸ ⢸⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡠⠋⠉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠙⢦⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏ ⠸⡄⠀⠀⠀⠀⠀⢸⠀⠀⡜⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⡀⠳⣴⠃⠀⠀⠀⣀⣀⣰⠃ ⠀⢣⠀⠀⠀⠀⠀⠈⢧⡾⣡⣤⣤⣤⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡿⠛⢿⣿⣶⣻⡀⠀⠀⠀⠻⣄⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠙⣿⡄⡇⠀⠀⢀⣠⣤⠤⢤⣄⠀⠐⣷⣿⣧⣤⣾⣿⣿⣿⢷⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠀⡟⣿⣿⣿⣷⣶⣿⣧⡇⡴⠊⠁⠀⠀⠀⠀⠀⠙⣦⡏⣿⣿⣿⣿⣿⣿⠏⢸⡀⣠⠜⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⣄⠀⣷⠹⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠻⣿⣿⣿⠿⢋⡠⢃⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣯⠳⢌⣛⣿⣿⣟⡡⠏⠹⣄⠀⠀⠀⠀⠀⠀⣠⠇⠀⠉⠓⣾⣿⣏⡉⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣨⠿⠿⠥⠤⣀⣀⣈⣲⠤⢄⣠⣤⣚⣁⠤⠴⠒⠋⠁⣀⡤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣄⣀⣀⣀⣉⣉⣉⣉⣁⣀⡠⠤⠤⢒⡾⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⡄⠀⠀⢹⣦⡀⠀⠀⠀⠀⢀⡞⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠸⣯⣶⣀⠀⠀⠀⡸⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠸⡄⠀⠀⠈⠻⠞⠀⠀⢠⠇⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣖⣯⠉⠛⠃⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡀⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠉⠉⠀⠹⠷⡀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⣤⡬⠵⢶⣦⣀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡸⠀⠀⡼⠋⠃⠀⠀⠀⠸⣗⠀ ⠀⠀⠀⠹⡀⠀⠀⠀⠀⢀⡏⠀⠘⣇⠀⠀⠀⠀⢸⣉⣓⣶⣶⠶⢶⡇⠀⠀⠀⠀⢠⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠙⠲⠤⠤⠤⠞⠒⠒⠒⠉⢳⣄⣀⣤⢿⣄⠁⠈⠉⠉⢩⣷⣄⣀⣀⡴⠓⠤⠤⣄⣷⣀⠀⠀⠀⢀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠙⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠶⡒⠒⠂⠀⠀⠀⡀⠤⡤⠔⠂⠉⠐⢄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠔⢁⠔⠈⡀⠄⠀⠀⠀⢀⠆⠀⠀⠘⡄⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⡠⠁⡠⠂⠀⠀⠀⢀⠔⠁⠀⠀⠀⠢⠍⣀⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠋⠂⠀⡟⢀⠎⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠠⠁⠠⠊⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃⠀⠀⡀⠔⠁⠀⠀⠀⠀⣀⡴⠓⠄⠀⠱⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣀⠔⠈⢀⣀⣀⠤⠐⠦⠛⣁⣠⠖⡜⡄⢐⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡏⠉⢿⣟⣿⡏⠁⠀⠲⣿⣿⣯⡙⡇⣇⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣷⡰⢀⣀⠨⠓⣋⡑⢤⡛⠛⠛⢱⣸⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢌⣉⠡⠒⣍⡀⠈⡢⡙⠶⠔⣵⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⣤⣤⡤⡤⢤⣤⣀⡉⢷⠱⡀⢀⣈⣈⣈⣀⠈⠒⡲⠁⠀⠀⠀⠀⠀⠀⠀ ⡗⠋⣿⠛⣈⣉⣏⣾⢒⠟⠑⢌⡇⢱⡀⠑⠒⠎⠀⡠⠆⠁⠢⡑⢄⠀⠀⠀⠀⠀ ⠸⢼⢻⢦⡀⠀⠀⠙⢯⠠⡀⠀⢿⡀⠗⠤⠀⠠⢺⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀ ⡏⠙⠛⠄⢹⣦⡒⠂⠈⢷⠈⢄⠀⠘⣴⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠪⠢⠀⠀ ⠃⡀⠀⠀⠙⠿⠧⡐⠂⠹⡀⠀⠢⡡⣻⡆⠀⠀⢣⠀⠀⠀⡀⠤⠐⠂⣀⣁⡑⠄ ⠀⠐⡀⠀⠀⠀⠀⠈⢢⣀⠨⢦⡀⠑⠌⠇⠀⠀⠀⢀⠔⣈⠴⢖⣌⡡⠸⠦⠀⠀ ⠀⠀⠱⠀⠀⠀⣀⠔⠁⢈⣤⣜⡈⠠⢈⢷⢀⠴⠭⡁⠄⡇⠁⣦⣅⢠⣉⡄⠃⠀ ⠀⠀⠀⠂⢀⠆⠁⣠⠶⠋⠀⠈⠙⠦⣀⠙⠟⠀⠀⠈⠦⡃⠀⡇⠈⠎⢻⡇⠁⠀ ⠀⠀⠀⠔⠁⣠⠞⠡⠀⠀⠀⠀⠀⠀⠈⠑⠇⠀⠀⠀⠀⠑⢴⠗⡀⢀⠃⡇⠀⠀ ⠀⠀⢰⠤⣺⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⣀⣈⢺⢃⠂⠀⡇⠀⠀ ⠀⠀⢾⠀⠹⣂⠀⠀⠀⠈⠀⠀⠀⠀⠀⡧⢀⣠⠔⠜⠋⠉⠉⠫⢫⡄⠀⠀⠀⠀ ⠀⢸⠐⠀⠀⠙⠦⡀⠀⠘⠀⠀⠀⡀⢊⡔⠈⣁⡠⠐⡈⠁⠀⠁⢣⢘⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡞⢀⡠⠀⠀⢀⠔⡐⠁⡼⠀⠀⠀⠀⠀ ⠀⢠⡤⠀⣀⣴⠖⠲⣦⢄⣀⣸⣂⠥⠒⢊⡡⠔⡲⠁⡐⠀⠘⠀⢀⡤⠀⠀⠀ ⢀⠼⣭⠄⡈⡻⠒⠠⠗⠛⢷⣌⢫⠑⢂⠀⢫⡏⣠⠜⠀⢀⠠⢊⠌⠀⠀⠀⠀ ⠃⣸⢸⢧⠏⠂⠄⡎⠉⢆⠀⣼⣿⣷⡄⢡⣸⣿⠿⡠⠒⣁⠠⠥⠒⡲⠀⠀⠀ ⢀⡟⠘⣼⢠⣸⣷⠳⠿⣽⢆⢻⡿⠘⣷⠸⣿⣡⠊⠁⢀⡤⠤⣐⣨⠤⣦⠄⠂ ⠸⡇⠀⡇⣾⣿⡀⠀⠀⠀⣴⣿⠃⢰⡟⣴⣹⠧⠐⠒⠻⡾⢟⠓⢒⡛⠁⠀⠀ ⢠⢇⠀⡛⠁⣻⡋⠢⣤⣶⣿⣿⠀⠘⢿⣿⠁⢀⡎⣄⢠⣣⣤⣤⣀⣀⠀⢀⡀ ⠀⢸⣦⡖⠀⠀⠃⣠⡚⣉⠔⡟⢤⣠⡟⠃⡠⣮⡓⢴⢯⡈⠫⡻⠋⠁⠀⠀⠀ ⠀⠘⣄⡡⠔⠈⠉⣹⡯⡀⠀⣉⡏⢿⡄⠀⣇⢻⣧⠸⠓⠺⢆⠈⠢⠀⠀⠀⠀ ⠀⠀⢿⡇⠀⠀⢰⣿⡇⠑⡴⣻⠀⡘⠃⠒⠁⠘⠻⡆⡆⠠⢀⠑⠤⣈⠢⡀⠀ ⠀⢀⣾⣿⠄⠀⠈⣻⠇⠀⠀⣿⠊⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠑⠤⣀⠉⠐⠀ ⠀⠀⠻⣿⣦⣀⢰⡿⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⡄⠆⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⡙⢿⡟⠀⠀⣰⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣷⡈⠁⢀⡴⠁⠙⠛⢿⣿⡦⢀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡄⠈⡶⠟⠀⠀⠀⢠⣾⡏⠱⡄⠱⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡇⡜⣿⣳⡀⢀⢤⢺⣅⠘⢄⠈⢆⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⣰⣿⣧⢹⡃⢸⢸⣿⣦⡈⢢⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⡎⣷⡾⣸⣿⣿⣷⡀⢣⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣾⣿⣿⣿⣿⣧⣷⣇⣿⣿⣿⣿⣷⡀⠳⠸⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣷⡀⢣⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡿⠋⣿⢸⣿⣿⣿⣿⣿⡇⠹⠌⣍⠙⢿⣿⣷⣄⡀⠀⠀⠀ ⠀⢸⠿⢿⡿⣿⡟⠀⠀⣿⠘⣿⡿⣿⣿⣿⠀⠀⢃⢹⠀⠀⢿⣿⣿⣿⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠓⠋⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠉⣀⢀⣀⠀⡔⠅⠀⠀⠠⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⠁⠄⠀⡈⢈⡀⠒⠛⠁⢠⣪⣥⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠘⢀⣰⡛⣺⠀⠈⠢⡈⠘⣾⣯⣀⠀⠋⠓⢒⠲⠤⣄⠀⠀⠀⠀⠀ ⠀⢸⠁⢀⠀⠀⠁⠸⣷⡻⢊⣜⢮⡿⠁⠀⠀⢉⡉⢩⣽⣷⣿⣦⣄⠑⢄⡀⠀⠀ ⠀⢸⠀⠁⠀⠀⠀⢉⡽⠂⢁⢀⢀⣘⡑⣴⣾⠿⠛⢁⣼⣿⣿⣿⣿⣿⣦⡹⡄⠀ ⠀⡏⠆⠀⠀⣠⠞⣏⣍⢩⠋⠉⡉⠉⣩⣇⢀⠴⠪⡏⠀⢙⣿⣿⣿⣿⣿⣿⡽⡄ ⠀⡇⠪⡕⢰⡏⢲⢣⠈⢿⢶⠦⣅⡞⠅⠩⢻⡀⡄⠙⡌⢆⣿⣿⣿⣿⣿⣿⣇⢸ ⢸⠁⢀⠀⠁⢿⣾⣆⣀⣘⡆⢂⠄⢳⡈⠄⡅⣇⣻⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⡏⠔⠁⡠⠀⡘⣿⣿⣿⣿⣿⣀⣘⣤⣇⣤⣾⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⡼ ⠳⣄⠁⠀⠀⠔⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢦⡀⠀⢹⣿⣿⣿⣿⣿⠏⡼⠁ ⠀⠈⠢⣄⠀⡠⠘⣿⡿⢛⣻⣿⣿⢿⡅⣀⣀⣀⠈⠁⢀⣼⡜⣿⣿⣿⢃⡼⠁⠀ ⠀⠀⠀⠈⠣⡐⠐⠨⡳⣾⠀⠀⠀⠀⡏⢁⠀⡏⢃⠀⡏⣰⡗⢚⡟⣡⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⣀⣐⣌⠓⠦⣤⣴⣅⣬⠴⠳⠴⢗⣛⠥⡴⠋⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣀⣀⣊⣉⣉⣋⣉⣙⣙⣂⣬⠴⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⠙⠲⢤⡀⠀⠀⢠⣄⢀⣀⡀⣴⠂⠙⣿⣿⣿⡀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣳⣶⣶⣶⣏⡋⠀⠀⠀⠉⠒⢤⣘⣿⣿⣿⣿⣾⠀⠀⠸⣿⣯⣷⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⡄⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣿⣿⣿⣿⣿⣿⣿⡿⠶⠂⠀⠀⠺⢿⣿⣿⣿⣿⣿⣯⠶⠂⢸⣿⣷⣷⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⡟⠈⠉⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⢿⠀ ⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⣟⡿⢿⠿⣿⣫⠀⠀⠀⣀⠀⠀⠀⣾⠙⠛⠛⠷⠀⠀⠀⣿⣿⣿⣿⡆ ⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠛⠁⠀⠀⠀⠉⠁⢠⣾⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇ ⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠁⠀⠀⠀⣤⡤⢀⣤⣶⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣶⣄⣸⣿⡂⠀⣤⠀⢀⡀⠀⡄⠀⢰⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣤⣸⡇⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⡛⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠮⠉⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⡀⠀⠀⠀⠀⠈⠳⣄⡀⢻⣿⣦⣤⣀⣈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡉⠙⠒⠒⢢⠤⠤⠾⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⠦⣤⣤⣤⣤⣤⣤⠴⠶⠒⠚⠛⢻⣿⣿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠈⢻⣿⣿⣿⢿⡋⠁⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣷⣶⣿⣿⣿⠟⣡⠞⠀⠀⠀⣴⣾⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡇⣼⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡃⣰⠏⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⢿⣟⠓⠒⠒⠛⠛⠛⢻⣉⡁⢀⠁⢀⣤⣾⣿⣿⣿⣿⢋⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣋⣀⣴⣿⣿⠛⢶⣤⣤⣤⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢹⡏⠙⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⣿⣶⣼⣿⡟⠁⣿⡟⠛⣿⣉⡭⠿⠿⠿⠿⠛⠛⠛⣿⡇⢸⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠈⣻⣿⠇⠁⠀⠀⢀⣴⣶⣶⣦⣀⣿⣷⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡌⡏⢻⣿⡼⠧⣄⣀⣁⠤⠤⠒⣒⠻⣿⣻⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣸⣟⠿⢷⣄⠃⠈⠂⠀⠀⠐⠒⠊⠉⠉⣱⣮⡻⣍⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣽⠟⢿⣿⢷⣤⣸⣆⠀⠀⠀⠀⣤⠤⣤⣦⣄⣀⠀⠛⠦⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⡿⠃⠈⠛⢿⣷⠀⣿⡀⢿⣿⠈⢧⡀⠀⠀⠹⣄⠈⢻⡿⠃⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣼⠁⠀⣼⡄⠈⢻⡇⣸⣧⠈⡇⠀⠀⠻⣶⣄⠀⠈⠹⠋⠁⣠⠔⠋⠹⣯⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣷⣄⠀⢸⡄⠀⣿⣷⢠⣞⡟⣿⣿⣆⢇⠀⠀⠀⠉⠛⣿⠶⠤⠒⠋⠀⠀⠀⠀⠘⣟⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣄⣀⣳⠀⣿⣾⠘⢿⣴⣿⠻⣿⣾⡀⠙⠦⢀⡴⣧⠀⠀⠀⠀⣀⠴⠚⠁⠀⠘⡦⠽⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⡟⠆⡿⢿⡀⠀⢹⣿⣶⣿⣿⣷⡀⢠⠏⠀⢸⡄⢀⣠⣤⠶⢖⣚⣉⣉⣉⣡⣀⣸⡆⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⢿⣿⡇⠀⡇⢸⡇⢠⣾⣿⣿⣿⣿⢿⣿⣿⠀⣀⣴⣷⣿⣧⣾⣿⡿⠛⠻⡅⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⣀⣆⠀⣿⢻⡿⠉⠛⣿⣿⣿⡿⠁⠀⣿⣸⣿⣿⣿⢿⣿⣿⣿⣌⣿⣿⡎⠁⢰⣿⣿⣿⣿⣿⣇⣤⢤⣿⣆⣀⣵⣤⠀⠀⠀⠀⠀ ⠀⣿⡗⢿⢸⡁⠀⠀⢹⣧⣄⠀⠀⠀⣿⣿⣿⡿⠃⠘⣿⣿⣯⠹⣿⣿⣧⣰⣿⣿⣿⣿⣿⠋⠀⡀⠈⣿⢿⣼⣧⣿⡇⠀⠀⠀⠀ ⠀⢸⠳⣈⡿⢿⣤⡀⠀⢻⣮⣷⡀⢰⣿⣿⣿⡅⠀⠀⢹⡿⣿⣄⡽⠋⠛⠛⠿⢾⣟⣿⣿⡀⣾⠇⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠙⢇⢸⣯⠹⢦⡈⣿⣟⣷⣌⣿⣿⣿⡇⠀⠀⢘⣧⣽⡿⠁⠀⠀⠀⠀⠈⣿⢿⣿⢿⣋⣠⣾⠟⣠⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠑⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⠉⠻⢶⣄⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⢠⣶⠂⠘⢿⣿⣿⣿⡆⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⢄⣤⣤⣤⣤⡺⠟⠀⠀⠀⠈⠙⠢⣄⣀⠘⢿⣿⣿⣿⣿⣶⣟⠀⠀⠘⣿⣿⣟⣿⡀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣱⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⣿⣹⣧⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣷⢿⡄⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠿⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠓⠀⢸⣿⣿⣾⣷⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣃⠀⠀⠀⠀⣿⣿⣿⣿⣼⡀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⡟⠻⠟⠛⢿⣷⡀⠀⠀⠀⣠⣄⠀⠀⠀⢸⠷⠉⠉⠁⠘⠛⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠉⠁⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠟⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀ ⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣇⠀⠈⣿⠀⠀⢠⡄⠀⢰⡆⠀⣸⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣄⣸⡇⠀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠖⠢⢤⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⣶⣶⠉⠐⠲⢦⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⡤⣄ ⠸⣄⠀⠀⠉⢳⣄⠀⠀⠀⠹⣦⠠⣤⣠⣴⡚⠉⠀⣿⣄⣰⣿⣄⣀⢀⡤⠟⠋⠉⠈⠓⢦⡀⠀⠀⣳⠀⠀⢀⣤⠞⠉⠀⠀⣼ ⢀⡼⠗⠂⣠⢤⡽⡇⠀⣠⠖⠚⠉⠉⠁⠈⠙⢯⠉⠉⠉⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⢷⡶⢚⡿⠀⢠⠟⠁⠀⠀⠀⠾⣅ ⠘⠧⣤⡶⢿⣄⣡⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠻⣅⠀⠸⣄⠏⠓⡆⠀⣀⡼ ⠀⠀⠈⠓⠋⠉⠀⢠⠇⠀⠀⠀⠀⠀⣠⠤⣤⣀⣠⠤⠤⢤⣄⣞⣉⣓⣤⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢦⠀⠙⠛⠋⠳⠤⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣇⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣤⠾⠋⠀⢀⡞⠁⢀⣤⣶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠈⢳⡄⠀⠀⠀⠸⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀ ⠹⣯⠀⠀⠀⠀⠀⢀⡞⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠻⠷⠄⠟⣧⡀⢰⡀⢻⡀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠈⠛⠲⠶⣶⠂⣼⠁⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠲⣶⠚⠋⠉⠉⡇⠀⠀⠀⡀⡀⠀⠉⢻⠶⣿⡍⠉⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⣷⠀⠊⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠼⠃⠀⠀⠘⠣⠇⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⢈⡇⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⢿⠀⢷⡀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⣠⠀⠀⠀⣼⣨⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣸⡿⣦⣸⣬⣳⡦⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠋⢹⠁⣼⣧⠾⣧⠞⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⢻⡙⠛⠛⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠷⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠷⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⢄⣀⠀⠀⠀⠀⢰⠀⠀⡠⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⣸⡀⠀⣇⢀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠝⠁⠙⠢⢄⣉⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠤⡀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⢶⣤⡀⠀⠀⠀⠀⡴⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠙⡄⢠⠋⠈⢣⡀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⣿⠃⠉⢻⠀⠀⠀⠀⠙⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢱⠇⠀⠀⠀⠻⡄⠀⠀⠀ ⠀⢀⣾⣿⠀⣿⣠⡶⠛⣀⣤⡴⢶⣶⣶⣾⠿⠿⠷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⢸⡆⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⣾⣿⢃⣴⣿⣯⣴⠾⢿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠀⠀ ⢸⣿⣵⣿⡟⣿⡟⠛⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⣰⡄⢴⡷⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⣿⣶⡿⣧⣴⠟⠁⠀⠀⡀⠀⡀⠀⠀⠀⢠⡿⠁⢸⣿⣿⠛⡿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⣿⣿⢿⣿⢧⣿⠏⣀⣤⡄⠀⢠⣾⢃⣠⣄⣴⣿⠥⣴⣿⣿⡟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀ ⣿⣿⡟⣼⣿⣿⣯⣤⡟⠉⠛⢷⣾⣛⣫⣵⣿⣯⣴⣿⣿⣿⠟⠀⣾⣿⡏⣿⣿⢀⠔⠙⠓⠢⠤⠤⠴⠒⠚⠉⠁⠀⣀⡙⣆⠀⠀ ⣿⣿⣷⣿⡟⣿⣿⠛⠳⠞⠋⢹⡟⢋⣽⣿⣥⣾⣿⠟⠋⠁⠀⠀⣿⣧⡤⣿⣿⠉⢰⣤⣤⣤⣤⣤⣤⣴⣶⡞⢿⣿⣿⣿⡌⠀⡇ ⣿⣿⣿⢻⡇⠘⣿⠀⠆⠀⠀⢸⣷⣿⣿⠟⣋⣭⡴⢶⠶⣦⠀⣼⣻⣿⠁⢹⣿⣆⢸⣿⣿⡇⠈⣿⣿⣿⣿⡇⠈⣿⣿⣿⡇⢠⠀ ⢸⣿⣿⡌⣿⡀⣿⣶⣷⣤⡀⢸⡇⣿⡿⡞⢡⣿⡟⠁⠀⣿⠟⠹⡏⢿⠃⢈⣿⣿⣾⣿⣿⣧⣰⣿⣿⣿⣿⣿⣶⣿⠿⠛⠁⡞⠀ ⠀⢿⣿⣷⡌⣷⠸⣿⣿⣿⠻⣿⣿⣿⡇⣷⡸⠟⠀⠀⣰⡟⠀⠀⠙⠷⠶⠾⠋⢿⣿⡄⠉⠙⠻⠿⠿⠛⠛⠛⢉⣠⠴⡦⣴⠃⠀ ⠀⠈⢿⣿⣿⣮⠀⢹⣿⣿⣷⣴⣿⣿⣇⠈⠛⠶⠶⠞⠋⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡏⠒⣶⠒⠒⢲⡶⠛⠛⢯⣀⡼⣧⠋⠀⠀ ⠀⠀⠈⢻⣍⠉⠙⠛⠿⢿⣿⣿⣿⡉⢿⣦⠀⠀⠀⠀⠀⠈⠐⠖⠋⠀⠀⠀⣠⣿⣿⠃⠄⠘⠧⠤⠟⠀⠀⠀⠀⢉⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠈⠉⠛⠿⣾⣿⣷⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄⠀⠈⠓⢤⣀⣀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣦⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣦⣤⣤⣄⣀⣀⣀⣤⣤⣴⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣗⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣚⣉⠭⢏⣉⡑⠲⢾⡇⠀⠹⠍⢈⣉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠉⠁⠋⠁⠀⠀⠀⠙⠂⠈⢹⣖⢦⡀⠀⣬⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣝⣮⣉⣩⢟⢲⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⣽⣎⣧⡀⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡼⠙⣆⠀⠀⠘⣇⠈⣧⡀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢠⡶⣿⡟⠃⠀⠃⠀⠀⣸⠿⠷⢦⣿⠀⠀⠀⣿⣰⠛⡇⠹⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⢨⣧⣿⣷⣤⣼⣴⣿⣟⣿⣿⣶⣦⣼⠀⠀⠀⣹⡟⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢀⠀⢾⡟⢿⣿⣿⣿⣯⠀⠀⠀⣽⣿⣿⣿⣿⢷⡦⠄⣿⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣞⡄⢸⣷⣾⣋⣿⣏⣿⡶⢶⡆⠘⣏⣿⢟⣾⡞⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⣼⡟⠿⣰⢿⣷⣸⡿⣯⣍⣩⣭⡟⠷⠀⠻⠦⢿⣿⡿⠟⡇⠀⢠⣿⣽⣧⣤⣖⡲⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣾⣿⡎⣑⣠⢶⠀⠈⢿⡞⣧⡀⠀⠀⠀⡀⠀⠀⠀⠂⡄⠀⠀⠀⣇⠀⣿⡏⠙⢧⣀⢀⣍⠳⣿⣿⣦⡀⠀⠀⠀ ⠸⣿⣿⢉⠹⢾⢯⣹⣼⣶⡴⠋⠻⣾⠧⣀⠀⠀⠳⢤⣤⡤⠼⠁⠀⠀⣠⣿⣸⠋⠛⠀⢹⢿⡋⠁⠀⠈⢮⠻⣷⠀⠀⠀ ⣀⣰⣶⣿⣷⣼⣞⢻⣿⠿⠁⠀⠀⠸⡆⠈⣷⣦⣄⣀⠉⣀⣀⢴⣶⠏⠁⣿⠋⠀⠀⣠⢀⣿⣧⡀⠀⣴⡶⠷⣾⡇⠀⠀ ⠻⣝⠗⠛⠋⠙⣻⡾⣿⠀⠀⠀⠀⠀⢱⡄⠈⣷⠀⠉⠉⠉⣠⡾⠁⠀⠙⠛⠀⢀⣤⣿⣿⢻⣿⣿⣶⣤⣠⣴⣿⠁⠀⠀ ⠀⠛⠀⠀⢀⣼⡿⢡⣿⣆⢸⡀⠀⠀⠀⢳⡀⠘⣧⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⡞⠉⢸⣿⡏⢸⣿⠙⢿⣿⣥⠇⠀⠀⠀ ⠀⠀⠀⢀⡞⣸⡷⢶⡿⠻⣆⣷⡀⠀⠀⠀⠁⠐⣿⢳⡾⠁⠀⠀⠀⠀⠀⢀⠀⣦⣿⣿⣿⢶⣾⣿⠸⣸⡹⡻⣄⠀⠀⠀ ⠀⠀⠀⣾⡿⢻⡏⢹⡇⠀⠙⢮⣿⣆⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⣼⣶⣿⡿⠋⢹⡏⢹⡿⣆⢷⡳⡿⢿⡆⠀⠀ ⠀⠀⣰⣿⠟⢻⡇⢸⡇⠀⠀⠈⠿⢾⣧⣄⡀⠀⠀⣿⣄⡴⠓⣖⣤⣖⣿⢿⣿⠛⠀⠀⢸⣧⢸⠀⠈⠲⠿⢦⣤⣵⡀⠀ ⠀⠀⣿⡇⠀⠀⠁⡼⠁⠀⠀⠀⠀⢀⣈⣽⣾⣟⣖⣿⣿⠷⠚⠿⠛⠛⠛⠛⠿⠷⠶⣦⠘⠛⣿⢀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⢰⣿⠃⠀⠀⢸⠇⠀⠀⢀⡴⣖⡿⠟⠋⠉⠉⠛⠯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡆⠀⠀⠀⠀⠀⣳⠀ ⠀⢸⣿⠀⠀⠀⡾⠀⠀⣴⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⠀⠀⠀⠀⠀⢻⡄ ⠀⠈⣿⠀⠀⢸⡇⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣿⠀⠀⢸⡇⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣿⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢽⡇⠀⠸⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠈⠁⠀⠀⠈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣰⠏⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⢛⣽⣟⣀⣀⣠⣴⠆⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣀⡀⠀⠀⠀⠀⠀⢀⣼⣧⣤⠞⠋⢁⣀⣀⣐⡿⠋⠁⠀⠀⣀⠀⣰⠋⠀⢀⡼⠁⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡖⣶⠄⠀⠀⣀⢀⣾⡿⠚⠋⠉⠑⠲⣭⡳⢶⣄⣀⣀⡘⣏⣉⣁⡤⠾⠭⠭⠭⣥⣀⣰⠶⠖⠉⢁⡞⠁⠀⢀⡞⠁⠀⠀⠹⠁⠀⠀⠀⣀⣴⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣯⣾⡄⠀⠈⠉⠛⢯⣝⣒⠛⠛⢛⡛⣇⣙⡷⣽⣶⣍⠙⠛⢿⡿⠲⣤⡀⠀⠀⠈⢳⣌⢳⣴⡔⠋⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣯⣤⣴⣶⣤⣀⠀⠀⢈⡾⠛⠉⢀⡴⣮⡿⠋⠙⠓⠻⣿⣷⣄⠈⢳⡀⠀⠙⢢⡀⠀⠀⠘⣧⣻⠀⢀⣠⣴⡏⠀⠀⠀⠀⢀⣠⠞⠉⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠚⠁⢠⡿⠋⣿⣆⠉⢳⣴⢋⢄⢈⠀⢀⣀⣈⣠⢦⠀⠀⠀⢿⠹⣿⣳⣜⣧⠀⡀⠀⠻⣄⢰⠀⢹⢻⣤⣿⣿⡏⠀⠀⢀⣠⠖⠋⠀⢀⡴⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⣾⡇⠀⣿⢻⣠⣾⡁⡌⠈⡼⠀⢸⠁⠀⠀⠀⣧⠀⢢⠘⣷⣾⣿⣾⣿⣧⣳⡀⠀⢹⣾⡆⢸⣾⣿⣿⡿⠋⢀⡴⠚⠁⠀⠀⢀⣈⣤⡴⠖⠋⠉⢩⡿⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⢀⣿⡇⠀⣿⠸⡇⢸⠀⠀⣠⣇⠀⣼⡄⢀⣀⣤⣼⣆⠀⠀⣿⣿⣿⣿⡟⢬⢿⣷⠀⠀⢷⡇⣼⡿⠟⠉⣠⣾⣥⠤⠴⠒⠛⠋⠁⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⣼⡿⠃⠀⠻⡆⡇⠘⣠⢀⣿⣿⡆⡟⢿⡡⣟⣣⣬⣿⣇⠀⠹⣿⣿⣿⠇⠈⢻⢿⡆⠀⣼⣿⣏⠤⣴⠞⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠞⠋⣀⣀⣤⣶⣶⡄⣀⡤⠖⠉ ⠀⠀⢀⣿⡇⠀⠀⠀⡇⢹⡀⣯⣼⣟⠙⣿⠇⠈⠉⠉⠽⠿⠟⠉⠷⣤⣼⣿⡟⠀⠀⣾⣸⡇⠀⢹⣿⡖⢺⡏⠀⠀⠀⠀⢀⣶⡿⠉⣁⣠⣴⡶⠾⠻⠻⢏⣍⣻⡿⠋⠉⠀⠀⠀ ⠀⠀⣾⣿⡇⠀⠀⠀⣧⠸⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠃⠀⢀⢷⣿⠀⢠⡞⠉⢻⣿⣀⣤⡤⠖⠒⢾⡿⣧⣾⠿⠿⣿⣿⡶⠶⠶⠾⠿⠏⠀⠀⠀⠀⠀⠀ ⠀⠐⡋⣿⡇⠀⠀⠀⣿⡀⣻⠟⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⣾⣿⠏⣰⣏⣧⣶⠛⠉⠁⠀⠀⠀⠀⠀⠉⢳⡌⠙⠓⠶⠤⣀⡤⠴⠶⠒⠒⠛⠛⠛⠛⠛⠛ ⠀⠀⣦⢸⠁⣤⠀⠀⣿⡟⢡⡀⠿⣍⢿⠉⠢⣀⠀⠀⣀⣴⣾⣿⣿⣾⣿⠃⠀⠀⠹⣿⣼⣿⣿⣿⠇⠀⠀⠀⣴⡿⠀⢀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡾⢰⣿⠀⠀⠼⠀⠀⠳⣤⣹⣆⡆⠀⠈⠓⢺⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⣰⣿⠀⢶⡿⠄⢠⣿⣤⣾⣿⣿⡛⠿⠶⢶⣶⣤⣄⣀⣀⣤⠤⠤⠐ ⠀⠀⠀⠀⢸⣿⣀⣠⣴⠆⠀⠀⠀⢀⡾⠁⠀⠀⢠⣿⡿⠛⠋⢁⣼⡟⢿⡄⠂⠀⠀⣰⣿⣷⠟⠀⠀⠀⣰⠛⢿⣤⠈⢀⣴⡟⠃⠈⠻⣟⠛⠿⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣅⣀⣤⠶⠋⠀⢹⡀⠹⣾⣄⣆⣿⠟⠁⠀⢠⡴⠚⢻⣶⣦⠉⠻⣿⡟⠻⢦⣄⠀⠈⠷⣄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠁⠈⠻⡄⠀⣀⡤⠶⠚⠏⣩⢿⣿⡿⠋⠀⠀⠤⣤⠟⠻⣶⡿⠻⣿⠁⠀⠀⠀⢸⢧⠀⢸⣿⣿⡆⠀⠹⣷⣦⣬⣽⣷⡀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣦⣤⣤⡷⠋⠁⠀⠀⠀⠀⠀⣶⣿⣿⣶⣄⠀⠀⠀⢀⣠⣿⠃⠐⣿⣷⣶⠀⠀⢸⣿⡆⠀⣿⣿⣿⠀⠀⡏⠉⠙⠛⠻⢧⡀⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠈⣿⡀⠀⢀⣿⢿⡏⠀⠀⢹⣿⡅⠀⢀⣨⠽⠇⠀⣿⣿⣿⣧⠀⢹⠀⠀⢀⠀⠀⠙⠦⣄⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠉⢻⣿⠏⢉⡟⠀⠀⣈⡿⠉⠛⠊⠉⠀⠀⠀⠀⠀⠙⢿⣿⡆⠸⡇⠀⠀⠲⣄⠀⠀⠈⠳⢦⣀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠁⠀⣽⣧⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢣⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⠛⠲⢤⣌⣳⡀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠆⣀⣀⣀⠀⠈⠙⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠸⡆⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠉⠛⠂⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⡀⠀⠉⠉⠀⠀⣴⣏⣿⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣼⣦⠀⡀⠀⣼⣿⣿⡅⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠸⡇⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣷⣿⣄⢩⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢻⠀⠀⠈⠋⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠈⢩⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣄⠀⠉⠛⠀⠀⠀⠀⢀⣿⠋⠀⠙⠻⣿⢿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⣿⣧⡀⢀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⠁⠀⠳⢄⣤⡾⣋⡴⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⠟⠉⢷⡄⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣨⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢷⡀⠀⠀⠹⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⣰⢿⣿⣞⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠻⣄⠀⠀⠘⢷⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣾⠁⣰⣿⣏⢹⣥⡀⠀⠀⣴⠶⢿⡏⢻⣷⣄⠀⠀⠘⢧⠀⠀⠀⢻⣆⢠⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⠏⢠⣿⣿⣿⡆⠙⢷⣤⡾⠋⠀⣿⡇⢸⣿⣿⣧⡀⠀⠈⢷⡄⠀⠀⠹⣧⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⢠⣿⣿⣿⣿⣿⡄⢸⢿⡄⠀⠀⣹⡇⢸⣿⣿⣿⣿⣄⠀⠀⠻⣆⠀⠀⠈⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢠⣿⣿⣿⣿⣿⣿⣷⠘⣯⣷⠀⢀⡿⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠹⣆⢀⡀⠈⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣆⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣧⠱⠄⣹⣮⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠉⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣷⠀⡉⣿⣦⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣵⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⣷⠐⢸⣿⣷⡽⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣧⠀⣿⣿⣿⣮⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⣆⢹⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢧⢣⠀⢻⡬⡿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⣯⢧⠈⣷⢣⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣆⡄⢹⣿⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⡘⠀⢿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠛⠛⠛⢻⡟⠈⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷⠀⢸⣇⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣻⣷⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠖⠀⠀⢀⠀⠀⠀⠀⠀⢀⡴⢠⠞⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⣡⠶⠛⠒⢲⣾⠏⠀⠀⠀⢀⠴⠁⢠⠋⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⢤⡄⠀⠀⠀⣴⠯⠟⠛⠯⢖⡦⣄⣀⡀⢸⣟⣋⣠⣖⠒⢒⣋⣁⡤⠴⠒⡴⠋⠀⣰⠃⠀⠐⠇⠀⠀⢀⣠⡖⠀⠀⠀⠀⠀ ⠀⠀⠀⣽⠽⡆⠀⠉⠙⢯⣅⣈⠉⠉⢣⣹⡶⣵⣯⡉⠻⣿⠒⢄⡀⠀⠈⢮⡳⣴⠊⠀⠀⡰⠁⠀⠀⠀⠀⣠⠔⣩⠋⠀⠀⠀⠀⠀⠀ ⠀⣠⠜⢓⣾⣟⡢⢤⣀⡼⠋⠄⠠⠛⠞⠁⠈⠉⢿⣿⣦⠘⡄⠀⠉⢦⠀⡀⢹⣿⢠⣴⡾⠁⠀⠀⣀⠔⠊⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⣼⠁⣿⡇⣠⡏⣘⢃⠀⢰⠋⠉⠙⡄⠠⠸⣌⣿⣿⣷⡴⡄⠀⢧⡇⢸⣼⣿⣿⠇⢀⡤⠛⠁⠀⠐⣋⡠⠴⠖⢲⠀⠀⠀⠀⠀ ⠸⠀⢸⣿⠀⣿⢹⠀⡇⢈⣼⠀⣼⣀⣀⠤⣼⡀⠁⣿⣿⣿⡟⣽⣾⡀⠸⣷⢸⡿⠋⣡⣶⠭⠤⠒⠒⠉⠉⠀⠀⣀⠴⠋⠀⠀⠀⠀⢀ ⠀⠀⣾⡏⢀⠙⣸⡄⡧⢠⡿⣷⡏⢧⡺⣵⢾⡿⣄⠘⣿⣿⠃⠈⡟⡇⢰⣿⣯⣒⡟⠁⠀⠀⢀⣀⡤⠤⠤⢒⣉⣤⡤⢶⣿⣆⠤⠚⠁ ⠀⢰⣿⡇⠸⠀⡇⣷⣿⣿⡇⠛⠁⠀⠀⠉⠉⠀⣭⣷⣿⠏⠀⢸⣷⡇⢠⡟⢷⡜⢀⣀⡤⢤⣾⣏⣴⣶⣿⣭⣥⣥⣵⣶⠏⠀⠀⠀⠀ ⠀⠛⣿⡇⠀⠀⣇⢘⡞⣿⣿⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⣿⡿⣠⢻⣠⡞⠛⠉⠁⠀⠀⠙⢻⠙⠒⠬⢍⣀⠤⠤⠀⠒⠒⠒⠒⠒ ⠀⢰⢸⢀⡆⠀⡿⠋⡆⠛⡜⠉⠳⣄⢀⣠⣶⣿⣾⣿⡏⠀⠀⠻⣷⣿⣿⡏⠀⠀⢰⡟⢀⡄⠀⣸⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⢸⡇⠀⣇⠀⠈⠒⢛⡗⠀⠈⣹⣿⡿⠟⢻⣿⣇⠀⠀⠀⣸⣟⡟⠀⠀⢠⢿⡄⠹⠋⣰⠟⠻⡿⢿⣭⣭⣽⡿⠛⠒⠒⠒⠉⠁ ⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠉⠀⢀⡴⣏⢁⣠⡴⠉⣇⠙⢾⣤⣰⡿⠋⠀⣠⠶⢿⣤⡙⠲⣾⠷⣤⡀⠘⢦⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠅⠈⢳⢀⡠⠔⠒⠋⠽⢿⣿⠋⠀⠂⠤⠋⢳⡾⢻⣏⠀⠀⠀⣿⡄⢸⣿⣇⠀⢻⣶⣬⣽⣆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣶⡞⠉⠀⠀⠀⠀⢠⣿⡿⠻⡦⠀⠀⣴⣾⠇⠈⣿⡿⠆⠀⢇⡇⢸⣿⣿⡄⠸⡄⠀⠈⠙⢦⡀⠀⠙⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠛⣦⡖⢫⡎⠀⢐⡿⠻⠔⠚⠉⠀⠀⠙⢿⣿⠀⡇⠀⠑⢄⠀⠈⠲⢄⡀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⣷⡀⠀⠀⠀⠘⣿⣷⡿⠀⠀⠉⢀⣿⡇⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠙⢆⡀⠀⠉⠓⠦⢌⣢⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⠟⠀⠤⠄⠀⢈⣿⡇⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠈⠉⠀ ⠀⠀⠀⠈⢻⣿⣿⡗⣄⢀⠀⢠⣿⣾⠁⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣹⣿⣿⣟⣞⣦⣈⡿⠁⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣇⠀⠈⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣏⠙⠿⢿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠿⠃⠀⠀⠀⣼⠏⠻⣿⣿⣿⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠂⠀⠀⣠⠞⠁⠀⠀⠀⠉⠈⢻⣿⣿⡿⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠳⣴⣞⡵⠂⠀⠀⠀⠀⠀⣰⣿⡿⠋⠙⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣯⣩⡀⠀⠀⠀⠀⠀⢰⣿⠟⠙⣄⠀⠈⢧⡀⠀⢣⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⡴⢁⣿⣟⣷⡀⠀⢀⣤⢶⠛⣿⣄⠀⠈⢧⡀⠀⠹⣄⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣪⠃⣼⣿⣿⡌⠻⣦⠞⠁⢸⠀⣿⣿⣧⡀⠀⠳⡄⠀⠈⢮⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⣿⣿⣿⣿⡈⣿⡄⠀⢸⠀⣿⣿⣿⣿⣄⠀⠹⣄⠀⠈⢯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⢰⡏⢰⣿⣿⣿⣿⣿⣦⠀⠙⣎⢢⠘⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⠈⣯⢻⠇⣾⣿⣿⣿⣿⣿⣿⣇⠀⠘⢧⢈⢻⣮⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣧⠘⣿⣷⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⡆⢿⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢖⡄⢹⡼⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⡞⡀⢷⡇⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⡰⠸⣾⠀⠀⠉⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠛⠟⠻⣿⠋⣿⣿⠋⠀⠀⠀⢸⣿⠃⢸⣿⣿⡿⠿⣿⣿⣿⣿⠀⠀⠀⠀⢣⠀⢹⡀⠀⠀⠘⣽⣿⣿⣿⣿⣟⣷⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣾⣶⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠻⠛⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣶⣤⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠀⠀⢀⣴⠞⠉⠉⠉⠉⢓⣦⣀⣠⡾⠟⠁⠀⠀⠈⢙⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⣿⣿⣿⣀⠀⣾⠁⠀⠀⢀⠆⡴⠋⠴⣿⣯⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿⣿⣿⣿⣦⣿⣶⣀⡀⡟⣾⠁⣀⣴⣿⣿⡇⠀⠀⠀⠀⠠⣄⣇⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠒⢺⣿⣷⡶⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠁⠇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠈⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣴⠊⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⢀⣴⣿⣧⣤⣶⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠉⠀⣈⠿⠀⠀⢿⣿⣿⣿⢿⣽⣫⡟⠉⠙⢶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢋⡿⠁⣴⣿⣿⠿⠟⠛⢻⣿⣿⣿⣿⣿⠟⣁⣽⣿⣿⣿⣿⠿⠿⣿⣶⡻⣿⣿⣾⠁⠹⢦⣀⠀⠀⠙⣧⠀⠀⠀⠀⠀ ⠀⠀⣰⠏⠀⣼⢇⣼⣿⣿⣷⣤⠴⢶⣛⣛⣿⠿⢟⣁⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⡀⠀⣯⠳⠄⣠⠟⠀⠀⠀⠀⠀ ⠀⣰⠇⠀⢠⣿⣿⣿⣿⣋⡭⠶⠿⠛⠛⠛⢿⣿⠟⠋⠙⣿⡀⠀⣶⠶⠿⠿⠿⠀⣿⣿⣿⣿⡅⠉⠉⠳⣿⣤⣾⡇⠀⠀⠀⠀⠀⠀ ⢰⣏⡀⠀⢸⣿⣿⣿⡸⡏⠀⣀⣤⣤⣤⣤⠈⣿⡆⠀⠀⢻⣷⡀⠿⠀⠀⠀⢀⣼⣿⣿⣿⠏⠈⠲⢤⣀⣀⣠⠟⢿⡀⠀⠀⠀⠀⠀ ⣼⡟⠀⠀⢸⣿⣿⣿⣷⣧⠚⠛⠉⠉⠉⠉⢀⣿⠇⠀⠀⠀⠙⠿⠶⡶⢶⣾⠿⠋⠁⣴⠋⠀⠀⠀⠀⠀⣸⠃⠀⢸⡇⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣦⣀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡷⢦⡀⠀⠀⠀ ⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣟⠿⠿⠿⠟⠋⠁⢀⣠⠴⠶⠶⠶⣶⠿⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠀⢸⠇⠀⠙⢦⠀⠀ ⣿⠀⠀⡀⠀⢿⡿⣿⣿⣋⡟⣷⡄⠀⠄⠀⠰⣏⣀⡤⠶⠖⣲⠏⠀⠀⠀⢀⣠⠞⠷⣄⣀⣀⣀⣠⣾⠇⠀⢸⢦⣿⣤⣤⣀⡈⢧⠀ ⢸⣇⠀⡇⠀⠈⠁⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⠿⠦⠤⣶⠏⠀⠀⣀⡴⠋⡏⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⣾⣾⣿⣿⠿⢿⣿⣾⡇ ⠈⢻⡄⣷⡀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣿⠀⣀⣶⡏⠀⢸⠁⠀⠀⠀⠀⠉⣿⠀⠃⠀⣴⡿⣿⣿⣁⣠⣾⣿⣿⡇ ⠀⠈⠳⣿⣧⠀⢀⠀⠀⠈⢿⣿⣿⠋⠈⢻⣷⣶⣶⢶⣾⣧⣾⠿⢿⡁⠀⣼⠀⠀⠀⠀⠀⣸⣇⣀⣠⡞⠉⠳⣜⢿⣿⣿⡟⣁⡼⠀ ⠀⠀⠀⠈⠻⣷⡘⣇⠀⠀⠀⣿⡏⠀⣰⠏⠀⢀⡤⠶⠋⠉⠀⢀⣸⡏⠉⢹⠀⠀⠀⠀⣰⣿⠟⠉⠀⠹⣄⠀⠈⠳⢽⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠷⣄⣀⣙⣄⣰⣏⡤⠞⠋⣀⡠⠶⠒⠉⠉⠁⢷⠀⠘⣦⡀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠳⢄⣀⢀⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣟⡿⠋⢀⡤⢞⣉⣠⡤⠶⠶⠶⣄⣈⣷⣀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⣽⣧⣠⣎⡤⣿⡍⠀⠀⠀⠀⠀⢹⡉⠉⢹⡟⡄⠀⠈⠙⡇⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⢀⡟⠉⠉⣿⠁⠀⣿⣧⠀⠀⠀⠀⠀⣸⡇⠀⢸⣷⠙⠒⠒⠚⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠖⠋⠉⠲⡀⢸⠓⠲⠚⣿⠀⠀⣿⠿⠶⣖⣖⡶⠉⢹⣷⣀⣀⣿⠀⠀⠀⣠⣿⣄⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⣿⣗⠛⢿⣶⠦⣤⣶⣶⣶⡿⠿⣿⡿⠿⠒⢾⣝⢿⣿⣿⣿⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⠤⠤⠶⣆⣠⠶⠋⠉⣿⢻⠋⠉⣙⠳⠶⣍⡄⠀⠀⠀⣸⣶⠞⠉⠀⢀⣀⠀⠹⣷⣝⣾⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⢰⣿⠇⢠⡏⡇⠀⠀⠀⡟⣿⠀⠀⣷⣿⣿⣦⡀⠈⠿⠟⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠳⡏⠀⣼⣿⠀⢸⠇⡇⠀⠀⠀⡇⢻⠀⠀⢻⣿⣿⣿⣿⣄⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⣿⣿⠀⣾⡀⣄⠀⠀⠀⣧⣼⠀⠀⠘⣿⣿⣿⣿⣿⣦⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣶⣿⣿⠀⢹⡏⣿⡄⠤⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠻⠿⠷⠶⠿⠛⠋⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠻⠿⠿⣷⣶⣤⣤⣤⣤⠤⠤⠶⠶⣶⡶⠿⠟⠋⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠀⠀⠈⠉⠉⠉⢿⡆⠀⠀⠘⣇⠀⠀⠀⠀⣀⣀⡤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢍⣉⠓⠒⠶⠦⢤⡤⠾⠁⠀⠀⠀⠉⠛⣾⠫⠭⠿⠇⠀⢧⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠲⠀⠀⢶⣉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠙⣆⠐⠒⠚⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣀⣀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠖⠒⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⠀⠀⣠⠴⠒⠛⢋⣠⠴⢝⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣶⠏⠀⢠⡴⠞⡉⠀⢀⡠⠷⠤⢀⣀⠈⠑⠲⢤⡀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⡄⢀⣿⢀⠎⢠⠔⠉⠀⠀⠀⠀⠀⠉⠙⠲⢤⣹⣏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⢹⣀⣸⢾⣿⣨⢠⠃⠀⠀⠀⠀⠀⠈⢣⠀⢢⡀⠀⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⣞⢹⣇⠈⡸⣿⣿⠀⠀⣠⠀⠀⠀⠀⠀⡇⠀⢱⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⣿⠘⣿⡄⣷⣿⣿⣤⡀⡇⢀⣿⢀⣠⢶⣧⣴⣿⣢⠄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⢿⣇⠿⣧⣼⣿⠙⡟⢻⢿⣿⣿⣽⡵⠛⠋⠙⠛⣿⣿⡟⠧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠀⢠⠈⣇⢀⣇⠘⡿⠀⣇⣿⣿⣿⣿⣿⠛⠂⠀⢰⣿⣿⡿⡏⠒⢤⡈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠸⡟⠯⠼⡇⢀⣧⣄⣻⠛⠋⠉⠀⠀⠀⠉⠛⢻⣧⠙⣤⠴⢛⠒⠒⠛⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⡇⢀⣣⠀⠀⢹⣦⠔⠁⢸⠙⠛⠋⣁⡀⠀⠀⠀⠀⡀⠀⣙⡿⠋⣡⠖⢁⡠⠤⠬⢍⣉⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⡇⣸⡟⠀⠀⡏⠙⣷⣶⣧⠀⠺⡿⠋⠀⠀⠀⠻⠿⣋⣀⡿⢷⣌⣠⣞⣡⠤⠒⢦⠄⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣹⠃⠀⡜⠀⠀⢹⡈⢻⣧⡀⠀⠀⠐⠒⢺⣿⡟⢫⣿⠀⠠⠀⢏⠈⢣⡀⠀⠀⢱⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢈⠏⠀⡸⠁⠀⠀⡄⢳⣘⣿⣹⣷⠦⠤⠤⠤⣄⣴⣿⣎⠀⠀⡆⢸⡀⠀⠻⡀⠀⠸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣡⡾⠀⢠⠇⠀⠀⠀⡆⢸⣿⣿⡿⠉⠀⢀⣤⣤⣀⠉⠻⣿⣄⠀⠑⡌⢷⡀⠀⣙⠦⣄⡀⠀⠀⠀⢷⡀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⣿⠁⠀⡜⠀⠀⠀⠀⡇⣸⣿⣿⠁⠀⠀⣸⣿⣋⣹⡇⠀⠈⢻⣿⣦⢸⡄⢣⠀⠘⢒⡾⡆⠀⠀⠀⠸⣿⣦⡀⠀⠀ ⠀⣴⡟⠁⡜⢸⠀⢠⠃⠀⠀⠀⠰⣵⢿⠃⢸⡀⣀⠀⠈⠉⠈⠉⠀⠀⠀⠀⢻⣿⣿⣧⣾⣆⠀⢼⠻⠿⣀⣀⣀⡤⠿⠛⡇⠀⠀ ⣸⡟⠀⢰⠁⡞⠀⢸⠀⠀⠀⠀⣼⠏⢸⠀⠀⣿⣍⡉⠉⠒⠦⢤⣀⠀⣀⠤⠞⢙⣍⣿⣿⣿⣍⡻⡆⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⡇⡇⠀⡇⢸⣧⠀⡆⠀⠀⠀⠀⡏⠀⢸⠀⠀⠘⣷⠀⠈⠉⠐⢢⡬⢉⡤⠒⠊⠉⠉⢿⣬⢿⣳⣍⠓⢦⣤⢤⡤⠴⡒⠛⣇⠀⠀ ⠉⢷⣸⠀⡟⢸⠀⡇⠀⠀⠀⢰⠁⠀⠘⡇⠀⠀⠹⢷⡀⡀⢀⣿⡾⡁⠀⠀⠓⢄⠀⠀⠙⢷⣄⠈⠠⡀⠘⢦⠘⡀⠘⡄⠸⡄⠀ ⠀⠀⢹⡇⡇⢸⢻⣿⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀⠀⠀⠉⠳⣾⣿⡇⠈⠢⡀⠀⠀⠑⢄⠀⠀⠙⢷⣄⢳⠀⢸⠀⢃⠀⢸⠀⢷⠀ ⠀⠀⠀⢻⣧⡘⢇⢻⣦⡀⢸⡀⣷⡀⠀⠈⢧⡀⠀⠀⠀⠀⠈⡟⠻⣧⡀⠈⠳⢄⠀⠀⠁⠆⠀⠀⠙⠻⣄⣸⠃⢸⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⢻⣷⠈⢆⠻⣿⢦⣣⠘⡌⠢⡀⠀⠻⣦⡀⠀⢀⡞⠀⠀⠀⠉⠲⢄⠀⠑⠤⢀⡀⠀⠈⠒⢤⡈⢿⣤⣸⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⢻⠀⠀⠑⢮⡛⢿⣧⡈⠀⠄⠉⠒⢼⣿⣦⣸⠁⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠈⠑⢄⠀⠀⠑⠄⠙⠿⣄⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠹⡔⢿⡩⡦⡄⠀⠀⠀⢻⣾⠻⣦⡀⠀⠀⠀⠀⠀⠀⡞⢻⠗⢦⡀⠀⠳⡀⠀⠀⢀⡀⠈⠻⣄⢀⡇ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠈⡟⠞⢌⠢⠀⠀⠀⢿⡆⠈⠻⣷⣄⣀⡀⠀⢰⣇⣾⠀⠀⠙⣶⣀⠙⠦⣤⠀⠉⠒⢄⠈⣻⣄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣀⡀⢀⡀⠠⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡶⠁⠀⠀⡀⠠⠚⠤⢀⠀⠀⠀⠀⠀ ⠀⠀⠰⢀⠀⠀⠀⠀⠀⡀⢣⡁⢀⠔⠉⠀⠀⠀⠀⠠⣑⢄⠀⠀⠀ ⠀⠀⠀⠈⢫⡉⡉⠔⠈⡨⢚⠓⡚⠛⢶⡀⠦⢀⠀⠀⢡⠙⡄⠀⠀ ⠀⠀⣀⡴⣿⠎⠀⠀⡰⠔⠚⠲⢚⡀⠈⡕⢄⠀⠑⠄⣀⠁⠂⣤⠤ ⠀⡀⠝⠪⠃⠀⢀⣠⢁⠀⢀⡤⠤⡇⠐⡈⡘⡄⠀⠀⢌⠫⡉⠀⠀ ⠠⠝⠯⡡⡤⠲⣭⢤⡜⠀⠈⢿⣖⢾⡄⣨⣐⡅⢀⠀⡬⡆⢡⠀⠀ ⠀⠀⠞⠋⡆⢀⡏⠹⠃⠀⠀⠘⠛⠀⢸⣮⣿⡇⠀⢀⡇⠈⣸⠀⠀ ⠀⠀⠤⣾⠔⠈⢹⠀⠀⠀⠀⠀⠀⠀⡸⣿⡇⠀⢀⠎⡇⠀⠏⠀⠀ ⠀⠀⠀⢀⠄⡝⡙⠡⢢⠀⠀⠀⡠⢚⢻⣼⣤⢀⠆⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢂⠁⠃⠃⠸⣦⣴⣾⢅⣸⠃⠈⠁⠙⢄⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠤⡬⠷⡀⠐⠢⡘⣿⡇⠘⢻⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⣰⠡⢄⠀⠀⠁⠘⣷⣶⣾⣿⢷⣤⣾⣷⠈⢤⢀⠀⠀⠀⠀⠀⠀⠀ ⢸⢀⡀⠁⠆⢀⠀⡾⠙⣾⣿⠁⠈⠉⢿⠀⠀⢠⠈⠐⢄⠀⠀⠀⠀ ⢨⠅⢓⣪⣑⢼⢠⠇⢀⣿⠇⠀⠀⠀⢈⠄⡠⠂⡐⠰⠀⡇⠀⠀⠀ ⠸⡮⢕⠢⠒⠫⣿⠀⢸⡸⠤⣄⡀⠀⠨⡄⠀⢠⢗⠡⣴⠇⠀⠀⠀ ⠀⢣⡽⠦⡭⣴⠇⠀⣾⠁⠀⠈⠙⠦⠀⠱⡄⢧⠕⠂⢻⡄⠀⠀⠀ ⠀⠸⣡⡚⢡⡟⠀⢀⣷⣄⣀⣀⣀⡀⠀⠀⠈⢢⠡⡀⠀⡇⠀⠀⠀ ⠀⠀⡍⢀⡎⠀⠀⢸⣿⡈⠙⠛⠿⢿⣿⣿⣿⣿⠗⠚⢂⠇⠀⠀⠀ ⠀⠐⡄⣾⡁⠀⣠⣿⠙⠷⣀⠀⠀⠀⠀⠉⠉⠙⠲⢄⠀⢡⠀⠀⠀ ⠀⠀⠘⠬⢷⣼⠟⠁⠀⠀⠀⠑⠲⢦⣄⣀⡀⠀⠀⢸⡗⣸⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠾⠒⠛⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠀⠀⡀⠤⠤⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⢲⠁⡴⢊⠁⡠⠑⠠⠍⣑⠢⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⣈⡶⣇⢡⠁⠀⠀⠀⠄⢄⠉⢺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⢸⢹⡄⣸⣇⠀⡆⣀⠀⣸⢠⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠸⡦⢧⣽⠫⢳⣳⣷⣏⠛⠙⣻⣾⠫⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⡇⢱⢾⣸⢠⡚⠿⠿⠂⠀⠸⢿⡙⢌⡢⠄⠦⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡇⠀⣧⡊⡈⢙⣩⠄⠀⣀⡄⢨⡏⠁⡠⢄⡊⠭⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣞⠁⡐⠀⢏⢳⣌⠁⠀⠠⣾⢲⡏⠙⢊⠢⡁⠘⡄⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⢆⡌⢠⠁⠀⡈⣾⣷⠗⠂⠀⠲⢿⡆⠸⡸⡀⠱⣀⠃⠀⠰⡀⠀⠀⠀ ⠀⢠⠞⣝⠀⡆⠀⠀⢃⡿⡏⠀⢼⡗⡷⠀⠹⣶⣰⢱⠈⢒⣧⠀⠀⢷⢤⠀⠀ ⢰⠏⡐⡸⢠⠀⠀⢨⠏⠁⢳⡒⠠⠄⡀⠀⣀⠿⡟⣿⣶⢸⠉⠒⠒⠈⢸⠀⠀ ⢿⣀⢁⢧⢸⠀⠀⡈⠀⡄⠈⢧⠈⠉⣐⠩⠂⡉⠉⢷⡫⠎⠒⢆⠖⠢⠹⡀⠀ ⠀⠹⣸⢸⣾⠀⠀⡇⠀⢃⠀⠈⠑⢶⣿⡑⢄⠈⠢⡀⠙⢦⣡⠈⡘⡀⠃⢣⠀ ⠀⠀⠻⣎⢜⢧⡘⡸⢄⠈⢢⡀⠀⢠⠋⠓⢄⠑⠄⡀⠀⠠⢉⢲⡁⡇⠀⠈⡀ ⠀⠀⠀⢹⠀⠙⢙⠷⣁⠌⠐⢽⣦⡇⠀⠀⠀⠈⢢⣈⠁⠂⠀⠀⠙⢧⡀⠀⠇ ⠀⠀⠀⠂⠀⠀⠈⠜⠮⠥⠀⠀⢻⠙⢦⣀⡀⠀⡆⡇⠑⣤⠱⣄⠐⠠⠈⣒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠖⠚⠋⠉⠉⠁⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠗⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡛⠛⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀ ⠀⣿⡀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⢀⣤⠾⠛⠉⣿⣛⠃⢉⣽⣧⠀⠀⠀⠀⣈⣽⠶⠒⠒⠲⠤⣄⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣤⠶⠋⠉⠀⢹⡆ ⠀⠘⢳⣄⡀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠈⣻⣭⣭⠷⠾⠻⢶⣤⣤⣤⣽⠿⠷⠾⠟⠛⠒⠒⣰⠾⠋⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢀⣴⣿⠀⠀⢀⣴⠋⠁⠀⠀⠀⣠⡿⠃ ⠀⢠⡾⠋⠉⠀⣶⠶⣶⢿⡇⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣏⠉⣾⠏⠀⢠⡟⠁⠀⠀⠀⠀⠘⠛⢶⡀ ⠀⠘⢷⣤⣴⡶⢿⣄⣉⣼⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠻⣇⠀⠀⠘⣇⠸⠋⠛⡆⠀⠀⣀⣸⡇ ⠀⠀⠀⠈⠧⠤⠾⠛⠋⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠀⢀⣀⠀⢠⡔⠛⠷⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⢷⡄⠀⠙⠿⠶⠶⢿⣄⣀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣴⣾⣭⠾⠛⠛⠚⠉⠉⠉⠙⠛⠚⠒⠒⠒⢮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡾⠇⠀⠀⢠⡟⠁⠀⠀⣀⣤⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠘⣶⡶⠒⠒⠛⠛⠉⠀⠀⠀⣰⡟⠀⠀⣴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣄⡀⢙⣷⣄⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠈⠙⢛⠛⠊⠋⡻⣷⣄⠸⣦⣈⣿⣄⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠶⠶⢶⡇⠆⣿⠁⠀⡅⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡖⠛⠋⠉⠁⠈⢳⠀⠀⠀⠀⡄⢀⡀⠀⠈⠉⣿⠷⣽⣯⠉⠉⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣏⠀⠴⠇⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣀⣼⡿⠀⠀⠀⠀⢷⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢿⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢠⠀⠀⠆⠀⡄⡀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡄⠸⢦⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⣠⡞⠀⠀⠘⢠⡇⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⢸⣷⣄⠀⣯⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠟⢉⡟⠀⣰⡟⣠⣾⢀⣴⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣇⠙⠷⠿⠙⠛⠋⠈⠉⠙⠛⠛⠶⠶⢶⡶⣶⣤⣤⡤⠤⠶⠶⠶⠶⢾⡏⠉⠉⠀⠀⠀⢸⢃⣼⠟⠟⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⢤⡀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣶⠶⢤⣄⣀⣹⣿⣄⠈⠙⠛⠛⠛⠒⠤⣀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣴⣦⡟⠣⢌⡙⠳⢶⣶⡿⣶⣤⣄⡘⢿⣌⣿⣾⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡻⣿⣾⣶⣿⠟⠋⢉⡏⠹⡻⣿⣿⠳⣝⢷⡝⣄⠀⣠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠋⢀⣼⡿⡟⢉⡿⠃⠀⣠⠾⡟⣸⣻⡾⣿⣷⡘⢆⠳⣬⣿⣿⣧⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠷⣾⣿⣿⣿⢿⡗⢺⠃⢀⠔⢡⣼⣷⣿⣻⣡⢼⣿⣇⠈⢷⡁⢸⣿⡾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⣿⣄⢸⠀⢀⣸⣿⣿⣿⠵⢛⣟⣻⣿⣯⠀⠈⠻⣿⡏⠟⠷⠙⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣼⣿⣿⠀⣤⣿⡿⠭⠀⢀⣨⣿⣯⣽⡇⠀⠀⠀⠹⢧⣀⣀⡠⠖⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣼⣿⠇⠀⢀⣴⡿⠋⣩⡏⠙⡇⠀⠀⠀⠀⠀⠈⢏⢳⣤⣾⣯⣉⠻⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⢻⣏⣿⠟⠾⠟⠋⢀⣀⣩⠴⢺⡁⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⠿⠿⣿⡟⠁⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣿⡿⢿⣿⡿⢄⡀⠀⠀⠀⠀⠀⠚⡿⠷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠻⣷⣤⣀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⣠⣾⡽⣻⣿⢻⣿⣿⣿⠈⠻⡀⠀⠈⠛⣶⡖⠒⠒⠈⠀⠀⠀⠙⣦⠙⣲⣄⣀⣀⡴⢾⣷⣄⠀⠀⢀⣿⠻⠷⣦⡀ ⠀⠀⢀⣀⣀⣒⣿⣽⣿⣿⣸⣿⠛⢿⡝⣧⠀⠈⠢⡀⠀⢸⣷⠀⣠⣴⣶⣖⢺⣷⣾⡿⠿⠿⠟⣿⢥⣼⠟⢻⣷⣄⠀⠉⠻⢉⣉⣿ ⢀⠖⠋⠀⠀⠀⠀⠙⣷⡌⠛⢻⣷⠾⣿⣿⠂⣠⣤⣼⣦⣾⣧⣴⣋⣿⣯⣿⣿⣿⡉⠀⠀⠀⣼⠁⠘⠁⠀⠐⣿⣿⢦⠀⠀⠀⢹⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠒⠉⢹⣿⣿⣿⣿⣿⣄⠀⠘⣿⠀⠙⣿⣿⡿⠿⣿⣿⣷⣄⠀⡜⠁⠀⠀⠀⠀⠀⣿⡟⠀⠁⠀⠀⠾⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣴⣶⠿⠛⠁⠰⠟⠿⣄⠑⣾⡏⠀⠀⠈⢳⣇⣀⣿⣿⣿⣿⣿⠀⠀⠀⠐⢂⣀⣸⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⡿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡟⡰⠀⣀⣼⣷⣿⣇⠉⣯⠉⠉⢹⠀⢀⣤⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣶⠻⣧⠊⠀⠘⣧⠀⠀⠀⠀⠀⢸⣇⢻⣰⠿⠛⢙⣿⣿⣟⠀⢸⡆⠀⠼⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠋⡟⠀⢻⡏⠙⠷⣄⠀⣿⣆⠀⠀⠀⣰⣿⠏⠉⠁⣠⡶⠟⢋⣹⣿⣆⢠⠇⠀⣠⣶⣆⣤⢄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢈⡿⠓⢄⠀⠘⢦⣼⡇⢀⣠⠔⢹⠇⠀⢀⣾⠏⠀⠀⣺⢴⣿⣿⡏⠀⠀⣯⣩⣽⣼⣭⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠁⠀⠀⠀⢡⠀⠈⠛⢷⣼⣇⠀⡏⠀⢀⣾⡏⠀⢀⡜⠁⣾⣿⡿⠀⠀⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠉⠙⣿⡇⠀⢸⡟⠣⠤⠋⢀⣼⠟⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢹⣷⡀⠘⣅⢀⣵⣶⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠺⣿⡿⡒⠚⠛⡹⣿⢿⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣈⣸⣾⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢌⠦⠀⠀⠠⠄⡴⠀⠀ ⠸⣻⣷⠠⠄⠀⠀⠀⠀⢀⠀⠀⢀⠯⡩⠝⠙⢖⡂⠔⣤⣤⢀⡀⠀⠈⠙⢄⠀⠀ ⡌⡿⠛⠉⢎⢄⠀⠀⠀⠀⠪⣉⠁⠄⠀⠀⢔⣾⠈⠳⢮⠻⡄⠈⠐⢄⠀⠀⢂⠀ ⠱⡡⡀⠀⢀⣂⢢⠀⠀⠀⢀⣁⠄⠀⣠⠞⠁⢸⡇⠀⢠⠷⠚⡄⠀⠈⠀⡖⠨⡀ ⠀⠑⡔⣞⡉⣉⡧⠥⠀⠑⠪⠐⠂⣟⠀⠀⠒⠚⣧⠀⢺⣿⣾⢘⠄⠀⠀⡧⢊⣥ ⠀⠀⠈⢾⡯⠭⣥⣂⠀⠤⠅⠆⢸⢹⡇⠈⣿⢢⢽⠂⢬⡛⡏⡘⡸⠀⢠⠡⣾⠏ ⠀⠀⠀⠀⠀⠀⠹⣷⢧⣰⠇⠈⢼⡆⠀⠀⠈⠀⢀⣽⢹⠵⠗⠊⡸⣀⠆⠀⣧⣤ ⠀⠀⠀⠀⠀⠀⠀⠹⣾⣇⣤⠤⠀⢨⡄⠀⢀⣠⣿⣯⠁⠀⠀⡰⢡⢁⣔⣘⠯⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢈⠈⣫⣿⣿⣿⣿⡧⢤⡊⠀⠈⡿⡿⠿⠿⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⢰⠊⠿⣿⣿⣿⠟⠉⠀⠀⣸⠓⢿⣦⡈⠂⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠜⠉⠀⠉⠂⢠⣾⢆⢇⠈⠈⠙⠠⣀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠹⣷⡂⠀⠀⠀⠀⠀⣾⣇⠔⠚⡄⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣇⠀⠹⣷⡄⠀⠀⠀⠘⢿⡿⡼⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡰⢻⠀⠀⢹⣿⣿⣦⠀⣰⡿⠁⡶⡇⢀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡸⢃⠀⠀⠻⣿⣿⣿⡾⠥⡤⠝⢧⣼⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠤⠖⡒⠶⠒⠂⠴⡓⠶⡁⠜⠁⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠊⠀⡐⠁⢀⡀⠤⠤⠒⠉⣆⣼⠮⢍⡁⠈⠙⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡶⣇⡠⠺⠠⠊⣟⣀⠤⡤⠒⠁⢰⠈⣷⡄⠈⠑⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⡕⠁⠀⣿⠹⣦⡀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣿⣠⠞⠁⠀⡇⢻⣢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⣭⣻⣦⠀⠀⠲⢟⣫⣍⢉⠀⢼⠋⠀⡙⠳⡅⠀⢇⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢟⢿⣎⢐⣆⣨⡒⠻⡽⠍⠲⢌⠀⠈⢀⠄⣲⠀⢿⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⠥⢁⡠⠌⠍⣛⢦⣐⡀⠗⠊⢁⠀⡏⠂⠁⢸⠰⡌⠀ ⠀⠀⠀⡠⠊⠺⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡬⠶⠐⡡⠟⠀⠀ ⠀⢠⠞⢁⠔⠁⠀⢀⡀⡄⠐⡀⢠⣬⢀⣀⢒⠢⠂⠀⠀⢀⣼⣧⢀⡮⠋⢽⠈⠀ ⡠⠁⢠⠁⡠⠐⠊⢁⠡⠂⠀⠱⠀⠉⣁⡈⠁⠀⠀⣠⡴⣿⡟⠈⣌⡄⠡⠀⣃⠠ ⠀⠀⠊⠁⢀⠄⠊⢀⡀⠤⠄⢠⠵⣴⣿⣮⣦⣴⣾⢟⣷⠏⠀⠀⠀⢹⣮⣍⡀⠈ ⠀⠀⠀⠀⡌⣠⡒⠁⠀⠀⢠⠃⠀⠀⢉⠉⢸⡻⠿⠟⠁⠀⠀⢀⠜⡡⢡⣾⠛⠿

⠀⠀⠀⠀⠀⢒⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢄⡀⠀⢂⠀⠀⠀⠀⠁⠀⠐⠂⠄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠢⠀⠁⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠉⠉⢂⠀⠀⠀⠀⠀ ⡀⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠾⣄⡀⠈⠆⠀⠀⠀⠀ ⠀⢄⡀⠀⠀⠀⡀⠀⡰⠀⠀⠀⠀⢀⠠⢲⠡⠁⠀⠀⢣⠀⡘⠀⠀⠀⠀ ⠀⠀⠈⠀⡂⠊⠀⠰⠁⠀⢀⣴⡦⠅⠂⡣⠥⣔⢌⣛⠞⡀⢸⠀⠀⠀⠀ ⠀⠀⢀⠔⢀⠄⠊⠇⣠⢴⠟⠛⣿⡛⡾⠓⣿⡟⠓⣦⣷⡷⡅⠀⠀⠀⠀ ⠀⠐⠋⠁⠀⠀⢰⢀⠿⡣⡑⠈⠒⣱⣡⣄⠙⠊⠐⢉⡏⣁⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢸⡤⠵⢯⠨⣐⠚⠉⢄⡀⠙⠖⣒⢕⠝⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠂⠁⠐⠁⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠉⠐⠀⡀ ⠀⠀⠚⠠⣄⠄⣀⠀⠀⠀⠀⠀⡗⠦⣌⣁⡴⠋⠃⠀⠀⠀⠀⠀⢀⡀⠌ ⠀⠀⡀⢸⢢⠉⠐⠾⠦⡀⠀⢀⠇⠀⠈⠉⠀⠀⡄⠀⠀⢠⣴⣎⣀⣠⣄ ⠀⠜⠠⠀⠑⣭⣤⣀⢠⡇⢠⠊⠀⠀⠀⠀⠀⠀⠘⣄⢠⣯⠀⠙⠛⡏⣬ ⠀⠀⠀⠡⠀⢈⣿⣿⠋⢇⠋⠂⠤⠤⠀⠀⢀⠤⠐⠉⡄⡍⠑⣶⣶⡧⠊ ⠀⠀⠀⠀⠣⠸⣿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⢻⡂⣿⣿⠀⠀ ⠀⠀⠑⠀⠀⢹⣿⡟⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢧⢻⡟⡄⠀ ⠀⠉⠉⠒⢢⡼⢫⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠍⢷⠴⠄ ⠀⠀⠀⠀⡼⣽⠋⠃⠤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠊⠈⢺⣏⠒ ⠀⠀⠀⣜⣾⡇⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠈⠉⠉⠉⠀⠀⠀⠀⠈⣿⡄ ⠀⠀⣰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠶⠶⠖⠲⣉⠋⢱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢀⠈⢳⡭⠗⣦⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⢀⣀⢀⠀⢠⣎⡄⠘⣹⡤⣷⠀⠀⠀ ⠀⠀⠀⠠⡏⢀⣽⣷⡶⠖⣷⣶⣇⣀⣿⡆⠀⠀⠀⠀ ⠀⠀⢀⡤⣹⣄⣿⣽⣽⠲⣸⣿⠏⢀⣿⣁⣀⡀⠀⠀ ⢰⡞⢯⣶⣄⠿⣇⠀⠀⣀⠐⠀⣰⡼⠉⣦⠏⢛⢦⠀ ⢶⠾⠺⣽⠋⠀⠡⠱⡒⠀⢲⠊⠼⢀⣤⣿⣦⣒⣻⠀ ⠈⢀⣾⣽⢧⣄⠀⠃⢱⡔⠁⠀⠀⢈⣼⣧⡏⣿⣇⠀ ⠀⡼⢿⢸⠀⠹⢦⣀⢸⣃⢤⣤⣾⡟⠁⣇⠓⠽⠍⡄ ⢠⡇⠀⡇⢀⡤⠶⠛⠻⠋⠉⠉⠉⠉⠁⠈⣦⠀⠀⢡ ⠘⡇⢸⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢸ ⠀⡇⢸⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸ ⠀⠁⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⠒⠒⠒⠒⠦⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⢛⡫⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⣭⠥⣀⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣠⣴⣻⠭⠕⣒⣩⠉⠻⠭⢿⣶⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣧⣠⡶⠛⠉⠉⠉⠀⢈⠑⠿⣿⣾⣝⣷⣦⣁⠀⠀⠰⠦⣄⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠟⠁⠀⠀⠀⠀⠀⣾⢚⣿⡆⠀⠈⠉⠛⠮⢽⣻⢶⣄⡀⠀⠉⠳⢤⣄⣠⢶⡠⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⠀⢀⠀⠀⠀⠀⢿⣿⡿⠓⠀⠀⠀⠀⠀⡀⢉⣛⠛⠿⣶⣄⣀⡀⠀⣁⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢨⣿⣦⣀⣀⡠⢴⣶⣶⣒⣒⣒⣉⣷⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣳⣿⣿⡿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣖⣒⣒⡄⠺⣿⣿⠛⣻⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣌⣹⣿⣿⣦⡀⠀⠙⣯⣿⡿⢿⣿⣟⣿⠁⠀⢸⡷⠂⡘⣿⡿⣿⡝⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⢿⣯⣽⣷⠿⢍⣧⠀⠀⠁⠈⠙⣿⣿⠯⠥⠚⠀⢸⣻⠀⢻⣿⣿⣽⣿⡜⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⠀⠉⠉⠀⠀⢸⣾⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⣼⠓⢢⣿⣿⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣿⣿⣿⣿⡇⣿⣿⣧⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡏⣿⣿⣿⡀⠀⠀⠀⠀⠙⠲⠊⠓⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⡄⠀⠀⠤⣠⠤⠤⠶⠒⠒⠋⠁⠀⠀⢠⡞⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠐⠒⠊⠉⠀⠀⠀⠀⡴⠋⣠⣿⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡟⣼⣿⣟⢻⡻⡟⠻⠿⠿⢦⣀⣀⠀⠀⠀⠀⢀⣤⠎⠀⣠⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⣧⣿⣿⡿⠛⠛⠾⢷⡤⠤⠤⣬⣍⣉⡉⠒⠒⠿⠤⣴⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣽⣾⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢿⠀⠀⠀⠀⠈⠉⠛⠷⠶⢦⣄⣈⣉⡉⠉⢛⣵⣿⣿⡿⢛⣥⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡇⠀⠀⠀⢈⢸⡆⠀⣀⡠⠤⠖⠒⠁⠀⠀⠀⠈⠉⠛⣻⣻⠟⣋⣥⣾⣿⣿⣿⣿⣿⣄⡄⠀⠀⠀ ⠀⠀⢻⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠀⠀⣼⣸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢱⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⣧⠀⠀⠀ ⠀⠀⠀⢻⡸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⣿⣿⡿⢃⡀⠀⠘⣿⡇⠀⠀ ⠀⠀⢀⣠⣷⠸⣿⣿⣿⣿⠉⠁⢰⠟⠛⠛⠋⠉⠓⢲⣶⢶⣶⣄⠀⠀⠀⠀⠀⢀⣠⠴⢒⣿⢸⣿⣿⣿⡿⠛⠀⠀⢷⡀⠀⠸⣿⠀⠀ ⠠⣾⠿⠋⡾⡆⢹⣿⣿⡏⠀⠀⢸⠀⠀⠀⠀⠀⣴⠟⢁⡞⠁⢻⡇⢀⣤⣴⣶⠿⠿⠛⢻⣿⣼⣿⡿⠫⡄⠀⠀⠀⢈⣧⣴⣾⢿⣆⠀ ⠀⠈⠀⣸⠁⣸⣈⣿⣿⡏⠀⠀⢸⠀⠀⠀⠀⢸⠏⣴⠋⠀⣸⡿⠟⠉⠉⠀⠀⠀⠀⢀⣼⣿⣿⣏⠁⠀⢻⡄⣠⠶⢿⣿⣿⢧⣌⣻⣧ ⠀⠀⠀⠇⢰⣿⣿⠋⠙⣿⠀⢸⣿⠄⠠⠤⠴⢁⣾⠇⢀⣼⡿⠃⠀⠀⠀⠀⢀⣠⣶⣿⣟⣛⣿⠏⠀⠀⠀⣿⣉⣴⠿⠋⠀⠈⠛⠙⠁ ⠀⠀⠀⠀⢸⣟⡟⠀⠀⣿⠀⠈⣿⣛⣿⣷⣶⣿⣮⣶⠛⠘⠁⠀⠀⣀⣤⣶⣿⣿⣿⡿⠋⣹⠏⠐⣆⢑⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⣤⡀⠀⢸⡆⠀⣱⣤⣼⣏⣉⡉⠉⠁⠀⠀⣠⣴⣿⣿⠟⠡⢼⡿⠁⠀⣴⠋⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠈⠻⣦⡈⠛⠓⠟⠋⠉⠉⠻⢿⠷⢤⣴⡾⣿⣿⠟⠁⠀⢠⣾⠁⢀⣾⠃⣠⠾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⠶⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠁⠀⠀⣄⡿⠃⢠⠾⠃⢀⢁⣈⡡⡀⣠⢄⣤⡴⠆⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠟⠁⠀⠀⠀⠴⠞⠹⠺⠚⠉⠉⠉⠈⠁⠈⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⡥⠔⠒⠤⠤⣉⡉⠁⠒⠒⠊⠉⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡔⠁⣀⠤⣀⣀⠃⠀⠈⠉⠒⠦⠤⣴⣯⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡴⠋⠀⠀⠀⠈⠉⠙⠒⠒⠲⠤⠤⣤⠔⠈⠉⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣏⠹⣒⠒⠤⢤⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠈⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠩⡲⢄⡀⢻⣣⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢄⠈⢺⡿⠟⠛⠋⠛⣦⡀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢬⣷⣯⣄⡀⠀⣀⣔⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡟⢻⣿⢿⣭⠽⣟⣿⡟⠉⣻⣦⣄⡀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⢻⠙⠛⣿⣿⠓⢾⣯⣤⣭⣀⣽⣿⡿⠋⠈⠙⢳⠶⢤⣤⣤⣤⠤⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠙⡄⠀⠈⢧⡀⡿⠿⠷⠶⠛⠿⠋⠉⠉⠀⠀⠀⠀⢀⡾⣁⡜⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⡁⠀⢳⠀⠀⠘⣷⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠒⠉⠁⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡶⠋⠙⡾⣦⠔⠋⠀⠀⠈⠓⠤⣀⠀⠀⠀⣀⡤⠖⣋⠅⠀⠀⠀⠀⢠⠧⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢧⣀⣴⣿⣁⣤⣼⠀⣽⣄⣀⠀⠘⣩⡿⠛⢁⠴⠊⠁⠀⠀⠀⣠⠴⠛⠒⠉⡹⠛⢻⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠈⠧⠤⠄⡀⢇⠈⠉⠙⣥⠄⠙⣿⠷⠶⣮⠄⣀⡀⠀⣠⠴⠋⠁⢀⠖⠀⠈⢳⣆⠀⠳⣬⡷⠔⠒⠉⠉⠉⠉⠳⡄ ⠀⢀⣀⣠⠾⡄⠀⠀⠀⣿⡿⣄⡠⠊⢀⣴⣋⣀⠀⠘⠧⡤⠜⠉⢫⠀⠀⠀⢠⡏⣀⠀⢀⣾⠋⣷⡊⢁⡤⠶⠒⠒⠦⣄⡀⠀⡇ ⢰⠋⣠⠋⠀⠙⣄⠀⠀⢹⣷⠏⢀⣴⡿⣿⣷⣦⡙⢦⠀⡇⠀⠀⠸⠀⠀⣠⠋⠀⠈⢉⣿⣿⣾⠄⣿⣯⣤⣀⣀⠀⠀⠀⠹⣄⡇ ⢸⢠⠇⠀⠀⢠⢾⢠⣴⣾⠉⠢⣾⣿⡏⠉⢹⠄⡇⢸⠟⠁⢀⣠⠦⠒⣻⠃⠀⠀⢀⡞⡟⠹⠋⣰⣿⠈⣆⠈⢻⣳⡀⠀⠀⢹⠁ ⠸⣿⠀⠀⠀⡟⣾⣸⠉⣿⣆⠀⠻⣯⣑⢒⣋⠞⣡⠞⠛⠉⠉⠀⢀⣴⣥⣄⣀⢀⡞⡜⠀⠸⣼⡟⣸⠀⠘⡄⠀⠻⡷⠀⠀⢸⠀ ⠀⢹⡀⠀⠀⣇⡿⣿⠀⡏⢻⣵⣶⣿⠛⠻⢖⠊⠁⣀⡤⠔⠒⣩⣿⣿⣿⣷⣿⢿⡴⣠⠒⢦⣿⣗⠉⣆⠀⡇⡠⠔⠃⠀⠀⡾⠀ ⠀⠈⠳⣄⡀⠻⣅⣹⣴⣃⣾⢿⣹⣿⠓⠠⠤⠿⣯⢥⡴⠛⡏⠘⣿⣿⣿⣿⣿⡾⠀⢿⡀⠀⢹⣿⣮⣼⠞⠋⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁⠀⠈⢿⣟⣤⠤⠀⠔⣡⠊⠀⠀⡸⡄⠘⣿⣿⠛⠋⢇⠀⡸⢷⣀⣰⠇⣹⣅⣀⢀⣀⣠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⠉⠁⠚⠁⠀⢠⠞⢀⡼⢆⠈⢿⣄⠀⠀⠑⠦⢄⣀⣤⡴⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢶⠤⠤⠤⠴⠧⠒⢁⣴⠉⢣⡀⠙⢷⣤⡤⠤⣤⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠀⠑⠢⠤⠤⠀⢊⠝⠁⠀⠁⠙⠦⣀⠈⠑⠢⠤⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⡇⢈⣙⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⢸⡃⠀⠀⠀⠈⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⣁⡀⠀⢸⡇⠀⠀⢠⠶⠊⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠋⠉⠉⠻⣦⢸⡇⠀⠀⡏⠀⢠⣖⣂⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣴⣶⣼⠀⢀⣿⣸⣷⣀⣀⣷⡀⠘⠛⡿⠏⣇⢀⡠⣬⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢠⣀⣹⠟⠃⠀⣼⠿⠋⠑⡀⠈⠛⢷⣄⠀⠉⠉⠁⠙⠚⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠱⢶⠿⠀⠀⠀⠀⠀⡼⠃⢀⣀⣀⣧⣤⣤⣄⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣠⣾⣷⣿⣿⣿⢟⣿⣿⣿⣿⣯⣷⣯⣷⣄⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⣠⣰⣿⣿⣿⣿⣿⣿⡿⢀⣸⣿⡟⢿⣿⣿⣿⣿⣿⣟⣄⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢦⠀⢰⣿⣿⣿⣿⣿⣿⣹⢿⠿⠿⠛⠛⠷⡾⣿⣿⡿⢿⣟⣿⣿⢇⠀⠀⢸⣿⡆⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠏⠈⣾⣿⣿⣿⣿⢛⣿⣿⣭⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣭⣝⣯⢻⣿⣆⠀⢸⠇⣿⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⠀⢸⣿⣷⣾⢣⡾⣿⣿⡿⢿⣷⢀⣠⣤⣼⣿⣿⣿⣯⣽⡿⣿⣾⣿⡿⣿⠀⢸⡆⢻⣦⠈⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣽⣿⡇⣤⠋⣸⣿⣿⢿⡇⢿⣿⣿⣿⢻⣿⡏⠙⣿⣯⢩⣿⣿⡿⠀⠛⣽⣿⣿⣿⠀⠀⠹⣌⣿⡄⢸⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣾⣻⣿⢠⠃⣰⣿⣿⣿⣷⣉⠈⠙⢉⣹⣿⠏⡀⠀⠀⠙⢷⣦⣤⣤⣴⡿⣿⣿⣿⣿⠀⠀⠀⢹⣿⡇⠀⠀⣿⡄⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⡇⡊⠀⠋⢹⣿⣿⣿⣿⡿⣶⡿⠋⠀⠘⣧⠀⠀⠀⠀⠈⠉⠉⠉⣰⣿⣿⣿⠇⠀⠀⠀⣿⣿⠃⠀⢀⣿⣿⣦⠀ ⠀⠀⢀⣾⣿⣿⣟⣿⣿⡀⠀⠀⠀⠙⢿⣿⣿⣏⠀⠀⠀⠀⣀⣀⡤⣤⣤⠄⠀⠀⠀⣠⣿⣿⣻⣉⣀⠀⣀⣸⣿⠛⠀⣁⣿⣿⣏⠀⠀ ⠀⠀⣼⢫⣿⣿⣿⣿⡿⣿⣦⣀⠀⠀⠀⡿⡿⠟⠁⠀⠀⡀⠀⠉⠩⠍⠁⠀⢀⣠⡶⠯⠟⠉⠙⠚⠛⣩⣿⣟⣁⣴⠾⠋⢩⣿⢿⡆⠀ ⠀⠀⣿⣾⣿⣧⣿⡟⠻⢮⣿⣿⣿⣿⣛⣫⡄⢀⠀⠀⠀⠙⠓⠦⠤⠤⠴⠚⣋⣁⣀⣠⣴⣒⣯⡿⠿⠛⠋⠭⠁⠀⠀⢀⣾⡏⠸⣿⠀ ⠀⢀⣿⣿⣿⣿⣿⣧⠸⣶⠈⢙⣻⣿⠿⠟⢧⣴⣿⣶⣶⣶⡶⣶⣾⣿⣛⣉⢉⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠻⣦⠀⢹⠀ ⠀⢸⠟⣿⣿⣿⣿⣿⡇⠐⣦⠀⠉⢁⣤⣾⠟⠛⠛⣉⠉⠉⠱⢦⣄⠀⠈⠻⣷⣤⣤⣶⣾⣤⣶⣶⣶⣶⣒⣺⣿⣿⠿⠀⠀⣿⣄⣸⠀ ⠀⢸⣠⣿⡇⠘⢿⣿⢿⣄⣽⣶⣾⣿⠟⠁⢀⠐⠁⠀⠀⠀⢀⠀⠉⠻⣦⡀⠀⠈⢻⡏⠉⠛⢿⣿⣿⣿⣿⠿⢫⡿⠀⠀⠀⠘⢿⣿⡄ ⠀⣼⣥⣿⠇⠀⠀⣿⣿⣿⣿⠙⣿⣿⡦⠀⠀⠐⢀⣀⣤⣄⣀⡤⠐⠀⠀⠙⠆⢀⣽⣿⡀⠀⠀⢸⣫⣿⡗⢪⡟⢁⣠⣄⡀⢦⠈⢻⣷ ⠀⣿⠀⠀⠀⠀⠑⣼⡟⠀⢠⣈⣿⣿⣮⡀⢠⣶⡾⣿⠁⠙⢿⣄⣀⣀⣠⣴⣾⣿⣿⡿⣿⣷⣦⣼⣿⣿⡟⠛⠶⣤⡀⠀⠑⣌⢳⠘⡈ ⠀⣹⠀⠀⠀⢀⣴⣿⣇⣶⣾⣿⣿⣿⣿⣿⣾⣿⣷⡏⠀⢀⣤⣽⣿⣿⠿⠛⣩⣾⣿⣿⣾⣿⣿⡿⠁⠻⣿⡄⠀⠻⣿⡄⠀⠘⢮⡇⣧ ⠀⡟⣆⣠⡶⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠘⠁⠈⢿⣿⣿⣿⡏⠀⠀⠀⣿⢻⡀⠀⢹⣿⡀⠀⠈⢹⣿ ⢠⣷⠞⣡⡴⢺⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠈⠀⠀⠀⠀⢸⡄⠘⣿⣿⣿⣧⡀⠀⣰⡇⢸⣷⠀⠀⢿⣧⠀⠀⢸⡇ ⢸⣿⠋⠁⢠⣿⣻⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⢓⣠⣼⣿⣿⣿⣿⠿⠋⠀⢸⣿⣀⣀⣾⣿⠀⠠⢿⠃ ⠈⡿⠀⠀⣸⡏⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣟⠀⠁⠀⠉⠁⡀⠀⣀⣤⣶⣿⣽⣟⣽⣿⣿⣯⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⢠⣿⠀ ⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢀⣴⣾⣿⣿⣿⣿⡿⠀⣴⣿⡇⠀ ⠀⣿⠀⢀⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣿⣿⣿⣿⣿⣿⣯⣥⡾⠟⢁⣧⠀ ⠀⢹⣧⡘⣿⣿⣿⣿⣿⣿⣠⣼⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠛⠋⢩⣿⣿⣿⠁⠀⠀⠸⢹⠀ ⠀⠀⠙⣷⣌⠙⠻⢿⣿⣿⣿⡷⢾⣿⣁⡉⠃⠉⠿⣿⣿⣿⣿⣶⠿⠟⠳⣴⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠰⢿⣿⣿⣿⣷⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡟⣿⣶⣦⣽⣿⣿⡿⠛⠛⠁⢠⣀⡀⣠⠀⠉⠉⠉⠀⠀⠀⠀⢹⣷⣦⣀⠀⣠⠜⠁⠀⠀⠀⣢⡟⣿⣿⣿⣿⣆⠀⠀⣸⠀ ⠀⠀⠀⢸⡇⠛⣿⣿⣿⣄⠀⢀⠀⠀⠀⠀⠈⠛⢛⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣷⠟⠋⠁⠀⠀⢀⣠⣾⠋⠀⠘⣿⣿⣿⣿⡆⠀⡿⠀

⠉⠉⠉⠀⠀⠀⠀⢀⠔⠛⣟⣿⣻⣿⢏⣴⣦⣔⠂⡔⣵⣶⣱⣀⠀⠀⠀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⣰⡥⠾⠛⠻⠿⢿⣥⣿⣿⣿⣿⣿⡴⣿⣅⡀⠈⠉⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⣀⣠⣿⣗⣤⣶⣦⣵⣿⣿⣿⣿⣿⡯⣿⢸⡆⠉⠻⢷⣦⣤⣤⣤⣀⢄ ⠀⠀⣤⠀⠀⡜⣷⣿⣿⣿⣿⣿⣯⠭⠛⣿⣿⡳⢹⣹⣿⣷⡄⠀⠙⠿⢿⣿⣿⣿ ⠀⠀⠘⠛⣆⠁⢻⣿⣿⣿⡿⠿⣿⡿⢃⣽⣿⣟⣾⣿⣿⣿⣏⢦⠀⢀⠀⠹⣿⣿ ⠀⠀⢶⠦⠚⠳⢶⠟⠟⡿⠓⠀⠀⠀⠥⡼⣿⡿⢿⣿⣿⣿⣿⣿⠓⠋⠛⣩⣿⣿ ⠀⡔⠁⢀⠐⢲⣎⡁⠐⠣⡀⠳⣂⡠⠀⠀⣼⡅⣻⣿⣿⣿⡟⠁⢠⣾⣿⣿⣿⣿ ⡞⠀⡰⢅⣴⣿⣿⣇⣀⣴⣛⣶⣕⡃⣀⣾⣥⣴⣿⣧⣶⣾⣴⣀⣸⣿⣿⣿⣿⣿ ⡆⣴⣤⡹⠿⢻⢏⣤⣾⠟⢁⣐⣽⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁ ⢻⡜⢿⡇⠀⣼⣿⣿⡏⢸⣿⣟⣿⣿⢿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡪⠍⠥⢄⡒⠀⠐⠒⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣌⢎⠔⠒⠚⠤⠀⢉⣀⣚⠂⠀⡲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⡰⢒⠠⠄⣿⠁⠀⠀⠀⠀⠀⠠⠂⠁⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠩⠒⢵⠿⠷⢆⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡖⣶⣧⣄⢠⣮⣷⢄⡀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠒⡓⢳⡞⢽⣏⣋⣱⡾⠋⠒⡤⢤⣀⠈⠶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠆⢡⠀⢱⣸⠛⠋⠉⠁⠀⠀⠀⣰⠳⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡮⠃⢢⡤⠊⢁⠑⠠⣀⡀⡠⢔⠪⠁⠀⢀⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢖⣛⠲⠢⠼⣒⠢⣔⣩⡐⠁⠀⡠⠔⢁⠤⠴⡈⠏⣂⠠⠄⠀⠠⡄ ⡠⢤⠳⠀⠀⢿⡦⢊⣴⣮⢄⠘⠀⠋⠉⠀⢠⠣⢀⣼⡹⣎⠅⠒⠒⠢⡀⠀ ⢡⠁⠀⠅⣤⡜⢥⣞⠟⢻⠡⠱⠂⣀⠤⠰⠁⠀⣼⠻⢏⡟⢋⠲⣦⠀⠘⡆ ⠇⠀⢸⣴⡇⡷⣄⣳⣥⣝⠅⠋⣉⡠⣴⣷⣤⡜⢎⣈⣾⠼⠈⡄⣘⠃⢀⠇ ⠘⢆⡘⢏⣧⡣⢿⣿⠂⠬⠶⡭⠒⡘⣿⣿⣿⡎⢯⠀⢻⣦⠷⠋⠀⢀⠞⠀ ⠀⠀⠀⠉⠀⠀⠈⢟⠲⠤⠕⠁⡠⢱⡘⢯⠁⠡⣈⠓⣊⠜⠒⠐⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡷⢂⠀⠘⢂⡵⠑⢌⠳⢤⠠⢔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⢁⠔⠀⠀⠀⠑⠠⢌⣁⣓⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠟⠛⠲⣼⠀⡌⢡⣄⠉⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⡀⠘⠟⡰⠟⠁⠻⠄⠑⠑⠋⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠈⠁⢀⣴⣷⣾⢿⣿⣿⣶⣄⠀⠀⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠢⣸⣿⢿⡿⠛⠛⢳⣿⣿⣿⣧⠀⡿⠡⠀⠀⠀ ⠀⠀⠀⣼⡟⡸⣿⣽⣿⣿⣦⢤⡿⣿⡟⣿⣿⡇⢇⡆⢇⠀⠀ ⠀⠀⣸⣿⠷⠸⣿⣯⣬⡽⠫⠀⠙⠒⠒⣻⣿⠃⠀⡿⠈⣧⡀ ⠀⣰⣿⣿⣧⡀⠘⣻⠇⠀⠐⠶⠖⢀⡰⠿⠧⢤⡾⡡⠼⣿⠀ ⠀⣿⣷⣿⠝⢻⡿⢷⣠⣤⡭⣴⣮⠡⠔⠚⠛⠉⠀⣀⠼⡏⡇ ⠀⣿⠛⢿⣎⣤⡴⠋⠁⠀⠈⠒⢄⠙⣶⠻⢿⣿⢿⡏⠀⢳⡇ ⢸⠉⠀⢸⠏⣸⣿⣀⣤⡞⠲⣀⣠⣵⣿⣦⣼⢿⠛⣄⠐⢥⡋ ⢰⣆⢔⣿⣾⣿⣿⣿⣿⣷⠞⠋⠁⠋⢿⣿⠋⢨⢧⠘⣇⠈⡿ ⢸⠋⣱⣿⣿⡸⣿⣿⣿⠀⠠⠀⠀⣘⣼⣿⣷⠊⢸⣤⣿⠀⡇ ⢸⠀⣷⣿⡿⣷⣿⣿⣿⣶⣶⣷⣿⣿⣿⡏⠁⣴⣿⣿⢏⡾⡀ ⠈⢧⡻⣿⣿⣼⣿⠿⢿⣿⣿⣠⢟⠛⠛⠛⠛⠋⣽⣿⡁⠀⡇ ⠀⠀⡿⣶⡟⠛⠉⠀⢴⠀⠀⠀⠀⢷⠤⠈⠀⡠⠚⣿⣷⡀⠇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢹⠇⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣀⡀⠸⡇⠀⢀⠔⠒⠚⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⢉⡀⠈⢻⠀⡇⠀⢾⠀⢰⣷⣤⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠐⢿⠟⠀⣼⡶⠟⠒⠺⣦⠀⠙⠓⠂⠾⠟⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢤⣶⠌⠉⠁⠀⡼⠁⢀⣀⣀⣀⣈⣳⣄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣤⣿⣿⣹⣿⣿⣿⣿⣷⡄⠀⠀⣿⡟⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⢣⣴⣿⣿⡿⢿⣿⡋⠉⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⡟⢧⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⠀⣾⣿⣿⣣⣿⣿⣿⣿⣄⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢧⢸⡆⢹⡆⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡏⡜⢹⣿⣿⡿⠜⣿⣿⣿⣿⠃⠙⢿⣜⠛⠛⠁⣹⣿⣿⣿⠀⠈⢿⣿⠀⠷⣄⠀⠀ ⠀⠀⢀⣿⣿⣿⠑⠀⠿⣿⣿⣿⣦⣤⣴⠟⠁⡄⠀⠀⠙⠛⠛⠛⢹⣿⣿⡏⠀⠀⢸⣿⠀⠀⣿⣆⡀ ⠀⢠⣾⣿⣿⣿⡆⠀⠀⠙⢿⣿⣿⡈⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣿⣿⣋⠁⠀⣀⣿⠃⢀⣼⣿⡋⠀ ⠀⣾⣼⣿⣿⣿⣿⣦⣀⣀⣀⣿⠟⠁⠀⢀⡀⠈⠉⠁⢀⣠⠴⠛⠋⢉⣙⣛⣿⣿⡥⠴⠋⢩⡿⣷⠀ ⠀⣿⣿⣷⣿⡏⣙⠻⢿⣿⣯⣷⡀⣤⣀⣀⣉⣙⣲⣮⠭⢤⣤⠴⠾⠛⠛⠉⠁⠀⠀⠀⣠⣾⡇⢹⡆ ⢸⢿⣿⣿⣿⣧⠉⡄⠐⠛⣈⣷⠿⠿⠛⠛⠻⣍⠙⠛⠶⣬⣁⣀⣤⣠⣤⣤⣤⣤⣴⣾⠏⠈⣷⣸⡀ ⢸⣼⡟⠘⢿⣿⣆⣷⣶⣾⠿⠁⡀⠀⠀⠀⠀⠈⠙⢦⣄⠈⢹⣏⠙⠻⢿⣿⣿⡿⢻⡏⠀⠀⠙⣿⣇ ⣾⠻⠇⠀⢀⣿⡿⠏⢹⣿⡇⠀⠀⣠⣴⢶⣤⠀⠀⠀⠈⣣⣼⣿⣄⡀⠸⣿⣿⣿⡏⠀⠂⢄⢢⡸⡿ ⢿⠀⠀⠀⢨⣿⢀⣴⣾⣿⣿⣦⣿⣿⡏⠀⢙⣷⣶⣶⡿⣿⣿⣿⣿⣿⣿⠟⣿⡄⠘⣷⡄⠀⠣⣧⣇ ⣾⡀⣠⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⠉⠀⠐⠋⢻⣿⣿⣿⠁⠀⢸⡿⡄⠈⣿⡄⠀⠹⣾ ⣿⣫⠴⢺⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⢱⠀⢻⣿⣷⣄⣀⡼⢰⣷⠀⢸⣧⠀⢠⡇ ⣿⠁⢀⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⠀⠀⣠⣵⣾⣿⣿⣿⠋⠁⠘⣿⣶⣾⡿⠀⢸⡇ ⡇⠀⢸⣧⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣶⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠟⠉⢀⣠⣾⣿⣿⣿⠇⣠⣿⠀ ⣷⠀⢸⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣧⠾⠛⢹⠀ ⠙⣧⡸⣿⣿⣿⣿⣶⣾⣿⡿⢿⠿⣿⣿⣿⣿⣁⣸⣟⠻⠿⠿⠻⠛⠻⠛⠛⠉⢠⣿⣿⣇⠀⠀⢸⠀ ⠀⠈⣿⢦⣌⣛⣿⣿⣿⠿⠗⠀⠀⠈⠛⠛⠛⠋⠉⠀⢻⣆⡀⠀⢀⠔⠀⠀⠀⣹⣿⣿⣿⡄⠀⢸⠀ ⠀⠀⢻⠸⣿⣿⣏⠉⠁⠀⠀⠈⠛⢛⡀⠀⠀⠀⠀⠀⠸⢿⡿⠛⠉⠀⠀⣠⡾⠃⠹⣿⣿⣿⡄⢸⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡤⠐⣶⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀ ⠘⠶⠯⢄⣀⡠⠁⠇⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⡀⠀⠘⢄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣵⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⣘⡀⠀⠀⠱⡀⠀⠀⠀⣠⠴⠁⠸⡀⠀⡇⠌⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡕⠆⠀⡗⠒⠋⠉⠀⢰⡀⢰⢣⡀⠠⡈⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠘⠀⠃⠀⠀⠀⠀⠀⠇⠸⠀⠑⢄⠑⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠃⠀⠀⢇⠈⡀⠀⠀⠀⠀⡆⢠⠃⠀⠈⠇⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠈⡄⡇⠀⠀⠀⠀⢁⠃⠀⠀⠀⠘⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠐⢡⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠁⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣔⣅⠼⠀⠀⠀⠀⢠⣎⡘⠄⠀⠰⡧⠜⠂⠀⠀⠀⣞⣅⠰

⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞ ⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠇⠀⠀⠀⠀⢀⣀⣠⣄⣀⣠⣤⣶⣿⣿⣿⣟⠀ ⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠹⠛⠓⠀⠉⠉⠐⠺⠀⠀⠘⣿⣿⣿⣿⣿⠿⢿⣿⣿ ⠛⠛⠛⠟⠛⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠙⠓⠒⠒⠊⠉⠛ ⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⣀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠈⠢⡀⡇⠀⠀⠀⠀⠀⠀ ⠀⡀⠄⠒⠃⠀⠀⠀⠀⠀⢀⡆⠀⠀⠓⠀⠀⠀⢀⠈⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢱⣎⠀⠀⢠⠃⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠦⠤⢀⡀⠀⠀⠀⠀⠑⠠⠀⣀⣐⣉⡑⢕⠖⠁⣀⣉⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠤⢀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡰⠊⠀⠀⠙⣄⠀⠀⠀⠀ ⠠⠄⠀⠀⣴⠀⠱⡀⠀⢣⠒⠒⠒⠒⠒⠒⠒⠒⢇⢰⡁⢀⣤⢤⡀⠈⢢⡄⠀⠀ ⠀⠀⠀⢀⣇⣄⠀⠘⣌⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡱⠋⠀⣣⡧⠂⡡⠼⡆⠀ ⠀⠀⠀⠀⠀⢘⣆⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⡾⢷⢠⣊⣴⠟⠀⠀ ⠀⠀⠀⢈⠏⠁⠘⠄⣀⠼⢆⠀⠀⠀⠀⢀⡤⠊⠀⣀⡴⠋⠧⠘⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣏⠀⠀⣀⣤⣶⠶⠶⠶⠶⣶⣤⣀⠀⠀⣹⣿⣦⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣷⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⣿⣿⣿⣷⡀⠀ ⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀ ⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⡇⠀⠀⢸⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⡇⠀⠀⢸⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣧⢀⣴⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣦⡀⣼⣿⣿⣿⣿⠃ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⡤⠤⠤⠤⣤⣤⣄⣀⡀⣠⣽⣖⣤⡀⢸⠋⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶⠛⢋⡩⠵⠛⠉⢀⡠⠴⠚⠉⠉⠀⠀⠀⠈⠛⢷⣄⠈⠛⢧⡀⢀⠞⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠓⢋⡵⠋⠁⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⢷⡄⠀⢹⣾⣠⠴⠒⠚⠛⠋⠉⠛⠛⠷⣶⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠉⢀⡴⠋⠀⠀⠀⣠⠞⠀⠀⠀⢀⣀⣤⡤⠴⣲⠶⠛⠛⠉⠀⠀⢈⣿⣀⣾⣛⠳⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣀⣵⡟⠀⠀⠀⣠⣾⡏⠀⠀⣠⢞⡿⣿⠋⠀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁⢈⡏⢻⣳⣄⠀⠀⠉⠓⠦⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣿⣷⣄⢠⣾⠋⢻⣀⡤⠞⠁⢸⡽⠁⢀⣀⣀⣤⢤⣶⠟⠉⠀⠀⠀⣰⣿⠁⠀⣻⣿⣦⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣸⠇⠈⠉⠛⠋⠀⠀⠀⠈⠀⠀⠀⠈⠙⠛⠋⠉⢁⣴⠟⠁⠀⢀⣠⡴⢊⣵⠃⠀⠀⢹⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⢿⡢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⢶⣊⣿⣯⣶⠋⠀⠀⠀⠀⣸⣿⠃⢻⣿⣦⡀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⡄⠀⠀⠀⣰⣿⠟⠀⠈⣿⠻⣝⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⢸⣼⠀⠀⣠⣿⡿⠁⠀⠀⠀⢸⡆⠘⣷⡙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣲⣲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣟⣭⣿⣿⡛⠳⢾⣿⣠⣾⣽⣋⣄⣀⣀⠀⠀⣸⡇⠀⠘⣿⡌⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠉⠙⠳⣽⣿⣷⣀⠀⠀⠀⠀⠀⣴⢿⣿⠶⠟⠋⠁⠀⠀⠀⠉⠀⠀⠘⢿⡟⠁⠀⠀⠀⢹⠻⣶⡟⠁⠀⠀⢸⣷⠀⢿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡏⢹⡭⡷⣾⣿⣽⣿⠀⠀⠀⠀⠀⠈⢛⣡⠤⠶⠮⣿⣷⡖⣖⠒⠒⠚⡉⡟⠀⠀⠀⢀⡴⠁⠀⠘⢿⡄⠀⠀⠀⢻⡆⢸⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣯⢻⠛⢿⣿⣿⣎⠙⠳⠤⠤⠤⠖⠚⢉⡤⠶⣶⡾⠛⣿⡟⠛⠳⡝⣆⠙⠆⠀⠀⡰⠋⠀⠀⠀⢀⣠⣿⠀⠀⠀⣾⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡘⢷⣘⠿⣿⣿⣆⢀⢞⢶⢦⡀⣤⢞⣀⡀⠘⠻⠿⠿⡛⢀⠑⡌⠋⣣⠆⠀⠀⡇⠀⢀⡠⠖⢋⣠⠾⡆⠀⢸⠇⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡟⠆⠘⢧⠀⠀⠀⠈⡕⠵⠑⢝⢎⡧⡀⢌⡉⡀⢀⠀⢜⢦⢳⡬⠞⢻⠀⠀⢠⡷⠚⣁⡤⠞⠋⠀⠀⡇⠀⡞⢰⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠓⠦⣤⣝⣆⡶⠖⠉⠒⠪⢤⣷⠑⢎⠢⠙⣈⣢⠤⠖⠊⠁⠀⠀⢸⡀⠀⠀⡗⠋⠁⠀⠀⠀⠀⣸⡇⢰⢃⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠛⢦⣀⡀⠀⣀⡼⠛⢀⣯⡞⠁⠀⠀⠀ ⢀⢀⠀⠀⠀⠀⠀⣀⡾⠋⠛⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠼⠛⠁⠀⣠⡿⠏⠀⠀⠀⠀⣀ ⠈⠀⠀⠀⠀⢀⡶⠋⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⣠⣾⣷⣶⣤⣀⣀⠤⠊⠀ ⠁⠀⠀⣀⣴⠋⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⠀⠀⢣⠀⠀⠀⣤⡤⠤⠤⠤⠖⠒⠒⠊⠭⢟⡶⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⢿⡆⠀⠀⣾⡥⠶⠶⠶⢾⡉⠀⠀⠀⠀ ⠀⠀⣰⠏⠁⠀⢀⡖⠁⠀⠀⠀⠀⠀⢀⡤⠖⠻⠤⠞⣿⠀⠀⠈⢧⠀⠀⠸⣿⣖⣒⣒⠒⣊⣡⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⠏⢳⠀⢸⠛⠦⣄⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⢠⠋⠀⠀⠀⡞⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡹⣷⣻⠏⠀⠘⣇⠘⡆⠀⠈⢣⡀⠀⠀⢳⠀⠀⢀ ⡴⠃⠀⠀⠀⣸⠁⣠⠴⠚⠁⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢰⣦⣦⠴⠂⠀⠀⠀⠀⠀⣀⣴⢾⢻⣾⡸⣇⣿⠃⠀⠀⠀⠹⣧⡹⣄⠀⠀⣹⢀⣤⡾⠒⠊⡩ ⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣹⣦⣠⣶⣪⣿⣬⢦⣻⣦⣀⣤⣴⣿⣟⣿⣸⡼⡇⣇⡟⠁⠀⠀⠀⠀⠀⠀⠙⠮⣯⣙⠉⡉⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣠⠤⠚⠋⠉⠁⠀⠀⢠⡾⠋⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣷⣿⡏⡏⣿⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⢻⣿⣷⡤⢄⣀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⡏⠉⢹⠁⠀⣿⣿⣎⣿⣿⣧⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢁⡴⠋⢀⣾⣿⡷⢶⣯⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⠀⠀⡟⡆⠉⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⣴⠋⠀⣰⣿⣿⣿⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠄⢀⣤⡤⠤⠤⢄⣼⠷⢦⣤⠏⠁⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⡩⠕⠊⠉⣀⠔⠊⠉⠀⠀⠀⠀⠀⠉⣷⣄⠈⠢⣴⢁⣀⠠⠤⠶⠶⢦⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⡠⠊⠀⠀⢀⠎⠁⠀⠀⣀⡠⠤⡴⠶⠒⠋⠉⢘⣇⣰⣿⠷⢤⣄⡀⠀⠀⠀⠈⠙⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣤⣾⠁⠀⣀⣾⠇⠀⡠⢺⣿⠏⠀⠀⠀⠀⣀⡤⠖⠉⢀⡝⠹⣷⣄⠀⠉⠓⠶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠟⠻⠷⠞⠃⠈⠒⠋⠀⠸⠧⠤⠶⠒⣻⠟⠁⠀⢀⡠⣺⠃⠀⢿⣿⣆⠀⠀⠀⠈⠻⢶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣖⣒⣾⣿⠞⠁⠀⠀⣸⡿⢻⣷⣄⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄⠀⢀⣴⡿⠃⠈⢿⠻⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣤⣀⣿⡅⣠⡾⠋⠀⠀⠀⢸⠀⠙⣯⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠻⢽⣷⣦⡀⠀⠀⠀⢠⣶⣿⠿⠛⠋⠉⠉⠂⠀⠙⣿⡟⠉⠉⠙⡳⣦⡿⠀⠀⢸⡇⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣶⣿⣽⣇⠀⠀⠀⢈⣫⠥⠒⢚⣿⣷⣲⡂⡈⢉⡝⠀⠀⢠⠞⠀⠈⢻⡀⠀⠀⣿⡄⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡸⣍⢿⣿⣧⠈⡙⣊⡉⠉⡰⠋⠹⣯⣽⣿⠅⢝⠾⢆⡁⠀⠀⠁⠀⢀⡤⢚⣇⠀⢠⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⠌⢣⡉⠉⠁⡟⠿⢿⣾⣯⡉⡀⡀⠀⠀⣦⣂⡡⢺⠁⠀⣴⠔⣈⠥⠒⠉⢸⠀⡘⠸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⡼⠒⠢⠬⠦⠖⠉⠑⠒⠼⣕⣃⣊⠬⠤⠒⠊⠁⠀⠘⡄⠀⢸⠉⠁⠀⠀⢀⡾⢀⣣⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠵⣿⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣑⣂⣠⠔⠋⢠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠙⠷⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⢀⣴⣯⣤⣀⡀⠀⠈ ⠀⠀⣠⠜⠁⠀⡠⠚⠀⠀⠀⠀⠀⣠⠖⣦⠀⠈⢆⠀⠀⣦⣤⠖⢒⣒⡂⠉⣛⠷⠃⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⢰⡷⠞⠒⠺⣍⠀⠀⠀ ⠀⡰⠋⠀⢀⡜⠀⠀⠀⣀⠠⠖⠉⠈⢉⡼⠀⠀⠘⡆⠀⠘⠛⠛⠣⠔⠒⠉⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⠋⠘⡀⢋⠉⠲⡀⠀⠘⡆⠀⠀ ⡴⠁⠀⠀⡜⢀⡠⠖⠉⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠸⡄⠀⠀⢠⣤⡤⠄⠀⠀⠀⠀⣠⣴⣿⡟⣿⣿⠃⠀⠀⢳⣜⢆⠀⢘⡂⣠⡧⠔⣪ ⠀⠀⠀⠘⠋⠁⠀⠀⢀⠴⠊⠁⠀⠀⢀⣀⡀⠤⠤⢤⣽⣦⣶⣾⣷⣷⣽⣦⣤⣶⣿⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠈⠛⣿⣍⣉⠀⠀⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⣠⠔⠉⠁⠀⠀⠀⣰⠏⠀⠈⠙⠻⡿⠿⠟⠛⣿⣿⣿⣿⣸⠿⠏⠀⠀⠀⠀⠀⠀⣴⠞⣩⠟⢻⣿⣶⣦⣧ ⠀⠀⠀⠀⠀⠀⠀⣏⣠⣼⣏⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⡇⠈⠀⢸⠯⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⣠⠊⣁⡔⠁⣴⣿⣿⠈⠙⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⠙⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⢈⢁⡒⠮⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⣿⣧⣄⠉⠁⠀⠈⠻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⣿⡿⣿⣶⣤⣤⣄⣈⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠉⠛⠳⠶⠤⠤⣤⣤⠤⡬⠿⠿⠿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣀⣀⡀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣾⣿⣿⣯⣿⣿⣿⣿⢶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣩⣉⣹⣿⣿⣿⣿⡿⠿⠟⠉⠉⠁⠀⠀⢀⣤⣾⣿⣿⣬⣽⡟⣼⡿⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⢈⣻⣿⣿⣿⡿⣋⡅⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣻⣿⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣛⣛⣻⣿⣿⣿⣿⣿⡿⢋⣴⠟⠀⠀⠀⢀⣤⣶⣿⣿⣿⣯⣿⣿⠿⣻⣿⣿⣿⣾⣿⣿⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠏⢀⣼⠃⠀⠀⠀⢀⣴⡿⢯⣭⣽⣿⠿⣛⣥⣞⣯⣾⣿⣿⢿⣿⣟⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣯⣤⣼⣇⣀⣀⣀⣠⣿⣿⣿⣿⣿⡿⠗⠚⠿⠟⠛⠋⢉⣾⣿⣸⣿⣿⣯⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠙⣶⣯⡍⠉⠉⠉⠉⠉⠉⠉⠰⢶⣤⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⣷⣄⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠋⣀⣠⣾⣿⣿⡙⠷⢶⣤⣀⣀⣀⣀⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠏⣿⡏⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⣿⣿⣿⣧⡀⣾⣿⡿⠟⢩⣿⣿⠿⣿⣟⠛⠛⣛⣿⣿⣿⣿⣿⡿⠿⠶⣾⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣧⣤⣴⡟⡗⠛⠉⠉⠁⠀⠀⢁⣀⠀⠀⠈⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣶⣟⣿⣿⣽⣿⣄⠀⠀⣬⣿⡿⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⢰⢿⣿⣾⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⡄⠿⠘⣿⣿⣠⠿⢦⣀⣀⣀⣀⣠⠤⠶⠖⡚⠿⣿⡛⣿⣿⡏⣿⣿⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠹⣧⣿⣄⡘⠟⠙⠢⠤⣀⣀⣀⡤⠤⠖⠚⠛⠙⢳⣌⠻⣿⡛⣰⣿⣳⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣿⣿⣿⣷⣿⣷⣌⠙⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠛⢳⣌⠛⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣾⡿⢿⣿⣿⣾⡇⠈⢿⣿⠙⣿⣶⣿⢷⡀⠀⠀⠀⠀⢸⡟⠛⠶⣿⠷⣶⣤⡤⠀⠉⠓⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢸⣿⠁⠀⠈⠻⣿⣿⡄⠘⣿⡄⠺⣿⡇⠀⢻⣄⠀⠀⠀⠈⢧⡀⠀⠙⣷⡿⠁⠀⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢠⡟⠁⠀⢰⣇⠀⠘⢿⣷⠀⣿⣇⠀⢻⠇⠀⠀⠹⣷⣤⡀⠀⠈⠙⢲⡶⠟⠁⠀⣠⡴⠛⢿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠈⡇⠀⠀⣿⡿⡆⠀⣨⡿⣦⣿⣿⡆⢸⡆⠀⠀⠀⠨⠻⢿⣶⣄⣀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠻⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡕⣧⠀⠀⢻⡀⠀⢿⡇⣧⢰⣯⡞⠁⣿⣿⣿⡈⣇⠀⣀⠀⠀⠀⠀⢪⡟⠋⠋⠉⠁⠀⠀⠀⠀⢀⣀⠀⠹⡄⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣽⣷⣿⣤⣀⡈⣷⠀⣸⣿⣸⠈⢿⣶⣾⡿⠹⣿⢿⣾⡀⠈⠳⠤⢀⣴⢿⡄⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⢹⡤⠎⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⡿⣿⣷⣶⣽⣿⡀⣿⢻⣿⠀⠀⠈⣿⣿⣦⣼⣞⢿⣷⡀⠀⢠⠟⠁⠀⣧⠀⠀⠀⣀⣀⣤⣴⠶⠶⠒⠛⠋⠉⡁⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠾⣿⣿⣭⡷⣾⢹⠁⠁⣿⠀⢻⡄⠀⢀⣿⣿⣿⣿⣿⣷⣿⣿⣀⡏⠀⠀⠀⢸⣄⣴⡿⢛⣩⣥⣶⣶⣶⣾⡟⠛⢿⣏⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣤⣤⣿⢏⡳⣿⡿⣯⢻⣿⣾⠀⠀⢻⡀⢸⣧⣰⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡇⣀⡤⠶⢻⣿⣿⣷⣿⣿⣿⣿⠉⠀⠘⢷⡀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣾⡄⠀⣿⠛⣿⠏⠀⠉⢻⣿⣻⣿⣿⠏⠀⠀⣸⣇⣸⣿⣿⣌⡿⣿⣿⢿⣿⣿⡄⣿⣿⣿⡉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣯⣤⣤⢤⣾⣷⣄⣀⣼⣦⡄⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⠲⣿⡀⡟⠀⠀⠀⠈⣿⢩⡍⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠸⣷⢯⣿⡇⠻⣿⣿⣿⣧⢀⣼⣿⣯⣿⣿⣿⣿⠏⠀⠀⠀⠘⣿⣯⣯⣹⣧⣼⡿⡄⠀⠀⠀⠀⠀ ⠀⢸⡟⣆⠸⣷⣿⣄⠀⠀⠀⠸⣷⡹⣦⡀⠀⢀⣿⣿⣿⣿⡏⠀⠀⠀⢿⣯⣾⣿⠀⢻⣿⠿⣿⣿⣿⣏⣽⣿⢻⣾⣿⠀⣠⣾⠃⠀⣿⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠈⢷⠘⢦⡿⠉⣿⡳⣦⡀⠀⢻⣿⣿⣷⡄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⠩⣿⣧⡼⠡⠀⠀⠀⠈⠉⢻⣷⣼⣿⣿⣤⣿⡏⠀⢀⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣘⣇⠈⢷⡄⣿⣷⡜⠿⣦⠀⣻⣿⣻⣿⣆⢹⣿⣿⣿⡇⠀⠀⠀⠀⣿⣤⣽⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡟⣻⣿⢿⣇⣥⣴⣿⡟⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠐⠒⠂⠤⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⠕⠀⠀⠀⠀⠀⠀⠈⠠⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢊⣠⣜⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣷⣏⡩⠒⠒⠂⢙⠿⣷⣶⣄⡀⠀⠤⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⢸⣽⠇⠀⠈⠁⠻⠷⢦⣀⠑⠒⢚⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣠⣶⣤⣤⠷⠶⠤⠯⠷⠾⠷⣶⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⠀⠀⠀⠀⣀⣠⣤⣄⡄⢿⡿⢻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⡆⠈⠟⢿⣿⣿⡡⢸⡇⢸⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⡇⠉⠉⠀⡇⠀⠀⠀⠉⠀⠀⠸⢑⣾⣿⣿⣧⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢿⣿⡀⠀⠀⠣⠄⠄⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣯⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⡄⠀⠰⢒⠂⠀⠁⠀⡰⣱⣿⣻⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠠⢹⣿⣿⣿⣟⠿⠦⠀⣀⡀⠀⡠⠊⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢀⣀⣤⣧⣾⣿⣿⠉⠉⣿⠀⠒⠒⠢⠭⣍⣛⠛⠿⢿⣿⣿⢗⣿⣿⡇⠀⠀ ⠀⡿⣿⣿⣿⣿⣿⡇⠀⠀⣹⡆⠤⠐⠂⠀⠀⠀⠉⢹⣟⣯⣶⣿⣿⡿⣤⠀⠀ ⠀⠱⡹⣿⣿⣿⡋⢉⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⢋⠀⢸⡆⠀ ⣠⡶⣧⢻⣿⡇⠀⡏⠉⠉⢉⡿⡹⢳⡀⣀⣀⣴⠮⣿⣾⣿⡏⠁⠀⢇⣀⣷⠀ ⠈⢰⢠⣼⣿⡇⢀⡇⠀⢀⢟⡞⢁⡿⠋⠉⠁⠀⣠⣿⣿⠅⠸⡤⢖⣿⠿⣬⡷ ⠀⠀⣾⡟⠀⡇⠸⣷⣾⣥⣮⡤⠛⠁⢀⣠⣴⣿⡿⢳⠏⠄⣤⠿⠋⠁⠀⠀⠀ ⠀⠀⣿⠳⣀⠱⢠⡷⠾⢦⣤⣀⣠⣶⡿⠋⢸⠃⣠⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠒⠚⠂⠀⠀⠀⠀⠀⠈⠉⡋⢀⣠⠟⠰⠃⣈⣨⣄⣤⢤⠂⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡸⡀⠇⡸⠀⠀ ⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢂⠁⠈⣐⠶⠂⠀ ⠀⠀⣰⣟⠲⡄⠀⠀⢎⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⢡⡌⠈⢢⠀⠀ ⠀⣰⡏⣹⡤⣃⣤⣔⣶⠶⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠓⠊⠈⡄⠀⠀⢣⠀ ⢰⣿⣼⢿⠿⢽⠟⠁⠀⠀⠀⣀⡄⣭⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⡾⣿⣷⣟⡶⠁⠀⠀⣠⠀⠀⣼⣁⣿⡏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⣿⣿⣧⡏⣓⣶⣓⣽⢿⣵⣿⠟⢱⡿⢹⣇⠔⠒⠠⠤⠐⠒⣈⣈⡦⠀ ⢿⣿⣿⠹⡇⠉⠀⣯⣾⡿⣛⡯⡤⡀⡼⣿⢹⣧⢸⣿⡏⣿⣿⣿⠹⣿⣿⢸ ⠸⣿⡜⡆⣷⣷⣤⣧⣿⡏⣾⠋⢀⠏⠹⣹⣠⢿⣿⠿⢧⣿⣿⡿⠾⢛⡉⡆ ⠀⠹⣿⣮⣸⣿⣧⣽⣿⠙⠒⠐⠊⡀⢀⠀⠀⢀⣿⠐⣖⠒⡖⠒⠪⣡⡟⠀ ⠀⠀⠹⣄⠀⠉⠛⠻⢮⣷⣄⠀⠀⠀⠁⠀⢠⣾⠏⠀⠈⠉⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⢿⡆⠈⠐⠀⠀⠘⠏⠀⠀⡄⡀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡖⠒⠒⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠤⣲⠶⠚⠉⠀⠀⠉⠢⣄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⣀⠀⠀⢀⡤⠚⠉⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⠁⠀⡠⠚⠁⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡇⣀⣀⡠⠶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢀⠞⠁⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠦⢌⣉⠀⠀⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⣀⣀⣀⣴⠃⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣙⠲⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡿⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢄⠙⢮⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠞⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣁⣄⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠎⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⠝⠋⠀⠘⣆⠀⠀⠈⣇⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⠀⣀⠶⠋⠁⠀⠀⠀⠀⣀⣀⡤⠶⣚⠩⠗⠋⠀⢀⣠⠶⢤⡾⡄⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀⣴⡺⢥⠤⣤⣶⣶⣾⣿⢿⣦⣤⣀⣀⣀⠤⢴⣲⣯⣷⢿⣤⣸⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢏⣿⡆⢀⠀⠻⣾⣯⡴⡿⢷⠄⠀⠀⠀⠙⠛⣻⠿⣿⣷⣄⠀⢹⢠⡇⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣎⣷⠀⡆⠀⠀⠈⠉⢉⣩⡴⠶⠶⢦⡄⠸⠿⣿⣿⣿⠿⠁⡇⣼⣷⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷⣌⣢⣤⡴⠒⠋⣁⡠⠤⠤⣀⠈⢳⣄⠀⠀⠀⠀⣸⢡⣿⡝⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣧⡀⠉⠀⣀⠴⠊⣡⠀⠀⠀⠨⡕⢄⠙⠷⣒⣤⣞⡵⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⡱⡘⢯⠉⠁⠀⠀⠙⠋⠶⠗⠲⠃⠀⠳⣄⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⢀⡔⣒⣖⣶⠶⠶⣒⡒⢶⣒⣒⣠⣾⡀⠙⣷⡀⠱⡀⠀⢤⣤⣄⣤⣤⣤⣀⠤⠀⠀⠉⣹⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠖⡾⢛⣿⡭⠟⠒⠊⠙⡏⢱⠘⡯⢭⣹⠃⠑⣄⢸⢧⠀⢳⠀⠀⠑⢦⣭⣭⠖⠃⠀⠀⣠⠜⠉⠲⢄⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⡆⢣⢸⣾⠀⠤⠶⠒⠒⠻⠿⡲⣇⡰⠃⠀⠀⠈⢿⣼⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⢆⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⢳⢼⠈⣯⣖⢄⡀⠀⠀⠀⠀⠈⢻⣣⠐⢄⠀⠀⠈⣿⣧⠀⢸⡙⠲⢄⣀⣀⠤⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⡀⠀⠀⠀⠀ ⣦⠼⢾⣧⣿⠈⠳⡽⣄⠀⢀⣀⡠⠤⠿⣧⡈⠳⡀⠀⠀⠇⠳⡀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠱⡄⠀⠀⠀ ⡇⠀⠀⠀⠀⠱⢄⢨⣿⣿⡇⠀⠀⠀⠀⢹⣷⠀⠘⢦⠀⢸⠀⢱⢸⡀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⢦⡀⠀ ⡇⢄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣠⠤⠔⠒⠫⣅⠀⠀⠈⠳⡀⢣⡸⣟⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠒⠒⠒⠛⠀⠱⣄ ⠀⠈⢆⠀⠀⠀⠀⠀⠈⠉⠁⠘⠦⡄⠀⠀⠈⠳⣄⠀⠀⠙⢆⠱⣿⣷⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠴⠚⠉⣀⣀⡤⠤⠔⡖⠒⠒⠒⠉ ⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡠⠤⠬⢷⣄⠀⠈⢣⠀⢻⠀⠀⠀⠀⠀⢸⢀⡴⠊⢀⡠⠶⠯⣙⡆⠈⣢⡠⠾⠚⢆⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠓⠤⡀⡼⠀⠓⣄⠀⠳⡘⡆⠀⠀⣠⠖⢻⠋⠀⡴⢯⠙⠲⣄⠈⢋⠁⡀⠒⠲⡀⠘⡄⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⣴⠯⠿⣢⣄⠀⠈⠓⢄⡙⣇⢰⠒⠉⠙⠣⣄⠎⠀⡼⠀⠀⢸⠯⠽⡄⠸⣦⡤⡟⠀⣳⠀ ⠀⠀⠀⠀⠀⢡⠀⠀⡠⠊⠀⠀⢀⣴⡻⠚⠁⠀⠀⠈⠙⠿⣦⣀⠀⠉⠺⡿⠀⠀⠀⠀⠈⠣⡄⠇⠀⠀⢸⠀⠀⠙⡤⠵⡿⡏⠉⠀⠀ ⠀⠀⠀⠀⠀⠈⣠⠎⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡾⣆⠀⠀⠀⢰⠃⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⢀⣼⠟⠁⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠱⡘⡄⠀⢀⠏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⣀⣴⠟⠁⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣱⢱⢀⠎⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣼⠊⠐⡜⡄⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡾⠁⠀⠀⢀⣀⣤⣤⣤⣤⢤⣱⡘⣄⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⡸⢹⠀⠀⠹⡝⡄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡠⢴⣺⠭⠓⠋⠉⠉⠉⠑⢍⢳⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⢸⠀⠀⠀⠙⣾⡄⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡴⠃⢈⡸⠟⠊⠁⠀⢀⣀⠤⠶⠒⠒⠲⢬⣆⠃⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⣻⡛⠈⠀⠀⠀⠀⠈⠮⠢⠄⠀⣀⠜⡀⠀⠀⠀⠀⢀⣠⢊⣀⣔⣁⡀⣀⣀⡠⣊⣁⣀⡀⠀⠀⡀⠀⠀⢉⡄⢀⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢶⠤⠄⣸⣦⡁⠛⠓⠢⢄⡲⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣏⣵⢶⣭⣻⡽⠷⠮⢷⣿⡿⣕⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣋⣼⣻⢹⠋⢀⢺⣳⣿⢿⡎⢜⠎⣿⢮⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣟⣏⢸⠀⣱⣿⡯⢷⣻⣷⠈⢳⡿⠿⠛⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⣏⣴⠟⠓⣠⠾⡷⠇⠀⠀⠓⢤⣔⢹⡷⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣻⣹⠒⠘⠅⠨⠅⣆⠀⠀⠀⠀⠚⠿⠻⢷⡋⠤⠀⢀ ⠀⠀⠀⠀⣠⡶⣿⣿⣿⠹⡏⠐⢤⡤⠤⠜⠉⠛⠕⢆⣀⠀⣬⣆⠀⠙⡶⣤⡀ ⠀⡀⠤⠶⢯⡿⣽⣏⣯⣧⠈⠢⡀⡷⢠⣴⣶⣾⡾⠛⠛⡿⡴⠛⣷⡄⠙⠩⣽ ⠈⠀⠀⠀⠀⢹⠔⢛⣿⣽⣾⡉⢹⡏⠳⣿⠿⣿⣧⡀⠜⠀⠀⠀⣿⠏⠂⠀⢧ ⠀⠀⠀⠀⠀⣤⢾⡛⠁⠈⠙⢦⡽⡀⠀⣽⡆⢿⠿⢿⠀⡀⣡⠖⠋⠀⠀⠀⠀ ⠀⠀⣀⡠⣞⣕⠁⢣⠀⠀⠀⣹⣫⠶⢓⣿⣟⠈⡇⠸⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢸⢠⠿⡈⠣⣸⠃⢀⢔⠏⢀⡴⠋⢴⣿⣣⠃⢐⢛⣲⣂⡬⠀⠀⠀⠀⠀ ⠀⠀⠘⠁⠀⠈⢄⠙⠲⢧⡘⠀⣾⠁⡐⢡⡿⠇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣿⡀⢇⣠⣴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡝⢭⣩⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣶⣶⡋⠀⠀⠀⠀⠀⠀⢠⣭⢝⣛⢿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⢟⠟⡩⢊⣥⣠⣶⡄⣀⣄⡐⠵⣶⢾⣿⣷⣿⣷⣿⣿⣟⢄⠀⠀⠀ ⠀⢠⣾⡷⣡⣾⣾⣿⣿⠟⠀⠙⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⠀⠀ ⢠⣿⣿⣽⣿⣿⣿⡿⠋⣠⣂⣉⣀⡈⠙⠛⠟⠋⡙⠛⠛⠛⠿⣿⣿⣿⣿⣇⠀ ⣸⣿⣿⣿⣿⣿⠃⠒⠚⠋⠉⠛⠛⢬⣐⠆⠀⠀⣵⠶⠭⠛⠂⠈⢻⣿⣿⣿⡄ ⣿⣿⣿⣿⣿⡏⢰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡀⠁⣿⣿⠇ ⢹⣿⣿⣿⣿⡇⠈⢦⣉⣲⢤⣀⡀⠀⠇⠐⠂⠀⠠⠃⠀⠀⡠⡏⠀⢰⣿⡟⠀ ⢸⣿⣿⣿⣿⡇⠀⠈⢿⢿⣶⣤⣬⣉⠉⠉⠁⠐⠒⠂⠈⣉⣀⡇⠀⣾⣿⡇⠀ ⠸⢻⣿⣿⣿⣿⡄⠀⠀⠑⠠⣉⠹⠛⠛⠛⠿⠿⢿⠿⢿⠿⠟⡇⠀⣿⣿⡇⠀ ⠀⠈⣿⣿⣿⣿⡌⠢⡀⠀⠀⠀⠍⣑⠒⠀⠤⠤⠤⠤⠤⠀⠒⡡⠂⣿⣿⡇⠀ ⠀⠀⠹⡿⣿⣿⣷⠀⠈⠐⠠⣀⠀⠀⠈⠑⠒⠂⠀⠤⠀⠐⠊⠀⢰⢿⡟⡇⠀ ⠀⠀⠀⡇⡏⣧⢻⣇⠀⠀⠀⠀⠉⠑⠂⠤⠄⣀⡀⠀⠀⠀⢀⡰⠃⠸⠃⠹⠀ ⠀⠀⠀⠠⡇⡏⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣴⡾⣿⢱⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢉⢑⠈⡸⠀⠃⣯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⣧⣀⡐⠉⠛⣉⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⡀⠀⡀⠁⠋⢸⣱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣏⠀⠀⢀⠌⠻⠏⢉⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢱⡖⠁⠀⠀⡘⠸⢿⠇⡏⣹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⡎⠀⠀⠀⡐⢰⣿⠍⡳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡖⠉⠀⠀⠁⢠⣠⣾⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡤⠊⠁⠛⠋⣹⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡄⠀⡀⠔⣈⣴⣿⣄⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⢹⠉⠀⠀⠹⢋⠽⡀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣦⡔⠂⠈⣷⣿⣟⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣥⣤⠢⣀⡹⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⠴⠊⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⡤⠤⣀⣀⡞⢻⡯⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠓⠖⠋⠑⠒⠄⠙⢣⢀⡁⠐⣪⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢌⣉⣝⢢⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢨⡯⢧⠀⢈⣏⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣠⣤⠄⢰⠀⠀⣠⣾⣁⣇⠀⠀⣧⡸⡆⢿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⢹⣼⣿⣀⣆⣴⡴⣷⣦⣌⣻⠀⠀⢻⣇⢰⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣿⡄⢰⡿⣿⣿⣿⡍⠉⠈⣵⣿⣿⢟⡶⠤⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⢸⣵⢘⣿⠯⠽⠧⣿⠚⢇⢸⣽⣿⣿⠁⠀⣿⢿⠃⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣦⠿⢅⣉⠚⢿⡼⡏⠉⠚⢋⠉⢁⣈⣉⠉⠉⠁⠀⣽⡿⢿⡛⠓⠯⡻⡦⡀⠀⠀⠀ ⢸⣿⢋⠹⡼⣻⣼⣤⡔⠱⡿⢆⠀⠘⠦⣤⡤⠜⠀⠀⣰⣇⡏⠓⠀⣿⡞⠁⠈⢮⠻⡆⠀⠀ ⣤⣶⣾⣷⣷⣛⣿⠋⠀⠀⢹⡄⠱⡦⢄⣈⣀⠤⡶⠋⣰⡟⠀⠀⣆⣼⣧⣀⠰⠶⢷⣿⠀⠀ ⠹⡎⠈⠁⣸⡟⣿⡀⡄⠀⠀⢱⡀⢳⠀⠀⢀⡾⠃⠀⠈⠁⢠⠾⣽⣿⢻⡏⣿⣶⢿⠇⠀⠀ ⠀⠀⠀⡴⣹⣥⣿⢷⢱⡀⠀⠀⠃⠈⡷⣤⠏⠀⠀⠀⠀⡀⢃⣴⣿⣧⣼⡗⡄⣿⢯⡀⠀⠀ ⠀⠀⣴⠿⢻⠒⡇⠀⠫⣿⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀⢠⣷⣾⡿⠉⡟⢻⠻⡸⡳⠷⢷⠀⠀ ⠀⢠⡿⠋⢹⢀⡇⠀⠀⠛⠺⢶⡄⣀⢸⣷⡜⣹⣷⣮⣟⣿⣏⠀⠀⣷⣼⠀⠘⠚⠲⠾⡇⠀ ⠀⣼⡇⠀⠀⡜⠀⠀⢀⣤⣔⡶⠿⠾⢾⠿⠋⠉⠉⠉⠉⠉⠉⠉⠃⠀⢻⢶⠀⠀⠀⠀⢹⠀ ⠀⣿⠁⠀⢠⠇⠀⣰⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⡄⠀⠀⠀⢸⡀ ⠀⢹⠀⠀⢸⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠸⡇ ⠀⢸⡀⠀⢸⡼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⡇ ⠀⢘⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡇ ⠀⠀⠁⠀⠀⠹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠨⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣉⣉⡙⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⠋⠉⣀⡤⠶⠚⠳⢦⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣋⠵⠚⢉⣠⣄⣀⣉⣉⠙⠲⢦⣌⠙⢿⣠⡤⠶⠚⢉⣀⣠⣴⣾⣶⣄⣀⡉⠙⠲⢤⡉⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⢩⡼⢋⣠⣴⣾⣿⣿⢻⣿⣿⡟⣿⣷⠀⢹⠗⠀⢹⣇⠐⣿⣿⣿⣿⣿⣿⢹⣿⡿⢻⡿⡆⢸⣇⡠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢤⣸⠀⢸⣿⣿⣿⣿⣿⡾⣿⣿⠛⠟⠿⠀⢸⣷⠯⠻⣿⠀⣿⣿⣿⣿⣿⣿⠘⠻⡇⠘⢃⡇⢸⣿⡞⡿⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⣿⠓⣿⡀⠀⣿⣿⣿⣿⣿⡇⠘⠋⠀⠀⡇⠀⢸⠁⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⢀⣠⡤⠔⠺⠁⣸⠳⣽⣷⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣀⣻⣯⠟⡇⠀⠻⠿⠿⠿⢿⣧⣤⠤⠖⠋⠁⣀⣼⠀⢀⡄⢻⣷⣤⣤⣀⣈⣉⣉⣉⣀⡤⠴⠖⠚⢃⣠⣾⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣯⣭⣀⠹⠶⠶⠶⠶⢶⣦⣤⡤⠶⠖⠛⣋⣡⣤⣶⣾⣿⣤⣀⣉⣉⣉⣙⣟⣉⣁⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣤⣤⡤⢴⣶⣶⣿⣿⣿⣿⣷⣶⣿⣷⣾⣿⣶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣝⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣷⣍⡩⠝⣿⠹⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢯⣿⢁⠤⣢⠝⢻⣵⠀⠀⠈⣇⢻⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠛⣌⣿⠥⠀⠹⡄⠀⠀⠀⠘⣿⠀⠀⠀⢸⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⡝⡱⣿⢇⣿⡿⣟⣻⡿⣿⣿⣿⣿⣿⡿⣿⡻⣭⠟⠙⠋⣄⠀⠀⣸⢷⣫⠵⠚⠻⣆⠀⠀⢸⣿⠀⠀⠀⢸⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⢿⣟⣽⡿⡫⠞⢙⡷⠋⠋⠀⠉⠉⠛⣶⣆⣴⡀⠀⠀⠘⢷⣾⣿⡏⠀⠀⠀⣤⣿⣇⠀⠀⢹⠀⣠⠶⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⡏⠀⣏⣿⡇⠀⠀⣸⠁⠀⠀⠀⢰⣿⡖⢻⡟⣿⡇⠀⠀⠀⠈⠙⠻⣧⠀⠀⠀⠉⠉⢹⡆⣆⣏⣸⣿⣷⣿⡀⠀⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣧⡜⢿⣷⡀⢸⡿⣄⠀⠀⠀⠀⠉⢀⣾⡽⣽⡇⠀⠀⠀⠀⠀⠀⠈⠛⡶⠶⠶⡒⢹⣿⣿⣹⣿⣷⠘⡟⢳⣆⣻⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠋⡇⡆⢻⣷⡘⣿⣿⣻⣶⣦⠤⠶⣿⠟⢵⣻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣡⢟⣿⣹⢿⣧⢯⡞⠃⠸⡄⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣄⠹⡍⠻⢧⣉⠈⠟⠛⢱⡯⠐⠋⢻⣟⢁⡤⠀⠀⠀⠀⠀⠀⠀⠻⡌⢿⣿⡉⣵⣿⣿⡇⠀⡷⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣦⢷⡀⠀⠉⠀⡀⣠⠟⠀⠀⣠⣚⣹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⣿⣾⡞⣰⡇⣀⣉⡁⠀⠀⠀⠀⠀⠀⡴⢋⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢳⡀⠀⠾⣿⠛⢁⡤⢺⡵⠿⠟⠛⠛⠓⠒⢦⡄⠀⠀⠀⠀⡀⣠⣽⡿⣿⡏⢸⣷⣿⣿⡾⠛⢿⠀⠀⠀⠀⠀⢠⢠⢊⣹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣳⡄⠀⠳⣄⡈⠀⢹⣿⠶⠶⠶⠶⠶⠾⠿⣿⠀⠀⠀⠰⢿⣿⡟⠈⢩⣷⠾⠟⠋⠁⠀⠀⣸⣦⣶⣶⡄⠀⢸⡿⡿⡢⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣦⡀⠳⢦⣖⡈⣋⣓⠒⠒⠒⠒⠒⣚⡭⠆⠀⠀⣠⣞⣁⣤⠞⠉⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡇⠀⢸⡿⣿⡾⡨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣼⣷⡙⢦⣄⠀⠙⠳⣿⠛⠛⠛⠛⠛⠉⠀⠀⣠⣾⡿⠋⢸⡇⣶⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⢋⣾⠀⠘⢧⡸⡇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣿⣧⠟⢺⣿⠄⠠⠙⠳⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⡿⠀⠀⢈⣷⣿⠀⣰⣿⣿⣿⣿⣿⣿⡿⢫⣴⣿⠟⢀⡄⠀⢹⡀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠘⣟⡆⠈⣿⠀⣔⠀⠀⠀⠉⠋⣋⣟⣽⠟⠯⣽⣿⣿⣿⣁⠄⠀⣼⡼⣸⢰⣿⣿⣿⣿⣿⣿⣿⠰⣿⠟⢁⣴⠋⠀⠀⡼⢇⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢾⡀⠀⠀⠸⣿⡀⣿⠀⡼⣆⠀⢀⡴⣵⡿⠋⠁⠀⠀⠀⢸⣿⣾⠇⠀⡸⢣⢿⡏⢸⣿⣿⣿⣿⣿⣟⡖⠐⣡⣶⠟⠁⠀⠀⣰⡣⢾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⢷⡀⠀⠀⢿⣧⣿⡾⣥⢷⣀⣠⣾⣟⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⠞⠁⣽⣿⢁⣾⣿⣿⣿⣿⣿⠋⣮⣾⡿⠏⠀⢠⠔⠚⡿⢀⡞⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢸⣧⡀⠀⠀⢹⣟⡼⢋⢿⡿⣿⣇⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠏⣠⠞⣡⣯⣾⣿⣿⣿⣿⣿⣷⣿⣷⡿⣁⠀⠀⣸⠀⠀⣹⢻⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣶⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠊⠁⠉⠉⠛⠻⢿⣻⣶⣿⣿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣠⠾⠠⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⢹⣿⠃⠀ ⠀⠀⢀⡤⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣹⣿⡿⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠛⠐⠢⠦⠄⠀⠀⡀⠀⠀⠈⠣⡴⠋⠉⠁⠐⢄ ⠘⠧⠀⠠⠄⠒⠒⠢⠤⢀⣀⡀⠀⠈⢫⠀⠀⠀⠐⢇⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡁⠀⠀⣀⣠⣄⡀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣤⠮⠤⠒⠒⠒⠒⠢⠬⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢁⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⢠⣶⡄⠈⢦⡀⠀ ⠀⠀⠀⠀⡞⢸⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠸⠿⠏⠀⠀⠙⢛⡁⡆⢁⡟⡆ ⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⢨⡀⠀⡱⢀⣤⡀⠀⣴⣰⠁⠀⠈⠉⠀⢸ ⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⡡⢤⣸⣿⡇⢀⡀⠬⣦⣄⠀⠀⢠⠏ ⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠤⠒⠣⣄⠀⣸⣾⡇⠉⢹⠉⠉⠑⢞⠁⠀ ⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠘⡛⠒⠛⠦⠼⢄⡀⠀⢈⠀⠀ ⠀⠀⣀⣼⠞⡆⠀⠀⠀⠀⠀⠀⠀⠒⡏⠁⣀⣣⣀⣀⡠⣤⣺⠏⠉⠉⡇⠀ ⢀⣼⠕⠋⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠜⢣⠖⠇⠀⠀⠀⡇⠀ ⠸⣅⠀⠀⠀⠀⢙⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠉⠉⠀⠀⠀⠈⠓⠒⠤⠤⠤⠤⠤⠤⠤⠒⠚⠉⠑⠒⠉⠉⠀⠀⠀

⠀⠐⡀⢸⠢⠀⠑⢄⠀⠁⢀⠈⣴⠀⠀⠀⣵⣦⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠋ ⠀⠀⠇⠈⠀⠐⢄⢀⣵⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣟⡛⠛⠛⠿⣟⣛⣻⣶⣤⣤ ⠢⡀⢰⠌⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡛⠛⠛⠛⢛⣋⣁⡉ ⠈⠺⢼⡔⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢹⠛⠍⡁⠠⢣ ⠠⡤⠔⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⠸⠀⠀⠀⠃⠈ ⠉⠀⡘⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⡿⢺⠂⢿⣿⣿⠲⠀⠠⠜⠀⠀ ⠂⠉⢸⠶⢺⣿⣿⣿⣿⣿⣿⠙⡄⠀⠀⠋⣿⡿⠁⠀⠀⢸⣿⣿⠀⠀⠀⠃⠀⠀ ⠀⠀⡼⠉⠹⢿⡇⠻⣿⣿⣿⡀⠈⠉⠁⠀⠘⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠈⠀⠀ ⠀⠰⡇⠀⠀⠁⠹⠲⣿⣿⣷⠑⠀⠀⡀⣀⣀⠀⠀⠀⢀⠾⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠃⠁⠀⠀⠀⠀⠀⢀⣯⡟⠻⡕⣂⣄⠀⢲⣤⡶⡞⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡤⠖⠋⡇⠰⠀⠈⡐⡏⣥⡟⡥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⢀⣀⣠⠄⣳⢄⢧⡇⢸⢸⠰⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠰⢠⠁⠈⢼⡟⡾⣧⣌⢼⠄⢃⠠⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⣸⠀⠀⠀⡏⠢⠠⠜⢹⣅⡀⠀⠈⣀⢌⠔⠀⢠⠀⠀⠀⠀⠀⠀⢗⣒ ⠀⠸⠀⠀⡏⠀⢀⣌⠈⢀⡃⠘⣿⣤⣤⣤⣤⣤⣤⣼⠀⠀⠢⠀⠀⠀⠀⠀⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠑⢔⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⣵⣾⣿⣿⣾⣿⣷⣶⣶⣶⣶⡠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠮⠚⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⡟⡹⡛⣛⣛⡛⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⣀⣀⣀⣤⣤⠤⢶⠾⡖⣛⣛⡛⡛⡛⣿⣶⣿⣶ ⠀⠀⠀⢀⣠⣤⣷⢶⡮⠟⠋⠉⢻⠣⣆⠂⢰⡇⠈⢄⠀⠗⣹⠙⡚⢿⣿⣿ ⢠⣶⣿⣿⣿⡟⣠⠈⡁⠀⢀⠀⠀⢆⠋⠙⣌⣇⠤⢌⢂⢰⡸⠆⠁⢱⠙⡄ ⠀⠉⠉⠉⢙⢇⡘⡀⢡⠔⢁⡠⢂⠈⢢⠀⠹⠃⡂⠀⢃⣾⠀⣿⠀⣸⠎⠀ ⠀⠀⠀⢠⢮⠆⢱⣴⣄⢛⠇⢀⠜⠀⠀⠉⠒⠠⠧⢗⢏⡟⠀⣿⡷⡇⠀⠀ ⠀⠀⠀⠁⢸⢸⢸⢠⢸⡆⢧⡀⠀⠀⠀⠀⠀⠀⡠⠂⡜⡇⠀⣿⡗⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢎⢞⠔⣅⠀⠈⠀⠀⠀⢀⣠⣮⣄⣺⣝⣖⣊⡏⠀⠀⠀⠀ ⠀⠀⠀⢉⢽⠤⠀⠉⠁⠈⠑⢤⣀⠀⣀⡏⠀⣠⣴⣶⠶⢒⣒⣛⣢⡀⠀⠀ ⠀⠀⠀⠈⠘⡄⠀⠀⠀⠀⠀⠉⠁⢠⠡⡇⣼⠟⣩⣴⣾⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠎⣏⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡟⡆⠀ ⠀⡯⢥⣄⣀⠀⠙⠀⠀⠀⢀⡴⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀

⡀⠀⠀⠀⠂⠄⡔⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢐⠀⠀ ⠈⠢⡀⠒⠠⢐⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡁⠀⠀⣼⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣇⡀⢀⠀⠀⠀ ⠀⠀⠀⢣⣴⣿⣯⡐⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⢛⡋⠭⠀⢊⣴⣗⣈⣢⠁⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠉⠟⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⠇⠇⠀⠀⠀⠀ ⠀⠀⠀⢠⡼⣠⡈⡤⠑⣏⣭⣉⣩⣏⠉⣩⣍⢡⣐⠢⡥⢀⣟⠞⣄⡆⠀⠈⠀⠀ ⠀⠀⠀⢸⢁⠇⡇⠈⢦⢋⠀⠉⠙⡼⢦⠸⡄⠀⠀⠈⠀⡸⡏⡤⠛⠃⠀⠀⠀⠀ ⠀⠀⢀⠧⠤⠍⠑⣆⡬⡧⡀⠀⠀⢃⠀⠈⠂⠁⠀⠀⡰⠁⠸⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠀⠀⠀⠘⠁⢈⣦⣑⢄⠀⠀⠁⠀⠀⠀⢀⠴⣇⣾⡯⠑⠒⠢⡄⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⢀⠋⠁⣹⣷⣷⣄⡀⠉⡩⣔⠣⣣⣿⣿⠀⠀⠀⣰⣠⡤⢤⠀ ⠀⠀⠀⠀⠀⡜⢻⡟⠀⢀⢇⣿⡻⣿⣾⣭⣴⣶⠿⠛⠋⡇⠀⠀⠰⡡⠋⠀⠘⡀ ⠀⠀⣀⠤⣎⠀⠈⡅⠀⢸⠿⠍⡉⠃⠹⡿⠁⠀⠀⠀⠸⠀⢀⠤⠊⣀⡀⠤⠤⣵ ⠀⠀⡗⠀⠈⣦⠀⢱⠀⣿⠀⠀⠈⠳⠠⠀⠒⠒⠒⢒⣣⠚⣁⣴⠞⠁⠈⠁⠀⠀ ⠀⠀⢹⠀⠀⢹⣧⡀⣿⣟⠀⠀⠀⠀⠀⠀⣀⠠⢤⡾⠓⠉⠒⠁⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡇⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡼⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⠏⠀⣠⠞⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢸⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⢿⣷⢀⣀⣀⣀⡀⠀ ⢸⡇⠀⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣒⣒⣿⣋⣥⣄⡉⢻⣆ ⢸⣿⠈⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢶⣿⠁⠀⢸⡇⢰⣿ ⠀⢻⣆⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣾⣯⣤⣴⠟⣡⣿⠃ ⠀⠈⢿⣎⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣭⣥⣴⡿⠟⠁⠀ ⠀⠀⠈⢿⣷⣄⠑⣦⡄⠀⠀⠀⣀⠀⢛⣻⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⣴⡶⠶⠿⠿⢿⣶⣤⣤⣤⣤⣽⣿⠿⠛⣛⣟⣷⡆⠀⠀⠀⠀⠀⠀ ⠀⠛⠷⠶⣤⣤⣤⣤⣴⣾⣿⣿⣶⣦⣤⣶⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀