°°°·.°·..·°¯°·._.· 𝒾 𝓌𝒶𝓃𝓉 𝓉ℴ 𝓁ℴ𝓋ℯ 𝒶 𝒷ℴ𝓎 𝓉𝒽ℯ 𝓌𝒶𝓎 𝒾 𝓁ℴ𝓋ℯ 𝓉𝒽ℯ ℴ𝒸ℯ𝒶𝓃 ·._.·°¯°·.·° .·°°°

⠀⠈⠳⣄⠀⢷⡦⠽⠻⣿⣿⣼⣷⡸⣿⣿⣷⣿⣯⢻⣿⣾⣿⣿⣿⣿⣖⠚⠿⢾⡿⣾⣯⡴⠦⣭⣻⣶⣤⣐⠓⢘⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣷⣿⣿⣷⣾⣿⣆⢦⡠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢻⣿⣷⠀⠀⠈⠻⣿⣿⣧⢿⣿⣿⣿⣿⣷⣻⣿⣝⠻⣿⢿⣿⣷⣟⠚⠛⠾⣿⣟⡿⠀⠀⠀⠈⠙⠳⣦⣜⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢷⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣆⠀⠀⠈⢿⣿⣯⡉⠈⠻⣯⢻⣿⣿⣿⣦⠈⠿⢻⣿⡻⣦⡀⠀⠉⠈⢷⣄⠀⠀⠀⠀⠐⠀⠙⢿⣦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⡆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡜⠻⣷⣦⡀⠀⠻⢿⣿⣶⣶⡏⠻⢮⣻⣿⣿⣷⣄⠘⢾⣿⣾⡿⣦⣀⠀⠀⠙⢦⡀⠄⠀⠀⠀⠀⠀⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⣨⡇⠀⠀⠀⠀⣠⡤⠾⣫⠄⠐⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢉⠓⢻⡀⢤⠘⠛⢾⣔⣿⣿⣿⡿⢷⣦⡀⠙⠻⢿⣿⣿⣷⣦⣙⢿⣿⣿⡻⣷⣄⠀⠀⠙⢮⠀⠀⠀⠀⣀⣀⣻⡀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⣠⡴⢞⡉⣴⡾⣡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣖⡞⠀⢈⣳⣀⠀⠀⠀⠉⠻⣷⣬⣹⣶⣉⠛⠷⣦⣠⡽⣿⣿⣿⣿⣷⣮⣿⣟⢷⣝⡿⣦⣀⢈⠳⣖⣚⣻⣿⣾⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⣿⡃⣠⠏⢀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠌⣼⠀⠀⠀⠁⣝⠃⢤⣀⠀⠀⠘⠻⣿⣿⣿⣷⣤⡈⠙⠻⢦⣽⣿⣿⡿⣿⣿⣿⡶⠿⣿⣾⣿⣷⣿⣿⣿⣿⠿⠿⢛⡿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠏⠉⢧⣏⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠐⠆⠀⡀⠛⠛⠟⠻⢿⣿⣷⣧⣄⡈⠙⠛⠿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣤⡬⠆⠙⢧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡀⠀⢚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣴⣿⣿⣿⣷⣤⣄⣈⢷⡀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣧⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠻⠟⠋⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣄⠀⡘⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢄⡖⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠏⣹⣿⣿⣿⣯⣽⣿⡁⠙⠘⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣾⣷⣾⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⡂⣿⣿⣿⣿⠟⠹⣿⣽⣿⣿⣶⣿⣿⣿⣿⡛⠂⠀⠀⠁⠙⢯⡀⠘⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣶⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⣾⣠⣿⣷⣿⣷⣴⡶⠾⢿⣿⠿⠻⣿⠟⠿⠈⠇⠀⠀⠀⠀⠀⠀⠙⠶⣽⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠙⠻⠿⣯⣿⣿⣿⣿⣽⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢄⠀⠐⣿⠛⠼⠛⠉⢉⠐⣤⡅⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⣀⠟⢀⠂⠀⠀⠀⠀⠀⠈⠿⣃⣹⣷⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠾⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠹⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⡿⠿⠀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠴⠖⠋⠁⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢷⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡈⢹⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⠿⣼⣿⡶⢬⡴⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣷⣼⣇⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⣼⡿⡿⣿⣿⣿⣿⠟⡿⠛⠙⠀⣠⡟⠈⠀⠈⠁⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠏⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣍⠀⠃⠘⢿⣇⠻⠀⠀⢀⡴⠞⠋⠀⠐⢠⠤⢠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⡾⠋⠀⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠳⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣦⡀⠀⠀⠉⠳⣷⣶⠋⣧⠀⠀⠀⠀⠀⠀⣼⣯⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠋⠄⠀⢠⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣶⡶⠶⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⣆⠀⠀⠀⠀⠛⠷⣤⣤⣈⠀⠞⠀⠀⢛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣠⡀⠀⠳⣾⣿⠿⣷⣇⡀⠰⠄⡴⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⣷⡙⠻⣕⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣻⣷⠀⠀⣹⣿⠛⠋⢻⣿⢮⣛⠃⠀⠀⣆⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣤⢄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀⠙⢿⣷⣈⠛⢿⠦⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡄⠀⠀⠀⠀⡍⠈⣹⣿⡛⢻⣄⣴⢎⡉⣖⠺⢷⣤⣔⡁⢸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⡀⣴⠋⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⣿⣿⣿⣌⢿⣯⣙⠗⠒⠒⢒⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣄⠀⠀⢀⣼⠄⣹⢿⣗⣾⠋⢀⣴⠿⠟⢻⠻⠞⠻⣿⣻⡄⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⣘⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠦⣤⣀⢼⠃⣈⠉⣻⣿⡿⠏⠁⠀⠀⠀⠀⠀⠈⠙⣿⣾⠷⣿⣍⠁⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⡠⡀⠘⠓⠚⢠⡏⢧⡁⣏⠐⠚⠀⠀⣤⠉⠀⠀⠀⠀⠀⠈⠛⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢄⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⢿⣿⣿⣿⣿⣦⡀⠀⠻⠟⠘⠳⠘⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣟⠻⢿⣿⣿⡛⠻⠻⣿⣿⣟⡋⢷⡈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢤⣢⡌⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⡀⠀⢀⠠⣀⡴⣾⠋⢡⣿⣿⣿⠋⢛⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠇⠘⢧⠈⠻⣿⣧⣯⡑⠁⢿⣿⣷⡄⠰⡘⣿⣿⡃⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡉⣹⣿⣿⡿⢿⣿⣿⣿⣶⣠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣡⡆⠀⣀⣼⢶⡞⠋⠁⠀⣹⣿⣿⠿⢻⣶⣶⡟⠀⠀⠀⡄⠀⠀⠀⠘⢠⠏⠀⠀⢸⠀⠀⠈⠻⣿⣷⣿⣦⣽⣿⣧⠀⠛⣟⣿⣷⡝⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣮⣹⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣯⣷⣾⡋⠉⠀⢀⣷⣤⡶⢿⡿⢛⢁⠀⠲⣽⠿⡀⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣿⣿⣟⠛⢻⣅⣀⡛⠛⢿⣷⠀⣈⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⣿⠻⠿⣆⠈⣯⠷⣠⠿⠉⠁⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡈⠉⠳⡄⠚⣿⣷⣉⠀⠀⠘⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠛⠿⢿⣿⣄⣀⠀⠀⠙⠿⠿⣿⠿⠟⠟⠋⢹⠏⢈⡇⡀⠀⠘⡆⢀⠈⢀⣴⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠸⣿⣬⣁⢷⡀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠿⣾⣿⣿⣿⣿⣯⡻⢾⣿⣿⣿⣿⣦⠀⠀⠀⠈⠙⠛⠷⢤⣤⣀⠀⠀⠠⠶⣧⣼⣿⣀⠘⠋⠇⠀⠀⡼⠷⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⢀⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣅⣀⡈⠻⠉⠀⠻⣄⠀⠀⠀⡈⠙⠲⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣅⠀⠲⠰⣄⠈⠻⢦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡐⢾⡧⠀⠀⠙⠶⣄⠈⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡿⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡙⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣞⡵⠋⠀⢀⣾⠋⢛⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠈⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⢠⠟⠁⢨⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⡀⠀⠈⠻⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣦⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣀⠀⠲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣼⢿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣄⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⣾⣿⣿⣿⡟⢿⣿⣦⡙⢿⣿⣷⣮⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣿⡗⣿⣿⡻⣶⣯⠈⠙⠆⠘⠿⢿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⣿⣿⣧⠘⢿⣦⡀⡀⠀⠀⠀⠈⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⢸⣿⣿⠀⠈⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⣿⡿⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⢇⠈⡟⣿⢸⣿⠇⠀⠀⠀⠀⠘⠊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢸⠀⡏⠈⡧⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀