Genshin Impact Chibi Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠠⣦⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠭⠌⠅⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡍⠉⠈⠁⢹⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⠞⣛⡩⠭⠭⠭⠭⠭⠭⠭⣙⣛⢶⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠸⡭⠓⠀⢉⣉⣉⣉⣉⣉⣉⡉⠘⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⣿⠳⢤⣿⡄⠀⠀⠀⠀⠀⣷⠴⢺⡟⠉⣸⠉⠙⢧⡙⠻⣷⠇⠀⠀⠀⠀⢀⣾⡃⠀⠀⠀⠀ ⠀⠀⠀⣸⣷⣄⡈⠙⢦⡀⠀⠀⠀⠸⡀⡏⠀⠐⢿⡿⠒⠒⠛⠁⢈⣶⣄⣠⣤⣾⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢾⡁⢸⣿⣿⠛⡿⠛⠳⢦⠀⠀⢱⢧⢩⠃⠀⠛⠯⢤⡤⠴⠊⣼⣿⡙⠫⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠙⢷⡋⢹⠟⢀⠀⡰⠃⠀⠀⢿⠈⠳⣤⣀⠀⠀⠀⠀⠀⢈⡡⠃⢣⠀⠘⣞⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠏⠀⠂⢠⡇⠀⠀⠀⣼⣆⠀⣷⡈⠉⠳⠒⠲⡾⠛⠀⡇⢸⡄⠀⢹⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⢠⠃⢸⠀⠀⠀⢠⢇⣸⣧⣼⡻⣄⠀⠀⠀⢸⣀⢾⣧⡃⢳⡀⠀⡄⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡠⠀⡞⠀⢸⡄⢀⣴⠟⠉⠉⠀⠈⠁⠺⠿⠖⠶⠤⠿⠛⠉⠙⠻⢷⣄⠀⡿⡆⠀⠀⠀ ⠀⠀⣠⠟⢠⡇⠀⡷⠀⠘⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣇⢻⡄⠀⠀ ⠀⣰⠏⢀⡼⠄⠀⡇⠀⠀⢸⡄⠀⠀⣤⣾⣭⣝⡂⠀⠀⠀⠀⠀⠒⣫⣽⣷⣆⠀⣼⠀⣿⠈⢧⠀⠀ ⢠⡏⡠⢋⡇⠰⢠⢳⡀⠀⠀⣧⣽⣾⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠘⠋⠉⠙⠻⣿⡷⠀⡇⡆⠸⣇⠀ ⢸⢰⣵⣿⠂⠀⠀⠳⣷⣤⣀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣷⣼⡟⠀⠀⣿⠀ ⠘⣶⡇⣿⡀⠀⠀⠀⠀⠈⠻⢼⣣⡀⠀⡀⠀⠀⠀⠀⠤⣀⣠⠆⠀⠀⠀⠀⠀⣀⣿⠋⡀⠀⠀⣼⡀ ⠀⠀⠁⣿⣷⣄⠀⠀⠀⠀⣀⠀⠙⠿⣏⣏⢻⢳⡄⠀⠀⠀⠀⠀⠀⠀⣠⢶⢯⢿⣇⣲⠃⣐⣻⢉⠁ ⠀⠀⠐⡿⣿⣿⣯⣒⡢⠤⠘⣯⢩⣿⢻⣟⣬⡄⠳⣄⣀⣀⣀⣀⣤⣴⠃⣨⣌⣿⣽⣷⠽⠟⠋⠀⠀ ⠀⠀⠀⠐⠀⠉⠛⡶⠻⠿⣿⣛⣻⣯⣬⣏⣅⠉⠓⣿⣿⣿⣿⣿⡯⢷⠴⢛⣭⣟⣿⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⡜⠀⢠⠞⢷⣆⣀⣼⣿⣿⣿⡿⠧⣄⡉⣿⠛⣋⣿⣿⣿⠿⣾⣿⣁⡤⠞⠻⣿⡻⣦⣀⡀⠀ ⠀⠀⠑⣥⣴⢿⡁⣸⠀⢠⣿⣞⢿⣿⣟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⡴⠟⣿⢠⣿⠁⠀ ⠀⠀⠀⠙⣻⣯⣞⣥⡤⠞⣇⣏⠟⡹⠯⠭⢭⣽⣿⡾⣟⢋⡟⣿⣿⣿⣿⡯⠔⠒⠚⠋⣿⡏⠁⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⠷⠶⠶⠿⢿⠿⠿⠿⢿⢿⠿⠿⠿⠿⢿⠒⠒⠒⠛⠉⠀⠀⠀⠀

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

⠀⠀⣰⡫⠛⢿⡿⠛⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠄⠀⠀⠙⢫⣿⠋⠙⢢⠀ ⠀⠀⢻⣴⡄⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠻⠿⢿⣿⣿⣟⠛⠻⣷⣶⣤⣀⡀⠀⠀⠀⠀⠻⣇⣄⣼⣷⣆⠀⠈⠀⠀⠀⠑ ⠀⢶⣾⡿⠁⢀⣄⢈⣿⡿⠀⠀⠀⣀⣴⡾⠫⠖⠉⠀⠀⠁⠈⠀⠄⠉⠛⢷⣄⠡⠄⢈⣙⠿⣶⣄⠀⠀⠀⠈⠙⢿⡮⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠻⢿⣻⠟⠀⠀⣤⣾⡛⣡⠞⡡⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⢀⢿⣦⠀⢷⠉⠻⣾⣝⢷⣼⡟⢶⡄⠀⠙⠲⠷⢄⠀⢀⠴⠀ ⡀⠀⠀⠀⠀⣀⢈⠟⠀⣠⣿⣿⢟⡴⠁⠀⠙⢃⣴⣻⣇⣾⠱⣤⡄⢤⣄⡬⠈⢿⣇⠚⠀⡀⠈⢻⣷⣿⣧⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀ ⣇⠀⠀⣸⡾⠛⠋⢀⣴⣿⡿⠁⠄⠈⠓⡀⠀⣾⢣⡿⢸⣿⠀⠀⠹⠀⠀⠀⠀⠈⢿⣆⢼⠁⠀⠀⠻⣿⡿⣧⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠋⠋⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⢰⢇⣾⣿⡿⠁⣾⣿⠀⡛⢳⣄⢰⠟⠙⢦⣸⣿⠎⠇⠀⠀⠀⠹⣿⣻⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⣴⠆⠀⠙⣾⣿⠁⠈⣸⣿⣿⣧⠀⠀⢻⣆⠀⠀⠀⠻⣿⡀⡀⠠⣦⠀⠀⢿⡗⣿⣰⣿⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⣼⡏⠀⠄⠄⣿⡇⠈⢲⡿⠛⠻⢿⡄⠀⠘⣿⡄⠀⠀⠀⣿⡇⠂⠀⣿⡄⠀⢸⣿⢹⣿⣥⣈⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠇⠀⣰⡿⠀⠄⠀⢵⣿⠀⢦⣿⠡⣄⠀⠀⢻⣎⠂⠘⣷⡀⠀⠀⢻⣿⡄⡂⠘⣿⡀⠀⣿⣼⣿⣿⠿⠛⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⣇⣿⡇⡆⠀⠀⣹⡟⢀⡾⠁⠀⠈⠙⠓⠦⢽⣦⡀⠘⣿⡀⠂⢺⡿⣷⡂⠀⠙⣷⡀⣿⣿⣿⣡⣤⣤⣤⠟⠀⠀⠀ ⠀⢀⣀⠀⠀⢸⣿⡇⣹⣿⣇⠂⠀⠀⣿⣧⡟⠁⠀⠀⠀⠰⠦⣄⠀⠀⠻⢦⣬⣿⡆⢸⣷⠘⢷⣄⠀⠹⣷⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⣉⡛⠶⣼⣿⣧⣿⡿⣿⡀⡀⠀⠹⣿⠑⢷⣶⣿⠿⠿⠿⣶⣄⠀⠀⠀⠈⠉⢷⡄⠹⣧⠀⠙⠷⢦⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣯⡰⣯⣹⠀⣤⣿⣿⣿⣷⢿⣧⠀⢠⡄⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣷⡀⠀⠀⢀⣿⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣤⣉⣼⠃⢹⣿⡿⠃⣀⣿⣧⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⢠⠔⠒⠲⠤⢤⣄⣀⠀⠀⠙⠻⠿⣿⣾⡿⣿⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣽⠂⠘⢿⣤⣼⠏⠀⢹⣿⡇⢿⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⢸⡇⠀⢸⣿⢿⡆⠘⢹⣿⠁⣿⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀ ⠀⣼⡋⠀⣼⠃⢀⣼⠋⣸⣿⣦⡾⠁⠆⣸⣿⣤⣀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣦⠏⢠⣾⠋⢠⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⣿⡛⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢁⣴⠟⠡⢄⣿⡟⢹⣿⣷⣿⣿⣿⠿⣏⠀⠤⠌⠙⢿⣿⣿⣿⣿⣽⣿⣿⣛⣉⣹⠿⣿⢿⣿⣿⣿⣷⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠟⠁⠀⢯⣿⠏⠀⢿⣿⣿⣿⣿⣿⡗⠂⠁⠀⠴⠒⢂⡽⣿⣿⢿⣿⠿⠿⣿⣿⣯⣒⠃⢸⣿⣿⣧⠈⣷⣤⣾⡟⠀⠀⣀⠀⠀⠀ ⢸⡟⠀⠂⠀⢠⡿⣿⣄⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣶⣾⣎⡠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢻⣿⣿⣷⣛⠛⠋⠀⠀⢠⡿⣷⠀⠀ ⢸⣧⠀⠀⢠⣿⢱⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠀⣙⣻⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣶⣤⣤⣼⠇⢹⡇⠀ ⠈⢿⣷⣦⣜⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⠃⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡿⣿⣟⡻⢿⢟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠠⠀⠄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣫⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠞⠛⠛⠛⠛⠛⠛⠓⠶⣶⣤⣀⣼⣿⣿⣿⣷⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢩⡿⢹⡿⠿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣼⢣⣿⣀⣴⡾⠟⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡀⠈⠀⠙⠻⢶⣤⣄⣀⣀⠀⢠⣶⣿⡟⣼⡟⠛⠛⠛⠷⣦⣄⡀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣦⣤⣤⣤⣬⣭⣽⣟⣛⣛⣿⡟⣿⣾⣿⣀⠀⠀⠀⠈⠙⠻⢦⣄⡀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⠙⣿⣶⠿⠻⠿⢿⣿⣶⣶⣤⣤⣤⣤⣽⣿⣦⡀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠷⣦⣌⡉⠁⠈⠻⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡶⠶⢶⡶⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡛⠛⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣶⣶⡶⠶⢶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⡿⣋⣭⣷⠶⠶⠶⢶⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢙⣿⠆⠀⠀⠀⢰⣿⢯⣾⣿⣧⣄⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⣴⡟⢁⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⣿⣀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡟⠀⠀⠀⢠⣾⠋⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣠⡿⠁⣠⣶⠿⠛⠛⠛⠛⠷⣦⡀⣠⣿⣿⠅⢙⣿⣦⣤⣀⡀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡟⠀⠀⠀⢠⡿⠃⠀⠀⠘⣷⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⢰⡿⠁⣼⣯⣥⣤⣄⠀⠀⠀⠀⠈⢿⣿⣿⣅⡀⠀⢀⣿⡿⠛⠁⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀ ⠀⢠⡿⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⣀⣴⠟⠉⣿⡄⠀⣿⠀⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠘⣿⠉⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠊⢻⣷⠀⠀⠀ ⠀⣿⠇⠀⠀⠏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠶⠟⠋⠁⠀⠀⠈⠻⣶⣏⠀⢸⡟⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣿⣆⠀⠈⢿⡟⠀⠀⠀⠀⠀⢠⣀⣠⣶⠟⠁⠀⠀⠀ ⢀⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣆⠀⠀⠀⠀⠀⠀⠈⠛⠂⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⡆⠀⠘⠃⠀⠀⢠⡄⠀⠘⣿⡉⠀⠀⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣶⣶⣾⣷⣄⣀⠀⣀⣤⠈⠛⢷⣤⣄⣀⣀⣠⣴⠾⢿⣄⣹⡇⠀⠀⠀⠀⠀⠸⣿⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀ ⠀⣿⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⣿⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠻⣿⡧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠛⠷⣶⣤⡀ ⠀⠹⣷⡀⢀⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁ ⠀⠀⠙⢷⣿⣷⡀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣾⠛⠀⠀ ⠀⠀⠀⠀⠙⠛⠿⣦⣄⣸⣧⣿⣿⣷⣤⣄⡀⠀⠈⠛⠦⢤⣀⡀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣯⣋⢻⣿⢷⣶⣤⣄⣀⠈⠉⠙⠒⠒⠒⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⣦⡀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠟⠛⠿⢷⣶⣿⣿⡟⣿⣿⣷⣶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡟⣿⡇⢀⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢰⡟⢺⣶⣾⠿⠿⢛⢽⣵⣿⢿⣿⠀⢩⣿⣿⣿⣿⣿⠿⢷⣶⣶⣶⣶⣶⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⣷⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣠⡿⠁⠀⣿⠁⠈⠻⢿⣿⣧⣾⠿⠟⣁⣾⡏⠀⢈⣿⡇⠉⠛⠿⣿⡿⠿⠿⠻⣿⣟⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣰⡿⠿⠛⣋⣀⣽⣵⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⣿⠙⢿⣿⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣿⠀⢠⣿⣟⠻⣾⣛⣛⠻⢿⣷⣤⣄⣀⡙⠻⠷⠶⠶⠿⣻⡟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣟⣋⣡⣠⣄⣿⡇⠀⠀

⠀⡘⠀⠀⠀⠀⠀⠀⣸⠵⣌⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢦⡀⢳⣂⠈⢻⡇ ⠀⡕⠀⠀⠀⠀⠀⣰⠏⠀⠈⢮⢧⠀⠀⠀⠀⠀⠀⠀⠀⡷⠦⠒⠑⣄⢻⡆⠀⠹ ⢀⠖⠀⠀⠀⢀⣴⠫⠤⠖⠋⠉⢾⡄⠀⠀⠀⠀⠀⠀⢰⣃⡤⠀⠀⠈⢣⡟⡀⠀ ⢨⠒⠀⠀⢠⡾⠃⠀⠠⠴⠭⡆⠈⣧⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⣀⡀⢻⡅⠀ ⢸⠌⡄⡰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⢿⣣⣭⣿⣾⣿⢿⠇⣻⡇⠀ ⢸⢎⣴⣋⣀⣀⣠⣶⣯⣭⣭⡷⠀⠈⡇⠀⢀⡴⢣⠿⠛⣿⣿⡇⣿⠘⠀⡷⣯⠀ ⢸⠉⢿⠻⠛⣿⣿⣿⡏⢻⡏⠋⠀⢀⣇⠴⡉⡴⠃⠀⠀⢿⣿⢷⡏⠀⠀⣿⣹⠀ ⢸⡀⠈⠃⠀⢹⣿⣿⢧⣼⡇⠀⠀⢨⢃⡶⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⡀⢳⣽⠀ ⠠⡇⠀⠀⠂⠀⠛⠋⠫⠍⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠁⠀⣼⣻⠀ ⠐⢻⠀⠐⠀⠠⠀⠄⢀⠠⠀⠀⠀⢤⣤⣤⣴⣾⣶⡞⠀⠀⠀⠀⠐⠀⣡⣿⢽⠀ ⠘⡸⣷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⠖⡜⣬⠻⡇⠀⠀⠀⠀⣠⣾⣛⣾⡻⠀ ⠀⠥⣹⣿⣷⣤⣀⣟⡉⠓⠦⡀⠀⠹⣎⠺⡜⢤⣫⠁⣠⠖⠋⠉⣹⢧⣏⡷⡇⠀ ⠀⠱⡠⢿⣿⣿⣿⣽⣮⡲⠀⠙⣄⣀⠈⠙⢚⣋⠥⠊⠁⢀⣴⣿⣿⣗⡾⣽⠁⠀ ⠀⠰⡁⠆⢿⣿⣿⣿⣿⣷⠀⠀⠘⠫⠿⠛⠉⠀⠀⣠⠖⣻⣿⣿⡿⣏⢷⡏⠀⠀ ⠰⠠⢌⠍⡢⢙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣿⣿⣿⣷⣿⠟⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣭⣷⣶⡦⠤⠿⠛⠒⠒⠠⠤⠸⢄⠀⢸⠦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⣂⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⢳⡀⠀⠀⠀⠀⠀⠙⢦⣶⣾⣿⣿⣿⣭⣕⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣄⣀⡉⠉⠻⢷⣗ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼⠁⠀⠀⠀⢠⠂⠀⢀⢞⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡀⠀⢹⣿⠿⠟⠛⠓⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣰⠁⠀⠀⠀⢀⠇⠀⠀⣼⠆⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⣧⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠜⠀⠀⠀⢠⠃⠀⠀⠀⢀⡞⠀⠀⢰⡟⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⣺⠁⠀⠀⢸⠛⣵⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣼⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠠⡾⠋⠸⠁⢠⠀⢸⠀⣿⢇⠀⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡰⠁⠀⢸⠀⠀⠀⠘⡇⠸⡎⢢⠀⠀⢣⣰⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿ ⠀⠀⠐⠁⠀⠀⠀⠘⠀⢢⣴⣁⡀⠢⢬⠀⠀⠀⠀⢱⡀⠘⣄⠑⢄⠘⡅⢸⡅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⣿⣿⣿ ⠀⣠⠃⠀⠀⠀⠀⠰⠶⣾⠟⢻⣿⣧⡈⣆⡀⠀⠀⠀⠳⢀⠌⠒⡴⠿⢿⣾⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢱⠀⢿⣿⡇ ⠀⡼⠀⠀⠀⠀⠀⢰⡆⢻⠀⣿⣿⣿⡷⠘⡾⡀⠀⠀⣠⠾⣾⠿⣿⣶⣦⣹⣧⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢇⢸⣿⣇ ⠀⡇⠀⠀⠀⣷⠀⠸⣧⡏⠀⢡⡀⢹⠃⡸⠀⠳⡤⠚⡡⠚⠁⣼⣷⣾⣯⣿⣿⣖⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⢆⣇⠙ ⠀⢹⢸⠀⠀⣿⣇⠀⢿⡆⠀⠀⠀⠀⡰⢥⣴⠾⠒⠉⠀⠀⠰⣇⠸⠙⢿⣿⣿⢿⠞⠀⠀⠀⠀⡰⠂⠀⠀⠀⡇⠀⠀⠈⣎⠑⠂⠤⠽⣄ ⢇⠸⣾⡄⠀⣿⣿⣷⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠛⣡⠎⠀⠀⠀⢀⡜⠁⠀⠀⠀⡸⠹⣴⡀⠀⠈⢆⠀⠀⠀⠘ ⠸⡄⣿⣷⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡠⠊⠀⠀⣠⠃⢠⠃⠀⠹⡝⠢⣀⠀⠳⣄⠀⠀ ⠀⡇⣿⣿⣷⣄⢿⠉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣀⠴⠊⠀⠀⢀⡴⠃⢠⠃⡇⠀⠀⠙⢆⡀⡏⠙⡟⠁⠀ ⠀⠃⢸⡿⠋⣸⣿⠷⣄⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⢀⣠⠔⠋⠁⠀⠀⢀⣴⠟⢁⡰⠁⢸⢡⠀⠀⠀⠀⣹⠇⠀⢻⢀⡴ ⡸⠀⢺⣇⡀⣿⡟⢧⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⣀⣠⡴⣯⣶⠟⣋⠴⠋⠀⣠⣿⠃⠀⠀⢠⣾⠃⡇⠀⣼⠟⠁ ⣓⡶⠴⠗⠭⢿⣇⠸⡆⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⡄⣺⣯⠟⠉⠉⠉⠉⠠⠔⢚⡵⠋⢻⠳⣤⣞⣿⣡⣄⡼⠒⡡⠋⣺⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢴⣷⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⢰⡟⠁⠀⡔⠀⠀⠀⢀⣴⣿⠃⣠⣼⣦⡀⠀⠈⠁⠀⣠⠞⢁⠜⠁⠀⠠⣶⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⠏⠀⢀⣾⣿⠤⠛⠻⢿⡟⢠⣾⠆⠀⣸⠇⠀⡠⠖⠁⢸⣧⡾⢋⣉⡙⢻⣿⣿⣿⠿⣿⣶⣷⣤⣤⣀⠀⢸⠒⠒ ⠒⠐⣚⡻⠿⠛⠉⠽⠁⣠⣴⠽⡿⠁⠀⢀⡴⠿⢧⠟⡎⠀⣶⣿⡶⠋⠀⠀⠀⣼⣿⣿⣾⣿⣿⡏⢹⣏⠁⠀⠙⢦⣴⡿⢋⡟⠀⠙⠛⠛ ⠀⢀⣠⠴⠒⠒⠋⠉⢉⡁⠤⠴⢅⣠⠎⢡⡼⠃⢸⢸⠀⠀⢻⠋⠀⡰⠠⠐⣈⣼⣋⣽⣿⡉⢥⣶⣧⡙⢧⡀⠀⢸⡇⢀⣞⣒⣲⣶⣶⣀ ⡄⡈⠁⢀⣠⠔⠒⠉⠁⠀⠀⠀⠀⠈⠀⠾⠒⠀⢸⣾⠀⠀⠘⣦⠞⠒⠈⠉⠀⢹⣿⣿⡿⠃⣸⠿⢿⡷⠌⢷⣀⣼⣧⠋⠈⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣉⠤⠒⠋⠙⣏⣿⠗⠊⠉⠉⠀⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣁⣤⣤⣤⡄⠘⠉⠀⠤⢄⣀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⢔⣪⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠑⠢⠤⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⠀⠀⠀⠀⠀⠀⢳⠤⠤⠖⢉⡰⣣⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠤⣀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣴⡟⣱⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⢱⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⢢⡀⠀⠀⠀⠀⠀⠀⠀⣰⡽⣱⣿⡿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⡿⠁⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠁⠲⡊⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣿⠿⠋⠀⢀⡠⠤⠲⣾⠀⠀⠀⠀⢃⠈⠉⡟⠙⢗⠒⢦⡄⠀⠀⠀⠀⠙⠦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⡶⠋⠀⠀⠀⣴⣴⣁⣧⢠⠀⠀⠘⡄⣰⣿⣶⣬⣷⣤⡇⢠⠀⢀⡀⠀⠀⠈⠙⣲⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣛⣀⣀⣀⣴⡿⢻⣿⣿⣾⣯⣧⠀⠀⠸⡟⣻⣿⣿⣿⡍⣿⡞⠀⢀⣿⡿⡆⠉⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠮⢄⣀⣤⠿⡇⠀⢿⠀⢈⣟⣻⡿⠃⡹⢷⣦⣀⡘⢧⠿⠿⠿⠃⣿⣡⠀⣼⣻⣠⠏⠒⠤⠬⠷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣰⠳⡀⠸⣧⣀⠀⠀⠀⠾⠗⠋⠀⠀⠈⠉⠁⠠⢤⡾⠋⢁⠞⢻⠿⠛⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢹⠒⠿⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣺⠁⠀⣼⠀⠀⠀⠑⢄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠀⡇⠀⠯⢦⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠴⡇⠀⠀⡟⡆⠀⠀⠀⠀⠓⠺⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠣⡀⢱⠀⠸⡀⠈⠓⠤⣀⡀⠀⠀⠀⣀⠔⠊⠁⢀⠃⠀⢸⠀⢃⠀⠀⠀⠀⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠱⡀⠀⣴⣶⣿⣷⣶⣋⣀⣀⣀⡴⠋⠀⣠⣿⣷⣾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣾⣿⠿⠟⠻⡄⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⢫⡽⠯⣍⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣠⠔⣶⣤⣀⣸⣦⡀⡘⢠⠿⡝⣲⠇⠀⠀⠀⠀⠀ ⠖⣧⠘⢆⠓⣦⣿⣏⣓⠒⠦⠤⣀⣀⣀⣴⣎⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡜⠁⣼⠏⠀⣸⣿⣿⠟⠡⠃⠀⠘⢅⠀⠀⠀⠀⠀⠀ ⠳⡌⠳⣉⣻⡙⣿⡄⠈⠉⠙⠓⠲⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⡔⠓⠀⡀⠀⠀⣀⣀⣤⣼⣄⠀⠀⠀⠀⠀ ⠳⢌⠢⢸⣿⠈⠻⠃⠀⠀⠀⠀⣠⠋⢼⡏⠉⠛⠛⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠹⢧⠡⣘⣒⣃⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⣷⣄⠑⢄⡟⠀⠀⠀⠀⠀⢀⠜⠙⡄⢸⡇⠀⠀⠀⠀⢸⠀⠀⢱⢸⠀⢠⠃⡞⠀⠘⢄⠀⠀⠀⡰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣷⣌⠷⠴⣒⠉⠉⠉⠛⡖⢤⣥⠘⡇⠀⠀⠀⠀⠀⡀⠀⠸⡈⣄⡎⡜⠀⠀⠀⠀⢹⠆⡖⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⡿⠋⠁⠀⠀⠀⠀⠀⠑⠀⠐⢆⠉⠲⡇⠀⠀⠀⠀⠀⡇⠀⠀⣇⡟⢰⠁⠀⢰⠦⠔⢊⡀⢣⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢦⠀⠀⠀⠀⢀⠔⠛⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⡙⣄⠀⠀⠱⣄⡠⠖⠁⠀⡴⠋⡰⠋⠉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣀⠠⠼⠚⢢⡀⠀⠈⠀⢀⡰⠮⠤⣚⡓⠒⠤⠤⣀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⣿⣤⠤⠔⠒⠉⠉⢦⣀⡠⠋⠀⢄⠀⠀⠈⠉⠒⢤⣠⣽⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢠⠋⢀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡼⠀⠀⠀⠀⣸⡄⠀⠀⠀⠲⣄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⠃⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⡁⢱⠀⠀⠀⠀⠈⠣⡀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡰⠁⠀⠀⠀⠀⠀⢠⢾⡇⠀⢰⠁⠀⠀⠀⠀⡇⢸⣧⠀⠀⠀⠀⠀⠹⡄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⠃⠀⠀⠀⠀⠀⣰⢃⠾⡇⠀⡜⠀⠀⠀⠀⢰⠀⣼⠀⢣⠀⠀⢀⠀⠀⠘⡄⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡗⢀⡇⠀⠀⠀⡘⠀⢰⣧⠊⠀⡇⢠⡇⠀⠀⠀⠀⡇⢠⠋⢆⠀⢇⠀⣸⣦⣀⠀⢣⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⡸⠀⠀⠀⠀⡇⢠⡿⠛⠊⠉⣏⣹⡇⠀⠀⠀⡜⢰⠟⠒⠚⢦⣼⣿⣿⣿⣿⠃⠈⡆⠈⠛⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⡇⠀⠀⠀⢰⣀⢿⣤⣶⣶⣿⣿⠛⡇⠀⢀⣼⡿⠃⣴⣶⣶⣤⣵⣼⡆⣿⡟⠀⠀⢼⠀⠀⠀⠑⠦⡀⠀⠀ ⣀⣠⠤⠊⠀⠀⠀⣸⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⠿⣇⡠⠞⠉⠀⠼⣿⣿⣿⣿⢿⣯⣷⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⣱⠆ ⠉⠛⠤⣀⣀⣀⣾⡏⠀⠀⠀⠀⣿⡟⠉⠀⣿⣯⣽⣿⠀⠉⠀⠀⠀⠀⠈⣿⣯⣽⣿⠀⠉⣻⣿⠀⠀⠀⠀⢸⣖⣀⣠⠤⠊⠀⠀ ⠀⠀⠀⠀⣠⠞⢰⠇⠀⠀⠀⠀⢹⣿⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠂⢠⣿⣿⠀⠀⠀⠀⠀⡇⠙⡄⠀⠀⠀⠀ ⠀⠀⠐⠻⡷⠷⣿⠁⠀⠀⠀⠀⠸⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣷⠀⠀⠀⠀⢰⡇⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⢸⠁⢸⡿⠀⠀⠀⠀⢀⠀⠇⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⡞⠀⣼⢸⠀⠀⡀⠀⠀⣧⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⢸⡀⡼⣷⠀⠀⠀⠀⣼⢤⢸⡀⢀⣹⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣏⠀⢀⠇⡸⠀⠀⡇⠀⠀⡼⢣⠀⣸⠃⠀⠀ ⠀⠀⠀⠈⢿⡇⡇⠀⠀⠀⠀⡇⠘⡄⢷⣿⠻⣟⠙⠻⠷⣦⣤⣤⠤⢲⡾⠟⠛⣿⣿⣷⠎⢠⠃⠀⢰⡇⠀⠀⡇⢸⣤⠋⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢳⠀⠀⠀⠀⡁⠀⢣⠘⣿⣆⢻⣇⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢈⣿⠏⡠⠋⠀⠀⣸⡇⠀⢠⣧⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⠸⡀⠀⠀⠀⢷⠀⠀⣧⡈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⡾⠁⠀⠀⣠⠃⡇⢠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⢳⡀⠀⠀⢸⠀⠀⢻⣿⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⡤⠔⠊⣽⡾⠳⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣆⣿⠀⠀⠘⣧⠀⠈⣿⣇⡽⠟⠁⢠⣿⣀⣀⣀⣤⣀⣀⡤⠾⠛⠉⠀⠀⠀⢡⠤⠀⠼⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣶⣶⣾⣦⣀⢸⣿⠀⠀⢀⣾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣠⠼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠈⠛⣿⣿⠟⢿⠄⠀⣻⠏⠀⠀⠀⠀⠀⠀⣠⠒⠤⠤⠤⠤⠔⣁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⣀⣀⡤⢾⡏⠀⠀⠀⣰⠟⠢⠄⣀⣀⡀⠴⠊⠀⠀⣀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢸⣧⣖⣠⠞⠋⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣖⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡟⣉⣽⣿⢿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⡗⠋⠙⡿⣷⢌⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣷⣄⣀⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣴⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡄⠀⢿⠀⠘⠃⠀⢼⡏⢸⡷⠀⠘⠃⠀⡿⠀⢠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⣆⠀⠋⠀⣠⡴⠶⠖⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⡀⠘⠁⢠⡶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⣾⡿⢻⡟⢻⡟⢿⣿⣶⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⢾⡃⢘⣷⠈⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣶⡀⠀⠀⢠⡀⠀⢀⣄⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀ ⠰⣶⣤⠶⠞⠃⠀⢀⣤⠄⢸⡟⢷⡀⠀⢸⡿⣦⡀⠉⠁⣄⡀⠀⠈⠻⠶⣤⣴⠆ ⠀⠈⠙⢻⡟⠛⠃⠈⠁⠀⣿⣀⡈⠛⢶⣤⣿⣌⣻⣦⡀⠈⠙⠛⠛⢻⡟⠋⠁⠀ ⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣿⠋⢻⡆⠀⠀⠉⣿⠉⣿⣧⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⣿⠀⢰⡇⠀⠀⣿⠙⠳⠞⣡⣤⣤⣤⠛⠶⠋⣿⠀⠀⢸⡇⠀⢿⡄⠀⠀ ⠀⠀⠀⣿⠀⠘⣧⠀⠀⢻⣆⠀⠀⢻⣄⣠⡿⠀⠀⢠⡿⠀⠀⣸⡇⠀⣸⠇⠀⠀ ⠀⠀⠀⠹⣆⠀⠹⣦⣀⠀⠙⣷⣶⣤⣀⣀⣠⣴⣾⠛⠁⣀⣴⠟⠀⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣤⣀⡙⠿⣿⣭⡅⠀⠉⠋⠁⢀⣭⣿⠿⠋⣁⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣿⣷⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠭⠿⢷⣶⣷⣶⣶⣶⣯⣭⣖⣲⢤⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠗⠋⠉⢀⣐⡿⢾⣶⣶⣶⣮⣟⡿⣿⣿⣿⣿⣷⣿⣶⣤⡀⠀⠈⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⡟⠀⢀⣀⣤⣤⣤⣭⣛⣿⣾⣿⣿⣿⣿⣿⣷⣝⡻⣿⣿⣿⣿⣿⣿⣗⡶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣼⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⢿⣿⣿⣿⣿⣿⣮⡻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣟⣼⣿⣿⣿⣿⣿⣶⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣾⣿⣿⢣⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠻⢿⢇⣸⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣷⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣭⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣾⣿⣦⣤⣀⡀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⢀⡇⣿⣿⣿⣿⢸⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⣟⣿⣿⣿⣆⠉⠁⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣷⣤⡀⠀⠀⢸⡇⢻⣿⣿⣿⡿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣟⢿⣿⣜⣻⣇⠸⣿⣿⣿⣿⡹⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⢸⢇⠀⠛⢿⣿⡿⠉⠛⢻⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⣩⡿⠿⢿⣍⠙⠛⢿⣿⣿⣿⣿⣧⢺⣿⣿⡘⣿⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⣿⣿⣿⡆⠀⣸⢸⠀⢀⣤⣿⠃⠀⠀⠈⢹⣴⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣛⡿⠋⢸⡿⢠⡶⢧⣤⣆⠀⠈⣿⣿⣿⣿⣿⣾⢸⣿⡇⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⡏⢸⢸⣸⣿⣿⣦⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢺⠿⣿⡷⡄⢳⣿⡆⠀⠘⣿⣿⣿⣿⣿⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢰⡾⡀⣇⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⢿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠙⠯⢤⣀⣩⠕⠈⠀⣿⢿⣿⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⣇⣷⠸⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣴⣶⣶⣾⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⢸⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠿⡼⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⡟⠧⣰⠚⣯⣯⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⣼⠀⢀⡤⠴⢶⡀⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠹⣿⣦⢿⣿⣿⣿⣿⣷⠻⣿⣿⣿⠃⠀⠹⣿⠛⠦⠽⠿⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠸⡇⠀⠀⠀⠰⠀⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣿⣎⢿⣿⣿⣿⣿⣷⣜⢿⣿⣦⠀⠀⠙⠓⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡰⠋⢹⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢣⠀⠀⠀⡄⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⣿⣮⢿⣿⣿⣿⣿⣿⣷⣶⣝⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠗⠉⠀⠀⠈⡆⠀⠀⠀⢀⡾⢶⣴⣀⡄⠀⠀⠈⢳⣦⣰⢁⡴⠂ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢻⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣾⡁⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀ ⠘⢿⣅⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⠀⢀⡿⠻⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⠄⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠞⠁⠀⠀⢠⡞⣈⣿⠦⢤⣀⣀⣀⣀⣀⡼⢻⣿⣦⡄⠀ ⠀⠀⠙⢷⡄⠈⠓⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢷⣄⠈⠻⣿⡛⠿⢿⣿⣿⣿⣿⡷⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣾⣿⣿⣷⡀⠉⠓⣢⡴⠋⠀⠠⡻⣿⣿⣠ ⠀⠀⠀⠀⠙⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⢦⣄⠈⠉⠛⠛⠀⠈⠙⢲⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠞⣳⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠘⢦⡀⠀⣀⡀⠀⢀⣠⡀⠀⠀⠉⠳⠄⠀⠀⠉⠁⠀⠀⠀⢀⡴⠋⠀⠁⠀⣿⠃⠀⠈⣷⣶⣶⣶⣶⣶⣿⡿⢾⣿⣿⣟⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⣠⡷⠞⠁⠉⢳⣏⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣿⡷⠛⠉⠀⠀⠀⢈⣻⡿⢿⣿⣖⣚⣛⣋⣛⣛⣛⠒⣾⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⣠⠔⠒⢦⡙⢦⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣿⣦⡀⠀⠀⠀⠀⡼⢹⣠⣿⠁⠀⠀⠀⠀⠀⣼⣷⣻⡁⠀⠀⠀⠀⠀⣾⣿⣿⠏⢩⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⠔⠲⡄⠱⡄⣱⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⢹⣿⣿⣶⠒⠒⠚⠛⠉⠁⢿⣦⣤⣤⣤⣴⣾⣿⣿⣷⣳⡀⠀⠀⣀⣼⣿⣿⠏⢰⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⡿⠿⠷⠤⢤⣽⣄⣹⣿⣿⣷⡀⠀⠀⠀⠀⢀⡴⢺⡟⣡⠔⠚⢿⣿⣿⣿⡆⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣻⢋⡏⠀⣿⣿⣿ ⠀⢀⣀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⡆⢀⣠⠞⠉⢀⣾⡟⠁⠀⠀⠈⣙⣿⣿⣧⡄⠀⢀⣴⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠟⣿⣿⠁⣴⣿⣿⣿ ⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⣰⠏⡏⠀⠀⠀⠀⠸⣿⣿⣿⡿⠇⣰⢟⠿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣤⠿⣯⣀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣃⣸⠁⠀⠀⠀⠀⠀⠈⣻⣿⣧⡼⠋⠋⢀⣀⣤⢤⣴⣻⣿⣿⣿⣿⣿⣿⠟⠛⢩⣰⠈⢆⠀⢻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠰⣿⣭⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⢳⡶⣿⣾⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣼⣧⡟⣼⢋⣥⠶⠲⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠈⠉⠻⠦⣤⣀⣀⣀⣶⣿⣷⣟⠋⠙⠳⢦⣄⡀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⡿⠶⠶⠖⠲⠿⠿⠿⣿⣻⣿⣿⣦⣄⣀⠀⠈⠛⢶⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠉⠙⠛⠿⣿⣛⠛⠋⠻⠄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡍⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣭⣍⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢙⣷⠀⠀⠀⣰⢟⣵⣿⣥⡀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⢀⣼⠋⣼⣿⣿⣿⣷⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⡾⠁⣀⣽⣦⣤⣀⡀⠀⢠⣾⠿⣧⣀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⢰⡟⠀⠀⢠⡾⠁⠀⢿⡛⠛⠛⠁⠀⠀⠀⠀⢠⣯⠀⠀⣰⠏⣰⣟⣉⡀⠀⠀⠈⠻⣶⣿⡛⠀⠈⣿⣷⠖⠀⠙⢷⣄⠀⠀⠀⠀ ⢠⡟⠀⢀⡠⠟⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⢀⣴⠟⠹⣆⢠⡏⢠⣿⣿⣿⣿⡆⠀⠀⠀⢹⡏⠻⣷⣶⡟⠁⠀⠀⠀⠀⠈⣻⡆⠀⠀ ⣼⠃⠀⠘⣤⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⠉⠀⠀⠀⠙⢿⣇⠘⣟⠛⠟⠋⠀⠀⠀⠀⢰⣧⡀⠘⣿⠀⠀⠀⠀⢠⣤⠾⠋⠀⠀⠀ ⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣤⣤⣤⡄⠀⠀⢀⠙⢦⣄⡀⠀⠀⣀⣴⣟⢸⡇⠀⠀⠀⠀⢿⠀⠈⢷⣄⠀⠀⠀⠀ ⢿⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠋⠉⠉⠛⠛⢾⡟⠁⠀⠈⠉⠛⠋⠉⠀⠙⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠉⠳⠶⣤⡀ ⠘⢷⣀⣤⠘⢷⣄⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠁ ⠀⠈⠛⠿⣦⡀⠈⣿⣶⣤⣀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣟⣻⣶⣦⣤⣀⡉⠑⠒⠦⠤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⢸⡇⣿⣄⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢿⣟⡙⣛⣿⣿⣿⢟⣿⣿⠶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⢀⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠃⣼⠈⢿⣿⣯⣡⣾⡿⢻⡿⠀⢺⡟⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⣿⣫⣥⣤⠀⠀ ⠀⠀⢰⡟⢷⣯⣤⣴⡇⠀⠀⠈⠉⠉⠁⣴⣿⡁⢠⣾⡷⣶⣶⠻⢿⣦⣄⡉⠓⠶⠤⠴⢶⡾⠃⢀⣠⣾⣿⣷⣾⣿⣛⣉⣉⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠒⠤⡼⣷⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠤⣖⡒⠒⢒⣷⣹⠴⣖⡓⠢⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠶⠒⠛⠫⠿⣻⢿⣤⣀⣉⣲⣄⡈⠲⡀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠥⠤⠟⠀⠀⠀⠀ ⠀⢏⠉⠉⠉⠀⢀⣠⢤⡤⠤⡆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠈⣳⠀⠀⡴⣿⣯⡉⠉⠙⢇⠀⠀⠀⡠⢺⠁⠀⠀⠀⣆⠀⠘⣆⠀⠀⠀⠀ ⠀⡴⠁⢀⠞⠸⡿⠿⠃⠀⠀⢸⠀⢀⠞⣴⡚⠋⠒⢤⣾⠉⢳⡤⠘⢦⡀⠀⠀ ⢰⠁⡄⠊⠀⠀⠙⠦⣀⣠⠔⠋⢧⡞⢸⣿⡿⠂⠀⠘⡍⢳⡟⠀⠀⣀⣨⠇⠀ ⢜⠀⢸⠀⠀⠀⠀⠀⠀⣹⣤⣤⣄⣉⣈⠢⣀⣀⣠⢼⣹⠀⠁⠰⡄⠻⣄⠀⠀ ⠸⣄⡘⢦⡀⠀⠀⠀⡞⠉⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢟⠀⠀⠀⡇⠀⠀⢉⠇ ⠀⠈⠛⠤⣹⣶⣤⣌⡑⠢⠄⣀⣀⣰⠃⠀⠀⠀⠀⡰⠁⠀⠀⠀⡇⡀⠀⡇⠀ ⠀⠀⠀⠀⣠⠻⣛⣻⡿⣿⣶⠶⣤⣤⣄⣀⣀⣀⣼⠟⠀⠀⠀⢰⣿⣻⣠⠃⠀ ⠀⢀⠤⣜⣁⠇⠙⠛⠚⣩⡟⣨⣧⣭⠿⣟⡙⠭⠀⠤⡤⢀⣰⣿⣭⣽⣒⣷⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⢉⣩⠿⠿⣶⠒⣿⣼⡤⠤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠴⠋⠁⠀⠀⠀⠸⣆⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠴⣲⣲⠶⠦⠀⠈⠀⠠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠔⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⣀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⠀⣠⡴⠚⢁⡞⣡⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡉⠉⠁⢠⣶⢏⣴⣿⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠈⠉⠳⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣳⠃⣾⣿⣿⠃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⣀⣸⡤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⣼⣿⣿⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⢱⣿⣿⠟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⡤⠔⠊⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣇⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠘⡄⠀⣤⣤⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣶⡿⠟⠋⣀⡀⢀⡴⠖⠋⠉⣿⢧⠀⠀⠀⠀⠀⢻⠀⠀⢰⡏⠈⠳⡀⠉⠙⡶⠄⠀⠀⠀⠀⠀⠀⠙⢦⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⢀⣼⣰⣋⡘⣆⢠⡀⠀⠀⠈⣇⠀⡿⣿⣭⣥⣬⣷⣄⣷⠀⢢⠀⢤⡀⠀⠀⠀⠀⠈⠙⢒⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⡿⠋⠀⠀⠀⣀⣴⣿⣿⣿⣿⣶⣽⣎⢧⠀⠀⠀⠸⣾⠿⣿⣿⣿⣿⣿⡛⢿⡆⡎⠀⠀⣽⣗⢲⠒⠒⠒⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠓⢒⡶⠒⠋⢿⡟⠁⣼⣿⣿⢿⣿⡍⢯⣧⣄⠀⠀⠘⣴⢻⡿⡯⣽⣻⠁⢸⡵⠃⠀⢰⢷⢹⠋⡷⣄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⢺⠏⢹⡀⠀⠸⣇⠀⠠⣯⣭⡤⠔⠁⣸⢉⣿⢝⠲⢤⣜⣮⡓⠛⠛⠉⢀⣼⣥⠂⢀⣯⣨⡿⣸⠁⠈⠉⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡞⢳⡀⠘⣝⢦⣀⠀⠀⠀⠠⠾⠗⠋⠀⠀⠀⠀⠀⠈⠁⢀⣤⡴⡿⠋⠀⣠⠋⢻⡽⠞⠳⢤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⡦⢬⣿⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠧⢶⡿⠁⠀⣿⠀⠀⠀⠀⠙⢆⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠘⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠤⢴⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⡆⠀⠀⠀⠀⠈⠳⣄⣀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢹⠀⠀⢻⠀⠀⣧⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⡿⠀⠀⢀⡇⢹⠀⠀⠀⠀⠀⠀⣈⠁⡲⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠎⢧⡀⠘⡆⠀⠹⡄⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⢠⠇⠀⠀⣼⠀⠸⡄⠀⠀⠀⠀⠀⠻⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠳⡀⠀⠀⣤⣴⣾⣿⣶⣶⡾⠋⠀⠀⠀⢀⣠⠏⠀⠀⣰⣿⣷⣠⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⠦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠼⠷⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣾⠿⠿⠿⠛⠛⠉⠀⠛⣆⠀⠀⠀⣤⠶⣜⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀ ⠞⢙⣤⠚⠳⣯⢽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢪⣷⡦⣤⣠⣼⣶⣄⢀⠇⢠⠞⢧⠉⣹⠃⠀⠀⠀⠀⠀⠀ ⡴⢏⣀⠱⣏⠛⢦⣌⣿⣍⠓⠲⠶⢦⣄⣀⡀⠀⠀⢀⣴⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⢯⠏⠀⠈⣿⣿⣿⣿⢏⡴⠋⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢦⠈⢱⣠⠼⢷⡮⣧⣹⡉⠙⠓⠶⠶⢦⣌⣉⠉⣷⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⢸⡘⠀⢀⣼⠋⠉⠛⠁⠉⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀ ⣤⠳⢄⠈⢦⣴⡷⢬⣟⣧⠀⠀⠀⠀⠀⠀⠀⡽⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣵⠀⡏⠸⡄⢀⡆⢀⣀⣤⣶⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⡉⠳⣌⠓⢾⣿⡄⠀⠙⠋⠀⠀⠀⠀⠀⢠⣾⠁⢰⢣⠀⠀⠉⠉⠙⠛⢻⡟⠻⠿⡿⢿⠿⠿⠿⣿⢿⡿⠻⡄⠀⠀⠙⢷⠙⢦⣍⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⣿⣦⡈⠳⣄⢻⠁⠀⠀⠀⠀⠀⠀⠀⣠⠋⢹⡀⠸⣼⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢿⠸⡀⠀⣠⠃⢰⠃⠀⠙⢦⡀⠀⠀⠀⢀⡼⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀ ⣿⣿⣿⣤⠈⣾⣀⣠⠤⠶⠶⠖⠲⠶⣧⣀⡀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡄⣇⢠⠏⢠⠇⠀⠀⠀⠀⠙⢶⠄⣠⠞⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⣿⣿⣿⣿⠟⠉⠀⠙⠦⠔⣀⣀⡀⠀⠸⡀⠛⢾⡄⢸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢻⡜⢀⡏⠀⠀⠀⠀⠀⢀⡼⠀⡇⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠘⣆⠀⠉⢻⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⣸⠃⡾⠀⠀⠈⢻⠛⠛⠋⣠⡄⠹⡄⠰⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢖⡒⠒⠚⠛⠻⢦⣄⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠙⠦⣄⡀⠀⠀⠀⢀⣀⡤⠖⣛⡉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠈⠉⠛⠓⠚⠛⠛⠉⠉⠉⠉⠙⠓⠦⣄⠀⢀⠀⠈⠂⠀⠀⢀⣠⣤⣌⠳⡄⠀⠈⠻⢤⣀⠀⠀⠀⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠓⢄⣀⠔⠉⠀⠀⠀⠑⢅⢀⣀⣀⠀⠻⡇⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⠋⠀⠀⠀⠀⠀⠀⢀⠈⢁⡾⠓⣄⠀⠀⠀⠈⢧⠀⠉⠙⠲⣽⣄⠀⠀⠀ ⠀⠀⠀⠀⣨⠟⢒⣦⠴⠒⠋⠉⢁⠜⠁⠀⠀⠀⠀⠀⠀⣠⣾⡽⠷⠿⠗⠶⠿⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠹⣆⠀⠀ ⣴⡶⠶⠶⠛⠛⠉⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢿⢧⠀⠀⠀⠀⠹⣆⠀ ⠈⠣⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣠⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣷⠀⠀⠀⢸⠈⣧⠀⠀⠀⠀⢻⠀ ⠀⠀⠈⡷⠲⠤⣤⡠⠞⠁⠀⠀⠀⠀⠀⢠⠏⢀⡞⢀⣀⡤⠤⠤⠀⠀⠀⠀⢸⢀⡿⠀⠀⠀⣾⣄⡸⡆⠀⠀⠀⢸⡇ ⠀⠀⠀⣧⣤⠖⠋⠀⠀⣠⠆⠀⠀⠀⢀⣼⠀⡾⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⡟⢸⡇⠀⠀⢰⠃⠀⠀⢷⠀⠀⠀⢸⡇ ⠀⠀⠀⣿⠈⠙⠓⠒⢛⡏⠀⠀⠀⠀⠀⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠇⢸⠇⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⣼⠁ ⠀⢰⠻⣿⣇⠀⠀⡴⣿⡇⠀⠀⠀⠀⠀⣿⡟⡇⣿⠤⠄⣤⣦⢚⡇⠀⢀⡟⢀⣾⠀⣠⣟⠛⣯⢹⡏⣿⠄⠀⢠⡿⠀ ⠀⢸⠀⠈⠛⣶⢶⡇⢻⣇⢷⠀⠀⠀⠀⣿⠇⠀⠙⢞⢳⠎⠁⣸⠃⠀⢼⠗⢫⣧⠔⠁⢿⣲⠋⣸⠁⡼⠀⣠⠟⠀⠀ ⠀⠈⡗⠀⠀⡏⣸⠇⣸⠛⢿⣷⡀⠀⠀⠸⡄⠀⠀⠈⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠼⢷⣾⠁⠀⠀⠀ ⠀⠘⣇⣠⣶⣿⢦⣘⣾⡞⠉⠉⠉⠢⣀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⠀ ⠀⠀⣘⠿⠋⠀⠀⣠⠸⡇⠀⠀⠲⠦⠈⠙⠒⣚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡼⠁⠉⢉⣽⠃ ⢿⡋⠁⠀⠀⢀⠔⠁⠀⠹⣄⣀⠀⠀⠀⣀⡶⢤⣉⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠐⢶⣾⣉⣀⠀ ⠀⠉⢓⣲⠞⠁⠀⠀⠀⡇⠀⠉⠉⠉⠉⠙⡆⠀⠙⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡚⠛⠉⠁⢦⡀⠀⠀⠀⣠⠴⠋⠀ ⠀⠀⠘⠯⠤⣤⣤⡒⠀⣧⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣉⣻⣿⣿⣹⣿⣿⣿⣿⣿⡿⣆⣀⠀⠀⣙⣳⠶⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⠗⠲⠴⠦⣤⣄⣀⣨⣿⣿⣾⠿⢦⣼⣿⣿⣿⣿⣩⣿⣷⣿⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠁⢠⠏⣰⣿⣿⣿⣸⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⡄⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⣿⣷⣤⣤⣴⡿⣶⡿⣿⡁⣿⢻⢿⣆⣼⠟⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢺⣿⡿⢉⣻⣿⣿⣧⡈⠻⢃⣼⣆⠙⠁⢀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⣶⡟⠁⠀⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣴⢫⣝⡾⠁⠸⣏⡽⢎⡷⣙⢮⢳⢭⢫⡝⣭⠻⣜⢧⡏⣷⡙⣿⣏⠷⣭⢻⡜ ⠿⣜⣯⣾⠃⠀⠀⡿⣜⢯⡜⣯⠞⣭⢞⣣⠻⣜⡻⡜⣮⠼⣥⠇⢹⣿⣹⠧⢯⣝ ⣿⢼⣿⣁⣀⣀⣀⢸⣝⢮⣚⣷⡻⣜⡺⣜⡝⡶⣍⡟⣖⡻⣼⣠⣤⣿⣿⣹⢳⣎ ⣽⠟⠉⠉⠉⠉⠙⠛⢿⡮⣝⣿⡵⣫⠵⣮⢝⡺⢵⣿⡜⣳⡟⠉⠁⠸⣿⡱⣏⣞ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣾⣿⣱⢻⡬⢯⣝⣻⣽⡺⣽⠀⢀⢠⣤⣿⣿⡱⣞ ⢀⣀⣤⠾⣻⣿⣶⢯⣐⠠⢽⣞⣿⣾⢣⣛⡧⣞⡼⣷⣿⡗⣪⠴⣿⣿⣿⣷⡻⣼ ⡏⢿⠁⢸⡿⣿⣿⣷⢘⡳⠄⠈⢻⣯⢳⣽⣷⡹⣖⣿⣿⢳⠁⢺⡟⢿⠟⣷⡻⣵ ⣷⠈⠣⡀⠢⡈⠅⡚⠀⣈⠆⠀⣰⣏⣿⣿⣽⡷⣭⢿⡟⠀⠄⣈⠢⠥⢔⣿⡽⢃ ⠻⣆⠀⠈⠁⠒⠊⠀⠁⠀⢀⠴⠟⠋⠀⠙⢷⣿⣾⢽⡃⠀⠀⠀⠀⠀⠀⠏⠀⣼ ⣧⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣷⡄⠀⠀⠀⠀⠀⠀⠰⢻ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠉⠛⠆⠀⠀⠀⠀⠀⢠⣿ ⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿ ⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡕⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢲⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠞⠛⣻⣧⣷⣾⣿⣿⣿⣿⣶⣶⣯⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢠⠀⠀⠀⢔⣾⣷⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢴⣿⣯⡻⣟⣵⣿⣿⣁⠨⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⡿⣹⣾⠷⡿⢿⣿⢿⣿⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⡠⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⠿⣽⣿⠁⢎⡀⢌⣠⠏⢻⡆⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢿⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀ ⢸⣯⢿⣿⡿⡀⣘⠎⠙⢶⡀⠌⣿⠑⣿⣯⢿⡿⣿⣿⣯⣟⡿⣿⣿⡿⣿⣽⣟⡿⣭⣟⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⢸⢯⣿⣿⣷⡑⠑⠲⡄⡖⠛⠒⣼⣿⣿⣽⣯⣿⣿⣿⡷⣯⣿⣽⣳⢿⣽⣻⣾⣽⣿⣿⣿⣾⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀ ⢸⣯⣿⣿⣿⠿⣧⣆⠻⣄⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠘⣷⣿⡙⠁⢀⣻⣿⣿⠛⠻⢿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢽⣥⣷⠂⡀⢠⣿⣯⣑⣠⣾⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀ ⠀⠀⠙⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀ ⠀⠀⢰⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣀⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀ ⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠻⢿⣯⡻⢿⣿⣟⣿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⢇⠀⠀ ⠀⢰⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣿⣯⠆⠀ ⠀⠺⣧⣄⣠⣿⣿⡿⠛⠻⣿⡿⣿⣿⡇⢀⣠⣤⣤⣤⣅⣒⠀⠀⠀⠀⠀⠀⠀⣮⣶⡾⢿⢷⠖⣿⣿⣿⣿⣿⡹⣿⣧⠀ ⠀⠀⢸⣿⣿⣿⡿⠠⠤⣄⡈⠧⢿⣿⣯⠛⠛⠛⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡜⣿⡆ ⠀⢠⣿⣿⣿⣿⣿⣄⠀⠘⠮⠖⠈⢿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣽⣿⣸⠇ ⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣽⣻⢿⣷⠦⠀⠀⠀⠀⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⡀⣠⠞⢉⣶⡤⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⣻⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣵⣶⣟⣳⢶⡄⠈⢻⣿⣿⣿⡿⣿⢿⠅⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣷⣾⠯⣿⣿⣿⣧⣀⠀⠀⠈⠙⠛⠿⢿⡿⣿⣏⣁⣀⣉⣙⣣⠀⣠⣿⣿⣿⣷⣿⣭⣶⣤⡆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⣱⣻⣿⣿⣿⠋⠚⠻⠭⠷⣲⢤⣀⠀⠊⠛⢤⡈⣻⠋⠈⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣶⠞⠘⠯⡲⣄⣀⣽⣅⣀⡞⠀⢹⣿⣿⣿⣿⣿⡿⣿⡿⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠉⣼⣯⣽⣶⣴⣶⣿⣿⣿⣿⣻⣻⢷⣾⡟⢿⣿⣯⣷⡿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⢿⣿⣛⡶⣤⣀⣀⣀⣀⣀⣿⣿⣷⣿⣲⣌⡻⣛⣿⣿⣿⣿⡿⠟⡻⣿⣷⣿⣿⣧⣸⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠓⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣷⠀⠀⣿⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠋⠉⠉⠙⣿⡄⠀⣿⢠⡇⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠁⠀⠀⠀⠀⠀⢀⣀⣿⣻⡿⢿⡿⠛⢤⠤⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⢀⣀⣠⣤⡴⠶⠿⢿⣟⣛⣛⣿⣦⣬⣷⡶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠿⠶⠶⠛⠀⠀⠀⢈⣉⣩⣩⣭⣭⣭⣤⣤⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣠⠿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡷⣤⣀⡀⠹⣷⣤⣀⣀⣀⠀ ⠀⠀⣾⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡟⠀⠀⠀⠈⠉⢩⡿⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⣠⡟⠁⠀ ⠀⠀⠀⠙⢷⣦⣤⣀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢳⡀⠀⠀⣾⡉⠀⠀⠀ ⠀⠀⠀⢀⣼⠁⠀⠈⡉⠉⠉⠁⢀⡔⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡼⠃⡇⠀⠀⠀⠀⠀⠀⡇⠻⡄⠀⠀⠀⠀⡀⠁⠀⠀⠈⠻⣦⣤⣤ ⠀⠀⠀⣾⠃⠀⢀⣾⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⣋⡀⢳⠀⠀⠀⠀⠀⠀⡇⠐⠛⣟⠒⠀⠀⢧⠀⠀⠀⡀⠀⠀⢀⡾ ⠀⢀⣾⠃⠀⠀⣾⠈⡀⠀⠀⣸⢻⡀⠀⠀⠀⠀⠀⡞⠁⠀⢈⡿⠋⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⢈⡳⣄⠀⢸⠀⠀⠀⢧⣀⣴⡿⠁ ⠀⣼⠇⠀⠀⣼⠇⠀⢇⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⡇⢀⣴⣟⣠⣤⣤⣤⣤⡀⠘⣆⠀⠀⠀⠀⣇⣴⣾⣿⠿⣿⣳⢜⡄⠀⠀⢸⡏⠁⠀⠀ ⢸⡇⠀⠀⢰⡿⠀⠀⢸⣶⠛⠋⢹⡇⠀⠀⠀⠀⠀⣿⣯⣿⡿⠛⣩⣿⣯⣿⣿⡆⠘⢧⣄⠀⠀⠸⣿⣿⣿⡇⢾⡿⠀⡇⠀⠀⠘⣿⠀⠀⠀ ⠘⣇⠀⠀⣾⠃⠀⠀⢸⣿⠀⠀⢶⣇⠀⠀⠀⠀⠀⣿⠸⠏⠀⢠⣿⣿⡿⣿⡏⠁⠀⠀⠈⠙⠲⠶⣾⢹⣿⡇⠀⣇⢰⠀⠀⡀⠀⣿⠀⠀⠀ ⠀⢻⣆⢸⣿⠀⠀⠀⢸⡿⣄⠀⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠘⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⣻⡼⠀⢰⠃⠀⣸⠀⠀⠀ ⠀⣀⣙⡿⠿⣇⠀⠀⢸⡇⠙⠛⠒⠲⣿⡀⠀⠀⠀⠈⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡤⠤⢶⠄⠀⠀⠀⣠⠟⠀⡰⣻⠀⠀⣿⠀⠀⠀ ⢸⣟⠉⠛⢛⣿⣷⣤⣀⣿⣄⡀⠀⣰⣿⠳⣀⠀⠀⠀⠈⢷⣤⣛⣂⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣼⣀⣠⣴⣾⠋⠀⠀⢠⠃⠀⢰⡿⠀⠀⠀ ⠈⢿⣇⠀⣠⣭⣿⣿⣿⣿⣿⣿⠷⠋⠈⢹⣿⢶⣄⡀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣿⣶⣶⣶⡶⣿⣿⣶⡿⠛⠁⠀⢀⣴⠋⠀⢠⣿⠃⠀⠀⠀ ⠀⢀⣭⣿⠿⣿⣿⣿⣿⡟⢻⡀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠛⣿⣿⣍⣛⡿⢿⣿⣿⣿⣿⣿⣟⠁⠉⠉⢳⠖⢟⡿⠁⣀⣴⢿⣥⠀⠀⠀⠀ ⠀⠸⣿⣤⡒⠻⣿⣿⣿⡇⠸⣃⠴⢦⣀⠀⣿⠀⠀⢀⡜⠉⠳⢮⡿⠿⡏⠛⠛⠛⠋⢹⣿⠉⠙⠷⣤⣀⡾⠛⠛⣶⠚⠉⠀⢀⡿⠀⠀⠀⠀ ⠀⠀⠈⠛⠻⠿⠿⠿⠿⣧⠀⠁⠀⠀⠹⡄⠸⣄⣀⣼⠀⠀⣠⠴⠦⢤⣇⠀⠀⠀⢰⡟⣿⠀⠀⠀⠈⢿⣦⣄⣸⣁⡀⣀⣠⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣦⡀⠀⠀⠀⣷⠶⠿⣷⣤⣠⠎⠁⠀⠀⠀⠙⣷⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠉⠛⣿⡟⢦⣤⣀⣠⢤⣀⣈⣿⣿⣦⣤⣄⣠⣤⣴⣻⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⢴⠁⠏⠳⠦⢌⡹⠿⡏⢉⡏⢸⠃⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠇⢸⡇⢸⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠷⣦⣤⣾⠻⠶⣤⣤⡤⠾⠋⠀⠀⢿⣬⣷⣤⣤⡴⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠷⡞⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠾⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠑⡆⢳⡆⠀⣿⠀⠀⠀⠀⠀⢭⢓⠿⠇⠀⠀⠀⠀⠀⣿⠀⢰⡟⠐⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⡹⡈⠿⡀⢹⡇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢹⠉⣀⠏⡽⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡜⠣⠬⠙⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠶⡟⠐⠃⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠛⠛⠛⠛⣤⣍⡏⠁⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⠀⢠⠟⠁⣀⣄⠀⠀⠈⣿⣩⣤⠛⠛⠛⠻⣤⣀⠀⠀⠀ ⠀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠀⢨⣿⠀⠀⠀⠀⣞⡇⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⠀⠀⠀⠀⢣⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣀⠀⣼⠇ ⠀⠻⢆⣴⣤⣤⣤⣯⣭⣵⣦⣤⣤⣼⣄⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣧⣤⣴⣾⣿⣿⣿⣤⣤⣼⣤⡼⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠗⠿⠇⠀⠀⠀⠀Pls don’t put innapropriet things here we just want to find cute emojis and have a good time. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⣸⠁⠀⠀⠀⠀⠀Younger children just want to find cute emojis, not see other things. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀pls spread the word and have a good day. <3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⣤⣶⣿⣿⣿⣿⣿⣭⡶⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠒⠤⠀⡔⠄⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣥⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢤⡀⠀⠀⢀⣀⠈⠂⠉⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⣀⢻⡟⠉⣷⠀⠀⠀⠀⠀⠀⢀⡤⠎⠁⣀⣿⣿⣿⣿⣿⣿⣿⠟⢉⣠⣶⡾⠋⠀⠀⠀⠀⣀⣠⡤⢶⡾⠶⠀⠀⠀⠀⠀⠉⠶⣽⣾⣿⣷⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣬⣺⡟⠀⠀⠀⠀⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⣣⣴⡿⠟⠁⠀⠀⣠⣤⣶⡿⠟⢉⣴⠋⠁⠀⠀⢀⡞⠀⠀⣦⠀⠙⢿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⣯⣶⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⢿⠋⡀⣀⣤⣾⠿⣿⡿⢋⣴⣾⠟⠀⠀⠀⠀⣴⠋⠀⠀⠀⢹⣦⠠⢪⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣻⢋⡞⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠟⠉⣱⡾⣯⡶⣿⡿⠃⠀⠀⠀⢀⡼⠃⢠⣆⠀⠀⣇⣿⡆⡜⡏⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠁⠀⠁⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢠⣾⣿⠟⢡⣾⣿⠅⠀⠀⠀⣠⡿⠁⣰⣿⢸⢸⡆⣿⣿⣿⣼⣼⡈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣹⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣰⣿⡿⠃⢠⣾⣿⠞⠀⠀⡴⣷⣿⠅⠀⣿⣿⢸⣾⡇⢻⣿⣿⣿⣿⣇⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡿⠁⣸⣿⡟⢠⢀⢠⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⣿⠟⠀⢠⣿⣿⡟⠀⢀⣼⣿⣿⡿⠀⢰⣿⣿⡟⣿⣇⢸⣿⣿⣿⣿⣿⠀⣿⣿ ⠀⠀⠀⠀⢰⡾⢶⣀⣥⣤⡀⠀⠀⠀⢰⡟⠁⣴⣿⣿⣧⡟⣾⢋⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⣿⠀⢀⣾⣿⣳⡿⠁⠀⡇⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⡀⢻⡏ ⠀⠀⠀⠀⢸⣇⠀⠻⣇⣸⡇⠀⠀⢀⡞⠀⣼⢿⣿⣿⣿⣹⡟⣾⡿⠋⠑⠦⠤⠤⣀⣀⣀⠤⣾⡿⠂⠀⢸⣿⣿⡇⢀⣾⡿⢱⡿⠁⠀⠐⠁⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠙⢷⣴⠟⠋⠀⠀⠀⡾⠀⢰⠃⢈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡏⠀⠀⠀⢸⣿⡿⢀⣾⡿⣇⡾⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠇⠀⠸⢸⣿⣿⣿⢋⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⢸⣿⡇⣾⡿⠁⡸⢣⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣠⠏⢀⡀⠀⣸⣿⣿⡏⢀⣹⣶⣶⣶⣿⣯⡒⢆⡀⠀⠀⠀⠀⠀⠀⢸⣿⢳⡿⠀⢰⠇⠀⠙⢦⡀⢀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣿⣿⡃⣼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠀⣼⢿⣿⣿⣱⡿⠋⠁⢠⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢮⡄⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⠞⠁⢀⣾⣿⢸⣿⡿⡿⠀⠀⣰⣿⣿⣿⣿⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⠈⢿⣿⣿⠈⣿⣿⣿⣿⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣿⣿⣿⣾⣿⣿⠃⠀⢠⡟⠉⠙⠛⢻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣤⣀⠀⡀⠀⠀⠀⠙⠚⢿⣿⣧⠸⣿⣿⣿⣾⣷⢰ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⢛⡥⢀⣴⣿⣿⣿⠟⠀⢹⣿⣧⠀⠀⠘⢇⠀⣀⡀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣿⣷⣿⣤⡀⠀⠀⠀⠈⢿⣿⣆⠸⣿⣿⣿⣿⣾ ⠀⠀⠀⢀⣠⠾⠋⢉⣴⣫⣶⣿⣿⡿⠋⠁⠀⠀⠀⣿⣿⡄⠀⠈⢿⡀⠈⠉⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠈⢻⣿⣆⠹⣿⣿⣿⣿ ⠀⠀⠀⠈⢱⣄⣾⣯⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⣼⠃⠙⢷⠀⠐⠚⠿⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠿⢿⣿⡏⢙⡏⠻⣿⣆⠀⠀⠻⣿⣷⣿⣿⣿⣿ ⡀⠀⠀⣠⣿⣿⣿⠟⣹⣵⣤⣤⣤⣤⣤⣤⡼⢿⡏⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⢘⣿⣿⠇⠀⠹⣿⡆⠀⠀⢸⣏⣿⣿⣿⣿ ⣡⣴⣾⣻⣿⠟⣩⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣳⠀⢤⣀⣠⠞⢉⡿⠀⠀⠀⢹⣷⠀⢀⣾⣾⣿⣿⣿⣿ ⣿⣿⢣⣿⣗⣼⣿⣿⡿⠿⢿⡟⠛⠛⠛⣷⠞⠋⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠇⢀⣾⣾⣿⢿⣿⣿⣿ ⣿⣿⠠⣿⠿⣿⡁⠈⠀⠀⠀⠑⣄⣠⠞⠁⠀⠀⠀⣀⡹⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣒⠖⠋⠁⠀⠀⠀⠀⠞⠁⣰⣿⣿⠟⢡⣿⡿⠋⠀ ⡋⠙⣸⠃⠀⠈⠻⣦⠀⢀⡴⣶⠟⠁⠀⠀⣀⡴⠚⠁⠀⠀⠀⠙⣆⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢟⡥⣺⣿⠟⠀⠊⠀ ⠀⠀⠃⠀⠀⠀⠀⢈⡿⠋⣰⠇⠀⠀⠐⠚⠁⠀⠀⠀⠀⣠⠴⠛⠋⠓⣆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣛⣻⠵⠚⢁⡴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⢸⣦⠀⠈⠳⠤⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠀⢀⣤⠶⠭⠄⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⠀⠀⠀⠀⢀⣀⣀⠐⠃ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⢀⠀⠀⢸⠀⠀⠀⡤⠤⠤⣤⡴⠒⠒⠒⢦⡖⠒⠲⠤⣄⣀⡀⠀⣀⣤⣾⡋⠉⠓⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀ ⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⡞⠀⢠⡞⠀⠀⠀⠈⡇⠀⠀⠀⢸⠇⠀⠀⠀⡇⠈⠉⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⢠⠀⠀⣠⣀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⡇⠀⢸⡓⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠉⢹⣿⠇⠀⠀⠀⠀⡇⠀⠀⠀⡸⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⣿⡿⠟⠳⠤⠖⠶⠤⣤⣴⣿⣌⢿⣿ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠁⡇⠀⠀⠀⠀⠇⠀⠉⠑⠶⢤⡤⠴⠞⠉⠄⣼⣠⠾⠿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠸⠁⠀⠀⢰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡹ ⠠⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠓⠤⢤⣤⣀⣀⣀⣀⣀⣠⡤⢖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡔⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠷⣶⣶⠶⣶⣶⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠉⠈⠳⠛⠼⣶⣦⣀⡀⠈⠐⠘⢻⣷⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⣠⣾⣿⡿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠑⢀⣄⠀⠂⣄⡈⠃⠀⠀⠙⣿⣿⣿⣿⣿⣅⡴⠀⢯⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢇⡆⠀⢂⣰⣟⡹⡄⠀⡟⠻⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠈⠎⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣼⡇⠀⢹⣏⣁⡀⣧⠀⡇⡏⠉⠻⣶⡄⠀⢹⣿⣿⣿⣿⠇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⡇⠀⢹⣿⣿⣧⠘⢧⣧⣾⣷⣶⣿⡀⠀⠀⣿⣿⡏⣿⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⠀⣷⠄⣼⠿⣿⣿⠠⠤⠈⣿⣿⣿⡟⢧⡀⠀⣿⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢿⡀⢿⠋⠀⠀⠀⢶⣿⣿⠇⣼⠂⣰⣿⣿⣿⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣷⣦⣄⣀⣰⣆⣀⣡⣣⣤⡟⢠⣿⣿⠟⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡿⣿⢿⡟⣿⣿⣿⠟⣿⠁⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣹⣿⠛⣷⢥⣾⢿⣾⠻⣇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣼⣿⣿⠁⢸⣏⢋⣿⣤⣿⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣠⣾⡿⠟⠃⠀⣿⡯⣍⣿⠛⢿⣷⡀⠀⢸⡇⠀⠀⡀⠀⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⣩⣿⠷⠀⢸⣿⠃⣸⡏⠀⠈⢻⣷⡄⢸⡏⠄⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣠⡶⠟⣩⣿⡇⣿⣿⡟⢋⠀⢠⣿⣿⢴⠟⣇⠀⠀⠀⢹⣿⣾⣧⡀⢄⠀⠀⠄⠹⣄⢻⣆⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠉⠉⠉⠉⢛⣯⡉⢻⣿⣶⣶⣿⣿⣯⣻⣋⣿⠄⠀⠀⠘⣿⣿⣿⣷⣬⣷⡄⠀⠀⠈⠛⠿⣷⣄⡀⠀⠀⠀ ⢸⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣧⣥⠟⠁⠀⢹⣿⣿⣿⡇⠲⡄⠀⠿⠋⢸⣿⣿⡟⣧⠀⠀⠀⠀⠤⠤⢈⣛⢷⣄⠀ ⠀⠻⠟⠛⠻⠏⠙⠋⠈⠀⠀⠀⣿⠠⠀⢰⣼⣿⣿⢿⣷⡰⣆⠠⡄⠀⣼⣿⢿⣽⢿⣷⣤⣤⢶⠶⠶⠾⠿⣷⣽⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣶⣿⣿⡿⠋⠈⠻⣿⣛⣿⣶⣾⣿⠿⠛⠁⠀⠈⠈⠁⠀⠀⠀⠀⠈⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡶⢫⣭⡝⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣹⡿⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠉⣗⣻⡃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⡴⣚⣽⡛⢦ ⠀⠀⣿⣨⣗⠀⢀⣤⡶⠟⠛⣉⣽⣶⣯⠿⠿⠿⢯⣷⢤⡀⠀⠀⠀⢦⣼⣿⠇⣸ ⠀⠀⠀⠀⢀⣼⠟⠉⢀⣴⠟⠋⠀⡀⠀⠀⠀⠰⣆⠈⠙⢷⣆⠀⠀⣤⣏⣴⠾⠃ ⠀⠀⠀⢠⣿⠃⠈⢠⡿⠃⠀⠀⣸⡁⠀⢰⠀⠀⢸⡄⠀⣄⠻⣧⠐⣯⣩⠟⠀⠀ ⠀⠀⠀⣿⡇⠀⠂⣼⠃⢸⡄⠉⣽⠀⠀⣯⠀⠀⡘⣧⠀⢸⡄⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠆⠈⢄⡟⠀⣸⠄⠠⣿⠀⠀⣿⠀⠀⣽⢷⡀⠈⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢠⡭⢠⡇⠀⢼⣂⣰⣿⣦⣠⣿⢯⣄⣾⣿⣦⣼⡇⢲⣿⡇⠀⠀⠀⠀ ⠀⠀⣼⡏⣰⠃⣾⣇⠀⢺⠟⣿⣿⣿⡅⠀⠀⠀⣿⣿⣿⣹⠇⣼⣿⠃⠀⠀⠀⠀ ⠀⢐⣿⠁⣯⠐⣿⢻⣀⠸⡇⠙⠿⠛⠀⠀⡀⠄⠈⠛⢋⢸⡄⣿⣏⠀⠀⠀⠀⠀ ⠀⠈⣿⡌⣷⡌⠻⣽⡜⣎⡧⠐⠂⠐⠀⡀⠀⢀⠠⠁⠂⣼⢃⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠉⣷⢾⣇⡳⢸⢷⣧⢻⣤⣤⣄⣡⣠⣔⣤⡴⡞⣿⣃⣾⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢿⣻⣿⣿⢾⣟⣯⣧⠰⠌⡍⠛⠹⣶⣿⣿⣿⢲⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣨⣾⣿⣿⣹⣾⡟⠙⠛⠉⡙⡙⣛⠉⠹⣿⣻⣿⣿⣝⡁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣧⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡿⠟⠉⠛⠻⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠂⢀⣾⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡶⣾⣿⢿⣱⣿⣿⣷⢶⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣹⣿⢿⣯⢻⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣯⣗⣻⡞⣿⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡿⠟⠉⠛⠷⣿⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠁⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠶⠶⠶⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠶⠶⠶⢤⣄⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿ ⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀ ⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣄⠀⠀⠀⣀⣠⠴⠛⠉⠉⠓⠦⣄⣀⠀⠀⠀⣠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡦⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⣷⠄⠀⠰⠤⣀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⢺⣿⣿⣿⣿⡄⠀⠀⣿⣿⢿⣿⣿⣦⣦⣦⣶⣼⣭⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡆⠂⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⠀⢸⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀ ⠀⠜⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⠄⣠⠀ ⠠⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⡿⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠉⠻⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⠀⠀⠀⠉⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠤⠴⠒⠢⠷⠤⣉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⠅⠀⠀⠀⠀⠀⠀⡀⠀⠲⢯⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠁⠀⠁⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⡆⠀⠀⠀⠀⠀⠀⣇⣀⡤⠞⠉⠀⠀⠀⣠⠀⠀⠀⠀⢀⠔⠁⣀⠔⠁⡀⠀⠀⠀⠀⡀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⡇⠀⠀⠀⣴⡖⠚⠉⣡⠞⠁⠀⠀⡠⠊⠀⠀⢀⣠⣖⠡⠔⠊⠁⢠⠀⡅⢂⠀⠀⠀⠘⢄⠀⠀⠀⠐⢄⣉⣒⣦⡄⠀⠀ ⠀⢸⣇⡇⠀⠀⠀⠈⢉⡿⠎⡰⠁⠀⢀⠎⠀⠀⠀⠈⣩⠏⠀⠀⠀⢀⢴⠏⡰⠃⡌⠆⠀⠀⠀⠈⢣⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⢀⡾⢁⡜⠀⠀⣰⠇⠀⠀⠀⢠⣾⠃⠀⠀⣀⡴⠃⣼⠞⠁⠀⠈⢾⡄⠀⠀⠀⠀⢡⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⣾⣿⡇⠀⢀⣴⢿⠷⠸⠀⠀⣤⡿⠀⠀⣀⠴⢿⣥⣄⡒⠺⠟⠀⠉⠛⠀⠒⠤⣀⠀⢳⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠸⡄⠀⠀ ⠀⢾⠇⠀⣶⡛⢁⠮⠃⠄⠀⢸⣿⠿⢚⡩⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⡀⠸⡀⠀⠰⠘⠀⠀⠀⢠⡀⠹⣄⠀ ⠀⢸⠀⠀⠈⢙⡏⢸⠀⡆⣠⣮⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⡇⢠⠁⠀⠈⠐⠀⡆⠀⠀⢹⡖⠾⠆ ⠀⣿⠀⠀⠀⣼⠀⡜⠀⢀⡿⠃⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠾⡿⣾⣿⣷⣬⠙⢶⣄⠀⢧⢸⠀⠀⠀⡅⠈⡇⠀⠀⠀⣳⠀⠀ ⠀⣿⠀⠀⠸⣷⠞⡇⢀⡾⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡟⢿⡇⠹⣿⡇⢸⣯⠀⠀⠀⣇⡇⠇⣇⠀⠀⢸⠄⠀ ⠀⣿⠀⠀⠀⠈⠀⠿⢿⠁⡇⣿⠁⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠃⣸⠃⠀⠘⠀⠠⢿⠇⠀⠀⣿⠿⡄⢿⢠⡄⠸⡀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⣧⢧⠀⠘⠀⠛⡼⠀⠀⠀⠀⠀⠀⠀⢀⠑⠤⠞⠁⠀⠀⠀⠀⠀⡸⠀⢀⣠⠟⢣⢹⢸⣾⡉⠢⡧⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣾⠀⡟⡄⢠⠀⠛⢺⡧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠋⠀⠀⠀⠷⠊⢻⡄⠀⢸⢸⢶⠃⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⣧⡇⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⢣⠏⡎⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⣿⡀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠭⠭⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣡⡴⠋⠻⠃⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢿⠀⡙⢣⡀⠀⠀⠀⠀⠘⡟⠋⠀⠀⠀⠀⠀⢀⣸⠂⠀⠀⠀⠀⣀⣴⠚⣿⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣿⡀⠙⢢⣄⡀⠀⠀⠉⠒⠒⠒⠒⠒⠉⠉⢀⣀⢠⣴⠖⠻⠾⣿⡞⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⡇⡇⠀⠈⣿⠉⠁⠒⠒⠢⢤⡤⢴⣖⠊⢉⡡⠔⠊⠁⠀⠀⠀⡸⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⣧⠠⠀⡤⠏⠀⠀⢀⡤⢺⠋⠀⢠⡝⣶⠛⣄⠀⠀⠀⠀⠀⣰⣡⠚⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⠎⠀⠀⠀⢠⠏⠀⡄⢀⠴⣿⣷⣼⣾⡿⠷⡀⠀⢀⡴⠋⠀⣠⠀⣀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡴⠒⠒⢎⠀⠰⠞⠓⠤⢾⣿⣿⣿⠧⠒⠛⠒⠊⠀⠀⣴⠇⠀⠈⢣⠀⢀⠈⢣⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡜⠀⠀⠐⢼⡀⠄⠀⠀⠀⢸⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⡖⠂⠢⢤⣧⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡗⠁⠀⢀⣰⣋⣿⠀⠀⠀⢀⣿⣋⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⠀⣀⢻⡤⣄⡀⢈⡇⠀⠀⠀

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠄⠀⢤⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠠⠀⠀⠄⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⣀⣾⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⠟⠀⠀⡀⠀⠀ ⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⡀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⣾⣿⠁⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⣾⣿⠇⡔⢳⣀⣸⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠠⠀⠀⠀⠀ ⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⡼⠀⠀⠀⠈⢹⠃⡀⠀⢀⠀⢀⠀⠀⡀⠀⡀⣠⣶⣿⡿⠋⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡏⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⢤⣴⣆⠀⢠⣾⣟⣿⣿⠗⠉⠰⠥⠄⣠⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠇⠀⠀⠀⠀⠀⣤⠼⠃⠀⠀⠀⠀⠉⠢⡙⠻⢿⣿⡿⠃⠀⠀⠀⠀⠛⢏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⡿⠿⠀⠀⣠⣤⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠲⣄⠀⠀⠀⠀⠀⣈⣳⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠳⡄⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⡆⠀⠀⠀⠀⠀⣷⡀⠀⠀⠘⢦⢤⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⠏⣇⠀⠀⡄⠀⠀⠀⠀⠀⢹⢳⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⢾⠁⠀⠀⠀⠀⠀⣰⣇⣀⣹⡀⢰⠁⠀⠀⠀⠀⣀⣼⣨⣇⠀⠀⠀⣸⣿⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡴⠋⠎⠀⠀⠀⠀⠀⢠⠃⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢠⠇⠀⠸⡄⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣇⡆⠀⠀⠀⠀⢀⡎⠀⠀⠀⢳⠀⠀⠈⢿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⣠⣔⣁⠤⠔⠒⠉⣷⠀⠀⠀⢠⠏⣀⣀⣀⣀⡀⢹⠇⠀⠀⠀⢀⡞⢀⣠⣤⣶⣬⣇⠀⠀⡼⢷⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢯⠉⠁⠀⠀⠀⠀⠆⠹⡆⠀⢠⣿⣾⢿⣿⣿⣿⡿⣿⠄⠀⠀⣠⡾⠡⣿⣿⣿⡍⠙⣿⠁⢀⣿⡆⠀⠙⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠹⡀⣼⡏⠁⣸⣿⣿⢿⡷⡇⠀⣠⠞⢹⠃⠀⡿⡟⢿⠃⠀⡟⡆⢸⠀⠑⠢⠤⠼⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠳⡇⢳⠀⢻⣄⠀⢰⢣⡧⠞⠀⠀⠀⠀⠀⢿⣀⡼⠀⢰⠇⠹⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⠀⠀⢸⡆⠀⠀⠀⠉⠀⢧⠀⢙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢠⣾⡀⠀⢸⠀⠀⣶⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡎⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⢲⣄⣿⡌⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⠃⠀⢸⠀⠀⢸⠟⠛⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⢀⣠⠃⠀⠀⠀⡔⢻⢸⡀⠀⠀⠈⡇⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠗⠚⠉⢸⠀⠀⠀⢠⡇⠀⠟⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡸⠹⡄⠀⢈⣇⠀⠀⣧⠀⠀⠘⢷⣶⣤⣄⣀⣀⣀⡤⠔⠋⢧⡿⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⢙⣶⣿⣿⡆⠀⣿⢦⡀⠀⠀⢹⣿⣦⣀⣩⠟⠀⠀⠀⠈⠁⢣⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⢣⡴⠋⠀⢿⣿⣿⡄⣟⣶⡻⣦⣀⢀⣿⣻⣿⣿⣄⡀⠀⠀⠀⠀⠈⢆⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⠴⠚⡙⠙⠲⣤ ⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣿⠃⣰⠟⠉⠙⢦ ⢦⡈⢁⣾ ⡟⠉⠳⣆ ⠸⠀ ⠙⣆⠙⢧⡀⢀⡴⠃ ⠛ ⢧⡀ ⢀⡴⠃ ⣰ ⠈⠓⢦⡈⢡⣰⠞ ⡈⠈⠓⢦⡈⢡⣰⠞⠁ ⠀⣰⠃⣰⡏⠀ ⠙⣆⠙⢧⡀⠀ ⢀⡴⠃ ⣰⠏⠀⠀ ⠈⠳⣄ ⠙⠶⣄ ⠈⠓⠲⠖⠚⠀⠀⠀⠀⠀ ⠈⠓⠲⠶⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⠶⠛⠛⠉⣩⣷⣶⣤⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠶⠶⠛⠛⠛⢉⣋⠀⠀⢰⣷⡀⠀⣸⣿⠏⠙⣿⣿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⢷⣤⡈⣿⣧⠀⣿⣿⡀⠀⣿⣿⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣏⠻⣿⡾⣽⡆⠘⢿⣿⣾⣿⠋⠀⠀⠀⢀⡀⠀⠸⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⠙⠟⠃⠀⠀⠀⠁⠀⠀⢀⣀⣼⠋⢧⠤⠖⠻⣆⠀⠀ ⡀⠀⠀⠀⠀⢀⣠⣍⠁⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣦⣀⠠⠀⠂⠙⣦⠀ ⣧⠀⢀⣀⣠⣼⡟⢸⣷⣿⣿⣿⣿⡿⣿⢿⣻⣟⣯⢿⡽⣯⣿⣿⣆⠀⠀⠀⠘⣦ ⠙⣿⣿⣏⣡⠤⠔⠾⣿⣻⣽⣳⢯⡿⣽⢯⡷⣟⡾⣯⣿⣿⡷⣯⣿⡆⠀⠀⠀⠹ ⠀⣿⣽⣏⠀⠀⠀⠀⣿⣯⢿⣽⡿⣿⣯⣿⣽⣻⡽⣿⣻⣷⣿⣿⣷⣿⡄⠀⠀⠀ ⢠⣿⣳⣿⡄⠀⠀⠀⢸⣿⢸⣿⣿⡿⠿⠿⠞⠛⠛⠋⠋⣀⣹⣷⣾⠻⣷⠀⠀⠀ ⢸⣷⢯⣿⣧⠀⠀⠀⠀⢻⣿⣋⣹⣿⣷⡄⠀⠠⠀⠀⢰⣿⣯⡹⢿⠀⢻⣧⠀⠀ ⢸⣯⢿⣿⣿⡆⠀⠀⠀⠸⣇⠹⡿⠩⢿⠇⠀⠠⢀⣴⣇⠈⢆⡐⢃⠆⠁⣿⡆⠀ ⢸⣿⣻⡇⠠⣷⠀⠀⠀⠀⢻⡆⡡⢁⠆⠠⠈⢀⣾⠛⣽⡆⢂⠉⢂⠌⢰⣿⣿⡀ ⢼⣷⣻⣿⣄⢸⡇⠀⠀⠀⠈⣷⡀⠃⠌⠐⠀⢸⣇⢣⣼⠇⠀⠈⢀⣠⣾⣿⡽⣷ ⣿⣳⢿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣇⠤⡄⢠⢀⢀⣉⡋⣁⣠⣤⣶⣿⣿⣿⣿⣻⣽

⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢠⡇⠀⢠⠇⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡄⠀⠀⠀⡸⠀⠀⢸⣀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠹⡄⠀⠀⡇⠀⠀⢻⠟⠀⣀⡠⣄⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⢦⡀⡇⠀⠀⠘⡦⠊⠀⢠⠏⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠙⢿⣤⣀⣀⡇⠀⠀⡾⠒⠛⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠀⠀⠹⠷⣈⠑⠢⠤⠧⣤⠚⠁⠀⠀⠀⣠⡴⠶⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⣈⣧⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠲⢤⣤⠖⠛⠓⣒⠀⠀⠈⢣⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡾⠁⠀⣀⣠⡇⠀⠀⠀⠀⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⢰⠃⡤⠊⡏⠀⣳⣄⣀⣤⠤⠾⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⣾⠁⠀⠈⠟⣇⠀⢣⣀⣿⡆⠀⣼⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⣆⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠈⠓⠒⣿⣿⡀⢀⡿⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣧⠛⢳⡀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⡏⠛⢹⠇⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠖⠛⠁⠀⠀⣿⣆⡈⢹⣤⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⢀⡞⠉⠁⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢏⣈⢀⣇⠀ ⢸⡄⠀⠀⠀⠀⣠⡞⠃⢰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⢏⡀⠈⣷ ⢸⡇⠀⠀⢀⣼⠉⠡⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣏⠀⢹ ⠀⣧⠀⠀⢺⠀⢲⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⢻ ⠀⠻⣦⣴⣾⣶⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠁⢰⣿ ⠀⣴⣋⠁⠈⠹⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⠰⡏⠀ ⠀⠿⢻⡀⢠⠶⠧⣤⣼⣧⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⠿⡇⢀⢾⡇⠀ ⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⢠⣀⣀⣠⣀⡤⠤⡄⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣹⠿⣿⡏⠋⡿⠟⡿⠇⢖⣯⣿⣯⢿⣏⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡀⣄⠳⣎⢾⠉⠀⠀⣄⣧⢾⣗⠻⠀⠃⣡⠝⢲⣡⣌⣇⣌⠱⠀⠀⠀⠀⠀⡗⠭⣿⢨⡑⠆⢃⣿⣿⡿⣽⣾⣟⣯⢿⣿⣠⠁⠁ ⠀⠀⠀⠀⠀⣆⡓⡻⢻⠈⠀⠀⢷⠀⡀⢧⣹⡹⡉⠻⠛⠚⠓⡚⡛⠻⠛⠛⠛⠛⡙⢿⣻⠚⠿⡷⣯⣟⣿⢿⣻⣿⣟⢿⣿⢿⡿⣾⣾ ⠀⠀⠀⠀⠀⠀⠀⣇⡹⣟⠖⠴⡷⣭⣦⣙⣼⢀⠀⠀⡀⣄⣳⡞⡏⣰⠀⠁⠀⣁⣀⣿⣷⣿⣾⣭⣻⣯⣛⢿⡽⣿⣿⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⣸⠀⠀⠀⣀⢧⡯⠀⠀⠀⠀⠀⠀⠀⣆⣹⠀⡀⠀⠁⠋⠛⡿⣿⢙⣷⣽⡿⣟⣿⣿⣿⣿⢻⠋⠛⠛⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠙⠀⠀⠉⠚⣖⠳⠋⠛⠻⠟⠿⠟⠛⡟⠉⠋⠗⣿⣿⣿⣿⣿⣿⣶⣾⣵⣭⣯⣟⣟⣮⡴⣤⣀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢼⣠⠀⠀⠉⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢠⠁⠀⠈⠁⠉⠍⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠉⡶⣤⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⡜⢻⣳⣮⣿⣿⣾⣶⣷⣭⣽⣾⣟⣶⣶⣤⣤⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⣤⢤⢳⠈⠁⠗⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣜⡹⣷⡹⢷⣭⣽⠾⣿⣯⣽⣺⣙⣻⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠋⡴⣀⠀⢏⣪⡥⣿⣾⣴⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⡜⡽⡜⢻⣮⡟⢧⣽⢿⣳⣟⣯⣿⣻⢿⠛⠛⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⡟⢰⠏⢠⠀⠀⠏⢫⢞⣠⢀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣟⣶⣿⣿⡀⢿⢧⣞⢶⣷⡽⣭⣻⣻⣷⡿⢷⣽⣿⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⣿⢠⠀⠀⠀⠇⠿⡿⢰⠁⡀⠁⡀⠈⡀⣷⠮⣟⠹⡄⣻⣽⣿⣧⣟⣣⣽⡻⢷⣯⣽⡾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⡇⢻⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠋⠙⠀⢧⡵⣿⠀⣇⡾⢏⣳⢯⣻⣿⡶⢿⣽⡽⣿⣿⡷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⡧⣿⠀⣿⣿⢿⡀⠀⠀⠀⠀⠀⡟⣿⣳⣿⢿⡇⡽⣿⠅⠀⣿⣏⡶⣞⠿⡿⣶⣟⣧⣟⣯⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⠀⡇⣻⠙⣷⢯⣿⢷⠻⠙⠈⠀⠀⡾⣿⣻⣿⣿⠁⣿⣿⠂⠡⣇⣫⣵⣟⢯⣻⣿⣟⣶⡾⣷⢝⠿⡿⡾ ⠀⠀⠀⠀⠀⠀⠁⠞⠤⣧⠀⠀⡇⣻⣮⡿⣿⣿⣿⣸⢤⣷⠻⠉⣍⣿⣷⣿⡿⣼⣯⣾⠄⠂⡇⣿⣯⣛⣻⣟⠷⡿⣾⣿⣹⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣽⢨⠀⠀⠀⠀⡟⡸⣤⠹⣀⣀⡁⢺⠀⠀⣄⣷⣘⡀⣀⠀⠀⠏⣷⢸⡀⠐⡇⣿⢮⣟⣫⡽⣻⡿⣟⣯⣟⢿⠓⠟⠟ ⠀⠀⠀⠀⠀⠀⣠⣀⢧⠹⠀⠀⡇⢻⠀⡀⢷⠬⠧⣸⠀⠀⠀⠀⣧⠻⠴⠧⡾⢀⡯⢠⡁⠀⡗⢿⣽⣭⣝⣻⣛⣛⣛⣿⡿⡶⣷⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠃⣹⡌⢸⠀⡀⣿⠙⠀⡀⢧⡟⠀⠀⠀⠀⠀⠀⣿⢞⣤⠀⠁⣼⠀⠀⠀⡿⣻⣵⢾⣫⢽⣾⡿⣿⢉⠀⠉⠉⠉⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣿⠉⡟⣶⣿⢿⠿⡤⢹⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⡏⢀⠀⠀⠇⢯⡱⣿⡶⢷⣭⣽⣯⣛⣲⣶⣖⡴⣤⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⡀⣄⣷⢺⠀⠀⣷⠀⠀⠀⠀⠀⠀⠁⢸⠀⠃⢰⠀⠀⠁⡼⣝⡲⣽⣮⣹⣽⡿⣴⢀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⠈⡀⢾⠙⠀⡆⠘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⡞⡴⡛⢧⣛⢧⣟⡾⣰⠋⠞⠵⠯⡽⣻⣞⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠳⠉⡀⠤⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣉⣬⠲⢥⡫⢶⣠⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⣋⢿⠿⠛⣼⣿⠻⠀⠀⠀⠀⠀⠀⠀⠄⣉⢉⠛⠷⡿⣾⠻⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣼⣤⡿⢷⡻⢶⣿⢿⣧⣿⣿⠿⠿⠿⠿⠿⣿⣿⣚⣿⣿⡿⠶⣿⣏⣽⡶⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⢽⣈⡇⠀⡀⢯⣎⣿⡦⣿⣡⠟⣤⣠⣀⡞⣄⠳⣌⠷⣳⣝⣯⠿⣿⡟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣶⡤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⡼⠛⠁⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠉⠽⠓⠒⠓⠒⠿⠉⠛⠒⠦⣤⡀⠀⣠⡶⠋⠁⠀⢠⡟⠀⠀⠴⠟⠛⢳⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⡀⠀⠀⢀⡏⡆⠀⠀⠀⢀⣼⣋⡅ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣸⠁⠀⠀⠀⠀⠉⠀⣸⡇ ⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⢀⣴⠏⠀ ⣤⡴⠒⠛⠉⠀⠀⠐⠒⠛⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣛⣒⣤⠿⠟⣶⠆ ⢹⣧⡀⠀⠀⠀⠀⠀⠀⣼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠀⠀⣰⠏⠀ ⠀⢿⡷⣄⠀⠀⠀⠀⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠛⣯⠀⠀ ⠀⠈⢷⣈⠙⢶⣒⠛⠋⢠⠞⠀⠀⠀⠀⠀⡴⠀⢠⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⡦⣴⠟⠁⠀⠀ ⠀⠀⠀⢹⡟⠂⠩⠛⢲⡏⠀⠀⠀⠀⠀⢰⡇⣀⣿⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠐⢺⢷⠂⠰⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠹⣟⡁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠲⢶⠀⡾⠀⠀⠀⠀⠀⢠⢸⡷⠫⢸⡆⢸⣆⠀⠀⠀⠀⠀⢳⠀⢀⡿⠘⢧⡀⢹⣄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⡆ ⠀⠀⠀⠀⠀⠀⠈⢹⠁⢰⠀⠀⠀⠀⢸⢸⡅⠀⠀⠻⣎⣿⢦⣀⠀⠀⠀⣸⡀⣼⣷⣾⣿⣿⣾⣿⢦⣿⠀⠀⠀⠀⠀⠀⠀⢷⠦⠴⠖⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⣿⠸⣇⠀⠀⠀⠈⠙⠂⠙⠷⣄⣀⣿⠟⢿⣿⡏⣀⡀⢙⣿⣿⣏⡀⠀⠀⠀⠀⢸⡀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⡀⠀⠀⢸⡷⢿⣶⣶⣦⣍⡢⠀⠀⠀⠀⠙⠀⠀⢸⣟⠉⠽⠿⠍⣻⣿⠟⠀⠀⠀⠀⠀⣸⠁⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣧⡿⢦⣄⡀⣷⠀⠀⠈⠉⠛⠻⢦⠀⠀⠀⠀⠀⠀⠠⠿⠤⠤⠤⢒⡿⠃⣠⡞⠀⠀⠀⣠⡏⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠟⠁⠀⠉⢉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡯⠴⣺⣿⠀⠀⢀⡴⣿⡖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠋⠁⠀⠀⠀⢀⡄⠈⢳⣄⠀⠀⠀⠀⠀⠠⣄⣠⣤⣀⡄⠀⠀⠀⠀⠀⢀⡴⠋⣯⣤⠖⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡶⠚⠉⢁⡆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠓⣶⣄⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⠟⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⣿⣿⣤⡉⠛⢿⡖⠦⠤⠤⠖⢛⣿⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠹⣷⣄⡀⠀⢀⡀⠀ ⢸⠀⠀⢸⡿⠁⢠⡄⠀⠀⠀⠀⡇⠀⠀⢀⡼⠛⠻⣿⣮⣙⣦⡈⣿⣆⠀⠀⢀⡾⠛⢷⣤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡄⠙⣮⡉⠉⠉⠁⠀ ⠘⣧⠀⡏⡇⠀⠸⡇⠀⠀⠀⠀⢻⠀⢀⡏⠀⠀⠀⠘⣿⣿⣿⣷⣽⣿⣦⣤⣼⡇⢀⡿⢸⠿⣆⠀⠀⠀⠈⣧⠀⠀⠀⢳⡄⠈⠻⣆⠀⠀⠀ ⠀⠈⢷⣇⣧⡀⠀⢹⣄⠀⠀⠀⠈⣇⢸⠁⠀⠀⠀⠀⠨⣿⣿⣿⣿⣆⢹⣆⣸⢡⣿⣷⡟⣠⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢆⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⠈⠙⠲⢤⣹⣦⣀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⠋⠈⢷⡄⠀⢀⡟⠀⠀⠀⠀⢹⡌⢷⡀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠓⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠹⣦⠞⠁⠀⠀⠀⠀⢸⡇⠀⢳⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠻⣏⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⣀⡾⠃⠀⢸⣇⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣀⣀⣀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣤⣤⣤⣤⣄⣀⣀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣍⣙⣲⣶⣖⣀⠀⠀⠚⠋⣉⠉⠉⠛⠛⠿⢿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡉⠛⢦⡀⠀⠀⡸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⣄⢀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡏⠉⠁⠀⠀⠸⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡜⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⢿⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⠋⠙⢆⠀⠀⠀⠀⠙⠟⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⢘⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠘⣿⣎⢦⠀⠀⠀⡀⠑⣄⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡹⣆⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢬⢻⣎⢣⡀⠀⠙⣄⠘⢦⡀⠀⢞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⡟⠀⠀⠀⠀ ⠀⢀⣠⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠃⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡵⢙⢧⣱⣄⠀⠈⢳⣄⠙⢦⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀ ⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣿⣿⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣹⣚⣢⡴⠒⢿⣷⡌⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢻⣿⣿⠇⠀⠀⠀⠀ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣇⣿⣿⣿⣧⣧⠀⡀⣿⠀⠀⠀⢀⣴⣫⠔⣠⣶⣿⣿⡋⠉⠙⣧⢴⣤⣹⣿⣦⣌⡑⠯⣻⣿⣿⡿⣿⣿⣿⡀⡄⠈⢻⣿⠀⠀⠀⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⠸⣿⡄⠀⠰⠟⠑⠛⣻⠿⣋⠿⠟⠛⡆⠀⠋⠘⡆⠈⣿⢛⡟⠿⢷⣾⠿⠿⠀⣿⣿⣿⣷⡼⡄⠀⢻⠀⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢹⢸⣹⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⡆⢺⣲⣼⣀⠀⠀⣷⠀⣿⣾⡇⠀⢸⣟⣀⡇⢠⣿⣿⢿⣿⡿⣷⡄⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⢸⡌⣧⡙⠷⠹⠝⠛⣛⣻⣭⣯⡉⣝⢷⡀⠀⠀⠀⠀⠀⠸⣄⣠⠼⠛⠁⠀⠀⣿⢠⠇⣿⢃⠀⢸⣿⠋⣠⣿⣿⣿⣿⣿⣿⣽⣷⡀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢸⡇⣿⣿⣿⠃⠺⣾⡟⠻⣏⠻⡿⡌⠙⠳⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡏⠀⣼⣏⡿⠀⣼⣿⣾⣿⣿⣿⣼⡇⢻⣿⣷⣽⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⢳⠸⣿⣿⡷⠾⢿⡀⠀⢿⠂⣇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣰⣿⣿⠃⣼⣿⣿⡿⣿⣿⣿⠏⠀⠀⣻⣿⡷⠿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣾⣿⣸⡄⢻⣿⣿⣾⡄⠙⠀⠼⠶⠊⠀⠀⠀⠀⢀⠴⠲⢄⡀⠀⠀⠀⠀⠀⢠⣧⣼⣿⠛⣳⣷⣿⡟⢉⡿⠘⢿⠋⠀⠀⠀⢹⢻⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠸⠟⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⣾⡏⠀⠀⠀⠙⣄⠀⠀⠀⠠⠛⢁⣿⠏⣰⣿⣿⡟⠚⢻⣿⣌⠙⢷⣤⠀⠀⠈⣇⠹⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠁⠈⠙⠿⣿⣾⣿⠀⡄⠘⢩⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⠟⣰⣿⣿⣿⠃⠀⣼⠃⠸⠷⣜⡆⠀⠀⠀⠘⣆⠙⣟⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⢰⡇⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡞⣰⣿⣿⡏⣽⡇⢀⣧⣤⣶⣤⡉⢧⠀⠀⠀⠀⠘⣦⠈⢿⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣫⠃⡇⢰⢨⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡸⠀⠀⠀⣰⢳⣿⠟⠋⢘⣽⠁⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠳⣜⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⢳⣾⡇⣿⣿⣿⣿⡳⣄⡀⠀⠀⠀⠀⠈⠳⢤⣀⡴⠃⠀⠀⢀⣿⣾⠏⠀⢀⣾⣟⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠚⠛⠛⠒⠤⢬⣳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⡛⢇⠘⣽⣿⣹⣿⣿⣿⣷⡀⠉⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⣀⣴⡾⣿⠛⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⢀⣤⡞⠀⢸⡀⣏⢿⣯⢿⣯⣿⣿⣧⠀⠀⠀⠀⠈⠉⠓⠲⠤⠔⢊⣽⣿⣇⣿⢀⣾⣯⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆ ⠀⠀⠀⠀⠐⠊⠁⠀⠀⠠⠞⠉⣾⠀⠀⢸⡇⢻⣿⣿⣯⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠿⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⡇⣸⡟⣦⡈⢿⣷⣿⣿⣿⡆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣸⣤⣀⣙⠲⠦⠤⢤⠤⠀⠀⠀⠀⠀⠐⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⡇⢹⠁⣿⣿⣦⣽⣿⡏⣿⣼⠀⠀⠀⢀⣿⣿⣿⣿⣏⡹⠿⠟⠋⠁⢀⣤⡤⢤⣴⣖⣿⣿⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⣃⣤⠖⠚⢤⡉⠻⣿⡇⣿⡟⡇⠀⠀⣸⣿⣿⣿⠟⠁⢀⣠⠔⢲⡶⢋⡥⠖⠉⠀⠉⠉⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣚⡽⠉⠀⠀⠀⠙⡆⣽⠁⠈⠁⠃⠀⢰⣿⢉⢻⠇⠀⡴⢻⢁⡴⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡏⣳⣄⣙⣅⠀⠀⠀⠀⠀⡇⣿⣿⣿⣶⣶⣶⣶⣶⠶⣾⢀⠎⣠⣴⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠗⠋⠙⠁⠀⠀⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣼⣿⣧⣄⠈⠁⠀⠀⠉⠉⠁⢠⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣿⣿⡣⠂ ⠀⠀⠀⠀⠀⢠⣎⣥⣤⣤⣤⣤⡝⣦⠤⠤⢤⣤⣤⣀⣀⠀⠀⠀⢘⣶⣶⣍⣿⣣ ⠀⠀⠀⠀⠀⣀⡴⠛⠉⣠⠔⠋⠉⠉⠙⠂⠁⠀⠀⢀⠈⠛⢦⡀⠀⠻⣉⣷⠽⠅ ⢠⡤⠤⠔⢚⡅⠀⠀⡜⠁⠀⠀⠀⠀⢶⠢⡀⢠⢴⠂⠁⠀⠀⢳⡄⠀⣿⠃⠀⠀ ⠈⠓⢦⡴⠋⢀⡠⠎⠀⠀⠀⠀⡀⠀⡧⠔⠽⠷⠦⣇⠀⢠⠀⠀⢈⠛⠒⣲⠀⠀ ⠀⠀⣸⡓⠚⠉⠀⠀⠀⢀⡀⠀⡇⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠻⡏⠁⠀⠀ ⠀⢀⠏⠉⠙⣻⠋⠁⠀⢸⠀⠀⡷⡀⢣⠀⠀⠇⠀⢸⠀⡜⣇⠀⢆⠀⢷⠀⠀⠀ ⠴⠋⢀⡀⠀⡇⠀⠀⢠⠏⠀⡘⠒⠓⢌⣧⠀⠀⠀⣿⠞⠁⠈⡄⠘⡀⡸⠀⠀⠀ ⠲⠒⡿⠁⠀⡇⠀⣠⠏⢀⣼⣤⣤⣄⣂⠀⠀⠀⠀⣨⣤⣤⣤⣼⡄⠱⡇⠀⠀⠀ ⣠⠞⠁⠀⣀⡧⢒⣁⡴⡯⠉⢏⠙⢟⡏⠀⠀⠀⠀⢹⡿⢋⡏⠉⡿⡢⢭⠆⠀⠀ ⠦⣤⣤⡾⢱⡉⢏⠀⢆⠱⣄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢦⢿⢸⠀⠀⠀ ⠀⠀⠀⠙⠉⠳⣮⢧⡀⢫⣏⠥⢤⡀⠀⠀⠀⠶⠂⠀⠀⣠⣤⣠⣇⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢧⢴⣟⣦⣹⣶⣶⣿⣦⣤⣤⣤⣤⣴⡾⣿⣿⠒⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⢪⡿⢡⣟⡉⣽⣿⢟⣟⠿⣾⡿⢿⣝⡿⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡀⡟⢇⠠⠿⢛⣿⣀⣠⣍⣿⣥⣺⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⣁⣀⣀⣀⡈⠉⣇⡔⠣⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⢓⠞⣉⠀⢄⡤⠀⠈⠠⠃⠀⠄⡀⢀⠀⡈⠱⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢎⠉⠉⣰⠗⡩⢄⡝⠉⠀⠀⡝⠀⠄⠁⡐⠀⢆⠐⠀⢁⠀⢳⡀⠀⠀⠀ ⠀⠀⡀⢨⠛⣺⢋⡜⣡⠏⠀⠠⠁⢸⠀⠈⠄⠁⠄⠈⠘⡄⠀⠂⠄⠂⢧⠀⠀⠀ ⠀⢸⣝⡻⡹⢆⠯⣴⠇⡐⠈⠄⡁⢾⠀⠀⠈⠀⠄⠂⠀⡇⠐⠈⠠⠐⠸⡄⠀⠀ ⠀⠀⢾⣵⣻⣞⡵⠚⠠⢀⠁⠂⠄⣿⠀⡀⢂⠐⠠⠈⠄⡇⢀⠁⡆⠁⠄⢉⠒⣤ ⣀⣀⡼⣞⡽⣤⣤⡴⠃⠄⠌⢂⢰⠟⣆⠐⠠⠈⠄⠡⢰⢻⣀⠈⣇⠈⡐⢦⡤⠃ ⠹⣯⣽⡾⣵⠷⢊⠡⢈⡰⠞⡩⠋⠉⠸⡄⠡⠘⡆⢑⡏⠁⢧⠀⠸⡄⠐⡈⠦⡄ ⠀⠯⣳⣻⣦⣤⡦⠶⠯⣵⣿⣶⣶⣮⡕⢈⣧⡐⠹⣾⣴⣶⣶⣿⠤⢽⣆⣐⠴⠃ ⠀⠀⠀⠈⢷⡍⡇⢰⠂⣏⠀⢷⡛⣿⠀⠙⠒⠉⠓⠻⣛⡷⠃⡹⢠⠆⡇⠀⠀⠀ ⠀⠀⠀⣀⠀⢣⡸⡌⠳⢬⠆⠠⢀⠀⠀⡀⣀⣈⠀⢀⠀⠠⢀⢙⡇⣼⠁⠀⠀⠀ ⠀⠀⠀⢣⣉⣉⠻⣟⣤⡉⢦⣅⣀⡀⠀⠀⠻⠃⠀⢀⣈⣠⣴⢋⣴⡃⠀⠀⠀⠀ ⠀⠀⠾⣉⣡⠦⢛⣽⣳⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⡟⡎⠜⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⡏⢰⠏⠈⡾⠛⠿⣦⠙⡓⢾⣿⣿⣿⣟⡾⢿⡟⣿⣿⣶⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⠃⠀⠸⠦⣝⣰⠈⣿⠿⠿⣻⣿⣿⣿⣿⢿⣭⠿⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⠐⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠓⠒⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⣿⢿⠈⢻⣆⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠻⢯⣉⠛⠉⠉⠉⠁⠀⠀⠀⠀⢨⣽ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠗⠈⢿⣶⣾⡿⠃⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡿⠁⠀⠀⣠⠖⠛⢉⣯⡉⠙⠳⢦⡀⠀⠀⠀⠀⢀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⣶⠰⣼⡟⠀⠀⢠⡞⠁⠀⠀⢸⣿⡇⠀⠀⠀⣿⠀⠀⠀⢠⡟⠉⠀⢹⣯⠛⢦⡀⢀⣴⣾⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣸⠟⠀⠀⠀⠈⣧⡀⠀⠀⠈⣿⢃⣠⡴⠞⢁⠀⢀⡀⢈⣧⡀⠀⢸⣿⠀⠀⢹⣼⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠁⠀⠀⠻⠶⠿⣷⡾⠋⡙⢦⣜⡛⠀⠀⣰⠏⢻⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣷⣶⣿⡁⠀⡈⠉⠻⠟⠁⠀⢸⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠈⢹⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡇⣿⡿⣶⣿⣟⣿⣿⡿⠟⠋⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣷⣄⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣙⢿⣿⠿⠯⠤⢤⣀⣀⣀⡴⠮⠋⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⡏⠉⠀⠛⣷⣄⡀⣺⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣀⣀⠤⠤⠈⠉⠁⠀⠀⠀⠀⣆⠀⠀⡀⠀⣤⡀⠀⠀⠹⣤⣀⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⢿⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠚⠋⠀⠀⠀⠲⢤⣄⡈⢙⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⢾⣷⣄⠈⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⠿⣿⣾⣽⣿⢿⣶⣄⣀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣶⣾⣿⣿⣟⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣿⣿⣁⠀⠀⢈⣙⣙⣻⢷⣿⣿⣦⡀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣣⣾⠟⠛⠛⢿⣿⡿⣿⡿⣿⣿⢿⠙⠙⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⡏⠀⢀⣠⣿⡿⠗⢾⡷⠶⣿⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣰⣟⢛⣭⡉⠀⠀⣹⠀⠀⠘⠿⣤⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⠓⠲⠤⣤⣤⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣟⡻⠶⣿⣷⣶⣿⣤⣤⣤⣤⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠓⠲⠤⢤⣤⣤⣄⣀⣬⣯⣿⣿⠉⠉⢻⡛⠛⠛⠛⠻⠿⠿⠿⣶⣶⠿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⡆⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⡟⠛⠛⠒⠶⠶⠶⠶⠶⣶⠊⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠖⠒⢻⡟⣻⡏⠉⠑⠒⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⣖⣿⡇⢫⣛⣶⡶⠶⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠖⠋⠙⠋⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢫⠁⠀⠀⠀⠀⠈⣲⣲⠂⠀⠈⠢⣀⣀⠀⠀⠀ ⠀⠀⢠⠃⠇⢀⠀⡇⠀⠀⡸⡉⠙⡧⡀⢀⢀⣀⡼⠀⠀⠀ ⢰⡊⠁⠞⢠⠇⠼⢡⠀⠀⠧⠐⢄⢣⠀⠀⢂⠈⠓⡲⠀⠀ ⠀⠉⢹⠀⢸⡾⢲⣶⡛⣦⡗⢻⣿⡻⠀⠀⢸⠙⡍⠀⠀⠀ ⠀⠀⠈⠀⢸⡆⠘⠻⠃⣍⡀⠘⠛⢀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⢰⣢⠀⢻⣶⣦⣼⣬⣷⣶⡞⢃⡀⠐⡮⣾⡤⡄⠀⠀ ⠀⠀⠀⢉⣱⡶⢯⣚⣟⡛⠽⠧⠀⠯⢤⡒⠳⡉⢂⡻⣹⡟ ⠀⠀⠀⢸⢸⠧⢼⠥⣀⡀⠀⠀⠀⠀⢀⠛⡷⢇⣁⠭⣁⠀ ⠀⠀⠀⠘⣍⠽⣤⠥⠬⣰⣤⣄⡀⠰⠥⣔⠣⠤⠤⠔⠊⠀ ⠀⠀⠀⠀⠀⠀⢸⡉⠉⡗⡌⠙⠙⢄⣀⠼⣄⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢩⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⡀⡢⢯⠑⡀⣆⣬⠣⠞⠖⣨⣉⣣⠩⠀⠈⠀⢿⣴⡉⠟⣿⣻⣽⢿⣿⢫⠛ ⠀⠀⡀⣿⢲⠤⢷⠥⣼⣀⣀⣄⠳⣜⣠⣀⣄⣧⣾⡽⣾⣟⣟⣿⣴⣀⣀⠁ ⠀⠀⠀⡆⢹⠀⠁⣌⠑⠉⠉⠛⡙⢩⠈⠟⡿⣿⢿⣿⣶⣿⣯⣾⢶⣤⣤⣠ ⠀⠀⠀⠀⡇⣰⢀⠋⠶⣷⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⣿⣿⣿⢚⠙⠛⠛⠾ ⠀⠀⠀⠁⡖⠥⡪⠁⠟⠿⣿⣿⣿⣿⣿⢻⣹⢮⡻⣖⢿⠿⣯⣟⣙⠈⠀⠀ ⠀⠀⠀⡼⠌⢀⠃⢫⡴⣠⢀⣀⣅⣦⣷⣿⢿⣦⡜⣻⢶⣽⢿⣯⣿⣷⣬⣤ ⠀⠀⠄⢸⢀⠀⡏⢀⠀⠄⡶⢠⠀⠀⠀⣄⡽⢺⣇⣺⣽⣳⣻⢻⣽⣿⠛⠛ ⠀⠀⠀⢇⠀⠀⣿⠇⢿⡘⠀⠀⠀⡟⣷⢿⡇⢿⡀⢾⣳⣽⢾⡽⣾⣿⢀⠉ ⠀⠀⠁⡚⢰⠀⣽⡻⣿⣿⣮⠳⠉⣯⣿⣿⡽⣾⠀⣟⣟⡯⣾⣟⣯⣜⣤⣠ ⠀⠀⣲⠑⠈⠀⣹⢄⡙⠉⢸⠀⣄⠹⢉⠋⡴⢸⡀⡝⣻⢶⣻⢷⣻⣿⠿⠶ ⠀⠀⠀⡗⢏⠀⣧⠙⡀⠿⢀⠀⠀⡆⠾⢀⡇⢀⠀⡿⣳⣼⣻⣿⣹⢉⠃⠛ ⠀⠀⠀⠀⡄⠽⣦⣿⣠⡇⠀⠀⠀⠀⢸⠁⢰⠀⠇⣭⡾⣟⣯⠾⣠⣀⣀⠀ ⠀⠀⠀⠀⠀⡀⠳⡌⠣⡄⠡⠀⠀⠀⠀⠀⠀⠋⢧⡎⣓⢮⣴⠆⠲⡒⣴⣤ ⠀⠀⠀⠀⠀⠀⠉⣋⠾⠛⡿⠹⠈⠀⠀⠁⡍⣋⢛⠷⣻⠛⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡙⣠⣤⣟⢺⣿⣯⣴⣥⣶⡼⣷⣭⣻⡿⣟⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⢲⡤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠔⠉⠁⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢀⡔⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⢀⡎⢀⠆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⡇⡜⠀⡸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠦⠀⠀⡜⢸⢠⠃⠀⡇⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡀⠀⠀⠀⠀ ⠀⠀⡔⢾⠃⣼⢸⠀⢸⡇⠀⠀⠀⢸⠘⡄⢠⠀⠀⠀⢷⠀⡄⠀⠀⠱⡀⠀⢠⡀ ⢀⠀⠀⣾⠀⢹⡆⠀⢸⡇⠀⠀⠀⠸⡤⠼⡜⡄⠀⠀⢰⢳⣱⡀⠀⠀⠱⡀⣈⠃ ⠀⠁⢀⠁⢣⣼⡗⠒⣈⣘⠒⠒⠒⠒⣃⣀⣈⣹⡖⠒⣏⠜⠁⢸⠀⠀⣀⡡⠁⠠ ⠀⠀⠈⠢⣒⡿⡷⢄⠀⠑⢄⠀⠀⠀⠉⠁⠀⠀⠀⠀⣁⡀⠤⠜⢀⢜⠟⠁⠀⠀ ⠀⠀⠀⠈⠁⢠⣷⡀⠈⠢⢄⠲⠒⠄⠀⠀⠀⣀⣠⣖⡁⠤⠐⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣏⡐⠠⠤⡵⡄⠐⣲⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡖⡟⡅⣰⢿⠯⣿⢋⣬⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⠉⠉⣻⣿⣿⣿⣿⠟⠟⠒⠚⢓⠖⣰⠌⠉⢹⣿⣿⠗⠀⠀⠤⠤⢄⠀⠀⠀ ⠁⠀⠀⡐⠀⠉⠉⠙⠒⠂⢠⠃⠒⠚⠋⠓⠠⠐⠊⠉⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡌⠛⠷⣦⣄⣤⣤⡶⢤⣤⣄⣴⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣦⡄⠀⠉⠁⠀⣿⠀⠀⣿⣿⣿⣿⠋⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⠛⠁⠀⠀⠀⢀⣿⠀⠀⣿⣿⡿⣿⣷⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⢻⣿⣿⣱⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢀⣴⣾⠋⠀⠀⠀⠀⠻⣿⣿⣯⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢾⣿⣴⣤⣤⣤⣀⣼⣿⡿⠀⠀⠀⣀⡀⠀⠸⢿⡿⣿⣿⣿⣴⣶ ⠀⠀⣰⣶⣦⠀⠀⠀⢻⣶⠾⠾⠟⠉⠀⠀⠀⠀⢠⣼⣿⣻⣦⠄⠀⠀⠀⣹⡿⠾⡟ ⠀⣼⡏⠀⣹⡇⠀⠀⠀⠙⢳⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⡾⠋⠀⠀⠀ ⢰⣿⠠⠔⢻⡇⠀⠀⠀⣠⡿⠉⢙⠻⠶⣤⣤⣀⣀⣀⣀⣤⡴⠾⠛⣿⡀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⠃⠀⢀⣾⣿⣼⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢼⣇⠀⠀⠀⠀ ⠘⢻⡆⠀⢸⡇⢠⡾⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀ ⠀⠀⢿⣄⠈⣿⣾⠃⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣄⣤⡀⠀⣸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠀⠀⣾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⣿⠀⢀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠶⠶⠷⠶⠶⠾⠷⠶⠿⠻⠷⠾⠟⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⡿⠋⠉⠁⢠⣿⠏⢁⣿⣿⣿⠏⠉⢸⣿⡏⠉⢻⣿⣿⡇⠈⠙⢿⣿⣿⣿⣷⡆⠀⠀⢇⠢⣈⡒⡤ ⣿⣿⣿⣿⣿⣏⣴⡇⠀⠀⠀⢠⡿⠋⠀⠀⠀⣰⣿⠋⠀⣼⣿⣿⠏⠀⠀⡾⣿⠁⠀⠀⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣄⢀⣿⣷⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣿⠇⠀⢰⣿⣿⡷⠀⣀⣜⣁⣻⣀⣀⣀⣸⢻⣿⡇⠀⠀⠀⠘⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⣿⡿⠛⣩⣿⠿⠛⢻⡏⠉⠉⢹⠉⢿⣿⡀⠀⠀⠀⠹⣿⣿⡆⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⡟⠀⠀⠀⢀⣾⣿⠀⠀⣸⣿⡿⢥⣶⠝⠁⠀⠀⠀⡇⠀⠀⡜⠰⡀⢻⡇⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣿⡿ ⣿⣿⢿⣿⣿⡃⠀⣼⣿⣿⡇⣀⣀⣤⣾⣿⡇⠀⠰⣼⡟⣠⠎⠁⠀⢀⣠⠔⠁⢹⣀⣠⣧⣶⣦⣤⣷⣤⣤⣠⣤⠼⣿⣿⡆⠀⢹⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣏⣁⣼⣿⣿⣿⠀⢠⣾⣟⡔⠁⠀⠀⠀⢸⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣇⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣟⣹⣿⣿⣿⡿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣾⢟⣻⡿⠛⢻⢋⣻⣏⣱⠞⠙⣄⡀⠀⣿⡽⣿⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡅⠚⠋⠉⠁⠀⠀⠀⠀⣔⣾⢏⢦⢄⣿⣧⣿⡆⠀⠈⣿⣿ ⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⢻⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⢂⢻⣿⣿⣿⡇⠀⠀⢽⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⣠⣾⣟⡖⢻⣿⣿⠃⠀⠀⣿⣿ ⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⠟⣻⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⠛⠉⠁⢰⢸⣿⡿⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠰⢟⣿⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⡇⣿ ⣿⣿⣿⣿⣿⣿⣏⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢾⣿⡟⠀⠀⠀⣼⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⠏⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣡⣴⣾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⠏⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠤⠚⠚⠉⠉⠉⠙⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⢽⣿⠿⠋⠉⠁⠀⢠⡆⢰⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⢠⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠇⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠈⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡗⠤⣀⠀⠀⠀⠀⠀⠑⢄⣀⡞⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠹⢇⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⣷⣦⣤⣀⡀⠀⠉⠀⠀⠀⣀⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠈⠳⣄⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠠⠎⣉⠀⢀⠉⣢⠄⠒⠈⠙⠉⠐⠂⡤⠔⠒⠐⠒⠠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠄⢈⠜⠉⠀⣠⡤⠀⠀⠀⣤⡄⠀⠐⠧⡀⠉⠂⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⣈⠖⠁⠀⠀⢀⠈⠀⠀⠃⠀⠀⡄⠀⠀⠀⠈⢲⡆⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⠳⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠇⢀⠀⠀⡃⢀⠀⠢⡙⢦⡀⠀⠀⣡⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⢀⠌⠰⢀⠞⠰⠀⡀⠀⠌⠀⣓⢄⡐⡌⢶⡀⠀⠈⡀⠀⠀ ⠀⠀⠀⠀⢃⠀⢩⣠⣶⢿⣻⣿⡧⣴⣄⣰⣴⣾⣳⠾⣿⣘⣗⡀⠀⡇⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⡉⣇⠈⠣⠫⠃⣸⠀⣇⠸⠙⠹⠁⢩⢉⡿⠁⢠⠁⠀⠀ ⢠⡨⠈⠘⢿⠀⠀⠑⢼⠆⠀⠀⠀⠁⠀⠟⠢⠀⠀⢤⡞⠋⢀⣴⡟⠰⡀⠀ ⠀⢃⠆⠀⠀⠑⡀⢆⢠⡙⡄⠠⣤⡀⠀⢠⣤⡐⠠⠋⣠⠔⣫⠏⠀⠀⢰⡆ ⠀⠀⠉⠀⠀⠀⠘⠈⢢⠑⢬⠙⠻⠧⢤⡬⢗⠫⠙⠊⡼⠀⠀⠀⠀⠀⡞⠀ ⠀⠀⠀⠀⠑⠢⢀⡁⠀⠑⢌⠂⠡⠒⠣⡈⡁⢖⡒⡠⢅⢀⡠⡢⠒⠉⠀⠀

⣷⣶⣶⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠣⡀⠙⢿⣷⣻⣿⣴⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡄⠠⣿⣿⣿⣿⣿⣿ ⠙⢿⣿⣿⡟⠁⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢣⠻⣿⣿⣿⣿ ⣤⣾⣿⡟⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡰⢻⠁⠀⢀⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢇⠹⡀⠀⠀ ⣿⠋⡜⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠀⣠⠞⠁⡜⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠱⡄⠀ ⢁⣰⠁⢠⠇⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⡶⠊⡠⠚⠙⠛⠶⣧⣄⡸⠀⠀⡇⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣠⢶⠀⢸⠀⠀⡇⠀⠈⢦ ⠉⡏⠀⡎⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⡷⡊⢠⠀⠀⠀⠀⡏⠻⣷⡄⠀⡇⠀⠀⠀⡜⠀⠀⠀⠀⣠⣶⢰⠇⢸⣤⣿⠀⠀⡇⠀⠀⠘ ⣰⠇⢰⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠲⢶⣷⠿⢿⣿⣷⣶⣶⣿⣦⡉⠁⠀⢳⠀⣠⠎⠀⠀⢀⡤⣶⣻⣿⢸⠀⠘⡿⡟⠀⠀⡇⠀⠀⠀ ⠁⠀⡎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣏⡖⢺⡻⣿⡛⢿⡿⣄⠀⣸⠖⢁⣀⣤⠞⠁⢀⠇⠀⡝⢸⠀⠐⢇⠘⡄⠀⡇⠀⠀⠇ ⠔⠺⡇⠀⢠⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠉⠚⠤⠽⠁⠈⢳⠐⠚⠛⠉⢹⣰⠃⠀⠀⡿⠀⠀⡇⢸⠀⠀⠈⠀⢸⠀⡇⠀⠀⠀ ⢀⣀⡇⠀⡎⠀⠀⠀⢁⠀⠀⠀⠀⠀⢣⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣦⣴⡄⡇⠀⢀⡇⡆⠀⠀⡰⠀⣿⢠⠃⣀⠀⣠ ⠉⠉⣧⣸⠀⠀⡆⠀⠘⡆⠀⠀⠀⠀⠀⡗⢄⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣿⡇⠀⢸⣾⠀⠀⢠⠇⠀⣿⡞⡀⠘⣄⠃ ⠀⠀⢹⡟⠀⠀⡇⠀⢀⠘⡄⠀⠀⠀⢆⢡⠀⠉⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⢧⠀⠈⢣⠀⠘⣷⣤⣤⣸⠀⠀⡇⣷⠋⠑⠚⠳ ⠀⠀⠀⣿⠀⢠⢷⠀⢸⡄⠘⢄⡀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡄⠀⢸⠀⠀⠀⢸⣿⡏⠀⠀⠁⡞⠀⠀⠀⠀ ⠀⠀⠀⣿⢀⡇⢸⢧⣸⢣⠀⢸⢿⠢⠤⠤⠬⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⡄⠀⠀⢸⣿⡇⠀⠀⢸⣁⠀⠐⠢⣀ ⠀⠀⠰⠁⢿⠀⢸⠀⠉⢈⢧⠸⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠉⠀⠀⣾⣿⣇⠀⠀⣸⠀⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⡞⠀⣠⢋⣀⣟⠇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⣦⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⣼⡵⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⢸⡇⠀⢤⡄⠀⠀ ⠀⠀⢀⠄⠀⣸⠛⠁⠀⢀⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⣿⣿⢿⣿⡇⡾⣇⠀⣿⣷⢠⣠ ⠀⢀⠎⠀⢀⠇⠀⠀⠠⠚⠁⣼⠤⠤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⢀⣾⣿⡏⠈⣿⣿⣗⢿⣵⣿⣿⣿⣿ ⡶⠃⠀⠀⡞⠀⠀⠀⠀⠀⢰⢹⠀⠐⠒⠮⣍⠒⢤⡀⠀⠈⠳⢄⡀⠀⠀⠀⢀⣀⣤⣶⠋⠁⢈⣿⣿⣿⡟⠀⠀⢸⣿⣿⢴⣿⡿⣿⣿⣿ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠇⡾⠒⠓⠒⠲⠤⢽⣦⡙⢦⡀⠀⢀⡙⢳⣶⣾⣿⣿⣿⣿⡇⣸⣿⣿⠛⠋⠀⠀⠀⠀⠻⡇⠀⠈⠙⢿⣿⣿ ⠀⠀⡼⠁⠀⠀⠀⠀⢠⠎⠀⣧⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣦⠎⠱⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢻⡷ ⣤⠞⠀⠀⠀⠀⠀⡠⢃⠄⠀⡿⢯⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢴⣦⠌⢻⡟⠛⢻⣿⣿⠛⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧ ⠁⠀⠀⠀⠀⠀⠀⣡⠊⣀⠔⠁⠈⢿⣿⣿⣿⣿⠛⠉⣡⣿⣦⣈⣿⢠⣿⣿⣿⣿⣿⡿⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣿⣤⣨⣿⡀⠀⠀⠉⠙⠷⣤⠀⠈⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠉⠉⠉⠉⠉⠛⠒⠦⣤⡀⠀⠈⢻⣆⠀⠹ ⠀⠀⠀⣴⢶⣶⡶⠖⢋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⣿⣠⡤ ⠀⠀⠀⣻⠦⢀⣠⣴⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀ ⠀⠀⠉⠀⢰⣿⣿⣿⣇⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣷ ⢧⣀⠀⠀⢸⣿⡿⠟⢋⣴⠋⣸⠁⠀⠀⠀⠀⠀⠀⣴⢻⡶⡄⠀⠀⠀⠀⠀⠀⠘ ⠀⢨⠃⠀⡿⠋⢀⡴⠋⠀⢀⡟⠀⡀⠀⠀⠀⣹⣾⣅⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⣰⠏⣀⡀⠀⢸⢷⡾⠁⣀⣤⠾⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠁⠀⠀ ⡇⠀⠀⠀⣰⠏⣾⣿⣿⠀⠀⠘⠓⠛⠉⠁⢀⣴⣶⣄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠙⠛⠋⠀⠀⠀⠀⠀⢀⠀⠺⣿⣿⡿⠂⠀⡟⠁⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⠶⠶⡶⣾⠋⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢸⣍⣻⣶⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⡇ ⠀⢰⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠈⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠟⠙⠿⠋⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡞⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣴⠶⠶⠟⣛⣛⣛⣛⣛⣛⣻⠶⢶⣦⣤⣤⣶⣶⣾⣿⣿⢿⡿⣿⡻⢶⣣⡽ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣭⡵⣭⣳⣽⢿⣿⡿⣟⡿⣭⢷⡶⣛⡿⣻⣭⣻⣭⣯⡽⣹⡞⣽⢯⡞⣽⣫⢟⣻⢿⣷⣿⣻⣽⣳⢽⣫⢷⣹ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡼⣳⢳⣧⣿⣻⡭⣟⡵⣯⠽⠞⠃⠉⢉⢀⣀⣀⠀⠀⠀⠉⠉⠓⠻⠞⣧⢯⢯⡽⣞⢮⢯⣟⡷⣽⡞⣧⢟⣧ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣾⡽⢯⡽⣎⡷⡽⢚⣩⡴⢖⣚⡛⣹⡩⠯⠉⠉⠛⠙⠛⠛⠒⠶⠤⣄⡀⠉⠓⢿⡼⣫⢷⣹⢾⣹⡽⣞⡽⣺ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⣾⡳⣽⢫⢷⠝⣡⠞⠋⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⡉⠻⣞⢧⣯⢳⡽⣎⡷⢯ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⡷⣝⣧⡿⣡⠞⠁⠀⠀⠀⠀⣜⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢻⡼⣏⢷⡻⣼⢯ ⠀⠀⠀⠀⠀⠀⣾⣿⣹⢟⣵⣾⠞⠁⠀⠀⠀⠀⠀⣜⡿⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⢦⡙⣞⢯⣳⢯⣞ ⠀⠀⠀⠀⠀⢰⣿⡏⣯⣟⣾⠋⠀⠀⠀⠀⠀⠀⡸⣽⡇⢀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢳⡌⢯⣗⢯⣞ ⠀⠀⠀⠀⠀⢼⡿⢸⣧⡿⡁⠀⠀⠀⠀⠀⠀⣰⣿⣹⣧⣸⠀⠀⠀⠀⠀⠀⠀⣧⣠⣄⣀⣀⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⢻⡜⣞⡯⣞ ⠀⠀⠀⠀⠀⣾⣧⡿⢋⡺⠁⠀⠀⠀⣠⠴⣻⠟⢱⢹⡇⢻⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠈⠉⠙⢺⣇⡀⠀⠀⠀⠀⠀⠈⡆⢻⣼⣳⢯ ⠀⠀⠀⢤⣼⣟⣍⣦⠟⠁⠀⠀⠀⠐⣡⡾⠋⠀⠘⡌⣷⢻⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⢸⣷⠈⠢⠀⠀⠀⠀⠀⢹⠸⣷⢟⡾ ⠀⠀⠀⢠⣿⢯⣿⠋⠀⠀⠀⠀⢠⡞⠃⠀⠀⢀⠀⡘⠼⣿⡷⣄⡀⠀⠀⠀⠀⠈⣧⠻⣦⠀⠀⠀⡸⢾⠀⠀⠀⠀⠀⠀⠀⠸⡀⢽⡾⣿ ⠀⠀⠀⣾⢯⣿⠃⠀⢀⠀⠠⠀⣼⢦⣠⣴⣾⣭⣯⣭⡇⠈⢻⣌⡛⠳⠶⢤⣄⣀⣹⣟⣚⣻⣦⡤⣃⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⡝⣷⣿ ⠀⠀⣸⣯⣿⡏⠀⣠⡇⠀⠄⢳⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠈⠉⠉⠒⠒⠣⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⡆⠀⠀⢀⠀⠠⡇⢻⣼⣿ ⠀⣰⡿⣼⣿⣧⢫⣱⠃⠠⠀⢀⣿⢋⠍⠤⢂⠦⠂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠤⡉⡉⢛⢻⡿⢿⠋⡆⠀⠀⠄⡀⢸⠁⡈⣿⣿ ⢰⣿⡳⣿⣽⢿⣷⡞⢰⠀⠁⣾⡇⡊⠤⠑⠂⠠⠁⡀⠄⠲⢧⣀⡠⠶⠤⠶⠞⠋⢀⠐⡐⠠⠉⢆⣾⠃⢀⡜⠇⠀⢈⠀⡀⡾⠀⠄⣿⣿ ⣿⡿⣱⣿⣯⣿⡿⣁⢾⠀⢁⢻⣧⡀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣁⣬⣾⡯⡚⢥⠻⠀⢀⢂⠀⣰⠇⢈⠀⣿⣿ ⣿⣷⡝⣿⣿⣷⣦⡷⣿⠀⠠⢸⣙⢻⣦⣄⣀⣀⣂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣚⣴⠟⣜⠩⡖⠁⡀⢂⡼⣰⢿⡀⢀⣼⣿⣿ ⠈⢻⣿⣼⣯⣿⣽⣿⡿⣧⣀⠈⢮⠹⣟⠛⣛⢛⣛⣛⡛⠻⠿⣷⡿⣿⣿⣿⡿⡿⣷⢷⣾⣽⣷⣾⣶⣭⣴⣶⢾⠿⣛⢭⣿⣷⣿⡿⣟⣾ ⠀⠀⢈⣿⡿⢛⣥⣿⢃⣼⠿⣷⠾⣷⢿⡿⣝⡯⣞⡽⣛⣷⣱⣿⣿⣿⢳⢧⣻⡵⣏⡿⡼⢶⢯⣝⡻⢿⣿⣿⣦⣷⣾⣻⣾⢿⣽⣻⢿⣽ ⢀⣴⡿⢋⣴⣿⣿⡏⣾⣝⣻⡼⣻⡝⣮⢟⡾⣱⢯⣳⢟⣼⣿⣿⢯⡷⣏⣟⡶⣏⡷⣽⣹⣛⣮⢏⣟⠷⣮⡙⢿⣟⡿⣿⣯⣿⢯⣿⢯⣿ ⣿⠟⣰⣿⢫⣿⣾⣗⢯⡞⣵⣏⡷⣽⢫⡾⡽⣭⢷⣯⡿⣻⣿⣟⣿⢿⣼⣣⢿⡜⣷⣣⢯⣳⠽⡾⣭⢟⡾⣹⢷⣍⠻⣷⣟⡿⣿⣯⣿⣻ ⢃⡾⢿⣜⢯⣿⢾⣿⣣⣟⣳⢾⣱⢯⣏⣷⣻⣾⣟⠟⣽⢯⣿⣿⣯⡿⣷⡽⣺⠽⣖⣯⢳⣏⠿⣵⣛⡾⣹⡽⣎⣟⡷⣜⢻⣿⣽⣻⡾⣿ ⣸⢻⣝⡮⢯⣿⢿⣽⣷⢯⣾⢷⣻⣾⢯⣿⣽⠗⣍⣾⢟⢺⣿⣞⣿⣽⣟⣿⢯⣛⡷⣚⣯⢞⣻⡵⣫⣞⢷⣹⡽⢮⣝⢯⣧⡹⣷⡿⣽⣿

⠀⠀⠀⠀⡠⠞⠁⠀⡀⢀⠀⣰⠏⠤⢿⡇⠈⠉⠛⠿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠖⠁⠀⠠⠐⠀⢠⡼⠃⠀⠀⢸⢇⡀⠐⢠⠀⠈⠑⠿⣦⡀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠌⢀⣀⡤⠿⢤⣀⣀⣠⠞⢈⡇⠀⠈⡷⠀⢀⠀⡉⠙⠛⠓⠶⠢⠦ ⣶⠁⠀⠄⠈⢀⡖⠋⢀⠂⣀⠈⣹⠃⠀⢸⡇⠀⠀⠸⡇⢠⡀⠐⢆⠀⠂⠀⠄⢀ ⡇⠀⢀⠂⣠⠟⠀⠐⠀⢀⡤⢲⡟⠀⠁⣿⠇⠀⠂⠀⣿⡄⢳⡀⠈⢷⡤⠖⡚⠉ ⠐⡤⢂⢠⡏⢀⠈⠐⢈⡼⣡⣿⣃⡀⣼⢫⡇⠐⠂⠀⣹⡽⣄⠹⣆⠈⣇⠀⣰⣾ ⢆⡀⣼⡟⠀⠀⡐⠈⣼⠧⠟⢧⣔⣻⠁⠸⣅⡀⠂⠀⣹⡇⠈⣧⣌⠳⣼⣴⠋⠘ ⢀⡼⡟⠀⡀⠁⢀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡾⣟⣷⠀⡗⢸⡑⣿⣿⣦⣀ ⢊⣼⠇⠐⢀⠈⣴⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣼⡇⠸⡇⣳⣿⠏⠀ ⢣⢾⡅⠂⠠⢘⣿⠻⢶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡐⡇⢿⣿⠀⠀ ⢣⢚⣧⡀⢁⠸⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣶⣷⣶⡋⣱⢞⣻⡇⠀⢸⣿⠁⠀ ⢣⢇⠞⣿⣄⠈⣿⢣⣄⠀⠀⢶⣦⣀⡀⠀⠈⠀⠉⢈⣿⣿⡎⣥⡟⠀⣴⣻⠀⠀ ⢣⢎⠽⣠⣿⢷⣸⡏⠉⣹⠶⣤⣬⢿⡽⣦⣤⡶⣴⣾⣿⣿⣣⡟⣃⣰⣿⡿⠀⠀ ⢣⢎⣳⡿⣽⢯⣟⣷⡀⣹⣋⣽⣯⢿⡽⣯⢷⡿⣽⣻⢿⣿⣿⣼⠿⠛⠉⠀⠀⠀ ⣧⣾⢿⡽⣯⡿⣾⣽⢿⣿⣿⣿⢯⡿⣽⢯⡿⣿⣳⢯⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠠⠤⠀⠠⠄⡀⠀⢀⠔⠂⠉⠉⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢃⠀⠀⠀⢠⢀⠱⠂⠀⠀⠀⠀⡠⠓⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠅⠄⣀⡀⠀⠹⢧⠤⠤⠐⡈⠂⢄⠀⠀⠈⠢⠀⠀⠀⠀ ⠘⠩⠥⠀⠀⠠⠀⠀⠀⠀⡠⠃⠀⠀⠈⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⢀⡤⢀⣀⣰⠀⠀⢜⠂⠀⠀⢬⠐⠀⠄⠢⡈⠄⠀⠀⠀⠀⠀ ⠀⠄⡌⠶⠊⠁⠇⠄⠈⠀⠀⠀⠠⣦⣀⣢⠀⡀⠱⠘⡀⠀⠀⠀⠀ ⢠⡆⢁⠀⠀⢰⣠⣶⢦⡀⠀⠀⠀⠰⠟⣿⣦⡇⠀⣦⣧⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⡾⠻⡇⠐⢷⠀⠀⠀⠄⠀⠉⢹⠇⠀⣘⣿⠀⠀⠀⠀ ⠀⠀⢻⠇⠀⠅⡆⠣⠀⠘⠀⠀⠀⠀⠀⠀⢡⠀⠠⠉⠀⠀⠠⠀⠀ ⠀⠀⠄⠀⠢⡆⣧⢀⠀⠀⠀⢇⡀⠀⠀⢀⡌⠐⢡⠀⠘⠠⠀⣡⡀ ⠀⠰⠒⠙⠄⠀⠈⠗⢢⠏⢩⣟⣿⡿⢧⢀⡏⢀⠎⡤⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⠌⠗⢡⠂⣙⠏⠉⢴⠸⣷⡜⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡄ ⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠒⠒⠒⠒⠒⠠⢀⠔⠊⡰⠁⠐⡳ ⠀⠀⢀⡠⠔⡪⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡁⠀⠈⡹ ⣖⠈⠁⠀⣙⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⠚⡱ ⠸⡂⢤⠔⡫⠀⠀⡀⠰⠁⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⣧⡨⠃ ⠀⠘⠠⣸⠁⠀⢀⡷⢣⢠⠀⠀⢂⢨⢻⡰⡈⡄⠀⠀⠈⠢⢤ ⠀⠀⠀⡆⢀⠀⢨⣇⡀⢙⠑⠢⡼⢺⣏⡙⣿⡇⠀⠀⠌⡍⠀ ⠀⠀⠀⠘⣬⠢⠼⡌⠉⠓⠂⠀⠀⠘⠒⣲⣋⡔⠀⣼⠔⠁⠀ ⢀⠠⢔⠊⠀⠀⠄⠑⢄⡀⠀⠠⠄⠀⢀⠠⠊⠓⠈⢸⠀⠀⠀ ⡇⢰⠃⠀⠀⠈⠀⡰⢿⣦⡝⣅⠀⡽⢅⡀⠀⢸⠀⢀⠳⡀⠀ ⠑⠿⡀⢃⠀⠘⡸⠀⠀⢻⣿⣟⣆⣧⣷⡹⡀⠀⠀⠀⣦⡑⢄ ⠀⠀⠀⠉⠓⠒⠆⠀⠀⠀⠙⠿⢿⣿⠟⠀⠑⢔⠀⠀⢸⠑⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠆⠀⠀⠈⠁⠊⠁⠐⠁

⠀⠀⠠⠤⠤⢼⢤⣤⣮⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⡔⢁⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⢼⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡂⠀ ⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠂ ⣰⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣻⣿⣿⣿⣿⣿⢹⣿⣿⣿⡗⢖⠋⠀⠀ ⠁⠀⣿⣿⣿⣿⣿⣿⡿⠓⢁⡀⢻⣿⣿⣿⣿⡏⠈⢿⣿⣿⡟⠀⢃⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⢁⣭⡴⠶⠆⢻⣿⡿⣿⣧⣌⣸⣿⣿⡿⠖⠊⠀⠀ ⠀⠀⠈⠙⣿⠿⢿⡟⠆⠀⠀⠠⠀⠔⠋⠀⠀⠉⠉⠸⣿⡙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠩⣒⠁⡰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣀⣰⠒⠋⠉⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⠉⢉⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡄⠆⠋⠛⢄⠀⠀⣖⢟⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⢘⢅⠠⣀⠀⠀⠢⠘⢌⠒⢷⢤⡉⡒⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⢠⠞⠉⢧⢀⡴⠚⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠦⣄⣰⠏⠀⠀⠈⠋⠀⠀⠀⠸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣸⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⡿⠂⠀⠀⠀ ⠀⠀⠀⠈⠛⢶⡴⠶⢶⣶⣶⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣴⣦⡁⠀⠐⡆⣠⣴⣿⣵⣶⣶⣶⡶ ⠀⠀⠀⠀⠀⣼⣀⠄⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⣿⡳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣥⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢲⣩⡔⢯⡀⠀⠀⡇⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⢀⡾⠃⣿⣇⡠⠃⠀⠀⡇⠀⠀⢀⢰⠉⠀⡠⠜⢧⢰⠀⠈⢿⡙⠛⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⣾⠁⠀⠘⠉⠀⡐⠉⠀⢱⣶⠀⡞⠯⠴⠛⡲⢀⡞⠀⢸⡶⢼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⡰⠀⡈⠉⠁⠈⠸⡜⠀⣄⠀⠊⣠⠞⢱⣤⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣜⡁⠀⠈⠁⠀⠀⠀⠀⢀⡈⢻⡉⣽⢤⣀⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⢶⠋⠉⠉⠉⠉⠉⠉⢹⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢼⡅⣯⢰⢀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡟⣿⣾⣾⣿⣿⣿⣿⢿⣿⣷⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢸⣿⣿⣿⣿⠿⣛⢿⣿⣓⣼⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢿⣥⣿⢇⡿⡉⠭⡑⢄⠣⣙⣦⣍⡛⠧⠹⣏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⣐⣉⣿⣿⢰⡇⡱⢂⠍⢢⡑⢄⠺⣽⣳⣬⣑⣤⠷⣋⢙⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠏⠀⣩⣾⣿⣿⣼⣧⣦⣵⣮⣥⣼⣌⣱⣧⣯⣽⣏⡰⢡⣶⠟⠛⠖⠲⣄⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⣸⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠛⠉⢻⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠙⢲⡖⠋⠀⠀⠀⢸⡏⢹⠋⢩⣼⠉⡌⢩⠉⡍⣽⡅⢰⣾⠀⠀⠘⣧⣴⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡰⢉⣛⡾⢡⡉⢜⡠⢃⣾⡯⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡱⢐⣣⠞⡡⠒⣌⢢⣴⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢡⠌⣻⣶⣋⠔⣡⢓⣼⢿⣵⣿⡿⢿⣱⡾⢋⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡾⡽⢃⠝⣷⣴⠟⠁⠀⠙⣿⠵⣋⠳⣝⢮⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⣿⣦⣾⣿⣧⣝⢷⣌⣒⣤⠟⠀⠀⠀⠀⠈⠳⣦⣱⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠻⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠳⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⣆⡀⠀⠀⢿⣄⠀⠀⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣿⣿⣻⣶⡆⠀⠻⣦⣀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠺⠛⠿⣿⣿⣿⡄⠀⠀⠀⠙⠛ ⣿⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀ ⡿⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣦⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠘⣔⣦ ⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⢀⡿⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣽⣷⡀⠀⠀⠀⣹⣇⠀⠃⠀⠀⢹⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣿⠂⠀⠀⢠⣾⡻⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠬⡼⣿⣆⠀⠀⡏⣼⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿⠇⡆⠀⣠⡟⠋⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠙⢷⣤⡓⢼⡃⠀⠀⢦⡀⠀ ⠤⡄⢤⠠⠤⠤⣄⠲⣾⠃⠀⠀⠀⠀⠀⠀⣿⠸⣁⡴⠋⠀⢠⠤⠤⠤⣿⡄⠀⠀⠀⠀⠀⠀⣿⠴⠦⢀⣀⣀⠀⠙⠻⢮⡇⠀⠀⢸⡅⠄ ⣮⡘⢆⣋⢎⡱⢌⣳⡏⠀⠀⠀⠀⠀⠀⠀⣿⡗⣋⣤⣴⡶⠶⠶⠶⢦⡀⢻⣆⠀⠀⠀⠀⠀⢹⣤⠞⢫⣿⣝⠻⣦⠀⢸⡏⠀⠀⠀⡯⣘ ⠉⠉⠛⠙⠋⣹⠟⢻⠁⠀⠀⠀⠀⠀⠀⢠⡟⠛⡉⡁⢠⣴⣿⣿⣿⣷⡈⠀⠙⢦⡄⠀⠀⠀⠘⣇⣾⣿⣿⣿⡇⠀⠙⣺⠁⠀⠀⠀⢿⠿ ⡆⠀⠀⠀⢠⣯⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⠐⣰⣿⣿⣿⠟⢻⣿⠅⠀⠀⠀⠙⠳⠤⣄⣀⢹⣿⠋⣽⣿⡇⠈⢐⡟⠀⠀⠀⠀⢸⡆ ⡹⣆⠀⠀⣼⢻⡀⣞⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⡀⣻⣿⠿⡏⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⢴⣿⡟⠀⠀⠼⡇⠀⠀⠀⠀⠈⣷ ⣧⠜⡳⡄⢏⠲⣙⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠉⠛⠚⠋⠀⠀⠀⢆⡿⠀⠀⠀⠀⠀⣿ ⢹⣧⡑⠮⣌⠳⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⠀⡀⠂⠀⠀⡀⠀⠀⣀⡤⠶⢶⣦⣄⡀⠀⠀⠀⠀⠈⢀⣼⣿⡇⠀⠀⠀⠀⠀⢻ ⠘⣿⣬⡓⣌⠳⡘⢼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⣀⡀⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⢷⣀⣀⣠⣤⡾⢟⣿⡞⠀⠀⠀⠀⠀⠀⣾ ⣄⡹⣟⠿⣶⣧⣝⣢⢿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⢀⣠⡼⠟⠛⢧⣒⢱⡾⠛⠀⠀⠀⠀⠀⠀⢀⣿ ⠈⠉⠁⠀⠀⠈⠉⣙⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⡿⣿⣿⣇⣀⣴⠾⠛⠉⡀⠄⠂⠠⠹⣏⡁⠀⠀⢀⣤⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⣰⡿⣅⠀⠈⢷⣦⡀⠀⠀⠀⠀⠀⠹⣶⣎⣹⠿⢯⡱⢺⣿⢻⡽⣆⠀⠂⡁⢀⠂⠁⢂⢀⡏⠻⣶⣶⣫⣇⣠⣶⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⠂⠈⠳⠦⠶⠮⣝⠻⠶⠶⡶⡶⠒⠋⠀⠉⠉⠋⠉⠉⢻⣧⠯⣽⢦⡁⠐⠀⣲⢥⣤⠞⠁⠀⣿⣟⡿⣿⣯⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⣠⢿⣄⠁⠂⠄⠠⢀⠈⣷⢲⢫⣽⠁⠀⠀⠀⠀⠐⢀⠄⠀⠈⣿⡿⢿⣿⣷⣤⡶⠋⠀⠀⠀⠀⢠⣿⢯⣟⡷⣯⢿⡿⣿⣶ ⠀⠀⠀⠀⣰⠋⠀⠙⠷⣤⣈⠐⠀⠺⢻⣇⡿⠃⠀⠀⣀⡀⠀⠀⠀⠉⢂⣀⣀⡀⠀⣻⢶⣧⣝⣛⣳⣶⣤⣴⣿⣿⣯⣿⣽⣻⣯⣿⠷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠿⠛⠛⠛⠛⠛⠛⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⣤⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠆⠀⠀⠀⠀⠀⠀⢸⣇⣀⠽⢦⣤⠀ ⠐⠯⣉⠹⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⢀⣀⡤⣴⢾⡿⢶⣺⡏⠀⠀ ⠀⢀⡤⠛⢻⡿⣯⠭⠭⣭⣉⣉⣉⣉⡥⠤⠔⠒⠋⣩⠔⠊⠁⢸⡇⠀⠈⢣⡀⠀ ⣰⠋⠀⢀⣼⡇⠈⠓⠦⣄⣠⠞⠑⢦⡀⢀⡠⠖⠋⠁⠀⠀⠀⢸⡏⠓⢦⠤⠛⠂ ⣧⠖⠉⠁⣿⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀ ⠀⠀⠀⡼⣿⡭⢉⣉⣟⣻⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠠⢼⡇⠀⢸⠀⠀⠀ ⠀⢀⡞⠀⣿⡄⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⠉⠉⠉⠉⠉⠁⠀⢻⣇⣀⣼⢣⠀⠀ ⠀⡞⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣿⠋⠙⠻⣇⠀⠀⠀⠀⠀⠀⣿⠻⡍⠁⠈⡇⠀ ⠀⡷⢣⣠⠋⠻⣦⣀⠀⣀⣠⡾⠃⠀⠀⠀⠻⣦⣀⠀⠀⣠⡼⠋⠀⢳⡀⡦⠝⠦ ⠀⠁⠈⠁⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⣶⢷⠢⣶⠁⢾⡦⠠⣠⣔⡖⡶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⣣⠀⠡⡠⠐⢀⢜⠕⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣔⣂⠥⠕⠄⢀⠔⡁⠚⠊⢅⣐⣠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠰⢁⠀⠈⢢⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⢀⠃⠈⠀⠀⠈⡆⠀⠀⠁⡀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⡠⣹⠀⡇⠀⠀⡀⡘⠄⠀⠀⠘⡄⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠰⠀⠀⡆⣰⡕⣸⣠⠀⠀⢠⢡⠱⡈⡄⣦⣀⢰⠈⡆⠀⠀⠀ ⠀⠀⠀⡐⠁⠆⠀⢠⡠⣋⣡⣼⢾⠀⢀⡦⢋⣈⣑⣿⣻⡟⠀⡆⠈⠢⡀⠀ ⢤⡔⠀⠀⣰⠀⠀⢸⣷⢿⣿⣿⡛⠤⠋⠀⢻⣿⣿⠿⣿⠀⠀⠰⡀⠀⢀⠱ ⠀⠈⢀⠜⡍⠀⠀⠘⡇⠘⠿⠟⠁⠀⠀⠀⠘⠿⠟⢀⣿⠀⠀⠀⡇⢎⠁⠀ ⠀⠈⡹⢸⡇⠀⠀⠈⡋⡄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠌⡟⠂⠀⠀⡇⠀⠆⠀ ⠀⠀⢃⡈⠆⠀⠀⠧⢃⢨⣦⣄⡀⠀⠀⠀⣀⣤⣎⢀⢃⠀⠀⠀⡘⡄⡜⠀ ⠀⠀⠈⡇⡀⠀⠀⠀⡌⣯⠹⡄⠉⠛⠚⠓⠉⠘⣿⢋⠌⠀⣿⠀⣇⠗⠀⠀ ⠀⠀⠀⢃⢃⠀⠀⡆⢸⣌⣻⣷⡀⠀⠀⠀⠀⠘⣳⠃⢀⢴⣈⠜⠀⠀⠀⠀ ⠀⠀⢠⣶⣮⣦⠀⢣⠀⢿⡹⠟⢠⣆⣀⣀⣀⠠⠟⠋⠀⢩⠀⠣⡀⠀⠀⠀ ⠀⠀⠀⠙⢛⡿⠛⠿⣶⣼⡇⠠⡞⠀⠀⠀⢀⢀⣀⣀⡠⢃⠠⠒⠁⠀⠀⠀ ⠀⠀⠀⠰⣏⣀⣀⠤⣻⠀⠀⡜⠂⠤⠠⠔⢉⡀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡠⠖⢓⣫⣃⠹⡇⠀⠀⠀⠀⡰⢁⣦⣄⣀⣀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⡰⠋⣠⠖⠁⠀⣈⠵⠧⣄⠐⠒⠚⠓⠛⠒⠓⠿⢽⣧⣀⣠⠴⠋⣸⠀⠀⠀⠀⠀ ⢁⠞⠁⢀⡠⢴⠁⠀⠀⠀⠱⣄⣀⣀⣀⣬⣭⣶⣤⣈⡑⠒⠢⢴⣧⢤⡀⠤⢤⠀ ⢼⡒⣲⠊⠀⢸⣆⠀⠀⠀⠀⡈⠓⣾⠱⣖⡒⢺⠈⠳⣍⠑⢤⡀⠈⠙⢦⡴⠋⠀ ⠀⣹⠁⠀⠀⢸⢈⠷⣔⡒⢮⡤⠤⠬⠷⠒⠒⠉⠁⠀⠉⢣⠀⠙⠄⠀⠀⠱⡄⠀ ⠀⡇⠀⡀⢀⡏⡏⡶⡎⠉⠙⢚⠷⠒⢲⠦⢄⠀⠀⠀⠀⠈⡇⠀⠘⣆⡀⠀⢹⠀ ⢸⡀⠀⢰⡜⣇⣛⡵⠃⠀⢠⠃⠐⠚⠁⠀⠀⠱⡄⠀⠀⠀⡇⠀⠀⢸⠹⡄⡼⠀ ⡸⡇⠀⠈⢧⠀⠀⠌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢰⠣⡀⢠⠎⠰⠟⠳⣄ ⠃⢣⠀⠀⠈⢷⡁⠀⠀⠀⠈⢇⠀⠀⢀⡠⠒⠒⠁⠀⣠⠋⠀⠈⡏⠀⣧⡀⠀⠘ ⠀⢼⡄⠀⠀⠀⠙⠦⣀⣀⠀⠀⡑⠒⠉⠀⠀⠀⣠⣴⣷⣶⣶⠒⡗⢠⣧⢼⡆⢀ ⢀⡎⠱⡀⠀⠀⠀⠀⠐⠶⣾⠭⣤⣤⣤⣴⣶⣿⣿⣿⣿⢿⡟⠚⠋⡡⢻⠈⠉⠁ ⠾⠤⡤⠛⣄⠀⠀⢠⢤⣀⣀⡩⠝⠛⡩⠿⣿⡿⣭⢁⣴⠋⠀⠐⢯⡀⣼⠦⣄⣀ ⠀⢠⡇⢿⣿⣿⡶⠾⢦⣀⣠⠀⣴⠊⣳⠚⠁⢀⣫⠏⠁⠀⠀⠀⢠⢃⠇⠀⠀⠀ ⠀⠘⣇⣆⢼⡟⠀⠀⣠⠚⠚⠀⠈⠉⡹⢶⡚⣿⠀⠀⠀⠠⡴⢚⡡⠋⠀⠀⠀⠀ ⠀⠀⠙⠚⠓⣇⠀⠀⠣⠤⢴⡿⠀⠘⠦⢞⣨⠟⠀⢀⣀⣴⠗⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠤⣄⣀⡀⠀⠀⠼⠿⠿⠿⣷⣶⣶⣶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠒⠦⡀⠀⠉⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢦⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠈⢿⣇⢻⡿⢿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢳⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡇⠀⠀⠀⠀⠈⢻⣮⢂⠀⠁⠀⢠⠀⠀⠹⣯⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣆⢰⠁⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠟⣏⢢⠀⠘⢄⠑⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡟⠀⠀⠀ ⣠⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠀⢣⠀⠀⠀⠀⠀⣠⠖⠈⠳⣷⡄⢈⣳⣌⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⣿⣿⣇⠀⢸⠀⠀⠀⣠⣞⡁⣠⣴⣾⠛⠻⣏⣌⣻⣷⣌⠻⡟⣿⣿⣿⣿⣿⡄⠀⠹⣿⠁⠀⠀⠀ ⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣤⣿⣇⠀⠐⠉⠛⠿⣿⡟⠟⢣⠀⠁⢹⠈⡟⢻⠛⢶⡿⠿⠃⣿⣿⣿⣶⡀⠹⡀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⣠⠞⢙⣿⠻⣿⢿⣿⣿⣿⣿⠿⢿⡄⠀⠀⠀⠀⠹⡃⠫⣿⡤⠀⢸⠀⡟⣿⠀⢸⣧⡜⣰⣿⣿⣿⣿⣷⡀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⠁⠀⢸⡟⣷⣼⠄⢤⣶⢾⣿⢷⡟⠻⢄⠀⠀⠀⠀⠓⠈⠁⠀⠀⢸⠀⢹⣿⠄⣸⣯⣴⣿⣟⣿⢻⣿⣿⣷⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣇⢿⣿⣷⠺⣇⠀⢿⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣿⡟⢰⣿⣿⣿⣿⡿⠃⠀⣻⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣼⣿⣿⠘⣿⣿⣷⡀⠀⠘⠃⠀⠀⢀⣠⠒⠓⢤⡀⠀⠀⠀⣰⢷⣿⢋⣿⣿⣏⣹⡇⢽⣁⠀⠀⢸⢿⣷⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⠻⢿⣿⣿⡇⠁⠘⢿⣷⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠱⡀⠀⠈⠀⣼⢃⣾⣿⡟⠀⡸⠛⣤⣹⠃⠀⠀⢣⠹⣿⡄⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⣿⣇⡇⠀⣼⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⢀⣧⣾⣿⢿⡇⢠⣧⣤⣤⣹⡆⠀⠀⠀⢣⡈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⢁⢰⣼⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠇⠀⠀⣼⣿⠏⠁⣸⡇⣾⣿⣿⣿⣿⣿⣦⣀⣀⣀⠑⢾⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⠘⣿⣿⣿⣿⣿⡝⠢⠄⣀⠀⠀⠈⠒⠊⠀⢀⣴⣿⠏⢀⣴⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠉⠐⢇⠀ ⠀⠀⠀⠀⢀⡀⠤⢄⠀⣠⡎⠈⡆⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠑⠂⠤⠤⢺⣿⣏⡇⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⠀⠀⠀⠀⠁⠀⠀⠐⠉⢸⡀⠀⡇⢹⣿⢷⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⢺⢹⣦⣝⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⡿⣿⣿⠿⠛⣛⣁⣀⣠⣤⣶⠿⠷⠶⠴⠾⠿⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣨⠼⢯⡙⢿⣿⢿⣿⠀⠀⣸⣿⣿⠟⠉⢁⠰⣶⠖⣋⠕⠋⠉⠉⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢪⡿⠁⠀⠀⠘⡄⣧⣈⡀⠀⠰⢟⣉⡏⢀⠊⣧⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠧⠟⠒⠳⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣭⣧⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣽⣿⣍⠙⠉⠉⠛⠋⢉⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿

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