Pokémon ASCII Art

Copy & Paste Pokémon ASCII Art Emojis & Symbols

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

Warning: This item may contain sensitive themes such as nudity.

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

Related Text & Emojis

If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!
AI Story Generator - AI Chat - AI Image Generator Free