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

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