𝘀𝗹𝗲𝗲𝗽𝘆𝗵𝗲𝗮𝗱 𝗞𝘂𝗿𝗼𝗺𝗶𝗠𝗲𝗹𝗼𝗱𝘆‹𝟹🧸ྀི Emojis & Text

Copy & Paste 𝘀𝗹𝗲𝗲𝗽𝘆𝗵𝗲𝗮𝗱 𝗞𝘂𝗿𝗼𝗺𝗶𝗠𝗲𝗹𝗼𝗱𝘆‹𝟹🧸ྀི Emojis & Symbols ⣿⣶⣶⣦⣦⣀⣠⢁⠣⡐⢡⠊⠤⠱⣀⠠⠔⡨⠄⠦⠡⠔⠢⢄⠠⡐⠦⠬⠰⢌⠰⢈⠄⡀⠠⠔⡨⠔⠤⠒⡌⠖⡠⠤⢌⠢⣁⢢⣥⣾

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

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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠀⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠀⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢻⡀⠀⠀ ⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒ ⠀⠀⠈⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀ ⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀ ⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⣶⣤⣴⡶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⣾⣿⣿⣷⣄ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣄ ⠀⠀⠀⣀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢇⠠⣏⡖⠒⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⣿⣿⡿⢋⠁⠀⠀⠀⠀⠉⡙⢿⣿⣿⡇ ⠀⠀⠘⣿⣿⠀⣿⠇⠀⢀⠀⠀⠘⣿⠀⣿⡿⠁ ⠀⠀⠀⠈⠙⠷⠤⣀⣀⣐⣂⣀⣠⠤⠾⠋⠁ ⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⢠⠞⠉⠉⠑⢶⠉⠀⠀⠀⠹⡄⠀⠀⠓⠒⠒⠐⠒⠒⠒⠚⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⢠⡏⠀⠀⢀⡴⠚⠀⠒⢄⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠈⠳⣄⡀⡎⠀⠀⠀⠀⢈⡆⠓⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠳⢄⣀⣀⣠⠞⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀ ⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⡿⢤⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⣨⠏⠁ ⠀⠀⠀⠀⠀⡟⠓⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⠤⢤⡔⠚⠁⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠉⠉⠉⠉⠐⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠸⡇⢀⣤⣾⠟⠛⠶⠦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⡇⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⡀⢱⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠉⠀⠀⠋⠿⠗⡇⠀⢀⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⣀⡤⠤⠤⠤⣄⠀⡠⠔⠒⠢⢄⡀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢹⠖⠁⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⠀⠘⢦⠶⢶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⢀⠜⠉⢆⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⠦⣀⣀⣀⠤⠊⠀⠀⠈⠢⢀⡀⠀⢀⡠⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣰⡿⠛⠛⠿⢶⣦⣀⠀⢀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠹⣷⣄⣤⣶⡶⠿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⢹⡟⠁⠀⠀⣀⣀⠘⣿⠉⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⡋⣽⠿⠛⠿⢶⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢈⣻⡏⠀⠀⠀⠀⣿⣀⠀⠈⠙⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⢷⣄⣀⣀⣼⣏⣿⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡉⠉⠁⢀⣠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠾⠟⠋⢹⣷⠀⠀⠀⠀ ⢀⣤⣤⣤⣿⣤⣄⠀⠀⠀⠴⠚⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣈⣿⣀⣀⡀⠀ ⠀⠀⠀⠈⣿⣠⣾⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡤⠶⢦⡀⠀⠀⠀⠀⠹⠯⠃⠀⠀⠀⠈⠉⢩⡿⠉⠉⠉⠁ ⠀⠀⣤⡶⠿⣿⣇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣯⣀⣀⠀⠀ ⠀⢰⣯⠀⠀⠈⠻⠀⠀⠀⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠉⠉⠁⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠈⠙⣷⠀⠀⠀⣴⠟⠉⠉⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⠟⠉⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⠀⠀⠀⠙⢧⣤⡶⠟⢀⣿⠛⢟⡟⡯⠽⢶⡶⠾⢿⣻⣏⣹⡏⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠙⠛⠛⠋⠀⠀⢀⣽⠟⠛⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠿⠟⠋⠹⣷⣤⣀⡀⠄⣡⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣉⣻⣏⣉⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
♡♡/ ̄ \   |  |  |  | / ̄ \ ( ̄v ̄)|/ \    \   > ○ <  ヽ_ノ (_人_)   \ |     / ̄ ̄ ̄\    |   \ (    ● o ●   ) ノ     >----------<       \_ノヽ_/
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⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣶⠟⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠙⠛⠛⠿⣷⣶⣶⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⣀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣯⣿⣻⢿⣿⣿⣿⣯⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠛⠿⢿⡿⣿⣿⣿⣿⣯⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣰⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠾⠟⣿⣟⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⡷⠷⡶⠀⠀⠀⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠧⠀⠀⠀⣤⣿⣿⣶⣴⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⣿⣆⣀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⢀⣼⡶⣷⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⣿⠃⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⣿⡍⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠛⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣻⣿⢿⣷⣦⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣈⣿⣿⣟⢠⣴⣿⣿⢿⡿⣶⣄⠀⠀⠀⣠⣾⡿⣟⢿⡿⣶⡄⣀⣴⣿⠟⠁⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡟⠃⠈⣙⣿⡿⠿⢾⣧⣛⢷⣻⣷⣠⣾⡿⣣⢟⡼⣳⣿⠟⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⣹⣯⡞⣵⢫⡟⣧⢻⢥⡻⡼⣿⣇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⣿⢣⡟⣼⢣⡟⣼⡹⣎⢷⡹⣝⣿⣇⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣼⡟⣮⢳⡝⣮⢳⡝⡶⣹⢎⡷⣹⢺⠼⣿⣷⣶⣿⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠉⠛⣿⣽⢎⡷⣹⢎⡷⢺⡵⢫⡞⣵⢋⣷⣿⡿⠛⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⠀⠀⠀⠀⠈⠻⣿⣞⣵⣫⢞⢧⣛⢧⡻⢼⣯⣿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠻⣷⣿⣎⠷⣭⢳⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣠⡿⠛⢿⣿⣼⡿⠛⢿⣧⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⢤⠴⠞⠋⠀⠀⠀⠙⠏⠀⠀⠀⠙⠻⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠠⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠿⢮⡿⣾⡖⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠒⢦⠸⣿⣄⠙⣧⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣷⣞⠳⣄⠘⡆⠙⢇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣯⡝⠻⣿⣏⠉⠻⣮⣷⣝⣶⣼⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⠈⠙⢤⠈⢳⡀⠀⠹⣌⢻⠀⠙⣧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠳⢤⣄⡑⠀⠹⡄⠀⣌⠀⢳⡀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣄⠀⠂⢻⡉⠑⣦⠹⡄⠸⡄⠀⢷⡄⡇⠀⠀⡇⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣝⠀⠀⠀⢿⡶⢧⠀⠸⡇⡗⠀⢀⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢻⣷⣦⡀⠈⠋⠈⢧⠀⠀⡇⠀⠈⠀⠔⠋⠀⠀⢀⣀⣤⣤⣤⡶⢶⣿⠿⠭⢥⢽⣁⣤⠀⠒⠿⠿⣿⣷⣆ ⠀⢀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⡘⣆⣼⣃⣴⣦⠀⠀⣀⡴⠞⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣛⣖⠲⠦⣄⣸⡿ ⢠⠾⠒⠶⠀⠀⠀⠀⠀⡀⠀⡙⢺⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⠞⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠤⣍⣙⣓⠶⣴⣶⠟⠁ ⡾⠀⠂⠀⠀⠀⠀⠀⠈⠑⠉⢡⣿⣿⠛⠲⣤⣯⣿⣿⣿⣿⣿⣥⡞⠒⠒⠚⠛⠓⠠⣀⠀⠀⠀⠠⠄⠀⠠⣤⣷⣌⢙⣿⣦⡾⠋⠀⠀ ⡗⠺⠤⠛⠉⠉⠁⠐⠉⠉⣹⣿⢿⢃⣠⣾⢋⣾⣿⣿⣿⣟⠻⠏⡿⣗⣦⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠀⠀⠀⠀ ⣇⣠⠤⠀⠀⠀⠀⢀⣴⡾⢛⡽⢋⣽⣟⣵⢫⣿⣿⣯⡏⢣⠀⠄⠀⠈⠉⢙⣻⠖⢦⣄⡀⠀⠤⢙⠶⣤⡀⠈⢳⣰⡟⠁⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⢀⡴⢪⠟⢩⠖⠋⢠⡾⢻⡟⢁⣿⣿⣿⡟⡀⠘⠀⣴⠀⣤⡐⠂⠈⠉⢗⣟⠿⣶⣤⡀⠲⣤⣹⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠈⠀⠀⠀⠀⡀⣠⠏⣴⠏⠀⢸⣿⠟⠻⢀⠆⠀⢀⠈⢳⡸⡗⢤⡀⠉⠪⠙⢧⡀⠉⠙⠓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⢀⡴⢂⣜⡥⠚⠁⠀⠀⠀⠁⢠⡆⢸⣰⠀⠈⣧⠀⠑⢿⠀⠙⢦⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣤⣖⣋⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢹⠆⠀⢸⡄⠀⠈⢷⡀⠀⠑⢦⡜⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⣾⠀⠈⢀⢳⡀⢠⡈⢻⣦⡀⠀⠙⢮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⡼⠀⠄⠈⠈⣇⠀⠹⣌⠹⣿⣄⠳⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⢻⠀⠀⠀⠀⠙⠂⠀⠹⡁⡈⡻⣦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡄⠀⠀⠀⠀⠀⢰⣄⣃⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢻⡀⠀⠀ ⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒ ⠀⠀⠈⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀ ⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀ ⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠴⠚⡙⠙⠲⣤⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣴⠃⣰⠟⠉⠙⢦⡈⢁⣾⡟⠉⠳⣆⠸⣇⠀ ⣿⠀⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿⠄⣿⠄ ⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡏⠀ ⠀⠙⣆⠙⢧⡀⠀⠀⠀⠀⢀⡴⠃⣰⠏⠀⠀ ⠀⠀⠈⠳⣄⠙⠶⣄⣀⠴⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⡈⢡⣰⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
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⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠛⢷⣄⢀⣠⣤⡶⠾⠟⠛⠛⠛⠛⠛⠛⠻⢷⡄ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿ ⠀⠀⠀⢰⣿⠀⠀⢰⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏ ⠀⢀⣤⣼⣿⠶⣦⡄⠛⢷⣤⣤⣀⣀⣴⡿⢶⣦⣤⣤⣤⣤⣶⣶⡶⠾⠟⠛⠁⠀ ⢰⣟⠁⠉⣁⠀⢼⣇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡶⠈⠛⣀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣶⡾⠛⠛⠋⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⠀⠀⠀⠀⣀⣤⡶⠟⠛⠋⠉⠉⠉⠉⠉⠛⠿⣦⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⣠⡾⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⢹⣧⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⢻⣆⠀⢰⡟⠁⢸⣿⠀⠀⠀⠀⣴⡄⠀⠀⠉⠁⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⣿⣇⠀⠈⠉⠀⠀⠀⢰⣶⡾⠇⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣷⣤⣄⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
ㅤ⠀⠀⠀⠀ ⠀⢀⣤⣄ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆ ⣠⣶⣿⣶⡀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⣾⣿⣿⣧⠀⠻⣿⣿⠿⠉ ⣰⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⠏ ⠀⠈⠛⠿⣿⣿⡟
⢆⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢆⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀ ⠀⠀⠣⡀⠀⠀⢀⣀⡀⠀⢡⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⢂⠀ ⠀⠀⡰⠉⠉⣱⠁⡀⠈⡆⠉⠉⠁⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠳⣀⡌⠀⠀⢰⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡁⠈⠐⣆⣁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⠆ ⠀⠀⢠⠋⠀⠉⠀⠀⢀⡀⠤⠤⠤⠄⢀⡀⠀⠀⠀⠉⠓⠒⡆⠁⠀ ⠀⠀⡆⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢀⠀⠀⠀⢹⠀⠀ ⠀⠀⠇⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢸⠀⠀ ⠀⠀⠘⡄⢇⠴⠛⠉⠒⠀⠀⠀⡄⠀⠀⠠⠶⠒⢦⣀⠀⢀⠇⠀⠀ ⠀⠀⠀⠈⠺⣆⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⢠⡠⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠵⢢⠔⠈⠉⠑⢔⠉⠀⠑⢄⢤⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⣠⠆⠀⠀⠀⠀⡘⠀⠀⠀⠈⣄⣵⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⡐⠱⡀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠈⠀⢒⠈⠀⠀⠈⠐⠒⠊⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆ ⢻⡈⠻⣦⣀⣀⣀⣀⣀⠀⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⣀⣠⣤⣤⣤⣤⡤⠖⠋⣸⠇ ⡿⠳⣤⣀⡀⠀⠀⠉⠉⠉⠳⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⡞⠉⠀⠀⠀⠀⠀⢀⣠⠶⢻⡆ ⠻⣦⣀⠀⠀⠀⡴⠶⢦⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠚⠳⡄⠈⢉⣀⣠⡾⠁ ⠀⠸⣍⣉⣁⡀⣇⠀⠀⠑⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠓⠀⢀⡇⢤⣈⣭⠿⠁⠀ ⠀⠀⠀⠙⠷⠤⠿⠶⠦⠶⠞⠋⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠈⠻⠦⠴⠖⠻⠶⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠴⠚⡙⠙⠲⣤⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣴⠃⣰⠟⠉⠙⢦⡈⢁⣾⡟⠉⠳⣆⠸⣇⠀ ⣿⠀⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿⠄⣿⠄ ⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡏⠀ ⠀⠙⣆⠙⢧⡀⠀⠀⠀⠀⢀⡴⠃⣰⠏⠀⠀ ⠀⠀⠈⠳⣄⠙⠶⣄⣀⠴⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⡈⢡⣰⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀-`♡´-
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢶⣶⣄⠀⣠⣴⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⠋⠀⠀⠈⠹⣿⡟⠉⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⠛⠻⢿⣶⠿⠿⠟⠛⠛⠛⣿⠇⠀⢠⣶⣶⣶⣿⣷⣦⣤⣀⣠⣤⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⣿⣼⡿⠁⠀⠀⠙⣿⣯⡁⠀⠈⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⢙⣿⣷⡀⠀⠀⢠⣿⣿⣿⡆⠀⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠙⠻⠷⠾⣿⡟⠛⠋⠀⣴⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⡶⠿⠛⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⣤⣤⣤⡄ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠘⠋⢹⣿⠀⠀⠀⠀ ⠀⣀⣀⣤⣿⣧⣤⡄⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⢠⣼⣿⣤⣤⡤⠀ ⠈⠛⠉⠉⠹⣿⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⢀⣠⡤⣤⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣿⣷⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡿⢶⣤⣄⠀⠀ ⠀⠀⠀⠉⠁⠀⠹⣷⣤⡴⠆⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣼⡟⣻⡇⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢀⣠⡾⠟⠛⠿⣶⣤⣤⣤⣄⣰⣿⣍⣀⡀⠀⠈⠙⠳⠿⢷⣦⣀⣠⣤⣶⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠋⠀⠀⠀⣰⡟⠉⠀⠀⠙⣿⣅⣉⣿⣁⣀⣠⣶⡀⠀⠀⠈⣿⡏⠁⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⣿⣧⡽⠉⠛⢉⣉⣘⣷⣄⣰⣿⣿⠇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⣻⡷⡄⣞⣳⠘⢦⣇⡈⠙⡿⢿⡇⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⢿⣦⣄⣠⣴⡿⠛⣡⣌⣿⢳⡞⠧⣿⣀⡙⠚⢿⣦⣄⣤⣴⠟⠙⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠈⠉⠉⢹⣧⠈⠳⠞⡉⢻⡷⢦⠸⢭⣧⣤⡿⠋⠉⠉⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⢾⣹⠆⠙⢫⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣤⣴⣾⡿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⠿⣷⣶⣿⣷⡀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣤⣀⣤⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠲⠶⣤⣀⣠⣤⣤⣤⡿⠛⠿⡴⠾⠛⢻⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠐⡿⣿⠿⣶⣤⣤⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠈⢯⣡⣿⣿⣀⣸⣿⣦⢓⡟⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⣄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠉⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾⠁⠀⠀⠀⠀
⠀⠀⠐⠀⠄⠀⣀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⣀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠰⣀⣔⠖⢡⣖⢿⡖⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠱⢤⣀⣀⣘⣧⡀⠀⠀⠀⠀⣷⢧⠀⠈⠛⠿⣿⡘ ⠑⠤⣀⠀⠀⠀⠀⡎⠀⡈⠧⢄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣦⡄⠄⠚⠃⠀ ⠀⠀⠀⠈⠹⣲⠒⡞⠀⠣⠤⠜⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡇⠁⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⡴⠉⠒⠒⠉⠁⢉⡀⠤⠄⠀⠂⠀⠤⢀⠀⠀⠀⠘⡒⣶⡾⠟⢃ ⠀⠀⠀⠀⣀⣴⠁⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢰⠐⠂⠈⠀ ⠀⠀⠀⢈⡷⠛⠀⠀⠀⡜⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣶⣌⠄⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠀⠀⠸⠀⢺⣿⣿⠟⠀⠀⠀⠀⠐⠀⠀⢻⣿⣿⢸⢐⠁⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⡡⡀⢲⠀⠀⠈⠁⠀⠀⠀⣰⠒⢲⡆⠀⠀⠉⠁⠘⡜⠀⠀⠀⠀ ⠀⠀⢀⠂⠀⠀⠈⠘⠦⣢⡀⠀⠀⠀⠀⠀⢯⣀⡼⠁⠀⠀⢀⡴⠛⠠⠀⠀⠀⠀ ⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⢏⠒⠠⠄⣀⣀⣀⣀⣀⠀⠤⡔⠉⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⣁⠢⠄⡀⣀⣀⡀⠡⣀⠀⡠⠊⠀⠀⢆⠀⡰⠁⠀⢀⡠⠚⠁⠀⠀⠀ ⠀⠀⠀⠠⠐⢄⡀⠡⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡐⢲⠌⣀⣀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠉⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠫⣉⣀⣉⠁⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠲⠶⣤⣀⣠⣤⣤⣤⡿⠛⠿⡴⠾⠛⢻⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠐⡿⣿⠿⣶⣤⣤⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠈⢯⣡⣿⣿⣀⣰⣿⣦⢂⡏⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⡄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠈⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠄⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀ ⠀⠀⠀⠀⢀⣀⠀⡊⣅⡕⠉⠑⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇ ⠀⠀⠀⠘⠀⢀⡑⠉⠉⠓⠠⡐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑ ⠀⢠⠂⠈⠌⠀⠈⡆⠐⢧⠤⠋⠒⢁⡀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠐⢄⠀⠀⠀ ⠀⢘⠤⢀⠈⠒⠊⣄⣀⠜⠀⠀⠀⡠⠃⠁⠒⠂⠐⠊⠀⠉⠒⠒⢆⡀⠀⠱⡢⢄ ⠔⠁⠀⠈⠂⡤⠒⠁⠀⢀⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠈⡄⠀⠀⢈⠮ ⠀⠀⠀⠀⡔⠀⠐⠒⠂⠁⢀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⢸⠂⢀⡇⠀ ⠀⢀⡠⠪⠁⠀⠀⡰⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⣀⡀⠀⠈⠩⠠⣌⢀⣾⠃⠀ ⣎⠁⢀⠁⠀⠀⠈⢡⠀⠀⠈⡙⡉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣡⡾⣿⢿⠉⠀⠀ ⠙⠢⡀⠈⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠤⡾⠉⠁⢿⡜⡀⠀⠀ ⠀⠀⠀⠉⢉⠋⠐⠂⠐⠊⠁⠒⠀⠀⠀⠀⠐⠒⠈⠉⠐⡄⢡⡀⠀⢀⡴⠃⠀⠀
⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⢻⣆ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢌⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣶⣿⣿⣷⡶⠀⠀⠀⣀⡴⣖⡦⡀⢀⣤⢤⡤⣀⠀ ⠀⠈⣿⣿⣿⠀⠀⠀⢰⢯⡽⣞⣵⡳⣟⢮⡗⣯⡽⡀ ⠀⠀⣿⣿⣿⠀⠀⠀⠸⣏⣾⢳⡞⣽⢞⡯⣞⣳⣽⠁ ⠀⢀⣿⣿⣿⠀⠀⠀⠀⠈⢺⡳⣏⣟⢾⣹⣳⡝⠂⠀ ⠀⠻⠿⠿⠿⠗⠀⠀⠀⠀⠀⠈⠙⢮⠯⠃⠉⠀⠀⠀ ⠀⠀⠀⢀⡄⣄⡀⢀⣀⣀⡜⠓⣄⠤⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠉⠉⠉⠩⣉⣀⣼⡒⠊⠁⡃⠀⠀⠀ ⠀⠀⠀⡝⠀⠀⠀⠀⠀⠐⠍⠵⢫⣧⡰⡔⠀⠀⠀⠀ ⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢁⣼⠤⠄⠀⠀ ⠀⠀⠨⣧⠀⠘⠃⠀⠀⡤⠄⠀⠙⠁⠀⣚⠒⠀⠀⠀ ⠀⠀⠠⠚⠹⢤⣀⣀⠀⠀⢀⣀⡤⠜⠉⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠳⣤⡀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⡶⠛⠳⢾⡃⠀⠀⠀⠙⣇⣸⣇⣤⡤⠤⠤⠤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⢀⣠⠽⢤⡄⠀⢤⣿⣋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣦⡄⠸⢧⣤⡴⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⡷⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠙⠷⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠲⠤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡛⢦⣄⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⢀⡾⠋⠀⢠⣾⡏⠁⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⢳⡆⠙⢧⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⢾⡟⣷⣦⣴⣿⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣦⣴⣿⡇⠀⠈⣇⠀⢸⡇⠀⠀⠀ ⠀⢀⣿⣦⣀⠀⡿⠁⠀⠀⠀⠸⣿⣿⣷⡿⠃⠀⣰⣀⣀⣙⣃⣀⣀⠈⠻⢷⣿⡿⠁⠀⠀⣿⡄⣼⠃⠀⠀⠀ ⣼⠋⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣽⣏⢛⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠓⢦⡀⠀ ⡇⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢷⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⠻⢯⣿⡿⠟⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀ ⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⢦⣤⣀⣀⠀⢀⣀⣠⣤⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀ ⠀⠀⠀⠀⠘⠶⣀⠀⠀⠀⠀⠀⠀⠘⢧⠻⠶⣿⡿⠃⠀⠈⢿⡽⠿⠋⣽⠇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⣇⣴⠟⠁⠀⠀⠀⠀⠙⢦⣴⡏⠀⠀⠀⢀⣴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣇⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⡆⢰⡵⣖⡢⢀⡀⢀⡀ ⠀⠀⠀⠀⠀⢀⡀⣤⣤⡀⠀⡜⠀⠀⠀⣀⣠⣇⣘⠁⠩⠇⢼⢾⡿⡇ ⠠⣲⢪⢭⡇⢹⣽⠯⠯⠇⢰⠃⠀⢠⠎⠁⠀⠀⠈⢳⠀⠀⠀⠀⠉⠀ ⠀⠻⠈⠁⠚⠀⠀⠀⣠⠔⠚⠁⠀⢸⡀⠀⠀⣠⠀⢸⠀⡤⢄⢀⡀⠀ ⠀⠀⠀⠀⠀⢄⢠⠞⠀⠀⢀⣀⣀⣀⠉⠒⠋⠁⠀⠣⡀⠣⣈⡰⠃⠀ ⠀⠀⠀⠀⢀⡞⠛⡖⢢⢪⣧⠀⠀⠀⠈⠑⠢⡀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⡡⡕⠒⠁⠈⣞⣋⡀⠖⠄⠀⣰⣷⠘⡀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡅⠁⠡⢄⠐⠭⠊⠙⢿⡉⣩⠱⠌⠁⠀⢣⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⢇⣀⢌⣈⠤⢀⡠⡤⢼⠬⣄⣁⣛⣀⣀⠜⠀⣀⠇⠰⢆⡠⡀ ⢀⢀⠖⡆⢇⠀⠀⠀⠀⠈⡢⠄⠤⠑⠒⢯⣉⠉⠉⠉⠁⠀⠘⠬⠔⠃ ⠙⠂⠚⠁⠀⠉⠉⠉⠉⣏⢣⣀⡖⠀⢀⠼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠁⠁⠀⠈⠉⠉⠛⠳⢦⣤⡀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣸⠀⠀⠀⠀ ⠀⣾⡋⢹⣷⣤⣤⣀⣀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⡀⠈⠉⡿⠓⡀⠁⠀ ⠀⠈⠛⢻⣿⣻⡟⠛⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⡷⠶⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠳⢶⣄⡀⠁⠰⠦ ⠀⠀⠀⢸⣿⣿⠇⠠⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣄⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠻⣦⡀⠀ ⠀⠀⠀⢸⣿⣿⣇⢈⣘⡀⡈⠿⣿⠿⣷⣦⣄⣀⠀⠀⠀⢰⡟⣉⡽⣿⡅⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠉⠀⠀⠀⣉⣭⠐⠢⡈⠻⣆ ⠀⠀⠀⠀⣿⣿⣿⣶⣾⣤⣴⣴⣴⣠⣴⣿⣿⣿⠛⠛⣿⡿⢿⣯⣥⣼⠇⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠈⠢⣹ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⠟⣿⣟⠉⠉⠉⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠶⠶⠶⢶⣏⣠⠇⢱ ⡄⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⢿⣿⢹⡿⣿⣷⣤⣠⣿⠉⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣄⠀⠀⠀⠀⠀⢀⣴⠟⠉⠘⠿⠀⢹⣬⣿⣿⠛⠛⢿⠇⠀⠀⣰⠃⢀⣀⣤⣤⣴⡦⠀⠀⠀⢈⣡⡶⠶⢶⣦⣀⣀⡀⠀⠀⠀⠀⠀⢀ ⠿⣿⣦⠀⠀⢀⣴⣿⡱⢾⠗⠀⠀⠀⢦⣿⣿⠇⠀⠀⢸⡆⠀⠀⡇⠚⠛⠋⢉⣽⠟⠁⠀⠀⢰⣿⣭⣄⣠⡿⠉⠀⠈⠙⢦⡀⠀⠀⠀⣸ ⠀⣽⣿⡆⣰⣿⠻⠟⠛⢶⣤⣶⣦⣿⣿⣿⡟⠀⠀⠀⣸⣇⠀⠘⡇⢀⡴⢶⡿⠋⠀⠀⠀⢀⡾⠋⠀⠈⢻⣇⠀⠀⠀⠀⠈⢿⡄⠀⣴⠏ ⠀⣿⢸⣿⣿⢹⡟⠒⣶⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠿⢻⣆⠀⢣⠘⠦⠞⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢿⠿⣧⡀ ⡀⣿⣾⣿⣿⣿⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠇⠀⠀⠙⢷⣄⠳⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⣧⡈⠻ ⣿⣿⣿⣿⣿⡟⠀⢀⣀⣠⣤⣄⠀⠀⠀⠀⠈⠋⠁⠀⠀⢀⣤⠀⠙⠳⣿⣶⣤⣀⡀⠀⣀⣿⠀⠀⠀⠀⠀⢠⡟⢷⡀⠀⠀⠀⠀⠙⢷⡀ ⣿⣿⣿⣿⣿⡇⠚⠛⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⣴⠾⠛⠩⠭⢯⠛⠛⠛⣿⠀⠀⠀⠀⠀⢼⣧⠈⠻⠆⠀⠀⠀⠀⠀⣿ ⠉⠁⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⡿⠀⠀⠘⠓⠚⠛⠉⢠⣾⠋⠁⣀⠤⢒⣋⡙⠆⠀⣀⣿⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠸⣿⣿⢿⡄⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣳⣿⠾⠟⠻⣦⢀⣾⠿⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢻⣷⣿⣿⣄⠀⠀⡞⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠋⠀⠀⠀⠀⢸⡟⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⣉⣩⣥⣶⣶⣶⣾⣿⣶⢶⣶⣶⠞⠁⠀⠀⠀⠀⠀⢀⡿⢀⡞⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇ ⢀⣤⣤⣄⣀⣀⠉⣙⣿⣿⣿⣿⣋⣿⣟⡈⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣴⡟⠡⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⢿⣶⣄⣴⣿⠟⠋⠁⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⢳⡽⣎⡟⣾⣻⣯⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣿⡿⢿⣿⣶⣶⣦⣤⣠⣤⣶⣾⣿⠿⠿⠟⢻⡿⣧⢟⣳⣿⣾⣷⣿⣿⡿⣷⣶⣄⣤⣶⣿⢿⡿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⡿⣵⣫⢿⣿⢧⣿⣟⡳⣟⣧⣛⣿⣿⣿⣼⢏⣾⢳⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣶⢫⣟⣻⣿⣿⣯⢳⣛⡶⣛⣾⣿⣟⣿⡿⣎⣯⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡿⣼⣣⣿⣿⣿⣟⣿⣣⣿⣿⣿⣿⣿⢿⣸⣻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠙⠛⠛⠉⢿⣾⣳⢭⣯⣷⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡷⠶⠿⠛⠓ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠉⠉⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⢠⣤⣿⣷⣤⣦⣤⡄ ⠀⠀⠀⠀⢿⣧⠀⢀⡀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⠀⢁⣿⡇⠀⠀⠀⠀ ⢠⣴⣶⡾⢿⣿⡟⠛⠛⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣀⡀⠀⠀⠀ ⠈⠁⠀⠀⠀⢻⣧⡀⢀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣧⣮⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠙⠛⡿⠷⠀ ⠀⠀⠀⢀⣤⣶⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠙⢿⣦⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠁⠀⠈⠉⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣾⡿⠿⠛⠉⢿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⢀⣬⣽⣿⣿⣿⣿⣿⣿⣾⡾⢿⠿⠿⠿⠟⠛⠛⣿⡿⢯⢿⣿⣄⠀⠀⠈⢻⣷⡄⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣟⠋⠁⣠⣿⣿⡹⡽⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⢽⡺⣟⣿⣆⠀⠀⠀⠻⣿⣄⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠘⢿⣷⣰⣿⣿⣼⣷⣟⣾⣻⣷⣤⣤⣀⣤⣤⣾⣿⢏⣷⣯⣷⣭⣿⣿⣧⣠⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⠀⣠⣿⠿⠛⠉⠉⠉⠛⢿⣷⡽⣏⣿⣛⣯⢿⣹⣺⣿⠿⠛⠉⠉⠉⠙⠻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣶⢻⣼⢳⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣳⡽⣺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢻⣜⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣻⢼⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣏⡾⣭⠷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠉⠉⠙⠻⠿⣷⣶⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⢀⠴⠚⠉⠉⠑⠦⠴⠚⠋⠉⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢘⡄⢷⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠈⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⡳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⣕⠢⢄⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠒⠦⣄⠀⠀⠀⠉⠉⠁⠀⠀⣀⡤⠤⢄⡀⠀⠀ ⢀⡞⠁⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠲⠏⠀⠀⠀⠘⢦⠀ ⢸⡇⠀⠀⠀⠀⢀⡖⢳⠀⣠⠺⡄⠀⠀⠀⠀⠀⠀⠀⢘⡆ ⠀⢻⠇⠀⠀⢀⣾⣶⡏⢀⣿⣴⠇⠀⠀⠀⠀⠀⠠⢀⡾⠀ ⠀⡏⢠⠖⠓⡾⢿⡿⠀⠸⣿⣿⢠⠀⠢⣄⠀⠀⠀⢻⠀⠀ ⢸⠀⠈⠛⠚⠁⠀⠀⠺⠃⠈⠁⠐⠦⣴⠿⠀⠀⠀⢸⡆⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀ ⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣧⠀ ⠀⠀⡯⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⡟⠀ ⠀⠀⢳⣤⢡⣤⠉⠛⣲⡶⠒⠲⣞⠛⢉⣀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠙⠓⠧⠴⠚⠉⠀⠀⠀⠙⢦⣀⠈⠁⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀ ☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩☾⋆。𖦹 °✩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠛⠳⠶⣤⣀⣠⣤⣤⣴⡟⠁⠀⠙⣷⠟⠋⠉⠉⢿⡀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠉⠀⠀⠀⡿⠀⢠⣟⣿⠿⠳⢦⣤⡴⣼⣇⠀⠀⠀ ⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣽⣏⠀⠀⢸⣷⡄⠀⣿⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⢾⡟⠛⢁⣼⣟⠀⠀⠀ ⠀⢀⣼⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣥⣽⢤⠀⠀ ⣀⣈⣷⣏⣁⠀⠀⢀⠀⠉⠙⠻⣶⣾⣳⣶⠟⠉⠁⢀⠀⠀⠀⠶⢻⡟⠒⠒ ⠀⠀⠸⣇⣀⠀⠀⠛⠉⠂⠀⢀⡿⣉⣉⢿⡄⠀⠒⠉⠋⠀⠀⠠⣼⠧⢤⠀ ⠀⠐⠛⠻⣍⣀⡀⠀⠀⢀⣠⠞⠙⠧⠼⠈⠳⣄⡀⠀⠀⠀⣠⣴⣟⡀⠀⠀ ⠀⠀⣠⠴⠛⢿⣭⠿⠿⢯⡅⠀⠀⠀⠀⠀⠀⣠⣭⣩⣭⣭⣿⣋⠈⠙⠂⠀ ⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣿⠶⠶⠶⠤⠶⣾⠇⠀⠘⣧⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⣰⠾⠋⠀⠀⠀⠀⠀⣧⡀⠀⠀⢿⣄⣤⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⋆。‧˚ʚ🍓ɞ˚‧。⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣦⢴⠟⠋⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢴⣾⡙⣻⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⢰⣿⣦⠤⠔⠀⢹⣧⣀⣀⠀⠀⠀⠈⠀⡀⠀⠀⠀ ⠀⠀⣸⣆⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠾⠂⠀⠀⠀⢻⡏⠀⠀⢾⡛⠻⣯⣉⠁⠀⠀⠀⢀⡿⣤⣀⡀ ⠠⣴⣟⣻⡷⢶⠀⠀⠀⣾⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⠛⠛⠛⣿⠛⠂⠀⠐⠻⣷⣼⠟⠉ ⠀⠀⠹⡿⠀⠀⠀⠀⠀⣿⣠⣀⣒⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠔⠀⠀⠀⠀⠈⠋⠀⠀ ⠀⣠⠀⠀⠀⠀⠀⢀⣤⣿⠟⣿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⢶⣤⡀⠀⠘⠟⢁⣿⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠤⣤⣄⠀⠀⠀⠀⠺⣧⡀⠀⠀⣴⠟⢿⡆⠀⠀⠀ ⠛⢷⣾⠋⠀⠀⠀⠀⣾⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⡁⢻⡀⢀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣤⠀⣿⠐⢸⡇⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⠄⠀⠀⠀⠁⠀⢀⣸⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡏⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠙⢾⣧⡄⠀⠀⠀⠀⠀⣁⡶⠋⠉⠀⠉⠙⢿⣄⠉⠉⠉⠛⠿⣿⡟⠉⠉⣙⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣤⣶⡾⠻⣃⣀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠹⣶⠄⠀⠰⣈⣁⣠⣤⣤⡤⣽⣿⣯⣹⣿⣿⣿⣷⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣞⡥⠖⠚⠛⠶⣝⢦⡀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣸⣯⡏⠀⠀⢻⡆⡆⢸⡏⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿ ⣾⡏⠀⠀⠀⠀⠀⠈⣇⠱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣹⣿⡇⠀⠀⢸⡇⡇⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣾⠁⠀⠀⠀⠀⠀⠀⡼⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢹⣷⣿⣄⣀⣼⣇⡀⢰⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣟⡱⣄⡀⠀⠀⣀⡼⣱⠇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⢿⣿⣿⣿⡿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠁⠙⠶⠭⠉⠉⣵⣾⠏⠀⠀⢳⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⡃⢸⣿⣿⣧⣄⣄⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠉⢻⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⠶⠢⢤⡔⠉⠉⢳⠀⠀⠀⣿⠷⠚⠋⠉⠉⠉⠉⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⡤⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⢀⡔⠋⠲⡤⢏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⢧⣀⡠⠃⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡀⠀⣠⠋⠒⠒⠁⠀⢀⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠉⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡝⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣠⣞⡤⠄⠒⠒⠒⠒⠒⠢⠤⢤⣈⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⢀⠜⢡⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡙⢆⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡴⠋⢠⣿⣿⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠈⢣⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⠀⣼⠁⠀⠈⠿⣿⣿⠟⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⣷⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡴⠁⠀⢀⡴⠃⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠻⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠞⠁⣀⠴⠋⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⣦⣀⠉⠁⠒⠢⠤⣤⣤⠤⠤⠤⠤⠤⠒⠊⢉⢼⣃⡴⠊⠁⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠉⠓⠤⢄⠤⠊⣁⣈⠓⢄⣀⣀⣀⡠⠶⠛⠉⠘⡆⠀⠀⠀⣠⣇⣀⣙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢡⠀⠀⠀⠀⠀⠈⡇⠀⠀⠑⣢⠊⠰⠁⠃⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⢃⡀⠴⠈⠀⢱⢰⠀⢀⠜⠁⠀⡄⠀⡼⠀⠀⠀⠀⠀⠀⢰⡀ ⠀⠀⡃⢠⠊⠁⠑⠘⠌⠈⠁⠀⠀⠉⠉⠀⠐⢇⠀⠀⠀⠀⠀⢸⢡ ⠀⠀⠀⡎⠢⠤⡔⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⡌⠀ ⠀⠀⡐⠣⠄⠔⢁⠠⠄⠒⠀⠈⠉⠁⠐⠂⠄⡀⠀⠈⠐⠲⡈⠀⠀ ⠀⡐⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠰⠀⠀ ⠀⠃⠀⠌⠀⣠⣾⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠡⠀⠀⡇⠀ ⠐⡀⠘⠀⠰⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⢁⠀⡇⠀ ⠀⠡⢰⠀⠀⠀⠉⠉⠀⠀⠀⠘⠓⠀⠀⠀⠈⠉⠀⠀⠀⠘⠰⠀⠀ ⠀⠀⠑⢆⠀⠀⠀⠀⣠⠶⠂⠒⠒⠒⠒⠢⡀⠀⠀⠀⢠⠗⠁⠀⠀ ⠀⠀⠀⠀⠑⠢⣀⠰⡁⠀⠀⠀⡠⠔⠒⠂⠇⢀⡠⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠘⠍⠀⢒⢾⠀⠀⠀⠀⢈⡫⣵⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠌⠑⠠⠬⠛⠈⠢⡀⠀⠀⠈⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⠃⠀⢸⠀⠀⠀⠀⠀⠈⡢⠀⠀⠠⣁⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⠤⢀⡀⠬⠤⠀⠀⠀⠐⠁⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠑⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⢀⣴⣋⢀⣯⠷⡍⣪⠉⠉⠒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠇⠰⠵⢀⡹⠽⠕⠛⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⠠⠮⠂⠉⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀ ⢰⠉⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰ ⠀⢁⡶⢲⠈⠁⠀⡤⢚⠒⠒⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠒⠉⠀ ⠐⠉⠀⢸⡄⠀⡹⣴⣿⡇⠀⠀⠀⠀⠉⠒⢲⠀⠀⠀⢠⠀⢃⠇⠐⠠⠄⠀ ⠀⠀⠀⠀⢣⣀⠇⠈⠛⠁⠀⠆⠀⠀⣼⣿⡆⢱⠢⠀⢸⠀⠈⢂⠀⠈⡄⠀ ⠀⠀⠀⢀⢴⠓⠳⢄⡀⠀⠐⠄⠀⠀⠙⠿⠃⠜⠆⠀⠈⢆⠀⢀⡆⠀⡇⢈ ⠀⠀⠀⠀⠢⠀⢠⠃⠈⠒⠤⠀⣀⠀⠀⢀⡜⠀⠀⡠⠂⠁⠉⠉⠁⠀⠈⠂ ⠀⠀⠀⠀⠀⠉⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠴⠥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⣑⣦⡄⢦⣀⠀⠀⠀⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠭⠰⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣶⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⢡⡿⠛⠀⠘⠻⣿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡷⠋⠀⠀⠀⠀⠀⠈⢿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡸⣷⣾⣷⣦⣤⡀⣀⣀⣠⠤⢤⣄⣀⠀⠀⠀ ⢸⣿⡏⠆⠀⠀⠀⠀⣿⡇⢀⣼⡿⠁⠀⠀⠀⠙⢿⡟⢻⡿⠋⠀⠸⢿⣿⡟⢆⠀ ⠸⣿⣿⡀⠀⠀⠀⠀⠙⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠹⣷⣬⡆ ⠀⠻⣿⣷⣄⠀⠀⠀⣀⣠⢿⣇⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⡆⠀⠀⠀⠀⣹⣿⡇ ⠀⠀⠙⠿⣿⣿⣶⣿⣷⣶⣿⣿⣿⣦⣀⠀⠀⣀⣴⣿⣁⣼⡟⠀⠀⠀⢀⣿⣿⠇ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠈⠛⠿⣿⣿⣿⣿⠋⠙⠛⠋⠀⠀⠀⠀⠈⠉⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢻⣿⣷⣄⠀⠀⠀⢀⣤⣤⣤⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣭⣛⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠛⢿⡿⠛⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢛⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣶⣦⡀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢀⣀⣤⣤⣀⡀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣭⣽⣶⣿⣿⣭⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⠿⣋⡷⣄⣀⣀⣰⠃⠀⠀⠀⣷⣦⣴⣞⣭⣟⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⡾⣿⣿⣷⣿⡟⠋⢠⣶⣶⡖⠋⠀⣏⢻⣿⣿⢷⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⢠⡞⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣧⣛⣿⣟⠽⠁⠀⢀⣹⣇⡀⢠⡄⠈⠛⠒⠛⠿⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⢸⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠉⠁⠀⠙⠲⣯⣥⣬⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀ ⠀⠉⠻⢿⣶⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠫⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣠⣤⠈⠉⠛⢿⠀⠀⠀ ⠀⠀⠀⢠⣿⡿⠋⠀⢀⣤⠀⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⡒⠒⡿⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣄⣙⡋⠀⢿⣗⡾⠀⠀⠀ ⠀⠀⠀⠘⣏⢰⣾⡄⢀⣉⣴⣧⣼⣿⣿⣦⣴⣦⣤⢤⣀⣀⣙⣋⣁⣀⣠⣤⣶⣿⣿⣿⣏⣿⣿⡾⡏⠉⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠛⣿⣹⢻⠿⣾⣿⣿⣿⣷⣟⣿⣿⣽⣻⡿⢯⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⠿⠛⢷⣿⣿⣿⠿⢿⣿⣿⣮⣻⣿⣾⣿⣿⣿⡟⠿⣿⣿⣿⣿⢷⢸⣥⠟⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣿⣿⣯⣿⣼⣿⣿⣿⣿⡟⢷⣍⣿⠿⣶⣯⣽⣿⣿⣿⡌⢦⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣆⣾⣽⣷⡀⢰⣿⣿⠿⢟⣫⠿⢿⠁⠨⢽⣗⣿⠛⠉⢹⢶⣍⡻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠿⠛⠁⣀⡙⡇⢸⣏⣤⣴⣶⣾⣿⣿⣄⣠⣴⣿⣿⣦⣀⣾⣿⣦⣝⡻⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⣶⣶⠂⠛⣳⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⡟⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠒⠒⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⢿⣿⣿⣷⣯⣳⠦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣾⣿⠷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⠙⣁⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠿⠿⡷⣿⢁⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣵⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣀⠀⠉⠛⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠿⠴⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⡳⣼⣆⠀⠀⢹⡄⠹⣷⣄⢠⠇⠻⣷⣶⢀⣸⣿⡾⡏⠀⠰⣿⣰⠏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡹⣟⡪⢟⣷⠦⠬⣿⣦⣌⡙⠿⡆⠻⡌⠿⣦⣿⣿⣿⣿⣦⣿⡿⠟⠚⠉⠀⠉⠳⣄⡀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣟⠛⠛⠙⠛⠉⠻⢶⣮⢿⣯⡙⢶⡌⠲⢤⡑⠀⠈⠛⠟⢿⣿⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠯⣙⠛⢉⣉⣙⣿⣿⡳⢶⣦⣝⢿⣆⠉⠻⣄⠈⢆⢵⡈⠀⠀⢰⡆⠀⣼⠓⠀⠀⠀ Nah ⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠖⠉⠻⣟⡿⣿⣭⢽⣽⣶⣈⢛⣾⣿⣧⠀⠙⠓⠀⠑⢦⡀⠹⣧⢂⠀⣿⡇⢀⣿⠺⠇⠀ ⠀I'd⠀ ⠀⣿⠀⠀ ⠀⠀⠀⠀⠐⠈⠉⢛⣿⣿⣶⣤⣈⠉⣰⣗⡈⢛⣇⠀⣵⡀⠀⠘⣿⡄⢻⣤⠀⢻⡇⣼⣧⣿⠀ Beef on this site⠀⡿⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⢍⡉⠛⠻⣷⡆⠨⣿⣭⣤⣍⠀⢹⣷⡀⠀⠹⣿⡄⠈⠀⢿⠁⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⣇⠀⠀ ⠀⣿⣇⣠⣾⣿⣛⣲⣿⠛⠀⠀⢀⣸⣿⣿⣟⣮⡻⣷⣤⡙⢟⡀⠀⠙⢧⠀⠀⠎⠀⠉⠁⠰⣿⠀⠀ ⠀⢀⡿⠀⠀ ⠀⠈⢻⣿⣿⣽⣿⣿⣿⣴⡏⠚⢛⣈⣍⠛⠛⠿⢦⣌⢙⠻⡆⠁⠀⠀⠀⣴⣦⠀⠀⠀⠐⢳⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠀⠀⠀ ⠀⠀⠈⠙⣿⣧⣶⣿⠿⣧⣴⣿⢻⡉⠀⢀⣠⣴⣾⡟⠿⠃⠁⣠⣤⡶⣾⡟⠅⠀⣀⡄⠀⣾⢸⣿⣏⢻⢶⣦⣤⣤⣄⢶⣾⣿⣡⣤⡄⠀ ⠀⠀⣠⣞⣋⣿⣿⣾⣿⡿⡛⣹⡟⣤⢰⡿⠟⠉⣀⣀⣤⣤⡠⠙⢁⣾⡿⠂⠀⣿⠟⣁⠀⣹⠀⣹⣿⡟⣼⣿⣿⣌⣿⣞⣿⣿⠁⠀⠀⠀ ⠀⢠⡿⢛⢟⣿⣿⣿⣿⣿⣿⡟⣼⣿⣟⢓⠛⣿⣏⣿⣵⣗⣵⣴⣿⢟⡵⣣⣼⣿⢟⣵⣶⢻⣶⣿⠀⠀⣈⢻⣿⣿⣿⢿⣾⢿⣧⠀⠀⠀ ⠀⠘⠃⢸⣿⡾⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣟⣾⡿⣫⣿⣿⣿⣽⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣴⡆⣻⣿⡏⣿⢻⣧⣿⡿⣿⡆⠀⠀ ⠀⠀⠀⠜⣿⣾⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣭⣿⣖⣿⢿⣿⡿⣿⣿⣿⡿⢡⢯⣿⣿⣿⣿⣿⣿⣿⣧⡿⣾⣷⣿⣿⢿⣿⡇⠉⠁⠀⠀ ⠀⠀⠀⠀⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⡇⣭⣿⣿⣿⣿⠃⠞⠟⣸⣿⠏⣸⣧⣀⠿⢿⣿⣿⣟⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢶⣦⣄⣿⠏⠀⣿⣟⣿⣶⠾⣿⣟⣋⣛⣿⣿⣿⣿⡇⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠛⠫⣿⣿⣿⣿⣿⡿⣧⠛⣿⠛⣿⣿⣿⣷⡌⠹⡟⠀⠀⠉⡟⠋⢠⣾⣿⣿⣿⡟⣿⣿⣿⣿⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⣾⣷⣿⣿⣧⠙⠀⠙⢣⠝⠛⠋⣽⣷⢦⠇⠀⠀⠘⠁⣤⣾⣿⠝⠛⠉⠘⢻⣿⣿⢿⣼⣷⡟⢻⣷⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣾⠟⠀⢸⣷⣿⡇⠀⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣆⠀⠛⠁⠶⣶⣶⣶⣶⣶⣶⡶⠆⠘⠋⣠⡾⢫⣾⡟⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠙⣷⡀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⢀⣴⠋⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣰⣦⡀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡄⢺⣿⡄⠹⣿⠻⢦⣤⣤⣤⣤⣶⣿⡟⢀⣀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡀⠹⡷⣦⣀⡀⡀⢸⣿⠏⢠⣾⣿⠀⠀⣾⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣷⣻⡟⠀⡼⠁⣴⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 🤞🤞🏻
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢎⠱⡈⠉⠙⠻⣟⡿⠛⠙⠻⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿ ⠧⢤⣤⠤⠄⡀⢣⠀⠀⠀⡝⠀⠀⠀⠀⠸⠿⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣘⣿⡤⠄⠠⢽⡄⠀⠀⡇⠀⠀⠀⠀⠀⠋⢹⠉⢹⡎⠙⡻⠟⠛⠛⢿⣿⣿⣿ ⡘⣿⡟⡀⠀⠀⢀⡼⠀⠀⡇⠀⠀⠀⠀⠀⣆⣸⣀⡸⣧⠊⠀⠀⠀⠀⢀⣿⣿⣿ ⡆⢸⠏⠻⠖⠲⡝⠃⠀⡤⢧⡠⠠⠀⠀⢠⠿⠯⠭⡽⠁⠀⠀⠀⠀⢀⠞⠈⠿⣿ ⣿⣼⡄⠀⠀⣤⠂⠀⡤⠲⣉⠇⠎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠞⠀⠁⠀⠘ ⡈⡏⡃⠀⠀⠀⠀⠀⠰⠒⠑⡲⠖⠒⠤⡀⠀⠀⠀⠀⠀⠀⢀⡔⠇⠀⠀⠀⠀⠀ ⠀⠡⠁⠀⠀⠀⠀⡰⠁⣠⠞⠒⠀⠀⠒⠨⢢⡀⠀⠀⠀⠀⠀⠸⡞⠤⠀⠀⠀⠀ ⠔⠁⠀⠀⠀⠀⢠⠁⡴⠥⢤⡀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠏⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡜⡇⠀⠀⠀⠉⠀⠀⠈⠙⠲⠀⠦⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠧⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢀⠀⢀⡜⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠣⠈⠢⢈⠒⢠⢄⠀⣀⣀⡀⢴⣴⠗⠁⠀⠀⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⢼⠈⠘⣤⠃⠂⠀⠒⠕⠁⠀⠀⡠⢘⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⢆⠈⡤⢃⣀⡠⠊⠀⠀⠂⣭⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⢃⠀⠀⠀⠀⢀⡠⢼⠀⠀⠀⢀⢔⣆⣀⣒⣼⠀⠀⠀ ⠀⠘⡄⡠⠒⠲⠇⠀⠀⡑⠒⠃⡆⢇⠀⠀⢨⢳⠀⠀⠀ ⠀⠀⠱⣇⠀⢰⠁⠈⡆⠑⡄⠀⠘⠄⣑⣒⡡⠒⢄⠀⠀ ⠀⠀⢀⠟⡏⠀⠑⠒⡁⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀ ⠀⢠⠃⠀⠑⡤⠠⠞⠀⠀⠀⣀⠠⠤⠤⠤⠄⡀⠀⠀⢣ ⠀⠆⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠑⢆⠸ ⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⣦ ⠀⡆⠀⠀⠀⠀⠆⠀⠰⠏⠉⠉⠀⠀⠀⠚⡀⠀⠀⠀⡟ ⠀⠘⢄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢀⠜⠀ ⠀⠀⠈⡱⠤⢀⣑⢄⡀⠀⠀⡀⠀⠀⢀⣀⢤⠂⠁⠀⠀ ⠀⠀⡸⠄⡀⠀⠀⠈⣉⡩⠅⠋⠉⠉⠁⠀⠀⢇⠀⠀⠀ ⣠⡞⠀⣀⣀⠉⠉⢀⣀⣀⣀⣀⣀⢀⡀⠀⠀⢀⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⢸⡄⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⢤⣄⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢧⠀⠀⠳⣄⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⠾⠽⠛⠛⠉⠉⣀⣠⠤⠖⠊⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣾⣆⠀⠀⠘⣷⣉⡭⠥⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠋⠉⠁⠈⠉⠉⠀⠀⣀⣤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣴⣶⡾⠽⢟⣛⣏⣤⣭⣟⡆⠀⠀⠉⠙⠓⠒⠦⠤⣤⣤⡤⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠒⠒⠚⠉⠉⠀⠀⠀⠈⠉⠛⠷⣦⣄⣠⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠒⠋⠉⠙⢳⣄⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢶⣾⡏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⢿⣍⣁⡿⡆⠀⠀⠀⠀⠀⣙⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡤⠖⠚⣋⡥⠴⠚⠋⠁⠀⠀⠀⢀⣀⡤⣴⡲⣏⠉⠙⢿⣦⡀⠀⠀⠀⠁⠙⠓⠒⠒⠒⠉⠁⠀⠀⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⠖⢋⣩⠤⠖⠚⠉⠁⠀⠀⣀⣀⠤⠔⠒⠉⠉⠀⠀⠀⠉⠲⢽⣒⠤⣝⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠯⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⢯⣉⠉⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢭⡏⣹⡷⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣷⣶⣴⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠉⠓⠲⢮⣍⣓⡲⡤⢤⣀⣼⠺⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⡟⠀⠀⠀⠀⠀⠈⣷⣿⠏⠉⠉⢻⣿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⣿⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣠⠴⠚⡙⠙⠲⣤ ⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣿⠃⣰⠟⠉⠙⢦ ⢦⡈⢁⣾ ⡟⠉⠳⣆ ⠸⠀ ⠙⣆⠙⢧⡀⢀⡴⠃ ⠛ ⢧⡀ ⢀⡴⠃ ⣰ ⠈⠓⢦⡈⢡⣰⠞ ⡈⠈⠓⢦⡈⢡⣰⠞⠁ ⠀⣰⠃⣰⡏⠀ ⠙⣆⠙⢧⡀⠀ ⢀⡴⠃ ⣰⠏⠀⠀ ⠈⠳⣄ ⠙⠶⣄ ⠈⠓⠲⠖⠚⠀⠀⠀⠀⠀ ⠈⠓⠲⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠀⠀⣀⣠⡄⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠛⠛⠛⠟⢂⣶⣆⡀⠀⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⢩⠇⠀⠀⠀⠀⠾⡇⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⣰⡟⣣⠶⠛⠙⢻⣦⠀⠀⠀⠀⠀⢀⣴⠶⠚⠳⣾⣿⡀⢠⠒⠲⡄⢀⣀⠀⠀⠇⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⢡⠀⢠⡿⣿⠋⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣿⣇⢸⡀⠀⠙⠉⠀⢹⠀⠰⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⣼⠇⠀⣰⣾⣶⠀⢀⣿⢂⣠⣄⣀⣼⡄⢰⣿⣶⡄⠸⣿⡀⢣⡀⠀⢀⣠⠎⠀⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⢠⣿⡿⠀⠀⢿⣿⠟⠀⢸⣿⡏⠁⠀⢙⣿⡇⠈⢿⣿⠇⠀⢻⣧⠀⠳⠖⠋⠀⠀⠀⠀⠀⠰⠀ ⡴⠉⠉⠓⠒⠒⠤⣄⡸⣿⣧⠀⠀⠀⣤⡄⠀⠀⠙⠿⠿⠿⠿⠋⠁⠀⠀⣤⡀⠀⣸⣿⣀⡤⠔⠒⠚⠉⠉⠳⡀⠀⠃ ⢧⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀ ⠘⢆⠀⠀⠀⠀⠀⠀⠈⣟⠙⠛⠷⣦⣄⣀⡀⠀⠀⢀⣀⠴⣲⢤⣀⣀⣠⣴⠾⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀ ⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⣿⠉⠀⠀⠀⣸⢿⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢧⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣲⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡒⠊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⢀⡇⠀⠀⠀⠀⢠⠴⢤⣠⠴⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢻⣀⣀⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⡇⠀⠀⠀⢠⠃⠀⡆⠀⠀⠀⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⠀⠀⠀⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠀⠀⠹⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠳⠤⠤⣹⣦⡀⠸⡄⠀⠹⡄⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠸⠀⢀⠼⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⣁⣀⣤⠾⠓⠒⠉⠉⠀⠀⠀⠉⠉⠑⠛⠢⠤⠴⠋⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠄⠠⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣶⡾⠋⢠⣶⠶⣾⣿⡖⢦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣿⠟⠁⠀⠈⢿⣿⣴⣿⣿⡆⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠤⠒⠷⣦⣀⣀⣀⣀⣈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⣦⠀⠀⠀⠀⠉⠛⢻⣿⣡⠇ ⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠈⢱⡇⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠿⣤⣀⣀⣀⣠⡴⡿⠇⠈⠆ ⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⢧⡀⠀⡴⠋⠉⠉⢢⡤⠼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⡽⢲⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣟⣻⡉⠒⡾⠉⠈⠓⠤⣀⠤⠊⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠉⠀⠀⠀⡀⠀⠀⢀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⠳⢄⡀⠀⣀⠞⠦⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⣀⣤⣶⣿⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⠤⠐⠒⠂⠈⠉⠉⠉⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠹⣍⣹⡿⠿⠟⠋⢉⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⢹⠀⠠⠤⠒⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⡄⣺⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡟⡇⠀⠀⠀⠀⠀⡸⠃⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡈⢆⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⡇⠀⠀⠀⠀⢰⠃⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣷⠘⡄⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡎⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⣿⣿⡿⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠠⡇⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢀⡴⠶⢤⣤⡀⠀⠀⠀⠈⠛⠛⠁⠀⡇⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠒⠁⠒⠦⣙⢦⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠙⠷⣦⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢀⣼⠟⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠉⠑⠒⠠⢤⣤⣄⣀⡀⠀⣀⣠⠤⠤⠒⠒⡻⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⡽⠋⠀⠀⠈⢧⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠲⠴⠒⠁⠉⠱⡒⠒⠠⢤⠤⠀⠀⠈⠳⠤⠤⠴⠊⠀⠀⠀⠀⠀⠈⢦⣀⡴⡇⠀⠀⣀⡀⠤⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠒⠦⠄⠀⠀⠳⣄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠉⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡖⠭⢿⣟⣿⠶⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠑⠤⣄⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⣤⣄⡀⠀⣠⡶⠚⠉⠙⠲⣄⠀⠀⢀⠸⣆⠀⣀⡀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠈⢹⠏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣤⠞⠛⠛⠲⢄⠀⠀⣰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⡞⠁⠀⠀⠀⠀⠈⣇⠰⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠊⢳⡦⠸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠙⠦⣄⣀⣠⠴⠋⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀ ⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠀⢸⡷⣄⡀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⠦⠤⠤⡤⠞⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⣀⣀⣀⣠⠴⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⠤⠤⠤⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⡿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿⡇⢀⣠⣾⡿⠟⠛⢻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣤⣤⣄⠀⠀⢸⠀⠀⠀⠀⣦⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠘⣧⠘⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠛⠋⠃⠀⠀⠩⠛⣿⣦⢼⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⣀⡤⠔⠒⠒⠲⢤⡀⢀⣠⠴⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠛⣶⠞⠁⠀⠀⠀⠀⠀⠀⠙⣏⠀⠀⠀⠀⠀⠀⠈⢧⣀⣤⣶⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢻⡅⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠹⣄⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡼⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠓⠢⠤⠤⠖⠋⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠴⠚⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠒⠒⠒⢺⢿⣿⢗⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣸⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡟⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡟⣴⣶⡄⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣧⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣏⣻⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⠙⣿⣷⣶⣤⣤⡄ ⠀⠀⠀⠀⢻⢇⣿⣿⣿⣿⣿⠹⠀⢹⣿⣿⣿⡇⠀⢟⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢘⣼⣿⣿⣿⣿⣿⡆⠀⢸⣿⠛⣿⡇⠀⢸⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣈⠻⠴⠟⣁⣴⣿⣿⠗⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⡏⠀⠹⣿⠿⠿⠿⠿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⢠⣿⣿⣿⣿⣥⣴⣾⣿⣿⡿⠿⠿⡗⠶⠃ ⣼⠀⠀⠀⢰⣗⠀⣹⠂⠀⠀⠀⠀⡿⠀⠀ ⢿⠀⠀⠀⠀⡁⠀⠉⣀⠀⠀⠀⢠⠃⠀⠀ ⠘⣆⠀⣠⣀⡉⠋⠉⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠈⡿⠿⣅⣀⣀⠤⠴⠚⠁⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⣰⢿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣇⡤⠞⠁⢸⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠠⡄⠀⠹⣿⣿⣷⣀⣤⣴⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⢸⣿⣄⠀⠘⣿⣿⡿⠿⠟⠋⠉⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣧⡀⠈⠉⣀⡀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠁⠀⠀⣿⣿⣿⣿⣷⣶⣾⠟⠁⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⡀⠀⠘⠲⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⡄⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡇⠀⢠⣿⣿⣿⠏⠀⠉⠙⠻⣿⣿⡄⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⣿⣿⡿⠁⠀⣸⣷⣄⣀⠀⠉⠙⠦⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢰⣿⠏⠀⢀⣴⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢀⡿⠃⠀⣠⣿⣿⡿⠉⠉⠉⠛⠻⢿⣿⣿⣷⣶⣬⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠈⠀⢀⣴⣿⣿⣯⣠⣤⡿⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⣠⣾⣿⡟⠋⢉⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⠃⠀⢀⣴⣿⣿⣿⡾⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣤⣶⡾⠿⠟⢛⣿⣿⡿⠀⣠⣿⣿⣿⣿⠟⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣿⣿⠟⣋⣁⣤⣴⣾⣿⣿⣿⢇⣼⣿⣿⣿⡿⢃⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣷⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⡟⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣧⠀⠀⠀⠀⠀⢰⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣷⠈⣿⣆⠀⠀⠀⢠⣿⠏⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢸⡿⢋⣼⣿⡏⢻⣿⣿⣿⣿⣆⢿⣿⠀⠀⠀⣼⣿⠀⣶⠈⢻⣿⣤⣄⣀⣀⣤⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣟⣠⣾⣿⠟⠙⢿⣦⡛⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠇⣰⣿⣧⡈⠛⠛⠛⣋⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠿⠋⠀⠀⠀⠈⠻⣿⣦⠻⣿⣿⣿⣷⣦⣀⠙⠻⣿⣿⣿⣿⣿⠉⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣜⣿⣇⠈⣿⣿⣿⠂⣾⣿⢟⣻⣿⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠙⢿⣦⣹⠇⣿⣿⠏⢸⠛⣡⣾⣿⣧⣈⠳⠌⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣀⠀⠀⠈⠻⣿⣦⣿⡏⢀⣴⣿⠟⠉⠈⠛⢿⣿⣦⣈⢿⣷⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣦⣄⣀⢈⣿⣿⣴⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣧⣠⣶⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⢬⣝⡿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⢿⣿⢠⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣻⣿⣿⣏⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣱⣾⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡿⣿⣿⣿⣦⣍⡛⢿⣦⣄⠀⣀⣴⠟⣋⣴⣿⣿⡿⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⢿⣿⣿⣿⣿⣶⣬⡛⠿⠟⣡⣾⣿⣿⣿⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⢻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡏⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢲⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⢋⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠙⢿⣷⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷⠆⠉⠻⣿⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⣀⣛⣋⣉⣉⣉⣉⣉⠙⣿⣿⣿⣿⣿⣿⡿⣠⣤⣶⣶⣶⣶⣿⣿⠿⠿⠿⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣷⡈⢿⣿⣿⣿⡿⢡⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣿⣿⣿⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡛⠛⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣤⣶⡿⣿⣿⠟⠻⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡌⠙⠋⠑⠿⣿⣤⣀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠃⠀⢤⣤⣀⣈⣙⣻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠾⣿⡇⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣿⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠙⢿⣷⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠳⣴⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀૮꒰ ˶• ༝ •˶꒱ა ./づᡕᠵ᠊ᡃ࡚ࠢ࠘ ⸝່ࠡࠣ᠊߯᠆ࠣ࠘ᡁࠣ࠘᠊᠊° i shoot u >:( ૮꒰ ˶> ༝ <˶꒱ა ./づᡕᠵ᠊ᡃ࡚ࠢ࠘ ⸝່ࠡࠣ᠊߯᠆ࠣ࠘ᡁࠣ࠘᠊᠊°.~♡︎ with love tho-
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⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠉⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⣀⠀⠀⠀⣀⡤⣔⡿⢏⡉⠒⠂⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡽⠓⠻⠿⠒⠋⠁⠀⠀⠙⠒⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀ ⠀⠀⠀⣠⠎⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⡼⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦ ⡞⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿ ⠹⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⣄⣹⣄⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠁⠙⢾⣧⡀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠈⠻⣾⣷⢠⠄⠄⠈⠀⠈⠉⢉⠈⢠⡶⠛⠉⠉⠉⠉⠙⢿⣧⡀⠉⠉⠋⠙⠻⢿⣿⣿⡿⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣇⠀⠀⣀⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣅⡀⠀⠀⢰⡀⠾⠋⠓⠀⠀⠉⠛⠺⣟⣟⠛⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⡞⣫⠿⠒⣂⣃⣶⠶⢦⡀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢠⣵⢶⡶⠶⠿⢿⣿⠛⠿⠿⣿⢷⣼⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣏⣡⠶⠛⠉⠉⠙⠻⢦⡙⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣼⡏⣿⠁⠀⠀⠈⣿⠀⣿⠀⣿⡇⣿⣟⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡿⠋⠀⠀⠀⠀⠀⠀⠈⢳⡌⢧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢹⡇⣿⡀⠀⠀⠀⣿⠀⣿⠀⢸⡇⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡆⢿⣿⣹⣧⠀⠀⠀⣿⠀⡟⠀⣸⣇⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡎⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⣼⣿⣿⡿⣷⣶⣶⣿⣷⣦⣤⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣌⠻⣦⡀⠀⠀⢀⣠⡾⣣⡾⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡟⢹⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠉⠻⢦⣍⣉⡉⢉⣤⢾⠿⠃⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡇⠀⣿⣿⣿⠯⢤⢠⡄⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠉⢿⣿⡿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⣷⣀⣀⡀⠀⡴⠚⠛⢲⡄⠀⠀⠀⢸⣷⣧⣤⡿⠿⠟⠛⠛⠛⠓⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣀⣀⡘⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⠏⠁⠈⠉⣺⣇⡀⠀⢠⡇⠀⠀⠀⢸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⡿⠚⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⡞⠁⠀⠙⢧⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⠞⢧⡀⠀⣠⠞⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠈⢹⠗⠤⠤⠴⠃⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠙⠦⠤⠴⠋⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠈⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⡤⠴⠶⠒⠚⠛⠓⠒⠲⠶⠦⢤⣀⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣴⠋⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡟⠀⠀⠀⠀⠀⣠⠞⢁⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠃⠀⠀⠀⢀⡴⠁⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⢀⡞⠁⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠾⠿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡃⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⢸⠟⣧⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⠀⠀⠀⠀⣠⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⡼⠁⠀⠀⢀⣶⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢿⡳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣠⠞⠁⠀⢀⡴⠋⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡙⢦⡈⠙⠲⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠾⢛⡽⠋⢀⣠⠞⠋⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢿⣦⣀⠀⠀⠀⠈⠉⣙⠿⠻⣿⠛⠛⠛⠛⠋⠉⠁⠀⢀⣴⣻⢤⡾⠋⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠉⠓⠦⢤⡴⠚⢉⣀⣄⡈⠻⢦⣀⣀⣀⣀⡤⠞⠛⠉⠀⠀⢹⡀⠀⠀⠀⠀⣠⣧⣀⣀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠙⡆⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⢭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⢀⣭⠍⣀⠀⡀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡨⠓⠒⠛⠊⠀⠑⠂⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠂⠈⠉⠉⠉⠁⠀⠐⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠀ ⠀⠀⢀⠔⠁⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀ ⠀⡠⠁⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠁⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⡆⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⡇⠀⠀⠙⠿⣿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿ ⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉ ⠀⠡⡐⠄⠀⠀⠀⠀⠰⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠻⢦⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢄ ⠀⡘⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈ ⠀⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠎⠀⠀⠀⠀⢸ ⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⢀⠃ ⠀⠈⡤⠤⡖⠐⢆⣇⡀⠀⣰⠀⠀⠀⠀⢀⠆⠀ ⠀⠀⣣⠰⢭⠂⢘⠆⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀ ⠀⡰⠣⠄⠊⠉⠁⣀⡀⠀⢀⣀⡀⠀⠀⠱⠀⠀ ⠀⡇⠀⢀⠤⢊⡥⠄⠀⠀⠀⠀⡤⢕⢤⠀⡇⠀ ⠀⣅⠀⠎⠀⢻⣷⡞⢀⠀⠄⡘⢷⡾⠀⢃⡸⠀ ⡏⠀⠙⢆⠀⠀⠀⠀⢿⣿⣽⡇⠀⠀⢀⠎⠉⢠ ⠣⡀⠀⠀⠁⠢⡀⠀⠀⠉⠉⠀⣠⠔⠁⠀⠀⡸ ⠀⠈⠢⡀⠀⠀⢩⢛⡟⠀⢺⡛⡏⠀⢀⠄⠈⠀ ⠀⠀⠀⠈⢢⠀⠀⠉⠀⠀⠀⠈⢰⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣼⠀⠀⢀⣤⠾⠋⠉⠉⠉⠛⢶⣄⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠛⠻⣄⠀⠀⠀⠀⣹⠀⢠⡟⢠⡶⠛⠻⣦⣤⠶⢦⡈⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⢀⣠⡤⢤⣤⣺⡏⠀⠀⠀⠀⠀⠸⣧⠤⠶⠶⠛⠀⡞⠀⣎⠀⠀⠀⠀⠀⠀⠀⢹⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⢠⡞⠉⠀⠀⠀⠙⠃⣀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⢧⠀⠹⣦⠀⠀⠀⠀⠀⣰⠟⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠼⣆⣟⠀⠀⠀⠀⠀⣰⠞⠉⠉⠓⣆⠀⠾⢷⣄⠀⠀⠀⠀⠘⢧⠀⠈⠳⣦⣀⣠⡾⠋⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡿⣄⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡆⠀⠀⡹⡆⠀⠀⠀⠀⠈⠑⢦⣀⣀⣉⣁⣠⠴⠋⠀⠘⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣮⣿⣿⠇⠀⠻⣤⣀⣀⣠⠏⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠇⢸⠃⠀⠀⠀⠈⠉⠉⢠⣀⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⣼⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⢿⡄ ⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡇ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⡇ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣿⠻⠗⠀⢹⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣴⡾⠟⠛⠛⡿⠷⠀⠀⠀⠀⠀⠀⢠⣴⣶⠀⠀⠁⠀⠀⠀⠀⠀⢼⡿⠁ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠐⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣃⠀ ⠀⠀⠀⠘⣷⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⠀ ⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣻⡷⢤⣀⡀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⠋⠁⠀⠉⠉⠓⠒⠶⠤⣭⣷⣦⣤⣤⣤⡤⠤⣶⣶⣤⣤⣀⣤⣤⠶⠞⠛⠉⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⠙⠶⢤⣀⣀⣀⣀⣀⣀⣠⠴⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⣀⣰⢫⡞⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣰⣇⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠁⠀⠀⠀⢀⡴⠉⠹⣆⠀⠉⠙⠛⠿⢿⣿⣿⣿⡟⢿⣿⣦⣿⣿⠿⢷⣿⣾⣒⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⣟⣟⠛⠛⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠱⣿⢿⣤⣾⠛⠁⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣥⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠾⠤⢤⣤⣤⡤⣤⠤⠤⣄⣀⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠅⠀⠀⠀⠙⠿⠿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣄⠀⠀⢿⣿⣿⡿⠀⠀⠀⠈⠙⠳⣤⣿⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠤⢴⣶⠦⠤⢤⣤⣄⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣦⡀⠈⣷⣿⣇⣤⣤⠤⠤⠤⠤⣬⣿⣷⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⣷⢈⡏⠀⠙⠛⢿⣿⡿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⡏⣦⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⡀⠀⣿⢸⡇⠀⢀⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿ ⠀⠹⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣽⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⠀⠇⠀⣿⢸⡇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⠤⠤⢽⣿⣿⣅⠱⣄⠀⠀⠀⠀⠀⠀⣴⢣⡏⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣯⣴⣶⣾⡇⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢉⣿⣿⣿⣿⣿ ⡆⠀⠈⣿⣼⣏⠣⣝⡳⠤⢤⠤⠴⢚⣽⡞⠀⠀⢰⠀⠀⠀⢹⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡉⡉⠉⢛⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⢹⣿⣿⣿⣿ ⣿⡀⠀⢸⡏⣿⠀⠈⠛⠒⠒⠲⡞⣿⠇⠀⠀⠀⠘⣼⠟⠉⠙⢧⠶⠋⠉⠙⡆⠀⠀⠀⠀⢠⡿⠟⠛⠛⠛⠛⠛⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠀⠛⠉⠛⢿⣿ ⣿⢿⡆⢸⡇⣿⠀⠀⠀⠀⠀⢸⢠⢸⢀⠀⠀⠀⡄⣿⣀⡴⠊⠉⢣⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠶⠶⠆⠀⠀⠀⢸⣿ ⢿⣷⡹⣿⣧⡿⠀⠀⠀⠀⠀⡼⣸⡌⠸⠀⠀⢸⡿⠋⠀⢧⣀⣀⠞⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠘⣯⣿⠟⢻⡃⠀⠀⠀⠀⠰⠇⡇⠇⠀⠀⠀⠈⢧⡀⢀⣠⠼⣁⠀⠀⡸⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⡿⠋⠁⠀⠈⠉⣹⠗⠋⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡴⠊⠁⠀⢀⡀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⣴⡯⠶⠚⠉⠉⠉⠉⠉⠉⠙⠲⠦⣄⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⠯⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣞⡟⠘⠋⠉⠙⢻⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣼⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠛⠟⠿⣶⡄⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣸⠃⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠓⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⣀⡤⠤⠤⣤⡾⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⢷⠀⠈⠳⣄⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣴⢃⡴⠊⠁⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠑⠦⣀⠀⠈⠉⠓⠶⣤⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣴⡯⣶⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⣿⠓⠶⠶⣺⠗⠚⢷⣄⠀⠉⠉⠉⠉⢉⣀⢴⣋⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⢤⣀⣿⠀⠀⠀⠹⣄⣀⡼⠀⠙⠢⠤⠤⠖⠛⠋⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⢻⠀⠀⠀⢠⡖⠒⢦⡀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⣀⡤⣴⠋⠁⠤⠚⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣸⣇⠀⠀⠘⢦⣀⡴⠃⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠐⣶⠊⢹⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⠈⠦⣀⣀⠴⠃⠙⠲⠤⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⣿⠇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢦⠀⠀⠀⠀⠀⠀⢠⡴⠒⠉⠉⠳⡀⢀⡠⢧⣀⠀⣠⡇⠀⠀⠀⠀⠙⡄⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⢣⡀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠟⠁⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼ ⠀⣀⡀⠀⠻⣦⠀⠀⠘⣆⠀⠀⡴⠒⠐⠲⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣄⠈⠉⠓⠒⠤⠤⠤⠤⠒⠋⠀ ⠖⣦⢬⡛⠲⣼⣷⣤⠞⠉⠁⢸⠀⠀⠀⠀⢘⠀⢀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⡈⠙⢯⡿⢍⠙⡏⠀⠀⠀⠈⠣⣄⣀⡠⠞⠀⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀ ⠫⡙⢦⡀⣙⢆⠑⣾⡀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣀⠤⠔⠒⠀⠈⠉⠉⠁⠒⠢⢄⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⢄⠈⠢⡙⣧⡈⢦⠘⡟⠒⠒⠒⠉⢳⣄⣀⣀⡤⠚⠁⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢹⣄⣀⠀⠀⠀⠀ ⠀⢳⣤⠼⢾⣧⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣬⣆⡇⠈⠙⠒⠤⢄ ⠚⣉⠬⠷⡊⢻⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠋⠁⠀⠈⠁⠸⣧⠀⠀⠀⠀⠀ ⡎⠁⠀⠀⠙⣾⡗⢸⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⠑⣆⡠⡖⠋⢁⣣⣼⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⣤⣶⡿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠉⣀⡠⠴⠚⠉⣴⡿⢧⠀⠀⠀⠀⠀⣿⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣴⠊⣷⣄⣀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡭⠾⢵⣤⣈⡷⠔⠛⠂⠐⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠈⠉⠒⠦⣄⣀⠀⠀ ⠀⠀⠀⠀⣀⣴⠋⠀⠀⢀⠏⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠳⢤⡀⠀⠀⠀⠀⠀⠀⠉⠑⠀ ⠀⠀⠀⠀⢠⣧⠀⠀⠀⢸⣤⣴⠛⠉⠀⠀⠀⠀⠉⣉⣳⣦⣼⣄⣀⣠⡤⠴⠒⠊⠉⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡠⠤⠚⠿⢟⣦⣀⠀⠀⣧⣝⠓⠤⠤⠤⢤⡴⠯⠅⠀⠀⠉⠻⣦⠤⣀⡀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠯⣉⠉⠳⣀⠙⠒⠲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⢲⠏⠹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⣱⣶⣤⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⢇⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠁⠀⠀⠉⠙⣍⡿⠿⢖⡢⢤⣤⣤⠒⠊⠀⠀⠀⠀⢸⠀⠀⢸⠀⠉⠓⠦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠙⢯⡀⠀⠉⠒⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⢠⠊⠉⢆⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣤⣄⠀⠈⠂⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⢀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⣤⠟⣠⣄⣼⠋⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⢀⡤⠞⠁⡟⢠⠟⠉⢹⡦⣤⡀⠀⠀⠘⡷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣦⠞⠁⠀⠀⠛⢻⠀⣠⢿⠀⠀⡿⠀⠀⠀⠻⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⡟⠙⠊⢀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢷⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⣴⣦⠀⢸⡇⠀⢠⣄⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠙⠛⠸⢽⡇⠀⠈⠉⡥⣀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠛⠃⢀⠈⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⣰⠇ ⠀⠀⠀⢀⣠⠾⠛⢦⡀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⣠⣤⣞⠋⠁⠀⠀⠀⠙⠳⢤⣄⡀⠀⠈⠓⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀ ⢹⣠⢫⠗⢦⡀⠀⠀⠀⠀⣿⠜⣽⢟⠛⢶⠒⢒⢺⣟⣉⣁⡀⠀⠀⠀⠀ ⠀⢷⠏⠀⠀⠹⡄⠀⠀⠀⡇⠀⣇⣠⡼⠞⣗⢰⠁⢸⡁⢠⡧⣄⠀⠀⠀ ⠀⢸⣧⣠⠤⠼⠃⠀⠀⠀⣧⠈⠙⣧⠀⠀⠘⢧⡑⣂⣩⡿⢺⣻⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣶⣶⣶⣶⣦⣤⣶⣶⣶⠂⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣆⠀⠀⠀⢹⣿⠿⣷⣄⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⠀⠀⠀⣿⠀⣈⣿⣷⣦⡀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀ ⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣴⣿⡯⣭⣽⣿⡿⣿⣧⡀⠀⣿⠀⣿⣿⣿⣿⣿⣦⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠟⠁⠀⠀⠀⠉⠻⣦⣝⢷⣤⠏⠀⠉⠉⣤⡶⠛⠛⠻⣦⣸⡿⣦⡀⠀⣶⣤⣤⣀⡈⣿⣧⠀ ⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⢸⣿⣦⡿⠃⢀⣴⣿⣿⣿⣷⣄⠈⠻⣇⠛⠀⠀⠀⣼⠃⢀⣴⣶⣶⣦⣝⠀⠹⣿⡀⠸⣧⠈⠙⠻⢿⣿⡄ ⠀⠀⣿⠀⠀⠀⠀⠈⣷⠀⠀⢸⣿⡿⠁⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⢰⡏⢀⣾⣿⣿⣿⣿⣿⡄⠀⢻⡇⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⣠⣶⣶⢿⡆⠀⢸⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠃⠀⠀⢸⡇⠈⣿⣿⣿⣿⣿⣿⠇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⣴⣿⠟⠁⠀⢻⣄⠘⣿⣧⠀⠀⠈⠻⠿⠿⠿⠋⠀⠀⣰⡟⠀⠀⣀⣈⣿⡀⠈⠻⠿⠿⠿⠋⠀⠀⣼⣷⣦⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⢀⣿⡏⠙⠲⢤⣀⠻⣦⢻⡟⢷⣄⣀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠈⠉⠋⠙⣷⣄⡀⠀⠀⠀⠀⢀⣼⠟⣿⡏⠿⣷⠀⠀⠀⠀⠀ ⢀⣼⣃⣸⣿⡇⠀⣴⡟⠋⠑⠈⠙⢧⠀⠉⠛⠻⠿⠿⠿⠛⠋⠀⣀⠀⣀⣤⣤⣤⣤⣬⣙⠻⠷⠶⠶⠟⠋⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠛⣻⣿⣧⠀⠸⣷⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣬⣿⣧⣀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠠⣾⣿⠆⣠⣾⠇⠀⣿⡟⠛⢉⣉⣙⣿⣿⣿⡿⠀⣠⣦⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠛⠿⣶⣤⣤⣴⣾⣿⣀⠀⠀⠉⠁⠀⢉⡉⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⠋⢀⣾⠟⠁⠀⢠⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⠻⡟⠛⢻⠻⢷⣤⣀⠀⠀⠙⠁⠀⠈⠛⠟⠛⠿⠿⠋⢉⠙⠁⠀⢀⣠⣴⡿⠋⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢻⡀⠸⣧⠀⠈⠛⠿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣿⣤⣶⢾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣧⡀⠀⠀⠀⠈⠉⠛⢛⣿⠟⢻⡟⠛⠋⠉⠁⠀⠀⠹⣿⣆⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀ ⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠛⠶⣤⣄⣀⣠⣴⠟⠋⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠈⠁⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⡀⢠⠏⠀⠈⢦⠂⠀⠊⠁⢄⣈⠙⠲⣤⠖⠋⣡⠴⡜⣦⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠘⠊⠀⠀⠠⡀⢇⠀⠀⠀⠀⠈⠉⠙⠛⠷⢤⡀⢠⠀⠈⢷⣠⣴⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠀⠈⠳⡀⠀⠀⠀⠹⢮⢣⠀⠀⠀⠀⠈⢳⡀⠀⣄⠑⠈⢧⠀⢸⠙⣏⡙⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡀⢄⠉⠲⠴⣁⠤⢍⡢⣘⠄⠀⢄⢧⠈⢷⣇⠀⠀⠀⠀⠀⣷⠄⠈⢣⡀⠘⣆⢸⡄⠙⠇⠙⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠹⡏⠀⢄⡀⠀⠀⠀⠈⠙⢆⠀⠘⣞⠆⠈⢻⡀⢀⠀⢄⠀⢹⡆⠀⢸⡇⠀⣹⠈⣇⠀⠀⠀⠈⠳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⢠⠀⠀⠑⠦⠈⠢⣀⠈⢧⠀⠘⢦⡀⠀⠃⠘⠆⠈⡇⣠⡽⡆⢸⣷⢃⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠱⡄⠀⠀⠶⣔⠨⣻⡢⣷⢔⠄⡳⣣⠀⢀⡆⣔⡇⢸⠀⣹⣾⠿⠋⢀⠜⠁⠀⠀⠀⠂⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠣⢄⣀⠈⠑⠲⣖⣄⠉⠊⠉⠉⠑⠋⠘⠘⠃⡼⠸⣿⣧⢸⡞⣧⢧⢠⠔⠁⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠒⠊⠀⠀⣀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⠈⠹⣾⠀⢹⣼⡇⠀⠒⠞⠡⣀⡀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠡⠀⠀⠀⢀⣰⣾⠃⠀⠀⠀⠀⠀⠀⢰⡄⠀⡟⠸⠃⠀⠀⣿⡆⠀⣿⡇⠀⠀⠀⠙⡾⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠁⣀⠤⠲⢺⠏⡀⠀⠀⣠⠤⣀⣀⠀⠀⢳⣰⠇⢠⡀⡀⠀⢿⡇⣠⢻⡇⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠤⣄⣠⣔⢉⡔⢁⡤⡾⠂⠙⢾⣟⠉⠉⢉⡭⢭⡓⣾⡟⣄⣸⠃⣇⠀⣘⡴⡁⠘⡇⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⢞⡴⠋⢠⡇⠀⠀⠈⠛⢷⣦⡿⠤⣂⣇⠘⣷⣿⠋⢹⣿⠾⣿⠟⠉⣙⡟⢶⣦⢄⢿⢻⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣥⣾⠚⠘⢦⡀⠀⠀⠀⠀⠀⠑⠒⠶⣿⣿⡇⠀⠀⣿⣜⠧⢴⣏⣨⡇⣀⣹⣷⡤⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠈⠲⠤⣀⣀⣀⠀⠀⠀⢸⠿⡇⠀⢸⣿⣿⠛⠒⠒⠉⠛⠛⠉⠉⠀⢸⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠊⡤⣓⢤⢠⡀⢿⠃⠀⠀⠸⢠⠗⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣸⣇⠀⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⣷⣼⢠⠁⡈⠘⢁⠉⡟⢲⡄⠀⠀⠛⠄⠼⢿⡿⠙⠛⠀⠀⠀⠀⣄⣀⠀⣸⣿⣏⣿⣮⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠏⡤⣿⣯⠙⠧⣇⣄⢸⠀⢹⣾⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡿⢠⣿⡿⢡⣿⠟⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⢸⡿⣧⣄⢋⠟⣾⢦⣏⣀⣠⣀⣀⣀⣀⣈⠉⠁⠒⠢⢄⣀⣀⣴⠟⠁⡾⢋⣿⡿⠁⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣼⡧⣌⣓⠈⠻⣾⡆⡏⢨⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣔⢀⡼⠃⢀⡼⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⠏⣰⡆⡏⣷⡀⠀⠙⠣⢼⡗⠒⠒⠤⠤⠤⣈⣉⣉⠛⠻⣿⡿⠋⠀⣠⣾⠃⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⢃⣼⡿⠀⡇⢹⣿⣆⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣾⣿⡏⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣡⣿⣿⡇⣰⡇⠈⣿⣿⣇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣡⢰⣞⣿⣿⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣥⣿⣧⠀⠸⣿⣿⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣿⣿⣿⡏⣿⣽⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠀⠀⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⠀⠀⠈⢻⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠘⡇⠀⠀⠀⠻⣿⡟⠛⠿⠿⣿⣿⣿⣿⠟⠁⠀⢠⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠹⠇⠀⠀⢀⣿⣿⣿⡟⠀⠀⢀⡾⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣿⠀⠀⢹⡀⠀⠀⠀⣰⣿⡿⣿⡟⠀⠀⠀⣸⡇⠀⠀⠀⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣺⠏⠀⠀⠈⣷⡀⠀⠀⠹⠏⢀⠟⠀⠀⠀⠀⢸⣷⡀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⢿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠛⠛⠉⠉⠈⠙⠲⢤⣀⢹⣷⡀⠀⢀⣰⡯⠖⠋⠙⠛⢿⣶⣿⣥⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠔⠁⢠⠏⣠⠞⣼⢁⡴⠋⣴⢻⢠⠋⠀⠀⢀⡔⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⢰⠃⣼⠟⢋⣀⣀⣿⣏⠚⠀⣠⠄⡾⢀⡆⡤⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠃⢸⣿⣃⣘⣰⣿⡴⠉⣀⡈⠑⠌⢱⡖⢁⡼⣥⣾⢻⣇⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⣅⣠⢼⡟⠁⣀⠉⠓⡇⢸⣿⣿⡆⢀⣸⡷⢋⣼⠟⢁⡾⣹⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡠⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⣁⠀⢼⡇⢾⣿⣷⠀⢹⣄⡙⢛⣡⣾⣿⣿⣿⣥⣀⣉⣴⣳⠋⣙⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢦⡀⠀⠀⠀⠀⠀ ⠀⢸⡇⣿⣷⠈⣧⠘⠿⠿⠀⣾⣼⣿⣿⣿⢟⣿⡷⠚⣻⣿⠿⣿⡇⣼⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠙⠂⠀⠀⠀⠀ ⠀⠀⠳⡙⣿⢃⣬⣹⣶⣶⣿⣿⡿⠟⢹⣷⣿⣿⣶⣿⣿⣯⡀⠈⠀⣽⣿⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⢿⣿⣿⣟⣻⣿⣿⣧⢀⡏⢽⣿⣷⡾⠟⠋⠉⠙⣆⠀⢻⣿⠿⣝⡳⢄⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠻⣾⡿⢿⣿⣿⠀⡀⠈⠿⡇⠀⠀⠀⠀⠘⡆⠸⣿⢷⣶⣛⠺⢧⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠛⣻⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⢀⣿⣸⣿⣿⢙⢦⢳⡄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⢦⣄⣰⡆⣀⣀⣀⠀⠀⠀⠀⣼⣿⣿⢹⣿⣟⢿⣞⠿⣗⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⢀⣱⣄⠀⠀⢿⣾⠿⠛⢋⡀⠀⢀⣼⣿⠟⢻⠸⣿⣿⣷⣽⣦⣘⢻⣷⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⢁⣴⡿⠓⣺⢟⣻⣿⣿⣿⣦⣄⠶⠤⣶⡟⠀⢀⣾⡿⠃⣠⠟⡆⢼⣿⣿⣿⣿⡿⣿⢿⣀⠀⠀⠀⠙⣶⠋⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⢠⣾⠿⠾⠛⠛⠋⣿⡇⠘⣿⡼⣿⣷⣦⣄⣤⣴⣿⣟⣰⢿⡇⠀⣇⢈⡟⣿⢹⣿⡇⠈⠳⣌⡙⠓⠶⠮⣤⣀⣠⣀⣀⣀⡀⠀ ⠀⡾⠀⢠⡿⠁⠀⢤⣀⠀⠀⠙⣧⠀⢸⣿⢿⣿⡇⠉⢻⣿⣿⣿⠡⡼⠁⠀⣿⣾⢡⡇⢸⡿⠁⠀⠀⠀⠉⢻⣲⢶⡾⠋⠀⠀⠀⠀⡹⡄ ⣾⠃⠀⣾⡇⢠⠆⠀⠈⠻⣿⣾⣿⣿⣿⣿⣾⡿⣷⡀⠈⠋⢷⣹⣄⣤⣤⢼⡿⣿⡿⣶⣾⣥⠤⠶⠺⠿⠶⠬⢡⣾⠁⠀⠀⠀⠀⢀⣷⣧ ⣿⡀⠀⣿⣧⡏⠀⠀⠀⠀⡼⣟⡦⠛⠻⢾⡽⡳⣿⣍⠳⣄⣸⣏⣷⠼⠞⠚⠳⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣼⣿⡇ ⣿⣷⡄⣿⣿⠁⠀⠀⠀⣼⣏⡿⠀⠀⠀⠀⠈⢻⣽⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠈⢿⠾⡆⠀⠀⢀⡀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣰⣿⣿⡟ ⢿⣿⣿⣿⣿⡄⠀⠀⠀⣯⢤⡇⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣷⠀⠀⠈⣷⠀⢀⣿⣯⠀⠀⣀⡴⣳⣿⣿⣿⡗ ⢺⣸⣿⣿⣿⣧⠀⠀⠀⢿⣋⣧⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡏⠀⠀⠀⢻⣧⣸⣿⣿⣦⣾⣿⣿⣿⣿⣿⠛⡀ ⣼⠛⢿⣿⣿⣿⣞⣦⠀⢾⣿⣟⣆⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣾⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠐⢄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀ ⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀ ⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀ ⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉ ⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⡀ ⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀ ⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⠀ ⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢠⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠀⠀ ⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣶⣿⣿⣿⣿⣛⣛⣛⣛⣻⠿⢿⣿⣿⣲⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⣷⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠙⠺⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠷⠛⠁⠀⣀⠀⠀⠀⢰⣖⣚⣦⠀⠙⣷⡄⠀⠀ ⠀⠀⠀⣸⡏⣟⡋⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀ ⠀⠀⢠⣿⠗⡫⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣴⣶⣿⠿⢿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⣿⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣏⠼⠦⠿⠯⣟⣺⢧⣿⣻⢷⣄⠀⠀⠀⠀⠀⢀⣤⣠⡄⠀⠀⠀⠘⣿⠀ ⠀⢸⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⣿⢓⠞⣻⣧⠀⠀⠀⠀⠈⠳⢿⠟⠀⠀⠀⠀⣿⡇ ⠀⣇⡀⠀⠀⠀⠀⠀⣀⣾⣧⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇ ⢠⣯⢟⣽⣿⠀⠀⠀⠈⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡶⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⣿⡿⣋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁ ⢼⣷⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢷⣾⠏⢠⡶⣄⠀⠀⠀⠀⣾⠶⠀⢰⣿⡏⠀ ⠁⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⢀⣀⣤⡴⣻⣿⣶⠟⠃⠀⠘⢿⠿⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀ ⠀⣧⣷⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⣿⡏⠀⠀ ⠀⠸⣇⡎⡤⢸⠏⡟⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠹⣴⢃⠏⣸⣸⠃⣿⡆⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠙⢾⣠⢇⡇⢸⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⢺⡆⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢾⣴⣯⠄⡈⠳⠦⠤⠤⠖⠒⠒⠦⣤⡀⠀⠀⠀⠀⣀⣴⠞⠏⣁⢠⠀⣾⣀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣇⣾⠀⡆⢀⠠⡆⢤⠀⡀⠉⡓⣒⠚⣋⣉⣤⢠⣿⡋⣼⣼⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠾⢼⣁⣜⣠⣇⣸⣀⣿⣰⣷⣿⣷⣾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠟⠉⠀⠀⠈⡛⢦⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⣴⠋⠁⠀⠀⠀⠀⠀⣶⠞⠛⠻⠋⠉⠹⣧⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⡀⣼⠃⠀⠀⠀⠀⠀⠀ ⣸⠇⠀⠀⠀⢀⣶⠀⠀⢻⣦⠀⣎⣱⠄⠀⣿⣥⣄⣸⠃⠀⠀⠀⠀⠀⠀⠀⢱⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⣠⣿⠃⠀⠀⢸⣇⠀⠀⢠⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠲⠛⠋⠙⠷⣄⠀⠀⠙⠓⢚⣋⣀⠁⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠰⢯⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠟⠀⣠⡴⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⣛⠶⣦⡀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⢠⡾⠋⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⢸⣯⡇⠈⠻⣦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⢰⡏⢀⣀⣤⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠺⡿⠃⠀⠀⠈⣷⠀⠀⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⢰⡟⠀⠀⣿⣷⠉⠁⠀⠈⢿⡄⠀⠀⢶⣿⡇⠀⠀⠀⢅⢀⡠⠀⠀⣽⠀⢨⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⡀⡄⣿⣿⡀⠀⠀⠀⢰⡇⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠷⣼⣯⣷⡀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠟⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⡀⠀⠀⠻⣝⠛⢛⣿⣟⠛⠛⠉⠉⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⢈⣿⡀⠀⠀⠈⠉⠙⡇⠙⣦⣀⠀⠀⠀⣰⠏⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠉⣿⠀⠀⣀⣠⣾⡇⠀⠀⠙⠷⣤⡾⠋⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣤⠾⠛⠉⠉⠉⠉⠈⠳⣄⡀⠀⠀⣴⡆⠀⠀⠀⠈⢿⡴⣦⠀⠀⠀⢀⡆ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣿⠁⠀⠀⠀⠀⣠⣿⡁⠀⢀⣠⠾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠴⠶⠛⠁⠈⠙⠛⠉⠁⠀⠀
⠀⢣⠀⠀⠀⡠⠂⠉⠉⡤⠔⠢⡤⠆⠀⠀⠘⠈⠑⣄⡀⠀⠀⠀⠀⠀⠀⡀ ⠀⣀⠑⡄⠀⢃⠀⡠⠒⠠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠛⢌⠑⠂⠠⠤⠤⠒⠁ ⡙⠼⣭⡻⡖⠁⠀⢄⠀⣀⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠫⡢⡨⢌⢶⣀⠀⡠⠂⠀⠀⡠⠀⢀⠠⠐⠂⠀⠉⠀⠒⠠⡀⢢⠀⠀⠀⠀ ⠑⣌⢾⡆⢺⠀⠀⠀⠁⠀⠉⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣂⡗⠂⠤⠀ ⡭⠊⠫⣹⠈⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⡇⠀⠀⠀ ⡢⠤⠒⡹⣴⠀⠀⠀⢠⠂⣠⡴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀ ⠐⠊⠁⠐⣫⢢⡀⠀⢸⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠛⡢⠕⠚⠀⠀⠒⠠⡀⠀⠀⠀⠀⠀⢀⣠⠂⠁⠉⠐⠠⢄⠀ ⠀⠀⢈⡇⠀⠀⣠⠖⠈⠉⠐⢒⣠⣸⣀⡠⠤⠐⠂⠁⠀⠹⠀⠀⠀⠀⠀⠀ ⠐⠊⠋⠛⢆⡤⠳⡩⠔⣒⠞⠀⠀⠈⠓⠒⠢⢀⡀⡤⡆⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠐⠨⣶⠬⠄⣀⣀⢀⠀⠀⠀⢀⠔⠀⢠⠉⢦⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠎⠉⠙⠏⠙⠠⠀⠀⢈⠀⢸⠀⠈⠑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠒⠲⠦⣄⣀⣀⣠⣤⣤⠎⠉⠉⢦⠶⠛⠉⢳⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠈⠉⠀⠀⠀⡏⠀⣴⢲⠼⠶⢄⣀⣼⣇⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢘⣯⠀⠀⢸⠶⡀⠀⡇⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠒⣏⠉⢀⡜⠀⠀⠀ ⠀⠀⠀⣯⣤⣴⣶⡶⠒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⣭⣿⠀⠀⠀ ⠐⠒⠚⣿⣿⣿⡏⠀⠺⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁ ⠀⠀⠤⢿⣿⣿⣡⣴⣾⣿⣿⡿⣕⣲⢿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠂⠀ ⠀⠀⠀⣠⠿⣿⡛⠿⠿⠛⠋⠀⠀⠀⠀⠙⠛⠿⠿⠛⣻⡿⠷⢄⠀⠀ ⠀⠀⠈⠁⠀⠈⠙⠲⠦⣤⣄⣀⣀⣀⣀⣀⣠⣤⠴⠞⠉⠀⠀⠀⠀⠀
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⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠈⠳⣄⣠⠎⠀⢠⠋⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⣠⠤⢄⡀⠘⡆⠀⠀⠀⠀⢀⡼⠋⠀⠀⡏⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠘⣄⣀⣀⣴⠋⠀⠀⠀⠹⡀⡇⠀⠀⠀⣠⠏⠀⠀⠀⢠⠁⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⢠⠋⠁⠀⡨⠔⠂⠤⡀⢰⠃⠧⠤⠤⠚⠓⠒⠒⠒⠠⠼⠤⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢧⠀ ⠀⠀⢨⠀⠀⡞⠀⠀⠀⠀⢹⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆ ⠀⠀⠀⠓⡄⠑⢄⠀⠀⢀⠜⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙ ⠀⠀⠀⠀⡇⠀⠀⠉⠈⡡⠤⠤⠐⠃⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⢀⡔⠛⢄⣀⣠⠜⠁⠀⣀⠤⠖⠒⠉⠉⠉⠀⠀⠀⠀⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠈⠑⠒⢎⠁⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⡇⠀⠀⠀ ⢸⠁⠀⠀⣠⠋⠀⠀⢠⣶⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⡀⠀⠀⠙⡄⠀⠀⠀⢹⠀⠀⠀ ⢸⠀⠀⢠⠃⠀⠀⣰⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠈⡆⠀⠀⢸⠀⠀⠀ ⢻⠀⠀⡏⠀⠀⠸⠿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀ ⠘⡆⠀⡇⠀⠀⠀⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⡇⠀⡎⠀⠀⠀ ⠀⠘⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡸⠃⠀⠀⠀ ⠀⠀⠘⢦⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠴⠶⠤⣤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠙⠒⠢⡇⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡖⠉⠉⣒⠿⠦⠤⣀⣀⣀⣠⠊⠀⠀⠀⠀⠀⠀⠐⣶⠾⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠑⠆⡀⠀⢀⡟⡟⠀⠀⠀⠀⠀⠀⠀⢀⣏⠴⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠢⣄⡀⠀⢁⠟⠀⠘⢄⠀⠀⠀⠀⠀⠀⠊⠀⠀⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠤⢤⡜⠁⠀⢀⡆⠈⠉⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠘⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⣀⠴⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⢫⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⠒⠤⢤⡤⠔⠒⠓⠂⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⢤⡀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠸⡆⠀⠀⠀⢀⣀⣀⡀⠀⣧⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⢻⠖⠒⢶⡉⠀⠀⠹⣄⣯⠤⠤⠤⠤⠼⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀ ⠀⠀⠀⢺⡀⠀⡶⠛⣲⠀⠚⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠉⢹⣅⣀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠀⠀ ⠀⠀⣰⠛⠦⠤⠖⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠉⠉⠙⠲⢤⡀⠀⠀⢸⡄⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⣠⠞⠁⣰⡞⠒⢦⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡝⢦⡀⠀⣇⠀⠀⠀ ⠀⢹⠁⠀⠀⡼⠁⠀⢸⡟⣷⣤⣾⠀⠀⠀⢀⡀⠀⢸⣷⣤⣾⡇⠀⢳⠀⢸⠀⠀⠀ ⢀⡼⠷⢤⣼⠃⠀⠀⠀⠻⠿⠟⠃⢀⣶⣤⣬⣥⣤⡀⠙⠻⠛⠁⠀⢸⣆⣟⡀⠀⠀ ⡏⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⡇⠀⠀⠀⠀⢀⡞⠁⠀⠈⢧⠀ ⣧⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀ ⠈⠲⣄⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢻⡻⣯⣿⡶⠂⠐⣶⣾⡿⣻⠃⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢳⣠⠟⠁⠀⠀⠘⠦⣠⡏⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠐⡦⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠛⠳⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣠⡤⠤⣤⣶⠒⣒⣲⢶⣿⣉⣀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠟⢁⣀⢰⠏⣭⠿⣭⠉⢷⡁⠀⠀⠉⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠉⢉⠿⢍⠀⠹⣿⣷⣤⢞⣠⣯⡇⠀⠀⠀⠀⠈⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡏⠀⠙⠒⠊⠀⣀⡼⠛⠻⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠄⠉⠉⠙⠦⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠴⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⠧⣄⣀⣀⣀⡤⠔⠊⠁⠀⠀⠀⢰⣄⣀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⣠⠤⠀⠉ ⠀⢀⣠⠾⠋⣿⠀⠀⠀⠀⢉⡽⠋⣁⡀⠀⠈⠀⠑⠦⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡔⠋⠀⠀⠀⠀ ⡴⠛⠁⠀⠀⣿⡀⠀⠀⠒⢻⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⡤⠀⠀⠀⠀⠀⢀⠀⠀⢸⢰⡇⠀⠣⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡇⠀⠀⣠⠏⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠳⡀⠀⠀⠀⠀⢸⠀⠀⠈⣿⠀⠀⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠈⡽⠀⠀⠙⠛⠁⠀⠀⠰⡆⠀⠀⠀⠀⣾⣿⣿⣷⠀⢸⡖⠦⠀⠀⢸⠀⠀⠀⠘⣆⠀⠀⠀⠸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣙⣿⡳⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⢠⡇⠀⠀⠀⠘⡆⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⢰ ⠀⠀⠀⠀⠀⢰⠎⡟⠉⠉⠙⠳⣄⡀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠛⠋⠁⢰⠃⠘⠀⠀⠀⠀⢙⣆⠀⠀⢀⣼⠀⠀⠀⣇⠀⣬ ⠀⠀⠀⠀⠀⠘⢾⡀⠀⠀⢀⡞⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⡴⠋⠈⠓⠒⠛⠉⠀⠀⠀⠘⠦⡈ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⠀⠈⠉⠑⠒⠶⠤⠤⠤⠤⠴⢿⣀⣀⣤⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣤⠎⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⣈⠓⢶⣄⣀⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢧⣶⣿⣿⡷⠤⣀⣀⣀⡼⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠦⠴⢚⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠈⠉⠑⠲⣌⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⠀⠀ ⢠⣖⣶⣤⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢀⣀⣀⣀⣠⣇⠙⠗⡀⡀ ⠀⠈⣿⣿⢛⢻⣿⣄⠀⠀⠀⠀⠀⢀⡀⣀⣰⠴⠛⠉⠉⠀⠀⠀⠀⠈⠙⠲⣄⠉ ⠀⠀⢿⣿⠨⡇⡝⢿⠳⣦⣄⣀⣀⣏⡭⣯⠀⠀⠀⡀⠤⠒⠊⠉⠁⢈⡽⠐⢌⢣ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⠠⢿⡟⠛⠋⡠⠐⠁⠀⠀⠀⠀⠀⠴⠯⠤⢔⣐⠹ ⣄⠀⠀⠈⠙⣻⠟⣿⢻⣹⣿⠷⣾⠁⢀⠌⠀⢀⣀⠀⠀⠲⣛⣀⡀⠀⠀⠀⠀⠀ ⢿⣆⠀⣠⣾⠷⠆⠀⣨⣿⠏⠀⢧⠀⡈⠒⠛⣹⠏⠀⢠⣮⢥⡼⠉⠉⠲⡀⠀⢰ ⢸⢿⣾⢫⠍⣩⣿⠿⠟⠛⠀⠀⡿⡄⢡⢘⡹⠁⠀⠀⡞⠀⠀⢳⠀⠀⠀⢹⣴⡃ ⣬⣿⣿⡗⠋⠁⠀⠀⠀⠀⡴⠎⠀⠘⢶⣣⡀⠀⠀⠀⡇⠀⠀⠈⣧⠀⠀⠀⢧⡙ ⣿⣿⣿⡇⠲⢾⣿⣦⠀⠀⠀⢀⣠⢃⣠⠞⠻⢗⠒⢺⡇⠀⠀⢸⡏⠣⠀⠀⠀⢱ ⠀⢹⣿⣇⠀⠀⠙⠛⠁⠀⠉⠉⠀⢯⡀⢲⣭⢿⡁⣲⡇⠀⠀⠠⠇⠀⠀⠀⠀⢸ ⠀⠈⢷⣿⣆⠀⣎⡠⠀⣀⣀⣀⠀⢀⠝⠉⠀⠀⡹⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⣀⣀⡙⢻⣷⣶⣟⣿⠹⣿⣿⡟⠁⠀⠀⢀⡴⡣⠓⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠙⡄⠀⠀⠀ ⠀⡴⠏⠀⠀⢸⡵⢤⠖⢢⡀⠀⣰⠋⠀⠀⠀⢀⡇⠀⠀⠀ ⢸⠀⠀⣠⠆⠘⡦⠨⠕⢘⡗⠤⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠘⠢⠚⠙⢤⠀⠓⢒⣋⡉⣀⣀⣀⣀⠀⠀⠼⣁⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⡴⠊⢡⡄⠀⠀⠀⠀⣼⡙⢦⡀⠀⢱⠀⠀⠀ ⠀⠀⡎⠀⣞⡠⠤⢾⠇⠀⣀⡀⠀⠻⠁⠀⢹⠀⣸⠁⠀⠀ ⠀⠘⣇⠄⡿⡀⠀⢨⠃⠀⠟⠀⠀⠈⠈⢀⣼⡴⠋⠀⠀⠀ ⠀⠀⠈⠙⠻⣳⣀⠀⠳⡤⠤⣤⠤⠤⠖⠋⡹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠹⣆⠀⠈⢉⡏⠢⣀⠀⡰⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⢆⣠⠞⠒⠒⠛⢦⡀⠈⣭⠁⠀⠹⣤⡀⠀⢠ ⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠉⢇⣀⣀⠤⠻⠤⠴⠊
⡄⣈⡳⠀⠀⠀⢠⠎⠁⠀⠉⢣⡈⠈⡹⠿⠍⠩⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡯⠒⠛⢕⠄⠘⠀⠀⠀⠀⠀⢣⠀⣾⡏⠉⡇⡍⣏⣿⡿⠋⠁⠀⠉⢿⣿⣿⣿ ⡟⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⡄⣿⣇⣀⣇⡁⣟⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠧⣢⠤⢤⣪⠆⢸⠀⠀⠀⠀⠀⠀⣧⢹⣿⡟⠛⢻⡏⠀⠀⠀⠀⠀⢀⡿⢿⣿⣿ ⠀⠀⠀⠈⠁⠀⢠⠆⠠⡔⠁⡄⠀⡷⠒⠛⠉⠉⡙⠀⠀⠀⠀⠀⠀⣜⠤⠤⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣦⢎⢀⠍⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⠟⠤⠌⠁⠉⡠⠐⠒⠢⢄⠀⠀⠀⠀⠀⠀⢾⡸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣠⠮⠄⠒⠒⠂⠠⠍⣦⡀⠀⠀⠀⠀⢻⡈⠂⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠀⠀⡠⢊⣤⡀⠀⠀⠀⠀⠀⢀⣤⣅⢄⠀⠀⠀⠈⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠔⠀⣿⣿⡇⠀⢠⡄⠀⠀⢸⣿⣿⠆⢢⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠘⡄⠀⠈⠉⠀⠀⢀⡀⠀⠀⠀⠉⠉⠀⡌⡇⠀⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢌⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠔⢀⠴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠦⣉⠀⡲⠲⢖⠒⠒⢀⡥⠮⠊⠁⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠆⠉⡆⠉⠉⠁⠀⠀⢣⠐⠊⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡔⠛⡄⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠆⠀⠀⠔⠉⠀⢱⠐⠑⢆⣀⠇⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠂⠁⠒⠒⠁⠀⢀⠄⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄ ⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠔⠁⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠐⠪⠐⠡ ⠀⠀⠀⢠⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁ ⠀⡀⢔⠁⡚⠀⠀⠀⡀⠤⠀⠒⠒⠒⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀ ⠀⠀⢠⠀⡇⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠈⡀ ⠈⠁⠒⠒⠇⣎⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠇ ⠀⠀⡀⡱⠐⡇⠙⠒⠚⠁⠀⠴⠦⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠆⠀⠀⠀⠰⠀ ⠀⢀⠘⠩⣙⣚⣂⣀⣀⣀⡀⡠⠄⢀⠀⠀⠀⠀⠈⠛⠛⠉⠀⡘⠀⢀⡔⠁⠀ ⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠓⠲⢥⠆⠀⠀⠀⠀⠀⣠⣡⡴⠋⠆⠀⠀ ⠀⠙⠄⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⡠⠤⢚⢿⣠⣤⡄⠀⠀⠀ ⠀⠀⣈⡢⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⢀⡠⠔⠉⠫⠀⢠⠀⠀⠀⠀ ⠀⠠⠤⠖⠾⣷⢀⠀⠀⠀⠀⠀⠀⡠⠁⠁⠈⠉⠢⡀⠀⠀⠀⠙⠅⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣎⣀⣀⣈⡉⠐⠉⠀⠀⠀⠀⠀⠀⠈⡢⡀⠀⠀⠀⠈⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⠢⢀⠄⠤⠊⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡞⠉⢧⠀⠉⠙⠛⠻⣿⣿⡟⢿⣿⡿⠟⠻⠿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡏⢉⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠳⠄⠈⣆⠀⠀⠀⠀⠈⠻⣿⡿⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣀⣤⣤⣤⣄⣀⣀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⣿⣟⠉⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣆⠀⢹⣿⣿⠃⠀⠀⠉⠑⢦⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⣶⠒⠶⣶⢌⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣀⣿⣿⡶⠒⠂⠀⠐⠲⣿⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⢹⢼⠇⠀⢉⡿⠟⠉⠁⠈⠉⠙⢿⣿⣿⣿⣿⣿ ⠈⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⣼⢸⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿ ⠦⠬⣿⣿⣄⢦⡀⠀⠀⠀⢀⣞⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣴⣶⣟⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣿⣿⣿⣿ ⣇⠀⢸⡿⡇⠻⢿⣀⣒⣊⣽⠟⠀⠀⠀⣤⠬⢷⣀⡤⠦⣄⠀⠀⠀⠀⣼⣿⣿⣤⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⠀⢸⠿⣿⣿ ⣿⣆⠀⡇⡇⠀⠀⠀⠀⡇⡉⠀⠀⠀⢸⡇⣠⠔⢯⡀⢀⡼⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⠤⠄⠀⠀⠈⣿ ⢿⣾⣿⣷⡇⠀⠀⠀⢸⢹⡄⠀⠀⢰⡟⠁⠣⣀⠼⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉ ⢸⠻⠏⠹⡄⠀⠀⠀⠈⠘⠃⠀⠀⠈⢧⡤⠔⠓⠤⣤⣎⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡤⠚⠁⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣴⡿⠒⠊⠉⠉⠉⠉⠒⠢⢌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢦⡀⠁⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣰⡏⠴⠒⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣰⣽⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠚⠒⢶⣄⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣯⢧⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⡀⠈⢦⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⡆⠀⠀⣀⣀⣀⡼⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠸⡄⠘⢦⡀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡴⣡⠖⠉⠀⠀⠈⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠒⢤⣀⠈⢑⣲⣦⡤⠤⠤⠀⠀⠀⠤⢾⡷⣾⠟⠁⠀⠀⠀⠀⠀⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⡇⠈⠉⣏⠀⢹⠲⢄⣀⣀⡤⠶⢛⡞⠁⠀⠀⠀⠀⠀⣀⠞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠙⡇⠀⠀⣨⠝⢥⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⣀⣤⠚⠡⠴⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡷⡀⠀⠙⣤⣜⠀⠀⠀⣠⠜⠁⠀⠀⠀⠟⠉⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠙⠒⠚⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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