Qiqi Dot Art

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣀⣀⣈⠐⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⣁⣴⣶⣿⣿⣿⣿⣿⣿⣷⣮⣕⠤⡀⠀⠀⠀ ⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣕⢦⠀ ⢀⣾⣿⣿⣿⣿⣿⠟⠛⠋⠉⢹⠛⠛⠛⠿⣿⣿⡏⡟⢹⠀ ⣿⣿⣿⣿⠟⢻⠏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⣿⡥⠊⠀ ⠘⢽⡟⠁⣠⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⣦⠀⢠⡀⠡⠀⠀ ⢀⠎⠀⢠⠃⠀⠀⠀⣰⠁⠀⢠⠀⠀⡰⠋⢯⠀⣿⠀⢡⠀ ⢸⠀⢠⠇⠀⠀⠀⣀⠃⢰⣆⠸⡤⠞⠁⠀⣞⡶⠋⢀⢸⡀ ⡜⣀⡎⠀⠀⠀⢰⣿⣶⡤⠇⠉⠁⣶⣶⠶⡟⢠⠀⣪⠞⠀ ⠐⠼⣀⠀⠀⠐⡟⠩⠍⠀⠀⠀⠀⠑⠂⢰⠁⣡⠚⠁⠀⠀ ⠀⠀⠀⠁⠪⢟⠳⣄⠀⠀⠀⠀⠀⢀⣴⢏⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠠⣙⠟⣶⣶⣴⠚⠉⠉⢿⣿⣇⢆⠀⠀⠀ ⠀⠀⠀⠀⡤⣒⣨⡟⢿⡟⠁⠀⠀⠀⠀⢘⠟⠘⣿⢇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡉⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠷⠿⠾⣩⠮⡙⢧⡚⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠚⠷⠤⡾⣼⡣⢐⣿⣿⠳⢧⣘⢾⡝⢫⡳⣏⠦⠛⠳⠖⠿⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠚⠿⣉⠻⣙⣭⡜⣷⢿⡿⣿⣿⣾⣤⣦⢿⡾⠿⢿⡾⢿⣛⡹⣧⠞⣏⡡⢿⠓⠉⠉⠋⠓⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⡿⣿⣾⣽⣿⣧⣾⡿⣿⣿⣿⣸⠁⠉⠟⣻⣽⣿⣻⣾⣜⣿⣻⢿⡞⣙⢻⣿⡻⢜⢛⣯⢛⣽⣶⣙⣮⣝⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⢾⣴⠂⡀⣀⣎⣿⣿⣟⢯⣿⣾⡡⢟⡻⣿⣿⣿⣼⡎⣧⣿⣿⣿⣽⣾⡽⣿⣿⣿⣛⣹⣶⣿⠿⣏⡜⣻⡔⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣬⣶⠿⠙⠉⡴⢟⣤⢿⠦⣽⣿⡿⣿⣷⣶⣿⣯⣿⢿⣐⣯⣿⣿⣿⣯⣿⣿⣟⣯⡜⣻⣯⣼⣿⣶⢿⣏⡣⢼⣛⢬⠓⠀⠀⠀⠀⠀⠀ ⢄⠀⠀⡁⣴⣯⡾⢑⣩⡞⢶⣝⢩⣿⣽⣿⣞⢫⣳⣿⣿⡙⣟⣽⣯⣿⣽⢿⡻⣉⣢⣭⢷⣿⠈⣷⣫⣵⣿⢻⣭⠷⣎⠽⣖⠪⠙⠀⠀⠀ ⠻⠈⠎⣻⣧⣾⡴⣩⢿⣿⣿⡿⣟⣾⡩⡞⣯⣻⣿⣿⣿⣿⣾⣐⡠⠜⡓⠄⣢⣔⢮⠳⡘⣧⢚⡑⣦⡿⢏⣧⣿⡹⢶⣚⡵⣞⡝⠳⠀⠀ ⣷⣟⣶⢌⣾⠉⠉⣏⣷⣻⢟⣿⡿⣟⣿⢿⣿⣶⣿⣿⣻⢾⠴⣤⣤⠧⠾⣥⣨⢔⡈⠱⣆⠬⢧⡈⠱⡌⣳⣾⡝⣿⣿⣿⣿⡞⣋⡴⢺⠀ ⡄⣧⠴⢬⢻⣷⣿⣧⠿⡙⣹⣾⣦⢘⣏⠻⡟⢾⣴⣠⢀⠂⠀⠀⠂⣲⡛⠓⠛⣉⠄⡐⠩⢄⠎⡁⠰⡌⠑⣬⢻⣹⣿⣿⣿⣿⢻⣬⣛⢧ ⠀⠀⣶⢿⡿⣿⣛⡻⣽⣿⡿⢉⠋⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⠛⢾⠛⡿⣿⡚⣶⠻⠈⢡⠄⠹⡑⠌⠢⠑⣄⡿⣎⣿⣿⣿⣿⣟⡻⢿ ⠀⠀⠀⠀⠀⣀⣤⣤⣧⣾⣿⣿⣟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠇⣼⢓⡤⡟⣹⢉⠄⠂⠀⢌⠠⠐⡆⠸⡀⢀⡜⠊⡄⣽⣿⣿⣿⣿⣻⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⢯⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠿⣿⣵⢛⡛⣛⢿⠛⠌⡀⠋⠞⢊⠒⠑⢆⠌⡐⡄⣿⣿⣿⣿⣿⣳⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡜⣿⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢇⡭⣈⠀⠄⠂⠁⡀⣏⡴⢃⣆⠘⢁⠠⣌⠌⡡⠀⣿⣿⣿⣿⣿⣽⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣏⢸⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠁⠋⠞⠶⣴⣤⠶⠓⠉⠞⣠⠁⡀⢳⣆⠙⠄⠂⠄⡊⠁⣿⣿⣿⣿⣾⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⢿⣮⠙⠈⡆⣝⢢⡱⡟⣿⠻⠀⣦⠳⠙⠈⠀⠡⠀⠟⣦⠙⠈⡄⠚⡀⢳⣄⠹⠄⡠⠐⡏⣿⣿⣿⣿⣼⣿⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⠙⣄⣦⣿⣿⣶⣠⣠⠀⠀⠀⡄⣹⣄⠶⠈⠂⡄⢳⠈⢦⡙⠄⠑⠣⢦⡌⢳⡈⠇⣿⣿⣿⣿⣽⡿⣽⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣽⣩⡈⢳⠞⡶⢶⠙⠈⠀⠀⠉⠛⠺⣧⠈⠀⠆⠄⠀⡈⢦⠙⡀⢦⠙⡀⠖⠄⡈⢏⣿⣿⣿⣿⣿⣾⣠⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣧⢻⠯⠦⡳⣌⠷⣽⣬⣀⠀⠀⣦⠘⠀⢂⠐⢈⠡⡀⢦⠙⡀⠦⠂⣁⠟⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⢳⡽⢩⡏⢰⣀⣤⠦⠶⠲⣟⠻⠙⠀⠄⠀⠠⠂⡀⢤⠻⠟⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣴⢦⠳⠛⠉⠀⠄⠀⠂⡀⣀⣄⠩⠋⠛⠛⠟⣿⣿⣿⣿⣿⣿⣵⢴⢠⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⡴⣤⣄⣿⣿⣿⣿⣿⣿⣾⣴⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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