Rin & len Christmas Emojis & Text

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

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⣶⣶⠋⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⡰⠻⡅⠙⠲⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠖⠚⠉⠉⠛⠲⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢀⣠⣤⡤⢤⣤⣤⣀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠻⣍⠳⠖⣃⣘⠓⠖⣩⡟⢦⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠀⢨⠿⠺⣇⣸⠗⠿⡅⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠛⠶⠚⠧⠼⠓⠶⠛⠀⣸⠧⣄⠀⠀⠀ ⠀⠀⣰⠋⠹⡄⠀⠀⠀⠀⠀⠀⢠⠯⣥⣶⡮⡷⣄⠀ ⠀⣸⢡⠞⠀⠙⠲⠤⣤⣤⠤⠖⠋⠀⣏⣀⣗⡷⠸⡆ ⣰⢓⡟⠒⠶⠤⠤⢴⣻⣟⣶⠤⠤⢶⡏⠉⢻⠀⠀⢷ ⢹⢻⣓⠲⠤⠤⠤⣼⡻⣟⣿⠤⠤⠬⠟⣛⡏⠀⠀⡾ ⠈⢻⣌⠉⠓⠒⠶⠤⠭⠭⠥⠶⠒⠚⠉⣁⡟⠀⡴⠃ ⠀⠀⠈⠻⣟⠒⠒⠦⣤⣤⠶⠖⠒⣻⣿⠥⠖⠋⠀⠀ ⠀⠀⠀⠀⢨⣏⣉⣉⡇⢸⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣀⣀⣀⡇⢸⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀

◽◽🌟 ◽◽🎄 ◽ 🎄🎄 ◽🎄⁣🎄🎄 🎄🎄🎄🎄 🎄🎄🎄🎄🎄 ◽🎁🎁🎁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⠒⠚⠛⠋⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣠⠤⢤⣄⣀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⣴⣤⠤⠞⠛⠋⠵⠚⠁⠀⠀⠀⠙⠛⠙⠖⠺⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⡾⠁⠀⠀⢀⣠⣴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡾⠁⠀⢀⢴⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣸⠇⠀⣰⠞⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⣴⠤⠶⢶⣆⣠⢤⡀⣄⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠚⠛⠳⣄⠀⠀⠀⠀⡴⠛⠛⠻⢿⣦⣤⠀⢸⣟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⢀⣄⣼⣿⣃⠤⠶⠲⠶⠶⠋⠀⠀⠀⠀⠓⠒⠚⠓⠮⣿⡟⢧⣴⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⢠⣼⠿⣿⠟⠁⡤⡶⠒⠦⣄⠀⠀⠀⠀⣰⣿⣿⣏⠓⢦⠘⡇⣾⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⢿⡀⡀⠀⠀⠀⣸⠋⢠⠏⠀⡞⣘⣿⣷⡄⠘⣆⠀⠀⠀⣿⣷⣾⣿⠃⠀⣷⣧⠻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠚⣿⣇⠀⣸⣿⣏⠀⠸⣄⣸⣧⣝⣿⣫⣀⣠⠼⠀⠀⠀⢿⠓⠾⠶⠚⣹⠛⠛⠓⢾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⢿⡟⢳⣬⣓⣶⡿⣁⠼⠛⠦⡀⠀⠀⠀⡠⠶⠖⠚⠛⠳⡄⢠⠟⠒⣄⠀⠀⢱⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⢰⠒⠚⢁⣾⡴⠊⠀⡟⠁⠀⠰⡏⠓⠀⢀⡠⠷⠤⢤⣄⣤⠴⠛⠲⠤⠴⠛⠀⠀⢸⡇⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⢦⣀⡴⠋⠀⠀⣻⠇⠀⠀⠀⠙⠲⠖⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣦⡀⢀⡀⠀⢀⣀⣀⠴⠋⠈⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⠀⢀⣀⣠⠼⣿⡛⠛⠿⢿⣿⣿⡏⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠙⠉⠀⠀⢠⠙⠲⠤⠤⠽⠟⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢶⣄⣠⣾⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈ ⠀⠀⠀⠀⠀⠠⠰⣀⠟⢣⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯ ⠀⠀⢐⡂⠉⠀⠀⠀⠀⠀⠀⠙⠿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠁⠀ ⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⠀⠑⢄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠙⠾⣢⣀⡀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠑⢿⡳⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣤⣾⡕⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠻⠤⠶⣤⣖⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⡢⣄⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⢦⣧⠀⢾⣿⠁⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣸⣦⡀⠀⠠⡀⠀⠉⠉⠉⠁⠀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⣤⣈⣓⣲⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢴⣤⣌⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

🎄🧑‍🎄🎅🎁🧦🎶🦌🧝☃️🌟🍪🥛🍴🎀

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

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🎄🎁🎅🏻❄

⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠖⠒⠶⠶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣤⣤⡀⠀ ⠀⠀⢀⡴⠿⣤⠀⡀⢀⠀⡀⢀⠀⠀⢀⠀⡀⢠⡤⣾⠁⠀⠈⢻⡄ ⠀⠀⣼⠁⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⠀⢻⣄⠀⢀⡼⠃ ⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⠉⠀⠀ ⠀⠀⣹⡟⠓⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠖⢻⣏⠁⠀⠀⠀ ⠀⣞⠉⠀⠀⠀⢀⡴⠶⢦⣤⠶⣄⡤⠶⢦⡀⠀⠀⠀⠉⢻⠄⠀⠀ ⢀⣽⠞⠳⣆⠀⢸⡅⠀⢨⡇⠀⢸⡅⠀⢈⡇⠀⣠⠞⠳⣿⡀⠀⠀ ⣼⠁⠀⠀⠹⡷⠦⠽⠟⠻⣦⣄⣤⠟⠻⠿⠴⢾⠏⠀⠀⠈⢷⠀⠀ ⣧⠀⠀⠀⠀⠙⢦⣀⣀⣀⣴⠛⢧⣀⣀⣀⡴⠋⠀⠀⠀⠀⣸⠀⠀ ⡾⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢻⡀⠀ ⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀ ⠀⠈⠉⢿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡼⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠛⠶⠦⠤⠴⠶⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠶⣶⣤⣄⣀⣤⡶⠾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠲⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣉⣳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠄⠀⠀⠀⢀⣠⠴⠒⠒⠛⠉⠉⠒⠒⠒⠒⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⢧⡀⢿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⣞⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠉⠉⠓⠺⣝⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⣹⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡞⠁⠀⠉⢳⡄⠀⠀⠀⠀⢸⡗⡞⠀⠀⠀⠀⠀⠀⠀⠙⣎⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡭⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢀⣠⠤⠾⢧⡀⠀⠀⠀⠈⢷⣷⠤⠴⠶⢶⣦⣄⠀⠀⠘⡆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣸⡇⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⢀⣤⣤⣤⣷⠄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡉⠳⢄⠀⢹⠀⠀⢹⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⠁⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠋⣛⣿⠿⠯⣤⡀⠀⠀⠀⠀⠀⠁⠘⠛⠛⠽⣄⠈⠛⠸⠂⠀⢸⠀⠹⣦⠴⠲⣶⡀⠀⠀⠀⠘⣆⣿⡟⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡏⠀⢰⣏⡧⠀⠘⣷⠀⠀⠀⠀⢹⡿⠀⡀⣸⠀⠀⠀⠠⢤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢰⡇⠀⢸⣧⣄⣀⣀⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢠⡖⠒⢦⡼⠀⠀⡼⢹⠀⠀⠀⣿⠀⠀⠀⠀⣼⠗⠛⠋⠁⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠷⣄⣈⣗⣠⠴⠛⠛⠿⠿⠛⠋⠙⠶⠶⠶⠋⠹⣆⡀⠀⠀⠀⠀⠀⠉⠳⡄⠙⣆⠀⠁⢸⠀⠀⢠⡿⠀⠀⠀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠛⢾⣟⡛⠭⠭⠥⠖⠃⢀⡽⠀⢸⠀⣰⠏⠀⣠⣾⣁⢀⣠⠾⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⡴⢆⠙⠦⣤⣤⣠⣤⣤⡀⠀⠈⠙⠓⠶⠶⠶⠞⠋⠀⢀⡾⢸⣁⣤⠖⠋⠘⢿⣻⣧⣄⢸⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⠦⠶⠞⠀⠀⠀⠀⠀⠀⠹⡆⠈⠉⠉⠉⠀⣠⠾⠛⠓⠦⣄⣀⡀⠀⠀⠀⣀⡠⠞⠀⢘⣇⠀⠀⠀⠀⠈⢳⡈⢻⣏⣿⣞⣆⠀⠀⢦⠀⠀⢀⣀⡠⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠽⠚⠃⠀⠀⠀⠀⠀⠀⢠⠙⢦⣄⣠⡤⠞⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⣿⡆⣠⡴⠂⠀⠀⣷⠀⣿⠈⠛⠻⠷⢦⣬⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢷⣄⡀⠀⣀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⡀⠀⠀⠶⢋⣼⠏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠛⠲⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢲⢸⣿⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⢸⠀⣿⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣸⣼⠀⡿⠀⠀⠀⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡞⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣎⣴⢾⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⢀⣀⣠⣤⠴⠿⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⠾⠛⠒⠚⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣧⣄⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠿⣶⣄⣀⠀⠀⠀⠀⠀⣀⣤⠞⠙⢷⣄⡙⠻⣶⣤⣀⡀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡻⠿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠈⣙⠛⠒⢛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⡾⠿⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠾⠟⠛⠛⠛⠛⣛⣯⣿⡏⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⣀⣶⡿⠟⠉⠻⣷⣄⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⢀⣼⡿⠻⣿⡄⠀⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣀⣠⣤⣤⣤⣤⣤⣬⣭⣀⣀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠟⠋⠉⠉⠀⠀⠈⠉⠉⠛⠻⢷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣤⣾⡿⠛⠛⠛⣿⡟⠛⢻⣿⠛⠛⠻⢿⣶⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠋⠻⠷⣶⡶⠾⠿⠃⠀⠘⠿⠶⣶⡶⠿⠋⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠃⠈⢿⣦⣀⠀⠻⠇⠀⣠⣴⣶⣦⣄⠀⠻⠃⠀⣠⣾⡟⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠙⠻⢿⣶⣶⣾⡿⠁⠀⠙⣿⣶⣶⣶⡿⠟⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣶⠿⠋⠁⠹⣿⣄⣀⣴⡿⠁⠉⠙⢿⣦⡀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣿⣏⠀⢀⣀⣴⡿⠛⠛⠻⣷⣤⣀⡀⠀⣻⡷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠙⠛⠛⠛⠛⠙⠻⣷⣶⣾⠟⠙⠛⠛⠛⠛⠁⠀⠀⢀⣾⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣽⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠋⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠋⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⣠⣶⣶⠶⣶⣶⣽⣿⣄⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⣠⡄⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⣹⡿⠿⠻⣿⣆⠘⣿⡘⢿⣇⠀⠀ ⠀⠀⢀⣾⠏⠀⣼⡿⠁⠀⠀⠈⠻⢿⣦⣤⣀⣀⣀⠀⣀⣀⣠⣤⣶⠿⠋⠀⠀⠀⣿⡅⠀⠀⢈⣿⠆⣿⡇⠈⢿⣦⠀ ⠀⠀⣸⡿⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠻⣷⣤⣴⣾⣯⣴⡿⠁⠀⠘⣿⡄ ⢀⣴⣿⣷⣾⡿⢷⣶⣦⣤⣤⣀⣀⣀⡀⢠⣾⠿⢿⠿⠿⢿⣦⡀⠀⣀⣀⣠⣤⣤⣾⠟⠉⠉⠻⣿⡅⠀⠀⠀⠀⢻⣧ ⣸⣿⠀⢠⣿⠃⠀⠀⠈⠉⠉⠉⠛⠛⠛⢻⣿⢰⣿⠿⣿⠀⣿⠟⠛⠛⠋⠉⠉⣿⣏⣀⣀⢀⣀⣸⣿⠀⠀⠀⠀⠸⣿ ⢸⣿⣶⣾⡿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⢸⣿⢀⣿⠚⣿⠀⠀⠀⠀⠀⠀⣙⣛⣻⣿⡿⣿⡟⠉⠀⠀⠀⠀⢸⣿ ⢸⣿⢀⣿⣧⣈⡉⠙⠛⠻⠿⠶⠶⠶⠶⢾⣿⡘⠛⢻⣛⣀⣿⡷⠶⠶⠶⠾⠿⠛⠛⠋⢉⣠⣾⣷⠀⠀⠀⠀⠀⣾⡏ ⠈⢿⣾⣿⠉⠛⠿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⣀⣀⣤⣤⣶⡾⠟⠛⠉⣿⡆⠀⠀⠀⣰⣿⠁ ⠀⠀⠸⣿⣦⡀⠀⠀⠈⠉⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⣀⣴⡿⠃⠀⠀⣴⡿⠁⠀ ⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⠿⠋⠀⢀⣴⡾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⠛⠛⠿⠿⠿⠿⢶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠟⠛⢛⣭⣿⣛⣡⣤⣴⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣤⣤⣤⣤⣾⠟⠙⢿⣦⣤⣤⣤⣤⣤⣴⡿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⣿⡇⠀⢺⣟⠉⠉⠉⠉⠉⣻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠶⠶⠶⠷⠾⣿⡇⠀⢸⡿⠷⠶⠶⠶⠾⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣿⠇⠀⢸⣷⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⣀⣀⠤⠤⠤⠤⠤⢤⣄⣀⡀⠀⠀⠈⢷⠈⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣄⡈⣇⠀⠹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⡤⡤⠖⠒⠒⠒⠒⠒⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠹⡄⠸⣇⠀⠀⠀ ⠀⠀⠀⠀⢰⡾⠀⠀⢀⣴⣾⣭⠦⠓⠒⠲⣤⡀⠀⠀⢀⣠⣤⣌⡉⠳⣦⡀⠀⠀⠀⣷⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢠⡾⠢⣿⡤⠤⠶⠦⠤⣬⡇⠀⢰⣏⣀⣠⣄⠈⠑⢶⠻⣆⠀⠀⢸⡆⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⢀⣾⡁⠀⠁⠀⣿⣿⡆⠀⢀⣠⣀⣀⠉⠉⣽⣯⡉⠛⠚⠃⢽⡆⠀⣼⣇⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠉⢹⣇⠀⠀⠀⠘⣯⣁⣾⠉⠀⠀⠉⢱⣄⠻⠿⠃⠀⠀⠀⢸⣷⣤⣿⠛⠛⠲⣄⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⢹⠛⠒⠒⠛⠉⠀⠈⠻⠶⠤⠖⠛⠉⠓⠦⣄⣀⣀⣴⠏⠀⠹⣧⠀⠀⠀⠘⣇ ⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠉⣡⡟⠀⠀⠀⠹⣧⣀⢀⣼⠏ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠶⠾⠿⠳⠶⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⢻⠋⠉⠁⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠄⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⣄⡀⣠⣀⣀⣀⣀⣀⢀⣀⣀⣀⣤⠀⢀⣀⣀⣀⣀⠀⠀⠠⣦⣤⣀⣠⣠⣀⢤⣤⣄⣤⢤⣄⣤ ⠘⢛⡛⠓⢛⢃⢚⡚⠓⣘⠛⢚⠛⡓⠛⠒⠑⢚⢚⡋⡇⠀⠀⠀⠋⡒⠛⠛⡒⠛⠚⡓⡛⠚⢘⢙⡛

⠀⠀⠀⠀⠀⠀⣠⠶⠞⠳⠶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⢀⡀⢀⡀⠘⣷⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣿⡀⢈⡁⢈⡁⢀⣿⣀⣀⣀⡀⠀ ⢠⡟⠉⠉⠙⠛⠓⠈⠙⠋⠁⠚⠛⠋⠉⠉⢻⡄ ⠈⠿⢦⣤⣀⣀⠀⠀⢠⡄⠀⠀⣀⣀⣤⡴⠿⠁ ⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠘⠃⠀⠀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⡞⠁⠀⢀⡾⢷⡀⠀⠀⢻⣄⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⣠⡟⠁⠈⢻⣄⠀⠀⢹⡆⠀⠀ ⠀⠀⠘⠷⣤⠶⠋⠀⠀⠀⠀⠙⠷⠶⠾⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⠀⢰⣿⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠈⢻⣷⣈⣿⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠙⠛⠋⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡿⠿⢷⣶⣾⠟⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⢀⣠⣾⠏⠀⠀⠀⠀⠀⢻⣧⣤⣤⣤⡆⠀⣤⣤⣤⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⠛⢻⣷⠀⠀⢀⣤⣤⣤⡀⠀⠈⠙⠛⣿⡿⠿⣶⣤⣄⣀⣀⡀⠀⠈⠉⣹⡿⠀⣰⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⢿⣧⠀⣿⡆⢸⣿⣄⣰⣿⠏⠁⣿⡇⠀⠀⠀⣴⡿⠁⠀⠀⠉⠉⠛⠛⠿⢷⣶⣾⠟⢁⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡁⠈⠻⠿⠿⠃⠀⠙⠛⠛⢁⣤⣾⠟⠁⠀⢀⣾⠟⠁⠀⣀⣤⣴⣶⣶⡶⣶⣶⣿⣿⣿⠟⠋⢀⣠⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠙⠻⠿⣷⣶⣿⢏⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⣶⡿⢋⣵⡿⠟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣤⣤⣴⡾⠟⠛⠿⠿⣶⣦⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⣸⡿⠃⣠⣿⠏⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣀⣴⣾⠿⠟⠛⠉⠉⠉⠙⠻⢿⠁⣴⡿⠁⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⣆⡶⢶⣏⣙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠾⠷⠶⣾⣿⣧⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣝⢷⣦⡝⣟⣉⣷⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣟⠛⠻⠿⣷⣶⣤⣤⣀⠙⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣭⣿⣿⠝⢻⣛⣻⣯⡤⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⣀⣉⣛⣛⣿⡟⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⣿⢻⣶⠆⡤⡟⢾⣯⠟⠀ ⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠟⢻⣿⠁⠀⠀⠀⠀⢰⣿⣉⡇⢸⣷⣼⡇⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠷⢶⣝⣹⣿⣉⡷⠀ ⠀⢰⠖⠲⣾⠛⢿⣦⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠈⠉⠀⠁⠀⠀ ⠀⢨⠿⢒⣉⢿⣧⣽⣿⣾⠞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⢷⠝⢚⣓⠈⢩⣶⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣴⡾⠿⢛⣫⣭⣥⣄⠀⠀⠀⠀⠈⠛⢿⣦⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠳⢾⡁⣿⣋⢸⣷⣿⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡿⠏⠉⠀⠀⣿⣉⣀⣠⡿⠁⠀⠀⠀⠀⠀⠈⢿⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣟⢹⡷⠷⠟⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⡟⠁⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⢀⡀⠀⠀⢀⣼⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⣿⣇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⢠⣾⠟⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡘⣿⣆⡀⠀⠀⠈⠙⠲⠶⠾⠟⠛⢁⣀⣴⣾⠟⢁⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣬⣛⠿⢷⣶⣤⣤⣤⣴⣶⣶⠾⠿⠛⠉⣀⣴⡿⢿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣟⠻⢿⣶⣾⣭⣭⣭⣭⣥⣤⣴⣶⣾⠿⢻⡏⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣧⡀⠈⣿⠉⠉⣏⠁⠀⢹⡀⢀⣸⣷⣴⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⠙⠛⠿⠿⠿⠿⢿⣶⣿⣾⣿⠟⢛⡛⠉⢉⣿⡇⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣀⣀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⣀⣶⠿⢻⡿⠉⠉⠉⣿⡟⠚⠉⠘⣷⠀⠹⣿⣀⠀⢀⣀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠻⣿⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⡾⠛⠦⠤⢤⣿⣇⣀⣤⡴⢿⡆⠀⣿⣿⠛⠛⠋⣿⠟⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢸⡏⣠⣿⣥⣀⠀⠀⣼⣿⠃⠀⠀⠀⢸⣷⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣄⠀⠈⠉⢩⣿⣿⠤⠤⠶⠞⢹⡿⠀⠀⣿⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⣿⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⠙⠿⠶⠶⠿⢻⣿⣄⣀⣀⣴⡿⠃⠀⢀⣿⠀⠀⢸⣿⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣼⡿⠀⠀⢸⣿⡄⠀⢀⣤⣤⣴⣶⣾⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣭⣭⣥⣄⡀⠀⣼⣿⠀⠀⠘⣿⡄⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⣴⡶⠟⢻⣧⣾⠟⠋⠉⠀⠀⠀⠙⣿⣿⣶⣶⣾⣿⡟⠉⠀⠀⠀⠉⠛⢿⣦⣿⠛⠿⣶⣤⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢶⣶⣶⣶⡾⠿⠉⠀⠀⠀⠀⠈⠻⠿⣶⣶⣶⣶⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠢⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⣁⠤⠒⠊⠉⠉⠉⠉⠉⠑⠒⠦⢄⡈⢇⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢸⡆⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⣠⣴⣚⣯⣉⡉⠉⠉⠉⠙⠒⠦⢄⠀⠀⠀⢹⡀⣧⠀⠀⠀ ⠀⠀⠀⣸⠀⢀⠞⢿⣋⡤⠤⣄⣹⠄⠀⣞⣉⣉⠁⠢⣽⣦⠀⠈⡇⢹⠀⠀⠀ ⠀⠀⠀⢿⣀⣾⠀⠈⠀⣿⡷⠀⣀⠤⢤⡈⠉⣿⡍⠙⠛⠸⡆⢀⣧⣼⠀⠀⠀ ⠀⠀⢀⡞⠁⠘⣧⣀⣀⡨⠷⠺⢤⣀⣀⡸⠦⣉⠁⠀⠀⣰⠿⣾⠋⠉⠑⣆⠀ ⠀⠀⡞⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⣴⡀⠀⠀⠈⠉⠒⣻⠃⠀⠘⣧⡀⢀⡼⠀ ⠀⡸⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠚⠛⠒⠤⠤⠤⠚⠁⠀⠀⠀⢸⡟⠛⠁⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⡀⠀⠀⠀⠀ ⠓⡛⠒⠛⠙⡻⠋⠓⠟⡛⠟⠃⠒⢻⣻⠃⠀⠀⠊⠻⠛⢻⠛⠛⠛⠛⠘⠛⠂

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡾⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠁⣠⣴⠿⢿⡇⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⢠⡾⢿⣄⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣠⣤⣴⠶⠶⢶⣮⣤⣀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⣾⠛⠛⢻⡿⠉⣿⡟⠛⠻⣷⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠻⣿⡀⠙⢻⡟⠛⢁⣀⡈⠛⢻⠟⠉⢨⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠈⠻⣶⣤⣤⣴⠟⠛⢿⣦⣤⣤⡾⠟⠁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⡾⠋⠉⢻⣦⣤⣼⠏⠉⠛⢷⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⢿⣤⣤⣴⣿⣏⣉⣹⡷⣦⣤⣼⡟⠀⠀⢰⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣷⣤⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣀⣴⠟⠉⠙⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣤⣴⣶⠶⣮⡿⣧⠀⠀⠀ ⠀⠀⠀⣼⠏⢠⣶⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⢸⡟⠋⠙⣷⡈⣷⠙⣷⡀⠀ ⠀⠀⢸⡏⢠⡿⠁⠀⠀⠀⠈⠛⠻⠶⢶⣶⡶⠶⠟⠋⠁⠀⠀⠸⣧⣀⣠⣾⣡⡿⠀⠸⣧⠀ ⠀⣠⣿⣦⣿⠷⢦⣤⣄⣀⣀⣀⣠⡶⢶⣶⠶⣶⣄⣀⣀⣀⣤⣴⠟⠋⠙⢿⣏⠀⠀⠀⢻⡆ ⢸⣿⣀⣾⣇⠀⠀⠀⠈⠉⠉⠉⢹⡇⣿⢻⣷⣿⡏⠉⠉⠉⠉⣿⣤⣤⣤⣬⡿⠀⠀⠀⢸⡇ ⠀⣿⢻⣿⡛⠻⠶⢦⣤⣤⣤⣀⣼⡇⠿⢾⡟⣿⣧⣠⣤⣤⣤⠶⠾⠛⢛⣿⠀⠀⠀⠀⣼⡇ ⠀⠻⣾⡏⠛⠷⣶⣤⣄⣀⣀⡀⠈⠻⠶⠾⠿⠛⠁⢀⣀⣀⣠⣤⡶⠞⠛⢻⡆⠀⠀⢠⡿⠀ ⠀⠀⠘⢷⣤⣀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⢀⣀⣴⡿⠁⢀⣰⡟⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⡿⠶⢶⣤⣤⣤⣀⣀⣀⣠⣠⣤⣤⣴⠶⠶⣿⡿⢋⣁⣠⡶⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣠⣩⡿⠻⣿⣍⣁⣀⣀⣠⡾⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⢀⣀⣹⡗⠀⣿⣁⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠉⠉⠉⢹⡇⠀⣿⠉⠉⠉⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣼⡇⠀⢿⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠢⣄⣀⡀⣀⣀⠀⡠⠔⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⠀⠀⠁⠠⡋⠀⠀⠙⠦⠀⠀⠀⠀⣧⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠑⠲⣄⣀⣠⠖⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣇⡀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠲⣄⠀⠀ ⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂⠀ ⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠐⠺⡄⠀⠀ ⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠁⡹⠀⠀⠀⣄⣀⡠⠟⢘⣯⣀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠺⡍⠒⣿⣀⣠⡀⠀⠀⠀⠀⠀⠈⠀⠈⡷⠀ ⠀⢸⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠺⡁⠀⠙⠚⠀⠁⡏⢧⣀⡄⠀⠀⠀⠀⠐⠒⣇⠀ ⠀⠸⣄⣀⣰⠀⠀⠀⠀⠀⠀⠲⣟⣿⡦⣷⠀⠀⠀⠀⢠⠁⣸⣿⣷⢶⡆⢀⣤⡀⣠⡾⠁ ⠀⠀⠀⠀⠱⣀⠀⢀⡱⠄⠤⠜⠋⠻⡄⠀⠀⠀⠀⠀⣸⣴⡿⣏⠀⢀⣭⣁⣀⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣿⡼⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⢋⣁⡀⠀⠀⠀⠀⠀⠘⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠙⠒⠤⣘⣗⠒⠒⠒⠚⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⛄❄️🎄🎁🦌🎅🎇🍪🔔🌟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⢦⡀⠀⠀⣀⡘⣧⠙⠚⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢧⣀⣴⠃⠀⠘⢯⣭⠉⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢲⣸⠄⢧⡼⣫⠇⢀⡼⠉⢉⣛⣒⣶⣫⠾⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣀⣀⣠⢮⣙⣒⣾⠴⠊⠉⠉⣈⠉⣷⢞⡽⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⢀⣠⣤⣤⣧⣀⡴⠚⠉⠉⠉⠃⣾⡤⠞⠁⠀⠀⢰⣲⣶⣵⣄⠀ ⠀⠀⠀⠀⠀⠈⠻⣍⣙⣒⣮⡍⠀⠀⡀⢀⣀⠀⠈⢧⡀⠀⠀⠀⣞⣿⡏⡿⡷⠁ ⢠⡤⣴⣶⠀⠀⠀⠀⠈⠉⢹⠀⠀⠘⠿⠘⠋⠀⠀⠀⢳⡀⠀⠀⠀⠹⠝⠊⠊⠀ ⢰⡕⡊⣻⣿⠃⠀⠀⠀⠀⢸⠀⢀⡤⠖⡺⢯⠉⠉⠓⢆⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠷⠛⠛⠀⠀⠀⠀⠀⢸⢰⠏⠀⠀⠓⠋⠀⡀⠀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣧⣄⣈⣒⣒⣩⠴⢚⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣏⣳⠻⠿⡷⠲⠛⣋⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣰⠃⠉⠉⢙⡿⡟⠋⣭⠍⢇⢳⡀⢀⣀⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⢻⠉⡏⠀⠀⠀⣏⡼⢉⣠⡗⠒⢹⠈⡏⢉⡏⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⣾⠀⡇⠀⠀⠀⣏⠓⠦⢞⣯⣩⠜⠀⡇⠸⡇⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠧⠖⢳⡖⠋⠉⢹⡶⠶⣾⠉⠉⠓⢶⠓⠦⠗⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠘⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠠⠒⠀⠀⠀⠐⠢⢄⣃⠣⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⠀⠀ ⠀⠀⢠⠃⢠⡴⠬⠭⡉⢉⠉⠒⡠⡀⠘⡸⠀⠀ ⠀⠀⢸⣠⡃⠋⣿⢉⠡⢈⢲⣖⠚⢱⠀⣧⡀⠀ ⠀⠀⠌⠀⢑⠀⠚⠙⢂⠐⠑⠤⠠⡜⠹⡁⠈⡆ ⠀⡘⠀⠀⠀⠁⠒⠒⠋⠓⠠⠤⠊⠀⠀⢹⠚⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠦⣀⣀⡤⠴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡦⠴⢦⠄⠤⠤⠆⠤⡤⠀⠰⠦⠶⠶⡶⠶⠆

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⢿⢢⡀⠸⣱⡀⢀⢤⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣤⡴⣴⠢⣧⣿⢤⣈⠺⡧⣺⠷⡟⠓⠃⣇⢧⣶⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⢠⠽⣇⣹⠓⠽⡌⠓⠹⢶⢿⠀⢠⠁⡈⡶⠓⠋⠙⢻⡹⢓⡶⠀⠀⠀ ⠀⣬⣿⡎⠓⠒⠻⢄⡀⢳⡀⠀⢸⠈⢦⢸⠀⣸⢇⠀⢀⣠⡞⢉⣡⣴⣲⠄⠀ ⢠⣽⣈⣇⣴⣲⠖⠀⠉⠚⠳⣄⢸⠀⠈⣿⠊⡼⡦⢏⠉⠀⠉⢙⠮⢱⡆⠀⠀ ⠘⢎⡇⠘⢧⡀⣀⣤⣤⠄⠀⠈⢻⣇⢀⣽⠖⢣⣣⡤⠤⠒⠚⣝⣆⠀⠀⠀⠀ ⠀⠀⠓⠢⠤⠽⢧⣀⠀⠀⠀⠀⠀⣿⠏⢹⡴⠋⠙⠒⠶⢖⢤⡀⢀⣤⣶⠗⠀ ⡢⢄⠐⠮⠷⢆⠀⠈⠙⠛⠛⠻⢶⣿⠀⣾⢀⣀⣀⣤⠤⡼⡓⢋⣿⠫⢕⡆⠀ ⠈⣻⠧⠤⠤⠤⠿⠗⠒⠒⠛⠶⣤⣿⣼⠛⠉⠙⠒⣶⡖⠳⡗⠺⡿⣤⣤⢄⡀ ⠰⣹⠀⠀⠀⢟⡆⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⢧⠇⠀⠀⠀⠀⠙⠮⡯⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠾⠛⣿⠙⠛⠶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠂⠀⠈⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠌⠀⢀⠜⠀⠀⠀⣀⣀⠴⠖⡲⠒⠀⠲⠦⠬⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⢠⠃⠀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⢀⠇⢠⠜⠛⠀⠀⠀⠀⣀⣤⣀⡤⠤⢄⡠⣀⡀⠀⢺⡀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠸⣰⠏⠀⠀⠀⠀⣴⢊⡁⣉⡡⠀⠀⠰⠉⠍⣳⢦⣘⡅⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣁⠀⠀⠀⣴⢻⠏⣡⣒⠢⡄⠀⠀⡶⣶⡐⢌⣴⠉⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠹⣆⠀⣦⡃⢈⣠⣰⣿⣃⡰⠀⠀⡯⠯⠄⡾⠣⢵⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⣘⡻⡱⡪⢻⠕⢉⠦⠀⠀⡆⠀⠉⣱⣐⢉⡆⠀⡗⢄⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠣⡠⠋⠀⠚⠀⠀⠑⠐⠁⠀⠈⠉⠀⠀⠀⠀⠀⣧⠀⠣⠀ ⠀⠀⠀⠀⠀⢡⠀⠀⡰⠁⠀⠀⠘⢄⠀⠀⠀⣠⡤⠶⢾⣦⡆⠤⠒⠈⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⡞⠀⢀⠃⠀⠀⠀⠀⠐⠈⠉⠉⠀⢈⠐⡒⢛⢠⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⢀⠀⠀⠣⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠉⠁⠀⠀⠀⠀⠀⠀⢐ ⢀⠀⠀⠀⠀⠀⠀⠉⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂ ⢀⠀⠀⠀⠀⠀⠀⠀⡭⠃⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠙⠦⣄⣀⣀⣠⠟⠁⠀⠀⠈⠋⠳⣄⣄⡀⠀⠀⡀⠀⠀⠀⠐⢀⣶⠫⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠤⠴⣄⠀⢀⠉⠀⠁⡠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡒⠒⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⣼⠆⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠀⠔⠊⠀⠈⠉⠒⠮⣵⣦⡀⠀⠁⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢾⠏⣐⣻⡂⠘⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⢿⣾⣿⣆⠠⠤⠤⣈⠙⠂⢄⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢦⣄⠙⠫⣷⡖⠛⠉⠑⠀⠀⠙⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠂ ⣿⣾⢿⣿⣦⡈⠙⢦⡀⠈⠂⠀⠀⠀⠈⢳⣄⣀⢀⣠⠤⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠖⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠛⢷⠙⢯⣿⣷⣄⠙⢦⡀⠀⠀⠈⠉⢝⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⢉⣀⣀⣀⣀⡠⠤⠤⣤⣤⣤⣤⣴⣶⠒⠒⠒⠒⠒⠒⠒⠛⠲⣶⣴⠀ ⠸⡇⢀⣴⠿⠿⠝⢟⣦⡀⠙⢆⠀⠀⠀⠈⢳⡤⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⡽⠏⠟⠋⢉⣠⠸⣆⣬⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀ ⡟⠛⠉⠴⣿⡿⠾⠚⠻⣿⡄⠈⢧⡀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠋⠀⠀⠀⠀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸ ⣿⣦⡀⠘⢿⣀⡀⢶⠂⠈⣿⡆⠀⢳⣤⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿ ⣍⣻⣿⣶⡎⣹⣧⠈⠃⠀⠻⣿⡀⠀⣿⠢⣤⣄⠀⢀⣴⣦⣤⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿ ⡿⣻⣏⣿⣿⠁⢀⣀⣦⡀⠐⠚⣧⠀⠘⡆⠈⠉⠉⠁⣉⣤⠤⠤⣀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣤⡤⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿ ⡞⠉⣿⣿⣿⠀⠀⣹⠀⠀⠀⠈⢻⡀⠀⢷⡄⠀⠀⣾⠃⠀⠀⠀⣈⣿⣿⡿⠋⠀⣀⡤⠖⠛⡋⠉⠙⠻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⠿⢿ ⡇⡰⠟⣿⢻⠀⠀⢩⣧⣠⠀⠀⣩⡇⠀⢸⡷⠀⡄⠈⠳⣤⢠⣾⣿⣿⣿⡥⣴⣯⣥⣤⣤⣴⣯⣤⣤⣤⣤⣿⣿⠿⣿⣿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀ ⣷⣾⣿⡏⢸⠀⠀⡁⠟⠳⠀⢰⣿⡇⠀⢸⡇⠰⠻⢀⡤⢾⡾⠿⠭⠿⠗⠒⣿⡖⠛⠛⠛⠛⠉⠉⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣽⠛⠀⢸⡷⢠⠇⠀⠀⠀⣸⣹⡥⠤⠚⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⣼⣇⣚⡤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣷⡶⠶⢶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⠉⠉⠁⠀⠀⠈⢻⣷⠉⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣤⡀⠀⠀⠀⢀⡀⠀⠀ ⠻⢿⣿⣝⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣄⡴⠃⠀⠀⠀⠀⣠⠤⢠⣾⣿⠁⣫⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸ ⠀⠘⢿⣿⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⣠⠔⠋⠁⢠⣿⢻⠋⣀⣿⣿⢿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣾ ⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠧⠼⠖⠋⠉⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⡾⡧⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢺⠀⠀ ⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⡇⢸⠀⣿⡿⣧⠁⣿⣿⣿⣿⣿⠀⠀⢸⢀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⢤⡄⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡇⣇⢸⠀⢿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠈⠉⢉ ⡇⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠋⠉⠀⠀⠀⣀⣠⠗⠀⠀⠀⠐⢫⡭⠿⠞⠉⣿⣷⣿⣮⣴⡞⣿⣿⡇⢿⣿⣿⣿⣿⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣯⣾⡇⣽⡛⠻⢿⣿⠀⢀⣠⣤⣾ ⡏⠀⠀⣀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣶⣶⣶⣶⣄⡀⠀⠀⠀⣄⣀⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⠃⠐⠚⠟⠛⣹⠿⣿⣿ ⣧⠀⢰⠛⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡍⢀⡿⠀⠀⠀⠀⠁⠀⠠⠊⡘ ⡟⠀⠘⠢⢌⣛⣛⣛⡟⠛⠛⠛⠋⠁⠀⠀⠤⢿⣿⣟⢛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⢃⣘⣊⣁⣠⡄⠀⠀⠀⠀⠀⠈⡀⠀⣹⣿⣿⣿⣿⣿⣿⣟⣫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡶⠶⢺⣦⣤⣭⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡦⣶⣦⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣀⣀⣨⣥⣶⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠠⢤⣤⣴⣷⣿⣾⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣦⣤⣤⣤⣶⣶⣴⣴⣴⣤⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⢁⠠⠤⠤⠤⠤⠬⢁⡒⠂⠄⡀⠀⠀⣀⠀⠀⠀ ⠀⠀⡼⠊⠀⠀⠀⠀⠀⠀⡄⡀⠀⠁⠢⡑⢴⠚⠉⠙⢶⡄ ⠀⡎⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⣆⡀⠄⡰⡤⠭⠂⠀⠀⣇ ⢸⠀⠀⠀⠀⡔⢈⣘⡝⠖⠤⠜⢹⠔⠒⢵⠧⣄⣀⣀⣾⠋ ⢸⠀⡀⠠⢏⠷⠁⣠⣈⠀⠀⠀⢠⣶⡆⣞⡀⠈⠉⠉⠀⠀ ⠈⢄⠫⠁⠼⠐⡨⠟⠻⠄⡨⠛⢻⡅⠀⠀⢸⢳⠂⠊⡆⠀ ⠀⠈⡻⠂⡵⡈⠀⠀⢀⡸⠒⠒⠊⠉⠀⠀⢁⡜⠀⠐⢙⠀ ⠀⢰⠀⠀⠘⢌⠉⠉⠁⠀⣀⣔⣗⡖⠒⠒⠊⠀⠀⠀⠹⠀ ⠀⠻⠀⠀⠀⠀⠐⠒⠉⠉⠀⠈⢚⠁⠀⠂⠄⠀⠀⠀⢀⠀ ⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⢷⠁⠀⠀⠀⠀⠀⡌⠀ ⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⠀⠀⣀⡀⠀⠰⣈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⣷⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠃⠀⠀⠀⢸⠿⣾⡟⠁⠀⠀⠀⠉⢿⡆⠐⡄⠀⠀⠀⠀⠐⣷⡱⡀⠀⠀⠀⠀⢤⠀⠀⢻⡄⠀⠈⢟⢿⠀⠀⠀⢀⠀⢨⢡⣀⠀⠀⢸ ⣿⡷⢹⣿⣿⡀⠀⠀⠀⢀⣴⠞⠋⠀⠠⢀⡖⠁⠀⠀⡟⣸⡟⠀⠀⠀⠀⠀⠀⠘⣿⡀⢻⡀⠀⠀⢠⠀⠈⢧⢳⡀⠀⠀⠀⡄⠳⣄⠀⢱⡀⠀⠘⣞⡇⠀⠀⠈⣆⠘⠏⢭⡄⠀⢸ ⣿⣿⣽⣿⣿⢧⣀⣠⣴⠟⠁⠀⠀⠀⡀⢸⠇⠀⠀⣸⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢷⠆⠀⡟⠀⠀⠘⣇⢳⡄⠀⠀⠹⡄⠙⣷⣄⢷⡀⠀⢹⣹⡄⠀⠀⢸⡆⠠⣄⣬⢠⣼ ⣿⣿⣿⣿⡗⢨⡽⣿⡷⠀⠀⠀⠀⠀⡇⡎⠀⠀⠀⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠄⢀⣼⣶⡛⣇⡸⠀⠀⠀⠀⠘⣎⢿⣆⠀⠀⠉⠂⠈⠋⠻⣷⣄⡈⣯⣧⠀⠀⠀⢿⢀⠈⠃⠈⣾ ⣿⣿⣿⣿⡷⠋⠀⡟⣷⠀⠀⠀⠀⢠⣇⡇⠀⠀⣸⢰⢃⠀⠀⡀⠀⠀⢀⣠⣴⠞⠋⠛⢿⡀⠘⣇⠀⠀⠀⠀⠀⠘⣆⢻⣷⣄⠀⠀⠀⠀⠀⠘⡎⠙⢻⣿⡄⠀⠀⢈⡾⡆⠀⠀⠹ ⡿⣿⣿⡟⠀⠀⠀⣇⢻⠀⢀⠀⠀⢸⣿⡇⠀⠀⡟⡏⠀⠀⠀⢀⣤⣾⠽⠛⠁⠀⠀⠀⠘⣷⠀⠸⣦⠀⠀⠀⠀⠀⠈⢦⢿⡛⢦⡄⠀⠀⠀⠀⢹⡄⢸⣿⣇⠀⠀⢈⣧⢧⠀⠀⠀ ⢶⣿⣿⡇⠀⠀⠀⣿⢸⡆⠸⠀⠀⢸⣿⠃⠀⢸⢳⢃⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢻⣧⡀⠀⠀⠀⠀⠈⢳⣳⡄⠙⠲⣄⠀⢀⡤⡟⠙⣿⢿⡎⢅⠀⣿⣼⠀⠀⠀ ⢋⣿⣿⠀⠀⡆⠀⣿⡏⡇⠀⠀⠀⢸⣿⠀⢀⣾⡿⠉⠀⠀⠀⠄⣀⡆⠀⠀⠀⠀⠀⢀⠀⠈⣯⢧⠈⡿⠿⣦⡀⠀⠀⠀⠀⠱⣿⡄⠀⣨⠿⣧⣠⣼⣶⣿⣼⣷⠀⠀⢹⢸⠀⠀⠀ ⣾⣿⡟⠀⠀⣿⠀⣿⣧⢿⡀⠀⠀⢸⣿⠗⠉⣿⡃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠀⠹⡜⢦⢹⠀⠈⠻⣦⡀⠀⠀⠀⠘⣿⣾⣵⣾⣿⣿⣿⡏⠙⢿⣿⣿⣶⣾⣤⣀⠀⠀ ⣿⣿⡇⠀⠀⢹⡇⣿⣿⡼⡇⢀⠐⣿⢿⡀⠀⡟⠀⢀⣠⣤⠴⠶⠖⠒⠲⠶⣤⡥⢤⠈⠀⠀⠀⢱⡈⢯⣧⠀⠀⠀⠙⠲⣄⠠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠈⢀⣿⣿⣿⠙⣿⡅⠀⠀ ⣿⣿⠇⠀⠀⠘⡇⢿⠏⢧⢿⡀⠀⡟⢸⣧⣴⣟⣋⣭⣤⣤⣴⣶⣶⣶⣾⡶⢮⣝⣶⣘⠀⠀⠀⠀⢷⡈⣿⡆⠀⠀⠈⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣸⣿⣿⣿⠀⣿⡇⠀⠀ ⣿⣿⠀⠀⠀⠀⡇⢸⠀⠘⣯⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⠛⠀⠀⠀⠀⢀⣿⠀⢻⡀⠀⠀⠀⣿⡿⣻⣿⣿⣿⣿⣿⣿⣏⡠⢴⣿⣾⣿⡿⢠⣿⠀⠀⠀ ⣿⡏⠀⠀⠀⠀⢳⢸⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠙⠳⢄⠀⠀⠀⠀⠀⠈⠈⠃⠀⢳⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠁⠀⠀⡾⢻⣿⡇⢸⣿⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⢸⢸⣄⣼⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡟⡄⠀⠀⣠⠾⣯⣭⣽⣟⣥⣂⣀⣀⣼⣧⣿⡟⠀⣸⣻⠀⠀⠀ ⣿⠀⠀⠀⠀⣀⣬⣿⡿⣿⣿⠀⠀⠉⠉⣹⣿⣿⣾⣭⣩⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡀⠀⣧⡀⠸⠷⢾⡟⠙⠇⠠⠈⣿⣿⣿⠁⢠⣿⡇⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⣟⣿⠘⢿⣄⣀⣐⣺⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢧⠀⠀⠉⠁⠀⠀⠀⠠⠀⠀⢀⣿⡿⠃⣠⠋⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⡼⠁⠀⠀⠀⠉⠛⡳⢿⣶⣶⣛⣭⣶⡾⠛⠉⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⢸⡿⢁⡼⡅⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⢿⣦⡀⠀⠀⠀⠀⢉⡿⠛⠛⠻⡏⠈⠛⠲⢄⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⠀⠀⠀⠀⠀⠀⣰⣿⢶⠋⠶⡷⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢹⡇⠀⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣉⣀⣈⡇⢸⣿⣶⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣧⡀⣿⠣⣀⠈⠳⢤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡟⠉⣰⣶⣶⣿⡜⢟⡁⠀⠀⠀⠀⣄ ⡀⠀⠀⠀⠀⠀⠀⢀⢣⢸⣷⡬⢗⣦⣄⣉⡛⠲⣤⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣴⣿⡿⢫⠞⢳⣸⠻⡄⠀⠀⡰⠔ ⠃⠀⠀⠀⠀⠀⠀⠈⠀⢧⢻⣍⠓⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡆⠀⢚⣥⣟⣻⣥⠞⠁⢀⠈⢳⣶⠇⢀⠼⡓⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠺⡏⠳⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢠⣋⢈⣴⣟⠭⠗⠋⠁⠀⠀⠘⢿⠟⢀⣴⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡷⠃⠀⠸⡄⢰⡀⠙⢢⣀⣴⣿⢻⣿⣿⣬⣙⡳⠦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣶⣿⣶⡄⠀⠀⠀⣩⡶⠛⠁⢱⠀⠀⠀⠀⠀⠀⢀⣸⠞⢋⣸⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢣⠘⠓⢀⡀⢻⢻⣽⢸⠅⠛⠓⠈⠉⠙⠛⠖⠒⠲⠶⠶⣟⢿⣿⣿⣿⣿⣿⠿⠀⣀⡴⠞⠃⠀⠀⠀⠀⠳⠄⠀⢀⣠⠞⠋⢀⡠⣯⠇⠀⠀⡀⠠ ⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⣷⣆⣀⣧⣘⠤⢽⣼⣧⣀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠹⠈⣿⣿⣿⠿⢋⣤⣾⣋⣀⣀⣀⣀⣀⣀⣀⣤⡴⠚⢁⣠⣔⣺⠵⢾⡟⠀⠀⡀⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣿⣷⣿⡿⣿⣼⣀⠀⠈⠛⢧⡆⠀⠐⠀⠰⠀⠀⠀⠀⠀⢀⡷⠛⢉⣡⣾⣿⣿⣿⡿⠿⠿⢿⡛⠛⠉⢻⣏⡤⠚⠉⠀⠀⠀⢀⠞⠀⢀⡴⠐⠁⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣿⣿⣿⣿⣿⡝⢟⡻⣿⣶⣦⣤⣛⠓⠦⢤⣠⡄⠀⠀⠀⢀⣾⣠⣴⣿⣿⣿⣿⣿⣻⡀⠀⠀⠉⠻⠲⣤⣼⠟⢧⡀⠀⠀⠀⣠⠏⠀⡠⣮⢎⠠⠈⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠞⢿⠫⣿⢿⣻⣿⣾⣙⡍⠉⠉⠉⠻⣿⣲⣶⣬⣍⣙⣒⣒⣿⣿⣿⠏⠁⠀⠀⠂⠈⣿⣟⣦⡀⠀⠀⠀⠉⢿⠽⢖⣾⡷⢶⡶⢃⣤⡾⠟⠛⠁⠀⠀⠀ ⠀⠀⠀⢠⠞⠀⠀⠐⠛⠉⢹⠖⠶⣶⣿⡿⣿⣯⣷⣁⣠⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⡟⠈⠳⣍⡲⠤⣄⣀⡈⠳⠤⠄⣠⣪⠴⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⠔⠁⠀⢀⢀⣠⣴⡴⠋⠀⠀⠈⠙⢿⣮⣛⢿⣿⣗⠒⠒⠒⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠒⠉⠀⠀⠀⠀⠉⠓⠦⠬⠭⠭⠟⠛⠉⣁⣀⣤⠤⠴⠒⠒⠂⠠⠤⢄

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❄🌨️🎅🏼🦌🎁🎀☃️☃⛄⛸️🎄✨🎋🍪🥛

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⣠⡖⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⡸⠁⢠⠃⠀⢀⣴⠟⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⣏⣀⡤⠚⠁⠤⠤⠾⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣧⢸⠀⠼⠋⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⢉⡓⠶⣤⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠋⠁⣠⠁⠀⠛⠋⠁⠀⠀⠀⠀⠀⠤⠤⣉⡒⠖⠤⢄⣈⠛⠛⠳⠤⢤⣤⣤⠄⠀⠀ ⠀⠀⠀⠀⡜⠁⢀⡤⠊⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠄⠀⠀⠉⠑⠒⠶⣈⡉⠁⠀⠀⠀ ⣀⣀⣀⠤⠖⠊⠁⠀⠀⢸⠁⠀⢀⠀⠀⠀⠀⡄⠀⠀⢶⠀⠘⣆⠀⠳⡀⠀⡄⠀⠰⢤⣤⠬⡭⣶⡶⠶ ⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠀⢸⡄⢠⠀⠀⣧⣷⠀⢸⡀⢠⠘⣆⠀⠱⡀⢻⠾⣆⢢⡹⣆⠀⠀⠀⠀ ⠀⠀⢀⣤⡾⡟⠀⡄⠀⡆⠀⠀⠀⢧⠸⡄⠀⢻⢹⡇⢼⢷⠈⡆⢹⢣⡀⠱⣼⡳⡙⢆⠱⠙⡆⠀⠀⠀ ⠰⠶⠟⠋⢰⠃⠀⡇⠀⢹⠀⢹⡘⡜⡆⢳⡀⠸⠈⣷⢸⣾⡆⠸⠸⡄⠑⡄⢻⡇⠱⡘⣷⣧⢹⡀⠀⠀ ⠀⠀⠀⠀⡎⡸⠀⢱⠀⠈⢧⠀⢇⢷⣽⡌⢧⠀⡷⢾⡀⡇⠱⡀⠃⡷⠒⠛⣺⣷⢄⠙⣽⣏⢧⣧⠀⠀ ⠀⠀⠀⢰⣿⡷⣧⠀⢣⡀⠈⡆⠸⢸⠙⣿⣄⣱⣷⣴⣧⣇⠀⠹⣿⣇⣴⣶⣿⣿⣈⢦⠘⣞⠘⠉⠀⠀ ⠀⠀⣤⠟⣱⣷⡟⣶⡤⢷⣄⣰⣀⣿⣄⣘⣬⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⡀⠳⣌⡇⠀⠀⠀ ⠀⠀⠀⠘⠋⣸⡷⡿⣇⡿⣶⡽⠏⠛⠉⠉⠙⢿⣿⣿⣿⣿⠏⠀⠀⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠁⢳⣿⡦⠋⣧⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠑⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠺⣍⢉⡟⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⡀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠈⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠹⢿⣶⣤⣄⣀⣀⣀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉⠻⣿⣷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣾⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠻⢿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠛⠁⠀⠀⠈⠉⠉⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⣤⡀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣿⣧⣠⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀ ⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀ ⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠟⠻⠿⠻⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⡿⠉⢿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⣠⣿⣿⣧ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠿⠋⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣇⠹⡄⠀⣀⠤⠤⢄⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⠠⠤⣀⠀⠀⣼⢋⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡄⢧⠀⠀⠀⠀⠀⠈⣒⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠊⠁⠀⠀⠀⠀⢰⡏⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⠸⡄⠀⠀⠀⠰⣿⣅⠣⠽⣢⣀⠀⠀⢠⠀⡎⠀⠀⢀⡠⢞⡩⢉⣶⠄⠀⠀⠀⡾⣸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠙⢿⣿⡿⠟⠋⠉⠉⣓⡒⠈⠒⠚⠛⠻⠶⠶⣿⡏⠀⠀⠀⢸⢷⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡄⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣾⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⡟⠁⠀⠀⠀⣠⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠘⢷⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⢿⣿⣿⣻⣿⣿⣿⡿⠇⠀⠀⠀⠀⢀⣼⡗⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⠒⢤⣀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⢀⣀⡤⠖⠋⠉⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣦⣤⣶⣶⣾⣿⡟⠁⠀⠀⢀⣠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⢻⣿⣯⣁⣀⣀⣿⣿⠏⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢫⣽⣻⣿⣿⡿⠃⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⠉⠉⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀ ⢸⣆⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣠⣤⣿⠀⢹⡆⠀⢠⣤⣄⠀⠀⠀⠀⣀⣀⠀⠀⢰⡏⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⠀⢀⣀⣙⠛⠋⠀⠹⣄⠀⠀⣼⠋⠹⣧⡴⠟⠀⠘⠓⢲⡄⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠋⣉⣩⣿⣶⡴⠞⠛⠛⠿⣧⡀⣠⡴⠖⠒⢶⣤⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⣠⠴⠚⠋⠁⠀⣼⠋⠀⠀⠀⠀⠀⠀⠹⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢄⡀⠀⠀⢸⡇⢀⣔⡆⠀⠀⢀⣀⠀⢹⠀⠀⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠒⣿⠀⠘⠟⠁⠀⠀⢸⡾⠀⡼⠀⠀⠀⣀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣄⠀⠀⢠⠚⠑⡦⠀⢸⡟⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠻⠶⣄⣉⣋⣥⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠲⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠛⠻⢯⡄⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⣻⣿⠀⠀⢸⣀⣀⣀⣀⣠⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⡿⠀⠀⣾⠉⠉⠉⢻⡍⠀⢿⢦⡀⠀⠀⠳⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢰⡇⠀⠀⡇⠀⠀⠀⠀⣷⠀⠈⢢⠙⠳⣄⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⣧⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣾⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠀⣿⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠇⠀⠀⠀⢀⡾⠀⠀⣼⠃⠀⠀⢀⡟⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠡⠬⠥⠽⠾⣥⣀⣀⡿

⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⠶⠶⠤⠤⣄⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⣠⡔⠂⠀⠉⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⠀⢠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡸⢠⠇⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠐⠀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢰⣡⠃⠀⠀⠀⠀⢀⠔⠝⠁⣀⠈⣦⠀⠀⢠⠚⠂⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠸⡇⠄⠀⢀⡀⡰⡇⢘⡀⣪⣯⡍⠉⠀⠀⣿⣭⠚⠁⠀⠀⠀⠀⠀⠀ ⢀⡄⠀⠘⡤⣻⠀⠀⡇⢸⡆⢃⣀⡀⠁⠀⠀⡠⠀⠉⠀⢑⡄⠢⢄⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⢘⢆⠀⣇⠘⡀⡌⡔⠍⣄⣠⡴⠑⠒⠉⡟⠋⠂⠧⠐⡇⠀⠀⠀⠀ ⠰⣀⠀⠠⢀⣴⣶⠿⠋⠑⢸⠣⡈⠒⠒⣉⠠⡔⠲⠶⢡⠒⠐⠒⠏⣠⠆⠀⠀⠀ ⠀⠀⠉⡗⠋⠁⢧⠃⠀⣢⡇⠀⠀⠉⠁⠀⠀⠠⣑⢒⡱⢀⠀⠀⠈⠛⠠⡀⠀⠀ ⠀⠀⢸⠱⠀⠀⠀⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠈⢢⡀ ⠀⠀⠸⢰⡀⡆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⠀⠱⢔⣄⢄⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⣄⣀⣰⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⡀⢀⣰⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⡚⠅⠊⠢⣤⣀⣤⠔⠓⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄⣀⣀⡤⠤⠶⠶⠶⠶⢶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠈⠉⠁⠒⢠⡀⠀⠀⠈⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠀⢀⠈⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢀⠠⠀⠒⠒⠒⣀⣤⣀⠀⠀⠀⠀⠀⠀⢥⠸⡄⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡔⠉⣢⠀⠀⢶⡊⣀⡀⠙⠕⢤⠀⠀⠀⠀⠀⢳⣱⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠥⣴⡇⠀⠈⠁⠠⣭⡃⠼⠀⡷⣄⣀⠀⠀⢀⡿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢄⠂⣎⠀⠀⠁⠠⡀⠀⠀⠁⡀⣠⠁⠮⠀⡇⠀⢸⠣⠌⠀⠀⢤ ⠀⠀⠀⠀⠀⣕⠊⠑⠉⠉⡉⠁⠒⠹⣤⠄⠀⠁⡌⡆⡀⢀⡇⣠⠾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡈⠕⠒⠒⢺⠈⠒⢒⠦⢌⣁⠀⢉⡠⢹⠒⠁⠩⠳⣴⣆⠀⡀⢀⠐ ⠀⠀⢀⠠⠒⠉⠀⠀⠀⢰⣑⣂⠡⠀⠀⠀⠀⠀⠀⠀⡷⡂⠠⣣⠇⠉⠑⡍⠁⠀ ⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠉⠀⠀⠀⢠⣸⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡇⣸⠻⠀⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⢀⢂⢔⠔⠁⠀⠀⠀ ⠘⣧⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⣰⣀⡠⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠙⢷⣄⠘⡀⠀⠀⠀⠀⢀⢡⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠓⢦⣤⣤⠴⠊⠓⡽⠶⠤⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⢷⣦⠸⣿⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠹⠿⠟⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠆⠀⠀⠀⣴⡿⠿⠶⠾⠃⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠈⠿⣦⣤⣴⣟⠀⠀⠀⠀⠙⠷⢶⣶⠃⢰⣶⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⣄⢸⣇⠈⣿⢀⣴⡿⢻⣧⠀⠀⢀⣿⠋⠙⠛⠷⠶⢶⣤⣄⣼⠏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣿⠀⠻⠿⠟⠀⠙⠛⠋⣤⣾⠃⠀⣠⡿⠃⢀⣠⣤⣤⣶⢶⣮⣿⣿⡾⠋⣀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⣀⣴⣤⣈⡛⠛⣿⣿⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⢹⣷⡾⢋⣽⠟⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠈⠙⠛⠛⢻⡿⠁⠀⠀⣠⣤⡶⠾⠿⠿⠶⣾⡟⢠⡿⠁⣀⣾⠏⠀⠀⠀⠀⠀⢀⡀⣀⣠⠶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⠶⣾⣿⣄⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠁⢿⣷⠾⠛⠁⠀⠀⠀⠀⠀⠐⣯⣽⢷⣽⣿⣟⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⡛⠛⠷⢶⣤⣌⣙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠙⢿⣽⣷⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⣿⡟⠀⠀⠀⠀⣤⢦⢀⣿⣷⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠛⠻⣿⣟⣸⠯⣽⢿⡀ ⠀⣠⠤⣴⠶⣯⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢿⡿⠀⠛⠟⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠹⠥⠟⠛⠉⠋⠀ ⠀⣹⢒⣉⣿⣯⣿⣾⣲⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡶⠶⠶⣶⣤⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣛⡇⣩⠄⣐⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⡾⠛⢋⡽⠶⢶⡆⠀⠀⠀⠈⠻⣦⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⡿⢶⣽⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡟⠁⠀⠀⠈⠳⠶⠛⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⣀⠀⠀⠀⢀⣠⠎⠀⢀⣼⢟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣜⢿⣤⣀⠀⠈⠙⠛⠛⣋⣁⣤⡾⠛⣡⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⣷⣯⣝⣻⣿⡟⡛⣛⣋⣉⣥⣴⡾⠋⢹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⣽⠉⢹⡟⠛⡟⠉⢹⡁⢀⣿⣤⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠙⠛⠛⠿⣿⣶⣿⣿⣟⣛⣋⣉⣿⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⢶⣦⣤⣤⣾⠃⠀⠀⠀⠀⢀⣾⠋⣹⣇⡀⢀⣿⠋⠀⢈⣷⠈⣿⣦⣤⣴⣶⡾⢷⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⣴⣏⡀⠉⢹⣿⠓⠉⠁⢹⡄⢸⡇⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⣧⡀⠈⢉⣿⣿⠤⠴⠒⣻⠇⠈⡇⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⣀⣸⣇⠈⠉⠛⠛⢹⣿⣦⣴⠞⠋⠀⢰⡇⠀⢸⣇⠀⣸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣿⣅⣤⡾⣿⣤⡶⠟⠛⠛⠛⢿⣦⣤⣤⣤⣾⠛⠛⠛⠻⢷⣤⣾⠷⣤⣄⣿⡶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⡀⠀⠀⠀⢀⣼⡏⠀⠀⠸⣷⡀⠀⠀⠀⢀⣹⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠾⠛⠋⠀⠀⠀⠀⠈⠛⠷⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡶⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠳⡸⣄⣀⡇⡇⠀⠀⠀⠀⠀⢠⣯⣇⣀⡴⢻⣏⡀ ⠾⠭⠽⠒⠒⠪⣅⢣⣀⣳⠾⣦⣔⣫⣼⣿⣛⠒⠒⠚⠃ ⠀⠀⠀⢏⣿⣳⣮⠏⠁⠀⠀⠀⢹⡿⣛⣷⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢩⠇⠺⠂⠀⠠⠿⠋⢻⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢧⠒⠉⠉⠉⢲⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠈⠣⣀⣠⠔⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡌⢺⡀⢁⠀⠀⢐⡆⠀⣰⠃⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⢝⣚⠦⢐⣊⡤⠚⠙⠋⠉⠀⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢀⠀⢰⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⣦⢤⣸⡄⡏⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⢹⠇⣯⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⡇⠘⡄⣿⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⡾⣄⡠⢷⣿⣠⠼⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠚⠀⠧⢠⡞⠙⠶⠞⡃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣠⣤⡤⠶⠖⠒⠒⠚⠛⠒⠖⠲⡦⢤⣤⣀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣡⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣄⠀⠀⠙⣄⠀⠀⣀⣮⣶⢿⣿⣶⡆⣦⢀⠀⠀ ⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢤⣀⡀⠀⠀⠀⠀⠈⠉⠦⣄⠈⠳⣶⠟⠉⠁⠀⠀⠀⠉⢻⣿⣦⠀ ⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠸⣦⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⢸⣿⡧ ⠀⢀⡾⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠟⠀⠀⠀⣧⠀⠀⣠⣤⣀⠈⠹⡷⠢⠤⠤⠞⠃⠀⠀⠀⠀⠀⣽⣯ ⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣦⣼⣉⡀⠉⠁⠀⠀⠀⣴⡿⣹⠋⠁⠀⠈⢳⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠘⠙⠻⣄⠙⠾⣗⡤⠤⠤⠴⠞⢰⣇⡴⠒⠛⠓⢄⢻⣾⣧⣤⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⠀⢀⡴⠒⠒⠲⢾⣦⡀⠀⠀⠀⠀⠀⠀⠘⠏⢀⠀⠀⠀⠈⣿⡏⠉⠙⠿⣶⣶⣧⣶⣿⢿⠟⠃⠀ ⢺⡇⠀⠀⠀⠀⠀⢀⣾⡋⢸⣶⡎⠀⠀⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣲⣦⣀⢸⡟⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀ ⠸⣧⠀⠀⣾⣄⣠⠞⠉⢳⠀⠙⠀⠀⣠⣴⡿⣟⢦⡀⠀⠀⠀⣀⢀⠀⠀⣿⢿⢿⣻⠄⠚⠛⠦⣄⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⢻⡀⠀⢿⣄⠀⠀⠀⣸⠀⠠⠤⠄⠘⣻⣿⣿⣯⡁⠀⠐⠛⣡⠾⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡯⣟⠦⠤⠠⠼⠛⢧⠀⠀⠀ ⠀⠀⠻⣆⢸⡍⠀⠀⢉⡝⠀⠀⢈⠴⠋⠉⠁⠀⠉⠉⢀⡴⠚⠁⠀⠀⠀⡿⠳⡄⠀⠀⠀⠀⠀⢠⠇⢸⡆⠀⠀⠀⠀⣸⣄⠀⠀ ⠀⠀⠀⠙⠿⣽⣷⠶⠛⣷⣀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠴⠦⣤⠾⠛⠚⠓⠒⠒⠒⠒⠋⠁⠀⣸⠇⠀⠀⠀⠰⠟⠻⡀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠸⣟⠻⣄⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣤⡇⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸⡀⠈⠑⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣄⣀⣀⣀⣀⣤⠔⠋⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⣿⣻⣗⡼⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀ ⠀⠀⣾⢰⠄⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣠⣬⠿⠿⠟⠁⠀⠀⠳⣬⣉⡥⠾⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢄⠀⠀⠀⠙⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢱⢳⡌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠈⣦⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀ ⠀⠀⠈⢿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠈⠹⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⣤⣶⣤⣄⣀⠀⠀⠀⠶⣦⣤⣀⡀⠀⠀⠀⢛⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠇⠀⠈⢙⠉⠐⠅⠀⠀⡦⢄⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠾⢄⠀ ⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠀⠀⠀⢀⡜⠁ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡸⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢠⡌⣀⠐⠀⠈⠘⠁⡄ ⠀⠄⠀⡀⠀⠀⠀⢠⣾⣃⠀⠁⠀⢙⣶⣀⠀⠀⠘⡧ ⠀⠀⠀⠀⠀⠔⠀⠘⠛⠀⠀⠀⢸⡾⠏⠀⠯⠀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⡀⠀⣀⠑⠤⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠻⢶⣀⣠⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠉⠉⠹⣧⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠉⠉⠛⣷⡤⠴⢾⣁⡀⠀⠀⠀⠀⠀⠀⠹⡧⠛⠉⠛⠛⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⢻⣆⣤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟⢹⣧⣀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⠟⠈⠉⠙⠷⠶⣶⣆⠀⣠⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⣤⠶⣶⡟⢁⣼⠁⠉⠓⠚⠉⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡼⠋⠀⠀⠁⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣳⣼⣿⢠⣰⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢴⣖⠀⠀⠀⠀⠀ ⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠿⢾⡆⠀⢳⣿⠈⡷⢯⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀ ⢸⣿⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⠿⡄⢀⠎⢘⠛⡿⢧⣤⣤⣦⠄⠀⣤⡄⠀⠀⠀⠀⢠⣤⢤⡤⣞⡥⣶⣄⣀⠀⠀ ⠀⠸⣷⣤⣾⣷⣀⣀⣿⣷⣠⣴⣤⡀⠀⠐⠒⠋⠀⠈⠳⣷⢤⡀⡎⢸⠁⠀⠈⡇⡍⠀⢠⣷⣷⣂⡤⠄⠀⠈⠛⠳⠷⠟⠀⠀⠀⠘⠋⣿ ⠀⠀⠀⠀⠀⠈⠛⢿⣯⡉⠉⣠⠏⠀⠐⣶⠆⠀⢀⣠⣤⡌⢲⠙⠃⣾⠀⠀⡼⣰⠓⢊⣡⠷⢯⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⢀⣀⣠⡼⠉⠙⠷⠃⠀⠀⡴⢡⠔⠚⠉⠀⠘⣿⡠⠖⢻⢮⠀⠀⠀⠀⣾⣩⣀⣄⣀⡱⠘⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠰⡿⠍⠁⠀⠀⠀⠀⠀⠀⠈⠴⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢛⡆⢸⢨⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠉ ⠀⠀⠀⠀⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠞⠁⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⢞⠛⠛⠃⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⣷⣠⠀⠀⠀⢀⣷⣀⠀⠀⠀⠀⢠⣤⠾⠚⠛⣧⠀⠀⢀⡼⢦⣴⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠶⠾⠻⡭⠟⠀⠀⠀⠀⢠⣉⣷⠀⠀⡏⠀⠀⣞⠀⠀⠀⠸⣏⡀⠀⠀⠀⠀⠀⠀⡶⠶⠶⠒⠾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠶⠴⠴⠷⠾⠉⠁⠀⢠⡇⠀⠀⢸⠀⠀⠀⠀⠈⠙⠛⣦⣠⠤⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⢻⡍⢳⡄⠀⠀⣿⠸⣆⠀⠀⣠⣤⣾⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⣀⠀⢸⢁⣿⡄⠀⠈⢷⣈⣿⠀⣠⣼⣦⣿⣴⣋⣡⠞⢻⠀⣿⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⡻⣿⠳⣾⡍⠻⣿⣾⢿⡛⠶⣦⡄⠈⣿⣏⣡⠞⠋⣻⠉⠉⡀⠀⢸⡶⢟⣽⡯⠥⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⣿⠀⢹⡿⠶⣼⣿⠀⠙⠶⢬⣷⣿⢸⡏⠀⠀⠀⡟⠀⢸⠹⣦⣾⠞⠋⠉⠛⠛⢿⠋⣻⠷⢲⣶⠆⠀⠀⠀ ⠀⠀⠀⢼⡿⣦⠸⣯⡉⠛⠷⣾⡃⠀⠀⢸⣇⠀⠀⠀⠈⣽⡇⢿⡄⠀⢀⡇⠀⢸⣠⡟⠀⠀⠀⠀⠀⠀⣸⣾⠥⠖⠋⠀⠀⠀⠀⠀ ⠀⠀⢰⣾⣧⢻⡆⠈⠉⠉⠙⠙⠻⣦⣀⠀⢿⣄⠀⠀⠀⣿⡇⠈⢻⣆⢸⡇⠀⣸⣿⢦⡀⠀⠀⣀⣤⣾⠋⠀⣀⣤⣶⣞⣉⡿⠆⠀ ⠀⠀⠘⣧⠈⢿⡃⠀⣀⣤⣤⣀⠀⠀⠙⠳⢶⣿⣦⡀⠀⣿⡇⠀⠀⢻⣿⣧⠞⢉⣿⣄⢻⡖⠛⠉⠉⠉⠉⠻⣿⣍⠛⣧⡀⠀⠀⠀ ⠀⢸⡿⢿⡷⠴⢷⡾⠥⠴⠞⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⣹⣇⠀⠀⠈⣿⡇⢀⡾⠉⣯⠛⠇⠀⠀⠀⠀⣀⣠⠞⠋⠓⠛⠟⠀⠀⠀ ⠀⠈⢷⡈⣷⡀⠈⠻⣆⠀⠀⢀⣠⡤⢤⣤⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⣼⣷⠋⢹⡀⣿⣀⣤⡤⠶⠒⠋⠹⣍⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣀⠀⠀⠙⠿⣦⡛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⢿⣧⣴⠟⢻⡇⢀⣤⠿⣿⣉⡀⠀⠀⣀⡀⠀⠈⠛⠛⠃⠀⢀⣠⣤⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠿⠿⣦⣄⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⠏⠀⢸⣷⠋⠁⠀⠀⠉⠉⠛⠛⣿⠙⢲⡄⠀⣀⣴⣾⡽⠾⠛⠀ ⢰⢦⣄⠀⠀⢴⣚⣛⣶⣶⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⣷⣦⣼⣿⡄⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣤⣬⡿⠶⠛⢩⣿⢯⣉⠛⢶⡄⠀ ⠘⢦⣌⣷⡄⠀⠀⠀⠀⠙⢶⣤⣀⡀⠀⠀⣀⣀⣀⣀⠈⠛⣿⣿⠇⣰⣿⣧⣶⣾⣿⠿⠿⠛⠉⠘⣧⢻⡄⠀⣾⢹⡆⠈⠙⠛⠛⠀ ⠀⠀⢈⡛⠷⠦⣤⣤⣤⡤⠴⠿⠿⠛⠛⠛⠋⠛⠛⠻⢿⣦⣼⣿⣠⣿⠋⠁⠀⠉⠙⠛⢳⣶⡞⠛⠻⣾⡏⠙⢿⡿⣧⣴⣶⠶⢤⣀ ⠀⠀⡟⢹⡄⠀⠀⠀⠀⡞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣁⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⠻⣞⠉ ⠀⠀⢷⡾⠀⠀⠀⠀⠀⠻⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⠟⠛⢻⣯⠙⠻⠿⠿⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠙⣛⣻⡶⠦⠴⠶⠒⠛⠛⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠁⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠁⠀⣄⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⣼⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⡤⠤⠤⠤⢄⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⣼⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠓⠒⠢⡀⠀⠀⠀⠀⠀⠈⢑⣢⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⢇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠏⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⣸⡋⠁⠙⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⡆⢀⣤⠖⣿⠉⠉⠛⠋⠀⠀⠀⣴⣏⡉⠒⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⣿⣀⠇⠀⠀⢀⡤⠤⣤⠏⢹⠀⠰⠄⠊⢠⡾⠿⠿⠥⠀⠀⠀⠀⣀⡻⢿⣿⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡤⠄⠈⠙⢻⣄⣸⡟⠀⠀⠀⣾⠁⠀⡟⡄⠘⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠤⠈⠀⠀⠀⠈⢳⡀⠰⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠃⠀⠀⠀⠀⠉⠉⢿⡀⠀⠀⣿⠀⠀⣿⠁⠀⡽⠊⡩⠖⠀⠀⠀⠀⢀⣾⣄⣀⣠⢤⣤⣤⣶⣾⡁⢰⡇⠀⣱⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢨⠳⣄⠀⢸⣆⠀⠹⡀⢸⠀⢜⠀⠤⢴⣦⠤⣶⡿⠄⠈⠉⠀⠀⢰⡆⠀⠀⠈⠙⠒⠉⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⢀⢰⡆⣼⣿⡿⠉⠳⠄⣹⠘⡄⠈⠳⠶⠶⠶⠚⠉⢀⣀⠤⣴⣤⣴⢛⢲⠤⢤⣤⣤⡴⠾⠋⠀⣵⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⢤⣀⡴⢁⣠⣾⡿⣿⠋⡟⠀⢀⠀⠀⡾⠀⠈⠢⠤⠤⠤⠤⠔⠒⠉⠙⢦⣀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢑⣲⡾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣹⠋⠉⠀⠀⢻⡀⠧⠀⠀⢱⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠉⠉⢁⣜⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⡀⠀⠀⠀⠀⠙⠲⠤⠖⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠒⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀ ⠀⠀⠀⠀⡿⢸⣄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠁⠈⢿⣄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣦⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⣷⣤⣀⠀⠀⠀⠀⠀⡤⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠴⠷⣄⣀⡞⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣠⠞⢁⡼⣁⠀⠀⠀⠀⠀⠀⢀⣰⣃⣤⠾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠾⠿⠥⠖⠉⠀⠈⠻⢶⣦⣤⣴⡶⠛⠉⢁⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠐⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⡀⠀⠀⠒⠽⣧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢁⡏⠁⠀⠀⠀⠀⠈⠙⡄⠀⢀⡴⠚⠉⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⣠⣤⠀⠀⡜⠁⢘⣦⣤⣿⣀⣀⣀⣀⡀⠀⠀⠀⠘⣶⠋⢀⣀⠄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡶⣹⠳⡇⠀⣸⠁⢀⣿⣩⡿⠄⠀⢸⣯⡙⢿⡉⠉⠐⡾⢧⣔⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⣿⡇⠐⠧⣤⡇⠀⠸⣿⣿⢷⡀⢀⡞⠉⠹⡌⠁⠀⠀⢻⣏⡁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⡟⠀⠀⠘⡇⠀⢠⣿⣧⣤⡅⣼⣧⡄⠀⣹⡤⠀⠀⠀⠀⠈⠹⡖⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣧⣴⠁⣸⡿⠿⠷⠽⣿⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⢰⣿⠉⣿⡟⠁⠀⠀⠀⠀⠀⠈⠁⢺⠟⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠔⢻⣀⠰⠛⠷⣿⣿⣎⠙⢦⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢈⠀⠄⠀⠐⠀ ⠀⠀⠀⠀⡟⢳⡀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⢹⣿⣍⣻⠦⠽⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠑⣶⠀⠤⠖⠋⠀⠀⠀⣀⠄ ⠀⠀⠀⡰⣇⠈⠻⡄⠀⠀⠀⠀⠀⠈⣦⣴⣊⣉⠈⠛⢿⣦⢄⠀⠀⠓⠂⠐⠂⠀⣀⡠⠖⠉⠀⠀⠀⡰⠃⠀⠀⠀⢀⣠⠄⠀⠼⠶ ⠀⠀⡼⠁⢸⠀⠀⢹⡀⠀⠀⢠⣔⣋⣁⣀⡀⠀⠀⠀⠀⠈⠙⠒⠦⠶⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⢰⠁⠀⠀⣀⣤⠟⠁⠀⠀⠀⠀ ⠀⢀⡇⠀⡇⠀⠀⠀⡇⠀⡴⠋⠀⠀⠀⠉⠛⠻⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡠⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠸⠀⠀⠀⢰⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠟⠀⠀⠀⣠⣇⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⠀⠀⢀⡝⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣀⣀⣀⡤⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⣄⣀⣤⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠉⠉⠲⢄⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣤⣤⣀⣀⣀⣀⣠⡤⠔⠊⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠟⠉⣿⣄⣄⣀⣠⠴⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠚⠋⠉⠃⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⢶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣻⡟⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠠⠟⠁⣸⡏⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⡤⢤⡤⣤⣄⣀⣀⣸⣿⣿⣿⣄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢀⡄⣿⣇⣤⡿⠛⠛⠛⠛⠉⠈⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣦⣤⣽⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣘⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣼⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢰⢲⣶⡖⠒⠒⠒⠊⠓⠒⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡇⡏⢣⠤⡟⢹⡏⣧⠀⠀⠀⠀⣀⣸⠁⡇⢹⠟⣏⠙⢶⣤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠋⠀⠸⠟⠑⡄⠸⡆⠀⠀⣀⡤⠖⡎⠉⢸⡀⠀⣿⣇⣸⣤⣇⡈⠀⣸⡞⡇⠀⢠⣧⣇⣀⣧⣟⣀⣸⡀⣸⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⣹⠀⠹⡤⠞⠁⠀⠀⡇⠀⠀⢳⣆⣿⡏⣽⣿⣿⣿⣿⠛⠻⢷⢀⡾⠟⣿⣿⣿⣿⣿⢻⣧⡇⠐⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⢀⡟⠀⠀⢷⠀⠀⠀⠀⡃⠀⠀⠀⠹⣿⠀⢛⣻⣿⣿⣿⠀⠀⢸⠟⠀⠀⣿⣿⡿⣿⠀⡟⡿⠁⢸⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣤⠖⠋⠀⠀⠀⣸⢰⠀⠀⠀⢱⠀⠀⠀⠠⣿⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⢸⡇⡇⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⠘⡆⠀⠀⡆⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⡇⠀⠀⠀⢿⠀⠀⢸⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡿⢀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢦⠀⠀⠈⣇⠀⠘⣧⣷⣄⣀⠀⠀⢿⠛⠲⡦⠀⣀⣠⡤⢾⠟⠀⢰⠇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡀⠀⠠⠈⠷⡄⠸⣿⣞⠙⠛⢿⣗⡒⢲⣾⢿⣍⡀⠀⣿⡀⠀⡏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣿⡀⣠⣶⣷⣿⣶⣿⣿⣦⡀⠀⠈⣿⣼⣷⡀⢹⣿⣶⣿⣧⣾⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣰⡏⢳⠀⢳⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡋⠳⡀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠃⠈⢿⣿⣿⣿⡟⢪⠻⣧⣼⣆⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠖⠛⠛⠛⠛⡇⠀⠹⢦⣴⣤⡀⢰⣿⣧⣀⣀⣀⣀⣀⢿⣿⢿⣿⣿⣟⣛⣻⣿⣷⢸⣿⣿⣿⡟⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣉⣉⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣾⣏⠈⠛⠛⠛⠉⠉⢸⣿⣿⣛⣛⣿⣿⢟⣩⣽⠿⣿⣭⢿⣧⠈⣿⡆⠀⠀⣀⣤⣤⣠⠤⠤⢤⢤⡀⠀⠀ ⠻⣭⢤⡄⠠⠖⠀⠀⣰⣿⣿⣿⣿⡿⠛⢷⣄⠀⠀⠀⠀⢸⣿⡋⣩⣽⣿⣻⡽⠟⠁⠀⠸⣿⡀⣿⡀⡟⣿⡶⠿⣿⣿⣿⣿⣦⠀⢘⢯⡁⠀⠀ ⠀⠹⠭⠴⠶⣦⣴⠾⣿⠛⣾⣿⡿⠁⠀⠈⢻⣷⣄⠀⠀⣿⣿⣶⣿⣿⡏⠉⠀⠀⠀⠀⠀⣿⡇⣸⡇⠁⢹⣿⡀⠹⣿⣿⣿⣿⣷⡀⡰⠿⣦⠀ ⠀⠀⠀⠀⠰⣿⣿⠆⢁⣴⣿⡟⠁⠀⠀⠀⠀⢿⣿⣷⣿⣿⠿⠋⣡⣿⣿⣠⣤⣤⣤⣤⣶⡿⣧⢿⡇⠀⢸⣿⡇⠠⠌⣿⣿⣽⣿⠧⣽⣦⣼⠇ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⡇⠀⢸⣇⠀⣾⢻⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⣄⠀⠀⢀⣼⠋⢹⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡁⠘⣿⣅⠋⠉⣽⣷⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣴⠟⠁⠀⣸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⣿⣀⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡁⠀⢀⣀⣿⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠈⠻⢦⣬⠉⣿⡿⠷⢶⣤⣄⣀⣠⣼⣿⡋⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠶⠶⠶⠶⠶⠷⠿⠿⠷⠶⠦⠴⠾⠿⠿⠿⠿⠶⢶⢿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⡠⠤⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠤⡀⠀⠰⠀⠈⡄⠀⠀⠀⠈⠃⠤⢌⠊⣄⣊⠀⢠⠔⠉⡇⠀⠀⠀⠀⠀ ⠀⢸⠀⠘⢄⠀⠣⠀⢠⢠⠋⠒⡀⠠⡒⠒⠀⡠⠘⠀⠇⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢣⠀⠈⠢⢀⣱⠘⡀⡃⠀⢡⠀⠉⠒⠀⣨⠖⠊⠀⠒⠮⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠀⠀⠀⠑⠒⠒⡺⠁⠀⠀⠀⠀⠀⠑⣄⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠠⠄⠂⡡⠒⠉⠉⠀⠀⠰⢿⣢⠀⠀⢸⠁⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠁⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣽⡦⣀⣀⡠⠄⣳⠤⠤⠜⠀⠀ ⠀⠀⠀⢠⠋⢘⠀⠀⠀⠀⠀⠀⠀⢠⡠⠎⠀⢠⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠰⠇⢠⣾⠇⡏⠀⠀⠀⠀⢠⡒⠠⣆⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠈⠒⠤⢀⣀⣀⡀⠸⡄⠀⣠⡑⠲⣀⣀⣄⠟⠀⡀⢸⡀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣌⠀⠀⠀⣤⡄⠀⠘⠚⣸⠁⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠦⠤⣀⡠⢤⢄⠂⠙⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢎⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠙⢆⠀⠀⠀⠀ ⠀⡔⠁⠀⠀⠀⢀⡞⠀⠀⢹⠉⠁⠐⠒⡆⠀⠀⢫⠀⠈⢆⠀⠀⠈⢣⠀⠀⠀ ⢸⠀⠀⠀⢀⠔⠁⢡⠀⠀⠈⡄⠀⠀⠀⢇⠀⠀⠀⢣⠀⠈⠆⠀⠀⢈⡄⠀⠀ ⢸⠀⠀⠀⣇⠀⠀⠀⢆⠀⠀⣸⠀⠀⠀⠘⡀⠀⠀⠀⠑⢄⠸⠤⠔⠊⠀⠀⠀ ⠀⡄⠀⠀⢈⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠛⠛⢛⡛⠛⠛⠿⠶⢶⣦⣀⡀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⣠⡿⢿⣆⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⢀⣶⠟⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⣀⣾⠋⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣴⣶⣀⠀⠈⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⢀⣾⠏⠈⢿⣆⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀ ⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⣠⡿⠉⠀⠀⠀⠻⣦⡀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀ ⠀⣾⠏⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠹⣷⡀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀ ⢨⣿⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⢿⡆⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⢿⣆ ⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢻⣦⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠛⠷⠶⠶⠶⠶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠟⠛⠀⠀⠀⢻⣦⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⢀⣾⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⣼⡏⠿⣷⣶⣤⣌⣉⣉⡙⠛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠛⠛⠋⠉⣉⣁⣀⣤⣶⡾⠿⣷⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⢠⣿⠀⠀⢻⡇⣼⡍⠉⠉⠛⠻⠷⠶⠶⠶⠶⠶⣶⣶⣦⣤⣤⣤⣤⣴⣶⡶⠶⠶⠶⠶⠶⠿⠛⠛⠉⣯⠉⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⢸⡏⠀⠀⢸⣇⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢸⡿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿ ⢸⠇⠀⠀⠀⠀⣾⡇⠀⠀⠈⣿⡄⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡇⠀⠀⠀⣿⡆⠀⠀⠀⠀⢠⣿ ⢸⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⢹⡇⠘⣿⣷⣄⡀⠀⢀⣀⣀⣤⡶⣾⢿⡟⢻⡟⣿⠿⣶⢶⣤⣀⣀⡀⠀⠀⣠⣾⣿⠏⠀⣼⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣷⠀⢻⣏⠙⣿⣿⠛⣿⡏⢩⡇⣿⣸⣧⣿⣷⣿⡀⣿⢀⣿⢙⣿⢛⣿⣿⠛⣩⡿⠀⠀⣿⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀⠀⢿⣆⣈⠉⢷⡇⣷⢸⣷⡿⣿⣿⡏⣿⠯⣷⢿⣼⣿⣼⢹⡾⠛⢳⢶⣿⠁⠀⢠⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣸⡇ ⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⣧⠀⠈⣿⣽⡄⠀⠉⢻⡿⠻⡗⠉⠹⠇⠛⢸⡿⠸⠋⠿⠃⠋⢁⢰⣌⣿⠁⠀⠀⣾⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃ ⢸⣧⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⣿⣷⣿⠂⣬⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣶⣿⢿⣿⠃⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⢰⡿⠀ ⠈⣿⡄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠹⣷⠀⠀⠘⣿⣽⣇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣻⣻⣾⠏⠀⠀⢀⣿⠃⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⣸⡇⠀ ⠀⢹⡇⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢻⣆⠀⠀⠘⣷⣼⠃⣿⣶⠀⠀⠀⠀⠀⠀⠀⢀⡀⡏⣿⠉⣿⠏⠀⠀⢀⣾⠇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⣿⠃⠀ ⠀⠸⣿⣄⡀⠀⠀⠀⠀⠈⠙⣷⣄⠀⠈⢿⣄⠀⠀⠹⣷⢀⣧⢿⣶⣀⠀⠀⠀⠀⠀⣸⣧⣇⠘⣾⠏⠀⠀⢠⣾⠋⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀ ⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠈⠻⣷⣄⡈⢿⣆⠀⠀⠹⣿⠋⢸⠟⣿⣧⣦⠀⢠⣼⣿⠹⣿⣼⠏⠀⠀⣠⡟⠁⢀⣴⠟⠁⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠈⠻⣿⡛⠿⣧⡀⠀⠹⣷⣿⠀⣿⢻⠿⣰⣸⣿⢿⢀⣾⠏⠀⣠⣾⠿⠶⣾⡿⠁⠀⠀⠀⠀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⠀⠈⢿⣦⠙⢷⣄⠀⠙⣿⣄⡇⢸⠀⡿⡏⣿⢸⣾⠋⢀⣶⠟⠁⢠⣾⠏⠀⠀⣀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀⠀⠀⠻⣷⡀⠙⠿⣦⣈⠻⢷⣾⣶⣧⣿⡿⢟⣡⣶⠟⠁⠀⣰⡟⢁⣠⣶⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡘⢿⣄⠀⠈⠛⠿⢶⣦⣤⣤⣶⠶⠿⠋⠁⠀⣀⣼⣿⠾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣦⣄⣀⠀⢸⣿⠈⢹⣯⣀⣠⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠾⠿⣶⠾⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣿⣀⣀⣿⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⣶⡀⠀⢀⣄⠀⠀⣀⣀⠀⠀⣠⡀⠀⢀⣶⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⣿⠻⣶⠟⠙⢷⡾⠋⠙⢷⡾⠋⠻⣶⠟⣿⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⣾⠃⠀⠀⢰⣿⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣿⡆⠀⠀⠘⣷⠀⠀ ⠀⢰⡟⠀⠀⠀⣼⣿⢷⣤⠞⠛⢦⣴⠟⠻⣦⡴⠛⠳⣤⡾⣿⣧⠀⠀⠀⢻⡄⠀ ⠀⣼⠇⠀⠀⢀⣿⣿⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⣿⣿⡀⠀⠀⠸⣧⠀ ⢀⣿⠀⠀⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⣿⡀ ⠈⣻⡶⠶⣶⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣶⠶⢶⣟⠁ ⠀⠿⠷⠾⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠷⠾⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠸⣆⢹⡄⠀⢸⠙⡇⠀⠀⠀⠀⠀⠀⠀⢀⡖⣶⠀⠀⢀⣾⣿⠇⠀ ⣀⣤⠤⢼⡈⠛⠲⠾⠇⣇⠀⢀⣀⣠⡄⠀⢀⡼⠛⢷⣶⣶⣋⣁⠛⢲⣦ ⠛⠓⠒⠋⣉⣉⣉⠓⢦⣘⣦⠤⠿⠛⠿⣶⣏⣴⣾⣿⡿⢥⡀⠉⠉⠉⠁ ⠀⠀⠀⠸⣇⣻⣟⡻⣶⠟⠁⠀⠀⠀⠀⠀⣿⡿⢛⣹⣷⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢻⠏⢸⡆⠀⠀⠀⣾⡶⠘⢿⠟⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣃⡤⠔⠒⠒⠢⢄⠈⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠉⢯⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠈⠳⣄⡤⠔⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠙⣏⠀⢸⠀⠀⠀⠐⡶⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣈⠳⠼⣦⣀⢤⠞⢁⣤⠞⠓⠖⠒⠉⠉⠉⠳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢾⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡄⠀⠀⠀⠀⢰⡀⢠⣏⣳⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⠀⢷⣒⣲⣿⡇⢸⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠀⢸⣽⢸⢹⠃⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⡆⠈⡇⠀⢸⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣿⠃⠀⢸⣀⣿⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡙⠒⣻⢻⠶⠖⠚⣿⣿⠶⠚⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠁⠈⠦⠤⣼⠋⠈⢓⠚⢋⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠓⠤⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠴⠋⠙⣦⠔⢎⡀⠀⠀⠀⠘⠖⠋⠚⠦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠤⣀⣀⡹⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡮⠹⠤⣀⢤⠀⠀⠀⠀⠀ ⢠⡞⠉⠀⠀⠀⠉⠓⠊⠉⠀⠀⢀⠀⢀⡔⠉⠉⠉⠉⠒⠁⠀⠀⠈⡑⠀⠀⠀⠀ ⢹⡆⠀⠀⠀⠀⠀⠀⠤⣦⡀⢛⡟⢴⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⠀⠀⠀ ⠸⡄⢀⡀⠀⣄⠀⠀⠀⢀⡹⠼⣣⠠⢉⢹⠣⠦⡖⢀⠶⠀⠀⢠⣔⣖⡅⠦⢄⣀ ⠀⠉⠉⠻⢾⣛⢊⠏⠀⡤⠀⡀⣬⠫⠂⡆⢀⢦⠇⡊⠽⡪⠁⠀⠀⠉⠀⠀⠀⢸ ⠀⠀⣠⠶⠚⠈⠉⠀⢌⠆⠉⠀⠘⠖⠙⢇⢠⣤⠗⠒⠒⠃⠉⠁⠀⠀⠀⠀⠀⡸ ⠀⠀⠸⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⣀⡠⠊⠂⡇⢀⣀⠀⠀⠀⠀⠀⢰⣖⡒⠃⠀ ⠀⠀⠀⠀⠑⠧⠤⠶⠷⠀⠀⢈⣫⠁⠘⠀⠔⠉⠁⢟⠀⠀⠀⠀⡤⠤⠴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠛⠀⠀⢆⠀⠰⠀⠀⠈⠉⠓⠖⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣷⠻⠛⣦⠴⠶⠤⣤⠞⠉⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢧⠀⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⣨⡷⠶⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠓⠾⣄⠀⠀⢀⡴⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠀⠀⠀⠀⠚⠉⠉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠧⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡄⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀ ⠀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢧⡀⠀⠀ ⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠖⠚⣧⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣤⡞⠁⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣦⣀⡀⢀⣠⠏⠀⠀⠀⠐⠶⠤⠴⠚⠁⠠⠿⠧⢤⡀⠀ ⠙⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠚⠻⡄⠉⣽⣄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆ ⠀⢘⡷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢶⡏⠀⠀⠙⠶⠋⠈⠁⡞⢿⣀⠀⣀⠀⠀⠀⠀⠀⠀⠴⠴⣟⡁ ⠀⢺⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣤⣴⢿⣧⡀⢳⡀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣥⣠⣄⡀⠀⢀⠀⠀⠀⣽⡇ ⠀⠀⠙⠦⠤⢾⠀⠀⠀⠀⣀⠀⠀⠀⠀⣻⣦⡿⠙⠛⠃⠀⠀⠀⠀⠀⣼⠀⣼⣯⡿⠛⠉⠿⠤⡤⠟⢣⡤⠿⠋⠁ ⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡼⠓⠒⠒⠚⠁⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⠻⣄⣀⢀⡼⠦⣄⣀⣰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⣿⣰⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠈⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠓⠒⠒⠒⠒⠒⠶⣤⣀⠀⠀⢶⣤⣀⣀⣀⣉⣙⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠾⡇⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⠀⠉⠉⠉⠀⠒⠤⡀⠀⢤⠈⢢⠀⠀ ⠀⠀⠀⠀⡠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣼⠀⢸⠀⠀ ⠀⠀⠠⡀⢃⢝⠍⠉⠭⡐⠶⠤⣄⡀⠀⠀⠀⠈⢆⡘⠀⠀ ⠀⡤⢄⣇⡿⡸⣀⠰⣿⡇⣾⣥⠈⠙⣱⢦⡀⠀⡜⣇⡀⠀ ⢸⠀⣾⣻⠁⠨⡒⠚⠚⠘⢝⡫⠤⣰⠼⠦⢽⢦⣏⠀⠈⡆ ⠀⢣⠈⢻⢠⡀⠘⠔⣂⣀⠤⠔⠂⠀⠀⠀⡜⠀⠙⣯⠉⠀ ⠀⠀⣱⡈⠙⠁⠅⡒⠠⠤⠀⠀⡀⠤⠄⢰⠁⠀⠀⢰⢡⠀ ⠀⠀⢧⠁⠀⠰⣰⣭⡆⡹⠀⠀⡸⠓⠚⠯⣢⠀⠰⠂⠀⡆ ⠀⠀⣘⣆⠀⠀⢱⠒⠊⠀⠀⢰⠵⢧⡦⠷⡡⠇⠀⠀⢀⠇ ⠀⠀⠡⣉⢿⡲⠼⢤⢀⣀⣀⣈⡢⠔⠁⠀⠀⢀⣀⣠⠎⠀ ⠀⠀⠀⠈⠈⠀⠀⠀⠧⠤⠽⠕⠣⠀⣀⣀⠠⠤⠊⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⣤⡶⠀⠘⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡏⠀⠻⣆⠀⠀⠀⢀⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢄⣉⡳⣄⡘⠋⢠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⢉⣾⠟⢡⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡒⠀⠀⠀⠱⠀⠈⠁⠹⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠻⣄⣠⠟⠁⣰⣿⣿⣿⣿⡿⠛⢁⣾⣿⡿⠃⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢿⣿⡿⠋⠛⠉⣽⣶⣿⡶⣤⣿⣿⡿⠛⠁⠀⠀⣼⡿⠋⠀⣀⣠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⡟⣾⣿⠀⠀⠸⠼⣿⣿⡿⢻⣏⠛⠉⠀⠀⠀⣧⣼⠿⢶⣛⣉⣁⣀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣷⢘⡇⠀⠀⠀⠀⠀⠙⠲⠦⡅⠀⠀⠀⠀⡀⠘⠿⠚⣿⣿⣷⠀⢟⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠒⠛⠛⠛⣠⣾⣿⣿⠁⠀⠉⠑⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢋⣽⣿⠇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠚⠉⠀⣠⣾⣿⠏⠀⠀⠀⠀⣴⡧⠶⠖⠒⠦⢤⣀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣿⠲⠤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣾⣿⡟⠋⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⣠⠬⠷⠲⠤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣆⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣠⣾⠏⠀⠀⢀⣀⡤⠞⠉⠒⠂⠡⠄⠉⠉⠉⠉ ⠀⠀⠀⣄⣰⠛⠛⠓⠒⠶⣼⡟⢦⠀⠀⠹⡆⠈⣇⢹⣻⣿⣿⣿⣿⣿⣿⣿⡿⠟⣟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠦⢤⣖⡋⠁⠀⠀⣀⣠⠮⠤⠒⠲⡖⠒⠀ ⠀⠀⠀⠈⢻⣏⡉⠀⠒⣆⢳⣳⠈⠓⠦⢀⢿⠀⢸⡄⢻⣷⡈⠻⣿⣿⡿⠋⠀⠀⠸⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠒⠾⠥⢄⣀⠀⠀⠀⠹⡀⠀ ⠀⠀⠀⠀⠈⣆⠙⣄⠀⠈⢿⣿⡀⠀⠀⠀⠈⡆⠈⡇⠀⠻⣧⣀⠼⡿⠀⠀⠀⠀⣀⡷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⡄ ⠀⠀⠀⠀⠀⠸⣷⣾⣤⣄⡀⢻⡇⠀⠀⠀⠀⢱⠀⢱⠀⠀⢻⠁⠸⠁⠀⣀⠴⠚⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣧⣄⣀⠀⠀⠸⡀⠸⠀⠀⢸⡀⣠⠴⢋⣡⠴⠛⠙⣄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⠛⢿⣿⣿⣿⣿⣿⣷⣷⣦⣴⣶⣶⣿⣥⣶⣏⣀⡤⠴⠖⣚⣱⠽⠾⠋⢁⡀⠈⠻⢿⡟⠀⢿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠒⠆⠂⠖⠎⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⢣⠀⠀⠀⠙⢶⠤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢧⠀⠀⠀⠀⠓⢄⠈⠉⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡿⠋⠀⠀⠀⠹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠱⡄⠀⠀⠀⠱⡶⢄⠀⠀⠀⢣⠀⢀⣤⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⡿⠃⠀⠀⠀⠀⣸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣄⠀⠀⠀⠈⢢⡀⠀⠀⠹⡌⢣⠀⠀⠘⣏⡇⠀⠳⣌⠉⠓⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠄⠀⡀⠀⢀⡀⢀⣰⣿⠁⠀⠀⠀⠀⢠⣿⣿⣷⣤⣀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⠱⡄⠀⠀⢱⡈⢧⡀⠀⠸⣡⠀⠀⡝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⠀⠀⠀⠈⠀⡞⠋⢙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠦⣄⠀⠀⠀⣱⣽⣄⡀⠀⠘⣆⠀⠀⢣⠀⠳⣄⣀⣿⠀⠀⢸⠀⠈⢣⣄⠀⠀⠀⢀⡠⠴⠍⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⠐⠀⣴⠃⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡞⠉⢸⢦⠳⡄⡀⠘⣆⠀⠘⣆⠀⠀⠉⠈⡆⠀⠈⣇⠀⢸⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠑⠂⢠⡾⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠘⠀⢣⡙⣏⠒⢋⠳⠤⠟⠀⠀⠀⠀⢻⠀⠀⠹⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀

⠀⠀⠀⠀⡀⠰⣄⠀⠀⠀⠀⡠⠐⣀⠄ ⠀⠀⠀⠀⠡⢀⣽⠃⠐⠲⢞⠂⠁⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⠠⣤⣄⢯⠃⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡟⠟⠹⣿⣿⡔⠀⠀⠀ ⠀⢀⡴⡺⠁⢙⣿⢤⣤⣾⢹⠹⣄⡀⠀ ⠰⡋⣐⣴⣲⡟⠈⠉⣿⡳⠹⣳⢮⡻⣷ ⠴⢺⣿⣻⡯⠃⠀⠀⢹⡇⠀⢴⣷⢏⡇ ⠀⣸⣿⠛⠁⠀⠀⡠⣾⣏⣆⣸⣻⠞⠁ ⠀⢸⣿⣄⠀⠀⠀⣹⣪⡿⠛⠁⠀⠀⠀ ⠀⣿⠉⠹⡍⣿⡏⢹⡎⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⢰⠃⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣧⣾⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠉⠇⠀⠀⠹⡎⢃⠀⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⣸⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⢿⢇⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣛⡄⠀⠀⠀⢭⡥⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣦⠤⠤⠴⠖⠒⠒⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡾⠀⢀⣠⠔⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢯⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡼⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⣆⠀⢾⣇⣼⡿⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⡵⠋⠀⠀⠀⠀⠀⠀⢀⣄⣴⢻⢰⣼⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣯⠄⠀⠀⠀⠀⠀⠀⠀⣸⡾⠁⢸⡾⣧⣳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡼⢹ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⡟⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⡾⠃ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡴⠻⣤⠀⠀⠀⠀⠀⡇⣰⣯⣹⡧⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⠞⠁⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⣎⠙⣇⠀⢨⣧⡀⠀⠀⠀⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡴⢁⡤⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠿⠶⠦⠤⣿⡀⠀⠀⠀⢸⠁⠈⢦⡈⢳⣸⣿⣧⠀⠀⠀⠈⢿⣿⣿⡷⠤⠀⠀⣤⣾⠜⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠸⠇⠀⠀⠈⠳⣟⣿⣿⠇⢀⣀⣀⡉⠉⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⢀⠀⠀⠀⠀⠀⠀⢀⣀⡟⢦⡀⣄⠀⠀⠀⠀⣰⠃⠀⠀⠰⢯⣶⠴⣛⡶⠒⠂⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⢿⠀⠀⠀⠀⠀⠀⢀⡟⠇⠈⠛⠿⠓⠲⠖⠚⠻⣄⡀⠀⠀⠀⣙⡉⠁⠀⣀⠤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠹⣆⠀⠀⣀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⣩⢽⠁⡰⠿⡄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⠤⣈⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⠜⠹⣀⣠⢾⠞⡥⠀⢀⠀⠘⣦⠴⣍⣉⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠟⠒⢦⠘⢣⡇⢰⠁⠀⠈⡗⠦⠥⠴⢯⣭⣍⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣒⠋⠉⠉⠀⠀⠀⠀⠀⠉⢹⠃⠈⠁⠀⠀⡇⠀⠀⡴⠋⣼⠀⠀⠀⠉⠉⠓⠲⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠉⠉⠓⣦⠤⣀⡀⠀⠀⢸⠄⠀⠀⠀⠀⢷⣄⣾⢖⡼⠁⠀⠀⠀⠀⣠⠴⠊⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣞⡉⠉⠙⠺⣍⠙⠒⠾⣅⡀⠀⠀⠀⠀⠙⣏⠁⠀⠀⠀⢀⡠⠞⠁⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⣿⠀⠀⠸⣶⣷⣆⢠⡞⠉⡇⠀⠀⠀⠈⠑⠦⣄⡀⣠⠏⠀⠀⣀⠴⣿⠶⠶⠶⠾⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠾⠭⠤⠤⠤⣿⠀⠀⠀⠙⠹⡟⢾⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣤⠞⠁⡼⢉⣿⣠⣤⡁⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⢹⠛⠛⡿⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠒⠒⠶⠶⠶⡿⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⢀⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⠃⣸⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣀⠀⡟⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣰⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⣸⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⢀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠈⠁⢲⠤⠤⠄⠀⠠⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⡀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀ ⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠃⢠⣖⠅⠀⠀⠀⠀⠀⢀⣠⠄⠀⠈⠱⡀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⢀⠋⡀⠖⠁⠀⠀⠀⡀⢀⡴⠁⠀⠑⢄⠀⠀⠈⢆ ⠀⠀⢸⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⠀⣸⣀⡷⡟⠁⠀⠀⠀⠈⢂⠀⠀⢈ ⠀⠀⢸⠀⠀⠀⢀⡾⠀⠀⠀⠀⢀⡟⠁⠟⢽⢧⠀⠀⠀⠀⠀⢸⠀⠀⠞ ⠀⠀⠀⡄⠀⠀⡜⠀⠀⠀⠀⠀⡜⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⡜⠀⠀⡜ ⠀⠀⠀⡇⠀⢰⠁⠀⠀⣀⠴⡊⢢⡀⠀⠀⣶⣿⡇⠀⠀⠀⡐⢁⠤⠊⠀ ⠀⢀⡠⠗⠒⠼⣄⠀⠀⡃⠳⢕⣼⣷⠀⠀⢹⡿⠷⠀⠠⡾⠊⠁⠀⠀⠀ ⢠⠋⠀⠀⠀⠀⣸⢆⣀⠁⠀⢀⠟⠋⢴⣶⢶⡤⠄⠀⢀⡇⠀⠀⠀⠀⠀ ⠘⢿⡀⠀⠀⢀⡟⠀⠉⠉⠂⠉⠢⠤⠤⣬⠁⡠⠒⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠄⠣⠎⠀⠀⠀⠀⢀⡤⠲⣠⡾⡋⢈⡈⡦⢊⣱⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠚⠉⠑⢸⠁⠃⠀⠉⠀⡹⡖⠒⠂⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⢉⡐⢶⡤⢀⣸⠀⠀⠀⠣⡾⠖⠁⠀⢀⠔⢨⠃⠀ ⠀⠀⠀⢀⡀⠤⠇⠀⢸⣦⡀⠞⡆⠈⠁⠢⠄⣀⠇⠀⡠⣶⠥⠴⡅⠀⠀ ⠀⠀⠀⠉⠀⠐⡆⠀⠀⢹⠙⠀⠇⠀⠀⠀⠀⠈⢱⠊⡐⡽⣷⠶⠃⠀⠀ ⠀⠀⠀⠓⠒⠒⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⠸⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⠀⣀⡄⠀⢠⠀⠀⠀⠀⠀⠎⠀⣃⠗⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠼⣀⠀⠀⠀⡘⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⢳⡀⢹⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠘⡈⡇⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⢸⠘⡆⠀⡇⢻⢠⠇⢸⡇⠀⡠⢲⠄⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⢇⠘⡇⠀⡸⠀⣧⣴⠃⠘⢿⡄⢸⡦⠞⢱⡏⡜⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣆⣸⠀⠿⠦⡇⠀⣿⣠⡤⢶⣾⠃⠈⠳⠶⠬⠟⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⠀⢻⣏⢀⣠⢶⡇⠀⠈⠙⠒⠉⠀⣀⣀⣀⣀⡀⠘⠿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡧⠤⠤⠧⡄⠉⠛⠛⠉⢀⣀⣀⣤⡤⠶⠛⠋⠁⠀⠀⠉⠓⠦⣈⠳⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⢹⠀⠀⣰⠞⠉⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⣏⣀⢀⣿⠤⠔⠉⠁⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠟⠉⣠⣄⠀⠈⠁⠀⠀⢀⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠖⠛⠁⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠘⢯⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣏⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢶⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠓⢛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⠶⠚⠉⠉⠳⡄⠀⠀⠀⠀⢀⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⡆⠹⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡠⡀⢘⢱⢰⢸⠐⢸⢀⢔⡄⡶⠀ ⠀⠀⠀⠀⠀⠓⣄⡁⠠⣈⠸⣏⣀⡽⠘⢭⡸⣠⠃⠀ ⠀⠀⠀⢰⣄⣠⡘⠧⠶⠋⠀⢀⣀⠤⠒⠒⠠⣙⢄⡀ ⠀⠀⠀⠀⠑⢢⣸⠀⢰⠊⡉⠁⡀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⢀⡠⠖⣩⠉⠁⠉⢀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⡴⡾⠁⠀⠀⠁⠀⠀⠀⢈⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⣇⠠⢄⡀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠑⢦⠀⠀⠀⠀⠀⠀⠀⠠⡾⠉⠀⠉⠲⡀⢠⠖⠉⢙⡦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⡀⠈⠁⡴⠒⠉⠀⠀⠀⣰⠞⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⠈⠳⡀⠀⠀⠸⡄⠀⠀⢸⠀⠀⣠⠤⣄⠀⠀⠀⠀⣀⣀⠈⡇⠀⠙⠋⢹⡇⠀⣼⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠀⠀⠹⡄⠀⠀⠙⣆⠀⠈⡇⠀⡇⠀⠀⠱⡀⠀⠸⡁⠈⠉⠁⠀⢰⠊⠁⠀⢠⠇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠈⠢⡀⠀⠈⢆⠀⢇⠀⠹⡄⠀⠀⢧⠀⠀⠈⠳⠤⣀⣀⣈⣙⡶⠶⠚⠓⠲⠦⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠓⠒⠛⠀⠈⠦⡴⠃⠀⠀⠘⢆⡀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⣋⡿⠷⠚⠃⠀⠀⠀⠀⣠⣤⢤⡀⠀⠀⠉⠛⢻⠟⠉⠉⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠶⠒⠒⠉⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠮⠽⠀⠀⠀⠀⠸⡀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⣺⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣄⣀⣀⡤⠴⣞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣄⣿⠲⣄⣀⢀⣀⣠⠴⠖⢚⡟⠶⠴⠶⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠛⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠀⢸⠀⠀⠈⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡦⠚⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⣠⣼⣿⠤⣿⡁⠀⠀⠀⠀⠀⠀⠀⢰⡗⠣⠤⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠻⠏⠉⠀⣿⡁⣀⠀⠀⠀⠀⠀⠰⡾⠇⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣠⡤⢼⣇⠀⠀⢠⡤⡄⠉⠹⣄⢀⡀⢠⣄⣼⠃⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡈⠛⠃⠀⠀⠈⠉⢉⡁⠀⠀⠀⠀⣏⣹⠠⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡀⠀⠀⠀⢯⡽⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣆⣀⣀⡀⠀⠀⣀⣀⣀⢠⠞⠉⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠶⠋⠀⡼⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠗⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢯⡀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⣏⠉⠉⠉⠉⠛⠛⢻⡇⠀⠀⠀⠀⢧⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⣠⠜⢹⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⢧⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢧⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠸⡄⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢷⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⢦⣀⣀⠤⠔⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠧⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⠲⣄⠀⠀⠀⣠⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈⠳⣤⠾⠁⢀⣀⡴⠏⠀⠀⠀⠀⣀⣤⠶⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠶⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⢤⣀⠀⠀⣾⣉⣁⣀⠀⠀⠀⢀⣾⠏⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠹⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⣷⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⣀⣀⠀⢹⠄⠀⠉⠉⠉⣹⡇⠀⠀⣾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⢳⡀⠀⠀⢹⠀⠀⣿⠀⠀⠀⠙⣆⠀⠀⠀⣟⠉⠉⠛⠛⠀⠀⢀⡴⠛⠁⠀⠀⣸⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⣄⠀⠸⡄⠀⠙⣆⠀⠀⠀⠹⡄⠀⠀⠙⠶⣄⡀⠀⠀⠀⠘⢧⣄⣀⣠⣠⣿⣀⣀⣀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠈⠳⣄⡀⠀⢹⠀⠀⢳⡀⠀⢹⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⣶⠾⠋⠉⠀⠀⠀⠉⠉⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠈⠷⣀⡀⠀⠀⠀⠀⣀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢶⣾⣤⠤⠶⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠛⠶⠶⣶⠖⠚⠓⢶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢄⣀⣀⣀⣀⣀⢀⣀⣀⣀⠴⠖⠉⠁⢀⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⣀⣀⣀⣀⣀⡤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡀⣹⣷⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⣿⣦⣀⣀⣀⣠⡼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠶⠿⠾⣧⠙⠻⠶⠦⠶⠶⠞⠋⠉⠀⢰⡟⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠶⠛⠁⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠈⠀⢀⣰⣾⣶⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⣞⣿⠷⠏⠀⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠈⠉⠹⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠉⠉⠀⠀⠀⠛⢷⡴⣶⠀⠀⠀⠀⠀⡀⠀⣹⡏⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⣤⣀⣀⣀⣤⠤⠴⠶⠖⣿⣄⠀⠀⠀⣶⣶⣆⠀⠀⠹⣦⣀⣤⣀⣠⣶⡤⠟⠁⠀⢀⣀⡀⠀⠸⣧⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⡀⠙⠟⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣉⣽⠠⢰⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢶⣀⠀⠀⠀⠀⠀⠀⢴⣟⣿⡆⠀⠀⠀⠀⠈⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠶⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠶⠶⢦⣀⠀⣀⡴⠶⣶⢦⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠿⠃⠀⢠⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠁⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠶⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢻⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠘⣧⣀⣀⣀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣆⠀⠀⠀⢀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠤⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠀⢠⠀⠀⠀⠀⣠⠀⣠⡄⠀ ⠦⠑⣚⢩⣆⠰⠆⣔⣽⠟⠒⠛⠂ ⠀⠈⠙⡻⡇⠀⢤⠸⠟⠁⠀⠀⠀ ⠀⠀⠜⠂⠉⠉⠂⠀⠂⠀⠀⠀⠀ ⠀⠀⡔⠆⡅⠀⠔⢀⠁⡀⣀⠀⠀ ⠀⠀⠀⠈⠁⠘⣀⠁⠀⠀⢀⢆⠀ ⠀⠀⠀⠀⠀⠀⠸⢃⢶⢲⢈⠉⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠸⢸⠘⡀⠀ ⠀⠀⠀⠀⠀⠸⠤⠛⣀⠟⠦⠇⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡀⠈⠛⠛⠁⢀⣤⣤⡀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿ ⣿⣿⠀⠸⠿⠟⠙⠻⠟⠋⠻⠿⠇⠀⣿⣿ ⣿⣿⠀⢠⣤⣴⣶⣤⣤⣶⣦⣤⡄⠀⣿⣿ ⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉ ⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠤⠾⠧⠤⠤⠼⠷⠤⣄⡀⠀⠀⠀ ⠀⠀⣴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣦⠀⠀ ⠀⢸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀ ⢀⡟⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⡀ ⣼⠁⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠈⣧ ⣿⠀⢸⡇⣿⣦⡴⠷⣤⣤⠾⢦⣴⣿⢸⡇⠀⣿ ⣿⣀⣸⡇⣿⣈⣀⣀⣈⣁⣀⣀⣁⣿⢸⣇⣀⣿ ⣿⣭⣽⠇⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⠸⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⠀⠀⡀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠃⠘⠟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢀⠘⣧⡀⠐⠢⠔⠂⢀⣼⠃⢀⣀⣀⣀⣀⡀⠀ ⢠⡿⠉⢈⡟⠉⠛⠛⠻⠿⠂⠀⠀⠐⠿⠟⠛⠛⠉⢻⡁⠉⢿⡄ ⠘⢷⣄⣾⡃⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⢘⣷⣠⡾⠃ ⠀⠀⠈⠉⠙⠛⠿⣶⡀⠀⠀⠈⠁⠀⠀⢀⣶⠿⠛⠋⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢾⡷⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣄⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢠⡟⢻⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣧⣤⣀⢠⡿⠀⠀⢿⡄⣀⣤⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠉⢉⣿⠁⠀⠀⠈⣿⡉⠉⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⠀⠀⠀⠀⠈⠓⠶⠞⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠁⠠⡦⠀⠀⢴⠄⠈⣿⡇⠀⠀⠀⠀⠀ ⠀⣀⣤⣤⣄⣘⣿⣆⠀⣠⣀⣀⣄⠀⢰⣿⣃⣀⣤⣤⣀⠀ ⣼⡏⠁⠈⠉⠙⠛⠿⠂⠈⠛⠛⠁⠐⠿⠟⠛⠉⠁⠈⢹⣧ ⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟ ⠀⠉⠙⠛⠿⢷⣶⡆⠀⠀⠘⠃⠀⠀⢰⣶⡾⠿⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠁⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣴⣶⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⣠⣾⠋⠙⣷⣆⠀⠀⠀⠹⣷⡀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⣼⡟⠁⠀⠀⠈⠻⣧⡀⠀⠀⣸⡇⠀⠀ ⠀⠀⠈⠻⠷⣶⠾⠋⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡟⢻⡟⢻⣿⡆⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠸⣿⣿⣻⣟⣿⣿⠇⠀⠀⣀⣀⠀ ⣾⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣷ ⠘⠛⠁⠿⠿⣿⣿⣿⣇⣸⣿⣿⣿⡿⠿⠈⠛⠃ ⠀⠀⠀⠀⠀⠈⣿⣿⡟⢻⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⠇⠸⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⣦⣭⣉⠋⠀⠀⠙⣉⣭⣴⡆⠀⠀⠀ ⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⣿⣿⠇ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⠿⠀⠀⣹⣿⣷⡄⠀⠀⢠⣾⣿⣏⠀⠀⠿⣿⣷⣦⡀⠀⠀ ⠀⣰⣿⡟⠋⠀⠀⠀⠀⠻⠿⠛⠃⣀⣀⠘⠛⠿⠟⠀⠀⠀⠀⠙⢻⣿⣆⠀ ⢠⣿⡟⠀⠀⠀⣾⣶⡀⠀⠀⠀⠺⢿⡿⠗⠀⠀⠀⢀⣶⣶⠀⠀⠀⢻⣿⡄ ⢸⣿⣷⣶⡆⠀⠘⢿⣿⣶⣤⣄⡀⠀⠀⢀⣠⣤⣶⣿⡿⠃⠀⢰⣶⣾⣿⡇ ⠈⠉⠙⣿⣧⣀⣤⡀⠈⠙⠛⠿⣿⣷⣾⣿⠿⠛⠋⠁⢀⣤⣀⣼⣿⠋⠉⠁ ⠀⠀⠀⠙⢿⠿⠿⣿⣶⣤⣀⠀⠀⠙⠋⠀⠀⣀⣤⣶⣿⠿⠿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⣿⠛⠛⠛⠛⣿⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡾⢿⣿⣿⣇⣿⣦⣤⣤⣴⣿⣸⣿⣿⡿⢷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠛⠉⠀⠀⠈⢻⣿⣿⣷⣤⣀⣀⣤⣾⣿⣿⡟⠁⠀⠀⠉⠛⣶⠀⠀⠀ ⠀⠀⢸⡏⢰⣆⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣰⡆⢹⡇⠀⠀ ⠀⠀⣼⠇⠀⣿⡀⢠⣄⡤⠀⠀⠀⠈⣭⣭⠁⠀⠀⠀⢤⣠⡄⢀⣿⠀⠸⣧⠀⠀ ⠀⠀⣿⠀⠀⢸⡇⠰⠛⠗⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠺⠛⠆⢸⡇⠀⠀⣿⠀⠀ ⠀⢸⡏⠀⠀⢸⡇⢀⣾⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣷⡀⢸⡇⠀⠀⢹⡇⠀ ⠀⣼⡇⠀⠀⣾⢧⣾⣿⣿⣷⡀⠀⢸⣿⣿⡇⠀⢀⣾⣿⣿⣷⡼⣷⠀⠀⢸⣧⠀ ⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀ ⢸⡟⠀⠀⠀⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣿⠀⠀⠀⢻⡇ ⣼⠇⠀⠀⠀⣿⣿⠃⠀⠀⠹⣿⣿⣿⠏⠹⣿⣿⣿⠏⠀⠀⠘⣿⣿⠀⠀⠀⠸⣧ ⠻⣶⣤⣤⣴⣿⠃⠀⠀⠀⠀⠹⣿⡟⠀⠀⢻⣿⠏⠀⠀⠀⠀⠘⣿⣦⣤⣤⣶⠟ ⠀⣿⣿⣿⣿⡇⠀⢘⣷⣏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣹⣾⡃⠀⢸⣿⣿⣿⣿⠀ ⠀⠈⠉⠉⠉⠛⣿⠿⣷⣷⣶⢶⣶⣶⡶⢶⣶⣶⡶⣶⣾⣾⠿⣿⠛⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣼⣿⣿⣧⣼⣿⣿⣧⣿⣿⣿⣤⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦ ⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠙⠛ ⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀ ⠀⣠⡾⠟⠀⣿⣷⠀⠀⣾⣿⠀⠻⢷⣄⠀ ⣾⠏⠀⣤⡄⠉⠁⣶⣶⠈⠉⢠⣤⠀⠹⣷ ⠿⣶⡆⠈⠻⢶⣦⣄⣠⣴⡶⠟⠁⢰⣶⠿ ⠀⠘⠟⠻⣶⣤⣀⣙⣋⣀⣤⣶⠟⠻⠃⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀

⢰⡏⠛⢦⡀⢸⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⡇⠀⣠⠞⢙⡦ ⠀⠙⢦⡀⠻⣼⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣧⠞⢁⡴⠟⠁ ⠀⠀⠀⣙⣦⠞⠁⠀⢷⡀⣰⢤⡀⠀⠀⠀⠀⠀⣠⢦⡀⣼⠃⠀⠉⣰⣏⡀⠀⠀ ⠀⢻⡉⣀⣀⡤⣤⡀⠀⠻⠃⢠⠏⠀⠀⠀⠀⠘⣧⠀⠛⠁⠀⣠⣤⣄⣀⡉⣽⠀ ⠀⠈⠉⠁⠀⠀⣈⡽⠆⠀⠀⠸⣆⣤⠤⠤⠤⣤⡟⠀⠀⠀⢾⣽⠀⠀⠈⠉⠁⠀ ⢰⡖⠒⠀⠒⠲⣽⣄⣤⡴⢦⡀⠙⠀⠀⠀⠀⠻⠀⣰⠶⣤⣤⣟⡴⠒⠚⠁⠒⣶ ⠀⢷⡀⠀⠀⠀⠈⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⡏⠀⠀⠀⠀⣠⠇ ⠀⠀⠙⠲⠤⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠰⢿⠿⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡖⡒⢦⡄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡈⠛⡟⠛⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠙⠒⠓⠒⠁⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⠛⠶⠤⣤⣤⡤⠤⠖⠻⣏⠱⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡴⠛⠉⠙⡆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣠⠇⠀⠀⠀⢿⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢀⢄⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⣄ ⠈⠢⡑⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢊⡴⠋ ⠠⡐⣚⣁⡀⠳⠊⡆⠀⠀⠰⡛⠞⠁⣀⣚⠒⡄ ⢀⡁⢀⣠⡛⢀⡀⢧⠒⠒⢲⢁⣀⠚⣇⡀⠈⣀ ⠸⣄⠀⠈⡻⠁⠈⠀⠀⠀⠀⠈⠈⢻⠁⠀⢀⠜ ⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀ ⠀⠀⠀⠀⡇⠀⠘⠛⣀⣀⡘⠋⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⡓⡗⡁⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⡲⠄⣈⣈⡠⠴⡚⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠃⡜⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀ ⠀⠀⢀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀ ⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠆⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠖⠑⡆⠀⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢚⠀⠀⠘⣒⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠓⣆⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠘⡆⢹⡄⠀⢳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢷⡀⠀⢱⠘⣇⠀⣸⠁⢹⡄⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠳⣦⠀⠀⠀⡇⢸⡇⠀⣼⠀⢿⣀⡏⠀⣼⠇⠀⣠⠎⣽⠇⡴⣻⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⢻⠀⢹⡆⠀⢸⠃⢸⣿⣴⠏⠀⠈⠻⣧⠀⢿⡷⠾⠃⣾⡇⡜⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣷⡄⢸⡆⠘⢷⡤⣼⠀⠘⣿⣁⣤⡤⢶⣾⡟⠀⠘⠿⣶⣤⡼⠟⢁⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⣿⡟⠁⠀⣀⣤⣾⠀⠀⠙⠻⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠈⣧⡀⠘⠿⣦⣾⣯⠽⠋⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠛⠛⠓⠦⣤⡀⠉⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡒⠊⠉⠻⣦⠀⠀⠀⠀⣀⣤⠤⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣹⣿⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⣿⠀⠀⠀⣾⠋⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣾⣏⣀⠀⣰⣧⣤⠴⠋⠉⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⢁⣀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠰⠿⠿⠃⠀⠀⠀⠀⠀⠀⠰⣶⡶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡶⢟⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠛⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⡶⠖⠛⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣴⠶⣦⡀⠀⠀⢰⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⣶⠀⠀⠀⣠⡶⣶⡄ ⠘⢷⣄⠈⠻⣦⡀⢸⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⣠⡾⠋⢐⣾⠏ ⠀⠀⠙⢷⣀⠈⠳⣾⣤⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡾⠋⢀⣴⠟⠁⠀ ⠀⠀⠀⠀⠙⣶⣤⠞⠁⠀⢻⣆⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⢠⣿⠁⠀⠛⠀⣴⡟⠁⠀⠀⠀ ⠀⢠⡖⠚⠛⠉⠁⠀⠀⠀⠀⠹⣶⡟⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⡉⠙⣷⠞⠁⠀⠀⡀⠈⠉⠙⠓⠲⣶⠀ ⠀⠀⣷⣤⠶⠶⠟⠋⠻⣦⡀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠋⠛⠲⠶⢦⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠂⠀⠀⠀⢿⣤⠴⠶⠶⠶⠶⢦⣼⠃⠀⠀⠀⠺⠷⣬⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⠛⠛⠛⠛⠳⢦⣽⣆⣀⣤⡴⢶⡄⠈⠻⠀⠀⠀⠀⠀⠸⠇⢀⣰⠶⣤⣄⣠⡿⣠⡶⠛⠛⠛⠛⠳⣶ ⠀⢿⡄⠀⠀⠀⠀⠀⠙⢯⣽⠏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠻⣯⡿⠁⠀⠀⠀⠀⠀⣰⡇ ⠀⠈⢳⣄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠀⠈⠙⠓⠶⠶⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠶⠶⠚⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣿⡦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠉⠉⠉⠀⢀⣀⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢰⣟⢩⡉⣿⡆⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡁⠙⠿⠾⠋⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠹⢄⡼⢦⣠⠇⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠋⠉⠛⠒⠲⠶⠶⠖⠒⠛⠉⠙⢷⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣆⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣴⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣴⠞⠉⠉⠳⣆⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡄⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠤⠾⠋⠀⠀⠀⠀⠘⠷⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠙⠛⠓⠒⠶⣿⣏⣉⣉⡉⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⡢⢄⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⡤⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡠⠤⠴⠒⠂⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⣧⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⡤⠒⠚⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢘⣧⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠀⠀⠙⡆⠀⠀⠀⢺⣿⡁⠀⣀⡀⠀⠀⠱⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⡀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡖⢊⣉⣹⡆⠀⠀⠀⠙⠋⢉⣉⡙⠳⢄⠀⢱⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢙⡻⠿⠧⣄⠀⠀⠀⠀⠁⠛⠻⠷⡀⠙⠸⠀⠀⡇⠳⡤⠴⢦⡀⠀⠀⠘⣼⡟⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⠁⢰⠋⠀⠀⠀⠀⠀⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⡽⠀⠈⡇⠀⠀⠀⣿⣁⣤⠇⠀⠀⠀⠤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢇⡀⢻⠀⣸⠷⣶⣶⠤⠤⢤⣀⣴⢧⡀⠀⠀⠀⠀⠛⢍⠙⢇⠀⠃⡇⠀⢀⡇⠀⠀⣠⡏⠁⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⠉⠉⠀⠀⠀⢰⡀⠀⠀⠀⠀⠰⢿⣲⠦⠤⠤⠂⢀⡇⠈⡆⡠⠃⢀⣼⡁⢀⡴⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣇⠀⠙⠳⠦⠤⠤⠤⢶⡊⣙⣦⣴⠶⠦⣄⡀⠈⠙⠒⠒⠒⠋⠀⡸⢫⡤⠔⠋⠈⢿⢷⣄⢸⣄⡀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠻⢷⣮⠁⠀⠀⠀⠀⠀⢣⡀⠀⢀⡠⠞⠉⠉⠓⠲⠤⠤⠤⠤⠚⠁⠀⣧⠀⢀⡀⠀⢣⠘⡿⢿⣷⣄⣈⣦⣤⠤⠒⠁ ⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢀⡀⢧⡈⠉⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣏⠀⠠⠜⣠⠇⠀⠀⠀⠹⣯⠁⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠒⠒⠚⠁⠀⠀⠀⠀⡀⢹⣇⠀⠀⠀ ⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⠀⠀⠀ ⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡇⣿⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣴⠟⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣠⠜⣡⠞⠁⠀⠀⠀⠀⠀⠀ ⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡏⠀⠐⢆⠀⠀⠀⠀⣀⣠⣴⠾⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⡅⠀⠀⠀⠀⠀⠀⠣⣄⡴⠿⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣦⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠷⢤⣹⣄⡀⠀⠀⠀⠀⠀⢀⡼⢦⡘⠷⣤⣀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⡶⠞⠋⠀⠀⠉⡓⠺⠿⠛⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠋⠉⠉⠉⠉⠙⠛⠓⠲⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠿⠶⠶⠶⠶⠶⠿⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⢀⣹⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⡇⠀⠤⣄⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣄⢀⣀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠐⠛⣏⠀⠀⠀⠀⣀⣴⣶⣶⡶⠿⢁⣤⣶⣶⣷⣶⣯⠉⠉⢙⣿⣿⣷⣤⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢿⠀⠀⠠⣾⠻⣿⣧⠀⢷⠀⠉⢠⣶⣛⣿⣶⠈⠀⢰⣿⣿⣶⣾⠟⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⢻⡄⠘⣧⣀⣴⡿⣄⡀⢉⡆⢸⣧⠄⠀⠈⠙⠙⠋⠀⢀⣸⡟⠛⠛⢻⡀⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠾⠶⣦⣸⡇⣰⠟⣿⠏⠀⢨⣿⡟⠀⠈⣇⠀⠀⠀⢀⣠⣯⣀⡀⠀⣹⡀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀ ⢀⣰⡟⠁⠀⠀⠀⠈⢿⣵⠋⠀⢻⡆⠀⢸⡿⠀⢀⡴⠛⠳⢶⠖⣩⣤⣀⣀⣹⣏⠀⣷⡴⠚⢿⣸⡇⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠈⣧⠀⠈⠀⠀⠀⠀⣧⣟⠒⠦⠤⠤⢾⣴⠋⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⣷⠀⢠⡏⠀⠀⠙⢧⡀⠀⠀⡀⠀⠀⣸⠿⠶⠶⠾⠛⣿⠀⠀⢦⣠⣿⣍⠻⣆⠀⠀⠀ ⠀⠀⢿⣄⣀⣀⣀⣠⣴⠟⠁⣀⡼⢧⡀⠀⠀⠀⠙⣦⢠⠇⢀⠞⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠙⣧⡽⠗⠛⣧⠀⠀ ⠀⠀⠀⠙⣩⡿⠋⠀⣈⡿⠋⢁⣠⣼⡇⠀⠀⣠⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣆⠀ ⠀⠀⠀⢰⣿⠁⠀⠀⠉⠉⠉⠁⠴⠯⠤⠴⢾⠋⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠛⠂⠀⢿⡀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣾⣀⡴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠻⣧⡀⠀⢰⠁⠀⠀⠀⠀⠀⠘⠋⠁⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⡿⠃⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠈⢿⣦⡏⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠛⣿⣦⡀⣇⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⣀⣀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠻⢿⣄⠀⠀⠀⠀⠀⠀⢿⡿⠛⠉⠁⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢷⣄⡀⢦⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⠶⠶⢶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠈⠻⢾⣆⠀⠀⠈⠻⣦⡀⠀⠀⠀⣴⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣤⣀⠀⠀⠀⠙⠳⣦⣄⣀⣀⣹⣦⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⢷⣦⣄⠀⠀⢸⡁⠀⠀⣠⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣿⡇⢀⣴⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣿⠏⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣤⣤⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠉⠛⢿⣷⡀ ⠀⠀⠀⠀⣰⡿⠛⠛⠿⠷⠆⢠⡄⠀⣤⠀⢀⡀⠀⣀⠀⢀⡀⠀⣤⡀⢠⣄⠀⡶⠿⢿⣿⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠘⠃⠀⠛⠁⠘⠋⠀⠋⠁⠈⠁⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣿⠇ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣤⣤⣴⠿⠋⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠈⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣼⡟⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠉⠀⠀⠀⠀⠀⠀⢀⣤⣷⣶⣦⡀⣠⣴⣶⣄⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⠀⠀⠀⠀ ⠀⠸⣿⡀⣀⣀⡀⠀⠀⠀⢀⣿⠋⠀⠀⠈⣿⡿⠁⠀⠹⣿⠏⠁⠀⠈⢿⣇⠀⠀⠀⠀⣀⣀⡀⣸⡿⠀⠀⠀⠀ ⠀⢀⣽⠿⠛⠙⢿⣦⠀⠀⠘⣿⡀⠀⠀⠀⣼⡇⠀⠀⠀⣿⡄⠀⠀⠀⣸⡟⠀⠀⢠⣾⠟⠙⠻⣿⣅⠀⠀⠀⠀ ⢠⡿⠃⠀⠀⠀⠈⢻⣷⣤⣀⣙⣿⣶⣶⣿⣿⡀⠀⠀⠀⣸⣿⣷⣶⣾⣟⣀⣤⣴⣿⠃⠀⠀⠀⠀⠻⣷⡀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⢿⣏⠛⠛⠛⠋⠁⠀⠙⠿⣷⣶⡿⠟⠁⠈⠉⠛⠛⠛⢋⣿⠇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣴⡿⠻⣷⣄⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠿⠛⠀⠀⠙⠻⠿⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀ ⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀ ⠀⠻⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡿⠋⠀⠀⠀ ⠀⠀⠀⠉⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠶⠿⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠷⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠉⢉⣉⣑⣒⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠁⠀⣠⠶⠒⠊⠉⠁⠀⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣠⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⠰⣇⠀⠀⠀ ⠀⠀⠈⢧⡈⢹⠀⢀⣤⣶⠲⡚⠴⣶⣿⡺⠄⣩⣿⣳⡞⠃⠀⠀⠀ ⠀⠀⢀⠀⢳⠘⣆⣼⠧⣙⡆⣧⠀⠉⠋⡃⠀⢟⠛⢻⠈⡆⠀⠀⠀ ⣠⠒⠉⠉⢾⡜⠹⡇⠀⡟⢀⠼⠤⡤⣊⣁⢢⠚⣄⠼⡆⡃⠀⠀⠀ ⢳⠀⠀⠀⠀⢧⠀⡅⠀⢇⠀⠀⠀⠑⢥⣒⣲⣷⠁⡀⢸⢧⡀⠀⠀ ⠸⣤⣀⡠⢴⣋⡠⢧⠀⠀⢱⣤⠃⠔⠁⠀⠀⠘⠄⠈⢻⠵⠻⡄⠀ ⠀⢠⡏⠀⠒⠑⠒⠝⠠⠴⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠄⢹⠀ ⠀⠘⣇⠀⢀⠃⠀⠀⢀⠧⠚⣇⠀⠀⠀⠀⠀⠠⠀⣰⠃⠀⠀⠈⡇ ⠀⠀⠈⢧⡎⠀⠀⠀⠐⠒⠚⢚⣷⣄⡄⠀⠀⠀⢻⣁⣀⡀⠀⠀⡇ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠠⠊⠀⠈⠳⢄⡀⡀⠈⢏⠀⠀⠀⠀⡃ ⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠲⠶⢤⣄⡀⠀⠙⠳⣄⠈⠓⢄⢀⡴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⢈⡏⠉⣩⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡾⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠒⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠁⢀⣀⣤⠤⠤⠤⠶⠦⠤⢤⣤⣀⡈⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣮⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠈⢢⡀⢀⣴⡶⠿⠷⢦⣄⡀⠀ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠤⡀⠀⠀⠀⠈⠳⡄⠙⢿⡁⠀⠀⠀⠀⠛⣿⡄ ⠀⢠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⡆⠀⢀⡀⠀⠻⣦⣀⣈⡳⠂⠀⠀⠀⢘⣿ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣾⣉⡉⠁⠀⠀⢰⣟⡟⠉⠈⠑⣄⢳⡀⠀⠀⠀⠀⠀⠀⣼⣿ ⢸⠁⠀⠀⠀⠀⠀⠀⡞⠁⢀⣀⣙⢦⠙⠛⠓⠒⠒⠉⢸⡖⠋⠉⠑⣼⡿⢷⣄⣀⣀⣀⣠⣾⣿⠁ ⣸⠀⠀⠀⠀⠀⣰⠋⣇⡴⠉⠀⠈⠙⠓⠀⠀⠀⠀⠀⠈⣠⣤⣀⠀⣾⠃⠀⠈⠙⠛⠛⠛⠉⠁⠀ ⢸⡄⠀⣶⣄⡜⠛⣆⠙⠁⠀⣤⣾⣶⣄⠀⠀⢀⣀⡀⢰⣿⣿⡿⠐⠛⠦⣄⡀⠀⠀⠀⣀⠀⠀⠀ ⠈⢧⡀⢻⡄⠀⣠⡏⠐⠂⢀⣹⠿⠿⠧⠀⠈⣡⠞⠋⢳⣄⠀⠀⠀⠀⠀⢹⠫⡓⠂⠐⠉⢃⠀⠀ ⠀⠀⠳⣼⣦⣀⢴⡅⠀⠔⠁⠀⠀⠀⠀⢰⡊⢁⣀⣀⣼⠭⠧⠀⠀⠠⠤⠊⢀⡇⠀⠀⢀⡾⡆⠀ ⠀⠀⠀⣠⠟⠁⢸⡟⢇⠀⠀⠀⠀⢀⣀⠔⠋⠁⠀⢨⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⣽⠀ ⠀⠀⡰⠁⠀⠀⠀⢳⡀⠉⠙⠒⠉⠉⠀⠀⠀⠀⣀⣼⡷⣤⣤⠤⠤⠤⠤⠚⠁⠀⠀⠀⠀⠸⡅⠀ ⠀⢠⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⣠⣤⣤⠔⠚⢻⡾⠷⣻⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢉⡉⠁⢀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣶⣎⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠒⠒⠤⠤⠬⠿⠒⠒⠤⠤⠬⠓⠁⠀⠀⠀⠀⠀⠀

⠂⠁⠀⠀⠀⠀⠀⢀⣤⡴⠋⣠⣴⣾⣿⣟⣿⣿⠟⢋⠩⠀⠈⠈⠈⠁⠉⠋⠻⢶⣤⡀⠀⠀⠀⠀⠉⠉⠛⠶⣬⣷⠶⣄⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⣿⠋⣠⡾⣫⡾⢋⣷⡿⠁⠀⠀⠀⠀⠀⢀⣠⣠⣤⣤⣤⣤⣤⣽⣿⣶⣄⠀⢀⣤⣴⠶⠶⠒⠛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⢟⡼⣣⠾⢋⡾⠋⢀⣾⠟⠀⠀⢀⣤⣶⣶⠿⠿⠛⠉⠉⠁⠀⠈⠉⠳⣍⠉⠙⠻⠿⣵⣦⣴⠶⠶⣟⣫⣷⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⢫⣾⠟⢁⡴⠋⠀⠀⣾⣯⠀⣤⡾⠟⠋⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⡀⠀⠘⠛⠿⢿⣿⡛⠛⠋⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⢁⡿⠋⣴⠟⠀⠀⠀⢸⣿⣷⡿⠋⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⢄⣀⠛⢿⣦⣀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡼⢡⡿⢁⡾⠃⠀⠀⠀⣠⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⣮⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠪⣿⣿⣿⡯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣧⣾⣷⡟⣠⣴⣶⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢳⣄⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠻⠼⠧⠤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⡾⠛⠁⠀⣠⣿⢻⣿⠃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠹⢷⣄⡀⠀⠈⠉⠉⠛⠲⠶⠶⠶⡒⠒⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⠟⠁⠁⠀⢰⣿⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⢇⠀⠀⠙⣦⣠⣤⣝⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣓⡄⠀⠀⠀⠀ ⣿⣿⡟⠀⠂⠀⠀⣾⡟⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢬⣇⠀⢸⡏⠀⣆⡈⠛⣿⠷⣄⠀⠀⢀⣀⣠⠴⠖⠊⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⣿⡟⠁⠀⠀⢀⣾⣿⠁⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣼⣧⠀⢻⣿⣆⡌⡇⠘⠓⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⣾⣿⡇⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠙⣿⣶⣗⣶⣻⡿⠃⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⠀⠀⠀⣿⡿⠀⠀⠀⣿⡄⠀⠀⠀⠀⢲⠀⠀⣷⠀⠀⠀⢀⣠⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢷⡙⢿⣿⡄⠀⠀⠀⢀⣠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣿⡄⠀⢰⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⠀⠈⣇⠀⢹⠀⢀⢜⡿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣰⠃⠀⠀⣀⡈⢷⣀⠽⣷⣤⡴⠞⠋⢹⠘⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠿⣶⣾⣿⠇⠀⡄⠘⣿⣤⠀⠀⠀⠀⠀⠘⣆⢸⡇⠀⣼⠀⢸⠀⢰⡇⠀⠀⠀⡔⠀⠀⣸⣿⠏⠀⣠⣾⣷⣿⡟⠛⢿⣿⣾⠇⠀⠀⠀⡆⣿⠈⠉⠑⠒⠲⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⡔⠀⢳⡀⢻⡇⠀⠀⠀⠀⠀⠀⠘⣎⣧⣼⠃⠀⢸⣤⣏⡇⠀⠀⣰⠃⢀⡼⠛⠃⠀⣼⣿⣿⣿⣿⢿⠀⡜⠁⠏⠀⠀⠀⣰⡇⡟⠀⠀⣠⡤⠖⣲⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡇⠄⠀⢳⣼⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣃⢀⣠⣾⣿⣷⣿⢶⣟⡵⠖⠋⠀⠀⠀⠀⠙⢿⣷⠱⠀⡺⠀⠀⠀⠀⠀⠀⢰⣿⠿⠴⠚⣉⡠⠴⢮⣁⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠘⣷⠿⣿⡿⣿⡾⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠞⠃⠀⠉⡿⠀⢀⣴⣿⣿⡤⠞⠛⠛⠋⢻⣿⠧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⡀⢀⡼⠫⣧⠀⠘⡆⠀⠀⠀⠀⠀⠈⠳⢿⡅⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣴⣿⡿⣷⣿⣤⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⠏⠀⠀⠙⣆⠀⢳⡀⠀⠀⠀⠀⠀⠘⣞⠙⠓⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⡿⢛⡿⠋⠀⣿⠀⠈⠻⣟⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠎⠁⠀⠀⠀⠀⠘⣦⡈⢷⣄⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⣤⡦⠿⠻⣿⠀⠀⠀⢀⡴⣿⣰⠊⠁⠀⢸⠇⠀⠀⠀⠈⠳⣌⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⢀⣰⠞⠁⣀⣀⣀⡤⠴⠒⠛⠉⢱⣄⢿⣷⣶⣤⣬⣴⣶⣦⠔⠈⠁⠀⠀⠀⠀⠀⢧⣄⣠⠾⠁⠀⣠⡖⠋⣨⠟⠁⠀⠀⢀⣿⡳⢦⣀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠛⠳⠶⢮⣥⠤⠤⠶⠒⢛⢻⠟⠛⠛⡿⣷⡈⠛⢻⣿⣿⡿⢿⣗⠦⠤⣄⣀⣀⡀⠀⠀⠀⢀⣤⣾⡿⠻⣭⠞⠀⠀⠀⠀⣼⣻⠇⠀⠈⠙⢦⣀⠀⠀⠳⡤⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠛⠁⣀⣠⡤⠤⣾⡏⠀⠀⣠⢿⡌⠁⠀⡼⢋⡏⠀⠀⠉⠙⣿⣯⡛⠻⣿⣭⣭⣿⣿⣿⡋⣻⡞⠁⠀⠀⠀⢀⡾⢷⣏⠀⠀⠀⠀⠀⠉⠳⣦⡀⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⢻⠗⡿⠛⠉⠁⠀⠀⣿⣥⠖⠋⠁⢸⡇⣠⠞⠁⣸⣄⠀⠀⢀⣴⣯⣀⣿⡋⣽⣿⣿⣿⣧⣼⣿⠏⠀⠀⠀⢀⡴⡋⠀⠀⣿⡀⠀⠀⠀⠀⠀⣰⣿⣿⣅⡀⠀⠀⠀⠀⠀ ⠀⠰⢃⣴⢋⠞⠁⠀⠀⠀⣴⠿⠻⢿⣿⣶⣄⡾⠋⠁⠀⢠⣿⠟⠙⠛⠉⠻⣏⠙⠻⢿⣿⣭⣿⣽⣿⢿⡏⠀⠀⠀⣰⣏⠈⠀⠀⣠⣿⣁⣀⣀⣠⣶⣿⡿⣿⢿⡏⠙⠳⢤⣀⠀⠀ ⢀⠀⢠⠃⠀⠀⢀⣠⣶⣫⡤⠤⠴⠟⣉⡿⠋⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⢹⡄⠀⠈⠙⠻⣧⣯⠗⠉⢱⠀⠀⣼⡟⠋⠳⠒⠺⣿⣿⣿⢿⠿⣿⣛⠽⠛⠁⢸⡇⠀⠀⠀⠈⠙⠷ ⣀⣀⣼⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⣠⠏⠀⣀⠀⠀⠀⣸⣿⣿⣄⡀⠀⠀⣠⠾⠷⡄⠀⢀⣴⣿⣿⣿⣦⣌⣧⢰⣿⠀⠀⠀⠀⠀⢸⡇⠹⣦⠁⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⣭⣀⡉⠉⠙⠓⠶⠶⣦⠀⠀⠀⢠⠏⢀⣴⡏⠀⠀⠀⣿⣟⠉⢹⡿⠉⠉⠁⠀⠀⠸⣶⣿⣟⠉⠁⠛⢿⣿⣿⣷⣿⣄⠀⠀⠀⣠⡾⠁⠀⠙⢧⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠓⠒⠲⡆⠀⡟⠀⠀⠀⠸⣄⡟⠈⢿⠀⠀⠰⣿⣿⠀⠀⢷⡀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⢀⡿⠋⠁⠘⠓⢶⣿⣿⠓⣶⠦⣴⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡇⠀⡇⠀⠀⠀⠀⠉⠀⠀⠈⢷⣄⡀⠘⢿⣄⡀⠎⠛⣦⣤⢤⣴⠉⠉⠳⣄⠀⣀⡀⢀⢾⠀⠀⠀⠀⠀⢸⡇⢸⡆⣟⠈⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣹⢿⡶⠞⢁⣤⢾⣿⡇⠀⠀⠀⠀⠀⣿⠞⠉⠉⠉⠛⢦⣄⠀⠀⢀⣼⡇⠸⣇⣿⠀⠀⠹⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠂⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣟⣴⠃⠘⣷⡞⠛⡇⠘⢿⣧⡀⠀⠀⢠⡾⡃⠀⠀⠀⡀⠀⠀⠙⡯⠛⠏⢸⡇⠰⣿⣿⡄⠀⠀⠻⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢄⠀⢿⢸⢣⠀⡀⠸⡶⡄⢱⡹⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠈⢮⠁⢸⢸⡄⢧⡙⣣⣗⠘⠶⣟⣙⣄⠈⢷⡀⢠⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡙⠧⣖⡈⠳⣼⡏⠙⠆⠓⠎⠿⣏⠒⠾⢮⣿⣷⢦⣻⣆⡳⢌⢳⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢣⡙⣆⠉⠓⠢⡝⠳⢶⡊⠦⠼⣄⡀⠀⡘⠳⣼⡦⠿⢿⣿⣌⡻⣷⡌⠻⣝⢿⣿⠶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⠈⢻⣢⣝⣘⠳⢍⣓⣻⡶⠤⣝⣳⣶⡿⠙⠉⠛⠻⠿⣽⣻⠲⢬⣻⣿⣿⣿⣤⣘⡻⡻⡗⣝⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡉⢸⣶⣚⣩⣖⣋⣉⡔⠖⠾⢿⠟⠉⠉⠀⣀⣤⣄⣀⣤⣦⡀⠉⠙⢦⣿⣿⣿⣿⣿⣿⣷⡄⠹⣮⡹⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣺⠟⠻⢦⡀⢀⠤⠶⠶⣶⣞⠒⠒⠊⠉⠀⣀⣠⠤⠴⢖⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠙⣶⣶⡿⠾⠋⠉⠉⠀⣀⡀⢀⡼⢋⣀⣤⠶⠋⠉⠠⠴⢶⣶⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⣿⣷⡾⢯⣛⣶⠴⠞⣿⠃⣠⢏⣨⠿⠋⠀⢀⡐⠛⠃⠀⢠⣴⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿ ⢸⠒⠒⠠⠤⠤⠤⠤⠤⠤⡤⠤⠤⠔⠖⠒⠶⠖⠚⠉⢹⣯⣉⣽⠏⠃⠀⠈⠉⠓⣾⢃⣾⣷⠋⠀⣠⡶⢒⡏⠀⠀⢀⣤⠽⠛⢋⡅⢀⣷⠟⠛⢻⣿⣿⣿⣿⣷ ⠘⣦⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣹⠃⠀⠀⠀⠀⠀⠀⣿⡿⣻⣭⣤⡞⢉⡴⠋⢀⣤⠞⠋⠀⠀⣰⢏⡴⠋⠁⠀⠀⣼⣿⣿⣿⣿⣿ ⠀⠈⢳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣄⡀⠀⠀⠀⠀⠀⠋⠸⣿⣷⣿⣶⣯⢦⡼⠋⠁⠀⣀⡴⠏⠁⠀⢀⣴⡆⣀⣰⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⣶⡶⠶⣶⣶⡶⣶⣤⢤⣤⣤⣤⣴⣤⣤⣷⣒⡖⠒⣾⣿⣶⣶⣶⣿⣿⣿⣶⣾⣿⢟⣡⣴⠷⠶⠛⠻⣯⣁⣤⠀⣠⡶⢛⡿⠁⣿⣿⡿⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠛⢦⣄⣭⠗⠆⠀⢀⠀⠐⠉⢉⡟⠛⠁⡹⠃⣼⣿⣿⣧⣾⣫⠿⠚⠿⢿⣿⣿⣿⣿⣓⣦⠄⠀⠀⣰⢋⣷⡿⠋⣰⣿⣧⡆⢿⡿⣇⢣⣿⡃⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣆⣂⠀⠁⠄⢽⡇⠀⠀⠁⣶⣿⣯⣾⡿⠋⠀⠀⠀⠀⢰⠿⠟⣿⠏⠛⠹⢷⠀⡰⠃⢰⣿⣷⣾⠁⣽⣿⣷⢺⣿⣿⣾⠟⢡⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢦⣦⣇⣷⡀⠰⣽⡟⣿⣽⡀⣰⠚⠓⠀⠀⡎⠀⠘⠁⠀⠀⠀⠀⠀⠀⢠⣾⡏⣀⡴⠚⢋⣿⣏⣼⣿⣿⠁⠀⢸⣿⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣧⠈⣻⣟⠁⠀⠀⢀⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠿⠋⠈⢠⣾⢟⡏⠉⢿⠰⡀⣴⣿⠋⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡋⠀⠀⠀⢸⡇⠀⢰⠀⠘⠆⣇⡿⡇⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⡟⠀⠀⠀⢸⡇⠈⢨⡇⠘⢀⣿⠘⣧⡏⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣥⣿⠟⠁⡀⠀⠀⢸⣷⠀⢸⡿⠀⣸⣿⣷⠋⠠⣘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣶⣤⣴⣶⣶⢿⣷⣯⡟⠃⣠⠀⠀⠀⠀⣸⣿⣷⣿⡇⣰⢟⡏⠰⣶⡖⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣽⠿⣯⣽⠏⣀⠉⠀⡴⠁⠀⠀⣶⡶⠿⠏⢹⣷⢻⡇⡾⣇⡄⠹⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠀⠉⣾⡾⠁⢠⠞⠁⠀⢀⣴⢿⡅⢀⣦⣼⡟⠿⡹⠁⠘⠃⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣤⣤⣼⣯⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿ ⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣴⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⠀⠀⠉⠉⠉⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀ ⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⢀⣠⣧⠀⠀⠀ ⠀⠀⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠈⢢⡟⠿⠹⣶⣤⠀ ⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡏⠁⠀ ⠀⢠⠯⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢀⡆⣾⣏⣢⣄ ⣀⢟⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠉⢰⡋⢹⡿⠟ ⢸⣿⣿⣿⡿⣻⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⢿⣟⣫⠿⣾⢿⣷⡦ ⠀⣸⡿⣿⢧⣴⣿⣽⣾⢇⠀⣆⡀⠰⣄⡀⠀⣵⢀⣶⢾⣽⣿⣾⣿⣿⣭⣀ ⠀⠉⠋⢹⣿⣿⣯⣿⣿⣾⣽⣿⣧⡀⣙⣿⣿⡟⣿⣿⣗⣛⣼⣿⣽⣿⡿⠟ ⠀⠀⠀⢀⣬⣿⣿⣿⡟⣻⠛⠻⣿⣿⣤⣿⣧⣿⡟⠛⣿⣿⣿⣯⡆⠉⠁⠀ ⠀⠀⠀⠀⠉⠻⣿⣤⡛⣳⢦⣼⡿⡁⢈⢻⣧⣼⣷⣿⡟⡷⠻⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠘⣦⡟⠛⠻⠏⠪⢵⣿⡽⠛⡅⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⢤⣤⣤⣄⣀⣀⣀⣀⣡⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⣩⣥⣤⣤⣤⣀⠉⠉⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣆⠀⣶⠋⠁⢺⣿⣿⠀⠈⣹⡄⢸⠏⠀⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢸⠀⠀⢻⡀⠈⠉⠑⠒⠒⠒⠊⠉⠁⠀⡟⠀⠀⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⣇⢀⣸⣧⡴⠶⠖⠚⠛⠛⠛⠛⠓⠺⠷⢶⣼⣟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣷⣦⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣠⣴⠶⠶⠶⢿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠂⣼⣿⣿⣿⠷⣶⣤⣀⠀⠀⠀⠀⠀⠘⠷⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⢸⠀⠉⠹⡿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢛⠋⠀⠀⢸⣾⡿⣿⣿⡏⠀⠀⠈⠙⠛⠒⢆⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⢷⠀⠈⢻⣿⣿⣿ ⣿⣿⣿⣿⠋⠀⢸⠀⠀⠀⢰⣿⢡⡿⣿⢧⣤⣄⣀⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠟⢿⣿⡙⣿⣿⣆⣀⣀⣸⣆⣀⣀⣻⣿⣿ ⣿⣿⣿⣧⣤⣤⣾⣤⣤⣤⣿⡇⣾⠇⣿⠀⠈⠙⠛⠛⠓⠦⠀⡰⠀⠀⠀⠀⠰⠟⠛⠉⠁⠀⠀⠘⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣷⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣵⡶⠒⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠫⠟⠛⠛⠟⠋⠃⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠤⠖⠒⠒⠋⠉⠉⠉⠉⠑⠒⠂⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣷⠏⡽⢿⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⡇⠀⢸⡏⠻⣯⢞⣥⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠞⠀⠀⢸⢀⠚⠛⠋⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡴⠃⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⡌⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢿⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠀⣸⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⡇⠄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⣇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣸⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⡿⠟⠛⠛⢿⣦⡀⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⡿⠀⡟⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠐⣿⣇⢸⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⠃⢰⠃⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣷⡀⠀⠀⢀⢀⣾⡇⠀⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣸⠀⢸⢠⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⢿⣶⣶⣷⡿⠟⠁⠀⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀⡏⢸⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡇⠋⠀⠀⠀⠀⠀⠀⢸⠀⣏⣦⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠆⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠖⠋⠉⠉⠙⠓⠒⠒⠒⠦⠤⠬⠷⣄⣀⠀ ⠀⢸⠁⢂⠀⠀⡰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻ ⠀⣿⠀⢈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⣿⢠⠋⠀⠀⠀⠀⢀⣠⠤⠴⠟⢲⠟⠉⠉⠓⠛⢏⡟⠋⠉⠉⠓⠲⡖⠒⢲⡞ ⠀⢿⠸⡀⠀⢀⣠⡞⠉⠉⡆⠀⠀⡇⠀⠀⢰⣾⡖⠈⡇⣶⣷⡆⠀⠀⣽⠀⠀⡇ ⠀⢸⠀⠉⠻⡏⠠⠐⠄⢰⠀⠀⠀⡵⢶⢤⣌⠚⢊⡼⣅⠑⠚⢁⣀⠴⣇⠀⢰⠋ ⠀⢸⠀⠀⠀⣇⠡⣀⠇⠀⡆⠀⠀⠑⢲⢆⠙⠚⠉⠀⠈⠉⢉⡀⠠⠴⠋⠀⣏⠀ ⢠⡞⠓⠒⠳⣿⡆⠀⠀⣀⢠⠀⠀⠀⢸⠀⠉⠐⡶⠲⡖⡖⢲⡟⠂⢀⣀⠀⡟⠀ ⣾⠀⠀⠀⠀⢸⠹⡄⠸⡀⠈⡇⠀⠀⢸⠀⠀⠀⠉⠈⠀⡗⠈⠀⠀⠁⠀⢹⡇⠀ ⠙⢦⣤⣀⣠⠞⠀⡻⢄⠈⠈⡇⡔⠢⡘⢍⡉⠋⠉⠢⣄⠇⠀⠀⠀⠑⠠⢂⡇⠀ ⠀⠀⠀⠈⠁⠀⢰⠃⠈⣇⠀⢃⠣⠠⠃⠐⠬⠭⠝⠫⠥⣜⣀⣀⡩⠜⢀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢳⢶⣿⣽⣿⣭⣿⣿⣿⣿⣷⣶⠾⢿⠭⠼⠬⠽⠿⢻⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⢹⠉⠉⠉⠉⠀⠀⢸⡅⢼⠁⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠊⢟⠲⡼⣤⠤⢤⡤⠤⠤⠤⠿⠿⠴⠶⡶⠶⣶⡾⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣷⠀⡦⠃⠑⢢⠤⠚⠁⠀⠀⠀⠀⢹⠒⠚⠁⠰⣷⡌⡦⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠈⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⣸⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠒⠤⡀⠀⠀⢰⣁⠀⠉⠉⢲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣤⡤⠇⠀⠀⠀⠉⠈⠙⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣶⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠊⠁⠉⠉⠛⠻⢿⣻⣶⣿⣿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣠⠾⠠⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⢹⣿⠃⠀ ⠀⠀⢀⡤⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣹⣿⡿⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠛⠐⠢⠦⠄⠀⠀⡀⠀⠀⠈⠣⡴⠋⠉⠁⠐⢄ ⠘⠧⠀⠠⠄⠒⠒⠢⠤⢀⣀⡀⠀⠈⢫⠀⠀⠀⠐⢇⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡁⠀⠀⣀⣠⣄⡀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢶⡞⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠈⣴⡧⠖⠒⠊⠒⠉⠉⠉⠒⠛⠻⢦⠤⠀⠀⠀ ⠀⠀⠀⣰⣇⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀ ⠀⠀⣰⣿⠇⠀⠀⠀⡀⢤⢖⡰⡶⠀⠀⢰⠆⣤⠤⡀⠰⠊⠀⠀ ⠐⠁⠈⢡⠠⡠⠂⡅⠱⣸⢺⣷⣴⢿⠰⢷⣶⡶⣶⢨⡅⠀⠀⠀ ⠐⠄⠤⠊⠀⣇⠀⠂⠀⢸⠘⠛⠃⠈⠁⠘⠛⢱⡇⠸⠑⠀⠀⠀ ⠀⠀⠀⠀⠰⠙⠀⠘⡀⢛⡁⠀⢀⡀⠀⠀⣠⢜⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⣑⣜⣿⠐⠲⣺⢪⣅⣇⣬⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠀⠀⠈⣿⠿⢿⣿⡷⢼⣁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣆⡉⠉⠀⢱⣶⣼⠃⠤⠒⣻⣿⣿⣟⡿⣿⣟⢻⠀⣀⣀⠀⣀⠀ ⠘⠧⢤⡤⢿⣿⠋⠱⣤⣀⣿⣾⣟⠉⠀⢹⣸⠈⣏⠻⣿⣧⢨⢄ ⠀⠀⠈⠓⢾⡇⠀⠀⢹⣿⠃⠸⣯⠉⠉⢹⢹⡠⢻⣀⣿⠿⠉⠉ ⠀⠀⠀⠀⠀⠈⠣⠔⠁⣼⠀⠀⣿⠀⠀⢸⠀⢣⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣈⣳⣿⣟⣒⠦⣾⣏⣨⡆⠀⠀⠀⠀⠀