Gemini Pog 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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠚⠛⠛⠛⠛⠛⠓⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⢙⠲⠤⠄⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⡤⢢⣦⣴⣶⡴⠏⢠⢟⠀⠈⢱⡀⠀⢰⢷⠀⠘⠪⠃⠙⢧⠘⢷⡀⠀⠀⠀⠀⣄⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⣡⠊⠀⠘⠋⠀⠉⢱⣼⡇⠇⠀⢀⡞⠁⢀⠀⣷⣧⠀⠀⠀⠀⠀⢳⡀⠹⡄⠀⣄⠀⢬⣙⢶⡦⣌⡱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢸⠃⠀⠸⡆⠸⣵⡀⠀⠀⠀⠀⠀⠹⡄⢹⡄⠈⣆⠀⠙⢦⡹⣮⡙⠪⣳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣠⠀⠀⠀⠀⠀⣶⠀⢀⡇⠀⢸⠀⠀⡆⠹⡀⠹⡿⣀⠀⠀⠀⠀⠀⠹⡀⢿⡄⢸⡄⠀⠀⠹⣌⢻⣄⠈⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢡⠀⢰⡡⠋⠈⣷⡇⠀⠀⠀⢿⠀⢸⣧⠀⢸⢸⣇⣧⣤⣿⣶⣬⣝⠢⡀⠀⠀⠀⠀⢧⢸⣻⣤⣷⡄⠀⠀⠙⣦⠙⣷⠀⠘⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⡄⣠⠋⢀⡼⡆⢸⡇⠀⡆⠀⢸⣆⠀⡿⡀⢸⣾⢿⢱⠀⠀⠈⠻⣝⣿⡺⢷⡀⠀⠀⢸⣿⠋⡏⢸⣿⣶⡄⠻⡜⣷⣜⣧⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣥⠟⢁⡴⡋⠀⡇⠈⣿⡄⢳⠀⢸⣹⡄⠘⣷⢿⡇⠈⢯⣇⡤⠤⣄⠈⠙⠓⠦⣭⣗⣤⣞⣿⣠⡇⢸⣿⠁⢹⡄⢹⣾⡎⢯⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⣴⡋⠀⠸⣸⠁⢰⡏⢷⠈⢇⠀⣧⠻⣄⢻⡆⢳⠀⠈⠛⣦⣀⣈⣳⠄⠀⠀⠀⠀⢹⣿⣿⣴⣶⣼⣿⡇⠸⣿⠀⣿⣷⠀⢿⡄⠀⠀⠀⠀⠀ ⢀⣿⡁⠀⠈⠙⠧⠤⠴⠃⠀⡼⡅⠀⣳⡜⢦⠸⡄⠈⠳⣽⣞⣆⢠⣽⠿⠛⠛⣿⣶⠗⠀⠀⠀⣠⡿⠟⢛⣿⣿⣿⣇⢀⣧⣄⡿⣿⡀⠸⡇⠀⠀⠀⠀⠀ ⠀⡿⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⣿⣟⠿⣳⣽⡄⠀⣾⣿⡟⠋⠀⠀⠀⢺⣿⠇⠀⠀⠀⠸⣿⣀⠀⠰⣿⣿⢻⢹⠘⣿⣿⠀⠁⠇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⠀⠀⠀⢀⡴⠋⣤⡀⢠⡀⠘⢎⠉⠀⡹⡙⢦⣀⠉⠛⣷⣖⣒⣒⣿⠿⠉⠀⠀⠀⢸⣿⣝⠛⠛⠿⢫⣟⣸⣤⣯⣿⡲⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢶⠊⣉⡴⠊⠹⣹⡀⠙⣄⠈⠳⡀⠈⢫⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠀⠀⣰⣵⢿⡏⠈⠀⠉⠉⠁⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⠟⠁⣀⣤⠔⢻⣵⡀⠈⠣⣄⠙⢦⡀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⠏⠀⣴⠟⣿⢿⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠋⣀⢴⠏⠁⢧⣀⠀⢳⣷⡀⠀⠈⠳⣦⣙⠶⣄⣈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣶⢤⣼⣿⣿⣗⡮⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡤⠚⢡⠞⠁⠈⠓⠀⠀⠈⠉⣀⣻⣳⡀⠀⠀⠘⣎⠻⣖⠮⢽⣷⡒⠮⠽⠟⠓⠀⠀⠀⠀⣠⡤⠞⣋⣥⣼⣿⠇⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠧⠤⢤⣤⣀⣀⣉⣉⣉⣉⣉⣀⣈⣹⣷⡀⠀⠀⠈⢦⠸⣳⡄⠀⠀⠀⣀⡄⠀⠀⢰⣶⣀⣀⣶⣾⣿⣾⢧⡿⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢄⠀⣷⣿⡟⢧⠀⠓⢆⠈⡆⢼⣟⣤⠄⠈⢸⡇⠀⠀⠀⠸⣌⠉⠻⡿⡯⡟⠉⣳⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠸⡆⠘⣿⡇⠈⢷⡀⠀⠑⢜⠦⡈⠻⢆⠀⢸⠀⣠⡄⠀⠀⠈⠳⣄⣀⣀⣴⠞⠹⣷⡀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⢹⡀⣿⡇⠀⠈⢻⣇⠀⠀⠀⠙⣄⠈⢧⠺⠚⠁⢧⠀⠀⠀⠀⢀⣤⣿⣿⡀⠀⠘⢟⣆⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡀⢸⡇⣿⡇⠀⠀⠀⠹⣷⡀⠀⠀⠈⢧⠈⢧⡀⠀⢸⡆⠀⠀⠀⠀⢈⡿⠻⡱⣄⠀⠈⢫⡷⡀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⢸⡇⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠳⡈⢳⠐⠺⠧⢤⣤⡤⠞⢻⣆⠀⠈⠛⠷⠄⠀⣙⢼⣆⠀⠈⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠀⢸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⢆⢳⣀⣴⠻⣿⣣⠀⠀⢻⣧⢆⠀⠀⠀⠀⠈⠻⡝⢧⣀⢳⡹⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡾⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠻⣿⣄⣿⣿⣿⣦⡀⠀⠹⣿⡳⣄⡀⠀⠀⡀⠀⠀⠘⠳⣄⠈⠫⡓⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠃⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡢⡀⠈⠹⣯⢿⣿⣿⡵⡄⠀⠘⢿⣌⠙⢶⣦⠀⠀⠀⠀⠀⠈⠓⢦⣈⢦⡁ ⠀⠀⠀⠀⠀⠀⢀⡞⢠⡏⠀⠰⣿⣇⡤⠤⣀⣀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠹⣄⠀⠀⠘⢿⣧⡉⠻⣟⢦⡀⠀⠙⠳⣤⣀⣉⡓⠒⠤⠄⠀⠀⠀⠈⠙⠛ ⠀⠀⠀⠀⠀⣠⠎⣠⡿⠃⠀⢠⡞⣡⠤⣄⣀⠉⠙⠲⠦⣄⡀⠹⣄⠀⠀⠀⠀⠈⢦⢠⡠⠄⠱⣝⢦⡈⠙⠻⠶⢤⣀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⣴⡿⠁⠀⢀⣿⠞⠁⠀⠀⠈⠃⠀⠀⠀⠀⠉⠳⢬⣣⡀⠀⠀⠀⠈⢳⡻⣌⠑⣬⢳⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⣤⣶⣶⣷⣿⠷⢮⡳⡙⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⠀⠀⠉⢿⣆⠀⠱⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠹⣆⠀⠹⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⠁⠀⠀⠀⠀⠀⠘⠟⠆⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠛⠋⠋⠓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠒⠒⠀⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⡄⢀⡀⠀⠀⡠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀ ⠀⢠⡿⠛⠓⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⣼⠃⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠁⠀⠀⠀⠀⠀⢹⠀ ⣸⣏⡎⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢆⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⠏⣷⣤⠤⠤⢀⢸⠀⠀⢀⣀⣤⣤⣤⣤⣤⡶⠚⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸ ⣿⣦⠼⣿⣄⣿⣾⡿⠍⠉⣿⣿⣿⡿⢫⡥⠙⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢹⣿⣄⠙⠻⢿⣿⡆⠁⠸⡟⡻⢿⣤⣈⣉⣸⣧⠞⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⣿⣿⣷⡄⣠⣿⡣⠀⢠⠆⡿⠷⢭⡉⠓⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠹⣿⣿⢿⣿⡖⣿⢀⠟⠊⣉⠉⠱⡌⢆⠀⢀⣠⠤⠂⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠙⣾⣿⣯⢣⠈⠻⡆⠀⠀⡇⠀⢡⠘⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠙⢿⣆⠱⡀⢰⠀⠀⠘⣄⠀⡆⠀⡃⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠧⣅⣼⡏⢹⠉⣯⡕⡎⡰⡍⣮⠥⠀⢀⣠⠔⠉⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠶⣛⣃⣓⣘⣓⣷⠶⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠀⠉⠉⠑⠢⣀⠀⠀⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢣⠀⠀⠀⠀⢠⡤⢤⡶⠖⠛⠛⠀⠀⠀⠀⠀⠀⠑⠒⠢⠤⡀⠈⢢⡀⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⢄⠀⢀⠎⠀⣀⠔⠒⠒⠒⠤⡀⠀⠀⠀⣠⠔⠒⠐⠒⠢⣀⠀⢣⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⣶⣶⣾⣿⣾⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣾⣷⣶⣿⣶⡆⠀⠀ ⠀⠀⠀⠛⣿⣿⣴⣻⣶⣛⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣜⣻⣶⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀ ⠀⠀⠀⠀⠈⢹⢿⣿⣾⣿⣶⣿⣿⣿⣿⣿⠟⠁⢀⠘⢿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣏⠘⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⣀⣱⠀⠈⠉⠉⠉⠉⠉⠉⠉⡿⠀⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢾⡀⠀⠀⠀⠀⣠⣤⣄⣀⣀⢀⣀⣀⣤⣤⣤⠀⠀⠀⠀⢠⠗⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⢲⠤⢤⣀⣀⣀⣀⣀⡠⠤⡖⠛⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⠟⡦⠶⣿⡧⠤⣼⣿⠓⢤⠟⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⢾⡀⠀⠀⢣⢱⢴⡏⡞⠀⠀⢀⡵⡄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⠀⢈⡱⠂⠘⣾⡀⣿⠃⠀⠾⡁⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠈⠢⡀⠀⢹⠀⡞⠀⢀⡴⠃⠀⣻⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠐⠚⣷⣤⡶⢷⣤⡀⢸⠀⢰⠇⠀⠀⠀⠑⡄⠈⣯⠗⡾⢿⡖⣶⠋⢹⠀⣶⡇⢀⣴⣶⠀⠀⠀⠀ ⢀⡤⣿⣿⣇⣀⣽⡿⣯⡴⣶⣤⣀⣴⠶⣦⣼⣆⠛⣰⢁⣿⠾⣿⠀⠘⢲⣷⠿⢾⣿⠖⢀⣤⢶⣄ ⠈⠻⣿⣿⡇⠀⢼⡇⢸⡇⠀⣿⠀⣿⠀⢸⡇⠘⠒⠁⠨⣿⢠⡟⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⠴⠋ ⣠⡴⣿⣿⣿⣶⡾⠃⠸⢷⣤⠿⠀⢿⡦⢺⣇⠀⠀⠀⣠⡿⠿⢶⣶⡤⠀⣿⠄⠸⢿⡤⠠⢿⣦⠴ ⠀⠀⢿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣜⠫⠭⠭⠍⣓⠲⢤⡉⢃⠤⠟⠙⣛⡛⠥⠤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠞⣩⣤⣤⣄⠀⠀⠀⠉⠢⣍⠕⣈⣁⠀⠀⠀⠈⠁⠢⣉⠻⣿⣿⣿⠟⠉⣀⠜ ⠘⣼⡏⠙⣿⣿⠀⠀⠀⠀⠰⢁⣾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠑⠋⢭⠏⢠⠞⠁⠀ ⠠⡘⢿⣿⡿⠋⠀⠀⠀⢀⡇⠘⣷⣤⣿⡿⠀⠀⠀⠀⠀⠀⡠⠒⡟⢠⠏⠀⠀⠀ ⠀⠫⠖⣒⣒⡒⠲⠶⠆⠁⠈⢢⠌⣉⠉⠀⠀⠀⢀⡀⠔⠊⡠⠂⡇⣸⠀⠀⠀⢰ ⠀⡤⠒⠥⠤⠤⠤⠤⠴⠃⢦⣄⡓⠤⠄⠉⠉⠭⠤⠒⠊⠉⠀⠀⡇⡇⠀⠀⠀⡿ ⠀⡖⠂⣉⡩⠭⠭⠭⢭⣍⣐⣒⠂⠭⢍⣁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⡇ ⠀⠙⢆⠳⡄⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠑⠒⠤⡀⠀⠀⠀⢣⠸⣄⣀⣠⡇ ⠀⠀⢸⠀⢿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢱⠀⠀⠀⢸⡀⢻⠀⠀⠀ ⠀⠀⢸⠀⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠎⠀⠀⠀⠀⢇⢸⠀⠀⠀ ⠀⠀⢸⠀⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡡⠋⠀⠀⠀⠀⠀⠘⡌⡆⠀⠀ ⠀⠀⢸⠀⡇⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠟⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⢄⡀ ⠀⠀⠸⣄⠉⠒⠂⠤⠤⠤⠒⢒⣚⠭⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠒⠢⢀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠄⠀⠡⠀⠀⠀⠀⢀⠠⠐⠂⢐⣒⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣼⣷⣂⡄⣀⠀⢃⠀⠀⠀⠀⡠⣲⠬⣿⣛⠛⢿⠷⣶⣤⡴⠃ ⠲⢾⡟⠉⡝⠷⠼⢹⡓⠀⢸⠀⠀⠀⠀⠉⠀⠸⠤⢭⠥⠤⡳⠾⠟⠁⠀ ⠀⠀⢹⠟⡙⣉⠡⢐⣀⡄⠁⠀⠀⠀⠀⠄⠁⠀⠀⠁⠀⠀⠐⠛⠛⠀⠀ ⠀⠈⠠⠕⠈⠔⠘⠉⠀⠀⣠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢊⣡⣤⣭⣍⣐⡂⢤⣄⠀⠀⢀⣺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡾⡿⣿⣿⡿⢿⡿⢿⡏⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠓⠁⢈⠇⢠⡑⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠠⡴⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠋⠁⠀⠀⠉⠁⠒⠤⡀⢀⡀⠤⠐⠒⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠒⠉⠁⠀⠀⠀⠈⠉⠒⢬⣆⠤⠤⠤⠀⠀⠠⠤⠤⢼⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⣒⣒⣀⡼⠦⡀⠀⠀⠀⠠⠤⠤⠤⠤⠭⢒⡄⠀⠀ ⠀⠀⠀⢀⠤⠐⣈⠤⠒⠉⠀⠀⠀⠀⠀⠉⠚⣶⠒⠂⠉⠉⢁⣀⣀⣈⣉⡚⣧⡀ ⠀⠀⠰⠍⣈⣉⣀⡀⠤⠔⣲⡞⣿⣧⣄⠀⠀⠹⠒⠀⠉⢁⣴⣛⣿⣷⣆⠀⠈⠃ ⠀⠀⠀⠀⠀⣑⠢⣄⠀⠸⣿⣟⣿⣤⣿⠧⠔⡧⠤⠀⢀⣸⣿⣽⣷⠼⠿⢦⡶⠁ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢴⠖⢒⣉⠁⢐⣒⢤⡠⠐⠊⠉⠐⠲⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠒⠒⠒⢠⠋⠀⠀⠀⠀⠀⠀⠀⠑⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢴⠁⠀⢀⣸⣅⣀⠀⠀⢀⢴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⡐⢈⡰⢹⠈⠛⠻⣕⣁⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣩⣿⡿⢿⣶⣤⡎⠀⣰⣽⠃⠀⠀⠀⠀⠀⢀⠀⢀⠜⠀⡇⠀⠠⠀ ⠀⠀⠀⣧⣾⡿⠁⠀⠘⣼⠎⠻⣆⢸⡝⠐⠀⢀⢀⡤⠂⡾⢲⠯⠥⠤⢦⣞⠁⠀ ⠀⡆⡆⣯⢘⡇⠀⣀⣀⣜⡒⠠⢙⣿⠘⠀⠀⢠⠋⢀⠾⡠⠋⠀⠀⠀⠘⡏⠙⠲ ⠀⣿⣇⣿⡞⠱⠀⠀⠂⠰⡡⠃⣆⠈⢰⡇⠀⣰⢀⢮⠗⢐⣒⣖⠂⠤⣆⣻⠀⠀ ⠀⠃⢹⣟⣿⠨⢵⢄⡈⠒⠒⠊⠉⠀⠀⠷⢀⢹⠌⠁⠈⣉⠉⣛⠛⢷⣯⣞⠀⠘ ⠀⠀⣸⠹⣾⢿⣥⢧⢲⠙⡠⣀⠀⠈⡀⠀⢻⠈⠀⠢⡎⢰⡦⢰⠣⠊⢈⣿⣕⠆ ⠀⢰⣿⠀⡿⠛⠗⠋⠋⠻⡷⣿⣯⠰⣱⠀⡀⢀⢀⠀⠥⢈⠂⡀⠵⡠⡞⠈⣿⠀ ⠀⢸⠸⠀⠟⠀⠀⣴⡀⠀⠁⠀⠙⡆⠡⢦⣡⣄⣀⠍⠂⢄⠀⠀⠀⡀⠤⢾⣿⠀ ⠀⢸⡄⢣⠀⠀⠀⡿⣈⠂⠄⡀⠀⠁⠀⠈⠙⢻⣷⢹⢸⣄⠫⣁⡢⢀⢔⠎⠘⢰ ⠘⡸⢟⣷⠣⠀⠀⢉⠱⡑⠠⢈⠢⠒⠒⠀⠀⠀⠸⡌⢟⣯⣷⡆⢀⣡⠃⠀⢀⠎ ⠀⠑⠎⠑⠡⢑⣤⠃⠀⢼⡅⠂⠤⢉⣀⠂⣒⡲⡾⠁⠈⠙⠛⢬⣭⣯⡶⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣄⠀⡞⠀⠀⠀⠀⠀⢀⠓⣺⠀⠐⣂⠤⠒⠉⢀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠃⠢⠄⠀⠤⠤⢤⣔⠝⠐⠒⣸⠉⣦⠀⣀⡴⡻⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣴⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣤⣠⣿⡷⠿⠙⠻⠟⠋⠠⠿⠶⣶⡴⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⢿⣧⣴⣤⠀ ⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⢀⡼⠛⠀ ⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄⣀⣀⢀⣀⣠⣴⠿⠛⠳⠶⠦⢤⣤⣀⡼⡧⠀⠀ ⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⢧⠀⠀ ⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠘⡇⠀ ⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡏⠀⠀⠀⢠⣿⠟⡛⣏⠉⠉⠙⠓⠀⢰⡾⠻⡿⠇ ⠀⣿⡇⠀⣠⣤⣤⡀⠀⠀⠀⢠⣾⠟⠂⠀⠀⠀⠀⠀⢀⡼⠿⣯⡀⠀⠀⢀⡼⢇⡰⡇⠀ ⠀⠹⣿⢰⣿⣿⣷⣯⡳⢦⡀⠘⣿⡀⠀⠀⠀⠀⠀⠰⠉⠀⢸⣿⡟⠀⠀⢸⡷⠻⢿⣟⠂ ⠀⠀⢹⡌⢫⣳⢰⣿⣿⠸⣿⡌⢛⣏⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠀⠀⠀⠀⠃⠀⢾⡇⠀ ⠀⠀⠀⢳⡜⣏⠘⠟⢹⣄⣿⡁⢙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀ ⠀⠀⠀⠈⣧⠘⢣⡄⠀⢹⠿⣷⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⣤⡄⢀⣰⣤⡿⠀ ⠀⠀⠀⠀⢸⡇⠀⣼⡓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢾⣁⡾⠃⠀ ⠀⠀⠀⠀⠸⢧⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⣤⣤⣶⣶⠊⣽⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠻⣴⣶⣶⣦⣤⣙⣶⣄⡀⠄⠒⠀⠀⢉⢅⠒⣆⠬⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⠟⠉⠙⡏⢏⣠⠋⠁⠀⠀⠀⠀⠀⠀⠁⠑⡀⠙⠕⢍⠣⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡽⣦⠀⠀⠀⠀⣄⡀⠂⣤⣀⣑⣦⣘⣄⠀⠀⠱⣌⠁⢀⠀⠀⠀⠀ ⣿⣿⢟⣻⡿⠡⠀⠂⠀⢚⡄⠙⢌⡳⠚⢯⡉⢢⣽⣻⣶⢠⠀⠹⠆⠈⣿⣧⡀⠀ ⢋⠴⠋⠀⠂⠀⠀⠘⢆⠀⡙⢆⠄⠱⣤⡀⣿⡿⢋⢁⣸⣷⠀⠀⠘⢀⢊⠉⠁⠀ ⠋⠀⠀⢰⠀⠀⠀⠀⢈⣿⠗⣤⣤⢤⢤⣈⢁⡁⡔⡝⠉⢷⡄⠀⠀⢸⣆⢦⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⡇⣈⡯⢦⣰⡿⠂⣀⠠⣿⠁⠂⠀⠀⢸⣧⠀⠀⠀⣼⠃⠡⡀ ⠀⠀⠀⠀⠀⠀⠡⣸⢸⣰⢀⡟⠂⢠⣿⠓⠀⣠⣶⡿⠻⡈⣸⠀⢠⠀⢻⡀⡄⡱ ⠀⠀⠀⢠⡇⠀⠀⠙⣵⡙⢯⠇⠊⠛⠁⠀⠰⣿⣄⠀⠀⢘⠱⣦⣨⣷⣞⠍⣿⡜ ⠀⠀⠈⠉⣰⡇⠀⡼⣌⠈⠹⠷⣦⡤⠤⠀⠀⠀⠉⠈⠰⡏⢀⣿⠫⣈⠽⣿⣿⡻ ⠀⠀⢀⣠⠻⣇⠀⢠⣷⣄⣒⣒⡬⠵⢾⣯⣟⡲⢬⠒⠊⠉⠁⣹⣇⣿⣶⡝⣿⡏ ⣄⣠⡼⠟⠀⣟⣇⠈⣿⡻⡿⠉⠀⠀⠀⠈⠃⡉⠱⣳⠂⠤⡼⢋⠹⢿⣿⣶⡸⠇

⠀⠀⠀⠀⠀⠀⡸⠗⠎⠁⠉⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠆⣱⣀⠀⠀⠀⠀⠀ ⠀⣠⠃⠀⠀⡰⢰⡜⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠋⠈⡀⠁⠀⠀⠀⠀ ⠀⢧⠀⠀⡐⠁⣞⡠⢄⣒⠆⢀⢣⠀⢨⠀⠀⠀⠀⠰⡸⠀⠀⡇⠀⡇⠀⠀⠀ ⠀⢀⢂⠎⣠⣾⣿⣿⡛⠻⣷⡊⡌⡠⢼⡆⠀⠀⡠⢎⣴⣮⣶⡁⡰⡇⠀⠀⠀ ⠀⠀⡅⣨⣿⣿⢿⣿⠿⠉⠙⠒⠉⠀⠘⠀⠀⢰⡡⣺⣿⣷⠤⣿⢰⠑⠀⠀⠀ ⠀⠀⢩⠉⢿⢿⠛⢉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡯⢻⡆⢀⠇⡎⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠙⠢⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⡁⠈⠀⡇⠀⠀⠀⠀ ⠠⠠⠤⠬⠢⠄⠀⠀⠠⠤⠤⠤⢤⠤⠤⠤⢤⣤⣄⡤⠤⠤⢤⣤⣥⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⠿⢿⣿⣷⣴⠄⠀⠀⠀⠀⣠⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣤⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠂⠐⠒⢒⣀⢖⣿⣶⣿⠿ ⠀⠀⠀⠀⠀⠀⠶⡦⢤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⡴⢿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠻⣿⠟⢿⣿⣿⣿⠭⠁⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⣿⣹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠤⣭⡖⠛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⣼⣿⣁⣵⡖⠛⠉⠉⠉⠙⠒⢦⠀⠀⣍⢙⠂⣯⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠈⠈⢩⡇⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢰⡟⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢠⡟⢀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠏⠉⢿⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢠⠟⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⡷⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡄⠀⠀⠀⠀⢠⠟⠀⠀⢸⡿⠁⣀⣤⠴⠲⠒⠺⡾⠀⠀⠀⡞⢰⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⡇⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣧⠀⠀⠀⣰⠋⠀⠀⢠⣿⢶⣞⣭⣤⣶⣶⣖⣋⡀⠀⢀⢸⠁⣸⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡼⠀⠁⠀⡀⠀⢀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠘⠆⢀⡾⠃⠀⢀⣼⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣦⠆⠀⢠⡏⠀⠀⣀⣀⡟⡄⠀⠀⠀⠀⠀⠀⢀⣼⠞⢁⣴⣾⣏⣭⣶⣟⠁⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣴⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⡻⣯⠛⠢⡼⢁⡴⠞⠁⠘⡇⠇⠀⠀⠀⠀⠐⢢⠟⠀⣰⣿⣿⣿⣿⠿⠿⣿⣷⣠⠞⠉⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠹⣟⢷⡴⠛⠋⠀⠀⠀⠀⡧⠀⠀⢀⡀⠀⢠⠏⠀⣴⣿⣿⣿⣿⣿⣆⡀⠈⣿⣟⠓⢲⡏⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⢀⣰⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠉⣻⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⣏⡴⠋⢱⣿⣿⣿⣿⣿⡇⠉⢳⣸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠋⠹⠻⣿⣿⣿⣿⣿⣾⡏⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣿⡏⣻⣿⣿⣉⠀⠀⠀⣿⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⠀⠻⣿⡿⣿⠀⠀⠀⣠⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠋⠙⣿⣿⠁⠀⢰⠏⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⣾⠃⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⠓⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡃⠀⠄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠶⠤⠤⠤⣤⡼⠷⠤⠤⠤⠤⠴⠦⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⢤⡤⡤⠤⣤⡤⠤⢤⣤⡤⠤⢤⣤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠬⠤⢤⣤⢷⡤⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⢀⣉⣁⡀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣤⣌⠀⠀⠉⠉⠛⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢾⣷⣀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣦⣴⣿⣿⠿⢾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣽⣿⣿⣤⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡾⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣦⡶⢉⣽⣿⣿⣿⣿⣿⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⡾⠋⠁⣨⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⣰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⠀⠀⠰⡿⠛⠛⠻⠿⡿⠿⠶⠀⠀⢠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣡⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠒⠒⠀⠚⢉⣠⣴⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠿⠿⠿⠿⠟⠛⠿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠔⠛⠉⠉⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢀⣴⠶⢀⠤⢤⡀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀ ⠀⢀⣼⠏⢠⠏⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⢀⣾⠃⠀⡸⠂⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀ ⣼⢣⠃⠀⡗⣛⢆⠀⠀⢔⣉⡑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢟⣾⠀⢀⠿⣒⡙⠀⠀⢸⣖⡱⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠘⢿⢸⡟⡏⠉⡁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠘⣾⣷⢈⡳⠈⠁⠡⠀⠀⠀⡔⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠈⠙⡥⣀⣀⣀⠀⢡⠀⠸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⢡⣿⣿⠟⠁⠠⠃⡄⠀⠀⣧⡆⠀⠀⠀⠀⡀⣀⣿⠀ ⠀⠀⠀⠀⢾⠯⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⢀⣇⣿⠇⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⠔⠉⣿⣿⣿⣾⣧⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⡾⠋⡹⠟⢻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠠⠔⠛⡇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠔⠀⠀⠀⠀⣀⠤⠀⠒⠒⠀⢄⠀⠰⡀⠀⠀⠀ ⠀⠀⠢⡀⠀⡐⠒⣚⢉⡁⠀⠀⠈⡁⠐⡀⠐⡀⠘⠀⠀⠀ ⠀⠀⣶⣾⢶⢶⣶⣶⣶⣶⣶⢶⡿⣶⢶⣶⣷⣶⣶⣶⡆⠀ ⠀⠀⠙⢻⣷⣵⣿⣿⣿⣿⠇⠈⢿⣿⣷⣿⣿⣿⣿⠛⠁⠀ ⠀⠀⠀⠣⣩⠉⠉⠉⠉⠁⠐⠈⠀⠉⡉⠉⠉⢹⡠⠃⠀⠀ ⠀⠀⠀⠀⠈⢢⠀⠀⠻⣿⣿⣿⣿⡿⠓⠀⠠⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠥⠦⠄⢀⣀⣀⣀⡀⡤⠦⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⢠⠓⠚⢳⣲⠻⠐⠱⡀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢠⠀⠱⠂⢿⠹⠇⠰⡉⢠⠸⠀⠀⠀⠀⠀ ⠠⢤⣠⢤⡀⡀⢸⠀⠈⠢⠘⣼⠤⡮⡤⢺⢀⠀⣠⡄⠀⠀ ⠠⣾⣿⢀⣿⣷⢳⡆⡖⢲⠣⡡⢡⡟⡇⠈⢲⠛⣿⠀⣖⡦ ⠠⢼⣿⠦⠟⠻⠼⠃⢧⠸⡄⠀⠠⠿⠴⠤⠸⠄⠿⠄⠧⠄ ⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠉⠉⠒⠒⠦⠤⣀⣀⠀⠀⢀⡇⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠾⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠑⠒⠲⠤⢄⣀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠊⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⠁⠀⠈⠓⢤⣀⡀⠀⠀⢿⠢⢄⡀⠀⠀⠀⢿⠢⣄⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢸⠀⠉⠉⠒⠺⠄⠀⠈⠉⠒⠢⠼⠆⠀⠈⠙⢲⠦⢼⡄⠀⣠⣶⢦⠀⠀⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⡼⠊⠉⠑⢦⠀⠀⣠⣖⠋⠉⠙⠒⠦⣄⠀⠀⠘⡄⠀⠀⡼⢹⣟⠃⣇⠀⠀⢾⠾⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡀⢾⠀⢰⡄⠀⠈⡇⠀⢏⠻⠆⠀⠀⠀⠀⢸⠄⠀⠀⢳⠀⢰⠃⣾⡿⡆⣿⠀⠀⢸⡆⠀⠀ ⢰⠤⣤⡞⠳⣤⠿⡋⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⡼⠁⠀⠈⠓⠤⠤⠤⠄⠒⠋⠀⠀⠀⠘⣆⡎⢠⣿⢀⣷⠏⠀⠀⡼⠁⠀⠀ ⠘⡟⠉⣇⠀⣿⢆⣻⡿⠁⠀⠀⠀⠀⠀⣹⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠘⢃⡞⠈⠉⠀⠀⠀⣼⣁⠀⠀⠀ ⠀⢹⡦⠘⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠓⠒⠤⡤⣤⣤⣤⣤⠤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⠓⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⠀⠀⠀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⠤⠤⠤⠄⠒⠚⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠲⠶⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⢀⡿⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣼⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠦⠤⣤⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠉⠙⠓⠲⠤⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣠⡴⠶⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡁⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠚⠋⠁⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠈⡟⢦⣄⠀⠀⠀⠀⠀⠈⣟⢦⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢸⠍⠛⠒⠦⢤⣀⣻⠀⠈⠙⠒⠦⣤⣀⡀⢹⡄⠉⠙⠒⠦⣤⣀⠀⢻⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣶⡶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠈⠉⠁⠀⠀⢀⣀⣀⣈⣉⠙⠃⠀⠀⠀⠀⠀⣏⠙⠚⠗⠀⢠⢞⡿⣏⢷⠀⠀⠀⠀⣀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡾⠋⠁⠀⠈⠳⣄⠀⠀⣠⢞⣋⠁⠀⠀⠉⠉⠳⢦⡀⠀⠀⠀⢹⠀⠀⠀⢠⡏⣼⣧⡉⠸⡇⠀⠀⠸⣿⠻⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣾⠀⢀⣤⡄⠀⠀⢹⡄⠀⢻⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣇⠀⢀⡾⢠⣿⣻⣧⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀ ⣀⣀⠀⢠⡴⣦⡀⣠⡶⡷⠂⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠙⠁⠀⢀⣾⠃⠀⠈⢷⣉⠀⠀⠀⠀⣀⣠⡴⠏⠀⠀⠀⠀⢹⡀⣸⠃⢘⣿⠋⣸⣠⡇⠀⠀⠀⣼⠀⠀⠀⠀ ⣿⡉⣻⢿⠀⠈⣷⡏⢸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⢧⡟⠀⡿⣽⣤⡿⠟⠁⠀⠀⣰⠇⠀⠀⠀⠀ ⢹⣏⠀⢸⣆⠀⢹⠻⣄⣩⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠘⠃⣼⠁⠀⠀⠀⠀⠀⠀⣴⣏⣠⠀⠀⠀⠀ ⠀⢹⣦⡀⠛⠓⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⠤⢤⣤⣄⣀⣀⣀⣀⣠⣠⡤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠲⠯⠿⣶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠶⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⢀⣀⣀⣤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣤⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀