⣏⢳⡭⢳⣹⡿⠁⠀⠈⢿⣆⠀⠀⠀⠀⠈⠉⠻⢿⣜⡣⢟⡼⣙⠮⣝⠮⡽⣙⢮⣝⣣⢏⡳⣭⠳⣽⣇⠀⠀⣀⣠⡴⠶⠚⠋⠉⠀⠀⠀ ⣎⡳⣜⢧⣿⣇⠀⡩⣀⠈⠿⣁⠀⠀⠀⠀⠀⠀⠀⡙⠿⣯⣶⣩⠳⣎⠽⡲⡝⢮⠶⣙⡮⣵⣎⣽⣲⣿⡷⠾⠋⠁⠒⠀⠀⠀⠀⠀⠀⠀ ⢮⠵⣎⣿⡟⢤⡹⠴⣹⠲⡸⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠙⠛⠛⠛⠛⠙⠉⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⡏⡞⣽⣿⠙⣦⡝⢣⡕⢣⠓⡎⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡅ ⡝⢶⣿⡟⣹⠲⣝⢮⡵⢫⡞⣵⣫⡞⣿⣦⣐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣔⣾⡟⣟⢫⡑ ⡝⣾⣿⣟⢶⣛⡮⢷⣹⢳⣟⣷⣯⣿⡶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⡟⡳⢉⢆⢣⠜ ⣝⣿⡿⣎⢷⣫⠽⣧⢏⡷⣾⣿⣿⣿⣹⣿⢃⠁⠀⢠⡤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠜⢦⣤⡀⠀⠀⠀⠐⠈⢿⡣⢅⠣⣈⠂⡉ ⣾⣿⣵⣫⣾⣽⣿⣾⣝⡞⣭⢫⡕⢡⣿⡏⡅⠀⠐⢿⣦⣾⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⡏⠂⠀⠀⠀⢑⠘⣿⠀⢤⣤⣐⣀ ⣿⡟⣾⣿⣿⣿⣿⣿⣿⣟⢦⠓⠌⣱⣿⠑⠌⠀⠀⠀⠉⠛⠉⠀⠀⣤⣤⣠⣀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⢻⡆⣻⣿⣿⣷ ⡟⡼⢻⡿⣿⡿⣿⢿⡿⠏⡂⠡⡜⣿⣷⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡰⢤⣄⠀⠀⢸⣧⢸⣿⣿⣿ ⡧⢍⡳⣜⠢⡅⣤⢢⠀⠐⠠⢁⢼⣿⣇⠶⣌⢯⡁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣈⣀⠀⠀⠀⠀⠀⠈⢸⢆⡛⢦⣝⠣⠀⢀⢻⡆⢹⣿⣿ ⠻⡜⢣⡜⢧⠻⣄⠟⣧⡘⡤⣀⣼⣿⢻⣧⣜⡟⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠀⠛⢿⠄⠀⠀⠀⠀⠀⠛⡜⡻⢤⢸⠇⠀⠀⠸⣧⡸⣿⣿ ⡰⢍⡳⣜⢣⠟⣬⢛⡴⣙⠶⣙⢾⣿⡀⢁⠉⠀⠀⠀⠀⠀⠀⠀⠄⣿⡎⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⠂⢻⡀⠀⠈ ⡰⣌⠐⠈⠃⠛⠀⠃⠈⠉⠉⠛⠈⢻⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⠲⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣷⠀⠡ ⡳⣇⢎⢤⣁⢂⡁⢌⣤⣷⣎⠰⠦⢾⡝⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡎⡀

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