⢯⡹⣍⢞⡱⣍⢮⡱⣍⢎⢧⡹⣌⢧⡹⡌⢧⡹⣌⢧⡹⣌⠧⢳⡌⢧⠹⣌⢣⠧⣹⣌⣳⠜⠃⠛⠒⠯⠚⠶⢭⡲⣍⠞⣌⠧⡹⣌⠧⣙⢬⢣⡝⡼⣡⠏⣮⣑⢣⡝⢬⢣⡝⣬⢓ ⣇⠳⣌⢮⡱⢎⡲⡱⢎⡚⢦⡓⡜⢦⣓⠹⣆⠳⡜⢦⠳⣌⣻⣴⡮⠷⠛⠚⠛⠉⠉⠀⠀⠒⠒⠒⠒⠒⠦⠤⣀⣉⡓⢾⣌⡳⡱⢎⠶⣩⠖⡣⢞⡱⢆⡛⣔⣊⠧⣜⠣⣇⠞⡴⣋ ⣎⢳⣉⠖⣭⢲⡱⣙⠎⡝⢦⡹⢜⡡⢎⡳⣌⢳⡹⣬⠗⠋⠁⠀⠀⢀⠀⠄⠀⡐⠀⠠⠁⠀⠄⠐⠀⠠⠀⢀⠀⠀⠈⠈⠉⠙⠓⢯⣜⡱⢎⡵⢋⠶⣩⠞⣰⢣⢹⡰⢫⢌⠏⠶⡱ ⣌⡳⣌⣫⣔⣣⣜⣡⣛⣜⣣⣜⣣⡹⣬⣑⣮⠗⠋⠀⠀⠠⠀⠁⡀⠂⢀⠀⠂⢀⠀⠁⡀⠌⠀⠐⠈⠀⠐⠀⠠⠈⢀⠐⠀⠠⠀⠀⠈⠙⠳⣜⣍⣚⣥⣚⡥⣎⣣⣜⣣⢎⣙⣣⣓ ⢭⡹⠭⡭⠭⣍⠭⡭⢭⠭⢭⠭⣭⠹⣍⡿⠁⠀⠠⠀⠁⠠⢀⣁⣠⣀⢦⠤⠶⠖⠲⣶⡦⠖⠓⠒⠶⠧⠤⠬⣄⣐⣀⣄⠈⠀⠄⠁⠐⠀⡀⠈⠛⢯⡭⢭⡹⠭⢭⠭⣍⠯⡹⢍⡝ ⣇⢎⡳⢱⣋⢬⠳⣑⢫⡜⢣⢞⡰⣋⡞⠀⣀⡢⠥⠖⠛⠉⣁⡀⠤⠤⣖⣦⡶⠞⠋⠉⠉⠉⠉⠉⠐⠒⠒⠠⠤⢄⣀⡈⠛⣷⣶⢬⣀⠐⠀⡀⠂⠀⠙⣦⢳⠹⣌⠶⣑⠮⣑⢫⠜ ⣎⠮⣑⢧⡚⣬⠳⣍⠶⣩⢓⡎⣵⠛⢁⣉⠤⠐⠂⠀⠉⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛⠷⣦⣍⠒⠦⣄⡁⠀⠘⢧⣋⢦⡹⢌⡳⢍⢮⡙ ⣎⠳⣍⠲⣍⠶⡙⢦⠛⡴⣩⠜⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠠⠀⡉⠓⠤⣈⣷⢎⡜⣣⢝⢪⠖⡭ ⡭⢳⣌⠳⣌⠳⡍⢧⢛⡴⢣⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠞⠋⠉⠉⠓⠲⠤⣀⣻⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢌⣹⡇⡞⡥⢎⢧⢋⡖ ⣝⠲⣌⢳⡉⢧⡙⢮⡱⣊⠵⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⣾⠓⠉⠉⠉⠉⠑⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢩⠖⣭⠲⣩⠜ ⣎⠳⣌⢧⡙⢦⡙⢦⡓⣍⢎⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⣙⠦⣙⠦⣙ ⣭⠳⡜⣢⠝⣦⡙⢦⡹⢌⡲⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢣⡝⠬⣎⡱ ⣭⠲⢥⣋⠶⣉⠳⣌⢧⠚⡥⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⢎⡕⢦⡹⣡ ⣆⠻⡔⣊⠶⣉⢳⡘⣆⡛⣜⢚⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣴⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⢎⡼⢡⠖⣡ ⣌⠧⣙⠬⢣⡙⢦⣱⢦⣱⣜⣮⣹⡄⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣌⣳⡌⢣⠚⠥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣻⡽⣷⣻⣦⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠋⠛⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⢀⣼⣿⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣟⡷⣯⢿⣽⣻⢷⣻⢿⣄⡀⠀⠀⠀⠑⠢⠄⣀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠊⠁⠀⠀⣠⣾⡿⣯⣟⡿⣷⣄⡀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣳⣯⢿⣻⣯⢷⣟⡿⣯⣟⡿⣽⣦⡀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⡀⠈⠉⠐⠒⠒⠒⠒⠂⠀⠀⣀⠤⠔⠒⠉⠀⠀⠀⠀⠀⣠⣾⣿⣻⣽⠗⠋⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣟⡷⣯⣟⣿⣳⢿⣯⢿⣽⢷⣻⢿⡽⣯⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠂⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣟⡿⣾⡽⠁⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⡠⠜⠋⠉⠛⠻⠽⣾⣷⣻⣟⣾⢯⣟⣯⡿⣯⣟⣿⣻⢾⣽⣻⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣟⡿⣾⣽⣻⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠐⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣿⢯⣟⡷⣿⣽⣻⢾⡽⣿⡽⣯⡿⣾⣽⣻⣟⡿⣿⢷⣶⣶⣶⣦⣤⣶⡶⣶⣶⣾⢿⣿⣻⢿⣽⣻⢾⣽⣻⢷⣯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢯⣟⣷⢯⣟⣯⡿⣷⣻⣽⣟⡷⣯⣷⣻⣽⢯⣿⣳⣯⣿⡿⣿⣳⣿⣻⢾⣽⣻⡾⣽⣟⣾⢯⣿⣳⢿⣻⡾⣽⣷⣶⣶⣶⣦⣄⡀⢀⡀⢠⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⢾⣟⣯⡷⣿⣽⣻⢾⣽⣻⢷⣯⣟⣾⣟⡷⣯⣷⢿⣽⣻⢷⣯⣟⣯⣷⢿⡽⣟⣾⢯⣿⣳⢿⣻⣽⣻⣽⣞⡷⣯⡷⣟⣿⣻⣿⡇⢹⡆

⡆⢹⡇⣿⣻⣿⣟⡷⣯⡷⣞⣽⣻⣽⣻⢿⣳⣿⢯⣾⣟⡽⢿⣷⣯⣟⣯⢷⣻⣽⢿⣷⣯⡷⣟⣾⣟⣯⢷⣻⣽⢾⣻⣽⣿⡷⣯⣟⢾⣻⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⢠⡀⢀⡀⣄⣦⣶⣶⣶⣷⣽⡾⣻⢿⣳⣿⢯⣾⣟⣽⡾⣻⣽⢾⣻⣿⣳⣿⡿⣿⣯⣳⣿⢯⣽⣻⣷⣯⡷⣟⣽⣻⣷⡿⣯⣟⢯⣷⣟⢯⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣯⢷⣻⣽⢾⣻⣽⢿⣻⣿⢿⣾⣶⣶⡶⣶⣤⣦⣶⣶⣶⢷⣿⡿⣟⣻⣽⣾⡿⣯⡽⣿⡽⢾⣻⣽⣿⡷⣟⢯⣿⢯⠳⠙⠈⠀⠀⠀⠀⠀⠀⠁⠐ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⣻⣽⣾⡿⣟⣿⣶⣤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣶⢿⣻⣽⢾⣻⣿⣟⣯⡿⣯⣟⢯⣾⣟⣻⣷⣾⠽⠻⠛⠉⠋⠜⡠⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠁⡽⣾⡿⣟⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⢿⣯⡽⢿⣻⢷⣽⢿⣯⢿⣳⣿⣟⣯⡷⣟⣿⣠⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠋⠗⣽⣻⣿⣾⣠⠀⠀⠀⠀⠀⠉⠒⠔⠤⣀⠀⠀⠂⠒⠒⠒⠒⠐⠉⠈⡀⢀⠤⠂⠐⠉⠀⠀⠀⠀⠀⡀⣦⣽⡿⣟⣯⡿⣟⢷⣯⣻⢿⣯⣳⣿⣾⢀⠀⠀⠀⠀ ⠀⠀⡀⣄⣷⡿⣟⣯⡿⣾⣠⠀⠀⠁⠊⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⣀⠄⠢⠑⠀⠀⠀⡀⣄⢿⣻⢷⣻⣽⢿⣯⡷⣟⣿⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣦⢿⣿⣼⢀⠀⠚⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⠻⠛⠋⠛⠟⠿⠛⠙⠀⠀⠀⠀⠀⠀⠀⢄⠑⠈⠀⠀⡀⣦⣻⣷⡽⣻⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⠈⠀⠀⣆⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠥⠚⢣⡌⣳⣌⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠈⠀⡄⣹⣮⣜⣱⢦⣱⢦⡙⢣⠬⣙⠧⣌ ⣡⠖⢡⡼⢎⡍⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⣦⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⢚⣜⡛⣆⡘⢳⣉⠶⣊⡔⠻⣆ ⣡⡹⢦⡕⢎⡍⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠚⢧⣌⠳⣉⠶⣋⢥⠲⣭ ⡱⣎⠬⡝⢣⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡲⢌⡹⢦⡙⣦⠝⣢⡜⠳⣭ ⣙⠦⣙⠦⣙⠧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢎⣍⡓⢦⡙⢦⡙⢧⣌⠳⣎ ⠜⣩⠲⣭⠖⢩⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠒⠑⠉⠉⠉⠉⠓⣾⠀⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠵⣊⡱⢮⡙⢧⡉⢳⣌⠲⣝ ⡖⢋⢧⢎⡥⡞⡇⣹⢌⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⣻⣀⠤⠲⠓⠉⠉⠋⠞⠶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢽⢣⡴⢛⢧⡍⠳⣌⠳⣌⢳⡭ ⡭⠖⢪⢝⣣⡜⢎⣷⣈⠤⠓⡉⠀⠠⠑⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣽⠜⣩⡴⠛⢦⡙⠶⣍⠲⣍⠳⣎ ⡙⢮⢍⡳⢌⡹⢦⣋⢧⠘⠀⡁⣄⠦⠒⣍⣦⠷⠛⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠁⠉⠀⠂⠐⠤⣉⢁⠛⣵⡎⢓⣩⠶⣍⠳⣬⡚⢧⣑⠮⣎ ⠜⢫⣑⠮⣑⠶⣌⠹⢳⣦⠙⠀⠂⡀⠀⠐⣀⢬⣶⣷⠛⡈⣀⢄⠤⠠⠒⠒⠐⠉⠉⠉⠉⠉⠋⠞⡶⣦⣖⠤⠤⡀⣁⠉⠛⠖⠥⡢⣀⠀⡞⣋⡰⢞⢣⡜⢫⣑⠳⢬⣋⢱⡳⢎⣇ ⡝⢍⡹⠯⣍⠭⢭⠭⡹⢭⡭⢯⠛⠈⡀⠀⠐⠁⠄⠀⠈⣄⣀⣐⣄⠬⠤⠧⠶⠒⠓⠖⡦⣶⠲⠖⠶⠤⢦⣀⣠⣁⢀⠠⠁⠀⠠⠀⠁⡿⣍⠹⣭⠭⢭⠭⢭⡭⠭⣍⠭⡭⠭⡹⢭ ⣓⣣⣙⢎⣣⣜⣣⣎⡥⣚⣥⣚⣍⣜⠳⠙⠈⠀⠀⠠⠀⠐⢀⠈⠠⠀⠐⠀⠈⠐⠀⠌⡀⠁⠀⢀⠂⠀⢀⠂⡀⠁⠀⠠⠀⠀⠋⠗⣮⣑⣬⡹⣣⣜⣣⣜⣛⣡⣜⣣⣔⣫⣌⡳⣌ ⡱⠶⠏⢌⢫⡰⢹⢣⣰⠞⣩⠶⢋⡵⢎⡱⣜⢯⠓⠙⠉⠈⠈⠀⠀⢀⠀⠠⠀⠐⠄⠀⠁⠠⠀⡐⠀⠄⠀⢀⠀⠀⠁⠋⠗⣬⡹⢳⣌⡳⢎⡡⢜⡹⢦⡝⠎⣙⡱⢲⣭⠖⣉⢳⣎ ⣋⡴⠞⣇⠣⣜⠧⣊⣔⡛⢆⡱⢞⡣⠖⣩⠶⢎⡱⡳⣌⢾⡓⣉⣀⠤⠦⠒⠒⠒⠒⠒⠀⠀⠉⠉⠛⠚⠛⠷⡮⣴⣻⣌⠳⢦⡜⠳⣆⠹⣓⢦⡜⡓⢦⡚⢎⡱⡲⢎⡱⢮⣌⠳⣇ ⢓⣬⡝⢣⢬⡝⢣⣑⣮⠏⣡⡼⡝⢣⢬⣙⠧⣌⡹⠧⣌⠞⣍⡲⢭⠶⠚⠯⠒⠛⠃⠜⣳⣌⣹⠧⢣⣌⠹⢧⡌⢳⠧⣌⡹⢧⣌⡹⢧⡌⡹⢧⣌⡹⢧⢎⣍⡱⢮⣍⡱⢞⣍⡹⢯