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