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