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