⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡖⣲⣶⣖⣲⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡖⣲⣶⣖⣲⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣶⣒⡺⡟⢒⡎⣇⣀⣫⣀⣀⡇⠒⢚⠒⣒⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣒⡾⠓⠒⣿⣀⣀⢫⣀⣸⢰⠒⢺⠒⣒⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣶⣚⣟⣅⣐⡇⣓⣒⣣⣖⣒⣒⣒⣚⣞⣒⣒⢸⣐⣺⣘⣲⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣋⣆⣐⡇⣓⣒⣳⣖⣒⣒⣒⣲⣼⢲⣚⢸⣐⣸⢚⣓⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣿⢁⣐⡺⣠⣖⣚⡗⠒⠒⠃⠒⠀⠀⠝⢖⡒⢲⣓⣲⣽⣐⣺⣘⣶⣤⣤⣀⣤⣤⣿⣋⣇⣐⣧⣖⣚⡗⡒⠒⡗⠒⡀⠒⡝⣲⢰⢾⣒⣲⣀⢇⣐⣸⣿⣄⠀⠀⠀⠀ ⠀⠀⢺⠟⢒⣲⣂⣖⣳⠛⠀⠀⡀⠐⠆⠀⠀⠀⠀⠆⠂⠐⠓⠝⣾⣳⣹⣐⣺⣛⠟⠀⢻⣛⣇⣐⣇⣞⡗⡣⣒⠀⠀⠶⠈⠀⠀⠀⢀⣿⢸⣿⠲⠝⢾⣲⣐⡖⢒⢻⡗⠀⠀⠀ ⠀⢠⣾⠝⢲⡚⢇⣸⠂⠁⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢾⣲⢽⣾⣲⠒⢞⣓⡺⣆⣷⠋⠀⠆⠁⠸⣏⣷⣎⣁⣙⣋⣋⠀⠀⢈⣋⣉⣉⣋⡈⢳⣆⡰⣧⡄⠀⠀ ⠀⣸⢧⣐⣺⡇⢸⠂⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢾⣹⢇⣐⡺⢏⣳⡛⠈⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⢶⢰⠚⠀⢰⠘⢰⡇⢸⢧⣑⡨⡇⠀⠀ ⢸⠋⠉⣹⡎⢱⡚⠄⡆⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠰⢹⢾⣉⣱⡺⠎⠁⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⢸⠀⠀⠈⡥⢼⢙⡎⢱⡎⠉⠟⡇⠀ ⣼⠷⠦⢾⡇⢸⠀⡀⠄⠀⠀⠀⠀⠀⠀⣀⡶⠍⠉⠶⠶⢶⣠⣀⠀⠀⠀⠀⠀⠀⠩⠙⠆⠁⠀⠀⠀⠀⠀⣀⣀⡶⠶⠶⠍⠉⠶⣀⠀⠸⣸⠉⠀⢿⣁⢈⣹⡇⢸⡽⠤⡶⡷⠀ ⢹⣤⡀⣺⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⣀⡿⠇⠀⠀⠀⠀⠀⠉⠹⢶⣀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⣀⡶⠏⠉⠁⠀⠀⠀⠀⠀⠿⣄⢸⣹⠀⠀⠈⠹⢺⠀⡇⢸⢧⠁⣥⣇⠀ ⢻⠉⠩⣹⢧⡸⢬⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡼⢧⡼⡏⠍⠏⡏⠀ ⠘⢿⡿⡯⢤⡇⢸⠅⠠⠬⠥⠥⠤⡬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠈⢹⡿⠭⠭⠭⠭⠭⢽⡏⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠤⠬⠭⠬⠬⡇⢸⡥⡭⢍⡏⠃⠀ ⠀⢸⣿⠬⠽⠧⡼⢄⠀⠀⠀⠀⠀⡅⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢿⠼⡏⠀⠀⠀⠀⠀⢸⠧⡤⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⢥⣼⠧⠭⡭⡧⠀⠀ ⠀⠀⢻⡯⠫⢽⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠬⠽⡟⠀⠀⠀⠀⠀⢸⠯⠥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡂⢸⡏⠯⠽⠇⠁⠀⠀ ⠀⠀⠈⣿⡭⡭⢭⡏⢡⠤⠤⠤⠤⠦⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠤⠝⢾⠤⠤⠤⠤⠤⡼⡫⠭⠭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⠤⠤⠤⣌⢹⡽⠭⢭⣿⠋⠀⠀⠀ ⠀⠀⠀⢿⣦⡬⢽⣉⣯⡟⣦⡏⠉⠯⡍⣿⡆⠀⠀⠀⡤⣤⠏⠈⠛⠀⠀⠀⠈⢡⢽⠤⢯⡍⠁⠈⠀⠀⠛⠉⠙⣧⢤⡄⠀⠀⠀⣼⠉⠄⢠⢽⣿⢻⢽⣉⢣⠬⣼⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⣿⡇⠣⢽⠧⡟⡏⣧⡄⠙⢯⠟⡛⣭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠟⠛⡩⠉⢨⡝⣿⢻⠼⣋⠰⢼⢿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢯⣯⡟⡖⡧⡗⣇⡧⡄⠈⣦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⠓⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⠁⠬⣽⣲⢻⢼⢲⢺⣭⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⣧⡬⡗⡟⣧⡗⣏⡻⡧⠤⢤⣤⣤⢤⢤⠀⠀⠀⠀⢠⣼⠛⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⠄⠤⠤⣤⠤⠤⣤⢿⣺⢺⢼⢛⢺⢬⣼⠽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣧⡤⣇⣙⣧⡗⣖⣖⣦⠀⠤⠈⢺⢤⠀⠀⢰⢼⠛⠀⠀⠀⠀⠀⠘⡧⡄⠀⠀⡤⡖⠀⠀⠀⠤⣁⣾⢚⢼⣉⣸⣤⣼⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣇⠳⡇⣙⣦⡗⣟⣿⡠⠈⢼⢸⠀⢠⢼⠿⠀⠀⠀⠀⠀⠀⠀⠻⡧⡄⠀⡇⡇⠀⡄⢉⣲⣚⣴⣋⢸⣘⢸⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢺⣆⣈⣒⣟⣲⣓⣒⣞⣺⣻⣒⣾⠟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⣗⣶⠟⢷⣻⣖⣚⣶⣻⣘⢒⣰⡖⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⣈⣒⣇⣙⣲⣓⣲⣙⢢⢢⡀⡀⠀⠂⠀⡀⠂⢀⢀⡐⠰⣣⣖⣚⣗⣃⣸⣘⣒⣳⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢺⣚⣘⣒⢀⣙⣾⣓⣲⣐⣐⢢⣆⣀⣰⠰⣎⣬⣖⣚⣗⣃⡀⣄⣒⣗⡖⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢾⣘⣘⣺⢀⣙⣒⢾⣒⣲⣈⣗⣛⣳⣒⣋⡄⣇⣓⣇⡖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢻⣸⣘⣺⣀⣀⣳⠒⣚⣄⣄⣇⡓⣇⡖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢷⣕⠒⡞⢛⣳⡗⣺⣷⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣾⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡿