⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⣟⡛⢷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠾⠛⠛⠉⠅⠀⠉⠅⣙⡇⠊⠑⠮⠉⠏⠻⢖⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⣻⠛⠁⠀⠀⠀⣀⣠⣤⣶⠾⠟⠛⠭⣝⣲⣦⣄⡀⠀⠀⠀⠋⠻⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠉⠐⠋⠀⢀⣠⣴⡾⠿⠟⠋⠉⠀⣀⣠⠴⠶⠒⠫⠉⠛⠻⢿⣶⣦⣄⠄⠀⠀⠈⠹⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢯⣄⠀⠤⠀⣠⣴⡿⠟⢋⣁⡀⠀⠀⣠⠖⠛⠛⢀⣀⣠⠤⠴⠶⠶⠦⢤⣬⡙⠻⣟⣦⣄⠀⠀⠈⣡⡭⠿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⡎⢧⠀⠀⣿⡗⢳⣰⠋⠀⡇⢠⠞⢁⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⡇⠙⣆⣸⠘⣿⡆⢲⣼⢫⣾⡿⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣄⡀⠸⣧⣜⣹⠘⡷⢧⣿⠁⢸⡏⠀⢰⣣⢏⡴⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢻⠀⢹⡏⠀⢹⢰⢿⡇⣏⡽⣦⣿⠇⣠⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⣌⠻⢶⣿⡇⠈⣿⠁⠸⣿⠀⠸⡇⠀⢸⣿⠏⠀⠀⠀⣀⣤⣶⡿⠟⠛⠛⠛⠛⠻⣿⣾⠀⢸⡇⠀⢸⢼⠀⡇⣿⠁⣿⣿⠾⢋⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠏⣇⠈⣷⡟⢯⣇⠀⢻⣇⠀⢻⡄⠀⢻⡀⣾⡇⠀⠀⢀⡾⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢰⠃⠀⣾⡟⢠⣿⠏⢀⡿⠉⣿⡏⢢⡙⢿⣦⡀⠀⠀ ⠀⣤⣾⣟⠗⢹⡿⣆⢸⣧⠈⢿⡆⠀⠙⣆⠈⢳⡀⠈⣇⣿⡇⠀⢠⢏⡼⠁⠀⠀⢄⣠⣴⣶⠿⢷⣶⣄⣸⢀⡾⠀⣸⡿⢀⡾⠃⢠⡟⠁⢠⣿⣧⡾⣿⠺⢻⣿⣶⡄ ⠐⣯⢿⣣⣥⠈⣇⠘⢯⡟⣇⠀⠙⢦⠀⠈⢧⡀⢳⡴⣿⢧⣧⠀⡟⢸⡇⠀⠀⢠⣿⠟⢁⣤⣄⠀⢈⣿⣧⣿⡥⣴⠋⣠⠞⠀⡰⠋⠀⢠⢟⣮⠟⢰⡟⣤⣵⡾⣹⡇ ⠀⠹⣷⣟⢶⣵⡙⣦⡀⠙⠿⣧⡀⠀⠳⡄⠈⠻⣾⣿⡜⡾⣾⡀⢷⡘⣧⠀⠀⠻⣽⣄⡘⣻⠿⢀⣾⣽⡟⠛⣜⣽⡿⠁⢠⠞⠁⢀⣠⠟⠋⠀⣰⢏⣛⣱⢏⡼⣟⠁ ⠀⠀⠈⢿⡜⣧⡉⠛⠿⣦⣄⠀⠉⠓⠲⢤⠰⣶⡮⠿⠃⢰⣻⣤⣀⣙⣾⣷⣦⣤⠬⠿⠛⠁⣴⣾⠟⣟⣇⠀⠯⢞⣲⡶⣣⠤⠚⠉⠀⢀⣠⡾⠟⠛⣡⡟⡸⢠⠇⠀ ⠀⠀⠀⠸⣇⣧⣙⣲⢤⣄⣉⡉⠉⠉⢀⠠⢾⣋⡛⠃⣰⣫⣿⡦⠞⠛⠉⠉⢁⡀⣀⣤⣶⠿⠋⠀⠀⢘⣎⣇⠘⣋⣻⠿⢃⣐⠒⢚⣉⣉⣀⣠⣤⣾⣿⠃⡇⢸⠀⠀ ⠀⠀⠀⠀⣿⢿⡉⠉⠉⠉⠙⠛⠋⠉⠉⢀⣻⣷⡲⢰⢷⠋⠀⠀⠀⢀⣴⠋⠉⢉⣩⡛⣷⡀⠀⢀⣴⣏⣹⣸⠀⣒⣚⣧⠀⠈⠉⠉⠈⠀⠀⠀⠀⢀⣨⢳⢣⠞⠀⠀ ⠀⠀⠀⠀⢻⣟⡿⠷⢶⣤⣤⡤⠴⠒⠉⠉⣾⣓⣶⠊⣟⣆⠀⣠⣶⢿⠟⣠⠀⠉⢛⣹⠛⠛⢾⣽⣹⣩⣯⠏⠀⠳⠿⣿⠛⠲⠦⠤⠤⠶⠶⠶⠾⠿⡇⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣷⢤⣀⣀⡀⣀⣀⣀⣠⠄⢻⣾⣓⡀⠙⢾⡻⣏⢠⡟⠀⠿⢷⣖⡘⠓⣟⠛⣻⣿⣿⠟⠁⠀⣌⣛⣭⡳⠤⣄⣀⣀⣀⣀⣀⣀⣴⡞⣹⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⢧⢿⣋⠉⠉⠁⠀⣀⣠⠽⢹⢯⡔⠒⣣⠉⠛⠿⠀⠀⠐⠫⠛⠀⠀⣸⣿⠗⠋⣀⠲⢌⡓⢶⣛⣎⠻⢤⣀⠀⠀⠀⠀⢀⣹⡾⢰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡾⡦⠈⣽⠗⠚⠉⠁⠀⠀⣻⣟⣞⣉⡤⣖⡮⢰⡆⠀⠀⠀⡀⠀⠀⠀⠁⠀⡄⠺⣗⢤⣙⣍⠓⢦⣀⠀⠈⠙⠛⠿⢿⡍⢠⣧⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⢻⣤⣤⣤⠴⠚⠉⠈⢓⣭⣟⠽⢃⠔⡀⢳⡀⣧⢠⠇⡇⣸⢡⣄⣄⠘⣦⣈⣿⠈⠳⢄⡀⠈⠙⠶⢤⣤⣤⣞⠡⣾⢹⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣿⢸⢢⢰⣿⣏⣁⣀⣠⠴⠚⠉⢀⣹⠞⣹⡔⣿⣯⡟⣏⢭⢤⣷⣷⢸⣸⣼⡷⡮⠧⠰⣄⠀⠀⠙⠲⢄⣀⣀⣨⣿⡟⢁⡟⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣏⣽⣿⡾⡀⣸⢸⡯⠉⢿⣁⣀⡤⣶⣋⣥⢋⣴⡇⣿⠛⢤⠸⣄⣼⡉⡼⢾⣿⣟⢧⠙⢦⣀⠈⠓⢦⣄⣀⠀⢻⠀⢰⡇⣧⣻⣿⣸⣟⣻⣶⡄⠀⠀⠀ ⠀⠀⠀⢸⡿⢗⣫⠞⠁⠃⡟⡾⠃⣠⠤⠾⢧⣀⠉⠳⡟⠚⠹⠽⢻⣿⡷⣆⣮⡁⡏⣧⢿⣿⣼⣌⣟⠒⠚⠛⠒⠚⣣⡼⠛⠋⣰⠋⢹⢹⡬⣧⠙⢿⣶⣋⣿⠀⠀⠀ ⠀⠀⠀⠈⢿⣏⠀⠀⠀⢸⣷⣏⡞⠁⠀⠀⠀⠈⠳⡄⠙⢦⡀⠀⠀⠀⢳⢸⣶⣷⡉⠁⣾⠙⡓⠚⠷⠤⠤⠤⠴⠛⠁⢀⣠⠞⠁⢀⡜⡯⡧⢹⠂⠀⢠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣧⡀⠀⣄⢻⣿⣇⠀⠀⡴⣶⣦⠀⢹⠀⢠⣿⣄⣀⠀⣼⣾⣿⣿⣟⣶⡟⠦⣤⣀⣈⣀⣀⣀⣮⠵⠖⠋⠀⠀⣠⢞⣜⡽⠃⠀⡖⣼⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣦⣻⣷⣽⢯⣧⡀⠳⢬⣡⡤⠏⠀⢸⣷⢻⣿⣽⣟⢹⡠⣼⣿⢋⣇⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣠⠞⣵⡿⠛⣁⠄⡄⡼⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣑⠛⢸⡳⠝⢿⣦⡀⠀⠙⢦⡀⠈⠉⠙⣱⡿⠉⢻⣿⠉⣦⣸⢹⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣡⡾⠋⠀⠀⠁⣠⣾⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⡈⢳⣄⠙⢿⣦⣄⠀⠙⢦⣀⠀⠁⠀⠀⢸⡏⣷⢯⡟⡎⢻⡖⠒⠒⠒⠛⠉⢉⣠⣴⡿⠋⣀⡠⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠀⠀⠉⠻⣷⣦⢤⣉⠓⠦⣤⣀⢸⠷⢻⠾⣽⢷⠼⢳⡀⠀⢀⣠⣴⡿⠟⠋⡀⠀⠃⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠒⣆⡉⠓⠮⣗⡦⣄⡈⢹⠀⢸⠀⠸⣎⣇⣈⣷⣾⠿⠛⢡⠖⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡀⠀⠂⠀⠉⠓⠯⣽⣓⣿⣴⣾⠿⢗⠋⠉⠀⠀⠀⠂⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣀⡠⠤⢤⡀⠉⠻⢷⣦⣄⡀⠁⠀⠀⠠⠉⠉⠁⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠠⠤⠀⠀⠀⠀⠈⠉⠳⠄⠨⢽⣿⣶⣤⣀⠀⠁⠀⠀⣀⣤⡶⣿⡿⠭⠄⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡴⠒⣲⡲⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠷⠿⠟⠛⠛⠋⠁⢀⣴⠒⠄⠀⠈⠁⠀⠀⢀⠈⠉⠉⠉⠉⠉⠿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢳⠀⣇⡇⢸⣤⠔⢦⠀⠀⠀⠄⠀⣐⣂⠀⢀⠀⣒⡀⠀⣀⠀⡞⢸⡠⠖⡢⡀⢀⡀⠀⢁⠁⢠⠀⠀⠀⠀⠀⠘⡶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⢀⡾⠀⠹⡇⡞⣧⢻⠈⡷⡜⣶⠹⡞⠁⠊⢱⡎⢪⡁⢳⡼⡅⢑⢧⢸⠀⣏⡇⢱⡇⠑⠐⠊⠅⢸⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣧⠀⣾⠸⡵⡇⠈⠀⣇⡇⣇⢠⡇⠀⠁⠀⠃⠘⠁⢸⣧⡃⠁⢸⢸⢆⠸⡇⣸⡇⠀⠀⣀⢀⠞⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢻⠀⡇⣇⢣⡑⠂⠜⠁⢣⡽⠊⠙⠲⠆⠀⠀⠀⠀⣸⢳⡳⡧⢦⢸⡘⠒⠷⠃⠱⣤⠋⠲⠋⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠀⠀⠀⠸⡰⠃⠸⣄⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠄⠀⠀⠀⠐⠒⠀⠀⢀⣒⣶⣀⣀⡤⠤⠶⠦⠟⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⣤⣀⣀⣤⠤⠤⠆⡤⠤⠤⣴⠒⠚⠑⠛⠁⠁⠈⠓⠋⠁⠀⠀⠈⠉⠑⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⣔⠒⢋⡁⡠⠴⠺⢧⣅⣀⠑⠶⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣺⠍⠠⣴⢚⢍⢁⠔⡊⠭⠄⠀⠨⢝⢲⣄⡈⣭⡲⡄⠀⠀⠀ ⠀⠀⠀⣤⢌⡗⢾⢢⠃⡇⣨⠝⠁⢀⣠⡤⠤⣤⡆⡆⢉⢺⡋⣼⡤⣄⠀⠀ ⠀⣠⠾⣧⣮⢳⠘⠄⢇⢡⣎⢀⠼⠋⣀⣠⣤⣀⡇⠇⡾⡸⢡⢋⣏⢾⠄⣀ ⠈⢾⣶⣣⡙⢦⡑⠌⢪⣞⢻⢨⣃⠀⢟⣰⠆⣼⠞⣮⢊⠔⣁⠎⢪⣓⣖⡛ ⠀⠀⡟⣂⣭⣒⣒⢡⡛⢃⡺⠔⢚⣋⣨⡴⠋⢘⣂⠛⡗⢉⡐⠊⠭⢾⡄⠇ ⠀⠀⢸⡗⠦⠄⠒⠠⣿⠲⢄⠴⡟⣄⢳⣓⣢⣧⠏⢀⣞⠂⠀⠐⢒⢪⠏⠀ ⠀⠀⠀⢗⡫⣍⠩⠔⢿⡳⡌⡙⡀⠚⠁⠵⠋⡕⡠⢟⡑⠤⢩⡭⣛⡎⠀⠀ ⠀⠀⠀⢸⡇⠱⡖⣈⠬⢛⢦⢠⡧⢚⢧⠑⡪⡚⠋⠂⢌⣐⣲⡕⢿⠀⠀⠀ ⠀⠀⣾⡾⠓⠿⡄⠷⢒⢗⠝⠼⡥⣕⣶⢽⣟⡬⠆⢵⠲⢀⠾⠏⡽⢿⡆⠀ ⠀⠀⠘⢆⢦⣷⠅⠀⡄⡃⡵⣄⣸⡿⣧⡧⠬⠋⠩⠧⠒⠁⣪⠍⢁⡞⠁⠀ ⠀⠀⠀⠈⠳⡺⢟⢦⡉⠢⡉⠹⠃⣯⣧⣡⣀⣀⠀⠄⣢⠞⠁⣡⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣅⠉⡳⢮⣔⠠⡟⠟⣓⣣⣠⢔⠋⢁⡡⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⡀⢙⠲⢅⡈⠉⠃⠓⠋⠉⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠨⠠⠄⠈⠀⠘⠷⠦⠤⠖⠛⡁⠄⠐⠒⣒⠒⠀⠲⡀⠀⠀ ⠀⠀⠀⠀⡄⠀⠜⢠⣜⠋⠀⠐⠢⠢⠲⢢⠔⣧⢡⢡⠀⠰⡄⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⡄⠀⢨⡈⡩⡒⠑⠉⠒⠀⠀⠜⠆⠿⠓⠊⠒⠓⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠈⣀⣀⡀⢀⡈⠀⠠⠤⠤⠤⠒⠂⠤⠀⠤⠐⠀⠒⠒⠉⠁⠀⠀