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