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