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