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