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