点阵图

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⢀⠀
⠀⠀⢘⢠⡑⠆⡌⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⠱⢌⡡⢌⠀⠀
⠀⠀⣈⠒⢌⡒⠡⠆⡅⠂⠌⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡁⢄⠲⢁⡑⠆⣌⠂⠌⠀
⠀⠀⠀⢍⡒⢌⠱⠀⠄⠃⡐⠠⠐⢈⠠⢀⠐⢀⠂⠰⣀⠂⡐⠠⠀⠄⠠⠁⠄⡁⠄⠃⡐⠠⢍⡒⠤⠃⠐⠀
⠀⠀⠈⠐⢌⠢⡑⠌⠠⠁⠄⡁⠌⠠⠐⠢⠌⠠⢈⠐⠆⡐⠠⢁⠸⢀⠁⠌⡐⢀⠂⡁⠄⣉⠒⢌⡑⠠⠁⠀
⠀⠀⠀⠈⠢⡑⠌⠠⠁⠌⡐⢀⠂⡁⠌⠑⢢⠁⠂⣈⠃⠄⡁⠤⣉⠠⢈⠐⢀⠂⡐⢀⠂⠌⢉⡒⠠⠀⠀⠀
⠀⠀⠀⠀⠁⠄⠂⡁⠌⡐⠠⢀⠐⢀⠂⡁⠣⠄⡁⠠⡍⠐⠠⣑⠠⠐⠠⢈⠠⠐⢀⠂⠌⢀⠂⠄⠂⠀⠀⠀
⠀⠀⠀⠀⢁⠂⡁⠄⠂⠄⠂⠄⡈⠠⠐⠠⢉⠂⠄⡑⠢⢁⠂⠤⢁⠂⢁⠂⡐⢈⠠⢈⠐⠠⢈⠠⢈⠀⠀⠀
⠀⠀⠀⠀⠂⡐⢀⠂⡁⠂⡁⠂⠄⡁⠌⡐⠠⢈⠐⢀⠃⠄⡈⠐⠠⢈⠠⠐⢀⠂⡐⠠⢈⠐⠠⠐⠠⠀⠀⠀
⠀⠀⠀⢈⠐⢀⠂⡐⠠⠁⠄⣱⣾⢿⣳⣄⠂⠄⡈⠠⢈⠐⠠⢁⢂⣾⣟⣿⢦⠐⢀⠁⠄⡈⠐⢈⠐⠠⠀⠀
⠀⠀⠀⠂⠌⠠⠐⠠⢁⠈⡐⢸⣯⣿⣻⠏⢀⠐⠠⢁⠂⠌⠐⠠⠘⣿⡾⣽⡿⠀⠂⠌⡐⠠⢁⠂⠌⡐⠀⠀
⠀⠀⠀⡈⠠⠁⠌⡐⠠⠐⢀⠂⠌⠉⡁⠐⠠⢈⠐⠠⠐⠠⢁⠂⡐⠈⠉⠃⠠⢈⠐⠠⢀⠂⠄⡈⠠⢀⠀⠀
⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠀⠈⠐⠠⢀⠁⡂⠄⣈⡐⢈⡐⠠⠐⠠⠁⠌⠠⠁⠂⠈⠐⠀⠈⠐⠀⠁⠂⠀⠀
⠀⠀⠀⠂⡁⠌⠠⢁⠂⠰⢀⠂⠄⡁⠂⡐⢀⠺⢡⢍⡣⢍⡳⠈⡐⢈⠠⠁⠠⠐⢀⠂⠄⡁⠂⡐⢀⠂⠀⠀
⠀⠀⠀⠐⠀⠂⠁⠀⠈⢀⠀⡀⢀⠀⡐⢀⠂⠌⡐⠎⡜⠂⠄⡐⢀⠂⢀⠀⠄⡀⢀⠈⠀⠀⠁⠄⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠠⠁⠌⠠⠐⢀⠂⡐⢀⠂⠌⣀⢤⣜⢣⣬⣐⠀⠂⠌⠠⢈⠐⢀⠂⠌⠠⢁⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠈⠠⠁⠌⠠⠐⠋⠶⢜⠲⠍⠂⠠⠀⠄⠨⠛⠼⠲⡙⠆⡈⠠⢈⠠⠁⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠌⡐⢀⠂⠄⡐⢈⠐⢈⠠⢁⠂⡐⠠⢀⠂⠄⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠂⠌⠠⠐⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⢶⡶⣶⢶⡶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⢶⡶⣶⢶⡶⣦⣤⣀⣀⠀⠀⠀⠀⠀
⠀⢀⣴⡶⣿⣻⢯⣟⣳⣯⡿⣽⢯⡿⣝⠣⡉⢄⠃⡜⠢⠡⢍⡘⢙⠺⢿⣽⢯⡿⣽⣳⢯⡿⣽⣻⢷⡶⣄⠀
⢀⣾⢯⣟⡷⣯⣟⡾⣿⣿⣽⢯⠛⢠⠂⡅⢌⠢⡑⢄⠃⣑⠢⠌⠢⡑⢌⡘⠿⣽⣿⣿⢿⣽⣳⢯⡿⣽⣻⢆
⢸⣯⣟⡾⣽⣳⢯⣟⣯⣿⠛⠠⠜⠢⡘⠠⠆⡑⢌⠢⡉⠤⡑⢌⡑⢌⠰⢈⡰⠙⢿⣾⣻⢾⣽⣻⣽⣳⢯⣿
⢾⡾⣽⣻⢷⣯⡿⣾⣳⡇⢌⡑⢌⡑⢨⠑⠢⣁⠆⡑⠌⡒⢨⠐⢨⠠⡑⠢⠄⡍⠒⣯⣟⡿⡾⣽⢾⣽⣻⢾
⢸⣽⣳⢯⣟⡾⣽⣳⢿⣌⠢⠌⡂⢌⠢⢌⡑⢄⠢⢅⠒⡁⠦⡘⢁⠒⢌⡑⠒⠤⡙⣿⢾⣽⣻⢯⣟⡾⣽⣻
⠸⡷⣯⡿⣾⣽⣳⣯⣿⠤⡘⢠⣁⣶⡷⣶⣌⠠⡑⠢⡑⢌⠒⢌⣶⣽⣶⣤⢉⠒⡈⢿⣾⣳⢯⣟⡾⣽⣳⠿
⠀⢻⣳⣟⡷⣯⣟⡾⣝⠠⢌⠢⣸⣿⣽⣻⡾⢠⢁⠃⡌⠢⣉⢸⣟⡷⣟⣾⠠⡑⢌⠹⣾⣽⣻⢾⣻⢯⣟⠃
⠀⠈⢻⢾⣽⣳⢯⡟⢡⠘⢠⠑⣸⡿⣾⣽⣻⠠⢌⡘⢠⠃⢤⢸⣿⣻⢯⣿⠐⣈⠢⢑⠛⣾⣽⣻⣽⣻⠊⠀
⠀⠀⠀⠙⠚⢉⡃⠤⠃⣌⠡⣘⢈⠛⠷⠏⣁⠒⠤⡈⢆⠸⠠⢌⠛⠽⠛⠢⡘⢠⠑⢌⠰⢁⠍⠛⠚⠁⠀⠀
⠀⠀⠀⠀⠠⣁⠌⠢⡑⠤⡑⠤⣈⠜⢀⠒⠈⠈⡐⠈⢀⠁⠌⠠⠘⠠⢉⠢⡁⠖⡈⠆⡑⢌⡐⢃⠀⠀⠀⠀
⠀⠀⠀⠀⠰⢠⠘⠡⢌⠒⠤⢁⠀⠠⠀⠄⣈⣴⣴⣶⢶⡶⣤⣁⠂⡐⠠⠀⠌⠢⣁⠃⡜⠠⢌⠢⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠆⡜⢁⠆⡉⢀⠠⠈⡐⠈⡀⠌⣿⣳⣯⡿⣽⣟⠏⠀⠠⠐⠈⠠⢀⠠⠑⠤⣉⠢⡐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⢀⠃⡜⠀⠠⠐⢈⠠⠐⠠⢀⠈⠛⣾⣽⠟⠈⡀⠌⠠⢉⠀⡁⠄⡐⢨⠑⢠⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠐⠠⠁⠂⡘⠠⢐⠘⠤⠀⠌⢀⠀⡀⠠⠐⠠⢀⠇⠢⠐⠄⠂⢀⠢⠘⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠁⡀⠉⢀⠂⡐⠠⣰⢦⡁⠐⢀⠂⠈⢁⠀⠂⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⢁⠂⠠⣤⠾⣭⡻⣵⢎⡠⠀⡁⠂⡈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡟⢦⡝⢮⡛⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⣙⡳⢼⣣⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⣀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣎⡳⢬⡳⣬⢳⢬⡳⣬⢳⣬⣹⣙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢎⡳⡜⠃⠉⠀⠀⠀⢸⠮⣅⠀⠀⠀⠈⢈⠓⢮⣙⡲⢄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣣⣝⠺⠁⢀⠂⠁⠌⠠⠁⢸⡓⡇⠀⠌⠠⠁⠂⠠⢀⠈⠙⢮⣱⢆⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣔⢣⠾⡑⠠⠀⠄⠂⠠⠈⡀⠐⠀⢺⣍⡇⢀⠂⡐⢠⢈⡀⣄⣈⣀⡓⢮⡺⣱⢇⡄
⠀⠀⡠⡔⢦⣋⡗⢮⣱⢎⡛⠶⣴⠲⣼⠲⣇⡗⢾⣸⢋⡟⡺⢴⣍⢯⡹⣍⡳⣭⣙⢦⡝⣬⣝⠳⣝⢮⡺⣱
⠀⢮⡱⢏⡳⣬⣝⠳⣜⠮⣝⡛⢦⡟⢦⡛⡦⣝⠳⣬⡛⣼⢹⢲⢎⡳⣝⠲⣝⠦⣏⠾⣱⢇⡮⣝⢮⡲⣝⢲
⠀⢧⣝⡺⣱⢇⡮⣝⢮⣹⠲⣝⠳⣼⢣⣏⡳⣍⣛⠦⣝⡲⣝⢺⣜⠳⢮⡝⢮⣓⢮⡳⣍⠾⣱⢎⡳⣝⢬⣫
⣀⠳⣬⠳⣍⠾⣱⢎⣷⡾⣿⣻⢿⣶⣝⠦⣝⡲⢭⡛⣼⢱⢏⡳⢬⣛⠶⣽⡷⣟⣷⢿⣮⡳⣍⠾⣱⢎⡳⢼
⣍⣛⠶⣛⢼⠳⣍⣾⣷⠏⠁⠉⠙⢺⣽⣗⠧⣝⡣⡟⢦⣛⢼⣩⣓⢮⣿⢿⠙⠉⠉⠙⢾⡿⣮⠳⣍⠾⣩⢳
⠮⣍⡳⣍⠾⣙⢮⣟⣾⠀⠠⠁⠄⣸⣿⢾⡱⢧⡝⢮⣓⢮⡳⢼⢬⡳⣯⣿⠀⢀⠂⠄⣸⣿⢧⡛⢮⡳⡝⠚
⠀⠀⠀⠀⠀⠀⠀⢻⣟⡿⣦⣶⢶⡿⣯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⢷⣦⣴⣶⣿⢯⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠯⠟⠿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠽⠯⠟⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡠⣔⠲⣔⢫⣝⢲⠲⣴⢠⡄⡀⠀⠀⠀⠀⠀⣀⢤⡰⢲⣔⢫⡓⢧⡒⡖⡤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⢎⡧⣓⠮⣝⢮⡳⢬⡏⣝⢦⡛⡴⢏⡦⢄⢀⢤⡚⣼⠲⣭⢳⢬⡳⢭⡳⣍⡗⢧⡇⡟⣤⠀⠀⠀
⠀⢠⢎⡳⢏⡶⣍⡻⢬⡳⣙⠾⣸⢣⡗⣭⡛⢮⡱⢏⡮⣓⡝⢦⡟⢦⣛⢼⣙⠶⣙⢦⣏⡳⣜⠧⣇⡟⣢⠀
⢠⡓⢮⡝⢮⣱⢮⣙⠧⣝⢮⡳⣍⠾⣸⢥⣏⡳⣝⢮⡱⢏⡼⢳⣜⠳⣎⠷⣼⢹⣙⠶⣬⡓⣮⣓⠮⣕⢏⡦
⠶⣍⡗⣞⢣⣝⠲⣍⡗⣮⠳⣍⢮⡓⣏⠶⣬⡓⢮⡳⢝⢮⡓⢯⡼⣙⢮⡓⣮⡓⢮⡓⡧⣝⢦⣍⡻⢬⡳⣕
⣛⠦⣝⢮⡹⢬⣛⠶⣙⢦⡟⣬⠳⣝⢮⡓⢧⣝⣣⡝⢮⡳⣍⠷⣼⢩⡶⣙⢦⡝⢧⣏⡳⢎⡳⢼⣩⠳⣝⢦
⣭⡛⣬⠳⣍⡗⡮⣝⢭⠶⣙⢮⡹⢮⡱⢭⡳⣬⠳⣼⠳⣝⢬⡳⢎⡳⣼⢩⡞⣼⠳⣬⣙⠾⣩⡳⢼⣙⢮⡲
⠰⣍⢧⡻⢬⡓⡗⢮⡳⣝⢭⠶⣹⠶⣭⠳⣝⠦⡟⢦⣛⣬⠳⣝⢺⡱⣎⡳⢎⡧⣛⠦⣭⣓⠧⣝⡺⢬⡳⢭
⠈⢮⡳⢝⢮⡹⣍⡳⣝⢬⡳⣝⢮⡓⢮⡝⢮⡳⢭⣓⠮⣼⣙⢮⡳⡝⢦⣏⡳⣕⢯⣙⠶⣍⡛⠶⣭⠳⣝⠎
⠀⠐⣝⢮⡳⢝⡲⣝⠮⣓⢭⡲⢧⣝⠳⣎⠷⣙⠾⣬⡛⢦⣝⠲⣝⢮⡳⢬⣓⢮⡳⣜⠳⢮⣹⠳⢮⣹⠎⠀
⠀⠀⠈⠶⣙⢮⡵⢎⡳⣭⠳⣝⡲⣼⣙⢮⡓⣏⡳⢦⡏⡗⢮⡝⣮⢲⢭⣓⢮⡳⣍⢮⣛⠳⣬⡛⠾⠌⠀⠀
⠀⠀⠀⠈⢝⡲⣝⢺⣙⠦⡟⢦⡝⡦⣝⡲⢭⣣⡝⡶⣍⣏⡳⢼⢣⡛⠶⣍⡶⣹⢬⡳⣜⡛⢦⣝⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠹⢬⣓⠮⣝⡺⢣⣝⠳⢮⣙⡳⢼⣸⢓⢮⡲⢭⡳⣝⠺⣝⡲⣕⢏⡶⣙⢦⣛⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠸⣹⠲⣭⡛⣬⡛⠾⣬⡹⠶⣍⠾⣱⢭⡳⣝⢪⣝⡲⣝⠮⡳⣕⢏⡾⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣝⢣⣝⠳⡶⢭⡳⢎⡟⣼⠲⣝⢬⡳⣬⣓⢮⡳⣝⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣝⣬⠻⣜⣣⣝⡺⣱⢇⡟⣬⠳⣝⠦⣝⡲⡝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢦⡳⢬⡳⣍⠾⣱⢫⡝⣎⡳⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢝⢮⠳⣍⠾⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠠⠁⠌⠠⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠐⠠⠁⠂⠌⢀⠂⡐⠠⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠌⠠⢁⠠⠐⠠⠁⠐⠈⡀⠄⠠⢀⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠄⠁⠌⠐⠠⠀⠄⠂⡐⠈⠠⢁⠠⢀⠁⠠⠈⠐⠠⠀⠂⢁⠐⢀⠂⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⢀⠁⠄⡁⠂⠄⡁⠐⢀⠂⠄⠈⠠⠀⠄⠠⠈⡐⠈⠠⠁⠠⠁⠂⠈⡀⠄⠂⢈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠈⡀⢀⠂⠐⠀⠁⠀⠀⠀⠀⠄⠀⠀⠁⠐⠀⠌⠐⠠⠁⠂⠌⠐⠀⠄⡈⠀⠌⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡁⠂⠄⠂⠈⠀⡀⠄⠀⠂⠀⠂⠀⠀⠂⠀⠄⠈⢀⠂⡐⠠⢈⠀⠂⡁⠐⠀⡁⠂⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠁⢀⠁⠂⠄⠂⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠄⠐⠀⠀⠀⠀⠁⠀⠠⠀⠀⡀⠀⠀⠐⠀⠀⠂⠀⠀⢈⠐⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠐⠀⠠⠀⠀⡀⠄⠂⠈⠀⠀⠄⠀⡀⠀⢀⠈⠀⠀⠂⠀⠈⠀⠠⢀⠁⠀⠀⠀⠀
⠀⠀⠀⢀⠈⠀⠀⠄⠂⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠂⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠂⠀⠀⢀⠈⠀⠀⠀⠀⡀⠄⠂⠁⠀⠄⠐⠈⠀⠀⠀⡀⠁⠀⢀⠀⠀⡀⠁⠀⡀⠀⡀⠀⠀
⠀⠀⠀⠀⡀⠁⠀⢀⠈⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠐⠀⠀⠀⠠⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⠀
⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠄⠈⠀⠀⡀⠄⠀⠂⠀⠀⠀⠁⠀⠀⠂⠀⠐⠈⠀⠀⠠⠀⠀⢀⠀⠀⠁⠀⡀⠀
⠀⠀⠀⠀⠠⠐⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠠⠀⠁⠀⠂⠀⠄⠀⡀⠂⠀⠀⠐⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠁⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠠⢁⠄⠠⢐⠠⢁⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⢈⡐⠂⠄⠃⡄⠌⡐⠠⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠂⠄⡡⠘⠠⠄⠒⠠⢁⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠑⠂⠤⠘⢰⠎⣹⢑⡂⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡄⠢⠐⠄⡂⠄⠠⢀⠀⢀⠢⣄⡘⠠⢁⠌⠓⡼⢁⠮⡁⠂⡄⠀⠀⡀⠄⡠⠐⢠⠂⠔⠠⢀⠀⠀
⠀⠀⣀⠃⠄⣁⠘⠠⡐⢈⠁⡂⠐⠮⣑⠦⣉⠆⠂⠤⠁⠀⠉⠐⢠⠁⠄⠂⠅⠂⡔⠠⢁⠂⠌⡠⠑⠂⠄⠀
⠀⠀⠀⠌⡐⠠⢈⠁⡄⠌⡐⢈⠁⡓⢬⡑⠎⠁⠌⡐⠀⠀⠀⡑⠂⡸⢸⢙⠢⣅⠠⢁⠂⠌⡐⠠⠌⠂⡈⠀
⠠⢀⡁⠒⠠⢁⠌⡐⢠⠲⢤⣁⠔⠠⠂⠄⠀⠀⠐⠠⢀⠀⡐⠠⠁⢘⠣⣎⡱⠆⡐⠂⠌⡐⠠⢁⠂⡁⢄⠠
⠐⢠⠀⠃⢌⠠⡐⠠⢏⡜⠲⣌⠂⠁⠈⠐⢀⠂⡁⠂⠄⡐⠠⠁⠀⠀⡉⠠⢁⠂⠤⢁⠒⠠⢁⠂⠌⡐⠠⠐
⠀⠂⠌⡁⢂⠰⢀⢁⠢⢉⠓⠌⡀⢀⠀⠀⠠⠐⠠⢁⠂⠄⡁⠌⡀⠑⠠⣁⠦⣌⡐⠠⠌⡐⠂⡉⠐⠠⢁⠊
⠀⠀⠁⠀⠊⠐⣀⠂⠔⠠⠌⡐⣠⢅⡌⠀⠁⠌⡐⠠⢈⠐⠠⠐⠀⠀⠰⣍⠲⢆⡍⢐⢀⠂⢡⠠⠉⠂⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⡐⢬⢃⠦⣑⠆⡀⠂⠀⠁⠄⠠⠁⠈⠐⠡⠘⠠⠛⠤⢉⠀⠈⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠄⠊⠼⠑⠎⡐⠠⣁⠀⠀⠌⡐⠀⠀⠀⠁⢊⠰⢈⠐⢠⠈⠄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢠⠀⢅⡘⢈⠐⠨⠐⠠⢏⡢⢝⢃⠆⠤⠁⢄⡰⢊⡇⠦⡐⠈⡄⠨⢐⠀⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢉⠠⢈⠄⣀⠂⡉⠐⠌⡘⠢⣍⠲⢍⠐⢠⠊⠰⣉⠞⣠⠗⠠⢁⠄⣁⠂⠌⡀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠌⡐⢠⠐⠠⠄⡁⠊⡐⠠⠁⠄⡁⠂⠈⠠⢈⡐⢈⠁⠃⠄⡑⠂⡐⠠⢈⡐⢀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡐⠠⠂⠌⠰⢀⡁⢁⠂⠅⠊⡐⠀⠁⠀⠁⠂⠄⡂⠁⠎⡐⠠⢁⠂⣁⠂⠄⡌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠄⡠⢁⠌⡐⠁⠂⠀⠀⠀⠀⠈⠐⠠⢉⠐⠠⢁⠂⠌⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡁⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣶⡿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⢿⡷⣦
⣿⣳⢵⠢⣌⠱⢛⠿⣷⣤⡀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣠⣴⡾⡟⢋⠦⣑⢦⣛⣿
⣿⢯⣀⠛⣦⡙⢬⡘⡑⠯⣿⣦⣄⠀⠀⠸⣟⣧⠀⠀⠀⠀⢠⣿⡻⠁⠀⢀⣠⣾⠿⣉⡑⠢⣍⡲⠮⡑⢬⣿
⣿⣻⠤⣙⠠⡝⢶⣨⢁⠳⡮⢱⢿⡷⣄⠀⠙⣯⣷⡄⠀⣰⣿⡏⠁⢀⣴⣿⠟⢩⡶⢠⢍⡳⢎⡑⠦⣉⢾⣻
⢹⣯⡗⢠⠓⣌⠲⢩⢾⣹⠂⡇⢬⡙⢿⣳⣄⠈⣷⢿⣴⢿⡓⢀⣴⣿⡛⠢⡜⣁⢞⡳⠞⣉⠆⡍⠲⣈⣿⣽
⠸⣷⢿⢠⡙⢠⠓⣌⠢⢽⣸⢠⠃⡜⢨⠛⣽⣧⣟⡿⣾⣻⢧⣾⠟⡡⢌⡓⠤⣃⠾⣉⠲⣁⠞⢠⠓⣬⣿⠾
⠀⢿⣻⡞⢩⡓⠟⢴⠛⠶⢭⣦⡙⢤⠓⢬⡑⢻⡾⣟⣷⢿⣻⠃⡜⢡⠒⠬⣑⢮⡗⠮⡓⢮⠚⢏⡛⣾⢯⠇
⠀⠘⣯⡿⣅⢌⡓⢢⢙⠒⠦⡐⢯⡰⢘⠢⣌⠃⣽⡿⣽⣻⠅⡜⢰⠃⡼⣱⠏⡒⠤⡓⢌⠦⡙⢢⣽⣟⡟⠀
⠀⠀⠘⣿⣻⢶⣌⡡⢎⡸⢁⠎⡲⢹⢎⠱⢠⡙⢸⣿⣳⣿⠘⢤⠓⣜⢲⠃⠦⣉⠲⣁⠎⣰⣥⣿⡾⡝⠀⠀
⠀⠀⠀⠘⠯⣿⡾⣿⣶⣵⣮⡶⣅⣎⣾⣱⢒⢬⣙⣷⢿⢧⣘⢢⣱⢮⣣⣼⣱⣮⣶⣮⡿⣟⡷⡯⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠉⢑⣛⣹⣿⣻⢷⠿⠿⣟⡯⣟⣿⣻⢟⠿⡟⣿⣽⢯⣟⣞⣓⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⡛⣙⠢⢍⡰⢌⡳⢎⣱⢿⣳⢯⡘⢳⣌⡢⢄⡋⡍⠻⢽⢿⣶⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⢿⠝⣨⠒⡡⠎⡸⣠⣝⠚⣡⠒⢬⣿⣻⢷⢈⠣⣘⠳⣦⡑⢌⡓⠢⡜⠸⢷⡿⣦⡀⠀⠀⠀
⠀⠀⠀⢠⣿⣏⠇⣜⣠⢣⣕⢮⣓⠏⣠⠙⢤⣉⣿⢯⣟⡿⣎⠱⢌⠲⢌⠻⣦⣥⡓⣌⡓⣂⠿⣯⣷⠀⠀⠀
⠀⠀⠀⢸⡷⣏⠛⡱⢉⡋⢬⡑⢽⢦⡁⠞⡰⣼⡯⣿⢾⡿⣻⡜⢠⢍⢢⡟⠆⠦⣙⢩⡙⢍⢻⡷⣿⠀⠀⠀
⠀⠀⠀⠘⣿⣻⣇⡑⢎⡸⢰⢈⠆⣳⣬⠣⣽⡿⠁⠘⠛⠀⠹⡿⣅⢪⡾⢁⠏⡲⢌⡰⢌⢢⣿⣽⡛⠀⠀⠀
⠀⠀⠀⠀⠘⢟⡾⣧⣆⠱⢌⡸⢰⢁⡾⣿⡛⠀⠀⠀⠀⠀⠀⠘⣿⣻⣄⠋⡴⢁⠦⣁⣮⣿⣳⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠳⣿⣻⣦⣵⣾⢾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣻⣴⣮⡷⣿⡽⠞⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡁⢌⡐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⠂⠆⣈⠢⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡌⠑⠢⢄⡁⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠒⠤⢉⠢⡐⢠⢁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢌⡐⠢⡐⠌⡠⢌⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢄⡀⢄⡀⢄⡀⢄⡀⢄⡀⢄⡀⠃⡜⠠⢠⢁⠢⢁⠆⠤⣈⠐⠂⡄⢠⠀⡄⡀⢄⡀⢄⡀⢄⠠⢀⠀
⠀⢠⠁⠆⡈⠤⢐⠂⠌⡠⢐⠂⠌⡠⢈⡑⠠⢑⠂⢌⠰⢈⠰⢐⠠⢉⠒⠠⠃⢌⠠⢌⡐⢠⠂⠌⡐⠌⠂⡄
⠀⠀⠘⢠⢁⠒⠤⡘⢠⠁⠆⡘⢠⠁⠆⡄⠃⠆⡘⢠⠘⢠⠁⠆⡁⠆⡌⡑⢈⠂⡌⠠⢄⠡⠌⡂⢅⡘⠐⠀
⠀⠀⠀⠀⠈⠐⠡⣀⠃⡘⢠⠁⠆⡘⠰⠠⢉⠂⡅⠢⡘⢠⠘⢠⢁⠒⠤⢈⠢⠑⢠⠃⡂⠅⡒⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⢌⠂⠜⢠⢁⠃⡜⢠⠘⠠⣁⠢⢁⠜⠠⢌⡐⠢⢌⡐⠉⡄⠢⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⢁⠂⡜⢀⠢⠌⡡⠠⠌⡂⠔⡁⠆⡠⢁⠆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢠⠑⠠⢌⡐⠂⢅⡘⢐⠨⢐⠁⠆⣁⠊⡠⢁⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⠠⢌⠑⠠⢄⡉⠤⣀⠃⢌⠂⣉⠰⠠⢁⠆⡌⡐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠌⡁⠆⡌⡑⠂⠌⡐⢠⠘⢠⠘⢠⠐⡁⠎⡐⢠⢁⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠌⡂⠅⡒⠠⠂⠍⡐⠁⠂⠈⠐⢈⠢⠘⢠⢁⠢⢁⠤⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠰⢀⠃⡄⠃⡜⠀⠁⠀⠀⠀⠀⠀⠈⠘⠠⠂⢅⠊⡐⠌⠢⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⡘⢠⠑⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠌⡠⠃⣁⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠄⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠄⠂⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠠⠀⠂⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡐⠈⠀⠌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠠⠁⠀⠄⠁⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠂⠐⠈⠀⠂⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠀⢀⠂⠌⠐⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠂⡁⠄⡐⠀⠠⠀⡐⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠂⠄⡁⠄⠂⠄⠠⠁⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠐⠀⠂⢈⠐⢀⠂⡁⠂⠁⠀⠌⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠂⠈⢀⠀⡐⠠⠁⢀⠂⠈⠀⠠⠀⠄⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⡀⢀⠀⡀⢀⠀⠠⠀⠄⠂⢈⠠⠐⠠⢀⠁⡀⠄⠀⠄⡀⠂⠀⠌⠀⠁⡀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠠⠀⠂⠈⢀⠐⠀⡐⠀⠐⠈⠐⠀⠠⠀⠠⠈⢀⠀⠄⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⡀⢀⠂⠀⡈⠐⠈⠀⠌⠀⡀⢁⠠⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣌⠳⣌⠣⡆⡀⡄⡄⣄⠠⣄⠠⡄⢠⡘⢦⡙⢦⡙⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢⣝⣶⢿⡶⣙⠦⡓⢬⡓⢬⡓⢬⡓⢬⡓⢬⡳⣾⢷⣮⡓⢼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⢾⣯⡟⡰⢍⡲⢍⡓⢬⡓⢬⡓⢬⡓⢬⡓⢬⡙⣿⢾⣡⠓⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠞⣰⢌⡣⢇⡝⢢⡝⢢⡝⢢⡝⢢⡝⢢⡝⢢⡝⣸⠣⣬⡙⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢡⢎⡱⢎⡼⣿⣻⠱⣌⠳⣌⢻⣽⡷⢌⡳⢬⡑⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢎⡱⢎⡴⠃⡍⣘⣦⣝⡦⠙⠤⡓⠮⣑⠦⣍⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⢍⡲⢁⠎⡰⢈⢿⡻⢍⡘⠰⢈⠳⣌⠳⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡙⢎⡰⢁⠾⣤⣬⠶⢍⠢⣍⠳⣬⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⠣⣝⡿⣶⣱⢎⡴⢤⢤⡒⢦⣙⣦⡿⣾⢰⢋⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡳⢌⡳⣬⠛⡷⢯⡿⣽⣻⢳⡿⣟⣟⠳⡟⢥⡞⣸⢰⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢎⡲⢍⡲⣙⢮⡙⠦⣿⣽⣳⣏⡻⣽⢯⣻⡕⢎⡳⣝⠢⣍⡚⡔⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣌⡲⢍⡲⢅⣯⡓⢬⡓⣿⠾⣽⢮⣙⣯⡿⣽⣏⠲⣅⢯⡓⢦⡙⢬⡓⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣤⡙⢦⡙⢦⢣⣝⢦⣙⢫⡛⣯⡓⢬⣳⢟⠣⡏⡜⣦⠟⡬⡓⢬⡓⣜⢢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢤⡙⢦⡙⢦⡓⢼⡣⣌⡓⢬⡃⣏⠣⡝⢬⡓⢬⡓⡧⣝⠢⣝⠢⡝⢤⡋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢍⡶⣝⠳⢭⡳⣝⢦⣙⠦⣙⠢⡝⢬⡓⢬⡳⣜⠳⡎⡟⠮⣝⢎⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢦⡑⠦⡙⠦⡑⠮⣑⠯⣶⣉⠳⣜⠣⣜⡳⢝⣨⠓⢬⠃⠗⣬⢪⣑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡙⢦⡉⠒⢌⠰⢈⡑⢪⡑⠶⡍⠓⠂⠙⢮⡙⠦⡁⡜⢠⡘⠰⢠⠓⣬⢁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢍⡲⢌⡑⠢⣉⠢⢌⠢⣍⡓⠀⠀⠀⠀⠱⢌⡓⠄⠦⡁⢌⡑⢢⡙⢦⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢍⡲⢌⡁⠆⣘⢠⡜⢢⡍⠀⠀⠀⠀⠘⢢⡝⣠⠃⡌⠢⣌⠲⢍⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢉⡳⢍⡲⠬⠃⠀⠀⠀⠀⠀⠀⠀⠸⠡⡝⢬⡓⠬⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡠⣄⠦⡢⢤⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡠⡔⢦⣠⠀⠀⠀
⠀⠀⢸⢱⢎⡳⣝⠶⣍⠾⣱⢒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣔⢎⡧⣝⡲⣝⢮⡳⢬⣛⠀⠀
⠀⠀⢘⡺⢼⣙⢮⡓⣮⠳⣍⡾⣓⠮⣜⢣⠆⡴⣀⠦⣐⢤⠂⣤⢰⡹⢬⣛⣬⠳⣕⠮⡵⣎⠧⣝⠳⢮⠀⠀
⠀⠀⢨⣝⡲⢭⠶⣍⢧⡻⢬⣓⠮⣝⡎⡳⢸⣁⠮⣑⠎⢦⣙⠢⣝⢼⡓⢮⡲⣝⢮⣹⢲⣍⡳⢮⡛⣞⠀⠀
⠀⠀⠰⢮⣙⢧⣛⣬⠳⣝⠺⣬⡛⢦⡓⣍⠲⢬⡑⠮⣘⠣⡬⣑⢎⡳⣍⠷⣙⢮⠳⣬⢳⡬⣝⡲⣝⠮⠀⠀
⠀⠀⢘⡳⢬⡳⢼⢬⣛⣬⡛⡦⣝⡳⣍⠦⣙⠲⢌⡳⢌⡓⠦⣃⠮⡵⢮⡝⣭⢺⣙⠦⡟⣴⢣⣝⢮⣹⠀⠀
⠀⠀⢨⣝⢣⡟⣺⠲⣍⠶⣍⡳⢧⣝⠦⡓⢬⣙⠢⡕⢎⣡⠓⣬⢱⣏⣶⣙⠶⣹⢬⣛⢼⢣⡛⣬⠳⡼⠀⠀
⠀⠀⠰⣎⡳⣜⢣⡟⣬⣷⡾⣽⢷⡾⣿⣌⡓⢬⡑⢎⡣⢬⣙⢢⣟⣾⣳⣟⣿⣻⢶⣯⡾⣱⡝⢮⣹⢚⠀⠀
⠀⠀⢘⠦⣝⣮⡿⣽⣻⣗⡿⢯⡿⣽⡳⢯⣙⢦⡝⢦⣝⠲⣬⡛⣼⠳⣟⣾⣳⢯⣟⡾⣽⢯⣟⡷⣮⣹⠀⠀
⠀⠀⣨⣟⡿⣽⣻⠷⣟⡾⣽⢻⣙⠧⣝⡲⣝⠺⣜⢳⢬⣛⠦⣝⠦⡟⣬⢣⡟⢿⡾⣽⢯⣟⡾⣽⣳⢯⡀⠀
⠀⠀⠘⠽⠻⠗⠯⠟⠋⣙⢦⣛⢬⡳⢧⡝⢮⡝⣮⣙⠾⣬⡛⣼⠳⣝⢮⡳⣜⠧⡉⠙⠛⠾⠽⠳⠯⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠲⣍⡳⣝⢲⢭⡳⣜⢣⡞⣵⠲⣝⠦⡟⣬⠳⣜⢮⡓⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠳⣬⡛⣼⢱⣎⡛⢶⣙⢮⡳⣜⢣⡟⣬⢳⣝⢲⠻⣬⠳⣍⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⣍⡛⡦⣝⢣⡟⣰⢏⡗⢮⡳⣕⠎⡳⣜⢣⡟⢬⡫⣝⡲⣛⠦⣏⡳⢥⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣐⠳⢮⣙⠧⣏⡳⣜⠧⡞⣭⠳⣕⢮⠁⠹⢬⣓⢮⡳⣝⠲⣝⢮⣹⠲⣭⠳⣥⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡰⣍⣛⠾⣸⢓⡮⡵⢎⡳⣝⠦⡟⣬⠃⠀⠈⡳⢎⡳⣝⢬⡻⢬⡳⢬⡛⢶⡛⢦⡗⡀⠀⠀⠀⠀
⠀⠀⠀⣐⠳⢮⣍⡳⢭⣺⢱⢏⡾⣙⢮⠳⣝⡒⠀⠀⠀⢙⠾⣱⢎⡳⣝⢮⣙⠾⣩⡳⣍⠷⣜⢣⡀⠀⠀⠀
⠀⠀⡰⣍⡻⠶⣬⠝⠚⠈⢝⡲⣕⢏⡾⣙⠶⠁⠀⠀⠀⠀⢛⡼⢪⣓⢮⡳⣜⠃⠃⠝⢮⡓⡮⣝⢲⠀⠀⠀
⠀⠀⠐⠃⠙⠁⠀⠀⠀⠀⠈⡳⢎⡳⣕⢫⠅⠀⠀⠀⠀⠀⠀⢵⡛⣬⠳⣍⠊⠀⠀⠀⠀⠈⠑⠋⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡫⣕⢮⠍⠀⠀⠀⠀⠀⠀⠀⠀⢭⡣⡟⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⢄⠠⡀⢄⠀⡀⣄⠒⣌⠢⡑⠦⡐⢄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢎⡱⢌⠲⡑⢬⠒⣍⠲⢤⡙⢤⡙⢌⡓⢌⡃⠖⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠓⢌⡢⢅⠎⡱⢌⠣⡜⢠⠓⠆⡜⠢⡜⢲⣼⢢⣍⡶⣥⢮⡼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣍⢢⡕⢪⡐⠇⡎⡱⢌⣳⢮⣱⣌⠓⣌⠲⢬⣛⡾⣱⣏⡾⣱⢮⣝⠶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡞⣧⡟⣠⣃⣬⣓⠶⣝⢯⣝⡾⣱⡞⣟⢧⡟⡾⣭⡳⣏⡾⣹⢏⡿⣼⣛⢮⡗⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣰⢧⡟⣧⣛⢧⡟⡶⣭⡟⡏⢷⢾⣱⢯⣝⢯⡳⣝⣳⠧⣟⢮⡗⣟⢾⣱⢧⢏⡿⣼⣛⠆⠀⠀⠀
⠀⠀⠀⢠⣏⡾⣱⢧⣏⡷⣝⣳⢧⠇⠠⢨⡷⣝⠾⣮⡳⣏⡯⣽⠀⢬⣗⢯⣏⡷⣝⠂⠠⣱⢧⣏⡿⠀⠀⠀
⠀⠀⠀⢸⣼⢳⣏⡷⢾⣱⢯⣝⠾⣤⣁⡾⣱⣏⡟⡶⣏⡷⣝⡾⣠⢾⣼⢳⢮⡳⣧⡌⣰⢏⡾⣼⢳⠀⠀⠀
⠀⠀⠀⠾⣼⢳⢮⣝⠓⠽⣺⢾⣹⢧⣏⡷⣏⠾⣹⢳⣏⡷⢏⡷⣏⡾⣼⣛⢾⣹⠶⣝⢯⡾⣹⢮⡻⠀⠀⠀
⠀⠀⠀⢸⢮⣛⡾⣼⣀⠂⣙⢾⣹⠾⣼⢳⡍⠐⠸⣻⢼⣭⡻⣵⢏⡷⢧⣏⡷⣭⡟⢾⡳⣝⢯⡾⠁⠀⠀⠀
⠀⠀⠀⠀⠻⣼⢳⢧⡟⡶⣼⢳⣝⢾⣣⠿⣼⣂⢡⡟⣾⢲⡽⢮⣛⣭⠷⣾⣱⠇⡀⠆⣽⢫⡷⠅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠫⣛⢾⣹⢳⣏⡿⣼⢳⣭⡟⡶⣏⡿⣼⢣⡿⣼⠛⢮⡳⣟⠶⣝⢶⣀⠶⣏⣻⠌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢳⣭⡻⣼⢣⣏⡗⢀⠙⢳⣏⢷⣫⢟⣼⡃⠌⠠⣙⡾⣝⢯⣳⣭⡟⣾⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⢮⡻⣼⣹⢧⣬⣠⣏⡷⣝⢾⣱⢯⣤⣁⡾⣵⢏⡷⣝⠶⣝⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⠶⣏⣾⣱⢏⡾⣱⣏⡷⣝⢾⡲⢯⣝⣮⡛⠀⢠⣟⡳⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣟⢮⡳⣝⢾⣹⢳⢮⡳⠏⠷⣽⢻⣼⢣⣇⣌⡾⣼⣹⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣽⢫⡷⣭⡟⣾⣁⢀⠂⢯⡻⣜⡻⣼⢣⡟⡶⣽⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡟⣼⢣⡟⣧⣏⡶⣼⢳⡟⣾⣹⢮⡻⣼⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣟⣽⢲⣭⡳⣏⡿⣼⢣⡟⣾⣹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢝⡶⣛⢮⣳⢭⠻⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⡔⢠⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡁⠜⣀⠀⢌⠰⢁⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠒⠤⠀⡀⠐⠨⡐⢁⠂⡀⠄⡐⠠⠁⡈⠠⢁⠈⠠⠁⠂⠌⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠄⣁⣂⡄⡊⣘⢰⣤⢦⣥⠦⡌⡑⢰⢤⣀⣄⡐⠠⢀⠂⠀⠄⡁⠂⠌⠀⠄⠀
⠀⠀⠀⠀⠀⠄⠂⣡⢤⡶⢏⡟⣭⡙⢠⢁⣬⣛⣬⡳⣼⢙⠠⡁⡟⣼⣙⠶⣝⡛⡶⣤⣅⠂⢀⠐⠠⢈⠐⠀
⠀⠀⠀⠌⡐⣴⠻⣍⡾⣜⣫⠾⣱⢉⠢⣜⣱⠮⣵⡹⠆⠬⡐⣼⢋⡗⣮⡛⡶⣝⡳⢮⣜⡻⢦⡌⠀⠄⠐⠀
⠀⠀⡈⢠⣏⡳⣛⢮⡵⢮⣣⢟⣣⠌⡰⢬⡳⣝⠶⡝⠢⡑⢼⡣⣟⣹⢲⡝⢧⡳⣭⡳⢮⡝⡾⣩⡇⠐⠈⠀
⠀⠀⠠⢸⢮⣹⢭⢾⣸⢳⢮⡳⢭⡖⣁⠂⡙⡮⣝⡇⠒⢌⡳⣝⠶⣭⢳⢭⡳⣝⢶⣹⢓⡾⢣⡷⢭⠐⠀⠁
⠀⠀⠠⠀⠳⢮⣓⠾⣼⣙⠶⣝⡳⢞⣣⡼⣴⢛⡶⢭⡃⠆⡌⢳⣛⣬⡻⢼⣙⢮⣓⢮⢯⣱⢟⡼⠃⠀⠀⠀
⠀⠀⠀⠀⠂⠌⠙⠽⣦⢏⣽⢲⣝⠻⣬⣓⢮⣛⡼⢳⡝⡶⣤⣛⡬⢧⣝⡳⢭⡳⢮⣛⠶⠝⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢉⠊⠳⠎⡟⠶⣭⢳⡭⡞⢯⣼⢓⡧⡞⣭⢳⠮⡝⠳⠍⠓⠈⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠁⠈⠉⠁⠈⠉⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀
⠀⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠀
⠀⠂⠄⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠈⠐⠀
⠠⢈⠀⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢀⠈⠠⢁
⢑⠂⡈⠐⠠⠁⢈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠂⠌⢀⠈⡐⠢
⠀⢑⠢⣁⠐⢀⠂⠄⠠⢀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡁⠐⢀⠐⢀⠂⠴⢁⠃
⠀⠀⠐⠌⡘⠤⡠⠄⡁⠀⠄⡁⢀⠂⡐⠠⢀⠀⠄⡀⢀⠀⠠⠀⠄⡐⠠⠁⠂⠈⡐⠀⡁⠤⡘⢠⠍⠒⠀⠀
⠀⠀⠀⠀⠁⠂⢅⠒⡁⢇⠢⢄⠂⡄⢠⠀⠂⢈⠀⡀⠂⢈⠐⠈⣀⠠⣀⠂⣌⠰⢄⠣⢌⡑⠌⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠍⠂⡱⢈⡡⣘⢉⠢⢍⡰⢉⠊⠬⡑⠢⡑⠤⡉⠤⠑⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣄⡖⡲⣼⢩⣏⡽⣩⡏⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡰⢎⡳⢮⣝⢶⡹⣝⡲⢏⡶⢭⡓⠮⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡲⣝⢮⡳⢭⣛⢭⡓⠎⠣⢍⠢⣉⠢⢔⠢⢌⡡⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣙⢮⡳⣝⠮⡓⢍⠓⢌⡰⢈⡱⢉⠢⡑⠢⢉⠂⡑⠂⢁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢮⣹⠶⣭⠳⠝⡨⠑⣌⠢⡙⠰⢈⠂⡁⠌⠐⢀⠁⠄⡐⠠⢈⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢧⣝⡳⢮⡓⠎⡑⢊⡡⠚⠠⠑⠈⡐⠠⠐⢀⠂⣁⠦⣸⠰⢆⡗⠮⣜⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢧⡏⡷⢮⡙⠢⢌⡒⢉⠢⠁⠌⡐⠠⢁⡄⣥⢚⡼⣉⢏⡲⢇⣝⠺⣌⡳⢎⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣼⢓⡾⠃⡖⢨⠑⠆⠌⠠⠐⢈⠐⣠⠓⢮⠴⣃⠾⣰⣍⡶⣝⢾⣸⠻⣼⢹⣋⡷
⠀⠀⠀⠀⠀⠀⢀⡔⢧⡟⡲⢏⡰⠑⢬⢁⠊⡐⠠⠁⣌⡢⢏⣥⢛⢣⡞⣼⠳⣏⠶⣝⢮⡳⢮⡛⢮⣙⠮⣱
⠀⠀⠀⠀⠀⢠⢇⡯⣓⠾⣉⠢⡔⣉⠂⠄⡐⠠⣁⠞⡴⢩⠶⣬⢾⣹⢼⣣⡟⢮⡛⣬⠣⣝⢢⣍⡳⢌⡳⢥
⠀⠀⠀⠀⢠⢏⡾⣱⠏⡱⢠⠃⡔⠠⢈⠐⢠⣑⠮⣙⠼⣙⢾⡲⢗⣮⠳⣜⢬⡓⣬⠣⣝⢢⠝⠄⠙⠊⠑⠊
⠀⠀⠀⢠⢏⡾⣱⠏⡰⢁⠎⡘⠀⡐⠠⣘⠮⣌⡳⣍⠷⣏⠷⣭⠳⣬⢓⣬⠲⣍⠆⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡏⡾⣱⠏⡰⢁⠎⡐⠁⡐⠠⣑⠮⣱⠦⣝⢮⣛⢮⡛⠦⣝⠢⡝⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡞⣼⢣⣏⠰⣁⠎⡰⠁⠐⠠⣱⢎⡳⢥⡾⢭⡳⣭⢓⠼⡓⣬⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡼⣸⢣⡟⠤⡑⠬⡐⠠⢀⠑⣸⠲⢬⡱⢾⢼⡳⣝⢢⣍⠳⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠳⣝⡺⢬⡑⠬⡑⠠⢁⠂⢌⡣⣝⠲⣝⠯⡶⣝⢢⠏⡴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⢹⠶⣝⠃⡌⡒⠌⡐⠠⠐⢮⣑⠮⣹⢮⣛⡵⢎⡣⣝⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⣛⡼⢮⠑⠢⢍⠂⠠⠁⢌⡳⢌⡳⣝⠶⣭⡓⢮⣑⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡗⣮⡝⡦⣉⠓⢢⠈⡐⠈⠲⣍⡺⢱⢮⣛⠶⣍⠳⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣝⢦⣝⡣⠤⡙⠢⠐⠠⠁⣛⢤⡝⢺⣣⡏⣟⠢⡟⢤⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⡂⠦⡑⢌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠬⣑⠢⢍⡒⠬⡑⢌⠪⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡒⢌⠢⣑⣌⡓⣤⢉⡒⠬⡑⢌⠪⡑⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣘⠢⡅⣍⢢⣿⣿⣿⣿⣿⣷⣮⡑⢌⠪⡑⢬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⢃⡓⢤⠃⡖⠤⠛⣌⠢⣍⠻⣿⣿⣿⣏⠢⡕⢊⡒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⡔⢌⠲⢄⠣⡜⢠⡙⠤⡃⡝⢠⡑⢢⡑⢌⣿⣿⡿⠰⢌⡃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣯⡷⣟⣾⠳⢡⡙⢤⠃⣍⠢⣑⢌⠣⣌⠱⢌⠢⡃⣌⠣⣘⠢⣽⠿⣁⠞⡰⠀⠀⠀
⠀⠀⠀⠀⢀⣴⢾⣯⣟⡷⣟⣯⠓⡜⠢⡜⠢⣉⠆⡱⢌⠢⣑⢦⣽⠶⡑⢌⡢⡑⢌⠲⣉⠲⢌⡰⠁⠀⠀⠀
⠀⠀⢀⣴⢿⣽⣻⣞⡾⣽⢯⠇⡜⣠⠓⢤⠓⣌⠲⣁⣮⣵⣟⡿⠾⡑⢌⠣⡔⣉⠆⡓⠬⡘⠤⠁⠀⠀⠀⠀
⠀⢶⡿⣽⣻⣞⢷⡯⣟⣯⡟⠰⣁⠦⡙⠢⢍⣠⡷⣾⣳⣟⡾⡝⢃⡜⢢⡑⠦⣁⠎⣡⠓⠌⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠈⠙⠹⢯⡷⡌⡓⠬⡰⢁⣯⡾⣽⣻⠷⣟⡾⢑⢌⠲⢌⡡⢌⡱⢈⠲⣁⠎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢬⣑⣼⣟⡷⣟⡷⣯⣟⠏⡡⢎⡰⢉⠆⡑⠦⡑⠎⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢄⠰⣩⣶⢿⣽⢾⣽⢯⣟⡷⢉⠲⣁⠦⡑⢎⡸⢁⡓⢬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠆⠌⡈⠀⣼⣻⢾⣻⢾⣻⢾⡻⢎⡁⢎⡱⢌⠢⡍⢢⡑⣮⣼⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⢈⡐⠠⢀⠁⣾⣽⣻⣽⣻⣭⠟⠡⠆⡍⠢⣅⢦⣱⣬⡷⣟⡿⣾⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠃⠆⡄⢁⠂⠄⠟⠳⠛⠜⢉⠠⡘⠑⠊⢳⣿⢾⣻⣽⣏⡿⣏⡿⣶⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡌⡘⢠⠂⠆⡈⢀⠂⠄⡐⢀⠢⠐⠌⠀⠀⠀⢫⡿⣽⢾⡾⣽⢯⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠤⢁⠆⠌⡂⡁⠆⡌⠰⢀⠎⢠⠉⠀⠀⠀⠀⠀⡿⢯⡷⣟⡯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡈⠒⢄⠢⢑⠠⣁⠒⠄⡃⠌⠐⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠉⠄⠒⠌⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠄⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠄⠀⡀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠐⠈⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣄⣄⡀⠀⠀⡀⠀⣁⣾⡿⣯⣟⣿⣻⢿⣆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣻⣟⡷⠀⠀⠀⠀⢼⣿⡽⠃⡍⣁⠻⣟⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠻⡽⠾⠉⠀⠀⠐⠀⠺⣟⣇⡘⢄⠢⢅⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠻⣼⣦⣽⠾⠛⠀⠀⠀⡀⠀⠀⢀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠄⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⢀⠈⠀⠀⠀⣀⣶⡿⣿⢿⡿⣶⣦⣀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠂⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠠⠀⠀⠀⠄⢐⡿⣯⣟⣯⡿⣽⣳⣟⡿⣷⣄⠀⠁⠀⠀⠀⠈⠀⠀⠐⠀⢀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⡀⠈⠀⠀⠀⠀⠂⠀⠘⣿⣟⣾⣽⣻⢿⣽⢯⣟⣯⡿⣆⠀⠀⠄⠈⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⢀⠈⠹⣾⣽⣳⢿⣻⢾⡿⣽⣳⣿⣻⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡀⠀⠀⠙⢳⡿⣟⣯⣿⣽⢷⣿⣳⠏⠀⠀⠠⠀⠀⠀⡀⠄⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠐⠀⠀⠈⠙⠛⠾⢝⠻⠞⠉⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠈⠀⠀⡀⠁⠀⡀⠀⡀⠀⠄⠀⠀⢀⠈⠀⠠⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀