⠨⠉⠉⠩⠁⠨⢀⠄⣤⣤⣴⣴⡀⠄⠢⠠⢠⢀⠆⡁⠂⣏
⠄⠄⠄⠄⡂⠁⣠⢈⣿⣻⡿⠣⠈⠄⠠⠄⠄⠐⢵⣜⡩⡧
⠈⠄⠐⠄⢠⡼⢟⣼⣔⣻⠅⠄⠄⠄⠄⠄⠄⠄⠈⢇⢇⣹
⠄⠄⠄⠄⠨⠈⣶⣿⣿⣷⣶⣦⡄⠄⠄⠄⠄⠄⠄⠘⡪⣲
⠄⠄⠄⠄⣦⣊⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠄⡀⠄⠄⡵⢆
⠄⠄⠄⡤⣼⣿⣿⣿⡿⠿⠿⢿⠿⣻⣿⠽⢿⢽⠜⢠⡪⣇
⠄⠄⠄⢱⣇⣽⣿⣯⣵⣤⠆⣠⣷⢠⡤⡖⢆⠄⠘⢠⢖⡉
⠄⠄⠄⠈⢿⣾⣿⣿⣿⣷⡾⣿⣿⠄⢱⣣⣤⠷⠁⠠⡳⢣
⠄⠄⡀⠄⠄⠄⣿⣿⣿⣯⡴⠛⠟⠅⢸⣿⢄⠢⠠⢳⢫⢽
⢂⠄⡆⠄⠄⢠⢿⣿⣿⡿⠫⠄⠄⠄⠸⢱⠉⠑⡍⣮⣎⡳
⠄⠠⠢⢀⣰⣾⣯⣿⢿⣮⣋⣉⣒⣗⣚⠝⠈⢀⠠⢹⣿⣿
⡡⢁⣤⢯⢿⣏⡿⣿⡿⢻⠟⠋⠨⠣⠂⢀⡠⡕⢠⡰⠼⣿
⣴⣿⣿⣞⢸⣿⣿⣾⡗⠰⠶⠄⡄⠂⠤⡬⠪⡐⣜⢸⣽⣿
⠿⣿⣿⣿⢸⣧⣗⣿⣿⣿⣶⣾⢁⠠⠄⢹⢜⡖⡇⣻⣿⢿

⠨⠉⠉⠩⠁⠨⢀⠄⣤⣤⣴⣴⡀⠄⠢⠠⢠⢀⠆⡁⠂⣏
⠄⠄⠄⠄⡂⠁⣠⢈⣿⣻⡿⠣⠈⠄⠠⠄⠄⠐⢵⣜⡩⡧
⠈⠄⠐⠄⢠⡼⢟⣼⣔⣻⠅⠄⠄⠄⠄⠄⠄⠄⠈⢇⢇⣹
⠄⠄⠄⠄⠨⠈⣶⣿⣿⣷⣶⣦⡄⠄⠄⠄⠄⠄⠄⠘⡪⣲
⠄⠄⠄⠄⣦⣊⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠄⡀⠄⠄⡵⢆
⠄⠄⠄⡤⣼⣿⣿⣿⡿⠿⠿⢿⠿⣻⣿⠽⢿⢽⠜⢠⡪⣇
⠄⠄⠄⢱⣇⣽⣿⣯⣵⣤⠆⣠⣷⢠⡤⡖⢆⠄⠘⢠⢖⡉
⠄⠄⠄⠈⢿⣾⣿⣿⣿⣷⡾⣿⣿⠄⢱⣣⣤⠷⠁⠠⡳⢣
⠄⠄⡀⠄⠄⠄⣿⣿⣿⣯⡴⠛⠟⠅⢸⣿⢄⠢⠠⢳⢫⢽
⢂⠄⡆⠄⠄⢠⢿⣿⣿⡿⠫⠄⠄⠄⠸⢱⠉⠑⡍⣮⣎⡳
⠄⠠⠢⢀⣰⣾⣯⣿⢿⣮⣋⣉⣒⣗⣚⠝⠈⢀⠠⢹⣿⣿
⡡⢁⣤⢯⢿⣏⡿⣿⡿⢻⠟⠋⠨⠣⠂⢀⡠⡕⢠⡰⠼⣿
⣴⣿⣿⣞⢸⣿⣿⣾⡗⠰⠶⠄⡄⠂⠤⡬⠪⡐⣜⢸⣽⣿
⠿⣿⣿⣿⢸⣧⣗⣿⣿⣿⣶⣾⢁⠠⠄⢹⢜⡖⡇⣻⣿⢿

⠀⠀⠀⠀⠀⣀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⢲⣹⡿⠛⣺⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠬⢾⠞⠻⣽⡿⣿⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⠀⠹⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠲⠶⢤⣤⢤⣌⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠋⠀⣀⡽⣿⡿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⡿⢻⣷⡿⠁⠀⠙⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⣅⠀⣼⠞⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⡆⠺⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⡄⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠆
⠀⠀⠀⠀⢀⡤⠍⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠞⠋⠀⠀⠀⠀⠤⣼⠃⠀

⠀⠀⠀⠀⠀⣀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⢲⣹⡿⠛⣺⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠬⢾⠞⠻⣽⡿⣿⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⠀⠹⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠲⠶⢤⣤⢤⣌⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠋⠀⣀⡽⣿⡿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⡿⢻⣷⡿⠁⠀⠙⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⣅⠀⣼⠞⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⡆⠺⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⡄⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠆
⠀⠀⠀⠀⢀⡤⠍⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠞⠋⠀⠀⠀⠀⠤⣼⠃⠀

⠀⠀⠀⠀⠀⣀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⢲⣹⡿⠛⣺⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠬⢾⠞⠻⣽⡿⣿⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⠀⠹⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠲⠶⢤⣤⢤⣌⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠋⠀⣀⡽⣿⡿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⡿⢻⣷⡿⠁⠀⠙⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⣅⠀⣼⠞⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⡆⠺⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⡄⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠆
⠀⠀⠀⠀⢀⡤⠍⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠞⠋⠀⠀⠀⠀⠤⣼⠃⠀

⠀⠀⠀⠀⠀⣀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⢲⣹⡿⠛⣺⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠬⢾⠞⠻⣽⡿⣿⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⠀⠹⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠲⠶⢤⣤⢤⣌⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠋⠀⣀⡽⣿⡿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⡿⢻⣷⡿⠁⠀⠙⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⣅⠀⣼⠞⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⡆⠺⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⡄⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠆
⠀⠀⠀⠀⢀⡤⠍⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠞⠋⠀⠀⠀⠀⠤⣼⠃⠀