Biological Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠈⡁⠀⠘⠀⠾⠂⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣦⡠
⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⡀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠷⠾⢓⣆⠀⠂
⠀⠀⠀⢠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣦⠖⣾⣯⡉⠀⠀⡀⠀⣴⣷⣿⣼⣿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠟⣷⢿⡏⠉⠂
⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠐⣴⣷⣏⣩⡅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣄⠀⠀⠀⠀⠀⢤⠿⠙⠍⠋⠈⠀⠀⠀⠀⣠⣤⢰⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⡀⢰⡤⠀⡀⠀⠀⠀⠀⢺⡃⢰⡆⠀⠈⡀⠀⠀⠀⠻⠀⠀⡅⢻⠋
⠀⠀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠁⠰⠆⠀⠀⠈⠁⠀⠙⣦⡀⣿⠀⠀⠀⠘⢶⡰⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢠
⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢶⣴⣇⣀⠀⠀⠀⡀
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⣾⣭⣻⢻⡷⡔⠚⠁
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠈⠀⠀⠐⣟⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⣼⣩⡄⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⣼
⠀⣀⠀⠀⠀⠰⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢀⣠⣞⠁⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠿⠀⠀⠀⠀⠄⠉⠙⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢈⠀⠀⠀⠀⠰⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠈⢘⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡄⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣲⣾⣿⣞⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡚⢲⡄⠀⠀⠘⠟⢻⣿⠛⠃⠀⠀⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠎⣰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠉⠳⡖⠀⠀⢠⠆⠀⠈⠀⠂⠀⠀⠀⡀⠠⢥⣮⣿⣿⣷⡀⠀⠠⠄⠀⣇⠀⠉⢸⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⠻⠟⠑⠦⠀⠀⠀⠉⠀⠀⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣴⠆⠁⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠒⠀⠀⠠⣤⠉⠀⠀⠄⠀⢨⠀⠀⡀⠀⢼⡴⠁⠀⣀⣀
⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⣀⡴⠒⣫⡟⠁⠀⠀⠀⠀⢰⡀⣠⡔⠀⠀⠀⠛⠀⠀⠀⠀⠀⠗⠀⠞⠀⠀⠈⠁⠐⣴⠛⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠐⠘⢿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢄⣸⣿⣯⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣸⣧⠖⠚⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢴⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⢠⣤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⡠⣴⡄⠀⠀⠀⢀⡤⣶⡀
⠀⠀⢸⣟⣛⣤⡀⠀⠀⠀⠑⠀⢠⣤⠀⢀⣀⡀⣴⠂⠐⠁⠀⠀⣿⡀⠀⢠⣤⣤⡴⠟⠀⣿⠁⠀⠀⢀⡎⢡⣟⣷
⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⢾⣤⡄⠀⠀⠀⠀⣈⣿⠆⠀⠀⠀⢈⣵⣦⢸⣿⡟⢇⣰⢛⡅⠀⠀⢠⣦⠉⢣⢿⣮⡀
⠀⠀⠀⢧⠈⠛⢿⣿⣄⣤⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠙⠃⠀⠐⠋⠀⢠⣤⣆⣸⣿⣾⡆⢻⣷
⠀⠀⠀⠈⠷⠂⣤⣼⣃⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣄⠀⢦⢒⣮⣬⣿⣿⡿⣿⠃⣼⡿
⠀⠀⠀⠀⠀⣴⣷⣿⠿⠏⠻⣿⣿⣷⣶⡄⣀⠀⠀⠀⠀⠀⠸⠋⠈⠀⠀⣀⠓⠀⠈⠷⣤⣿⣿⣿⣿⠻⢷⡄⠈⠁
⠀⠀⠀⠀⠰⠟⠛⠁⠐⠮⢍⣈⣻⣿⣯⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠼⠿⣷⣌⣛⣋⣩⡄
⠀⠀⠀⠀⠀⠀⠀⣉⢸⠇⠀⠈⠉⠀⢉⣉⡁⠀⠀⠀⠠⠤⠄⠦⡤⠄⠀⠀⠀⢀⣀⡀⠘⠛⠛⠛⠋
⠀⠀⠀⠢⢥⡈⠄⡀⠀⠀⠀⣠⣤⡀⠘⣷⣀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢀⣐⠯⢚⣿⠃⢰⣿⣦⠀⠀⠀⠀⠀⠀⡠⠏
⠀⠀⠀⠀⠈⠙⠋⠀⠀⢀⣚⡛⢿⡇⠀⠘⣷⡆⠭⢉⡣⡀⢀⠐⢁⣜⠩⠅⣠⣾⡃⠀⢸⣿⢿⣧⠀⠀⠀⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡆⠀⠚⠚⠎⠒⠒⢽⣠⣿⡷⠆⠁⠰⢷⠗⠁⠀⣽⣏⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠁⠀⠘⣳⠄⠀⣀⠘⡄⣿⠃⠀⡀⠄⣜⠇⠀⠀⣻⠋⣿⣿⣇⠀⠀⠰⢀⡀
⠀⠀⠀⠸⣿⣤⡀⠀⣼⡉⠃⠀⠀⡀⢂⠀⠀⠘⣣⣼⡁⠀⠈⠁⠐⢘⣤⡸⠋⠀⠀⢸⣿⢀⣿⣿⡧⠀⠀⠆⢀⡀
⠀⠀⠀⠀⠘⢿⡿⡆⠘⢿⣟⡀⠀⠀⡞⠀⠀⢀⣿⠈⠀⠀⠀⠀⠀⠈⢳⣧⠀⠀⠐⢸⣿⣸⡿⠋⠀⠀⠀⠹⢿⣷
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠘⠻⠓⠂⠀⠀⡠⠜⠁⠀⠀⠀⣤⣦⠀⠀⠀⠈⠲⣄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠈⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠠⡀⠀⠘⠿⣿⣷⣤⣄⡀⠀⠀⢠⣾⣶⢆⣀⠀⠀⠀⠀⣤⣌⣿⣿⠃
⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⡀⣠⣴⣿⣿⣿⡿⠃⠀⠀⠀⠘⠠⠤⠤⣄⠉⢻⡇⠀⠀⣟⠹⣟⣿⣷⣄⣄⣾⣿⣿⡿⣽⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠀⠈⠛⣧⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⣿⣾⣿⣿⡏⠻⠋⢿⣿⣾⣿⡄
⠀⠀⠀⠀⠈⠿⠟⠋⠀⠁⠸⣿⣿⣿⠟⠀⠀⢸⢯⣴⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠛⠿⣿⠟⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠋⠁⠀⠀⠀⠘⣶⣿⣱⣛⣤⣤⡠⢶⢾⡿⢚⡟⠀⢠⡄⠀⠀⠰⡄⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢳⣄⣠⣾⡿⠆⠀⢀⣞⣷⡆⠀⠿⣮⣿⡻⢿⣿⠻⣿⣿⣿⡏⠀⢀⣾⣿⣿⡷
⠀⠀⠀⠀⢀⣠⠙⠟⠉⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠘⠁⠈⠙⠛⠋⢀⣴⣿⣿⠛⣭⡖⠀⣠⠀⠀⠀⢀⣤⣤
⠀⠀⠀⢆⠟⠁⠀⢀⣤⡀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡿⢋⣵⢇⣿⠃⠀⡠⠀⠀⠀⡉⢸⣿⡇
⠀⠀⠀⠀⢀⠠⢶⣿⣯⠟⠀⠀⠀⢰⣎⠙⣿⣿⣿⣷⣦⠀⠀⠀⢠⣾⡿⢛⠡⣾⢻⣿⢸⡏⠀⠴⠁⠀⠀⠀⠆⣀⢹⡇
⠀⠀⠀⠀⣿⣿⡿⠟⠁⠀⠀⠀⢀⣴⣿⣷⣿⣏⣿⣿⣿⠀⠀⠀⣿⠟⣡⣿⣥⡿⣽⣿⠿⠁⠀⠀⠀⠀⠀⠀⠛⠻⢿⡇
⠀⠀⠀⠀⠈⠉⠀⢀⣀⠀⣀⣤⣾⣟⡟⠿⣍⠙⠛⠻⠋⠀⠀⠀⠛⠚⠛⠛⠋⢁⣬⠵⣶⣿⢤⣄⣀⡀⠀⠀⠀⠈⠿⠃
⠀⠀⠀⢀⠀⡘⠻⣿⣽⣿⣿⣿⣿⣿⣧⡁⠘⠃⠀⠀⣀⡀⠐⢂⣶⣶⣶⠶⠀⢀⣤⡬⣽⡻⣷⣤⣿⣙⢻⠷⣆⣄
⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣴⣯⣤⡽⢿⡏⠉⠁⠀⢠⠾⠟⠛⠶⠈⢏⣉⣩⣴⣾⣶⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠾⠟⠋⠀⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠃⠉⠛⠛⠉⠁⠉⠛⠒

⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡄⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⡀
⠀⠀⠀⠀⠐⢄⡀⠺⣏⡁⢀⣾⣷⠄⠀⠀⠀⠀⣘⠀⣛⡃⠀⠀⠀⠀⠀⠀⠀⣼⣿⡤⠐⠁⠘⠄⠸⠟
⠀⠀⠀⠠⣠⡿⠀⠰⣾⡟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠒⠀⠉⠁⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⡀⠀⠐⡞⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⣿⣿⣦⠀⠀⠀⠂⡱
⠀⠀⠀⣀⠄⠀⠀⠀⢀⡤⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠈
⠀⣶⣾⠆⢀⣀⠀⡀⡀⠄⠀⠊⠉⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⢻⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⠃⠀⠀⠉⠉⣩⠀⣠
⠀⢀⠟⣛⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣻⣿⣿⣿⠁⠀⠀⠚⠉⠀⠰⠋
⢠⡬⠾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣼⣻⣿⣿⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡻⣿⣿⣿⡿⣿⣿⣽⣲⠄
⠀⠀⠀⢄⡄⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⣿⣿⣷⡟⢯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠂
⠀⠀⠀⠘⣿⠆⣿⠃⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢿⣿⠋⠀⠀⠀⣀⣤⣶⡂⢀⣶⣶⠞⡏⠀⠀⠀⠂
⠀⠀⠀⠀⢸⣷⡷⣶⣿⠿⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⣾⠏⠀⠀⠈⠁⠚⣻⣿⣷⣌⠁⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⣠⣿⣿⠇⠁⠀⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠃⠉⠉⠈⠉⠉⠀⠀⠠⣄
⠀⠀⢀⠋⠉⢁⠀⢰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⡠⠃⠘⠑⠀⢀⣠⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣀
⢀⠟⠀⠀⠀⠀⠠⣨⣨⣻⢿⣽⣿⠄⠀⠀⠀⢠⣴⣶⣦⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣁⣹⣯
⠀⠀⠀⠀⣤⣁⣢⠥⣾⣿⣾⡿⠋⠀⠀⠀⣴⡻⢽⣘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠿⠋
⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣸⠏⠃⢴⢲⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢈⣠⣄⠠⢤⡀
⠀⠀⠂⠈⠀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⡿⣖⠢⢼⣨⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣠⣽⣿
⠀⠀⠀⠛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣗⡾⠐⣻⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⠋⡁⣀⣀⡰⣶⣶⡄
⠀⠈⠀⠀⠛⣷⣿⣿⣧⠀⠀⠀⠀⠀⠨⣯⣦⠮⣷⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⠲⣯⣏⣾⣿⣿⣿
⠀⠀⠀⢈⣿⡀⢻⣿⣟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣺⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣽⣻⣟⣿⣿⡿⠃
⠀⠀⠀⠀⠠⠿⠛⠛⠿⣧⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠟⠟⠛⠁⠀⠀⠀⠐⣤⡀⢸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⢠⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠁⠀⠀⡀⡀⠀⠠⠀⠁⢀⠀⢤⡀⠀⡀⡀
⠀⠀⢀⢀⠀⡀⡀⠀⠊⠀⠀⠀⣠⡀⠀⣀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠄⠨⣄⣄⠀⠠⠀⠀⠀⠙⠀⠂⠂
⠀⠀⠈⠂⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠨⡹⢚⠃⠈⠉⠀⠀⡆⠀⠀⠀⠀⠈⠍⠍⠉⠉⠀⠀⠀⠀⠀⠀⠠
⠀⡀⢄⠋⡀⠓⠀⠠⠀⠀⠀⢕⡁⠰⠠⠈⡁⠐⡂⡀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡀⣠⡄⡦⠀⢀⠀⢀⠀⠂
⠠⠀⠀⠀⠁⠀⠀⠈⠀⠀⠢⠈⢁⠈⠈⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⡀⠀⢀⡘⠁⡡⠄⣀⠀⠀⠄⠉⣄⠁
⠀⠁⡈⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠀⠋⠀⠈⠁⠉⠀⠀⠀⠀⣶⠀⠀⠀⠂⠓
⠀⠰⡅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠠⠀⠀⠁⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⢀⠈⠀⠀⠀⠐⢐⠷⠶⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠂
⠈⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠕⠀⠠⠀⠂⠅⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠄⠀⠀⠀⠁

⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡠⠀⠠⠄⠀⠀⢀⣀⡀
⠀⠀⠀⢩⠄⡠⠀⠄⠛⠀⠀⠄⠀⠀⠀⢀⣾⣯⣿⣿⣦⣄⡀⠹⢿⠀⢤⠿⠇⡈⢀⣬⣣⡀⠐⠀⢿⡏⢹⡆
⠀⠀⠀⠀⠤⠂⠰⡄⠣⢦⣁⡘⠀⠀⠀⢸⣿⣿⣿⣿⡷⠿⣻⣶⣄⡀⠠⡿⠀⠐⣉⠷⠙⠋⣄⡀⠀⢿⣾⠏
⠀⠀⠀⠀⠀⠀⠴⣩⣛⡎⣰⠯⠄⠀⢠⠀⠙⠻⣷⣿⣴⣿⣶⣿⣿⣿⡆⠀⠀⣀⣻⣄⢀⡞⢸⡇⡀
⠀⠀⠀⠀⠀⠀⣋⡑⡵⠿⣟⠷⢀⠆⠘⡷⢾⠇⠒⠤⣌⠙⠻⠿⠿⠟⠁⠀⠀⢸⠉⠀⣍⣩⣹⡇
⠀⠀⠀⠀⢀⠀⠀⣈⢻⡶⠿⣎⠄⠀⠀⠈⠓⠲⠦⠼⠜⠃⠀⠀⠀⠀⠀⠀⠀⠈⣶⠞⢃⣤⡸⣇⠀⠀⢀⣤⡄
⠀⠀⠀⢤⣈⠣⡀⠈⠀⠀⠀⠀⠀⢀⣤⣦⡿⡿⣶⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⢋⣻⣿⣧⣾⡆⠀⢸⣻⡇
⠀⠀⠀⢥⣈⢷⣝⠀⠐⢶⡄⠀⠀⠸⣏⣤⣦⣤⣼⠇⠀⠀⠀⠸⡇⡞⠀⠀⠀⠀⠀⢠⠹⣿⣿⣽⣧⠀⠸⠿⠁
⠀⠀⠀⠀⠉⠛⠽⡷⣭⣶⡀⣤⣀⡀⠛⢟⣫⡀⣶⣤⡄⠀⠀⠀⢱⣀⠀⠀⠀⠀⠀⠀⠡⡹⢿⣿⠇
⠀⠀⠀⢰⡞⡹⢛⣿⢟⡞⢿⣿⣿⣤⠀⢿⡋⢃⣹⣿⣏⠀⠀⠐⠀⠙⡄⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⢡⠏⡠⢍⢲⣷⢹⣿⣾⣇⠈⠛⠚⠁⠉⠁⠀⠀⠀⠀⢠⠁⣿⠇⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⣤⣶⡀⢼⡴⣮⠿⢺⠯⠛⠛⠃⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⢠⠀⠀⠂⠀⠀⠀⢀⣾⣿⢿⣿⡦⠠
⠀⠀⠀⢻⡌⡇⢠⡴⠯⠆⠈⠀⣀⢠⡀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⡇⠀⠀⠀⠀⠀⠀⠙⣿⣹⣿⣗
⠀⠀⠀⢸⣿⠇⠸⠇⠀⠀⢠⠃⠉⠁⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⢀⡀⠀⠀⠀⠀⠀⢨⠁⠛⠟⠄
⠀⠀⠀⠀⢀⣠⠤⢄⠀⠀⢸⠀⠀⠀⠀⠋⡤⠀⠈⡀⠀⢀⠐⠊⠁⠀⠃⠘⡌⠀⠀⠀⠀⠀⠀⠝⢘
⠀⠀⠀⠀⡞⠀⠠⠄⠑⠄⠀⠃⠀⠀⠀⠀⢖⠱⠀⢁⠀⠀⠀⠀⠀⠁⠀⠈⠡⠀⢠⣾⣟⠇⠀⠀⠁
⠀⠀⠀⢀⣅⠀⠠⠄⠀⣸⢀⠴⠷⠶⠚⢲⡄⠀⠲⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⣤⢠⠇⠸⣿⣰⣶⣦⣤⠁⠀⠀⠀⠈⠀⠀⠀⠤⠐⢦⡀⠘⠲⢤⣶⠧⠬⡟⢷⡚⠁
⠀⠀⠀⠀⡆⠀⠀⠂⡜⠀⣀⡀⣀⡉⠁⠀⠀⢠⣄⡠⣴⣠⢴⡶⣠⣄⡀⠉⠛⠋⠉⡡⠶⠋⠺⣿⠷⠄⢀
⠀⠀⠀⢠⡇⠐⠀⠠⠃⢸⣽⠿⠿⢷⢶⡀⢰⠾⣿⣼⣻⣧⣾⣧⣿⣈⡗⠀⢀⡔⠉⣠⠴⢃⠰⠂⠀⣴⣿⡆
⠀⠀⠀⠈⠳⠴⠔⠁⠀⠘⢻⡟⢳⣾⢻⡁⠸⣧⡼⠻⢿⣏⠳⣼⡏⠋⠁⢠⠊⠀⢺⠁⠀⠈⣤⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⣩⢿⠆⠀⠀⠀⠚⠓⠉⠉⠛⠁⠀⠀⠀⠘⠂⡁⢾⠀⣀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⢀⣴⡜⠿⣿⣀⠀⢀⣄⡰⡶⣾⢛⣇⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌
⠀⠀⠀⢸⣟⠤⣢⠙⠋⠀⠀⠉⣾⠻⣏⣿⢿⡟⠀⠉⠈⡙⠶⠤⢤⣤⣤⠀⠀⣠⠀⠀⠜⠀⠤
⠀⠀⠀⠀⠘⠺⠛⣁⢾⣿⣀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠐⠀⠲⠒⠻⠛⢉⠁⠘⠛⠚⠖⠀⠻⠖
⠀⠀⠀⠀⠀⠀⠛⠛⠂⠙⠋⠀⠀⠀⠀⠀⠀⠲⠞⠁⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠦⠐⢒⣂⠠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡐⠂⠀⠠⠀⠆⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⠶⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⣤⣤⣄⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣿⡆⠀⡀⠀⠂⠀⠍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠈⠁⠀⠀⠀⠔
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛
⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⢦⣼⡇⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⢧⠁⠀⠀⠀⠂⠀⠀⠀⡀⠀⣀⣀⣀⠀⣤⣼⣿⡟⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠛⠛⠛⠰⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢇⠀⠀⠀⠸⠃⠀⠀⠀⠀⣶⡄⠀⠀⠈⠀⠀⠂⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠘⠀⠀⠀⠀⠀⠀⢠⣤⡤⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⢿⣿⣦⡯⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢚⡿⣻⣿⣈⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠋⠀⠀⣀⡄⠀⠀⠀⠀⢺⣷⣿⣬⢿⡷⠦⠀⠆
⠀⠀⠀⠀⠀⠞⠲⣄⡀⠀⠀⠀⠀⠛⠀⠀⠀⠜⠁⠀⠀⠀⠀⠘⢿⣿⣯⣄⢻⡆⠬⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠨⠿⢾⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠤⢔⡉⢡⠾⣿⣷⣴⢻⣇⠀⠀⠀⠀⣠⡄⠀⠀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠤⡙⢿⡀⠀⠐⠟⠑⠀⠀⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠈⠁⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠⠀⠈⠁⠰⠀⢀⡀⠰⠤
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡞⠂⠛⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢀⡗⣴⠚⠉⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠠⠀⠀⠀⢠⠿⠋⠠⠀⢀
⠀⠀⠀⠈⠉⠹⢷⠀⠀⠀⠀⠀⠀⠀⠰⠃⠰⠄⠀⠀⠀⠀⢄⠾⠁⡄⢀⠀⣅⡘⠀⠀⠀⠀⠀⠀⠀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠸⠷⣦⢡⡜⠃⢻⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣦⠀⠀⠀⠀⢹⡄⡄⠀⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⠁⠀⣀

⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣶⡆⠀⠀⠀⠀⣀⠰⣶⠀⠀⠀⣠⡶⣆
⠀⠀⠀⠀⢿⣵⣷⡄⠀⠀⢈⡄⠛⠂⠐⠒⠘⣧⡌⠀⠀⠘⢆⡀⢺⣶⡆⢁⢴⠃⠀⢀⡘⠄⣢⡻
⠀⠀⠀⠀⢾⢙⠿⣷⣄⣀⡀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⢷⠾⠧⠈⠨⠞⠀⣄⡌⢻⣦⣯⢻⣦
⠀⠀⠀⠀⠀⠳⠀⣬⣟⣬⣧⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⠀⠄⣲⣭⣿⣿⠿⡟⣸⡟
⠀⠀⠀⠀⠀⢀⣾⣾⠟⠋⠙⢿⣿⣷⢆⣄⡀⠀⠀⠀⠙⠀⠀⠀⢨⣁⢀⣕⡶⣿⣿⡿⠙⠳⠀⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⡍⠑⠲⠛⠛⠛⠛⠃⠀⢀⢀⣀⢀⡀⠀⠀⠉⠉⠉⠿⣶⣶⠶⠁
⠀⠀⠀⠀⠀⢂⣀⠈⠑⠁⠀⣠⡄⠸⣷⠐⢢⡀⠀⠈⠀⠈⠀⢀⢐⡎⣾⠇⢠⣦⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠙⠉⠀⢠⣾⣛⣿⠀⠙⣷⡈⠉⠡⡀⠀⣀⠔⠉⠁⣼⡛⠀⣸⡿⣷⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⢙⡟⠀⠀⢲⢶⣿⠓⠀⠘⣛⠁⢀⣿⢰⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠠⣤⡀⠀⢀⠟⠛⠉⠉⠄⠀⠘⢧⣠⠔⠀⠺⠁⡠⡈⢴⠃⠀⢠⡷⢸⣿⣗⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠹⢿⣦⠈⠇⣆⠀⠀⠰⠀⠀⢸⡏⠃⠀⠀⠀⠐⢿⡇⠀⠀⢸⣇⣼⠿⠁⠀⠀⢶⣷
⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠈⠛⠐⠀⠀⠀⠉⠀⠀⢀⣴⣄⠀⠀⠀⠢⠀⢉⠉⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⣿⣿⣷⣦⠀⠀⠀⣀⣠⣴⣦⠀⠀⠀⠈⠻⠛⠳⠦⣄⠀⠐⣯⣿⣴⣄⠀⠀⣰⡾⣽⢿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣗⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠉⠑⠂⠹⠃⠀⠧⣎⢻⣿⣿⣾⣿⣿⣷⣟⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣷⣿⣿⡏⠿⠹⣿⣵⣿
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠁⠸⣿⣿⠟⠀⠀⡿⢵⣦⡀⠀⠀⠀⢀⡀⣤⠀⠀⠛⠻⠟⠁⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣄⡀⠀⢠⣄⠀⢸⡟⣾⣴⣶⣶⣽⣿⣯⠝⠀⣰⣦⣠⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⣀⢻⠞⠋⠉⠀⢠⣿⣿⣧⠀⠉⠙⠀⠻⠁⠿⠿⠛⢀⣴⣿⢿⣻⠀⢀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠚⠁⠀⣠⡀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣿⢟⣹⣪⡟⠀⢈⠀⠀⠈⠹⣿⠄
⠀⠀⠀⠀⠀⣠⣰⣿⡿⠛⠀⠀⠀⣾⡉⣿⣻⣿⣷⠀⠀⢠⣾⠟⣁⢲⣟⣿⣾⠁⠐⠀⠀⠀⢐⣤⣹⠇
⠀⠀⠀⠀⠀⠻⠟⠋⠀⠀⠀⢀⣶⢿⣿⠿⢾⣿⡿⠀⠀⠸⣫⣴⠿⠟⠙⢟⣩⣄⠀⠀⠀⠀⠈⠙⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣿⣿⣿⣧⠊⠳⠀⠀⠀⠀⠄⣠⣤⣤⡄⠀⣉⣹⣻⣷⣍⣿⡲⣦⡤⣀
⠀⠀⠀⠀⠀⠈⠿⠿⠿⢿⣿⣿⠿⣿⣷⠄⢠⣶⣭⠽⠾⠉⠉⠀⠠⠾⠛⠧⢸⣋⣭⣭⣵⣶⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠰⠟⠛⠁⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠃⠀⠉⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⢄⠀⣄⢄⣴⡤⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣤⢸⣇⡦⡄⠀⠚⠛⢤⠛⠚⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⡀⢘⠀⢼⢿⡀⠨⢁⠆⠀⠙⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠁⡈⠛⠀⠘⠀⡄⢢⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠠
⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⠄⠀⠀⣀⠀⠰⠂⠓⣀⠀⠐⠹⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⢤⡈⠛⣁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠋⠀⠀⠙⠋⠈⠀⡐⠀⠈⠓⡄⠀⠈⠃⠀⠀⢄⠀⠀⠀⢐⠆⠀⠶⣈⠳⣄⠀⠙⣃⡈⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠨⢇⢁⠀⠀⠀⠄⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⢀⠀⠈⣧⣄⠀⠀⢳⠂⢀⠼⢶⡍⢂⡀⢡⠤⢈⡴
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⢑⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠗⠄⠈⠟⡗⣠⠀⠻⣠⣬⡙⣻⠎⠁⢓⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢠⡀⠁⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠐⠈⠳⠌⠡⣤⠁⠆⡈⠉⢿⣀⠉⢈⠀⡀⠈⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠙⣷⢂⡠⠀⠀⠀⠀⡠⠀⠶⠀⠒⡄⠈⠲⠄⣩⢭⣤⣬⡁⡴⠴⠚⠉
⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠁⠀⠚⢡⠀⠠⠀⡀⠀⠀⠀⠶⠁⠦⠒⠐⠀⠀⠳⢈⢜⡃⠀⢨⠇⣠⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣀⠀⣀⠀⠀⠠⢄⡀⠀⠀⠀⠁⢀⡉⢠⠀⠀⠠⠈⠂⡁⢠⠞⠈⠉⠉⠀⠈⠉⠛⠟⠛⠷⠶⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠉⠄⠀⠉⡀⠈⠀⠠⠀⠀⠀⠀⠀⠅⠆⠀⠀⠀⠀⠁⠄⠂⠐⠀⡺⠁⠀⠀⠀⠐⠥⠂⢀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⡭⠀⠀⣶⠀⠤⠀⠁⠀⠀⠀⠀⠀⡀⠀⠴⠂⠀⠀⠀⠀⠀⠈⢢⡜⠁⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⢀⠀⢦⠀⠈⠂⢐⡄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠈⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⡔⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠄⠠⠀⠒⠋
⠀⠀⠀⠀⠐⠀⠰⠀⢉⠀⡁⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼
⠀⠀⠀⠀⠀⠚⠇⡀⠀⠀⠁⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠐⠂
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠆⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠂⠰⠇⠀⣠⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠆⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠒⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡆⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⢢⠈⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢓⡀⣀⠠⠰⠔⠚⠉⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠙⣄⠀⠀⠀⠀⠁⡠⠀⠀⠄⢠⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⠀⡀⢂⠄⠀⠀⠘⢆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⡀⡀⠀⡄⠀⠐⢂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠘⡄⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠀⠠⡤⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠙⣄⣠⠄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⠶⠾⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠤⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣴⣶⣾⣿⡏⠀⠀⠀⠀⢠⡇⣦⡤⢠⣴⡶
⠀⠀⠀⠀⠀⠀⢴⣿⡿⣦⡶⠚⢻⣾⣿⡇⠀⠙⠷⠀⠀⠀⣿⢸⣿⣿⡀⢠⣿⣧⣤⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠶⡀⠀⠸⣿⣷⠀⢠⡄⠀⢺⠆⠼⣿⠉⡷⢣⣞⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠠⠣⣄⠀⠀⠀⠀⠀⢻⣿⣷⣿⠃⠀⣸⡁⢠⣯⠀⡁⠛⣿⡷⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣇⢁⠁⠀⠀⡄⠀⠰⣤⢺⣿⣿⡇⠀⢸⡏⠀⠉⠀⠀⢸⣿⠿⠃⠈⠉⠍⢹⢿⠳⣆
⠀⠀⠀⣠⠖⠋⠙⠉⠉⠉⠘⠂⠐⠀⠛⣧⣼⣿⡇⠀⢸⠃⠀⠀⠀⠀⠼⠁⠀⠀⠀⢀⡴⠛⠁⠀⠈⠃
⠀⠀⠀⠲⣤⠤⠤⠠⢀⠀⠀⠀⡀⠉⢶⣼⣿⣿⣿⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣙⣿⣿⣿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠰⢶⣭⣄⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣆⡀⠀⠀⠀⠀⢀⠐⢁
⠀⠀⠀⠀⠀⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⣤⡀⠀⠠⣦⣶⣷⡟⣤⠖⠒⠂
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣴⣤⣤⡤⠶⠛⠛⠋⠉⠉⢿⣿⣿⣦⣄⠀⠈⠙⡟⠛⢷⡄
⠀⠀⠀⠀⠀⠐⣧⠁⠉⠛⠛⠛⠋⠁⠀⠀⠘⠀⠀⠀⠀⢀⣈⣽⢿⣿⣿⡄⢨⣇⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠹⣦⣤⣤⣀⡀⠉⠀⠀⠀⠀⠀⠠⠔⣾⣥⠚⠹⣻⣃⣾⣥⡄⣿⡄⠈⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠚⠉⠁⠀⢠⣶⡶⡟⠁⣀⡿⠿⠛⠉⣰⠆⣿⢧⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠋⠀⠀⠀⡼⠀⠀⡀⠞⠁⠀⡿⠈⢇⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠞⠀⠀⢰⠇⠀⠀⠘⡇⠀⠘⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣠⠟⠀⠀⠀⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠏⢨⠐⠀⠀⣴⠶⠻⠋⠁⠀⠀⠀⠀⢀⢀⠠⠀⠀⣠⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠂⡀⣀⠀⠘⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠀⢠⠖⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⠀⢠⢤⡄⠈⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠎⠀⠠⠂⠀⠀⣀⣀⠄⠀⡠⠗⠀⠀⠀⠀⠀⠐⠠⢠⠄⠂⠀⡀⠀⠀⠀⢀⠔⣾⣰
⠀⠀⢰⠂⠀⠀⢀⠀⠀⠈⠁⠀⠀⡦⠀⠀⠀⠒⣎⠿⠤⠊⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠲⣿⢠⡸⣭
⠀⢀⠂⠀⢀⠈⠄⠒⠀⠀⠄⠀⠈⠁⠀⠀⠠⠈⣠⠄⠀⠠⠇⠀⠀⠀⢀⣆⡀⠀⠀⠀⠰⠆⠀⠀⠀⠈⣉⣤⣗⡶⠂
⠀⢸⠀⠀⠘⠃⠀⠀⡀⠐⠂⠠⠀⠀⠁⠀⢈⠰⠁⢀⠣⠀⢠⡆⠀⠐⡑⠊⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠘⢿⡱⠈
⠀⣸⠀⠀⠀⠠⠤⠈⠁⠀⠀⢀⠀⠀⣔⠂⣽⠂⢀⣿⠀⢳⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⣄⢠⡀
⠀⣩⠀⢸⡶⠀⠀⠀⠀⠌⠁⡘⠒⠀⢧⠐⢉⢀⡾⡻⡔⡏⠀⠀⠀⢠⡄⠐⢻⡄⠀⠀⠀⠐⠀⠄⠀⠀⠀⠉⡄⡘⠂
⠀⢀⡀⣶⣀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠈⢧⣀⡏⠀⢁⠙⠁⠀⠧⣽⣷⢂⠀⠈⠀⠲⠀⠀⠐⠤⠤⠤⠀⣶⢀⠀⠉
⠀⠙⠃⠀⢹⠿⠂⠀⠀⠀⠁⢄⡠⠀⠁⠀⠙⠂⡘⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⢠⣢⡶⠀⢀⡴⠒⠒⢻⠁
⣀⠀⠀⢀⡄⠂⠀⠠⠒⣂⡭⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠈⠉⠀⠀⢸⠀⠀⣀⠜⠀⣤
⢘⡱⡰⠏⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠠⠂⠀⠀⠚⠀⠄⣀⡛⠀⠀⠀⡴⠒⠚⡗⠉⠁⠀⠈⢘⡆
⠸⣟⣧⠞⠁⠀⠀⠠⠂⠀⠁⠀⠁⠀⠀⠀⠀⢀⡀⠀⡰⢄⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⣇⣠⡴⠃⠀⠀⢄⠀⠀⠁
⠀⠀⠃⠀⠀⠀⠄⠀⡀⠈⠀⠂⠈⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⣀⠚⠁⠀⠀⡞⠉⢹⡆⠀⢀⢸⣿⠗⠺⢳⣆
⠀⢀⣦⠀⢄⠀⠂⡀⠂⠈⠀⠀⠀⠀⠀⠀⢀⡑⠐⠀⠄⠈⠄⠀⠀⠀⠢⠀⠀⣀⣧⠴⠊⠀⣀⠀⠉⡴⠀⠀⠀⡉⠁
⠀⠈⠏⠀⠈⢆⠀⠀⠠⡲⠀⠐⠚⠛⠉⠉⠈⠉⠀⠀⣀⣀⣶⣶⣶⠶⠀⠀⣸⡵⠋⠀⠀⠒⢏⠀⠀⠈⠺⣀⠚⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣟⣿⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠄⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠈⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⠄
⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⠀⠀⣀⠁⠠⢶⡄⠀⠀⠀⠀⠀⡸⡄⣀⠃⢀⠀⡐
⠀⠀⠀⠀⠀⠄⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢀⠈⣬⡝⢄⣈⡀⠂⠠⠀⠙⠠⣀⣁⣉⠴⠁⠀⡀
⠀⠀⡀⠀⠀⠀⢀⣔⠆⡀⠀⠀⠠⠀⠀⠁⢀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡀⡠⠀⠀⠀⠀⢀⠀⠀⠀⠠⠆⡔⠄⠄⢠⠀⠀⠀⠀⣀⢨⠶⠤⠤⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⡀⢀⠀⠄
⠀⠀⠂⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⣧⠀⠂⠐⠠⠀⠀⠀⢠⠐
⠀⠀⠈⠐⠀⠀⠀⠀⠁⢀⣄⠠⠀⠀⣂⠀⠀⠀⠀⠀⠊⠐⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠤⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⠀⠀⠀⢉⠀⠀⠀⣀⢤⡠⠄⠀⠀⠀⠴⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠓⠆⠠⠀⢀⡄⠗⠀⠐⠉⠆⠁⠀⠠⡀⠀⢠⠃
⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠌⠑⠂⠀⠀⢀⣀⣀⣀⣋⣀⣀⡀⠀⠀⠈⠀⠀⣦⡀⢐⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠙⠂
⠀⠀⠇⠂⠀⠀⠲⠿⡀⣶⣤⠀⠀⢀⠀⡀⠀⢀⡀⠠⠄⠀⠀⠀⡼⠤⠥⠤⠬⠥⠥⠼⠀⠀⠀⠀⠈⠁⠀⡀⠈⠉⠀⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠐⠁
⠀⠀⠁⠀⠀⠀⢦⡐⠃⣠⠀⠀⠀⠀⠂⠉⠐⠂⠀⠀⠂⠉⠀⠀⠀⠙⠀⠁⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⠁⠀⠂⠁⠥⠨⠀⠑⠂⡀⡀
⠀⢀⡤⠤⡄⠀⠀⠉⠉⠀⠀⠀⠀⣠⣀⠀⢀⣤⡀⠀⢀⣤⣄⠀⠀⣄⠀⠀⠀⢀⣤⣄⠀⠀⣀⣤⣄⠀⠠⣄⠀⢀⡄⠀⠀⠀⠄⠂⡀⠂⠀⠀⢡⠁⢄
⠀⡎⠀⠀⠘⡄⡀⠠⣤⠢⡄⠀⠀⣿⣸⠇⠀⣿⠀⢠⡿⠀⠹⣇⠀⣿⠀⠀⢠⡟⠀⢹⡇⢰⡏⠀⢉⡁⠀⠹⣆⣾⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠱⠄⠜
⠀⢃⠐⠂⣠⠃⠉⠀⡏⠀⠀⠀⠀⣿⠙⡇⠀⣿⠀⠸⣧⡀⣠⡟⠀⣿⢀⡀⠸⣇⠀⣸⡇⠸⣇⠀⣹⡟⠁⠀⣹⠃⠀⠀⠀⠀⠀⠐⠀⢀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⠛⠋⠁⠈⠉⠁⠀⠉⠛⠉⠀⠀⠉⠉⠉⠀⠙⠛⠉⠀⠀⠙⠛⠋⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⢀⠠⠀⣀⠂⢠⠂
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣀⡀⢀⡄⠀⠀⠀⢀⣀⡀⣤⠀⠀⠈⠒⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢐⠓⡀⠀⣀⠀⠀⣲⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣃⣀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠿⠿⠇⠛⠁⠠⠀⠀⠀⡜⠀⠠
⠀⡠⣶⠀⠀⠂⠀⠀⣦⡀⠀⠈⠀⠀⢽⡂⠀⠀⠀⡀⠀⠂⠀⠀⠀⠘⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⢉⡠⠈⠉⠀⠀⠀⠀⠊⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠨⢄⣸⠀⠀⠀⠴⠚⠉⠀⠐⠚⠁⠀⢀⠀⠀⠠
⠀⢀⠰⢂⠔⣐⢀⠀⠀⠀⠀⠰⠀⡔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡀⡀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠂⠀⠀⡀
⠀⠀⠉⠘⠀⠀⠈⠃⠀⠀⠉⣁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠠⠁⠄⠀⠀⠀⠀⠀⠤⠠⠁⠀⠈⠄⠨⠀⠀⠀⠀⠁⠀⠀⠁⠈⠀⠁
⠀⠠⠠⢀⠐⠉⠄⠀⠀⠀⠀⠁⠀⠁⠀⠀⠤⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⢘⠀⠀⠐⠀⢠⠀⠀⢀⠀⠀⡰⠂⠚⢀
⠀⠀⠀⠈⢀⠘⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠚⢀⠞⠀⠀⢔⠀⢑⠀⠁⠈⠉⠁⠀⠁⠀⠄⠀⠀⠀⠈⠐⠀⠁⡀⠀⡌⠀⠉⠦⠀⢀⠀⢠⠀⠔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⢊⠀⠀⠀⠀⢀⠘⢡⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠠⠄⠢⡀⠀⡐⠒⢂⠀⠀⠀⠀⠁⠄⠠⠃
⠀⠀⠀⠀⠀⠁⠞⠁⠀⠀⠈⠁⠀⠀⠰⣠⡈⠈⠀⡀⠐⢪⠄⠀⠀⠀⠠⠀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠄⠀⠀⠄
⠀⠀⠈⠆⡀⠀⠈⢀⠄⠀⠀⠄⠀⠀⠀⠉⠁⠀⠤⡑⠂⠀⠀⠀⠘⠀⢀⠁⠀⠀⠄⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠘⣄⠀⠱⠄⢢⣠⠀⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣇⣴⣾⣭⣽⣷⣷⣿⣟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠙⢿⣿⡿⠛⠉⠻⣿⣯⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠄⠀⠀⠀⠀⣠⡴⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⣠⣴⣿⣧⠉⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⢀⣀⣤⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⡁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⡠⠉⠀⠀⠸⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂⠈⠁⠀⢀⠄⠈⠀⢀⣤⣤⣄⡀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣶⣿⣎⢄⠀⠁⠐⢂⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢺⣿⡿⠫⠉⠀⠀⠀⠉⠁⠀⠙⠿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⠀⠄⠐⣾⣿⣿⡠⠔⠀⠀⠀⢄⡈⠦⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠆⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠶⣤⣬⡗⣮⣤⠌⣡⣿⡉⡀⠀⠄⠈⠁⠀⠈⠀⠠⢀⡀⠀⠈⠙⢿⣿⣿⣿
⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⣱⠟⢋⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡇⠀⠀⠀⠀⠙⠿⣿
⠀⠢⣔⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣿⣿⣿⣷⣾⢦⢶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠈⠙⠻⢤⣌⣅⣈⡭⠡⠤⠰⠀⡀⠰⠂⠐⠶⠘⣻⢟⠏⠉⠁⢠⠔⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠘⠛⠙⠋⢀⡠⠞⢂⡠⠄⠁⠁⠀⡠⠞⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⣃⡶⠞⣩⣵⠀⡥⠄⠀⠂⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣛⣭⠟⠋⠉⠀⣼⢋⠆⡼⠁⠀⡇⠢⣹⡄
⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⠋⠁⠀⠀⠀⣴⡏⣿⡿⠀⠀⠀⠙⣶⣃⢹⡀
⣶⣤⡄⣚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣈⡿⠁⠀⠀⠀⠀⠘⠧⣼⣷⣦⣤⣀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠀⠀⠉⠀⢀⡀⠀⠶⠐⠂⢀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁
⠀⣀⡀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠠⠴⢖⣇⠀⠀⠀⠀⣠⠀⠀⠀⠀⠐⣂⠀⠘⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢐
⣴⣿⠃⠀⠀⠀⠈⠀⠀⢠⢞⡋⠀⠀⢸⡇⠀⠀⠀⠿⠓⡞⠈⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⢩⠀⠀⠀⠀⠀⢀⠦⠔⠁⣰⠀⠈⠀⠀⠠⣾⣿⠀⢠⡄⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⢀⣺⣿⠋⠀⣼⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣄⣴⡘⠿⠂⠀⢰⡶⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡿⠏⠀⠀⠈⠀⠀⠜⠁⠙⠀⢀⡤⠀⠀⠄⠀⠈
⢷⠀⠀⠀⠀⠀⠀⠀⠛⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⡼⠃⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠠⡠⢄⠄⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠃⣶⢀⣭⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠑⠤⡀⠀⢸⡆⢒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⡀⠀⢀⡶
⢲⠒⣧⣄⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢾⠆⠀⠀⠰⠁⠀⢸
⡐⢛⡫⠈⠉⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⠠⡀⠙⠀⠀⠀⠈⢀⠀⠀⣀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠋⠁⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠒⠄⠃⠀⠀⠀⠀⢀⠀⠀⠀⠘⠠⡀⠀⠀⣈⣁⠀⠐⠲⠀⠈⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠐
⠀⡤⠀⡄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠘⠋⠀⠀⢀⡀⠀⠀⠈⠀⠀⠈⠓⠀⠠⠆⠀⠻⣄⠰⠀⠌⠃⢀⠐⡄⠀⢀⠀⠀⠀⠀⡀⢲⣶⡦⢂⡀⠛
⠃⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢧⠀⠀⡘⠳⢤⡀⠄⠀⢠⡅⠒⠋⠀⠈⠩⠀⠈⣩⠉⠀⠈⠉⣣
⠘⠀⠁⠀⢠⠀⠀⠀⢀⠀⣀⡄⠀⠀⠀⡄⠀⠛⠀⠀⠐⣈⣦⡔⢀⡆⠀⠀⠈⠢⡀⠇⠐⠠⠙⢦⡀⡾⠀⢀⠀⡁⠈⠰⠄⠀⣧⡄
⠀⠀⠀⢦⣼⣀⡀⠑⠒⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⢼⠋⠛⠈⠀⠀⠀⢡⡀⠈⠃⠠⠀⠀⠀⠹⠁⠀⠀⠀⠀⠄⠐⠀⠀⠀⠙⠀⠀⠃
⠀⠀⠀⠀⡯⠉⠉⠉⠳⣄⠀⠀⠙⠳⣌⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠠⠤⠄⡀⠀⠄⠀⠀⠀⠀⢤⡀⠀⠀⣠
⠀⢀⡀⠀⢣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠌⡉⠐⠢⠄⠀⠀⠀⠀⠧⠀⠂
⠀⡾⠀⠀⠀⠉⠛⠦⢤⣿⣤⣤⣄⠀⠀⠀⠀⠸⡦⠀⠀⠀⢈⣧⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢆⡀⡿⢺⠛
⠰⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⢡⡤⠀⠀⠀⠀⠀⠠⠆⡀⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠂⠀⣀⠀⠈⠀⠀⠀⠀⠀⠘⣷⠊
⠀⠀⠀⠀⡠⠒⡀⠀⠀⠻⢦⣄⣰⣇⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠂⠀⠈
⢠⣶⠚⠷⠼⣿⣿⠀⠀⠀⠀⢠⡏⠉⠙⢷⠀⠀⠀⠁⠶⠀⡀⠄⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤
⠘⠁⠀⠀⠀⢀⡙⠖⠁⠀⠀⠈⠧⣀⠀⢸⠀⠀⠀⠐⢀⡈⠁⠀⠀⠀⡰⠀⠀⠀⠀⣐⣨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠄⠀⠈⣿
⢠⡄⠀⠀⣀⢨⠇⠀⠀⢀⠰⠀⠀⠀⠉⣿⠲⣄⠀⠀⠐⢂⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⡤⢤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⢁⡀⠕⠋⠀⠀⠀⢨⠇⠓⠀⠀⠀⠘⠦⣼⡀⠀⠀⠈⠙⠛⠻⠿⠿⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠂⠀⢆⠂⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠠⡄⠀⠀⠀⠰⢶
⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⢨⡁⠀⠀⠀⠁⡀
⣿⢿⡿⠿⢿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣻⣿⣿⣿⣿⣟⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣟⠛⣷⠀⠀⠄⠁⠀⠈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⣻⣿⡋⠄⠀⠀⠠⢀⠠⢀⠀⠄⡁⠂⠈⠀⠀⢀⠀⠐⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠂⠐⠈⣉⣉⠛⠉⢁⠀⠀⠨⠕⠢⠀⠤⠔⠠⠄⠤⠆⠉⠒⠁⠀⠀⠀⣰⢶⠀⠀⠐⠀⠈⠑⠂⠤⢀⡀⣤⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢞⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢷⡻⡧⣬⣤⣧⠌⣁⠂⢄⠨⢘⣿⡔⠟⡽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⡋⣰⣤⣀⣶⣿⣿⠴⠀⠉⠀⠀⣏⣻⣧⣤⣙⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠃⠐⣰⢃⣯⣠⣼⠛⠁⠀⠀⠀⠀⠀⢰⡯⣷⡄⠍⡁⠸⠅
⠀⠀⠀⠀⣠⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣴⠛⠓⣘⠛⣿⣡⣬⡿⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠛⡳⢷⡆⠆
⠀⠀⠀⠀⠘⡀⠀⠀⠐⣚⠃⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠿⡡⢠⣨⡁⣾⣷⣶⠏⠀⠀⠀⠠⠄⡐⠲⡌⢿⣧⠀⠀⣯⡈⡇
⠀⠀⠀⠀⠀⠈⣦⠀⠥⠏⠀⢀⡪⠁⡔⠊⠛⣛⠛⣻⢻⡓⠄⢲⣓⣾⡿⠷⠋⠉⠁⠀⠀⢀⠐⠁⠀⠀⠠⠗⢈⣾⠀⠀⠶⠁⠁
⠀⠀⠀⠀⠀⠀⠈⢔⣻⡁⠀⠰⠁⣾⠂⠀⠀⠿⢷⢶⡾⣡⣼⣾⣏⠒⡀⠀⠀⠐⠀⠀⠀⠀⠈⠐⠀⢨⠔⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠰⠀⣷⢀⡀⠀⠀⢀⠈⣿⣿⢟⠛⡉⣴⣧⣤⣀⡐⢀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠉⠁⠀⠀⣰⣿⠁⠴⠇⢙⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⡟⠀⡁⠀⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠓⠛⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣿⠤⢚⠦⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠄⠐⢶⣖⣴⣌⣷⡀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣑⢂⠠⢈⣿⡀⠀⠀⠀⠀⠀⣀⣤⣾⣸⡽⣧⡀⠀⢨⡿⡿⢿⣿⡟⠀⠆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡎⣴⢧⣺⢿⣦⣤⣤⡴⠿⠋⠁⣡⣿⣧⢸⡇⠀⠈⠀⠀⠀⢹⣿⠶⠀⢠⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠲⠶⣤⣀⠻⣿⣶⣌⡿⣶⣿⡿⣥⢀⣀⢰⣟⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡈⣬⡟⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣦⣴⣴⣶⣧⣡⠀⣉⡛⢮⡝⠻⢿⣿⣿⣷⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⢀⣠⠠⡴⣿⣤⡔⣷⣿⣥⣤⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡼⣿⠟⠁⠀⠈⠙⠻⣿⣿⠆⠈⡓⢦⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⢻⣿⣿⡾⣿⠻⣿⣤⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡀⠀⠀⠀⠀⠀⠈⠛⢧⣲⣍⡂⢈⠑⠦⢤⣀⣀⣀⣀⣄⣠⣤⡴⢘⣛⣤⣤⣰⢶⣋⣿⠟⠙⠷⣦⣤⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⢳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣀⣤⣤⣄⣨⠿⣿⣡⣿⢔⡠⠿⣿⢟⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⢻⡶⢤⣀⡀⠀⠀⠀⠀⣀⠉⠛⠿⠿⣷⣿⣽⣶⣷⣾⡶⠀⠀⠈⠿⣟⡁⠀⠀⠀⠆⠀⠓⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⣾⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⢿⣶⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣍⣾⢽⣿⣿⣛⠿⡿⠿⢻⣯⣡⣾⣟⣼⣭⡶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣿⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡹⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣩⣿⣿⡟⠛⣩⠉⣹⢫⡮⢹⣿⣿⣿⣿⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣷⡝⢎⣹⣶⣿⣿⣿⣿⣟⣻⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣮⣿⣿⣿⣟⣭⡉⣶⠏⠉⣻⡿⣿⣽⣿⡶⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣿⣹⣫⣿⣸⡕⢎⣶⣿⣴⣿⣿⣿⣿⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣮⣿⣯⣾⢿⣿⣿⣿⣷⣤⣴⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣻⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⡟⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣏⣾⣿⣿⡿⠵⠁⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣴⣾⣗⣽⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⢿⢿⡿⠿⠛⠿⠿⠦⢿⢿⣿⡟⠭⠿⢿⠷⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⣀⣭⢤⣄⣀⠀⠈⢇⠐
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⠄⠠⡀⠀⠀⣴⠻⣿⣿⢿⢾⣽⣳⣲⢄⣖⡀
⠀⠀⠀⠀⠀⢷⣿⠙⢸⠁⠀⠀⠀⠀⡜⠾⢩⢿⠷⠦⢴⡯⣛⠿⣿⡿⠛⢷⣿⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⣷⡴⢩⣵⠛⡷⢾⢦⡏⣹⣏⢫⣶⣾⣿⣿⣷⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠲⠧⠀⠀⠀⠀⠘⡟⠞⠋⢠⠒⡇⢺⠉⢠⣶⡼⢹⣟⣿⣿⣷⡿⣿⢿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠁⡞⠐⡇⣯⠀⢶⢀⣜⢻⡦⣽⣟⣿⣿⡿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠬⢀⡿⡗⠀⣤⠈⠁⡻⠿⢷⣬⠛⣿⣿⣿⣿⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡂⢸⡇⢰⠄⢍⠁⢨⣉⣟⢠⡜⠓⢻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣂⣸⣁⣼⣿⣮⣤⣹⡗⢿⠈⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣋⢪⡿⣿⣏⠉⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⢢⠀⠀⠀⠀⠀⠺⣿⠋⠙⢻⣿⣿⣾⣾⣷⣤⣼⣧⣼⢿⡿⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃⠈⢢⣀⣘⣀⡀⣤⡀⠀⠀⣿⡀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣆⢷⡹⣧⡘⣿⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠡⠄⠀⠀⠛⢉⣿⡗⠈⠁⠈⠉⠉⠁⠀⠀⠀⡟⠈⠻⣿⣿⣿⣿⣿⣾⣎⢳⣜⢿⣿⣇
⠀⠀⠀⠀⡔⠉⠀⠀⠀⡀⠂⣀⡴⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠠⣸⠃⠀⣼⣿⠻⣝⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣄⣀⠀⣀⠘⢦⣴⠁⠀⠀⣘⣇⠀⠀⠈⣿⠋⠻⣿⢿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⣶⣶⣾⣾⣿⣿⣿⣤⣾⣿⣿⡇⡀⡤⢿⣤⣶⣤⣿⡀⠀⠘⢷⡈⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⡛⠉⠙⠛⡛⢛⠿⢿⣿⣿⣷⣷⣧⢸⣿⣿⣿⣿⡇⠀⠀⠈⢹⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠏⠳⠦⠤⠀⠀⠴⣿⣿⣿⣿⣿⠘⢿⣿⢁⣿⠁⠀⠀⠀⠀⠗⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠀⢘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠌⠈⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠔⠁⠈⠈⠓⡄⠀⢸⠀⠀⠀⠰⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢀⡤⠖⠊⢉⠉⠉⠉⠑⠲⢄⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠐⠈⠁⠉⢲⠀⢸⠀⢰⠀⠀⠀⠀⠀⡇⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⡀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠈⠉⠛⠒⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢡⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⢀⠈⠀⠀⠀⠓⠀⠒⠊⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠐⠂⣀⢀⠀⠁⠐⠀⠈⠀⠀⠊
⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡎⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠀⠘⠃⡈⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠈⠉⠉⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡈⡸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠸⠁⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣄⣀⣀⣀⣀⣠⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠞⠛⠋⠉⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢉⠉⠉⠉⢉⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠄⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠌⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠐⠆⡠⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠄⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠋⡀⠀⠁⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠁⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠠⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠠⠀⠀⢠⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠰⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⠳⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠐⠁⠀⡐⠂⠐⠂⠀⠑⠒⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠀⠀⠀⠼⢤⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠂⢤⣀⣀⡁⠀⠀⢧⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠂⠠⡂⠀⠀⠀⣠⠄⠀⠀⠠⠀⠀⠀⠀⠐⢄⠀⠀⠀⠁⡦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⡎⠀⢀⡀⠀⠀⠐⠀⠀⢀⡀⠀⢐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⡈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢾⣽⣿⣿⣿⣿⣯⡗⠀⠀⠀⠀⢀⣤⠴⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠇⣀⠁⣀⣀
⠀⠀⢿⣿⡿⠁⠎⢻⣿⡿⠀⠀⠀⠀⣾⣿⣷⠰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠘⠃⠨⠄⠉⠁
⠀⠀⢫⢿⣿⠀⠀⢸⣿⣍⠁⠀⠀⢸⣏⠉⠀⠁⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⣿⣤⣤⣼⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡖⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣀⣈⣉⣩⡅⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⠀⡀⢀⡀⢀⡀⣀⢀⢀⠀⢀⢀⢀⠀⣀⢀⠀⢀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀
⠀⠀⠀⠀⠀⣔⣆⠆⠀⠀⢶⣌⠉⠀⠀⠀⣱⢸⠀⠺⡇⣿⢾⢸⠇⢿⢸⢹⠀⢿⠈⡇⢸⠀⢻⡇⡟⡇⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢹⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣿⡎
⠀⠀⠀⠙⠁⠙⠛⠈⠋⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢶⣦⠿⠚⠿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⠶⣿⡇
⠀⠀⠀⢠⣤⡀⢀⣀⡄⠀⠀⠈⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⣷⣶⠇⠀⠐⠀⠘⣷⣶⠀⠀⠀⠀⠀⢿⣿⡤⡀⠀⠁⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⢐⣂⣀⣉⣭⡅⠀⠀⠀⠘⠇⠀⠀⠀⠿⠁⠀⠀⠀⣶⣾⡀⠀⠀⠀⢀⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢰⣿⢲⣶⣾⢿⡧⠉⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣶⡇
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣉⡛⠈⠀⠀⠀⠀⣴⣶⡖⠀⣨⣭⣅⠀⠐⣶⣶⠆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠇

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⢿⣄⠄⠀⢤⡤⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠸⣽⣷⣦⣀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢂⣶⣿⣷⣾⣿⣷⣦⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠁⢀⢤⣽⣿⣿⣷⡄⠀⠀⠀⡇⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡟⠻⣷⣒⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡿⣏⠋⢹⡇⠀⠀⠀⡇⠀⢸⠀⠀⢸⠋⣿⣪⡟⢸⡇⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⣃⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠉⠁⠉⠉⠐⠟⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⢘⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣴⣆⣴⣤⣄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠄⢀⡀⠴⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⢿⡏⢛⡻⣿⣗⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣠⣯⣥⣬⠆⠀⠀⠀⠀⡇
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣍⣃⡈⢠⣿⣿⣦⠄⠀⡇⠀⢸⠀⠀⢀⣀⢂⣩⣟⣻⣝⡁⠁⠀⠀⠀⡇
⠀⢀⣻⠁⠀⠛⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⣶⣾⣿⣿⡟⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠁⢿⢹⡯⡟⠐⠓⠁⠀⠀⡇
⣾⡿⠋⠤⠠⠀⢤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⢺⡿⠿⠋⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣷⣶⠄⠀⠀⠀⠀⠀⡇
⠉⠃⠈⣶⣿⣤⡷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡇
⣧⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣶⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢾⠆
⠀⠀⠀⠀⠀⠀⣂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⠀⠀⠙⠒⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠙⠛⠳⢦⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣠⡾⠁⢀⡴⠞⠋⠉⠙⢻⡟⠺⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡤⢀⠀⠘⠀⠀⠀⢸⡿⠁⠀⠀⣼⠿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢿⣧⠤⠀⠁⠀⠀⢸⡇⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢡⣾⡇⠀⠀⠀⣿⣇⠀⢠⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⣾⡏⠀⠀⠀⢀⣿⣿⠷⠾⠏⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⡏⠀⠀⠀⢰⣿⠣⣈⠀⢤⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢈⢷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣿⠇⠀⠀⠀⠀⢸⡏⢰⡷⣯⠘⠀⠀⠀⠀⠀⣀⢀⡀⣼⣤⣢⣤⣠⣦⡆⣴⣿⣦⣤⣴⣶⣶⣿⡿⣿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣣⣶⠀⠀⠀⣠⣴⡾⣿⣁⠀⠀⠀⠀⠀⢠⣵⠟⠛⠛⠻⢿⡇⢩⣿⣿⣿⠛⠟⠋⠉⠉⠁⠄⠀⠈⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠀⣰⣿⡼⠂⠁⠀⠀⠀⠀⢀⣴⠿⣿⠿⠟⠛⠛⠛⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⣀⢀⣀⣨⣶⣿⣧⣾⣷
⠀⠀⠀⠀⠀⢠⠀⠀⣠⣶⣿⣿⣿⣿⣯⡻⢄⡿⢁⡸⠧⢴⠄⠀⠀⢠⣿⣿⣟⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠶⠄⢀⡀
⠀⠀⠀⠀⠀⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡾⢯⡘⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⢿⠿⠻⣿⣿⣿⡿⣟⣉⣁⡐⣶⡶⣶⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣭⣿⣿⡙⠛⠁⢠⣗⠫⠽⠖⠀⠀⠀⢺⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣯⠿⣯⠳⡄
⠀⠀⠤⠀⠀⣾⣿⣿⣿⣿⡟⣋⣭⠏⣡⣶⣾⠄⣩⠜⠂⠀⠀⠀⠀⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠙⠛⠻⠷⠋
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⡙⢻⣿⡆⠙⠉⢱⠎⣿⣼⡦⠄⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣠⠦⣄⡀⠀⠀⢹⡆⠀⠀⠀⠄
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⣤⡙⠋⢷⣿⡷⣷⣿⢈⣀⢀⣼⣿⠋⠀⠄⢀⣦⠔⠂⠀⠀⠀⢀⣼⠁⢀⣤⣤⡾⠛⠀⠀⠘⣀⠀⢸⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣯⣴⠿⠛⠉⠉⠙⣿⠳⠷⠀⣴⡟⠁⠀⠀⠀⠀⢠⣾⣿⣴⣿⣿⣍⠁⠀⠀⠀⠀⠘⢿⣼⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡟⢻⣧⣼⣶⡟⠁⠀⢀⡀⠀⠀⠈⠓⠓⢾⡟⠁⠀⠀⠀⠀⠀⢳⣿⣿⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣍⣽⣿⡿⣿⠫⠘⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⢈⡇⠰⣀⣠⡀⠀⠀⡈⢿⣿⣿⣇⠀⢠⡅⠀⠀⠀⠐⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡟⣿⣿⢿⢏⡝⠀⣴⠾⡏⠁⠀⢻⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠁⠈⠉⠀⠀⠙⣗⣿⣿⡄⠘⠷⢎⢀⡀⠀⣸⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣾⡏⣾⠁⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⢷⣦⡹⢯⣿⣻⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⡇⣿⠀⠀⠧⠀⡆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⢷⠻⠀⠀⠙⠛⠟⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⡏⢰⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣶⣼⡧⡴⠞⢠⣼⣾⣷⣄⠀⠀⣤⣤⣴⣶⣦⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣧⡟⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠉⠉⠁⠀⡀⠚⡟⠁⠉⠛⡇⠈⠉⠉⢿⡥⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠴⠀⠹⣿⣷⣿⣿⣷⣿⣾⡙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⢠⡶⠿⠀⢠⣿⠶⢡⣄⠀⢰⣄⠀⢶⣾⠟⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⣻⡿⠆⠀⠀⠀⠀⠀⢀⠤⠤⣾⠇⠃⠀⠀⠀⣤⣷⡀⠀⢀⣠⡀⢸⣧⡈⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⢀⠟⠀⠀⠀⠀⢠⡿⠏⠀⠈⠀⠙⠁⠸⣇⠉⠉⠉⣹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⠁⠢⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⣿⡤⣿⣦⣀⡀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⣞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡄⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⣤⣤⡤⠲⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣗⣻⣣⡀⠣⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⡾⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣏⣌⢀⡛⡉⠓⠀⢀⡄⠀⠀⠀⢰⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⡐⢦⠀⡄⠀⢀⣠⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠠⢈⠦⠙⠒⡏⢉⠂⠀⠀⠀⠀⠆⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠐⠁⠠⠀⠒
⠀⠀⠀⠀⠐⠁⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⢀⠊⠀⠀⠘⠀⠀⠢⡀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈
⠀⢀⠂⠀⠀⠀⠀⠡⣠⠄⠈⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠚⠂⠐⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⠁⠀⣧⣄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣰⡟⠡⢠⡤⡄
⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠈⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠘⠃⠀⠀⢨⣞⠁⠀⠈⠂⠤⡀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠘
⠇⠀⠀⠀⠀⠀⠀⢀⠀⠠⢠⠄⡀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⠙⢁⠂⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠈⠠⠀⠧⠑⠀⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠂⠀⠠⠀⠀⠀⢀⣐⠀⢀⡒⢲⣌⠀⠀⢈⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⡠⠂
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢉⡀⠠⡂⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠑⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠐⢷⠓⡶⠀⠁⠐⠄⠀⠂⠁
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⡄⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⢐⠀⣋⠀⠈⠂⠀⠀⣄
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⡔⠐⡒⡀⢀⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢹⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢘⡧⣀⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢹⡇⠀⣨⠻⠉⠁⠉⠐⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢯⡁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣉⣧⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⡉⠉⡉⠉⡉⠁⠀⠀⢀⡞⠙⢦⠀⠸⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠄⠀⠀⠀⢀⡏⠀⢀⡈⣷⠒⠲⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢳⠀⠀⠂⠀⠂⠀⠂⠀⠂⠀⠀⠀⠀⠀⠳⣄⣉⣴⠇⠀⠀⢸⠆⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠹⣤⣧⡾⠀⠀⠀⠁⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⡘⠲⠤⠴⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⣈⢳⡄⢸⡇⠀⣠⠴⠲⡆⠀⠀⢀⣤⣴⠶⡶⢶⣤⣀⠀⠀⠋⠀⠀⢰⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣭⣶⡃⢸⡇⢸⢃⡄⢀⡇⠀⣴⠯⣴⣧⣠⣧⣬⣧⡼⢷⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠇⢨⡟⠶⠋⠀⢸⠃⠀⣿⠀⠀⡇⠀⢸⡆⠀⣷⠀⣾⠓⠶⣄⣀⣀⣀⣠⡴⠚⢻
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣹⣷⣋⣀⣀⡀⠀⢸⡉⠉⣿⠉⠉⡏⠉⢹⡏⠉⣿⠀⢹⡀⡴⠋⠁⠀⠉⠙⢲⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡤⢿⡶⠶⡷⠶⣾⢤⣴⠃⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢒⡒⠒⡒⠲⡄⠀⠀⠙⠦⢷⣤⣧⣼⠷⠞⠁⠀⠰⣯⣄⣀⠐⠀⠀⠀⠂⢀⣀⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣀⣈⣡⣤⣥⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⠙⢳⣛⣳⠋⢉⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠰⣤⠞⡉⠙⢲⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⣍⣽⠉⣳⡀⠀⠀⠘⣿⠀⠀⢠⠴⠓⠛⢛⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠋⠈⣿⢉⡷⢤⡀⠀⠸⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠴⠃⠀⠀⠀⢤⣄⣀⣈⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠄⠂⠁⠀⠀⠁⠤⠠⠠⠂⠀⠀⠀⠀⠚⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⢀⠀⠀⠄⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠐⠂⠀⠁⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠤⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⠁⢀⠀⠠⠂⠀⠀⠀⠤⠂⠀⠀⠀⠀⠒⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⢡⡄⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠌⠐⠀⢀⣉⠀⠰⡄⠈⠀⠉⠀⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢀⡄
⠀⠀⠀⠀⠠⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠂⠀⠃⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⡦⠀⠐⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠋⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⢤⡄⠀⠀⠀⠈⠙⠀⠀⢀⡀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠇⠀⢈⣀⣀⣀⢀⡈⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣁⣀⠀⠰⠀⠐⠂⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠱⠂⠈⠀⠀⠀⠆⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠁⠠⠑⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠂⠰⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⣐⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠋⠀⠀⠰⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡈⣐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠓⠂⠊⠉⠀⢀⢀⡤⢘⡇⠀⠀⠀⠀⠈⠀⠀⠁⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠙⠄⠀⠀⠀⠀⠂⠐⠀⠒⠈⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠴⠀⠀⠀⠀⠰⠁⠀⠀⠈⡄⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠠⡀⠀⠀⠨⠀⠀⠀⠚⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⡰⠀⠁⠘⠀⠀⠀⠀⢉⠠⠄⠀⠰⡀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡠⡄⠒⠀⠀⠀⠀⠈⠁⠂⠀⠀⠤⠄⠀⠀⡀⠀⠁⠀⠐⠂⡄⠀⠀⠈⠁⠀⠀⠀⠀⠠⠂⠀⠀⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡈⠻⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣿⠈⠻⣦⣈⣻⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⣷⣄⠙⢷⠌⠉⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠻⣯⡙⠃⣿⡏⠻⠿⠛⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣄⠰⣶⣾⡄⢻⣤⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠻⣦⡈⠻⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢶⣄⠙⢷⣌⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡈⠻⣦⣨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⡙⢷⣄⠙⠷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣶⣤⣸⣿⢠⣌⣻⣦⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⠛⣧⠘⡿⠿⠆⠙⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⣯⡉⠻⣦⡀⣿⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣀⡐⢷⣄⠙⢿⠀⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⢸⣿⠟⠿⠿⠿⠿⠿⠿⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣥⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀⠠⡀⠀⠤⢠⠄⢸⡇⠀⢸⣿⠀⠀⠄⠀⠠⡄⡤⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⡷⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠛⠱⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁



⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢟⣭⣭⡉⢙⣛⣉⠉⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣟⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠛⣿⣿⣷⣿⣾⡄⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⢼⣿⣿⣭⣴⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄⢈⣿⣿⣿⣿⣷⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠍⠡⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⢸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣶⣾⣶⣾⡀⠙⣿⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⢪⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠦⢹⣏⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠏⠀⠉⠠⠈
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣿⣼⣯⡟⣻⠶⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣶⣄⣀⣀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⣾⣾⡏⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⢄⠠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⡿⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠿⣇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡿⣿⣿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠙⠿⣶⣼⣿⣧⡀⠈⠟⠿⣿⣿⣿⣿⠿⢃⡾⠚⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠤⠶⠏⠁⠀⠈⠀⠠⠀⠈⠀⠀⠀⠀⠉⠀⣀⣿⣿⣿⣿⢏⣴⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣠⠀⣤⣄⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣏⢸⣯⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣏⢸⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡙⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢨⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣺⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⣿⣿⡿⠯⠁⠀⠉⠻⣿⣿⣷⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⣿⣿⣿⣿⡧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣱⣿⣿⠏⠀⠀⠊⠀⠀⠀⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⣴⣾⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢋⣉⣉⣤⣤⣤⣤⣉⣉⡙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⣁⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠉⠻⢷⣦⡈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⢁⣴⡿⠋⠀⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⠀⠀⠀⠀⠙⢿⣦⡈⢻⣧⡀
⠀⠀⠀⠀⢀⣾⠏⢠⣾⠏⠀⠀⢀⣿⣿⣷⠶⠓⣠⣤⣤⣄⠀⠀⠹⣦⣼⠋⠀⢀⣤⣤⣤⡀⠙⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣾⡏⢠⣿⠃⠀⠀⢀⡿⣹⡏⠀⠀⠀⢻⣆⣀⣹⢷⣴⠾⠋⠙⠷⣦⡾⣃⣀⣼⠇⠀⠘⣿⡄⢹⣷
⠀⠀⠀⣸⡿⢀⣿⠇⠀⠀⠀⣼⢷⡟⠀⠀⠀⠀⠀⠉⠋⠙⣷⠀⢈⣀⠲⠂⠀⣾⠋⠉⠁⠀⠀⠀⠸⣿⡀⢿⣇
⠀⠀⠀⣿⡇⢸⡿⠀⠀⠀⢰⣏⣾⠃⠀⠀⠀⠀⠀⣀⣤⣤⡿⠀⣏⣍⣳⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⢿⡇⢸⣿
⠀⠀⢀⣿⠀⣿⡇⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⣼⠏⠀⣱⡟⠻⢾⡍⣥⡶⠛⢷⣍⠈⢹⡆⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⣸⠇⢻⣄⠀⠀⠙⠛⠛⠁⠀⠀⠀⢸⡿⠀⣿
⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⢸⡟⢿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣾⡏
⠀⠀⠀⠀⢿⣇⠘⣿⡄⠀⠀⣿⣼⡇⠀⠀⠀⠐⣶⣼⡷⢦⣤⣤⠶⠾⠛⠛⠛⢷⣴⡟⠀⠀⠀⢠⣿⠃⣸⡿
⠀⠀⠀⠀⠈⢿⣆⠘⢿⣆⠀⢸⡇⣿⠀⠀⢘⣻⡏⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠃⠀⣰⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣧⡈⠻⣷⣌⠛⠛⠀⠀⠉⣹⣷⣬⣀⡐⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⣠⣾⠟⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⢷⣦⣀⠀⠀⠉⠰⠟⢹⠟⠛⠛⠉⠉⠁⠀⠀⣀⣴⡾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⢉⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣌⣉⣉⠛⠛⠛⠛⣉⣉⣡⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠉⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣀⠀⠀⣀⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠛⠃⣀⣴⠟⠹⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠏⠻⣦⣀⠘⠛⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⡤⠶⠛⠉⣀⡴⠂⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣀⠉⠛⠶⢤⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢉⡠⠖⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⠃⠀⠲⢤⡉⠁⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢠⠖⠋⣀⠘⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠃⣀⠙⠲⡄⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠰⠛⣁⡄⠘⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣿⠃⢠⣈⠙⠆⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠚⣁⡤⠆⠘⣿⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⠃⠰⢤⣈⠓⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠉⠀⠀⠀⢨⣿⠂⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠐⣿⡅⠀⠀⠀⠉⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣀⣤⣾⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣷⣤⣀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡶⣿⡟⢿⡌⢿⣦⠀⠈⠻⠿⣶⣶⣶⣶⠿⠟⠁⠀⣴⡿⢩⡿⢻⣿⢶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢻⡌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⡟⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠘⣿⣆⢻⡌⢻⣧⠀⣀⡀⠀⠀⢀⣀⠀⣼⡿⢡⡟⣰⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡈⠉⠛⠛⠿⣶⣦⠀⠀⠘⢿⣆⢻⡄⢻⣿⢛⣿⡇⢸⣿⡛⣿⡟⢠⡟⣰⡿⠃⠀⠀⣴⣶⠿⠟⠛⠉⢁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⢀⡴⢻⣿⠀⠀⢠⣾⣿⡆⢻⣠⣵⡿⠋⠀⠀⠙⢿⣮⣄⡟⢰⣿⣷⡄⠀⠀⣿⡟⢦⡀⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡀⢀⣴⣯⣀⣸⣿⠀⠀⢿⣷⣶⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣾⡿⠀⠀⣿⡇⣀⣽⣦⡀⢀⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⠉⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⠿⠟⠛⠉⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣇⢠⡆⣰⡄⠉⣩⣍⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⡛⢛⣛⣛⣉⠉⡥⢤⡄⣶⡄⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⡾⢠⣧⣽⣸⡇⠈⢣⡏⠉⠓⣼⢸⢷⣸⡇⣼⢳⡈⢹⠁⢸⢸⡇⢀⡟⣿⠙⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣶⣬⣄⣈⡋⠓⠶⠋⠳⠤⠗⠿⠸⠀⠻⠧⠟⠛⠇⠸⠀⠘⠈⢛⣋⣠⣤⣶⡾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠿⠛⠛⠋⠉

⠀⢠⣴⠶⢶⣶⡿⠿⣶⣤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⠁⣼⡤⣏⠰⠶⣿⠰⠶⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⢔⢐⣴⡆⡄⣀⠴⢄⢤⠢⣖⠂⠀⢈⠄⠀⠀⠀⠀⠀⡄⠃⢀
⠀⠙⠷⠤⠴⠻⢷⣾⡿⠿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⣀⣀⣀⡀⢀⡀⢀⣠⠜⠀⠀⡠⠊⡀⢸⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠗⠁⠀⠀⠀⠐⠁⠀⠡⠞⢩⠙⠂⠤⣈⠂
⠀⠀⢀⡶⠀⠀⠀⠀⠀⠲⡔⢒⡊⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠛⠖⠚⠀⠀⠀⠥
⠀⡰⠁⡇⠑⡀⠀⠀⠎⡔⠉⠀⠀⠀⢢⡀⠄⠀⠀⠀⠀⠳⣴⣫⠗⣠⠞⠆⢠⠎⠙⣧⢀⣡⢀⡞⠀⠀⠀⢘⡿⡅⠈⠀⠀⠐⢄⠀⢰⠀⠀⠀⡠⠂
⠀⣇⠀⡇⠀⡱⠈⢰⠰⡀⠁⠀⠀⠈⠀⠇⡀⠒⠀⠀⠀⠀⠻⠤⠴⠻⣤⡤⠛⣦⡤⠎⠀⠈⠉⠀⠐⠀⢀
⠀⠈⠒⡇⠀⠀⠀⠄⢀⠱⣀⠠⠤⠊⠠⠁⢋⡀⠀⠀⡀⠀⠠⢄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠘⢘⠀⢢⢤⣀⠖⠃⠀⠀⠀⢸⠀⠒⠒⠃⢠⠁⣠⣈⡧⢀⠄⢀⡉⢢⡀⠀⢠⠁⠀⠒⠤⢠⡤⠴⠊⠁⠀⠀⠇⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⣀⣠⡀⢸⡀⠔⠂⠀⠀⠘⠀⠀⠀⢸⠀⠁⢹⠀⣇⠀⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠁
⡰⠨⢤⠉⠄⠀⢀⢰⠂⠐⠊⠐⢀⠀⠀⠰⠁⠀⠉⠿⢤⣀⣀⠀⠸⣄⣀⣀⡀⠸⣀⡀⠈⣠⠇⠀⠀⠀⣀⠤⠒⠁⠀⠈⠱⠄⠀⠀⡀⠀⠀⠐⠄
⠑⠊⠩⠔⠂⠀⠀⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠀⠀⠙⠛⠛⠁⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⣾⡆⠀⠈
⠀⠀⢀⣤⡖⠒⠂⠒⠒⣲⣤⡀⠀⠀⠀⠀⠀⠀⣰⣊⡉⠉⠉⢱⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠄⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⣠⡙⢻⡷⠀⠄⠐⣋⣭⣿⣿⣦⠀⠀⠀⠀⢠⠀⠇⢮⡁⢠⣷⠣⢹⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠱⣀⠀⠀⠂⠁⢈⠕⠀⠀⡐⠀⠀⠀⠀⠂
⢰⠹⠟⣃⡀⠀⠀⠼⠛⠟⠿⢿⣿⡇⠀⠀⠀⠎⠀⠈⠉⠑⠆⠘⡇⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⡇⢸⠒⠊
⢸⣷⣿⣿⠁⠀⠀⢠⣾⣿⣧⣙⠿⡇⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀
⠀⣿⠉⢁⡀⠀⠀⠙⠿⠿⣿⡿⢡⠇⠀⠀⠀⢸⠈⢀⡀⠀⠀⡰⠁⠀⠀⡎⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠰⠿⠿⠿⠇
⠀⠘⢿⣿⣿⣶⠀⠀⠀⠀⢿⡧⠊⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠇⠀⠀⠀⠣⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⣀⠀⠀⠀⠀⢀⣀⣀⣈⣥⣤⣄⠀⠀⠀⠀⢰⣁⠯⠆⡈
⠀⢠⠊⠁⢀⠀⠀⢀⠀⠀⠀⠄⠸⠀⠘⠇⠒⠒⠒⠀⠀⠀⠀⠏⠀⠀⢀⡤⠚⠙⠀⠀⠀⠘⡇⠀⠀⢠⣿⢩⡍⢹⠁⠌⣿⡇⠀⠀⠀⠀⠀⠐⠁
⠀⠸⣀⡡⠃⠉⠡⠏⠌⢹⠐⠂⠂⠀⠀⠀⠀⢠⠀⠀⠠⡄⠀⠀⠀⢰⠏⠠⠀⠀⠀⡀⢀⣀⠇⠀⠀⠈⠻⢶⣶⡿⢗⣶⡿⢶⣦⡀⠀⠂⠀⢶⡄
⠀⠀⠀⠐⠒⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⡀⠠⠀⠀⠀⠀⣄⠀⠀⢀⠴⠭⠤⢤⡟⠐⠀⠀⠀⠀⢀⣿⣇⡛⣉⣇⣄⣻⡷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⠈⠀⣀⣠⠭⠶⠆⠀⠀⠀⠀⠠⠀⣀⣀⣀⠠⠆⠀⠀⠉⠀⠠⠋⠀⣀⡴⠋⠀⡘⠀⠀⠀⣼⡏⠛⢹⡏⣿⢩⣹⣿⠁⠀⠀⠀⢀
⠀⢀⡀⠀⠞⠋⠋⠁⣀⠔⠁⠀⠀⠀⠀⠖⠰⢠⠂⠖⡔⠂⠀⡇⠀⠀⠀⣜⣴⣞⡉⠤⠀⠀⠀⠀⠀⠀⠻⣧⣷⣾⡷⢿⣮⣿⡿⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠿⠒⣴⠞⣴⠛⣱⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⣿⡏⣀⠁⡐⢃⡴⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠔⠚⠘⣿⠿⢆⣿⣴⢳⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣴⣿⣦⠀⣘⠙⠿⣟⠻⠈⣾⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣤⢾⣴⣫⣍⡻⡎⣶⡕⢸⡿⢼⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠋⣾⣏⠙⢓⣣⣿⣷⢈⣽⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢿⣦⣭⣭⣿⣧⣤⡰⣾⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣽⣿⡟⠁⠘⣷⠘⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⣋⡾⣮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠉⠙⣿⣿⣿⣿⠟⠳⣬⢳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠸⣿⣿⡇⠀⡄⠘⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣇⠀⣠⣿⣿⣿⣶⣿⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⡟⠛⠉⣿⠏⠉⠙⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢻⣦⡀⣿⡆⠀⠀⡿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢿⣾⣷⡀⠐⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢦⠀⠀⠀⠑⢦⣁⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⠀⠘⡐⠓⡀⠀⠀⠀⢻⠻⣄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠂⠀⠂⠀⠋⠀⠀⠀⠀⠀⢿⠏⠳⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡔⠈⠂⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠠⠀⠀⠀⠁⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣄⠀⠀⠁⠂⠀⡀
⠀⠀⠀⠀⠀⣱⡀⠜⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠓⢀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⢉⠀⢄⠀⠀⠀⠀⠀⠀⠉⢀⡀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡀⢈⡆⠀⠀⠀⠀⠠⡄⠀⢛⣆⠀⠸⣅⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠇⠈⠁⠀⠀⠀⠀⠈⢠⠄⠘⢀⠱⡀⠀⢰⠄⠀⠀⠀⠀⢐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠙⣷⠀⠀⠐⠁⠀⠁⠈⠀⠀⠄⠀⠀⠲⣄⠀⠀⢐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠳⣮⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠙⣆⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⠏⠳⣄⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣂⣀⣀⣀⣈⣁⣀⣀⣀⣀⣠⣚⣁⣀⣀⣌⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡟⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢀⣤⣴⠶⠶⠶⠶⠶⢦⣤⣤⣀⣀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣀⣠⣤⣤⡶⠶⠶⠶⠶⢦⣤⣀
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡿⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠉⠛⠳⢶⣤⣤⡶⠛⠋⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⠶⠛⠉⠙⠻⢦⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣴⠟⠋⢸⡇⠀⠀⠀⠀⢠⡶⠛⠛⠛⢷⣄⠀⠀⠀⠀⠈⣿⠈⠙⢷⣄⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣾⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣿⠀⠀⠀⠉⠻⣦⡾⠋
⠀⠀⠀⠀⠀⣠⡾⠋⠙⢷⣄⠀⠀⢸⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⣿⠀⠀⢀⣴⠞⠋⠻⣦⡀
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠉⠻⣦⣸⡇⠀⠀⠀⠀⠀⠙⠷⠶⠶⠛⠁⠀⠀⠀⠀⠀⣿⣠⡶⠛⠁⠀⠀⠀⠈⠻⣦⣀⣀
⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⢻
⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⢀⣤⡶⠛⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣴⣿
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠛⢷⣦⣴⡞⠋⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⡶⠟⠋⠁⠉⠛⠷⢦⣤⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢷⣄⣀⠀⠀⣴⠟⠻⣦⣀⣠⣤⡴⠾⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡿⠶⣦⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣴⠟
⠀⠀⠈⠉⠛⠛⢷⣀⣀⡾⠉⠁⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⢀⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠤⢆⡉⠉⠁⠩⡉⠈⠈⢉⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠠⢈⠗⡖⠃⠒⠲⣤⣌⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠒⡁⠀⣣⣀⣈⡠⠃⢍⡠⠔⣛⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠈⠑⠬⣋⡀⠀⠀⣀⣀⠠⠴⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⡑⠦⢀⠀⠀⠆⠀⠛⠀⠟⣡⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⢤⠄⠀⠈⠀⢸⠠⠀⠀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡖⠀⠀⠠⢠⠆⠀⠀⠇⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠀⠀⠐⠄⠀⠀⠀⡠⠊⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⢠⡊⠁⠢⡀⢀⠌⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠆⠈⠘⡤⠤⠔⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢀⠀⠐⠀⠠⠤⠄⢤⠐⠊⠠⠀⠐⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠒⠠⠄⡼⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⡗⠠⠄⣀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠈⠣⣀⠀⠀⠀⢁⡁⠟⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠤⠀⠠⠊⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣿⣛

⠀⠀⠀⠀⠀⡠⠲⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠝⣶⣶⡿⣏⠀⠀⠀⠀⠀⢀⢀⣦⠙⠀⠀⠀⠰⠿⣿⣿⡿⢿⣆⠀⠀⠀⠀⠀⠈⢀⣮⣄⠄
⠀⠀⢠⠊⡀⠸⠿⠣⡈⢦⠀⠀⠀⡀⣨⡿⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠛⢛⠛⠀⠈
⠀⠀⠘⠚⠓⠒⠒⠒⠚⠒⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣷⠆⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⢰⣶⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠔⢲⣶⡦⢄⠀⠀⠀⠀⠉⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⠀⠰⠀⠁⣤⠀⠈⠁⠀⠀⢀⣀⡘⣟⢀⣀⠂⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠈⠒⠊⠑⠆⠀⠀⠈⠁⠀⠀⠺⡿⠋⠉⠻⣿⠂⠀⠀⠀⢀⣠⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠈⠀⠀⠀⠀⠸⢿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⡶⠠⠄⠐⡠⠀⠀⠀⢠⣌⠡⠦⠀⠀⠐⠆⠀⠀⠀⠀⠘⣾⣟⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⣧⠀⠁⠀⢛⠀⠀⠀⠈⠉⢠⣤⠛⣈⡃⣀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠈⠀⠁⠄⠀⠿⠀⠀⠀⠀⠶⠊⢩⡀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡇
⠀⠀⢸⢷⣤⣾⣧⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠓⠒⠒⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣀⣨⣇⠀⠀⠀⠀⠀⠀⠀⠲⠆⠰⠶⠀⠶⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⠀⠀⠀⠀⡠⣴⠒⠲⢤⡀
⠀⠀⠈⢩⡟⢩⡗⠀⠀⠀⠀⠀⢰⠆⠒⠒⠐⠒⠀⠶⠀⠀⠀⢀⣤⣴⡉⠉⣿⡆⠀⠀⢈⡼⢧⡀⣠⠷⣴
⠀⠀⠀⠈⢛⡿⠛⠛⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠍⣿⣷⣾⠟⠁⠀⠀⠈⠀⠀⢰⠀⡀⠈
⠀⠀⠀⠀⠀⠙⠛⢻⠟⠂⠀⠀⠘⠛⠛⠛⠚⠛⠚⠓⠀⠀⠀⢠⣶⣾⣿⣷⣶⡄⠀⠀⠀⠁⠛⠋⠛⠑⠁

⠀⠀⠀⠀⠀⠀⣴⠀⠝⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡤⠀⠴⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⣠⠀⠀⠈⠃⣴⠃⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⣿⠏⠀⠀⠀⣄
⠀⠀⠀⠀⠈⣷⠀⠀⣤⠃⣰⡇⠀⠀⢠⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⣿⣄⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣀⠀⣠⠆⠃
⠀⠀⠀⠀⠀⠸⣆⠀⢁⣠⢿⠁⠀⠀⠀⠀⠀⠀⠙⠙⠗⠀⠀⠠⠆⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻
⠀⠀⠀⠀⡄⣰⠹⣶⡈⣧⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠂
⠀⠀⠀⠀⢱⡏⠐⠋⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠁⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣆⣠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠄⠀⠀⠀⢀⠤⢴⠲⠶⠶⠛⠉⠃⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡿⢦⠄⠤⠼⠛⢻⠀⠇⣠⠀⠀⠀⡈⣠⢆⠀⠈⠇⠀⠤⠆⢠⡖⠀⠀⠀⢸⡇⣠⠛⠢⠀⠐⠁⢀
⠀⠀⢠⠃⣰⡇⠀⠀⠀⠀⠀⠀⣇⣼⠇⠀⢀⣴⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⠃⠀⠀⠀⠀⠀⣸
⠀⠀⢸⣾⡁⠧⠶⠄⠀⠀⠀⠀⠸⠿⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢀⣤⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠒⠊⠉⠊⢀⠒⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠠⠤⠓⠂⢒⣸⠓⠂⠀⠠⣭⣥⣤⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡠⠒⠀⢈⣩⡭⠭⠤⢈⡁⠈⠛⢍⠭⠉⠷⢻⠁⠀⠒⠂⠀⠀⠀⠐⢒⠂⣭
⠀⠀⠀⠀⠀⠛⠂⠀⠠⠬⠬⠉⠭⠭⠤⠀⠐⣁⡄⠀⣨⢾⡀⠀⠀⠀⠀⣜⢜⢕⠥⠪⠞
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⢔⠔⠐⠀⠀⢺⣠⣆⠠⠀⣹⠷⠲⠤⠴⠤⠷⠚⢶⡕⠄
⠀⠀⠀⠀⠀⠀⠃⣤⣀⡀⠐⠐⠅⠔⡕⣑⢹⣛⡙⠂⣠⢸⠁⠀⠈⠉⠉⠉⠉⠁⡀⢀⠀⡄
⠀⠀⠀⠀⠀⢀⠜⠉⣁⡈⠉⠉⠋⠉⠁⢋⠓⠷⡀⡄⠀⠈⠀⠀⠀⠀⠀⠠⠪⠦⠨⠘⣀⡇
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠉⢉⢉⢉⠄⢀⠤⠂⣇⡂⠀⡂⠀⢨⡉⠀⢒⠒⡒⢂⡉⣉⢰⡇
⠀⠀⠀⠀⠀⡟⠢⠤⢀⡀⠀⠁⠀⠀⠐⠉⣉⠁⡇⣀⠀⡇⠀⢸⡈⡄⠽⣘⠀⢀⠀⡏⢻⡅
⠀⠀⠀⠀⠀⣷⣴⡆⡄⠄⣉⠉⠉⡉⢉⠡⠂⠀⡇⠀⠎⡇⠀⢸⣹⣶⡠⠭⠂⠨⠄⠒⠚⠄
⠀⠀⠀⠀⠀⠯⣈⠁⢆⠸⣀⠠⠀⠑⣌⢈⡁⠀⡇⠀⡀⠅⠀⢸⠀⡫⠑⣋⣉⡀⠀⣒⠀⡆
⠀⠀⠀⠀⠀⣾⠶⣭⡒⢒⠂⠤⠤⡤⠄⢒⠊⠁⡖⠒⢛⡀⠀⠀⠲⣦⠍⡀⠂⠀⠀⣀⠤⡇
⠀⠀⠀⠀⠀⢲⣅⣒⠀⠈⠝⠉⠀⠇⢸⡗⠀⡆⡏⠉⠉⢙⠀⠀⠀⠀⢉⣒⣒⣎⠩⠀⠀⡏⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⡙⠪⢕⡀⠸⠓⠂⠀⠀⠈⠀⣀⠃⡧⠀⠀⠈⠢⡙⢤⣐⠛⡬⣍⣸⣶⠟⣸⣒⢒⣒⡂⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠁⡀⠀⠀⡉⠐⠒⢒⠂⢀⡊⣠⠂⣗⣒⡂⠀⠀⠈⠑⠪⢥⣬⣬⣬⣴⡛⠠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠘⢜⡦⣀⠨⠲⠃⠔⣤⢦⣴⠟⡾⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠪⢍⣊⠗⠒⠚⢉⢠⠚⣁⠀⠀⡀⠠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠉⠠⠤⠠⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⡉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⠰⠀⠒⠄⠀⠀⠀⠀⠀⠠⠰⠀⠀⠄⠆⢀
⠀⠀⠀⠀⠀⠀⠸⠤⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⢃⢀⠞⡍⠌⣂⠄⡀⠀⠀⠀⠀⠐⢯⢨⠭⠅⠭⠝⠹⡆
⠀⠀⠀⠀⠀⠓⠖⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⡤⢁⡀⣤⠀⠀⡖⠒⠀⠀⠀⠀⠀⢀⠉⠲⡠⠔⣇⡄⠴⠀⠀⠀⠀⠀⠇⡀⠀⢆⠂⠀⠠⠇
⠀⠀⠀⠀⠀⠰⠉⠈⠉⠡⠀⠀⠀⠀⠀⠀⠀⠨⠀⠨⠤⠄⠅⠀⠑⠀⠀⠀⠀⠀⠀⠈⠚⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠀⠀⠈⠀⠠⢀⠄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠄⠀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠊⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠰⣤⠚⡖⣰⠒⠀⠀⠀⠀⠀⠀⢠⣾⠒⢠⡘⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠠⡢⠀⣠⠀⡔⠄⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠈⢬⡱⡀⠰⠹⠀⠀⠀⠀⡔⠁⠀⠈⣤⡀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣈⠉⠀⡀⠡⠂⠀⠀⠀⠀⡄⠀⣠⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡠⢀⠁⠐⢄⠀⡠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⢦⠀⢤⠂⠀⠀⠀⠀⠀⠀⢀⡔⠓⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⡀⠀⢀⢀⣀⢀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠘⠐⠂⡤⠀⡸⠀⢸⠀⡠⠠⠄⠀⡇⠐⠀⠒⢄⠑⡆⠀⠈⢠⠤⡄⠱
⠀⠀⠀⠀⠀⠀⡜⠁⡔⠁⠀⢸⠀⣀⣀⡀⠀⡇⠠⡠⠠⠊⢀⠂⠀⠀⠆⠀⢠⠀⡀
⠀⠀⠀⠀⢀⠎⢀⠌⠀⠀⠀⢸⠀⡤⠤⠃⠀⠇⠀⢄⠀⠂⠁⠀⢰⠀⠀⠀⠘⠀⡃
⠀⠀⠀⢀⠎⠠⠏⠀⠠⡀⠀⠸⠀⠇⢀⡀⠀⠀⢦⠈⢢⠀⠀⠀⠀⡀⠣⠠⠂
⠀⠀⠀⠘⠤⠤⠤⠤⠤⠂⠀⠰⠤⠤⠤⠃⠀⠦⠂⠁⠤⠃⠀⠀⠀⠐⠠⠠⠐⠁

⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠒⢲⠀⠀⠔⠐⠄⠀⠀⢀⠖⠉⠉⠲⡀⢰⠀⠀⠀⠀⠈⠀⠀⡀⠀⠖⠂⠀⠐
⠀⠀⠀⠈⡄⢰⠀⠀⡠⠤⡀⠀⠀⠃⡀⠀⠐⠀⠀⠘⠀⠀⡂⢰⠁⠀⠉⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⡇⠈⠉⠉
⠀⠀⠀⠀⢡⠀⡆⠰⢡⡄⢱⠀⠰⢀⠁⠀⡀⢈⠁⠀⠀⠀⠑⠄⢉⣁⠐⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠰⠤⠤
⠀⠀⠀⠀⠘⡄⠰⠇⠎⢸⠘⡀⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⡖⠀⠈
⠀⠀⠀⠀⠀⢃⠀⡜⠀⠈⡄⠓⠁⠇⠀⢈⠀⠔⡄⠀⠀⢐⠁⣀⣀⠠⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠣⠤⢤
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠒⠊⠀⠀⠐⠐⠀⠑⠒⠀⠀⠑⠂⠀⠒⠁⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠘⠂⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡈⠙⠲⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣶⣶⣶⣒⣴⣧⡀⠀⠙⣿⣷⡄⢹⡎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣮⣿⣿⣿⢷⣄⠀⠈⣿⣧⡀⠁⠂⠹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣾⠁⣿⣷⣶⣦⣾⣿⠍⠀⠠⠄⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡛⠿⣿⣿⡟⠛⠀⠀⠀⢀⣴⠀⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⢻⣿⠛⠻⣤⠉⠛⢠⠈⠁⠈⠉⠁⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿⣿⣿⣷⣾⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⡿⠋⢉⣿⡿⣷⣀⣀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⣾⡿⠃⠸⠛⠛⠋⢻⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠁⠉⠛⠛⠛⠉⠉⠀⡀⠀⠀⠀⠘⢿⠀⠀⠘⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡤⠄⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡔⠃⠀⠀⠈⠉⣉⣱⡦⠶⠆⠀⢀⣴⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⡀⢁⡠⢔⣰⣿⣿⣏⣴⣶⣶⡾⠟⠛⠁⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⣬⣶⣼⣿⣿⣿⣿⠟⠛⠁⠀⠰⣤⣄⠂⠀⠀⠀⠄⠀⠀⠀⠀⢀⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⢠⣰⠂⠀⠀⠀⢂⣤⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣾⣯⣧⣿⣿⢻⠛⣿⠁⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡦⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡚⠐⠀⠐⠐⠓⣄⠀⠀⠀⠀⠀⣀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠀⠀⠀⢿⠢⣀⣤
⠀⠀⠀⠀⠀⠀⠼⢰⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠈⣑⡂⠉⣉⠁⢰⠀⠀⠀⠀⠀⡛⠁⠲⣆⣀⢴⠄⣶⡄⠀⠀⢀⠴⠚⢿⡉⠁
⠀⠀⠀⠀⠀⠀⢷⠎⠑⠀⠁⠀⠀⢰⣶⡦⢀⠀⠀⠀⠀⠀⠀⠘⡤⠠⠄⣀⣀⠀⠠⡼⠀⠀⠀⠀⠀⡸⠶⡚⣴⡎⣲⣠⠊⠀⠀⠀⢸⣌⡒⣼⠇
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠇⢀⠀⠀⠀⢇⠰⣶⠉⠢⣀⠀⣀⠀⠀⠈⠲⢔⡀⠀⡠⠎⠀⠀⠀⠀⠀⠸⣀⣀⡯⠶⢴⡃⠈⢂⠀⢠⡖⠛⢿⡉⠁
⠀⠀⠀⢩⠙⡁⠀⠀⡘⢀⠆⠀⠀⠀⠈⢢⠀⠀⠀⠈⢦⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⠎⠈⠁⠁⠀⠀⠉⠊⠲⠇
⠀⠀⠀⠀⢢⣤⣷⣷⣴⡅⠀⠀⠀⠀⠀⠀⠟⢤⣀⣠⡾⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠘⠛⠉⠉⠉⣁⣰⠀⠀⠀⠀⠀⢃⡆⠈⠫⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠘
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠢⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠐⠒⠒⠠⡀⠐⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡲⠶⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡲⠁⠀⠠⢀⠈⢻⢆⠀⠀⠀⠀⠀⠀⠀⡇⠒⠀⡏⠀⠀⠀⠀⠀⠂⠃⠀⣀⣠⢠⠀⠀⡆⡀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡔⠁⠔
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠰⠁⠀⢀⠻⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡇⠀⠀⠀⠀⠀⠀⠘⠄⢸⠁⠁⠀⡔⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⣀⠀⣀⣠⠺⠁⠀⠀⠀⠀⠀⠀⠠⣀⣤⣤⡰⡀⠀⠀⠀⠀⠐⠁⢀⠈⠀⠐⢰⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⠉⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⡠⢉⠏⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣿⣿⣿⣷⡑⡀⠀⠀⠀⠀⠀⠘⠁⢀⡀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡜⢠⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡐⡀⠀⠀⠀⠀⠈⠓⠂⠀⠊
⠀⠀⠀⠀⠀⠸⣀⠏⠀⠀⠀⣄⣂⡡⠔⢇⠀⠀⠀⠠⣛⠛⣛⢛⠛⣻⡛⢛⠓⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠔⠉⠀⠶⠁⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠈⠱⠄⠀⠸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸⣄⡀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠒⠀⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠛⠓⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠀⠛⢟⠻⠋⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚
⠀⠀⠀⠀⠀⠐⡎⠉⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣤⣾⡍⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⢀⠄⠁⠀⠈⠚⡝⠁⠀⠀⠀⠀⠀⡜⠀⠈⢻⣿⠁⢀⣀⡀⢁⠀⠀⠀⠀⠠⣂⣽⠩⠽⠀⠸⡀⠀⠀⠀⠀⠅⢬⡑⢄⠀⠀⢀⠔⢊⡥⠂⢀⠄
⠀⠀⠀⢠⢁⡀⠄⠀⠤⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠿⣿⣿⡇⠘⠀⠀⠀⠀⠀⢹⠀⢡⠀⠒⠀⢡⠀⠀⠀⠀⠐⢌⠁⠾⣀⠠⢣⡟⠀⢀⠤⠊
⠀⠀⠀⠀⢆⠢⠀⣀⡀⠔⠜⠀⠀⠀⠀⠀⠀⠄⠻⣿⡿⠁⠀⠀⠉⢡⠃⠀⠀⠀⠀⠀⠀⢂⠀⢃⠰⣷⠄⠆⠀⠀⠀⠀⠀⠁⠀⠙⡷⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠁⠂⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠁⡀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⡶⠿⡀⢀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢶⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢇⠈⢧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣧⠈⢇⠈⢆⠈⢇⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠠⣦⠘⢇⠘⣇⠘⣇⠙⢧⠈⢆⠈⢆⠈⢆⠈⣦⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣈⣿⣿⣿⣿⣿⣿⡙⡇⠘⣄⠈⣆⠘⣆⠈⣆⠸⡧⠸⠇⠸⠇⠸⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠛⠋⠈⠛⠛⠿⣿⣿⣿⣿⣧⠘⡄⠈⡄⠘⡄⠈⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⢋⣬⠐⡄⠘⣄⠸⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⡷⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡠⠞⠋⠁⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⣀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡋⣀⠀⠉⠛⢒⣲⣷⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⠤⠤⠉⣻⣅⢹⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡐⠂⠈⠻⠿⠟⣫⣽⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠂⣿⣿⣆⠀⠀⢀⡤⠀⡰⢊⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡅⠡⢷⣾⡟⠋⠀⠀⠳⠌⢹⣂⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⠒⠒⠚⠿⠇⢀⣴⣧⡀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣤⣤⢤⣄⡀⠀⠀⠙⡿⠋⣀⣴⣾⣿⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⢉⣿⣿⡿⠁⣐⣶⠋⣴⣾⣿⣿⣿⣇⣀⣠⣶⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡻⠖⠛⠁⠁⠘⠿⠿⣦⡙⢿⣿⣿⣿⣿⠿⠿⠋⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⢀⣀⠀⣀⣀⡀⢻⣿⣶⣝⡻⢿⣤⣴⢦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⣿⣿⣿⣁⢿⣟⢻⣿⣿⣿⣿⣿⠃⠨⢯⣤⡅⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⠽⠛⠁⠈⠙⡿⢿⣿⣻⣽⣶⣿⡿⠁⡸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣠⡼⢀⣘⣿⡿⠿⠿⣿⢧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⡽⠿⠇⢸⣿⡋⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⢀⣴⡾⠃⣼⣿⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠙⡿⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⣺⡁⠀⠀⢠⠏⠀⠀⠀⣠⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⡞⠀⠀⠀⣼⣿⡿⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣠⣅⠀⠀⠀⠹⣿⣿⣿⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠛⠛⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠒⠒⠷⣿⡖⠐⠢⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⡠⠒⢒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠙⠲⣶⣶⣦⣀⢈⡿⠶⠴⠁⠀⠀⢻⣦⣤⣤⣄⣍⣑⠖⠀⣠⣤⡿⠋⠁⣠⡑⣀⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⠲⢶⣿⣀⠀⠈⢻⣿⢿⠟⠁⠀⠀⠀⠀⠀⠘⠿⢿⠿⠟⠻⡇⠀⣸⡿⠋⢀⣼⣿⡟⠋⢉⣁⣌⠃
⠀⠀⠀⢀⠊⢀⣼⣿⣶⣤⣤⣾⣿⣿⣷⣶⠾⢱⢺⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣦⣼⠘⠀⣠⣿⠇⠀⣸⣿⠏⠀⣰⣿⣿⣿⡀⠆
⠀⠀⠀⢘⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⡧⣼⡦⠤⣄⠀⠀⠀⠀⡖⠒⠀⠀⢺⠘⠶⠋⢰⠀⣰⣿⣿⣤⣾⣿⣿⣿⣟⣳⠈
⠀⠀⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠄⣰⠊⠀⠀⣠⠞⠀⠀⠀⠀⡆⠀⠁⠀⠙⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢡
⠀⠀⠀⢘⠈⠋⠹⢛⣿⣿⣿⣿⣿⢿⣿⣶⣯⣤⣴⡿⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣾⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡆
⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⢾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱
⠀⠀⠀⠠⠀⢿⣿⣿⣿⡟⣿⠁⣿⣿⣿⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠸⡆
⠀⠄⠀⠘⣣⣉⣿⣿⣿⣇⢻⡄⠻⡟⠋⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡘⡻⣿⣿⣿⣿⣿⣿⣯⣤⡈⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⢾⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠛⠻⣭⠁⠀⠀⠉⠈⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⣠⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠄⠀⠄⠀⠀⡰⠃⠱⡀⢠⠇⢩⠀⠀⠈⢣⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠄⢠⠄⠘⠄⠀⠀⠱⡴⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠙⠻⠧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠶⡒⠒⠂⠀⠉⠹⡀⠂⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢀⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡦⠀⠀⡀⠀⠱⡀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⡔⡥⠦⠤⠠⠤⠄⡄⠁⠀⠀⠀⡠⠃⠪⠤⠤⠤⠤⠤⠬⠴⠖⠗⢠⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⡄⢸⡎⠀⠀⠀⠀⠀⠀⡏⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠑⢦⡀⠀⠠⠀⠀⠃⢀⠀⠀⠘⢦⠀⢰⡂⠀⠀⣀⣀⡤⢞⡙⢫⣄⠀⠀⢀⠀⠴⡉⢋⠒⢄
⠐⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠈⠠⡀⠀⠀⠑⢾⠉⠉⠁⢍⠀⢴⣿⣦⣥⡍⠀⠄⠠⠾⠾⣿⣿⣣⢨
⠛⠄⠀⠛⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠈⠢⢅⣇⠠⠉⠁⠈⠄⠀⠘⠦⣉⣋⣡⠎
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⣶⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢹⣦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣭⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠉⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠤⠾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⣄⣤⣤⣤⡀⠉⠁⠀⢳⠀⠀⢀⣶⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠏⠁⠈⠛⢻⣂⡀⠀⠲⣷⠀⢼⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡆⠀⠀⢀⣀⡈⠻⣗⠀⠀⠜⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⢶⠶⠞⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠟⠉⠀⠑⣄⠀⢀⢀⣠⣠⣄⢤⡈⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠺⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣽⣿⠟⢻⠉⠛⠯⠟⠳⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣴⡾⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣠⡄⠂⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣰⣿⢀⡆⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣼⠋⠀⠘⠄⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠀⠀⠀⡼⠛⠿⠟⠋⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⣀⣠⣤⣾⣿⣯⣷⣞⡿⣿⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⣴⣏⠀⣴⣾⣷⣾⡿⣿⠛⠻⣿⡿⣁⣿⣆⠀⣎⠀⠀⠀⠀⠘⠀⠀⣼⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣿⢿⣼⣿⣿⣿⣿⠋⠋⠒⠶⠿⠟⠛⠋⢹⠀⠹⡄⠐⣄⢳⢁⣼⠏⠙⢿⣜⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠟⣾⣿⣿⣿⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠸⡆⢸⡎⢈⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣴⠟⠻⣿⣉⣿⣿⣿⣿⣷⣿⡿⢻⡟⢻⣿⣭⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠉⠀⡀⢀⡀⣿
⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⡿⠿⠟⡛⣋⣀⠟⢁⣸⣿⣿⠀⠘⣦⢻⡿⠓⠿⢳⡶⠆⠀⠀⡆⠀⠘⢆⡀⢠⠁⠀⠀⣿
⠀⠀⠀⠸⣿⣦⣶⣿⣿⣿⣷⣤⣤⡿⠯⡉⣀⣾⠈⠻⣿⣔⣛⡁⠈⠐⢦⣆⣈⣧⠀⠀⢤⣷⠐⠂⢨⣿⣿⠂⠆⢰⣿
⠀⠀⠀⠀⣸⣹⣹⣿⠿⠥⠾⠷⠦⠶⣾⣿⣌⡙⠛⠚⠚⠛⠛⠓⠒⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⣀⣤⣤⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣻⡇⠸⢏⣿⡟⣾⡋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠿⠶⠶⢦⣭⣴⣭⡉⢷⣀⠀⠀⠀⠀⢻⡆⠀⠀⠘⠻⠾⠿⠿⣦⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣹⠃⠀⠀⣠⡼⠃⠀⢀⣀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢻⣄⢀⡾⠁⠀⠀⠀⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣭⣉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢰⡟⠳⣦⠀⢰⡟⠁⣀⣀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠁⠈⠙⠛⢾⣝⠛⣿⣆⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⢹⡆
⠀⢸⡇⠀⢿⡇⢸⡇⠀⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠋⠀⠀⠀⠀⢀⣾⣯⣤⣈⢻⣆⠀⠀⣿⠀⠈⠻⣦⠀⠀⢸⣇
⠀⣸⡇⠀⠈⣿⠚⠷⠚⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⢿⣿⣛⣿⣯⡄⠀⠐⣿⠀⣤⢴⡏
⠀⢻⡇⠀⣾⠏⠀⠀⠀⠀⠈⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠙⠛⠃⢸⡇
⠀⢸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢠⡶⠟⠀⠀⠀⣠⠶⠶⠶⣿
⠀⠀⢹⣏⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣼⠏⠀⠀⣸⡏
⠀⠀⠀⢻⡄⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣷⠀⠀⣰⡟
⠀⠀⠀⠀⢻⡄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢰⣏⣀⣴⡟
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣿⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣾⠉⣿⠞⠁⠈⣩⡿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠹⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⡾⠃⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣙⠷⣄⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⡶⠶⠶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⢶⣶⠶⠶⠶⢶⡶⠶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⢉⣓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡤⠂⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠐⠣⣀⣘⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠙⠇⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡴⠛⡆⣠⠁⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⢀⡔⣁⠤⠼⠒⠲⠤⣄
⠀⠀⠀⢀⣞⣀⣠⡇⠘⢦⣀⣠⠞⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢰⣀⠞⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⣠⠊⠉⢰⠃⠀⠀⠀⣀⠯⠂⠀⠀⠈⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⡴⠁⠀⠀⢀⡱⠖⠂⠉⠀⣀⠀⣀⡄⠀⠀⠈⢆⠀⠈⠀⡗⠂⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⡼⠳⣶⠖⠈⠀⠀⠀⣀⠔⠊⠁⠙⠳⠇⠀⣏⠛⠢⢦⠀⠀⠛⠀⠀⠐⡎
⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⣦⠐⠀⠀⠈⠣⣀⠀⠀⠀⢀⠇⠀⠀⠂⠀⢸⡎
⣀⣀⡠⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡌⠂⢄⣀⡼⠓⠢⣀⡸⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠈⡦⡀⠀⠨⡃⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⢠⠃⠈⠢⢄⠘⠤⣀⢀⡎⠈⠒⢄⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⡼⠀⠀⠀⠀⠑⠒⠈⠉⠀⠀⠀⠀⠈⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠘⠋⣡⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢈⣤⡀⠈⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⠟⠿⣿⡀⠈⠑
⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⢠⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣈⣥⡦
⠀⠀⠀⠀⢀⡀⡁⠀⠀⠠⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣄⠋⠁⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⡂⠀⠀⠀⠀⠀⠀⠃⠻⠀⠀⠀⠀⠀⢰⣶



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣋⣍⣹⣟⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⢦⣶⠛⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠀⠀⠀⠙⠘⡀⠀⠀⠀⠁⠉⣦⠂⠆⣔⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⢎⣱⣿⠷⣶⠉⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⢻⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠄⠈⢋⣿⠢⠁⢄⠈⢸⣏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⣧⠘⠺⠅⠀⠀⠔⡀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡛⠃⠀⠐⠚⠻⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⡟⠀⠀⠠⠀⡗
⠀⠀⠀⣀⠀⠐⠈⠀⠀⢀⣔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢄⡂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡀
⠀⠀⢸⣿⠀⠀⠀⠀⣤⡼⠟⠒⠒⠀⠰⠂⠀⠀⠀⠀⢰⡀⠚⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢤⡏⠁⡀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⡆⠀⠀⢂⣀⠃⢉⡽⡀
⠀⠀⢸⣿⡇⠀⠀⠈⠛⠚⣁⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣆⠀⠀⣤⣦⣞⡜⠁
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠿⠟⠻⢿⡿⠇⠀⠀⣽⠝⣸⣃⠄⠀⡀
⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⠄⠒⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⢬⠀⣴⠞⠶⣿⡿⣿⣶⠋⠀⣿⣿⠆⣸⠃
⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠀⠀⢰⡟⡰⠁⣄⡠⠄⠀⠀⠀⠀⠀⠀⢁⡂⠀⠈⠙⠻⠆⠠⣈⠋⣈⢫⣤⣤⣿⣿⣿⣇⣆
⠀⠀⠈⢿⣿⣿⣿⣄⣆⠀⢀⣤⣶⠀⠀⣿⣷⡇⠀⡀⣰⡷⠀⠀⠀⠀⣤⣦⣄⢀⠀⢀⡄⠀⠀⠀⢻⡿⠿⠿⣿⡿⠿⠿⢛⡠⠝⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣧⣡⠍⠀⢸⣿⡇⣠⡘⢛⣻⣿⡀⡀⡄⠍⠁⠉⠻⠀⣣⡜⡂⠀⠀⠀⣾⡇⠀⠠⣶⡄⠒⠒⠁⠐⠀⣀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⢙⣇⣼⢻⡟⣀⣸⣿⠛⠉⠀⠀⠙⣯⠀⠀⠀⡀⠸⢿⣿⣷⣶⠄⡀⣿⣧⣾⣦⡛⠂⠀⠀⢠⡶⠋⢁
⠀⠀⠀⠀⠀⠉⣶⣿⣿⡏⠋⠻⢿⣷⣾⠃⠀⠈⣷⠀⠀⠀⠀⢰⣧⣤⣀⣤⡇⠀⣤⣷⠚⡛⠊⢳⣿⡿⠟⢻⣿⡆⠀⠀⡎⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢀⢸⣿⣿⠈⣷⣤⠏⠀⠀⠀⠀⠈⢻⠿⢫⠥⠁⠀⠛⠉⠀⢛⣛⣤⣶⣷⠆⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠈⠘⠛⢿⡈⠿⠿⠦⣀⣤⣤⣤⡤⠜⠀⠀⠀⠀⠤⠴⠶⠿⠿⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⢀⠀⠀⣤⣤⣤⢀⣠⣒⣢⣼⠶⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢳⡀⠀⠀⣴⣆⠀⠀⠀⠀⠀⢠⡴⠊⠻⠋⠛⢰⠋⠘⢀⠁⠈⠉⠉⠉⠛⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⣠⠆⠀⠐⢲⡟⣧⠀⠀⠈⢶⣌⡀⡀⣀⡤⠏⠁⠀⠀⠀⣀⠘⠀⠀⡈⠀⠀⢀⣠⣰⣾⡿⠋
⠀⠀⠀⠄⠀⠀⣤⣰⣶⣶⣶⣶⣿⠙⠛⢿⣷⡶⠿⠦⠞⢇⣀⡀⠴⠿⠻⠋⠀⠀⠀⠀⠉⠙⠙⠛⠀⠀⣀⣄⣠⣤⣼⣷⣷⣾⡿⠾⠿⠿⠿⠟⠉
⠀⠀⠀⣀⣿⣶⠿⠛⣫⣾⣿⣿⣀⡀⠀⠀⣿⠶⠦⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⠆⠴⠶⣦⣌⡁⠀⠀⠙⠉⠹⡏
⠀⠀⠸⣾⣿⣁⠀⢠⣿⠟⡉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠯⠽⢜⣦⣅⣀⠁⢈⣷⣄⠀⠀⠁
⠀⠀⠀⠙⠉⠛⠛⠛⠁⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣶⣿⣿⣿⣿⣤⣔⣛⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡆⠀⠀⠈⠙⠇⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠽⠿⠿⠿⠿⠛⠁
⠀⢀⠀⣠⣤⠀⠀⢀⠀⡄⠈⠈⠁⠀⠀⠀⢀⡄⠀⠀⢠⣔⠻⣿
⠀⠀⠁⠋⠉⠁⠉⠛⢋⠀⠀⠀⠀⠠⠀⠉⠘⠁⠀⡹⠊⣿⡒⠻⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠄⠀⣠⠼⢃⡀⠀⢲⣤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠒⠚⠋⠀⠀⠁⠀⢭⣿⣴⡆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⣦⡖⣷⡀⣠⠇⢀
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠆⣀⣤⢴⣦⠾⢷⠷⠾⢿⢛⡗⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣀⠀⠘⣺⠯⣿⣽⠟⣈⡿⠿⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠐⠋⠟⠢⠜⠆⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂