Mutation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡉⢉⣉⣉⣉⣉⣉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡘⢶⣶⠶⠶⠶⠶⠶⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣉⠩⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠓⠶⣖⡂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣝⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠳⣄⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠵⠶⠾⢿⣿⣧⠀⠀⡼⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣞⣙⣙⣀⠀⠈⢿⣿⢟⣠⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠰⠶⠶⠶⠶⣿⣋⡁⠀⠤⢶⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣟⣉⣋⣉⣙⡁⠶⢾⣿⣟⣋⡉⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠶⠶⠶⣶⣿⣿⠃⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣍⣉⣉⡉⠁⠀⣸⣿⣏⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠶⣿⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠈⠻⣏⡀⣠⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡝⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢳⣤⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠛⠛⠓⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣤⣬⣭⣭⣽⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠛⠛⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⢛⣶⣴⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠙⣦
⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣧⣤⣤⣤⣤⡀
⠀⠀⣠⣞⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠈⢷
⢠⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⠿⢻⡟⠲⣦⡀⠀⠀⠀⠀⠈⠳⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⢈
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢸⡇⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢠⡞
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧⠀⠀⢸⡇⠀⠀⣸⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⣠⠟⠛⠛⠛⠻⣆
⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣸⣇⣠⡴⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠙
⠀⠙⢷⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠙⣧⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⠀⠀⠀⠀⠀⠈⣷⠤⠤⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠉⢛⣶⣴⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠛⠁
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣿⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣀⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡁⠉⡀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠉⠉⠁⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣀⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢀⠀⣀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢁⡀⣀⣹⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⣀⣙⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠈⣱⠀⠁⠀⢀⠤⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⣁⣩⣵⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣾⣥⣤⣴⡋⣀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⢿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠑⠒⠂⠸⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠂⠀⠼⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉⠒⠂⠤⢀⢀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠒⠢⠠⣀⠀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⣤⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡤⢄⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⢟⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢿⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠫⠤⠄⠭⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠤⠄⠭⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠤⠤⠄⠤⠤⠬⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡤⠤⠄⠤⠤⠬⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠒⠂⠤⢄⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠒⠠⠤⣀⡀⣀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢼⠇⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⠦⣤⣦⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣝⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢗⣈⣻⣿⣦⡀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢇⣉⣉⣉⣹⡿⠿⠀⢚⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡌⣭⣭⣭⣭⣿⣿⠀⢤⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⣴⣿⠟⠁⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡝⠿⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠟⠓⠖⠒⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢊⡑⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡸⢏⣸⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣶⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⣠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣤⡀⠀⣾⡿⠀⣰⣿⠋⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣸⣿⠁⢠⣿⡇⠀⣿⡇⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⢹⣿⠀⠀⢠⣿⡇⠀⢸⣿⠀⢸⣿⣷⣄⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠘⠿⠃⠀⣾⡟⠀⠀⢸⣿⠀⠘⣿⡏⠻⣷⣄⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠈⠀⢀⡀⠈⣿⡇⠀⣿⡇⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢠⣾⠿⠿⠿⠿⣷⣶⣿⣿⣤⣀⣀⣈⣻⣷⣄⣀⣀⣤⣾⡿⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⢿⣷⡀⠀⠀⢻⣿⣶⣤⣤⣄⣀⡀⠉⠉⠛⠛⠛⠛⠿⠿⠿⠛⠛⠋⠁⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⣠⣶⡿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠛⣿⣿⠿⣿⣶⣶⣶⣤⣤⠀⠀⢴⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⢠⣾⣿⣿⣄⠀⠀⠀⠀⠰⣷⣄⠀⠀⠀⢸⣿⠀⢸⣿⡄⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⢠⣿⠏⠀⠙⢿⣷⣄⠀⠀⠀⠈⠻⣷⣄⠀⢸⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⣿⣄⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⠻⣷⣼⣿⠃⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⠛⢿⣷⣄⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⡿⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡀⠀⠙⠿⠆⠀⠀⠀⠀⠙⢿⣷⣄⠀⣰⣿⠃⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢸⣿⡆⠈⣿⡇⠀⠀⠀⠀⢠⣦⣄⠀⠀⠀⠙⣿⣿⡿⠃⢠⣾⡟
⠀⢀⣠⣴⣾⡿⠿⠿⠛⠛⠛⠻⠿⠿⠿⣿⣶⣿⣷⣄⣀⣀⡀⠀⠙⣿⣷⣤⣴⣾⠿⠋⢀⣴⣿⠏
⣴⣿⠟⠉⢀⣠⣤⣤⣴⣶⣦⣤⣤⣤⣄⣀⡀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠉⢀⣠⣴⡿⠟⠁
⢿⣷⣤⣾⡿⠛⠉⠉⠻⣿⣯⡉⠉⠙⠛⣿⣿⠿⣷⣶⣶⣦⣤⣤⣤⣴⣶⣶⡿⠿⠛⠉
⠀⠉⠉⠻⣷⣄⠀⠀⠀⠈⠻⣿⣦⡀⠀⢹⣿⠀⢸⣿⡉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣿⣦⣸⣿⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣿⣿⠇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢸⣿⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣠⣿⠏⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈⠀⡀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡁⠌⠂⠀⠀⠀⠀⠁⠠⠀⠀⠀⣠⠂⠉⢀⠛⡦
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠄⠀⠤⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⢄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣬⡢⠀⠀⠀⠄⠀⠀⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠟⠀⠀⠠⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠊
⠀⠀⠀⢀⠈⠀⠀⠀⠀⠁⠂⠀⠲⠄⠀⠠⠈⢡⣲⣦⠆⢦⣵⡄⠀⠀⠢⢤⠀⠀⠀⠐⠁⠀⠀⠀⢠⣤
⠀⠀⠀⠈⡁⠢⠀⠀⠀⠀⠀⠀⢐⠀⠉⠀⡀⠀⡀⢀⠀⣀⠁⠵⠀⢀⠀⠀⢈⠀⠀⠀⠠⡀⠂⠄⢀⠉⠀⡀⠀⣤
⠀⠀⠀⠀⠀⠁⡀⠀⠅⢀⠀⢀⠀⠀⠀⢢⠁⠀⠀⠀⠁⠠⠐⠀⠇⠀⠀⠘⠃⠤⠀⠠⡀⠀⠁⠀⠀⠠⠄⠀⢀⠈⢃
⠀⠠⠀⠀⢀⣀⠀⠀⠄⠀⠁⢠⡄⠀⠢⡅⠀⠀⠀⢠⣤⠠⠀⠀⠘⠁⠀⠀⠀⡀⡌⠅⢀⡈⠁⠀⠀⠥⠈⠥⠄⠂⢩⡀
⠀⠀⠂⠀⠀⠀⠈⠐⠒⠀⠀⠐⠂⠀⡴⢁⢀⠀⠀⣬⡅⠀⠀⠁⠰⠇⠄⠁⠈⠉⢑⠒⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠁⢀⡸⠁⣀⠈⠁⣠⠀⡁⢀⠈⠂⠈⠀⠀⠀⠀⢀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠠⠩⠁⢀⠀⠀⠀⠢⡀⠉⠀⠠⠌⠀⠈⠉⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠂⠈⠀⠀⠈⠀⠁⠀⢐⠒⠉⠈⠑⡀⠀⠐⠒⠒⠁⠀⠰⡀⠀⠀⠀⣀⠁⢠⡄⠂⠀⠀⠀⠀⠈⠀⠀⠠⢀⡀⠰⠆
⠀⠀⠄⠀⡄⢀⡴⠂⢀⠏⠉⠙⣄⡀⠠⠈⠛⢐⠂⠀⡀⠀⢢⠡⠐⠴⡀⠡⢉⣀⡀⠘⢿⠣⢀⠀⠀⠈⠀⠀⠐⠄
⠀⠀⠠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠲⠈⠑⠂⠀⠀⠀⠈⠁⠀⣤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⠄⠀⠀⠸⡥⠀⢀⣤⠀⠀⣀⡀⠀⠀⠀⢀⣌⠀⠉⠀⣀⠠⠀⠀⣁⠀⠀⠀⠀⠀⠈⠄⠉
⠀⢀⠆⠀⠁⠀⠀⠉⠀⠀⢀⢀⠀⠀⠘⡅⠣⣈⡁⠀⣀⠚⠇⢄⠛⢀⠀⠉⠀⠌⠀⡋
⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠀⠠⠁⢰⠐⢄⡉⠁⡠⠢⠄⠴⠉⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠐⠀⠨⠀⠀⠠⣄⠪⡀⠐⠄⠀⠈⠁⠀⢀⣀
⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠐⠒⠂⠁⠀⣄⣀⠀⠂⡄⠆⢈⢀⠤⢀⡀⠀⠀⣀⠈⠂⡔⠂⣔⣤⡐⠨⠓⠄⠈
⠀⠀⠀⠀⠀⢉⠋⠒⠒⠢⡒⠒⠒⠲⠊⠀⢐⠲⠆⡉⠀⡒⠋⡴⢠⠅⠠⠤⠀⠀⣀⠈⡇⠀⠖⢀⠰⠀⠂⠀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠒⠉⠀⠤⠛⠀⠈⠁⠀⡈⠀⢸⡃⣶⢀⡀⠀⠁⠁⠈⠁⠀⠀⢀⡁⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠒⠃⡀⠀⠀⠀⠀⠐⠒⡀⠀⠀⢀⡢⢼⡀⢀⡀⢀⢆⠀⠀⢡⠌⠓⠂⠁⠀⠀⢠⡖⠀⠑⠂⠀⠁⠀⣀⠒
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠁⠙⠄⠃⠉⠘⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠿⠿⠿⠿⠟⠿⠿⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⢿⣿⣿⣦⣄⠀⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠈⠙⢿⡿⠃⠀⠛⠛⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣥⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⣠⣾⣿⠟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⢀⣾⣿⡟⠁⠀⠺⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠈⠻⣿⣷⣄⠀⢴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠈⠻⣿⣦⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⢀⣤⣾⣷⡄⠀⣴⣤⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠟⠉⠀⠀⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣿⣿⣿⣿⣻⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣻⣻⣿⣛⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡛⢿⣿⣿⡿⢛⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⣿⢈⣭⣭⡁⣿⢸⣿⣿⣿⣦⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⣿⢈⣉⣉⡁⣿⢸⡿⣿⣿⣿⣷⠀⠀⣄⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠹⣦⡙⠿⣷⣦⣼⣷⣿⣿⣿⣿⡇⠀⠉⠉⠛⣷⣾⣿⣷⣦⡀⠀⠀⢸⣿⢹⣿⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢃⣼⠟⠷⣦⡙⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⣙⣿⣦⡀⢸⣿⣾⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⣾⠣⠾⠷⠜⣷⢸⡟⢿⣿⣿⣿⢃⡄⠀⠀⠈⠻⣷⣝⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⣿⢰⣶⣶⡆⣿⢸⣿⣿⣿⣿⠏⣼⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠿⢰⣶⣶⣆⠿⢸⣿⣿⠿⣣⣾⣿⣿⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠿⠛⣛⣩⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠟⣋⣥⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣤⣶⣶⣶⣌⡛⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⡿⠟⠛⠛⠓⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠇⣶⣶⢀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠉⠉⠈⠛⠃⣾⣿⣷⣄⠀⠀⠀⠈⠻⢿⣿⣿⣿⡷⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠉⠉⠛⠃⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⢰⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢋⣴⣄⠀⠀⠀⠀⠀⠀⠀⣩⣭⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣮⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣱⣶⣤⣄⣀⣠⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠛⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡟⠃
⠀⠀⠀⠀⠀⢀⣀⣤⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⣄⣀
⣠⣟⡀⢀⡶⠋⠁⠀⠀⠀⠉⠛⢦⡀⣠⡽⣆⠀⠀⠀⠀⠀⢀⡾⣥⡀⣠⠞⠋⠀⠀⠀⠀⠉⠳⣄⠀⣸⣧
⠉⠀⢹⡏⢠⣤⡀⠀⠀⠀⣠⣄⠈⢿⡁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⣹⠃⢠⣤⡀⠀⠀⠀⣠⣄⠈⣿⠁⠈
⠀⠀⢸⠀⠹⠶⠏⠀⠀⠀⠷⠾⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⠶⠃⠀⠀⠈⠷⠾⠁⢸
⠀⠀⠸⣆⠀⠀⣠⠶⡄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡴⢦⡀⠀⢀⡾
⣦⣤⠞⠛⢦⡀⠙⠞⠃⠀⠀⣠⡼⠛⠶⣤⡖⠀⠀⠀⠀⠀⠰⣦⡴⠞⠻⣄⡀⠀⠀⠓⠞⢁⣠⠞⠛⢦⣴
⠈⠓⠀⠀⠀⠉⠛⠲⣶⠒⠛⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈⠙⠓⢲⡶⠚⠋⠁⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⢰⡇⢸⡆⠀⠀⠀⠀⢰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡌⠳⣤⣶⠚⠛⠀⠈⠛⠓⢦⣤⠴⢋⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⠀⠉⠀⠀⠀⠀⣠⢤⡈⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡏⠈⢠⠖⠲⣆⠀⠀⠙⠚⠁⠀⠀⢹⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠖⠚⠛⠁⠀⠹⣦⣤⠟⠀⠀⢀⣀⣀⠀⠀⠙⠛⠲⠖⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⢲⡆⠀⠀⠀⠀⠀⠀⠀⣿⠁⢈⡇⠀⢶⡞⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠀⠀⠀⣴⣳⡄⠈⠛⠋⠁⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢁⣤⡶⠀⠈⠉⠀⠀⠀⢠⣀⡀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣴⠋⠀⠉⠓⢶⡀⢀⡶⠚⠉⠈⠙⢦⣙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣒⠋⠉⣓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢸⢹⣒⣚⣿⠀⠀⠙⡄⠀⢠⠀⠀⠀⠀⠀⢠⠔⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⢏⠧⣈⠛⠈⠀⠀⢸⡈⢉⡗⠉⢙⠢⡀⡇⢠⠀⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣎⡔⢪⢱⣀⠉⠀⢸⡇⠘⣄⢠⡈⠁⠈⢧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⢸⣍⣩⣿⡀⠀⢠⠎⢸⠀⠈⠳⣄⠀⠀⠈⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢍⣀⣀⣉⠤⠖⠁⠀⠀⡇⠀⠀⠈⣑⣲⠋⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⣀⠀⠀⢸⠀⡔⠉⠀⣈⣑⣦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⡬⣉⠒⠾⠂⡇⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠴⠾⠤⡎⠉⠢⡀⠙⢄⡀⠉⢑⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⠢⡀⠀⡸⠲⡏⠀⠀⠀⠈⠳⡄⢈⠦⣀⠉⠉⠛⣄⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠉⢙⡶⠁⠀⠀⠀⠀⠀⠈⠣⣀⠎⠑⠒⠚⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⣄⠀⢀⠀⠀⠀⠄⡄⡀⢀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⡄⣤⣤⡄⢠⡄⢤⡤⣤⣠⢤⣠⣄⡄⠀⢠⣀⡤⢠⡤⣄⣤⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠃⠘⠂⠋⠓⠘⠃⠛⠛⠚⠙⠙⠃⠀⠘⠙⠒⠛⠒⠋⠋⠛⠚⠛

⠀⠀⠀⣆⢶⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⢠⣤⣶⣦⣤
⠀⠀⠀⠙⢮⣾⠁⠀⠀⠀⠀⠀⢠⢖⡉⠉⣑⢄⠀⠀⠀⠀⠀⢸⠉⡇⠾⢶⠀⠀⠀⠀⠀⠈⢻⠿⠿⠏
⠀⠀⠀⠀⢰⢏⠳⡄⠀⠀⠀⠀⣟⠛⠳⡞⠛⢻⠀⠀⠀⠀⠀⢎⣀⡙⣶⣾⠀⠀⠀⠀⢀⣶⣾⠷⢿⣶⣦
⠀⠀⠀⠀⠸⡜⠇⠃⠀⠀⠀⠀⠈⠢⣾⣻⠤⠋⠀⠀⠀⠀⢎⣚⣛⣛⣿⡿⠀⠀⠀⠀⠘⠿⢿⣂⣸⡿⠟

⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⢀⣴⡾⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⣤⢏⣱⣂⢽⣧⡀⠀⠀⠀⢦⣐⣟⣶⡆⠀⠀⠀⠀⠀⢶⣱⣎⡶⠀⠀⠀⠀⠀⠀⠺⣙⣏⡠⠂
⠀⠀⢸⡏⠀⢹⡇⠀⣿⠄⠀⠀⠀⠀⢸⣟⠉⠀⠀⠀⠀⠀⢰⠃⢸⡇⠘⡆⠀⠀⠀⠀⠀⣶⣜⣿⢰⣾⣶
⠀⠀⠈⠻⠦⠏⠧⠶⠋⠀⠀⠀⠀⠀⠾⠹⠀⠀⠀⠀⠀⠀⠈⠣⠾⠻⠜⠁⠀⠀⠀⠀⠀⠉⢸⠹⠄⠈


⠀⠀⠀⣄⣀⣠⡈⣄⠀⡄⠀⢀⡀⠀⠐⡖⢤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⢒⣤⡀
⠀⠀⠀⠘⢿⣾⣵⣷⠋⠀⠰⡏⠠⣀⠀⢈⣳⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣿⣿⠋⢱
⠀⠀⠀⠀⠀⠙⢱⢻⡀⠀⠀⠈⠓⠒⠀⠀⣼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠟⠻⣧⠎
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠆⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠑⢌⢧⠠⣄⣸⢻⡄⠀⣠⣄⣤⣤⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠸⠎⣷⣌⡛⢇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⢟⣭⣏⠽⢻⣾⣿⣛⣿⣿⣿⣿⣿⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡴⣠⣶⣿⣿⣿⣿⡟⠉⢈⡷⢹⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⠉⠙⢿⣿⣿⣿⣿⣷⣦⣤⣷⣿⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣄⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⣀⣤⠾⠛⠁⠉⢻⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣤⣀⢹⣿⣿⣿⣻⣷⣦⣀⣴⡟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠜⠴⡯⠋⠁⠀⠀⠉⠻⠿⡇⠈⣹⣿⣽⣿⣿⡿⣷⣄⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⢿⡿⣧⡈⢻⠉⠋⠑⠲⢦⣈⠙⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⣌⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣯⣝⢿⡶⣄⠀⡀⠘⢿⡿⣄⠀⠈⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠜⢦⡁⠀⢈⠻⢫⣑⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠠⡁⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⢾⠷⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⣀⣠⣤⢼⡦⢤⣄⣀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠖⠋⠉⠀⠀⠘⠀⠀⠀⠈⠙⠳⢤⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠞⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢦⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⡇⠈⣉⣉⣉⣉⡁⢸⡇⠀⠀⠀⠈⢳⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⠃⠀⠀⠀⠀⠀⣧⠀⢩⣭⣭⡍⠁⣸⠁⠀⠀⠀⠀⠈⣧⠀⢸⡄
⠀⠀⠀⠀⠀⣀⣰⣇⣀⣿⣀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⡤⠞⠁⠀⠀⠀⠀⠀⣀⣸⣀⣈⣇⣀
⠀⠀⠀⠀⠀⠉⠹⡏⠉⣿⠉⠀⠀⠀⠀⠀⠀⣠⠖⠊⠙⠲⢤⡀⠀⠀⠀⠀⠀⠉⢹⠉⢉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⡄⠀⠀⠀⠀⠀⡞⠁⠐⠒⠒⠒⠀⢹⡀⠀⠀⠀⠀⢀⡟⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢳⡀⠀⠀⠀⠀⡇⠈⣉⣉⣉⣉⡁⢸⡇⠀⠀⠀⢀⡼⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⡀⠀⠀⠁⠀⠉⠉⠉⠉⠁⠈⠀⠀⠀⣠⠞⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠦⣄⣀⠀⠀⢠⠀⠀⠀⢀⣠⠴⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠉⠙⠛⢺⡗⠚⠋⠉⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⢾⡶⠶⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠂⠀⠀⠀⠀⠀⠤⠄⡀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⣤⠄⠀⠀⠈⠁⣀⡀⠀⠀⠀⢄⠉⠀⠈⠁⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⣶⣿⠃⠀⡠⠚⠋⠉⠁⠀⠀⠀⠀⠈⠳⣄⠀⠢⢀⡀⠀⠀⣬⡿⠛⢻⣷⠟⠃⠙⢳⣶⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣿⣿⡇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠛⠀⠀⠈⠀⠀⠒⢉⠀⠰⢠⠀⠀⠈⠀⠀⠀⠀⠈⠛⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠻⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠰⣤⡀⢫⡀⠁⠤⠂⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠐⣿⣥⠀⣿⡇⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⡼⣏⢁⡘⠀⠠⡀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⡾⢿⡟⡰⢛⡷⠈⠀⠈⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡘⠦⠀⡗⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡆⠁
⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠎⠁⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⢻⡴⠀⠤⡲⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠢⣄
⠀⠀⠀⠀⢠⣿⣵⣷⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡀
⠀⠀⠀⠀⠸⢸⠏⠀⢠⡞⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⢄⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠀⡈⠀⠀⠀⠀⣰⠏⠀⠸⢜⡀
⠀⠀⠀⠀⠀⠀⢀⠈⠧⣄⡀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠇⠀⠀⠀⠀⠀⢹⠀⠀⠰⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢰⠇
⠀⠀⠀⠀⣢⣤⣗⡄⠀⣆⠀⠀⢀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡈⠈
⠀⠀⠀⠀⢿⣿⣿⣷⡀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠙⠷⣦⣀⡀⠀⠀⣀⡴⠋⠀⠀⢠⠁⠀⢀⣀⣠⣤⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡿⢀⠆⣤
⠀⠀⠀⠀⠈⠻⠿⠿⡿⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠋⡀⠐⣏⢀⡈⠻⠛⠛⠉⠁⠀⠀⠤⢄⣈⠙⠲⠤⠤⠤⠶⠛⢁⡜⣆⡠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠁⠈⠉⠁⠉⠋⠃⠀⠀⠁⠚⠢⠴⠀⠤⣾⡉⢩⠛⠣⠿⠶⠂⠀⠀⠀⠀⠀⠀⣽⣦⣵⣦⣀⣀⣀⣀⣤⠛⣙⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠉⠉⠉⠙⠉⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠠⠀⠀⠄⠀⠠⠄

⠀⠀⠀⣰⣿⠿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⢿⣿⣆
⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⡿⢿⣟⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣻⡿⢿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠙⣿⣟⣿⣿⠉⣹⣷⣾⡿⢏⣙⣿⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣿⣋⡹⢿⣷⣾⣏⠉⣻⣿⣻⣿⠋
⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠉⠙⠛⠶⡟⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⢻⠷⠛⠋⠉⢻⣿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠖⠒⠢⠤⠷⣄⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣠⠾⠤⠔⠒⠲⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⣀⣈⣑⣦⣀⠀⠀⠙⢷⣄⠀⢀⡀⠀⣠⡾⠋⠀⠀⣀⣴⣊⣁⣀⣀⣀⣀⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠙⢦⣾⣷⡴⠋⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠈⠙⣲⣿⣿⣖⠋⠁⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡿⠿⠿⠛⠻⢿⣛⡻⡿⠿⠿⣿⣿⣿⣿⠻⠿⢿⣟⣛⡿⠟⠛⠿⠿⢿⣯⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⠤⠴⠒⢒⡲⠋⠀⠀⢀⡠⠚⣹⣿⣿⣏⠓⢤⡀⠀⠀⠙⢶⡒⠒⠦⠤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢋⣀⠤⠔⢺⠏⠀⠀⣀⠔⠉⢀⠜⡸⣿⣿⢏⠣⡀⠉⠢⣀⠀⠀⠹⡗⠢⠤⣀⡙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠉⢀⡠⠖⢻⠖⠒⣹⠃⠀⣠⠋⡰⠡⣿⣿⠈⢆⠙⣄⠀⠘⣏⠒⠲⡟⠲⢄⡀⠉⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢶⡋⠀⢠⠋⠀⢰⠃⠀⡼⠁⣰⠃⠀⣿⣿⠀⠘⡆⠈⢧⠀⠘⡆⠀⠙⡄⠀⢙⡶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢶⡇⠀⣠⠃⠀⡜⠀⢠⡇⠀⠀⢻⡟⠀⠀⢸⡄⠀⢣⡀⠘⣄⠀⢸⡶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣦⢾⣀⣠⠟⠀⠀⠀⠘⠃⠀⠀⠀⠻⣄⣀⡷⣴⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⢻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⢸⠟⠻⡟⠙⢿⠻⣏⣵⣼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠻⡉⢻⠙⣿⣦⣿⡇⠀⡇⠀⠎⢀⢿⣧⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠓⢄⠀⣈⡃⠡⢸⣿⠁⠀⠁⢀⠶⠚⣻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠲⢦⣝⡇⠙⠦⣼⣿⠀⠀⡴⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠓⠦⣌⠻⣄⠀⢿⡇⠀⠘⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠑⢈⣳⣼⣇⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠶⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⣠⠔⣨⠞⢿⡏⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠤⠒⢋⣥⡞⠁⢀⣿⡇⠀⢠⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠴⠚⢋⢴⣀⡴⠋⢿⣇⠀⠀⠳⡀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠚⢁⠌⢰⠀⡆⣼⣿⠀⠀⠀⠘⠲⣤⡝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣤⣯⣼⠿⠋⣿⠀⢸⠀⠀⡆⢰⣾⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⣦⣾⣦⣴⣷⣾⡉⡏⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣷⣧⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠒⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡆⠀⠁⠈⠀⣀⠄⣀⠀⣠⣀⡋⡐⠀⢠⢊⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠈⢰⠤⠐⠉⠉⠈⠁⠀⠀⠐⠢⠄⠁⠈⠓⠲⢂⡂⢊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠈⠐⢄⠁⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠐⠂⠀⡴⠉⠀⠁⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢠⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⡐⠎⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠨⠀⠀⠠⠄⠀⠹⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢡⡀⠀⡀
⠀⠀⠀⠐⢀⣀⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣱⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⡆⠀⠠
⠀⠀⠀⠈⠀⢸⠀⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⣃
⠀⠀⠀⠀⠰⣽⠀⠀⢠⣙⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠂⠀⠀⠀⠀⡍⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⠐⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠇⢀⡆⠂⠈
⠀⠀⠀⢤⠄⠀⢃⠀⠀⠀⠀⠀⠒⣀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠈
⠀⠀⠀⠀⠀⠀⢘⣆⠀⣁⠀⠀⠑⠃⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣸⡇⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⣶⠋⢀
⠀⠀⠀⠀⠀⢀⡀⡠⠊⠻⣦⣀⡀⢲⣀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣤⡞⠇⠀⠦
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢈⡾⢷⣄⠀⠀⢀⠀⣄⠂⡀⠀⠀⣤⡠⠀⠀⠀⠀⠀⠀⣈⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠻⠶⢻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠛⠁⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⡔⠋⠁⡽⠙⠛⠷⠒⠲⠖⠦⠨⠛⣏⠉⠀⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣠⠀⠘⠒⠂⠸⠀⠀⠀⠀⢀⠴⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠓⢦⡀⠀⢠⠖⠃⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣳⠀⠀⠀⠀⠀⠀⢸⠃⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣨⠇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣇⠀⢀⠀⠛⢦⣀⣠⠴⠖⠋⣿⠀⠀⠀⢿⠓⠲⢤⡀⠀⣠⠞⢁⡴⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⡄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠋⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠆⠀⠀⢀⡴⠚⠉⠙⣦⠀⠀⠀⠀⠀⠀⠠⠞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⣄⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⣾⣠⠴⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢴⠋⠙⠳⣄⠀⠀⠈⠛⠓⠲⠶⠤⠴⠋⠉⢳⡀
⠀⢀⡞⠉⠙⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠞⠀⠀⣀⣤⣤⣤⣤⣤⡄⠀⠀⢸⠇
⠀⠘⡇⠀⠀⢠⠤⠖⢶⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠙⠦⠴⠋
⠀⠀⠙⠦⠤⠞⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣞⠉⠉⢙⡆⠀⠀⠀⠀⠀⢠⡀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡴⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠹⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⣄⠀⠈⠛⠉⠙⡆
⠀⠀⠀⠀⠀⢀⣀⣀⡞⠁⢀⡴⠋⠉⠓⠦⣤⣦⠀⠀⣇⣠⡤⠶⠛⠁⠈⡗⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⣧⡀⠀⠀⠀⠀⠀⠳⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠙⢦⣀⣀⡿⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢼⣶⣀⡀⠀⠀⠀⣀⣲⣿⠀⢸⡿⣒⣄⠀⠀⠀⠀⣀⡲⢶⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠐⣿⣷⠦⡀⠀⠀⢴⣿
⢸⣛⣭⣵⣄⣤⣮⣭⣍⣻⠀⠀⡿⠉⠛⢷⡀⢠⠞⠛⠛⣿⠀⠈⠳⢉⣾⣿⣶⣴⣶⣾⣿⡌⠼⠁⠀⠹⢿⣀⣱⣤⣀⣠⡿
⠀⢿⣿⣿⠟⡟⢿⣿⡿⠄⠀⠀⢈⠔⠂⠀⢹⡏⠀⠀⢠⠁⠀⠀⠀⠘⠙⠉⢸⡿⣿⠈⠋⠟⠀⠀⠀⠀⣞⠁⠀⠋⠀⠙⣷
⠀⠀⠻⠇⠀⠁⠈⡿⠃⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠆⠀⠳⠿⠁
⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠑⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⡾⠛⠁⢀⠀⠀⢀⠀⠉⠛⡇⠀⠹⣿⢶⣄⠀⠀⠀⠀⣠⡾⠿⠃⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢰⡿⠒⠀⠀⠀⠀⠀⠒⠻
⠁⢴⣿⡁⠀⡄⠀⣽⣷⠄⠀⠀⠀⢻⣆⣻⣷⣀⣠⣾⡏⠸⡎⠀⠀⠀⠀⣠⣾⣤⣶⣀⠀⠀⠀⠈⢀⣴⡖⠁⣀⠈⢑⣶⡄
⢰⠻⣿⣥⡴⡷⣄⣽⡿⠰⠀⠀⠀⠰⠋⣀⠘⠻⠻⢃⣄⠱⠀⠀⠀⠀⢼⡙⠟⠉⠿⢙⡆⠀⠀⠀⠾⣿⣏⣠⣿⣄⣹⣿⠇
⠀⠀⠈⠙⠁⠁⠙⠉⠀⠀⠀⠀⠀⠀⠣⡴⠟⠀⠐⠿⢆⠊⠀⠀⠀⠠⠜⠛⠀⠀⠘⠛⢥⠀⠀⠀⠁⠈⠛⠋⠈⠘⠟⠋
⣠⢤⣀⡀⠀⠀⠀⠀⢀⣄⡦⣄⠀⠄⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⣄⠀⠀⠀⠀⠀⠀⠀⢠
⣷⠛⠉⣀⡀⣀⣀⢀⣀⠉⠛⡎⠀⠀⢸⣧⡀⠀⠀⢀⣾⠄⠀⠀⢸⣿⠿⣢⠀⠀⣠⡺⢻⡿⠀⠸⣄⣾⣦⠀⠀⠀⣠⣶⢠
⠙⢒⣻⣟⣯⣿⣟⣟⣿⡟⡒⠃⠀⠹⣟⣙⣿⣤⣴⣿⣉⣿⠇⠀⠀⠙⡆⠛⣷⣶⠛⢠⠛⠁⠀⠀⠻⡎⢻⣷⣤⣼⡟⢩⡞
⠀⢿⡿⣿⡾⢙⠹⣿⣿⣧⡗⠀⠀⢀⡾⢿⡿⢻⡿⣿⡿⣦⠀⠀⠀⢸⣿⠸⠁⠉⢇⣼⠇⠀⠀⠀⠀⣾⣟⡉⢻⢉⣟⣶
⠀⠈⠙⠛⠁⠀⠀⠈⠋⠉⠀⠀⠀⠈⠻⠞⠁⠀⠀⠘⠻⠛⠀⠀⠀⠐⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠈⠋⠀⠀⠀⠛
⠐⠰⣠⡀⠀⠀⠀⣀⠠⠒⠀⠀⢠⣤⣄⡀⠀⠀⠀⣠⣴⡆⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⢰⣦⣤⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠈⢢⣦⡚⠈⠀⠀⠀⠀⠀⣏⡉⠉⢀⡀⠈⠉⠙⡇⠀⠀⡂⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠘⣿⢰⠋⠀⣠⠀⠘⢷⢹
⠀⠀⠌⠃⠺⡟⠃⠯⡠⠀⠀⠀⠀⢉⡷⠾⢿⡿⠗⠶⣌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢨⣾⠟⠉⢹⠉⠳⣾⡎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠷⡴⠋⠙⢳⡴⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠧⣀⠀⠘⠀⣠⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⠶⡄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣟⠀⣀⣨⠓⣅⣀⢀⣿⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⣠⢤⠀⠀⡠⠋⠉⡤⢤⠀⠀⠀⠉⠸⢄⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⢹⢴⡃⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠑⠺⢕⠊⢀⡀⠀⠁⠉⠀⠀⠯⡵⠀⠀⠛⡫⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢎⠣⠴⢒⣋⡀⠉⠓⠦⢜⡴⠚
⠀⠀⠀⠀⠀⠀⠀⡜⠀⢯⠟⠀⠀⢯⣱⠀⠀⢠⠴⡄⠀⢧⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠘⠒⠁⢠⢤⡄⠘⢄
⠀⠀⠀⠀⣏⡱⢮⡁⠀⠀⠀⠀⠀⣀⣤⡀⠀⠈⠋⠀⠀⢈⠴⣍⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣙⣒⠚⠀⡤⡄⠀⠀⠀⠈⠉⠀⠀⠈⢒⣒⣉⡳
⠀⠀⠀⠀⠀⠀⠀⢣⠀⢞⣳⠀⠀⠑⠚⠀⠀⣴⣲⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠓⠁⠀⠯⡷⠀⠀⣞⠝⠀⡏⠀⠈
⠀⠀⠀⠀⠀⡴⢲⡯⠤⡀⠉⠀⠀⠰⣋⡗⠀⠈⠁⣠⠖⢽⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀⠀⢀⣄⡀⠀⠀⣀⣀⠀⠰⣇⣀⡀
⠀⠀⠀⠀⠀⠙⠊⠀⠀⢈⣆⣤⣀⣀⠀⢀⣀⣤⢺⠁⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠋⠙⠦⣈⠓⠃⠀⠈⠓⣁⠴⠋⠲⣄⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡸⠀⠀⢈⣶⠉⠀⠀⣷⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡔⠒⠒⠒⢆⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⠳⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⣔⠋⢳⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⡀⡇⠀⠀⡀⣸⠃⣇⠀⠀⠀⢸⢆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠑⠒⠋⢉⠁⠀⠈⠉⠉⠒⠋⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢦⡀⢀⠞⠁⠀⠀⢼⣁⡽⠀⠀⢀⢤⣀⠀⠈⠳⡄⣀⡴⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠓⣌⠁⢀⣠⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠂⠀⠀⠈⣡⠖⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⣀⠇⠀⠀⠐⣍⢱⡄⠀⠀⠀⡠⢤⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠦⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠧⠜⠀⠀⠀⠧⠤⠖⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠊⠉⢳⡀⠀⠀⣀⠀⠀⠀⢀⡖⢛⡆⠀⠀⠀⢀⠀⠀⠀⠀⡎⠉⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠸⣉⣱⠀⠀⠀⠉⠉⠀⠀⠀⢴⢉⡵⠀⠀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⣃⢤⡀⠈⠁⠀⠀⠀⢰⠚⣳⠀⠀⠈⠉⠀⢀⠤⢌⡳⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠏⠀⠀⠑⢦⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡔⠋⠀⠀⠹⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣠⠒⠲⠤⢤⠀⡤⠤⠔⠒⢄⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡜⠀⠀⠀⢀⡇⡇⠀⠀⠀⢸⡃⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡹⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⢠⣹⣴⣤⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⣽⣿⣿⣿⣿⣾⢃⡀⡀⡆⡀⢀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⢹⢿⣿⣿⢿⡳⢮⣵⣿⣿⣷⣯⠄⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⠈⠙⠂⠘⢫⣿⣿⣿⣿⡿⠝⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠐⠋⠟⣟⠻⣱⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢀⡀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠒⣼⣶⣶⣧⣖⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠰⢽⣿⣿⣿⣿⣧⠶⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣀⣩⠿⡿⡿⡟⣭⢠⠄⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢢⣷⣾⣾⣼⡓⠃⣛⣽⣾⣾⣴⣃⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠮⣿⣿⣿⣿⣿⡥⠖⣻⣿⣿⣿⣿⣗⠆⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⡄⡈⣽⣻⢿⢿⣻⡅⡀⣽⢻⣿⣿⣿⣴⢢⣷⣿⣿⣼⣺⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀
⠀⢾⡿⢍⠳⠈⠛⠙⢶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⠋⠟⠡⠞⡩⢿⡇
⠀⠸⣗⠄⡱⣚⠭⠭⠶⢷⣬⣟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣛⣥⡾⠶⠭⠭⣓⣎⠠⣻⠃
⠀⠀⠹⡗⢽⣱⢊⣭⠤⠬⢜⣛⣿⢷⣽⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣯⣾⣽⣋⡡⠥⠬⣭⡑⣾⡇⣺⠏
⠀⠀⠀⠹⡆⢿⢺⠀⢲⡖⠐⠠⠭⡝⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⢿⢫⠭⠄⠂⢲⡖⢀⡇⡿⢰⠏
⠀⠀⠀⠀⢹⡄⢦⠑⢤⣙⡢⢄⣀⠀⠁⠂⠝⣺⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣝⡫⠒⠍⠀⣀⡠⢔⣃⡤⠋⡼⣠⠏
⠀⠀⠀⠀⠀⣷⠈⡷⣄⡤⠉⣑⠒⠡⠕⣴⣄⡈⠚⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⡝⠓⠁⣀⣦⠪⠘⠒⣈⠉⢄⣠⣾⠡⡾
⠀⠀⠀⠀⠀⢸⡅⢻⣦⣉⢉⠈⠳⠥⠤⠶⡉⡙⠷⣠⡛⣽⢟⣷⡀⠀⠀⠀⠀⠀⠀⢀⣞⡿⣫⢋⣤⠖⢋⢉⠖⠤⠭⠞⠡⡉⣉⣴⡟⢨⡇
⠀⠀⠀⠀⠀⠸⣇⢸⠟⣩⡥⠤⡤⠤⣀⡀⠙⠢⠄⢂⠙⠿⣿⡿⣿⡄⠀⢀⡀⠀⢠⣟⢯⣿⠟⠋⡐⠠⠔⠋⢀⣀⠤⠤⠤⢬⣍⠻⡇⣺⠇
⠀⠀⠀⠀⠀⠀⢿⡼⣜⢧⣠⣰⣰⣀⣸⣈⣹⡐⢠⢈⡳⢅⠨⠻⣼⣿⡔⣿⣿⢢⣿⣳⠟⠅⡸⢞⠀⡄⢒⣏⣀⣅⣀⣇⣆⣄⡼⣣⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠮⣓⣤⣀⡉⠀⠀⢀⣀⠈⠉⠓⠺⠶⣄⡀⠘⢿⣷⣿⣿⣾⡿⠁⢀⣠⠶⠓⠊⠉⠁⣀⣀⠀⠀⢉⣀⣴⣛⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢲⣴⣶⢢⣤⣤⣩⣵⣄⣀⣩⣷⡾⣿⣧⣾⡿⢷⣾⣍⣀⣠⣮⣁⣥⣥⡔⣶⣦⡖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡉⢱⢁⡛⠀⡇⢻⠙⠉⢹⣿⣿⣮⡿⣿⣿⢿⣤⣿⣿⡏⠉⠋⡟⢹⠀⢛⡈⡌⣉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠠⢇⠀⡇⢼⡐⠂⠀⠸⠛⣿⡇⣿⣇⢸⣿⠛⠇⠀⠐⢂⡇⢸⠀⡼⠄⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⢣⠈⣻⡀⠹⡀⢹⡀⠂⠀⠀⢹⠀⣿⣿⠈⡏⠀⠀⠒⢀⡏⢀⠏⢀⣟⠀⡜⣄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⢀⡒⡀⠐⢣⡀⠙⣄⠉⠱⣄⣡⠇⠀⣿⣿⠀⠸⣌⣠⠊⠉⡠⠋⢀⡜⠢⢀⢒⡀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⢘⡒⡄⠉⠷⣄⠀⠙⠲⢼⠏⠀⠀⢻⡗⠀⠀⠹⡦⠖⠋⢀⣠⠾⠉⡠⢐⡁⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠤⠦⣀⠁⠟⢲⡾⠁⠀⠀⠀⠈⠁⠀⠀⠀⠘⢷⡖⠻⠈⡠⠴⠥⠀⢸⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣜⢂⣭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣭⡐⣣⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠀⢸⢖⠣⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡸⠀⠠⠄⠘⠀⠈⠀⠀⠀⠀⠳⠈⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠁⢀⡀⠀⡀⠠⡇⢀⡀⢠⡀⣀⠀⠉⠄⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⢠⡜⠁⠁⠉⠚⠛⠋⠉⠀⠀⠙⢦⡀⠀⠀⢐⠒
⠀⠀⠀⠀⠀⡀⠈⠠⠌⢁⡀⠢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠠⠤⠔⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠂⢀⠀⢸⡇⠀⢠⠞⠁⠀⠀⠀⠉⠑⠀⠀⢸⣇⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣷⣀⡔⠒⠖⢤⡀⠀⡴⢈⣝⠰⣾⠃⠀⢀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡟⠅⠀⢀⣽⡦⢁⣉⠘⢳⣦⠀⢼⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⡼⠀⢃⠀⠀⠘⡻⢞⠄⠘⡄⠀⠁⠠⡼⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡞⢀⢑⠆⠈⠒⠫⠄⠀⠺⠓⣰⠎⡯⠀⢄⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠈⢲⡀⠀⠒⠤⣄⣀⡴⠞⢠⠞⠁⠀⠀⠀⠀⢀⡔⠉⢠⠀⠉⠉⠠⣆
⠀⡆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣤⠀⠈⠀⠁⣠⠞⠂⠀⠀⠀⠀⠀⣸⠀⠀⢾⡁⠀⠀⠀⡯
⠀⠘⡄⢳⣠⠎⠁⠀⠀⠀⠀⠀⠀⣀⡠⠚⢢⠙⠒⠛⠛⠁⠀⢰⡟⣀⠀⠀⡼⠋⠀⠀⠀⢱⣀⠀⡀⠁
⢀⡄⠀⡀⠙⠀⢰⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠱⠆⠚⠐⠀⠴⠁⢻⡀⠼⠁⠀⠀⢀⠆⠈⠁
⡤⠀⠀⠐⡆⠀⠈⡄⠀⠀⣿⠀⠀⠀⠀⠘⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⡸
⠑⠀⡸⠀⠛⠀⠀⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠧⣀⣀⠇
⠀⠀⠈⠢⡀⠀⠀⢰⠀⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⡀⠀⢨⠉
⠀⠀⠀⠀⣦⠀⠀⠐⣇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠀⠀⠀⢻⡀⠁⠀⡄
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⢸⡀⠀⠀⠀⠀⠂⠀⠀⠄⠇⠀⠀⠀⢸⡇⠀⢨⠇
⠀⠀⠀⠀⢸⢀⡀⠤⠜⢯⠄⢸⡇⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⠸⣇⢀⡟
⠀⠀⠀⠀⠈⠻⡄⠀⠀⠸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠤⣿⠊
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣠⠟⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠏⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⢠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢛⡏⠀⢲⠀⠁⠉⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠃⠀⠸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠷⡄⠀⡸⠀⠀⠀⠀⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⡀⢰⠁⠀⣣⠔⠀⠀⠀⠐⠒⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠒⠒⠂⢤⡀⢹⠇⠈⡗⢂⢁⠒⠉⠁⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡀⠀⠈⠉⠉⠢⢠⠟⠀⠀⠀⠀⠘⠁
⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣙⠲⣤⣤⣀⡀⣉⠀⠤⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⢿⠿⢿⠿⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⣟⣛⣿⣿⣿⠿⠿⠿⠿⡻⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⠀⢀⠔⠀⠀⡤⠊⠁⠀⠠⠾⣖⣋⠉⠀⠀⠠⠂⠄⠸⡄
⠀⠀⠀⠀⠀⢄⡀⢠⣄⠲⢶⣶⡀⠁⠰⣶⠁⠔⢖⡋⠀⢶⣀⡀⠒⠒⠂⠒⠻⠫⣙⡃⠋⠠⡀⠒⠲⣄⠰⠒⠒⠒⠒⢲⡆⡀⡒⡆
⠀⠀⠀⠀⠀⠀⠑⠤⠀⠢⢀⣙⢣⠀⠀⠉⢧⠀⠈⠱⡄⠀⠀⠈⠁⠀⠀⠀⠀⠁⠏⡆⠀⠀⠀⠀⠉⠀⠉⠁⢠⠀⠀⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⣀⡀⠈⠈⠂⠀⠀⠀⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⢀⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠤⠀⢀⠱⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠉⠀⠑⠄⠘⠡⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡶⠀⡂⠀⠙⠒⣠⡀⠈⠢⢈⡆⠀⠀⢀⣀⠀⠀⠀⠄⠀⢀⣀⡀⡀⠀⢠⡀⠀⠀⠀⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠙⠒⠒⠒⠒⠚⠛⠚⠛⠛⠀⠀⣿⣿⣧⠀⠀⠐⠚⠃⠤⠉⠛⣠⠝⡳⠆⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⡀⠀⠠⠁⠀⠀⠀⠐⠊⠀⠔⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠩⠍⣉⡙⠛⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢉⣿⠋⠉⠀⠀⠀⠀⠀⠀⠃⠦⣀⠀⠀⠑⠢⢄⡀⠉⠙⠫⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣶⡤⠚⠉⠻⡇⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠈⠒⠤⣀⠀⠉⠲⢶⣦⣄⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⠋⠀⠀⠠⠂⠙⣦⡀⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠈⠑⠂⢤⠀⠀⠉⠒⠤⠀⡈⠻⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⡿⠁⠀⠀⢀⠆⠀⠀⢨⠿⢦⢄⡀⠀⠀⠈⠁⠒⠠⠄⣀⡀⠀⠀⠀⠈⠁⠒⠒⢀⣤⠼⠛⣻⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠁⠀⢀⡴⠃⠀⢀⠔⠁⠀⠀⠉⠒⠭⣐⠒⠠⠤⠄⠀⣀⣀⣉⠉⠩⠭⠽⠿⠯⢁⣤⡴⣊⣩⠃⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⢀⡴⠊⠀⡠⠖⠁⠀⣠⡴⣁⣀⡀⠀⠀⠀⣠⠶⠦⣀⠲⠶⢦⡄⣤⣤⣤⣤⡤⠤⢦⠄⠀⠈⠉⠀⠉⣛⡆⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⢻⣿⡖⠒⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⢇⠰⢆⣬⡴⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿
⡿⠛⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠙⠻⠿
⣿⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠎⢌⣱⠎⠁⠒⠤⣄⡛⠿⠆⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⣠⠈⡜⠀⠙⠤⣀⠀⠀⠀⠈⠓⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⢧⠆⡐⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢐⠧⡌⠄⠀⡀⠀⠀⠀⠠⢤⠀⠀⢀⠀⠉⠲⠓⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠎⡘⣈⡠⠞⠉⡇⠀⢀⣅⠤⠚⣷⠉⠑⢄⠀⡘⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠒⠚⢴⠛⠉⠀⠀⠐⠁⠀⠄⠙⡶⠎⠽⠃⠀⠀⠉⠹⡦⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠒⠛⡶⠚⠲⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠒⠒⣭⠶⠶⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⡤⠤⠳⠤⡤⢀⡀⠀⠳⠂⠉⠰⠞⠀⠀⠀⣠⣤⠮⡤⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⣆⡀⠀⠀⠀⠀⠈⠉⠒⠚⠀⠀⠀⠓⢒⠛⠛⠥⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠐⠁⢰⡆⠀⢈⣉⠳⡦⣄⠀⠀⠀⡜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⠻⣤⣹⠃⠀⠣⠤⠜⡗⠈⡟⠓⠶⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⣤⣤⣴⢻⡇⠀⠀⣔⠀⢰⡇⠀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⠉⠙⠉⠉⠉⠘⡀⠀⠉⠀⡇⠀⣷⠀⠀⡇⠀⠀⠀⠀⠛⠉⠉⠉⠉⠈⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡁⠀⣿⠀⠀⡇⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠓⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠑⠤⠤⠤⠤⠚⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡟⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣤⣀⣀⣀⣄⣀⣧⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢩⣴⣶⣒⣒⣒⣛⣭⠀⣿⠀⣥⣴⣶⣶⠶⣶⣾⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠜⣅⠢⡀⠀⠀⠀⠀⠀⠀⡡⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢿⡟⠈⠳⣄⠀⠀⠀⠀⡤⠊⠁⣻⠗⠀⠀⠀⣿⡇⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⡆⣿⡇⠀⠀⠘⢻⡷⡦⣄⠀⠀⠀⠀⠀⣠⣴⡾⣿⠓
⠀⠀⠀⡉⠁⠀⠈⠁⣴⡄⠊⠀⠀⠈⣩⠀⠀⠀⠀⠸⣷⡙⠻⣤⣇⢀⣄⢀⣧⡼⠛⣱⡿⠀⠀⠀⠀⠫⢿⡹⡟⠀⣀⣸⣀⡠⠘⡟⣽⠯⠃
⠀⠀⠀⠛⣳⠖⠶⠖⣿⡗⠲⠖⠲⡛⠋⠀⠀⠀⠀⠀⠙⣷⡾⠉⠉⣹⣿⡉⠉⢹⣾⡟⠁⠀⠀⠀⠀⠀⠻⣿⣛⡈⣹⣿⣏⠁⣘⣿⡟⠁
⠀⠀⠀⠘⡀⢠⠔⠀⣿⡇⠑⢤⠀⣈⠀⠀⠀⠀⠀⠀⠸⣿⣷⠘⠻⠏⠏⠿⠛⢸⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⠁⢸⠈⢠⣟⣿⣿⣆
⠀⠀⠀⠀⢳⣀⣀⠂⠀⠀⠂⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡞⠂⠀⠛⣾⣿⡟⠃⠀⠀⠀⠀⠀⠸⣨⣻⣴⠇⠀⠀⠀⠘⣧⣝⣉⡇
⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱
⠀⢿⣿⣶⣦⢀⠀⠀⠀⠀⢀⠀⡠⣴⣾⣿⡇⠀⠰⣄⣀⣶⣶⢤⡀⠀⠀⠀⣠⢴⣶⣆⣀⡶
⠀⠈⣿⡯⠨⠈⠳⣄⠀⠀⡠⠋⠩⠁⣿⡏⠀⠀⠀⠘⢷⣮⡁⠀⠈⣶⣷⡎⠀⠀⣩⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢸⣿⣀⣈⣀⣈⣶⣞⣁⣊⣀⣰⣿⠃⠀⠀⠀⠀⠈⢿⡿⠛⣋⣹⣿⣉⡛⠻⣿⠏⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⢺⣿⡗⠂⠀⠀⠀⡰⡾
⠀⠀⠀⣿⠁⠈⣉⠉⣿⣏⢉⡉⠀⠹⣯⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⡉⠃⣉⠁⢠⡿⠀⠀⠀⠀⠀⠀⠈⠀⡤⡖⠉⠘⣿⡇⠈⢐⣤⡄⠋
⠀⠀⠀⢿⣥⣀⡀⠘⠙⠙⡀⣁⣡⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠲⠚⠁⠀⠙⠲⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠿⠄⠀⠀⠄
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣾⣷⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿
⠀⠴⠀⠶⣤⢀⠀⠠⢴⡤⠀⢀⡀⡴⠖⠰⣄⠀⠀⡏⠁⠂⠀⠉⠢⣠⣦⡠⠚⠁⠀⠂⠉⡇⠀⠀⠹⡶⠻⠹⠊⠶⡄⠀⢀⡶⠂⠏⠝⠳⡏
⠀⠻⣷⡀⠀⢀⣠⠔⢻⡃⢤⣄⡀⠀⡐⡾⠋⠀⠀⠑⠒⣶⠶⠦⠤⣾⣿⡦⠤⠴⢶⠒⠒⠁⠀⠀⠀⠷⣀⣀⣀⣀⣸⣶⣏⣀⣀⣀⣀⠸⠃
⠀⠀⠈⢃⠈⠉⠀⠀⣼⡄⠀⠈⠉⠀⠛⠁⠀⠀⠀⠀⠘⠁⢀⠄⢀⡿⡿⣇⠀⢤⠀⠙⠀⠀⠀⠀⠀⢰⡏⠀⠈⡀⠘⣿⡧⠀⡉⠀⢘⣦
⠀⠀⠀⠈⠢⢀⠠⠜⠁⠈⠢⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡦⠀⠠⠃⠀⠀⠈⠣⠀⠠⣆⡀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠋⠹⠙⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠛⠁
⢀⣤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣄⠀⠀⢰⣿⣿⠳⢄⠀⠀⠀⠀⢀⠴⢻⣿⣷⠀⠀⠀⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷
⠀⢿⠂⠀⠙⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⢘⠟⠀⠀⠘⣿⡏⠂⠀⠐⠀⠀⠀⠀⠀⠊⣿⡟⠀⠀⠀⠘⣿⣿⠷⣟⣳⣄⠀⢠⣖⣻⡾⣻⣿⡏
⠀⠀⡛⢐⠢⠀⠈⠀⢰⡄⠔⠁⠠⠐⠘⠋⠀⠀⠀⠀⠹⢿⡥⠄⠐⢶⣷⠖⠀⠤⣽⠟⠁⠀⠀⠀⠀⠘⣿⣷⡉⣿⣿⣿⣿⣿⣉⣴⣿⠏
⠀⠀⠈⠂⢠⡤⠀⢠⣾⣧⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠾⡟⠆⠀⠂⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣧⡀⢸⣿⡅
⠀⠀⠀⢰⠏⠀⠀⠀⢿⡇⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠀⠁⠸⣦⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠉⢹⣿⣿⡿⠃
⠀⠀⠀⠈⠃⠼⠄⠀⠀⠀⠀⠤⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⡆⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣤⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⡏⠀⠀⠀⠀⠀⠀⢀⡴⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣦⣀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣤⣤⡤⠴⠿⡧
⠀⠀⠀⠀⠀⢸⣦⣄⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠞⠋⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠛⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⠖⠚⠛⠛⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣹⣿⣿⣿⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⡍⠁⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠉⠻⣿⣿⣿⣿⣿⣟⡁⢉⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⠞⠁⠀⠀⠀⠀⠀⠀⣸⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠸⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢻⣿⣿⣿⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⢀
⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⣿⡇⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠈⠁⠀⠉⠘⠀⣿⡇⠀⣿⡇⠁⠉⠀⠀⠁⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣻⣽⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣿⡇⠀⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⡿⠿⠿⠿⡿⠟⠁⠀⠙⠿⠿⠿⠿⢿⠿⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢰⡾⢿⡆⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣽⠆⠀⠀⠈⢻⡟⠁⠀⠀⠰⣿⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠈⠉⢿⡄⢀⣿⣀⣸⣇⣀⣿⡀⢀⡿⠉⠁⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⡀⠀⢷⣤⡾⠟⠛⠉⠉⢉⡉⠉⠙⠛⠿⢷⣤⡿⠀⢀⣿⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠟⠁⠀⣤⣶⣄⠀⠈⠁⠀⣠⡶⣦⡀⠉⠻⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡆⠀⠛⣷⡟⠁⢠⡄⠈⢿⣴⠟⠀⠀⠀⠀⠹⢷⠾⠃⢀⡀⠈⠻⣾⠋⠀⢰⡾⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠛⠷⣾⠏⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⣁⡀⠀⢹⣷⠾⠛⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡿⠀⠰⣿⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⣿⠄⠀⢿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⣄⣀⣸⡇⠀⢀⠉⠉⠁⠀⠛⠀⠀⢰⡟⢻⡆⠀⠰⠆⠀⠈⠛⠋⠀⠀⢸⣇⣀⣀⣴⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠟⠉⠉⢹⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⡤⠀⢸⡏⠉⠉⠿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣧⠀⠀⣼⡟⣻⡆⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡶⣦⡀⠀⠀⠀⣼⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⡶⢿⣆⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⠃⠀⠀⣰⡿⢶⣤⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⠃⠀⣠⡿⣧⡀⠀⢠⡄⠀⠀⢰⡾⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣤⠀⠸⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⣀⠀⠀⠀⠘⠷⠟⠃⠀⠀⠖⠀⠀⣀⣴⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣿⠁⠀⣾⠛⢷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣴⡾⠛⢷⠀⠈⣿⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢀⣀⣾⠁⠈⣿⠉⢹⡏⠉⣿⠁⠘⣷⣀⡀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⠆⠀⠀⢠⣼⣧⡀⠀⠀⢰⣿⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠸⣷⣾⠇⠀⠀⠀⠉⠉⠁

⢰⣶⡶⠖⠛⠛⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠒⠛⠓⠶⣶⣶
⣿⡋⡉⠀⠀⠀⠀⠔⠂⠀⠀⠈⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠒⠄⠀⠀⠀⠈⡉⣻
⢻⣀⡀⠠⠄⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠤⠀⢀⣸
⠀⠛⢦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⢠⣴⣤⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠞⠃
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣀⠠⠀⠀⠉⠐⠀⠤⢀⣀⣙⣷⣴⣿⣷⣴⣟⣁⣀⠠⠄⠀⠈⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⢶⡖⠒⠉⠁⠀⠀⠀⠀⢀⣠⡤⠖⠚⠛⠛⠻⣻⣿⣿⠛⠏⠛⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠉⠑⠒⣶⠎
⠀⠀⠀⠀⠀⠀⠳⣦⣀⠀⠀⢀⣠⡶⠋⠁⡀⠄⠤⠀⠀⢀⡞⣿⡟⣆⠀⠀⠠⠄⠄⠀⠉⠳⣦⣀⠀⠀⢀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠉⠀⠀⠀⠀⠄⠀⠀⢀⣾⠐⣿⡇⢸⣆⠀⠀⠀⠄⠀⠀⠀⠀⠙⢿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠃⠀⠠⠂⠀⠀⠀⠄⢸⣿⠀⢿⠇⢸⣿⠁⠄⠀⠀⠀⠢⠀⠀⠱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⡠⠁⢀⠀⠀⠀⠀⠀⢻⠀⠘⠀⢸⠇⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡐⠀⢀⠂⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢣⠀⠐⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⠆⠀⠀⠀⡆⠀⢀⠀⣃⠀⢀⡇⠀⠀⠀⠆⠀⠀⠀⢂⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡜⠀⠰⠀⠀⠆⠀⢸⣠⡏⠀⠈⣧⣸⠀⠀⠂⠀⠘⡀⠈⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡇⠀⢠⠀⢀⣼⠋⠀⠀⠀⠈⢻⣄⠀⢰⠀⠀⢇⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⢾⡿⠛⠛⠀⠀⠀⠀⠀⠘⠛⠻⣿⠾⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡤⢤⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢄⠀⠀⠀⠀⠈⡇⢸⠁⠀⠀⠀⠀⡠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡞⠁⠀⣀⡴⠀⠀⠀⠀⢠⠇⠸⡄⠀⠀⠀⠀⢦⣀⠀⠈⢳⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢳⠀⠀⠀⠈⠳⠴⠯⣉⣧⠤⠖⠛⠋⠉⠓⠚⠋⠙⠛⠲⠤⣼⣀⠽⠦⠞⠁⠀⠀⠀⡞⠉⠉⠳⣄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡇⠀⠀⢀⣴⡋⠳⢤⣀⣀⠞⠁⠀⠀⡴⠋⠉⠙⡆⠀⠀⠀⠀⢰⠋⠉⠙⢦⠀⠀⠈⠳⣀⣀⡤⠞⣙⣦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠦⠖⠋⠉⠉⠙⢦⣀⡼⠀⠀⠀⠀⠱⢤⣤⣾⡁⠀⠀⠀⠀⢈⣷⣤⡤⠞⠀⠀⠀⠀⢧⣀⡴⠋⠉⠉⠙⠲⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠷⠟⠀⠀⠀⠀⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⡾⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢿⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⡷⢤⡇⠀⢠⠏⠉⠙⣄⡤⣄⠀⠀⠀⡞⠉⠉⢳⠀⠀⠀⣠⢤⣠⠏⠉⠹⡄⠀⢸⡤⠾⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢧⠀⢈⡷⠚⡇⠀⠘⢦⣀⡴⠋⠙⠃⠀⠀⠀⢦⣀⣀⡴⠀⠀⠀⠘⠋⠙⣆⣀⡴⠃⠀⢸⠓⢾⡁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⢷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡾⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⣖⡦⠀⠀⠀⠀⣴⣲⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⡰⠒⠲⢄⣀⣀⣤⠞⠁⣱⠀⠀⠀⠀⡴⠋⠙⢻⡀⠀⠀⠀⠀⢀⡟⠋⠙⢦⠀⠀⠀⠀⡏⠈⠳⢤⣀⣀⡠⠖⠒⢆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣄⡴⠚⠉⠉⢣⡀⠀⠀⠱⣄⣀⣰⠃⠀⠀⠀⠀⠸⣄⣀⣠⠎⠀⠀⢀⠜⠉⠉⠓⢦⣠⠟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡼⠀⠀⠀⢀⡶⠒⢞⣁⡟⠓⠦⢤⣤⣠⠤⠤⣄⣤⡤⠴⠚⢹⣉⡷⠒⢶⡀⠀⠀⠀⢧⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠉⢑⠀⠀⠀⠀⠘⡆⢰⠃⠀⠀⠀⠀⡎⠉⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠀⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⠀⠙⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠖⠒⠋⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡽⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠄⢀⡀⠀⠀⠀⢀⣠⣠⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⢀⣼⢇⡄
⠀⠀⠀⠀⠨⠵⢞⣳⡟⠻⠂⠀⠀⠀⣠⣀⣤⡀⠀⠀⠀⠈⢢⣄⣠⡄⠃⠀⠀⠀⣿⣿⡟⠁⠀⣀⣾⣿⢋⠈⠀⠀⠀⠀⠀⠀⠐⣯⠁⡄
⠀⠀⠀⠀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠰⣿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠠⠔
⠀⠀⠀⠀⠀⠀⠀⡎⠰⠃⠀⠀⠀⠈⢾⣿⣽⡞⡗⠀⠀⠀⠀⢲⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⠀⠀⠀⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠉⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⣤⠀⢘⣦⠾⠁⠀⠠⠐⣦⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢠⣤⢞⠀⠀⢀⠈⡄⢠⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠔⠋⠀⠊⠀⠀⠀⠀⠀⠀⠅⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠋⠉⠁⠀⠀⠈⠀⢑⡺⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡇⠀⠀⠀⠀⠀⠈⠰⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢀⡄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣨⠁⣉⠀⠀⠀⣶⡶⠀⠀⠀⡇⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢉⠀⠀⠀⠀⠆
⠀⠄⠀⠀⠀⠀⣀⠀⡦⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡃⡿⣃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠀⠀⠀⠾⡷⠄
⠀⠂⠀⠀⠀⠀⠈⢰⡖⠚⠀⠀⠸⠿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠉⠳⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣾⠆⠄
⠀⠂⠀⠀⠀⠀⠀⠘⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⡂
⠀⠁
⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢡⣤⣤⠈⠻⣦⡠⠀⠀⢰⣀⣀⣐⡂⠀⠀⣁⣰⠗⢀⡢
⠀⠀⠀⢀⠔⣀⠘⠒⢶⣦⡀⠈⣿⢿⠏⠀⠀⠀⠀⠘⠿⡿⠟⠻⠀⣸⡟⢁⣼⡿⠛⣉⣩⡃
⠀⠀⠀⢁⣴⣿⣷⣶⣿⣿⣿⡟⠡⢳⡀⠀⠀⠀⠀⢰⡞⠛⡾⣄⣴⢛⠀⣸⣿⢁⣼⣿⣿⣧⠂
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡛⠀⡬⠋⠁⣸⠂⠀⠀⠀⠀⠀⠺⠀⠀⠘⢺⣿⣿⣿⣿⣿⣿⣾⠀⡀
⠀⠀⠀⠈⠙⣛⣿⣿⣿⣿⣿⣾⣧⣴⡟⠀⠀⠀⠀⢰⣶⣶⣾⣠⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⡇⢡
⠀⠀⠐⢰⣿⣿⣿⣿⠏⣾⣿⣿⡿⡩⠀⠀⠀⠀⠀⠙⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡄
⠀⠀⠀⣀⣻⣿⣿⡸⡄⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣏⡀⡇

⣰⠋⡻⠻⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⢟⠙
⣿⣷⡿⣖⣿⠿⣆⡙⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢋⣰⠿⣿⣲⢿⣾
⠻⣿⣍⣺⣿⣷⣾⠟⠛⠉⠃⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠘⠉⠛⠻⣷⣾⣿⣗⣩⣿
⠀⠹⣿⣿⣿⣿⠍⢑⣒⣤⣤⠾⣦⣟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⣴⠷⣤⣤⣖⡊⠩⣿⣿⣿⣿⡏
⠀⠀⢹⣿⡏⣙⣶⣶⣾⣿⣿⣶⣾⡿⠷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⢿⣷⣶⣿⣿⣷⣶⣶⣋⢹⣿⡏
⠀⠀⠀⢻⣿⡍⣽⣿⠿⠛⠁⠀⠈⢧⡀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⡼⠁⠀⠈⠛⠿⣿⣯⢩⣿⡟
⠀⠀⠀⠸⣿⣶⡿⣇⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠹⣿⣧⡀⢀⡀⢀⣼⣿⠏⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⣿⠇
⠀⠀⠀⠀⠹⣄⣷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⣠⠏
⠀⠀⠀⠀⠐⣿⣿⣄⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣥⣤⠿⣿⣿⠿⣤⣬⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠈⠛⠛⣻⡿⢿⣟⡛⠛⠿⢛⡿⠟⠉⠁⠀⠀⣿⣿⠀⠀⠈⠉⠻⢿⡛⠿⠛⢛⣻⡿⢿⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡰⣿⠖⠊⠈⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠹⠦⠀⠀⠁⠑⠲⣿⢆
⠀⠀⠀⠀⠀⠀⠀⡟⢹⣡⠄⠀⠀⠀⠼⠓⠒⠂⠀⠀⠀⠀⣿⡯⠀⠀⠀⠀⠐⠒⠺⠧⠀⠀⠀⠠⣬⡏⢻
⠀⠀⠀⠀⠀⠀⠀⢻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠙⠃⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠗⢦⡆⠀⠀⢠⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⡄⠀⠀⢰⡴⢺⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣟⣿⣖⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⣲⣿⣻⡽⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣀⠴⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠂⠀⠀⠤⠚⠁⠀⠉⠐⠉⠀⠀⠀⠀⠐⠂⢙⠉⢥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⠤⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠑⢆⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⠀⢀⠁⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠜⠉⠣⠄⠠⠒⠉⠓⠦⣀⣀⠤⠆⠁⠠⠄⣈⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠖⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⠑⠆
⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸
⠀⠀⠀⠀⠀⡐⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢃
⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⠁
⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠁⠲⠶⠀⠀⣀⣉⣤⡉⠀⠰⠶⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⡙⠋⠀⠒⠒⢠⡄⠀⠀⠄⣤⠐⠒⠒⠂⠛⡍⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠸⠁⠲⣄⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⣠⠔⢺⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠃⠀⠀⠈⠓⡄⢨⡇⠀⠀⠀⣿⠀⣠⠊⠁⠀⠀⠲⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢠⠉⠀⠀⠀⡠⠎⠀⢸⡇⠀⠀⠀⣽⠀⠈⢢⠀⠀⠀⠀⢡⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⢄⠀⠀⡇⠀⠀⠀⠸⠀⠀⡰⠃⠀⠀⠀⠀⠦⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠳⣀⠇⠀⠀⠀⢀⢀⠎⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⢀⠴⠖⣨⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⣶⢀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠓⠐⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⣥
⠀⠀⣀⡤⠊⠀⠈⠑⠢⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠤⠒⠁⠀⠣⢄⡀
⡤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣶⡟⠁⠀⠀⠀⠀⠀⠀⠉⠓
⠉⢰⠆⢀⡀⠀⠀⠀⠀⣀⡴⢄⠀⠀⣠⡞⠋⠉⠉⢛⢻⣶⡦⠤⢤⡤⠤⠴⠦⠤⠀⠀⠀⠀⠀⢸⠀⢀⡿⠀⡄⠀⠀⠀⠀⢀⠀⠰⡆
⠀⠈⠶⣟⠁⣰⠆⢀⣤⡀⣷⢀⣇⢠⡏⠀⠀⠀⠀⠀⠈⢹⡇⠀⠐⠇⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⢨⡏⠀⠇⣀⡀⠠⣄⠈⣷⠶⠃
⠀⠀⠀⠈⠒⠉⠒⠂⠈⢻⡉⠃⢧⡘⣧⡀⠀⡀⠀⠀⠀⣼⡇⠀⠐⡆⠀⠀⡇⠀⠀⠀⡰⠺⣷⣦⠀⣼⠛⡀⢸⠁⠐⠀⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⢸⣦⣬⣷⣶⣤⣤⣤⡾⢁⡦⠀⢠⡇⠀⠀⡇⠀⠀⠘⢤⡀⢘⣿⢠⡏⣭⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⣌⣤⣤⣤⢱⣿⠀⠠⢄⠨⣟⠀⢸⡇⠀⠀⡇⠈⠀⠀⠀⣹⣏⣹⣿⣀⡤⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠱⠆⠠⠄⠴⠋⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠈⠲⠄⠀⠠⠴⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠐⡇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠺⢿⣭⣭⣤⣤⣬⣽⡋⢸⡏⠘⢯⣭⣭⣭⣭⣽⡟⠿⠃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠛⠃⠀⠀⠀⠀⠈⠉⠁⣼⠣⠘⠃⠀⠀⠀⠀⠀⠰⠟⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢭⠴⠆⢀⣀⡀⠰⢦⡁⠞⠓⢨⠴⠆⣀⣀⣀⡀⠰⠮⠓

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠠⡀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠄⠂⠈⣉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠉⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡀⠒⠂⢀⠀⠐⠀⠀⢤⡀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠐⣀⠀⡈⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠨⢀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠆⠀⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠸⠀⠀⡀⠦⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠒⢄⠀⠸⠂⠊
⠀⠀⣰⡶⠶⠶⠶⠶⠶⠶⠶⢶⣆⠀⠀⢰⠀⠎⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⡱
⠀⠀⡿⠐⠄⠀⠀⠀⠀⠀⡠⠀⢿⡀⠀⢸⠀⠑⠀⡆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢀⠀⠀⡜⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡇⠀⢸⠀⠀⣄⠈⠒⠂⢇⠀⠀⣠⡀⠀⠀⣀⡀⠼⠀⠥⠤⡤⠄⠠
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⣣⠀⠀⠀⢅⠒⠤⣀⠀⠀⠀⠠⠭⠋⠀⠀⣀⠄⠒⡡⠀⡀⠀⠀⣐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠮⠷⠤⠤⠤⠤⠥⠽⠤⠬⠴⠤⠥⠤⠤⠤⠭⠤⠭⠭⠤⠤⠧⠾⠥⠭⠬⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠥⠤
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠆⠀⠀⣀⣀⠀⢀⣜⣫⣿⡂⢤⡀⠈⡩⠖⢶⡋⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⣟⣩⣿⣽⣷⣶⠖⠁⠳⣵⣾⡶⢠⢦⡘⡇⠀⠀⠄⠀⢠⠶⢦⡄⠀⢀⣴⡏⢱⣦⣀
⠀⠀⠀⠁⡀⠀⢀⣀⣠⣀⠀⠀⠀⠀⣠⢠⠀⠀⠀⠀⠈⠻⠏⠛⠛⠃⠀⠀⢀⣨⣭⣽⡟⡾⠛⠉⢂⠀⢸⡀⠀⠀⠀⠀⠀⢸⣷⣿⣍⡿⢇⡳
⠀⠀⠀⠀⠀⠈⢣⣾⣿⣿⣶⣤⡀⠀⠈⠎⢇⠀⠀⢀⠀⢀⣤⣄⠀⠀⠀⠀⠇⢹⣿⡽⣷⣟⡱⢀⠀⢣⠘⣷⠄⠀⠀⠀⠁⣾⠿⣟⣷⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢙⠛⢛⡻⣾⠁⠀⣀⠸⡌⢣⠀⠀⠀⡿⣿⣿⣿⣷⣶⡀⠘⠶⣑⣰⠆⠀⠀⠘⠀⣠⢓⡸⢂⠐⡲⢄⢰⣿⣷⡏⡫⢩⡃⢀⡀
⠀⠀⠰⠒⡂⢤⠤⣬⢭⠤⡁⠁⣄⡾⣽⡆⠹⢄⣱⡀⠀⠹⠿⣿⣷⢿⣿⣷⡄⠀⢉⠅⢐⢀⡀⡀⠀⠈⠛⠃⢸⡀⠀⠼⢼⠿⡻⠟⠛⢿⠃⠀⠁
⠀⠀⠀⢡⡁⣈⠾⣤⢃⢳⣾⠶⡿⡿⣷⣿⣯⠤⠀⢀⠶⠀⠀⠘⠢⠿⠻⠃⠀⠃⠂⠠⢘⣖⠇⢀⡤⠠⠤⡈⣧⠿⠶⠃⢀⡠⠀⠀⢀⢀
⠀⠀⠀⠀⢻⠑⢉⣭⠩⠋⢸⣴⣱⢻⣷⣿⡏⣰⡟⣿⣶⣤⡀⠀⢀⠀⠀⠠⡀⠉⠃⠀⠉⠁⠀⠘⣶⣖⠒⠃⡿⡇⡄⠀⠈⠁⠂⠈⠁⣢⠂
⠀⠀⠀⠆⣘⠚⠋⠁⠀⠀⢀⣻⢽⣷⣽⠋⠀⣡⣾⣿⣿⣿⡿⠀⣈⡁⠒⡲⢅⠈⢀⢈⡇⠀⣼⢹⡸⠏⠓⠀⠹⠉⠆⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠃⢨⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⣯⣿⡿⣿⣧⡄⠻⠿⡤⠒⠌⠀⠓⠉⢼⡈⣣⢴⣷⠂⠀⢧⠄⠀⠀⠘⠓⡈⠓⠀⠀⠀⡴⠀⠛
⢀⠀⠐⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⠻⡿⠻⠷⠂⠴⠤⠆⠀⠀⠈⣀⡄⠉⠉⢄⠏⠀⠀⠀⠀⠀⢀⡄⠋⠉⠉⠛⣂⠀⠁⠄
⡘⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⡷⠶⠀⠐⠀⠀⠀⠀⠀⢠⡌⠚⠠⣀⡀⠃⡄⢨⠉⢰⡿
⣤⣬⣃⠨⢧⡄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠲⠁⣀⣀⠀⠀⠀⠀⠀⠺⠆⠀⠠⠌⢿⣿⣀⣭⡆⢈⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠿⢻⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⠀⠀⠉⠀⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢸⠁⢿⡣⢰⣶⣶⡿⠁⠀⠀⣶⣖⣶⣀⣀⣀⣀⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⡟⠹⠿⣷⣄⢨⡄⠀⣀⠚⠉⣽⠇⠀⠀⠀⣇⠄⠉⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡠⣰⠃⠀⠁⣈⡽⠖⠒⠢⠽⢳⣀⠛⣠⡞⠁⠀⠀⠀⠀⣇⡩⠆⠀⠀⠀⠀⡇
⠀⠀⢀⡤⠚⢹⠇⢇⠴⡎⠉⠁⠀⠀⡣⠀⠀⣯⡧⠽⡟⢳⣄⠀⠀⠀⠀⣃⡕⠂⠀⠀⠀⠀⣧
⠀⢠⠏⠀⠀⠈⣻⠛⠀⡇⠀⠀⠀⠀⡆⠀⢘⣗⠛⠇⢀⡼⠈⠑⣤⠀⠀⠹⡞⠇⠀⠀⠀⠀⡇
⢰⡃⠀⢀⣀⣾⣇⣀⡼⠁⠐⠀⠀⠀⢁⠀⢸⣄⠒⠀⢨⡆⠀⣼⢿⠀⠀⠘⢿⠃⠀⠀⠀⠀⡇⠀⠀⣀⡀
⠀⠉⠉⠙⠛⠚⠉⢹⡇⠀⠄⢁⠀⠀⠈⡀⠈⠀⡝⣆⠈⠧⣤⣀⣺⠀⠀⡰⢄⡆⠀⠀⠀⠀⣇⡴⠋⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⡤⢼⡇⠀⠈⢂⠂⠀⠀⢀⢸⠁⡏⠈⢦⡇⣸⠉⠛⡆⠀⡁⢎⡁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠑⠢⠀⠀⢸⠀⡇⠀⠱⡔⠋⠀⠀⢱⡀⡣⡊⡁⠀⡠⠊⣠⡔⠲⣤⣠⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠧⡿⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠹⡄⣼⢇⠀⠀⠀⡼⠃⡅⡜⣃⣈⣓⡉⠀⡇⣸⠁⢸⠀⠸⡀
⠀⠚⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⢲⠋⠀⠀⠀⠹⡗⠒⠚⠒⠚⣧⣤⣧⣉⣿⠀⠰⣷⣶⣷⠗⠒⢺⠒⠒⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣶⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢍⡱⠋⠉⠀⠀⠉⠒⢰⠆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠻⠿⠓⢟⣀⠬⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⣳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢿⣠⣤⡀⢼⣇⠀⢀⣞⠀⢲⣾⣿⣶⠛⠃⠀⣤⡙⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣿⣷⣾⣿⣿⣿⣧⣶⡿⠊⣡⣤⣤⡐⢀⣀⡤⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣏⢹⠉⠁⣞⣵⣷⣤⡎⣿⣿⣿⣿⣿⠯⠃⠉
⠀⠀⠀⠠⠤⠤⡄⢸⠀⠀⣆⡖⠀⠁⠃⣸⠘⣿⢻⡋⣰⡏⠻⠛⡌⣽⣿⣿⣿⡅⠎
⠀⠀⠀⠀⠈⠂⠀⢸⣇⠀⣡⠁⠀⠀⠂⠘⠆⢻⣆⣿⣿⣧⢀⣰⢧⣻⣿⠯⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠛⠗⠀⠀⠀⠀⠐⠂⠹⣦⣽⣿⣮⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠓⠀⡤⠊⠁⠀⠀⠀⠀⣄⣾⣿⣿⣿⠒⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢿⡧⠄⠀⠤⠀⠀⠀⠀⠀⠘⢛⣿⠛⣿⣽⣿⡿⠘⢹⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣤⣠⣼⠷⠶⠓⠒⠀⠀⠀⠀⠀⢀⡟⠙⢯⣜⣥⣿⢥⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠂⠈⠉⠙⠙⠆
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠐⢀⠸⡇⠈⠑⢄⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠳⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡈⠃⠀⠀⠤⠀⠀⠈⠀⢀⠀⠱⡀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄
⠀⠀⠀⢀⠐⠂⠐⠂⡃⢸⠀⠀⠈⠀⠀⢀⢀⡀⡀⠀⠀⠙⠢⣽⣀⡌⠀⣀⠶⡤⢤⣀⠀⠀⠀⣶⢰⠟
⠀⠀⠀⠀⡠⠐⠀⠀⠁⢨⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣣⠏⠀⡄⠀⠀⠀⠀⠤⣴⣯⣀⢀⡀⠀⢀⠶⡃
⠀⠀⠀⠀⠀⣠⠖⣃⠀⠀⢀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣯⣭⣭⠛⠀⠁
⠀⠀⠀⠀⠀⠨⠁⠙⡂⠀⠈⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠛⢿⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠂⠀⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠢⣀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⠴⠒⢢⡀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣎⣁⣀⣀⡀⠙⢄⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣰⢋⣩⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠀⠀⠉⠓⠮⡑⢤⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠋⠴⢚⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣈⣛⣰⡀⠀⢴⡄⢸⠖⠋⠀⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣝⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠛⠉⠲⠤⠴⠋⠀⣤⣠⠞⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⡷⡀⠰⠤⠴⠀⠀⢀⡴⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡿⣼⡄⠀⠀⠀⠀⠀⠰⢇⣈⣓⣶⠴⠶⠒⠋⠀⡧⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣻⣙⣛⡩⣷⠈⠁⠀⠀⠀⠀⣠⠖⣻⠟⢱⠟⠳⣄⣠⠴⠚⣳⠈⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠀⠀⣿⠀⣴⢲⣄⣠⠞⠁⠾⣅⡀⢸⣄⣴⡿⡅⠀⣰⠃⠀⢸⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣠⡏⠉⣿⠁⠀⠀⢠⠞⠁⢸⠈⢹⠀⠱⡾⠃⢀⣀⣈⡇⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⣧⣴⣛⠉⠙⠒⠾⢧⡀⢸⠀⡟⢀⡼⠁⠀⠻⡄⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢀⣟⡭⠤⠀⠀⠀⠀⠀⠉⢿⡀⣧⠞⠀⠀⣠⠔⠃⠀⣀⠔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣈⡯⠾⣉⣁⣀⣀⣀⣀⠀⠀⠙⢧⡀⢠⠞⠁⠀⠀⡴⠁⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⢉⡝⠀⠀⠈⠳⡄⡏⠀⠘⢦⣀⡠⠏⣹⠓⢤⡀⠀⡾⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢹⣄⡰⠃⠀⠀⠉⢺⡁⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠖⠒⠒⠒⠲⢄⣿⠀⠀⢀⡞⡼⠃⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣸⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢄⣀⣀⠴⠁⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢇⠀⠀⠀⠀⠀⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠓⠁⠀⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠈⠒⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡄⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⡀⣀⡀⠠⡇⠀⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣁⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣠⠀⠀⠠⠆⠒⠈⠁⠁⠈⢈⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠒⠒⠚⠉⠁⠀⠉⠙⠄⠤⠠⠤⠠⠦⠤⠴⠦⠤⠖⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠁⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣯⣽⣿⣭⣿⣯⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢺⠟⢟⠀⠤⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⡀⠒⠒⠄
⠀⠀⠀⠀⠀⠀⢀⠈⠂⠈⠆⠀⠀⠀⢀⠅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡟⡉⠉⠂⢰⠤⠐⠓
⠀⠀⠀⠀⠀⠀⠈⠁⠸⢄⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠈⠃⠀⠠⠈⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⢀⠀⠀⠀⠠⡀
⠀⠉⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀
⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡄⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡠⠀⠤⠶⠈⠊⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⡆⢀⡀⠑⠠⠐⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢦⠧⢄⠉⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣷⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⡿⠿⡛⠛⢻⠻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢂⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡘⣯⣦⣴⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⢛⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡏⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣻⣿⣿⣿⠟⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣿⣿⣿⡷⠶⠶⢒⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠛⣿⠿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠿⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢐⡆⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡆⠙⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⣸⣿⣿⣿⣿⠃⠇⣴⢹⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣹⡄⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⢹⣗⣿⣿⣿⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢐⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⠏⠀⢀⣀⣾⣼⣿⣿⣿⣋⡷⠰⣞⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣸⣟⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⣾⠁⢀⠹⣾⣿⡿⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠸⣿⡆⠀⠙⢿⣿⠒⠛⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡅⣸⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⣀⣹⣿⣷⣾⣿⡈⢷⡄⢀⣀⣥⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⢂⡿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⡹⣷⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢏⣰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠃⠈⠿⣶⡂
⠀⠀⠀⠀⢀⣀⣀⣾⣟⣧⠞⣻⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠘⢿⡿⠟⠋⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣭⣭⣭⣭⣭⣭⠉⠁⠀⠀⠀⠀⣨⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣤⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣟⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⡀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣯⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠿⠿⠿⠿⠿⠿⠿⠷⣿⡇⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⣭⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠶⠾⠿⠷⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠦⡀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠉⢠⣄⣀⠀⠀⠀⠀⢱⣼⣷⣾⠄⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⡀⢤⣚⣿⢿⡟⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠑⠤⣄⡀⠀⠀⠀⠀⠀⢈⡄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣿⣿⣻⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⡠⡀⠀⠀⠂⠄⠐⠰⢄⣀⢀⡠⠀⠠⠉⠀⠐⠀⠀⢹⢿⣿⡿⠄
⠀⠀⠀⠀⠀⠸⠅⠀⠀⢀⠄⠉⠀⠀⢰⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠃⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠀⠀⠸⡺⣄⠀⡀⠀⠀⢃⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠤⠄⣀⠈⠻⢿⣾⣷⡤⠂⠁⠀⠀⠸⠁⠀⣤⣀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⡠⢮⡿⠁⡀⠀⠠⠬⠿⢻⣿⣿⢷⡦⠤⠖⠚⠁⠙⢷⡏⠿⠛⠀⠀⡁⠀⠐
⠀⠀⠀⠾⠁⠉⠀⠀⠈⠁⠀⠀⡄⢀⣨⠶⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠜⠃⢨⠀⣠⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⠌⠀⢀⡏⢓⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠠⣿⡃⠀⠀⠑⠒⠀⠒⠂⠁⠀⠀⠀⠩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠰⠄⡈⠗⠈⠁⠐⣁⡠⠀⠀⢴⠋⠀⠀⠈⠑⠢⢄⡀⢀⡀⠆⠒⠒⠒⠶⣀⠀⠀⠀⣠⠺⠚⠰⠷⢄⠄⠀⠀⠘⡀⠢⠵⠀⠆⣀⠔⠀⠀⠀⡄⡈⢁⡱⠀⢠
⠀⡤⠤⠁⠀⠀⠀⠀⠈⠤⠆⠀⠘⠖⠖⠂⠦⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⡸⠀⠐⢸⡍⠀⠀⠂⠀⠻⠄⠀⠀⡐⠃⠀⠀⠀⠀⠀⡣⠀⠀⠀⢀⢗⠈⠃⡇
⠀⢀⡰⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠈⠉⠀⠀⠉⠉⠁⠁⠀⠀⠈⢫⣄⢀⣀⡰⠛⠈⠀⠀⢑⠅⠀⠀⠀⠀⠀⡤⠈⠀⠀⠈⠀⢤⡄⠀⠰⠆
⠀⠀⠀⠞⠀⣀⠀⠢⠄⠀⠀⢠⠀⠒⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠎⠈⠱⠂⠀⠀⠀⢀⠀⠀⠍⠈⠐⢀⠀⠀⠀⠄⠸⠰⢀⡄⠦⠉⡁⠀⠀⡀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠘⠠⡈⠂⠀⠀⠀⠀⢰⠄⠀⠂⠈⠒⠀⠀⠀⢀⠀⠀⣐⠆⠞⠠⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠟
⠀⠀⠀⡔⠒⢢⠀⠀⠀⠀⠀⠀⠢⠀⠈⡀⠀⡈⠀⠀⠠⠐⠄⠠⠂⠀⠆⠀⠁⠄⠀⠀⠉⠀⠀⣩⠄⣀⣀⠓⠠⣠⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⠂⠈⠀⠀⠠⠐
⠀⠀⠰⠀⠠⠀⠀⠀⠴⠀⠠⠁⢰⢐⠈⠡⠀⠀⠀⠈⠈⠀⠈⠀⠀⠠⡄⠄⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠱⢵⣄⡈⠉⠛⠲⣤
⠀⠀⠂⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⣀⣀⡀⠀⠤⠤⠐⠉⠉⠢⡄⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠑⡥⠀⠀⠀⠂⡀⠀⠔⠂
⠀⢘⠀⠀⢠⠃⠀⠰⠉⠈⠱⠀⠀⠀⠀⠀⠒⠀⠀⡄⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⡸⠀⠀⣠⠮⠃⠘⣵⠀⠈⡗⠀⠀⠀⠀⠀⠀⠁⠀⢁⠂
⠀⠈⢲⠐⠁⠀⠀⡄⠀⠀⠌⠀⠀⠀⢀⠀⣀⠀⢂⠈⠀⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡀⠠⠄⠖⠁⠀⢬⠋⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠈⠈⠄⣅⢆⠂
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⢀⠀⠈⢀⠀⠀⠀⠆⢠⠀⠈⠑⠒⠰⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⠜⠛⠋⠀⠰⠀⠀⢸⠀⠂⠀⠘⡄
⠀⠀⠂⠀⠀⠀⠀⡄⠀⡸⠀⠀⠀⠈⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⢀⢀⣀⣀⣤⣴⣶⣾⣶⣶⣤⡀⠀⠀⠀⠋⠀⠀⠀⠰⠓⠁⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣤⠀⠀⡗⠀⡀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠟⣛⠻⠻⡟⠟⠉⠹⠿⣿⣏⠉⡹⢿⣿⣿⡆⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡄⣀⠀⠢⣀⣄⡀⢁⠠⠆⠀⠠⣼⡏⢸⢰⡄⠀⠈⠰⢧⠙⡆⠹⡿⠷⠂⢹⣯⣥⣾⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⡀⢡⠀⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡁⠀⣋⠀⢀⡀⠀⢰⣿⡇⠀⣸⣇⣸⣤⣷⣴⣷⡴⢾⡿⠶⢾⡟⢛⠛⠙⡆⢁⢻⡇⠀⠀⢀⠄⠡⠂⠀⠄⠐⠌⠁⢄⡰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠋⠁⢀⡀⠀⠀⠐⣿⠟⡛⢿⠉⡝⢿⠀⣦⣶⣶⠸⣇⠘⠛⣣⡈⠠⣆⠁⢸⣾⡷⠀⠀⠸⡀⠀⢀⠈⡀⠉⡡⢀⠀⢀⡀
⠀⠀⡴⠒⠒⠲⣄⠀⠀⠀⠀⠀⠈⠁⠀⠴⠀⠀⠀⠀⠀⠀⡹⣧⠡⣜⠃⠰⣄⠡⡙⠋⢹⣧⢹⡄⠙⠛⢣⢠⣈⣀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢄⠀⢠⠈⠢⠬⠤⠃
⠀⢼⠀⠀⠀⠀⢈⡄⠀⢀⠀⠴⠀⠀⢤⠀⢠⠀⢀⡀⠀⠀⠀⠨⠛⠶⢾⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠋⠁⠀⣀⠀⡔⠆⠀⠀⠀⠑⠂
⠀⠘⢦⣀⣀⣀⠜⠀⠀⠀⠀⠀⠀⠓⢤⠦⢤⡔⢁⡀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡬⣃⡟⢠⣌⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⠀⠀⠀⣀⠤⠤⢄⡀⠘⠀⠀⠹⢄⣠⠏⠀⣀⠀⢀⡄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⢖⣄⣸⠶⠛⠉⠉⠀⠀⠀⠠⡀⠐
⠀⢘⠁⢸⠆⡼⠁⠀⠀⠀⠘⡆⠀⠒⠀⡐⠀⠦⠀⠈⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⡰⠋⠙⡆⠀⠀⠀⠐⠢⠼⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠀⠁⢀
⠀⠈⠉⠉⠀⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⡎⠀⠈⢡⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⣠⢠⣤⣤⣤⠲⣾⣩⠻⡍⢣⠀⠉⠀⠀⡀⠀⠀⡠⠀⢀
⠀⠀⠄⠀⠀⠈⠓⠤⡤⠤⠊⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠑⠄⠔⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠐⣩⡆⣿⡞⠷⠍⠛⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠘⠀⢀⡀⠀⡀⠀⠀⠤⠀⠀⡀⠀⠀⢀⡀⢀⡀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠄⠀⠈⠀⢈⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢀⠂⢒⡠⡀
⠀⠀⣐⠂⢘⠀⡀⡎⢃⢩⡩⠤⠼⢄⡠⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠄⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⢀⡀⢀⠄⠲⠒⠠⡀⢀⠀⢀⠎⠂⠱⠀⠀⠼⢈⠆
⠀⠆⢨⠖⠉⠉⠈⠁⠈⠀⠀⠈⠉⠀⠓⢼⠀⠀⠀⣠⠴⠟⠉⠋⢹⡆⠀⠀⠀⣠⠖⠑⢠⠅⠂⠀⠀⠀⠁⠀⠀⢨⡠⠀⠀⠀⠐⣩⠀⠀⢨⢰⠀⡄⠀⡄⠀⠰⠈
⠀⡌⢸⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡀⢫⡉⠀⢠⠞⠁⣠⠤⠤⠖⠛⠀⣀⡠⠔⠁⠀⢀⡜⠀⠀⠀⠒⠀⠀⠀⠐⠨⢴⡄⠀⠀⢄⠈⠀⠀⠀⠢⡑⠄⢀⠀⢔⠡⠂
⠀⠀⣃⠜⡘⠤⠤⠄⢂⠠⡌⣤⠗⠈⠆⠀⠀⢯⡼⠊⠁⠀⠀⠀⢰⡋⠉⣀⣀⠤⠒⠉⠀⠀⠀⠠⠆⣀⠀⠀⠀⠀⢠⠂⠋⠣⠁⠀⠀⠀⢀⡀⠀⠁⠀⠈⠁
⠀⠀⠀⠈⠀⠆⠖⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⡄⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠁⢠⠀⡀⢠⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠠⠃⠈⠑⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡶⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡻⠻⠆⠀⠀⠀⠀⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⠀⠀⢀⣠⣆⣠⠀⠀⠃⠀⢀⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⡿⠁⠀⢠⡋⠉⠹⢃⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠶⠆⠂⠀⠺⢿⢇⡀⡀⠀⡸⠿⠛⢀⡿⢶⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⢻⡃⢠⠇⠀⢠⠂⠀⠠⠀⠀⠀⣴⣿⠟⠲⣄⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢠⠏⠀⠀⡇⠀⢠⣿⠟⠻⠀⠀⢹⠆⠀⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢠⣄⠀⠘⢀⡄⠀⠃⠀⠉⠉⠀⡴⠞⠀⠀⠀⠀⢠⡆⠈⢢⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠈⠀⠀⠀⠞⢷⡛⠱⠄⠀⠀⡴⠀⠀⠀⠀⠀⠀⠐⠿⠃⣀⣸⡟⠦
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡄⢲⡆⠀⢠⣷⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⢸⡋⠁
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡎⠑⠇⠀⢘⠉⠘⡇⢢⣿⡶⠊⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠃⠀⠠⡘⢾⡄⠀⣏⡼⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⣷⡄⡟⢀⣶⣇⠀⠀⠀⠲⢀⣄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⢠⡄⢱⠙⡄⢸⣿⢋⡀⣘⣀⠀⠘⠛⠛⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠱⣾⡇⢸⡄⠁⠀⡇⢈⠷⠛⡟⢃⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⣤⣾⣶⡷⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠈⡇⣸⣷⣷⡿⠟⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⢳⡏⣿⠥⣶⣶⣽⣿⡴⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠠⣄⡀⠀⠀⠀⣸⠇⣿⣠⣨⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠙⢦⡀⠀⣿⡔⡿⠃⠛⠛⢿⣼⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢿⡆⢿⡿⡇⠀⢀⣀⡀⠋⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣿⠾⠃⠀⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣿⡛⣛⢻⣾⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠋⠛⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢖⡶⣄⣠⢾⠝⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠈⠁⠇⠘⠤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⢨⣀⡄⢀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⢄⠀⠀⠒⣿⣿⠏⠀⠠⠀⠠⠂⠿⣿⢷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⡈⠁⣱⠠⢉⡄⢀⠀⠀⠀⠐⠀⠐⠈⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴⠖⠂⡆⠂⠀⠀⠐⠉⢠⡁⠀⢸⡇⠈⢿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠸⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠡⣀⡴⢖⡠⠖⠲⢶⠦⠈⠆⠀⡘⢻⡿⢀⡴⠋⠀⠀⠀⣀⠀⣤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⣦⣠⣴⣾⣯⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠱⡏⠀⠐⠒⠤⠀⣿⣾⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠼⠿⠛⠉⠉⠉⠉⠉⠉⣷⣄⠀⢀⡀⢀⣄⡎⢧⠀⠁⢀⠀⠀⡀⠘⢻⡇⠀⠀⠀⠀⢀⣀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣧⣵⠸⡆⠐⡇⠠⠄⡀⠀⠸⠃⠀⠈⠉⠑⢏⠡⡀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡩⠍⠉⠡⠞⠛⢻⣄⡇⠀⠑⠀⠀⠈⢰⣶⡶⢤⣀⠀⠀⢸⠇⡵⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠱⡀⠀⠀⠀⠀⣾⣧⣤⠠⠀⠀⠀⠀⣾⣿⠃⠀⠈⠛⠲⣾⢠⣧⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠑⠀⠀⠀⠜⠛⠛⠁⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠁⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⠞⢻⣭⠭⢽⡓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⡯⠭⣭⡟⠳⡄
⠀⠀⠀⠀⣿⠀⠻⠿⠁⣀⣈⠑⢄⠙⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠿⠋⡠⠊⣁⣀⠀⠿⠟⠀⣿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠻⠟⠁⠀⠑⣄⠈⠢⡑⢄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⡠⢊⠔⠁⣠⠊⠀⠈⠻⠟⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠹⡄⠀⣤⣤⠀⠀⠔⠋⠀⢱⣄⠈⢆⡑⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣠⢊⡴⠁⣠⡎⠁⠉⠢⡀⠀⣤⣤⠀⢀⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠛⠛⠀⡌⠀⣀⣠⠃⠈⠳⣜⠛⢌⠳⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠜⡡⠛⣣⠞⢁⠘⣄⣀⠀⢡⠀⠙⠛⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣤⡅⠘⠿⠟⠀⠋⠀⠈⢳⣄⠱⣝⢄⠀⠀⠱⡀⠀⠀⠀⠀⢀⠎⠀⠀⡠⣋⠎⢠⡞⠁⠀⠙⠀⠹⠿⠃⢈⣤⣦⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠙⠋⠁⢀⣤⣤⠀⠀⠀⡰⢅⣈⠳⣌⠁⢧⡀⠀⠱⠀⢀⡀⠀⠎⠀⢀⡼⠛⣩⠞⣁⡈⠆⠀⠀⠀⣠⣤⡀⠸⠙⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡘⡈⠛⠛⡀⠀⠀⡇⠀⠋⠙⠪⣑⠦⣙⢦⡀⣨⣿⣿⣅⢀⡴⣋⠴⣊⠔⠊⠙⠁⢸⠀⠀⢀⠛⠛⢃⢂⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⡀⠀⠡⣾⣿⠧⣀⣉⠉⣁⡲⣵⣬⣓⢿⣿⢻⡟⣿⡿⣞⣥⣮⣴⣊⡉⣉⣀⠸⣿⣷⡌⠀⢀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡈⠄⠀⢣⣠⠤⠷⢒⠒⡉⠩⣿⣭⣍⣛⣿⣿⣿⣿⣛⣩⣭⡿⠍⢉⠐⡒⠾⠤⣤⡜⠀⠠⢃⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠟⠋⠁⣀⣠⣤⣈⡑⠾⢦⠶⢾⣿⣻⣿⣿⣿⣿⣿⣿⡷⢶⡴⠷⠊⣁⣤⣄⣀⠈⠙⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠊⠍⣙⡽⢃⠠⢀⣶⢶⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡶⢦⡀⠄⡘⢯⣋⠩⠙⢦⡀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣺⢟⣪⠴⠛⠉⢀⣠⣶⣫⣽⠿⣻⡿⠃⣸⣿⣿⣇⠈⢿⣯⠻⣼⣝⡶⣄⡀⠉⠛⠦⣕⡻⣗⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⢉⠁⠀⠀⡀⠘⠋⢉⠔⠁⡼⢻⠁⣠⢿⣿⣿⡿⣆⠈⡛⢷⠈⠢⡉⠙⠓⢄⠀⠁⠈⡉⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠔⠁⠀⢀⢸⣿⠀⣐⠁⢠⠟⠄⡄⢠⠇⢸⣽⣯⡇⠸⡄⢡⠠⠻⡄⠈⣂⠀⣿⡇⠀⠀⠈⠢⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠁⢸⡏⣸⡿⠀⣟⡜⡐⢀⡎⠀⢸⢾⡷⡇⠀⠱⡀⢂⢳⣳⠀⢿⣧⢹⡇⠈⠄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠂⠀⠈⢰⡿⠁⠀⠟⡰⠁⡸⠀⠀⠘⣿⣿⠇⠀⠀⢧⠈⢆⠻⠀⠈⢿⡆⠁⠀⠘⣀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⠆⠀⠀⠀⡰⢁⣶⠇⠀⠀⠀⠛⠛⠀⠀⠀⠘⣶⡈⢆⠀⠀⠀⠐⠀⢀⡴⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⠴⡀⠀⣀⣠⡷⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢾⣄⣀⠀⢀⡦⠞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠙⠊⠉⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠉⠑⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠛⠛⢦⡀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠈⠛⢦⡀⣰⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢹⡿⠟⣻⣿⢿⣿⡟⢡⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣷⢿⡏⢘⢩⣧⣸⢿⣿⣿⡟⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢻⣿⣼⣷⣽⣯⣿⠏⠈⢿⣿⠇⠘⣿⣿⣿⣿⣶
⢠⣾⠶⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⢻⠀⢠⣿⣿⣿⣿⣿⣷⡀
⢸⣿⠀⣿⣿⣷⡀⠀⠉⠻⣿⣿⣿⡇⢸⣇⠀⣴⢸⣿⣿⣿⣿⣿⣿⣷⡀
⠈⠹⠀⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⠘⣿⣤⣿⢸⣿⢿⣿⠿⢿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠛⢿⣿⣿⣷⠀⠀⠈⣿⣿⣿⡀⣿⣿⣿⢸⣿⠦⣶⣶⣾⠿⠿⠛⢋⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠻⢿⣷⡀⠀⠘⢿⣿⡇⢹⣿⣿⡀⣿⠇⣶⣶⣿⣶⣿⡇⣿⣿⡟⣩⣆⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢈⣿⣇⣸⣿⣿⣿⣿⠁⣈⣙⣩⣿⣿⡇⣿⣿⡇⣈⣩⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⢿⣿⣿⣿⠀⢹⣿⠟⢛⣿⣿⣿⣿⣤⣼⣿⢱⣿⣿⣈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣿⡿⠀⢸⡟⠀⢸⡟⣀⠈⣿⠏⡙⠻⢿⣿⡟⠻⠿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢰⡆⢠⡄⢸⡗⣿⢠⡏⢸⣿⣿⡆⢻⡇⣶⣶⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣧⣼⡇⢸⡇⠃⣼⠃⣈⠙⣉⣰⣿⠁⣿⠟⣡⠟⢩⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣾⣿⣿⢇⣼⣇⣠⡿⢠⣿⣷⠘⣿⡟⢠⣄⣼⡇⢠⣿⡏⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠛⠿⣿⣿⣿⣿⣿⣿⠃⢈⣻⣯⡀⣿⡇⢸⣿⣿⠃⡛⠛⢠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠘⣿⣿⣿⡿⠿⣾⣿⣿⣿⣿⣿⢀⣼⣿⡏⣸⣿⣷⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣼⣿⡏⢠⣶⣤⠹⣿⣿⣿⠿⠛⣿⣿⣤⣿⣿⣿⣨⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣧⢻⣿⣿⣇⢿⡏⢀⣤⣄⠘⣿⠀⣴⣿⣿⠿⠋⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⡿⠀⠙⣿⡄⢿⣿⣿⠘⣿⡜⣿⣿⣾⣿⠀⣿⠋⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⣾⣿⠃⠀⠀⢹⣧⠈⢿⠋⢰⣿⣿⡈⢿⣿⣿⠀⣿⠀⢴⣿⣿⣿⣷⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⠀⣿⣿⠀⠀⠀⠀⢿⣷⣦⣀⡟⢿⣿⡇⢸⣿⡟⢠⣿⣦⡀⠙⢿⣿⣧⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣿⣿⣇⠸⠟⠃⣨⣿⠁⣸⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠈⠙⢿⣿⣦⣴⣿⣿⡏⠀⣿⡿⣿⣿⣿⣿⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠘⢿⡿⠟⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡄⠀⢀⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⠀⠀⠀⠻⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠑⠒⠄⢀⠐⢂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠨⢤⡠⠀⠀⠀⠀⠀⠀⠘⠂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠚⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠘⠛⠛⠶⠄⠀⠀⠀⠀⠀⠀⠱⠢⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⠀⠀⠄⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⡠⠴⢦⡀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⣤⠀⠠⠤⣦⢸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣰⠀⢸⣿⠀⠀⠐⠂
⠀⠀⠘⡢⠤⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠒⠂⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠴⠋⢸⠀⠀⣎
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⢤⠔⠚⠁⠀⠀⠀⠀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠔⠀⡲⠊
⠀⠀⠀⣗⣀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠊⠈⠳⣄
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⢄⠀⠑⠲⡤⠤⣤⠤⢠⠔⠖⠚⢙⣫⠀⠀⠀⠀⠀⠈⠳⣄
⠀⡞⠁⠱⣄⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⢀⠊⠀⠀⠀⣡⠀⠀⡖⠁⠀⠀⢞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⢀⠡⠤⣄⠚⢀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠑⠢⡀⠀⠙⣠⠎⢀⣠⠄⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢇⡀⢀⣈⠆⢸⡟⠃⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠈⢧
⢨⡉⠉⠙⡄⢸⡇⠀⡘⠉⢧⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢧
⠰⡉⠙⡏⠀⢸⡁⠎⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠸
⠀⠈⠉⡇⠀⢸⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠰⢄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠇⠀⢸⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⢀⣀⣀⡀⢇⡘⠦⡀⠀⠀⠀⢀⣀⣤⠔⠋⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢧⣀⡼⠀⠘⠋⠑⠦⣀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠄⢀⣀⣀⣀⣀⠈⢽⠀⠀⠙⢏⠉⠀⠀⠀⣂⠀⠀⠀⠀⢀⠜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠈⠄⠀⠀⠀⠨⡄⠀⣠⠔⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣀⠀⠀⠠⠋⠀⠀⠀⠀⠀⢰⠀⠀⣀⠠⠖⠈⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⣤⣤⣤⣤⠖⢀⠄⠀⠀⢠⠏⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠀⠀⠀⢀⡠⠂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠉⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠤⠤⠤⢤⠤⠄⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠢⠤⠤⢤⡤⠤⠤⠤⠤⠤⢤⡤⠄⠀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠄⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠸⠆⠀⢀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⣤⣤⠀⠀⠶⠖⠛⠋⠙⠥⠄⠤⠄⠖⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣤⣤⣤⣤⣚⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡌⣡⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠨⣽⣇⠀⣠⣴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠶⠦⣄⢀⠘⣄⠀⢰⣏⣿⠀⠀⠀⠀⠀⢟⣿⡀⠉⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠢⠤⣤⠤⠀⠀⠀⠀⠀⠀⢻⣦⣠⡾⢟⣁⡘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠉⣯⠀⣄⣤
⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡟⠃⠈⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⢻⡞⠑⣵⠒⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣘⣆⠀⠀⠀⠀⠀⠰⢻⠯⡄⠀⠀⢠⢪⣦⠞⠻⠛⠛⠋⢀⢰⡇⠠⠀⣄
⠀⠀⠀⠀⠀⠀⢸⣟⢛⣧⠀⢰⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⢇⠀⠀⠀⡠⠾⢽⣦⠤⡀⠠⠲⠋⠋⠀⠀⠀⠀⠀⠀⠈⠂⠞⢀⣣⣴
⠀⠀⠀⠀⠀⠀⢘⣓⣛⣷⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠈⠁⠀⠉⠀⡀⠄⠠⡤⠀⢀⣼⡿⢷⡿⣿⢿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⢘⣯⣶⣺⡁⠀⠀⠀⠀⠀⠀⡇⠠⠀⡰⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⣤⣤⡶⢿⠔⠀⠀⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡈⠙⢿⣿⠀⠀⠀⠀⠀⠈⠐⠂⠤⠞⠋⠉⠐⠀⠂⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠙⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠀⢀⠏⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠇⠮⠞⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡔⢓⡒⠛⠑⢀⠀⢠⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⠐⠐⠈⠳⣤⣒⡊⠀⠻⣇⠈⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⢤⡄⣶⢂⢶⢦⡀⠀⠁⠀⠰⢨⠀⠊⢾⠁⠀⠉⠳⢼⡜⣆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡯⢩⡉⣸⠑⡭⠀⡆⣠⢨⢰⡍⠂⠀⠀⠀⠈⢁⠀⠇⠀⢉⣭⠤⢄⢈⡴⠃⢚⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠤⠖⠛⠟⠒⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣋⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣭⣭⣿⣯⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠘⠃⠀⠤⠂⠀⢀⠀⢀⡀⠚⡀⠀⠁⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠠⡀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠀⠂⠀⠀⠀⠒⠀⠸⡀⠄⠁⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠀⠠⡆⠀⠀⡀⠊
⠀⠀⠀⠠⠄⠂⠀⠀⣂⠂⠀⠁⠁⢀⠤⠄⠀⠂⣀⠄⠀⠢⢄⠀⡴⡄⠀⠀⠀⠉⡉⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠨⠃⠀⠀⠂⠀⠒⠁⠀⠀⣂⠀⠀⠀⠀⠔⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⠬⠍⠉⢩⡯⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠁⢀⡄⢀⣂⢤⡄
⠀⠀⠀⠀⡼⠈⠀⠀⠀⠀⠀⠐⠀⠺⠥⠛⠉⠴⣖⡀
⠀⠀⠀⠀⠑⠀⡀⠂⠀⠀⠀⡆⠀⢰⣠⠾⡿⠿⠛⠋
⡆⠁⠀⠀⡮⠈⠀⠀⠀⠀⠰⠀⠀⠀⠁⠠⠔⠒⠒⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠄⣠⣤⣴⣶⣾⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢀⡀⠘⠞⠉⠈⠉⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠁⠈⠁⠒⠛⡛⣛⠉⠃⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣖⣀⣀⠀⣀⣠⣤⡔⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠛⠋⠉⠙⠛⠛⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⡶⠖⠠⠿⠿⢛⡋⠀⠼⠌⢆⢨⠓⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠁⠀⠀⠂⠊⣉⣡⠶⠀⢸⡔⠮⣱⢤⣧⠀⠷
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠁⢀⡀⣠⣄⠴⣿⡯⢕⣤⢄⢳⣉⠒⠉⠚⠙⣆⡐⠆
⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠻⠷⠏⢐⠟⢁⣴⣟⣶⡌⢯⣭⣛⢓⣀⢳⡈⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠔⠋⢠⡌⣼⢸⣹⣧⡈⢉⠻⣦⡀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⢸⡇⢹⠜⢷⡐⣍⣷⣑⠦⢅⠀⡀⠰⡮⠉⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠘⠫⠀⣿⠈⠳⠄⠘⢧⡈⠀⢠⡄⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⢤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣆⠶⣿⡿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣦⣹⠆⢋⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠲⣦⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣿⡏⠀⣰⣿⣯⠋
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡦⣄⡀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⢿⣮⡂⠀⡀⣿⣏⡇
⠀⠀⠀⢠⣤⣻⣿⡿⢆⣷⣿⣿⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣦⠝⠉⠛⠈⠘⢿⣷⢀⣴⣿⡗⡁
⠀⠀⢀⡦⣿⣿⣿⣀⠀⠀⠙⢿⣳⣼⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣉⣣⣤⣴⣶⣦⣔⣠⣤⡞⠉⢹⡿⠝⢄
⠀⠀⠀⠲⠙⡿⢻⡏⢴⣿⣿⠿⡻⠛⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠿⠿⠛⠛⠼⡻⠟⡿⡻⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠢⣄⢠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡈⢑⠀⠈⠀⠀⠀⣀⠀⢆⡀⠙⡿⠛⠁
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠨⠄⣶⣿⠁⠀⠰⣤⠺⠝⠋⠀⠀⠀⠀⢀⣤⣾⣯⢹
⠀⠸⣿⣏⢛⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⣴⣛⡯⢰⡯⣽
⠀⠀⠘⣿⣿⠩⠭⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣅⣿⣗⡏
⠀⠀⠀⠘⣷⠖⠂⣀⣀⣀⣀⣱⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣯⣷⣈⣷⠙⣧⣀
⠀⠀⠀⠀⣿⡛⠻⠋⠉⢉⣩⣿⢿⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡹⠿⠿⣿⣿⣧⡽⣳⠖⠛⠃
⠀⠀⠀⠀⠹⣧⣀⠘⢀⣾⡿⠃⢸⡇⠀⡈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣄⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠛⢻⡏⠠⠊⣸⡇⢀⢀⡤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡛⠂⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣘⣧⣼⣠⣧⣟⡻⣧⠀⠀⠀⠀⠀⠀⠀⠉⠩⠛⠛⢉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠛⠻⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⡻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣄⠀⠀⠀⠀⠀⣀⣀⠀⣠⠀⠀⠀⢀⣤⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⠀⠈⢉⡹⠿⠟⠀⠀⠀⠀⠘⠏⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡆⠀⠀⢴⣦⠀⠀⠀⣀⣰⠈⠀⠀⠀⢀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢊⠉⣀⣤⡄⠀⢀⡀⠀⠚⡛⠁⠀⠈⢻⣾⣧⠀⠀⠰⢻⠃⠀⠀⠀⠀⠀⣶⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣢⣤⣽⣿⣶⣿⣠⠱⣦⡆⠀⢿⣿⠀⠀⢿⡏⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣦⣾⣿⣿⣿⣿⣿⣷⣷⣎⡟⠻⢶⣿⣿⣶⡶⢠⡄⣠⠀⢿⠇⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠰⠳⢦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡛⣾⣏⡓⡸⣦⡍⢀⣀⡀⠀⠰⣄⣠⠀⠦⠾⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠀⠀⠰⢿⠇⠀⠉⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⢒⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠸⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡴⠀⠀⠀⠀⠘⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠞⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⠀⠈⣻⠿⣿⣿⣿⣿⣿⣿⡿⠿⣏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢸⡏⠉⠉⢹⣄⠀⢙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣼⣥⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣡⣏⣾⣥⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢋⠏⢁⡼⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠖⣦⠔⠉⡠⠞⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⠁⢰⣃⠔⠊⢀⣠⣾⠟⠁
⠀⠀⠐⣿⣿⣗⢶⣶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⢀⣴⣿⣟⣥⣴⣶⣤⣄
⠀⠀⠀⠈⠻⣦⣿⠧⣽⡿⠛⢿⣷⣦⣀⠢⠀⠀⠀⠀⠀⠀⢸⠀⡰⢀⣴⣿⡿⠛⣁⠤⠊⢉⡻⢿⣧
⠀⠀⠀⠀⠀⠈⠻⢿⣯⡉⠙⢻⣄⡉⠛⠻⢷⣤⣀⠀⢀⣀⣿⣠⣷⠿⡫⠾⠶⠭⠴⣂⣉⠠⠄⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⣀⠀⠭⠓⠒⠀⠤⠭⢿⣾⣿⣿⣯⣴⣫⡤⠤⠤⣤⡒⠉⠑⠢⢤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⣤⣴⣶⡿⠿⣋⠝⣿⣿⣿⣒⠤⢄⣀⠀⠈⠉⠒⢤⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⡻⢖⠉⠀⡌⢸⢻⢻⣖⠱⢦⣀⠉⠑⠒⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⠞⣄⣸⠀⠈⡆⢣⢿⣦⠀⠈⠉⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⠣⠱⡀⠡⠀⢿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⣦⣶⡾

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⠈⠡⠀⢷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣤⣦⣤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠢⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢏⡜⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠈⠙⡆⠈⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡼⣄⣀⡂⠀⠀⠀⣇⠀⠀⠠⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣡⠤⠶⠚⣟⠁⠀⠀⢠⠝⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠾⠵⠒⠶⣅⣀⢸⡆⡀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠁⠈⢣⡀⠀⢰⠀⠈⠉⠑⢢⡤⠂⠀⠀⠀⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⡤⠀⠀⢀⠀⡀⠈⠳⡀⠀⠀⢸⡆⠀⠀⢁⢀⠀⠀⠇⠀⠀⠀⡔⡠⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣠⠀⠀⠀⠀⣀⣀⡀⠐⠄⠀⠀⠙⠀⠐⢌⡴⢂⠀⠀⠀⠀⣐⣎⠋⠀⠉⠂⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠈⠢⠀⠀⠸⡄⠀⠐⠀⠀⠈⢢⠹⢦⣾⠠⠂⠀⠀⠠⠀⠐⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠁⢀⡊⠀⠀⡄⠤⠆⠀⣤⡀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠀⢠⡀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠠⠶⠂⠒⡻⢆⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠂⣷⡋⠂
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡇⠐⠚⠞⠁⠀⣈⣀⠤⠤⠬⢶⡀⠀⠀⠀⠀⣤⢤⡀⠀⠀⠀⠀⠆⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⣀⡤⠂⠉⠁⠀⡀⠠⠀⠐⠳⠆⣀⠀⠀⡇⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠈⢀⠄⡜⠱⠶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢄⡄⠤⣠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠖⠉⢶⠞⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠙⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⠦⣴⡟⠠⠄
⠀⠀⠀⠀⢀⠀⠂⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠆⠀⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⡈⣤⠀⣤⣄⡂⠀⠀⠀⠀⠀⢀⢤⠔⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢻⣿⡾⢿⡿⣿⣿⣿⣿⣿⡿⠁⠆⢸⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⡄⠀⢸⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣾⣁⡞⠁⣻⣿⡿⢡⡷⢀⡇⣿⣿⣿⡧⠀⠀⠀⠸⣿⣿⡇⠀⠀⢾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⢿⣇⣠⡇⣿⣿⡏⢀⣾⠃⢻⣿⣿⡇⡀⠀⠀⠀⣿⡿⠀⢰⠆⠺⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠘⢻⣷⠊⣿⡃⣼⣟⠀⠘⣿⣿⡇⢻⡀⠀⠀⣿⡇⠀⡈⠀⣤⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⢆⠀⠈⣿⢧⣿⣧⡿⠋⠀⣤⢻⣿⡇⢸⡃⠀⠀⡿⠀⠀⠀⢠⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡌⠰⠀⢾⣿⡙⠉⠀⠀⢈⡟⢸⣿⣷⠘⣇⠀⣾⡇⢰⡆⠀⢸⣿⣿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣇⣤⢳⣜⣿⣿⠶⠦⢀⣼⠳⠒⣿⣿⠀⠈⢄⣿⠃⢸⠁⠀⣿⣿⣿⡿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⢥⡙⠿⣿⣿⣿⣦⣀⣾⣿⣧⣼⡏⢻⡆⠀⠸⡟⠀⡿⠀⣸⡷⣾⣿⡗⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣇⠔⣯⡒⠠⠉⠛⢿⣿⢿⣿⢹⣿⡇⢸⣿⠀⠀⠀⠀⠁⢠⣿⡿⢿⣿⠁⢿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠹⣿⣿⠂⠘⣧⢀⠀⠐⠠⢸⣎⣷⣿⣿⡟⢸⣿⡆⠀⠀⠈⠀⣾⣯⡟⣾⢫⡎⢸
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢘⣿⡇⠀⠹⣷⡓⠀⣱⣼⣿⣿⣿⡏⠀⢸⣿⠀⠀⢠⠄⣸⡿⢶⢼⣿⡿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸⣿⣷⠀⠀⠈⢿⣦⡈⣿⣿⣿⡿⠀⠀⣾⣿⠀⠀⠀⢀⣿⡷⠾⢼⣿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⣸⡟⢷⣿⣿⣿⡇⠀⠀⣿⣿⠀⢀⠀⣼⣿⣴⠾⣿⡟⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠀⢐⣿⠇⣸⣿⣿⣿⡇⠀⢠⣿⣿⡀⠄⣰⣿⣿⠃⣸⣿⡻⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⢸⣿⢠⣿⠟⣿⣿⠃⠀⢸⣿⣿⡇⣰⠿⣿⣇⢀⡇⠈⣿⡄⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣀⣿⣧⣿⠃⠀⣿⣿⡄⠀⠸⠟⠏⣰⠏⢠⣿⣿⡾⢃⠀⡏⢹⣦⠈⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⣿⣿⣾⠇⠀⠀⣿⣿⡇⢀⣴⢊⣼⣿⡄⠀⣿⣿⣿⣼⡀⡁⢘⡏⢣⡀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⣿⣿⣷⣿⣱⣾⣿⣿⣷⡀⢹⣿⣿⣿⢿⣿⣬⣃⠸⡷⢤⠀⠀⣆
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠁⢀⢆⣼⡏⢹⡟⣸⣿⣷⣼⣿⣿⣷⡀⢿⣿⣿⣦⠙⣯⣻⣤⡿⢈⠿⡄⠘⠄
⠀⢀⣾⣿⣿⢿⣿⡿⠏⠙⣀⣿⣿⣿⡟⢠⣿⣾⠿⡇⣾⢃⣿⣿⣿⡇⢻⣿⣿⣷⡌⠻⣿⣿⣷⣦⡙⢿⣷⣿⡆⣃⡄⠂
⣴⣿⣿⡟⣱⣿⣿⡇⡀⠀⢻⣿⣿⣿⣷⡟⢻⠃⣼⣿⣿⢸⣿⢹⣿⡇⠀⢿⣿⣿⣿⣆⠈⠉⠻⡻⢿⣦⣽⣿⠘⣿⣧⣤
⣿⠋⡏⣴⣿⣿⠋⢻⣇⠀⢸⣷⣿⣿⡿⢀⣿⡄⣿⠻⣿⡆⣿⡄⣿⡃⠀⠈⣿⣿⣿⣿⣷⣄⠀⠈⠲⡈⠻⣿⡀⠆⢉⠉⠉
⡋⠀⣼⣿⣿⡇⠀⠀⠟⠀⣿⡿⣿⣿⡃⠘⠁⣴⣿⣷⣿⣷⣾⣷⣸⣧⣀⠀⠘⢿⣿⣿⣿⣿⣦⠀⡀⡉⢦⠙⢿⣿⠺⡏⠳⣄
⠁⣴⣿⣿⣿⠷⠄⠀⠀⢀⣿⠇⣿⣿⠋⠀⣰⡟⢸⡏⢹⣿⣿⣿⣿⡍⢷⡤⣤⣜⣿⣿⣿⣿⣿⢷⡌⡜⢤⢣⠈⢿⣇⠘⠃⠘⠫⠑
⣹⣿⣿⣿⣿⠀⠀⠁⠠⣎⠹⣇⢹⡿⠳⠞⢻⡇⢸⣇⢀⣿⣿⣿⣿⣧⡈⢷⣀⠈⠉⠻⣿⣿⣿⣿⡿⣼⣂⢧⠇⠘⣿⣿⣇⠀⠦⠙⣧⡆
⣿⣿⡿⠁⢻⡇⠀⠀⠀⠈⢦⣼⣿⡇⠀⠀⢸⣇⣾⣿⣾⠿⢹⣿⣿⣷⡀⢠⡹⣷⣄⠀⠙⣿⣿⣿⣿⣿⢫⡜⣴⠀⢻⡄⠉⠳⣦⠀⢈⣻⠆⡀
⣿⣿⠃⠀⠈⣷⠀⠀⠀⠀⡈⠻⣷⣿⡇⠀⠟⣿⣿⠛⣏⣰⣿⡿⢿⣿⣿⣄⣹⣿⣿⣶⣄⠙⣿⣿⣿⣿⡟⣤⠛⡄⢸⠉⣲⡤⠬⢷⡀⠉⠀⠉⠢⡀
⣿⡏⠀⠀⠀⢹⡆⠀⠀⠀⠃⠀⢿⣾⡁⢸⣷⡿⣃⣘⡿⠿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⠀⡇⠘⠋⠀⡈⠳⡄⢻⣦⣦⣀⣤⣤⢦⣀
⣿⠀⠀⠀⠀⠀⢷⠀⠀⢀⡀⠀⢸⣿⠁⣾⡿⢡⣿⠛⠀⠀⠀⣿⡎⠹⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⡇⠀⠀⢸⣦⣾⣿⣶⣼⣿⠀⠉⢤⠀⠉⢦⡘⠋⠂
⡇⠀⠀⠀⠀⠀⠘⣧⣴⣿⣿⣶⣿⣿⣾⣿⣷⣾⣿⠀⠀⠀⢰⣿⡦⣀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⢸⣿⡿⣿⣿⣿⣿⣿⣤⡀⠀⢰⡆⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⡿⠟⢋⣥⣾⡏⢩⣿⣿⠀⠀⠀⣾⢯⣛⣽⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⣿⡿⣷⣏⠻⣿⣿⣿⡉⠳⣄⣼⣇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡤⢀⣾⣿⣧⠙⣿⣿⣽⠀⠀⢀⣿⡶⢉⣬⣿⣿⡇⠀⠻⢿⣿⣧⣼⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⣧⡙⢿⣿⣿⣦⣙⣯⠀⢂
⠀⠀⠀⠀⠀⠀⢀⣼⡃⠈⢠⣾⣿⠿⣿⡴⣿⠇⣿⣄⣠⣿⣯⣿⣿⣿⣏⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⠀⢠⡘⢿⣿⣦⡙⢿⣿⣿⣿⣇⠀⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⣿⣿⣴⢿⣿⣿⣰⣿⣻⣿⣿⣿⠟⢻⣿⠏⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⣻⣿⠉⢿⠀⢸⣧⠀⠙⢿⣿⣦⡈⢿⣿⣿⣠⠉⠢⡀
⠲⣤⡀⠀⠀⢠⣿⣿⣧⣸⣿⣿⢻⡿⣯⣿⣿⣿⣿⣿⣿⡏⠀⣠⣾⠋⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⡏⠹⣿⡀⢸⠀⢠⢹⣧⠀⠀⠙⢿⣿⡌⣿⣿⣉⠓⡄⠈⠷
⠐⠺⠿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠈⢻⣯⣀⣿⣷⣾⣿⢻⡾⣠⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⣿⡿⣿⠀⡀⠀⠙⢷⣄⠀⠀⠉⢻⡼⣿⣿⣏⠳⣄⢀
⠟⣿⣿⠟⠉⠛⢿⣿⣿⡷⣿⣿⣿⣿⢏⡟⠀⢈⠻⣿⠛⣿⡿⠁⢸⣇⡿⠀⠀⠀⢸⣿⣿⣿⡿⠁⠸⣿⣷⠻⣧⡘⠈⠛⠳⢶⣤⣿⡷⣀⠀⠀⢷⣻⣿⣿⡀⠀⠉
⡜⢡⡏⠀⠀⠀⣾⡞⠟⢀⣿⣟⣸⡿⢦⡄⢀⠘⡆⢽⣤⣿⠁⠀⠀⣿⣇⠀⠀⠀⠞⣿⣿⣿⠇⠀⢀⢹⣿⠀⠛⣿⡄⠀⠀⠀⠈⢻⣆⠈⠙⢆⠘⣧⢿⣿⣧
⣠⡿⠀⠀⢀⡾⠟⡿⠀⣾⣿⣿⠇⡷⢸⠃⢺⠀⣷⣾⣿⠇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⣿⣷⠀⢹⣿⢶⣤⣀⣀⣀⣿⣄⠀⠀⠀⢿⡝⣿⣿⣷⣤
⠟⠀⢀⡴⣻⣷⣄⠃⣼⣿⣿⡌⢠⡘⣿⠀⣼⢰⣿⢹⣿⠀⠀⠀⠀⢹⣿⣆⣀⣠⣶⣿⣿⣯⡀⠀⠀⠀⣾⣿⡀⠸⣿⣧⡈⢻⣿⠿⠿⠟⠓⠆⢤⣤⣵⣌⠛⢿⣿
⠀⠀⠈⣴⠟⢿⣿⣾⣿⣿⣿⣄⣸⣅⡿⠀⣼⣾⣿⠘⣿⠀⠀⠀⠀⣼⣿⡏⠉⣹⣿⣿⡿⠉⣹⣷⣶⣷⣿⣿⣧⠐⣿⣿⣿⣤⡙⡄⠀⠀⠀⠀⠀⠈⠉⠋⠑⢦⡈
⠠⢀⣾⠏⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣧⣾⣿⢻⣿⣴⡿⠿⠶⠶⢿⣿⣿⣷⣾⣿⣿⡿⠿⣿⣿⢻⡏⠉⠉⣿⡏⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⠟⠁⠀⠀⠀⠘⣿⣿⣧⣼⣿⣿⣿⠛⣿⣧⠾⠟⠉⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⡟⠁⠀⠈⠻⣾⠇⠀⠀⣿⡷⣆⠈⢿⣿⣿⣿⣿⣮⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠿⣧⠞⠉⠁⠀⡆⠀⠀⠀⠀⠀⠀⢀⡇⡸⣿⡟⠀⠀⠀⠀⠀⢹⡆⠀⢀⣿⡇⠈⠳⡀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⠿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡐⠀⠀⠀⠀⠘⠛⠉⠙⠙⠛⠳⠻⠞⠿⠻⠛⠉⠋⠻⠉⠁
⠀⠀⠀⠀⠀⢀⣤⣴⣾⠟⠁⠀⠀⠀⠀⠹⢿⣶⣶⣤⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⣀⣰⣶⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣴⣶⣄⡀⠀⠀⠀⠀⠀⠘⣿⡿⣶⡆⠀⠀⠀⠙⠋⠛⠟⣯⡽⢟⣦⡀⠀⠀⠀⢀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣾⣾⣿⣿⣹⣷⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠘⠛⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢻⣧⠀⠀⠀⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠰⣿⣿⠿⠷⠟⠿⠛⠋⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣗⣿⡟⠀⠀⠀⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣴⣴⡄⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⢹⣵⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⡾⢽⣻⣦⠀⠀⠀⠀⠀⣀⣤⡾⣿⡍⣽⣼⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⢾⡇⠀⠀⠀⣶⣿⡿⠷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠛⠻⢾⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣾⣿⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡇⠛⠉⠀⠀⠀⠀⠈⠛⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⠀⢴⣾⣿⣿⠀⠘⠈⠙⠓⠀⠀⠒⠀⠀⠀⠐⠁⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⡿⠀⡀
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⠀⠀⠀⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠄⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾
⢀⠔⠈⠁⠈⠁⣀⠀⠀⠀⠀⢠⣖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢀⣾⣏
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤⠀⡴⠊⠉⠉⠐⢄⠀⠀⠀⠁⢄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣀⡀⢀⣤⣿⣿⣟⡡
⠁⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠦⣄⡠⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⡀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡻⣿⣿⣷
⠙⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠴⠊⠁⠀⠀⢀⣿⡟⠃⠀⠃⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢱⣄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠈⢆⠀⠉⠁⠀⢄⠵⠶⣦⠀⠀⠀⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⣾⠇⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⣀⢀⡀⠉⠉⢻⣿⣿⣧⢠⣿⣷⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⠁⠀⠠⡄
⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠃⠀⠁⠈
⠀⠐⢄⢿⡄⡀⠀⠀⠀⠀⠕⠀⠄⠀⠀⠀⠀⠀⠀⠒⢂⣩⡴⠋⡉⠀⠙⢷⡀⠈⠀⠀⠐⠒⠒⠄⠠⠄⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠙⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠅⡔⠁⠀⠋⠀⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣴⣶⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠖⠀⠀⠀⠀⠀⠀⠁⠰⣀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⠀⠀⠀⠈⠙⠙⠓⠚⠠⢄⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠉⠉⠒⠆⠒⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⢠⠀⢀⣴⣿
⠀⠀⠀⠀⠇⠑⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢺⣧⣠⣿⣿⣿⣿⠏
⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠸⠁⠀⠀⢀⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⣀⠀⠀⠀⠈⢻⣿⣷⣀⢠⠀⠀⣤⣿⣿⠋⢀⠀⠠⠠⠀⠠⠄⠀⡸⠉⠐⠙⠧⣐⠀⠤⠤
⠲⢀⠈⠁⠀⠁⠀⠀⠠⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠈⠻⣿⣿⠛⠃⢸⣿⣿⡡⠊⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠒⠒
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣶⣦⣉⡀⠃⢌⣿⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠐⠚⠉⠉⠉⠻⠛⠛⠛⢻⡿⢿⠁⣠⡆⢫⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠍⢉⣉⡸⠟⢛⠖⠀⣈⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢠⠠⡒⠐⣐⡇⢀⣀⡀⠀⠤⠤⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠱⣤⡀⢀⢐⣛⣏⣉⣈⡭⣼⣋⠁⠀⠀⠰⠿⠿⠷⠖⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⢠⣤⡤⠶⠶⠤⣄⠀⠈⠙⢪⠬⠬⠭⠝⢻⠀⠉⠁⠐⠒⠒⠒⡒⠒⢂⠪⠡⣠
⠀⠀⠀⠀⠀⠀⡟⠒⠤⠤⠤⠤⠬⠉⡉⠉⠡⠤⠤⠐⡊⣂⢀⣐⣉⡺⡐⠀⠀⠀⠀⠀⡨⡢⠋⢕⢕⠝⡼
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡠⢂⢄⢔⢔⠕⠕⠕⡍⣀⠒⢸⠀⠙⣖⡦⣤⣤⣴⣩⣬⡥⠷⣆⡳⡀
⠀⠀⠀⠀⠀⠀⠀⢅⡀⠀⠀⠀⠠⣊⢔⠕⡠⡡⢊⠪⢦⠗⣾⣉⠀⢀⠞⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⡉⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠷⢖⢦⠤⠥⢬⠬⣤⢕⣶⣝⢷⠒⠒⠒⠚⢸⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⡢⢸⠀⢽
⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠤⢄⣀⣀⣀⣀⣀⠀⠠⠌⠛⢳⣒⡂⠀⢸⠀⠀⣤⣀⠀⠀⠀⠡⠊⢊⣐⣊⠥⠞
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢄⠔⡠⠢⣪⠔⠃⢸⠤⠁⡆⢸⠀⠀⡧⡄⠉⣉⠉⣩⡉⡩⠁⣤⡀⡇
⠀⠀⠀⠀⠀⠀⡟⠒⠤⣀⣀⠀⠀⠀⠐⠠⠂⠊⠊⢉⣋⢸⠈⣀⠀⣺⠀⠀⡇⢠⡆⠯⡀⡃⠀⡇⠀⢯⠱⡇
⠀⠀⠀⠀⠀⠀⣧⡄⡆⢀⢤⠈⡉⠉⠁⠀⠀⠉⣩⠥⠐⢸⠀⠰⡎⣿⠀⠀⡯⢛⡬⢄⣉⡓⢂⣉⡠⠤⠒⡇
⠀⠀⠀⠀⠀⠀⡟⠫⠻⢸⠀⢸⠉⠁⡇⠸⡄⡇⠷⠀⠐⢸⠀⠈⡄⢻⠀⠀⡏⢱⡯⠧⢴⠒⡒⠀⠸⠭⠀⡇
⠀⠀⠀⠀⠀⠀⣩⣑⠢⢌⣋⣈⠲⠂⠃⠀⠈⠇⣓⡢⠄⢘⢀⣠⣦⢸⠀⠀⢃⣁⡪⠥⡐⢒⠒⠀⢐⠒⠀⣷
⠀⠀⠀⠀⠀⠀⡻⢝⠻⠖⠂⢨⣬⠭⠍⢹⠍⠭⡕⠂⠀⢸⣤⣥⢤⣦⠀⠀⠀⠑⠭⣒⣀⣀⢀⣀⡠⠴⠊⣭⣉⣁⣀
⠀⠀⠀⠀⠀⠀⣹⢶⣭⣑⠀⠐⠊⠉⠀⠸⠀⢹⢏⠀⠐⢸⠂⠀⠀⢨⠀⢀⠀⠀⠀⣠⣬⣬⡽⡢⠢⢀⠄⡟⠀⠀⠀⣐⠀⠒⣒⣒⣂
⠀⠀⠀⠀⠀⠀⡍⠒⢍⣂⠀⠚⠉⠈⠀⢘⠀⠨⠈⢁⠄⢸⠄⠀⠀⠀⠳⣌⠳⣤⣈⠛⣴⢦⣀⣻⣿⠻⣰⣓⣒⣒⣒⡒⠒⢒⠒
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠉⠙⠒⠒⠠⠴⠄⠠⠂⣁⡄⢸⠤⠤⠤⠀⠀⠈⠙⠢⠭⣍⣐⣑⣉⣭⣴⣚⣓⣒⣒⡒⠀⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠸⣜⢆⡀⠪⢐⢥⠪⢒⢅⣀⣉⣠⡷⢥⠮⠭⠭⠥⠄⠄⠀⡀⠀⠀⠈⠉⠉⠁⠀⠁⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠲⠤⣤⢆⣑⣨⡧⡚⠗⣡⠎⠈⠉⠉⠭⠅⠀⠐⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢮⣀⡈⣤⡔⠚⣒⠒⠂⠈⠥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠂⠨⠍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⣀⠀⠀⢀⡤⠴⠖⣚⠛⠋⠩⠍⣁⠐⠒⠠⢀⡀⠀⢀⠤⠤⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡀⣽⣎⡀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠈⠑⠢⢀⠀⠙⠠⢀⡀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⠔⠂⡠⠋⠀⡈⢳⡉⠓⠀⠄⡀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠉⠒⠠⢀⠉⠉⢄⡢⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠜⠀⠀⢀⠁⠀⠙⣦⣀⠀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠁⠒⠠⠄⠈⣀⣢⠼⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠌⠀⠀⡠⠃⠀⢠⠊⠀⠉⠫⢔⠂⠤⢀⣀⠀⠈⠁⠐⠒⣒⢒⣶⠶⢊⣉⡤⠐⡃
⠀⠀⠀⠀⠀⠰⠀⢀⠔⠁⢀⠄⠊⢀⣤⢌⣁⠀⠀⠀⢀⡤⠤⣀⠶⠤⣤⢈⣥⣠⣀⡤⠤⡄⠐⠊⠉⠈⠛⣣
⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⡒⠂⠈⠁⠀⠀⠀⠀⠀⠉⠙⡀⢒⡸⠶⠀⠌⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢰⠀⠀⠀⡀
⠀⠀⠀⠀⡸⠁⠀⢠⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢆⠀⠀⢄
⢀⡀⠤⠒⠁⠀⡠⠃⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠈⢄⠀⠈⠣⢄⡀
⠣⢀⣀⣀⠠⠒⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⠢⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠠⢁⣂⠖⠀⠠⢠⡐⠳⠆⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⢤⠡⠁⠉⠂⠄⡀⠀⠀⠁⠲⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡰⢲⠢⠁⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⡝⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠠⢑⠣⠃⡠⢄⠀⠀⠔⠒⣄⡠⢄⠀⠉⢉⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⢁⡦⠖⠈⠀⠘⠀⠀⢃⣁⠜⡇⠀⠑⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠤⠶⡤⠧⠄⠀⠀⠀⠀⠈⡁⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⠶⣵⠶⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⢤⡤⠤⠑⠤⠄⣀⠀⠘⠂⠉⠰⠂⠀⣀⣠⣤⠦⠤⢀⡠⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠒⠤⣀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⣍⠍⠓⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⡉⠒⠦⣄⡀⠀⠀⠀⠀⣜⠎⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⠤⢤⣄⢰⡇⠀⡖⠂⣽⠱⣦⢄⣘⠮⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⣿⠁⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⡮⢱⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠦⣤⣴⣞⣏⠀⠀⡆⠀⡞⠀⢸⠀⢸⠆⠀⠀⠀⠀⠀⣀⢁⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠉⠉⠉⠁⠈⡄⠈⠁⠀⠀⢸⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢆⠀⠀⠀⢀⠃⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠆⠀⠀⠀⠀⠀⠐⠃⠀⠸⠀⠀⠢⠤⠤⠤⠤⠤⠤⠄⠤⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⣤⡄⣬⢀⣤⣤⣤⢤⣤⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠨⠷⠾⠟⠯⠭⠴⠄⡿⠠⠶⠾⠟⠛⠲⠾⠅⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⡠⠄⠀⠀⠠⢄⡪⠳⢕⡠⠀⣀⣀⠀⢤⡲⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣶⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡓⠒⢲⣯⡄⠑⢮⠟⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣡⠚⠉⠛⡈⠃⠈⠇⢀⠀⢸⣙⠀⢸⡉⢦⡀
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⣄⡀⣀⣄⣀⣀⣰⡠⢤⣴⡞⠉⠻⣏⠀⠠⠐⡄⣤⣸⣤⡤⣾⣴⣀⣿⣍⡧⡽
⠀⠀⠀⣠⣄⣹⣷⣶⣆⡽⣾⣯⡀⢻⣏⣄⠈⢹⣿⣇⠀⢻⡟⠆⠆⢹⣖⣰⣲⠓⠆⠈⠙⢷⣇⣹⣿⢀⣳⣤⠤
⠀⠀⣀⣸⣎⢹⡇⡜⣯⠱⢸⡇⠠⢸⣿⠈⠆⣸⣿⣀⠃⢸⣇⣐⣦⣼⠛⠋⡁⠀⠀⣀⣠⠭⠿⠒⠋⠉⠁
⠀⠀⣿⣿⣿⣶⣧⣄⣽⣧⣼⢷⣦⣼⠿⣿⣷⡞⠻⣿⣷⣞⣙⣿⢿⠒⣂⡩⠴⠚⠋⠉
⣀⣀⣻⣿⣿⣏⣩⠩⠤⠬⠴⠾⢿⠓⠚⠻⠿⠛⣛⡿⣟⣉⣩⣟⠋⡉⣀
⠻⣯⣿⣿⣿⠶⠶⠶⠶⠒⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠒⠒⠀⠀⠁⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⠄⠀⠈⠙⠀⠉⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠴⠉⠑⡆⠀⣤⠀⠀⠠⠛⠉⢳⡄⠀⠀⠀⠀⠀⢸⣄⠀⡀⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣌⠑⠆⠠⠴⠃⠀⠈⢷⣄⡀⠀⠀⠈⡧⠀⠀⣾⣦⣴⣦⠈⠉⠈⢦⣀⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⡰⡁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢸⡏⡼⠏⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣠⡄⠰⠚⠲⢤⡀⠀⠀⠈⣴⠀⢀⡴⠋⠛⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢰⠃⠀⠀⡀⠀⠀⠙⠲⣄⠀⠘⠶⠉⠀⠀⢀⡟⠀⣰⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢄⡠⠂⠀⢸⡇⠀⡼⠀⠀⠀⠷⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣷⠀⠐⠛⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡽⢆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⢠⡀⣠⠇⠀⠀⢀⡄⠀⣤⠀⠀⠀⠀⣼⠃⠸⣿⣇⠀⠀⠀⢹⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠀⠀⠉⠁⠂⢀⣀⡞⠀⠙⠀⠀⠀⠀⠘⣷⡐⠢⠿⠿⣿⠖⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠈⠁⠁⠀⠀⢀⡀⠀⢠⣊⣀⣤⣬⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠹⡄⠈⠉⠋⠁⠀⠀⠀⠀⢠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⣿⢻⡆⠀⠈⠓⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡺⠈⣿⣤⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠳⡄⠀⢠⡷⠤⠀⠀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⢻⣆⠀⠀⠀⠀⠈⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠐⠒⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠒⠚⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⢋⣿⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⡴⢋⣴⠟⣡⡾⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⣿⣷⣟⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣀⡴⠋⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣤⣤⣤⣤⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡴⠋⢀⣴⠟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣌⠳⣴⠟⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢷⡿⢷⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣉⡉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⣭⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡟⢹⡇⠀⠀⠀⠀⠀⠀⣿⢘⣛⣃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣿⢨⣭⡉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣤⣤⣤⣾⠃⠀⠀⠀⠀⣾⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⠰⠶⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢿⡀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠐⠒⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⡀⢸⡇⠀⠀⣴⠟⠀⠀⠙⢷⡀⠀⠀⠀⠀⣿⠈⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⡿⣰⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠉⠉⠉⠉⢹⡇⢸⡇⠀⠀⣿⠀⠀⣶⠶⢾⡇⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⣿⡀⡀
⠀⠀⠀⠀⠀⢀⣤⡀⠈⠁⠀⠻⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⣷⠀⢸⡇⠀⠀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⣾⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠻⠦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⡟⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣄⣀⣀⣀⣸⡇⢸⡇⠀⠀⣿⠀⠀⠷⠶⢾⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣉⣉⣩⣍⣉⣤⡿⠀⠀⠀⠻⣤⣀⣀⣠⡾⠃⠀⠀⠀⠀⣿⣛⣛⣛⣛⣛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⣾⣿⣯⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣏⣿⣷⡆
⠀⠀⢿⣿⣿⣿⣿⢿⣿⡏⣿⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣲⣿⡯⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠈⢿⣟⣿⣿⣛⣻⣷⣿⣿⣿⣿⣗⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣴⣾⣿⣭⠿⣿⣿⣏⣻⣿⣻⣿⡟⠁
⠀⠀⠀⠀⠻⣿⣏⣿⣟⠉⠙⠛⢿⣟⠛⠛⢿⣦⣄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠊⣠⣾⡿⠿⢿⣿⠟⠛⠙⢛⣿⣿⣻⣿⠏
⠀⠀⠀⠀⠀⢹⣿⣷⡿⠓⠛⠛⠛⠿⠷⣤⣀⠉⠻⣷⣌⠀⠄⠀⢀⡤⠊⣠⣾⠟⢉⣢⣶⠿⠟⠛⠻⠛⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣷⡦⠶⠶⠶⠶⠶⠛⠛⠓⢶⣮⣻⣦⣈⣷⣇⢠⢾⣿⣵⠿⠛⠛⠛⠳⠶⠶⠶⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⣀⣠⣤⣠⣀⣀⣀⣤⣤⣮⣿⣿⣿⣿⣿⣯⣾⣯⣥⣤⣤⣤⣤⣤⣤⣀⣐⣂⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⣿⠛⠛⠿⠿⢿⣿⣭⠽⢿⣿⣿⣿⣿⣷⠿⠯⣽⣿⣿⡿⠿⠿⠿⢿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣡⡤⠶⠒⢛⣿⠋⠀⢠⡿⣻⣿⣿⣿⣟⣷⡀⠀⠙⢿⡶⠶⣤⣄⣈⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⢁⣠⠴⢟⠟⠁⣀⣴⠏⢠⢯⠿⣿⡿⡟⣎⠙⢦⣄⠈⠙⣶⢦⣌⠩⣛⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢙⣽⣿⡖⡋⢀⡴⢿⡶⠟⣿⠁⣰⠏⠸⠈⣿⡗⢼⡘⣎⢎⢿⣿⢶⣿⢦⣌⠛⠶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣴⠋⢠⡟⠀⣼⠋⣰⡏⢀⡇⠀⣿⡇⠘⣇⠹⣎⢎⢿⣤⢻⡄⡝⢷⣱⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣴⣰⣯⣼⣿⣧⡿⠀⠀⢿⡇⠀⠹⡀⣿⡼⡎⣷⣃⣿⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣭⣀⣀⣸⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢋⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠇⠀⠀⠀⠀⠀⠀⣼⡏⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⡁⣷⠀⠀⠀⠀⢀⣠⣤⣼⣿⢤⣤⣀⡀⠀⠀⠀⣿⠳⣜⠦⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠟⢠⣿⡄⣠⡴⠞⠋⠉⠀⠀⠀⠘⠃⠈⠉⠓⢦⣀⡇⣀⣬⡷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣯⣤⣻⡇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢲⡄⠀⠹⠿⣏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡙⠇⣿⠀⠀⠀⠘⢷⣀⣠⠾⣧
⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⢸⡟⠛⠾⠋
⠀⠀⠀⠀⠀⠀⢀⡈⣷⣤⣀⢰⣷⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣿⢸⠀⣉⣭⣿⠗⠀⢀⡾⢋⣠⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⠤⠴⣶⡟⢻
⠀⠀⠀⠀⠀⠀⠹⣧⡾⠛⠉⠀⠘⢧⡀⠸⣧⣈⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⢶⣀⣟⡶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠈⢿⣇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⡶⠋⣷⣤⡀⠀⠀⢰⣦⡴⠚⠁⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣄⣀⣿⠈⠉⠉⠉⢹⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡴⠭⠙⢻⡆⠀⠀⠀⢸⣗⣠⠿⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⢸⣯⣵⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠒⣷⠀⠀⠀⢰⣿⡄⠀⠀⢠⣏⢳⣄⠘⠀⠀⠀⠀⠀⢀⣀⣴⠋⡄⠀⢰⠀⠀⠀⢿⣇⠉⢀⣤
⠀⠀⠀⢀⡀⡠⠗⠀⠀⠀⢭⠀⢹⠀⠀⠀⢸⣏⡧⠀⠀⠈⢻⣿⣯⠈⠀⠀⡀⢤⠘⢋⡘⢃⢹⡇⠀⢸⠀⠀⠀⣈⡿⠆⠀⢧⠖⣆⠀⣀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢩⢕⣸⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢻⣆⢠⠀⠠⡛⢎⠀⢯⣀⠘⡄⠇⠀⢸⠀⠀⢀⣿⠄⠀⢀⣶⠞⠛⠛⠃⢰⠃⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣒⠾⠀⠀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠙⢺⠀⠀⠀⠉⠀⠘⠁⠆⠀⠀⠀⢸⠀⠀⠉⠙⠚⠂⠈⠀⣀⠀⣠⣤⣤⣬⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⡶⠏⠀⠉


⣶⡶⠶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣤⣤⣤⢤⢀⣀
⠀⣿⣿⣻⣿⣶⣌⣙⣲⣤⣀
⠀⠙⣿⡟⢿⣿⡿⠿⣟⣿⣿⣷⣶⣄⡀
⠀⠀⢙⣿⣿⠿⣗⣀⣻⡏⠉⢉⣿⣿⣷⣄⢀⠀⠀⠀⠉⠂
⠀⠀⠀⢹⣿⣛⣿⡤⠜⠧⡀⢿⣿⠋⠉⣯⣳⣀
⠀⠀⠀⠈⢻⣟⣻⣷⡊⠈⣉⣒⣤⡀⢾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠨⣫⣭⣽⣯⣀⠀⣀⣹⣿⣷⣮⢅⡀⢻⣷⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠘⣷⠶⢾⡤⠀⠀⠠⠿⠿⢷⣄⣉⣳⣿⣧⣠⡞⣿⡿⠂⠀⠀⢀⣀⣠⣤⣤⣤⣀⣴⡴⠤⠤⢀⣀
⠀⠀⠀⠀⣠⡿⢻⣋⣉⣽⠖⠒⠉⠉⠉⠁⠐⠚⣭⣿⣿⣿⣿⣿⣷⣶⣟⡛⠋⠛⠉⣹⣿⡟⠓⣾⣯⠭⣝⡛⠶⣬⣻⡦⣤⡀
⠀⠀⠀⠀⢺⡿⢻⣧⠀⢇⠀⠀⠀⠀⣀⡴⠒⠉⢉⣽⡿⢽⣿⣿⡛⠿⣍⠉⠛⢀⣶⣿⣟⡁⢰⣿⠃⠀⢈⣿⡙⢻⡿⣿⣭⣿⠦
⠀⠀⠀⠀⣿⡟⣛⣿⡔⠉⡙⠓⢒⡿⠃⠀⢀⡔⣡⣟⣿⡿⠛⢡⡀⠀⠠⡙⠲⣾⣿⣿⠛⠟⠙⠗⠒⢶⡛⢤⣽⠿⣟⠻⣯⣹⡷
⠀⠀⠀⠰⣿⣟⣫⣿⣷⣾⣇⣠⣏⡀⢀⣴⠟⣰⣿⣿⠟⣰⠁⠀⣇⠀⠀⠘⣷⢌⣻⣧⣵⣄⢀⣤⣴⣶⡿⣿⣻⣧⡽⠗⠛⠃
⠀⠀⠀⠀⣼⠿⠛⣍⣿⡿⣻⣿⣿⣿⣺⡎⢰⣿⡿⠋⡼⠃⠀⢀⡟⣦⡀⢀⡜⢦⣹⣾⡿⠿⣿⢽⣷⠾⡿⠛⠛
⠀⠀⠀⣸⡡⠀⠀⠫⠋⠙⣿⠈⠉⢭⠎⠀⠈⠁⠀⣼⣟⢷⡄⢸⠀⣘⠈⡀⣧⣼⢻⣿⠇
⠀⠀⡼⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡏⠘⣋⣾⣷⣾⣀⣿⣶⡿⢷⣙⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢻⣿⣿⣏⣿⢸⣯⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⣧⣿⣿⣿⣿⡿⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⣀⠠⠤⠤⠤⠖⣉⡀⠀⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⡁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠓⢄⠀⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⢢⡴⠂⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢷⣄⠀⢸⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠆
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⡇⠈⠉⠁⠈⡆⠑⠢⢤⠠⠤⣄⣀⣀⣠⠤⠄⢤⠤⠃
⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⡄⠀⠀⠀⢀⣘⠤⢼⣤
⠀⠀⠀⠀⠀⠀⠘⣇⡄⠀⣰⢀⢰⠀⣀⡀⠀⠀⣇⣤⡖⠒⠈⠙⢲⢺⡁⠀⡄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠉⠀⠲⡤⡎⠓⠜⠁⠈⢧⡀⠈⣀⢏⠀⠙⠦⠤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠈⠉⠀⠀⠙⢁⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣕⡒⢶⢤⠤⡤⠴⡒⡍⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠙⠣⣤⡓⠐⣇⢧⠀⢸⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠈⠑⡤⠛⠚⠓⠁⠚⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠳⢄⡀⠀⠀⠀⠀⠀⢰⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡏⠒⠲⠤⠤⠰⡾⠋⠀⠀⠑⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⢸⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⠀⠀⠀⠀⢀⠆⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠈⢷⠤⠴⢚⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠸⢄⣀⡀⣀⣀⣰⣀⡠⠤⢤⠒⠊⠉⠀⠀⡖⠒⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⡀⠀⠀⠀⠀⡠⠚⠫⡀⠀⠄⣬⣀⢀⣼⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⡠⠊⠘⢠⣀⡈⢒⡺⠄⣀⠠⠾⣦⡀⠀⠀⢀⠇⠀⠸⢀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⡆⠀⡅⠀⠀⠀⢇⠈⢉⡷⠀⠈⠂⠐⠁⠙⡄⠐⠁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⡀⢣⠀⠀⠀⠀⠉⠉⠀⡇⠀⠀⠀⢀⡰⠁⢡⠀⠀⠀⠀⠀⡘⠀⠃
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠐⠁⠈⠢⢄⡀⠀⠀⢀⡠⠋⠁⠒⠈⠁⠀⠀⠀⠑⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠱⠄⠈⢁⣀⣵⡙⠳⡿⠄⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⢀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢕⣤⠀⠀⣠⠊
⢀⣴⣕⠄⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠉⠀⠛⠀⢀⡀⠀⠀⠀⡔⢠⠀⠀⠀⠘⠁⠀⠜⠁⠸⣆
⣝⠂⠙⢀⣴⠄⠓⠀⠀⠀⣠⠰⠲⠲⠆⠁⠀⠀⠴⠀⠒⠠⠀⠀⠈⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠠⠀⠀⠈
⡙⠂⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡚⠶⠄⠀⠀⢀⠥⠒⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠘⠉⠁⢢⠀⠀⠀⠈⠀⠀⢸⠒⠒⢀⡀⠀⠀⠀⠁⠀⠔⠀⠀⠀⡠⠚⠁
⠀⠀⢠⠀⠤⠰⠇⠀⠀⠀⢰⠃⠚⠁⠠⡄⠀⠀⢁⠇⠰⠀⠀⠀⢰⠤⠐⣀⠸⠂⠒⢀⠰⡄⠀⢀⡀⠀⠀⠀⠠
⡰⠈⠙⠂⠀⠈⡱⠔⠶⠤⠌⢠⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠸⡀⠀⠉⣠
⠳⠦⠀⠀⠀⠀⣁⠀⡤⠬⠗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⠄⠀⠠⠅⠀⠠⠒
⣦⠀⠀⠀⢰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢈⠂⠀⠀⠉⠉
⠀⠈⡁⠀⠘⠠⠂⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⡤⠤⠄
⣤⡦⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣴⡶⠖⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣼⡷⠖⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⢴⡶⠟⣋⠄⠀⠀⣠⠔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠢⣌⠙⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠈⠰⢧⡤⢣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣋⠝⢃⠂⡀⠀⣀⣀⢴⡠⠀⠠
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠤⠤⠀⠁⠀⠈⣴⢤⡀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⡠⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠱⡛⠣⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣉⣤⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠊⠁
⠀⠀⠀⠀⢀⠈⠉⠀⣬⠧⠀⠀⢤⡄⠀⠀⣠⡄⠀⢀⡀⠀⡀⠀⢤⡄⡄
⠀⠀⠀⠀⠀⠀⠔⠂⠉⢷⡀⠢⠾⠷⠫⠞⠿⠅⣤⢛⠉⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣄⣠⠴⠈⡈⠀⠄⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⡿⠿⠶⣄⡀⢀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡷⠀⠰⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⢹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢦⣄⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⠛⢯⣏⡁⠉⣹⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣦⣙⣿⡿⢼⣿⣠⣽⣌⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣮⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣼⣿⣿⣿⣿⡛⡟⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⡟⠉⠉⠙⠻⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣆⠈⠻⣿⣷⣈⠛⢦⣄⡀⢈⣿⣿⣿⣿⣧⡀
⠀⢀⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⠈⠻⣍⡳⢤⣈⠙⣿⣿⣿⣿⣿⣿⣷
⠀⢸⣿⠁⠙⢺⠟⠛⠛⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠁⠀⠙⠀⠀⠀⠈⠙⠶⣝⠷⣾⣿⣿⣿⣿⣿⣿⡇
⠀⢸⡏⠀⠀⣿⠀⠀⠀⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠸⣇⠀⢀⢀⡀⡆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠟⠋
⠀⠸⣧⣀⣀⣯⣀⣀⣠⣧⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣿⣶⣿⣿⣿⣷
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠛⠛⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⠀⢀⠀⠠⡀
⠀⠀⢀⠤⠤⡀⠀⠀⠰⢄⣀⡸⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⢄⠠⠃⠀⠈⢆⠀⠀⠁⠀⣡
⠀⠀⠑⢤⠖⠁⠀⠀⠀⢰⠁⠀⠀⠤⠀⠐⠂⠁⠀⠀⠀⠀⠀⠠⡀⠢⠀⠀⡀⠐⡄⠐⡀⢄⣈⠀⠈⢆⠀⠀⡀⠀⡆⠀⠀⠀⠇
⠀⠀⠀⠘⡄⠀⠀⢀⠠⠘⣇⠀⠀⠀⠠⡀⠀⠀⠀⠀⠐⠄⠠⡀⠈⢢⠈⢢⠀⣄⡀⠀⠀⠀⠀⢀⠀⠘⠀⠉⠀⠀⠇⠀⣀⢤⡇
⠀⠀⠀⠀⠹⡄⠂⠁⠀⠀⠘⠆⠀⠀⠀⠀⠳⡐⢄⠀⠀⠈⢂⠐⢄⡠⠀⠀⢃⠀⠀⠀⠀⠆⠈⠈⠀⠀⠂⠀⠀⢠⠤⠴⠶⠚⠁
⠀⠀⠀⡠⠊⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠃⠀⡆⠀⢂⠀⠀⠀⠀⠘⡀⠉⠁⠀⠠⠀⠀⠀⠈⠀⡴⠊⣻
⠀⠀⡐⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⠒⠃⠀⠈⡄⠐⠒⠁⠀⡇⠀⠀⠀⠀⠀⢀⣠⠖⠛⠓⠚⠁
⠀⢠⠁⠀⠀⠀⠰⠆⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⢀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣁⡼
⠀⢸⡀⠀⠀⠀⢄⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡏
⠀⠀⢧⠀⠀⠀⠀⣧⣀⡠⢾⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⡤⢤⡔⠉⠉⠉
⠀⠀⠈⠳⣀⠀⠐⠃⠐⠂⠈⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠒⡾⠀⠈⠑⠋
⠀⠀⠀⠀⠈⠑⠲⠤⠤⣤⣤⣤⣤⡤⠤⠴⠒⠒⠚⠉⠉⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡀⠀⠀⠀⠀⠀⣀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠈⠀⠰⠀⢅⡠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢃⣤⢁⢀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠘⠓⠉⠁⡈⢀⠃⣀⠶⠚⠃⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡈⠕⠊
⠀⠀⠀⠀⠐⠀⠀⡀⠄⠢⠌⠉⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⣠⠄⠒⠁
⠀⠀⠀⠀⠄⡰⠊⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠢⡔⠀⠠
⠀⠀⠀⠀⠌⠀⠠⡀⠀⠀⠀⣄⣀⣀⡜⣂⠀⠀⠀⠂⠐⠄⠀⠀⡀⠀⠀⠠
⠀⠀⠀⡌⠀⡄⠀⠀⠀⠀⠀⢻⠀⣮⢧⣉⡠⠀⠀⠂⠀⠘⡬⡄⠠⠀⡀
⠀⠀⢀⣲⠀⠓⠒⠈⠀⠀⠀⠈⠳⠤⢎⡤⢀⣀⣀⠐⠀⠁⠃
⠀⠀⠀⡄⠀⠀⡀⡀⠀⢀⠀⠀⡠⠂⠚⢀⡄⠂⠉⠀⠠⠘⡇⠀⢀
⠀⠀⠀⢱⡀⠀⠐⠄⡀⢀⠀⠀⠗⢠⡜⠁⢀⠤⠒⠀⠀⡰⠁⠀⠈
⠀⠀⠀⠀⠑⡹⠂⠀⠀⠈⠀⠀⠀⠃⡠⠊⣡⠄⠀⠀⡰⠁⠀⠀⠁
⠀⠀⠀⢀⡀⠉⠢⣀⠀⠀⠀⠘⡥⠊⠀⠈⠀⢀⡠⠊⠁⠀⠆
⠀⠀⠀⠀⠈⠒⠀⠈⠉⠓⠤⠤⠤⠤⠤⠴⠊⠁⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡀⠀⠀⢀⡀
⣿⣿⡿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⠒⣂⠠⡀⠀⠉⠂⠰⠁⠀⠀⢀⠀⢊⠠⠀⢀⠄⠳⢄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢏⠀⠀⠂⣈⢾⣆⠐⠀⠀⢧⠀⠀⡀⠀⡀⠐⠰⠀⠠⣔⢀⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠋⠀⠀⠜⠲⢔⣄⠀⢤⣾⣖⣀⣤⡾⠋⠹⣄⠀⠈⠙⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⡲⠄⢸⠀⠀⠈⠙⠻⣬⠠⠼⡧⠋⠀⠀⢸⣇⠱⣶⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⡀⠓⣦⣤⣤⢄⣸⠀⢸⣟⣥⣤⣤⣪⣷⣞⡐⠁⠀⠐⡂⠀⠉⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠫⠁⠃⠀⠉⠙⠙⣆⣽⣿⠛⠉⠁⠄⠘⡕⠨⠀⠀⠀⠁⠡⢀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⡂⠀⠀⠀⡀⠛⢣⢳⢩⢆⠐⠀⠂⠘⡆⠰⠀⠀⠀⠈⠀⠀⠑⢄⢀⠅⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢧⢤⡤⢀⠠⠁⠸⡼⠀⠣⢑⢄⣐⡊⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡅⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢎⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⢻⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠁⠀⠀⠀⠘⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠈⠀⠀⠀⠀⠀⡭⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢆⠠⠘⠀⢈⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠑⢂⠀⡆⢰⠀⡄⢠⠆⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡁⠀⠀⠂⠀⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠌⢂⣰⡶⠗⠓⠺⣷⣡⠤⠢⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠠⠀⠀⡈⣠⠠⠀⠀⢢⢠⠉⠁⠀⠀⠀⠘⠶⠤⠒⢣⠐⠀⢀⡔⠈⢉⡎⠃⠀⠀⠀⠀⠘⡉⠀⠀⠐⠀⡃⡀⡀⣰⢯⠀⠀⠀⠀⡅
⠀⠀⠀⢈⣄⢀⠀⠄⢈⡀⠀⣣⣰⣮⠉⠁⠀⠀⠀⠀⠀⢹⡿⠒⣀⡠⢹⠥⢸⡶⢫⡧⠀⠀⠄⠀⠂⠁⡀⠄⠀⠀⠀⠢⠤⣉⠃⣸⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠉⢔⣷⠬⣬⠖⣻⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⣿⣟⣀⢴⠾⠋⠉⠁⠀⠀⠀⠒⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠈⠁⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠐⠈⠉⠉⠑⠢⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠙⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠀⠀⠤⠄⠀⠀⡄⠀⠀⠀⠑⠖⠖⢀⣀⠄⠀⠀⢀⣄⣀⠄⠀⠀⠈⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠒⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⢀⡉⢣⠀⠀⠀⠀⠐⠦⠤⠄⢀⣀⡀⠀⠢⠤⠔⠊⠒⠃⠀⣠⢀⠄⠀⠀⢠⠀⠀⠀⠈⢢
⠀⠀⠀⠰⠊⠁⠀⢀⠀⠀⣈⣧⣀⠉⡉⠀⠙⠓⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡜⣠⠀⠀⠀⠀⠁⢳
⠀⢀⡤⠂⠀⠐⠊⠹⣄⡀⢀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⢀⡜⠀⠀⡀⠈⠹⠄⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠀⡴⠀⠀⠈⠀⢤
⠀⠊⠀⠀⠒⣆⠀⠀⣀⡍⠀⠀⠀⠑⢪⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠠⣄⡀⠐⠆⠀⠒⠁⠒⠒⠋⠀⢀⠦⠔⠄⠈⠇
⡀⠀⠀⠀⢤⡈⠁⠀⠰⡁⠀⠸⣄⠀⡀⠑⠂⢄⠀⠰⣄⡀⠄⠀⠀⣀⠀⠀⠣⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⣰⠤⠂⠈⠋⠁⢀⠄⠀⠀⡀
⢇⠱⠄⠀⠀⣉⠁⣠⠀⠉⠀⠀⢀⠉⡀⠀⠀⠀⠉⠁⠀⢀⠀⣉⡉⢀⣀⡠⢄⣈⠉⣉⣁⡀⠠⣄⣠⡄⠀⠀⢤⡀⠀⠀⠈⠉⠁⠠⠖⢊⡁
⠈⠢⠀⡄⣄⠈⠀⠻⠀⠀⠙⠤⠈⠉⣁⡜⠐⠋⠈⡐⠊⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⣀⣜⠃⠀⠀⠀⠠⠴⠒⠊⠀⠄⠈⡄⠊
⠀⠀⠀⠈⠢⡁⠀⠤⡀⠄⠐⠂⠀⠀⠀⠈⠋⠉⠉⠀⣿⠀⠀⠀⢰⠀⡇⠰⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠉⠒⠂⠐⠤⡍⠉⢀⣐⡊⡐⠒⠀⠀⠖⡿⠀⠀⠀⢸⠀⢇⡇⠀⡈⠠⢸⠃⠒⠓⠒⠂⠀⠀⠉⡈⣁⣀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠑⠄⠀⢺⡀⢈⠸⠈⡇⠸⠀⢃⠇⡆⡿⠖⠤⠒⠐⠊⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡆⡀⡇⡄⠠⣸⢰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⡇⠁⠀⡇⡏⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡼⢇⡠⠴⢧⣇⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠌⠉⠁⠀⠀⠀⠀⠀⠁⠘⠋⠳⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢠⣴⠦⣴⠠⢤⣤⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠲⠄⠠⣿⡇⣿⠀⢸⠀⢸⢣⠔⠢⠤⠆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡿⠀⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⡇⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢳⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠴⢦⠀⠀⢈⠤⢤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠣⠀⠀⠀⠀⠋⠑⡀⠀⠀⠉⠀⠀⠁⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠀⠀⠔⢢⡤⡈⠂⢀⡀⢩⠤⠒⢤⢤⡀⠙⠀⠐⠳⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠀⠠⠄⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠑⠲⠀⠈⠓⠀⠈⠈⠋⠂
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢠⠀⢠⠤⡀⠀⠀⢈⠀⠉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢄⠀⢸⠀⠀⠸⠀⠀⠀⠸⠀⠎⠀⠐⢢⠀⠀⡔⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣢⠘⠖⠂⠉⠉⠉⠁⠃⠘⠒⠰⢥⡁⢀⠔⠁⣀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢢⠀⡠⠖⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠢⠈⠁⠰⡉⢀⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⡀⠛⠀⡀⢀⠈⠀⢱⠀⠀⠀⠀⠀⠀⡨⠢⣤⠄⠀⠀⠀⠈⠱⡨⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⡔⠁⠁⠀⠀⠈⠂⠴⠋⠑⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣈⡠⠄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠡⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠊⠉⠑⣏⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠅⠄⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡰⠒⡄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⡌⠀⠠⠒⠢⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠘⢃⣉⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠀⢓⠀⢠⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠒⠐⠊⠉⡄⠈⡇⢀⡀
⠀⠀⠀⠀⠀⡏⠁⠒⢂⣁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡆⠀⠀⠆⠀⠀⠐⠒⠦⣠⠃⢰⠃⠀⠍
⠀⠀⠀⠀⠀⠑⡠⠂⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⢐⠈⠑⡄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠂⠀⠀⡼⠉⠑⢦⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣤⠀⠀⠀⠀⠉⠲⠁⠀⠀⠀⠀⠀⠀⠀⢰⠔⠛⠀⠀⠀⠀⢀⠼⡣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠒⢄⠀⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠔⠀⠀⢶⠃⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠄⠀⡠⡱⠢⢄⢀⡀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⡤⠚⠑⡈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⢀⠆⢨⠉⠒⠒⣶⠒⠒⠒⠆⠹⡉⠀⡨⠂⠀⢐⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⡣⠀⠠⠠⠆⠀⠸⡀⣀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⣄⣤⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡋⠀⠀⣀⡀⠀⢀⣀⡀⡀⠀⠀⠀⠀⣧⣿⣿⣿⡟⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⣠⠞⣻⣿⢿⣿⢠⠶⠴⠋⠀⠀⠀⠀⠘⣿⡿⢿⠥⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠁⠀⠀⠀⠳⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠸⡇⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⠀⠀⠀⠠⣵⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢣⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡄⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣾⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣤⡿⡇⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⠀⠀⡎⠀⠁⢘⠀⠀⠀⠡⠀⠔⠁⡤⢄⠀⠀⡔⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⠀⠱⡀⢣⠤⠞⠚⠒⠒⠲⠃⠸⠤⢤⣣⠊⠀⡰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀⠉⣪⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢌⠑⠊⣠⠚⠉⡡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠱⠞⠁⠀⠠⠂⠐⠄⠀⠀⠀⠀⠀⠀⢰⢄⢀⠸⠀⠀⠈⠑⢮⢐⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢉⡝⠀⠀⠉⠀⠡⠀⡠⠛⠄⠀⠀⠀⠀⠀⠁⠠⠋⠀⠀⠀⠀⢀⡈⠁⠈⢣
⠴⠂⣀⣀⠀⡀⠀⠀⠀⠠⠂⠼⣐⡎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠄⠤⠠⡼⣀⡀⠀⠀⠀⠀⠀⣠⠴⠖
⢹⠁⠀⣿⠍⠐⠶⣤⠀⡇⢀⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⢥⡼⣀⠤⣀⠔⠋⢀⣴⡍
⢨⠀⠀⠀⠀⠘⠀⠈⡳⣎⡁⣠⠇⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⠿⠗⠁⠀⢹⠀⡴⠁⢸
⠀⡀⠀⣦⠀⠀⣮⠟⠁⢣⠤⣽⠀⠰⠁⠀⢹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠤⠠⡀⠠⡶⡺⠋⠙⠺⢿⡅⠀⢨
⢀⠀⠀⡿⣀⡴⠋⣰⠲⠧⠤⠾⠂⠀⠑⠀⠋⠁⠂⠀⠨⠀⠀⠈⠀⠀⠀⠀⢀⠖⠁⠁⡄⠀⠀⣀⣀⣀⠀⠇⢀⡟⡓⢲⠰⢅⠸⡣⡄⢸
⢀⣄⣠⡿⠋⣀⠔⠻⡀⢀⠔⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠀⠀⠀⠀⠀⠢⠀⠔⠀⠀⠀⠀⠀⠈⠈⠀⢼⣀⠔⣁⣀⠈⠑⢀⠈⢺⣄
⠒⠚⠓⠒⠊⠁⠀⠀⠙⠁⣀⠠⠜⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠤⢬⡉⠀⢸⠂⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠊⠀⠘⣄⠀⠀⠀⠀⠰⠧⣀⠄⠀⠀⠀⠀⠀⠀⠀⢄⢀⣦⠀⠠⠀⠀⠀⢠⣏⠀⠀⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⢃⡀⠀⢁⣀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡰⠀⠀⢀⡴⠉⠪⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠇⠈⢢⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⣠⡀⠻⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠀⡔⢱⠋⠉⠇⢰⢤⣀⣀⢀⡀⠀⣀⠀⣤⠴⠖⠫⡀⠈⠆⠀⠈⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠜⠀⠸⡀⠀⠈⢩⠉⠉⡸⠀⠘⢆⠐⠚⠁⠀⠰⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠄⣀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣀⢄⠀⠀⠈⢀⠠⠐⠈⠀⠀⠈⠀⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⠈⡗⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠢⠧⣀⣀⠜⠲⣤⠖⠛⠓⢦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢇⠀⠀⠀⢨⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⢵⣊⠈⢉⠛⠑⠒⢤⡀⠀⠀⡀⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠰⠀⠀⠀⠀⠇⠐⠐⠁
⠀⠀⠀⠀⠀⢤⢠⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠠⠀⠠⠔⠁
⠀⠀⠀⠀⢀⠚⠘⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠗⡀⠀⠀⠈⠃⠀⠒⢦⡔⠒⣶⣶⣾⣿⠿⠿⣿⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠋⢸⡔⠁⠀⠑⠀⠀⠀⢀⠀⠀⠈⢿⣿⣿⡟⠉⠉⠀⠀⠜⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠀⠄⠀⠀⠐⠀⠀⠀⠢⡀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠔⠓⠒⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⣀⡀⠀⠀⠈⠂⡤⠀⣀⣀⡀⠀⠀⠀⠐⠈⠀⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠤⢱⠄⠁⠀⠀⠀⠀⠀⠂⠈⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣆⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠉⡀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⢂⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠉⠀⠈⠢⡀⠀⠤⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠉⠂⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀⣬⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⡴⠿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠙⢿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀
⠀⢀⣤⣶⣦⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢦⠈⠀⠂⢀⠔
⠀⣾⣿⣾⣿⡧⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⢹⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢱⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣤⣻⣄⠈⢯⢾⣎⠇
⠘⣯⡽⣞⠿⣶⡸⡀⠀⢀⡴⠀⠀⠀⠀⢰⣿⣿⡁⠇⠀⢀⡼⠁⠀⠀⠰⠀⢠⠀⠀⡆⠀⢠⠞⠀⠀⠀⠀⣰⣿⡟⢿⡇⠀⠀⠈⠉⢡
⠀⠱⣿⡽⣞⡱⣧⣇⣠⠎⠀⠀⠀⠀⠀⣸⣿⣾⣯⡘⣠⠞⠀⠀⠀⠀⠀⠐⠺⡇⠀⢹⡶⠋⠀⠀⠀⠀⣰⣍⢻⢻⣐⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠹⣿⣯⣷⣷⢼⠁⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⡃⢻⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢧⠀⠀⠀⠀⠀⣯⣭⣛⡛⢠⡀⡮⠀⠀⠀⠀⢡
⠀⠀⠀⠘⢿⣿⣿⡼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⣦⣴⡉⡱⠷⣻⠇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠙⠿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⠿⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠘⠿⣇⢀⣸⡿⠥⠤⢼⣅⠀⣠⣄⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⣫⣾⣿⠟⠁⠈⠁
⠀⠀⠀⠀⣤⣄⡠⢟⣩⣴⣶⠟⠻⣿⣾⣿⣿⣍⠀⣠⣶⡄⠀⠐⠻⣿⣽⡟⠉⠀⠀⠀⠀⢀⣼⠿⣦⡙⢾⣿⠟⠁
⠀⢀⡀⠀⢙⡟⣱⣿⡟⢻⣿⣦⣴⣿⠛⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⠟⡁⠀⠈⠻⣦⡁
⠀⠿⠿⠶⡾⣰⠟⢻⣿⡿⠿⣿⣿⣿⣷⡟⠉⠉⣿⣧⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣁⠀⠙⠦⠀⣠⠞⠛⠂
⠀⠀⢀⣀⡇⣿⣶⣾⣿⣧⣠⣿⣯⣠⣿⣿⣶⣾⣿⡯⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⣁⠀⠙⠷⠀⣠⠞⠁
⠀⠀⠘⠟⢷⣿⣿⣅⣽⣟⢛⣿⣿⣿⡟⢻⣿⣏⣹⡿⠶⣾⡦⠀⠀⢀⣴⠟⣥⡀⠈⠳⠀⣠⠞⠁
⠀⠀⢀⣤⣼⢿⣿⣿⡟⢻⣿⣿⠁⠈⣻⣿⣿⣿⣿⣄⠀⠈⠀⢀⣴⠟⢡⡀⠈⠛⠀⣠⠞⠁⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠙⠟⠁⠀⣹⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⠃⠙⠋⠀⢀⣴⠟⣁⠶⣾⣯⣶⣶⠞⠁⠀⠀⢸⡇⣾⠀⠀⣾⣾⣾⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠙⠁⠀⣹⡟⠛⢻⣿⠉⠀⣿⣦⡀⢀⣴⠟⣁⠺⣿⣷⣽⣿⠟⠁⠀⠀⠀⠀⠘⠷⢿⡦⠴⠿⠿⠿⢿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠈⠉⠀⠀⠈⢉⣴⠟⣡⡘⢿⣷⣾⣿⠟⠁⡴⢦⡀⠀⠀⠀⠀⣀⡼⠀⠰⠶⠶⠦⠸⣄⡀
⠀⠀⣀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⣿⣿⣿⣾⣿⠟⠁⠀⡼⣰⠀⢧⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⢠⣙⣦⡗⣾⣶⣂⣤⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⣿⣿⣿⠟⠁⠀⠀⢰⠃⠏⠀⠘⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠒⢾⣟⣿⢻⣿⣏⣻⠦⠀⠀⠀⠀⠀⡠⣢⣮⡻⣿⠿⠟⠁⠀⠀⠀⠀⠘⣔⠀⠀⣠⠇⠀⣿⢈⡁⠀⣉⣉⣉⣉⣉⣉⣉⣉⢸⡇
⢈⣻⣿⣿⣿⠻⣿⣿⠓⠂⠀⠀⢀⣪⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⢧⡀⠀⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠈⠁⠚⢻⠟⡿⢻⡌⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⣁⣀⣀⠹⡄⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⣿⣿⣿⡇⡇⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⡇⡇⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⣿⣿⣿⡇⡇⣿⢸⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣿⣿⡇⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣛⣛⣛⣛⡡⠃⠘⢦⣍⣉⣉⣉⣉⣉⣉⣉⣉⣭⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠹⣧⢀⣿⠇⢰⡿⣧⠀⣰⡿⠛⠻⢂⣾⠟⠛⠓⢸⡇⢸⣿⣦⣸⣿⠀⣰⡿⣧⠈⠛⣿⡟⠃⣿⡇⣰⡿⠛⢻⣦⢸⣿⣦⣸⣿
⠀⢻⣿⠏⢠⡿⠷⢿⣧⠻⣧⣤⣤⠈⢿⣤⣤⡤⢸⡇⢸⣿⠙⢿⣿⢠⡿⠷⢿⣧⠀⣿⡇⠀⣿⡇⠻⣧⣤⣼⠟⢸⡿⠙⢿⣿
⣶⣾⠿⠶⠿⠷⣶⣶⣿⣷⣾⣿⣷⣶⣶⣿⣿⣶⣾⣿⣾⣿⣶⣾⣿⣿⣷⣶⣾⣿⣶⣿⣷⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⣶⣾⣿⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿