Moving house Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⡀⠀⠀⣠⣴⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠿⣷⣤⣿⣿⠁⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠛⢿⣷⣄⡀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠉⠉⠁⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣿⡄⠀⠀⣀⣤⣶⣆⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⠀⢹⡇⠀⣾⡟⠉⢿⣿⠀⣿⡄
⠀⠀⠀⡀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠈⣿⡆⢹⣷
⠀⣴⣿⠟⠛⢶⣾⣿⣷⣶⣤⣄⡀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢀⡀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⣷⠀⠀⠸⣿⡌⣿⡆
⣸⣿⠁⠀⠀⣸⡿⠃⠀⠀⠈⣉⡛⣷⡀⠘⣿⡀⠀⣠⣴⠿⢿⣷⠸⣿⡄⠀⠀⠀⠀⠀⠀⠸⣧⠘⣿⣷⣴⣶⣿⠇⢿⣧
⣿⣯⠀⠀⣰⡿⠁⠀⠀⠀⠀⠻⠇⠸⣿⠀⢻⡇⠀⣿⡇⠀⠀⣿⡀⢻⣷⠀⢾⣶⠀⠀⠀⠀⣿⡀⠈⠉⠉⠉⠀⠀⢸⣿⡄
⠹⢿⣦⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣧⠀⣿⡇⠀⠀⢹⡇⠈⣿⡆⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠙⢿⣇⠀⠀⠘⢷⣤⣀⡀⠀⣠⣿⠀⠀⣿⠀⢻⣧⠀⠀⢸⣷⠀⠸⣿⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠉⠙⢻⣿⣿⣿⣄⠀⣿⣇⠸⣿⣦⣤⣴⣿⠇⠀⢻⣧⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢀⣠⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠿⠶⣶⣶⡿⠛⠁⠈⠙⢿⣿⣿⡆⠈⠛⠋⠉⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⣹⣿⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⣤⡀⠀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣴⡶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠻⣿⣤⡀⠀⠀⠘⣿⠀⠀⣠⡀⠀⢀⣠⣴⡾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠈⠙⠿⣷⣤⣀⣻⣆⣰⣿⣷⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠙⠻⢿⣿⣿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣄⣀⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⣾⠟⣻⣿⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⣠⣾⠟⠁⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⠋⠀⠀⣸⡿
⠀⠀⠀⠀⣾⡏⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⣰⡿⠁
⠀⠀⠀⢀⣿⠇⠀⢿⣿⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⣀⡀
⠀⠀⣴⣿⡏⠀⣀⣈⣁⣀⣀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣔⢀⣠⢒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⠵⠩⠼⠀⠉⠁⠘⢄⡀
⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠁⣤⢦⣤⠤⢶⣤⡤⡤⣤⠤⣦⡤⠤⠽⡅
⠀⠀⠀⠀⠀⠆⠁⠘⠂⠀⠀⠀⠀⠀⠠⣟⣟⡄⠀⢠⣘⣾⣀⣵⣚⣷⣷⣤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢂⣀⡀⠂⢀⠀⢀⣀⣠⣤⣀⢀⠀⠛⠛⢻⡆⢸⡗⠉⠉⠉⠀⠉⣋⣉⣉⣃⣀⣐⣄⡄⠤⠤⣤⠄⣀⣠⢤⡀
⠀⠀⠘⠉⠽⠤⠀⠚⠫⠕⠉⠝⠛⠋⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠽⠫⠿⠯⢥⠿⢯⡷⠀⠀⠀⠄⠐⠓⠀⠉⠹⠄
⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠒⠒⠚⠓⠚⠲⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢨⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⡆
⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⠶⣶⠶⠶⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠉⠉⠉⠉⡇⠀⡏⠉⠉⠉⠙⡇⠀⡏⠉⠉⠉⢹⡄⠀⡇⢰⡟⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢸⠇⠀⡇⢸⡇⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠶⠶⠶⠶⠇⠀⠷⠶⠶⠶⠶⠃⠀⡇⡆⠀⠀⢸⡇⠀⡇⠀⠙⠉⠉⠉⠋⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⡇⠀⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢀⣀⣄⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡼⠁⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠷⠶⠶⠶⠾⠁⠀⡇⠀⠀⣰⠋⠀⠀⠈⢳⡄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣇⠀⠀⠀⠀⣸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⠀⠀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⡴⣿⡇⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⣿⡇⣿⡇⣿⡇⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣿⣷⣿⣷⣿⡷⣄⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⠂⠃⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣒⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠰⠿⢻⣦⣀⡀⠻⣿⠗
⠀⠀⠀⢀⣴⣿⣿⣿⣦⠀⢴⣿⡧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣿⣆
⠀⠀⠀⢿⣅⣿⣿⣿⠛⠷⠾⠿⠋⣤⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠙⢷⣄
⠀⠀⠀⠀⠙⣿⡿⣿⡆⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⢿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⣿⡇⢿⣇⠀⠀⠀⠀⠀⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠘⣿⡄
⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠛⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀⠀⠀⣿⡟⢻⣿⣿⣿⠛⢻⣿⣿⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⡖⢿⣿⠇⠀⠀⠸⣿⠟⠀⠀⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⢹⡆
⠀⠀⠀⠬⣷⣶⣷⣶⡄⣰⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡆⢀⣶⣾⣷⣿⣖
⠀⠀⠀⢰⡏⣿⣿⡏⣿⣿⣿⣿⣿⣿⡆⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⢠⣄⠻⠿⠷⠟⢹⣿⣿⣠⡟
⠀⠀⠀⠿⢰⣿⣿⣷⠸⠟⣿⣿⣿⠽⠇⠴⣶⠦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⣿⠁⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣾⣿⣿⣇
⠀⠀⠀⠀⠻⣿⢿⡿⠃⠀⣿⣿⣿⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠘⢿⡿⣿⡿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⣿⣿⣿⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣇
⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠛⠋⠛⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠁⠀⠀⠀⠉⠀⠙⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⡀⣶⣾⢒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠃⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢀⡁⠀⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣄⠀⢰⠀⠀⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣴⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣿⣿⣿⣷⣿⣿⣶⣶⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣀⣀⣀⣱⡀⠐⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⢿⣿⣿⡇⠀⠀⠈⠅⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢼⢙⣿⡟⢹⡧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠊⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣙⣿⡟⢹⡄⠀⣀⡤⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⠛⡏⣿⠉⡛⣦⡀⠀⢀⠔⣾⣿⣿⣿⣷⢀⣬⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢉⡠⢾⢁⣿⣇⣸⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⢐⠀⠸⣷⢹⠀⡇⣿⢘⡆⡏⢹⢦⣌⣎⣿⣿⣿⣿⣿⡇⣻⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢉⡤⠖⠋⠀⡜⠘⠛⠛⠘⣄⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⣿⠸⡃⣗⢸⠀⡏⢸⡞⢿⣿⠟⡟⢹⢈⢻⠁
⠀⠀⠀⠀⠀⠀⠔⢉⡠⠖⠋⠀⠀⠀⢰⣟⢛⣛⣛⢛⣿⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⡀⡀⠸⣿⣷⣸⣁⣏⣸⣁⣏⣸⣁⣏⣸⣉⣏⣸⣙⣏⣋⣺⣾⠇
⠀⠀⠀⠐⠂⠀⠈⠋⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿⠀⠀⠀⠀⠂⢀⠀⠂⠀⠀⠀⠀⠀⠰⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢼⣿⢌⡇
⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⠘⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠿⠿⠧⣇
⠀⠀⠀⠀⠀⠀⢸⡛⠛⠛⢛⣿
⠀⠀⠀⢰⣤⠚⢺⡟⠛⠛⠫⠿
⠀⠀⠀⢸⣿⠀⢸⠏⠁⢘⣑⣶⡀
⠀⠀⠀⢸⣿⣿⠿⠿⠿⢸⣾⣶⠂
⠀⠀⠀⠀⠃⠀⠀⠀⠂⡀⠀⡁⢀
⠀⠀⠀⢀⣤⠤⢤⣄⠀⠅⠀⠅⠠
⠀⠀⠀⢈⣿⣶⣯⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⠀⠀⡆⢱
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢹⠀⡆
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⢟⣵⣵⣄⠀⠀⠘⡆⢱
⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⣸⣱⣿⣿⣿⣿⣿⢢⡀⢧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⢶⣿⠿⣿⣿⡿⣁⢀⣽⣼⣄⣧⣤⢤⠤⡤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣾⡸⠀⡏⢲⣾⡿⡏⢰⢸⠉⡇⣺⢸⠀⡇⠀⠙⡏⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣮⣅⣏⣸⣹⣅⣇⣹⣸⣁⣇⣹⣸⣁⣏⣷⡇⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠻⠛⠛⠛⠻⠛⠻⠇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡽
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠳⣄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄

⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠘⢿⣿⠏⠉⠁⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣶⣿⣶⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠘⠿⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⡅⢲⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠁⠚⠈⠁⠉⠀⠚⠀⠀⠀⠛⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠴⡢⠖⡠⠄⡬⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠍⠭⠆⠨⠭⠭⠁⠉⢡⣆⡀⠀⠀⠀⠀⣀⢸⠴⣄⡇⠀⢠⠟⢁⡲⠲⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠉⢐⣦⣶⠂⠀⢠⣆⠀⠀⢻⣷⡄⡆⠀⠀⠤⣤⣴⣾⣽⠶⠷⣶⢹⠛⠛⣚⣺⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠐⠂⠠⠊⢀⡴⠁⠀⠐⠛⠚⠃⠀⠬⠞⠏⠀⠀⠹⡿⡇⠀⠀⢂⣩⠭⠿⠦⢠⠞⠾⡟⢋⣻⣥⣤⣹⠆
⠀⠀⠀⠀⡀⡀⠀⠀⡂⢲⡂⠀⠀⠀⢠⡎⠁⣀⡀⣀⠀⠀⠀⠀⢤⡄⣤⠄⠀⡀⢱⡤⠀⠐⠂⠀⣀⡔⢢⣾⣹⣿⡗⠁⡉⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢾⠁⠀⣱⠏⠀⠀⠘⣡⣧⠀⡴⡄⠆⠸⣫⣴⡀⠐⠑⠈⠀⠀⠀⠀⠊⠀⢁⣾⡏⣉⢹⡇⠀⡆⡘⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠸⠗⠠⠰⠀⠁⠁⠁⠀⠀⠀⠀⠉⢁⢉⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⣎⣸⢑⣟⣻⠇⠀⡇⣇⠰⠁
⠀⠀⠀⠀⠤⠥⢤⡥⣤⣤⠤⠤⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣤⠄⠥⠬⠀⠀⢸⠀⠀⠀⠈⠀⠺⠷⠉⢸⡾⣿⢦⣤⡚⣇⣀
⠀⠀⠀⠀⠀⠀⢠⠟⣪⢾⠀⠀⠠⡄⠠⠀⢰⢠⢶⡢⡀⠀⠀⠈⣋⢰⣖⡁⠀⠔⢺⠀⠀⠀⡆⠠⠶⠤⣴⢨⣄⣿⠮⣽⢧⡤⠼⣇
⠀⠀⠀⠀⠀⠀⠈⠊⠙⠛⠀⠀⠀⠀⠀⠀⢸⠀⠉⠅⠁⠀⠀⠀⠁⠀⠉⠈⠀⠀⠸⠀⠀⠀⢹⠆⢠⡤⣬⠿⠧⠴⠢⠿⡿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠈⡄⢽⠐⠀⠀⠀⠀⠄⠀⠀⢀⠐⠒⠒⠄⣸⠀⠀⠀⠘⠂⣠⡶⠂⢸⡖⠒⠒⠒⠲⠀⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠈⠁⣰⠀⢾⠻⠒⠀⢈⣟⢉⠁⠉⠉⠉⠁⠉⠀⠀⠀⢠⠃⢰⡟⠂⠀⠙⢀⣄⡀⢀⠇⣈⢀⠄⠺⠗⠶⠤⣄⡰⢠
⠀⠀⠀⠀⠈⠀⠀⢄⠀⠁⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠁⠀⠀⠀⠓⠋⠉⠙⣏⠐⠉⠉⠉⠙⠻⡏⠠⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡉⡉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁

⠀⠀⠀⣀⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣠⠤⣀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡴⠋⠀⠀⠈⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠴⡇⠀⠀⠀⡤⠤⠤⠤⢤⠤⠤⠤⢤⠀⠀⠀⠙⡦⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⡏⠉⠉⠉⠉⢉⣉⣓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⠤⠤⠄⣼⣀⣀⣀⣼⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⡏⠉⠁⠉⠈⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⣺⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⣀⣀⣀⣿⣀⣀⣀⣸⠀⠀⠀⠀⡇⢠⡇⠀⠀⠀⢧⣄⣀⣀⣀⣀⣤⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⢧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡖⠉⠉⠲⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠶⠶⢾⠀⠀⠀⠀⡳⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⢺⠀⠀⠀⠀⡟⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⠚

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⢶⠶⢶⣶⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠐⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠩⣶⡄⠀⠢⣴⡎⠁⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠤⢀⣄⠈⠢⣗⣄⣃⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠋⡠⠋⠀⠙⠀⠀⠙⠻⢂⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⠈⢀⠎⠁⡀⠀⠀⠤⡑⠢⠢⡄⠉⠛⢽⡶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠖⢀⡴⠁⠀⠀⢸⣭⠰⠅⢱⠀⠀⠈⠊⠢⡀⠬⣉⠚⠫⢏⠄⠀⠈⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⡙⠃⡠⠋⠀⠀⠀⠀⣰⠶⠘⠧⢈⡇⠀⠑⠜⠰⠀⠁⠀⠋⠈⠉
⠀⠀⠀⠀⢀⠶⠌⡠⡞⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠃⠀⠃⠀⠀⠀⠀⠀⣠⠄⠀⠠⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⢄⠆⠠⢱⠀⠀⠀⠀⠠⠘⢛⣁⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠂⢸⠟⠳⡸⡄⠀⠀⠀⠩⠄⠀⠀⠡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠷⣤⠸⣤⣤⣄⡇⣠⠠⠄⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢤⠀⠀⠈⠀⠀⣧⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⡀⠀⠀⠀⡆⣇⢀⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⣤⣀⣤⡄⠤⠤⠤⢴⡀⠓⠓⢀⡠⠩⡉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡤⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⢳⡄⠀⠀⠀⢣⡠⠂⠁⠐⠂⠘⢆⠀⠀⠀⠀⠀⠊⠀⠋⠢⠤⡘⠒⠛⠋⠀⠀⠀⠀⠀⠀⠰⢒⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢠⠝⠉⢂⠀⢀⠀⠀⠈⣀⠔⠉⠙⠺⠇⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠂⠀⠐⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⠀⠀⠈⠢⡀⠀⠑⢅⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠠⠀⠀⠀⠀⢈⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⢅⠁⠀⠀⠀⠀⠈⠀⠀⡤⠠⠀⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠂⡡⠨⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣷⣤⣴⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠛⠛⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠛⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡀⢀⡴⠋⢰⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡀⢀⡴⠋⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣄⢀⡴⠋⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⣄⣠⠖⠁⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⣄⣠⠞⠁⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠨⠓⠁⠀⠉⢀⠀⠙⠴⡀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠂⢀⣂⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⠀⠀⠘⡖⡇⠀⠀⠀⢠⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠠⠀⢀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⣀⡀⣀⣀⠄⢁⣀⣀⢀⠄⣀
⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⠐⠤⠀⢤⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⡄⠈⣁⠀⠢⠀⠾⠙⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠈⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠴⠒⠄⠀⢰⡀⠂⠀⠄⠄⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⣀⠐⢀⠀⠀⠀⠀⠠⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣼⣁⣀⣀⣀⣀⣈⣇⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠒⠒⠒⢳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⡘⠒⠒⠒⠒⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⡛⢰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡄⢹⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣈⣉⣀⣀⣀⣀⣀⣈⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠧⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣏⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡖⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡤⣥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠄⠚⠂⠠⢓⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡰⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠳⡾⠁⠀⠀⢀⡃⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣧⠊⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠓⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⠙⣶
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⢐⠀⠀⡀⡀⠀⠀⠀⠀⢀⣴⠾⠿⣶⣆⡀⠀⠀⠠⠅⠠⠅⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠄⠀⠙⣿⡇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠠⣒⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢁⡿⠋⠀⠀⠀⠐⠒⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⠀⣀⣀⠀⠀⠀⠀⠘⠓⠀⠶⠛⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⣶⣴⡟⠀⠀⠄⠡⠄⠀⠀⠀⠈⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢘⣵⡿⠛⢿⣧⠀⠀⠀⠀⠉⠁⠀⢀⡄⡀⠴⡀
⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠁⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⢃⠁⠈⠀⠠⢹⢃⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⢀⣿⣧⣀⣀⣠⠁⠀⠀⢻⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠁⠀⠈⠀⠴⠆⠤⢀⠁⠞⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠤⢀⡶⢾⣷⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠓⠒⠀⠀⠈⠀⠀⠀⠀⡴⠖⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⡇⣄⠀⠀⠀⠒⠁⠀⠀⠀⠀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠂⢀⡀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡗⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁⠐⠀⠀⢀⠀⠀⠀⠠⠁⣠⡄
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠀⠀⠀⠀⠃⠠⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⢂⠈⠁⠉⠀⠀⠀⠀⠀⠐⣆⠂⠘⠀⠀⠀⠀⡀⣠⣶⣷⣾⣧⣄⢰⣿⣿⡇
⠀⠀⠀⠀⠂⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠊⠀⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⢽⣿⣿⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⠀⠈⣿⣿⣿⣿⠀⠀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⡇⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠛⠛⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢒⡲⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⡍⠀⢸⢣⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⠀⠒⠒⠁⠀⠀⠘⠳⠦⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠒⠒⠒⢺⠀⡠⡶⠖⡲⢖⠦⣠⢤⡤⣠⣀⣀⡀⡀⠀⠀⣈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠉⠂⠀⠈⠁⠲⠤⠤⣬⠤⣅⣈⣐⣁⡊⠐⠁⠉⠜⠵⠫⠻⡏⢰⣿⣒⠀⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠉⠉⠙⠙⠓⠒⠒⠒⠚⠟⠉⠉⠁⠐⢲⡈⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⠉⠙⠃⠘⠓⠒⠂⠰⠶⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⡄⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⢰⠁⠀⡀⠉⢃⠔⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡄⠀⢸⠀⠪⡘⠤⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⠀⠈⠙⠋⠑⠖⠁⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢠⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠠⠒⠒⠒⠤⡤⢖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⢘⠀⢰⠳⣤⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣖⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡈⠀⠀⠘⠦⠤⠧⠼⠁⠀⠀⠀⠀⠤⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠀⠀⠘⠀⢸⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠆⠐⡒⢲⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠀⢚⠹⠞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠂⠌⠢⠜⠁⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠸⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠰⠆⠀⠀⠀⣴⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠐⠂⠤⠁⢈⣁⣐⠒⠀⠀⠤⠤⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⠀⠀⠉⠐⠒⠒⠂⠠⠤⠀⠉⣁⣐⠒⠂⠀⠠⠬⠥⣥⣀⣀⣒⠖⠀⠀⢠⠅⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠂⠀⠀⠀⠉⠀⠀⢸⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠙⠳⠶⠦⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣭⠆
⠀⠀⠀⠀⠀⠀⠀⣆⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠋⠒⠲⠒⠶⢲⠖⡲⠆⡤⢄⡤⢤⡤⠇⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠽⠷⢶⡖⣤⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠑⠓⠀⢨⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠣⠾⠹⠯⠟⣷⢂⡶⣴⢦⢤⡤⣀⢀⣀⡂⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠚⠛⠋⠮⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣀⠠⠄⢀⡠⠤⠀⣀⡀⠤⠀⣀⠠⠄⠂⣀⠠⠄⠀⣀⠠⠄⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠒⠈⠁⠀⠒⠈⠡⠄⠂⠉⠄⠐⠀⠩⠀⠒⠨⠡⠄⠐⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⠀⠀⠄⠙⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠉⠀⠁⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣤⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣤⣀⣠⡴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡴⣆⠀⠀⢸⡇⣿⠀⠀⠀⣀⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠉⠁⣿⣿⣿⣷⡀⠀⠀⢀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣼⣃⣿⠤⠒⠉⠁⠀⣠⣤⡾⠿⣦⠀⠀⠀⢀⣤⡴⣤⡀⠀⠀⠀⠉⠲⢄⣸⣿⣿⣿⣿⣷⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⣿⣇⠀⢀⢿⡄⠀⠀⢸⡏⠀⠈⡇⠀⠀⠀⠀⠀⢀⡿⠿⣿⡿⠿⡿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⡀⠸⠋⣿⣿⡄⣠⡄⢠⣄⡙⣶⣾⣇⣠⣶⠀⠀⢀⣾⣼⣿⣤⣾⣭⣽⣥⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⠉⠒⣾⣿⣿⣿⠀⠀⠀⠀⢙⣿⣿⣿⠀⠀⠀⠀⠸⠿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠾⠿⡿⡿⠿⠃⠀⠀⠀⠀⠻⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣜⣈⣧⣀⣀⣀⣀⣀⣀⣠⣇⣣⣄⣀⣀⣀⣀⣀⣤⣇⣧⣀⣀⣀⣀⣀⣀⣀⣤⣇⣀⣈⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⣤⠀⣠⡟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠈⢻⣷⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠘⢿⣦⡿⠁⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡠⠍⠘⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠒⢠⣦⠀⠀⣇⡀⠀⢠⠔⢀⣄⡀⢤⣤⡄⢀⠉⣙⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠱⣤⠀⠀⠄⠠⡆⠻⠒⠐⢾⣿⣿⠛⢲⠀⠄⠇⠀⠀⠀⠈⠾⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⠀⠀⣤⡔⠀⢻⡇⡄⠀⠀⠀⠀⠀⢸⡀⠀⡀⡀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⣩⣭⣍⣷⠀⠘⣿⡇⠀⠀⠀⠈⠀⣸⡟⠏⠉⠉⠉⠉⡝⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠀⢹⣇⠀⢻⣿⡏⠋⠿⠿⠍⠹⡇⠠⠂⠀⠀⠚⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣤⣀⡠⡤⠮⣿⡖⢺⢺⡂⠀⠀⠀⠀⢸⣷⡁⢀⣀⣀⢀⣙⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡆⢠⠀⢹⡧⠸⣿⠳⡙⠛⠓⢒⠾⣿⠀⠀⠀⠄⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⡄⠒⠀⠒⠒⠒⣒⡒⠒⠢⡤⠤⠴⢈⡆⠸⣷⠀⢻⠀⠈⣱⠊⠁⠀⣿⡀⢀⢋⡃⠀⡛⠁⣀⣐
⠀⠀⠀⠀⡔⠀⡇⠈⠀⠀⠀⠠⡉⣳⠀⠀⣥⠤⠴⡮⠿⠦⠟⠲⣾⠀⠀⣨⠀⠀⠀⣿⢀⣀⢀⣅⢰⡇⢠⠄⢨
⠀⠀⠀⢀⠁⠸⡅⢀⣀⠀⡀⢑⠬⣺⠀⢀⣗⠀⠀⣷⣒⣆⠀⡆⢹⡒⠚⠓⢺⠛⠒⣿⠛⢍⡉⠉⢛⡽⢛⠉⠉
⠀⠀⠀⡘⢀⢌⠆⣿⢸⠫⡢⡑⠥⡶⠀⢸⣿⠀⠈⠙⠉⠋⠀⠁⢸⠂⢀⣼⣾⣤⠀⣿⠀⠀⠈⢺⠁⠀⠸
⠀⠀⠀⠇⡭⡠⡍⣮⢸⢕⠌⠪⡑⡆⠀⢸⣿⣀⣄⣀⣤⣠⣄⣴⣾⣆⣀⣀⡀⣀⣀⣿⣤⢀⡀⣸⣀⣂⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡸⠓⠛⠋⠀⠉⠊⠛⠓⠛⣈⡁⠀⢸⣧⣨⣨⣬⠎⢏⢤⣮⣯⣭⣭⡩⢭⡽⠿⣽⣽⣽⣽⣽⣽⣽⣽
⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡭⠭⠬⢭⠮⠮⠎⢬⢖⢒⣛⢛⠟⠑⣓⣱⢛⠳⡵⣜⣼⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⢘⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣬⣬⣬⣤⣵⣥⣿⣭⣭⣭⣭⣭⣬⡴⣥⣡⣎⣄⣕⣵⣡⡹⠀⠀⠀⢀⠔⠦⠠⢤⠖⡁⣤⠐⠇
⠀⠸⠀⠀⠀⢀⢾⡵⠒⠚⠺⢽⣄⠀⢠⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡥⠛⠲⣿⡍⠉⠉⡟⣷⡄⠀⢀⠄⠉⠀⠀⠀⢀⠑⢄⠀⠀⠀⠀⡴⠲⠊⠒
⠀⠶⠂⠀⠀⣾⡞⢰⡟⠙⡷⠀⣿⣂⡀⢉⠁⢀⡀⣀⡀⣀⢀⣀⡀⡀⣀⣠⢿⢰⢟⡶⢸⢷⣠⠞⠀⠓⠃⠈⢠⠀⣀⠔⡐⠂⣈⡰⠊⠀⠀⠀⠀⠁⠂⠍⠓
⠀⠘⣛⡚⢛⡁⠘⣄⠙⠛⢁⡰⠡⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠉⠁⠁⠁⠁⠘⢆⡉⡡⠖⠂⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⠉⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠉⠛⠁⠀⠀⠈⠀⠀⢠⣿⣿⠏⠀⠈⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⢀⣀⣤⣄⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠈⠛⠳
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡈⣿⠘⣿⣿⣿⣷⡀⠀⣇⠀⠀⠀⠀⣄⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡇⢠⣿⣄⠀⠈⠃⠀⠈⠁⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡄⠄⠀⠀⢠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠻⣿⡿⢻⣿⣿⣿⣿⡄⠈⠙⠛⣑⠦⠤⠞⣂⠉⠉⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⡀⠀⢠⣿⣷⣶⣾⣿⡆⠀⠀⠀⢸⣿⣿⠀⣀⡀
⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⢿⣿⡿⠋⠀⠀⠉⡛⠿⢾⣿⢿⣿⣿⣿⠉⣿⡀⣠⣶⣿⡟⢿⣿⣭⠁
⠀⠀⠀⠀⡀⢈⠁⠀⢸⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⣿⠀⠘⡿⠛⠛⠁⠀⠈⠻⢿⣷
⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣿⣿⠀⡀⠚⠀⠀⠁⠀⠛⠀⠈⠀⣴⣿⣿⣿⣆⠀⠁⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣦⣄⣀⣀⣠⡄⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠙⠀⠀⠘⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣆⢠⣾⣶⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⠟⢿⣿⣿⣿⣿⡜⢋⠝⠛⠛⠛⠛⠛⠫⠤⠀⣿⣿⣿⣿⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⡇⠘⣷⣿⣿⣻⡟⣛⠁⠀⠀⠀⢀⡀⢀⣀⠀⠀⠈⢛⡋⢙⣛
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠃⠀⠛⠙⠿⠟⠁⠿⠦⠀⠐⠛⠉⠀⠀⠉⠁⠀⠀⠚⠛⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢄⠀⠐⠒⠂⠀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠠
⠀⠀⠀⠀⠀⢀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣀⡒⠀⠀⠀⠀⠀⠂⠀⠆⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢹⣿⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⢍⠉⠁⠉⠋⠉⠉⠙⠋⠉⠉⠉⠉⢉⠑⠒⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣶⣶⣶⣦⣤⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠈⠁⠒⢄⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⡑⠄⣀⠀⠱⡀⣿⣿⣿⣿⣿⣿⣿⣏⠦⢄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣒⣲⣦⣾⣿⣛⣛⡻⣷⡘⠿⠿⠿⠇⢿⣿⣿⢿⣿⡿⡿⠟⠐⠿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣀⠀⢀⣾⣿⣿⣿⡿⠛⠛⢷⡜⣷⣶⡶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁⢤
⠀⠀⠀⠀⠀⠀⠀⢻⣇⣸⣿⣿⣿⡿⠛⠛⠛⣿⣿⣿⣿⣿⡏⠀⠹⡿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠐⠈⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠟⠛⠃⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠠⠀⣿⢸⣿⣦⢤⣤⠤⡶⢶⣶⣶⣶⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣾⢣⣿⣿⠃⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠷⠛⠋⠁







⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠂
⢹⣿⣿⣷⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠏
⠘⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠃
⠀⠹⣿⣿⣿⣷⣄⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠹⣿⣿⣿⣿⣷⣤⣀⠈⠉⢁⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣶⣭⣭⣙⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⢡⣶⣬⡻⣿⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠀⣿⣿⣿⣿⣷⠘⣿⣿⣷⡜⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣦⣄⠙⠿⣿⡿⠟⠁⣠⣾⣿⣿⣿⠃
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⡹⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⠟⣋⡙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣤⣄⡀⠘⠿⣿⣿⣿⠟⠁⣫⣴⣿⣿⠇⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⡿⣫⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡙⠿⣿⣿⣿⣿⣿⣿⣟⢡⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡟⠀⢸⣿⣿⣿⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢹⣿⣿⡏⣿⣿⡏⠀⣿⣿⣿⠇⠀⠀⠿⣿⠇⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⠀⢿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣤⡄⣷⣶⣤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⠛⠉⠉⠁⠛⠛⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣛⣷⡄⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣽⡿⠯⠿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⣀⠀⠠⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠒⠈⠁⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⡿⢻⡄⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠚⣿⡟⣻⠀⠀⣀⡄⣾⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⡿⢻⠉⡏⣻⢦⣀⠀⠀⡠⣴⣿⣿⣿⣦⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣡⢼⢋⣿⣇⣹⠀⠈⠉⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠲⡶⠃⢸⠀⡇⣿⢸⠙⣦⣄⣧⢿⣿⣿⣿⣿⠎⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣡⠔⠋⠀⣜⣘⣛⣛⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠇⢸⠀⡇⠿⢸⠀⠇⢸⠈⣎⣻⣿⠟⡏⢩⠁⣿
⠀⠀⠀⠀⠀⠰⠊⣠⠔⠋⠀⠀⠀⠐⣏⣉⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠹⣿⣷⣍⣸⣁⣅⣨⣀⣁⣏⣸⣉⣏⣿⣹⣁⣏⣷⡿
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⣯⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠰⡿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⡗
⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠐⡏⠉⠉⠉⠹⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⣤⣤⣤⣤⣤⣤⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢶⣄⢀⣴⠟⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠟⠁⠀⠀⠀⠀⠙⠋⠛⠛⠛⠛⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡾⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣦⡀⠀⣠⡾⠋⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⠿⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⣶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠿⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⢠⡏⠀⠀⡀⠀⠀⠀⣠⣾⣿⡷⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣾⣿⣧⣤⣾⣾⡿⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣉⡄⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠉⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⡤⢤⠤⣶⠀⠀⠀⠀⡔⠒⡐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠑⠂⠀⠀⠀⣤⣔⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣾⡷⠶⠾⠷⠧⠶⢿⠀⠀⠀⠀⠠⢈⡀⠝⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣯⣬⣭⣭⣭⣿⠋⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⢙⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠈⢹⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢹⡆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡤⠐⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡄⢸⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢡⠐⣁⡫⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡯⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠤⠉⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣷⠀⠀⠀⠀⢰⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣽⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⢹⡆⠀⠀⠀⠀⠸⠀⠀⠀⠀⡎⢉⡉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⣾⡼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠬⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⢨⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⢰⡷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠇⣷⠀⡀⠀⠀⠠⠤⠤⠠⠤⠤⢤⣤⡤⣠⣠⣤⣤⣤⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⢸⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠂⣼⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠉⠁⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢜⣭⢝⡶⠶⠒⢲⢦⣤⠤⢤⠤⠤⣤⠤⢤⠴⣶⠶⠶⢶⠖⠶⣶⢶⠆⣶⢶⠤⢤⡤⣠⢤⣤⡴⢶⡿⡣⡏
⠀⠀⠀⢠⠖⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠓⠚⠓⠛⠷⠾⠷⠶⠶⠶⠶⠶⠶⠷⠦⠶⠶⠶⠾⠿⠯⠽⠥⠥⢤⣮⣭⣴⣯⣍⣤⣯⣬⣼⡧⠤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠘⠧⣤⣤⣠⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣤⣀⣤⣠⣄⣤⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠋⠁⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡋⠃⡀
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⢾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢂⢀⣀⣀⣀⡇⠀⡀⢀⢀⣀⡀⡀
⠀⠠⠀⠑⣀⠁⡀⠘⣮⠂⠈⢀⠌⠠⣅⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡡⣬⣴⣯⡥⠬⣷⡞⢿⣿⣿⣿⣿⣇
⠀⠀⢀⡀⠇⠀⠁⠂⣯⠀⢡⣿⡀⠒⣌⡴⠉⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠛⠒⢲⡲⠷⢶⡒⡶⠖⢆⣾⠿⡟⡟⠛
⠀⠀⠀⠀⠀⠐⠀⠀⠛⠒⠚⠒⠓⠂⠓⠛⠐⠓⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠚⠂⠘⠛⠛⠑⠀⠸⠴⠟⠓⠘⠀⠀⠂

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠦⣤⡴⠛⠛⠛⠶⣤⡀
⠀⠀⣠⡴⠛⠉⠉⠉⠛⠶⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⢰⡏⠀⠀⠀⠀⣀⣤⠶⢦⡀⠀⠀⠀⠀⠀⢹
⣸⠇⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇⢀⣠⠶⠛⠉⠀⠀⠀⠙⠳⣤⣀⡀
⣿⠀⠀⠀⠀⠀⣀⡤⠞⠋⠈⠳⣦⣀⡀⠀⠀⠀⢸⡇⠀⠀⢸⣧⡟⠁⠀⠤⠄⠀⠀⠀⠀⠠⠤⠍⠙⠛⣧
⣿⠀⠀⣾⠛⠉⠑⠲⠀⠀⠀⠀⠖⠋⠙⢛⣿⣀⠈⣇⣀⣀⢨⣟⣡⣀⠀⠰⠆⠀⠀⡀⠀⠀⠶⠀⠀⠀⢙
⣿⠀⠀⢹⡄⠀⠘⠃⠀⠀⡄⠀⠘⠃⣰⠏⣠⡿⠛⠉⠉⠉⠙⠻⣧⠉⢷⠀⠀⢀⠀⠋⢀⠀⠀⠀⢀⡾⠛
⢻⡀⠀⠀⢻⣄⠀⠀⠠⢈⡀⠄⠀⠀⢻⣶⠏⣀⣤⠖⠛⢦⣄⡀⠈⣷⣾⡁⠀⠈⠉⠉⠁⠀⠀⣠⠟⠁
⠘⣧⡀⠀⠀⠙⢦⣄⠀⠀⠀⠀⣀⡴⠋⣿⡟⠭⡆⠀⠀⠀⠈⡿⠛⣿⡋⠛⢶⣄⣀⣀⣠⡴⠟⠁
⠀⠈⠛⠶⠦⣤⣤⣽⣿⠲⠖⣿⢯⣤⣤⣯⣀⠀⠁⠀⠰⠀⠀⠁⢀⣹⡇⠀⢠⣿⣉⣉⣹⣇
⠀⠀⠀⠀⠀⠀⣀⡼⣿⣿⣿⣿⣧⣀⠀⠈⠹⣦⡀⠀⠉⠁⠀⣠⡞⠉⣠⡴⠟⠻⠿⠿⠿⠛⢶⣄⡀
⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠈⠙⣷⣶⣶⡛⠁⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠞⢉⠀⠈⠛⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣇⣀⣿⣛⣻⣇⣀⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠉⠉⠀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢀⡀⠠⠤⠤⠬⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⢀⠃⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠸⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠾⠰⡦⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣧⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡜⠀⠑⢧⠈⠉⠒⠒⠀⠒⢄⠀⡇⠀⢀⢼⠀⠀⠀⣴⠄⠀⠀⠀⠀⣰⡆⠀⠘⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠘⡀⠉⢑⢈⠸⠀⠀⠀⠉⠀⢰⠀⠀⠀⠉⠀⠀⠀⠑⠁⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡏⠀⠀⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢡⡥⠊⠈⠒⠇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⢰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠘⡀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢧⢂⠀⠀⠀⠀⠘⢄⡀⠄⠀⠀⢀⠎⠈⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⢀⢦⡠⡄
⠀⠀⠀⠀⣤⢄⣀⣄⠀⠀⠀⠙⢷⠢⢀⣀⠀⠀⣀⡀⠤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⣤⠤⠤⠐⣆⠁⠀⠀⠸⠙⠂⠃⠖⠱
⠀⠀⠬⣓⠀⠀⠁⡎⠀⠀⠀⠀⠀⠁⠀⢀⣠⢠⠇⠀⠀⠘⠂⠠⡤⢀⡀⠀⠀⠀⠀⡀⠴⠙⠦⡀⠀⡀⠟⠢⢄⡠⡒⠃⠀⠀⢀⠇
⠀⠀⠀⠉⠂⠢⡀⠈⠢⡀⠀⠀⠀⠀⢰⣫⠶⡁⠀⠀⠀⠀⠀⡠⠁⠀⠈⠑⠢⢔⠉⠀⠀⢀⠀⢉⡞⠀⠀⠀⠀⠈⠢⡉⣖⠂⠉⣆
⠀⠀⠀⠀⠀⠀⠑⡄⠀⣈⠦⠀⠒⠚⠣⢄⡀⠑⠢⠀⠠⠄⠊⠀⠀⠀⣀⡀⠀⡠⠓⠢⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⠜⠉⣆⡠⠄⠀⠒⠒⠠⣈⠢⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⡲⠅⠀⠒⠘⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⡄
⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢧⠵⢌⠑⡆⠀⠀⠀⠀⣷⣊⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⣴⢤⡀⠨⠇⠀⠀⣴
⠀⠀⠀⠀⠀⠘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢀⣈⢣⠀⠀⠀⣽⠁⠀⠑⠂⠿⠲⠆⠀⠀⠀⠀⠇⠀⠀⠀⣿⠀⠙⠳⠦⣤⣤⠟
⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⢏⠈⡎⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠁⢸⠀⠀⠀⡇⠀⠀⠀⠙
⠀⠀⠀⠀⢠⠚⢪⡖⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⡼⢄⡞⠀⡦⢤⠤⠒⡀⠈⠁⠀⠀⠀⠖⠀⠀⢄⠄⣀⠃
⠀⠀⠀⠀⠸⡀⢇⢀⡠⡀⠀⠀⠀⠐⠈⣀⠤⣎⡠⠚⠣⡜⠀⠓⡄⢇⠑⢄⠀⠙⠀⠂⠀⠀⠀⠀⣠⡮⢀
⠀⠀⠀⠀⠀⢄⠀⠀⢀⠌⠡⠒⠀⢂⡽⠀⠠⠦⠄⠀⣠⠃⠀⠀⠱⡈⢳⠆⠷⢰⠂⠠⣤⠴⡖⠋⡩⠄⠚⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⠂⢻⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠉⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠟⠀⠘⠉⠉⠁⠉⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⣄⣀⣀⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⣄⣀⣀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠁⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢮⠀⠀⣸⢤⡀⠀⠐⡄⢸⠀⡖⠀⢀⣠⢼⡀⠀⢨⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠉⠀⠀⠈⠓⢄⠀⠀⠀⢀⡔⠋⠀⠀⠉⠉⠁⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡴⢾⠉⡏⠉⡏⠉⠉⢩⠉⣉⣉⡉⣉⠉⢹⠲⡄⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⡇⠀⠀⢸⠀⠀⠒⠒⠂⠀⢸⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⠟⠙⠇⠀⠀⢸⠀⠠⠄⠤⠤⠄⢸⢀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⢸⠀⡀⢀⣀⣀⠀⢸⠀⠀⠶⠶⠶⠆⢸⢐⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣀⣀⡀⢀⠀⢸⠀⠒⠒⠒⠀⠂⢸⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠁⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⣠⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣄⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠖⠒⠚⠛⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠛⠃⠒⢲⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠂⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢠⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⣰⣷⣤⣀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡼⠁⠈⢹⠏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠾⠁⠀⢸⠀⠀⢸⠀⢀⡞⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠀⠀⢸⣠⠏⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⠀⠀⣸⠋⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢸⡞⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠎⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⠀⡟⠓⢦⡞⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢾⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣤⡀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠿⣿⠿⠿⠆⠀⠀⣾⡿⠉⠉⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠀⠰⠀⠰⠆⠀⠀⠀⠉⠁⠀⠘⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣶⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠛⠛⠛⠀⠀⠈⠁⠀⣤⠀⠀⣠⠀⠀⠀⠀⠀⣴⣷⣀⣭⣄⣾⣦⠀⠀⠀⠀⣠⣤⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠘⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡆⠀⠀⠀⣸⠟⣿⣿⣿⠟⢿⠻⣇⠀⠀⣾⡟⠻⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⣤⣄⡀⠐⠒⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⣿⠀⣿⣿⣿⣷⣡⠀⣿⠀⠀⣍⠀⠘⠃⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣶⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠐⠋⠀⣿⣿⣿⣿⣿⠀⠘⠀⠀⠾⠆⡀⠉⠁⠚⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⠉⣿⣿⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣿⣿⠇⠀⠀⠀⠀⠸⠅
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣤⣤⣄⠀⠀⠀⠀⢠⣀⡀⢠⣀⡀⠀⠀⠀⢀⣴⣿⣿⣀⣿⣿⣦⡀⠀⠀⢀⣤⣤⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠉⢳⡀⠤⠤⣄⣉⠑⠢⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡰⠓⠦⠤⠤⠤⡄⣧⠀⠀⠀⠈⢙⡆⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠉⠉⢉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣠⠊⡝⠁⢹⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣄⣀⠴⣏⠀⠀⠀⠀⠀⠀⢀⣡⠴⠧⠤⠼⠦⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠘⢇⡀⠀⣀⠞⠓⠦⣄⠀⠀⠀⠙⡞⠉⠉⠉⠉⠉⠑⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⢦⠀⠀⢣⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢳⢄⡀⣠⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡤⡖⢻⡀⠉⠁⣸⠃⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢣⠀⠉⠛⠋⠁⢀⠇⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠣⣀⡴⢦⣠⠞⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠈⠦⣤⡇⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⣅⠀⠀⠀⠀⠀⠀⡧⠤⠤⢸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⠤⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠦⣌⠙⠒⠤⠤⠤⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⠶⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⣀⢀⡄⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣛⣒⣂⡉⢹⣿⣽⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣵⣟⡿⣫⠍⠁⠀⠀⢼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣮⣵⣿⣿⡿⠋⠀⣠⣶⠈⣀⣾⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣀⡀⣠⡶⠟⣛⣯⣽⣿⠟⠀⢠⣾⣿⣿⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⣉⡵⠀⣯⣶⣜⡻⠽⢑⢿⡀⠀⣿⣿⣿⣿⣆⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡟⠁⢀⣼⣿⠁⠀⠈⠻⣮⣝⡻⢾⠃⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣸⣿⢟⣻⣿⣿⣿⣿⠁⠀⣾⣿⣿⠀⠀⠀⣘⢼⡻⣟⡳⢦⠀⠀⠀⠹⣿⡿⠀⠀⠀⠘⢛⣿⠁
⠀⠀⠀⠀⢀⣆⡿⣱⣿⠟⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠘⢷⣝⢶⣍⠳⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⣠⢾⣿⣼⣿⢏⠀⢻⡇⣿⣿⡇⢈⣿⣿⣿⣧⠀⠀⠀⠈⢻⣷⣹⡇⠀⠀⢀⠀⣿⣿⣧
⠀⢀⣮⠵⣿⣿⣿⣏⣼⠀⠘⣷⠸⣿⣇⡾⠉⠻⣿⣿⣧⡀⠀⠀⢈⡟⢱⣷⣶⠾⠋⣸⣿⡿⠃
⠀⢀⡴⣞⣯⣿⢟⣽⣿⠀⠀⢻⠀⣿⡿⠁⠀⠀⢈⠛⠿⣿⣦⣀⠈⠀⣼⠋⠑⠶⣼⣿⣿⠁
⠀⣴⠿⣿⣛⣵⣿⣯⣝⠂⠀⢸⡆⠋⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠙⣿⡏
⠀⠙⠳⠾⠯⢭⡙⠻⢿⣷⡀⣸⣇⡆⠀⠀⣴⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣿⡇⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡝⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⠇⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣬⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣟⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁
⣿⡿⠿⡿⠻⢿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠚⠉⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡀⠄⠒⠀⠐⠂⠄⠀⠀⠈⠖⠀⠀⠀⠀⠀⠂⠀⠀⡆
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠠⠒⠀⢀⠑⠄⢀⡏⠀⠁⠀⠀⠀⠀⠀⠐⠇⠠⠈⢀⠤⠀⠀⠀⠀⠀⠀⠄⠀⡅⠠⢤⠀⠠⠈⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠂⢁⠐⠘⠆⠀⠀⠀⡂⠀⠀⠀⠀⠄⠀⠀⠁⠀⠑⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⣠⠁
⠀⠀⠀⠀⠀⢀⠀⢀⠔⠡⠀⠀⠈⠀⠈⡤⠀⠀⠄⠀⠀⠀⠀⠀⢀⠌⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣆⠀⠇⠀⠀⠀⠠⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠒⠙⡀⠀⠀⣀⡅⠀⠀⠆⠀⠀⡀⠒⢤⠤⠤⡰⠋⠄⠀⠀⠀⠀⠀⢁⣀⠀⠀⠠⠌⠐⠀⠈⢐⢦⠀⠀⡤⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⠤⠤⡠⠐⣇⠀⠀⠌⠀⡄⠀⠀⠀⢀⡴⠒⠒⠂⢄⠑⠤⣄⡁⡤⠴⡇⠈⡆⠀⠀⠠⠀⠀⠁⠀⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠑⠀⠘⠊⢀⠀⠀⠀⢀⡁⠀⠀⢀⠃⠔⣮⠉⠨⠄⣏⠄⠠⠜⢀⠀⠘⠄⡅⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⢲⠩⠘⠂⠠⣠⠔⠀⠐⠀⡀⠀⢡⠆⠀⢀⠈⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣃⢀⢘⠀⢂⠰⠂⠒⡒⠊⡅⠀⠰⠀⠐⢀⡄⢴⠐⡡⠂⡅⠀⠀⠀⠀⢐⠋⠁⠀⠀⠀⢋⢊
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠭⠉⠈⠉⠀⠈⡚⢸⢴⡀⠁⣀⠀⢠⠅⠸⠁⠀⠈⠉⢧⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⠈⠀⠀⠈⠝⡂⠀⢀⠑⣀⢡⡅⠀⠀⢸⢄⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠀⠀⠀⢾⡇⠀⢰⣷⠋⠇⡏⠉⡉⠙⢸⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠨⣄⣀⣠⣭⡄⡄⠰⠰⠗⠸⠀⠁⠒⠰⠐⠆⠈⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢘⣇⠡⠀⠀⠀⠀⣾⠀⢹⡞⠀⠊⠀⣬⣨⣄⠀⠀⢰⠴⠤⠆⠀⠀⠀⠀⠀⠀⢨⢃⡓⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⣴⠀⠀⠀⠀⠀⠀⣀⡄⢀⡢⢀⣠⠀⣰⠀⠀⠀⠀⠠⣤⠀⣐⣶⠖
⠀⣶⠀⠀⠀⠀⢀⡈⠁⠈⠁⠀⠁⠀⠉⠀⠉⢀⠀⠀⠠⣦⠀⠘⠁
⠀⣶⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣁⠚⠀⠠⣦
⠀⠶⠀⠀⠀⠐⡹⠁⠀⠀⠀⣰⠄⠈⠀⠀⠀⠈⠘⠀⠰⡶
⠀⠶⠀⠀⠀⠀⢲⠀⠀⠀⠐⣧⠄⠺⠂⠀⠀⠉⠔⠀⠐⠶⠀⠀⠇⢀⡀
⠀⠀⣀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠠⠄⠂⠀⢠⣆⠀⡆
⠀⠁⠀⠀⠊⠀⠉⠈⡁⠆⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⢸⡏⠀⡅
⠀⠀⠀⠀⠀⠚⠀⠀⢀⡐⠁⠀⠀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠐⠇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡀⠀⠒⠂⢀⣀⠐⠂⠀⢀⣀⠂⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⡃⠀⠀⣀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⢇⠀⠀⠀⠀⠙⢬⡴⠀⢛⢟⠀⠀⠀⠀⠁⢂⣀⠈⠐⠀⠀⠁⡂⠀⠈⠐⠀⠀⠁⠂⠀⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣿⠆⠀⠀⠀⠀⢤⠈⠀⢴⣶⠄⠀⠐⡀⠀⠛⠶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠲⠀⠀⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀
⢀⡆⠀⠀⠀⠀⠀⠀⠙
⢀⡉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⢠⡖⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⣴⣾⡛⠁⠀⠀⠀⠀⠀⠀⠀⣶⠗⠀⠀⠀⠀⢤⢰⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⣏⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣰⡆
⠀⠈⠳⣿⣷⠀⠀⠀⠀⣠⡴⣾⣽⣿⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡌⠢⡄⠀⠀⠀⣸⣿⠻⢦⣠⠤
⠀⠀⠀⢸⣿⣇⠀⠀⠈⠁⠠⠇⠸⣿⣆⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠀⠠⣇⠀⣾⡟⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⡏⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠋⠉⠳⣄⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀⢀⣿⡏⠀⠀⠐⢢⡀
⠀⠀⠀⢠⡏⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⢠⡄⣢⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠀⠀⢠⠞⢿⡟⠀⠀⠀⢠⡟⣻⡇⠀⠀⣸⣠⡇
⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⢸⠁⠀⠀⠀⠈⣷⣿⡇⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣶⠀⠀⠀⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣄⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⣿⠀⠀⠀⠸⣷⣄⣠⡼⠇⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡯⠉⠛⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⢠⡏⠀⠛⠀⠀⠀⢀⣾⣿⡏⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⢀⣼⣷⣦⣀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢈⣿⣿⠉⠁⠀⠀⠀⣀⣤⣹⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⢧⠀⠀⠀⠀⠀⠀⠈⠀⣿⣇⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣾⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⢷⠀⠀⠀⠀⠀⠀⠀⡰⠋⢹⡇⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠇⠀⠀⠀⠀⣸⠉⢸⠇⠀⠀⣰⣟⣤⢓⡤⠀⠀⠀⡀⣀⡃
⠀⠀⠀⠀⣿⣴⣆⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⣿⣿⡿⠟⠁⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⡀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⢀⡾⣿⢻⡄⠀⠀⠀⠀⠀⢀⣧⣤⡄⠀⠀⠀⠀⠀⢸⡀⣿⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⣿⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠸⢰⣿⡆⠇⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡇⠀⠀⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠙⠃⠘⡿⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢸⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣸⠁⠀⠀⠀⠀⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀⠘⡇⠈⢻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡇⠀⠀⠀⠀⠀⠇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⠀⠿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠇⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡁⠀⠀⠀⠀⠀⠀⣠⣀⠐⡆
⠀⠀⠀⠈⡇⣤⡴⠗⠀⠀⠀⠀⠀⠀⠀⠀⣾⡬⠀⠀⠀⠀⠀⠐⣥⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣧⠖⠒⠆⠀⠀⠀⠰⣧⣼⡁⠀⠀⠀⠀⠀⠀⢳⣾⡶⠇
⠀⠀⠀⠀⢿⣿⣷⠾⠉⠓⠀⠀⠀⠀⠠⠶⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⡟⠛⠓⠈⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢰⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠋⢻⡄⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠆
⠀⠀⠀⠀⢸⡏⢹⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⣸⡇⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⢻⠉⣿
⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⣿⠀⠘⠓⠀⠀⠀⠀⠀⠀⣿⠇⠀⠉⠁⠀⠀⠀⠀⠀⢸⠇⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉
⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠤⠀⠀⣴⣥⡀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠞⠁⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⢠⡄⠀⠀⡄⠀⠀⠀⠁⢶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠂
⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠰⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⢠⣴⠢⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠘⠠⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠄⡀⠀⠀⠀⡠⠢⠤⠁⠀⠀⠀⠒⠰⠀⠀⠀⠀⠄⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠊⠂⠀⡀⢈⠔⠀⠈⠢⡑⠢⠐⠍⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠑⠁⠁⠀⠀⠀⠀⠈⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠏⡅⡊⠉
⠀⠀⠑⠂⠠⠤⠄⠀⠀⠀⢀⡀⠀⠀⠀⣀⣼⣠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠇⣇⡇⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠳⠿⠆⠆⠢⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡎⠀⠀⠀⠀⠀⢀⡄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⡶⣶⡶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠤⠤⠄⠀⠀⠤⠤⠤⠤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣧⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⡠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⡿⢀⠀⠀⠀⠀⠐⠒⠂⣶⢋⡙⠃⢸⣀⣀⣀⠁⠁⠀⠀⠀⠀⠀⢀⠀⠘⡩⢆⠀⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠴⣾⣔⣡⣀⣠⣀⣠⣠⣀⣾⢧⠏⠠⣼⣿⣟⠀⣠⠀⠀⠀⠀⡀⠄⢊⠠⠐⢀⡠⢞⡧⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐⠠⠀⠀⠀⠉⢰⠋⣝⡍⠙⠉⠘⢋⡛⠛⣯⡝⠽⣻⢿⡿⠿⠞⠙⠀⡀⠐⠈⡠⠀⢀⡤⢚⠭⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡦⣌⢤⡜⢀⠏⠰⠿⠀⢰⡔⠀⣿⠃⠠⠿⣽⢶⣿⣿⠁⠠⠀⠖⠈⠠⠂⣁⠤⢊⠧⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠐⢰⡾⠠⢁⡞⢀⢠⠄⠀⠀⠀⠀⠀⢠⣅⢀⣀⣾⣾⡇⡠⢏⠀⠀⣡⠔⣚⠤⠚⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⡞⠀⠾⠏⠀⣼⡛⢹⠀⠀⠼⣷⡷⣻⣿⣏⡎⠀⠀⢺⡧⠖⠊⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠁⠁⠀⠦⠴⠇⠀⠀⣀⣰⣟⣀⣯⠀⠈⡀⠀⢰⣿⡿⠛⠯⣼⡡⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠒⠒⠀⠴⠄⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠉⠉⠁⠙⠛⠓⠐⠜⠀⠀⠠⠐⠤⠂⣄⣀⣸⠃
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠉⠉⠩⡹⠋⠒⠂⠄
⠀⠀⠀⠈⠙⠒⠢⠦⢤⠤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠈⠙⠁⠂⠒⠒⠒⠖⠴⠠⠠⠤⢤⢤⣤⣤⠞⠨⠆⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠉⠁⠀⠀⠀⠀⠀⣤⠟⠻⠀⠀⠈⠀⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠦⠤⣤⠀⠀⣀⣀⡀⠀⠀⠀⢀⠀⣤⣠⡄⠀⠀⠀⢶⠄⠈⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣶⡝⢿⣷⣷⣿⣷⣿⣿⢿⣿⡄⢀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢧⡀⠀⠀⠀⠀⢸⡤⠛⠛⢻⣿⣦⠛⣽⣿⣿⣿⡁⠀⣩⣀⠀⠀⠀⠀⠀⣠⢤⣤⡀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢺⣿⠃⡈⣳⣤⡀⠀⠀⠀⠀⠋⠘⢛⣿⣿⣷⡹⡿⣿⣿⣧⣴⣿⣿⣶⣤⠀⠀⠀⡇⠀⠄⠇⠀⠘⣿⡇⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣀⣿⣿⣿⠀⢀⢀⣆⠀⣰⡟⣿⣿⣿⣿⠖⠉⡙⣿⣿⣿⠋⣳⠙⣦⠀⠀⢡⠀⠀⡄⠀⠀⡿⢿⣾⠋⠻⡆⢠⣯⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠁⡘⣿⣿⣿⣷⠌⢹⣿⠿⡦⢞⢆⣿⣿⡟⣰⢏⡇⢃⠰⠀⠀⠀⠀⠁⠀⠀⣿⣿⣇⠀⢠⣿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⢰⣀⠉⠉⠉⡏⠀⢾⣧⢐⠄⠀⡺⣿⣿⣷⠿⢸⠃⢸⠀⠀⠀⠀⢠⠄⢀⠀⣿⣺⣿⣶⣌⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⡘⠀⠀⠀⠀⠟⠷⢻⣿⠏⠀⠄⠿⢿⣿⡇⡤⢸⠆⠘⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⠃
⠀⠀⢐⠳⠀⠀⢠⣾⣿⣿⣯⣭⣉⡁⠀⠁⠀⠀⠀⠀⡀⣄⢈⡧⠤⠀⠀⠀⣾⣿⠀⣤⢻⡄⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣯⣭⡏⡀
⠀⠀⠀⠀⢰⣷⠾⣿⣿⣿⣿⠡⠀⠀⢀⠀⠀⣠⣴⢶⠀⡟⠁⠛⣷⠎⠀⠀⣿⣿⣤⡀⢰⣷⣦⣀⠀⠀⠀⠀⠀⠀⣶⡉⢉⣿⠿⠏⠰⠇
⠀⠀⠀⠀⠀⠨⣦⠘⠻⣿⣧⠀⠈⣸⣺⡤⠎⣡⡜⢉⠀⡏⠀⠹⠇⢀⡆⠸⡿⠂⠼⣏⣠⠁⠈⠸⠿⠷⡾⠿⠛⠀⢧⡀⢀⡽⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⣷⣄⣩⣽⣇⢸⣿⢷⣥⠞⠁⠀⣠⡿⠋⠀⢿⡇⣼⣇⣠⣶⡀⣸⣿⣷⣜⠃⠠⠀⠀⠀⠀⠀⣰⡿⠁⠘⣧⣰⣷⣾⣆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⢯⡽⠹⠻⡻⠽⣄⠀⠀⡇⣿⠁⠀⠀⠘⣿⣿⣿⠟⠻⢿⠿⣿⣿⣿⡀⡀⠒⠀⠀⠀⠀⡿⠁⠀⠀⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡟⢦⣴⠃⠀⢩⣴⣿⡆⠀⡇⣿⠀⠀⠀⠀⢹⣿⣧⣤⣤⣀⡉⠩⢽⣿⢹⡵⢦⣤⡛⠆⢰⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡭⠀⠀⠀⢿⣸⠇⠠⡅⣿⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣷⢸⣿⣸⡏⠘⢈⣿⡆⢸⣤⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣤⣤⣤⣞⠁⡀⢀⢀⣇⣀⣀⣀⣀⣸⣿⡿⠠⠤⠄⣀⣍⣸⣿⣏⢷⣀⢸⡷⡇⢰⠉⠉⠛⠉⠙⣿⣿⣯⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣠⣠⡤⣌⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⠀⠈⢻⣿⣿⣾⠳⡾⢿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠳⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⣌⠀⠀⠈⢻⣿⣿⣶⣤⣾⡇⠰⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⣙⢿⡷⠶⠶⣤⡾⠙⡏⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠀⢸⣿⠀⣶⣾⠀⠀⠀⢠⣶⣟⢿⡟⠀⣬⠀⡼⠯⠈⠀⣠⡄⠀⠀⠀⢸⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⡈⣿⡼⠳⠃⢰⣶⠀⣥⡌⠀⠀⠀⡀⠘⢳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠢⣹⠈⢿⣈⡇⠰⠚⠀⠉⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⢰⣶⡄⢼⣶⠀⠀⠠⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠸⠷⠋⠀⠘⣧⡼⠁⠀⠀⠀⠀⠀⠑⠊⠃⠀⠂⠀⢀⡀⠉⠻⠷⠿⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⡋⠉⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⡤⠤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡛⣶⢿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠉⠉⠉⠀⣠⠆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡓⣶⢿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠉⠉⠉⠀⣠⠆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⠀⠀⣰⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣶⣮⣟⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡳⣦⢿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣳⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠙⠉⠋⠀⣠⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢘⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⣤⣄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡳⣤⢿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣴⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠛⠉⠛⠀⣠⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣾⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣤⣤⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣵⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡳⣤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⠛⠉⠛⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣱⠿⣿⣿⣿⡿⠁⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⣹⠏⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠖⠋⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠢⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⢺⠁⠀⠈⠉⠀⢐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⡶⠋⠀⣐⠀⢠⢔⣀⣀⣤⢼⡇⠾⠨⠀⡄⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠝⠁⢠⡟⠓⡿⠀⠀⠛⠀⠀⣿⣺⡇⣤⠤⢠⡄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⠐⠢⠌⠉⢘⠲⢤⣭⠐⠆⠀⠀⠀⣇⠀⠈⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠔⠠⠀⡠⠔⢺⠀⠀⠂⠀⠉⢽⡏⠁⠀⡶⠶⡴⡽⠄⣀⣴⣧⠄⠧⠅⠠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡇⠀⠐⢰⠀⢀⡀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⢼⢯⢿⡆⠈⠁⢰⢒⠒
⠀⠀⠀⠀⠀⠀⡋⠘⠲⠚⠂⠂⠒⠚⠀⡋⣓⠐⠒⢶⣖⠒⠒⠲⡀⢤⠤⠀⠼⠗⠚⣇⣀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠓⡀⢤⢺⢠⣠⢸⠀⠀⠀⠀⡇⠀⠒⠀⠀⠀⡀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠏⠈⢀⠀⠀⠀⠀⠤⠀⢨⠤⠤⠤⠼⠦⠀⠠⠄⠧⠀⠀⠀⠐⠠⠁⠱⠦⠀⠸⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠟⣀⢊⣥⠦⠮⡾⡬⡤⢟⠛⠛⠛⡛⠛⠛⠛⢻⣷⠶⠿⡓⠔⣖⠶⠶⣶⡶⢒⣒⣒⢇
⠀⠀⠀⠀⠀⠀⠲⣋⠜⠁⠀⡀⢨⠯⠿⠿⠄⠀⠀⠀⠀⠀⠴⠿⠃⠄⡄⢨⠶⠁⢀⡄⢨⠿⠷⠷⠽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠠⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠀⠂⠐⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⢠⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢐⠒⠒⠛⢿⣛⣛⣛⣛⣛⣛⣛⣛⡛⣛⡟⠛⠒⠒⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⠄⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣿⠀⠀⠀⣴⣧⣈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⢀⡜⠀⢉⠏
⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⣿⢠⠎⠀⣠⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⡰⠃
⠀⠀⠀⠀⠀⠀⣿⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⡞
⠀⠀⠀⠀⠀⠀⣿⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣞⡀⣠⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠝⠁⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⢰⣶⣶⣦⠀⢰⣦⣰⣦⠀⠀⣦⠀⠰⣶⣄⣶⡄⠀⢶⣴⠖
⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢁⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⢻⣿⠀⠀⣿⠀⠀⣿⠙⣿⡇⠀⢸⡟⢷
⠀⠀⠘⡰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣰⠞⠛⠀⢶⡆⠀⠀⡠⠒⠒⠦
⠀⠀⠀⠑⠄⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⡰⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠛⠃⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⡄⠀⢠⠀⠀⠀⡀⢠⠀⠀⡄⠀⢀⠄⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⠈⠁
⠀⠉⠀⠴⠄⠉⡄⠀⢰⠀⠙⠀⠀⠸⠀⠀⡇⠀⢺⠀⠉⠶⠂⢸⠀⠀⡇⠀⠸⡇⠀⢸⠀⠏⠉⠀⡇⠈⠹⠖⠸⡀⠀⠳⠆⠀⠀⠠⠘⠃
⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⡈⠀⢸⠀⠀⡇⠀⢀⠙⢢⡈⠀⢸⠀⠀⡇⠀⡆⠀⠀⢸⠀⠤⠆⠀⡈⠓⣄⠀⠀⠉⠲⡄⠀⠀⢠⡄⠀⡀⣠
⢀⡄⠀⠀⠀⠂⠀⠀⢸⣀⣈⡠⠀⢨⣀⣈⣁⠄⠹⣀⣈⣠⠀⢸⣀⠀⢁⡀⠹⣀⡀⢸⣀⣀⣀⠈⢇⣀⣁⡠⠘⣄⣈⣁⡄⠀⠀⠁⠀⠀⠉
⠀⣷⡶⠄⠀⢀⡀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣱⠀⣿
⠀⡇⠀⠀⠀⠀⠉⠄⠀⠉⠈⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠂⠀⠈⠀⠀⠂⠠⠀⠀⠠⠀⠀⠞⠁⠀⠿
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣅⡠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠈⠀⠀⠈⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠰⠶⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⢁⠄⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠃⠀⢸⠃⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠉⠀⠈⠡⠀⠀⠀⠀⡃⢠⠀⡆⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⢀
⠀⠀⠱⠖⣂⢖⡂⡎⠀⠀⠀⢀⣀⠀⠀⠀⢠⡀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠠⠄⠀⠘⠀⠁⠀⡈⠁⠀⠉⠁⠀⣶⣶⣶⣶⠖⠀⠈⠀⠀⠀⢀
⠀⠀⢒⣚⣒⠳⠞⠃⠀⠀⠀⠘⣟⠀⢀⡀⢸⡇⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡀⢰⠆⠂⠀⠀⢻⣿⠟⠁⠀⢀⠄
⠀⠀⠌⠀⠀⠀⠀⠂⠀⠀⠀⠀⠿⠀⠷⠄⠘⠇⠻⠾⠙⠥⠴⠿⠀⠨⠨⠅⠸⠀⠄⠀⠀⠠⠤⠸⠄⠄⠀⠀⠀⠁⠂
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠖⢋⢝⠛⠓⣲⢦⠒⠻⣤⠀⢹⡮⠖⠣⣹⠖⠚⠦⠠⠖⢊⢌⡿⠐⠲⠾⣕⣭⠀⠩⣕⠸⣀⡿⠀⠀⠠⢮⡁
⠰⡈⡍⠳⢶⠞⢻⠛⣃⡀⠈⡇⢸⡃⠀⠀⠱⢾⠬⣉⡉⣉⣡⣾⠤⠒⠒⣦⠈⢻⠇⣴⣨⠵⠹⡄⠄⡙⠓⣎
⠀⠈⠀⠀⣺⠿⠷⢤⠋⠛⠂⣠⣿⠛⠲⠎⣷⣯⠦⠦⠈⠁⡩⠐⠘⣿⢣⡽⠀⣼⣨⠾⠡⡉⢲⡉⠀⣌⡹⠂
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠀⠀⠁⠒⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠊⠀⠀⠀⠈⠉⠐⠋⠒⠁
⠀⠀⢸⠀⠀⠴⠦⠴⠦⠴⠶⠆⠀⢈⠀⡇⠀⠐⠠⠴⠤⠤⠴⠰⠀⠀⠁⢸⠀⠤⠦⠦⠶⠦⠤⠤⠖⠆⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⠐⠒⠲⠶⠶⠲⠲⠲⠀⢘⠀⡇⠀⠀⠖⠶⠲⠶⠲⠂⠀⠀⠁⢸⠀⠰⠴⠒⠲⠶⠰⠶⠲⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠀⠘⠙⠉⠉⠙⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠂⠐⠒⠒⠒⠒⠀⠀⠀⠀⠘⠀⠂⠀⠂⠒⠒⠒⠂⠀⠐⠀⠀⠃⠀⠒⠐⠒⠒⠒⠂⠀⠀⠂⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡿⢧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀⠀⣀⣩⣽⣄⡀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣿⡇⠹⣷⠃⢸⣿⢏⡁⢠⣴⣿⣿⣍⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⢛⣭⣍⢩⣙⣿⣏⣺⣧⣼⣿⣄⣹⣿⡿⠓⣻⠿⠉⠋⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠈⣻⣵⣿⡏⢈⣻⣿⣿⣿⠟⣿⢛⣋⣽⣯⣤⣿⢯⣽⡿⠁⢀⠀⢠⡠⣞⣷⡀
⠀⠀⠀⠀⠰⡾⡿⠟⣿⣿⣿⠸⢿⣿⣿⠛⢻⠋⠉⢈⣁⠟⣉⠋⠈⠋⡀⠀⡀⢰⣧⣽⣌⡏⡇
⠀⠀⠀⠀⠀⠆⠓⢲⠏⣿⣿⣠⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡄⢄⢳⣼⢿⢿⣿⣇⡄
⠀⠀⠀⠀⠀⠄⠐⢺⡆⣿⡿⡿⠷⠢⠀⣿⣿⣿⣿⣟⣉⠙⣿⡏⡿⢿⣿⣮⡳⠬⡿⠿⣻⠏⡖
⠀⠀⠀⠀⠀⣀⠀⢸⣀⣿⣿⣿⣿⣿⣿⣟⣛⣿⢟⣛⡷⠲⣾⠿⠿⠌⠿⠿⠿⠿⠿⠿⠿⠯⠳⠿⠯
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⠟⠀⢂⡞⣿⡇⢀⣸⣿⣀⡄⠀⢸⣿⣿⣷⣶⠄⣰⣿⣂⡀
⠀⠀⠀⠀⠀⢈⣈⣉⣿⣿⣿⠿⣿⣿⣿⣿⣼⣶⣾⣿⣶⣿⣷⣿⣿⣿⠿⡟⠏⣶⣶⢰⢿⣿⣿⣿⣾⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠙⠛⠿⠿⠷⠽⣿⣿⣻⣿⣿⣿⣿⣿⣟⢤⢷⣿⠸⠿⡟⡟⢿⣿⣷⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠉⠙⠿⠟⠻⡿⠿⢶⠾⡿⢶⣶⡾⣾⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣀⣀⣀⣘⣆⣀⣀
⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋

⠀⠀⠠⠄⠀⠀⠐⢀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠁⣀⡀⠈⠀⠀⠀⢸⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠉⠔⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠠⣀⠀⠀⠀⠀⢀⣀⠀⠈⠡⠐⡭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⣀⠀⠀⠰⠚⡁⠐⣀⠄⢀⡄⠂⣧⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠋⡁⠐⠈⠆⠈⠤⠊⡁⠀⣁⠔⠊⠀⠀⠀⠙⠂⠐⠳
⠀⠀⠀⠀⠀⠀⢂⡀⠀⢙⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⣴⡆
⠀⠀⠀⠀⠀⠀⢈⡥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠄⠁⢉⠤
⠀⠀⠀⠀⣀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠤⠐⠁⡠⠖⠀⢀⡀
⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⢀⡠⠔⠈⠀⠔⠈⢀⡠⠖⢵⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⢀⠴⡊⠁⡀⠂⠀⣀⠔⠊⢁⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠛⠁⡀⠛⢡⣀⠠⠚⢃⡠⠒⣥⣤⣤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡀⠀⠀⠒⠁⣄⠀⠁⠀⡠⠚⠁⣠⠔⠉⠀⠀⠀⠀⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉⠐⠈⢀⠠⠈⠁⢀⠔⠈⢀⠐⡨⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠠⠐⠁⢀⠠⠚⢃⡠⠊⠁⢀⠁⠀⠀⠀⠀⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠄⣵⣤⠐⠁⠀⠀⣈⣀⠃⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠈⠀⠛

⠀⠑⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠐⢶⣿⣦⣀⠈⠻⣿⣷⡄⠀⠰⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠿⣿⣷⣤⠀⠈⣻⣿⡷⠀⢈⣿⣿⡦⠀⠙⣿⣧⠀⠘⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⣿⣶⠄⠀⣼⣿⠃⢀⣼⡿⠋⠀⣴⣿⠟⠉⢀⣤⣶⣿⠿⠃⠀⢹⣿⡆⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⠀⢀⣿⡟⠀⡸⠟⠳⠶⣾⣤⡈⠙⢿⣦⡀⠙⢿⣯⠉⢫⣤⡠⣴⣾⣿⠿⠟⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⠀⢸⠟⠑⠛⠿⣷⣶⠀⢨⣿⠏⢀⣴⡿⠋⣀⣼⡿⠇⠀⢻⣷⠀⢱⣤⢠⣤⣴⣶⣿⣧⠀⢸⣦
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⡆⠀⣿⠗⠾⠿⠿⣿⡆⢀⣿⣇⣠⡛⠓⢶⣮⡉⠲⣾⡙⢫⣤⠴⢾⠟⠛⠁⣈⣿⡆⠉⣍⠉⠉⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠸⣿⡇⣠⣷⣶⣶⡆⢰⣿⢥⣾⣥⣄⠉⣿⡗⢠⣿⠋⣠⡾⠟⣀⣽⡧⠈⣿⡞⢻⡛⠛⠁⠀⣿⡏⠻⡿⢿⣿⣿⠀⢠⣦
⠀⠀⠀⣤⣴⣶⣿⡆⠀⠿⢃⣀⣀⠀⣿⡇⣼⣷⣦⠄⣸⣏⣰⡛⠲⢯⡌⠻⣧⠘⣾⡉⢧⡴⠶⠿⠃⠈⣿⠘⠿⠿⠿⠇⢸⣷⣀⣀⡀⠀⣸⣿⠇
⠀⠀⠼⠛⠋⠉⢿⣿⡠⠿⠟⢻⣿⢀⣭⣤⣤⠀⡿⠠⠷⣦⠈⣿⣁⠞⢥⡚⢥⡾⢏⡡⡾⠗⢘⣗⢻⡛⠛⠀⣿⡶⣶⣦⣼⣿⠈⡻⠿⣿⣿⡟⠀⢠
⠀⠀⣀⣤⣶⡄⠈⢟⣠⣤⣦⠀⢿⣉⣁⠀⣿⠴⠷⣶⢀⣟⠺⣶⢉⣟⡰⢏⡼⣋⢼⢃⣹⡏⣏⢩⣼⡏⢹⠛⠻⠁⣼⣌⡉⠁⢠⣿⢄⣀⠈⠀⢠⣿⡆
⢀⣿⡿⠛⢿⣿⣄⠿⠛⠉⢿⡦⠟⠛⢻⡇⠶⠺⣇⣩⣭⠹⠇⢯⡙⢆⡿⣴⢣⢞⡼⢇⣷⢲⣛⣸⡦⣤⣼⠏⡷⢶⡿⢈⡿⠿⣿⡟⢈⡿⣿⣶⣿⡟⠁
⠈⠁⢀⣄⠀⠻⣇⣤⣶⣆⠈⣧⡶⣷⣈⡷⢾⣆⡷⢶⣸⣭⢹⡺⣍⡳⡗⣿⣮⣞⢽⣫⢖⣞⣩⢭⣴⡗⣤⣴⡗⣦⣤⣼⠗⣤⣀⢀⣼⣧⡀⠉⠛⠀⣠
⣠⣶⣿⣿⣧⡀⡿⠋⠉⢻⡷⢁⣤⡘⢧⣴⣆⡱⠶⡬⠶⢮⡳⡽⡷⣟⣾⣯⣿⣻⣽⣫⢏⠼⡡⠞⡦⣴⢣⣌⣰⢧⣉⠋⣠⡏⠻⣿⠟⠀⣿⣶⣄⣴⣿
⡿⠛⠁⠈⠻⣿⢀⣴⣷⣄⢹⠟⠙⢷⢉⣤⡙⡷⠷⣜⣙⡮⣝⣿⣽⣿⣿⣿⣿⣿⣿⢗⣽⣯⣽⡛⡱⢦⠞⣌⢉⣬⠛⢿⠟⢱⣦⡀⣠⣾⠀⠙⢿⡿⠋
⠁⢠⣾⣷⣄⠀⡿⠋⠈⠻⢇⣴⣷⣤⡛⣁⡙⣴⠳⢏⣬⣞⣻⣟⣷⣿⣿⣿⣿⣿⣿⣟⣿⣝⡺⣍⡝⢶⢾⡌⠛⣁⢷⣄⣴⡇⠙⢿⠟⠁⣿⣦⡀⢀⣤
⣴⣿⠟⠙⠿⣷⠁⣴⣷⣦⣸⠋⣠⣈⢳⠏⡙⢣⠟⠺⡴⢪⡞⣹⣻⣞⡯⣿⣿⣿⣟⢾⣞⢮⡹⢶⡚⠶⢎⠹⠞⢳⡌⠛⣁⢼⣧⣀⣠⣾⠈⢻⣿⣿⠿
⠸⠋⠀⣤⣀⠈⢹⡿⠁⠉⠛⢴⡟⠙⠻⢴⠟⠛⢼⢟⣓⣋⡭⠵⣪⢗⡯⡻⣿⢾⢯⣙⡬⣇⣛⡏⠷⢾⠹⡷⢾⡈⢿⠾⢻⡄⠹⠿⠛⢹⣦⠀⠙⠁⢀
⠀⢀⣾⣿⠿⣿⣾⡁⣼⣿⣶⣾⡁⣾⠷⢾⣠⡟⠛⠺⡏⣭⠧⢿⣱⡟⡵⢳⠝⣾⢹⣌⣳⢸⣇⣛⣛⢹⡦⠶⢺⣧⣠⣴⠺⣷⣀⣤⣶⠙⣿⣧⣤⣾⣿
⠀⢸⣿⠃⠀⡀⠉⠑⣿⠃⢀⣈⡙⡿⢀⣦⣤⣅⣸⡟⣋⣻⡘⣏⢡⡗⣩⡞⣱⠎⣽⡁⠿⡬⣽⠁⠿⢶⠆⣿⠀⢉⣉⣷⠀⠻⠛⠋⣵⡀⠘⠿⠛⠉
⠀⠀⠃⠀⣼⣿⣿⣶⣮⡀⣿⡟⠛⠿⠼⣿⠀⣤⣬⣧⢽⡅⢴⡾⢋⣱⡾⢓⡬⢓⡶⢉⣿⡀⠛⢶⠒⣾⠀⠛⠛⣛⠁⣿⣧⣴⣶⠊⣿⣷⣀⣠⣤⡖
⠀⠀⠀⢰⣿⡏⠀⠈⠉⠉⢿⡇⢰⣶⣶⣾⡄⣿⡀⢠⣶⠶⠞⢓⣈⡿⡄⢻⣦⣘⣳⠦⣭⠏⢹⡏⠐⠻⢿⡟⢹⣿⠀⠈⠉⢡⣷⠀⠸⣿⠿⠟⠛
⠀⠀⠀⠀⠻⠃⠀⣿⣿⣷⣾⣦⣸⣿⠀⢀⣤⣬⣧⡜⣷⡀⢺⣟⠉⣴⡾⠋⣠⣿⠃⢼⣿⣀⡙⢛⡿⢓⣿⠇⠸⠿⠿⢿⠋⢸⣿⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣀⣀⣙⣀⠸⣿⡉⢀⣤⣴⡷⠖⠛⣢⣌⡿⠦⣈⣻⠷⢤⣬⠋⢹⣿⠁⠸⣿⣶⣶⡶⢴⣿⠀⠸⡿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⢻⣿⠿⠟⠛⠋⠛⢇⠀⢿⣧⠀⢰⣾⡟⠉⣠⣾⠟⠁⣰⣿⡃⠀⠿⢿⣶⣤⢄⣴⡇⠀⣿⣿⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣴⣶⣿⡿⠟⠊⠛⣣⣀⣻⣷⣄⠈⠻⣷⣄⠈⠛⡿⠶⢦⣴⡎⠀⣼⣿⠁⠀⠛⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⣿⣇⠀⢠⣶⣿⠿⠛⠁⣀⣴⣿⠟⠁⣠⣾⡿⠁⢠⣿⡟⠀⠐⠿⣿⣷⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡄⠀⢻⣿⣄⠀⠺⣿⣿⡁⠀⢾⣿⣯⡀⠀⠛⢿⣿⣶⣤⣀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠦⠀⠘⢿⣿⣆⡀⠉⠻⢿⠷⠄⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠐⠢⡀
⢂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠁⠀⢠⠂⠐⠀⠀⠐⠀⡀⢀
⠀⣤⣶⣦⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠻⠛⠉⣻⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢁⠀⠰⣻⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢂⠀⠈⢿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠄⠀⢪⣿⣄⠀⠀⢸⠀⠀⣾⠟⠛⠛⠛⠛⣿⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⡇
⠀⠀⠀⠀⠘⡄⠀⠋⠉⠀⠀⢸⠀⠀⣿⠀⠀⣠⡞⠁⣿⠀⢈⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠰⡀⠈⢄⠀⠀⢸⠀⠀⣿⠀⠻⠋⠀⠀⣿⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠱⠀⠘⡀⠀⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠡⢸⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢻⠀⠀⣿⠀⠀⠀⣠⠀⣿⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠂⠀⣿⠀⣦⡾⠁⠀⣿⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⢿⡶⢤⣶⣶⣶⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠲⠈⢷⣶⣶⣶⣶⣶⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⣤⠀⢀⡴⠀⣿⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡟⢶⠟⠁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠷⡶⣶⠶⢶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀
⣿⣿⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣟⣁⠀⠀⠀⠀⢈⣛⣿⣟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣿⡆⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣛⣱⣿⢿⣿⣿⣿⣿⢿⣷⣸⣿⢿⣿⣿⣿⣿⢻⣷⣙⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⠘⣿⣿⡟⢸⣿⣿⣿⣿⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⢰⣿⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⠛⢡⣿⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠈⢹⣿⡟⣿⣿⠉⠀⠀⠀⢸⣿⡇⣿⣿⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⢸⣿⡇⣿⣿⠀⠀⠀⠀⢸⣿⡇⣿⣿⠀⠈⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠀⠀⠸⠿⠇⠿⠿⠀⠀⠀⠀⠸⠿⠇⠿⠿⠀⠀⠿⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠶⠶⠶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⠤⣄⣠⢠⠄⡤⠤⣤⠀⡄⢀⣠⡄⢠⠄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠂⠉⠘⠘⠂⠓⠈⠋⠀⠛⠚⠁⠛⠘⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡔⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠹⣿⡿⠃⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣆⠀⠙⠁⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠉

⣶⡶⢶⢶⢶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⡶⣶⣶⣶⢶⣶⣶

⠀⠀⢤⡤⣫⣿⣗⣚⣩⠾⣿⢿⣹⣁⣸⣾⠠⢄⡏⢍⢳⠀⣄⢤⣏⡁⢨⠙⣳⣭⣶⣍⢰⡞⠃⠀⠈⣠⡴⢖⣒⡲⢤⡈⠈⠳⢰⠈⢦⠆⣰⡀⠈⢙⠚⡒
⢠⡮⠒⢀⣦⡉⠿⣻⠺⢿⣏⣡⣷⢒⢦⡘⣿⣱⠷⠃⠼⠧⡐⠀⣀⣭⠀⢦⢇⢹⠁⣌⡾⠁⣀⣤⢾⣡⢌⢕⡩⣾⢢⣳⢸⡀⠠⠀⠂⠀⡼⢋⠋⣡⠀⠈
⠘⠖⢒⠯⣋⠉⠲⣆⠘⢷⠼⡟⣡⠯⣞⣩⢅⢸⡛⠓⡮⠕⠀⠟⢏⢼⣶⠤⣹⣿⣷⠛⠙⠻⢉⡠⢞⡥⣺⣋⠀⠿⣴⠞⣸⠁⡐⡠⠀⡀⠁⠸⠄⠀⢈⡫
⠀⠀⣀⠃⢤⡭⣉⡮⢴⠝⣳⠰⠪⡵⢏⠃⢾⠠⡓⠐⡂⠔⣱⠗⢮⡟⡘⢓⣫⣿⣯⡽⡿⠟⡿⠌⠻⢆⢻⣤⠁⣈⣀⠈⣠⣁⠠⠀⠈⡦⠼⠤⠠⢞⠉
⠀⠀⠈⠀⠞⠀⠸⠋⠀⠀⠘⢯⣤⣄⣼⠠⡴⢙⠄⡠⣃⠄⠘⠲⠛⠉⠉⠿⣬⡤⠿⠲⠟⠥⠚⠁⠈⠢⠥⠤⠐⠻⠟⠐⠻⠊⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⢰⠶⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡶⠶⢰⠴⠦⡶⠲⠀⠀⠀⠀⠀⠀⠰⡴⠶⠶⠶⠶⠲⠆⡦⠶⠴⠖⠆










⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⣀⣀⢀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⢀⣀⣀⢠⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠈⠉⠉⠉⠉⠁⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣤⣠⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣦⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣤⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⠁⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣄⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⠋⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣄⠀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⠋⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣴⠒⠦⠀⠀⢀⣀⡀⠀⠀⠀⣤⣶⣶⣶⠀⠀⢰⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⣿⠀⠀⢾⣿⡟⠉⣡⠀⠀⠈⡅⠀⠀⠀⠐⠛⢷⡄⠀⠀⠁⠀⠛⢻⣷
⠀⠀⠀⣾⣿⣿⠀⣷⡆⢀⣴⠀⣿⠆⠀⢰⡾⠏⠰⣷⠀⠰⣶⣄⣱⡆⠀⢠⣤⠘⣷⠄⠀⠀⠀⣀⠰⠋
⠀⠀⣰⣿⣿⣿⡆⢸⣿⢸⠀⠀⣿⠀⠈⠀⠀⠀⠀⠈⠇⢸⣿⣿⣿⡇⠀⡜⠀⠀⠀⠈⠀⠀⠠⠈⠀⠈⡂
⠀⠐⠿⢿⣿⣿⠇⣸⣿⢸⠀⠀⠙⠁⡀⠆⠀⠀⠀⠠⡌⣿⣿⣿⣿⡿⠤⣷⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠸⣿⣿⠀⣿⣿⣤⣤⢀⠀⠀⠧⠇⠀⠀⠀⠀⠇⢻⣿⣿⡿⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠁⠀⠀⣟⠀⠉⠈⢣⣜⣧⡞⠁⠀⠀⠘⠀⠐⠀⠀⠾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⢀
⠀⠀⠀⠀⠀⠀⡇⠔⠀⠘⠆⠀⠘⠛⠟⠃⠀⢀⠀⠀⢠⡦⡀⣤⣦⣔⣿⢠⡀⣀⢤⡄⠀⠀⣸⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⢤⢸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠻⠀⠃⠈⠀⠀⠀⠀⠀⢠⣿⡿⠛⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠠⡄⢀⣀⡀⡀⠀⠀⠈⠁⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⡅⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠐⠚⠈⠀⠀⠋⡓
⠀⠀⠀⠀⠻⠆⠻⠾⠇⠷⠰⠗⠰⠇⠀⠀⠷⠀⠷⠀⠀⠸⠦⠘⠶⠧⠀⠀⠰⠃⠼⠂⠐⠛⠀⠀⠀⠀⠠⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣶⣶⣶⣾⣥⣽⣶⣶⣶⡆⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠙⠉⠙⠙⠀⠈⠛⠿⠿⠿⠿⠿⠟⠋⠀⠘⠉⠛⠉⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣷⣶⠟⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢿⡿⠋⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠟⠁⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣶⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠰⡆⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣦⢸⣿⡟⠛⠛⠈⠁⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣿⣧⠀⠀⠐⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃