⢀⢀⡴⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⡤⠞⠉⢳⠀⠀⠀⠀
⢀⡇⠘⠋⠓⣆⠀⠀⠀⣀⣠⠞⠀⢀⣴⣫⠶⠚⠛⣷
⣿⠀⠒⠘⣠⡾⢀⡴⠋⠉⠀⠀⠀⠉⠋⠁⢀⣠⠶⠃
⠈⠙⣏⣿⢧⢿⡏⠀⠀⢠⠄⠀⠀⠀⠀⠀⢻⡀⠀⠀
⠀⠀⠉⠘⣟⣾⡄⠀⠀⠀⠈⠓⠘⠃⣀⠀⢈⡇
⠀⠀⠀⠀⢿⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢙⡆⠀⠀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋

⢀⢀⡴⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⡤⠞⠉⢳⠀⠀⠀⠀
⢀⡇⠘⠋⠓⣆⠀⠀⠀⣀⣠⠞⠀⢀⣴⣫⠶⠚⠛⣷
⣿⠀⠒⠘⣠⡾⢀⡴⠋⠉⠀⠀⠀⠉⠋⠁⢀⣠⠶⠃
⠈⠙⣏⣿⢧⢿⡏⠀⠀⢠⠄⠀⠀⠀⠀⠀⢻⡀⠀⠀
⠀⠀⠉⠘⣟⣾⡄⠀⠀⠀⠈⠓⠘⠃⣀⠀⢈⡇
⠀⠀⠀⠀⢿⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢙⡆⠀⠀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋

⣿⣿⣿⠿⢛⠉⢉⡙⠿⣿⠿⠿⠿⣿⣿⡿⠟⢛⠛⡛⠻⢿⣿
⣿⣿⠋⡴⢛⠛⢂⣥⣴⣶⣶⣶⣶⣶⣆⣰⢋⣴⡶⠟⠳⣄⢻
⣿⣿⡀⠇⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣿⡷⢸⣿
⣿⣿⠃⠜⣛⠻⣿⣿⣿⣿⡿⢟⠻⢿⣿⣿⣿⣿⡗⠠⠴⢊⣼
⢋⣴⠾⡀⠁⢀⣿⢛⣿⣿⡅⠙⠁⢸⣿⣿⣿⣿⣿⣿⠈⣿⣿
⢸⣿⣷⣾⣿⣿⣬⣤⣥⣿⣿⣷⣾⣤⣾⣿⣿⣿⣿⣿⡀⢿⣿
⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿
⣿⣶⣌⠛⣿⣿⣿⠛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸
⣿⣿⡇⣼⣿⣍⣛🤍⠿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⡿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⠇⡘
⣿⡀⢷⡈⠻⣿⣿⣿⣿⣿⡇⢴⣦⣹⣿⣿⣿⣿⣿⠟⢃⣈⣡
⣿⣿⣶⣤⣤⣄⣉⣉⣛⣛⣓⣀⣙⣛⣛⣛⣋⣩⣤⣾⣿⣿⣿

.⠀⠀⢠⡶⢦⡀ ⠀⠀⠀⢀⣴⠖⣦
⠀⠀⠀⡿⢀⠀⢳⡀⠀⢀⡾⢁⢤⠘⡇
⠀⠀⢸⡇⡇⢣⢸⡧⠶⢼⠃⡜⢸⠀⡇⠀
⠀⠀⢸⡀⢃⠞⠀⠀⠀⠀⠀⠉⠁⠀⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⡀
⠀⠀⣾⠁⠀⣤⡀⠀⢀⠀⢰⣿⠀⠀⡲⣿⡖⠂⠀⠀⠀
⢒⣲⣟⠀⠀⠉⠁⠀⠈⠈⠀⠀⠀⠀⣀⡿⢁⣤⠖⢲⡆
⠀⠈⠳⣤⣄⣀⣀⠀⠀⠀⠀⠀⠰⣾⠋⠀⡜⠁⠐⢸⠃
⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠙⡇⠀⡇⠀⠀⡏
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⡇
⠀⠀⠀⡼⠁⢀⠀⠀⠀⠠⢀⠀⠀⠀⠜⣷⠇⠀⠀⡇
⠀⠀⣴⠃⠀⢺⠀⠀⠀⠀⠈⠀⠀⠀⠐⠠⠂⠑⢰⠇
⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⡆⠀⠀⡆⠀⠃⣠⠟⠀⠀
⠀⠀⠈⢦⡀⠀⢰⠀⠀⢠⠀⡇⠀⠀⠁⠀⣿⠁
⠀⠀⠀⠀⠈⠛⠢⢷⣤⡬⠤⢧⣠⡼⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⣴⠟⠛⠓⠶⣤⠴⠶⢶⡿⠁⣶⣽⣯⠉⠁⠹⡆⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡁⢼⣿⡏⠙⠻⣾⡛⢿⣆⠀⠀
⠀⠀⠀⣻⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠷⣤⣼⣯⠟⣸⡟⠀⠀
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⢙⣆⣀⠀
⢠⡶⢾⡶⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠚⢩⡏⠉⠁
⠀⢀⣼⣷⠒⠀⠈⠋⠀⠀⠀⢶⡲⠀⠀⠀⠛⠁⠀⡈⣹⠛⠛⠀
⠀⠀⢠⡼⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠷⠆⠀
⠀⠀⠈⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀

⢀⢀⡴⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⡤⠞⠉⢳⠀⠀⠀⠀
⢀⡇⠘⠋⠓⣆⠀⠀⠀⣀⣠⠞⠀⢀⣴⣫⠶⠚⠛⣷
⣿⠀⠒⠘⣠⡾⢀⡴⠋⠉⠀⠀⠀⠉⠋⠁⢀⣠⠶⠃
⠈⠙⣏⣿⢧⢿⡏⠀⠀⢠⠄⠀⠀⠀⠀⠀⢻⡀⠀⠀
⠀⠀⠉⠘⣟⣾⡄⠀⠀⠀⠈⠓⠘⠃⣀⠀⢈⡇
⠀⠀⠀⠀⢿⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢙⡆⠀⠀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋