Worry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠛⠉⠉⠉⠙⠓⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣰⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣀⠀⠹⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⠀⡾⠙⡆⠐⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣠⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠏⠀⠙⠚⠃⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⢷⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢠⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⣧⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢰⡋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠛⠛⠛⠛⠓⠒⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈


⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠇⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⢸⡃⠉⡆⢸⠈⢹⠉⢀⢳⡀⢸⣉⡇⢸⠀⠀⣏⡉⠀⠐⢏⡁⠈⢻⠁⣿⢉⡇⡔⠉⠙⡆⣥⡜⠁⣏⣉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣀⣘⣅⣠⣃⣸⣀⣸⣀⣏⣈⣃⣸⣠⣇⣸⣤⣀⣧⣀⣀⣀⣀⣝⣀⣸⣀⣿⣈⣇⣱⣄⣴⣃⣇⣙⣄⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠠⢴⡦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣶⠦
⠀⠀⠀⠀⠀⠈⠈⠁⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⠿⠟⠻⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠈⡛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠐⠀⠀⠀⠘⠈⠂⠀⠀⠀⠀⠀⠀⠰⠁⠁⠐⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠚⠿⠷⢀⠀⠀⢀⣴⡇⠁⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠄⡀⠀⢀⠐
⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠈⠁⠀⠀⠀⠂⠄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠠⡀⠀⠀⢸⠛⠀⠀⢠⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣠⢋⣤⣤⠶⠞⡍⡁⠀⢀⠤⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢲⣿⣽⣋⡵⠛⣳⣶⢿⠓⣶⢣⢤⣞⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠚⡿⣠⣿⡾⠛⠃⣤⡞⣠⠟⣾⡜⡱⢰⣿⡏⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣲⢦⣾⣿⣅⡤⡾⠛⠋⢁⣤⣿⢰⡇⣼⠈⣄⠘⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣹⣯⢡⣿⠿⢯⣈⣿⣗⠶⣤⣞⡻⡞⠀⡆⣻⣴⠻⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠫⣷⣾⡿⠚⠉⣿⠛⣯⣶⡤⢾⣿⢻⣌⡙⢯⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⣸⢷⣆⠀⣰⢃⡽⢷⡜⣻⣿⣥⣬⡧⠿⢾⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡽⣿⠛⣿⡿⡿⣾⠶⣞⡟⡻⣝⣍⣳⣷⣶⣏⣈⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣟⠾⡇⢽⣿⣦⡿⠛⣾⡟⢻⠾⣿⣿⣿⣀⠀⠘⣯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⢺⡛⢳⡀⡰⢃⡤⠞⢲⣿⡿⠿⡿⣿⢾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⣌⣲⢿⡦⣈⢷⡶⣻⣿⠥⡶⠶⠚⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢤⣉⣳⣦⣟⣻⣿⣯⣏⣀⣀⣠⡾⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢘⣇⣉⠠⠤⣀⣻⣯⣿⠶⠶⠯⠥⠖⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠛⢻⣟⣷⣶⢿⢻⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⣤⣤⣶⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣀⣠⣄⣄⡴⠖⠲⠄⠀⠀⢀⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⣖⣞⣡⣼⣿⣿⣿⣷⣿⣿⣿⢶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣯⣿⣟⣙⣿⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡍⣹⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾
⡿⠟⠿⠿⠟⠛⠛⠒⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⠀⢀⣠⣽⣿⠻
⣦⣤⣤⣤⣀⣤⣤⢤⣂⠾⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠓⠀⠀⣴⣿⣿⣿⣿⣿⣿⣾
⣛⣛⣛⣟⣛⣛⣛⣛⣃⣒⣓⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣓⣒⣒⣒⣾⣿⣛⣛⣛⣛⣋⣉⣉
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣤⡴⠲⣆⠀⠀⠈⣧
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠻⠿⣿⣿⣿⡿⠟⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⡿⠁⠀⠈⢧⡀⠀⠘⣇
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⣠⡟⠀⠀⠀⠀⠈⢷⡀⠀⢻⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣷⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⣰⠇⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠟⠀⠙⠳⠦⣤⠴⠞⠁⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢋⣝⣛⡒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢿⣃⢀⣾⡿⠋⠉⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⣿⣿⢫⣍⡀⠀⠉⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠟⠁⠁⠀⢹⣿⣶⠋⣟⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠉⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡀⠈⠙⠇⠑⠶⢄⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣠⡖⠂⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠑⠀⠈⠙⠒⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣉⠀⠤⠀⢀⠄⠀⠀⡀⠀⠀⠀⠀⡄⡰⠋⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣞⣠⠔⣿⡦⠀⠘⠁⠀⠀⠀⠀⢀⠃⣀⠀⠀⠠⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡏⢹⡄⠀⢀⡀⠀⢀⠀⢰⣌⠺⠕⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣇⠀⣾⠁⢀⡌⠀⡼⢋⠄⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡖⠂⠴⠀⢠⠀⠨⠳⠦⣝⣿⣿⣿⣿⠿⣿⣿⣿⡈⣿⣸⡏⢀⡞⢠⡾⠒⠁⠀⠀⠀⠀⠀⠀⣠⢐⠜⡇
⠀⠀⠀⠀⠠⠚⡄⠛⠀⠀⠁⠀⠀⠸⡄⠘⣿⣿⡟⠋⠀⢿⣿⣿⡇⣿⣿⡇⣼⣴⠯⠐⠀⠀⠀⠀⠀⠀⠀⡴⡤⠀⠀⣿
⠀⠀⠀⠀⠶⣄⠹⠖⠀⠀⠀⠀⠀⠀⣹⠋⡙⠙⠀⠀⠤⠬⠿⠿⠷⢿⡿⠒⢻⣐⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠛⣓⠂⡀⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠋⠒⠒⠲⢼⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⢤⣤⣀⣀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠶⠬⠿⠶⠦⠤⠤⠞⠁

⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢫⢿⣬⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣻⡻⣿⡇⣿⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣾⣿⣿⣿⡿⠟⠁⠀⠈⠉⠹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠁⠈⠁⠀⠀⠈⠁⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠀⠀⢀⡀⠀⠀⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠄⠄⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⢠⡄⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣿⣿⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⢴⣾⣿⣯⣭⣶⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⠉⠉⠉⠁⣀⣀⡀⠀⠀⡤⠖⠓⢶⣿⣾⡇⠞⢫⣿⣿⣿⡿⢟⣛⣲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠈⣠⣾⣿⣷⣮⣿⠇⠀⠘⠛⢡⣿⣿⣯⡭⣍⡗
⠀⠀⠀⠀⠀⠀⠀⣾⣡⡤⠖⠚⢻⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠃
⠀⠀⠀⠀⠀⢀⡴⠻⣅⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢰⡏⠘⣿⣿⣟⡛⠂⠀⠀⢀⣀⣀⠀⠀⠀⢸⡆⠀⠀⠐⠢⢄⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠈⠂⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠸⣇⡀⡙⠿⣿⡯⠀⠀⠰⠟⠉⠁⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⢈⠑⠦⣄
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣷⣶⣿⣄⣦⣁⣀⡀⠀⠀⠀⢀⡄⠀⠀⡤⠀⡤⢿⠤⠤⠴⠖⠚⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠀⠀⠘⠃⠀⠀⡇⠘⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⢖⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠐⠁⠀⣀⣀⣀⣀⣀⡈⠑⠊⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠛⢡⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠤⠦⠀⠙⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢫⣶⣾⣿⣿⣿⣿⡇⢸⠓⣦⡤⣀⣀⣀⣀⠤⠴⠛⠁⠀⠀⠠⠤⠤⠤⠴⠐⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⡿⠀⢸⣞⣿⠄⠋⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠇⠀⠀⢠⣾⡿⠃⠀⠀⣀⣀⣀⡀⢀⣀⣀⣠⣤⠴⠚⠉
⠀⠀⠀⠀⣀⣠⡤⠶⠚⢻⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⡟⠉⢀⣀⡤⠄⠈⣻⣶⣿⣿⣿⣿⣿⣿⣿⠟⢀⣀⠉⢹⣿⣿⡿⠟⠁
⠀⠀⠀⣸⠟⠋⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠳⠞⠋⠈⠙⠾⠻⣅
⠀⠀⠈⠳⠤⣄⠀⣰⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠸⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⣾⠃⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠻⣄⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠈⠓⠦⣰⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠘⣇
⠰⣿⣇⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⢻⡀
⠀⢸⣿⣆⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠸⡇
⠀⠸⣿⣿⣧⠴⠛⠁⠀⠀⠀⣆⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢀⣀⡧⠔⠋⡿
⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠦⠸⣿⡄⣀⣤⠾⠛⣉⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⢤⣤⢤⠀⠀⠀⠀⠀⠛⢻⣿⠇⡔⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣧⣴⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢹⡄⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠰⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡤⠀⠀⠀⠀⠀⠀⠀⣿⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠙⠷⣦⣌⣻⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⡶⠓⠀⠈⠉⠉⠉⠉⠉⣉⠉⠙⠙⣿⡿⣦⣀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣰⣿⡟⠁⠀⣀⣴⣶⣿⣦⡀⠀⠀⣠⡿⠛⠳⢦⣜⣷⡄⠙⣦⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⢀⣠⡴⢟⣿⠋⠀⢠⡾⠋⠀⢀⣴⣬⡝⣦⢸⡏⢀⣤⣄⠀⠙⣿⣿⣦⠈⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠐⠛⠋⣩⣴⣿⠃⠀⠀⢿⡁⠀⠀⠈⠻⠿⢋⡾⠻⣷⡸⠿⠟⠀⠀⣾⢿⡏⢷⡄⠀⠀⠀⠀⠈⢳⡄
⠈⠉⠉⠁⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⣿⠀⠀⠰⣬⣳⣤⣤⣤⣤⡴⠟⠁⠀⠙⢿⣶⣤⣤⣼⣋⡼⣷⠀⠻⡄⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⢰⣆⠀⠀⠀⠀⢹⡏⠛⠛⠋⠀⢻⡟⣷⢻⠀⠀⠀⠀⠀⠘⣷⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⢹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⠶⠟⠁⠀⠀⠀⠀⢀⣰⡏⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠳⣤⡀⠀⠀⠀⢻⡌⠻⢿⣷⣄⣀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⡶⣶⣶⢤⣤⣤⣤⣄⠈⠻⣇⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣼⣿⣶⣤⣤⣤⣭⣤⣴⣿⡟⠁⢀⣴⣿⠋⠙⣧⠀⠈⣷⠀⠀⣼⡇⠀⣼⡇⠈⣹⣷⡀⢻⡇⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣭⣭⣍⠀⠀⡿⠀⣼⣿⡇⣻⣄⣴⣿⣦⡴⣿⢶⣤⣿⣧⡶⢿⣟⠛⢿⣿⣦⣾⣇⣀⣀⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⢳⣼⣧⠀⠙⣻⡿⢋⣿⠋⢀⡿⢀⣿⠀⣿⡏⠙⢷⡀⠙⣧⡀⢻⡎⢻⡟⠻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠻⢿⡟⠀⣼⠃⠀⣸⠇⠸⠏⠀⢻⣷⡄⠈⠻⠀⠸⡧⠘⣿⠘⣿⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣄⣄⢺⡇⠀⠁⠀⠀⠉⠀⠀⠀⠀⢸⡇⠙⣦⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣹⡎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢻⣦⡄⠀⠀⠀⠀⠀⠀⣼⠇⠀⣿⡀⠀⠀⠀⠀⠰⣿⣤⡤⠶⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⣀⣸⣿⣁⡴⠟⠁⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠈⢷⣄⠀⠀⠀⠀⠈⠿⣤⣤⣀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠶⠛⠉⠉⠁⠈⣹⡿⠋⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠉⠻⣍⡛⢶⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣤⡶⠾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠘⠷⠈⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⣾⡟⠁⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣤⡀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠉⠻⢿⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠶⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠐⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣟⣿⣿⣿⡛⣆⣀⣰⠊⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣛⡟⢿⠿⣿⡆⢸⣿⠻⢿⣿⣧⣤
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢋⣭⣭⣾⡇⠈⡁⢘⣁⣀⠛⢿⣿⣿⠏⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡟⣿⣥⠿⣿⠟⠛⠙⢿⡿⠎⢹⠏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠳⣄⠀⠀⠀⠐
⠀⠀⠀⢀⠤⢤⣤⡤⠤⠤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠚⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣻⡁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣉⡽⢋⣁⡀⠀⠈⠷⣄⡀
⠀⠀⢰⠏⡀⠀⠉⢤⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⡄⠀⡀⠀⣠⠤⠀⠀⠀⠙⠯⢿⢷⣀⡀⣄⣀⣀⠀⠀⠀⡄⠊⠉⠀⠀⠀⠀⠀⠀⠄⠊⢳
⠀⠀⠘⡆⠀⠑⠠⠀⠙⠂⠀⢈⠒⠒⠈⠁⠀⠀⠀⠀⠀⢀⡇⠒⠈⠀⠈⠉⠉⠀⠀⠀⠀⠈⣸⠋⠠⠾⠿⣍⣉⠒⠾⡄⠀⠊⢁⣠⡀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠘⢦⡀⠀⠀⢀⡀⠘⢻⢷⣦⡀⠀⠀⠀⠀⠀⢀⣀⣷⠀⠀⠀⠄⠑⠀⠀⠀⠀⠀⣿⣿⠂⣴⠿⠿⣈⣿⡆⢀⠜⢣⠴⠏⠁⠀⢠⠇⢀⠀⡰⠋
⠀⠀⠀⠀⠀⠹⣦⡀⠏⠀⢸⠀⢃⠁⢳⠻⡖⠖⢄⡀⢹⣿⣿⣆⠘⠖⣒⡲⠆⠀⠀⢀⡂⣿⡇⡀⠻⣿⣿⣾⣿⡷⠃⠀⠋⠳⠆⠀⢠⠏⢀⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢇⠌⠀⠘⡄⢿⠀⠈⠀⠙⢛⡿⠛⠳⡀⠀⠀⠀⢀⢴⠋⠀⣳⢀⣨⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⢠⠋⠠⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⢦⠀⠀⠁⠸⡀⠀⠌⠁⠘⠁⠀⠀⠈⠒⠂⠈⡁⢁⠔⠔⠁⠉⠉⠉⠋⢁⠁⠈⠀⠀⠀⠀⠀⠀⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠇⠀⢠⠀⠀⠀⠀⠀⠀⢸⣠⠊⡐⠁⠀⠀⠀⠀⠀⠀⠆⢸⠀⡆⠂⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠀⡇⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⢸⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢠⠂⡘⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠇⢀⠆⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡞⢀⡞⣰⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⡞⢀⡜⢠⠇⠀⠸⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢹⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠔⣋⣠⠞⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡆⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢒⡒⠲⠟⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠊⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠐⠀⠘⠀⠀⠐⠒⠶⢞⣓⠒⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠋⠉⠉⠉⠉⠙⠓⠒⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣙⣲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⣀⢀⡤⠤⠤⠶⠒⠂⠈⠁⠢⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠓⠀⠀⠈⠲⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢶⠤⠳⡄⠀⠀⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣤⠀⠀⠀⠀⠀⣟⠀⠀⠜⠁⡀⠂⡄⠀⠀⠀⠀⠀⣧⠀⠘⢆⠀⠀⠀⠐⢒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡆⠀⠀⠀⠀⠀⠘⡆⠀⠠⠊⠀⢰⠈⠀⠂⠀⠀⠀⢸⠀⠀⠈⢧⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠸⠖⠒⠉⠁⠈⢦⠀⢱⠀⠀⠀⠀⢀⠜⠲⣤⣤⣠⡤⠃⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⡴⢒⣈⣚⠓⠾⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⡠⠔⠦⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢸⡁⠉⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢊⠀⣀⡤⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠞⠀⠀⠀⠉⠓⠒⠒⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠠⠄⠰⣚⠟⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢎⠀⣀⡰⠖⣁⣀⣀⡀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠤⠭⠵⠒⠉⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⠀⠀⠀⢰⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣸⠀⠀⠀⡼⢻⡽⠝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠙⢀⣀⣀⡈⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠈⠁⠀⠐⠆⠢⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠒⠒⠒⣶⢲⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠛⢻⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⣀⣀⣠⣼⠤⣤⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠶⠶⢶⣾⣿⢾⣷⡾⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢠⡿⢁⣤⠞⠋⠉⣉⣙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠛⠛⠛⠛⠷⢾⣷⡋⠀⣠⣶⡛⢿⡍⠙⣷
⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠾⣧⣄⠻⡄⢹⣴⡟
⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⡤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣼⠟⠀⠀⠀⠀⠀⣠⡤⠤⢤⣄
⠀⠀⠀⣰⡟⠁⠀⠀⢀⣤⠖⠋⠀⢀⡴⠞⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣾⣿⣟⣲⣤⣄
⠀⠀⣰⡏⠀⣠⡴⠞⠉⠀⣀⡤⠞⠋⠀⢀⡴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢰⢋⡽⣞⣿⣿⣿⠿
⠀⢠⣿⡴⠛⠁⢀⣠⠶⠛⠉⠀⢀⣤⠞⠉⠀⠀⢀⣼⢿⡆⠀⢠⡀⠘⣦⠸⣧⠀⠀⠘⢿⣿⣉⣿⣿⡧⠴
⠀⣾⣇⣤⠶⠛⠉⠀⣀⣠⠴⠚⠉⠀⠀⢀⣤⡾⢋⠁⡈⢿⣄⡈⢳⣄⠈⢷⣿⠀⠀⢀⡾⠶⣌⣻⠋
⠀⣿⣉⣠⣤⣴⠖⠛⠉⣀⣴⣦⣤⡶⠞⢛⠁⣷⣼⠀⡇⢸⠻⣧⣇⠙⢦⣄⣿⡄⠀⠀⢹⣿⠟⠁
⢀⣿⣧⣶⠶⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠘⠀⠇⢸⠙⡟⢻⠛⡏⣟⠻⢶⣬⣿⣇
⣿⠁⣿⡆⠀⠀⢠⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⣄⠃⠋⠀⢸⡿⠀⣻⡆
⢿⡄⢸⡇⠀⠀⠈⣽⡿⠿⠿⠗⠀⠀⡤⠀⠀⠺⠿⠿⢿⣯⠅⠀⠀⠀⣸⡇⢀⣿⠁
⠈⠻⣾⣿⣴⣶⣷⣶⡄⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⢀⣿⡶⠟⠁
⠀⠀⠀⠸⣧⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣼⠇
⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⢀⣤⣀⣠⣄⣀⣤⡀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠉⠀⠈⠁⠈⠁⠀⠉⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⡶⠶⠶⠶⢾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⡇⠀⠀⠀⢼⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠙⢧⣄⠀⠀⣀⣤⠞⠉⠉⠻⢶⡄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠟⣦⡴⠞⠋⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡈⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⣀⣰⡀⠀⠀⣸⡆⠀⠀⢸⣆⠀⠀⠀⣷⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⠀⠀⠀⢻⠁⠑⠦⡴⠁⠘⢦⡤⠞⠚⠣⣀⡠⠋⠘⠲⠤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠺⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡐⠳⢤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠄⠠⠄⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣇⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢠⡊⠀⠉⠉⠀⠉⠫⡉⢹⠀⠀⠀⠀⣀⡾⠁⠀⣀⣤⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡼⠷⠶⠤⣤⣀⡉⠉⠉⠁⠐⠒⢒⣛⣁⣤⣤⠶⠞⠋⢀⣠⠞⠉⢠⡖⡦⣬⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉⠛⠷⢤⣤⣤⡤⠶⠋⠙⣦⡴⣤⣾⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⠉⠁⠹⡄⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⢃⣦⣰⠿⠞⠋⠉⠉⠉⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣠⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡤⣤⣀⣀⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠉⠉⠑⠒⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⢻⠀⠀⠀⠀⣠⡴⠋⡷⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣦⠴⠖⠛⠁⠀⠀⡇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣽⡆⠀⠀⠀⠀⠀⠛⣟⣙⣛⣉⣙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠶⠋⠀⠀⠀⠀⠀⠀⠛⠚⢳⡄⣿⠀⠀⠀⠀⠀⠀⠓⠦⠤⠞⠁
⠀⠀⠀⠀⢀⡴⠚⠋⠛⠛⠉⠉⠛⢦⡀⠀⠀⠀⠀⢠⠟⣰⠏⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠓⣦
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣟⣸⠃⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⡏⠀⢰⠀⠀⠀⠀⠀⣶⠀⠸⡆⠀⠀⠀⣼⢿⡄⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⣧⠀⠀⠀⠙⠚⠁⠀⠀⠀⢠⡇⠀⣿⠀⠀⠀⠀⠀⣧⠀⢹⡀
⠀⠀⠀⣸⠀⢀⣿⡆⠀⠀⠀⠀⣿⣧⠀⢸⡀⠀⠀⢀⣀⠀⠀⠀⠀⡾⠀⢸⡇⠀⠀⠀⠀⠀⢻⡆⠀⢷
⠀⠀⠀⢿⣀⣸⢻⡇⠀⠀⠀⠀⢸⢸⡀⢈⡇⠀⣼⠉⠉⢳⡀⠀⢸⡇⢀⣿⡇⠀⠀⠀⠀⠀⢸⡿⣄⣸⠇
⠀⠀⠀⠀⠉⠀⢸⠀⠀⣿⡇⠀⢸⠀⢉⣭⣄⣀⠙⢤⣤⠞⣀⡤⠶⣍⠉⢸⠁⠀⠀⠀⠀⠀⠈⡇⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⡇⠀⢸⠀⠘⠦⣄⣈⡉⠛⠛⠋⣁⣤⠴⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⣷⠀⢸⡇⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⠀⠀⠀⠙⢶⠶⢶⣶⡶⠶⣶⠛
⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠀⢸⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⢿⠀⠀⡇⠀⠀⠀⠀⡟⠀⣦⠈⡇⠀⠀⠀⠀⠀⣿⠀⢸⡇⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠹⠤⠼⠃⠸⢤⡴⠃⠀⠀⠀⠀⡇⢸⣿⠀⣷⠀⠀⠀⠀⠀⠻⣤⡼⠃⢧⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡼⠻⣤⡼


⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠓⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓
⠀⠀⠀⠀⠀⠀⢠⡖⢠⠂⢄⡄⢲⠂⡠⡀⡔⡄⡄⠀⡔⠀⢠⡖⠀⡶⢠⢢⣄⠔⢤⢠⡠⢠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠛⠛⠛⠛⠛⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣄⢄⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣨⣭⣿⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⡠⠔⠋⠀⡇⠀⢰⠒⠒⠒⠒⢻⠆⠀⢸⡇⠀⠀⠀⠀⠀⠒⣺⠽⣿⠟⠛⠻⢿⣿⣿⣿⡀
⠀⢰⠚⢁⣀⣀⣀⣀⡇⠀⠈⠉⠉⠉⠉⠁⠀⠀⢸⢹⠀⠀⠀⠀⠀⣀⣀⡰⢁⠈⠂⠀⢸⣿⣿⡿⠁
⠀⣼⠀⠠⠤⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢧⣀⡀⠸⠀⠀⠀⠸⠛⣿⠁
⠀⡏⠀⠰⠶⠤⠤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠖⠟⠀⣀⢴⣤⡄⣪⡵⡧⠤⠤⠤⣀
⠀⡇⠀⠘⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠘⡟⠺⢯⠃⡞⢱⢟⣿⡾⠁⠀⡀⠀⠀⠑⢆
⠀⣧⠀⠈⠉⠉⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠉⣲⡜⣆⠀⠀⠈⣾⡽⠀⠀⣧⡄⠀⠀⠈⣇
⠀⢹⠀⠀⢰⡶⢰⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢠⠞⠻⠿⣿⣷⣲⣻⣿⡤⠀⣸⡿⠀⠀⠀⠀⡿
⠀⠈⠓⠦⢄⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠀⠀⠘⢀⣴⡟⢀⣀⣠⣴⡚⢱
⠀⠀⠀⣀⣀⣤⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⠃⠤⢤⣾⢧⣄⣀⡤⠶⠛⠛⠛⠛⠛⠋⠉⠀⠀⡇
⠀⣰⠞⣉⣁⣀⣀⣀⣹⣤⣤⣤⣤⣤⣤⣤⣶⣶⡿⡄⠀⠀⠀⢣⠀⠠⣠⡇⠀⠀⡀⠘⠲⣤⣀⣀⡀⢀⣀⣀⣠⡼⠓
⠀⢹⡀⢯⣤⣤⠤⠤⠤⠤⣤⣤⣤⠤⠤⠤⣤⣤⠤⠇⠀⠀⠀⠈⢧⡀⠀⢳⡀⠀⠈⠙⠛⠻⡉⠉⠉⠉⠉⠀⠀⠀⣀
⠀⠈⡇⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢀⣠⣽⠶⣤⣽⣦⡀⠀⠀⠀⠘⢿⣟⣛⣛⣩⣭⣽⣿
⠚⠛⠁⠀⣸⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣼⡀⠀⢀⡴⠚⠻⠿⠿⢛⣡⠤⢶⣿⣷⣤⣤⣤⣤⠟⣟⢛⡇⢸⠁⢀
⠀⠀⠀⢸⣗⣲⣱⠀⠀⠀⠀⠀⠀⠀⠰⡷⣋⢇⡇⠀⠘⠿⣶⣶⠶⢯⡵⠞⠛⠛⠿⠿⠋⣈⣉⣀⠴⠋⠉⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠟⢿⣯⢸⣿⣿⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⣀⣾⣿⣿⡿⠟⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣠⣿⣿⣿⣿⣷⣄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠑⠊⠉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡐⠁⠀⠀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣤⣴⣿⠟⠋⠙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣥⡀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣟⠀⢀⣾⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣧⡘⠉
⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⣶⠟⠉⢐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣵⣿⣿⣧⣀⠆⠠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠂⡠⢂⢏⡠⠈⣀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠋⠛⢤⢾⣷⠀⠬⠄⢲⡛⠒⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⠿⠀⠓⠤⠊⠀⠉⠋⠀⠀⠀⠀⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⡀⠀⠄⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠆⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡅⠀⠀⠠⠀⠐⠤⡀⠀⠀⠀⠠⠀⠀⠀⢠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⢀⠀⠀⠈⠑⠢⠄⣀⣀⣀⣀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⢁⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠑⠢⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡤⣀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠰⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠷⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⣀⡄⢀⡞⣧⠀⠀⠀⠀⠀⠀⠀⣤⠊⠥⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⡶⡊⠑⠃⡀⠘⡀⠀⠙⠉⠀⡀⢊⠈⠑⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠧⣤⢦⡀⡀⠀⢰⠠⠂⠀⢰⠀⠈⠫⠬⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⡼⠀⠈⠙⢼⢃⣠⢼⡖⢶⣲⣺⠿⠲⡆⠐⢢⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠃⠀⠚⠿⠿⠿⣯⢴⣯⣾⣿⣿⣿⣿⣷⣿⣷⣿⣿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠧⣈⣳⡀⢠⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠐⢏⡩⠽⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢛⠻⢿⣿⡏⠀⠀⠀⠀⣶⠖⡤⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⣿⡿⠁⠶⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⢠⣿⠃⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡴⠁⢘⢷⡀⠈⢦⣉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡸⠃⠀⠀⠀⠀⠀⣤⡼⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⣿⠏⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⢷⣄⠀⠀⠀⠀⠀⠉⠀⠒⠙⠀⠀⠀⠀⠀⢠⡾⠳⣶⣦⣀
⠀⠀⠀⣀⡴⠖⠲⠞⠉⠀⢀⣀⣀⡾⠉⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡿⠠⣄⡼⠃⢙⢧⡀
⠀⠀⢸⡋⠀⠀⠀⠀⠠⡶⠋⠁⠉⣹⠖⠂⠀⠙⠿⢭⣿⣷⣶⠖⠒⠻⣏⠁⢀⡿⠀⠈⠓⢶⡁⣰⠇
⠀⠀⠀⢿⣀⡀⠀⠀⢀⡟⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡜⠷⠋⠀⠀⣴⠦⠴⠛⠁
⠀⠀⠀⠀⠙⢧⡴⠷⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠶⠞⠁
⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⢸⡦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣠⠞⡱⠋⢹⣆⡀⠘⣇⠀⠈⠉⠙⠛⠶⠦⣤⣄⣀⠀⢀⡟
⠀⣠⠞⡡⢊⡤⣴⠏⠈⠙⢦⣾⡳⣤⣀⠀⠀⠀⠀⠀⢠⠟⠻⣿
⣼⣣⠎⢱⣭⡵⠛⢦⡀⠀⠀⠈⠙⢲⡽⠛⠓⠶⠦⢤⡏⠀⠀⢈⡇
⠈⠛⠛⠋⠁⠀⠀⠀⠙⠶⣤⣤⠴⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢧⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠠⣀⠸⢭⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣅⠢⢍⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡾
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣿⣇⠀⢀⣤⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠛⠛⠻⠷⣶⡿⠙⢿⡾⠛⠉⠀⢿⠷⠶⠟⠛⠛⠛⠳⠶⣦⣀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⢠⣿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠁⠀⠀⠈⠛⠠⠤⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⣷⠄⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣭⣄⠀⠀⠀⠀⠀⠀⠀⣡⡾⠁⠤⣤⡀⠸⡀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢰⡿⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⣴⠉⢠⣤⠈⣧⠀⠀⠀⠀⠀⠀⠋⠀⣴⣦⠀⢹⡆⢁⡀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢿⡀⠈⠉⢀⡟⠀⠀⠀⠀⠀⠀⣧⠀⠈⠁⢀⡬⠁⡸⠇⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠀⠈⠙⠶⠚⠉⢠⡴⠖⠀⠀⠀⠀⠈⠳⠶⠶⠋⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠈⣻⣶⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⢠⡜⠋⣉⣉⠙⢦⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠛⠃⠀⠀⠀⠀⠀⣀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠙⠷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠻⣟⠻⣷⠀⠀⠀⠀⣿⣏⡉⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠙⣤⣤⣤⡴⠟⠉⠉⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣸⡇
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠴⢦⡀⠀⠀⣠⣿⠉⠻⢶⡾⠟
⠀⠀⠀⠀⠈⠻⠶⣤⡤⢶⣿⣦⣀⣀⡠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⣠⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣤⢦⣤
⠀⣀⣀⣴⡾⠋⠁⠀⠀⠀⢀⣴⠟⠁⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⢠⠌⠀⠀⢴⣾
⣾⡟⣉⡉⠙⢦⡀⠀⠀⣠⡿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⣿⣦⣤⣀⣤⠁⠀⠀⠘⢶⣾
⣸⡿⢋⡄⠀⠀⠙⢶⡾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣦⣼⣶⣿⡾⠋
⠛⢷⣿⣡⣾⠀⣤⢸⣷⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠉
⠀⠀⠉⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⣤⠤⠤⠄⠲⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⣤⡴⠒⠶⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠛⠛⠛⠓⠂⠤⢤⣶⣶⡦⠄⠤⠔⠛⠉⠀⠈⠛⢦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣤⣶⣶⣾⣿⣿⣶⣶⣶⣞⣋⣛⣷⣤⣶⣶⣶⣶⣶⣶⣷⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⢀⡀⢀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣠⡤⠴⠖⠒⠒⠒⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢈⠦⠄⣀⣀⢀⣀⡠⠄⠀⠀⠀⠀⠀⢀⡠⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⢨⠃⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⠀⣀⣤⣘⡳⠀⠇⠤⠦⢀⣀⡀⠀⢠⠛⡄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡸⠁⠀⠐⠛⠉⠁⠀⠀⠈⠛⠛⠻⠟⠀⠌⠀⡇⣠⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⣬⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⢀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢎⠐⠒⠂⣄⣀⡈⠉⠩⠭⢭⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣴⠿⠿⢿⣿⣿⣛⣛⣉⣙⣛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣧⣴⣶⣤⣤⣤⡄⠀⠤⢀⣀⡽⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⠉⠉⠭⠭⠭⠭⠍⠉⠻⠋⠉⢌⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢻⢯⣍⠙⠓⢒⣀⢀⣀⣉⣭⢿⢾⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⠟⠛⠛⠒⠒⠒⠒⠛⠻⠬⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣤⣤⣤⣤⠤⠤⣤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⣿⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠽⠶⠿⠿⠭⠭⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠊⠙⡊⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⠄⠀⠀⢠⡄⠊⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠁⠁⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠐⠂⠀⢀⣀⣀⡀⠀⣠⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢄⠃⠀⠈⣤⠍⠁⠀⠰⡖⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆⠀⠀⠀⠀⡀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⢀⠀⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⢧⣀⢸⢢⠀⠈⢡⠀⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡝⠀⠰⠀⠫⡙⡆⠳⠖⠁⠈⠈⢱⠈⠑⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠜⠀⠀⠀⣇⠀⢨⣇⠀⠀⠀⠀⠀⢡⠣⠆⠤⡀⠀⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⡤⠸⠆⠀⠀⠀⢹⢴⠃⠞⡆⠀⠀⠀⢀⠎⠀⠀⠀⡇⠀⠀⡠⠂⢰
⠀⠀⠀⠀⠀⠀⢸⠁⢀⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢇⢻⣸⣁⡒⠤⣴⠃⠀⠀⠀⢠⠇⠐⠀⡠⢠⣟
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⢉⣁⣲⣄⠹⣄⠀⠀⠀⠀⠘⣰⠃⠀⠈⠑⠢⢵⠀⠀⠀⡸⠀⣀⢀⠀⡡⣟
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠁⠀⠉⠁⠙⣦⡀⠀⠀⣠⠃⠀⠀⠀⢀⠆⠄⡃⠀⠀⡧⢊⣁⠈⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠤⠔⠒⠒⠀⠀⠈⢷⡄⣠⠃⠀⠀⠀⢠⠆⠀⡴⠁⠀⠸⠐⠌⡟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⢰⠃⠀⠀⣀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡤⣂⣤⡜⠁⠀⠀⠒⡄⠀⢠⡞⠘⡄⠀⢸⠃⢀⡏⠀⣐⡥⠊⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠛⠊⢡⠎⠀⠀⠀⠀⠀⠀⠀⣾⠡⠀⢳⠀⠘⠀⢸⡠⠖⠋⢉⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠏⠀⠀⠀⠀⠀⠀⢠⠞⢹⠀⠀⠈⡳⠤⠒⠁⠀⠀⠀⠀⠈⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣆⠀⠀⠀⠀⠀⠀⠂⡴⠋⠐⠚⠒⢏⠁⠀⠀⢀⣀⣀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠳⣄⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⣀⠈⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠠⠔⠒⠺⡝⣆⣨⠽⠞⠋⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⣰⠞⢩⣿⡛⢿⡷⣦
⠀⠀⢠⣏⣰⣿⣿⣿⣶⣿⡟⣷⣄
⠀⠀⢀⣟⣹⣯⡼⢻⣿⢻⣧⣿⢹
⠀⠀⢸⡟⢿⣟⣿⢿⣿⣾⣿⣷⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠈⢷⡈⠻⢭⣽⣿⡿⠿⠿⠃⠀⠀⠀⣀⡴⠞⠋⠁⢀⣀⣤⣤⠀⣀⠀⣉⡙⠳⣤
⠀⠀⠀⠀⠉⠛⠛⠹⣇⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⣶⡿⠿⠛⠉⠉⢠⢚⣼⡿⡑⠄⣤⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⡾⠁⣀⣰⣿⠟⡁⢅⠂⡥⠌⣠⣴⠿⠋⢂⢃⣼⣿⣦⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⢤⣾⢟⡠⡔⢁⣐⣬⣶⡿⠛⢁⠌⠒⣡⣾⡟⠀⡙⣿⣤⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣱⡿⠃⣪⣴⡾⢟⡛⢉⠑⠐⠎⣣⣬⡾⠋⠀⠻⣶⣔⠈⢿⣦⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠸⠟⣠⡿⢋⡁⢒⣠⣤⣶⠶⠶⠟⠋⠁⠀⠀⠀⠀⠈⢻⣮⠘⢿⣆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣌⢇⣾⢟⡔⣢⡷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢲⡀⢀⡀⠀⢻⣯⠸⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⣼⡏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⢻⡇⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣹⣟⣼⠋⠀⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤⠀⠀⠘⣿⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⣿⠁⠀⠀⢿⡀⠀⣿⠀⠀⠀⣠⠄⠀⠀⠘⣇⠀⢠⡟⠀⠀⠀⣿⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣿⠀⠀⠀⠈⠛⠛⠁⠀⠠⣾⣁⠀⠀⠀⠀⡈⠛⠋⠀⠀⠀⠀⢿⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠈⠁⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⣾⣿⣭⣙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⡇⠀⠀⢠⡾⠛⠙⠓⣦⠀⠀⠀⡗⠀⠀⠀⢠⣿⠐⡩⡻⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⡻⢷⠶⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁⠈⠛⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠛⠛⠛⡛⣛⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⣍⠙⠛⠁⠀⠈⠋⢋⣽⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⣤⡀⠀⠀⠀⡾⠀⠊⠀⠙⠷⣦⣀⣀⣠⣾⠛⠁⠈⣠⠈⣷⠀⠀⠀⣠⡴⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣬⠿⠛⠀⠀⢹⡆⠀⢀⡇⢨⣄⠀⠀⠀⣿⠉⠉⠈⣿⠀⠀⠀⣠⡀⢹⡄⠀⢰⡃⠀⠀⠛⠻⣯⣀
⠀⠀⠀⠀⢠⡾⠋⢀⣠⣤⢶⡞⢛⢿⡄⢸⡇⢸⡏⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢿⡇⢸⡇⢠⣿⡛⢲⡶⢦⣄⡀⠙⢶⡀
⠀⠀⠀⠀⠻⠴⠞⠋⠁⠀⠀⢿⡀⠊⣿⡄⡇⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⣇⣾⠣⠀⡾⠀⠀⠈⠙⠛⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠜⣿⡇⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢺⡇⢸⣿⠫⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠃⠘⣷⣸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣾⣧⣾⢃⠇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⠀⠽⠛⠿⠄⠀⠐⢿⠀⠀⠀⡿⠀⠀⠂⠿⠛⠋⠐⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡓⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⢀⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡁⠠⠤⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠄⠀⠘⠀⡀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠄⡰⠊⠉⠀⠀⠀⠀⠀⠉⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠁⠈⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡔⠁⡜⠀⠀⢀⠔⠈⠉⠀⠒⠂⠤⠤⢀⣀⠈⠑⢄⠀⠀⠀⠀⠀⠢⡉⠒⠤⠀⠁⠀⠄⡇
⠀⠀⠀⠀⠀⡸⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⢆⠀⠀⠀⠠⠀⠈⠢⢄⠠⠀⢀⠀⠑⠒⠒⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠀⠀⠀⡟⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠋⠻⠤⠀⠢⢄
⠀⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠉⠁⣀⣀⠠⠔⠁⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠈⠑⢒⠒⡀⠉⠉⠁⠀⠀⠀⠂⣠⠋⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠘⢦⡀⠱⣀⠀⠀⠈⠀⠈⢀⡀⠠⠤⠄⠒⠶⠍⢏⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢃⣀⣑⠬⣐⠒⠈⢀⠠⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠌⣉⠄⠉⠉⠉⠉⠀⠀⠀⠀⠆⠂⠀⠀⠀⠘⡀⠀⠀⠀⠂⠒⠂⠄⠂⠤⠖⠐⠂⠀⢀⡴⠙⠚⠡⠀⡀
⠀⠀⠀⠀⡀⠄⡌⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣀⠀⠄⠀⠀⠂⠀⠀⠀⠁⠀⠰⠄⠉⢁⠀⠀⡸⠀⡇⠀⠀⠀⠠⠄⣀
⠀⠄⠂⠉⠀⠂⠚⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠐⠀⠈⢀⠂⠠⠅⠊⢀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡂⠔⠂⠀⠑⠤⠄⠐⠊⠀⡀⠘⠀⠁⠕⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠚⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⡠⠄⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣀
⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀
⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠂
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠉⠉⠙⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠉⠉⠉⠛⠳⢶⣄⡀
⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠉⠙⣦⠙⢷⡀⠀⠀⠀⠀⢀⡾⠋⣼⠋⠁⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇⠈⣷⠀⠀⠀⠀⣾⠁⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡄⠈⠻⣦⣄⣤⡴⠋⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠙⢦⣤⣠⣴⠟⠁⢀⡴⠶⣄
⣿⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣸⠇
⢿⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⢀
⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣤⣤⣤⡴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢦⣤⣤⣤⡤⠶⠞⠛⠁
⠀⠀⠀⠀⠀⣴⠶⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠛⠶⠶⠶⠚⠛⠁⠀⠀⠀⠀⣤⡾⠛⠋⠉⠛⠻⣶⠟⠉⠀⠀⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣠⣴⣾⣿⣿⣶⣦⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡶⠛⠓⠶⢶⣇⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⢛⣛⣛⣛⡉⠀⠰⣶⣾⣿⡿⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠛⠿⠿⢋⡴⢊⣥⡀⠀⠀⠛⠿⠟⣯⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⢀⢎⡞⠁⢀⠀⣾⢡⣿⣿⣿⣿⣿⡇⢀⠠⣤⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢸⡸⣧⣿⣿⣇⠻⢸⡿⠿⠿⠟⠁⠀⠀⠙⠛⠛⡉
⠀⠀⠀⠀⠀⢠⠇⠀⠛⣲⣤⠀⠑⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠹⣦⡀
⠀⠀⠀⠀⢀⣟⠀⠀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣸⣷
⠀⠀⠀⠀⢸⣿⣆⠀⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⣿⠂
⠀⠀⠀⠀⠀⣿⣿⡆⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢄⡀⠸⣿⣿⣀⡀
⠀⠀⠀⠀⠀⢻⣿⠇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⠁⠀⢿⣿⣿⡝⢷⡄
⠀⠀⠀⠀⠀⢸⣿⢀⣾⡇⠀⠀⢀⣠⡤⠶⠶⠶⠀⠙⠀⠀⡀⠀⣠⣼⡟⠻⠇⠀⠘⣷⢿⣽⣼⣿
⠀⠀⠀⠀⠀⢘⡏⢾⣿⣷⠀⠠⠋⠀⣠⣴⡖⣀⠀⠀⡀⠀⡇⠈⠁⠙⠚⠃⠀⠀⠀⣿⣾⣿⣿⠏
⠀⠀⠀⠀⢰⠟⣿⡎⠻⠛⠀⠀⠀⠺⠋⠿⠇⠂⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡀
⠀⠀⠀⠀⣿⠀⠛⣷⣿⣷⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣿
⠀⠀⠀⠀⣸⣷⣶⣿⣿⣿⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⠟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟
⠀⠀⠀⢸⣿⡏⣿⣧⣼⣿⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣯⣿⠁
⠀⠀⠀⠈⢿⣧⣻⣿⣿⣿⣿⣷⠀⢠⡀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⠂⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣧⠀⠳⡀⣠⠖⠒⠤⢬⣙⠛⠛⠛⠁⠀⠀⠀⣼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣇⢀⡴⢁⡔⠀⠦⣤⣄⠳⣄⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠎⣰⠋⢀⡴⠂⠪⣑⡍⠉⢀⣀⡤⠞⢹
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠁⠴⠋⢀⣴⣤⠈⠃⠀⠀⠀⠀⠀⢸⣦⣀
⢻⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⡴⠃⠙⣦⡰⣄⠀⠚⢡⠰⡆⡧⣄⠀⠀⠀⠀⣺⣿⣿⣷⣶⣤⣀⣀⣀
⠀⢿⣿⣿⣦⣤⠶⠖⠛⠉⠀⢿⠀⠀⠈⠳⣄⠀⠀⠀⠐⢟⡃⠘⢦⠀⠀⠀⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠙⠛⠁⣤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠙⣆⠘⣧⣤⣾⣷⠀⠀⢿⡙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⢸⢦⣿⣿⣿⣿⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠛⣼⣿⣿⣿⡿⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡏⠙⠿⠙⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣷⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⠀⠿⠿⠿⠿⠿⠈⠿⠿⠿⠿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⣤⠄⠀⠀⠀⠙⠉⠉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⣉⣙⠻⢿⠀⠀⠀⠐⠒⣶⠖⢄⠀⠀⠆⢀⠤⣶⡖⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⠄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⣀⣀⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡐⠐⠀⠀⠀⠠⣀⡀⣀⡈⠃⠁⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⡆⣸⣷⠄⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⠘⠁⡃⠀⠠⢀⡟⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢾⠁⠙⠃⠀⠀⠐⢤⠀⡄⠀⠀⠀⠀⣀⠀⠀⠁⢀⠀⠈⢁⡘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⢸⡇⠀⠸⠃⠀⡀⠂⠀⠐⣶⣴⠀⠀⠀⠀⠐⠋⠁⠐⠒⠒⠒⠒⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⢡⣄⡀⢆⡀⢀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠐⠂⠂⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⢸⡇⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣀⠀⣤⣤⣀⡀⠀⣄⠀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⣹⠀⠘⠟⠃⠀⠀⠘⠂⠀⠀⣀⠈⣁⠀⠀⠀⡄⣈⢻⠎⠀⠀⠀⢀⡁⢀⡠⠤⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠓⠄⠀⠒⠀⠰⠷⠞⠣⠈⠋⠠⣿⠀⠋⣠⠋⠁⠻⠦⠄⠒⠂⢠⡟⠈⠀⠀⠀⠹⣦⣀⡄⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠀⠀⢠⡿⣆⠀⣤⠀⢡⣄⡀⠈⠀⠊⡠⣄⠀⠀⡀⠉⠀⠀⠉⢳⠄⠀⠂⠐⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠙⠿⣦⡈⠀⢨⣿⣁⢠⠀⣩⠅⣰⣦⣄⣴⣷⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠐⢈⣞⣁⣈⠀⢉⣷⣿⣿⠇⣨⣷⣶⡈⠁⡐⢳⣤⡀⠁⢑⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⡬⣧⠙⠶⠶⠠⠘⠋⠡⡄⠀⣀⠛⠉⠀⠈⠑⠀⠀⠀⠈⣔⢂
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣤⠀⠉⠓⠠⠐⢃⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠠⠀⠠⡀⠄⠠⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠩⠄⠀⠈⠐⠀⣸⢠⡄⢸⠇⢸⠗⠛
⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠊⠀⢠⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠘⠷⠀⠀⠐⠛⠐⣦⠇⠃⠈⠁
⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣦⡈⠉⠀⠀⠀⢠⠀⡄⠀⠾⠀⠀⠋
⠠⢠⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⡄⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠈⣧⠀⠚⡃⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡟⠀⠠⣤⣄⣀⠄⠀⠀⠀⠃⣀⠀⠀⠄⠀⡀⢸⣏⠹⠇⠀⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠇⠋⠁⠀⣀⠉⣀⡀⠀⠀⢰⡇⠀⠀⣄⠈⠃⠀⠁⠀⣠⠀⠿⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⡶⢫⠹⠸⣿⡟⠀⠀⢸⡇⠀⠈⠁⠀⠈⠀⢰⡀⠃⣈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣷⠀⠀⠀⠻⠄⣠⣶⣴⠀⣀⠰⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢀⠀⠀⠸⠿⠋⢀⣀⡰⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢟⠜⢳⣄⣀⠀⠠⢾⣿⡃⠄⠀⠀⠄⠀⡀⠀⣀⣀⠀⠀⢀⡀⠀⠈⠉⠀⠀⠐⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣾⣿⣷⣿⢉⠀⠀⢀⠛⠁⣠⣴⣶⠾⠿⠻⠄⠉⠈⢻⠆⣤⣭⡆⡟⠁⠀⠀⣀⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡷⢺⣿⣿⣿⠟⡢⣶⠧⣈⠓⠾⠋⠀⠀⠀⠀⠀⠀⠠⡀⠀⠓⣼⠿⣹⡟⠀⢀⡷⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢛⠋⣿⢿⣍⢠⡷⠁⣨⠝⠲⡇⠀⣰⣾⡇⢰⡿⡄⠀⢳⠞⠀⠙⠷⠈⠀⣤⣄⡙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢆⣉⠀⠈⡫⠉⠁⠀⠀⠃⣀⢀⡶⠀⣧⣰⠂⢰⣀⠃⠀⠽⢃⡸⠃⠀⢀⡀⠀⠙⠁⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡻⢁⡚⠛⡛⠂⢾⣿⡂⠁⣦⡈⠛⠀⠀⠉⠀⠀⣦⠀⠇⠀⠀⢸⣷⢀⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⢥⣾⡟⢃⡤⢛⠁⢴⠈⠰⠀⣴⣧⠀⠀⠀⠋⣦⡚⠀⠀⢘⣭⣸⡇⠐⠁⢈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠈⢻⣟⠀⠈⡄⠀⠂⠈⠈⠀⠀⠀⠀⢱⣾⡆⠀⠈⠀⠀⠁⠀⠉⢹⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠆⠀⠀⠠⠿⠀⠀⠰⠀⠀⠀⠂⠀⠀⠀⢀⣀⠙⢡⡀⠀⢶⣠⣄⣀⣀⣸⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢒⣃⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠃⢸⣷⡦⢶⠀⠀⠀⠀⠀⠘⣿⠤⠤⠤⠠⠤⣼⣁⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠀⠉⠀⠉⠛⢛⠀⠀⡌⠀⢰⣦⣤⡄⠀⠀⠀⠀⠀⠔⠁⠄⠀⠀⠀⠀⢙⠉⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⡉⠉⠀⠘⠀⠀⣨⣭⣭⡇⠀⠀⠀⠀⠀⣴⡧⠀⠀⠀⠀⠤⠈⠁⢸⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠤⠀⠀⠀⢓⡆⠀⠠⠄⣰⣉⢉⢉⢃⠃⠀⣠⡀⠀⢻⡿⠀⠀⠀⠀⠒⠀⠂⢘⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⣤⠞⠛⠛⠛⠛⠋⠳⡜⠁⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠈⠀⠁
⣿⣿⠟⠛⣿⠿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣏⣈⣷⣶⣴⣶⣶⣶⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠄⠀⢠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⢄⠀⠀⢀⡈⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠒⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢨⠀⡠⠄⡸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠈⠁⠁⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠈⣿⠀⢸⡇⠀⢠⡤⠖⢒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⣀⣉⣉⣉⣭⣭⣤⣤⣬⣽⡛⢳⠀⠀⣀⡀⣀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⢇⡼⠋⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡇⢸⡏⠀⠈⣷⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠈⠳⠤⠔⠃⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣄⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⠀⣹⠃⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠒⠊⠁⠀⠀⡇
⠀⠀⠀⣿⠀⢸⣇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠈⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⠉⠙⢣⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠻⠤⠤⠟⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡄⢀⣤⠤⣤⣄⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⡏⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⢖⣋⣀⣼⠁⠸⣇⠀⣀⡟⠀⠀⣿
⠀⠀⠀⢹⠀⠀⣿⠀⠘⠓⠒⠒⠒⠒⠛⠒⠛⠛⠛⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⣸⣿
⠀⠀⠀⠈⢻⣷⡿⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⢳⣶⣿⣿⠟⠛⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⢸⡟⠁⠏⠹⣿⣄⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠀⠀⢿⠉⠁⡏
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠁⠈⠉⠙⠛⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢀⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⣾⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢡⡉⢯⠀⡇⢀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠛⠃⡰⢸⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠈⢷⣍⣈⡳⢿⣌⢣⡘⡔⡆⢲⠀⡇⡜⢀⡀⢐⡴⠋⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀
⠀⠀⠀⠀⠀⠈⠉⠀⢀⣿⡧⠙⡀⠁⢘⣨⣤⡒⠉⠛⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠉⠉⠉⠁⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠾⠁⠀⠉⠀⠀⠀⠀⠀⠉⠛⠛⡛⣥⡀
⠀⠀⠀⠀⢀⡤⠞⣽⠃⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠻⣆
⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠈⡇⠀⠀⠀⠀⠸⣦⣀⣤⠤⠖⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⡽
⠀⠀⠀⠀⠛⠦⠄⢻⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢷⠚⠻⢶⡀⠀⡟⠀⠰⡀⠀⠓⠦⠤⣤⠤⠤⠤⠤⠤⠤⠞⢯⡉⠉
⠀⠀⠀⠀⠀⠀⡾⠛⠛⠓⠶⠖⠒⠚⠃⠹⡇⠀⠀⢹⠀⠀⣸⠃⠀⠳⣄⡣⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠿⠖⢒⢙⡶⡟⠁⠀⢀⣰⡞⠛⠛⠛⢷⣦⣄⣀⣀⣀⣀⣀⣀⣠⣴⢋⣀⣀⡀
⠀⠀⠀⠒⠀⠀⠈⠍⠛⠛⠛⠛⠿⠿⠿⠅⠻⢿⣸⠗⠛⠁⠀⠀⠀⢀⣘⡛⣒⡚⣒⣂⣉⡉⠛⠉⠉⠉⠉⠁⠀⠨⠭⠭⢥⣤⢄
⠒⠒⠀⠀⠀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⣉⣁⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠡⠈⠠⠭⠭

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⢐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠈⠐⠢⠄⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠄⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⡀⢀⠀⠀⠉⠐⠂⠀⣀
⠀⠀⠀⠀⠃⠁⠀⠀⠀⢐⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡤⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠤⠄⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⣤⢬⠽⢭⠂⣠⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄⡀
⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⡠⠀⠉⠉⠑⠢⠤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠲⠄⣠⠀⢉⠏⠀⠀⠀⢠⠐⢲⡆⠀⠀⠀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣸⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠒⠀⡂⠐⢀⠜⠁⠀⠀⠀⠀⠀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡎⠀⡀⠀⡀⠈⠀⢿⠁⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⡐⠀⠀⡎⢀⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡀⠖⠂⠐⠾⢡⡊⣀⣀⣀⣀⠀⠀⢀⡀⠀⠤⣭⡖⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⠤⢒⠡⠶⠙⡿⠶⢖⢤⠞⠛⠨⠲⠤⡑⢬⡈⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⡄⠁⠁⡄⠸⡍⠛⠙⠃⠛⠓⠚⠁⢨⠀⠀⠀⠀⠀⠈⡐⠤⡀⠀⠀⢘⠉⢳⣠⣄⡀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⡔⠒⣇⡀⠯⠂⠒⣰⣤⠖⠁⠀⠀⠑⢄⠀⠀⠀⠀⠢⠀⠀⠑⠢⢄⣀⠉⠐⣯⠛⠻⢅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠑⢀⡠⠄⢖⠈⠀⠉⠑⡄⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠁⠀⠀⠤⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠙⠄⠀⠘⢤⠀⠐⠂⠀⠀⠀⠸⠀⠀⡀⠤⠤⠈⢶⣄⠀⠀⠀⠀⠑⢄⠀⠁⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠑⠢⠤⣀⣀⣀⡜⠚⠀⢀⠀⠀⡀⠌⠀⠑⠤⡀⠀⠀⠀⠑⢄⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠬⠖⠀⠀⠀⠀⠙⠦⠤⠤⠤⠴⠒⠒⠂⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠿⠿⠿⢶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⣰⡟⠉⠀⢙⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣴⠾⠃⣀⣤⣤⣀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠈⢻⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣧⣀⠀⠀⠀⠀⠀⠘⡇⠀⢀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⣋⣭⣿⣿⣿⠉⠉⠛⠿⢷⣶⣶⣶⡾⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⢁⣠⣾⠿⠋⢹⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⣠⣾⠟⠁⠀⠀⣼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⣾⡿⠁⠀⠀⠀⠀⣿⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢠⣿⠏⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢿⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⡀⠀⠀⢀⣀⣀
⠀⠀⠀⣰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣤⣶⣿⣿⣿⣿⣶⣤⣄⢀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣯⣭⣭⣥⣦⣴⣶⡶⠶⠒⠒
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣯⣥⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠠⠻⠟⠛⠛⠛⢋⣽⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⠄

⠀⠀⠀⠀⠀⢀⡴⢒⣶⠶⣶⢦⡀
⠀⠀⠀⠀⠀⣾⣠⣿⣿⣿⣼⣿⢳⣦
⠀⠀⠀⠀⠀⣿⣹⣯⣞⣿⡟⣿⣸⢻⠆
⠀⠀⠀⠀⠀⣏⢻⣯⣟⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢦⣝⣳⣾⠟⠛⠛⠁⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⢀⡴⠋⢀⣠⣴⠶⠿⠶⢶⣤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⣴⠟⠉⢀⣀⣤⣄⣀⠈⠻⣦⡈⠑⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⡀⣀⡴⠃⠀⠈⠁⣠⡾⠛⠉⠉⠉⠉⠻⣶⡘⠃⢀⣤⣤⣀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⡉⠉⠀⠀⠀⠀⣴⠟⠀⠀⣠⣶⣶⣶⣤⡈⠛⠀⠈⠉⠈⠙⣷⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⢶⣤⣤⣤⡾⠋⠀⠀⣰⠿⢦⣍⠳⡌⠻⠄⠶⠶⠶⣄⠀⢹⡇⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⣀⠈⠉⠀⠀⠀⢀⣼⠋⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠘⣧⠈⢿⡀⣧⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠃⢨⡟⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞⠀⢸⣆⡈⠳⠦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⠀⠘⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡼⠛⣿⠀⠀⠈⣇⠀⣸⠁⠀⢀⡴⠀⠀⠀⠸⡀⢀⡾⠀⠀⠀⣿⠛⢷⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣤⣿⠀⠀⠀⠈⠉⢁⣀⠀⠛⠶⠀⠀⠀⣀⡉⠉⠀⠀⠀⠀⣿⣤⡼⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⡀⠀⠀⠀⣰⠋⠁⠀⢀⣀⣀⡀⠀⠈⠙⢷⠀⠀⠀⢀⣿⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⡄⠀⠀⠘⠀⠀⠰⠏⠁⠀⠙⠦⠀⠀⠘⠀⠀⢀⡾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⣶⡶⢶⣶⡖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⠾⠏⠉⠉⠉⠽⠒⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⡞⠁⢀⠹⣧⡀⠀⠀⠀⣠⡾⠁⠆⠙⣧⠀⠀⠀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣽⠷⠂⠀⠙⣆⠀⢸⡇⣠⡥⠠⠌⠛⠛⠾⠛⠋⠐⡄⢠⡁⢹⠀⠀⣾⠁⠀⠐⠿⣯⡀
⠀⠀⠀⠀⢠⠞⠉⣀⣤⠶⣾⠛⢻⣆⢸⡇⣿⠁⢣⡄⠀⠀⠀⠀⠀⠀⢈⢸⡇⢸⡆⣰⡟⠛⡶⠶⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠘⣆⠀⢻⣼⡇⣿⡄⡆⡁⠀⠀⠀⠀⠀⠀⠈⢸⡇⢸⣷⡟⠀⣸⠃⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⢿⡇⢿⡇⢁⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⡐⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⠌⢿⢼⡇⢈⠀⣀⠀⣂⡒⠂⠀⢂⣸⣷⡟⠐⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠙⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⠉⢷⡀⡠⠀⣀⣀⡀⢀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣴⡆⢻⠗⠊⣉⠈⠙⢦⠑⣄⠀⠀⠀⢠⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠙⠦⣀⣀⣀⡤⠀⣿⣠⣾⣿⡿⢡⠈⠀⢸⣿⣄⠀⠀⠇⠘⠀⠀⠀⢸⣷⡌⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠈⠉⠁⠀⠀⡟⠛⠛⠉⠀⣿⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣀⣀⡤⠆⠀⡇⠀⣴⣦⠀⢸⡇⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠉⠀⠀⠀⡇⠘⠛⢹⠄⣰⠃⠀⣠⣿⣆⠀⠈⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⣢⡤⠞⠁⠀⢠⠋⠛⣹⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣉⠁⠀⠀⠀⠀⢤⡤⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠯⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⣀⡶⢤⣀⢀⡏⠈⠛⢷⣄⠀⠀⢀⠀⡈⠒⠄⠀⠀⠀⠀⠀⢿⡿⢿⢏⡡⢴⠶⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡞⠀⣠⣌⡙⣆⠀⠀⠀⠀⠀⠀⠘⣆⢱⠈⠆⠀⠀⠀⠀⠀⠀⠀⠋⠋⡰⢋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠠⠏⠀⣰⠃⠀⣉⣛⢦⣤⣤⣄⠀⠀⠀⢹⠀⡆⠘⠀⠀⠀⠀⠀⢀⠀⠀⠞⣰⡟⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⠏⠀⡼⠁⠈⠉⠛⠻⣿⣷⠀⠀⢘⠀⠃⠀⠃⠀⠀⠀⣠⢋⡾⣦⣼⠟⠀⠀⢸⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠸⠁⣠⠞⠉⣛⠒⢿⣿⡇⠀⢸⠀⠁⠀⠀⠀⠀⣴⠃⡼⠁⠀⠀⠸⣧⡀⠀⠳⡌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠑⠄⠿⠁⠀⡘⠀⠀⠀⠀⢠⡞⠁⣸⠁⠀⠀⠀⠀⢧⠱⣄⠀⠙⠢⠜⠁
⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠋⠀⢠⡇⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⢹⣷⠀⠀⠀⠀⢸⣷⣤⣉⠒⠤⠤⠒⠁⠀⢀⣠⡶⠛⣁⠠⠀⣸⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀⠀⣿⠈⣹⢿⠿⢷⣶⣶⠶⠿⠟⠛⠊⠉⠀⠀⢀⣯⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⠟⠀⠀⠀⠀⣿⣠⡏⢸⡄⠀⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠘⢯⡀⠀⠀⢀⡴⣋⣼⠀⠀⣇⣰⠃⠸⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠈⠳⢤⡔⠋⢸⣿⣿⣿⣶⣼⣧⣤⣤⣷⣤⣤⣤⡄⠀⢰⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⢦⣼⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⡟⠀⢠⡟⠀⠀⠀⠀⢀⡼⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠙⣿⠁⠀⠀⠀⠀⠈⠛⢿⣿⡟⠀⢠⡟⠀⠀⠀⣀⠴⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡜⠁⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⡾⠁⠀⠀⠀⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⠀⠀⠀⠀⠀⡤⠖⠃⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⡼⠛⠛⠛⠛⠙⢦⠀⠀⣀⣠⣿⡿⢿⣆⣿⠀⠀⢀⢤⣤⣷⣤⣄⠀⠀⠀⢀⣽⣿⣿⣿⣾⣿
⠀⠀⠀⡇⠀⠔⡀⠢⠀⡸⠀⠀⣿⠀⠀⡾⢻⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⢲⠀⠀⠀⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠘⠦⣀⣉⡠⠔⠁⠀⠀⣏⠀⠸⠃⣠⠚⢂⠀⠀⠈⠻⣿⣿⠿⠋⠁⠀⠀⠀⠈⠉⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⢦⡀⠀⠀⠀⠈⣧⣿⣧⡀
⠀⠀⢠⠀⠀⣰⣷⡀⠀⠀⠀⠀⡯⠐⡖⢀⢠⡄⢹⡀⠀⠀⢰⢿⣿⡏⣧⠀⠀⠀⠀⢰⠉⠉⠉⣿⡂
⠀⠀⢸⣠⣼⣹⣿⣽⣦⣄⡄⠘⢧⣈⠁⠚⠈⠁⡴⠁⠀⠀⠀⢸⡏⣷⠀⠀⠀⠀⡄⣈⠩⢉⡉⢉⢀⡄
⠀⠀⠸⠉⠉⠹⠩⠏⠉⠉⠇⠀⠜⠋⠙⠋⠉⠉⠀⠀⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠁⠉⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠈⠓⠑⠀⠀⠀⠀⠀⠀⢀⡾⣿⣷⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⣋⣻⣷
⠀⠀⠀⣿⣿⢻⢻⣹⡟⢦⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⢰⠀⠠⠏⣰⠪⠇⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⢧⣽⣿⡿⠉⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠻⠿⣿⣿⡏
⠀⠀⠀⠐⠒⠚⠓⠒⠂⠀⠀⠀⠀⠀⠈⠋⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢙⠛⠉
⠀⠀⠀⠀⠀⣠⣦⠀⠀⣤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⣿⣗⡀
⠀⠀⠀⢀⣨⣿⡿⣷⣄⣿⠀⠀⠀⠀⢾⡿⣿⠆⠀⠀⢀⣼⣿⣿⠿⠋⠻⢷⡄⠀⠀⢠⡟⣿⣿⢧
⠀⠀⠀⣿⠀⢀⡾⣻⣿⣿⠀⠀⠀⣠⣤⣿⣷⣤⠀⠀⢸⣏⠀⠤⢀⠠⠄⢸⣿⠀⠀⠈⢠⡟⣿⠈
⠀⠀⠀⣇⠀⠼⠁⡠⠓⣄⠀⠀⢰⡟⣿⣿⣿⣿⠇⠀⠸⠿⠦⣄⣙⣀⡤⠿⠿⠀⠀⠀⠸⡇⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠚⠛⠛⠛⠛⠓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⣀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⣀⣀⣠⣼⠃⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡬⠿⠟⠛⠛⠉⠁⠉⢷⠀⠀⠀⠘⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣀⡤⠶⠆⠀⣀⣀⣀⡤⠟⠀⠀⠀⣀⣡⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⣠⠴⠚⠉⠀⣠⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡼⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⡞⠁⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⣠⠞⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢰⠏⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣀⣠⠴⠋⠁⠈⠙⠺⠟⢷⣄⠀⠀⠀⠀⣸⠋⠳⣄⣤⠖⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⠀⠀⠀⠀⠀⠘⢧⣀⠀⢀⣀⣤⣤⢤⣤⡀⠀⠀⠘⣧⠶⠖⠛⢉⣠⡶⠀⠀⠀⠀⢦⣀⠀⠉⠓⠶⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠄
⢿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣹⠀⠀⠀⢿⡀⠀⠈⣩⣥⣀⠀⠀⠀⠀⣀⣭⣉⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⢹⡇⠀⠁⠀⠉⠀⠀⠀⠀⠉⠀⠈⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠙⠳⣦⠀⠀⠀⠀⠀⢿⣄⣀⣤⡤⠶⠦⣄⠀⠀⠹⣆⠀⠀⢠⠖⠃⠑⠒⡄⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⡟⠓⠒⠒⠚⢻⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣄⣀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⣀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠦⢤⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣤⣤⠴⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢦⠤⠽⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠿⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠢⣀⡛⣄⠀⣀⠸⡓⠀⠀⡠⠔⠒⠃⠀⠀⠀⠀⢠⡤⠒⠋⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠾⠱⣿⡄⠀⠧⢤⣈⠀⠀⠀⠀⠐⠺⣜⣠⠤⠖⠛⠒⠛⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⡤⠔⠊⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣒⠿⠛⠉⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠠⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠈⡙⢲⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⡙⠁⠘⡆⠈⢶⢤⣀⠀⠰⡶⢄⠀⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢦⠀⢸⡀⠀⠇⠀⠘⣆⠈⠉⠐⠛⠈⢺⠥⠤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⠀⠀⠃⠀⠈⠀⠀⠘⠆⠀⠀⠀⣰⡃⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡧⠤⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢾⣿⡀⢿⠿⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⣖⡀⠛⢁⡀⠳⡄⠰⠒⣻⠁⠀⠀⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣇⣠⣅⠀⢠⠇⠀⠀⠀⠀⠈⠒⡛⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠦⣀⠀⠀⠈⢑⣿⠉⠬⠤⠞⠢⠄⠀⠀⠀⠀⠘⢅⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⠴⠒⢦⠀⠀⠀⢠⠞⠁⢀⣀⡀⠈⠲⡀⠀⠀⠀⡔⠉⠀⣀⣀⠈⠑⢄⠀⠀⠀⣠⠊⠁⢀⣀⡀⠉⢢
⠀⠀⠀⢼⢁⡤⣶⣾⠀⠀⠀⡇⠀⠰⢉⣤⡜⠀⠀⢱⠀⠀⢸⠀⠀⠎⣠⣴⠁⠀⠘⡀⠀⢀⠃⠀⠔⣡⣤⡇⠀⠀⠇
⠀⠀⠀⠀⠈⠩⣷⡷⠀⠀⠀⢇⠀⠀⠈⠻⡇⠀⠀⡜⠀⠀⠸⡀⠀⠀⠙⢿⠀⠀⣰⠀⠀⠀⡆⠀⠀⠈⠻⡇⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⣼⠤⢄⣀⣀⣀⡠⠊⠀⠀⠀⠀⠑⠤⣀⠀⢀⣀⠔⠁⠀⠀⠀⠈⠢⣄⣀⣀⣀⠤⢌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⢠⠋⠀⣀⠤⢄⠀⠙⡄⠀⠀⠀⠀⠀⣀⣀⣤⢄⠀⢀⠀⠀⠀⡰⠉⢀⣀⣠⡤⡀⠱⡄
⠀⠀⠀⠀⠞⣡⣤⡇⠀⡎⠀⡇⠀⠸⢡⣶⡞⠀⠀⢸⠀⠀⠀⠀⢠⡿⣿⣿⣿⠀⡜⠀⠀⠀⡇⠀⣾⢿⣿⣿⡇⠀⠡
⠀⠀⠀⠀⠀⠈⠻⡇⠠⠃⠀⢳⡀⠀⠀⠙⠇⢀⡠⡎⠀⠀⠀⠀⠈⠛⠿⠿⠛⠀⠃⠀⠀⠀⢣⠀⠙⠻⠿⠟⢃⢤⡇
⠀⠀⠉⠉⠐⠒⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⠤⠜⠤⢮⣄⠀⠀⠈⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣤⠤⠾⠤⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⠀⠀⠁⠀⠀⠀⣀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣀⠀⠈⠁
⠀⠀⠀⣠⠖⣲⣞⣟⢲⠀⠀⡰⠋⢀⡠⣠⡤⡀⠑⡄⠀⠀⢀⠎⠀⣀⣄⣤⢄⠈⢦⠀⠀⠀⡴⠁⢀⣠⣠⣤⡀⠱⡀
⠀⠀⢀⣿⢻⣿⣾⣿⣿⡀⠀⡇⠀⣸⢻⣿⣿⡇⠀⢸⠀⠀⢸⠀⢠⡟⣿⣿⣿⠀⠈⡄⠀⠠⠁⠀⣿⢻⣿⣿⡇⠀⡇
⠀⠀⠘⢝⣶⣿⣛⣿⡿⠁⠀⢣⠀⠙⠻⠿⠿⠃⢀⠎⠀⠀⠘⡄⠈⠛⠿⠿⠛⠀⡸⠀⠀⠀⢇⠀⠙⠻⠿⠟⠁⢠⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠾⠐⠢⠄⣀⠤⠔⠉⠀⠀⠀⠀⠈⠲⠤⡀⣠⠤⠊⠀⠀⠀⠀⠀⠑⠤⢄⡀⠤⠖⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣭⣛⡛⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⣿⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠷⢣⡖⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏⠏⠉⠈⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡍⠿⣶⣅⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠈⢢⡀⠁⠈⠉⠻⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⢢⡀⠉⢲⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⠃⠀⠀⠈⣇⠙⢦⡀⠰⠧⡀
⠀⠀⠀⠀⠀⠀⠀⡰⢱⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠰⠁⣿⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡇⢯⠸⡀
⠀⠀⠀⠀⠀⢠⠃⢸⣿⠀⠀⠀⠀⠀⣸⣠⣀⣤⠖⡀⠈⡇⡇
⠀⠀⠀⠀⠀⡜⢠⣿⣿⠀⠀⠀⠀⢠⣭⣽⡧⠔⣹⠇⣠⡇⢇
⠀⠀⠀⠀⢀⡇⠘⢻⣿⠃⠀⠀⠀⠀⡿⠛⣞⣿⣵⡿⠁⢿⣾
⠀⠀⠀⠀⠘⡇⣦⢸⣿⡀⠀⠀⠀⢠⣇⠀⠀⣼⡯⠃⠀⢸⢻
⠀⠀⠀⠀⠀⣷⣿⡄⣿⠗⣉⡑⠛⢦⣹⠀⢠⣿⣷⡀⢀⣼⠆
⠀⠀⠀⠀⠀⡘⢻⣿⣿⣾⣯⠍⠙⢦⡻⠀⢸⡈⠓⠞⠒
⠀⠀⠀⠀⢀⡇⠀⠹⣿⣿⢹⡆⠀⠈⠁⠀⠈⡇
⠀⠀⠀⠀⠈⢧⣳⣤⣹⣿⣆⣇⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠄⠀⣶⣾⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢂⠈⠻⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⠁⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⠆⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡻⢿⣿⣿⣧⣤⡙⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡳⣍⠀⠉⠙⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣴⣿⣿⣶⣶⣶⣾⣿⣦⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⢻⣛⣭⣭⣴⣮⣭⣼⣝⣹⣟⣿⣿⣷⣦
⠀⠀⠀⠀⠀⣠⣴⣴⡿⢋⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠛⠟⠁⠉⠀⠀⠉⠻⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠘⢿⣿⣷
⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠠⣄⣠⠴⠖⠲⢦⡀⠀⠀⠀⠀⠀⢠⣟⣉⠙⡖⠸⣿⠻⢦
⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠄⣼⠃⠀⠀⢀⣠⢽⡆⠀⠀⠀⠀⠈⢭⡙⡹⠃⠀⢻⣄⣼⣤⣄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⢿⣠⠴⠾⠟⠀⢠⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠈⠳⣄⣀⣀⣠⠟⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡀⠀⢨⡇⠀⠀⠀⠀⠀⣿⣿⡿⠛⠋
⠀⠀⠀⠐⣿⣿⣿⡟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⢰⠿⠋
⠀⠀⠀⣿⣿⣿⣿⣷⣄⣥⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠶⠓⠄⠀⠀⠀⢀⡟
⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⡤⠊⠉⠉⠉⠉⠑⠢⣄⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠋⠁⢳⡄⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⣦⣤⣀⡀⠀⣀⡤⠞⣉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⠞⢻⠁⠈⠉⠉⠉⠉⠀⠀⢹⡟⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡽⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⢳⡀
⠀⠀⠀⠀⢀⣀⣤⡼⠁⢾⠁⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠳⠤⣤⣀⡀
⠀⢀⡴⠚⠉⠁⣠⣤⢤⡌⠙⢦⡀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡏⢀⡴⠋⢠⠶⠶⢤⣀⠈⠙⠲
⠀⢮⣀⣠⡴⢿⠃⠀⠀⠹⣄⣠⡇⠀⠀⠘⢷⡄⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠸⢦⣤⠏⠀⠀⠈⣟⠳⣤⣄
⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⣷⠀⠀⣤⠂⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⡟⣿⢻⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣯⣀⣿⣈⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⣟⠛⠉⠻⠿⠇⠀⣯⠀⠸⠿⠟⠉⠉⡻⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣴⣤⡞⣦⢠⣖⣄⢲⡄⣿⣴⣲⣒⣶⢒⣶⠓⣰⣠⣻⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⢠⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠀⠀⠀⠁⠠⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠐⠖⠀⠀⠈⠢⡀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠃⢀⠀⢢⠀⠀⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠠⡀⠀⡠⠁⠀⠐⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⢊⠀⠉⡁⠀⠘⠢⢄⠀⠑⢄⠀⠀⠀⣀⡠⠔⠒⠒
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠑⢄⠶⡀⠀⠀⠀⠉⠦⡀⠑⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠀⠂⠀⠀⠀⠘⠂⠠⠄⠠⠤⠀⣀⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠁⠁
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠠⣤⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠉⠈⠳⣄⠀⠀⠀⣠⠞⠛⠻⢿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣷⣠⡾⠃⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣄⣀
⠀⠀⠀⢀⣠⣤⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣶⠶⠤
⠀⠀⠋⠉⠉⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠤⣿⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡷⠖⠒⠛⠉⠉⠹⣏⠉⣹⣍⣿⠟⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣤⣼⣭⠿⠁⠀⠉⠉⠉⠉⠒⠒⣿
⠀⠀⠀⠀⠀⠸⣿⠀⢀⡠⠄⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⢹⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣿⣷⠀⠁⠀⠀⢠⠀⠀⠀⠀⠐⠲⣄⡀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⢽⣠⡾⠁⠘⠷⣄⡀⠀⣮⠁⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣬⠇⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠈⠙⠛⠧⠤⠤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠋⠉⠙⠻⣿⣿⣓⠾⣯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣈⣷⣮⣝⣷⢯⣝⡳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠉⠛⠻⢧⣍⣷⠮⣝⣓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣯⣙⢲⣭⣛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⣿⡒⢬⣝⡲⢤⣄⣀⣤⠶⠶⠶⢤⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢧⣽⣗⠮⣭⣀⣤⣶⠦⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⢿⣿⣷⢤⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⠿⠿⠋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠈⠀⠀⠀⠀⠀⢀⡀⢀⠀⠋⠈⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⡆⣠⣷⠦⠀⠀⠀⠀⠖⠀⠀⠀⠈⠠⣈⡟⠸⠀⠀⠂⣼⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢾⡃⠘⠃⢀⠄⠀⠤⡀⢤⠀⠀⠀⠀⢄⡀⠖⠁⣀⠀⡈⠁⡀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢸⡇⠀⠸⠃⠀⣀⠊⠀⠐⣶⣧⡆⠀⠀⠀⠀⠚⠋⣀⠒⠒⠒⠒⠒⠈⠁⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⢡⡄⣰⢦⣀⠀⣤⠓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⢿⡆⠀⠀⠀⠐⠀⠐⠢⠀⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⢻⡇⠀⢠⡆⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣧⣀⠀⣠⣶⣤⣄⠀⢤⠠⢀⠠⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣄⣹⡆⠘⠿⠃⠀⠀⠘⠃⠀⠀⣀⡀⣃⠀⠀⠀⣤⢨⡋⡾⠈⠁⠀⠀⣌⠀⣰⡤⠶⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠉⠓⠤⠀⠔⠀⠐⠶⠾⠃⠘⠋⠠⢿⡭⠟⣠⠞⠉⡙⢧⠤⠒⠒⢠⡟⠂⠁⠀⠀⠘⢷⣀⣀⣶⡖⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⡀⠀⢀⡿⣇⠀⣤⡀⢨⣤⡀⠘⠂⠊⡩⢀⠀⠄⢀⠈⠁⠈⠉⢻⡄⠀⠒⠀⠒⠋⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡄⠙⠻⣦⡈⠁⠈⣿⡋⢀⡄⢉⡝⢠⣧⣄⠴⣿⣆⣠⡀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⡘⠁⠀⠀⠈⠁⠉⣐⣋⣈⠀⢉⣽⣿⣿⡿⢠⣿⣶⣂⠀⠠⠛⣦⡀⠘⠀⡀⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⡀⠙⡄⠀⠀⠁⠀⠀⠙⡛⠉⠀⣬⠵⠾⠥⠤⠄⠘⠛⠉⣤⠀⢀⡹⠋⠀⠀⠙⠀⠀⠀⠀⣩⠄
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠌⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠢⠀⠘⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠛⠠⠐⠒⡈⠀⠀⡀⠀⣿⢁⠠
⠀⠀⠀⠀⠀⢀⡅⠀⠀⠁⢤⡀⢀⡀⠄⠄⡀⠀⢠⠀⡄⠀⠀⠀⠠⡀⠀⠀⢴⢟⠀⠀⠀⠀⠀⠀⠈⠥⠀⠈⠐⢂⢸⠇⣄⠠⡿⢠⡷⠚⠠
⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠰⣆⠀⠐⠀⠀⠁⠀⠷⠂⠀⠀⠺⠃⢬⠽⠘⠂⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣸⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢤⡀⠉⠀⠀⠀⢀⡄⡤⠀⠸⠆⠀⠚⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠠⠠⣎⠉⠀⠀⠈⠀⠀⠀⠀⠀⠂⠰⡄⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠂⣳⠀⠒⢋⠀⠈⠀⠉⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡟⠀⣀⣤⣄⣀⠀⠀⠀⠀⠛⢠⠀⠀⠆⠤⠀⠘⣿⣹⠟⠀⢸⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠐⠇⠚⠁⠀⣈⠉⣀⡀⠀⠀⢠⡇⠀⠄⢂⠀⠛⠀⠁⠀⢀⠀⣸⠀⠀⠀⠠⣅⡀
⠀⠀⠀⠀⠀⠀⡾⢻⠹⢰⣿⡟⠀⠀⠸⣇⠀⠀⠉⠀⠀⠰⢠⡄⠘⣄⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣷⡄⠀⡀⠻⢄⢠⣶⣶⠀⣀⠰⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⢁⠀⠀⠈⠿⢋⠀⣌⣸⠓⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⣀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⣟⡽⢫⣆⣀⠀⠀⢾⣿⣏⠄⠀⠀⠤⠀⡀⢀⣀⣀⠀⠀⢀⣀⠀⠈⠉⠁⠀⠀⠾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢀⣾⣿⣷⣿⠅⠀⠀⢈⠛⠁⣀⣴⣶⡶⠿⠛⢤⠈⠉⠻⡗⣠⣭⣯⣰⠃⠀⠀⢀⣘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢾⣷⢘⣿⣿⣿⡟⠢⣶⠗⣬⠹⠶⠛⠀⠀⠀⠀⠀⠀⠀⡄⠀⠟⣼⡿⢿⣿⠃⠀⡲⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠘⢛⡋⣿⢿⣍⢀⡷⠇⣈⡝⢳⡆⠀⢠⣶⡧⢠⣿⡆⠀⢰⢾⠓⠙⠳⠄⠀⢠⡄⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡈⡁⠈⣛⠉⠁⠀⠀⠃⣀⣀⣳⡀⢸⣀⠇⢸⣄⡄⠀⠸⠇⣠⠟⠀⠀⣀⠀⠙⠛⠀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢿⠁⡖⠛⡛⠂⢼⣿⡃⠈⣤⣀⠙⠀⠀⠉⠀⠀⢦⡀⣿⠀⠀⢀⣿⡄⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢭⣾⣿⢇⡤⠜⠓⢠⠇⠹⠀⢠⣶⠀⠀⠀⠘⢧⣼⠀⠀⠈⣻⣡⣿⠀⠇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠈⢳⣿⡁⠀⠃⠀⠀⠘⠚⠀⠀⠀⠀⢸⣿⣧⠀⠈⠉⠉⠉⠀⠘⠛⣷⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠿⠄⠀⠘⡄⠀⡀⠁⠀⠀⠀⢀⣈⡘⢣⡀⠀⢷⣤⣀⣀⣀⡀⡟⠃⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣦⣴⣦⠀⠀⠀⠀⠠⠀⠀⠸⠀⣷⣦⠶⠀⠀⠀⠰⠀⠘⢿⡥⠤⠬⠤⠤⣼⠋⣼⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠩⡭⠉⠉⠉⠛⠛⡃⠀⡰⠀⢀⣧⣤⣴⠀⠀⠀⠀⠀⠠⠃⡄⠀⠀⠀⠀⢘⡛⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠉⡟⠋⠀⠰⠀⠀⢨⣉⣭⣏⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠤⠤⡌⠟⢈⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⠤⠤⠤⠀⠗⣦⠀⢢⡄⣀⣋⠋⢉⢻⠂⠀⣠⢀⠀⢹⣿⠀⠀⠀⠀⠰⠀⢰⠀⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠈⠉⠛⠃⠀⣤⡴⠛⠻⠿⠿⠛⠳⠤⠏⠀⠀⠈⠛⠒⠂⠀⠀⠀⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠩⠿⣁⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣎⠒⠶⢤⠘⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡨⢠⠈⢀⡰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⠁⠀⠈⠑⠢⢤⣠⡏⠀⠀⠁⠃⠀⠨⠓⢄
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢴⡾⡋⠢⠤⠄⠀⠀⢀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⢀⣠⠖⠋⠁⣀⠐⢱⠀⠀⠴⠆⠑⠂⢄⡀⠀⠈⡌⠀⠀⠀⠀⠀⠀⠜⢀⡀⠀⠑⡀
⠀⠈⢻⣄⠀⠘⠄⠸⠃⠈⠢⡀⡀⢀⠤⡪⠀⣈⡴⢻⠁⠀⠀⠀⠀⠀⠘⠀⠀⠑⠀⠀⠈⠠⡀
⠀⠀⢸⠈⠓⢤⡀⠀⡀⠈⢆⣀⠍⠓⣨⠴⠚⠓⠂⠣⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢄⡠⠣⡀
⠀⠀⢸⠀⠀⠀⠙⠢⡉⠀⢀⣠⠖⠋⠁⠀⢀⠴⠋⠀⠀⠉⠓⠂⢀⡴⡀⠀⠀⠀⠀⠀⠀⢑⡢⡈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⢹⠚⠉⡇⠀⠀⢺⠚⠁⠀⠀⠀⢀⣠⠔⠚⢁⣀⡜⠀⠀⠀⠀⠀⠀⠐⠠⠬⡀
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⢖⠈⣿⠀⠉⠉⣏⢸⡇⠀⠀⠀⠀⠀⠈⠒⠤⠥⠃
⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⡜⢆⠀⠀⠈⡄⣿⠀⠀⠀⡿⠈⡇⠀⠀⠀⢠⣶⣻⣛⡏⣻⢙⣓⡄
⠀⠀⠈⠳⡄⠀⠀⠀⢸⠀⠀⣿⠀⠀⡇⠈⢆⠀⠀⠸⡇⠀⠀⠀⡇⠀⣷⠀⠀⠀⠈⣿⣟⣏⣹⣉⣯⣿
⠀⠀⠀⠀⠙⢦⠀⠀⢸⠤⠒⠋⠉⢹⠀⠀⠈⢧⠀⠀⢣⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡀⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⣄⢸⠖⠒⠋⠉⠁⠀⠀⠀⠈⢧⣀⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣄
⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠻⡄⠘⡏⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣼⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⢀⠴⠧⠀⠠⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⢐⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠇⠀⢀⠀⠙⠦⠀⠀⢹⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣄⠐⣡⠞⡡⠢⠔⡁⠀⣀⡀⠀⠀⡜⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠁⠴⠂⢁⠀⠀⢦⡟⣦⠀⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠴⠑⢉⠝⠘⡇⠸⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣨⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠖⢁⡠⠀⡇⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣠⠄⢂⣈⣀⣀⡸⢨⠃⠀⠧⠇⡴⣾⠁⠀⠀⠀⠀⠀⡀⠀⢾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⣼⣥⡾⣿⣿⣿⡿⠛⡾⠀⠀⢐⠛⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⣾⠟⠁⢰⣿⣿⡟⠀⢻⡇⠀⠀⠀⢪⠠⡄⠀⢀⣤⣤⣤⣤⣀⣤⣼⣿
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢠⣿⠃⠀⠀⣾⣿⡿⠁⠀⠸⠛⠂⠀⠁⠀⠰⠁⣠⢛⣯⡠⠀⠤⠤⠀⠚⠙⠳⣤⣀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⢀⣿⣿⠇⠀⠀⠀⢇⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣄
⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⡀⣾⣿⡟⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠉⠙⢷⡀
⠀⢠⠎⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠐⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⢸⡇
⠀⡞⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⢸⠇
⢸⠃⠀⠀⠀⠀⠀⣠⣿⣃⣠⣴⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⢷⠀⠀⣀⣴⣾⣿⣿⣧⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢠⡟
⢸⣄⡀⢀⣀⣤⣾⣿⣿⣿⣿⣿⡿⠟⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⣿⣿⣿⣿⡿⠛⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠻⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠹⣿⡿⠟⠋⠀⡼⢛⡿⣿⠻⠆⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠰⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⣆⠀⠀⠀⠀⠘⠁⣿⠀⠀⠀⣠⣾⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⡆⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⣠⣾⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣠⣤⡾⠛⢁⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣾⣆⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣰⣷⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠾⠇⠙⠃⠙⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠋⠘⠋⠸⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠈⠳⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠞⠁⠀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠀⢀⣀⣀⠈⠀⢀⣴⠶⠞⠳⠶⣦⡀⠀⠁⣀⣀⡀⠀⠨⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠉⠀⣴⠏⠀⠀⠀⠀⠀⠀⠹⣦⠀⠉⠻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠆⢸⡇⠀⣀⣀⡀⢀⣀⣀⠀⢸⡇⠰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢻⡾⠋⠉⢻⡟⠉⠙⢷⡟⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠟⠁⠀⢀⣼⣧⡀⠀⠈⠻⣦⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠁⠀⠀⣠⡞⠁⠈⢳⣄⠀⠀⠈⢷⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠼⠋⠀⠀⢀⡾⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣧⣤⣤⣤⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣼⣧⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⢄⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⠠⠜⠉⠒⠚⢦⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠑⠢⢄⡀⠀⠀⠴⠘⠀⢀⣀⣀⠀⠀⣀⠀⠀⠀⠚⣄⠀⠀⠀⠀⢀⡀⠠⢄⡁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠢⣄⠀⠀⠈⠓⢴⠂⠀⡰⢁⠄⠀⠈⠁⠀⢈⡑⣄⠀⢻⡤⠔⠂⠉⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⣍⠓⠦⢄⡠⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠈⠘⠂⢸⡀⠀⣀⣠⡖⠉⠀⢀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⡀⠀⠈⢦⡀⠀⠀⠒⠆⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡠⡴⠋⠉⢀⡞⠀⠀⢀⠎⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⣄⠈⠣⡀⠀⢀⣀⣀⣉⣁⡒⠦⡀⠀⢁⡄⠀⣠⠎⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⢣⡀⠘⢄⠈⠻⠉⠙⢉⣙⡿⠃⣀⠉⢀⡔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⣀⠄⠀⠀⠐⠀⠀⠈⢳⡀⡤⠁⠈⠢⡀⠑⡄⠀⠀⠀⠈⢡⠔⢁⡴⠋⢣⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠈⡲⠇⠀⠀⠀⢰⠳⡂⠁⠀⠀⠀⣹⠄⠀⠀⠀⠀⠂⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀⠀⠀⠘⡀⠈⡦⠠⣖⠉⡠⠁⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠐⠊⣙⢾⢃⠙⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡀⠀⠀⠀⡏⠸⠈⠀⠀⠀⢠⡇⠀⠀⠀⢐⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢷⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⢀⠃⠀⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⢤⡀⡈⢣⣌⢀⡠⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠐⠒⠆⠀⠘⠀⠁⠛⣧⠀⠀⠀⠜⠡⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⢠⡘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡄⠀⠀⠀⢸⡄⠀⠀⢡⠀⠀⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠇⠀⠀⠀⠀⡆⠀⠀⠀⠘⡇⠀⠀⠘⠆⡀⠴⠅
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⡉⠥⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⢋⠉⠄⠒⠈⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡅⠀⡀⠀⠠⠄⠀⠒⠂⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⡞⠀⢠⡀⣠⠀⡀⠀⠀⠀⣹⠃⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣆
⠀⠠⠀⠀⢀⠌⠀⠀⠆⠰⠂⠠⠀⠀⠀⢠⠃⢀⠠⠓⠒⠠⠤⠄⢼⢄⡀⠀⢀⡽⣀⡀
⠀⡀⠀⢠⠏⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⠃⠰⠃⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⢀⠄⠈⠒⠒⠻⠚⠛⠛⠛⠉⠈⠉⠁⠀⠙⠀⢤⡤⠴⠶⠞⠋⠁⠒⠀⠒⠠⠤⠀⣀⢠⠆
⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢻⡿⢿⢻⡟⣙⠛⣿⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣛⣻⣿⣛⣛⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⡾⠒⠵⠋⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡋⠀⠀⠀⠀⠀⡀⠀⡶⠒⠢⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠹⠀⠱⡀⠀⠜⡧⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢀⠀⠀⠀⠀⡠⣚⠀⠀⠙⠢⢤⠏⢉⠒⠒⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠒⠈⠃⠛⡀⠀⠀⠀⠀⠀⠀⠙⢔⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣕⠄⣶⡿⣄⠀⠀⠀⠀⠀⠀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐⠊⠀⠀⠈⠢⣀⠀⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡜⠀⣇⣀⡀⡜⢰⠆⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠚⢤⣀⠀⠈⠸⡅⠀⠀⡕⠦⡠⠖⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠶⠸⠟⠂⢠⠳⠴⠘⢄⠠⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⢀⠀⠤⡀⠃⠀⠀⠈⠀⠀⠘⠁⠀⠚⠀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠘⡦⢄⣈⠀⠂⠈⠀⠨⠀⡀
⠠⡐⠶⠶⡆⠀⠀⡀⢄⠀⡔⠁⠀⠌⠀⠀⠀⠀⠀⠉⠐⣶⠖⠒⠚⠃⠁
⠘⠃⠀⠐⠁⠸⠢⢀⠋⠆⠁⠁⠀⠀⠀⠀⠀⠀⢠⣔⣀⠖⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡴⠟⠛⣢⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣉⣰⢸⢁⢎⢜⢃⡾⠣⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⢸⡅⣪⣣⠾⢃⡸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⡇⠸⢼⡧⠇⢀⢞⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠂⣤⠀⠀⠀⠀⠀⠀⠀⠈⣀⡅⣰⣿⢏⢀⠒⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠈⡉⠂⠀⠀⠀⠀⠀⠀⣶⣊⡀⣋⢪⢡⡷⢱⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⣠⣥⣌⠛⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠄⣰⣷⡷⠀⠀⠀⠀⠀⠀⢠⣭⣤⠆⣗⢀⡝⡱⣻⢿⣿⡅
⠀⠀⠀⠀⢀⡼⢭⣴⠟⠛⢁⢀⡀⢀⠀⠀⠀⠀⠀⠈⠀⣠⠀⢸⣽⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⡇⠴⢰⢡⠟⣽⣿
⠀⠀⠀⣰⣿⣿⣿⣛⣖⠚⣁⣀⣠⡭⡜⠀⠀⠀⢀⣤⣶⠖⠎⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣿⡇⢠⣃⣋⣰⣿⣿⣀⣀
⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠷⠧⠤⠶⠿⠿⠋⠁⠄⠸⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠢⠊⠓⠰⠾⠯⣝⣻⢠⣽⠟⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⠀⠐⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠠⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠋⠀⠀⠢⣦⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠉⠢⡈⠲⣌⣦⡖⠠⢥⡒⠷⠠⠀⠀⠈⣶⠏⠀⠀⠀⠀⢁⠀⠁⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠡⠀⠀⠀⠀⣻⣋⠐⠓⢠⣐⠁⠈⠆⠀⠂⠀⡀⠻⠀⠀⠀⠀⠀⠘⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⢸⡁⠑⢌⡀⣈⠬⠘⠂⢬⠀⢀⡼⠀⠐⣇⠀⠀⠀⢸⡔⡀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠌⢀⠄⡞⠀⠒⠀⠠⠤⠂⠀⠀⠊⠉⢀⠛⠀⠀⣤⠆⢀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠈⡔⢀⡀⠛⠀⠀⠀⠀⠀⠀⢀⠒⠂⠐⠁⠀⠡⡐⠈⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢷⠊⠉⠁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠐⠒⠒⣲⠚⣯⡀⠁⠱⠒⠁⠁⠺⠀⠂⠀⠀⠠⠠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠭⠧⡐⠀⠀⢃⣘⡀⢬⠈⠀⠀⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢀⣀⢪⠁⠀⠔⠢⠤⠅⠀⠈⠙⡛⠁⢘⣀⠤⡐⠐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠒⠚⠦⠤⠄⠓⠶⠤⣲⡄⢠⠄⠀⠄⠠⡤⣀⡉⠀⣀⣡⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠄⣰⡃⠠⠀⠉⠐⠺⡁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⡀⠀⠀⠈⠸⡁⠈⠈⠀⠤⠆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠈⢄⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⠀⡀⠀⠐⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⡀⠀⠀⠀⡆⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠴⠖⠒⠒⠚⠛⠉⠉⠙⡦⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⢀⣠⣴⠿⢄⠘⢿⣦⡄⢼⢇⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠁⢺⠧⡎⠉⠀⡆⠀⣵⡇⡎⠉⠙⠲⡇⢀⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡶⠶⠶⢷⢠⢾⡆⠈⠒⠒⠒⠒⠁⠛⢶⠒⠲⢊⡔⡵⠀⠀⠈⠛⠶⠦⢤⡀
⠀⠀⠀⣤⣶⠾⠟⠛⠋⠉⠉⠀⠀⣄⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢀⡀⠀⠀⠚⠀⠀⠁⠊⣰⣋⣁⠀⠀⠀⠀⠀⠙⠄⡰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠛⠒⠒⠛⠋⠀⡖⠉⠉⠁⠀⠈⠉⠉⠓⠲⠦⣄⡠⣢⡀⢀
⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⠀⢈⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⣨⣅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠈⢻⡄⠀⢸⠀⠀⢆⠈⠲⣤⣠⣴⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢬⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢈⡇⠀⢿⡀⠀⠘⣆⣰⣿⣿⣿⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠒⠄⠘⣇⢹⣿⣿⣅⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⢤⡇⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢠⡔⠁⠘⢾⣿⣿⣣⠖⢁⢞⣠⠴⡶⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠈⠳⠄⠀⠻⠋⠀⡴⠟⠉⣠⡾⣴⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⢴⠏⠀⠀⠀⠀⣎⠠⢀⠀⠀⠀⠀⠀⢀⣿⣦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠚⠦⠤⠤⠄⠀⠀⢲⣤⡄⠀⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⢸⠁⠀⠀⠉⠐⢖⠒⠒⠋⠀⢈⣹⠶⢍⣹⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⡇⠀⢀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⡮⠀⠀⠀⠀⠀⠀⠉⠒⢖⡫⣭⣶⡛⠻⢤⣀
⠀⠀⠀⠀⠀⠀⠔⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢾⡗⠈⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⡄⠃⠀⠀⠀⠀⣀⡤⠶⢿⣓⣲⡯⠵⠟⠀⣠⠼⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡨⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠸⠗⠈⢺⣿⠀⠀⠀⣀⠐⣶⣶⠾⠿⠿⠟⣓⣛⣳⡤⠴⣾⠛⠚⠋⠉⠁⠀⣀⡤⠖⠋⠁⠀⡏
⠀⠀⠀⠀⠀⣶⣋⠁⠀⠀⣹⢛⡖⠒⠒⠲⠶⠶⠶⢶⠶⢶⣦⣤⠶⣿⠀⣽⠯⠉⢢⠐⣒⣚⣯⠭⠭⢷⣖⣒⣻⡧⠌⠳⣄⣠⡤⠖⠋⠁⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⡇⠈⠓⢦⡼⠁⣞⡀⠀⠀⠀⠀⠀⠀⢸⡇⠐⣛⣚⣉⣽⠀⢻⠀⠀⢀⣣⣀⣒⣊⡉⠭⠭⢤⣶⡶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠷⠦⠬⢭⣝⣓⡒⠶⠤⣤⣼⠃⢈⣉⣀⡤⣼⠀⠈⣩⠭⠭⠽⠶⣒⣚⣻⡭⠵⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⢾⡇⠠⠴⠒⢒⣻⣤⣶⡶⠶⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣠⣤⣾⣿⣿⠟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠉⠉⠙⠛⠿⠿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦
⠀⠀⠀⣠⣾⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣦⣀⠀⠀⠀⢀⣤⣾⣿⠿⣿⣿⣷⣤⣀⡀⣀⣀⣠⣤⣶⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉⠛⠿⣿⣿⣿⡿⠿⠿⠛⠉⠉⠉⠻⣿⣿⣶⣄⣀⣤⣄⠀⢾⣿⣏
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠀⠈⢿⣿⣷⡄
⠀⠀⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠙⣿⣿
⠀⠀⢹⣿⡇⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢻⣿
⠀⠀⣸⣿⡿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⢸⣿
⠀⣼⣿⡿⠁⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⣼⣿
⠰⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⣀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣿⣿⡄⠀⠀⣴⣿⡿
⠀⢿⣿⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⡄⠀⢿⣿⣧⣤⣾⣿⠟⠁
⠀⠘⣿⣿⣄⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠈⠛⠿⠿⣿⣿⣆
⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⢰⣿⣿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠁
⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋
⠀⠀⠘⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠈⠻⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠀⠀⠀⠀⠉⠉⣻⣿⣿⡟⠛⠉⠉⠁⠀⠀⠀⠈⣻⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⡿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠉⠙⠻⢿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠿⠛⠋⠁⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⢀⣿⣿⠛⣿⣿⣄⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣷⣄⡀
⠀⠀⠀⣠⣶⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⡀⠀⣼⣿⡟⠀⠙⢿⣿⣦⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣄
⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣷⣤⣤⣾⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣁⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠁⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠻⣿⣿⣿⡿⠛⠀⠀⣀⡴⢤⣀⠤⠒⠩⠍⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⠄⠀⠀⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠁⠀⠀⠀⠈⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⣼⠁⠀⠈⠻⣆⠀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⢸⡇⠀⠀⠀⠀⢹⣇⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠛⢷⡀
⠀⠀⣸⡟⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢸⡇
⠀⠀⣿⠁⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⠇
⠀⠀⣿⣆⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⡟
⠀⠀⠘⢿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣤⣼⡟⢳⣄⣀⣠⣴⢾⣯⣤⣴⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⣘⣿⣥⣿⠍⣸⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠙⢷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠖⠒⠒⠒⠛⠛⠛⠉⠉⠛⠛⠛⠓⠒⠒⠶⠤⢄⡀⢠⠞⠙⠲⣄
⠀⠀⠀⠀⠀⠀⢠⠏⠁⠉⢷⣠⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣀⠤⠒⡶⠀⢀⣀⡤⠶⠒⠛⠉⠉⠉⠉⣑⣲⠦⠈⠉⠀⣀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠸⠤⣀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⡴⠋⠁⠀⣼⠤⠚⠉⠀⠀⠀⠀⠀⢀⣤⣖⡋⠭⠄⣀⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⡀⠀⠀⠀⠀⢠⠋⠰⢃⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⠏⡘⠁⡇⠀⠀⡀⠀⡆⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠄⠀⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡈⠰⠿⠿⢧⠀⠀⡁⠠⠁⠀⠀⠀⠀⠀⡠⠴⠒⠋⠉⠉⠉⠉⠁⠊⠁⠀⠀⠢⡀⠀⠁⠄⠀⠁⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣼⠀⠀⣘⡄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡠⠔⠒⠒⢮⡓⠀⠰⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⢻⡆⡞⢁⢤⠀⠀⠀⠀⠠⡓⠀⠀⠀⠀⢠⠞⠁⠀⢀⠎⠀⠀⠀⠀⠀⠹⡄⠀⠱⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⡀⣿⣶⣾⣿⣿⡇⠙⠁⡏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⠂⠀⠢⡎⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠇⣅⣠⣤⣤⣼⡇⠀⠘⠷⠒⠒⣚⢳⡀⢀⡇⠀⠀⠀⠀⠀⠀⣤⠚⡖⢤⣤⣀⡀⠀⠀⡟⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⡇⠀⢠⠖⠉⣉⣄⣈⡉⠉⠀⠀⠀⠀⠅⠀⠀⠈⣰⡇⠉⠁⠀⠈⢉⡾⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⣦⣤⣶⣶⣶⡇⠀⣿⠀⠈⠙⠒⠚⠉⢀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠙⠿⠶⠶⠚⣋⣀⡀⠀⠀⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡄⡏⠉⠉⠉⢉⡇⠀⠘⠳⠦⠤⠶⠒⠛⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠉⠀⠀⣹⠀⢀⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡁⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠉⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢳⣡⣤⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠘⢀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠂⠦⠄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠸⣸⡏⢉⣉⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠲⢄⡀⣀⣀⣤⡄⠀⠀⠒⠈⠁⠈⠒⠁⠀⠀⠀⠀⠐⠿⣿⣷⡖⠢⡄
⠀⠀⠀⠀⠀⠀⢣⢻⡿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠳⣄⠔⠀⢻⡠⠊⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠋⢳⣶⣿⠁⠀⠀⠀⠀⢀⡴⢢⠞⡿⢲⡆⣀⠀⠀⠘⠛⠀⡄⢣⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⣀⡤⠂⠉⠉⠈⠉⠉⢭⠉⠉⠓⠘⠢⠓⠊⠀⠁⠉⠉⠉⠉⠙⠛⠛⢆⣸⠀⡏⢳⣄⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⡀⠔⠋⠁⠀⠰⣖⠒⠀⡔⠁⢸⣤⠄⠤⠐⣦⡤⠤⠤⠤⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢆
⠀⠐⠉⠀⠀⠀⠰⠚⠉⠉⠣⠀⡀⠀⠰⠊⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠑⠒⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡉⡆⠀⠀⠀⠀⠀⠚⠃⢂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢴⡥⠤⢀⣀⠉⠀⠒⠒⠚⠋⡠⠒⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡁⠒⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠁⠉⢐⠉⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⣤⣀⣈⠤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣋⣯⣶⡤⣙⠤⠐⡀⣀⣼⣽⣯⣤⡀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⢽⣄⣰⠋⣠⠆⠀⠀⠀⠐⠍⡳⣹⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⡇⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⡆⠑⢄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠒⠀⠀⠀⠀⢀⠤⠄⣀⣀⣠⣤⣀⠀⢸⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⠀⠀⠀⠀⢇⢰⣿⣿⠟⣭⣉⣉⣛⣿⡇⣸⣀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡕⠒⠲⠎⣹⠻⠿⢒⣂⣀⣛⡛⠯⠺⠉⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⠀⣿⡇⡄⠀⡄⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸⠀⠀⠀⠀⣿⣷⠀⠀⢠⠸⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢸⢹⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠤⠤⠶⠬⠽⠤⠤⠤⠶⠶⠤⠤⠭⠭⠙⠛⠛⠛⠒⠂⠈⠉⠉⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡥⠤⠤⠤⠤⠠⡄⠀⠀⠀⢀⣠⡤⣠⣤⣤⢤⡤⠦⣶⣶⣖⢢⠀⠀⠶⣖⣒⠶⠶⠶⡒⠒⠄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠎⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣸⣿⣻⣚⣲⣓⣎⣉⣝⣭⣫⣌⠆⠳⠀⠀⡇⠀⠀⠉⠉⠀⠀⢰⠀⠈⠲⡄
⠀⠄⠀⠀⠀⠀⠀⠀⢀⢌⠎⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣧⣭⣭⣭⣭⣭⣭⣤⣴⣶⣶⣶⣶⣾⠗⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠠⢪⣥⡤⠶⠤⣶⣶⠶⠶⠒⢂⡜⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⣽⠥⠤⠅⠛⠛⠿⠶⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣀⣴⣷⢟⢢⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣤⠌⢀⣄⠑⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠊⠀⠠⠀⠓⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⠦⠤⡞⢓⣈⠀⠀⠀⠀⠀⠀⠀⠀⡞⡄⠀⡈⢀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠐⠀⠁⠀⠐⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⠤⠤⠀⠀⡺⠒⢀⡾⠁⠀⠂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠊⢀⣀⣀⣨⣡⡠⡠⠿⠀⠀⠈⠰⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠃
⠀⠀⠀⠀⠀⠵⡶⡆⠀⠀⠀⠀⠀⣻⣶⣦⣤⣤⣾⣿⣶⢿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠳⡌⡤⣤⣤⣄⢀⢀⣀⡀⣀⢠⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠧⠴⡆⠴⠀⠀⣿⡅⠐⠀⠀⢐⠀⣸⠏⢀⠐⠂⠠⡄⠢⠀⠁⡄⠃⡠⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠲⠶⡴⠶⠐⠶⠲⠶⠆⠴⠶⠅⠀⠈⠢⣘⠄⠂⠠⠅⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠉⠁⠈⠀⠉⠐⠑⠻⠖⠚⠓⠛⠒⠚⠓⠛⠒⠚⠲⠓⠲⠶⠟⠢⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⣠⣴⣾⣿⣿⣶⣄⢀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠉⠛⠛⠛⠉⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⢿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⣀⣤⣶⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⡀⠀⠀⠀⠀⠈⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠙⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⠄⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣈⠁⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡛⠿⣿⣷⣄⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⣾⣿⡏⠻⣿⣿⠟⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠹⣿⣿⡿⠃⠀⠈⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿
⠀⣀⣤⣶⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⣿⣿⣤⣤⣄
⣼⣿⡿⠛⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣄⡀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⢿
⢿⣿⣦⣀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣴⣿
⠈⠛⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⢀⠖⠈⠀⢀⣠⡽⠛⣋⣉⣙⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⣀⣷⣯⣴⣁⣴⣿⣿⣴⣿⠿⠃⠀⠸⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢿⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣷⣦⠠⡝⢻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠾⠛⠋⠙⠉⠋⠀⠀⠀⠀⠀⠐⣌⠻⣿⠻⠗⢾⣤⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢻⣮⣱⡇⠘⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠗⣶⣖⣂⣀⠀⠀⠀⠀⠀⠀⢠⣿⡷⢿⣿⣎⠉⡀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣧⣶⣶⣶⣶⣶⣶⣶⣤⣾⣿⡿⠃⢹⣿⡟⢁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡿⢿⣿⣿⣿⠉⠿⢿⣿⣿⣿⣿⣶⢨⡿⢻⣿⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⠁⣸⡟⡟⠿⠤⠀⠀⠘⠉⠉⠙⣿⣿⣷⠀⣿⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡏⠀⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⢱⡿⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⣿⣿⠶⠒⠄⠀⠀⠀⠀⢀⣼⣇⣏⡆⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⠁⠀⠀⠀⠀⢤⠀⠀⠈⢷⣽⣿⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢻⠒⠉⡉⠙⠂⠈⠃⠀⠀⠘⢻⡟⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠛⠇⠀⠀⠶⠤⠀⠀⠼⢋⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⡀⢀⣄⡀⠀⠀⣀⣤⣶⣿⣿⣿⡀⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠸⢻⣿⣿⣿⣿⣒⡒⠻⠛⠻⢿⣿⣿⣿⣷⣸⡿⣿⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⠿⠟⠛⢻⣄⣜⢿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠱⠃⣼⣿⣿⣿⣤⡀
⠀⠀⠀⠲⣄⣠⣴⡾⠿⠟⠛⠛⠉⠉⠀⠀⣴⣶⣼⣿⡟⢦⡻⢯⣿⣿⡇⠀⣀⣴⣿⣿⡿⢟⣋⠄⢀⡼⠁⠈⠙⢿⣿⣿⣷⣤⣀
⠀⠀⠀⢹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣆⡙⠢⣭⡛⠛⠛⠉⣉⠉⠁⠐⠛⢁⣠⠟⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⡀⢀⡤⠒⠦⡀
⠀⠀⠀⠾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠲⢌⣁⣀⣀⣈⣉⡡⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡏⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠉⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⠈⠀⠀⠀⠀⡤⠀⠠⠔⠒⠐⠙⠄
⠀⠀⠀⠠⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠊⠀⣈⢵⣂⠢⠀⠐⠈
⠀⠀⠀⠄⢈⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠇⠀⢠⣈⢡⠇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠁⠀⠈⠐⠃⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠢⠤⡀⠀⠀⠀⠐⠂⠑⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠐⡀⠀⠠⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⣀⡀⠀⠀⠀⣀⣀⠀⡈
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠠⠠⠄⡐⠁⡢⠥⠈⡅⢰⢠⡄⢐⠁⠊⠁⠉⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠂⠁⠘⠒⠀⠅⠃⠀⠀⠀⠀⢼⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠡⠀⢘⠚⠀⠠⢀⠔⠉⠉⠑⠄⠀⠸⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⠄⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠉⠉⠚⠒⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠪⢀⣠⠀⣀⣀⣀⡀⠀⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠢⢄⣀⠆⠈⠀⢠⢾⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠂⠄⠀⠀⠀⠈⠲⢇⣀⣄⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠶⣄⠀⠀⢹⡿⡇⠀⡗⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡒⠈⠀⠀⠀⠀⠀⠐⠓⠙⠂⢀⣣⡰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⣓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠘⠿⢿⡿⠏⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⢤⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⣰⡆⠀⠀⡄⢸⢿⡇⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠸⠏⠻⡆⠀⣇⠈⠒⠁⠀⠹⡄⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⠒⠀⠀⠘⠄⢰⠦⢄⠀⠘⣤⢔⣩⡤⣄⠉⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⡞⠒⠒⠋⠀⠀⠱⣞⡵⣏⡮⠊⡝⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠀⠀⠀⠸⠀⠀⠀⣀⡠⠖⠉⠉⠀⠻⢁⠞⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⢧⠀⠀⡇⢀⠔⠊⠴⠂⠀⠀⠀⢀⡼⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣥⠃⠀⠀⠀⢀⠀⠀⣠⢾⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠦⣄⠘⣆⠀⠀⠀⠀⠑⢋⡴⣫⡤⠴⠷⣤⠞⡽⠲⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢹⠻⡄⠀⠀⠀⠐⠉⡆⠀⠲⢄⠸⢁⡞⠁⠀⠈⠓⢄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡌⠀⢱⡀⠀⠸⡇⠀⡇⠀⢀⠠⠓⠘⠦⣄⠀⠀⠀⠀⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠄⢣⠀⠀⢹⡀⢸⠀⠉⠢⢄⡀⠀⠈⠙⠦⣄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠀⠈⢇⠀⠘⣇⢘⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠈⠆⠀⣿⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠘⠄⢿⡆⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣻⢦⡴⠭⠷⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡿⠉⠁⡞⠀⠀⠀⠀⠀⠈⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢰⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠦⠤⠀⠀⠀⠦⠒⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠋⠀⠀⠙⠒⠋⠉⠛⠚⠉⠉⠉⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠀⢩⠂⠐⠒⠚⠉⠉⠉⠉⠲⠰⡤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠁⠂⠧⣀⠤⠸⡠⠤⠀⠀⠀⢀⡗⠑⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠲⣄⣀⠈⠇⣀⡈⡢⠠⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⢒⠞⢤⠢⠶⠦⢐⠖⠒⠋⠉⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢀⣜⣁⡱⠭⠭⠭⠬⣄⣲⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠉⠉⠀⡧⣤⡤⠠⢤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠨⠗⠙⠄
⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⡄⢀⡤⠊⣀⣀⡤⠤⠶⢞⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠈⡷⢤⣀⡈⠳⣄⠀⠀⠀⠀⠀⡧⣤⠤⢾
⠐⢰⠤⠼⠆⠒⡰⠿⠆⠒⢖⠛⠋⠉⠁⠀⠀⠒⠒⠊⢳⠦⠼⠀⠀⠀⠀⠀⠀⠀⣇⠜⡲⠖⠊⠐⠒⠊⠉⠓⠾⢷⡐⠒⠒⠂⡇⠀⠀⢸⠒⠒⠒
⠀⢸⣉⣹⠀⢸⣦⠤⠤⠤⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⢾
⠀⢸⣀⣸⠀⢸⣋⠀⠀⠚⢩⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣄⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⡀⢤⠠⠀⢀⠀⠀⠀⠀⠀⠣⠤⠤⠊
⠀⠈⠉⠉⠀⠘⠲⠬⠭⠔⠀⠀⢀⣠⣤⣤⡀⠐⠛⠉⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣤⡶⠶⠟⠛⠉⠁⠀⠀⠲⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣴⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⣰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⢀⠀⣴⣾⣿⣿⣿⣿⣿⠛⠛⠃⠛⠋⠛⠛⠃⠙⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⣿⣿⣷⠈⣷⠂⠄⠀⠀⠀⠀⠀⠀⠄⣶⡿⢻⣿⣿⣿⣿⣿⡙⢿⣿⠁
⠀⠀⠀⠀⠈⠉⣵⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠰⠛⢉⣷⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢋⣾⣿⣿⡿⣿⣿⣶⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡍⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠫⣾⣿⢿⣿⠙⠛⠛⢹⣿⣿⣿⣷⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⡄⢢⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡑⢤⡀⠀⠀⠀⠀⢸⡇⠀⠳⣄⡼⡀⠀⢠⠎⡇⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠉⠲⣄⣀⡷⠾⠁⠀⠀⠀⠀⠈⠐⠋⠀⢱⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠉⠀⠀⠀⠉⠁⣀⣀⣀⣀⡀⠤⠤⠄⣀⡀⠘⠳⠚⢩⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⠒⠀⢀⠀⠘⡁⠚⠁⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣀⠀⠸⣀⢠⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠻⢄⡀⢠⠎⠀⠀⠀⠀⠀⠀⣀⠦⡀⠀⠀⠀⠀⠀⢸⠆⠀⢁⣸⠦⠚⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠀⠀⢙⠏⠀⠀⠀⢀⠠⠤⠚⠁⠀⠈⠁⠂⠠⣄⠀⠸⠗⠊⠉⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠙⠷⢤⡔⠁⠀⢀⠔⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢢⡀⠀⢀⠀⠂⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡟⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⢶⠁⠀⢀⡞⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠱⡀⢠⠁⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢲⠀⠀⠀⢣⣠⠏⠀⢀⣀⠤⠬⠽⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠃⠀⠠⣄⡙⢾⠀⠀⠀⠧⣤⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⣈⡈⠀⠀⠀⠀⣣⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⡆⠁⢆⠀⠀⠀⠀⣧⣤⣤⡇⠀⠀⠀⠰⢋⡀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⢄⢡⡀⠀⠀⠀⠀⠑⢄⠀⠀⢩⠍⢍⠃⠀⠀⡠⠁⠈⠃⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠙⢦⣤⣀⣀⣠⡄⠓⣤⡄⣈⣀⣀⡠⢶⡆⠠⠄⢤⡶⠊⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠊⠁⠁⢉⠳⡄⠀⠀⠱⡄⠈⠀⠀⠀⢉⡡⠎⠀⠀⢀⡞⠀⠀⢠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡥⠤⢜⡀⠀⠀⠈⣶⠀⠀⠀⣸⠁⢀⠀⢀⡞⠠⠤⢄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣼⣤⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡁⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠀⢤⠀⢠⠤⣄⠀⠀⠀⢈⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⡔⠈⠑⢀⢸⠄⠀⣤⣤⠀⣘⠠⠃⡠⠌⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠀⠤⢶⠔⠀⣄⠀⠀⡇
⠀⠀⠀⠀⠁⠀⠀⠄⡐⢻⢦⠀⢠⠺⢉⠰⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡴⠂⠀⣠⣤⡂⠒⠁⡀⠀⠋⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠄⣳⠛⡀⠉⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠉⠀⠀⠀⠀⠒⠂⢻⢖⣆⡀⠠⠉⣈⠓⠹⠤⠥⠀⢳⠤⠀⢠⣤
⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠧⠀⠠⠄⠐⠁⡦⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠉⠀⠂⠀⠀⡄⠀⠀⢀⡄⣸⡄⠀⠈⠉
⠀⠀⠀⠀⠀⠸⠐⠀⠀⣄⡀⠀⠀⠤⠤⡖⠀⢀⣀⣀⡼⠂⣤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⠙⠓⠊⠀⠙⠻⡁⢠⠉⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠠⣅⣀⠀⠠⠀⠀⢀⠆⣈⢉⡤⣂⡬⠋⠀⠀⡦⠠⠤⡤⠤⢤⠄⠸⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠽⢦⠄⠀⠀⠀⠓⠀⠹⡂⣉⡁⠀⠀⠀⣧⠀⢀⠀⠀⢠⡄⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠖⢛⠔⠁⠂⠀⠀⠀⠄⠀⠄⠀⠉⠁⠢⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠤⠄⢀⡁⢈⠓⠀⢀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⡀⠀⠀⠀⣠⣄⡀⠰⠀⣂⠀⢀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠠⠀⠀⠀⢈⣀⡁⠂⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠈⠂⢀⠘⡀⠀⠺⠛⠛⠷⠀⢀⠁⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡄⠞⠛⠋⠁⢀⠠⠀⢉⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠘⠀⣀⠀⠀⣀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠲⣄⠀⠀⠀⢀⡀⠂
⠂⠀⠀⠀⠀⠀⠀⡀⠈⠉⠀⠀⠐⠂⢉⢀⡀⢄⡠⣄⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⠀⠈⣙⠚⢉⡉
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⢀⠰⠂⠀⠀⠀⡈⢁⠂⠈⢃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠶⠋⢌⠁⠉⠃⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄⠌⠀⠀⠠⠀⠼⢄⠨⠁⢀⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⢡⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡉⠁⠀⠀⠀⠀⠈⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡀⠈⠶⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⢈⡙
⠀⠀⠀⠀⠀⠆⠀⠘⠃⠰⠘⠂⠤⠖⠂⠀⠉⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀
⠀⠀⠀⠀⠀⡤⢤⠲⠎⠅⡛⠗⠓⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣭⠤⠴⢭⢅⠉⠦
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠄⠀⠀⡡⢱⢀
⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⠀⠀⢰⢡⠀⠣⡀⡄⠂⠀⠠⣀
⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠀⠀⠀⢄⣾⠘⢄⢹⠈⠢⡀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⢀⠄⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠔⢡⡿⡖⠀⢻⠀⠀⠀⠑⠤⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⢡⢸⠀⠀⠀⠠⢒⠕⡊⠤⠠⠀⠀⣀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠮⣀⣘⠀⠀⠀⠀⠀⠈⡆⠀⠀⢈
⠀⠀⠀⠀⠀⢸⢸⠨⢐⣥⡞⢥⡊⠁⠀⠀⡠⠚⢡⠀⠀⠀⠔⠀⠀⠀⠀⣤⣶⣲⣶⢰⠀⠶⡖⠀⠀⣠⠀⠠⠐⠈⢢⠣⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠄⢴⡁⠀⢀⠀⡠⢃⠴⠋⠀⠀⡸⠄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢱⡅⠀⢤⠀⣀⣀⣠⠴⠥⠤⠜⠀⠀⢄⠀⡇⠀⠀⠀⠃
⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠊⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⢂⡐⢠⠒⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰
⠀⠀⠎⠥⠀⣀⠀⡀⢀⠄⠊⠁⠀⠀⡠⠊⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠀⠀⢀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠊⠀⠀⠀⠺⠀⠤⠀⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⢸⠂⠺⠭⠯⠭⠽⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⣠⠞⠀⠀⠀⠀⠀⠰⠀⡤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⡤⠸⠃⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠧⠤⠤⠄⠀⣀⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠑⠒⠒⠒⠂⠉⠉⠉⠉⠉⠁⠂⠉⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢿⣍⣉⣉⣉⣽⡟⠁⠀⠀⠀⠀⠀⠻⣯⣉⣉⣉⣩⣿⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⣯⣤⡶⠶⠿⠿⠶⢶⣦⣽⣷⡀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣤⣤⣤⣤⣴⡶⠾⠟⠛⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣠⠖⠉⣠⠔⠁⣼⡡⠖⠚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠘⠋⠀⢀⡞⠁⢠⠞⠉⣀⡤⠤⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⣠⣯⠴⠖⠛⠚⠊⠁⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⡠⠠⢄⡀⠀⠀⢀⣀⣼⠁⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⠄⠠⡄
⠀⠀⠀⠀⠀⠀⠣⠤⠤⠼⠆⠀⣴⠟⠙⣦⠟⠁⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠾⠤⠤⠴⠃
⠀⠀⠀⠀⠀⢠⠤⠤⣤⠀⠀⢰⡇⠀⡜⠁⠀⠀⠀⠸⠟⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⢻⡀⠀⠀⢠⡤⠤⢤
⠀⠀⠀⠀⠀⠘⠶⠚⠁⠀⠀⢺⠏⣸⡇⠀⠀⠀⢠⠖⠋⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⢀⣀⣉⠀⠈⣇⠀⠀⠀⠙⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣇⠀⠀⢠⡏⠀⠀⠀⠀⣀⣹⡆⠀⠀⠆⠀⠀⣿⣁⣈⣳⠀⢿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠖⢻⡀⠀⠈⣷⠖⠚⠋⠛⠋⣼⠀⠀⠀⣦⠀⠀⠣⡌⡩⠋⠀⢸⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆⠀⢧⠀⠀⠘⠦⣤⣀⡤⠞⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣁⣠⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⡴⠋⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡼⣿⣿⣷⣼⠆⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠰⠦⣌⣻⣿⡟⠀⠀⠀⢀⡴⠋⠀⠀⢀⣸⡁⢸⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣄⡀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠙⠁⠀⢀⡴⠋⠀⠀⠀⠀⡏⠀⢈⡇⢀⠎⢙⡆
⠀⠀⠀⢀⣠⠤⠤⠴⠊⣉⠴⠚⠉⠉⠉⣿⣉⠉⢻⡄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢳⠀⠙⠉⠙⡶⠊
⠀⠀⡾⠋⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠈⠉⣻⠇⢛⡗⠶⠦⠤⠴⠚⣏⠙⣦⠀⠀⠀⠀⢀⡰⠋⣠⠖⠀⠁
⠀⠀⠳⡞⠀⠀⠀⡀⢀⠇⠀⠀⠀⠀⠀⠀⢠⡟⠁⠘⠀⠀⠀⠀⠀⢨⢻⡷⠛⢶⣦⣤⣶⡯⠴⠋⠁
⠀⠀⠀⠙⢾⣁⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡀⠀⣸⠇⢰⣦⢀⠘⡇
⠀⠀⠀⠀⠀⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⣀⡈⠃⠐⠾⠃⠐⠀⡇
⠀⠀⠀⠀⠀⠀⣰⠟⡹⣧⠀⠀⠀⠀⢰⡿⠶⣤⣤⣉⣉⠛⠛⠚⠚⠃⢠⡇
⠀⠀⠀⠀⢠⡾⢣⠞⢀⡼⡆⠀⠀⠀⣸⣯⠀⠀⠀⠈⠉⠙⠛⠳⠶⠦⣼⠃
⠀⠀⠀⣴⠟⡴⢁⣶⣿⡔⢻⡄⠀⣾⠉⠙⢦⣀⡀⠀⠀⠀⠰⢤⣤⣴⡋
⠀⣠⡾⣡⢮⠀⢠⡿⠁⠹⡄⠙⣛⡿⠳⡤⠞⠉⠛⠷⢦⣤⣀⣤⣶⣿⣧⣤⣀
⣴⢏⡔⢁⣠⡷⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⢳⡦⠉⡷
⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠯⣴⣿⣶⡶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠢⠤⢤⡬⣉⣀⣀⣰⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠺⠶⠶⠦⣤⣭⣭⣉⣗⣻⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⠿⠟⠛⢋⡋⣙⣛⣟⢛⠿⠿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⠟⡻⠋⣉⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣩⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡃⠀⠀⠀⠀⠀⠀⢀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⢜⠁⠀⠉⠳⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣠⠔⠋⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⣾⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⢿⡄⠀⠀⠀⢀⣤⠴⠶⠦⣄
⠀⠀⠀⠀⠀⠺⣄⣠⠶⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠘⣧⠀⠀⠀⠀⠙⠲⢤⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⣥⣤⣄⣈⣷⠀⢸⣷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⢻⡶⠶⠶⠛⠋⠛⠿⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢉⡽⠃⠀⠸⣧⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠈⢷⣄⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠙⠋⠀⠀⠀⠀⣿⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⣿⣿⣿⠄⠀⠀⠀⠉⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠐⠀⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣐⠒⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠛⠋⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⣍⣻⡆⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡟⠙⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⡾⠛⢻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠘⠛⠶⠶⢿⣿⣿⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠶⣧⣀⣼⠋⠉⢻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⢈⣿⠀⢰⠏⠈⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡶⠟⢋⣡⡴⠾⠛⠛⠛⢿⡿⠛⠗⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⢻⠛⠾⣯⣤⡼⠃
⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠁⢀⡴⠛⠁⠀⠀⠀⠀⠀⠐⠷⣶⣤⣤⣼⢷⣤⣀⠀⠀⠀⠀⠀⣀⣤⠾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⣀⣤⠄⠞⠁
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠈⢛⠿⠿⠿⠿⠟⠋⠱⣦⣼⣿⣦⠀⠀⠄⠠⠖⣀⣴⠞⣁⣴⡾⠋
⠀⠀⠈⢳⣾⠃⠀⠀⠀⠀⠠⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣷⠿⣿⣷⣶⣶⣶⣿⣿⣥⠾⠟⠁
⠀⠀⠀⠀⠻⣦⣴⠃⠀⣾⠗⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡧⠄⠀⠈⠉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠻⢦⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣻⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡿⢁⡾⠁⢘⣷⠀⠀⠀⠀⠀⠀⣿⠗⠀⠈⠉⠙⠛⠛⠷⠶⣦⣤⣄⣀⣀⠀⣸⡇
⠀⠀⠀⠀⠀⣠⣾⠏⣰⠏⠀⣤⡾⢹⣇⠀⠀⠀⣀⣴⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢻⡟
⠀⠀⠀⢀⣴⡟⢁⡼⠁⣸⣿⣿⣷⠋⠹⣆⠀⢸⣿⡅⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠲⠶⣤⣴⣟
⠀⠀⣠⡾⠋⣴⡏⠀⠀⣹⡿⠃⠘⣧⡀⠻⠿⢻⣿⠿⣦⣠⠾⠋⠙⠻⢶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣄⡀
⢀⣴⡟⣡⠞⠁⢱⣆⣼⠟⠀⠀⠀⠘⣷⣤⡶⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠛⠷⢿⣍⡙⠻⢶⣄
⣾⣯⣴⣏⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣼⠏
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣍⣩⣿⣵⣤⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠈⠉⠻⠿⠿⠃⠈⠉⢉⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣍⣙⣛⠒⠲⠖⠲⠤⣤⣤⣤⣯⣀⣀⣀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠶⣶⣶⣦⣼⣤⣭⣉⣙⣉⣻⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣷⡎⠉⠙⢣⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠁⠀⠀⠐⠲⢦⣀⠹⣏⣿⣍⠉⠙⠋⢱⣮⡛⣾⣿⣿⠩⣷⣿⣟⣾⣿⣷⣧⣾⣡⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⡿⢛⣀⡤⠤⢤⣿⣾⣷⡿⣸⣎⡓⢄⠀⠀⠉⠁⢦⣍⡛⠯⢿⡿⢿⣿⣿⣏⠈⣿⣿⢅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⢾⣿⡿⠊⠁⠀⡠⠤⣶⣶⣿⣿⡷⣘⣋⣭⣤⣷⣄⠀⠀⠙⠛⠀⠀⠀⠀⢠⣭⣍⠀⣀⡉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠟⣾⢋⡔⠀⢀⣡⡴⠟⠋⠉⡡⡿⢀⡟⢻⡙⢯⡂⠙⢷⡀⠀⠀⠀⠀⠀⠀⢘⠟⠁⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡏⡟⣸⢃⣾⣧⣴⣿⣏⣠⣤⣤⠔⠀⠀⡈⣀⢸⡧⢀⣹⣄⠈⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠏⣼⢸⠁⣿⣸⣿⣿⣿⣷⣿⣿⣿⣵⣿⣾⣿⣿⣏⣼⠇⣿⣷⢿⣷⣼⡆
⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠟⢠⢇⣿⣿⣿⣿⣿⢻⣿⣿⠿⠻⠇⣿⡿⠻⡿⠿⡿⢋⣼⠿⠿⠿⢿⣿⠁
⣿⣟⣿⢿⣿⣿⡷⠫⠉⠁⢀⣾⣼⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⡉⢄⠉⠉⠁⠀⠀⠀⠀⠶⠒⠒⣼⡿
⣿⣿⣿⣈⣹⣭⠅⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⠀⠱⢟⠛⠿⠙⠃⡄⠀⠰⠶⠶⢾⡆⠈⢸⡇
⡟⣿⣿⡿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢸⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⡰⣼⠁
⢮⡙⣻⣅⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣸⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡿
⡎⢰⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⢀⣿⣿⣿⠃
⣿⣮⠿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⡄⠀⠀⠀⠀⠐⠀⣠⠤⠔⠚⠛⢿⣇
⣿⣿⢂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣰⠎⢀⠠⠄⠈⢁⠀⠀⠐⠀⢠⡀
⢻⣟⣽⡗⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠳⣦⣄⡀⠈⠉⠈⣠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠑⢆
⢙⠘⠿⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⢀⡟⠀⠀⠀⣰⣤⡤⠀⠀⢸
⣯⡂⢀⠀⠀⠀⠀⣀⡤⠜⠛⠿⣿⣿⣿⣿⠿⠛⠁⢄⠀⠀⠀⠀⠀⠉⣿⣿⣿⣷⣾⣇⠀⢀⠀⣿⣿⠗⠆⠀⠸⡄
⠃⠁⠀⢀⣴⡞⡋⠁⠀⣰⣶⣿⡂⠀⠀⠀⣧⠀⠀⠀⠙⠢⡀⣄⠀⢠⡟⢿⡿⠿⠿⢉⣧⠄⠸⠻⣿⠀⠀⠀⠀⢇
⡿⠁⡔⠀⠀⠳⣦⡀⠘⢿⣿⣿⡀⠀⠀⠀⠹⣇⠀⢀⣴⡶⢿⠘⢦⠘⢇⠀⠙⢾⣷⣦⡉⢶⣧⡀⣿⡀⠀⠀⠀⠈⢆
⠆⡼⠀⠀⠈⢧⡘⢿⣦⡀⠹⣿⡇⣀⣀⣀⣠⣤⣴⣿⣧⡀⠈⠀⠘⡆⠀⠑⡄⠀⠙⠌⠙⠚⠛⢛⢮⡛⠂⠀⠀⠀⠸⡄
⢰⡇⠀⠀⢀⠘⣷⡀⠻⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠱⡀⠀⠘⢤⣤⣤⣤⣴⡖⡜⢧⣱⠀⠀⠀⠀⠀⣷
⣾⠀⠀⠀⣹⡆⢹⣿⡄⠹⣿⣧⡈⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⢄⠀⠈⣆⠀⣸⣿⣿⣾⣿⢻⡦⠖⢂⣭⣥⣍⣀
⡿⠀⠀⣄⢘⣿⡄⢻⣿⡄⠹⣿⣷⡸⣿⣿⢻⣿⠈⢿⣿⣿⣿⣿⡄⠀⠀⠀⠱⣄⢸⡀⡿⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⣿⣿⡀
⡇⠀⠀⣾⣯⣿⣿⡈⢿⣿⣦⠘⣿⣷⣿⣿⢸⣿⠃⠈⠏⠃⠙⢿⣿⡄⠀⠀⠀⠈⢦⡇⢧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⣇⠀⣄⠸⣿⣜⣽⣷⡜⣿⣿⣷⡘⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠈⠋⢻⡄⠀⠀⠀⠀⢷⡸⠀⠹⣿⣿⣿⠏⢛⣭⣽⢃⣴⢀⣿
⣿⠀⢿⣦⠘⢿⣿⡋⡿⡜⢿⣿⣷⣽⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⠇⠀⠀⠹⣿⡏⢠⣿⠿⣫⣾⡟⣼⣿
⣿⡄⠸⣿⣷⣄⠻⣿⣷⡾⣎⢻⣿⣿⣮⡁⣼⣿⠀⠀⠀⢠⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠀⠀⠀⠀⢹⣿⢸⡇⣰⣿⡿⣱⣿⢣⡞⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠠⡤⠄⢰⣀⡀⠠⠤⠤⠤⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⣠⠔⠋⣱⡀⠄⠀⠀⠒⠐⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠴⢦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣠⣒⠁⠈⢆⣀⠤⠒⢉⡠⠒⣽⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢤⡀
⠀⠀⠀⠀⡠⠛⠀⠀⠹⣤⡤⠀⠀⢿⣿⣿⣿⣿⣿⠟⡥⠞⢻⣿⠉⠉⠹⢤⠖⢁⡠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠳⣀⡀⠀⢀⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠊⠡⠽⡗⠒⠒⢞⠉⠉⠙⠟⠛⠛⠋⢩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢦⡀⠀⢸⠁⠀⠀⠘⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠓⠦⣾⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠈⢳⣿⣿⡿⢏⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⣼⠀⠀⣸⣷⠀⠀⠀⠀⠀⡏⠉⠉⠁⠈⢦⣀⡀⠀⣀⣀⣸⣄⣀⣀⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⡤⠤⠴⠁⠀⠀⠀⠀⡿⠻⠴⠚⠁⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠣⠤⠤⠤⠴⠦⠤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⠤⠤⣤⣤⣤⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠿⠿⣿⣷⣤⢃⣔⣥⡶⠶⢄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢈⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⢦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣴⣿⣿⣿⡟⣩⡦⠀⠈⣿⣿⣿⡏⢛⣿⣿⣦⡙⠂
⠐⡀⠂⠠⠀⠂⠉⠀⠀⢸⢫⣾⣿⢃⠹⠠⢁⣀⠀⢸⡟⢸⠇⣀⠛⡜⢿⣿⡍⠒⠢⢄⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠈⠀⠴⣟⠫⠥⡀⠀⠀⠘⠿⣷⠀⠈⣿⣿⡄⠀⠀⠈⠑⠢⢄
⠀⠀⠙⡦⠀⠀⠀⠀⢀⠀⣿⣿⡇⠀⠀⢰⠁⠠⠀⡀⠀⢀⡀⠘⠈⠀⢠⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⣸⠃⠀⠀⠀⢊⢊⠴⡿⢿⠃⠀⠀⠸⡀⠀⠈⠁⣀⠈⢀⡜⠀⠀⣼⣿⣏⠈⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢠⡏⠀⠀⠀⠀⢠⠏⠀⢢⣄⠀⠀⠀⠀⠒⠛⠁⢤⡠⠟⠛⠈⠀⠀⢻⣭⢌⢧⢙⠀⠀⠀⠀⣰⠀⠀⣷
⠀⣸⠁⠀⠀⠀⠀⠘⣆⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡼⠋⢊⡞⠀⠀⠀⠀⢠⡏⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠈⠲⠶⠾⢧⣀⣀⠀⡴⠖⠒⠒⠚⢁⣀⡤⠖⠿⠤⠶⠋⠀⠀⠀⠀⢀⣿⠁⠀⢀⡇
⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⣐⠤⠑⣂⡥⠾⢶⣶⠂⢠⠞⠛⢿⣿⠀⠐⠢⢄⡀⠀⠀⠀⠀⢌⠆⠀⠀⢸⠃
⠀⣿⠀⠀⠀⠀⠀⠸⠶⡋⠄⠂⠁⡳⠂⣸⣦⡁⢠⣮⣶⠒⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡟
⠀⢻⡀⠀⠀⠀⠀⠀⣁⠀⠀⡠⢊⠝⣼⣿⠃⣿⡟⠸⣿⡆⠠⡀⠳⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡾⠁
⠀⠘⣇⠀⢀⠂⢁⡎⠀⠈⠈⣀⡏⣼⣿⡏⢠⣿⣧⠀⢻⣿⡀⢱⡀⠘⣦⠀⠀⠀⠀⢠⠁⠀⢀⡾⠁
⠀⣀⠿⠶⠺⡀⠈⣇⠀⣆⠀⡏⠉⠉⠉⠓⠺⠿⢟⠒⠉⠉⠉⠉⠉⠑⠚⠢⢤⣀⠀⠘⠀⢠⡟⠁
⠈⠀⠀⠀⠀⠉⠒⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣴⠏
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⣱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠙⢦
⠀⠀⠀⠀⠀⠀⢠⣒⡈⠙⠛⠛⠁⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⢀⠐⣶⣌⢦
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⡿⣦⠀⢸⠀⢏⡃⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠡⡸⠀⠈⢆⠠⣀⠀⠀⢳⡀⡠⠖⣂⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠦⠤⠴⠁⠈⠢⡠⣫⢞⣽⠝⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢨⠈⠁⠀⠀⠀⡌⠀⠀⠀⢀⡠⠒⠛⠉⡟⢁⠞⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢇⠀⠀⡇⣠⠔⢫⠄⠀⠀⠀⢀⡿⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡗⠁⠀⠀⠀⡄⠀⣠⢾⠀⠰⣅
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⢄⡘⡄⠀⠀⠀⠈⢊⡴⣯⠴⠾⢷⡴⢫⠟⢦⡀
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⠹⡀⠀⠀⡀⠉⢃⠀⠐⢆⠚⣠⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⡇⠀⢳⠀⠀⢻⠀⢸⠀⢠⠒⠁⠉⠳⢤⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠂⢣⠀⠀⣇⢸⠀⠀⠁⢲⠄⠀⠀⠉⠲⢄⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⠀⠀⠈⢆⠀⢿⢸⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⡄⢸⣧⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣾⣷⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢟⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⡋⠉⠳⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠙⠓⠲⠾⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢾⣉⣀⣨⡽⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠙⣿⣿⣿⣿⣿⡟⠀⢀⣠⠤⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠐⠲⢦⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣿⣿⣿⣿⡿⠁⠀⠙⠷⢤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠦⣤⠀⢸⣿⣿⣿⣿⠃⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠟⠀⠺⠿⣿⡿⠁⠀⠀⠹⣍⠙⠳⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠉⠁⠀⠀⡈⢐⣿⠀⠀⠀⠀⠀⠙⠳⠴⠋
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠁
⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠁⣀⣠⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⣉⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⠉⢹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠙⢯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⡴⠟⠛⠿⠛⠉⠀⠀⠀⣀⣀⢠⡿⠀⠉⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⡟⠀⢦⣠⡼⠃⠀⣸⣿⡄
⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠙⠛⢷⣶⢤⠀⠈⠻⢿⣟⣛⠷⠶⢶⣦⣤⣦⡶⢶⣾⠛⠉⠀⢸⣧⠀⠀⠻⢧⣠⡞⠋⢀⡿
⠀⠀⠀⠸⣷⡆⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⡀⠀⠙⣧⡀⣠⡾⠁⠀⠀⠀⠀⠈⢳⣴⠟⠁
⠀⠀⠀⠀⠹⣧⣀⡄⠀⢀⡄⢀⣾⠃⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣴⠟⠛⠁⠀⠀⠀⣰⡟⠛⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠻⣦⣄⣼⠷⠟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣤⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄⠀⠀⠀⠀⣿⡶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢀⣴⠟⢁⠖⠙⢷⣄⠀⠀⢸⣇⠀⠀⠉⠙⠛⠛⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣠⡾⢁⡔⠁⠀⢠⡾⠛⢷⣄⡀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢷⣶⣦⡾⠃
⠀⣠⡾⢋⣴⢋⣠⡏⢲⡟⠀⠀⠀⠉⠻⠿⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⣴⠋⡠⠋⠉⣞⣀⡹⠊⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠛⠶⢶⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠙⠿⢷⡴⠾⠛⠉⠀⠀⠀⠈⠻⣦⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠷⣦⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠣⣄⡀⠀⣾⣉⡽⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣌⡑⠢⢄⡙⢲⠾⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣙⠳⢄⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⣿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⡄⠀⠀⡇⠀⠀⣤⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢿⡀⠀⡅⠀⢠⡏⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠹⡆⠘⠃⠀⠇⠀⠚⠀⡴⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣴⣖⠒⠒⠒⣲⣦⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣟⠛⠛⠛⠛⠛⠛⣿⠛⠛⢻⡟⠛⠛⠛⠛⠛⢛⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⢸⡇⠈⠳⣄⠀⠀⠀⠀⣿⢀⣀⢸⡇⠀⠀⠀⢀⡴⠋⠀⣿⢠⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤⡴⠃⠀⠈⢿⡇⠀⠀⠈⠳⣄⠀⠀⠿⠋⠉⠻⠇⠀⢀⡴⠋⠀⠀⠀⣿⠟⠀⠀⠻⢤⡴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣠⡤⠶⢤⣼⡇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣿⣤⠴⠦⣤⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠏⢀⡞⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣆⠀⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣦⠀⠳⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠴⠃⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡈⠙⠛⠋⢸⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣿⠉⠛⠛⠁⣀⡀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠙⣇⠀⣰⢿⡇⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⢳⡀⠀⡾⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣠⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⢤⣄⡀⠀⠀⠀⠀⠀⢀⣤⢤⣤⡀⠀⠀⠙⢦
⠀⠀⠀⠀⢸⠃⠀⠀⢠⡟⠁⠀⠀⠙⣧⠀⠀⠀⠀⣾⠁⠀⠀⠈⢷⡀⠀⠀⠀⣼⠃⠀⠀⠈⢳⡀⠀⠀⠀⢰⠋⠀⠀⠀⢹⡆⠀⠀⠘⡇
⠀⠀⠀⠀⢸⡄⠀⠀⠘⣇⠀⠀⠀⢠⡟⠀⠀⠀⠀⢿⡀⠀⠀⢀⡼⠁⠀⠀⠀⢻⡀⠀⠀⠀⣼⠁⠀⠀⠀⠸⣄⠀⠀⠀⣸⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢳⣄⠀⠀⠈⠛⠒⠚⠋⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠙⠓⠒⠋⠁⠀⠀⠀⠀⠀⠉⠓⠒⠛⠁⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠞⠉


⡏⢙⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡋
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⡎⠑⣆⠠⠀⡒⠀⡰⣆⠀⣎⡲⢠⠀⠀⣖⠁⠀⠠⡊⠀⠐⡎⢠⡊⡢⢠⠊⠳⡄⣆⡔⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⣇⣠⠇⣀⠀⣀⢀⠃⢹⣀⣇⣹⢨⣀⣀⣏⣀⠀⢀⣈⡇⢀⡇⢈⡋⢃⠸⣀⣰⠃⣏⢱⣀⣇⣀
⣿⣿⡟⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣼⣿⠀⠉⠉⠙⠒⠒⠦⠤⢤⣤⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⢀⡈⠉⠢⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⣰⠋⠀⠀⢰⢦⡀⣿⠾⢦⣱⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⣇⢸⡀⡀⡜⢊⠙⠃⠲⠀⢯⢸⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⢘⠶⢧⠟⠁⠈⠀⣀⡁⠀⢸⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⢥⣀⠘⠃⢮⠥⢇⣠⡾⠉⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⡟⠻⢧⣀⣸⣿⠾⣇⣰⣻⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⡏⠉⠲⣌⡿⠁⠀⢈⣽⣿⠿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣠⢻⡄⠀⠸⠀⠀⢠⠎⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠹⡦⣀⢀⣴⡡⠞⢹⣿⠀⠀⠀⢰⠒⢒⣒⣒⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢛⣉⡤⠞⢹⣿⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠘⣦⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢯⡀⠑⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠓⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢻⣿⡤⠤⠤⠤⠖⠒⠒⠒⠛⠛⠛⠓⠃

⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⣀⣀⠀⡀⡀⠀⡀⠀⠀⠀⣀⣀⡠⠤⠤⠴⠖⠒⠒⠒⠒⠛⠛⠋⠉⠙⠛⠛⠒⠒⠒⢶⠤⣤⣀⣀⣤⠞⠉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢳⣀⡠⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⠔⡶⠀⠀⢀⣠⠤⠶⠒⠚⠛⠉⠉⠛⢒⣢⣤⠈⠉⠀⡀⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡴⠚⠁⠀⣼⡡⠖⠛⠉⠀⠀⠀⠀⠀⢀⣤⣖⣛⣉⣁⣀⠀⠀⠀⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⡀⠀⠀⠀⠀⠀⡴⠋⡽⢀⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⣴⠚⠋⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⠋⣇⠀⠀⠀⠀⢸⠃⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡠⠽⠆⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣿⣶⣿⠀⠀⡗⢄⣿⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠒⠒⠢⠤⠞⠉⠉⢤⣀⠁⠙⣇⡠⠜⠃⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠇⡏⣈⣉⣹⡆⠀⠹⣄⠁⠀⠀⠀⢀⠄⠊⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⡤⣍⡳⢄⠈⢂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣸⣿⠿⠿⢿⡇⢰⠖⢉⡀⠀⠀⠀⠉⣐⡄⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠀⠙⣆⠀⠈⢆⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡏⣯⣤⣤⣤⣼⡇⢸⡴⢹⠃⠀⠀⠀⠀⠙⣦⠀⠀⠀⠠⠚⣡⢤⣄⣰⠃⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠛⠛⠛⡇⠀⠀⣿⣀⣀⣀⣤⡀⠀⢸⡇⠀⠀⠀⡞⠁⠀⠈⢻⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⢼⣿⣿⣿⣿⣿⡇⠀⠀⢈⣩⠤⠤⠤⠷⠤⣼⠁⠀⠀⠰⡧⠖⠚⠿⠁⡏⠹⡿⠒⠶⠤⣄⣸⠃⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣸⡁⠀⠀⣀⢀⣧⠀⢠⠏⠀⡠⣖⣒⣦⠄⠀⠀⠀⠀⠀⠳⣄⠀⣀⣴⢷⣄⣀⣀⣀⣠⡼⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⡿⠿⣿⠀⢸⣄⠀⠀⠈⠉⣀⣀⢤⡀⠀⠀⠀⠀⠘⠛⠛⠉⠀⢉⠙⠉⡉⠥⠤⠦⣄⠀⠀⡟⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢸⣼⣇⣀⣀⣄⣀⣿⠀⠀⠉⠙⠛⠛⠉⠉⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢁⣝⠐⣠⡀⠀⣀⣠⠟⠀⢰⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡏⡿⠟⠿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⡇⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢷⢿⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠐⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠾⣿⣿⡶⣶⣤⣤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡼⣏⣉⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠓⢦⣀⣀⠤⢤⣴⠒⠚⠋⠉⠁⠀⠉⠉⠁⠀⠈⠈⠉⠛⠻⢿⣿⣟⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢳⢻⡿⠿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠳⣤⠖⠁⢹⣤⠊⠉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢳⣾⣿⡇⠀⠀⣀⣀⣀⣠⠖⣶⢻⠗⣲⣇⣀⣀⣀⠈⠛⠃⢰⢸⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠉⠉⠉⠉⢉⠽⡍⠉⠙⠒⠓⠼⠲⠋⠀⠀⠀⠉⠉⠉⠉⠛⠛⢶⣀⣇⣸⣉⣦⣀⣀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠰⣦⠒⡒⡤⠊⠀⣧⡤⢤⠤⢲⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣞
⠀⠀⠀⠐⠉⠀⠀⣀⠤⠖⠛⠉⠣⡙⡄⠀⠈⠖⠁⠂⠀⢀⡥⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠙⢃⠈⠀⠈⠀⠀⡠⠚⠁⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀⡀⠀⠀⢀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣊⣀⠀⠉⠘⠒⠀⠤⠦⠚⠒⡠⠖⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣈⠒⠠⢽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠉⠉⠉⠓⠒⠒⠢⡔⠋⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⣄⣀⡀⠀⠀⠃⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠐⠂⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠇⠀⠀⠏⠀⢀⡴⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡄⠀⠀⠀⡏⠉⠒⠪⠥⢒⣦⢤⣀⡀
⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⢠⢖⡀⠀⠀⠉⠙⠛⠯⢦⣠⡄
⠀⠀⠀⠈⠙⠂⠀⠀⠀⡴⠒⠈⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠐⡿⢲⡶⠆⢴⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡌⠚⡟⠀⠀⣀⠔⠒⠦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢙⢘⠋⠀⠙⠁⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡸⠄⢠⢨⠇⡜⠁⠀⠀⣠⢺⠀⠀⠀⠀⠑⣢⠄⣀⠠⠏⢿⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢰⡃⣰⠚⣋⣀⢣⡀⠰⡉⢀⣈⡄⡤⢀⠉⠀⠀⠀⣀⠭⠷⠲⣤⣄⡀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡟⠙⢼⢸⠉⣹⠀⣨⣞⣠⡖⣻⡠⠇⠀⠊⠙⡦⠤⢈⠑⠒⠤⡌⠕⠈⠙⠲⠶⠓⠠⢄
⠀⠀⢀⡤⠤⠤⢄⣀⡼⠀⢣⡠⠾⠋⡼⢁⡞⠁⠀⠀⠈⠳⣹⡦⠊⡤⠒⠃⠀⠀⠈⠐⠢⢄⣀⠀⠀⠀⠀⠀⢀⠤⠚⡇
⠀⢠⠏⠀⠀⠀⠀⠈⠑⠦⣄⠙⠤⠾⢂⡞⠀⠀⠀⠲⣤⣎⠉⣠⠞⠀⠀⢰⠀⢰⠀⠁⠀⠄⣀⠉⠒⠦⡔⠊⠀⠀⠀⡇
⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢯⣽⠀⠀⠀⠀⢀⡇⠉⠫⢁⠀⠀⠀⢸⠀⢸⠀⠀⢀⡠⠔⢻⠀⠀⡇⠀⢀⡠⠖⠃
⠀⠀⠈⡏⠀⠐⠦⣄⣀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⢸⡧⢬⡐⠠⣈⠒⠤⢀⢉⡡⠔⠊⣁⣤⠖⢹⠢⢤⡧⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⢠⡀⠀⠀⠀⠀⠀⠘⣧⠼⠋⣉⡭⠧⣄⠉⠒⢤⣍⣠⠖⠋⠁⢸⣸⡸
⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⢀⡀⢹⠔⠊⠁⠀⣀⡤⡇⠀⡇⠈⢸
⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⢀⣠⠔⠊⠁⠀⡇⠀⠣⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⣀⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⣿⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠙⠒⠤⣀⠤⠊⠁⠀⠀⠀⠈⠢⣀⡠⠤⠒⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠉⠉⠉⠑⠂⠒⠊⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠃⠀⠸⢄⣀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢸⠈⠁⠊⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠙⠒⠉⠀⢇
⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡜⠀⠀⠀⡄⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠁⠀⠀⢸⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢄⡀⠀⠀⣀⠤⠒⠢⢄⠀⠀⠀⠀⠁⣀⡠⠔⠤⣀⠀⠀⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡇⠀⠈⠀⢀⡤⠚⠓⠒⠒⠒⠒⠠⠤⠤⠄⢀⡴⠁⠀⠀⠀⠉⠊⠉⠀⠀⠀⠀⠀⠉⠲⠖⠚⠉⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⢰⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠸⡀
⠀⠀⢀⠔⠺⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢛⠑⢦
⠀⠀⡎⠀⣥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⡆⠈⡇
⠀⢠⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢱
⢠⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢣⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰
⠀⠑⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢤⣀⣀⡀⠀⠀⠑⠂⠤⠤⠐⠁⢀⣀⣀⡤⠤⠒⠊⠉