Honey aesthetic Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⣞⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠷⣌⡷⠞⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠷⠶⢿⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠳⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⡞⠉⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠶⣿⣧⣤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢹⣏⡡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣤⣶⢦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠖⠛⠉⢷⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣷⣽⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠞⠉⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀
⠀⠀⣠⣴⢚⣉⣭⡥⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠒⠒⠒⠿⢭⣻⠶⣄
⠀⣾⠁⢻⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠉⠀⠘⡆
⠀⢹⡆⠀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣤⠀⠀⢀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⢸⡇⠀⠀⠀⢠⠞⢳⡄⢀⡇⠀⢸⣄⣠⠏⠀⠈⣇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣤⠀⠀⠀⢸⠋⠙⢿
⠀⣼⠁⠀⠀⠀⣾⡃⠈⠳⠛⠀⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠉⠙⢶⡄⠀⠀⠀⠀⠀⡎⠀⠀⢸⡀⠀⠀⢨⣀⡤⠋
⠀⣿⠀⠀⠀⠠⣟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡇⠀⠀⠀⢰⣇⠀⠀⠀⠀⣼⣀⣀⣠⠼⠷⠶⠚⠛⠉⠇
⠀⣧⠀⠀⠀⣼⠋⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⡟⠉⠉⠉⠉⠉⠙⢧⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠈⣿⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠁⠀⠀⢀⣀⣀⣀⣰⡇⠀⠀⠀⣡⠄⠤⠴⠶⠖⠊⠉⠉⣆
⠀⢠⡿⠉⠙⠛⠛⠓⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⡉⠳⣦⡴⠶⠃⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠘⣏⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢘⡄⢠⡞⠙⣆⠀⡟⢦⣸⡆⢸⠁⠀⠙⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌
⠀⠀⠈⣷⢮⣀⣀⠀⠀⠀⠀⠀⠀⠻⠀⠉⠓⠈⠓⠖⠃⠀⠁⡀⣉⣃⣈⣛⣃⣀⡘⠀⠤⠤⠤⠤⠤⠒⠒⠚⠉⠁⢸
⠀⠀⢸⢋⠄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⢧⣎⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢴⠁
⠀⠀⠀⠀⢸⠓⠶⠶⠆⠀⠠⢤⣤⣤⣤⣄⣀⣀⣄⡠⠤⠤⠤⠤⠤⠶⠶⠶⠶⠖⠒⠒⠛⠛⠉⠉⠉⠉⠁⠀⠀⢸
⠀⠀⠀⠀⠸⣧⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠙⢧⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⠴⠶⢺⠃
⠀⠀⠀⠀⠀⠀⠀⣧⣈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣚⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠤⠔⠒⠒⠒⠒⠚⠋⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣧⣤⣤⣤⡤⢤⠤⣤⠤⠤⡤⣤⢤⡤⢤⡤⠤⠤⡤⢲⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⡦⠶⠴⠦⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠿⠟⠛⣋⣉⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡐⠒⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢈⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⢸⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣱⣿⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠉⢹⣿⠛⠛⠉⠈⣿⣆⠀⠹⣷⣍⡱⣿⡿⣣⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⣹⣿⠀⠀⠙⢿⣷⡌⠺⣿⣟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠰⣿⠃⠀⠀⠀⠀⠙⠿⠄⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠓







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⠿⠛⡿⢻⡿⢻⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⣴⣴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣀⡀
⢀⠠⠘⣿⣿⣿⣟⠶⠛⠃⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⠇⣀⡵⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡯⢁⢼⡇
⠈⠏⠂⠉⠝⠋⠛⠂⠀⠙⡟⠁⠀⠀⠀⠀⡀⠌⠐⢢⠀⠀⠁⠠⠊⠀⠀⠀⠀⠀⠑⡂⢀⣾⠕⠚⠻⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡊⠀⠓⠀⠀⡀⠑⠇⡀⠆⠀⠀⠀⠐⢋⣹⠛⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢉⡀⠀⢳⠆⢰⠂⠀⠀⠀⠀⠀⠘⠿⣿⢯⠙⠦⠄
⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠈⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⢶⡾⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣦⣴⣦⣴⣶⣶⣴⣴⣦⣶⣶⣶⣶⣶⣶⣤⣴⣴⣦⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠊⠁⠀⠀⠀⠀⠀⢠⠂⢿⡻⠛⣗⣲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰
⠀⠀⠀⠀⠀⠀⠐⢂⣀⠰⠐⠀⣀⣀⢠⢗⣿⣀⣄⠄⡏⡯⠏⢀⠀⠀⠀⠀⠀⣠⠙⠂⠀⠀⣀⡀⠀⠠⠤⠀⠁⡶⢁
⠀⠀⠀⠀⠀⠀⠲⠶⠈⠁⠀⠂⡃⡀⢾⣀⠋⠫⡧⠠⡆⠙⣂⠭⡄⠀⠀⠀⠋⠚⠂⠠⣁⡀⠂⠀⠀⢀⣀⣰⣿⣅⡸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠹⠡⠚⠛⢲⠬⣝⠬⡆⢀⣞⠟⠁⠀⠀⠆⠀⠀⡀⠀⠀⡜⠁⡈⠉⠟⢻⣿⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⢶⡤⣊⣤⡇⡘⠁⠭⠭⠌⠂⡊⡄⠀⠀⢀⠀⣠⢶⠋⠿⣀⠔⡁⠀⢤⡀⡰⢀⠀⠀⡈⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠙⠟⡀⠥⠄⡐⠛⠈⡬⡐⠃⠀⠘⠙⠛⡷⠃⠚⠋⠁⠀⠀⠀⠀⠘⠑⠲⠤⡄⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⣉⡀⠀⠘⠂⢈⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢿⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⡈⠲⡀⠀⠀⠀⠉⠓⠤⢄⠀⠀⠀⠀⠀⠀⠃⡀⢁⠆⡀⠀⠀⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠀⠈⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠰⣄⠉⠓⠤⣀⠐⠦⠀⠀⡄⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠉⠓⢤⣤⣀⠀⢀⢀⠀⡄⠄⠀⢤⡀⠀⠀⠀⢠⢀⠠⠄
⠀⠀⠀⠈⠙⠒⠀⡀⣹⣷⣶⣤⣻⣯⣤⣄⣳⣴⠿⠾⢤⠀⠀⠀⠀⢀⠀⠀⣀⠀⠈⠙⢲⣎⣸⠀⡐⠀⡀⠀⠂⠀⠀⠁⢀
⠀⠀⠀⢀⠔⠀⣠⣾⣿⣿⢀⣀⡠⠄⠛⠓⢤⢤⣀⢀⣰⣄⠀⠀⢀⡀⡇⠰⠛⠀⠀⠀⠀⡟⢻⣰⡇⣰⠀⢠⠁⠡
⠀⠀⠀⠃⣀⠤⢋⠀⣿⠟⠉⠀⠀⠀⠀⠀⠈⠒⠛⠉⠙⠟⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⢹⡤⣿⣤⠏
⠀⠀⠀⠀⠀⢀⠏⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⢤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢴⡺⠳⠆⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠌
⠀⠀⠀⠀⠀⠃⠀⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⡏⠊⣴⠆⠀⢱⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⣤⠀⠛⠋⠀⢨⡌⢀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠻⢂⠤⣤⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄

⠄⢃⣶⢶⣄⠀⠀⢠⡾⣷⡄⠀⠀⠀⠀⠀⠘⠧⠐⣰⡟⢷⡄⠀⠀⣼⠿⡷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡹
⠀⠈⠿⠶⠃⠀⠀⠈⢲⠿⠀⠀⠀⠀⠀⠀⢰⡿⣿⡜⢗⡚⠀⠀⠀⢘⡚⠋⠀⠀⠀⠀⠀⠀⣼⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠹⠷⠿⠁
⠀⠠⠟⠉⠀⣀⣀⢠⠉⢀⡄⠀⠀⠀⠀⠀⠈⠛⠛⠻⠋⠀⢀⣀⡀⢎⠁⢰⠀⣀⡀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠰⢍⢹⡆⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣈⣹⠊⠉⠁⢾⡏⢻⠂
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠀⢤⢤⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣯⣿⠗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡀⡀⣸⡶⣶⠤⠤⠤⠤⠤⠤⠤⠠⠄⠠⠿⠤⠄
⠀⠀⠀⠘⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢆⣸⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠋⠉⠉⠄⠒⠒⠀⠀⠀⠈⢡⠃
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣼⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⢰⣏⡉⠀⠀⡆⠀⠀⠀⠀⠈⠐⠒⠢⢄⣀⠀⠐⠂⠁⠀⠶⢀⠀⠀⠀⠀⠀⢄⡟⠉⠉⠉⠉⠁⠀⠁⠈⣻
⠀⠀⠀⠀⢀⠜⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠀⠀⠋⠁⠀⠀⠀⠀⠒⣸⡄⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⡆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠒
⠀⠀⠀⠀⠃⠀⠀⢀⣶⡠⠀⠀⠀⠀⡀⠀⣄⣤⢦⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⡀
⠀⠀⠀⠀⠙⠀⠀⠀⠘⢶⡤⢰⡆⠀⠀⠀⢾⣇⣀⠷⠀⠀⠀⠀⠀⠀⠀⠿⠷⠋⠀⠀⠀⠀⢀⠈⡆⡀⠀⠀⠀⠸⢿⣿⠿⡧⠤⠄
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡹⠁⠀⠀⠀⠐⢡⡏⢖⡭⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠁⠂

⠀⠀⡄⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⣶⣿⠷⠃
⠀⠈⠀⠀⣴⠆⣴⣿⣿⣷⡾⠟⠋⠀⠀⢣⣠⡴⠆
⠀⠀⠀⠘⢻⡾⣷⣿⣿⠟⠁
⠠⣤⠞⣲⠏⠙⠿⡭⠋⠀⠀⢀⢀⣐⣰⣷⡷⣀
⠀⠀⠀⠁⠀⢢⠎⠀⠀⠀⠀⢨⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣄⣀⣀⣀⠀⠄
⠀⠀⠐⣺⣏⣭⣹⣆⡀⠠⠀⠀⠀⠀⠀⣠⣶⡖
⠀⠀⠊⠩⡛⠻⠻⣿⣷⠀⠀⠀⣠⡀⠈⠉⠁
⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆⠀⣖⠰⡄⢰⠂⠀⢰⣆⡧⢖⢠⠴⡂⡖⢆⡦
⠀⠀⠀⠀⣤⣟⠛⣿⣃⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢐⣶⣿⡅⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠻⠟
⠀⠀⠀⠀⠾⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠹⢶⠛⠉
⠀⣄⠀⠀⡀⣴⣶⣴⢄⠀⠀⠀⠀⠈⠻⠿⠀⡀
⠀⠘⢄⡜⣤⣿⡿⠋⠛⠀⠀⠀⠀⢀⣰⢾⣿⡗⠈
⠀⠀⠘⡿⣿⠋⠳⣀⠀⣁⡆⠀⠀⠀⠀⠀⢸⣷⢀
⠀⠀⠀⠘⡜⢧⣀⣸⣷⡼⠃⠀⠀⠀⠀⠀⠀⠻⡇
⠀⡀⠀⠀⢸⣦⡉⠉⠁
⠀⣿⣧⣄⠀⠙⠃⠀⢀⣴⡆⠀⠀⠀⠀⢀⡠⠄⡀⣀⣤⠴⠒
⠀⠹⠛⢛⡄⠀⠀⣴⣍⣛⠁⠀⠀⠀⢸⣻⣷⣾⡿⠏⠀⠀⠀⡀
⠀⠀⠘⠉⠀⠀⠰⠾⣿⣿⡇⠀⠀⠀⠸⠛⠛⠋⢀⣠⣴⣦⣶⣢⣾⣂⢄
⢀⠄⢠⠀⠀⢰⣆⡀⢈⠏⠀⠀⠄⠀⠀⠀⠀⠐⣿⢿⣿⣾⣿⣿⣷⢾⡣⣶⡆
⠿⣿⣟⣶⡂⠀⠈⠙⠋⠀⠀⠀⠀⠑⠀⠀⠀⠀⠙⢿⣿⡿⠿⣿⣿⣿⣿⠅
⣀⣹⣻⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⡞⢻⣷⠄⠀⠀⠀⢀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⢧⣾⡿⠀⠀⠀⠀⠳⣞⠽⠀⠀⠀⠀⢘⣠⣿⠇⠀⠀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣙⣧⣠⣀⡀⠀⣠⣟⠁⠀⠀⢈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣷⣟⣶⣿⣧⠤⠴⠾⠿⠿⠿⢟⣷⣿⣿⣿⣦⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣩⡿⢽⣿⡞⠻⣻⢿⣟⡛⣿⣿⠼⣿⣿⢾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣼⣷⣻⣏⠀⠾⠺⠿⠷⠋⠿⠿⢹⣾⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣴⣶⣟⣿⣾⣿⢛⡍⣹⡟⣙⣃⣻⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠳⢮⠿⠛⠀⠀⠃⠀⠀⠈⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣄⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠙⢦⣀⣠⣶⣦⣶⣶⡄⣀⡤⠊⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢹⣿⣿⣿⣿⣿⢿⠉⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⣿⣿⣿⣿⣿⡞⠀⢸⡿⠁⠀⠀⠀⠀⢀⣀⡀⠠
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣴⣿⣿⣿⣿⣿⣧⣾⣟⡁⠀⠀⠀⠀⠐⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠈⠛⣿⣿⣿⣧⣈⢉⣿⣿⡏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣴⣶⣻⣿⣿⣿⣿⣿⠟⣤⣤⡀⠀⠀⠉⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠹⣿⡟⣛⠉⡁⠀⠉⠙⠛⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠃⠀⢀⣴⣾⣶⣵⣿⣿⣷⣬⣲⣶⣄⠀⠀⠲⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠋⠀⠀⠀⢀⣾⠁⢠⡿⣿⣿⣏⡙⡉⠷⠈⠛⣦⠀⠀⠀⠈⠻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⡿⠀⣼⣿⣿⣿⠿⣿⣷⣴⡇⠀⢿⡇⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⠀⠀⢿⣿⣿⣿⣷⣾⣿⣿⠃⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠸⣿⣯⣿⣯⣿⣿⣾⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⣰⣟⡉⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠹⢷⣦⣤⣀⡛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣶⣄⣈⠙⠲⢤⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣦⣤⡈⠉⢉⠝⢛⡶⢶⣤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⡏⣴⠃⡴⠋⡱⠢⣤⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⡇⣼⡁⣼⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠰⢢⢀⣄⠀⠀⠀⠀⠀⢈⣙⠻⣿⣷⠿⠟⣸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠲⣧⣘⣧⣸⡃⡸⠴⢄⡤⠖⣋⣭⠥⠗⢤⡘⠒⢠⠃⠈⠉⠙⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣯⡉⢓⣿⣿⣟⡿⣿⡇⡴⢫⣶⣿⠵⣖⣛⣯⡭⡯⣭⣽⠀⠀⠀⠀⡀⢦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠨⣿⣿⣿⣿⣿⢻⠃⣿⣿⣾⣿⡭⠶⣖⣒⣗⣓⣿⡀⠀⠀⡐⢬⡳⣌⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡠⢍⣻⣻⠯⣼⢙⣏⣿⢺⣟⢮⡻⢿⣿⣿⣯⣭⣥⣧⣭⣿⣿⣻⣷⣾⣿⠟⣠⣿⣇
⠀⠀⠀⠀⣀⣀⡀⡇⠀⢳⡇⠀⣿⠋⢹⢯⣿⣿⣷⣍⠒⠈⠉⠛⠛⠛⠛⠛⠛⣛⣛⣉⣥⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠳⡀⠉⣻⣦⣤⣷⣼⣿⣀⣀⣿⡿⣮⡛⠯⣝⡳⠶⢤⣤⣬⣭⣭⣭⣭⠽⠿⣿⣿⣿⣿⣿⡷⣿⡤⢄⡞⢢⡔⢲⣀⡀
⠀⠀⢮⡉⠉⢛⣷⣾⣿⡿⣛⡻⣿⣿⠡⣿⡻⢦⣉⠓⠂⠌⠁⠀⠀⠀⠀⠐⠒⠒⢚⣛⣩⣽⣿⣿⣿⢾⣿⡇⣤⣿⣼⣷⣟⣠⠧⢤
⠀⢀⡔⠛⠓⠲⣿⣿⣯⣶⣿⣿⣿⣿⡆⣿⣟⡶⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣉⣉⣭⣴⠾⣿⣿⣿⣟⣽⠣⣿⣿⣽⣽⣿⣷⠴⢎
⠀⠀⢹⠖⠒⠒⠻⣿⣿⣿⣿⣿⡿⢯⡛⢹⣿⣿⠶⣭⣁⠀⠀⠀⠀⠀⠀⣀⣩⣭⡤⠴⠶⣿⣿⣿⣿⣿⣯⡤⠚⡿⣿⣿⣿⠟⠲⡞⠁
⠀⠀⠈⢳⡖⠂⠉⣩⠟⠁⣼⠁⢱⡀⢽⣿⣿⣿⣿⡶⢬⣍⡀⠀⠀⠀⠀⠤⠤⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣴⡞⢀⡎⢹⡁⣷⠒⠃
⠀⠀⠀⠈⠛⠛⣿⣤⣤⣞⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡦⣭⣍⣙⣓⣒⠒⣛⣛⣛⣿⣿⣿⣿⣿⣿⣭⡭⠽⠿⠿⠷⠾⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⣉⣉⣉⣉⣉⣉⣭⣽⣿⣿⣷⣶⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠶⠶⠶⠶⠶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢛⣛⣛⣛⣛⣉⣉⣉⣉⣉⡉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⢀⣤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⣷⡀⠖⠒⠲⢤⡀⣀⣀⡤⠐⠢⠀⣠⡮⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠈⣄⢀⠀⠄⣀⣉⡑⠲⢤⣀⠀⠻⣧⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⣰⡿⠃⠀⣀⡠⠔⡲⠋⠁⠀⠀⢈⠆
⠀⠀⠈⠢⡀⠀⠀⠀⢄⣁⣂⡈⠙⠶⣽⣿⣶⡛⠁⠀⠀⠈⠋⠳⣾⣿⡥⠖⠋⢡⡁⡁⠝⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠈⠢⠤⠤⠼⠦⢔⣂⣀⣤⣥⣴⡿⣷⠀⠀⠀⠀⢠⣟⣿⣛⣃⣘⣛⣣⡠⠼⢤⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⢙⡉⠁⠀⣠⠿⣏⡀⡀⢀⡀⢀⡝⠳⡉⠉⢉⣋⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⣥⣤⠤⠒⢁⣀⠾⣷⣿⣿⠿⠿⢆⣀⠙⠢⣀⣀⣀⡠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠃⣠⣴⡿⣯⣤⣄⣀⣠⣤⣤⣾⡿⣷⣄⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣿⣿⠀⣿⣟⠀⣿⣿⣿⣿⣯⡅⠿⣿⡆⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢹⣟⡦⣿⣟⣛⣿⣿⠁⠠⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠈⠻⣧⢚⣿⣿⣿⠁⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⣨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⡤⣄⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣶⣾⣶⣾⣷⣷⣦⡀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠻⣿⣿⡿⠿⠿⣿⣿⠃⣠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠂⢒⡾⠿⠋⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣸⣏⠀⠀⠀⠀⠀⠀⢹⣿⣶⣶⣶⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⡹⣿⣿⣆⣀⠔⠐⠤⡄⣻⣿⣽⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⣿⠡⢾⣺⣿⣶⣿⡟⠧⡹⣯⡑⢯⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⡃⢁⣉⠚⢿⠿⠿⢿⠿⢿⢿⢃⢻⢶⡀⠉⢉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠼⢁⡾⢳⣟⠺⠷⠂⠧⠘⠿⣗⣼⡈⢧⡝⡦⠀⣱⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣡⡳⡻⠁⢸⡙⢿⢷⣶⣶⣶⡿⠟⣡⡇⠀⠳⣌⢌⠛⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣴⢿⠟⠁⠀⠸⣿⣷⣤⣄⣠⣼⣾⣿⣿⠀⠀⠀⠙⢿⡆⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡵⠋⠀⠀⠀⠀⠹⣿⣯⣟⣛⣻⣽⡾⠃⠀⠀⠀⠀⠀⠙⠦⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⣭⠿⠋

⠀⠀⡴⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢡⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⢀⡶⠆⠊⣁⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡀⠀⢢⠀⠁
⠀⠀⠀⢆⠀⠱⠀⠀⠀⠀⠸⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢰⠋⠀⠀⢀⣤⠞⠉⠀⣀⣴⠇⠀⠀⠀⠀⠀⢂⣤⣀⠀⠠⠤⣄⣠⠴⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠀⢀⠂⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⢷⠘⢀⡴⠊⠁⠘⢢⡴⠞⠁⠃⡴⠀⠀⠐⢈⠍⠰⠀⠀⠠⠘⠉⠁⠐⠀⠀⠀⡄
⠀⠀⠀⠀⠰⡀⠀⠂⠀⠀⠀⠈⠀⠀⢀⡂⠀⡀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠉⠑⠀⠐⠛⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠒⠓⠀⠀⠀⠀⠢⠉⠐⢆
⠀⠀⠀⠀⠀⢣⣀⡠⠤⠤⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠠
⠀⠀⠀⠀⢀⠌⠁⠄⠀⠉⣉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠤⠀⣀⠀⠨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠
⠀⠀⠀⠀⠸⡏⡀⠔⠂⠉⢁⣈⣱⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠿⢁⡠⠒⠈⠀⣀⠈⡇⠀⠀⠀⠀⢸⠀⠀⡘⠀⡄⠀⠀⠀⡾⠀⠀⣾⠀⢀⠇⠀⠀⡿⠀⢀⡆⠀⠀⠰⡙⠀⠺⠿⡿⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠈⢏⢠⠤⠊⠉⠉⠀⢹⠀⠀⠀⠀⡆⠀⠀⡇⠀⢇⡀⠀⠀⢇⠀⠀⡏⠀⠘⠄⠀⠀⠁⠀⢸⠃⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠊
⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⠀⡠⠔⠁⠀⠀⠀⠠⠇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠈⣀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⣀⠀⠴⠋⠁
⠀⠀⠀⠀⠀⠈⠍⠀⠀⡅⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠐⠥⡿⠁⠀⠀⠀⡁⡅⠀⠀⠀⠀⠀⣀⠂⠐⠢⣄⠀⠀⠈⠀⠀⠀⠀⠀⢀⠠⠁⠀⠀⠀⠀⠀⢰⠊⡀⠀⠀⠀⡹⠀⠀⡰⠄⠁⠀⠀⠀⠈⠀⠀⢀⠕
⠀⠀⠘⣁⠏⠀⠀⠀⠀⠑⠀⠀⠀⠗⠷⠄⠼⠷⠤⠲⢾⣿⠿⠾⡟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠤⠋⠰⠀⠀⠇⠐⠒⠀⠀⡄⠠⠤⠀⠐⠊⠱
⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⢻⠛⠈⠈⠀⠐⡰⠎⠦⠐⠢⣦⡰⡠⠃⠀⠀⠀⠀⠐⠀⠀⠳⠄⠀⠀⠈⠀⠠⠀⠂⠀⠀⠀⠀⠈⠇⠀⠀⠑⠀⠀⠀⠀⠀⠖⠄
⠀⠀⠠⠀⠄⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣀
⠀⢠⠐⠀⢠⠂⠁⠀⡀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠌⠀⠀⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣤⠘⢁⠸⣄⡀⡠⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠈⠀⠒⠀⠁⠀⢈⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⡄⠀⢁⠀⠱⡆⠁⠀⠀⠈⡃⠀⢠⠀⠀⠀⠀⠰⣄⣁⠀⠀⠀⠀⠀⢀⠄⣠⠃
⠀⠀⠀⠀⠂⠂⠂⠐⠀⠀⠀⠀⠀⠀⠈⠁⠂⠒⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠂⠈⠂⠉⠀⠀⠀⠠⠄⠠⠆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣶⣈⣀⣈⠭⠔⠁

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢨⠼⡀
⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠩⠀⠀⠂⠀⠠⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣼⣤⡆⠀⠀⠀⠇⠀⠀⠀⠠⠀⠈⠋⠙⠀⠲⠂⠒⠐⠒⠀⠀⢤
⡐⠀⠆⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⡃⠀⡇⠀⠋
⠯⠀⡇⠀⠀⢸⠀⠽⢅⠀⠠⠀⠠⢸⡟⠛⠘⡟⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠐⢲
⠆⠀⡇⠀⠀⠠⢰⡆⠀⠀⢸⣏⠂⠈⠃⠀⠀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣷⣬⣹
⢀⣸⣇⠀⠠⠌⠈⠀⠀⠀⢀⣯⣤⠄⡁⠀⠂⡇⠀⢀⣀⣻⠀⠈⠀⠀⠀⠀⠀⠀⢉⡀⠧⠄⠀⠠
⢉⠩⠀⠃⠇⠲⠀⠀⠀⣈⠈⠉⠀⠀⠀⠀⠁⠆⠀⠉⠁⠹⡶⢶⠀⡀⠀⠄⣀⠔⠂⠁⠉⠀⠀⠀⠀⢠
⢶⣐⢸⡆⣶⣰⣠⣤⣴⣾⡾⢦⠀⠄⢀⣌⢶⠃⠀⠀⠀⠚⠃⠻⠤⡅⠀⠀⣷⠆⣀⡄⠉⢃⣻⠀⠀⢸
⢎⣡⣈⣥⡟⢾⢿⣿⢙⣻⢿⠟⣿⣷⣭⣿⠿⠥⠬⠯⢏⡿⠿⠧⣿⠷⢌⣥⣥⣤⣶⣯⣵⠾⠶⠎⠖⠸⠖
⣉⠉⠉⠉⢠⠄⠤⠶⠶⠞⠒⢳⣤⣴⣠⣤⣮⡅⠁⠚⠛⠛⠛⠓⠛⠈⠈⠉⠉⠉⠉⠉⠉⠋⣻⣥⠿⠷⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡄⠻⠿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⡀⠀⠀⠀⠀⢠⣦⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⡀⠀⠀⠀⠈⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠿⠇⠀⠺⠿⠀⠀⠿⠇⠀⠸⠿⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣤⠀⠀⣤⡄⠀⢠⣤⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠉⠁⠀⠈⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠁⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠉⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⣴⣷⡀⠀⣾⠆⠀⢰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠸⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠈⢳⠀⠀⠀⢀⣀⣘⣿⡁⡨⣰⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣠⠀⠀⠘⣿⣿⡄⣠⣷⣿⣿⣿⢟⣹⣿⣿⣿⡋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠒⠓⠒⠦⣄⠀⢀⡔⣭⣾⣿⠗⠛⠉⠀⣿⣿⣿⣿⣿⡿⠛⣿⣜⠻⢟⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣦⣀⠀⠀⢱⣿⣾⣿⠿⣷⡿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡛⢿⠟⢹⣿⣯⠙⠿⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⣿⣿⣷⣤⣿⣿⣿⢋⣀⣤⣏⣽⣶⢶⣾⠿⣿⡿⣿⡟⢿⣿⣿⡌⠓⠴⠻⠋⠀⠈⠀⠀⠀⠀⣠⣴⡆⣴⡇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣛⢿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⢿⣼⣿⣇⠿⢷⣤⣼⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢟⡴⡫⠴⢶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⢀⣽⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠁⠀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢀⣤⣼⢟⣵⣿⠯⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣠⣴⣿⣿⢟⡝⣿⣿⣿⣿⣷⡄⢀⣀⡤⠞⠈⠀⠀⠀⠀⠀⢀⣀⡀⢀⡎⢠⣾⡽⢿⣮⣸⡟⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣷⣽⣿⣾⡿⠀⢸⣿⣿⢿⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⣾⣦⣷⣿⣿⣟⣦⣼⣿⣿⣷⠮⢶⡄
⠀⠀⠀⠀⠀⠀⣠⣶⠥⠁⣴⣽⡏⠹⣼⡆⠀⢸⡿⠙⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣀⣹⣿⣿⣿⡿⠿⣛⢡⠟⣿⡗⠈⠁
⠀⠀⠀⠀⠀⣼⡿⢉⣰⡼⣻⠋⠀⠰⣟⢷⣀⠘⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣋⣤⢠⡿⠟⢛⡻⣿⠉⠫⠀⠀⠁⠘⠁
⠀⠀⠀⠀⢰⣿⡷⠟⠋⣰⡟⠰⡆⢰⡟⠀⠈⠙⠁⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠈⠉⠉⠀⢺⠀⠠⠌⠱⣝⣷
⠀⠀⠀⠀⠈⠀⠀⠀⣴⠏⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣇⡧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟
⠀⠃⠀⠀⠀⠀⠀⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡷⣦⣤⣀⣀⠀⠀⠀⠑⢄
⠀⠀⠀⢀⣠⣶⣿⠿⠿⠛⣛⣛⣻⠿⣬⡀⠀⠀⠉⠁⠀⠀⣀⣩⣽⣿⣿⣿⣷⣦⣄⠀⠱⡀
⠀⠀⣴⣿⠛⢉⡀⠴⠚⠉⠉⠉⠉⠙⠲⢍⠓⢄⠀⠀⢔⣻⠝⠛⠋⠉⠙⠒⢬⣙⠻⣷⣄⠁
⠀⣾⠟⣡⠞⣋⣤⣶⣾⣿⣿⣿⠖⠒⠀⠀⠉⠀⠀⠀⠙⠛⠿⣿⣿⣷⣦⣄⠀⠈⠳⡌⢻⣦
⣼⠏⣼⣯⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣦⡀⠹⣤⢿⡆
⣿⠀⣿⣿⣿⣿⣿⣿⣿⡟⢀⣴⣾⣷⣶⣄⠀⠀⠀⢀⣠⣤⣄⡀⠈⢻⣿⣿⣿⣿⣿⣶⣧⢸⣧
⢿⡀⣿⣿⣿⣿⣿⣿⡿⠁⠘⢿⣿⣿⣿⣿⣇⢀⣼⣿⣿⣿⣿⣿⠀⠼⣿⣿⣿⣿⣿⣿⣿⢸⡏
⠘⣧⢻⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢘⣽⣟⣿⣿⣿⣿⡇⣸⡇
⠀⠘⢧⡙⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣿⣿⠟⠋⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⣠⡟
⠀⠀⠈⠙⢦⡈⠻⣿⣿⣿⡂⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⡿⠟⣩⡴⠋
⠀⠀⠀⠀⠀⠙⢷⡈⢿⣿⣷⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⠟⣳⠶⠛⠓⠒⠂⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣼⢌⠛⠿⣿⣷⣶⣶⣦⣤⣤⣶⣾⣿⣿⣿⡟⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⢠⠀⣷⣿⣷⣶⣤⣀⡈⠉⠛⠘⠛⠛⠛⠛⠫⣩⣾⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠘⢦⣍⡛⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣷⣶⣾⣭⣭⣭⣿⣛⣛⣛⣛⣛⣛⣛⣻⣥⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠒⠀⠀⢠⡄⠀⠀⠀⠀⣛⡅⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣴⣴⠶⠾⠩⢿⠷⠒⠻⠷⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠁⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⢷⠤⡃⢀⣰⣶⡾⠃⣦⢰⣄⣠⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠧⠇⢂⠂⢀⡅⠀⣀⡖⠀⢀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⢤⠉⠙⠁⠈⢋⠁⠀⠀⢈⠁⠈⠀⠀⠀⠀⠀⠀⠆⠸⠄⡆⡤⠤⢸⢃⡼⢇⣛⠀⢀⡒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠓⠺⠃⠀⠀⠀⠀⢿⡑⠗⠀⣩⣥⡶⠀⠀⠀⠀⠀⠀⢙⣟⠀⠀⠉⠉⢸⡎⡄⠋⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠑⠀⣠⣄⢀⣀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⢀⠀⠈⠂⠖⡤⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⢠⣄⣼⣽⢹⣿⡴⠀⠀⠀⢩⣅⠉⡁⠀⠀⠀⠀⠀⠈⡀⠆⠈⣶⣤⠀⢠⣄⣀⠀⠀⢠⣤⢀⣄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⢃⣿⠛⢾⢡⢾⡏⢀⣔⣋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠐⢿⣽⠇⠁⠀⠐⠁⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠼⠵⠿⠎⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠳⢀⠐⠄⢀⠀⣼⠇⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠠⠄⠐⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠒⠉⠉⠈⠉⠛⠈⠷⠀⠀⠀⠉⠁⠀⠀⢾⢏⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣤⡒⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣼⡦⠀⢠⡖⢲⠆⣠⢀⣀⡁⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠆⠀⠄⡠⠀⣈⠀⠹⠇⠀⠈⠃⠀⠂⠀⠀⠀⠘⠧⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣿⠄⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡀⠀⡀⠀⠈⢯⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⣰⣤⡄⠀⠀⠰⢉⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠁⠀⠀⠉⠀⠀⠰⠽⠟⠀⠀⠀⠀⠀⠀⡰⠀⡴⠃⠀⠈⠡⠈⠀⠀⠀⠒⠋⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⣀⢀⠄⠻⠄⠀⠐⠳⠒⠖⠂⠀⠀⠐⠚⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⡿⡷⠀⢀⠀⠀⠈⠋⢀⢀⠀⠀⢰⣻⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠊⠀⠉⠀⠀⠁⠠⠒⠒⠉⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠘⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠶⣆⡀⠘⠁⠀⠀⠀⠈⢷⠀⠀⠀⠀⢻⣿⣷⡀⠀⠂⡀⠀⠀⠀⢀⡔⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠑⢦⡀⠀⠀⠘⠈⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠒⢈⣿⣿⡇⠀⠀⠀⠀⠀⢶⣥⣥⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠄⠀⠈⠂⢀⣈⡀⠀⠀⠀⠀⠀⠒⠠⢤⣀⠀⠀⡠⠔⠊⠁⠀⠀⢠⠠⡺⠃⠈⠷⠀⠤⠒⠀⠀⠀⠀⠉⠙⠓⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢘⢤⡀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⡴⠃⠊⣀⡤⠴⢄
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢱⠶⠂⠀⠈⠀⠀⣶⠖⠋⠁⢀⡴⠊⠁⠀⠀⢿⣤⡀
⠀⠀⠀⠀⠘⢦⡀⠠⠀⠀⢰⠀⠀⠀⠀⣷⣦⣀⠀⠀⠀⠀⠀⠑⢺⡇⠙⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠠⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠈⠢⠀⠀⠀⣿⣿⠉⠛⠳⠒⠉⠀⠉⠙⠻⡀⢠⠟⣴⣦⡀⠀⠒⠤⢀⡀⠹⣿⡄⠀⠁⠀⠱⠀⡀
⠀⠀⠀⠀⠀⠂⢀⡤⠞⠁⠀⠀⠀⠀⠐⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠀⢿⣿⣿⠾⠳⠶⠋⠀⠀⠈⠙⠂⠀⠀⠇⠈
⠀⠀⠀⠸⣄⠀⣅⠀⠀⠀⠀⠀⢀⠜⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠉⠊⠓⠂⠀⠀⡠⠕⠊⠉⠉⠁⠺⡀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⣀⠀⠠⠋⠀⠠⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣡⣠⣤⣾⣂⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⢀⣿⣿⣿⣿⣿⠡⠤⠰⠂⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⣤⠏⠀⠴⢿⣿⡿⠿⠃⠀⠀⠢⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⠎⢀⠔⠗⡀⢀⠀⡛⡀⢈⡁⠀⠀⢀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⠆⠀⠀⠀⠈⢠⠃⠐⠀⠀⠀⠀⠀⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠛⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠔⠁

⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⣶⠄⠈⠱⡀⠀⠀⠀⠀⢰⡾⣋⣵⣾⠇⠀⠀⠀⠀⣸⣿⣤⣶⡇⠀⠀⠀⠤⠠⡤⢀⡀⠂⠀⠀⠀⠀⠀⡄⠄
⠀⠀⢹⡤⠶⠀⠀⠀⠀⠀⢠⠁⢂⣈⠟⠁⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠠⠈⠒⠖⠀⠂⠀⠀⠀⣄⡞⠓⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠋⠉

⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣬⣭⠀⢀⣭⣅⠀⠀⠀⠀⣀⣤⣤⡼⠿⢿⠀⠀⠀⠀⠚⢯⣿⣿⣷⠀⠀⠀⢠⡄⢺⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠
⠀⣿⣿⠁⠈⠉⠉⠀⠀⠀⠻⢏⣕⣊⡭⠝⡂⠀⠀⠀⠀⠀⠀⡿⠛⠋⠀⠀⠀⠘⠟⢈⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠉⠉⠁⠈⠀⠈⠀⠀⠀⠁⠒⠲⠶⠒⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⢀⠴


⠀⢠⣶⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⣰⣾⢟⣿⡇⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⣶⣤⣄
⠀⢀⠉⣁⡀⠘⠛⠀⠀⢸⣟⢿⣶⢟⣵⣿⣿⠃⠀⠀⠀⠻⠀⢀⡾⠇⠀⠀⠀⢰⣿⣿⣿⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠭⠿
⠀⢿⡿⠋⠁⠰⠆⠀⠀⠀⠉⠉⢰⣿⠉⠉⠀⠀⠀⠀⢤⣤⡤⢞⠵⠃⠀⠀⠀⠘⠻⠿⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠟⠲⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠆⢀⣀⡤⠴⠖⠻⢿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠀⢀⣠⠖⠛⡄⠀⠉⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠒⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠤⠄⣾⠀⢸⡄⠀⠀⠀⠀⠀⠀⠜⣿⣤
⠀⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠙⠙⠆⢠⠀⠀⠀⠀⣀⣀⣀⠙⢩⣿⡷⢏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠈⠿⢻⡇⣶⣶⡶⢶⣶⣶⠀⣠⡠⠄⣠⣷⣦⣦⢙⣭⢤⣟⣡⣄⣠⣾⡏⢉⢽⣗⠈⢍⣷⠸⠀⠀⣇⡄⠀⡀⡀⠀⠀⠀⣿⣿
⢠⡐⢻⠿⢧⠏⡍⣧⢘⣛⡿⢠⠌⠳⢢⣿⣿⡏⢹⡄⡿⠿⣂⠘⠷⠻⢁⠙⠛⠊⠻⠆⠀⡀⢱⣶⢤⣤⣤⣄⣠⣤⣤⣤⢤⣿⣿
⢸⣿⡿⠆⠀⠘⡇⠀⠀⡛⢁⣨⠘⠁⠊⠿⠈⠀⡌⠀⠀⠀⠀⠐⢤⣄⢰⣴⡷⠂⣤⣇⣛⣿⢾⠘⠙⢘⡇⢙⣿⣿⣿⣿⢸⣿⣿
⠀⢐⡹⢀⣠⣨⡓⠦⣤⢈⠘⠋⢸⡄⠀⠀⢸⡆⢈⠀⠀⠄⠀⢰⣾⣻⣽⣟⢳⢴⣼⣿⢩⣍⠁⢆⡀⠘⡃⠸⣿⣿⣿⣿⠐⣿⣿
⠀⠘⠀⣲⣶⣶⣿⠟⠿⠆⠀⠀⣸⡏⢠⡀⠉⣱⠛⠀⠀⣀⣿⣾⠇⠀⠀⢿⡀⢸⠗⢸⣧⡝⢿⠊⣡⢀⡄⠀⠿⣿⡿⠟⢈⣿⡋
⠀⠀⠀⣧⡿⠩⠉⠀⠀⠀⠀⢉⡁⣀⢸⠃⣸⡟⠖⠸⢱⠔⣟⠉⠀⠀⠀⠀⠙⢤⣀⠞⣿⠃⠺⢧⣤⣄⣰⣶⣶⣤⢽⣷⣻⣟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⡏⠁⠀⠈⠘⠤⠀⠁⠀⠀⠀⠀⠀⢀⣈⣿⡀⣌⡀⣀⣨⠇⢀⠀⢀⣭⣅⠘⠯⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⠛⠋⢧⠀⠀⠈⠉⢀⣘⠛⠉⠉⠉⢏⢆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡏⠀⠀⠀⠀⢀⠈⠀⠀⠻⣯⣤⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣤⡀⢀⡀⣀⢄⢀⣄⠀⣀⠀⣀⣀⣀⡄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠘⠛⠇⠛⠃⠳⠶⠸⠻⠴⠛⠆⠏⠟⠳⠄⠺⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⣴⢲⡤⣖⢠⣆⣴⢰⡆⢰⡖⢰⢠⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠊⠁⠚⠉⠁⠈⠘⠂⠈⠁⠘⠀⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⢻⢻⢶⡄⠀⢠⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⣺⣟⣿⠭⣽⠐⢯⢔⢪⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣼⣸⣼⡴⠧⣀⣀⠭⠭⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⢰⢲⢢⡈⠀⢣⣘⣾⢣⠖⡱⠁⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⣆⠃⡇⡰⡡⠯⣼⢏⠙⡄⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠳⡀⠀⠈⠓⠾⠓⠒⠒⠉⠒⠴⠃⣀⣀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣘⡀⠈⢂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣸⠀⢸⣿⣿⣇⠀⠀⠀⠀⢠⢞⣔⣓⣒⣛⣎⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠀⠰⠗⣲⣶⡚⡇⠀⠀⠀⢸⢹⢠⠤⠤⢠⢠⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠰⠆⢙⡙⠡⡗⢆⢀⠞⢹⢸⠨⢷⣶⠾⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠘⡄⠀⠀⢠⡇⠀⠁⠀⢸⡺⡀⠠⠥⠄⡠⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠀⠉⠈⠉⠉⠉⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠿⢠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣆⣀⠀⠖⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⡜⠛⣉⣉⣬⢋⠉⡋⠆⠀⠀⠀⡀⡀⠀⠀⠀⠀⢩⣰⠀⣀⠀⡆⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⠂⠒⠻⠿⠡⢾⠓⠟⠋⠰⠀⢺⠁⠁⠀⠀⠀⡀⢠⢨⢀⣒⡂⡇⣰⣶⡧⠀⠒⡳
⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⢶⠇⠀⠀⠀⢰⡇⡦⠀⣺⣀⡝⠂⠀⠀⢠⠀⢲⡦⠈⠐⠒⠀⡇⡳⠟⠃⠀⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠈⠙⠀⣠⡉⣉⡉⠀⠀⠀⠠⠄⢸⠇⠀⢀⠀⠀⠇⠅⡤⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣄⣬⡟⣿⣧⠀⠀⠀⢹⡉⢹⡁⠀⠀⠐⠀⠈⠰⠄⢰⣦⡄⠀⣄⣀⠀⠀⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠐⠠⠟⠻⣡⡿⢛⠟⡺⣟⠁⣶⣫⠸⠹⠁⠀⠂⠀⠀⠀⠀⠀⢂⠙⡁⠺⠽⠇⠁⠀⢊⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠛⠞⠟⣽⠂⠈⢀⠃⠰⠐⠀⠀⠀⠀⠀⠀⠀⠼⠋⢹⠶⠐⠂⠠⠠⡿⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⣬⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠯⠮⠤⠖⠆⢼⡀⠀⠀⠢⠀⠀⢀⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠴⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⠀⢀⡤⣤⠄⡀⠉⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠐⢰⡦⠀⠀⣨⡀⠀⠈⠻⠀⠈⠁⠸⠀⠁⠁⠁⢦⠀⠀⠀⢨⠀⠀⠀⠀⠀⡐⠀⣠⣏⣃⠄⠈
⠀⠀⠀⠀⠀⠀⢀⡉⠅⠀⠀⢱⡿⠁⠐⠂⠀⡳⠀⠀⠀⠀⠀⢀⠀⡄⡀⢀⢚⣶⣤⠀⠀⠸⣅⢠⣍⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠌⠉⢀⡀⠀⠀⢀⠹⣎⣶⠁⠀⢉⠄⠁⠀⢀⠉⠉⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣾⡄⠀⢀⠀⢿⣷⠀⠀⠀⠐⢰⡇⠟⠛⠊⠁⠘⠛⠚⠊⠉⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠤⢛⡇⠀⢼⠀⠁⣉⡠⠀⠀⠀⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⡶⠛⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣄⡀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠀⠈⠙⣾⠋⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⣠⠟⠛⠛⢶⣄⣀⣠⡾
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⣤⠾⠦⣤⣄⣤⠶⠖⠺⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠶⠚⢷⣄⣀⣀⣴⠟⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣤⠞⠓⠒⠒⢦⡾⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⣠⡴⣇⠀⠀⠀⠈⠙⢯⡀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠀⠹⣦⣀⠀⠀⣀⡴⠛⠳⠶⠖⠛⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡼⢷⣄⣀⣀⣠⣾⠋⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⣸⡇⠀⠀⠉⠉⠀⠙⠳⣦⣤⡤⠴⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⣇⠀⠀⠀⠀⠀⠀⣰⠇⠘⢷⡀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣤⡤⠾⠋⠀⠀⠈⢻⡄⠀⠀⣸⠃⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⢤⣤⣄⣀⠀⠀⠀⠀⢿⡀⢀⡟⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠰⢯⣅⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⠀⠈⣧⢸⡇⣠⠞⠁⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣸⣿⣴⠋⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⣀⣀⣀⣀⣀⣹⣿⠃⠀⣀⣀⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠿⠛⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠭⢍⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠑⣲⢄⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡹⠀⠀⠀⠀⠉⠊⠀⠐⠆⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⡀⢠⠃⠀⢠⠇⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠤⡀⠙⣄⠐⠎⢁⠆⣄⣴⠧⠒⠉⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠓⠀⣈⣢⣬⣟⣦⡞⠃⡰⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣠⡒⠋⠩⠭⠑⣯⣯⡛⣿⣿⣿⢥⡄⣨⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢀⣀⠈⠀⠀⡠⠘⠌⠠⣠⣨⣄⡀⠀⠀⠀⢀⠤⠖⠊⡰⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠁⠀⠀⠐⠁⡟⠀⠀⣈⠈⠙⠻⠶⣤⠮⠥⠖⠒⠋
⠀⠀⠠⠂⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠈⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⠠⢄⣱⣄⡀⠀⣀⠀⠀⢀⡔⠁⢸⡀⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠙⠯⣁⡤⠖⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⡿⠿⠆⠀⠰⡂⠀⠦⠀⢀
⠀⠀⠀⠀⡧⢄⣀⡀⠀⡟⠓⠚⢶⠦⢤⣐⣴⠿⠱⡖⠤⢤⣄⣀
⠀⠀⠀⢰⡇⠀⠀⠀⠉⠉⠛⠓⠒⠳⠤⣄⡙⢧⣠⣝⠄⠀⣈⠙⠛⠶⠦⡤⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⡔⠀⠀⠀⠱⢄⠀⠀⠈⠳⣿⣟⠛⠛⠶⢦⣤⣤⣀⣀⣀⠈⠉⢲
⠀⠀⠀⣼⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠈⠻⡳⣾⠀⠀⠑⠤⣈⠉⠉⠛⠛⠚⠀⢴⣶⣦⡤⠭⠭⠭⠉⡽⠃⠠⣄⣀
⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⢱⠈⠳⣄⢀⠂⠀⡄⠈⠀⠀⠂⠀⠀⠈⠛⠻⡉⢐⣚⣛⣛⣉⣂⣘⡿⢷⣦⣶⣤⣀
⠀⠀⠀⡇⠀⡘⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣇⠀⠉⢯⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⠀⣠⠎⠉⣉⠽⠛⠛⣿⣽⣏⣹⡄⠄
⠀⠀⠸⣇⡘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢹⢦⣤⡤⠹⣦⠀⠀⢩⠉⠐⠒⠒⠂⠀⠀⠀⠙⣿⠛⠓⢤⡺⠁⠀⠔⡡⠀⢈⠀⡦⢻⣦⡀
⠀⠀⠀⢸⡯⠤⠶⠦⠤⠤⠤⠤⠤⠤⠀⠀⠤⢷⠤⠤⠤⢰⡏⠉⠉⣹⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠹⠀⡇⢀⡇⠀⠈⢀⡇⢰⠈⠉⠁
⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣤⣤⣤⡧⡤⢤⠿⠒⠲⠶⠖⢷⠒⠒⠒⠒⢲⠀⠀⠀⠘⣦⣄⠀⡀⣦⠃⠐⣷⠢⠠⠘⡇⢸
⠀⠀⠀⠀⡏⠉⠉⡏⠉⡏⠉⠉⡛⠙⠉⡏⣿⠸⠦⢶⠶⠶⠶⠶⠶⠶⡦⠦⠦⠤⠾⠦⠤⠶⢲⢺⠓⠒⠒⢺⠁⢉⡉⠀⠈⡀⠀⡏⠀⢒⡤⣧⢸⠀⡁
⠀⠀⠀⠀⣇⠀⠀⡇⠀⡇⠀⠀⢽⣠⣀⡇⣿⠠⠄⢠⡇⠀⠀⠀⠀⣷⠇⠀⠀⣠⠀⠐⣦⣽⣆⣿⡄⠀⢰⠸⡗⠀⠇⣼⡉⠺⢠⠷⢾⠀⠦⠮⣸⢀⠀⠆
⠀⠀⠀⠀⣿⠀⠀⡷⠒⡇⠀⠀⠉⠈⠀⠀⢹⠁⢀⠈⠇⠀⠀⠀⠠⣿⡄⠀⠀⢹⣦⣆⣰⠠⣌⡁⠀⠀⠠⠄⣷⣀⡲⢯⠻⣇⠸⡀⡢⣆⡀⢰⣮⡈⠛⢁
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡇⠀⠀⢰⡀⠉⡇⢸⡤⢠⡀⠀⢳⡄⠀⠀⣯⠆⠐⠫⠀⠀⠉⢣⠀⠀⠑⢄⠀⠀⠀⠈⠀⠀⠀⢣⠘⠂⠙⠁⢅⢀⠋⢁⠹⡞⠻
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡇⠀⠀⠜⡿⠿⠇⣼⣀⣸⣧⡄⢈⡙⠳⡦⣿⡦⡄⡀⠀⠀⠀⠀⡇⠀⢀⣿⡀⠀⠃⠀⠀⠀⢀⢸⡔⠀⠀⠀⡈⠨⡄⢼⡤⠁⡀
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡿⠀⠀⣿⠀⠀⢄⠈⠻⣷⠙⠋⠀⡀⠀⡟⠁⠈⠉⢃⠀⠀⣆⠀⢷⠀⢸⠇⢷⣸⡄⠀⠀⠀⢸⡆⠃⡄⠀⠀⠃⠀⠙⠉⠀⠀⠇
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡷⠒⠂⣿⠀⠀⠀⠋⢀⣼⠀⢀⣉⠠⢰⢁⡶⠴⢦⡈⠛⠆⠈⢳⠈⢃⢸⡆⢸⣶⠃⠀⠀⠀⡀⣏⡛⢋⡐⠀⠀⢀⠀⣀⡴⠀⡓
⠀⠀⠀⠀⣿⠀⠀⡇⠀⣇⣀⣤⣿⣀⣀⡬⠞⠁⣟⠏⠉⠀⠀⢰⣟⠁⡀⠀⠹⣊⣀⣀⢀⠏⠉⢨⡏⠉⢉⠀⢀⠀⠈⣃⢯⡤⣾⣿⣠⣿⠿⠿⠷⠶⢾⡏
⠀⠀⠀⢀⡿⣤⠴⠷⠾⢿⢿⡍⠉⡀⠀⠀⡀⠀⢹⡄⠀⠀⠀⠈⡏⠉⠙⠛⠀⡏⠉⠉⠩⠀⡀⣼⣏⢍⣉⡀⢈⠀⣈⢉⣸⣇⣿⣿⣿⣿⣒⣲⣶⠤⡾⣇
⠀⠀⠀⡎⠀⠉⠈⠉⠉⠉⠂⢹⠀⣷⠀⠀⠇⠀⠸⣇⣤⠤⠖⠲⣦⠤⠔⠒⠒⡞⠀⠀⣤⣠⣧⠟⠋⡿⢻⡁⠈⠀⠈⠁⠀⠛⠃⠿⠚⠏⠀⠀⠀⠉⢷⣈
⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠀⢱⠀⡇⠀⢡⠀⡆⠀⡧⠀⢠⠀⠀⡃⠀⢠⡇⠈⡆⠃⢐⠀⠀⠹⠆⠒⢣⠴⠉⠀⠀⠀⠀⠀⡀⠀⡆⡤⣬⠁
⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡆⠀⠀⡇⠀⠘⡆⣹⠀⠁⠀⡜⠃⠀⡇⠀⠈⠰⠀⡇⡄⠠⡄⠁⢀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⡇⢸⠃⡏
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⠀⣀⣘⠷⠶⢿⠄⠀⣄⣩⣿⡏⢀⠌⠀⡇⢀⠇⠀⠀⠀⠍⠅⠄⠘⠳⣇⣿⣇⡐⠁⠀⠀⠀⠀⠀⠀⠀⢳⡼⡶
⠀⠀⠀⢸⢷⣀⣀⣀⣀⢀⠀⠸⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠰⢄⣈⠀⠀⣇⣀⠶⠿⣦⠶⠤⠚⠃⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠤⡴⠖
⠀⠀⠀⠘⢊⠉⠉⠉⠉⠑⡐⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣬⠆⠀⢨⣤⣵⡶⠒⠁
⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠹⢟⠛⠋⠉⠹⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⠈⠟⢰⠀⠀⣀⠀⢸⣦⠀⠸⣿⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠣⡄⡘⢦⣦⢺⣄⣶⣄⢻⡄⡀⢠⣰⡇⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⡠⣌⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⡔⢻⣟⣋⠀⠚⠛⠛⠉⢩⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⠃⢀⠲⡶⣿⣿⣿⣿⣿⣿⢿⡹⣇⢹⣾⡿⣼⡿⠁⣃⠀⠀⢀⣴⣿⡿⡟⠛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣷⡀⢀⠘⢁⠶⣿⢻⣿⡿⣽⢷⣏⢳⣼⡞⠹⡿⣿⠇⣠⣿⠋⢀⠛⠻⣿⣿⣷⣤⡟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⢹⡦⢷⣼⡇⠙⣧⣍⠙⢾⡊⠿⠉⣻⣦⣠⣃⡎⣠⣿⣷⣾⡥⠀⣠⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⣂⣀⣴⣍⣽⣾⣆⣙⣾⣾⣿⣷⣤⣾⣿⣿⣿⣶⡿⢿⡏⠉⢛⠿⠁⠀⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠤⠒⢫⣥⣼⣍⡙⣻⡟⠻⢟⣿⣿⣿⣿⣿⣧⣾⣇⣄⣼⣶⣾⡟⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣶⣼⠋⠘⢣⣌⣉⣥⣿⡟⠿⢿⠹⠿⢻⣿⡂⠙⣿⢻⣿⣇⠀⠁⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⢲⣿⣿⡿⠋⢿⡿⣷⣀⣰⣷⢤⣾⣥⣀⣤⣬⠂⢿⣟⠛⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅⣨⣵⣶⡿⠁⢀⣠⣤⣾⡿⢧⡀⠀⢸⣟⢿⣿⣷⣶⣦⣁⣀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣏⠹⢀⣶⡾⠿⣹⣿⣧⠀⠙⢢⣄⣩⣧⠹⠯⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣾⣿⡅⠀⣯⡴⣿⣿⣶⡼⠋⣸⣿⣷⣄⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢤⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠀⡀⣀⣼⣤⠞⣀⡤⠀⠀⠀⡀⠀⠀⠠⠃⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢈⡑⣶⣿⣿⣿⡧⢞⠁⠀⢶⡚⠁⡔⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢋⣻⡟⣛⢁⠨⠉⠀⠀⡁⢸⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢤⡤⠴⠋⠊⡇⡇⠈⠁⠀⠀⢸⠁⠀⣣⠴⠾⠚
⠀⠀⠀⠀⠀⢤⠠⠀⠀⢀⠀⠀⠀⠀⠤⡀⢸⠀⠀⠀⠀⠀⠈⢢⢤⠀⠀⠁⢀⡴⠁⠀⡠⠀⠀⠠⡀⠀⣠⠬⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠎⠀⠈⠂⡁⠢⠀⢀⣀⠠⠊⠈⢧⢀⠔⠋⠀⠒⠺⣅⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⡇⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠙⠓⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠠⢀⣇⠀⠙⠀⢠⠆⠀⠀⠈⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⠔⠒⠛⢄⠑⢢⡟⠡⡀⠄⠀⡜⠀⢀⡞⠁⠀⠀⠀⠀⢀⠠⠊⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⢉⠾⠄⡀⢙⠒⠈⠀⣠⠞⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠐⠂⠔⡺⠉⢀⠤⣤⡋⠐⠒⢶⡇⠀⠀⠀⠈⠁⠀⠀⢂⡀⢀⡀⣰⢁⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⢀⡠⠖⠁⠀⠀⠈⠀⡕⠀⠀⠘⡇⠀⠀⡀⠀⡄⡀⠀⢀⡤⢏⣈⠉⢦⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠛⢹⡤⠊⡀⠀⠈⠁⠂⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⢀⠔⠉⠐⠋⠄⠀⢂⠑⠀⠀⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁

⠀⠀⠄⠀⠄⠁⢨⠀⠁⣸⣛⡇⠘⠀⠀⡢⠄⠂⠀⠘⡇⠀⣁⡁⢘⣈⠀⠸⠠⠄⡄⢠⡄⡅⢨⠀⢹⡇⠸⠳⢻⠠⣯⢠⠄⣆⡀⠀⢀⣀⣰⣀⣀⣀⣀
⠀⠀⠁⢀⡀⣁⢘⡀⢀⠛⠛⢳⠀⠀⠨⣀⣀⠇⠀⠘⡇⠀⠤⡄⢨⢤⠀⢠⠰⠂⠦⠰⠄⠄⢠⣀⣼⡇⢠⡄⠰⠀⡷⠀⡆⣥⠠⠄⡄⡤⡈⠻⢿⠠⢤
⠀⠐⠀⠠⠀⠤⠀⢤⠤⠁⠉⠁⠐⡆⠀⠀⠀⠀⠀⠀⣇⡀⠲⠦⠴⠴⠤⠾⠴⠦⡖⠐⠂⠆⢸⠀⠀⠀⢠⡄⢘⠐⡗⠀⠇⣎⠀⠈⡅⣐⡀⢠⢤⣤⣤
⠈⡁⣁⣎⠁⠐⠀⠛⣂⣉⣉⣉⡁⣯⠄⠀⠀⠀⠀⠀⠇⡄⠉⡈⠉⠉⡏⠃⠉⠑⢘⢈⠁⠃⢸⢹⡏⠁⢠⡀⢈⣈⣊⡉⠁⡛⠺⠒⠟⠶⢁⡀⠀⢠⡀
⠀⠀⠂⠀⠀⠀⠀⡅⣨⣀⣡⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⡅⠀⠟⡃⠃⡇⡋⠉⠉⠨⢈⡁⣁⠈⢸⠇⡆⢠⣀⣨⣀⣏⣀⣀⡇⠈⠐⠁⠈⠉⠁⢈⠐⢈
⠀⠀⣃⠁⡀⢀⠀⡂⣥⢤⢤⡤⠌⡁⡀⠀⠀⠀⠀⠀⣀⣰⣆⠈⡏⠉⡏⡉⠉⠁⠠⠠⠄⢠⠀⢸⠷⡇⢠⡈⠉⠀⠈⠉⠛⠁⠀⠁⠀⠀⠀⠀⣎⠀⠹
⠐⠂⠒⠀⠂⠠⠀⡇⠤⠤⠤⠤⠀⡁⠀⠀⠀⠀⡀⠀⡙⢉⣉⠈⡉⠉⠏⠉⠉⠃⠀⠀⠀⠀⠐⢸⢐⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⠀⠄⢈⡁⣉⡔⠃⢀⢀⢀⢠⣤⢉⠛⠉⠀⠈⠉⠐⢦⡐⣶⠐⡗⠓⠓⠚⠚⠃⡏⢐⠚⢲⠸⠴⠺⠇⢨⡄⢐⠂⠀⠀⡔⠐⠒⠂⠒⠀⠀⠉⠀⠀⠈
⠀⠀⢠⡀⠀⡄⠀⠀⠤⠤⢤⠸⠠⠔⠐⠀⠐⠐⠁⠀⠀⠀⡀⠈⡇⠃⠃⠉⠙⠃⡇⠘⠀⠈⠀⠀⠀⠀⢰⡄⠈⠀⠉⠀⡇
⠀⠈⣸⣀⣉⡑⠀⠤⠄⠆⠴⠰⠲⠂⠀⢀⠀⠠⠀⠀⠀⠀⠁⠐⡇⠗⠆⠐⠚⠃⡆⠠⠄⠆⠠⠀⡄⢀⠸⡄⣠⣀⠤⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠴⠸⠡⠅⠇⠛⠒⠦⠆⠆⠒⠒⠚⠂⠉⠤⠠⠠⠄⢀⡀⣠⡀⠐⡇⠖⠒⠚⠚⠂⡇⠐⠀⠀⡥⠀⡶⠒⠒⠒⠛⠛⠛⠛⠻⠆⢀⡁⡁⣀⠀⠀⢀
⢐⠒⡒⢒⢐⠒⡂⢰⢃⢓⣂⣀⣚⣂⠘⠀⠀⠀⠀⠘⠀⠀⠙⡦⠆⠖⠶⠰⠶⠆⡧⠴⠄⢀⢿⣼⡇⢀⡁⢈⢈⠀⠀⢀⠄⡯⡭⣓⣀⣡⢨⣀⣈⣤⣀
⣈⢈⡁⣉⢈⠉⡁⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡧⠤⡤⢴⢰⠴⠄⠂⠀⠂⠀⠂⠒⠀⢐⠂⣀⢐⠐⣂⢐⢀⣡⠰⠯⠋⠍⠶⠶⣖⣶⣶
⠠⠠⠄⠤⠠⠠⠄⢠⣀⣀⣀⣤⣤⣤⡄⠉⠀⠈⡀⠀⠀⠀⠁⣧⠔⡆⢠⠠⠤⠄⠂⠀⠐⠀⠀⠐⠆⠤⠀⠄⠠⠀⠠⠀⠀⢠⠤⠆⠦⠰⠀⠀⡃⠉⠉
⠐⠐⠂⠲⠰⠀⠂⢈⠀⠀⠀⠀⠀⠈⡇⢀⠀⠀⡀⡀⠀⠀⡄⠰⠀⠒⡖⠐⠒⠂⠁⠶⠄⠂⠀⠐⡇⢓⠀⡀⢐⢐⠈⢀⠀⢈⢀⡁⣉⢈⢈⠀⠂⣀⠔
⢘⠀⡁⢉⢈⠀⡁⠴⠶⠦⠤⠶⠦⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⡧⢀⠀⣠⠄⢉⠁⠆⢄⠀⡇⡈⠠⠄⠤⠠⠈⠀⠀⠠⠠⠄⠄⠠⠠⠀⡷⠊
⣈⢈⡅⣈⢈⡀⡁⠀⡖⠊⠃⣸⢚⠀⠀⠠⠠⠀⠀⠀⠀⠠⠀⠀⣀⣈⠁⣀⣀⣉⣀⣀⣈⣀⣀⡈⠁⠒⠀⠂⠈⠀⢐⠀⠀⠐⠀⠂⠒⠐⠐⠀⠓⠒⠒
⣤⣠⣄⣤⣠⣄⡄⠀⡶⢄⡀⣶⠔⠀⠀⠀⠀⠀⠂⠀⠐⠐⠀⠀⠀⢘⢐⡃⡂⢰⠰⠂⠇⠇⠏⠅⠀⠄⠨⠁⠌⠠⠁⠈⠀⢈⢀⡁⡉⢈⢈⠀⠀⠉⠉
⠀⡀⡀⢀⢀⠀⠀⠤⠤⠤⠤⠤⠬⠤⠄⠐⠀⠀⠑⠁⠈⠉⠀⠀⢀⠀⢀⣀⣄⣀⣈⠉⣉⣉⢍⠃⠀⡀⢐⠂⡉⠐⠁⠂⠀⠠⠠⠄⠤⠠⠠⠄⠀⠐⠂
⠀⠤⡄⠰⠤⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⢐⠉⠆⠀⠁⠈⣀⠄⠤⠽⠽⢿⠭⢭⡙⣛⢸⡄⢀⢠⠀⠀⠇⠠⠀⠆⠀⠀⠀⢠⠐⠀⠂⠒⠐⠀⠂⠀⠒⠂
⠀⠒⠂⠐⠒⠀⠀⠂⠀⢠⠀⢸⠀⢀⡘⠈⠉⠁⠉⠃⢤⡇⠀⠀⠀⢀⡀⣀⠈⡇⠀⣘⠉⠉⢹⠀⠀⠀⢠⠤⡀⢔⢀⠀⢸⠀⢀⡠⣠⢄⠀⠀⠀⠤⠄
⠀⣉⡁⢈⣉⠀⠐⠛⠒⠺⠆⠘⠻⠾⠀⠶⠴⠀⠯⠲⢰⡯⠤⠤⠤⠤⠤⠤⠤⠷⠈⠀⠈⠹⣶⣤⡀⢀⣸⡀⣆⣸⠀⠀⣈⢀⠼⠠⠠⠄⠤⠰⡀⢤⢤
⠀⠤⠄⠠⠤⠀⢤⠄⠠⠤⠤⠤⠤⡠⠄⠒⠒⠀⡒⠘⠠⠀⡴⠤⠖⢐⣲⠶⠀⣠⣤⠤⠤⢤⣬⢡⣡⣠⠄⣤⣡⣠⣄⣤⣠⣈⣇⠀⠀⢀⡆⠀⡆
⠀⠒⠂⠐⠒⠀⠡⠚⠒⠐⠁⠘⠛⠀⡀⠉⠉⡀⢉⢉⢀⠀⣉⣀⠅⠨⢅⣨⠀⠘⠛⠄⠄⠴⠂⠀⢀⠀⠀⡄⠀⡀⣀⢀⢀⡀⣣⢠⠀⠂⠟⡽⠁⣠⠠
⠀⣉⡁⢨⣉⠀⠐⢀⣀⣀⣀⠈⠀⠈⠍⠉⣋⠛⢛⠛⠻⡀⠓⠈⠋⠈⠉⠀⠀⡰⠤⠦⠶⠶⡆⠓⠐⠀⠂⠂⠒⠂⠊⠘⠀⠀⠠⡄⠄⠀⠆⠤⠀⠄⠂
⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⢤⣤⠀⢀⡀⠄⠀⠀⠀⡀⠉⠁⠁⡈⠉⠉⠉⠉⠃⢀⠰⢄⡀⣞⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⡆⠈⠹⠐⠀⠂⠐⠀⠐⠒
⠀⠀⠀⠰⠶⠀⠀⢀⣀⣀⣀⠨⠽⠀⠘⠁⠀⠀⠀⠀⠈⠀⠀⠀⠰⠐⠅⠀⠀⠂⢰⢈⣠⠉⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠄⠐⠀⠀⠂⠠⠄
⢀⣀⣀⠈⠚⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⣄⣤⣠⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠸⠀⠸⠀⡇⠀⠀⠀⠀⠓⠒⠒⠒⠉⠛⠁⠀⠘⠃⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⢺⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣿⣧⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⢀⡴⠶⠖⠶⠶⣄⠀⠀⣿⠏⠉⠉⠙⡀⠀⠀⠀⢠⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⡀⠀⠈⠉⠀⠀⢳⡀⠀⠀⢰⡟⠀⢰⣿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⡠⣄⡀⠀⠀⠀⠈⣷⠀⢀⡟⠀⠀⣼⡏⠀⢀⠀⠀⠘⡀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⠁⠀⠀⠀⠀⠉⣳⣤⣶⡿⠿⠿⠿⠿⠦⢤⣿⠁⠀⢸⠀⠀⠀⢣⠀⣀⣼⠿⠾⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡵⠁⠀⠀⠀⠀⠀⠈⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢸⠀⠀⠀⢸⡾⠋⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⠿⣷⣶⣶⣶⣶⣶⠶⢷⠈⣆⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢸⠀⠀⠀⢸⡷⠦⣤⣤⣤⣤⡤⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣭⣭⣥⣶⣶⣾⣇⠘⣶⣤⣤⣀⣀⡀⣼⡟⠀⠀⢸⠀⢀⣀⣘⢧⡀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠘⣦⣌⣉⣛⣛⠋⣰⠟⠿⣿⣿⣿⣿⣿⣿⡿⠀⣍⣂⣀⣀⣐⣋⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣥⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁






⣶⡶⠒⣶⢶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣥⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⡄
⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠙⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠂⠘⠃⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠁⠀⠀⠀⠀⠨⠹⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⠀⠰⠚⢷⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠰⠀⠀⠀⠀⠀⠀⡤⠘⠀⠀⠆⠀⠀⣀⠔⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡀⠝⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⢰⣠⠄⠈⠀⢀⠃
⠀⠀⠀⠀⠀⡄⠘⠉⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣠⠈⠃⠤⠀⠀⠀⣰⣾⣿⡆⠁⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢣⣶⠂⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠑⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⢸⡿⣖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠆⠈⠉⢿⣿⣿⡆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣀⡀⢀⡌⠀⠀⠀⠀⠀⠡⠀⠘⣀⣀⠀⠈⠿⡟⠢⢀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠡⡉⠺⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⢢⡘⢅⠀⠀⠑⠂⢀⡠⠂⠐⠢
⠀⠀⠀⡠⠂⠈⠁⠉⠉⠑⢀⠀⢀⠠⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⡗⠂⠐⠀⢘⠀⠀⠀⠀⠇
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣸⣬⣿⣟⡛⠁⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⣀⣼⣾⣷⣇⡴⠐⠂⠤⡀
⠀⠀⠀⠣⡀⠀⠀⠀⢀⣦⣾⣿⡿⡿⣍⠦⡀⠀⡀⠔⠈⠀⠀⡠⠊⠀⠈⢾⣿⣿⣿⠂⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠈⠑⠀⡔⠁⠈⠈⡟⣷⡛⠈⠀⠀⠀⠀⢢⠀⠀⠀⡁⠀⠀⠀⠸⠑⠛⠀⠉⢢⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠒⠖⠖⡅⠀⠀⠀⠀⢸⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠀⠀⢀⡔⠙⢆⣀⣀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠄⠂⠀⠑⠠⠤⠤⠄⠀⠀⠀⠀⡄⠀⣀⠊⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣴⣾⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠓⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⣇⣄⠉⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⢳⡇⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠓⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠤⢾⠃⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⣷⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠜⡿⠠⠜⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠨⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠈⢿⣶⡄⠀⠀⣿
⠀⠀⠀⠀⠀⢀⡼⢁⠌⠀⠀⠀⠀⠀⠪⢦⠀⠀⠀⠀⠀⠀⠈⣿⠈⠆⠀⠀⠀⡔⡇⠀⠀⠀⠀⡀⠈⠡⠘⠎⠀⠀⠀⣄⢡⣼⣤⣴⡏
⠀⠀⠀⠀⠀⡾⠁⡎⠀⠀⠀⠠⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠠⣿⡀⣇⠀⣰⢰⣿⠁⠀⠀⠀⠀⢡⡀⠐⠀⣤⢌⣁⣶⣿⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⣧⣿⣠⣿⡾⠃⠀⠀⠀⠀⠀⠀⠁⣀⣟⣧⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠂⢠⠠⠶⠞⠿⢶⠶⣄⢀⠄⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣀⣀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣰⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠭⠝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡭⣹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⢠⣖⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠁⣏⢹⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⢺⣇⣰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢾⡛⢛⣿⡶⢶⠠⠀⠀⠀⠀⠀⠀⠀⢸⣎⣿⡄⣣⣿⡎⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢹⡄⠀⠀⠀⠀⠀⠀⣶⣤⣠⠁⠀⡀⠀⢉⣤⣴⡇⠀⠀⠀⠀⠀⢀⢀⢈⣯⣥⣽⡿⣇⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣏⣿⠄⠀⠁⠀⣼⠙⢸⡇⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⡀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⢻⠠⡀⠀⠀⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠹⡄⢀⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢤⣼⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢦⣬⠀⢈⣉⠉⠙⡊⠁⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⡢⣴⣤⠀⣀⣀⣤⡀⢈⠀⠁⠈⠁⠂⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣷⠿⠿⠿⠿⠋⠉⠙⠿⢤⠆⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⢒⠁⠀⣠⣇⠀⠀⡀⠀⠀⠐⠂⠀⠀⠁⠒⠀⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢆⣈⠆⢻⣿⡏⠀⠀⣀⠀⠀⠀⠰⠀⠀⠀⢀⠄⠀⠁⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠞⠁⠀⢇⠟⠃⠀⠀⠈⠀⡀⢀⡀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⣁⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠙⢀⠀⠀⠐⠂⠀⠉⡠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠢⡀⣤⠊⠡⠀⠄⠀⠐⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⢀⡀⠀⠰⠂⠄⠋⣀⢀⢀⡠⠆⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠙⡄⢰⠀⠀⠠⢀⡀⠀⠀⢀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⢠⠑⡄⠀⠀⠀⠀⠀⠈⠑⡂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠃⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡠⠄⢠⠒⠤⠴⠶⠢⠤⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡠⢀⣠⠤⠒⠊⠁⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠇⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⠒⠒⠂⠉⠓⡄⠀⠀⠐⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢲⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣠⡾⠁⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡠⢰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠙⠟⢻⣏⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠰⠖⠀⠈⠉⠁⠙⠻⠷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠘⠀⠀⡐⠋⠐⠂⠉⠀⠀⠀⠈⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⣿⡟⠀⠀⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⣛⠓⠶⢓⣄⠀⠀⠉⠀⠀⠈⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡆⢀⡟⠋⠉⠉⠳⠀⠀⣁⠴
⠀⠀⠀⢴⠀⢠⡄⠀⠀⢿⡟⠉⠉⢰⡆⠀⣀⠀⣤⣀⢛⡀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⡆⠀⠀⠘⠂⠈⠓⠒⠶⠾⣿⡶⣤⣼⣷⠖⢉⡀⠀⠛⠀⡉⠒⠒⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡛⠙⠁⢘⡁⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠙⣥⣄⠀⢈⠇⠀⠉⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠀⠤⡀⠀⠠⢤⡙⠛⠶⠶⡤⣀⣀⣀⡀⠤⠶⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⢸⡀⢻⣄⠐⠂⠁⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠳⣄⣹⠆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡄⣤⡀⠈⠁⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠻⣦⣀⡤⠋⠀⠀⠀⠀⠀⠀⢀⣾⢹⡇
⠀⠀⠀⣀⠀⢠⡆⠐⠒⣀⣠⡶⠀⣾⠉⣠⠀⠀⠀⠀⠀⠀⢠⠘⡇⠸⡇
⠀⠀⠀⠙⠀⠀⠙⠛⠋⠙⢿⠷⣤⣿⠀⢿⠀⠀⠀⠀⠀⢠⠌⣷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⠊⠀⠛⣿⣧⠘⡄⠀⠀⠀⠠⠇⢀⠋⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⠁⠀⣿⠀⠀⢀⠟⠀⢸⠆⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠁⠀⢿⠀⢀⠛⠀⢀⡌⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠸⠀⠀⢸⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⡘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣿⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠒⠒⠒⠒⣠⣾⠀⠀⠀⠀⠀⠈⢷⣤⡤⠐⠒⠒⠒⢠⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⡟⠋⠻⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⢀⠀⠆⠐⠀⠀⢠⠂⠀⠀⡁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣆⠀⠀⢠⠀⡠⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠌⠢⠤⠔⠛⣡⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠔⠁⠤⠂⠀⠰⠁⠀⠀⠀⠀⠀⢄⡤⠂⠀⠀⠀⠑⢂
⠀⠀⠀⠀⠀⢐⠈⠑⠢⠀⠀⠀⠀⠀⠉⠲⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢆⠀⡀⠀⣇⠀⠀⠀⢀⡼⣂⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠢⠰⣎⣠⡆⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢼⠀⠁⠂⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡛⢣⣮⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠄⠀⢤⡀⠀⡤⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠀⣀⠴⠃⠑⠈⢣⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠈⠐⠚⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⣧⠠⠄⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⠁⠀⠀⡀⠀⠀⠀⠀⠦⢀⠀⠐⢛⣬⡀⠤⣎⠈⠀⠉⢉⣢⠀⠀⠀⠀⠀⢣⢀⣀⢀⡰⠀⠠⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠑⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠋⠶⣿⣿⣤⡀⣀⠀⠀⠀⠹⠄⠀⠀⢀⠀⠀⡀⠉⠉⠀⠀⠉⠁⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⡏⠙⠛⠡⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢠⣡⣂⣀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣀⡀⠔⠀⠁⠉⠈⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠈⡆⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢴⠀⠀⠀⢠⠃⠀⠀⠀⡀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠲⠋⠀⠀⠀⠉⠉⢣⠁⠀⠀⢆⠢⠠⠄⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⣠⠂⠀⢀⠆⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠒⠀⠀⠀⠀⠀⠈⠢⣀⣀⡑⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢘⠀⠀⠁⠒⢄⠀⢠⣄⠀⠀⣆⠂⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠉⠐⠒⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠚⠫⠀⣐⣋⡵⣴⠀⠒⠛⠛⠛⠚⠋⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠐⠂⢾⢇⣀⣶⠀⡄⢀
⠀⠀⠀⠀⠀⠀⡀⢠⡖⠀⠲⢻⣿⣷⣧⠀⠀⠀⢀⠀⠈⡇⠀⠄⠀⠀⠈⠁⢠⣷⡀⠸⡀⠀⠺⠿⠟⠟⠾⠿⠿⠂
⠀⠀⠀⡀⠃⡀⣧⠼⠇⢀⡀⠀⠉⠻⣷⠶⠦⠺⠿⢓⠀⠀⠀⠀⠀⠀⠀⠀⣝⠷⠇⠀⣀⣼⡅⢠⣿⢠⡄
⠀⠀⠀⠀⠀⠁⠁⠀⠠⠈⣰⣦⡬⠛⣋⢹⢿⡿⢖⣩⡀⠀⠀⠀⠀⠀⠀⠐⠮⣳⡄⢻⣿⣿⣿⣾⣿⡿⠠
⠀⠀⠀⠀⠐⠀⠀⠀⢁⣿⣿⡿⢿⠡⡼⢼⣛⣛⣿⠏⠀⠀⠀⠀⠀⣴⠆⠀⢀⣀⢙⡄⢸⣿⣿⣿⣿⡄
⠀⠀⢀⡀⠀⠀⠀⠀⠈⠙⠻⢶⣿⣾⣿⡿⠿⠟⠁⠀⠀⢀⠀⠀⣰⡿⠀⡤⠀⠁⠀⠀⠸⠚⢟⠋⠀⠁
⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⣀⢀⣿⡕⠈⡁⠃
⠀⠀⠀⣨⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠸⣿⣿⡄⠈⠢⡐
⠀⠀⠶⠼⠛⠁⠀⠀⠸⣖⡂⠤⡤⣤⡠⢤⡆⠀⠀⠀⠷⠆⠀⠀⠘⣿⣧⠀⠀⠙⢷⣶⢄
⠀⠀⠀⠙⠃⠁⠀⠀⠀⠘⠣⡴⣁⣳⣵⠟⠀⠀⠀⠀⠀⠀⠀⢲⣴⣿⣿⠤⠴⠶⠾⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠁⢠⣉⡀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠐⠂⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠈⠁⢦⡀⠀⢀⠄⠈⠈⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠂⠡⣤⠇⠀⠀⠀⠈⠀⠈⠆⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠂⣄⣀⣧⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠈⡼⠁⠀⠂⠠⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠄⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⢀⣀⡤⠦⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠔⠒⠈⠉⢉⡀⠒⠢⢤⠊⠀⢀⠄⠊⠁⠀⠀⠀⠈⠐⠄⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠛⠶⠄⡀⠀⠀⠀⠀⡠⠊⠀⠀⠃⠀⠂⢠⠀⠀⠀⠰⠃⢶⠁
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠈⠀⠀⠀⠀⠀⠉⠀⠒⠎⠀⠀⠀⠀⠈⡀⢠⡄⠀⠄⠰⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠘⠂⠀⠀⠀⠀⢃⡀⠀⠀⠀⠤⠐⠚⠋⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢚⡷⠒⠈⠉⠀⠀⠰⠀⠀⣠⠠⡄⢠⠂⠀⠤⢤⠈⢁⠀⠀⠀⠀⠏⠐⠂⠤⢄⡀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠀⠁⠀⠑⠒⠒⠀⠀⠅⠜⠀⢀⠜⠀⠀⠀⠀⠀⠈⠳⠦⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠕⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠐⠄⡀⠀⠀⣀⣠⠔⠁⠀⠀⠈⢐⠂⠤⠤⠤⠤⠐⡆⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠾⠋⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠒⢤⣄⡀⠀⠐⣁⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠐⠄⡀⢀⠀⣠⠟⡧⠀⠀⠀⠀⠀⠀⢼⢷⡄⡀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⠈⠁⠀⠡⡁⠀⠀⠀⠀⢀⠌⠀⠙⠂⠄⠀⠤⠐⠁⠀⠀⠠⠄⠂⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢠⡄⠔⠉⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⢀⠀⠀⣠⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⣀⠀⣘⣠⠞⠋⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠶⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠋⡀⠀⣠⠁⠰⣃⡴⠛⠉⠈⠉⠁⠌
⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠉⠀⠀⠐⠚⠃⠀⠀⠤⢀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⣸⠁⢠⣡⡴⠟⠋⠤⠶⠦⠄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠲⢄⡀⢠⠀⠀⢠⠀⢂⠀⠈⠑⢄⠀⠀⢸⡇⠀⠀⠀⠇⣩⡴⠋⠁⠀⠤⠤⠤⠄⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠐⠒⠛⠺⢦⣀⠈⠆⠈⣦⠀⣧⠈⠓⠀⢸⠇⠀⠀⣰⠞⢧⣌⣛⣛⣓⣲⣦⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⣀⡀⠤⠌⠛⠳⢦⣤⡀⠸⡆⠠⡄⢠⡄⢠⡜⠁⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠠⠤⠒⠂⠀⠙⣳⢦⣠⡄⢠⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠤⠀⠀⠘⠉⠀⡄⠛⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⡀⢸⡇⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀⢸⠀⠑⣼⡇⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠙⠀⠀⠈⠀⠀⠘⠈⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⢠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠂⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⣶⡼⠀⠀⠀⠀⢀⠀⠈⠁⠀⠠⢰⠀⠀⠀⠀⣸⡼⠀⠱⠪⣭⣁
⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢤⠀⠀⠀⠀⠀⣄⢀⣒⡿⠀⠀⠠⢀⠀⠠⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠈⣠⡾⠋
⡔⠆⢠⡄⠀⠀⠀⣈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠈⠃⠰⡀⢌⠠⠾⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⣷⡦⠖⠋
⠡⣀⠚⠁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠁⠈⠑⠁⠀⠀⡄⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠆⠸⠁⠀⠀⠀⠀⠀⣠⠷⠔⠀⠀⠀⠀⠐⡇⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠺⠗⢀⠞⢬⣵⢦⡄⣼⡄⠠⢄⠀⠀⣄⡀⠀⢤
⣤⠄⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠸⠂⠀⠀⠈⠉⠙⠁⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⣄⣈⡿⢸⠁⡿⠁⠀⠀⠀⠀⠈⣸⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠂⠈⠀⡀⠀⠀⠰⠋⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠴⠄⣘⣃⣀⣀⣀⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠖⠁⠀⠀⠀⢠⣈⣁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠯⡀⠀⢮⣓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠈⠘⣩⡁⢐⠎⠀⠀⠀⠀⠄⠀⠀⠀⠰⣁⠀⠀⢀⡀⠀⠀⢀⣴
⡌⠃⠀⠀⣀⠀⠀⠀⠀⢧⡀⠀⡀⢀⣨⣷⠟⠂⠀⠀⡂⢀⣀⣀⡥⠼⠀⠀⠀⠹⠖⠘⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢨⢃⣤⠠⠟⠀⢀⡆⠈
⠀⠀⠀⠀⠀⠁⠀⢀⡀⠈⢷⡄⣠⢛⣄⣶⡂⠀⠀⠀⠀⠀⢣⣬⣆⣄⠀⠀⠀⢀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠘⠿⠃⠚⠡⠈⠡⡠⠦⠀⠀⠏⠁⠉⠁⠉⡆⠀⢠⣺⠟⡀⠇⢰⠀⠀⠀⠈⠀⠀⠠⢿⣷⠁
⠀⠀⠀⠀⠐⠄⣀⠊⠀⠀⢀⠀⠀⠀⠀⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠀⠉⠀⣠⠃⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⡜⠀⠀⡜⠀⠀⠈⠰⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠰⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⣀⣐⠠⢀⠄⠈⠀⠀⠆⠀⠀⢐⡖⣦⠰⢤⢀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠺⠾⣍⡠⠂⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠘⢛⠁⠀⠠⠖⣊⠄⠀⠀⠀⠈⠁⠀⠀⢄⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⢀⠀⠤
⡀⠀⠀⠊⠀⠀⣀⠀⠀⠀⠀⠀⢢⠁⠦⢤⡤⢀⣇⠀⠀⠀⠀⡆⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠁⠂⠀⠄⠀⠀⠀⣀⠂⠀⢀⠀⡀⠀⠀⠈
⠀⠀⠀⢀⣸⠗⡀⠇⢰⠀⠀⠈⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⣧⡤⠤⠴⠾⠿⠃⠀⠀⠀⠀⣴⣄⠀⠀⠀⠁⠘⠋
⠀⠀⠀⠀⠛⠀⠉⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⡆⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⡄⠀⠀⠀⠀⠀⣰⠀⠀⢀⠀⠀⡄⢠⣲⡂⢄⠀⠀⠀⠀⠶⠤⢄⣤⠼⣧⡈⠂⠀⠀⠀⢀⠤⠤⣀⡀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⡟⠋⡙⠉⢸⠆⠀⠀⢰⠓⠀⠈⠀⣤⠀⠁⠀⠀⠀⠀⣮⠀⠀⠀⠂⠄⡰⠄
⠢⠀⠀⠂⠀⠈⠀⠀⠀⠀⢆⠃⠀⠀⠀⠀⢀⠀⠀⠀⠈⡦⠆⠀⠙⡷⠉⠋⣠⠤⠀⠀⠀⠀⠀⠀⠈⠀⢠⣾⠃⠀⠀⠈⠃⠀⠄⢀⣾⣣⣢
⠄⠀⠀⠀⠠⠀⠀⠀⠀⢸⡾⠠⠤⣀⣀⣆⡘⠀⠀⠀⠀⠁⠀⣀⣀⡚⠀⡠⠇⠁⠀⠀⠀⠀⠲⡶⣆⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠰⠁⠉⢿
⠀⠀⠀⠘⣀⠀⠘⠂⠀⠀⠀⠀⠀⠂⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣔⠆⣲⡂⠀⠀⠀⠀⠀⢾⣦⡰⢾⡡⠀⠉
⣿⣿⠿⢿⡿⢿⠿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⣄⡀⠀⠤⡄⠀⠈⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢲⠀⠈⢢⡀⠀⡢⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⡉⠛⢄⡀⠀⢱⣴⠃⠀⠀⢸⠁⣠⣡⡤⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣘⠇⣸⣲⣜⢶⣽⡿⢷⣤⣄⣾⡞⠁⢻⠀⠀⢰⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠉⢇⠈⠙⠃⢽⡇⠈⢿⣽⠁⠈⢻⡿⠃⠀⠀⡄⢀⢔⠎⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠰⠂⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢢⡀⠀⠀⢃⠀⠀⣹⠀⠀⢘⠁⠀⠀⣰⣾⠟⠁⠀⠀⠀⠀⠀⠀⣠⠇⢸⢃⠀⠀⡠⠞⡃
⠀⠀⠀⠀⠀⢀⡈⣥⡀⠉⠁⠉⠀⠂⣼⣄⣃⡏⠀⠀⣸⣀⣰⠾⠉⠁⠀⠀⠠⠀⠀⠀⠀⠐⡟⠀⣸⡟⠰⠄⠀⢺⡇
⠀⠀⡖⠛⠛⠛⠉⠋⠛⠶⠠⠤⣄⣀⣀⣩⣽⣧⢴⣾⣯⣭⣀⡀⠀⡀⣀⡤⠄⠀⠀⠀⠀⠘⣇⣰⢏⡄⠀⠀⢀⡾⠃
⠀⠀⠀⠉⠂⠀⢀⠀⠀⠄⢀⣀⣀⣨⠟⠋⠁⠀⠀⣾⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣼⣿⣠⡶⡫
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠋⠁⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡀⠠⠔⠒⠘⠉⠁⢀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡁⠀⢀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢼⠆⠀⢀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠎⠀⠀⠜⠀⠀⠀⠀⢠⡀⠸⡄⢀⢊⠁⢰⠶⠀⠀⠀⠄⠁⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠏⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⣶⠾⣿⣎⣴⣷⣴⠶⠀⠀⠛⠓⠀⠀⠀⠐⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⢀⠀⠂⠀⠀⠀⠐⠉⡤⠶⣯⡈⣭⢍⡙⠀⢤⡐⠐⠦⠴⣦⠤⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠏⠇⠀⠈⢄⠀⠀⠀⠀⠔⡠⠔⠀⠀⠁⠀⠈⠙⠳⠤⠀⠀⠄⠀⠀⠀⠀⠈⠉⠲⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠀⠀⠈⠳⣤⡶⡈⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⢸⡀⠀⠀⠀⠈⠳⢦⣄⣀⣠⡀⠄⠀⠐⠀⠀⢀⠀⠂⠀⠀⢤⡴⠂⠀⠐⢂⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣹⡿⠛⠲⠶⠤⣤⣤⣠⣤⣀⠀⠀⢄⡀⠢⣄⣀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣘⠇⠀⠀⠀⠀⣦⠃
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣇⠀⠀⠀⠀⢀⣀⣇⠀⡀⢀⣠⣏⢀
⣿⡟⣉⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⣄⠀⠀⠀⠀⠀⣀⣀⣲⠶⠦⣄⠀⠸⠗⠁⠀⣀⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢶⣤⡀⠈⠛⠛⠃⠀⢀⡶⠛⢉⣭⡽⠿⠿⢾⣷⣤⡀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠉⣠⡾⠋⢁⣠⢶⡿⠟⠳⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⣻⠷⠆⠀⠀⣰⠏⠈⣛⣭⠖⠋⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢰⣶⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢰⡞⠛⠶⢤⣀⡀⢀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡶⠶⠷⣿⡷⣤⡀⠈⠓⠶⠖⠛⠉⠉⠉⣠⡼⠃
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⣆⠀⢀⣠⣤⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⣴⠋⠀⠈⡻⠳⢶⣦⡤⢤⣴⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣠⡤⣤
⠀⠀⣀⡤⠖⣿⠏⠀⠀⠀⠈⢷⡫⢴⣾⣷⣴⠋⠁⠀⠀⢀⣀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠙⠉⢫⣠⠷⢾⡟⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠻⣯⡳⡆
⣴⠛⠁⢀⡼⠃⠀⠀⠀⠀⠀⠈⢷⡀⣹⠎⣷⠀⢀⡤⠞⠉⠈⠓⠶⠤⠼⣧⣤⣤⣤⠤⢤⣶⠟⠀⢀⡿⠀⠀⠀⠉⠛⠿⠶⣶⣶⡶⠶⠞⠋⠁⠀⠀⠈⠁
⠸⣆⠀⣾⡗⢲⡄⠀⠀⠀⠀⠀⠀⢻⡴⠛⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠖⠉⠀⠀⠀⢸⡇
⠀⢹⣞⠛⢷⣯⣥⣤⣤⣀⡀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠈⠛⠚⠛⠛⢻⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⣉⣷⡶⠶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⡀⠀⣀⣤⠶⠛⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠈⢷⡞⠉⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠻⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⣀⣠⣿⣦⡀⠀⠀⠀⠀⣠⣾⣧⣀⠀⠀⠀⣠⠶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡏⠉⠛⠻⠿⠛⠋⠈⠙⠓⠖⠚⠛⠉⠉⠛⠿⣷⡄⣼⠃⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡖⢲⣄⠏⠀⠷⠾⠉⠻⠶⠟⣶⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⡉⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡬⠇⠀⠀⠀⠀⢀⡠⣄⠀⣀⣀⣠⠖⢦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⡄⠀⠀⠀⢈⡇⠈⠉⠀⠀⠀⠀⠙⠢⡄⠀⠈⠳⣌⠱⣆
⠀⠀⠀⠀⠀⠀⡴⠀⠀⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠲⢦⡄⠀⠀⠀⠀⠀⠸⣏⣥⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢲⡄⠘⣇⢹⡆
⠀⠀⠀⢀⠀⣸⠃⠀⣴⠒⠃⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⡤⠾⢲⣋⠉⠀⠀⠀⠀⡠⠴⠲⢤⠀⠀⠀⠀⢻⠁⠀⣿⠘⠁
⠀⠀⠀⣸⠀⣿⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠛⢲⠀⢹⠀⠀⠀⠀⠰⡁⠀⠀⣸⠀⠀⠀⠀⢸
⠀⠀⠀⢻⡀⣿⠀⠀⠀⣞⣁⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⡟⠉⠀⢈⡄⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠘⡦
⠀⠀⠀⠘⣇⠸⡆⠀⠀⠉⢉⡷⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠀⢯⡠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠙⠁
⠀⠀⠀⠀⠘⠂⢹⡄⠀⠀⠘⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡍⠁⠀⠀⠀⠀⠙⠦⢤⡀⢀⣀⣀⣤⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠖⣤⢀⣀⣀⠀⢠⠤⡄⣰⠙⠷⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠨⣤⡀⠀⠀⣶⠀⠀⠀⣈⡀
⠀⠀⠀⡄⡀⠀⠹⡄⠀⠀⠘⣀⢀⣠⠻⠆
⠀⠀⣄⠰⢼⡀⢀⣷⣤⣤⡴⠉⠈⠉⣇
⠀⠸⠄⡿⠦⠛⢫⠟⠛⠛⣧⠀⠐⠾⠀⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⡟⠙⠦⢄⠀⠀⠀⠀⠀⢳⡀⠀⠂
⠀⠀⠀⠀⠀⢄⠀⠀⢀⠌⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠣⡀⠠⡀⠀⠢⠀⠀⠑⠀⠁⠈
⠀⠀⠀⠀⠱⠰⠛⠈⠙⣦⣤⣄⠀⠀⠀⠲⣌⠉⠉⠒⠢⠬⣒⣜⣢⡘⡃⠚⠤⠀⣠⡀⠀⠀⢠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠙⠁⠀⠀⠠⠈⠙⠢⠤⠀⠀⠀⠀⠀⠉⠙⠢⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢁⡶⠦⠤⠂⠀⠉⡉⠁⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠙⠛⠺⠷⠶⠶⠖⠋⠀⠀⠀⣗⠤⡀⠀⠀⠀⠀⠀⠈⠐⢖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡟⠳⢬⣂⡴⠦⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠁⠀⠀⠀⢠⣷⠀⠀⠈⢴⠀⠈⠉⠙⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠟⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⠔⠁⠒⠉⠀⠀⠀⠙⠢⠄⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⣩⣍⡂⢾⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⡃⠀⠱⠀⡦⠄⠙⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⢠⠁⠀⠀⠀⠀⠦⠄⢤⠄⠰⠖⡄⠰⠀⠀⠀⠀⠀⠀⠈⢼⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⢄⡀⡐⢢⠁⠀⡀⢀⡀⠀⠀⠀⠀⣾⠀⠀⠀⠘⠀⢈⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢧⣬⠜⠑⠒⠂⠀⠀⠀⠄⠁⠀⠀⠀⠀⠈⠀⠐⠢⠘⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢐⠀⠀⠀⠃⠄⡀⠀⠀⠀⠁⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢆⠀⠀⠀⠀⠉⠀⠁⠀⠠⠈⣼⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠞⣦⢧⢘⡃⠀⠀⣀⠀⣀⣀⣀⣀⠀⠤⠀⠂⠀⠛
⡄⠀⠀⠀⠀⠀⠒⠄⠀⣄⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⠁⠀⠲⡀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠍⠀⠐⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⡇⠐⣒⣢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠆⠀⠂⠀⢠⠀⠠⢄⠑⠄⣠⠀⣀⠀⠀⠀⠀⠀⠀⠉⠖⠀⠀⠀⠀⠗⠺⣿⡛⠉⠰⣀⣀⠂⠀⠀⠀⠔⢀⠉
⠀⠀⠸⡀⠀⠀⠀⠀⠂⠀⠱⠀⠛⠀⠉⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠓⠻⡀⢸⡇⠠⠁⠹⠅⠀⠀⠀⠀⠀⠈⠀⠒⠂⠠⠄⣀
⠀⠀⠀⢁⠀⠀⠀⢀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⡽⡟⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄
⠀⠀⠀⠈⡄⠀⠀⠀⢀⣀⢈⡀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢁⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀
⠀⠀⠀⠀⠰⡀⠀⠦⡤⠛⠀⠅⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡉⠢⢠⡆⠀⠈⠉⠉⠀⢀⠄⡐
⠀⠀⠀⠀⠀⠉⠦⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢐⠉⠀⠀⠀⠀⠀⠐⠂⠤⢀⠀⠀⠀⠀⠁⠂⣾⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠄⠀⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠈⢱⠆⠀⠀⡠⠁⠠⠀⠀⢴⡶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⠑⡌⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢲⣆⠀⠀⠀⠀⢠⠘⠂⠀⠀⢀⠃⠀⡴⣋⣁⠀⠤⠤⠀⠊⠠⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠲⠆⡔⠀⡌⠂⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠛⢹⡄⠀⠀⠀⡘⢢⠀⠀⠀⠂
⠀⠀⣀⣀⣀⣀⣀⠀⣉⣁⢀⠤⢄⣁⣠⠤⠤⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⡀⠀⠀⠹⠄⠀⠀⣀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⡄⠀⠀⠑⠀⠬⢆⣠⢀⠀⠀⠉⢢⡄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠤⣄⠀⡀⣠⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡧⠀⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⢃⠀⢀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡇⠈⣄⠈⡄⠀⠀⠀⠈⡄
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠀⡇⠀⠰⠄⢠⠀⠀⠀⠂⠰
⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⡄⠀⠀⠈⠀⠃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣤⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣷⣤⣠⣤⠒⠀⠀⠀⠀⠀⠐⢥⣄⣠⣤⠴⢶⣿⣿⣿⣷⣦⣤⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣧⣤⣤⣭⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿