Musical organization Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠲⠀⠦⣤⣤⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⢀⣤⣄⢧⡀⠀⠀⠀⠰⠿⠀⠀⠀⠀⣰⣿⠓⠀⠀⠀⢀⠀⠱
⠀⠀⠀⠀⠀⠀⠐⢇⣠⢀⣷⡌⠉⡑⠻⣶⠶⢶⣶⣿⡇⠀⠀⠶⠆⠀⠀⢀⣴⣾⠿⠛⠉⢀⣀⣤⣤⣄⠀⠀⠀⠀⢤⣴⡿⣁⣛⣶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠒⠓⠤⠞⠀⠀⠉⠻⠁⠀⠀⠀⠀⠐⠞⠋⢩⡤⠶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠛⠸⠇⣘⡽⠟⢀⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠙⢷⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠘⠿⣶⠂⠙⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⡶⠶⠶⠶⣶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠛⣿⣿⣿⣿⣿⣿⣶⣽⣿⣷⣦⣀
⠀⠀⠀⠀⠀⢰⣿⠚⠓⠒⠒⠒⠀⠀⠁⢽⠄⣸⠇⢠⣾⣿⣆⠀⠀⠀⠀⢀⠀⣤⡀⠀⠙⢿⣤⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠓
⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠈⣓⣀⣠⣄⠣⣾⣧⣶⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠈⠶⠀⠀⠀⠙⢷⣄⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠻⠿⣿⣼⣿⣿⣿⣿⣿⣿⡮⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⠀⠀⠀⡀⠀⠄⠀⠀⡀⠙⢿⣦⡀⠉⢿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠉⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠌⠁⠀⠈⠻⣿⣦⡀⠘⠻⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣠⣴⣶⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠈⠢⡀⠘⠂⠀⠀⠙⠁⢀⠀⠈⠠⠀⠀⠀⠀⢀⡀⠀⠀⣀⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠛⠉⠁⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠀⠠⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⢈⠁⠀⠀⠐⠛⠀⠀⢈⡠⣄⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⡟⠁⠀⢤⠀⠈⣦⠦⠈⠁⠃⠨⠀⠳⠂⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁⠈
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠙⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⣄⠀⡀⠀⠁⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠁⠀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠚⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣛⡉⠀⠠⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣤⣾⣾⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⢀⣤⡄⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠻⢷⣶⣿⣭⣿⣿⣛⡿⠟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣬⠤⠋⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀
⠀⠀⠀⠲⢶⡆⣠⣤⣉⣉⠉⣛⠛⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡏⠀⠐⠠
⠀⠀⠀⠀⠈⡇⠈⠉⠙⣾⠛⠿⠇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡟⠀⠀⠀⢸⠀⢰⣦⣀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠈⢂⣤⡶⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⣴⡦⠉⠉⠀⠀⠘⠀⠉⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⢦⣤⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣿⡿⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠑⠅⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⣠⡄⣿⡇⣺⣹⡆⠾⢿⠆⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⣤
⠀⠀⠀⠀⠠⡀⠛⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠘⠛⠛⠁⠉⠈⠃⠀⣽⣟⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⣀⡀⠀⠈⠉⠙⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣡⣀⣠⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠉⠉⠃
⣧⣼⠆⣤⠀⣠⣤⣴⣤⣄⠀⠠⠠⠀⡠⠀⠁⠀⠀⠀⠐⠠⢤⣀⡀⠀⠀⠀⣀⡉⠁⠉⠉⠛⠻⢷⣎⣀⠀⠉⠀⠀⠀⠀⠀⢀⣴⣶⣤⡇⢠⠀⢀⣤⣴⣤⣤⡀⢠
⠶⠝⠓⠇⡸⡟⠁⠀⠀⠙⢷⠀⢀⡀⡇⠘⠀⠀⠠⠆⠀⢀⡞⠿⠇⠰⠛⠈⠁⠀⢸⣆⠀⠀⠀⠀⠉⠛⠁⢀⣀⣤⣦⣦⢘⡙⣥⠷⠏⠓⠷⠰⣿⠉⠀⠀⠉⢻⡄
⠀⠀⠀⠀⢣⣧⡀⠰⠀⣀⡾⠀⣘⡛⠛⢦⡀⠀⠀⠈⣡⣼⣁⣀⠀⠀⢷⡀⠀⠀⠀⢿⣆⠀⠀⠀⡂⠀⠛⠋⠉⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⠰⠃⢀⣼⠃
⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⢁⠀⠈⠁⠀⠂⠭⡙⠑⠫⢁⠓⢾⣿⠀⠀⠈⣷⡄⠀⠀⠀⠻⣧⠀⠀⠑⡀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⢃⡀
⣛⠛⠛⠛⠆⠀⢀⡄⠀⠀⠈⠘⡤⠤⣄⡀⣄⠀⠈⠀⠀⠐⢬⡇⠀⠀⠀⠘⢿⣆⠀⠀⠀⠹⣧⡀⠀⠇⠀⠀⠐⠾⠛⠛⠛⢛⠻⢟⠛⠳⠛⠷⠀⠀⡀⠀⠀⠀⠈
⠙⠙⠺⣤⡀⠀⡾⠁⠀⠀⠀⠈⠠⢤⣠⡙⠚⠷⢄⣀⠀⠀⠀⠀⠀⠀⠠⡀⢻⣞⣗⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠰⠇
⠀⠀⠀⠀⠉⠠⣤⠀⠀⠰⡀⠄⠀⠀⠽⡑⠶⢰⣴⠉⣻⢔⠢⠀⠀⠀⠀⠀⠘⢿⣮⣧⡀⠀⠀⠘⣿⣄⠀⠀⡀⠀⠐⠄⠀⠛⣠⠀⠀⠀⠀⠉⠠⢤⠀⠀⠐⣆⠔
⠀⠀⣀⣀⣀⣀⣈⣀⡀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠂⠀⠀⠀⠀⠈⠋⠁⠗⠀⠀⠚⠀⢉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣁⣀⠀⠈⠇
⡄⢠⠁⡁⣿⣟⣋⣉⣃⡀⢠⡖⠲⡗⠒⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⢠⢤⡄⢀⠀⠀⡄⠀⠀⠀⠉⣿⣶⡆⠀⠀⠀⠀⠀⣧⠤⢠⡅⡀⢻⣿⣋⣉⣹⣀⢀⣖
⡀⠈⢠⠀⢹⣍⡁⡐⠬⣧⣼⠿⠠⡆⠀⠀⠀⢠⡆⠈⠁⠀⠁⠀⠘⡉⠉⢡⡠⡄⢠⡄⠀⠻⠄⠀⢘⠀⠙⣿⠗⠂⡨⠁⠀⠐⣯⣁⠀⠁⡄⢸⣯⣉⡐⢮⣭⣼⡿
⠉⣿⠃⠀⠀⠈⢡⠈⣆⢐⢸⠃⠠⡆⠀⠀⠀⠘⡇⠀⠀⠀⡀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠀⠀⠀⡍⠉⢹⠋⠀⠀⠀⠙⡄⢤⠐⠂⠃
⠠⡅⠀⠀⠀⠀⠀⣤⡙⠸⢸⡶⠄⠿⡄⠀⠰⠀⣷⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⠠⣌⠀⠀⠀⠀⠀⣠⣘⠐⢀⡶
⠀⠑⢤⡀⢀⣤⠮⠞⠔⠏⠛⠒⠉⠓⣜⠀⠀⠀⢸⡄⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⡞⢷⡀⠀⢀⠀⠀⠙⠀⠂⣀⠀⠀⠀⠁⠄⠀⢠⠉⠢⡀⠀⣠⠾⠽⠡⠏⠙⠒
⣄⠀⠀⠀⢀⠀⠀⠀⠀⠁⢀⠤⠂⠀⠀⠀⠠⠀⠘⣇⠀⠀⢻⡇⠀⠀⠀⠀⠲⢾⠧⣨⡿⣟⠋⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⡀⠀⠀⠀⠀⢀⡤
⠈⠳⣄⠁⠂⠠⠀⠀⠒⠈⠁⠀⠘⡆⠀⠀⠀⠀⠀⣿⡀⠀⢸⡇⠀⢴⣿⡆⠀⡈⠀⠈⠁⠱⡀⠀⡠⠈⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢤⡀⠂⠀⠄⠀⠐⠂⠁
⠶⠶⠮⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢹⠇⠀⠸⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠦⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠈⢹⣉⠙⠛⢶⠄⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⡀⠀⢁⠘⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠙⣏⡉⠛⠺⡄
⢈⡀⠀⠀⠀⠈⠈⠳⣆⡀⠀⣨⡟⠀⠹⡥⣆⠀⠀⠀⢀⡄⢀⣿⡅⠀⠀⠀⢀⣀⠈⠉⠓⠒⠤⠄⣀⡀⢠⠄⠠⠤⠒⠓⠀⠀⠰⠀⣁⠀⠀⠀⠀⠉⠙⢦⡀⠀⣀
⠈⢉⣰⣤⠤⡤⢬⣠⣌⠣⣀⠉⠀⠀⠠⢴⡹⣷⡄⠀⠃⠁⠀⡿⢷⡆⠀⠁⠚⠙⠻⠿⣶⣦⣄⣀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⣦⡤⢤⢤⣄⣄⠁⢀⠉
⠀⢸⣉⡛⠐⠃⠃⠼⠉⠀⠈⠃⠀⠀⠀⠘⣳⡿⡤⠆⠀⠀⠀⢉⣏⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠛⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⣇⣛⢃⡃⠘⠰⠋⠀⠈⠳
⠀⣼⣻⣓⡿⣿⣲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠷⠲⠆⠀⢠⠃⠀⢾⣴⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⡏⡓⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡄⢸⢻⣟⡿⣽⣓⣶⠂
⠀⣷⣯⣿⣿⣷⢿⡏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠘⢀⡴⠀⠀⠀⠉⠀⠀⣄⠃⡃⠀⠀⠀⠀⢀⠂⢀⠀⠀⢸⠁⣾⢿⡿⣿⣿⣿⡿
⠾⠟⠺⠻⠷⠿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗⠀⠀⠀⠀⠀⠈⠃⠀⣠⡴⠞⠁⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠟⠚⠛⠷⠿⠽⡇
⠀⢴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠒⠀⠀⠠⠶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣾⣤⣾⣦⣤⡄⢀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠈
⠿⢾⣁⠟⢀⣴⠿⠟⠿⢶⡄⠐⠈⠁⡖⢠⠂⠀⡀⡀⠀⠐⣳⣴⡆⠀⣀⡀⠴⠂⢀⠀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⢠⢴⠿⡟⢾⣇⠼⠂⣴⡾⠟⠻⢷⣄⠐
⠋⠉⠉⠁⡬⡇⠀⢀⡀⠀⢿⠀⢠⣤⡧⠈⠀⠀⠈⠡⠤⢴⠏⠉⠁⠘⣄⠀⠀⠀⢸⣧⡀⠀⠀⠀⡀⢀⣀⡤⣴⡾⠷⠿⠜⠂⠛⠙⠁⠉⠉⠈⣟⠀⠀⡀⠀⢹⡆
⠀⠀⠀⠀⠘⣷⣤⣉⣠⣴⡟⠀⠶⠎⣀⠳⣦⣠⣀⣠⠴⡟⢠⣶⠀⠀⠻⣄⠀⠀⠀⠹⣷⡀⠀⠀⣇⠈⠁⠀⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣦⣈⣁⣤⡿⠁
⣀⣠⣀⣀⡀⠀⠉⠉⠉⠁⠠⢀⠀⠀⠀⠈⠀⠂⠤⣁⠐⠈⠹⡿⠀⠀⠀⢿⣆⠀⠀⠀⠘⣷⡀⠀⠈⡆⠀⠀⢀⣀⣄⣉⣶⣤⣄⣀⣠⣀⣀⡀⠀⠉⠉⠉⠉⠠⢄
⢯⣅⣈⠈⠉⠀⢰⠆⠀⠀⠀⢀⠞⠑⠲⣤⣲⡀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⣯⢷⣀⠀⠀⠈⢿⣄⠀⠁⠀⠀⠈⠋⠁⠀⠈⠡⠉⢫⣍⣈⠁⠉⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⠀⠒⠂⠐⠒⠒⠂⠐⠒⠀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠴⠶⠶⠶⠶⠦⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⡀⠀⡀⠀⡀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡇⢸⡇⢸⡇⠺⣯⡀⢸⠀⣿⠉⡁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠃⠈⠛⠛⠁⠘⠛⠁⠘⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⢢
⠀⠀⠀⠜⠀⠀⠀⢀⡾⠁⠀⣠⣶⡾⠿⣷⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣄⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠣⡀
⠀⠀⠌⠀⠀⠀⣠⠏⠀⠀⢼⡟⠁⠀⠼⠋⣠⣤⣴⣿⢁⣤⠀⣤⡄⢀⣤⣄⠀⣠⣤⣤⣬⠉⣿⠏⢉⣭⣅⠀⢀⣿⣅⠀⢀⣤⣤⡀⠀⠀⠹⣄⠀⠀⠀⠱⡀
⠀⡜⠀⠀⠀⢠⠏⠀⠀⠀⢈⣿⣶⡆⠀⢰⡿⢁⣿⠇⣾⡏⣰⡿⢡⣿⠋⡿⢰⡿⢁⣿⠇⣸⡟⢠⣿⠻⣿⠗⣿⢁⣿⠆⣿⡏⣾⠛⠀⠀⠀⠹⣆⠀⠀⠀⢡
⢰⠁⠀⠀⢠⡏⠀⠀⠀⣴⡿⠋⠀⢀⣴⣿⢃⣾⣿⣼⣿⣴⣿⣇⣾⡏⢀⣴⣿⣃⣾⣿⣴⣿⣥⣿⡇⣰⡟⣼⠃⣼⣏⣼⠙⣿⡄⠀⠀⠀⠀⠀⠹⡄
⡆⠀⠀⠀⡼⠀⠀⠀⠀⠻⠷⣶⠾⠋⠀⠻⠟⠙⠛⠙⠿⠋⠛⠋⠙⠷⠟⠉⠻⠏⠙⠟⠙⠿⠋⠹⠷⠟⠀⠟⠀⠻⠟⠙⠷⠟⠁⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⣀⡀⠀⢀⠀⠀⡀⢀⠀⢀⠀⣀⣀⠀⠀⡀⠀⣀⣀⡀⢀⠀⢀⣀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⡏⢹⡇⣿⣹⡇⢸⢉⣏⠀⣾⣇⠀⣿⣾⠁⣿⠀⢩⡟⠀⢸⣿⡀⠈⣿⠁⣿⠀⡏⠙⡇⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁⠛⠙⠀⠘⠶⠋⠘⠋⠙⠀⠛⠙⠀⠛⠀⠻⠖⠀⠛⠙⠃⠀⠛⠀⠛⠀⠛⠚⠃⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣼⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼
⠰⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡟⠼⡟⢳⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠇
⠀⢃⠀⠀⠀⠹⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⠏⠀⠀⠀⡰
⠀⠈⢆⠀⠀⠀⠙⣆⠀⠐⢁⡶⢂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⢳⡈⠃⠀⣰⠏⠀⠀⠀⡰⠁
⠀⠀⠈⢆⠀⠀⠀⠈⢧⡀⠀⠁⠛⠣⣾⢠⡦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣶⡌⠻⠊⠀⠀⢀⡴⠃⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠣⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈⠁⠀⢮⠉⣴⣦⣴⡄⡄⣤⠀⣀⡀⢀⡀⣀⡀⠀⣤⡄⣴⡄⡎⠻⠈⠓⠈⠀⠀⠀⢀⣠⠏⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠀⠃⠁⠘⠃⠙⠃⠀⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠦⠤⠤⠤⠴⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠒⠊⠉

⠀⠀⢰⣄⣰⡀⠀⠳⡖⠀⠐⠋⡴⣾⣿⣿⠿⠃⣀⠀⢰⣶⣦⠐⡆⣶⣶⠀⠀⢸⠀⠀⠀⢰⠳⠀⡆⠀⠳⣄⣰⡄
⠀⠀⣾⣿⣿⣿⣶⣤⣥⣤⣤⣤⣤⣾⣿⣧⣤⣾⣧⣤⣾⣿⣿⣴⣧⣼⣿⣷⣼⣾⣦⣦⣤⣾⣤⣤⣧⣼⣿⣿⣿⣿
⠀⠀⢹⣿⢿⠿⠛⠉⠉⠛⢉⡟⠉⡟⣩⠟⠉⣿⣯⡉⡟⠉⢻⣽⣏⣹⠉⠙⠹⣿⣿⠿⠋⡟⠉⢹⣿⡟⠉⠙⠿⠟⠁
⠀⠀⢸⣹⣠⣤⠄⠀⠀⠀⠎⠤⠾⠿⠥⠀⠈⠿⠛⠠⠁⠀⠠⠿⠿⠿⠀⠀⠃⠀⠀⠀⠀⠁⠀⠸⠿⡿⠀⠀⢀⣤
⠀⠀⢈⣭⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣌⠈
⠀⠀⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠇
⠀⠀⡠⠔⡚⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣤⠔⠊
⠀⠀⣤⣾⣿⣦⠀⠀⡈⠓⠿⠃⠀⠴⢛⣰⣦⢊⣤⣄⣙⠻⠿⠿⠃⠀⣼⠀⢾⠄⠀⠀⡦⠈⡇⠀⠆⢠⣤⣤⡑⢄⠀⢂⠙⠃
⠀⠀⢺⠟⠉⠁⠀⠀⡉⢀⠀⢻⣿⡀⠻⠿⠏⣸⣿⣿⣿⡷⠀⠀⠀⣀⣁⡀⢸⠀⣀⣄⠀⠀⢸⠀⠀⠸⢿⣿⠀⡆⠱⣌⠀⡀
⢤⣤⣀⠀⠠⠦⠀⠀⣾⣾⣦⣄⠈⠀⠀⠀⠈⣹⢿⡿⠉⢀⠶⠂⢀⣿⣿⠟⢸⡄⠻⢿⠄⠰⣨⣆⡀⠀⢸⠈⠀⠇⠲⣼⣷⣇
⣿⣿⠧⠀⠒⠂⠀⠀⠈⣿⣿⡿⠀⠀⡀⠀⡴⠁⠐⢁⠔⠁⡀⠀⠀⡌⠙⡄⢘⡇⠀⠀⢃⠀⣽⣿⣷⡀⠈⠀⢀⣀⡀⠈⣿⡟
⣿⣿⠃⠀⣤⣤⠀⠀⠀⠉⠁⠀⠀⠀⢀⠞⣀⣼⡴⠋⠀⢼⣿⠷⠰⠁⠀⢹⣿⣷⣾⠀⠀⢄⠛⠛⠋⠁⠟⠀⢸⣿⣇⠀⠈⠁
⠀⠀⠐⠂⠻⣿⣶⠛⠀⠒⠛⠓⠀⣰⡎⠸⣿⣿⡟⠁⡀⠊⠃⠀⠃⡀⠀⣾⣿⣿⣿⡆⠀⠠⣄⡄⠀⠠⠐⠀⠈⣉⡁⠤⠐⠒
⠀⠀⠀⠀⠐⣅⣠⠇⣼⣿⡄⠀⠀⠁⠀⠀⠀⠉⢠⠄⠀⢢⣤⣖⡏⠭⠄⠉⠛⠛⣋⣡⡀⠨⠀⢈⢅⣍⠋⠈⠀⠀⢤⣴⣿⡄
⠀⠀⠀⠀⠀⠘⠓⠊⠟⢛⡡⠚⠋⠁⠀⠀⢀⠀⠠⠠⠐⢶⡊⡱⣗⣢⡀⠀⢠⣾⣿⣿⣿⠀⠩⠾⠉⠉⠉⢀⡠⠔⢚⠟⢛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠖⣭⡀⠐⢛⡛⢉⣀⠀⠀⠀⠀⠀⠊⠁⠀⢀⣬⣄⠀⠀⠙⢻⣿⣿⡷⣄⠀⠀⠒⣋⣁⣴⣉⡠⠖⣩⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⣿⣿⣿⠖⠒⠒⠒⠉⠉⣩⣤⡀⣼⣿⣿⣿⣟⠀⠈⠃⠈⢧⠀⠀⠀⣿⣿⣿⣿⣏⠀⢶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠙⠋⠈⠁⣐⠖⡋⠳⠈⢿⣿⣇⠀⠀⠈⡃⠀⠉⠒⠢⢄⣀⠳⡀⠀⠙⢿⡿⠋⣠⠔⠹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢚⠶⣈⠈⠀⠀⠘⢀⡙⠚⠀⠈⠈⡌⠀⠀⣀⣈⠁⠂⠤⢀⡀⣌⣁⠙⢄⠀⣠⡤⢊⡠⣀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠳⢤⡜⠉⣀⠴⠚⢉⣠⠄⣠⣄⡀⠘⡀⠸⣄⡼⠀⠀⠀⠐⠛⢿⣿⠇⠘⠇⠀⠀⢿⣄⣼⡓⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⣄⡀⠀⠄⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⣶⣶⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠾⠿⠿⠿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠙⢻⣏⣹⣿⡏⠣⡀⢀⠴⠁⢀⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢸⡿⣿⣌⠳⡝⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠙⢾⡻⣷⣎⠲⠉⢀⣀⣀⣀⣀⣀⠀⠀⠀⡼⣿⣇⠀⠿⠿⣤⡆⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠶⣮⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⢿⣿⠇⠰⠘⠛⠿⣦⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿⡿⣼⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠶⣶⡆⠀⠀⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣇⡀⣿⡇⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⡙⣿⠀⣿⣿⣿⣿⡇⢸⣿⣉⣿⣿⣿⣿⠿⣿⣿⣽⠁⢭⢡⠤⠡⢄⡎⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⣶⣿⡀⢿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠛⠇⠾⠲⠶⠶⠶⠶⠾⠶⠶⠶⠾⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⡺⣓⣾⣂⣺⣿⣷⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠀⠈⠻⣦⡉⠛⠿⣿⡿⠶⢾⣿⠿⠋⠀⠀⣠⣟⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣀⣀⣀⠀⠀⡨⠛⠷⢦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠸⣿⣶⣶⣶⡶⠲⠖⠒⠒⣶⣶⣶⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⠟⣿⣿⠀⠚⠀⠀⣰⣶⣴⣶⣶⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠿⠿⠀⠀⠀⠐⣿⡟⢻⣷⣿⡏⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠘⠻⠿⠿⠛⢠⣤⠀⠀⢿⣿⣯⣨⠟⣹⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⣀⡰⣿⠟⣡⠞⣡⡾⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠾⢋⣴⠟⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⡀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠛⠙⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⢈⠘⠂⠀⠐⠀⠂⠀⠀⠭⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠁⠀⣂⠀⠸⠀⠀⠀⠂⠒⠲⠀⠀⠀⠀⠉⠲⢀
⠀⠀⠀⠀⠀⢀⡄⠠⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠈⠓⢴⠀⠀⢠⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠀⠙⠋⠓⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠑⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠋⠀⢀⣠⠤⠄⠖⠲⠆⠀⣀⡀⠻⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⠀⢀⠶⠂⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡿⣤⡆⠙⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⢀⡤⠀⠀⣰⠤⡂⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡃
⠀⠀⠀⣰⠀⠀⣀⠐⠀⠀⠈⢻⢡⣪⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⢉⠁⠀⡅
⠀⠀⠀⡓⠀⠀⡏⠀⠀⠀⢀⡄⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢠⡄⠀⠸⣧⠀⠀⠀⠊⠋⠈⢁⣤⠀⠀⠀⠀⠀⠀⢴⡏⠀⣼⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠐⠂⠀⠀⠙⢀⠀⠀⠀⠠⣶⡄⠉⠀⠀⠴⠖⠛⠆⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘
⠀⠀⠀⣀⠀⢀⠐⡙⠄⠀⠀⠀⠈⠁⠢⠚⣶⡖⢶⢶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢀⡴
⠀⠀⠀⠙⠄⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣠⠈⡅⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠢⣻⠆⠁⠀⢀⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡔⣺⠅⣈⣴⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣙⠶⢬⣙⡒⠩⠅⠤⠞⠋⠹⠫⠝⢓⣀⣭⠴⠛⠧⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠝⢿⠀⠀⠀⢀⣚⣻⡹⠿⠄⠓⠁

⠀⠀⠀⠀⠐⠲⣖⣶⣲⣖⣖⣶⣶⣒⣖⣖⣲⣒⣖⣖⣲⣒⣖⣖⣲⣒⣶⣖⣲⣲⣖⣖⣲⣲⣶⣶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠉⠉⠉⠉⠉⠈⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃



⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢤⡀⠂⡄⠀⠦⢀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⣠⠊⠘⠀⠀⠔⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⣀⠌⠁⣀⠀⠀⢂⡠⠀⠸⠆⠘⡂
⠀⠀⠰⢧⡄⠐⡄⡄⠊⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠚⢲⠈⠁⠰⠀⠠⠐⠁⠀⢀⠔
⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠁⠀⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠈⠀⠠⠄⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢀⡤⠒⠂
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⠄⠊
⠀⠰⡄⠀⠈⢇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠘⠀⠀⠀⠀⠉⠛
⠀⠀⠹⣆⢰⠋⡶⠶⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⣠⢭⠂
⠀⠀⠀⠹⣎⠂⠅⠱⡜⠁⣤⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡌⠣⣦
⠀⠀⠀⠀⠙⡆⠀⠛⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡦⠈⠁⠀⠴
⠀⠀⠀⠀⢘⠁⠀⠀⠠⠄⣈⠅⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠒⠒⠁⠀⠀⠩⢀⢠⡀⠀⠤⠤⠂⠈⠀⠀⠀⢀
⠀⠀⠀⠀⡔⣀⢠⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⡀⠀⠦⠀⠀⠀⠌⡁
⠀⠀⠀⡜⣿⢹⠇⠀⠀⠀⠀⠀⢡⠄⠀⠀⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⣀⠀⠁⠂⠀⠀⠀⠁
⠀⠀⠀⠣⠬⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠿⠀⣠⡄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠓⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⢀⡠⢤⣤⣄⣀⠸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⣴⠞⠴⠠⠎⢿⣿⣷⡿⡿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠄⢴⠇⠠⠀⠠⠄⢬⣮⣿⣷⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⢀⡀⣠⣿⣿⣿⣧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⣸⣀⣀⣆⣶⣿⣿⣿⣿⡆
⠀⠀⠀⣘⣿⡒⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊
⠀⠀⠀⡻⠟⢠⡉⠉⠀⠾⠿⠷⢶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠘⠻⠿⠶⡶⠾⠃⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⣤⠀⠀⠀⠀⡜⠀⠀⡰⠀⠀⠀⠀⠀⠀⡀⠀⠾⡦⠤⣤⣀⣀⡀⢀⠀⠀⠀⠀⠀⠉⠳⢄⡀⣠⣴⣦⣾⣿⡿
⠀⣿⠃⠀⢀⣿⣷⡀⠀⣭⣄⢀⠀⣀⣀⢀⣻⣦⠂⠈⠙⠛⠓⠚⠉⣻⣿⣿⣿⣻⣷⣷⣀⠀⣽⣿⣿⣿⣿⣿⠙
⢸⣿⣳⡆⠸⣿⠏⠁⠚⠛⠛⠁⠘⣿⣿⣯⠃⣿⣿⣦⠀⢀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⠋⡀
⠀⢨⣽⠐⠻⡀⠀⠀⠀⢚⣷⣴⣆⢸⣿⣿⣧⠘⣿⣿⠇⠀⠐⢀⣽⣿⣿⣿⣿⣿⣿⡿⣿⣷⣀⠘⠿⠟⡻⣧⡀
⠀⠀⠀⠀⠀⣷⣶⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠄⠀⠈⠛⢿⣿⢻⣿⣿⣿⣿⣱⣿⠛⠀⠀⠀⠘⣆⠁
⠀⠀⠀⠀⠐⠻⢟⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣯⣿⡿⣿⣟⣿⠛⠃⠀⠀⠀⠀⠘⡆
⢀⠀⠲⢂⢶⠴⣿⣿⠟⠋⠀⢀⣉⡛⠛⠋⠀⠀⠀⠀⠀⠀⢠⠄⠀⣠⣾⣿⣿⠙⠉⠙⠛⠀⠀⠀⣴⣶⣶⣦⣿
⠨⠃⠰⢈⠀⢸⣿⡿⠃⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠻⠿⠇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣾
⠀⡤⠘⢹⣿⣿⣷⠀⠀⠀⠀⣴⣿⣷⡆⠀⢀⠀⠀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿
⢰⠀⣀⢸⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⠀⣼⠟⠧⡅⣨⣶⣶⡄⠀⠀⠀⢠⣾⣟⠋⠀⢰⣟⣿⣾⣿⣿⣿⣿⣿
⠀⡄⠇⠠⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⠁⢰⣿⣤⣤⣬⣿⣿⠿⠃⠀⠀⠀⣼⣿⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣧⠀⠀⣸⢸⣿⡇⠀⠉⢹⣿⣿⡿⠀⠀⠈⠉⢹⣿⣿⣿⣷⡄⠀⠀⣠⣿⣿⣿⣭⣽⠿⢿⣿⣿⡿⠿⠛⢛⡿
⠀⢹⣦⡀⣿⡌⡿⣿⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⡏⢿⡄⢸⣿⢿⣿⠉⠙⣿⣇⢰⣿⡿⠁⢀⡰⠋
⠀⠀⠻⣟⣿⡇⣿⢻⣷⣆⠀⣹⣿⣷⡀⠀⠀⠀⠀⢿⣿⣿⣿⣾⠇⢸⠇⠀⣿⠀⠀⢿⣿⣤⣿⣤⣾⣋⡀⠀⡀
⠀⠸⢿⣿⣿⡷⣿⣿⣿⣿⣷⣾⣿⣿⣷⣤⣤⣤⣤⣾⣿⣿⣿⠟⠀⢀⡄⠀⠀⢀⣀⣤⡶⠟⣻⡗⣼⣍⣷⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡀⢃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡰⠋⡆⠀⠀⠀⠀⠀⢀⠀⠈⠠⢦⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠀⠀⢄⠓⠦⠄⠤⠸⢱⠀⠀⠀⠀⠀⠀⠀⠐⡘⡸⠦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⢀⠀⢀⠀⡀
⠀⠀⣠⠻⣧⡆⠀⠀⠙⠟⠳⢦⣤⣵⡄⠀⠀⠀⢣⢣⠀⢀⠄⠠⡀⢀⠄⠌⠀⠀⡨⢐⣀⡽⠃⠀⠀⠀⠀⢠⣾⠿⠿⠿⢿⣿⣶⣯⣾⡗
⣠⣤⣧⠤⣉⣻⠆⠀⠀⠀⢹⠆⠈⠟⠃⢀⢀⠀⢸⣾⡧⠠⢌⠑⢸⣮⠊⢀⣴⣏⣴⡺⠋⡰⠃⠀⠀⠀⠀⠀⠉⢠⣤⡀⣠⣿⣿⣿⣯⡴⠖
⢨⣿⣿⠞⠉⠁⠀⠀⠀⠀⠀⡀⠀⣀⠴⡡⠎⠀⠈⣿⣷⣔⣀⣡⣼⡿⢡⣿⠯⠵⡏⠀⡪⣀⠀⣀⡀⠐⠄⠀⠀⢀⣝⠿⠿⣿⣿⣿⣿⡷⠆
⠀⠋⠉⠪⡓⠋⣶⣿⣶⣤⠀⡇⣠⣷⡴⠃⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⠁⠀⠀⠀⠶⠀⡀⠀⡀⢀⠁⢀⠀⠀⠐⠌⢿⠿⠿⠓
⠀⠀⢰⣶⣿⣿⣿⣿⠿⣧⢀⣼⢟⡝⣁⣴⣆⣾⠚⠛⠛⡗⠲⢽⣧⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⣤⠴⢤⠤⠨⡔
⠀⠀⢸⣿⣿⣿⠿⠿⠀⣷⡿⢉⠉⡀⠟⢶⠀⡏⠀⠀⢠⠁⠀⡀⣎⣠⣄⣲⡴⢷⣶⣤⣴⣞⣛⡛⠟⠶⠶⠶⠶⢤⣤⣄⣉⣢⣼⣶⣤⡀
⠀⠀⢸⣿⢿⡏⣠⡔⠘⠻⣷⢈⣧⢔⣇⠘⣶⣻⣧⣤⣼⣤⣰⣗⡏⡏⠁⠀⠀⠀⠉⢿⠉⠉⠉⣹⠛⠛⠿⠶⢶⣦⣶⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠙⣄⢡⡔⠚⠃⢠⠟⡍⠀⢸⢸⡄⢻⡟⡫⢵⣶⣶⣶⣶⣭⡳⢤⢀⣲⣢⣿⠼⣇⠀⣰⠃⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢲⣶⣿⠀⡆⠀⢘⠀⢧⡀⡫⣦⣿⣿⢿⡿⣿⢿⣿⣎⢋⣽⠀⠀⠀⠸⡼⠃⠀⠀⠀⠀⢀⣴⡿⠃⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣆⡃⠀⢸⠀⡈⣿⣾⣯⢀⣅⢈⠀⣡⠘⣡⣿⡄⣿⠀⠀⠀⡼⢧⠀⠀⠀⠀⣴⣿⡟⠀⠀⣰⣿⣦⡀
⠀⠀⠀⠀⠀⢀⡴⢊⣤⠞⡽⢯⠭⠽⢧⢇⢻⣿⣷⣿⣿⣿⣾⣿⣾⣿⣿⠁⣿⢣⡀⣰⠃⠸⡄⠀⠀⣠⠟⠉⠀⠀⣰⠃⠸⣿⣿⠄
⠀⠀⠀⠀⡔⠉⢰⠟⠀⢀⣇⣨⣀⣀⣸⣈⣎⢻⣿⣿⣟⣛⢻⣿⣿⡿⠃⡄⢸⡄⢳⡇⠀⠀⣇⡀⡰⠃⠀⠀⠀⣰⠃⠀⠀⢧⠙⢦
⠀⠀⢀⣠⡗⠰⠯⣀⣀⣈⣉⣉⣉⣉⣉⣿⣿⣷⣌⡛⠿⠿⠿⠛⣋⣤⣾⡴⣾⣷⡟⠛⠛⠛⠛⠚⠒⢶⣶⣤⣴⣧⣤⣀⣀⣸⣄⣔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⢤⠀⡀⠀⠀⣀
⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠉⠈⠙⠆⠀⠀⠀⠀⠢⠄⢀⠺⠭⢭⢌⡓⠐⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠠⣾⠀⠀⢀⠀⢀⠔⠁⠀⠀⡆⢰⠀⠰⠀⠆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⢔⠀⠀⢀⡠⠟⠁⠀⠠⠁⠀⠂⠀⠀⠘⠀⠀⠌⠀⠀⠆⠈⠄
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡱⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⢄⠠⣀⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠐⠙⠒⠐⠤⢄⠀⢀⡠
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠞⢆⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡇⢸⡄⠀⢸⠀⠈⢳⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⡴⢄⡠⡀⣠
⠀⠀⠀⠀⠀⠀⠀⢷⠀⣼⠁⠀⢻⡀⣿⠀⠀⠀⠹⣄⠀⠀⠀⠇⠀⠀⠀⠀⢀⡀⠄⠀⠠⠀⢀⠤⠄⠬⠁⣉⢀⠑⠂⡀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠀⠀⠀⢳⡟⠀⠀⠀⠀⠘⠇⠀⠀⠀⡀⠀⣠⠖⠁⠀⠀⠀⠀⠀⡁⢀⠀⣀⠀⡀⠀⠁⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠸⠇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠢⡉⠃⠀⠀⠀⠁⠈⠊⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠑⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠘⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⣾⢿⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⢸⡌⣬⣤⠀⢠⣤⡄⣅
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠈⠀⠀⠀⠀⢱⠄⠠⠤⠀⠀⠀⡀⠀⠀⠀⠀⠛⠻⠀⠸⠇⠟⠻⠀⠸⠻⠇⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡀⣀⣠⣀⠀⣀⣠⠇
⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠰⠄⡀⠀⠀⢀⠀⠰⠧⡀⠀⡆⠀⢿⠂⠀⠈⠁⠈⡀⠀⠀⡀⠄⠀⠀⠀⢠⠀⢰⣶⠀⣦⠀⡀⠄
⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠀⠀⢸⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠲⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠼⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠄
⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⡈⠀⠀⠀⣘⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡞⠀⠀⠀⠀⡏
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⡇⠀⢂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠿⠀⠀⠀⠸⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠐⠂⠄⠄⠀⠀⢀⠀⠀⠒⠆⠀⠀⠀⠀⠘⠉⠀⠀⠀⠒⠆⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠠⠀⠀⠀⠒⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⢿⣧⡐⠠⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣴⡆⠀⠀⢱⡄
⠀⠀⠀⣰⣿⣿⣿⠋⠁⠀⠀⠀⠈⢻⣆⠀⢢⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⠀⢸⣇
⠀⠀⣸⣿⣿⡿⠁⠀⡶⠀⡶⠆⠀⠀⢻⣿⣿⣇⠀⢸⠟⡿⣿⠛⢿⢻⢿⡟⢻⡟⡿⠛⣿⢿⢻⠛⠛⣿⠀⠘⣿⣿⡇⠀⠀⣺⡿
⠀⢀⣿⣿⣿⠁⠀⠀⡇⠀⡇⡁⠀⠀⠸⣿⣿⣿⡀⢸⠀⠇⠿⠀⠺⠸⠸⠇⠸⠇⡇⠀⠿⠸⢸⠀⠀⣿⢀⣠⣿⣿⣇⢀⠈⢸⣧⣀
⠀⢸⣿⣿⣿⠀⠀⠀⣗⠀⡇⠀⠀⠀⠀⣿⣿⣿⠁⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⠘⣷⣿⣿⣧⣤⣤⣼⣿⡟
⠀⢸⣿⣿⣷⠀⠀⠀⣿⠀⣷⠚⠀⠀⠀⣿⣿⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠸⣿⣿⣿⣿⣿⠹⠁
⠀⠀⣿⠉⠉⡀⣀⠀⠀⠀⠀⣠⠤⣠⣴⣿⣿⣿⠀⢸⣿⣰⣾⣿⣿⣿⣿⣿⣿⠀⡷⣦⢶⢶⣶⣶⣾⡇⠀⠸⣦⣝⣻⣿⣟⣥⡾
⠀⠀⢹⣶⣾⡿⣫⣭⡒⣠⠊⡴⢊⣴⢊⣿⣿⣿⠀⢸⣿⣿⣿⣟⣛⣿⣿⣿⣿⠀⣄⣤⡈⢁⣬⣿⣿⡇⠀⠀⠀⠙⢻⣿⠛⠉
⠀⠀⠂⣇⣿⣇⢿⣿⣿⣿⣿⣰⡟⣱⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠦⢦⣤⣼⣶⣶⣿⠆⠀⠀⠀⠀⢰⣶
⠀⠀⢼⣿⣿⣿⣮⣻⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⠳⠆⣳⢹⣿⠀⠀⠤⠴⠶⣾⣭
⠀⠀⠈⠻⡿⣟⣿⣿⡿⠟⢿⢿⣿⣿⣿⣿⡾⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠯⢕⣒⣡⣾⠏⠀⠰⣤⣄⣀⣈⣰⣶⣶⣤⡶
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠠⠖⠀⠁⠀⡒⠿⠛⣓⡶⠀⠀⠀⡅⢀⣀⠀⠉⠉⠀⣤⡤⢴⡶⠶⠶⠒⠛⣛⠛
⠀⠉⠐⠫⡡⠐⠐⣀⠤⠄⠉⡠⠔⠊⠁⠀⠀⠀⠀⠜⠉⠉⠀⢀
⠀⠀⠀⠀⠐⠾⣗⢀⠠⠒⠁⠀⠀⠀⠊⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⢀⠀⠐⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠀⠀⠠⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⢠⢾⡝⠋⡅⣿⠀⣀⠀⠀⠀⠀⠀⠢
⠀⠚⠀⠀⠀⠐⡀⢀⠀⠈⡀⠀⠀⠀⡙⢯⠉⠉⢿⠀⢻⣤⣾⣿⡄⢐⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⣀⡷
⠀⠀⠀⠀⠀⠀⠸⣍⠀⠠⠞⠀⠀⠸⡈⠄⣣⠀⠈⣧⠀⢿⣿⣿⡇⠈⠀⠀⠴⠀⠀⠀⠀⢄
⠀⠀⠀⠆⠀⠀⠀⢻⣤⠀⢀⠀⠀⠀⠱⡌⢘⢧⠀⠘⣧⠘⣿⠟⠋⠀⡠⠀⠀⠀⠀⠀⠰⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠊⠀⠈⠀⠀⠘⡄⢩⠗⠀⠹⠖⠁⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⣇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢀⠁⠀⠀⢸⣇⠀⠀⠁
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⠘⠁⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠈⣧
⠀⠐⡄⠀⠀⣤⣀⢀⡀⢀⠀⠀⢁⠀⠀⢐⣗⣁⠤⠔⠂⣁⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⠒⠤⠀⢸⡇
⠀⠀⡄⠀⠀⣸⣿⡌⠀⢨⡀⠀⠈⠀⠀⠀⣽⠻⠿⠿⠟⠚⡅⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠓⠀⠀⠐⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠁⠀⠀⠀⠂⠀⠀⠀⠀⠤⢤⣤⡤⠶⠛

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⠀⢠⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠇⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣟⣼⡇⠀⠀⢠⣄
⣿⣿⣿⣿⣿⡏⣠⣤⣼⣿⣿⠟⢀⣴⣿⣿⡿⢸⣾⣿⣿⠟⢻⣿⡇⠀⠀⠀⠀⠀⠀⡿⠟⠛⡇⠀⢀⣴⣿⠏⠀⠀⢀⣸⠘⠀⠀⣤⡄
⣿⣿⣿⣿⡿⠷⣿⠛⠋⣿⡇⡴⡋⣉⠻⣿⣦⣼⣿⣿⣿⢰⣾⣿⡆⠀⠀⠀⠀⠀⣀⣿⢠⣴⣧⠀⣾⣯⣽⠶⣦⠀⠘⠛⠀⠀⣄⡏⠁
⣿⣿⣿⣿⣧⣤⣿⣷⣾⣿⣧⡹⠿⠿⣠⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⠀⠀⠀⠀⠛⠋⠀⠉⠁⠀⠹⣯⣈⣇⡼⠃⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⢸⣿⣿⠿⠿⣿⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡯⣯⠀⠀⣠⣄⠀⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⢠⣴⣿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠉⠛⠁⠀⠀⡟⠋⠀⡏⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠋⢉⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⣶⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢀⣤⣤⣿⠀⠀⠀⠀⠀⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⡆⠀⠀⠀⠀⠈⣇⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠸⡏⠉⠁⠀⠀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠁⠀⠀⢀⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣧⡀⠀⠀⠀⠀⠀⠀⣰⡟⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⢷⡀⠀⠀⠀⠀⣴⠏⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⠷⠶⠶⠶⠶⠿⠿⠾⠿⠶⠾⠶⠾⠿⠾⠿⠷⠷⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⣿⠟⠛⢻⡿⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣿⣀⣀⣸⣧⣀⣀⣿⡇⠀⠀⠀⣠⡶⠟⠻⢶⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠉⠉⢹⡟⠉⠉⣿⡇⠀⠀⢰⡟⠀⠀⠀⠀⢹⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣿⣦⣤⣼⣷⣤⣤⣿⡇⢀⣀⠘⣷⡀⠀⠀⢀⣼⠇⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⢸⡏⠀⠀⣿⡇⢯⣨⠇⠈⠙⠛⠛⠛⠁⠰⣏⣹⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠾⠿⠷⠿⠾⠿⠾⠾⠿⠿⠾⠿⠾⠾⠾⠿⠿⠿⠾⠷⠿⠷⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⡤⢤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡐⣃⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣇⣛⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⠀⢸⠀⠀⠚⠚⠓⠒⠚⠆⠀⠀⠀⣈⣍⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢿⣮⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⣾⠡⡆⣳⢸⠀⠀⠉⠀⢰⠉⠁⠁⠀⠃⢰⠋⡴⢹⡆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⠘⠳⠖⠃⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠓⠶⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠶⠾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠲⠖⠲⠶⠲⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⠀⠀⠀⠀⠀⡄⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠃⡰⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠇⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⡏⢸⡟⢠⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣴⡿⢠⠄⠀⠀⠀⠀⠁⢿⠇⠀⠀⠀⠀⠀⠀⣿⢰⠇⣼⢀⠃⢀⠂⢠⠁
⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⠈⠀⣠⣴⠟⡠⠂⡠⠀⠀⠀⠀⠀⠃⣼⠆⠀⠀⠀⠀⠀⠀⣿⢸⢠⡇⠄⠀⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠴⡾⢂⡅⢊⠄⠺⣇⠀⠀⠀⠀⠀⠥⢹⠁⠀⠀⠀⠀⠀⠀⣿⡟⣼⡇⠀⠌⢀⠾⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠀⣄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⡤⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⣰⢫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣔⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣟⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⣦⣤⣤⣤⣤⡶⠾⣿⠁⢸
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⣀⡙⠶⠞⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⢸⡇⠀⠀⢸⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣸⡇⠀⢸⡇⠀⠀⢾⠀⠀⣿⠠⠊
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⠇⠀⠠⠾⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⡀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡄⠀⠀⠀⠐⡆⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⣩⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠰⢳⡀⠀⠀⢰⠔⠉⣩⡄⠀⠀⠀⣀⣀⡀⡐⠠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢈⠢
⠀⠀⠀⠀⠈⡝⣇⠀⠀⠀⠲⠞⠃⡄⠀⠀⠀⠀⠀⠀⢀⠀⠼⠀⠀⠀⠀⠑⠂⠀⠙⢄
⠀⠀⠀⠀⠀⠩⢼⣄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠰⡭⢿⠉⠑⢈⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠄⠀⢸⠽⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠁⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣦⠷⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡌⣈⠃⠀⠀⠀⡀⠈⡛⢧⠀⠀⠈⠭⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠘⠁⣠⡜⠀⠈⠣⡀⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⠂⠀⠀⠘⢄⡆⠀⠀⠂⠀⠀⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⡧⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠇⠤⠶⠀⢠⡀⡀⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⢄⠠⠇
⠀⠀⠀⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠛⠀⡟⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠲⠤⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁
⠀⠀⠀⢠⡔⠁⡴⠄⠀⠀⠀⣘⡳⢤⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠑⠚⠁⠆⠀⠀⠀⠈⠀⠀⠂⠩⠐⢒⠒⢒⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠒⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠘⢠⠐⢚⢻⣛⡷⣄⣀⠀⠀⠀⢀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⣻⡟⡓⠂⡄⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⡏⠒⠡⢮⣹⣿⣞⣀⣱⠍⢢⢀⠎⠀⠟⠉⣷⢦⣄⠀⠀⠀⠀⠀⠀⣀⣤⠴⣶⣚⣿⡍⢹⣊⣁⣻⣿⣟⡱⠬⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣟⠀⠀⠀⠀⢀⣽⠈⠉⠁⠉⢡⠂⠀⠀⠀⠀⠁⠠⠏⢱⠆⠀⠀⠀⠸⡁⠛⠀⢿⣷⠠⣾⡛⡃⠉⠈⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡇⠀⠀⠀⣠⡾⠋⠀⠀⠀⢠⣃⣴⠄⢀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣡⡀⠀⣻⣿⠀⣿⣧⢱⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢽⠇⢀⡴⣾⠋⠀⠀⠀⠀⠀⠈⠛⢝⡲⢿⡀⣤⠀⣎⠤⠷⢿⡽⢾⣽⠾⠦⡨⢦⡈⢹⣶⣾⣷⣤⡆⠀⠀⠀⠑⣷⢦⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣏⣼⡀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⢷⡴⠁⠀⠀⢸⠃⠀⡇⠀⠀⢡⡼⠛⠍⣷⣿⠈⠁⠀⠀⠀⠀⢀⣈⣻⢑⢟⡣⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣜⣫⣼⣳⣤⣄⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢻⣿⣿⣸⠾⠷⢕⣶⠶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⢸⡆⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⢀⣠⡾⠟⠛⠉⠉⠉⠉⠙⠻⢷⣦⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣻⠉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⢠⡿⣾⠇⠀⠀⢸⡇⠨⠀⠸⠃⠀⠸⠃⠀⠸⠇⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⢻⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣟⣿⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡗⠛⣿⠚⢻⡗⠚⣿⠂⡟⢷⠆
⠀⠀⢀⣀⠀⡶⡿⠿⣿⣀⡴⢣⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⠤⢄⡀⠀⠀⠀⠀⠀⡆⡷⡇
⠀⠀⡇⣈⠙⣿⠛⠒⢧⠀⢠⠃⢸⡇⢠⣀⣸⣇⣀⣸⣇⣀⣸⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣿⣿⡇⠀⢹⣤⣼⣧⣤⣿⠄⣿⡇
⠀⠀⡇⠀⠀⠈⠉⠙⠋⡀⣾⠀⢸⡇⠈⠉⠉⠉⠉⢹⠋⠉⠉⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⠝⠛⠻⣢⢸⠀⠀⠀⢸⣽⠀⣿⡇
⠀⡜⠁⠀⢀⣤⣀⣀⢀⡇⠸⡀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠀⠀⢀⢧⠀⢣⠀⠀⢸⣻⠀⣿⡇
⡈⠀⠀⠀⠸⠦⣤⣼⡟⠀⣀⢣⣼⣇⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⣼⠏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠁⠀⠀⠱⡀⣸⢿⠀⣿⣇
⡇⠀⠀⠀⢤⣤⣀⡾⠠⣆⣛⢹⠋⠻⡆⠀⠀⠀⣸⢻⠻⣆⠀⣴⠏⠀⠀⠈⠙⠿⠷⣶⣶⣶⣶⠶⠿⠛⢹⠀⠀⣤⠀⢤⣀⡀⠰⠀⠀⣥⠟⠙⣿⠉⠹⣆
⠘⢦⡀⠀⠀⠀⠉⠀⠰⠆⣩⠏⠀⠀⠹⢄⠀⡼⠇⠀⠀⢹⡎⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⣠⡟⢀⠼⠉⡧⠀⠹⢆
⠀⠀⠈⠓⠢⣤⢤⠤⠖⠊⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⣀⣀⣠⡄⠊⠉⠁⠀⠉⠀⠉⠀⠀⠁
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣒⠄⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠁⠀⡀⠤⠀⠒⠀⠁⠀⠀⢄⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⣴⠿⠂⠁⠀⢠⣶⠦⠀⠤⠀⠀⠀⠉⠁⠠
⠀⠀⠀⠀⢸⢙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢀⡠⠂⠁⢀⠠⠂⠁⠀⠀⠀⠀⠀⠰⠶⠄
⠀⠀⠀⠀⢈⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⢀⣶⠇⠁⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁
⠀⠀⢀⡴⢏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⠚⠋⠀⠀⣀⠔⠊⠀⣀⠄⠂⠀⣶⡝⢶⠁⠀⢀⣠
⠀⢠⠋⠀⢚⠙⢧⠀⠐⠂⠀⢶⠇⠀⠒⠀⠈⠁⠀⠀⠀⡠⠔⠊⠀⣠⠖⠊⠀⢀⠔⠊⠉⠀⠏⠀⠀⠈⠁
⠀⠸⡄⠀⢸⠀⡸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠄⠐⠈⠁⢀⠠⠐⢉⣠⣀⠄⠊
⠀⠀⣨⡓⡾⠋⠁⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠀⠂⠉⠀⠀⠠⠛⠋⠀⠀⡠⠐⠁
⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⠀⠀⠀⠀⠀⠀⣀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠋⠉⣉⠀⣀⠀⠠⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣬⠃⢴⠇⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣬⠋⢷⣿⣿⣿⣿⣷⡄⠀⠀⠈⠙⠒⠦⡀⠈⣴⣶⡻⢧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡱⠃⠀⠀⠀⠀⣴⣾⠿⡻⢿⣿⣷⣿⣿⣿⠀⠀⠀⠹⡄⣰⢿⢒⡰
⢋⣦⢸⣎⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠚⠛⠉⠻⣦⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣾⣛⣼⣿⣿⡿⠟⠁⠀⠀⠀⠀⠘⣟⣸⣟⣧
⣁⡿⢫⣾⣿⠿⠛⠛⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⢿
⣥⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⠀⠀⢀⡄⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⣀⣠⡖⠀⠀⠀⠙⢷⣤
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣠⠟⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠈⢿⡅
⠀⠀⠀⣀⣠⣤⣴⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⢠⣿⣮⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡄⠀⠀⠀⠀⣰⣿⠁⠄⠀⠸⣿⡄
⣤⣶⣿⣿⡿⠟⢉⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⣾⢿⣩⠽⠛⢿⠀⠀⠀⢠⣿⣿⢰⣶⣶⠄⣿⣷
⣿⣿⣿⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣀⣀⣄⡤⠖⠃⠀⠀⠀⠻⢄⡀⠠⠀⠸⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⡻⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣻⡭⠿⠿⣿⠇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠨⢿⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣡⣤⣼⣧⠀⠀⠈⠛⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢛⡛⠛⢳⣦⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢀⣠⢴⡶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⢥⡾⢉⣼⢷⣿⡯⢻⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⡻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣠⣾⣿⣯⣾⢹⣖⡀⢙⢷⠗⣬⡏⠳⣄⠀⠀⠀⠀⢹⣆⠀⠀⠀⠈⢧⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣉⢛⣿⣿⣿⣿⠟⠀⠀⠀⠐⣿⣿⣿⣿⣿⣧⣽⣄⠈⡟⠶⠆⢒⡿⠁⠀⠈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢧⠀⠁⢿⣿⣿⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠎⠓⠷⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣾⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⣶⣼⣶⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⠀⠀⠀⠀⠀⣠⡄⣤⡤⠞⠃⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣄⣀⡀⠀⢀⣀⣤⣤⣶⣿⡿⠂⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠰⢻⡿⠈⠀⠀⠀⠀⠘⠁⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⣀
⣿⣿⣿⣤⣿⣿⣿⣿⡟⠩⣤⣶⡤⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⣠⣴⣾⣿⠂⠀⠀⠀⠀⠀⠀⢨⠙⠛⢿
⡟⢻⣣⣿⣜⣻⣿⣿⣥⣄⡆⠀⠀⠀⠀⠀⠀⠘⠿⣿⣭⢬⣝⣻⢿⣧⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠻⢿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⣠⣤⣬
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡇⠐⠀⠀⠀⠀⠀⢠⢿⢄⣠⡲⢞⠛⢆⢹⣧⠀⠀⣼⣻⠿⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠙⢿⣷⣌⢻⣿⣷⣧⠀⠀⠀⠀⠀⡀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠑⢡⣔⣷⠞⢸⡟⠀⠀⠙⢿⣿⡿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⡇⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⣤⢦⣾⡀⠀⠀⠀⠀⠈⢧⣣⡸⠷⢿⣿⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠤⠇⢈⠋⠉
⠛⠿⣿⣿⣿⠿⠛⡄⠈⠀⠄⢹⠰⡀⠀⠀⠀⠀⠀⠉⢓⡶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣶⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠈⢻⣭⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠶⠶⣾⡿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢠⣝⣿⣿⢀⠈⠲⠆⢤⣄
⣶⣶⣶⣶⣦⡄⠀⠀⢀⣾⣿⡜⠟⠉⠁⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢹⣧⠀⠀⠀⠀⠁⠀⠀⠀⣰⠃⠀⠀⠙⠧⣤⡀⠘⠀⡠⢲⣿⠀⠀⠀⢠
⣶⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠁⠀⣠⣤⣄⡀⠀⠀⠙⣾⡿⠀⠀⠀⠀⣰⣿⡇⠘⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⣠⡾⠅⠀⠀⠀⠀⠀⠀⠹⣶⣾⣷⣿⠋⠀⠀⠀⠙
⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⡟⣻⠟⠷⡀⠀⠀⠈⠉⠁⠀⠀⢠⣿⣿⠁⣤⣤⣤⡄⣿⣿⣇⠀⠀⠀⠸⡻⠿⠀⣰⣾⣿⣿⣦⡀⠀⠈⠉⠉⠁
⢲⣤⡀⣠⣶⣤⣄⣀⣀⢀⣀⣺⣟⡊⡁⣠⢀⡙⢲⣄⡀⣀⣀⣀⣀⣸⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣀⣀⣀⣀⣀⣀⣼⣿⣿⣯⣻⣿⣿⣆⣀⢀⢀⣀⣀⣀⣀⣤⠖
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠉⠉⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣮⣝⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠉⠀⠀⣀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢿⣿⣦⠹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⢿⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣅⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠙⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣷⣶⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣀⣼⣿⡿⠋
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠉⢹⣿⣿⡿⠋
⠀⢰⣿⣿⠋⠉⠀⠀⠉⠙⣿⣿⡇⠀⠀⣠⣴⣾⣿⣿⣿⣶⣤⣾⣿⠟⢿⣿⣶⣿⡿⠋
⠀⠈⢿⣿⣷⣦⣤⣤⣴⣾⣿⡿⠀⢀⣾⣿⠟⠉⠁⠀⣹⣿⣿⣿⣧⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀
⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠉⠀⣠⣾⣿⠋⠀⠀⣠⣾⣿⠟⠁⢙⣿⣿⣿⠋⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⠟⠁⣠⣶⣿⣿⣿⣅⢀⣴⣿⡿⢻⣿⣧⠀⠀⣾⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⢁⣀⣀⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣿⠿⠛⠋⠉⠁⠀⠀⢰⣿⡿⠉⠉⢻⣿⣿⡿⠋⠀⢀⣿⣿⠀⠀⣿⣿⣧⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⣠⣼⣿⡏⠀⠀⢀⣼⣿⠏⠀⠀⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠁⠀⠀⣿⣿⡇
⠀⢀⣿⣿⠃⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋⢀⣤⣶⣿⡿⠋⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣏⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣿⣿⡇
⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⢀⣀⣠⣄⣀⣿⣿⡇⠀⠀⠀⠀⣴⣿⡿⠟⠛⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⢠⣾⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣷⣤⣤⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⢻⣿⣯⣀⠀⢀⣀⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⢠⠶⡈⠁⠢⡀
⡸⠒⠘⡄⠀⢸⠄⣠⠤⡤
⠉⠲⠠⠧⠴⠋⠈⣩⣿⣜⠚
⡀⠂⢴⡀⠆⢀⠻⣿⣿⣿⣷⣤⡀
⠐⠠⡋⠐⡗⠉⠢⠽⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠉⠊⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢿⣿⣿⣿⣿⣷⣤⡴⠖⠛⠋⠉⠉⠉⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢿⡷⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠙⢾⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠻⣿⣳⣝⢿⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣟⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⣝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣝⣿⠿⡛⠢⠀⠀⠀⠀⠈⠳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⡉⠢⡈⠢⡁⢠⣶⡐⠒⢦⡈⠳⣦⣀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠶⠛⢋⠉⡇⢻⣆⠀⠉⠛⠛⠛⠛⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⣀⣠⣄⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⡶⠉⠀⣈⣤⡴⢇⠀⠹⣷⣀⠀⠾⣷⠄⠀⠀⠉⠻⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⢸⠋⠀⠈⠙⠶⣄⠀⠀⠘⡇⠘⠁⠀⠇⣰⠞⠉⢄⠀⢀⠑⢄⠈⠙⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠶⠶⠤⣄⠘⢧⡀⠀⠹⣆⠀⠀⠘⠁⠀⠑⢄⠀⢄⠁⠤⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⣄⠹⡄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠱⣢⡭⠖⠉⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠞⠀⠸⣇⡼⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠙⢦⡘⢦⡀⠀⠀⠀⠀⣠⠞⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠉⠙⠲⣄⠀⢳⠀⠙⣆⠀⣠⠞⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣷⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢧⡤⠾⢿⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠳⣄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠛⣧⠀⢸⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⠻⢶⣼⣧⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠁⠀⣀⡼⢧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣤⡤⠶⠛⠉
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠠⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⡟
⠀⠀⠀⠀⢠⡀⠈⠂⠄⡀⠀⠀⠀⠀⠀⢀⡿⠁⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡴
⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠀⣾⠇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢀⠀⠄⠐⠀⡜
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⠜⢿⡟⠀⢰⡟⠀⢲⡖⠀⠀⠀⠀⠀⡸⠳⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⡀⠈⢧⠀⠀⠀⡴⠋⠀⣿⢧⢀⣿⠁⢠⠏⠸⡄⠀⠀⠀⡰⠁⠀⠘⢦⡀⠀⠀⡸⠁⢀
⠀⠀⠀⠀⠀⠰⠄⡈⣆⣠⠞⠀⠀⣼⠇⠈⣿⡇⢀⠎⠀⠀⠹⡀⠀⡰⠁⠀⠀⠀⠀⠑⣄⣰⠁⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠑⠂⠄⢰⡿⠀⢠⣿⣦⡞⠀⠀⠀⠀⢱⣴⠁⠀⠀⠀⠀⠠⠀⠊⠉⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠂⣶⡆⢰⡤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⡏⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢸⡏⢠⣿⠀⣾⡇⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⣠⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠎⠀⠀⢿⡇⠸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠄⢀⣾⡃⠀⣿⠏⠀⠀⠒⠒⠒⠂⠀⠐⠐⠒⠀⠀⢀⡉⠀⠀⠀⠂⠀⠀⠀⠀⢸⣇⠀⣿⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡀⣸⡟⠀⠐⠒⠀⠀⠀⠠⠤⠶⠰⡖⢀⣁⣀⣀⠀⠀⠀⡀⠀⠄⠀⠀⠘⣿⡀⢹⣧⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⣠⣿⠁⠀⠐⠀⠰⠓⢒⣒⠪⠽⠟⣿⠋⢉⡁⠀⠀⠀⠀⠰⡀⠈⠄⠀⠀⢹⣧⠀⢿⣆⠘⣿⣄⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⠻⣧⡈⢻⡦⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



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

⠊⠉⠁⠁⠀⠀⠀⠀⠈⢩⡍⠈⠁⠀⠀⠀⠀⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⢀⠆⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⢀⠋⢀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢀⣴⣤⡶⢾⡛⡛⠆⠀⠀⠀⠀⠀⠀⢀⡤⠖⢾⣦⡀⢹⣿⣷⣄⡀
⠀⠀⠀⠀⠁⡠⢠⣏⡠⢉⡄⠀⠀⡇⠀⠀⠀⡇⢀⣠⣴⡾⢟⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠘⣾⢤⣾⣿⡤⢿⣼⡿⠟⠛⠓
⠀⠀⠀⣴⣦⣿⣿⣿⣷⠃⠀⠀⠀⡇⠀⠀⠀⡇⠈⠀⢯⣀⣾⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣟⣹⣠⣿⠟⠁
⠄⠀⠀⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⡃⠀⠀⠀⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁
⠣⠤⠤⠄⠬⠉⠩⠥⠤⠤⠤⠄⠄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⡅⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠆⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣷⠀⠀⠀⠀⣶⡦
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢀⣤⣾⣟⢍⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⢰⣯⡇
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣀⣴⢿⣫⣵⣿⣟⡱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣧⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⡇⠀⠀⠀⡇⠈⠉⢿⣿⣿⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣾⣿⡇
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡆⠀⠀⠀⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠋⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢞⡃⠀⡁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⣠⠔⠛⠁⣠⠞⠁⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠈⢻
⠂⣀⡴⠞⠉⠀⠀⣠⠞⠁⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⣠⡞⠁⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⣿⣿⠏⣉⡙⢿⣿⡇⠈⡆
⠄⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⣠⡾⠃⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣉⣡⣾⣿⡇⠠⠈
⠄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡾⢋⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠿⠋
⠆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⡀⠀⢀⠠⠀⠀⠔⠀⠂⠀⣀⠀⠀⠀⡀⠀⢠⡄⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⠀⣀⣀⣀⡀
⠀⠀⠀⠄⠂⠑⠀⢀⠀⣠⡔⢿⡁⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠤⠤⠤⠇
⠀⠀⠀⠁⠀⢄⠀⠠⠙⠦⡀⠰⠟⠀⠀⠀⠀⣠⠀⠀⠀⠰⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⠤⠤⠤⡇
⠀⠀⠀⠀⠴⣍⢀⡀⣿⠘⡉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠒⠒⡇
⠀⠆⣸⠇⢠⢡⡴⠟⠁⠀⠀⠀⠀⠎⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠅⠉⠉⠙⡇
⠀⠘⢇⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠄⠀⠀⡀⢀⠠⢀⡀⠠⠀⠀⢀⢄⢀⣀⣀⠀⠀⠐⠃⣛⣛⣓⡃
⠀⠀⠉⢀⠀⠀⠈⠐⢃⡀⠀⠀⠁⠀⠀⠀⠘⢄⣁⠀⡄⠋⠀⢙⡄⢰⡄⠸⢸⡇⠚⠢⠑⠀⠀⠅⠈⢉⣉⡁
⠀⠐⠀⠈⠑⠄⠀⢀⢀⣥⠀⠈⠁⠀⠀⢀⠠⠀⢀⠈⡇⠀⢀⢄⡾⢨⠸⠻⠸⢗⢄⢶⠒⡀⠀⡁⠨⣭⣭⡅
⠀⠀⢀⠀⠀⠀⢀⢉⠀⠀⠄⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⢑⡀⠀⡄⠐⠒⠒⠆
⠀⡄⢀⢀⣶⠀⣼⢀⡤⢄⢚⢀⡀⠀⠀⠀⠀⠀⠀⡚⣀⡎⠏⠈⠉⠃⠔⠺⠇⡇⢰⠀⠈⠀⠀⠁⡄⠀⠀⠡
⠀⠱⣯⣭⠾⠀⠈⠓⠱⢸⣂⠈⡚⢀⡀⠀⠀⠀⠠⠏⠿⠸⠳⠳⠆⠠⠄⠰⠳⠿⠶⠶⠈⠁⠀⢀⠀⢠⡖⢰
⠀⠀⠰⣦⡆⠀⢸⠀⢀⠘⢶⡚⣇⠾⠂⡴⣀⠑⡤⢀⠄⢂⠁⢀⣈⣁⠀⠈⢀⠀⠛⠀⠘⠀⡀⠀⠀⠾⣢⠟
⠀⠀⠀⠉⠁⠄⠈⡇⢸⠀⣦⣅⠫⡄⣤⣤⢹⣄⠀⠀⠀⠀⠃⠈⠉⣵⠃⠻⢾⡆⠀⠀⠀⠀⣠⠴⠆⠚⠁⠀⠁
⠀⠀⠀⠀⣀⡃⠀⢹⣿⠀⠁⠈⠀⠀⠈⠣⠏⠻⢠⠀⠀⠀⠈⢀⠤⠎⠘⠲⠀⠻⠆⠀⠀⣺⡧⠶⢣⡗⢰⢾⠈
⠀⠀⠀⠀⠠⠄⠀⠀⢿⠀⠀⠀⠈⠀⠀⠀⠀⠑⢽⣄⡀⠰⠊⠁⠆⠉⠈⡃⢏⡔⢷⡆⠠⠙⠷⣦⡍⣥⠥⠛⠼
⠀⠀⠀⠀⠠⠈⠁⠀⠘⡇⢀⠀⠀⠀⠀⠀⢀⠷⠆⢉⣥⣤⠂⠘⣘⢂⠀⡄⢸⠀⠈⠁⠀⠀⠉⢀⣠⡇⠀⠋
⠀⢀⣭⣴⡶⢶⡶⢦⣄⣳⠘⢛⡀⡈⠤⣤⠠⠖⣾⠘⠷⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠍⠀⠀⣠⡆
⠀⠸⣧⣿⣄⠀⠀⣸⣿⣿⡄⠀⣝⢸⡐⢸⠤⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠘⠻⠇⠀⠀⡄⢰⠉⠁⢻
⠀⢇⠨⠻⠿⠷⠾⠿⠿⠛⠀⠀⠚⠀⠁⠁⠀⠀⠀⠹⠒⠚⠁⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠠⣄⠁⠞⠃⠀⣸
⠀⢀⠳⢤⡀⠀⠀⠠⠀⠀⠐⠄⠀⠀⡀⠤⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢠⠀⠀⠙⣆⠳⢴⠒⠡
⠀⠀⠙⠦⠙⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠐⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠤⢤⠀⠀⠘⠛⠉⠠⢀⣠⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠃⠀⠀⠀⠀⠀⢐⡄⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⢀⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠆⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡅⢰⡅
⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⠻⠊⣾⡥
⠀⠀⠀⠀⠀⠸⠐⠂⣀⠀⠀⠀⢠⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⡿⠆
⠀⠀⠀⠀⠀⠰⠀⠅⢸⡆⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣰⠀⢠⣟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⣷⠀⠀⠀⠠⠐⣎⠡⠐⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠅⠉⠋⢸⣏
⠀⠀⠀⠀⠀⣸⠤⠜⠒⠉⠀⠀⠀⠀⠀⠡⣁⠤⠔⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⢧⠅⣾⠀⠀⢀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠘⡱⠇⢠⡀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡄⡀⠀⣅⠀⠐⠀⠀⠀⡀⠀⠐⢄
⠀⠀⠀⠀⠈⠄⠀⣤⣴⠈⠁⠀⠀⠐⠈⠁⠸⢰⠁⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣀⢆⢠⣈⡁⢠⠈⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣹⠉⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡈⢙⠀⢠⣍⡁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠄⠀⠀⠀⣨⠠⠤⠁⡤⠐⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠟⠧⠄⠀⠠⡇⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠁⠈⡅⠤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠠⠀⠐⠱⠂⠀⠀⠀⠀⠀⠀⠀⡬⣾⡽⡴⠉⢢⣻⠇⠉⣦⠀⠄⠀⠉⠀⡌
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠞⠵⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣹⡇⠻⠤⢊⣍⠀⠀⡾⡐⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠊⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠖⠢⠨⠉⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠾⢸⣄⠄⣥⡴⠂⢲⡀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠰⠠⡀⠀⠁⠀⢀⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠲⠂⢇⣀⢸⠀⢲⡠⠞⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣃⠰⠇⠒⠈⠁⠀⠁⠀⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤⠀⠈⡅⠈⡔⠁⠙⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢄⠀⠀⠀⢀⠐⠀⠀⡆⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠉⠀⠀⣅⠀⠥⣀⣰⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⣀⠈⠀⠀⠁⠀⡃⠄⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⢸⡀⠈⠁⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠐

⡿⠉⠙⡟⢛⠛⠟⠟⠻⣟⠻⠟⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣻⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠠⠀⠠⠖⠐⢛⣤⠀⠀⠲⠀⠀⠀⠀⠤⠀⡄⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡂⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⢠⠂⠀⠀⢐⠡⡠⢓⡀⢘⠉⠙⠁⠐⠀⠢⠄⠀⠀⣠⣶⣄⢤⡀⡱⠒⣀⡀⠂⢄⠀⠴⠫⠄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⣦⠀⢙⠉⠁⠀⠀⠀⠀⠁⠀⠂⣤⡌⠙⠿⣿⡛⢿⣿⠀⠊⠹⣷⠐⠀⢱⣦⣄⣿⠷⠆⠀⠀⠠⢀⠀⠀⠀⠁⠐⠁⠀⠂
⠀⠀⠀⠀⡇⠀⠀⠀⠠⠘⠗⠈⠀⠀⠈⠢⣀⢐⠀⠀⠀⠘⡄⠓⢀⡈⢣⠀⣌⠳⢶⣾⠟⠀⠀⣸⡿⢏⣡⣾⣿⣿⠖⠂⢄⡹⡀⠀⠀⠄⠀⢀⠀⡁
⠀⠀⠀⠄⢿⠀⠀⠀⠀⠺⠀⠢⠀⠀⠀⠀⣿⣿⣿⣶⣄⡀⠩⡄⠠⠀⠚⠆⠘⡑⢢⡁⡶⠂⠉⡉⠃⢺⣿⠟⠋⠀⠄⠒⠈⠁⠐⠀⠀⠀⠐⡀⠀⠐⠁⠀⠠
⠀⠀⠀⢀⠘⡁⠀⠀⠀⠀⠠⡀⠀⢉⣀⠸⠋⡟⣽⢻⡟⠻⣦⡙⡆⠀⢀⠀⠀⢱⡎⠀⠀⠀⠐⠀⡖⠘⠃⠀⢂⡠⠖⠂⢐⣚⡴⣄⠀⢢⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠄⠀⠱⠀⠀⠁⠀⡀⠈⠀⠨⢉⣐⠀⠠⠄⢈⡘⢆⠀⣉⠺⠄⢂⠀⠀⢘⡧⠀⠀⢠⠁⡀⠀⠿⠔⠀⣨⠄⠒⠲⢫⡇⠙⠨⡆⠀⠀⢀⡇⠄⢀⠀⠆
⠀⠀⠀⠈⡁⠀⢠⡀⠄⠀⠀⠁⠐⠠⠄⣀⠈⠁⠳⡂⠀⠉⣂⠀⠁⠢⠄⢢⣃⡌⢉⠑⢄⡆⠰⢃⡄⡀⠸⠊⠀⢀⡰⠀⠺⠀⠀⠀⢡⡔⠘⡧⠈⠀⠀⠄⠄⠀⠑
⠀⢰⠀⠀⠀⢀⣀⠀⠑⠉⠀⠀⠤⠀⠀⠀⠀⠈⠀⠑⢄⠢⠈⠀⠐⡈⢢⠈⠃⢱⡄⣥⠈⡷⠶⠊⡠⠀⠄⠀⠀⠈⠃⡠⠁⠀⠀⠀⡀⣠⣴⠆⠲⡡⠆⡀⠘⠃
⠀⠀⠁⠀⢰⡿⠁⡠⠀⣠⣿⠓⡠⢄⣠⡀⢀⠀⠒⠆⠘⢦⡀⡀⣤⡉⠀⠋⢀⡤⠶⡚⢠⡓⠠⡎⠀⢈⡀⠧⠐⢚⡐⢁⠔⠀⣀⣼⣴⣿⠁⣴⠌⡁⢢⠈⠂⠀⠂
⠀⠀⠀⠠⠘⡇⠀⠁⢰⣿⣿⠉⠁⠀⠀⢿⣿⣿⣿⣿⠖⢁⠀⠈⠉⠙⠻⣄⡐⠒⠋⠐⠋⠉⠲⠘⠉⠀⠀⠀⠀⠀⠉⡉⠔⠋⠁⠀⠉⠛⢀⣙⣀⣇⡸
⠀⠀⠀⠂⠁⠈⠻⣷⣾⣬⡍⠠⠰⠀⠀⠀⠉⠉⣽⠁⠠⣈⢂⠀⢀⡀⡇⢨⡤⠔⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⠐⠂⠁⡀⠠⢀⠁⡤⠈⠂⠨⠉⠙⠟⠁⠀⢀⡀
⠀⠀⠀⠀⠠⠂⢐⣾⣿⡏⠀⢰⠷⠌⠁⡔⠀⠀⠉⡀⠂⣤⠊⠀⠀⠀⠘⣉⠐⠄⠀⠀⠀⢀⠠⠔⠂⠀⠀⠀⠀⠀⠠⠄⠂⠈⠀⠀⢀⡀⠢⠀⡄⠈⡁⣠⣾⣷
⠀⠀⠠⠈⠀⠻⣿⡿⠟⡡⠶⠊⠀⠀⠈⠀⠈⠺⠣⡈⠐⠀⡀⠀⠀⠦⡀⠐⠀⠀⠀⠒⠈⠀⠀⠄⠀⡈⠠⠀⠂⠁⠀⠀⠀⡀⠀⠘⠃⠠⣤⡀⠁⣰⣿⢿⣿⠁
⠀⠀⠀⠀⣀⠀⠟⠁⠀⢀⠄⠐⠂⣀⠀⣀⢀⣇⠠⣘⢓⡒⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠐⡈⠵⠀⠁⠀⠠⠀⣂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⢿⣾⡟⡡
⠀⠀⢀⠀⠣⡎⡸⠁⡔⠁⣨⣴⣶⡦⢉⣤⡴⠡⠁⠀⠀⢠⠤⢔⣈⠦⢀⠀⠀⠀⠱⠘⠁⡀⠠⠀⡂⠀⢀⠀⢈⠁⡐⠀⠀⡄⡁⠀⠀⠀⠀⠀⡀⠠⠀⠋
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡟⠛⠻⡇⠸⣷⣤⠂⠀⠀⢰⣯⠀⣹⠙⠛⠋⠁⠢⢀⡰⢆⢀⠠⠘⠡⡇⠀⠇⣘⢧⠀⠥⠁⡐⠈⢠⠀⠀⠀⠄⠀⠀⠁⠈⡀
⠀⠀⠂⠀⣠⠋⠁⠈⠀⠸⢷⣴⠇⢰⠤⡈⠙⠇⠃⠀⠀⢼⡀⠸⣄⢈⢀⣀⠠⠔⠛⠉⠀⠠⣀⠀⠘⠤⣀⡀⠄⢉⣶⣦⣌⡀⠀⠈⠠⡐⠀⠂⠀⡐⠀⠁⢀
⠀⠀⠀⠀⠃⠐⠀⠀⠂⡐⠀⠀⣺⠞⠐⢄⠴⠂⠀⠀⠀⠘⡗⠀⠈⠲⢤⣀⡀⢠⡀⠀⠀⠄⠀⠈⢃⣼⢶⣦⠒⢉⡛⠿⣃⠀⠼⢂⡦⠀⠀⠂⡀⠍⠀⢀⠀⠂
⠀⠀⠀⠀⠁⠄⠠⣤⣶⣅⣈⣨⢻⠃⠀⠀⠀⠀⠀⠀⣀⣴⣥⠀⢄⠀⠐⠀⠐⠋⠀⡡⡄⠀⢁⣄⡹⣟⠋⠅⠀⡄⠰⠶⠘⠁⢠⣾⣧⡴⠀⢈⠁⡄⠀⠰
⠀⠀⡀⠀⠀⣀⡀⠈⢻⣿⣿⣯⡟⡀⣀⣀⣀⣀⣄⠻⣿⣧⣿⠿⠶⡦⢈⡍⢉⣉⣀⠠⣴⠦⠿⠥⠄⢻⣿⣶⢦⠔⠲⡄⠀⠀⢣⣤⣤⣤⣶⡿⠋
⠀⠀⠀⠀⠚⡅⠀⠁⢀⠝⢿⣝⣓⣒⣐⣐⣐⡀⣒⢂⠟⠁⠀⠀⠰⠀⠀⠁⠈⠐⠋⣀⠷⡒⠒⠲⠂⢺⡭⠓⠓⠄⠀⠈⣖⠛⠟⣋⠉⠉⠀⠈⠀⢀⣴⠁⢀⠎
⠀⠀⠀⠐⠆⠌⢢⠌⡀⠀⢀⢻⣿⡟⠻⠟⠋⠁⢨⡅⠄⢠⠔⡀⢷⡀⠿⢆⣀⢀⡈⡧⢓⣄⣠⣠⣔⠉⠣⡀⠻⠂⣱⠖⠊⠁⠀⡀⠹⠲⢈⣤⣶⠿⡟⠔⠁
⠀⠀⠐⡄⠢⢀⡉⠆⠀⠀⡨⠑⠃⠐⠀⡄⠀⢀⣡⣶⣿⡈⠤⠓⢈⠷⡀⠀⠹⠀⠀⡹⢛⡠⢑⠬⠒⡱⢄⠈⠢⠾⠓⢈⡠⠄⠙⢶⡾⣷⠘⣿⡧⠀⠂
⠀⠀⠀⠈⠢⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⢼⣿⡿⣿⣿⣄⠀⠙⠀⠠⡙⠓⠞⠀⢠⡗⢊⡔⢊⡐⢈⠠⡁⢷⡋⠈⡅⣴⣶⠂⣸⣷⣶⡜⢰⠋⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀⠀⠀⢁⠀⠈⠛⢿⡷⠤⢄⣀⣀⣠⣤⣾⡗⠠⢃⠄⠃⡄⢂⡐⡀⢺⠠⠁⠀⠘⠁⡀⠀⢈⠁⠀⠁⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠉⠁⠛⠀⠁⠀⠀⠙⠻⢿⡿⣿⠿⢴⡉⠢⡡⠄⢡⠘⣤⣏⣀⣀⣠⡆⡀⠀⠀⠠⠄⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠀⠁⠀⠀⠀⡠⠀⠀⠁⠀⡀⠀⢙⠃⠰⠈⠀⠚⠻⢿⣿⡿⠋⠀⠃⠠⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣠⡄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⣠⣀⣀⣀⣀⣤⣤⡄⠀⢠⠀⠀⠀⠀⣤⡄
⠀⠀⢠⣾⡇⠀⠀⣷⠀⠸⣿⣿⣿⣳⠦⢤⣀⣼⢃⣀⣤⠠⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⡄⡄⣼⣿⣿
⠀⠀⣾⣿⡧⠀⠀⣿⡆⠀⠻⢿⠿⣏⠀⠀⠁⠷⠸⢿⠇⢠⡄⠀⠀⠀⠀⠀⠀⠀⢠⡼⠶⠶⢦⣼⠟⠁
⠀⠀⣸⣿⡇⠀⠀⣿⡀⠀⠄⠀⠀⠀⠀⠀⣀⡀⠐⠀⠀⠈⢷⠈⠙⠓⠒⢦⠀⠀⡠⠔⢲⡖⠢⢤
⠀⢻⣿⣿⣧⣀⣤⣿⡟⠂⠖⠂⠐⣂⣥⣴⣿⣿⣏⡁⠈⠁⢸⡄⠀⠀⠀⣼⡀⢠⣀⣀⠀⠀⣀⣀⡄
⠀⠀⠙⢿⣿⣿⣿⠏⠁⠀⣀⣀⣀⣀⡀⠀⠉⠁⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⡷⠘⠻⣿⣿⣿⣿⠟⠃
⠀⠀⠱⢌⣉⣋⣩⠔⣁⣼⣿⣿⣿⣿⣧⣤⣴⡆⠀⡇⣸⠃⠘⣿⠀⠀⠀⣿⣳⡀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⢸⡏⠀⠀⠈⠛⢿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣦⠠⢻⣆⠀⠀⢿⣸⢫⣷⠆⣼⠏⠀⠀⢱⣆
⠀⠀⢀⣀⣸⡧⠀⠀⠀⠀⢸⠀⠀⡏⠉⢹⡏⠸⠀⠀⣴⠋⠄⢸⡗⠀⠀⢿⣪⢾⡅⠀⡿⠀⠀⠀⢸⡿
⠀⣄⡀⠀⠙⢩⣄⣀⣠⠀⠈⠀⠺⠷⠀⢸⡇⠀⠀⠀⢿⠀⠀⢿⠃⠠⠀⢽⠰⣿⡇⠀⣹⣿⣶⣶⣿⡧
⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠈⠛⠀⠀⠈⠛⠋⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⡜⠀⠀⠀⢀⡤⠆⠀⠻⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠰⠂⣤⣴⠁⢀⡴⠚⢉⡄⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠀⣰⠟⠀⣀⠁⠠⠀⠉⠁⠀⠀⡄⠚⠀⡖⣒⠖⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠡⠀⠻⢄⠘⠋⠀⠀⠾⠀⡀⣒⢀⣄⡀⠤⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠡⠄⢀⠄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠐⠂⢃⡀⠀⠀⠀⠀⢠⢦⣤⣄⡀⠀⠀⠀⢼⠈⣯⡫⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⠀⡌⠁⠀⠀⣤⣤⠃⢀⡀⡨⠃⠀⠀⠀⠈⠳⠦⠚⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠤⢠⢾⢥⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⢀⣠⠀⠾⡐⠂⠘⡚⠊
⠀⠀⠀⠀⠀⠀⡀⠀⡴⠓⣀⠃⢄⠘⠋⠀⠀⠉⠀⠀⠁
⠀⠀⠀⢨⠉⡍⠉⠉⢑⡀⠋⠀⠀⠷⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢵⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠘⢧⣅⡑⠀⠀⠀⠀⢠⠶⠚⠛⠃⠀⠀⠀⢄⢀⡀⠀⠠⠄⠀⠀⠆⠀⢀⠞⠐⠂⢀
⠀⠀⠀⠀⠠⠄⠀⢀⣀⡀⠈⠳⠶⠊⠡⡦⠀⠀⠀⣀⡄⠀⣴⠆⠀⠀⠀⠸⣌⡢⡀⠶⠘⣠⣤⠀⠰⠋⣄⠃⠴⢠⡅⠀⠑⣀
⠀⠀⠀⠀⠀⠀⣀⣫⢔⡉⠁⠀⠀⠀⠠⢄⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⠀⢂⠈⠁⠀⠀⠂⠀⠀⠀⠀⠈⠙⠲⠶⠆
⠀⠀⢈⠃⢀⠀⠉⢀⣩⠶⠋⣀⠀⠀⠙⠀⠠⡶⠀⠀⠀⢠⡆⠀⠀⠀⠀⡄⡄⠠⣄⠀⠋⠀⠄⠉
⠀⠀⠘⠀⠼⠀⠰⠋⣀⠘⠂⠁⠀⢀⣤⣤⠀⠂⠀⢰⠖⠀⢢⡀⠀⠘⢁⠴⠀⠒
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡴⠃⠈⢁⡤⠀⠖⠀⢢⡴⠛⢡⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠶⠒⠀⠀⠀⠀⠀⠈⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡏⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⢤⡀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠒⠀⠈⠀⠀⣀⠤⠛⠈⡀⠄⠊⠁
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⣶⣦⠀⠙⢢⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢤⡀
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠺⠿⠟⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡀⠘⠁⠀⠀⠙⠲⠤⢄⠠⠄
⠀⠀⠀⠘⡆⠀⠀⠀⠒⠀⠀⠀⠀⠐⠉⠁⠈⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣀⣥⣴⢂⡆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢐⣤⣾⡙⣟⠝⠋
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠰⣺⣿⢟⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡤⠤⠤⠤⠄⠤⠄⣀⡀⠀⠀⠀⠀⠠⠀⠀⠔⠀⣘⡯⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠓⠦⢤⣀⣠⠆⠀⠈⠉⠒⠤⠀⠀⠣⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠉⠟⠛⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⡜⠀⠀⠀⠀⠴⢤⠀⠠⣴⡴⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠞⠇⢀⣠⣬⣅⠀⠐⠠⣀⠀⠀⠰⠸⠀⢢⡠⠖⠻⣟⠛⠐⡗⣠⣤⡶⠄⠀⠀⢰⢰⠄
⠀⠀⠀⠀⠀⠀⠀⣧⠏⠁⠀⠀⠭⠒⢢⠘⡣⠐⠚⠐⠒⠢⢥⡬⠥⠤⠤⢬⡇⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠠⠐⠂⠀⠂⠀⠀⠡⣀⣀⣀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⡧⣄⣀⣀⡀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠡⡁⠀⠈⠹⠁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠰⣧
⠀⠀⠀⠀⢀⠈⠀⠒⠏⢄⠈⠠⠀⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⡄⢰⢷⠁⡀⠀⠀⠀⠀⠀⢸⡄⣀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠂⠀⠌⠀⠀⠑⠤⣀⣀⣀⣀⡠⡴⠃⠴⠙⠦⢸⡽⠀⠈⠄⠀⠀⠣⠤⢬⣤⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢒⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠓⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠀⠄⠀⠀⠀⠀⠈⠁⠊⠰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠹⣷⣵⣊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠌⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⡀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢟⣻⡀⠀⠀⠛⠁⠀⠀⠀⠀⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣳⡊⠀⠀⠀⠴⠂⠀⠀⠀⠀⢷⠚⠉⢘⣇⠀⠀⠀⠀⠀⠀⢠⠎⣠⠂⣀⡜⠁
⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⣿⣽⣿⣽⣿⣷⠂⠀⠀⠀⠀⠀⠀⣸⡀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠉⠉⠉⢉⠉⠀⠒⠲⠏⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⡀⢆⠀⠀⠀⢚⡃⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠐⢰⠀⢰⡠⢄⠤⣀⢠⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠑⠢⡀⠀⠁⠀⠀⠠⠀⠂⠈⠠⠖⠀⠀⠀⠀⠈⠈⡀⠁⠀⡀⠀⠀⢀⡀⣼⠃⡀⠀⡀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠋⡟⢽⢰⡓⢹⡡⣞⠏⢾⠰⡇⠾⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⡀⠀⠀⠀⠀⠀⡘⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⡌⠑⠀⠀⠀⠀⠈⠃⠰⠀⠀⠀⠀⠀⢻⡪⡃⠈⣙⠒⠤⣤⣀⣀⣀⡀⠀⠀⢀⡀⡕
⠀⠀⢀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠦⠀⠀⠉⠪⢅⠪⢅⣐⠲⠈⢠⣍⡉⣉⣩⠉⢼⠃
⠀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠑⠲⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠨⠇⠴⢶⣶⠄⠀⠶⠞⠀⠀⠀⢀
⠀⠀⠀⠀⢈⠑⠀⡀⠀⠀⣀⣠⠔⠡⠑⠀⢁⡴⠍⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠂⢀⡁⠀⠀⠐⠛⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠈⡤⠗⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⡇⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢐⡵⠒⠛⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠈⠃
⠌⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣠⠔⣹⠆⠀⠀⠀⣀⠤⠀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢎
⠋⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠠⢔⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠫⡔⣊⡠⠀⠀⠀⣞⡉⠀⠀⠰⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣯
⠤⢒⠭⠛⠀⠀⠀⠀⠀⠀⠈⠃⢄⠑⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠱
⠉⠤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⡀⠀⢰⠄⠀⠐⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠁⠀⠒⠄⠰⠄
⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣈⢦⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠰⠶⢄⠦⠈⠀⠈⠎⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⡠⡤⣀
⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠑⠐⠠⢄⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠑⠀⠀⣿⢉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢔⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⡿⠘⢸⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⢤⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢠⠇⡖⡈
⠀⢈⡀⠀⠀⠀⠀⠀⠀⢀⣁⠐⢠⠷⣄⠀⠀⠀⠀⠀⠢⡀⠀⠀⡱⢄⡀⠢⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡟⢀⢡⢁⠂
⠀⠨⣹⡀⠀⠀⠀⠀⠀⠛⢌⡠⠺⢤⠀⠉⠢⠀⠀⠀⠀⠈⠁⠉⠀⠀⠙⢦⡈⢦⡀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠘⠀⠀⠀⠀⢀⡼⠁⠋⡌⠎
⠠⠉⠉⠙⢄⡀⠀⠀⠀⠄⠂⠉⣕⡢⣁⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡙⢆⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣰⠟⢠⠃⣼⠌
⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠈⠙⢦⡢⢄⠈⢢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢯⣆⡀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢋⠔⢀⠾⠋
⢀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠁⠀⠈⠁⠮⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠼⠁⠀⠀⠀⠀⠀⠀⠉⠻⠲⣠⡴⠕⠁⠀⠀⠀⠀⣠
⠀⠡⡀⠀⢀⠀⠀⣠⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⢠⠀⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠟⠀⠈⠁⢰⡖⠀⠠⠀⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠲⠇⠀⠀⠀⠀⢀⡀⠈⠁⠈⠐⠃⠀⠶⠀⠀⡂
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⠀⡠⠃⠐
⠠⠤⣶⠆⠀⠀⠀⡀⠤⠀⠒⠒⠂⠄⠀⠀⠀⠀⠈⢉⠦⠀⠀⠀⠀⠀⣀⠀⢤⡤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠀⢀⠄⠁⠀⠐⠂⠁⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠉⠀⠉⠀⠀⠈⠉⠛⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡪⠛⠉⠁⠀⢰⡁⠀⠀⠀⠂⠲⠤⣤⣀⡀⠀⠀⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠐⠁⠀⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⢤⣀⠀⠀⠀⠉⣦⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣌⡁
⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣀⢀⣀⠀⠀⠰
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠄⠒⠖⠊⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠤⠤⠀⠤⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠶⠂⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢠⠼⠦⠺⠛⠖⡀⠉⠄⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢀⣇⣀⡎⡦⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣎
⠀⠀⠀⠀⠘⠂⠀⠀⠈⠃⡰⠃⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢸⡀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡉⢀⠉⠡
⠀⠀⠀⠀⠸⠦⢤⡤⠤⠟⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⢷⠂⠀⠀⠡⠀⠀⠀⠄⠀⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠑⢄⠀⠀⠀⠀⠀⡠⠃⢀⢃⡌⠡⠘⠀⠀⢣⠀⠀⠀⢀⣠⠴⠦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠈⠉⠁⠀⠂⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⢲⡀⠀⠀⣄⠈⢷⢤⡀⢸⣄⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⣿⣆⠀⠀⠀⠈⠷⠮⣸⣝⢷⠀⠀⢷⣹⠦⡀⣧
⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⠀⢀⠹⣿⣿⠀⠀⣀⠀⠈⠅⠉⡟⢻⣠⣤⡀⠉⡄⠁⡏⢷⡰⢠⢄
⠀⠀⠀⠀⠀⠉⠙⠂⠤⢀⣰⠁⡠⣿⣿⢶⣠⣤⣄⡸⠿⠀⠇⠘⠉⠩⡇⢠⣾⠀⡇⠠⣃⡰⢞⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠖⠀⡀⢹⣿⡆⣿⣇⢸⣟⠷⡉⢻⡄⢛⡇⠀⢀⣠⠆⠈⢡⣤⡷⢶⡭⠟⠁⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⢤⣏⣁⠀⠹⠷⣽⣥⠬⠻⣄⠙⠃⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠂⣬⠿⣫⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠰⠀⠸⠉⠓⠲⣦⡀⢰⣶⡸⠀⠀⢀⡀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠲⡭⢗⡸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣤⢚⡟⢾⡀⢿⡿⠀⠀⠀⠀⠀⢸⡇⡇⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠿⣾⠐
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠳⠀⠸⡙⠡⠀⠧⠀⢂⠀⠀⠀⠀⠀⢸⡇⣯⣫⡭⡽⠀⠀⠀⠀⣠⢀⣰⣦⣀⣶
⠀⠀⠀⠀⠀⠀⠀⢈⣍⠉⠳⡒⠳⡒⠳⣤⣥⡀⣢⣀⡄⠀⠀⠸⠇⠿⠿⠸⠧⠀⠀⠀⠀⡁⢜⠛⠬⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠹⢧⠘⣄⠻⢏⣨⣍⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣏⠀⣱⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠣⣀⠗⢅⢙⣏⢠⡾⣛⠋⡂⠀⠠⠖⠀⠶⢴⠂⢿⡀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⡿⠚⠉⠶⡈⠙⢟⣉⣓⡉⠢⡈⠂⣀⠀⠀⠀⣎⢆⢀⡷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⢴⡺⣧⠀⡈⠖⢌⠙⠿⠁⠢⠀⠸⢏⠐⢧⣀⣼⠆⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⢷⡜⣷⡀⠀⢀⡡⠶⣿⣿⣆⠐⢆⣠⣼⠟⢁⠀⠦⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⠷⠂⢁⡰⠦⠈⣴⢎⠑⠸⠟⠁⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⣼⡇⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⣀⣤⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢢⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⢀⣴⣦⡞⠁⠀⠀⠀⠀⠀⣾⣿⠿⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⣼⣤⣼⡄⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⡄
⠀⠀⢰⣟⢿⣧⣼⠟⠀⠀⠀⠀⠀⠀⣿⣿⡤⣠⣿⢺⠉⡅⠀⠀⠀⠀⠀⢿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠸⣷⣤⣾⠇
⠀⠀⠈⠿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠿⠳⠂⠈⠁⠀⠀⠀⠀⠀⠑⣨⣐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⣠⠖⠚⠒⢦⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠈⢀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⢰⣖⣾⣿⢸⡇⡘⠀⠀⠀⠀⣔⠉⠀⠀⠀⢉⡂
⠀⠀⠸⣿⣇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⢸⡇⠡⠀⠀⠀⠀⢉⡟⣷⣶⡞⣿⡁
⠀⠀⠀⠙⠋⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣴⣟⠇⠀⠀⠀⠀⠀⠀⢰⣶⠀⠘⣿⠀⠀⠀⠀⠀⣶⣶⠶⠶⢶⣶⣶⠀⠀⠀⠀⢸⠀⡇⠀⠇⢘
⠀⠀⠀⢀⣴⣯⠟⠁⠀⠀⠀⠀⠀⠀⣤⣼⣿⢀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠟⠻⠛⠿⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠸⠀⠏⠀⠇⠸


⠀⠀⠀⠀⠀⢀⣀⣤⡆⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢰⡶⠶⢶⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⡇⠀⠀⠀⠀⢸⠀⠶⢈⡁⠀⠀⠀⠀⣠⣶⢲⣶⣶⣶⢲⣦⡀
⠀⠀⠀⠀⢸⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀⣷⣤⠘⢫⠉⠉⠁⠀⠀⠀⠀⢸⣷⠶⣿⡇⠀⠀⠀⠀⠀⠁⣴⣶⠄⠀⠀⠁
⠀⠀⠀⠾⠟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠒⠒⠓⠐⠒⠒⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢯⡏⡭⣯⣿⡏⣺⡀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⣰⡯⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠷⠶⠛⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡁⠧⡷⠀⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⡤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⢀⠀⠀⠀⠙⠋⠀⠈⡆⠀⠀⠀⣀⡀⠊⢑⠤⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠰⠀⠀⠈⡂⣎⠁⠀⠀⠄⠺⠥⠐⠀⠀⢸⣾⣿⣃⠀⠀⠀⢀⠀⠘⢦⣈⠓⠁⠀⠀⢀⣄⡀⠀⠀⠈⠀⠟
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⣶⠒⢌⠋⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⠉⠀⠀⠰⡌⢻⡟⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⣀⠀⠀⠶⠂
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⣀⠀⠀⠀⢀⣀⠐⠈⠀⠀⠀⢠⠀⠳⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⡇⡇⠸⢿⣯⠀⠀⢀⠀⢈⠀⠀⡈⠀⠀⠒⠁⡀⠃⠀⠀⠀⠐⣎⠀⠀⠁⠀⠀⠀⢀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠛⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⠀⡇⠈⠁⠸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠁⠘⠃⠘⠂⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⣀⣀⡀⠀⠀⠀⠉⠷⣤⠀⠀⠀⡤⣀⡀
⠀⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠰⣿⣟⢻⠷⣶⣄⠀⠀⠀⡶⡟⢹⣏⣵⡿⠁⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⠋
⠀⠀⠀⠀⣠⡄⠀⠉⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⠶⢾⡞⠀⠀⠈⠙⠛⠛⢉⠁⢠⠀⠀⠀⢀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⣸⠼⠇⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠈⠣⠴⠷⠶⠄⠈⠰⡀⢠⠄⠁⠺⠷⠗⠒⠀⠀⠈⠉⠀⠀⣀⣀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢷⣤⢀⠀⠀⠀⡀⠀⠀⠀⠐⠛⠘⢻⡟⠐⠛⠋⠀⠀⣄⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠻⠟⠁⠀⠀⠃⠀⡄⠀⠀⠰⠂⠀⠂⠀⣀⠀⠀⡆⠁⢰⠶⠦⡐⢿⣿⠏⣴⡌⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠴⠯⢗⣀⠀⠙⠳⣭⡶⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡗⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢐⠀⢁⣀⠀⠘⣁⡍⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠙⢇⠸⠵⡄⠀⠀⠀⠀⠀⠠⠚⢫⠈⠁⠁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠆⠠⠣⠴⠀⠈⠂⠀⠈⠁⠀⠞⠃⠣⠀⠆⠀⠀⠘⠂⠀⠀⠀⠀⢀⢀⢀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡼⠶⠷⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢄⠒⠜⠘⠉
⠀⠀⠀⣠⠄⢀⡀⠀⠘⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉
⠀⠀⠀⠀⡩⠡⡢⢠⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⡁⠀⠀⡀⠀⢀⠀⠄⠈⠀⢀
⠀⠀⠀⠋⠁⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠠⠋⠀⠈⢁⠔⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣩⣿⣿⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢯⣘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣸⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣐⣲⣞⡛⠲⣷⣷⣶⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⣧⠀⠀⠀⠀⣶⣿⣿⡥⠚⢛⠒⢂⣄⠨⠽⣿⠯⠽⠽⠿⢯⣽⣿⣿⣿⣿⣿⣿⣭⡶⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡀⣿⣾⣷⠀⢻⡧⠀⢀⡴⠚⠩⠁⠀⠒⠒⠀⢈⣉⣉⣉⡉⠉⠉⠉⣩⣿⣿⡿⠛⠛⠛⠻⠽⣿⣿⣶⠘⠖⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠿⠒⠻⡄⠘⠉⠁⠀⢠⣤⠀⠀⠀⠀⣠⠞⣫⣽⣿⣿⣿⣿⣶⣾⣿⡿⠋⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢰⠀⠀⠀⠀⠉⠁⠀⠀⢀⣾⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⢀⣤⠀⠋⠁⡀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⠀⠀⠀⠀⠀⡀⠴⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠀⠀⠀⠀⣀⡴⠾⠻⣦⣤⣶⣿⣿⢏⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡟
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡾⢋⣴⣾⣿⣿⣯⣠⣛⣵⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣻⣿⢟⣩⣾⣿⠟⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⣿⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠈⢢⣴⣿⣿⣿⣧⣴⣄⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⢏⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢀⢴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢆⠀⢀⣀⣴⣺⣿⣿⣯⠄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣍⠙⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⠶⠖⠒⠂⠀⠀⢀⣀⡤⢼⣾⣿⣻⣿⣻⣿⠿⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡞⠀⠐⠶⠦⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢖⣒⢯⣭⣿⡿⣿⣿⣿⣿⠿⠋⠁⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣠⣿⠉⠠⢤⢤⢤⣀⣀⣀⡐⠀⠈⠉⣀⣒⣦⣭⣷⣶⣯⢽⣲⠭⠗⠋⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⣇⣼⣿⣦⢹⡭⠅⠒⣶⣿⡿⠍⠛⢒⡰⢾⠭⠽⠒⠊⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⣟⠸⠧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎

⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠀⠀⠀⢴⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⢶⢟⣿
⠀⠀⠀⠺⠆⠀⢸⡆⠒⠀⠀⠀⠰⣎⣁⣽⠃⠀⠀⠀⠀⠀⠉⡽⠁⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⠁⠤⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⢸⢚⡆⠀⠀⠀⠀⠀⡇⠀⠀⢰⣾⡿
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣴⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣤⣴⠶⠶⠶⢾⡆⠀⠀⠀⠀⠀⣠⣤⡶⠶⠾⢻⡇⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣿⠿⠃
⠀⠀⠀⠀⣿⠋⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠈⠑⠀⠀⠀⠀⡟⠛⠉⠉⠉⢹⠀⠀⠀⢸⠟⠛⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⣾⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣤⡏⠀⠀⠀⣾⣿⠃⠀⠀⠀⢀⣤⣿⠀⠀⠀⠉⠉⠀⠀⠀⢠⣴⣾⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⣀⣸⠀⠀⠀⢸⣦⣴⠶⠶⠶⠇
⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠿⠿⠃⠀⠀⠘⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣦
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠓⢻⡟⠛⠛⠛⠛⣿⠀⠀⠀⠀⠠⣿⢾⠂⠀⠀⠀⠀⠐⣇⣼⡿⠁
⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⢀⠤⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⢻⠁⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⢿⡿⠀⠀⠀⠀⠙⠦⠋⠀⠀⠀⠘⠓⠋⠀⠀⢠⣶⡟⠀⠀⠀⣾⡿⠃⠀⠀⢠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⣷⣦⣄
⠀⠀⠀⠀⣠⣤⣤⣤⣤⢶⡶⠶⠶⠟⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠁⣿⠋⡇⠈⢻⡆
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⢍⡂⠀⠀⠀⠀⠀⣿⢍⠂⠀⠀⠀⢻⡀⠙⠀⡇⠀⣸⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢨⡗⡆⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⡟⠓⠌⠀⠀⠀⠀⠙⠲⠶⡷⠚⠁
⠀⠀⢠⣶⡿⠀⠀⠀⣴⣶⡇⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠈⠛⡇⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀⢠⣶⡄⡇
⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⣴⠟
⠀⠀⠀⠀⠚⣿⣿⡿⠋⢀⣠⣤⣀⡀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣴⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡌⢿⣿⣧⣀⣤
⠀⠀⠀⠀⠰⠋⠈⢃⣴⣿⣿⣿⣿⣿⣦⣤⣶⠾⠛⠉⠀⠀⠀⠀⠀⡀⠀⠰⡀⠀⠰⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⣦⡸⣿⣧⣴⣬⡿⡎⠙⠋
⠀⠀⣤⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⢹⡀⠀⢁⡀⠀⠀⠈⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⠀⠀⠀⢶⣾⣿⣟⢧⣽⣧⠐⠞⠁⠀⠀⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⠈⢿⡅⠻⡷⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠘⢿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠛⠋⠁⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠀⠀⣠⣤⡤⠊⠀⠀⠀⠀⠑⡄⠛⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠈⠻⢿⣿⠿⠋⠀⠀⠀⣶⡗⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠀⢠⠄⠀⠶⠀⠀⠀⠀⠰⣃⣤⣀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⡶⠀⡀
⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⢀⣤⣤⣄⣤⣤⣤⣦⣄⣀⣀⣠⣤⣤⣼⣿⣉⣿⣧⣶⣦⣄⠀⠀⠀⠀⢀⡠⠊⠀⢀⠀⠀⠀⠈⠈⠃⠈⠀⣰
⠐⠂⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠈⠿⠋⠈⡇⠈⣿⠋⢿⠋⣁⡈⢻⡟⠉⣿⠋⣠⣈⣿⡇⠀⢀⣴⣿⠇⠀⠀⢸⠀⠀⠀⠀⠀⠖⢈⣀⡁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⡆⠀⠀⢀⡀⠀⢀⣿⠀⣀⣀⡀⢸⡇⢸⣿⠀⢨⠘⢿⣶⣾⡇⠀⡇⢰⣿⠉⠉⠀⠀⠉⠋⠁⠀⠀⣀⡜⠀⠀⠀⣀⠀⠚⡉⠉⠉⠳
⠀⠀⣀⣠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠐⠀⢸⣿⠀⣿⣿⠃⢸⣇⠘⠟⠀⣼⣷⣄⠈⢻⡇⠀⣧⠘⣿⣶⣦⡀⠀⠀⠠⠀⠀⠀⠉⢡⠀⠀⠚⠋⠀⣠⠷⠒⠲⣤
⠀⠘⢿⣿⠟⠀⢀⡄⢳⣄⠂⠀⠀⠀⠀⠀⠀⢸⣿⣀⣿⣿⣆⣀⣿⣄⢀⣰⣿⣏⠙⢁⣼⣇⢠⣿⣆⡈⢁⣿⠇⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠰⠤⠔⠘
⠀⠀⠀⠉⡠⢼⡁⠙⠄⠀⠀⠀⠀⠀⢀⠀⠀⣀⠙⠛⠋⠈⠛⠛⡉⠛⢛⠋⠈⠛⠛⠛⠋⡛⠛⠉⠙⠛⠛⠋⢀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓⠒⢶
⠀⠀⣠⠚⢢⡄⠉⠀⣠⠤⡀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⣿⣿⢸⡇⢸⣿⠀⠀⠀⢸⡏⢸⣿⠀⠀⠀⣿⡇⢸⣿⢸⣿⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠤⠚⠡⠤⢤
⠀⠀⠙⠲⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⢹⡇⢸⡇⠸⣿⠀⠀⠀⢸⡇⢸⡧⠀⠀⠀⢿⠇⠸⠿⠸⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡤⠤⢤⡈
⢀⡉⠁⠒⠂⢄⡀⠀⠠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠁⠆⠀⠀⠙
⠰⠏⣀⣀⠐⠤⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⢉⠉⢹
⠀⡐⠋⠠⣜⠳⣌⠂⣤⠁⠀⠀⠀⠀⢀⣀⣤⣀⣠⣾⣿⣷⠀⠀⡄⠀⠀⠀⡀⠀⠰⠶⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣃⣈⣀⣈
⠀⠉⠛⠛⢄⣵⣔⠻⡜⢂⢀⣢⣠⡀⣿⣿⣿⣿⣿⣿⣿⡟⠀⢤⣿⣾⣤⠔⠋⠀⠀⠀⡀⠀⢺⡇⠀⠀⠀⠠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠠⠀⠀⠤⠘
⠀⠀⠀⠀⠀⠡⡀⢦⣾⡌⡁⠀⠈⠁⠙⣿⣿⢿⣿⣷⡞⠀⠰⠚⣿⣿⠓⠀⠀⠀⠀⢠⣄⠀⣿⣇⠀⠀⠀⠀⠀⠀⡀⠒⠀⡬⠂⠉⠈⢀⢀⢀⡠⠀⠀⠀⠀⡀⢲
⠀⠀⠀⠀⠀⠀⢣⣬⡉⣏⣡⡀⠁⠀⠀⠀⠙⠻⢿⡏⠀⠀⠀⠀⠀⠹⠀⣀⠀⠀⠀⠀⡁⠀⡿⠋⠀⠀⠀⠄⠤⠀⢌⠐⠀⠁⠁⠀⠁⠁⠀⠀⠀⠀⠈⠉⠉⠁⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⣀⠀⠀⡲⣄⠀⠀⠀⢀⡀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠁⡤⠀⠀⠄⠀⠀⠰⠂⠀⠀⣴⠄⢀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠸⢊⠆⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠒⠒⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠂


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⣐⠀⠨⠥⠤⣀⣈⣓⣀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠉⠀⢀⡀
⠀⠀⠀⠀⠈⢇⣒⠀⠀⠀⠋⢐⡖⠂⠬⠭⠭⣝⣚⣒⣒⣒⣶⣒⠒⢲⡖⠒⠒⠒⡾⠉⠉⠀⣀⠄
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠒⠒⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⢀⣠⣧⣤⣬⣤⣴⣶⠮⠍⣉⣽⡋⠉⠉⠒⠒⠢⠤⠾⣀⣀⠐⠀⠀⠀⠀⠐⣒⠚⠉⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠉⠑⠒⠢⠭⢍⣓⡒⠤⢄⣐⡀⠀⠀⣨⠉⠁⠀⠰⠋⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠛⠛⠓⠒⠒⠂⠀⢠⠀⠰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠔⠒⠀⠃⠀⢀⠀⠀⠀⠈⠁⠠⣄⠀⢠⣄⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⡈
⠀⠀⠀⠀⠀⢐⠀⢀⠎⠐⠈⢀⠀⢀⡀⠀⠀⡾⢷⢦⠠⠀⡈⡀⠉⠛⣿⣿⡷⣶⡈⠀⠀⠀⠐⠒⠀⠀⡉⠀⠐⠀⠀⠀⢄
⠀⠀⠀⠀⢀⠄⠀⠈⡄⠐⠀⠀⠄⠀⠂⠘⢦⣀⡂⠀⠆⠀⢠⠀⠀⠀⠈⠅⠀⢻⣧⡄⠀⠀⠁⠄⠈⡲⢁⠆⠀⠀⣅⠀⠢
⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠁⠀⠐⠀⠘⢁⠐⠀⠳⣤⣀⠠⠂⠡⣀⠀⡀⢀⣠⣾⣿⠀⠀⠀⢀⠀⡘⠁⠐⠀⣀⠈⠉⠀⠂⠰
⠀⠀⠀⠀⠈⢂⢀⠀⣀⣆⠀⠆⠀⢀⠀⠡⠀⠀⢄⠙⢿⡀⠄⠠⡁⠀⠑⢀⠉⠀⠀⣠⡀⠠⠥⠔⠁⠄⠀⠀⠨⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠄⢢⠸⣿⣿⡄⠘⡀⠀⠀⠀⠐⠀⢀⣦⠈⣧⠀⠄⠃⢠⠀⠀⠀⠀⠊⠀⠈⠖⠶⠀⠘⠀⠄⠂⠷⠀⠀⠀⢀
⠀⠀⡀⠀⠐⠖⠘⣷⠜⢛⠛⠀⠁⠀⠀⠀⢀⣠⡾⢋⣴⣿⠁⠀⣀⠢⡀⠐⠀⢸⠀⠀⠐⡬⠣⣤⢴⡁⠀⠀⠀⡐⠀⠀⠀⠈
⠀⠀⠀⠀⠠⢀⣺⢁⣾⣦⠹⣆⢲⣶⣶⣦⣙⣋⠴⢧⡀⠻⣶⠾⠂⣐⡄⠀⠐⢸⠀⠀⢰⠅⣰⢒⡠⣧⣀⣀⠘⠁
⠀⠀⢀⠀⢿⡸⣿⣦⣭⣿⣷⠄⣾⣿⡾⠋⠁⠀⠁⠢⡙⠊⠁⠲⠞⢻⡏⠐⢢⠎⠀⢀⠈⠔⠋⠙⠁⢸⡿⢃⣄⡀⠰⠂
⠀⠀⠀⠀⠰⣷⣌⣙⢛⣋⣥⣶⡘⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠤⠊⡰⠎⠁⠀⠀⠀⠈⠀⠀⢐⣤⡟⠁⠡⠊⡄⠀⢁
⠀⠃⠀⠀⠀⠈⠛⠛⠛⠋⣉⢻⠁⢤⠀⠀⠃⡘⠀⠀⠠⠄⡀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⡙⠟⠀⠀⡀⢀⡔⡀⠡⣤
⠀⠀⠀⠀⠠⢂⣤⣶⡄⠸⣿⣼⠗⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠈⠒⠀⠀⠁⠿⢿⠸⡄⡸⣐⡸⠴⠀⠀⣿⡆⠆
⠀⠀⠁⠀⠀⠠⠿⠁⢈⠀⠠⣤⣶⡿⠦⠀⠀⢀⠈⢀⠀⠀⠀⣀⢚⠢⠀⠈⠁⠀⠀⠠⠀⠀⣼⡿⢠⠓⣌⠻⣗⠀⢢⡾⠋
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠂⠛⠁⠀⠀⠈⠀⡄⠁⡢⠀⠄⠂⠡⠴⡀⠋⠦⣀⣀⠀⢂⣀⠜⢛⡡⠦⠀⠘⢵⡹⡛
⠀⠀⠀⠀⠈⠀⢿⢟⣤⠔⡘⠀⢀⠰⣶⠀⠀⠀⠉⠀⠀⠀⠷⠉⠀⣄⡑⠄⠀⠈⡇⠁⠁⠉⠁⠀⢀⠀⠽⣯⡅⡇⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⡘⢡⠈⠰⡀⠀⠀⠀⠀⠀⣠⣵⠂⠀⠀⠀⠀⠈⢁⡀⡈⡣⠋⠁⠄⡂⠐⢏⢀⠨⠫⠀⢈⢃⠃⠀⠠
⠀⠀⠀⠄⠀⠀⢠⠀⠂⠀⡐⢨⣷⣤⣤⣶⡇⣿⡇⠀⠀⠁⣶⠄⠀⠀⠁⠐⠀⠀⢐⢓⠄⠐⢾⢇⣄⣀⡠⢫⡶⠀⡠⡁⠉
⠀⠀⠀⠀⡀⠁⠰⢸⠄⠀⠀⡿⣿⡿⠻⢾⣇⢹⣷⡄⠀⠐⠀⠈⠀⣀⡀⠈⣶⣄⠀⠊⠀⡠⠰⡘⣛⣩⣴⠟⢀⡀⡁⠀⠐
⠀⠀⠀⠀⠀⠁⠘⢂⢃⠀⠡⠘⢟⣤⡆⢸⣿⣦⠉⢈⡂⣠⣤⣤⣾⡿⢋⣴⣿⣿⣷⣦⣀⠀⠀⡠⠉⠛⠋
⠀⠀⠑⠄⠀⠀⠀⠀⠀⠤⣄⡀⡀⠀⠀⠚⠛⢙⣿⣦⣬⠩⢉⡉⠁⠀⠈⠙⡧⠏⠙⢿⣿⣷⡶⠀⠄⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠈⠀⠂⠀⠄⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡟⣿⠀⢸⣿⡟⣿⠀⠀⠀⣿⠀⠀⠀⣿⡟⣿⠀⢸⣿⣿⢻⠀⢰⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⣿⠀⢸⣿⡇⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⣿⠀⢸⣿⣿⢸⠀⢸⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⣿⠀⢸⣿⡧⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⣿⠀⢸⣿⣿⢸⠀⢸⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⡿⠀⢸⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⠀⠘⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⡟⠃⠀⠀⢻⣿⠃⠀⠀⠀⣿⠀⠀⠀⠙⡟⠋⠀⠀⢻⣿⠋⠀⠀⠙⣿⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡯⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠼⠧⠤⠤⠤⠼⠿⠤⠤⠤⠴⠿⠤⠤⠤⠤⠷⠤⠤⠤⠼⠿⠤⠤⠤⠤⠿⠤⠤⠤⠤⠇








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣄⡉⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢼⠁⡜⠄⠉⠓⡀⠁⠄⡀⠀⠄⠀⠀⡀⣀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⢀⡘⡌⢠⡟⡤⠭⠶⠄⠛⠒⠐⠛⠈⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⣤⣁⣂⣬⠃⡼⣠⠀⠀⣀⣀⡀⣤⠤⡤⠐⠖⣂⠒⢆⣰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢀⠊⠀⠀⠀⠀⢀⡿⢪⠀⠀⠫⠾⠒⠛⠚⠒⢋⡉⢉⣉⡁⢄⠀⠀⡅
⠀⠀⠀⠀⠀⠀⢀⠂⠤⢁⠚⢄⡀⣀⠀⠄⣼⣹⠿⠀⠀⠴⣶⣒⡿⣽⠛⡮⣁⠃⡬⢁⠾⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡘⢠⠌⠚⠉⠁⢀⣀⣀⣀⢹⣿⠀⠀⣿⢷⣟⣳⢧⣟⡳⢏⡜⠠⢍⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⢠⢙⡀⠀⢰⢾⣩⠿⠼⢿⡿⣽⠀⠀⣿⣿⣾⣿⡿⣼⣋⠾⣬⠃⠦⣹⠀⠀⣃⠂
⠀⠀⠀⠀⠀⠄⡐⠂⠌⣃⠀⠈⣡⢴⣶⢻⣿⣿⢿⠀⠀⣿⣿⣷⣯⣿⢳⣏⣱⢢⡝⡰⢎⠀⠀⡇⡐
⠀⠀⠀⠀⠀⠀⢀⠙⠠⢉⡄⠀⢻⡾⣭⣟⣾⣭⣿⠀⠀⡿⣿⣟⡿⣭⣟⣾⠭⠟⠂⠓⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⡌⠁⠎⣱⠀⠈⡗⠋⠉⠀⠀⠀⠀⠀⣿⢷⣿⣻⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠐⠠⠉⠰⢨⡆⠀⢱⠀⠀⠀⠀⠀⠀⠀⣯⡟⡶⣍⡟⡇⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠌⢁⠂⣼⠀⠈⡆⠀⠀⠀⠀⠀⣠⠏⣼⣳⠎⣜⠻⠦⣄⢀⣀⣀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡠⠇⠀⢹⡖⠲⢤⡔⠺⢉⡚⢠⢉⡲⢠⠉⠰⢁⠛⠠⢁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠈⡏⢁⠂⡌⠁⠎⣘⠃⠌⣁⠂⠌⠁⠂⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠈⡐⠠⠉⠐⢀⠉⠰⢀⠐⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠒⠈

⣎⢹⣿⣿⣿⣦⡀⠀⠉⠐⠂⣠⣶⣟⠂⠀⠀⠀⠻⢿⣿⣿⣿⠯⠃⠀⠀⢠⣾⣿⣿⣿⣿⣿⠇⠀⠈⢣⡼⣣⡔
⢘⡟⣿⣿⠿⠿⠇⠀⠀⠀⠀⠈⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⠾⠛⠋⠁⠀⠀⠀⠀⢷⡿⣿
⡴⠾⠋⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠙⢦⠀⠀⣠⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠰⣦⡤⣴⠆⠀⠈⠳⠦
⠀⠀⠀⢀⣀⣤⣤⡶⠖⠋⠁⠀⠀⠀⠀⢠⡀⠀⢠⣴⠃⠀⠀⠉⠁⠀⣀⣀⡀⠀⠀⠀⣰⡏⠀⢸⣆
⣤⣶⡿⠟⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⠉⠀⠀⠀⠀⠀⡾⠯⠿⢿⠀⠀⢰⣿⣠⣤⣄⣿⡆
⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀⢀⣤⣤⣼⠁⠀⠀⠀⢠⣦⠶⠊⠁⠀⠀⠙⠆⠀⠈⢧⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠸
⠉⠉⠉⠉⠁⠈⠁⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠈⠉⠀⢀⣀⠀⠀⠀⠀⠺⠿⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣶⣦⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣠⡞⡫⢍⣙⣶⡄⠀⠀⠀⠹⡄⠀⠀⠀⡤⠶⣶⣿⣿⣿⣿
⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣀⣼⣿⣼⣧⡉⢿⡯⣹⠢⡀⠀⠀⠹⡄⠀⠀⠡⠀⠸⣿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠹⣿⣏⣹⣿⣿⡟⠀⠀⠐⣿⣿⣿⣷⣽⣄⡛⠒⣲⠏⠀⠈⠀⠀⠀⠻⠀⠀⠀⠣⠀⢹⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⢤⣀⣀⣤⠀⠀⠑⠚⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⢠⣤⡤⠖⠀⢀⡤⣄⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⣀
⣶⣤⣀⣴⣶⣾⢿⣋⣀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠉⠋⠀⠀⠀⠈⠀⠈⢳⣄⠀⠀⣀⣤⡄⠀⠀⠀⠈⠻⢿⣶
⡿⣏⣯⣻⣿⣯⣄⡉⠉⠀⠀⠀⠻⣿⢯⣟⡿⣦⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠹⣧⡾⢿⣿⣧⠀⠀⠀⠀⢀⣠⣼
⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⡞⣠⠞⢫⣙⢼⡇⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣦⣻⣿⣇⠀⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⠇⢀⣤⡄⠀⠀⠀⢣⣍⠶⢿⣯⡼⠃⠀⠈⠉⠉⠉⠁⠀⠀⣄⠀⠀⠀⠻⢿⣿⡿⠀⠀⢀⡄⡛⠛
⠙⠻⠿⠟⠋⠀⠀⠀⠑⠀⠀⠀⠀⣉⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⢠⣷⠄⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣶⣤⣤⣴⡖⠀⠘⡅⠀⠀⠀⠈⢙⢦⣾⠃⠤⢀⡀
⣶⣶⣶⣤⠀⠀⢴⣶⠒⠉⠁⠀⠑⢤⣀⠀⠀⠀⢀⣾⠁⠀⢹⡆⠀⠀⠁⠀⠀⡴⠀⠈⠻⠤⡀⢀⣄⣿⠀⠀⣠
⠿⠿⠿⠋⠀⠀⠀⠀⣠⣶⣶⣄⠀⠐⠿⠇⠀⢀⣾⡇⢀⣀⠈⣿⡆⠀⠀⢰⣾⠀⣠⣤⣄⠀⠙⠿⠿⠃⠀⠀⠈
⣢⣀⣠⣤⣄⣀⣀⣀⣿⣈⣁⣈⣲⣄⣀⣀⣀⣸⣿⣧⣿⣿⣧⣿⣟⣀⣀⣈⣀⣼⣿⣟⣿⣷⣀⣀⣀⣀⣀⣠⣔
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⣧⣠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠈⠙⢦⡀⠀⡀⠀⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠉⠒⠀⠊⠀⠀⠀⢀⡠⠔⠋⠁⢀⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠹⢦⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠀⠀⡀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠀⠀⠠⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢁⡴⠋⠀⠀⠠⣄⣉⠁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⡀⠀⠀⠁⠛⠛⠁⠀⣀⣀⠈⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢀⢆⢸⡀⠀⠀⠀⠀⠀⠉⠉⠑⡖⠚⠃
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣠⣦⣶⡍⢩⠆⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠐⣠⣴⣞⢻⡿⣫⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⣀⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠐⢀⢤⣾⣿⡿⢛⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⡠⠔⣵⡿⢛⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣶⡛⠛⠛⠛⠓⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠘⡄⠀⠴⠃⠀⣀⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⣴⠂⠀⠀⠀⠉⠓⠢⣄⠀⠀⠱⣄⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠑⠒⢲⠶⠶⠶⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⣸⠚⠎⠉⠀⠀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⡃⠀⣠⣤⣤⣧⣀⠉⠐⠲⢤⡀⠀⠀⠸⠆⠛⠀⠸⣤⠶⠛⠩⣯⠉⠉⠈⡫⠉⣵⣶⠶⠆⠀⠀⠀⢀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⡞⠉⠀⠤⠤⠬⠙⠶⢤⡤⠟⣡⠤⠒⠃⠒⠢⠤⣉⣀⣌⣭⣥⣠⣄⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⢀⣀⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠑⠀⠸⡖⣶⡒⠒⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠤⢤⣄⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠱⣜⠀⠀⠈⠈⡇⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠤⣼⢂⠀⠘⠀⡀⠀⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⢀⠔⢤⣯⡓⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⡜⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡼⡇⠂⣪⠾⠀⠈⢆⠀⠀⠀⢀⡖⠀⠀⠿⠈⢳⣤
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠉⠓⠦⠤⢤⡤⠴⠖⠻⠁⠀⠊⠀⠙⠑⠚⠚⠁⠀⠀⠃⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡏⢠⠝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⣻⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⣿⢐⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢠⡟⢸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣀⡾⠁⠸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢃⣿⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠉⢙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⣾⠏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⢿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠔⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢶⢷⣄⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢰⠿⠒⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢠⡀⠀⠀⠙⣦⣀⣿⣼⣶⣿⣶⣶⣦⡄⢠⠾⠒⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣶⣾⣷⣿⣯⣿⣿⣟⢿⣿⣯⣿⣿⡎⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣏⢶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣿⣿⡟⡛⠿⠁⠀⠀⠀⣿⠟⠛⣾⠟⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣹⣾⣿⠁⠀⠀⠀⠀⣠⣴⣿⣤⣼⣿⣦⣄⣀⣤⣶⡿⠋⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⣀⣠⣴⣿⣿⡧⣽⣻⣶⡌⠛⠛⠟⠛⠉⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡕⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⠈⣩⣿⣿⣿⣿⣿⡿⢻⡿⠛⠓⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣫⣴⣞⡿⣿⣿⣿⣿⣿⢿⣻⣿⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢫⣶⣿⣦⣌⣻⣿⢫⣿⣶⣿⡍⠉⠉⣠⣤⠀⠀⠀⣿⣿⣿⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢻⣿⣿⣿⣿⣿⣿⣶⣯⣭⣛⣡⣷⣦⣬⣁⠾⠗⠀⢿⣿⠈⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣼⣏⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢀⠀⡀⠉⠻⣷⣶⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⠉⠛⠿⢿⣿⣿⡿⠀⢀⠎⠁⣀⠉⢂⠀⢹⣿⡿⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢸⣿⡏⠙⣦⣼⣄⣡⣭⣤⣼⣄⣾⡏⢠⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠁⠀⠀⠀⢸⣿⡗⠀⠹⣿⣿⣿⣯⣿⣿⠿⢸⡇⢸⡟⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠉⠹⣿⢿⠃⠀⢸⡇⠺⠗⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⢼⠀⠀⢸⡇⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⡇⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠘⠁⢸⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⣀⡀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⣄⡀⣀⡀⢀⣠⣤⣤⣤⠀⠀⣠⡤⢀⠀⠠⠐⣶⣤
⠀⠀⠀⣪⣾⡅⠀⠀⠀⣷⠀⠈⣿⣿⣿⣟⡷⣴⣶⣒⡒⢢⡿⠂⠀⣠⠀⣤⣤⣤⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣴⣀⣀⡀⣼⣿⣿⡇
⠀⠀⢠⣽⣿⡇⠀⠀⠨⣿⡅⠀⠪⣿⣿⣽⣿⢷⠀⠉⠻⢿⣁⣿⣿⡿⠀⠀⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⣏⣉⣈⣁⣩⣿⠟⠃
⠀⠀⠘⣿⣿⡯⠀⠀⢐⣿⡇⠀⠀⠈⠙⠉⠛⠊⠀⠀⠀⠀⠁⠈⡽⠃⠀⢿⡄⠀⢤⣄⣀⣀⡀⠀⠀⠀⠛⠋⠉⠉⠉⠙⠛⠁
⠀⢠⣠⣿⣿⡏⠀⠀⢐⣷⣆⡄⠐⠢⠀⠀⠀⠀⠀⠀⢠⣤⡉⠁⠀⠀⢀⠘⣧⠀⠀⠀⠈⠉⣿⠂⠀⠠⠒⠉⠙⠿⠉⠙⠲⠄
⠀⠘⣿⢿⣿⣧⣤⣤⣤⣿⣿⠃⠰⠛⠉⠹⣩⣩⣥⣼⣿⣿⣯⡄⣀⡀⠈⠀⢹⡀⠀⠀⠀⠀⣞⠅⠀⣥⣀⣤⠁⠀⠠⣥⣀⡄
⠀⠀⠹⠸⣿⣿⣿⣿⣿⡇⠻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⣿⡦⡄⠻⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠱⣄⠙⠻⡿⠿⠋⣀⠆⠐⣶⣿⣿⣿⣿⣿⣀⣀⣀⣀⠀⢰⡆⢠⡶⠂⢸⣿⠐⠄⠀⠀⣿⣷⡄⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠈⠙⠲⡆⠖⠋⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠃⢸⣇⠀⠸⣿⡀⠀⠀⠀⣿⣲⣧⢤⣀⡀⢀⣴⡟⠋⠙⢆⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣿⣿⣿⣿⡿⣄⠈⠀⠀⢸⡇⡄⣿⣿⠀⠀⢸⢻⢒⡏⣾⠻⠁⣼⡏⠀⠀⠀⠘⣿⡆
⠀⠀⢀⣀⣀⣠⡇⠄⠀⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⢹⡯⠀⠗⠀⠀⣴⠋⠡⠃⢹⡟⠈⠂⠈⢿⣹⠸⣿⠇⠀⣿⠇⠀⠀⠀⢀⣿⡇
⠀⢀⠀⠀⠉⠙⠋⣆⡀⠀⢀⡀⠀⠁⠀⠰⢿⡤⠀⢸⡇⠀⠀⠀⠀⢿⠀⠀⠀⣿⠇⠀⡀⢀⣸⠴⣼⣿⡄⠀⢸⣾⣷⣦⣴⣿⣿⡄
⠀⠈⠛⠶⢶⣶⣶⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠃⠀⠀⠹⠀⠀⠀⠀⠘⠱⠿⠟⠀⠀⠘⠿⠿⠿⢿⣿⡿⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡤⢤⣀⠱⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣼⠃⢰⢃⡈⠀⠷⢃⠉⠠⠄⠀⠂⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠠⡌⠀⠖⡜⠀⡾⠆⣀⠛⣠⣌⣐⠦⠤⠭⠴⠖⠒⠓⠒⠋⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⡈⠀⠆⣀⠉⢰⠃⢠⠇⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠂⢀⠈⠀⠆⣠⠿⠴⠬⠴⠟⠀⣜⡰⡇⠀⠀⣴⢖⡖⠲⣾⢉⡛⣩⣍⣁⣶⣤⠬⠤⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠄⣀⠃⡜⠀⠀⠀⠀⠀⠀⢀⣟⠃⡇⠀⠀⠙⠚⠛⠛⠉⠉⠉⣉⣀⣀⢀⡤⣤⠤⢤⠀⠀⡇
⠀⠀⠀⠀⡀⠂⢤⠁⠐⠳⣀⠀⢀⣀⣀⣀⣼⣁⡿⡇⠀⠀⡴⣶⡖⣻⡿⣩⡛⢴⡌⣐⠓⣤⠉⠰⢾⠀⠀⡷
⠀⠀⠀⠀⠁⠐⠀⣈⠡⠖⠚⠉⠁⠀⠀⠀⠀⢹⣱⡇⠀⠀⣿⣿⣽⠟⣶⣏⣹⠗⣤⠋⠲⢆⣌⠃⠜⠀⠀⡇⠄
⠀⠀⠐⢀⡈⠀⢾⠀⠀⠀⣀⣤⠶⣾⡟⣻⢿⣽⡟⡇⠀⠀⣿⣾⣏⣿⢷⣼⣛⡶⢇⣜⠃⣶⢁⡚⢲⠀⠀⡗⢀⠈
⠀⠀⠀⠄⢀⠛⢠⣇⠀⠀⢣⡽⠔⠊⣉⣉⣙⣏⣿⡇⠀⠀⣿⣿⣿⣻⣾⣯⣿⢳⣾⣉⡿⢠⡌⠁⢾⠀⠀⡧⠄
⠀⠀⠂⢠⠈⠐⠆⣸⡀⠀⠀⣤⠚⣿⣍⣿⢷⣾⣛⡇⠀⠀⣾⣾⣯⡿⢷⣾⣙⡿⣤⡝⠱⠶⣠⠛⢸⠀⠀⡇⠠
⠀⠀⠀⠂⣀⠁⠰⠀⣇⠀⠀⢻⡺⢧⣼⢛⣾⣯⣿⡇⠀⠀⡿⣷⣿⣻⡿⣤⡟⢳⣮⠴⠟⠒⠛⠙⠋⠀⠀⡷⠀⡀⠁
⠀⠀⠁⠠⠀⡘⠂⣤⢉⡄⠀⠈⣧⠖⠋⠉⠁⠀⠀⠀⠀⠀⣿⡿⣭⡟⣷⣏⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄
⠀⠀⠐⠀⡌⠁⠲⢀⡘⢣⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣶⣏⣹⠿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢀⠈⠀⠄⢀⠛⡆⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣬⢋⠾⢦⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠂⢠⠉⠰⢿⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⣼⠋⠾⢠⡝⠣⡶⣁⡛⢲⡤⢤⠤⣤⡤⠤⠞⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠴⠇⠀⠈⣿⠓⠲⢲⡖⠛⠷⢀⡛⠡⡮⣁⠛⢠⡍⠁⠆⣠⠉⠰⠄⡀⠃⠠
⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⢹⡌⠁⠦⢀⡛⠠⡌⣁⠓⢠⡍⠐⠆⣀⠉⠰⠄⡀⠃⠠
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⠠⠌⠀⠂⢠⠉⠰⠆⣀⠃⠠⠀⡐⠂⠄⠁⠐
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⣀⠉⠰⠀⡀⠃⠠⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠁⠀⠀⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠈⠁⣼⡍⢐⡄⠀⠀⠀⡔⣿⡿⢿⣿⣦⠀⠀⢠⢇⣯⠀⠀⠀⠐⠀⠢⠄⠀⠀⠀⠀⠀⣤⣤⡄
⠀⠀⠰⠀⣿⣁⡎⠃⠀⠀⢸⣵⡏⡀⠀⢹⢟⡇⠀⠘⣮⠍⠀⠀⠀⢐⠈⢐⠀⠀⠀⡀⠈⠀⠁⠉
⠀⠀⠀⠀⠈⠩⢉⣓⠀⠀⠈⠻⣿⣷⣶⣿⠞⠀⠀⠀⣨⡄⠀⠀⠀⠀⠉⠁⠀⠀⠘⠛⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣶⠄⠀⠀⠀⢉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠈⢥⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣔⣤⡀⠀⠀⣶⣶⢲⣤⠀⠀⠀⠘⠿⠊⠀⠀⢸⣀⠈⠓⢆⠀⠀⠀⢸
⠀⠀⠆⠢⠀⠀⠠⡆⠀⠀⠀⠈⠛⠁⠀⠘⠛⠥⠽⡟⠀⠀⠀⢊⠀⠀⠀⠀⢰⣻⠇⠀⠈⠀⠀⠀⠸⠃
⠀⠀⠷⢄⡰⣀⠶⣀⠀⠀⠀⢀⣔⠠⠀⢀⡀⢀⠀⡀⣀⣀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠈⣿⢸⣿⣿⣏⣹⣾⡿⣿⡁⠀⢠⠃⠀⡄⠀⠻⡇⠀⠀⠀⡀
⠀⠀⠈⠀⣈⠀⠀⠌⠀⠀⠦⠐⣽⠀⠀⣤⣉⣬⣨⠉⣭⣭⡬⣥⢉⣥⡄⠀⢀⠘⠁⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⢻⣦⣿⣽⣧⣿⢻⣧⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎⢋⡂
⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⣶⠀⠤⡀⠀⠇⠀⠀⣀⢓⡂
⠀⠀⣸⣾⣆⠀⣠⣤⣤⣄⣤⠀⠀⠴⠀⠀⠔⢂⣌⣁⣌⣣⣀⡐⡄⠀⣀⡀⠈⠳⣄⠀⠠⡧⢴
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠠⠿⠟⠿⠿⠿⢠⠃⠀⡇⡵⠀⠀⡠⠀⠐⣷⠈⠀⢸⡄
⠀⠀⡄⠀⢲⡿⠛⠛⠓⡖⡆⠀⠀⠀⠆⠀⠀⠂⠒⠐⠂⠑⠊⠁⠀⠀⠀⠀⠀⢰⡁⠀⠀⣧⠠⠀⠀⠙
⠀⠀⠀⡀⢸⠀⠒⠀⠂⠀⡇⠀⠁⢾⡞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⠀⠀⠀⠉⠂⠀⠀⠀⢠⣄⣀
⢀⠔⠒⠂⢸⠀⠀⠀⠀⠀⡇⠀⠀⣦⣴⠀⠀⠰⣄⠤⠄⣤⠴⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⢘⣡⢶⡄
⠈⠒⠓⠒⠾⠟⣛⡛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠄⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⢨⣇⣬⡄
⠀⠀⢀⠤⠄⠀⠀⠛⠀⠀⠀⢠⣀⠄⠀⠀⠀⠄⠀⠀⠀⣤⠀⠀⢔⡀⠀⢂⠀⠀⠸⠀⠰⠀⠀⢰⣯⣍⡀
⠀⠀⠈⠁⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠋⠉⠉⠉⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⠿⠃⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⣉⣩⣉⠓⢦⣄⠀⠀⣾⢻⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠠⠶⡿⡿⡿⣝⠢⠹⣷⠀⢿⢸⣧⠀⢀⡤⠴⠖⢋⡿⠁⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠁⠁⠀⠀⠀⣿⡇⢸⡸⣿⠀⣸⡗⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠸⡇⣿⠀⣿⠇⠀⠀⢀⣀⠀⢠⣿⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⢀⣠⠤⠶⣤⣄⠻⣧⣀⠀⠀⠀⠀⣀⡴⠟⣡⣧⠀⢧⣉⢉⣿⠀⠀⠀⠈⢿⡍⠋⠛⣢⡄⠀⠀⠀⠈⢿⣆
⠀⠀⠀⣴⠟⠁⠀⠀⠈⢿⣎⢆⠉⠙⢷⡛⢋⣩⣴⠞⠋⠈⣧⠀⠀⠈⠁⠀⠀⠀⠀⣼⣡⣴⣿⠁⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣼⠏⠀⢠⣲⡄⠀⠈⣿⢸⡀⠀⠀⠻⣍⢁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⠁⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⣿⠸⣀⠀⠀⠀⠙⢿⣦⡆⠀⠀⠀⠘⣧⠀⠲⣀
⠀⠀⠻⢤⣀⡀⠀⠀⠀⠀⠈⠓⢮⡓⢤⡀⠀⠈⢻⣿⣠⠀⠀⠀⠸⣧⠈⡽⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠾⠇
⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣀⡀⢀⣽⠃⣽⠀⠀⠀⠹⣿⣇⠀⠀⠀⠹⣆⢉⣩⣤⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⢿⣴⡄⠀⠀⠹⣆⢉⡤⠀⠀⠀⠐⢦⣄⡀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠻⣷⢀⠀⠀⢻⡄⠞⠙⠀⠀⠀⠀⠈⠛⠶⣤⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⢯⡙⠚⠡⣇⡀⠀⠀⠙⣿⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢀⣼⣁⣄⣰⡖⠛⠁⠀⠀⠈⢻⣧⡄⡀⢷⡀⠀⠀⠀⢠⣶⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠉⠉⠀⠈⠻⠇⠀⠀⢠⡄⠀⠀⠸⣟⠛⠻⣇⠀⠀⢻⡏⢉⡛⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠉⠛⠋⠁⠀⠀⠸⠗⠛⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠀⠀⠀⣴⡦

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀
⠀⠀⠀⢤⣴⣧⠄⠀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣾⡅
⠀⠀⠀⠘⠉⢃⣴⣿⣿⣿⣦⣤⡶⠞⠋⠁⠀⠀⢀⠀⠆⠀⠂⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣔⣾⡯⢤⡿⡝⠛
⠀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⠄⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⣷⠿⣿⢾⡇⠙⠁⠀⢰
⠀⢿⣿⣿⣿⣿⡿⠛⠿⠿⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⣀⣀⠔⠈⠈⠐⡌⠧⠉⠁⠀⠀⠀⡠⠃
⠀⠀⠛⠿⠿⠋⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⣣⣤⡀⠸⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⠾⣶⡶⢶⠿⣶⢶⡶⠶⢾⡿⢼⡿⠛⢷⡄⠀⠀⣠⡎⠀⠀⠀⠀⠀⢈⠠⠠⠃
⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⣿⢀⡈⡀⣸⢠⣧⠈⠱⣯⣼⡇⢸⢁⡿⠛⠃⠀⠛⠋⠀⢀⡀⠀⠀⠀⠠⠒⠒⢢
⠀⣀⣠⡄⠀⠀⡀⠀⠀⠀⠐⠂⠀⣿⢸⣿⡇⢹⠈⠋⢸⣷⣄⠙⡇⢸⡀⢿⢶⡄⠀⠀⠀⠀⠈⠡⠀⠘⠁⠠⠟⠒⢲
⠀⠘⠿⢁⡄⢦⠙⠀⠀⠀⠀⠀⠀⢿⡼⠛⠷⠾⢷⣴⠟⢷⣤⠾⢷⡾⠷⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡭⣅
⠀⢀⠔⢤⠙⠀⡀⠀⠀⠀⢰⡆⣾⠀⠀⢰⡆⣶⢠⣶⠀⠀⣶⠀⡷⠀⠀⣶⠀⣶⢰⡇⠀⠀⠀⠠⠀⠀⠀⠀⠔⠠⢬
⠀⠈⠙⠀⠀⠀⠀⡠⠀⠀⠸⠇⠻⠀⠀⠸⠇⠿⠘⠟⠀⠀⠻⠐⠇⠀⠀⠛⠀⠛⠘⠃⠀⠀⠀⠀⣠⣄⠀⠠⠖⠒⢦
⢰⠆⠀⠀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠠⠧⠤⠤
⢀⡚⠀⠖⠄⠀⡄⠀⠀⠀⢀⣠⣄⣠⣾⣶⠀⢠⠀⠀⢀⠀⠰⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣄⣈⣤
⠀⠉⠉⠲⠒⡑⣉⠤⠖⠦⢺⣿⣿⣿⣟⡟⢀⣾⣿⡖⠈⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢡⣙⢻⢒⡀⠀⠀⠙⠿⣿⠏⠀⠀⠈⠹⠀⠀⠀⠀⠛⠀⡿⠀⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢧⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠃⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢴⣶⠄⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣈⣽⣿⡟⢧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣄⣀⠀⣷⠀⠀⡀⣤⣶⣦⣠⡴⣘⣫⡵⣿⣿⣷⣶⣶⣶⣤⣤⣀⣠⣾⠟⠋⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⣿⡃⢸⡇⠀⠔⠒⠉⠁⠀⠀⠀⠠⠠⠼⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⠀⠤⠆⠀⠀⠀⣠⡤⣶⣶⣤⣄⠀⢀⣴⣿⡿⠋⠙⠛⠿⣿⣾⡄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣵⣾⣿⣿⣿⣿⣿⣿⠟⠁⢀⡀⢠⠄⠀⠀⢈⡑⠀⠉
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⠀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢶⣤⣤⣶⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣾⣿⣿⣯⣀⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⡿⣫⣶⡿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⡏⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⢁⣤⣾⣿⣿⣋⡛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣴⣾⣿⣿⣿⣿⣿⣿⢇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣔⠉⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠈⠻⠿⣿⣿⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⢈⣡⣴⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡼⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣯⠁⠲⠄
⠀⠀⠀⠀⠀⠀⠀⢰⢻⣇⡀⠀⠙⣗⢂⠤⢀⣀⡀⠀⠤⢀⣙⣯⣻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢞⣻⡇⠀⠀⡏⠀⠘⠻⠟⠋⠛⠃⠾⠯⠷⠙⠻⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠉⠉⠐⢄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠑⣄⠀⣠⡊⠀⠝⠢⡀⠀⠀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣀⠠⠤⠔⣚⣛⡩⠭⢭⢭⠅⢶⠋
⠀⠀⠀⢀⣀⣤⡳⣄⡀⠀⠀⡿⢈⢄⣵⡈⠱⢆⡈⠢⣌⠖⣩⣿⣥⡃⠀⠀⠀⠀⠀⠛⣲⠛⠇⠀⠀⠆⠀⠀⢸⡄⢸
⠀⠀⠀⠘⠷⠴⠃⠀⠉⠉⣏⢔⠷⣫⡶⣛⣦⠈⠁⠀⢘⢢⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣿⠀⡇⠀⠀⡆⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡾⡫⣻⡿⢋⣵⡄⠀⠳⡀⠹⡟⠛⠛⠀⠀⠉⠀⠀⠀⢸⡀⢣⠀⠀⣧⣀⣀⠴⠷⠚⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢾⡩⡺⢟⣽⠾⣆⠀⠙⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⣞⣓⣉⣉⠉⠥⠤⠦⠒⠒⢾⣭⣤⣄
⠀⠀⢀⠔⠀⠀⠀⠤⠄⠰⠿⠂⠀⠀⠙⢶⢛⢥⡾⣻⣧⠀⠈⠁⠸⣄⡀⠠⠤⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠤⠘⠀⠀⠀⠀⣀⠴⠒⠂⠉⠀⠉⡆⠈⢻⣕⡽⣿⣥⢿⡄⠀⠀⢻⠉⠙⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿
⠇⣀⣀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⢰⠃⠒⢒⠻⣝⣫⣵⡿⢏⠀⠚⣢⠀⠀⡀⢫⣎⡰⠇⢤⡀⣀⡤⠰⡾⣿⠿⣿⠿⠿⠿⠋
⠀⠀⠀⠧⠢⡀⠀⠀⠀⢈⢿⣖⠈⡏⠻⣱⠓⠤⢻⣿⣭⣶⠟⠋⠁⠀⣀⠼⣌⢯⠑⢊⣁⠀⡻⢿⣿⣆⠠⠁⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠈⠑⠒⢰⠋⠁⠈⢢⠥⠤⢅⣀⡀⢰⣿⣿⠟⣀⡠⠔⠉⠀⠀⠈⡎⢃⣀⠤⣶⡁⠀⢻⣿⠃⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠧⠤⣠⠃⠀⠀⠀⠘⠃⢹⣿⠧⠊⠁⠀⢀⣠⠴⠒⠋⠓⠋⠸⠗⠑⠁⠀⢸⠇⡤⠀⠀⠀⠀⢰⠶⠶⠇
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠊⠀⠀⣀⡤⠚⠉⠀⠀⠀⣠⣤⣦⣤⡀⠀⠀⠀⠼⡪⠛⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠰⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⠀⣞⠀⣀⡠⠔⠊⠉⠒⠤⣀⠀⠀⣸⡿⡍⠛⣿⡷⣄⠀⠀⠠⠀⠊⠀⠀⠀⠀⣷⣶⡄⠉
⠀⠀⠀⠀⠀⣤⡄⠀⣇⠀⠀⡃⠀⠀⠀⠈⠻⢤⣄⣀⡀⠀⢐⠄⠈⠀⠀⠘⣿⡋⣠⣾⡖⠁⠁⠢⡀⠀⠀⠀⠀⠀⢰⣿⣿⡿
⠀⠀⠀⠘⡄⢻⢣⠀⠈⠑⠚⠀⠀⠀⣀⠀⣀⣠⣿⣿⣿⣿⡶⢦⣄⣀⠀⠀⠀⠉⠙⠉⠒⠀⠉⠀⠆⠑⢄⠀⠀⠀⡘⠛⠉
⠀⠀⠀⠀⠿⡌⠛⠁⠀⠀⠀⠀⠀⠐⠁⠀⢹⣿⣿⣿⣿⣿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣵⣄⠔⠁
⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠒⠀⣀⠠⠔⠊⠁⠀⠀⢻⣿⣿⣶⣿⣿⣿⡀⣀⣠⡤⠔⠒⠈⠣⣄⠀⠀⠀⡤⠭⢕⣦⡈⠉⢢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠀⠀⡔⠈⠁⠐⢦⠀⠻⣿⣿⣿⣿⣿⡿⠟⣉⣀⡠⠤⠀⢠⣄⣑⠢⣠⠓⠀⠀⠁⢱⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢇⠀⠀⠀⠀⡇⠀⠹⣿⣿⠿⠋⠀⠈⠣⡀⢠⠁⠀⢸⠟⠉⠀⢋⠑⠢⠤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠑⠀⠐⠊⠀⠀⠀⠙⡁⡤⠐⠒⠒⡄⢱⠇⠀⠀⠀⠀⠀⠀⠀⠑⠂⠰⡀⠀⠀⡠⠋⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⣔⠑⡆⠀⠀⠸⡌⢉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⢈⣉⣤⣴⣶⡿⠁⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣛⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡛⢛⣛⢛⡛⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠁⣀⠈⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⢄⡄
⠀⠀⠄⠀⠀⠀⠑⢷⢈⠀⠀⢠⠖⠉⠉⠛⢦⡀⢀⠀⠀⠀⠀⠁⠀⠐⠛⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠁⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⢀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⣨⢚⣿⣶⠀⠀⠀⠀⠀⠀⢄⠀⠰⡄
⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡟⠀⠠⣄⣠⠤⠙⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠂
⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣗⡞⣞⣾⣸⣵⣇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠴
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠞⢀⡉⢉⡉⠈⠁⠀⠀⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡡⠔⠂
⠀⠀⠀⢠⣄⣀⠀⠀⠆⠀⠀⠀⠀⢤⣤⣤⠀⠀⠏⢠⣞⡵⡾⡋⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠉⠐⠀⠀⠀⠀⠀⠀⠈⢣⠞⠀⣀⣴⠻⡟⣸⢱⣷⣧⣷⣿⣴⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠙⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢖⠒
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠
⠀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⡠⡄⠀⠠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⢠⠀⢽⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠍⢡⣨⠆⠄⠀⠀⠘⠂⢰⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢠⡇⠘⠄⠀⠀⠀⠀⠀⣝⠃⡞⢉⢹⣦⣐⣫⠵⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⢸⡇⠀⠀⠀⠀⠐⠀⣾⠏⠀⠘⠊⠹⡿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠄⠉⢉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢹⡀⠀⠀⠀⠀⠀⠀⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠋⠉⠘
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⢸⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠛⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢼⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠘⠟⠋
⠀⠀⠀⠀⣠⣾⡿⠛⡇⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠐⠿⠛⠁
⠀⠀⠀⢠⣿⠏⠀⣠⣷⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋
⠀⠀⠀⢸⣿⠀⢸⠏⢹⠀⠈⢻⡇
⠀⠀⠀⠀⢿⣆⠈⠃⠸⡆⢀⣼⠃⠀⠀⠀⠀⠀⡞⠛⠛⠛⠛⠗⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⣿⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠉⠛⠶⠶⡷⠋⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⢹
⠀⠀⠀⠀⠀⢿⣿⠇⢀⡞⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⣴⣶⡶⠀⠀⠀⣠⣶⣶⠀⠀⢀⣴⣶⡆⠀⠀⢠⣶⣶
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁

⠀⠀⠀⡴⠚⠉⠉⠙⢶⣄⠀⠀⢠⣤
⠀⠀⠀⣇⣴⣶⡄⠀⠀⣿⣷⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠙⠿⠟⠁⠀⠀⢸⣿⡆⢰⣶⠀⢰⠀⠀⠀⠀⠀⠀⣇⣸⣤⠀⠀⠀⠀⠀⣏⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠿⡟⢻⠉⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⢸⠟⢻⡇⠀⠀⣠⣷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⢸⡤⠟⠀⠀⠀⠉⡏⠸⠀⠀⠀⣴⣿⡿⠀⠀⢀⣾⣿⠇⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣟⡷⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡟⠁⠀⣀⢶⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣛⡮⣄⢠⣮⣻⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢮⣪⡪⡪⣳⠟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣕⢝⣷⣕⢜⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣮⡪⡻⣮⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢷⣷⣝⢿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⣿⡪⡻⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠉⠀⠀⠉⢑⣶⢝⢟⢾⣈⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣠⣮⡻⡻⣷⣑⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⢼⣿⣾⢿⣾⡮⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠁⠀⠀⢀⡠⢄⣸⣷⣵⣝⢷⠟⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⢀⠞⠁⢀⢞⠮⣻⣿⠛⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⣅⣑⢕⠝⠁⡇⠀⠀⠀⠀⠀⡸⠹
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡪⡫⡺⠋⠀⡰⠁⠀⠀⠀⢀⠔⣡⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣔⣕⢝⢟⠾⠤⠐⠊⠀⠀⠀⡴⢊⡡⠔⠁
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢞⠳⣮⡫⡲⡳⠃⠀⠀⠀⠀⠀⠀⠸⡰⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠙⠪⡙⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢖⠤⣀⣀⠀⠀⠀⢀⣀⠠⠒⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠬⠍⠉⠠⠤⠒⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⢀⣠⣤⣶⠄⠀⠀⠀⠀⣿⣿⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⣾⠇⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢁⣿⠏⢠⣿⠏⠀⢀⣴⣾⣿⣿⣿⣷⣦⣿⣿⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⡿⠀⣿⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠰⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣷⠀⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⣿⣆⠘⣿⣆⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⣴⡿⠃⣼⡿⢠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡈⢿⣦⡈⠻⣷⣤⣀⠈⠉⠉⠉⢁⣀⣴⣾⠟⢁⣼⡿⢡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠙⢿⣦⣈⠙⠛⠿⠿⠿⠿⠿⠛⢋⣠⣴⡿⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣉⠛⠿⣷⣶⣶⣶⣶⣶⡾⠿⠛⣡⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣦⣤⣤⣤⣤⣤⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⠁⢁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣓⣿⣏⣿⡠⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⢷⣽⡟⣿⣩⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⣿⠓⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⣿⠃⢸⡏⠓⠶⣄⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢶⡂⣿⠀⢸⡇⢠⢄⡈⢳⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡘⡒⠄⣿⠀⢸⡇⠈⠑⠢⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠨⠀⣿⠀⢸⡇⠰⠖⠄⣾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣆⠳⠦⣿⠀⢸⡇⡀⣰⠖⠻⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠁⠛⠟⠛⠃⠁⢿⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠃⢰⠋⠁⠀⠀⠉⣇⠘⢷⣤⣀⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣸⠀⠀⢷⠗⠀⢸⠀⠀⠀⣾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠐⠁⠃⠀⣤⢤⣤⣤⡌⠣⠓⢘⢹⣆⠀⠀⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⠀⣠⣶⠀⢸⣿⣿⡟⠠⣠⠒⢈⠀⣿⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠙⠯⠓⠀⢸⣿⣿⠀⠀⠈⠈⢂⡴⠃⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⢤⣀⣸⣿⣿⡠⠤⠴⠚⠉⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⣿⠀⣿⣿⠀⣿⡆⣿⣷⠀⣸⡇⢸⣿⡇⢸⡆⢰⣿⡇⢸⣿⠀⣿⣿⢀⣿⠀⣿⣾⠀⣿⡆⣸⣿⡀⢰⡇⢸⣗⡇⢸⡧⢰⣸⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣤⠄⣠⠄⣠⣤⠀⣤⠀⣤⣤⠀⣄⠠⣤⡄⢠⡄⢠⣤⡀⢤⡀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠐⠛⠃⠘⠋⠐⠛⠋⠘⠛⠐⠛⠃⠀⠛⠀⠋⠙⠈⠛⠀⠙⠛⠀⠙⠂⠙⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⢰⡆⠸⠀⣦⠀⣀⢀⡄⠘⠀⠧⠀⠀⠀⠀⣴⠆⠿⠆⢠⡀⠀⠀⠀⠄⠸⠻⠀⡆⢀
⠀⠀⠀⠃⠈⠀⠀⠀⠈⠀⠚⠈⠀⠀⠀⠀⠸⠀⠾⠁⠁⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠄⢰⠀⡖⡆⢰⠀⡆⡆⢠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠃⠸⠄⢶⡆⢠⡄⣀⡀⢀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠘⠀⠗⠇⠸⠀⠛⠃⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢤⡄⢦⠀⣤⡠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⡀⣧⠘⠿⠄⠳⠈⠛⠂⠑⠈⠓⠌⠢⠱⣄
⠀⠀⠀⠀⠀⠀⠐⠦⠤⠀⠀⣀⡄⢀⠄⣠⠄⠰⠀⠚⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣿⡇⠀⠀⠀⠀⢁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⢛⣿⣿⣿⣧⣴⠶⠟⠛⠛⠛⠛⠛⠛⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢁⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣶⣿⣿⣿⣿⣿⣿⣿⠏⢀⣤⣶⡿⠿⠛⠛⠛⠛⠛⠿⢿⣷⣦⣀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠿⠛⢁⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣾⠃⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣠⣤⠉⠀⠀⣼⠇⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⢻⡇
⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀⣿⠀⠀⠀⢸⣿⠃⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣿⡇⠀⠀⠈⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⣇⠀⠀⢠⣿⡟⢻⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⣾⡏⠀⢸⠁⠀⠀⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⢸⢸⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⢠⠏⠀⠀⠀⡔⣥⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣾⠿⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⢀⣧⡴⠋⠀⠀⠀⠀⠣⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠙⠻⠿⢿⣿⣿⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⢋⣴⠟⢿⠁⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢠⡿⠁⠀⣸⣦⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠁⠀⣾⡿⢿⠛⠛⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠋⠉⣿⠀⠀⢿⡁⢸⡇⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⢠⡄⠀⠀⢻⣆⡀⠀⠁⠀⣷⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠀⠀⠀⠙⠻⢶⣶⣤⣿⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠾⠳⡄⠀⠀⠀⠀⢠⣤⣤⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡎⠁⠀⠀⠀⠀⣿⡿⠿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⣁⣤⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠟⠛⢛⣉⣽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣿⣧⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣼⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⠀⣿
⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⡄⠀⠀⡿
⠀⠀⣼⣿⡿⢻⣿⣿⣧⠀⠀⢠⡇⠀⠀⠀⢸⣿⣇⢿⣿⣿⣿⡇⠀⢸⡇
⠀⠀⢿⣿⡃⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⢠⡟
⠀⠀⠘⢿⣧⣙⣿⣿⣿⠃⢀⡟⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣧⡶⠋
⠀⠀⠀⠀⠙⢿⣿⣿⣋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⠷⢶⣶⣶⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡉⣿⣿⣆⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣿⣿⡟⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⣀⠤⢶⣶⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠔⠋
⠀⠀⠀⠀⢱⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⠤⠙⠯⡻⣿⡀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣖⠁
⠀⠀⠀⠀⠀⢣⠀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣇⢚⢙⢙⠻⢹⡇⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠣⣀⣼⠿⠛⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣹⣜⣿⣟⣡⠞⠀⠀⠀⠀⠈⢿⣯⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢰⣄⣀⣀⣴⠂
⠀⠀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣷
⠀⠀⠀⢀⣼⠋⠉⠉⠉⠉⠉⠋⠉⠙⠙⢣⡄⠀⠀⠀⠀⠀⠀⣠⣴⠟⣻⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣷
⠀⠀⠀⠈⠉⢹⠋⢹⠋⠉⠉⠉⠉⠉⣿⠉⠁⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣬⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⢶⣦⣀⣀⣀⠀⠀⣀⣀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⡾⣿⣿⡟⠱⠶⠖⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣴⠋
⠀⠀⠀⠀⠀⣾⣿⣿⣶⣾⣷⣾⣿⣿⡷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⣽⢿⣿⠂
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣟⢿⣿⣶⡿⠋
⠀⠀⠀⠀⠁⠀⠀⠘⢿⣿⣿⣿⠟⠀⠈⠙⠀⠀⠀⠀⠀⠛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉