Astrology sing Emojis & Symbols

⠀⠀⠀⣠⡤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⡀
⠀⣰⠟⣥⠀⣰⢶⣤⡙⢧⡀⠀⠀⠀⡴⢋⠀⢀⠀⢀⡈⠙⣆⠀⠀⠀⢠⡞⠩⡄⠀⠀⢀⡌⠳⡄⠀⠀⠀⣰⠟⣡⣤⣄⣤⣤⡙⢷⡀
⢰⡇⠀⠸⣆⡏⢸⠶⠃⠈⣧⠀⠀⢸⠁⠈⠷⠏⠳⠞⠹⠄⢸⡆⠀⠀⡿⠀⢀⣹⣀⣀⣿⡀⠀⢻⠀⠀⢰⡏⠀⠧⠀⢸⠀⠠⠇⠀⣧
⠘⣇⠀⠀⣿⠁⣾⠀⠀⢀⡟⠀⠀⢸⡄⠘⣆⡞⢦⡼⢳⠀⢸⠇⠀⠀⢷⠀⠀⣽⠉⠉⢿⠀⠀⣼⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⢀⡟
⠀⠙⢦⣀⠀⠰⠇⢀⣠⠞⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢷⣜⠁⠀⠀⠈⣃⡼⠃⠀⠀⠀⠙⢦⣀⠀⠘⠀⢀⣠⠞⠁
⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⢀⡴⢋⠉⠀⠈⣉⠳⣄⠀⠀⠀⠀⣠⠞⣋⠁⠀⠉⣙⢶⡄⠀⠀⠀⠀⣴⠚⠉⣁⣈⠉⠛⢦⡀⠀⠀⠀⢀⡴⢋⡭⠶⠮⣍⠳⣄
⢀⡟⠀⢈⡷⠶⠾⣏⠀⠘⣇⠀⠀⢰⠃⠀⢈⡏⠉⢿⠁⠀⢹⡄⠀⠀⣾⠁⠴⠋⠉⣽⠛⣦⠈⢷⠀⠀⢀⡟⠀⢺⡁⠀⠀⢸⠇⠘⣇
⠸⡇⠀⢾⠀⠀⠀⢹⠀⠀⡿⠀⠀⢸⠀⠀⢸⡇⠀⣺⠀⠀⢸⡇⠀⠀⣧⠀⣴⠛⣳⠘⠛⢋⠀⣸⠀⠀⠸⡇⠰⣏⡷⠀⣰⠏⠀⠀⡿
⠀⠳⣄⠈⠳⠦⠶⠋⢀⡼⠃⠀⠀⠈⢧⡀⠴⠓⠒⠻⠦⣠⡞⠀⠀⠀⠙⣆⠈⠛⠿⠶⠚⠋⣠⠏⠀⠀⠀⠻⣄⠀⠀⠀⣇⣀⣄⡼⠃
⠀⠀⠉⠓⠶⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠞⠉⠀⠀⠀⠀⠀⠈⠛⠶⠤⠴⠶⠛⠁⠀⠀⠀⠀⠀⠈⠓⠶⠤⠴⠟⠋

⠀⠀⣠⡶⠛⠛⠛⠲⢦⡀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠶⣄⠀⠀⠀⠀⠀⣠⣴⠚⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠲⢦⡀
⠀⡾⠁⡗⢳⡞⢳⡀⠀⠹⡄⠀⠀⢠⡟⠀⠀⡤⠶⣄⠀⠈⢳⡀⠀⠀⣰⠋⣿⠚⡖⠛⣆⠀⠘⣧⠀⠀⠀⡾⠁⠀⠀⠀⢠⣶⠆⠹⡆
⢸⡇⠀⡇⢸⡇⢸⠙⡆⠀⣿⠀⠀⢸⠀⢐⣚⣃⣀⡘⣒⠀⢸⡇⠀⠀⣏⠀⣿⠀⡇⢀⡟⠀⠀⢸⠀⠀⢸⡇⠀⠀⣄⣴⠋⠈⠀⠀⣿
⠈⢧⡀⠃⠘⠃⣸⡼⠁⣰⠇⠀⠀⠸⣆⠈⠉⠉⠉⠉⠉⠀⣼⠃⠀⠀⢻⡄⠛⠀⠃⡞⢠⣶⢀⡟⠀⠀⠈⢧⡀⡴⠋⠉⠁⠀⠀⣰⠇
⠀⠈⠳⢦⣄⣉⣉⣽⠟⠃⠀⠀⠀⠀⠈⠳⣤⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠙⠦⣤⣀⣉⣩⡴⠋⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣠⢞⣽⠿⣶⡄⠀⠀⠀⠀⡀⠃⠑⣶⡥⠀⠀⠀⠀⢀⣤⡾⠰⣇⡀⠰⣄⠀⠀⡖⡞⠀⠄⠘⣶⡆
⠀⠀⠀⠈⠒⢉⣯⣶⡜⣿⡀⠀⠀⣠⠝⢘⢯⢹⣷⠀⠀⠀⢠⣾⠑⠊⠀⠈⣿⣛⣼⠀⠀⠙⠁⣎⠈⠙⡍⠁
⠀⠀⠑⢶⣾⣟⣋⡼⢻⡸⠁⠀⢰⣿⢀⠤⠎⢸⡁⠀⠀⠀⢸⣯⣼⠃⠀⠀⢠⣿⠽⠀⠀⠈⣶⠻⢠⢧⡿
⠀⠀⠀⢰⣯⠤⠤⠖⠃⠀⠀⠀⠘⢿⣸⠀⠀⢽⡧⢤⡀⠀⠈⠳⠙⠛⠦⢰⠟⠋⠀⠀⠀⠀⠅⢀⠏⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⡠⠤⣿⠤⣀⠄⠀⢀⠐⢲⡅⡄⠀⢀⣀⣀⠀⠀⠀⠀⢴⠤⣤⣼⣯⡤⠀⠀⠀⠀⡾⠂⡇⢺⡆
⠀⠀⠀⠀⠃⠀⡇⠀⠙⠀⠀⠀⣖⣩⠶⠃⠀⣀⠀⢤⠗⠀⠀⠀⢀⠄⠀⠘⠿⠀⠀⠀⠀⠀⡳⣴⡇⡼⡃
⠀⠀⠀⢷⣞⢗⡷⠲⣞⡿⠀⠀⠘⣷⣷⠰⠻⡿⠧⡀⠀⠀⠀⢠⠁⣰⣶⠶⢻⡽⠀⠀⠀⢈⢽⢿⣯⢿⢏
⠀⠀⠀⠀⠀⣬⠟⢄⠀⠀⠀⠀⢠⡟⣰⠇⢠⡿⢠⡇⠀⠀⠀⠀⠐⡅⠹⡀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠒⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⢸⡇⠀⠀⠀⠀⠀⠀⢬⣉⢭⠇⠀⠀⢿⣶⣜⣙⣤⣾⠇
⠀⠀⠀⢠⡶⡌⠉⠀⢠⠄⠀⠀⣠⡤⢶⠛⢋⣩⣴⣿⡀⠀⠀⠰⠆⣤⣀⡀⣤⡆⠀⠀⠀⠀⠉⠛⣧⡟⠁
⠀⠀⠀⣰⠛⢿⡷⢦⣼⠑⠁⠈⠁⠀⠈⠙⢿⠻⡟⡍⠂⠀⠀⣠⠾⡟⢉⣿⡿⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠒⠃⠀⠴⠃⠀⠘⠂⠀⠀⠀⠐⣲⠞⠋⠀⠁⠀⠀⠀⠀⠷⠀⠹⠆⠸⠆⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡴⠦⣄⠀⠀⠀⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⡤⠆
⠀⠀⠀⠀⢸⡀⠀⠘⣆⠀⣼⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠈⠃⠀⠀⢹⣰⡏⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⣤⣤⣼⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠃⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠊⠉⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠙⠊⠉⠘⠀⠃
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣰⢿⣆⡴⢿⡄
⠀⠀⠀⢀⡞⠋⠙⢦⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⣿⠁⢸⣧⡶⣆
⠀⠀⠀⠘⣆⣀⣀⡾⠀⠀⣰⠚⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⡟⠀⣿
⠀⠀⠀⢀⡈⠉⠉⠀⠀⠀⠻⣄⢀⣠⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⣷⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⡇⢀⡿
⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠋⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠇⠀⢸⣧⠟⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢷
⠀⠀⠀⠀⠀⠢⠐⠗⠙⠪⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠲⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠐⡼⠢⠂
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣠⣤⠀⡠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⡿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣰⡾⢻⣇
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡿⠋⠀⠀⡿
⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⢷⣄
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠀⠀⠀⠉
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣴⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠦⠤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⠠⡠⠄⡄⠤⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⡴⡆⣤⠤⠤⡄⡄
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠉⢿⡄⣰⠟⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢀⣠⣄⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠸⣧⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠛⠁⠹⠶⠛⠁⢻⠾⠋⠁⢻⠄⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⣿⣠⠶⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⣿⠶⠶⢿⡷⠶⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣻⣏⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀⣠⡶⣷⣀⣠⠶⣧⣀⣤⠾⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠙⠚⠋⠀⠀⠀⠀⠀⠐⠛⠁⠀⠘⠋⠁⠀⠙⠋⠁⠀⠙⠂⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠠⠠⠦⠴⠴⠰⠄⠴⠴⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠄⠦⠤⠴⠆⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠰⠤⠠⠦⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡲⢤⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠤⣄⣀
⠀⠀⠀⠀⠀⣠⠾⢫⣴⣿⣛⠿⣯⣦⠀⠀⠀⠀⠀⢠⣤⠀⠀⣈⣹⣿⡟⠃⠀⠀⠀⠀⠀⢀⣴⣾⠟⠀⢻⣧⣄⣠⡙⣦⠀⠀⠀⣯⣹⡇⠀⠐⣀⠀⣹⣿⡇
⠀⠀⠀⠀⠐⠁⠶⠈⢉⣧⣾⣆⠹⣿⡇⠀⠀⠀⢀⣴⡍⠃⡝⣫⠄⣿⣷⠀⠀⠀⠀⠀⢴⣿⠋⠖⠀⠀⠀⠈⣿⠟⠳⠘⡆⠀⠀⢈⠏⠀⣿⠁⢈⠉⣏⢹
⠀⠀⠀⢇⣀⣤⣴⣾⡿⠟⢹⣿⡇⢹⡇⠀⠀⠀⣼⣿⠀⠀⠊⠴⠃⣿⠋⠀⠀⠀⠀⠀⡿⣿⠃⣶⡄⠀⠀⠀⠈⢻⣿⢰⡃⠀⠀⠘⢂⣠⣿⡄⢸⡄⣽⡆
⠀⠀⠀⠀⠹⢋⣿⡿⠦⠔⠛⢁⡆⠜⠀⠀⠀⠀⣿⡟⠀⡞⠛⠃⣀⣿⠀⠀⠀⠀⠀⠀⢻⡙⣿⣷⣀⠀⠀⠠⣨⣽⡟⠋⠀⠀⠀⠀⢠⢿⠈⢇⣼⢸⢿⡇
⠀⠀⠀⠀⠀⢾⣵⡴⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⢸⠿⢀⡇⠀⠀⢠⣿⣤⠴⣤⠀⠀⠀⠀⠛⠦⠙⠛⢷⠂⢰⡿⠉⠁⠀⠀⠀⠀⠀⠘⡀⢀⡼⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⣀
⠀⠀⠀⠀⠀⡀⢀⣀⣸⣇⣀⡀⢀⡀⠀⠀⠀⠀⠶⢽⡝⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣆⣀⣀⡠⣽⣟⣂⣤⠄⠀⠀⠀⠀⢠⣯⡆⢸⠀⢾⡇
⠀⠀⠀⠀⠀⢹⡏⠀⢹⡏⠀⢨⡏⠀⠀⠀⠈⢄⡤⠞⢁⡼⠀⠀⠈⠙⠋⠉⠲⡄⠀⠀⠀⠀⠀⠣⠈⠉⠁⢧⣽⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⢈⣷
⠀⠀⠀⠀⢠⠃⠘⡀⢸⡃⢀⠊⠈⢂⠀⠀⠀⢾⣤⠞⡋⠉⠀⣈⣤⣄⠀⢹⠚⠁⠀⠀⠀⠀⣠⡔⠂⠀⠀⠈⣙⣃⣀⠀⠀⠀⠀⢀⡲⣝⣺⣿⣀⣟⡥⢂
⠀⠀⠀⠀⢿⣶⣛⡻⢺⠷⠺⣶⣛⡻⠂⠀⠀⠈⢳⣾⣿⡄⠿⠻⣿⡿⢦⡘⠀⠀⠀⠀⠀⢠⡆⠀⣼⣿⡶⠿⠞⣧⠽⠀⠀⠀⠀⠀⣉⣿⣿⣿⣸⣿⣏⡁
⠀⠀⠀⠀⠀⠉⠉⠀⣻⡷⡁⠈⠉⠀⠀⠀⠀⠀⢠⡿⠉⣷⠀⠀⢹⡆⠀⣱⠀⠀⠀⠀⠀⠉⠀⢴⠉⠸⡅⠀⠘⠋⠀⠀⠀⠀⠀⠀⠁⠊⢐⣿⣗⠈⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠿⠎⠁⠹⠂⠀⠀⠀⠀⠀⠐⠛⠓⠚⠗⠀⠰⠛⠃⠺⠛⠂⠀⠀⠀⠀⠀⠀⠘⠇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠹⠂


⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠟⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠾⠿⣆⠀⠀⠀⠸⣄⡀⢀⡏⣧⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠋⣉⣁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡤⠸⡶⠏⠀⠀⠀⠸⣿⣿⣾⡤⢠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⣰⣤⠤⠉⠁⠀⠀⢤⢀⠀⠀⠀⢀⣤⣀⣒⡻⠛⠛⢉⣡⣴⣿⣇⠀⠀⠀⠀⢤⡖⢀⣄⠀⢁⠁⣄⣶⠁⠀⠀⠀⠀⠀⠈⠙⠋⣿⣈⡛⠋
⠀⠀⠀⠀⠀⢸⣏⣾⣴⣦⣤⠈⡷⢤⡇⠀⠐⢋⠊⠀⠈⠵⢶⣾⣿⣷⣿⡿⢌⠑⠀⠀⠀⠀⢃⣼⣿⠿⢿⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⠆
⠀⠀⠀⠀⣰⠏⠀⠚⢻⡏⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠉⢹⠆⠇⠈⠁⠀⠀⠀⣴⠋⠹⣇⠀⠶⢾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠓⠋⠀⠀⠠⠞⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠊⣛⡿⠛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠹⠦⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡥⠙⣷⡄⠀⠀⠀⠀⠀⢈⡷⢢⣄⣀⣤⡀⢀⡷⠀⠀⠀⠀⠀⠀⠀⣴⣾⠉⠀⠀⠀⠀⡈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣧⣠⣾⡇⡀⠀⠀⢠⣾⣯⣄⣿⠃⠉⣽⣷⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢋⣤⣶⣷⣦⣌⠛⣿⣧
⠀⠀⠀⢠⣶⡟⢛⠿⣽⣿⣿⣿⣮⣭⢆⠀⠀⠈⠉⢻⣿⢰⡏⠉⠻⣿⡆⠀⠀⠀⠀⠀⠦⣀⡙⢻⣿⣿⣿⣿⣿⣿⡿⠛⣁⡠⠂
⠀⠀⠀⠈⢯⠻⠀⠀⠉⠻⢭⡝⢣⠌⠀⠀⠀⠀⣀⣸⣿⣷⡓⠂⣸⡿⠿⡶⣶⡄⠀⠘⠲⠶⣷⣾⣿⣿⣿⣿⣿⣿⣷⣾⡷⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠴⠴⣶⣾⡟⠃⠀⠀⠀⠀⢸⠋⣉⣹⣿⢧⣾⡟⠁⢀⠴⠛⠁⠀⠀⠀⠾⠀⠏⠉⠀⠀⠁⠀⠈⠉⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠒⠋⠈⠉⠀⠀⠀⠀⠀⠀⠛⠒

⠀⠀⠀⠀⠀⠀⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠐⢦⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠶⠶⠖⠿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠂⠀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣤⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠃
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠴⣾⣿⣿⣿⣶⣷⣦⠶⣦⡀⠀⠀⠀⠘⣿⣿⣿⡿⠿⢿⣿⠿⢷⣤⣄
⠀⠀⠀⠀⠠⢴⣿⣿⣿⣻⣿⠋⠟⠿⠟⠉⠀⠀⠀⠀⠃⣅⠈⠙⠉⢿⣿⢧⠀⠘⠉⠀⠀⠀⢸⡏⠾⣍⣀⠀⠘⣿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠘⠓⠀⠈⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⡀⠀⣤⡀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣄
⠀⠀⠀⠶⢿⣦⡀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣶⡄⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢰⣾⣿⣿⡏⠀⠀⠈⠻⢷⣤⣀⡀⠀⠀⡼⢫⣿⣿⣿⣿⢿⣧⡟⠀⢹⠁⠀⠀⠀⠀⠀⢻⡏⢿⢿⣿⣧⣿⠄
⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠽⠟⠀⠿⠟⠀⣾⠋⠀⠀⠾⠁⠀⠀⠀⠀⠰⠞⠃⢸⠐⣿⠟
⠀⠀⠀⠘⠹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⠐⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⡿⠀⠀⠀⠀⠀⠻⠛⠛⠛⠉⠙⣿⠋⠉⠉⠉⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⢠⣤⣤⠀⠀⣾⣿⡿⢿⣿⣯⠉⢹⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⠛⠋⠿⡇⠀⠀⠀⠠⢿⣿⣿⠷⠂⢀⣼⣿⣇⠀⠀⠈⠀⠀⠀⠙⠛⠰⠿⠉⠀⠀⢸⣿⣏⣩⣿⡇
⠀⠀⠀⠀⠀⢻⣻⣄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣦⣤⡾⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⡶⢶⣄
⠀⠀⠀⠀⡀⢶⣶⣶⢀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠙⢿⡆⠀⠀⠐⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢻⡇
⠀⠀⠐⠲⠰⣆⣿⣷⠚⠶⠀⠀⠀⠠⡄⢰⡟⠉⢷⣼⠃⠀⠀⠀⠘⡿⠻⠿⡗⡛⠀⠀⠀⠀⢻⣷⡀⠀⠰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠿⠶⠛⠁⠀⠀⠀⠀⠈⠑⠀⠐⠈⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⢠⣤⠄⠀⢄⠀⠀⠀⠀⠀⣠⣦⣴⣶⣄⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⠘⠉⢱⣀⣬⡀⠀⠀⠀⣰⡞⠉⠉⠉⠻⠃⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢳⣄⣴⣀⠹⠛⠀⠀⠀⠀⠙⠃⠀⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠶⠠⠄
⠀⠀⠀⠀⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠒⠂

⠀⠀⠀⠀⢀⠀⠠⣀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣴⣆⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠠⢤⠤⠤⢤⢟⠀⠀⠀⠀⡟⠠⠍⠉⢩⣄⢻⠀⠀⠀⠀⠘⠁⢸⡄⠀⠀⠀⠀⠀⠀⣴⡒⠀⠀⠒⠢⠄
⠀⠀⠀⠀⣯⢿⣼⣿⡿⠀⠀⠀⠀⠿⠘⠒⠀⠀⠻⠿⠀⠀⠀⠠⡤⡤⢸⡇⠤⣤⠀⠀⠀⠀⢽⣧⣤⣤⣤⠀⠁
⠀⠀⠀⠀⠈⠀⠁⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠟⠛⠛⠛⠛⠛⠛⠷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣉⠀⠀⢧⠀⢹⡿⣦⣾⣿⠂⢸⠃⢠⡌⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢁⣤⣀⣿⣴⠀⠘⡄⢀⠁⢿⠃⠁⠀⡏⠀⣸⣷⣦⣀⣀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣾⠟⠳⣄⠀⢨⡽⣿⠛⠶⠀⢡⠀⣀⣈⣀⡀⠰⠁⠸⣿⠀⣹⡟⠉⢀⠔⠉⢻⣄
⠀⠀⠀⠀⣠⡿⠁⣶⢆⣈⠳⣄⠀⠛⣀⣤⠶⣛⣫⣭⣭⣭⣭⣛⡳⢦⣍⠋⠛⢁⠔⠁⠀⢴⣤⡙⣧⡀
⠀⠀⠀⢰⡟⢀⣼⠛⣼⠏⠀⠀⣱⡾⣫⣶⣯⣿⣿⢿⣯⣽⣿⣿⣿⣷⣮⡻⣶⡁⠲⣦⡾⢋⣹⣇⠘⣷
⠀⠀⢠⡿⠁⠈⠃⢿⠃⠀⠀⣼⢫⣾⣿⣿⣽⣷⣿⢋⣉⡉⠉⠛⠻⣿⡟⣿⣮⢳⡄⠘⣷⠋⠁⠉⠁⢸⣧
⠀⠀⣼⠟⠓⠲⠤⠌⣀⡀⣼⢣⣿⣾⣿⣿⡁⣀⠀⠉⠀⠙⡆⠀⠀⠉⣻⣿⣻⣧⢻⣄⡈⠥⠤⠒⠛⠉⢿⡄
⠀⠀⣿⠀⡀⢀⣤⡄⠀⢨⡟⣾⡷⣿⠋⠉⠉⠉⠀⠖⠀⣐⢇⢰⠂⠀⠐⢿⣿⣿⡏⣧⠀⢠⡆⣶⣳⣄⢸⡇
⠀⠀⣿⠀⣴⡾⠷⠿⢦⢸⡇⣿⢷⣿⣤⠄⠀⠀⢨⠀⠈⠉⢇⡀⠉⠀⠀⢸⣷⠻⡇⣿⠀⢸⣧⣭⡉⣿⢸⡇
⠀⠀⣿⠠⠟⠛⠁⠀⠀⢘⣧⢿⣾⣿⣇⠀⠀⠀⠀⢣⡀⠐⢺⠕⠀⠀⢀⣿⣿⣿⢇⣟⠀⠈⠻⠾⠓⠋⢸⡇
⠀⠀⢹⣧⣤⠤⠖⠚⠉⠁⢻⣞⣿⣿⣿⣿⡟⠀⠀⠀⡠⠀⠘⠀⠀⣠⣾⡷⣾⡟⣼⠃⠀⣉⠓⠒⠦⢤⣾⠁
⠀⠀⠈⣿⡀⣀⣠⣖⣰⣆⠀⠻⣮⢿⣽⣿⣿⣶⣶⣻⣷⣦⣤⡶⣿⡿⢿⣿⢏⡾⢃⢀⣾⣽⣇⡁⠀⣰⡏
⠀⠀⠀⠘⣧⡈⠛⠏⢹⠏⠓⠀⡙⠷⣭⡻⢿⣽⣿⣛⣿⣿⣿⣷⣿⠿⣻⡵⠟⢄⠛⡉⢳⣌⣉⣷⢰⡟
⠀⠀⠀⠀⠘⢷⡀⠀⠀⢂⡴⠊⠶⣦⠈⠙⠳⢾⣭⣽⣿⣿⣯⣽⠶⢛⠉⠀⠀⠀⠑⢄⠀⠈⠉⣱⠟
⠀⠀⠀⠀⠀⠈⠻⣦⡴⠋⠀⢀⡴⢋⠀⡀⠀⡐⢀⡄⢀⡀⢀⡘⡔⢿⣳⡰⣄⢹⣤⡈⠳⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⠷⣯⣰⠇⢠⠇⠽⣷⠊⢻⣯⠆⢳⠈⠉⢷⡽⠛⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⡛⠀⣾⠀⠀⢿⣤⡜⠃⠀⠸⡆⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣦⣤⣤⣤⣴⠶⠶⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣀⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣈⣹⣿⣷⣌⢻⣷⡄⠀⠀⠀⠀⠀⢀⣤⣿⣿⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣨⣟⣿⣿⣿⣿⣧⢻⡇⠀⠀⠀⢠⣶⡻⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢀⣾⠟⠋⠉⠻⣿⣷⡀⠀⢠⣾⣿⠏⠉⠛⢿⣦
⠀⠀⠀⠀⠀⣾⠃⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠸⠃⠀⠀⠀⣿⣿⣿⡾⠿⠿⠍⠉⠉⢿⣿⣦⣤⣄⠀⠘⣿⣀⠀⣠⡷⢹⣿⣷⣤⣿⣿⠁⣧⡀⠀⣸⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠙⣿⡁⠀⠀⠀⠀⠀⠀⣹⡋⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠈⠛⠻⠛⣱⣾⣿⣿⣿⣿⣿⣷⡝⠛⠛⠛⠁
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⣀⣈⣁⠀⠀⠀⠀⣠⣴⣿⡇⡀⠀⠀⠀⠀⠀⢀⣠⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⠟⢻⡇
⠀⢀⣴⢶⣾⣿⣿⣿⣿⣿⣿⣄⠸⡏⣹⣿⡇⠀⠀⠀⠙⠛⢻⣿⣧⣄⣀⣘⣿⣶⡻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣿⣿⣿⠟
⠀⢸⣯⣿⣿⣿⣿⢿⣧⢨⣿⣿⣷⣾⡿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⣛⡿⠃
⠀⠀⠙⠛⠋⠀⠙⢷⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣠⠄⠤⡀⢀⣴⣾⣿⣿⣷⣄⠀⢠⠄⠠⡀⠀⠀⠀⠘⣶⣄⣸⣦⣷⣼⣷⣼⣧⣾⣠⣴⡗⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠘⣧⡲⠴⣣⣿⣿⣿⣿⣿⣿⣿⣷⡸⠤⢂⡿⠀⠀⠶⣶⣿⣿⡿⢿⣿⣿⣿⣧⣿⢿⣿⣿⣷⡶⠂⠀⢸⣿⣷⣤⣤⣀⣤⣤⣤⣤⣄⣠⣤⣴⣿⣿
⠀⠀⠉⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⡟⠻⠛⠛⠁⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⠄⠀⠀⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⡿⢿⣿⣿⡿⠿⣿⣿⣿⣯⣥⣀⠀⠀⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠈⢙⣻⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⡋⠁⠀⠸⠿⠃⠘⣿⠛⣿⣿⣿⣿⡿⢻⡿⠀⠙⠿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⡟⠁
⠀⠐⢤⣊⣀⣤⣿⣯⡉⣿⡟⣩⢿⣯⣄⣀⣠⠄⠀⠀⠐⠛⢛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠈⠉⠁⠸⡀⣠⠟⢧⡀⡀⠃⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋
⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⡀
⠀⠀⣾⡇⠘⣦⠀⠀⡀⠃⠘⢀⠀⠀⣴⠁⢸⣷⠀⠀⠀⠀⠀⣀⣤⠶⠟⠻⡏⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⠞⠋⠙⠛⣿⣄
⠀⠀⠛⢧⡾⠋⠀⠀⣃⠀⠀⣘⠂⠀⠙⢷⡸⠛⠀⠀⠀⣠⠞⠉⠀⠀⠀⢠⡇⠀⠀⠀⠈⠛⢦⡀⠀⠀⢠⣾⣯⡉⠀⠀⠀⠀⢿⡏
⠀⠀⠀⢹⣏⠀⠀⠸⣿⣶⣶⣿⠇⠀⠀⣸⡏⠀⠀⠀⠀⢁⠀⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡿⠿⡃⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢿⣦⣠⣾⣿⣿⣿⣿⣷⣄⣴⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣷⣦⣤⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠙⣋⢿⣿⣿⣿⣿⡿⣙⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣷⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠛⠋⣟⠳⣦
⠀⠀⠀⢀⡴⠊⡡⠖⢉⠻⢿⡉⠒⢌⠑⢤⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⣼⣿⡀⠀⠀⠙⠿⠿⠟⠀⠀⠀⡞⠁⡽⠛⣿⠿⣿⡁⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠣⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠃⠀⠘⢿⣤⣖⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣄⡁⠀⣁⣸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠻⣧⡄⠀⠀⠀⠀⢀⣤⡻⠃⠀⠀⠀⠐⢉⠉⠉⠉⠉⠙⠛⠿⣿⣶⣄⡀⢀⣠⡴⠂
⠀⠀⠀⠀⠀⣼⣿⣿⣁⡄⠀⣄⣹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢫⣿⣷⣶⣶⣾⣷⣿⠁⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⢀⡛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⠛⠙⣿⣿⣿⡇⠀⠀⠀⢀⡤⢾⣿⣿⣿⣿⣿⣿⣿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣆
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⠉⠙⡇⠀⠀⢰⣿⡇⣾⣿⠻⣿⣿⡟⣻⣿⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠃⠀⠀⠸⠟⠃⠈⢻⣿⣿⣿⣿⡟⠁⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⢠⠞⠉⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⢦⣀⣀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡼

⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢰⠏⣉⡉⢿⡇⠀⠈⣷⠀⠀⠀⠀⠐⢯⣤⢹⣆⢀⣰⠏⢠⣌⣿⠀⠀⠀⠀⠀⠛⠉⠛⡶⠶⢶⡟⠁⠈⠁⠀⠀⠀⠀⠀⣴⠞⢯⡉⠉⠙⠳⣦
⠀⠀⠀⠀⠸⣆⣈⡷⢸⠀⠷⡤⠟⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠛⢦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⡼⠃⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠠⡟⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣴⣀⣼⠷⠶⠾⣧⣀⣴⡄⠀⠀⠀⠀⠀⠈⠻⠯⣤⣤⣽⣶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣴⠛⠉⠙⢷⡀⠀⠀⠀⠀⠀⠛⠂⣿⠋⠙⡟⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡟⠉⣿⠛⣦
⠀⠀⠀⠀⣀⡰⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⣿
⠀⠀⠀⣾⠉⠹⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⣧⣶⡄⠀⠀⠀⠀⠀⢾⣦⣤⣽⠆⠀⢿⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢿
⠀⠀⠀⠙⠳⠞⠋⠀⠸⣇⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⣼⠇⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠋⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⢴⣦⣴⣾⠂⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢻⡄⠀⠀⠀⠀⠀⠀⠘⠃⣿⠁⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠹⡿⠉⢷⠏⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣼⠁
⠀⠀⠀⠀⠠⣄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣠⡴⣄⡴⣦⡀⠀⠀⠀⠀⠀⠀⠰⣿⣼⡷⠖⢾⡿⣶⠄
⠀⠀⠀⠀⠀⣸⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣷⠞⣷⠀⠀⠀⠀⠀⠀⠼⠃⠘⠟⠀⠻⠃⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣧
⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠴⠿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠘⠧

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⠿⣿⣟⠛⢻⣿⡟⠿⢶⣶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠿⠛⠉⣿⡂⠀⠀⠰⠀⣄⠑⢡⡄⡀⠀⠀⠀⢸⡟⠉⠛⠿⣳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠛⠀⠀⠀⠀⠸⣧⠀⠀⠀⠁⠙⠀⠈⠁⠀⠀⠀⠀⣿⠃⠀⠀⠐⠍⠍⠙⠿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠫⡐⠨⠄⠓⡆⠀⠀⠀⢻⡄⢀⣀⣀⣀⣦⣇⣀⣀⣀⡀⣸⡏⠀⠀⠀⠔⡉⢈⢀⡄⠽⠙⠯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡛⠁⠀⠀⠀⠮⠄⠊⠂⢀⣦⡤⠶⠚⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠙⠓⠶⢤⣀⣃⠂⠐⡠⠀⠀⠀⠀⠈⣫⣿⣄
⠀⠀⠀⠀⠀⠀⣠⣾⠗⠙⢿⣦⡀⠀⠀⠀⢠⣦⠶⠛⠁⠀⠀⢃⠀⠀⠀⠦⠀⠀⢠⡠⠀⠺⠀⠀⠀⠀⠀⠈⠙⠻⢥⡀⠀⠀⠀⢀⣼⠟⠁⠻⡷⣄
⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠙⠻⣄⣀⣴⠋⠀⠀⡀⠀⠀⠈⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠰⠀⠙⢲⣄⣴⠟⠁⠀⠀⠀⣈⢞⢧⡀
⠀⠀⠀⢀⣾⡟⡉⠹⢂⠄⣀⠀⢀⡼⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡘⢳⡄⠀⠀⠀⡠⠃⢢⠫⣳⡀
⠀⠀⢀⣾⠏⠜⢀⠂⠘⣀⠁⣰⠋⠀⠀⠓⠀⠀⠀⡀⢠⡄⠀⠀⡄⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠁⠀⠹⢿⣌⠡⡂⠜⢀⡑⣽⣳⡀
⠀⠀⣾⡏⠀⢄⡍⠊⡀⠃⣼⠋⠀⠀⠐⠠⢠⡂⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠠⠄⠀⠀⣀⡀⠀⠀⠀⠀⠶⠀⠀⠘⢧⣆⢠⠊⠀⠈⠀⢡⢳⡀
⠀⣼⡿⠀⠀⠀⠀⠐⠂⣼⠁⠀⠠⠄⠀⢠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠠⠆⠀⠀⠀⣤⡀⠈⣿⠁⠀⠀⠀⠀⠀⢛⣧
⢠⡿⠷⠶⣦⣤⣀⡀⣰⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⠲⣄⠀⠈⠢⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠸⣇⣠⣤⠶⠶⠛⠛⣻
⢸⣿⠀⠀⠀⠀⠉⠉⣿⠀⠀⣄⠁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⠃⠑⢤⡀⠀⠙⡆⠀⠀⠈⢆⠀⠾⠆⠀⠀⠀⠀⢠⠄⠀⡀⠀⢠⡤⠀⢻⡁⠀⠀⠀⠀⠀⣷
⣿⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠄⠀⠀⣸⠁⢠⡌⡇⠠⡀⠀⠈⡆⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣤⠄⠠⡀⢠
⣿⠁⣀⣀⠇⠏⡆⢸⡇⠀⠀⠠⠀⠀⠀⠛⠀⠀⠀⠶⠀⠀⠀⣁⡌⡀⠀⢾⠀⠀⠀⣧⠀⠀⠀⠀⠇⠀⣄⡀⠀⠀⠀⠀⠀⠠⡴⠀⠀⣶⠀⠈⣿⠀⠁⠌⠡⡈⢆
⣿⣻⠀⠒⡆⠁⠒⢿⡇⠀⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠣⠁⢀⠀⠈⣧⡀⠀⢹⠀⠀⠀⡘⠀⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⢀⡟⢄⠩⡍⣂⠃⡾
⣿⡏⠁⠀⠀⠀⠀⢸⡇⠀⠋⠀⠀⠁⠀⠈⠀⠀⠀⠀⠻⠃⠀⠀⠀⠶⠈⠓⠨⡞⠀⠋⠀⠀⠊⢀⣤⠀⠀⠠⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠑⠂⠉⠈⠘
⢹⣟⠀⠀⠀⠀⠀⢀⣿⠀⠀⡀⠀⠀⢀⡔⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⣾⣅⣀⠀⠀⠀⠀⣞
⠘⣿⣤⣦⡶⠶⠛⠋⠹⡇⠴⠀⠀⠀⣀⠉⠀⠀⠆⠀⠁⠀⠀⠀⠀⠙⠁⠂⠀⠐⠂⠀⠀⠈⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⢰⡏⠉⠙⠛⠿⠶⣶⣾
⠀⢻⣯⠀⠀⠀⣀⠀⠀⢹⡄⠀⢀⠁⠀⠀⢀⡀⠀⠤⢀⣀⠈⠄⠀⠀⠐⠂⠀⠀⠄⠀⡔⢦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⡈⠀⠰⠀⢀⡟⠀⠀⠀⠀⠀⠀⣆⡟
⠀⠈⢿⣧⠠⠊⠰⠁⡔⡂⠻⣄⠈⠐⠀⠀⠙⠃⠀⠀⠈⠉⠀⠠⡆⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠒⠀⠈⠁⠀⠀⢠⣞⣀⠃⠌⢁⠀⠀⡜⡼⠁
⠀⠀⠈⢿⣦⣀⠇⢲⢀⠌⠵⠙⣦⠀⠀⠀⢀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡶⠀⠀⠀⣀⠀⠀⠐⠇⠀⣰⠟⣁⠤⡑⢆⡢⢑⡴⡽⠁
⠀⠀⠀⠈⢿⣧⠀⠀⠉⠀⠀⠀⠈⢳⣄⠀⠛⠁⠀⠀⠀⠀⢀⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢠⠀⠀⠀⠙⠁⠀⠀⣠⡞⠁⠀⠀⠀⠈⠐⠐⡞⡽⠁
⠀⠀⠀⠀⠈⢳⣵⡄⠀⠀⠀⠀⣠⠞⠉⠳⣤⡀⠀⠀⠈⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠲⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⢀⣤⠞⠉⠹⣦⡀⠀⠀⠀⢠⢎⡞⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣦⢀⣴⡿⠋⠀⠀⠀⣶⡿⠷⢤⣀⠀⠒⠀⠀⠀⠀⠉⠀⢀⡄⠀⠀⠀⠈⠋⠀⠀⠀⢀⣤⣶⠋⠁⡀⠀⠀⠈⠻⣷⣄⠴⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣫⡀⠀⠀⠀⠀⠀⢃⡦⣀⠈⠙⠳⢶⣤⣄⣀⣀⣀⣀⣁⣀⣀⣀⣠⣤⡶⠖⠛⠩⣯⡍⢶⡻⡌⢄⠀⠀⢀⡬⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣶⣄⠀⠀⠎⡼⢱⢏⠇⠀⠀⣸⠇⠀⠉⢩⠛⠛⠛⠋⢩⠉⠀⠘⣷⠀⠀⠀⠠⡸⣆⠳⡜⣦⡷⢖⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣶⣾⣅⢏⣈⠀⠀⢠⡿⠀⠀⠀⠸⡉⠹⠸⠉⡹⠀⠀⠀⢻⡆⠀⠀⠀⠀⣈⡵⣟⡭⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢯⣶⣤⢀⣼⡇⠀⠀⠀⠀⠠⠑⠐⠡⠂⠀⠀⠀⢸⣿⡀⢤⣒⡭⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠿⢿⣶⣶⣶⣘⣯⣠⣶⣦⡿⠿⠷⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⠀⣴⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣛⡛⣷⣮⣿⢿⣿⣷⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⢠⣳⣷⣿⣻⣷⡜⣏⣿⣿⣿⣦⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⣰⣿⣿⡟⠁⠀⠻⠍⣉⣿⣟⠟⠋⠁⠁⠉⠹⣿⣷⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⣿⣿⣿⡃⠀⢀⡄⠚⠉⠁⠐⢂⡒⠀⣄⠀⣠⣿⣿⣇⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠴⠀⠀⠀⠀⠄⠄⠀⢘⠀⠀⢸⣿⣿⣿⣷⡀⢸⡄⠀⠢⠀⠈⠀⠀⠀⠈⡛⠛⠿⣿⣿⠀⠀⢘⠀⠀⠄⠄⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠸⣿⣿⣿⡏⠀⠚⠙⡂⢀⣀⠸⢠⠀⠀⠀⠀⠀⠀⣹⡟⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣤⡀⠀⠀⠂⠉⠀⠈⠁⠀⠀⢠⣾⣷⣾⣿⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻⣿⠿⠇⢀⢆⣠⣀⡀⠀⠀⠀⠀⠰⣿⣿⡿⠁⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣟⣃⣼⣟⠃⠀⣀⣠⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⠛⠛⠉⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⢀⣀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⢻⣤⣀⠄
⠀⢠⠞⠉⠀⢀⣀⡁⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡀⣎⡤⢦⠻⠀⢠⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⢶⡆
⠀⠘⠻⠧⢀⡏⠠⠂⠀⢼⣇⡀⠀⠀⠀⠀⠀⠀⠘⢶⡃⡀⠈⠛⠗⢶⡦⢳⣔⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠰⣿⣄⡤⢩⡑⠢⣄⢴⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠐⣤⡿⣨⢀⡇⡪⡥⣾⠇⠀⠀⠀⠀⠀⠀⣟⠛⠀⠀⣠⠄
⠀⠉⠁⠀⠀⡠⠖⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢰⠏⢨⡺⢇⡴⡿⠀⠀⠀⠀⠀⠀⠀⠚⠷⠶⠿⡋⢀⠀⠠⠠⠶
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢤⣄⢁⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠈⠳⣦⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⢋⡿⠻⣋⢳⣄⡀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠈⢉⠙⠙⠛⠦⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠺⠦⢁⣙⣀⣀⣘⣈⢠⡟
⠀⠀⠀⠀⠀⠐⣷⠀⠀⠐⢌⠁⠘⠅⠀⠀⠀⠀⠑⠆⡁⠴⠀⠀⠀⠀⠚⠛⣿⣡⠀⠀⠀⠀⠀⠀⠀⡴⠰⡉⠡⡈⠉⠬⠉⣆⠴
⠀⠀⠀⠀⠀⠀⠻⣦⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠷⣞⠂⠁⠰⠆⣿⡿⡇⠀⠀⠀⠀⠀⠀⠑⠚⣽⢧⡴⠧⡴⢯⡟⠚
⠀⠀⠀⠀⠀⠀⠠⠤⠙⠲⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠶⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⡄⠀⢀
⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢁⠒⠲⡌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡶⠃⠠⠀⠀⡆⢷
⠀⢷⣸⡧⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⣄⡤⠴⢷⡄⠀⠉⠱⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠆⠲⠆⠰⠤
⠀⠈⠢⠑⢀⡄⠰⠿⠃⣔⣐⠢⣄⡀⠀⠀⠀⠀⠀⠁⠈⣀⠀⠀⠀⠻⡖⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⡏⣿⠠⡛⢹⡆⣺
⠀⠀⠀⢠⣏⡄⠆⢠⡾⠳⠎⠑⣨⡝⠖⠀⠀⠀⠀⢿⣄⡀⠁⠸⣄⡀⠢⣤⣦⣤⠶⣌⠁⠀⠀⠀⠀⠀⠀⠀⢸⠟⣷⢈⠓⠏⢿
⠀⠀⠀⣀⠀⢀⣤⡴⠁⠘⣛⣩⢕⠛⠛⢆⠀⠀⠀⠈⠻⠶⠴⠶⠉⠙⠳⣤⣤⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⠇⡹
⠀⠀⠸⠷⠘⠁⠀⣴⠀⠁⠉⠀⠠⡕⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠒⡆⠀⠀⠀⢠⠒⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡞⠠⠀⡈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣠⡦⣄⠀⢠⡤⣄⠉⡀⠀⠀⠀⠀⠀⠀⢠⣏⡍⢫⡭⠹⣷⡆
⠀⠀⠀⠀⠀⢀⣉⠰⠲⣌⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢙⣢⣤⠌⢤⣴⡋⢀⡅⠀⠀⠀⠀⠀⠀⢰⣿⡉⠀⠙⢾⣿⡧
⠀⠀⠀⠀⠀⠈⢹⡷⡷⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠛⢁⣹⣦⣟⡈⠙⠳⠖⠀⠀⠀⠀⠀⠀⡸⣿⡟⠶⡞⢙⡍⠃
⠀⠀⠀⠀⠀⠀⠘⢣⠤⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡷⣤⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠻⣽⣀⣯⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠡⠉⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠕⠀⠠⢖⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣻⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢄
⠀⠀⣿⣿⣷⣤⣤⣤⡤⠀⠀⠀⣠⣶⣿⣿⣿⣦⡄⠀⠀⠀⢠⠪⡆⠉⢹⡿⡆⠀⠀⠀⠀⠘⢦⣶⣶⡴⠃
⠀⠀⠈⣿⡟⠛⡟⡏⠀⠀⠀⠀⠀⠹⢾⠛⠛⢻⠃⠀⠀⠀⠈⣰⠂⣻⡃⢀⡀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠛⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠉
⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡔⣿⣿⣦⣤⡍⠀⠀⠀⠀⠀⠊⠉⢉⣿⣿⠀⠀⠀⠀⢀⣤⣀⡴⣿⣷⠤⡄⠀⠀⢀⣾⡏⠉⢿⣶⣤⡀
⠀⠀⠀⡖⢻⣿⣿⠓⠀⠀⠀⠀⠁⠀⣡⠞⠙⢯⠀⠀⠀⠀⠈⠜⠿⠿⣿⣿⡃⠁⠀⠀⠈⠙⠛⢷⣀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠐⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⣀⣀⣀
⠀⠀⠐⠙⠻⣿⡿⠳⠀⠀⠀⠀⢹⣿⣿⣦⠀⡀⠀⠀⠀⠀⠈⠃⢀⣴⡄⠀⠋⠀⠀⠀⠐⠻⠢⠐⣿⣿⣽
⠀⠀⠀⣤⠞⠉⠷⡀⠀⠀⠀⠀⡦⢴⡿⣿⣷⣟⠉⠀⠀⠀⠀⠀⠉⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠂
⠀⠀⠚⠉⠀⠀⠀⠈⠂⠀⠀⠀⠁⠋⠂⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⣶⣒⣒⣛⣛⣒⣲⣶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢖⣻⣭⣾⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣹⣿⣿⡿⣶⣭⣝⡲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣫⣵⣾⣿⣿⣾⣿⡿⡽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣵⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢿⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣟⢦⡀
⠀⠀⠀⠀⠀⣰⢟⣼⣿⣿⣿⣟⢿⣿⣷⣿⣿⣷⣿⣿⣿⣿⡧⢿⣿⣯⣿⣿⣿⣿⡟⢣⣿⣿⣯⣽⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣧⡹⣆
⠀⠀⠀⢀⣼⣣⣿⣿⣿⣿⣿⣾⣷⣝⢿⣿⣿⡟⢻⣿⣿⡿⠇⠘⠋⢩⣍⣭⡉⠙⡙⠺⠿⣿⣿⣿⣿⣿⣿⡿⡻⣫⣾⣿⣿⣿⣿⣿⣌⢧⡀
⠀⠀⢀⡾⣱⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠿⣿⣿⠟⢋⣱⡄⠀⠀⠀⠈⢸⠋⠀⠀⠀⠀⣰⣄⡙⠻⣿⡿⣻⣯⣾⣿⣿⣿⣿⣿⣧⣽⣿⣎⢷⡀
⠀⠀⣼⣱⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⠌⠁⠀⠀⠻⠙⣀⣴⣶⢶⣶⣶⠶⣷⣦⣄⡳⠛⠀⠀⠈⠠⣿⣛⣿⣿⣿⣿⣿⣾⣿⣿⣈⣹⣎⢧
⠀⣸⢧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⢀⠀⠀⣠⣴⣿⣿⣹⣿⠟⡛⠛⠿⢿⣯⣿⡿⣦⣆⠀⠀⢀⡌⢿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣘⣇
⠀⡿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠏⡼⠁⣴⡿⣷⣿⣫⡍⠛⠋⠉⢧⠀⠀⠈⢻⣷⣿⢻⣦⠙⡿⠛⠂⢿⣿⣿⣿⣿⣿⢿⠿⣟⣻⣿⣯⢻
⢸⣧⣿⣿⣿⣿⣿⣿⣿⣽⣮⣉⣛⠃⠀⠀⣁⣼⣿⣶⠟⠻⠿⠟⢻⠖⠠⠬⡁⠠⠄⠀⢹⡿⢿⣿⣷⡀⠀⠀⠘⣋⣭⣤⣶⣶⣿⣿⣿⣿⣿⣿⡘
⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⡟⠀⠀⠀⢺⣿⢿⣿⣿⣇⣀⣀⡂⠀⠘⠃⠇⠘⠂⠀⠈⣿⣿⡿⢿⡗⢁⣀⡀⢹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣾⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡇⣤⡞⠣⢸⡿⣾⣿⡟⠿⠋⠉⠳⡀⠀⠀⣿⠀⠀⠀⢰⡟⢻⣿⣿⡇⢿⣝⣳⢸⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⡇
⢸⣸⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣷⠀⠀⢀⢸⣿⡿⢻⣿⣶⣶⣄⣠⣿⣢⢄⡬⠀⠀⣠⣿⣿⣿⣿⣿⡧⠀⠁⠀⣸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣩⡒⠀⠀⠈⢿⣿⣿⣿⡿⣯⣭⣶⣾⣯⣥⣤⣴⣾⣿⣿⣿⣦⣿⡿⠁⠀⠀⢠⣾⣍⡿⣛⣿⣿⣿⣿⣿⣿⣿⢣
⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⠗⡾⠄⠻⣿⣿⣶⣿⣿⣿⣏⣻⣿⣭⣿⣿⡿⢷⣿⣿⠟⠴⢾⣷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼
⠀⢹⡏⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⠻⣷⣿⡿⢻⣿⣿⣿⣿⣟⣿⣷⣾⠟⠋⠀⠀⠀⢁⣾⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣻⢣⡏
⠀⠀⢻⡹⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣙⣿⠆⡀⠀⠀⢰⣆⠉⢻⠿⠿⠷⠾⠿⠿⠟⠋⣦⣤⣄⠀⢀⡐⢿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡾
⠀⠀⠈⢷⡹⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⡾⢿⢶⣄⡻⠿⠁⠀⠀⠀⣿⢻⠆⠀⠀⠀⠙⢛⣫⣴⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢏⡾⠁
⠀⠀⠀⠈⢳⡝⣿⣿⣿⣿⣿⡿⣫⣿⣾⣿⣿⣿⣟⣿⣿⣷⡶⢤⣤⣄⣉⣉⣠⣤⡴⢰⣾⣿⣏⢹⣿⣿⡿⣷⣝⢿⣿⣿⣿⣿⣿⣿⢋⡞⠁
⠀⠀⠀⠀⠀⠙⣮⢻⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣿⣿⢿⣿⣿⣿⣷⢮⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣽⣾⣿⣿⡟⣡⠏
⠀⠀⠀⠀⠀⠀⠈⠳⣽⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡻⣿⣿⣿⣿⣿⣿⠋⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣝⡻⢿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⡿⢟⣫⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠮⣝⣛⠿⣾⢿⣿⣿⣿⣿⣿⣽⣿⣯⣹⣿⡿⣿⡿⣛⣫⠵⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠭⠭⢭⣭⣭⠭⠭⠭⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠤⣄⠀⠀⠀⠀⢀⡠⠴⠒⠢⠤⣀⠀⠀⠀⠀⣀⡤⠖⠒⠦⢄⡀⠀⠀⠀⠀⣠⠤⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡞⣥⣦⣄⢀⣤⣤⡑⡄⠀⣠⢫⠖⠀⠀⠀⠐⢮⢧⠀⠀⡜⢡⣶⣦⣠⣶⣦⠙⣄⠀⢠⢊⣴⡂⠀⠀⣐⣎⢳⡀
⠀⠀⠀⠀⠀⠀⢸⢸⡟⣽⣿⣿⣯⡹⡧⢹⠀⡇⢈⣿⣿⣿⣿⣿⣏⠈⡇⢸⠁⢺⣿⡿⠹⣿⣿⠆⢸⠀⡟⠘⢿⣥⣤⣤⣼⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡌⠷⠀⢻⣿⠃⠼⢃⡏⠀⢳⡀⠀⢻⣿⣿⠃⠀⣰⠃⠘⣆⢀⣿⣷⣴⣿⣇⢀⡞⠀⢹⡈⠙⢿⠿⢿⢿⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣈⣁⣠⠴⠋⠀⠀⠀⠑⠦⣈⣛⣋⡤⠞⠁⠀⠀⠈⠳⢬⣙⣛⣉⠤⠊⠀⠀⠀⠙⠦⣌⣀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡰⢋⠀⣰⣶⣦⣍⢢⡀⠀⢀⠞⡉⢠⣦⡄⠈⠑⢄⠀⠀⡠⠊⠁⠀⡆⠀⠉⠲⡀⠀⢀⡔⡭⠖⠶⡄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢸⠁⠛⢻⣿⣿⣿⣿⡄⢷⠀⡎⠘⣁⣠⣿⣿⣄⣰⠘⡆⢰⠃⠲⠋⠉⡏⠉⠳⠒⢱⠀⡾⢸⡇⠀⢢⣿⡔⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠙⢛⣿⣿⣿⣿⠇⡞⠀⢧⠀⢀⣤⣾⡿⠙⠋⢠⠇⠸⡄⢶⡶⠀⡇⠐⣶⠆⡼⠀⢳⠀⠀⣠⠼⠛⠧⣅⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠑⢌⡛⠿⠻⠟⣡⠞⠁⠀⠈⠣⣙⠻⠿⠿⢛⡠⠋⠀⠀⠙⢤⡀⠀⠧⠀⣀⠜⠁⠀⠈⠳⣄⠈⠃⠀⢘⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠙⠲⣄⠀⠀⠀⡠⠖⣉⡭⢍⠓⢦⡀⠀⠀⢀⠔⠋⠉⠉⢉⣓⢄⠀⠀⠀⣠⣖⣭⣭⣭⣑⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠃⠘⠷⢀⡴⠒⠋⠈⣇⠀⡼⢁⣸⣿⡇⠀⠀⣄⠹⡀⢠⠏⠀⣰⠚⢻⣿⣿⣆⢣⠀⣸⠁⣿⡿⠟⠉⣩⢧⠘⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡴⠋⠁⡀⠀⠀⣸⠀⡇⡿⣿⣿⣇⠀⣀⣿⢇⡇⢸⡀⠀⢿⣄⡙⠛⠛⠃⣸⠀⣧⢀⣉⡀⠀⣀⣠⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡠⠃⠀⠀⠸⠟⡠⠃⠀⠙⣄⠈⠙⣿⣿⡯⢁⡜⠀⠀⠳⡻⠾⣿⣿⠀⠀⡠⠃⠀⠘⢎⠻⣤⣴⣿⣿⣇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠒⠋⠀⠀⠀⠀⠈⠑⠲⠤⠽⠒⠉⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠀⠀⠀⠀⠀⠙⠒⠭⠽⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠿⣿⣿⠛⢻⣿⡿⠷⢶⣶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠃⢻⡇⠀⠀⠰⠀⣄⠐⢡⠄⡁⠀⠀⠀⣾⠇⠙⠻⢟⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⡟⠃⠀⠀⠀⠈⣿⠀⠀⠀⠉⠉⠀⡌⠉⠀⠀⠀⢰⡟⠀⠀⠀⠸⡹⡈⠛⢟⡶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠙⠠⡑⠇⠈⡱⠀⠀⠀⠸⣄⣀⣀⣀⣀⣶⣇⣄⣀⣀⣀⣼⠁⠀⠀⢠⢊⠤⠈⠠⠠⠋⠛⢟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡋⠀⠀⠀⠘⠤⠘⠁⢂⣶⢤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣜⣌⣒⡁⠂⠀⠀⠀⠀⣡⣿⢶⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠃⠙⢿⣆⠀⠀⠀⢀⡾⠖⠋⠀⠀⢀⠁⠀⠀⠀⠓⠀⠀⠠⡤⠀⠛⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⢀⣴⠟⠁⠙⢝⢦⡀
⠀⠀⠀⠀⢠⣾⣏⡀⠀⠀⠀⠉⠳⣤⡴⠋⠀⠀⣀⡀⠀⠀⠄⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠂⠀⠙⢦⣴⠋⠁⠀⠀⠀⡨⢿⣷⡄
⠀⠀⠀⣰⡿⢋⠃⡎⠡⢠⡄⢀⡴⠋⢀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠘⢦⣀⣄⡀⠔⣃⡐⠙⣽⣄
⠀⠀⣰⣿⠡⠊⡌⢱⢁⠔⢠⡞⠁⠀⠈⠁⠀⠀⣄⠠⠆⠀⠀⠒⠀⠀⠀⢨⡄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠐⠗⠀⠀⢀⠀⠈⠻⡦⡀⠎⠂⠡⢌⠾⡽⡄
⠀⢠⣿⠃⠀⠲⠀⣅⠎⢠⡏⠀⠀⠀⠁⠂⠯⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣤⠀⠀⠀⠀⠘⠃⠀⠀⠘⣞⣐⠁⠀⠀⠀⠱⣻⡄
⠀⣾⣋⠀⠀⠀⠀⠈⢡⡟⠀⠀⠒⠀⠀⠖⠀⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠤⢀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠘⠁⠀⠀⣴⠢⠀⢺⡄⠀⠀⠀⢀⣀⣥⣷
⢸⣯⠛⠛⠷⠶⠤⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡄⢔⠘⠟⠙⣧⠀⠀⠙⢦⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⠶⠒⠛⠉⠉⠉⣾
⣼⡏⠀⠀⠀⠀⠀⢸⠇⠀⠰⠂⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠠⢁⠀⢹⠖⠀⢠⡇⠀⠀⠀⢣⠀⠉⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠛⠀⠘⡇⠀⠀⠀⠀⠀⢿
⣿⠇⠀⢀⠤⢄⠀⢸⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⠀⠀⠘⠷⠡⠀⠀⣚⠀⠘⠃⡇⠙⠀⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⣧⡌⢹⠩⡌⠢⣸
⣿⣤⠒⣘⡈⠄⣂⣾⠀⠀⠀⠃⠀⠀⠀⢠⠀⠀⠘⠁⠀⠀⢐⠇⠂⠀⠙⡄⠀⠀⢿⠀⠀⠀⢰⠀⠰⠷⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠃⠀⣿⡄⠤⠵⠘⠆⣿
⣿⡾⠔⠀⠁⠀⠈⢹⠀⠠⠄⠀⠚⠀⠀⠄⡀⠀⠀⢠⣄⠀⠀⠁⣐⠢⡄⠻⣲⠀⡜⠀⠀⡰⠁⠀⠀⠀⢀⢄⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⡇⠐⢌⡃⠼⠠⠋
⢿⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠓⠀⠀⠙⠊⠀⠀⠀⠀⢀⠀⠀⡀⠀⢠⡇⠀⠀⠀⠀⠀⣾
⢸⣷⢀⣀⣤⣤⡶⠾⣷⠀⡈⠀⠀⠀⠻⠞⠀⣀⠀⠂⠀⠀⠀⡀⠴⠆⡄⠀⢠⠀⠀⠀⠲⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠀⠀⠀⣤⠀⣼⠓⠶⠦⣤⣤⣀⣳
⠀⣿⣛⠋⠉⠀⠀⠀⠘⣧⠁⠀⠠⠐⠁⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠀⠀⣠⡀⠀⠀⠔⠷⠂⠀⠀⠀⠀⠀⣠⠆⢠⡄⠀⣼⠇⠀⠀⠀⠀⠈⣿⣿
⠀⠘⣿⡄⢀⠔⣱⠀⡤⠘⣆⠀⠂⠄⠀⠰⠷⠀⠈⠀⠻⠃⠈⣀⠀⢠⠀⠀⠠⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠟⠀⠀⠀⢸⠏⡴⣒⣦⠀⠀⣰⣿⠇
⠀⠀⠹⣿⡰⢀⡄⢌⢀⡓⡘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠊⠉⠀⠀⠀⠀⣴⠀⢀⡾⠟⣉⠳⣭⢌⠳⢠⢻⠏
⠀⠀⠀⠹⣿⡍⠀⠈⠂⠀⠀⠈⠳⣄⠀⠸⠗⠀⠀⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⠀⠀⠠⠷⠂⠀⠀⠁⠀⠀⠘⠗⠀⠀⠀⣠⠟⠁⠈⠁⠑⠢⠉⣼⣫⠏
⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⢀⣠⠞⠳⣄⡀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⠈⢀⠀⠀⠀⢀⣠⠞⠻⣦⡀⠀⠀⠀⠀⡴⡵⠃
⠀⠀⠀⠀⠀⠈⢻⣷⡄⢀⣴⡾⠃⠀⠀⣨⣽⣶⣄⡀⠈⠰⠀⠀⠀⠀⠛⠀⠀⡀⠀⠀⠀⠘⠓⠀⠀⠈⢁⣠⡶⠋⠁⠀⠀⠈⠻⣦⡄⢠⣮⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣋⠀⠀⠀⠀⠀⡘⢠⠀⠉⠛⠶⢤⣄⣀⢀⠀⠀⠈⠁⠀⠀⠀⣀⣀⡤⠶⠛⢩⣏⠣⡔⣎⠂⠀⠀⠀⣨⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠰⢠⠏⡞⡙⠀⠀⢀⡏⠉⠉⢩⠙⠿⠛⠫⢭⠉⠁⢹⡄⠀⠀⠀⠍⢧⡙⣎⢧⣱⡤⣪⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⣶⣯⣸⢱⠁⠀⠀⣼⠁⠀⠀⢸⡉⠻⢸⠋⡻⠀⠀⠘⣷⠀⠀⠀⠈⠐⣉⡾⣻⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣤⡄⢰⡟⠀⠀⠀⠀⠣⠃⠔⡡⠁⠀⠀⠀⢹⣧⢠⢤⣶⡭⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠿⠶⣶⣶⣶⣬⣿⣰⣶⣶⠾⠼⠾⠛⠛⠉

⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⢤⣤⣄
⠀⠀⢰⣿⡿⣿⣿⡿⣆⣀⣠⣿⣾⣿⢿⣿⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⠿⠷⠂⠀⠀⠀⠒⠿⢿⠇
⠀⠀⢸⡏⢀⠙⠛⣿⣿⣿⣿⣿⠛⢋⠀⣹⡇⠀⠀⠀⠀⢛⣛⣾⣿⣿⣿⣷⣿⡛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣦⣀⣠⣤⣤⣤⣄⣀⡴⠁
⠀⠀⠈⠛⠚⠁⠀⣿⣻⣿⣿⣻⠀⠙⠚⠋⠀⠀⠀⠀⠘⠛⠋⣿⣿⣿⣿⣿⡍⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠬⢿⣿⣿⣿⣿⣿⠯⡥⠚
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠁⢘⡯⢻⢿⣿⠿⣟⢭⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⢺⣿⣿⣿⣿⣷⣤⣤⣄⠀⠈⠀⠻⣄⠀⣠⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀⣾⠏⡀⠀⠉⣉⡛
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⢿⣿⢿⣿⣧⢠⣦⣤⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢈⣁⢀⣀⡠⠖⠁
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣞⣻⡷⠂⠀⠀⠀⠀⠹⠟⠋⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣄⣀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠏⠀⠀⠀⢲⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠋⢺⠙⠁⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠘⠋⠏⠛⠿⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡁⠀⠀⠀⢩⠀⠀⠀⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢴⡷⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠻⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠺⠛⣳⣿⣿⣿⣿⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢶⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⢀⣤⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⢻⣿⣿⡃⠀⢤⡄⠀⢀⣿⣧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣷⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠈⣿⡟⠀⠀⠙⠉⠀⣾⢿⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⠿⠿⠿⠛⠉⠉⠉⣹⠇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢻⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠉⠉⠛⠂⠀⠀⠀⠄⠀⠀⣤⣶⣶⣶⠖⠁⠀⠀⠀⠀⠀⠘⣶⡶⠶⠶⠖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⢠⣶⠀⣸⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠰⠒⠒⠒⠒⠒⠒⠒⠐⠆⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠑⣄⠱⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠶⡈⠑⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠉⠀⡷⠀⠁⠀⠀⠀⠀⠀⠀⠀⡽⠏⠀⠁⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠒⠀⠀⠈⠀⠐⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⡤⠚⢀⡤⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⣶⣶⣾⣷⡄⠀⠈⠀⠢⠀⠀⠀⠀⢀⠴⣢⡱⣄
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠔⠊⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣉⣺⣿⠋⠀⠐⠶⡔⠒⠤⡀⠀⠀⠁⠀⠀⠋⠞⡵⠁⠈⢢⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣱⡏⡶⣻⠀⠀⣠⣦⣴⣶⣿⠁⠀⠀⠀⠀⠀⢀⠪⡀⠀⠀⠀⠱⡄
⠀⠀⢀⠎⠀⠀⠀⠀⢀⠐⠀⠀⠀⡰⠀⠀⡠⠄⡀⣄⠀⢀⣯⠀⢹⣿⠾⣷⣄⠀⢰⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠘⡄
⠀⠀⡜⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠣⠀⠐⠇⠘⠆⠉⠀⢸⣧⠀⡨⢿⣶⣽⣯⣀⡀⠻⠲⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠱
⠀⡸⠀⠑⠶⠄⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣦⣍⣈⣹⡛⠻⣿⣶⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⢠⠤⣄⢣
⠀⠇⠈⠈⠉⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠈⠙⠿⢿⣯⣟⣿⣍⣺⣿⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⡄⡦⠊⠘
⢸⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠈⢧⠀⠀⠲⢍⡉⢻⣿⣿⣿⣟⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡀⠀⡀⠀⠀⠀⠑⠀⢈⣻⣿⡿⢹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠠⢝⠀⠀⠀⠀⠀⢡⡿⡿⣡⡿⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠸
⢸⡄⣀⠀⠀⠀⠘⠀⣀⣤⡶⢶⢖⠀⠀⡰⠀⠐⢄⢀⣀⣀⣀⣀⠀⠑⣄⠀⠃⠂⠻⢿⡿⠿⣣⣈⣲⣦⠀⠑⠀⠀⠀⠀⠀⡇
⠀⡞⠤⢀⣠⡤⢴⡿⠋⠀⡀⠀⠀⠀⡀⢀⣤⣤⣀⣉⡉⠉⢉⣁⣠⣶⣿⠂⢆⡉⠀⠈⢣⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠐⠀⠀⣁⡒⢦⢸
⠀⠰⡴⠋⠀⢠⣿⠎⠐⠈⠐⠀⠀⢈⡵⢿⢿⠿⠛⠛⠛⠛⠟⠉⠉⠀⠀⠙⢦⡉⠁⡀⠀⠣⡀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠁⠈⠳⡐⣮⠝⡝
⠀⠀⢣⠁⠀⠘⣿⣄⣠⣶⣶⣶⣾⡏⠀⠙⢌⡀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⡄⠀⠳⢦⣤⠇⠀⠀⣠⡀⠀⠀⠀⠀⡸
⠀⠀⠈⢆⠀⠀⡃⢍⢉⠻⣆⠉⠿⠁⠀⠀⠀⠙⢦⣀⡐⢈⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣄⣠⠃
⠀⠀⠀⠈⢦⠈⠑⠛⠚⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣄⡀⠀⠈⣉⣰⣾⡻⡏⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠐⠉⠑⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢚⣻⣿⣧⣶⡝⣿⡶⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠘⢮⡉⠉⡆⠚⠀⠀⠈⠀⢢⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠐⣿⣿⣿⣿⣿⣿⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠀⢀⣀⣀⡀⠀⠤⠔⠂⠉⠈⠀⠀⠀⠈⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⢸⠁⡒⠂⠀⠀⠀⠀⠀⠀⠀⠐⢂⠈⠁⡂⠀⠀⠀⢈⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠠⠎⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⢀⡠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠐⠒⠠⠤⠤⠤⠤⠤⠤⠤⠒⠒⠚⠉⠁
⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣷⢀⣤⡀⢠⣄⢀⡁⣆⢀⡇⣠⣀⢠⣄⢈⢡⠀⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠑⢤⣨⠤⣷⣏⢨⢸⡏⡏⠹⣯⠥⢸⢸⠀⢸⢸⡀⣇⡱⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠥⣈⣹⠀⠁⠁⠀⠁⠉⠉⠀⠀⠈⠀⠉⠁⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣀⡁
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠛⠋⠀⠀⠀⠠⠄⣉⠉⠀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⢿⣿⣆⣀⠁⠀⠀⠀⠸⠿⣣⡾⠋⢹⠄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠀⠀⠀⠀⠀⣴⠟⣁⠀⠻⢄⡉⠀⠀⠀⠀⠀⠀⠻⢿⡆
⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⣻⣿⢀⠀⠀⢹⠄⣀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠁⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⡿⠃⠀⠀⠘⠋⠸⣿⠂⣾⠟
⠀⠀⠀⠀⠀⠁⠀⢻⣇⠘⠿⡿⢇⣄⠐⠃⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⣀⠀⠙⠀⠁⢰⣿⣴⠆
⠀⠀⠀⠀⠀⠸⢿⣦⡀⠀⠀⠀⠸⠃⢴⡄⣠⣤⣴⣶⣶⣶⣶⣶⣷⠀⢸⣦⣧⣈⠀⠀⠀⠀⢈⣙⡋
⠀⠀⠀⠀⠀⠀⢠⣠⣀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⠿⠿⠟⠿⡟⢛⣣⡀⠻⣿⣿⣶⠀⠀⠀⢙⣉⠁⠴
⠀⠀⠀⠀⠀⠀⢺⣿⡯⠀⠀⠄⠀⠠⣆⠁⢸⠀⠀⠀⠀⠀⢤⡙⠈⠛⡵⣢⡙⢿⣿⣇⢀⡠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠈⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⠈⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢠⡀⡀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠃⠀⠈⢻⣿⣿⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠀⢀⣿⡟⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⡟⢀⣿⡿⣀⠀⠀⠀⠀⣀⣀⡀⣀⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⢁⣾⣿⠛⢋⣵⣶⣿⣿⣿⣷⠁⢫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⡰⠒⠐⠒⡄⠀⠐⢀⠀⠀⣀⠀⠠⠑⠀⠀⠐⠠⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢰⠀⢰⠃⠀⠀⠀⢳⠀⣃
⠀⠀⠀⠀⠀⣇⠀⠀⠐⢀⡀⠀⢠⠀⡀⠀⠀⡎⠀⠀⠀⡂⠤⡀⠀⢢⠄⠂⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⢀⠕
⠀⠀⠀⠀⠀⠙⠦⠀⠈⠢⣁⠀⡡⠊⠀⠠⠜⠁⠀⠀⠀⠘⠄⡁⠀⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄⠀⠀⠀⠀⢀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⢸⠃⠀⠀⠀⢳⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠴⠳⢄⡗⠀⢠⣏⠛⠆
⠀⠀⠀⠀⠀⠀⠨⠀⠐⢁⠀⢀⠑⠀⢠⠀⠀⠀⠀⠀⢰⡠⠄⠀⠠⠄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⡏⠀⠀⡗⠦⡍
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠂⠀⢠⠄⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠈⡌⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡂⣐⡠⠄⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⡑⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣴⠧⠊⠀⠀⡀⠀⠀⠈⠁⣀⣠⡬⠁⠀⠉⣉⠀⠖
⠀⠀⠀⠀⠀⢀⣶⡄⢀⠀⠐⠁⢁⠀⣼⠀⡦⠄⠀⠰⠄⠴⢀⠀⠀⣀⠐⠀⠴⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⣱⠀⠀⠀⠈⣉⠀⠁⠀⠀⠀⢾⠖⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠍⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠈⠐⠊⠈⠀⠀⠀⠀⠀⠰⣖⠒⠀⢀⠁⠀⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣠⣴⣖⣆⣦⣶⣵⣵⣰⣲⣢⡄⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣰⡼⠼⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠳⢏⣖⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣲⠾⠋⠁⠀⠀⠀⠀⡀⣴⡀⠀⠀⢰⡆⠀⢀⢀⢰⣦⠄⠀⠀⠀⠈⠙⠷⣆⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⠾⠋⠀⠀⠐⣄⠀⠀⠀⠍⢅⣼⡇⠀⠀⢀⡄⠀⠀⠉⠙⢿⡄⠀⠀⠀⣠⠃⠀⠀⠙⠷⣓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⠟⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡜⠁⠳⠀⠀⢠⡄⠀⠀⣠⢼⡆⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠻⣕⣄
⠀⠀⠀⠀⠀⠀⢀⣜⡾⠃⠀⠀⠈⠃⣠⡀⠃⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡤⠁⢠⣿⣇⣈⡀⠀⠀⠀⠘⢷⣣⡀
⠀⠀⠀⠀⠀⠠⣺⠞⠀⠀⠀⠀⠀⠐⢿⠃⠀⠀⠀⠈⢣⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠜⠁⠀⠀⣿⣾⣿⠇⠀⠀⠀⠀⠀⢳⣗⠄
⠀⠀⠀⠀⠠⣰⠏⠀⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣔⣦⠦⠷⠞⠚⠚⠒⠶⢭⣖⡤⣄⠀⠀⠀⠀⠁⠈⠉⠒⠀⠀⢀⡤⠒⠀⠹⣞⡄
⠀⠀⠀⢀⣳⡏⠀⠀⠀⠀⠀⠐⠂⣄⡀⠀⠀⠀⢀⣔⣯⠟⠋⠀⠀⡒⡄⠀⠀⠰⣦⠀⠀⠙⠳⣯⢤⡀⠀⠀⠀⢀⣠⠐⠂⠁⠀⠀⠀⠀⢹⣖⡀
⠀⠀⠀⣜⡾⠀⠀⢀⠀⣰⣦⣀⠀⠀⠉⠒⠀⡰⣾⠞⠁⡤⠀⠀⠀⢁⡠⡠⡄⣀⡁⠀⠀⠤⠠⠈⠻⡼⣀⠀⠒⠉⠀⠀⡤⠀⠠⢄⠀⠀⠀⢷⣣
⠀⠀⢀⢾⠇⠀⠀⢻⡿⣿⣿⠉⠀⠀⠀⠀⠰⣱⠋⠀⠀⠀⢀⡴⣮⠶⠛⢋⡙⠓⠫⣕⡦⡀⠀⠀⠀⠙⣷⣆⠀⠀⠀⠀⠻⠿⠿⠿⠀⠀⠀⠸⣾⡀
⠀⠀⢸⢽⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣱⡏⠠⢀⠀⢠⣺⡞⣁⣸⣷⣾⠋⠚⢇⣈⢻⡵⡀⠀⣴⠆⢸⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠅
⠀⠀⠨⣿⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢘⢺⠁⠀⠀⠀⡐⡿⢀⣽⣿⣛⣧⠘⠃⡈⢋⡀⢿⠅⠀⠀⠀⠐⡯⠇⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⣯⠁
⠀⠀⢐⣿⠀⠀⠈⠉⠀⠉⠀⠉⠉⠀⠀⢠⢼⡄⠀⡀⠀⠱⣷⠈⣹⣿⣿⡇⠀⠀⠁⣜⠁⣾⡢⢀⠀⠀⠀⣗⡆⠀⠀⠈⢩⡀⢉⡀⠉⠁⠀⠀⣿⡀
⠀⠀⢸⣺⠀⠀⠀⢸⣿⣶⡀⠀⠀⠀⠀⠈⡭⣇⠘⠀⠀⠘⢽⣧⡉⢹⡿⣿⡦⣴⡎⢉⣼⡳⠃⠀⠀⠁⣸⢳⠀⠀⠀⠐⢯⡅⣸⡿⠀⠀⠀⠀⣗⡇
⠀⠀⠈⠿⡆⠀⠀⠠⢼⣿⣿⣾⠃⠀⠀⠀⠰⡹⣄⠀⠀⢀⠈⠻⢟⠶⣤⣌⣡⡤⠔⡫⠗⢁⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠸⢛⡿⢇⠀⠀⠀⢰⣷⠃
⠀⠀⠀⢫⢷⠀⠀⠈⠉⠁⠘⠛⠀⠀⣀⠄⠀⠐⡽⢦⡐⠂⠀⠀⠀⠈⠑⠑⠓⠉⡁⠀⠀⠀⠀⢀⣴⠫⠏⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡝
⠀⠀⠀⠈⠽⣇⠀⠀⠀⠀⠀⠠⠄⠋⠁⠀⠀⠀⠀⠫⡟⣦⣄⠀⠀⠘⠀⠀⠀⠰⠒⠀⠀⣠⡴⡿⠇⠁⠀⠀⠀⠈⠙⠠⠄⠀⠀⠀⠀⠀⣸⠯⠁
⠀⠀⠀⠀⠘⡹⣆⠀⠤⠚⠁⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠑⠫⠟⢖⡶⢤⢤⢤⠤⠶⣒⠯⠗⠋⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠈⠓⠤⠀⣰⠯⠃
⠀⠀⠀⠀⠀⠐⠽⢦⠀⠀⠀⠀⠀⢠⠾⡇⠀⠀⠀⢀⡔⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢢⡀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⡴⡯⠂
⠀⠀⠀⠀⠀⠀⠈⢯⢷⡄⠀⠀⠠⠋⠀⠘⠀⠀⢀⠚⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠀⣀⣄⠠⠀⠀⠃⡀⠀⠠⠇⠚⠁⠀⠀⠀⢠⡾⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⣦⡀⠀⠁⠀⠀⠀⢀⠌⠀⢰⣿⡁⠶⣶⣤⠀⠘⠃⠠⣾⣿⣿⣿⣦⠀⠀⠡⡀⠀⠀⠀⠀⠀⢀⣴⡣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⢶⣄⠀⠀⢠⠋⠀⠀⠈⠙⢻⡤⠼⠋⠀⠘⠃⠀⠈⠻⠉⢉⠃⠀⠀⠀⠙⡄⠀⠀⣠⡶⡭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠹⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡏⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠽⢳⢶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⡴⡎⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠚⠚⠩⠯⠯⠟⠟⠻⠻⠽⠹⠭⠓⠓⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠍⠀⠄⠀⢠⣤⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⣤⡋⠁⠀⠀⡀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡆⠀⠀⠈⠴⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣴⣶⣶⡆
⠀⠀⠀⠈⣿⣿⡆⠠⠤⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⡶⠶⢦⡀⣿⡇⠀⠀⢀⠈⣤⣵⣶⣶⣮⣤⠀⡀⠀⠀⠀⣤⣾⢫⣿⣿⣿⣍⢷⣤
⠀⠀⠀⠀⠈⠻⣷⣤⣤⣾⡿⠋⠀⠀⠀⠀⠀⢶⡀⢿⣄⠀⣨⣷⠟⠀⠀⠀⠈⠀⡈⡍⣻⣿⠩⢉⠈⠁⠀⠀⠀⠈⠁⠈⠿⠿⠿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⢠⣰⣿⣿⡆⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠘⠓⠂⠈⠀⠀⠀⠀⠀⠀⠠⠛⠿⢷⣿⣯⣧⣀⠀⠀⠀⠀⠀⢀⠖⠆⠀⠹⠂
⠀⠀⠀⠀⠟⠉⠻⠉⣿⣧⣶⡄⠀⠀⠀⠀⠙⢀⣤⣄⣀⣀⡐⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠁⠙⠂⠀⠀⠀⠠⣟⣛⣍⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⡀⣶⢀⡹⠟⠁⠀⠀⠀⠀⠀⠨⢿⠿⠿⣻⡷⠂⠀⠀⠀⠀⠀⠋⠀⠀⠰⠶⠤⠀⠴⠂⠀⠀⠀⠈⠐⠊⠁⣠⡾⣷⠂
⠀⠀⠀⠀⠀⠙⠳⠌⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣄⠜⠈⠀⠀⠀⠀⠀⠀⠀⠈⣀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠙⢬⠭⠃

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣰⡶⣆⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣐⣠⣤⣦⣤⠂⠀⠀⠀⠀⠀⠀⠉⠉⠀⢿⠀⠉⠛
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠨⢹⣿⡕⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠿⡿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⠀⠒⠶⠖⠠⠿⠀⠲⠒⠒
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡤⠴



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⡄⠀⠀⠀⠀⢀⡀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣀⣿⠀⠀⠀⣠⣞⣱⡟⢚⣷⣞⠁⠀⠀⠀⠀⣾⡷⢂⣤⣤⣐⢾⣷
⠀⠀⠀⠀⠀⠀⠀⣶⡛⠛⣽⡿⣷⠄⠀⠀⠈⠉⣿⣱⡋⠙⣿⡀⠀⠀⠀⠀⠉⢳⣿⣿⣿⣿⡟⠋⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⣀⣡⡆⠀⠀⠀⢠⠤⠿⣿⣉⡾⠛⢛⡿⠀⠀⠀⠈⠶⠛⠛⠛⠛⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠂⠐⠉⠉⠉⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣀⠀⠀⠀⠀⠀⠲⢶⣿⡄⠤⠠⠀⠂⠀⠰⡁⠀⠘⠄⢀⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⣿⣷⡄⠀⠀⠀⠀⢨⣿⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⣿⣿⠆⠀⠀⠨⠙⠻⠿⣿⣿⠙⠷⠀⠀⢠⡿⣿⠋⠙⣿⠉⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠃⠀⠀⠀⠘⠓⠈⠉⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⢠⣾⣿⡏⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡀⠂⠀⠀⠀⢺⣿⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡄⠘⢿⣏⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⠻⡇⠀⠀⠀⢠⣾⣿⣿⡟⣁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠙⠷⠂⠀⠘⣷⠛⣿⠏⣽⠏⢀⡇⠀⠀⠀⢠⡿⢹⢹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⢿⠀⠀⠀⠀⠶⠒⠒⠒⡟⠒⠀⠂⠀⠀⣠⣾⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣖⠀⠀⠀⣀⣀⣀⠀⢰⣿⠀⠰⠶⠀⠠⣿⢟⣿⠯⠉⣿⡷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠁⠈⠟⠀⠀⠀⠙⠛⠉⠀⣾⣿⡆⠀⠀⠀⠀⠀⠈⣡⣄⣠⡿⠷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣥⣶⣿⣿⣯⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣽⣿⣿⣶⣬⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠛⠉⢁⡀⠀⣀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢠⠓⠃⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⡐
⠀⠀⠀⠀⠀⠀⠀⠐⣠⣿⣿⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠁⠁⠀⠀⠀⠀⣀⣀⠀⠙⢷⣟⣿⣄
⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⠏⠀⠀⠐⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠈⠀⠈⠀⡤⠈⠀⠀⢠⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⢦⠀⠁⠀⠁⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⡿⠀⠔⠤⠂⠄⠀⠀⠀⠀⣠⠀⠀⠀⣀⠰⣄⣧⣼⣠⠆⣀⠀⠀⠀⢀⠀⠀⠀⠀⠜⡃⠀⠁⠀⢿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⡇⠀⠁⠉⠈⠁⠀⠀⠀⠀⠁⠀⠀⠢⢬⣿⣿⣿⣿⣿⣿⡥⠔⠀⠀⠈⠀⠀⠀⠀⠀⠂⠘⠁⠀⢸⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢒⣻⣿⣿⣿⣿⣿⣿⣟⡒⠀⠀⠀⠀⠀⠼⠆⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠘⣿⢿⡇⠀⠀⠤⢠⠀⠀⠀⠀⠀⡀⠀⠈⢉⡽⢿⣿⣿⣿⣿⡿⢯⡉⠁⠀⢀⠀⠀⠀⠀⠀⠔⠄⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣯⣷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⠀⠀⠀⠰⠋⡼⢹⡏⢧⠙⠆⠀⠀⠀⠊⠀⠀⠀⠀⠾⠠⠁⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠸⣿⢿⡆⠀⠀⠈⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣷⣿⣄⠀⠀⠀⠀⠀⢀⡀⠓⠀⠀⠀⠑⠂⠀⠀⠀⠀⠐⠊⠀⠀⠀⠞⢀⣀⣀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⢀⡠⠊⠁⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⡀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣷⣄⠈⠁⠀⠀⠀⠀⠠⡤⡤⠀⠀⠈⠁⠀⢀⠤⠀⠀⠀⠀⠈⠈⠸⠇⣠⣾⣿⣿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠃⠁⣀⠀⠀⠀⠀⠼⠀⠸⠄⠀⠀⠀⢀⣠⣾⣯⣿⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣻⣶⣶⣶⣶⣶⣶⣶⣶⣻⣻⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⡰⢻⣿⣿⣶⡀⠀⠀⠀⠀⠀⣠⣤⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢰
⠀⠀⠀⢣⠀⣽⣿⠉⠁⠀⠀⠀⠀⢸⣿⡀⠀⠿⢯⣷⣤⠀⠀⠀⠀⠀⢹⣿⣷⣤⣤⡠⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣮⣄
⠀⠀⠀⢈⡼⠋⠘⢇⠀⠀⠀⠀⠀⠈⠻⠻⠧⠀⣈⣿⠏⠀⠀⠀⠀⠀⠈⢿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠈⠹⣟⣿⡿⡿⣿⣿⠂
⠀⠀⠠⠞⠇⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠜⠜⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⠄⡠⠃⠃
⠀⢰⣶⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⡤⡆⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⢲⠂⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⡆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢺⣶⣴
⠀⠀⠸⡯⣦⠉⢹⣿⠷⠀⠀⠀⠀⠠⣐⠋⣁⣀⡉⢙⡢⠀⠀⠀⠀⠀⠴⣿⣿⣤⣌⡁⠀⠀⠀⠀⠀⠀⠈⠟⠒⣿⣿⣿
⠀⠀⠈⢀⡅⢶⡏⠃⠆⠀⠀⠀⠀⠀⠉⠻⢿⣿⡿⠯⠁⠀⠂⠀⠀⠀⠀⣫⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠹
⠀⠀⠀⡜⠃⠞⢆⠱⡄⠀⠀⠀⠀⠀⢀⡆⠀⠁⠀⢠⠈⠀⠀⠀⠀⠀⠀⠁⠙⠛⠻⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲
⠀⠀⠠⠤⠈⠀⠈⣀⡀⠀⠀⠀⠀⢠⢤⠄⠀⢀⠀⠈⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠤⠄
⠀⠀⠀⣰⣒⠒⣿⣦⠀⠀⠀⠀⠀⠀⠀⠁⢀⣄⠀⠋⠀⠀⠀⠀⠀⠀⣀⠀⣠⣿⣷⢀⣐⠀⠀⠀⠀⠈⡿⣿⣿⣆⠀⡀
⠀⠀⠠⠄⠠⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠼⢻⣿⣷⣾⣿⣏⠸⠀⠀⠀⠀⣀⣉⣿⣿⣿⣧⣼⠖⠂
⠀⠀⠀⠀⢠⠏⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⡀⠀⠀⠀⠀⠀⠀⢐⠋⠋⠙⠻⢿⢦⠀⠀⠀⠀⠀⢨⣨⢟⡙⠛⣿⣿⡇
⠀⠀⠀⣀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢀⢠⠄⠀⠀⠀⠈⠉
⠀⠀⠘⠒⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃

⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠄⠀⠀⢠⠀⠀⠀⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠐⢀⣀⣀⡀⣸⣀⢀⣀⣐⠀⠀⠀⠉⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢫⡀⢀⡀⠤⠐⠂⢉⣀⡀⠀⠀⢸⠀⠀⢀⣀⡈⠑⠒⠠⠄⠀⠀⣨⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⢀⠤⠻⠁⠀⠀⠰⠿⣿⠿⠿⠆⠀⠸⠀⣼⣯⠽⣷⡾⠷⣦⠀⠀⠹⠣⢄⠀⠀⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⡠⠀⠀⠀⠀⠐⡀⠀⣾⠀⠀⣀⣀⣾⠀⢰⠀⢾⠿⠀⣿⣮⣶⡿⠀⡐⠁⢀⣀⠀⢠⡀⢀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⣠⣤⣤⣄⡄⠀⠹⣄⠘⠐⢿⡟⠛⠁⠀⢸⠀⠀⠀⠐⠛⠈⠙⢀⡔⠀⠀⣾⣉⠁⠀⠙⢢⡀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣊⠀⢀⠔⠀⠀⣿⣿⣿⣿⣇⠀⠀⠈⣄⣀⡤⠶⠒⠚⠉⢹⠁⠘⠒⠂⢤⣄⣀⡞⠀⠈⢩⣼⣿⣷⡀⢰⡀⠀⢀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⢰⠏⡈⢳⠮⣄⡀⠀⠼⢟⢿⣿⡯⠀⣀⡴⠛⢧⠀⠈⡶⠇⠀⢸⠀⠈⠸⠁⠆⢠⠟⠳⣄⡀⣿⡿⠿⣽⠛⠋⠀⣀⡬⢶⠋⠈⢷
⠀⠀⠀⠀⠀⢠⠏⠄⢁⠎⠀⠀⠙⠲⢤⡈⠉⠉⢁⡞⢁⠔⢀⠈⢧⣠⡥⠶⠶⠛⠒⠶⠦⣤⣠⠏⠀⢀⡂⠙⣆⠀⠀⠈⣡⠴⠊⠁⠀⠈⢆⠀⠈⢧
⠀⠀⠀⠀⠀⡾⠀⠀⡌⢀⣤⡶⠷⠶⣄⠉⠓⣶⣏⠐⢁⠖⢡⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠠⠋⠀⢈⣷⡖⠋⠀⣠⣶⣶⣤⣄⠈⡄⢠⠸⡆
⠀⠀⠀⠀⢸⠃⠈⠀⠀⢻⣿⣷⢰⠋⢹⡆⢰⠇⠈⠙⠲⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠚⠉⠀⢷⡀⠸⣻⠻⠏⠛⠿⡄⠰⠐⡀⢛
⠀⠀⠀⠀⠸⠠⠄⠂⠀⢸⣧⠉⢀⠙⡻⠃⡟⢀⠐⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠂⠨⠈⡇⠐⢶⣾⣷⣾⡞⠀⠀⠂⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠉⠏⠉⠉⠉⠉⠁⠉⠉⠙⠉⠉⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⣉⠈⠉⠉⠉⠉⠉⠈⠈⠏⠁⢸⡇
⠀⠀⠀⠀⢷⠀⠀⡀⠀⠀⠀⣠⣤⣔⠀⠀⡆⠲⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⢀⠀⠆⡟⠀⠀⣀⣠⢤⣦⡀⠀⡁⠀⢸⠇
⠀⠀⠀⠀⢸⡄⠁⢡⠀⠉⣿⣏⣻⣿⠀⡀⢻⡀⠀⢀⣨⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣀⠁⠀⣼⠁⠀⣸⣿⣿⠏⠉⠁⢠⠀⡂⣼
⠀⠀⠀⠀⠈⣧⠀⠀⠆⠀⠉⢀⡟⠛⠃⠀⣀⣷⡞⠉⠀⠆⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠈⠙⣶⣇⡀⠀⠘⠟⢿⣧⠖⠀⠇⠈⢠⡏
⠀⠀⠀⠀⠀⠸⡄⠀⠘⡄⠀⠈⢀⣠⠴⠋⠁⠀⠙⣦⠢⣀⠀⠀⡽⠳⠦⣤⣤⣀⣠⣤⡤⠶⠻⡅⠐⣆⡠⢀⡞⠁⠀⠉⠲⢤⣀⠀⠀⠀⡜⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠐⡤⠖⠋⠀⣠⠞⢛⣿⡆⠈⠓⢦⣀⡼⠁⢠⠀⡄⠀⢸⠀⠒⠠⠀⠀⠹⣄⣠⠞⠋⣠⣶⣿⣷⢦⠀⠈⠑⠀⣔⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠻⡎⠀⠘⢆⠀⠰⣿⠟⢻⣿⡗⠃⠀⠀⠟⠓⠶⣤⣁⡀⠀⢸⠀⣈⣀⡁⠵⠖⠛⣇⠀⠀⡟⢿⣿⣫⢸⡦⠀⢀⠖⠀⠉⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⠻⠄⣰⣿⡆⠀⢠⠞⢀⡀⠲⣶⣤⡄⠉⢹⠁⠉⣁⠀⣤⣄⡀⠘⢆⠀⠻⣿⣿⠀⠾⢃⡴⠋⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⠀⠀⠀⠀⢠⠋⠀⠀⠀⢠⡟⠀⠶⠄⠸⠀⢸⣿⣣⣿⢿⣿⡄⠀⢂⠀⠀⠀⠀⠀⠋⠄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⣸⠁⢀⠀⠀⢰⠀⠸⣿⡅⣿⣷⣽⠃⠀⠀⢡⡠⠔⠉⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡰⠃⠀⠢⠤⣀⡰⠿⠀⠀⠀⠀⢸⠀⠀⠈⠛⠀⠈⣁⠠⠤⠒⠉⠳⣄⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠐⠀⢤⠉⠑⠒⠒⠂⢺⠒⠒⠒⠂⠉⠁⠄⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⠤⠀⠀⠸⠀⠀⠠⠤⠴⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠀⠀⡴⠀⠀⠠⠁
⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⢠⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣯⣤⢿⡆⠠⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠆
⠀⢀⠀⠠⠀⠔⣤⢸⣇⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠈⠃⢞⠀⠁⠀⠀⢰⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠐⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠠⠄⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠆⠀⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠆⠐⠀⠀⠀⠀⠂⠀⠀⢤⠤⠄⠀⠀⠘
⠀⠊⢳⡎⠁⢈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣴⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⢰⣠⡀⠀⠂⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⣸⠇⠀⠀⠀⠐⠂⠒⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⡀⠄⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠈⢺⡆
⠀⠀⠀⠀⠀⠀⣫⡔⣮⡂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠸⠃⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⢜
⠀⠀⠀⠀⠂⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠓⣊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠆⠠⠂
⠀⠄⠀⢈⠃⠀⠀⠡⠀⠀⢄⠀⢀⣀⡀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠖⢆⠀⠀⠀⠀⠀⣀⣄⣤⡀⢀
⠀⠀⠠⠈⠀⢀⠀⠀⠀⠀⣀⠀⠿⠽⣉⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠸⢆⠇⠀⠀⠀⠀⠀⠹⠘⢈⡁
⠀⠀⠀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠑⠚⠒⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⠀⠀⠀⠠⠀⠂⠰⠤⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡊⠇⠀⠀⢠⠂⠀⠀⠀⠚⡰⠄⠣⠔⠂⠜⣂⠀⢀
⡄⠀⠀⠀⠀⠀⡆⠀⠈⡀⢀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣐⡶⠃⡄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢉
⠁⠉⠀⠀⠀⠀⠁⡀⣀⠀⠉⠀⠰⠀⠀⠁⠀⠈⠄⠀⠀⠤⢀⠀⠀⠈⠋⠰⠟⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠃⠀⠀⠀⠀⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⢀⡘⠀⢀⣀⣄⣠⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⡀⠀⡀⠀⢠⡘
⠀⠀⠀⠀⢠⠛⢣⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠥⠀⠀⡅⠀⠀⡏⠈⠀⢃⡀⠀⠀⠀⠀⢀⣀⠶⠀⠀⢀⠁⠈⡁⠂⠁
⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⠚⠁⠀⠠⠤⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⢄⠖⠓⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢈⠆⠒⡃⡐⠁⠀⠈⠉⠃⠀⠀⠀⠀⠰⣉⢭⣓⡃⠀⠀⠀⠀⠀⠛⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⡀⠀⠀⠀⣀⡋⠉⠂
⠀⠀⠘⣡⣄⣵⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠉⠀⠀⠀⠀⠀⠐⠀⣰⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡞⠁⠡⠀⠀⡠⠀⠙⡆
⠀⠀⠀⠀⢈⠅⢀⠀⠀⠀⠈⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠘⡀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠶⠧⠀⠀⠀⠀⠠⠶⢆⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠘⠂⠀⠀⠐⠀⢀⠀⠆⢀⠀⠀⠀⠀⡀⠏
⠢⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⡀⠀⠀⠀⡀⢠⠀⢀⠀⠀⡀⠀⠀⠠
⠀⠃⢸⣗⡄⠘⠂⡄⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⢻⠃⠀⠁
⣀⣀⣀⣀⣀⣐⣂⣉⣀⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣈⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠒⠂⢓⣚⣓⡚⠂⠳⠶⠴⣄⡀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⡠⠔⠙⠉⠀⠀⠀⠀⠀⠸⡟⠉⠉⠛⠋⠛⠛⠶⢮⣌⡒⠆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⢉⡀⠀⠀⠀⠀⢰⣶⣦⡀⠐⣗⠀⠀⡀⣠⠀⠀⠀⢠⡟⠀⠀⠈⠚⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠛⠋⠙⢧⣀⠀⠀⠻⣟⠋⠀⠀⠩⠀⠘⠋⠀⠘⠀⠠⠶⠀⢀⡐⠀⠀⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⣀⠟⣡⣿⠀⣠⢦⠀⠀⠹⢦⡀⢀⣠⣤⣴⣶⣾⣶⣦⣦⣂⣠⢄⠂⠀⠀⠋⢉⣷⠘⠀⠀⢀⡙⡄⠣
⠀⠀⠀⠀⣰⢶⠒⣤⡟⠁⢾⠁⠀⡀⠀⢀⡜⣯⠴⣿⡉⠀⠀⠀⢸⠄⠀⠀⠉⡿⠾⣷⣄⠀⠀⠀⢀⣠⡶⠟⠷⣄⢠
⠀⠀⠀⠀⣀⠇⠘⠾⢦⡄⠀⠀⠀⢀⣔⡵⠋⠀⠀⠘⣷⡀⠀⢀⣸⣄⡀⠀⡼⠁⠀⠈⠛⣿⡤⣴⠍⠉⢀⣀⠈⢻⡘⠳
⠀⠀⠀⢀⡍⠀⠀⠀⠀⠈⠳⢦⣠⣶⡾⠷⣄⡀⠀⣤⠶⣚⠩⠥⠔⠇⠭⣝⠢⣀⠀⣠⠶⠋⠱⡽⡄⣸⣿⣿⣷⠈⢿⡀⠇
⠀⠀⠀⢴⠁⠀⠆⠈⠅⠀⠀⢀⣾⡟⠀⠀⠈⢩⡾⡡⠞⠂⠀⠀⠀⡀⠀⠈⠙⢪⡣⡁⠀⠂⠀⠹⡜⡀⠉⠷⠁⠀⠀⡧⢨⡄
⠀⠀⠀⡻⠀⠀⠀⢄⠀⠄⠀⣺⣿⠁⠀⠀⢀⡟⡸⠁⠀⠀⠠⣴⣴⣆⡀⠀⠀⠈⢻⣹⣤⠤⠤⠴⣷⡃⣀⣀⣀⣠⣴⣶⠘⠠⡄
⠀⠀⠈⡇⠀⠀⠀⠉⠀⠀⠀⠾⣿⣤⠶⠶⢸⠁⡅⠀⠀⠀⣺⡏⠁⠙⣿⠤⠀⠀⠐⡃⡗⠀⠀⡄⣼⣯⠉⠉⠀⠀⠀⠀⢈⡖⠁
⠀⠀⣄⡖⢰⣶⠶⠶⠒⠂⠛⡆⣧⠀⠄⠀⢿⡆⣆⠀⠀⠀⢺⣷⣤⣾⠟⠉⠀⠀⢰⢃⡇⡈⠐⠀⣿⡯⢀⡶⠶⠀⠀⠀⢀⢂
⠀⠀⠀⢰⠀⢒⠀⠀⡀⠀⠀⢷⢹⡀⠀⠀⢘⣿⡘⣀⠀⠀⠀⠟⠏⠈⠀⠀⠀⣠⢍⡾⠀⠛⠶⣄⣿⠇⠘⡇⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠘⡄⢸⡄⠀⣋⡄⠀⠈⠄⢷⣠⡶⠋⠈⠻⣌⡓⠄⣀⢀⠀⡀⣀⡤⢚⣵⡷⠃⡀⠀⢀⡼⣱⡀⠀⠈⠃⠀⠀⢀⣧
⠀⠀⠀⠀⢹⠈⢷⠀⠀⠀⠀⠀⣀⢿⣷⣆⠀⠀⠀⠈⢛⣶⣾⣭⣵⢩⡤⠖⠓⠋⠙⣦⡀⢠⠞⡕⠀⠈⠓⠶⣄⣀⠀⡨⠒
⠀⠀⠀⠀⠀⠡⡌⢱⣀⣀⡴⠞⠋⠈⠹⢿⣷⣤⡀⣠⡿⠀⡀⠉⠉⢰⡇⠐⠀⠄⢀⣼⣿⠣⠞⣀⠏⠁⡀⠀⢀⠋⠴⠻⠆
⠀⠀⠀⠀⠀⠠⡓⣀⠋⠁⠀⠀⣴⣤⣦⠀⠘⠿⠛⡿⠧⣤⣁⣀⣀⣘⣛⣤⣴⣾⡿⠟⡋⠀⠘⠋⢀⠐⠀⣰⢋⡤
⠀⠀⠀⠀⠀⠀⠉⠸⠧⡀⠀⠀⠛⠛⠛⠀⠀⣰⠋⠉⠓⠢⠴⠨⠍⣭⠑⠛⠙⠈⠁⠀⠘⢆⠀⠀⢀⡠⠞⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⣄⠀⠀⠀⠀⣰⠃⠀⢠⠆⠀⡀⠀⠀⢹⠀⠠⠀⣶⡄⠀⠀⠀⠻⠶⢉⠥⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠤⣀⡸⢧⡄⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠊⠉⠃⠀⠀⣀⡀⢼⣤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠗⠐⠤⣍⢙⣓⡒⠶⠶⠖⠾⠀⣀⡀⠀⡰⠴⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠘⠌⠃⠽⠆⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠



⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⢠⡀⠠⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢿⣷⠀⠀⠀⢠⡆⠀⠚⢻⠹⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⣙⣿⣧
⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⢶⣄⡀⠀⠀⠀⠀⠀⣠⡴⢦⡀⣿⠇⠀⠀⠀⢰⣿⣷⣶⣷⣤⢤⠀⠀⠀⠀⣿⣧⠠⡤⢁⣾⣿
⠀⠀⠀⠀⠈⠁⠙⠻⠟⠟⠀⠉⠀⠀⠀⠀⠹⣄⣿⣀⣀⡿⠏⠀⠀⠀⠀⠉⢍⠉⠉⣙⠕⠃⠀⠀⠀⠀⠘⢿⣧⣤⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⣴⣿⣿⡏⠐⢠⠀⠀⠀⠀⠀⠰⢾⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠐⠄
⠀⠀⠀⠀⢸⠋⠛⠉⣿⣶⣶⡄⠀⠀⠀⢠⣾⠉⠁⠈⠈⠟⠓⠀⠀⠀⠀⡄⠀⣻⣿⡐⠀⠀⠀⠀⠀⠈⡚⠀⠀⣀⠀⠐⡃
⠀⠀⠀⠀⠘⢧⣤⣷⣤⠟⠋⠀⠀⠀⠀⠀⢉⠀⠐⠓⠢⠤⠆⠀⠀⠀⠀⠓⠄⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠈⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠈⠀⠛⠺⠿⠖⠋

⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⣴⣍⣁⣨⣭⠲⠀⠀⠀⠀⣸⠏⣝⠛⠉⣋⠉⢷⠀⠀⠀⠀⢸⠋⠉⡏⠉⠉⠁⠀⠀⠀⠀⣠⠿⠄⠀⠤⠧⡄
⠀⠀⠀⠀⠸⢳⣿⣗⣺⣿⡲⡁⠀⠀⠀⢹⢾⠿⡅⠈⡹⢿⣾⠀⠀⠀⠀⣀⠀⢠⣷⢀⣀⠀⠀⠀⠀⠈⢿⣇⣀⣀⡀⣸⡍
⠀⠀⠀⠀⠀⠋⠟⠹⢝⡟⠅⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠉⡉⠈⠉⠈⡉⠁⠀⠀⠀⠀⠘⢽⠋⠉⠙⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀

⠀⠀⣠⣤⡄⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⡀
⠀⠀⠁⠀⢻⡄⡿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠷⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠑⡆⢀⣀
⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⢻⠋⠈⣣
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡵⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠴⠆⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⣤⠤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠤⠤⠤⠄



⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⣤⢶⣤⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡴⢶⣤⠶⣄
⠀⠀⠀⣀⣘⠃⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⠀⢸⡤⣤⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⢿
⠀⢠⡟⠁⠉⢷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠻⠀⢸⡇⡼⠁⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⢸
⠀⠘⢧⣀⣠⠞⠹⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⢁⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣆⢀
⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢂⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣄⣠⢄⣄⡀⡀
⠀⠀⠀⠀⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈


⠀⠀⠀⠀⠠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠶⠶⠞⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⣸⠃⡀
⠀⠀⠀⠐⣲⣏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⠙⢦⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢤⡀⠀⣠⡴⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢻⠉
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠃


⠀⠒⣀⣀⣀⢠⢄⣀⡀⣀⡀⠀⠀⠀⠀⠀⠤⠆⡀⡀⣀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡀⢀⠀⡀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠁⠁⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁

⠀⠀⣴⠲⣄⣰⠖⡆⠀⠀⠀⠀⠒⣦⠀⢀⡴⠂⠀⠀⠀⠀⠒⣶⠶⢶⠖⠀⠀⠀⠀⠀⢀⣤⡤⢤⣄
⠀⠀⠈⠀⢻⡏⠈⠁⠀⠀⠀⠀⠀⣼⠛⠻⡄⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⠼⠃⡖⣦
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠃⠀⠀⠀⠀⠀⠤⠿⠶⠾⠦⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀
⠀⠀⠀⠀⡖⠓⣦⠀⠀⠀⠀⠀⢸⡏⣿⢹⣤⡄⠀⠀⠀⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⠀⢻⠛⡟⣿
⠀⠀⠀⣞⣷⢠⠏⠀⠀⠀⠀⠀⢸⡇⣿⢸⣧⡇⠀⠀⠀⠀⢤⠷⠀⠼⠧⠀⠀⠀⠀⠀⢸⠀⡇⣿
⠀⠀⠀⠈⠁⠻⠶⠀⠀⠀⠀⠀⠈⠁⠩⠼⡟⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠈⠀⠁⠻⣤


⠀⠀⠀⠀⠀⢶⣶⠀⠀⠀⠀⠀⠘⣶⢳⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣄⣤⠀⠀⠀⠀⠀⠐⢦⠀⣴⠂
⠀⠀⠀⢙⣶⡋⠘⠀⠀⠀⠀⠀⠀⠇⢸⣶⢳⡆⠀⠀⠀⠀⢉⣬⣡⣍⣬⠁⠀⠀⠀⠀⠐⢺⠖⣿⠂
⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠉⠀⠀⠀⠀⠀⠉⠈⠁⠉⠈⠁⠀⠀⠀⠀⠐⠋⠀⠙⠆

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢷⡀
⠀⠀⢀⠔⠋⠁⣉⠙⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⢔⣩⣴⠃⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠙⠡⣤
⠀⠀⣘⠛⠆⣜⠐⠊⢸⣷⡀⠀⠀⠀⠀⠀⠓⠏⡄⠈⠻⡲⡆⢷⣜⡆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙
⠀⠀⠿⠖⠒⠪⣐⣶⡿⠋⠁⠀⠀⠀⠀⠀⠘⠂⢈⣾⢣⠇⣧⡔⢺⡇⠀⠀⠀⠀⠀⣮⣁⣠⡴⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢴⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⣀⠋⠣⠟⠀⠀⠀⠀⠀⠀⠈⠍⠭⠢⠰⣤⣌⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠋⠀⠤⠤⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠤⠶⠶⠦⣄⣄⣀⠀⠀⠀⠀⠀⠀⢴⡚⠱⠃⠈⠆⢓⣢
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢒⠃⠰⠀⠀⠀⠈⠧⢉⠴⠀⠐⠀⠜⠛⣣⡀⠀⠀⠀⠀⠀⡴⣁⠋⠙⠋⡉⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠗⠁⠐⢨⠿⠇⠀⠀⠀⠀⠀⠙⠻⠷⠔⠣⢜⠯⠋
⠀⠀⠀⠀⠀⠀⠐⠂⠉⠑⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀
⠀⠀⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠔⣂⢍⠀⠀⠀⠀⠀⠀⠀⡈⡷⠂⠀⠐⢢⢷
⠀⠀⠹⡾⠆⠀⢀⣦⠀⡀⡀⠀⠀⠀⠀⠀⠰⠻⠒⠚⡙⢧⣀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⡕⣰⣈⣧⣜⣚
⠀⠀⠀⠀⢰⠃⠨⢁⡾⡟⠮⣓⠦⠀⠀⠀⢰⡆⠒⠀⣀⠈⠁⢀⣀⡀⡘⠃⠀⠀⠀⠀⠀⢸⡿⣌⠨⡽⢿
⠀⠀⠀⢀⡈⢁⡀⡜⠐⢓⣪⠝⠓⢢⠀⠀⠀⠛⠥⠤⠜⠛⠶⣉⣩⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⢀⠄
⠀⠀⠀⠘⠓⠀⠀⠖⠈⠉⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⢠⠄⡄
⠀⠀⠀⠀⠀⠀⡌⡀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠙⣠⢤⠀⢠⢬⡜⠁⠀⠀⠀⠀⠀⢰⣫⠋⡍⢳⣄
⠀⠀⠀⠀⠀⢀⣅⢼⢣⣠⡇⠀⠀⠀⠀⠀⠀⠘⢄⣹⢶⡊⣲⢾⣅⠜⠀⠀⠀⠀⠀⣸⣯⡁⢉⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠟⢻⡋⠄⠀⠀⠀⠀⠀⠀⠈⠋⠁⣐⣿⣟⡀⠉⠋⠀⠀⠀⠀⠀⣼⣿⡉⢇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠫⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡄⣼⡗⠀⠀⠀⠀⠀⠀⠀⠈⠈⣙⠟⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⢄⣠⣂⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢀⠂⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣦⡄⠀⠀⠀⠀⠀⢠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠉⠻⣿⣿⣿⣿⡆
⠀⠀⣼⠞⠛⠛⠛⢦⠶⠀⠀⠀⠰⢦⠞⠛⠛⠛⢼⡇⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⠂⠀⠀⠙⠁⣿⣿⠇
⠀⠀⠙⠀⠀⠀⠀⢠⡤⡤⠀⠠⠤⣼⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣿⠁⠒⠉⠀⠈⠓⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⣀⢀⡤⠈⢿⡆⠀⠀⣾⠟⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⣶⣶⣾⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣯⣿⣿⣿⣿⣿⣭⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠾⢿⣼⣯⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡋⠀⣀⠄⢀⡀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠉⠛⠉⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠈⢿⣿⡇
⠀⠀⠀⠀⣀⣤⣈⣷⡋⠀⠀⠀⠀⣳⡞⣠⢄⡀⠀⠀⠀⠀⠀⢸⣏⣿⣿⣿⢠⣤⠀⣤⡄⢿⣿⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⡀⠈⣿⣧
⠀⠀⠀⠀⢋⣀⣈⣿⣿⣿⣿⣿⣿⣿⣯⣀⣈⠃⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⡀⠀⠀⠀⢀⣿⣿⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠹⢿
⠀⠀⠀⠀⡏⠀⣤⠞⠻⠿⠿⠿⠿⠟⢦⡄⠈⡷⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣇⠀⠛⠀⢸⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠷⠄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣵⠃⠀⠘⣮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠠⠄⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡠⠤⠂⠀⠀⠀⠀⠀⠀⢸⣏⢁⡀⠀⢀⡈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⡻⣿⣶⣿⢟⣉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⣿⣿⣿⠢⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⣿⣿⣿⠑⡚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠀⠉⠁⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠆⠔⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣰⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⡄⠀⠀⠀⠀⠀⠀⠐⠿⣿⣷⣤⣘⠂⢄⡉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⢀⡀⠀⠀⠀⠠⣖⠁
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣤⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣤⣀⣀⣥⠴⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠘⣁⡈⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣮⡅⠀⠀⣩⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣽⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢠⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠢⣤⣉⣀⣠⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⠿⢿⣿⣿⠿⠿⠿⡿⠿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⡆⢰⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣏⣿⣽⣿⠿⢿⣿⣟⡇⢙⣿⣿⠿⠿⣿⣯⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣄⢿⣿⢿⣛⣯⣽⣶⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣶⣯⣽⣻⠿⣿⡿⣠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⢟⣄⢰⣿⡟⠋⠁⠙⠛⠉⠛⢿⣿⡇⢸⣿⠁⠈⠉⠉⠉⠙⠻⣿⣿⡆⣠⡻⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⡿⣫⣾⣿⣿⣧⢻⣿⣶⣄⠀⡀⠀⠀⠘⢿⡇⣸⣟⣀⣄⠀⠀⠀⠀⠀⣿⠟⣼⣿⠿⢷⣝⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣵⣿⣿⠿⠿⠓⢾⣷⡹⣿⣶⣶⣷⣶⣿⡿⢣⡇⢸⣷⣾⣿⣿⠀⣼⣷⣶⢎⣾⣿⠅⢿⣿⣿⣿⣮⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣫⣾⣿⣯⠁⠀⠀⠀⢈⡹⣷⡙⣿⣿⣿⣿⣶⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢃⡾⣫⠅⠀⠀⠙⠿⠿⠟⣷⣝⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣤⣝⠛⢵⣿⣯⣝⠁⠀⠀⠀⣀⢶⣽⣾⣿⡜⠿⢛⣫⣭⣵⣶⡆⠀⠀⠈⠉⠙⠛⠿⢣⣿⣿⣿⣿⣿⠄⠀⢀⣠⢄⣻⣿⡮⠛⣫⣤⡀
⠀⠀⠀⠀⢀⣾⣿⣟⣴⣶⣭⣛⢯⣾⣶⣤⡜⢿⣧⣿⡿⠋⠁⠈⢿⣿⣿⠿⠿⡇⢀⠀⠀⠀⠀⠀⣠⣮⣙⢿⣿⣿⣯⣦⣾⣿⣿⠿⣛⣭⣶⣦⢻⡿⣷⡀
⠀⠀⠀⠀⣼⢻⡿⣼⣿⣿⣿⣿⣷⣮⣝⠻⣿⣾⡿⠋⠀⠀⠀⠀⣈⠱⠖⣛⡉⠥⠬⣍⣛⡳⠆⣀⠿⣿⣿⣷⡝⢿⣿⣿⠟⣫⣵⣾⣿⣿⠿⣿⣯⢿⣿⣧
⠀⠀⠀⢰⣿⣿⢳⣿⣿⣼⣿⡏⣤⣉⣽⢻⣶⡍⡁⠀⠀⠀⣴⢟⡥⠚⠉⠀⠀⠀⠀⠀⠉⢻⣷⣬⠳⣌⠻⣿⡿⠊⢩⣶⣿⣿⠟⠉⠁⢘⣾⣿⣿⡞⣿⣿⡄
⠀⠀⠀⣾⣿⡟⣿⣿⣿⣿⠟⠀⣿⣿⣿⣿⡟⣰⣿⣷⢄⡘⣡⠋⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⣿⣿⣿⣌⢃⡀⠀⠀⠀⢿⡯⣭⠀⠀⠐⠃⠉⠉⠛⣷⢻⣿⣷
⠀⠀⢀⣿⣿⣧⣿⣿⣟⠀⣴⡈⣿⣿⣿⣿⢇⣿⣿⡟⣼⢱⠃⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣿⣿⣿⣿⡌⣧⠀⠀⠀⠸⣿⣿⣿⣧⣶⣶⣶⡔⣤⣿⣼⣿⣿
⠀⠀⠸⠿⠿⠹⠿⠿⠿⠶⠿⠧⠿⠿⠿⠿⠸⠿⠿⠧⠇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣧⠸⠄⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠇
⠀⠀⢰⣶⣶⣰⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠐⡆⢃⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⢲⣶⣾⡆⣶⣶⣶⠶⣒⣒⠶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⣿⣿⡟⣿⣿⡟⠙⠿⠟⠛⣠⠼⣿⡆⠀⠀⠀⢿⡘⡄⠀⠀⠀⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⢃⡟⣼⣿⣿⢱⣿⠿⠃⠘⠛⢿⣿⣎⢿⣿⢻⣿⣿
⠀⠀⠀⢿⣿⣧⣿⣿⠄⢀⣀⠀⠀⠀⠀⣻⣷⠀⠀⠀⠈⢡⡙⣄⠀⠀⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⡿⢋⡌⠱⢿⣿⠏⣾⡏⠲⠀⠀⠀⠀⠛⢻⣾⡿⣼⣷⡿
⠀⠀⠀⠸⡿⣿⡼⣯⣤⣸⣿⣧⣤⣤⣤⣿⠿⣃⡠⣾⣿⣧⡙⢮⡓⢤⣘⢿⣿⣿⣿⣿⣿⣿⡿⢋⡴⠋⠀⠀⠀⢀⣘⠿⣷⣿⣤⣈⣤⡄⠀⣀⣿⢧⣟⣿⠇
⠀⠀⠀⠀⢻⡾⣷⣻⣿⣿⣿⣿⡿⢟⣫⣴⢿⣿⣷⣜⢿⣿⣿⣶⠉⠰⠦⣭⣉⡛⢛⣉⣭⠴⢆⡉⠀⠀⠀⠀⣠⣾⠛⠻⣦⣝⡻⢿⣿⣿⣾⣿⣟⣾⣿⡟
⠀⠀⠀⠀⠈⢿⣿⣯⠻⠿⣛⣥⣾⡿⡿⠉⠚⢿⢿⣿⣷⣍⡻⠋⠀⠀⠀⠀⠀⠁⢰⣶⣶⣿⣿⣷⠀⢀⣠⡾⢿⣿⣿⠆⠙⠻⢿⣶⣭⣛⠿⢟⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠛⣫⣤⡺⣿⣿⣭⣕⢇⠸⣳⠀⣿⣿⣿⡿⢣⣶⣤⣄⣀⡀⠀⠀⠻⠿⢟⣛⣫⣥⣶⡜⣿⣷⣦⠛⠀⠀⢀⣴⣿⣿⣿⣿⢗⣤⣝⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣝⢿⣿⣿⣞⠆⣹⣯⣔⣹⡿⣡⣿⡿⠿⠋⠉⠛⢿⡇⢸⣿⣿⣿⠻⢿⣿⣿⣌⢿⣿⣆⠀⢠⡿⣿⣿⣿⡿⣫⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡻⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⡀⠀⠀⠈⠃⢠⡇⢸⣿⣿⣿⠃⠈⢹⣿⣿⣎⢻⣿⡧⠀⣱⣿⡿⢫⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢷⣝⢿⣿⣿⡟⣼⣿⣿⡿⠃⠀⠀⠀⣤⣼⡇⢼⣟⣋⠁⠀⣴⣿⣿⣿⣿⣧⢻⣾⣿⡿⣫⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣮⠋⠸⣿⣿⣏⣁⠀⣀⣤⣷⣿⣿⡇⢸⣿⣿⡗⠀⢸⣿⣿⣿⣿⣿⠇⠙⣵⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⣾⣿⣶⣯⣟⣻⠿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣷⣿⠿⣟⣻⣽⣶⣿⣷⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣶⣶⣿⣿⡅⢨⣿⣿⣶⣶⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠇⠸⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣢⣤⣤⣤⣄⡀⠀⠀⠀⢰⣄⣀⣀⡦⠀⠀⠀⠀⠀⠀⠀⢲⣴⣶⣴⠂⠀⠀⠀⠀⠀⠀⠀⣠⢂⣾
⠀⠀⠀⠀⡀⠀⠀⠀⣸⡿⠛⡿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⣿⣿⡁⠀⠀⠀⠤⠀⠀⠀⠻⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠿⢻⠟
⠀⠀⠀⠀⢀⠀⠀⠀⠋⢀⡜⢁⠇⢹⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⠀⠀⠠⣴⣾⣿⣦⣴⣶⣿⣶⣄
⠀⠀⠀⠄⠀⠐⠂⠀⠀⠀⡠⡀⠀⠚⣽⠋⢩⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡁⠀⠀⢀⡠⠏⠀⠀⠀⠀⢸⡆⣿⢩⡟⣿⠀⠀⠀⠀⠀⠰⠿⢠⡏⣻⣿⣿⠿⠁⠀⠀⠠⢞⡽⢁⡤⠟⣻⡿⠉⠋
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⠺⣇⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⡾⠻⣶⡄⠀⠀⣰⣶⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡿⠿⠍⡂
⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⣿⣁⡈⢿⣷⣿⣿⣶⡄⠀⣸⡟⢻⡇⢹⡿⢃⡀⠸⣿⠀⢸⣿⣿⣿⣄⣀⣀⣄⣀⣤⣴⠀⠀⠘⢹⣿⣷⣄⣀⣀⣀⡤
⠀⠀⠀⠀⠒⠀⠀⠀⣰⣿⣿⡟⠹⠆⠀⣴⠞⠛⣿⠀⢸⡆⢸⡇⠀⠀⠧⣹⢀⣿⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⠉⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠠⡀⠀⠁⠀⠀⠀⢸⣦⠿⣿⠀⢰⣧⠀⠀⣴⠏⠀⠈⢿⣌⡻⠦⠤⢖⣣⡾⠃⠀⠸⣇⢸⡟⠛⠛⠻⣿⢿⡄⠀⠀⠀⢠⠞⢻⠟⠛⠻⢿⣿⠁
⠀⠰⠁⠀⢀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠛⠓⠚⠉⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠿⠸⠁⠀⠀⠀⠛⠀⢸⠀⠀⠀⡏⠛
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠈⠂
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⡀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠘⣇⢿⣿⠏⠀⢀⡀⠀⠀⢠⣾⡟⠁⠀⣀⣤⣤⣄⠀⠀⢠⡟⢻⠆⠀⠀⠀⣿⣿⡇⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠆⠀⠀⠀⢀⡤⠤⡌⢱⣿⣞⠛⠉⠁⠀⠀⣿⣿⣷⣄⣰⣿⣿⣿⣿⡆⠀⠸⢿⢶⣿⣿⣶⣾⣿⣿⠃⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠄⠀⠀⠀⣏⢰⣃⡼⠘⣿⣿⡷⢶⡄⠀⠀⠹⣿⣿⣿⣿⡿⢿⢻⣿⠃⠀⠀⠀⣸⣿⡿⠿⢿⡿⣏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠏⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠙⠦⢤⠤⠖⢹⣏⣀⠺⠇⠀⠀⠀⢈⠛⢛⠁⠀⠀⠈⠃⠀⠀⠀⠀⢻⡘⣧⠀⠀⢷⡘⠦⠀⠀⠀⠛⠼⠁⠀⠼⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡤⠠⠄⠠⠀⠀⠀⠀⠀⠑⠀⠀⡐⠤⠄⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠐⠐⠀⠀⠀⠂⠂

⠀⢠⠴⣄⠀⣤⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠠
⠀⠀⠀⠸⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡎⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⣥⡤⢤
⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠸⠥⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠁⠈


⠀⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠐⠳⡖⠳⡖⢳⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠦⡄⠀⠀⠀⠀⠀⠀⠚⢶⠚⣶⠛⡆
⠀⣠⠖⠲⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠸⡏⡷⠀⠀⠀⠀⠀⢸⡅⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⡇
⠀⠻⣄⣀⠟⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢁⠀⠀⠀⠀⠀⣉⣥⣤⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠑⠑⠂


⠀⠀⠀⠈⠒⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠀⠀⠀⠀⠀⠀⠀⠴⠒⢦⣀⣠⠖⠲⠄⠀⠀⠀⠀⠀⠀⢠⡀⢠⠂
⠀⠀⠀⢤⡞⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠐⢤⠀⠀⠀⠀⠀⠀⣠⢤⣀⠉⢁⣤⢤⡀⠀⠀⠀⠀⠀⠀⢺⡷⢿⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂

⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠐⠀⠁⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠉⠋⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⢰⡿⠻⣦⢀⣴⠟⣷⡄⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠻⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠿⠿⠷⢶⠄
⠀⠈⠛⠀⢻⣿⡇⠐⠟⠀⠀⠀⠀⠀⠀⠀⢈⣿⡶⢾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠉⣻⡇⢠⡾⠿⣶
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠋⠀⣘⣷⣶⡿
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠟⠛⠛⠻⠷⣦⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁


⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⡶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⢶⡶⣶⡶⣦
⠀⠀⠀⣾⡏⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⢷⡄⠀⠀⠀⠀⠀⠀⣠⣍⣉⡛⠛⣋⣉⣥⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿
⠀⠀⣴⢿⣧⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿⣸⡏⠀⠀⠀⠀⠀⠀⠈⢹⡿⠁⠀⠹⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿
⠀⠀⠿⣶⡿⣾⡇⣠⡤⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠁⣿⣤⣄
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣠⡄
⠀⠀⠀⡀⠈⢉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢿⣾⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣦⡿⣦⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢸⡟
⠀⠀⠈⢻⣶⡟⠁⠘⠗⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡿⠛⣷⡆⠀⠀⠀⠀⠀⠉⢉⣤⣉⣤⣈⣡⣌⠁⠀⠀⠀⠀⠀⠀⠐⠾⢿⡿⢿⡿⠿⠂
⠀⠀⣴⠟⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣼⠟⠿⠛⠁⠀⠀⠀⠀⠀⠶⠾⠛⠿⠋⠻⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣥⡴⠶⠤⠆⠴⡲⠶⠢⠴⢤⣦⣥⡀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣀⣱⠶⠟⠋⠉⠁⠀⠀⠀⢸⣿⠟⠻⠶⠾⠿⠶⣶⣭⣝⡚⢦⣭⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠒⡋⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠇⠈⠙⠧⣦⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⣫⣶⡿⢧⣦⡀⠀⠀⢰⣿⣿⡷⠀⠀⢿⠀⠠⣶⡤⠋⣤⠀⠀⣼⡛⠀⠀⡀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣩⡞⠃⠀⠀⠀⠻⣵⡄⠀⠀⠻⠇⠀⠀⠀⣸⡀⢀⣀⠀⠀⠉⠀⡘⠋⠀⢠⡤⣤⡀⢀⠀⠀⠙⣷⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⣴⣿⠃⣠⣞⠇⠀⠀⠈⠻⣦⡀⣤⣶⣾⡿⠿⠿⢿⡷⠾⠾⢥⣶⣶⢅⡀⠀⠀⠀⠼⡷⠀⠀⠀⣠⣄⠱⡈⢃
⠀⠀⠀⠀⢀⡞⢾⢃⣬⡟⠀⠺⠯⠀⢀⡀⠀⣠⢞⣫⠖⠻⣯⠀⠀⠀⠀⢸⡇⠀⠄⠀⢨⡿⠻⢿⣦⣄⠀⠀⠀⣀⣰⡿⠟⠛⣷⡐⣶
⠀⠀⠀⠀⢄⣼⠃⠙⠾⣶⣄⠀⠀⠀⠀⣠⢞⣵⠏⠁⠀⠀⠹⣧⠀⠀⢀⣸⣇⣀⠀⠀⡟⠀⠀⠀⠙⢿⣷⠄⡮⠝⠉⠀⣀⠀⠙⣧⡙⡆
⠀⠀⠀⠀⣘⠇⠀⠀⠀⠀⠈⠛⢶⣄⢰⣶⡾⣷⣄⡀⠀⢀⣴⠴⣚⢫⡭⡅⠮⠩⣉⡛⢦⡀⠀⣀⡴⠟⠛⢮⢧⠀⣸⣿⣿⣷⡆⠹⣷⢸⠇
⠀⠀⠀⢀⡞⠀⢠⠄⠘⢇⠀⠀⠀⣠⣿⡝⠀⠀⠈⠛⣷⠟⣥⡚⠉⠀⠀⠀⠀⠀⠀⠙⠳⢝⢦⡉⠀⠠⠀⠈⢧⠷⠉⠙⣿⡽⠁⠀⢹⡆⣍⡀
⠀⠀⠀⢰⡇⠀⠀⢀⡀⠀⢀⠀⠠⣿⡿⠁⠀⠀⠀⣰⢋⣞⠂⠀⠀⡀⢠⣤⣼⠀⠀⠀⠀⠘⣧⢻⡄⣀⣀⣀⣸⡏⡇⠀⠁⠁⠀⢀⣨⣇⢼⣡⡀
⠀⠀⠀⢼⡁⠀⠀⠀⠷⠀⠉⠀⢸⣿⣇⣀⣀⣀⢰⡏⠸⠀⠀⠀⠀⣼⡿⠟⠻⣿⣖⠀⠀⠀⢘⡟⣿⠉⠉⠉⠉⣿⡶⠶⠿⠛⠚⠛⠛⠛⠸⣀⡇
⠀⠀⠀⢞⡀⣀⣀⣀⣀⣀⡄⢠⣌⢹⡟⠛⠉⠉⣸⡇⣋⠀⠀⠀⠀⣻⣇⠀⢀⣼⡯⠍⡀⠀⠀⡆⣿⠀⠄⡀⠀⣿⡿⠀⢀⣀⠀⠀⠀⠀⠸⣣⡇
⠀⠀⠸⠼⡀⠻⡟⠉⠉⠉⠁⠀⠹⠼⡇⠀⠣⠀⢹⣽⠸⣂⠀⠀⠀⠉⣿⡿⡿⡟⠄⠀⠀⠀⣸⢡⡏⣤⣀⠀⢀⣿⡏⢠⡟⠛⠂⠀⠀⠀⢸⡴⠁
⠀⠀⠀⠘⡧⠡⣇⠀⠀⣔⡒⠄⠘⣇⢿⡄⠈⠀⣀⡿⣧⠡⡄⠀⠀⠀⠎⠃⠀⠀⠀⠀⢠⡴⣣⡟⠀⠈⠙⠻⣾⠿⠃⠀⢧⡀⠀⠀⠀⠀⣿⢆
⠀⠀⠀⠀⢻⡀⣾⡄⠀⣭⡴⠸⠀⠱⠊⢷⡴⠟⠋⠀⠙⢷⣌⡑⠦⣄⣀⡀⢠⣠⡴⠴⡫⣾⣽⠁⣀⡀⠀⣰⢏⣽⣀⡀⠀⠉⠀⠀⠀⣸⡧⠂
⠀⠀⠀⠀⠈⣇⠈⣷⡀⠀⠀⠀⠀⢀⡸⢷⣿⣆⠀⢈⠀⠀⠈⣛⣶⣶⣶⣿⡮⣤⠶⠛⠛⠉⠉⣁⡀⢀⣼⢋⠙⠀⠙⠛⢷⣦⣀⡀⣰⣿⣾⠃
⠀⠀⠀⠀⠀⠈⢧⡙⣷⣀⣀⣠⡶⠟⠉⠈⠹⢿⣷⣦⣀⠀⣴⡟⠀⠀⠩⠉⠁⣾⠀⠂⠠⠰⢀⣨⣿⠯⡤⢋⡸⠟⠣⣀⠀⠈⡿⢻⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢘⠷⡈⠛⠋⠁⠀⢀⣤⣰⣄⠈⠹⢿⡾⢽⣿⣄⣐⠃⠀⠀⠀⢿⣇⣀⣤⣶⣿⣿⠻⠀⠀⠿⠉⢀⠰⠁⢀⡾⢡⡚⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢹⣆⡀⠀⠀⠐⣿⢿⡿⠀⠀⢀⡶⠚⠲⠌⣍⣛⢛⡛⣛⠛⢽⠟⠿⠙⠃⠀⠙⢆⠀⠀⠀⠈⢀⡴⢋⣼⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣆⡀⠀⠀⠁⠀⠀⢀⡾⠁⠀⢀⡀⠀⠈⠈⠁⢹⡅⠀⠀⠀⣀⠁⠀⠀⠈⠳⣦⣠⠶⠋⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣦⡄⠀⠀⢀⣾⠁⠀⠀⠛⠀⠐⠆⠀⠀⠸⡇⠀⢅⡸⠿⡇⠀⠄⠀⠀⠙⣡⠰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠱⠴⣌⣛⠷⠤⣤⣀⣂⠀⠀⠀⠀⣐⡇⠀⠀⠀⠀⠀⠀⣀⡤⡤⠍⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⢇⢳⡔⢭⡭⣍⢛⣛⢛⡛⣃⡀⣤⡔⠢⠝⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠈⠀⠙⠒⠛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠠⠤⠴⠄⠂⠒⠲⠀⠠⠶⠤⠄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠣⡰⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠀⠀⠀⠀⠀⠀⠓⠈⣷⠉⠅⠀⠀⠀⠀⠀⠀⠀⠐⣤⠊⠘⠃⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡐⢣⣴⠶⠛⣛⠛⠒⢤⡠⠄⣈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢫⣽⣿⣿⣿⣷⡀⠀⠐⠂⠀⢰⡛⣿⡘⢣⠉⡆⠀⡀⠱⠀⠀⠀⠀⠂⠄⠀⡀⠀⠀⠀⠀⠀⠀⢈⠳⢄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢩⣼⡟⣃⣾⡿⠟⠅⠈⠀⠀⠀⠀⣼⡟⣻⣷⣾⠟⠓⠪⠁⢾⡃⠀⠀⠀⠀⠀⠁⠪⢀⢄⠀⠀⢀⡴⢋⠟⡮⠳⡄
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡔⣿⠃⠒⢀⣄⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢡⠎⠀⠀⠘⢆
⠀⠀⠀⠀⡴⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⢼⡟⠻⡰⠀⡈⠙⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠄⠀⠀⠀⠈⢧
⠀⠀⠀⡼⠀⠀⠀⠉⠛⢿⠟⠅⠀⠀⠀⠀⣀⣄⠚⢋⢥⣌⣿⡘⣿⠀⠣⢔⣓⣤⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀⠀⠀⠀⢣
⠀⠀⡸⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⣀⣜⣯⠐⣀⣠⢌⣣⣿⣿⣻⣷⡄⠀⠐⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠀⠀⠀⠀⠀⠀⢧
⠀⢠⠇⠘⠢⣄⣀⠀⠠⠀⠀⠀⠀⢰⣿⣅⡤⠦⣤⣹⣿⡿⣻⣫⣾⠫⣽⣿⡿⣛⣽⣿⢿⣿⡕⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣀⣀⠘⡆
⠀⡼⠀⠒⠺⠢⡀⢠⠃⠀⠀⠀⢠⣾⡿⠉⠀⠀⠀⠈⠿⡽⣱⡟⢦⣿⣿⢏⣴⣿⡿⢍⣶⠿⠉⢢⢴⡖⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⡇⢁⣀⠇⢛
⢀⡇⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⡟⣽⠀⠀⠀⠀⠀⠀⢸⣇⡟⢬⣿⡿⣱⣿⣿⠯⣹⠞⡗⡀⣪⣾⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠘⠀⠀⢸
⠈⠃⠀⠀⠀⠀⠀⢁⠀⠀⠀⣸⡇⣿⡀⠀⠀⠀⠀⠀⢸⠟⣿⣷⣿⢳⣿⡿⢍⣾⣫⠁⢄⢾⣽⢿⠅⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠰⠄⠄⠀⠀⠀⠠⠐⠀⠀⢀⣿⢿⣿⣧⠠⢄⠀⠀⠀⢸⣿⣿⣿⢇⣿⣿⣝⣲⣯⠅⢣⣟⣿⣃⢨⡴⠇⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐
⠈⡀⠀⠀⠀⠀⠀⡈⠀⢠⣾⠙⣸⡟⣿⠀⠀⠀⠀⠀⠸⡇⢿⡾⡿⣿⣟⢢⡟⡔⡈⣞⣾⠋⢃⡾⡄⡟⠭⣰⠏⠁⡗⠂⣴⡄⠀⠀⠀⠀⡀
⠘⡇⡠⠄⠀⠀⠀⢃⠀⠀⣿⣦⣿⠃⡻⡆⠀⢀⠀⠀⠀⣷⣤⡝⢾⣺⣷⣾⣱⠣⢹⢿⡟⢎⢸⣧⣽⣖⣹⠃⠀⡘⠀⣾⣿⠃⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢰
⠀⢼⠒⠤⢤⡤⠄⠘⡀⠀⠀⢸⣿⡀⢳⣷⠀⠀⠳⠀⠀⠸⠦⠿⠷⠽⠿⠿⠟⠛⠛⠉⠁⠀⠀⢤⡤⠋⣱⣄⠀⡧⢰⣿⠏⠀⠀⠀⠀⠀⠆⡀⠬⢍⣓⣶⡘
⠀⠸⣠⠊⠁⠀⠀⠀⠰⠀⠀⢠⢹⣿⣅⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣗⣁⣾⡄⠀⠀⠀⠀⠀⡌⠈⠙⢖⢲⡬⢧⠇
⠀⠀⢫⠉⠁⠀⠀⠀⠀⠑⠄⠘⠻⣿⣿⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠍⠁⠿⣿⣿⡏⠀⠁⠰⠄⠀⢀⢎⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⠪⠀⠀⠙⠛⠿⢿⣿⣦⣤⣴⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⢄⣪⠟⠏⠐⠀⠐⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠻⠿⠟⠋⠉⣙⠛⠻⠿⠿⠟⠛⠛⠉⠉⠉⠉⡉⠉⠈⠁⣀⡀⢀⠀⠒⡀⠄⠀⠊⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠤⠤⡙⠄⠀⠀⠀⠀⠀⠀⡀⣻⠀⠀⡦⢠⢠⠄⠀⠤⢠⠄⢦⠠⠄⡄⢀⡀⠀⠈⠐⠘⡛⠀⠀⡄⢐⠄⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠠⠤⠼⡀⢀⡄⠀⠁⠐⡄⡀⢀⠀⠀⠃⠘⢒⠃⠚⠚⠘⠒⠃⠈⠀⠂⠘⠒⠃⠂⠁⢀⡠⡀⠊⠀⠊⠑⢄⠈⠉⢆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡍⠁⠀⠀⠀⠀⠀⠐⠐⠤⣀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⠀⠒⠀⠀⠴⠔⠲⠤⠄⠉⠓⠀⣩⡤⠤⠄⡀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⢀⠇⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠠⠀⡄⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡠⠾⢀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠚⣋⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠒⠛⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⡶⠶⡶⢶⣶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠻⡏⠉⠠⣤⣤⡀⢀⣠⣤⡀⠀⣹⠛⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⣠⠀⠀⠀⢿⠀⠂⢿⠛⣿⣿⢟⡿⠁⢠⡟⠀⢰⣆⠀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣀⣀⡀⣿⣤⡆⠂⠸⡇⠀⠀⠀⢹⡋⠀⠀⠀⣼⠁⠀⣨⣿⣶⣄⣈⣀⡈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣦⠀⠄⠨⢉⣿⣿⠻⣧⣤⠀⢹⠀⠁⠀⠘⠁⠐⠂⢠⠇⠀⣾⣿⠉⠉⣿⡟⠛⠁⢀⡴⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⣀⢈⠳⣄⠀⠘⡀⣿⠀⠀⠀⣀⣬⣶⡶⠶⠶⠶⠶⢶⣾⣤⣀⠈⠿⣶⠾⡿⠃⢁⡴⠋⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⣰⡿⠃⢀⣹⡏⣤⣤⠈⠳⢄⠀⢉⣠⡶⠟⣫⣥⣶⣶⣿⣿⢿⣿⡶⣶⣬⣝⡻⢶⣄⡀⢀⡴⠋⠀⠐⢈⣹⣿⣧⠈⢿⣆
⠀⠀⠀⠀⣰⡿⠁⢠⣿⠉⣶⠾⠂⠀⠀⢈⣵⡿⣫⣴⣿⣯⣿⣿⡟⣿⣿⣶⣿⡿⣿⣯⣿⣿⢶⣍⠻⣯⡀⠛⢷⣾⠟⢁⣤⣿⣆⠈⢿⣆
⠀⠀⠀⢠⣿⠃⠀⠘⠇⢻⡟⠂⠐⠂⢠⣾⢋⣾⣯⣿⣿⣽⣿⣼⡿⠛⠉⠉⠉⠙⠛⠿⣥⣿⡿⢿⣷⡜⢷⡄⠀⢻⣶⠛⠉⠈⠙⠃⠈⣿⡄
⠀⠀⠀⣾⡿⢦⣤⣀⡀⠘⠃⠀⠀⢠⡿⢡⣿⣉⣿⣯⡿⠋⠉⠉⠑⠾⠋⠹⣦⠀⠀⠈⠐⠝⣷⣾⣿⣿⣎⢿⡄⠀⠘⠒⢀⣀⣤⠴⠶⢻⣧
⠀⠀⢀⣿⠁⠀⠀⠈⠉⠉⠑⠒⢤⣿⢃⣿⢻⣿⣿⡿⠷⢔⣴⠄⠀⡀⠀⠃⢘⡆⠀⠀⠀⠈⢎⣿⣷⣿⣿⡌⣿⠖⠊⠉⠉⡀⣀⣀⠀⠀⣿⡀
⠀⠀⢸⣿⠀⠄⠀⢠⡶⢦⠀⠁⢸⣿⢸⣿⠿⣿⢃⠀⠀⠀⠀⠀⣀⠃⠐⣩⡝⡧⢨⡍⡀⠀⠀⢸⣿⢿⣿⣧⢻⡇⠀⢠⣟⣸⣿⣹⣷⡄⣿⡇
⠀⠀⢸⣿⠀⣤⣶⡾⠷⠿⢷⡄⢸⣿⢸⣿⣿⣿⣦⡤⠖⠀⠀⠀⣸⠀⠀⠉⢨⣃⣀⠉⠀⠀⠀⢸⣿⡿⠿⣿⢸⡇⠀⢸⣧⣤⣍⡉⢻⡇⣿⡇
⠀⠀⢸⣿⠀⣾⠿⠟⠃⠈⠀⠀⠸⣿⢸⣦⣼⣟⣿⠀⠀⠀⠀⠀⠈⣆⠀⠀⠤⢾⡡⠄⠀⠀⠀⣸⣿⣿⣾⡏⣼⠇⠀⠈⢽⣯⣿⢇⡟⠃⣿⡇
⠀⠀⠈⣿⡄⠀⠀⠀⣀⣀⡤⠤⠚⢿⡆⢿⡟⣿⡿⣶⣤⣤⠀⠀⠀⠘⠀⠀⠀⢺⠀⠀⠀⠠⣢⣿⣉⣿⣿⢡⡿⠓⠒⠤⢤⣄⣀⡀⠀⢀⣿
⠀⠀⠀⢻⣷⠖⠛⠋⠉⠄⠀⠀⠀⠘⢿⡜⢿⣿⡷⣾⣿⡇⠈⠀⢀⣀⠢⠁⠀⠁⠀⢀⣪⣾⣿⣏⣿⣿⢣⣿⠃⠀⣀⣤⣄⢀⠉⠉⠛⣿⡟
⠀⠀⠀⠈⣿⡄⢀⣀⣰⣞⣀⣸⣆⠀⠈⢿⣮⡻⣷⣿⣿⣿⣷⣾⣏⣿⣿⣖⣶⣶⠾⢿⣿⡟⣿⣿⠟⣱⡿⢁⡄⢠⢿⣤⣿⣀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠘⣿⡄⠙⠻⣏⠉⣿⠟⠻⠀⠀⡹⢷⣮⡻⢿⣿⣭⣿⣿⠛⣿⣿⣿⣿⣷⣾⣿⡿⢟⣡⡾⠯⡀⠸⠋⠙⢷⣄⠉⢻⡤⢰⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠀⠉⠀⠀⡠⢋⣀⡀⠉⠻⢷⣮⣝⣛⡿⠿⠿⠷⠿⠿⣛⣫⣥⡶⠟⠉⠀⠀⠙⢦⡈⠀⠈⠙⠿⠟⢡⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢀⣴⠋⠀⠈⢉⣿⠀⠐⠀⠈⠉⡟⠛⠛⠿⠟⠛⠛⠛⡋⢡⣶⡄⠀⡀⠰⣄⠀⠙⢶⣄⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡟⠁⠀⠁⣴⠏⣡⠆⢂⠀⠀⣸⢀⣴⡆⢢⣄⣀⣠⡔⣥⠉⢷⣹⡆⢳⣄⣸⣷⣄⡀⠙⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠻⢶⣯⣠⠾⠀⢠⡇⠨⢾⣷⠏⡩⣿⣿⠆⢸⡆⠈⠉⠿⣶⠿⠛⠁⢉⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠉⠻⡇⠀⣼⠁⠀⠸⣿⣄⣠⠿⠀⠀⠀⢿⠀⠀⠀⠀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣴⣧⣀⣀⡀⠈⠙⠋⠀⢀⣀⣀⣸⣧⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣾⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡀⠀⣤⢀⡀
⠀⠀⠀⠀⠌⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⠎⣸⠵⡇⠰⠧⠸⢏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⡌⠰⠀⡄⠄⠀⠀⠀⠀⠀⢷⡟⣁⡈⣴⠓⠾⠓⠀⣢⠾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠋⠀⢀⢄⡨⠂⠥⡓⢀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢁⡟⠀⢹⠀⠘⠐⡁⡉⠰⣣⠀⠀⠀⠀⠂⠀⠐⢀⣴⡆⠀⡞⠀⠀⠠⠂
⠀⠀⠀⠀⠐⢦⡀⢀⠠⠉⠷⡖⠛⠈⠓⠀⠀⠀⠀⠀⣸⣄⡆⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⡇⢸⡈⡆⠀⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⢀⠂⠀⠩⢩⠄⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠋⢻⣧⠐⠀⠀⠣⡁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣷⣄⡀⠘⠇⠀⠤⠁
⠀⠀⠀⠐⠀⠀⠀⡤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠓⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓

⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢴⡠⣄⡀
⠀⠀⠀⣏⠑⠄⠂⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠠⡇⣰⢀⡄⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠤⣤⠀⢐⡛⠁⣷⣔⠋
⠀⠀⠠⣟⣲⣮⢶⣄⣠⡥⠂⠒⠀⠀⠀⠀⠀⢠⠙⣷⣌⣿⡆⢷⠈⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢾⠠⠄⠁⠈⠓⠀⢦⡄
⠀⠀⠀⢾⣽⣯⡿⣿⡅⢀⣀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢈⡝⠀⠸⠾⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡀⢀⡀⡀⡀⠀⢠⡀
⠀⠀⠀⢻⣿⠟⣿⣿⠓⠈⠙⣹⠀⠠⢸⠀⠀⠀⠀⠀⠘⡇⢄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠉⠁⠀⠀⠀⠰
⠀⠀⠀⡈⠘⠀⠹⠈⠂⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠈⢻⡈⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡅⠤⠸⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⣜⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⢀⠰⢖⠣⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣤⡖⠒⡃⠀⡑⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠓⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣄⣀⣀⡰⠀⠀⠀⠀⠀⠋⢥⠀⡁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠴⠈⠁⠣⠀⠀⠀⠀⠀⠠⠚⠀⢸⢁⡀⢀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠣⠤⠿⠫⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣄⣄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠛⠘⠁⠀⠰⠲⢢⣄⠀⠈⠋⠚⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⡋⠢⠀⠀⠀⠀⠀⠈⠸⠁⠀⡀⠀⢠⠔⢐⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠑⠊⢄⢀⠨⠄⠀⠒⠒⠀⠤⠅⡀⠀⠀⠣⠀⠀⠀⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠗⠁⠀⠀⠀⠄⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠠⠀⠀⢀⢈⣻⡄
⠀⠀⠀⠀⠀⠀⠠⠏⣜⠢⠉⠁⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⢂⣡⡘⠸⡄
⠀⠀⠀⠀⠀⢀⡛⠀⠀⠈⠀⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⣙⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⣺⠰⢆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢄⢠⠀⣗
⠀⠀⠀⠀⠀⢿⠀⠀⠑⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠈⠁⡯
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠄⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠈⣩⠀⠀⣄⡀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⠀⠀⠀⠀⣽⠁
⠀⠀⠀⠀⠀⠀⠘⣇⣔⡡⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠁⠯⣵⠚⣾⢏⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣬⡀⠀⠀⠀⠂⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠐⠀⠀⠀⢘⣿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠠⣀⠀⠈⠉⢐⠒⠀⠤⠄⠀⠒⡂⠁⠀⢠⡀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠑⠋⠀⠀⠈⠀⠀⢂⡘⠀⠀⠀⠀⠀⣘⠈⡊⡔⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⢠⡀⠀⠀⠈⠁⠀⠀⠀⣄⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠙⠛⠛⠋⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣴⡄⠀⠁⡌⠀⣘⡼⠂⡀⡂⠀⢀⠀⠀⣠⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⡗⣶⡤⣦⡌⠈⡾⢛⣂⡁⠁⠀⠀⠈⠲⡀⠀⠀⠕⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⠪⠃⢀⠀⠘⣳⡫⠞⠛⠁⠊⣹⠟⡇⢄⠀⠀⠀⢀⣂⡠⠐⠺⠃⠐⠐⢇⠀⠑
⠀⠀⠀⠀⠀⠀⢀⠄⠁⠚⠙⢹⢏⣿⡔⡎⢡⠀⠰⠻⣆⠘⣉⡿⠀⠀⠀⠀⣠⠟⢩⠁⠠⠀⠈⣤⡁⠡⡄
⠀⠀⠀⠀⠀⡠⠁⠀⠀⢀⣠⠞⠋⠈⠢⠁⢺⣦⡀⡷⢈⠓⠳⣶⡀⠸⢆⣿⣄⣴⡇⠀⢀⣉⣙⠖⠋⠀⢏⣿⡀⠈⠤⡑⡀
⠀⠀⠀⠀⠔⠁⠀⠀⠓⠶⠃⠀⠀⠀⠇⠳⡿⠻⡇⠔⢻⣰⣼⡀⣻⠻⠌⡃⠘⡟⠀⢨⡎⠍⣁⣤⡀⠐⡀⠙⢗⣀⡠⠠⠉⡆
⠀⠀⠀⡌⠄⢀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠛⠋⣿⠤⠛⠉⠉⠀⠀⠀⠀⠉⠈⠛⠦⣬⠈⠙⢿⠿⡌⢂⠀⠀⠈⠓⠑⠛⠈⠀⠂
⠀⠀⡸⢀⠀⠋⠠⠀⠀⠉⠈⢃⠊⠀⠀⠢⡶⠀⠁⠀⠀⠀⠀⢰⡉⢻⠗⠀⠀⢐⢢⣄⠘⢦⣨⠟⢡⡴⣀⣀⡕⠀⢠⠀⠚
⠀⠀⢀⠚⠀⠀⠛⠀⠀⠂⡆⠉⢰⡶⠀⠖⠀⠄⠀⠀⠀⠀⠀⠀⡰⠦⠰⠄⠀⠈⠇⠼⠷⠄⠱⡶⠟⣠⡉⣻⡀⠉⠀⠢⠈⡉⡑⡺⠄
⠀⠀⠘⣄⣤⠀⠀⠀⠄⢀⣹⢘⠓⠥⡍⠀⠀⠀⣴⣤⠀⢀⣿⡾⡡⠤⠷⢠⣠⡤⠀⣄⣀⣀⢀⠠⠀⣚⣿⡿⠷⠀⠀⠀⣄⡀⠷⠦⢠
⠀⠀⠀⠈⠁⢸⠀⠀⠀⠁⠘⠉⠁⠠⠀⠈⠈⠉⠀⠴⢐⠿⠏⠀⢐⡶⢶⣾⢅⡀⠈⠀⠀⠀⠘⠀⢀⣨⡤⢦⡇⠒⠀⡀⡛
⠀⠀⠀⠀⠀⠹⠀⢀⠀⠤⣼⠀⠀⠀⠀⡄⠀⠴⠾⠷⢇⣤⠦⠄⠈⠀⠡⠶⠶⠤⠡⠀⠀⠀⠀⠀⠈⠀⢶⠤⠐⢄⠀⡃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠸⢀⢀⡐⠃⣾⢠⣤⣓⠀⠈⢳⠀⠀⠀⠈⢰⠒⡒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⢢⣄⣛⠻⡦⠄⠄⠀⢠
⠀⢠⠀⡄⠀⠆⠉⠉⠁⠚⠋⠉⠉⣈⡀⠀⠄⠰⣤⠜⢀⠁⠶⡄⠀⣀⣠⠤⠰⡆⣄⡀⣾⡤⠆⠀⠀⣀⠤⠌⠀⠈⠁⠀⠀⣒⢀⣀⠘
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡡⠂⠀⣦⣿⣰⡨⠁⠘⠰⠒⣛⣿⡟⠃⠈⢀⣞⣶⢛⠿⣠⣦⣀⠀⡀⠀⠀⢀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠸⢆⠀⢘⡰⠢⡀⠑⠀⠢⡈⢈⣍⣁⣂⠠⡆⠀⠉⠀⠀⠀⢠⡄⣯⣀⡞⠀⡈⠉⢽⡴⠁⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢉⣡⠘⢻⠳⣄⣸⢢⣄⡀⠘⠛⠻⠟⠮⠭⠷⠀⠀⡠⠔⠉⢢⡄⡧⠉⠀⠀⠉⠀⠦⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⢤⠄⡦⡀⠘⠁⠀⠘⠃⠘⠿⢳⢃⣠⣷⡆⢀⠒⠒⣲⡖⠓⢄⣶⣦⠀⢿⣾⣟⡋⢀⠀⠀⠐⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠧⢈⠀⠀⠀⢴⢂⠢⠔⠿⢒⡏⠙⢿⣤⣈⠀⣿⣸⣼⢃⣠⡞⣙⡁⠀⠀⠹⢜⠥⠂⠈⣹⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠲⠋⠱⠞⠂⢀⣠⡟⠀⠂⠈⠻⠶⠷⠁⢾⣾⡏⢹⠏⠉⠋⣀⢨⡍⠢⡈⠖⠉⣠⠔⢋⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠐⡌⠀⠠⢀⠂⠀⠀⠀⠀⠀⠙⡅⠀⠀⠀⢀⡁⠄⠐⠀⠀⠀⣴⠇⢂⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⢤⠑⠒⠀⠀⣀⣀⠀⠀⠲⠄⢒⡂⠀⡸⣿⠿⡗⣳⡄⠀⠀⠈⡡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠉⠉⡂⠀⠓⠘⢢⡉⠊⠀⠞⠷⣿⡃⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠠⠤⠄⠤⠀⠀⠀⠄⠒⠊⠉⠁
⣶⣶⡶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠉⠑⡀⠁⠬⠄⠐⠒⠒⠒⠒⠂⠀⠤⠀⢀⡀⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠔⠊⠀⠀⠀⠀⠀⢰⠋⠙⣆⠀⠀⠀⠀⠀⠀⡞⡷⣶⡀⠀⠀⠀⠀⠀⠑⠢⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⣶⡤⠿⠀⠀⠀⠀⠀⠀⠁⢣⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠈⠳⣄
⠀⠀⠀⠀⢀⡴⠃⢀⠎⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⣄⠀⠈⠳⡀⠈⢦⡀
⠀⠀⠀⢀⡞⠀⡰⠁⠀⠀⠀⠺⣝⠮⠢⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⢃⡤⠎⠀⠀⠀⠈⢆⠀⠳⡀
⠀⠀⢀⡞⠀⡜⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢂⠀⠹⡄
⠀⢀⡾⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢱⡀
⠀⣸⠁⠠⠀⠀⣀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⠘⠀⠐⠂⡤⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡄⣆⢳⠀⠈⡄⠀⣇
⠀⡏⠀⡀⠀⠀⠏⠑⠲⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡎⠽⠀⠀⢰⢐⢸
⢸⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⡇⠀⠀⠲⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸
⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⠄⠀⢸⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠃
⢸⡇⠂⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠘⠻⣿⣿⣶⡿⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⠤⢀⡄⠀⢰⢀⢠
⠀⡧⠀⠂⠀⠀⢐⡭⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠂⣼⠀⠀⠄⠠⢸
⠀⢹⡐⠘⡄⠀⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡏
⠀⠀⢧⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡼⠁
⠀⠀⠈⢧⠀⠱⡄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠀⠀⠀⢠⠆⠀⣰⠁
⠀⠀⠀⠈⢧⠀⠘⢄⠀⠀⠰⣤⠀⠹⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣀⣨⠗⠂⠀⠀⡠⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠳⡄⢀⠣⡀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⠞⠄⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢦⡐⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢼⢤⡂⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⡀⠀⠀⠀⠀⠀⠀⡠⠔⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠑⠢⣀⠀⠀⠀⠀⠐⠁⠘⠀⠀⠀⠀⠀⠀⠀⢲⣤⠓⠐⠃⠀⠀⠀⣀⠔⠊⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠉⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠉⢀⠀⠐⠒⠒⠒⠒⠀⠈⢈⠉⠄⢀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠶⠒⠒⠋⠉