Snorkeling Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦
⠀⠀⠀⠠⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⠶⣤⣀⣀⣀⣀⣤⠶⣤⣀⣀⣀⣀⣤⠆⠀⠀⠈⢷⡸⣷⣤⣄⣀⣠⣤⠞⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⢠⡞⢷⡀⠈⢷⡹⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠈⠛⠋⠀⠀⠈⢷⣹⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⡋⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⠇⠀⠀⠀⠀⣠⠟⠉⠀⠀⠉⠻⣦
⠀⠀⠀⢀⣤⡴⠞⠋⣡⡄⢈⣿⠞⢿⡀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣀⣤⣤⣤⣤⡏⠀⠀⢀⣤⣄⠀⢸⡇
⠀⠀⠀⠘⣧⣀⡴⠟⣩⡴⠋⠁⠀⠀⠻⣦⠀⠈⠻⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣤⠶⠛⠋⠉⣠⠶⠂⠀⠉⣀⣴⢿⣄⠙⣷⣼⠇
⠀⠀⠀⠀⠈⠛⠶⠞⠉⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⠓⠒⠒⠒⠚⠋⠁⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢿⡀⠀⢶⡴⢿⣅⢀⣩⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢳⣦⣤⣀⠙⢦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣃⠀⠉⠛⠻⠿⣭⣹⠟⠋⠉⠻⣦⣤⣄⣀⣀⣤⣤⠴⠶⠛⣿⠛⢻⡟⠛⢷⡄⠘⠷⠶⠶⠶⠶⠶⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢻⡏⠉⠛⠶⣤⣀⡀⠀⠁⠀⠀⣠⠾⠋⠀⠈⠉⠉⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡶⢸⠇⠀⠀⠀⠀⠈⠙⠳⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣸⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⣹⡟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠺⢧⣄⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠲⠶⣄⣠⡴⠶⠛⠛⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⢀⣀⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠋⠀⠀⠀⢰⠆⢀⡶⠈⠻⣦⠀⠀⠀⠀⠀⠀⢸⡇⣹⠟⠉⠀⠀⢨⡝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⣄⠰⠟⠀⠀⠀⠈⠷⢀⣴⠟⠀⠀⠀⠀⠀⠀⣸⣇⣼⢷⣄⣀⣀⣈⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠤⠶⠋⠙⠳⠶⣤⣤⣤⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⢺⠅⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣾⣅⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠌⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡃⠀⠙⠷⣤⣄⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⡷⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⢉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠉⠒⠒⠒⠒⠊⠉⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣀⣀⣠⡤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⣀⡠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣂⠉⠉⠑⢆⠀⠀⠙⢧⠈⢻⠑⢤⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠉⠁⠈⠀⠀⠀⠘⠀⢰⠀⠀⠀⠀⠀⠈⠃⠈⡶⡄⠀⠀⠀⠀⠀⢠⡏⠉⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⢄⢸⢀⠤⠀⣀⠤⠀⠀⠀⠆⠘⠞⠆⠀⠀⢀⡟⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⠄⠀⣠⠶⠒⠒⠓⠒⠚⠃⠀⠈⠉⠒⠚⠛⠛⠠⢤⡀⠀⣸⡀⠀⣼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⡜⠁⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⢱⠀⠉⣥⢠⠇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢸⣀⣠⣒⣉⣁⣀⣤⣤⣤⡤⠤⠤⠤⠤⣬⣭⣶⣤⣠⣀⠀⣽⣼⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣋⣭⣭⣭⣦⣤⣤⣤⣤⣤⣀⣀⣤⡴⠶⠶⠶⠶⠶⣦⣤⣭⣍⣛⢧⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣾⠟⠛⠉⣩⡯⠶⠶⠶⠤⣄⠀⢀⣄⠀⠀⣀⣠⡤⠤⣤⣘⡄⠀⠉⢻⠹⣷⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⡏⠀⡐⠀⡧⠒⣲⣶⣶⣤⣾⢷⣻⣉⡓⢯⡤⢒⣊⣉⡒⠺⣿⠀⠀⢸⡇⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣷⠀⡇⠀⡇⠘⠉⣯⣿⡿⡳⢋⡤⠤⡉⢦⣱⡹⣿⣿⠻⣤⠇⢀⡇⠀⡇⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢻⠀⠀⠠⡁⠀⠐⠀⣼⡟⣱⠏⠀⠀⠈⢦⡱⣷⡉⠩⠀⢸⡆⠀⠀⢀⡇⡎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⢌⡓⠦⠤⣵⣄⡤⣾⢏⠞⡉⠀⠂⠀⠀⠀⢿⣜⢿⡢⠤⠼⠷⣒⡿⠽⣊⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣯⡶⣶⣶⡾⠟⠋⠀⠇⠀⡀⠀⢰⠀⢸⠈⠳⠬⠭⣭⠭⢶⡖⠋⣽⠉⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠈⡆⠀⠑⢄⠀⠀⠀⠦⠴⣂⣂⣺⣦⠆⠐⠀⢀⡜⠁⢀⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⡀⠀⠈⠑⠂⠴⠴⢦⣄⡠⠶⡶⠦⠤⠖⣋⣤⠖⠋⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⡒⠒⠚⠛⠛⠛⠛⠚⠛⠉⠉⠁⠀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠐⠓⠶⠶⠶⠶⠶⠶⡶⠶⠒⠒⢚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠓⠒⠒⠛⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣱⢤⣀⣀⣀⣀⣀⣀⡴⠋⠀⠀⣀⡠⠤⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠒⢦⣴⣄⣀⣀⣀⣀⣠⣤⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣠⣴⡏⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢳⣟⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠦⠤⠤⠶⢒⣺⣟⡥⢺⡇⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠉⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠈⣧⠀⢸⡄
⠀⠀⠀⢠⡶⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠛⠓⠲⣆⠀⢹⡀⠀⣧
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠛⢉⣉⣀⣤⣤⠤⠶⠖⠚⠛⠻⡆⠘⡆⠘⣇⠀⢹
⠀⠀⠸⡇⠀⠀⠀⢀⣴⠟⠋⣉⣤⠤⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢷⠀⢿⠀⠸⡇
⠀⠀⠀⢷⠀⠀⠀⢸⡇⢰⡟⠉⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡄⢸⡆⠀⣧
⠀⠀⠀⠘⢧⡀⠀⠸⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠈⠻⣦⣀⣿⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⠾⠁⣸⠃⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢧⣀⠀⠀⠀⣀⣀⣤⠶⠋⠉⣉⣉⣉⣉⣉⣉⣁⡤⠞⠁⠀⣾⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠉⠛⠛⢋⣉⣁⣤⠴⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡼⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣠⡴⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠉⠉⠀⠈⣿⣁⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⣀⣠⡤⠴⠀⣀⣠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠶⠖⠚⠋⠉


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

⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠂⠀⠒⠒⠐⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡞⠀⠀⠀⢠⡄⠀⠴⠆⠀⠀⠀⡇⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠐⢃⠀⠀⠀⢀⠚⠉⠑⠤⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠠⠤⠤⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠆⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡜⠁⠀⠀⢀⡀⠀⢀⣀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⢇⠀⠀⠀⠈⡡⠐⠬⡉⠀⠀⠀⢰⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢌⠂⠀⠈⠒⠤⠄⠊⠀⠀⠀⠙⠀⠤⠐⠁⠀⠀⡁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⡀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠂⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⡀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⠑⢀⠁⠄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠉⠒⠚⠀⠀⠈⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠈⠣⡤⠤⢤⠜⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠬⠤⠤⠤⠤⠤⠀⣀⡀⠀⠀⠡⠀⠁⠤⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡾⠁⠀⠀⢠⡀⠀⣠⡀⠀⠀⠈⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡄⠻⡀⠀⠀⢈⠔⠒⠪⡀⠀⠀⢀⠟⠠⠘⠀⠐⠀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠈⠁⠀⠀⠀⠁⠐⠒⠉⠀⠀⠀⠄⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠀⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀
⡀⡀⢀⢀⢀⡀⣀⣀⢀⠀⠀⣀⣀⢀⠀⣀⢀⣀⣀⣀⣀⣀⠀⣀⠀⣀⣁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⢀⡀⣀⡀⢀⣀⠀⣀⠀⠀⣀⣀⢀
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢋⣡⣤⣴⣶⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣤⣶⣶⣤⣤⣉⠻⣶⡀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⣧⠘⣷⣠⣿⣀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢀⣾⠋⣠⣶⢶⣦⡉⢻⣆⠀⠀⠀⠀⠀⢀⣿⠀⣿⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⢿⣄⠀⠀⠀⢠⡿⢁⣾⣿⠇⠀⣿⣿⣆⢹⣇⠀⠀⠀⣀⣼⠇⣸⡏⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡙⠻⠷⠶⠟⠁⣼⢃⣿⠀⠀⢸⡇⢿⡄⠛⠷⠶⠿⢛⣡⣾⠟⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡶⠶⠶⠟⠋⢸⡇⠀⠀⠈⣿⠈⠛⠷⠶⠶⣾⡟⠉⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣿⠟⠛⠛⠻⢿⣇⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⢀⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣦⣀⣀⣰⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠛⠋⠀⣼⡇⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⡀
⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄
⠙⢿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⣠⡀⢀
⠀⠀⠈⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢈⡁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣶⣦⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠙⠃

⠀⠀⠀⢠⡖⠋⠓⣺⣷⡄
⠀⠀⠀⢸⠀⠀⠬⠄⣿
⠀⠀⠀⢸⠀⠀⠤⠭⣿
⠀⠀⠀⢸⢀⠀⠶⡫⣿
⠀⠀⠀⠘⠀⠀⢑⠀⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⢸⠀⠀⢝⠄⡇⠀⠀⠀⢀⡴⠅⠒⠛⠉⠙⠛⠛⠷⠶⠶⢤⣤⢤⣤⣤⣤⣤⣴⣒⣂⠩⠄⠐⠒⢚⠛⠿⣦
⠀⠀⠀⢈⡀⣀⣵⣂⡅⢀⣀⣔⡿⣪⣭⣄⣄⣄⣴⣶⣦⣖⣒⣮⣤⣭⣭⡍⣍⣵⣶⢶⠶⠦⠶⠶⢶⣿⣦⡒⢣⣿⣇⡀
⠀⠀⠰⠏⠀⠀⠀⠁⠀⣠⠊⣻⣸⡽⣩⢁⡤⠠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⠙⣌⢢⢿⣻⡃⣰⡀
⠀⠀⢀⠀⡀⠀⠈⠄⠀⣷⣰⠈⢷⠃⡏⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢽⠈⠐⣿⡟⡐
⠀⠀⠀⠒⡏⠉⠉⢉⡞⠛⣧⢸⣻⠀⡇⣀⢸⡆⠀⠀⠀⠀⠀⡀⣿⠃⠀⢹⣟⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡄⠁
⠀⠀⠀⠀⡇⠀⢐⠄⡁⠀⠈⣿⣺⠀⢣⡀⠀⠀⠊⠀⠀⠀⡐⡸⠁⠀⠀⡂⢿⣾⣦⠀⠀⠁⠀⠀⠀⣀⠔⢽⢸⣶⡿⣦
⠀⠀⠀⠀⡁⠀⠘⠀⠀⠀⠀⢸⡿⡄⠀⣈⣙⣛⣛⣛⡡⢋⠔⠀⠀⠀⠀⢆⠘⣿⣎⠩⠉⡥⠀⠩⡡⠐⠐⢗⣿⠈⠳⡽⢡
⠀⠀⠀⠀⠀⠀⢐⠔⠀⠀⠀⠈⠻⠶⠦⢤⣤⣤⣤⣤⣴⠿⠒⠤⡀⡀⡀⢀⠖⢼⣮⣑⣒⡒⣐⣐⣒⣈⣡⣾⠇⠀⠐⣡⣿⠄
⠀⠀⠀⠀⠀⠀⢀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠙⠦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣁⣄⣴⡿⣺⠷⠋
⠀⠀⠀⠀⢐⠀⢐⠁⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣑⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⡯⠗⠊⠉
⠀⠀⠀⠀⢰⢀⣀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣤⣀⣉⠓⠢⠤⣀⣀⢄⡲⡞⣋⠗⠋
⠀⠀⠀⢠⠗⠈⡉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠻⠿⠻⠿⠯⠧⠛⠁
⠀⠀⠀⢸⠀⠀⡀⡀⣠⡀
⠀⠀⠀⢘⠐⣏⣋⣩⣽⠗⡀
⠀⠀⠀⠸⠀⠈⠉⠉⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢰⣤⠀⠀⠀⠀⡤⢤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠋⠛⠿⠶⠖⠶⣶⠚⠋⠂⠁⢹
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠒⠈⠐⠠⣀⠀⠀⠀⠀⠀⠀⠙⣷⠆⠀⠀⠤⠲⢀⡀⠐⠈⡫⠃
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠖⠀⠂⠁⠀⢀⠀⢤⠂⠼⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣈⠊⠀⠀⠌⠀⠄⠄⠀⢀⡠⠔⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠉⠀⡀⠀⠀⢈⠁⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠐⠀⠂⠀⠀⠂⠨⠔⠄⢊⠔⠔⠨⠂⠅⠀⢊⠀⠔⠨⠀⠄⠀⠨⠀⠔⠔⠠⠀⠀⠀⠠⠊⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠀⠀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣉⠤⠐⠂⠁⠉⠉⠁⠁⠒⠢⢌⡁⠂⢄⡀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠉⡆⠀⠀⢹⠉⡚
⠀⠀⠀⠀⠀⠀⠘⡀⢨⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⠀⠀⠀⠀⠀⠀⡆⢀⠁⠀⠀⢨⣉⡅
⠀⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⠀⠀⡔⠀⣠⣄⠈⢆⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⣤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠳⣀⣀⠔⠁⡘⢰⠈⡄⠀⠓⠤⡠⠊⣠⠊⠀⠀⠀⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡤⠒⠒⠤⣑⠼⠤⣃⠴⠊⠉⠀⡖⡙⠀⠀⠀⠀⠀⡗⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠑⢄⠀⠀⠀⠈⠀⠀⠀⠀⡠⠎⢠⠃⠀⠀⠀⠀⠀⡏⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⡐⠂⠀⠀⠐⢒⡉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠧⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠍⣉⣉⠉⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠤⠤⠤⢰⠄⠀⢀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⢔⠁⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠑⠒⠒⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢄⠂⠶⢦⡠⢐⢦⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡭⠭⡅⠓⠂⠀⠙⠂⠑⢮⢪⢣⠀⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠒⠀⢀⣠⢖⡀⢀⡀⢀⡠⠠⠀⣏⡃⠀⠀⠀⠀⠀⠔⠊⠉⠉⠳⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠦⠤⠴⠁⠘⠈⡔⠉⠉⢢⡠⠀⢯⠂⠙⠀⠀⢀⠄⠀⠀⢀⡀⠀⠀⠘⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⠀⢄⣲⡆⠀⢀⢸⠀⠀⠀⠰⠑⠀⢀⠃⠰⢰⠊⠉⡶⠊⠉⠉⡃⠀⠀⠀⠈⠅
⠀⢲⠀⠀⠀⠀⠀⣰⣀⠀⣸⠀⠼⡑⡠⠄⠐⢄⡘⠘⢄⣀⣠⢜⠕⢚⠧⠄⡦⡜⠒⠂⠧⠤⢠⠔⠁⠀⠀⠀⠀⠈⠄⠀⢀⠐⢁
⠀⠨⠤⠀⠐⠂⠚⠁⡾⠋⠉⠙⠷⠀⠮⠐⢀⠻⠓⠤⣉⠉⠡⡖⠡⢐⡯⠎⠀⠈⠫⠂⠄⠀⠀⠀⠀⠀⢰⠅⠀⠀⠈⢻⡏⢠⠌
⠀⠀⠀⠀⠀⡀⢀⣀⡄⣆⠀⠈⡄⠀⡠⠖⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⡱⢄⡀⠀⠀⠀⠺⣍⠀⢠⠠⠂⠙⠉⠈⡆
⣀⠄⠂⠁⠀⢀⠼⠏⠿⠮⣂⡀⠌⠚⠀⠑⠕⢢⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠁⠈⠒⠄⠠⠤⠚⠓⢾⠀⠀⠀⠀⠈⠁
⠉⠒⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠳⠶⢶⣦⣤⣤⣤⣤⣶⡶⠶⠞⠛⠛⢶⣄⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢠⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠉⠻⣿⣶⣿⠀⠀⣿
⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⣸⠃⠀⢠⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠈⢿⣿⣦⣀⠀⠀⠘⠁⢀⣴⣿⡿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣶⣾⣿⡿⠛⣁⣀⠀⠀⠉⠻⢿⣿⣷⣶⣿⡿⠟⠋⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠙⢷⡄⠀⠀⢠⡾⠋⢉⣿⠀⠀⠀⠀⣿⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⡛⠛⠟⠛⣁⣴⣞⣁⣀⣀⣠⣴⠟⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡛⠛⠉⠉⠉⠙⠉⠉⠁⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣤⣤⣤⡴⠶⠟⠋⠁

⢀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣷⡠⣀⠀⠀⠀⠀⣠⣦⣀
⠈⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠙⠳⠶⠶⠞⠛⠉⠙⠻⠶⠶⠶⠛⠉⠀⠀⠀⠀⠘⣷⡉⠛⠛⠛⠛⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣨⣥⣴⣤⣄⡀
⠀⠀⠀⢀⣠⣴⣶⣎⠿⠟⣭⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠠⣶⣿⡿⣛⣵⠿⠋⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⢶⣶⣄⣿⣿⡿⣣⣮⡻⢿⡇
⠀⠙⠵⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡟⣴⣿⡿⣿⠏⢫⣾⣮⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣷⡁⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣶⣤⣀⡀⠈⠛⠛⠛⠛⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠈⠛⠿⣿⣿⣿⣶⣤⣤⣾⣿⣿⡿⠂⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣶⣶⢴⠶
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣿⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⢀⣾⣿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠱⠷⠆
⠀⠀⠀⠀⠀⠉⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢀⣠⣦⣀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠈⠙⠛⠛⠛⠛⠉⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀⣠⣤⣶⣶⣶⣶⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣬⣑⣆
⠀⠀⠀⠀⠀⠀⢹⣿⡟⣼⣿⣿⢿⣿⣧⣿⡟⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣟⢼⣿⣿⣿⣿⢹⣷⠄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠜⢿⣯⣾⣿⣿⣿⣿⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠈⠛⠻⠿⢟⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠛⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢖⢷⡀⠀⠀⠀⢀⣀
⠈⠓⠲⠶⠒⠋⠙⠒⠶⠖⠚⠉⠓⠶⠶⠒⠋⠙⠲⠶⠖⠛⠙⠓⠶⠶⠚⢉⡤⣄⠘⣯⢿⠛⠒⠚⠉⠉⠙
⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠓⠋⠀⠘⣎⣧⣀⣀
⠀⠀⢀⣠⡤⠾⣏⣀⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⠇⠀⠀⠀⣰⠋⠁⠀⠈⠻⡄
⢶⠚⢉⣤⢖⣠⠟⠉⢳⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢒⣒⠒⠧⠀⣠⡞⢦⣀⣿
⠈⠷⢯⡴⠋⠀⠀⠀⠀⠙⢦⠀⠙⠦⠤⠤⠴⠖⠛⠛⠲⠴⠖⠛⠉⠁⠀⠀⣿⠁⢠⣠⣿⠉⢙⡶⠛⠃
⠀⠀⠀⠀⠀⠀⡴⠛⣶⢤⣈⡳⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⠈⠙⠉
⠀⠀⠀⠀⠀⢰⣇⣠⡯⣄⡈⠉⠛⠻⠿⠋⠉⣙⡷⠦⠤⠤⠶⠒⠛⢹⡏⢹⡏⠉⢧⠈⠓⠒⠒⠒⢲⣖⣶
⠀⠀⠀⠀⢠⡟⣀⢹⠀⠀⠉⠓⠶⢤⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⠳⢤⣈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⢀⡞⢠⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣈⢹⡶⣤
⠀⠀⠀⠺⠦⣼⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣀⣤⡴⠲⢤⣄⣠⡤⠖⠦⡄⣀⡀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣄
⠀⠀⠀⠀⢸⡛⠓⣦⠴⠚⠋⢙⠛⠳⢦⡀⠀⠀⠀⠀⠀⢤⠦⣄⡤⠿⠿⢦⣀
⠀⠀⠀⠀⢸⡇⠰⣇⠀⣤⠀⠋⠀⣏⠀⣹⠆⠀⠀⠀⠀⢸⠀⣯⡀⠀⠀⢇⣹⠇
⠀⠀⠀⠀⢸⣤⡴⠟⠳⢤⣄⣤⣤⡴⠚⠁⠀⠀⠀⠀⠀⠙⠋⠉⠉⠿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠔⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡀
⠀⠀⠀⠀⢠⠟⠻⣦⠀⠀⠀⠀⢀⡞⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⢻⠦⢠⣼⠇⠀⢠⠖⠉⠐⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⣏⠀⠘⡇⠀⠀⡜⠁⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟
⠀⠀⠀⠀⠹⡄⠀⢹⡀⠀⢷⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢳⡀⠀⢧⠀⠀⠳⡀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⡤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⢳⠀⠈⢧⠀⠀⠈⠢⣄⡁⠒⠒⠀⢀⣠⠴⠖⠦⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⣧⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣍⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠛⠲⠦⠤⠤⠴⠶⠒⠚⠋⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢦⣤⣴⣤⡤⠤⠴⠖⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠶⢶⣤⡀⠀⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣆⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠋⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠛⠿⣿⣷⣄⣿⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡀⠀⠈⢿⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⣿⣧⡀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠹⣿⣷⣄⡀⠀⠀⠀⠋⠀⢀⣴⣿⡿⣿⣦⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⣶⣶⣶⣾⣿⠿⠃⠀⠀⠀⠈⠻⢿⣿⣷⣶⣶⣶⣾⣿⠿⠋⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁⣴⠿⠻⣶⡄⠀⠀⠀⠈⣹⡿⠻⢿⣏⠁⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⢿⣦⣤⣤⣼⠏⠀⣠⡾⠃⠀⠀⠀⢀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣭⣥⣤⣶⠿⣿⣤⣤⣶⠶⠿⠛⠁⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⣶⣶⠶⠶⠾⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠲⠦⣄⡀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢁⡤⠒⠒⠓⠒⠒⠒⠒⠶⠦⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠦⡀⠙⢆⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡖⣦⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⣄⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡟⣿⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡴⠃⠈⢣⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡟⠋⢰⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠹⣄⠀⠀⠀⠀⢀⡤⠋⢀⠞⠁⠀⠀⠀⠱⣄⠘⢦⣀⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⢸⡗⠶⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠙⠛⠛⠋⣉⣠⢴⣉⣀⠀⠀⠀⠀⣀⣈⣷⢄⣈⠉⠛⠛⠛⠉⣠⠞⠀⠀⠀⢸⠯⢭⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⢉⣉⣀⣀⣀⣈⣉⣉⠉⠉⠉⠀⠀⠀⠀⢀⡾⢝⡲⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡴⠶⠤⠤⠬⠵⠤⠤⢤⡤⡤⣖⠻⣕⠦⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⢪⣱⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⣀⡈⠛⠛⠋⢉⣉⡽⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⣴⡾⠿⣶⣀⣀⣤⡾⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠞⠉⠀⠀⠀⠀⡍⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⣠⡾⠁⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⠶⠀⣠⠶⠆⣸⠟⠁⠀⣰⠟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠞⢁⣠⠞⠁⠀⠀⡴⠃⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡜⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠋⢠⣴⣞⡉⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢠⡴⢿⣥⣀⠀⠈⠉⠙⠳⠶⣤⣾⣿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠰⣮⣥⣤⡀⠈⠙⢷⣶⣶⡶⠶⠾⢿⡋⠀⠀⣠⣼⠷⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠉⠙⠛⣶⣿⣿⠋⠀⠀⢀⣾⣿⠟⠛⢉⣤⣶⣿⠿⠿⠛⠻⣷⡄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⢰⣿⣿⠁⠀⠀⣠⣿⣿⠋⢀⣾⠿⠟⠋⠁⠀⠀⢀⣠⣼⣿⡄⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⡏⠀⠀⢠⣿⣿⣧⠞⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⠟⢻⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⣤⣤⣾⡿⠉⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋⠁⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣾⣿⣿⠿⠿⠛⠉⠁⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣦⣤⣤⣤⣶⣶⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⠛⠿⠛⠉⠁⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣶⣤⣤⢀⣠⡤⠀⠀⠀⠀⢀⣴⠟⠋⣉⣤⣀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠛⠛⠋⠑⠋⠁⠀⠀⠀⠀⣴⠟⠁⣠⠞⢛⡝⠋⠀⣈⣤⣄
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣤⣀⣀⣀⣤⣤⣤⣶⡇⠀⠀⠀⣼⠇⠀⠘⠁⠐⠊⠀⣰⣾⠋⠉⠹⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠰⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣶⣠⡟⠁⠀⠀⠀⢀⣀⣀⠀⢀⡀⣸⣇
⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣀⣀⣀⡠⠤⠠⢶⣾⣿⣿⣿⡟⠀⠁⠔⠀⠰⠏⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⢻⠋⡩⠽⣇⠀⠀⠀⠀⠀⠀⢤⣤⠂⠀⠐⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⠉⠉⠙⣄⡀⠀⠀⠱⣾⢀⡐⠀⡌⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⢙⣦
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣴⣿⡇⠀⠀⠀⢹⣿⣷⣄⠁⠀⠀⠀⣰⠿⠋⠉⠀⠀⠰⠟⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠿⢿⡇⠀⠀⠀⠀⠛⠀⣿⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡜⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣾⣇⠀⠀⠀⠀⣷⣶⣿⣇⠀⠀⠀⠀⠈⠳⢄⣀⣀⠴⠛⣠⡟
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⠀⠙⢷⣄⡀⠀⠀⠀⠛⠉⠉⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣅⠀⠀⠀⠀⠙⣿⠛⢷⡖⠒⠒⠉
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣆⠀⠀⠀⢸⣿⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣧⠀⠀⢰⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⡀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⡤⠤⠒⠛⢋⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⡇⠀⠀⢻⣇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠌⠀⠒⢛⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢠⠀⠀⠈⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣈⣁⣤⡤⠒⠒⠉⠉⠀⡉⠈⠉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⢙⡇⠀⣇⣰⠶⡆
⠀⣤⡤⠶⠖⠋⠉⠁⠀⢀⣀⣤⣴⣶⣾⣿⣶⣦⣄⣀⠀⠉⠻⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣤⡴⠲⠻⢧⣤⠿⠋⢸⣧⡴⠛⣿
⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⠀⠀⣀⣠⣤⠶⢋⣁⠴⠞⠁
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⢇⠀⠀⢰⠋
⠈⠛⠛⠋⠈⠛⠿⣿⣿⠿⠟⠛⠛⠉⠁⠀⣀⡀⠀⠤⠤⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⠘⣇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠖⠛⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⡀⢰⠉⡄⢻⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⢸⠀⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢾⣀⣧⣤⣽⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⣦⣴⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⣀⢠⡀⠄⠒⠶⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠶⡲⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠣⠛
⢠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⠀⠀⠀⣀⠀⠀⢀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠠⡈⢀⣠⣾
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢰⠿⢾⡿⢿
⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⢀⣀⣀
⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⢀⣼⣿⡟
⠀⠀⠀⠙⢿⣶⣤⣤⣤⣤⣴⣶⡿⠏⠀⠀⠀⠀⠀⠻⣿⣶⣦⣤⣤⣤⣤⣾⡿⠋⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠁⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣟⣀⣔⣀⣴⣢⣴⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⣴⣶⣶⣶⣶⣶⣶⣶⡆⠄⣤⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣹⣿⣧⡀
⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣿⣿⣿⣥⣄
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠻⠿⣷⣿⣷
⢀⣶⣤⡻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣿⣼⣿⣿⣶⠄
⠀⠀⢹⣧⡛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⣿⣿⠇
⠘⢷⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠠⣴⢮⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣷⣬⣠⣤⢀⣀⣻⣿⣿⣷⡄⠀⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⡇
⠀⠁⠉⠀⢈⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣤⣸⡿⢿⢿⣽⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣵⠾⣼⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣠⣤⡴⢦⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡤⠤⣀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣤⣴
⠀⠀⠭⠥⠶⠦⣌⣿⣿⣿⣿⣿⡇⠀⠀⠐⠋⠹⠶⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣋⣭⣭⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⣤⠤⠤⣤⠀⠀⠀⠀⠉⠋⠀⢰⣶⣿⣿⣿⣷⣓⣰⠛⠒⠀⠈⠉⠈⠛⠉⠀⠀⠙⠛
⠀⠰⢶⣶⠶⢦⡀⠀⢠⣤⣄⡀⠀⠀⠤⠦⣬⣷⣤⣿⣿⣿⣶⡄⠈⠙⣿⣿⡿⠋⠉⠁⠀⢾⣿⣿⣿⣷⠆⣀⡴⣶⡒⠲⠆
⠀⠀⢀⣠⠶⣌⣷⣴⣶⣿⣿⣿⣦⠀⠀⠀⠀⠈⠉⢉⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠻⠿⠋⠉⠉⠁⠉
⠀⠈⠉⠀⠀⠈⠛⠋⠁⠹⢟⡉⠿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣧⡄⢀⣀⣀⣀⣠⣼⣧⣠⡴⠚⠉⠀⣶⣿⣷⣦⣤⠶⢆⡀
⠀⠀⠀⣀⣠⠶⣄⠀⢠⣤⣤⣧⣤⣀⠀⠀⢠⣤⡴⣾⣿⣿⣿⡀⠀⠁⠈⠉⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⢷⣤⡟⠙⠒
⠀⠀⣘⡿⠷⠶⠿⠶⠿⠿⣿⣿⡿⡟⠀⠰⠶⠛⠗⣻⡋⠁⠈⢧⡀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⣀
⠐⠋⠉⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⡄⠙⣷⣄⠀⣀⠀⠀⣀⣷⠎⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⣀⡾⣹⠟⠛⠂
⠀⢰⡒⠊⠉⠙⢦⡀⢠⣶⣶⣿⣶⣦⠀⠀⠀⠈⠹⣿⣿⣷⣿⡾⠇⠀⠉⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋⠀⣀
⠀⠀⠙⠚⠛⠶⢬⣽⠿⠻⡿⣿⠻⠉⠛⠉⠁⠀⠀⠻⡿⡿⠟⠁⠀⠠⣤⣄⣀⣀⡀⠀⠰⠚⠁⠋⠉⠀⠀⠀⠀⢾⣽⣧⣐
⠀⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⡠⠖⠚⣿⣿⡇⠈⢀⣠⣶⣶⣶⡂⠀⣠⢦⡤⠄⢼⣿⣿⡏
⠀⢹⣿⣿⣿⠿⣾⣿⣿⣟⠁⠰⣿⣿⣿⣿⣿⣤⣞⣩⢭⣀⠈⠀⠀⠀⣿⡿⠁⠀⠈⡿⠿⢿⠿⠿⢾⠿⠉⠑⠀⣸⠿⣿
⠀⠀⣉⣚⠟⠳⠟⠉⠛⠋⠁⠀⠀⠉⠋⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⣰⠁⠀⠈⣀⣀⠀⠀⠀⠀⡾⠁⠀⡿
⠸⢿⣿⣿⣿⣿⣆⣀⣤⡴⡶⠄⠀⠀⢀⣶⣶⡄⠀⣀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠀⠀⢰⣆⣤⣭⣿⡇⠀⠀⢸⡇⠀⢰⡇
⠀⣤⠙⠛⠏⠛⠻⠿⠋⠀⠈⠑⠀⣠⣼⣿⣿⢿⣄⡏⠙⠛⠛⠃⠀⣲⣄⣀⣠⠤⠒⠂⠉⢿⣿⣿⣿⡴⣷⡀⠀⠀⠘⠓
⢀⣈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⠻⠃⠈⠉⠁⠀⠀⠒⠒⠛⢿⣿⣿⡀⠀⠀⠀⡀⢰⡟⢉⡏⠀⠀⠀⠀⢀⣆
⠀⠉⠉⠹⣷⣄⣰⣶⣾⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠀⠀⠀⠀⠓⢬⡁⠀⣀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠙⠛⠛⠻⡿⠿⢿⣷⠤⠀⠀⢠⣤⠀⠀⠀⠀⠀⣀⣘⣷⠋⠀⠀⣀⣀⣀⣀⣀⠀⢙⣷⣿⣧⡀⠴⠹⣿⣿⡿⣇
⠀⠀⠀⢀⡀⠀⠀⣠⢁⣀⣀⠀⢠⡄⠀⠘⣿⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠘⠻⠷⠦⠭⣽⣿⣿⡿⠛⠱⣄⠀⣿⢿⡇⠈
⠀⠀⢘⣻⣿⣷⣶⣋⡾⠀⠀⣀⣀⣻⣀⣼⣿⣯⣄⣤⠤⠒⠃⠀⠀⢀⣀⣀⣀⣀⠀⢀⡴⠛⠚⠒⢦⠀⠀⠀⠀⠹⡌⣧
⢀⡴⠟⣿⣿⣿⣿⡟⠁⠀⠀⠈⠀⠹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⠞⣁⣤⠶⠒⠋⠀⠀⠀⠀⣰⡇⣿
⠈⠁⠀⠉⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⠟⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠿⠛⠛⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠉⠛⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⣀⣤⣴⣶⡾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⢷⣶⣦⣤⣀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠻⣷⣄⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⣠⣾⠟⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠉⠻⢷⣶⣤⣤⣴⡿⠋⢀⣤⣶⠿⠿⣶⣤⡀⠙⢿⣦⣤⣤⣶⡾⠟⠉⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣤⣄⣀⡀⠉⠁⣀⣴⡾⠏⠁⠀⠀⠈⠙⢿⣦⣀⠈⠉⢁⣀⣠⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠸⣿⡛⠛⠛⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠉⠻⣷⣦⣤⣴⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠈⢹⡿⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣾⣇⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣒⣠⡤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⢏⡾⣿⣿⣿⡟⣸⡆⣦⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠸⡄⢿⣣⡟⠁⡕⠪⡿⠼⠿⢃⠟⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠳⣌⣽⣿⢌⢂⠀⠀⠈⠂⠉⠀⠈⠀⠀⠈⠀⠀⠁⠀⡀⠀⢠⢠⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⢆⢢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⣨⣢⠽⢃⠎
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠐⠄⢣⠀⠀⠀⢫⢹⣀⠀⠀⠀⠀⠙⢾⡷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠡⠀⢣⠀⢰⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠀⠀⣧⠀⠁⠀⠪⡛⢝⠿⢿⣿⠟⢶⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⡞⠉⢧⠀⠀⠀⠈⠢⡉⠢⢄⠀⠀⠑⢄⠈⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠸⡀⠀⢧⠀⠠⠀⠀⠈⠒⢄⠈⠲⣤⠞⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⣇⠀⠡⡀⠀⠀⠀⠑⠀⡈⠓⠆⡀⠈⠑⢤⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠡⠘⣆⠀⠱⡀⠀⠀⠀⠀⠀⠠⡀⠉⠢⣄⠀⠈⠢⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢣⡰⣘⣤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠲⢄⠈⠙⢦⡐⣮⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠓⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣧⣤
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡋⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣿⣟⠿⠇
⠀⠀⠀⠀⢰⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣿⣿⣧
⠀⠀⠀⠀⢸⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠿⣯⡉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠻⣷⡶⠖⠚⠛⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠸⣧⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⣄⣾⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⠉⠉⠻⠿⠟⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣤
⠀⠀⢀⡿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⣾⣿⣿⣿⣿⣿⡻⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣏⠹⡀
⠀⠉⠛⠛⠀⠹⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⣿⠻⣿⠈⠃
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⣿⡿⠿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⣣⠀⠀⠀⠀⠀⠀⣀⡴⠇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⢴⡿⠋⠀⠀⠀⠀⢻⣷

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠛⠛⠛⠓⠲⢦⣄⢰⠋⢳⠀⠀⣀⡀⠀⠀⠀⠀⠳⣀⡀⣀⡰⠃
⠀⠀⠀⠀⢀⡞⠉⠈⠙⡄⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢻⡉⠁⢠⡏⠁⠈⡇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠈⢷⣀⣀⡴⠃⠀⠀⠀⣿⣡⣴⠃⢀⣀⠤⠊⠀⠈⠢⡀⠀⠀⣷⡖⢢⠓⠦⠖⠃⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡴⠒⢤⠁⠀⠀⠀⠀⢀⣿⡤⣤⡾⠶⠾⣚⣛⣛⢷⣤⠗⠚⠉⢻⠉⠉⠀⠀⠀⠀⠀⠀⢰⠋⠉⣳
⠀⠀⠀⠘⢧⣀⡼⠀⠀⠀⠀⠀⣿⣾⡟⢉⠭⠁⠀⠁⡔⢌⣾⢿⣆⡠⠔⣿⡿⠿⢿⣦⠀⠀⠀⠀⠈⠓⠚⠁⠀⣠⡀
⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡘⠜⢲⣿⣶⣈⣁⣿⡿⠁⠀⢠⣿⣤⣤⣼⢿⣦⣄⡀⠀⠀⢾⣩⠆⠀⠓⠁
⠀⠀⠧⡤⠇⢰⠋⢳⠀⠀⠀⠀⠀⠙⠿⣿⠿⠛⣀⣘⡛⠛⠋⠀⣀⣴⣯⠿⣭⢭⣉⠉⠁⠀⠙⢦⠀⠀⠀⡴⠚⠓⣄
⠀⠀⠀⢀⣀⠈⢉⣁⠀⠀⠀⠀⠀⠀⠀⢈⣷⣾⣿⣿⣿⣠⡴⠚⠁⠀⠀⠀⠇⠀⠈⢳⡀⠀⠀⠈⣇⠀⠀⠳⣀⣀⠞
⠀⠀⠀⠸⠼⠃⠘⠛⠀⠀⢀⡀⠀⢀⣼⣻⣿⣿⣯⣥⣂⣀⣧⣀⣄⠀⠀⢰⠀⠀⠀⠀⢷⣀⣀⣀⣿⠀⠀⠀⠀⢀⡠⣀
⠀⠀⢀⣤⢶⣻⣿⣿⣽⡷⠮⣍⡓⢾⣿⣿⣿⢹⠉⠉⠉⠉⠉⠉⠉⣷⠀⢸⠀⠀⠀⠀⢸⡀⢀⣂⣿⠀⠀⠀⠀⣇⠀⢈⡇
⠀⣠⣞⣿⣫⡁⠀⠀⣿⣟⠓⠦⣍⠃⠈⠻⣏⠘⠶⠶⠶⠶⠶⠶⠶⠃⠀⢸⠀⠀⠀⠀⢸⣯⢿⣿⣿⠀⠀⠀⠀⠈⠙⠉
⡒⣶⣾⡛⢸⡇⠀⠀⠙⠮⣍⣛⡒⠀⠀⠀⠈⡇⠉⢢⠤⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠗⠶⠶⣿⠀⠀⠯⠇
⣨⠤⠴⣙⠈⢧⣤⣤⣤⠴⠇⠀⠀⠉⢰⣶⣤⢣⠀⠰⠀⠀⠀⠀⠉⠐⠒⠒⠀⠀⠀⠀⣼⠉⠳⠀⢻
⠒⢤⣶⣞⠁⠀⢘⡶⠈⢷⠀⠀⠀⣠⢿⣯⣿⡉⠘⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢀⡴⠁⢸⠀⠀⢏⡽
⠀⠈⠻⣿⣿⣶⣌⠁⣀⣞⣀⣠⠴⠃⢸⣯⣷⣇⠀⠀⠀⠀⠈⠉⠐⠂⢤⣄⣀⣀⣠⣴⣿⡋⠀⠀⢸
⠀⠀⠀⠀⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⢻⣽⣿⣬⣀⣀⣀⣰⡶⠿⣽⠋⠡⠉⢿⡾⡿⣿⡥⠤⠄⢼⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⢤
⠀⠀⠀⠀⠀⣞⠁⢉⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⣿⣿⣵⡒⠓⢫⣄⠀⢀⡼⢋⠕⠉⡇⠀⠀⢸⡆⠀⠀⠀⢀⡤⠾⡉⠉⠑⡌⣧
⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠒⠤⣀⠉⠉⠀⠉⠉⢉⠔⠁⠀⠀⢿⠀⠀⢸⡇⠀⢀⡴⠋⠢⢀⣨⠀⠀⣠⡿⡆
⠀⠀⠀⠀⠀⠀⠿⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣆⠀⠀⠉⠒⠠⢀⢀⠆⠀⠀⠀⠀⢸⡆⠀⢸⣇⡴⠋⠀⠀⢀⣴⡿⣶⣾⡿⡇⢹⡄
⠀⠀⠀⠀⢀⣀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⣢⡾⠋⠀⠀⢀⡴⠋⢸⡇⣨⢰⠇⢠⠀⢷
⠀⠀⠀⠀⢯⣨⠇⠀⣈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠸⡋⠀⠀⠀⡴⠋⠀⠀⢸⠀⠛⢸⣶⠘⡀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⡶⠄⠀⠀⠀⠀⣠⢀⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣸⠀⡆⠀⣾⠀⢃
⠀⠀⠀⠀⠀⠶⠆⢈⢿⡟⢉⣀⠀⠀⣄⡠⢼⣯⡶⠂⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣿⠀⠁⠀⢺⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣽⡶⣷⣾⠅⠀⠐⣷⣮⠞⠛⡉⠀⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠲⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⢸⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠉⢳⣮⣿⠀⢀⣿⣿⢏⠀⢀⣿⣾⣽⡂⠀⠀⠀⠀⠈⠳⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣀⡀⢸⠀⣀⢃
⠀⠀⠀⠀⠀⢤⢴⡄⠈⠻⢿⣦⣸⡻⣞⡖⣲⢟⠷⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠉⠹⣼⠞⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣾⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣗⢍⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠙⢿⣿⣷⡿⡝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣀⠀⢹⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⣿⣿⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⢦⣻⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⡿⠂⠀⠀⠒⠒⠒⠶⠶⠖⠚⠛⠛⠋⠁⠀⠀⢀⣈⣿⡟⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣞⡽⠷⠶⠚⣛⣛⣛⣛⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⠚⠿⢿⣿⣷⢭⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⡵⠶⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠙⠛⠻⢶⣤⡿⢷⢿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣌⡛⢛⣿⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠭⠭⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣯⣛⣛⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠛⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣗⣲⣖⣺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣭⣓⡶⢶⣖⣺⡿⠋⢠⡿⠁⢸⣇⠀⡙⠻⣿⣦⢤⣀⣀⣀⡤⢞⣿⣾⡷⠭⠽⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡍⢩⡁⠀⢾⣩⣀⠀⣀⣤⣤⣻⡄⠀⠉⠛⢒⠒⠒⠚⣫⣴⣟⢯⣝⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣇⣠⣤⡶⣻⣿⣿⣷⣶⣥⣄⡀⠀⢠⣯⣤⣾⢻⡿⣞⠪⣝⣲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⡿⠫⣻⣿⣼⣷⡿⢮⣽⣿⣿⡿⡞⣿⢹⡜⢎⢧⣙⣮⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠹⠷⠾⢷⣝⠀⢉⡿⢘⣧⡻⣌⣷⣽⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠳⢶⣶⣿⡟⠉⢠⢞⣽⠟⠟⠉⢨⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠸⣧⣤⣬⣾⠃⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⣤⣶⣶⣤⣭⣍⣤⣤⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣩⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢡⡾⠉⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⡟⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠁⢠⡅⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⢠⡜⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠃⠀⠀⣠⡾⠁⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣴⠟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡾⠋⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⢠⡄⠀⣠⠋⠀⢀⡀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠘⠁⣴⠟⠀⢠⡟⠃⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣀⣀⣀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣾⣿⣿⣿⣿⣷⣦⣉⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⠿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠁⠀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⠟⠁⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⠿⠿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢤⣶⣤⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⣿⠇⠀⢻⣿⣿⠿⠋
⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣀⣤⣤⠴⠒⠒⠒⠲⣦⣄⠀⠀⠀⠀⠀⠸⣿⠀⢴⣯⣀⠀⢸⣏⠁
⠀⠀⠀⠂⠀⠀⠀⣠⡾⠛⢻⣀⠀⠀⠀⣠⣶⠶⠟⠙⠛⣶⣄⠀⠀⠀⢹⡇⠈⠀⢹⣷⠀⣿⡆
⠀⠀⠀⣦⠀⣀⠾⠉⠀⠀⠀⠙⠷⠶⠾⠟⠁⠀⠀⠀⠀⠀⠙⣷⠀⠀⢸⡇⠀⣠⡿⠃⠀⣿⡇
⠀⠀⠀⢸⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡦⠀⠀⠀⠈⠿⡀⢸⣧⡴⠟⠁⠀⠀⣿⡇
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⠻⣷⣄⠀⠶⠶⠶⢦⣀⠀⠀⠀⠀⠀⣿⡶⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⣄⡀⠈⠻⢷⡀⢀⣤⡀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠘⠛⠿⣆⠈⡇⠀⠙⠛⠀⠉⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠋⢱⡆⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⡟⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠒⠂⣤⣤⣈⡉⠙⠻⠿⠟⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣽⡏⠈⠛⠃⢤⡤⠤⡤⠛⠁⠅⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣀⡾⠁⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⣀⡴⠋⠀⠀⢀⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣿⣤⡾⠋⠁⠀⠀⣤⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⣄⣉⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣿⠛⢀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠐⠒⠀⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠓⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎
⠀⠀⠀⣠⠤⠖⠒⠛⠉⣉⣁⣀⣠⣤⣔⣒⣚⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣓⣒⣦⣤⣄⣀⠉⠉⠙⠒⠒⠦⢄⡀⠀⠀⡞⠀⢣
⠀⡰⠋⠀⠀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀⠀⠀⠈⠢⣀⠇⢸⢸
⡼⠀⠀⡠⠊⠀⡠⢔⡺⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣒⢤⡀⠈⢦⡀⠀⠀⢹⠀⡏⡇
⡇⠀⡰⠁⢠⠎⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⢄⠀⢡⠀⠀⡏⢠⢱⠁
⢧⢀⠇⠀⡏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡄⠀⣇⢠⠃⣸⡼
⠘⣾⠀⢰⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣇⠀⢻⣹⠀⡇⡇
⠀⢸⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⢸⡇⢰⢹
⠀⠸⡀⠀⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⣉⣉⡓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⣿⠁⡼⡞
⠀⠀⢧⠀⢱⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡴⣫⠴⠒⠲⢍⠲⣌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠀⢰⡿⢀⢇⠇
⠀⠀⠈⢆⠀⠱⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⢎⣞⣁⣀⣀⣀⣀⡙⣌⢦⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠜⠁⢠⠋⡇⢸⢸
⠀⠀⠀⠈⠳⣄⠈⠑⠮⢗⣦⣤⣤⣤⡤⠶⠋⢁⣴⡵⠋⠉⠀⠀⠀⠀⠀⠉⠉⠢⡑⢄⡙⠲⠦⣤⣯⣽⣦⣶⠿⣽⠃⢀⡴⠃⢸⠀⡟⡏
⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⣶⣤⣤⡇⢉⠒⢂⡈⠈⡗⠁⠀⢀⡟⢠⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⣦⡀⠣⣞⡁⢀⣠⠎⡠⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢍⡒⠤⠭⠭⠔⢋⠴⠋
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣽⣿⣶⣶⣿⣥⣶⣶⣶⣦⣶⣶⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⣤⣀
⠀⠀⠀⠙⠻⠷⣶⣤⣤⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⣴⣶⣄⠀⠀⠘⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣠⡴⠾⠷⣮⣽⣷⣶⣄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⡀
⠒⠈⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠹⠗⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣄⠀⠀⣠⡿⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⢻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣬⡿⢿⣿⣿⣿⣿⣶⣿⠇⠀⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠙⠻⢷⣭⠉⠉⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠈⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠛⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏
⠀⠀⢀⣀⣴⣾⠿⠿⠟⠋⠁⠘⣿⣿⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⣤⡄
⠀⢀⣾⡟⠁⠀⠀⠀⣠⣴⣤⣶⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⢩⣿⡟⠁⠀⠀⠀⠀⠀⢀⣿⣿⡟
⢀⣾⡿⠀⠀⠀⠴⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⣼⡿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠋⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠸⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⢸⣿⡇
⠲⠿⣦⣸⣿⢿⣿⣿⣿⣿⣷⣤⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⢸⣿⡇
⠀⠀⠈⠛⠃⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣀⡤⠶⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠙⢿⣿⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠀⠀⠀⣰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣿⡵⠶⠶⠶⠶⣦⣤⣀⡀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠦⣽⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⢀⣴⠾⣛⣭⣴⠶⠾⠛⠛⠷⣦⣌⣉⠛⠛⠛⠛⠛⢋⣉⣤⡶⠟⠛⠻⠶⢶⣬⣍⡻⢶⣄⠀⠀⠀⣿⣿⣿
⠀⣰⠏⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡌⢷⡀⢀⣿⣿⣿
⣿⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣿
⠿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⢿⣿⣿⣿
⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⢶⣄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣿⣿⣿
⠀⢻⡆⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣡⡟⠁⠀⠀⠙⣧⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣼⠃⢠⣿⣿⣿
⠀⠈⢿⣌⠻⠶⢦⣤⣤⣤⣤⣤⣼⢋⣼⠏⠀⠀⠀⠀⠀⠈⢻⣌⠻⣤⣤⣤⣤⣤⣤⠶⠾⢋⣴⠏⠀⢸⣿⣿⣿
⠀⠀⠀⠉⠛⠳⠶⣶⣤⣤⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣤⣴⡶⠶⠛⠋⠁⠀⠀⢸⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠶⢤⣄⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⢀⣼⣇⠀⢀⣠⣴⣶⠛⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠤⠤⠤⢤⣤⣀⣀⣀⡀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠛⠒⠒⠒⠛⠓⠲⠦⢤⣀⣀⣀⣠⠤⠶⠒⠛⠓⠒⠒⠚⠳⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⠤⠶⠒⠒⠚⠛⠛⠛⠒⠦⢤⣀⣀⣀⣠⠤⠶⠚⠛⠛⠛⠒⠒⠲⠦⢤⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣀⡈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠁⠘⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣾⠀⠀⠀⢸⣆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⢤⣀⠀⠀⠀⠀⠀⡼⠁⡼⡇⠀⠀⠀⠀⡿⣄⠹⡄⠀⠀⠀⠀⢀⣠⠞⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣬⣍⣛⣒⣒⣚⣡⠞⠀⡇⠀⠀⠀⠀⡇⠘⣦⣙⣒⣒⣒⣋⣩⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠉⠉⠹⣇⢰⡇⠀⠀⠀⠀⣷⢀⡿⠈⠉⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡬⠿⣅⠀⠀⠀⢀⡽⠯⣄⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠉⠉⠁⠢
⠀⠀⠀⠀⡠⠄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠭⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠤⠀⠂⣀⣡⠌⠹⠑⡀
⠀⠀⢀⠎⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠒⠉⠉⢈⠠⠁⠐⣤⠈⢀⡤⢧⡂
⠀⠀⡀⠀⠀⠈⠐⠠⠄⠀⠀⠁⠁⠒⠠⠤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠚⠋⡏⠩⠐⡀⠀⠤⠀⣼⠁⠀⠈⡆
⠀⠀⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢹⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⡇⠀⠀⡇⠀⠑⠨⠢⠴⠚⣥⠀⠠⠊
⠀⠀⠠⠀⠤⠀⠒⠀⠀⠀⠂⠤⠀⡜⠀⠀⢸⠠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⢁⢀⠀⠠⠠⠔⠛⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠘⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠻⠀⠑⣐⣎⣀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠂⠀⠈⠩⠁⠘⠁⠀⠀⠀⠠⠊⡩⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠕⠀⠀⠐⠀⠤⠀⢠⠄⠀⠀⠀⠀⠀⠐⠈⠀⠀⠘⠀⠀⠀⡇⠰⠀⠀⠀⢀⠃⠊⠐⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡡⡈⠂⠤⠚⢁⠔⠀⣀⠔⠁⠀⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢐⡖⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠖⠀⠑⠀⠁⠙⠆⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⡜⠃⠒⢣⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⡁⠀⠀⠀⠀⡨⠷⠦⣤⣀⣈⣻⡉⠙⢄⠀⠀⠀⠀⠀⠀⠀⠉⣓⡶⠶⢖⠒⠀⠁⠀⢠⠊⠔⠈⢑
⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠐⠀⠈⠑⠂⠀⠒⠁⠀⠀⠀⠀⠈⢙⠟⠉⠂⠀⠓⠀⠠⠤⠤⠀⢶⡟⠁⠀⠀⠀⠈⠁⠒⢰⠂⢀⠒⠫⠭
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⡲⠄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀⣀⡀⠤⠚⡆⠈⠒⢠
⢀⠠⠒⠉⠀⢀⠄⠀⠀⡠⠊⠀⠀⠈⠉⠒⠲⠤⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠐
⠃⠀⠀⠠⠊⠀⠀⠄⡔⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄
⠘⢄⠀⠀⠀⠀⠐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠐⢄⡀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣶⠟⠉⠉⢉⣁⣀⣁⣀⣈⠉⠉⠙⠻⣶⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠎⠑⣚⣛⣋⣉⠭⣭⣥⠄⣠⣌⣭⠥⢭⣬⠍⣉⢋⣛⠒⡈⠷⠦⣀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣩⣶⠞⠛⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠊⠛⠛⢷⣶⣍⠢⣀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡹⣧⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⣶⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣇⢿⡄⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢰⣿⣿⣿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣿⢸⡇⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡴⠉⠀⠀⠀⠙⢆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⡏⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢷⣧⠀⠀⠀⠀⠀⠀⠀⣰⢃⣾⠁⠀⠀⠀⠀⠀⠈⣷⡙⡄⠀⠀⠀⠀⠀⠀⢀⣯⡟⡸⠀⠀⢸⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡳⢷⡀⠀⠀⠀⣠⠞⢡⡿⠅⠀⠀⠀⠈⠄⠀⠀⠹⣷⡈⠢⣀⠀⠀⠀⣠⡮⢋⡴⠁⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠬⠭⠭⠭⣤⣞⠳⢤⡤⣖⣒⣢⣤⡖⣒⡲⢤⡴⢞⣲⣤⠭⠭⠭⠥⠒⠉⠀⠀⠀⠀⢸⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠈⠉⠉⠁⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣄⣨⢷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⢀⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠐⠒⣸⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠄⠀⢼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⢹⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠶⠶⠚⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠒⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠨⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⠀⠀⢀⣀⣠⡖⠛⠋⠉⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠟⠁⠀⠀⢀⡤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⣤⣤⣄⣐⢸⡇⢀⣠⣀⣴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠒⠒⠒⠈⠉⠉⠉⠉⠉⠒⠒⠒⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠴⠒⠊⠉⢀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⣀⠉⠙⠒⠦⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⢸⢸
⠀⠀⠀⠀⠀⡠⠖⠋⠉⢁⡠⠤⠤⠐⠒⠒⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠦⠤⢄⡀⠀⠉⠉⠒⢄⠀⢸⠁⡇⡇
⠀⠀⠀⢠⠎⠀⠀⡤⠊⠁⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠈⠑⢦⡀⠀⠀⠑⡾⢰⢧⠁
⠀⠀⠀⡎⠀⢀⠎⠀⡰⢪⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣕⢦⠀⠱⡄⠀⠀⠇⢸⡸
⠀⠀⠀⡇⠀⡎⠀⡜⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢳⠀⢹⠀⢸⠀⣇⡇
⠀⠀⠀⠸⣰⠁⢰⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⡗⡞⢰⢻⠁
⠀⠀⠀⠀⢹⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡇⠀⣧⠇⣸⡜
⠀⠀⠀⠀⠸⠀⠸⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⣿⠀⣇⡇
⠀⠀⠀⠀⠀⣇⠀⢇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⢖⡫⠭⢍⡲⢌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⠀⢰⡇⢰⢸
⠀⠀⠀⠀⠀⠘⡄⠈⢦⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡔⡵⠉⠀⠀⠀⠉⢦⠳⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠁⢠⢯⠃⡼⡏
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⠪⣗⣤⣄⣀⣀⣀⡤⠔⠋⣠⣪⠞⠉⠉⠉⠉⠉⠉⠉⠳⣝⢤⡙⠲⢤⣄⣾⣹⣦⣤⣾⣙⠏⢀⡰⠃⡜⢀⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠉⠉⠉⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣶⣤⣀⡏⢙⡿⢶⠚⠉⡖⠋⠀⢀⠇⡸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢼⣧⡀⢧⡔⠁⠀⣠⠊⡠⣣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⡒⠬⠭⠭⠔⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⣉⣉⣉⣉⣉⡉⠛⠛⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡠⠖⠋⠁⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⢤⣉⡙⠓⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠙⠻⣦⡀⠀⠀⠀⠀⢀⣶⣟⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⢻⡄⠀⠀⠀⣾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⣉⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⣿⠀⠀⢰⡏⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⠦⣄⡀⠀⠀⠀⠀⣠⠎⢀⡾⠉⠈⢻⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⡾⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣉⡉⠙⠛⠉⠁⣠⠟⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡿⠀⣰⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⣾⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⢧⣠⡏⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣠⠴⠃⢀⡾⣧⣀⡿⠓⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣌⣉⡉⠛⠋⢉⣁⣠⡶⠛⠀⠀⣽⠓⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⢀⣼⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠉⠛⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡭⢽⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠙⠳⠦⣤⣤⣤⣤⣤⠶⠞⠋⠁⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠉⠢⢀⠀⠀⢀⣤⠞⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠑⢦⣾⣿⣤⣶⠈⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⠛⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⠻⣿⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⢀⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⢀⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋⠀⣠⣦⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⡿⠁⠀⠀⠈⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⡀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠠⣯⡄⢀⠜⢕⠻⠛⠐⠂⠀⠀⠴⢖⣶⠋⠀⠀⠀⠀⠠⠄⠀⢀⠀⠤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠁⠀⠀⠀⡀⠂⠤⠀⠠⠸⡅⢈⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠈⠳⠦⠤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠂⠀⠀⠐⠷⠾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⡿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀
⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠟⡟⠻⢿⣿⣿⣿⣿⣿⣿⠿⠶⠄
⠀⠀⠀⠚⠓⢦⣄⣀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣷⣟⠘⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣄⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣳⢤⣀⣠⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠶⢾⣿⠿⠇⠉⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣭⣤⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣶⣿⣿⣿⣛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠑⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠳⣌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡝⣷⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⣀⣴⡞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡼⢁⠀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣇⠈⠄⠀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⣇⠌⢦⡈⠂⢌⠢⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠈⠳⢶⣭⣓⠶⣌⡢⡑⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣤⢺⠇⠈⠡⠐⠀⠀⠀⠀⠀⠉⠛⢦⣳⠐⡄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣳⠝⠁⡞⠀⠀⠡⠀⠔⣀⡀⠀⠀⠀⠀⢀⠿⠶⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠦⣞⠁⢀⣠⣤⣄⡀⠒⠁⠀⣠⢤⣶⣯⡓⠛⠫⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⠇⢠⠏⡔⠛⠲⣝⣦⣀⣠⢾⠍⠂⠑⢝⢷⣘⡚⠒⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⢸⢸⡁⣀⣤⣸⣇⢣⣹⣅⠀⣾⡷⠀⢢⢻⡁⠉⢸⠈⢧
⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣠⠴⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠓⠚⠛⢛⣧⡄⢹⢸⢋⠕⠋⢷⡄⠀⠀⠀⢣⠃⡀⢸⠀⣸
⠀⠀⢻⠀⠀⡉⣉⣉⣉⠥⠴⢒⡿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠲⣤⣤⡤⠖⠋⠉⡀⢸⠟⡜⣖⠤⠤⢊⡷⠸⠿⠇⠈⢰⠀⠀⣤⠏
⠀⠀⡸⠁⡰⠀⠀⣼⠀⠀⢀⣿⡀⠀⠀⠱⣄⠀⠀⠀⢀⣀⣴⠛⢿⠉⠁⠀⠀⠀⢀⡠⠛⠻⢤⣘⣦⡉⠛⣉⢣⡡⣀⠠⣸⣞⣠⠶⠃
⠀⠀⢧⣀⣉⠒⢆⠘⣦⠖⠉⠀⢳⡀⠀⠀⠈⠳⠴⠚⠉⠀⠘⡄⠘⣄⠠⠔⠒⠉⠁⠀⠖⢄⠀⣹⢆⡿⠲⠤⠤⠛⠋⠛⠚⠙
⠀⠀⠀⠀⠈⢳⢸⣾⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣄⠀⠀⠀⠀⠈⢁⣨⣴⠃⠀⠑⢤⣀⣀⣀⣀⡴⣳⡤⣤
⠀⠀⠀⠀⠀⣏⡴⠁⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣠⣤⡀⠀⠘⣆⠘⢦⣀⣠⠤⣞⡽⠛⠉⠳⣄⠀⠀⠈⠉⠁⠀⢧⠀⣯⢽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡶⡶⠒⠲⠦⠤⠤⠤⠖⠋⠀⠀⠀⢈⡷⠲⠯⠔⠋⠁⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠒⠚⠒⠭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⣠⠴⣋⠜⡽⠁⠀⡗⠲⠶⠤⠤⠤⣤⡤⠴⠊⠁
⠀⠀⠀⠀⢰⡊⢡⣊⣁⢰⠃⠀⡼
⠀⠀⠀⠀⠀⠙⡄⠀⡰⢉⠳⣾⠁
⠀⠀⠀⠀⠀⠀⢇⠸⣔⠉⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣿⣿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡉⠻⡄⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⡉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⣷⠀⠀⣿⣤⢤⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣋⣍⡛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⠀⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣸⠃⠀⢹⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⣧⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⠃⠀⠀⠀⢹⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⠦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣸⠃⣿⠀⠀⠀⠀⠘⡇⠸⣆⡀⢀⣀⣀⣀⣀⣀⣀⣠⣤⠾⠁⢸⠇⠀⡿⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⠤⣤⣤⣉⣉⣉⣙⣛⣛⣛⣁⣰⠇⠀⠀⠀⠀⠀⢻⣄⣈⣉⣉⣉⣉⣉⣉⣡⣤⣤⠤⠶⠞⠋⠀⣰⢇⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⢣⡞⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⡤⢤⣄⠀⠀⠀⠀⠀⠀⣀⣠⣴⣞⣭⠞⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣴⢛⡿⠿⠿⠿⠷⠦⠤⠾⠶⠶⠒⠚⠛⠛⠋⠉⠉⣁⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠸⣅⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣜⣳⣞⣿⣟⣿⣟⣩⡽⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⡶⠶⣶⣶⣶⠶⠶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠛⠓⠒⠾⠍⠀⣀⠀⢀⣛⠿⠿⠷⠒⠛⠛⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠰⠒⠛⠀⣿⣿⣿⣿⣶⣦⠀⠂⠀⢠⣴⣶⣿⣿⣿⣷⠛⠛⠒⠄⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢀⢀⡀⡀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢁⡟⢸⣿⢻⡈⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠺⠁⢸⣿⡞⠗⠘⣿⣿⣿⣾⠀⠀⠀⠀⠘⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⣿⡿⡁⠀⢀⠀⢸⣿⡇⡀⠀⢘⢿⣿⣿⠀⠀⠀⢀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣷⣄⠀⠐⣤⢀⠟⠁⢠⡀⢸⠄⣿⣿⡿⡇⣄⠈⠈⠻⣿⣤⠂⠀⣡⣞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣡⣾⠟⠉⠑⠦⣈⣩⣴⣤⣿⣇⠟⠚⠉⠉⠂⢟⣽⣤⣠⣦⣉⣡⠴⠋⠙⢿⣦⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣾⠋⠀⠀⠀⠀⠀⠘⠿⣿⣷⣦⠉⠐⠀⠀⠀⠐⠈⢡⣾⣿⣿⠿⠁⠀⠀⠀⠀⠈⢻⡆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⢄⣀⡤⢂⡂⠀⠀⢐⣸⡿⠃⠂⢘⠃⠀⠀⢛⠀⠂⠻⣿⣐⠂⠀⠀⣂⠢⣄⣀⠴⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⠿⠓⠒⠒⠚⠛⢇⠀⠀⠀⡆⠀⠀⡆⠀⠀⢀⠟⠛⠒⠒⠒⠻⢷⣶⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡘⢲⣿⠀⢸⣷⠞⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢇⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣦⣤⣤⣴⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣦⣤⣀
⢀⣴⣾⣿⢿⣛⣋⣭⣥⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠉⠙⠛⠛⠋⠉⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣬⣭⣙⣛⡿⣿⣷⣦
⣾⣿⢉⣴⣿⠿⠟⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⣿⣧⠀⠀⠀⠀⣼⣿⠋⠁⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠿⣿⣦⡉⣿
⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿
⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿
⣿⣿⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣿
⢹⣿⡄⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢠⣿
⠸⣿⣇⠘⢿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡿⠃⣸⣿
⠀⠻⣿⣶⣦⣍⣛⠻⠿⢿⣿⣷⣶⣶⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣶⣶⣾⣿⡿⠿⠟⣛⣩⣴⣶⣿⠟
⠀⠀⠀⠉⠛⠻⠿⣿⣿⣶⣶⣶⣤⣭⣭⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣭⣭⣥⣴⣶⣶⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⠋⠛⠛⠉⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠉⠛⠛⠛⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣤⣴⣶⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣶⣦⣤⣤⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠉⠻⣿⣷⣤⣤⣾⣿⠟⠉⠉⠉⠉⠛⠛⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣲⣾⢋⢉⣁⠀⠈⣁⢀⣉⡈⣉⣻⣶⡢⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⣛⣂⣭⣭⡥⡌⠲⡶⠤⠴⠶⠦⠐⢶⡀⡍⣭⣭⣁⣘⣓⠤⢀⠀⠀⠀⢸⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡱⣄⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢸⡄⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⣿⣿⣧⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢄⡇⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⡜⡠⠊⠀⠀⠈⠣⡘⡄⠀⠀⠀⠀⠀⠀⠀⣈⣿⠸⠁⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⣧⠀⠀⠀⠀⠀⢀⠜⣴⠇⠀⠀⠀⠀⠀⢷⡌⢆⠀⠀⠀⠀⠀⢠⣿⢣⠃⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⠳⠄⡀⠠⠔⢉⡜⠋⠀⣀⠀⠀⢀⣀⠈⠛⣌⠓⠤⠀⠀⠴⢛⡵⠃⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠛⠧⠬⠿⠵⠖⠽⠿⠕⠦⠽⠯⠤⠟⠋⠉⠉⠈⠁⠀⠀⠀⠀⣸⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⠩⠉⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⢲⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠦⠶⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣏⡐⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠒⠢⠴⠲⣤⣄⣠⠴⠶⠋⠉⢀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣿⠈⠃⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠳⠷⠼⠛⠒⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⠟⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠈⢉⣁⣀⣀⠀⠀⢠⣿⡟⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⢻⣿⠄⣴⣿⠿⠻⢿⣿⣆⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⠟⢸⣿⡇⠀⠀⠀⣿⣿⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣾⣿⠏⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠀⠀⠀⣠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⣠⣾⡿⢋⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣠⣾⡿⢋⣴⣿⠟⠁⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢠⣾⡿⢋⣴⣿⠟⠁⠀⠀⠀⠀⣰⣿⠟⠛⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠉⠀⠙⠛⠁⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣶⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣶⣾⣿⠿⠛⠁⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⣀⣾⣿⠃⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠐⢾⣿⣿⣤⣤⣤⣤⣴⣾⡿⠟⠁⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠻⣿⣷⣄⡀⠈⠉⠛⠛⠛⠛⠋⠉⠀⣀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⠟⠀⠐⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠟⠛⢦⣀⡤⠾⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠶⠶⠤⠶⠈⠀⠀⠀⠀⡠⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠙⠂⠉⠀⠀⠀⠀⠀⢀⠄⠀⣴⠞⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠥⠀⠀⢀⣀⢀⣠⡖⠁⢀⡾⠃⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢁⡠⠞⣩⡼⠋⠀⣠⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣡⠞⠁⠀⠀⣰⠏⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡾⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣏⠀⠈⠙⠓⠲⢤⣄⣤⣶⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢤⣆⣈⡀⠉⠛⢷⣶⣶⣶⠤⣾⡟⠉⠀⢀⣨⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⡀⠀⠀⠈⠉⠙⠓⢶⣾⣿⠋⠀⠀⣼⣿⡷⠞⢋⣡⣴⣿⣿⡿⠿⢶⣄⠀⠀⠀⢸⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⢠⣿⣿⠃⠀⢀⣾⣿⠏⢀⣴⡿⠟⠉⠁⠀⠀⢀⣼⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡏⠀⠀⣼⣿⡧⠒⠋⠁⠀⠀⣀⣠⣴⣾⣿⠟⢻⡿⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠧⠤⢴⡿⠋⠀⣀⣠⣤⣶⣿⣿⣿⠿⠛⠁⠀⣸⠇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣿⠿⠿⠟⠋⠉⠁⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠈⠉⠉⠀⠀⠉⠁⠀⠀⢀⣠⡴⠤⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⠿⣧⠶⠛⠀⠀⠀⢀⣾⠟⢁⣤⣶⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡿⠁⠰⠋⢠⠊⠀⣠⡴⠶⠦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣧⣀⡼⠋⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⠀⢤⣶⣾⣿⣿⡿⠁⢋⡄⠀⡴⠋⠈⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠛⠉⠿⢇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠈⠹⢀⡀⠀⠀⢢⢀⡀⠐⡬⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠘⢻⡄
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣤⣴⣿⡆⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠜⠏⠀⠀⠀⠀⠟⠛⠘⡏
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⢻⡇⠀⠀⠀⡇⠀⣯⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⠄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡇⠀⠀⠀⣿⠿⠿⣆⠀⠀⠀⠀⠈⣓⠀⠀⠐⠉⣠⠏
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⡁⠀⠀⠈⠳⣤⣄⣀⣀⣉⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢧⡀⠀⠀⠀⢸⣏⠉⢻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢳⡄⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⣀⣤⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢸⡇⠀⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⢀⣀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠒⠉⠉⡏⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿⠀⠀⠘⣿⠀⣿⢠⣤⡄
⠀⠠⠤⠔⠒⠋⠉⠁⢀⣀⣠⣤⣴⣶⣿⣶⣤⣀⡀⠉⠛⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣤⡤⠶⢿⣤⣿⠞⢺⣃⣠⠖⣶
⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠉⠀⠀⢀⠀⡀⠴⢛⣩⡤⠞⠋
⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡀⠀⢰⠋
⠀⠈⠉⠀⠀⠉⠻⠿⠟⠛⠉⠁⠀⢀⣀⣠⠄⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⡄⡦⢰⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡇⢸⢀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢷⡾⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⡀⠀⠀⠀⢀⡀
⠠⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣷⢻⡟⢿⣿⣿⣿⣿⣿⡿⠷⠄
⠀⠘⠓⠦⣤⣀⠀⠀⠐⡶⣿⣿⣿⣿⣾⡁⠋⢙⡛⠋⠁
⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⣷⣤⡾⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣯⣷⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣙⣿⣿⣿⠿⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠉⠻⢿⣿⣿⣿⣦⣤⣴⣶⣶⠶⠟⠛⠋⠉⠛⠛⠻⠿⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢦⡙⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠋⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠻⣦⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣏⣠⣴⠶⠟⠛⠛⠛⠛⠛⠛⠷⠶⠶⣦⣤⣤⣤⣤⠶⠶⠶⠛⠛⠛⠛⠛⠛⠻⠶⢦⣤⣸⡇⠀⠀⠀⠀⣿⣤⣤⣤⣾
⠀⢀⣤⡴⠾⠛⠉⠁⣀⣤⣤⡶⠶⠶⠶⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⡶⠶⣶⠶⠶⠶⢦⣤⣀⡈⠉⠛⠳⠶⣤⡀⢸⡇⠀⠀⣿
⣰⠟⠁⣠⣤⠶⠞⠛⠉⣡⠟⠁⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠉⠉⠉⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢉⡿⠻⠶⣤⣄⠀⠹⣿⡇⠀⠀⣿
⣿⠀⢸⡏⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢹⡇⠀⣿⡇⠀⠀⣿
⣿⠀⢸⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⣤⣴⣶⣦⣤⣾⡁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⣿
⣿⠀⢸⣷⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣰⠟⠉⢀⣀⣄⣀⣀⠈⠻⣦⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣤⢾⡇⠀⣿⡇⠀⠀⣿
⣿⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣰⠏⠀⣼⠋⠉⠉⠉⠙⣷⡀⠸⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢸⡇⠀⣿⡇⠀⠀⣿
⢻⣄⠈⠛⠶⣤⣄⣀⡴⠋⠀⠀⠀⠀⠀⣰⠏⠀⣼⣿⠀⠀⠀⠀⠀⢿⣷⡀⠹⣧⠀⠀⠀⠀⠀⢀⡤⠞⣁⣤⡶⠟⠁⣠⣿⡇⠀⠀⣿
⠀⠙⠷⣦⣄⡀⠉⠛⠷⣦⣄⡀⠀⠀⣰⠏⠀⣼⢿⡏⠀⠀⠀⠀⠀⢸⡟⣷⠀⠹⣧⠀⠀⢀⣠⣾⠷⠛⠉⢀⣠⣴⠾⠋⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠉⠛⠷⠶⠋⠀⣼⡏⢸⡇⠀⠀⠀⠀⠀⢸⡇⠘⣧⡀⠙⠷⠾⠛⠉⢀⣠⣴⠾⠛⠉⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣤⣴⠾⠋⠛⠛⠻⣦⣤⣀⣤⣴⠿⠛⠛⠙⠳⣦⣤⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⢀⣤⠾⠋⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⣠⡾⠁⠀⣠⡶⠛⠁⠀⠀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣏⠉⢀⣴⠞⠉⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⠋⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡋⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡶⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣟⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣞⠛⣆
⠀⠀⠀⠀⠀⣿⠀⢿
⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠖⠒⠒⠒⠒⠒⠲⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⡤⠖⢋⣉⡤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⢬⣉⠓⠦⣄
⠀⠀⠀⠀⠀⡇⠀⢸⡴⠋⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⠙⢦⡀
⠀⠀⠀⠀⢠⠷⠖⢺⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢳⣤⡄
⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⡇
⠀⠀⠀⠀⠘⡶⠒⣾⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⣸⠷⠃
⠀⠀⠀⠀⠀⣧⡤⣿⠹⣄⠙⢦⣀⡀⠀⣀⣠⠔⠁⠀⢀⣀⣤⣤⣀⡀⠈⠳⣄⣀⣀⣀⣠⠴⠋⢀⡴⠃
⠀⠀⠀⠀⠀⡇⠀⢹⠀⠈⠳⢤⣈⣉⡉⣉⣀⣠⠴⠞⠉⠁⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⢷⠤⠺⡆⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢸⡄⠀⢳
⠀⠀⠀⠀⠀⠀⢳⣀⡼⢧⡀
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡰⠋⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⢀⡏⠈⠉⠛⡖⠒⠒⠚⡏⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠴⣧⣤⣤⠴⠧⠖⠋⠁