Exciting Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠄⢐⣶⣒⠒⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⡥⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠚⠉⠁⢦⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⠀⠀⠀⠀⡇⢀⡤⠭⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⣤⢀⠟⠁⠀⠀⠁⠀⠀⠀⢩⠃⠀⠀⠀⠀⠀⠐⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠂⢳⡀⠘⠗⣏⡀⠀⠀⠠⠀⠀⠀⠀⢸⣀⣀⣀⠀⠀⠀⠙⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡖⠠⢙⠂⠘⣏⣡⠔⠁⠀⠀⠀⠇⠀⠠⢤⣦⣌⠙⡎⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠁⠀⠘⠁⠀⠀⠀⡠⢃⠆⠀⠠⣄⡉⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠐⢀⡼⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠑⠢⣄⡀⠀⠀⢷⠤⠀⠀⢘⡂⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢂⡄⠄⠀⠸⡆⢈⡑⠠⠄⠀⠠⡤⠼⠇⠀⠀⠘⠞⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠂⠀⠀⠈⠁⠄⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠙⠑⠒⠒⠒⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⡋⡐⣷⣦⠤⠤⢀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠒⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⠀⢐⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠓⡞⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⠀⠐⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠉⣿⣿⣿⠿⠿⠟⠛⠉⠉⣀⣠⠉⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⢀⣀⣰⣤⣤⣴⣶⣾⣿⣿⠏⣿⠀⠀⣾⠘⣸⣿⡄
⠀⠀⠀⠀⠀⠀⣧⠀⣠⣇⠀⠦⣇⡀⠁⠰⠤⠄⠒⠦⠝⣿⠿⠟⠛⠛⠿⡋⡁⠐⠿⢄⣡⣿⡄⠞⠀⠈
⠀⠀⠀⠀⠀⢸⡿⠰⠋⠉⡠⠆⢁⠉⠁⠈⠀⠰⠆⠒⠀⢀⠀⠂⠀⣧⠀⠈⠈⠐⢲⡦⡀⠈⠱⠔
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⡰⠀⠁⠀⠀⠀⡆⠀⡀⠀⣸⣴⣿⡀⠠⠄⠀⠀⠀⠀⠀⢰
⠀⠸⠀⠄⠀⠀⠀⠀⠀⠰⣶⣶⣶⠀⠀⠋⠀⠲⠸⣿⠘⢋⠄⠉⠉
⠀⠀⠀⠀⠀⠂⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡄⠀⠀⠀⠀⢀⡟⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠙⡾⠁⠀⠀⠀⠀⣸⠁⠀⢀⣿
⠀⠀⠀⠀⠀⣠⣀⠀⡾⠙⡆⠀⣠⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡴⠛⠁
⠀⠀⠀⠀⠸⡇⠈⠳⠇⠀⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡴⠚⠓⠲⣄⡀⠀⠘⠟⠋
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢳⡄
⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣴⠋⠀⢷
⠀⡼⠁⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⢀⠀⠀⠀⡟⠦⡀⠀⢠⠞⠣⣀⠀⢠⢷⡀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢠⠞⠁⠀⠀⢸
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠤⠞⠁⣀⣀⡀⠁⠀⠀⠈⠙⢡⠀⠉⠒⣠⡤⠖⣾⠁⠀⠀⠀⠀⣴⠋⣀⣀⣠⣤⠼
⡿⠀⠀⡀⢠⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠇⠀⢠⠊⠁⠀⠉⢢⠀⠀⠀⠀⠈⢇⡔⠉⣀⡈⢳⣼⠀⠀⠀⠀⠀⠉⠉⠉⠁
⡇⠀⠀⠉⠁⠀⠀⠀⠀⠑⠁⠀⠘⠁⠉⠀⠀⢸⠀⢰⣿⡇⠀⡇⠀⠀⠀⠀⢸⡇⠘⠿⠟⢀⣿
⢷⠀⠀⠀⠀⠀⢀⡤⠒⠒⢦⡀⢀⠆⠀⠀⠀⠘⢆⡀⠈⣀⡴⠁⠀⠀⠀⠀⠈⡗⠤⢀⠠⠞⠹⡆⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣀
⠸⡆⠀⠐⠂⠀⠏⠀⠀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠙⢦⠀⠀⠀⠉⢹
⠀⠹⣄⠀⠀⠀⡆⠀⠚⠙⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⡟
⠀⠀⠈⠷⣄⠀⠈⠲⠤⢤⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠚⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠹⣄⡾
⠀⠀⠀⠀⠈⠓⠦⣄⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠠⣼⣧⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⡀⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⢠⡞⠁
⠀⠀⠀⠀⣀⣤⣤⣼⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⢐⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⡼⠋⠀⣴⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠳⢤⣀⡾⢄⠀⠀⠀⣠⠟
⠀⠀⢸⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⢈⡀⠞⠀⠀⣰⠃
⠀⠀⠀⢧⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠸⡆⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⡾⠛⢦⣀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠑⢤⡀⠀⡴⢿⡄⠀⠀⠈⠙⠲⠤⠤⠤⠖⠋
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣩⠞⠁⠀⢻
⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⠞⠧⣄⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⣇⣤⠞⠁⠀⠀⠀⠉⠓⠾⠇
⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠦⣄⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⠔⠀⣴
⠀⠀⠀⠀⠳⡄⠈⢳⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠙⢦⡀⣠⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢼⡁⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠻⠿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⢀⡱
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⡏⣠⠀⠀⣠⡀⢻⡆⠀⠀⠀⠀⢀⣴⡿⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢻⣦⡀⠀⠀⠀⢺⠃⠈⠀⠃⠈⠀⢸⢧⠀⠀⢀⣴⡿⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠙⠿⣦⡀⠀⠺⡇⠰⣿⣽⡖⢀⣿⠆⠀⣰⣿⠋⠀⠀⣠⡾⢁⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠈⠻⣦⡀⠹⣦⣀⣁⣤⣾⢁⣠⣾⡿⠃⠀⣠⣾⢟⡴⠉⠁⠈⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠘⢷⡀⠇⣈⠉⣁⢿⡿⠛⠉⠀⢀⣾⠿⠃⢸⠃⠃⠆⠘⠃⠘⠷⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠈⠃⠀⠟⠛⠿⠀⠀⠀⠀⢠⡿⠃⠀⠀⢸⡂⢶⣶⡷⠀⢠⠞⠁⠀⢉⢳⡠⠊⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠳⣌⣉⣡⠆⣿⠀⠀⠀⢼⠘⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⠀⣨⣿⠀⠀⢹⣤⡀⠀⣸⠇⠀⣰⠃
⠀⠀⡀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⠿⠿⣿⣿⣿⡇⣶⠿⠥⠈⠷⠾⠇⠀⢛⣿⠋⠀⣰⠃
⠀⠀⣧⠓⢦⣜⡎⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⢃⡀⠀⠀⠤⠙⣿⣿⡀⠒⠒⠒⠒⠛⠛⣻⠟⠁⠀⣴⠏
⠀⠀⠈⢷⣄⠈⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⢀⣾⣿⡇⢠⡄⠄⠀⣴⡄⢸⣿⣿⡆⠛⠛⣛⣉⣿⠏⠀⢀⣼⠋
⠀⠀⠀⠀⠙⠳⢦⣄⠈⠻⢷⣤⣀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣿⣿⡇⠈⠁⠀⠀⠈⠀⠘⣿⣿⡟⠉⣉⣡⣿⠏⠀⢠⡾⠣
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠈⠙⠻⢷⣦⣄⢸⣿⣦⣀⡀⠈⢿⣿⣧⠀⢶⣊⣑⡶⠀⣰⣿⡿⠁⢈⣽⡟⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠙⠿⣿⣇⠈⠉⠛⠃⠙⠛⢦⡈⠛⠟⠁⣰⡟⠋⢀⣴⡿⠛⣄⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⢶⣄⡀⠀⠈⠙⢻⡿⣶⣶⣤⣄⡀⢻⡖⠶⠋⢹⡇⣴⣿⣿⣦⡀⢨⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣼⠁⢀⣿⣿⣿⣿⡿⣧⣀⣀⡼⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢶⣾⣿⣿⣿⣿⡇⠈⣹⣏⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠿⠿⠿⠿⠟⠛⠿⣿⠿⠿⠟⠿⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠻⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⣿⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠠⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠆⠀⠀⢀⣿⣧⡈⠢⡑⢄⠀⠀⠀⠠⠄⠒⠊⢡⠠⠂⠀⠀⢸⠂⠀⠀⠀⠀⡠⢂⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⡿⠀⠑⣶⣿⣿⣿⣿⡀⠈⠢⠑⠤⣀⠃⠀⠀⠀⠈⡶⡀⠀⠀⡌⠀⠀⠀⡠⠊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⠉⠀⢁⠀⠀⡀⠍⢻⣿⣿⠗⠀⢀⠼⠀⠀⠀⠢⢀⡀⡀⠁⠈⠰⠊⠀⠄⠊⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⡄⠀⠀⠀⠀⡷⠀⠘⣿⣿⠆⠀⡁⠀⠐⠄⠀⠀⠈⠢⡀⠀⠀⠀⠜⠇⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⢀⠃⠀⠀⠀⢀⡇⠀⠀⠡⠀⠀⠀⠈⠀⠀⠀⣱⠂⠀⠀⠀⠁⠀⠀⠀⠈⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠌⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠾⠀⠀⠀⠀⡐⠀⡇⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠶⠀⠀⠀⢰⠃⠀⠁⠀⠘⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠂⠀⠀⠀⠀⡉⠀⠀⢀⠀⠀⠀⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣾⣤⣶⣶⣶⣶⡅⠀⠀⠨⡄⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢱⠆⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠖⠀⠀⠑⠙⠆⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠹⢿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢉⠻⢿⣿⣿⠿⠛⢫⡀⠠⡀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠡⠀⠀⠀⠀⠁⠲⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⢀⠃⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠂⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣘⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉

⣶⣶⣶⣶⣶⡷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⢷⡾⠿⠿⠷⢶⣶⡶⠶⠶⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣆⣿⡀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠰⣙⡋⢉⠀⠝⢈⠆⢉⣠⣴⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠔⢁⣴⡽⠿⠿⠉⠄⣀⠀⠀⠀⠀⠀⠰⡐⣤⠻⢾⣕⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⣴⣆⠞⠁⠀⢀⡴⠂⠀⠘⠛⢄⠀⠀⠀⠀⢸⡀⠓⢀⡝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⢸⠇⠀⠀⠠⡆⠀⠑⠼⡁⠱⡀⠀⢀⣼⡣⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡌⠀⠀⠀⡠⠤⠀⠘⠂⢁⠀⣧⢀⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠐⠘⠑⣖⣂⣠⣭⡟⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⡀⠄⠘⠻⠿⠛⡁⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣕⡢⢔⣪⣾⣿⣿⣿⣿⣥⡶⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣿⣿⣿⡿⠈⠒⠽⡋⠛⠛⠻⠗⠛⠿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠑⢃⠀⠈⢦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠿⣿⢿⠟⢒⠶⣤⣀⠀⠀⠉⠁⢓⠈⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡌⡀⠀⠀⢷⠘⠻⣦⣠⡶⠚⢲⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡿⢷⠀⡄⠌⡀⢀⣡⠡⠁⢁⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢳⢋⢰⠡⠀⣡⠞⠁⣡⣶⢏⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⡆⠈⠘⠁⢻⠞⣡⡶⠛⠉⠉⡎⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣰⠀⡄⣠⡿⠟⠉⠈⠻⣤⢠⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣦⠟⠉⠀⠀⠀⠀⠀⠙⢷⣁⣤⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠿⠿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣪⣿⡿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡻⠿⠿⢇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠻⣿⣿⡿⠋⠚⠛⠛⢹⣟⠙⣿⣿⠟⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣟⣆⢻⣿⣷⠀⠀⠀⠀⣈⡁⠈⠀⠈⣿⠆⠀⠀⠀⠀⠑⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⡇⠀⠀⢾⣿⣿⣟⡇⠀⣿⣧⠇⠀⠀⠀⠀⠀⢶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠻⠃⣸⣿⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠇⠀⣀⣾⣿⡿⡿⣻⣿⣧⣄⣀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⢹⣿⢫⢏⣴⡏⣿⣿⠙⠿⠿⠖⢶⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠡⣤⣀⢀⣾⣿⣿⣸⣿⣿⣿⡿⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣷⡄⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⢿⡟⢿⣿⣿⣼⣟⣿⣿⠃⠀⠀⠀⢠⡿⠿⣿⣿⣿⣿⣤⣤⢠⣾⣿⣿⣿⣿⣹⡳⣭⣷⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢸⡏⢦⢻⣿⣿⣿⣯⡻⣗⣀⠀⠀⣿⠷⢳⣿⣿⣿⣿⣿⢏⣾⣿⣫⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⠀⠀⢀⣿⡙⣼⠈⡛⢿⣿⣿⣿⣮⠙⠷⣴⠇⠀⠘⢿⣿⣿⣿⢃⣼⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⠀⠀⠀⠀⣾⣟⣷⣧⣶⣇⠰⠼⣿⣿⠟⠀⠀⠘⠃⢀⠀⠀⣿⠛⢿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡋⠀⠀⣠⣴⣿⣿⣿⣿⣿⡟⡄⠒⠋⠀⠀⠀⠀⠀⠉⠀⠆⠀⠘⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⣉⣹⡿⠛⠙⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⠀⠀⠘⣿⣿⣷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⣶⣶⣄⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⢿⠛⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣻⡿⠿⠛⠁⠀⠀⠀⠈⠀⣠⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣿⣿⣿⣿⠋⠀⠀⠀⢀⣤⣶⣾⣷⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠸⣿⣿⢛⠛⢛⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⠠⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒
⠀⠀⠀⠀⠀⠰⢶⣶⣴⡏⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠛⠛⠛⠉⠙⠛⠛⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡘⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠏⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠟⠟⢃⣶⡞⡏⢿⢀⡇⣸⠏⣹⣦⣁⠑⠉⠙⠛⠋⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠛⠙⠀⠀⢀⣿⡇⣧⡏⣿⣸⢧⡏⣸⡟⠉⣿⡃⠀⠀⠀⠊⠁⠈⠙⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣿⣿⣿⠟⠛⠉⣥⢾⠿⠋⠁⠀⠀⢀⠀⠈⣽⣷⣿⢣⢧⣿⡞⣰⠟⣰⡾⣻⣿⡆⠀⠐⠀⢀⠀⠀⠀⠈⠻⢿⣦⣍⠙⠛⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠿⢿⡽⠄⠀⠀⢀⠐⠀⠀⠀⢠⣿⣿⣿⣿⣯⢏⡼⢣⡼⣋⣰⣿⣿⡁⠀⠀⠀⠀⠉⠐⣄⠀⠀⠠⢾⣹⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠃⠀⡀⠈⠃⠀⠀⠀⠀⠑⠦⣤⣤⣿⡿⣿⣻⣿⣵⣿⣿⢋⣼⠿⣻⣥⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⡛⠁⢀⡴⠏⠉⠀⠉⠉⠉⠙⠛⠻⣷⣾⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣩⣿⡀⣤⣴⣤⡀⠀⠀⠀⠑⠄⠀⠀⠉⠉⠳⣄⠀⠙⣻⣿⣿
⣽⣿⣟⠭⠒⠿⠛⠂⠀⡠⠈⠀⠀⠀⠀⠀⠸⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡽⠋⠀⣿⠉⣿⣿⣦⣀⠀⠀⠀⠀⠠⡀⠀⠚⠻⢇⠺⢟⣿⣿
⣿⣿⣀⣤⡁⠀⢀⠠⠈⠁⣄⠀⡀⢀⡔⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠟⠃⠀⢸⣿⠀⣿⣏⠟⢿⣷⣄⠀⠀⠀⠁⠠⡀⠀⠈⣱⣄⣹⣿
⠁⠝⠛⠿⠮⣶⢗⠀⠀⠀⠙⣿⣿⠂⠘⠁⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣰⡟⠀⠀⣤⣿⡏⢠⣿⡿⣿⣗⣍⣙⣷⣤⡀⠀⠀⠘⢗⡮⠾⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠁⠀⢀⣠⣴⣶⡹⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⠃⠀⣿⣿⣿⢣⣿⣿⣷⣿⠟⠙⠛⠻⢿⡏⣷⣄⠀⠀⠀⠀⠀⠀⠈
⠊⠥⣀⠀⠀⠀⠀⢀⣤⡾⢏⣡⣴⣾⣿⣿⣿⣿⡷⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣷⠀⠀⣼⡿⠁⣹⣿⣿⠛⠁⢀⢀⣀⣠⣸⣿⣿⢿⢷⣦⠀⠀⢀⣠⠌
⠀⠀⠀⠈⠀⣠⣶⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣟⣿⣿⣿⣿⣾⣿⣷⣶⣛⣡⣾⣿⣿⣿⣶⣷⢿⣽⣿⣿⣿⣿⣯⣶⠖⠺⣧
⠀⢀⢀⣴⡿⠿⠛⠛⠋⠉⠉⠉⢩⡿⠛⠛⠻⠿⣿⡇⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣣⣯⣿⣿⣿⡿⡋⣰⣶⡾⢿⠀⠀⢀
⠀⢸⠹⠼⠶⠖⠂⢂⡀⠀⠀⠀⠸⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣫⣤⣾⡆
⠀⠸⣅⠰⠾⡟⣟⣻⣿⣯⣄⡀⠂⣙⡻⠿⠟⣷⡄⠀⠀⠀⠀⠀⣿⣾⣿⡏⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⡟⢙⣿⣿⣿⡇⢀
⠀⠀⣿⣿⣿⠿⠛⠛⢻⣿⣷⠲⣶⣿⠁⠀⠀⢸⣿⡀⠀⢀⣴⡾⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓⣾⣻⣿⣿⣿⣿⣿⣿⣷⣷⣶
⠀⣴⣟⣖⠿⠶⢦⣶⣾⠿⠤⢶⢿⢿⡀⠀⠀⠈⢿⠳⠄⠘⠯⣿⡿⠿⣿⣥⣼⣿⣿⣿⡿⠿⠟⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⠟⠿⠿⠟⠛⠛⠛⠛⠛⠁
⠀⠈⠻⠽⠭⠭⠭⠭⠭⠭⠿⠯⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣷⢷⣯⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣖⣾⣯⠽⡿⣯⣽⣖⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢮⣷⣿⣿⣿⣿⣿⣿⣌⢿⣿⡟⢻⣮⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠿⠿⢿⣿⣭⣾⣿⣿⣿⣶⣬⣗⣘⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠿⣿⣿⣿⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠛⠓⠂⠀⠀⠐⠒⠒⠭⠻⣿⣦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣿⡇⢶⠷⠂⠹⠄⠀⠀⠶⠶⠦⠀⢻⣿⡿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣵⣶⣿⣿⠀⠀⠀⠀⣠⡀⣀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣽⡀⠀⠀⢀⣈⠩⢤⣄⠳⡀⠀⢰⣷⣿⣿⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠹⠿⡿⣿⣿⣇⠀⠈⢿⣶⣶⣶⣾⠟⠁⠀⣸⣾⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣆⣴⡃⠀⣠⣿⣿⣿⡄⠀⠈⢩⣍⡉⠁⠀⠀⢠⣿⣿⣿⣷⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⠟⡛⠛⠿⣿⣿⣿⢿⣿⡶⠾⠛⠋⠀⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠻⠈⢿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠻⣍⣿⣿⡟⠹⢿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⢻⣷⣾⣿⡿⠿⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⣤⢱⣻⡹⣿⣇⡀⠂⠿⣧⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⣻⡿⡿⠀⠀⣀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢿⣿⣿⣧⢿⣿⣿⣷⣦⣌⡓⢄⠀⠀⣠⠟⠁⣀⣤⣾⠿⠃⢠⠀⣾⣿⡾⠁⠱
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⡞⣏⢸⣿⣯⠿⢿⣿⣦⡵⣼⣥⣶⡿⠿⠉⠅⠀⠀⣿⣾⣿⣿⠁⠀⠘
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠠⠀⠀⠀⠈⡏⠻⡟⢿⡇⠀⠀⠀⠀⡴⠁⢸⣼⣿⣿⠇⡰⣶⠆⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣀⣤⠴⠶⠒⠚⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⣠⠶⢦⡀⣼⠁⠘⣇⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣏⣠⠾⠋
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠉⠻⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠛⠉⠙⠳⢦⡀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢀⣠⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢹⡆
⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣷
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢤⡰⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡏⠳⢤⡀⠀⣠⠏⠙⢦⣀⠀⢠⠟⣦⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠤⠴⠋⠀⢀⣀⡀⠁⠀⠀⠀⠀⠈⠙⢩⡀⠈⠙⠢⣤⣤⠴⠲⣟⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣀⣤⣼
⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⠞⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠈⣧⢀⡴⠋⠉⠉⠳⣄⣿⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠁
⢸⠁⠀⠀⠧⠰⠃⠀⠀⠀⠀⠣⡤⠀⠀⠰⡦⣤⠴⠁⠀⠀⡏⠀⢀⣤⣤⡀⠘⡄⠀⠀⠀⠀⠀⢸⡿⠀⣴⣿⣷⠀⢸⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣧⠀⠘⠿⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠋⠀⣸⢿
⠸⡇⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠉⢣⣀⣀⡾⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢻⠙⠲⠤⠄⠞⠁⠸⡆⠀⠀⠀⠀⠀⣠⡴⠶⠤⣤⣤⣄⣀⣀
⠀⢿⡀⠀⠘⠂⠀⢰⠏⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢹
⠀⠈⢷⡀⠀⠀⠀⢰⡄⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⡟
⠀⠀⠈⠻⣄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⡞
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠉⠑⣿⠀⠀⠀⠀⠀⠀⠀⣯⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣯⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⠛⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠤⣠⠴⠛⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⢀⣤⠖⠛⢛⡿⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢠⡴⠏
⠀⠀⠀⢀⡾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⡏⠳⡄⠀⠀⠀⣠⠟
⠀⠀⠀⢸⡇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣠⠼⠃⠀⠀⣰⠏
⠀⠀⠀⠀⢷⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢀⣼⠋⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠉⠲⣄⡀⣠⠏⠻⣆⠀⠀⠀⠀⠀⠉⠛⠛⠒⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣠⠾⢧⣄⡀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠞⠁⠀⠀⠈⠙⠲⣤⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⣩⣤⣤⣤⣤⣤⣤⣈⡉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⣿⡿⠿⣿⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⠛⠛⠉⠀⠉⠛⠛⠛⠋⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⡭⣵
⠀⠀⠀⠀⠀⠀⠀⠀⢜⣩⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠤⠀⠀⠘⠃⠀⠀⠀⠀⠀⢇⠘⠀⠀⣀⣀
⠀⠀⠀⠀⢀⢀⠀⠀⢋⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠂⠀⠰⣼⡞⠣⠇⠀⠀⡀⠀⠀⠀⠚⣳⠺⠗⠀⠀⠀⠀⠀⠀⢠⣿⡄⢸⠒⠛⣷⡂
⠀⠀⠀⠰⣼⠞⠃⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠑⠰⣄⠚⢾⣣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠃⠀⠀⠉
⠀⠀⠀⠈⠉⠀⠀⢌⠂⢄⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡀⢔⡠⠀⠢⣈⠐⠿⣶⣶⣶⡄⠀⣴⣶⣾⣿⠟⠋⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡈⠐⠨⡀⠀⠤⢀⡀⠀⠀⢀⣀⡀⠠⢐⠨⠒⢁⠔⠈⠀⠀⠀⠀⠁⢢⡄⠈⠛⠁⠐⠉⠋⠁⢀⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠍⠀⢄⡴⢀⠀⠧⡠⠐⡂⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠂⠀⠀⠀⠀⢺⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠠⠄⠀⠀⠐⠈⠱⠀⠠⡤⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⡀⠀⠀⠀⠀⢀⠤⣼⠌⡆
⠀⠀⠀⠀⠀⠀⠀⠔⠡⠋⠒⠄⣀⠁⠐⠠⠄⠀⣀⡀⡀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠐⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠺⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠂⠁⠀⠩⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠐⠈⠁⠀⠡⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⡁⢸⠎⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠁⠔⠊

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠥⠀⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⢤⣰⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢀⢀⣀⣀⡀⠀⢀⣤⡸⠃⠛⠀⠀⠘⠿⠀⠀⠀⠠⠒⣈⠈⠛⠛⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡴⠁⡨⠛⠉⠻⠁⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⢹⣂⣀⣀⣙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠰⢶⣿⣶⣿⣿⠟⠀⠁⠳⢛⠙⣤⡀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⣠⡞⠁⣡⢋⠉⠉⠉⣩⠉⠁⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⢤⢆⠀⠀⡌⠈⣄⠈⠒⠤⢄⡀⠀⠀⠀⠀⡠⠈⠙⠶⠊⠁⣀⡑⠀⡠⠋⡄⠀⠆⢹⠇
⠀⠀⠀⠀⣠⡀⠀⢹⣿⣿⠇⡜⣤⣌⠀⠀⠈⠀⠛⢠⡄⠒⠊⠀⠀⠀⠀⠘⠀⠀⠒⠒⠀⠉⠻⠅⠊⠀⠀⠁⠀⠁⢰
⠀⠀⢈⣮⣿⡆⠀⠀⠻⣇⠃⣿⢀⠐⠔⠀⠀⢰⣄⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈
⠀⠀⠀⣼⣯⠃⠀⠀⠀⠈⣿⡌⢢⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠀⢣⢰⠀⠀⠀⢀⠜⠁⠀⠀⢀⠇
⠀⠀⣀⡈⢻⡄⠀⠀⢀⣉⠉⠷⣸⡇⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠰⠀⢐⢦⣃⠐⢸⠀⠀⠀⠰⠁⠀⠀⡠⠔⣽⣆⠀⠀⠐⡃
⠀⠀⠈⠙⠜⣧⠀⠀⠉⠉⠃⢠⠙⠃⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢋⠢⡄⠀⠐⣆⣰⡦⠔⠉⢀⣾⣿⣿⡆
⠀⢸⣿⠀⠀⠁⡆⠀⠀⢀⡸⢧⣄⣀⡀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠂⠐⡸⢂⡁⠀⠀⡿⣿⡇⠀⣠⣿⣿⣿⣿⣷⠀⠀⡌⠠
⠀⠀⠉⠀⢩⠆⢠⡤⠶⣭⡳⠄⣈⠙⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⣴⣅⡄⠰⣋⣥⣾⡄⠀⢰⣯⠁⣴⣿⣿⣿⣿⣿⣿⣇⠀⢀
⠀⠀⠀⠀⠈⠀⢸⠃⠀⢹⠀⣴⡽⠋⠑⢶⢫⣿⡄⠀⠀⠀⠀⠀⠈⠙⠁⠁⠀⢻⣿⣿⣷⣀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁
⠀⠀⠀⠀⠀⢠⠃⠀⠀⡾⣡⡄⠀⣾⢓⠾⠈⠕⢁⢀⣀⠀⠀⢀⡴⠴⠤⠧⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡄⢀⠇⠀⠀⡜⠸⠛⢘⠖⠘⠁⣀⠤⠢⠕⣒⣭⠛⡄⠈⢫⡭⠍⠓⠀⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢠⣞⡇⡎⠀⠀⢐⢡⡶⠷⠁⠰⠿⢿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠿⢿⡿⡇⠀⠀⠈⠐⠒⠓⠠⠤⢤⣮⠄⣤⠐⣲⣞⠋⢉⡽⢷⡀⠀⠀⠀⡟⠛⠀⠀⠀⡠⠒⠒⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢢⣀⠈⣻⣏⢀⡙⠁⡠⡉⠁⠚⣷⠄⣀⣤⣷⡆⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢾⢞⣿⠟⢀⠸⠛⠁⠰⠇⢙⣯⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢶⣼⡀⡋⣴⡟⠃⣠⡾⢀⣴⡟⡋⠹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀
⠀⠀⠀⢷⠤⠔⠲⠀⠠⠠⠤⣾⣿⣿⣿⣿⣷⡠⠖⠓⢺⢏⠁⠀⢷⡀⠀⢈⡿⣿⣿⣿⣿⣄⢻⠀⠂⠀⠃⠀⠠⠶⠿⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⡿⠏⢃⠀⠀⠂⠈⢣⡀⠈⢷⡀⢸⡇⠘⢿⣿⣿⣿⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⢨⠁⠀⠀⢃⡀⠀⠹⣾⠀⠀⠀⠹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣌⣀⠘⣆⠀⠀⠘⢿⡿⢿⣿⣶⣤⣤⣀⣸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡘⠀⠀⠀⢿⠛⠻⢿⣶⣤⣀⡀⣗⣠⡇⠈⣉⣽⣿⠿⠋⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡿
⠀⢊⠥⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠃⢘⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡀⢀
⠀⠁⠀⠀⡖⢦⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⣀⣤⠼⣄⠀⢀⣴⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⠞⣹⠂⠀⠘⡄⠱
⠀⠀⢎⠒⢜⣦⠱⣼⢠⠊⠀⠀⠀⠀⢀⡾⣥⠆⠀⠀⠀⠀⠀⢀⣉⠳⡄⠀⠀⠀⢼⣉⢍⠺⣄⠀⠸⠵⢲⡄⠀⣧
⠀⠀⡀⠍⠶⠁⡞⠁⠘⡆⠀⠀⠀⠀⢸⠃⢸⢣⡀⠀⠀⠀⠀⢀⣼⡇⢹⡄⠀⠀⠀⠀⢸⠀⠈⠇⠀⠾⡉⠀⠀⡇
⠀⠀⠁⢒⠖⣀⠀⢀⠘⢅⠀⠀⠀⠀⣸⡀⢸⠀⠉⠓⠲⠶⠒⠋⠀⡇⠈⣧⣀⠀⠀⠀⡸⢃⡤⠴⠊⠓⠋
⠀⠀⠀⠙⠉⠈⠉⠉⠱⣄⠳⣄⠀⠸⣅⡀⢸⣷⣄⡀⠀⠀⠀⢀⣠⡇⠀⣀⡼⠀⢠⠞⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⡄⢹⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢀⡴⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢻⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⣹⠋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠈⢧⡉⠙⠛⠛⣿⠋⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢢⡀⠙⠶⠶⠛⢁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⢤⣀⠙⠲⠦⠤⠶⠋⠀⢀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠓⠒⠒⠒⠚⠋⠉⠀⢸⡀
⠀⠀⠀⠀⠀⠀⡔⢁⠤⠤⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠤⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠘⠀⢸⠉⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⣦⠈⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣤⡞⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢦⡀⠀⢙⡷⡦⣤⣄⣀⣀⣀⣤⣤⣤⢶⡾⡃⢀⡤⠚⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⠲⠎⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠋⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⢀⣀⣀⣒⣒⢂⣀⣀⣠⣀⣀⣤⣤⣤⣤⠤⠄⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⠇⣠⣾⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣯⡌⠁⠠⠄⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⢋⣵⣾⣿⣿⣿⣿⡍⠻⠗⠚⠟⠻⠋⠉⠸⠋⠙⠉⣀⠀⠀⠀⠀⠈⠿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡌⠹⠿⠟⢿⢿⡀⠸⣿⣿⣿⣿⡏⠀⠀⠠⠴⠆⠀⢤⠄⠀⠀⠀⣴⣿⣿⣷⣤⣶⣦⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣠⡶⠾⣷⣦⡘⣷⣄⠙⠿⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠹⣿⣿⣷⣿⠇⠈⣻⡷⠀⢨⣿⣾⣿⣿⣿⣿⣿⢻⣿⣶⣦⠀⠀⠀⠀⡈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢻⡟⠉⠁⠀⠘⠛⣣⣴⠀⡍⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⠀⠀⠀⠈⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠃⣤⡄⢀⣴⣿⣿⠿⢤⠇⠀⣿⣿⣿⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠏⢿⣿⡟⣭⣤⣤⣤⣾⣿⣿⣩⣯⣉⣘⣻⣿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠆⠀⠹⣽⣿⠟⠉⣁⠀⠠⢬⠻⠉⠉⠙⠻⣿⣷⣶⣤⡀⠀⠀⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢾⠁⢠⡇⢀⣿⡏⠀⠩⠠⣤⡀⡀⠀⠀⠀⠐⢂⡄⣉⠛⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⣆⢘⣳⡿⠋⠀⠢⠀⠀⠀⠀⡠⠀⠁⠀⠀⠈⠀⠻⠓⡦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣉⣣⣴⠇⡔⠀⠨⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢀⣂⠚⠁⠀⢀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⡇⠁⢠⣄⣀⠀⠀⠑⠴⠀⠀⠀⠀⠒⠀⠀⠄⠀⠉⠀⠀⢀⠀⣖⣾⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡍⣹⣯⠀⠸⣿⣿⠦⡀⠀⠀⠠⠱⢶⣄⡀⠀⣀⣀⣀⣴⣦⡀⠈⠀⠹⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣽⣿⠀⠀⣿⣿⢠⡈⠀⠀⣀⠀⠀⠈⠙⠛⡋⠁⠈⣿⣷⢻⡄⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⣿⣿⠇⠻⢴⣦⣴⡦⣄⠀⠀⠀⠂⢹⡿⢿⣿⡆⠀⢠⠋⡄⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣶⣿⣿⣿⣷⣾⣿⣧⡀⣘⣿⡷⢶⣿⣿⣇⣴⣿⣷⠇⡁⢼⡇⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣟⣸⣽⡏⢿⣿⣿⣿⣿⣾⣯⣶⣮⣤⣤⣜⣛⣿⣿⣿⣿⢻⡆⢩⠤⠃⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠉⠛⠛⠟⠛⠉⠁⣿⣏⢟⣿⣋⡁⠆⢀⣽⣿⣻⣿⣿⡿⢻⡇⠀⠌⠩⠽⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠰⣶⠶⣶⡆⢀⣏⠀⡲⣅⠠⠀⠀⠀⠉⠉⠉⠙⠛⠃⠸⡧⠐⣤⣀⣉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠛⠛⠉⢁⠜⠛⠢⠙⠓⠀⠀⠛⠛⢲⡄⠀⠀⠐⠀⠀⠐⣻⠎⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣤⡶⠀⠈⡄⠀⠀⠀⠀⠀⠀⡀⠀⢾⣥⣄⣀⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠠⠼⢶⣽⣿⠿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠃⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠻⡼⠀⠀⠀⠀⣸⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢰⠛⢦⠀⣠⠴⠚⠉⠉⠁⠀⠀⠀⠀⠉⠉⠓⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠻⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠋⠉⠲⢄⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⣿⠀⠀⠀⠀⠀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⣠⢦⡀⠀⢠⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠞⠁⠀⢹
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⠤⠴⠁⣀⣁⠈⠁⠀⠉⠒⣁⠈⠂⢤⡤⠴⡞⠁⠀⠀⢀⡴⠃⣀⣀⣠⡼
⠀⠀⠀⠀⠀⢀⡇⠀⡄⢠⠀⠀⠀⠀⠀⠀⣀⠀⡸⠀⢠⠊⠁⡈⠑⡄⠀⠀⠀⠸⣴⠋⣠⡈⢣⣧⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⢈⠉⠀⠀⢸⠀⠺⠿⠂⡄⠀⠀⠀⠀⢷⠈⠛⠋⢸⣧
⠀⠀⠀⠀⠀⠀⣇⠀⢀⠀⠀⠔⠉⠁⠙⠦⠜⠀⠀⠀⠀⠑⠤⠤⠖⠁⠀⠀⠀⠀⢸⠉⠒⠀⠁⢸⠀⠀⠀⠀⣶⠒⠒⠒⠤⢤
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠨⠀⠀⠴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠳⢄⣀⡀⠀⠀⠀⠀⡋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠤⠤⠇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠹⡄⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⢸⠇⠀⠀⠀⠀⢠⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡞⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠑⠲⠤⠤⣀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣀⡤⠒⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣳⠃⠀⠀⠀⢀⠀⠀⠀⠀⠈⠢⣀⠀⢠⡏⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠇⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⠓⠋⣸⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠉⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠑⡄⠀⠀⠀⠀⣰⠛⠦⣄⡀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠢⣄⣀⠞⢧⠀⠀⠀⠉⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⡔⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣠⠞⠉⠉⠓⠦⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡟⣿⠇⠀⠀⠀⠀⠀⢀⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⡇⠋⠀⢄⠀⢘⡿⠿⣿⣿⣿⣿⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⢀⡀⢀⡔⠂⠉⠞⡸⠎⠀⣶⣤⣀⠙⣿⣷⣤⠀⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣦⠈⠂⡌⠀⠠⠀⠂⡀⠈⠄⢌⡙⠛⠋⠏⠉⠉⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⡯⠂⣀⡑⠄⠀⠘⡧⣀⠠⢆⡸⢨⣄⠀⠆⠀⠠⢛⣽⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠭⢤⠰⣶⣙⣷⣼⡆⠀⡕⠁⠀⠀⠀⡀⠉⠑⡄⠀⠈⠙⢿⡷⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢠⣸⠀⠠⢋⠟⢫⣁⠉⢁⠢⡈⠃⣀⣬⠀⡀⡈⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢘⣆⠀⠃⠀⣠⠽⠜⠃⠀⣎⣰⠝⢃⠚⠄⡨⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣆⠸⣄⠈⠋⠈⠁⠰⢃⡠⠈⠀⢀⣀⠻⡫⢰⡔⢈⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣾⠁⠓⠀⣈⠀⠀⡇⠈⠃⠛⠋⠀⢣⠊⠀⢺⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢰⠀⠘⠟⠟⠀⠀⢀⠠⠀⠸⠇⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠏⠉⠉⠉⠉⣉⡉⠉⠉⠹⣿⣿⣿⠋⠉⠉⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢁⣀⡀⠀⠀⣾⣿⣿⡆⠀⠀⠈⠉⠀⠀⢠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠅⠀⠀⡀⣀⣴⣶⣶⠄⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠚⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⣶⣿⣶⣯⣭⣿⣧⣿⣿⡿⣿⣿⡧⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠟⠹⠿⠟⢻⡟⢻⣿⡶⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡷⡌⣿⣿⡆⠀⠀⠀⢈⠉⠉⠈⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⠀⠀⢺⣿⣿⣿⠀⣸⣇⡇⠀⠀⠀⠀⠀⣶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠛⢀⣿⠿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀⢤⣾⣿⣻⢋⣿⣿⣶⣤⣀⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢰⣿⡽⣱⣿⣼⣿⡇⠙⠋⠉⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠙⢶⣤⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⠀⢀⣠⣤⣴⣶⠿⣿⡿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠘⡟⢜⢿⣿⣿⣷⡻⣧⠄⠀⠀⣾⣧⣭⣿⣿⣿⣿⡟⣼⣿⢟⣿⣿⣿⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⣰⡿⢸⠘⠿⣿⣿⢿⣟⠛⢦⣠⠏⠀⢺⣿⣿⣿⠟⣱⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣍⠀⠀⠀⢠⣿⢣⣯⣴⡇⠨⣿⣿⡿⠃⠀⠘⠂⢀⠀⢹⡿⢻⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⣠⣾⣿⣿⣿⣿⣿⠀⠚⠁⠀⠀⠀⠀⠁⠘⡀⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣇⣀⣩⣿⠟⠉⢻⣿⣿⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⣇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢣⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣭⡤⠀⠀⠀⠰⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠶⠿⡥⠀⠀⠀⠀⠀⠀⠇

⣿⣿⣷⣀⠀⠈⣳⡸⣴⡛⠒⢛⣴⠨⢙⡮⠿⣯⣾⣿⣿⡿⣿⣎⣻⣯⣭⡝⠃⠀⠸⡏⠠⡇⠈⣿⠈⠻⠇⠙⠻⢯⢶⣆⡿⠃⠡⡾⠃⠀⡛
⣿⣿⣿⣿⣿⣿⣥⣠⣘⠛⠐⠀⠓⢦⠀⢻⢦⣿⢯⣼⢿⣷⣽⢿⢻⣩⣿⣧⡔⠘⠂⡶⠀⠐⠀⣄⠀⠀⠀⠀⠀⠘⡿⠁⠀⢦⠀⠁⣀⡠⢿
⣿⣿⣿⣿⣿⣏⢛⣧⣌⢶⣦⣠⣀⠀⠠⠉⢀⣆⣽⠾⢾⣿⠷⠾⢷⣭⣝⠰⠁⢠⣴⣿⣿⣷⣷⠀⠀⣀⠀⠀⢀⡀⠃⠀⠰⠀⠈⣧⠉⣠⣶
⣿⣿⣋⣉⣉⡽⠋⣿⡇⣬⣥⡏⠀⢀⠀⢀⡸⢯⠉⠓⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⢃⠀⣿⢡⠋⠂⠠⠍⠒⢠⠀⠉⠐⠀⠀⠠⢾⡟⠋⠉
⣿⣿⣿⣿⣿⣧⣾⣿⣛⣋⣡⣶⡯⠧⣄⣮⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠏⠀⠁⠀⠀⠺⠇⢠⡄⠀⡙⢸⡖⠀⠂⠀⠚⠁⠀⠐⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⡬⠇⠋⠀⠀⠈⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣁⣧⢰⠃⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⡇⣤⣤⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣤⡤⡟⣝⣰⣟⣟⡦⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣇⣤⡀⣠⡀⠀⠀⠀⠠⠴⠒⠒⠀⠀⠀⠀⠀⠐⠆⠀⢀⣩⠤⠃⣟⢩⠾⣼⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠀⠀⠀⠀⠐⠶⠠⠀⠀⠀⠀⠃⢀⠀⠐⠦⠀⠀⠀⢛⣀⢔⡇⠀⠐⠂⠀⠀⠀⢶⣆⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣥⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⢡⣤⠰⣌⡐⠘⠁⠀⠀⠀⠀⠀⠀⠤⠻⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⢎⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠶⢠⡔⠁⠀⠀⢀⠀⠀⠐⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡵⡛⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠆⠈⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢯⣾⠁⠀⠀⠀⠀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣸⠶⠀⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⢎⠟⣷⡶⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠋⠠⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⠷⠦⢠⢀⠀⠀⠀⠀⣠⣭⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠺⢫⣦⣧⣀⢀⢹⡚⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠙⢩⣤⣸⠥⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣳⡟⢠⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢰⢉⣼⣧⡖⠀⠈⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢘⠠⢤⣀⣸⡾⣇⣙⣿⡧⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⡐⢄⣶⡿⠏⣋⣿⡟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠾⡅⠀⠺⣪⣿⠏⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠴⣓⡛⠂⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⠳⣄⠀⠀⠀⠀⠀⣠⠞⠑⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠖⠉⠙⠦⣀⠀⠀⠀⢸⠁⠀⠈⠓⠦⣄⡀⢰⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⠲⠤⣬⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡰⠓⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣠⠶⠚⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠘⠦⣀⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⢢⠀⣀⠀⠀⠈⠁⠀⡜⠉⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢹⡹⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿
⠀⣴⣤⣶⢀⠀⠈⢇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⡀⣶⣤⣦
⣻⣽⠞⠻⢯⠇⠀⠘⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠃⠀⠸⡽⠟⠳⣿
⠙⢯⡀⠀⠸⢤⡀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠃⠀⢀⡤⠃⠀⢀⡽
⠀⠀⠈⠳⡀⠀⠙⠦⣀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠉⠉⢉⠏⠀⠀⠀⠀⠀⢀⣠⣯⠞⠀⣀⠴⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠙⢦⠀⠀⠈⠳⢄⡀⠙⠻⣦⣄⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⣠⣴⠿⠋⢀⡠⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠉⠳⢤⡀⠉⠛⠷⢦⣤⣤⣀⣀⣀⣀⣤⣤⡴⠾⠛⠋⢁⡤⠞⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠉⠳⡶⣄⠀⠀⢘⡇⠀⠀⢸⡃⠀⠀⣠⢶⠞⠉⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⡰⠃⠀⠙⠒⠋⠱⢤⡤⠞⠙⠒⠋⠀⠈⢆⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠏⠀⠀⠘⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢾⠖⠇⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠆⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛
⠀⠀⠀⠀⠀⣠⣶⡦⠀⠀⠀⠀⣠⣶⡶
⠀⠀⠀⣀⠀⠙⠉⠀⠀⠀⠀⠀⠉⠉⣠⡆⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠁⠀⣤⣤⣀⠀⠀⠀⠀⢠⣤⣄⠁⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠙⠻⠗⠀⢠⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⣀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⢦⣾⡄⢠⠾⢁⡐
⠀⠀⠀⠀⢰⡄⠈⠆⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢈⣄⠀⠀⠀⠁⢠⠄⠁
⠀⢀⠀⠀⠀⠙⣄⠈⢀⠀⡀⢰⠀⠀⠀⡀⠀⢀⠀⠀⠀⠛⢥⡄⠈⠉⠓⠒⠲⡄
⠀⠈⢢⡀⠑⢆⡀⠆⠈⠴⠗⠈⢀⠀⠘⠀⡤⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠈⢢⣄⡙⠞⠁⢀⡠⠤⠛⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⠀⡀⠀⠃
⠀⠀⢠⡄⠀⠉⢁⡀⠀⠘⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢂⠀⠂
⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⢤⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠚⠁⣼⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣀⣈⣧⠀⢡⡀⠀⠀⣀⣀⣀⣀⡠⠴⠶⠚⠋⠁⠀⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⡀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠙⠛⠀⠉⠉⠉⠉⠙⠛⠿⣷⡀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢡⠀⠀⠀⣠⠶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠲⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣃⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠋⠁⣠⣿⡆⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢠⠀⠀⢷⡖⠒⠀⠶⠶⠶⠊⠉⠁⠀⠀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠄⠀⠀⢲⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣦⠄⠀⠀⠀⠀⠀⠀⠀⠤⠒⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠁⢆⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁⠉⠁⠈⣿⡿⣿⠇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠙⠻⢇⣀⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠈⡍⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠉⣠⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣠⣾⡋⠀⠀⠀⠀⠀⠀⢀⣰⠞⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠉⡛⢿⠓⠒⠒⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠶⢶⣶⠶⠖⠋⢻⠉⠲⣤⠀⣃⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⢨⠷⡀⠀⣾⠀⠀⠀⠈⠋⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⢤⣤⡀⣀⣀⣀⣀⠀⣤⡴⠛⠁⠀⠀⠈⠀⢃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠴⣦⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠈⢃⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘⠃⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠤⠖⠛⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⢀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠀⠀⠀⠀⣸⠘⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣠⠾⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠳⣄⣀⡴⠉⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⣉⣠⠶⠛⢳⣄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠉⢀⣴⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⡀⣀⣠⠤⠚⠛⠉⠁⠀⠀⠀⠹⣦⠀⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡏⠻⡀⠘⠿⠒⠲⠶⠒⠒⠒⠘⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⠦⣀⠀⠀⠀⠀⢀⡟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠈⠓⠶⠶⠶⠋⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠴⠤⠴⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠴⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⣄⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⣾⡿⠁⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢾⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣖⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣆⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⡞⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡄⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣥⣿⣽⣿⡌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⡹⠿⣿⣿⣿⠦⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⡜⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣾⡟⠛⠛⠛⠛⠛⠛⠋⠓⠒⠒⠒⠒⢶⣶⣶⣶⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⢀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠔⢺⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠢⠠⠬⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠁⠀⠀⠀⠀⠀⣠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⢸⣿⠀⣾⢋⣤⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⢹⡇⠀⠰⠂⠀⠀⡿⠀⠃⠈⠉⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⢀⠀⠟⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⡀⠀⣠⡶⢶⣿⠁⠀⠠⠄⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⣠⡾⢉⠇⣰⡿⢠⠇⣴⡟⢠⣿⠇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣧⡼⣾⡏⢻⡾⢾⡟⣠⢿⡿⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣤⣴⣶⡄⣼⡏⢀⡞⢠⣿⣠⠏⠀⠸⡷⠋⣾⡇⠀⢀⡾⠁⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉⠉⢁⡼⠃⠹⠷⢋⣠⣬⡿⠷⠦⣄⠀⠀⠀⣿⡇⢀⡾⠁⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡶⠛⠉⠀⣴⠂⠀⡼⠀⠀⠀⠘⠳⠛⡁⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠸⣿⣄⠀⢀⣠⡾⠋⡀⠀⣼⠏⠀⠀⠀⢰⡏⣠⠞⣱⠆⢀⣾⠀⣰⠟⣹⠇⠀⠀⠛⣥⣴⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠈⠛⠛⠛⠁⠀⠀⠁⢸⡏⠀⠀⠀⢀⣿⢿⡅⢠⣿⡴⢻⡏⣸⣿⠞⠁⣠⠄⣀⠀⠰⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠀⠀⠀⠀⣠⣴⡾⠿⠿⠿⣷⣄⠀⠀⣼⡇⠀⡟⠀⠉⢀⣾⠷⣿⠁⠀⣰⠏⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠗⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠛⠀⠀⣿⠀⡼⠁⢀⡴⢻⡟⠀⠻⣶⠾⠋⠀⠀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠻⠟⠁⣠⠏⠀⣾⠁⢠⣶⡆⠀⠀⠀⢰⡿⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀⠀⢠⡏⢀⣼⠃⢠⡞⣯⡀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠛⢁⡀⠀⠉⠀⢁⣀⣠⣿⠃⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣠⡞⢹⠄⠀⣴⠋⡷⠀⢀⣾⠟⢩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⣿⢃⣾⣿⠀⣜⣠⣾⢿⣴⣃⣠⣿⠁⣠⢿⡟⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⢀⣼⠇⣼⡇⠘⡿⠉⢸⡇⣴⠋⠉⢸⣇⡴⠃⢸⡇⠀⣠⡟⠀⠀⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⣀⣀⣤⣿⣿⠀⣿⣠⡞⠁⠀⠸⠟⠁⠀⠀⠀⠉⠀⠀⣼⠛⠞⠋⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⢁⣾⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡆⣸⠇⢀⣤⠄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢠⣦⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⣼⠀⣰⡇⢀⣾⠃⠀⣴⣿⣾⠿⠋⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⣼⢇⣼⣿⠀⣼⠇⣠⢞⣿⣿⡁⠀⠀⠀⢀⣾⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣾⡿⠀⠀⠀⢀⣀⡀⣿⠟⢸⣧⡾⠻⠶⠃⣸⠇⠘⢷⣤⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⣿⠷⠶⠿⠿⠟⠛⠁⠀⠀⠀⢉⡀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⢹⡇⠙⠀⠀⠀⠰⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠆⢾⣋⣉⣛⣋⣩⣉⣉⣋⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣴⣦⣦⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣪⣵⣾⣿⣟⣭⣯⡹⣿⣿⣷⣦⣕⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣾⣿⣿⣿⡿⢻⣿⣿⣷⣜⠻⣿⡇⢹⣿⣝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣘⢛⣛⣻⣵⣾⣿⣿⣿⣿⣿⣿⣶⣥⣌⣩⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⠿⠋⠁⠀⠈⠙⠿⢿⣿⣿⣿⠟⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠛⠛⠓⠂⠀⠀⠐⠚⠒⠒⠌⢻⣿⣦⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⣿⣿⡿⢠⡶⠶⠄⠹⠄⠀⠀⠴⠶⢦⡄⠀⢿⣿⡿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣿⣻⠇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⣿⣹⡆⠀⠀⠀⠀⠛⠓⠈⠀⠠⡀⠀⠀⢰⣧⣿⣿⣏⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⢰⣾⣡⣄⣍⣝⣶⠽⠀⠀⣼⣹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⣠⠄⠉⠋⣽⣿⣿⡄⠀⠀⠻⠿⠻⡿⠟⠋⠀⠀⢀⣿⣿⣿⣍⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣤⣤⣼⣿⣿⣿⣷⣄⠀⠀⠒⠖⠂⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣤⡾⢻⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣛⣛⣙⢛⡛⣻⣿⣿⣿⢿⣿⠿⠛⠋⠉⠀⠘⣿⣿⣽⣷⣶⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⢫⡹⣿⣿⣿⠋⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡌⢿⣧⣼⣿⣿⠿⠟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⢀⡀⣆⢧⢻⣿⣇⠀⠐⢝⢿⡄⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⢻⣿⣿⠇⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣼⣿⣼⡞⡆⣿⣿⣿⣦⣤⡀⠙⢦⡀⠀⠀⠀⣰⡿⠃⠀⣀⣴⣿⡇⠁⠀⢀⣾⣇⡴⠉⢣
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡿⣿⣷⠹⡼⠻⣿⣿⢿⣿⣷⣦⣑⢄⢀⡾⣁⣤⣶⣿⠟⠋⠁⠀⢰⣀⡾⣿⣿⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠫⠀⠛⠛⠃⠁⢻⠻⣿⣷⡿⡟⠛⠛⠉⠀⠀⠀⠀⢠⣸⣽⣿⣿⠏⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠈⠃⠘⠃⠙⠛⠀⠀⠀⠀⠀⠚⠀⠀⠛⠻⠻⠋⠀⠛⠛⠁⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢘⠄⠀⠀⠀⠀⢀⣄⠤⠀⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆
⠀⠀⡀⠛⠀⠀⠀⢤⢈⠇⠀⠀⠀⠀⠀⠀⡀⢾⡆⣴⠀⣷⡆⠀⠀⠀⠰⠰⣶⠀⣀⠙⠃⠰⠐⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢉⡡⢒⠂
⠀⠀⠯⠀⠂⢆⢠⡎⠀⠀⢀⠀⠀⠀⠀⠀⢹⡶⡦⢴⡶⣿⠀⠀⠀⠀⠀⠀⢀⣈⠛⢠⣤⠀⠀⠀⡐⢻⡆⠀⠀⠀⠀⢰⣧⡄⠀⣐⢰⣯⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠀⠈⠀⠀⠀⠀⠈⠋⠛⠋⠛⠙⠁⠀⠀⠀⠀⠀⠈⠋⢰⡦⠀⡀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠇⠀⠆⠈⠀⣇⡀⠐⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠙⠛⠆⠀⠀⠀⠀⠒⠀⠀⠀⠀⠅⠓⠀⠰⠆⣻⣣⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠿⡿⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠠⣀⣶⠀⠀⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄
⠀⠀⠐⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢆⠀⠉⠉⠀⠜⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠒⡦⠐⠀⣂⠀⢀⠀⠀⠶⢤⡀⠠⡀
⠀⠀⠀⠀⠀⣴⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠰⣿⡗⠀⢰⣾⡄⠀⠀⠀⠀⡠⢀⣴⠞⠈⣠⣄⢼⠇⢷⣛⣃⠛⠱⠿⠛⣀⣤⠀⡹⠀⡇
⠀⠀⠀⠀⠀⠙⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⡠⢊⡼⠋⠠⣶⢷⠌⠉⠀⠑⠈⠁⠈⠀⠉⢈⠛⡻⣻⡵⢁⠜⠁⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠂⡛⠀⠀⠀⠀⠁⠸⠀⢰⣴⣶⠦⠀⠀⠀⠀⠀⣀⠠⣤⣀⣛⠿⠛⡁⠔⠁⠀⣀⣔⡛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠛⠛⠳⣄⠀⠀⠀⠀⢀⠀⠈⠡⣠⣶⡿⢡⣿⡯⠸⠿⠖⢛⡉⠤⠐⠀⠀⠀⠀⠰⣯⣯⣭⣼⣿⡆
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡰⠁⠀⢶⡆⠙⢦⡀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢾⣣⠀⠈⠳⠀⠀⢀⡀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⢀⠀⢠⡤⠄⡀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⢀⠀⠊⠀⠀⠟⠇⠀⠑⣰⣾⣾⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠆⠢⣍⠀⠐⣂⠀⠶⢑⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⢺⣿⠟⠁⠀⡇⡄⠀⡒⠂⠒⣤⡔⣀⣂⣒⠒⡄⠒⣒⣒⡐⠂⠆
⠀⠀⠀⠀⢠⡄⠉⠠⣭⣶⠻⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⡷⡇⠛⡻⠊⢸⣻⡇⠋⠛⠈⢸⠘⡀⢋⠃⠁⢠⡇
⠀⠀⢄⠀⠈⠁⠀⢰⣿⠇⢒⡇⠅⠀⠀⠀⢰⠀⢀⡀⠀⠀⠈⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠓⠀⠈⡟⡇⠘⠓⠀⠀⢠⡁⠘⠂⠀⢘⡆
⠀⠀⠀⠑⠢⣀⠀⡆⠶⠀⠈⠑⠀⠀⠀⠀⠀⠉⠒⠀⢼⡂⢰⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠙⠛⠓⠉⠛⠛⠉⠋⠀⠛⠙⠋⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⢚⡿⠀⠀⠀⢀⣶⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⢳⡄⠀⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠺⡏⠙⠹⠓⠗⠛⠉⡷⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠇⠀⠀⢀⣠⡴
⠀⣀⡀⠀⠀⠀⠀⠈⢳⡝⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡄⠀⣧⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣾⠤⠶⣾⢕⡠⠶⠚
⢀⣬⡿⣷⣶⡖⠶⠒⠉⠀⠀⠙⡆⠀⠀⠀⠀⢀⡾⠀⡾⠀⠀⢸⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠠⡿⠟⡒⠒
⠀⢬⣭⣻⣯⠶⣠⡤⠦⢤⡀⠀⣷⠀⠀⠀⠀⣼⠃⢸⠇⠀⠀⠈⡷⠶⠶⢶⡞⠀⠀⠀⢹⠀⠀⢻⡄⠀⠀⠀⠀⠀⣸⠃⠀⡴⠛⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠾⠖⠋⠁⠀⠀⠀⣧⠀⢸⡄⠀⠀⢰⡏⠀⢾⠀⠀⠀⠀⢷⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⠀⠀⢠⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣇⠀⠀⣿⢄⡀⠘⣆⠀⠀⠀⢸⡄⣰⠃⠀⠀⠀⢀⣿⠀⠀⠀⠸⡆⠀⠀⠀⡞⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⠀⢰⠇⠀⠉⣱⠘⢧⣤⠤⢬⣧⣏⣀⣀⡀⢀⡾⠙⣧⣤⠴⠞⣧⠀⠀⣸⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣇⡏⠀⠀⣰⠏⠀⣎⣵⣤⡴⠷⠾⢤⣀⡿⡾⠁⠀⠘⣇⠀⠀⠸⡆⢠⠏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡿⠀⠀⢠⡏⠀⠀⠀⢈⣆⣀⣀⣀⠀⠈⣹⠇⠀⠀⠀⠘⣆⠀⠀⠙⠞⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠀⠀⣠⡴⠋⠁⠀⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢦⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡾⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠋⠙⠁⠀⢀⡤⠁⠈⠙⠿⠛⡲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣁⡤⠖⠂⠀⠀⠙⠒⠀⠀⠀⠰⠬⠭⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣻⣿⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣠⣹⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣼⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡧⠋⠀⠀⠚⠀⠀⠀⠀⠀⠘⠀⠀⣴⢠⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢋⣾⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣽⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠿⠟⣻⠟⢫⣽⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⡏⢽⡿⡏⠉⢀⡖⢼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⠑⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⡀⢰⣿⣤⣿⢰⠁⠀⠘⠃⣿⣿⣸⣿⣿⣿⣿⣿⠴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣹⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣼⣿⣿⣸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⣀⡀⠀⠀⠀⠀⣼⡿⢟⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠐⣹⣿⣿⣿⣷⡟⣿⣿⣿⣶⣾⣿⡷⠿⠟⣋⣁⣀⠀⠀⢠⣭⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠂⢉⢿⣿⣿⣿⣷⣿⡿⣿⣿⣿⠛⠔⠖⢀⣘⠡⠏⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡂⠐⠒⡀⠙⢧⡤⠨⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠐⠐⢺⣿⣿⣿⣿⡽⣿⣿⣇⣻⣿⣯⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⠟⠛⡛⠛⠿⠿⠿⠿⠶⠮⠉⠉⡁⠡⢬⣅⣤⣾⣿⣿⡿⣯⢿⢽⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣻⣾⣿⣿⣿⣿⠦⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢁⣤⣤⣶⣶⠦⡄⣼⣿⠋⢱⡆⣠⣾⡿⣀⠀⣰⣿⠏⢠⣿⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡟⢼⣿⠟⣻⣿⠃⠀⢸⣿⠃⢀⣿⢰⣿⠏⢠⣿⢰⣿⠏⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣴⣿⠃⠀⠀⢿⡟⢀⣼⠃⣿⡿⠀⣾⠇⢸⣿⣠⡟⢹⣿⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠘⣿⣇⣠⣾⠟⠁⠀⠀⠀⠈⠛⠚⠁⠀⢿⣧⡼⠋⠀⠀⠉⢡⣾⡆⠙⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢀⣾⣿⠀⢀⣀⠀⠀⣤⣾⣿⣧⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⣾⣿⡏⣠⣿⡟⢀⣾⡿⠫⣿⡟⣠⣾⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢸⣿⣟⣴⣿⣿⠁⣼⣿⠁⠀⠈⠀⣼⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢈⠻⠛⠁⣿⡇⠀⢿⣇⣠⡴⠂⢠⡿⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣠⠏⠀⠀⠀⠘⠓⠚⠁⠈⠉⠀⠀⠘⠃⠀⠹⣿⣧⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⣛⣻⣉⣁⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⣾⠋⠀⠀⠀⠉⠛⢿⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⢟⣿⠥⠤⠄⠹⢿⢾⡿⡟⠇⣿⡀⠀⠀⠀⠀⠀⠀⠙⢦⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢾⣩⣷⣶⠰⣿⠀⠀⠀⠀⠀⠀⠀⠇⠙⡄⠘⢳⣄⠀⢀⠀⠀⠀⠀⠈⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⣵⠋⠹⣿⣿⡓⠙⠷⣆⣀⠀⠀⠀⠀⠈⢆⠈⣢⣶⣝⠷⣤⣀⠀⠀⠀⢀⣾⠈⠳
⠀⠀⠀⠀⠀⠀⣀⣤⡔⣂⡠⠽⣿⣿⡌⢿⣄⠀⠈⠢⡉⠂⠄⣨⣭⣛⣓⡲⠶⠦⠴⠷⢿⣿⣿⣿⣮⠙⠛⠛⠛⣋⣡⣄⡰
⠀⠀⠀⠀⠠⠊⠉⣵⠋⠁⠀⠀⢿⡿⣟⠂⠙⠿⢦⣤⡄⣁⣂⣿⣿⣿⣿⣿⣿⠤⠤⠤⠤⠙⣿⣿⡟⠒⠠⠤⠌⣿⣿⡿⠁
⠀⠀⠀⠀⣷⣶⡌⢿⣀⡀⠀⠀⠈⠳⢌⠑⠒⠤⣴⣶⣷⣿⣭⣏⣀⢀⡉⠍⢛⠰⢀⡠⠚⠛⡋⠢⢬⣅⣐⠂⠐⠛⣉⣀⡀⠠⠠⢤⢠⡀
⠀⠀⠀⠀⢻⡿⢟⡀⠙⠛⠻⣶⣶⡶⠶⠿⠒⠢⠿⣿⣿⣿⣿⡇⠀⠤⠀⠂⠁⣼⣛⠻⠄⣈⢉⣀⠄⡫⠜⡆⠀⠸⡉⢫⣀⣀⠀⠀⠤⠮⠦⡀
⠀⠀⠀⠀⠀⠙⠢⢀⠉⠐⢾⣿⣿⣿⣿⡇⠀⠂⠉⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁⠒⢨⡗⣩⠀⠚⡇⠀⠈⠈⠾⠁⠀⠀⠀⢒⣀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡆⠀⠀⡇⠁⠀⢰⡇⠀⢀⠆⠈⠀⠀⠀⣀⡈⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⡇⠚⡠⠘⠀⠀⠈⠄⠢⠀⣀⡀⠉⠁⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠓⠈⠀⠀⠀⠀⠀⠀⠻⠀⠉⠁⠤⠀⠒⠊



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⢭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣧⢻⣧⡙⢿⣆⣻⣷⡘⢷⡌⠙⠿⣶⣶⣤⣬⣿⣿⣿⣿⣷⣿⣿⡏⣠⣾⣿⣽⡾⠟⣩⣾⣯⣴⣾⣿⠟⢀⣼⢟⣴⠟⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⢻⣷⡄⠈⠻⣿⣿⣶⣿⣷⣦⣀⠉⠙⠛⢿⣿⡙⢻⣿⣿⣿⣰⣿⣿⢟⣭⡾⠟⣛⣿⣿⣿⣿⣷⣾⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⢻⣿⣆⠀⢹⣿⡟⠛⠻⠿⣿⣿⣦⣄⠈⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⡿⠿⠛⠛⢻⣿⠏⣴⣿⣿⠟⢫⣿⡏⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⡆⢸⣿⢠⡶⠶⣤⡀⠉⠻⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣀⣤⠶⢶⡘⣿⣿⣿⠟⠁⣠⣿⠏⢸⣿⢣⣿⣿
⣿⣿⣿⣿⣯⢻⣿⣧⡀⢻⣿⣿⡏⣼⢲⣶⣂⣙⢷⡀⠀⠹⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⠿⠋⠀⣠⢞⡉⣦⡕⢺⡇⢿⣿⠃⣠⣾⡿⠃⢀⣿⢃⣾⣿⣿
⣿⣿⡹⣿⡻⣷⡙⣿⣷⡌⣿⣿⡇⣿⢸⠸⢮⣽⣂⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡡⣿⣺⡜⡀⡇⢸⣿⣾⡿⠋⠀⣠⣿⣷⣿⣿⣿⣿
⣿⣿⣧⠹⣷⡙⢿⣮⣿⣿⣾⣿⡇⣿⢸⣷⣯⣭⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⣿⣿⠆⡇⣼⣿⠏⣀⣴⣾⣿⣿⠟⣩⣾⣿⣿
⣿⣟⢿⣧⢻⣷⡀⠙⢿⣿⣿⣿⣿⡽⣎⣾⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⣗⣼⣿⣿⣿⣾⣿⣿⠿⣋⣵⣾⣿⢟⣿⣿
⣿⡿⣷⣿⣿⣿⣿⣶⣤⣙⣿⣝⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⢛⣻⣿⣿⣷⣿⣿⡿⣋⣴⣿⣿⣿
⣿⠷⠦⠈⠙⠻⢿⣿⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣽⣿⣿⣿⣿⠿⠿⠛⢿
⣿⠷⠛⣛⣛⣻⣿⡿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⡾⠋⠉⣹⡟⢦⡀⠀⠀⠀⠀⠀⣠⡾⣻⡍⠉⠙⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠷⠖⠖⠉⠃⠀⠀⠀⠀⠀⢷⠀⠀⣿⡇⠀⢷⠀⠀⠀⠀⢠⡏⠀⣿⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠖⠶⠿⣿⣿⣿⠿⣿⣿⣷⣿
⣿⡿⢋⣵⣿⣯⣷⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢿⠇⢀⡞⠀⠀⠀⠀⠈⢧⡀⢻⡇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣶⣿⣿⣿⡶⣬⣙⣿
⣿⣴⠿⢋⣽⣿⡟⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠤⡤⢄⠀⠀⠉⠋⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣶⣍⣻
⣿⣧⣾⣿⣿⡟⣠⡶⠛⣩⣷⠿⠛⠋⣻⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡟⠉⠛⠿⣯⡛⠳⢦⡈⢿⣿⡿⣿⣿⣿
⣿⣭⣾⣿⣿⣾⠋⢀⣾⠟⠁⠀⠀⣴⡿⡿⠀⠈⠙⠳⢦⣄⣀⠀⠀⢀⣠⣷⣀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠘⡟⢿⣄⠀⠀⠀⠹⣦⠀⢻⣾⣿⣧⣾⣿⢿
⣿⣿⣿⠟⣿⣿⠀⣾⠃⠀⠀⠠⠚⠁⣠⣷⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡼⡟⣦⠟⠉⠉⠉⠀⠀⠀⠀⠀⢰⣷⡀⠉⠳⠀⠀⠀⠈⠃⠀⣿⣿⡟⣿⢃⣾
⣿⣧⣿⠀⢹⣿⠀⠃⠀⠀⠀⠀⠀⠀⢁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣇⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣦⣧⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣿⣾⣿
⣿⣿⣿⣇⠀⢻⣇⠀⣆⠀⠀⢀⣀⣴⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⣿⣄⠹⣆⠀⠀⠀⠀⠀⠀⠘⣿⡟⠷⣤⣀⠀⠀⠀⡄⠀⣾⠃⡟⢀⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠻⡄⢿⣶⣄⣉⣁⣠⣾⡿⣿⣰⠀⠀⠀⠀⠀⣼⠃⡼⠁⡇⠹⣆⠹⣆⠀⠀⠀⠀⢸⣦⡿⢿⣦⣄⣀⣀⣤⣾⡇⡸⠋⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣀⣈⣳⣬⣭⣽⠟⠋⠀⢹⣿⢠⠆⠀⠀⣸⢃⡾⠁⠀⡇⠀⠘⢦⠹⡄⠀⠀⢢⢸⣿⠃⠈⠙⢿⣯⣭⣴⣋⣀⣀⣠⣴⣿⣿⣿⣿⣿
⣿⡻⢿⣿⣏⠛⠻⠿⢿⣿⣿⣿⣛⠛⠻⣦⡀⢻⣿⠀⠀⢀⣧⡏⠀⠐⠀⣇⠀⠄⠈⣷⣿⠀⠀⠈⣿⠏⣠⡶⠟⢛⣻⣿⣿⣿⡿⠿⠛⠋⣽⣿⡿⣫⣿
⣿⣿⣆⠻⣿⡆⢀⣾⣿⣿⣿⡿⣿⣿⣦⡘⣷⠀⣿⣄⠀⠈⣿⣷⠀⢀⠈⠛⢀⡀⢀⣿⡿⠀⠀⣰⣿⢠⡿⢠⣾⣿⣿⢿⣿⣿⣿⣦⠀⣼⡿⢋⣴⣿⣿
⣿⣿⣿⡆⠘⣿⣾⣿⣿⢨⣿⣇⣿⣿⢿⣷⣽⣇⣿⠉⢳⡀⢹⣿⡄⠒⠀⣆⠐⠈⢸⣿⠇⣠⠞⠹⣿⣼⣷⣿⢿⣿⡇⣿⡏⢰⣿⣿⣷⡿⠁⣼⣿⣿⣿
⣿⣿⣿⣷⠀⢸⣿⡟⣻⣷⣿⣿⣿⣟⠀⣿⣿⣿⡏⠀⠀⠹⣼⣿⡇⢠⡊⠈⣠⠀⣾⣿⣰⠃⠀⠀⣿⣿⣿⣿⠄⣿⣿⣿⣷⣾⢟⣻⣿⠁⢀⣿⣿⣿⢿
⣿⢿⣿⣿⡄⠈⣿⣧⣃⣿⣿⠁⡻⠿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣷⠈⠀⠀⠀⠀⣿⣿⠏⠀⠀⠠⠙⣿⣿⣿⣿⢿⡇⢹⣿⣗⣠⣿⡟⠀⣸⣿⣿⡇⣸
⣿⡈⢿⣿⣷⡀⠘⢿⣿⣿⣥⣄⣸⣶⣾⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣌⣽⣝⣿⣿⠿⠃⣠⣿⣿⠟⣠⣾
⣿⣿⣷⣿⣿⣿⣷⣤⣭⣝⣛⡻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣹⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⣛⣋⣭⣤⣴⣾⣿⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⣂⡄⡀⡔⠒⡀⠀⢀⠀⡤⠔⠒⠠⡀⠀⠀⢀⠀⡤⠔⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡈⠀⡨⣜⢰⢅⠃⡰⢁⠊⠅⡄⠂⠄⠑⠀⡰⢡⠊⠁⡄⠢⡀⠱⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠡⡀⡁⡘⢹⠁⢀⠃⡌⠀⠃⡈⣒⠽⠀⢠⠁⡀⠀⢆⡈⣒⢽⠀⠇⠀⠀⢀⠠⠤⢤⣃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠊⠀⠀⠆⢘⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⠇⠀⠀⠀⠀⢸⠀⡀⢀⢊⠔⠁⡑⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠇⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⡘⠀⠿⠀⢠⠀⠀⠀⠀⡌⠀⠃⠁⢌⠀⠀⠇⠁⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⢀⠄⠄⠀⢣⠀⠑⠤⠤⠊⠀⡔⠀⢣⠀⠑⠤⠄⠊⠀⡌⠀⡀⠐⡀⠀⠈⢻⠧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠤⠊⠀⠀⠀⠑⠠⠀⠠⠄⠊⠀⠀⠀⠑⠠⠀⠠⠔⠊⠀⠀⠑⠢⠄⠁⠩⠊⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠀⢈⠀⢡⠀⠠⠪⢪⢢⠀⠀⠀⡠⡊⠥⢈⠑⢄⠀⠈⡀⡅⢀⠆⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢤⠀⠀⠈⡄⢸⠀⢀⢠⠌⡘⠀⠀⠌⠔⠀⠄⡂⠂⢘⠀⠀⢠⢠⡌⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠈⠎⢀⠁⠀⡘⠘⠀⠀⠈⠢⠤⠊⠀⠀⢠⠌⡞⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠆⠁⠀⠌⠀⡌⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⡆⠃⠈⢢⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠧⠊⢀⠌⠈⠀⠆⠁⠰⠀⠀⠀⠀⠀⠠⠀⢰⠀⡇⠀⠀⠀⢃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡇⣗⠂⠠⠤⠤⢲⡆⠀⠀⢀⠌⠀⠀⠀⢰⠐⠄⠑⠄⣀⠀⢠⠖⠀⠠⣀⡣⠁⠀⠈⢌⠒⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠜⠀⠈⠁⠒⠂⠁⠑⠤⠐⠁⠀⠀⠀⠐⠊⠀⠀⠑⠒⠒⠂⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣀⡄⢀⠈⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠡⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠀⢠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻⣾⣷⣷⡆⢃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡄⣸⡄⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠤⠤⣴⣦⣴⣦⣤⣀⠀⠀⠘⢿⣿⣷⣼⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⢰⣿⡇⠀⠀⢙⡿⣩⠟⢋⠤
⠀⠀⠀⠉⠉⠛⠿⣿⣿⣦⡀⠀⢻⣿⣿⣣⠘⡄⠀⠀⠀⢀⠌⠀⠀⠀⢸⣿⣿⡁⣠⣴⣫⢞⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣤⡹⣿⣿⣧⣃⠀⠀⠀⡆⠀⠀⠀⠀⣦⣿⣿⣿⢟⣿⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡀⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡎⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⣠⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⢉⠁⢀⡀⠈⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣀⣶⣦⣿⠁⢸⡇⠀⣿⣷⣰⡦⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡌⠻⣿⠏⠛⠀⠘⠃⠘⠋⠸⢿⠁⠴⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣶⢶⡶⢶⡶⣶⣶⢶⣶⣶⡶⣶⢶⢶⣶⣶⢶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⡿⠿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣷⡄⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣇⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠒⠀⠀⠀⠀⠒⠆⠀⠀⠀⠂⠦⠈⡇⠀⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠠⡶⠰⠶⠀⠀⣤⡆⣴⡆⠀⢠⡦⢰⡦⡇⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢻⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⣶⢶⡆⢲⡆⠀⠀⢰⣶⡆⠐⢶⣤⡶⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⣿⠟⠃⣿⣧⣤⢀⣾⠿⣿⡀⢸⣿⠀⠁⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠻⠿⠃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⠀⠘⠺⢝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⣽⣶⡶⢾⡥⠤⠤⠤⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡹⠊⠛⠉⠉⠀⠤⣄⠀⠀⠀⠀⠀⠈⣧⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠔⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⢠⢆⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠔⠂⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠞⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⠈⠀⢀⡠⠖⡆⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠄⢀⣠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢔⠀⠀⠀⠀⠰⡒⠊⠉⣀⠄⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠹⣌⡉⢅⡾⠀⠀⠀⠀⣠⠏⠀⠀⠠⢐⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠉⠉⠀⠀⠀⣠⠔⢁⣀⠴⢳⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⢴⠒⠋⡍⡉⠀⠤⠒⠊
⠀⠀⠀⠀⡀⠈⠤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠐⢊⣠⠀⠑⠚⠁⢡
⠀⠀⠀⠀⠠⠀⠀⢁⣀⡠⠖⠀⠤⠤⠔⠚⠤⠐⠒⠉⡜⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠤⢍⡑⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠄⢄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣇⣀⠀⠈⢑⠖⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⡭⢷⡀⢀⣀⣀⣈⡑⠲⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢸⢀⠇⠉⠉⠈⠁⠈
⠀⠈⠂⠀⡀⠀⠀⡴⢢⠜⠁⠀⠀⠉⠉⠀⠀⠀⠈⠐⠢⢤⣠⠀⠉⠉⠒⡖⠀⠀⡠⣇⠜
⠈⠢⠠⡄⠈⠑⠲⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣸⢅⠀⠥⠒⠉
⠀⠀⠀⠪⡲⢄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣤⣤⣤⣤⣬⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡾⣿⠟⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡤⠶⠿⣯⠞⠁⠀⠀⠈⢷⣀⠀⢀⡴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠁⢁⣰⡶⠶⣦⠀⠀⠀⢀⣤⣠⡴⠛⢁⠁⠱⠀⠒⢠⡄⠀⠀⠀⠀⢈⠻⠋⠀⠼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠻⣦⠐⠠⠐⠏⠤⠀⠈⠀⣰⡄⠀⣼⣿⠀⠀⢀⢴⡿⠒⠀⢀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠔⠂⣠⠆⠀⣹⣿⣰⣿⣿⡦⠊⠑⠀⠀⢈⠰⢏⣨⣿⡆
⠀⠀⠀⠀⣰⣄⡀⠀⠐⣡⠞⠀⠀⠀⠀⠀⠀⠀⣻⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡤⠀⠀⢀⣡⣴⠟⠉⠁
⠀⠀⠀⠀⠉⠙⠻⢿⣼⣱⣶⣄⡀⠀⠀⠀⠀⣠⣿⠄⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆⣡⣄⡀⣾⣶⣷⡇
⠀⠀⠀⠀⠀⠀⠀⢤⡙⠛⠁⠁⠉⢷⣄⣤⣾⡿⠋⠀⢰⣿⣄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣿⠿⠛⠋⡉
⠀⠀⠀⠀⠀⠀⠀⢈⡙⠓⠤⣄⡀⠀⠉⠙⠛⠒⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⢠⣴⣿⣃⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣠⣴⠶⠊⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠘⠓⠲⢤⢀⡀⠙⠿⣄⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⣰⣮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠳⣿⣦⣾⣿⣿⣿⣿⣿⠿⠻⠟⠻⠛⠉⠀⠀⢀⣄⣀⡠⠀⠀⢀⡴⠟⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢁⣾⣿⣿⠿⠛⠛⠀⠀⠀⠀⠐⠀⢠⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡆⠀⠀⠀⠀⠀⡠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠑⠲⢄⡀⠀⠀⠀⣀⡤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡴⠋⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢞⠁⣱⠀⠀⢸⠀⡴⠒⢢⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠞⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⡀⠓⠤⠞⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡆
⠀⠀⠀⠀⠀⢰⠁⠀⠊⠡⠂⠀⠈⠑⠲⠦⠤⠤⠴⠒⠋⠁⠀⡀⠙⠦⣀⡀⠀⠀⣀⣠⠖⠁⠀⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢻⠁⠀⠀⠀⠉⠉⠉⠁⠠⠊⠴⠂⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡴⢄⠀⠀⠀⡷⠴⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⡇⠈⡆⠀⠀⡇⢸⠁⠀⢠⠞⠉⡇⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⡇⠀⢸⣀⠀⠘⠃⠀⢠⠏⠀⣼⣁⣀⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠈⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠐⡶⠦⢤⠤⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠏⠀⠸⣀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⢸⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠈⠷⠁⠀⠀⠀⠀⡟⠀⠀⣸⠇
⠀⠀⠀⠀⢠⠤⣄⣸⠉⣧⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⣀⠀⠀⠀⠀⢰⣇⡴⠚⠁
⠀⠀⠀⠀⢹⡀⠈⠛⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠋⠉⠙⠲⣄⠀⠈⠉
⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠋⣧
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⣠⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⢀⡜⠁⠀⢸
⢰⠇⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢰⣄⣀⠜⠀⠑⠂⠚⠁⠈⠓⠤⠊⠙⠦⣀⣀⣀⣤⠚⠁⠀⠀⠀⡰⠋⠀⠀⠀⣈
⡾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⡠⠚⠉⠑⢄⠀⠀⠀⠀⢹⣀⡔⠊⠉⢢⣸⡀⠀⠀⠀⠘⠓⠒⠚⠋⠉⠉
⡇⠀⠈⠒⠃⠀⠀⠀⠑⠂⠀⢱⠒⠊⠀⠠⡇⢠⣶⣦⠈⡆⠀⠀⠀⠀⣿⠀⢿⡿⠀⣿⡇
⣧⠀⠀⠀⠀⠀⣠⠤⠀⢤⡀⢠⠀⠀⠀⠀⢣⡀⠉⠁⡰⠃⠀⠀⠀⠀⢸⠢⢀⡀⠴⠛⡇⠀⠀⠀⠀⣀⣀⣀⣀
⠸⡄⠀⠂⠀⠸⠁⠀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠳⡄⠀⠈⠉⢩
⠀⠹⡄⠀⠀⢰⠀⠀⠉⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣆⠀⠀⡞
⠀⠀⠘⠦⣄⠀⠙⠲⢤⡄⠀⠀⠀⠀⢸⠈⠳⣄⠀⠀⠀⠀⠀⠀⠐⠒⠒⠃⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⢧⣼⠁
⠀⠀⠀⠀⠈⠙⠶⡄⢸⠀⠀⠀⠀⠀⠸⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠺⢷⡏⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⡀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⣀⠴⠀⠁⠀⠀⣠⠟⠁
⠀⠀⠀⣠⠖⠛⡻⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⢄⠀⠀⣰⠃⠀⠀⠀⢠⡼⠁
⠀⠀⢸⠃⠀⠸⡁⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠙⠒⠋⣱⠀⠀⣰⠏
⠀⠀⠸⡄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢰⠏
⠀⠀⠀⢳⠀⠀⠈⢦⠀⠀⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠈⡆⠀⠀⠀⠳⣄⠀⠀⣠⣏⠀⠀⠉⠓⠦⣄⣀⣠⡴⠋
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢑⠞⠁⠈⣇
⠀⠀⠀⠀⠀⣧⠀⠀⣠⠶⠧⣄⡀⠀⢹
⠀⠀⠀⠀⠀⢸⣠⠞⠁⠀⠀⠀⠉⠓⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣿⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⢠⣤⠀⠀⠀⣿⣬⡾⡀⠋⣴⢿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣌⠀⠀⠀⠀⣿⣿⣿⣮⡿⠂⢀⣶⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⡞⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡈⠻⣿⣿⣯⣿⠿⠁⠀⠘⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⢀⣴⡛⢻⢿⣿⣦⡀⠉⠉⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣷⠆⢸⣿⣀⣦⣙⡫⠈⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢾⣿⣿⣾⣿⣿⣿⣬⣽⣿⣿⣷⢄
⠀⠀⠀⡀⠀⢈⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⡛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠠⢄⠀⢠⣶⡦⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠳⠶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣀
⠀⡀⠀⠾⠷⠀⠈⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠹⠉⠀⠈⠁⠀⠀⠀⠠⣴⣀⣟⢇
⠈⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⣯⣼⡆⢀⡀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣶⣼⠵⢛⣁⡼⠟⠃
⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠘⠇⠀⠀⠀⢠⣤⣀⠘⣾⣦⠿⠛⣁⠤⠋⠁
⡀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⣼⡵⠞⠋⠁
⣷⠀⠀⠀⠀⠘⢛⡆⠀⠀⠀⠀⠘⢿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣤
⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⡏⠀⣀⣀
⣀⣽⣧⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠼⣿⡿⠁⠀⠙⠉
⠿⣿⣿⡄⠀⠀⠀⠀⣷⣤⡁⠀⠀⠀⠈⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠸⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣆⣀
⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⣅⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⢛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣖⡒⠶⠶⣤⣀⣾⢁⠀⡀⠀⠀⢉⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡒⠂⠨⣀⡢⢍⡻⣿⣆⠞⡴⢀⠀⠀⠔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⠀⣀⡒⠭⣓⠯⣺⢎⡞⠐⢁⠄⡀⠐⡿⠀⣀⣤⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⠀⠀⠬⣕⡪⢝⠊⢳⠀⠀⠀⠈⣠⡾⣡⠞⡙⠀⠁⠐⠀⠋⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣙⢦⣤⣙⡒⠍⠀⠀⢠⡆⡔⠀⣠⠏⡴⠏⠰⢁⠄⡠⢀⠀⠀⠀⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠁⠀⠂⠈⢢⡙⢷⣮⡙⠺⣄⡀⢀⢸⡏⡴⡴⢃⠞⠁⠀⠀⢈⠜⡡⢃⢎⡄⡀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠢⣈⠢⠁⠀⠀⠉⡳⢤⡙⠦⣙⣏⣞⡵⠳⢂⣞⡰⠤⠤⣞⢼⣱⢿⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠐⠬⣑⠮⣑⠀⠀⠠⣑⣊⣑⣉⣓⣻⣿⣿⣖⠻⡛⠉⠀⠀⢤⡲⢝⠮⡓⢍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣦⣽⣶⣹⢦⢟⢀⠀⠁⠉⠱⢫⠞⢩⠿⡽⢍⡓⢦⣀⢀⠢⡑⢌⠢⡑⢌⠢⠁⢈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⡵⡱⢣⢣⢎⠄⡄⡀⣴⠋⣰⢏⠜⣷⠒⠝⢦⣌⠳⣵⡘⠂⠁⠉⠀⠀⡐⣌⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⠰⢡⢣⠏⡎⡜⣰⡼⢡⢞⠁⠀⠀⠺⣏⠣⠀⠈⠳⣮⡙⠦⣷⣼⣤⣦⠽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⢀⠁⠀⠈⠀⠀⢠⣟⣵⠟⣩⢖⡄⡠⠀⣐⢀⠀⣀⠒⠤⢉⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⣴⣠⣥⡷⠞⠉⣾⠅⢈⠔⣫⢞⠔⡱⣯⡢⣕⠢⣉⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠰⡷⠂⠀⢊⠵⣫⢎⢜⣵⢝⠮⡑⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣿⡥⢀⠁⢊⠔⠁⣾⠿⣧⠁⠀⠀⠀⣈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡟⠀⠀⠀⠀⠀⠘⢶⣥⣔⣡⡴⠞⠁⠀⠈⠛⠶⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣖⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⣊⣁⠀⠀⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠒⠒⠒⠉⠀⣿⠀⠯⠿⠀⢠⣤⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⣉⡁⠀⠀⠹⠶⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⡀⠀⠀⠀⠀⠀⠀⡿⢀⣴⣆⠰⣾⣿⡦⠀⠀⠰⣾⣿⡦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣉⡁⠀⡄⣀⠀⠀⢶⡗
⠀⠀⠀⠀⠀⠀⢀⡀⣷⠀⣧⣇⠀⢀⡀⠀⠀⠀⡇⠈⠻⠋⠀⠈⠁⠀⢠⣤⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠶⠂⠀⢋⣁⡤⣅⠙⠃
⠀⠀⠀⠀⡴⠊⣁⠀⠸⡆⠙⣉⠀⣼⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠰⢿⣿⠶⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠒⠉⠁⠀⠀⠀⠑⢄⠘⠷⢰
⠀⠀⠀⠀⢣⠀⡼⢣⠀⣧⠀⢿⡗⠈⠛⠃⢠⣷⡇⠀⠀⠀⠀⢰⣶⠀⠈⠉⠀⢰⣶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠐⠿⠆⠀⠀⣠⣤⠀⠀⠀⣘
⠀⢀⡴⠊⠉⢣⠀⣤⡀⢹⡀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠘⢿⡿⠗⠀⠀⠘⢿⡿⠗⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠈⣉⠤⠖⠊⠁
⠀⠘⣇⠸⡧⢸⡆⠻⠏⠸⡇⠀⠀⠀⠀⣶⣄⢠⡇⠀⠀⠀⠀⠀⠀⢀⣰⣶⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡈⠂⠒⠛⠉
⠀⠀⠘⡄⢁⣄⣳⠀⠀⠀⢿⠀⠀⠀⠘⠿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠔⠡⠾⡀⠀⢀⡤⠉⠑⢶
⠀⠀⠀⠘⡜⠿⠛⣇⠀⠀⠸⡇⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⢀⣴⣧⣄⠀⠀⢠⣴⣶⣄⢀⣴⣦⢨⡇⠀⠀⢀⠴⠊⣵⡆⠀⢚⣡⠀⠈⡠⠀⢠⡜⣇
⠀⠀⠀⠀⠘⡄⠀⠹⡄⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢹⡿⠁⠀⠀⠈⠹⡿⠁⠀⠹⠏⢸⡇⠀⠀⢦⠀⠀⠀⠠⠤⢌⣉⡠⠊⠀⠀⠛⠃⢹⡄
⠀⠀⠀⠀⠀⠰⡄⠀⢳⠀⠀⠘⡇⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡶⢸⡇⠀⠀⠈⡆⠀⠀⣀⠀⠀⠀⢧⠀⠀⢰⡷⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢳⠀⠈⡇⠀⠀⢷⠀⠀⠀⠈⠻⣅⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⠗⣸⠇⠀⠀⠀⢱⠀⠀⢿⡷⠀⠀⠘⠀⢀⣤⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢹⡄⠀⢸⡀⠀⠀⠀⠀⠈⠉⠩⠉⢩⠉⠭⠉⣟⣻⡟⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠈⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢳⡀⠀⣇⠀⠀⠀⠀⣀⣀⣤⢤⣴⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⢄⣀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣇⠀⠈⠳⠲⣚⣩⣭⣷⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⠳⣶⣞⡿⠟⠛⠉⠁⠀⢀⣠⣴⠆⠉⠹⠛⠻⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠎⠁⠀⠀⠀⠀⠀⠀⠀⠰⠛⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣰⠂⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣠⠀⣀⠀⠀⠀⠀⣀⣠⡿⠋⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣧⣴⡷⢤⣤⡶⠾⠋⠁⢀⣠⣼⣿⠏⠀⠀⣀⣀⣀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠯⢶⣶⣾⣶⣿⠿⠛⠉⠁⠀⠀⠈⠁⠀⠉⠀⠀⠘⠉⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⡾⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⡉⠰⠂⠀⠀⢀⠀⠀⠱⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⠶⢤⣰⣴⠶⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠶⠀⠘⠛⠛⠀⠠⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢛⣡⣄⠀⠀⠀⠀⠀⢀⣠⣜⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠿⢿⠁⠀⢸⣿⣿⡆⠀⢹⠿⢧⠀⠀⣀⣄⠀⠀⠶⠶⠄⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡟⠂⠀⣶⣶⡎⠀⠘⣿⣶⣀⣲⠶⠎⠁⠀⠀⠀⠀⠀⠀⠈⠱⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣥⣦⠄⠛⣛⣃⡀⠀⢭⣯⣭⠉⢰⣿⡟⠀⢠⣶⣶⡄⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⣘⠛⠇⠀⠀⠿⣿⣇⣀⠀⠻⣟⣤⣦⠌⠁⣀⣈⡛⠛⢧⣶⣤⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠁⠀⣴⣶⣶⠀⠈⣻⣿⠄⠶⢾⢇⣀⣀⡿⣿⣏⣀⠀⠿⣿⣌⣉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡖⠉⠉⣿⣶⡆⠈⠙⣿⣷⣠⡾⢿⣇⡀⠰⣿⣿⡇⠀⢈⣿⠗⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣷⠖⠀⢻⣿⣧⣠⣴⠏⠁⠾⠟⣩⡽⡅⠀⣾⣿⣧⠀⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢀⣼⡯⠀⠉⠀⠀⠀⠀⣴⣶⣦⠀⠐⠻⢟⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆⣀⣀⠀⢠⣴⣦⡀⢀⣙⣋⠀⠠⣤⣬⡍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⣿⡇⠀⠘⠿⠋⠁⢸⣿⣿⠇⠀⠸⠟⠃





⣿⣿⠻⠿⢻⠿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⢶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢟⣛⡇⡁⢿⣯⣟⣈⠀⠈⠉⠙⠛⠻⠷⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢐⡀⢺⢿⣯⣫⣤⣿⣯⣭⣄⣀⣀⢀⣀⡀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢯⣄⣭⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡩⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠀⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⢻⡄⣿⣿⣿⣯⣩⣻⣟⣛⣛⠓⢟⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠈⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢸⢸⠀⠀⠘⠛⠛⠉⠁⠀⠀⠉⠉⠙⠛⠻⠟
⠀⠀⠀⠀⠀⢸⣠⣤⣿⣶⣾⣿⣦⣄⣀⣸⣸
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⣿⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿⣿⣿⣿⢿⣿⢻
⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠉⠉⢉⡉⠉⢉⣸
⠀⠀⠀⠀⠀⠈⠉⠉⣙⣿⣛⣛⣛⣉⣹⣿⣿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⣀⣀⣤⠼⠗⠚⠋⠉⣦
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢫⡥⠶⠒⢛⡭⠭⠤⠶⣶⣶⣶⡖⠒⠚⠒⠒⠒⢲⡀
⠀⠀⠀⠀⠀⠀⢾⠁⣴⣦⢹⡀⠾⠆⢸⠀⣼⡦⢸⠃⣤⣬⠉⠉⠛⠓⠒⠶⠾⠧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⢧⠉⠀⠈⣇⠀⠀⢸⡀⠀⠀⡾⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢹⡀⠀⢸⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣧⠀⢸⡇⠀⢸⠁⠀⢀⣶⣿⣷⡄⣠⣤⣤⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡄⠈⡇⠀⡟⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢷⠀⡇⢰⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⡆⡇⣸⠀⠀⠀⠀⠀⠙⣿⡿⠟⠁⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣴⣦⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠲⠶⠤⠞



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡎⠁⠉⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⣤⣷⣿⣵⣯⣯⣽⣟⣋⣾⣿⣿⣿⣿⣿⣷⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⣿⣿⣿⢿⣿⣿⣿⣷⣭⡭⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣿⡉⢻⣿⣿⡁⠀⠈⠉⠀⠸⠷⠠⡞⠻⣯⡀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡄⣿⣿⣧⠀⠀⠀⢀⣤⣤⣄⣀⠀⢸⣏⢡⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣯⡿⠀⣾⣿⡾⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠃⢰⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⣠⣾⣿⡿⣻⢛⣿⣿⣷⣤⣄⡀⠀⠀⠀⢠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⢈⣿⣏⡿⣡⣿⢹⣿⣿⠙⠿⠟⠛⢲⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠑⣤⣀⠀⣼⣿⣿⣤⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣦⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠈⢿⣿⢻⣿⣿⣯⣿⡻⣿⡿⠁⠀⠀⠀⢀⣿⠿⣿⣿⣿⣿⣧⣤⡄⣴⣾⣿⣿⣿⣿⣹⡳⣭⣿⡦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡅⠀⠀⠀⠸⡏⢣⠹⣿⣿⣿⣿⣝⢿⡖⡀⠀⠀⣿⡷⠶⣾⣿⣿⣿⣿⣿⢓⣿⣿⣫⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣾⡛⢸⠇⠿⢿⣿⣿⢿⣷⡟⠻⣦⣰⠇⠀⠘⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡉⠀⠀⠀⠀⣸⣿⢇⣾⣄⡾⠀⣌⣻⣿⣿⠏⠀⠀⠹⠖⠀⠀⠈⣻⡿⢿⣷⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣇⣇⢀⡽⠋⠉⠀⠀⠀⠀⠒⠈⡄⠀⠸⠇⠈⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡂⠀⠒⢻⣿⡿⠿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⡶⠟⠋⠀⠀⠹⣿⣿⣿⡈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢇⣐⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⣸⣿⣿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣭⣅⠀⠀⠀⠀⢰⠄⠀⠠⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣯⣽⣉⠁⠀⠀⠀⠀⡀⠀⢰⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⢟⣻⣙⣯⣍⠛⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⠋⠃⠀⠘⠛⣛⠛⠋⠀⠀⠀⣠⣄⡙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣿⣷⠄⣀⣴⣾⠿⠿⠿⠿⠿⣷⣦⣈⠻⣿⣆⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣯⣿⣿⢁⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣊⠁⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠚⣿⣿⣿⣻⣿⢯⡍⢉⣉⡉⠛⠒⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄⠀⠀⣿⣿⣷⣺⣇⣻⡆⣏⠀⣹⢰⠟⠳⡄⣠⣌⡉⠓⠶⢤⣀⡀⠀⣿⣯⣺⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣸⡿⠛⣿⣿⣷⣤⡤⣌⣉⣁⡘⠦⠾⢡⡏⣀⡗⠀⢠⠆⠈⠙⠳⢿⣟⣺⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣋⡀⠙⣿⠁⢠⣿⣟⡺⠿⢠⣿⡏⠉⠉⠛⠓⠦⣌⣉⡀⠠⢯⡀⢠⡟⢀⡆⢈⡙⠧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡴⠋⠀⢸⣿⡒⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⢤⣘⠲⠟⣴⠋⠙⠆⣈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⣾⣿⢭⣀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⣌⡓⠃⡾⣷⠒⠂⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣹⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠧⣿⡟⢳⣤⣙⠀⠀⣰⠏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⢾⣿⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠋⠁⠀⢠⣿⠃⠙⢳⡞⠁⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⢣⣅⠀⣠⣿⠃⠀⢀⣾⣤⣤⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣲⣿⠏⣴⣿⠁⠀⠀⢸⡟⣫⡃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠁⠀⠉⠀⠀⠀⠀⠀⢀⣴⣿⡿⠍⠈⠻⢃⣾⡿⠁⠀⠀⠀⠀⣿⠋⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣯⡀⠀⠰⣿⣿⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠁⠈⢿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠋⠉⠀⣿⣿⣿⣿⡿⠯⠿⠟⠛⣛⣋⣡⣴⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⠛⠁⠀⠀⣠⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⢤⣈⣭⣤⣤⡶⣶⣾⣿⣿⣿⣿⣤⣿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣦⣀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⠿
⠛⠛⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠻⡛⠿⡿⣿⣿⣿⣶⣦⡀⠈⠻⣏⠛⠛⣿⡁
⣠⣤⡄⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠛⣉⣡⣴⣶⡀⣿⣾⠳⣦⣴⢰⣿⣿⣿⣿⡻⣦⠀⠈⠣⣌⢹⠷⣿⡿⠎⠇
⠙⠛⠁⠀⠀⣿⣿⣿⢇⡄⠈⠉⠉⠤⣶⣿⣿⣿⣿⣿⣷⡈⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇⣿⡀⠀⠀⢈⠻⠃⠈⠁⠀⠁
⠀⣀⣀⡀⠀⠛⢛⠋⣾⢡⣶⣦⢠⣤⣀⠈⠙⠻⠿⣿⣿⣧⠰⡀⣿⡸⣿⣿⣿⣿⣿⢿⣯⠃⢠⣀⡈⠂⠀⠢⠀⠲⣶
⠈⠻⠋⢠⣴⣶⠏⠀⠀⠀⠛⣻⣿⡿⠟⢻⡗⠀⠀⠀⢉⣿⣧⢡⠘⠷⣿⣿⣿⣿⣋⣙⠉⠓⠜⠛⠀⠀⠀⣠⣷
⠀⠀⢣⠘⣿⠏⠀⣰⣶⣶⣶⣿⢏⣀⣀⣼⡇⠀⠀⢀⣾⣿⣿⣇⢣⡀⠈⠛⠻⠿⣿⣿⣿⣶⡾⠀⠀⠀⠀⠉⠁
⠀⢰⣿⣧⠙⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⡿⠟⣈⣿⣄⠀⠀⠀⠀⠉⠛⠁⢀⣴⣿⠀⠀⢀⣤⣄
⣦⡀⠀⠀⠀⢠⡿⠿⠿⢻⣿⣿⣧⣴⣶⣷⠂⠀⡼⢛⣩⣴⣾⣿⠿⠿⠟⠳⣄⠀⠀⠀⢀⡴⠿⢿⣿⡇⠀⠙⠛⠛
⠉⠁⠰⠀⠀⢰⣿⣶⣾⣿⣿⣿⣿⣿⠾⠇⠀⠐⠛⠉⠉⠁⠀⠐⠂⠈⠀⠀⢻⣷⣤⣴⡟⠀⠀⠀⠉⠓⠠⢀⣀⣄⡀
⠀⠀⠀⠀⠀⢸⡿⠋⠉⠉⠈⠁⠀⠀⠀⢀⣤⡤⢦⣶⣿⣦⠀⠀⢼⣷⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⡀⠀⠀⠀⢨⣯⣐⣶⠀⠀⢀⡠⠠⠤⣬⣽⣷⣴⣿⣿⣿⣷⠀⠀⠀⠴⠀⠀⠛⠛⣀⣀⣠⣤⣤⡄
⠀⠈⠙⠶⣤⣀⠈⠉⠛⡀⠀⣷⡶⠸⡁⢹⣿⣿⣿⣿⣿⣿⣿⡐⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄⠀⢸⣯⠀⠀⢠⣿⣿⣿⣟⣿⣿⣽⠗⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢾⣾⣿
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⢁⣴⡄⠀⠹⣿⣿⣿⣤⢰⡶⠀⢀⠈⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠈⠛⠉
⠀⠀⠀⠀⢀⠾⠿⠁⠀⠀⠀⠀⠀⠙⢁⠀⠀⠈⠉⠁⠀⣀⣀⣀⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⣀⢩⣤⡤⠐⠒⠘⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣽⣿⡆
⠀⠀⢀⣾⣧⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣄⣀⣿⣿⣿⣧⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣃⣾⣿⣿⣿⣿⡀⠀⠀⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡶⣠⣶⣿⣿⣟⠙⠇⠿⠼⢭⣿⣿⣷⣦⡰⣶⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠝⠿⣿⣿⣏⣛⣇⣶⣰⣤⣼⣿⡿⠛⠴⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠶⣦⢤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⠤⠶⣾⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⡀⣿⢸⣿⡇⢹⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⣿⣸⣿⡿⢟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⢻⠿⣷⣾⢿⣿⣿⣿⣿⣶⡶⠿⣿⠟⠛⣩⣵⣾⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣸⣀⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⣿⡀⢸⣿⣿⣿⠘⡿⢛⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⠟⠛⣿⠋⠉⣇⢸⣉⣡⣿⠀⢡⣿⣿⣷⡄⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⣿⣸⣿⣿⣸⣿⣿⣿⣿⣿⣀⣀⣿⣀⣤⣿⢸⣭⣴⣾⣇⣸⣿⣿⡿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⡏⣿⣿⢹⣿⣿⣿⣿⣿⡏⠉⢹⠁⠀⣿⢛⣋⣿⣿⣿⣼⡇⠐⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣷⣾⣧⣿⣿⣼⣿⣿⣿⣿⣿⣥⣤⡼⠦⣶⠸⣿⣿⣿⣿⣿⣷⣚⡀⣵⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⣿⢸⣿⡏⢹⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⣿⣠⢹⣿⣿⣿⣿⣿⣿⣄⣼⣾⣿⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠛⡾⢿⣷⣾⣿⣿⣿⣿⣿⣴⠶⢿⡾⠛⢻⡏⣧⢻⡛⠋⠙⢿⠃⠻⣿⣿⡿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣀⡇⣸⣿⡇⣿⣿⣿⣿⠿⢇⣀⣨⣥⣤⣤⣥⡴⠀⠓⠀⠲⠟⣷⡀⠪⣍⣡⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⢛⠉⠁⠀⢙⣿⣿⣿⣿⡟⣟⢻⣿⣶⣶⣥⠲⣿⣿⣿⣦⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣤⡴⣠⣾⣿⣿⣇⣈⡁⣁⣉⠉⣻⣿⡿⠋⠜⠛⣻⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠧⠙⠻⠿⣿⣧⣬⣷⣿⣞⣻⣿⣍⣀⡤⠖⢿⠙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⡶⢤⡤⣤⣼⡿⣿⣿⣿⣿⣿⡏⠉⢹⡇⠀⣸⡧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠘⣇⢹⣿⡇⣿⣿⣿⣿⣿⣧⡤⠼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠈⠉⠉⠉⠉⠉⠰⠆⣀⠀⢀⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠰⠶⠀⠀⠀⠐⠶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⠀⠈⠁⠐⢶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠉⠁⠒⢀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠒⠛⡀⠀⠐⠤⡀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠘⢦⣀⠀⠈⠳⢄⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠤⠤⢱⣄⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢡⡌⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠰⠀⠀⠀⠀⢰⡆⠀⢰⠀⡄
⠀⠈⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢰⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣠⠸⣏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⢙⠀⠏⠢⡈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⢀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠀⠐⠛⠋⠀⠀⠀⢠⡀⠀⠀⢀⡴⠋⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠘⠠⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠑⠂⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠾⣠
⠀⠀⢃⠔⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠈⠑⠒⣤⠄⠤⠐⠒⠲⣋⢣⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎⢠⡉
⠀⠀⠀⠠⢃⠀⠀⠀⠀⠀⠈⠓⠤⢀⡀⢠⠞⠁⠀⠀⠀⠀⠀⠐⠦⢄⡀⠀⡄⠀⠀⣩⡌⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡄
⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄⠀⢠⣤⠀⠀⠀⡀⠀⠀⠉⠚⠛⣤⠊⣡⢂⠈⢣⡀⠀⠀⠀⠀⠀⣀⡤⠒⠁⠀⢰⠇⠁
⠀⠀⠀⠀⢀⡘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠄⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣹⠀⠠⡀⠉⠒⠒⠒⠒⠺⡉⢀⣔⣀⠔⠀⠆⠙⢤⠆
⠀⠀⠀⠐⠈⠀⠀⠙⠦⣀⠀⠀⠀⢀⡠⠜⠃⡠⠀⡠⠒⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠱⡀⠀⠀⠀⠀⠀⠉⠈⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠈⡀⠔⢁⠄⠊⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣄
⢀⡄⠀⠀⠀⠀⠄⠀⢀⡔⢳⠤⠘⢋⡠⠚⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠱⡄⠙⠦⡀⠀⠀⠀⢀⡀⠀⠀⠠⠊⢀⠙⢄⡀
⠶⠀⠀⠠⡀⠀⠀⠘⠇⠀⠀⡶⠜⠁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠦⡀⠈⠃⠤⠀⡜⠳⡀⠠⠃⠀⠋⠁⠤⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠛⠓⢤⡅⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠳⢄⡀⠀⡇⠀⡜⠁⠠⠂⠈⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠙⠃⡀⠶⠄⠔⠈⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢬⡥⠤⠒⠂⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠉⠀⠒⠒⠨⠤⠤⠄⢀⡀⠀⠀⣤⠤⠤⠤⠀⢀⣀⣀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠺⠆⠀⠀⠀⠀⠀⢰⣄⠤⣤⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠰⠖⠶⠊⣄⠀⠀⠀⡌⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⢣⡄⠀⠁⠀⠀⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⣦⠀⠀⠀⠀⠈⡄⢿⣄⠀⠀⢀⡜⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⣤⣤⣤⠞⠀⢸⠈⠑⠒⠉⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⣀⡿⣦⣤⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠀⢸⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡏⠀⠀⠀⠀⠀⡿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣀⠀⢰⠛⢦⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⢀⡴⠛⠁
⠀⠀⠀⠀⠀⡏⠉⠳⣾⠀⢸⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡴⠶⠦⣄⡀⠀⠀⠸⠶⠋
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣀⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠈⣇
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⡴⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡴⠋⠀⠀⢹
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⢰⣄⣀⡸⠁⠈⠒⠀⠚⠁⠈⠑⠦⠴⠈⠳⢄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢀⡴⠒⠒⠦⡀⠀⠀⠀⠀⠘⡆⢀⡤⠚⠛⢤⡘⡇⠀⠀⠀⠀⠸⠧⠶⠶⠒⠛⠋⠉
⡏⠀⠀⠦⠼⠂⠀⠀⠀⠢⡄⠀⠐⣦⣤⠜⠀⠀⡎⠀⣠⣤⡀⠹⠀⠀⠀⠀⠀⢹⡏⠀⣶⣶⠀⢷⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢁⠀⠀⠀⠀⢧⠀⠙⠿⠃⢠⠇⠀⠀⠀⠀⠈⣧⡀⠙⠋⢀⡿⡇
⢻⡀⠀⢀⠀⠀⢠⠞⠉⠀⠈⠦⠤⠎⠀⠀⠀⠀⠈⠳⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⣧⠉⠒⠒⠉⠀⢹⠀⠀⠀⠀⠠⣶⠒⠒⠲⠶⠤⢤
⠈⣧⠀⠀⠁⠀⡇⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣸
⠀⠈⢧⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠇
⠀⠀⠀⠙⢦⣀⠀⠙⠓⢲⡆⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏
⠀⠀⠀⠀⠀⠉⠛⢦⡄⢸⠇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⣯⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣄⣀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢀⣤⠤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢑⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣴⠋⠀⢰⠋⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡾⢄⠀⠀⠀⢠⠞⠁
⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠜⠀⠀⢠⠏
⠀⠀⠀⢷⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠘⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢠⡞⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠑⢄⡀⠀⢀⡴⣏⠀⠀⠈⠙⠳⢤⣄⣀⣠⡴⠟
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣢⠞⠀⠘⡆
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢀⣠⠞⠁⠀⠈⠙⠶⣄⣸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠀⡀
⠀⠀⢀⠈
⠀⠀⠀⠀⢸⢹⡤⠃⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⡸⠈⡄⠀⠰⠁⠀⠄⠄⢀⠤⠤⡀⢰⠤⠠⠀⠠⠠⠄⡠⠄⠄⣀⠤⠠⡂⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢈⡀⢀⡁⠀⠀⠀⡀⠀⠀⠁⠀⡀⠤⠬⣖⣒⣂⣒⣐⢂⡐⣂⣒⣐⣒⣒⠥⠤⠄⣄⢲⣢⠐⡖
⠀⠀⠀⠀⢁⠈⠁⡈⠀⠀⠀⠈⠢⡀⠀⣁⠀⠀⠀⠘⠀⡇⢠⡍⠀⠀⢩⡌⢸⠀⠃⠀⠀⠂⡇⠰⣺⡀⠄⡼
⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠉⣉⣹⢤⠃⠀⠀⠀⠀⠀⠀⠈⡤⢏⣈⠉⠑⠣⡀⠀⠄⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣉⠉⡀⠀⢀⣠⣄⡀⠀⠀⢉⣩⠀⠀⠀⢀⠍⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡉⢋⡓⢄⠀⠀⠀⠀⡠⢊⣉⢉⣅⠀⠀⢸⣉⡁⠈⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣀⣉⡏⢹⣉⠀⢀⡀⠀⣉⡋⢹⣉⣀⠂⠠⡃⠀⠀⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠐⠦⠼⡚⢛⠭⠽⣃⣘⠯⠭⡛⢛⠢⠴⠀⠀⠀⢰⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠂⠀⠀⠀⠀⠉⠁⠐⠊⠡⠌⠱⠂⠈⠁⠀⠀⠀⡠⠔⠁⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣔⠈⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⡔⠈⠀⠀⠔⡩⠭⣝⡫⠝⠭⣂⡀⠀⠀⠉⡒⠤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠜⡀⢦⢤⢤⠜⠈⠁⠉⣸⠀⠀⠀⡗⠃⠀⠀⢠⠀⠀⠈⠗⠢⢄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⢠⠁⠐⠀⢸⠀⠀⠀⠀⠸⠀⣠⣪⠛⠀⠀⠀⢸⢀⡀⠠⡇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⣠⣀⠸⠤⣀⣀⣀⡹⣌⠉⠁⠉⠒⡎⠋⠉⠰⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⠀⠉⠁⡇⠀⠀⠀⡤⡯⠋⠀⡆⠀⠀⠀⠀⡅⠀⠀⢀⠃⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠢⢼⡀⠀⠀⠃⠀⠀⢰⢽⠀⠀⠀⣍⢀⢀⡀⡔⠓⠓⢳⠒⡴⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠂⠼⣀⠀⠀⠈⠫⢗⣔⣪⣍⣒⣊⠔⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠝⠒⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⡀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⢀⠐⠉⠀⠀⠀⣀⡀⡴⠂⠒⠲⠲⠆⠀⣀⠀⠀⠉⠓⢦⡄⢢⠔⠋⠀⡧⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠔⢲⢥⣬⣗⢶⠦⠴⠖⢶⢦⠿⠞⠳⠄⠀⠈⠻⠃⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠀⠀⢨⠒⠤⠉⣈⣇⣨⣿⠖⠞⠒⠲⣿⣇⣾⣆⠐⠶⠒⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣉⡀⢈⣉⡇⠀⠀⢙⣁⣌⡡⠊⠀⠀⠀⠀⠑⢌⣡⣈⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠐⠀⣐⠀⠀⢀⠀⣋⣁⠁⠀⠈⠙⠋⠁⠀⠈⣀⣙⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠀⠉⢂⢄⣀⣉⣱⠚⡀⠀⠀⠀⠀⠀⠀⢀⠓⣎⣉⣀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠐⠈⡧⠆⢸⠠⠀⠀⢠⠀⡅⠘⣃⠀⠀⡘⢃⢘⠀⠄⠀⠀⠈⢉⠀⠈⠢⡀⠀⠀⠀⡈⠀⡀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠯⠧⠝⠘⠒⢒⠭⠭⠩⠭⠭⠌⠠⠍⠭⠩⠅⠽⡒⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠒⠈⠐⠐⠊⠀⠐⠂⠁⠂⠒⠅⠈⠒⠒⠁⠐⠒⠀⢀⠆⠀⠸⡀⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠁⠈⠉⠈⠉⠉⠉⠈⠁⠀⠈⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⢠⠚⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠒⠒⠀⠁