Humorous Emojis & Symbols

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠠⢤⣀⠀⢤⣄⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⢀
⠀⠧⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠀⠀⠉⠐⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨
⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣶⣂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⠀⠤⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠲⢄⡒⠦⣌⣹
⠀⠁⢠⡁⠀⢁⢀⠀⠀⠀⡀⠀⢀⣀⡀⢀⣀⠀⣈⠀⣉⡉⣀⠀⢀⢀⡉⠀⣀⠈⢀⠀⠀⢀⡀⡀⣈⢉⡀⢀⣉
⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢐⢮⡢⡈⢦⡈⢿⡜⣆⠈⢸⡇⠀⡋⠀⡎⠀⢀⡞⢕⢕⠕⢋⡴⠋⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣕⡪⡪⠂⠑⠄⠻⡜⡄⠀⡇⠀⠀⠐⠀⠀⠊⠀⠀⣡⠖⢁⣠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠲⢄⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⡶⢟⣫⡵⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡫⠕⠚⠉⠁⠈⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⠒⠀⣀⠠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣚⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⡀⠀⠒⠤⢍⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⣡⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡽⣄⠀⠀⠀⠈⢓⢤⣀⠀⢬
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠊⡠⡢⡀⡴⠁⠀⠀⠀⠀⠀⡇⡀⢹⡹⣦⠐⢄⠢⣔⢕⢯⡳⢶
⠀⠃⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⢈⡴⣫⢮⢎⡞⠀⠀⡄⠀⠀⠀⠀⣷⢣⠀⢳⡹⣧⡈⢳⣌⠳⣕⢮⡳
⠀⠓⠀⢂⠚⢀⡀⣈⠃⠀⠀⠈⠀⠈⠁⠈⠈⠁⠁⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⢤⣤⣶⣦⣤
⠀⣟⣋⣉⡑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢛⢩⣭⣭⣿⣾
⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⢿
⠀⣿⣿⣿⣿⣿⣶⠒⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢙⣿⣿
⠀⠋⠛⠟⠛⠛⠖⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⣴⣦⡤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⡤⠤⠤⠂
⠀⠀⠀⠀⢸⣿⣿⣽⣧⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⣡⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠘⢛⣭⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⠛⡩⠭⠭⣙⠻⣷⡄
⠀⠀⠀⠀⠀⠈⠙⢻⡏⠀⠀⠀⠀⠀⠀⠐⢷⣦⣀⠀⢿⣿⣧⣎⡤⠒⠢⣌⠳⣌⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣾⣿⣿⣷⣬⣁⣉⢎⠣⠈⢦⡙⢿⣦⡀
⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠉⠉⠀⠀⠀⢠⡾⠋⠁⠀⣈⡙⢿⡉⠙⠛⠿⣷⣵⣄⠙⢦⠙⣿⣄
⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠿⠍⣼⠇⠀⠀⠀⠈⠙⣷⣗⡄⢳⢸⣿
⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣾⣸⢸⣿⡄⢀
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡸⣧⠙⠛
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⣦⣤⣀⠀⠀⠀⠀⢻⣿⣷⣽⣷⡄
⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣷⠉⠀⠀⠀⡾⠟⠻⣿⣿⠿⠊
⠀⠀⠀⠈⠙⠛⠿⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠿⠆⠀⠀⠀⢀⣼⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣀⣀⣠⣤⠶⠛⠁⠀⢀⣼⡇⠀⠀⠀⢿⣦⣶⡿⠋⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠹⣯⠀⠀⠀⣠⣴⣿⣿⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣿⣿⡿⠛⠁⣰⠟⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⣶⣦⣤⣾⣧⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⢀⣾⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⠉⢉⣿⣿⣿⡿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⠀⠀⣸⡟⠀⠀⠀⠀⣀⣴⡿⠋⠉⠉⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣍⣉⣛⡓⠒⠒⠶⣆⠀⣠⠤⠦⠴⠶⠶⠶⠲⣿⡃⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠶⠶⠶⢾⣿⠛⠋⠉
⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣸⡇⠀⣹⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠀⢀⡟⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⠿⠆⣼⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠿⠴⠞⠛⠛⠿⢶⣦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠷⠶⠶⢶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⠈⢿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠐⡄
⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠥⢇⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢈⢳⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠄⠠⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡂⠀⡦⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠂⠐⠲⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⢀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠁⠈⠉⠉⠐⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣄
⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠠⠀⠁⠀⡈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠂⠅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠏⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠋⢹⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠓⡂⠠⢄⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⠈⠰⠃⠀⠀⠀⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠲⠄⠀⠀⠀⠀⠴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⠀⠀⡷⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠐⠢⠀⠀⠀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢺⠀⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣠⡞⢅⡀
⠀⠀⠀⠀⢀⠄⠒⢉⠀⠀⠚⠓⠒⠻⢦⠀⠀⠀⢦⡄⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⢩⢉⡏⢀⡇⠀⠙⢦⡀
⠀⠀⠀⠀⠠⠊⠀⠁⠀⢀⡀⠀⠀⠀⠀⠠⣄⡀⠤⣌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠛⣄⡌⢠⠎⠀⠀⣄⠀⠑⢄
⠀⠀⠀⠀⠰⠀⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⡇⠀⠘⠗⠁⠀⠀⠀⢏⢱⡄
⠀⠀⠀⣂⡀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢘⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⣠
⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢺⠀⡀⡈⠀⠀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠲⠾⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠇
⠀⠀⠀⠀⢢⠀⠀⢰⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢰⡄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢺⡏⠁
⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⢻⠉⡗⠐⠴⠀⠀⠀⠀⠀⠠⢫⡇⠀⠀⠀⠀⠀⠀⠀⢉⠉⠛⢛⡓⠒⠒⠒⢾⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢳⡄⠀⠀⢸
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⢸⡄⡏⠀⠀⢈⡇
⠀⠄⠈⠀⠀⠀⢀⠀⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠖⠀⠀⠀⠀⢀⠴⠒⠉⠉⢉⡙⣧⠷⠦⠴⠖⢋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠉⠀⠀⠀⠀⠡⡇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡨⠝⠛⠛⠂⠀⠀⠀⡀⠁⠀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠔⠁⠈⠑⢄⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠤⠱⡀⠀⠳⡄⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⡀⠈⠏⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⢁⠨⠀⠀⠀⢀⣀⠀⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠈⠈⠢⢤⠤⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢍⣁⡐⠀⠤⣧⡇⠁⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠘⢳⠖⢀⠔⠚⡇⠀⠡
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠦⢀⣇⠀⠁⠈⠋⠒⠤⠤⢀⡀⠠⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠐⢇⣀⠎⠀⠀⠰⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠐⠓⠒⠓⠒⠒⣾⣧⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⡄⠸⢀⡠⠔⠢⣄⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢺⡁⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⢾⠟⠋⠉⠉⠉⢀⠀⠀⠀⠀⠀⢀⠇⠖⠁⠤⠴⠀⡟⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠤⡕⡀⠀⠀⠀⠀⠀⠈⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡜⢠⡄⠀⠀⢀⠔⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢆⠀⣸⡌⢢⡀⠀⠀⠀⠀⣅⠀⠀⠀⠠⠐⠐⠀⠤⠖⠑⠂⠒⢒⡉⠟⢠⠎⣈⠟⠋⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠩⠥⠼⣄⠙⠢⣀⠠⡤⠘⠟⠀⠂⠀⠀⠀⠀⠀⠀⠍⠀⡀⠈⠀⣤⡣⠊⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠐⠂⠀⠀⠈⠁⠀⠀⠈⠀⠐⠀⠀⠀⡠⠔⠊⠀⠀⠀⠉⠀⠀⠁⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⡆⢣⣀⠀⠇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣠⠆⠀⠀⠀⢸⢷⡷⠜⠀⠹⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠌⠀⠀⠀⠀⢸⠸⠁⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣤⠀⠀⠌⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠺⠀⠀⠀⠀⢀⠄⠁⡆⢿⣿⡏⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠖⠀⠉⠁⠀⠀⠹⡀⠳⠀⢀⠔⠁⠀⠀⠹⠇⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢱⠴⢇⠀⠀⠀⠀⠀⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣀⣤⣴⣾⠥⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢫⣍⢳⠖⠯⠭⣽⣿⣛⣛⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⠀⠸⠆⠄⠀⠀⠀⠀⢐⠒⠊⠉⠉⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠒⠂⠐⠀⠂⠆⠂⠒⠀⠀⠂⠀⠐⠐⠐⠐⠂⠀⠀⠀⠀⠐⠀⠃⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠀⣀⠉⠁⠠⠄⠀⠀⠀⠀⠀⣀⣠⠛⠋⠈⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⢀⣠⣤⣮⠀⠀⠀⠀⠀⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⠆⠉⠀⠀⠈⠉⠲⣤⡀⠈⢢⣤⠖⠉⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠠⠶⠶⢆⣀⢀⡀⠀⠈⢣⣰⠇⠀⠀⠀⠀⠀⠋⢦⡀⠀⠀⣤⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠻⣟⠦⠀⠀⠙⢧⡤⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⢾⠃⠀⠀⠐⠒⢦⡀⠀⠀⠈⠒⠂⣄⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⣧⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠶⠂⣦⠀⠀⠀⠀⠀⠈⠉⠀⠤⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠖⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⣦⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠚⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⣸⣷⠛⠱⡎⠉⠁⠶⣤⣤⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠀⠀⢸⡄⠀⠀⠈⠛⠛⠀⠀⠀⠀⡧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠸⣧⣤⣤⣤⣬⣍⡁⠀⢠⣶⡃⠀⠈⣦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡀⠹⣟⡁⠹⣧⡀⠶⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⣧⡼⠏⠀⠀⢹⡇⠀⠀⠈⠙⢦⡀
⠀⠀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠹⣄
⠀⡼⠃⠀⢠⡀⢀⡴⠛⠳⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⠀⠀⠀⠀⠸⣆
⢸⡇⠀⠀⠸⣦⠟⢰⡟⠛⠛⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠤⠖⡿⠟⠛⠛⠛⠋⣤⠋⠀⠀⠀⢾⠀⠸⣆
⣿⠀⠀⠀⢰⡟⠀⠸⣦⣴⡖⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠇⢀⡴⠋⠀⠀⠀⢀⡴⠃⠀⠂⠀⠀⠀⡆⠀⢻⡀
⢻⡄⠀⠀⢸⠇⠀⠀⠀⠀⢰⠀⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⡿⠋⠀⠀⠀⢀⡾⠋⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⢿
⠘⢧⡀⢰⡟⠀⠀⠀⠀⠀⢸⠃⠀⢰⡿⡀⢀⣤⠀⠀⠀⠀⣠⠞⠃⠀⢰⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠸⡇
⠀⠈⠙⢾⠇⠀⠀⡀⠀⠀⢸⡀⠸⢧⡀⠙⡏⣰⠿⠶⠶⠎⠁⠀⠀⠀⢺⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⢱
⠀⢀⣠⡿⠀⠀⢠⡇⠀⡀⢸⡟⠃⠀⠘⢿⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⣀⣠⣶⣦⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠶⠀⠉⠀⠀⠀⢸⡇⠀⡇⢸⡇⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢀⣤⡴⢻⡝⣿⣿⠋⢩⢷⡈⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⡏⠀⠀⢸⡇
⠀⠈⠳⣄⡀⠀⣼⠁⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠉⠲⠷⠶⠛⠉⠀⣸⠂⢼⡟⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣷⠀⠀⢸⡇
⠀⠀⠀⠈⢣⡀⣿⣀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢿⡄⠀⢸⠃
⠀⠀⠀⠀⠈⠹⡿⠈⢻⠃⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡇⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⢂⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡉⠂⠾⠆⠀⢀⣀⣀⣀⣀⠸⣷⡀⠀⠀⠀⢀⣼⠷⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠓⠂⠀⠀⠠⠍⠉⠉⠐⠛⢷⣄⣀⣤⣾⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⣤⡐⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣹⠟⠓⠶⠶⠶⠚⣿⠃⠀⠀⠀⣰⡄⢻⣀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠞⢡⠟⠋⠁⠀⣏⠀⠀⠤⠄⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠏⠀⠀⢶⠀⠀⠀⠈⠉⠿⣤⠄⢿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠠⢾⡁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢠⡏⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠻⠦⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠸⣿⡄⠀⠀⠀⠀⡼⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⢷⣤⣀⡀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠘⣧⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⠶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡇⠀⠀⢸⠇⢄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⠛⠛⠛⠛⠓⠀⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⡇⠘⠛⠶⠾⠟⠂⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚⠛⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣠⣴⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠤⠤⠄⣀⣀⣀⣀⣀⣀⢠⣤⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢤⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠛⠛⢿⣄⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣞⠻⠷⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠛⠛⠛⠒⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⣀⠜⠛⠋⠉⣉⣉⢑⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠞⠋⣿⠟⠉⠀⠀⠀⣀⣤⣴⣖⣚⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⡼⠁⠀⠀⣰⠏⠀⠀⠈⠁⠀⠀⠀⠀⠊⠉⣽⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⣰⠇⠀⡀⠀⣀⣀⣠⣤⣤⣤⣤⣼⣧⣄⣀⠀⠀⠀⠀⡀
⠀⠀⣿⠙⠲⣤⡀⠀⠀⠀⣤⣄⠀⣀⣿⡤⣶⣿⡟⠉⠛⠁⠀⠀⠉⠀⠀⠈⠀⠉⢳⠀⠀⠀⢈
⠀⠀⢸⠀⠀⠠⡙⣦⠀⣰⠃⢀⣿⣿⣿⠀⠘⣿⡇⠀⣿⣿⣷⠀⠀⠈⠍⠒⣦⣴⠋⠳⡀⠀⠈⠓⡆
⠀⠀⠈⢧⡀⠀⢜⡾⢷⡗⢲⣿⠀⠻⡿⠀⠀⠀⠀⢰⣿⣷⣾⠀⠀⠀⠀⠈⠁⠀⠀⠀⠹⡄⠀⠀⢱
⠀⠀⠀⢀⡗⠀⢀⡇⠈⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⣿⣓⣤⣀⣀⣀⣀⣀⣀⣠⡴⠃⠀⠀⢸⡄
⠀⠀⠀⣾⠀⢀⣡⠟⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠛⠻⣿⢿⡤⠋⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⡿⠖⠋⠁⠀⠀⢷⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⢸⣾⢳⣤⠖⡆⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢆⠀⠀⢯⣑⠢⢄⠀⠈⠑⠢⠤⣤⠜⠉⠁⠀⠀⡇⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢧⡀⠹⡏⠁⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠐⠒⡅⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠢⠤⠀⠠⠄⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢄⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠑⠄⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣠⡤⣶⠟⠉⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠘⣅⣤⣭⡅⢀⡴⠃⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣤⣀⣀⣀⣀⣈⣉⣯⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔
⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⠁⠀⠁⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⠾⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠄⠘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤
⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣽⣾⣿⢷⣶⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⢹⠛⠙⡛⠀⠀⠈⢻⢇⣑⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢪⠀⣹⠂⠀⠀⠈⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠐⢲⠲⠤⠀⠀⠀⠀⠀⠀⠉⠙⠈⠋⠀⠀⠀⢀⡳⠀⠀⠑⡄
⠀⠀⢀⣀⣀⡠⠚⢭⣉⠀⠂⠀⠀⢆⣀⠴⠃⠀⠀⠤⠄⠂⠁⠀⠀⠀⠀⠈⢆
⠀⠀⠉⢙⣿⠃⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡤⠒⠉⡅⢉⠐⣄
⠀⠉⠂⠈⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠤⠠⠇⠀⠀⢠⠒⠀⠀⠀⠀⢀⣀⠠⠤⢲⠧⡌⢀⠌⠃⡐⢡⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⣡⠁⠈⠀⡀⠀⠀⠈⠉⠉⠀⠀⣀⡤⠾⡁⠀⣇⠀⣆⡨⠣⠀⠂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢁⠆⠀⠀⠀⠈⠁⠒⠒⠒⠒⠋⠉⠙⢆⠀⠙⡄⠈⢳⡚⣶⣖⡶⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠠⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣱⠀⠀⡤⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠹⠵⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⠈⢆⠉⠉⠉⠁⠀⠐⠀⠐⠒⠒⠒⠒⠒⠒⠒⡲⠋⠉
⠀⠀⠀⠀⠀⠔⡯⡴⣯⢓⠄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠲⡶⠤⠤⠤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⠤⢤⠵⠀⠀⠂⠠⡔⢶⠶⠶⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠀⠀⠀⠀⠀⢱⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠂⠈⠐⠢⠴⠊⢚⣠⠀⣀⠀⢔⠵⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠋⠉⠉⠀⢨⠊⠀⣀⠤⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠒⠒⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣀⣠⡼⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣄⡀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠶⠞⠋⠉⠀⠀⢀⣀⣀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠲⠟⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰⠞⢋⣉⣤⠴⠞⠛
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠋⠁
⠒⠋⠉⠉⠉⠁⠀⠀⠉⠙⠒⠶⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣁⡈⠁⠀⠀⠀⢀⣐⣀⣼
⠀⢀⣀⣤⣤⠤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⢿⠟⣿⠛⠛⢛⣉⣉⣉⣉⣙⣑⣦
⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⠶⠚⠋⠉⠉⣉⣩⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣾⠂⠈⠙⣧⢹⡉⠉⠙⠛⢿⡙⣿
⠀⢀⣀⣠⣤⠴⠶⠞⠋⠁⠀⢀⣀⣠⣤⠴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡖⢿⡀⠀⠀⠸⣆⠙⢦⣦⠀⢸⡇⢸⡇
⠛⠋⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣷⠛⠉⣷⠀⠀⠙⢦⣀⢻⣆⣀⣷⢸⡇
⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣴⢲⣖⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣼⠃⢠⡶⠛⠀⠀⠀⠀⠉⠛⢿⠉⠹⣾⣷⣆
⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢛⣩⣭⠵⢿⡄⣏⡉⠉⣹⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⠁⢀⡿⠀⠀⠀⠀⠀⢀⣠⠄⢸⣇⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣟⣩⠴⡄⢸⡃⢀⣼⡄⣿⠈⣿⠉⢻⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⠁⠀⣀⣤⡶⠞⠋⠁⠀⠀⣿⡄⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⠀⣠⠿⢿⡟⠋⢼⡟⠛⠲⣾⣤⣿⣦⡀⠀⠀⠀⠀⠀⢺⡄⠀⣼⡇⠀⠘⠋⠁⠀⠀⠀⠀⠀⢸⣧⡿⣄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⠞⢁⣤⢶⠟⠀⠈⣷⠑⣦⣄⠙⠷⠈⠻⣄⠀⠀⠀⠀⠈⠳⠞⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠈⠓⢄⠀⠑⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣴⡏⢸⣼⡇⠀⠀⠘⢷⣌⣉⣷⣦⣀⢀⣹⠂⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⡇⠀⠀⠀⠀⠑⢦⠨⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣰⡟⣿⡿⠾⠋⠀⠀⣀⡤⠀⠀⠀⢻⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⣶⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠳⡷⡿
⠀⠀⠀⠀⢀⣤⠶⠦⣄⡈⠀⠻⣿⠃⠀⣤⠶⠛⠉⠀⢀⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⢸⡇⣿⠀⠀⣼⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⢀⣤⠾⠋⠀⠀⠀⠀⢉⠀⠀⣿⣀⣤⣤⣴⡶⠾⠿⠛⠛⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸⡇⢻⡄⢀⡇⠘⡇⠀⠀⠀⠀⠀⢸
⠶⠟⠁⢀⢄⠀⢀⡜⠛⠛⠀⡴⠋⠉⠉⠀⢀⣀⡀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⢸⡇⢸⡇⠘⠇⠀⣿⠀⠀⠀⠀⠀⡏
⠀⠐⠒⠁⠀⠉⠉⠀⠀⠀⡼⢡⡆⠀⢀⡴⠉⢉⡇⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⢠⣄⡴⠄⠀⠀⠀⡴⠁⣼⠁⢀⡾⠁⠀⢸⡇⠀⠀⣾⠁⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⢻⣄⣀⣀⣿⠀⠀⠀⠀⢸
⡴⠢⠀⠈⢀⣤⠀⠀⡼⠁⢰⡏⢠⡟⠀⠀⠀⢸⡇⠀⣸⡏⠀⢸⡇⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⣸
⠐⠀⠏⡅⠈⠀⠀⢸⡀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠉⠀⠀⢸⡇⠀⠀⠀⠈⠛⠦⠀⠀⠀⠀⠀⣰⣏⠉⠉⢹⡇⠀⠀⣿⠀⢉⣩⣷⡀⠀⠀⡏
⠀⠀⠀⠋⠙⠆⠀⢸⡇⠀⠀⠀⣸⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⠛⠀⠀⢸⡇⠺⠆⠘⣦⣈⠳⣾⣷⡀⠀⡇
⠀⣠⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⣠⣾⣿⠿⣆⠀⠀⠀⠀⠀⠀⠀⣯⣈⢁⣀⡤⠶⠞⠁⠀⠀⠀⠉⠙⢻⣦⣼⡇⡀⠛⠿⠿⠿⠿⠿⠿
⠸⠃⠀⢣⡖⢲⡆⢸⡇⠀⠀⠀⣿⠀⡰⠒⢦⡀⠀⠈⠳⣾⡿⠛⠁⠀⠹⣆⠀⣀⠀⢀⡴⠛⠉⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠙⠳⣦⡀⠀⣀⣀⡀
⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⠛⠂⠀⠙⣦⠀⠀⠀⣸⠟⡀⢀⣴⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠳⡜⠿⠿⣿
⠶⠶⠶⠖⠲⠖⠀⢈⡏⠀⠀⠀⢸⡀⠤⣤⣤⣤⣄⣀⣀⠀⡸⠿⢃⡴⠛⣀⡥⠞⠉⠉⠉⠳⣦⡴⠶⠶⠶⣤⡀⠀⠀⢀⡴⠞⠛⠉⠉⠙⠛⢶⣄⠀⠀⠙⣤⣀⣈
⣀⣀⣀⣀⠀⠀⡾⣿⢄⣀⣠⣤⡾⠁⢀⣀⣀⡀⠀⠈⠉⠀⠙⠒⢋⣵⠞⠉⠀⢀⣀⣀⣀⣀⡈⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⢶⡶⢶⣶⣶⡤⠤⠼⠓
⠛⠛⠛⣻⡃⠀⠙⠛⠋⠙⠁⠀⠁⠀⠈⠛⠛⠛⢀⣀⣀⣉⣀⣠⠟⠁⣀⠐⠛⠻⣥⠤⠬⠍⠉⠓⠲⣤⣠⣤⠶⠶⠶⠶⠶⢤⣤⣀⠀⠀⠴⠶⠶⠶⢦
⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠒⠒⠖⠛⠩⠷⠎⠿⠿⠯⠾⠯⠭⠽⠦⠀⠄⠰⠤⠤⣤⠀⠀⠀⠙⣿⣦⡀⠀⢀⣀⣀⣀⣉⣹⣆⣤⣀⣶⣶⠛⠉⠉⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠉⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠦⣀⠐⣋⠁⠀⠀⠀⣆
⠀⠀⢀⠠⡄⠤⠀⠀⠀⠌⠀⠀⠀⠀⠀⠂⠀⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠻⠋⠻⣏⡀⠁⠀⠀⠀⠘⡆
⡔⠋⠀⠀⠀⠢⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⣠⠠⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡅
⠑⣄⠀⠀⠀⠀⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠈⠀⠀⠀⠈⢶⣶⣿⠌⠆⠀⠀⡜⠀⠒
⠀⠈⢂⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠘⠅⠀⠋⠀⠀⠐⠀⠱⠀⠀⠀⠐
⠀⠀⠀⢃⠀⠀⠀⠀⣯⣀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠈⠄⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠚⠙⠂⠀⠀⠀⢸⠀⠀⢹⠠⡀⢀
⠀⠀⠀⠀⡂⠀⣠⠂⠁⠀⠀⠀⠀⠀⠂⠠⠒⠄⠀⠀⠠⠀⠀⠀⢀⠄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⣹⠈⠃⠀⠨
⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠐⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠨⠒⡄⠀⠀⠀⠀⠲⠴⠬⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠜
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣀⣀⡠⠤⡤⠖⠚⠅⠤⠀⡀
⠀⠀⠀⠀⠀⠈⠒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡀⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣶⣶⣶⣶⣦⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠂⠀⠀⠐⠂⠀⠀⠀⠀⡠⠊⠁⠈⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠐⠂⢄⣀⠁⠢⡀⢀⡤⠒⠚⡄⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢁⠄⣀⡄⠀⠉⠓⢄⡘⠋⠀⠀⠀⠠⢄⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠻⣓⠄⠀⠛⣤⠀⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢻⠀⠀⠐⠉⠆⠀⠀⠈⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⣤⢀⡀⠀⠀⠀⠉⠛⢠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠰⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠠⠖⠂⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠰⣆⡀⠐⣇⠾⣀⠢⠄⣀⢀⠀⠀⠀⢀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⡷⠀⠸⡆⠀⠈⠹⠗⠀⠀⠀⡀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠧⠤⠤⠔⠛⠓⠒⠾⣅⠀⢷⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣶⢈⡧⠀⢹⡖⠚⠓⢤⡀
⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠙⠉⠀⠀⠘⣷⡀⠀⠀⠘⢦
⢀⠾⠀⢀⠀⡨⠕⢂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⠀⣹⠃⡄⠀⠀⠈⢣
⡸⠀⠀⢸⡷⢱⡞⠉⡉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠛⡛⠋⠉⠉⢁⡆⠡⠀⠀⢠⠀⠆
⡗⠀⠀⢸⠇⠀⠛⠛⡅⠸⢇⡀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣤⠞⠁⠀⢀⡴⠋⠀⢰⠀⠀⠈⠀⠸⡆
⠸⣆⠀⡾⠀⠀⠀⠀⠃⠀⢠⡟⠀⡀⠀⠀⠀⣀⠔⠁⠸⠃⠀⠀⠀⠎⠀⠀⠀⢸⠀⠀⠀⡇⠀⢹⡀
⠀⠉⢻⠃⠀⢰⠀⠀⣁⣐⠧⣈⡛⢱⠓⠒⠚⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡇
⡀⠴⠊⠀⠀⠀⠀⠀⢈⠁⠀⠈⠵⡀⠀⠀⠀⠀⠀⡠⢿⣁⣠⠴⡟⠃⠀⠀⠀⡏⠀⠀⠀⡇⠀⠀⠁
⠈⠢⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠈⠶⣤⡤⠶⠋⢀⠈⡹⠅⠂⠈⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⢆⠀⣇⢀⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡄⠀⡆
⠀⠀⠀⠈⠛⠋⢹⠆⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⢳
⠀⠀⠀⠀⠀⠀⠸⠶⠶⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⣀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠀⠍⠉⢡⣤⠍⠉⠙⠷⣄⣀⣠⡞⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠨⡭⣤⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣠⠟⠉⠛⠛⠛⡛⠁⠀⢀⠴⣄⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⡴⠋⠀⠀⠀⠀⣼⠁⠀⣠⠊⠑⠀⠀⠀⠒⢤⡈⢰⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⢞⠁⠀⠀⠀⠀⡼⠁⠀⢰⡇⠀⠀⠸⡀⠀⠀⠀⠹⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠾⡄⠀⠀⠀⣾⠀⠀⠠⣎⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣟⠀⠀⠀⠙⣄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡟⠀⠀⠀⠀⠈⢳⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⠃⠀⠀⠀⠀⠀⠀⢳⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣯⣀⣸⡇⢤⠀⠀⠀⠀⠀⠈⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠉⠀⠰⠀⠀⠀⠀⡠⢶⣧⣤⣼⡅⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⠇⠀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⠠⣇⣠⠴⠒⠛⠀⠀⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠶⠶⠶⢤⢽⡏⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡿⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣛⣓⣚⣛⣒⣉⣉⣉⣑⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣎⣥⣄⣿⣄⣼⣠⣴⣷⣥⣴⣮⣱⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡴⠞⢤⡀⣡⢦⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⡆⠀⠸⡄⢡⠘⣣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠉⠙⠒⠂⠴⠤⠤⠴⣯⡴⠖⠒⢚⣛⠒⡖⠿⣼⣉⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠤⠤⠤⠒⢚⣯⠄⡇⠀⠀⢀⡤⠴⣇⡿⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡇⠦⢀⠎⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⣠⣚⡛⢢⣼⠀⠁⠀⠀⢸⠀⠀⠀⢀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣸⡀⠀⠱⡀⠀⢸⡁⠀⠀⠘⣹⠀⠀⠀⣀⠞⠀⠀⠀⡎⠀⠀⡸⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠙⣌⢂⠀⡇⡠⢄⡉⠉⢺⠟⠀⠉⠈⠉⡇⢀⠤⢄⠀⠸⡀⠞⡱⠁⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⣉⢑⡈⠋⠀⣿⣀⡠⣈⠖⠁⠀⠀⠀⠀⠀⡞⢁⠶⣎⠀⡠⠃⠛⢡⣋⡩⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⣩⠀⠀⠀⠉⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⡇⢜⡲⠮⡉⠃⠀⠀⡠⢤⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠔⠋⠀⠦⡄⣠⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄⣅⠀⠀⠀⢘⠄⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡇⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⠞⠀⢸⠃⠈⡏⢱⢰⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠈⠑⠒⢢⠴⠖⠊⠁⠀⢀⡇⠀⡰⠃⡌⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠸⠀⠀⢀⡤⠒⠒⠚⣦⣀⡔⠳⣄⡜⢠⠞⠁⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢇⠀⠀⡏⠀⠀⠠⠒⢩⠉⠀⠀⢀⡴⠁⠀⠀⢀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢌⠳⡀⠳⠤⠔⠁⠀⣾⠀⠀⢠⠎⠀⠀⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣉⡶⢄⠀⠀⠀⡇⠀⡰⠁⠀⣠⣄⣠⠤⣫⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠒⡞⠀⢸⠦⠲⠚⢁⣡⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠠⣇⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⢋⣭⣀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡤⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⢆⡁⠀⠳⣄⠀⠀⡜⠀⠈⠑⢤⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡙⠲⡉⢻⣣⠶⠁⠀⠀⠀⠀⠹⠙⠢⢄⡀⠀⠀⠀⠠⢤⢀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢈⠪⡃⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⢳⠒⠒⠒⠒⠋⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣠⣿⣦⡄⠀⠈⡶⢄⠀⠀⢠⠁⡇⠀⠀⠀⠈⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⢏⠣⣙⢦⡄⢳⠀⠙⠻⡾⠶⠤⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠱⣌⢲⡿⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⣀⣀⣤⣀⣀⣈⣉⣀⣀⣀⡀⠀⣿⣴⣤⣤⣤⣤⣤⠤⠤⠿⣾⠿⠻⠿⡍⠉⠩⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠊⠉⠁⠉⠉⠀⠉⠋⠉⠋⠉⠉⠀⠀⠈⠑⠒⠂⠠⠬⠭⠍⠉⠉⠉⠂⠘⠬⠉⠩⠭⠵⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠿⠶⠤⡄
⠀⠈⠉⠉⠁⢸⡏⠛⠛⠿⠿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⣶⣶⢀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠛⠋⠉⠀⠸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡟⠻⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠀⢨⡏⠸⣇⠀⠈⠣⠴⠛⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣤⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣶⠛⠋⠉⠉⠉⠉⢹⡛⠛⠓⠲⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠧⠤⠴⠿⠴⠶⢶⡶⠶⠶⠿⠒⠒⠒⠒⢾⠛⠛⠛⠉⠉⠉⢩⡿⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡀⠀⣾⠋⢳⣄⠀⠀⠀⠀⠀⣀⣿⣀⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣄⣀⣿⡃
⠀⠀⠀⠀⡇⠀⠹⣆⡀⣙⣦⡴⠶⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒
⠀⠀⠀⠀⠻⣄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⡶⠆⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠀⠀⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠈⠀⠁⠂⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⢄⡀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⢠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⢠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⣉⠉⠀⠀⠀⠄
⠀⠀⣀⡀⠀⡀⠀⠈⢀⠜⢄⡀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⡠⠧⣀⠀⣀⠜⠀⠀⠀⠀⠀⣠⠄⠐⠀⠀⠀⠉⠑⠀⠀⠀⠔
⠀⠈⠙⢄⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠅⠤⠤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠈⡁⠢⠄⢀⠀⠀⡀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢙⠂⠄⠀⡀⠀⠠⡤⠒⠁
⠀⠀⠀⠀⠘⢤⠤⠤⠤⠤⠧⠄⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠑⠠⠤⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠆⠀⠀⠀⠀⠒⠂⠀⠣


⠀⠀⠀⠀⠀⢀⣤⡤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠄⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠠⡀⠀⢀⠀⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⢀⡀⠀⠀⠀⠉⠉
⠀⠀⢀⠄⠀⠚⠛⠃⠀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡈⢂⡀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣌⠲⣨⣀⣤⠀⡀
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⡈⠁⠀⠀⠀⠄⠀⠀⠀⠀⣀⡀⠀⠀⠻⣿⣿⡿⢈⠻⣿⠟⠁⠄⠀⠤
⠀⠀⠀⠀⠓⠠⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠤⠊⠉⠒⠀⠒⠉⠀⠀⠀⠀⠀⠈⡄⠀⠈⠠⠈⠡⠔⠉⠑⠂⠐⠈⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠶⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠌⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠀⠀⠀⠀⠴⣦
⠀⠀⠀⠒⠿⠶⣶⣤⣄⣀⣀⣀⣤⡴⠶⠟⢟⠃⠀⠀⠀⠀⣠⠴⠚⠋⠁⠐⡎⠈⠙⠒⠂⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠢⣀⠄
⠀⠀⠀⠀⢆⠀⠈⠙⠉⡹⠛⡉⠙⠀⠀⢀⠌⠀⠀⠀⠀⠀⠸⡀⠈⠙⠁⠀⡅⠉⠋⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢠⢤⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠑⠂⠐⠊⠁⠀⠈⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠊⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠶⣀⡀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⢀⠠⠀⡖⠀⠀⠒⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⢠⠮⠭⠤⡄⠇⠀⠔⠒⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢟⢠⠠⠤⠇⠂⠐⠒⠒⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡾⠛⠃⠀⠀⠶⣦⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠋⡠⢤⡀⢀⣤⣄⠈⠃⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⢸⠀⢿⣿⡏⠸⠿⡇⠀⠀⠀⢿⣆⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⠁⠀⠀⠘⠳⠖⠋⠈⠒⢚⣁⣤⡴⠶⠟⠛⠋⠉⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣬⠄⠀⢀⣠⣄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠈⠁⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣀⣀⣀⣀⣀⣤⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡄⠀⠀⠀⢠⠇⠀⠀⠀⠈⠉⢹⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢦⣀⠀⠀⠙⠶⠤⠴⠋⠀⠀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣡⣿⠀⠈⠛⠶⢾⣶⣶⣆⣤⣤⣤⡶⠾⠛⠁⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣠⠞⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠙⢦⡀
⠀⠀⢴⠲⢄⣀⣀⣤⣤⠞⢉⡴⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⣄⠙⢦⡀
⢠⠒⠒⠛⠂⠉⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠙⢦⣄⠀⠀⢀⠄⣆⣀
⠯⣀⡀⠤⠄⠀⣀⡤⣀⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⣄⠙⠉⠙⠋⢚⣡⣜
⠀⠧⠤⠒⠚⠉⠀⠀⢸⡈⠳⣄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣤⠔⠚⢡⠦⣄⠀⠠⣬⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠓⠚⠁⠀⠈⠓⠦⣄⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢳⡀⠀⠀⠀⠀⠈⠉⣟⢻⡷⠶⠶⠶⠶⢶⡶⡶⠿⠛⠋⠁⠀⠀⢀⣤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢻⣦⣤⣤⣤⣤⣄⣿⠘⡇⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⣀⡴⠋⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠉⠃⢷⡄⠀⠀⢠⠞⠁⠛⠉⠉⠉⠉⠙⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⢦⣤⣤⣤⣴⠇⠀⠀⠘⠷⣤⣤⡤⠴⠶⠶⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⣿⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠛⠻⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠷⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠿⠿⣶⣄⡀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⢀⣾⡿⠛⠉⠀⠀⠀⠀⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⢀⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠾⠛⢋⣿⡟⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠰⢶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠾⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⡀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠠⠀⠠⠀⠒⠀⠢⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠈⠀⡀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠂⠀⠡⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⢠⠊⠀⠀⠂⠂⣀⠀⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢁⠀⠈⡆⠀⠜⠀⠀⠀⠀⠀⠀⠐⠠⠄⢀⣀⠠⠀⠀⠀⠄⠷⠀⡄⠠⠂⠀⠀⡠⠀⠀⢈⣀⠀⠀⠀⡇
⠀⠐⠀⠐⡀⠀⢢⠀⠀⠀⠀⢸⠟⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⣰⠀⠀⢀⠌⠀⡕⠀⠀⠒
⠀⠀⠀⠀⠄⠒⠌⠳⠤⠊⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠈⠂⠐⠓⠒⠋⠄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣿⣭⣽⣭⣮⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡤⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⡖⢶⣋⣛⣧⣀⣄⡀
⠀⠀⠀⡞⠉⢀⣀⣀⢀⣷⠀⠀⠀⠀⣀⢶⣶⠿⢿⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⢿⡆⠀⠀⠀⡞⡡⠲⠤⠃⠐⠠⣞⡿
⠀⠀⠈⢻⣟⣁⠀⣀⣹⠁⠀⠀⣀⡼⠑⢦⠄⠚⣤⠌⢡⡀⡀⠀⢘⣃⠀⠙⠛⠋⠀⣠⠷⠀⠀⠠⢭⣃⢄⠀⠀⠤⠄⠄
⠀⠀⠀⢧⣀⣨⢹⡁⣂⡘⠀⠀⠣⡇⠀⠂⢄⣀⣨⠀⠂⢷⠁⠀⠐⠿⠗⢀⣀⣀⡼⢿⠇⠀⠀⠀⠸⠟⠸⠀⣸⠟⠡
⠀⠀⠠⣤⣷⣿⣬⣧⣧⣤⡀⠀⠀⢿⠄⠀⢴⡈⣥⠀⠰⡿⠀⠀⠀⢠⣴⣾⣿⣿⣶⣆⠀⠀⠀⠀⠀⢰⠀⣤⣄⢸
⠀⠀⠀⠀⢸⠈⠉⢉⠏⠁⠀⠀⠀⠀⠀⠀⠠⠈⠀⠠⠞⠀⠀⠀⠀⠀⠱⡉⠘⠋⡜⠁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠔
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠒⠁
⠀⠀⠀⢰⣿⣟⣿⣷⣤⠀⠀⠀⠀⠀⢀⡠⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⡠⢄⣀⡀⠀⠀⠀⠀⠀⠀⣶⡳⠂
⠀⠀⠀⣸⣏⠙⠻⠿⣿⡄⡀⠀⢀⣰⠋⠉⠓⠈⠢⠺⠦⠀⠀⠀⠀⣠⣤⣴⣿⣿⣦⣶⠌⡆⠀⠀⠀⠀⡜⣿⡁⢳⡼⣄
⠀⠀⠨⣿⣽⣿⠀⣻⣯⣷⡄⠀⣺⡇⠶⢔⠀⠀⢰⢒⣶⠦⠀⠀⣺⡟⣏⢻⠛⠋⠯⡝⣶⡌⢣⠀⠀⠸⠄⠀⠈⠉⢁⣈⡀
⠀⠀⠈⡇⢸⣟⣶⣻⠇⡞⠀⠀⠀⢣⡀⠘⠦⠤⠜⠀⠠⠎⠀⠀⠸⠷⢾⠦⠀⠴⣶⠼⣿⣷⠞⠀⠀⠾⣷⡖⠂⠈⣱⠾⠛⠁
⠀⠀⠀⠳⠛⢁⡉⠙⣾⠃⠀⠀⠀⠀⢳⡀⠐⢮⡲⠗⠁⠀⠀⠸⠤⢷⠀⣀⡒⡂⠀⢀⣏⣹⠀⠀⠀⢠⡀⣬⣃⠤⣁⢀⡜⠃
⠀⠀⠀⠀⠑⠀⠉⠴⠃⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⠡⠎⠀⠀⠀⠀⠀⠀⠑⠙⠉⢈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢀⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⠻⣧⡀⠀⠀⠀⠀⢠⠂⠉⠉⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠘⡿⠿⢿⡁
⠀⠀⢲⣾⠟⣉⠈⣉⠻⣿⠿⠃⠀⠀⠀⡞⠙⠦⠜⠉⡆⠀⠀⠀⡆⢀⡎⠉⠉⠉⠹⡄⢸⠀⠀⠀⠀⢻⢻⣟⣛⣿⣿⢩⠁
⠀⠀⢼⣻⡏⢳⠀⢸⣿⠽⡴⠀⠀⣠⣴⣧⣆⡄⣄⣴⣷⡆⠀⠀⠳⢶⣷⣦⠀⣷⣾⡟⠚⠀⠀⠀⠀⠀⢾⡙⡎⠛⣉⠓
⠀⠀⣸⣄⣤⣼⢶⣾⣤⣠⣧⠀⠀⠘⣸⣀⡤⣇⣴⢤⣯⠁⠀⠀⠀⢰⠍⠭⠀⡸⠉⠧⠀⠀⠀⠀⠀⠀⢸⡿⣅⡰⢿
⠀⠀⠉⠛⢯⡉⠛⠋⣠⠟⠉⠀⠀⠀⠨⢴⠤⠿⠶⢦⠗⠀⠀⠀⠀⠣⠴⡛⠛⠋⡹⠒⠁⠀⠀⠀⠀⠀⠸⣧⣿⣧⡼⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢦⣓⡠⠃⠀⠀⠀⠀⠀⠀⠀⠙⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣁⠅


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠒⠒⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣀⣠⡼⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⢤⣄⣀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠞⠋⠉⠀⠀⢀⣀⣀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠶⠟⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⡠⠞⢋⣉⣤⠴⠞⠛
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠒⠋⠉⠉⠉⠀⠀⠀⠉⠙⠒⠶⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠴⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣉⡀⠁⠀⠀⠀⢀⣐⣀⣸
⠀⢀⣀⣤⣤⠤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⢿⠟⣿⠛⠛⢙⣋⣉⣉⣉⣉⣙⣶
⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠚⠛⠉⠉⣉⣩⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣾⠂⠈⠛⣧⢸⡉⠉⠉⠛⢿⡉⢿⡀
⠀⢀⣀⣠⣤⠴⠶⠞⠋⠁⠀⢀⣀⣠⣤⠴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡗⢿⡄⠀⠀⠸⣆⠙⢦⣦⠀⢸⡇⢸⡇
⠛⠋⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⠛⠉⣷⡀⠀⠙⢧⣄⢹⣆⣀⣷⢘⡇
⣠⣤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣴⢲⣶⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣼⠃⢠⡶⠛⠀⠀⠀⠀⠉⠛⢿⡉⠙⣿⣷⣆
⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢛⣩⣭⡵⢾⡄⣏⠉⠉⣹⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⠁⢀⡿⠀⠀⠀⠀⠀⢀⣠⠄⢸⣇⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣟⣡⠴⡆⢸⡃⢀⣼⡄⣿⠈⣿⠉⢻⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⠁⠀⢀⣤⡴⠞⠋⠁⠀⠀⣿⡆⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⠀⣠⠿⠿⡟⠋⣼⡟⠛⠳⣾⣧⣿⣦⡀⠀⠀⠀⠀⠀⢸⡇⠀⣼⡇⠀⠘⠋⠁⠀⠀⠀⠀⠀⢸⣧⡿⣄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⠞⢁⣤⢴⠟⠀⠈⣿⠑⣶⣄⠙⠷⠌⠻⣄⠀⠀⠀⠀⠈⠳⠾⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠳⢤⡀⠑⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣴⡏⢸⣸⡇⠀⠀⠈⢷⣌⣉⣷⣦⣀⠀⣹⠂⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠙⢻⡇⠀⠀⠀⠀⠑⢦⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⡟⣿⡿⠾⠋⠀⠀⣀⡴⠀⠀⠀⢻⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢠⣶⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠳⡷⣿
⠀⠀⠀⠀⢀⣤⠶⠦⣄⡀⠀⠻⣿⠃⠀⣤⠶⠛⠉⠀⢀⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⢸⡇⣿⠀⠀⣸⢸⡇⠀⠀⠀⠀⠀⢠⡇
⠀⢀⣤⠞⠋⠀⠀⠀⠀⢉⠀⠀⣿⣀⣤⣤⣴⡶⠾⠿⠛⠛⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⢸⡇⢹⡄⠀⡏⠀⣧⠀⠀⠀⠀⠀⢸⠁
⠶⠟⠁⢀⢄⡀⢀⡜⠛⠛⠀⡴⠋⠉⠉⠀⢀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⢸⡇⠸⣇⠐⠇⠀⣿⠀⠀⠀⠀⠀⡟
⠀⠐⠒⠁⠀⠉⠉⠀⠀⠀⡼⢡⡆⠀⢀⡴⠉⠉⡇⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇
⠀⠀⢠⣄⡴⠄⠀⠀⠀⡼⠁⣼⠁⢀⡾⠁⠀⢰⡇⠀⠀⣾⠁⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⢻⣄⣀⣀⣽⠀⠀⠀⠀⢸⠃
⡴⠲⡀⠈⢀⣤⠀⠀⡼⠁⢰⡏⢠⡟⠀⠀⠀⢸⡇⠀⣰⡏⠀⢸⡇⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⢸
⠐⠀⠏⡅⠀⠀⠀⢸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠉⠀⠀⢸⣇⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⣰⣏⠉⠉⢹⡇⠀⠀⣿⠀⠉⣉⣷⡀⠀⠀⡟
⠀⠀⠀⠋⠙⠆⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⠛⠀⠀⢸⡇⠺⠆⠘⣧⣈⠓⣾⣷⡀⠀⡇
⠀⣠⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⣠⣾⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣈⣁⣀⡤⠴⠞⠁⠀⠀⠀⠙⠉⢻⣦⣼⡇⢀⠻⠿⠿⠿⠿⠿⠿
⠸⠃⠀⢣⡞⢲⡆⢸⡇⠀⠀⠀⣻⠀⠰⠖⠤⡀⠀⠀⠳⣾⡿⠛⠁⠀⠹⣆⠐⣀⠀⢀⡴⠚⠉⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠳⢦⡀⠀⣀⣀⡀
⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⠛⠂⠀⠙⣦⠀⠀⠀⣰⠟⡀⢈⣴⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠳⡌⠿⠿⣿
⠶⠶⠶⠶⠶⠖⠀⢈⡏⠀⠀⠀⢸⡀⠤⣤⣤⣤⣤⣀⣀⠀⣸⠿⢛⡴⠛⣀⡥⠞⠉⠉⠉⠻⣦⡴⠶⠶⠶⣤⣀⠀⠀⢀⡴⠞⠛⠉⠉⠙⠛⢶⣄⠀⠀⠙⣦⣄⣈
⣀⣀⣀⣀⠀⠀⡾⣿⡄⣀⣠⣤⡾⠃⢀⣀⣀⡀⠀⠈⠉⠀⠙⠒⢋⣽⠞⠉⠀⢀⣀⣀⣀⣀⡈⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⠶⠶⣶⣶⣶⡤⠤⠜⠓
⠛⠛⠛⣻⣃⠀⠙⠛⠋⠙⠁⠀⠁⠀⠈⠛⠛⠛⢀⣀⣀⣉⣀⣠⠟⠁⣀⠐⠛⠻⣥⠤⠬⠍⠉⠓⠲⢤⣠⣤⠴⠶⠶⠶⠶⢤⣤⣀⠀⠀⠰⠶⠶⠶⢦
⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠒⠒⠒⠛⠉⠷⠎⠿⠿⠯⠶⠯⠭⠽⠦⠀⠤⠐⠤⠤⣤⠀⠀⠀⠉⣿⣦⡀⠀⢀⣀⣀⣀⣉⣙⣆⣤⣀⣶⣶⠟⠉⠉⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠛⠛⠳⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢶⣦⡀⠀⠀⠀⠀⠀⣿⡄⣠⠒⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠤⣾⣿⡇⠀⠀⠀⠀⠀⣿⠇⣿⠖⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠟⠁⠀⠀⠀⠀⢀⡿⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⢀⣠⣴⣶⣿⣿⣶⣦⣄⡀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠘⠿⠋⠉⢿⣧⠀⠀⠉⠛⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣽⠛⠷⢶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡶⠏⣽⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣼⠇⠀⠀⠀⠀⠈⠉⠉⣿⠛⠛⠛⠛⠛⠛⠛⠛⢹⡏⠉⠁⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡟⠛⠛⣿⠟⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⣀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠿⢷⣦⣤⣤⣤⣤⣴⡶⠿⠿⠛⠋⠉

⢀⣠⣤⡀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⠀⠀⠀⠀⡄⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⣠⣤⣤⣄
⠈⠉⠁⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠪⠟⠀⠀⠀⠀⠪⠟⠀⠀⠀⠀⠀⠀⣿⠥⠾⠯⢵⡀⠀⡎⠤⠟⠯⣿
⣴⣶⡄⠀⠀⠀⠀⠀⠀⣾⣳⡆⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠁⣤⡀⠀⠀⠁⠈⠀⠀⢠⣤⠈
⠙⠛⠃⠐⣦⣀⣠⡞⠀⠉⠋⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠁⠀⠠⡀⠀⠀⡠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⢦⡀⢀⡰⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠤⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⠀⡴⢦⡴⣆⠀⢠⡶⣤⢲⡄⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⢠⢤⡀
⠀⠙⢎⡴⠁⠀⠀⠳⠤⠊⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠉⢁⣀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠐⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⠃⠀⠀⠀⠳⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠀⠀⡀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠐
⠀⠀⠀⠘⠧⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁



⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠢⠤⠄⠀⠀⠀⠢⡤⠖⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠆⠀⠀⠀⢮⣁
⠀⠀⠀⡤⣀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣾⢷⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠬⣭⠥⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠊



⠀⠀⣠⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠘⢜⠟⠀⠀⠀⠘⢜⠟⠀⠀⠀⠀⠀⠀⠐⠦⠤⠆⠀⠀⠀⠦⠤⠒⠀⠀⠀⠀⠀⠀⠀⡎⣷⠀⠀⠀⠀⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠉⠀⠀⠀⠀⠉⢉⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⣟⣡⣤⣤⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇⠀⠀⠢⠔⠂⠀⠘⠯⠋⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣠⠖⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⣁⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣈⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠒⢤⡀⠉⠲⢤⡀⠀⠀⢀⣀⣀⣠⣤⠤⣤⣄⣀⣀⡀⠀⠀⢀⡤⠖⠉⣀⡤⠚⠉⠁⣼
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠳⣄⠀⠉⠳⠞⡏⠁⠈⣧⡇⠀⢸⡇⡇⠈⢉⡷⠞⠉⠀⣠⠞⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣬⢿⠟⠂⠀⢻⠀⠀⣿⡇⠀⢸⣿⡇⠀⢸⠁⠘⠻⡿⣥⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⣤⠏⠉⠀⠀⠀⠀⠸⣄⣠⠟⢧⣀⡼⠛⢦⣠⠞⠀⠀⠀⠀⠉⠹⣄⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣀⣀⣀⣸⠀⠀⠀⠀⠀⢀⣤⠖⣺⣿⡗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣽⠀⠀⠀⠀⠀⠈⢻⡀⢿⣿⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⣰⢄⣀⣀⡴⠧⠀⠀⠀⠀⠀⣏⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣤⢼⡄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⢰⣧⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢹⠁⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢳⠀⠀⠀⠀⢀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣿⣿⣸⠀⠀⢀⣴⣫⣾⣿⠀⠀⠀⠀⠀⣀⡠⠤⢲⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⢿⣷⣾⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⠃⠀⣀⣤⣶⣿⣷⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣯⣭⣉⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⢿⣿⡟⠿⣿⣗⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠛⠛⠲⢦⣄⠉⠳⣄⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣩⣿⣿⡿⠋⣠⠴⠒⠛⠋⠙⠛⠓⠲⢶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⠈⠳⣄⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡿⣡⣾⣿⣿⡟⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⢳⡀⠀⣴⠟⠉⠀⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⢠⣟⣼⣿⣿⣿⡟⢀⡟⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⢹⣄⣴⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⣾⠃⠀⢠⣾⡿⠻⣶⣄⠀⠹⣇
⠀⠀⠀⠀⠀⣾⡿⠋⢰⣿⣿⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⡟⢿⣿⡗⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⢻⡆⠀⣿
⠀⠀⠀⠀⠀⠟⠁⠀⣾⡾⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣧⣀⡀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠉⣉⣻⣿⡿⠿⣿⠿⠶⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡥⠶⠚⡏⠉⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⠈⠳⣄⠀⠀⠀⢰⡶⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢿⣄⡀⠀⠀⢀⣠⣴⣿⡿⠋⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣸⣄⣀⣼⣦⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⠀⠀⠙⠛⠛⠛⠋⣩⠞⠁⢹⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣀⣼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠉⠁⠀⠀⠀⠀⢀⡼⡇⠀⠀⠸⡇⠀⠀⠀⠀⣸⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿
⠀⠀⠀⠀⠀⢠⡟⠀⢀⣴⣶⠆⠀⠀⠀⠀⠀⣼⠁⣧⠀⠀⠀⠙⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣧
⠀⠀⠀⠀⠀⢸⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢹⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⢩⡟⠀⠀⠀⠀⠀⠈⢙⣿⠿⢿⣿⠏⠈⢿⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣦⠀⠈⠻⠷⠄⠀⠀⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠀⠀⠀⣠⡴⠶⣄⣿⠁⠀⠈⢿⣇⠀⠘⡿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⣀⣤⡴⠛⠙⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⠶⠟⢷⡌⣧⠀⠀⠈⢿⡆⠀⠀⠈⣿⣄⡼⠁⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⢧⡀⠘⢿⣿⣿⣿⣿⣏⠁⠀⢻⡅⠀⠀⠀⠹⣿⡆⠀⠀⠈⢿⡄⠀⠀⣸⠏⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⢿⣿⡏⠉⠻⣆⠀⠀⢳⡀⠀⠀⠀⠹⣿⡀⠀⠀⠈⣷⡴⠊⢁⣤⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠙⢿⣦⡀⠘⢧⡀⠀⠳⣄⠀⠀⠀⢘⣧⠤⠖⠋⢁⣠⠴⠋⣁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠓⠶⠤⠿⠦⠤⠼⠓⠚⠉⠁⠀⠰⠶⠛⣉⣥⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠈⢙⠃⠀⠀⠀⠀⠀⢀⣠⣤⣾⠿⠄⡀⠀⠀⢴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠈⠖⠁⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⡲⠆⠀⠀⡀⠀⠀⠀⠀⡄⠀⢃⠀⠛⠀⠜⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠚⠀⡘⠘⠃⠀⠀⡘
⠀⠀⠀⢂⠀⠀⠀⠀⠄⠊⠁⠂⠀⠈⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠈⠀⢀⣀⡀⠔⠉⠒⠠⠤
⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠈⡠⠀⠀⢀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⡀⠡⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡧⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⡀⠀⠀⠀⡉⠛
⠀⠀⠀⠀⠀⠀⠈⠙⠷⠀⠈⠉⠳⠀⠀⠀⠀⠀⠀⢤⣶⣤⣄⣀⠀⢀⠀⣀⣤⣴⠶⠖⠂⠀⠀⠀⠀⠀⠄⢠⡶⡶⣤⠱⢪⡴⡦⠔
⠀⠀⠀⢠⠁⠀⠀⠀⠐⡁⣀⠀⠀⢱⠀⠀⠀⠀⠀⠘⡀⠀⠉⠛⠙⠛⡛⠛⠃⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⣠⣽⣷⡆⢠⢀⣽⣿⠇⡘
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⠀⠀⡜⠀⠀⠀⠚⠇⠀⠈⠒⠀⠐⠈⠀⠈⠐⠂⠒⠁⠀⠠⠀⠀⠀⢋⠀⠀⠀⠉⠉⠄⠊⠑⠀⠄⠊⠀⢠⠂
⠀⠈⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠈⠐⠤⠀⣀⠀⣀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡶⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⡖⠒⠒⠀⠀⠈⠁
⠀⠀⠀⠀⠹⡄⡄⠄⠄⠀⠤⠠⢤⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣃⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠑⠀⠄⠀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠂⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠿⠇⠀⠀⠀⠀⠷⣆⠀⠀⠀⠀⠀⠀⠀⣴⠾⠇⠀⠀⠀⠀⣀⣀
⠀⠀⠚⠛⠷⢶⣤⣤⣠⣤⣤⡶⠞⠛⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⡀⠀⣋⣉⠉⠀⡀
⠀⠀⠀⠣⡀⠀⠉⢀⠍⠡⡈⠁⠀⡠⠊⠀⠀⠀⣀⠀⠀⠀⠀⢠⡄⠀⠤⠄⠀⠀⠀⠀⣄⠀⠀⠀⠣⠀⠀⠈⠀⡠⠓⠀⠀⠁⠀⠠⠃
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⢀⠜⠢⢀⡀⠔
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤
⠀⠀⠀⠀⢤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠘⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠠⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣛⣉⣉⣙⣛⣛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⣻⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡟⢰⣿⣿⣿⣿⣿⣿⡿⣿⠈⠁⡈⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢻⣜⣿⣿⣿⣿⣿⣿⣳⡏⣠⣴⣿⣿⣿⡿⠟⠉⠀⠉⠢⡀⡀⠉⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⣤⣤⣤⣤⣸⣦⣾⣿⣶⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⡙⠀⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⣬⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠸⣎⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢏⡻⣄⠀⠀⠀⠐⠿⠛⠉⠁⠀⠈⠉⠀⠀⠀⢿⣜⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⣾⡆⠀⠀⠀⠀⠀⠤⢭⣇⡀⠀⠀⠀⠀⠀⠻⣿⡿⡫⠭⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡿⠿⡿⢿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡠⠄⠂⠁⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⣀⣠⣶⣿⣧⣀⣄⡀⣅⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢤⣤⣤⣤⣤⣤⣤⣤⡢⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢣⠀⣷⣤⣤⣤⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⣯⣭⣽⠿⠋⠀⠀⠀⠀⠀⠀⢀⠔⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠂⠁⠀⠄⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠠⡤⠒⠈⠁⠀⠀⠀⠀⠐⠀⣿⣯⣀⣠⣀⠀⠀⠁⠃⢀⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣧⣿⣶⣿⣇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠒⡞⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⢹⡉⠋⠑⢒⠢⢤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡒⠈⠉⠌⡵⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡀⠌⠁⠈⠠⠈⠄⠀⠌⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⠰⢀⠠⡀⢶⠁⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⡰⡁⠄⡁⢀⠠⢈⠠⠀⠄⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠠⠐⠀⠀⠄⢃⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠂⠈⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⠄⠢⠄⠠⠐⠠⠐⢄⠂⠄⠢⡐
⠀⠀⠀⠀⠀⠀⠀⠃⠆⠈⠠⠈⠠⠀⠆⠙⠦⣀⣀⣀⣀⠤⠔⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠠⠁⠄⠁⠌⠰⠈⠰⠁⠀⠁⠆⠑⠈
⠀⠀⠀⠀⠀⠀⠂⠁⠂⠂⠐⢈⠐⠈⠂⡁⠂⡑⢈⠐⢈⠐⡀⠂⡉⠒⠂⢤⠤⣤⠤⡐⠒⡚⢁⠐⢈⠐⡀⠂⠁⠂⠐⠈⠐⣀⠂⠁⠂⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠐⠀⠂⡀⠂⠐⢀⠐⢀⠂⠀⠂⠐⠀⠑⢈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠉⠉⠉⠉⠙⠻⢿⣷⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠤⠴⠶⠶⠶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣦⣄⡀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⣿⠀⠀⣻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠗⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠘⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡾
⢀⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣀⣀⣀⣀⣀⣉⣻⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠈⠉⢙⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠦⣤⣀⠀⢀⡼⠁
⠀⠀⢘⡻⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⢸⡇⢿⡆⠸⣆
⠀⠀⢸⣇⠘⣷⠀⠹⣆
⠀⠀⠀⣿⠀⢹⡆⠀⠘⢦⡀
⠀⠀⠀⢿⡆⠀⢻⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀
⠀⠀⠀⢸⣷⠀⠀⢻⡄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣿⣶⡄
⠀⠀⠀⠀⢿⣇⠀⠀⠹⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠀⠉⠋
⠀⠀⠀⠀⠈⣿⣆⠀⠀⠈⠢⡀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣠⡞⠁
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠉⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠋⠉⠉⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣀⣀⣀⠀⠀⣀⣤⣤⣀⠀⠀⢻⡾⠁⢀⣀⣀⡀⠀⣠⣤⣄⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣾⠟⢹⣿⣿⣾⣿⣿⣿⣿⣷⡀⠀⢿⣰⡟⢉⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⠉⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣼⠀⠀⠀⢀⣤⠶⢶⣶⣄
⠀⢀⣴⢿⣟⠛⠳⠄⠀⠀⠀⢷⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣰⣯⡀⠀⠀⠙⠻⠿⠛⠉⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⣼⠀⠙⠃
⠀⠈⠀⠘⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⢀⣴⠏⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⢀⣀⣤⡶⠛⠁⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⢤⣀⡀
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢘⡔⠀⠀⠀⡔⠂⠉⠉⠒⠂⢤⣤⣦⣀⣸⢤⠀⠀⠀⠀⠀⠀⠈⠀⢠⣬⠀⢂⣠⡀
⠀⢀⡀⡀⠠⠀⠀⣠⣤⠄⢀⠀⠀⠀⠀⠈⠒⡶⠒⠲⣿⡏⢶⣶⠀⠀⣳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠗⠁⠀⠧⠆
⠀⠀⠒⠀⠀⠛⠶⠈⠁⡀⠊⠀⠀⠀⠀⠀⠀⠱⠀⠀⠈⠀⠈⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⢀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠔⠀⠀⠂⠀⠠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⠄⢀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⠄⠀⢣⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠠⠔
⠀⠀⠀⠀⠀⠈⠿⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠀⠀⢚⣃⠀⡜⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠆⠀⠀⠃
⠀⡠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠈⠴⠤⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠃⠀⠀⠉⠀⠀⠠⠀⠤⠤⠜⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠠⠢⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠡⠌⢉⠉⠒⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠁⠒⢀⡈⠱⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠀⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⣄⢀⡀⣒⣀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣶⣄⠁⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⠈
⠀⠀⠀⠁⠀⠘⠦⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⠠⠔⠊
⣀⡀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡇
⠀⠀⠀⢸⠉⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⡆
⠀⠀⠀⠈⠓⠒⠒⠒⠓⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠚⠁
⠀⠠⠒⠀⣀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠻⠿⠛⠛⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⢿⣟⠷⢦⡄⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⠒⠄
⠀⠈⠉⠉⣀⣤⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠈⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠉⠛⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠤⢤⣀⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣠⠴⠾⠷⢦⡀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⢀⡔⠉⠀⠀⠀⠀⠉⠳⠀⠀⠀⣠⡿⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣤⣄⣀⣀⣀⣤⡤⠶⠖⠛⠉⠀⠀⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢁⠤⢄⣀⣀⣀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡰⠣⠆⠀⠀⢈⡉⠀⠀⠀⠢⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠠⠄⠀⠄⢀⠁⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢰⠀⠀⠠⠂⠀⠰⠂⠀⠀⠀⠀⠀⠀⠤⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡂⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠎⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠒⢂⢛⠋⡩⢉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠁
⠀⠒⠒⠒⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠁⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠈⠢⠤⠤⢤⣤⣤⣤⡤⠤⠤⠤⠤⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠁⠀⠀⠀⠈⠀⠓⠀⠣⠄⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠁⠀⠒⠁⢈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠶⠦⢤⠴⠒⠒⠒⠒⠶⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣠⣦⠀⠀⣠⠞⠙⢧⡀⣠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡴⢧⡀⡰⠋⠘⢦⡼⠁⠈⠓⠚⠁⠀⠀⠈⠛⠃⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡼⠁⢠⣙⣡⠤⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⠃⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠴⠀⣠⠖⠀⠀⠤⠤⣤⣀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠈⣴⣡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠙⣧⢿⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠙⠓⠚⠛⠋⠁⣀⣀⣀⠀⠀⠀⠉⢸⡄⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡿⠻⡆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢩⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣹⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡿⡇⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡥⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⣷⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢀⣀⣀⣤⣼⣄⡀⣿⠀⢹⡀⠀⠀⠀⣿⠻⣦⡀⠰⠶⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇
⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⣻⢺⡄⢸⡇⠀⠀⠀⣿⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⣄⠀⢀⣀⡀⠀⠴⢿⠈⣷⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⣷⠀⠀⠀⠀⠀⢸⠃
⠀⠀⢰⣇⠀⠈⠀⠀⠀⣠⣿⠀⢸⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⠶⠶⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢹⠋⠀⠉⠁⠀⠠⢿⣠⠟⢸⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠘⣷⣒⠀⠀⢀⣠⠞⠁⠀⣿⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢠⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⢿⡄⠀⠀⢀⣤⡀⠀⠀⠀⣠⢴⡄⠀⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⢀⠴⣄⠀⠀⠀⠈⢷⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⡰⠋⠀⠙⢦⡴⠋⠈⠳⣤⣀⠜⠁⠀⠙⠳⢦⣤⠞⠁⠀⠈⠻⢦⣤⠞⠁⠀⠘⢧⡀⠀⣠⠌⢿⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠙⠳⢦⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠋⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡄⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⢁⡴⠋⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠛⢦⡈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢻⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠶⠦⣤⣤⣤⠶⠛⢡⡿⠁⡇⢰⡏⢿⡌⠛⣶⣦⣤⡴⠶⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠳⣦⣀⡘⠛⣁⣴⠏⠀⢰⡇⠘⣇⠈⠻⣄⡛⠛⣀⣴⠞⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠙⠋⠉⠀⠀⠀⣸⠃⠀⢿⡀⠀⠈⠙⠛⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠘⣧⡀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣤⡤⠞⠁⠀⠀⠀⠀⠈⠛⠶⣤⡴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠛⡏⠉⠉⠉⠉⡟⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡄⠀⠀⠀⢹⠀⠀⠀⢠⠃⠀⠀⢀⣼⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣶⣤⣼⣧⣤⣤⣾⣶⣶⣶⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀
⢀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⡄
⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢤⣄⣳⣾⣭⣻⣯⣿⣭⣭⣭⣉⣉⡉⠛⠲⣄
⠀⢙⣲⣾⣿⣿⣿⡿⠿⢻⡏⠹⣿⣿⡍⢻⠳⢦⣀
⠀⢷⣿⣿⣿⣿⣿⣷⣤⣈⢧⠀⠛⠋⢀⠟⣀⣤⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠶⠶⣤⣀
⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣦⣤⣄⣀⣀⣀⣀⣤⣴⣾⡿⣿⣝⡛⠶⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠙⣯⠻⡟⠻⣟⢿⣌⠛⢦⡈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣄⣦⣠⣠⣀⣈⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣷⣦⣌⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⣼⣟⣾⠟⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⣤⣤⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⠿⠗⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢀⠴⡿⢃⡞⠙⢧⡈⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠞⠁⣞⣠⠞⠁⢸⡷⠋⠀⠀⠀⠉⠀⠀⣷⠋⢳⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠋⠹⠋⠀⠀⠘⢇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⠉⠳⣄⠀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⠀⠀⠀⢀⣠⠶⠒⠒⠒⠒⠲⢦⣀⠀⠀⣧⠀⠀⠀⠀⣀⡤⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⡷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠀⢰⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣘⣷⣤⠔⠊⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣆⠀⠈⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⡘⢦⣀⡏⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠶⣄⣼⡇⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⠓⠀⠠⡙⠦⣽⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣀⠀⠀⠀⢧⡀⠀⠀⠀⢸⡟⣣⠀⢀⡮⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠲⢌⣙⣻⠀⠀⠀⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣷⣦⣄⡉⠀⠀⠀⢸⣟⡥⠀⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠠⢍⣒⣚⢻⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣦⠀⠀⢸⣯⠞⢀⣠⠾⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠒⠦⣽⠋⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⢸⡏⠀⠉⠁⢠⠞
⠀⠀⠀⠀⠀⠀⢠⣴⠞⠂⠀⠀⠀⢰⠃⠀⠘⠛⠛⠉⠉⠉⠉⠉⠻⣅⣀⣀⠀⠀⠀⠀⢠⡶⠶⠶⣶⣚⣿⡟⠛⠛⡶⠂⠀⣼⠁⢀⡞⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣷⠀⠀⡏⠀⠀⢺⡛⠛⢻⣏⣫⣿⠛⠛⣻⠋⠉⠀⠀⠀⠀⠸⣷⡀⠀⠈⠉⠉⠀⢀⣼⠇⠀⠀⡿⢀⡞⠋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣼⠋⣀⠸⡄⠀⣿⠀⠀⠀⠳⣄⣀⠈⠉⢁⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢿⣍⠲⠶⣤⣴⠾⢛⠟⠀⠀⢸⠇⣼⠀⡤⡖⠘⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⢳⠀⠸⡀⠀⠀⠀⠘⠛⠿⠿⠟⢫⠟⠀⢀⣠⣤⠤⠤⣤⡀⠈⠣⠑⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠓⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⢸⣒⡶⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢰⡏⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡇⠀⡇⠀⠀⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣯⢳⣄⡸⣇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⡤⠾⠋⠀⠀⠀⠀⠀⣠⠟⠉⠀⢰⣇⣼⣳⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡁⠈⠑⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠛⠁⠀⠀⠀⠀⠉⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⣋⣥⣾⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⣋⣉⣩⣤⣴⣶⡿⠛⣿⠃⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠟⠉⠀⣉⣤⠞⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡀⠀⡀⠀⠀⠉⠛⣛⣛⣩⡴⢆⣴⣦⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣄⣀⠀⠀⠀⠀⣁⣴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉
⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠋⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠿⠶⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠐⠀⢄
⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡀⠘⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠘⡠⠂⢉⠂⠤⣤⣀⡀⣀⢀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢁⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠿⠃⢸⡿⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⡤⠄⣤⡤⣤⠀⡤⢄⣀⣀⣀⣀⣀⢡
⠀⡔⠋⠀⠘⠷⡄⠀⠀⢤⣄⡀⠀⠄⠼⢑⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣆⠀⠀⢀⠀⣠⡆⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⠛⢁⠀⠐⠼⠿⠷⠋⣸⠋⢸
⠀⠡⣠⠀⠀⠀⠀⠀⠀⠒⠉⠅⢀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠰⣾⣿⠇⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠠⠀⠀⢀⠴⠃⠀⢸
⠀⠀⠀⢄⠀⠀⠐⠂⢀⠆⠀⢀⠞⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠙⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⠠⠤⠖⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠑⢤⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠛⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠉⠑⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡴⠖⠚⠛⠛⠿⣿⣿⣽⢞⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⢀
⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠐⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠉⠀⠀⠐⠲⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⡀
⠀⠀⣾⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠄⠀⠀⣠⣶⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⡀
⠀⠀⠃⠀⣿⠁⠀⠀⠐⠒⠒⠐⡂⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠹⠛⠤⠈⠛⠋⠀⠀⢠⠥⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠂⡆⠀⠀⠀⠀⠐⠀⣠
⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣾⣿⡇⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠒⠀⠀⠀⠈⡹
⠀⠀⠠⠀⠈⠯⠈⠉⠉⢉⡉⠟⠁⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠂⠀⠀⠀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠡⢄⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⢀⣀⠀⠔⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠤⠐⠊
⠀⠀⠀⠀⠀⠉⠁⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠙⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⡀⠀⡠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⢁⠀⠨⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⢁⠘⠳⢆⠈⠀⠀⢀⡅
⠀⠐⠀⣀⣀⣀⣴⣂⣀⣀⣀⣀⣠⣤⡀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⡁⣾⣽⠆⢰⣿⣵⠇⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢠⠁⠀⣶⣻
⠀⡇⠀⠀⠀⠀⠀⣶⢤⠄⠀⠀⢲⣶⠂⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠈⠁⠀⠉⠉⠁⠀⠀⡍⡨⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠟⠀⠣⢄⠨⠋⠀⠀⠀⡄⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢀⣀⡀⠤⠀⠀⢠
⠀⠀⠀⠤⠬⠦⡀⠀⠑⠀⠀⠀⢀⠤⠫⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠁⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠐⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠁
⣿⣿⣿⣿⣿⣿⣿⣂⣐⣒⣒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣂⣀⣒⣒⣒⣶⣶⣶⣶⣶
⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠚⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢸⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⡄⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⠋⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⣿⣄⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠿⠿⢿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣶⣤⣙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣤⣤⣤⣉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠙⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣄⣀⣀⣀⣤⣤⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣷⣄⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠛⠓⠲⠦⣤⣀⠀⠙⣿⡇⠀⠀⠀⠀⠀⣠⣤⠶⠶⠚⠛⠛⠲⠶⣤⣄⠈⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡈⠃⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣞⠁⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠁⠀⠀⠀⠠⠄⠀⠠⠤⠤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⠛⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀⠀⠀⣸⡟⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠖⠀⠰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⢀⣤⣶⣾⣿⡿⠿⠷⣦⣄⠀⠀⠀⠀⠉⠛⠶⣤⣀⣀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⡀⠀⣀⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠈⠛⠉⠀⠻⣷⡀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠉⣻⡷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢠⡟⠀⠀⠈⠉⠙⠛⠻⠿⣶⠴⠶⢤⣴⠶⠶⠶⠿⠿⣿⠟⠛⠛⠉⠉⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣼⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⡀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣠⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠷⠶⠶⠶⠶⠶⠿⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⣦⡈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠥⠘⠟⠛⠝⠻⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣶⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⢦⣄⠀⠀⠀⠀⢠⡾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣌⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣶⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠣⠌⠗⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠻⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠋⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣍⠁⠀⠀⠀⠀⠈⠉⠁⢀⣤⣶⣴⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣅⣹⣬⣟⣁⠀⠀⠀⠀⠀⠀⢀⣚⣉⣿⣿⣯⣽⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⣰⣶⣯⣯⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠋⠉⢙⡋⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⢈⠨

⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⢀⡾⠛⠛⠛⠻⠿⢿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠿⠿⠛⠛⠻⢷⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣾⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣠⣶⣻⣯⣿⣿⣿⣿⣽⣗⡦⡀
⠀⠀⠀⠀⠦⣴⣿⣿⣿⣿⡿⢻⣿⠿⡿⣿⡟⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠚⠿⢿⣷⣶⣤⣬⣿⣿⣾⣿⡥⠤⠆⠽⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠘⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⠿⠿⠿⣿⢿⠿⣿⠿⠟⠃

⠀⠀⠀⠠⠾⠇⠀⠀⠠⢦⡀⠀⠀⠀⠀⠀⣰⠶⠀⠀⠀⠚⠦⠀⠀⠀⠀⠀⣀⣠⣴⢆⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠀⠀⠀⠀⠉⠉⠀⢀⠈⠆⢀⠀⠉⠁
⠀⢀⠀⠀⠀⠚⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢁⣌⠉⠀⠀⠄
⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈
⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠶⣆
⠀⠀⠀⠒⠒⢦⠀⠰⠦⡄⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⣀⣄⣀⡄⣀⣄⡠
⠀⠀⠀⠀⠀⠀⠆⣀⠀⠀⡀⠀⠀⠀⠀⡈⠉⠛⠛⡾⠚⠛⠉⢀⠄⠀⠀⠀⠀⠀⢀⣹⣷⡅⡀⣹⣿⡆
⢀⡀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠹⡀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠄⠀⠀⢉⠀⠀⠈⠉⠀⠉⠀⠀⠈⢀
⠀⠣⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⡀⠀⠄⠈⠀⠀⠀⠀⠠⡄⣀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⢠⠁⠐⠀⠐⠀⢡⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠨
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠅⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⠞⠛⠀⠀⠀⢠⣤⡄
⠀⢀⠉⠛⠛⠺⠗⠻⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠒⠀⡆⠐⠒⠀⠀⠂
⠀⠀⠁⠀⠂⠁⠀⠁⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠉⠠⠌⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡠⠤
⠀⠀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⠀⠀⠘⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⣼⡀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠓⠀⠀⠈⠙⠓⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣶⣤⣤⣤⣤⣿⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⠿⠿⢿⣿⠿⠛⠛⠛⠻⢿⣿⠛⠛⢷⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠉⠁⠀⠀⠀⢰⣿⣡⡤⠤⣤⣤⣤⣀⣹⣧⠀⠀⠉⠻⠶⣧⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⡄
⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⣷⠟⠀⢹⡿⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⢀⣀⡼⠃
⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣀⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣆⡀⠀⠘⣯
⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠦⣬⠿⠆
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⡀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠿⢿⣿⣦
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⡆
⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣾⡿⠁
⠀⠈⠻⢿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣹⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠠⠞⠛⠋⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢿⣿⠏⠀⠀⠀⠀⢠⡿⣇⠀⠀⣠⢿⡛⢧⡀⠀⣼⢿⡇⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠋⠉⠀⣾⡟⠀⠀⠀⠀⠀⣼⠃⠹⣦⡼⠁⢸⠃⠈⣷⡾⠃⢸⣧⠀⠀⠀⠀⢀⡄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⢰⣿⠁⠀⠀⠀⠀⢀⡿⠀⠀⠘⢧⣀⣿⣠⠾⠋⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣾⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡆⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣧⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⣿⡿⠋⣽⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠙⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⡄⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠃⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⢀⣀⣀⣾⣇⣀⣠⣤⣤⣤⣾⣿⣾⡿⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠛⠛⠛⠋⠉⠉⠉⠹⣧⣤⣴⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣶⢦⣤⣤⣄⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⡀⠀⢰⠄⠀⠀⢉⡉⠛⣦⡀⠀⠀⠀⠀⠀⠀⣠⡟⢉⡀⠀⠀⠀⡇⠀⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠶⠾⠿⠛⣿⣤⣼⡇⠀⠀⠀⠀⠀⢰⣯⣀⣸⡟⠻⠶⠶⢷⡶⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⣠⠴⠶⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣢⣶⣾⣛⣿⣿⣿⣿⣿⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⠿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⡀⣶⣼⣄⣤⣦⣤⣰⣩⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠘⠛⠿⢿⣿⣏⠁⢿⡙⠿⠾⢋⡟⠀⠉⠳⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣤⣴⣶⣿⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠺⠿⠛⢾⣿⠶⢶⠿⠖⠶⣶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣯⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠹⡈⠛⠙⢌⠙⠊



⢀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣀⡇⡿⢼⠀⠀⠀⠀⣰⢺⠘⡴⢡⡏⠀⠀⠀⢸⣇⢿⡾⢾⠽⡇
⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⠛⠀⠚⠀⠀⠀⠐⠛⠘⠚⠙⠊⠁⠀⠀⠀⠚⠁⠘⠀⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠔⠒⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠄⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⡏⠀⢀⣴⣶⣄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⣿⣇⡇⠀⠀⠀⠀⠐⠒⠋⠉⠙⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠻⠿⢫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢿⣿⣦⣤⣉⣉⠉⠛⠓⠒⠒⠒⢛⣋⣉⣩⣥⣼⣿⠏⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠈⠙⠻⠿⢿⣿⣿⠿⠿⠛⠉⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠁