Squid ascii Emojis & Symbols

⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⣠⠎⠉⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢆⠀⠶⠚⠉⠉⠉⠳⢆
⠀⠀⠼⠀⠀⠀⢀⣀⣠⡶⠷⠤⠤⢀⢀⣀⠀⠀⠀⠀⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢲⣄⡀⠀⣾⡛⡟⠀⠀⣀⠀⠀⢻⡀⠀⢘⠉⠻⡛⢷⣾⠿⠇⠀⠸⠿⢷⡄⠀⠀⢧
⠀⠀⠀⠉⠻⢦⠀⠉⠻⣄⢸⣏⣷⠀⠈⡇⠀⢹⡄⠀⢙⠃⠀⢳⡆⠀⠀⠀⠀⢹⠀⠀⠘
⠀⠀⠀⣀⠶⠴⠀⠀⠀⠈⡟⢧⡀⠁⣴⠃⢀⣀⡄⠀⠰⠀⠀⠈⡇⠀⠀⠀⠀⠘
⠀⣼⠁⠀⠀⠀⠀⠀⠀⣠⡇⠀⣡⠀⠉⣇⠀⠉⠀⠀⢀⠀⠀⠀⡇⠀⢂⣀⡀⠚⠀⠀⢠⡀
⠀⣧⠀⠀⠀⠀⠀⣀⣴⠞⠻⠿⣿⠀⠀⢸⣦⣀⣤⣦⣾⡄⠀⣠⣧⡀⠀⠀⠀⠀⣀⣠⡟⠁
⠀⠙⠿⠿⠿⠿⠿⠏⠁⢀⣶⠟⢹⣀⣴⡟⠉⠉⠉⠀⠈⠿⠿⠟⢻⣿⣿⠿⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢠⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡄⠀⠀⠀⠀⡀
⡀⠀⠀⠂⠀⠀⠀⣴⣿⠾⠋⢡⡿⠀⠀⠀⠈⡟⠲⢤⣄⠀⠀⠀⢠⢸⣿⣷
⠁⠀⡀⠀⠀⠀⢰⡏⠷⠶⠶⠟⠀⠀⠀⠀⠀⢧⠀⠀⠉⢻⣶⡄⢠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⢰⣷⠀⠀⠈⠻⠶⠿⠛⢁⢄⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠄
⠈⠈⠀⠀⡀⠀⢸⣿⡄⢀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⢦⣬⣽⣿⡟⠃
⠀⠀⠀⠀⠀⡀⠀⠹⣿⣿⣦⣆⡀⣿⣷⠀⡀⠀⠀⠀⣼⣷⣾⣿⣿⠏
⠀⠃⢀⠀⠠⠐⠠⠄⠈⠻⠿⣿⣷⣮⣉⣾⣧⣿⣷⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡄⠀⠀⠀⠀⢈
⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⢀⣸⣿⣿⣿⠉⣻⣯⣽⡿⢿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣔⡠⠀⠂
⢀⣼⡾⣦⡄⠠⣀⠀⠘⠀⠀⠀⣿⢹⡏⣿⠀⣹⡇⢸⡇⢸⠃⠀⠀⠀⠀⡀⢠⣿⢿⣿⣷⡄
⢹⢿⠃⠀⠹⣦⠀⠀⠀⠀⢀⣼⠃⣿⢸⣿⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠠⠁⣸⠃⠀⢸⣿⣿⠰
⢻⣿⣆⠀⠀⠘⣧⣤⣤⣴⠟⠁⣠⡗⢸⡇⠀⣼⡇⠀⣷⠘⣷⡀⠀⠀⢀⣴⠇⠀⠀⢨⣿⣿⢀
⠀⢿⣾⣷⣤⠀⠀⠈⠉⠀⢠⣰⠟⢀⣿⠇⠀⣿⣇⠀⢻⣧⡈⠳⠾⠷⠟⠁⠀⠀⠀⣿⣾⠇⠚
⠀⢡⣿⣿⣿⣿⣾⣶⣦⣷⡾⠉⢀⣾⡿⠀⠘⣿⣷⠀⠈⢿⣿⣦⣤⣤⡀⣤⣠⣴⣿⣿⠇⡈⠰
⢰⣿⣿⡁⠈⠀⠉⠉⠉⠁⢀⣴⣿⣿⠇⠀⣾⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⡁⠀⢀
⠈⢻⣯⣷⣮⣁⣤⣤⣄⣤⣿⣿⡿⠃⠀⠀⣿⠇⢿⣿⣧⣄⠀⠀⠈⠛⢿⣶⣦⠄⠠⠉⠀⠈
⠀⠀⠉⠿⠿⠿⠿⠿⢿⣯⣿⠏⠀⠀⠀⠈⣿⠂⠀⠙⢿⣿⣿⣦⣶⣤⣾⣟⣿⡇⠀⠀⠠
⠀⠂⠐⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⣄⣸⡿⠂⠀⠀⠀⠈⠉⠛⢻⣿⣿⠿⠛⢁⠀⠑⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣷⣤⣶⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨
⠁⠀⠀⠏⠀⠀⠀⠈⠀⠙⠿⠿⠿⠿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠃⢠⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢿⣝⣶⢯⡙⠛⠉⠉⠽⠛⡆
⠀⠀⠘⡎⠻⣧⠉⠓⢦⣤⡀⣼⠁
⠀⠀⠀⢱⠀⠈⢧⡀⢤⡉⠋⠙⠲⢤⣀
⠀⠀⠀⠸⡇⠀⠀⢻⡜⠍⠀⠀⣀⠀⠈⠓⢦⣄
⠀⠀⠀⠀⡧⣠⠞⠁⠙⢆⠀⠀⠈⠙⠂⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠙⢢⡀⣸⢢⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⠀⠖⣨⡴⠊⢄⠉⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠾⡝⢒⡲⡄⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢮⡉⠐⠀⢀⡀⠀⠲⢄⣀⠐⠲⢴⡦⣴⣬⣅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣀⠀⠑⣄⠢⠠⠀⠠⢄⠐⠈⠪⡲⣳⣔⣍⡂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⡶⡀⢈⠻⣿⣆⠈⠲⣥⡀⢅⡈⠫⢌⡙⠻⢧⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠛⣽⠦⣄⡀⠈⡓⢄⡘⢪⠑⢿⡯⣦⢄⠑⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⠳⣍⠹⡷⢄⠀⠱⣄⠑⣤⣙⡀⠘⠓⠀⠙⠒⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣌⡖⣳⡌⢷⣀⠐⡌⠉⠐⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⣥⢷⡀⠳⣕⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠻⢿⡟⠠⢙⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠃⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠉⠉⠈⣙⡢⠀⠀⠀⡞⠁⠈⢳⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠃⠀⠀⡟⠀⠀⠀⣀⠀⠒⠂⠀⠠⡀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⢠⠀⠁⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢁⠀⠀⠀⠀⠋⠇⢀⣠⠔⠁
⠀⠀⠀⠀⢦⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⡄⠐⠒⠚⠁⢀⡔⠀⠀⢀⠿⠋
⠀⠀⠀⠀⠀⠑⠦⣀⠀⡐⣧⡌⠑⠂⠦⠆⠞⠛⣲⠤⠤⠐⠁⢀⡤⠐⠉
⠀⠀⠀⠀⡀⠤⠀⠀⢙⡟⠐⠚⠓⠂⢄⣀⣀⣀⡄⠀⢀⣴⣞⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠩⠉⠛⠀⢰⡿⠋
⠀⠀⠀⠐⢀⠀⠀⠀⠀⠊⠉⠠⠰⠶⠉⠑⢰⡇⠀⢾⣥⠔
⠀⠀⠀⠀⠀⠀⢰⠖⠀⠁⠁⠀⢀⡐⠈⠉⡝⢱⣄⠙⠥⢀⢀⡀⣀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢨⠝⠁⠀⠀⠀⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠣⡀⠀⠀⠀⠀⠎⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠑⠄⠈⠁

⠀⠀⠀⠀⢏⠓⠦⢤⣤⠤⠤⠤⠤⢤⢤⡀
⠀⠀⠀⠀⠈⣷⣦⡀⠈⠉⠂⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢸⣿⣿⡢⣄⠀⠀⠀⠐⠤⣄⣧
⠀⠀⠀⠀⠀⠘⣿⣿⠙⢮⡳⣄⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠙⣮⡳⢤⡀⠀⠀⠀⠈⠙⣦⣄
⠀⠀⠀⠀⠀⠀⠘⠦⣝⣒⣄⣈⣿⣦⡛⢦⡀⠀⠀⠀⠈⠙⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠢⣝⢶⣄⠀⠀⠀⠚⠉⠙⢲⡀⠀⢀⡠⠔⣊⠭⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣿⠗⣿⣄⠀⠀⠀⣓⠚⠻⠶⢮⡥⠤⠴⠮⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠥⣼⠷⡍⡛⠯⢿⡷⢾⣟⠉⢉⡷⣮⡳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢿⣿⣿⡲⢬⡪⣿⣲⠟⠉⠙⠎⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢧⡻⣦⢻⣳⣭⡚⢿⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠟⢨⡇⡟⡇⣏⡇⢹⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢸⠰⡁⣇⠻⣄⡀⡇⣷⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣿⣝⢏⡀⠹⠤⠖⠛⠛⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠁⠉⠒⠚⠿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠈⠀⠛⠉⠛⠙⠋⠉⠀⠈⠓⣄⠀⠀⠀⠀⠀⣠⣾⣿⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠟⣛⣭⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⣾⠿⠛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣾⠟⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⣼⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⠿⣶⣦⣤⣤⣠⣤⣴⠾⠋⠀⣠⡿⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿
⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣰⣿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⢿⣿⣿⠏
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠁
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣄⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⣘⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣠⡤⠶⠶⠒⠶⠤⢤⣀⡀
⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠙⠻⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡀
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣦⣴⣿⢳⣶⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣉⣽⡿⣿⡿⠱⠛⠛⠛⣽⣿⢟⣯⠿⠛⠛⣽⣿⣿⣿⣿⢋⣴⠄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿
⠀⠀⠀⠀⢀⣼⠋⠁⢰⡿⢁⣠⡴⢶⣾⡟⠃⠈⠀⠀⢀⣿⣻⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣸⠃⠀⢠⢿⡵⠋⠁⢀⣾⠿⠀⠀⠀⠀⠀⣼⢳⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣿⠀⣰⠋⡞⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠘⣧⣿⣿⣿⣿⠪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠠⢄⠊⠁⠠⠀⠀⢀⣾⠋⠀⠀⠀⢀⣰⣶⣿⠟⠡⣿⣿⡿⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⣤⣼⠿⠛⢹⡏⠀⠐⠿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⠿⠋⠀⠀⣠⠏⢀⣄⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⣰⠟⠁⢀⡀⠴⠊⣡⡶⠟⠉⣹⡏⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⣰⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⢎⠀⢠⡤⠴⠞⠉⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣹⣾⣮⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⣿⣿⣿⣿⣷⣻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⡞⣾⣿⣿⣿⣿⣷⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⣸⣿⣿⣿⣿⣿⣿⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣾⣿⣿⣿⣿⣾⣯⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢨⣟⡿⠿⠿⣟⢱⡤⠤⣤⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣴⣿⣿⣿⣿⢸⣿⢧⡙⠷⣦⣽⣆⣀⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠋⣼⣿⣿⣿⢸⡟⠀⢹⣷⣦⣄⡙⠻⠷⣶⣶⣿⠿⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠿⡇⠀⣼⣿⣽⣿⡿⣸⣧⠀⠀⢻⣷⡈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⣼⡏⠀⠇⢰⣿⢹⡿⣿⣇⣿⣿⡇⠀⠘⣿⣧⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢻⡄⠀⠀⣸⡇⢸⣷⣿⣿⠇⢹⣿⠀⠀⣿⣿⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠈⠃⠀⠀⢹⣧⠈⣿⡿⠃⠀⢸⣿⠀⠀⣿⠇⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⢧⠀⠀⢸⣿⠀⠀⡿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠻⣿⡄⠀⠀⠀⠀⢿⠀⠀⠇⠀⠀⠀⠀⠀⣿⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠙⢿⣄⣀⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣶⣿⣿⣄⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⢰
⠀⠀⠀⠀⢀⣴⣠⡬⠄⠀⠂⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣦⣶⣷⣄⣴⣿⠃⣀⣤⡶⡿⠶⠒⡒⠖⠂⠤
⠀⠀⠀⡔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣄⣿⣯⣭⣿⣿⣽⣦⣤⡄⠀⠀⠈
⠀⠀⠀⠈⠓⠶⡦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡋⠁⠉⢿⣿⣿⣿⢶⣮⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠒⣶⡶⠂⠀⠀⠀⠀⠹⣿⡿⠻⡿⠶⢷⣮⣝⢿⣷⣦⣤⣤⣀⡀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡀⠧⠉⠛⠻⠾⠯⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⠁⠀⠀⠀⠀⢃⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢼⠁⠀⠀⠀⠀⢻⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠠⡷⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠲⠀⠀⠁⠁⠀⠀⠁⠁⠀⠰⠂⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠢⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠄⠐⠄⠀⠀⠀⠀⠠⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠠⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠂⠀⠀⣀⠤⢄⡀⠀⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠂⠤⠔⠊⠁⠀⠀⠈⠒⠤⠄⠚⡁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣾⣼⣿⣝⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢹⣿⣿⣎⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⢋⣾⣿⣿⣿⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⠙⣷⣄⠀⠀⢀⠎⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣡⣦⠄⠀⢸⣿⡆⠀⠌⢀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠙⠻⠀⣴⣿⣿⣽⣿⣷⣟⣀⣾⣿⠇⠀⢀⣾⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⢷⢿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣾⣿⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣯⡻⠿⠿⠟⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⣻⣿⢿⣿⣿⠙⠿⢿⣿⣧⡀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠁⣄⣀⣀⣀⣴⣿⣿⢸⣿⣿⠀⠀⠀⠀⠹⡇⠀⡌
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠈⠿⣿⣆⠀⠀⠀⠀⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⢌⣉⠃⠀⠀⠀⠀⠀⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣫⠿⠓⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠒⠆⣄⡁⣀⡀⠀⡤⠤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠠⠀⠹⣂⠂⠄⠀⠀⣀⡀⠈⠻⣦⣬⣉⠘⢃⢤⣤⣀⣉⠁⡂⠤⠤⠤⠄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠻⡄⠀⢠⡈⠉⢳⢈⡉⠈⠸⢏⣉⡂⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠑⢌⢳⣾⡀⠘⠛⣷⠀⡉⠳⡬⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⡿⡇⠀⡆⢸⠀⠻⠀⠰⣧⣠⡆⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⠇⣻⠀⣧⠋⡆⣴⠀⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠠⡠⠀⠬⢐⡏⢀⠁⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠉⡇⢨⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡑⠀⠀⠀⢠⠀⡏⠀⠀⠈⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡇⠀⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣷⡀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣦⣀⣲
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠖⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣦⠲⠿⣵⡢⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠂⠉⣉⣉⠻⣿⡄⠄⠳⣾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢤⣊⣡⠄⠀⠀⠀⠀⠀⢸⡗⣹⠀⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠒⠒⠈⠉⠀⠀⣀⠀⢀⢀⣀⣤⣾⣯⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢴⣷⣦⣀⣴⣿⣷⡀⣠⠖⣶⣦⣠⠶⣶⣶⣟⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠯⣟⣵⣿⣿⣿⣄⣛⣿⢁⣟⢻⠉⢰⣟⣁⡟⠉⣯⣀⣈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣠⡿⢛⠉⠀⠈⡇⠈⠉⠈⠙⢏⠉⠹⠋⠙⡏⠀⠉⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠌⣾⣯⢠⡟⠀⣯⠄⠀⠈⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⡰⠀⠂⠀⠀⠀⣠⣾⣿⣿⣼⠃⡼⠻⠀⠀⣼⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢂
⠱⠀⠀⠀⠀⣼⣼⣿⣿⡿⠏⣰⠇⠀⠀⡰⠇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢀⠀⠀⠈⠂
⠀⠉⠛⠛⠛⠩⢟⡟⠋⠀⠀⠀⠀⠈⣰⠋⠀⠀⠀⠀⠀⠀⠀⣈⡓⡀⠀⣿⢍⡑⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠃⡸⠃⠠⡄⠀⠀⠀⢰⡿⣻⣴⣄⠠⣀⠀⠈⠀⠉⠻⡇⢀⡿⠀⡀⠴⠀⠀⢸⡿
⠀⠀⠀⠀⢠⣣⡧⠀⠀⢹⠀⠀⡄⣿⣿⡏⠠⠌⣴⢻⣦⠀⠀⠀⢀⣿⠶⡷⠂⢠⣬⡆⠀⢸⠛⠗
⠀⠀⠀⠀⠀⠃⠀⠀⢀⣾⠀⠀⠁⣿⣧⡟⠶⠞⠋⣁⣠⣠⡿⡋⠏⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⠈⣃⢸⣿⣧⣴⣶⣿⣸⣿⡇⠀⠀⠀⠀⢀⡄⢀⡀⢀⠀⠀⠈⠃⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠐⠄⠹⢆⠀⠈⠉⢀⠹⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⣶⣾⣿⣿⡿⣋⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢌⡓⠤⠬⠴⠿⠟⠛⠋⣁⠀⠀⠀⠀⢠⠔⠲⡤⠐⠾⠁⠀⠐⣶⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢶⣤⠀⢤⣤⣰⠟⠉⠀⠀⠀⠀⡀⢀⡀⢀⣤⣀⣴⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠛⠆⠀⢁⣀⣠⠼⠫⠟⠛⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠶⠖⡒⠀⣷⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⢀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⠤⠿⠛⠁
⣿⣟⣻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⢀⣀⣤⢤⠴⠶⢶⠶⠶⢦⣤⣄⣀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⣶⣶⠂⠀⠀⠀⠘⠋⠓⢦⣄⡀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣠⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠙⢷⡄
⠀⠀⠀⠀⢀⣼⠋⠀⢀⣾⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠹⣦
⠀⠀⠀⢀⡾⠁⠀⣰⠋⠀⠀⠀⠀⢀⠄⠊⡀⠀⠐⠒⢀⠀⣾⠐⡿⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⣧
⠀⠀⢀⡾⠁⠀⣴⠋⠀⠀⠀⠀⠀⢀⢀⡌⠃⠀⠀⠰⡈⢸⣿⠀⠀⠐⠀⠀⠀⢀⡠⢆⠀⣀⠀⠀⠀⠈⠹⣆⠀⠘⣧
⠀⠀⣼⠃⠀⢰⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⣦⠀⠀⣤⣾⣿⠀⠀⠠⠐⠄⡀⠈⠀⠀⠀⠁⣀⡤⠒⠀⠀⢿⡄⠀⢹⡆
⠀⢀⡿⠀⠀⣟⠀⡀⠀⠀⣸⠃⠄⠀⠀⠀⢉⠈⢷⣄⠸⣿⣿⠀⠀⠀⠠⠞⠀⢐⣠⣤⡶⠟⠉⠆⠀⠀⠀⠀⣷⠀⠀⣿
⠀⢸⡇⠀⢸⡇⣠⡀⠀⢀⡀⠀⠀⣀⠠⠂⠀⠀⠀⠛⣷⠼⢛⠐⢄⢀⣠⣴⣾⣿⣟⠁⣀⠀⠀⠠⠀⠀⠀⠀⢹⠀⠀⢹⡀
⠀⢸⡇⠀⢸⡗⣭⣿⡇⠀⠓⠦⢤⣤⣤⣤⣤⣤⣴⣾⣏⠰⣿⡷⠆⣿⡿⠛⠛⠛⠛⠛⠛⠓⠒⢀⠀⢸⡿⡿⢺⠀⠀⢸⡇
⠀⢸⡇⠀⠘⣇⠉⠀⠀⠀⡃⠀⠀⠀⣂⣼⣿⠿⠟⠋⠉⠀⠈⣠⡜⢷⣤⡀⠀⠀⠀⠄⠀⠀⠴⠈⠀⠀⠀⠀⣸⠀⠀⣼⠁
⠀⠈⣷⠀⠀⣯⠀⠀⠀⠀⠠⣠⣾⠿⠛⠏⠁⢠⠔⠀⠀⠀⠀⣿⣿⠂⠙⢧⠀⢀⠀⠀⠀⢀⠉⠃⠀⠀⠀⠀⡏⠀⠀⣿
⠀⠀⢻⡄⠀⠘⡖⠀⠀⠴⠚⠋⠀⠄⠀⠀⠀⠀⡘⠀⠘⠆⠀⣿⡏⠤⠒⠀⡁⠈⠀⠐⠆⠀⠆⠀⠀⠀⠀⣾⠁⠀⢸⠇
⠀⠀⠈⢷⡀⠀⠹⣤⠀⠀⠀⠀⠰⠀⠀⢤⡀⠀⢠⠀⣀⠀⠀⣿⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢠⡟
⠀⠀⠀⠈⢷⡀⠀⠙⣦⠀⠀⠀⠀⠈⠀⢴⠀⠐⠀⠀⢄⠀⠀⡏⠈⠉⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⡟
⠀⠀⠀⠀⠈⢻⣄⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠄⣴⠟
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠏⠁⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠂⠀⠉⠓⠦⣤⣀⠀⢀⠀⠀⢛⠃⠀⢀⠀⢀⣰⡤⠴⠛⠁⠀⢀⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠈⠉⠙⠓⠒⠚⠓⠒⠛⠉⠉⠁⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡤⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠑⠘⠀⠀⠀⠀⢀⣏⣱⣀⡤⠶⠂⠑⠂⠄⠀⢈⠠⠻⣶⠟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠑⣀⢀⠒⡯⡭⣼⠏⠀⠀⠀⠀⠀⠀⠰⣤⠴⢾⡇⣞⢉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡇⠀⠀⠉⠂⠡⣸⣀⡏⠀⠀⠀⠀⠀⡀⠀⢀⡇⠀⢸⣇⠙⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣉⣂⣄⠄⠀⠀⣀⠔⡲⠢⠄⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣠⢷⡀⡀⡏⠳⠚⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢉⠟⠀⠄⠀⠀⠁⠀⣇⠀⠀⡒⠛⠀⠀⠀⠀⠀⢀⣠⣾⡟⢀⠟⠁⠀⡀⠀⡿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⠏⠀⣾⡧⠀⢸⡆⠀⠈⣑⣭⡁⠀⠀⠀⢀⡄⡀⢹⣿⡿⠁⠀⠀⢠⠜⠀⠀⢳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⡤⣠⡀⠰⠙⣿⣿⣿⠟⠀⠀⠀⠀⢈⣴⣷⠿⠛⠀⠀⠀⠀⠀⢱⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧⠃⠠⠂⢼⣷⣿⠏⠀⠀⡀⠀⠀⠸⠟⣻⣤⠛⢀⣔⣀⡢⠄⠀⢸⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠂⠐⠀⠒⠋⠉⠁⠀⣜⡰⠁⠀⠀⠀⠹⣿⠄⣠⡀⠀⠀⠀⠄⠀⠜⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠋⠑⠤⢤⣤⣤⣤⡶⠶⣦⡾⠋⠀⢀⠀⠀⠀⠀⠀⠢⠀⠙⢿⡿⣀⠁⠀⠄⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠄⠱⡬⣷⢀⣿⠶⠊⠁⠀⠀⠀⠼⠀⡀⠀⠀⠀⠀⣀⠀⠀⠑⢆⠀⢀⣄⡴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢡⠊⢀⠼⠉⠀⠀⠀⣀⣠⣴⠶⢤⡀⠄⠀⠀⠀⠀⠱⣤⠐⠄⠀⠙⡌⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠘⡄⠃⠀⣠⡴⠞⠩⡙⠂⠀⠓⢀⡵⣄⠀⠀⠀⠀⠀⠛⢳⡄⡀⠀⠀⠁⠈⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⠀⠐⠾⣃⡀⡀⠀⠀⠈⢹⣀⠈⠀⢸⠓⠀⠀⠀⠀⠁⣀⣇⢘⣦⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠂⠀⡀⠀⡈⠉⠉⠉⠉⠘⠳⣄⠀⠀⢀⠄⢀⠔⠒⡌⠀⠈⡿⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠄⣌⠀⣙⠈⣣⠀⢆⠀⡀⠀⠀⠀⠉⠒⠀⠀⡀⠐⢀⡧⢀⣠⠃⣿⡠⠔⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠑⠤⠞⠉⠁⣀⡠⠀⡀⢠⠀⠄⠈⣿⠁⠄⢸⡇⠀⠇⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢿⡀⠀⢀⠁⠀⢘⠒⢎⠀⠀⡲⠤⠾⣦⠄⠚⠻⣦⣤⠞⠁⠀⠘⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠙⠒⠎⠀⢀⠂⠀⠀⠑⠛⣆⠐⢀⣽⣀⣉⡰⠃⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠺⠆⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠐⠀⠀⠀⡠⠖⠋⠉⣉⠉⠉⠙⠦⣄⠀⠀⠀⠀⠐⠀⠀⠁⡄⠴⠀⠀⠀⠉
⠀⠐⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠁⠀⠈⠀⠀⠈⣧⠠⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠐⠁
⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⡇⠀⠐⠀⠀⠑⠀⠄⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢻⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡏⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣥⡁⢂⡀⣠⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⢈⠀⢻⠂⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡇⢐⣞⡠⠎⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠙⠚⠚⠃⠉⠀⡀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⡅⢠⠔⠂⠀⠀⠀⠀⠀⠁⠁⠀⠠⡄
⠀⠀⠀⢀⠀⠴⠞⣀⠄⠀⠉⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⠀⠐⠂⠙⡌⠁⠀⠐⠂⠘⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢠⢀
⠀⠀⠀⠀⠀⢠⣀⣠⣥⡤⠆⢠⡄⠤⠀⠀⠀⠙⠂⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢱⢀⢘⡉⢃⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⡀
⠀⠀⠀⠀⡷⢤⠓⠞⠀⡀⡸⣠⡤⢤⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠠⠈⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠉⠀⠀⠘⠰⣿⠟⠁⡿⠁⣩⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠂⣀⠈⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢀⢄⠀⠀⠀⠀⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢁⡄⢈⠈⠀⠰⣀⠶⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⡦⢤⣟⢃⡉⣶⣦⠐⣣⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣘⠀⢿⠌⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠚⠃⠀⢠⡄⠀⠘⠀⠀⠔⠀⠀⠀⠴⠤⠟⠏⠉⠁⠂⠀⠀⠀⠀⡀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠁⠀⢐⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣈⠀⡀⠂⡞⠀⠓⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠈⠁⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠺⣤⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠑⠀⠘⠀⠀⠀⠀⠀⠉⢿⠱⣆⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠃⠀⠀⠀⠐⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈
⠀⠀⠀⠀⠀⠐⠀⣤⣠⠄⠀⠀⠀⠀⠀⠹⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠁⠀⠀⠉⢣⡏⠀⠀⡀⠀⠀⠀⢤⢿⡃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠀⢙⠀⠀⠀⠁⠀⣀⡥⠤⠀⠀⡀⠀⠀⠀⠂⠌⡤⠠⠄⢀⡀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠃⠀⠂⠈⠈⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣏⣹⣉⣿⣭⣭⣽⣯⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣽⣯⣭⣽⣿⣯⣽⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣴⣾⠿⠛⠉⠉⣿⡏⠉⠙⠛⠿⣶⣄⡀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠋⠀⣀⠤⠒⢺⣿⢟⠒⠆⢤⡀⠈⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⡰⢎⣀⡴⠚⢻⣿⠸⠛⠲⢦⣈⡷⡄⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⡜⢀⡼⠻⣶⣄⣿⣿⠀⡇⣠⣴⠟⣦⠘⢆⠀⠹⣷⡀
⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠀⣾⡇⠀⢸⢀⣾⣀⠀⠹⠿⣿⣿⣤⣿⣿⣧⣤⣸⣧⣘⡄⠀⣿⡇⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠸⣷⢿⣾⠁⠀⠒⠶⣿⡿⠿⣿⣶⣶⣶⣶⣶⣶⣾⡀⢀⣿⠛⠛⠛⠛⣛⣛⡿⠿⣿⡿⠒⠒⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⠀⢻⡉⢉⣽⣿⡏⢹⣿⣿⣿⣍⠉⢠⠏⢰⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠳⡈⢳⣾⠛⠁⠄⢸⣿⡇⠙⢻⣷⡏⢠⠆⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠙⠯⣈⠛⠶⢴⢸⣿⢧⠖⠋⣀⠝⠁⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⣷⣄⡀⠈⠑⠒⠼⣼⣿⠴⠒⠈⠀⢀⣴⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠈⠙⠿⣶⣦⣤⣄⣿⣧⣤⣤⣴⡾⠟⠋⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠯⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣤⡀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠹⢿⣿⣿⡄⠀⢠⣾⠋⠀⠀⠀⠀⠀⣠⣄⣴⣾⣿⣿⣿⣗⠄⣤⡀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣄⠀⢿⣿⡇⢰⣿⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣿⣿⠁⣿⣿⠀⠀⠀⠀⢀⣴⠞⠁⠁⠙⢿⣿⣿⣿⣿⠁⠀⢰⣶⡆⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣧⣀⣀⣴⣿⡇⠀⠐⠀⠀⠀⢹⣿⣿⣿⣿⣧⡿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣿⠆⠀⡀⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣙⣿⣶⣶⣶⠿⣹⣿⣿⣿⣾⣷⣤⣿⣿⣿⣿⣿⣿⡿⢶⣤⣤⣀⣀⣀⣤⣾⠿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⣿⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⣿⣿⣿⠿⣿⣧⣌⣳⡀⠀⠀⠁⣠⣿⠿⠛⠛⠻⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⠟⢩⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣏⣡⣾⣿⣿⣿⣍⣳⣤⣀⢰⡿⠁⠀⠀⠀⠀⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠸⠁⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⠋⣹⣿⣿⣿⣭⡍⠻⣿⣿⣿⡶⣦⠰⠆⠸⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣆⠀⣼⣿⣿⣿⡇⠀⠀⠀⠂⠀⣸⡿⣠⣿⠃⠈⠻⣿⣿⣦⠀⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣿⣿⣿⣿⠀⠀⠀⠀⡆⠀⠟⣰⣿⠏⠀⠀⠀⠈⢻⣿⣧⠀⠀⠈⠳⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠠⡀⠙⢿⣿⣿⣟⣿⡀⠀⠀⠀⢿⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠋⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⣾⣿⣷⣀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣤⣈⣿⡿⣿⣿⡇⠀⢸⣿⣿⠉⠛⠷⣶⣶⣾⡿⠿⠛⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⡄⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⡀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠙⢷⣿⣿⡦⡶⣤⣴⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⣄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠉⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡶⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠆⠄⠤⠄⠘⠛⢃⣨⠐⢧⣤⠢⣠⣤⢰⡤⣠⣶⠀⣤⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡄⠀⠀⣄⣠⡄⣦⡀⠀⢈⣉⠁⠰⢦⣵⣌⣉⡈⠑⠛⠙⠛⠿⠶⣴⣦⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⢚⡯⣽⠻⣇⠀⠒⠛⠛⣀⣘⣛⠯⣍⣘⢿⣿⣒⠒⢠⡄⠀⠻⡛⢃⡶⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢁⡀⣶⢆⠙⣯⡤⣤⣀⢹⣄⢴⡞⠻⠍⠛⠉⢙⣲⣍⡓⠦⣍⡉⣉⡙⠻⢷⣿⣸⠀⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢖⣸⠂⠙⣋⣾⠈⢹⣠⣌⣬⣿⡏⠀⠉⠉⠓⠒⠦⣤⡙⠻⢿⣿⣶⣤⡈⠙⠳⢦⣬⡛⠷⣦⠈⠢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢐⣴⠿⠓⣦⣍⢿⣷⣋⣥⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡿⠎⠛⠻⣜⠻⢶⣮⣝⠲⣬⣧⡀⢱⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡾⣟⠠⠄⢀⠟⢳⣌⠽⣟⣀⡀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠶⣄⠀⢬⣓⣄⡈⠛⠳⣜⡙⢧⢰⡃⠈
⠀⠀⠀⠀⠀⠀⠐⠀⢾⢠⠀⠄⣰⠛⡿⢿⡉⠙⣿⠆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠈⠛⢦⣈⠻⣿⡲⢤⡀⢳⣴⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⣛⠰⡟⠀⠀⣿⣿⣶⣶⠀⠀⠲⣀⣶⣶⣶⣦⡀⠀⢀⣾⠋⠀⠀⠀⠀⡉⠓⢤⡁⠈⠳⣆⢉⡓⡔⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠹⣷⠂⠠⠞⠛⣿⠚⢠⢰⡿⢻⣿⣿⣏⢳⡄⠘⣿⠀⠀⠀⠀⡞⠁⠀⢀⠙⢦⡀⠙⣦⠀⠙⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠙⢉⠑⠂⠀⠛⣀⠀⠀⠛⠶⣿⣿⣿⣿⠃⢀⡿⠀⠀⠀⠀⠁⠀⠀⣤⠀⠈⢻⡄⠈⢧⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠐⠦⠀⣀⣀⣡⠎⠈⣱⢞⡥⠀⠙⠃⠀⠄⠀⠀⠙⠛⠋⠁⠠⣾⡇⠀⠀⠈⢉⡀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⠰⠎
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣙⣡⣦⣤⣀⡌⠁⠘⠁⢰⠞⠀⠀⠀⠀⠡⢰⠀⡀⠙⠛⠶⠀⠀⠻⠶⠂⠀⣀⡀⠀⠀⠀⠹⣦⠈⠷⠂
⠀⠀⠀⠀⠀⠘⠓⠀⠘⠃⣿⣿⡿⠿⣿⣿⡿⢁⣴⣋⠀⣶⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠖⠉⢀⠀⠀⠀⠀⠠⣿⣶⡜
⠀⠀⠀⠀⠀⠀⣆⣠⠄⠈⠡⣤⣶⡶⠳⠦⠟⠛⣭⢿⣶⡃⢠⢠⡄⡀⠀⢀⣼⠀⡀⠲⣿⣿⡿⢻⡿⣧⣀⡀⠠⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠹⠅⠀⠀⠐⠈⠷⠂⠠⠈⠟⠂⠘⡛⠉⢛⣦⡀⠀⠙⠰⣽⣿⡄⡇⠀⣌⠁⢠⣿⣷⣿⡿⠃⠀⡤⠀⣴⠃
⠀⠀⠀⠀⠀⠀⡀⠀⣤⠄⠂⣶⠀⠰⢶⣺⠖⢛⣽⠀⢀⣰⣿⣟⣿⣦⣴⣿⣿⣧⠀⠀⠀⢀⣿⣿⠏⢡⡀⢠⣾⣡⣴⡁⠂
⠀⠀⠀⠀⠀⠀⠇⢾⠀⠀⠀⢠⢿⡟⠩⣅⠀⣤⣥⠀⠙⠉⢠⡝⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣄⣤⣤⠞⢩⡿⣧⡀⣤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⢰⣧⣤⡤⠄⠓⠀⢠⣄⡰⣎⣁⣈⠋⢉⣻⣿⡿⠀⠀⠀⠼⠿⠿⢛⣋⣁⣠⠾⡷⠋⢿⠀⣟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠋⠀⣧⣰⠿⠛⠆⠑⡬⣽⡧⢈⢉⡿⠋⢁⠠⠊⠁⠀⠀⡄⠀⣾⣙⣽⡃⠄⠙⣾⣅⢂⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀⠀⠁⠧⠀⠒⠀⣺⡽⠂⢁⣫⠞⣡⣾⠅⠀⡞⠀⠀⠘⠀⢀⣿⣿⣭⣴⣚⡁⢹⡶⠛⠁⢹⣆⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠆⠰⠞⠓⢴⡶⠛⠋⢠⢻⠏⠀⠀⢂⣡⣤⣤⠶⣶⡿⣿⠿⣤⣍⡁⠀⢼⡟⣂⣄⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠓⢠⣤⡄⢀⡀⠀⢘⡠⠃⣾⣄⠴⠒⠋⠛⠉⠀⠀⡟⠰⡟⣧⠉⠀⠉⢱⣿⢭⡁⢠⡟⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠰⠀⠀⠈⠱⠁⠚⠁⢦⠈⢡⠀⡇⠀⢲⠶⢶⢀⣰⣦⣔⠀⠀⠇⠈⣇⣀⡼⡟⠛⠷⣤⡿⠁⠀⢊⠃
⠀⠀⠀⠀⠀⠀⠀⢶⡆⢿⣄⠀⢠⡄⠀⡀⣀⡀⠀⠘⣶⠋⠀⢣⠔⠂⠀⡀⢼⠋⠉⢹⠉⡾⢷⢀⡟⠉⠓⢷⣀⣴⠛⠁⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠾⢁⠀⠹⠲⢾⡇⠀⠰⣿⡄⣄⢠⣿⠾⣶⡄⠀⠠⢄⣄⡀⠈⠁⣼⡎⠀⠀⢻⣇⣠⡤⠾⠋⠀⠠⠄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠴⠀⠶⣄⡄⠉⠀⡽⠇⠀⠀⢿⠀⢴⠖⠀⠉⠛⠀⠀⢻⠉⠩⠉⠉⠉⠁⠉⠐⠆⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢰⣦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⢶⡖⠠⢀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠉⠉⠉⠀⠀⠀⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣅⢀⡀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢾⡵⡍⢲⣞⣥⠆⠀⠀⠀⠀⠀⠀⢀⡴⡉⠀⢈⠙⢶⣬⠀⠈⠀⢘⡄⠀⠀⠀⢀⢌⠔⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⠆⢹⠋⠀⠀⠀⠀⠀⠙⠻⣿⡀⠝⠀⢸⡇⠀⠀⠀⠠⣶⣿⡧⢀⣄⢖⣥⠎
⠀⠀⠀⠀⠀⠀⠀⢠⣷⣠⣠⢦⠆⠀⠀⠀⠀⢠⣶⣷⣾⢃⡀⣶⠛⠇⠀⠀⡀⢀⡈⣾⣰⠩⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢣⡟⠀⠀⠀⠀⠀⠁⢹⡟⠹⣦⡀⠁⠀⡀⠀⠀⣷⠈⢳⡈⠻⣼⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⠀⣰⡄⢀⠸⣁⣤⡾⠁⠀⡀⣿⠀⠀⢻⡄⢀⢳⡄⠸⠇⡀⠀⡠⠒⢈⣁⣒⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⠟⣧⠸⢦⠋⠌⠁⢀⡼⢣⣿⠀⠀⢸⡇⢸⠀⠀⠀⠀⠈⠙⠚⠵⠷⠿⠛⠃⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣞⣈⣉⣁⠧⡀⣟⣰⣿⡏⠀⣠⡞⢁⣾⡇⠠⠀⢸⡇⠈⡇⠀⡀⢶⣤⡀⢀⠀⠀⠁⣠⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⡹⢿⣷⣿⣷⡻⠝⢩⠁⢰⠋⠀⣾⣿⠀⠆⠀⣿⠣⠀⠸⡄⠐⡼⣿⣿⣿⣿⣿⠿⢯⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠛⠋⠉⠁⠀⠀⡌⠀⠃⠀⢸⠏⠀⢸⠀⠀⠇⣠⡀⠀⠹⡄⠙⢟⡿⣏⣤⣿⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣤⣀⣀⣀⣠⣾⠀⠀⠀⠀⢎⡄⠀⠀⠀⠀⢸⣿⡍⠂⠀⠈⠢⣈⠣⢼⡁⢰⡿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡉⠛⣙⣾⣿⣿⠗⠀⠀⠀⢀⣾⡏⣄⢰⠀⣦⢸⠏⣁⣀⣉⢦⣄⡈⠑⠢⣌⣉⡇⠇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢓⣿⣻⡟⢉⠄⠀⠀⢀⡞⠉⢡⣿⠈⡆⢷⢸⠊⢹⢿⢙⡧⣉⣻⢷⣤⣤⣿⠀⢠⠓⠨⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠖⠁⠀⢀⣾⠟⣽⣶⢾⣿⣆⠘⡌⢮⣂⠌⢸⠸⢰⠁⠈⠉⠛⠻⢿⢀⢮⡛⢦⡀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠁⢀⣠⡄⡲⠛⠁⠀⡏⠇⡘⠾⠋⠁⠈⡢⠙⠦⢀⢰⡅⠀⠀⠀⠀⠀⠸⣽⡇⠉⢟⣻⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⡿⠏⠁⠀⠀⠀⠀⠙⠤⠤⠶⠙⡄⠀⢷⣦⡕⠂⠭⢑⠢⢄⠀⠀⠀⠀⠉⠋⠀⠀⡣⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢧⣀⡴⡍⢫⣢⠀⠀⠀⠀⠀⠠⠃⡼⢨⡍⠛⣓⢤⡀⠈⢲⣦⠀⠀⠀⢀⠔⣩⣤⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣄⡀⠀⠉⠀⠘⣿⠀⠀⠀⠀⠀⣷⣼⠀⠀⠻⣿⡿⠵⠯⠓⢸⣷⠀⠀⠀⠐⡘⢏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⡷⠠⢴⣯⣕⣦⡀⠀⠀⠈⠉⠀⠀⠀⠣⣰⣾⣫⣝⢦⠘⠃⣂⠭⠀⢈⣂⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢽⠧⠀⠀⠀⠀⠀⠀⠀⢀⠜⢉⡙⢫⠞⠉⠉⠁⠀⠀⠈⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣇⠀⠀⠀⠀⠀⢠⣧⣾⣟⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣷⠀⠀⠀⠀⠈⣿⠏⡌⠀⠀⣀⡤⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⠀⠈⠒⡉⣢⠊⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠊⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡇⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣾⡿⠟⠋⠉⣿⡇⠉⠉⠛⠿⣿⣦⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠻⡄⠀⠀⢠⣿⡇⠀⠀⠀⠰⠋⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⢰⣄⢸⡿⠇⢠⡾⠃⠀⠀⠀⢻⣿⡄
⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⢻⣿⣶⣶⣶⣾⣿⣧⣤⣤⣀⣀⣀⣀⠀⢀⡀
⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠙⣿⣟⠛⠻⠿⠿⠿⡄⠀⠀⢀⣀⡀⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢴⠇⠀⣾⣿⠈⠛⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡴⠀⠀⠀⠀⣿⡏⠀⠀⠀⣳⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠻⣿⣶⣤⣀⡀⣿⣇⣠⣴⣾⡿⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠇⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠦⠴⢸⣧⠶⢠⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠗⠉⠁⠀⠀⠀⢸⣷⠀⠀⠀⠉⠻⠶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠞⣉⡲⠄⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢰⠎⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠫⠤⠤⠉⠀⠀⠀⡀⠀⠀⢸⣿⡇⠀⡐⠀⠀⠈⠤⠎⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠁⠀⠀⠀⠀⠈⠓⢤⡐⠀⠀⢸⣿⣷⠀⠀⣠⠋⠀⠀⠀⠀⠀⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣙⣇⠀⢸⣿⣿⣠⠞⠁⠈⠀⠀⠀⠀⠀⠘⣧
⢲⡀⣶⠀⠀⣀⣀⣠⣤⣿⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⣸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢰⡆
⠀⠟⠘⠇⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⣻⠋⠋⠉⠁⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀⡀⠄⠀⣴⠟⢻⣿⡇⠀⠈⣯⡉⠀⢀⠀⠀⠀⠀⠀⢠⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢠⠞⢁⠈⢸⣿⡇⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠞⡴⢀⠁⠀⠂⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠫⢦⣁⠙⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⣓⢔⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠵⣦⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⣴⡾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠸⡇⠰⠸⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢐⢳⠈⠟⠱⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠠⣬⣿⣾⠂⠀⢭⠀⠀⠀⠀⠀⢀⣤⢶⣖⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠖⠀⠠⢩⣿⠀⠀⠘⡀⠀⠀⠀⠀⢻⠒⠛⣾⢽⠳⡳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⢀⣼⠀⠋⠀⢀⠀⠳⡀⠀⠀⠀⢌⣂⣂⠏⠀⠱⢻⠵
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⣜⣿⠏⠀⠀⠀⢸⡆⠀⣜⢄⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⣀⣼⣿⣿⠃⠀⠀⠀⠀⣼⣷⡀⠘⢦⡑⠠⢀⡀⠀⠀⠀⢀⡧⢭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⢫⣤⣾⡯⢀⣼⣿⢿⣇⠀⠘⢿⢷⣄⠈⢠⠀⠀⣮⡽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⣴⣿⡿⠋⡰⡩⣿⠗⠉⣾⣗⠦⠀⠙⢿⣻⣴⣠⣜⠖⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⣛⡭⠙⠀⢚⣩⣾⣿⡄⢠⣾⡽⢿⠻⢤⣸⢯⠿⢘⣥⣾⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠫⡌⠉⣀⣴⣾⡿⣛⠛⣿⣧⣼⢁⢀⠞⢠⢎⡟⡽⠿⠷⣿⡿⣿⣯⠢
⠀⠀⠀⠀⠀⠀⠀⠨⣿⡟⢠⣾⡯⣺⠏⣿⠏⣴⡿⣻⠎⢂⣂⣀⣼⣽⢤⠃⠀⠀⠀⠈⠙⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣯⣍⣶⢏⢿⡄⡨⢋⣰⢿⣿⣻⡥⡶⢮⢺⢪⢆⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠻⠽⠎⣧⢨⡙⡟⢓⣭⡾⢻⢿⠁⢿⣏⠜⠷⣺⡷⣄⡀⠀⠀⢰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⣬⣿⠰⣲⣟⠉⢨⠆⣘⣻⡀⠀⠀⠀⠀⠈⠙⠳⢮⡐⢄⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣳⣿⣧⣀⠃⠟⢃⠰⣽⠟⢫⣴⣦⣀⢥⣈⣷⣦⠀⠑⢶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢷⣼⢿⣿⣋⣑⣤⣴⣾⢻⡽⢙⣈⠑⠦⢀⠀⠀⠀⠀⠀⠘⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣔⡺⢧⣹⣧⣖⣿⣽⡯⠊⠈⣛⣷⠸⣗⡋⢄⡂⡠⠄⠀⣑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣾⣾⠭⠞⠁⠀⠀⡜⠠⣨⢇⡟⠻⠯⠿⠿⠯⠯⠶⢌⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣴⡞⡡
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠄⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠐⡇⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡰⠀⠀⡈⠀⣀⣀⡈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⠶⠦⠰⠂⠀⠀⠠⠤⣄⠠⠶⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠶⠀⠉⡀⠀⠀⠀⠀⠃⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⡴⠒⠁⠸⠠⠁⠀⠠⣤⠀⠀⠀⠀⣶⡌⠁⠀⠀⠀⠀⠀⠀⠀⠶⠆⡸⠀⠠⠀⠠⠀⠁⡀⠀⠀⠁⠀⠂⠢
⠀⠀⠀⠀⠚⠂⠃⠀⠀⠀⠀⠀⠒⣀⣄⣴⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠄⢀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⣻⠀⠂
⠀⠀⠆⠀⠀⡐⢠⠖⣦⠀⠀⠁⠉⢉⡈⠋⠀⠀⠀⠀⣠⠤⠀⠴⠖⠒⣤⠰⠖⠀⠦⣀⡈⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⡀⠀⠀⠦⠠⠈⠁⢠⠒⠉⠛⠂⠁⢀⡠⠈⠈⠉⠁⠀⡄⠀⠀⠀⠁⠀⠀⠀⠰⠏⠀⠈⠀⠀⠀⣠⠤⡄⠞
⠀⠀⠈⠀⠀⣦⠀⠀⠰⠀⠄⠀⠀⡠⠖⠉⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠁
⠀⠀⡆⠀⠚⠘⠖⠢⠞⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠁⠂⡀⠀⠀⢀⠼⡇⢠⠞
⠀⠀⠀⣀⠐⡆⠀⠀⠀⢀⠙⠉⠀⠀⠀⠀⠀⠀⣠⡦⠀⡠⠤⠿⠶⠂⠀⠒⠛⠛⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⠂⠀⠹⢀⠀⢺⠀⠒⠛⢀⡄
⠀⠀⡴⠎⠋⠀⠀⠀⣠⠁⠂⠀⢀⠀⠀⠀⠀⠈⠀⠀⡼⠄⠂⣶⠂⠐⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠄
⠀⠀⣅⠀⠀⠀⠀⡰⠃⠀⠀⠀⠉⠁⠀⢀⡤⠀⣰⠀⠁⢀⣀⡷⠤⢾⣈⠩⠧⠴⠗⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠈⠃⠀⠀⠀⠀⠠⡄
⠀⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⡠⠂⠀⠈⠁⠀⡈⠀⠄⠀⢀⣀⣀⡠⠀⢀⣀⡀⠀⠖⠀⠑⠛⠁⠀⢠⠔⠂⢤⡄⠀⢀⠃⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⡆⠀⠀⣤⠦⢼⠖⠻⠋⠈⣯⠉⣷⠆⠉⣟⠙⣧⡀⠀⠀⠀⠀⡴⠾⠶⠆⠀⠀⠁⠀⢀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⣠⠞⢹⠀⢸⠇⢀⠖⠂⠉⠛⠩⠒⠒⠉⠈⠛⠋⣿⣷⠛⣦⠀⢀⣾⠀⠀⠀⠀⠀⠈⠀⠀⣀⠸⠟⠛
⠀⠀⠁⠀⠀⢸⠀⡄⠀⠀⠀⠀⢀⠔⠁⠀⠘⠶⢸⡆⠘⠀⠀⣤⣀⠀⠀⢀⣀⠀⢰⠄⠛⠙⠙⠻⡥⠼⡴⠆⢻⠄⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡰⠋⢀⠔⠃⠀⠐⢸⡇⠘⣁⣸⣯⡨⠶⠂⠘⣻⠁⣯⣀⣀⣄⣀⣀⣀⡀⣠⠀⢩⠰⠀⠀⠄⠀⢠⡿
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡰⠁⡴⠁⠀⠀⢀⡤⢴⡧⠼⠂⠀⠀⢀⠐⠀⠀⠀⠀⣩⡹⠬⠿⣿⣏⣠⣹⣲⡄⡞⢀⡄⠀⠀⡀⠸⣇
⠀⠀⠀⠀⠀⠀⠳⠖⠀⠶⠤⣤⣀⠀⠠⠞⠁⠀⢈⣇⣀⢠⣄⣀⣼⣀⠀⣀⣀⠀⣿⠀⠀⠀⠰⠋⠉⠈⠁⢀⣧⠸⠆⠀⠰⠋⣸⠋
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢤⣄⠉⠙⠳⣤⣤⣠⡶⢿⣷⣤⣧⣿⢘⣏⣀⡏⣏⣶⡺⣷⢠⣄⣴⡖⡞⣲⢿⣿⣿⣿⢿⡿⠂⢀⡟⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠡⡈⠁⠀⢡⣄⠓⠘⢘⣷⣯⡴⢤⣯⠭⢭⣽⡿⠯⠭⠿⣾⠛⠱⠒⠊⣠⠴⠷⠁⠗⠀⢠⡋
⠀⠀⠀⠀⠀⣠⠊⠙⣦⠀⠀⠀⠀⠘⠆⠠⠚⢻⡶⠛⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⣀⠠⠄⠀⠀⠲⣿⣀⠁⠀⠀⠀⠀⣠⠋⢈⡂⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠁⠈⠀⠳⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠀⠀⠀⢀⡴⠁⠈⠀⠀⡶⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⡈⠀⠈⠲⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢠⣆⠀⠊⠀⠔⠙⠀⠀⢰
⠀⠀⠀⠀⠄⠁⠂⠀⠀⠀⠀⢀⡀⠈⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠴⠀⠉⠀⠀⠀⡨⠾⠇⠀⠀⠀⡀⠀⠐⠛⠋
⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠊⠁⠒⠀⠀⠀⠸⠀⠓⠃
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡈⠰⡌⢈⡁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠘⢋⠀⠀⠀⠀⠀⢴⠶⠆⣀⣤⠴⣄
⠀⠀⡀⠁⣀⠀⠀⠀⠈⠀⢠⠖⠀⠸⠤⠅⠀⠀⠀⠀⠀⢈⣀⡀⠁⠠⠀⠰⠇⠀⣠⡆⠀⠀⠂⠀⡄⢀⠄⠚⠃⠈⠉
⠀⠀⠀⠈⠁⠀⠀⠀⠞⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠙⣆⠀⠈⠀⠀⠚⠉⠘⠿⠙⠶⠀⢠⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⠈⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢐⠁⣠⠏⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠙⢋⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂
⠀⠀⠀⠁⠀⠠⠀⠐⠇⠞⠃⠀⠀⠀⠀⢀⠁⠈⡀⠀⠈⡀⠉⠀⡀⢀⠀⠀⠠⠀⠉⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⣤⠒⠢⡀⠀⠈⠑⠀⠂
⠀⠀⠀⠘⠃⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠤⠠⠄⠀⢀⡍⢡⡆⢠⠈⠀⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠁⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠂⣤⠤⠀⠀⠀⠀⠐⢠⠀⢀⠁⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⢀⠀⠀⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠄⠠⠄⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠈⢠⠯

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣈⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⢒⣿⡀⠤⠤⡇⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣳⣤⣤⣷⣴⣶⣾⣿⣿⣿⠁
⠀⠀⠈⠀⢀⣀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⣯⣟⣿⣆⠀⠀⠀⠀⠐⠦⠄⠐
⠀⠀⠠⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣏⣽⣿⠟⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠉⢉⡉⠁
⠐⠚⠛⠿⠷⠶⠾⣟⠛⠛⠹⠛⠿⣷⣿⠟⢻⣿⣿⡿⠿⠽⠛⠛⢛⣖⣿⢿⣿⡟⠉⠉
⠀⠀⠉⠛⠛⠀⠰⠦⢭⣍⣉⣁⠀⠈⠛⠋⠬⠽⣿⠅⠀⠒⠒⠒⠒⣂⣉⡭⠉⠉⠀⠒⠒⠒⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠁⠀⠈⠉⠑⠒⠀⠀⠀⠉⠉⠓⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠒⠒⣿⡂⠤⠤⣯⠀⠀⠀⠀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣦⣤⣼⣴⣶⣾⣿⣿⣿⠏
⠀⠀⠈⠁⢀⣀⣀⡀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣋⣯⣽⣻⣇⠀⠀⠀⠀⠀⠲⠄⠐⠒
⠀⠈⠡⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣟⣽⣿⠟⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠈⠍⣉⠁
⠒⠚⠛⠿⠷⠶⠾⣟⡛⠛⠫⠛⠻⣷⣾⠿⢛⣿⣿⣿⠿⠯⠟⠛⢛⣷⣛⡿⣿⣿⠉⠉⠁
⠀⠀⠉⠛⠛⠀⠐⠦⠭⣍⣉⣁⠀⠈⠛⠋⠥⠽⣿⡧⠀⠐⠒⠒⠒⣒⣀⡭⠉⠉⠀⠐⠒⠒⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠃⠀⠀⠉⠑⠒⠒⠀⠀⠈⠉⠙⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡤⢴⠲⠒⡦⢤⣀⠀⠀⠀⠈⠁⠉⢄⠀⠀⠄⢀⠀⠈⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠈⠀⠀⠞⠄⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡠
⠀⠀⠁⠈⠀⠀⠀⢀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠀⠀⠁⠀⠖⠈⠀⠀⠀⠀⣖
⠀⠀⠀⠀⠀⠐⠀⢸⡒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⡟⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠃⠦⠀⠀⣠⡰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠠⢰⡄⠀⠂⠀⢠⡼⠃⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠛⠳⡄⠃⣈⡟⠂⠼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡘⠛⠣⠆⣠⣠⣀⣄⠰⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⠠⣤⠘⠀⠚⠒⠋⠀⠰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠀⠘⠀⠀⠀⠉⠁⠀⠐⠀⠀⠀⣀⣄⡀⠀⠴⡀⠀⠀⠈⠀⠁⠐⡂⢠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣠⡄⠀⠇⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠐⠴⠟⢠⠆⠀⠀⠁⠀⡀⠦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢴⠀⠀⣤⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠁⠀⠰⠒⠉⢦⠃⢀⠀⠤⠂⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠃⠀⠀⠄⠀⠋⠁⠐⠀⠀⠲⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⣀⣘⣀⣠⠀⢀⡀⢀⠀⠀⠀⠀⠳⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠠⡄⠀⢶⠺⣽⠛⠉⢉⡀⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢱⡆⠸⠆⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠠⠀⠀⡀⠀⠀⠀⠠⠀⠁⠀⡀⠀⠀⢤⠁⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣀⠈⡘⠲⢋⠉⣀⣤⣀⠲⣶⡖⣙⢶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠁⠈⢃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡈⠐⠿⠟⠁⡈⠏⠠⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⡀⠀⠀⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠆⠠⡀⡀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⢠⠰⠓⣀⠀⠁⠉⠀⠰⠀⣰⡀⠀⠀⢤⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⢤⠠⠶⠆⠸⠰⣤⡇⠰⡆⠀⠀⠀⠀⠈⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⢲⠙⣧⡙⠹⠃⠶⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁⣀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠶⢻⠄⠉⠋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠀⠶⠈⠁⠀⠁⠀⠀⠀⠰⠆⠀⠀⢀⠀⠘⠂⠀⠀⠀⠛⠉⠘⠉⠂⠀⠀⠁⠀⠀⠀⠁⠀⢄⠀⢠⡄⠀⡤⢤
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠀⠰⠄⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠊⢰⠃⠈⠉⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⡀⣠
⠀⠀⠀⠀⠀⡄⠈⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠡⣇⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠠
⠀⢸⡄⠠⡄⠀⣴⠀⠀⠈⠁⠀⠸⠶⣶⢦⡀⠀⢠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⠄⠂
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠸⠄⠀⠀⠀⠀⢁⣰⢢⡆⠀⠀⠀⠈⠁⠀⠀⢻⣀⣀⡈⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠓
⠀⢰⡄⠀⠀⠀⠀⠈⠻⡼⠀⠀⠀⡀⠀⠀⠀⠰⢠⢿⠃⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⢸⠃⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⣁⡀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣣⡀⣉⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠁
⠀⢐⠀⠀⠀⡀⠁⠀⠀⠀⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠘⠦⠀⠀⠈⠐⠒⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠉⡄⠀⠀⠀⠀⠠⠂
⠀⢸⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⢿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣀⣴⣿⠿⠛⠉⠀⠀⠀⣿⣿⠀⠀⠀⠉⠙⠻⣿⣶⣄⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⣀⡤⠒⠚⢹⣿⡟⡋⠑⠒⠤⣀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⣤⡊⠁⣠⡤⠶⣿⣿⡇⡟⠷⢦⣄⠈⠑⣦⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢀⠞⠀⣹⣿⣍⡀⠀⣿⣿⡇⢠⠀⠀⢈⣿⣿⠀⠑⡄⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⡎⠀⣼⠃⠈⢿⣿⣶⣿⣿⡇⢘⣤⣾⡿⠃⠈⢷⡀⠸⡄⠀⠘⣿⡇
⠀⠀⠀⠀⠀⢠⡄⢠⡄⢠⡄⠀⠀⠀⠀⣸⣿⠀⠀⣸⣀⣸⡇⠤⠤⠤⠛⠻⣿⡿⠷⣾⣿⣿⣷⣶⣤⣼⣧⣀⣧⣀⡀⣿⣷⠀⠀⠀⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠈⣿⡾⢿⣿⠃⠀⠐⠒⠶⣿⣿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⡀⠀⣸⡟⠛⠛⠛⠛⠛⠛⠛⣛⣿⠿⣿⣿⠟⠒⠒⠀⢸⣿⣓⣛
⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⡀⠹⣏⠉⠛⢻⣿⣿⡟⢻⣿⣿⣿⣶⡆⠉⠉⢹⡏⠀⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢧⠀⠹⣆⣰⣿⠿⠛⡆⢸⣿⣿⠛⢿⣿⣆⣠⡿⠀⡰⠁⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠈⠣⣀⡽⢿⣅⡀⠀⠃⢸⣿⣿⠀⠀⣨⡿⢿⣀⡼⠁⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠙⠦⣀⠈⠙⠳⢾⢸⣿⡿⠾⠛⠉⣀⠴⠋⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣦⡀⠀⠀⠉⠒⠢⠼⣼⣿⡧⠴⠒⠊⠁⠀⢀⣤⣾⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠛⢿⣷⣦⣄⣀⡀⠀⣿⣿⠀⠀⣀⣠⣤⣾⡿⠟⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⡠⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⡄⢀⠰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠃⣄⠲⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣀⠀⡖⠀⠐⠀⠀⢀⣤⣴⡄⢦⡤⠄⣿⣿⡤⢖⡿⠒⢂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⢿⣦⡄⠐⠀⡸⠻⣿⡏⢸⡇⣠⣾⣿⣿⣯⡤⠀⠁
⠀⠀⠀⠀⠀⠐⠁⣰⠎⢱⠀⢠⣤⢀⣤⠿⢀⠀⠀⠙⣿⠛⠳⢬⣵⣿⡿⢻⣿⢿⡅
⠀⠀⠀⠀⢀⡄⠀⢣⠀⠘⠒⠪⠷⠚⠁⠀⢹⠀⠀⠀⠀⠳⡄⠈⠻⢿⡇⠘⠁
⠀⠀⠀⠀⡀⢿⠀⠀⠀⠐⠀⣀⣤⡼⠀⡀⠈⠀⡠⠀⠀⠠⠀⠑⠒⠦⣌⠛⠓⠶⠶⠶⠆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠠⠳⢤⠤⣴⠞⠋⠀⣀⣠⣇⣤⣏⢀⣸⡀⠀⠀⠓⠀⠀⠐⠉⠠⣸⣿⣿⣷⡀⠀⠀⠀⠠⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡴⠞⠋⢁⣈⡀⠈⠁⠆⠀⢀⡀⠅⣄⣄⣀⠀⠀⠉⠛⠛⠓⠛⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠻⢓⠄⠀⡆⠉⠀⠀⠀⠙⠻⣄⠀⠄⠀⠀⠰⠖⢢⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢒⠒⢂⠄⣠⠇⠐⠀⡍⠀⠀⠀⠀⠀⠓⠄⠈⠀⠀⠐⠀⢰⠮⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢚⣿⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢆⠀⠀⠀⡄⠀⠀⠀⡀⠀⠠⠤
⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠎⢉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠂⠀⠁⠀⠀⡰⢀⠀⠀⠋
⠀⠀⠀⠐⠒⠢⠀⢀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⢀⠖⢣⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠂⢀⠙⢁⠤⠂
⢀⠄⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⢠⡀⠀⠀⠀⠀⠊⠀⠁⢀⡤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠈⠁
⢦⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡠⠀⣀⠤⠁⠀⠀⠀⠞⠁⠀⠀⠀⠈⠓⠤⠤⠦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⣛⣩⣭⣥⣤⣾⣷⣦⣤⣭⣍⣛⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣩⣴⣾⣿⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣦⣍⡻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣍⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⣡⣾⣿⠟⠁⠀⣠⣠⡟⠀⠀⢀⣀⣤⣿⣧⣄⡀⠀⠀⢀⡀⠀⠀⠀⠈⠛⢿⣷⣌⢻⣦⡀
⠀⠀⠀⠀⠀⢠⣾⠏⣴⣿⠟⠁⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⢹⠉⠉⠁⠀⠀⠀⠽⣤⡦⠀⠀⠀⠀⠻⣿⣦⡙⣿⡄
⠀⠀⠀⠀⢠⣿⢃⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣶⣾⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡘⣿⡄
⠀⠀⠀⢀⣿⠇⣾⣿⠁⠀⠀⠀⠀⢀⣤⣾⠃⠀⠀⠶⣾⣿⣿⣿⣿⣿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠘⣿⡀
⠀⠀⠀⣼⡏⣸⣿⠇⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢸⣛⣛⣛⣛⣛⣇⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠘⣿⣇⢹⣧
⠀⢀⣠⣿⠃⣿⡿⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⡄⠀⠀⣼⠉⠉⠉⠉⢩⢹⠀⠀⢀⣼⠿⢩⣭⣻⣿⠄⠀⠀⠀⠀⢻⣿⠘⣿⣄⡀
⢀⣾⣿⡿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠀⠀⣿⡀⠀⠀⠀⢈⠘⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⡆⢿⣿⣷
⢿⣿⣯⡐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠂⠀⠀⠀⠐⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢂⣽⣿
⠀⠹⣿⣿⡀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⣿⣿⠟
⠀⠀⠀⢻⣇⢻⣿⡄⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⢠⣿⡟⣸⡿
⠀⠀⠀⠘⣿⡌⣿⣷⣤⣽⣿⣿⢿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣶⣶⣿⣿⡿⠿⠫⢥⣾⣿⢡⣿⠃
⠀⠀⠀⠀⠹⣷⡘⣿⣿⣿⡿⢿⡳⠾⣯⣽⣛⡿⠷⢿⣻⣷⣿⣭⢛⣯⣥⣝⡛⢛⣛⣛⣻⣿⣿⡿⢿⣛⣻⣿⣿⢃⣾⠏
⠀⠀⠀⠀⠀⠹⣷⡌⢿⣿⣿⠿⣟⣛⣓⣲⠿⠿⣿⡿⠿⣟⣯⣾⣯⢽⣷⣯⣭⣧⡭⠿⢷⣮⣔⡾⠿⣿⣿⡿⢡⣾⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣦⠹⣿⣿⣿⣭⣿⣯⣭⣟⣻⣿⣿⣛⣫⣵⣾⣿⡶⣖⣒⣲⢾⣿⣷⣶⣭⣻⣿⣿⢋⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡛⢿⣿⣿⣿⣿⣷⣿⣾⣿⡭⢍⣛⣋⣑⡻⠿⣿⣿⣷⣯⣭⣽⣿⡿⢋⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣍⠻⢿⣿⣶⣶⣶⣶⣚⣛⣯⣭⣽⣟⣿⣶⣮⣿⣿⡿⢟⣩⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣬⣍⣛⠛⠿⠿⠿⣿⣿⠿⠿⠿⠛⣛⣩⣵⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣷⣶⣌⢡⣶⣾⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠂⢐⢧⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⢸⡌⢀⣤⡞⠐⠃⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⡂⢀⠔⣸⣿⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⡉⣰⡿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣤⠾⢂⣾⣿⠀⡟⣧⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⢈⠘⠁⠀⣾⣏⡏⠀⡇⢿⡀⠀⠀⠐⠒⠀⠀⠀⠸⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡤⠁⠀⠀⣾⣿⣿⡇⠀⡇⢸⡇⠀⠀⠀⠀⠑⡀⠀⢠⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⢎⡀⠀⢀⡿⣿⣿⣿⠄⠠⡇⠀⣿⡂⠀⠀⠀⠀⠈⠆⢀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⣉⣀⠀⡀⠀⡇⠀⢻⣏⠀⠀⠀⠀⠀⠀⠸⡷⡶⢦⣤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣤⣼⣶⣤⣤⣤⣃⣀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⢠⣴⠶⠾⠿⡭⣤⣒⡚⠛⣛⠛⠛⠻⠿⠟⠛⠻⠿⠿⠿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⠁⠤⠤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠃⠀⠤⠖⠊⠉⠩⠵⠖⠛⢳⡖⢀⣤⡴⠶⠶⢟⣩⠴⠤⣤⣴⣶⡆⠨⢤⡤⠉⠀⢀⢀⡤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠴⠤⠈⠭⢉⣉⡥⠴⠶⠒⠒⠒⠲⠄⠈⠉⠉⠀⠀⠀⠉⠛⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⡊⢉⡅⠂⠈⠐⢀⣯⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣒⠩⠅⠂⠉⠙⣬⢋⠖⠂⠤⡠⠀⣀
⠀⠀⠀⠀⡖⠉⠙⡌⢆⢁⢀⠖⠺⡈⢠⠁⠌⠉⢣⠁⢢⠉⠑⠢⢄⣀⠤⠐⠊⣙⢣⡘⢄⡀⠀⠀⢀⠞⡇⣌⠔⠉⠀⠈⣱⢸
⠀⠀⠀⠀⡇⠀⠀⠘⡌⠢⡄⠤⠤⡴⠓⢣⠤⣴⡄⠄⠸⢰⠀⣀⡀⠄⢀⡔⢢⠗⠈⣗⢡⡙⢄⠀⡸⠠⠁⣏⢀⠔⢊⠉⠄⢸
⠀⠀⠀⠀⡷⡁⡱⠀⠈⠢⡈⠢⣀⠦⠤⠴⠠⠉⢃⠀⡆⣬⠊⠀⠘⡂⢰⠇⠘⣦⣴⡗⠀⣣⠈⠒⣁⣠⠄⢇⢁⣘⡀⠐⠀⠡
⠀⠀⠀⠀⡇⠘⠀⢈⠉⡀⠈⠒⢌⡑⠢⣀⠃⠀⠐⡞⡐⡘⠀⠀⡰⠁⠙⠳⠖⠓⠐⠓⣒⠞⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻
⠀⠀⠀⠀⡀⠎⠈⠀⠿⠀⡜⠓⢄⠈⠒⠤⡉⠂⡔⡱⢹⣁⡠⣎⢕⡨⠥⢭⣉⠲⡤⠊⠁⠀⢀⠤⣐⢂⡈⢣⢰⠒⠂⠤⠄⡜
⠀⠀⠀⠀⡇⠈⠏⠀⡤⠊⠀⠀⠀⠉⡆⠀⢈⠏⡴⡉⠢⣀⣾⢛⠥⠀⢅⡠⢀⠇⠀⠀⣠⢞⠕⠋⠀⠀⠙⢈⢰⠀⢠⢁⢂⡄
⠀⠀⠀⠀⢟⡒⠤⣀⠑⠂⠤⡀⠀⢠⠃⢀⠎⠜⡀⠌⠢⡈⠣⡐⢤⠂⠀⡳⠃⠀⢀⣄⠱⡸⣀⠀⠀⠀⠸⡈⡘⣘⣀⠊⠉⡇
⠀⠀⠀⠀⢀⡨⢕⡢⣑⠢⡀⠈⠉⣁⣀⡜⠸⣠⡀⣂⡁⡜⢄⠑⢌⠴⠊⠀⠀⡠⢋⢀⡳⡈⠢⣈⠢⢄⢾⡱⠁⠀⠙⡀⠐⡇
⠀⠀⠀⠀⢘⢣⠀⠈⣉⣗⢌⢳⠉⢀⡌⢢⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⢀⡠⠊⡐⠁⠀⠙⠮⡓⠤⣁⠒⠳⢅⣉⣀⠈⠁⢀⠇
⠀⠀⠀⠀⢸⠸⣴⠿⠋⠀⠈⡆⡧⢴⠇⠘⣗⣲⠉⣦⠤⠤⣀⠤⣔⡒⣄⠱⡀⢇⠀⠀⠀⠀⢸⠐⢠⢁⠓⡲⠤⡤⠬⠭⢬
⠀⠀⠀⠀⢸⠔⠁⠀⣀⠔⠊⡇⡏⠽⢡⠤⢻⣟⠀⢘⣅⢸⠰⢘⠀⠈⢮⠣⡈⢪⣢⠀⠀⠀⠘⡌⢸⢸⡎⠀⠀⠀⣱⠀⣸
⠀⠀⠀⠀⢸⢀⡠⠊⠅⠀⠰⢡⠷⠝⡟⠻⣦⠛⠒⠒⢳⢣⠇⣀⠳⣀⠀⢑⠌⢦⡙⢷⡤⢀⠀⠈⡜⡀⢗⠤⣒⢝⠫⣅⣸
⠀⠀⠀⠀⠘⠃⠈⠀⠀⡰⢣⣾⡄⡘⠛⡄⡙⢕⠦⡠⢃⢎⠎⠀⠑⠤⣉⠁⠆⠀⠙⠦⡉⠢⢍⡒⢡⠘⢌⠒⡕⠱⠋⠀⢸
⠀⠀⠀⠀⠀⡀⢠⢀⡔⡡⢣⠉⢹⣀⣀⣠⠁⠂⡼⣠⡣⠃⠀⠀⠀⢠⢊⠐⢠⢀⠈⠀⣌⠵⠦⢈⡐⠬⡀⠑⢌⢪⢢⠀⡀
⠀⠀⠀⠀⠀⡇⡠⢊⠞⠀⠆⠀⠀⣧⠠⢄⣀⠎⡔⢱⠁⠀⠀⠀⠀⠸⠀⢀⠀⣀⠴⠊⠁⠀⠀⠀⠈⠉⠙⠓⠬⢆⣣⠓⡇
⠀⠀⠀⠀⠀⣏⣔⡡⠤⠒⠒⠉⠁⠀⠀⠀⠈⠉⠒⠢⢅⣒⠒⠤⣀⡰⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⣠⠖⠁⡠⠀⠘⠀⠀⢀⣴⣾⠃⣠⣤⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣀⣠⠇
⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠻⣤⡀⠳⣤⣀⡀⠀⣾⣿⣿⣿⣿⣽⡃⢠⡞⢻⣣⠀⠀⠀⣠⠖⠛⠉
⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡀⡈⢿⣦⣌⠚⢳⠀⣿⣿⣿⣿⣿⣿⣥⣾⣀⣴⣿⠀⠀⣶⠁⠀⠀⠀⠀⢠⠒
⣽⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⣇⠀⠘⢫⣽⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡀⠀⣀⣠⣤⡟⢀
⠉⠛⠿⣯⣟⣿⣶⣄⠀⠀⠀⠘⢷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣠⣤⣣⣀⣉⣧⡄⠀⠘
⡄⠀⠀⠈⠛⠿⣷⣿⣛⣶⣤⠄⣰⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣽⠟⠀⡀
⣿⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡋⣱⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⢷⣮⢩⣿⠁⣤⡀⢨
⡿⠀⠀⠀⠀⠀⢀⣀⣴⡶⠿⣁⣸⣾⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣧⣤⣿⣿⣯⣟⣦
⣿⡀⠀⠀⠀⣤⣾⣟⠉⣷⣤⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠉⠉⠛⠤⣿⣯
⣽⣿⣿⣷⡔⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢾⣿⣿⣿⣷⣟⢻⣿⣿⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣿
⠉⢉⣉⣙⣽⣾⣧⠄⠋⢉⣿⡿⣿⡿⢿⣏⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢷⣈⣦⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠊⢁⣉⣿⣿⠟⠁⠀⠀⢼⣿⡟⢿⣷⣴⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠓⠿⠿⣷⣶⣦⣤⣤⣴⢿⡏⠁
⢀⣼⣿⡿⠁⠀⠀⠀⢀⣾⢟⢳⣾⣿⣿⣷⣿⣿⡿⢿⣏⣹⣿⣿⢷⡾⢻⡆⠀⠈⠿⣿⣿⣿⠛⠛⠂
⣧⣿⡿⠁⠀⠀⠀⣠⣿⣿⡷⢿⣟⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⠉⠾⠻⡟⣿⣄⠀⠀⠈⢹⣿
⡿⠉⠀⠀⠀⡀⢸⣿⣿⣏⣷⣾⣿⣿⣿⣿⣿⡀⠀⢉⣿⣯⣿⡇⠀⠙⢿⡿⣿⣷⡀⠀⠘⢿
⡟⠋⠛⠓⢟⣿⠿⣇⣀⣿⣿⣿⢻⣿⣿⣙⡟⠷⣤⡘⢻⡿⣿⡇⠀⠀⠀⠘⠋⣿⣛⣶⣄⡀⠉⡑⠄
⣿⢄⠀⢀⣼⣿⣄⣼⣿⠋⣿⣟⣿⣻⡇⢿⡀⠀⠀⢻⣿⣀⣿⡟⠀⠀⠀⠀⠈⠛⢿⣌⣿⡟⠀⠁
⠉⣿⡆⢸⣿⣀⣿⡿⠁⠸⢿⣿⡟⡹⢳⡾⠁⠀⢠⣾⣟⢹⣿⡇⠀⠀⠀⠀⢀⡀⠀⢻⣿⣿⣾⡃⡀
⣾⡿⢷⣾⣿⣿⠟⠁⠀⢐⠛⣿⡴⢳⣾⠃⠀⣠⣾⡟⢙⣿⠟⠀⠀⠀⢠⡖⠁⠀⠀⢸⣿⡇⠙⣿⣗⡀
⠉⣦⣾⣿⡟⠁⠀⠀⠀⠠⡿⢿⣽⠿⢷⣶⡾⠻⠋⣹⣿⣿⣸⡋⠛⠛⠛⠁⠀⠀⣰⣿⡟⠀⠀⠘⣿⣅⡀
⠰⣼⣿⠏⠀⡀⠀⠀⠀⠀⣷⡾⣿⡀⠀⠀⣀⠀⢸⡏⢹⣿⠘⢧⡀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠸⣿⡅
⢻⣿⣟⠀⠀⢿⡄⠀⢀⠀⠸⣧⣾⣷⡄⠀⠀⠳⡈⢟⣻⣿⡆⠈⣿⡀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⡗
⠘⣿⣿⡄⠀⠀⠻⣦⡀⠀⠀⠈⠳⣾⢻⢶⣄⡀⣻⠀⣽⠟⣿⣴⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠙⣿⣷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠙⢶⣛⣿⠟⠷⠿⣿⣿⣿⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⠅
⠀⠀⠰⣿⣷⡄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣉⣁⡀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠙⣷⣄⡀⠀⠀⢀⣠⣿⠋
⣄⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠹⣦⠀⠀⢸⠁⠀⡱⠀⠀⣰⣿⡹⠇⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠛⠁
⠙⠻⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣉⣉⣤⣴⣾⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡀⠤⠤⢸⡤⠤⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠣⠔⣈⠠⠄⠒⠀⠁⢸⡇⢀⠐⠂⠌⢁⠂⠜⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣠⠄⢀⠈⠠⠀⢘⣠⣌⡄⢸⣧⣠⣄⡊⠀⠄⠉⠀⢀⠄⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠀⢄⠀⡡⣴⠞⠓⠈⠁⠀⢸⣿⠈⠉⠛⠹⢶⢔⠁⣠⠈⠔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⡀⠐⠄⣠⡪⠊⠀⠀⡀⠐⠀⠀⢸⣿⡀⠂⠄⡀⠀⠙⢝⢄⠠⠂⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⠐⠂⣰⠝⠀⠀⠐⢦⡀⠀⠀⠀⢸⣿⡇⠀⠀⢀⠴⠀⠀⠹⣣⠐⠂⠡⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⢠⠁⠒⣰⡝⠀⢀⠂⠀⠀⠙⢷⣄⠀⢸⣿⡗⢀⣴⠋⠀⠀⠀⠀⢸⢇⠐⠀⠆⢀⠉
⡃⠀⢀⡀⠀⠀⠀⠀⠀⡇⣄⢐⣀⣽⣁⣀⣤⣤⣴⣶⣾⣦⣝⠆⢸⣟⠴⠋⠁⠀⠀⠀⠀⠀⠀⠿⠀⠂⢰⠸⠀⠀⠀⠀⠀⢠⣀⣀⣠
⠖⣋⣩⠄⠀⠀⠀⠉⠉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⡄⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⢶⠖⠒⠒⠀⠀⢀⠀⠄
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠇⢁⠒⠂⢭⡄⠀⠀⠀⠀⠐⣠⡶⢋⣾⡇⠈⢦⡉⠫⠉⠉⠉⡉⠀⢀⣳⠀⠒⡈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⡈⡄⠂⠘⣶⡀⠀⠠⠀⡴⠋⠀⢸⣿⡇⠀⠈⠙⠶⣄⠀⠀⠀⠀⣴⠃⠐⠀⠁⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⡐⠉⠘⢕⣄⠀⠈⠠⠀⠀⠨⣿⡇⠀⠀⠀⠀⠈⠂⠀⢀⣾⠂⠈⠂⠌⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠈⠁⣨⠳⢷⢄⠀⠀⠀⠀⢿⡇⠀⠀⠈⠀⠀⡠⣴⠟⢁⠈⠁⠀⠐⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠂⢉⠚⠶⢤⣀⣼⡇⠀⣀⣤⠶⠻⡊⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢈⠀⠀⠀⢌⡀⠐⠀⠀⢸⡇⠀⢠⠀⠐⠀⡠⠄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠆⠉⠒⠤⢀⡁⢐⣚⡇⢐⡂⢈⡁⠤⠐⠈⠰⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠱⠄⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⢦⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠂⢾⡷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠙⠆⢆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠸⢻⡏⠀⡇⠸⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠁⡌⡇⠀⢧⠀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠇⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢘⡀⠀⡈⢿⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣇⠀⠦⠈⠟
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡑⢀
⠀⠀⠀⠀⣸⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠷⢀⠀⠀⠀⠀⢀⡹⢦⣶⡀
⠀⠀⠀⢀⣿⣿⣦⠂⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⠶⣽⣾⣿⣿⣦⡀
⠀⠀⠀⠈⠛⠛⠷⠾⠷⣤⣤⣤⣀⣀⣸⣻⣰⣀⣀⣠⠀⡀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠉⠙⠛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣄⣼⣭⣭⣿⣿⣡⣶⠰⣧⣧⣤⠧⣀⣸⣦⣤⣴⠶⠒⠒⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣴⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠹⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡲⠿⢻⡟⠀⠙⠻⢷⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⢀⡴⢋⡴⠶⣄⠀⠀⢱⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣋⣰⠋⠀⠀⠀⣷⣀⣼⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠈⠙⢧⡀⠀⣶⡾⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⣀⣀⣽⣶⣷⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢀⣠⣴⠶⠚⠋⠉⠉⠉⠈⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⡤⣞⣽⣊⡥⢴⣲⣭⣵⣶⡶⠶⡶⠶⣶⣦⣤⣔⣢⢤⣀⠹⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⢔⣯⣾⠿⣫⣵⠾⠛⡋⠉⣀⣀⣤⣤⣤⣤⣄⣀⠈⠉⠛⠿⣾⣝⡻⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣼⣡⣿⢟⣵⡿⠋⠁⣠⣤⠿⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⡾⢦⣔⠀⡙⠻⣮⡟⢿⣮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⢯⣾⡟⣵⡿⠋⢤⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠉⠻⣦⣠⠈⠻⣯⡻⣿⣝⣆
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣰⢣⣿⢏⣾⠏⠀⣤⠟⠁⠀⠀⠀⠀⠀⣀⣤⠤⠰⡇⠠⢄⣼⠇⠀⠀⠀⠀⠈⠹⣦⡂⠙⣿⡝⣿⡎⢧
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⡯⢣⣏⣾⠇⠀⣾⠃⠀⠀⠀⠐⣦⡔⠉⠀⠀⠂⠀⣿⠀⣾⡯⠉⢲⣤⠆⠀⠀⠀⠘⢷⡂⠘⣿⡼⣿⠘⣆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡾⢀⡿⣼⡏⠀⣽⠃⠀⠄⠀⠀⣴⠉⢻⡓⢤⡀⠀⠀⣿⣾⣿⡡⣺⡿⠉⢢⡀⠀⠀⠀⠈⣷⡁⠸⣷⢹⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢰⡇⢸⣇⣿⠀⢰⡟⠀⠀⠀⠀⢸⠀⠈⠀⠑⢄⣨⣶⠀⣽⣿⣧⣾⠏⠀⠉⡀⢡⠀⠀⠀⠀⢸⡇⠀⣿⡏⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠃⣸⢹⣿⢀⢸⡇⠀⠀⢀⣀⡇⠨⠀⠀⠀⠈⠛⠉⣼⣿⡟⠙⠃⠀⠀⠀⠅⢈⣄⣀⠀⠀⠈⣿⠀⣸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⢸⣸⣿⠀⢸⡇⠀⠀⠀⠈⡏⢙⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⡋⢙⠉⠀⠀⠀⢠⣿⠀⢸⡇⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡗⠺⣭⣿⠀⠸⣧⠀⠀⠀⠀⠸⡀⢀⠀⡠⣣⣾⣿⡟⣿⠿⢿⣌⢂⠀⡀⠀⡜⠀⠀⠀⠀⢸⡇⠀⣾⡇⠀⣤⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⢸⣷⠤⢿⣄⠀⠂⠀⠀⠻⣀⣼⡶⠋⣿⡟⠀⣿⠀⠀⠙⠳⣿⣀⡜⠁⠀⠀⠀⢀⡿⡀⢰⡿⠀⣰⣿⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⣏⢿⣆⠀⢿⣏⠓⠶⢤⣤⣟⡣⡄⣸⡿⠀⠄⣿⠀⠂⠈⣠⠜⠛⠆⠀⠀⠀⢠⡾⠅⢠⣿⠃⢠⣇⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣮⢿⣆⠀⠹⣦⡀⠀⠀⠈⠉⢙⡟⠒⠲⠶⡷⣶⣋⣉⣀⣀⣀⣀⣀⣀⣰⡟⢤⣤⡿⣳⣾⢯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⢾⣧⡻⣷⣄⠊⠛⣦⣄⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣴⡟⠛⢀⣴⢟⣽⡿⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠳⣝⡏⠈⠻⣷⣄⡀⠙⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⢶⠛⠙⠀⣠⣶⢟⣵⣿⢟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠙⠻⢷⣦⣄⣀⠀⠉⠉⠉⠍⠉⠉⠁⣀⣠⣤⣶⢿⣫⣷⡿⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠙⠦⣄⡠⣀⡈⠉⠛⢛⣻⡿⢿⠿⢿⠿⠛⠛⠉⣁⣠⠿⣛⡽⠚⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠽⣶⣾⣿⡿⠿⠿⠷⢶⣖⣛⠯⠽⠒⣋⣥⠴⠖⠛⠉⠉⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠶⠖⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢹⣄⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠂⢀⣾⣿⣿⠿⠿⠛⠛⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠞⠽⡆⠀⡟⢝⢢⣠⡤⠄⠓⠀⡂⠀⠀⠀⠹⡄⠀⠀⠀⠁⡤⣤⠈⠿⠟
⠀⠀⣤⢤⠀⠀⠈⠀⠀⠙⠛⡿⡮⢤⣹⢼⡥⠞⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⢄⡀⠈⠀⠀⠄⠙⠂
⠀⠀⠛⠁⠀⠀⠀⠀⢀⠀⠀⣧⣥⠴⢺⡾⡍⢓⢶⡿⣤⡀⠀⠐⠛⢋⠁⢸⡇⠀⢣⠀⠀⠀⠉⠁⠠⠊⠀⠀⠀⢀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠛⠷⣕⣾⣠⣹⣯⠞⠁⣀⠀⠀⠀⠶⠶⢯⡼⡷⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠁⠙⠆⢀⡘⣧⢀⡤⠀⠞⡿⢽⡛⠓⠀⠀⣤⡀⣴⡄⠀⠒⠆⠀⠀⠃⠀⠀⠚⠦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠛⣿⢻⣍⡀⠀⢠⠇⠀⠀⠀⡀⠀⠀⡽⢫⡄⠀⢠⡶⠶⢤⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠉⠀⠀⠀⠀⠀⠸⡏⢠⠎⠀⠀⠀⠀⠸⣄⠀⠀⠙⡆
⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠐⡈⠁⠀⠀⠀⠄⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⠛⠀⢀⣤⡀⣸⡇⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠐⡂⠔⣀⠀⠀⠀⠀⠀⣄⢠⠀⣄⢠⠀⡤⢤⡤⢤⢠⠶⡀⣤⢠⡄⠀⣠⣶⡟⡌⠉⠉⠀⠀⠀⢃⡀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⡿⠆⣀⠀⠀⠀⢿⣾⢠⢿⢸⠀⡇⠀⡇⢸⢸⠀⢰⣿⢸⡇⠀⠉⠈⠉⢀⣀⠀⠀⠀⠐⢠⠊
⠀⠀⠀⠰⠉⠉⢲⠀⠀⣸⡧⠸⢣⠆⠀⠀⢸⢻⣸⠉⡷⣄⡇⠀⡇⢸⡞⣄⢾⠹⡖⣇⡀⣠⣶⣿⣿⡇⢀⣷⣦⠀⠈
⠀⠀⢠⠃⠀⠀⠘⠀⠀⢿⣧⣴⢏⡼⠁⠀⠀⠀⠀⠀⠀⡀⠄⢠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠛⠉⠁⠙⢿⣿⣧
⠀⠀⠺⠀⠀⢠⣇⠀⠀⠀⠙⠿⠚⠁⠀⠀⠀⠀⠀⠀⠁⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣈⠉⠉⠀⠐
⠀⠀⠀⣰⡄⠀⠀⠀⠁⠠⢤⡤⠤⠴⠊⠀⠀⠀⣀⠀⠀⠰⠵⠀⠀⠀⡠⠤⠎⠀⠀⠀⠈⢿⣿⠏⢰⣶⣾⣿⣷⠆⠀⠀⢀
⠀⠀⣤⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠁⠀⠀⠁⠀⠘⠛⠛⠉
⠀⢄⣀⡉⡄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⡀⠀⠀⠀⣰⡀⠠⠀⠰⠂⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⠀⠀⠀⠀⢂⡀
⠀⠀⡀⠈⠁⠀⠀⠀⠐⠢⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡉⠁⠀⢰⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠘⠀⠀⠀⠰⠿⡅
⠀⠀⠀⠀⠐⠾⣷⠆⠀⢠⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠏⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠄⠀⠀⡤⢶
⠀⢸⠁⡀⠀⣴⣿⠀⡐⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐⡂⠀⢠⣴⣶⣦⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒
⠀⠛⠛⠃⠄⠝⡇⡈⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⡆⠁⠀⠀⠙⣿⣿⣿⣿⣷⣄⠀⠀⠈⠑⠶⠈⠀⢰⡄⠀⠀⠀⠀⠠⠞⠂
⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⣤⠷⠀⢻⣿⣿⣿⣿⡿⠇⠀⠀⠀⢾⡟⢹⣿⠻⠿⠿⠀⠀⡀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⢀⢀⢁⡙⢊⡒⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⢀⣀⣄⢃⣤⢒⠐⣐⠀⠀⠀⠀⠀⡁
⠀⠀⠀⢜⠀⠆⢦⠰⢤⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠛⢘⢼⢀⠽⠒⡽⠊⠰⢛⠆⠀⠀⠀⠀⠂
⠀⠀⡔⡒⠀⡐⡀⡄⠀⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠊⠘⠀⠃⠈⠁
⠀⠀⠁⢠⠁⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠃⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⠐⠂⠐⢳⢘⢂⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠁⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠈⢠⠤⠤⠰⢀⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⡦⡦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣤⡴⢦⣦⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣮⣾⣶⣬⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣠⡤⠼⠗⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⡤⠤⠶⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠖⠛⠋⠉⠁⢸⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣻⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡏⣄⣀⡠⠤⢲⠚⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣤⡤⠶⠒⢺⠏⠁⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⢀⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⢀⡠⣆⣴⡟⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠴⡶⠛⠭⠠⢠⣏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⡾⡔⠚⠋⡀⠟⢀⣠⣴⣶⣖⣾⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠉⠀⢀⡧⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣗⣊⣥⣴⣾⣿⣿⣿⠿⠛⡿⣿⣿⣿⣋⢀⡀⣀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠈⣛⠛⡛⠋⣋⣯⣍⢓⣻⣷⡎⢿⣻⣯⠙⣿⣿⣿⡟⠛⠶⣶⣿⣷⣞⣉⣀
⠀⠀⠀⠀⠙⠉⠀⠀⡠⠙⣉⣠⣿⣭⣽⣿⣿⡞⢛⣯⣥⣶⣿⣟⡛⠟⢛⣩⣶⡈⠀⣍⣛⣛⠛⠻⣿⣿⡿⢶⣿⣯⣟⡛⠁⡤
⠀⠀⠀⠀⠀⠒⠒⠂⠉⠉⢭⣥⠄⢘⣿⣛⡉⠉⠥⠼⠛⠋⠉⠩⠔⠂⣸⡿⣟⠁⠀⢶⣭⣹⡧⣠⠤⢴⣶⣶⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⠄⠀⠉⠁⠀⠀⠀⠉⠙⠉⠀⠀⠒⠬⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⡀⢤⣶⣂⡔⠒⢦⣤⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠶⠒⠒⠓⠒⢐⣀⣂⣂⣒⣒⠢⠤⠤⢉⣛⠱⢤⡑⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠠⠔⠊⣍⡤⠤⠐⠒⠉⠉⣰⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⣈⠙⠦⣤⡀⢀
⠀⠀⠀⠀⠀⠀⡠⢀⠕⠊⢀⡠⠒⠋⠁⠀⠀⡀⢀⠀⢠⡏⠀⠀⢀⠰⡀⠀⠀⠀⠀⠀⠀⠙⠢⣈⢻⣦⠉⡀
⠀⠀⠀⠀⡠⢊⠔⠁⡠⠒⠁⠀⠀⡀⠀⠀⠈⠀⠀⢀⣾⡇⠀⣀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⢢⣿⠁⠈⡋
⠀⠀⢀⠊⡰⠁⡤⠊⠐⠀⠀⠐⠛⠋⠠⢤⡀⠀⢀⠞⡛⡇⠚⠁⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣷
⠀⠀⠉⡸⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠰⢈
⠀⢀⣶⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡐
⠀⢸⢿⡜⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠂⠀⠀⠀⠐⠀⠠⠌⣠⠇⠀⠄
⠀⠈⢝⡇⠰⠀⠀⠀⠀⠀⠀⠀⢀⢄⠘⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⣰⡟⠀⠀⠈
⠀⠀⠐⡟⢄⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠊⡸⠁
⠀⠀⢀⠀⠀⣛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠁⠄⠀⠁
⠀⠀⠈⢳⣄⠀⠀⠁⠻⠗⠄⠀⠀⢀⣀⣀⣀⣁⣀⡀⠤⡤⠔⠒⠈⠁⠀⠀⠄⠀⢀⠠⠐⠁⠀⡀⠊
⠀⠀⠀⠀⠙⢭⡂⢤⢀⠀⠠⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠈⠀⠀⢀⢹⠏
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡈⠁⠒⠀⠠⠠⠤⠀⠠⠀⠠⠀⠠⠀⠀⠂⠈⠉⠀⢀⡶⠐⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠒⠰⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠂⠉⠉⠉⠢⡀⠀⠀⢀⣀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⡉⠀⠁⠀⢱⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⢋⢰⢆⡆⠀⣼⣡⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠀⠠⠩⠙⠳⢦⣄⣀⣀⢀⣴⣿⣦⣶⡿⣣⣾⣰⡾⠿⠷⢄
⠀⠀⠀⡠⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠉⠙⢻⣿⣿⣿⣷⡴⣤⡀⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠞⢿⢡⣿⣧⡘⠯⡙⠓⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⢀⡀⠀⢈⣉⠽⢋⠀⡠⠋⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡰⠦⠃⠀⠀⢻⡿⠟⠈⠉⡀⠰⠄⠀⠀⠀⠀⠀⠄⠀⠀⠈⢳⡆⠈⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡫⠀⠀⠀⠑⠢⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⢲⣒⣒⢒⣤⣤⢶⣤⣤⡤⠀⠒⢤⣄⣀⡤⠐⠀⣤⢤⣴⡦⣤⣤⡒⣒⣒⡒⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠐⠀⠈⠆⠀⠁⢀⡀⠺⢏⠉⠶⣤⣙⠲⣤⡾⠟⠛⠛⠻⢷⣤⠞⣛⣤⠶⠉⣹⠗⢀⡀⠉⠀⠐⠋⠀⠒⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠎⢀⠴⠀⠀⣠⣲⣀⠀⡯⢫⡇⠀⠓⠀⣠⢉⣽⠋⠀⣤⣴⣄⣤⠀⠹⣿⡉⣀⠀⠛⠀⢸⡏⢽⠀⣀⣞⡁⠀⠐⢤⡀⠳
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⣋⣶⠈⢿⣿⣾⣇⢼⡗⢲⣦⠀⠻⣾⡇⠀⠸⣿⡿⢿⣿⠇⠀⣹⣷⠟⠀⣴⡐⢺⡇⣼⣣⣿⡿⠈⣦⣉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣀⣠⡄⠀⡟⢡⠆⠻⠛⣿⣿⣉⠄⢙⣿⣿⣆⣤⠼⣷⠀⢠⣾⣤⣶⣽⡁⠀⣾⡧⣄⣴⣿⣿⡋⠠⣭⣿⡿⠙⠟⠱⡌⢻⠀⢀⣇⣀⡀
⠀⠂⠠⠐⢉⡽⠟⣿⡋⠘⢣⡀⣰⣤⠛⣄⠙⢳⡤⢄⣘⣩⣥⣤⠼⠗⢺⣟⠱⠽⠿⡝⠺⠧⣤⣭⣌⣃⡤⢤⠞⠋⣈⠳⣤⣄⢀⡜⠃⢙⣿⠡⠯⡉⠀⠠⠒
⠀⠈⠀⠀⠀⠀⠈⢹⣿⣦⠀⠙⣩⡤⠋⠀⠀⠂⠀⠈⠉⠉⠀⡠⠖⣀⠉⠛⠿⠖⠛⠋⣀⠶⣄⠉⠍⠉⠁⠀⠀⠀⠀⠙⢦⡉⠋⠀⣤⣿⡏
⠀⠀⠀⠀⣠⠉⢲⠈⠳⣶⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢰⣷⠟⠁⡞⠈⣤
⠀⠀⠀⠀⠀⠠⢎⠀⠀⠉⡗⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⢸⠉⠀⢀⡱⠄⣀
⠀⠀⠀⠀⠀⠀⡙⠁⠀⢿⠇⢠⣿⣥⠆⠀⠐⠂⠤⠤⢴⡄⣶⠄⠛⠀⠀⠈⠀⠀⢠⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣿⡄⠘⡿⠀⠀⠋
⠀⠀⢸⠀⠀⠈⠣⣤⠔⠋⠀⢸⣇⠷⢶⠀⠀⣀⣀⣴⡶⠻⣄⡀⠀⠶⠀⠀⠀⠀⣾⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡶⡛⢼⡇⠀⠙⠢⢤⠜⠀⠀⠀⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣾⠛⣁⣋⡟⠠⠐⣿⠉⠉⠀⠀⠋⠀⠀⢀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣙⣈⠛⣷⡆⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⢰⡇⡠⢾⠑⢦⡔⠉⢤⣿⡙⠁⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⠠⠄⠀⠂⠒⢀⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢋⣿⡄⠉⢣⡴⠈⡿⢄⠸⣆
⠀⠀⠀⢹⡆⠁⠀⠀⠀⠛⣄⠀⢰⡁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⡀⢠⣄⡀⠀⠀⣈⣡⣀⠕⢀⡀⠀⠀⠀⠀⠀⠈⡶⠀⣠⠛⠀⠀⠀⠀⢰⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⠿⢵⡆⠑⠀⠀⠀⠀⡀⢀⠌⠁⢰⣆⣙⡉⠈⠹⠟⠁⠀⠀⠀⢹⡤⠤⠊⠘⠋⠀⠀⠀⢀⠀⠈⠱⣮⠿⠦⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⡆⢀⣤⢀⠰⣆⣷⢾⠗⠁⠂⠀⠀⠀⠁⣾⠛⣀⡜⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠲⡷⣴⣳⠞⢀⣰⣀⢠⠇
⠀⠀⠀⠀⠙⣆⠈⠉⠰⠟⢿⠃⣠⠆⠀⠀⠀⠀⠀⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⡟⠛⠂⠘⠁⣠⠃
⠀⠀⠀⠀⠀⠟⠓⠠⠤⣴⠞⣰⠏⡎⡀⠀⠀⠀⠀⣸⡇⢰⡆⠀⠀⠀⠀⠀⢠⠀⢀⠄⠀⠀⠳⠞⢻⡀⡄⠧⡀⠀⠀⠀⠇⠹⡆⢻⣦⠤⠀⠚⠙
⠀⠀⠀⠀⡀⠀⠈⢠⠛⠛⠛⢿⡿⢻⡇⠀⡄⠀⣶⠘⡿⠊⠈⡇⠀⠀⠈⢀⣀⣹⣯⢶⣴⠋⢰⡂⢻⡴⠂⡾⠋⠀⠀⠸⡟⢿⡿⠛⠋⠛⠃⠁⠀⠠
⠀⠀⠀⡀⠀⠀⠒⣾⣿⣿⣿⣿⣡⡏⠀⠀⣷⣀⡉⠀⡇⢀⠀⣁⠠⣼⣿⣿⡇⢸⠅⠌⠉⠀⢸⠁⠉⠀⠀⠁⢀⠀⠀⠀⠘⣌⣳⣿⣿⣷⣾⡒⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠈⡹⢋⣿⠷⠛⣹⠇⠀⠀⠙⠛⠀⠀⠀⠙⠿⠋⠳⣾⠟⠋⠀⠀⠐⠀⠈⠀⢈⠀⠀⠈⠀⠀⠘⠀⠀⠀⠈⣿⡙⠟⣽⡎⠻⣁
⠀⠀⠀⠀⠀⠘⠋⠀⢺⣄⣀⣹⡯⣤⣀⠀⠀⣾⣦⡿⡄⠀⠀⢲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⣯⡁⣠⣾⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠉⢳⠞⡇⢿⣌⠿⣄⠀⠁⠀⠀⠘⡿⢏⠤⣀⣠⠊⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⢀⡿⢇⣿⠸⡗⠲⠉
⠀⠀⠀⠀⠀⠀⠘⡀⢻⣿⡀⢶⡜⣆⠀⠀⠀⠀⢹⡌⠀⣿⠟⡠⢀⣄⣻⡄⢹⣿⣄⠉⠙⣷⣶⣀⣷⣆⢠⣿⣍⣡⡄⠀⢀⡿⢰⢀⣻⡟⠁⡆
⠀⠀⠀⢀⣂⣀⠘⠳⡀⠋⠑⣼⣿⣋⡀⠀⠀⠀⠀⢱⣜⣽⣾⣷⣾⣿⣿⣷⣿⣿⣿⣷⣼⣿⣿⣿⢉⣿⣬⣀⣷⠀⠀⢀⣈⣻⣯⡄⠉⢠⠞⠃⢀⣘⣰
⠀⠀⠀⠈⢛⡀⠀⣴⠏⢀⣠⣾⠁⡧⡅⠀⠀⠀⠀⠀⠿⠿⣿⣿⡿⢋⠻⠷⠀⣹⣿⣯⣙⣻⣿⣿⣿⣿⣹⣿⡇⠀⠀⢠⡴⠋⠿⣦⡀⠘⣦⠀⢀⡙⠃
⠀⠀⠀⢀⡄⠀⠀⢿⡀⠘⠣⣤⣤⠳⠀⠀⠀⠀⠀⠀⠀⢠⡜⠻⣷⠛⠛⣉⡉⡀⠉⠉⠻⠿⠷⠾⠿⢿⡿⠿⢦⠀⠀⠀⠜⣢⣤⠔⠋⢀⡼⠃⠀⢐⡄
⠀⠀⠀⠸⠆⠀⠀⢘⠞⠀⠀⢸⣍⠃⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⠊⠀⣼⠛⠆⠐⠀⠰⠆⢰⠊⠛⠳⠴⠛⠀⠀⠀⠀⣯⡽⠀⠀⠘⠆⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣁⡞⠀⠀⠀⣌⢹⠀⠀⠀⠀⠀⠀⠀⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠄⠀⠈⠂⠀⠀⠀⠀⡼⢩⣄⠀⠀⢸⣠⠎
⠀⠀⠀⠀⢠⡔⢿⡷⢀⣴⣤⢹⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣺⣠⣴⣄⢸⣯⢓⣤
⠀⠀⠀⠐⢳⠋⠀⣷⠈⠉⠐⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠚⠭⣥⡄⠹⣧⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠲⠛⠀⠀⠉⢰⡇⠈⢶⢓
⠀⠀⢀⡏⡋⢀⡀⣉⠀⠀⢰⣶⠶⠂⢀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢄⠙⠄⡶⣖⣺⡁⢠⠞⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⢲⡖⠀⠀⣀⢁⡀⠈⡋⡇
⠀⠀⠈⢀⡇⠀⠙⠻⠟⠳⠜⢁⡴⠘⠛⠻⠋⠀⠀⠀⠀⠀⠀⠱⡴⢶⠃⡱⣟⣋⣀⠿⣦⡗⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠋⢤⣌⠁⠔⠛⠛⠋⠁⠀⡇⠄
⠀⠀⠀⢠⡗⣤⣆⣠⡤⠂⡰⢏⠀⠄⢒⡦⢀⡀⢤⠴⠸⣴⢄⢀⡄⢻⣿⢷⣌⣁⣠⣶⡾⣠⣄⡀⢴⡶⠠⠆⠄⣀⠠⡖⢢⠄⢘⢣⠀⠲⣤⣰⣦⡘⠤⠂
⠀⠀⠀⠀⠀⢡⣌⣩⠀⢠⣵⣾⢷⣛⡿⢗⢫⠴⣾⡷⡖⣟⣫⡤⠺⣿⣿⣷⣤⣬⣷⣻⣿⣗⠢⣼⣗⢶⡲⣟⠶⡭⢒⡿⣛⣚⢫⣶⣇⠀⢬⣉⡄⠁
⠀⠀⠀⠀⠀⠄⢠⡏⠀⠘⠾⠷⢏⣀⡙⣋⣦⡘⠶⠿⣿⢬⣧⣏⠷⡨⠛⡛⡻⢟⠛⠙⢯⡈⣏⣯⣤⢽⠟⠿⢎⣡⣞⣍⣁⣈⡿⠳⠎⠀⠘⣥⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠐⠛⢣⠀⠙⠳⣝⣃⣐⡥⠞⠁⠸⠂⠀⠈⠀⠙⠊⠁⠁⠀⠀⠋⠀⠑⢮⣃⣔⣛⠵⠛⠓⢈⠛⠓⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠈⠲⠋⠀⠀⠀⠈⠑⠂⠁⠀⠁⠀⠈⠳⠊⠀⠀⠀⠀⠀⠘⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠒⢲⠈⠉⢹⡍⠉⠁⡖⠂⠠⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⡊⠀⠀⠃⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠘⠀⠈⢱⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠙⢦⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⡏⣿⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣁⡴⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠁⠈⠻⣷⣄⡀⠀⠀⣀⠥⠐⠂⠉⢹⠇⣿⡉⠉⠐⠂⠭⣀⠀⠀⢀⣤⣾⠟⠀⠈⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠄⠀⠀⠀⠀⠙⢮⠻⣶⣊⠀⠀⠺⠇⠀⣸⠀⣿⡇⠀⠸⠇⠀⠀⣱⠶⣫⡾⠁⠀⠀⠀⠀⠰⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⡠⠳⣌⠻⣷⣤⡀⠀⠀⣿⠀⣿⣧⠀⠀⢀⡴⠚⣡⣾⠛⢄⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⢤⡄⡜⠁⠀⠈⢧⡈⠻⣿⣦⣄⡇⠀⣿⣿⣠⠖⠋⣠⣾⡟⠁⠀⠈⢆⢠⡤⠀⠀⠀⠀⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠀⠀⠀⠀⠀⠀⡸⠀⠸⠇⠀⠀⠙⣄⠈⠻⣿⠇⠀⣿⣿⡅⣠⣾⡿⠋⠀⠀⠺⠃⠈⡆⠀⠀⠀⠀⠀⠀⠤⡆
⠀⠀⠀⢄⠤⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣆⣀⣠⣤⣤⣤⣤⣾⣷⣶⣿⣷⣄⣿⡿⠛⠛⠛⠷⠤⠤⠤⣤⣄⣀⣰⣀⡀⠀⠀⠀⠀⠀⠁⠀⡄⢠
⠀⠀⠀⢀⡖⣿⠀⠀⠀⠛⠒⠺⠿⠿⠿⢿⣭⣝⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠿⠿⠓⠒⠾⠀⡼⢉⠁
⠀⠀⠀⠈⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠉⠉⠉⠉⣹⣶⣶⢾⣿⣿⠈⢻⣟⠛⠻⣏⠉⠉⠉⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⢀⡘⡀⠸⠇⠀⢀⣴⣿⠟⠁⣸⣿⣿⠀⢸⣿⣷⣄⠘⢦⡀⠀⠺⠆⢠⢃⡀⠀⠀⠀⠀⠀⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠀⠀⠀⠀⠉⠁⠱⡄⠀⣠⣿⠟⢁⡴⠊⠁⣿⣿⠀⣸⠈⠛⢿⣷⣄⠱⣄⠀⣠⠃⠈⠉⠀⠀⠀⠀⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢈⣾⠟⣡⠞⠉⠀⠀⠀⢿⣿⠀⡟⠀⠀⠀⠉⠻⣷⣌⢳⡁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⠁⠀⠀⠀⠀⣰⣟⡵⠛⠣⣀⠀⠻⠃⠀⢸⣿⠀⡇⠀⠘⠇⠀⣠⠜⠛⢷⣝⣆⠀⠀⠀⠀⠘⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠄⢠⡾⠟⠁⠀⠀⠀⠀⣍⡂⠂⠤⢼⣿⢸⠥⠄⠖⢀⣭⠀⠀⠀⠀⠈⠻⣷⡀⠠⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠋⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⢙⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡆⠀⠀⢀⠀⠀⢸⡇⠀⠀⡀⠀⠀⢲⣀⡠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⠠⠄⢼⠅⠀⠀⠓⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄⠀⠀⠀⠀⡰⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⡠⠖⣊⣉⣉⣉⣙⡧⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⣷⣿⠀⠀⠀⠀⣿⣾⡄⠀⠀⠀⠀⠀⠀⢀⣤⠀⢼⣋⣉⣉⣉⣑⠲⢄
⠀⢠⠊⡴⠛⠉⠀⠀⠉⠉⡇⠀⣆⠈⠓⢄⠀⠀⠀⠀⠀⣳⡁⠀⠀⠀⠀⢈⣞⠀⠀⠀⠀⠀⡠⠚⠁⣰⠀⢸⠉⠉⠀⠀⠉⠛⢦⠑⡄
⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠳⣄⡀⠑⠢⠄⠤⢔⡉⠀⠀⠀⠀⠀⠀⢝⡢⠤⠠⠔⠊⢀⣠⠞⡹⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⡀
⠀⠈⠌⡆⠀⠀⠀⠀⠀⠀⠙⣤⠈⠓⠬⢝⣳⠦⠦⠖⢋⡆⡀⠀⠀⠀⠀⢀⢰⡝⠲⠴⠴⣖⡋⠥⠚⠁⣤⠋⠀⠀⠀⠀⠀⠀⢰⠡⠁
⠀⠀⠀⠸⠀⠀⠀⡠⠔⢚⣉⡛⠛⠶⣤⣄⣠⣰⠤⢶⠏⠀⡇⠀⠀⠀⠀⢸⠀⠹⡷⠤⣆⣄⣠⣤⠾⠛⠛⣉⡓⠢⢄⠀⠀⠀⡇
⠀⠀⠀⠘⠀⢀⠞⡠⠊⠉⠉⠉⠓⢦⣀⠙⠒⠒⠒⠁⢀⡴⡇⠀⠀⠀⠀⠸⢦⡀⠈⠒⠒⠒⠋⣀⡴⠚⠉⠉⠉⠑⢤⠳⡀⠀⠃
⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠖⠚⠉⡠⠁⠀⣼⢇⠀⠈⢄⠉⠓⠲⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠈⠜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⡼⠁⠈⢧⣀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠃
⠀⠀⠀⠀⠀⠀⠈⠪⢆⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣀⡤⠖⠉⠀⠀⠀⠀⠉⠲⢤⣀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⡴⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠔⢉⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⡉⠲⡄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠡⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢀⣀⣀⣰⣿⣀⣄⣀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⣀⣠⡶⠟⢻⠉⠁⠀⡙⣿⡁⠀⠉⢹⠛⠵⢦⣤⣀⡤⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⣠⡴⠛⢏⠁⠀⠀⠘⠀⣀⣀⠃⣿⣇⣀⠀⠈⠀⠀⠀⢈⠟⠷⡤⢀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡝⠁⡀⠀⠈⣂⠤⠒⠊⠉⠀⠘⠀⣿⣻⠀⠈⠉⠒⠠⠄⡊⠀⠀⢀⠛⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠁⡤⠜⢉⠔⠉⠀⠀⠀⠀⠀⠀⡸⠀⣿⣿⡄⠀⠀⠀⠀⠀⠈⠐⢄⠙⢷⠄⠑⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢎⠀⠀⢀⠔⠉⠳⣦⡀⠀⡠⣔⡲⠘⡇⠀⣿⣿⡿⠴⣒⡤⡀⠀⣠⣴⠋⠑⢄⠀⠀⢈⢶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠁⢀⠎⠀⠀⠀⢉⡻⣿⣶⡉⠀⢸⠀⠀⣿⣿⣿⠀⠀⣁⠞⣫⣟⠁⠀⠀⠈⢂⠀⠁⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⠀⠀⡌⠀⠀⠀⢀⣊⠟⢊⠻⣿⣦⣌⠀⠀⣿⣿⣿⡤⠚⣡⣾⠟⢟⣢⠀⠀⠀⠈⣄⠀⠀⠘⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⢘⠀⠀⠀⠀⢾⠃⠀⠀⢡⡈⠻⣿⣆⠀⣿⣿⠏⣠⣾⣿⠃⠀⠀⢣⠆⠀⠀⠀⠸⠀⠈⠉⢩⡄
⢤⡄⣀⠀⡄⠀⠀⠀⠀⡇⠀⢀⣀⣃⣠⣤⣤⣾⣷⣶⣾⣿⣿⣿⣶⣬⡿⠛⠉⠛⣾⠟⠋⠁⠉⠉⠐⠚⠛⠦⠠⠤⣀⣇⣀⠀⢈⡗⠀⠀⠀⣤⠤
⠈⣷⠙⣦⠃⠀⠴⠶⠶⣿⣿⡿⠿⠿⠷⠿⠿⠟⠻⠟⠛⠿⠛⠿⠛⢻⠀⢸⣿⠆⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡷⠶⠶⠆⣹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡏⠑⠒⠂⠰⣤⠤⠀⢀⣀⣀⣤⣾⢷⣤⣤⢴⣟⠻⢿⣿⣿⡿⠿⢿⣿⠛⠛⠋⠉⡍⠉⠀⢸⡇⠀⠀⠀⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣄⠀⠤⠱⠀⠀⠀⠀⢛⣆⠀⠀⣼⣿⠟⢁⣾⣿⡇⠈⢿⣷⣄⠙⢄⠀⢀⣚⠃⠀⠀⠀⢰⠡⠄⢀⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣵⡄⠀⠀⢇⠀⠀⠀⠀⢡⣷⣾⠟⣡⠔⢻⣿⣿⡇⠀⢀⠛⢿⣷⣌⢲⣧⠉⠀⠀⠀⢀⠎⠀⠀⣠⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣀⡠⠌⢆⠀⠀⠀⣠⣟⣥⡾⣁⡀⢸⣿⣿⡇⠀⠸⠀⣀⡽⣻⣷⣅⡀⠀⠀⢀⠎⠤⣀⡰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢯⡄⠀⢀⠳⣀⡼⠟⠁⠀⠀⠉⠺⢿⣿⣿⡇⠀⣿⠿⠚⠁⠀⠀⠙⠻⣄⡰⠊⠀⠀⣸⠟⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠃⢆⡈⠳⢀⡀⠀⠀⠀⠀⠀⢻⣿⡇⢠⠃⠀⠀⠀⠀⠀⣀⠤⠊⢤⡗⣀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢷⣄⠀⠀⠀⡈⠑⠠⠄⢀⡀⢸⣽⡇⢰⠀⣀⠀⠤⠐⠉⡀⠀⠀⢀⣴⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠐⠃⣠⣎⡀⠀⠀⠀⠄⠀⠈⣿⡇⡌⠀⠀⠄⠀⠀⠀⡈⣦⡔⠃⠁⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠐⠋⠉⠉⠓⠦⣾⣤⣀⣀⣹⣧⣁⣀⣠⣼⡦⠶⠋⠋⠉⠓⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠉⢹⣿⠉⠈⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢷⡄

⠀⠀⠀⠀⣠⣴⣶⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠒
⠀⠀⣰⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷
⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣦⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦
⡏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢃⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠈⣧⠈⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⣠⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⢳⡄⠹⣿⣷⣦⣤⣀⣀⣀⢀⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠙⢦⡈⠙⢿⣭⢉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢀⣰⠋
⠀⠀⠀⠀⠀⠻⣶⣄⠙⠻⢴⡂⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⡾⠛⠁⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠙⠳⢤⣉⠙⠛⠛⠻⠷⠶⠮⠥⠤⠤⠤⠀⠐⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢠⣤⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢡⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⡀⠤⠄⠠⠤⠄⢀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣠⠔⠉⠁⠀⠀⠀⠀⠀⠈⠐⠢⡀⠀⠘⢿⣦⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡿⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡾⢋⡾⢋⠁
⠀⠀⠀⠀⠀⠀⠉⠲⠄⣀⣀⠀⠀⣀⣀⡀⠀⠀⠁⢀⡴⠋⣰⡟⢠⠀⠘⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣴⠏⠀⠈⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⠀⠰⣀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣼⡟⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣸⣿⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⣿⡇⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡏
⠀⠀⠀⣀⡤⠤⠤⠤⠤⣿⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣷⠀⠀⠀⠀⣾⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣾⠤⠤⠤⠤⢤⣀
⢀⡴⠊⣡⠴⠶⠶⠶⠴⣾⠃⢸⠓⠦⡀⠀⠀⠀⠀⠀⠀⢻⡹⠟⠀⠀⠀⠀⠻⢏⡟⠀⠀⠀⠀⠀⠀⢀⠴⠚⡇⠘⣷⠦⠶⠶⠶⠦⣌⠑⢦
⡞⣰⠏⠁⠀⠀⠀⠀⠀⢸⡀⢸⣷⣄⠈⠳⢄⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⡠⠞⠁⣠⣼⡇⢀⡇⠀⠀⠀⠀⠀⠈⠙⣆
⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢆⠙⢷⣄⡀⠙⠒⠀⢒⡭⡂⠀⠀⠀⠀⠀⠀⢸⢭⡒⠀⠒⠋⢀⣠⡾⠋⡰⠁⢐⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠘⡼⡆⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠑⠢⠭⠿⠷⠖⠚⢋⣼⠁⡄⠀⠀⠀⠀⢠⠈⣧⡙⠓⠲⠾⠯⠭⠔⠊⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢰⢧
⠀⠐⢱⠀⠀⠀⣠⠔⢊⣉⣉⠙⠛⠷⣦⣦⣴⣤⡦⠶⡿⠁⢸⡇⠀⠀⠀⠀⢸⡇⠈⢿⠶⢴⣤⣆⣴⣴⠾⠛⠋⣉⣉⡓⠢⣄⠀⠀⠀⡎⠂
⠀⠀⡜⠀⢀⡞⣡⠞⠉⠉⠉⠙⠳⣦⡈⠙⠒⠶⠒⠋⠠⣄⡿⡇⠀⢰⠆⠀⢸⢿⣠⠄⠙⠒⠶⠒⠋⢀⣴⠞⠋⠉⠉⠉⠳⣌⢳⡀⠀⢣
⠀⠀⠀⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⠴⠤⠦⠼⠛⠁⡸⠀⠀⣼⣧⠀⠀⢇⠈⠛⠧⠴⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆⡇
⠀⠀⠀⠀⠘⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡼⠃⠘⢧⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠃
⠀⠀⠀⠀⠀⠘⢜⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢀⣠⡼⠛⠁⠀⠀⠈⠛⢧⣄⡀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣠⠔⠋⢁⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡈⠙⠢⣄⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠞⢁⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀⠱⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣜⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣑⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣊⠥⠚⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⡀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠶⣤⢄⡴⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠵⣢⢄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠐⠛⠓⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠤⠤⠤⠴⠤⠀⠐⠒⠒⠒⠀⠀⠊⠉⠉⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢖⣤⣀⠤⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠙⡵⠀⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠈⠶⡀⣀⡤⠒⠈
⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠚⢿⡀
⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠊⠁⠀⠀⠀⠈⢷⡄
⠀⠐⠀⠀⠀⠐⠉⠓⠠⣀⠀⠁⠀⠀⠀⢀⡠⠔⠊⠁⠀⠠⠀⠀⠀⠀⠀⡀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠁⠀⠈⠐⢄⡀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣤⡤⠋⠀⠁⢀
⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠈⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠢⠤⣀
⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐
⠀⠀⠈⠙⠶⣄⡀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢈⡝⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⣤⣀⠀⢀⠴⠉⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀
⠀⢉⡿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡴⠋⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠓⠲⢤⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠉⠉⠓⡶⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⡙⠗⠲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣄⣀⠀⠀⠎⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠶⢤⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⡠⠐⠑⡡⠒⢃⠉⠙⠓⠶⢤⣄⣀
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡠⠒⠁⠀⢀⠜⠀⠀⠈⣆⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⣀⠔
⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣀⠔⠉⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⡶⢮⣄⣀
⠀⠀⠀⠩⠉⠓⢦⣄⡀⠀⢀⠆⡠⠐⠁⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉
⠀⠠⠐⠀⠀⠀⠀⠀⠉⣳⡾⢊⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢀⣀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⢣⠀⠈⠑⠒⣤⠼⣄⠀⠄⠀⠀⢀⠄⠠⡀⡀⠠⠤⠤⠳⡒⠉⠀⠀⣸⠟⠉⠉⠓⠒⠠⠄⣀
⠀⢀⡴⠤⠒⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣧⣴⣤⣦⣶⣴⣤⣤⣴⣶⣶⣴⣦⣴⣷⣶⣶⣦⣶⣦⣤⣤⣤⣦⣤⣶⣶⣶⣶⣦⣤⣾⣧⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣾⣄⣀⡀⠀⠀⢀⣀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠠⠾⣿⠧
⠀⠀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣤⡄⠀⠀⣺⣿⠆
⠀⠀⠀⠀⠘⠟⠉⠙⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠻⣿⣿⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠋⠉⠁⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣿⣦⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣶⣶⡤⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣿⣿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀
⠀⠹⢿⡏⠀⠀⠀⠨⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⣾⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⣠⣾⣿⣷⠀⠀⠀⠀⠀⢸⣿⠿⣿⣇⠀⠀⠰⣶⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⠉⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⢸⣿⣿⣦⣠⣤⣤⡄⠀⠀⠀⣤⣤⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣦⣶⣶⣶⠆
⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀
⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢲⣶⣿⣤⡀
⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣠⡄⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⡀⠀⠸⠛⢿⠁
⠀⠀⠀⠀⡿⠋⠁⠀⠀⠀⠈⠀⢀⣴⡀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠘⠟⠃⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣧⣀⡀⠀⠈⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣷⣶⡶⠀⠀⠼⣿⠇
⠀⠀⠀⠀⠰⣾⣿⡶⠄⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠉⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠆⠀⠀⠀⢀⣿⠟⠛⠻⠿⠀⠀⣠⣤⣿⣦⣀⡀
⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⢈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣿⣗⠦⣄⡀
⠀⠀⠀⠀⣀⡴⠞⠉⠀⢘⠵⢻⡧⡙⠢⢝⡳⢦⣀
⠀⣠⡴⠚⣁⣤⠤⢤⣄⠉⡠⢺⡷⢌⡒⠄⠀⠀⠈⠛⣦⣄⡀⠀⢀⣀⣀⣀⣤⡤⠤⠶⠶⣶⣆
⠀⣿⠀⣰⠋⣴⠲⣦⠈⣧⢀⡰⡏⠒⢍⠂⠀⠀⠀⠀⡙⠪⣿⣩⠍⠉⠀⢠⡀⢀⣠⢄⠌⣽⡌⢷⡀
⠀⢸⡀⢻⡀⠙⠶⠋⢠⠇⠉⠀⣿⠓⠤⠀⠀⠀⠀⠀⡉⠢⣸⢁⣔⠀⠀⢀⡽⢿⡁⢀⠜⣿⡘⠀⠹⣄
⠀⠸⡇⠘⣧⠀⠀⢀⡟⠀⠀⠀⠙⠈⠐⢀⣀⣀⠀⠀⢌⠢⣸⡿⠋⢀⡄⠀⠀⠀⠉⡠⢊⡇⢡⠀⠀⠘⢧
⠀⠀⣧⠀⠈⠳⣤⡾⠀⠀⠀⠀⠀⣠⠆⠈⠁⠀⠐⢶⡄⠑⢼⡇⠀⠟⠀⠀⠀⠀⢀⠔⣹⠳⠀⠂⠀⢀⡏
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠁⢦⡈⠃⢰⡀⠀⠀⠀⠀⠤⠊⣹⡄⠁⠀⠀⣸⠁
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣘⠃⠀⠀⢀⡴⠖⠲⠶⣄⠈⠳⠄⠈⠁⠀⢤⣀⡀⠐⠉⣿⠘⠀⠀⠀⡿
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡟⢰⣄⠀⢸⡁⣞⠙⣷⢸⡆⢀⠀⢶⣀⠀⠀⠈⠁⢲⣴⣧⠁⠀⠀⢀⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡈⢀⢼⣯⡳⡜⣇⠉⠛⢁⡞⢀⢸⢀⠀⠙⠀⣀⡀⠀⡼⣿⠀⠁⠀⠀⢸⠃
⠀⠀⠀⢹⢠⡞⢛⣦⡴⠋⠀⡣⣼⡷⢌⠢⠘⢦⣠⠟⠀⡈⢻⠁⣀⢀⠄⠀⠁⢀⣠⣿⠀⠀⠀⠀⣼
⠀⠀⠀⢸⡎⠛⠋⠁⠀⠀⠸⢋⣡⣿⣆⡀⠀⠀⠁⠀⢠⡘⢼⠞⣡⠋⠀⠀⢐⠡⡾⢃⠃⠀⠀⠀⡟
⠀⠀⠀⢸⡇⠀⢀⣠⡤⠖⠛⠉⠁⠀⠈⠙⠓⠲⢤⣄⡀⠑⣼⠖⠁⠀⣀⣀⣥⣾⠳⡀⠂⠀⠀⢠⡇
⠀⠀⠀⠈⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠖⠛⠉⠉⠀⠀⠈⢳⡁⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠉⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢄⢀⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⡀⢀⠄⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⣨⡖⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠰⠀⠀⠸⠀⠙⠣⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⡱⢄⢀⡴⠒⠛⠛⢲⣦
⠀⠀⠀⠀⠀⠀⢊⡴⠒⠲⣦⡁⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⢢⠀⠐⠢⢌⣁⣀⠀⠀⣂⡼
⠀⠀⠀⠀⢀⠃⡟⠀⠀⠀⢈⡇⣅⠔⠋⠀⣠⠀⠀⠀⠀⠀⠈⡆⠀⢤⡀⠈⠻⣭⠉
⠀⠀⠀⠀⠀⢄⠁⠀⠀⠠⣼⢹⣁⣀⠠⠦⠬⠡⠀⣴⡀⠃⠀⠛⠀⠤⠀⠐⢦⡼⠃⢰⠤⣀⣠⡰
⠀⠀⠀⠀⠀⠀⠑⠂⠤⠖⢻⠋⣁⡥⠖⠚⠳⣶⣴⣦⣶⣴⡎⢿⡿⣖⣶⣢⣽⣶⠖⠛⢦⡀⠙
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⢋⡔⠉⣀⣤⡶⢛⡏⠈⠙⢠⣌⠀⢐⡇⠀⠉⢻⣯⣿⣄⠀⠀⢁⠀⡀
⠀⠀⠀⠀⠀⠘⠀⡠⠊⠤⢖⣴⡦⠈⢳⡦⠴⡶⠤⣀⣸⠸⡄⠀⢻⣆⠀⠀⣽⡷⣯⠁⠒⠁⡰⠃
⠀⠀⠀⠢⠔⠒⠩⠄⠇⣀⡿⠋⠀⠘⣔⡇⠀⡇⠀⢈⡿⠀⠹⣄⠀⠫⣷⣞⡿⣺⠉⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢽⢇⠀⢀⣼⡿⠇⠀⣇⠀⠸⡇⠀⠀⡟⠳⡤⠤⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⠋⣉⡩⠊⠀⠀⠸⡄⠈⣿⡀⠀⢡⡀⢂⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠻⣦⣀⣑⣤⣉⣙⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣈⣁⡥⠞⠉⠳⠦⠤⠂

⣿⡟⠀⠀⣰⣿⣿⠃⠀⢀⣾⣿⡿⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠈⠙⢿⣿⣷⣄⠀⠀⠻⣿⣿⣆⠀⠀⢻⣿⣷⡀
⡿⠀⠀⣰⣿⣿⠃⠀⢠⣿⣿⠟⠀⠀⣰⣿⣿⠟⠁⠀⣠⣴⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣄⠀⠀⠙⢿⣿⣷⡀⠀⠘⣿⣿⣦⠀⠀⢻⣿⣷
⠁⠀⢰⣿⣿⠃⠀⢠⣿⣿⠏⠀⠀⣼⣿⡿⠃⠀⢀⣼⣿⡿⠛⠁⠀⢀⣤⣴⣶⣾⣿⣿⣿⣶⣶⣤⣀⠀⠀⠙⠿⣿⣿⣄⠀⠀⠻⣿⣿⡄⠀⠈⣿⣿⣇⠀⠀⢻⣿
⠀⠀⣿⣿⡏⠀⠀⣾⣿⡟⠀⠀⣼⣿⡿⠁⠀⣠⣿⣿⠟⠀⠀⣠⣾⣿⣿⠿⠛⠋⠉⠉⠉⠛⠻⢿⣿⣿⣦⡀⠀⠙⢿⣿⣧⠀⠀⠹⣿⣿⡄⠀⠘⣿⣿⡆⠀⠘⣿
⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⠁⠀⢰⣿⣿⠋⠀⢀⣾⣿⡿⠋⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠈⠻⣿⣿⣄⠀⠈⢿⣿⣧⠀⠀⢹⣿⣧⠀⠀⢹⣿⣷⠀⠀⢹
⠀⣾⣿⡏⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⡏⠀⢀⣾⣿⡟⠀⠀⣠⣾⣿⡿⠿⠿⠿⣿⣿⣦⡀⠀⠙⣿⣿⡆⠀⠈⣿⣿⡇⠀⠈⣿⣿⡆⠀⠈⣿⣿⡆⠀⠸
⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⢰⣿⣿⠁⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⣰⣿⣿⠋⠀⠀⡀⠀⠈⢻⣿⣷⠀⠀⢹⣿⣿⠀⠀⢹⣿⣷⠀⠀⢿⣿⣇⠀⠀⣿⣿⡇
⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⣿⣇⠀⢀⣾⣿⠆⠀⢸⣿⣿⠆⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇
⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠘⣿⣿⡄⠀⠸⣿⣿⡀⠀⢸⣿⣿⡄⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⣸⣿⣿⠀⠀⣸⣿⣿⠀⠀⣸⣿⡿⠀⠀⣾⣿⡏⠀⠀⣿⣿⡇
⠀⢻⣿⣧⠀⠀⢿⣿⣇⠀⠀⢿⣿⣇⠀⠀⢿⣿⣧⠀⠀⠻⣿⣿⣄⠀⠀⠈⠉⠉⠀⠀⢀⣴⣿⣿⠃⠀⢠⣿⣿⠇⠀⢀⣿⣿⡇⠀⠀⣿⣿⡇⠀⢀⣿⣿⠇⠀⢠
⠀⠸⣿⣿⡀⠀⠸⣿⣿⡀⠀⠘⣿⣿⡄⠀⠈⢿⣿⣧⡀⠀⠉⠿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⠟⠁⠀⣠⣿⣿⠟⠀⠀⣼⣿⡿⠀⠀⣸⣿⣿⠀⠀⣸⣿⣿⠀⠀⣸
⠀⠀⢿⣿⣧⠀⠀⢻⣿⣷⡀⠀⠹⣿⣿⣄⠀⠈⠻⣿⣿⣦⡀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠉⠀⠀⣠⣴⣿⣿⠋⠀⠀⣼⣿⡿⠁⠀⢠⣿⣿⠃⠀⢀⣿⣿⠇⠀⢀⣿
⡄⠀⠈⣿⣿⣆⠀⠀⢻⣿⣷⡀⠀⠙⣿⣿⣦⡀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⡿⠛⠁⠀⣠⣾⣿⡟⠁⠀⣠⣿⣿⠏⠀⢀⣾⣿⡟⠀⠀⣼⣿
⣷⡀⠀⠘⣿⣿⣆⠀⠀⢻⣿⣷⣄⠀⠈⠻⣿⣿⣦⣀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⢀⣠⣾⣿⡿⠋⠀⠀⣰⣿⣿⠋⠀⢀⣾⣿⡟⠀⠀⣰⣿⣿
⣿⣷⡀⠀⠘⣿⣿⣦⡀⠀⠙⣿⣿⣦⡀⠀⠈⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠋⠀⠀⣠⣾⣿⡟⠁⠀⢠⣾⣿⡟⠀⠀⣰⣿⣿⠃
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⡜⣆⣀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢠⡆
⠙⣤⠁⠡⡜⠁⠀⠀⠈⠳⠀⠀⣩⠋⠀⠀⠀⠉⢛⡽⡻⠋⠀⠀⠀⠀⢩⠰⠆⠅⠁⠀⠀⠀⠑⠀⠀⡈⠉⠀⠀⠀⠘⢻⡭⠶⠉⠁⠀⠀⠈⠻⡭⠀⠈
⠀⠷⠊⠑⠇⠀⠀⠀⠀⠸⠊⠁⠺⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠀⠀⠀⠀⠀⠛⠁⠙⠂⠀⠀⠀⠀⠘⠃⠈⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⢖⢣⢗⠆⠀⠀⠀⠀⠛⣟⠙⡴⠂⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠘⣭⠁⠈⣭⠃⠀⠀⠀⠒⠆⠉⠲⠂⠀⠀⠀⠐⠖⠈⠐⠛⠂⠀⠀⠘⢭⠁⠀⢩
⠀⠘⠁⠑⠀⠀⠀⠀⠀⠸⠃⠛⠆⠀⠀⠀⠀⠀⠶⠀⠸⠀⠀⠀⠀⠀⠻⠖⠲⠟⠀⠀⠀⠀⠀⠟⠈⠳⠀⠀⠀⠀⠀⠴⠃⠸⠇⠀⠀⠀⠀⠠⠕⠒⠭

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⢖⣚⣓⠖⠀⠀⠀⠀⢶⣾⣿⣶⠆⠀⠀⠀⢈⠉⠀⠈⡡⠀⠀⠀⠠⣄⠁⠀⠒⠂⠀⠀⠀⠠⣤⠻⡤⠀⠀⠀⠀⠰⣖⠋⢓⡶⠀⠀⠀⠰⢦⠈⠀⠒
⠀⠘⠛⠛⠀⠀⠀⠀⠀⠰⠿⠻⠧⠀⠀⠀⠀⠀⠡⠤⠄⠃⠀⠀⠀⠀⢀⠤⠀⢣⠀⠀⠀⠀⠀⠛⠛⢃⠀⠀⠀⠀⠀⠺⠖⠾⠆⠀⠀⠀⠀⢠⠔⠀⢷

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣄⠊⠂⣤⠄⠀⠀⠠⡆⠀⠈⠀⡦⠀⠀⠀⢤⠐⠁⠓⣠⠀⠀⠀⢰⣟⠃⠘⢻⡆⠀⠀⠀⢤⡀⠃⢤⠄⠀⠀⠀⠤⠀⠀⣀⠠⠄⠀⠀⠠⣤⠘⠑⢤
⠀⣸⠴⢮⡅⠀⠀⠀⠀⢰⡀⠀⣀⠀⠀⠀⠀⠀⣇⠤⣘⡅⠀⠀⠀⠘⢿⣤⣤⡿⠃⠀⠀⠀⠀⡤⠀⢦⠀⠀⠀⠀⠀⡁⢲⣿⡗⠀⠀⠀⠀⢨⡤⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⡠⠧⣀⡀⠀⠀⠀⣀⠴⠋⠢⢀⠀⠀⠀⢀⣀⣰⣀⠀⠀⠀⠀⢀⡠⠞⠀⠳⢆⠀⠀⠀⣀⠠⠇⠤⢤⠀⠀⠀⠀⠚⠁⠁⠙
⠀⠠⠛⢏⠀⠀⠀⠀⠀⠈⡧⢠⡍⠀⠀⠀⠀⠀⢆⣀⣰⠃⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⢹⠀⣀⠐⡏⠀⠀⠀⠈⠓⣠⠐⡆⠀⠀⠀⠘⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉

⣀⠤⠎⠣⠤⡀⠀⠀⠀⣀⣰⢧⣀⡀⠀⠀⠀⢀⣀⣾⣄⣀⠀⠀⠀⠀⠤⠎⠱⠤⠀⠀⠀⠀⣀⠀⡗⢀⡀⠀⠀⠀⣀⠠⠏⠡⢀⡀⠀⠀⠀⡀⢠⢇⣀
⠘⡆⠀⠀⡖⠁⠀⠀⠀⠙⣆⡀⣞⠁⠀⠀⠀⠈⣿⣥⣿⠋⠀⠀⠀⠈⡢⠀⠀⢔⠁⠀⠀⠀⠉⣃⠀⣍⠁⠀⠀⠀⠉⣷⢀⡀⡞⠁⠀⠀⠀⠙⢊⡺⡍
⠀⠓⠉⠑⠂⠀⠀⠀⠀⠘⠉⠈⠉⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠀⠙⠋⠉⠊⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠘⠉⠀⠉

⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡰⢳⣀
⠀⠨⠀⠈⡄⠀⠀⠀⢠⠀⣻⢿⠃⡠⠀⠀⠀⠑⠄⠀⠀⠌⠀⠀⠀⠈⢫⠀⢈⡝⠁⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠈⢣⠰⠷⢠

⠈⢦⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠈⠎⠀⠀⠀⠀⠀⣇⠀⠠⠢⠂⠀⠀⠀⢸⡀⠀⠀⠀⡸⠀⠀⠀⢀⡼⠁⠀⠀⡨⠳⣄
⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⠤⠶⠒⠒⠚⠋⠉⠙⢆⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣰⠃⠀⠀⢠⠞⠀⠀⠠⠊⠀⠀⡈
⠀⠀⠀⣳⠀⠀⠀⢀⡠⠴⠊⠉⢦⡀⠀⠀⠀⣀⣠⠤⠶⠚⢗⠒⠲⠦⢤⣏⡀⠀⠀⡰⠁⠀⠀⣰⠋⢀⠀⠔⠡⠄⠐⠊
⠀⠀⢸⣁⡠⠔⠛⠁⠀⠀⠀⠠⠀⢱⡖⠚⠉⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⢹⡉⢑⠾⣁⠀⢀⡼⠉⠃⢀
⡠⠔⢺⡁⣳⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠂⠄⢀⠀⠀⠀⠀⠍⠠⠄⣀⡼⢠⠎⠀⠈⣱⢾⣀⠀⠀⠀⠑⠄
⠦⠤⣄⡵⠋⠀⠀⠀⣀⠠⠀⠐⠂⠈⡇⠀⠀⠀⠀⠈⠙⠅⠈⠢⠀⠀⢠⡽⠛⠳⣄⡼⠃⠀⠈⠑⠓⠒⢺⠒⠲⢖⠒⠚⠉
⠀⠀⠀⠙⠚⡦⠜⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠰⠐⠪⣀⡴⠋⠀⠀⣠⢏⠙⠳⢦⣄⡀⠀⠀⡿⠀⢀⠈⠑⢄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⡤⠞⠙⢦⠀⢀⡾⠁⠀⢣⠀⠀⠈⠙⠳⣴⣇⣀⣈⣀⠀⠀⠠
⠀⠀⣀⣀⣮⣤⣤⣤⣄⠀⠀⠀⠀⡶⢺⡶⠖⠒⠚⠛⠉⣁⠠⠀⠀⠀⡵⢏⢀⠀⠀⢘⡆⠀⠀⠀⣰⠋⠀⠈⠏⠉⠉⠙⢛
⠋⠉⠉⠉⡇⠀⠀⠀⣹⠖⢲⡚⠉⠃⠈⡇⠂⠀⠉⠈⠁⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⢸⠓⠦⣀⢰⠃⠀⠀⠰⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢳⠀⢀⣠⡟⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡼⠁⠑⢄⠀⠀⠀⠀⡞⠀⠀⠨⠛⢦⡀⠀⡂⠀⠀⠀⠠⠉
⣀⠤⠴⡖⠺⡉⣁⣸⣇⣤⣤⡬⡧⠶⠶⢾⠶⠒⠒⠚⠚⠛⠋⠀⠀⠀⠀⠢⡀⠀⡼⠃⠀⣀⠀⠀⠀⠈⠳⢧⡀⠀⡠⠁
⠀⠀⠀⢳⠞⠋⠉⠁⠳⡄⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠂⠠⣀⠃⠀⠉⠲⡅
⣤⡤⢤⣿⡀⠂⠀⠀⠀⠘⢆⠀⠀⣷⠒⠚⠒⠒⠛⢹⠟⠲⠤⣀⠀⠀⠀⠀⡰⠁⠀⠐⠠⠄⣀⢀⠴⠉⠐⢄⠀⠀⠈⢦⡀
⠀⠀⡾⠁⠉⠳⣄⠀⠀⢀⡰⢳⡉⠙⡆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⠒⠦⣴⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠒⢀⠀⠈
⠀⡼⠁⠀⠀⠀⠈⢳⡔⠉⠀⠀⠙⣆⢹⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠑⠶⠤⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⣼⠁⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠈⢻⡄⠀⠀⢹⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠐⢀⣀⣀⣉⣒⣤⣄⣀⣤⣤⣤⠤⠶⠖⠚
⠧⢄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠶⡧⠤⠤⢼⠶⠶⠖⠒⠒⢺⠛⠛⠛⠉⠉⠉⠉⣯⠉⠉⠀⠁⠉⠓⢦⣀

⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠐⠒⠒⠂⠂⠒⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢐⡾⠷⠶⠇⠘⠳⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠉⠁⠐⠀⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⢰⡖⠒⠈⠀⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⡌⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠠⠄⠈⠀⠢⠀⠠⠰⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡀⠀⠉⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠁⠀⠠⣾⡀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⣴⡗⠂
⠀⠀⠀⢀⠀⠀⠀⠙⠛⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⠄⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠞⠛⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣠⠐
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠂⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠤⠐⠀⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠈⠂⠀⠀⡀⠈⡛⠀⠀⠤⠴⡃
⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠙⠀⠛⠉⠀⠐⢲⣅
⠀⠀⠀⠀⠐⠈⠀⠀⡜⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⣤⡄⠴⣤⡀⠀⠀⠀⠀⠀⠠⠤⠀⠶⠀⣾⢿⣆⣠
⠀⠀⢠⠀⡀⠀⠀⢴⣿⡾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠸⠟⠀⠽⡇
⠀⠀⠈⠂⠁⡀⠀⠂⠐⠀⠀⠀⠀⢠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠑
⠀⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢹⣆⠀⠈⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠻⠆
⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣄⣤⣤⣤⠤⢄⣀⣄⣄⣠⡤⢦⠤⣄⣄⣀
⠀⣠⣄⣠⡀⠀⣄⣀⣠⣤⣤⣤⣦⣷⣷⣶⣻⡁⠂⠐⢂⠀⠀⠂⠀⡀⠀⠀⠀⡀⣀⣀⣿⣿⣷⣶⣷⣾⣶⣷⣤⣦⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠿⣿⣿⣿⣿⣿⣙⣀⣈⡀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⠉⠉⠉⠙⢉⣻⣿⣿⣷⣾⣷⣶⠖⠀⠠⠂⠁⠀⡀

⠀⠀⢀⠀⢀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⢀⠄⠀⡀⠈⠀⠠⠀⠁⢁⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣭⠀⠀⠀⠀⠀⠢⣤⣥⡤⠂
⠀⠉⠠⠀⠀⠀⠀⠀⠁⠀⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⣻⣿⣾⠟⠁⢠⡀⠀⠂⠐⠆
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⣤⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠚⠀⠠⠟⠋⠛⢇⠀⠙⠛⠀⠠
⠀⠀⠈⠀⣄⠀⠀⠁⠀⣣⢬⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠞⠙⠇⠀⠀⠀⠀⠀⣀⣀⣠⠃⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠠⣤⠞⠘⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠉⠲⡔⠀⠀⣠⠊⠀⠀⠴⠆⢠⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⢨⣃⣤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠈⠀⠀⢸⣥⠖⠦⣸⡀⠀⠀⣤⣤⣾⣧⣤⡤
⠀⠀⢈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⢇⠀⠀⠐⠐⠀⠐⠀⠀⠀⠈⠀⠀⠀⠈⠡⠀⠀⠀⣹⣿⣿⡏
⠀⠀⠈⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣤⣾⣿⣏⣤⣤⣄⡄⠀⠀⢶⣶⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠋⠁⠈⠓⠀⠀⠈⣇
⠀⠀⠀⠐⠀⢀⡾⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠠⣄⠀⠋⠀⠐⠦⡤⠀⠀⠀⠀⠈⠛⠻⣦⣯⣤⠔⠂
⠀⠀⠲⢶⠶⢋⡴⠟⣻⣶⣦⠶⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⢸⣿⡿⠿⣿⣷⠀⠀⢀⣀⣼⣧⣀⡀⠈⠁⠀⠀⢠⡀⠀⠀⢤⣦⡤⠀⢀⡿⠁⢷⡀
⠀⠀⡀⠈⢶⡿⢁⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠛⠁⠀⠀⠈⠙⠂⠀⠀⢹⣿⢿⡏⠀⠀⠖⠉⠀⠐⠇⠀⠀⠘⠉⠃⠀⠈⠀⠀⠀⠉
⠀⠘⠋⠀⢨⢶⠿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠂⢀⣀⡰⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⡆⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠂
⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠠⣤⠤⠶⠞⢀⠈⠳⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠸⠛⠉⠛⠇⠠⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⢀⡄
⠀⠲⣶⣶⣿⣿⣷⣶⠖⠀⠀⠄⠀⠈⠳⡄⠘⣿⣿⠂⡴⠊⠀⠀⣤⠀⠀⠰⣶⣶⡿⠧⢀⡄⠀⠀⠀⣀⣴⣆⣀⠀⠀⠁⠀⠀⠀⠀⣀⡤⠞⠙⠤⢀⡀
⠀⠀⠈⣿⣿⣿⣿⠁⠀⠂⠀⠀⠐⠂⠀⡇⠀⣁⣉⠀⢧⠀⠐⣾⣿⡶⠂⠀⠈⣹⣮⣶⡏⠀⡀⠀⠀⢙⣿⣿⡁⠀⠀⠀⠀⠀⠐⠀⠈⢲⠀⠀⢰⠋
⠀⠀⠸⠛⠁⠈⠛⠇⠀⠀⠂⠀⠃⠀⠸⠗⠉⠀⠈⠙⠻⠀⠀⠋⠉⠓⠀⠀⠀⠉⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠙⠺⠄

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

⠀⢐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠰⠀⠀⠀⠀⠠⠐⠀⠀⠘⠂⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⡂⢀⣀⠀⢀⠀⠀⡀⢲⠀⢸⡆⣀⢠⠀⠀⠄
⠄⠒⠀⠀⠀⠈⣶⣀⠀⢠⠤⠀⠀⠀⠇⠈⣤⡆⠴⠀⠈⠁⠐⠛⠿⢋⠓⠆⠅⡆⢥⣀⠡⠁
⣶⡔⠰⡂⡀⠀⠈⠉⠀⠀⠀⠀⠀⠰⠖⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⢦⣍⡑⠆⠛⠒⠈⠁⠀⣄⣀
⠉⠛⠒⠛⠋⠀⠀⠀⠒⠶⢖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠙⠷⠶⣦⣤⣴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣳⣶⣤⣄⣀⣀⣐⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⡀⠀⣿⠽⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢂⡀⠀⠀⠀⡜⠀⠀⠠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣭⣿⠉⣷⣦⣅⣀⣀⣀⢀⠀⢘⡇⠀⠀⠈⣀⠀⠠⣀⣑⣤⡶⠂
⠀⠀⠀⠀⣀⣒⡒⢶⣶⣦⣤⣤⣦⣄⣸⣿⣿⣿⣿⡶⠶⠿⠤⠿⠤⠬⠥⠼⠷⣶⣾⣟⣛⠉⣛⠽⣁⡀
⠀⠠⠄⠀⢻⡛⠛⣿⣯⣽⠟⢛⣻⣏⣙⠛⠃⣿⣿⣿⣍⣻⣶⠿⠀⣲⣿⢗⠓⠿⠯⠀⠿⢿⡋⠤⠟⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠈⠀⠰⠴⠂⠨⠤⢈⣭⠉⠷⠾⢤⣀⠈⠑⡊⠁⢤⠘⠻⠿⠓⠂⠈⠁⠐⠂⠀⠠⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠿⣦⣻⣤⡀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠱⣀⣭⡽⠶⠶⢦⣄⣛⣩⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣡⣶⡄⠀⠀⠈⠹⣆⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡼⠁⠀⠀⠀⠀⠀⣤⣸⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢧⠀⠀⠀⠀⠀⢸⡿⣸⢇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⢧⡀⠀⠀⠀⠠⠞⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠔⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣈⣙⠻⠿⣧⣄⡰⣶⣹⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠈⠒⠖⠋⠉⠉⠙⠻⣦⡈⠙⢿⣌⣨⠽⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢲⣷⠈⠀⠀⠀⠀⠀⠀⠘⣿⡄⠘⣿⡅⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢸⡇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣶⣄⢿⡞⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⡴⠃⠐⣡⣾⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣤⣶⣭⠉⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⠙⡄⠀⠀⠀⢀⣈⣀⠀⠀⢤⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡴⠒⠒⢬⢇⢇⣤⠶⠛⠛⠻⡍⠉⠓⢦⡈⠻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⣀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠁⠀⠀⢸⡿⠛⠁⠀⢀⠀⠀⡗⠀⠀⠠⡹⡄
⠀⠀⠀⠀⠀⠀⢀⢸⠰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⠀⠀⠀⠀⠉⠉⠀⠀⠔⢀⠇⡇
⠀⠀⠀⠀⢀⣤⡻⡇⢣⡙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣢⡾⣱⡇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠠⠊⠜
⠀⠀⠀⠀⠀⠩⣾⢂⡴⠿⢦⣙⠲⢤⣤⣤⣤⣤⠴⢚⣩⠞⣫⡆⢿⣿⠘⠿⠿
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠙⠓⠒⠶⠖⠒⠛⠉⠀⠸⠟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢄⣴⠿⠛⠋⡙⠉⢹⣿⡿⣷⣆
⠀⠀⠀⠀⠀⠀⣯⠸⡇⠀⠀⣾⣷⣶⠞⠛⠓⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢧⣌⣒⠄⠙⠿⣿⣄⡀⣀⣸⣿⠇⢀⣀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠶⢿⣿⣿⣿⠿⠛⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⣡⠖⣱⠺⣾⣤⣤⣴⡤⠤⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡃⣠⣾⣿⣶⢿⡀⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢰⢱⣿⡿⠋⠀⠑⠉⠢⡀⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣾⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⡇⣿⡟⠀⠀⠁⠀⠀⠀⠈⠢⡀⠀⠀⢦⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⣿⠠⡀⠀⠀⠀⠀⠀⠀⣄⠈⠦⣀⠙⢦⣆⠫⣀⣘⡇⣀⣤⡶⠿⣿⣽⡧⠌⠻⣿⣿⣿⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣇⠇⢀⡄⠀⠀⠀⠀⠀⠀⠈⠓⠂⢀⣂⣈⠟⠂⠈⢉⣘⢉⣴⣒⡉⠙⠋⠉⠀⠳⡽⣿⣿⣿⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⣿⡄⢀⠠⠀⢀⣀⣀⠀⠀⠀⣀⣤⣾⣿⣿⣦⣤⣄⠼⢳⠉⠀⠀⠉⠀⠀⠀⠀⠀⢇⢸⣿⣿⣧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⣷⡀⢠⠠⠟⠉⣙⣿⡟⢛⡿⠃⠈⠻⣿⣿⣿⣤⣰⡞⠤⢤⣄⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠘⣿⣄⠣⡐⢾⣿⠿⢻⡧⠀⠀⠀⢠⣧⠈⠉⠙⢤⡀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠰⡇⣿⣿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡈⠻⣷⣄⠀⠁⠀⠉⠀⠀⠀⠴⠋⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⣿⠏⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡼⢋⡾⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡢⠀⢀⣠⡴⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣄⡉⠛⠻⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣥⣤⣶⠾⠛⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣦⣄⣀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣮⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠶⠖⠒⠚⠋⠉

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠛⠫⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡘⠀⠀⠀⠙⠫⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⡶⠶⠶⢶⣿⣟⣛⣛⣛⣛⣛⣻⣿⡷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠒⠒⡄⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⠀⢹⠀⠀⠀⡇⠹⠀⠀⡏⠀⠉⠑⢻⠽⣻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠇⠀⠀⠘⠢⡀⠀⡞⠉⠉⢹⠒⠒⠊⠉⠉⠉⠀⠀⡎⠀⡇⡠⢲⢄⣀⣀⣀⡜⠀⠀⢈⠟⠻⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠢⠒⠢⣄⠀⠙⠒⠃⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⠇⠸⠔⠁⡜⠀⠀⠀⡀⠀⠀⠀⠧⣄⣘⠤⠞⣹⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⡏⠓⠲⣄⡸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣠⠔⢃⡔⢙⠆⢀⠇⠀⣰⠋⠈⠑⠄⠀⠀⠈⠀⠱⢤⣿
⠀⠀⠀⠀⠀⠀⠀⣼⢷⢦⠀⠀⠀⠀⠀⡸⠉⢲⠀⢸⠀⠀⠀⠀⠀⠀⠑⢄⡙⠒⠋⠀⢸⠀⢰⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢧⠀⠀⠀⡠⠁⣤⠀⠓⡗⡄⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡏⠀⣇⠤⣒⡂⠒⠚⠀⢠⠠⢄⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣯⣣⢄⠀⠳⠤⠴⠁⢶⠆⠀⢀⠃⢇⠀⠀⣠⠤⢄⠀⠀⠀⡇⠀⢀⠃⠀⠀⠈⣓⣁⠀⠀⠀⠀⠑⡄⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣢⣄⠀⠀⠀⠀⠀⢸⠖⢲⠑⠚⠁⠀⢀⠇⠀⢠⠇⠀⢸⠀⠀⢰⠋⠀⢸⠀⢀⡴⠊⠚⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡢⣄⠀⠀⡞⠓⠁⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⡎⠀⠀⠀⠣⡀⠈⠓⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣕⣤⣇⠀⠠⠤⠤⠤⠤⠤⠷⢧⣤⣤⣤⡧⣀⡀⢀⠴⠁⠀⣏⣉⡇⠀⢀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠷⢾⣽⣖⣦⣄⣀⡠⠒⠒⠋⣾⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠷⢿⣷⣶⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣨⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⠀⣴⣄⡀⠀⠀⡀⠀⠀⠉⠚⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠼⡇⠀⠀⠀⣰⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣤⠀⣀⡄⠠⠀⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠀⠀⠀⠢⠄⠀⠠⢿⡄⠀⠀⠐⠀⣘⡶⠿⠂⠀⠐⣯⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠁⠁⠀⠀⠀⠀⣶⣟⢀⣀⣷⡄
⠀⠀⠀⠠⢤⣤⠀⡀⠀⠀⠤⠤⠴⡞⠦⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠢⠤⠾⠶⠾⠶⠶⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⡀⠘⡀⠤⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠆⠀⠀⠶⡆⠀⠉⠐⠀⠀⡈⢄⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠂⢀⡀⡄⠃⢀⠀⠀⠀⠠⠕⢈⠣⣤⡀⠀⠀⠀⢀⣀⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠡⠀⠀⠈⠑⠀⠤⢀⠴⡄⠉⠀⠠⣭⢡⠉⠰⡇⢠⠈⢳⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢄⠀⠀⠀⠀⠀⠙⠍⠀⢄⣀⠈⣠⢶⣧⣀⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠘⡇⠈⠀⠀⠀⠀⠀⠀⠂⠀⣠⠑⠆⠈⠀⣣⠍⠉⢸⠀⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⣦⣄⣀⢀⠀⠀⠈⠀⠀⠀⠀⢸⣟⢐⡄⣈⡅⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣶⢶⣋⣿⣿⣿⣿⣞⣟⣻⢦⣤⣄⠀⠠⠀⢸⡋⠉⠁⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠼⢋⠟⢩⣾⣽⣯⢩⣿⣿⡛⡟⣿⣿⠛⣿⡟⣶⣺⣷⣶⣶⣾⢳⡶⢶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢼⣳⠀⠉⣌⠀⢿⡐⣷⡾⣁⠘⢠⠬⠒⠳⣃⠻⠌⠩⠛⣤⠀⣹⠛⣻⢻⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠫⢘⠟⢀⡷⠙⡆⡉⠀⠘⠀⠀⢀⠟⠁⠀⣶⠆⠀⣤⣌⠀⠴⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠅⠀⠄⠐⠄⠀⠁⡇⢸⠁⠘⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠐⡈⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⣀⠀⢄⠀⢺⢣⠷⠴⣤⢀⠀⠀⠀⠀⠀⠁⠀⣀⢀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠹⡄⠀⠀⠀⠀⢿⢿⡤⢘⠛⠃⠀⠀⠁⠀⠀⠀⠤⠽⠦⠘⣛⢀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡀⠀⠉⠀⠀⠀⠛⠂⡉⠁⠀⢠⡈⠈⠓⡀⠀⢀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡀⠀⠠⠒⠃⠉⣑⣣⡄⠀⠁⠆⡐⢤⣂⡠⠇⢲⠄⠀⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠑⠊⠁⠊⠒⠈⠁⠈⠉⠠⠀⠒⠦⢤⠀⠀⢁⡉⠀⠞⠀⠀⠈⠛⠁⠀⡁⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠓⠢⠤⡠⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠆⠄⠀⡀⠀⠠⢀⠀⣈⠉⠈⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠁
⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⡀⠀⠂⠀⣠⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠽⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠿
⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠈⠁⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿
⡀⠀⠀⠀⠠⠀⠀⠀⢹⡿⣿⡁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢻⡿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣶⠀⠀⠀⢴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢴⡦⠀⠀⠠⣼⣷⠄
⠀⠀⠀⠤⣽⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⢀⠀⠀⠀⠰⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠃
⠃⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠟⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⢀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⢸⣿⡷⠄⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⣻⣿⡶
⠿⡗⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⢿⠂⠀⠀⠨⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡦
⠀⠿⠆⠀⠀⠀⠀⠂⠀⠀⠛⠙⠂⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠠⣼⣧⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀
⡦⠀⠀⠀⠀⠈⠛⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⢲⣿⠄⠀⠀⠀⠀⠘⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⣶
⠁⠀⠀⢀⣠⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⢀⣄⠀⠀⠀⢀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⢠⣄⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⢰⣀⡀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡿⠿⠄
⡦⠀⠀⠈⠝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⣴⣄
⣴⡄⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠚⠛⠏⠀⠀⠀⢠⣴⡀⠀⠀⠰⣿⣗⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠛⠻⠇
⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⣀⣶⣄⣀⣀⣀⣀⣀⣀⣈⣿⣿⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣦⣀⣀⣀⣀⣀⣀⣀⣈⣿⣯⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖
⠀⠀⠀⠙⠻⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣄⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣴⣾⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⡸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⢃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢠⡟⣀⡾⠋⠁⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⡟⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡜⡿⠁⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡼⠁⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⡼⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⣠⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠉⠉⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⢀⣴⢟⣁⣤⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠸⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠂⠀⢀⣴⣿⣿⣿⣭⣤⠴⠶⠖⢻⣿⣯⣤⣤⣤⣀⣀⣀⣀⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠲⠿⠻⠭⠉⣡⣀⣀⣀⣀⣴⣁⣀⣀⣠⠤⠤⢤⠤⠤⡌⣿⡓⠒⠂⠀⠤⠠⠤⠀⢀⣠⣤⣤⣤⣤⣤⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣛⡛⠻⠿⣯⣭⣄⣀⡈⠃⠸⠧⣬⣍⣀⣀⣀⣀⣀⣀⣀⣀⣐⠆⠀⢉⡿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⡿⠛⠛⠛⠻⢿⣿⣟⠶⠶⠶⠶⣬⣭⣭⣭⣤⣤⣤⡶⠶⠚⠋⣁⣠⡾⠀⠠⠔⢒⣋⣥⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠁⠀⠀⠀⠙⢿⣷⣤⡀⠀⠚⠁⠀⠉⢻⣿⣿⣿⣿⠿⠛⠛⠉⣀⣤⡶⠾⠛⠉⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠀⠀⠀⠀⠉⠻⢿⣟⣓⠛⠀⢀⣠⡟⠈⠙⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⡰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⣆⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣦⡀⠙⠶⢤⢤⣠⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠶⠞⠉⠉⣡⠂⢁⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠝⠳⣦⣄⣀⡘⡉⠁⡉⠁⠀⠀⡀⠀⣀⣀⣠⡤⠖⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣀⡏⠀⠀⠀⠁⠁⠁⠀⠐⠛⠛⠉⠉⠁⢀⣤⣤⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⢤⣀⣀⣀⣀⣀⢀⢀⠀⣠⠴⠈⠉⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠷⡄⠀⠨⠩⠥⠥⠴⠒⠋⠁⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠒⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣾⣖⣤⣀⡬⣌⣤⣾⣡⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠉⠉⠉⢹⣶⢫⣆⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣔⣀⣠⣿⣯⣤⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⣽⡟⠉⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠘⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣻

⠀⠀⠀⠀⠀⣀⣠⣴⣶⣄⠀⠀⠀⣠⡄⠢⠀⢐⣀⠶⢟⣿⣷⣦⣶⣶⡄
⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣦⣺⣛⣼⣩⢶⡇⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠉⠁⠀⠀⢀⠄⠀⢀⣤⣶⣆⣀⣄⣀⣤⣄⣠⣀⣤⣤⣄⣀
⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⢋⡡⠾⠃⢀⣾⠿⠟⢛⣀⠀⠀⠀⢀⣤⣦⣄⢀⣁⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⣷⠀⠀⠈⠃⠀⠀⠈⠁⠀⠀⣴⡿⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠘⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣟⠀⠀⠀⠀⠀⠀⠀⢤⣧⣠⣮⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⠂
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣁⣀⠙⠻⠹⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠆⠴⠃
⠀⠀⠀⠈⢹⣿⡟⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⣶⣦⡴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⢧⣞⠀⠙⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣾⠎⠉⠻⣿⣿⡟⠛⣿⣿⡟⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣇⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣛⠁⠀⠀⠀⢹⡏⠀⠀⠈⡟⠿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⣵⠄⢀⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣘⠋⠊⠀⠘⠲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣿⣶⣦⣤⣶⣶⣶⣶⣶⣤⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀
⠀⠀⠀⠱⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠐⠁
⠀⠀⠀⠀⠁⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀
⠀⠀⠈⠆⠀⠀⠤⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡖
⠀⠀⠀⠀⠀⠀⢂⠁⠀⡰⠃⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⡄⠀⠀⡀⠀⠠⡀⢩⠀⠀⢠⠀⠀⢀⡘⠁⠀⠒⠂⠀⠀⠀⠀⠠⠀⢖⠀⠴⢀⡀⠀⠀⠀⠀⠀⠀⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠂⢰⡇⠀⠀⠓⣮⠒⠀⠘⣧⡄⠈⢅⢀⡀⠲⣆⣒⡆⠀⢠⠊⣤⠈⠀⠂⣈⠀⢋⠁⠀⠀⡀⠀⠾⠂⠀⡄⠀⠀⠀⠀⣀⠀⠀⠼⠶⠧⣄⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠚⠛⠀⠀⠖⠛⠁⠘⠚⠞⠃⠈⠀⠈⠈⠀⠈⠓⠀⠀⠀⠀⠀⠚⠂⠀⠀⠚⠃⠀⠁⠐⠚⠋⠀⠀⠀⠐⠚⠀⠈⠀⠰⠖⠛⠁

⣿⣿⣿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣶⣴⣧⣾⣯⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⡤⠷⠖⠚⠛⢸⡟⠓⠲⠶⢤⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢀⠀⠤⠠⠀⢸⣿⡆⠠⠄⡀⠀⠀⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠫⠀⠄⠁⢀⠤⠚⠁⠀⢀⣄⠀⢸⣿⣧⣀⠀⠀⠓⠀⠀⠈⠀⠀⠈⢳⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠄⠛⣦⣀⠴⠛⠉⠁⠀⢸⣿⣿⠉⠙⠢⣄⣤⠞⠡⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠚⠀⢀⡼⢻⣷⣄⡀⠀⠀⢸⣿⣿⠀⣠⣶⡿⠻⡄⠀⠘⠄⠀⠀⠀⢻⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠇⠀⠀⠀⡌⠀⢀⡞⠀⠀⠹⣿⣿⠀⢀⢸⣿⣿⣿⣿⠟⠁⠀⠹⡆⠀⢨⡀⠀⠀⠈⣧⠁
⠀⠐⣶⢲⡖⠀⠂⠀⠀⠀⠀⣼⣀⣠⣠⣴⣤⣴⣾⣶⣶⣿⣿⣿⣿⡟⠁⠀⠐⠙⡄⠀⠀⠀⠀⠀⠁⠀⠀⠲⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣤⠀⠄
⠀⠀⠹⡆⢷⠀⠀⠀⠉⠋⠉⣉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡍⡄⠀⠀⠺⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⠖⠒⠒⠂⠀⠀⣿⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠀⠀⠈⡄⠀⠳⡆⠀⠐⠀⣤⣤⣾⣶⡭⠔⠚⢿⣿⡟⠛⠛⢋⡏⠋⢩⡍⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠀⠀⠽⡄⢠⣾⣿⠟⣿⣿⡇⠀⠀⠻⢿⣿⣄⢀⡾⠁⠀⡐⠀⠀⠀⢰⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠹⡀⠀⣽⠿⣋⠀⠀⢻⣿⡇⠀⠀⠀⠀⢉⡿⣿⡀⢀⠜⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣄⠀⠀⠀⠈⠻⡁⠀⠈⠓⠲⢼⣿⡇⠀⢠⠴⠚⠉⠀⢀⠹⠊⠀⠀⠀⢠⠞⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣰⠈⠀⠀⠈⠘⠢⢄⣀⠀⣿⡇⠀⠀⢀⡀⠄⠒⠀⠀⠈⠀⢄⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠙⠲⣄⡀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠉⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠨⠝⠲⢤⣄⣀⠀⠀⢸⡇⠀⠀⠀⣀⣀⡤⠶⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠙⠛⡇⠘⠛⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢖⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠉⣩⣿⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣤⡆⣀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠚⢛⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⢠⡖⠉⠁⠀⠀⠀⣠⣴⠶⠒⠤⣀⠀⠀⠀⢠⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣷⡿⣓⠏⠉⠉⠓⢾⣿⣧⣶⠴⠤⠄⠉⠒⣺⣿⠿⠒⡛⠋⢉⡒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡝⣼⠃⠀⠀⠀⠀⠀⢹⣯⡞⠉⠉⠉⠛⣩⡟⠁⣀⡧⠞⠛⠉⠛⠳⣄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⣿⠀⢀⠀⠀⠀⠀⠈⣿⡇⠀⢀⡴⢾⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⣽⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⢷⣾⠀⡀⡀⠀⠀⠊⡉⢉⣡⣴⠟⣵⣡⡴⠒⠉⠉⡉⠉⠒⠶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢈⣄⣱⠀⡀⠹⠆⠀⠈⠇⣌⠙⠛⣯⣷⣿⣷⡾⠞⣲⡗⠓⢻⣤⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠛⠛⠉⠋⠀⠳⠀⠀⠀⠀⠀⠀⠘⢛⣛⣿⣿⡛⠛⠒⠚⠛⠒⠚⠱⠿⣧⡥⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⡀⠀⠀⣀⣠⡄⢀⠄⠀⠀⠀⠀⠀⠀⢲⣤⣽⣿⣯⣥⣶⣶⣶⣶⣶⣶⣶⣖⠶⣌⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⣾⠿⠛⠛⠻⣿⣿⣇⡼⠀⠀⠀⠀⢡⣠⡀⠱⣟⠿⠛⠋⠉⠉⠁⠀⠀⢀⡼⣣⠛⠻⣎⣇⢱
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠃⠀⠀⠀⠀⠀⠹⡿⢷⠀⠀⠀⣼⣠⣷⣝⢦⣙⠢⢄⡀⠀⠀⠀⠀⢀⣿⡾⠁⢰⢩⢯⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣲⡄⢧⡀⠀⠀⠀⠀⠀⢠⣯⠏⠀⢀⡾⢿⢿⣿⣿⣷⣮⣕⣦⠈⠑⠦⣄⠀⠈⡏⢣⡀⠈⢻⡾⠇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣿⣦⣌⡉⠑⠒⣲⣦⢾⡏⠀⣰⣡⠞⠁⠀⠀⠉⠙⠚⠿⢮⣙⡢⢄⠀⠑⣦⡘⠲⠬⠭⡅⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠛⠻⢿⣿⠀⣰⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢆⠀⠙⣷⡄⠀⢰⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢽⢻⣿⠀⠀⠀⢰⢫⠭⣍⢢⠀⠀⠀⠀⠀⢱⡄⢸⣷⠀⠈⣜⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣤⡟⡇⠀⠀⠈⠳⢷⣌⣾⣇⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠈⠙⠒⢲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⣿⠟⣠⣷⡤⠤⠤⠤⣼⡟⢣⢾⡄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢺⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡠⠟⡞⠓⠒⠊⠛⠻⠖⠶⠶⠦⢤⡭⢟⢎⣚⡲⢤⣤⢜⣿⢋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠑⠶⠼⠦⠿⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣇⠀⠀⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠐⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢱⣶⡟⢛⡟⠻⣶⡎⠀⠀⠀⠰⠴⠿⠿⠆⠀⠀⢀⠀⠀⠀⣸⠅⠀⢀
⠀⠀⢠⠖⢂⣤⠄⣠⣿⡥⣤⡤⠖⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣿⡃⣑⣶⣷⣎⢈⣿⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠑⠊⠉⠉⢹⠉⠉⠁⠒⠁
⠀⠀⠈⠉⠁⠀⠀⠁⢹⠀⠀⠀⠘⠋⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡠⢻⡟⢅⣠⣿⠁⠀⠀⠲⠒⣻⣿⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠷⣾⣷⠾⠟⢅⠀⠀⠀⠀⠘⢻⣿⠀⠀⠰⡁⠀⠀⢠⣘⠀⠀⠀⢀⡆
⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠑⠄⣠⠀⢸⡁⠀⣠⠈⠁
⠀⠀⠿⡂⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠉⠛⠯⠛⠉
⠀⠀⠀⠘⠦⣄⠀⠀⣸⡄⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢻⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠉⠻⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠛⠁⠀⠀⠈⠁⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡶
⠀⠀⠀⠀⠠⠄⠤⠼⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣰⣀⣁⡈⠀⠀⠀⠀⠀⠴⢂⣀⣀⡸⣃⣀⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡅⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢠⣤⠤⠠⠜⣏⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡦⠀⠀⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀
⠀⠀⠀⠀⣰⣶⣠⢴⣀⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⢠⣄⣷⣶⡶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠡⠁⠙⠁⠀⠘⣇⠀⠀⢰⡀⠀⠀⠀⢘⠃⠀⠀⠀⣀
⠀⠀⠀⣀⣘⠻⣿⣿⣿⣧⡀⠞⡁⠀⠀⠀⠀⠀⠀⠀⡀⠙⡅⠀⢰⣾⣿⣯⣿⣯⣿⠇⠀⠀⠠⣜⣻⣃⣴⣖⣢⣄⠀⠁⢹⠈⠀⠈⠣⡀⡤⠀⢸⡇⠀⢀⡠⠋
⠀⠀⠀⠟⠛⢪⠛⠿⢿⠃⠐⠺⠯⠉⠁⠀⠀⣁⣈⠛⠱⡶⠞⠓⠒⠛⠛⠿⠛⠛⣃⠀⠐⠶⠀⠈⠻⣿⣿⣿⣿⣿⣄⣀⡞⠀⠀⠀⠀⠀⠛⠶⣎⡷⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡟⠀⡀⠀⠠⠴⠀⠀⠀⢀⡀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⣀⣠⡄⠀⠠⢄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⣀⣤⢾⡟⣿⠛⢛⡀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣩⠿⠼⠓⠋⠻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠁⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢀⡀⢴⡶⠚⡿⠇⠀⠀⠸⣗⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡨⠀⢀⣤⣾⡯⣶⠚⣿⡾⣤⣼⡦⠴⠶⠾⣶⡿⠦⠴⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣷⠾⢛⣉⡥⠷⠞⠒⠛⢟⠉⠉⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠠⣄⠸⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣛⠿⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣤⠶⢺⡿⢸⣶⣞⢫⣾⢿⣿⣿⣿⣙⡻⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠛⡉⠀⢸⣷⢞⣵⣞⣷⣾⣿⣿⣿⣿⣿⣿⡦⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣟⣷⡿⠺⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⠇⠀⠁⠀⠀⠈⠹⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠦⣤⡶⠶⠖⠒⠲⢶⣶⣤⡽⠿⠿⠉⣤⣦⡀⢀⣀⣰⣶⣇⠀⢠⡀⠃⠐⠶⠖⠀⠀⠀⠀⠒⠶⠖⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⡗⣰⡿⣶⣶⣶⣤⠀⠐⠒⣯⣷⡷⠈⣽⣾⣿⡏⣀⡘⠻⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠡⣶⣾⣍⠙⣃⣠⡔⢛⡿⠃⠀⠚⠿⣻⣥⠙⢿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠙⠛⠚⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠟⠟⠉⠙⠋⠙⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⠃⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⢀⡛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠂⠇⠉⠀⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⣥⠈⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢲⡿⢟⢉⣿⣿⢿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣼⣿⣿⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⠟⢀⡀⣖⠠⣅⠾⠡⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡆⠀⠄⢀⠼⣧⣨⣿⢍⣥⣦⠛⢠⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣦⡰⣿⣽⣦⢀⣄⢠⠄⠀⠀⢰⣄⡰⠇⢠⣼⢊⣳⠿⠉⠑⢲⣬⣿⣬⣿⣿⣿⣿⣿⣿⣶⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣇⣼⣛⣤⣄⡀⢠⣞⠋⠀⣾⠁⢜⣃⣠⣶⣶⣿⠿⣿⣼⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣻⣿⣧⣨⠋⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠷⠾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢦⣄⠀⠀⠠⡇⠀⠀⢹⣦⣀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣯⠑⢦⣀⣇⠀⠀⠸⣿⡷⡑⢢⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡃⠸⠀⠀⣹⣿⠄⠀⢸⠇⡇⠀⠀⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢼⣿⠀⠀⠸⠁⠀⠀⠀⠀⡼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⢇⠀⡚⠀⠀⠀⠀⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣷⢸⠀⠇⠀⠀⠀⠀⠀⠀⢹⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣻⡋⡞⠀⠀⠀⠀⠀⠀⠀⢸⣻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡄⠀⠀⠀⢀⠀⣸⢾⣶⠃⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⢂⠀⠀⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣅⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡅⢣⠀⠀⠀⠀⠀⠈⣀⠚⠉⠃⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⢀⣠⣤⣽⣿⡧⠖⣂⣉⣀⠀⠀⠀⠀⠸⣿⣧⢸⠀⠀⣀⡀⠀⢈⣵⡖
⠀⠀⠀⠀⠀⠀⣰⣿⠁⣀⠔⠀⠀⠀⢀⡈⢻⣷⣶⣭⣿⠭⠍⣡⠄⠀⢀⣈⣿⣿⣬⠁⠀⣁⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠨⠷⠩⠿⣁⣈⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣶⣃⣤⣶⣿⣿⣿⣿⡟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⡏⠉⣿⣷⠂⢀⣠⣤⣾⣿⣿⣿⣿⠿⠋⠉⠙⠿⢀⠴⠃⠀⠄
⣠⣄⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣴⡿⢓⢀⣷⠀⢸⣿⡇⢀⣆
⣿⣿⣿⠿⢿⠂⠉⠚⠦⡀⣶⣬⣀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣇⠉⢈⣉⣶⣾⣿⣿⣿⡀⣿⡿⠛⢸⣿⣦⣤⣀⣀⣠⠤⢢
⠉⠉⠉⠛⠢⠀⠀⠀⠻⣦⣤⣈⠉⠛⢿⣷⣾⣶⣷⣿⣿⣷⣾⣿⡿⠿⠿⠿⣾⣟⠿⠿⣿⡿⠿⠁⠹⠆⠀⢿⣿⣿⣏⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⡤⠌⠉⠉⠉⠛⠶⡿⠍⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⡯⠀⠘⢷⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠀⠀⠁

⠀⠀⠀⠀⠀⣴⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⣰⣾⠿⢧⣄
⠀⠀⠀⠀⠀⠋⠉⠀⠉⠙⢿⣿⡄⠀⠀⠀⠀⢻⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⠀⣀⠀⠠⠃⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠻⣿⣄⢛⣪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⢠⣾⣿⠿⢿⣆⠀⢸⣿⣿⡇⠀⣠⣦⣄⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⢀⡴⠶⠃⠉⣀⣤⣿⠟⢁⠀⢀⣿⠀⠛⠛⠉⠁⣸⣿⣿⣿⣇⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠏⠀⢠⣶⣿⣿⢿⣿⠀⠀⠓⠈⠀⠀⠀⢠⢊⣩⣭⣿⠛⠹⠃⠀⠀⠰⣄⠀⠀⠀⠀⢠⠀⠀⢀⣥⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠃⣿⠞⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⠃⠀⠀⠀⠀⠀⠘⣗⠀⣀⣴⣯⡀⣠⣿⡇⠀⠀⠀⣰⣿⡿⠛⠉⠉⠙⢿⣿⢃
⠀⠀⠀⠀⠀⠀⣸⡏⠀⢿⣷⣿⣿⢿⣦⣀⡀⠀⢀⠀⢦⣦⣀⡴⡏⠠⠀⡀⠀⠀⠀⡀⠘⢦⡙⢿⣿⣿⣿⣟⡀⠀⣀⣼⡿⠁⠀⠀⠀⠀⠀⠈⣿⢿⡇
⠀⠀⠀⠀⠀⣆⣸⠇⠀⠘⣿⣿⣿⣿⣧⢬⣄⣷⣴⣾⣿⡿⢋⡾⠀⠀⢀⡇⠀⠀⠀⢳⡀⠀⠻⣆⠉⠻⠟⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⣾⠇
⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡥⢀⣠⣾⠃⢰⡄⠀⠀⢡⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⠏
⠀⠀⠀⠀⠈⣻⡿⣧⣀⣀⢠⠤⢄⠈⠻⢿⡏⢀⠀⢀⡠⠀⣀⣶⣯⣽⠏⠀⣾⣷⣄⠀⠀⠛⣤⣶⣶⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣠⣴⣿⠃
⠀⠀⠀⠀⠀⢿⣧⣼⣷⣿⣾⡟⢿⣄⣤⡜⢷⣄⣤⣾⣷⣶⣿⣴⣿⠟⠀⢸⣿⣞⣿⡆⢀⣾⡿⣿⣯⡉⠉⠛⣿⣦⢹⣿⣷⣶⣶⣾⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢀⣾⣿⣿⣻⣿⣾⣿⠁⢹⣿⣿⣆⣀⣸⣿⣾⣿⣏⠉⠈⠉
⠀⠀⠀⠀⠀⣷⡄⠀⠀⠉⠛⠛⠻⠿⠿⠿⠟⢛⠛⠛⠉⠁⠀⠀⢀⣠⣿⣿⣷⡟⣹⣷⣾⣿⣿⡎⠙⢿⣿⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠚⠋⠁⠀⢸⣷⣶⣶⣿⣿⣿⣿⣿⣿⠛⠋⢽⣿⣿⣯⣅⣀⣀⣉⣡⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣠⣤⣤⣶⣿⠄
⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠛⠿⣿⡿⢿⣿⠿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⢿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁⠒⠒⠁⠑⠤⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣤⣶⠾⠿⠿⠿⠿⠶⣶⣤⣉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣶⡾⠋⠁⣀⡤⠶⠶⠶⠶⢤⣄⡈⠛⢷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⢠⡾⠋⣀⣴⠋⠁⣀⠠⠼⣧⠄⣀⠈⠙⢦⣀⠉⢷⡆⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⡿⠁⢰⠏⠀⡰⠊⡡⠐⠃⣿⠂⢌⠑⢆⠀⠹⣆⠈⢿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢠⡏⠀⡚⠀⠊⢀⣠⠤⠿⣆⠀⠑⡀⢃⠀⢹⡄⠈⣿⡁
⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠈⠻⣿⠂⢸⡧⠶⡟⣛⠛⠻⡇⠀⠀⢸⣤⣤⣭⣽⠶⢼⡇⠈⣿⠟⠁⠀⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠘⣇⠀⢣⠈⡄⠀⠹⣶⠒⠋⠉⢠⠁⡜⠀⣸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⣷⡀⠹⣄⠀⠱⣄⠐⠤⣿⢠⠄⠒⡡⠎⠀⣰⠏⠀⣾⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⣷⡀⠉⠳⣄⠀⠙⠒⢻⡖⠒⠋⠀⣠⡾⠉⢀⣾⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠁⠈⠻⢦⣄⡈⠛⠓⠶⠶⠶⠶⠚⠛⢁⣠⡶⠟⠁⠙⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢷⣶⣴⣤⣤⣶⣶⡾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⣄⣠⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⢀⢺⣿⠋⣽⣿⣿⣿⣿⡏⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢐⣢⣀
⠀⢠⣤⣤⣀⣤⣻⣶⣔⣟⡷⢦⡀⢸⣿⣿⠿⠁⠀⠀⠀⣠⣤⣀⢀⣊⣠⣶⣶⣿⣿⣿⣶⣦⣴⣶⣤⣀⣤⡀
⠀⠸⠿⠿⢿⣿⣿⣿⣿⡏⠁⣼⣃⠈⠛⠁⠀⠉⠀⠀⢶⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡿⠛⠉
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⡟⠆⠀⠀⠀⠀⠈⢷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢘⣯⣌⠙⡓⣶⣿⣽⣿⣿⣿⣿⣿⣿⣏⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⡿⠻⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⣶⣄⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠀⠀⠈⠃⠀⣉⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠈⠁⢀⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⠇⠚⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣇⠠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⠀⠀⠀⠀⡀⢀⣀⣧⠜⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠦⠶⠒⠚⡟⠉⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢬⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡢⠐⠀⠀⠈⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠚⠋⠉⠁⢸⠇⠀⠀⠀⠀⠰⡆⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢻⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡃⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠷⣾⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢤⠖⠻⠟⠁⠂⡂⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣀⠦⡜⡾⠉⠉⡠⠘⢁⣤⣴⣾⣿⣯⣷⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⡀⠿⠐⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣬⣥⣶⣿⣿⣿⣿⣿⣋⠻⢿⣿⣿⣿⣁⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⢀⡖⢮⣙⣛⡛⠉⢩⣽⣭⣙⣋⣿⣶⠳⣿⢿⣯⢙⣿⣿⣿⠝⣛⠷⣴⣶⣶⣾⣍⣀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠠⠌⠋⣁⣬⣿⣭⣿⣿⣿⡞⢛⣯⣥⣶⣿⣿⣛⠛⠛⣉⣵⣆⠁⢨⣉⣛⣛⠙⠻⣿⣿⠿⠶⣿⣯⣟⡛⠁⠠⠄
⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠉⣭⣥⠀⢼⡿⠛⠋⠁⠤⠼⠛⠋⠉⠩⠕⠂⢀⣿⠿⡋⠀⠰⣮⣍⣻⠥⠤⠤⢴⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠁⠀⠀⠀⠘⠻⢿⣷⣶⡄⠀⠒⠉⠀⠀⠀⠈⠙⠛⠉⠁⠀⠢⠭⣭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠀⢠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⢀⡀⠀⣬⠀⠀⠀⠀⠀⠀⢀⠖⢒⡆⠀⠊⠀⠠⠀⡴⣐⠆⣸
⠀⠀⠀⠀⢀⡴⠞⠉⡃⠓⠀⣁⡀⠀⠀⢠⡍⠃⠀⠀⠀⠀⠀⡠⠤⠸⠄⠠⠀⡀⠃⠀⠀⠘⠀⠀⢌
⠀⢀⡄⠀⠛⠀⠀⠀⠀⡐⣂⣤⣶⣄⡔⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠔⠵⠈
⠀⠘⠇⠀⡎⠰⠹⠀⢈⣀⣠⠤⠉⠀⣀⠤⠤⠒⠀⠀⠉⠽⠈⠁⠐⣢⠤⠀⠀⠀⠀⠀⢹
⠀⠐⠀⠀⣉⠀⠀⡀⠁⠀⠀⣀⠴⠊⠁⠀⢀⡄⠃⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠐⢍⡈⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⢠⠀⠠⠻⠤⣬⠍⠁⣠⠊⠀⠀⠀⠀⢀⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠢⡀⠀⠀⡠⡦⢀⠭
⠀⠀⣀⡀⡆⠀⠀⢀⢜⠁⠀⠀⠀⠀⢀⡶⠂⠠⠴⠷⠆⠠⠒⠓⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣆⠀⠇⠐⠛⢠⠄
⠀⢰⠃⠉⠀⠀⡠⠃⠂⠀⡄⠀⠀⠀⠀⡀⠸⠀⢐⡃⢂⡀⢴⡶⢧⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇
⠀⢐⠃⠀⠀⣠⠁⠀⠀⠀⣰⠀⠐⠂⠀⡇⢀⠔⠚⠉⠙⠒⠈⠉⠉⠀⠠⢅⡤⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠸⠁⠀⠀⡅⠀⠀⠀⠀⣷⠀⠀⣠⢤⡧⠴⠖⢰⡖⢳⡄⠐⡖⢲⡀⠀⠀⠀⣠⡤⢥⠄⠈⠀⠀⢀⠀⠂⣀⣀⢸
⠀⠀⡁⠀⢸⠀⠀⠀⠀⠠⠋⢀⠜⠉⠀⡷⢀⠖⠈⠛⠛⠗⠘⠃⠙⠋⡻⣖⢳⡀⢠⣎⠀⡀⠀⠀⠉⠀⣀⠛⠿⠂
⠀⠈⠀⠀⠸⠀⠀⠀⠀⠁⠀⠁⠀⠘⠒⢷⢚⡠⢠⡤⠄⠀⢠⣄⢰⡆⠉⠉⠉⠱⠚⠒⠀⠗⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⠀⠘⡀⢀⠀⡀⠀⠀⠀⠀⣹⢠⡄⠐⠓⠚⠀⠀⠛⠲⠀⠰⣶⣦⠀⣤⠖⠀⠀⡀⠀⠂⠀⣿⠀⠀⠐
⠀⠀⠀⠀⠠⢦⠄⢠⢈⣀⠁⠀⠤⠀⠁⣿⢁⢁⡀⢀⣆⠀⠀⠀⢰⠊⠈⠈⡯⠚⠛⠈⢰⣀⣄⠀⡰⠆⡷⠂⠈
⠀⠀⠀⠀⠀⠈⡀⠀⠠⣌⠉⠒⢤⣄⣠⠿⣿⣬⣯⡇⢻⣡⡏⣓⡾⢷⢀⣄⣶⠲⣲⣿⢿⣷⢾⡗⠀⡸⠂⠀⠐⠄
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠣⡀⠀⢠⣅⠉⢁⠿⠧⢬⠿⠛⠛⠿⠿⠯⠽⠝⠛⢙⡃⡴⠚⠚⠚⠀⡴⡁⠀⠀⠀⢀
⠀⠀⠀⠀⢴⠐⢸⡀⠀⠀⠀⠁⠀⠁⠙⠋⠀⠀⢀⠀⠀⡀⠈⠀⠐⠐⠀⠀⠀⠛⠦⠀⠂⠀⢀⠞⠀⠘⢀⠄⠠⠸
⠀⠀⠀⠀⠀⢒⠈⠀⠀⠀⡀⠀⠀⠄⣀⠀⠐⢄⠀⠁⠀⠘⡄⠀⠀⠄⠀⠀⠀⠐⠒⢀⠄⠰⠋⡠⠆⠀⠋⡀
⠀⠀⠀⢂⠁⠈⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠠⠀⠀⠠⠀⠀⠀⠀⠰⠀⠁⠀⠀⠠⠿⠁⠀⠠⡄⡔⠆⠒
⠀⠠⠔⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠁⠂⠠⢀⣀⠀⢀⠀⠀⠀⣀⠀⠠⠀⠊⠁⢊⠀⠀⠠⠀⠙⠃
⠀⠀⡀⠒⠀⠀⠀⠔⠆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠐⠠⠈⠉⢩⡁⠃⢀⠀⠀⠀⠰⠋⠃⣴⠚⠷
⠀⠀⠃⠖⠀⠀⢠⠀⢰⠂⠀⠉⠁⠀⠀⠀⠄⠐⠒⢆⠀⠀⠈⠠⠾⠻⣄⠤⡀⢈⡰⡁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⢀⠀⠀⠀⠀⢃⡸⠀⠀⠀⠀⠀⡀⠀⢀⠑⠚⠁⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠐⠉⠀⠐⠀⠈⠰⠃⠀⠀⠀⠀⠀⠨⠀⠈⡀⠀⢀⡀⡀⠀⡁⠈⠀⠠⠈⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠀⠙
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢙⠒⠀⠀⠀⠀⢛⠐⠀⢬⠀⡁⠀⠀⠀⠀⠀⠠⠀⠀⠐⢠⠀⠀⠈⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠓⠉⠀⠀⠆⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠀⡖

⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⢈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⢀⢈⠀⠈⠀⠀⠀⠉⠁⢀⡀⠀⠓⠀⠐⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⠤⠄⠀⠀⠀⠸⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠒⠐⠒⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠀⣀⡈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠐⠒⠠⠠⠦⠦⡄⠠⠄⠈⢀⠀⠀⠀⠀⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢠⠄⠀⠀⠀⠀⡀⠀⠀⠁⠠⠀⠀⡀⠀⠐⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⡀⢀⡄
⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠄⠊⡀⡀⠄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⣉⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⠘⠓⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠃⠀⠀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠓⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⣧⠀⢻⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣽⡄⠈⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡀⢨⣿⡄⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠠⠐⠒⠁⠈⠉⠀⠀⠀⢸⣧⣼⠟⢻⡄⠀⠰⡀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⣿⣄⠀⠀⢀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⢿⢸⡆⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⡾⠿⠯⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⠛⠃⠒⠶⠶⠦⢤⣤⣴⡇⠀⣠⣾⣦⣴⣯⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠉⠙⠻⠿⢯⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⠸⢿⢰⣶⡤⣬⣤⣤⣀⣄⡄⠀⠀⢀⣀⣀⣤⠤⡶⠃
⠀⠀⠀⠀⠀⠰⣬⣵⣾⣿⣿⡏⠉⠉⠀⠀⠀⣀⡀⣀⣒⣒⣴⠺⣥⡿⣿⠶⠞⠛⠫⠉⠑⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⣿⣦⣦⣤⣤⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠬⠽⠷⠶⣿⣿⠠⠔⠒⠤⠄⣀⣀⣤⠤⠀⠀⠤⣤⣤⣤⡼⠛⠛⠁⢠⣤⡤⠤⠄
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⣉⡉⠀⢀⣀⣀⣀⣉⣉⣉⣀⠀⠄⠀⠀⠀⣉⡥⣤⣄⣓⡙⠉
⠀⠀⠀⠀⠀⠀⠠⠔⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠒⠒

⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠈⠉⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣠⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁
⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠁

⠀⠀⢼⡿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠃
⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠻⠂⠀⠀⠀⠀⣲⣿⡥⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⣄⣠⠀⠀⠐⠀⠠⣴⣄⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⢻⠟⠂⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢿⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠀⠀⠀⠀⠀⣺⣷⡥⠀⠀⠀⠀⢀⣠⡄
⣶⡇⠀⠀⠀⠀⠀⠀⠄⢠⣷⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠄⠀⠀⠘⠻⠋
⠛⠉⠀⠀⠀⠀⠀⠃⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠄⠀⠀⠀⠀⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠏⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⢀⠀⠐⠂⠀⠁⠀⢀⣄⠀⠀⠀⠀⠀⠚⠟⠃⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⢠⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⢻⠁⣿⡟⠓⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⡾⠀⣿⣷⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣉⠀⠀⠀⣠⠴⠖⠛⢹⡇⠀⣿⣿⡉⠛⠲⠦⣄⡀⠀⠀⣉⣶⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠘⢎⠑⠶⣋⠁⠀⠀⠀⢸⠀⠀⣿⣿⡇⠀⠀⠀⠈⣙⠶⠊⡱⠃⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡼⢧⡀⠈⠓⢦⣀⠀⡏⠀⠀⣿⣿⣿⠀⣀⡴⠊⠁⢀⡜⢧⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡞⠁⠀⠱⣄⠀⠀⠈⢻⠃⠀⠀⣿⣿⣿⡟⠁⠀⠀⢠⠎⠀⠈⢷⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣼⠁⠀⠀⠀⠘⣦⣀⣀⣼⠀⠀⠀⣿⣿⣿⣧⣀⣀⣴⠃⠀⠀⠀⠈⣧⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣠⣤⣧⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⡿⠋⠀⠀⠀⠉⠉⠙⠒⠒⠶⠾⠤⣄⣀⣷
⠀⠀⠀⠶⠶⢾⣟⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣳⢯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⡷⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⠒⡶⠶⠤⠤⣄⣀⣀⠀⠀⠀⣠⣾⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⠛⠉⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⡀⠀⠀⠀⢠⠟⠉⠉⢻⣿⣿⣿⠀⠀⠀⡟⠉⠉⠻⡄⠀⠀⠀⢀⡟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⢧⡀⠀⡰⠋⠀⠀⢀⣼⣿⣿⣿⠀⠀⢰⣧⡀⠀⠀⠙⢆⠀⢀⡾⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢳⡜⠁⢀⡠⠖⠉⠀⣿⣿⣿⠀⠀⣸⠀⠉⠳⢄⡀⠈⢣⡞⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢠⢎⡠⠶⣍⡀⠀⠀⠀⢸⣿⣿⠀⠀⡇⠀⠀⠀⢀⣩⠶⢄⡱⡄⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⣉⠀⠀⠈⠙⠳⠦⣤⣈⣿⣿⠀⢸⣇⣤⠴⠖⠋⠀⠀⠀⣉⠿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⢿⣿⠀⡼⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣼⣿⢀⣧⡤⠤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣷⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣍⢻⠄
⠀⠀⠀⠀⢀⡔⢻⣿⣿⣿⠼⠛⢨⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⡃⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣟⢛⡛⠛
⠀⠀⠀⡼⣿⢰⡶⣶⣶⣦⡀⠀⢸⣿⣶⣤⠀⠀⠀⢐⢆⣼⣿⡋⣟⢃⠀⠿⠞⡆⠀⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠉⠒⠙⢿⣟⣿⡿⠟⠑⠚⠉
⠀⠀⠀⢿⣿⣿⣙⢿⣻⣿⡇⠀⢼⣿⣿⡇⠀⠀⢀⣬⣼⣿⣿⣋⣿⠁⠀⢸⡎⠀⢶⢎⣀⡀⠀⢀⣿⣿⣿⠿⣿⣿⣿⣗⠀⠀⠀⠀⠈⢻⣿⢷⡄
⠀⠀⠀⣈⣿⣝⣿⣶⣹⡿⢪⣤⡈⢛⡏⠀⠀⠀⠀⠀⣬⣿⣯⣤⣬⣦⣤⣴⣴⣤⣨⡿⠋⠁⠀⠀⠙⠯⣿⣾⡿⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⣬⡁
⠀⠀⠀⣼⣿⣿⣯⣅⣠⣠⡼⠿⣿⣿⣶⡦⠀⠀⠀⠀⠻⣿⣿⣿⣯⣍⣩⣽⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⣿⡇⣿⠧⣘⡑⢠⣥⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⢀⣶
⠀⠀⠀⢛⣷⠂⣤⣉⣭⠛⣽⣟⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⣤⣤⣀⠀⠀⢀⡀⠀⠀⠀⣠⣿⡟⢻⠇⠀⠀⠀⠀⢘⣿⣶⠀⠀⠈⣿⣿⣿⣄⡀⠀⣶⣿⡇
⠀⠀⠀⠀⠛⢕⣤⣴⣄⣐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⣤⠃⠈⠙⠿⢶⣿⣿⣤⣴⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠘⠛⢿⠷⣶⣾⣿⣿⠸⢿⣿⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⣠⣴⣶⣿⣿⣋⣼⡿⠃⠀⣠⡞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠺⢷⣿⣿⣾⣾⣿⠋
⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⠈⣹⣿⣛⡉⠉⢠⣾⠋⢯⣿⠶⠋⠁⢉⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁
⠀⠀⢠⣿⣣⢿⣝⢿⣆⠀⠀⠀⠀⢠⣠⣦⠈⠶⠻⡀⠀⠀⢸⣿⠋⠀⠁⢠⡿⠁⠀⣨⣽⡿⢶⣤⣼⣤⡴⠋
⠀⠀⣿⡛⣿⣿⣧⢶⣷⠀⠀⠀⠀⣾⠛⡇⠀⠀⠀⠉⠒⠀⠘⣯⡓⠚⠛⣾⣇⣠⡾⢁⡿⢅⠀⠀⠉⠀⢠⣶⣾⣷⣶⡀
⠀⠀⠘⢿⣧⣿⣼⡿⠋⠀⠀⢀⠴⣿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠞⠃⠀⠁⠀⠈⢇⣸⠂⠀⠀⢰⣻⣯⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣼⣻⡧⠎⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣡⣤⣤⣄⡿⠃⠀⠀⢴⣆⣉⠛⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡽⠃⠀⠀⠀⠀⠀⠀⠀⣼⣷⡽⠿⢿⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠙⠃⠀⠀⠀⠈⠹⣿⣿⣿⣿⢤⣰⣷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠞⡏⠈⢣⣀⠞⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠻⠯⠿⠺⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠏⠀⠀⠀⠀⠀⠀⠀⠙⠚⣮⡗⠒⢻⣭⡒⠓⢻⣿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⢻⡶
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⡏⢀⣹⣴⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⢹⡇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⠟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠚⠛⠋⠉⠋⠁

⠀⢀⣀⡀
⠈⢀⢈⡁
⢉⣁⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⢠⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦
⢠⡤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠠⠤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋
⠰⠶⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠐⠒⠘⠃⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡁
⠘⠛⠘⠃⠸⢴⣂⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡎⢆⡀
⠈⣉⢈⡃⠀⠀⠀⡴⠖⠋⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⣇⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⣰⠇
⢈⣉⢈⡁⠀⠀⠀⠙⠛⣳⠀⠔⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣷⣿⡇⢻⣿⣿⣿⣆⠀⠀⠓⠒⢦⠀⢠⡶⠛⠁
⠀⣀⢬⡁⢠⡤⡄⣰⡟⠁⠀⠀⡆⠀⢀⣼⣿⠟⣿⣿⣿⡇⣞⣿⣿⣿⢸⣿⣿⣿⣿⡄⢸⡉⠉⠉⢰⡿⠀⠀⣀
⠀⡠⢤⣽⣃⡵⠦⢼⣷⣤⣠⡊⢁⣴⣿⡿⢣⣾⡿⢃⣿⣇⣸⠇⣿⢿⡎⣿⣿⠘⣿⣷⠀⢸⡆⠀⣾⡇⡀⣸⠁
⠀⠤⢠⣼⠧⢠⣀⠜⠀⠉⡿⣿⣿⣟⠁⢠⣿⡟⠀⣼⠟⣼⣿⠀⢸⣿⣷⣽⣿⠀⢹⡟⣿⠋⠀⣼⡿⠤⣄⣀⡤⠶⢦⣄
⠀⠤⠠⡜⣆⠀⢀⠀⠀⣼⣽⡿⠛⢿⣷⣾⣿⣤⣾⣿⢾⣿⣿⠀⢸⣿⡟⢻⣿⣷⣿⣿⣾⣷⣾⠟⢠⡶⠚⡏⠀⠀⠀⢹⡆
⠀⠤⠰⠆⠈⠱⢦⣷⢾⡿⠋⠀⠀⠀⢉⣻⣿⣛⣋⣁⣼⣿⡏⠀⣼⣿⠃⠀⠻⣿⣿⡟⠉⠻⣿⣄⠈⢳⣄⠙⢆⢀⣠⡾⠁
⠐⠒⠰⠆⠀⠀⢸⠁⠈⠻⣶⣴⣶⠿⠯⠹⣿⡿⠿⠿⠟⠋⠀⠀⣿⣿⠀⠀⠀⣸⢿⣿⡄⠀⠘⢿⣦⣀⣻⣶⠞⠛⠁
⠀⠒⠐⠆⠀⠀⠘⠆⠤⠖⠛⢳⣄⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣿⠷⠂⢻⣷⣄⠀⠈⣉⣿⠟⠁⠀⠁
⠀⠒⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉
⠀⠛⠘⠃
⠈⠉⠈⠃
⠀⠉⠈⠁

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀