Monstrous Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠖⠛⠒⠲⠆⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⢛⠁⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠂⠀⣠⠃⠀⠀⠀⠂⠀⠀⠀⠘⣦⠀⢈⠿⣿⡀
⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⣰⡆⣀⠀⠀⡄⠀⠀⠀⠀⡈⣷⡰⢤⣾⣄⡀⡀⣠⢠⠸⣀⣤⣰⣿⠀⡄⠀⠻⣿⡀
⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠠⠀⣿⣾⢿⠿⡦⢧⠰⠶⢤⠾⢿⣿⠃⠐⣿⡟⠿⠛⠛⡾⠟⠉⠉⢉⣿⡆⠀⠀⠀⠙⣷
⠀⠀⠀⠀⢠⣿⠓⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⢸⠁⠀⠈⢀⣼⠇⢠⠀⢙⣷⡀⠀⠀⠇⠀⠀⢀⡼⡋⠀⠀⠀⠀⠀⠽⣇
⠀⠀⠀⢀⣾⠷⠀⠀⠀⠀⠀⠀⠈⢹⡛⣦⣤⣤⣤⣤⡴⠟⠋⠀⠈⠀⠈⢨⡿⢶⣤⣤⣴⣶⠟⠁⠁⠀⠀⠀⠀⠡⢠⣿
⠀⠀⠀⣸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡥⢻⠟⠷⠆⠀⠀⠰⠄⠀⠀⠀⠁⠀⠒⠛⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⢹⣧
⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣿⢀⣼⣿⣶⣾⣶⣤⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠰⠄⠀⠙⣿⡀
⠀⢠⣾⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣷⣴⣥⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇
⠀⢰⡷⠀⠈⠀⠀⠀⠀⠀⠀⣰⣷⣦⡈⢿⣿⠛⠿⣿⠿⣿⣿⣯⣤⣄⣠⣤⣴⡶⣾⠉⣟⢡⣴⡄⠀⠀⠀⠀⠀⠄⠀⠀⢸⣿
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠓⠇⡀⠂⠀⠛⠂⠋⡍⠙⠛⠿⠏⠁⠈⠀⠉⠀⠁⢺⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⣾⣧⠀⡀⠀⠀⠀⠀⠀⠐⡿⣿⡿⠀⠰⠃⠀⠀⠀⠀⠘⠁⠀⣼⠀⠀⠂⠀⢾⠀⠐⠀⢺⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣇
⢠⣿⠃⢨⡀⠀⠀⠀⠀⠀⢀⢱⣿⣧⡀⠀⢠⡈⠀⠃⠀⠆⠀⠐⢁⠐⠀⠀⠀⠀⠀⠀⠀⣼⣧⠃⠀⠀⠀⠀⣄⠀⠀⠀⣠⢿⡇
⢀⣿⡠⠞⠁⠀⠀⠀⠀⣀⠈⢲⣿⣿⠃⠀⠈⠁⠀⠀⠀⣀⣼⣿⣻⣧⣦⡀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠰⠈⢀⣻⡇
⠈⣿⡅⠀⠃⠀⠀⠀⠀⠈⠂⠈⣿⣟⠃⠀⠀⠀⠀⠀⠐⢾⡿⠟⠛⠻⣿⣿⣢⠄⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠁⠘⠀⠐⣀⢾⡇
⢠⣿⣿⡁⠈⠀⠀⠀⠀⠀⠀⠰⣿⣿⡗⠀⠀⠀⠀⢰⣧⡿⠁⠀⠀⠀⠈⢿⣯⠄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⢂⢾⣺⡇
⠀⢸⣿⡡⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠃⠀⠀⣻⣿⠃⠀⠀⠀⠀⠀⠘⣿⡞⠀⠀⠀⠀⣿⣧⠀⠀⠀⠖⠀⡀⠀⢀⣸⢻⣇
⠀⢸⡿⡟⢹⢀⠀⠀⠀⠀⠀⠀⠙⣻⣷⠀⠀⢀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⣿⠱⠀⠀⠂⠀⠀⠀⠀⣌⡃⣽⡟
⠀⢸⣿⣧⠊⡈⠀⠀⠀⡀⠀⠀⠀⢿⣧⠀⠀⠈⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⣠⡍⢷⢹⡇
⠀⠘⣿⣾⣧⣏⢲⠐⣌⣣⠀⠀⣔⣻⣿⡀⠀⠠⢶⣼⡃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠁⣿⢻⣛⡄⡆⢀⡠⢘⣽⢻⣾⣿⡃
⠀⠀⣿⣿⣯⣼⣿⣿⣶⣷⣾⣾⠟⠋⠻⠿⡁⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠘⣿⣿⣿⣅⣡⣴⣰⣮⣷⣿⣷⣾⠃
⠀⠀⠈⠻⣿⡿⠋⠙⠏⠉⠁⠀⠀⠀⠀⠀⠀⠠⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⡤⠋⠈⠙⠛⠛⠛⠉⠛⠙⢿⣿⠇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠖⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡘⠚⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡜⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠆⢆⡀⠁⠀⠴⠀⢀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠸⣄⠈⠀⠀⠈⠀⠀⠹⡄⢸⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠉⢀⣿⣶⣶⣷⣦⣴⣷⣧⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⠒⣀⣀⣠⠀⢀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⣀⡴⠞⠉⠉⠉⠀⠉⠼⠉⠉⠉⠉⠙⠟⠛⠂⠀⠀⠀⠀⠀⣴⠿⠟⠻⠋⠻⠛⠛⠛⢿⠻⣿⠻⠿⣧
⠀⠀⠀⠔⠚⠁⠐⠂⢀⡤⠀⢀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣤⠀⠀⢸⠇⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠈⠣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⡴⠆⠈⠉⠀⠀⠐⠄⠀⠀⠀⠀⣼⡇⠀⣾⠋⠳⢦⣀⣀⠀⠲⣤⡘⠃⡈⠓⠀⠈⢦
⠑⡦⠀⠀⢀⡠⠂⠀⣀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢿⣄⠈⠷⡄⠀⠉⠛⠳⣤⣀⠙⢦⠈⢂⠈⢂⠈⣧
⠐⠠⠄⠒⠛⠀⠀⣼⠛⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠙⠳⠦⠟⠀⠀⠀⠀⠀⢻⡀⠀⣁⠀⠀⢸⡄⢻⡄
⠀⠀⠀⠀⠰⠂⠋⠈⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣛⢘⡇⢸⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⡸⠦⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⢂⠀⠀⠀⠀⠈⢳⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠾⠿⢤⣀⡜⠛⡛⢟⠲⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢰⡇⠀⣠⣄⣿⣄⢺⣧⡾⠀⣀⡤⢤⣄⡉⠉⠛⠓⠶⢤⣤⣤⡤⠖⠋⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⠤⠄⠒⠺⡆⠀⠀⠈⠳⣤⣙⣿⠃⠈⠛⠉⠀⡞⢁⣀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠘⠢⡀⠱⣄⠀⠀⠀⠀⣀⣻⡄⠀⠀⠀⢀⠎⣡⣤⠀⣤⡀⢺⡇⢾⣯⡴⠀⠀⣹⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⢀⡤⠒⠲⣏⠀⠀⠀⠙⣄⠀⠉⠙⠋⠉⠉⠈⣷⠀⠀⠀⠾⠄⠀⣀⣀⣀⣀⠸⠳⣄⠉⠀⢀⣴⢏⠀⠀⣀⣴⡞⠉⠀⡀⠀⢀
⠀⠀⢠⠏⠀⠀⠀⣙⠶⠶⠞⠀⠈⠳⣄⠀⠀⠀⠀⠀⢻⠀⡖⠀⢀⡴⠊⠁⠀⠀⠈⣷⣄⠉⠛⠛⠛⠒⠁⢠⡞⠁⠀⠈⠉⠉⢀⡴⠃⢀⡴⠒⠉⠉⠓
⠀⠀⡏⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⢠⠇⣠⣏⣤⣤⣤⣴⣤⣤⣿⡈⢳⡀⠀⠀⠀⢠⡏⠉⠓⠶⠶⠶⠒⠋⠀⢀⠎⠀⠀⡀⠀⣠⠟
⠀⠀⠳⣔⠋⣹⣃⣰⢃⡀⠀⢹⠟⣆⠀⢸⠀⠀⠀⠀⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⢠⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠙⠛⠉⠳⡄
⠀⠀⠀⠈⠀⡏⠉⠣⣯⠩⠶⠋⠀⢸⠀⢸⠀⠀⠀⠀⣿⣿⡯⠤⠀⠠⠤⢄⣈⡉⠉⣻⠟⠻⣿⡆⡆⢀⡿⣀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣀⠀⣀⡶⠀⠀⢸
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⡞⠀⠀⢇⠀⠀⢠⡿⡏⠀⠀⠀⠀⠤⣤⣄⣉⠙⠛⠦⢄⡈⢻⡇⢸⣇⠈⠓⠲⠤⠤⠒⠈⠁⠀⢀⡎⢀⠸⣇⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⠤⣼⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⠘⠷⣤⣀⡀⢀⣀⣀⣠⠶⠋⠹⣄⡀⠉⣩⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣠⡟⠀⠀⣴⠟⢳⡀⠀⠀⢀⡶⠲⣄⠀⠀⠀⣿⠁⠘⣆⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠾⠋⠀⢀⡾⠁⠀⢸⠇⠀⠀⡞⠀⠀⠈⠳⣄⠀⠁⠀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⢀⣠⡤⠶⠋⠀⠀⠀⣸⠀⠀⢸⠃⠀⠀⠀⠀⠈⢷⡀⠀⠘⢦⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⡷⣄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⠘⡄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⠀⢳⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠘⡄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠹⡄⠀⠹⣄
⠀⠀⠀⣀⡤⠶⠶⠶⠶⠤⣤⡏⠀⠀⡼⠤⣤⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⣿⠀⠀⠀⠹⣦⠀⠈⠷⠤⠄⠒⠒⠒⠒⠒⠲⣤
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣤⠤⣤⣤⡿⠀⠀⠀⢸⣄⣀⣀⣀⣠⠤⠿⠆⠀⠹⣤⣄⣀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡇
⠀⠀⠻⣄⣤⣼⠷⣄⡀⠀⠀⣀⣶⣄⣀⣸⣤⡾⠁⣰⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⡀⠉⠉⢳⡄⠀⣦⠀⠀⠀⠀⠨⣍⢣⡀⢀⣤⡀⠀⣴⢀⣠⠞⠒⠚⠋
⠀⠀⠀⠀⠁⠀⠀⠈⠉⠛⠛⠉⠁⠈⠉⠉⠀⠀⠀⠘⢦⣤⡶⠟⢦⣀⠀⢠⠄⠀⠈⣷⠤⠶⠛⠦⠴⣏⠀⠀⠀⠀⠀⢈⡟⠉⠉⠁⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠚⠛⠁⠀⠀⠀⠀⠀⠈⠓⠶⠴⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣋⡤⠐⣀⣠⣔⣾⣿⣿⡦⣥⡀⠉⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠘⢃⡴⣾⣽⣿⣿⣿⣿⣿⣿⣻⢿⣷⣤⣦⣵⡔⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠰⠃⠐⣩⣾⣿⡿⠛⠛⠋⠸⠋⠍⢛⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣮⡞⠠⢟⣴⣿⢿⣋⡙⡀⡀⠀⠀⣤⡀⣀⡁⢨⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣴⣳⣿⣿⣿⣿⣛⣛⣿⠇⠀⠐⠛⣿⣟⣛⣶⣾⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠉⠈⢁⣤⣤⣤⣀⠀⠈⠙⢫⣙⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠰⢒⣿⣻⣿⣁⡀⠀⠄⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢰⣿⠟⢻⠉⡛⡿⣦⣰⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣷⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣾⠛⢋⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣻⣿⣟⣿⣿⣿⣍⣿⣿⣿⣿⣿⡘⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡆⣼⣿⣿⣿⣿⣿⣿⡝⢻⡼⣯⣭⢵⡿⢿⣿⣿⣾⢻⣿⣿⣿⣿⣷⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⣿⠿⠿⣿⣿⡿⣿⣿⣧⣠⣀⠀⣄⠀⢀⣼⣿⣿⡷⢸⣿⣿⣿⣿⣿⣟⡿⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢙⡏⠀⠐⢻⠟⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣽⣿⣿⡇⠈⠻⣿⣿⣿⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣤⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣼⡇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠹⣿⡟⠀⠿⣿⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣤⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣋⣹⣯⣿⣿⡏⣽⠷⢦⢋⣠⣄⠐⠀⠻⡌⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣕⠛⣛⣛⣉⣩⣿⣿⣿⣿⣿⣿⣶⣆⣄⢸⣿⣷⣦⡳⣍⢲⢷
⠀⠀⠀⠀⠀⢀⣀⣶⠀⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣷⡳⠟⢿⣿⣿⣿⣷⢸⢧⠤
⠀⠀⠀⠀⠀⢳⣿⣿⣟⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⡄⢴⣄
⠀⠀⠀⠀⢠⡏⣿⡿⠛⠁⠞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢪⢁⢳
⠀⠀⠀⠀⣾⣹⣿⠁⢸⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⠙⣎⡃
⠀⠀⠀⢠⣿⡿⠃⠀⢸⢇⣀⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢡⣳⣾⡄
⠀⠀⡠⣼⣿⣷⣀⡔⠃⣺⣿⣿⠇⢯⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⢯⢣⢿⢻⡆
⠀⠀⣆⣿⣿⡿⢣⠀⠀⣿⣿⡏⠀⢠⡉⢙⣿⣿⢟⡰⢋⣼⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣯⡀⠌⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣦⣤⣴⣾⣷⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠛⢿⣿⣿⣿⣿⣎⣿⣿⣿⣿⡑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⢽⠟⣁⡀⠙⣿⡿⢥⠙⣧⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣶⢷⡞⢹⣯⣷⣬⣧⣨⣷⠛⢇⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠛⠷⠦⠷⣿⣟⣸⣧⣀⠧⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣤⣀⣀⣈⣭⣽⣿⣿⡗⠀⢂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣯⣿⣿⣿⣯⢿⢿⣷⡀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢿⣿⣿⣿⣧⣤⣴⣷⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⠿⣿⣿⣿⣿⣿⠏⠁⠀⢨⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠉⠛⠛⠃⠀⠀⠀⠚⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣺⠟⠋
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢠⣴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⣴⡿⠛⠇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⣠⣾⣿⡛⠿⣆⢀⡀⠀⠀⠀⠴⣾⠟⠁⠀⢠⣾⠋⠀⠀⠀⢀⣤⠀⠀⣠⡦⢛⡴⠾⠒⡲⠿⠟
⠀⠀⠐⠊⠉⠀⠀⠈⠙⢤⡉⢻⣧⡀⠀⠀⢰⣿⠀⠀⣴⣿⠃⠀⠀⠀⣠⡾⢃⡤⢚⣡⠶⠋⣠⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠹⣷⡀⠠⢸⣿⢠⡾⣿⣿⠀⠀⣠⡾⢋⡔⢉⡴⠋⠁⠀⠀⠉⠉⠀⢀⣸⠋⠀⣀⣠⣤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠈⠻⣦⣸⣿⡇⠘⣿⣿⣴⣿⣿⠷⢋⣴⣿⡗⠀⠀⠀⠀⣠⣤⡾⠟⠋⣉⣭⣽⡿⠿⠛⠛⠛⠛⠛⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠘⢿⣿⡇⣰⣿⣿⣿⣿⣿⣶⣿⡿⢻⣶⣟⣩⣶⠟⢋⣡⣴⣾⠟⢛⢋⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣸⣧⡈⣿⣷⣿⣿⡟⣹⣿⣿⣿⣿⣟⡉⠻⢿⣿⣶⣾⣿⡟⠁⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⣚⠛⣿⣿⣿⣿⣿⠿⣷⣬⣻⣾⠛⠤⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣿⣿⣿⣷⣼⣯⣤⣃⣱⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣝⡍⠻⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣣⠶⠉⠁⠀⢠⣬⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣬⡶⣿⣽⣿⣿⣿⣿⠟⡿⠛⠋⢹⡿⣽⣿⣿⣯⣀⣄⠀⢠⣤⡿⢛⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡷⢀⡿⣦⢼⣿⣏⣿⡿⣿⡈⠓⠀⢀⣼⠃⣿⣿⢟⡟⣩⢿⣶⣶⣿⣃⠈⣟⡢⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠷⡢⣄⣿⡅⠛⣋⠿⠏⢻⡿⣿⣷⣾⣿⣿⣸⠇⡄⣻⠺⠯⣸⡿⠀⢿⢿⣤⡏⢀⣠⣿⣶⠂
⠀⠀⠀⠀⠀⠀⠀⢐⣖⠳⢶⣟⢻⣿⠀⠀⠀⠀⠀⣆⢷⣿⣿⣿⣿⣿⣿⠰⣼⡁⢠⣦⣇⣄⠀⠀⠶⣹⣿⡿⠁⣀⡛⢋⣀
⠀⠀⠀⠀⠀⠀⢂⣿⠉⠀⠀⢙⣿⠁⠀⠀⡼⠆⣰⣿⣯⣿⣿⣿⣿⢿⡧⢻⣿⣷⣿⡟⠋⠘⢗⠀⠘⡹⢛⣷⡟⠋⢀⠠⣝⠁
⠀⠀⠀⠀⠀⠀⢈⣍⠀⠠⠴⡿⠏⠀⠀⠀⠆⠀⠆⢀⣿⣯⣿⣿⣷⣿⢢⣿⣿⣯⡟⢱⡆⠀⠘⣧⠀⠁⠈⣿⢿⣿⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣏⣀⠰⠶⣷⡄⠀⠘⡗⢀⠀⢀⣼⣿⣿⣿⣽⣉⣷⡸⢿⢹⣿⡿⢻⡟⠀⠀⠘⣧⠀⠀⠀⠀⣼⣟⠁⠈⣿⡀
⠀⠀⠀⣠⠀⠀⠂⣿⣥⡤⠴⣷⠀⠀⡾⠀⢉⡠⠂⢸⣿⣿⣿⣿⣾⣿⣷⠶⣾⣿⠃⠚⠋⠁⠀⠀⠘⠓⠤⠀⠀⠙⡿⠲⢏⡽
⠀⠀⢠⡏⠀⠀⠀⠃⢸⣷⢀⣇⠀⣰⠃⠀⠉⢀⡴⣿⣿⣯⣻⣿⡏⠠⠷⠰⣿⠿⠀⠀⠀⢀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠄⢸⣧⣆⠀⠀⠀⢀
⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⡎⠚⠂⠀⠀⢰⠋⠈⢠⣿⣿⣼⣿⣿⡀⠒⠃⣠⡅⢘⠃⠀⠀⠾⠀⠈⢀⠓⠲⣀⡆⠀⠀⢾⣼⣿⣿⡗⢤⣶⣿⠃
⠀⠀⢻⡇⠀⠀⠀⠀⠀⣈⢻⣠⡀⢠⣀⣀⠀⠀⠐⡯⠞⠛⠶⠂⠘⠙⠋⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠉⠠⣼⢧⡼⠁⠛⡋⠁⢰⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠁⠏⠀⠆⢸⠟⣿⡆⢦⣌⡱⠂⢸⣤⡶⠒⢶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣶⣴⡆⣠⢶⢁⡈
⠀⠀⠈⠻⠀⠀⠀⠀⢠⡗⠠⡄⠳⠈⢴⠌⣿⠃⠈⠉⡼⠀⠙⠳⣄⠀⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣮⡿⢟⣷⣠⡿⠾⠛
⠀⠀⠀⠰⡄⠀⠀⠀⠘⢿⣶⣦⠈⣷⣠⠏⠋⠀⢠⡾⣄⣀⣀⣠⣟⠲⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠋⣀⣀⢽⡀
⠀⠀⠀⠀⠀⠀⠆⣄⠀⡬⠭⣿⡤⠛⠁⠀⠀⠀⠉⣠⡾⠿⡋⢉⣀⣠⣌⣀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠉⠀⠀⣸⡿⠧⠀⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠀⡷⠀⠈⠁⠀⠀⠀⠀⠀⠀⣝⣀⣼⣿⣿⠟⠛⠉⣹⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢙⠀⠀⣈⡦⠛⠁⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣟⠻⠋⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡾⡿⢓⣮⣀⣁⡀⠀⠀⠀⠀⠀⠀⡛⠒⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⣡⣄⠚⢿⡷⢻⣅⠲⠀⠀⢮⡉⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⠀⠀⠈⠉⢹⡶⠆⣠⠄⣉⠉⠐⠻⠀⠂⠄⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⣀⣤⣀⣶⣶⣤⣔⣚⣉⡈⠋⠤⣶⡶⢟⣣⣬⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢲⣄⠀⠀⠀⣠⡾⢛⣿⣿⣿⣤⣍⡛⠛⢿⣿⣿⡷⢿⣟⣿⡿⢛⡿⠟⢙⣛⠀⠀⠒⠒⡐⠒⠾⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠂⢀⣤⣴⣤⣴⣶⣦⢉⣡⣾⣿⠋⠉⠛⢿⣿⣷⣤⣬⣭⣽⣶⣾⣿⣶⡄⠃⣦⣴⡟⠉⠒⠦⣾⣷⣶⣶⣶⣶⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠟⠀⠠⠀⣤⣿⠛⠉⠉⠿⣿⠿⠟⠉⠓⠶⠄⡁⠚⢿⠿⠟⠛⠉⣤⡾⠃⠚⠛⠛⠛⠓⢦⣤⣬⣿⡟⠁⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣷⣿⣷⣶⣴⣹⣶⣧⣤⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠆⢀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠦⣄⠂⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡁⠀⢀⠴⠛⠙⠛⠛⠿⠟⠟⢻⣿⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠀⢀⡠⠖⠒⠒⠒⠦⡀⠀⠀⠀⠀⣀⠴⠒⠒⠒⠲⢄⠀⠀⠘⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⠎⠀⠀⣀⣀⡀⠀⠈⢆⠀⠀⡴⠁⠀⢀⣀⡀⠀⠀⠱⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⢾⣿⣿⠛⣆⠀⢸⠀⠀⡇⠀⢰⣿⣿⠛⢳⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⡄⠀⠘⢿⣿⣿⠟⠀⡜⠀⠀⢧⠀⢈⢿⣿⣷⡿⠀⢠⠃⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠘⠢⣄⣀⣀⣀⠤⠊⠀⠴⠄⠀⠓⢤⣁⣀⣀⡠⠔⠁⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣸⢻⣷⠀⠀⠀⠀⠀⣖⣶⡖⠒⢲⣶⣶⣶⠒⠒⣲⣾⣛⣆⠀⠀⠀⠀⠀⣿⠃⢇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣇⠀⠀⠀⠀⠙⢿⣿⣶⣿⡿⢿⣿⣷⣶⡿⠛⣿⠇⠀⠀⠀⠀⣸⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢳⣤⣿⡿⣧⣄⠀⠀⠀⠀⠈⠙⠛⠦⠤⠿⠿⠛⠓⠊⠁⠀⠀⠀⢀⣴⢿⣶⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠹⣷⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠎⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢹⣿⣶⣦⣷⣦⣦⣤⣤⣶⣶⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠉⢿⠈⠁⠉⠃⠉⢀⡿⠻⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣷⣋⣀⣀⣸⣶⣶⣶⣶⣶⣾⣇⣀⣀⣹⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢧⠉⣳⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣠⡴⠖⣾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠻⣥⠿⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡴⠻⣌⣳⡞⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠂⣀⠙⢦⣽⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣞⣠⡴⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣠⡴⠛⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠺⣦⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣾⠛⣷⢀⣤⡀⠀⠀⠀⢸⡆⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣄⠻⠆⠿⠋⣀⡟⠀⠀⠀⠀⣧⠀⠀⠿⣄⣀⣤⡤⠴⠶⠶⢤⣄⡴⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠾⡇⠸⠋⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣉⡄⠀⠀⠸⣏⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⢻⣦⠀⠀⣠⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠳⣄⡀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⠤⣤⡀⠀⠹⣆⢀⣠⡴⠛⠁⠀⢠⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⠓⠋⠀⠀⣠⠶⡾⠛⣲⠛⢳⣖⠚⣻⣄⣀⡼⠀⠀⠙⣆⠀⠛⠋⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣀⠀⠀⠀⡼⠁⠀⠛⠞⠋⠓⠋⠉⠉⠁⠈⠁⠀⠀⠀⠀⢸⠀⠀⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣄⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢧⠀⠀⠀⣰⠛⠉⠙⢲⡏⠀⠀⠈⢳⠀⠀⢀⡏⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⢼⡀⢀⡜⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⢧⡀⣸⠦⣄⡴⠲⣼⠋⣻⣃⣀⡷⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠙⠳⠦⠼⠗⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠻⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡶⠶⠶⠶⠶⠖⠛⠋⠉⠀⠀⠀⠉⠳⣦⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠘⡷⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⡘⢳⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣄⣀⣀⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡥⣀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣧⣤⣤⣤⣤⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡜⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠱⡀⢀⠠⠐⠈⡁⠀⠉⠀⢄⠀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⠑⠂⠀⠈⠛⠶⠄⠀⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢠⣤⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠙⡄
⠀⠀⠀⠀⢀⠀⢂⠀⠠⠤⠄⢀⣿⠀⠀⠐⠂⠀⠀⠀⠀⠐⠤⠄⡀⠀⠀⠀⠀⠀⣇
⡔⠁⠁⠀⠀⠊⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢰⠿⡁⠐⠠⡀
⠁⠰⠛⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠁⠢⡈⢀
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠌
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢀⠀⠰⡄
⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣄⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⡂⡀
⠀⠀⠀⠀⡶⠪⠉⠀⠁⠈⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡆⠀⠀⠀⠸⠻⠀⠀⠀⠀⠀⠀⢰⠋⣉⠻⡄⠀⠀⡰⣼⡿⢸⢰
⠀⠀⢐⠏⠀⢀⡀⣀⠀⣀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢛⡦⠠⠤⢼⡀⠀⠀⠀⠀⠀⠀⠸⢤⣩⠐⣇⠀⠀⠑⡌⢨⠕⠁
⠀⠀⣮⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⢀⠌⠠⢂⣅⠢⠙⠄⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⢦⠀⠀⠃⡌
⠀⠀⢷⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠓⠚⠀⢧⡀
⠀⠀⠰⣆⠐⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠰⠖⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠢⡱⡀
⠀⠀⠀⠉⠶⢄⣀⣀⢀⣀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠳⠚⢧⡞⠋⠁⠈⠁⢢
⠀⠀⠀⠀⠀⣾⣿⡇⠉⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢠⠀⡁⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠔⠒⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣁⣀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⣶⣄⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠉⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣫⡕⠀⠂
⠀⠀⠀⢠⠀⡁⠉⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⢋⠁⠀⠀⠽⠀⠸⠆⠀⠀⠉⠒⣄⠀⠀⠀⠀⠀⠀⠐⢀⠈⠁⢀⠂
⠀⠀⠀⠀⠰⠀⠀⢰⣶⡆⠀⠀⢀⠀⠀⠀⠀⢸⠀⢿⠀⠰⣁⣤⣠⣄⣄⣥⠀⢸⢃⢘⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⠔
⠀⠀⠀⣌⠀⣀⠀⠈⣉⡁⠀⠀⢠⢦⠀⠀⠀⢸⠀⡏⢦⠀⠻⢻⡟⢿⣻⠇⢀⡼⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠈⣎⠀⠀⠀⠀⣀⣀⡤⠂⠠⠶⠀⠀⠀⠙⠛⠃⠈⠳⣄⠀⢀⡀⠀⣠⠊⠘⠳⠛⠀⠀⠀⠀⢀⣶⣀⠔⠁⠀⠀⠀⠤⠶
⠀⠀⠀⠈⣇⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡋⣽⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠙⠒⠚⠁⡀
⠀⠀⠀⠀⠀⠀⠇⠂⠀⠘⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡇⢸⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠁⠘⠖
⠀⠀⠀⠀⠀⠘⠆⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠦⠀⣀
⠀⠀⠀⠀⢀⠜⣤⠀⠀⠠⡶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠛⠁⠈⣙⣳⡅⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⢠⡀
⠀⢀⡀⠀⡘⠂⣤⣠⣤⣤⡆⠈⢠⠀⠲⡆⠀⠀⠠⢶⢦⠋⣺⣿⠢⣾⣿⢽⡏⣮⡟⠃⠀⠀⠀⠀⠸⠀⠀⠿⠁⠀⠸⠏⠀⠀⠰
⠀⠻⠤⠆⡁⠀⠈⠛⠛⠉⠀⠀⠀⠘⠁⠁⠀⠀⠀⠈⢻⡀⠀⣈⣀⣙⣿⠋⠀⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⣟⣿⣿⠀⡼⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⢄⠀⠀⣠⠾⡁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢐⠀⢠⠄⢢⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠀⠑⠖⠁⣀⢡⡀⠀⠀⠀⠀⠀⠰⢆⣀⡀⣀⣀⣀⣀⣀⣀⣀⣠⠄
⠀⠀⠀⠀⠘⠀⠀⠘⠀⠘⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠖⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⢀⡰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⡤⢤⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠐⣴⡂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⢒⡊⢀⠓⢒⣠⠀⠠⣄⠀⠀⠀⠀⠀⠀⡎⠀⠈⢾⡷⠃⡀⢸
⠀⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠈⠁⠈⠁⠈⠁⠐⠀⠈⠀⠀⠀⠀⠀⠀⣷⣾⠷⣦⡶⢿⣿⡾
⠀⠀⠀⠀⢀⠀⢷⣄⣀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠻⠾⠾⠟⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⠡⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠨⠴⡵⠂
⠀⠀⠀⠀⠀⢰⡆⣤⠄⣴⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣕⡠⠄⠰⡚
⠀⠀⠀⠀⠀⠘⠁⠙⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠑⠊⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣤⢀⣴⣠⣀⣤⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣀
⠀⠀⢠⡾⣋⢉⡙⢳⡀⠀⠀⠀⢛⡶⢛⠛⢿⣦⠀⠀⠀⣠⢼⣿⠟⠿⣿⣖⡄⠀⠀⢸⣏⠐⠖⣸⠇⠀⠀⢀⣀⣠⣤⡞⣻⣿⡟⣿⠏
⣠⢀⡿⣤⣩⣨⣡⣤⣷⢀⡀⠀⢸⣇⠻⠟⣸⣿⡆⠀⠀⣙⣿⣷⣙⣡⣿⣿⡄⠀⢀⡾⠛⠛⠛⠡⣴⡶⠄⠹⠛⠇⣾⣿⣿⢤⣟⡏⠙⣷⣦
⠙⢾⣧⡙⠛⠛⢛⣃⣿⡞⠁⠀⠀⣿⣿⡟⣛⠻⡇⠀⠰⣼⡇⡂⠉⠰⠚⣿⡾⠀⠘⢧⣤⣶⣶⣦⠜⠀⠀⠀⠀⢠⣿⠿⠿⢿⣿⠃⠀⠁⠈
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣻⣷⣬⣴⣷⠀⠀⣿⣧⡿⣶⣷⣶⣿⡇⠀⠀⠈⢹⣷⣴⣿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢻⡄
⠀⠀⠀⠋⠘⠁⠛⠈⠓⠀⠀⠠⠞⠻⠋⠛⠙⠛⠉⠃⠀⠻⠸⠃⠟⠸⠘⠃⠇⠀⠀⠠⠞⠁⠀⠹⠦⠄⠀⠀⠠⠾⠀⠀⠀⠀⠀⠷⠤
⠀⢀⣤⣤⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠻⣿⠟⢷⠀⢠⠟⢿⣿⠇⠀⠀⠺⣧⣴⣶⣼⠛⠀⠀⠀⠀⠐⢿⣤⣀⣀⣀⣀⣽⠀⠀⠀⡞⠉⠛⠓⣦⠀⠀⠀⢻⣤⡶⢶⣶⡟
⠀⠀⠈⢀⡼⠛⠛⢦⡀⠀⠀⠀⠀⣰⡟⣭⢩⡙⣷⡀⠀⠀⠀⠀⣠⢹⠟⠻⡿⢋⠁⠀⠀⢸⡇⠉⠘⢠⡇⠀⠀⠀⠀⣿⣮⣵⣻⣷
⠀⠀⠀⢸⣇⠘⠃⣸⠇⠀⠀⠀⣼⣿⣷⣦⣤⣴⣿⣷⠀⠀⠀⠀⢉⣿⣌⣡⣗⠋⠀⠀⠀⠸⢻⡿⣶⢾⠀⠀⠀⣤⠀⣿⣐⡸⢿⣿⡇⠀⣀
⠀⠀⠀⠀⢉⡟⢻⡁⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⡞⢹⣯⣤⣼⠋⡇⠀⠀⢠⠁⢸⠃⡏⢈⠀⠀⠀⠉⢓⣧⣪⣷⣾⣿⡷⠚⠁
⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⡿⠿⢿⡄⠀⠀⠀⠏⠁⢸⠀⡇⢸⡧⠀⠀⠀⢠⣭⣍⣱⣿⣿⠇
⠀⠀⠀⠀⣼⠷⠶⣦⡶⠀⠀⠀⠨⠏⠹⠋⠯⠹⠍⠣⠄⠀⠀⠀⠸⠀⠀⠈⠇⠀⠀⠀⠀⣀⡼⠀⢧⡀⠀⠀⠀⠀⠈⢛⣿⢿⡟⠋
⠀⠀⠀⠸⣯⠸⠶⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢠⠠⠀⠀⡠⡀
⠀⠀⠀⢀⡿⠛⠺⣟⠁⠀⠀⠀⠀⠀⣸⣥⣤⣜⠃⠀⠀⠀⠀⠰⣇⣴⠶⣿⣄⠀⠀⠀⢧⣀⣤⠴⠶⢤⣤⠖⠁⡔⡐⡀⠐⡅⠀⣠⠬
⠀⠀⠀⠸⣧⣛⣡⡟⠀⠀⠰⣷⢀⣼⡟⣉⡉⢿⢀⡷⠀⠀⠀⠀⠛⣯⣒⣼⣿⡄⣰⠄⠀⢿⣇⣈⣙⣨⡿⠀⠀⠀⠈⢳⣸⡇⣼⠁
⠀⠀⠀⠀⣟⠥⢹⡇⠀⠀⣶⡉⢻⣿⣧⣌⣡⣾⣯⣀⣶⠀⠘⠦⣽⡟⠍⠊⢻⣏⠁⠀⠠⠃⠨⠉⠹⠋⢱⡀⠀⠀⠀⠀⡿⠛⢻⡀
⠀⣀⣠⠤⣿⠟⣿⠤⣄⣀⠈⠙⢻⣯⡈⠛⠛⢡⣿⡏⠀⠀⠀⠀⣾⣃⣂⣀⣉⣿⠀⠀⠐⠂⢰⠀⢰⡀⢸⠇⠀⢀⣤⠶⣿⡿⠛⠛⢦⡄
⠀⠘⢉⣠⠛⠛⠙⣀⠉⠃⠀⠀⠀⠻⣿⣷⣾⣿⠟⠀⠀⠀⠀⢰⡿⣿⠿⣿⠿⣿⠀⠀⠀⠀⣸⡀⢘⣧⡀⠀⠀⠸⡇⠀⢿⡀⠀⠀⢀⠇
⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉⠀⠁⠀⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⣀⠀⠁⠀⢀⡀
⠀⠀⣠⣷⣶⣶⣾⡁⠀⠀⠀⠀⠀⢠⣄⣠⣿⣄⣤⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⡀⠀⢰⡤⢒⡒⠂⣐⠒⣷⠀⠀⠀⠀⢈⣤⠴⢦⣬⡀
⠛⣴⠿⣿⢛⡻⡿⡻⡖⠃⠀⠀⣴⣴⢿⣛⣛⢟⣿⣤⠀⠀⠀⣿⢢⣴⣶⣜⢸⠇⠀⠘⣷⣬⣭⣤⡭⠴⠟⠀⠀⠀⢰⡟⠑⠂⠃⢹⣿⡄
⠀⣿⣭⣿⣬⣵⣷⣵⡇⠀⠀⢠⣼⣿⠡⢜⡯⢯⣽⣧⡀⠀⠀⣿⠹⠿⠿⠋⣸⠀⠀⠀⠀⠀⠀⢹⠀⣀⣤⠀⠀⢀⣼⣷⣬⣤⣤⣾⣿⠧⡄
⠀⢨⣭⣭⣼⣿⣿⡿⠣⡀⠀⠀⣿⣿⣿⣾⣮⡾⣿⣿⠀⠀⠀⠈⢻⡟⠛⣿⠁⠀⠀⠀⠘⢛⠀⣸⡄⢈⠇⠀⠀⠉⠀⠙⢿⣿⣿⢿⡃
⠀⠈⣛⡿⠿⢟⠋⠁⠐⠙⠂⠀⣿⣿⣿⣭⣥⣴⣿⣿⡀⠀⠀⠀⠘⣿⠿⢟⠀⠀⠀⠀⠀⠀⢱⣿⣿⡅⠀⠀⠀⠀⠀⠀⡸⠀⣿⠈⢇
⠀⠀⠉⠀⠀⠘⠃⠀⠀⠀⠀⠸⠿⠛⠻⠿⠿⠻⠿⠟⠛⠀⠀⠀⠴⠛⠾⠾⠶⠀⠀⠀⠀⢀⡜⠛⠛⢣⡀⠀⠀⠀⠀⠴⠇⢀⣼⡀⠸⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠠⡿⠉⠀⠀⠠⡄⡀⠀⣀⠀⡄⠀⠀⠀⣀⢤⠀⠀⠀⣿⣇⣄⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣶⣀⠠⠀⣀⣹⡂⠲⠏⠐⠃⠀⠓⠾⠃⣇⣀⣠⣤⣿⠛⠟⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣾⡿⠋⣀⡤⠤⢤⡀⠀⠀⠀⣠⠤⠤⢄⡀⠈⠙⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠆⣴⣱⠀⠀⠀⠈⢢⢠⣞⡕⠀⠀⠀⠙⡄⠀⠀⠻⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠹⣧⢿⡀⢰⣶⡆⡸⢸⡟⣇⠀⣶⣶⢀⡇⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡠⢄⡘⠷⣭⣤⡭⠖⠁⠀⠙⢮⣥⣬⠵⠊⢀⡀⠀⠀⠈⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠁⣾⣿⣷⠲⢶⡶⢶⣶⠶⣶⡶⢶⣖⢒⣟⣿⣷⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡄⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢨⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠙⣿⣿⣷⠘⢏⡿⠻⣿⠿⣿⡿⠿⣿⣿⠿⣿⣟⣻⠟⠀⠀⠀⣠⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣼⣿⣿⡷⢄⡙⠒⠻⠦⠿⠧⠶⠾⠿⠖⠛⠉⢀⠄⠁⠀⢰⣿⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠁⠀⠀⢰⣿⣿⣿⡇⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣇⠀⠀⠐⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠄⠀⠆⢈⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠅⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣿⣷⡐⣦⣤⣹⣿⣿⣿⣯⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣴⣿⣣⣴⡇⡼⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⣿⡀⠠⠇⢹⣿⡿⠿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡁⠻⠀⣠⣿⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣿⣏⠀⠀⠊⢻⣷⣶⣦⣐⣤⣀⣴⣢⣴⣿⡃⠀⠀⠈⢂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⡸⠙⠻⠿⠿⠿⠿⠿⠛⠻⣿⣷⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠲⠾⠟⠓⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢗⣂⠐⣶⣆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣿⣿⣿⣷⣿⣿⣿⣶⣿⣶⣶⣶⡖⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠴⠖⠒⠛⠛⠉⠉⠙⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣩⠽⠀⠀⢰⣒⣒⣋⡋⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠉⠉⠀⠒⠊⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠔⠁⡇⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⢞⡭⠗⠒⠚⠻⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⣤⣶⠶⣷⣤⣀⠀⠀⠀⠀⠀⢳⠀⠀⣼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⣀⣼⣯⣶⠶⣤⡈⠙⢷⡄⠀⠀⠀⠘⡆⢠⣷⠿⠟⠛⠛⠛⠛⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢳
⠀⠀⠀⠀⠀⠀⡰⠋⠠⣠⡶⠟⠛⡋⢩⡴⠖⠲⢦⡉⠢⠈⣷⠀⠀⠀⠀⣷⢹⣷⡤⠀⠶⠶⣟⡛⠓⠒⠲⢤⡉⢷⠀⡀⠀⠀⠀⠀⠀⠈⢎⣇
⠀⠀⠀⠀⢠⠎⢀⠔⣽⠋⠀⠀⠀⣧⣿⠀⣴⢢⠀⢻⡄⠀⣿⠀⠀⠀⠀⢸⢸⣏⠀⣾⠛⠳⢦⣍⡓⢄⡀⠴⠷⠛⠀⠱⡀⠀⠀⠀⣀⠤⣀⢻⡆
⠀⠀⣠⣴⡥⠖⠉⣰⠏⠀⠀⠀⠀⠘⢿⣄⡛⢛⣠⣾⡴⠂⠘⢧⣀⠀⠀⡟⠀⠻⣆⠘⣧⠀⠀⠈⠙⢦⡙⢄⠀⠀⠀⠀⢳⠀⠀⡜⠁⠀⠀⠱⣿⡄
⠒⠛⠛⠲⢤⡀⢠⡏⠀⠀⠀⠀⠀⣠⡶⠾⢿⣭⣉⠁⠀⠀⠀⠀⠈⠙⠺⣤⣤⠤⠽⡧⠘⢧⡀⠀⠀⠀⠙⣎⢧⠀⠀⠀⠀⢇⢰⠃⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠉⣻⠀⠀⠀⣤⡄⠀⣿⣷⣀⣿⣯⢉⣷⣄⠀⠀⠀⠀⢠⡾⢩⡴⠾⣷⣦⣄⣸⡇⠀⠀⠐⢾⣋⣸⠀⠀⠀⠀⠘⣼
⠀⠀⠀⠀⠀⠀⡏⢀⣶⢸⡏⠙⡄⢻⣿⣿⣿⣿⣾⣏⣼⣧⠀⠀⠀⠘⠁⠋⠀⠀⠘⣷⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣹⡇
⠀⠀⠀⠀⠀⠀⢧⠸⡿⡄⡇⠀⢣⡾⢭⡛⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⠶⣤⣀⣀⣀⡤⠔⠋⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠸⡄⢣⠳⡔⡀⠀⠀⠀⠉⢓⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣆⠈⠓⠀⠀⣠⠞⣋⡭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠛⠷⣤⣄⣀⣀⣤⠾⠋⠉⠉⠛⠷⣤⣀⣀⣀⣴⠟⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠚⠳⠞⡵⠚⠁⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⠆⣠⡸⡄⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣼⡗⢦⣀⠀⠀⠀⠀⣀⣀⣤⠶⠟⠿⢶⣤⣀⣀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠁⣼⠉⣧⢻⠀⠀⠀⠀⠀⠀⣰⠋⣰⡞⠛⠛⠛⠛⠿⠟⠛⠋⠁⠙⡆⢹⠛⠛⠛⢛⣫⣍⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢠⡇⠀⢹⢸⠀⢠⢤⣤⣤⣀⠘⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠞⠀⠀⢰⠏⣠⣄⢹⡱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⢸⣿⢰⠇⣼⢁⡤⡌⠧⣄⣙⣌⠳⣄⣀⡀⠀⠀⢀⡴⠋⣴⣁⣀⣀⣀⡾⢠⡇⠈⣇⡇⡧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢸⡏⣻⣮⠹⡾⠀⠹⠦⣤⣬⣉⣁⣈⣉⣽⠆⠀⢯⣄⣤⣤⡤⠤⠭⠤⠶⠟⠀⠀⠟⠳⢷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠀⠀⡏⠉⡆⠀⠀⠀⠀⣠⠀⢀⡔⠒⢢⡀⠀⠀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⢈⠣⣄⣘⠤⠴⠃⡴⠁⠀⠀⠀⢰⢈⡦⠊⠀⠀⠀⢘⡤⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⡏⠀⠀⡜⠀⠀⠀⠀⢀⠼⢏⡀⠀⠀⠀⠀⠸⡀⢠⠎⠀⠄⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⢰⠁⠀⠀⢀⣶⠁⠀⠀⢣⠀⠀⠀⠀⠀⠉⠁⠱⡀⠀⠁⢀⡎⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢸⠀⠀⣠⣿⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠞⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘⡀⢰⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠄⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠱⠉⠒⠒⠒⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠖⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢱⠤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠚⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠈⠑⠢⡀⠈⠌⠹⡗⢒⣲⣶⠉⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⠀⠀⡀⠀⡐⡹⠴⠑⠒⢦⡂
⠀⠀⠀⠀⠀⠀⠦⠂⠉⠀⠀⠈⠑⠂⠌⡒⠄⢀⢈⣿⠿⡿⠀⠀⡸⠀⢠⠁⠀⠀⠀⢸⠀⣄⡬⠔⠋⠁⠀⠀⠀⠀⣸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠥⢤⣉⡡⠀⣲⣿⠃⠀⡰⠁⢀⡎⠀⠀⠀⠀⡰⠚⠁⠀⠀⠀⣀⠤⡄⠀⢰⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠈⠉⠘⠛⠁⠀⡰⠁⠀⡜⠀⠀⠀⠀⠘⠀⠀⠀⠀⡠⠊⠁⠀⢣⠀⠸⠜⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠂⠀⠀⠀⣀⠜⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠙⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡠⠚⠁⠀⠀⡜⠀⠀⣀⣀⡀⠤⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⠋⠓⠢⠒⠉⠀⠀⠀⢀⠎⡎⠈⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠀⡇⠀⠃⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⠁⠀⡀⡸⠀⠀⠈⠉⠉⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢅⣀⡀⠤⠚⠁⠤⠤⠤⠔⠁⠣⢄⣀⡀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⠒⢄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢤⡀⢸⢇⠳⣠⠎⣠⠈⢣⡔⡁⢸⠀⡠⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⣸⣐⣬⠶⠚⠛⠉⠉⠉⠉⠉⠉⠛⠚⠯⣤⣀⡇⣠⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⣰⢃⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⢀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣄⠀⠘⢿⡔⡊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠉⠢⡀⠀⠀⠀⣿⠀⠀⠀⠹⣤⢗⢚⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠆⠀⢀⠇⠀⠀⣰⡇⠀⠀⠀⠶⠈⠻⣼⢰⢺⠀⠀⠀⠀⠀⡴⢺⣷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⠊⠉⠉⠳⡄⠀⠀⠀⠀⠀⠈⠦⡀⠀⢀⡠⠊⠀⣠⡔⠃⠼⠀⠀⠀⠀⢿⡷⠘⢷⣾⡎⣇⢄⠠⠖⠻⣾⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⣶⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⡤⠞⢍⠅⠀⠀⠀⠀⠀⠀⠀⣤⣬⡋⣭⡳⠯⢦⣿⢼⡞⠷⢸
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠢⠄⠤⠔⠁⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠋⣥⠛⣥⣷⣦⡁⢚⣛⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⣀⣠⣤⠶⠚⠋⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⢉⣛⡛⢡⡜⠋⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠉⠉⠻⣙⠉⠑⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠺⠿⠗⠈⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠳⡄⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠲⠶⠋⣰⠋⠉⠉⠉⠙⢷⡄⢀⣤⠴⠶⠒⠛⠛⢳⡀⠘⡇⠀⠀⡴⠃⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠞⠁⠀⠀⠀⣀⣀⣸⠇⣼⠁⠀⠀⠀⠀⣀⣼⠃⠀⣽⠀⠘⠷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣭⣥⣤⠿⠀⠀⠀⠀⠸⢧⡤⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣒⣶⣿⣿⡿⡟⣋⡉⠉⠶⠶⢶⣤⣀⣀⡀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠘⠻⣿⣿⣿⣿⡇⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣯⠻⣷⣇⡀⠀⠙⠻⢿⡇⠀⠀⢸⣿⢸⣿⠀⠀⠀⣀⣤⣶⣿⣿⠿⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠻⢿⣦⡀⠀⠀⠀⠀⠀⠘⠛⣼⣿⣶⣶⣿⣿⣿⡿⠟⢁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣝⣻⣷⣤⣠⣤⣤⣤⣤⠛⠛⠛⢛⡿⠟⠋⡠⠔⣋⣥⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠿⠿⠿⠿⠿⠿⠿⠯⣒⣋⣉⣥⠄⣠⣦⡸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣾⣿⢿⣿⣮⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣿⣦⡀⢀⣼⣧⠀⣿⠃⠙⢿⡿⠏⠈⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠛⠛⠻⣿⣿⠇⠀⣿⣧⠀⠀⣤⣤⣶⠖⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⢻⠟⠀⠀⣿⣿⣆⣠⣅⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⡄⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢈⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠛⠛⠿⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣩⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠋

⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠉⠢⢀⠀⠀⠀⠀⢀⠠⠐⠂⠁⠁⠀⠀⠀⠀⠉⠐⠠⢄⠀⠀⠀⢀⡠⠊⠀⢡⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠂⠄⡀⠑⠢⡠⠊⠁⠀⠀⡠⠐⠈⠀⠀⠀⠈⠐⢄⠀⠀⠈⠂⢔⠁⢀⠄⠊⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠊⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠈⠂⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠑⠈⢀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠰⠀⠀⠀⠐⠀⠂⠀⠐⢧
⠀⠀⠀⠠⠐⠠⡀⠀⠀⠀⠀⡘⠤⢃⠀⠁⠃⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠰⢀⢁⠉⡀⠀⠀⠀⢀⠔⠀⢢
⠀⠀⠀⢁⠀⠀⠈⠄⠀⠀⠀⠃⠀⠅⠅⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠇⠀⠀⢀⠃⠀⠀⠘⢀⠀⡀
⠐⠁⠈⠐⢦⡀⠀⢰⠀⠀⢀⡤⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠑⠠⢄⠀⠀⢸⠀⠀⡴⠋⠀⠀⠈
⢇⠀⠀⠀⠀⠙⠀⠈⠀⠈⠁⡠⠂⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠢⡀⠈⠁⠁⠀⠈⠀⠀⠀⠀⡠
⢀⠁⠖⠂⠤⠄⠀⠀⢀⠔⠊⠠⠀⡈⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠈⡀⢀⠁⠑⠤⡀⢀⣀⠒⠐⠛⠁⠂
⢀⠀⠀⣀⣠⠂⠀⠈⠑⠠⡀⠈⡤⠁⠰⠀⠀⠀⠀⠀⠘⠁⠒⠠⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠘⠀⠐⡌⠀⡠⠐⠉⠀⠀⢱⠦⠄⣀⡠
⠀⠈⠀⠀⠄⠂⠄⣀⡀⠀⠈⠒⠁⠀⡀⠀⠀⠀⠀⠀⠃⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠊⠀⢀⣀⣠⠴⠡⠂
⠀⠀⠀⠀⢀⠂⠉⠉⠉⠉⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠐⡀⠀⠀⢀⡠⠔⠀⡄⠰⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢠⠀⠒⢤⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠉⢁⠋⠀⠀⡸⡀⠀⡁⢀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢘⠀⢀⢆⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠔⠀⠀⠁⠀⠈⠀⢀⠉⠒⠠⠄⠀⢀⣀⠀⢀⣀⣀⠀⠀⠤⠰⡊⠀⢁⠀⠀⠈⠁⠀⠑⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⡀⠐⠤⣴⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣈⣠⠐⢂⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠀⠀⠀⠀⣀⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠁⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠢⠀⣀⡀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⢠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⣯⣵⣿⣿⡟⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⣠⡿⠃
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠸⣿⣍⡛⠛⠛⣉⣤⠾⠋⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣀⣤⣿⣟⠛⠛⠉⠉⠀⢠⡄⠀⠀⠀⠀⠀⣻⣷⣤⣠⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠰⣽⣿⣿⣿⣿⣿⣿⣄⣴⠀⠀⠀⢸⡇⠀⠀⠀⣦⣠⣿⣿⣿⣿⣿⣿⣯⠆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣆⠀⠀⠾⠷⠀⠀⣰⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠐⣮⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⡧⣿⣿⣿⣿⣿⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣿⣿⣧⡀⢻⣿⢿⡻⢟⣿⣽⡻⢟⡿⣿⡟⢀⣼⣿⣿⣿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣦⣁⡀⠀⣿⣿⣿⣿⠀⢀⣈⣴⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⡿⠟⢻⣿⣃⠙⠻⠟⠋⣘⣿⡟⠻⢿⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣌⡙⠛⠛⢋⣡⡞⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠌⠙⠓⠚⠉⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⣄⢤
⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⢤⡄⠀⠀⠐⡤⡀⢀⠀⠉⠁⠀⠀⠀⠀⠁⡄⠀⠀⠆⢀⠀⣯⡼⠏
⠀⠀⠀⠀⠀⠀⠀⢐⣦⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡏⠀⠀⠶⠛⠀⠀⢀⡴⢮⣿⣤⠀⠈
⠀⠠⠚⡠⠟⠀⠖⡾⠋⠁⠉⠑⠠⣀⠀⠀⠀⢒⠢⢈⣻⠋⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠙⢏⡺⣄⠸⣯⡀
⠀⠑⠚⠁⠀⢀⠋⠀⠀⠀⣿⣶⣄⠀⠑⠄⠀⠉⠀⠞⠩⣠⠄⠀⠀⠄⢀⣴⡶⢶⠆⠀⠀⠀⠈⠙⢅⠀⠈⠁
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⣿⣿⣤⡀⠀⠀⠐⡀⠀⠀⠚⠁⠀⠀⢀⣲⠋⣞⣲⣶⠂⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠹⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠈⢾⣓⣒⣲⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠙⣿⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠳⠶⠆⠀⠀⠀⠑⠤⢀⡀⢀⣀⠀⠀⠀⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠈⢁⠈⠒⠂⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃
⠀⠀⢰⡇⡶⠄⠀⠙⠧⠀⠀⠀⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠰⣄⠀⢀⣤⢄⣀⣀⡀
⠀⠀⠀⠙⢤⣤⡀⠀⠀⠀⠀⠀⠁⣤⠾⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢹⡄⠀⠻⢆⠰⠖⠚⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢠⠞⠁⢠⡀⠀⠀⠠⠖⣸⠆⡇⠀⠀⢸⠀⠀⠀⠈⠓⠦⣄⡉⠉⠀⠀⢷⡂
⠀⠀⠀⠻⠖⠀⠀⣠⠞⠀⠴⠃⠀⠀⢸⠀⢠⠀⠙⠋⠀⠀⡇⠀⠀⠸⡄⠀⠀⣦⠀⠀⠀⠉⠲⣄⡀⡀
⠀⠀⠀⠀⠀⢀⡴⢃⡀⠀⠀⣷⠀⠀⢸⠀⢘⠀⢠⣤⠀⠀⡇⠀⠀⢨⡅⠀⠀⡧⠀⠀⢀⠀⠄⠈⠉⢫
⠀⠀⠀⠀⡰⠋⠀⠀⡇⠀⠀⣿⠀⠀⣸⠀⢸⠀⠈⠳⠂⠀⡇⢠⠀⢘⡃⡀⠀⡏⠀⠀⠀⡅⠐⠀⠀⠀⢧
⠀⠀⠠⠎⠀⢲⠀⣀⣇⣀⣤⣿⣠⣤⣿⣄⣼⠀⠀⠀⠀⠠⠧⠼⠶⠾⠦⠷⠴⠷⠤⠦⢤⣇⣀⠀⠀⠀⠈
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠴⣄⣀⠀⠀⠀⠀⡀⠀⡰⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢉⣇⣠⣤⡄⢀⣀⢰⠞⠀⠀⠺⢃⡇⠀⢠⠫⠁⠀⠀⣠⠤⠷
⠀⠀⠀⠀⢀⡱⠖⠁⣀⡟⣹⣖⣢⡾⣿⠃⢨⡿⠉⠻⠀⠀⠀⠛⠃⠀⠈⠈⠉⠀⡴⠕⠀⣀⠐⣄⠀⠀⢀
⠀⢁⢀⣑⣺⠁⠀⣿⣛⠐⠂⣿⠁⠀⠋⣡⡴⠆⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠆⠸⠍⠀⣿⠀⠀⠠⣄
⠀⠘⣠⠄⢸⢇⣀⢿⢟⢀⢀⡹⠖⢋⠄⠉⠁⠈⠁⠀⣠⡨⠤⠀⠠⣀⣀⣈⠀⠀⠀⠈⠂⠶⠚⠁⢀⢔⠀⢀⠠
⠀⠈⠀⠀⠰⠺⠿⠞⠟⣄⣀⣉⣼⣀⠀⠄⠂⠀⠠⡎⣸⠻⢌⣪⡝⢤⠛⠳⠄⢀⡀⠂⠀⠀⠐⠊⠝⠄⣶⠀⠁
⠀⠀⠈⠓⢢⣬⣓⠆⢀⣠⠬⠋⠋⠁⠀⠀⠀⠁⠀⢙⡉⣹⢞⡿⠧⠾⠒⠁⠀⠉⠁⠀⠀⠀⠈⡁⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠡⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠛⠛⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠁⠀⠀⠀⠉⠻⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠰⠶⢶⣤⣀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠙⠳⣄⠀⣸⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠹⣧⣿⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠈⠀⠉⠉⠈⠉⠉⠈⠁⠁⠉⠀⠈⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠁⠀⠀⠈⠉⠻⠇⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢠⣤⣤⣼⣿⣿⣥⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠈⠛⢻⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⣀⣸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁


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

⢀⣤⠀⣔⣃⡠⠤⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡀⠀⠀⠀⡴⢦
⠘⢬⡎⠉⢀⡄⡀⠀⠔⠩⢍⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣦⠎⢱⣠⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⢱⠀⠀⢰⠇⢸
⠀⠀⡀⢠⢬⡀⠁⣀⣃⣈⣁⣀⠀⠀⠀⠀⠀⢀⡖⠢⠴⠃⠀⠋⠀⠘⠁⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠀⠈⡆
⠀⠀⡇⣷⠀⠙⠫⠿⡼⣇⠧⠟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢠⡎⠰⠰⠆⠰⣂⣒⡏
⠀⠀⡇⠙⢄⣀⡀⣲⡐⡤⣂⠔⣆⠀⠀⠀⠀⣘⠰⣍⣱⣀⠝⠀⠯⠮⠝⢺⡴⡄⠀⠀⠀⠀⢸⠘⢞⣣⠛⣤⢣⠟⣜⣧
⠰⣆⡇⠀⠀⠀⠉⠉⠉⠉⠁⠀⣇⣴⠆⠀⠀⡏⠐⠲⠿⠶⠷⠮⠷⠾⠽⠞⠒⠛⠳⡄⠀⠀⠸⡄⠀⠀⠀⣀⣁⣁⣀⡠⠁
⠀⠉⠑⠤⣀⡀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⣧⡤⢤⡀⣀⣀⡀⢀⣀⣀⢀⣀⢀⣀⡝⠀⠀⠤⢵⠀⠀⠈⠉⠉⠀⢠⠅
⠀⠀⠀⠀⠀⠡⡌⠉⡽⠏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠀⠀⠣⠏⠉⠙⠼⠙⠞⠉⠃⠀⠀⠀⠀⠣⠜⠀⠀⠈⠻⠍
⠀⠀⠀⠀⣀⡄⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡐⡄
⠀⠀⠀⡼⠁⣁⠐⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢡⠍⢲⠼⠶⠞⠁⢠
⠀⠀⢀⠗⠀⠉⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠑⠶⣾⢁⣄⢀⡄⢀⣀⡙⡽⠄
⠀⢠⠃⡤⢤⡦⡄⢰⠱⢋⠎⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡞⠁⠀⠀⠀⠈⢢⡀⠀⠀⠀⢸⠈⠉⠉⠙⠛⠣⠯⢼
⠀⡎⢀⡉⣉⠉⣁⡀⣩⣁⢄⡇⠀⠀⠀⠀⠀⢰⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠇⠘⠚⠤⠿⠤⠿⠴⠯⠜⢳⠀⠀⠀⠀⠀⠈⡎⢧⡀⢀⠇⠀⠘⡗⠀⠀⠀⠘⠦⡠⠤⠃⠀⠀⠀⠀⠀⠀⢰⠃
⡰⢋⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢉⠆⠀⠀⠀⠀⠙⢄⡉⠁⠀⣠⠇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠑⠉⠈⢲⠄⣀⣀⡀⢠⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡉⡦
⠀⠀⠀⠘⠜⠁⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠌⠙⡖⢢⠤⠤⠀⠒⠒⠛⢄⠜
⠀⠀⡀⠀⢀⣴⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠀⠀⢀⡄⡀⢠⠀⠤⠤⠤⠤⠤⣄⣄⣠
⠀⠈⢯⠒⢁⡤⡄⠀⢏⣂⠶⣀⡠⢤⠎⢳⡀⠀⠀⢀⠔⠒⢤⠖⢲⠎⣀⠉⢱⡀⠀⠀⠘⠋⠸⢠⡪⠏⣱⠀⡖⠶⠢⢸⠈
⠀⠀⠀⡇⠘⠤⠂⠀⣠⢲⡶⠭⠧⠚⠒⠁⢸⠀⠀⢺⡘⣃⠴⡄⠘⢄⣉⣠⠜⠁⠀⠀⠀⠀⡇⢀⢩⡭⣄⢤⢈⣭⡥⠚
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⡞⣷⢢⡜⡏⠀⠀⠀⠀⠀⢀⠴⠃⠀⠉⠑⠉⠋⢹⣉
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⡰⠋⠉⠉⢹⠃⠀⠀⠀⠀⠀⠷⢹⠀⠀⠀⠀⠀⠀⢸⠳⡇
⠀⠀⠀⠈⢙⢲⢲⠀⡎⠈⢳⢸⠉⡏⡟⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡀⠀⠀⣀⡼
⠀⠀⠀⠀⠸⡍⠸⠀⠃⠀⠸⠎⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠱⣲⠖⢜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠵⠉⠉⠹⡍
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⢀⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠲⠂⢀
⠀⠀⠀⠀⢠⡤⠋⠉⠈⠋⠙⠃⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠸⢻⡇⠀⠀⠀⠀⠀⠀⢠⡖⢊⠐⣦⠀⠀⠀⠡⢸⣷⠄⡎⡂
⠀⠀⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡧⡀⠀⢀⡸⡌⠀⠀⠀⠀⠀⠀⠀⠰⣆⠚⢃⢼⠀⠀⠀⠢⡙⠉⡚⠵⠁
⠀⠀⣠⠋⠀⠀⠛⠀⠛⠀⠘⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⠀⠠⢀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⡈⢣⡀⠀⠀⡇⢸⠁
⠀⠀⢹⡁⠀⠀⠀⢠⣄⣀⡄⠀⠀⠀⢀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠠⠷⠈⡆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠱⣄⣠⠁⡇
⠀⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠀⠀⠊⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠈⠀⠀⠙⢦
⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⣁⣋⣀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀⠀⢀⣈⡶⢣⣀
⠀⠀⠀⠀⠘⠓⣤⣄⣠⣀⣀⣤⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⠉⢣⠎⠉⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠰⠿⡿⡇⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⠠⠀⡌⠸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠤⠒⠂⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣁⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⢤⣦⡀⠀⠀⠀⢠⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠰⣀⡓⠀⠂
⠀⠀⠀⠀⠠⠘⠃⠓⠒⠒⠒⠚⠚⠂⠀⠀⠀⠀⠀⠀⢀⡔⠚⠁⠀⠀⡆⠀⢠⡄⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠙⠃⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⡆⠀⢠⠀⡠⠄⠀⠀⢰⠀⠀⡶⡀⢣⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠴⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠻⠿⠟⠀⠀⠀⢠⠀⠀⠀⠀⠸⠀⢸⢃⠀⠸⣾⣿⣾⣷⣿⣾⠀⠀⡇⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠜⡆⠀⠠⠄⠄⠠⠄⠀⢀⠀⠛⡂⠀⠀⠀⢰⣤⣼⠈⢦⠀⠙⠸⠃⠙⠘⠃⢀⡖⣹⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠀⢄⠀⢀⡀
⠀⠀⠀⢈⣄⠀⠀⠀⠀⠤⠤⠔⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣠⣄⠀⢰⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠾⠷⡔⠁⣀⠀⢀⡀⠉⠚⠃
⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⢸⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠁⡀
⠀⠀⠀⠀⠀⠀⡀⠄⠡⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⡇⢸⡀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⢀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠲⣄⡀⢀⣀⡸⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣤⡀
⠀⠀⠀⠀⠀⢀⡖⣀⠀⠀⢀⣄⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡵⠖⠂⠀⠒⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠃⣀
⠀⠀⠀⠀⠀⣦⠀⡋⠀⠀⢀⣉⠠⢃⠀⣀⢤⡀⠀⠀⠀⣠⣤⡠⠏⣴⣶⠄⣴⣻⡓⣜⢂⢰⡻⠄⠀⠀⠀⠀⢠⡄⠀⠠⣶⠀⠀⢰⡖⠀⠀⠙⡄
⠀⢼⠃⡀⠐⠀⠀⠻⣾⣿⠿⠏⠀⠈⠁⡤⠠⠇⠀⠀⠀⠈⢤⣧⠀⠛⠛⠉⠿⣽⣧⠏⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢡
⠀⠈⠋⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣶⣶⣦⣿⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⠋⠿⠛⠁⡼⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢋⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠦⡀⠀⡠⠚⢡⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠨⠀⢰⠂⠰⡄⠸⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠰⡀⠈⠚⠁⢰⣈⣆⠀⠀⠀⠀⠀⠀⠀⠳⡤⡠⣀⢄⡤⠠⠤⢄⠠⣤⠄⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠔⠂⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢠⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠉⣀⣀⠘⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠰⠐⠤⠠⠤⢀⡈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡵⣏⡇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠄⠀⠲⠂⠰⠆⠐⠖⠁⡤⠈⠂⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣈⣉⣴⣶⣤
⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣯⣝⣛⣫⣹⡾⢋⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠉⠙⠉⠉⢠⠉⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠚⡵⠋
⠀⠀⠀⠀⠀⠀⣼⠆⣶⠆⢺⡎⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⣉⡰⠂⡐⠏⡁
⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠄⠒⠀⠀⠈⠃⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠀⢀⢀⣀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠄⠀⢸⠞⠉⢆⠀⠀⠀⢀⠉⠀⢀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡀⢀⠈⠙⠖⡋⠘⠂⠂⠀⠚⢂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠉⠐⡀⠚⡅⠛⠐⠧⡤⠀⢶⠀⠆⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠸⠖⠌⠀⠸⠧⡇⠀⡀⠠⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⠷⡀⡁⠞⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⡄⠀⡐⠂⠄⠈⠙⢱⠾⠶⣁⠀⠀⠒⣈⠦⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠘⠛⠲⣄⢸⡆⢠⡄⣵⢀⡔⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠈⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠠⠀⠀⠀⠀⢀⠊⠘⡁⡀⠀⠀⢀⣸⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠸⠷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠞⠀⠀⠀⢱⠈⠑⠔⠀⡆⢥⡀⠀⠀⠀⠻⣄⠀⠀⡾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⢄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠁⢀⢧⠀⠀⠀⠀⠈⠀⠀⠙⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠟⠴⡆⣿⢳⡄⠧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⢀⣬⠀⠀⠀⢿⠠⠃⢰⠀⢀⠀⠀⠀⠐⠶⠄⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣁⠛⢢⡀⠀⠸⣧⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣍⡄⠀⠳⠀⠀⡿⣇⢰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣧⡟⢰⡗⠀⣰⠇⣇⣿⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠈⠀⢀⣤⡠⠞⡩⠀⡞⠀⡐⠛⣠⣿⠟⠀⠸⣁⠉⣠⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⠂⠀⠴⠦⡈⠀⠄⠀⠊⢀⣼⠁⠐⣇⠀⢼⡸⣟⡄⠁⠀⠀⢨⣄⠠⠀⠀⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⢄⡑⠆⠀⠑⠲⡆⠰⠶⠋⠉⠃⢰⡿⠄⠀⠓⠿⠄⠒⠀⡴⠕⠘⠧⠀⣀⠀⠀⠀⢀⡀
⠀⠅⠀⠀⠀⡠⠄⠀⠈⠀⠘⠉⣔⠊⡇⠀⠀⠱⠀⢢⡀⠁⠸⠸⠫⢶⡀⢢⣴⠲⠶⢏⡁⠀⠈⠦⠘⠋⡈⢰⠐⠊
⠀⠂⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠈⡠⠇⣘⠂⢀⡲⡦⢄⢠⡴⢐⠁⢺⠀⣠⠀⠀⠐⢀⠱⠀⠁⠀⠆⠀⠐⢣⣄⠀⡁
⠀⠀⠀⠀⠀⠀⠘⡂⠀⠘⠑⠄⠘⣠⠠⣀⡼⠏⠀⠀⠀⡈⢤⢀⣀⠈⠻⠑⡀⢠⠀⢀⠠⠃⠂⠉⠤⡷⠄⠀⠀⠈⠉
⠀⠃⠀⠀⠀⠈⠒⠓⠖⣠⡄⠐⠀⡠⠏⠈⠀⠚⠀⠀⠀⠈⠠⠠⠈⡼⠀⢈⠲⢈⡕⠠⠆⠠⡄⠹⠏⠀⠉⠁⠠⠐⠐⠒
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠘⠂⠀⠀⠀⠀⠀⠚⠒⠈⠁⠀⠁⠀⠉
⠀⠛

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄
⠀⠀⠷⣅⣡⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠠⣆⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢄⡀⠀⠀⡾⢋⣷⠍
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢄⡀⠀⠀⡄⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⡀⢡⠆⣴⠇⠀⢀⣠⡄⠀⠀⠀⠀⣈⣦⣤⡀⠉⠀⠆⠀⠙⠋⠁
⠀⠀⠀⣀⠀⣀⠀⠐⠀⣠⣿⡿⢐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢺⣶⠟⠀⠀⠛⠉⠀⠀⢀⡠⠜⠛⠻⠿⣿⣁⠠⣀⠀⢀⡄⠄
⠀⢀⠊⢡⠄⠟⠀⣘⢛⠋⠁⠀⠀⠀⠈⠑⢄⡀⠀⠀⠈⢢⣙⠆⢀⣝⠁⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠈⠫⣘⡛⡆⠈⢷⣼
⠀⠘⠒⠋⠀⠀⠀⠈⠁⠀⠀⠀⢘⢿⣦⣄⠀⠈⠲⡀⠀⠉⠀⢑⠞⢩⣱⡄⠀⠀⡔⠁⣠⡴⣶⣶⡶⠀⠀⠀⠀⠁⠉⠻⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣞⣿⣿⣉⠀⠀⠀⠀⢤⡀⠀⠀⠀⠶⠋⠀⠀⠄⣤⡴⢷⠾⡤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⢓⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠐⠓⣇⣼⣁⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣸⣷⢿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⠻⠽⠥⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠏⠀⠀⠀⠀⡘⠀⢀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠑⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠘⠗⠶⡦⠀⠀⠀⠙⠢⢄⠀⠀⠀⢀⡀⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠲⠶⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢴⣾⠻⠆
⠀⠀⠀⢠⡤⢀⡀⠀⠀⣶⡆⠀⠀⠀⠀⠀⡀⠀⣸⠇⠀⡆⠀⠀⠀⠀⠀⠃⠀⠘⠓⠂⠀⠀⠀⣀
⠀⠀⠀⠸⡤⠊⠁⠄⠀⠀⠙⠁⠀⠀⠰⡎⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠈⢷⠀⠀⢸⣏⠑⠶⢦⡒⣤⠄
⠀⠀⠀⠀⠈⠠⠵⢦⠀⠀⠀⠀⠀⠀⠀⢀⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠂⢸⡇⠀⠈⠛⢦⣊⡋
⠀⠀⠀⠀⡀⠀⠀⣸⠃⢀⠀⠀⠀⠀⣠⠟⠀⠀⣤⠀⢰⠀⢀⡴⠆⣼⠆⣄⠀⠀⠀⢸⠀⠀⠀⠠⠀⠙⠳⢤⣄⡈⠉⠁⠀⠈⢿⡆
⠀⠀⠀⠀⢯⡴⠀⠁⠀⢀⡶⠂⢀⡼⠃⠀⠀⠀⢸⠀⢸⠀⠘⠞⠋⠁⠀⣿⠀⠀⠀⢸⠄⠀⠀⠀⣄⠀⠀⠀⠈⠙⠢⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⡄⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠻⠀⠀⠀⠁⠄⠀⠈⠻⠶⡶
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠒⣦⠀⠀⠀⡿⠀⠀⢀⡛⠀⢸⠀⠐⣯⠓⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⠀⢰⠄⠁⠆⠀⠀⠘⣆
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⢸⡇⠀⢸⠀⠀⠀⠉⠀⠀⣿⠀⡦⠀⢨⡄⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠂⠀⠀⠛⡄
⠀⠀⠀⠰⠋⠀⢐⡆⢀⣀⣧⣀⣴⣼⣯⣠⣤⣼⣧⣤⣼⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠾⠷⠾⠷⠶⠶⠦⠴⢦⣼⣦⡀
⠀⠀⠀⠐⠀⠈⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠚⢻⡇⠀⣀⣀⠀⠀⠄⠉⣨⡿⠀⠀⢀⣶⠀⡷⠀⠈⢠⠖⠆⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠤⡀⢀⡤⠀⢠⡤⢀⢀⡀⢀⣸⣿⠀⠸⣷⡷⣿⣾⠃⠀⠚⢀⣿⡄⠀⠀⢀⣡⠔⠁⠀⣰⠋⠊⣀⡀⠀⠑⠛⠉⠉
⠀⣀⠀⡀⠀⢰⣦⠛⠁⣠⣄⡫⠉⠙⣮⡵⠿⢻⣧⡀⢸⠟⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠜⠁⠁⢀⣤⡀⢳⡄⠀⠀⠀⠄
⠀⠨⡈⣅⣙⣹⡇⠀⠈⣿⣋⡉⠉⢙⡿⠀⢀⠚⢀⣽⡗⠒⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠸⠀⠻⠅⠁⣸⡄⠀⠀⠀⣦⠄
⠀⠀⠃⣀⡀⢸⣗⣀⣀⡿⠶⠂⡀⠀⢯⠔⠋⣀⠈⠙⠁⠊⠉⠀⠀⡀⣈⣄⡀⠠⢀⠀⠀⠀⡉⠀⠀⠀⠀⠑⠠⠤⠾⠊⠀⢀⡜⠁⠁⠀⡄
⠀⠀⠒⠑⠀⠀⣤⣽⣇⣻⣮⠄⠉⠀⠂⢀⠊⠁⠀⣀⠠⠄⢀⣤⡾⣹⣯⡒⠠⡞⢟⣉⠹⣾⣄⠀⠀⠀⢠⡒⠄⠀⢀⡤⠒⢷⡈⣤⠀⡙
⠀⠀⡐⢠⣄⠈⠠⣌⣉⠈⠉⠄⠰⠶⣚⠯⠗⠊⠉⠀⢀⢀⠉⠙⣕⠾⢬⣉⣿⣿⠂⢸⣇⣤⠉⠁⡐⠶⠀⠀⠀⠀⢠⠤⠈⢴⠇⠘⠃
⠀⠀⠀⠀⠈⠘⠳⠮⢅⡀⢠⠴⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣴⣭⣽⣛⣛⣋⣉⠀⣀⠀⠀⠀⠀⠀⠀⠀⢘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠐⠒
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣥⣬⣧⣴⣤⣵⣬⣼⣯⣵⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⠉⠁⠀⠀⠀⠀⠠⠀⠀⣛⡋⢿⡿⢿⣿⣿⣿⡿⠛⣛⣁⣼⣿⣿⣿⣿⣿⡷⠀⣿⣿⣿⣿⠃⡞⣿⠯⢻⢿⠾⣿⠿⠿⢿⠿⠇⣿⢻⣿⣿⠏⣾⣯
⡟⠀⠀⢠⣶⣾⣆⢿⣄⠀⠘⢟⣣⡝⢣⣾⣿⣿⡏⢰⣿⣿⣿⠛⠉⠉⠁⠀⠀⠀⢀⣿⣿⣿⣿⡇⢿⣷⣶⠄⡉⠀⠀⠀⠀⠀⠈⠴⣡⠔⢛⣥⢖⡣⠬
⣧⠀⢄⠹⠿⠿⠟⠘⠃⠈⠀⠙⠿⢃⣼⢼⣿⣿⡅⣿⡯⡉⠀⢠⣶⠀⠀⠃⠀⠀⠈⠿⠿⠻⢿⣿⢀⣥⡏⢧⠀⡀⣤⢀⡀⠀⠸⣵⠇⠚⠁⠀⠉⠲⣀
⣿⣦⠄⣉⣒⡂⠀⠀⠀⢀⡀⠀⣸⣛⠉⠸⣿⣿⣧⠺⣹⠍⡄⠀⠀⠐⠀⠀⠄⠂⣠⣴⣶⣦⡀⠙⠘⡿⠃⠀⢀⠼⣷⠷⡷⠀⠀⠦⡀⠀⠉⡠⠐⢃⡄
⣿⣿⣷⣌⢠⠀⠰⡆⠺⠿⠿⠛⠋⣶⣌⡠⠈⠊⣿⣶⣝⠺⠁⠀⠀⠀⠀⠀⡑⡄⢿⣿⣿⣿⣧⡀⠀⠓⠓⠀⠈⠚⠛⣷⣼⢶⣤⠂⠈⡀⠀⠶⠂
⣿⣿⣽⡛⣴⠟⣶⣧⣤⣶⡤⢤⣤⡼⣿⡅⠉⠒⡂⠿⡧⠀⢠⣄⣀⠀⠀⠀⠀⠀⢀⠁⣀⣤⣤⡥⣖⠀⠖⠟⣃⠀⠀⢸⡿⠖⢎⣡⣰⣹⣭⣹⣠⠄
⣿⣿⣿⠁⡅⠀⠀⠀⠉⠉⣹⡟⣿⣾⡟⠀⠀⠀⠘⠃⠁⢀⣿⣿⠿⠃⠀⠀⠀⢀⠈⠙⠽⠻⠛⠟⠃⠀⢐⠺⣜⢧⠶⠞⡕⣦⠆⠄⠺⠟⣛⣿⢿⢣⡅
⣿⣿⣿⣆⠓⢄⠀⠀⡄⢲⣨⠃⢙⣒⡇⢤⣤⣴⣤⡤⢈⣧⣃⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠸⠃⡉⢦⡞⠓⠀⠀⠀⠀⠘⠃⠛⠧⠜⢚⠂
⣿⣿⡿⠏⠴⢀⡐⠼⠷⠘⢁⣴⣏⡹⠇⠠⡄⠈⣤⣤⡈⠉⣍⠀⠶⠦⣲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠙⠀⠀⠀⠀⠀⠀⡀⠀⡠⠐⢊⣂
⣿⣿⣾⠂⠈⠺⣷⣶⡜⠻⣿⣿⣿⠃⣾⠄⢹⡛⠟⠁⣻⣳⢉⣤⠑⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠂⢀⣄⢻⣷⡝
⣿⣿⣿⣶⣆⠀⣿⣹⡆⠀⠸⢟⣾⣦⠛⠰⣆⣀⠐⢛⣫⢳⣾⣿⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠐⠀⠀⠀⠀⣾⠁⢠⠀⡶⠂⣂⣨⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠀⡅⣿⡇⠀⠀⠉⠛⠉⢀⡈⣿⣿⡇⢮⣦⣿⣾⠟⡃⠾⢷⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠻⠦⡤⠀⢿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠀⠀⠈⠶⣰⣷⡐⣢⢠⡔⣮⣷⣤⣩⡙⢂⣀⡁⠧⠸⠿⢶⡆⢸⣿⣿⣷⣤⣾⣞⣠⣴⢿⣿⡗⠀⠃⠀⠀⣀⣶⡆⠈⠀⠀⢸⢿⣿⣿⣿⣿
⣿⣿⠄⠀⠀⢈⠀⢀⡿⢟⣣⡿⠜⠃⠉⠙⠛⠨⢑⠸⠷⠍⢶⠉⣾⡀⠀⠀⠙⠛⠛⠉⣡⡆⠘⠿⠿⠛⠁⠈⣻⣿⡁⠀⠈⠀⠀⠀⢀⡄⠀⢻⣿⣿⣿
⣿⣇⠀⠀⠀⣠⡄⡯⠀⠉⠛⡴⣀⠀⣄⠀⢀⠀⣼⠢⠰⢐⢂⢠⡞⡥⣤⢠⠄⠀⠀⠰⠋⠙⠀⠀⠀⣀⡀⣠⣿⣿⣿⣿⠽⠀⢀⣼⣿⡗⠀⣸⣿⣿⣿
⣿⣿⣤⠛⠓⠋⠠⣴⣷⠀⡸⣆⠛⣠⠟⠊⠻⡁⢘⠁⠀⠨⡘⣾⣷⣿⣿⣿⣖⣭⠀⣄⢠⢀⣠⡞⣿⣿⠻⠨⣿⠿⠿⠁⠀⣠⣿⣿⡟⢀⣾⣿⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠆⢭⠙⠻⠇⡀⡉⠣⠰⢈⣤⡀⠀⠀⠀⠘⣿⢿⡿⠎⠁⠖⠈⠉⠀⠉⠉⠀⠉⠙⠛⠋⢀⣼⣿⣿⡗⠀⢠⣿⣿⣿⣅⠘⠿⣻⣿⣿⣿
⣿⣿⣿⣿⣄⡀⠀⠄⢿⣿⠞⠀⠀⠑⣾⣿⠸⢇⣀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢀⡄⢀⣄⢠⣤⠀⢠⣶⣿⣿⣿⣿⡃⠀⢸⣿⣿⣿⣿⡟⣈⣀⢄⢹⣿
⣿⣿⣿⣿⣟⣳⣦⣤⣀⢠⡔⠖⣀⣽⡈⣱⣽⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿⠻⠾⠼⣈⣏⠜⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⡿⠿⠛⣱⢟⣿⣾⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠄⠁⠈⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣀⠆⠀⠀⠀⠀⠀⡐⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⢀⡠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠎⠀⠀⢀⡄⠀⠀⠀⠀⠀⢆⠀⠰⣆⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠆⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⡀⠀⠀⢈⡀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⢀⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣴⠿⠟⠃⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡠⢤⣀⠀⢿⣧
⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠙⠒⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠙⡀⠈⣿⡆
⠀⠀⢀⣾⠏⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠇⠀⠸⣿⡀⣴⣶⡄
⠀⠀⣼⡇⠀⣤⡶⠟⠛⠛⠛⠛⢿⡛⠛⠿⠿⢷⣶⣤⣍⣙⠲⠦⣀⠀⠀⠀⠀⠀⠀⠈⣤⡀⠀⠀⡇⠀⠀⠹⣿⠏⢸⣧
⠀⠀⣿⡀⠀⢉⠧⣤⣄⣀⣀⣀⣀⣉⣑⣶⣦⣤⣤⣬⣽⡿⠿⢶⣤⣍⡐⠀⠀⠀⠀⠀⠈⠙⠃⠈⠀⠀⠀⢰⡿⠀⠸⣿
⠀⠀⠹⣷⣄⠹⣦⣀⣈⣙⣩⣿⣿⠟⠋⠁⠀⠀⢀⠀⠀⢀⡀⢀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢐⢻⣇
⠀⠀⠀⠈⠙⠻⢾⣿⣿⣾⣟⣁⣤⢔⣢⣴⣦⣼⣷⣴⡶⠞⠛⢿⣰⣄⣇⣴⠀⠉⠙⠻⣶⣤⣀⣁⠀⠀⢰⡟⡔⠂⠌⠤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣟⣥⣈⣩⣿⠇⠀⠀⠀⠀⠈⠋⠛⠻⠟⢷⣷⣤⣶⣤⣿⢯⣙⣛⣿⡟⠁⠃⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⣿⠋⠛⠛⣿⡟⢀⣾⣧⠀⠀⢀⡀⠀⠀⣷⢸⣷⣬⣴⣾⣿⠶⣮⣽⡿⠁⠄⠀⠀⠀⠄⣰⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢼⡇⠀⢠⣿⠀⣼⣿⣿⠀⠀⣾⣿⡆⠀⢟⢸⣿⠷⣿⣿⣿⣿⠿⠛⠀⠀⠀⢀⠀⠀⠀⠈⠒⢁⡼⠃
⠀⠀⠀⠀⠀⠀⣀⡴⣏⠀⢀⠐⢸⣧⠀⣼⠇⠀⣿⣿⠇⠀⢸⣿⣿⠀⠀⠈⠈⣿⠀⠀⠀⢾⣇⡀⠀⠀⠀⠀⠘⠂⠀⣀⣀⣴⠾⣅
⠀⠀⠀⢀⣴⠞⠋⠐⠁⠀⠀⠀⠀⣿⣀⣿⠀⠀⠟⠋⠀⠀⠸⠿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⣹⡟⠛⠶⠶⠶⠶⠾⠟⠛⠉⠠⣀⣿⠇
⠀⠀⠀⢾⣥⡄⠒⠚⠛⠛⠠⠤⡀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⣿⣏⣤⣀⢀⣰⣄⣦⣀⣶⠶⠛⠁
⠀⠀⠀⠀⠛⠿⢶⣶⣤⣦⣦⣴⣄⣰⣿⠁⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣧⣠⣤⣤⣄⣈⡉⠉⠛⢻⡏⠛⢻⣿⠁
⠀⠀⠀⠀⠀⠀⣾⠁⢨⣿⠉⠉⠉⠙⣿⠀⢰⣿⣿⣿⣷⣤⣾⡆⠀⠀⠀⠀⠀⡼⠛⠉⠉⠉⠉⠙⠛⠻⢿⠿⠃⠀⢀⣿
⠀⠀⠀⠀⠀⢸⣿⠀⢸⣷⣀⣀⣀⢀⡟⠠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⢿⣦⣀⣉⡉⠉⠉⠛⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠶⠶⠶⠿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡀⠀⠁⠘⣿⣿⠿⠿⠋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⣿⡟⠀⠀⠀⠛⠹⠿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣧⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠻⢿⣷⠀⠀⣀⡀⠀⠸⣿⠋⡰⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣆⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡏⠀⠀⠈⠀⠀⠈⣧⠘⠇⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⢏⣹⠏⠰⣟⠳⣶⣤⡀⠀⠀⠀⣼⠋⣷⡀⠀⣠⣤⣀⣄⢀⣴⢟⣷⡄⠀⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠰⡋⢰⠈⠓⣀⣄⡽⠆⠀⠈⢷⡄⢸⠿⣿⠀⢸⣇⣴⠋⢹⡏⢹⡟⣿⠈⣼⠃⠲⠆⠙⢷⡀
⠀⠀⠀⠀⣠⡄⣀⣤⡉⠁⡀⠈⠁⠊⣱⡀⠀⠀⣼⠻⣿⡇⠙⠀⠺⠛⠇⠀⣿⠁⠘⠐⠇⠀⠀⠀⢢⡀⠀⠸⠇
⠀⠀⠀⠀⠈⠤⠉⠁⠉⠁⠀⠀⠀⠤⠟⠁⠀⠀⠄⠀⠀⢀⠄⢀⠠⠄⠀⠀⠠⠤⠀⠐⢿⡂⠀⠂⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠿⡟⠿⢿⠟⠛⡿⠿⠿⢿⠟⡿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣼⣦⣾⣧⣶⣿⣶⣶⣿⣧⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⣀
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢺⡷⣾⣿⣷⢾⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡤⣾⡖
⢀⣴⡆⢸⠀⣶⣤⠀⠀⠀⠀⠀⠘⠇⢻⣿⡟⠸⠃⠀⠀⠀⠀⠀⣿⡏⠉⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⡇
⣾⣿⣿⢼⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣿⡇
⠛⠛⠛⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⡹⠃⠀⣤
⠀⣤⣴⣯⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠀⠀⠀⠀⠀⠀⡤⠒⠊⠀⢤⣄⣠⣿⡆
⠐⢷⣿⠟⠳⣤⣀⠀⠀⠀⠀⠀⠸⣿⣿⠳⢤⣀⡀⠀⠀⠀⠀⢠⣾⣿⣤⣤⣀⣘⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢹⣿⡇
⠀⣼⠛⣧⠸⣿⠿⠇⠀⠀⠀⠀⢸⡿⢿⡄⣿⡿⠷⠀⠀⠀⠀⢘⣿⣷⢾⡏⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠸⠏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⠿⢠⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇


⠀⢀⣠⡤⣤⣀
⣰⠛⡿⠤⠼⢿⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢀⣀⣠⣆⣰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⡷⢺⡗⠒⠒⢾⠒⡇⠀⠀⠀⠐⣶⣾⡏⢯⢹⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣶⡆
⠹⣶⣷⠒⢒⣿⡴⠁⠀⠀⠀⠀⢿⠿⠷⣖⣫⡭⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠿⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁

⠀⠀⠠⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠰⠀⠀⠀⠠⠜⢻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⢂⠀⠀⠀⢒⠀⠀⢆⠀⠀⠀⠀⠀⠐⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠒⠀⠀⠁⠀⠀⠁
⠀⠰⠤⣤⡐⠀⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠂⠂⠈⠓⠒⠄⠀⠀⡀⠀⠀⠀⠃⠀⠃⠈⢃⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠠⠀⠒⠋⠀⠀⠖⢀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢁
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⡂⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠅⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⡐⠈⠀⠀⠐⠀⠀⠒
⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠠⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠴⡇⠀⠀⠗⠄⠀⠀⠀⠀⠠⠊⠀⠀⠐⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠚⠃⠀⠈
⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠀⠄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠈⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣤⠄
⠀⠀⠀⢠⠠⡀⠀⠀⠴⠦⠀⠀⠀⠶⠀⠀⠀⠡⠒⠀⠠⡂⠀⠀⠐⠀⠢⠀⠀⠀⠐⠀⠀⠈
⠀⠠⠄⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡈⠀⠁⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠠⠈⢄⠀⢉⠀⠄⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠈⢁⠀⠀⠁⠂⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠠⠉⢀⠀⠀⠐⠒⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⢰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠒⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠰⠔⠊⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠈

⠀⢀⡠⠄⢤⣀⠀⠀⠀⠀⠴⠖⠒⠀⠀⠀⠀⢀⣴⡾⣆⠀⠀⠀⠀⢠⢲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣧
⠀⢻⣿⣤⣤⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⢺⣿⣿⣧⣽⡶⠀⠀⠐⢡⠏⠀⠀⠀⠀⠀⠲⣿⣿⡿⡀⠀⠀⢰⡄⠀⡀⢰⣆
⠀⠘⠿⠿⠿⠕⠀⠀⠀⠀⠈⠁⠀⡇⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢼⣶⣶⣾⡇⠀⠀⠉⠁⠀⠀⢩⡍
⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⣏⠀⠀⠂⠀⠅⡆⠀⢠⣶⣶⣶⣶⠄⠀⢰⣿⣿⣿⣿⡇⠁⠀⠀⠀⣱⣀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠄⠀⠀⠰⡥⠤⢽
⠀⣇⠀⠀⠀⠀⣃⡇⠀⢰⢘⢘⣋⡃⡄⠀⢸⣿⣿⣤⣼⡟⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⣹⣿⣿⣿⣿⠂
⠀⠈⠁⠀⠀⠀⠉⠀⠀⠘⠤⠤⠤⠠⠂⠀⠈⠻⠿⠿⠿⠍⠃⠀⠀⠀⠈⠛⠉
⠀⠀⠤⠀⠀⠀⠀⠀⢠⠤⠤⢤⡀⠀⠀⣤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⢠⡤⠤⠤⡄⠀⠀⢀⣀⣀⣀
⠀⠀⠨⣧⠀⠀⠀⠀⠀⠐⠲⡆⡇⠀⠀⡇⣤⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡽⡀⠀⠀⢸⡧⠐⠀⡇⠀⠀⠸⠤⠶⢿
⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠔⢃⠀⠀⢸⡀⠀⠀⡇⠀⠀⢸⠩⠭⢹
⠀⠀⠓⠒⠒⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠈⠉⠀⠉⠁⠀⠀⠈⠉⠉⠉
⠀⡴⠒⢦⣤⣤⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣄
⠀⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣧⣤⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠉⠁⠀⠀⠸⡿⣹⣿
⠀⠛⠛⠛⠛⠛⠃⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠀⠐⠒⠶⠖⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⣠⡶⠒⠶⠀⠀⠀⢠⡖⢲⡄⠀⠀⢀⡤⠲⢤⠀⠀⠀⢀⣀⣀⢀⠀⠀⢀⣤⣄⡀⣄⠀⠀⠀⣴⠛⡆⠀⠀⠀⠀⣠⣄⡀
⠨⣿⡿⠏⠀⠀⠀⠀⠺⡷⠂⠀⠀⠀⢾⢦⣈⢻⡇⠀⠀⢰⡎⣀⣰⡆⠀⢸⣿⣿⣅⣙⠀⠀⠀⣿⣛⣿⠀⠀⠀⠐⣿⣿⠇
⠀⠈⠛⠛⠛⠀⠀⠀⠘⠛⠲⠂⠀⠀⠈⠳⠴⠚⠁⠀⠀⠃⠀⠀⠐⠁⠀⠘⠛⠛⠛⠛⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠘⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣄⠀⠀⡀⠀⠀⣠⡦⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⣰⠏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣾⠁⠸⣆⡼⢳⣤⠞⠁⢹⠀⡀⢠⠞⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀
⠀⠀⠀⠀⣰⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣯⠀⠀⣿⠃⠀⠟⠀⠀⣾⠾⣷⡎⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⡄
⠀⠀⠀⠀⡟⠀⠀⠀⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢉⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠻⠁⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠹⡄
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⢀⣠⡴⠶⠛⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣤⣼⡁⠀⠀⠀⠀⠀⠀⣠⡴⠞⠃⠀⠀⠀⣇
⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠠⠀⠀⣠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⣤⠶⠋⠁⠀⠈⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠀⠀⠀⠐⠀⢰⠇
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡶⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⢴⡶⠂⠘⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⢹⠉⠉⠙⣿⠛⠛⠛⣿⠟⠛⠛⢻⡟⠛⠉⢹⣏⠉⠉⠙⣿⡀⠀⠀⡇⠀⠀⠀⣉⠀⢈⠀⣿
⠀⠀⠀⠀⠀⠀⠈⡆⠐⠀⠐⠀⠀⢸⣄⣀⡴⠛⠶⠶⠶⠛⠦⣤⣤⡾⠻⣤⣀⣴⠟⠲⠶⠚⠁⠙⠓⠛⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢧⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⡇⠀⠀⠀⠉⠙⠛⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⡤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⣦
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢧
⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢳⡀
⢠⡟⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠳⡄
⡜⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢳⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠙⢦⣀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠈⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣯⠙⢦⣀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠙⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠛⠲⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠖⠛⠉⠁⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⠉⠉⠉⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣀⣤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠶⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣶⣶⡦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠒⠉⡶⠀⠠⣄⠈⠐⠽⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠊⠀⠀⢀⠁⣐⠀⣇⠱⡦⠀⠈⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠀⠀⠀⢸⠺⣿⠇⣇⠼⡄⠀⠀⠈⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⡄⠀⠀⠀⠀⡇⠀⠀⠀⡤⠚⠂⠉⠀⠀⠀⠘⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⣴⠶⠞⠛⠉⠀⠀⠀⠀⠙⣛⢦⡀⠀⢇⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⢹⠃
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠠⠼⠟⣂⡿⠀⠘⢎⢄⠀⠀⠇⠀⠀⢀⡀⠀⠐⠈⠠⣢⠏
⠀⠀⠀⠀⠀⣠⠴⣲⠿⣷⣶⣶⣶⣶⣿⣿⡟⠉⠀⠀⠀⠈⠳⢕⡤⣘⠈⠀⠀⠀⣀⠠⣢⠕⠁
⠀⠀⠀⠀⠊⣠⠞⢁⡾⠁⠀⠀⠀⠀⠨⠭⠽⣦⠀⠀⠀⠀⠀⠀⠉⠓⠒⠿⠾⠓⠚⠉
⠀⠀⠀⠀⠘⠁⢠⡞⠁⠀⢀⡠⠢⠴⡈⢹⣭⣽⣧
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡆⢴⢰⡆⠤⠄⠤⠤⠼⣇
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢰⢠⡄⡝⠄⠩⠭⠭⢽⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠐⡒⠬⠸⠇⠆⡰⠴⠧⠉⣋⣽⣿⣿⠛⠐⠒⠒⠲⠖
⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠈⠒⠤⢆⠮⢥⣀⣀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠸⣇⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠙⠓⠀⠤⠀⢤⢀
⠀⠀⠀⠀⠀⠈⠙⠓⠾⣦⡀⠀⠀⠀⠀⠈⠉⠒⠛⣿⣿⣤⠄⣀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠒⠛⠀⠀⠀⠀⠿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣼⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⢠⡇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⠻⣏⠀⠀⠘⢶⣄⣠⡞⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠘⣧⠀⠀⠀⣜⣿⣇⢰⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⣿⢿⣿⠋⠉⠙⣿⣿⣷⣿⣧⠀⢀⡼⠋⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠀⠏⠁⠨⠁⢰⣶⣿⣿⣿⣿⣿⣿⣶⣼⣷⣴⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣴⠀⠉⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⡿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡖⣦⢄⣻⡇⠀⠙⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠏⠳⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣿⣿⡿⣿⠿⠟⠛⠷⣶⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⡇⠇
⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠈⠢⡀⠀⠀⠀⢠⣿⣿⣿⡽⢛⡟⣯⣿⣧⡀⠊⠀⠈⢹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⢦⣄⡀⠀⠀⠈⠂⡀⠀⣼⣿⣿⣿⣤⣀⢠⣿⣿⣿⡛⠷⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡴⣾⡇⠀⠉⠳⠄⠀⠀⠈⢦⣿⣿⣿⣿⣿⣿⡅⠀⠀⢙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⠻⠿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⣤⣾⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠲⢦⡤⣀⣉⡻⢷⣦⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢻⣿⣷⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⢻⣽⣟⡿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠉⠉⠉⠀⠀⠀⠙⠛⠿⠛⠙⠛⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⢀⣴⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢀⣬⣤⠄⠀⠀⠀⠴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣴⣿⣿⣶⣦⣄⡀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣟⠛⠛⠉⡉⣠⡆⣁⣾⡟⠛⣛⠉⢻⣿⢿⣿⡝⢄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢱⡷⠿⣿⣏⢉⣿⣇⡜⠻⣷⣬⣯⢞⣿⣿⣦⡙⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⠿⣿⣼⣦⠻⣿⠿⠿⠵⠇⢀⣿⣿⣿⣮⣿⣿⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠶⢂⣠⠿⣿⣿⣿⠉⠃⠀⠾⣷⡶⣶⣿⣿⣿⡿⡿⡿⢿⣿⠿⢿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠁⠀⠀⠀⠀⢰⣿⠯⡴⠴⠶⣾⡿⠁⣿⡿⣿⡿⢧⣰⡉⠈⠛⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⡄⠀⢀⠄⠸⣿⢿⠗⠛⠉⢉⣰⣾⣯⡴⣋⡵⢞⣽⣿⣷⣶⢻⣿⡿⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⢸⣄⣀⣹⣦⣤⣤⣶⣿⣿⡿⠟⣫⣥⣶⢿⣻⢿⣿⡟⠛⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡇⢀⣀⣼⠯⠝⣻⠟⠿⢿⡭⢭⠴⠒⣫⣾⠿⣛⣿⠟⢠⢾⠃⠀⠀⠀⢻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⢏⠈⣷⡿⡏⠀⢻⡲⡍⢽⣯⣾⣏⣤⣾⣿⣏⡄⡄⢠⡗⠁⠀⡀⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡿⠹⣦⣤⣐⣦⡍⣹⣬⣿⣿⣿⣿⣿⡿⣿⣽⣇⣀⣸⠁⢠⣾⣿⣶⣶⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣝⢿⣾⠿⠛⣙⣋⣬⣿⡿⣿⣿⡿⢩⣾⣿⣟⡿⠙⣫⣴⣿⣿⣿⠟⢹⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⣯⣄⢙⢦⡟⣻⡝⠫⣿⣿⣿⣿⣴⣿⠿⠟⠀⠀⣞⡿⠋⠉⡉⢁⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠘⣦⣬⡅⠈⠀⠈⣉⣵⣇⢸⣿⣿⣿⡙⠀⠀⠀⠀⣸⣿⣆⡠⠂⣰⣿⣿⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢨⡿⠱⠂⠠⢾⣭⣭⡿⢿⣭⣿⡿⠛⠂⠀⢠⢚⣿⣿⠟⣡⣾⠿⠃⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠁⢀⣤⣾⠉⠁⠀⣶⣿⢱⣿⣶⣆⣾⣿⡿⢃⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡦⠞⠙⠁⢠⢠⣿⠟⠉⣩⣿⣿⣿⣿⢏⣴⣿⠿⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠁⢀⣤⣶⣾⡏⡀⠀⠐⠉⢻⠟⣡⢞⣿⣿⣧⡀⠀⠉⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⡁⠽⣉⣹⣏⠁⠀⡀⢠⣴⣦⠄⣼⡷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡤⠉⠓⢻⡿⡿⢀⣿⣵⣿⣿⠏⠀⢸⡇⣿⣿⡟⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠘⣧⣼⠋⣹⠃⠀⣼⠇⣽⣉⡋⣠⡾⠏⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣠⢟⣀⡴⡅⣼⣿⣿⣿⡋⢡⣤⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⠶⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣶⣄⣀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⠉⡶⢤⣀⡰⠋⠀⠀⠀⠙⢯⡻⣦⣀⡀⣀⣀⣀⡀
⠀⠀⠀⢠⠞⣠⠖⠋⠉⠉⠉⠙⠓⠶⣄⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣳⡌⢻⡙⢯⠀⠉⠉⠻⣦⣄⡀
⠀⠀⢠⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡀⢧⠈⢣⠀⠀⠀⣷⠀⠙⠳⣄
⠀⠀⣾⡟⠉⠙⡆⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢷⡀
⠀⢠⢟⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⡠⡄⠐⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠉⣿⠀⠂⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠙⣦⡀
⠀⡜⠈⠒⠒⣿⣿⣿⣿⣿⣿⣿⡇⠁⠈⠈⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢩⠏⠀⠀⣻⡇⠀⡆⠀⠀⠀⠀⠸⠀⠀⠀⠠⡀⢩⠳⡄
⠀⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⣸⠁⠐⠁⣀⠴⠧⣄⠀⠀⠀⠁⠸⠀⢻
⠀⢷⠀⠀⠀⣿⣿⣿⣿⣿⣉⣿⠁⠀⠀⠀⠀⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⡟⣰⠟⠋⠉⠉⠁⠀⠀⠈⣯⠁⠀⡇⠀⠀⢸⡆
⠀⠸⡆⠀⠀⠘⠿⣿⣿⣿⠟⠡⢳⣿⡆⣠⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡧⠀⠀⢸⠃
⠀⠀⢻⣆⠀⡐⠀⠀⠀⠀⠀⠀⠈⢉⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡇⢠⠂⡞
⠀⠀⠀⠻⣝⠦⣄⣀⣀⣀⣠⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⠀⠀⡼⠁
⠀⠀⠀⠀⠈⢷⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢁⡴⠋⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣧⣀⠤⣀⠀⠀⣠⡴⠋⢀⡔⠋⠁⠈⠉⠛⠲⠶⢶⣖⣚⠉⠁⠀⢔⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⡀⠀⢀⣀⣀⣤⡤⠿⠛⠁⠀⢀⡎⠀⣴⡯⢤⣄⣀⠤⠀⢀⣀⣤⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠳⢤⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⢀⠏⠳⣄⠀⡰⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠒⢄⣘⣀⣱⣮⣤⣦⣬⣎⣥⣘⡠⠞⢹⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢒⣾⠼⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⢼⡤⠒⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⢔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢧⡎⠤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠐⠒⢄⠀⠀⠀⠀⡇⠀⠀⠻⣎⣰⡡⡆
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣤⠀⠀⡇⠀⠀⢰⡇⠀⠀⢠⡌⢳⣠⣃⠴⠀⠀⠀⠀⢀⡠⢴⡄
⠀⠀⠀⠀⠀⠀⢸⠃⢀⡔⠂⠐⠢⡀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠜⠁⢀⡴⠫⠵⠀⠀⠀⢰⣶⠙⢾⣼⠔⣆⣄⢠⠬⣧⡟⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣴⠄⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠉⢁⣠⠶⢉⠀⠀⠀⠀⠀⠀⠀⢩⣤⡛⣙⡳⢯⣬⣮⣴⠞⡅⡃
⠀⠀⠀⠀⠀⠀⢸⡀⠈⠣⠄⠠⠔⠁⠀⠀⠀⠀⠀⣀⣠⢴⠚⠋⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠛⢡⠛⣡⣷⣤⠁⢻⡃⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣀⣀⡤⡴⢖⢛⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⢈⣛⡋⣤⡝⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠉⠙⢭⠁⠑⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠃⠈⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⠞⣰⠶⠒⠲⠦⣤⡀⠀⢀⣀⣀⣤⠤⢤⡀⠀⡞⠁⠀⢈⡇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡼⠁⠀⠀⠀⠀⢈⡇⣼⠋⠉⠀⠀⠀⢀⡷⠀⢹⡀⠠⣯⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⣒⣛⣀⡿⠀⠀⠀⠀⣶⣋⣡⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⢸⣦⣀
⣼⣿⣿⣷⣤⡀
⣹⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⡟⠁⡠
⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⠃⢀
⠻⢿⣿⡿⠄⠛⢢
⠀⠀⠉⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⢀⣀⣀⡠⠄⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠹⣟⠁⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⠛⣤⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠈⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⠀⠻⡀⡓⢤⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢸⠀⣀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⠄⠀⠠⠀⠀⠀⢹⠀⡴⠁⠀⠀⡇⢠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠂⠂⠀⠰⠀⡀⠀⠈⠀⠂⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠂⠀⠰⠀⠀⠀⣸⠀⠇⠀⠀⠀⡇⠐⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠀⢸⠀⡃⠀⠂⠀⡇⢐⡁⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁

⣶⣶⡶⠶⠶⢶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⡇⠳⢴⡮⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣷⡴⠋⡤⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣌⠑⢤⡇⠀⠀⣷⣄⡈⠿⠛⢲⣦⠤⢀⣀⡤⢤⣶⠚⠛⠿⣁⣴⡏⠀⠀⢥⠔⠉⣠⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠏⢙⣧⡀⠀⢀⡞⠋⠈⠻⣿⠿⠛⠁⠀⠈⠉⠀⠀⠈⠻⢿⡿⠛⢁⠛⢦⠀⠀⣠⣞⠉⢳⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠀⡞⠉⢻⣆⡎⠀⠀⠢⠀⠤⠔⠀⡀⠄⠀⠀⠀⠀⣀⠐⠠⠄⠠⠌⠀⠈⣇⣼⠛⠙⣧⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢧⡀⠁⠀⠙⢦⡀⠀⣠⠴⠊⠁⠀⠘⠂⠀⠐⠂⠀⠉⠒⢤⡀⠀⣠⠜⠁⠀⠁⣠⠟⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣹⡆⠀⠀⠀⠉⠀⠁⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠤⣤⡄⠀⠰⠁⠀⠀⠀⢼⡃⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⣀⠔⡄⠀⠀⠀⠀⡇⠀⠖⠒⢢⠤⡤⢤⠖⠒⠂⠀⡇⠀⠀⠀⠀⡤⢄⡀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠸⠀⠀⠀⠀⣿⣶⣶⣦⣼⣀⣇⣠⣦⣴⣶⣶⡇⠀⠀⠀⠐⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠈⡏⠙⠿⠿⠟⠋⠟⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣄⠠⣇⠀⠀⠀⠀⢀⣷⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠂⠈⠑⠂⠤⠢⠤⠶⠌⠒⠉⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠈⠉⣟⠉⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠀⠀⠀⠿⠀⠀⢀⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⣀⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠾⠀⠀⠀⡄⠀⢀⠀⡄⢀⠀⣀⡄⠀⠀⣷⣣⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⣀⣤⣼⠈⠛⠈⠁⠈⠙⠁⢧⣤⣶⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣽⡿⠋⢀⣀⠀⠀⠀⠀⢀⣀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢡⣾⠁⠀⠉⢢⢠⣾⠁⠀⠉⠂⠀⠀⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠻⣿⣄⢰⡷⡸⢹⡿⣄⢾⡆⡜⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠗⣤⣝⣓⣒⣋⣁⣀⣙⣓⣒⣫⣤⣆⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡀⣿⣿⣦⣿⣦⣿⣼⣿⣼⣷⣾⣿⡿⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢻⣿⣧⠻⣽⠻⡿⢿⡿⢿⣿⡿⣿⣛⠟⠁⠀⢀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣸⣿⣿⠗⠬⠉⠛⠚⠓⠒⠛⠛⠉⠁⠀⠀⠀⢸⡇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢨⣿⡆⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠸⢻⣷⣠⣤⣸⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣀⠎⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠯⠀⠙⣸⡿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⣠⠄⠰⢌⠃⠠⠿⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⢿⣿⣶⣶⣴⣷⣿⣿⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡽⠷⠄⠀⡂⠀⠈⠉⠉⠉⠀⠈⣿⡧⠄⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣶⣷⣾⣿⣶⣷⣶⣶⡶⢶⢶⣶⣾⣿⣿⣿⣿⣿⣷⣦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡀⢀⡤⠖⠊⠉⠉⠉⠒⠢⣄⠀⡠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠉⠀⠀⠀⣀⣀⣀⣀⣀⠀⠉⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠙⣆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠃⣀⣀⠀⠀⢀⠔⠋⠉⠳⡜⡆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇⡎⣀⠀⢱⠀⢸⡀⠲⠂⢀⠇⢹⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠀⠑⠬⠤⠾⣄⢀⢝⠒⢒⣁⣀⠈⡇⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⢀⢤⠤⢴⢥⢤⡪⠴⣅⠼⠈⢷⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡜⣴⠁⠀⠑⠃⠀⠀⠀⠀⠀⣀⣀⣾⢣⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣼⠃⠹⣗⢄⣀⢄⢀⠴⠒⠒⣦⢗⡵⠁⢸⠀⠀⠀⠙⢤⣀⣀⣴⣧⡀
⠀⠀⠀⢀⣦⣀⡠⠞⠁⠀⢀⡼⢹⠀⠀⠈⠑⠪⠽⠿⠶⠾⠭⠒⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⢹⠅⠀⠀⠀⢀⡤⠊⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠤⣀⣀⡠⠔⠋
⠀⠀⠀⠈⠑⠒⠒⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢰⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠦⣀⠀⠀⣠⠊⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡾⠏⠀⠀⠻⠶⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠉⠀⠉⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⠉⠉⠉⠙⣿⡏⠉⠉⠉⠉⣿⡟⠉⠉⠉⢹⣿⠋⠉⠉⠉⠙⣿⡏⠉⠉⠉⣿⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡄⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⣤⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠇⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⢿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⣿⣷⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢄⣀⠀⠤⢒⣀⣠⣤⣤⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡢⣄⢤⣀⣤⣤⣴⣮⣵⣶⢾⣷⣽⣾⣽⣿⣬⣮⣽⡿⠿⣿⣿⣟⡲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠮⣛⣩⣔⢟⣯⣫⣝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⠾⢿⣿⣿⣿⣿⣿⣿⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣪⠐⢁⣪⣼⣾⡶⠿⠟⠛⠛⣫⢙⢛⡻⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⢔⣴⣷⣿⣿⡿⡟⢻⠡⡆⢸⢠⠀⣮⡶⣿⣛⢷⣽⡯⣮⣦⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿
⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⢡⢰⣧⣸⢁⠇⢨⢧⠺⣿⣿⣿⡟⢸⣧⢃⣿⣿⣃⣿⣿⣎⣽⣻⣟⡻⣍⠙⠛⠿⠿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⢰⣿⠟⠋⠋⠁⠀⡌⢷⠙⢦⠺⢠⠈⢸⠀⢹⡿⣥⡴⢏⣠⣾⣿⡿⣻⣿⣿⣿⣿⣟⣁⡈⠀⠀⠦⠬⣶⣾⣍⠾⣹⣿⣿
⠀⠀⠀⠈⠁⠰⣦⣔⢲⣲⠁⣦⠷⢚⣷⢩⣦⣻⡥⣐⣩⣭⡶⢛⣿⡿⢻⣹⡭⢁⣌⣼⣟⣂⣽⣿⣄⡀⠀⠀⢀⢈⠶⠮⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠿⠇⠹⡦⠘⢇⠋⠻⠈⠉⣉⢈⣉⣭⣷⣾⠿⠿⣷⣥⣷⣿⣿⢿⢿⡟⡙⢻⣿⣿⣿⡖⣬⣐⡂⠲⠶⠾⠁
⠀⠀⠀⡶⢀⢄⢦⣬⣆⡸⣡⣀⣠⣶⡁⢖⢓⠻⡟⣟⣿⣽⣧⣾⣿⣿⡯⡼⣏⢎⣏⡖⠐⢥⣄⡿⣿⣿⣷⣄⢔⢄⣀⣀
⠀⠀⠐⢁⣾⢿⣿⣿⣿⣷⣦⣄⣩⠹⡏⠻⣿⠿⢿⣿⡿⣿⡿⢛⠻⠷⠑⡝⡗⡤⠨⠈⡅⠈⠴⢘⠴⣝⣿⣿⣿⣷⡪⠈⠁⠂
⠀⠀⠀⣼⣿⣞⡿⣿⣻⣿⢿⣿⣿⣿⣿⣶⣿⣿⡶⡮⠽⠍⢊⣆⠕⠇⣀⠍⠌⡡⣅⣡⢰⠀⠂⢩⡌⣼⣿⣿⣿⣿⡓⠄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡹⠄⠿⡃⣜⡀⠀⠟⢇⡡⢃⠂⢠⣎⣽⢯⣿⣿⣿⣿⣛⡲⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣭⣐⣮⣾⣴⣼⣴⣷⣦⣿⣿⡿⣾⣿⣿⣿⣿⡟
⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠯⡹⣿⣿⢇⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠔⠖⠠⡶⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⡿⡟⠋⠤⢤⡀⠀⢠⡄⠘⠢
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋⠀⠀⢀⡄⠈⠁⠠⢀⠙⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠈⠉⠙⠛⠛⠛⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠊⠁⢀⡄⠀⠀⠀⡀⠘⠡
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⣿⣿⣿⣿⡿⣿⠆⠀⠀⠀⢰⡦⡤⣾⠟⠁⠀⣤⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢺⠣⠻⣿⠿⠋⣡⢿⡟⠀⠀⡼⢀⠊⠀⢰⠇⠀⠀⠀⠁⠋⠛⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⣴⡿⠃⠀⠀⠀⡀⠀⠀⠠⠾⢃⣀⢀⡀⣠⣴⣶⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠐⠀⠀⠝⠉⢈⣴⣿⣟⣿⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠂⠆⠀⠀⣔⣠⣿⡿⡋⠱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣾⣿⣿⣾⣾⣾⣾⣿⡏⢯⠊⠀⠀⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠅⢡⠀⠀⠀⠁⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣗⣿⡀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠁⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂
⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠐⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠗⣃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⢠⣁⠀⠠⣀⠀⢠⡔⣫⣼⣟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠯⠣⢾⠶⠋⢯⠋⠹⢏⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢶⠆⠀⠀⡄⣀⠆⠀⣴⠂⠘⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠀⠀⠀⢠⠂⠀⠀⠀⠀⠠⣼⠲⠇⠀⠀⠀⠑
⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠬⣀⣤⢈⡆⠀⢀⠆⠀⠈⠀⠀⠀⡀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠐
⠈⢿⠀⠈⠁⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣧⠈⠻⣄⠡⠴⠖⠶⠋⡞⠁⠀⣼⢰⠀⠀⠀⠂⠀⠀⠀⠙⡇⠀⠀⠁
⢸⠸⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣧⡀⡟⢤⣀⣈⡀⡤⢳⣀⣰⡇⢸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠨⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣧⡿⠟⠛⠃⠁⠀⠀⠀⠁⠀⠈⣿⡟⡹⠾⢿⡿⠂⠁⠈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠐⠀⠀⠀⠑⠂⠀⠀⠋⠁⠀⠀⠀⠐⠂⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠠⠀⠂⡩⠀⠀⠀⠀⠀⠄⠀⠀⠁⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠢⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢻⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠴⢿⡄⠀⠀⠳⠻⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⢀⡴⠶⢤⣒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣴⠋⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠑⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢫⠀⠿⡀⡛⢦⡁⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠐⠃⠀⠀⠀⠀⠀⠀⠀⠉⠆⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠁⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠐⠀⢲⠐⠀⠀⠀⠠⠄⢲⠀⢀⡄⠀⢀⠀⠀⣀⠐⢀⠀⢀⢀⡆⢀⡄⣀⠀⠀⠀⣠⡐⢀⡆⢠⠐⠐⠀⠀⠂⡒
⠀⠀⠀⠂⠀⠀⡆⠀⠀⠀⠀⡀⡄⢀⢀⢰⠀⠀⢸⠀⡼⠀⠀⠀⣇⠈⡇⠀⠀⢠⠈⠀⣁⠈⠀⠠⠀⠀⠂⠀⠀⡆
⠀⠀⠀⠸⠀⠀⡇⠀⠀⠃⠀⡄⡇⢀⢸⢸⠂⠀⢻⠀⡟⠃⠀⠘⣏⢀⡇⠀⢸⢸⠀⡀⢸⠀⠀⠪⠀⠀⡞⠀⠘⡇
⠀⠀⠀⠐⠒⠒⠃⠀⠀⠒⠒⣀⡇⢀⣸⠘⠒⠒⠚⣀⡗⠒⠒⠂⢻⡀⠓⠒⠒⢸⣀⡀⣸⡐⠒⠒⠀⠀⠒⠒⠒⠃
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡇⢀⢰⠀⡁⠀⢀⣀⡇⠃⠀⠂⣹⢀⠀⠀⢈⢸⣀⡀⢸⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⡇⠀⢨⢰⠀⠀⢺⠀⣇⠀⠀⠀⣯⠠⡖⠀⠰⢸⠀⠀⢼⠀⠀⠠⠀⠀⡐⠀⠀⡆
⠀⠀⠀⠸⠂⠂⡇⠀⠀⠂⠐⠆⡇⠀⠰⢸⠂⠀⢻⠀⣟⠀⡄⠀⡷⠀⡗⠀⢸⢸⠠⠄⠴⠀⠀⠺⠀⠀⠚⠀⠐⡇
⠀⠀⠀⠐⠒⠒⠃⠀⠀⠒⠒⠒⠇⠐⠚⠘⠒⠒⠚⠒⠏⠀⠀⠀⠓⠒⠓⠒⠚⠸⠂⠀⠘⠒⠒⠒⠀⠀⠓⠒⠒⠃
⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠐⠒⠀⠓⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠐⠚⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⠀⠀⢀⡖⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢠⠃⠀⠀⠀⠀⢑⡆⡞⢀⣀⣤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣒⣒⣒⣚⠃⠑⠒⠒⠚⠉⠉⠀⠉⠉⠀⣀⣠⣤⣀⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠖⠉⠁⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⣀⠉⠳⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⠁⠀⠀⠀⡤⢶⣤⡀⠀⠈⣧⠀⠀⠀⠀⢀⡏⠀⠀⣾⣉⣿⣷⠀⢻⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢻⠀⠀⠀⠸⣷⣾⣿⡇⠀⠀⣿⠀⠀⢀⡀⠘⣇⠀⠀⠛⠿⠿⠋⢀⡟⠀⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⢆⠀⠀⠀⠉⠛⠉⠀⠀⣠⠇⠀⢰⡏⠉⢢⡈⠢⣄⣀⣀⣀⡴⠋⢀⡼⠁⢸⠿⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠓⠦⣤⣄⣠⣤⠴⠞⠁⠀⠀⠀⢧⠶⠗⠃⣠⡄⠀⠁⠀⣠⠶⠋⠀⢠⠏⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⠀⠀⠀⠀⠀⣤⠤⣤⣤⠤⡤⢶⢋⢿⡇⠀⢠⡞⠁⠀⣠⠴⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠘⣧⢉⡀⠒⢈⡁⢌⡿⠀⠀⠀⠙⠛⠉⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⡀⠀⠀⠀⠀⠀⠈⠻⠴⠧⠾⠼⠋⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⡴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡞⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠻⠋⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣼⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡛⠶⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠚⢉⡇⠀⢀⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⢿⠉⠳⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠋⠀⠀⢸⠀⠀⡴⠋⠳⡄⠀⡇⠀⠳⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠁⠀⠀⠙⠚⠁

⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⢀⣀⡀⠀⠀⠀⡀⢰⡅
⠀⠀⠀⠀⡀⠢⡉⠓⠆⠉⠉⠀⠰⣦⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢳⢊⡅⠀⣀⠤⠒⢊⣰⡿⠁
⠀⠀⠀⠀⠐⣦⣉⠳⠤⠄⠤⢄⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡖⠋⡠⣔⡺⠛⡩
⠀⠀⠀⠀⠀⠻⠿⠿⠶⠦⠦⢄⢠⣜⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣋⣥⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⣾⣦⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⣿⣿⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡙⠇⣠⣶⣦⣀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡆⠘⢃⡞⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣧⠀⣿⣿⣙⣿⣻⣶⣶⣶⣾⣟⣻⣯⣿⣇⠀⢼⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⠀⠘⠛⠿⠟⣹⣋⣼⣿⣿⣯⠛⢿⣿⠻⠀⡾⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡆⠀⢀⡈⡴⢿⣿⣿⣿⣿⡿⠳⠖⠂⠄⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⢄⣀⡾⡽⡿⡿⡿⠷⣦⡤⠂⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢹⣇⣒⡀⡂⠂⣰⡿⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢝⣛⣛⡛⡛⠱⠃⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣾⣿⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⢉⠙⠂⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠄⠀⠀⠠⠀⠀⠱⡤⠶⠚⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡴⠒⠂⠉⠀⠲⠴⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠠⠀⣠⣤⣤⣠⢀⣐⣦⡶⠚⠻⢦⠜⣿⣶⠾⣿⠷⠞⠛⣛⣀⢂⣤⢠⣀⣤⡴⠊⠀⠀⠀⠀⠀⠀⠀⠞⠀⢰⣧⣶⣀⣠⣶⣆⡸⢃⠀⠀⢀⡤⠰⡄
⠀⠀⣠⣄⣠⣼⡿⠏⠀⡉⣭⣦⠑⠋⠀⢀⣤⣄⢀⡈⢻⡌⡁⠘⠓⠛⢩⣿⢈⣩⡼⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡘⡀⠀⡇⠀⠀⣇
⠒⠢⣹⣿⣦⡾⢿⣗⣩⡅⠛⢁⣀⡰⡄⠉⣛⡁⢾⣿⣿⣅⢉⣉⣼⠞⣴⠿⢏⠹⠀⣤⠀⠀⠀⠀⠀⡴⣯⢱⣠⠀⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠹⡄⠀⠈
⠶⠟⢹⣇⣹⣷⠾⠏⣉⡅⢄⠿⠿⢢⣶⡞⠻⣷⣿⡟⠛⢼⠇⠈⢻⢀⣶⠺⠦⠵⢶⣿⡄⣼⣿⣦⠀⢉⣶⢴⡷⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠄⢠⡀
⣷⠏⠀⠙⣋⣻⣴⡜⢿⠿⡘⢳⠄⠉⠻⣷⠚⣿⠉⢁⣈⣶⠸⣿⣦⠀⠿⡆⢠⡄⠚⢁⠀⣉⣤⣿⣏⠋⣉⢹⡇⠀⢀⠎⠸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢸⠟⣛⠻
⣡⣼⠿⠟⢙⣿⠿⠿⣴⣿⣤⡤⠐⠦⠄⠙⢦⡈⠈⠿⠛⠉⣦⠄⢠⣤⣶⡎⣤⠀⣆⡉⠩⠁⢽⢠⣾⡆⠽⣶⣇⠲⠈⠀⠀⠟⢡⣿⡿⢿⣿⠉⠈⠀⠀⣾⣿⣿⠟
⠿⠿⢷⣬⡿⠁⢠⣤⡄⢤⣥⣤⣶⣶⣶⡾⠛⢿⠆⠀⠤⠈⢻⡗⠸⣿⢃⣤⣮⡁⣟⣥⠀⠀⡀⠈⢋⢀⣤⡶⠚⡆⠦⡀⠀⠀⠈⠙⠃⢸⡿⠃⠀⠀⣡⣿⠏⠰⢶
⢳⠆⠀⠉⠐⢂⠛⠟⣁⡼⢿⡟⠉⠙⠿⣇⣀⣿⠶⠀⠀⠀⠉⢱⡜⠁⠈⠉⠙⠡⣼⠿⣧⡀⠀⠀⠀⠻⡿⠃⠀⠃⠀⢨⠀⠤⣀⠀⠀⠀⠀⢀⠠⠊⠙⣧⣴⣿⣶
⣤⢀⣠⡴⠞⠙⣿⣦⡁⣠⣄⢠⣠⣀⣐⡛⠻⡏⠀⠀⣀⣀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⠀⠀⣤⠄⠀⠀⠀⠀⠁⠀⣠⣾⣛⣻⣶⣎⠁⠀⠀⡀⠘⠩⢋⣽
⣿⣦⣤⡀⢋⣴⣿⡟⠁⣼⣿⡈⠉⠣⠀⠀⣴⣧⣤⣶⣴⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠲⡀⢠⡷⣎⣠⠀⣄⠀⣀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠰⠁⠀⠀⣠⣾
⠀⠙⣿⡏⢨⣿⠉⠁⠃⠻⣿⡏⠠⡀⠀⣴⣿⣿⣿⡿⠿⠥⠴⠀⠀⠀⠀⠀⠀⠀⣀⣰⢾⣟⠀⠘⡇⣠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⣯⣍⠉
⣠⡴⠊⣥⡀⠁⢀⡀⣀⣀⣨⣿⣤⣿⣾⣿⡿⠁⠀⠀⠀⠐⠂⠁⠀⢀⢐⡀⢴⣾⣿⣿⣟⣭⣤⣶⣿⣿⡿⠟⢁⢀⡠⠄⠀⠉⠛⢿⣿⣿⣿⣿⣦⣤⡾⣿⣿⣿⠇
⠁⣠⣌⢹⣿⣶⡈⠙⠛⣉⣤⡀⠐⢿⣯⠀⣰⡀⠀⠠⠤⣤⣄⡈⡻⢿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⡿⠋⠀⢀⠘⠈⠧⠤⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠻⠿⠛
⣷⡟⠉⠙⢿⣇⣤⣼⡿⠋⠉⠙⠗⠚⠷⢿⣿⣷⠀⠀⠀⣿⠃⡞⠀⢯⠈⠘⣫⡿⢿⣿⣿⣿⣿⡟⠀⠀⢠⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣷⣦⣄⣀
⣽⠇⠀⠀⠀⢀⢤⡈⠁⢠⣾⣷⡈⣿⠶⣿⠟⠛⠷⡀⣠⢷⠀⠙⠄⠀⠐⠺⠿⠿⠀⣹⣿⣿⣿⡇⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⡀⠀⢰⣄⠀⢰⣦⡀⢙⣿⣿⣿⣿
⠋⡀⣀⣠⣶⠟⠈⢀⣄⠹⣿⠟⠀⠀⠀⣰⡕⣶⣶⣿⣧⠈⠓⠤⠤⠤⡀⠀⠀⢀⣴⣿⣿⣿⣿⡇⢰⣷⣄⠀⣀⣀⠀⠀⣶⣿⣿⣦⣸⣿⣤⣼⣿⣿⠿⢿⣿⣿⡿
⢈⣿⣬⡀⠠⠶⠈⠉⠙⢦⠀⢀⡀⢺⣿⣿⡇⢈⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠈⢿⣿⣠⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠆⠘⢿⡋
⠻⣿⣿⠿⠂⠸⣷⣶⣶⣶⢠⣀⠁⣀⠉⢉⣀⣃⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⠿⠿⠛⠛⠛⣙⡆⠀⠻⣿⣿⣿⡟⢻⡟⢿⣿⣿⠉⠃⠻⠟⠀⠀⠀⠀⠀⣿⠘

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠛⢤⣶⣿⣿⣦⣝⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⡵⠀⠘⠛⠀⠺⡗
⠀⠀⠀⠀⠀⠀⡩⢙⠹⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠛⢀⠀⠀⠺⢵⠂⠀⠀⢀⣀⠀⠀⠀⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠈⡈⠀⡀⠄⠀⣤⡄⠀⠀⠀⠘⠋⠄⠀⠀⢰⣤
⠀⠀⠀⠊⠀⠁⠀⢐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠁⠉⠁⠀⠀⠀⠉⠄⠀⠀⠠⠄⠐⠁⠀⠁
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠠⡀⠀⠁⠀⠂⠃⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇⢰⡇
⠀⠀⠀⠀⣀⣀⡈⠀⠀⢄⣀⣠⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠠⠾⠇⠸⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠿⠿⠿⠿⠇⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠰⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⡀⠀⠀⢐⣂⡂⠀⠀⠀⡄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢂⠀⠀⠀⢸⣦⣀⠀⠀⠀⠀⠀⢈⣁⣶⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⢺⣿⠟⠀⠀⢀⠀⠈⠀⠀⠀⠆⠀⢀
⠀⠀⢠⠛⠀⠀⠀⠈⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠰⠀⠀⠒⠒⠂⠀⠀⠃
⠀⠀⢼⠀⢂⠀⠐⠠⠐⠊⠁⠀⠠⡇⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⠂⢲⠂⠈⠑⠂
⠀⠀⠀⠀⠀⠁⣐⠒⠀⣒⡀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠈⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠚⠂⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣒⠂⠐⢂⡀

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⢠⡀
⠀⠈⠳⢬⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⣤⡠⠀⠀⠀⠠⣀⠀⢀⡀⠙⠃⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⡀⠀⣏⣹⠞
⠀⠀⠀⠀⠀⠀⠀⡀⠢⣠⣄⣰⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⣰⣃⡿⠁⢀⣤⠖⠀⠀⠀⢀⣜⣶⣦⡀⠀⠃⠀⠉
⠀⠀⡤⠖⢴⠄⢸⣤⣾⠟⠋⠛⠣⣀⡀⠀⠀⠀⢀⢠⡀⠀⢼⠟⠁⠀⠀⠀⠀⠀⠤⠒⠉⠉⠋⠛⣧⣂⣦⠀⢰⡐⡄
⠀⢰⣠⠎⠁⠀⠸⠔⠁⠀⠀⣤⣄⡀⠙⠢⡀⠀⠠⠗⠂⣴⠿⢀⠀⠀⠀⡐⠉⢀⣀⣀⣀⠀⠀⠀⠀⠲⣧⠃⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢠⣾⣾⠟⠀⠀⠈⠂⡀⠀⠈⢃⣨⠟⠁⠀⠜⣀⣼⣭⣋⣙⣁⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠘⠿⢿⣷⣶⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠸⢽⣰⡗⠛⡛⠁⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣤⣌⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠈⠻⢭⡭⠼⠃⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠛⢻⠿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠈⠀⢤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠁⠀⠀⠛⠲⠆⠀⠀⠀⠑⠢⠀⢀⣀⣤⠀⠠⡀⠠⠔⠊⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛
⠀⠀⠀⡾⢰⠦⡀⠀⠻⣥⠀⠀⠀⡀⠄⠀⡜⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢉⠀⠀⠀⢠⡄⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠙⢍⣠⣁⠀⠀⠀⠀⠀⠀⠁⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⢷⡄⠉⡽⠀⠚
⠀⠀⠀⠀⠀⠉⢩⡆⠀⠀⠀⠠⢂⣰⠏⢀⡀⠀⠄⠀⢠⣤⣶⡄⡆⠀⠀⠀⣿⠀⠀⠄⠘⠧⣄⡀⠛⠶⠃⠀⢠⣤
⠀⠀⠀⢰⣂⡤⠉⠀⢈⣤⢈⢁⡾⠉⡇⠀⡿⠀⡀⠀⢿⡿⠋⠀⡇⠀⡁⠀⣯⠀⠀⢠⡐⠦⡀⠙⠿⢦⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠉⣄⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠐⠀⠀⠙⠶⢶⣤
⠀⠀⠀⠀⠀⢠⠞⠁⠰⡆⠀⠀⣿⠀⠀⢀⡃⠀⡇⠀⠾⡛⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢉⠀⠀⠐⣄⠀⠀⠀⠀⢣⡄
⠀⠀⠀⢀⡴⠃⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⡇⠀⠀⠉⠀⠀⡇⠀⡆⠀⡇⠀⡄⠀⠀⠀⡀⠀⣧⠀⠀⠀⠀⠀⢣
⠀⠀⠀⡋⠀⣨⣇⣠⣴⠧⠴⠶⠿⠤⠷⠾⠷⠤⠇⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠚⠛⠛⠛⠒⠓⠶⠷⠤⠄⠀⢀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢤⡀⠀⠀⠀⠀⠒⡦⢤⡀⠀⡠⠀⠠⡀⠀⠔⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⢹⣄⣤⣆⡄⠀⣀⠀⡞⠁⠀⠀⠟⢠⠇⠈⢠⠫⠁⠀⠀⣀⡤⠼⠇
⠀⠀⠀⠀⠄⣈⠿⠞⠉⣀⠟⠙⣑⣆⣴⢿⡏⠀⣽⣟⠙⠿⠀⠀⠀⠚⠛⠀⠀⠀⠚⡁⠀⡰⠕⠀⠀⠀⢤⠀⠀⠀⢀
⠀⢓⢐⣒⢲⡟⠀⠐⡿⠟⠓⠈⣿⠏⠁⠼⢃⣢⠥⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠊⠀⡄⢰⣏⠁⣸⡇⠀⠀⢨⡀
⠀⠸⠃⠈⢉⣿⠀⢀⣿⡷⠀⠀⢽⣢⠎⣀⠘⠛⠒⠚⠁⠀⢀⢘⣁⠀⠀⠀⣀⢀⣘⠉⠀⠀⠐⠤⣤⠴⠟⠀⢀⡌⠘⠉⢀
⠀⠀⠊⠃⠀⢭⣽⣧⣷⣞⠈⢀⠳⢀⡞⠉⢁⡠⠤⠀⣀⡴⠹⢿⠄⢠⡶⣏⡩⣶⢇⠀⠀⠀⡄⠂⠀⢀⡤⢒⣏⠨⡄
⠀⠀⠐⣤⣈⠀⢬⣍⠈⠍⠊⢵⢖⠿⠗⠊⠁⠀⡄⡈⠙⢷⠶⢮⣹⣷⡟⢈⣧⡤⠈⠀⠰⠺⠀⠀⠀⠰⠤⠈⢾⠄⠋
⠀⠀⠀⠈⠐⠛⠳⠦⠤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠾⣴⣿⣭⠭⠥⠄⠠⠀⠄⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠿⠟⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣀⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⣤⣄⠀⢀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣬⠀⠀⠁
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⡴⠿⡿⢟⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣿⣿⣦⡐⠲⠟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⣿⣿⣿⣿⣿⣿⡛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡃⢸⣷⣿⣿⣿⣿⣿⣿⣷⡄⠰⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠻⢿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣷⣠⣤⣄⠀⠀⠀⠀⠀⢠⡇⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠙⣿⡇⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⡇⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠈⢿⣦⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡄⠀⠀⠀⢹⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⡇⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⡿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⡿⡏⠚⠏⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣀⣴⠦⠄⠀⠀⠀⠀⠠⢤⣄⡀⠀⡔⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠔⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠢⡀⠀⡌
⠀⠀⠋⠀⠀⡀⠀⠀⠀⠔⠄⠠⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢲
⠃⠀⢉⠀⠉⠜⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠢⠁⠆⠂
⠀⠀⠓⠊⠑⠅⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠀⠀⠀⠁⠢⢹
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠈⠐⠠⡄⠀⢀⣀⠀⣀⣀⡀⠠⠔⠊⠁⠀⠀⠀⠀⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢁⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣀⢄⢀⠠⠄⠀⠀⡀⠀⠀⠀⠘⡀⢀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠅⣀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠤⠒⠊⠁⠀⠀⠀⡄⠀⢀⠀⠡⡀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠑⠐⠒⠀⠒⠂⠒⠠⠤⠄⠀⠤⠐⠂⠀⠤⠤⠍⠁⣀⡀⠀⠠⠤⠐⠒⠀⠒⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠷⣀⠀⠀⢀⡠⢼⡋⣱⢖⡛⠛⠉⠉⠉⠉⠉⠉⠉⢛⡷⣏⢹⠷⢤⡀⠀⠀⣀⠾⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡰⢩⠗⡞⠁⠀⠀⠻⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠟⠀⠀⠈⢶⠺⡙⡆⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣧⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣴⣦⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠻⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡇⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⠀⠀⠀⠀⠀⡏⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠉⢣⠎⠀⠀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⢷⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡠⣼⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠞⠘⠦⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠒⠲⡶⠶⠦⢤⠤⠤⠤⠤⡤⠤⠤⢶⠔⠒⠒⠋⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣼⠀⠀⠀⠀⣇⣀⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠕⠀⠀⠁⠪⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⡥⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⣀⣀⡐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠐⠁⠀⠀⠀⠑⠌⠄⡀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠠⠦⠤⠶⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠘⢏⠘⠁⡃⠀⢀⠀⡁⠀⠉⠀⠀⠐⠒⠊⠉⢉⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⠃⠀⠀⢣⡁⠀⠀⠀⣀⣀⣀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⣉⣁⠀⢄⠀⡄⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠤⣖⣤⡶⠄⡀⠀⢀⠈⠉⠉⠉⠉⠉⠈⢁⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⠀⠀⠨⢆⠈⢀⠰⣠⠀⠀⠀⠀⡃⠠⠀⢀⣀⣀⣀⡠⠔⡇⠀⠸⠦⢤⠤⢠⣤⣶⣾⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⢀⣀⣤⠇⠀⢀⡦⠀⠀⠀⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠈⠓⠒⠲⠅⣀⠀⣇⡀⠉⠉⠛⠛⠛⠙⣸⠀⠀⠀⠁⠀⠀⠀⠤⠰⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢠⠀⠉⠉⠂⠐⠂⠀⡇⠀⠙⠀⠀⠄⠤⠤⢶⠞⢿⠀⠀⠰⠇⠀⠀⠀⣀⣀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠶⠶⠦⠀⡀⠀⠾⠁⠀⠠⣤⣤⣤⣦⡇⠀⢠⡓⠀⠀⠀⠀⠀⢀⡼⠀⠀⢐⠀⠀⠀⠈⠈⠁⠁⢤
⠀⠀⠀⠀⠀⠀⣆⠈⠀⢐⠀⠒⠒⠉⢀⠀⢠⡀⠀⠈⠉⠉⠉⠁⣧⠀⠀⢀⠁⠀⠚⠓⠛⠩⢰⠄⡀⠈⠀⠀⠀⠤⠤⠤⠶⠟⡇
⠀⠀⠀⠀⠀⠀⠑⠠⠄⠠⢤⢤⣤⡴⠊⠁⠘⠢⠤⣀⣤⢤⡤⠶⠁⠔⠈⠀⠅⣀⡤⣤⣤⠔⠋⠀⠀⠲⣌⣀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠁⠀⠀⠉⠉⠙⠛⠳⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠠⠀⠀⠀⠀⠀⠀⢀⣤⠼⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⢹⠇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣠⣀⣀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⢸⡀⠀⣠⠖⢛⣿⣿⡍⠉⠉⢳⡅⠀⠉⠉⠙⠳⢤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢀⡴⣋⣀⣤⣀⣀⠀⠀⠀⠀⢙⣾⣷⣴⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣹⠃⠀⢀⣤⠴⠶⠶⣤⣄⢹⡄
⠀⠀⢰⠿⠊⠁⠀⠀⠀⠈⡿⣠⣤⣀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡇⠀⠀⠀⢠⠦⠞⠁⠀⣴⡏⠀⠀⠀⠀⠀⠉⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⠄⠠⡌⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠛⠛⠉⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣀⡴⠋⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠹⠦⠤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣤⣀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡶⠦⣤⠟⠉⠙⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀⠀⢀⣀⣀⠀⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠉⠉⠙⠳⢿⣿⣿⠇⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⡤⢤⣄⣠⡾⠟⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⡼⠇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⡀⠀⠀⠐⢿⣆⣀⣀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⣀⣀⡤⠞⠁⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠋⠉⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⢤⣄⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣀⣀⣤⣤⣤⣾⠀⠀⠀⠀⣠⠖⠛⠛⠒⠒⠋⠉⠁⠀⠀⠀⠀⠈⢳⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⠁⠀⠀⠀⠀⠸⣇⠀⠀⠀⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢧⡀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⢸⣆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⡉⠳⡄⠀⠀⠀⠀⠉⠛⠛⠛⠛⣻⡆⠀⠈⣧⠀⠀⠀⠀⠀⢾⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠇⢀⡟⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡀⢂⠀⣆⠀⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠻⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣆⡇⢸⠀⣻⠀⣿⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣢⠀⠀⠀⢻⣧⠀⣗⢦⠀⠀⢀⡀⠀⠹⡇⠀⢠⢶⡄⠀⠀⢠⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⡿⠁⡟⠀⡿⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⠀⠈⠂⠘⠮⣷⡀⠸⣿⡀⠀⠀⠀⢼⠀⣧⠀⠀⣾⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⢁⡼⢃⣰⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠣⣧⠀⠠⣶⣄⡀⠀⣀⠈⠓⠀⠀⠀⠀⠀⠹⠶⠶⠟⠀⠿⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡽⠛⠛⠛⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠈⠁⠀⠈⠙⠛⠂⠻⣷⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠶⠀⠀⠀⠉⢛⣳⣦⠀⠀⢠⠏⢠⡏⢠⠏⢀⡎⢀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⣀⣀⠀⠀⠀⠀⠈⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡽⠋⠀⠀⣿⠀⢸⡀⣼⠀⢸⠀⢸⠀⡧
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⣀⠔⠋⠉⠉⢻⡄⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⢰⡞⠒⠶⠶⠶⠚⠋⠀⠀⠀⠀⠘⣆⠘⣇⠹⡄⠸⡄⢸⣴⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⣸⣵⠟⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠛⢦⢿⠶⢿⣏⠁
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⡀⠃⠀⠐⠻⡄⠀⠀⢠⡇⣸⣷⢃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡀⠱⡄⣇⠘⡜⣧
⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡾⠛⣧⣼⡞⠀⠀⠀⢸⠁⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⡇⢠⡇⡟⠀⡇⣼
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⠀⠀⢀⣸⠃⠀⢰⢷⡞⢻⣁⡿⠀⠀⠀⢸⠠⢋⣿⡶⣿⠃⠀⠀⠀⠀⠀⢳⣎⡜⣱⠏⡼⠁⣼⣡⠏
⠀⠀⠀⠀⠀⠀⠹⣄⡀⢀⣠⠞⣽⠓⠲⡚⠁⠀⢀⣟⣠⣿⠞⣿⠀⠀⠀⠀⣾⠀⠈⢉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣾⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⠀⣿⣶⠟⠁⠀⠀⡾⠉⣷⣸⢿⠁⢀⠘⣆⠀⣿⣀⠀⠈⢉⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡇⠀⠀⠀⣸⠳⡟⢹⣥⠾⠀⠘⢦⡈⢷⣯⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣿⡴⢳⣁⣼⣷⠇⠀⠀⠉⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⠀⠀⢀⠀⣀⡀⠀⣀⠀⣠⢶⡦⢶⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⢶⣲⣾⠷⢿⡾⢹⣏⣿⣸⠃⠀⠀⠀⢸⡧⠠⠴⣶⡶⠂⠀⠀⠀⡟⢷⡠⡿⠦⠛⠗⢛⣿⠞⠟⠃⠁⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠛⠿⢭⣍⣹⣿⣹⣷⢻⣏⢿⡼⣧⣶⠛⣯⢹⡇⣹⡇⠀⠀⠀⠸⣷⣶⣿⠵⠶⣶⡶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠷⠿⠷⠿⠶⠦⠤⠴⠶⠶⠶⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣤⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡷⢚⡶⢻⡗⢻⡧⠽⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠆⠸⢣⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⢁⡞⢠⡟⠀⢀⣤⣄⠀⢹⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⢠⠂⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣯⣾⣥⡏⠀⠀⠂⢈⠋⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣾⣽⣷⣯⣴⣋⢉⡑⣌⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠖⠰⢈⠲⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣿⣇⠛⢙⢿⡟⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠘⠚⠉⠀⢀⠀⠀⠀⠀⠤⣿⣿⣿⣿⠋⠀⠘⠻⣓⠒⠉⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⢴⠀⠀⠙⠁⠀⠈⠢⠆⠉⠀⣤⠉⣥⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠊⠀⠀⢀⠀⡀⠀⠐⡓⡘⠃⡀⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠨⠀⠀⠈⠄⠁⠁⠀⠁⠁⠄⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠀⣂⠀⠀⠀⠄⠀⠁⠰⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠁⠀⢀⠀⠀⠀⡁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⢐⠀⠐⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢀⡴⠂⣤⣿⠟⠁⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣴⠟⢡⣾⣿⠋⣠⣾⡿⠁⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⣿⡿⢣⣾⣿⠟⠀⠀⠀⠀⢸⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⣿⣿⣿⡗⡰⠀⠠⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣫⣿⣿⣿⣷⣇⣴⢁⣰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣥⣤⣾⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠛⠿⢶⣤⣄⡀⠙⢿⣿⣿⣅⣘⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣍⣀⡀⠀⠀⠀⠈⠙⢿⣷⣮⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⠟⠿⠷⣿⣤⡐⠺⠅⠘⠋⠀⠀⠀⣠⣾⣿⣤⣤⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⠀⣾⡀⠛⣀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠋⣠⣾⣿⣉⣩⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠷⠾⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⣶⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣿⢷⣶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠷⣿⣿⣽⡟⠋⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣝⢿⣿⠿⠿⣿⡧⠀⠀⠀⠀⢀⣤⠀⠀⠀⠁⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠉⢸⣧⣈⣛⣠⣴⣿⡄⠀⠀⠀⠀⢼⣿⠀⠺⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣦⡀⣬⠈⣿⠛⠛⢡⠉⠁⢀⣀⣤⣶⣾⣷⣿⣆⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⡀⢿⠀⠀⠀⠀⢻⣿⢻⣿⣿⣿⣿⠉⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠰⣦⣙⠿⣿⣿⣿⣿⣄⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣰⠀⠀⣤⡀⠟⠻⣶⣿⣷⣈⠉⠀⠻⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⠻⣷⠈⣄⠈⠀⢙⣿⡷⣄⣼⠂⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⠀⠙⢷⣿⣷⡄⢹⡇⠱⠿⡟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠈⠇⠀⠘⠏⢿⣷⣼⡇⠀⠹⠇⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠐⠆⠀⠀⢁⣸⣏⠿⠀⠀⣦⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⡄⠀⠈⢻⣇⠀⠀⠀⣿⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠆⢰⣧⠀⠀⠀⢻⣷⡀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⣿⣿⡇⠀⢀⡿⣻⡇⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠁⠀⢸⣷⡟⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⠀⠀⠀⢸⣿⡷⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗

⠀⠀⣀⠀⢀⡠⠤⡤⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠈⡄⡁⢀⠀⠀⠀⠀⠀⣈⠄⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢁⠀⠀⢀⡈⠄⠀⠠⠄
⠀⠀⡐⠀⠀⠀⣍⠑⠂⠉⣎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠄⠀⠀⣘⠀⠀⠀⠐⠂⠐⠂
⠀⠀⢇⠀⠀⠀⠐⠀⠀⠀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠉⠀⠱⡦⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀
⠀⠀⠀⠓⠒⠠⡤⠀⠠⠠⠤⠐⠁⠀⣀⡀⣀⣀⠀⠀⠀⠀⡀⠤⠒⠒⠂⠧⡀⠀⠀⠀⠀⠀⠄⣴⢁⠆⠀⠀⠀⠀⠀⡰⠀⠀⠈⠉⡂
⠀⠀⠀⠁⠀⠀⡇⢀⠆⠀⠐⢢⠂⠁⠀⠀⠀⠀⠉⠢⣀⠞⠉⠈⠀⠀⠠⢀⠈⢂⠀⠑⠤⠤⠒⡩⣥⠃⠳⠊⢓⠖⡖⡅⢡⣄⣀⠃⡇
⠀⠀⢸⠀⠀⠀⡇⢰⠀⠀⡇⡈⠀⠀⠀⠀⡄⠀⢤⠀⢹⠀⢀⠀⠀⠀⢀⡀⢀⠀⠆⢀⠴⣎⡹⠤⠀⠂⠀⠠⠄⣠⠀⣄⠉⠉⠁⠀⠂
⠀⠀⢸⠀⠀⠀⣠⠜⡨⢁⠀⠣⣢⠀⠀⠀⠀⠀⠄⠀⠸⠀⠉⠀⠀⠀⠈⠁⠀⠀⢛⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢀⠃
⠀⠀⢸⠀⠀⠀⠩⠀⠀⠉⡀⠀⣆⠠⠄⠀⠀⠀⠠⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡀⡄⠀⢀⠋⠆
⠀⠀⠐⠂⠀⠀⠀⡆⠀⢘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⢋⠀⠀⠀⠀⡌⠀⠅⠀⡄⠀⠀⡀⠀⠀⠀⠠⢄⡼⠤⠤⠤⠵⠏⡐⡎
⠀⠀⠀⡅⠀⠀⠀⠘⡀⢈⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢘⠀⣶⠦⠐⣇⠜⠁⢈⡕⠃⡌⠀⠀⡆⠨⠒⠠⠃⠀⠀⠀⠀⠀⠈⠱
⠀⠀⢠⢰⣀⠠⠤⠀⠋⠁⢡⣀⡄⠀⠀⡀⠀⣴⡎⠛⡰⠉⠉⠁⠀⠀⠀⢀⠔⠋⠀⠀⣈⠦⣸⢦⢁⠀⡀⣰⢠⡇⡄⢰⠀⣄⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣤⣼⠀⠘⣿⠶⢾⠿⠛⠃⠰⠁⡀⠀⠀⠀⣠⢰⣁⠀⠀⠀⠀⠛⠀⠀⠰⢸⠸⡇⠙⡌⢣⢧⡜⣼⣿⣰⠇
⠀⠀⠸⠀⠘⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠙⠈⠛⢻⣶⣄⠀⠀⠀⠀⠀⠎⠃⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⠀⠀⢀⠤⠒⠉⠁⠀⠁⠉⠒⢄⠀⠀⠀⠀⡇⠀⠀⠠⠀⡀⢂⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⢄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⡃⠀⠈⠀⠀⠀⠀⠀⢰⣿⡟⠹⢛⠃⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠓⠒⠠⢄⡀⠀⠠⢶⣻⣿⣧⣀⠎⠀⠀⠀⡀⢠⡀⠀⠂⠄⠠⠐⠈⠀⠀⢠⠀⡄
⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⣀⠀⠀⠀⠙⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠇⠈⡧⠐⠂⠉⠒⠀⠈⠐⠠⣜⠀⡇
⠀⠀⠃⠀⠀⠀⠀⠿⣼⣇⣴⣀⡄⣠⠀⡌⠀⠉⠀⠃⠉⠢⡀⠀⠞⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠃
⠀⢀⠀⠀⠈⠆⠀⠀⠈⠙⣿⣿⣿⡏⡸⡆⠀⠃⠀⠀⠄⠀⠈⠲⣆⠠⠆⠒⠒⠊⠉⠁⠉⠁⠉⠓⠅⣔⠢⠀⠀⢠⡀⠀⠀⠀⠙⢺
⠀⢨⠀⠈⢆⣰⠀⠀⠀⠀⠈⠻⡿⢀⡆⠁⠀⠀⠀⠀⠀⡀⡘⠁⠀⠀⠀⢀⡀⠄⠀⡀⢀⠀⠀⡀⠐⠋⡐⠀⠀⠘⠁⠄⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡎⠈⠁⠈⠀⠀⠈⠀⢁⠀⠀⡀⠈⠀⠀⢰⠜⠦⠹⠊⠎⠎⢱⠁⠀⢤⣤⣤⠤⠴⠂⠠⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠈⠈⠂⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⠔⠁⠀⣀⠀⢶⠀⢰⠈⠤⢐⠀⠀⠀⠀⠀⠀⡃⢠⠁
⠀⠈⡀⢀⠃⠒⠀⠀⠀⠒⡀⡰⠁⡄⡤⠤⠤⠄⠠⢄⠜⠀⡀⠄⣀⣤⡁⠀⠒⣁⣄⠀⠀⠀⢀⡬⢤⡂⠀⠐⠖⠦⠀⠀⣉⡉⠨⠆
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠄⠂⠀⠀⠈⠀⠀⠀⠀⠋⢤⠀⠀⠀⠀⠗⠂⠀⢀⡀
⠀⠀⠀⣤⠀⠠⠀⠂⠀⠁⠀⠀⠈⢀⠄⠤⠀⢄⡀⠀⡀⠀⠀⣀⡀⠀⠀⠸⡁⠀⠀⠰⡢⠤⡄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠰⠁⢐⣢⠀⠀⠑⠀⠀⠀⠀⣧⡱⠀⠀⠀⠃⠀⠐⠀⠙⠁
⠀⠀⠀⠀⠄⠀⠀⡖⡇⠀⠀⠀⢡⠀⠀⠀⡆⡂⢀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠓⠀⠸⠂⢠⠘⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠑⠄⣉⡮⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⠦⠒
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠈⡀⠤⠀⠤⠤⠒⠀⠀⠀⠈⠀⠀⠀⠀⠁⠘⠁⠀⠀⠒
⠀⠀⠀⠀⠈⠧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠐⠀⠀⠤




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠜⠐⢄⡀⠀⠀⠀⠀⢀⡠⠄⠂⠀⠉⠁⠀⠈⠉⠀⠐⠢⠄⡀⠀⠀⠀⢀⡠⠊⠀⢢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠚⠂⠄⡀⠈⠒⢄⡠⠂⠁⠀⠀⢀⠔⠂⠈⠉⠉⠀⠐⠤⡀⠀⠈⠑⠠⡔⠁⢀⠤⠂⠁⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠊⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠈⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠰⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⡄⠀⠀⠀⠣⡀⠄⠀⠨⡆
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣏⣹⠀⠰⠐⠄⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠄⠄⠈⠠⠻⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠈⠀⠀⠑⠄⠀⠀⠀⢸⠀⠠⠐⡆⠉⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠑⠁⢈⣹⠀⡇⠀⠀⠀⡔⠀⠀⠀⠇
⢀⠔⠂⠌⣆⠀⠀⠘⡀⠀⠀⠐⢀⠠⠈⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⡀⠁⠀⠀⢰⠀⠀⢀⡼⠐⠁⠐
⡆⠀⠀⠀⠈⠳⡀⠀⠇⠀⠄⠊⢁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠄⡈⠑⠢⠄⠘⠀⠠⠊
⠑⠄⣀⡀⠀⠀⠀⠀⠀⠀⣀⠔⡁⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⢂⠀⠈⠆⢄⠀⠀⠀⠀⢀⣀⣠⡤⢂
⠐⠈⠉⠉⠉⠁⠤⠄⢤⠊⠀⠀⠁⢠⠁⠘⠀⠀⠀⠀⠈⢢⠄⣀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠈⠆⢰⠀⠀⢉⠦⠀⠒⢠⡀
⠐⠄⠠⠄⠚⢇⠀⠀⠀⠈⠐⢄⡸⠃⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠘⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢆⣀⠄⠁⠀⠀⠀⡠⢛⠀⠒⠒
⠀⠀⠀⠀⠐⢂⠓⠠⠤⢤⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠴⠶⠭⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠡⣀⣀⣀⡤⠊⠁⠰⠀⠠⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠱⠀⢱⠀⠈⠲⢤⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢠⠫⣀⡀⠃⠘⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠠⢀⠠⠣⡀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠐⠁⠀⠀⠀⠀⠂⠀⠐⠀⠁⠐⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⢫⠀⠀⠃⠀⠀⠀⠀⠀⠈⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠄⠰⠦⣤⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣧⠴⠀⠀⣐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⡀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⡈⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⠢⠀⣀⡀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣘⣿⡾⣯⣳⣔⣄⡞⣿⡶⣿⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⠀⠀⠀⠀⠂⢠⣀⣹⣿⣾⣿⣿⣷⣿⣿⣿⣹⡭⠿⠿⠷⣯⡀⠀⠠⠀⠀⠰⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠋⠀⠰⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⣠⠞⠉⠁⠁⠉⠀⠈⠛⠛⠙⠉⢻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠏⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠈⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⣇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣼⠁⠀⠀⢀⣠⣤⣄⡀⠀⠀⠸⡆⠀⠀⣰⠃⠀⠀⢀⣤⣤⣄⡀⠀⠀⠈⣇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠐⣿⣿⣿⠟⠻⡆⠀⠀⣷⠀⠀⣟⠀⠀⠔⣿⣿⣿⠛⠻⡄⠀⠀⢸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⢧⠀⠀⠀⢿⣿⣿⣶⣴⡟⠀⢀⡏⠀⠀⢻⠀⠀⡄⢿⣿⣿⣦⣾⡇⠀⠀⡾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠈⢧⡀⠈⠢⢙⡛⠛⠟⠁⣠⠞⠀⠀⠀⠈⢳⡀⠈⠢⢙⢛⠻⠋⠀⢀⡜⠁⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠉⠳⠤⠤⠤⠤⠴⠚⠁⠀⠐⠛⠂⠀⠀⠉⠓⠦⢤⡤⠤⠴⠚⠉⠀⠀⠀⠀⣸⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⣿⠀⠀⠀⠀⠀⠀⠰⡟⣶⣶⠒⠒⠒⣶⣶⣶⣶⡖⠒⠒⣻⣿⣏⣛⣆⠀⠀⠀⠀⠀⠀⢀⣿⠃⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⣾⣿⣿⣿⣿⣷⣤⣴⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣽⣿⣦⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡏⠀⠙⣿⣿⣿⣿⣟⣠⠴⠛⠀⠀⠀⠀⠀⠀⣰⣿⣁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢷⡿⠿⠙⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠿⢿⡾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣔⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠁⠙⠻⢻⣿⣶⣤⡄⣲⣤⣠⣄⣄⣀⣀⣤⣬⣴⣶⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡿⠻⣿⠛⠟⠛⠿⣿⠻⠟⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣶⠾⠃⠈⢻⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠹⢶⣶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣾⣁⣀⣀⣀⣼⣶⣶⣶⣶⣶⣶⣶⣾⣇⣀⣀⣀⣸⣮⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣦⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠀⠤⠤⠤⠀⠤⡄⠀⠀⠀⠀⢀⠜⡀⠠⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠸⣧⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠳⣄⠀⢀⡠⠒⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠂⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢐⣈⢀⠇⣛⣾⠇
⠀⠀⠀⠀⠯⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠷⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣦⠀⢀⡄
⠀⠀⡀⢀⣀⡠⠎⠀⠀⠈⠉⠉⠙⠙⠉⠉⠀⠀⠀⠀⡀⠀⢀⢰⠀⠀⣮⣤⣦⣴⣶⠀⠀⠀⠀⠙⢀⠀⡀⣻⠇⠉
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠚⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣁⠒⠉⠐⠴⠴⠒⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠤⠀⠀⠀⠀⠀⠀⠀⠛⠓⠦⠆⠀⠀⠐⠀⡁⡀⠖⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠆⠀⠀⠀⠀⣠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢀
⠀⠀⠀⠀⠀⠠⣤⡦⠶⠟⠉⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠓⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⠀⠘⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⣸⡏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣿⢁⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣷⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⣿⣶⣖⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⣂⠀⢹⣿⡰⣣⡦⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣿⠀⢻⠟⠛⠉⣀⣀⣈⢙⠒⠒⠒⠒⡠⠤⠞⣁⡴⢂⡀⣉⣁⠰⢾⡗⣿⣿⠀⣿⠇
⠀⠀⠀⠀⠀⣴⠻⡆⣼⢃⣶⣿⣿⣿⣿⣿⣿⣦⡯⠁⠂⣤⣭⣵⣾⣿⣿⣿⣿⣷⡀⢿⣶⡏⢠⡟⢛⣦
⠀⠀⠀⠀⢰⣿⡄⢻⣿⢿⣿⡿⢛⣉⡙⢿⣿⣿⠅⢤⣠⡹⣿⣿⡿⢛⠛⡳⣝⣿⣷⡘⣿⠁⡼⣠⣿⣹⡆
⠀⠀⠀⠀⣼⠹⣷⡼⢟⣿⣾⣧⣈⣛⣃⣼⡿⣿⡆⣤⡸⣿⠟⢿⣄⣘⡻⣃⣸⣿⢿⢇⡘⠆⢱⣏⠋⣿⠃
⠀⠀⠀⠀⣿⢰⣿⡀⠐⠿⡿⠿⠿⠧⢯⣿⡇⡜⣸⣿⣿⣜⢷⣷⣞⠛⢩⢭⠴⢚⣣⠞⠀⢠⡟⣿⡇⡿
⠀⠀⠀⠀⠹⣎⠻⣧⣀⣀⣀⠄⠉⠉⠁⠉⢀⣾⣿⣿⣿⣿⣧⢻⣟⣆⣈⢉⡙⣉⢩⣤⣶⡿⢱⠟⢱⡇
⠀⠀⠀⠀⠀⠙⣧⠆⢙⢻⣿⢀⡀⢎⠄⠀⠘⠛⠟⢡⠻⠿⠟⠘⠁⣄⣠⣾⡇⣿⣿⣿⡟⡇⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠹⣦⣼⡆⡿⣾⣷⡏⡆⡄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⢻⡏⠘⣿⠋⡿⣴⣷⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⢳⣹⣿⡴⠷⣷⠷⣾⠷⡾⢤⡴⢾⡾⣦⣴⣼⡹⢰⣿⣸⢿⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⢹⣿⣷⣤⣿⡀⣸⡀⣇⣸⣠⣼⣄⣴⣤⣿⢹⣴⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠀⢟⠛⠿⠿⢿⠿⡿⢿⣿⠟⣿⡟⢻⡿⠟⣨⠟⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠰⡌⠻⣶⢧⣼⣠⡄⣰⣿⣀⡦⠵⢊⣴⡞⢁⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠰⡉⠀⠲⣦⣬⣥⣤⣤⡶⣶⡟⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡿⣦⡀⠚⣄⠀⠉⢩⣤⣴⡆⠈⢀⣴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢾⡜⣠⣶⢰⢠⣤⣠⢴⢾⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⣷⠇⠸⡿⠞⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⣉⣉⡉⠉⠉⢉⣉⣉⣉⣉⣉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⣛⡛⠛⠀⠀⠛⢛⣛⣛⣛⠛⠃⠀⠀⠛⢛⣛⣛⣛⠛⠁⠀⠘⠛⣛⣛⣛⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣭⣥⣄⠀⠀⣠⣬⣭⣭⣭⣥⡀⠀⠀⣠⣭⣭⣭⣭⣤⡀⠀⢀⣤⣭⣭⣭⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣉⣉⣉⣉⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣈⣉⣉⣉⣉⣉⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡦⠀⠈⠛⢟⡜⠿⠚⠀⢆⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⡟⣾⠛⠀⠀⢸⣧⣠⣈⠀⠀⠀⠀⢛⡼⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣤⣶⡀⠀⠈⠉⢋⢹⣤⡀⣴⣦⣤⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠈⣿⢼⣿⡄⠈⠘⣿⡏⢰⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣍⢾⡙⢃⣀⡲⠿⠴⣏⣀⠐⣯⡄⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢄⣦⣿⣀⢅⡸⢇⣤⣰⢀⣿⡛⡄⢮⢘⡿⢛⣧⡀⣴⣇⡴⠘⠋
⠀⠀⠀⠀⠐⢀⣤⡰⣶⢛⣁⠚⣹⢳⣷⠄⣷⠶⢀⡸⢺⣿⡗⣔⠏⣾⡒⣰⡯⣭⢻⠿⢿⠃
⠀⠀⠀⠀⠀⠈⢁⢉⣰⣿⣿⣶⡛⣋⣡⡇⢹⠧⡾⠋⠘⠻⠃⠛⣣⣟⣷⣨⣷⡏⠀⣠⠃
⠀⠀⠀⠀⠀⠀⢸⠋⠋⠙⢟⣬⢣⣯⡉⠈⠀⣐⠃⠀⠀⠂⢀⣠⡖⢉⠿⠿⠋⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⡀⣽⡄⠀⠀⢽⡝⢲⣤⡶⢋⡿⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣇⣾⠇⠂⣀⣴⢿⡏⢀⣙⣿⢧⣀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡿⠛⠀⠉⠉⠛⠛⣿⠙⣹⠋⠛⠉⠁⠀⠀⣥⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢁⠀⠀⠀⠠⠖⠀⠙⣷⠋⠀⠀⠁⠀⢤⡀⣷⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠄⡦⠄⠀⠀⠹⢸⡇⢀⣤⣴⣶⣦⡀⠀⠀⣴⣿⣿⣿⣷⡆⢿⡏⠀⡀⠀⢀⣠⠦
⠀⠀⠀⠀⠀⠀⠈⠑⢢⣤⡰⠢⡿⠃⣿⣿⣿⣿⣿⢇⣶⣌⢿⣿⣿⣿⡿⡧⠘⣆⣊⢴⠺⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠉⠿⠿⡇⠀⠙⢻⠛⢟⣿⢸⣿⣿⡤⣍⠛⠛⠛⣀⣴⠿⠃⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡃⣰⡿⢖⠲⣶⡆⠀⠀⣿⡿⠿⡇⠈⠁⣶⣿⠩⠛⢸⡛⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢥⡄⠠⢭⡄⢩⡇⣀⠀⠈⡄⠈⠋⠀⢀⣿⡆⢴⣟⡀⠀⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣣⣆⣦⡽⠟⣧⡘⣷⠑⠀⢡⠦⠴⡘⡔⢚⣼⠁⣾⠉⠱⢎⣷⠼⣃
⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣉⡀⠀⠚⠁⢻⠹⢝⣸⢹⣶⠀⡔⠞⠻⠟⣸⠣⠀⠓⠀⠄⠈⠛⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⠀⠀⠀⠀⠀⠈⢆⠀⠀⠉⠋⠚⠉⠉⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠉⠙⢇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢓⠦⠤⢵⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠈⢆⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠈⠢⣛⠛⠛⠿⠿⠟⠋⣠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣤⣤⣶⣶⣾⣿⣭⡉⠓⣰⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⠮⡁⠄⠉⠀⢼⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣫⣬⣝⣚⣷⣆⡲⣈⠻⠽⣿⣷⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣶⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢽⣿⣿⣿⣻⠋⠻⠿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣾⣿⣿⡿⠏⠀⠀⠀⢸⣿⣿⣽⡇⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠁⠀⠈⠻⣿⣿⣇⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢹⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠿⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⢠⠾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣆
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢀⣠⠴⠚⡇⣰⣯⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣏⠀⠀⠀⡿⣟⠀⣼⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⣆⢴⡾⠁⠈⣹⣏⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⣎⠀⠀⣰⠧⠞⠓⢦⣀⣠⠏⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿⡄⢰⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠈⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢀⠞⠉⠛⢤⡀⠀⠀⢀⣠⠴⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⡰⠋⠀⠀⠀⠀⠙⠢⣴⠋⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣠⡞⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⢀⡀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠐⡁⠨⠠⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠉⠉⠉⠉⠉⢉⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠉⠉⠉⠉⠉⠉⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⠒⠒⢲⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⡖⠒⠒⠒⠲
⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠈⣅⣀⣀⡨⠁⠀⠀⠀⢅⣀⣀⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⠇⠀⠀⠀⢩⣀⣀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡖⠲⠒⢲⣾⣿⣿⡇⣴⠠⠦⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠠⡆⢸⣿⣿⣿⣤⠀⠦⠠⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⢀⡀⣸⣿⣿⣿⡇⣿⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡇⢸⣿⣿⣯⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣟⣀⣖⣐⣣⠀⠀⠀⠀⠀⠀⠀⣞⣀⣖⣐⣣⢸⣿⣿⣷⣟⣀⣶⣐⣳⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢸⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡤⠤⠤⢤⣼⣿⣿⡇⣠⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⠤⡄⢸⣿⣿⣿⣤⠤⠤⠤⣄⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⡐⠀⡞⠁⢆⠀⢸⠀⠀⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⣿⠀⠉⠈⡇⠀⡧⠤⣧⠤⢼⠀⢹⠀⠉⠈⡇⢸⣿⣿⣿⣿⠀⠉⠈⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣦⣼⣿⣿⣿⣧⣿⣤⣤⣤⣧⠀⣇⠀⣇⠀⣸⠀⣽⣤⣦⣤⣧⢸⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢸⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡠⠍⠉⠉⠩⠀⠀⠀⠀⠍⠉⠉⠩⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠇⠀⠀⠀⠸⠉⠉⠉⠅
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⢀⡀⠠⡆⠀⠀⠀⠈⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣿⣸⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠡
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⢻⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠹⡷⠈⠉⢀⢐⠂⠀⠀⠀⠀⢀⠀⠺⠇⠀⠀⠂⠀⠀⠀⠈⠉⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠒
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡔⠀⠀⠀⠀⠆⠀⠀⠀⠺⢠⣠⠔⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣐⠂⠁⠐⠚⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠂⠂⠐⠒⠁⠀⠀⢀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠳⠜⠜⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⡆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈
⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠲⠒⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠠⠶⠀⠀⠀⠀⠀⡀⠀⣠
⡿⠋⢁⡄⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢠⠜⠀⠀⠀⠐⣠⣴⣿⣿
⠁⠀⠺⡤⠀⠀⢸⣿⣿⣿⡿⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡄⠀⠀⠤⠄⠀⣼⣿⡿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣶⣤⣤⣴⣾⡿⠋⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠄⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠈⠀⠁⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡐⠠⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡿⢋⠀⠀⠀⠑⠀⡀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠀⠀⢀⠄⠀⠀⠀⠀⠀⢿⣿⣿
⠁⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠈⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠲⠄⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢄⣀
⡠⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⠖⠐⠀⠁⢀⠤⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲
⠀⠀⠀⠁⠀⠀⠀⡀⠀⣄⠀⠈⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⢓⡆⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡖⠀⠘⡅⠀⠀⠀⠀⠀⢉⠂⠐⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⠀⠉⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠒⠢⡁
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠿⢤⡀⣀⠠⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⣀⠫⠀⠀⡀⣀⡴⡃⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣠⡾⣿⢻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠛
⣇⠀⠀⠐⠀⠀⠀⠀⣀⣤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣀⣿⢸⣷⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘
⠀⠄⠀⠀⠀⠀⢠⣿⣯⢿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣾⣿⣶⣄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠋⠉⠙⠛⠒⠦⣄
⠀⠀⠀⠀⢠⠖⠋⠀⣠⠤⠖⠒⠒⢒⠦⣄⡀⠈⠳⣄
⠀⠀⠀⣰⠋⠀⣰⠋⠁⠀⠀⡤⠶⢾⡀⠀⠙⣆⠀⠈⣇
⠀⠀⢰⠇⠀⣸⠁⠀⠀⠀⠘⣧⠀⠀⠙⠀⠀⢸⡆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢛⣉⣉⣉⣉⣉⣉⣉⣙⠓⠲⢤⣀
⠀⠀⠸⡆⠀⠸⣆⠀⠈⢳⡤⠴⠞⠀⠀⠀⣰⠋⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡴⢋⣉⡵⠀⢀⣠⠖⠒⢲⣭⠽⠳⡄⠈
⠀⠀⠀⢻⣆⠀⠈⠳⢤⣌⣀⣀⣀⣤⠴⠋⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠲⠤⣽⣛⣋⣁⣀⣀⣨⡥⠴⠚⠁⣠
⠀⠀⠀⠀⠙⣿⣦⣄⣀⡀⠀⠀⢀⣀⣠⣴⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣯⣟⣻⣿⠿⢿⣿⣿⠿⢿⣿⣛⣯⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠖⠲⠶⠶⠤⢤⣀⣸⡿⣷⣯⣟⣻⣿⡿⠿⠿⠿⠿⣿⣿⣻⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⠴⢖⡒⠛⠛⣛⣻⣖⡲⠦⣤⡉⠛⣷⣯⣿⣻⣿⠿⢿⣿⣿⠿⢿⣿⣛⣯⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠻⣔⡒⠻⢤⠤⠞⠁⠀⠀⠟⢉⣠⠟⠀⢸⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣭⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣈⡉⠙⠛⠒⠒⠒⠒⠛⠋⢉⣁⣤⣶⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣝⣿⢿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⢿⣫⣾⣿⣻⣿⣿⡿⠿⠿⣿⣿⡿⢿⣿⣻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣽⣻⢿⣷⣿⣿⣯⣭⣭⣽⣿⣿⣶⣿⢿⣫⣿⡿⠛⠉⠀⢀⣀⣀⡀⠈⠙⠻⣿⣻⣽⣾
⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣄⣀⢸⣷⣝⣿⢿⣷⣿⣿⣭⣿⣿⣭⣿⣿⣶⣿⢿⣿⡟⠀⢀⡴⠚⠉⠉⠉⠉⠛⠦⣀⠈⠻⣯⣿
⢀⡴⠋⣉⡤⠴⠶⠒⠒⢒⣒⣶⠶⠤⣌⡙⠻⣿⣿⣿⣷⣿⣿⣿⣭⣭⣿⣿⣿⣷⣿⣿⣿⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠘⣿
⣏⠀⠸⣁⠶⠾⣥⣤⡴⠋⠁⠉⠿⠛⢁⡽⠀⢈⣿⣷⣿⣯⣽⣿⣿⣿⣿⣯⣽⣿⣾⣿⣇⠀⢸⡇⣤⣾⠁⠀⠀⡴⠚⢶⡄⠈⣇⠀⢹
⣿⣶⣄⣈⠙⠓⠒⠲⠶⠶⠶⠒⠒⠋⢉⣀⣴⣾⣿⣷⣿⣯⣽⣿⣿⣿⣿⣯⣽⣿⣾⣿⣿⠀⠘⣇⠀⠙⢦⣤⠞⠁⠀⣰⠟⠃⣿⠀⢸
⣿⣝⡿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⣟⣽⣿⣷⣿⣿⣭⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣧⠀⠘⣆⠀⠀⠀⠀⠀⠀⠉⠀⢠⠏⠀⢸
⣿⣝⡿⣷⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿⣶⡿⣟⣽⡇⠉⠙⠛⠛⠛⠿⠿⠛⠛⠛⠋⠉⠀⠻⣿⣷⣄⠈⠓⢦⣄⣀⣀⣀⣠⠴⠋⠀⢠⠏
⠘⠿⣿⣷⣾⣯⣭⣿⣿⣿⣿⣯⣽⣿⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠉⠉⠉⠀⠀⣠⠴⠋
⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣷⣶⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠰⢚⣻⢶⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠈⢀⡽⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠹⣭⠿⡖⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢐⢠⡀⠀⠡⣴⢈⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡆⠀⠀⠀⠀⠃⣨⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⣀⠀⠀⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⠀⠠⠔⣿⣤⡁⠶⡀⠀⠀⠀⠰⠂⠸⠷⠯⠉⠀⠀⠘⠍⣻⣦⣤⡝⣌⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⡀⠈⠁⠀⠀⠀⠉⠛⢂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠛⠉⣹⣷⣾⣏⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣑⣒⠂⠖⢤⣀⣱⣿⣴⣃⠀⠠⣀⣤⣖⡀⠀⠀⠀⠀⢠⠀⠴⣤⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣴⡷⠂⠀⠈⠙⠲⠄⠈⠿⠀⠀⡀⠁⠀⡿⠛⠿⢿⣼⡆⠂⠂⠊⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣴⠖⠚⠻⠛⠶⣄⡁⠀⢀⡴⠆⠒⠀⠀⠀⠀⢀⣩⣤⣤⡴⠗⠂⡠⡶⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⡀⠀⠀⠀⠀⠘⢿⣦⡇⠠⠂⢐⠀⠉⣥⠈⠁⠀⠀⠘⠀⡠⠊⡔⢁⠞⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⣿⢻⣧⡀⠀⠀⠀⠀⠀⠝⠓⠠⡈⠀⠤⠈⣿⡆⠀⠀⠀⠀⣾⡄⠀⠆⠀⠀⠀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣿⢸⣧⢻⣦⡀⠀⠁⠀⠀⠀⡠⠁⠑⠲⠸⠛⡁⠀⠀⠀⠀⠰⣏⠀⢌⠀⣠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⣿⡆⢯⡟⣦⣤⠶⠀⣈⠄⠀⠀⠀⠀⠈⠉⠀⢊⠹⣠⠀⢸⠀⠀⠀⠹⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣇⠀⣟⣀⡜⡇⢣⢉⢲⡄⠁⠀⠀⠀⠈⠠⠌⠠⠐⠾⠄⠐⠀⡈⠇⠀⠀⠀⠀⠀⠀⢠⢅⡀
⠀⠀⠀⠀⢀⡀⠈⠻⣄⠾⢙⣽⣿⣿⣷⣤⡀⠀⢣⠀⣶⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⢞⠀⠀⠐⢠⠇⠀⢿⣾⣿⣤⣶⢒⣦⣶⣶⣶
⠀⠀⠀⠀⠀⢀⣤⣴⠠⣴⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⠈⠋⢻⣧⣀⢀⡀⠀⠀⡄⠀⣇⣐⣂⣸⣃⡐⣛⣸⣦⣄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠈⠈⠩⣙⠛⠉⣿⣟⢿⠿⣿⢿⣿⣿⢓⣀⠀⠀⢸⣿⣿⣾⣿⣿⣷⣶⢂⣽⣽⣿⣿⠭⠄⠉⠉⢣⠀⠈⡶⠟⣿⣿⣿⣿⣿⡏⣁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠘⠃⠀⣴⢿⠿⠋⠉⠁⡴⠀⣾⣿⣿⣿⣿⣿⢿⠯⢭⣟⣻⣿⣿⠀⠀⠀⠀⣴⣽⣟⣢⣶⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠐⠁⠀⣈⠁⠐⡀⠀⠀⠀⠓⠠⢭⣥⣀⠮⠹⠿⢿⡄⠂⠀⢠⢿⠇⠸⠯⣛⠊⠑⢒⣶⣿⣟⣛
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢀⣃⣠⣶⣦⣮⡷⠶⠀⠋⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⢀⣠⣾⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣦⡀⡶⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠦⠈⠷⡀⣠⣴⣾⠿⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⢀⡙⢂⡓⠢⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡠⣄⣀⣀⠀⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⣿⠉⠉⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡏⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⢰⣷⣿⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣿⠟⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠿⠋⠀⠀⠈⠉⠙⣻⡇⢻⡏⠉⠀⠻⣄⣠⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣠⣴⡶⠾⠿⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⣰⠾⠋⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣀⣀⣀⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢶⣤⣤⡴⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠘⠃⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⡤⠴⠶⠶⣶⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠒⠒⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠛⠓⠶⣾⠉⠁⠀⠀⠉⢳⣦⣶⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣀⣤⡾⠋⠁⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣤⣤⣤⣤⣤⡶⠶⠛⠛⠉⠁⠀⠀⠀⠈⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣉⡀⠠⢄⠀⠀⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡁⠄⠂⣿⡋⣿⡇⠂⢈⡐⠈⢶⡉⠓⠲⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣤⠀⠈⠠⠀⠁⠀⠀⠀⠹⠧⠟⠁⠀⠀⠈⠀⠤⠙⠰⢤⣀⡀⢌⣫⣙⠩⡉⠑⠀⠑⢦⡀⡀
⠀⠀⠀⠀⢨⣹⢤⣐⣃⣠⣴⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠉⠉⠛⠛⠓⠒⠒⠒⠚⠀⠀⠉
⡠⢠⠤⣄⣀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡆⢰⠀⠀⡂⠀⠀⠀⠀⡀⠀⢰⠀⡀⠀⢰⠀⠂⠀⠀⠀⠀⠀⣀⣠⠀⠠⠤⡤⢀⠔⠂
⠙⢿⣦⣸⡏⠙⠦⠀⢀⣠⠴⢚⣱⠈⠀⠀⠁⠈⠁⠂⠀⠀⠂⡇⠀⢁⡀⠅⢀⣥⣀⡤⠤⡤⢶⣞⣋⠁⣀⣀⡤⠖⠉
⠀⠀⠈⠉⠋⠛⠓⢷⣋⣘⣴⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡦⢧⣤⠀⢀⣀⣁⡤⠾⠛⠛⠉
⢠⣆⣖⠒⣦⣄⡀⠚⠛⠋⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⡀⡇⠀⠀⠀⠈⠢⣊⠉⠛⠓⠒⠶⢶⡶⡶⠒⠒⠒⠀⠲⢤⠀⠄⡀
⠀⠙⠻⢷⢯⣄⣈⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠔⠦⠤⠥⢤⠽⠦⠴⠤⠤⠴⠒⠛⠀⠁
⠀⠀⠀⠀⡀⡬⠽⣯⠤⠤⡀⢀⠀⢀⠀⠀⡀⢀⡀⠀⠀⠀⠀⡇⠀⡄⠀⡀⠀⡂
⠀⠀⠀⢸⣷⣿⣶⣿⣶⣶⡿⠬⠤⠤⠥⠬⠤⠬⠽⠀⠀⠀⠼⠥⠤⠭⠤⠥⢼⣯⣀⡞⠛⠛⠛⠻⠛⢿⡛⠟⡛⠓⠂⠰⢤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣶⣤⣤⣤⣴⣶⣿⣶⣷⣶⣶⣶⣮⣤⣥
⣀⣀⣀⣘⣛⣿⣿⣻⣿⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣴⠟⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣤⠟⡁⠀⠀⣀⣝⠳⣤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠞⠛⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⡾⣫⡾⠙⠛⢛⠋⠉⠻⢦⣝⠳⣶⣶⡶⠶⠖⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣤⣄⣀⡾⣡⡶⣫⡾⠋⠀⣠⣤⣈⠻⢦⣄⣀⠈⢻⡆⠉⠛⠶⣤⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠈⠙⠿⣯⡴⠋⠀⣀⣀⡙⢷⣍⠻⣦⠉⠛⠀⠸⣇⠀⣠⡾⠋⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⢿⡉⠛⢦⡉⠛⠾⠃⠀⢀⡴⣫⣾⡋⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⢦⡿⠀⠀⣀⡶⣋⡶⣿⡈⢻⡄⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣠⡾⣫⡾⠋⣼⠋⠀⠀⣻⡄⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡾⠋⢀⣤⠿⢀⣤⠾⠋⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠻⣶⡟⣋⣥⠾⠋⠁⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠛⣦⣠⡴⠶⠶⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢻⣍⣀⣀⣀⣀⣀⣀⣀⣸
⢿⣤⣤⣤⣤⣤⣤⡾⠁⠀⠀⠀⣼⠏⠀⠀⠀⠈⣷⠟⠉⠉⠛⣦⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠙⢿⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣿⠋⠉⠉⢻⡄⢤⣤⣀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠈⠳⣄⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣾⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⡇⠀⠈⠙⠛⠶⣤⣀⠀⠀⠉⠳⣤⣀⢀⣈⡿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣴⡏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⠳⠶⢦⣤⣄⣀⣀⣉⣻⡶⠶⠶⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⢦⣤⣀⣠⡾⢷⣤⣀⣀⣰⡟⠛⠶⣤⡀⠈⣿⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣈⣉⣉⣉⣀⣀⣀⣈⣙⣳⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿