Pluto Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠶⠶⠶⠶⠶⠦⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠛⠻⠷⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣈⣩⣽⡷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠿⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠓⣒⡒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⣤⠴⠶⢤⡀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠉⠉⠛⠛⠓⠶⣄⣀⣀⡀⠀⠀⠻⣭⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⣛⣁⣀⣠⣤⣬⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⠲⠶⠶⠤⠤⣤⣤⣤⣭⣭⣉⣉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣉⣭⣭⣭⣭⡭⠵⠶⠖⠚⠛⠉⢳⡄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⡴⠶⠶⠶⠒⠒⠒⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣴⣃⣀⠀⠀⠈⣳⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣧
⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢰⠟⠛⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠀⣸⣇
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠰⣟⣉⣉⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣭⠽⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠸⣅⢹⡄
⠀⠀⠀⣼⠦⣤⣤⣤⣤⣤⣤⠤⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣞⣁⣤⣤⠴⠶⠶⠋⠀⣷
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⡄⠀⠀⠀⠀⢰⣛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠲⠶⢤⣤⡀⠀⠾⠿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⢸⡗⠲⠶⠶⠶⠶⠖⠒⠒⠶⠶⠶⠦⣤⣀⠀⠀⠀⢰⣖⣓⣲⡆⠀⠀⠀⠀⣀⣤⠶⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠻⡆⠀⢸⡇
⠀⠀⢸⡧⠤⠤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠓⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⣦⠀⠀⠙⠛⢺⡇
⠀⠀⠈⣇⢀⣤⠴⠶⠚⠛⠛⠁⠀⠀⠀⠸⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣁⣀⣀⣀⣀⣼⠃
⠀⠀⠀⢿⣟⣁⣀⣀⣠⣤⡤⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⡄⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⡿
⠀⠀⠀⠘⣏⠉⠉⣉⣀⡀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠶⠖⠚⠛⠋⠉⠉⠙⢳⡄⠀⠰⣏⣉⣉⡷⠀⠀⣸⠃
⠀⠀⠀⠀⠹⡆⠈⠻⠿⠛⠀⠀⠀⣀⣨⣉⡉⠉⠉⠁⠀⠀⣸⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠈⠉⠉⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠘⠷⠤⠼⠃⣀⣠⣤⠶⠛⠁⠀⠀⠀⠸⣏⡉⠉⠉⠙⠛⠛⠛⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣙⣛⣋⣉⣹⠏
⠀⠀⠀⠀⠀⠀⠹⣶⠶⠶⠒⠚⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠛⠶⠶⠶⠶⠖⠚⠛⠋⠉⠉⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⠶⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠾⠃⢀⣤⣄⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠛⠛⠋⠉⢙⣷⠀⠀⣠⡴⠖⠛⠋⠉⠁⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠶⠶⠾⠃⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⢰⡞⠛⠋⠁⠀⠀⢻⡀⠀⠀⣠⡤⠶⠶⢤⣄⠀⠀⢀⡴⠶⠒⠛⠛⠛⠛⠛⠛⠛⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⢀⣀⣀⡼⠁⠀⠀⠙⠲⠶⠶⠶⠋⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣅⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠞⢋⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠾⠟⠛⠛⠛⠛⠻⢿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠀⠈⠉⠛⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣠⣴⠾⠛⠉⢉⣉⣻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣴⡾⠋⣀⣤⡶⠞⠛⠉⠉⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣰⡿⢫⡄⢸⡇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣴⡿⢋⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⢀⣾⠏⠀⣾⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁⠀⣠⡾⠋⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⣷⡀
⠀⠀⢀⣾⠃⠀⠀⠉⠀⠀⠀⣀⣠⣤⡶⠶⠟⠛⠛⠋⠉⠀⠀⣠⡾⠋⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠘⢷⡄
⠀⢀⣾⠁⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⣠⡾⠃⠀⠀⠀⠀⠀⣀⣠⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣼⠃⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠉⣀⣠⡾⠋⠁⠀⠀⠀⣠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⢰⡏⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠋⢉⣥⡶⠾⠛⠋⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣠⡴⠾⠛⢷⡆⠀⠀⠀⣠⡿⠁⢹
⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢀⣴⠟⠋⠀⠀⢀⣼⠃⠀⠀⣰⡟⠁⠀⠈
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣰⡿⠁⠀⠀⢀⣴⡿⠃⠀⠀⣴⠟⠀⠀⢀⣼
⣿⠀⠀⠀⣀⣀⣀⣠⣤⣶⠟⠁⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢰⡟⠀⠀⣀⣴⠿⠋⠀⠀⢠⣾⠋⠀⠀⢠⡾⠃
⣿⢀⣴⠿⠛⠉⢉⣉⣁⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠘⠷⠶⠟⠋⠁⠀⠀⢀⣴⠟⠁⠀⠀⣴⠟⠁⢠
⢻⡿⠁⠀⣠⡾⠛⠉⠉⠉⠛⠻⠶⣦⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⣠⡾⠋⠀⢠⣿
⢸⡇⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⡾⠋⠀⠀⣰⡟⢱
⠀⢿⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⣠⡾⠋⠀⠀⣠⡾⠋⢀⡿
⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⣀⣴⠟⠋⠀⠀⣠⡾⠛⠁⠀⣼⠃
⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠁⢀⣠⣴⠾⠋⠁⠀⣠⣴⠟⠋⠀⠀⠀⣼⠏
⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⠋⠉⣀⣤⣴⠾⠛⠉⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠀⠀⠀⣠⣴⠟⠋⠁⠀⣀⣤⡶⠟⠋⠁⡀⢀⣶⢰⡿⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣸⡏⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⣼⠇⠸⠃⢈⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⢀⣾⠋⠀⠀⠀⠀⠀⢀⣾⠋⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣧⣀⡀⠀⠀⠀⣰⡿⠁⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣾⣯⣤⣄⣀⣾⣇⣀⣀⣤⣤⣴⡶⠾⠟⠋⠉
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠨⠁⠑⠊⠙⢶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠏⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣳⡀
⠀⠀⠀⠀⠀⢠⡞⠩⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣆
⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠹⣆
⠀⠀⠀⠀⡾⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⢻⡄
⠀⠀⠀⢰⡇⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⠡⠘⣇
⠀⠀⠀⢸⠇⠀⠀⢄⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢀⢀⠀⠀⠀⠀⠴⠀⠠⠀⢈⣿
⠀⠀⠀⢸⡅⠀⠀⢈⡈⠂⠀⠀⠁⠀⢀⢀⡼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢂⠀⣿
⠀⠀⠀⠸⣇⠁⠀⠀⠀⡀⠀⠀⠀⠀⡁⠀⡀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇
⠀⠀⠀⠀⢻⣊⢂⠀⡀⠁⠀⡀⠀⠰⢂⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠈⠁⣼⠁
⠀⠀⠀⠀⠈⢷⡁⢀⠀⢠⠲⠀⢀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⡀⠈⠃⣰⠃
⠀⠀⠀⠀⠀⠈⢳⡏⡿⢤⡐⠀⢶⠾⣂⡀⠔⢦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⠤⠤⠊⠔⢠⢰⡕⢺⡓⠠⠀⠄⡀⠀⠀⠀⠀⠀⣀⡦⢒⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣅⡔⡋⠀⠑⠬⠁⠨⠑⠀⠀⠀⠀⠐⠀⠀⠈⣉⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⣌⣀⢐⠀⠀⠀⣀⣀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡴⠆⠂⢀⡀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠅⠀⠂⠀⠠⠀⠀⠁⠀⢀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡁⠀⠀⡀⡇⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⠁⠱⢄⣀⠔⠱⢄⠠⠂⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⢀⠀⡠⢄⠀⠀⠀⠀⠀⢸⠀⠀⢀⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⢄
⡀⠇⣈⠇⠈⢆⠀⠀⠀⠀⣿⠀⢀⠜⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⣿⠀⠀⠀⠀⡐⠃⠸⡁⠸
⢣⠄⠀⠀⠀⣀⣉⠀⠐⠂⢿⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⠁⠀⡿⠐⠂⠀⢁⣀⠀⠀⠀⠠
⠐⠒⠂⠀⠉⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠁⠀⠀⠀⠉⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⣀⣀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠦⢤⡇⢸⡇⢸⡤⠴⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⠤⠤⠤⠤⠤⠤⠼⠧⠤⠤⠤⠤⠤⠤⠬⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢸⠇⠀⢁⠸⣆⠀⠀⠀⠀⠀⠀⣰⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠡⡈⢆⠀⠀⠀⢀⡤⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠰⣶⡄⢻⣾⣄⡤⠚⠋⠀⠈⠙⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠂⠀⠀⠛⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠦⣀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠈⡆⠈⣿⣶⣶⢴⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢀⡇⠀⢹⠻⣿⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡴⣿⠀⠀⠀⣄⠈⠂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠹⡧⣀⠡⣜⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠣⡈⠪⢕⣂⣧⣀⣀⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠂⠄⣀⠠⠊⠀⠀⣇
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠳⡄⠀⠀⢀⡔⠒⠢⢄⠀⠀⠀⠀⠀⠘⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣠⠤⢄
⠀⠀⠀⠀⠀⢻⠀⠀⣘⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠨⠳⠋⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠸⡇⠀⢹⠀⠀⠀⠀⣠⠀⠙⢦⡀⢸⠃⠀⠀⢰⡀⠀⠀⠀⠀⡀⠁⠸⡼⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣧⠀⠈⢇⠀⠀⠀⠈⢆⠀⠀⠈⡻⠀⠀⠀⢸⠀⠀⠀⠀⢀⠁⠀⠀⢃⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢦⠀⠀⠀⠀⠑⢄⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⡐⠀⠀⠀⠸⡀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠱⣄⠀⠀⠀⠀⡙⠀⠀⠀⠀⢸⠀⠀⠀⡰⢃⠀⠀⠀⠀⢣⠈⠉⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⠖⠊⠉⠓⠀⠀⠠⠁⠀⠀⠀⠀⢸⠀⠀⡰⣅⣈⠀⠀⠀⠀⠠⠦⠌⠴⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣅⠂⡀⠀⣀⠤⠤⠴⠞⠐⠂⠀⠀⠀⢸⡠⠞⠁⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠒⢌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢦⡜⡡⠂⢀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣱⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣍⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠛⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⢶⡀⠀⠀⠀⠀⢹⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡾⠁⠀⠀⢀⣠⠟⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢼⠁⠀⠀⣾⠁⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠸⣆⣀⣰⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⣤⣀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢸⠇⠀⠀⢀⡴⠶⢤⣀⣠⠞⠀⠀⠀⢠⡶⢦⡀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⣇⣀⡴⠛⠉⠉⠉⠙⣧⠀⢀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⣿⠦⠤⠴⠞⠁⠀⠀⠈⢀⣤⢦⣄⠀⠀⠛⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⡼⠃⠀⢀⡴⠋⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢳⡀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢠⡟⠁⠀⠀⠀⠈⠳⠦⢤⣤⣤⣤⠤⣤⣤⣀⠀⠀⠀⠘⣧⠀⠈⠻⠦⣤⡀⠀⠙⠦⠴⠶⠛⠳⣆⠀⠀⠀⢸⡇
⠀⠀⠘⣿⠉⠉⣇⣀⣠⣤⣤⣤⣄⡀⠀⠀⢠⡟⠀⠀⣰⠟⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢠⡏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣸⠇
⠀⠀⠀⣿⠀⠀⠈⠉⠀⠀⠀⠀⠈⠙⣷⠀⣼⠁⠀⢰⠏⠀⠀⠈⠻⠦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠈⢷⡀⢷⡀⠀⣠⠶⠚⠁⠀⣀⡤⠶⢦⡄⠀⢸⡀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠇⠀⠛⠞⠁⠀⠀⠀⠀⠙⠶⠶⠶⠃⠀⠈⣷⠀⢰⡇
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⢀⡿
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣠⡴⠚⠋⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⣀⠀⠀⠀⠀⠀⢰⡏⠙⠶⠶⢦⡄⠀⠀⢻⡾⠁
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⢧⠈⣷⠀⠀⣿⠀⠀⠀⣼⠋⠀⠀⠀⢀⣠⣤⠖⠋⠁⠀⠀⢠⠞⠉⠻⣦⠀⠀⠀⠘⣧⡀⠀⠀⢀⣿⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣾⠀⠘⢧⡀⠈⠷⣤⡴⠃⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠈⢷⡀⠀⠀⠈⠙⠛⠛⠋⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣿⠀⠀⠈⢳⣄⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢀⣴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠻⣤⣀⣤⠶⠶⣄⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠹⣦⡀⠀⠀⠙⠷⣄⡀⠀⣼⠀⠀⣼⠋⠛⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠈⠙⠳⠶⠒⠶⣌⠙⠛⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠈⠛⢦⣄⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⠈⠘⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠄⠉⠀⠁⠊⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠉⠙⠿⠿⠿⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠹⣿⣿⣿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣴⣿⡖⠚⠅⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⠟⠻⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⢤⡄⢤⡄⠀⠀⢰⡴⠀⠀⢴⢦⠶⣦⠶⡄⢀⡤⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡤⠟⢸⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⣿⠀⢠⡏⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠠⡇⠀⠀⢸⠀⠀⣿⠀⠘⣧⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠚⠓⠒⠚⠀⠙⠒⠒⠋⠀⠀⠛⠂⠀⠈⠓⠒⠒⠉


⣿⠿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡖⠂⠁⠀⠀⠀⠀⠀⠈⢙⠣⢐⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠍⢑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠂⡨⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠠⠊⣠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣷⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⣿⣿⣿⣿⣿⣿⣻⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⢿⢿⡟⢛⢛⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⢟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣖⢼⡤⠛⠉⠈⠋⠿⣿⣿⣿⣿⣿⡟⠟⢟⣿⣿⣿⡇
⠀⠀⠀⠈⠀⠠⠀⢒⠠⠀⠂⡀⠀⠀⠀⠀⠄⡀⢌⠀⣡⡪⠋⠀⠀⠀⠀⠀⠈⠫⡻⣿⠟⠋⠀⠀⠀⢼⣿⣿⠃
⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⢀⣀⣠⣠⢔⡨⣂⣰⣬⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣿⡟
⠀⠀⠀⠀⠈⢇⣰⢷⣶⣚⡉⣕⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣟⣋⣀⣀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠘⠀⠄⠀⢟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠺⣿⣧⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡓⢐⡏⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠰⣦⣄⣠⣆⠀⠀⡇⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢫⠁⣠⠦⠂⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡙⠀⠸⣯⢿⡇⢙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣘⢽⢀⢰⡆⠀⠀⠀⠀⢴⢸⡆⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣿⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣄⡅⠐⠀⠀⠀⠀⠀⢸⢫⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣥⠄⠀⠀⠀⠀⠀⢀⠉⠻⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣦⠀⠄⢀⡀⢿⠹⣆⢹⣿⡉⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣗⡀⣰⣿⣿⣿⣿⣾⣭⣁⣲⡖⠂⠀⠀⢸⣿⣿⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢨⣿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁




⡾⠓⢲⠶⠷⠶⠾⠶⡶⠶⠶⠶⡶⠷⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⣶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠒⠒⠒⠒⠒⠲⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⢙⡆⠀⠀⠀⠀⡾⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⠃⠀⢀⡴⠋⠀⠀⣀⡴⠚⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢹⡀⠀⣸⠃⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⢤⣀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠈⠓⢦⣀⣀⣀⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⡾⠀⠀⢀⡶⠛⠲⠤⠶⠃⠀⠀⠠⣞⠲⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠸⣤⡴⠋⠉⠀⠀⠈⢧⣀⣤⠶⠲⣄⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⢰⡟⠓⠚⠋⠀⠀⠀⢀⡴⠚⠲⣄⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡿⠀⠀⢀⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠳⣆⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠶⠒⠛⠁⠀⣰⠏⠀⠀⠈⠳⣄⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠹⣆⠀⠘⣆⣀⠀⠀⠸⣄⣀⣠⣤⣄⠀⠀⠀⠀⡇
⠀⠀⢸⡶⠒⢶⠀⠀⣀⣀⣀⠀⠀⠀⠀⣸⠃⠀⢠⡶⢦⡀⠈⠉⠉⠉⠉⠉⠉⠙⠶⣄⠀⠀⣿⠀⠀⠀⠉⢳⡄⠀⠈⠉⠀⠀⠈⣧⠀⠀⢀⡇
⠀⠀⠸⡇⠀⠘⠛⠋⠉⠁⠉⠙⢲⡄⢠⡏⠀⢠⡏⠀⠀⠙⢦⣀⣀⣀⣀⠀⠀⠀⠀⠈⢳⡄⢿⡀⠀⣀⡤⠞⠁⠀⣀⣤⣤⡀⠀⣿⠀⠀⢸⠇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⡇⠀⠳⠾⠁⠀⠀⠀⠘⠧⠤⠴⠃⠀⢸⡆⠀⡿
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣠⠶⠃⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⡇⣸⠃
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⣿⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⣠⠴⠋⠀⢀⣀⣀⠀⠀⠀⠀⣿⠈⠓⠒⠲⡄⠀⠈⣷⠏
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠘⡆⠹⡄⠀⢻⡀⠀⢠⡏⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⢠⡟⠁⠉⢷⡀⠀⠀⠹⣦⣀⣀⣠⠟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢰⡇⠀⠹⣆⠀⠙⠒⠋⠀⢀⡴⠋⠁⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠳⡄⠀⠀⢀⣉⠉⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣇⠀⠀⠈⠳⣄⠀⠀⠀⡞⠀⢀⡤⢤⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠋⠉⠳⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠈⠳⢤⣤⣤⣌⠓⠦⠴⠃⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠈⠓⢦⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠶⠶⠶⠖⠒⠛⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠂⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠑⢄⠀⣀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⡞⢀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠺⡀⠀⠀⠈⢀⣇⠈⠀⠀⢸⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡀⠀⠘⠢⠤⠔⠋⠈⠳⠤⠔⠃⠀⢀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⠄⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡼⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢧
⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⡎⠉⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡠⠃⠀⠀⠀⠄⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⢈⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡄⠈⠐⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢸⡇
⠀⠀⠀⢀⡤⠖⢚⣇⠀⠀⠘⠂⠠⠤⠤⠤⠤⠤⠁⠀⠀⠀⢀⡔⠒⠒⠒⠀⠂⠀⡁⠀⠀⠀⣸⡓⠲⢤⡀
⠀⠀⡰⠋⣠⠖⠉⠹⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠲⣄⠙⢆
⠀⢰⠁⢰⠃⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⠔⠒⠒⠒⠀⠐⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠘⡆⠈⡆
⠀⢨⠀⠘⢤⠀⠀⠀⠀⠙⢦⡀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⡶⠃⠀⠀⠀⠀⡤⠃⠀⡅
⢠⠋⠀⠀⠈⠧⣄⠀⠀⠀⠀⠙⠶⣅⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⣠⠼⠁⠀⠀⠙
⡏⠀⡜⢟⠢⠴⠊⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⢤⣤⣀⣀⣀⣀⣤⡤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⡻⢣
⠣⡤⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢸⠀⡇⢸⢨⡇⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠉⠉⠛⠀⣇⣸⠀⠛⠉⠉⠀⠀⠀⠉⠙⢦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠆⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⡀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠙⡄⡠⠊⠉⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⠀⢸⠁⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢻⡀⠀⠀⠀⠈⠀⣼⡀⠀⠀⠀⠀⡼⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠳⣄⣀⣀⣠⠞⠁⠳⣄⣀⣀⡴⠃⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣝⢢⡀⠑⢄⡀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⠊⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠖⠲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣆⣧⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠤⠤⡼⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠇⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣈⣷⡀⠀⠀⠀⠀⠀⣏⠀⠀⠴⢷⠤⠞⢤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣝⣛⠟⣛⡥⠚⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡴⣩⣶⣾⣷⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠢⣍⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠒⠉⢈⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠄⠀⠉⠓⠢⠤⣀⣿⣿⣿⣿⣿⡿⠛⠻⡟⠛⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠑⢜⡻⠿⢟⣿⠀⠀⠀⢀⡴⠋⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠋⠁⠀⠀⣀⠤⠦⣄⠀⠈⠻⢿⣿⣿⡃⠀⠀⠀⠀⠀⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⠋⠉⢉⣿⠒⠚⠛⠉⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢴⢡⣿⣿⡆⣇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⣿⠒⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠼⣇⠀⠀⠀⠀⢳⠝⡫⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠴⠖⠚⠉⠀⠀⠀⢀⡿
⠀⠀⠀⢀⡴⠚⠉⣀⡤⢿⡄⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣺⠇
⠀⠀⢠⠞⠀⢠⠞⠁⠀⠈⣷⡔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠚⠉⠀⣰⡟
⠀⠀⡟⠀⢠⡏⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⡀⣲⠟
⠀⠰⡇⠀⠘⣇⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣀⡤⠔⠒⠉⠉⠁⠀⠀⢀⠖⣭⣬⡳⡎⠀⠀⠀⠀⠀⠀⠀⠐⢦⡼⠋
⠀⣠⠇⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠈⠳⣖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⠿⡿⢃⠇⠀⠀⠀⠀⠀⠀⣀⡴⠋
⢰⠃⠀⢀⣀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡇⠀⠀⠀⠀⣀⣴⠞⠋
⡟⠀⠠⡟⢏⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣤⣀⣀⣀⣀⣀⣤⣤⠶⠞⠛⠉
⢧⡀⣰⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⢹⡏⢸⡇
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠦⢤⣄⣀⣿⠀⣿⢸⡇⢸⣇⣀⣤⠤⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⣿⢸⡇⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠔⠂⠉⠉⠁⠀⠢⡀⠀⠀⠀⠀⠀⡠⠐⠐⠉⠉⠁⠒⠠⠀⠀⠀⠀⠀⢀⠄⠂⠈⠉⠁⠀⠠⣀⠀⠀⠀⠀⠀⡠⠀⠀⠉⠉⠀⠀⢄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡜⠁⠀⠀⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠐⠄⡀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠲⢤⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⠀⠀⠀⢀⡀⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⢀⡠⢀⣠⠤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠀⠀⠀⠠⣢⠔⠋⠧⠀⢠⠯⠁⢀⠔⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⠀⠀⢔⡵⠊⠁⠀⠀⠀⢳⠅⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢈
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢐⡜⢇⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠉⠂⠤⠄⠀⠀⠐⠋⠀⠀⢀⡎⠀⣠⡷⠠⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠑⠀⢀⡀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠑⠀⢀⡀⢀⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠆⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠊⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡆⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠰⢂⡜⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠡⠄⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢱⠀⡀⠠⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠐⠦⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣭⣸⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠠⠀⠀⠐⠀⢀⠤⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡀⠀⡀⠀⠀⠈⠀⠄⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣧
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠠⠂⠀⠀⠁⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠐⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠈⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠠⠀⠀⠀⢀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠤⣤⣤⣤⣤⣤⡤⠴⠶⠖⠛⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⠶⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⡿⠿⠂⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢛⣲⣶⣶⠄⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠭⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣤⣤⣤⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣇
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠶⠶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⠶⢦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣏⣁⣀⣀⣀⣀⣀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢿⣭⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠈⣯⠉⠉⢩⣽⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠉⠉⠉⠉⠉⣩⣿⣟⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠳⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⢻⡆⠀⠀⠀⠀⢀⡟⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣤⠞⠁⠀⠀⣀⡴⠟⠁⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠁⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠘⢧⣀⣴⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣰⠖⠒⠲⠶⢤⣀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⢀⣸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢀⡟⠀⠀⠀⣠⠖⠶⣤⣠⡴⠋⠀⠀⠀⣴⠶⢦⡀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⣀⡴⠛⠉⠉⠉⠉⢻⡄⢀⣠⡤⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠷⠤⠴⠞⠋⠀⠀⠀⠀⣠⡴⢤⡀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢹⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⡀⠀⠀⠀⠀⠀⢀⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣀⣠⡾⠀⠀⢀⡴⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⡆⠀⠀⠀⠀⢸⡁
⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣰⠏⠀⠀⠀⠀⠈⠳⢤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠈⣷⠀⠀⠙⠦⣤⡀⠀⠈⠷⣤⡴⠶⠚⢶⡀
⣿⠟⠉⢿⠀⣀⣀⣤⣤⣄⣀⠀⠀⠀⢰⠏⠀⠀⣰⠟⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⣇
⢸⡄⠀⠈⠉⠉⠁⠀⠀⠀⠉⠳⡄⢀⡿⠀⠀⣸⠃⠀⠀⠈⠷⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠈⢳⡀⢻⡄⠀⢀⣤⠶⠛⠀⠀⣠⣤⣤⣤⠀⠀⣿⠀⠀⢀
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⡇⠀⠹⠶⠏⠀⠀⠀⠀⠘⠷⣤⣤⠾⠁⠀⢹⡆⠀⣸
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡟
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠦⣤⣤⣄⠀⠀⠘⣧⡾
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡆⠀⠘⣇⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⡴⠛⠳⣦⠀⠀⠀⠀⢷⡀⠀⠀⠀⢹⡆⠀⢀⡾⠁
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⡿⠀⢻⡄⠀⠻⣄⣀⣰⠇⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⢷⡀⠀⠀⠈⠛⠶⠶⠶⠛⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⢠⡇⠀⠀⠹⣆⠀⠈⠉⠁⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⣠⣤⣄⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⣼⠁⠀⣠⠶⠶⢤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠉⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠛⢦⣤⣤⣤⣌⠛⠶⠶⠏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠈⠳⢦⣀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠉⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⢤⣤⣤⣀⣀⣀⣠⣤⣤⡤⠴⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠂⠀⠀⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠦⡀⠀⠀⢀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⣟⠀⠆⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⢄⠀⠀⠀⠀⣰⢻⡀⠀⠀⠀⡠⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣀⠀⠀⠈⠓⠦⠶⠚⠁⠀⠙⠢⠴⠊⠀⠀⠀⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⡞⠉⠙⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣠⠖⠺⠀⠀⠇⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣀⣀⡀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠹⣄⠀⠈⠀⠂⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡴⠂⠀⣠⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⠀⠀⠀⠀⢀⡇⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡇⠀⢀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢸⡇⠀⠀⠀⣠⠞⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡴⠃⠀⠸⠀⡠⠄⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀⢘⡷⠖⠒⠋⠁⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠺⠀⢀⡰⢺⠋⠀⠂⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠞⠉⠉⢹⡷⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⣀⠠⠼⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠃
⠀⠀⠀⠀⡤⠚⠁⣠⠄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢀⡞⠁⢠⠞⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⢸⠁⠀⡏⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣠⠖⠉⠁⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⢐⣠⠀⠀⠀⠀⠠⣤⡾⠁
⠀⠀⢿⠀⠀⠧⡀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⢈⣶⠟
⠀⢠⠟⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠈⠛⢦⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⢀⡏⠀⢠⡴⣄⣀⣀⡽⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠉
⢸⡇⠀⣾⠘⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣶⠲⡖⢶⠖⣶⠛⠉⠉
⠀⠓⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⡀⠀⣿⠀⡇⢸⠀⣿⠀⢀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠉⠉⠛⠿⠀⡇⢸⠀⠿⠚⠉⠉⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠟⠺⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡬⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠃⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠂⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡤⢤⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠋⠀⠀⠙⣆⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠃⠀⠀⠀⠀⠘⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡇⠀⠀⠀⠀⠀⠀⢸⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡷⠶⠖⠒⢿⠛⠛⠓⠒⢾⠈⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡛⠉⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⡆⢻⢹⡝⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⢆⠉⢣⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣇⢸⡆⢧⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠤⣀⠀⠈⢧⠀⢧⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⠈⡇⢸⡀⠀⠀⠀⠹⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠈⢦⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⣷⠀⡇⠀⠀⠀⠀⢹⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠠⢳⠀⢰⡄⠀⢃⠀⡇⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⡄⢻⠀⡇⠀⠀⠀⠀⠀⣇⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠇⢸⠀⡇⠹⡀⠈⢆⡇⠈⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠎⠀⡜⠀⡇⠀⠇⠀⢸⡇⠀⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⡇⢸⠀⢣⡀⠀⠀⠀⠀⢸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⠇⢸⠇⠀⢸⠀⠀⠃⠀⠘⡀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡞⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠔⠋⠀⢀⡏⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⢰⡇⢸⡀⢠⠁⠀⠀⠀⠀⡜⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡸⠀⠀⠀⠀⢣⠀⠀⠀⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⢸⡇⢸⢇⡘⠀⠀⠀⠀⢠⠃⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠴⠁⠀⠀⠀⠀⠈⡆⠀⠀⠀⠇⠀⡸⠀⢀⡀⠀⠀⠀⢸⡇⢸⠈⠃⠀⠀⠀⢀⡞⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢠⠃⠀⠸⠃⠀⠀⠀⣸⠀⣿⠀⠀⠀⠀⢀⡞⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⢠⠃⠀⢰⠃⡇⠀⠀⠀⣿⠀⡏⠀⠀⠀⢀⠞⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡇⠀⠀⠛⠁⠀⢠⠃⢀⠃⠀⠀⢰⡟⢀⡇⠀⠀⢠⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡼⠀⠀⠀⠀⠀⢠⠃⠀⣨⠀⠀⠀⠎⡇⣸⠁⠀⡰⠃⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⡰⠃⠀⢠⠇⠀⠀⡘⢰⠁⡟⢀⣴⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢺⠷⠤⠤⢮⣤⡤⠴⠥⡞⢠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⡆⠀⠀⠀⠀⠀⠀⢠⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢱⠀⠀⠀⠀⠀⠀⡎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⡀⠀⠀⠀⡜⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠑⠤⠤⠞⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠣⢄⡠⠞⠑⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⣄⠀⠀⠀⢠⠚⢇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢰⠇⠄⠀⡤⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢾⠀⠀⢠⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣧⡠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠈⠉⡷⠒⠒
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢰⠃⡴⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⡇⠀⣇⠀⠀⠀⠳⣄⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⣴⠏
⠀⠠⠃⠀⠈⠀⡀⠀⠀⠈⠳⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠠⢻⠒⠒⠃⠀⠀⠀⠀⠀⠉⠑⠂⠠⣤⣀⣤⣤⠠⠖⠈⠁
⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠐⠒⠲⠤⡇⣶⡆⢸⠤⠖⠒⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠟⠧⠤⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠃⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠓⢤⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠞⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠈⠀⠀⡀⠀⠀⠀⣠⠟⣆⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⡄⠀⠀⠈⠓⠐⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⡞⠂⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠹⡆⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠊⠀⢀⡖⠒⠒⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠃⠀⠠⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⢸⡇⠀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⣀⡀⣠⠀⠂⠈⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⢀⠤⠤⢼⡏⠉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠀⠀⠈⠉⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢸⠏⠉⠁
⠀⠀⠀⠀⢀⣠⠄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⣰⠎⠁⣠⠖⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⢰⠇⠀⡼⠁⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂
⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠀⠀⠠⣈⣿⠋
⠀⠀⡽⠀⠀⠁⣀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠛⠁
⠀⡾⠁⠀⢀⠀⠘⠓⣦⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠰⠋
⢸⠇⠀⡌⠈⠓⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⡦⢀⣤⣀⣀⣀⣠⡀⠴⠶⠂⠉⠁
⠘⢇⣠⠯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠘⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⢸⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠛⠲⠶⣼⡇⢸⢸⡇⢸⡤⠶⠚⠛⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⢼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠃⠀⠠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⠢⢀⠄⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣀⠀⠀⠠⠀⡇⠠⠀⠀⣆⡂
⠀⢀⡤⢄⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠘⢄⣀⣀⠴⠳⣀⣀⡰⠁⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡠⢤
⡎⠙⡄⢈⡁⣸⠤⡀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣀⣤⣼⣶⣶⣶⣶⣧⣤⡀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⠤⣇⢈⡁⢠⠋
⠘⡆⠈⠰⠊⠁⡠⠃⠀⠀⢀⡞⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢳⡀⠀⠀⠘⢄⠈⠑⠆⠁⢰
⠀⠈⠢⡄⠀⡞⠁⠀⠀⠀⡞⢀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠋⢳⠀⠀⠀⠈⢳⠀⢠⠔⠁
⠀⠀⠀⠹⡄⠘⢄⡀⠀⢸⠋⠁⠀⢸⠀⠀⢸⣿⠿⠿⠥⠌⠤⠼⠿⠿⣿⠇⠀⠀⠀⠀⠀⠘⡇⠀⢀⡠⠃⢠⠇
⠀⠀⠀⠀⠈⠲⠤⣉⣉⣻⠀⠀⡔⠁⢀⣠⠐⠀⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣀⠤⠤⣟⣉⣉⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠐⣄⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠊⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⠤⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣱⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢧⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⡶⣤⣤⢶⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠓⠒⠒⠤⡇⣿⣿⢸⠤⠖⠒⠛⠒⠲⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡂⢀⣄⣴⣤⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡄⠀⠀⠀⠀⠀⣄⠀⣿⣿⡿⢿⣟⢩⣼⠇⡐⢴⣶⠀⣠⣼⣿⣷⣾⣿⠀⠀⠀⠀⠀⠈⠱⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠀⣀⢸⣿⡆⠀⠀⠀⠀⠣⠀⢹⡿⠀⠈⢻⣿⡏⢠⠀⣴⣏⣾⣿⣿⡇⢈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠔⡁
⠀⠀⠀⠀⠀⠀⣠⡼⠶⢀⡀⣸⡇⠀⣰⡇⢨⡿⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣀⡀⠻⣁⠀⠀⠀⣹⣛⣋⡉⠀⠈⠁⠀⠀⠀⠀⠀⠠⢲⠆⣶⡇
⠀⠀⠀⠀⢰⡖⢻⣶⣾⣼⠋⠉⠀⣸⣿⡏⣸⣳⣦⡀⣤⣀⠀⠀⠐⢢⠙⣦⣩⣿⡦⠈⠲⣾⡛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢇⢠⣾⠃⠙⠃
⠀⠀⠀⠀⣿⣱⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡎⣿⡇⠀⡀⢀⠱⠈⡏⠹⠃⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣾⡿⢿⢦⠴⡀
⠀⠀⠀⢸⣿⣿⡟⢛⣯⣤⣦⢴⣄⡀⣠⣿⣿⣿⣻⣿⠃⣿⣿⣦⠉⠙⣷⣬⣷⠠⣆⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣿⠡⠼⣿⣿⡗⠘⣿⣾⡇
⠀⠀⣠⠏⠐⣽⣿⠋⡞⠉⠙⠶⢏⣟⠙⠿⣯⡈⠻⣿⣄⠸⣿⡿⠀⠐⣿⣿⣿⣇⣾⣄⠀⢀⣼⣿⣿⣿⣿⣷⡤⠀⠈⢷⣶⣿⣿⡇⣀⣈⣟⡁
⠀⠀⣿⣄⠄⠈⡿⠀⡏⠏⠀⠀⣎⠙⣝⠲⣿⣇⠀⠀⠹⡇⠉⠁⠀⢰⣿⣿⣿⡻⠟⣿⣠⣤⣤⡬⣽⣿⣽⣿⠂⠀⢀⣾⣏⡀⣿⡇⣿⣿⣿⡇
⠀⠀⣿⣿⣤⣀⠃⠀⠷⠀⠀⠀⠋⠁⠙⠃⢸⣉⠙⠲⢤⣳⠀⠀⠰⣾⣿⣿⣿⣷⣄⢻⡻⣾⣶⣶⣶⣶⠀⠀⠀⠀⠘⠋⠁⠘⢻⡟⣿⠿⡿⠇
⠀⠀⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠸⠏⠁⠐⣲⡾⢿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣷⣝⡿⢻⣿⣫⣿⣧⣦⣄⠀⣤⣶⡆⣴⣾⣿⣆⣳⠆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⠙⠙⠿⠿⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠒⠒⠛⠛⠛⠛⠒⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠈⠉⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡽⠀⠀⠀⢀⡾⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣼⠀⠀⣰⠋⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠸⣄⣠⠟⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠙⠲⢤⡀⠀⠀⣸⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⡟⠀⠀⢠⡤⢤⣀⣠⠞⠀⠀⢠⡤⣄⠀⠙⠓⠚⠉⠀⠀⠀⠀⠀⢿⣀⡤⠖⠛⠉⠙⢦⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠷⠴⠖⠋⠀⠀⠈⣠⠴⢦⡀⠀⠙⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⣼⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡿⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠓⣆⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠶⠶⠚⠁⠀⡴⠋⠀⠈⠳⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢧⠀⠘⢦⣀⠀⠀⢻⣄⣀⣀⣤⡀⠀⠀⠀⣿
⠀⠀⢻⠖⠒⡆⠀⣀⣀⣀⡀⠀⠀⠀⡼⠁⠀⣠⠶⣄⠀⠉⠉⠉⠉⠉⠉⠓⢦⡀⠀⢸⠇⠀⠀⠉⢳⡄⠀⠉⠉⠀⠀⢹⡀⠀⠀⡟
⠀⠀⢸⡄⠀⠙⠉⠉⠁⠈⠉⠳⡄⢰⠃⠀⣸⠁⠀⠈⠳⣤⣤⣤⣀⡀⠀⠀⠀⠙⢦⠘⣆⠀⣠⡤⠞⠁⢀⣠⠤⢤⠀⢸⡇⠀⢠⡇
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⠇⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣸⠀⠈⠒⠃⠀⠀⠀⠘⠳⠶⠞⠁⠀⣷⠀⣼⠁
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⢸⡇⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⣿⢰⠇
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢿⡀⣧⠀⠈⡇⠀⠀⢠⠖⠋⠁⠀⠀⢀⣠⠴⠋⠀⢀⡤⢤⣀⠀⠀⠀⢿⠀⠉⠉⢳⡄⠀⢸⠏
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⡇⠘⣆⠀⠳⣄⣀⡟⠀⠀⣠⠶⠚⠉⠁⠀⠀⢀⡞⠀⠀⠘⢦⠀⠀⠈⠳⠤⠤⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢸⡇⠀⠈⢧⡀⠈⠁⠀⢠⠞⠁⠀⠀⠀⢀⡴⠖⠋⠀⠀⠀⠀⠈⢳⣀⣀⡤⢤⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠳⣄⠀⠀⠙⢦⣄⣀⣾⠀⢰⠋⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡈⠙⠛⠙⠲⣌⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠙⠲⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⣤⣤⣤⣤⠤⠤⠶⠒⠛⠉⠁

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⣤⣾⣿⣿⣿⣿⣿⣷⣦⣀⣀⣠⣤⣤⣀⣀⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⣿⣿⡿⠋⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣦⡦
⠀⠛⠿⢿⣦⣄⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠈⠛⣿⡿⠋⠀⠀⠀⠀⠉⠻⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡤⠴⢶⣦⠖⢈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣨⠿⠗⠛⢪⠛⠛⠳⣦⣀
⠀⠀⠀⢁⣀⣀⣭⣤⠀⠀⠀⠒⠈⠀⠀⠀⠈⠏⠿⠷⠀⠀⣀⡼⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠸⣿⡿⠋⠹⠄⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⣀⣴⡄⠀⡀⢩⣭⣽⠆
⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢀⠠⣤⣀⡄⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡈⠈⠉⠉⠉⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⡀⠀⠀⠀⣶⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⢀⣔⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢠⠚⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠐⣩⣅⡂⠀⢉
⠀⠰⢥⣿⣅⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⣷⣯⣿⣯⡛⢢⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣼⣿⣿⣿⣯⡕⣿⠀⠀⡀⠀⠀⠀⠈⠣⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡧⠀⠀⠀⠀⡀⢻⡄⢘
⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠘⢿⣶⣴⣴⣮⠀⡄⣷⣰⡇⠰
⣿⣿⣿⣿⡟⡧⢁⣧⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣭⠙⠀⠰⣯⠼⣗
⣿⣿⣿⣿⣷⣇⠛⣽⢂⠀⡦⠀⠀⠀⠀⠀⢠⡄⣧⠠⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⡃⠋
⢹⣿⣿⣿⣿⣿⣷⠬⢎⠀⠅⠀⠀⠀⠀⠀⢨⡟⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠘⠃⠀⢀
⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⡾
⠀⠺⣿⣿⣿⣿⣿⣿⢝⡁⡀⠀⠀⠀⠀⠀⣴⣠⡄⠡⣤⣄⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠃
⠀⠀⠻⣿⣿⣿⣿⣯⣿⣿⣭⢭⠔⠂⢰⣤⣹⣏⣿⡄⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣀⣤⣿⣿⣿⡿⠃
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣂⣹⣷⣿⣿⣿⣿⣿⣦⣤⡹⠯⠉⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠈⠀⠀⠀⠀⢰⣻⢿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⠿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⠀⠀⠄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠋⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣓⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠃⠀⢀⠂⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣻⣿⡳⠆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣅⣸⡇⠀⡀⠀⠀⠀⠙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠀⠀⠀⠀⡀⢷⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠻⣷⣥⣴⣦⠀⠀⣿⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣳⢀⣵⠖⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠝⠃⠐⣿⠹⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣘⢿⢃⡀⡶⠀⠀⠀⠀⠀⣶⢹⣆⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢿⡁⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣔⣽⠀⠂⠀⠀⠀⠀⠀⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠈⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣽⣦⡤⠤⣀⠀⢀⠘⣿⢷⡄⢻⣶⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣵⣿⣾⣿⣾⣟⠃⢤⡤⠤⠄⠀⠀⣼⣿⣷⣶⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠛⠥⢄⠀⠀⠀⢠⠤⠭⠵⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡉⢅⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⡠⠛⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠠⠼⠀⠈⠐⠂⠤⡀⣀⣀⠄⠀⠀⣀⡀⠔⠊⡠⠊⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⠂⣉⠉⠤⣼⠁⠀⠉⠀⠀⠐⠒⠠⢄⡀⠀⠀⠀⢀⠀⠤⠤⠀⠒⠉⠀⠀⢀⠔⢉⠽⡄
⠀⠀⠀⠀⠀⠀⡞⠁⠀⡠⠊⠁⠀⠀⠰⡄⠀⠂⠤⠀⣀⣀⣀⠀⠀⠈⠑⠒⠀⠤⣈⠁⠀⠐⠒⠂⠀⠊⣁⠔⠁⠀⠰
⠀⠀⠀⠀⠀⠀⢣⡀⠀⢣⡀⠀⠀⢀⠧⣀⠁⠐⠐⠒⠂⠠⠤⢀⡉⠒⢄⡀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⢳⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠙⠢⢄⣸⠀⠀⠈⠉⠐⠒⠢⢄⡀⠀⠈⠑⠦⣈⠒⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢾⠑⠦⣌⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡉⠒⠤⣄⡙⠬⡁⠀⠠⢈⡑⠤⣀⡀⠀⠑⠢⠤⣤⠀⠀⠈⠉⠉⠉⠁⠀⠠⠄⠒⢹⠀⠀⠈⠳⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠲⠤⣌⡁⠚⠦⢀⡀⠈⠑⠢⢌⣁⡂⠠⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠄⠀⠀⡘⠀⠀⠀⢀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠄⡀⠈⠛⢕⠒⠤⠌⣉⡑⠒⠠⠤⠍⣉⣀⡈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢠⡃⣀⡠⠴⠋⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠐⠂⢍⡑⠦⣈⠁⠐⠀⠤⠄⣀⠀⠀⠒⠲⠦⠬⠭⠬⠭⠉⢉⣉⣈⣈⣉⣀⠀⠤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠐⠢⣈⠑⠢⣁⠀⠀⠤⠀⢀⣈⣀⣀⠀⠂⠀⠙⠛⠓⠂⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣅⠀⠀⣀⠀⠉⠑⠒⠒⠒⠒⠒⠒⠤⠤⢀⣀⠉⠉⠈⡠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠈⠑⠒⢐⣒⣈⠉⠉⠉⠑⠒⠤⢄⣀⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠥⢤⣀⣀⣈⣉⣀⡤⠶⠒⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡏⢀⣀⠀⣀⡀⠀⠀⣀⠀⡀⢀⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣀⢾⢁⠏⠈⢸⢁⡼⢠⡏⢠⠁⡁⣼⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠈⠀⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠛⠋⠀⠀⠀⠀⠀⠉⠙⣻⠿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣯⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⢀⡀⠀⢀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⢿⣧⣀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣶⢦⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⢉⣉⠉⣉⣉⣉⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠽⢸⠀⠀⢸⡇⠀⢘⠀⢸⠁⢰⠃⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡀⢀⠘⣇⠀⡸⠀⢸⡀⠘⢄⡀⣀⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠆⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⡀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠙⡄⡠⠊⠉⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣀⠀⢸⠁⣀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢻⡀⠀⠀⠀⠈⠀⣾⡀⠀⠀⠀⠀⡼⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠳⣄⣀⣀⣠⠞⠁⠳⣄⣀⣀⡴⠁⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠢⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠐⠂⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠖⠲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠤⠤⡼⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣏⠀⠠⠴⢷⠤⠞⢤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⠉⢷⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠄⠁⠀⢠⠖⠒⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢠⠇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⠀⠀⠀⢀⡴⠋⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⠀⠀⠀⢀⠼⢿⣿⣿⣿⠇⠀⠀⠁⠀⠈⣿⣿⣿⣿⠏⠀⠀⣬⠀⠀⠀⠀⢀⣀⡀⣻⠒⠚⠋⠉⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⡀⠔⠛⠁⠀⠀⠈⠙⢛⠓⠒⠒⠂⠀⠀⠙⠉⠉⠀⠀⠀⠈⠐⠈⠀⣠⠞⠁⠀⠈⣿⠒⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠼⣇⠀⠀⠀⠹⣄⣀⣀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠀⢀⡿
⠀⠀⠀⢀⡴⠚⠉⣀⡤⢿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⣸⠇
⠀⠀⢠⠞⠀⢠⠞⠁⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⡟⠀⢀⡏⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠂⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠆⢀⠄⠀⠀⠀⠀⡀⣲⠟
⠀⠰⡇⠀⠘⣇⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡲⢺⠃⠀⠀⠀⠐⢦⡼⠋
⠀⣠⠇⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⢰⠃⠀⢀⣀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⡟⠀⠀⡟⢏⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢦⣤⣤⣀⣀⣀⣀⣀⣤⣤⠶⠞⠛⠉
⢧⡀⣰⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⢹⡏⢸⡇
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠦⢤⣄⣀⣿⠀⣿⢸⡇⢸⣇⣀⣤⠤⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⣿⢸⡇⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡠⠶⠄⠀⠀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠠⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⠀⠠⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠰⠄⠂⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⢀⠂⠘⠁⠀⠀⠀⠀⠳⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠶⠀⢀⠀⠀⠀⠂⠉⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⠉⠂
⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠠⡄⠀⠐⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢀⠒⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠖⠉⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠸⠀⡀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⡠⣴⣋⠁⠋⠀⠀⠀⠀⠀⢀⡄⠀⠉⠂
⡾⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠁⠀⢀⡀⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⣗⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⣐⠀⠀⠀⠀⠮⠀⠀⢀⠀⠀⠙⠁⠀⠀⠀⠀⠰⠾⡴⠀⠀⠐⢤⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠀⠈⡁⠐⠀⠀⢁⢒⡀⠀⠀⠀⠀⠀⠘⠁⠀⡀⠈⠠⠀⠒⠲⠌⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠾
⢿⡄⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢈⣣⠘⠀⠀⡠⢉⠉⠀⠀⠀⣠⠀⣤⠀⠀⠉⠀⠀⠠⢤⡀⠐⠦⠰⠮⠀⢀⠉⢳⣤⠄⠠⠒⠊⠉
⢸⣧⠆⠀⠀⠐⣀⠄⠴⠖⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡴⠀⠀⠈⠀⠰⠆⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠐⠦⢀
⠈⣿⡆⢀⣁⠈⠃⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠤⠀⠈⠀⠐⠀⠀⠀⠀⠀⡀⠀⣆⣈⣄⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢹⡷⢲⡈⢀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣴⠀⣀⠀⠀⠀⢠⠄⠀⠀⡄⣄⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⢠⠓⠀⠀⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠄
⠀⠀⢻⡻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⠀⠀⠃⠸⠗⠀⠁⠀⠀⠀⠀⡋⠒⣍⡀⠀⠈⠀⣀⠀⠀⠁⠀⠀⠀⠨
⠀⠀⠈⢷⣦⣕⠲⣆⠀⠀⠈⠢⣔⣠⣶⣠⡤⠒⠀⠆⠐⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣄⢀⡄
⠀⠀⠀⠈⢿⣮⡍⣀⠰⣄⠀⠀⠀⠈⠉⠇⠀⠴⠀⠰⠂⠀⢰⠆⠘⠃⠀⣄⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠻⣿⡯⠰⠘⠷⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠁⠀⠠⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⢶⡳⡌⠶⣈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣃⣡⠠⣆⣉⢄⡐⠀⠀⠀⠀⠀⠙⠊⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⣌⠓⠋⡶⢤⣁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣾⣩⣮⡍⢉⠞⠦⣤⣤⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⣷⣽⣓⣴⡅⣁⠈⡥⠥⣤⡀⠀⠀⠀⢀⡀⣀⡤⢀⠀⠀⣀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣶⣿⣶⣷⣶⣾⣽⣶⡾⠖⠛⠚⠈⠁
⣿⣿⡿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣺⠉⠉⠉⠉⠉⠉⠉⠉⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢰⡃⠀⠀⠀⠀⢠⠚⠉⢙⠆⠀⠀⣨⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⡇⠀⡰⠋⠀⡠⠚⠁⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠑⠴⠃⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⣠⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢸⠉⠉⠓⠦⣀⠀⢈⡇⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠒⠦⠴⠃⠀⠠⣖⢤⠈⠉⠉⠀⠀⠀⠀⠸⡤⠞⠉⠉⠙⣦⡤⠔⢤⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠀⠀⡔⠉⢳⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠧⠤⠞⠀⡰⠋⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠱⣀⠀⠀⣇⢀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⢢⣀⣠⢤⣄⡀⠀⡰⠁⢠⠖⢦⡈⠉⠉⠉⠉⠙⠢⡀⢠⡇⠀⠈⢱⠀⠀⠉⠀⠈⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⢠⠇⢀⡏⠀⠀⠑⠒⠒⠲⡄⠀⠀⠈⡆⠳⣠⠒⠉⠀⢴⣒⡲⠀⢧⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡼⢸⠀⢸⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⡰⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢧⠸⡀⠸⡀⠀⢠⠞⠉⠀⢀⣠⠴⠊⠀⡠⠤⡀⠀⠀⣇⠈⠉⢳⠀⢨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢸⠃⠳⡀⠳⠤⠋⢀⡴⠊⠉⠀⠀⣀⠜⠁⠀⠘⢆⠀⠈⠓⠒⠉⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠸⣄⠀⠙⢦⡀⠀⡞⠀⡤⠤⠤⠋⠁⠀⠀⠀⠀⠈⠓⠚⠉⢳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠓⠒⠒⢌⡉⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⡉⠓⠚⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉

⠀⠀⢻⣦⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠚⠛⠛⠛⠿⠿⠿⣧⡀⠀⠈
⠀⠀⠈⢿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠘⣧⡀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢿⡅⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠐⠀⠀⠘⠻⠋
⠀⠀⠀⠀⠸⣿⡀⠀⠀⢸⣿⣿⣿⣿⢃⣤⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠹⣿⣄⠀⡸⠛⠉⢹⣿⣾⠟⢀⡄⢰⠦⠿⠰⠂⠉⠋⢉⣿⣿⣿⣿⡿⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢹⣿⣷⣷⣶⣶⣿⣿⡏⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⣯⣀⢰⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠟⠛⣟⠛⠋⠹⣿⣯⣾⡆⢹⢿⣧⣶⡀⢀⣴⢀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡗
⠀⣀⠀⠀⠀⠀⠐⠀⠀⢻⠀⠀⢠⠘⠋⠻⠀⠐⢄⠘⢻⡇⠘⠣⡿⠃⠀⠀⠀⣾⣿⣿⠛⠿⠿⠟⠁
⠀⡽⠿⠿⢻⣿⡇⠀⠀⣸⠤⠂⠀⠓⠤⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⣿
⠀⠀⠀⠀⢸⣯⣉⠓⠂⠁⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⣰⣇
⢀⣷⣶⣿⣿⣿⣿⣇⣒⠀⢸⣿⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⣤⣀⣀⣈⣁⣤⣤⣾⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠂⠀⠀⠀⢠⣤⣤⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⣿⣿⣿⣿⣿⣿⣟⡉⠉⠹⣿⡄⠀⠰⠆⡴⢀⣀⣼⠸⣿⠀⠀⠀⢰⠛⣟⠛⠛⠉⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢰⣃⣴⡿⠿⠃⠀⢿⡇⠀⠀⢸⡀⣸⡀⠀⠀⠀⠀⠀⢀⣀
⠈⣿⡿⠿⠟⠛⠻⠿⢯⠍⠉⡉⠉⠉⠉⠉⠀⠀⠀⠀⢴⣼⣷⠀⠀⣇⠻⢬⣅⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⣿⡇⠀⠀⠉⣄⣀
⢠⣤⣶⠀⠀⢀⣴⣶⣤⣿⡶⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠈⢿⣷⠀⠀⢸⣿⠇
⢸⣿⣿⡆⢠⣾⣿⣿⣿⣿⣀⠀⢘⡇⠀⠀⢀⣀⡤⠒⢿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡄
⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣠⣼⡧⠀⠚⠉⢻⠀⠀⣾⣿⣿⠆⠀⠀⠀⠀⠀⠈⠛⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⠀⣴⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⣀⣀⣼⣿⣿⠿⠛⢻⣷⡄⠀⠀⠀⠀⠀⠀⠤⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⡀
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠻⣷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣰⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠿⠟⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠄⠀⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⢀⣀⠤⠤⠴⢦⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⢀⡠⠖⠊⠁⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⡠⠒⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡠⠒⠊⠉⡱⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡇⠀⢀⣀⣀⢀⣠⠇⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠓⠒⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠓⠦⣤⠤⠄⠦⣄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠳⡀⠈⢣⡀⢺⣉⠓⠦⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠑⢄⠀⠙⠢⢄⣀⠉⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⢄⠀⠀⠀⠀⠉⠉⠑⠲⡄⠀⠘⡆⠀⠀⠀⠀⢀⡤⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠢⢄⣀⠀⠀⠀⠀⣹⠀⡴⠀⢀⣠⠤⠚⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡈⠉⠉⠐⠊⠁⠀⠁⠉⣉⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⡆⢰⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠐⠁⡼⢰⠁⣸⠀⡍⠀⢰⠋⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠘⠒⠛⠀⠓⠃⠘⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⢿⢿⣿⣿⡿⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣷⠆⠀⢠⣤⣤⣤⣤⠌⣿⣿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢪⠻⡿⠟⠀⠀⠀⠀⠉⠛⠋⠀⣿⡏⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣶⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣧⣴⣿⣿⣮⡀⠀⠀⠀⠀⠀⢺⠏
⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣠⠏
⠀⠀⠀⢀⣾⣟⡻⠚⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⢿⣍⠉⠉⠉⢀⣠⣤⣾⣇
⠀⠀⠀⢸⣻⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⠿⠿⠷⢾⣿⣶⣴⣿⣿⢫⣿⣿⡆
⠀⠀⠀⢸⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⡀⠀⠀⠈⠳⣟⠻⠟⠁⠈⢻⣿⡇
⠀⠀⠀⡏⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠈⠒⠢⠤⠄⠋⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢀⠀⠉⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠘⠳⣤⣿⣷⣄⡀⠀⠀⢀⡇⠀⣿⣿⣿⡀⣤⣤⡀⠀⠀⠀⠀⣠⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠙⢯⣄⣽⠿⢶⢶⣿⣷⣾⣿⣿⣿⣿⣯⣵⣭⣦⣴⣶⣾⣿⣿⣿⣿⡷⠋⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢵⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡇⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡿⣿⡟⠀⠀⠠⠇

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢸⠁⠀⠀⡔⠉⠉⠉⠑⠢⢄⡈⠙⢦⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⢀⡤⠤⣀⡀⠉⠢⣄⠈⠳⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⡏⠀⠀⠀⠉⠲⢄⡈⠑⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⣄⣈⡷⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⢻⠀⠈⡄⠀⢇⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⢰⠀⠘⡄⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠄⠀⢣⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⠸⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⢧⠀⠑⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⢧⠀⠘⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⡀⠘⢆⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡄⠈⢢⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠱⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠘⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠳⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠑⢄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠳⣄⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢧⠀⠳⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣀⠀⠑⢄⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢣⠀⠱⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣄⠀⠙⢦⡴⠚⠁⠀⠀⠀⠀⠀⠀⣧⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠶⠶⠦⠟⢦⡀⠀⠑⢄⡀⠈⠲⢄⡀⠀⠀⠀⠀⠀⣸⠀⠘⡂⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠉⠢⣄⠀⠉⠑⠢⠤⠤⠔⠁⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠙⠒⠤⣀⠀⠀⠀⠀⢀⡴⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠉⠉⠁⠈⠁⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣀⣀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⠃⢀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⡘⠁⢀⣀⣀⣀⣀⠉⠻⢤⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⢿⣿⣿⡿⠿⠿⠿⣿⠿⠿⢿⣶⣄⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣼⣷⣦⠠⡀⣝⠁⠀⠠⠐⠈⠁⠀⠃⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢹⣿⣿⠇⠀⢈⠻⡆⠀⠀⠠⠂⠀⠘⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⢀⠹⠀⠁⠀⠈⠄⠀⠙⠒⢂⠀⢠⡄⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⣆⠀⠙⢄⠀⠀⠀⠀⣀⠔⣂⣀⣸⣧⠚⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠤⠉⠁⠀⠙⠁⠀⣁⡴⠞⠁⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⢀⣠⠘⡝⢣⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠉⠁⠉⠉⠉⣀⠀⠈⠇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠴⠇⠀⢋⡀⠆⠀⠀⠈⢄⣠⠂⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⢂⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢠⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⣮⠀⠀⠀⠠⠒⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⡄⠀⠀⡇⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢦⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⣄⠀⠇⠀⠀⠀⠀⢂⢀⠑⣄⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠳⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠏⠳⢼⡀⠀⠀⠀⠀⢿⠀⠘⣦⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠑⢄⠀⢸⡇⠀⠀⠀⠀⠸⠀⠀⡧⠀⠀⠀⠀⠈⢇⠀⠘⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡗⣀⡇⠀⠀⠀⠀⠀⡇⠀⢰⡆⠀⠀⠀⠀⠘⣇⠀⠸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⢰⠈⡷⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠸⡆⠀⢣⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠈⠒⠤⣀⡆⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⡄⠀⠀⠀⠀⠀⢻⡀⠸⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠾⠧⢉⠘⠋⠀⠀⠀⠀⠀⡱⠚⠂⠤⢀⠀⠀⠀⡇⠀⢼⠁⠐⠒⠠⢄⡀⠀⢷⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠊⣡⠀⠀⢀⡀⠀⠑⠄⡀⢀⣀⠀⢀⣡⠄⢀⠀⠀⠈⠒⢄⣧⡀⠠⢦⣤⣄⠀⠀⠈⠒⢄⣧⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠣⠀⣜⠀⠀⢀⠀⠒⠈⠉⠉⠢⡀⠁⠈⠠⠀⠀⠀⠀⠀⢙⠉⠂⠀⠀⠀⠀⠀⢀⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠣⣴⠊⢀⡠⠤⠄⠈⠦⡀⠀⠀⠸⡀⠀⠀⣘⠀⠀⠀⠑⠄⡀⠀⠓⠄⢀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⠄⣀⠀⠀⠀⠈⠀⣀⣀⣀⠴⠝⠉⠁⠀⠐⠀⠀⠒⠛⠒⠒⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢘⣘⣣⣄⣤⣀⡀⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⢼⣿⣿⣾⡙⢿⣿⣦⣀⠀⠀⣨⣯⣤⣤⣀⣤⠀⡾⣀⣠⣦⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣦⡉⣿⠟⠃⠘⠿⠿⣿⣿⢋⡁⠛⠙⠻⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢁⢀⡆⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣹⣷⣶⣾⣿⣿⣿⣷⣶⣤⣾⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⣴⠖⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠻⢦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠛⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠁⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢠⡿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠷⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⣧⠀⠈⣷
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢺⣅⣈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⢸⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⢸⡇
⠀⠀⠀⢸⣇⣤⡴⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⢶⣤⣤⣤⣄⣀⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠛⠁⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠲⠶⠶⠶⠶⠖⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣇⠀⠀⠀⠀⢿⣅⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠉⠉⠉⠛⠛⢶⡄⠀⠀⠀⠀⠀⢿⣄⣸⡇⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⡀⠀⠀⠀⣀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⡾⢻⡏
⠀⠀⠀⠀⠀⢿⣤⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⠶⣦⣤⣤⣀⣀⣀⡀⠈⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⢠⡿
⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠷⠶⠶⠶⢦⣤⣤⣤⣤⣤⠤⠴⠶⠾⠛⠋⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⠶⠶⠶⠛⠛⠛⠋⠉⠉⠉⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠋⣩⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⣽⠂⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⣦⣤⣤⣄⣀⣀⣈⣉⣡⣤⣤⣴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⠿⠉⠉⣹⠇⠐⠲⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⣿⡻⠋⠀⠀⠀⠁⠀⢀⣼⡿⠏⠉⠉⠀⢄⡀⠀⠀⠀⠀⠀⠀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⣾⣿⠻⢦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡔⣼⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⠅⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠁⣀⣨⠟⣰
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠨⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢠⣿⢏⣾⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡟⣡⣾⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠀⠊⠀⢀⡤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣴⢋⣼⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⢀⠀⠊⣤⡀⠤⠀⠀⢀⣤⣄⣬⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡾⣱⣿⢿⠛⠉⣽⣿⣿⡇
⠀⠀⠀⠀⢸⠇⠿⠛⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⡠⣫⣾⠟⠀⠡⣤⣾⣿⣿⡏⡇
⠀⠀⠀⠀⠘⡀⣠⣤⣶⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⢞⡿⠟⠁⠀⠀⣠⣼⡿⠛⠙⢡⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⣠⢞⣵⡿⠀⠀⠀⠀⣠⡞⠃⠀⢀⣸⣿⠃
⠀⠀⠀⠀⠀⢘⠻⢿⣛⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠋⠀⠀⣤⢾⡁⠛⠛⠃⢀⣀⣤⣾⡿⠋⠰⣢⣿⣿⡿
⠀⠀⠀⠀⠀⣸⣧⡀⢛⣟⣰⣦⣄⣀⣀⣤⣾⣿⠿⠛⣀⣰⣾⠞⣡⣿⣏⡉⠉⠈⣈⣭⡝⠉⠀⠀⢢⣿⣿⡿⠁
⠀⠀⠀⠀⠠⠀⠀⠁⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢡⢦⣯⠟⣡⣾⡿⠋⠀⠀⢠⣴⠏⠃⠀⠀⢀⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣬⣿⣾⢟⣵⣾⣿⡏⣀⣤⣴⣾⠟⠁⠀⢀⣠⣶⣾⡿⡿⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣛⣦⣰⣠⣿⣿⣿⡿⠋
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠑⠉
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠻⠿⠿⠿⠿⠿⠾⠛⠛⠉
⢀⠀⢀⡀
⠀⢦⡀⠉⠉⢁⡀⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⣀⣀⣀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⢀⡠⠔⠊⠉⠁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢀⠤⠊⠁⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢎⡁⢀⣀⠴⠋⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣇⠀⣀⠤⠤⢤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠉⠓⢦⡤⠖⠒⠲⢄⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢣⡀⠀⠳⡀⠰⡏⠑⠢⢄⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠱⣄⠀⠙⠢⣌⡉⠉⠈⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠳⣀⠀⠀⠉⠉⠉⠀⠒⠢⢄⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⣠⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠓⢄⣀⠀⠀⠀⠀⠀⠀⢳⠀⢀⠇⠀⠀⢀⣠⠔⠊⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠒⠢⠤⠀⠤⠊⠀⠏⠤⠖⠊⢉⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⠤⣄⣀⣀⡠⠤⠤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢨⠇⡼⢀⡀⢀⡀⢼⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⠉⠀⡇⢸⠀⣸⠁⡸⢀⢰⡇⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⠋⠉⠀⠘⠋⠀⠑⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⢀⡠⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠿⠋⠀⢳⡀⠀⠀⢀⡤⠞⠓⣢⣐⣊⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠈⡷⣄⢠⢋⣤⡤⠚⠁⠀⢠⢃⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠁⢹⠳⡿⠋⠀⣠⣄⡴⠃⠀⠈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢸⣤⣾⣟⠋⠀⠀⠀⠀⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⢀⡶⣄⠀⠘⣶⠀⡤⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡏⠉⠉⠉⢩⠋⠀⢀⡤⠤⢾⡏⠉⠁⠀⠀⠀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡼⣤⠖⠉⣹⠃⠀⢰⢫⠃⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡰⠁⠀⣶⠃⡀⠀⢸⢸⣖⢢⣄⢹⣧⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡇⡴⠁⠀⡟⢸⡞⡼⠈⣶⢿⣿⣤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣸⣋⣀⣤⠞⣡⢞⡞⠁⢠⡏⠀⠻⣿⣿⣷⣶⣾⣧⣄⠨⣴⣤⡀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠒⠶⠦⣤⡀⠀⠙⠒⠚⢱⢟⢁⡠⢟⡵⠋⠀⢠⠞⠀⠀⠀⠈⠛⠿⠿⡿⠿⡟⠀⠀⠀⣿⣦⠴⠚⠋
⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠘⢮⡕⠚⠁⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡉⠉⠁
⠀⠀⡞⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣰⡉⠑⠒⠋⠁⠀⠀⢀⣶⠕
⠀⠀⠳⡏⢀⡔⠀⠀⠀⡀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⢀⡠⠞⠁⠀⠀⠀⡀
⠀⠀⠀⠙⠾⢧⣀⣀⡴⠋⠉⠉⠙⠓⠻⣄⡀⠀⠀⠀⠀⠀⠀⠙⠲⡖⠏⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠻⣥⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠉⠓⠲⠶⠺⣭⣄⣀⣀⣀⣠⡤⠴⠞⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⡹⢷⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠐⢶⣼⣟⡛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠤⢤⣀⣠⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⣀⡄⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⢀⢀⠾⠋⠁⠀⠀⠘⠅⠃⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡆⢠⢣⠋⠀⠀⠀⡀⠀⠀⠀⠀⣠⠤⠤⠤⣄⠘⠲⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⣤⣀⠜⠉⠁⠑⢄⠀⠀⠀⠁⠀⠀⡠⢊⡁⠀⠂⠀⠈⠓⢄⠈⠇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠈⠆⡀⠀⢠⡂⠙⠒⠀⠀⠀⠀⢱⠈⠉⠀⠀⢀⣀⠀⢈⠀⠀⣤⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣸⠊⢸⡛⠉⠛⠄⠀⠀⠀⡄⠀⠀⢣⡘⠃⠀⠣⠜⣠⠎⠀⢤⣸⣤⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⠃⠀⠈⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠊⠁⠀⠀⣠⡇⠸⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡖⠀⠀⠀⣀⡤⠖⠂⠀⠀⠈⠀⠟⢹⡍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣄⣈⠗⠊⠰⠤⠄⡨⠁⠀⢀⠤⠤⠤⢄⠀⠀⠀⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠚⠦⢰⠀⠀⠀⣀⣠⠼⢡⡀⠀⣠⡶⣉⡀⠀⢀⠃⠀⠀⠀⠀⠉⢢⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠉⠀⠉⠀⠀⠊⠁⠀⠀⠀⢡⠻⡆⠈⠉⠀⠀⠸⡀⠀⠀⠀⠀⢀⠊⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠠⠀⠀⢀⢤⠀⠤⡀⠀⠀⢸⠀⠹⡄⠀⠀⠀⠀⠈⠒⠠⠤⠤⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢧⡀⠠⠀⠘⡆⠀⠘⠀⠀⠙⠀⠀⠀⢀⠄⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⡑⠓⠘⠂⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⣀⣠⠤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠄⠒⠚⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢣⠃⢃⢠⠭⠕⢸⠁⠁⠎⠉⢠⠀⣰⢀⠏⠙⢰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠐⠂⠀⠀⠀⠑⠊⠈⠂⠁⠈⠀⠀⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠷⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⢣⢀⠔⠊⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠈⡏⢀⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⡄⠀⠀⠀⠀⠁⢰⡇⠈⠁⠀⠀⢀⡗⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠙⣄⣀⠀⣀⡴⠋⠘⣄⡀⠀⣠⠞⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢶⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡴⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠤⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⠂⠀⠀⡤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠜⠀⠀⢸⠀⣀⠄⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⡃⠀⠂⡠⢼⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠂⠀⢀⠔⠋⠉⠑⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⠀⠀⠀⠹⡄⠈⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠔⠁⠀⠀⠀⢠⣯⣀
⠀⠀⠀⠀⢀⡴⠚⠉⢀⣿⡀⠀⠀⠀⠈⠑⠛⠓⠓⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣇⠉⠙⠲⣄
⠀⠀⠀⡴⠋⠀⡴⠞⠉⠘⣧⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⡟⠈⠙⠲⡄⠈⠳⡄
⠀⠀⣼⠁⠀⡞⠁⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡟⠀⠀⠀⠀⠙⡆⠀⢹⡄
⠀⠀⡇⠀⠰⡇⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠩⠀⠀⠀⢤⣈⣶⠏⠀⠀⠀⠀⠀⠀⡷⠀⠀⣇
⠀⠈⡇⠀⠀⠓⣦⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⢠⡖⠃⠀⠀⡇
⢀⡞⠁⠀⠀⠀⠸⠤⣄⠀⠀⠀⠀⠀⠀⠙⠷⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢀⡤⠼⠀⠀⠀⠀⠙
⣼⠀⠀⡴⡖⢤⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢧⣴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠔⡶⡄
⣇⠀⢀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⡟⢻⡟⣿⠛⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣇
⠙⠲⠞⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢸⡇⢸⡇⣿⠀⣿⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠉⠛⠳⢾⡇⢸⡇⣿⠀⣿⠶⠛⠉⠉⠉⠉⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇

⠀⠀⠀⠀⢀⠠⢂⠀⠄⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡴⠶⢄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠢⣄
⠀⠀⠀⠀⡬⣁⠂⣐⠐⡂⣆⠀⠀⠀⠀⠀⢰⣥⣀⣤⣴⡶⢶⠀⠀⠀⠀⠀⠀⠈⠿⣟⣁⠀⠸⡆
⠀⠀⠀⠀⣕⠠⢉⡐⢰⣤⠇⠀⠀⠀⠀⠀⠠⡀⠔⠍⢀⣐⡺⠀⠀⠀⠀⠀⠀⡀⠀⠺⣿⣿⣦⠇
⠀⠀⠀⠀⠀⠚⠿⠿⠛⠉⡀⠀⠀⠀⠀⠀⠀⠑⠺⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠒⠾⠿⠟⠋
⠀⠀⠀⠀⠉⠛⠃⠚⠋⠀⠎⠀⠀⠀⠀⠀⠀⠛⠚⠓⠃⠰⠆⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠘⠛
⠀⠀⠀⠀⠀⢀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣔⣾⡊⣟⣻⣏⡀⠀⠀⠀⠀⠀⢠⢛⠓⠉⠉⠍⢦⠀⠀⠀⠀⠀⠀⣴⣷⣶⣷⣾⣿⣿⣿⠇
⠀⠀⠀⠀⣿⣖⢺⡿⢿⣫⡇⠀⠀⠀⠀⠀⢪⠄⠢⣐⣮⣽⣾⠀⠀⠀⠀⢀⣴⣟⣳⣶⣶⣾⣿⡏
⠀⠀⠀⠀⠘⠿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠿⠃⠀⠀⠀⠀⠻⠟⠛⢿⣿⣶⡾⠟⠁
⠀⠀⠀⠀⠠⠤⠤⠠⠠⠖⠀⠀⠀⠀⠀⠀⠠⠤⠶⠦⠴⠄⣶⠀⠀⠀⠀⠀⠀⠶⠶⠢⠴⠦⢰⡀

⠀⠀⠀⠀⣠⠾⠽⠬⣗⣦⡀⠀⠀⠀⠀⠀⢀⢤⣉⣛⣻⠷⠄⠀⠀⠀⠀⠀⠀⣠⠞⡿⠉⣽⣦⡀
⠀⠀⠀⣀⣋⣉⣉⣭⣉⣀⣯⠟⠀⠀⠀⠀⣈⣶⣶⣶⣒⣚⣛⠀⠀⠀⠀⠀⢠⡯⠀⠶⠀⠛⣿⣧
⠀⠀⠚⠿⠿⣿⢞⣻⣟⡿⠃⠀⠀⠀⠀⠀⠐⢄⣶⣶⣶⣿⠟⠀⠀⠀⠀⠀⠀⢻⣠⣄⣸⣶⣿⠃
⠀⠀⠀⠀⣀⣈⣉⣋⣉⢠⡀⠀⠀⠀⠀⠀⣀⣈⣉⣛⣉⠁⣤⠀⠀⠀⠀⠀⠀⢀⣉⣙⣛⣉⣤
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⡴⠀⠀⣖⠀⠢⣰⣴⣶⠶⣶⠶⣶⠆⠰⠶⠶⠶⠶⠶⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠹⠦⠼⠛⠷⠟⠩⠿⠿⠄⠿⠠⠾⠇⠰⠶⠶⠶⠆⠶⠖

⠀⠀⢀⠴⢤
⠀⠀⠈⢤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣠⢶⣫⠵⠚⠋⠉⢻⡄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠉⠙⠷⣄⠀⠀⠀⣼⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣼⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⢷⡀⠀⠙⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠃⠀⠙⢦⡀⠀⢀⣤⠞⢁⡴⠛⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡏⠀⠀⠀⣀⣽⠟⢋⣠⣾⣯⣤⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠻⠶⠶⠛⣉⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠋⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠋⠛⢿⣯⠁⢸⣾⣷⡶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁⠀⠀⠀⠀⢄⣀⠹⢻⣶⡿⣿⣿⣃⣿⣿⣿⣯⣶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⣤⣤⣀⡘⠛⠛⢛⣽⣤⢾⡿⢿⣿⣿⣿⣿⣿⡻⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣦⡤⢄⠀⠀⣉⡿⠓⠡⣄⣄⠂⣮⠉⣻⣿⠗⣺⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡠⣾⣿⡷⠚⡀⠸⢯⢗⣧⠀⠿⠿⠋⠀⠀⠈⠪⠀⠛⡻⠀⠾⢿⣿⡿⠯⣷⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⠳⣹⡟⣛⢈⠦⢄⠄⣠⣞⢿⠀⠀⠀⡀⠀⠀⡀⠠⠄⠄⠀⠀⠈⠉⠉⠑⢊⣿⣧⣄⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⣯⣽⢼⣿⣾⣿⢼⣷⣻⣾⡓⣬⠖⠶⢀⡠⣤⠆⡴⠠⠀⠁⠀⠐⠏⠁⠈⢾⡊⣿⣿⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠟⣸⠟⠋⢱⣿⣿⣿⡿⢿⣿⣿⢿⠋⠉⠂⠀⢺⡿⠃⠍⠁⠀⠀⠀⣠⠐⠉⠀⠀⠙⠿⢿⣿⣿⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠽⠢⣰⣿⣿⣿⣧⣝⣿⣿⣷⠇⢀⢄⠀⠀⠀⠰⠀⠀⠠⠀⠀⠆⠀⠀⢀⠀⠰⣿⠁⠐⠩⠹⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⡀⠈⣉⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣶⣄⢀⣤⡾⠂⠀⢠⡄⠒⠂⠀⠀⠻⠀⠁⢰⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡧⣼⢲⣽⣶⡿⠸⣿⣿⣟⣿⣯⣼⣇⣠⢤⣆⠉⣻⣷⣿⡟⢡⠋⢴⠇⠀⠀⠀⠀⠐⠂⠀⠀⠘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⠈⣿⡐⠦⣍⢶⣭⣿⣿⣿⣯⣿⣶⣿⣿⣿⣿⣿⣆⠂⣈⣶⡄⠀⠀⠀⢠⣲⠄⠀⠠⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⠀⠇⡿⡸⣯⣶⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⡶⡂⠀⡀⢽⣿⣧⣀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠉⣹⡿⣟⣻⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⡝⣬⡛⠉⢡⠀⠀⠀⠈⢹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠉⠀⠀⠬⢃⡺⠿⡿⣿⡏⠰⠂⢀⠀⠀⠈⢿⣿⠏⠁⡴⠀⡤⠐⣀⠀⠀⠘⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠤⠄⠸⠽⢇⠶⡿⣧⠀⠀⠀⠀⢠⣀⣿⣟⡀⣀⠀⠀⠀⡀⠀⣰⣼⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⠀⠀⠁⠙⡳⠶⠤⡄⢴⣿⣿⣿⣿⣦⡿⣦⣴⣴⣿⣿⣧⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢭⣿⡄⠦⢿⣷⣾⣂⣰⡾⣿⣿⡍⣿⣟⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠪⢯⣍⡹⡛⣶⣿⣛⣵⣶⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠒⠟⠀⠴⠅⠀⠀⠀⠤⣀⣤⣠⣴⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠋⠈⠀⠀⠀⠀⠂⠀⠤⠄⢤⣤⣤⠄⠤⣠⣤⣤⣶⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣑⣛⣛⣛⣯⣨⣽⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡷⠐⠂⠤⠤⠤⢤⢠⠄⡠⡠⣜⢿⡱⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽⡟⠻⡷⠵⣦⡨⠤⣤⣤⣉⠁⠃⠘⠀⣐⣦⠶⣽⢿⡽⢿⣷⡟⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣾⣾⣖⣰⣄⣴⣵⣄⣦⣶⣤⣱⣟⣑⣤⣬⣹⣤⣆⡶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠚⠿⠠⣭⠯⢬⡙⣋⡑⢋⡓⠻⠝⠛⠷⠶⣷⠚⠻⠻⡙⢿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠶⠆⠐⠀⠀⠀⣌⠄⠠⠑⠀⠈⠀⠈⣸⣦⣼⠦⠀⣐⠚⢳⢿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠄⠀⠂⠘⠁⠡⡀⠀⠀⠀⠈⢯⡉⣀⣾⡃⠀⠐⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⣄⢀⠠⠁⠀⠀⠀⠁⠀⠃⠐⠀⠀⠀⠈⠡⢀⠄⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢥⡁⣀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⠀⢠⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠦⢅⢨⣡⡥⠀⡐⣃⣀⣀⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠲⢦⣄⠀⠀⠀⠀⠀⠀⢀⡞⣹⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡌⠳⢧⡉⠓⢦⡀⠀⠀⢀⡼⢿⣿⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⠸⡀⠀⠀⢈⡢⣿⣿⣄⣠⠾⠀⠀⠀⠀⢰⣸⠃
⠀⠀⠀⠀⠀⠀⡠⠤⠶⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠃⠀⠙⣄⠀⠹⢿⣿⡜⡿⠁⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣄⠀⣤⡄⠈⠱⠤⠤⠞⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣭⡷⣏⡁⠀⠀⠶⣦⣀⣀⣀⣀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢠⣾⣿⣿⣷⣿⣿⣿⡿⠟⠋⠁⠀⣨⣿⠓⠲⣦⡈⠻⣿⣿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠀⢀⣀⣠⣴⣾⡿⠃⢀⣀⢽⡽⡄⠙⣇⠀⠈⠂⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠟⠋⠀⣾⣑⣯⣭⣗⣷⠰⡜⢿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠳⣝⣿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡴⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠦⠤⠴⠖⠚⠉⠘⠦⡤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⢀⣠⢴⠎⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠉⠀⠀⢠⣼⠀⠀⠀⠘⡆⠀⢀⣸⡴⠗⠒⠂⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⢀⠤⡷⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⢸⠇⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢳⡀
⠀⠀⠀⠀⠀⠀⢰⠇⢀⡀⠀⣼⠀⠀⠀⠀⣰⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⢦⣄⡀⠀⠀⠲⣄⠀⢹⣬⠇
⠀⠀⠀⠀⠀⢀⡟⠀⢻⠀⠈⡇⠀⠀⠀⢠⠏⠀⠉⠙⠲⢶⠤⣤⣤⣄⣠⣤⠤⢤⡾⠶⠤⠶⢶⡞⠋⠁⠀⠀⠀⠀⠀⠀⣏⠀⠀⢠⡟⣀⡾⠋
⠀⠀⠀⠀⢀⡞⠀⠀⠸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⢳⣀⡞⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⣄⡀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣠⠏⠀⠀⠀⢠⠏
⠀⠀⠀⣇⠀⠀⢀⡜⠀⣠⠈⣩⠏⠁⠀⠀⠀⠀⢀⣔⠋⠓⠺⠉⠙⣤⠞⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠿⣭⣤⠾⠵⠞⠁⠀⠀⠀⠀⠀⡞⠉⠀⠑⠀⠀⠲⠋⠀⠀⠀⠀⢀⡴⢧⠀⣠⠶⠛⠛⢿⡉⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⣷⠋⠀⠀⠀⣸⠃⢀⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠤⠴⠖⠛⢹⡀⠀⠐⢩⠃⠀⠀⠀⠀⠁⠠⢊⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠃⠘⠂⠧⠀⠈⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠳⢦⣀⡠⠖⠛⠛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⡀⠈⢧⡴⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠀⠙⡆⠘⣠⣤⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠋⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿⡼⠁⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠇⠀⣀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⡿⠁⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠧⠶⠚⠁⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⢸⣿⡆⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢷⣀⣴⠖⠓⠶⣤⣀⣿⣿⠏⠀⠀⠀⢀⣿⣿⠃⢠⡏
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⣽⠁⢀⣀⠀⠀⠙⢯⠁⠀⠀⠀⠀⡼⡿⠃⣠⠏
⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⢿⠀⠀⠻⡙⢦⠀⠈⠇⠴⠒⠛⠛⠛⠓⣲⣥⣀⣀⣀
⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠸⣇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠭⠽⠶⢤⣀⣤⠖⠛⠉⠉⢛
⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣀⣠⠞
⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠘⢦⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢹⡄
⠀⠀⣿⣿⣿⣿⣇⣤⣶⢿⣶⣶⡏⠀⠈⡗⠀⠈⣇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⢀⣿⣿⣿⣿⡟⣽⢁⡏⠱⠋⠀⠀⢀⡇⠀⠀⢹⡀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⡶⠛⣿⣿⣿⣿⠀⣿⠘⣇⠀⠀⠀⠀⢸⡇⠀⠀⠈⣧⠀⠀⠀⠈⡏⠛⠓⢶⢶⠖⠒⠉⠓⠒⠚⠛⠉
⠀⠀⢻⣿⣿⣿⠀⢹⡀⢻⡄⠀⠀⠀⢸⡃⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢸⠸⡆
⠀⠀⠀⠉⠁⢻⡀⠀⢧⡀⢻⡄⠀⠀⢸⡇⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⢀⡼⢰⡇
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠳⡀⠹⣆⠀⠀⢻⣄⠀⠀⠀⠀⠀⠉⠓⠲⠖⠋⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⢦⡈⠳⣤⣠⠟⡷⣦⣀⡀⠀⠉⣓⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠉⠳⠤⣤⠴⢃⡏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⣀⣼⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⠲⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠓⠶⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⣤⣤⣭⠽⠷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⢯⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠶⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣋⣀⣀⠀⠀⠀⠉⠉⠉⠉⠙⢛⣛⣛⡛⠛⠛⠛⠛⠛⠉⠉⠉⠉⢠⡶⠶⠶⣦⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡉⠉⠉⠉⠉⠉⠛⠶⣤⣄⣀⣀⣀⣙⣷⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣋⣁⣤⡤⠤⠶⢾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠙⠛⠓⠒⠲⠶⠶⠶⠶⠦⣤⣤⡈⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣭⡭⠭⠭⠥⠶⠶⠶⠖⠚⠛⠉⠉⠁⠙⢦
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢴⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢀⣾⣤⣤⣀⣀⣨⠷⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢷⡀
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠀⠀⠀⠀⢠⠞⠉⠀⠀⢀⡴⢷
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠻⠤⣤⡤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠋⠀⠀⠀⢀⡿⠀⠀⠀⠀⢈⣧⠘⣇
⠀⠀⠀⡟⠛⠓⠒⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠖⠲⠒⢒⣒⣺⡯⠴⠶⠚⠛⠉⠉⠁⠀⢻
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣙⡷⠀⠀⠀⠀⠘⠧⢤⣤⣤⣀⣀⣀⡀⠀⠀⠀⢀⣠⣴⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⣛⣶⠄⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠒⠒⠲⠶⠦⣤⡀⠀⠸⡇
⠀⠀⢸⡇⠉⠉⠉⢉⡉⠁⠀⠀⠉⠉⠉⠙⢳⡆⠀⠀⠘⠳⠶⠾⠃⠀⠀⠀⠀⠶⣯⣍⣀⣀⣀⣀⣠⣤⡤⠤⠶⠶⠶⠶⠶⠤⢤⣀⠀⠀⠿⣤⣠⡇
⠀⠀⢸⡏⠉⠉⣉⣩⣭⡭⠷⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣧⡼⠋⠉⠀⠀⠀⣀⣀⠀⠀⠀⠙⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⠀⠀⠿⡽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠒⠒⣿
⠀⠀⠀⢹⡖⠶⠒⠚⠛⠉⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣤⡤⠴⠶⠶⠶⢤⣀⠀⠀⡴⠶⠶⢦⠀⠀⢠⡏
⠀⠀⠀⠀⢷⠀⠰⣾⣷⠆⠀⠀⠀⠙⠓⠒⠒⠒⠛⠛⠋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⠓⠚⠋⠀⢀⡾
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢶⣋⣙⡷⠀⠀⢀⣀⡴⠞⠁⠀⠀⢰⡖⠒⠒⠲⠶⠦⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠖⡾⠁
⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⠤⠤⠴⠶⠶⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠘⠧⣤⣤⣤⣤⡤⠴⠶⠒⠛⠛⠛⠋⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡽⠇⢀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⠷⠶⠖⠚⠓⢶⡄⠀⢀⣠⠴⠶⠒⠛⠋⠉⠀⠀⠀⠘⠛⠋⠀⠀⠀⠿⣭⣭⠿⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⡴⠶⠚⠋⠀⠀⢸⡅⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⢀⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣄⠀⠀⠀⢀⣸⠇⠀⠀⠘⠦⠤⠤⠴⠛⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣠⡴⠚⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣍⣁⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⠞⠃⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⠶⠦⠴⠶⠶⠶⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣃⡀⠀⠀⣀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣄⣑⠂⡄⢳⣰⡋⣿⣷⡀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢡⡿⠿⢿⠟⣡⠓⠰⠻⣧⣾⣷⣽⡀⠀⠀⠀⠀⡜⡆⠀⡀⣰⣄⣀⠆⢳⡀⡁⣄⣀⡤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠙⠰⣲⠀⠆⠀⢀⠰⡸⡷⠾⡝⠛⠋⠀⠄⠀⢪⠸⡀⠸⢟⣻⣿⠁⢀⢧⠆⢸⢿⣇⡽⠆⢠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠒⡏⢠⡠⢤⣴⡏⢀⠀⠀⡃⢀⡀⠀⠀⠀⡺⠀⠈⡄⢀⣿⡿⠂⢨⠈⢳⡈⣮⢷⡀⠄⢠
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠀⣇⠹⠋⠶⠁⢀⡞⠀⠀⠁⢀⠆⡠⠂⠀⠹⡀⠀⢧⡉⠛⠙⢁⣿⡀⠸⣧⠿⢿⣷⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠋⠀⠘⠤⠚⠂⡎⢳⠏⠀⠀⠀⠠⡤⠃⠀⠀⠀⠀⢓⡶⠊⡀⢠⣮⡟⣀⠀⢙⠏⡛⠛⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣞⣽⠂⠆⢰⢰⠫⠃⠀⠀⠀⣰⣁⡀⠀⠀⠀⠀⠈⠬⠑⣌⢽⠃⠀⠀⠘⣾⣀⢷⣴⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠅⠴⢀⡜⣷⡄⠀⠀⠰⠁⠉⢢⡄⠀⠀⠃⠀⠀⠀⢸⡾⣀⠀⠀⣀⣹⣿⣋⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠴⡋⢰⠃⠀⠀⠀⠒⢀⣄⠈⢈⠓⢄⣡⠀⠀⢠⣿⠁⢸⠓⢼⣻⢷⣾⣻⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢀⡿⠀⠀⠀⢀⡜⠉⠈⠔⠁⠀⠘⠊⣠⣰⣿⠇⠀⠘⠂⠜⠚⠾⣿⡼⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠋⠑⣴⠚⠉⢃⡀⠂⢀⡞⠀⠀⠀⠀⠀⠔⡔⡈⠀⠡⠺⡄⠀⠀⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠉⠀⠀⣁⡠⠀⡜⠀⢠⣄⠀⠀⠘⢈⡟⡀⢍⣉⠟⣎⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠈⠃⠀⣉⠁⡀⠀⠀⠀⠀⠀⢸⣇⠀⣝⣚⣅⣟⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠁⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⣠⣴⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢩⡿⠛⠋⠁⣸⡟⢹⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠓⠀⠀⠀⠉⠁⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠻⢿⣿⣿⣿⣾⣶⣀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⡿⠛⠛⠉⠁⠈⣿⣿⣿⣿⠃⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠘⠿⠟⠉⠿⠇⠀⠀⠀⠿⠛⠿⠃⠈⠛⣛⣠⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⠀⠀⠀⠀⠲⣤⣠⣼⣷⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⡀⠀⣰⠞⠛⠉⠀⣿⣿⡏
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⡟⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠛⠛⠛⠉⣿⣿⠛⠉⠉⠛⠃⠘⠃⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢦⠀⠀⠀⠀⠘⠓⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣷⣤⣤⣠⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⢫⡣⡻⣄⢝⣳⡝⢿⠿⣿⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⢀⠈⣢⣑⢝⡎⠈⢑⣢⣤⣶⣾⣿⡷⢯⣿⠟⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠳⣤⡒⠁⠀⠈⠀⠑⠨⠑⠒⣒⢂⠾⠥⠖⠶⠟⢛⠪⠓⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡻⡚⠳⢌⠪⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠉⠀⠀⠀⡀⠀⡂⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣼⠙⢷⣌⠢⣤⡁⡀⠤⣀⠉⣖⡒⠤⠤⠤⠀⠄⠀⠀⠀⠀⠀⢀⠀⢀⣩⠤⠚⣆
⠀⠀⠀⠀⠀⢰⡇⠀⠈⢻⡿⡄⠁⣈⠀⢀⡀⠒⠬⠍⠀⠀⠀⠀⠈⢛⣻⡿⠿⠛⣦⠤⢾⢛⠋⢹⡄
⠀⠀⠀⠀⠀⣸⠀⠗⠀⠀⠑⠉⢲⣄⡉⠒⠈⠉⠉⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠒⠂⠐⠒⠊⣉⠈⡇
⠀⠀⠀⠀⠀⢹⡄⠂⠀⠀⠀⠀⠀⠌⠉⠒⠒⠦⠭⠭⠉⠀⠀⠤⠈⣐⡒⠒⠒⠊⠠⠄⢒⠛⠉⠅⣷
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠁⠀⠀⠰⠖⠀⡟
⠀⠀⠀⠀⠀⠈⣿⢨⡉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⣀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣈⠷⢭⣒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠢⠄⠀⢀⣀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣎⠳⢶⣬⡛⢟⣈⠋⠿⠻⣷⣶⣦⣆⣤⠄⡠⢤⡤⣤⠤⠖⢒⡛⠩⢭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠌⠛⠶⣾⣯⣀⡢⠦⠵⠶⠐⠐⣒⣀⣈⣉⠉⠩⠝⣲⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⣅⠀⠈⠍⠉⠛⠛⠒⠶⠶⠶⠿⠿⠒⢒⠻⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣤⣶⣤⣤⣤⣤⣭⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠁⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡗⠀⢀⠀⢀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠿⣇⣀⢰⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣤⣤⣤⣠⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠈⢉⡙⠛⣛⣋⣉⣁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡽⢸⠁⠀⢸⡇⠀⢸⠈⢸⠁⢱⠋⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡀⢀⡘⡇⠀⣸⠀⢸⡀⠸⣄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠀⠀⠈⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠸⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡄⠀⠀⣤⣶⣴⣶⣦⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠛⠻⢿⠿⠟
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⣴⣿⣷⣽⣿⣿⣆⠀⠀⠀⢰⣶⣤⡀⠀⠠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⠀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠗⠹⢿⣿⣟⣿⣿⠆⠀⠀⢤⠻⣿⣿⣦⡀⠄⠀⠀⣿⣿⣿⡟⠛⠿⣿⡇⠀⢸⣿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠳⣄⡘⠛⢉⣬⠟⠀⠀⠀⠀⠁⠈⠻⣿⡿⠃⠀⠀⠹⣿⣿⣷⣀⣶⡿⠃⠀⠀⠻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁

⣿⡏⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠒⠽⢋⣁⠒⠋⣾⣿⣿⣾⡵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠁⣤⠆⠈⠁⢺⣿⣿⣿⣧⠨⠁⠈⣀⣀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⡟⢀⡞⠀⠀⠀⢴⣿⡏⣁⣿⣿⣦⣀⡟⠙⠁⠀⠀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⢧⣿⣾⢡⠏⠀⠀⣀⠴⠨⣿⢶⣿⣿⡛⣿⠯⠠⠀⠀⢶⠂⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⡰⣿⣿⠇⢸⣿⡿⠈⠀⠂⠀⠈⠀⣀⣴⣞⣿⡿⣿⠁⠐⣦⠰⣤⢢⣄⠀⠀⠑⠠⢯
⠀⠀⠀⠀⠀⣀⠜⣹⠀⢨⡿⠁⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⡖⠦⣄⣴⠿⣿⣿⣿⣿⣶⣶⣶⡄⠀⠀⢢
⠀⠀⠀⠀⠀⡏⢀⠋⠀⢸⡻⠀⠀⠀⠀⠀⠀⠀⠠⢝⣿⣿⣿⠓⠋⠁⢠⣿⣿⣿⣿⣾⣿⣿⢻⡇⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⡆⠐⠀⠀⠀⠹⣤⡄⣜⣿⣿⣿⠖⠀⢀⠀⣭⣿⣿⣿⣿⣶⣿⣿⣶⣦⠀⢀⠸
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⡿⠟⢃⢀⣴⣾⣿⣿⣻⣿⣾⣿⣿⣿⣿⣿⡿⡸⢠⠇⠁
⠀⠀⠀⢸⢀⠁⠘⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⡌⠁⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⡉⠸
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠷⠀⠈⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢱⡄⣹⡆⢤⠈⠐⠀⠀⠀⢲⠀⠁⠀⡘⠺⠁⢒⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠔
⠀⠀⠀⠀⠀⢿⣷⡘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣠⣄⡔⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⢐⣦⠀⠀⠉⢨⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣲⡄⠀⢀⡀⠛⠁⢠⣖⠰⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⠀⢧⡄⠀⠻⣷⡐⠊⠛⣻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣷⣧⡰⣄⠩⠀⣹⣿⣿⣿⣿⣿⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠷⠼⠿⠿⠟⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⢿⡯⣮⣾⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⢟⣬⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠤⣾⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡺⣻⣿⣿⣿⣿⣵⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡨⣛⠽⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣟⠵⣺⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣾⣿⣿⣿⣿⣷⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣽⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣭⣁⡠⢄⣀⠂⡀⠀⠀⠀⣀⣠⣴⣞⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣓⣿⣭⣩⣧⣿⣷⣼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⠿⠟⡋⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠀⠨⠔⠂⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠋⠉⠁⠀⠀⣀⣤⣄⡀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⣷⡀⠉⠉⠑⢄⠀⠀⠈⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⡈⠓⠀⠀⢀⣵⠾⠛⢿⣀⡀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⣀⠜⠀⣀⣤⣶⣿⠟⠁⠀⢀⣴⠾⠛⠛⠛⢷⣦⡾⠋⠀⠀⠀⠀⡀⠈⢢⡀⠀⠘⢿⣷⣄
⠀⠀⠀⣰⣿⡿⠁⠀⣠⡶⠶⣤⣄⡛⢻⡿⠟⠛⠷⣦⠀⣼⡇⢀⣶⡛⣶⠀⣿⡇⠀⠀⠀⠀⠀⠐⢄⣀⡇⠀⠀⣠⠽⣿⣦
⠀⠀⣼⣿⡟⠀⠀⠀⠉⠀⠀⠀⠈⢹⣿⢡⣾⣱⡆⢹⣇⣿⣇⠀⠻⠿⠟⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣧
⠀⢰⣿⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣿⡄⠙⠋⣠⡾⠋⠀⠻⢷⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠹⣿⣇
⠀⣿⣿⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠘⡄⠀⠈⢦⠀⠀⢻⣿
⢸⣿⡇⠀⢠⠤⢯⡀⢀⡤⠂⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⢀⣀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠜⠉⢳⡄⠀⠙⠒⢻⣿
⣾⣿⠃⢀⠃⠀⠀⣿⠋⠀⠀⠀⠀⠀⢰⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⡇⠀⠀⠀⠀⣿
⣿⣿⠀⠸⡄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢩⠁⠀⠀⢿⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠐⢉⣸⡀⠀⢰⡇⠀⠀⡠⢄⣿
⣿⣿⠀⠀⠉⢻⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢸⡇⠀⠈⣷⠀⠀⠀⠀⠀⡠⠞⠉⠀⢳⠴⠋⠀⠀⡸⠀⢈⣿
⣿⣿⡆⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠓⠴⠋⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⡇⠀⢸⣿
⢸⣿⣧⠀⣀⡀⠀⠀⠀⠀⠀⢠⠒⢄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢦⣤⣿⣿
⠈⣿⣿⣾⠀⠙⣆⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⣸⣿⡿
⠀⠸⣿⣿⡀⠀⠘⡆⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠹⣿⣷⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢶⣶⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠹⣿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠲⢄⠬⢄⡀⢀⡀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣦⡀⠀⠀⠘⠀⡀⣘⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣭⡙⢿⣿⣿⣿⣿⡟⣡⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⡑⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣦⣭⣍⣛⣛⠛⠿⠿⠿⠿⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣝⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠿⣣⡀
⠀⠀⠀⠀⠀⠀⢀⡘⢿⣿⣷⣍⣛⣛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣶⣶⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣦⣍⣛⡛⠋⠿⣿⣿⣿⣷⣶⣶⣭⣙⡻⠿⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⠮⠻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⡛⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⢃⣶⣶⣶⣤⡉⢛⡻⠿⠿⠿⠆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣮⡙⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣩⣭⣭⣭⣭⣭⣙⣛⣛⣛⣛⣛⣥⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⢛⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣶⣦⡙⢿⣿⣿⣿⣿⣧⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣶⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢶⣬⣭⣉⣉⣭⣴⣿⣿⣿⣿⣿⢿⣿⣧⣝⣛⣛⣛⣛⠩⠿⣿⣷⣶⣭⣙⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠇⣽⣿⣿⣿⣿⣿⣷⣶⣬⣍⣛⠻⠿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣶⣷⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢛⣥⣶⣲⡿⢻⣿⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡟⣹⣿⢿⣿⡿⣿⣾⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠿⠟⣸⣿⣿⡟⣼⢿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠐⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⠲⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⡭⠟⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠶⠦⠤⠤⣤⡀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣒⡛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠿⢦
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠬⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣈⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⡾⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⣀⣀⣤⡤⠤⠶⠶⠶⢶⡆⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡏⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠶⠶⠶⠶⠶⠶⢾⡇
⠀⠀⢸⡇⠀⠻⠶⠶⠶⠶⠒⠶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣩⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠒⠒⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⢴⡏
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣃⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠿⠀⢀⡾
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⢓⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢒⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⣒⣶⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠒⠒⠒⠛⠛⠛⠉⠉⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠒⠒⠶⠶⢶⣶⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠴⠶⠶⠶⠒⠛⠋⠉