Big love Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠀⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠉⠉⠉⠛⠶⣤⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣆
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣿⡦
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠿⢿⣿⣯⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣄⠤⣽⣶⣿⢿⡯⠂
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢚⣻⣤⢿⣿⣻⣽⣁
⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣾⣣⣐⣿⡍⣻⣿⣿⡟⠂
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⡷⣾⢿⣿⣏⣽⠷⣟⣠⣚⠃
⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⢓⣾⣭⠳⡤⣟⡛⢿⣤⣛⠻⣿
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣼⠣⣎⣫⣦⣵⢇⢸⠙⣼⠁⣠⠶⣥
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢬⠿⡈⠳⣛⣳⣖⣡⣮⢎⡴⢉⡞⣉⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⣰⣳⢤⢠⣉⣳⠦⢽⣄⠹⣑⡚⠒⠒⣋⣔⣉⣴⠞⢧⡭⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠭⣿⣾⡿⠿⠶⣶⡿⢀⡿⣖⣺⢏⣉⣀⠴⠊⠛⠓⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡙⠻⢿⠗⢾⣿⡇⣈⣀⡤⣔⣮⡉⢃⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣧⡴⠋⠷⠋⠉⠓⠋⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢶⣿⡿⣟⢿⡿⣶⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⡶⢨⡽⣿⣿⡧⢸⡇⢿⣧⣇⠿⣿⣿⣿⣯⣿⣷⢤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⡿⣿⣿⣿⢶⣧⣤⣷⣾⣿⣿⣾⣷⣶⡄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣴⣾⣿⣿⣟⣇⣯⣔⣿⣿⣧⣆⣏⣿⣿⣿⣻⣛⣟⣿⣿⣻⣓⣀
⠀⠀⢀⣤⣪⣯⣩⣿⣿⣿⣿⣷⣾⣿⣿⣇⣿⣿⣿⡟⣛⢿⢿⣟⣟⠻⣿⣿⣧⡄⠀⠈⢹⣏⠉⢹⣿⣿⣿⣿⠈⣿⠀⠛⣿⢻⡟⢻⠛⣿⣿⠛⠛⠻⢻⠛⠃
⠀⢀⣼⣟⣛⣟⡟⣿⣿⣛⣻⣿⣿⣿⢿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⡿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣾⣿⣿⣷⣿⣿⣿⣶⣿⣾⣿⣷⣶⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡘⣯⡺⣺⣎⣾⡀⣿⣿⣷⣸⡰⢇⣇⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣯⣿⣤
⢠⣤⣴⣶⣾⣿⣠⣦⣦⣴⣼⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡛⢛⡟⠛⢻⣿⣿⣿⣿⣏⣇⣉⣉⣁⣿⣩⢈⢙⣿⣿⣿⣻⣛⣻⣿⡟⢛⢛
⠈⠉⠉⢹⣿⡏⠙⠉⠉⢹⣿⣸⣿⣇⣥⣀⣵⣀⣧⣀⣿⣿⡆⣼⣄⣨⣄⣸⣿⣿⣧⣶⣾⣧⣦⣼⡏⣽⣿⢹⡏⣭⣯⠉⣽⢡⣽⣿⡍⢩⣯⡍⡏⡏⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣿⡏⡿⠻⡟⣿⢟⣿⣿⣻⡟⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣻⠷⣿⢿⣶⠶⣶⡿⠶⡿⠶⣾⣿⣷⣾⣷⣶⣷⣶⣿⣿⣿⣤⣮
⣿⣧⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣾⣿⣾⣽⣯⣿⣿⣼⣭⣾⣧⣿⣤⣿⣿⣼⣿⣥⣿⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣧⣭⣬⣽⣏⣠⣌⣿⣿⣇⢈⣀⢸⡏⡀⡁⣿⣿⣿⣏⢸⡇⢸⡇⢾⣇⢙⡇⢨⣿⡇⢩⡁⣿⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣻⣉⣿⣿⣿⣿⡿⣿
⠀⣏⣿⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⡟⠟⡿⣿⣿⠻⡟⠻⠿⣿⣿⢻⣿⡏⠟⡟⠛⢻⣿⡟⠛⠛⠛⢻⣿⣟⣿⢿⣿⢿⣿⣿⠿⡿⣿⣿⣹⣿⣇⣟
⠀⠸⡇⢸⣭⠉⣏⠩⣿⣇⢉⡏⢹⡉⢹⣿⣿⣿⣿⣿⣿⣷⣿⡿⣼⡿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣶⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠹⣿⣿⡿⠿⡿⠿⣿⣿⢿⡿⣿⣿⣿⣻⣛⢛⣿⠛⡛⣿⣧⣿⣤⣭⣥⣬⣤⣽⡅⣨⣥⣭⣭⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⣿⣛⣻⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⢿⣿⣿⣿⣻⣿⣿⢰⣿⡏⢿⢠⡼⢟⣿⣽⣽⣿⡏⡩⡃⣤⠟⣉⠉
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⠶⣶⣷⣾⣾⣾⣿⣷⣶⣷⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡙⣿⣟⠛⠛⠛⠻⠛⢿⡟⠛⠛⠻⠛⢻⣿⡏⢹⣿⣿⢙⣿⡟⣿⡟⣏⣿⣻⡏⣯⣿⣿⣟⠿⣿⢻⣟⢿⢻⣏⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣋⠋⢻⣶⣿⣧⣽⣼⣬⣼⣵⣾⣇⣁⣽⣼⣷⣾⣿⣗⣸⣿⣿⣘⣿⣧⣛⣷⣿⣆⣿⣃⣷⣻⣿⣿⣂⣿⣘⣿⣾⣜⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣯⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⠿⣿⣿⡏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣧⣿⣴⣶⣶⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⡿⢿⣶⣶⣿⣿⣴⣶⣿⣿⣽⣿⣯⣭⣽⣿⣏⣭⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣯⣽⣿⣿⣿⣧⣿⣯⣿⣿⣯⣼⣿⣿⢹⣿⡇⢿⡡⠆⣷⢡⡇⢼⣿⣿⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡍⠉⣿⣿⣿⣿⡟⣿⡿⠿⠻⠿⠿⠿⢿⡿⠿⠿⠿⠟⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⣿⣿⣿⣧⣿⣧⣵⣤⣌⣤⣯⣼⣇⠑⣱⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⠙⣿⣿⠉⠉⠉⠙⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⡟⣿⣿⣿⡿⠟⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠚⠛⠛⠛⠛⠓⠒⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣀⣤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⢤⣤⣤⣤⣤⡤⠤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡂⠀⠀⢤⣄⠀⠂⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⣰⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠐⠀⠀⠐⠢⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠁⠀⠀⢐⠖⠉⠙⠂⠀⡀⢀⠈⠁⠒⢤⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣟⠀⠀⠀⡞⠀⠀⠀⡀⠒⠀⠈⠂⠀⠀⠼⠀⠀⠀⠸⡇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⢈⠁⠀⢀⢻⠀⠀⠂⢿⡀⠂⠀⠀⠀⠀⠀⢀⠄⠀⢰⠣⠀⠀⠀⣗⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠎⠁⢐⡀⢸⣇⠀⠀⠚⢧⠀⡀⠀⠀⠀⠀⠀⠀⢐⡎⠀⠀⠀⠄⡿⠂⠰⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠤⡇⠀⠀⠀⠈⠻⢄⣸⠀⠀⠀⢘⡴⠋⠁⠀⠀⠀⢠⡧⠂⣀⡇
⠀⠀⠀⠀⠀⠀⡀⠈⠱⠲⢤⣀⡏⠀⠀⠀⠀⠀⠎⠙⠳⣤⣷⢋⠄⠀⠀⡌⠀⠁⢸⣇⡴⠋⠴⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⡇⠀⠐⠀⠀⣄⣠⡶⠛⡁⠈⠛⠳⣶⣮⡀⡀⠀⣿⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠌⣷⠀⠈⣁⣴⠟⠓⠆⠂⠐⠀⠀⠀⢀⠨⡟⢷⣦⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢹⣆⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠹⣿⣿⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠠⠄⣐⠀⠀⠀⠤⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⢸⣿⡿⠀⠀⣰⠇⠁
⠀⠀⠀⠀⠀⠀⠼⣇⠠⡜⢃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣟⠃⠀⢀
⠀⠀⠀⠀⠀⢀⠤⠉⠛⠛⠚⢶⣄⣿⣿⠈⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⣾⡿⢿⣿⡀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠐⣿⣿⠀⣿⣷⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡀⠀⠀⠀⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠈⣿⡟⠁⢿⣏⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⡇⠀⠘⣿⡆⠀⠀⠀⢸⣿⣿⡇
⣀⣀⣀⣀⣀⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣷⣤⣤⣼⣷⣷⣤⣴⣿⣧⣤⣤⣤⣾⣿⣿⣿⣤⣤⣤⣤⣤⣀⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣿⣷⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⣿⠿⣿⡿⠉⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠿⠀⢹⡇⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣭⣭⣭⣿⣿⣷⣶⣤⡀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠈⠀⢠⣿⡿⠁⠀⠀⢀⣠⣤⣶⣶⣖⣛⣛⣉⡀
⠀⠀⠀⠀⢀⡀⣠⣀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢿⣿⣷⡀⠀⠀⣰⣿⣿⠃⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣇⠀⢠⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⣠⡤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢸⠀⢇⠀⣸⠃⠀⡤⢤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢳⠀⠀⣠⣤⢦
⠀⠀⠀⠀⠀⣠⠞⢳⠹⣄⣀⡼⢀⣀⡽⠷⢄⠀⣇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⠛⠳⡌⠲⢋⡤⡀⠹⣄⡼⠁
⠀⠀⠀⠀⠀⠹⣄⡼⢀⣤⡉⢰⡃⠈⠀⠀⠀⢳⠈⣛⣁⡀⢠⠤⠒⡄⠀⠀⠀⠀⢸⠀⠀⠀⢰⠋⠛⠾⠀⡿
⠀⠀⠀⠀⠀⠀⢠⡶⠏⠀⢹⠈⣧⠀⠀⠀⣰⠋⠑⠃⠀⢳⠘⠤⠴⠃⠀⠀⠀⠀⢘⡶⠦⡀⠘⣦⡀⠀⢰⠟⢦⡏⢹⡄
⠀⠀⠀⠀⠀⣠⠞⢧⠀⠀⢸⠀⠈⢧⣄⡀⠹⡄⠀⠀⠀⣼⠀⣰⠚⠳⠛⡆⡾⠛⠞⠀⠀⣷⡼⠁⠉⠛⢻⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠘⢯⣀⣠⠟⣒⠃⣴⠒⠏⠀⣷⠴⠛⠦⣄⣠⠇⠀⢻⠀⠀⢠⠇⢻⡀⠀⠀⢠⢇⡴⠴⠉⢳⠀⣷⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠈⡤⠞⠉⡇⠙⣆⠀⢀⡇⠀⢀⠀⢀⡴⠦⢄⡈⠣⡤⠞⠀⠀⠱⢤⡤⠎⠘⡆⠀⣶⠉⠳⠇⠈⢹
⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⡇⠀⠈⠓⠋⢀⡞⠉⠉⠋⠀⠀⢠⠗⠦⣄⣰⠋⠙⣆⢠⠤⠞⣦⠘⠦⠽⡄⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⡠⠖⠒⢦⡀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁⠀⠀⢸⢸⡄⢀⡟⡤⣤⢦⡙⢦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠀⢀⠴⢧⣰⠛⢦⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⡀⣙⣋⠈⣇⠀⢀⡇⢠⠴⠒⣦
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠙⢦⣤⠴⠋⢧⠀⠀⠀⢀⡼⠁⠙⠃⢸⡆⠈⢓⡋⠀⢿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣸⣆⠀⠀⠀⠀⢠⠏⠀⢠⠖⢲⡓⠦⣶⡋⠹⣄⠀⠀⡼⠉⠻⢋⣹⢦⣈⡽⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⣁⣈⠳⣄⣀⣠⠏⣼⠉⠉⠀⢨⡇⢰⡇⠈⢹⠜⠶⠞⣇⠀⠀⠘⣆⡀⠉⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣧⠀⣀⡴⢲⡹⣄⠀⢀⡞⠀⠈⢧⣠⠞⡴⠲⠚⢺⠙⠒⠚⣁⣙⠲⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡿⢸⠉⠁⠀⣇⠈⠛⢹⠋⠉⠛⠹⡄⢸⡇⠀⠀⡼⣴⠛⠾⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡘⣆⠀⣠⠏⢳⣤⠞⢱⠀⡴⠛⠳⠏⠱⠤⡞⠁⢿⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠘⡎⠹⡇⠀⠀⠁⢀⠾⠤⢷⡀⠀⠀⣠⠴⣇⢀⣈⢦⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠇⠀⠙⢆⣀⡴⢫⠴⡤⠶⡝⠦⣴⡇⠀⠈⠋⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠶⠳⡄⣿⠀⢀⣤⣇⡠⢦⢳⣀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠇⠘⢤⡽⣄⠈⠁⢸⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠷⠶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣠⣴⠶⡶⠿⢷⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠑⠒⡂⠈⠑⠆⠁⡤⠩⠿⣦⡀⢀⣴⣟⠏⠀⠀⠈⠑⠁⠀⠀⢈⠟⢷⣄
⠀⠀⠀⠀⠀⣴⠟⠀⠉⠢⠂⠁⢀⠀⡀⠀⠑⢄⠄⠚⣿⣾⠃⢀⣀⣀⡀⠀⢀⠤⢄⠀⠀⠒⢬⠻⣦
⠀⠀⠀⠀⣸⡿⠤⠀⠀⠀⠀⠐⣅⠈⢀⠅⠀⠀⠀⠀⠘⠟⠀⠧⡀⠀⠖⠀⠈⠒⠈⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣿⡡⠐⢀⠔⠤⠂⡄⠀⠙⠀⠀⢠⠒⠄⢢⠀⠀⠀⠀⠈⠀⠀⠀⠀⡎⠑⠈⡢⠀⠀⠠⠺⣿
⠀⠀⠀⠀⣿⡁⠀⠀⠒⢤⠐⠁⠀⠀⠀⠀⠈⠢⡤⠊⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠰⠊⠀⠀⠀⠘⢢⣿
⠀⠀⠀⠀⠸⣿⠒⢑⠀⠀⠀⠀⡔⠑⠊⢢⠀⠀⠀⠀⠘⢄⠀⡠⠃⠐⢍⠱⠀⠀⠀⠀⡔⠢⠒⢀⣼⠇
⠀⠀⠀⠀⠀⠹⣷⣀⡠⣀⢄⠀⠈⠰⠆⠁⠀⡔⠔⡄⠀⠀⠉⠀⠀⠀⠀⢀⢀⡀⡀⠀⠑⠢⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡠⠃⠀⠀⡠⣀⠄⡀⠉⠀⢠⠒⠔⢢⠀⠀⠀⠣⡀⢀⠜⢠⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⡘⠦⣀⠠⠃⠀⠀⠈⠢⡄⠊⠀⠀⠀⠀⢈⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⡀⢄⠀⠀⠀⠀⢎⣢⣵⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿
⣼⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⣤⣤⣤⣤⣤⡴⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣳⣶⣶⣶⣶⣶⣶⣶⣶⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⢾⢿⡷⢳⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⠿⠷⢶⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣼⣿⣿⣾⣮⣿⣿⣿⣿⣯⣿⣶⣄⠀⠀⣠⣼⣿⣿⣉⣽⣯⣉⣻⣿⣟⣟⣿⣗⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣷⣿⣷⣴⣿⣯⣽⣻⣯⣹⣿⣦⣀⣹⣏⣹⣿⣿⣍⣇⣉⣩⣭⣏⣿⣍⣩⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠿⣿⠾⠿⢾⣟⣿⣹⣹⣍⣯⣹⣿⣩⣻⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠰⠿⢿⡿⠶⠿⣾⢻⡟⠛⢛⢛⠛⣿⠛⡛⠛⢻⣿⣏⣩⣏⣹⢿⡿⣿⠷⠶⡞⣴⡼⢿⠿⠿⣿⣯⣭⣇
⠀⠀⠀⠀⠀⠀⣾⠿⢿⣿⣺⣗⣛⣛⣟⣿⣿⣛⣛⣿⡿⡿⠿⣿⠿⠿⡟⣿⠿⢾⢷⠶⣾⢷⠷⡿⣷⣿⣶⣷⣿⣿⣭⣧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣛⣿⣟⣻⣿⡟⠛⣿⠛⢻⣿⡟⣛⢻⢻⡛⡛⢻⡟⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⡿⢿⢽⠿⣿⠿⠿⡿⢿⣿⣿⣙⣛⣿⢛⣛⣻⣿⣻⣏⣛⣛⣿⣟⣛⣛⣿⣿⣛⣛⣿⣛⣻⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣾⡶⢷⢿⡷⠷⣷⣾⣿⢿⣿⠿⣿⣿⣙⣻⣯⣿⢻⣻⣿⣿⣿⣿⣽⣿⣿⣯⣽⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣶⣽⣿⣴⣿⣇⣿⣇⣄⣏⣽⣺⣿⣈⣄⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢻⠛⠛⠛⠛⡟⠛⢛⠛⣷⢹⣿⣻⣿⣿⢿⢿⡟⣿⣶⡛⡟⣿⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣟⣿⣿⣿⣟⣷⣾⣿⣿⣿⣾⣿⣷⣿⣾⣿⣾⣷⣿⣿⣷⣿⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢿⣷⠾⣿⣿⡷⠶⣾⡷⠶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣟⣿⣿⣭⣽⣿⣯⣿⡟⣿⠻⡯⣟⣻⢻⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣉⣿⣿⣟⣿⠛⠛⠛⣛⡟⠉⠛⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣻⣟⣛⣛⣿⣿⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⡏⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠒⠛⠛⠋⠉⠉⠉⠛⠛⠓⠒⠶⠦⣤⣀⡀
⠀⠀⠀⠀⣠⠖⠋⣠⡴⠞⠋⠁⠀⠀⠀⢀⣀⣀⣀⣀⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠚⢁⡴⠋⠁⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⣄⡀⠀⠀⠀⠉⠳⣄
⠀⡴⢃⡴⠋⠀⢀⣠⠖⠋⠁⠀⠀⢀⣀⣠⡤⠴⠶⠶⠒⠒⠒⠒⠶⠶⠤⢤⣄⣀⠀⠉⠓⠦⣄⠀⠀⠈⢷⡀
⠸⢡⡟⠀⢀⡰⠋⠁⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠈⠳⣄⠀⠀⢳⡄
⢀⡟⠀⣠⠟⠀⠀⣠⠖⠋⠀⠀⠀⢀⣠⡤⠤⠶⠶⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢧⠀⠀⢻⡀
⣼⠀⢰⠏⠀⢀⡼⠃⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢤⣌⡉⠓⠦⣄⠀⠀⠀⠙⣆⠀⠈⣧⠀⠈⡇
⡿⢀⡟⠀⢀⡞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⠈⠙⣦⠀⠀⢹⡄⠀⢸⡄⠀⡇
⡇⢸⠇⠀⣼⠁⠀⣸⣧⠴⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⢈⡇⠀⢸⡇⢠⡇
⣷⡼⠛⠛⠻⣤⡾⠋⠀⠰⡆⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⢾⣧⠖⣛⠓⢾⡁⢰
⣿⠀⠀⠀⠀⠉⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⣸⠀⣸⠃⢰
⠘⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣩⠞⠁⠐⠋
⠀⠀⠙⠳⣄⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡴⠚⢁⡴⠋
⣀⣀⣀⣀⣈⣳⣏⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣚⣉⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⣀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡃⣣⣀⠀⠈⠒⠠⠐⠈⡆⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠤⣵⣊⣀⠀⠀⠑⠄⠀⠀⠀⢀⠇⠸⣿⡆⢠⣶⣄⣾⡞⣿⢼⣟⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢘⣧⡀⠈⠷⠀⠙⡆⠀⢸⠤⣤⠴⠋⠀⠀⣿⡇⠘⠧⠃⠘⠟⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡔⠁⢸⠹⡀⠘⠲⠚⣉⡒⠚⠃⠀⠑⡄⠀⠀⢿⣿⣤⣦⠀⠄⢦⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠀⠘⠀⠈⢆⠐⣟⣻⣻⠀⠀⠀⠀⢸⠀⠀⢈⡉⢉⡀⢀⣠⠀⣠⣤⢰⡆⣴⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠊⠀⠀⠀⡰⠀⠀⢸⠀⠈⠙⠉⠀⠰⡂⠆⡐⠀⠀⢸⣷⠌⣷⠛⠻⠎⡉⢻⡄⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⠦⣤⣤⡤⠖⠧⠀⢀⣾⠀⠀⠀⡀⢀⠀⠔⢉⣀⠀⠀⠈⠛⠀⠉⠀⠀⠀⠘⠺⠇
⠀⠀⠀⠀⠀⠀⠀⢘⠙⠤⠩⠔⠃⠀⠀⢀⡿⠐⠁⠀⡷⠀⠀⠀⠀⢂⡌⢀⠀⠈⠁⢢⡀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⢀⣠⠊⠀⠀⢀⡴⠠⠀⠀⠀⣀⣈⣁⠀⠇⢆⠂⠁⢈⠆⠀⠠⠤⠄⢀⠨⢐⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠉⠉⡩⢕⡒⢿⣆⡈⠁⠊⠀⠀⠰⡀⢀⡀⠀⠹⠀⠀⠈⠉⠀⠀⠀⠀⠞⠐⠢⠄⣐⢕⣖⣄⠀⢄
⠀⠀⠀⠀⠈⠀⣀⠀⢘⠈⠁⢁⠔⢉⠄⢀⡍⠀⠀⠀⠀⠀⠀⢀⠼⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡛⠋⠀⠀⠰
⠀⠀⠀⠀⠀⡎⠹⣃⠌⠉⠋⠁⡰⠋⠔⠁⡇⠀⠀⠀⠠⢀⣠⠶⠀⠈⢢⠃⠀⠀⠀⠀⢀⠔⠀⠀⠐⢀⠀⠀⠀⠀⠀⠈⠐⡀⡂⡀
⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⡤⠊⠀⡨⠉⢁⡅⠀⢀⢔⠁⠁⠸⠀⠑⠔⠁⢀⠅⠉⠑⢤⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠠⢀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢉⣡⡂⣀⡔⠁⡔⠉⠀⣰⠁⢈⠆⠀⠀⠀⠀⠀⠀⠈⠐⢆⡀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠁⠀⠀⠏⠀⠀⢀⠃⠁⠆⠀⠀⠰⠤⠄⣀⠀⠀⢀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⡈⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠑⠢⣀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡷⠄⠠⠤⢶⠀⠀⠐⡤⠤⠔⠛⡀⠀⡀⠀⠀⠀⠉⠂⠀⠈⢄⠀⠀⠀⢀⣠⠀⠘⠃⠴⢤⠦⡸⠋
⠀⠀⠀⠀⠀⠢⡀⠀⢀⠀⢀⠀⠣⠄⣀⣀⠠⠇⠒⠈⠑⠠⡤⠄⠃⠀⠁⠀⠀⠀⠀⠃⠀⡀⠀⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⡆⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠡⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⡁⠂⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠤⠠⠂⠀⠀⠈⠈⠁⠀⠀⠀⡀⠀⠤⠂⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈
⠀⠀⣀⠀⢀⠀⡀
⣿⣯⢩⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢉⣉⣉⣉⣉⣉⣉⣉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠛⢉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡈⠙⢿⣿⣿⣿⣿⣷⡀⢂
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⡄⢣
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢻⣿⣿⣿⣷⡀⢧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⡿⠛⠋⣁⣠⣤⣤⣤⣤⣤⣄⣀⡀⠉⠛⠻⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣇⠸⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢰⣿⣿⣿⠟⠉⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠙⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⠀⣷
⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⣿⣿⣿⠋⢠⣾⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⡄⠸⣿⣿⣿⡇⢸⡀
⠀⠀⠀⠀⢸⣿⣿⣿⠃⢸⣿⣿⠃⢠⣿⣿⣿⡟⠁⢀⣠⣴⣾⣿⣿⣿⣶⣦⣄⠈⠻⣿⣿⣿⣿⡄⢻⣿⣿⡇⠀⢿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠀⣾⣿⡏⢀⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣷⠈⣿⣿⣿⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⢸⣿⣿⡏⠀⣿⣿⠁⢸⣿⣿⡿⠀⣼⣿⣿⡿⠋⠀⠀⠄⠀⠈⠻⣿⣿⣿⡀⠸⣿⣿⣿⡆⢸⣿⣿⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⠀⣾⣿⣿⠇⢰⣿⣿⡟⠀⢰⣿⣿⣶⣿⣿⡄⢻⣿⣿⡇⠀⣿⣿⣿⡇⠘⣿⣿⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⠀⣿⣿⣿⠀⣼⣿⣿⠃⡀⠸⣿⣿⣿⣿⡿⠁⢸⣿⣿⣧⠀⣿⣿⣿⠃⠀⣿⣿⠀⢸⣿⣿⠀⣾⠁
⠀⠀⠀⠀⠈⠿⠿⠿⠀⣉⣉⡀⠙⠛⠛⠀⠻⠿⠿⠀⣿⠀⠈⠻⠿⠋⢀⡆⠘⠿⠿⠏⠀⠉⠉⠉⢀⡀⠛⠉⡀⠘⠛⠋⢠⡿
⠀⠀⠀⠀⠀⠠⠴⠶⠾⠛⠉⠀⠈⠉⠉⠁⠐⠒⠒⠚⠛⠀⠀⠀⠠⠾⠛⠁⠀⠒⠖⠒⠚⠋⠉⠉⠉⠁⠈⠉⠉⠀⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠐⠂⠈⠉⠀⠉⠉⠉⠀⠐⠒⠒⠂⠠⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⠴⠒⠒⢤⡀⠀⡠⠖⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢄⡀⠀⡠⠖⠒⠒⠦⡀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡌⠀⢐⠄⠀⠈⠎⠀⠤⡊⠔⢀⠈⡆⠀⠀⠀⠀⠠⠁⠀⡂⠄⡀⠑⣜⠀⢔⠡⢊⠀⢹⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠰⡀⠀⠄⢊⠔⡀⠔⣊⠔⡊⠅⢠⠁⠀⠀⠀⠀⢸⠀⠨⢔⠩⢂⠀⡠⢐⠡⢂⠕⠀⠐⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠄⢊⠔⡪⢔⠨⠐⡠⠁⠀⠀⠀⠀⠀⠀⢆⠀⠠⢊⠄⡨⢐⠡⢊⠅⠊⡠⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠩⢂⠥⣢⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠁⡨⢂⠥⢊⠕⢊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠡⠊⢔⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠃⠌
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⡀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⡀⠆⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡠⠀⠠⠁⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣁⣈⠀⠂⠐⠂⠀⠁⠀⠊⠐⠁⠊⠀⢁⣠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠐⠊⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⡀⠄⠀⡀⠄⠂⢀⠠⠀⣀⠤⠀⡀⠄⢀⠠⠀⣀⠄⠀⢀⠄⠀⡀⠄⢂⠠⠒⡀⠄⢂⠀⠀⡀⠄⢈⠡⠀⡁⠀⡠⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠡⠔⠊⢁⠄⠒⢈⠤⠒⣁⠠⠒⡁⠄⠊⡁⠔⢊⡠⠔⢈⠠⠐⡉⠔⢈⠠⠐⢉⠤⠂⡡⠐⠉⠠⠂⠁⠔⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠂⠁⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠙⠳⢦⡀⠀⠀⣀⡤⠶⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣦⠞⠁⠀⠀⠀⢀⣀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣰⡟⢻⣿⣶⣿⣿⣿⣷⠀⢸⣤⡞⣹⣿⣾⣿⣿⣷⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⠇⢀⡿⣿⣾⣿⣿⣿⣿⣿⠁⠀⢸⠇⠀⠀⠀⢀⡀
⠀⢀⣤⣤⣤⡀⠀⠀⢳⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠋⠀⣸⠃⠈⠻⢿⣿⡿⠛⠁⠀⢀⡾⠀⠀⠀⠛⠉⡟⠷⡄
⠀⠋⠉⣧⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠙⠻⠛⠉⠀⢀⣴⠋⠳⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⣀⣀⣤⠶⠋⠁⠀⠀⠈⠙⠓⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⡤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡛⠛⠿⠟⠛⠛⡉⠩⠍⣛⡻⠯⢝⣫⢿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠪⠓⠢⢍⠉⠉⠩⠤⠔⠂⠀⠥⢒⠈⠁⠈⠁⠊⠙⠙⢚⢗⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡬⠷⡶⠖⡷⠿⢷⠥⠀⠈⠰⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠒⠀⠉⠛⠻⠿⣿⡿⢿⣿⡟⠛
⠀⠀⠀⠀⠈⢿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣫⣤⣦⣶⣶⣼⣿⣧⣦⣶⣡⡂⠘⠙⠰⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠁⢀
⠀⠀⠀⠀⠀⡩⠳⠚⠐⠻⢻⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣶⣤⣈⠙⠻⢶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⣤⣶⣖⢠⣠⡖⢶⣦⡀⠉⠛⠻⢿⣿⣿⣷⣀⣉⠛⢿⣴⣤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠿⠿⣿⣿⣿⣿⠅⠀⠀⠀⠀⢸⣿⢯⢙⣼⣤⣀⣽⣿⡇⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣦⡉⠻⢿⣮⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠋⢀⣾⠟⠛⡩⣷⠀⠀⠀⠀⠀⠀⠻⠉⠛⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⡆⠄⠙⠻⣯⣢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠈⠻⠒⠒⠚⠻⠧⣀⠀⠀⠀⠀⠀⠑⢿⣶⣶⣾⠟⠀⠀⠀⠀⠀⠀⠁⠡⠈⠀⠁⠞⠉⠻⠿⡷⠂⠀⠀⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣲⠦⣄⣈⠃⠶⡠⠄⢀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣦⣤⣀⣁⣀⣀⢀⡀⣀⣀⣀⣠⣤⡴⡾⢯⠣⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠉⢉⡛⠛⠛⠛⠿⠛⠋⠙⠙⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⢣⠀⠀⠀⠌⠙⠃⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⢒⠀⠀⡀⠀⠐⠉⢃
⠀⠀⠀⢠⣀⡀⠀⡄⠓⠂⠋⠈⠈⠈⠈⠒⠒⠄⡀⠀⢀⡤⡀⠀⠀⢀⠱⠆⠊⠁⠁⠁⠉⠑⠐⠢⢀⠀⢀⡀⡀
⠀⠀⠀⡄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⢀⠂⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢀⢀
⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⡀⠠⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠠⠦
⠱⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠
⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠔⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⢻⡆⠀⠀⠀⠀⠀⠀⢰⠟⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⡀
⠀⠡⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⡀⠃⠀⠀⠀⠀⠀⠀⠸⣄⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⠄⠄⠆
⠀⠀⠀⠠⢥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀
⠀⠀⠠⠁⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠀⡐
⠀⠀⠀⠈⠈⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠁
⠀⠀⠀⠀⠀⠠⠈⠙⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠉⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠃⠈⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠑⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠑⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠨⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠓⡀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠄⠁⡱⠦⢤⠀⣀⠤⠶⠌⠐⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠌⠉⠐⢀⠠⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣶⣶⣶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣄⣤⢀⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣧⣤⣄⣀⡀
⠀⠀⠔⣒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠉⠲⡆⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣧⢿⣿⢹⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡒⣳⡖⣄
⢠⣀⡀⠀⠀⠋⣁⣹⣥⡁⢻⡟⠁⠏⠉⠧⠾⠐⠿⣿⠿⠹⠟⠀⠈⠉⠸⠿⣿⢣⣶⣿⢻⣿⠋⠿⣼⣿⣭⣽⣿⡿⢿⢶⣅⡦⣰⣷⣄
⠀⠻⣿⣿⣿⣶⣶⣭⣿⣛⣛⠿⠷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠡⣴⣿⣾⠿⣿⡟⠹⠄⡠⣎⡴⢡⡤⠉⠀⠛⠷
⠀⠀⠙⢿⣟⡿⣿⣿⣿⣿⣿⣿⣾⣦⣶⠖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠛⠚⠟⠷⠸⢷⢾⣧⠾⠂
⠀⠀⠀⠈⠛⠋⠿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣦⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⢶⡶⣦⣶⣶⣶⣶⣾⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣶⣶⣀⣠⡀⢀⢀⠀⠀⢀⣀⣀⣄⣮⣳⣞⣿⣿⣦⣳⣼⡿⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⡿⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣽⣿⢿⣿⣿⠟⢛⣩⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢉⣥⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⠿⢿⣿⡻⠿⠟⠛⠈⢋⡽⠚⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡰⠁⠀⠀⠈⡇⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠃⠀⠀⠀⠀⠸⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡰⠁⠹⡄⠀⠀⠀⠀⠈⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠚⠀⠀⡰⠁⠀⠀⠱⡀⠀⠀⠀⠀⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢠⠃⢰⠛⢄⠀⠱⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠳⡀⢳⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡆⢇⠀⠀⠀⢳⠀⡇⣀⣀⣀⣸⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡤⠒⠉⠉⠙⠒⢤⡀⢈⡷⠋⠉⠀⠈⠉⠓⣌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜⠀⡴⢦⠀⠀⠀⠀⠙⠞⠀⠀⠀⠠⣎⣳⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠉⠁⠀⡀⢠⣀⣇⣰⣁⡆⡄⠀⠈⠀⠀⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢄⠀⠀⠀⢸⡊⠉⣞⣳⠀⢉⡽⠀⠀⢀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠳⣄⠀⠀⠏⡲⢪⠥⡖⠻⠈⢀⡴⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡑⢦⡀⠀⠈⠀⠀⠀⡠⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡓⢄⡀⣠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⣠⠤⠒⠂⠉⠉⠉⠈⠉⠉⠑⠒⠤⢄⡀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡤⠊⠁⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠑⠦⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⠔⠁⠀⠀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠈⠳⡄⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡰⠁⠀⢀⠔⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠈⢢⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡜⠀⠀⡰⠋⠀⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠈⢦⠀⠀⠱⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡼⠀⠀⡼⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢳⠀⠀⢣⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠃⠀⢰⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢇⠀⠀⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡼⠔⠒⠛⠤⡀⠀⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⣤⠴⠒⠚⠢⢄⣰⠀⠀⠇
⠀⠀⠀⠀⠀⡠⠤⠼⠤⠋⠀⠀⠀⠀⠀⠈⢾⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⡡⠋⢸⠁⠀⠀⠀⠀⠀⠙⠤⠐⠓⠤⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠿⠎⠒⠉⠉⠉⠉⡟⠓⠊⠀⠀⣰⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠙⢶⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⢠⠊⠀⠀⢀⡀⢀⡄⠀⠀⢠⡀⢸⣞⣁⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⣱⣀⣀⡀⢀⣀⣱⡎⣤⡄⠀⠀⠀⢠⣤⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠉⠉⠀⢄⡠⠈⢉⡽⢫⠐⠒⠨⣫⠕⠒⠢⡑⣄⡰⢫⠔⠒⠪⣉⠕⠂⠲⡙⢄⠀⠘⠤⠃⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠢⣀⠀⣀⡀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠁⠀⠀⠀⡅⡠⡀⠇⠀⠀⠀⠀⠀⠀⠀⡑⣠⠃⠀⠀⠀⠀⣠⢄⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠚⢛⡳⡘⣄⠀⠀⠀⠀⠀⡴⣱⠁⠰⡘⣄⠀⠀⠀⠀⠀⡰⡡⢿⠻⠤⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡅⢹⡮⡓⠄⣀⠤⣊⡴⡇⢻⠃⢈⠢⡑⠤⣀⠠⢊⠔⠁⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢄⠑⠪⠕⠒⠪⠟⠀⠙⠈⠑⠁⠀⠈⠑⠒⠊⠁⢀⠜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠒⠒⠒⠒⠊⠉



⡿⠉⢙⡟⠿⠻⠿⠟⠿⡛⠿⠻⠟⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠉⠉⠉⠉⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠘⢆⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠉⠓⢴⡁⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠈⠙⠢⣄⠈⡆⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠁⠀⠀⠀⠠⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢣⡜⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣌⡉⠛⠻⠂
⡞⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣴⡟⠻⣿
⡇⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣿⣧⣴⣿
⣇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠻⢷⣄⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠘⣷⡀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⣞⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠘⢷⣄⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠙⠻⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠒⠉⠀⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⢀⢔⣿⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⣾⣵⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢗⣦⣀⠀⠀⠀⠀⠀⠀⣀⠤⢺⣧⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣿⠀⠉⠲⢤⣤⠒⠉⠀⠀⠀⢿⡄⠀⠀⢸⡟⠢⠤⠖⠊⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠁⢸⡿⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⢸⣷⣄⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠷⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠰⠿⣿⡿⠄⢸⡇⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠷⡄⠀⠈⠻⣦⡖⠤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠸⣀⠀⠈⠲⢄⠀⠀⠀⡠⠼⠧⡄⠀⠀⠀⢀⡤⠿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠃⠀⠀⠀⠀⠀⠉⠢⡄⠀⢱⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠀⢣⠀⠀⠇⠀⠀⠀⠀⠸⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⡤⢃⡤⠒⠒⠋⠀⢸⠀⠀⠀⡠⠔⠒⠁⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠛⠛⠻⠷⣶⣤⡀⠀⠀⠀⢀⣤⣶⡾⠿⠟⠛⠻⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠀⠀⠀⠀⡘⣄⠳⣀⣀⠀⠀⠐⠘⣟⣿⣿⠋⠐⠲⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣌⠑⢦⣤⣤⡼⢾⣿⣽⣷⣭⣶⣾⣿⣿⣿⣿⣷⣶⣤⣧⣀⠈⠙⣷⣆⡀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢤⣬⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠙⢦⡀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢒⣲⣿⣿⣻⣿⣿⠋⢯⣹⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠙⠦⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠹⣿⣿⡇⠀⠘⢻⣿⣿⠟⠺⢷⣿⣿⣿⣿⣿⡟⣿⣿⡿⠻⣿⣮⣳⡀⠈⠂⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠁⢻⣻⣿⠀⠀⠈⣿⣂⠖⠈⠙⢿⣿⣿⣿⡿⠫⢿⡟⠀⠀⢿⢻⣷⡝⠄⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢰⢿⢿⣧⣄⠀⠘⢿⡀⠀⠀⠀⠏⠉⣉⣋⢠⠟⠀⠀⠀⠈⠀⢙⣿⡄⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠁⠀⠹⣿⣿⣷⣄⠀⠙⠦⣴⡊⡈⠸⡁⢘⠁⠀⠀⠀⠀⠀⢀⣄⢉⡿⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢹⡗⣿⣿⣿⣷⣶⣤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠊⠉⣿⠛⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⣿⠇⠙⣿⢶⡟⠉⠙⣏⡉⠉⠉⠉⠀⠠⠤⠐⠀⠀⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣿⠀⠀⠘⣿⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⣤⡾⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⣦⣿⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⢻⢷⣦⣀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⣀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⡀⣸⠀⣆⠀⡇⠀⢰⡇⡒⢰⡧⣴⡇⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣇⢠⡘⡦⣇⣻⣇⣿⣄⣷⣷⣿⠃⣇⣾⢣⣿⣼⣿⡿⣄⡴⣴⡆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⢌⣿⣧⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⢟⣿⣿⣾⢋⣿⣯⣾⣣⡞⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠦⣀⣻⣖⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⡾⣃⡴⠋⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣨⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⠉⠉⣍⣉⡟⢩⢋⠻⡿⣿⣿⠿⣿⣿⣿⣿⣿⣻⣵⣿⣿⣾⣯⡴⢟⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⢹⣿⠁⠀⠀⠀⣶⡿⠻⠟⠛⣷⠎⠀⠘⣿⣿⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⣴⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣿⣿⡿⠋⠀⠀⠀⠀⠸⣿⡛⠀⠀⢘⣿⣧⡀⠀⣠⣿⣖⡁⠀⢿⡿⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣭⣥⣤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⣧⡠⢔⡩⣻⠿⠷⠾⠿⡃⠀⠀⢀⣾⠁⢀⣠⣤⢤⣶⣴⣾⣿⠿⡿⣍⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢚⣋⡙⠻⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⠻⣿⣧⠞⡅⠀⠀⠀⠀⢳⡌⣠⠞⠁⣀⣢⣤⣶⣿⣿⣯⠛⢫⢔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⠟⢿⣶⣶⣿⣯⣭⣤⣌⣙⣿⣶⣦⣤⣤⣤⣶⣿⣷⣾⣿⣿⡿⢿⠛⠓⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀⠈⠈⠁⠋⠉⠋⠙⠛⢛⠛⠟⠛⢿⠛⣿⠛⠏⠙⡟⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁









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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠉⠉⠛⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣤⠴⠶⠶⠦⣤⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⠞⠁⢀⣠⠶⠚⠛⠛⠓⠶⣄⠀⠈⢳⡀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣰⠋⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⡄⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣰⠃⢀⡞⠁⠀⢀⣠⠴⠶⠶⢦⣄⠀⠀⠈⢧⠀⠙⡆⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⣠⠏⠁⢀⣀⣀⠀⠈⠳⣄⠀⠈⢧⠀⠹⡄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢠⠇⠀⡜⠀⠀⡼⠁⢀⡴⠋⠁⠈⠙⢦⡀⠘⣆⠀⠈⢧⠀⢹⡀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡞⠀⣸⠁⠀⡼⠁⢠⠞⠀⠀⢀⡀⠀⠈⢳⡀⠘⣆⠀⠘⡆⠀⢧⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣸⠁⢠⠇⠀⣸⠃⢀⡏⠀⢀⡼⠉⠙⢦⠀⠀⢳⠀⠸⡆⠀⢹⠀⠘⡆⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡏⠀⡼⠀⢀⡏⠀⡼⠀⠀⡼⠀⠀⠀⠈⣇⠀⠈⣇⠀⢻⠀⠈⣇⠀⢻⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣸⠀⢠⡇⠀⣸⠀⢰⠃⠀⢰⠃⠀⠀⠀⠀⢸⡄⠀⠸⡄⠈⡇⠀⢹⡀⠘⡇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⡇⠀⢸⠀⢀⡇⠀⡞⠀⠀⡞⠀⠀⠀⠀⠀⠀⣇⠀⠀⢧⠀⢹⠀⠘⡇⠀⢻⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠁⠀⡏⠀⢸⠁⢰⠇⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠸⡇⠀⢧⠀⠸⡆⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣾⠀⢠⠇⠀⡿⠀⣸⠀⠀⢸⠀⣴⠙⠦⠞⢳⠀⠸⡇⠀⠈⡇⠀⣧⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠀⡟⠀⠀⣾⠀⠸⡄⠀⢀⡞⠀⠀⡇⠀⠀⣷⠀⢹⠀⠘⡆⠀⢻⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⣼⠀⢰⠃⢀⡇⠀⠀⡏⠀⠀⠘⢤⠞⠀⠀⠀⣷⠀⠀⢸⠀⢸⠀⠀⡇⠀⢸⡀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⠀⠀⡿⠀⢸⠀⢸⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡀⠘⡇⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡟⠀⠀⡇⠀⢸⠀⢸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡇⠀⡇⠀⣿⠀⠀⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⣾⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⡇⠀⠀⡇⠀⡿⠀⠹⣄⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠇⠀⣇⠀⣸⠀⠀⢸⡀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠙⠒⠒⠚⠉

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

⠀⠀⠀⣠⡶⢤⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⢀⣀⣤⣶⣶⣶⣤⣤⣤
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣾⡿⠾⣿⣦⡀⠀⠀⠀⣠⣾⠿⠛⠛⠿⣦⡀⠘⠻⢿⣛⣫⣵⣿⢋⡿
⠀⣿⣿⣯⣥⣤⣤⣬⣽⣿⣇⠀⢰⣿⣭⣤⣤⣤⣶⣿⣿⠀⠀⢩⣭⣥⣀⣀⣀⣠⣬⣥⠀⠀⠈⠻⣿⣿⠿⠋
⠀⠹⢿⣿⣿⠿⢿⣿⣿⣿⠏⠀⠘⠻⠟⠿⠿⠟⠿⠛⠋⠀⠀⠘⠻⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⣠⣀⣤⣀
⠀⠀⠀⣩⣭⣍⣩⣭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢰⣶⣄⠀⠀⠀⢠⡾⠟⠛⠋⠻⣧⡀
⠀⣠⣾⣿⡿⠿⠿⢿⣿⣷⡄⠀⢀⣀⣤⣴⣶⣶⣶⣤⡄⠀⢠⣴⠏⠉⠁⠈⠈⡙⢷⡆⠰⣯⣤⣄⣤⣀⣤⣾⣷
⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣿⣿⣿⢿⠟⠛⢫⣷⣶⡆⠨⢽⣿⣾⣿⣿⣿⡥⠔⠃⠈⠛⠿⠿⠿⠿⠟⠛⠁
⠀⠀⠀⢉⣉⢉⣉⠉⠁⠀⠀⣿⣿⣿⠗⠀⢀⣴⣿⣿⡟⠀⠀⣠⣼⣿⣯⣥⣤⡀
⠀⣠⣾⣿⣿⣿⣿⣷⣦⠀⠀⢿⡿⣿⣴⣾⣿⣿⣿⠟⠀⠀⠀⠻⣿⣶⣄⣭⣽⣿⡦⠀⠀⣠⣦⣤⣤⣦⣀
⠘⣻⣽⣿⣧⣬⣭⣟⣭⡇⠀⠀⢠⣿⡿⠿⠟⠋⠀⡰⠃⢀⠀⡀⠉⠛⠻⠿⠟⠋⠀⠀⣼⣿⣿⠟⠛⠛⢛⡁
⠀⠉⠻⣿⠿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠡⡏⠊⠟⠀⠀⠀⠀⠀⠀⠀⠘⢛⣻⣥⣄⣠⣾⣿⣧⠎
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⢀⣶⣿⣾⣿⣿⢷⣦⡄⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠉⠁⣡⣄⣠⣶⣦⣤⡀⠀⠀⠀⠀⠁
⠀⢀⡾⣋⣍⣁⣀⣴⣶⡟⠁⠀⠀⢀⣴⡿⠿⠿⢿⣦⡀⠀⠀⢠⣾⣿⣿⠿⠿⠿⠿⣿⠄⠀⠀⢀⣠⣄⣤⣄
⠀⠀⠈⠻⠿⡿⠟⠛⠋⠀⠀⠀⠰⣿⣷⣦⣤⣤⣶⣿⣿⠄⠀⠛⢛⣩⣄⠀⢠⣶⣾⣿⡟⠀⣀⣉⣉⡀⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠐⢿⣿⣿⣿⣶⣿⡿⠏⠀⠀⠉⠛⠛⠛⠛⠋⠉
⠀⠀⣠⣤⣶⣾⣿⣿⣷⠖⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⣰⣿⣿⣿⠛⠁⣨⣿⣿⠏⣠⣶⣿⣿⢿⣿⡿⢿⣿⣦⡄⢀⢈⡑⢶⣇⣴⢠⠄⠀⠀⢀⣴⠾⣿⣿⡿⢷⣦⣀
⠀⣿⣿⣿⢀⣠⣴⣿⣿⠏⠀⠩⣿⣿⣷⣦⣴⣿⣿⣿⡿⠆⠘⣷⣽⢦⡉⠙⠿⣾⡁⠀⠐⢴⣶⣤⣤⣤⣶⡶⠂
⠀⠘⢋⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠉⠀⠀⠀⠈⠻⣦⣭⣛⠳⠦⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠋⠉⠉⠉⠛⠛⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣄⡀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⡔⠉⠀⢀⡤⠞⠉⠀⠀⢀⣀⣤⠤⠴⠶⠶⠠⠤⠤⣄⣀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠉⠙⠲⣴⠋⠀⢀⡴⠋⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⣤⣀⠀⠀⠈⠓⣄⠀⠀⠈⢧⡀
⠀⢀⡤⠤⠤⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡿⠒⠋⠉⠉⠉⠉⠓⠦⣄⣀⣀⣀⣤⣤⣀⡠⠖⠋⠉⠀⠀⠀⠈⠙⠦⡀⠀⠈⠳⡄⠀⠀⠳⡄
⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠙⣆⠀⠀⢱⡄
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠘⡆⠀⠀⢳
⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⢹⡀⠀⠘
⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠈⡇
⣸⠁⠀⠀⠀⠀⠚⠷⣤⡾⠇⠀⠀⢀⠘⠷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠞⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⠀⣿
⠈⠳⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⠏⠀⠀⢀⡇⠀⠀⡏
⠀⠀⠀⠉⠙⠉⠉⠙⢦⣀⠀⠀⠀⠀⢀⡤⠞⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠉⠉⠓⢤⡀⣼⠀⠀⢸⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠤⠤⠿⢤⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠟⠛⠂⢀⠀⠀⡀⠐⠛⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠒⠒⠚⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣶⣤⣤⣤⣖⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠦⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⢦⡀⠀⠀⢀⣴⣋⢀⡴⠚⠛⠲⣄⠀⣠⠖⠛⠛⢶⡄⣈⣷⡀
⠀⠀⠀⢠⡏⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠛⠻⢿⣷⡄⠈⢷⠀⡼⠋⠁⠉⠛⠀⠀⠀⠀⢸⠆⡏⠀⠀⠀⠀⠛⠉⠉⠉⢳⡀
⠀⠀⠀⡿⠀⢰⣿⠟⣋⣉⣀⠀⠀⠀⠀⢠⣾⣷⡆⠙⠟⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠀⠈⠁⣾⠿⠿⠿⣷⠀⠀⠀⠸⣿⣿⡷⠤⢤⡀⢀⣿⠿⢶⣤⣀⠀⠀⠀⢀⡞⠀⠀⠀⢻⡄⠀⠀⠀⢀⣠⠶⢿
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠹⠏⠀⠀⠀⠘⡏⠓⢦⣤⡞⠀⠀⠀⠀⠀⠻⣄⡴⠞⠉⠀⠀⣿
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠚⢙⠆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠠⣦⣄⣀⡀⠀⠀⣀⣠⣴⡄⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠤⠬⠃⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⢧⡀⠀⠀⠙⢦⣉⠉⠉⠉⣉⡴⠏⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠷⣄⣠⠞⠁⠀⠀⠛⢦⣀⠀⠀⠈⠉⠛⠋⠉⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⡤⠤⠴⠖⠛⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⣤⠤⠴⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠒⢤⡤⠤⠴⠤⣤⠔⠚⠉⠉⠙⠲⣄
⠀⠀⢀⣠⠴⠒⠒⠦⣤⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⢣⠤⠖⠒⠲⢤⣀
⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⣸⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢹⡀
⠀⢀⡇⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣀⣠⠤⠒⠉⠀⠀⠀⣇
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠉⠉⠙⠛⠓⠒⠒⠒⠛⠛⠉⠉⠉⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠦⣄⣀⣀⣀⣀⣀⣀⣀⣠⠶⠒⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢀⣀⣀⣀⡀
⠀⠀⢀⡴⠛⠉⠁⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠈⠉⠓⢦⡀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⣽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏
⠀⠀⢰⠇⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⢹⡀
⠀⠀⣾⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠈⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣠⣤⣤⡤⠤⠶⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣀⣀⣀⡀⠀⢀⣀⣀⣀⡤⠤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠉⠉⠉⠉⠑⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣀⠤⠔⠒⠒⠂⠐⠒⠒⠦⢄⣀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⡀⢀⠔⠁⣀⠔⠉⢀⣀⠤⠔⠒⠒⠒⠲⠤⣄⡀⠈⠑⠦⡀⠈⠳⡄
⠀⠀⢀⣀⣀⣀⠞⠁⠀⠀⠀⠈⠻⣀⡼⠥⠒⠒⠫⢄⡀⠀⣀⣀⣀⡠⠔⠒⠛⠓⠦⡀⠈⢢⡀⠘⢆
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠫⡀⡴⠋⠀⠀⠀⠀⠀⠀⠘⣆⠀⠱⡀⠈⢆
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢱⠀⠸⡀
⠀⢀⠞⠀⠀⢀⡀⢀⡀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⡇⠀⡇
⠀⢸⠀⠀⠀⠀⠙⠉⠀⣄⠄⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⠀⡇⠀⡇
⠀⠀⠳⢄⣀⣀⡀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣤⣎⠀⢠⠃⢀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠊⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡔⠁⠀⠀⠀⠈⠑⣞⣀⣼⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠦⠴⠀⠈⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⢄⣀⣠⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠔⠂⠠⢄⡀
⠀⠀⢀⠃⠀⠀⠀⠱⡀⡠⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⡍⢩⣭⡖⠢⣝⢆
⠀⠀⠘⡆⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠈⠢⢉⠠⠊⠀⣹⠂
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠒⠒⠂⠈⠉
⠀⠀⠀⠀⠈⠢⡄⢀⡀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠠⠤⠐⠀⠀⠉⠉⠉⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢗⡒⠂⢐⣂⣉⡀⠀⠤⠔⠙⣄⡀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠠⡤⠒⠒⠐⠈⠐⠒⢄⠀⡼
⠀⠀⠀⠑⡶⢇⠀⠀⢀⡠⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠁⠀⠀⢇⡔⠒⠒⠒⠤⠤⠤⠞⢧
⠀⠀⠀⠀⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠂⠈⠉⠁⠒⠠⣡
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⢀⠀⠠⠐⠀⠀⠡
⠀⠀⠀⠀⠀⠁⠒⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢢⠀⠀⡠⠄⠂⠄⡀
⠀⠀⠀⠀⠀⢠⡶⢳⠒⢒⣀⠤⣉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡠⢣⠊⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠙⢤⠀⠣⣈⠋⣀⠜⠑⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡔⡠⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠄⠀⢙⠂⠤⠭⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢇⠀⣀⡤⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣤⣀⣀⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣤⣤⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠟⢋⣉⠁⠀⠀⠀⠀⠀⠀⠈⣉⡙⠻⢶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠻⣶⡾⠛⠛⠻⢷⡄⠀⠀⢠⡾⠟⠛⠛⢷⣶⠟⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣿⡄⢠⣿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠻⣷⣄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣠⣾⠟⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠻⢷⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡾⠟⠁⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣾⠛⠲⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠛⣷⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢿⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠈⢀⣀⣀⣀⣀⣠⣤⣤⣶⡿⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠙⠛⢿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠴⠆⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣄⣠⣤⡤⠶⠚⠉⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⢶⣶⣶⠶⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⢙⣿⣿⣦⣤⣾⣿⣿⣦⣴⣿⣿⣿⠉⠛⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⣿⣿⡷⠞⠛⠉⣉⠀⠠⠄⠀⡄⠀⢉⠉⠛⠶⢾⣿⣿⠛⢷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣴⠟⠁⡀⢀⡃⠐⢢⡄⠡⠄⠡⠄⢒⡈⠠⠰⠀⠀⠉⠻⣤⣴⣿⣷⡄
⠀⠀⠀⠀⠀⣼⠏⠹⣿⠟⠀⠤⠀⠆⠄⠈⢁⣠⣤⣴⣶⣶⣤⣤⣄⡘⠂⢘⠈⡀⣀⠈⢻⣿⠉⢻⣆
⠀⠀⠀⠀⣼⣿⣶⣶⠃⠠⠄⠘⠘⢀⣤⣾⠿⠛⣉⣩⣭⣭⣍⡙⠻⢿⣶⣄⠠⠅⢠⢀⠀⠹⣶⣾⣿⡆
⠀⠀⠀⣸⠟⠻⣿⠃⠠⠄⣃⠉⣠⣿⠟⢁⡴⠛⠉⠀⠀⠀⠈⠙⠳⣄⠙⢿⣧⡀⠂⢠⢀⠀⢹⣿⠛⢻⡄
⠀⠀⢀⣿⣤⣴⡏⠠⡄⢉⠈⣰⣿⠋⣰⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢻⣷⠀⠂⣈⠀⠀⣷⣦⣼⣧
⠀⠀⢸⠿⢿⣿⠀⣀⠘⡈⢠⣿⡏⢰⡏⠀⣾⣿⣿⣦⡀⢠⣾⣿⣿⣆⠈⣷⠈⣿⣇⠐⢀⡉⠀⢸⣿⠿⢿
⠀⠀⣾⣀⣠⡿⠀⡀⠂⠁⢸⣿⠀⣿⠀⠀⢿⣿⣿⣿⣷⣿⣿⣿⣿⡏⠀⢸⡆⢹⣿⠀⠂⡀⠃⠘⣧⣀⣸⡇
⠀⠀⣿⣿⣿⡇⠀⠑⠊⠁⢸⣿⠀⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⡇⢸⣿⠀⠒⠁⠂⠀⣿⣿⣿⡇
⠀⠀⣿⠀⢙⡇⠈⠡⠌⠁⢸⣿⠀⣿⠀⠀⠀⠀⠙⠻⣿⡿⠟⠁⠀⠀⠀⢸⡇⢸⣿⠀⠶⠉⠆⠀⣿⠁⢸⡇
⠀⠀⠻⣶⡿⠃⠀⠃⠌⠃⠸⡿⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⡿⠀⠤⠃⠄⠀⠻⣷⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⣦⣌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣰⣶⡀⣠⣶⣠⠄⣼⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡴⣿⢻⡟⢿⣿⠃⢀⡟⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣠⣶⣅⣰⣅⣠⣇⣸⡟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⡄⠳⣾⣿⣿⣾⣧⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣿⣿⣿⣿⣿⣿⣷⣄⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣀⣸⠀⠀⠀⠀⠀⣠⠴⠖⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠛⠛⠛⠻⠿⣧⣀⠀⠀⠈⠙⠻⢦⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠈⠳⣄⢘⡀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠠⢃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠑⠿⡏⠉⠛⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⡠⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠑⠶⣇⣀⢸⡟⠛⠻⣷⣶⣤⣤⣀⣀⣀⠀⣀⣀⣀⣤⣴⣾⡿⠛⠁⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠉⠙⠛⠒⠶⠿⠿⠟⠛⠛⣿⡿⠛⠉⢉⣹⡿⠋⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢀⣴⠟⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣾⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠀⠠⠄⠛⡟⠀⠀⢰⡇⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⣶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡔⢲⣯⣭⣉⣩⣭⣭⣉⣥⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠉⣉⣀⣀⠈⠉⠉⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⣀⠤⠒⠊⠉⠁⠀⠀⠀⠉⠉⠑⠒⠤⣀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣠⠖⠋⣀⡠⠴⣒⣚⣉⡉⣉⣉⣓⠲⠤⣀⠀⠈⠑⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠊⢀⠔⢋⡥⠒⠉⣁⣀⣤⣤⣀⣀⠈⠙⠲⢄⠙⠢⡀⠀⠱⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠊⠀⡔⢁⡔⠁⢀⠔⠋⣀⠤⠖⠒⠶⠤⣉⠒⢄⠀⠱⡄⠘⢆⠀⠘⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠁⢀⡞⢠⠋⠀⡰⠃⡠⠊⠁⠀⠀⠀⠀⠀⠈⠑⢄⠱⡄⠹⡄⠘⡆⠀⠸⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⡸⠁⠀⡼⢠⠃⠀⡸⠁⡜⠁⠀⣀⡀⠀⠀⠀⢀⣀⠀⠈⢆⠹⡄⠹⡀⢸⡀⠀⢃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⢀⠇⠀⢠⠃⡎⠀⢰⠃⡼⠀⡰⠋⠀⠈⠱⣄⡔⠁⠀⠙⢆⠘⡄⢱⠀⢱⠀⡇⠀⠘⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⡼⢰⠇⠀⡎⢰⠃⠀⠃⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠀⢧⠘⡄⠸⡆⢿⠀⠀⣧⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⠀⡇⠀⡇⢸⠀⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⡇⠸⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠀⡇⠀⡇⢸⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⠨⡄⠀⡇⢠⠀⠀⠀⠀⠙⠦⣀⣀⡤⠞⠁⠀⠀⠀⠸⣀⠇⠀⢅⣰⠀⠀⢸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢰⢀⡆⠀⠱⠔⠃⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣾⣿⣿⠀⠀⠀⠀⣿⣿⣷⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡄⠀⠘⠛⠻⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠉⠛⠿⠶⢶⣶⣶⡶⠶⠿⠛⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣄⣀⣀⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡈⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠛⠲⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⢿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡶⠀⠀⠀⠀⠀⠉⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⡦⣄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠟⢠⣿⣀⠆⢀⠀⠀⠀⠙⢿⣿⣿⣷⡍⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⡈⠿⠟⣰⡏⠂⡤⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⠿⠿⠿⠿⠒⣿⣆⠁⠀⠀⠀⠒⢀⣿⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⡀⢠⣻⣿⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠉⢿⣿⣿⡗⢲⡄⢠⠐⠀⣤⠘⠶⣾⣧⠀⢀⡄
⠀⠀⠀⠀⠀⢀⣵⣿⣿⣿⡿⡿⠛⠻⠟⠛⠉⠉⠁⠀⠄⠀⠀⠀⣿⣿⡷⠘⠃⣸⠃⠾⠿⡿⣷⠟⣿⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣴⡾⠛⠛⠋⠁⠀⠀⠀⠀⣀⠀⠀⠒⠀⠀⠀⠃⠀⠚⠛⠛⠿⣿⣿⣿⣿⣶⣟⣿⡁⠀⠈⠃⠀⠀⠛⠉⠀⠈⠂
⠀⠀⠰⠿⢋⠀⠀⣀⣤⢠⣶⣦⣈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠀⠀⠉⠻⢿⣿⣭⣩⣭⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠉⠛⠀⠳⠿⠃⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠒⠷⠶⣄⡀⠠⣄⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠛⠿⠷⠶⢶⣤⣤⣄⣀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⣀⣩⣴⣤⣆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣤⣀⡀⠀⠀⢐⢢⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⣄⠙⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⡛⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠟⠛⠻⢿⣿⣿⣿⡿⠛⠛⠋⠉⠠⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⣧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⢀⡀⠠⡄⠀⠄⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣠⣤⣤⣴⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠋⠉⠉⠉⠉⠛⠛⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠛⠳⢦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⢀⣴⠾⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣧⣀⠀⢀⣠⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠤⠀⢹⡄⠈⢮⠉⠻⣍⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠸⣇
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠔⠀⠈⠳⢄⠞⠀⠒⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⢹⡆⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢠⢤⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⣰⠃⠸⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⠀⢠⠇⠀⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠁⠀⠉⠀⠀⢀⡟⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⣠⢷
⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⠖⠛⠉⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘



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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⠶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⢿⣿⣏⣩⣿⣿⣤⣾⣿⣇⣈⣿⣿⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣿⣦⡾⠟⠋⠉⠀⠀⠀⠀⠀⠉⠙⠻⣿⣤⣼⣿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣾⠟⠉⢀⣠⠴⠖⠒⠛⠛⠓⠒⠦⣄⡀⠀⠙⢿⣤⣀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣤⣿⡟⠁⣠⠖⠉⢀⣤⣴⣶⡾⡳⣶⣦⣄⡀⠉⠳⣄⠀⠻⣿⣏⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣋⢹⣿⠋⢠⠞⠁⣠⣾⠿⢿⢫⠶⣄⣓⡛⠍⡙⠿⣦⡄⠈⠳⡄⠙⣿⣿⡿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⣸⣿⠟⣿⣿⠃⣰⠋⢀⣼⣿⠟⣘⣪⣶⠾⠟⠛⠻⠾⣿⡈⠼⠿⣦⠀⠙⣆⠘⣿⣦⣸⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⠃⢠⠇⢀⣾⢛⠿⣐⣸⡟⠁⠀⠀⠀⠀⠀⠈⠻⣧⣵⠹⣧⠀⠘⡆⠘⣿⡟⠛⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣄⣹⡏⠀⡞⠀⣾⣿⢢⠾⣿⡟⠀⠀⢠⣦⣴⣶⠀⠀⠀⢹⣏⢢⣼⣇⠀⢹⠀⢹⣷⣾⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣟⢻⣿⠁⢰⠃⢸⡿⠻⡌⣵⡿⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⣿⡰⠊⣿⡀⠈⡇⠀⣿⣯⢀⣿⣿⡀
⠀⠀⠀⠀⢸⣿⠟⢿⡏⠀⣼⠀⣾⣧⢉⠵⣿⠇⠀⠀⠀⡀⠙⢋⣤⠀⠀⠀⠀⢻⣿⠣⢹⡇⠀⢻⠀⢸⣿⠿⢿⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⡏⠀⣿⠿⡧⣩⣾⠀⠀⠀⢰⣿⣷⣿⣿⠇⠀⠀⠀⢸⣿⢜⢻⣿⠀⢸⡄⠀⣿⣆⣼⣿⣷
⠀⠀⠀⠀⢸⣿⣄⣿⠀⠀⡇⠀⣿⡎⡵⢿⣿⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣤⠇⣿⠀⠈⡇⠀⢹⡟⠛⣿⣿
⠀⠀⠀⠀⢸⣿⠛⣿⠀⠀⡇⠀⣿⠷⡄⣼⡿⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⣿⡏⡒⣸⡇⠀⡇⠀⢸⣿⣾⣿⣿
⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⡇⠀⣿⡌⡼⢿⡇⠀⠀⠀⣾⣷⣄⣴⣿⡇⠀⠀⠀⠀⢻⡗⠍⢿⡇⠀⣇⠀⢸⣯⠉⣿⣿
⠀⠀⠀⠀⢸⣿⣤⣿⡇⠀⣇⠀⣿⠟⡌⣾⡇⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⣿⠆⢿⡇⠀⣿⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠋⢻⡇⠀⢻⠀⢸⣷⠸⢻⡇⠀⠀⠀⠀⠙⢿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣐⣿⡇⠀⣿⠀⢸⣿⣄⣼⡇
⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠘⠆⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠛⠀⠘⠿⠿⠟⠁