Hairstylist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⠀⠀⠺⣧⠀⢠⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢿⣷⡀⢰⣿⣿⡇⣶⠀⢻⣆⠸⡇⠰⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠻⢮⡿⠓⠈⣿⣿⣿⣿⠀⠈⠻⡄⠁⡰⠀⠙⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠁⣰⣦⠀⡔⠐⠠⡀⠘⢿⣿⡇⠀⠀⠀⠘⡀⠃⠀⠀⠀⣙⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣾⡿⠃⠀⣀⡬⠝⠀⠀⢈⣉⡁⠀⢤⡀⠀⠑⠀⡄⠀⣰⣿⣿⠋⠉⡤⠾⠛
⠀⠀⠀⠀⠀⣸⠁⠀⢠⣿⠟⠀⢶⠟⠁⢀⣤⠶⠀⢿⣽⢷⡄⠀⠹⣄⠀⢀⡇⢸⣿⡿⠁⢀⣴⣾⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⢀⡏⠀⣠⠞⠁⠀⠀⣠⣴⡞⠋⠁⠀⠀⠈⢷⣜⣷⠀⠀⠉⠀⢸⡇⣿⠟⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⠚⠁⡴⠃⠀⠀⠀⠀⠛⠉⠀⠀⢀⣶⡦⠀⠈⠻⢿⡁⠀⠀⠀⣼⡇⠀⠀⡀⠀⠈⢹⣿⣿⣿⣿⣿⠋
⠀⠀⡔⢛⡔⠂⠀⣰⡆⢀⣠⣤⣤⣴⣶⣾⣿⣿⣿⠄⠀⢀⡈⢳⡄⠀⠀⣿⣧⠀⠀⣇⠰⠶⠦⠍⠛⠛⠛⢁⡄
⠀⠀⠈⠀⠰⠀⣰⡟⢰⣿⣿⣿⣿⣿⡿⠛⠉⣤⠀⠀⢸⡿⣧⠈⠻⠀⠐⠿⢿⠟⠀⠛⠀⣀⠔⢠⣦⠀⣰⡿⣡⣾⢃
⠀⠀⠀⠀⣠⣴⣟⠀⠈⠿⣿⣿⣿⡉⠀⠀⡼⠁⠀⠀⠀⠹⡇⠀⠀⠀⠀⠄⠀⢀⣠⠶⠋⠁⠀⢸⣿⣶⣿⣿⣿⣷⠟⠁
⠀⠀⠀⠘⢰⣿⠃⠀⢀⠀⠀⠹⣿⣷⡀⠀⠀⠀⣰⣿⠆⠀⢻⠀⠀⠂⠲⠂⡩⠛⠁⡀⣶⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⣰⣾⠃⢀⡴⠁⠀⠀⠀⠹⣿⡇⠀⠀⣴⣿⠋⢀⣀⠈⠄⠀⠀⠃⠹⠁⢠⡀⠘⢿⡇⠺⣿⣿⣿⣿⠟⣋
⠀⠀⠰⠿⠃⣠⡞⠀⢀⣴⠆⠀⠀⠙⠿⠀⢸⡿⠃⢀⣿⠏⠀⠀⠀⢈⠀⢤⡀⠘⣿⡀⠈⣿⠀⠀⠙⠟⢁⣼⡿⠓⠂
⠀⠀⠀⠀⣴⣿⠀⢴⣻⠿⠳⢄⠀⢀⡤⢠⠏⠀⠀⡾⠃⠸⠗⠀⠀⠙⢷⣄⠙⠂⢹⣧⠀⢸⠀⠰⠢⠀⣾⣟⠏
⠀⠀⠀⠀⠉⠈⠀⠀⣿⣷⣀⠀⠔⠋⢰⠃⠐⠳⠦⢄⠀⠀⠀⡀⠀⠀⠈⠻⣧⡀⠀⢻⣆⠀⠀⢇⠌⣼⣿⡡
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⢀⣀⢸⣦⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣦⠈⢿⡄⠀⠀⣴⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃⣤⣿⣷⣽⣷⣄⣿⡆⠀⠀⢸⣿⣧⠀⢠⡀⠀⠙⢧⡈⣷⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣬⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⢻⣿⡄⠀⠈⠳⣄⠈⠻⣬⣃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡷⢀⣾⠈⣿⣷⡀⠀⠀⠻⠷⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠀⢼⡝⠀⠸⡿⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⡤⡶⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣞⠟⠁⠀⠓⠤⠔⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣼⣿⣯⣤⣠⣴⣶⢒⣶⣶⣤⣀⠀⠀⠀⠸⣧⡄⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣥⣾⣷⣦⣾⣟⣩⣿⠿⠛⠿⣿⣧⠘⠿⠟⠛⠙⠛⢦⣄⣀⠀⢀⣠⣿⡇⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⣾⢣⡾⠆⣿⡿⣿⣿⡟⢋⠀⠀⠀⣿⠎⠷⠶⣶⣆⠛⣽⣿⡿⠛⠛⢿⣿⣟⣁⣀⣀⡼⠃
⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⢮⣨⣷⣾⠝⣦⡁⠈⢡⠤⢿⣿⣤⡎⠀⠀⠀⠙⣿⣾⣿⠛⠛⣧⡾⢿⣧⣺⣷⡀⢿⡿⢋⣭⡁
⠀⠀⠀⠀⣼⢟⣭⣭⣝⢻⣦⣿⡿⠧⣶⣶⡇⢠⠃⣠⣾⣿⣿⣿⣿⡿⣦⡀⠘⠻⣟⡷⣦⣈⠉⠀⣉⣿⠭⣣⡘⣧⡈⠻⠿
⠀⠀⠀⠀⢿⡸⣅⣀⣽⣿⣿⣿⣷⡷⣸⣿⣧⡀⠳⢬⡥⢃⣿⣿⠟⣡⣮⢷⣄⠀⠈⣻⣮⠙⢷⣄⠙⠿⡿⠛⠳⣬⣙⣃⣤⡄
⠀⠀⠀⠀⠀⢙⣾⡿⠛⣉⣄⣉⠙⢣⡟⣥⣽⡿⡲⣶⣶⣿⡿⢃⣼⣿⣿⣦⠝⢁⡈⠛⠁⠀⣸⣿⣦⣠⣷⣤⣼⣧⣽⣹⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠰⣿⡿⣿⣧⠀⢙⣈⡛⢷⣶⣿⣿⠋⢀⣼⣿⣿⠟⠁⣠⣿⢿⣦⣤⣾⠿⠟⠛⠛⠉⠉⠉⢻⣿⣭⠉⠻⡆
⠀⠀⠀⠀⠀⠛⣿⣿⣦⣤⣼⣿⣿⠀⢸⣿⣿⣦⠀⣌⠁⣠⣿⣿⣟⣥⣴⣾⡿⠴⠞⠛⠛⠋⠀⠀⠀⠀⢀⣀⣀⣼⣿⢉⠀⢀⣿⠒⠉⠀⠙
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣋⢉⣛⠀⣾⣿⣏⣛⣠⢫⠾⠻⢿⣿⣟⣛⣭⣥⣶⣾⣿⣿⣿⣿⣷⡾⢿⡿⣻⣿⣯⣿⣷⢤⢀⣿⡟
⠀⠀⢀⡀⢰⣿⣿⣿⣿⡁⢧⡙⠛⠀⣿⣌⢟⣟⣵⣿⣾⠇⢸⣟⡙⠻⣿⣥⣈⣉⠛⠛⠿⢿⣿⣧⣻⣟⠿⠟⣤⣈⣿⣾⣷⠟⢁⣠⡄
⠀⠀⠀⣙⣿⣿⣿⣿⣿⣷⣄⣉⣀⣠⣼⣷⣿⣿⣿⡟⣡⣴⣿⣏⢻⣦⣄⠙⢿⣿⣿⣷⣶⡤⣄⡀⢶⣶⣾⣿⣿⣿⠋⣩⣶⣶⠹⣿⣿⡄
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡛⣿⡏⣼⠋⣉⡉⢿⣦⢻⣟⣓⣄⡈⠻⣿⣿⡦⣈⣹⢇⡙⢿⣿⣿⠏⣠⣿⣿⣿⣷⡙⣿⣿⡆
⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⢏⣥⣶⣶⣾⣦⡛⠛⠇⠙⠀⣿⣷⣾⣿⣧⠙⢿⣿⣿⣿⣦⣉⠻⣿⣇⢿⡿⢸⣿⣯⣴⣿⣿⣿⣿⣿⠗⠉
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠿⠏⣿⣿⣿⣿⣿⣷⠷⣦⠘⣿⣿⣿⡿⣧⠀⠈⢻⣷⡈⠻⣷⣦⣉⣻⣿⣿⠟⠉⠉⣷
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣯⡟⢙⣿⡆⢹⡿⢿⣷⣉⣠⠴⠊⢻⣷⡀⠙⠟⣸⣿⠟⠁⠀⠘⠒⠋
⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠈⣧⠈⠻⣿⣀⣠⡶⠟⣁⣹⣿⣿⠟⠁⠀⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⠿⢃⣼⣿⣷⡀⣻⡉⣡⡄⣈⡽⢟⣫⠄⠊⠀⠀⠀⠀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣏⣉⣰⣟⣛⣻⣭⣵⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠃⣬⢻⣿⡿⠿⢿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠁⠀⣼⣿⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⣾⣿⣿⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣤⣶⡶⢶⣶⣦⣀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣯⣶⣶⣦⣄⠙⢿⣧
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠒⠒⠒⠀⠉⣉⣁⣀⣀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣾⣿⣿⣛⣛⣻⣭⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠟⣹⣿⡛⣿⣿⣿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠰⣄⣀⣥⡿⠿⣿⢿⣿⣿⣿⣿⠀⢀⣀⠀⠀⢀⣤⣄⣒⣻⣿⣿⣿⣿⣿⣿⣿⣦⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣭⠖⣚⡿⣿⣯⣿⣿⣿⣿⣿⠙⠏⠙⠂⣿⠁⠉⠉⠏⢹⣿⣿⣿⣿⣿⣿⣿⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⡞⠉⠳⣻⣿⣿⣿⡀⠀⠀⠀⠀⠋⡠⢀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠶⣶⣿⣿⣿⣿⣿⡀⠀⢈⣁⣩⣤⠄⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢠⣟⣿⣿⣿⣿⣿⣿⣦⡀⠀⠂⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⢸⣿⡏⠻⠿⠿⢛⣻⣿⠹⣷⠶⠾⠛⣿⣿⣿⠿⢿⣿⣿⣿⡿⠃⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣯⠛⠛⢻⣿⣇⣠⣀⠀⠉⣽⡟⣧⣤⣁⠐⠾⣷⣛⣿⣿⡇⢨⠉⠉⠀⠀⣄⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⣿⣿⣿⡏⣿⣿⠉⠀⡹⢿⣾⣍⣛⠿⣣⣾⣿⣿⣿⠀⢀⣥⢄⠀⢠⣌⠳⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⡌⣫⡿⠏⢀⠀⣹⠟⣄⠀⠳⣾⠻⠿⣿⣿⡟⢻⣿⡾⡁⣠⡿⢁⣼⣿⡆⢿⡇⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⡶⠶⡿⠠⢏⣄⢘⣷⡀⠈⠛⠀⣸⡋⠁⢸⡏⠀⠀⣿⢁⣾⡿⢻⣷⡄⣰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⣨⣶⣿⡟⠛⣿⡿⠶⣀⠀⠉⠀⠀⢸⣷⠀⢰⡇⣨⣿⣿⡎⢟⠳⠟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⢿⣷⣶⣿⠀⢷⣏⣤⣽⣄⠀⢸⣿⡴⣯⣾⡿⠿⠻⠶⠿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⢸⣟⣿⣿⣄⠀⠈⠉⠛⠋⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠈⠻⣿⣿⣯⣥⣸⣧⣾⣶⣾⣼⣿⣽⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡿⣣⣴⣶⣯⣍⠛⠷⣶⣶⣾⣿⠿⠿⠿⠷⠠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡟⢸⡿⠻⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣦⡙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠈⠁⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⡀⠀⠀⣀⣀⣤⣤⣶⣶⣯⡍⠛⠻⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠉⢛⠿⠿⠿⠛⠋⠉⠀⠈⠙⣿⣿⣿⠀⠀⢀⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⣷⡄⠀⠀⢰⣆⠀⠀⠀⠘⣿⡟⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠓⠀⠀⠀⣿⡇⣿⣆⡀⠀⢿⣦⡀⠀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠻⣿⣶⣌⡻⣿⣶⣄⣀⢣⣀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⣀⣀⠀⢳⡀⠀⠘⣿⣯⡻⣿⡙⠻⢿⣯⠻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⣿⣭⣿⡷⠀⢻⣆⠀⢸⣿⡇⢹⠃⠀⠀⢙⡇⣿⣷⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠠⠀⠀⠉⠁⠀⢠⠈⣿⣧⣾⠏⢀⠊⣀⣤⣶⡟⢠⣿⠏⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠒⠒⠊⠀⠀⢹⣿⡏⢠⣡⣾⣿⣿⠏⢠⡟⠁⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⢹⡿⣿⣿⡏⠀⣿⢠⣾⡿⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⢠⣿⡏⠻⣷⣿⣮⡛⢧⡀⠀⣿⡏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠄⠀⠀⠀⠀⢀⡴⢫⣿⠁⠀⠈⠻⣿⣿⣦⡹⣄⠙⢷⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡌⠀⠀⠀⠀⣠⡏⠀⣾⣿⡀⠀⠀⠀⢻⣿⠈⣻⣿⡆⠀⠸⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⣿⣿⡄⠙⠿⣷⣄⠀⢠⠟⠁⠀⣨⣿⣟⡔⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⢉⣿⣧⠀⣠⡾⠟⣽⣿⡀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⢠⡿⠟⢡⠞⠁⠀⠸⣿⣿⣿⣦⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠺⣷⡀⣿⠀⠀⠀⠀⠈⡻⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⣿⠀⠈⢹⣟⠀⠀⠀⣼⠈⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠹⣆⠀⠀⢿⣧⡀⠀⠙⠦⣀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠙⠆⢀⣼⡿⠃⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⡴⠛⠉⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠛⠛⠛⠻⢮⠳⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⢀⣀⣤⡤⠤⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⣀⣴⠞⣋⡁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡞⣠⣾⠋⣵⠞⢡⣴⠛⠁⠀⠀⠀⠀⠀⣿⠀⠈⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⣿⣼⡟⢁⣾⡟⢠⣿⡷⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⣿⡟⢀⣿⡿⢀⣿⡟⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢿⡄⠘⣿⠁⣼⣿⡇⢸⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⢸⣧⠀⠙⠀⣿⣿⠁⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⠤⠄⠀⠀⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣇⣐⣠⣾⠏⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣤⣶⠟⢋⡁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⣭⠴⠋⢀⣄⡾⢹⣿⠀⣿⡟⣿⣿⣧⠀⠀⠉⠀⠀⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣤⠴⠞⠫⠊⠀⠈⣿⣶⣿⠁⢻⣿⣿⣷⡀⠀⠐⠻⢿⣿⣿⡿⠁⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⠇⢹⣿⠏⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣡⡴⠊⠀⢀⣀⣠⣤⣶⡿⠋⠠⠾⣿⠀⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⣠⣴⣾⣿⣿⠟⠋⠁⠀⠀⣰⡄⣿⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⣿⣿⣿⣁⣤⣤⣤⣶⣿⠟⢠⡟⠀⠀⡄⠀⣿⣿⡇⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣼⣿⣿⠿⠿⠿⠛⠛⠛⠋⠁⠠⠚⠀⠠⠞⠀⢀⣿⡿⠀⠀⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣤⠤⠴⢊⣠⣾⡟⠀⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣰⠃⠀⣴⣿⡿⠛⠉⠀⠀⠀⠐⠒⠒⠚⢋⣡⣾⠃⢠⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠃⠀⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣮⠀⢀⠄⣠⣴⣾⣿⡿⠿⠛⢁⡀⣦⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣤⣯⣾⣿⠿⠋⠁⠀⢀⣠⣾⢃⣿⣇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⣿⡿⠁⠀⣀⣤⣶⣿⡿⢋⣼⣿⣿⠀⣼⣿⠏⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣴⣾⣿⠿⠟⠋⣠⣾⣿⣿⡏⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⠟⠁⠀⡰⢀⣾⣿⣿⣿⣫⣾⣿⠟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⢃⣿⣿⣿⣿⣿⡿⠟⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢸⡟⢸⣿⣿⣿⣿⠋⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸⣿⣿⡿⢡⡆⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠻⣿⡃⣿⣧⡸⣅⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⢻⣿⡛⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡀
⠀⢸⣿⠇⠀⠀⢠⠞⠉⢙⢦⠀⡄⢀⠄⢀⡠⠤⣀⠀⠀⠀⠀⠀⣴⣿⣯⣌⢆⠀⠀⣰⠃
⠀⣸⣿⣀⠀⠀⠸⡀⠠⠋⡜⠀⠸⣼⠀⡎⠀⠀⡸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⡐⣴⡇⠀⠀⢀⣠⠄
⠀⣿⣿⣿⣷⣤⣄⣈⢳⡎⢀⠔⢩⠟⠍⢳⠈⠉⢀⠶⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣵⣶⠾⠋⠁
⠀⠹⠿⠿⠋⠉⠛⠛⢹⣿⠀⠀⢊⠀⠈⢠⠑⠊⠁⠀⠀⢀⡴⠶⢤⣀⣠⠴⠿⣯⣿⣯⣷⣅⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡼⠋⠀⠀⠀⣿⠙⢿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡏⠀⠀⠙⢿⣿⠟⠁
⠀⠀⢀⡠⠤⠤⠤⣀⠀⠀⣴⡧⠂⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⣇
⠀⡰⠁⠀⠀⠀⠀⠈⠳⠎⠀⠀⠀⠉⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡞
⠀⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢠⢀
⠀⢘⣶⣿⣧⡄⠀⠀⠀⠀⠀⠀⣀⠀⢠⣾⠿⠿⠿⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⣀⠀⠀⡀
⠀⠈⠻⣿⣿⣿⣶⡀⠀⠀⠀⢰⣇⡰⠛⠁⠀⠀⠀⠀⠀⢘⣃⡝⡰⣡⢦⢰⠲⡆⢸⡏⠀⢧⡾⠜⡗⣼⢧⣤
⠀⠀⠀⠈⠻⣿⣿⣿⠆⠀⣠⡼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠹⠋⠓⠛⠛⠁⢋⡶⠙⣞⠛⠦⣈⣻⠇⠙⠂⠁
⠀⠀⠀⠀⠀⠈⠉⠈⢢⠞⣛⠅⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣄⢀⠜⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠯⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠋⠈⠲⠾⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠞⠀⡀⠀⠀⠀⠀⠀⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⠁⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⢀⣽⢿⠿⠟⠋⠀⠀⠀⠠⣾⣿⣿⣿⣿⡿⣫⣶⣄
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⣙⠻⢦⣄⡀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣉⠛⠷⣤⣀
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣌⡙⠷⣤⡀
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣄
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⢟⡄
⠀⠀⠸⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⠇
⠀⠀⠀⢻⡄⠀⣠⡾⢡⡖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⠛⠛⠻⠿⢣⡾⠟⠋
⠀⠀⠀⠀⢻⣾⣋⡴⢋⡼⢋⡶⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠀⠀⢠⣾⣿⣿⡿⠉
⠀⠀⠀⢰⣿⣿⣿⣴⣋⡴⢋⡴⢋⡾⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡏⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣟⣴⢏⡴⢋⡴⢃⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⢀⣤⠞⠛⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣿⣵⢟⣴⢋⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣬⡻⢦⣀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣼⠏⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣝⠳⣤⡀⢀⣴⠟⣱⠟⠛⠻⣆⢀⡼⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡇⠈⢹⣿⡁⠀⢿⣄⣀⣠⡟⢾⡁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⠈⣿⠀⠀⠉⠉⠁⠀⠈⠛⠶⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣉⣭⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠺⠏⠙⠹⡿⠉⠈⠛⠁⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠠⡞⣣⠔⣋⢾⣻⣿⣷⣄⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠞⣤⠿⠿⣻⣿⣿⣷⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢀⠀⣶⡾⣋⣶⢿⣿⠟⢻⣿⡇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣈⡶⢁⡤⣿⣧⡾⢁⡶⠛⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠰⢫⡵⠋⠀⠀⠀⠰⠿⣿⣷⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢉⣠⣶⣶⣷⣶⣶⢤⣈⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⣟⣉⡀⠀⠀⠈⡡⠾⣿⣆⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢀⣼⣿⣿⠉⣉⠀⠀⠀⣁⠠⣿⣿⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣾⡵⠿⡇⠀⠉⠁⠀⠀⠉⢀⣹⣿⢷⡶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⠀⠀⠀⠹⡆⠀⠀⣠⣄⠀⣾⠃⠈⠛⢋⣡⠶⣾⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠡⠦⠘⠳⣄⡀⠀⢸⠀⠄⣉⣁⣴⠃⠀⢀⡴⢋⡀⠀⠛⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣘⣆⣀⣛⠉⠛⣦⡘⣁⠀⠈⠉⣹⠀⢶⡏⢀⣘⣁⣀⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣉⠛⠛⣷⣾⠟⣹⡏⠑⠶⠞⢁⣴⡏⠀⠈⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠙⠋⠀⢉⡋⠉⠻⠃⣸⠋⢻⣾⡓⠐⢻⡉⢠⣾⠀⣶⡌⠉⠲⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠸⠷⠀⠀⠙⠁⠀⢀⡀⢹⣆⠠⠙⠻⠷⢈⣠⣿⠟⠀⠀⠀⣠⡄⠈⢳⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⣠⡄⠀⠀⠙⠁⠀⢻⣄⠹⠟⠛⠋⠉⠁⠐⠓⠀⠀⠉⠁⠀⠀⣀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠠⡦⠀⠈⠁⠠⣶⠂⠀⠄⠀⣻⣦⣄⠀⠘⠃⢀⣠⣤⠶⠾⠟⠒⣶⠀⠉⠀⢀⡀⢸⡇
⠀⠀⠀⠀⠀⣴⠏⠡⡆⠀⠀⠀⢠⡄⠀⡀⠀⠀⠀⠀⠉⠉⠛⠟⠐⠚⠛⠉⠀⠀⠀⠀⠀⣿⠰⡶⠀⠈⠉⢀⣿⡄
⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⣤⡄⠀⠀⠀⠁⡠⢦⠛⠐⠀⠀⠀⠀⡇⢸⠀⠀⠀⠠⠤⢀⡀⣿⡀⢀⣄⠀⣴⠟⠉⠳⣦⡀
⠀⠀⠀⠀⠿⢧⣀⠛⠀⠀⠈⠀⢘⠿⠈⠈⢹⣦⢇⡔⠀⠀⠀⠀⡇⠈⠀⠀⠀⠰⢶⡇⠀⠉⠙⠶⣅⠀⢿⣀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⠄⠀⠀⠙⠧⢀⣀⣴⡶⠀⠀⢀⣀⣤⠿⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠛⠁⢤⣤⣄⣀⡉⠛⠂⠽⣶⣤⣤⠄⠀⠙⣷⡀⠀⠀⠀⠈⠃
⠀⡴⠋⠀⠀⠀⠀⠀⠈⠉⠁⣠⡴⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠘⠃
⣼⠃⠀⠀⠀⠀⢀⣤⡴⠶⠿⣿⣷⣶⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⢀⣤⠖⠛⠃⠀⢠⣬⠙⢷⣦⣤⡀⠀⠀⠀⣸⡗⠀⠀⠰⠆
⢿⣶⣶⣶⡾⢿⡟⢁⡈⠛⣶⠈⢻⣇⢀⡄⠙⠃⠀⠠⠤⣀⣀⡀⠀⠀⠁⠀⠀⢴⣌⣁⡀⠀⠀⠀⠀⠀⠄⠁⢤⣀⠈⠻⠛⠿⠟⠋⠁
⠀⠈⠉⠁⠀⠈⢷⣦⡶⠶⡄⠀⢸⣿⡆⠀⢠⣄⠀⠀⠤⢀⣠⣿⣿⣿⣿⡿⢦⡀⠀⠉⠻⢷⡆⠰⣠⠆⠀⢀⣤⣦⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⡟⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠟⠁⠀⠀⠙⣦⠠⣦⠀⠁⠀⣿⡀⢠⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⣿⢧⣴⡟⢁⣤⣾⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⢹⣆⠉⠀⠀⢠⣿⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣀⠀⣁⣼⡿⠁⢠⣿⣿⣿⣿⡿⠁⠀⠘⣦⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠛⢿⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⢿⣜⣿⣿⣷⠄⣼⣿⣿⣿⣿⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⠘⣿⡆⢰⣆⠀⠀⠈⠳⣈⡷
⠀⠀⠀⠀⠀⠀⢀⣿⡴⢿⣼⢿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⢾⠄⠀⠀⡇⠀⠀⠀⠀⠀⢹⣿⡈⠉⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⢸⡟⠇⢸⡏⢸⣿⣿⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠻⠆⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡇⢠⡿⠁⣼⣿⣿⠾⠆⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠙⣿⣿⡄⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⣿⣿⡆⠸⠟⠀⠀⠀⠿⠂⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣿⣿⣷⣤⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⣰⡄⠈⢿⣿⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⣿⣿⡇⠀⠀⠻⠇⠀⠀⠀⠾⡷⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠈⠁⠀⠀⡀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣇⠀⣀⠀⠀⠀⣤⠀⠀⠀⠀⢠⣾⣿⡄⠀⠘⠃
⠀⠀⠀⠀⢀⣿⡿⠃⠀⣤⡄⠀⠀⠈⠛⠀⢠⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⠀⠙⠁⠀⠀⠛⠀⠀⢀⡀⠀⠙⣿⡇
⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⠀⠀⠀⠀⢀⡴⠋⠀⠻⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⢻⣷⡤⠶⠶⣤⠀⣀⠀⠸⠟⠀⠰⣿⡇⠀⡀
⠀⠀⠀⠀⠀⢻⣷⡀⠶⠆⠀⠘⢣⡴⢻⠀⠀⠀⠀⠈⠙⡇⠀⠀⠋⠻⣿⣿⣿⣿⣿⡿⡇⠀⢰⠀⠈⣷⠀⠀⢼⠀⠀⠹⣦⡀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⢶⣯⠀⠈⠀⠀⠀⠀⠀⢀⡇⠀⡆⠀⠀⠈⠛⠿⠿⠋⠀⢸⡆⠀⠀⢀⡟⠀⢠⡎⠀⠀⠀⢸⣿⡀⣼⡏⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢿⡆⢰⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢻⡇⢠⡏⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⠀⠀⠀⠀⠀⠈⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣈⣥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣸⠀⠀⠀⠀⠀⠘⡂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡇⠀⠀⠀⠀⠀⠠⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷

⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠦⠀⢀⣾⣶⣦⠀⠀⠀⡀⣀
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠘⠉⠒⠀⠀⠀⠀⠀⠙⠀⠀⢠⣠⡤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠃⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠩⠗⣄⠀⠀⠀⠀⣠⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠀⠀⠙⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⡠⠊
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡖⣳⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠈⠃⠀⢀⠀⠀⠀⠑⠘⠃⠀⠀⠂⠀⠀⠃⢨⠀⠀⠀⠀⠀⠠⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠄⠀⢀⣤⠎
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⢸⡆⡇⡏⡆⢸⠉⠂⣧⢸⠀⡎⣻⣦⡇⠀⠀⠀⠐⢏⠠⠀⠀⠀⢀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡟⢣⡖⢧⡁⡷⡁⢀⢑⣴⠺⣸⡀⢇⠙⠹⡇⢀⡔⠀⠀⡀⠋⠀⠀⣴⣿⠏
⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⠈⣁⢁⠁⠈⢉⠀⠀⢀⠉⡈⠀⢀⠀⠈⠇⠠⠈⢀⠄⠒⡄⠘⠃⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠛⠁⠀⠀⠀⠐⠀⠂⢤⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠞⢡⠄⠀⢢⡀⣧⠀⠀⠀⠀⢀⣴⠏⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⢀⡰⠋⠀⢢⠀⠀⠀⢳⣿⠀⠀⢀⠐⠛⡿⠀⠀⠀⠀⠁
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢲⣎⠁⠀⠀⠀⢀⡏⠙⠶⢤⡈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⣐⢦
⠀⠀⠀⠘⡆⠀⠀⠠⠀⠙⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢇⠅⠀⠐⠂⠓⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⠀⠁⣴⠊⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⢋⠶⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠂⠀⠀⢉⡈⠀⢸⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠰⠿⡿⢧⠀⢸⡇⠀⢸⡇⠀⠈⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠀⠈⡁⠀⣄⣤⠀⠀⡇⠀⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠁⠁⠛⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠈⠉⠁⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠐⠈⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠐



⠀⠀⠀⠀⢀
⠀⠀⠀⢴⣿⣷⣄⡀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⠟⣠⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠀⠀⠀⠐⠪⣷⣄⠀⠑
⠀⠀⠀⢀⣼⡿⠛⠉⠉⠉⠀⣸⡿⠁⢠⠊⠀⠀⣤⣤⡀⠀⠀⢀⣤⠄⠀⠀⣶⡆⠀⠘⠉⠹⣷⣄⠀⠀⠀⠀⠀⠉⠳⡤⡄⠀⠀⠀⠢
⠀⠀⠠⠟⠉⠀⠀⠀⠀⠀⣰⣿⢁⡠⠁⠀⠀⣰⣿⣿⠁⠀⢸⣿⣿⣷⠀⠀⢹⣗⠀⠀⠀⠀⠹⣿⣦⡀⠀⡏⠉⠆⢀⡰⢃⡀⠑⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⢛⡿⠏⠀⠀⢸⣿⣿⣿⠀⠀⠈⣿⡄⠀⠀⠀⠀⠹⣿⣷⣄⡈⠁⡛⠁⢸⠁⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠈⠂⡸⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠃⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⡠⠄⠒⠲⡧⠤⣀⡀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⠀⠀⠀⣰⠃⠀⠀⠈⠉⢺⣿⣿⣿⣀⡀⠀⠀⠘⡄⠀⠀⠀⣀⡠⠜⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠒⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠉⠉⠉⠉⢹⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⡀⠀⠀⡔⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⢀⡠⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⢀⣴⠟⠀⠳
⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠃⠟⠀⠀⠀⠀⠀⠀⠰⠃⡠⠞⠁⠀⣤⣄⡀
⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠘⠤⠘⢠⣶⠟⠙⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⣀⠀⡀⢘⣮⡙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠤⠖⠛⠁⠈⠉⠀⠉⠉⡟⠛⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⢀⡀⢀⣾⣄⠀⠚⠀⠀⠀⠀⠀⠀⠶⠂⢀⠇⠀⠙⢷
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠒⠸⠈⠁⠀⠤⠆⠀⠀⠀⠀⠀⢀⣠⣶⠄⢹⠄⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠹⣾⡖⣠⠇⠸⠀⠀⢳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠄⠐⠚⣇⡿⢓⣾⣆⠀⠀⢇⣤⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠋⠁⠀⠀⠠⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠁⢀⡾⠋⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣀⣠⣴⠟⠁⠀⠀⠀⠀⣰⠋⠁⠀⠀⠈⢻⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⠀⠀⠀⢠⡀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣡⣴⣶⣦⡤⠄⣀⡀⠀⠀⢀⣼⠃⠀⢀⣴⠋⠁⠀⠀⠀⠐⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⣿⣿⣿⠋⠀⠀⠈⠙⠛⠿⠟⢃⠀⣰⠟⣁⡤⠶⠂⠀⠀⠷⡄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢿⣿⠃⠀⠀⠀⣴⠀⠀⠀⣴⣿⡟⠁⠀⠁⣀⠀⣀⡀⠀⢠⡀⣀⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣠⣾⡟⠀⣀⣼⡏⢹⡇⠀⠀⠈⠉⠛⠉⠁⠀⠀⠙⢾⣟⡻⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣠⢌⣠⣴⣾⡿⣏⣴⣾⣿⠏⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢟⣽⠿⠛⢩⣾⢫⣿⡟⠁⠀⡀⠁⠀⣀⣀⡀⠀⠀⠀⠀⡴⠟⠁⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣾⣿⢸⡁⠀⠀⢸⡇⢻⣿⡇⢀⣾⠁⠀⢾⣿⣿⡿⠂⠀⠀⠈⠀⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠹⣿⡄⢻⣷⣦⣀⠁⡀⠹⣧⣿⡇⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠈⢻⡄⠹⣿⣿⣷⡜⡄⢹⣿⠁⠀⠀⠙⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢻⣷⡄⡿⠀⢹⣿⡿⣿⢃⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⡿⠁⣠⠟⣡⣾⣿⡿⠋⢿⢷⡈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠟⢁⣼⣡⠾⣿⣿⠋⠀⠀⢸⣧⠻⣦⡀⠀⠀⠀⠀⢠⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠇⠀⣸⣿⠇⠈⣿⡇⠀⠀⠀⣸⣿⡇⢈⣿⣄⠀⠀⠀⠀⢇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠰⣿⣿⣦⠀⠈⠻⣄⣠⡴⠟⠛⠁⣼⣿⡿⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢀⣴⣿⣿⡙⠳⢦⡐⢿⣯⡀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣾⣿⣿⡿⠁⠀⠀⠹⡆⠙⣿⡀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠫⠀⠀⠀⠀⠀⣧⣴⠟⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⡷⠀⠀⢠⣿⠀⠀⢠⡇⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣠⠔⠋⠀⠀⢰⣿⠇⠀⢠⣿⡵⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠻⣷⣄⠉⠈⠇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠉⠃⢀⡘⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠲⠦⣌⠳⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠸⣁⣱⠆⠀⠀⠀⠀⠀⠛⠣⠀⠀⠀⠀⠀⠀⢀⡴⣋⡥⢤⡁⠈⠇⡇⣸⠇⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠔⠉⠀⢠⠄⠱⡌⢣⡀
⠀⠀⣞⠉⠉⠉⠀⡴⠋⠱⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡞⡼⠋⠀⠀⠀⠀⠀⠸⢥⡄⠀⠀⠀⠀⠀⣰⠃⠀⡴⠃⡠⠶⠚⠁⠀⠀⢸⡄⢷
⠀⠀⡿⠟⠀⣠⠤⣙⡆⠀⣒⠀⠀⣒⠀⠙⢊⡇⠀⠀⠸⡇⠇⢤⠀⠖⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⡟⠀⣼⠁⡀⠀⠀⠀⠉⠁⠘⠀⣇⠸⡇
⠀⠀⠹⠒⠂⢙⡶⠞⠁⠀⠀⠀⠀⠀⠀⣴⢋⠀⠀⠀⠀⢳⡀⠀⡀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⣇⠀⣏⠀⠉⠀⠀⠀⠀⠀⡄⠀⣿⠀⡇
⠀⠀⠀⠀⠠⠇⡀⠄⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⢦⡀⠀⠀⠠⠀⠀⠀⠀⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠨⠁⠀⠀⠀⠀⠀⡰⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁

⠀⠀⠀⠀⣠⡤⢤⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠸⠀⡤⠠⠖⠄
⠀⠀⠀⡾⣵⣚⠏⠁⠈⣉⣩⡭⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠉⢀⡴⢋⡩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⡄⠲⢄⡀
⠀⠀⠀⢧⠀⠀⣈⣉⣩⠏⠁⠀⠀⠠⠀⠀⠀⠀⢀⠴⠚⠉⠉⠁⠀⢀⣴⠋⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⡀⠂⠀⠐⡀
⠀⠀⠀⠀⠑⠀⢨⢉⠀⠀⠀⠰⠆⢠⠀⠀⠀⠐⠁⠀⠀⣀⣠⣤⠴⠛⠁⣸⠃⠨⠅⠀⠼⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠰⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠠⠀⡍⢀⡄⠄⢒⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡠⠀⣦⠈⢦⠀⠄⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠁⠀⠉⠰⢃⠀⠀⠀⠀⠀⠀⠀⢠⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡜⢀⠇⢠⠃⠀⠀⠀⠈⠀⣰⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⡀⡆⠀⢀⢀⠀⠀⠉⠀⠀⠀⠀⠀⡔⠈⢀⣤⠞⠀⠀⠀⢤⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠁⢸⠀⣼⠀⠲⠀⠀⠤⢲⡏⠀⠀⠀⠀⠀⠀⠈⠀⣄⠰⢀⡀⠀⠸⡈⠇⠀⠄⠀⠀⠀⠀⠀⠑⠄⠸⡦⠂⠀⠰⠆⠘⠲⡌⢢⠰⡀
⠀⠀⠀⠀⠀⡌⠀⣿⠀⣯⠀⠀⠀⣀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠖⠀⠠⠇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⢠⠟⠀⡀⠀⠀⠀⢺⡁⠂⠀⡸
⠀⠀⠀⠀⠐⠀⠀⢻⠀⢃⠀⠀⠀⠁⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠑⠀⠈⠒⣄⠀⠀⠀⠀⠾⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠻⠍⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠂⠉⠐⠒⠛⡇⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣀⡴⠶⠒⣺⠗⠚⠿⡿⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡾⠋⠀⠀⠀⣧⡘⠃⣀⡇⠀⠀⠀⠉⠛⠶⣄
⠆⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⢀⣾⠁⠀⠀⢀⣀⡀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠃⠀⠀⢠⠎⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡶⠆⠀⢀⡇⠀⠀⠐⢆⣳⠶⣦⣤⣤⣤⣤⡤⠴⠞⠋
⠀⠰⡧⠀⠀⠀⠀⣀⡀⢀⡞⣸⠀⠀⠀⠈⣇⣀⡠⠃⠀⠉⢹⠇
⠀⠀⠛⡄⠀⠀⠀⣇⠓⢋⣠⢿⠀⠀⠀⠰⢤⣭⠄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡀
⠀⢀⢃⢘⣒⠀⠀⠀⠉⠉⠀⢸⡇⠀⠀⠀⠴⠷⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡞⡵⠙⣳⠘⡆
⠀⢛⣿⣿⣿⣄⠀⢀⣀⣠⡴⣾⠛⠒⠒⠲⠶⢶⠶⢶⡶⡖⢻⣤⡀⠀⠀⠀⠀⠀⡇⠱⠤⠊⣀⠉⠒⢤⠤⠤⠤
⠀⠀⠀⠉⠙⠉⠉⠉⠉⠀⢀⡏⠀⠀⢀⡞⠀⡏⢣⡞⢡⠘⡜⣇⠙⠳⠶⣤⠴⣿⣤⡔⠒⠉⠀⠙⠲⡇⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡠⢧⠀⣧⠃⠘⣮⠀⡇⢻⡀⡀⠀⠀⡐⢰⣿⠃⠀⠀⠀⠀⠀⠘⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣶⠧⢤⡤⠼⣇⠇⠸⡇⠀⠸⠰⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⣤⣤⣄⣼⠛⠛⠛⡟⢻⣤⡤⠷⠀⡇⢸⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢼⣇⠀⠀⠀⢀⣯⡤⠤⢤⡀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⣶⣒⣬⣆⣀⣀⣮⣔⣒⣖⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠊⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⣀⣴⣾⣿⠿⠛⠛⠛⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⣠⣾⣿⡿⢋⣤⡶⠛⣉⣤⣤⣤⣌⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⢀⣼⣿⣿⠏⣠⣿⠋⣠⣾⣿⡿⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⢠⣿⣿⣿⠃⣰⡿⠁⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⣰⣿⣿⡿⠁⣰⡿⠁⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣰⣿⣿⡿⠁⢰⣿⠁⠀⢸⣿⣿⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⣰⣿⣿⡿⠁⢠⣿⠃⠀⠀⢸⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠃⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⢀⣼⣿⣿⡿⠁⢀⣿⠇⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠁⠀⣠⣿⣿⣿⡿⠁⢀⣾⠏⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠀⠀⣠⣾⣿⣿⣿⡟⠁⢀⣼⡏⠀⠀⡆⠀⠀⢀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠲⢤⣀⣀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⡿⠋⠀⢀⣾⠏⠀⠀⢠⡇⠀⠀⣿⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢀⣴⠟⠁⠀⠀⢀⣾⠇⠀⢀⣿⠀⠘⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠠⠔⠚⠋⠁⠀⠀⢀⣴⣿⡟⠀⠀⣸⡟⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠋⢀⠀⢰⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠉⢀⡠⠃⢠⣿⡟⠀⣠⠀⠈⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⠀⢀⣠⣴⠟⠁⣰⣿⠟⠀⣰⠇⠀⠀⣿⣿⣿⣿⣿⠃⣸⣧
⠀⠀⠀⣠⣾⣿⠿⢛⣩⡥⠖⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠁⢀⣾⡿⠋⣠⣾⠏⠀⠀⢀⣿⣿⣿⣿⡟⢀⣿⡿
⠀⠀⣼⣿⠟⣡⣴⠟⠉⠀⢀⣤⣶⣿⡿⠿⠛⠋⠁⠀⢀⡴⠟⠉⣠⣶⣿⠋⠀⢀⠄⣸⣿⣿⣿⡟⠁⣼⣿⡇
⠀⢰⣿⠁⣴⡿⠃⠀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠟⠁⠀⣠⠏⣰⣿⣿⡿⠋⣠⣾⣿⡿
⠀⢸⡇⢸⡿⠁⢠⡾⠋⠁⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⡾⠃⡰⠟⠋⢁⣤⣾⣿⣿⠟
⠀⠀⠀⣿⠃⠀⠈⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⣀⣠⣴⡿⠋⠀⢀⣠⣴⣾⣿⣿⣿⠟⠁⡀
⠀⠀⠀⡏⠀⠀⣠⣾⣿⣿⣿⡿⠟⠋⠉⢀⣀⣤⣴⣶⣶⣿⠿⠛⠁⣠⣴⣾⣿⣿⣿⣿⠟⠋⠁⢀⡼⠁
⠀⠀⠀⠃⠀⣰⣿⣿⣿⡿⠋⠀⢀⣴⣾⡿⠿⠛⠛⠉⠉⠀⣠⣶⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣠⣴⣿⠟
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠞⠁⠀⠀⣠⠖⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣠⡞⠁⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣼⡟⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⢀⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⡿⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢹⡏⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⣧

⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⡀⠀⠀⢀⣦⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢋⠉⠉⠀⠀⣾⠿⢛⠛⠀⠀⠀⠐⠠⣆
⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⡶⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠁⠀⠀⠉⠀⠀⠰⡦⠾⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠳⣄⠀⠀⠀⠀⠀⣠⠞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠣⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⢤⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠬⠁⠀⠀⠀⠈⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⢴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠘⢔⢾⠇⠀⠀⡀⠀⠀⠀⠂⢡⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣆⠀⠀⠀⠀⢀⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠄⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠄⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⡀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠸⡇⢨⢿⢱⠀⢯⠈⠃⣿⠀⡇⢰⡍⣿⣇⡇⠀⠀⠀⠀⠘⢏⠐⡀⠀⢠⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡗⣇⡷⢷⢸⡸⢎⠀⣀⠱⡄⠿⡇⡇⠸⡁⠇⠹⡇⠀⣠⠂⠀⠀⠀⠟⠁⠀⠠⣶⣿⠍
⠀⠀⢀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠈⠊⠉⠘⠀⠙⠚⠉⠀⠁⠙⠃⠉⠀⠀⠁⠀⢋⠀⡀⠂⠁⣀⠤⣄⠈⠻⠁⠀⠀⠀⠀⣤
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠐⡀⠀⠀⠁⠀⠈⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠋⠈⠀⠁⠈⠀⠀⠀⠁⡠⠀⢨⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣠⣴⠾⠛⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢣⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⠞⢁⠻⠀⠀⠱⡄⢸⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠂⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⢄⡔⠁⠀⢈⠆⠀⠀⠀⠹⣾⡇⠀⠀⢠⠂⠉⠻⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠓⠒⠲⣖⠁⠀⠀⠀⠀⢀⡟⠉⠳⡦⢄⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠉⠁⢲⡄
⠀⠀⠀⠀⠛⡀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⣏⣹⠀⠀⠠⠤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⢐⠁⣠⠖⠉⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠑⠲⠖⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⢀⠀⠀⠀⠞⠋⠂⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣼⣶⣤⠀⠀⢰⠀⠀⢰⡇⠀⠀⢸⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠈⠉⠋⣉⠄⠀⢸⠀⠀⠘⠇⠀⠀⢸⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡄⠀⠲⠒⠃⠀⢸⣀⡄⣿⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⢀⡴⠋⠁⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠠⠶⠛⠀⠀⠀⢠⠎⠁⠀⠀⠙⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣠⣀⣀⠀⠀⠀⠀⣠⠏⠀⣠⠔⠀⠀⠀⠷⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⣾⣿⠟⠀⠀⠙⠛⠿⢋⣀⡾⢃⠤⠂⠀⠐⠆⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡏⠀⠀⣰⠇⠀⣰⢿⡇⠀⠠⢤⡤⠄⠀⢦⣤⣽⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡈⣀⣤⣾⣟⣤⣾⠏⢸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⡽⠟⢩⡿⣿⡟⠁⣀⠀⣀⣤⣀⠀⠀⢀⠞⠃⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢿⡇⢧⣄⠀⠇⠻⣇⣴⠇⠀⠛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠻⡌⢻⣿⣦⣀⢹⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣧⡛⢀⣿⢿⣟⣼⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠟⣠⢎⣴⣿⠟⠁⢸⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠅⢠⣿⠏⢻⡇⠀⠀⣸⣷⢘⣧⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢺⣿⣦⡀⢙⣤⠞⠋⠁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣴⣿⣿⠀⠉⢪⡛⢷⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⠀⣧⠞⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡰⠃⠀⣴⠇⠀⣼⡀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⢿⣄⠘⠹⠁⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠄⠀⠀⠀⠈⢑⡀⠀⠀⢀⠼⠁

⠀⠀⠀⠀⢀⠴⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠐⢀
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒
⠀⠀⠀⠀⠉⣉⣽⣿⠿⡏⠁⠀⢠⠊⠙⢲⣀⡞⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⣿⡿⠏⠁
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⢸⡀⠀⡰⠉⢧⡀⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⢁⣠⡆
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡇⠀⠀⠀⠠⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠏⣀⣤⣶⡇⠀⠀⠀⠀⠈⢄⢄⠀⠀⠂⠀⠀⠀⠠⡈⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⠇⠀⠆⠀⠐⠀⠠⠤⡴⡆⠀⠀⠀⡟⣁⣤⣶⡇
⠀⠀⠀⠀⠀⣿⠿⠛⢁⡇⠀⠀⠀⠀⠀⠈⡀⢱⠄⠀⠀⠀⠀⠀⠑⢀⣀⣀⡐⠁⠀⠀⠀⠀⠀⡜⠀⡈⠀⠀⠀⠀⢐⠒⠺⠅⠀⠀⠀⣿⡿⠛⠉⡀
⠀⠀⠀⠀⠀⣁⣤⣾⡿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠹⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⢒⣚⣩⡅⠀⠀⠀⣏⣤⣶⡿⠇
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇⠀⠌⠀⠀⠀⠀⠀⠠⣬⣤⡇⠀⠀⠀⡿⠛⢉⣠⡦
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠌⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠨⠥⢖⡂⠀⠀⠀⣵⣾⡿⠟⠁
⠀⠀⠀⠀⡀⠋⢀⣤⣾⢇⡀⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⠀⠀⣘⠓⠒⠇⠀⠀⡀⠛⢁⣤⣶⠗⡀
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠤⢀⣀⣀⣀⣀⠉⠉⡉⣙⣁⣀⣈⠥⠂⠀⠀⠀⠀⠀⠂⠈⠭⠅⠀⠀⠠⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠈⠢⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⢠⠀⠀⢠⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣤⡏⠀⠁⠀⠀⠀⠂⢸⣧⡆⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡟⡤⠀⠀⠀⠀⠀⠀⢠⠙⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠓⠶⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⡀⠀⠀⠀⠀⠀⠀⡰⠃⢠⣥⣤⡤⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠶⠂⠀⠀⠀⠈⠬⣿⡗⠢⠀⠀⠀⠀⠴⢪⣿⡯⠂⠀⠀⠀⠀⠀⠀⢈⡧⠄⢻⡇⠀⣹⠢⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣄⢀⠀⠀⡌⢠⡘⣉⠀⠀⠀⠀⠀⢀⣤⠎⠈⢻⣆⡌⠛⠛⠡⠀⣶⠋⠁⢦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⡿⠅⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠈⠓⠖⠒⠒⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠆⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠋⢉⠉⠙⠳⢌⣡⣴⣾⡷⠗⣂⣤⣤⣾⢟⣡⣶⣿⣿⣿⣶⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠈⠉⣶⣿⡿⣱⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⢀⣴⣾⣿⣿⣿⡆⢻⣿⣧⢻⡀⢸⣿⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣯⣿⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⢀⣾⣿⣿⣿⢿⣿⣿⣆⡙⢿⣮⣧⡈⢿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣾⣿⣿⣿⣿⣧⡛⢿⣿⣿⣦⣝⡻⣿⣶⣭⣛⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⡿⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⠀⢰⣿⣿⣿⣿⣎⢿⣿⣷⣝⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣟⣛⣋⣥⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢸⠀⢸⣿⣿⣿⡝⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⡄⠀⣿⣿⣿⣿⣮⣻⣿⣿⣾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢿⣧⠀⠸⣿⣿⣞⠋⢉⠙⣿⠏⠀⠀⠀⠀⠲⠒⠒⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣇⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⣄⣳⣤⣤⣤⣀⣀⠀⠙⠛⠃⠀⠀⣀⣤⣄⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡘⣿⣿⡀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠐⡻⣿⣛⠿⠿⣿⣿⠀⠀⠀⣠⣀⡁⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣧⢻⣿⡇⠀⣇⢻⣿⣷⣆⠀⠀⠀⠀⠀⠨⠛⠟⡖⠃⠁⠀⠀⢰⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⠿⣿⣿⣿⡇⢠⣿⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⢿⣿⣿⡇⣾⣿⣆⣿⢻⣿⡍⠻⣄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠁⠀⡾⣹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⡙⣿⣿⠛⠉⠙⢻⣿⣿⣿⢸⣿⡇⠀⠈⠻⣦⡀⠀⠀⢈⠛⠛⠋⢀⣤⡾⣵⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠏⣾⣿⣾⡇⣸⠃⣾⣿⣿⡄⣿⣿⡏⣾⣿⡇⠀⠀⠀⠘⢿⣦⡀⠀⢉⣡⣶⣿⣿⣾⣿⡿⢛⣉⣁
⠀⠀⠀⠀⠀⠀⣾⣿⣆⠻⣿⠟⢀⠇⣸⣿⣿⣿⠃⣿⡿⣱⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡶⢖⣫⣴⣿⣿⣿⠏⣴⣿⣵⣿⣿⠏⠘⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⢟⣽⡿⣹⡏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣵⣿⣥⣾⣿⣿⡿⠟⠁⠀⠀⠈⠂⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣯⡻⢿⡿⠿⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠁

⠀⠀⠀⣿⣿⢾⣿⠟⣼⣷⢸⡟⣿⢿⣿⠟⣷⡟⠀⢰⣿⡆⣿⣾⢻⡟⣷⠀⢸⣿⡇⣼⣷⢸⡟⣿⣿⠀⠰⣿⣗⢸⣿⡘⣗⣀⣾⢻⣾⣷⣿
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠛⠋⠘⠛⠀⠚⠃⠀⠛⠛⠓⠛⠛⠘⠛⠛⠀⠚⠛⠓⠛⠛⠚⠓⠛⠛⠂⠘⠛⠛⠛⠙⠛⠛⠛⠛⠛⠙⠛⠛

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣘⣉⣉⣉⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠗⠦⠀⠀⠀⠀⠈⢉⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡍⡍⠄⠀⠀⠀⠀⠐⠀⠀⠁⢸⠀⢸⠀⠀⠀⡀⢠⠀⡄⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠉⠄⠂⡀
⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠨⠀⠀⠀⢸⠀⢸⠀⠁⠀⠀⡎⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡍⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠘⠀⡇
⠀⠀⠀⠀⠀⡒⡒⠒⠀⠀⠀⠀⠩⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠡⠤⠤⠀⠀⢀⣀⣐⠀⠀⠀⠀⢠⠁⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠘⣛⣉⣁⠀⠀⠤⠤⠀⠀⠀⠀⠈⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⢂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠪⡑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣑⣒⣲⣤⣴⣲⣤⣴⣦⣤⣶⣤⣶⣦⣤⣖⣚⣁⡀⠀⢆⠐⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⡄⠈⢦⡀⠈⢷⣄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠭⠛⠒⠻⠓⠻⠛⠛⠿⠗⠿⠽⠛⠻⠭⠥⠄⠃⠀⠀⢹⡀⠈⢷⡀⠀⠙⢧⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠄⠀⠀⠀⠈⣧⠀⠀⠻⡀⠀⠀⢧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠻⠄⠀⠈⢂⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠥⠶⠒⠦⠖⠾⠷⠳⠿⠞⠯⠽⠿⠮⠭⢉⣑⡆⠀⠀⠀⢎⠀⠀⡀⠻⠆⠀⠀⠀⢀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠚⠉⠙⠚⠉⠑⠋⠙⠚⠉⠓⠋⠉⠓⠲⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉

⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣟⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠀⣸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣶⣿⣿⣿⠟⢀⣴⡿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⠿⠟⢋⣠⣴⢟⣽⣿⡟⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⣛⣉⣩⣤⣶⠾⠛⣉⣴⣿⣿⠏⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠶⠛⠛⠛⠉⠉⠀⣀⣴⣾⣿⣿⣿⣵⣿⠟⢁⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢁⣀⡠⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⠋⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⢟⡥⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢶⢶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⠗⣡⣾⣿⣿⣿⡿⢋⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠸⡟⣸⣿⣿⣿⢿⡟⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⢸⡇⠀⣿⣿⣿⡿⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⠘⣷⡀⠙⣿⣿⣧⡞⠀⠢⡀⠈⠉⠉⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⠈⠻⣦⡈⠻⣿⣷⠀⠀⠈⠂⠀⠀⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠓⠄⠈⠻⣦⣄⠙⠷⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠐⢄⡀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣍⡒⠤⣄⡀⠠⣌⣙⠷⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣭⣷⣤⡙⣿⣦⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⣌⣙⢿⣿⣿⣷⠘⣿⣿⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⡿⢋⣼⣿⡿⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣵⣾⣿⣿⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁

⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⣈⠀⠈⠘⣿⣿⡇⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⢉⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡌⢈⡉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢻⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠚⠋⢸⣿
⠀⠀⡠⠖⢒⣛⣛⣛⠒⠲⡄⠀⠀⠀⣾⣿⡿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡦⢐⣷⡆
⠀⠀⡓⠶⠤⠭⠭⢭⢤⠔⣻⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡂⠀⠐⠹⠆⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⢏⠒⠦⠤⠤⠤⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠗⠷⠚⠛⠒⣄⠀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⢸⣿⣶⣿⡿
⠀⠀⠀⠁⠒⠀⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠸⡇⢠⠤⠔⠒⢲⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠸⡜⢋⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢹⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠄
⠀⠀⠀⠀⠀⠰⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⣰⢶⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠈⠻⣏⣀⡇
⢀⠤⠚⠆⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢠⠑⠁⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⡒
⠀⠀⠄⠀⢃⠀⠀⠀⠀⠀⠈⠉⠛⢦⣘⣷⠀⡀⣠⣛⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣦⠀⠀⠀⠘
⢂⠉⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠁⠀⠀⠀⠀⠀⠀⠀⢷⣺⣿⣿⣿⡿
⠀⢣⠄⢀⠈⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠛⠛
⠀⠀⠳⡤⢤⠊⡧⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⢀⠀⠰⠷⣶⣶⡶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡆⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠊⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠤⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠢⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠉
⠀⢰⠀⠀⠀⠀⠀⠤⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⢀⠀⠼⠂⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡾⠑⠒⠓⠒⠬⣉⠹
⠀⠀⠓⠀⠀⠀⠀⡀⠙⢄⡠⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠈⡀⢀⢠⠀⢑⡬⠂⠀⠀⠀⠀⠀⠀⠁⣀⣠⣶⣒⣓⣓⣶⣀
⠀⠀⠀⠀⢀⡴⠛⠷⡤⠊⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⠠⠄⠀⢠⡤⠒⠁⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠢⡀⠀⠒⢀⡤⠚⠁⠀⠀⠀⠀⢀⣸⡍⢆⠀⠀⠀⠘⣿⣿⣉⣉⡉⠛⠛⣿⣿⡇⠀⠀⠀⢠⣤⡴⢦
⠀⠀⠘⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⢈⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢧⣠⠏
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡤⠴⠶⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣀⣠⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢦⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠝⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠰⠍⠉⠉⠋⠙⠭⡆⠀⠀⡠⠤⠤⣤⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠂⠀⠰⠂⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢲⡐⣀⣿⠀⠀⠈⢹⠁⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠄⠁⠀⣠⢀⡀⠀⠀⠈⠀⠁⠁⠀⠀⠀⢸
⠀⢀⡴⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠈⠉⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠠⠆⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠰⠃⠀⠀⠐⠀⠀⠀⠠⣂⠄⠀⠀⢰⠀⠀⠃⠀⠀⠰⠘⡄⠀⠀⣗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡠⠄⠈⠁⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠌⠂⠀⠀⠀⣀⠔⠉⢀⡴⠊⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠄⠂
⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⢀⠤⠊⢀⡠⠞⠁⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⡠⡠⠁
⠤⠈⠀⡀⠄⠀⠀⠀⠀⡠⠖⠁⣀⠔⠋⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⠂⠀⠀⠀⠒⠀⠀⠀⣴⣾⣧
⠘⠁⠀⠀⠀⠀⣀⠔⠊⢀⡤⠚⠁⠀⠀⠂⠀⠀⢀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠀⠸⣿⣿⡡
⠀⠀⠀⠀⡠⠞⣡⢀⠖⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⣠⠺⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⠀⣀⠔⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⣀⠈
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣤⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣠⣈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⠾⣦⣝⡻⣶⢬⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣴⣝⡻⣶⡽⣪⣝⠻⣮⣕⡻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⡾⣶⣝⡻⢗⡽⣪⣝⡻⢶⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢧⡀⠀⠀⠀⠀⢀⠞⠀⠀⢠⣟⡻⢶⣭⣺⢕⡻⢶⣭⡻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢳⡄⠀⠀⢠⠎⠀⠀⣰⢷⣭⡻⢷⡯⣞⣝⡻⢶⣭⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠹⣄⢠⠏⠀⠀⣰⡻⢶⡭⣛⢕⡫⢶⣭⡛⠷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢧⠀⠀⣰⣯⡛⢷⡮⣗⣽⡻⢷⣬⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡾⣾⢳⣰⢷⣮⣛⢿⣺⢷⣯⣛⠷⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡍⠁⠀⠹⣷⣮⢕⣯⣚⠷⣮⣙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⣆⣀⠀⠈⢾⣕⣮⣛⠷⣮⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⡄⢹⠳⢤⡑⢮⣝⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠔⢳⡘⡗⠲⠽⣮⡻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⡰⠁⠀⠀⢃⢣⠀⠀⠀⠑⣌⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⡼⠁⠀⠀⠀⠘⡌⢆⠀⠀⠀⠈⢆⠀⣩⠭⢭⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⣧⠈⢦⠀⠀⠀⢸⢸⠁⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⡆⣠⠤⣽⣲⣄⣸⡼⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡜⣼⠁⠀⠀⠙⢯⣧⠞⢝⠦⣄⣠⡴⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢱⣹⡀⠀⠀⠀⢸⣿⡄⠀⠉⠓⠒⠋⠣⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢦⣀⣀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠙⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠓⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠂⠇⠀⠀⠈⠈⡃⠀⠀⠀⠃⠀⠀⠀⢀⠄⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠂⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣤
⠀⠀⠴⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢱⡆⠀⠀⠀⠀⠀⠄
⠀⠀⡇⢀⠖⠉⠁⠉⠢⡀⢰⠉⠉⡆⡊⠀⠙⠄⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠞⠃⠀⢀⠀⠀⠀⢀
⠀⠀⡇⡌⠀⠀⠀⠀⠀⠱⠈⡲⣒⠁⢙⡶⡊⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⠀⠠⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠄
⠀⠀⡇⠡⡀⠀⠀⠀⠀⡔⢸⠀⠀⡇⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⡅⠀⠬⠀⠀⢀⣀⣀⡀⠀⠠⠀⠰⠀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⣇⠀⠑⠢⡤⠄⠊⠀⠀⠉⠉⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠌⡆⠀⠀⠀⡇⠘⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⡈⠂⠀⠰⠰⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠁⠀⠀⢮⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡾⢩⠏⢿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⢀⠠⢄⡀
⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⡅⡆⠀⠹⢍⡘⢹⠀⢀⠔⠛⠋⠲⡄⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⢻⡀⢀⢈⡬⢷⡾⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⢠⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠢⡉⠓⠛⠛⠉⠀⠀⠀⠓⠤⠤⠖⠁⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⢄⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠀⠘⠀⠀⠀⠀⠸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢡⠇⠀⠀⠀⠀⠀⠀⠰⣶
⠀⠀⠀⣄⠀⠀⠀⢷⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⡴
⠀⠀⠀⠸⡄⠀⠀⠸⡆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⢷⠀⠀⠀⢻⡀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡼⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠈⣧⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢩⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠃⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⢹⡄⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣰⠇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢷⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡰⠋⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠛⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠉⠀⠀⠀⠀⣎
⠀⠀⠀⠀⠀⣠⠖⠁⠹⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡇⠐⣆
⠀⠀⠀⠀⡼⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⢃⠄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠘⢧
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡘⣆⠀⠀⠰⡷⢋⠆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⣧
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢷⣜⣦⠀⠀⠀⡼⢀⡶⠀⡄⢀⡀⣸⠁⠀⠀⠀⠀⢸⡆
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣄⠸⡄⠉⠀⠀⢠⡇⣸⠇⢼⠃⣾⢁⠇⠀⠀⠀⠀⠀⠀⣷
⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⢻⠰⡆⢹⡆⢻⡄⢡⠀⠀⠀⠸⠠⢹⠠⢿⢰⢹⠸⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⣼⠀⠀⠀⠀⠀⡴⠹⡆⠀⠈⣇⣿⡈⡿⡌⣿⣼⠀⠀⠀⠀⠃⠨⠜⠀⠌⠈⠀⠀⢰⠣⡄⠀⠀⠀⠀⣧
⠀⣿⠀⠀⠀⠀⠀⡇⠀⢿⠀⠀⢩⡇⢣⢳⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢻⡀⠀⠀⠀⢹⡄
⠀⡏⠀⠀⠀⠀⢸⠇⠀⠸⡆⠀⠀⠀⠘⠞⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡇⠀⠀⠀⠈⣇
⢰⡇⠀⠀⠀⠀⣼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢻⠀⠀⠀⠀⢻⡀
⢸⠇⠀⠀⠀⠀⡟⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⡆⠀⠀⠀⠸⡇
⢸⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⢿
⡏⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸
⠃⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⠀⠤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⠶⠾⠟⠛⠛⠛⠉⠉⠉⠉⢉⣛⠛⠛⠻⠷⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠉⠉⢛⡛⠛⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠓⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠀⠐⠂⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡠⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠹⡿⠋⠀⠀⢀⠀⠚⠉⡛⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠠⠱⡱⣠⣠⠃⠀⠐⠄⠃⠀⠀⠈⢛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠦⣄⣣⣿⣿⣿⠃⣠⡀⠀⠀⠀⠲⢄⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠉⠉⢻⣿⡀⢹⣷⡀⠀⠀⠃⠈⠴⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⠶⠟⠛⠾⠟⠋⠉⣩⡽⠟⠋
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠙⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠷⠦⠄⣀⣤⠔⠉⠒⠦⡤⠠⠄⠀⠀⠛⠿⠷⠟⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿⣷⣆⡀
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠐⠶⣖⠀⢡⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡠
⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣈⠲⣄⠀⠀⠀⠀⠀⠀⣸⣷⣦⣄⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠿⠛⣇⠈⢻⡇⠰⡀
⠀⠀⠀⠀⠀⢹⣶⣄⡀⠠⡀⠀⠁⠀⣱⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢰⣿⠀⠘⠀⠀⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣬⣲⣤⣰⡾⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢿⡄⠀⠀⣸⠇
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣡⣼⡿⠿⠿⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⠃⢡⠀⠀⢻
⠐⠿⠿⠟⠫⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣸⠁⠀⠘
⣀⣀⣀⣀⣀⣉⣛⣉⣀⣙⣛⣛⣃⣻⣿⣿⣿⣿⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣋⣀⣀⣀⣃⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣿⣯⣽⣿⣽

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⣼⡏⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢉⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣧⢀⣴⠟⠁⣸
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢨⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⣥⡤⠔⠁
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢹⣿⠄⢉⡆⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠶⠿⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠦⠄


⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⢸⠁⠙⢿⣝⢮⡹⣧⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡟⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⡄⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢀⣀⢨⣿⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⡇⣿⠆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣾⣫⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠘⠉⠉⠉⠁⠙⠖⠃⠀⠀⠀⠀⠀⠀⠿⠶⠶⠇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠿⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠺⠋⣀⠀⠀⣀⠛⠗⠀⠀⠀⠀⠀⠀⠀⢪⢔⡵⡃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⣫⢞⡅
⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣕⣡⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠃

⠀⠀⠀⠀⠀⢴⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⡀⠀⠀⠀⢠⣶⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣠⠂
⠀⠀⠀⠘⣿⣿⣿⣿⣧⢠⣿⠀⡀⠀⣸⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡞⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣼⣿⢀⣷⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⡴⠋⡏⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⠃⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢹
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⡟⠀⠀⠠⠚⠻⢀⣼⠀⠀⠀⠀⠀⠀⡔⠛⡏⢀⡎⠀⠀⠀⠀⠀⠀⠊⢩⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠇⠀⢸⣿⣿⣿⠟⠀⠀⠀⠐⠄⢻⠃⢨⠀⠀⠀⠀⠀⠀⠃⠐⢻⠁⡹⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢯⠀⠁⠀⠀⠀⠀⠀⠀⣴⣿⡟⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢟⠔⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠗⠅⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟
⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢝⢝⠏
⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠂⠀⠀⣴⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⠀⠺⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣠⣶⠀⠀⠀⣼⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡌⠁⠙⢷⡀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⣼⣿⠁⠀⢀⣼⡿⠃⠀⠀⣰⠟⠁⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⢠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣠⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⣾⣷⣷⡇
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠛
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⣿⠛⡿⢿⡿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢻⠿⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⡠⠶⠖⠀⠖⠀⠆⠀⠆⠀⠛⠒⠠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀⣈⠁⠀⢠⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣀⠀⢐⠀⠀⠁⠀⠀⠄⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡯⠖⠀⠀⢹⠁
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⢒⠒⠐⠂⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠓⠋⠉
⠀⠀⠀⠀⠠⡀⢰⠀⠀⡆⡆⠘⠀⠀⡇⠀⠀⡏⠀⠀⡔⢸⣽⢲⡄⢁⣈⠀⠀⢀⡀⠐⠃⠀⢀⠉⠀⠀⠘⡁⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠁⠈⢀⠟⠛⢻⡁⠀⢠⡇⠄⢠⠃⠀⠸⣚⣚⣗⣰⡇⢀⠀⠀⠀⠈⠀⠀⠀⣰⠛⢿⡄⣴⠀⠀⠀⠀⣄⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠈⠁⠀⠀⠙⢋⠏⠃⠄⢀⠁⠀⡀⢠⠀⠀⠀⠘⠳⠾⠃⢸⠀⠀⠀⢰⡟⠊⠃⠀⢠
⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⣿⠀⠘⠓⠀⠀⢸⢠⡖⠀⠸⠀⢰⠀⢸⠀⢀⣇⢀⠀⠀⢰⠛⠉⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠈⠆⠀⢰⠏⣀⠯⠀⠀⠀⠈⢸⡇⠀⠀⠀⢸⠀⠈⠀⠐⠶⢺⡀⢀⡀⠧⠔⠰⠶⠆⠀⠀⠐⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢒⡋⣀⢹⠀⠀⡄⠀⠀⠠⠁⠆⡏⠀⢸⠀⠀⢠⡆⠀⠀⠀⠈⢱⢸⠀⠀⢆⠉⠀⠀⠀⢰⡇⠀⠁
⠀⠀⠛⠒⠋⠁⠀⠀⠀⠸⡝⠹⢸⡀⠀⠳⠀⠀⡄⠀⠀⠁⠴⠞⠀⠤⢹⠀⠘⠌⠀⠀⠈⢘⠀⠀⢸
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠑⠃⠀⢡⣤⣤⡄⢰⠁⠀⠀⠀⢠⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠇⠀⠀⠀⣀
⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠓⠒⢢⣤⣤⣤⡄⢸⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⢀⡃⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠘⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠃⠀⠀⠳⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣾⡥⣄⠀⠀⢄⠀⢀⣠⠀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠁⠀⠀⢦⠀⠀⠱⠂⠀⢀⣀⣀⣨⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠖⠁⠀⠙⠛⠁⠀⢀⣀⠁⠊⡠⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣸⡇⠈⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣼⡇⠀⠀⠐⠒⠉⡄⠀⠸⣠⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⠆⠀⠛⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠁⠀⠀⠀⠡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠀⠀⣀⡜⠁⣀⠆⠀⠀⠀⠀⠀⠘⣄⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠆⠘⠀⠀⠀⠀⠀⢄⡀⠀⠌⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⠿⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⢞⡽⢐⣯⣷⣮⣍⡻⣆
⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⣿⠼⣩⣶⢿⣛⣲⣉⠳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⡄⠘⠷⣿⢸⣇⠾⢋⣤⣤⣌⠛⢾⡆
⠀⠀⠀⠀⠀⣼⠟⠉⠀⠉⠉⠀⠉⠀⠉⠉⢭⣿⢷⡀⠀⠀⠀⠀⠀⠀⢠⢞⣛⣛⡛⠳⠦⠙⠳⠙⠂⠀⠀⠉⢻⣧⢠⠁
⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⣴⠟⡛⣩⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣸⢠
⠀⠀⠀⠀⠈⣥⠤⠴⠦⠤⣤⠤⣤⠤⠶⠤⢦⡤⠉⠁⠀⠀⠀⠀⠀⢀⣴⢏⠾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⡟⣸
⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⡏⠀⢻⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⡿⢋⡴⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣿⣻⣄
⠀⠀⠀⠀⠀⣧⠉⠉⠉⠉⠀⠀⠈⠉⠉⠋⠁⡾⠀⠀⠀⠀⢀⡴⢛⣱⡿⢣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⠙⢷⣉⠁
⠀⠀⠀⠀⠀⠸⣇⡀⣠⣤⡶⠐⣶⣤⣄⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡖⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠹⣧⣐⢮⣥⣤⡤
⠀⠀⠀⠀⠀⢠⣧⣉⡉⠉⢀⡀⠀⠉⢉⡭⣼⡄⠀⠀⠀⠀⠀⠀⢀⣨⣾⠟⣴⢸⡆⠀⠀⠐⣿⣛⣿⡆⠀⠀⠀⢙⠿⠦⠭⠤
⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡘⣿⣇⣀⣾⣇⡿⠃⠀⠀⠀⠀⠀⠉⢉⣭⡴⠟⣡⢸⣷⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡼⣿⣌⢷
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⣘⣿⣮⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⢹⣎⢻⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢻⡇⠀⠀⠀⠀⠀⠀⢀⡟⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠘⠅⠃
⠀⠀⠀⠀⠀⠀⠠⣦⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢁⣴⠃⠀⡀⠀⣀⢄⢰⡄⢠⠀⣿⠃⣸⠇⣠⠀⣰⡿⠋⠉⠳⠀⠀⢠⡎⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣿⢀⢹⡇⣾⡉⣸⣧⡞⢸⡇⣼⢀⣿⢀⣿⢠⡇⠀⢹⣷⠀⠀⣀⡤⡀⣿⠀⢜⣤⣀⢀⣤⣄⢀⣶⠴⣄
⠀⠀⠀⠀⠀⠀⠘⠻⣧⣾⠃⠈⠉⠈⠉⠓⠉⠋⠻⠚⠿⠊⠈⣽⠃⠀⢀⣿⣿⣸⣋⣼⠃⣿⡀⢸⡏⢸⢸⡏⢸⣇⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡿⠀⠀⣾⣀⣿⠋⠉⠻⠂⠙⠧⡼⠷⠚⠀⠻⠛⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠞⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠤⠴⠖⠒⠲⡒⠉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢼⠉⠑⢌⠻⢆⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣣⣀⣨⠶⣀⡸⠀⠀⢉⣲⠖⠂⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⣟⢰⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠤⠤⠴⠆⠀⠀⣠⣿⠘⡀⠀⢠⣗⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⠤⠒⠊⠈⣿⠀⣇⢤⠖⠥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⢾⣻⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢭⢈⣀⣉⠶⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡀⠀⢨⠀⢈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣰⠚⠧⡀⠸⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡏⠬
⠀⠀⠀⠀⠀⠀⠀⠳⣚⣉⣽⡙⠒⣳⠸⡿⢣⡌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⠓⢤⠇
⡰⠊⠉⠉⠉⠉⠉⠉⠉⠀⠈⠛⠉⠑⡖⠀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⢂⠔⠀⠰⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⣯⣄⣠⠀⢧
⠈⠢⣄⣀⣀⣠⡤⠔⢪⠋⠀⠀⠀⡸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢽⠗⡸⢁⣠⠔⠊⠉⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⡠⠞⠁⠀⠀⢠⠀⠀⠀⠀⠀⢠⡄⠤⢴⣒⠒⢡⡪⢊⠜⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀⣀⣀⡀⢸⢳⠊⠢⣀⡀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠱⣤⣄⡀⠀⠀⠑⠒⠐⠒⠒⠊⠉⠉⠙⠦⠬⠥⡀⢹⠳⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢫⣉⣉⣉⣙⣉⣍⠁⠀⠀⠀⠈⠋⠰⠢
⠀⠀⠀⠀⠀⡅⠀⠑⠂⠄⠀⠀⠀⠀⠀⢀⣉⠁⠂⠆⢠⣀⣀⣀⣀⠀⠀⣀⣠⠇⠆⣸⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠒⠢⠤⢤⠀⣀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠘⡀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢍⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⡀⡰⠲⡄⠀⠀⠀⠀⠀⡆⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠎⠀⠀⠈⢡⠎⣀⠀⠀⠀⠀⠀⡇⠒⠒⠒⠂⠠⠬⢁⣀⣀⣀⡀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠑⡄⠰⢦⠀⠜⠀⠀⠀⠀⠀⠓⠊⠉⠉⠉⠁⠒⠒⠂⠤⠤⠀⠀⢠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚

⠀⠀⡠⠐⠈⠉⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⢀⠎⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠀⠶⢶⣤⣀
⡾⠀⠀⠀⠀⣀⠤⠀⠉⠀⠀⠀⠀⠀⡀⠀⠤⠄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢿⣶⣦⡄
⣇⠀⣤⡾⠋⠁⠀⢰⠁⠀⠀⠀⠀⠀⠈
⠹⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⠒⠊⠉
⠀⠙⠿⣦⡀⠰⠊⡀⠀⠀⠀⢀⣤⡆⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠘⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⣠⣤⠤⣤⠀⠀⠀⠈⠑⠲⠶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⠛⠛⠉⠁
⣼⣿⢱⡟⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠈⠳⢤⣀⣀⡀⠀⢀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠶⠒⠒⠒⠛⠛⠛⠛
⠹⣿⣌⠛⢁⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠉⠉⠁⠀⠱⣄⠀⠀⠀⠀⣀⠤⠖⠋

⠀⠀⠀⣠⣤⣠⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢻⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣿⣿⡇⠀⢰⡇
⠀⠀⠀⢸⣷⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⣿⣿⣷⠀⠸⠇⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣾⠀⠀⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡏
⠀⠀⠀⠀⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡞⠂⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡷⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡇
⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⣴⣧⠀⣿⡇⠀⠀⠀⠀⣿⣇⡀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⣿⢰⣾⣷⡆⠀⠀⢀⣘⣿⣧⣇⡀
⠀⠀⠀⠀⢿⣿⣿⠃⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⢠⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⢸⣿⢈⡇⠀⠀⠘⣿⠂⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠈⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣀⣤⣄⣀
⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢹⣶⣾⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⡾⠋⠀⠀⠙⢷⡄⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣋⣠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣿⣿⢶⣶⣶⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠉⠉⠉⠉⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢹⡄⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠲⠒⠓⠓⠚
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠙⢶⣤⣾⡷⠏⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⢚⣛⣾⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣈⡇⠀⠀⠀⠀⠀⣾⠉⠙⠻⣿⣿⠟⠋⠉⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⡆⠀⠀⠀⢠⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠦⣄⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⣴⡾⠃
⠀⠀⠀⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠙⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠋⠀⠀⠀⠠⣄⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢀⡀⠀⠀⠀⢈⡙⠶⣄⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢀⠀⠀⠀⠒⠙⢷⡄⠀⠀⠀⠀⠘⣆⠀⠀⠂⠙⢿⠛⠓⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠱⣄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⢧⣀⡠⠋⣀⣀⣤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⢷⡈⠳⣄⠀⠀⠀⠈⢦⠀⠀⠀⠀⠘⣶⡀⠀⠀⠈⢯⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠳⡄⠀⣠⣬⡲⡌⢳⡀⠀⠀⠀⠱⡀⠀⠀⠀⠘⡝⣆⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡴⣊⠢⣜⢿⡿⠂⠀⠹⣄⠀⣠⣦⣌⢄⠀⠀⠀⠹⡜⣆⠀⣾⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⡴⠊⠀⠈⠀⠀⠁⢀⣠⣴⡶⠞⢧⡙⣿⣿⣿⠇⣾⣿⣦⢻⠘⢦⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠋⠀⠀⠀⠀⣀⣴⣾⠟⠋⢡⡀⠀⠀⠉⠊⢛⣁⠀⠘⣿⣿⡧⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠋⠀⠀⠀⠀⣠⢞⡭⠊⠁⠀⠀⠀⠀⣀⣤⠶⠛⢉⣥⠖⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠛⣉⠀⠀⠀⢀⣠⠞⠕⠁⠀⠀⠀⢀⡤⠖⠛⠉⠀⣠⠾⠋⡁⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⡴⢛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣤⠞⠁⠀⠀⠉⢀⣤⠶⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠘⠿⠛⠡⠞⣩⣾⣿⠇⠀⣠⡴⠛⠁⠀⢀⠤⠚⠉⠀⠀⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢟⣡⠴⠚⠁⠀⠀⢀⣤⣶⣶⠄⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣟⡫⠤⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣞⣷⠦⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡈⠉⠳⢬⡙⢾⣅⢦⣀⠀⠀⠁⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢄⠈⠛⠯⡙⠣⣝⢳⣄⠀⠀⠀⠔⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠹⢦⣍⠻⣌⢷⡀⠀⢀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠉⠙⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⣦⣄⠈⠙⢦⣀⠙⠳⠈⠀⢷⡈⢩⢟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⢠⡆⠀⠀⠀⠹⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡄⠘⠈⠷⣄⠀⠁⠀⠀⠀⠀⠘⢷⡉⢀⣿
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣸⣿⠃⠀⢠⠿⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⢂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⣧⠉⠯
⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⣿⡇⠀⢰⣃⠜⠁⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⡧
⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⡇⢀⡀⠈⢁⡟⠹⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⡀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣴⠋⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡷⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠰⠄⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣵⣿⣿⠀⠀⠀⠀⢀⠏⢠⠓⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠙⠏⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢿⡇⠀⠀⢠⡾⠋⣽⠎⠀⠴⢣⣾⣿⣿⠇⡀⠀⠐⠁⠀⠠⣂⣾⣿⢿⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠐⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⢿⣥⠾⣇⠀⢐⣵⣮⣿⣿⣁⠀⠀⠀⠀⢀⠔⠀⠹⡎⠁⢹⣷⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠹⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⣠⢒⣀⣭⣶⠿⠚⣧⠙⠂⠀⠀⠂⠀⠀⠀⠀⠀⢀⣼⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⣻⠖⠥⠶⣣⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⠈⠒⠉⠙⣇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃


⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⣀⠤⠔⠛⠛⢻⣿⣿⣿⣿⣿⡻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⣞⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⢬⡿⢿⣝⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠘⠶⣄⡀⠀⠀⠀⠙⠿⣿⣿⡄⠀⠀⠈⠓⠯⢟⡿⣿⣿⣿⣶⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠃⠀⢄⡀⠀⠛⠀⠀⠀⠈⠉⠽⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⢀⣤⣆⡀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠁⢀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⢧⠀⠀⣠⠾⠥⠤⠤⠐⠀⣰⠋⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⢣⠀⠈⠻⣿⣿⣧⠰⠇⠀⠀⠀⠀⣄⡰⢁⡞⢠⠆⡞⠀⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⡀⠈⠀⠀⠀⢈⣿⡿⠀⠀⡠⠀⠀⠜⠁⠁⠈⢀⠎⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⣼⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠖⠀⢀⠔⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⣠⠂⠀⡠⠊⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁⠀⡐⠁⠀⡔⠁⠀⡠⠔⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢀⠈⠀⢠⠊⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠴⠋⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⡆⠀⠀⠈⣹⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⡄⠀⢸⡇⠀⡀⠀⢿⣿⠂⠀⣴⣶⣶⣶⣦⣴⣶⣶⣶⡄
⠀⠀⠀⣼⣿⣧⡀⠀⣾⣿⣿⣆⠀⠘⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣶⠀⠀⡇⠀⢸⡇⢰⡇⠀⢸⡟⠀⠀⡿⠉⠙⡟⠉⠙⡟⠉⠙⡇
⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢾⣿⠀⠀⣿⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠻⠦⠶⠿⠦⠾⠷⠦⠾⠃
⠀⠀⠘⣿⣿⣿⠃⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢺⣿⠀⠀⣿⡇⠀⣿⠀⢠⣷⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠐⠀⠐⠒⠒⠒⠒
⠀⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⠀⣿⠇⠀⣿⠀⠐⣿⠀⢸⡇⠸⡇⠀⠀⡇⠀⠀⠚⠂⠚⠛⠛⠛⠒⠒⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⣯⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⡟⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⡟⡇⠀⠀⢠⣤⡹⢿⠃⠀⢰⣿⣦⣤⣤⣴⣾⣷⣶⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⠀⠀⠀⠀⣬⣬⡉⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⡇⠀⠀⠼⠿⠇⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣷⠀⠘⢠⣶⣿⣿⣷⣤⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⡏
⠀⠀⢸⣿⣿⡗⠀⢁⠰⠶⠀⡇⠈⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⠀⠀⣼⣇⠀⠀⣼⣷⠀⠈⡏⠀⢠⣿⡈⠄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠿⠿⠇⠀⠸⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠸⠿⠿⠃⠘⠿⠿⠃⠀⠁⠀⠻⠿⠗⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⢿⠿⠿⠿⠷⡿⠿⠿⢿⡇
⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣄⣄⣄⣤⣠⣀⣠⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⢹⣟⢸⠠⠀⠆⠀⠀⠀⣿⣿⣧⣤⣼⣿⢿⡃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⡿⢻⡟⡝⠙⢻⣷⡀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠿⠶⠶⠶⠶⠷⠶⠶⠾⠇
⠀⠀⢸⡇⢸⢐⠀⡇⠀⠀⢸⡏⠈⡉⠀⠉⠁⢹⡇⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣿⢠⡿⡱⠀⢀⡿⢻⡷⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⡀
⠀⠀⢸⡇⢸⢈⠀⡇⠀⠀⠘⡅⠀⠁⠀⠀⠀⢨⡇⠀⠀⡆⢡⣠⡌⢰⠀⠀⠘⣿⣿⡱⠁⢀⣾⣣⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣞⣩⣶⠟⠋⡲
⠀⠀⢸⡇⢸⠘⠀⠇⠀⠀⠀⡟⠈⠉⣿⣿⣿⣿⠁⠀⠀⣇⠈⠉⠀⣾⠀⠀⢀⠈⢻⣿⣶⣾⣿⣿⠋⣀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠛⠁⢀⣤⡇
⠀⠀⠈⠃⠘⠈⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠒⠛⠋⠀⠀⠈⠛⠛⠓⠒⠒⠚⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⣀⠴⠚⠳⠦⣴⡋⣸⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⣦⣄⠀⣀⡴⠛⠁
⠀⠀⢈⣩⠿⠛⠻⢯⣉⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⢠⡟⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⢿⢏⣤⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣷⣶⡆
⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠋⢋⣼⣿⣧⡀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣧⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⣿⣦⣤⣄⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠔⠁⠀⠘⣿⣿⣿⠆⠀⠀⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠙⠲⠦⠶⠚⠋⠀⠀⠀⠀⠻⠿⠛⠤⠬⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡍⣿⠛⠿⠿⠿⠻⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⣋⣩⣭⣬⣭⣉⡙⠛⠿⣷⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡾⠃⣠⣶⡿⠟⠋⠉⠉⠉⠉⠙⠓⠄⠈⠻⣷⣽⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⣴⡿⢁⣴⣶⣿⣿⣿⣷⣶⣄⠙⢦⣄⠀⠈⢿⣧⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⣿⣿⢰⡿⢀⣾⣿⡿⠿⠿⣿⣿⣿⣿⣷⡈⢿⣷⡰⡌⣿⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣿⠈⣇⠸⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣿⣷⣷⠈⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣉⠻⠿⣧⡈⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡿⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⣙⠛⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢀⣿⣿⡿⠁⣼⡿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⢀⣠⣤⣀⣀⠀⠀⠀⠀⢠⣿⣿⡿⢡⣿⡿⠋⢠⡾⠋⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠉⠛⠿⣦⡄⢀⣿⣿⠟⢰⣿⢏⠀⢀⡡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡇⠀⢿⡟⠛⠓⠆⠀⠈⠀⢸⣿⡟⠀⣿⠃⡆⣠⡾⠁⠀⠸⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠃⠀⢼⣿⣦⣤⣤⠄⠀⠀⠸⣿⡇⣆⢻⡀⢷⣿⣇⢠⣀⠑⠒⢛⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠻⣇⢻⣦⡑⠈⢻⣿⣦⡈⠙⠛⢛⠋⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣶⣄⡙⢿⡿⢷⣦⣬⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⢉⠻⢿⣷⣝⣦⡈⢉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣄⡀⠀⠀⠀⢻⣷⣌⠻⣿⣷⠈⣿⣶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⣿⣿⣿⣿⠏⢀⣀⣠⣾⢿⣿⡇⣹⡟⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣫⡵⠿⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠾⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣠⣿⣿⡿⠛⠛⠻⠛⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠿⠿⢿⣿⣿⡄
⠀⠀⢸⣿⣿⢿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⣼⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣏⣿⣿⣿⢻⡿⠃⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠈⣿⠟⠁⡼⠁⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠐⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠉⣹⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡛⠿⠄⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡄⠀⠀⠀⠀⠀⣰⣿⢿
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⢠⡟⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⢷⣦⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣾⣿⣿⡵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠠⡟⠋
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⣾⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀⣿⡿⠟⠛⠛⠿⠿⠿⠿⢿⣇
⠀⠀⠀⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⣼⣿⣿⣿⠻⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠊⣿⡇⠀⠀⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡦⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠁⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠿⠻⢷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠠⢾⣿⣿⣿⡿⢸⣿⣿⣿⠹⣿⠈⢿⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⢿⠀⠀⢹⣿⡇⠹⣿⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠻⣿⣿⠀⠟⠀⢸⣿⢿⠃⠀⠀⠀⢸⣿⣿⡟⣿⠈⢿⣿⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠉⢿⣿⣿⣿⠘⠀⠀⢸⠏⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠘⠃⠀⠀⢀⣾⣿⠘⠀⠀⠀⠀⠈⣿⢿⡇⠈⠀⠈⠗⠀⠀⠀⠀⢸⣿⡟⠃⠀⠀⠀⡼⢿⣿⣟⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠀⠀⠀⠀⠀⠀⠘⢿⣏⠂⠀⠀⠀⠀⠀⠀⠀⣽⡟⠉
⠀⠀⠀⠀⠀⠸⢻⣄⠀⠀⠀⠀⠀⠀⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⠀⠀⠀⠸⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⢠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⡠⢿⠷⡄⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠇
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠂⣤⠀⠀⠀⠀⢠⠎⠢⠀⡰⠚⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣹⡃⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⠠⢶⡎⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠿⠀⠀⠀⠀⠀⠀⠘⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠲⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠
⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⢰⠉⠀⠀⠀⠀⠀⠌⠀⢀⡠⣀⠀⠈
⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠠⢄⠃⠠⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠏⠀⠈⠃
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠐⠰
⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠀⢀⣄⣀
⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⠎⠀⠀⠀⠀⠀⠀⠀⠸⣧⡤⣦⠀⠀⢸⡧⣤⠀⠀⠀⠀⣠⠤⡄
⠸⠀⠘⡞⢳⠿⡖⣦⢤⠀⠀⠋⠤⠙⡎⠳⠳⡖⣦⢤⠀⠀⠀⢿⣀⣤⡄⠀⣾⠤⡄⠀⠀⠀⠀⠧⡄⢺⠋⠻⠱⠖⣦
⠀⠀⠀⠇⠸⠀⠀⠈⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠈⠀⠀⠀⢸⣇⣀⣄⢀⡷⢤⠄⠀⠀⠀⠌⠂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣡⠘⠓⠶⠀⢠⠂⠀⠀⢠

⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠙⠿⢿⣿⣧⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠒⠀⠀⠄⠊⠹⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠲⠤⠀⠀⣠⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠰⢻⠉⠛⠒⢞⠋⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⡠⠾⣿⡿⠋⠸⣟⣧⡀⣆⠀⠀⠈⠀⠀⣸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢣⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⡘⡠⠛⠦⣄⣀⣀⡙⠿⣿⠛⠗⠒⠃⠀⢠⣇⡤⠜⠋⠉⠉⠉⠉⠉⠒⡴⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸
⡿⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠄⠂⠈⢢⡿⢴⡀⠀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠤⢤⣀⠀⠀⠀⠀⢸
⣷⠀⢀⠄⠀⢼⠘⢧⡀⠀⣥⠄⠀⣠⠞⠁⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⢳⡄⡀⠀⢸
⣿⠀⣾⠀⠀⠈⢿⡄⠙⠓⠲⠖⠛⠁⠀⠀⠀⠀⣸⠀⣠⡴⠖⠲⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣡⣀⣠⠤⠴⠚⠀⣷⠀⢸
⣿⠀⠘⢷⣄⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣣⠞⠁⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⢸
⣿⠀⠀⠀⠙⠻⢦⣤⣈⠑⠒⠢⠴⠖⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿
⣿⣿⣿⣿⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣟⣛⣿

⠀⠀⠀⠀⢠⡄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢸⡃⠀⠺⢄⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣽⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⠾⠂⠀⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⠀⣯⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡶⢒⣒⣲⣶⣤⠀⢿⢸⡇
⠀⠀⠀⠀⣇⣽⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠸⣿⠀⠈⣿⠁
⠀⠀⠀⠀⢡⣻⠀⠀⢀⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠤⠤⠤⠤⣤⢼⣿⡇⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⣼⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡇⠀⢰⠒⢦⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣇⣣⣀⡀⣼⡟⠀⢰⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠘⡇⠈⢷⣴⠚⠛⠀⣤⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣾⣿⡀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣿⡇⠀⠀⠇⠀⠈⣿⣇⠐⢤⣿⡟⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⡏⢸⡇⠀⢻⣿⡀⠀⠀⠀⠀⣠⠴⠋⠀⢸⢻⠃⠀⢠⠀⠀⢀⣿⣿⡆⢘⠏⠀⢀⣴⡏⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⡇
⠀⠀⠀⠀⡇⢸⡇⠀⠈⢿⣷⡀⠀⣠⠞⠁⠀⠀⢠⢏⡏⠀⢀⠃⠀⠀⣼⣇⢻⣿⡦⢊⣦⡼⠋⠀⠀⣶⠀⠀⠸⡀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠈⢿⢷⣤⡏⠀⠀⠀⣠⢏⠞⠀⢀⡞⠀⣀⠴⠿⠚⣾⠟⢠⣾⣟⡁⢀⣴⣾⣃⠀⠀⣆⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣧⢸⡇⠀⠀⠀⠀⠹⡻⣇⠀⠀⣰⢿⠋⠀⠀⡸⠐⠋⠁⠀⠀⠀⢧⣆⢰⠎⣡⢮⡞⠋⠁⢈⡇⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠑⢸⣆⣰⣯⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⠎⣺⢟⣡⣇⣴⣾⣿⠃⠀⣿⡇⠀⠀⠀⡟⡇
⠀⠀⠀⠀⢸⣼⠁⠀⠀⠀⠀⠀⠀⣸⢉⡉⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁⠉⠉⠙⠛⣏⣠⡿⠁⠀⠀⣿⡅⠀⠀⠐⡅⢱
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢠⠇⢘⣻⡿⡀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⣿⡇⠀⠀⠀⣷⢸
⠀⠀⠀⠀⠀⢠⣴⣶⡄⠀⠀⠀⠘⣰⡏⢹⣿⠃⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠹⠀⠈⠟⠀⠀⠀⠆⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣰⣿⣿⣀
⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⢄⡀⠀⢀⣴⠟⠁⠀⠀⣠⡶⠿⠿⣿⣟⣿⣿⣿⣷⡦⡀
⠀⠀⠀⠀⠀⢰⣿⡄⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠑⢠⣈⣿⠟⠁⠀⠀⠀⢸⣟⠀⠀⠀⢻⡯⣿⡏⠀⠈⢻⣼⡄
⠀⠀⠀⠀⢀⣴⣼⡧⠿⣄⡀⠀⠀⣿⣭⣭⣭⣭⡿⠛⠟⠛⢶⣽⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⢸⣷⣿⡇⠀⠀⠘⡏⡇
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⣧⠀⠀⢿⣭⣯⣭⣽⣷⣴⣶⣶⣾⡽⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢀⣾⠏⣿⢧⡀⠀⣸⣯⠃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠿⠋⠀⠈⠳⢿⠿⠟⠁
⠀⠀⠀⠀⣿⣀⡀⠀⢀⣸⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠠⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣠⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠉⠉⠉⠉⠉⠋⠉⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⣯⢺⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠘⣎⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠙⡆⠀⠀⠀⠐⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣮⣿⢫⣿⣿⣦⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣷⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢮⡙⢿⣿⣿⣷⣄⠀⠀⠀⢀⣧⣤⣤⣤⣤⣤⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣿⣿⣿⣦⡀⠀⢰⣿⡀⢀⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡜⠁⢺⣿⣿⡄⠘⣛⣣⣬⣭⣭⣭⣭⣄⣀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢀⣀⣤⣶⣦⡀⠀⠀⠀⠻⣄⠈⢛⣩⣶⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣷⣌⡻⠀⠀⠀⣰⡟⢀⡄⠈⢙⣿⣿⣿⡿⠃⠀⣠⣶⣦⣄⡀
⢾⣧⡤⢿⣿⣿⡟⡆⠀⠀⠀⠈⣱⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⣰⡟⢠⣾⠁⢠⣾⣿⣿⡿⠀⠀⠀⡇⠀⠈⠙⢿⣦
⢺⣿⣷⠀⣿⣿⣷⢹⡄⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⣠⣿⠃⢠⣿⣿⣿⡿⠁⠀⠀⡜⣰⡀⠀⠀⠀⢹⠂
⠈⢿⣿⣧⢻⣿⣿⣧⢻⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠟⢤⣿⣿⣿⡿⠁⠀⢀⣼⣿⡟⢡⠆⣠⠎⠁
⠀⠘⣿⣿⣇⢻⣿⣿⣯⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣾⣿⣿⡿⠁⠀⣠⣾⡿⠋⣰⣿⡿⠁
⠀⠀⠸⣿⣿⡆⠿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⣿⣿⠙⠺⣿⣿⡿⢁⣤⡾⠋⠎⢀⡼⣿⡿⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠹⣿⣿⣷⠹⣿⣿⣿⣷⠀⠀⠀⣠⣴⣾⡿⢿⣛⡿⠭⠭⠭⠭⠭⠽⣟⣿⢿⣿⣧⣄⠀⣼⡿⢡⣾⣿⣦⣀⠀⠞⢱⣿⠁⠀⢠⠂⢿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣆⢻⣿⣿⣿⣧⣴⣿⣿⡯⠗⠋⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠺⢻⣿⣿⣿⢡⣿⣿⠛⣿⣿⣷⣤⣼⣿⠀⣰⠟⣡⣿⡿
⠀⠀⠀⠀⠀⢿⣿⠈⣦⡹⣿⣿⣿⣿⡿⠋⢀⡠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⢹⣿⣿⣿⣿⠧⢄⣿⣿⣿⣿⣿⠃⣴⠃⣴⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠛⠛⣾⣿⣿⠏⢀⠔⠉⠀⠀⢀⣄⣀⢸⣧⣀⡤⢖⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣧⢀⣼⣿⣿⣿⣿⠃⠚⢅⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣸⣿⣿⡀⠁⠀⠀⠀⠀⣀⡤⠟⠋⢻⣥⠶⣈⣭⠉⢀⠀⠀⢀⣼⣿⣿⣿⣿⣸⣿⣿⣿⣿⠇⠀⠀⠀⣰⣹
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣻⣿⣧⡳⣄⠀⠀⠐⠿⢥⣭⣶⣒⣻⡧⠞⣋⡤⠖⠁⣀⣴⣿⣿⣿⣿⣿⣏⣝⣻⣿⡿⣵⡆⠀⠀⡴⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠙⣿⣿⣷⣬⡑⣢⣄⣀⣀⠀⠀⠉⠉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⡿⠛⣽⣽⡇⢀⣼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠀⠀⠀⠑⢦⡙⠻⢟⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⣉⣠⣽⣿⠟⠀⠀⠀⠀⠀⠀⢰⢸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣥⣴⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⣠⣾⣾⣿⡟⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢶⣤⣤⣤⣿⣾⣿⡿⢋⣤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣤⣄⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢠⣿⠛⢦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠈⣿⡀⢸⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠹⣧⠀⠀⠀⢿⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣿⡄⠀⠀⢸⣷⠀⢹⠀⠀⠀⢀⣿⣿⡇⠀⠉⢹⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣹⣷⠀⢠⣾⣿⡖⠘⣿⡇⠀⢸⣿⣿⡇⠀⠀⡞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⣹⠿⢇⠈⣿⣿⣷⠆⢿⣿⠀⢸⣿⣿⠃⠀⢰⠇⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠸⡀⣿⣿⣿⡂⠸⣿⡇⢸⣿⡿⠲⠤⡜⠀⡼⢁⣼⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣷⣾⣿⣿⡇⠀⢸⣇⣿⣿⡇⠀⣾⠃⡼⢡⣾⣿⡟⠀⠀⠀⢈⡿⠛⠋⠉
⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣷⡀⠸⣿⣿⣿⡯⢉⣿⡼⣡⣿⣿⣿⣄⡀⠀⢠⠎
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⣿⣿⣿⠙⢺⡿⣵⣿⣿⣿⣯⣀⣼⣷⠋⠀⠀⢀⠀⠀⢐
⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⠁⠀⣼⣿⣿⣿⣿⣟⣵⣿⣿⣷⡶⣶⡆⢸⣷⣴⡟
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢹⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⡇⣿⡇⢸⠛⠛⡇
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣷⡼⢤⣤⠧⣄⠠
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⠀⣸⣿⠀⢸
⢻⣿⣿⣦⣀⡀⠀⠀⢀⣀⣤⣶⢿⣿⣿⡿⠛⠉⠉⢙⣿⣿⣾⣿⣿⣿⣿⣿⣀⢐⣗⣀⣽⠀⢸⣿⣿⣿⣿⠁⣿⣿⠃⢹
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠋⠉⠻⣦⣤⠞⠋⠀⢈⣹⢿⣿⣿⣿⣿⣮⣽⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢹
⠀⠀⠉⠛⠛⣻⣿⡿⠋⠉⠉⠻⣦⣴⠞⠋⠉⢙⣷⣶⡞⠉⠀⢀⣉⣿⣿⣿⠫⣭⣿⣯⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢸
⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⠶⠋⠉⠙⣷⣶⠞⠋⠁⢀⣙⣷⣾⣿⣿⣿⡿⢿⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⢸
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⠖⠋⠁⠉⣻⣶⣾⣿⣿⣿⣿⠿⠛⠉⠀⢸⡇⢸⣿⣿⣿⠀⠘⠻⠿⠿⠟⠓⠛⠛⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣦⣷⣾⣼⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣯⣭⣬⣿⣬⣭⣧⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦

⠀⠀⠀⠀⣤⠀⠀⠀⣠⠤⠤⠄⠤⡤⠤⡤⠄⠠⣤⠀⣤⢤⡶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣯⡀⠈⠣⢴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠃⠀⠀⠀⠀⠀⠀⣿⢸⡀
⠀⠀⠀⠀⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⠭⠭⢿⣷⠀⢻⣸⠇
⠀⠀⠀⠀⣤⡇⠀⠀⢀⢾⠇⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⣿⣿⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⢧⡇⠀⠀⡞⡎⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣀⡀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⢻⠛⠀⠀⠀⣿⠀⢸⣿⡀
⠀⠀⠀⠀⣼⡇⠀⢸⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⡀⠀⡇⠙⢦⢀⣠⣤⠀⠲⡄⠀⠀⠀⠘⠦⠶⠦⠾⠋⠀⢸⣿⡇
⠀⠀⠀⠀⣿⣧⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠇⠀⠠⠀⠘⣿⡄⢀⢀⣿⡧⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⡇⣿⠀⠸⣿⡄⠀⠀⠀⠀⠀⣠⠞⠁⣸⣿⠀⠀⡁⠀⠀⣿⣿⡄⢸⡟⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇
⠀⠀⠀⢀⡇⣿⠀⠀⢻⣷⡀⠀⢀⡴⠋⠀⠀⢠⢧⠇⠀⠰⠀⠀⢰⡟⢻⣷⡌⠄⡄⡼⠋⠀⢐⡄⠀⠀⡆⠀⠀⢸⣾⡇
⠀⠀⠀⠀⡇⣿⠀⠀⠀⢻⣷⣄⡞⠀⠀⠀⢠⢯⠏⠀⢠⠃⠀⣠⠿⠝⣼⡿⢁⣼⠟⠁⢀⣤⡞⠀⠀⣀⠁⠀⠀⠈⣿⡇
⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠱⡻⣇⠀⠀⣰⣻⠋⠀⠀⡇⠐⠉⠀⠀⠀⢏⡄⢠⠕⣡⢣⠞⠋⠉⣱⠀⣿⡆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠘⢼⣆⣰⢳⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⠄⡺⢓⡽⣢⣴⣾⡟⠀⣿⡇⠀⠀⠀⣟⡀
⠀⠀⠀⠀⢧⣿⠀⠀⠀⠀⠀⠀⣸⢁⣉⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠁⠉⠁⠙⠻⣅⣼⠋⠀⠀⣿⡇⠀⠀⢸⡅⢇
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⠏⣈⣹⣿⠀⠀⠀⢸⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⣿⡇⠀⠀⠀⣇⡌
⠀⠀⠀⠀⠀⢰⡶⣦⠀⠀⠀⠀⣾⡇⢹⣿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠘⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣀⣀⣤⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⣿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠐⠤⣀⣤⡾⠁⠀⠀⢠⡾⠋⠉⢻⣿⣿⡿⠛⠻⣗⠄
⠀⠀⠀⠀⠀⡟⣷⢸⡇⠀⠀⠀⣤⠤⠤⠤⢤⡤⣤⣤⣤⠤⡀⠀⠐⣶⡾⠋⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟⣿⡇⠀⠀⢹⣞
⠀⠀⠀⢀⣾⠟⠛⠉⢻⣦⠀⠀⣿⢿⡿⠿⢿⣏⣉⣁⣉⡿⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⣿⣿⣇⠀⠀⢸⣇
⠀⠀⠀⠈⡏⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠘⢷⣦⣴⡿⠃⠘⣮⣶⣴⡿⠊
⠀⠀⠀⠸⣇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠛⠿⠶⠶⠟⠋⠀⠐⠒⠒⠒⠲⠒⠛⠿⠿⠷⠖⠶⠶⠿⠿⠿⠿⠿⠿⠷⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠒⠒⠒⠒⠒⠂⠒⠆⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⡔⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡚⠀⣀⣀⢘⢲⡀⠐⠀⠀⠀⢰⠒⢢⠤⠄⠀⠀⠠⠄⠀⠀⠀⠀⢃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡔⠃⠊⠙⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠘⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂⠘⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠖⠲⠖⠒⠒⠒⠂⠒⠂⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⡠⠒⠂⠐⠒⢤⠀⠀⡴⠂⠑⢢⠀⠖⠉⠙⢆⢸⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠇
⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⢱⡀⢣⡀⢀⡼⠀⢦⣀⣀⠎⢸⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠄
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣠⠆⠠⢄⠀⡴⠒⠢⡄⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠧⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⡇⠱⡀⠀⠀⠀⠀⠀⣰⠁⣇⠀⠀⣸⠀⣄⠀⢀⡄⢸⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠰⠄⠀⠀⠠⠄⠄⠤⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡇⠀⠈⠢⠤⠀⠤⠞⠁⠀⠈⠉⠈⠁⠀⠈⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡀⠀⢀⣄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠉⠒⢄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢀⣀⣀⣀⣀⡀⠠⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣅⠼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠊⢠⠘⠅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠀⡀⠤⢀
⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠄⡀⠀⠀⠀⠈⠀⠄⠀⠀⠤⠂⠀⠘⡆⠀⢀⡔⠚⠒⠒⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠀⠀⠀⢨⣀⠠⠀⠠⠐⠨⠀⠐⡇⠀⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⡠⠀⠀⠀⠀⠑⢤⡐⣀⢶⠡⡈⠎⠀⠀⠡⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠉⠑⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠛⠂⠑⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⢐⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡦⠀⠀⠠⠄⠀⢠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠁⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠑⠛⠻⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠐⠚⣙⠛⠛⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠉⠀⠀⠀⠐⠚⠛⠉⠉⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⠀⠀⠀⠀⠀⠀⠖⠒⠛⠛⣒⣶⣤⠀⠀⢀⣀⡠⡠⠴⢶⣿⣿⣶⣿⣿⡿⠿⠗
⠀⢀⣀⠀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⢯⣏⠀⠀⠀⠀⠀⠀⠤⠀⢰⣤⣤⣙⣿⣥⣴⣋⣬⡤⠖⠒⠛⠛⠉⠉⠁
⠀⠀⠈⠉⠉⠙⠛⠛⠛⠿⠿⠦⠦⠞⠛⠉⡙⣻⣷⣶⣶⣶⠶⠶⠮⠽⠟⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⠂⢀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⡜⠀⡴⠃⣠⠃⡼⠁
⠀⠀⠀⠀⠀⠀⡼⠁⡼⠁⢐⠃⠌
⠀⠀⠀⠀⠀⠀⠀⠜⠁⠁⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣛⣛⣛⣛⣛⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣄⣀⣛⣛⣛⣛⣛⣛⣥⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠘⢿⣿⡋⠉⠈⡇⢰⣿⣿⣷⡄⠀⠘⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⠁
⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣆⠀⠀⠘⠛⣷⡀⠸⣿⣷⡀⠀⣷⢸⣿⣿⣿⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡰⢃⣼⣿⠃
⠀⠑⠤⡀⢀⣠⣴⣄⠀⠀⠀⠀⠹⣉⠀⠀⠀⢸⣿⣧⠀⢿⣿⣷⡀⢹⠀⣿⣿⣿⣿⠀⢸⠀⠀⡿⠀⠀⠀⠀⢠⣮⣀⣿⣿⠃
⠀⠀⠀⠈⢻⣿⣿⣿⣦⡀⠀⠀⠀⢻⣧⢣⠀⠈⡿⣿⣆⠘⣿⢿⣿⣹⡇⢻⣿⣿⣿⡆⢸⠐⠒⡇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⢻⣧⢣⡀⢹⣿⣿⡄⢹⣽⣿⣀⣷⢸⣟⣿⣿⣇⢸⠈⠉⡇⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣶⣦⣤⣌⣿⣧⢳⡀⢿⣿⣷⠀⢿⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⢸⡇⠀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡳⠘⣿⣿⣧⠸⣿⣿⣿⡇⢹⢹⣿⣿⡟⠀⣼⣿⡏⠉⠛⠿⣿⣃
⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⡟⠙⡆⢻⣿⣿⣿⠘⡟⣿⣿⡇⢸⣿⣿⣿⣿⣶⣦⣄⡙⠳⣦⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠀⢹⡈⣿⣿⣿⡄⣧⢿⣿⡇⠀⣿⣿⣿⡿⠟⢿⣿⣿⣶⣄⡙⢦⡀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠻⢇⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢧⢹⣿⣿⣇⢸⣸⣿⡇⢰⣿⢿⣷⣍⠀⠀⠉⠛⢿⣿⣿⣦⣽⡄
⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣠⣔⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⡆⢿⣿⣿⣼⣷⣿⣦⣼⣯⣾⣿⣿⣷⣦⣀⠀⣰⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣅⣀⣠⣴⣿⠾⢋⣽⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⠸⣆⣽⣾⣿⠿⣛⠛⠉⠙⢛⡻⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡃
⢻⣿⣿⣿⣿⣿⣿⣿⣯⢁⣤⣾⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⡿⣰⣿⡿⣫⣖⣭⡶⠾⠟⠛⠛⠻⢶⣌⠻⣿⣿⣆⠉⠛⠻⠿⠿⠟⠁
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠐⠂⠈⠳⡜⣇⠘⣇
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⡿⠿⠟⠛⠛⢿⣿⣿⣿⠃⠀⠠⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⢹⣿⡄⣿⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡁⠀⠤⢤⣤⡀⢸⣿⣿⡏⠀⠰⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠈⠳⣌⣧⣾⣀⣀⣸⣿⣿⣷⡀⠀⢨⠙⠓⠀⠀⠀⠀⠀⠆⠀⠀⣸⣿⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⡏⠀⣤⣀⣀⣤⢀⣀⠈⠓⢦⠜⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢯⣾⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉⠹⣿⠌⠉⠑⠂⢁⣤⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣤⣤⣤⣤⣶⣾⣿⢟⣫⠶⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⡄
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿
⠀⠀⢀⣨⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⡀⠘⢛⣿⣿⣟⠀⡀⠀⠀⠀⠀⢀⠀⠃⣸⣿⣿⣃⣀⠀⠀⠀⠀⠀⣀⣸⣦⣿⣿⣿⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⡆⡇⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⠁⡇⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⠛⠿⠿⠿⠿⠛⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣇⠀⢸⣿⣿⣿⢰⠇⠀⠀⠀⠀⢸⡆⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢹⣀⠸⣿⣿⣟⣼⠀⠀⠀⠀⠀⠀⣇⣀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣸⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠐⣿⣿⣬⣅⢩⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⣷⣾⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣾⣿⡆
⠀⡀⠐⠊⠁⠀⠀⠀⠁⠂⠠⠀⠀⠀⢤⣴⣭⣤⣤⣤⣬⣵⣤⡄⠀⠀⢀⡤⠶⠿⠿⠿⠿⠷⠦⢤⡀⠀⠀⣀⣀⣶⣿⣿⣿⣿⣦⣀⡀
⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠻⢿⠿⠻⣿⣿⠀⠀⠀⢸⡇⠀⣠⣄⢀⣠⡄⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠇⠀⢸⣿⣶⣴⣿⡗⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⣰⣿⣿⠀⠀⠀⢸⡇⠀⠹⣿⣿⡿⠃⠀⣸⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⢿⡿⠟⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣿⣿⣿⡿⠀⠀⠀⢸⣇⠀⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠿⠟⠁⠀⠀⠀⢸⣿⣦⣀⣀⣀⣀⣠⣼⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠹⡿⠋⠀⠀⢀⠀⠚⢉⡛⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠠⡱⡷⣰⣠⠃⠀⠐⠄⠓⠀⠀⠈⢛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠦⣆⣧⣾⣿⣿⠃⣠⡀⠀⠀⠀⠲⢄⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠉⠉⢻⣿⡀⢹⣷⡀⠀⠀⡃⠀⠴⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⠶⠛⠛⠾⠟⠋⠉⣩⡽⠟⠉
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠦⠄⣠⣤⠖⠁⠒⠦⡤⠠⠄⠀⠀⠛⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿⣷⣆⡀
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠐⠶⣎⠀⢡⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣌⠳⣄⠀⠀⠀⠀⠀⠀⣸⣷⣦⣄⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠿⠛⣇⠈⢻⡇⠰⡄
⠀⠀⠀⠀⠀⢸⣶⣤⡀⠠⡀⠀⠁⠀⣱⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢰⣿⠀⠘⠀⢀⡷
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣬⣱⣤⣰⡾⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢿⡄⠀⠀⣸⠇
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣡⣼⡿⠿⠿⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⠃⢡⠀⠀⢻
⠐⠿⠿⠟⠫⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣸⠁⠀⠘