Canned beans Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⡄⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢄⣀⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠒⠤⠤⠤⠤⠄⠒⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⣿⠛⠛⠲⢦⣄⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠈⣆⢮⠷⠸⣏⡿⣷⣄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣾⢁⡀⠀⢲⣾⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠛⢋⢘⡿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⠉⠙⣄⠠⣤⣼⢷⣛⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢀⣘⠚⠠⠤⢤⣼⡧⠟⣍⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢴⣟⣇⠼⢧⡶⣃⣸⢧⣼⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠈⡛⠛⠿⣤⠾⢒⡛⣷⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣿⣿⠃⢀⣐⠈⣄⣆⣷⡁⡟⠿⡿⢯⣙⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⣋⡥⠴⢒⠺⣅⢹⣷⣧⡤⢇⣻⣼⣏⣡⡿⢮⣤⣿⣻⡿⣷⡦⢭⣙⠲⢤⡀
⠀⠀⠀⠀⢀⡼⠋⣠⠞⠁⠀⣾⠁⠀⠳⣴⠿⣯⣷⣆⢿⣿⡿⠿⣦⠾⣏⡹⠿⣾⣫⣷⠦⣌⠑⢦⡙⢷⡀
⠀⠀⠀⠀⣾⠁⣰⠃⢀⣀⣴⠛⡟⢋⠟⠋⢻⣧⣠⣿⡋⣹⡟⠉⠙⡦⢾⣷⡶⠻⠟⣷⣶⣬⡷⠀⢳⠀⢻⡄
⠀⠀⠀⠀⢿⡀⠸⣴⠁⢀⣟⢛⣯⣈⣷⡚⣽⡶⠒⠻⣍⣩⣿⣉⣹⣷⡼⢛⣿⡶⠾⡟⣻⠷⡄⠀⡼⠀⢸⠇
⠀⠀⠀⠀⠈⢷⣄⠘⠻⢯⣀⡤⢧⣰⣭⣄⣨⠗⣶⢒⣿⣉⣽⡉⣹⡆⣀⣯⣤⣼⠆⠙⠛⢞⣣⠞⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠈⠙⠛⠻⠿⣽⣀⣠⣟⡉⡉⣙⣿⡛⣻⣍⣨⣧⣤⠤⠴⠖⠛⠉⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⣀⠉⠉⠉⠉⠉⠉⠁⠀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⠖⠚⠙⠳⠶⠦⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣀⡤⠒⠒⠒⢤⡀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⠆⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠃⠀⢠⠴⠒⠒⢦⡀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇⢀⠤⣄⠀⢳⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡆⠀⠱⠬⠴⠋⠀⡜⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠙⠦⣄⣀⣠⠴⠊⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠒⠒⠒⠛⠛⠒⠒⠒⠲⠦⠤⢵⡄⠀⣀⣀⠀⣀⡤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⡀⠀⠀⣀⠤⠤⣀⠀⠀⣀⠀⢀⡀⠀⠉⠛⢭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢾⣝⣉⠌⢻⡟⠐⣯⡽⢌⡹⠯⢭⢑⡒⢻⣍⡶⠆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠀⠀⠉⠉⠛⠛⠛⠛⠒⠒⠓⠒⠛⠊⠉⠁⠀⠠⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⡤⠴⠶⠶⠢⡖⠒⠒⣾⣀⣀⡀⠀⠀⠐⠂⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⠤⠤⠍⠚⠀⠀⣠⠬⠭⣉⠣⠤⠤⠛⠤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⣀⣀⡀
⠓⠤⠤⢀⣀⡀⠀⠙⠢⠤⠴⠃⠀⣐⠊⢁⣩⠎⠀⠷⠊⣆⣀⠀⢀⡀⠀⣒⣈⠥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⢉⣁⡤⠀⠀⢠⣤⣀⠉⠳
⠀⠀⣠⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⣀⣀⣀⣀⣈⡭⠅⣚⠭⠥⠤⠶⠖⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⣉⣉⣉⣀⣀⣀⣀⡉⠉⠉⠉⠉⠀⢀⡠⠔
⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣀⣀⣀⣀⠠⠤⠤⠴⠒⠒⠚⠋⠉⠉⢽⣋⣁⣀⣀⣀⣀⣀⠀⠉⠉⠉⣭⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⠿⠿⠿⠿⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢋⢩⡄⠀⠀⢀⣀⣀⣀⣀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⣈⡤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠲⣄⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⣠⠞⠉⠀⣀⡤⠖⠛⠛⠛⠛⠓⠶⣄⠈⠳⣄⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⣰⠃⢀⡴⣋⡵⠖⠉⠉⠉⠉⠉⠙⠶⣌⠳⣄⠘⣆⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⣸⠃⢠⠏⡴⠋⠀⠀⣀⠤⠤⠤⢤⡀⠀⠘⢆⢸⡆⠸⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡟⠀⡇⣼⠁⠀⢀⡜⡥⠞⠋⠛⢦⡙⡆⠀⠘⡄⣧⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢺⡇⢸⠀⣵⠖⢦⣼⢻⠁⠀⠀⠀⢸⠇⣯⢀⠀⡇⣿⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⡇⠸⡀⣿⠀⠀⠘⢇⡳⢤⣠⣴⣫⠞⠁⠘⣷⢡⡧⢤⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠈⣧⠀⢳⡈⢧⡀⠀⠀⠙⠛⠛⠉⠁⠀⢀⡴⢣⠞⢀⡞⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠘⢧⠀⠙⢦⡙⢦⣄⣀⣀⣀⣀⣤⠶⣫⡴⠋⢀⡾⢡⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡈⠳⣄⡈⠙⠢⠤⢥⣭⢭⡤⠴⠚⠁⢀⡴⠛⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠙⠲⠦⢤⣀⣀⡀⠀⣀⠴⠞⠋⠀⢠⣿⣿⣶⣦⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⣈⣩⠉⠀⢀⣈⣉⣥⣿⣿⣥⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⢷⣶⣤⣤⣶⣾⡿⠿⣿⡿⢿⣿⡿⠿⠿⣿⣶⠟⠛⣻⣯⣽⣿⠷⣮⣝⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⣠⣼⡿⠟⠛⣿⠿⠛⠛⢿⣄⣴⣿⣴⠶⠶⣶⡿⠷⢾⣏⠉⠉⢻⣦⣤⣽⣿⡌⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠻⣿⣧⡶⠟⢿⣦⣤⣤⣼⡿⠛⠻⣷⣤⣤⣤⣿⣦⣤⣹⡿⠻⣿⡃⢀⣠⣿⠇⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣦⣈⠛⠷⣤⣼⣏⡀⠀⠈⣿⠀⢸⡏⠁⠀⠈⣻⣆⣈⣿⣥⣤⠾⠟⠛⣉⣤⣾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠦⣍⠻⠿⣷⣦⣭⣍⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⡛⣛⣉⣉⣥⣴⣶⣾⠿⠿⠛⣡⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠙⠲⠦⣬⣍⣙⡛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣉⣉⣤⣤⠴⠖⠋⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣄⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉⠁⠀⠀⠀⢚⡥⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢙⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣭⣓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⣋⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣬⣉⣛⠛⠓⠒⠶⠶⠶⠶⠶⠒⠚⣋⣉⣥⣶⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣶⣶⣶⣶⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠔⢒⡒⣒⣒⣀⣀⣀⡀⠀⠄⠨⠁⠀⠐⠒⣒⣂⣤⡤⣤⣀⣀⡀⣀
⠀⣠⡤⠶⣚⠋⠉⠁⠀⠀⠀⠀⣈⣭⣥⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣤⣄⠀⠉⠉⠙⠛⠿⣝⡓⠦⣄
⢸⡁⠀⣿⣁⠀⠀⠀⠀⠀⠀⠘⠿⢭⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣭⡿⠇⠀⠀⠀⠀⠀⢀⣽⠀⢈
⣿⠉⠒⠤⣉⡙⠓⠶⠶⢤⣤⣤⣄⣀⣀⣀⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣠⣤⡶⠟⣁⡴⠛
⣼⠀⠀⠀⠀⠈⠉⠛⠓⠒⠶⠦⠬⠭⣭⣭⣭⣍⣉⣉⣛⠛⢛⡛⠛⠛⠛⠛⠋⠉⢉⣭⠉⠭⠥⠒⠂⠉
⣿
⢸⠀⢸⡏⢩⣍⣉⡉⠑⢦⠀⢶⠖⠒⠒⠒⢦⠀⠀⡤⠤⠤⡄⠀⢠⠦⠤⢦⠀⡖⠶⢀⡖⣋⣉⣦⡀
⢸⠀⢸⡇⢸⣄⣤⠎⠀⣸⠁⢸⠀⣖⡒⠶⠾⠀⢸⠃⣠⡀⢵⠀⢸⠀⠀⠀⢷⡅⣼⠛⡇⠸⣽⣤⠏⠑⢤⡀
⢸⠀⢸⡇⠈⣥⠤⣄⡈⠙⣦⢸⡆⢉⣉⣉⡃⠀⡗⠀⣯⠇⢸⠀⢸⡇⢰⡴⠋⠀⣿⠀⠈⢢⡀⠳⡄⠀⠀⠙⣤
⢸⠀⢸⡇⠰⠧⠤⠼⠃⠀⡾⢸⡇⠸⠭⢤⡄⢸⠃⣠⢤⡀⠸⡇⢸⡗⢿⢣⠀⠀⣿⡏⠻⣀⠇⠀⡇⠀⠀⠀⢸
⢸⠀⠈⠛⠒⠂⠐⠲⠖⠊⠁⠘⠷⠤⠤⠼⠃⢿⣴⠅⠀⢧⣤⣧⢾⣄⡽⠀⠷⠴⠇⠙⠦⠠⠴⠊⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠒⠒⠒⠒⢤⣸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢰⡄⢻
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠛⠋⠉⠛⣗⢦⡀⠀⠟⣡⢿
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⡾⣏⡠⠷⠶⠾⣁⢸
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⣠⠤⠞⠂⠒⠒⠒⠲⢦⠔⠊⠀⠀⠀⢠⣦⡈⣿
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡔⢉⡀⠀⠀⠀⠀⠀⠀⢠⣏⣤⠤⠤⣤⣄⡸⠟⢁⣾
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡁⣾⣳⣄⡀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⢀⠙⡞⠁⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠙⠲⠭⠍⠥⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣏⡇⡶⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⠜⠁⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠛⠳⠦⢤⣀⣀⣀⠠⠤⠒⠁⠀⠀⠀⢸
⠸⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠈⠙⠻⢷⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⡀⠀⢀⣀⣀⡤⠴⣚⡥⠞
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢗⣒⣂⠤⠤⠤⠀⠀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠠⢤⣤⣌⣛⣻⡭⠭⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠛⠛⠉⣉⣉⣁⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢀⣉⣉⣉⠙⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⡠⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⣈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠳⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⠛⠉⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⠤⣀⡀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠓⠒⠲⠶⠶⠶⠖⠚⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⣀⡠⠔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠒⠒⠢⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠄⠒⠒⠈⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡏⠉⣿⡆⠀⣀⣀⠀⠀⢀⣀⣀⠀⢀⣀⣀⡀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣷⠾⣯⡀⢸⣏⣹⣷⠀⠿⠋⣻⡇⢸⡟⠙⣿⠀⣿⣅⡛⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣇⣠⣾⡇⢸⣏⣩⡭⢠⣿⡋⣻⡇⢸⣿⠀⣿⠀⣶⣍⣿⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠈⠙⠛⠁⠀⠙⠛⠛⠃⠘⠛⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠊⠉⠉⡉⠉⠉⡉⠑⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠴⠋⠁⡀⠒⠀⠒⢢⣈⠦⡀⡩⠅⡌⢁⣱⡀⢂⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⢃⠀⠎⡰⠓⢺⠙⢊⣀⢸⠆⡸⠆⡄⠁⠙⠢⣀⠮⣄⠊⢁⣄⢱⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⢚⣌⠣⣎⠁⡶⡀⡉⠸⢅⠐⡄⠲⡂⢁⡞⠓⣠⠼⣤⡏⠀⣮⠎⣼⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡟⠈⠳⢬⣙⠳⠼⢷⣔⣉⠑⡜⢒⠊⣁⣝⣉⣽⡤⠥⠚⣋⠴⢪⠤⣱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⠭⢍⣉⣉⠩⠥⠤⠤⠒⢚⠭⣀⣀⠜⠀⡝⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀⠤⠚⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠉⠑⠒⠤⠤⢀⣀⣀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⣀⣀⣀⠠⠤⠔⠒⠉⠁⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠛⠁⣀⠤⠤⣀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⠔⠉⠀⠀⠀⠀⠱⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠇⠀⣠⠔⠒⠤⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢰⠁⣠⢤⠀⢘⠀⠸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠘⡆⠀⠓⠐⠚⠀⡸⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠳⡀⠈⠲⠤⠤⠖⠊⠀⠀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠑⠚⠂⣤⡤⡤⠤⠒⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣀⡠⠶⠦⣄⣠⢒⡈⢑⠦⣀⡰⢄⣀⣤⠄⣀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢈⠙⠒⠧⠼⢶⣶⣟⣉⣱⣄⡸⠭⠦⠚⠃⠉⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠤⢤⣅⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠠⠍⠴⠆⠀⢀⡈⢀⡐⠯⠀⠽⠆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀
⠀⠀⠀⠃⠤⠀⣀⢀⠀⠙⠢⠤⠼⠀⢀⠔⠀⢉⠖⠁⠧⠘⣀⡀⠀⠀⠀⢐⣂⡡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⡀⠀⠀⢠⣄⠉⠒⡄
⠀⠀⠀⠀⠀⡔⠂⠉⠀⠀⠀⠀⠀⢀⣀⣁⣉⣀⡀⠀⠀⠀⠀⠭⠋⡨⠭⠥⠔⠶⠒⠒⠒⠚⠛⠉⠀⢈⣉⣉⣉⣉⡉⠀⠠⣄⣉⠉⠉⠉⠁⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠄⠒⠒⠈⠉⠉⠉⠀⠾⠥⠠⠤⠤⠤⢤⡀⠀⠈⠡⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠄⠀⠒⠀⠀⠠⠤⠤⠤⠤⠄⢀⣀⡀
⠀⠀⠀⠀⣀⣤⡔⠊⠉⠉⠀⠀⠙⢋⣉⣉⠉⠡⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠼⣿⣵⣦⣤⣀
⠀⠀⢀⡎⡿⠛⠉⠀⢀⡤⠖⣋⠭⢐⣂⡤⠴⠞⠓⠒⠛⠉⠁⠀⠀⠀⠀⠠⣤⣀⠠⢄⡈⠉⠓⢦⡈⠙⢻⡷⢱
⠀⠀⠈⢧⡸⣦⣄⣀⢸⣇⡘⠧⡀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢇⡠⠟⢀⡜⠼⠗⢴⡿⣣⡞
⠀⠀⠀⢸⣿⣷⣿⣭⣅⣀⣀⡀⠉⠉⠓⠒⠂⠀⠀⠒⠒⠒⠒⠂⠐⠂⢀⣴⣶⣿⣿⣶⣆⣁⣠⣤⣶⣾⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡙⢛⢻⡟⡛⣿⢛⣟⠿⢻⣿⡟⢛⠋⠙⡏⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠙⢻⠿⡿⢿⣿⣷⣿⣶⣾⣧⣧⣿⣤⣿⣠⣿⣿⣷⣾⣷⣶⣿⣶⣿⣿⠿⣿⠟⠻⢹⠁⢾⣿⡇
⠀⠀⠀⢸⣿⣿⠀⢸⠀⡇⢠⠈⡇⠉⠏⢹⡏⢉⣹⡍⠙⠋⣹⣿⣟⠉⠉⢹⡏⠠⢼⡏⠀⢸⡇⡀⢘⣃⣼⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣾⣦⣧⣀⣠⡇⢠⡀⢸⡇⠠⢼⣿⠀⢰⣿⣿⣿⠀⠆⢈⡇⢀⣻⣀⣤⣤⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⡛⠉⢉⢝⣉⣉⠐⠄⠀⠒⠨⣀⠀⢁⡢⣀⡈⠉⢉⠙⠛⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡿⠛⢡⠚⣲⡮⠭⠽⠥⣅⣄⠀⠙⢶⣄⡀⠀⠀⠈⢫⡴⢡⡔⠀⠈⠀⠀⠀⡙⠙⢿⣿⣿⡇
⠀⠀⠀⠈⣿⣿⡟⡕⠒⢸⠋⠁⢀⣀⣤⠖⣈⣯⣳⠦⠤⠏⠹⠿⢦⣰⠊⠀⢠⡽⣄⣒⠾⠛⢩⠅⣉⠊⢿⣿⡇
⠀⠀⠀⠀⣿⣿⠁⣾⠷⣼⠄⠐⢭⠛⠛⠛⠻⢏⡠⣤⣀⣀⣀⣀⡀⢘⠀⠀⢸⣯⠟⢁⠠⠚⠛⠈⠏⠙⡘⣿⡇
⠀⠀⠀⠀⣿⣿⠀⢩⣙⡃⠀⢰⣷⡤⠖⠒⠀⠄⠌⣲⡶⠒⠀⡀⠀⠚⠂⠉⠙⢧⠊⠁⢀⣀⡤⢎⡜⢠⠁⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠈⡀⠢⢬⣽⠟⠒⠲⡶⢤⣤⣀⠈⡷⢴⠁⢀⣤⣤⠴⢞⣡⠾⠤⠤⢝⠛⢹⠉⢱⣬⠀⣿⡇
⠀⠀⠀⢠⣿⣿⡀⠨⡳⣄⠀⡏⠀⠀⢠⣿⣿⣠⡀⠈⠓⢄⠉⠒⣶⠟⠉⠀⠀⠀⠀⣀⢀⠜⠀⠀⡾⠁⢸⣿⣷
⠀⠀⠀⢸⠙⣿⣧⠀⠘⡶⠶⣧⠀⠀⡎⠀⠀⠙⣝⢦⡀⠀⣻⠵⠛⠐⢏⡉⠊⠁⠀⢀⣄⠖⠊⢸⡕⢀⣿⡿⢁
⠀⠀⠀⠈⠳⣮⣟⢦⣀⠳⣄⡨⠽⠯⠷⠼⢷⣢⣿⣷⡵⠋⠀⢀⣤⡞⠼⠀⠀⣤⡶⠛⠁⢀⠔⢈⣠⠾⣫⡾⠂
⠀⠀⠀⠀⠀⠈⠛⢧⣌⠙⠚⠳⠶⢤⣀⣀⣀⡈⠛⠛⠀⠠⠴⣋⡃⣄⠀⠀⣀⣀⣈⣴⢾⣛⣿⣉⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠤⢀⣀⣉⣉⣉⠉⠉⣉⡉⠉⢩⣭⣽⣿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠇⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣴⠀⠀⠀⢙⣷⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡼⢣⣤⠀⠀⠛⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣫⠴⠯⠤⠬⠭⣤⣤⣤⣄⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⣚⣛⡿⠿⠿⠿⠿⠿⣛⡓⢚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣉⠉⠉⠉⠉⠉⠉⣉⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⢸⣔⣲⠭⠭⠭⠭⠤⠭⠭⠭⣖⣂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢯⢽⣟⣛⣻⣻⣿⣿⣍⢭⢹⡇⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣴⢾⡇⠀⠀⠀⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢩⡟⣿⣿⢝⣛⣿⣿⣿⢟⣡⣽⢻⡇⠀⢶⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡇⣿⣿⣾⡿⢸⣿⣿⣿⣟⣮⢻⡇⠀⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠾⠧⠾⠿⠭⠽⠯⠬⠿⠑⢾⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣼⠩⠭⠭⣽⡟⠛⣛⣻⣯⠭⠭⠽⣧⣤⣤⣤⣤⡄⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡦⠤⠤⠤⠤⡤⣤⡤⠤⠤⠤⢴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡝⠛⠛⠛⠛⠃⠚⠂⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠚⠁⠛⠃⠒⠶⠠⠤⢀⣀⠨⣿⣿⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢸⣿⣶⣷⣾⣿⣤⣿⣿⣿⣿⣾⣿⣿⣶⣦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣄⠀⠒⠲⠶⢤⣬⣭⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣩⣥⣤⡤⠔⠒⠀⣀⣀
⠀⠀⢀⣠⡴⣖⣚⠭⠍⠒⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠊⠭⠴⣒⣠⣄⣀
⣠⣾⣿⡵⠚⠉⡁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡈⠙⠻⣽⣷
⣿⣿⣿⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠀⢸⣿
⣿⡟⠿⣷⣦⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⣤⣶⠟⠋
⢻⣷⣄⠀⠉⠉⠛⠻⠶⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡴⠶⠞⠛⠉⠁⠀⢀⣴
⢸⡟⠛⠿⣦⣤⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠉
⢸⡇⠀⠀⠀⠈⠉⠛⠛⠷⠶⢶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠛⠛⠉⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⢸⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡶⠋⠉⠉⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣠⡤⠤⢤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠟⠁⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢨⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠴⢤⡀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⠂⠽⠦⢠⡀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠘⣆⠀⠀⠀⣾
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠷⠤⠒⠠⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⡾⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠛⢶⣤⣤⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⢠⡞⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣤⣤⠴⠶⠛⠋⠁⠀⠀⣰⠟
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠶⠶⠶⠶⠒⠛⠉⠁
⢸⡇
⢸⡇
⢸⡇
⢸⣷
⣾⣷
⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾
⣿⣇⠉⠛⠿⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠉⢀
⠙⠿⣦⣄⡀⠀⠀⠉⠉⠙⠛⠛⠷⠶⠶⠶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠶⠶⠶⠛⠛⠋⠉⠉⠀⠀⠀⣀⣤⠾
⠀⠀⠈⠉⠛⠿⠶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠈⠑⢄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠊⠀⠀⠀⠀⢄⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠁⠀⠀⠀⠀⠀⠀⡀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠈⢆⠀⠀⠀⠀⠀⢀⡇⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡀⠱⢄⠀⠀⢀⡪⠣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡀⠈⠑⠋⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢉⣓⣴⣲⣽⡿⠋⢻⡏⠁⣸⣦⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢩⣶⣞⡿⠦⡏⣨⣿⠋⣱⣿⠛⢺⡁⣨⣷⠀⣰⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠙⢧⡧⠾⠧⡉⠁⠠⠿⠇⠸⠟⢉⣉⣥⣰⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⣤⡈⠑⠂⠠⠄⠉⠉⠉⠯⠿⠙⠚⣳⠟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢑⠠⠈⣙⠂⠸⡀⠀⠀⠀⠀⠀⠨⠞⡂⠈⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢈⡐⠒⠀⢠⠊⠀⠀⠀⠀⠀⠑⢣⠐⠈⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⠠⠀⣉⠀⠀⡥⠀⠀⠀⠀⠀⠀⡇⡂⠩⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠍⣐⠠⠄⠈⠈⡀⠀⠀⠀⠀⠀⠠⢒⡒⠈⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠠⠉⡐⠂⠠⠃⠀⠀⠀⠀⠀⠐⡄⠐⠈⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡐⠀⠀⠭⠀⠣⠀⠀⠀⠀⠀⢨⡍⠀⡐⠬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⢉⡀⠒⠀⡃⠀⠀⠀⠀⠀⢠⠃⢁⠒⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠂⡀⠬⠅⠈⡂⠀⠀⠀⠀⢠⠃⢀⣨⢅⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⡀⠈⠥⠀⠃⠀⠀⠀⠀⢌⣋⣬⣵⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠶⠶⠶⠶⠾⠿⠟⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⡤⠤⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⣀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠤⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡀⠛⢠⠉⠁⠈⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢸⣄⣤⢄⠌⢀⠴⠖⠄⢀⢤⠶⡤⢢⠀⠒⢀⡀⠂⢀⠄⠲⠆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠉⠉⠂⠀⠆⡦⠶⠁⠄⠀⢀⠃⡄⠀⢸⠏⠀⠀⢸⣌⢢⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠴⢚⣠⡤⠔⠀⠡⠐⠤⠞⠣⠐⠞⠇⡲⠟⡈⠀⢀⠰⠻⣫⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠤⠐⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣟⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣭⣿⡿⢿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⣯⣼⣿⣯⡅⣿⣿⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢥⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣾⣿⣙⡿⠧⣿⣇⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣿⡞⣩⣿⣿⣶⡨⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢏⡹⢛⠟⠻⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⣶⣷⡷⠶⢶⡶⡾⢿⠿⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣶⣦⣦⣶⣾⣷⣷⣶⣶⣶⣶⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣯⣽⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠟⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠉⠉⠉⠙⠛⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠐⣚⠤⠴⠒⠒⠒⠒⠒⠤⣀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⢀⡴⠋⠀⣀⠤⠒⠒⠒⠒⠢⢄⡈⠣⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠎⢀⡴⣩⠖⠋⠉⠉⠉⠉⠓⢦⠙⣄⠹⡈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⡎⢠⢎⡜⠁⠀⣠⢔⣒⣒⠢⡄⠀⢳⠸⡀⢣⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⣰⠁⡌⢸⣀⡀⡰⡝⠁⠀⠀⢱⢸⠀⠀⡇⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⠀⡇⢸⠀⠈⢱⡳⣀⢀⡠⣎⠞⠑⢦⢃⣇⣸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⡆⠘⡌⢧⡀⠀⠉⠛⠛⠋⠁⠀⣠⢎⠎⢠⠃⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣄⠈⢦⡙⠦⢄⣀⣀⡠⠴⣊⠵⠋⣠⠏⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣈⠳⣄⡈⠒⠒⠒⠒⠒⠊⢁⣠⠖⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠉⠉⠒⠒⠦⠴⠚⠉⠤⠄⣼⡿⠛⠻⠿⠿⠿⠷⢶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣤⣘⣈⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣽⠿⠿⣿⣻⣿⣽⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⣿⠿⠻⣿⠿⠓⢿⣅⣼⣯⡤⠤⣬⡿⠶⣾⡋⠉⢿⣤⣭⣷⣍⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠻⣿⡶⠛⢻⣤⠶⢴⣟⠛⢻⣦⣤⣤⣿⠶⣬⡿⠛⣿⣁⣠⡼⠃⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠻⣶⣬⣙⠶⠾⣧⣤⣀⣽⣄⣿⣅⣀⣤⣽⣦⡼⠷⠖⢛⣉⣥⣴⡿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⠢⢍⡛⠛⠿⠶⣶⣶⣥⣬⣤⣤⣤⣤⣤⣶⣶⠶⠿⠛⠛⣉⡥⠖⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠉⠒⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠉⠁⠠⣶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⠏
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⣗⡢⠤⢄⣀⣀⡀⠀⠀⠀⠀⢀⣀⡠⠤⢒⣫⣵⡿⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⣶⣤⣤⣬⣉⣉⣉⣭⣥⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣄⠀⠀⣠⣾⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀
⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⢛⡛⠻⠿⣿⣿⣿⣉⣉⢻⣿⡏⠛⢹⣿⣏⢛⣹⣿⢛⣿⣿⣽⠟⠻⣯⣹⣿⡟⠋⢻⣿⡏⠙⢹⣿⠉⠋⢫⣿⣏⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿
⣿⣿⣷⣾⣿⣿⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠸⠇⠈⠉⠛⠛⠿⠿⠿⠷⠾⠿⠿⠿⠿⠛⢫⠛⡻⢿⣿⣿⣿⣭⣭⣭⣿⣿⣶⣿⣿
⣿⣿⣿⢿⢻⣝⢦⣹⣿⣼⣿⣿⢿⡛⠭⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢉⠻⣿⣾⣿⣞⣽⡇⡟⣿⣿
⣿⣿⣿⣸⣼⣿⣷⣿⣿⡿⠋⠶⠈⠁⠀⠀⠀⠀⠀⣀⣤⢴⣶⣲⣿⣿⣿⣿⣿⣿⣟⣛⣓⣲⠶⠦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣌⠻⣿⣿⣿⣧⣷⣿⣿
⣿⣿⡿⣿⢿⣿⣾⠟⣉⠘⠁⠀⠀⠀⠀⠀⣠⢖⡯⠗⠚⠻⠷⠶⠒⠒⣒⣒⣒⣒⣒⠶⠿⠭⣭⠛⠒⠶⢬⣍⣛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⢿⣿⡿⣿⢿⣿
⣿⣿⡇⢀⣾⡿⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡮⣙⠶⢤⣄⣛⡛⠒⠶⠷⠶⠤⠤⠤⠤⠶⠶⢶⣚⣋⣤⡤⠶⢟⣣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡹⣷⡀⢸⣿
⣿⣿⡇⣾⡟⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠛⠒⠮⢭⣽⣛⣛⣛⣛⣛⣛⣛⣛⣉⣩⣭⡥⠶⠖⠛⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠹⣷⢸⣿
⣿⣿⣷⡟⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⠠⠤⠄⠀⠉⠉⠉⠭⠁⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡹⣿⣿
⣿⣿⣿⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣔⠢⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡆⠀⠀⠶⢻⣿
⣿⣿⡏⠒⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⠀⠀⢸⡇⠀⠀⠀⢁⢹⣿⡛⠏⣿⠰⡏⣿⠉⠋⣭⢉⣿⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⢈⠻⠿⠿⠿⠿⠉⠀⠀⠀⠘⣙⣿
⣿⣿⣇⡃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇⠀⢸⡇⠀⠀⠀⣒⣨⣿⣧⣶⣼⣬⣷⣿⣾⣴⣥⣽⣿⣑⡀⠀⠀⠀⠀⣼⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿
⣿⣿⣏⣷⠀⠀⠀⠈⠙⠿⠛⠻⠛⠁⠀⠀⢸⡇⠈⢰⣿⠟⠛⢻⡟⣉⣽⣿⠉⢿⡏⠙⡟⢹⣟⡛⠿⣿⡎⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣿
⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡄⠛⠸⡇⢉⣽⡇⠤⢸⡇⢀⠁⣼⡿⢁⣾⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿
⣿⣿⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣧⠘⢀⣧⣈⣹⣥⣾⣤⣧⣾⣦⣟⡀⠛⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⣿
⣿⣿⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠒⠀⢸⡇⠀⠀⢹⣿⡿⣿⣿⣿⣿⣿⣛⣟⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣿
⣿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⣿⣿⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣿
⣿⣿⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠀⠀⢀⣷⠀⠀⠀⠀⠀⢀⣶⣷⣄⠸⣇⡀⣿
⣿⣿⣿⡋⠀⠀⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⣟⣹⢗⣻⣞⣭⣿⡿⠻⣷⣴⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⢼⡿⢠⡀⠀⠀⠀⠘⠻⡟⠋⠀⣼⠟⣿
⣿⣿⡏⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡈⢿⣭⣽⣡⣽⣖⣻⣟⠙⢻⣯⣤⡟⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⠸⣟⣘⣿
⣿⣿⣷⢃⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⣟⠀⠀⠐⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠁⢠⣿⣿⣿⣿⣧⠻⣬⣿
⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣧⠶⢿⣿⣿⣿⣿⣧⢀⣴⡆⠀⠀⠀⠀⢀⡀⣿⡇⣹⢁⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⠃⣸⣿
⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣸⡟⣽⣥⣀⣀⠀⠀⠀⠁⠈⠠⠀⠈⠀⠀⠀⢀⣤⣤⡴⢞⣿⣿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠉⠙⠛⢠⣿⣿
⣿⣿⣿⣷⡈⢿⣿⣿⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣶⣿⣶⣾⣭⣽⣟⣓⣶⣶⣶⣶⣶⣶⣶⡿⣿⢿⣶⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⣼⣿⣿
⣿⣿⠟⢹⣧⣈⡛⡋⡃⠀⠛⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⣰⣿⢻⣿
⣿⣿⡗⣏⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⢿⠿⢿⠿⣿⣿⣿⣿⡿⠿⢿⢿⠿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⣿
⣿⣿⣷⣏⣿⣿⣿⣄⢠⡞⣁⠀⠉⠳⣄⠲⢠⠞⠉⢀⣀⡙⢷⠀⠀⣀⣴⣿⠛⣿⣦⣄⢠⡞⠉⣠⣄⠀⠈⠙⣦⠚⣠⠞⠉⠁⢀⣤⣌⢹⡆⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣿⠿⡿⣿⣿⣧⣽⠇⠀⠀⠹⣦⡟⠀⠀⢸⣝⣁⣼⣷⣾⣿⠿⢿⣞⡿⠿⢿⣿⣿⣦⣭⣼⠃⠀⠀⠘⣷⡏⠀⠀⠀⠸⢧⣭⣼⣷⣿⣿⣟⣿⣿⣹⣿⣿
⣿⣿⣧⣸⣿⣾⣶⣤⣽⣿⣷⣶⣶⣶⣶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣯⣿⣷⣿⣿⣿⣬⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣴⠖⢲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⡇⠀⠀⣿⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢙⠆⠈⣿⣿⠀⠀⣿⠁⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣿⣿⠀⠀⢸⡇⠀⣿⣿⠀⢸⡇⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⣿⡄⠀⢸⡇⠀⢻⣿⣆⣾⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡠⠈⣿⣿⡄⠈⡇⠀⢸⣟⣿⡇⢀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⠸⣿⣷⡴⠷⠆⣸⣿⣏⠀⠘⠟⠉⠃⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡀⠀⠀⠘⣧⡀⠸⠿⠃⠀⠀⠀⠈⠁⠀⣀⡆⢠⣤⣀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⣿⣷⣿⡀⠀⢀⡿⠈⠀⠀⠀⢀⣤⣾⣮⣿⡷⣿⠿⠊⣿⠿⣿⣦⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡇⢹⣿⣿⡇⢀⡞⠁⠀⢀⣤⣶⣿⠟⣿⣿⢉⡄⠨⣅⣈⣀⣐⡉⢻⣿⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⣿⣿⣷⡟⠀⠀⠀⠠⣿⣿⡛⣾⣿⣿⣿⣿⣷⢻⣿⣿⣿⣷⣷⣉⣻⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⢘⣿⣿⡟⢀⠀⠀⠀⣠⣿⠇⣜⣶⣿⣿⣛⣿⠟⠠⠿⠿⠟⠛⠛⠛⠛⠓⠾⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢨⣿⣿⢱⡇⠀⠀⢠⣿⠏⠱⣿⡿⢿⣿⡟⠃⠀⠀⠀⠀⠀⣠⣤⣤⣤⡤⢀⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠘⢻⡟⣾⠀⠀⠀⣾⡿⣦⣼⣿⠀⣾⡟⠀⢀⠐⣂⣷⡞⠇⠉⢉⣩⣟⡳⠆⠙⢃⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠙⠛⠾⣷⡯⠀⠀⣾⣿⣿⣿⣿⣿⡻⣿⠇⠀⢈⣰⣿⣟⠋⣀⣤⣿⣷⣾⣿⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⠰⠋⠀⠀⠀⠀⢸⣿⡀⣠⣿⣿⣿⣿⣿⡏⣾⡿⠀⢠⣞⣿⣿⡟⣠⣿⣿⣏⢻⣿⣿⣛⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣀⠿⠂⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣶⣿⣿⢱⡿⠆⠀⢸⣿⣿⡋⠀⣿⡿⠉⢻⡿⠛⣩⣿⡛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣤⣽⣿⣤⣴⣾⣦⣤⣼⣿⣿⣿⣿⣿⣿⠏⢩⣶⣟⠉⠀⢀⣽⣿⣿⣿⠀⣿⣿⣤⡟⠃⣼⣿⣭⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⣿⣿⣿⡿⣿⠁⠋⢹⣿⣿⣿⣿⡿⠛⠁⠐⠈⠉⠁⠰⢦⣿⣿⣿⣿⣿⡗⣿⣿⠛⢷⣦⠙⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⣿⡿⠋⠀⠈⠎⣠⡞⣿⣿⠏⣠⡄⠀⣠⣄⣀⣤⣠⣤⣤⣬⣍⢙⠛⠿⠛⢿⣿⣦⡈⠛⠂⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣿⠃⠠⠀⢲⣄⣽⣿⣿⠏⣸⣿⣦⡀⠳⠛⣿⡿⠿⣿⣯⣻⣟⣭⣷⣿⣧⠈⣿⣿⣿⣾⠛⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢠⣿⣿⣿⡶⢤⣬⣿⣿⢟⢁⣴⣁⢈⠙⠛⠀⠀⠁⢣⣾⣷⠿⢟⠿⣹⣿⢻⡙⠣⣙⢿⡿⠛⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠰⡙⠟⣻⣶⣮⣽⡿⢏⠀⢠⠟⣉⠀⢀⠀⠀⢄⠀⠄⠀⠛⠀⠈⣶⠜⠀⢻⣿⡀⠈⠀⣀⡤⢒⣈⡉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣿⣿⣿⠿⠋⠀⠀⠀⡌⠋⣀⣴⣦⣶⣦⣾⣃⣴⠋⠒⣀⠀⡁⢀⠀⡸⣿⠓⢠⡞⣻⣿⣿⣿⣿⣧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⠋⠡⠀⠀⢀⣠⣾⣇⣼⡿⣿⡹⢻⣿⣿⣿⣇⡙⢷⠁⡆⠛⠀⠰⠟⣿⣠⣿⠀⣿⣿⢿⣿⣿⣿⣦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡄⠀⠀⠀⢸⡟⢡⡦⠙⣵⣌⠰⣜⣿⣟⣹⣾⣳⠄⠳⡀⢶⠋⠀⢰⡟⠛⠃⣰⡇⠈⣿⣿⣿⣿⣿⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⠀⡝⠀⠀⠻⡄⠉⢠⣶⡙⢻⣧⣼⣿⣾⢦⣾⣳⡾⠋⠑⣆⡵⠊⣀⣰⠟⣱⢿⣴⣛⣻⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢰⡏⠀⠀⠹⠀⢴⢸⣿⣧⠘⡏⢬⣹⡔⠂⡸⢍⢰⠆⠚⣉⣤⡿⣿⠁⢰⡟⢻⣿⣛⢋⣷⣾⣿⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢸⣿⡄⠀⠘⣀⣆⣸⣿⣿⣿⠋⠂⡘⢏⡠⠁⣸⠇⠔⠊⠙⢧⠙⠁⣶⠎⢁⠞⢹⣧⡝⣳⢾⣿⡏⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⣿⣿⣷⡄⢿⡟⣿⣿⣿⣿⡀⠂⠀⠂⠠⠀⠡⣶⠄⠀⢠⣾⠀⣾⢋⣴⡟⢠⠟⣻⠰⣍⡾⣩⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡌⢿⣿⣞⠳⣝⠻⡿⢹⠿⡇⠠⠒⢀⣠⣏⡐⢀⡠⠲⡄⠁⣼⢃⡽⠁⣼⡿⢠⡿⠓⡈⠻⠈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣮⣿⢯⣷⠜⣁⣄⣀⠀⡧⠀⣤⣟⣥⣿⣿⢟⠁⣴⠀⢐⣃⣜⣱⣾⢛⣿⡟⢁⡖⠀⢂⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣻⣿⢼⣯⡧⣀⣿⣌⢿⡿⢿⣿⡶⠂⡀⢀⡀⢏⣹⣟⠿⣧⣴⠟⢳⣬⠃⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡙⢿⣷⣧⣼⣿⣿⠛⠻⠋⠀⠀⢀⠎⠁⢰⡏⢠⡾⢿⡅⣨⠳⣄⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣭⠓⣏⢉⡱⣟⢀⢠⡔⣰⣁⣌⡁⢲⣤⡉⢱⣿⣬⠟⢶⠆⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣡⣬⡵⠏⢰⠋⣀⡞⠓⠾⣟⣁⣿⣠⣷⢾⠉⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣈⣷⠶⣻⣿⣿⠇⣿⡿⢁⣅⢹⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⣿⣧⣠⡽⣧⡾⠿⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⡃⠠⠃⠰⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⡿⣷⣶⡌⠁⠀⠀⣠⣶⣶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠿⣿⣧⣿⠃⠀⠀⣰⣿⣿⣋⡛⢻⠿⠛⠉⣻⣿⣧⣶⡾⠆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣿⣾⠁⠀⠀⢰⣿⣿⠏⠉⠈⠁⠀⢠⣾⣿⣿⣿⠟⠱⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣏⢀⠀⢠⣿⣿⢿⢀⠀⠀⠀⢀⣾⡟⠋⠉⠀⠀⠐⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢀⣸⠿⢿⣿⡴⢻⣿⣿⣾⠘⠁⠀⠀⣸⣇⠀⠀⠀⣠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⢸⣿⣾⣿⣿⣟⠅⠀⠀⠀⣿⣣⣴⣾⣿⠟⠂⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⢇⠀⡀⢼⡻⣿⡟⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣀⣠⡟⠁⠹⣿⣿⣿⣷⣧⣚⠡⠞⢿⣤⣄⡀⢀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢰⣽⡿⠁⠀⠀⠐⠋⢿⠉⠀⠁⠀⠂⠀⢙⠻⠟⠳⠾⠷⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⢀⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣬⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡍⠀⠀⠀⠀⠂⠐⢒⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠾⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠴⠊⠀⠆⠀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡗⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢠⠀⠠⠃⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣶⣞⠿⠟⣠⡧⢀⣷⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣮⣟⣦⣼⣧⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠁⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣄⡀⢀⠀⣿⠃⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠋⠙⢿⡄⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢴⣾⣣⣂⠀⠀⡀⠀⠀⣀⣴⣿⣿⡟⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧⠀⠀⣿⣿⠟⠉⠀⠀⣀⣄⣠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠁⠀⢀⣴⣾⣫⣽⡿⠖⠀⠀⠀⠀⣴⣶⠟⠋⠁⠀⠁⢦⣤⣶⡿⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣏⡴⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⣷⠿⣟⠿⠋⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠆⠀⠀⢰⣿⣿⣿⣿⣿⡏⠸⠂⠀⠀⢸⣿⣿⠀⠀⠀⠼⣽⠞⠁⠀⠀⠀⡄⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣾⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇
⢀⡠⢐⠒⣿⣽⣿⣿⣿⣿⣿⣿⡏⠐⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢀⠀⣾⣿⣷⡴⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⡃
⣞⣿⡋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢸⣿⣿⣿⣿⣏⡂⠀⠀⡎⠃⣘⣿⣿⣿⣎⡥⢀⡀⠀⠀⠀⢼⣿⣿⣿⣦⣀
⢹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣻⣷⡄⠸⣿⣿⣿⣿⣿⣿⠳⣄⣤⣾⣿⣿⣿⣿⣿⣿⠉⡆⠀⠀⠐⢸⣿⣿⣿⣿⠿⠛⠋
⠀⠙⠛⠛⠉⠀⠀⠀⣼⣿⣿⣿⣿⠬⢽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡾⠁⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⠀⠀⣠⣤⡴⣶⣶⣾⣿⣿⣿⣿⣿⡇⡀⠈⢡⡀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⡃⠀⠀⡀⠀⠸⣿⣿⣇⡙⢷⣿⣷⣠
⠀⠀⢰⣯⢵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⠶⠒⠉⢄⠀⠀⠈⠀⢿⣿⣿⣤⠌⢿⡄
⠀⠀⠸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣫⣿⣿⡷⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⢀⢾⠻⢷⣦⣼⣀⡴⣄⠀⠀⠀⣿⣿⣷⡄⠈⣧
⠀⠀⢠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⢟⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠿⣇⠀⢤⡰⠉⢿⢿⣿⡚⠳⢄⣴⠋⢿⣿⣧⡰⡏
⠀⠀⢘⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣻⣝⣷⣮⣷⣿⣿⣿⡿⢻⣿⣿⣿⢣⡀⣈⠲⢄⠴⢃⢰⢧⣿⣷⣿⣶⠋⠀⠀⢹⡛⣿⠁
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⢁⣾⣿⡿⢣⡈⠙⢿⣷⣬⣤⠀⣪⣷⣿⣿⣿⣧⠄⢐⠀⠀⢧⠘
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡏⠀⣼⣿⣿⣿⠋⣢⢐⣶⣿⣿⣿⣮⠙⠦⣿⣧⣼⣯⠀⢀⠐⣜⠢⡄
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣯⣠⡈⢿⣿⣿⢿⣉⣷⢾⡟⣷⣼⢿⣷⣿⣾⣟⡿⠏⠀⢰⠄⠈
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⢳⡌⠻⣿⣧⣴⣿⣿⣿⣿⡿⢫⢼⣿⣿⣿⣿⡆⠀⠋⠀⠀⢀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⣽⡧⣾⣏⡿⢉⣿⣴⣦⣻⣿⣿⣿⠛⠉⠹⠀⢈⣿⣿⣿⣿⠀⠐⣄⠀⠀⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠁⣾⣯⡿⣿⣿⣿⠟⠉⠀⠐⡈⣿⣧⣿⡿⠀⡉⠸⣷⡄⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣟⠀⣿⣿⡟⣼⡿⠿⡄⠀⢠⣄⣀⣛⣿⣿⡇⠸⠁⠀⢻⡛⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣶⣯⣸⣿⣿⣦⣀⣈⡐⢂⠈⠙⠻⣿⣯⡄⣷⢀⠀⢾⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣻⣿⣗⣢⠌⢹⣿⣿⣿⢹⢾⡖⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⡟⢤⢿⣿⣿⣇⠿⠾⣅⡦⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣴⠿⣽⣿⠀⣶⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⣰⣿⠉⣆⠺⢻⡿⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣍⡿⣿⢧⣶⣼⣿⢏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡌⠀⠀⡀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣈⠀⣈⡀⢄⠱⡀⢆⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⢂⠐⠒⠩⠠⡠⠄⠊⢠⡄⢄⠁⠌⡄⢡⢾⠀⣀⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢔⠣⡖⠠⡀⠀⢀⡀⢈⢃⠀⠀⠔⠟⠌⠴⠄⣒⠇⠸⠇⠀⠉⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠁⠢⠀⠠⣐⠭⠄⢀⡂⠀⠦⡘⠠⠌⡁⠡⠔⡩⣁⠶⡤⠀⡞⣠⢜⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠈⢈⡀⡡⠘⡸⢃⡔⠐⡆⡔⢈⠨⡉⡀⠓⠫⠙⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠑⠈⠀⠂⠐⠀⠙⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣄⣀
⠀⠀⠐⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣉⣿⣛⣙⣯⣉⣿⣏⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⡶⠶⠿⠿⣿⣿⠿⠿⠿⢶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣀⣤⣶⢾⣿⣿⣽⣿⣿⣷⡿⠿⠛⠛⠛⠿⣿⡿⠿⠿⠿⣿⣿⣿⣯⣭⣛⡻⢷⣦⣄⡀
⠀⢀⣴⡾⢛⣥⡶⠟⠛⠛⠻⣿⣿⣿⣇⣀⣒⠶⠤⣤⣼⣇⠐⠲⢦⣤⣝⣿⣧⣤⣄⣈⣷⣮⣝⠻⣦⣄
⢠⡿⢋⣴⣿⣿⣤⣤⣬⣿⣷⡼⠀⠀⠩⠟⠛⢿⣿⠋⢉⣈⣉⡙⣿⡟⠋⠉⣉⡛⢿⣿⣿⠿⠿⣷⣌⢻⣦
⣿⠇⣾⡏⠉⢉⣹⣿⣿⣿⣿⠀⠀⢀⣴⣶⣽⠟⠛⠓⠒⠶⣾⠟⠉⠁⠀⢈⣻⣿⣧⠏⠀⢠⣶⠘⣿⡆⣿
⢿⣇⠹⣿⣦⣤⣹⡟⠁⣠⣼⣶⡾⠟⠛⢿⣯⣀⣈⣽⣿⠖⠽⣷⣶⣶⣶⣿⣧⠟⠉⢀⣴⣿⣟⣼⡿⢁⣿
⠘⣿⠀⠈⠋⢁⡘⢃⡚⣛⣿⠋⠀⣠⢞⣵⣿⣿⣿⣿⣇⠀⠐⢤⣽⣿⡿⠿⢇⣀⣘⣩⣶⣾⡿⠋⠀⢸⣿
⠀⣿⠀⣶⠀⠀⠙⠻⠿⢿⣿⣤⣤⣷⣿⣿⡿⠛⢛⣛⣿⣷⣶⣶⣿⣏⣠⣾⣿⣿⠿⠿⠛⠉⣠⣴⡆⢸⣿
⠀⣿⡀⣿⠀⠀⠀⠀⠀⣀⡀⠈⠉⠙⠛⠛⠳⠶⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁⣀⣀⣤⣴⣶⣿⣿⣿⣷⣼⣿
⠀⣿⣇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠻⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣈⡳⠄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣁
⠀⠀⠀⠀⣾⣿⣿⣿⣶⣄⣀⠲⠮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢛⣩⣴⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⡋⠉⠉⠀⠀⠉⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡩⠖⠒⠉⣉⣉⡉⠉⠓⢄⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⡰⠋⣀⠴⣚⠭⠭⠭⠭⣍⠳⣄⠱⡌⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⡰⢁⡜⡵⠋⠀⢀⣀⢀⣀⠀⠱⡌⣇⠱⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣇⢠⠃⡜⡼⠁⠀⣴⡵⠒⠐⢮⢳⠀⢹⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⠀⡇⡞⠈⠲⡽⡀⠀⢀⡜⡸⠠⣸⢯⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠘⡄⢳⡹⡄⠀⠙⠺⠿⠟⠊⠀⢠⢏⠏⡹⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠱⡄⠑⣌⠲⢄⣀⣀⣀⡤⢞⡵⠋⣰⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡘⠢⣀⠑⠒⠒⠐⠒⠊⢁⡠⠞⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠉⠑⠒⠲⠔⠚⠁⠤⢠⣾⣟⣛⣛⣻⣿⡷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⢶⣤⣩⣴⣶⡿⣿⡿⣽⡿⠿⢿⣯⠟⢻⣿⣻⡿⢯⣟⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢡⣾⠟⣋⣿⠛⠉⢻⣤⣾⡶⠒⠲⣿⠛⢿⣅⣈⣷⠶⠾⣷⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⠻⢿⣉⢹⡟⠛⠻⣏⠉⡽⠛⠓⢿⡟⢳⡏⣉⣿⡴⠖⣋⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⣝⠻⢶⣭⣭⣛⣒⡲⠿⠶⠿⠖⠖⠚⢛⣛⣉⣭⣤⡶⠿⢛⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠉⠒⠤⠭⢉⣙⡛⡛⠛⠛⠛⠛⣛⣛⣋⣉⡡⠤⠔⢊⡉⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠰⡂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢙⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣕⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣫⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣬⣉⣉⣐⣒⣒⣒⣂⣩⣥⣴⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣿⠿⠋⠀⠀⠀⢀⠀⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠲⣄⢀⠀⢀⣾⣿⡿⠏⠈⠀⠀⢀⡠⠄⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣿⣿⡗⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠛⢁⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣆⢠
⠀⠀⠀⠀⢸⣿⣿⣿⣏⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠿⠛⠛⣿⣿⡿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠰⠞⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠾⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣮⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠣⡀
⠀⠀⠀⠀⠘⢿⠹⡌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⡔
⠀⠀⠀⠀⠀⠘⡅⠁⠄⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠛⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣭⣤⣤⣶⣶⣿⣿⠉⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣷⣠⡢⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠻⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠟⠋⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣶⣾⡧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣇⠀⠀⠀⠀⢀⣠⣶⣿⣟⠉⠀⠀⠀⠀⠀⣠⣾⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣻⠂⠀⠲⣿⣿⣿⣿⣅⡀⠀⣀⣠⣶⣾⢿⠁⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⡾⠛⠻⡛⢁⣀⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢐⣒⣒⣀⣂⠉⠉⢉⠉⠍⢩⠉⢍⠁⢆⡐⠂⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣴⡾⢻⣋⡥⢦⣡⡏⠀⢀⣀⣀⡠⠖⢰⡊⡖⠛⢺⡟⠛⣶⡤⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠉⠛⠛⠐⠾⠧⠘⠷⠾⠤⠼⠟⠣⠸⠿⠗⠐⠒⠛⠛⠉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠾⢿⣄
⠀⠀⠀⠀⢀⡀⠔⠚⠩⠘⠤⠃⡝⣀⠋⠏⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⢤⣀
⠀⠀⢀⣴⠋⠑⡂⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠤⠒⠒⠀⠐⠒⠒⠤⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠣⡀
⠀⢀⠎⠀⠐⠀⠁⢀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⡞⠀⠁⠠⠈⠆⠀⠁⠀⠀⢂⠀⣀⣨⡴⢁⠀⠀⠀⠀⠆⠁⠀⡲⠀⠀⠈⢣⠙⢶⣄⡀⠈⠀⠈⠀⠀⠀⠀⠀⢡
⢸⠑⠀⠀⢀⠀⠀⠈⠀⢀⡤⠒⠒⠋⠉⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣀⣉⡉⠙⣆⠀⠀⠀⠀⠀⠀⡇
⠘⠈⠀⠀⠀⠠⠀⠁⠀⡎⠀⡖⠂⠀⠠⡔⢲⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⡀⠘⠀⠀⠀⠀⠀⠀⢰
⡄⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⢖⡓⡠⠏⠐⠟⠂⠀⠙⠆⠀⠛⠀⠙⠋⠛⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡆⠀⠀⠀⠀⢤⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠀⡸⠀⠀⠀⠀⠀⠀⢸
⢡⠀⠀⠀⠀⠀⠀⠁⠀⣣⠀⠘⢄⠀⠀⢀⣸⡀⢉⠄⠰⠏⠀⠛⠄⠈⠙⠑⠀⠹⠆⠀⠠⠀⢠⠃⠀⠀⠀⠀⠀⠀⡸
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠘⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠒⠀⠐⠊⠉⠒⠀⠒⠒⠉⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠙⡄⠀⠀⠀⠁⢀⠀⠀⠁⠀⠀⠀⠀⠉⠒⠒⠤⠤⠤⠀⠀⠀⠠⠤⠒⠊⠁⠀⠀⠂⠠⠀⠀⠀⠀⠀⢀⡋
⠀⠀⠀⠹⡄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⢁⠞
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠢⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠾⢿⢿⣶⣦⡤⢤⢄⣤⣤⣄⣀⣀⣠⡤⠤⠴⢶⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣯⣥⢋⡬⢦⣄⡁⠀⠩⠘⠛⢿⣷⣿⡷⠓⠒⠛⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣽⡏⢰⠾⢧⡀⢹⡟⠛⢳⣤⡤⢤⢈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢫⠈⠣⣤⠚⠙⡏⠙⢶⠗⠛⣆⡼⠦⡀⠘⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡈⠉⠚⠳⠤⢼⣀⣾⣬⣇⣠⣯⢄⣀⡩⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠦⠤⢤⣠⣤⡤⠴⠶⠶⠶⠶⠤⣤⣀⡀⠈⠙⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠲⢤⣀⠈⠉⠓⠢⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⡀⠀⠉⠃⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠤⣄⠀⠈⠉⠒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀

⢸⡎⣇⢻⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠈⣿⣽⣼⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢻⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⡉⠠⣄⣠⣿⡿⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠸⣿⠟⠈⠉⢩⠀⠀⠀⠀⠀⣠⣛⢁⠉⢉⣿⡿⢋⣤⣿⣶⣏⣭⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅
⠀⠀⠻⣷⡆⣠⠇⠀⠀⠀⠀⠀⣿⣷⣾⠿⣿⡟⣶⣿⣍⣙⣷⢼⣿⣦⢿⡿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠁⡇⠀⠀⠀⠀⠀⢠⣝⣿⢀⣷⣾⠙⣿⢷⣿⣛⣳⣄⣽⣧⣼⣇⣹⠗⠀⠀⠀⠀⠀⣿⠟⣿⡇
⠀⠀⠀⢸⢰⣷⠀⠀⠀⠀⠀⠸⢿⣿⣿⣯⣼⡦⣷⣴⡛⣉⡿⠭⢿⡿⠉⣟⣹⣄⡀⠀⠀⠀⢸⣿⠀⢹⡇
⠀⠀⠀⠈⡌⣿⠀⠀⠀⠀⢠⣤⣾⢋⣑⣟⢛⣷⣿⣿⣿⣿⡷⣶⣾⣷⣾⡿⢿⡇⠀⠀⠀⠀⢸⣿⣧⣨⡇
⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠸⠏⣩⠋⣹⣿⠿⣧⢘⣿⡿⠹⣷⣾⣏⣤⣾⣦⣾⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢷⣿⡀⠀⠀⠀⢰⣟⣿⢾⣿⣿⠇⡛⣿⣦⣅⣴⣧⣾⣉⣉⣹⣯⣭⠇⠀⠀⠀⠀⠈⢻⣭⣭⡇
⠀⠀⠀⠀⣸⣿⡇⠀⢀⡇⢸⣿⣿⣄⣿⣿⣿⣿⣿⣿⠟⠳⢾⣿⣿⣌⣿⡷⠏⠀⡀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⣿⣿⣷⡀⠘⠂⠀⠙⢿⣿⣿⣉⣠⣽⣀⣿⣲⣶⡟⠛⠟⠛⣁⣀⣀⣤⣀⡜⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠑⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆
⣀⣀⣀⣀⣸⣿⣇⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣧
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⠄⢠⣄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⢀⣠⣤⣀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠑⠞⢹⣧⣭⣦⣾⠿⠋⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠰⠆⢺⣿⠩⣄⠿⣾⡿⠻⡏⡿⣻⣟⣶⠀⠠⠀⠀⢀⠀⠀⠒⠶⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠀⠀⠀⠀⠀⠲⣄⠉⠩⠟⠹⠿⠷⠿⠾⠟⠛⠿⠻⠋⠀⠠⠂⠀⠈⢧⡀⠀⠀⠀⢀⡴
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣻⠖⠆⠻⠦⢴⡶⠄⠀⠀⠀⠉⠿⣓⣒⣒⠒⠒⠒⣖⣒⣒⡶⠟⠁⠀⠀⠀⠀⠈⠛⠀⠐⠛⠋
⠀⠀⠀⢼⣤⣦⡀⠀⠀⠀⡇⠀⠀⢠⣴⡿⠀⠠⠠⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠉⠛⠻⢦⡴⢊⣷⣤⣶⠿⠋⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⢤⣦⠰⡟⡄⠀⠀⠀⠀⠀⡯⢸⡇
⠀⠀⠀⠲⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠻⣦⣄⣶⣶⡄⠀⠀⠀⠃⢸⡇
⠀⠀⠀⠀⣴⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠆⣀⡀⠀⠀⠈⢞⣡⠀⠀⠀⠀⠀⠀⠀⠰⣿⡖⢻⣿⡀⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠃⠀⠀⠀⣸⡀⠀⠀⠀⠈⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⠄⣍⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠠⠂⠐⣢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠃⠀⠀⠀⠀⠐⠘⠋⡉⠀⢠⡀⠈⠁⠀⢀⡄⠀⠀⠀⢀⠀⠀⠀⣼⣆
⠀⠀⠀⠀⠀⠇⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣤⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣷⠀⠀⢀⣾⠀⠀⣠⣿⣿⢀
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⣀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⠀⠀⠀⠀⠀⢿⡅⠀⠐⠾⢿⣧⠀⠀⢸⠟⠀⠀⠀⠈⠙⢧
⠀⠀⠀⣦⣹⣿⣇⡄⡀⠢⢄⡈⠉⢺⡧⣔⠢⣀⡀⠀⠀⠀⠀⣀⣠⠖⠀⢀⣷⡠⠀⠀⠀⠀⠘⢿⣦⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠺⣧⠿⢷⣿⣶⠦⣤⣄⣾⠻⢿⣷⣦⠁⣠⣉⡥⣓⣅⣶⣿⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠘⠛⠻⡍⡭⢛⡽⠛⠛⠒⠋⠉⠁⠉⠉⠈⢉⣁⣠⡴⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠐⠒⠐⠀⠀⠀⠀⠐⠒⠘⠉⠉⠀⠀⠀⣀⠠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠝⡷⣽⣗⢋⣀⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠛⡶⣏⢻⣯⣂⠀⠒⠦⠤⠤⠀⠂⠀⠀⠈⠁⠀⠀⠀⠔⠟⠋
⠀⠀⠀⠀⣀⣤⠒⠈⠅⠠⠀⠠⠀⠠⠲⢶⡤⢀⡠⠤⠒⠒⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠉⠀⠂⠀⠀⠀⠉⠠⣤⡀⠀⡡⠾⠙⠆⠀⠀⠀⠀⢀⠀⢠⡰⠤⣀⡨⣆⢲⡀⠤⠠⠀⠀⠀⠈⠀⠀⣠⣀⣤⣔⢰⣴⣤⣔⠀⡀
⠀⠀⠠⡌⢠⣀⠀⠀⠀⠀⠀⠴⠼⠥⣬⡁⣀⡞⢠⠀⠀⠀⢀⣀⠭⡐⠊⠉⠒⢒⡈⡀⠊⣉⡑⢤⠀⡄⠀⠀⠀⠓⠋⡩⢙⣿⣿⠭⢸⣔⡆
⠀⠀⠀⠀⠔⡍⠉⠈⠀⠒⠒⠒⠓⠒⠉⠉⠛⠡⠤⠄⠀⠸⠦⡥⠲⠬⠇⠈⠄⠀⠦⠌⠁⠤⠌⣉⠠⠁⠀⣀⢂⠄⠒⣺⢭⣾⠿⣷⣌⡫⠄
⠀⠀⠀⠀⠀⢌⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠀⣀⡀⠀⠀⠠⡌⠉⠒⠊⠏⠄⠶⠃⠤⠐⠛⣒⡽⠀⠀⠀⠙⠻⣍⣭⣵⡿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠒⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁

⠀⠘⠀⠀⠛⠀⠈⠁⠀⠈⠀⠀⠁
⠀⠰⠆⠀⠶⠀⠐⠂⠀⠐⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢠⡄⠀⣤⠀⠠⠄⠀⠤⠀⠀⠤⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠆
⠀⣠⡀⠀⣤⠀⢠⡄⠀⣠⡀⠀⣤⠀⢀⡄⠀⢀⡀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⠁
⠀⢈⠀⠀⣁⠀⢀⡀⠀⢀⡀⠀⣀⠀⢀⡀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠉
⠀⠙⠀⠀⠉⠀⠈⠁⠀⠉⠁⠀⠉⠀⠈⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣠⣾⡿⠟⠉
⠀⠛⠃⠐⠛⠀⠘⠓⠀⠛⠃⠀⠛⠀⢠⡿⠿⣿⣿⣿⣿⡿⢟⣻⣿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠟⠋
⠀⠶⠆⠰⠷⠀⠸⠇⠀⠺⠃⠐⠇⠀⠈⠀⠀⠀⠙⠛⣡⠂⠛⣿⠟⠒⠆⣀⠈⡊⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣴⡄⢠⣶⠀⣴⣦⠠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠐⣆⠉⠀⣣⠀⢉⡄⢸⣤⣴⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣤⡄⢠⣤⡀⣼⣧⣀⣼⣇⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠺⠋⠠⠀⠙⠀⠀⠃⠀⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣙⠁⢈⣿⠁⣹⣏⢉⣿⣏⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⢀
⠙⣿⠋⢛⣿⠛⢻⡟⠛⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠂⠐⠀⢲⠀⢒⠒⠀⡀⠀⠈⢁⣬⢀⣧⡿⣿⣿⣿⣿⣿⣿⡿⠈
⠒⣿⠗⢺⣿⠿⢿⡿⠿⣿⡿⠀⠀⠀⠀⠀⠀⢸⡋⠁⠠⡅⠈⠉⠀⢀⠀⠁⠀⣻⡂⠘⣿⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⠀⠘⠁
⢤⣿⡦⢼⣿⡶⣾⣷⡶⣿⣷⡆⠀⠀⠀⠀⠀⠀⢻⡇⢀⣀⢐⠀⢀⣈⠤⡄⠀⡁⣠⡄⠻⣤⣼⡋⣿⣿⣿⣿⣿⣿⣿⠁⠰⠆⠀⠰⠆⠀⠐
⣠⣾⣤⣼⣿⣤⣼⣧⣤⣿⣧⣴⡄⠀⠀⠀⠀⠀⠈⠳⣤⠻⣿⠓⣪⢤⣀⣄⡘⠃⣉⢳⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⡤⠀⢠⡄⠀⢠⠀⠀⠤⠀⠀⠄
⢀⣽⡁⣨⣿⣀⣹⣏⣈⣿⣏⣹⣷⡄⠀⠀⠀⠀⠀⠀⠘⠶⣾⣹⣅⡤⣿⣁⠿⢿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⡀⢀⣀⠀⢀⡀⠀⢀⡀⠀⣀⠀⠀⡀
⠀⠉⠁⠙⠛⠉⢻⡟⠙⣿⡛⢹⣿⠛⢀⠀⢠⣶⣶⣄⣷⣶⣬⣝⣛⣿⣿⢿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠀⠈⠉⠀⠈⠁⠀⠈⠁
⠘⠿⠇⠺⡿⠓⢿⡿⠻⣿⠟⠻⣿⠟⢿⣷⠄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠚⠃⠀⠛⠃⠀⠛⠀⠘⠃⠀⠘⠃⠀⠙⠀⠀⠁
⢰⣿⠆⢼⣷⠤⣾⡷⢴⣿⡦⢾⣿⡶⣾⣿⠶⣿⣶⢍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢱⠶⠀⠼⠧⠀⠶⠆⠀⠶⠀⠰⠶⠀⠰⠆⠀⠰⠂⠀⠒
⢠⣦⡄⣴⣧⠀⣼⣇⣀⣽⣄⣰⣿⣄⣼⣧⣤⣼⣧⣠⣿⣅⢠⣾⡍⣭⣿⡛⣻⣏⠩⣽⡄⢠⣶⡀⢠⣤⠀⢠⣤⠀⣤⡄⠀⣤⡄⠀⣄⠀⢠⣤⠀⢠⡄⠀⢤
⢈⣍⠀⣉⣏⠀⣹⡁⢈⣿⠁⢈⣏⠀⣹⣏⠀⣹⡋⠈⣿⡁⢈⣟⠀⢈⣉⠀⣉⡁⠀⣉⡁⠀⣉⠀⢈⣁⠀⢈⣁⠀⢈⡀⠀⣈⡀⠀⣀⠀⢀⣀⠀⢀⡀⠀⣀
⣘⣟⣁⣻⣟⣈⣻⣋⣘⣿⣃⣹⣟⣁⣻⣟⣉⣻⣋⣙⣿⣃⣘⣟⣁⣙⣛⣀⣛⣋⣀⣛⣃⣈⣛⣃⣘⣛⣀⣘⣛⣀⣙⣃⣀⣛⣃⣀⣛⣁⣈⣉⣀⣈⣁⣀⣈
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⡀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣊⡘⡁⠀⠀⠀⢹⣧⠀⠀⠀⠉⠀⠀⣼⡿⠀⠀⠀⠀⣠⡾⠛⠾⢿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠻⢷⣤⣠⡁⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣠⡾⠋⡠⠞⠚⠛⢿⣿⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⢸⣿⠀⠀⣴⠟⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⣳⣦⠀⠀⣸⡏⠀⣰⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⣸⣿⣕⠀⠀⣿⣷⣤⠛⠉⠀⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠇⢀⣿⣿⣿⣤⣾⡿⠃⠀⠀⠀⠀⠀⣄⣀⢀⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⢟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣟⠀⠀⠸⣿⣼⣿⠿⠉⠀⠀⢀⣴⣤⣶⣿⣿⣿⡟⣿⣿⣿⣦⣴⣶⡶⠿⠿⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣠⣾⣿⣿⡿⠃⠀⠀⢠⣾⣿⣧⣤⣤⡿⡯⠼⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡃⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⠟⠛⢻⠿⣿⣿⣏⣉⡙⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣏⡠⢿⣿⣿⡅⠀⠀⢿⣿⣿⣿⠟⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢟⣾⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢾⣿⣿⣿⣀⣀⣿⣿⠟⡟⠀⠀⠀⠀⢀⡿⠀⠀⠀⣀⡀⠀⠀⢸⣧⠀⠀⢉⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⡿⢷⣾⣿⣿⣿⣿⣿⠏⠁⣾⡵⠦⠤⠀⢀⣾⠃⢀⣠⣴⡟⠻⢷⡀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣧⣾⠛⠉⠉⠹⣿⣻⢋⣿⡟⠁⠀⠀⠀⣾⣿⣾⣿⣯⠋⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣿⣿⢿⣿⠁⠀⠀⠀⠀⠈⠉⢻⣿⡀⢤⠀⠀⠀⣿⣿⣿⡟⢠⡄⠀⠀⠀⠀⢿⡇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢟⣼⣿⠄⠀⠀⠀⠀⠀⠀⣼⠁⠙⢾⠢⠤⠀⠸⣿⣿⣇⠸⣃⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣷⣾⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠈⠛⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢷⡀⠀⠀⠈⠉⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠂⣤⡴⠶⢾⣿⠀⠀⢻⡆⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⠀⡤⠞⠁⠀⢀⣿⡏⠀⠀⠀⢹⡄⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣼⠟⢹⡄⠀⠀⠀⠀⠈⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⠏⠀⠀⠗⠀⠀⠀⢀⣠⣶⣿⡟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀⢠⣞⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣤⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡞⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣾⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⡄⠀⠀⣰⣇⠐⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⣼⣟⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⣴⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⢈⣿⣿⡿⠉⠀⣠⣞⠉⠙⠻⣷⣴⣿⠾⠗⠛⢋⣉⣬⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⣤⣿⣿⡟⠀⠀⣼⣿⣿⣿⡿⠛⠉⠁⢀⣀⣴⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠁⠀⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⡇⠀⠀⢀⣼⠟⠛⠙⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠐⠋⠸⣿⣿⠀⠀⣿⣿⣿⣿⣿⡁⠀⠀⣿⣿⠀⠀⠀⠉⠘⢻⣏⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠐⠒⣿⣿⣇⢠⣿⣿⣿⣿⣿⡶⢦⣾⣿⣿⠀⠀⠀⢸⣟⠻⠿⠷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣀⣶⣴⣟⡛⠉⠈⠻⠿⣿⣿⣿⠁⢰⣿⣿⣿⣤⣀⣤⣼⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⠀⠀⠀⠀⠀⢹⠿⣄⠈⣿⣿⣿⣿⣿⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢿⣾⡷⠂⠀⠀⠀⠀⢢⠀⠈⠛⢊⠹⣿⣿⣿⡄⠸⣿⣆
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡻⡖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣼⣆⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⣷⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣵⣆⡀⠀⠀⢀⣆⣀⣀⣠⣴⣿⠛⢷⣔⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⡀⠀⣠⠞⠋⠉⢠⣿⠃⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡗⣨⠃⠀⠀⠀⣾⠏⠀⣬⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣃⣄⠀⠀⣴⠋⢀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⣴⣼⡿⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡆⣀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀⣀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢴⡋⠀⠀⢈⡇⠀⠀⢙⠖⠉⣀⡉⣦⣠⣠⠖⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡜⠁⠀⠀⣠⠇⠀⢰⣋⣠⠤⠤⣾⠀⡎⠀⢸⠁⠀⢧⣀⠀⠀⠀⢣⠤⢄⡀
⠀⠀⠀⠀⠀⢀⣠⠶⢾⡁⠀⢣⡀⠀⣾⠏⠓⠒⠋⣸⠀⠀⡠⠚⠺⡁⠀⠘⡄⠀⠀⠉⡿⣀⣠⢾⠀⠀⢳⣄⡀
⠀⠀⠀⣠⠾⡟⠁⠀⢀⣇⠀⠀⠉⣹⠙⣆⠀⣰⡏⠙⣄⠀⡇⠀⠀⠳⢤⡾⢬⡓⣖⠉⠀⠀⢀⡞⠀⢠⠎⠈⠻⡷⣄
⠀⠀⢰⠃⠀⣇⠀⠀⠸⡀⠙⠲⢾⡁⠀⠀⡟⠉⠀⠀⣠⠿⠓⢄⡀⠀⣠⠇⠀⡽⠚⢶⣤⠔⠛⠒⠒⢷⣄⠀⠀⢀⠘⡄
⠀⠀⠈⢇⠀⠈⠓⢤⠾⣅⠀⢀⡰⠛⢦⡴⠻⢦⠤⠖⢣⣀⠀⣀⣽⡉⠀⣠⠴⠁⠀⠀⡧⣳⣄⣀⣠⡜⠻⣤⣤⠏⡸⠁
⠀⠀⠀⠘⣗⠤⣐⠃⠀⣀⠽⠋⠀⡠⠜⠀⠀⢈⠧⡀⡠⠬⢽⠵⠚⢿⠛⢧⡀⠀⣀⣼⡹⠁⠈⢳⠃⠱⠄⣀⠴⢺⠃
⠀⠀⠀⠀⠘⡆⠈⠉⠒⠦⠤⣀⣘⠂⠀⠀⠠⠞⡀⢨⡅⠀⠀⠀⠀⣸⣄⢀⠉⠉⠽⠉⠀⣀⣀⠬⠴⠒⠉⠀⢀⠏
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠒⠒⠒⠶⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠶⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠁⠶⣉⣉⣉⡉⠉⠉⣉⣉⣉⡲⢌⣉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠒⠒⠒⠂⠠⠤⠐⠒⠒⠊⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠤⠔⠒⠒⠒⠲⠤⢤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠒⡟⣆⢀⣏⡆⡿⡁⢺⠅⡏⢪⠑⡆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⢹⣤⠛⠀⡁⢀⡉⠈⢠⢓⠁⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠽⣸⠄⡮⣥⡿⣜⡓⡄⢀⠃⢸⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠉⠉⠛⠒⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠺⢌⣉⣁⣁⡈⣀⠩⠜⠋⠉⠀⢸⠀⠀⣴⠋⠁⠀⠀⣀⣠⠤⠤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⡄⢸⠀⠀⢻⠑⠦⣾⡍⢤⠀⡔⣒⠆⠀⢰⣂⠶⠀⡜⣗⣢⡴⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠁⠀⢸⠀⠰⠊⠉⠑⠢⡀⡇⠀⠀⡇⢸⠀⠀⠘⣆⠀⠀⠉⠙⠛⠛⠓⠺⠿⠶⠴⠖⠒⠛⠋⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢦⠀⠀⢳⠘⠢⢄⠀⠀⢸⠘⢦⡠⠆⢸⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡉⠒⠁⠀⠀⠈⠢⠤⠞⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠉

⠀⠀⠀⢠⡤⣄⡤⣤⡄⠀⣤⢠⣄⣤⠀⣤⣄⣤⣠⣠⠤⠀⡤⣄⢤⡄⣤⠀⣤⣄⡤⡄⣤⠀⡄⣤⣄⡤
⠀⠀⠀⠐⠋⠘⠃⠙⠋⠀⠓⠘⠀⠚⠁⠙⠀⠃⠛⠙⠛⠀⠛⠁⠋⠃⠋⠀⠋⠀⠛⠁⠃⠠⠇⠋⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠦⣅⠀⠀⢠⠁⢠⠖⠐⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⠀⢨⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢰⣿⡶⠋⢀⣀⣤⣤⣶⣀⣀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣾⡟⠁⢠⣾⡗⠚⠙⠉⢀⣀⣠⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣻⣧⠀⢹⣿⠇⠀⢠⠚⠉⠉⢻⠧⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣽⣿⣶⡟⣩⠀⢀⡎⣠⡴⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠙⢻⣁⠀⢸⣿⢃⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⢦⣶⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣰⠳⡀⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠊⢀⡟⠀⢰⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⢀⠞⠡⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⡎⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣿⣧⡶⠟⢋⣁⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡶⢶⣄⠘⢿⣛⣥⣤⣾⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣯⡿⢟⣽⣷⡄⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⣤⠖⣊⡤⢚⣩⡶⢟⣫⣵⣾⣿⢿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢪⣤⡾⢋⢔⣷⡿
⠀⠀⠀⠀⣀⡘⣷⠚⣛⢉⡥⢞⣵⠶⠋⣡⣶⣿⣿⢿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣊⣾⣿⢿⡿⣯⡾⠋
⠀⠀⠀⠀⢿⠉⢿⣽⠻⡧⠞⠋⣁⣴⣿⡿⢿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣾⡿⢏⡴⢫⣾⠟
⠀⠀⠀⠀⢀⣄⣀⠻⡆⣻⣶⣿⣿⠟⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣾⡿⢛⣷⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠛⠻⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⣀⠠⣄⣾⠟⠋⣸⡿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠘⠏⢿⠿⢿⣶⣾⡿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠰⡆⠀⠌⣩⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠤⠌⠳⡀⣿⢀⣴⠟⠋⠀⢒⣶⡶⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠈⠱⣶⣶⣶⣽⡉⢻⡿⠷⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢿⣯⢿⢯⣀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⠛
⠀⠀⠀⠘⠃⠈⠀⠀⠀⠤⠶⠟⠛⠉⠐⢁⡏⢿⡀⠙⠙⠛⠷⠞⠓⠀⠒⠀⠀⠀⠀⠀⠘⠾⢿⠿⠿⢿⠿⠟⠟⢿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠃⠘⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠚⠒⠈⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠓⣼

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣛⣝⢳⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡛⠒⠑⢽⣿⣿⠿⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢠⣾⣻⣝⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣁⣀⡀⠀⠀⢀⣴⢞⡉⠛⠆⠀⠹⣿⣿⡖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⡖⢾⣿⡿⠻⢟⠣⠒⠀⠀⠙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢉⣿⠀⠷⣄⡁⠀⡜⠀⠀⠀⠀⢀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⠊⣿⠀⠀⣩⠴⢷⣿⣦⣤⠀⠀⠈⡹⠻⣶⡌⠉⠛⠒⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣟⠀⠤⠚⠹⠧⡏⠀⠀⡸⠁⠀⣾⡇⠀⠀⢂⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠿⠇⠀⡠⠀⢀⠀⡴⠁⠀⠀⣿⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣾⣿⣿⣦⣤⣤⡾⠋⣩⠞⠁⠀⢀⡆⣿⠇⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡝⠙⢯⣿⣿⣿⢹⣿⣿⣿⣿⡛⠁⠀⠀⠀⡾⢀⣿⠀⠀⠀⢀⣈⣆⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⢀⡄⢀⡀⠉⢸⡇⠀⠈⢋⡿⣿⠼⣿⠃⢿⢿⠃⠀⠀⠠⡾⠁⣾⣿⠀⠀⠈⠛⠋⠉⠃⠀⠀⢀⠎
⢠⣄⣠⣴⢾⡇⠀⣷⢆⢘⡆⢀⠀⠀⠙⣿⡇⣿⣡⣾⣿⢷⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⣠⡄⠀⢰⣿
⠀⢸⡉⡛⠛⠛⠓⣶⣦⣅⠁⠀⠀⠀⠀⢉⠇⢻⣿⣿⣿⣿⣧⠎⠀⠀⣿⣿⣿⠀⠀⠀⠀⣴⡟⠁⠀⣹⢣
⠀⠀⢯⣉⣉⣻⣿⣿⣿⡚⢿⣀⣄⣤⣤⣯⣅⡐⣿⣿⣿⡏⠠⠂⠀⠀⠛⠟⣿⠀⠀⠠⣾⡟⠀⠀⠀⠙⣤⡆
⠀⠀⠀⠙⠦⡖⠒⣺⡟⠀⢈⠉⠋⠉⠉⠩⠡⡤⢽⣷⠟⠁⠀⢀⡴⡊⠑⠲⢟⡀⠀⠀⠘⠃⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠱⣌⠉⠁⠀⠀⠘⠰⡛⢎⣋⠁⠉⠀⠻⡍⠀⠠⡎⢁⣼⠇⠀⠀⠀⠙⠲⠼⢷⣶⡦⢄
⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⢤⡤⣤⡽⠧⠤⣤⣄⣀⣀⡀⠀⠈⠉⠀⠒⠀⠀⠀⠀⠀⠀⠈⠙⢄⠱⡀
⣠⠖⠚⠉⢉⠀⣤⣤⣶⣶⣶⣿⣿⣱⡶⢶⣶⣤⣀⣐⢄⡈⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⡄
⠙⠤⣀⡀⠚⠿⠿⣷⣭⣿⣿⢿⣿⣿⣿⣿⣶⣿⣽⠻⠿⠟⢀⣀⡤⠞⠁

⠀⠀⠀⠀⠀⢀⢔⡶⠞⠳⢄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠈⢃⠀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢦⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⣀⣁⣤⡼⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠿⠶⠶⠩
⠀⠀⠀⠀⠀⣠⠎⠳⡄⠘⣧⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠅⢢⡀⢈⠢⡘⣧⠀⠀⠢⡀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠃⠀⠠⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⢆⠁⠀⠱⣌⢾⣷⡄⠀⠈⠓⢦⡈⠻⣦⡀⠀⡼⡉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⢒⠚⠓⠊⠀⠀⠤⡀⠀⢀⠔⠈⠳⣄⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⢧⡙⢿⣆⠀⠀⠀⠙⠷⣌⡻⢦⡀⠑⠄⠀⠠⡀⠀⢀⠀⠀⠇⠀⠀⠀⢀⠔⠁⢀⠀⠘⢦⠀⠀⠐⠂⠀⠳⡄⠀⡼⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠀⠀⠙⢦⡻⣧⡀⠀⠀⠀⠀⠙⢮⣷⣤⠀⠀⠀⠑⠀⠈⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢁⣰⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡾⠉⠉⠙⠳⣤⣀⠀⠙⢌⠻⣤⡀⠀⠀⠀⠀⠈⠻⢷⣄⡐⠆⠀⢀⡀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢷⠤⡤⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄⡀⠀⠉⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠢⡉⠻⣦⢤⣨⣤⠟⢻⡄⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠘⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠙⣆⠀⠀⠻⣆⠀⠀⠀⠈⡳⢦⡀⠀⠀⠀⠈⠀⠈⠳⢦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠦⣦⣄
⠀⠀⠀⠀⡜⠀⢄⣳⡄⠀⠀⠉⠳⣄⠀⢻⣧⡀⠀⠀⠙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⠖⢲⡶⠓⠛⠉⠀⠐⠒⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠐⡇⠀⠀⠱⣿⣄⡀⠀⠀⠘⣧⡾⠦⠿⣦⡀⠀⠀⠈⠳⢽⣷⣄⠐⢦⠀⠀⠀⠀⠈⠳⢦⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡉⠓⠒⠚⡇⠙⢦⡀⠀⠉⠓⠲⢤⡀⠀⠉⠻⢿⣦⣑⠀⠀⠀⠀⠀⠀⠙⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠶⡶⠚⠉
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠙⠲⢄⠠⡇⠀⠀⠻⣦⡀⠀⠀⠀⠳⣤⡀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑
⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⢷⠀⠀⠀⠀⠙⠪⣽⣦⡀⠀⠀⠀⠀⠀⠙⢦⡑⠢⠀⠀⠀⠀⠀⣠⡿⠀⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣭⡿⠶⠖⠋⡎⣷⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠉⠳⣄⠀⠀⠀⠀⠀⠙⠳⢶⣤⠤⠶⠛⠁
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⣀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡀⠀⠀⠀⠈⢦
⠀⠀⡏⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⠙⢷⣄⠈⠙⠳⢶⣤⣠⣤⣴⠾⢿⣆⣰⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠘⡆
⢀⣠⣤⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⡆⠈⠳⣤⣀⠀⠀⢀⣀⡼⢧⣤⡼⠋⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣴⡏
⠛⠛⠉⠠⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢀⡤⠤⠤⠭⠭⠭⠭⠴⠖⠋⠁⣠⠾⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⠋⠁⢀⣰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠙⢦⣀⣠⣤⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠛⠛⠷⠶⠶⢶⣶⣶⣿⠭⠥⠤⠤⠤⠤⠶⠶⠖⠛⢉⣠⣞⣀⣀⣰⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣄⣠⣤⣤⣴⡋⠁⠀⢀⣠⣤⣤⣤⣄⠀⢀⣀⣤⠶⠋⠁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠳⠶⠤⠤⠶⠶⠶⠶⠖⠛⠉⠁