Bowel Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⢀⣴⣾⣿⣿⣶⣄⣠⣤⡤⠄
⠀⠀⢀⣤⣤⣤⣀⡉⠙⠻⣿⣿⣿⣦⣴⣾⣿⣿⣿⣦⣤⣴⣶⣶⣦⣤⣴⣶⣶⣶⣤⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⠿⠋⢁⣤⣶⣶⣶
⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠿⠿⢿⣿⠟⠋⠉⠉⢠⣶⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣄⠉⣉⣁⣀⣈⡉⠉⢉⣠⣤⣤⣤⣄⠉⣠⣴⣶⣶⣦⣤⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣰⣿⣿⣿⣿⣿⣿⢿⡛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠁⢿⣦⡙⠿⣿⣿⣿⣿⡿
⢿⣿⣿⣿⣿⣿⡿⢸⡷⠀⢠⣌⠉⠉⠻⢷⣝⠿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⠟⢋⣀⣀⣀⡀⠀⠀⠀⠀⣽⣿⠆⣸⣿⣿⣿⣧
⠘⣿⣿⣿⣿⠟⢁⣿⣅⠀⠀⠙⢷⡀⠀⠀⠹⣇⠀⠈⠀⠀⠀⠀⠀⢹⡿⠻⠟⠛⠉⠀⠀⠀⠀⠈⠻⣾⠋⠉⠉⠉⠙⠛⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⡟
⣰⣿⣿⣿⣧⠀⢻⣿⣿⣷⡀⠀⠈⣿⠀⠀⢀⡿⠀⠀⠀⣦⠀⠀⠀⠘⣧⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠸⣇⠀⠰⣦⡀⠀⠀⠀⠀⢻⣿⣧⢨⣿⣿⣟
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⢸⡆⠀⠘⠃⠀⠀⢀⡿⠀⠀⠀⠀⠘⠷⠀⢀⠀⠀⠹⣧⠀⠀⠀⢀⡿⠀⠀⠈⠙⠳⠶⠶⠞⢻⣿⡇⢸⣿⣿⣿⡆
⠈⠻⣿⣿⡟⠀⣾⣿⣿⠛⠀⢀⣀⣼⠃⠀⠀⠀⠀⢀⣾⡷⠞⠛⠷⢶⣄⠀⢀⡿⠀⠀⣰⡟⠀⠀⠀⣸⣧⣄⣀⣀⣠⣄⠀⠀⠀⠸⣿⣇⠸⣿⣿⣿⠃
⠀⣰⣿⣿⣷⣆⠈⠻⣿⣷⣄⠛⠉⠙⠷⣤⣤⣤⡶⠛⠁⠀⠀⠀⠀⠀⠉⠻⣟⠁⠀⣰⠟⠀⠀⠀⢰⠏⠀⢈⣩⣭⣭⣀⡀⠀⠀⢀⣼⡿⠀⣹⣿⡁
⢰⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢷⣤⡟⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠉⠻⠆⣴⣿⡿⠁⣰⣿⣿⣷⡀
⠸⣿⣿⣿⣿⣿⡿⠀⣿⣿⣏⠀⠀⠀⣀⣤⣄⡀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠙⢷⡀⠉⠛⠶⠶⠞⠛⠉⠀⠀⠀⣸⠇⠀⠀⠀⠀⣿⣿⡇⢰⣿⣿⣿⣿⠃
⠀⠘⢿⣿⣿⣿⡁⠸⣿⣿⣿⣷⡄⠛⠉⠀⠉⠛⠻⠛⠋⠁⢀⣠⡄⠀⠀⠀⢸⣧⣤⣴⣤⣤⡀⢀⣤⡴⠶⢶⡏⠀⠀⠀⢀⣤⣿⣿⡄⢸⣿⣿⣿⠃
⠀⢀⣾⣿⣿⣿⣿⡆⢸⣿⣿⣿⠇⠀⠐⢦⣀⠀⠀⠀⠀⣰⣟⣁⣀⡀⠀⠀⠾⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⣁⣠⣼⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⠇⢸⣿⣿⣏⠀⠀⠀⠀⠙⠛⠶⠶⠶⠛⠋⠉⠉⠙⢷⡄⠀⠀⢸⡇⠀⠀⠀⠋⠀⠀⢀⣴⣾⣿⣷⡟⠁⣰⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠻⣿⣿⣿⡏⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⠀⢀⣤⣶⣶⣿⡿⠛⠋⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⢸⣿⣿⣷⣦⡈⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⣿⣤⣤⣤⣿⣦⣴⡿⠛⠛⠛⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⢹⣿⣿⣿⠀⠉⠛⠛⠶⠶⠞⠛⠁⠀⠀⢀⣰⣿⠿⠛⠋⠉⠉⠉⢠⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⣿⠏⠈⠓⠦⣤⣀⣀⣠⣤⠶⠚⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠖⣊⣉⠐⣢⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠚⠋⢉⠲⡄
⠀⠀⡴⠓⠺⢿⠧⡎⠉⠉⠉⠈⡳⠒⠖⠶⢄⣀⣤⡤⣄⣀⣀⣀⣀⣀⡤⠴⠤⣴⡻⠟⠉⠙⠁⣠⠤⠴⠓⢉⠠
⠀⠰⣇⡶⠁⣠⠞⠈⠳⡤⢤⡠⢁⡀⠀⠀⠼⠛⠀⠀⠘⠋⠀⠀⠻⣇⢀⠀⣀⠿⠀⢀⡀⠀⠊⠁⠀⠀⠀⣿⡇
⠀⣾⠟⣧⠀⡇⠀⢀⡞⠀⠀⢈⠑⠚⠛⠩⣭⠷⣶⠤⡔⢒⣤⠶⠦⠭⣩⠛⠉⠉⠉⢩⡠⠠⡜⣦⣤⣤⡞⣿⣿
⠀⡙⠁⠈⣿⣿⣿⣿⣧⡀⠀⢸⡄⠀⠀⠀⣦⠀⠀⠀⠰⡏⠀⠀⠀⠀⢻⡄⠀⠀⠀⢈⡿⢻⠻⢿⣷⡟⠃⢘⣿
⠀⣱⡄⠀⢿⠀⠋⠉⢻⠛⠛⠛⠹⢿⡶⠶⠿⣄⣀⣤⣠⣷⣄⣀⣤⣠⠔⠉⠙⠛⠋⠉⢀⡼⠖⢒⢹⠻⠿⠯⡟
⠀⣿⠀⠀⣦⠀⡀⢀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢁⢀⣼⡀⠀⠀⠀⣷
⠀⢻⣄⣀⢿⠀⣴⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢤⠉⠓⠷⢤⣾⠋
⢀⡞⠉⠛⠈⠆⠀⠐⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⢨⠀⠀⠀⠐⣿⡆
⠘⡧⠀⠸⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⣿⠂⠀⣘⡟⠁
⢀⠟⠦⡄⢸⠀⢤⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡅⠀⠃⠀⠀⠀⢼⡄
⡾⠀⠀⢠⢸⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⢠⡆⠀⠀⢰⣿⠁
⢻⠀⣀⡌⢸⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣹⠃⠀⡘⠈⠉⠻⢿⡇
⢠⣿⠛⢣⡘⡟⠛⠻⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠀⠸⡇⢀⠀⠐⣸⠇
⣾⠁⠀⠀⢿⡁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡴⣛⠛⠓⢤⠤⣵⠲⠶⢤⣀⣤⢄⣰⢿⠷⢀⡠⠃⠘⠿⢿⡏
⢹⣴⢀⡀⣸⡗⢀⣄⡴⢿⢿⡄⠀⠀⠀⠀⣸⠀⢠⣤⣀⣀⠀⠘⠳⡤⢴⡏⠁⠀⡿⠂⡠⢎⠁⠀⠀⠀⢰⡇
⠀⠙⢷⠶⡟⠉⠺⢷⣀⠀⢀⡇⠀⠀⠀⠀⣿⠀⢹⡾⢯⣿⡛⡀⠀⢠⣗⠾⡷⠎⡩⠛⠛⠉⠀⠠⢀⣨⡿⠃
⠀⠀⣿⡆⠀⠀⠀⠈⢪⣐⡊⣀⠀⠀⠀⠀⠙⡄⠘⠀⢠⣼⣿⣿⣴⣿⡘⠄⡃⠀⢠⠀⣀⡀⣠⣿⠟⠋⠁
⠀⠀⠹⣍⡦⢀⠀⢰⣾⠯⣻⢪⡆⠀⠀⠀⣰⠉⠀⢀⠈⡿⣿⣇⠀⠀⠙⠒⠶⠖⠋⠙⠓⠒⠛⠁
⠀⠀⠀⠈⠛⠒⠒⠿⠤⠴⠟⠀⠉⠀⠀⢠⠇⠀⠀⢸⠀⠐⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⡀⢸⣤⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡆⠁⢸⠌⣸⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⣳⢸⠀⣧⡤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡦⢀⡟⣱⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣯⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠋⠁⠀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⠉⠙⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠻⢦⣤⡴⠶⠶⠶⢦⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣿⠋⠁⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢹⡿⠶⠤⣤⣤⠶⠶⣤⣄⣀⣠⣤⠶⠶⢶⣶⠞⠋⠁⢸⠇⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣾⠋⠉⠁⠀⢀⣴⠟⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠀⢻⣤⡴⠶⠶⠶⠾⢷⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⠄⢸⡷⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠙⠿⣟⠛⢻⡿⠉⠁⠀⠀⣾⠁⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢿⣄⣠⡴⠶⠶⢦⣄⡀⠀⠀⠙⣷⡟⠀⠘⢦⣄⠀⢿⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠈⠙⢷⡄⠀⠈⢻⡄⠀⠀⠉⠳⢾⡧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣷⣄⣀⡀⠀⣸⡇⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣶⡟⠁⠀⠀⠛⠲⠶⢦⣤⣤⣤⣤⡴⠟⠀⠈⠉⠉⠉⣹⡇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣠⡤⠶⢦⣴⠟⠉⠷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣠⣴⠟⠉⠛⠶⠶⣤⣤⣤⣴⡟⠁⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣇⠀⠀⠀⣀⣤⣤⣄⣠⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠍⢤⣭⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⠉⠑⠒⠉⠐⠣⠄⠂⠐⠠⠘⠉⠁⠒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠼⠗⠀⠀⠀⠾⠓⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣀⠀⢀⠀⣀⠀⠄⠁⠀⠀⠠⠤⠐⠀⣀⡀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠁⠂⠁⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢈⠄⠀⠠⠀⠀⠐⠀⡁⢀⠀⠀⠀⢀⠘⠀⠁⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠂⠀⠀⠄⠠⠠⠀⠐⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⢀⣀⢀⠀⠀⠀⠄⠀⠀⠐⠉⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠫⠁⠉⡥⠎⠉⠀⠀⠀⠠⠀⠒⠂⠁⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠀⠀⠀⠀⢀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠔⠃⠀⠘⠤⢦⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣱⠒⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠠⣄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠴⠝⠒⠤⡀
⠀⠀⠀⠀⠀⠄⠀⠉⠓⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⢀⣀⠐⠀⠀⠀⡁⡀
⠀⠀⠀⠀⠀⢄⡀⠀⠠⠀⠈⠐⠢⡀⠀⠀⠀⢀⠀⠀⠀⣀⠠⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⣀⣠⡐⠃⢠
⠀⠀⠀⠀⠀⠀⠃⠛⢆⠀⠀⢀⠄⠉⠉⠑⠰⠖⠐⠒⠂⠲⠄⠐⠈⠉⠈⠁⠀⠀⠀⠀⠔⢁⢈
⠀⠀⠀⠀⠖⠀⠀⠀⠨⠁⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠅
⠀⠀⠀⢘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠀⠀⠎
⠀⠀⠀⢀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠨⠃⠐⠤
⠀⠀⠀⠰⠀⣀⣠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠰
⠀⠀⠀⢠⠀⠐⠁⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠄⠒⠛⠉⠉⠂
⠀⠀⠀⠠⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⡖⢃⠦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡉⢀⠒⠀⠈⠀⠀⠀⠀⢀⠔⠒⠂⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⠒⠀⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠑⠀⠀⢶⠀⠀⠀⠱⢄⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡔

⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠤⠒⠤⠒⠀⠀⠐⠢⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠒⠊⠉⠉⠱⠄⠀⠠⡀
⠀⠀⡔⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡄
⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠢⠤⠒⠒⢄⠠⠐⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸
⠱⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠶⠆⠒⠁⠍⠀⠀⠀⠀⠀⠀⠘
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠁⠒⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢂⠀⠀⠀⠠⠄
⠑⣄⠀⠀⠀⠀⢀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠑⠂⠐⠂⠒⢄⠀⠀⠀⠀⣀⠀⠀⠀⣀⠔⠒⠂⠊⠁⠀⠀⠀⠀⠀⠎
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⠔⠁⠀⠀⠀⠂⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢀
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠘⢤⡀⠀⠀⠘⠀⠀⠀⠐⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⡤⠖
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠀⠀⢰
⠀⢄⠀⠀⠀⠀⠂⠀⠀⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠠⠀⠀⠐⡃
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠣⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⠤⠰⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠁⢣⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⣀⠔⠤⠤⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣠⠔⠻⣦⡀⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠐⠊⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢀
⠀⠀⠀⠀⠀⡠⠂⠉⠉⠠⠤⣉⡉⠲⠠⣄⣀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠈⢁⡠⠀⠀⡄⢱
⠀⠀⠀⠀⠀⡣⠀⠤⣀⣄⠀⠀⠘⠳⠒⠤⢀⡀⠘⠀⠀⠻⠋⠈⠑⠊⠉⠉⢈⡃⠤⢔⠢⠁⠁⢜⠔⠃⡸
⠀⠀⠀⠀⠀⢇⠀⠐⠀⢸⠒⢺⠆⢀⣴⡀⠀⢀⣄⠉⠀⠉⠉⠉⠉⡁⠀⠀⠀⠀⣀⡰⡤⠔⠹⠀⡤⠀⢸
⠀⠀⠀⠀⠀⡮⠀⢠⡇⢉⡄⠑⢕⡂⢆⠉⠉⢹⠈⡷⡉⠙⠂⢖⡉⠚⠠⠤⠊⣉⠩⣐⠅⠀⡎⢀⡇⠀⣹
⠀⠀⠀⠀⠀⡸⡂⢸⠃⠰⡕⢄⠀⠀⠀⠑⡠⡪⠃⠈⠂⠅⠄⣀⠀⠉⠐⠲⡎⠀⠀⡠⣒⠈⡅⠐⡇⠠⢌
⠀⠀⠀⠀⠀⢂⡀⢸⠀⢐⡯⠠⡈⠐⣊⠛⠊⣔⠊⠉⠉⠈⠤⠭⠉⠢⡀⠀⠊⡦⠮⡀⠁⠀⡢⠀⡇⠴⡸
⠀⠀⠀⠀⠀⡾⠂⠀⡀⠀⣷⡀⠀⠩⠒⠂⠞⠀⠀⡀⠀⣠⠤⢄⠀⠀⠇⠀⠀⡄⠀⠘⢄⠀⡡⡀⡇⠀⡸
⠀⠀⠀⠀⠀⠣⠄⠀⢧⠀⣪⠀⠈⢻⢄⢠⠁⠀⠰⠀⢰⢠⠀⡌⢖⠠⠤⢔⢴⡀⠠⣔⢄⠑⠪⠀⢹⠀⣱
⠀⠀⠀⠀⠀⢧⠀⣀⠸⠀⠰⠤⠀⡇⠳⢺⡀⠀⠻⠆⡀⠳⢕⡬⣂⠉⡡⢐⡡⠇⠀⠏⠢⢁⠓⠀⠹⠈⢜
⠀⠀⠀⠀⠀⠀⡟⠁⠀⢣⠀⠰⢇⠕⠁⠜⡇⠀⠠⢇⠈⠔⣤⢈⠁⠉⠑⢄⣀⢠⠊⠎⠠⣀⠷⠀⠆⠀⡺
⠀⠀⠀⠀⠀⠀⠑⢤⠂⠀⠑⠀⠐⡀⠤⡢⠜⠢⠀⠼⣀⠀⣀⠀⢁⠀⢘⠎⠀⠀⠣⡀⢀⡼⠇⠀⠃⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁⢂⡏⠀⠀⠀⠀⠀⠀⢀⠋⢠⠀⠢⣅⡙⠈⠑⠖⠉⠁⠀⢀⠀⠁⠀⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢈⠓⠐⠉⠐⢦⡉⣓⠒⠒⢒⠐⢨⡁⢐⠔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⠀⡁⡅⠀⠀⠉⠂⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢧⠀⠀⠈⠉⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⣦⠤⠦⠤⠀⠀⠈⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠠⠤⣇⡀⠀⠘⠦⣀⣀⣤⣋⠉⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠈⠱⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⢹⡠⠾⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣠⠋⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣢⠤⠤⣤⠒⠉⢳⠒⠋⠁⠀⠀⡠⠂⠀⠀⠘⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠁⠀⣰⡇⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠤⣖⠊⠁⠈⠲⠤⠤⠘⢦⣀⡀⠀⠀⣰⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠙⠆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠻⡍⠀⠀⠀⡗⢤⣀⣀⣀⡠⠖⠋⠉⠓⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⡠⢄⣀⠀⠀⣀⠜⠁⠀⡼⠁⠀⠰⢤⡀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⠈⠙⢯⠴⠒⠲⢼⡁⠀⡀⠀⠀⠃⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢤⠀⠀⠀⠈⣆⣀⣀⡀⠙⢆⠙⠦⣀⣀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢺⠀⠀⠀⢠⠇⠀⠀⡽⣆⠈⠳⣄⣀⠴⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠁⢀⣠⠔⠁⠸⣄⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠓⠲⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠉⠳⠎⠁⠀⠉⠳⡴⠛⠉⠙⠳⣴⠋⠉⠉⠙⠳⠖⠋⠙⠲⡎⠉⠙⠻⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣼⣦⣀⠀⢀⣠⣧⡀⠀⠀⠀⣠⠶⣤⣀⣀⣀⣤⠞⠙⢦⣤⣤⠂⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠉⠛⠛⢉⣀⣙⠓⠚⠛⠁⠄⠀⠉⣉⠉⠀⠐⠒⢄⠀⣺⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣸⠀⠀⢢⠉⠀⠐⠒⢄⠀⠈⠠⠀⠀⠠⠊⠀⠠⠀⢀⠀⣀⢈⠀⢈⡷⠄⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠀⠀⠙⣆⠀⠔⢠⠊⠁⠀⠀⠂⡠⠄⠊⠀⡁⠀⠀⠐⠄⠁⠀⢨⠀⢀⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀⡠⠀⣂⠉⣁⠀⠪⡀⠀⠈⠀⢀⠠⠀⠀⠀⢆⡐⢁⠄⢺⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣼⠀⠀⠈⠀⠀⢀⠉⢢⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⡃⢰⠙⣧⠀⠠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⠙⡆⠠⡀⠀⠀⢀⠀⢸⠀⢢⡈⢤⠂⠀⠀⣀⠤⡀⠠⠓⠄⠀⡞⠑⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡇⠀⠀⡠⠔⠁⢀⡘⢆⡀⢂⠘⠀⠀⡌⠀⡀⠄⠀⠀⠂⠘⣇⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⡄⠀⠀⠈⠳⣤⠟⠊⠉⠉⠢⠙⡄⠘⡄⡰⠀⠀⡇⠀⢀⠀⠐⢀⠈⢠⠿⢦⠀⠈⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⢀⠄⢀⠀⠐⠈⠀⠀⠀⠀⠀⡰⢡⠊⡡⠄⣀⠁⠀⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠰⣏⠓⠀⠀⣣⡀⠁⠀⣀⣐⠀⠊⠀⠁⠈⠀⣠⠴⠗⠚⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢹⠉⠉⠂⠈⣩⠽⠛⠲⠴⠒⠛⠛⠳⢦⡼⠁⠀⠀⠀⠀⠀⠀⠠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⢀⡜⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠊⠀⠀⠀⠀⢻⡀⠀⠀⠀⠠⣤⠼⢦⣀⣀⣠⡴⠳⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⣿⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠖⠛⠒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠟⠉⠀⠉⠀⠀⢀⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠙⠓⠛⠛⠲⣤⡤⠤⣤⡀⣀⣀⡀⣀⣤⣤⣤⡴⠚⠓⠲⡏⠀⠀⠀⠀⠀⣀⡠⠔⠚⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⡀⠀⠒⠦⣄⣀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠉⠉⠙⠋⠀⠀⠈⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠤⠤⣀⣀⣀⣀⣀⠤⠤⠤⠤⠖⠒⠊⠉⠉⡀⠀⠀⢀⣼⣀⣤⠀⠀⠀⡄⠀⠈⣷
⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⢄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⣀⣀⡴⠓⠶⠒⠋⠀⠀⠹⣄⠀⠀⡇⠀⣰⠇
⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⢻⡗⠒⠚⠳⢤⣤⣤⠴⠷⣤⣤⠴⠛⠳⠶⠶⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇⠀⢀⡿
⠀⠀⠀⠀⠈⣧⡠⠄⠀⡇⠐⠂⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠂⠀⡇⠐⠻⣆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⡇⠀⠀⣹
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⡀⢠⡇⢀⣴⠏
⠀⠀⠀⠀⠀⠸⣆⡠⠀⠘⡆⠀⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢸⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢱⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⡼⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢧⠐⠂⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠁⢠⠃⠀⠊⢿
⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⠀⠈⢧⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠀⢀⡎⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠳⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣠⠴⠶⠦⣤⣠⣤⣤⣠⠶⠒⠾⠃⠀⠀⢀⠞⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠃⠀⢀⡾⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠴⠃⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⡤⣴⠛⢧⠀⠀⠀⠀⢸⠁⠀⠀⠀⠒⠤⢄⣀⣀⣀⡠⠤⠖⠊⠁⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡾⠀⠀⠀⠀⢠⡏⠉⠂⠀⠀⠀⠀⢠⠤⠶⠛⠛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠀⠀⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠃

⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣟⣿⣿⡿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢰⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡰⠏
⠀⠀⠀⠀⠀⢀⣤⣶⣶⢤⡄⣀⡀⠀⠀⠉⢓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣰⣦⣴⣶⣦⣤⣀
⠀⠀⠀⠀⢠⣿⣿⠋⠛⠈⠹⠟⡿⢿⣶⠀⠦⢈⡄⣴⣤⣤⣤⣤⣠⡄⣶⣶⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣮⣖⡀
⠀⠀⠀⠰⢿⣿⣷⠀⠀⠀⢀⣀⣀⣀⡀⠀⠐⠈⠁⡈⠁⠟⡙⠿⢻⣟⣿⢿⠛⠷⠌⢓⣼⣿⣿⣍⠋⢿⣿⣿⣿⢧
⠀⠀⠀⢐⣿⣿⠇⠀⠆⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣄⣄⣠⣥⣤⣦⣴⣦⣾⣿⣿⣿⣿⣿⡆⢫⣿⣿⣿⣟⡃
⠀⠀⠀⢠⣹⠁⢀⡟⠀⢾⣿⠏⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠛⠛⡛⢸⡷⠨⣞⣿⡯⠼
⠀⠀⠀⢀⡀⠀⢨⣏⠀⠈⣿⡇⠀⠀⠀⡀⠁⠈⠛⠿⣿⡟⠛⠿⠟⠿⡛⠛⠀⠀⠀⡀⠀⠀⠇⢸⡇⣰⣜⣋⡁
⠀⠀⠀⠀⠀⠀⢸⡀⠃⠀⣿⡅⠀⠀⢠⡄⠀⠀⢠⡆⠀⠰⠀⠀⠀⠀⣿⣴⠟⠛⠀⣼⠀⢸⠀⣿⡃⣾⡮⣽⠇
⠀⠀⠀⠲⠀⢦⠈⣷⡰⠆⢿⣇⠷⢶⠖⠿⢦⡄⠀⠀⢄⣀⠀⣤⣤⣿⠏⠩⠀⠀⢰⠋⠀⡈⠀⣿⢰⣿⠄⠞
⠀⠀⠀⢀⠀⢸⡆⠙⠀⠀⢀⢿⣧⠐⣀⣀⡤⣀⣀⢀⡼⠁⠛⠉⠉⠓⠀⢀⣀⣤⠞⠀⠀⠁⠀⣿⠸⢯⠄⡤⢄
⠀⠀⠀⠘⣦⠘⡷⠀⠀⠀⠀⠈⣿⡷⠌⣋⠀⢠⡉⡅⠀⢶⡀⠈⠉⡦⠦⠞⠀⠚⠀⠀⠀⠂⡀⢹⣦⣿⠧⢀⠘⢧⡀
⠀⠀⠀⠀⠱⣄⠸⡄⠀⠀⠀⠀⣿⡇⠄⠀⠀⠀⠀⠛⠄⠀⢿⠂⡴⠃⠀⠛⠗⠛⠒⠃⢠⡆⢥⡀⢿⡞⣷⢥⡄⠘⣷
⠀⠀⠀⠀⠀⡅⠀⠁⠀⠀⠀⠀⣿⣇⠀⠈⠀⠘⠓⠦⠄⣤⠁⠀⠀⣠⣧⡀⠀⠀⣰⢿⣭⡁⠰⠁⠀⢳⣿⣷⡶⠓⢿⡇
⠀⠀⠀⠀⠀⡻⠦⠀⣾⠏⠀⠀⣿⠻⠀⠀⠀⠀⠀⠀⠀⠆⣀⡰⢿⡿⠉⢻⡟⠛⣹⡆⠀⢠⠾⠀⠙⠈⣿⣿⣀⡀⣸⣷
⠀⠀⠀⠀⠀⢹⠀⢸⡧⠤⠀⢸⣿⠺⡄⠀⠐⠚⠛⢷⡤⢤⡏⠀⢸⡀⠀⠘⢧⣀⢀⣀⣠⡿⠀⠀⠈⠆⢹⣿⠐⠇⣿⣿⠆
⠀⠀⠀⠀⢈⡀⠀⢈⠅⠀⠀⣾⡏⠀⠙⠦⣶⠃⠀⢸⣷⠴⣧⡀⠈⢁⡟⠁⢰⠏⠙⠉⠛⣀⡼⠃⠸⠀⣼⡿⠮⣤⣿⡟
⠀⠀⠀⠀⠈⠉⠀⣶⣆⠀⢰⣿⣇⠀⠀⠀⢹⡦⠐⠺⢇⣀⣄⠙⢿⡀⢉⣠⣿⣶⠟⢛⣿⣏⣀⢼⣀⡼⣛⠀⢰⣿⡿⠃
⠀⠀⠀⠈⡇⠀⠀⣿⡁⠀⠸⣿⣏⠲⢄⠀⠀⢀⡀⠀⠈⠉⢧⡀⠈⠁⢈⣿⠍⣤⣾⡿⠟⠛⠛⠛⠹⠖⠄⠁⢼⣿⠁
⠀⠀⠀⢸⠀⠀⠀⢹⣥⠀⠆⣻⣿⣦⣄⠉⠒⠛⡁⠀⠉⠰⠎⠀⢉⣿⠟⠋⢼⣿⣿⡗⠰⠀⠀⠀⣀⠀⢀⣴⣿⡿
⠀⠀⠀⠘⡷⠁⢰⡄⠻⣤⢘⣶⣤⣄⡿⠷⢦⡀⠈⠛⣥⣠⣴⣤⡀⠀⠀⢠⠘⣿⣏⠛⠂⠷⣶⣦⣤⣾⣿⣿⣿⠇
⠀⠀⠀⠀⢳⡀⠈⣿⡄⠘⠿⣽⣿⣿⣿⣷⣾⡿⣤⠀⠀⠉⠀⢈⠁⠀⢀⣼⠀⠈⢿⣆⣄⡀⠘⣝⠛⠻⠿⠋⠁
⠀⠀⠀⠀⡀⢹⣆⡘⣠⣧⣤⡠⣾⣯⣽⣿⣿⣴⣿⡇⡀⠀⠰⡏⠛⠛⢛⣁⣤⣤⣄⡙⣿⣷⣀⢸⡆
⠀⠀⠀⠀⠀⠀⢻⣽⣌⠛⡙⢿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠀⢠⠃⢀⣶⣿⣿⡿⣿⣿⣿⣿⡿⠬⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣰⣾⣿⣿⣿⣿⣵⣿⠇⠀⡟⠀⣼⢀⣿⡿⢿⠛⠂⠀⠈⠉⣃⡁⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠛⠛⣿⠀⠀⠁⣠⣇⣾⣿⠋⠘⠀⠀⠀⠀⠁⠲⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠶⠋⠸⠿⠏⢀⠇

⣦⣶⣴⣦⣤⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣦⣴⣶⣦⣤⣶⣶
⣿⣿⣏⣀⣁⣠⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⠂⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢻⡷⣄⠀⠀⠀⠀⠀⢀⠘⠀⢋⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠘⣅⢀⠋⠲⠀⣰⡿⠖⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡴⠛⠛⣻⠟⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⣩⠃⡀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⣆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣾⠟⠀⢸⠃⠄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠹⣿⣆
⠀⠀⠀⠀⠀⣼⡏⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣬⣻⡄
⠀⠀⠀⠀⠀⣉⠇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⢺⡉⣷
⠀⠀⠀⠀⠀⠙⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡏⢀⠘⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣱⠀⠁⢻
⠀⠀⠀⠀⠠⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡟⠀⠀⠸⡇
⠀⠀⠀⠀⢲⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⡙⡆⠀⠀⡇⠀⠀⠀⢠
⢦⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠢⠄⠀⢠⡇⠙⠀⠄⡇⠀⠀⢀⡎
⢸⡇⠀⠀⡆⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⢸⠀⠀⡇⢀⡴⠉⡇
⢸⣿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⢸⡄⢠⠃⠉⠀⠘⠃
⣼⣏⢷⣄⡰⢀⡇⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢸⡇⠘⠠⠃
⠛⠀⢆⠀⢛⠾⡇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢿⢹⡞
⠀⠀⠈⢁⡞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢺⡀
⠀⠀⠀⠀⠱⢸⡿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢨⠞
⠀⠀⠀⠀⠀⠛⠇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⢂⡄⠙⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢀⣤⢻
⠀⢾⡀⠀⠀⠀⣼⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢨⡇⡟⠀⠀⠀⢠⡀
⠀⢨⡷⢄⡀⠀⠀⡆⢠⠈⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⣧⠤⣷⡆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠐
⠀⠀⢳⠀⠉⠣⠚⠧⠀⣀⢼⢄⠀⠀⠀⠀⠀⢀⡴⢀⡟⠀⢐⡇⠈⠂⢤⣼⠅⠀⠠⠈
⠀⠀⢸⠑⢄⠀⠐⢄⠈⠉⣸⣀⠂⣀⣀⠠⠔⠁⠈⣤⠁⠀⡼⠃⠀⣰⠁⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢧⡉⠙⢁⣠⠲⠒⠶⠂⣤⡀⢾⠖⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⢻⠶⢎⡩⠓⠭⡴⠾⠤⣆⠁⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠶⠆⠰⠚⠓⠀⠷⠶⠤⠾⠅⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣤⣿⣤⣷⣒⣒⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠤⠀⡀
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠠⢄⡘⠒⠢⡤⠤⢀⡀⠀⡀⣀⣀⠀⢀⣀⡀⢀⡀⠔⠋⢈⣠⠄⠀⠰⠈⡄
⠀⠀⠀⠀⢀⠆⠐⠢⠴⡄⠀⡈⠁⠋⠐⠠⠤⠈⣀⠀⣙⣁⣀⣈⡁⡀⠀⠡⠅⠒⠌⠂⢁⡐⠕⠉⠰⠁
⠀⠀⠀⠀⠈⡆⠀⢠⠀⡏⢈⢟⠀⠔⠦⣀⣀⢦⡀⡀⣄⠀⠀⣄⠀⠀⠀⣈⠠⠤⢲⠒⠁⡃⢰⠀⢢⠃
⠀⠀⠀⠀⠀⢄⠀⣾⠀⢾⡀⠑⠩⠘⢄⠀⠈⡄⠫⡦⡀⠉⠋⠄⣁⡐⠊⡠⠀⠢⠓⢀⢼⠀⡾⠀⡠⠆
⠀⠀⠀⠀⠀⠪⠀⡟⠀⣱⠌⡢⢀⠠⢤⢔⠕⣁⠠⠌⢀⣊⣤⢄⡀⠀⢙⢄⠀⡐⠨⠂⠘⠀⠇⠀⡙⡄
⠀⠀⠀⠀⠀⣱⠀⠃⠀⠽⠁⠒⠥⢐⠀⢀⠮⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠋⠐⠄⠀⠨⠃⢠⠈⠳
⠀⠀⠀⠀⠰⡈⠀⢰⠀⢘⠇⠠⢬⡐⠀⡘⠀⠀⠔⢀⠒⠉⠡⢀⠀⠀⡀⡠⠀⠀⡈⠢⣰⠕⢸⠀⢴
⠀⠀⠀⠀⠀⠎⠀⠀⡇⠀⡃⠀⢠⢏⣂⠃⠀⢸⡀⠘⣜⢄⠣⠑⠩⠍⡒⢷⠀⢸⠪⠂⢠⡁⢸⠀⢄⠇
⠀⠀⠀⠀⠀⠡⡴⠂⠡⠀⠈⣡⠘⡘⢀⡇⠀⠠⢏⠢⢄⡙⠫⠖⠠⢊⠐⠉⢀⢌⠆⠈⢣⡀⢸⠀⡸⡄
⠀⠀⠀⠀⠀⠀⢄⣀⠀⠑⡄⠉⡏⢀⡀⢰⢄⠀⢙⠀⠉⠘⠑⠂⠀⢠⡓⠀⠹⡀⠀⠁⣮⠀⠈⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠃⠤⠠⠄⢄⢐⠂⠈⠀⠀⠁⠁⠁⠖⢀⠉⣑⠒⠮⠀⢤⡄⠾⠁⠉⠀⡠⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠸⠦⠸⠂⠠⣙⠲⠦⠬⠀⠠⠄⡒⠉⢤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠀⠢⠉⠁⠑⠂⠐⠓⠐⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⢀⠤⠴⠠⠔⠂⠀⠐⠲⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⠒⠉⠉⠉⠢⠀⠀⢄
⠀⠀⠰⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠢⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠒⠒⠦⠄⠀⠢⢄⡠⠄⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠋⠀⠀⠀⠀⠈⠀⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡁⠂⠀⠀⠀⠤
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈
⢣⡀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠓⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⢄⡀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠀⠀⠀⠀⠠⠀⡈⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠤⠐⠃⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠴⠚⠻⣦⠀⠇⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣤⣤⣴⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠠⠄⣀⢀⠔⠒⠒⠒⠁⡠⠔⠚⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠈⠓⠊⠁⠀⠀⠈⠋⠀⠀⠀⠀⠁⢀⣀⠤⠒⠋⠀⠀⣠⠃⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⡀⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠋⢉⡁⠀⠀⣀⠼⡁⠉⠸⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠉⠀⠀⣀⠀⢀⣴⢲⡤⠤⠔⠋⢗⠒⠒⠊⠁⠙⠛⠛⠒⠒⠞⠀⢸⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠄⡤⣔⠉⠉⠁⡜⠀⢣⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠰⡀⢸⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡜⠁⢩⣀⣠⠴⡅⠀⠀⠑⠦⣀⠀⠀⠀⠈⠉⠉⠙⢯⠀⠀⢰⠁⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢰⠁⢠⠇⠀⠘⠀⠈⠢⢄⡀⢀⣀⣈⠉⡉⠁⢖⠢⠀⠈⡆⠀⠘⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢣⠀⠀⠀⡀⠀⠐⡄⠀⢹⠉⠉⢣⠀⠀⢸⠀⠀⠀⢰⠀⢰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠇⠀⣸⡀⠀⠀⢡⠀⠀⢰⠀⠈⠄⠀⠀⠣⡀⠀⠆⠀⠀⠸⠃⢈⠆⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢇⢹⠀⠀⠀⡇⠀⢨⠀⠀⢰⠰⡀⠀⣑⡦⠼⢦⣀⠀⠀⢸⠀⠸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡄⠀⣜⠈⠀⠀⡰⡁⠀⠘⠆⠀⠀⠀⠈⡟⠁⠀⢄⠀⠈⠉⢉⠋⠀⠇⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠙⣉⡂⠉⡀⠙⢦⣀⣀⣠⡞⢩⣉⡉⠲⠤⠤⢑⠤⡤⠼⠂⡜⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢇⠀⠘⠤⡉⢺⡁⠀⠘⡄⠜⠁⡀⠀⠀⠈⠒⠤⣀⠀⠉⠀⣠⠞⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠈⠢⣀⠀⢸⠀⠑⠀⢀⢼⠀⠀⠑⢤⣀⣀⣀⡀⠀⠈⠉⠉⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣈⡳⡦⠤⣤⠤⠊⢠⠂⠀⠀⠰⡀⠀⠀⠈⠑⠂⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠁⠒⠺⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁



⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢯⣭⡶⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⣠⢞⡵⢿⠉⢻⡀
⠀⠀⠀⠀⢠⣾⣉⣓⠢⣶⠋⢀⡽⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡁⠀⢨⣣⣾⠀⠈⣷⡟⣧
⠀⠀⠀⢰⡏⢮⠀⢈⡷⣄⠙⢿⡀⠀⢀⠟⠛⠓⣦⠤⢤⣀⡤⣄⣠⠴⠢⣶⠖⠲⣶⠋⠙⢧⠀⣹⠶⣫⠃⠀⢱⡾⢀⣀⣾
⠀⠀⠀⢸⣇⡘⣄⡸⠀⢘⠷⣄⡙⠶⣯⣀⡀⠐⠃⠀⢸⡇⠀⠈⡇⠀⠀⢸⡆⣀⣸⣦⠴⠞⢛⣡⠜⠛⢦⣠⣾⣥⢸⠀⢹
⠀⠀⠀⢿⠈⠙⠻⠿⣤⡟⠀⠀⣹⠦⣄⡈⠉⠙⠓⠢⠾⠧⠤⠴⠷⠒⠒⠚⠋⠉⣁⣠⡤⠚⠉⠳⡄⠀⠀⢹⠀⠉⢸⠛⢻
⠀⠀⠀⣸⠧⠤⣼⠁⡿⢻⡀⢠⠇⠀⠀⠉⡿⠛⠒⠒⣶⠲⠶⠶⡶⠒⠊⠉⢻⠉⠁⠀⠹⠀⠀⠀⠘⣦⡴⠛⠓⢾⠸⣄⣸⠁
⠀⠀⠀⣿⠀⠀⡸⢠⡇⣠⡟⠛⣆⡀⠀⣰⠃⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠸⣇⠀⠀⢀⣷⠦⠤⠖⠁⢳⣄⡀⠸⡄⡏⠙⣧
⠀⠀⢠⣿⠶⠶⡇⡼⠋⢹⠀⠀⠈⠉⠉⠉⠛⠲⠒⠛⠛⠲⠶⠶⠛⠓⠶⠶⠞⠛⠛⠛⠋⠁⠀⠀⠀⠀⢸⡉⠙⠻⢇⢣⣴⣏
⠀⠀⣿⠁⠀⢸⢰⣁⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠘⡘⡀⢹⡆
⠀⠀⣿⠒⠛⡟⡟⠁⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠉⠙⡇⡟⠛⢧⡀
⠀⢰⣧⡤⣾⢃⡟⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠶⡇⢷⡤⣾⠁
⠀⢸⠁⠀⡟⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢱⠸⠀⠘⣆
⠀⢸⠖⢺⡇⢸⠋⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠺⡆⣦⠴⢿⡀
⠀⣇⠀⣸⠇⢸⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢃⢃⠀⠀⣥
⢰⠏⠉⢹⡀⢸⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⢻⠸⡗⠒⢿
⢸⣀⣠⣼⡇⢺⠦⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠺⡇⡿⠒⠲
⡸⠋⠀⢸⡇⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣤⣴⡄⣷⣤⣤
⡇⢀⡠⢼⡇⢸⠓⠚⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⣿⠁⠀⠀⡇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠙⡟⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⢠⠟⠒⢶⠀⣷⠤⣤
⣿⠀⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣀⣴⡟⢦⡀⠈⠙⠳⣄⠀⠀⠀⢀⣿⡀⠀⡞⢸⠇⠀⣸
⢸⡄⠀⠀⣷⡞⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠀⠉⠢⣝⠲⢤⣀⠈⠻⣶⠶⣟⠉⠙⡾⢁⡏⠀⠀⡟
⠀⠻⣤⢤⣿⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢠⣄⠀⢀⣠⡀⠀⠀⠀⠈⠳⢤⣈⡉⠒⠷⠤⠼⠗⠋⣠⠞⠳⣄⡼⠁
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⠛⠋⠉⣿⣦⡀⠀⠀⠀⠀⠈⠉⢳⠶⠶⠶⠲⣞⠁⠀⢀⡟
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠙⢦⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠀⣰⠟
⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⠒⠒⠿⠤⠤⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠉⠉⠙⠻⢦⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡶⠶⠶⣦⡀
⠀⠀⠀⠀⠀⣸⠏⠀⠲⠶⢦⣄⡀⠀⠉⠻⠞⠛⠛⠛⠶⡶⠞⠛⠛⠛⠋⠁⠀⠀⣠⣤⠶⠆⠈⢿⡀
⠀⠀⠀⠀⢀⡿⠀⢠⡄⠀⠀⠈⠛⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⢠⡆⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠻⣤⣀⡀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠶⠒⠛⠛⠛⠉⠁⠀⠀⠀⣠⡟⠀⠀⠀⣿
⠀⠀⠀⠀⢈⡷⠀⠀⣶⠈⠉⠻⣦⣄⡀⢀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⡶⣶⠞⢋⡀⠀⠀⢠⡿
⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⣿⠉⠉⠋⠉⠛⠳⠶⠶⠛⠋⠛⠛⠛⠛⠁⢸⡇⠀⠈⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠈⣧⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣾⠁
⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⢠⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠃⠀⢀⣼⠃
⠀⠀⠀⠀⠀⢹⣄⠀⠸⠇⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠾⠇⠀⣴⠏⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠙⠷⢦⡄⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠾⠋⠀⢀⣀⣴⠞⠃⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⣓⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣴⠶⠛⠋⠉⠀⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⣿⠁⢠⣤⣤⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢷⣄⡙⠋⠉⠻⣷⣤⣤⣀⣀⣀⡀⢀⣀⣀⣠⣤⣤⣶⠟⠋⢀⣠⣴⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣤⠉⠛⠷⣦⣄⣀⠀⠉⠛⠛⠉⠛⠛⠋⠙⠋⢁⣀⣤⣶⠾⠛⠉⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⢸⡿⢶⣶⣦⣀⣉⠙⠛⠿⠶⠶⣶⣶⠶⠶⠾⠛⠛⠉⢁⣤⣤⣴⡿⣷⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣼⡇⢰⣿⠉⠛⠛⢷⣶⣶⣦⣠⣤⣤⣠⣤⣄⣤⣶⣦⡾⠏⠉⣿⡆⣿⡆⠰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠁⢀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⣿⡄⢸⡇⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠘⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣸⡟⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠘⣷⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣴⠟⠃⣰⡟⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⢹⣧⠀⠀⣿⡆⠀⠀⣠⡾⠛⠿⣿⡏⠙⠛⠋⠉⠛⢉⣉⣴⠾⢋⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⠀⠀⠹⣷⣾⠋⠀⠀⠀⣿⡇⠀⠀⠘⠿⠶⠶⠶⠶⠿⠛⠋⠁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⠾⠋⣿⡄⠀⠀⣼⡟⠀⠀⢶⣄⠀⣀⣀⣠⣤⣤⣴⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧⠀⠀⣿⡀⠀⠀⠈⠙⣿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢆⠀⠐⡘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⡀⠀⠀⠀⠀⠀⠀⠄⢙⠀⠈⠀⠀⠁⠸⡄⠀⠀⠀⠀⠀⠀⢀⣼⡷⢌⣄⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣆⣠⣽⣷⡦⢄⡀⠀⠀⠀⠀⡀⠰⠀⠀⢸⠀⣃⠀⠀⠀⠀⢙⣉⣿⣿⠿⣟⣏⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⣀⠙⢟⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⢐⣧⣤⠀⠀⢸⣀⢻⠒⠒⠀⠀⠉⢉⡡⠾⠿⢛⣫⣽⠶
⠀⠀⠀⠀⠀⠀⠠⠄⣘⣻⠢⡈⠻⢦⣙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⢻⣿⡀⠃⢠⣿⠏⡆⠀⠀⠀⠀⠀⣲⣾⢟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣌⡻⢷⣤⣽⣿⣟⣻⣿⣶⡄⠀⠀⠀⠃⢨⣿⣷⠴⣿⣿⢀⣿⠀⠀⠀⠀⠿⣛⣳⡤⢠⣴⠤⠀⠀⡀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠫⣙⢿⣦⣽⣿⣿⣿⣿⡿⡈⠀⠀⠀⣼⡇⢸⣿⣿⠀⣽⣿⣿⣿⡆⠀⠀⠲⣿⣿⣽⠋⠑⣠⣴⠶⠋⣀⡤⠂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠙⢿⣧⡙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣷⣼⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠙⠉⢋⣠⣶⣿⣿⣷⣾⠟⣉⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣄⢀⠙⢿⣆⠻⣿⣿⣿⣟⠿⣶⣤⣰⣿⣿⣿⣿⡝⠀⣿⣿⣿⣿⣿⣀⣤⣶⣾⣿⣿⣿⣿⣿⢟⣴⢟⢃⣔⣥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡐⣦⡙⣿⣦⡛⢿⡛⢁⠠⡄⢸⣿⣿⣿⣻⣿⠀⢸⣿⣿⣿⣿⠈⠁⠹⢿⣿⣿⡿⢋⣴⣿⢿⣧⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⣡⣿⣾⡙⠮⢛⣿⣤⡀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢾⣽⣿⣿⣿⣿⣧⠀⠀⠐⠋⢹⣿⣬⣛⠮⠊⣀⡴⠊
⠀⠀⠀⠀⠀⠙⢶⣼⣿⣿⣾⣿⣿⣿⣦⡈⢿⡉⠄⠀⠀⣰⣿⣿⡿⣫⣿⣧⢶⣿⡽⣿⣟⢿⣿⣆⠀⠀⠈⠋⠛⣿⠿⠁⣀⣄⣠⣶⣶⣾⣧⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣧⡀⠁⠠⠀⣤⣽⢟⣫⣾⣿⣿⣷⣛⢿⣿⡌⢿⣤⡙⠿⣣⡀⠀⠀⢉⠤⣶⣿⣿⣟⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠐⠓⢤⡐⠿⣟⡿⠿⠿⠿⠃⠀⠀⣴⣿⣷⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⢻⣿⣿⣿⣾⠷⢦⠀⠀⠚⣻⣿⠿⠿⢟⣯⣭⣴⣦⣵⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣶⣦⣑⣀⠂⠀⠀⠀⠀⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣿⣟⣿⣿⣇⢀⣠⣶⣞⣤⣀⣀⣀⣀⣀⣤⣼⣿⣿⣿⣟⣯⣿⣤
⠀⠀⠀⠀⠀⠀⢤⡄⢻⣟⣻⡟⡿⢿⣿⣿⣿⠟⣿⣿⡏⠌⢹⣿⣿⣿⣿⣼⣿⣿⣿⣿⣟⣿⣧⣤⣴⣯⡿⢟⣿⣌⣉⣹⣿⣿⠿⢿⣿⡿⢻⡿⠻⠒
⠀⠀⠀⠀⠀⠐⢬⣻⣿⣆⣝⠃⣤⣀⠉⠿⠋⠀⢿⣿⣿⣷⣿⣶⣶⢻⣿⣿⣿⣿⣿⣟⣶⣶⣿⣿⣿⣿⣣⣾⣿⡿⠟⠋⠉⠀⣬⣻⡵⠖⠋
⠀⠀⠀⠀⠀⠀⡀⠸⠩⣛⡿⢷⠟⡋⣱⠀⠐⢢⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣃⠙⠛⠋⠀⡠⠀⢈⣁⣀⡨⣆⡠⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣍⣟⡚⡿⡷⡰⠄⠀⠀⠈⢸⣿⣿⠟⠛⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣷⣟⠿⢯⣴⣭⣥⣴⣶⡟⣩⡄⠉⠉⠀⠈⠁
⠀⠀⠀⠀⠀⢀⢶⣄⣹⣿⣿⡿⢷⣿⢓⡆⠰⠀⣀⠐⠉⣽⢿⣥⣿⣿⣿⠏⠀⠈⠛⠛⠛⠛⠋⠙⣡⣥⣍⣨⣭⡿⣿⣿⣞⡻⣧⡱⠶⠒⠂
⠀⠀⠀⠀⠀⠀⢻⣮⣟⣷⣾⣟⣷⣿⣿⣿⣷⠶⡋⣔⢄⠀⠀⠛⠛⠻⣿⡃⠀⠘⣆⠀⠀⠲⣶⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣷⣿⣯⣍⠐⠂
⠀⠀⠀⠀⠀⠈⠛⠧⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣧⣶⣦⣷⣦⣤⣶⡞⠁⠀⠁⠀⠙⣧⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠤⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡉⠒⠤⣈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣌⡓⢦⣍⠛⠰⢄⠀⠀⠀⠀⠈⠀⠀⠀⠈⠱⢄⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠷⢦⣄⠁⠒⠤⣀⠀⠀⠀⠀⡐⠀⠈⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠒⠲⠶⠿⣿⣶⣤⣀⡉⠲⠄⡚⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢆⡄⠀⠀⠀⠀⢠⡞⢉⣤⣶⣶⣷⣶⣶⣤⣍⡛⠻⢿⡇⠀⠉⠠⢀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⡀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⣤⣀⡀⠀⡀⠀⠉⢢⡀⠀⠀⡀⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢼⣧⠘⢿⣿⣿⣿⡇⠉⠛⠛⠁⣚⣿⣿⣿⣦⣌⠂⠀⠀⠙⢶⠊⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠉⢻⣿⣶⣾⣶⣤⡷⠿⠿⣭⣿⣿⣿⣦⡀⠀⠀⠀⠃⡀⠰⡄⠈⡀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⣿⣿⣿⣿⣿⣶⣄⠐⠀⠹⠿⣿⣿⣿⡄⠠⠀⠀⠰⠀⠡⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⣿⣿⣿⣿⣿⡟⠐⠂⠀⠀⠻⣯⢿⣿⣿⡄⠁⠀⠀⢶⡀⠀⢨⠄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣭⣄⡉⠀⠀⠀⠀⠠⠿⣿⣿⣧⠀⠀⠀⢠⠄⠁⠁⡆⠸⠃⠀⠀⠀⠸
⠀⠀⠀⠀⣤⠤⠒⠂⠉⠉⠀⠀⠀⠉⠉⠔⠲⡄⠀⠀⠸⡇⢸⣿⣿⣿⣿⣭⣟⣛⣁⡀⠀⢉⣀⠐⢶⡝⣿⣿⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⠀⠘⢦⡀⠈⣇⠈⣿⣿⣿⣿⣿⣻⠯⠅⠀⠀⠈⠉⣀⣀⣿⣿⡟⠠⠀⠀⠠⠁⠄⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠆⠙⠦⣼⠀⠈⢿⣿⣿⣿⣷⣶⣦⣌⠋⠀⢶⣬⣿⣿⡟⠁⠄⠀⢀⡛⠐⠀⡌⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠄⢀⣽⣿⣶⡶⣌⣛⢫⡁⢲⡾⣹⣿⠟⠁⠀⠀⢀⡞⠉⠲⠔⢁⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⣓⠀⠀⠀⢠⣾⣿⣿⠆⠃⠀⠘⣿⣿⣿⣿⠟⠃⠄⠀⠀⢐⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠃⠀⡌⣸⠏⠀⠀⢠⣿⣿⣿⡟⠂⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⢀⡠⢋⡴⠊⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⠀⠒⢸⠟⠀⠀⢀⣾⣿⣿⡿⠀⠀⢶⣴⠟⠁⠀⠀⠀⠁⠀⠤⣈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⢀⣦⠜⠁⠀⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⠀⠀⠆⠀⠀⣿⣿⣿⠀⠀⣰⡏⠀⢂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡿⠀⢀⠀⠀⠀⢿⣿⣷⣦⡶⣿⣇⠀⠀⢀⠀⣀⡀⠁⣀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢃⡤⠃⠀⠀⠠⣄⡙⢿⡀⠀⠀⣿⡀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠫⠴⠿⣦⡖⢢⠀⠀⠨⠁⠈⣿⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠰⠀⠀⠀⠀⠈⣿⠸⠀⠀⠀⠀⠀⣿⣿⠀⠀⡿⣧⠠⠄⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢶⣋⣡⣔⣀⣀⣀⣀⣀⠀⠀⠀⣏⡀⠀⠀⠀⡀⢀⢸⣿⣄⠀⢸⣿⠀⠳⠘⠀⠀⠀⠀⠀⣀⣠⠖⠁⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢿⡉⠌⢉⠈⠉⣉⣩⡄⠤⢈⠀⠈⢠⠊⠁⠀⣇⡈⠀⢿⣿⣶⠦⠿⠷⢀⣀⣠⠤⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⠑⠛⠒⠒⠒⠒⠀⣁⠀⡀⠠⡀⠠⠄⠀⠘⠚⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠄⠀⠈⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠤⠤⠀⣀⣀⣀⡤⠤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠒⠒⠒⠶⠖⠒⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⢀⣆⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢠⣿⣇
⠀⠀⠐⣿⡆⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⢹⠃⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⠟
⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⣸⠀⠀⠀⢸⣿⣿⣿⣆⣄⠀⠀⠀⠀⢠⠃⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⢰⣇⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠟⠀⠀⠀⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢿⣷⣄
⢰⡇⣸⣿⡀⠺⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣼⡇⠀⠀⠀⣠⣤⠀⣀⣤⣀⡀⢀⣼⣿⣇
⠀⠻⣿⢿⣿⣦⣤⣾⣿⣿⣿⣿⣿⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢻⣿⣿⣿⡳⢤⣐⣿⠱⠿⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠓⠈⠻⠿⠿⠛⠛⠛⠉⠀⡆⣀⡸⡇⠀⠀⠀⢀⣾⣦⣤⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠉⠁⠐⢦⠀⠻⠿⠿⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋

⠀⠀⠀⠀⣠⠖⠒⠛⠯⣝⣒⣒⣒⠢⢄⣠⠤⠤⠤⣀⡤⠤⠤⠤⠤⡤⠔⠒⠒⠲⠶⣋⡉⢉⣹⠗⠒⠲⢄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠁⠀⠀⠈⠉⠖⠒⠊⠉⠛⠲⡶⠚⠉⠉⠉⠓⠞⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⡞⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⢧
⠀⠀⠀⡇⠀⠀⠛⠓⣾⠷⠤⢄⣀⡰⣄⡀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣀⡠⢴⡟⠋⠀⠀⢸
⠀⠀⠀⡸⠂⠀⠀⠀⡇⠀⠀⠀⠙⠄⠀⠀⠙⠏⠉⠉⣿⠛⠉⠉⠉⠛⢿⡟⠊⠉⠉⠈⠙⠀⠀⡆⠀⠀⠠⣞
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠙⣆⠀⠸⡆⠀⠀⠀⠀⢀⡏⠀⠀⢲⠀⠀⠀⠙⣄⠀⠘⢆⣀⣀⣼⠁⠀⠀⠀⢸
⠀⠀⠀⢰⠄⠀⠀⢠⡇⠀⠀⡼⠀⣰⡇⠀⡶⠂⠀⢸⡀⠀⠀⠀⠓⣄⠀⠀⠈⡆⠀⠀⠀⠀⢹⡦⠀⠀⠀⢼
⠀⠀⠀⡆⠀⠀⠀⠀⢱⠀⠀⣇⠀⠀⠀⡼⠀⠀⠀⠶⠓⠂⠀⠀⣠⠼⠃⢀⡴⠟⠛⠙⠛⠀⢸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⢰⠄⠀⠀⠀⣸⣄⠀⠀⠙⠲⣿⣀⣀⣠⠤⠤⠤⠤⢤⡎⠀⠀⠘⠋⠀⣠⠔⠉⠉⢳⣾⠧⢀⠀⢀⣴⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠈⣎⡷⠤⢄⣀⡀⠀⢀⣀⡠⠤⠤⢀⠀⠈⠓⠲⠶⠒⠋⢁⣠⠦⠀⡸⠁⠀⠁⠀⠀⢸
⠀⠀⠀⠰⡄⠀⠀⠀⢀⡏⠀⠠⡄⠀⠉⠉⠉⠀⠀⠀⠀⢀⡗⠊⠉⢢⡤⠖⠊⠉⠀⣠⠴⠓⡀⠁⠀⠀⠀⡘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⡀⠀⠙⠒⠒⠒⠒⠒⠒⠢⢄⠈⠃⠀⠀⠀⠁⠀⢀⣀⣼⠁⠀⠈⠀⠀⠐⣄⠔⠁
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⠧⠤⢀⡀⠀⢀⡠⠄⠀⠀⠈⣧⣀⣠⣦⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⢹⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⡷⠒⠦⠤⠤⠤⠤⠴⠒⣟⠀⠀⠀⠀⠀⠀⠀⣆⡀⣀⡠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣯⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣀⣀⣤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡣⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠙⠉⢿⣦⣴⡿⠉⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣧⣼⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢰⡟⢻⡆⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⡶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣀⣀⣀⠉⠛⠉⠉⠙⠛⠿⣦⣤⣤⣤⣶⣦⣤⣄⡀⣀⣤⣤⣶⣶⣦⣴⡾⠛⠉⠉⠉⠉⠉⠀⣀⣀⡀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠉⠛⠿⣶⣤⣀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠙⠻⠛⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣤⡀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⣴⡆⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠙⠻⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢰⣷⠀⠀⠈⠙⣿⣦⣄⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣾⢿⣿⠟⠋⠁⣄⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣹⡏⠙⠛⠛⠛⠛⠛⠿⣶⣦⣤⣴⣶⡾⠟⠻⠷⢶⡶⠾⠟⠛⠁⣼⡏⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣾⡇⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⢸⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠗⠀⠀⢠⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⣼⡟⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⣰⡿⠁⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠘⠛⠀⢀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠛⠀⢀⣴⡿⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⡄⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠋⠀⠀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣌⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢀⣠⣤⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣰⡿⠋⠉⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⠁⠀⢰⣶⣤⣤⣴⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠸⠿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢊⠁⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⢀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠄⠀⠀⠀⢂⠀⠡⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⢀⠠⠀⠅
⠀⠀⠀⠠⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠈⡀⠄⠈⠐⠀⠄⠀⠀⠀⠺⢦⡄⠀⠀⠠⠀⠀⠀⠈⠀⢠⠀⠂⠈⡀⠀⠈⠐
⠀⠀⠀⠠⠀⠀⠀⠓⠀⠂⠐⠀⠀⠀⡀⠀⢤⠘⠚⠀⠈⠀⠠⠀⠀⠀⠀⠀⡰⠐⢘⠿⠀⠂⠀⠀⠀⠀⣀⣀⣤⣐⣰⣥⣶⢦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⡀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣀⢼⡤⠀⠄⠀⠀⠀⡀⠀⢷⠻⣇⡼⣽⣫⡽⠀⠀⡀
⠀⠀⠀⠘⠀⠀⠀⠄⠁⠀⠂⠀⠉⠄⠀⠁⠁⠅⠠⡀⠀⡂⠆⢀⠀⠀⠀⠀⣋⢈⣸⡇⠁⠀⠂⠀⠈⠇⠀⠈⠉⠏⠈⡿⠋⡂⠠
⠀⠀⠀⢈⠀⠀⠀⠠⠠⢄⠀⠂⠀⣈⠁⠈⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠐⣋⠀⠜⣇⢀⠌⠀⠆⠀⢀⠁⠈⠀⠈⡀⠀⠀⠀⠄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠐⢀⡀⠈⠀⠀⠠⠀⠁⠀⠀⠀⠀⠓⢄⣉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠂⠀⠉⠐⠰⠀⠢⠐⠈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠐⠂⠀⠉⠑⠐⠄⠢⠐⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣨⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀⠀⠀⠀⠀⢀⡀⠀⢠⡀⣀⢀⢀⠀⢀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠐⠋⠉⠏⠃⠀⠀⠀⠀⠋⠉⠚⠙⠁⠋⠉⠙⠘⠀⠙⠉⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠈⠉⠁⠉⠀⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠆⢤⣤⣤⣤⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⣄⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⢄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⡀⠈⠃⠀⡠⠋⠀⠀⢀⣄⠀⣀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠆⢀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⡎⠀⢈
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠟⠀⢀⣤⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡴⠀⠀⠸
⠀⠀⠀⠶⠶⠲⠖⠂⠀⠀⠀⣀⠄⠁⠀⠀⠈⡅⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⣼⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⣴⢞⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠖⠁⠀⡀⢀⣠⠞⠁⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠁⠴⠀⠀⠠⠀⠀⠀⠄⠐⠒⠊⠁⠀⢀⡀⣤⠔⠉⠀⠰⠀⠀⡇⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠴⠆⠴⠂⠀⠀⢈⠀⠀⠀⢂⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⡀⢀⣄⠀⠀⢀⣀⠴⠂⠀⠐⢲⠟⠋⠉⠠⠀⡔⠀⠀⠀⠀⣈⣀⠀⠀⡂⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⢀⣈⡀⢀⣀⡤⠞⠁⢀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠁⠀⠐⡀⡕⠀⠀⠃⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⠀⢠⡌⠑⠀⣀⣠⠀⠀⠀⠀⠀⢇⠀⠀⠀⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠘⠂⠄⣀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⢀⠃⠘⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠢⠄⠐⠐⠃⠠⣀⠀⠀⠀⠀⠸⠀⠐⠆⠀⠈⠣⡀⠀⠀⠚⠣⡄⠘⠆⠀⠀⠀⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠏⠀⠀⠈⢂⠀⡄⠀⠀⣆⠀⠀⠀⠀⠂⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠆⠁⠀⠆⠀⢀⡀⠀⡠⠀⠀⠐⠊⠁⠳⠀⠀⠂⠀⠀⠘⢀⡴⠁⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠴⢀⠀⠀⠀⡴⠋⢠⠂⢀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⡰⠁⠀⠀⡀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠁⠀⢀⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠔⢠⠂⠈⠀⠀⠠⠘⠉⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠁⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠄⠀⠀⠀⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠡⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⣴⠒⠀⠀⠀⠬⠶⠶⠖⠶⠖⠲⠾⠖⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⣧⢀⡀⠀⠀⠁⠀⠀⠹⠡⠶⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠂⠒⠀⠉⠁⠀⠀⠀⠀⠤⠴⠶⠶⠆
⠀⠀⠀⡁⢠⣦⣤⣤⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⡿⠛⠛⠓⠛
⠀⠀⠀⣤⡠⣤⢤⣤⢤⡤⣤⡄⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠂
⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣤⣀⣀⣠⡄⢀⣀⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠦⠲⠶⠖⠆
⠀⠀⠀⠉⠉⠉⠉⠁⠈⠈⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡌
⠀⠀⠀⣠⣀⣄⣠⡄⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠉⠁
⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶
⣿⣿⣿⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡟⢻⣿⣿⣿⣿⣷⣤⡔⠒⠛⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣦⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠴⠿⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢫⡾⠛⠓⢒⣶⣶⣶⣶⣾⠟⠻⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⣭⡛⠉⣿⣿⣤⣬⣿⡿⣻⡽⠟⠠⣂⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠢⣹⣿⣿⣿⡿⢛⠁⠐⣩⡖⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣷⣦⣭⣨⣈⣤⣷⠶⡛⠋⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⢀⠘⣯⣿⣿⣿⠿⡟⣙⢊⠙⣂⣀⢰⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢄⡁⠟⣿⣯⣽⣦⣸⣯⡸⠿⣿⡏⢰⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣬⣵⣿⣿⣿⣩⡆⠿⣛⣷⢀⠃⡈⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣿⡕⣆⣿⣿⡟⢰⢒⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣧⡿⣿⣷⠟⠁⡼⢠⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠋⠀⢰⡟⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡁
⠀⠀⠀⠀⢀⠀⠢⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠠⠀⢀⠰⠀⠄⠀⠀⠀⢁⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠀⠈⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⡀⢐⠀⠈⠀⠂⠀⠀⠀⠘⠢⣄⡀⠁⠂⠀⠀⠠⠀⠠⠄⠐⠀⣀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢈⠃⠘⠀⠀⠀⠀⠠⠀⠐⠄⠉⠀⢀⠈⠐⠀⠄⠀⠀⠀⠑⠀⢸⠉⠀⠀⠀⠀⠀⠠⢤⢴⣀⠥⣵⣺⣷⡄⠂
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡠⠀⢃⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⡀⢸⠂⡀⠀⠀⠀⣠⠀⠘⣍⣻⡴⣸⣷⡾⠁
⠀⠀⠀⢀⠀⠀⠐⠀⠀⡈⠀⠀⠐⠀⠀⠀⢀⠀⠅⠀⠄⠀⠠⠀⠀⠀⠀⡍⠰⢺⠀⠀⠈⠀⠀⠀⢀⠀⠀⠘⡀⠸⠛⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠈⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠂⠄⠀⠀⠀⠈⡄⠀⢍⢇⠐⠂⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠂⠐⠄⠁⠤⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠉⠂⠒⠊⠀⠀⠀⡀⠐⠀⠠⠀⠰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢈⠁⡁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⡁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇

⠀⠀⠀⠀⠀⠦⠖⢰⠴⠀⠀⠀⠀⠢⠶⠤⠾⠇⠤⠖⠢⠲⠔⠴⠦⠖⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







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

⠀⠀⠀⠀⢀⡠⠤⢤⡤⠒⠒⠒⠒⠦⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠐⠖⠊⠉⠉⠉⡄⠤⠤⢄
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⣀
⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⣀⡠⠤⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆
⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠒⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠒⠊⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣄
⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⢄⣀⡀⠤⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⡰⠃
⠀⡝⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠐⠘⠒⠶⠶⠆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⠢⣄⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠸⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⠀⠙⡅
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠱⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠂⠀⠀⠀⢡
⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢩⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡤⠂⠁⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⢄⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠑⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡔⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⣀⡤⣶⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⢀⡠⠞⠁⠀⠀⠙⠂⠈⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣽⣤⣵⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠋⢉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣄⣀⣀⡀⢀⣾⣿⣧⣴⣶⣿⣷⡀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⠀⠈⢙⣿⣿⣿⣿⠏⠁
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠠⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⡏
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡷⠂
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣧
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠠⣃⣼⣿⣿⣿⡁⠀⠀⢘⣿⣿⣿⣿⣿⣷⣄⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠿⠿⠿⠿⠿⠀⠀⠀⠀⢠⣿⣿⠟⣿⡿⢹⣿⣿⡆⠀⠀⠘⢿⣿⡿⠿⠛⠛⠻⠷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⢀⡟⣱⣤⣹⣿⡀⠀⠀⠀⠘⣀⣀⣤⣀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠋⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠛⠛⠻⠿⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⢤⡴⠖⠒⠒⠲⠶⠦⣴⠖⠒⠚⠛⠙⠚⠛⠓⠶⣤⡴⠖⠒⠒⠒⠒⠒⠒⠒⠶⠶⣦⡴⠶⠤⣄⣀
⢀⡤⠴⠖⢚⣋⣩⡤⠤⠤⡄⠀⢀⡶⠶⠶⠲⣦⠀⠁⢠⡖⠒⠲⠦⠶⠶⠤⣄⠀⢠⠤⠤⠴⠶⠒⠒⠒⠶⢦⠀⠉⢀⡤⢤⣄⠉⠓⣦
⣯⠀⢺⠉⠉⠀⠀⠀⠀⠀⢹⠀⢸⠁⠀⠀⠀⠘⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⡼⠀⢠⠏
⢹⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⠀⢹⡄⠀⡇⠀⠀⠀⣴⡆⠀⠀⠀⢹⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⢠⠃⢀⡏
⠘⡇⠀⡇⠀⠀⠀⢸⠋⠉⠉⠀⡇⠀⠀⡤⡀⠀⠈⣷⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⡾⠀⠈⡽⠀⠀⠀⣶⠒⠛⠁⣸⠀⠀⡼⠀⡞
⠀⡇⠀⣷⠀⠀⠀⠈⠉⢳⠀⢸⠁⠀⠀⠋⠁⠀⠀⢸⣇⢻⠀⠀⠀⠀⠀⣠⠤⠊⠀⠀⢰⠃⠀⠀⠀⢿⠀⠀⠀⣇⡀⢠⠇⡸⠁
⠀⢹⠀⣿⠀⠀⠀⢴⠛⠋⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⡏⠀⠀⠀⠀⢸⠀⠀⠀⣀⣉⠉⢴⠃
⠀⠸⡆⢸⡆⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢠⢆⠀⠀⠀⣘⣿⠀⠀⣸⣆⠀⣀⣀⣹⠄⢸⣤⣄⣀⣀⣀⣸⠇⠀⢞⠁⢈⡇⢸⠇
⠀⠀⣷⢸⣧⣤⡤⠼⢠⡄⠸⠗⠒⠚⠛⠉⢠⡙⠉⠉⠀⣉⣉⠉⢁⡈⠉⠉⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠉⢉⣠⠏
⣀⣀⣘⣤⣤⣤⣤⣶⣚⣷⣤⣤⣶⣶⣒⣒⣛⣉⣉⣉⣉⣉⣉⣉⣉⣙⣒⣒⣚⣛⣉⣛⣋⣉⣉⣉⣛⣛⣙⣋⣉⣛⣉⣀⣀⣀⣀⣀⣀
⣿⣿⡋⢙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣄⠀⠈⠑⠒⠠⠠⠀⠀⠂⠀⠀⢠⠏⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠠⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡎⠀⠀⢦⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢸⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣵⣫⣽⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⣤⣴⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⠔⠶⠄⣀⢢⠂⢀⠠⠤⠄⡀⢀⣀⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠠⠄⠤⠤⠤⠤⠄⢀⣈⣉⣉⣀⣶⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⠠⣌⣥⠤⠤⠤⠤⣤⣁⣠⡤⠤⠀⠀⠤⢥⣤⠔⠒⠒⠂⠀⢄⠉⠀⠀⠀⠉⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠙⠳⣶⡷⠦⢄⣀⣀⣀⣷⣄⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣴⠀⣀⣤⣾⡟⠉⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠈⣧⡀⠀⢸⠀⠀⡟⠀⠀⠀⠈⠻⣇⠀⠀⠉⠓⢶⠒⠒⠚⢿⣿⠷⠒⠒⠒⠒⠾⣿⣶⣶⠆⠐⠚⠛⠛⠻⡄⠀⢸⡇⠀⡀⠀⠀⣰
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⠀⠸⡇⠀⠰⢆⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⠀⠀⠈⠻⣇⠀⠀⠀⣠⠀⠀⠈⠀⢸⡟⠂⠁⠀⠈⠹⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⡘⠁⠀⠀⠈⣇⠀⠀⠀⠀⠘⢦⡀⠀⠈⠳⣤⣤⣴⣏⠀⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡷⠤⠀⢸⠀⢼⡃⠀⠀⠀⡾⠀⠀⣼⠀⠀⣸⠛⠉⠀⠘⣇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢹⣦⠀⢡⠀⠠⠾⡅
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠆⠀⢳⠀⠀⢰⡇⠀⠀⠈⠀⣰⠃⠀⠀⠀⣤⡾⠶⠤⠄⠀⠀⢀⣨⠇⠀⠀⣠⡿⠶⠒⠒⠶⡇⠀⢸⠁⠀⠌⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡀⠀⢸⡆⠀⠀⠙⠶⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⢀⣴⡾⠋⠀⠀⣠⠶⠶⢤⣀⣼⡄⢰⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠅⠀⠚⡳⣄⠀⠀⠀⠀⠙⠳⠶⠶⠶⠒⠚⠛⠉⠉⠙⠛⠿⣆⡀⠀⠀⠁⠀⣀⠰⠚⠁⠀⠀⠀⢻⠟⠋⠀⠂⠀⠔⢺⡇
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠰⠀⠀⢳⡼⠿⠶⠤⣄⣀⠀⠀⠀⣀⣠⠤⠶⠖⠲⢄⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⢀⡴⠖⠀⢠⠂⠀⠠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢠⠀⠀⡸⠀⠀⢀⣠⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢱⠞⠋⠁⢢⣀⡤⠖⠂⠈⠀⠀⢀⡠⠾⠆⢀⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠂⠀⠀⠱⡄⠀⠀⠻⠄⣀⣀⣀⣀⠀⢤⡄⣀⡀⠀⠙⠇⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⣴⠋⠀⠀⠂⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⢸⠀⠀⢀⣀⡤⠶⠒⠚⠣⢀⠌⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⢠⠞⠓⠒⠦⠄⣀⣀⣀⡤⠾⠤⠄⠀⠀⠈⣧⣄⣤⠾⢷⡶⠋⡁⠄⠂⠀⠀⠁⠁⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠣⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠳⣦⢤⣄⣀⣀⣀⣀⣀⣀⣠⡤⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡤⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⣄⢲⡞⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⢤⣤⠴⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠟⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠗⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠛⠓⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠏⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠈
⠀⢀⡟⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠒⠈⠉⠉⠉⠙⠒⠢⣄
⢠⠟⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠈⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠈⢳⡆⠀⠀⠐⠒⠉⠉⠉⠀⠀⠀⠀⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠄⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠀⠀⠉⠒⢲⡶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⡀⠀⠀⠉⠉⠒⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠐⠻⣍⠉
⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠄⠀⠀⢀⡴⠒⠲⣌⠢⠀⠀⠑⠲⢄⡀⠀⠀⠀⠉⠁⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢄⣀⡼⠀⠀⠀⠀⠀⢀⣈⠑⠄⠀⠀⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⣹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⣿⣿⣶⢿⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣰⣟⢩⣭⢿⣷⠋⣶⣾⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠞⣁⣴⣿⡿⠛⡯⢚⣿⣿⣿⣟⣻⣻⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣰⣿⣿⣿⣿⣿⣶⣿⡿⣬⡟⠛⠛⠟⠛⠦⠐
⠀⠀⠀⡀⠀⠻⢱⠜⣿⣿⣿⣿⣿⡿⢿⠋⣽⠛⠓⠃
⠀⠀⠀⠸⠷⢸⣿⣼⣿⣿⣿⣿⡿⢶⠖⢛⡇
⠀⠀⠀⠀⠀⠹⠿⣿⡿⢿⡛⢿⡷⣬⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠈⠁⠀⠀⠈⢻⣷⡠⢀⣀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠤⠄⠀⠀⠚⠛⠚⠻⠿⠶⠿⠿⠿⠷⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠛⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⡀⠲⡿⠒⠀⣀⠀⣷⠀⠒⣿⠒⠲⠂⠀⠀⣀⠀⠀⣀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠇⣿⠎⣿⠀⡇⠀⣾⣩⠇⡿⣦⠀⣿⠀⣿⠀⣿⡎⣽⠀⣾⣩⠗⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠀⠿⠀⠿⠜⠷⠔⠻⠄⠴⣥⡿⠖⠻⠔⠻⠤⠻⠀⠻⠴⠻⠤⠔⣥⡼⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠉⠀⠀⠀⠀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⢀⣀⠀⣀⠤⠄⠈⠀⠀⠐⠀⠀⠀⣠⠟⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠙⠓⢤⣀⡀⠀⠀⠀⠀⠐⠀⠠⠄⠀⠄⠠⠤⠀⠀⠀⠁⠀⠀⡀⣠⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⢀⠀⢀⠘⠦⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣠⣞⡉⠉⠉⢣⡀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢡⠈⣦⠈⠻⡄⠀⢈⡇⢹⡛⠛⣶⠶⠖⣷⣶⡞⠉⠻⡄⠀⡀⠁⠀⠀⣰⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⢡⠀⠸⠀⠀⣿⠀⠈⠁⣸⣅⣀⡉⠓⠆⠀⠈⢃⠀⠀⡇⣀⡉⢉⡉⠙⢇⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠢⠐⡀⠀⠒⠻⣤⠤⠺⡋⠀⠈⠉⠲⣅⣀⡴⠃⠤⠞⠉⣈⣁⡉⠀⢀⡜⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⠃⠈⣆⠀⠀⣀⡀⠀⣀⠤⠖⠒⠦⡈⠻⢄⣀⡠⠔⠋⠁⠀⠁⠙⢯⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠋⠉⡀⠉⠉⠀⢀⠀⠀⠀⣹⠀⠀⠠⣀⠐⠒⠛⠁⠀⠀⣤⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⠀⠀⠱⢲⠖⠒⠚⡱⠊⠉⠀⠉⠁⠢⠧⠀⠀⠀⣦⠖⠚⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⡷⢄⣀⡀⣀⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⢦⣀⡀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢀⡴⢞⠙⠦⠤⠔⠻⡄⠀⠀⠈⢲⠖⠚⠳⢄⣠⠴⣄⡀⢀⣶⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠉⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡅⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣥⡜⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⢀⡎⠱⣤⣼⡏
⠀⠀⠀⠀⠀⢠⣞⣙⣻⣩⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢹⡄⠀⠀⠀⠀⣰⡿⠋⣱⡿⠰⣤⣼⣿⡇
⠀⠀⠀⠀⢀⣾⣟⣰⣿⠿⣿⣿⣛⣷⣶⣶⣖⣦⣄⢀⡀⠀⢸⣇⠀⣨⣧⣀⣠⣤⡾⣛⣠⣾⠋⢤⣄⣼⠟⣽⡇
⠀⠀⠀⠀⢰⡟⠙⣿⣷⣰⣾⠃⣹⠓⠻⣿⢯⣟⣛⣛⣛⡿⣟⣛⣿⢿⣉⣭⣥⡼⠷⣟⠁⠈⣷⣤⡿⠿⣟⣿⡇
⠀⠀⠀⠀⢸⡷⠞⣻⡿⣿⡿⣾⣿⣀⣾⡇⠀⣼⡍⠉⠉⣿⠉⠙⢻⡏⠉⠉⣷⡀⢀⣸⣧⣴⠿⣋⠀⠀⢹⣿
⠀⠀⠀⠀⢺⣇⣬⣿⣀⣽⡇⣾⡏⠉⣹⠿⠿⡿⠿⣶⠾⣿⢤⣤⣼⠿⢤⣶⣿⣙⣛⣉⣠⣤⠞⠃⠀⢀⣾⣿
⠀⠀⠀⠀⡟⠈⠀⣿⠉⢿⡆⠹⡇⠀⠙⠶⠞⠀⢠⡇⠀⡇⠀⢻⡇⢀⡞⠁⢀⣀⣀⠈⠀⣀⣀⣀⣠⣞⣹⣿
⠀⠀⠀⠀⣿⠶⢾⣿⢠⣾⣧⡀⠙⢤⣀⠀⢀⡴⢋⡇⠀⣇⠀⢸⡇⢸⡇⠀⠀⠉⠉⠙⠋⠉⠉⠉⣉⡈⠉⢳⡀
⠀⠀⠀⢸⡇⣀⣰⣏⢀⣿⡌⠛⠷⠀⠈⢹⣥⠤⡼⠀⣸⠇⠀⢸⢧⡈⢧⣴⣶⡟⠛⠛⠲⠤⠶⠛⠉⢀⣀⣴⡇
⠀⠀⠀⣸⠟⠻⢿⡿⣿⡟⠻⣄⣀⣀⣠⡾⠁⡀⢧⡀⠁⢀⣠⠟⠛⢻⡏⠀⠀⠘⣦⠤⠤⣤⣤⣶⡚⠉⢁⣿⡟
⠀⠀⠀⣿⣤⣤⣿⣠⣸⣿⣤⣈⠉⠉⣉⣠⠾⠃⢈⡿⠋⢉⡴⠀⢀⣼⣣⢿⠁⠸⢧⡤⠖⠋⠀⠀⠉⣮⠽⢿⣷
⠀⠀⢠⣟⠉⢙⣿⠙⢻⣧⠞⠙⠻⢿⡏⠀⣤⡴⠟⠁⣰⡏⠀⠰⠋⣰⠧⣬⣳⣤⣀⣀⣠⣤⠞⠀⢀⣾⣄⣨⣿
⠀⠀⠀⣿⠖⢛⣿⡗⢿⣿⣇⠀⢶⡈⠷⣄⣤⣤⢤⡞⠹⣦⣠⣤⣴⣃⣀⠀⠈⡏⠉⠉⣡⣤⣤⠴⠛⠁⠈⡟⢿⡆
⠀⠀⠘⣿⣤⣬⣿⣷⠾⣿⣮⡇⠈⢿⡀⢹⡄⡇⠀⣧⠀⠚⠁⡼⠛⠛⠿⣿⣆⡙⢦⣀⣀⣀⣠⡴⠏⢁⡼⣿⡟
⠀⠀⠀⠸⣏⣅⣾⣿⣏⣙⣿⣷⣤⠟⡇⠐⣇⣿⠀⢸⢲⠖⠊⡁⠀⠀⠀⠀⠈⠙⠓⠪⠭⣍⣡⡤⠔⣋⣠⣿⠇
⠀⠀⠀⠀⠈⣿⣤⣼⡿⣧⣤⣾⠃⠀⠻⣄⠈⠉⢀⡞⢸⣆⠘⢧⣧⣦⣤⠀⣀⠀⠀⠀⠀⣰⡀⣀⣤⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠷⠤⠼⠋⠉⢷⡀⠀⠉⠛⠛⠉⣰⠃⠉⠓⠂⠈⢛⣿⠿⢾⣾⣮⣦⣿⠿⠛⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⣿⠀⠰⢦⣤⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠙⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣝⣴⠶⠀⠐⠻⢷⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠺⠀⠀⠀⢈⡔⢢⠀⡴⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡤⠤⠼⣦⢸⠀⣧⡀⣨⠷⠒⠒⠀⠐⠂⠄⠀⠀⠠⠒⠋⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠉⢹⠀⠀⠀⠈⠧⠤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⡳⢤⣀⡐⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠐⠒⠀⠐⠀⠀⠸⠤⠄⠀⠠⢏⠉⠉⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢶⣚⣠⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠉⠀⠀⠀⠂⠈⠁⢈⢧⡀⠀⠀⠉⠀⠈⠙⠒⠦⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡶⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠓⡤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⠞⠳⢄⣀⠀⣀⣠⠴⠋⠳⣄⠀⠀⠀⣀⡴⠋

⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠐⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⡀
⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠋⠉⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣵⡄
⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡀
⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⣶⣤⣶⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣰⣿⠃⠀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⡽⣟⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠮⠙⠉⡙⣿⠄⡀⠏⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⢱⣄⢟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣷⡁⢠⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡀⡐⠋⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⡝⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⡖⢳⠜⢷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡧⠀⠀⡃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣝⠫⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢻⣯⠠⢀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢼⣷⣘⣿⢿⣗⣄⠀⠀⠀⠀⠀⠀⠀⢀⠸⢸⣿⣤⡤⣅⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⢻⡏⠹⣾⣿⡿⡳⡀⠀⠀⠀⠀⠀⠀⡳⡘⢻⣿⡔⢸⠉⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢩⠀⢻⣿⣷⡘⣿⠀⠀⠀⠀⠀⢀⣡⣝⣻⣿⣿⣬⡆⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢀⡢⢀⠈⣿⣿⣧⣌⡇⠐⠠⠈⠀⠁⠀⢲⢻⣿⣿⣿⠧⠉⠀⠙⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⢿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⡄⡹⡿⠋⠘⠀⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠜⠫⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⢀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⢢⡄⠀⠀⠀⠈⠙⠛⢹⠀⢀⠠⠔⠊⠀⠙⠦⠄⢀⣀⡤⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠄⠠⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠆⠠⠀⠲⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠙⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠛⠛⠶⣤⡀⣠⠞⠁⠀⠀⠀⠂⠠⢄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣤⣀⡀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢻⡄
⠀⠀⠀⠀⣰⠚⠁⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀⣴⣷⣆⠀⠀⠀⠀⠀⠰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡟⠀⠆⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢄⠀⠀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠛⠉⠙⢷⣄
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠶⠀⢸⡀⠀⠶⠀⠀⠀⣸⠸⠘⠀⠀⠀⠀⠀⢰⠄⠀⠹⣆
⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡎⣇⠀⠀⠀⠀⠀⠀⡸⠳⣄⠀⠀⢀⡰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢦⣀⠀⠀⣀⠔⠁⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠠⣾⣧⡀
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⢰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣾⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⣄⠀⠀⠀⢀⡠⠔⠢⠤⣀⡀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜⠀⢀⠟⠙⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢀⠄⠀⡾
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠁⣠⡾⠁
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠷⠶⠾⠟⠉
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⡴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠠⠤⠔⠊⢀⣠⡾⠋⢿⣦⣀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠓⠲⠶⣶⣶⠾⠛⠁⠀⠀⠀⠉⠛⠟⠛⠛⠋⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠋⠉⠉⠉⠛⢦⣠⡞⠁⠀⠀⠀⠐⠂⠄⠈⢳⡄
⠀⠀⠀⠀⢀⡠⠖⠒⠒⠲⢤⣀⡎⠀⠀⣀⡀⠀⠀⠀⠈⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠛⠒⣄
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⡀⠐⠆⠀⠀⡠⠆⠃⠀⠀⠀⠀⠴⠀⠈⣧
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠠⠠⢧⡀⠀⠀⠀⠀⠀⠑⢤⣀⣠⠴⠁⠀⠀⠀⢤⠀⠀⠀⠀⢀⡞
⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⠦⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⠓⢤⡀
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡠⠤⣄⣀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠘⣧⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠅⠀⡸⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼
⠀⠈⠻⢶⡄⠀⠀⠀⠀⠀⠀⠳⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢠⠏
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⣀⣀⣠⡴⠋
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠓⣄⡀⠀⠀⠠⠤⠐⢁⣠⠞⠻⣦⣀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠒⠲⠶⠖⠛⠁⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⡤⠒⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠁⠀⣰⣾⠛⠓⣦⡀⠢⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⢟⣋⣭⣌⣉⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⢸⣏⠛⠀⠀⠈⢿⡄⠂⠀⠀⠀⠀⣾⠿⣫⣤⣶⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡦⣄⠀⠈⡇⡀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⣻⣯⣽⣿⣛⠿⢷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⣦⠉⣱⣿⡆⢠⢇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣿⣿⡿⢿⣿⣿⣾⣾⣼⡻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣴⣧⣴⣿⠟⢠⡞⡌⠀⠀⠀⠀⠀⠈⣹⣿⣿⠟⢻⣿⢶⣿⣿⢿⡟⠻⢿⣿⡜⠿⠇
⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⣉⠔⠁⠀⠀⠀⠀⠀⠀⠰⠾⢤⣄⣀⡻⣶⣭⡴⠟⢁⡠⢤⡾⠻⡀
⠀⠀⠀⠀⠀⢄⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⡁⠙⠙⠙⠟⠋⠋⠑⠀⢁⡤⠄
⠀⠀⠀⠀⠀⠈⠙⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⢤⣶⡶⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠠⢉⡁⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⡀⠀⠀⢄⠀⠀⠀⠀⣠⣦⣄⣀⣀⣼⣿⣦⣀⣠⣄⣶⣾⣧⣄⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠿⠿⠷⠤⠀⠀⠢⠀⠀⠀⠀⠘⢿⣿⡛⠛⠿⠿⠻⠻⠿⠿⠿⠿⢛⣋⣽⡟⠁
⠀⠀⠀⠀⠀⠀⡔⣠⣞⣗⣲⣤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡟⠋
⠀⠀⠀⠀⠀⣼⣷⣝⣛⠻⠛⣿⠗⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠛⠉⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠠⢄⠀⠀⠀⣀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠀⠒⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡼⠁
⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⡿⠉⠓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀
⠘⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠈⢿⣅⡀⠀⠠⠀⠀⠅⠀⠒⠠⠄⠀⠀⠀⢀⡀⠀⡐⠁⠀⠀⠈⠑⠀⠀⠀⠐⠢⣀
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⢌⠐⠀⢈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠢⡈⠂⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠑⢄⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⡤⡄⠆⢀⢤⡀⡠⣄⠀⢀⠤⠀⢤⠀⡤⡄⢠⠄⢀⢄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠘⠤⠜⠀⠸⠤⠃⠇⠸⠀⠸⠤⠰⠽⠀⠇⠘⠣⠄⠫⠬⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠴⠚⠉⠙⠒⠦⣤⠖⠛⠉⠛⣶⡶⠟⠛⠛⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢀⣤⣦⣤⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⠴⠶⠒⠒⠀⠀⠒⠀⠤⠤⠤⢼⣿⠤⠴⣿⣿⣿⣿⣷⠀⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣿⣄⠀⠙⠿⠿⢿⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⢀⡴⠋⠙⠒⠒⢋⣉⡉⠓⠲⢾⡻⣿⣷⣀⣀⣸⣧⡾⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⣄⠹⡆⠀⡏⠙⣆⠉⢿⣍⡉⢹⡄⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠀⠀⠀⣸⠀⣴⠒⠒⠶⠤⢞⣠⣹⣞⣁⣠⠟⠀⠀⡿⠁⠀⢳⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠀⠀⢰⡃⠀⠈⠉⠓⢦⡀⠘⢦⣠⡤⠴⠶⠶⣄⠀⡇⠀⠀⢸⠂⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⣷⢰⠒⠒⠒⠉⢀⡴⠒⠒⠒⠶⠶⢚⣁⣤⠷⠀⠀⡼⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⢀⡏⢈⣉⣉⣹⠆⢸⣀⡤⠤⠤⠴⠞⠉⠀⠀⢀⣠⠞⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢸⠀⠀⢺⣄⠀⠀⠁⠀⠀⢸⠏⠀⢀⣀⡠⠤⠤⠶⠞⠋⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠀⢸⠏⠙⠒⠶⠦⢴⡏⠀⣰⠋⠀⠀⠀⠀⠀⠀⣸⠒⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⡤⠋⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⢰⡶⠦⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⢀⣠⣴⠟⠁
⠸⣿⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⢀⣿⠀⠀⠀⠀⠀⢷⣀⠀⢀⣀⡴⠞⠋⣡⠴⠚⠉⠁
⠀⠙⠷⢬⡉⠙⠻⢦⣀⠀⠀⠀⣠⡴⠛⠋⣩⡤⠞⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢡⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡟⢁⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠿⢿⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠟⢋⣴⣿⠿⣟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣬⡙⠷⣾⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣤⣿⠿⢋⣡⣾⣿⣿⡿⣻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢟⠙⣿⣿⡿⣿⣷⣬⣙⡛⠿⠿⢿⣿⣿⣿⣶⣿⣷⡾⠿⠿⠟⣛⣩⣴⣾⣿⣿⠉⣯⣽⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢠⣾⣽⣶⡝⢿⣿⡿⢻⣿⣶⣶⢶⣶⣤⣤⣴⣶⣶⣶⣾⣿⡿⠿⠟⠻⡿⠃⠸⣿⣿⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣍⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠋⠁⠙⠛⠋⠀⠉⠉⠁⠀⠀⠀⠀⠀⣴⣿⣿⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡏⢸⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢸⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡆⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡙⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠛⠢⠃⠀⠀⠀⠀⠀⠀⢠⢊⣥⣬⣍⡛⠻⢷⣦⣠⣄⡀⠀⠀⠀⠀⠠⣾⣿⡿⢸⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣌⣙⠻⠷⣤⣶⣄⣾⣿⡿⠟⣠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣭⣤⣶⣾⡯⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠉⠈⠻⠿⠟⠹⢿⣿⠟⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⣠⡤⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠑⣦⣄⡀
⠀⢠⣾⣡⣤⣀⣀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⠀⠀⢀⣴⠟⠀⠙⣄
⢀⡟⠋⠉⠉⠉⠻⢷⣦⡀⠀⠈⠓⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠁⠀⠀⢀⣠⣴⠿⠉⠀⠀⣰⠛⡆
⢸⠁⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⠉⠉⠉⠙⢦⣠⠤⠤⣄⣀⡤⢤⣀⡴⠒⠲⠤⠊⠁⠀⢀⣠⣴⡾⠿⠋⠁⠀⠀⣠⣿⡇⠀⢧⡀
⠈⢧⣀⣠⠴⣦⡀⠀⠀⠀⠀⠙⠻⠷⢶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠾⠿⠛⠋⠁⠀⠀⢀⠖⣾⠋⠁⣿⠁⠀⡼⠁
⠀⠘⡇⠀⠀⣿⡟⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉⡇⠀⠀⣿⠀⠀⡷
⠀⣰⠃⠀⠀⣿⠁⠀⠀⡸⠉⢓⡶⠚⠋⠉⠳⢄⣀⢀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣤⠤⢤⠴⡞⠉⠙⢻⣹⡁⠀⢀⣰⡇⠀⠀⣿⠀⠀⣧
⠸⡅⠀⠀⠀⣿⠀⠀⠈⣷⠋⠉⠀⠒⣄⡠⠖⠚⠙⠛⠳⢤⡀⠉⡩⠖⠦⣍⠉⡟⠉⠉⢢⡀⠙⣆⠀⠀⠉⢀⡴⠋⢸⠁⠀⠀⣿⠀⠀⡇
⢀⡿⠀⠀⢸⣿⠀⠀⣠⠏⠀⣀⣠⣤⣼⡅⠀⠀⠀⠲⣄⠀⠙⠶⠃⠀⢠⡈⠳⠃⠀⢀⡀⠙⢦⣹⡄⠀⣠⠞⠀⠀⣸⠀⠀⠀⣿⠀⠀⣇
⢸⠀⠀⠀⢸⣿⠀⠀⢹⣆⡞⠁⠀⠀⠀⠈⠂⠀⡀⢀⡽⠳⣄⣀⡤⠴⠒⠛⠒⠲⠦⣼⣙⣆⠀⠀⠉⠉⠁⠀⠀⢀⣿⠀⠀⠀⣿⡇⠀⢸⡄
⠘⡆⠀⠀⠘⣿⠀⠀⢼⡙⣄⠘⠳⠶⠟⠛⠉⠉⠉⢻⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣄⡀⠀⢀⣠⡴⠋⢸⡄⠀⠀⣿⡇⠀⢸
⣸⠁⠀⠀⠀⣿⠀⠀⠀⠑⣌⠓⠶⠶⠶⡶⠋⠉⠁⡼⠋⠀⠀⠀⠀⣀⡤⠶⠒⠲⡄⠀⠀⢸⣃⡴⠛⠉⢹⡞⠁⠀⠘⡇⠀⠀⣿⡇⠀⠈⣧
⣸⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡆⠀⣄⢸⡀⠀⠐⠚⠁⠀⠀⣀⠴⠊⢁⡞⠁⠀⡴⠁⠀⣠⠎⠁⣠⡀⢀⡞⠀⠀⢠⡄⢳⠀⠀⢹⣧⠀⠀⡏
⣇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⢧⠀⠘⣆⠙⠒⢶⣦⡶⣶⠋⠳⡄⢠⠾⢦⡀⠀⡇⠀⠀⠁⠀⡴⡿⠀⠘⠁⢀⣴⡿⠁⠈⡆⠀⠘⣿⠀⠀⠙
⢸⡀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠘⣧⠏⠉⠑⢤⡏⠀⢻⡇⠀⡄⢹⡿⠀⠀⢹⠀⣸⠶⢤⡴⠚⠰⡇⠀⠀⣠⡾⠋⠀⠀⠀⣇⠀⠀⢿⡇
⢸⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢠⡟⢀⣄⠀⢸⠃⡀⢸⡇⢠⠇⠈⠁⢠⣦⠸⠾⠁⠀⠀⢹⣀⡴⠛⠒⠛⠉⠀⠀⠀⢀⡴⢹⠀⠀⢸⣷
⢸⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡼⣧⡜⣿⠀⠸⠀⡇⠘⠁⢸⣆⠀⢀⣼⣳⣄⣀⡴⣇⠀⠘⠿⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⢸⠀⠀⢸⣿
⠸⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⠀⠀⣿⠀⠀⠀⣇⠀⠀⢸⣬⣿⣿⣤⣄⠀⠉⠉⠉⠓⢦⣀⣀⣠⠏⠙⠛⣻⠉⠀⠀⣀⡼⠀⠀⣸⣽⠀⢠
⠀⠙⢦⣀⡀⠀⢀⣠⠴⠋⠀⢿⡄⠀⠸⡄⠀⢠⠏⠳⠴⡿⠁⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠙⠉⠓⢦⡠⠞⣁⠀⣀⡰⠃⠀⠀⣠⣻⠃⠀⢻
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢘⣷⠀⠀⠙⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣄⣀⠉⠉⠉⠉⠁⢀⣀⣤⣾⠟⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣆⡀⠀⣀⣀⡀⠀⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠉⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠉⢻⠉⠀⠳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡄⠀⠀⠄⠀⡀⢠⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⢀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⣻⣷⣄⠀⠀⠀⠀⡆⡀⡀⠀⠀⠄⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣴⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠃⠉⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠉⢝⣟⡠⠃⡃⠀⠠⠨⠐⠀⠀⠀⠐⠠⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢜⠿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⢡⡹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠈⠃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣯⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⣎⣿⡆⠠⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠙⣿⢻⣽⣿⢆⠀⠀⠀⠀⠀⣦⢺⣟⡉⡧⠀⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠘⠄⢻⣷⡜⣧⠀⠀⢀⢀⢴⣿⣿⣿⣦⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡐⢣⡜⣿⣿⣾⠈⠈⠀⠀⠀⢎⢻⣿⠟⡄⠀⠻⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠽⠻⣿⣿⣧⠀⠀⠀⠀⠸⣄⡇⠀⠀⠀⣄⡸⠂
⠀⠀⠃⠀⠃⠀⠃⠉⠀⠁⠈⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠉⠻⣦⡤⠀⠁⠈⠛⠇⠢⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣊⠀⢁⣠⠜⠁
⠀⠁⠨⠘⠀⠀⠀⠀⠁⠘⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⣠⠁⠠⢀⠀⠠⠀⢀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠠⠦⠠⠀⠈⠚⠀⠮⢗⠀⠀⠀⠀⠀⠐⢋⠄⠪⡇⠀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⡠⡈⠈⠀⣠⡀⠀⠀⠀⢔⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⠇
⠀⠀⠀⠀⠀⠈⠁⠙⠑⠊⠀⠀⠀⠀⡀⡀⠀⠙⠓⠁⠀⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠇⠰⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠨⠆⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠗⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠧⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠄⠀⠆⠀⠀⠀⠐⣅⠹⠍⡆
⠀⠀⠐⣃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⠐⠓⠔⡄
⠀⠈⢂⠘⢁⡂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢀⠉⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠪⠂⠟⠆⠉
⠀⠐⠑⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠔⠁