Hindu deity Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⡻⢭⡕⢤⠒⡭⢿⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢎⣹⡦⠿⢚⡻⠋⢿⣛⠺⠧⣾⣹⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣟⣡⡶⠛⡟⠁⠀⠀⠹⡟⠲⣤⣙⣶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣦⡿⠋⠀⡼⠀⣔⡮⣦⠀⢹⡀⠀⠹⣧⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣹⡟⠀⠀⠀⣇⠀⠘⠿⠟⠀⢈⡇⠀⠀⠈⣿⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡿⠁⠀⠀⠀⠙⢦⣀⣀⣀⣤⠞⠀⠀⠀⠀⢻⣥⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⢾⡧⠀⣠⠴⠒⢒⣒⣋⠩⣍⣓⣒⠒⠢⢄⡀⢸⣷⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⢺⣧⢊⣴⣾⠿⠿⠷⣖⡤⣖⡷⠿⠿⣷⣦⡉⣸⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⢙⣷⡟⣉⡤⣄⡀⠀⢸⠀⢻⠀⠀⣀⡤⣈⡻⣿⣏⣹⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⢆⠈⡊⠐⡦⢌⣉⠷⡇⢀⢀⣿⡏⡩⢽⡂⠁⠋⢰⠟⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠷⡇⢾⠳⠴⠿⢠⡏⠹⠉⢧⠸⠦⠜⣻⢃⡦⠋⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠠⢀⡄⡗⠀⠈⠈⠁⡾⠀⣈⡒⠘⡇⠁⠁⠀⢸⡇⣀⠠⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⢁⣴⣋⣰⢿⡀⠀⠀⢰⠁⠈⠙⠉⠁⡇⠀⠀⠀⣼⢧⣘⣧⡀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣰⡋⣿⠏⠁⠈⢧⣠⣖⣾⠀⢚⢛⡒⢀⡷⢒⣆⣰⠇⠀⠉⢿⠋⣢⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⠋⠀⠀⠀⢼⣉⣩⣿⠐⠂⠀⠂⣼⣅⣇⠈⠻⡀⠀⠀⠈⢿⣿⠇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢸⡏⠀⠀⠀⠀⠀⠈⠙⣿⠀⢉⣍⠁⣇⣠⠞⣩⡟⠛⠖⢦⡀⠸⣯⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠤⢀⠰⡟⠁⢰⣗⠊⢀⢤⠀⠷⡀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠒⡩⢻⢤⣾⠢⠄⡸⢸⡶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠀⠀⣰⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠼⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⢷⣿⢿⡿⢧⣹⣿⣿⢿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠾⠿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣧⣤⣄⠀⠀⠀⢸⣿⣿⣿⣟⢻⣆⠀⠀⠀⡶⠛⢻⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⠿⠁⠀⠀⠀⠀⠙⣿⣿⡿⠿⢿⠀⠀⠀⠿⠋⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠇⠀⠀⠀⠀⠀⢠⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡄⣶⢺⡿⡏⠀⠀⠀⠀⠀⢀⣾⠀⣿⣿⣿⣧⣀⠀⠀⠀⢀⣿⣿⣿⠆⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⠞⢠⠆⠀⠀⠀⠀⣴⣿⢃⣼⣿⣿⣿⣿⣿⠀⠀⠀⣿⣹⣿⠟⣿⡦⠀⢿⡗⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢀⣤⠿⠋⠛⢿⣄⢻⣿⣿⣿⡀⠀⠀⢿⣿⣧⣾⣯⠀⠀⠈⠹⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⡀⠀⠀⢀⣾⡅⠀⠀⠀⠈⣿⡧⢿⠿⣿⣷⣀⠀⠘⠟⢻⣿⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⠸⠧
⠀⠀⠀⠀⠀⠀⠈⢿⠿⠋⠀⠀⡔⠀⠙⣳⠄⣤⠀⠀⠘⡇⠀⢦⠀⢻⣿⣶⣄⠀⣿⠋⠀⠀⢠⠀⠀⠀⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⠰⡇⣶⣴⣿⡄⣿⡄⠀⠀⣹⡀⠀⣹⣿⣿⡿⢛⠀⠸⠀⡀⠀⣾⠀⠀⣸⡍⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢠⣿⠀⣿⠟⠀⣿⣿⣿⣿⣿⣿⠀⠻⢿⡛⠛⠃⣠⡷⣼⡗⠈⠻⣿⢧⣠⡏⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣾⣿⣧⣼⣅⣰⣿⣿⣿⠛⠛⣿⠀⠂⣠⣿⡇⢀⣿⡇⠈⠀⠀⠀⠈⢳⣾⣿⣷⢉⠢⢰⡦⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠁⠀⠉⠁⠜⠃⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠆⠀⢺⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣄⡀⠀⣀⠀⢀⣇⠀⠀⠀⠀⠀⠀⢸⠿⠿⠶⡶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣽⣿⣿⣿⣿⣷⣄⣿⣿⣵⣿⣤⣤⣸⡏⠠⠀⠀⠀⠀⣠⣼⡄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣄⢙⣿⢛⡇⢀⣼⣿⣷⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⠙⠛⢿⣿⣿⣿⣿⡿⣿⣿⣿⣟⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⠀⠀⠀⠐⣶⣶⣿⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣷⣶⣿⠿⠛⣽⠛⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⠏⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⢹⡄⣿⣷⡀⣄⢀⠀⠀⠀⠀⠠⣝⣛⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣼⣿⣿⡗
⠀⠀⠀⠀⠀⢢⠀⢣⣿⣿⣿⣿⡟⣿⣽⣿⣿⣿⣼⣆⣠⢀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠵⣄⠙⠿⣿⣿⣾⡋⠉⣿⣧⣿⣿⣿⣷⣯⠳⣄⡀⠐⢤⣤⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢳⣦⣙⠻⠿⣷⣄⣻⣿⣿⣯⣿⣿⣿⣷⣬⣿⣶⣤⣤⣭⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣠⣴⣠⡤⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣶⣾⣶⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠼⠛⠛⠛⣻⣟⣛⡛⠛⠻⠿⠿⠿⠋⠁⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡃⠀⠠⡃⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢉⣿⡌⢉⣽⠎⠉⢹⣤⣍⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣼⣧⣶⣿⣶⣶⣶⣾⣿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡏⠉⢹⡏⠉⠉⠉⢿⣏⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣴⣬⣄⡄⠩⠴⠶⠶⠶⢿⠩⣄⣬⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠄⢿⣶⣤⣀⡄⢠⡿⣆⣾⣿⣦⣾⡿⢿⣆
⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⢠⣈⢀⣶⣄⣼⠛⡃⢀⣠⣀⣧⣠⠟⠿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⡀⣠⣾⣿⠁⠀⠀⠀⠀⠹⢾⣿⣿⣅⡀⢐⣸⠿⢿⡿⢿⡘⠜⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⢤⠀⣷⣶⣄
⠀⠀⠀⠈⠛⠿⣩⠀⠀⠀⠀⠀⣠⢨⣿⣿⠹⠽⠉⣿⠶⢴⣾⡿⠙⣿⣏⢻⡏⣿⣦⡀⠀⠀⠀⠀⢻⣟⢛⣛⠇
⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠿⣟⢸⣿⣿⠁⠀⣠⣟⣆⣁⣨⡔⢸⣿⡧⣾⡏⣻⣿⣷⡆⠀⠀⠀⢼⣿⡞
⠀⠀⠀⠀⠀⠰⣞⠿⣦⡄⠀⠀⠈⠸⣿⣿⡄⠱⣿⣿⣻⠃⠙⡆⢸⡉⣹⣿⠁⣿⣿⣿⣷⠖⠀⡐⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢿⡧⠉⠀⣀⣤⠶⠞⢿⠿⣧⠉⣗⡠⠋⠀⠁⠁⣾⣿⣿⣿⣤⡿⠟⢛⣛⠃⠀⢸⡿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣥⣤⣤⣤⣴⣿⣷⣾⠟⣷⣛⡴⢂⣤⠘⣿⠛⠉⠛⣾⣶⣙⣷⣴⠏⣀⣴⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠔⡱⣹⣿⣸⡿⣹⣿⣿⣿⣿⣿⣹⠁⡿⠉⣴⣋⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡤⢊⠔⣰⢿⣿⡟⣱⣿⣿⣿⣿⡟⡻⣷⢆⡴⣾⠿⣿⣿⣿⠟⠀⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠀⡤⠊⣴⢣⠟⠉⣸⣿⢻⣿⣿⡿⢓⡤⠚⠋⠀⠶⠾⠟⠛⠁⠀⠀⢺⣞⢿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠃⠀⡾⣡⠀⢀⣼⡿⢫⣿⡿⠋⠻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⠻⡟⠂⠀⢻⣿⣿⣿⠉⢉
⠀⠀⠀⠀⠁⣴⠟⢡⣾⣿⣡⡿⢟⠀⠀⠀⠘⢿⣿⣳⣶⠅⣰⣆⣤⠀⠀⠀⠀⠀⠻⣄⢷⡄⢀⣸⣿⠋⡝⠀⡌
⣀⣀⣀⣠⣾⡏⣰⣿⣿⡿⠉⠀⠈⠳⣀⠀⠀⠀⣸⣿⣿⣶⣿⠿⠿⣿⡷⣷⣶⣶⣶⣿⣌⣿⣿⣿⣿⡟⠀⡠⣹
⣿⡟⣻⣿⢋⣴⣿⠏⢿⡇⠀⠀⢀⣴⣿⠳⣤⡠⡿⠛⠛⠁⠀⠀⢀⣠⣴⠾⠋⠀⠈⠉⢻⡾⢿⡈⢽⣷⣾⣷⣿
⣾⣷⣾⣱⣿⣿⣿⣄⣈⣷⡄⢠⠋⠹⠿⠘⠀⠀⠀⠉⢉⣉⣭⡿⠛⠁⠀⡀⠀⠀⠀⠈⣿⣿⡌⢿⣿⣿⣿⣿⣿
⠉⢉⣩⣿⣍⣩⣹⣅⣸⠂⠙⠛⠿⠒⢀⣤⠀⠚⠚⠛⠛⠉⠀⠀⠀⠀⠀⠘⣦⠀⠀⢠⡟⣿⣿⣽⣿⣿⣿⣻⣿
⠆⣿⣬⣿⡏⠉⠉⠉⠉⣤⣔⣠⡶⣶⣿⠋⠀⠀⣴⠀⠀⠀⠀⣼⣦⣄⣀⣼⡟⣿⠀⢩⣥⣿⠋⠉⠉⠸⣿⣿⣻
⠀⠈⣤⣽⡇⠀⠀⠀⠀⠀⠉⢩⣤⣹⣏⠓⣒⣻⠟⠱⢤⣴⠞⣡⠟⢩⣝⣋⣰⣃⣀⣸⡏⠋⠀⠀⠀⢀⣿⣿⣿
⠀⠠⠉⠿⠅⠀⠀⠀⠀⠀⠀⠈⠟⠻⣿⡟⠋⠱⠶⠟⠲⣶⡞⠛⠲⠟⠉⠛⠛⠉⠛⠛⠃⠀⠀⢀⠀⠰⡧⠼⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣻⣿⣿⡟⣿⣿⣿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣷⣽⣿⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣧⣠⡀⠀⠀⠀⣿⣿⣿⣟⢷⣄⠀⠀⠀⠶⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡿⠃⠀⠀⠀⠈⣻⣿⣿⠿⢿⠀⠀⠀⠿⠃⢸⣷⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⡄⢸⣿⣿⡀⠀⠀⠀⠀⢀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢴⣰⢺⡿⠏⠀⠀⠀⠀⢀⣼⠇⣸⣿⣿⣷⣤⠀⠀⠀⣸⣿⣿⣇⠀⠳⣄⡀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⣬⣿⠛⠀⠇⠀⠀⠀⢰⣿⣏⣴⡿⢿⣿⣿⣿⠀⠀⠸⣿⣹⡿⣻⠗⠀⠹⣟
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⠞⠉⠘⠙⣷⡜⣿⣿⣿⡄⠀⠀⣿⣿⣾⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣿⣿⣶⠂⠀⠀⠀⢿⡄⠀⠀⠀⠸⡟⠙⡉⠛⣿⣦⡀⠈⢠⣿⠇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠘⣯⠁⠀⠀⡇⡂⢀⣏⢰⡧⠀⠀⢻⡀⠙⢄⣼⣿⣿⡦⠘⡇⠀⠀⢠⠆⠀⢀⡿⠄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⢀⣧⠛⣿⡿⠘⣿⣤⣤⣾⣧⠄⢼⣿⣿⡧⠀⢠⡁⣶⠀⢾⣦⣄⠚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⣿⣄⣿⡀⣸⣿⣿⡿⠿⣿⡄⠀⣙⣷⡀⢠⣿⠉⠋⠀⠀⠙⢿⣻⣷⡰⠦⡀⣠⡘⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠘⠛⠁⡸⠋⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⡞⣠⠋
⠀⣤⣄⣀⢀⠀⢀⣠⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢼⡀⠀⠀⡀⠀⢰⡀⠀⠀⠀⠀⠀⢰⠿⠧⣤⣴⡶⢛⣁⣠⠄
⢠⣿⣿⣿⣿⣷⣿⠋⠙⠟⠛⠿⠛⢉⣻⣿⣻⣿⣷⣄⣺⣿⣣⣾⣥⣄⣾⠃⠀⠀⠀⠀⢀⣼⡄⠀⠄⠀⠈⠁
⣿⣿⡿⠟⠀⠙⠀⠀⠀⠀⠀⢀⣴⡿⠋⢻⣿⣿⣿⣿⣿⣿⣅⣈⡿⣻⡃⣠⣿⣶⠶⠞⠋
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠴⣿⣟⠀⠀⠀⠙⢻⣿⣿⣿⣿⣟⣿⣿⣿⣏⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡀⠀⣀⣀⣶⣿⡿⠋⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠛⣩⡞⠃⣸⡏
⣿⣧⠀⠀⡀⠀⠀⣠⣤⣿⣿⣷⠹⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠐⠿⢁⣠⣿⡇
⣿⣿⡇⠀⠠⠀⢰⢿⣿⣿⣿⣼⣦⢿⣷⣼⡆⣄⠀⠀⠀⠀⠶⣬⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠟⠛⣿⡅⠀⠀⠀⠀⢀
⣿⣿⣿⣆⠀⠣⡀⠻⣿⣿⣿⣧⠿⢾⣿⣻⣿⣿⣶⣶⣦⡀⠀⡀⠉⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣠⣿
⠛⠛⠛⠛⠳⠦⠿⢦⡈⠻⢿⣿⣦⡘⣿⣿⣿⡿⣿⣿⣯⣻⣦⣄⡙⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠺⠿⠟
⣤⣤⣤⣀⠀⠀⠀⠁⠙⢷⣶⣿⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡠⢀⣀⠴⠶⠿⠅
⣈⣿⣿⣿⣷⣤⣀⠀⠀⠸⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⣤⣶⣾⣿⣿⣿⡀⠀⠀⠀⠲⡶⠶⠒⠒
⠀⠈⠙⠛⢿⡿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣮⠿⣿⡿⠿⠿⠿⠿⠷⠿⡿⢿⠿⠋⣿⣯⣽⣛⣏⣉⣤⣴⡶⠋⠁
⠀⠀⠀⢠⡤⠤⢶⡾⠿⣿⣿⣷⣶⣼⣴⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣶⣾⣿⠿⠿⠛⠋⠉
⣼⣿⣶⠀⠈⢠⠀⡧⢠⡿⠋⣉⣳⣄⣉⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣾⣿⣿⠶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣏⡉⠛⠆
⣿⣿⣿⡟⠋⠉⣿⣿⣿⣿⣿⣿⣟⠉⠉⠓⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣲⣶⣶⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⣻⣷⡖⣶⣿⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣈⣥⣯⡀⢨⣧⣍⡀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠚⠂⠚⠚⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡃⠀⠈⣸⡇⢠⡄⠐⠀⣤⠈⣿⠨⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠂⡇⠀⠀⠠⠀⠀⠀⡗⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢹⢦⠀⠀⠀⠀⢸⠁⠤⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠐⠁⠀⢀⢨⣼⡀⠀⠀⣾⣧⠀⠀⢀⡀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⡘⠀⠀⠈⠘⠈⣇⠀⠀⠀⠡⠇⠐⠀⠚⠇⡠⠊⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣗⡶⣤⣠⠀⠀⠸⡄⠀⠀⣤⠀⠀⡅⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⢤⡄⠀⠀⠀⠙⢦⠞⠁⠀⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠁⠀⣬⡀⠀⠁⠀⠀⠀⡀⠂⠒⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⡀⠱⣤⡌⢠⣉⣡⠀⣤⣴⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠇⠐⣯⡗⠀⠁⠠⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⢈⡠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣧⠀⠀⠀⠀⠀⣀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡁⠠⢀⠀⠀⢀⡸⠋⣂⡙⠛⠖⠄⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⡔⠉⠀⠀⠈⢀⡞⣟⠀⠀⠃⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣙⣿⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣹⣻⡿⣿⣿⣦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠆⠀⠾⠽⠽⣏⡙⣋⢱⡯⠝⠉⢁⠺⡘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢃⡁⣴⢳⠐⢇⡞⢷⠀⢁⠁⠀⠈⢣⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⣼⠙⣵⢇⣩⡑⢊⡿⢽⡇⠀⢑⡀⠀⡄⡹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠚⢠⣼⠯⣆⣿⠚⢻⢉⠁⡇⣼⡗⣀⣰⣎⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠐⠛⠉⢙⣆⢨⠁⠀⢡⡸⠇⠛⠟⠉⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⣠⡆⡄⡄⣴⠳⡆⠠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⡇⢙⣿⠷⣇⡹⢇⠀⣿⢥⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠀⣸⡿⡀⠈⠓⢤⣀⢿⡤⠈⢷⠈⠣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢀⡿⠁⠙⢢⣀⠀⠈⢸⣿⠅⠈⢂⠀⢿⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢔⡔⠀⢀⣿⢃⡤⠖⣾⣿⡙⣲⡼⠹⣧⢂⠀⠙⣼⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⢸⠀⡐⠙⠈⢥⠀⡇⠀⢻⣆⠂⠀⢩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡁⢀⢸⡊⠐⢤⡲⣶⣷⡁⠀⠀⢻⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣄⠅⡑⢠⠄⠑⡖⢲⠛⢦⠇⠕⡢⢈⠿⣦⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⡄⠉⠀⢺⠀⢨⢇⢌⠀⡸⠪⢒⠀⠠⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠂⠐⠀⠂⢐⠁⢀⠒⠒⠀⣔⠈⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠍⠭⠭⠽⠭⠭⠯⠤⠬⠿⠽⠽⠼⠭⡭⠭⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢀⠖⠀⠀⠊⢁⢀⠔⣂⠀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡆⠐⣦⠀⠘⡃⠀⠸⣇⠀⠘⢏⠀⣻⠂⣀⣇⡤⠀⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤⡄⠀⠸⣇⠀⠐⠂⣀⠋⠀⠿⠁⠀⠀⢈⡺⠧⠀⢈⡿⠀⣠⣧⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⡆⠀⠹⢒⣠⣤⣶⡿⠋⠉⠀⠲⢤⣤⣦⣤⣥⡤⠴⠋⡈⠁⠐⢦⣭⣀⠰⡟⠉⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣀⠠⢋⣤⣶⣿⣿⡿⠿⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡄⢡⠈⣿⣿⣷⣤⡐⠮⠁⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⣀⠀⣩⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠇⠰⠉⠙⠻⣿⣿⣶⣌⠫⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢁⡀⡠⢁⣾⣿⣿⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢛⣿⣖⠚⠐⠈⠉⠀⠀⠀⠔⠀⠀⠀⠙⢿⣿⣧⡘⢞⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠝⣰⣿⣿⡿⢄⠑⣃⠔⠀⠀⠀⠀⠀⠀⠀⣀⠀⡿⠎⠈⣟⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣠⠂⠘⣿⣿⣿⣎⠳⠜⠋⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠑⠎⣰⣿⣿⣿⠓⠀⠀⠈⢸⣁⠆⡀⠀⠀⠀⡀⠠⠘⢯⣄⣐⣤⠧⢐⠱⠀⠀⠀⠀⠀⣠⢲⠂⠁⠀⠀⣿⣿⣿⣿⣧⠡⡤⠾⠅
⠀⠀⠀⠀⠀⠀⠀⠈⢠⡴⢠⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠁⠛⠘⠲⠓⠀⠁⠀⠙⠛⠉⠐⠳⣆⠰⢄⢶⡐⠢⠈⠁⠀⠀⠀⠠⣿⣿⣿⣿⣿⣇⠡⡀⢀⡄
⠀⠀⠀⠀⠀⠐⣆⡀⣴⠁⣾⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣁⠀⢀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠃⠉⠁⡠
⠀⠀⠀⠀⠀⣤⠤⠒⠉⣈⢉⡙⠛⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠤⠲⠄⠀⠀⠏⠀⠈⠷⠄⠂⠈⠃⠀⠠⢄⣀⣀⠀⠀⢀⣼⡿⠿⠿⠿⠿⢿⣿⣷⠘⠶⠋⢀
⠀⠀⠀⡰⠆⢀⣤⠖⢻⠉⢉⡟⠙⠲⢤⡙⢿⡷⠆⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠄⢴⠁⣠⠀⣄⡀⡀⠀⠀⠉⠛⢿⣿⠟⣁⡤⠴⠶⠒⠒⠦⣌⠛⢦⣄⡄⠊
⠀⢀⡼⣡⡖⠋⠀⠀⠃⢴⠋⠀⠀⠀⠀⠱⡌⢷⣀⣠⠴⠈⠁⠉⠀⠀⠀⠀⠀⠠⠀⠘⠈⠀⠀⠉⠈⠉⠙⠓⠶⣶⡟⣵⣞⠉⠀⠀⠀⠀⠀⠀⣈⠳⡌⢳⡀⣢
⢠⢞⡿⠉⢠⠀⠀⠀⠀⠪⠕⢀⠀⠀⠀⠀⠘⢦⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⣿⡉⣹⠆⠀⠀⠀⠀⠀⠀⠀⢄⠸⠀⢿⡀
⠿⣿⣷⣴⠛⡤⣀⡀⠀⢀⡀⣈⢈⣐⢣⡿⣄⣰⠘⠦⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⡄⡀⠀⠀⠀⣀⠴⠃⢸⠟⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⡄
⠀⠀⠉⠛⢍⡁⠁⠉⠉⠈⠁⠉⠈⠀⠀⠀⠀⠀⢦⣠⣤⣭⠀⠲⢄⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⣠⠖⣩⡴⠶⠶⣾⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⠤⠚
⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢆⠺⠆⠈⠇⠃⠀⠀⠀⠐⠤⠀⠀⠀⣰⠃⠜⠁⣴⠗⡄⢻⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡃⠈⠑⠒⠂⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠉⠀⠘⡆⠉⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢚⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⡼⠃⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣦⡀⠀⣠⡞⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣴⡊⠀⠀⠀⠀⢀⡠⠘⣻⣿⣿⣿⣦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠂⠘⠛⠻⣿⣤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⢊⣩⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢸⣙⠻⡅⣐⠀⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢉⣅⠜⢻⣿⣷⠖⠠⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣯⣈⠿⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡴⠖⢉⠝⠁⠀⣠⣿⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢸⣭⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣧⣀⠀⣸⠿⣿⡦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣯⠗⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢴⢛⡧⢴⡏⣷⠀⠀⠀⠀⢻⠂⠀⠀⠀⠀⠀⠾⠁⠀⣴⡿⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣤⢛⣇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⠦⠾⠌⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⠀⣨⠗⠀⠀⠀⠀⠀⠀⣀⡠⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣴⣤
⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢀⠀⣴⡄⠀⢀⠀⠀⠈⣉⠁⠠⠺⣿⣿⠒⠄⠀⡀⠀⠀⢀⠀⢀⡄⠀⢀
⠀⠀⠀⡀⠘⣛⣛⣟⠀⡄⠀⠀⠠⡄⢠⠿⠿⡀⣠⠀⠀⠀⠨⣹⣿⣧⡀⢺⠀⠀⠀⠻⠶⣶⣷⣾⣷⣶⣦⡾⠃⠀⠀⠘⢦⣼⣿⣤⠏
⠀⠀⠀⠉⠻⣿⣿⣿⠛⠁⠀⠀⢀⡽⠗⠀⠀⠻⣅⡀⠀⠀⠳⠿⣿⠿⢧⣄⠃⠀⠀⠦⠶⢿⣿⣿⣿⣿⠷⠾⠿⠀⠀⢀⡼⠀⠸⠿⠃
⠀⠀⠀⠀⠀⠈⠈⢸⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣴⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⢰⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⡀⠀⠀⢶⠰⣄⣇⣸⣿⣀⣇⡤⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠂⢳⡿⣿⣿⠁⠀⠀⠀⢠⠀⣿⣿⡿⣆⣠⠀⠀⠀⠀⠳⣶⣌⠭⣾⠏⠁⠀⠀⠀⠐⠺⣻⠊⠁⣿⠛⠒⠀⠀⠀⢀⡆⠉⢱⡀
⠀⠀⠀⢠⠎⠀⠉⠉⠃⠀⠀⠀⠀⠘⠏⠙⠳⠀⠙⠀⠀⠀⠀⠺⠋⠁⠀⠀⠛⠃⠀⠀⠀⠀⠸⠁⠘⠛⠈⠓⠀⠀⠀⠀⠊⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠘⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⣀⠀⢀⡄⢀⡀⠀⠀⠀⠀⣤⡀⢀⠀⣤⡄
⠀⠀⠀⣨⠁⠀⣁⠀⠘⢇⠀⠀⠀⢀⠝⢁⣉⣁⠙⢁⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠹⣆⣠⣿⣇⣠⡎⠀⠀⠀⠙⣆⣺⢿⢿⣀⡞⠁⠀⠀⠀⢤⣼⣿⡆⠀⠀⠀⠀⠘⣦⣾⣻⣦⣠⣶⡄⠀⠀⠀⠀⠸⣉⠃
⠀⠀⠀⠀⠀⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢽⣿⣿⣅⡀⠀⠀⠀⠀⣼⢿⣿⣷⡄⠀⠀⠀⢀⣹⣿⣿⣿⣁⣉⣁⠀⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠜⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠈⠉⠹⠇⠀⠀⠈⠉⢠⣶⣾⣦⠈⠉⠁⠀⠀⠀⠸⠟⠉⠹⠃
⠀⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⡏⠀⠀⠀⠀⠀⣤⠁⣴⠚⣷⠐⠈
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⡴⠟⢤⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣧⣌⠐⢼⠀⠀⠀⠀⣄⡠⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⣹⠷⠘⡄⠀⠀⠉⡆⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⢀⠠⡀⠀⠀⠘⠋⠁⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠀⠀⠀⠀⠀⢀⣀⣠⣆⠀⣀⣠⣀⣔⡹⠂⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠐⠀⠀⠀⠐⡀⠈⠻⢹⠛⡟⠺⡻⠃⠈⠱⡄⠀⠴⣼
⠀⠀⠀⠀⠀⠠⣶⠄⠀⠈⠃⠀⠀⠐⠠⢦⠄⣆⢀⠤⠆⢠⢷⠁⣀⣤⣤⣀⠄⠀⠸
⠀⠀⠀⠀⠀⠀⢪⠁⠀⣰⠂⠀⠒⠠⠀⠀⢠⡟⢈⣂⢀⣠⣏⣀⠯⠉⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠠⢠⡿⠀⠘⡅⣀⣿⡀⡀⠀⠀⠀⠆⠂⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⠉⡙⣿⡆⢀⠴⣭⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⡿⠈⠀⠁⠸⡇⢸⠀⡾⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠸⡀⣗⠤⡄⠀⢰⠃⣧⡄⢠⣿⡶⠓⠀⠰⣷⣟⣾⡜⠀⠀⠀⠀⠀⠀⡐⠆⣸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠆⠀⠀⢈⡄⢀⡡⠊⣃⠑⠠⣀⣢⡟⠀⠉⠳⣄⡀⠀⠀⠀⢀⣴⣾⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⠦⢄⣸⠷⠾⠁⢠⡸⠄⠐⠉⢡⣨⣤⠶⡄⠈⠓⢄⠤⠚⣯⠤⠉⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⣄⡌⢀⠖⢺⣿⡤⠠⡄⠂⠨⠃⢀⠀⠈⠓⢄⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢀⠜⠁⡸⠄⢈⣊⡁⠠⢘⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡩⠐⠁⠀⠀⠈⡇⢟⢰⣷⣽⡖⢲⣦⢿⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠠⠐⠚⠁⢀⣀⠤⠊⡷⢤⣻⠀⠇⠁⣿⠁⢸⡷⠿⠟⠓⠉⠉⡿⠿
⠀⠀⠀⠀⠀⠀⠘⣆⣀⡀⣀⠤⠛⠉⠀⠀⠀⣸⡅⣾⣿⠐⣆⣾⢷⡀⠈⠛⠲⠷⠿⠮⢾⣟⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⢸⣤⠟⢹⠀⠹⣿⡆⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡌⠁⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠑⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠭⠤⠤⠤⠃

⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢄⢠⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⠄⣀⠀⣀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣽⡪⣯⣿⢦⣀
⠀⡀⠀⣀⠒⠦⠤⠤⠤⠂⣈⠀⠀⠀⠀⠀⠀⠀⠐⠬⠉⠁⠀⠧⠀⠾⠀⠈⠩⠥⠂⠀⠀⠀⠀⠀⣠⡶⣶⡼⣟⠙⡄⢋⣗⢴⣿⣷⣄
⠀⠁⠘⠅⠈⠐⢠⣤⠒⠁⢨⠃⠐⠀⠀⠀⠀⠀⠬⠭⠅⠀⠀⠞⠀⠓⠀⠀⠨⠭⠅⠀⠀⠀⠀⠈⣿⡿⢲⣴⣿⣺⢶⣧⣿⣴⡞⣾⣿
⠀⢸⣿⡓⠦⠄⢻⡟⢠⠴⢚⣳⡟⠀⠀⠀⠀⢠⠋⠱⡄⠄⢲⡀⠴⢀⡓⠠⢠⠞⠑⡄⠀⠀⠀⢀⣛⢇⠠⠁⠀⠀⠀⠀⠀⠨⠀⡞⣃
⠀⠈⡉⠃⠀⠚⠀⠁⠒⠀⠘⠉⠁⠀⠀⠀⠀⢻⡀⣠⡟⠂⠀⠹⠤⠏⠀⠐⢻⣄⢀⡟⠀⠀⠀⢸⡁⢹⡈⢶⠒⠤⠀⠔⢒⠖⢹⡅⢨
⠀⠀⠄⠪⠄⠀⠠⠄⠂⢠⠖⠢⠄⠀⠀⠀⠀⠈⠙⣿⣄⠠⢠⠠⠀⢂⡄⠄⣠⣿⠉⠀⠀⠀⠀⠀⠓⢌⣷⠀⠣⠀⠀⠀⠆⢠⣏⡀⠊
⠀⢀⠐⣀⣐⠆⣀⣀⠠⢂⣈⡀⣀⠀⠀⠀⠀⠀⠀⣭⡿⠈⢠⠄⠀⠠⡄⠁⢿⣬⠀⠀⠀⠀⠀⠀⢀⡐⢰⡀⠀⠀⠀⠀⠀⢰⡀⡀⡀
⠀⠈⠄⠈⠉⢌⡒⠂⡁⠌⠁⠠⠅⠀⠀⠀⠀⠀⠀⠈⡇⢠⠾⡒⢀⢒⠷⡄⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠬⠶⠐⠒⠀⠶⠄⡁⠀⠄
⠀⠀⠚⠃⠄⠀⡀⢀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⡼⢀⣧⣸⠿⠋⣬⠙⢿⣇⣼⠀⢇⠀⠀⠀⠀⠀⢠⠄⠹⠀⢀⣀⣀⣀⠀⠈⠁⠠⡄
⠀⠀⠀⠀⠀⠀⢳⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠙⠤⠂⠤⠋⠀⠀⠁⠘⠂⠀⠀⠀⠀⠈⣭⢰⡥⣻⣇⣀⣿⡇⢥⠠⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠀⣠⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣘⣟⡀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄
⠀⠐⠦⠀⠀⠐⠄⢬⠠⠜⠀⠠⠠⠆⢡⠀⠀⠀⠀⠀⠜⢦⢄⠝⢘⣛⠘⢁⢤⡞⡄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠐⠎⢠⠉⡆⠄⢠⡄
⢩⠞⠀⠂⠀⢲⠀⠀⠀⠴⠀⠐⠂⠱⡜⠀⠀⠀⠀⠀⠈⠻⠄⣢⣉⠉⢀⣎⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠃⠀⠀⠀⠈⠧⠘
⠛⠀⠀⠀⠀⢀⣠⡶⣤⢀⢀⠀⡀⠐⠞⠀⠀⠀⠀⠀⢰⣆⠀⠈⠘⠚⠈⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⠶⡀⠀⠀⠐
⠀⡀⣷⡔⠋⠀⡈⠀⠁⢀⠘⢛⣾⢀⠀⠀⠀⠀⠀⢀⣮⣊⠙⣦⠘⠜⢀⡞⠉⣩⢧⠀⠀⠀⠀⠈⠁⠃⢐⡀⠀⠙⢤⠚⠁⠀⣁⠀⠃
⠀⣐⡻⡀⠀⠊⠋⠀⠘⠙⠂⠀⡹⣓⠀⠀⠀⠀⠀⠀⣥⡙⢂⡚⠠⠠⠈⣂⠚⣡⡄⠀⠀⠀⠀⠀⠀⢞⠀⢞⣛⣥⠀⣠⣝⣛⠄⠐⠃
⠀⡥⡄⡷⠀⠘⣤⣀⣤⠌⠀⢸⢀⣤⠀⠀⠀⠀⠀⠀⢸⠋⠁⢤⡃⠀⣡⡜⠉⢹⠀⠀⠀⠀⠀⠀⠓⠞⢡⠀⢀⠦⢤⠴⢆⠀⢀⠓⠚
⢰⣦⣓⠆⣀⣭⡑⠿⠆⣭⣁⠠⣞⢵⠆⠀⠀⠀⠀⠀⢨⡅⢸⣉⡒⡝⣊⣽⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡙⠶⠶⠶⠚⣁⠈
⠘⠛⠜⢾⡚⠶⠯⣿⠩⠶⠒⡾⠛⠙⠋⠀⠀⠀⠀⠀⠀⣧⣛⠻⠙⠟⠩⢋⣣⡅⠈⠀⠀⠀⠀⠀⠀⢀⠛⣄⡀⠀⣴⡀⠀⣀⠜⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⢯⣤⣟⠛⣻⣦⡼⠄⣁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣁⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠺⣿⣭⡿⡟⠛⠒⠒⠒⠲⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠉⠁⠀⠀⢀⣶⢴⢤⢤⢤⢴⣦⡄⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠰⡇⡦⢰⠞⣰⡞⠶⠾⠧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠄⠐⠀⠀⠀⠀⠆⢠⡞⠒⠒⠀⠀⣿⡇⠀⠀⠐⢺⡀⠀⠀⠀⠔⠀⠀⢀⠀⠂⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⣠⣄⠘⠀⠀⠀⠀⣯⣕⠀⠀⠐⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡞⠀⠉⠁⠀⠀⠀⠐⣇⣨⠄⠀⠀⠀⠈⠻⣿⣷⣦⣄⡐⠀⠀⠀⠀⢀⠄⠀⠐⠀⠀⠙⣦
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⣶⣿⡟⠁⠈⡀⠀⠠⠀⠀⢀⣿⣿⣦⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⠄⠀⠀⡀⠈⢳⣄
⠀⠀⠀⢠⠞⠀⠀⠠⠀⡈⠀⠀⠀⠀⣴⣾⣿⣿⣿⣇⠄⠐⠀⠀⠀⠀⣦⡞⠉⠀⢽⣶⡄⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⡀⠆⠀⠠⠀⠹⣦
⠀⠀⢠⡏⠀⠀⠐⠀⠠⠀⢀⣀⢴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⠀⣤⡿⠀⠁⣤⠈⠹⣧⡄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣷⠄⠤⠄⠀⢈⡀⠀⠀⠀⠸⣇
⢀⣀⣏⠀⠀⢒⡛⠈⠈⠉⠉⣉⠉⠛⠿⢿⣿⡇⠀⠀⠀⣀⢀⣀⣀⣼⣇⠐⢠⣤⠖⠀⣹⣁⠀⡀⠀⠀⠁⠀⣿⡿⠟⠋⠡⠐⠒⠂⠀⠀⠺⠶⢦⣀⠁⠀⠸⣆
⠈⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⡀⠉⠡⣀⣶⣞⡯⠧⠟⠓⠙⠁⠀⠈⢸⠀⠀⡻⢿⡽⢟⣳⣦⣀⠔⠉⢀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢤⣽⣄
⢰⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣄⠀⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⢀⠀⠀⠀⠈⠁⠓⢻⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾
⣸⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠀⠀⠀⠄⠀⠀⠀⠈⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢸
⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠸
⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠃
⣇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⢸⠀⠀⣤⣤⣤⣄⠀⠀⢨⠀⠀⠠⠀⠀⢀⣠⣶⡦⣤⠀⡌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡯
⣿⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠠⡜⢿⡿⢇⠀⠀⠀⠀⠀⠀⠀⠟⢛⣛⡰⠃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⢸
⢸⠀⠀⠉⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠛⠂⠚⠀⠀⠀⠂⠀⠀⠀⠃⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⣸
⠸⡆⠀⠀⠀⢉⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠀⡟
⠀⢷⠀⠀⠂⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣣⡀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣄⣼⢁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠑⠂⠐⠀⠀⣸⠃
⠀⠘⣇⠀⠀⡀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠘⣿⠃⠀⡄⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠘⣿⡇⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠠⡀⢀⠀⠀⣰⠏
⠀⠀⠹⣆⠀⠈⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⣼⡿⠀⠘⡇⠀⠀⠀⠤⠀⠀⠀⠀⢀⡗⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⣠⠏
⠀⠀⠀⠘⣧⡀⠀⠀⣐⠃⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠃⠀⣰⡇⠀⠀⠠⡄⠀⠀⠀⠀⣼⣧⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⢳⣄⠜⠉⠀⠀⠀⠀⡀⠀⠒⠘⢿⡿⠟⠁⣠⣾⡿⠁⠀⠀⠤⠀⠀⠀⠀⣰⣿⣿⣷⣄⣸⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠯⣀⡀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠒⠻⣿⡿⠑⠀⠠⠆⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠈⠀⢀⡀⠀⠀⠀⠙⡄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠑⠀⠀⠀⠀⡀⠀⠀⠐⠼⠁⠂⣤⠀⠄⠀⢀⣴⠿⣿⡛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠁⠂⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠈⠀⠀⠀⠂⠠⠀⡀⠄⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢠⠀⠂⠀⠐⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠁⠀⢸⢁⠀⠘⠀⠀⡃⠀⠀⠀⣦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣘⡄⠀⠙⡀⠠⠓⠠⠄⠀⡈⠒⡘⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠉⠠⠆⢠⠆⢇⣉⣾⣤⣤⡶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠤⠴⠄⡠⢤⣄⡀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠉⢉⠉⠀⠀⠖⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠈⠀⠠⠄⠀⢀⢀⡐⢥⠁⠉⠝⠴⠀⡠⠎⢆⢰⠃⠫⡀⠈⠀⠀⡀⠀⠀⠀⡉⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⢁⠄⡬⠒⠉⠉⠀⠀⠀⠈⠉⠈⠐⠒⠄⢫⡴⠀⡀⢀⠈⡿⠐⣆⠀⠀⠀⠀⠀⠀⠤⡂⠠⠜⢶⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⣨⠃⠀⠀⢀⡠⠔⠲⠒⠒⠢⠄⠠⡀⠀⠞⠀⠙⢤⠚⠅⠜⠂⢨⣶⡄⠄⠀⡀⠀⠀⠀⠀⠀⠞⠃⣄
⠀⠀⠀⠀⠀⠀⢠⡉⠤⢰⠇⠀⢀⠶⠁⡄⣐⠥⠈⠃⢤⣄⢤⠴⡟⣵⠆⠴⠀⠀⠀⠀⠀⠉⢋⡵⣚⣄⣦⠀⠀⠀⠀⠐⠂⠤⠈⡀
⠀⠀⠀⠀⠀⠀⢸⡅⢠⡄⠀⢠⡟⠀⢊⠅⠀⠀⠀⠀⢀⠥⠀⢐⡇⠁⢀⠐⠒⠠⠐⢀⠀⠀⠙⠂⣙⢡⡿⠀⠀⠀⠀⠀⠀⠀⠄⣢
⠀⠀⠀⠀⠀⠀⢸⠁⢀⢰⡀⠀⡆⠀⣸⠂⠀⠐⠀⠀⠁⠀⠠⣾⡵⠀⠘⠳⣠⠂⠹⠟⣌⢈⢦⣁⣫⡄⢹⣶⠃⠀⠀⠀⠀⡇⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⢇⠀⠲⣄⡀⣠⢠⠀⠀⠀⠀⠀⢀⠈⠁⠳⡟⢀⠅⠄⠠⠊⢀⡈⠻⢯⠑⣼⠂⠠⠀⠀⣴⢶⣭⣍⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⣴⠢⠀⡈⢛⢿⣌⠁⠀⢀⣀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⢀⡸⢢⠿⠙⢀⠀⠐⠃⢹⡟⢹⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⡼⠋⠀⠉⠷⠴⠛⠾⣀⣉⣠⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣦⣤⠁⢀⠀⡁⡄⣀⠀⢸⡇⢼⣄⡠⠃⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⣛⣴⠛⠊⠳⠘⠊⠀⠀⠀⡀⠠⠔⠐⢈⡜⠀⣚⡿⡏⠺⡠⢘⢟⣙⣎⠀⢰⣴⣖⠺⣥⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⣻⢶⠇⠐⠒⠒⠂⠉⠉⠑⢠⡀⠀⠀⠈⠁⠈⠀⠁⣴⡆⢹⣿⣼⣿⣿⣷⢮⠥⣿⣦⠘⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⣸⣙⣦⣤⣶⠶⠆⢈⡡⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠘⣿⣿⡿⢛⡁⠶⠟⡉⢙⠓⢆⣘⢿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⡢⠠⡄⠹⣿⡏⠀⢀⣀⠀⠀⠀⠀⠀⠙⢷⡄⢀⡀⠀⢀⣀⣀⠈⢱⠟⣃⠶⣋⣵⠆⠙⠄⡤⠛⠀⠈⠳⣞⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⢀⣿⡇⠀⠀⠈⠣⡀⠀⢿⣿⡶⠈⠁⠀⠀⢘⢋⡁⠀⢰⡷⢋⣤⠚⠛⠉⠀⠀⠀⠀⠁⢀⡤⠖⠸⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⣸⡟⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⡿⠏⠀⢀⣀⡀⠀⠰⠆⠀⠾⣁⠠⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢿⣏⣴⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⡇⡟⢀⡴⠚⠉⠉⠛⠛⠀⠀⠀⠿⠿⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠉⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⣿⣇⣧⠀⣀⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠃⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠀⠀⢰⣿⣿⡧⢾⡇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⣾⢇⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡠⡌⢀⣿⣿⡇⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⣀⠀⠈⠉⡷
⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⢀⡀⠀⢛⡂⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠰⠟⢿⣿⣇⠀⣽⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣿⣿⠃⠀⢠⣜⠃⠘⠷⣿⣀⠀⠀⠀⠀⠀⠀⠁⠂⡀⣀⠀⣀⠀⡄⡀⠀⠀⡼⣿⣿⣿⡟⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠⠄
⡀⢠⠄⢠⡤⠛⠓⠠⣤⡄⠉⠀⠀⠀⠈⢉⡐⠖⢂⣐⠛⠀⣤⠛⠃⠠⠄⣉⢡⣦⣤⣤⣤⣬⣾⣿⡏⣶⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉
⠃⠐⠀⠀⠀⠈⠉⠀⠘⠛⠀⠀⠀⠀⠀⠀⠙⣾⣷⡆⠤⢀⣄⡤⢠⣄⣮⠿⢛⣿⣿⣿⣿⣿⣿⣿⣧⣈⢄⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠲⢦⡄⢄⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢉⠻⠛⢟⠿⠛⠉⠩⣀⣾⠉⠉⠉⠉⠉⠀⠀⠈⠙⠿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠙⢤⠃⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠶⠆⠺⠄⢰⢆⡀⣀⢀⢀⣀⡀⣰⣦⠗⢦⣄⡀⠀⠀⡆⠀⠀⠀⠀⠀⠁⣯⠻⢶⣀⡀⠀⠀⠀⠀⢠⡜⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣙⢶⠾⠋⣯⠛⡝⢀⡑⠘⣿⣿⣿⣿⣷⠂⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠚⠰⠶⡟⣡⣧⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣛⡏⣡⡑⢢⡴⠀⢂⠁⡐⠈⠉⠛⠛⠟⠀⠁⣀⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢼⢷⣌⣏⠀⠀⡃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠐⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠀⠨⠍⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢡⡟⣿⡾⡏⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⣼⣷⣶⣦⣤⡿⠋⠁⠀⠀⠀⠀⠈⠹⠆⠆⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠓⠀⠸⠂⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠣⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡱⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶
⣿⣿⣏⣁⣍⣋⣀⣏⣉⣯⣁⣽⣟⣝⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣟⣻⠄⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢰⠟⢿⣭⣧⢠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⡶⣌⣷⣶⣿⣭⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣯⣿⠻⠻⠿⣿⣿⣿⢿⣿⢿⣦⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣄⠃⡀⠀⠐⣿⢿⡼⠿⣿⣏⣿⣷⣶⣿⣏⢨⣿⣿⣿⢿⣿⡄⠀⢠⣞⣄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⡠⠂⠀⡼⠿⠶⠿⠦⢿⡥⣠⠈⢳⣤⠄⣿⣧⣤⠻⡰⠎⢃⠘⠹⣇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠘⠁⠀⠀⠘⣖⠀⢳⠂⢀⣽⣏⠉⣁⣏⠉⢨⣿⢡⠀⢰⡗⠀⡶⠁⠀⠈⢢⣥
⠀⠀⠀⠀⠀⠀⢀⡀⠸⠁⠀⠀⠀⠀⠀⢸⣤⣘⠤⢾⡋⢙⡧⢘⡃⢴⡟⠙⣿⢂⡄⢢⣄⠁⠀⠀⠀⠀⠹⣾⡷⠾⠃
⠀⠀⠀⠀⠀⢀⠚⠀⠁⠀⠀⠀⠀⢀⡴⡯⢶⡛⣾⡏⠙⣉⠳⠶⠶⠚⣿⡞⢛⣷⡚⡄⢍⠳⡄⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠈⠳⡴⠇⢸⡀⠀⠀⢰⢻⣟⠀⡇⣼⣿⠁⣶⣼⣧⡐⣂⡴⣿⠉⣼⣿⡅⢀⠀⢢⢝⣄⠀⢀⣾⣀⣴⠉⠁
⠀⠀⠀⠀⠀⠈⠑⣦⠶⠧⠀⠀⣈⣿⣍⣻⠖⣻⣏⡞⠻⢿⡄⠉⠉⢀⡇⠀⢮⣿⣏⡏⠀⠘⣤⡜⠀⠈⠉⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣴⠛⢏⡛⣭⣻⣟⡹⡟⡆⢈⡸⢇⢤⠄⢸⡇⢸⢻⣿⠆⢶⣒⣻⣿⣿⡟⡳⢆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣀⡴⠛⠉⠉⠉⠘⡿⣇⠈⣵⡆⠀⢀⠸⢥⣌⣸⡿⢅⠉⠹⠟⠉⡵⢀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⣀⣀⣀⣠⢤⠚⢫⠃⠘⡇⠠⢏⠰⠀⣽⣨⡀⠀⠀⠀⠀⠀⠀⡸⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⣿⣿⣎⣶⢸⣾⠅⡷⠀⣿⠀⣾⠏⠉⣿⡏⢹⠖⣶⣶⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⡯⢋⡏⣼⣿⣿⣀⣷⠀⢿⣾⡇⠘⡄⣿⣯⠙⣬⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣹⢻⡗⢸⠤⣿⣿⣟⠙⠻⣷⠞⠉⢡⠞⠀⣻⣿⠉⡞⢹⣿⣇⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠰⢌⠹⡇⡜⢲⣿⣿⣏⠓⠄⢉⠻⢾⣁⠀⢀⢼⣿⣍⢱⠀⢿⣿⣤⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠄⠄⢀⡓⢠⠋⣼⣿⡍⢳⣅⠀⠀⢢⡀⠚⠛⠷⡏⢻⣿⣈⡇⠘⢧⠙⠀⠀⢘⡿⣶⡤⣄
⠀⠀⠀⠀⡤⠰⡎⢦⠓⠀⠀⠈⢀⡒⠀⠐⢲⣿⡏⠀⢰⠉⠙⢦⣄⠀⠂⢌⠞⠉⣻⣿⣧⠼⠄⠈⢷⡄⠀⣀⡿⣿⠇⣽
⠀⠀⠀⠀⠘⡀⠘⣄⠳⡀⠀⣠⠎⠀⠴⢤⣿⣯⢀⠇⠀⣀⣤⢾⣿⣷⢦⣤⠲⡅⣽⢹⣿⡶⠚⡀⠀⠙⢦⣝⠀⣿⠀⢿
⠀⠀⠀⠀⠀⠐⢤⡈⠶⣉⡶⠃⠀⠘⢤⣾⡿⢹⣧⠶⡟⠏⣾⣿⡟⣿⢲⣫⠿⣦⡟⠀⢿⣿⡎⢡⠀⠀⠀⢣⣺⡏⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡘⠃⢀⠘⢠⣻⡿⠁⢸⡇⠑⠀⢘⠿⢻⡇⠽⢃⠀⠾⢹⡇⠀⠈⣿⣿⡁⣦⠀⠀⠀⢫⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠈⣰⣿⡿⠁⠀⢸⡆⠄⡰⠏⠄⠘⠃⠀⠻⢒⡀⣾⠃⠀⠀⠘⣿⣷⡄⢃⠀⠀⠈⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣼⣙⠏⠀⠀⠀⢸⡷⢎⠁⠰⢤⣤⣤⣤⢶⣟⣯⣿⠀⠀⠀⠀⠸⣿⣷⡈⣥
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣒⢾⣶⠎⠰⢆⣠⠛⢉⡶⠤⣉⡙⠚⠛⢒⠛⣻⣻⠦⠾⠎⣡⠂⠰⠒⠸⣿⣿⠤⠓⡀
⠀⠀⠀⠀⠀⠀⠠⠄⣸⣿⠿⠐⣆⢣⠬⣁⠞⢢⣅⣀⣠⠍⣻⠛⠛⣏⠛⠻⢤⡗⠮⣀⠛⢣⡔⢠⡟⣿⣍⣉⣹
⠀⠀⠀⠀⠀⠀⠀⠁⠾⣯⡆⠙⢻⠄⡶⢩⡔⠂⡬⠀⠀⣀⣿⠀⢠⡟⠢⢤⣰⠗⡴⢁⡙⢣⡄⣾⠁⠈⢋⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢁⣹⠀⡗⠃⡄⠋⣴⡋⠉⢠⡾⣄⠼⢦⣀⣀⣽⠛⡰⢮⣕⠃⠄⢱⠄⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣤⡏⣘⡐⠃⣤⠙⢈⡁⣀⣈⠰⢉⡖⢈⢄⣀⣯⠘⠑⠖⣀⡛⢣⣈⡦⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣁⣉⡁⢂⢀⣀⣀⣀⣀⣨⡄⠀⢀⣀⣀⢀⡀⢀⡈⠻⣄⣀⢀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣔⡉⠘⠃⣻⣟⢙⣿⡟⠉⣙⣿⡟⢋⣺⡏⢛⣿⠋⣻⣟⢛⡛⢻⡋⢛⣋⢙⠛⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠘⠃⣀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠶⠂⠏⡉⢁⠈⢉⠹⠐⠶⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣰⢿⣚⣉⡏⡞⠁⠈⢫⢫⣙⣒⡿⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⡿⢉⢄⡰⢏⢇⡀⢀⣼⡝⢆⡠⡉⢿⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢙⡿⠜⠓⠚⠓⠯⠭⠚⠓⠛⠣⢿⡋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠼⣥⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⣴⠧⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⢄⢤⣤⠈⡟⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⢻⢁⣤⡤⡤⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠁⡠⠀⠈⣿⠐⣉⣍⣍⣙⠁⠀⠀⠈⣋⣩⣩⣉⠒⣿⠥⡠⢄⠈⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠈⡷⠾⡟⢿⣻⣻⡇⠀⠀⢸⡟⣿⡻⢻⠷⢾⠁⣀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢇⠀⠙⠶⠾⠳⠃⠀⠀⠘⠞⠿⠶⠋⠀⡼⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠠⠾⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠄⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠚⣦⡀⠈⢴⠁⠀⠀⠈⡶⠁⢀⡴⠓⠀⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠁⣺⣤⢀⠀⠀⠀⠀⠀⣬⣕⠨⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡺⠴⣡⣉⡄⠀⠀⠀⠙⢌⡦⢗⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣉⡙⡄⠀⠀⠀⠀⠑⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣤⠀⠀⣠⣄
⠀⠀⠀⣀⠴⠶⠶⠛⠋⠉⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⠃⠈⠀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠀⠀⠀⠛⠀⠦⡄
⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⣄⠀⠀⢀⡆⢀⠀⣀
⠀⠀⠊⠉⠉⠉⠉⠀⢀⡈⠀⠈⠀⠒⣎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣿⠀⠀⢸⡇⢸⠈⠀⠂
⠀⠀⠀⠀⠀⢀⡤⣤⠴⠀⢰⠓⠉⠉⠁⠀⢰⡟⠂⠀⠀⠀⠀⠀⠀⠶⠱⠜⠃⢀⠙⠀⠀⠙⣠⣾⣄⠀⢀⢰
⠀⠀⠀⠀⡀⣿⠁⠻⠎⣰⠃⠀⠀⠀⠀⠀⡸⠮⣺⣿⢀⡆⠀⠀⠠⡐⠀⠀⠀⣀⣽⠂⠐⡊⠀⠈⠙⠻⣦⡀⢰⠦
⠀⠀⠠⠿⠰⣧⡛⠀⣽⡇⠀⢲⣤⣤⣤⣤⠁⠀⢸⡟⣧⡀⠀⠀⠉⣀⡀⣀⣀⣤⠤⠴⠤⠄⣠⣀⡀⣀⣹⡏⠉
⠀⠀⠀⠀⠈⢿⠇⢠⣿⣧⠀⣿⣶⣮⠙⣿⣆⠀⠸⣉⣁⡀⠀⠀⡀⠠⡤⠄⠀⠐⠒⠒⠒⠒⠂⠨⢿⣿⣿⡏
⠀⠀⠀⠑⠀⠀⣠⣥⠽⠿⢒⡉⣿⠏⢰⣿⠿⠏⢀⣿⠏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸⠿⠿⠿⠿⠧

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠉⠑⠀⠀⠑⠚⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⠀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠂⢲⠒⣷⠀⠀⠀⢀⣖⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⢂⡈⢸⣴⠾⢷⣾⠉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣃⠀⠀⠀⠈⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠘⢁⠋⣹⠃⠔⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡤⢦⠌⠶⠰⠾⣿⠀⠀⠀⡠⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠀⠀⠀⠀⢀⣠⣴⣦⡉⠴⠷⢀⠀⠀⠀⠀⠃⣿⢷⣄⠀⣀⠠⣞⠁⡰⣃⠐⢂⣼⡃⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⣀⠀⡀⠦⠀⢠⠈⢸⣷⠀⠀⠈⠀⢘⠢⠑⠢⠄⠼⡁⠸⡍⠗⣉⠁⠔⣾⢠⡟⠄⠀⠉⡗⢀⣼⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣍⠩⣧⣀⡁⠠⡄⣀⠄⠋⢀⡀⠀⠀⠩⡇⠀⠈⠖⠷⣬⣏⠀⠙⠁⠀⠀⣹⣿⢀⡀⡐⠀⢀⠞⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠇⠈⠀⡄⠀⠈⢀⣅⠠⡀⠫⠿⠂⡀⠀⣣⠊⠀⠠⠶⠁⠁⢂⠀⢀⠀⢀⠛⡟⠹⣷⠈⢢⣄⣒⠃⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⠁⠀⢰⡷⢼⠶⠋⠁⠀⠈⠢⠄⠊⣀⡴⠭⣐⣤⣇⠂⢀⠄⢱⠃⠃⢀⡞⡹⢧⠀⠉⡰⠋⠉⣷⣶⢤⠔
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣗⠀⠀⠘⠀⠀⢈⡦⡈⠓⠤⠤⣀⠀⠁⣠⡶⠛⠳⣮⣒⠶⣱⣾⠀⠀⠀⣽⠧⡇⠀⣠⠁⠀⢠⣑⣈⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⡓⠶⠂⣼⠌⠀⠈⠙⠒⠒⠒⠚⢦⠀⠀⢆⠀⠀⠘⠷⣷⠃⠀⠀⠲⠃⠀⠀⠜⡀⠀⡈⠔⠁⠫⢧⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠄⠀⢈⡟⡾⠀⠀⠀⠀⠀⠄⢰⠁⡗⠐⢋⠁⡠⠀⠀⡿⡀⢀⣾⠃⠄⣀⠎⠈⢉⠀⠐⠉⠀⠀⠐⢿⣦⣀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣄⠟⣾⣡⠏⠀⠀⠀⠀⣠⠞⠀⠁⠘⠟⠁⠀⣀⣺⣇⣽⠶⠥⣄⠀⠻⢀⢘⡿⠁⢤⣳⠀⢀⡀⠀⣌⣻⣿⠷⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡴⢡⠎⡤⠠⠐⠔⡋⠁⠀⠀⠀⠀⠀⡁⡀⣾⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣄⢩⣺⣾⡿⠉⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠷⠀⣁⡚⢆⡼⣁⠖⠖⠀⠠⢈⠽⢄⡟⠋⠀⠀⠀⠀⠀⠀⠀⠸⢤⢤⣤⣀⣀⣤⣵⣤⡘⢟⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⢀⠏⠀⠀⠉⠒⠒⠋⠢⠵⠞⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠑⠸⡦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠙⠀⠀⠀⠈⠘⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠉⠁⠀⠀⠄⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⢀⣄⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠿⠾⠀⢀⣴⣿⣿⡧⡀
⠀⠀⠀⠀⠀⣼⣿⣽⣿⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⠂⠀⠀⠀⠀⠀⠀⡆⣾⣿⡇⠀⣰⠀⠀⠀⢰⣆⢀⣁⣤⣻⣟⣡⣈⠀⣰⡆⠀⠀⠘⡆⠀⣾⡆⠀⡾
⠀⠀⠀⠰⣄⣨⣶⣶⣧⣀⡼⠀⠀⠀⠘⢧⣜⠛⠛⢣⣴⠗⠀⠀⠀⣀⣲⣿⣿⣷⡄⠘⡄⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⡟⣡⣤⠀⠀⠀⠙⣞⠻⣿⣾⡁
⠀⠀⠀⠀⠈⠙⣿⣿⢿⡇⠀⠀⠀⠀⢤⠞⠋⠀⠀⠈⠳⣦⠀⠀⠀⠙⠛⠟⠟⠛⠳⠦⠁⠀⠀⠘⠛⠛⢹⣿⣿⣿⣿⡟⠛⠛⠋⠀⠀⠀⡼⠁⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣹⣤⠀⠀⠀⠀⠀⠀⠀⡀⢠⣬⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⢀⡀⠸⠀⡤⢠⣶⡄⢠⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⡀⢀⠀⣹⣿⣤⡀⠀⠀⠀⠀⠀⠸⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⠀⠰⢿⡿⢄⣠⡤⠀⠀⠘⠋⠘⢦⣧⡼⣿⢧⣼⡴⠃⠀⠀⠀⠀⠀⠾⣿⠇
⠀⠀⠀⠉⠈⣻⠿⣿⣿⠀⠀⠀⠀⠀⠢⢀⣿⣿⣿⠿⣄⡄⠀⠀⠀⠀⠘⣳⣿⡤⠒⢿⡃⡀⠀⠀⠀⠀⠙⠛⣽⢃⣀⡸⣏⠛⠋⠀⠀⠀⠀⡸⠀⠀⠺⣄
⠀⠀⠀⠀⡼⠁⠀⠉⠈⠉⠀⠀⠀⠀⠀⠘⠏⠉⠉⠇⠀⠡⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠘⠁⠈⠉⠁⠈⠃⠀⠀⠀⠀⠚⠁⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠀⠘⠃⠀⠀⠀⠀⠀⠀⠐⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⢤⠆⢀⠘⠃⢐⣤⠀⠀⠀⠀⠠⢾⡇⢠⢄⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⢠⡆⠀⠀⣴⡀⠀⢹⡄⠀⠀⠀⣤⠂⠀⣦⣴⡄⠀⣠⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣶⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠻⣄⣸⣿⣧⣠⡾⠀⠀⠀⠈⠘⢧⣜⣛⣻⣛⣴⠇⠀⠀⠀⠀⠐⠶⢾⣿⡆⠀⠀⠀⠀⠀⠸⣤⣿⣽⣷⣤⢾⣧⡄⠀⠀⠀⠀⠀⣋⣘⡁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣾⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⢀⣉⡀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠜⠛⠋⠈⠙⠃⠀⠀⠀⠀⠀⠀⠛⠛⠁⠉⠛⠀⠀⠀⠀⠀⠀⠘⠛⠹⠇⠀⠀⠀⠈⠉⢠⣮⣷⣦⠈⠉⠉⠀⠀⠀⠀⠀⠿⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣟⠁⠀⠀⠀⠀⠀⢀⡔⢠⣤⢲⡄⠤⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠿⠀⠀⠀⠀⠀⠀⠛⠃⠸⠇⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⣠⠀⠀⠀⠀⢼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠁⢀⣴⡿⠃⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⣘⠿⣁⠀⣿⡿⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠉⠛⠛⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡿⠀⠀⠡⠄⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣿⣷⣦⡷⠷⣴⡄
⣀⠘⠃⠀⢀⡀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣼⠃⠀⠘⠋⠀⠰⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⡈⢷⣧
⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠃⠉⠛⣿⣿⣿⣷⣼⡏
⠀⠀⠀⠀⠐⢀⠀⠀⠀⢸⣿⣿⣿⡟⠹⠟⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠂⠐⣗⠀⠹⣿⣿⣿⡇⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⢿⣳⣠⠀⠀⠀⠠⡞⢃⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠾⢀⣤⣠⣴⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⠀⣄⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠹⣿⣿⣋⠀⠁⠀⠀⠀⠀⠀⠀⢄⣀⠸⡏⢻⡿⠃⠀⠀⠀⠀⢸⡛⠻⠟⠿⢿⡄
⠀⠀⠀⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⢹⡀⢈⡛⢮⠈⠃⠀⠀⠀⢀⡀⠀⢸⣿⣇⠀⢀⣤⣄⣀⢀⣠⠐⠋⠀⠀⠀⠀⡀⢹
⠀⠀⠀⢠⡞⠀⠹⠗⠄⠀⠀⠀⠀⠀⢸⠂⢃⣼⣷⡈⠙⠂⠀⠀⠀⡈⠁⢀⠘⠛⠃⢴⡟⢿⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡅⠙⠳⠆⠀⠀⢀⡘⠃⡤⠻⣄⠀⠀⠈⣄⠠⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠛⣳⠄⠀⠀⠀⣈⠣⠀⠙⠦⣿⣿⡇⠀⠹⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠛⣳⠆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠻⠁⠀⢻⠃⠀⢀⡈⠿⠀⠠⠀⣀⠀⠱⡦⠴⠐⠂
⠀⠀⠀⠀⢀⡜⠁⠉⠀⠀⠀⠀⠖⢠⡿⠃⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠸⡿⣦⠀⢀⠀⠉
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠃⠀⢠⠀⠀⠘⠒⠀⢀⡸⠋⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠀⠀⠀⠀⠀⢠⣤⣀⣀⠄⣠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠢⠷⢷⣾⣷⣼⣿⣿⡍⢣⡵⠦⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣄⠠⢼⡟⢻⡉⠉⠹⡛⠧⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣰⣾⣿⠿⣿⣿⣿⡉⢆⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⢀⡀⢠⠄⠔⠀⠀⠀⠸⠿⠿⠋⠅⢸⣆⣼⡿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠉⠁⠁⣀⠀⠄⠀⠀⠀⠀⠀⠀⢢⡀⠋⢁⠄⠀⠀⠙⡃⠀⠰⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠂⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠛⠀⠀⠀⠀⠀⠀⡄⣠⡁⣴⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠎⠙⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⡆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠛⠀⠲⠾⠇⠀⠀⠀⠐⣷
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣤⠀⠸⠁⠀⠀⠀⠀⠀⠀⢩⠆
⠀⠀⠀⠶⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠐⠂⠀⣤⡦⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⣠⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠈⠋⠑⠂⠀⠒⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⣴⠆⢠⣤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠊⠙⡿⢠⠀⠼⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡀⠁⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠠⠈⢁⠀⠻⠆⠀⣄⢀⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⢉⠠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠶⠇⠀⠀⡀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⠉⠠⣾⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣀⠀⠀⠀⠀⣡⠏⡈⠠⠜⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡈⠀⠀⠀⣤⡄⠀⠀⠶⠀⠀⠀⠸⠛⠀⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠂⠉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡄⠀⠀⠀⢦⡈⠀⠀⠀⠀⠀⠀⠁⠀⠖⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⢦⠀⠂⠉⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡤⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠃⡈⠙⢋⠀⡸⢉⡉⣯⠹⢈⣿⠟⡻⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣤⢤⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠨⠀⡀⠀⡗⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠒⠲⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢐⡂⣿⡇⠇⠀⠀⠀⠀⠀⠀⡀⢀⠠⡤⠦⣦⠀⠆⢀⠀⠀⠀⠾⠄⢀⣸⠀⢸⣀⠠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⠶⠀⣿⡇⠠⠤⠼⠆⠀⢀⠸⠦⠼⠃⠃⠀⠉⠻⠜⠿⢀⠀⠠⠾⡟⠉⠩⠉⠉⠉⠉⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠆⡺⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢚⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣗⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠂⡄⠀⠀⠀⠀⠀⠀⢀⢹⣿⣄⣡⣼⡖⢁⠀⠀⠀⠀⠀⣸⣿⣭⡏⣿⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⢐⠠⡀⢠⠐⠀⠀⠐⠀⠀⠀⠀⠸⠖⠀⠀⠒⡇⠸⠀⠀⠀⢀⣼⢷⡟⢶⠇⢷⠞⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠬⠉⠁⠉⠈⠥⠤⠀⠀⠀⠀⡅⠈⣷⣤⣤⣶⡇⢨⡀⠀⠀⣤⡟⣾⡛⡾⠀⢸⡗⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⡀⠀⠀⠀⠀⠀⠈⠁⠈⠉⢁⣀⣀⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠒⠿⠧⠀⠀⠀⠀⠀⠀⠀⡔⡩⠤⠬⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠠⠿⠿⠿⠿⠆⠀⣴⠀⠀⠀⠀⠀⠧⠤⠦⠥⠼⠀⠀⠀⠀⠀⠀⠀⣧⠁⠴⠆⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢶⢶⢶⡶⣶⡖⠀⣿⢠⠀⠀⠀⠀⠹⢻⠀⠳⠿⠀⠀⠀⠀⠀⠀⡀⠽⠀⠁⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⣴⣲⢆⢰⣶⣶⠂⢤⠨⠀⠀⠀⠚⣹⢿⠿⢿⣏⡛⠂⠀⠀⠀⢰⣦⠠⣴⠂⡤⠸⠇⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢘⡃⠀⡄⢠⣇⣸⡀⣸⠀⣿⢀⠀⠀⠀⠀⠈⣟⡀⣸⡁⠀⠀⠀⠀⢠⣿⣿⣠⣬⣤⣴⣦⣄⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠸⠸⠿⠿⠈⠀⠀⠀⠁⠁⠀⠴⠶⠾⠶⠿⠶⠿⠶⠦⠀⠀⠤⠤⠾⠿⠿⠿⠿⠿⠿⠧⠼⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⡂⠐⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠈⠑⢦⠀⠀⢩⠁⢀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢠⠞⡇⠠⠤⢄⣀⡤⢤⡀⠼⠁⠀⣂⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣄⠀⣠⣿⡀⢀⣟⡀⢀⣰⠿⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣯⠔⠋⠁⠀⠁⡘⠀⠈⢟⡉⠉⠓⠶⡄⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠄⠀⠈⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⣀⠄⡀⡀⠀⠀⢀⣾⠃⠢⡀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠤⠀⢄⣀⠀⠤⠤⠽⠀⠈⠯⠀⠀⠁⠲⣀⠀⣠⠞⠀⠀⢀⣠⠖⡒⢦⠀⠀⢀⠤⢄
⠀⠀⠀⢀⠀⠀⢀⠀⠈⠁⠒⠒⠒⠒⠒⠺⢶⡄⠄⢀⠤⠖⠚⠓⠀⠀⠀⠒⠓⠤⠀⠀⠈⡾⠓⠒⠒⠛⠉⠀⡀⠀⢸⡇⠀⡼⠒⢺
⢐⠀⠀⠀⠀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣆⠙⠀⠀⠄⠀⠒⠈⠁⠀⠀⠸⠀⢸⠁⠀⠈
⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⡼
⠀⠀⠀⠀⣃⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠳⠦⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⢸⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠃⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⢱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡎⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠝⡇
⠀⠀⠀⠠⠶⣌⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⡔⠋⠀⠀⠀⠂⠹⠀⠴⢶⡁
⠀⠀⠀⢀⠀⢸⠁⠀⠀⠀⠳⡄⠀⠀⠀⣠⠴⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⡲⢦⣄⡀⠀⠀⢨⡆⠀⠀⠀⠀⠀⡀⠘⠀⠀⣧
⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠘⣆⡀⠐⣰⠀⠀⠀⠀⠹⣆⠀⠀⠈⠢⠍⢿⡛⠛⠋⠀⠀⠀⠀⠀⠀⢙⠀⠐⠒⠃
⠘⣀⠀⠀⣀⠣⠄⠀⠀⠀⠀⠀⠈⢀⡠⢤⣄⠀⠀⠀⠉⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀
⠀⠉⠁⡈⣠⡤⠴⣀⠀⡀⠀⡠⠖⠉⠀⠀⢸⠂⣄⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⢀⣀⣀⡠⠚⠁⠀⠀⠑⠐⡄
⠀⠹⠀⠁⠀⠀⠀⠈⢛⠀⢸⠀⠀⠀⠀⠀⢸⡦⡀⠁⠐⠀⠀⠀⠈⠓⠶⠂⠤⣤⢴⣾⡋⠁⠀⠀⢹⠀⣈⣁⡀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠐⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡇⠀⠀⠀⠈⠞⠉⠙⠻⣄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠑⠠⠄⠤⡠⠄⠂⢀⠀⡇⠀⠀⠀⡀⠠⢀⠀⢠⠀⢀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⠇⠀⠈⢰⡇⠇⠸⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⠀⠐⢢⣤⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⢀⠏⠀⠀⠀⢘⣷⣜⣦⣧⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠄⢀⠀⠀⠀⠠⠀⠊⢀⡤⠊⠀⠀⠀⢀⣼⠟⠉⠉⠁⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠓⢦⡈⠐⠲⠲⠖⠒⠋⠁⠀⠀⠀⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡓⠢⢤⣀⣀⠀⡐⠂⠀⢉⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⡱⠀⠀⠀⠉⠙⠻⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⡀⠀⠔⣊⠔⠡⠞⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠉⠀⢀⣀⣀⡠⣤⠤⠤⠤⠴⠶⠴⠷⠤⠄⣀⠀⡀⠤⣤⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠊⠣⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢿⣿⠟⠀⢰⢂⠸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⢿⣏⠈⠀⠰⠀⠁⢈⣿⡿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⡿⠋⠀⠀⣀⠀⠀⠘⢿⣧⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠎⠓⠀⠀⠀⠐⠆⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣿⣿⣷⣿⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣆⡜⠻⣿⣿⣯⣿⣿⢻⣿⣿⣹⣿⣿⠏⢸⠏⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⢼⡀⠀⠜⠙⠿⣿⣿⣼⣿⣿⠟⠉⠑⢄⠈⡢⠈⣄⢺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⢀⠠⢢⠈⠙⠿⠋⠁⠀⡐⠢⡀⠁⠀⠄⠘⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠧⣄⡸⠀⠀⠀⠀⠀⠀⣇⠤⡤⠤⣀⠀⢠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠂⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠑⣎⠁⠂⡵⠋⠀⠀⠀⠀⠴⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣀⠉⠙⢉⣀⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠒⠒⠀⠘⠤⡴⠤⠎⠀⡠⠊⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠛⠀⠀⠀⠒⠒⠒⠉⠐⠳⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡾⢞⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣉⠀⠈⠃⢀⣿⡄⠹⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣾⣽⣟⠂⣰⢆⡟⠻⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢀⡄⠁⠉⠀⢠⠀⣉⣄⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⡾⢁⣆⡀⢰⣄⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⠁⠀⠉⠀⠈⠉⢹⣿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⢀⡠⣅⡠⢤⣤⠚⠀⣄⠿⠿⣷⠇⠀⠀⠤⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠈⠋⠉⠈⠀⢀⠀⠀⠈⠀⠀⠨⡟⠠⠿⢆⡀⠁⡰⢺⡿⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠒⠂⢺⠀⢀⣰⠀⠀⢠⡇⢐⠀⠀⠹⡟⢡⡿⠋⠑⠂⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⢷⡉⠉⢀⠀⠙⠅⣍⠀⠀⣸⠷⣍⠂⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠈⠈⠀⢀⠀⠀⠀⠚⠁⠀⠙⡄⠄⠂⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⡆⠁⠠⡀⠀⢠⠀⠀⢀⠀⣀⣠⠄⠁⠀⠀⠘⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠃⡀⠸⠀⡀⠀⢾⠀⠇⠀⢩⠴⡏⠀⠀⠀⢹⣾⠀⠐⣁⠀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠈⡋⠀⡇⠀⠀⠡⠀⢸⠀⣀⠠⣀⠀⠀⠀⠠⡀⠀⢻⠀⠀⢿⠀⠀⠀⠀⠀⢤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡇⠀⡆⠆⠀⠀⠀⣼⠂⣯⣉⣌⠀⣍⣀⡀⠑⠀⣅⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⢀⣟⠂⠀⠀⠈⠉⠸⠗⣟⣿⢸⡟⠠⠉⠉⠙⠷⠀⠃⠐
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡏⠸⠃⠀⠀⠃⠀⣸⠉⡀⠀⡄⠀⢀⠀⠸⠀⠀⠀⢈
⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⢵⠄⠀⠘⠐⠇⠀⡻⠀⠃⠀⡄⠂⢀⡘⢦⠂⠀⠁⠈
⠀⠀⠀⢻⠀⠀⠀⠸⠀⠀⠀⠀⠀⠞⠀⡎⠘⠸⡇⠀⣿⠀⡀⢠⡄⠀⠀⠙⣦
⠀⠀⠀⠈⡄⠀⠀⠀⢀⢠⡄⠀⠐⠃⠰⠁⡀⠂⢉⡀⢛⠐⢡⠋⠀⠁⣀⠐⡌⠀⠀⢀⠀⠀⣠
⠀⠀⠀⠀⢰⡀⠀⢀⣠⡼⠦⢀⡼⠂⢘⠛⠀⠀⠀⣽⠛⢻⠟⢿⡀⠀⠈⢦⠁⠈⠁⡄⠀⠾⠁⣰⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠈⠣⠀⠁⠀⠀⠉⠈⠉⠛⠙⠂⠀⠀⠀⠛⠡⣴⡿⠊⠁⢦⡀⠀⠀⠀⢈⡁⢸⡿⠂⠉⠈⠐⠐⣤⣠⡉⠌
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠓⠈⠀⠀⠠⠃⠉⠀⠀⠄⠀⠈⠈⠛⢿⣇
⠀⠀⠀⢤⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⢾⡟⢀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⡰⠊⢀⠀⠀⠀⠀⠀⠀⢀⠀⠛
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠈⢠⡆⠀⠀⠀⠀⠂⠒⠀⡀⠞⠃⠠⠀⠈⠀⠀⠀⠿⠋⠀⠈⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡘⠲⠇⠀⠄⠀⣿⡟⠀⠀⠀⠈⡄⠀⠶⠁⠀⡀⠻⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠁⠀⡀
⠀⠂⠀⠉⣀⣀⡄⠈⠛⠁⠀⠀⠀⠀⠀⢹⡤⠀⠄⠀⠀⠀⠀⡴⠂⢀⢀⠚⢩⣧⣰⣆⠀⠶⠀⠀⠀⠠⡌⠀⠂
⠀⠀⠀⠀⠿⣼⠽⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⠀⡄⠀⢠⢀⡁⠀⠀⠘⠁⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠐⠄⠘⣂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⣈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⠇⠀⠀⠀⠀⠀⠀⠿⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⡷⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀⠘⢶⣄⣀⡀⠉⣉⣁⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠛⠉⠙⢻⣿⡷⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⣿⣶⣶⣴⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡌⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠋⠉⠉⠉⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⣿⣿⣦⣀⣀⢀⣀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿⠟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢠⠀⢸⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣥⡿⣦⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢰⠃⣸⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡴⠖⠊⠿⣛⣛⣻⠗⠛⠲⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢸⣄⣹⣇⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠞⠉⠀⠀⠘⣿⣩⢨⣹⣟⠀⠀⠀⠙⢷⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠙⢹⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⠃⠀⠀⠀⠀⠸⣿⣜⠾⣻⠹⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣸⠃⠀⠀⠀⠀⠀⣾⡿⢣⣷⠺⣿⡆⠀⠀⠀⠀⠀⠸⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣤⡟⠀⠀⠀⠀⢰⠶⣩⣾⣇⠇⣸⣿⡡⢶⠀⠀⠀⠀⠀⡷⢀⣜⢫⣄⠀⠀⠀⠀⠀⠈⣿
⠀⢀⣿⣶⣄⠀⠀⠀⠀⠀⠶⣾⣯⣻⣿⣷⠆⠀⠀⠀⠀⢂⣳⣿⣽⣿⣽⣧⣇⢃⠀⠀⠀⠀⠀⠟⠇⣆⠖⡥⡟⠃⠀⠀⠀⠀⠸⣷⡄
⢠⣿⣿⠛⠀⠀⠀⠀⠀⡀⠀⢜⠛⣿⠋⢻⣠⠀⢸⠀⢸⢏⣿⣿⣿⢾⣿⣿⣏⢻⣀⣠⡤⠀⢠⡇⠈⢚⣉⡆⠀⠀⠀⠀⠀⠀⢸⢿⣿
⠙⣿⣿⠀⠀⠀⠀⠠⠤⠼⢿⣿⣤⠤⠤⠬⠽⣿⣿⡦⢾⣦⣶⣿⣿⣽⣿⣯⣢⣿⣿⣏⠁⢀⡟⠠⠁⠀⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣙⣻⡄⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⢀⠀⣿⣿⢻⣼⣹⣧⠾⣝⠻⣿⢛⣿⣳⣿⢿⣶⣯⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠈⢹⣶⣦⡀⠀⠀⠀⠘⢿⣏⢀⣤⡾⣿⣷⣿⡿⣠⢻⣿⣿⣷⣮⣤⣷⢿⣿⣿⣷⣾⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⡟⢿
⠀⠀⢸⢿⣿⣿⣦⡀⠀⢈⣻⣿⣾⢻⣿⣿⣿⣋⣙⣻⣿⣿⣿⣿⣳⠖⢣⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣴⣿⣿⡶⠀⢰
⠀⠀⢸⠀⢻⣿⣿⣷⢸⣮⢻⣿⣿⣿⣭⡻⣿⡿⣿⢻⣿⡻⣿⣿⣿⣷⣿⣿⣿⡌⣿⠿⠛⠿⣿⣿⣿⣿⡟⣰⣦⣰⣿⣿⣿⠟⠀⠀⠘
⠀⠀⢘⠀⠀⠹⣿⣿⣿⣿⠸⢿⣿⣿⣿⣿⠉⠀⣿⡀⠙⢿⣿⡿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠫⣾⣿⣿⣿⣿⣿⠋
⠀⠀⢸⠄⠀⠀⠈⠉⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⢻⣇⠀⠀⢩⡷⠘⣉⣸⣿⣁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠁
⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⢾⠏⣿⣿⣿⠻⢗⡄⢹⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢣⣶⣧⣝⣈⠽⣺⣥⣴⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⡿⢿⣾⣿⣾⣽⣺⣿⣿⣿⣿⣿⣿⡿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣭⣿⣿⣭⠝⢀⠾⣿⠟⣛⣿⣛⡳⣿⠉⠉⠉⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠋⠀⢀⣴⣿⣿⡾⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⡇⠀⠀⣀⡀⣶⣶⣿⣿⠟⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣝⣛⣻⣾⠏⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢘⣷⣶⣿⣿⣿⠿⠿⠿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡭⠛⠋⠁⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠿⠿⠿⠟⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⣴⣦⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢀⠀⠀⠈⢛⠃⠀⠔⣿⣿⡗⠄⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⡀
⠀⠀⠀⡀⠸⢿⠿⡿⠃⢀⠀⠀⠀⣠⠂⣸⣿⣇⠀⣀⠀⠀⠀⢘⣹⣿⣇⠀⢺⠀⠀⠀⠹⣦⣴⣶⣾⣿⣶⣦⣤⠾⠀⠀⠀⢻⣀⣿⣧⣠⠇
⠀⠀⠀⠙⠶⣿⣿⣿⡷⠋⠀⠀⠀⢈⣿⠂⠀⠰⣿⣁⠀⠀⠐⢦⣿⣿⣿⣇⣀⠇⠀⠀⢤⣤⡼⣿⣿⣿⣿⣿⣥⣿⠗⠀⠀⢀⡼⠈⢽⣿⠂
⠀⠀⠀⠀⠀⠈⠉⢉⡇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⡀⣶⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⣀⡀⡃⢰⠠⣾⡄⢠⠀⠀⠀⠀⠀⠀⢠⣶⠄
⠀⠀⠀⡄⣄⣨⣿⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠠⣄⣀⠻⠟⣢⡤⠖⠀⠀⠉⢁⣑⣾⡞⠿⢳⣾⣚⣁⠀⠀⠀⢀⡚⠿⢃
⠀⠀⠀⠀⡨⠛⠻⠿⣅⠄⠀⠀⠀⠃⣸⠿⣿⡝⠳⠆⠀⠀⠀⠀⣨⡿⠗⠉⠛⣥⡄⠀⠀⠀⠀⢀⡼⠣⣤⡜⢦⡀⠀⠀⠀⢀⡼⠁⠀⠙⢦
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⡄⠀⠀⡤⠀⠀⠀⠀⠀⠀⣤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄


⠀⠀⠀⠀⡴⠀⡀⠆⠀⣄⠀⠀⠀⠀⢰⣶⠀⣄⠠⣷⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢰⠀⠀⣰⡄⠀⢹⡄⠀⠀⢀⡔⠀⣴⣤⡆⠀⣤⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⢰⡆⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠈⠧⣤⣿⣿⡤⠞⠀⠀⠀⠀⠹⢤⣟⣛⣻⡴⠃⠀⠀⠀⠀⢲⢾⣿⡇⠀⠀⠀⠀⠀⢳⣾⣿⣷⣤⢾⣷⠀⠀⠀⠀⠀⣹⣼⣁
⠀⠀⠀⠀⠀⠸⣿⣿⢧⣄⡀⠀⠀⠀⠀⠀⢿⣿⡿⣤⣀⠀⠀⠀⠀⠾⢿⣿⣿⡇⠀⠀⠀⣀⡼⠿⣿⠿⢧⣠⣥⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢘⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙
⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⣿⠀⠀⠀⠀⠀⢠⣾⠀⣿⢸⡇⠊⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠍⠭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠠⠴⠡⠱⠤⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠅⠀⡚⢀⠘⡂⠂⠽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡤⠴⠤⣿⠄⢼⠧⠴⠬⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡴⠂⠒⠫⠦⠮⠓⠂⠲⣬⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⣉⣉⣻⣻⠃⠀⠀⢀⣰⣀⠀⠀⠀⢻⣻⣋⣉⣉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠚⠙⠀⣻⡧⢧⢈⣉⠓⠈⠉⠉⠐⢋⣉⢠⠧⣿⡇⠘⠙⠊⢣
⠀⠀⠀⠀⠀⠀⠠⢅⠀⠀⠀⠈⠛⢳⡇⠀⠈⠃⠀⠀⠀⠀⠋⠀⠀⣷⡛⠋⠀⠀⠀⢀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠉⣇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣦⣤⡀⠀⠒⠀⠀⢷⣤⡎⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⢀⢿⢳⠃⢀⡁⠀⢰⡤⢻⢇⠠⡀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣶⣓⡡⢺⡀⠀⡄⠀⡞⠙⠢⣑⣳⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣦⡀⠣⡀⠠⠄⠻⣄⣠⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢇⠈⠓⠻⠦⡘⠁⠈⠳⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠳⠤⣄⣀⣈⡷⡄⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⠶⢤⣤⡤⢤⡾⢠⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣀⢀⣠⣌⠉⠋⠒⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⣀⣻⠉⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠟⢋⡤⣭⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠈⠀⠀⠀⠀⣀⡉⠓⣺⣿⡿⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢦⠆⠀⠀⠈⠆⠑⠾⠏⠉⣀⣠⡤⠀⠀⠀⠀⣠⢤⠦⠐⢉⣡⣾⠿⠛⠶⣶⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⣄⡠⣻⠏⣠⡔⢙⣻⠁⠈⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠐⠂⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣦⣷⣾⣿⢾⣁⡠⠟⣲⣥⣾⡇⠀⠗⣿⣟⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⣶⡒⠆⠀⠀⠀⡀⠀⠀⢀⣠⣤⣤⣻⢿⣿⣿⣿⣦⣴⠴⠋⠉⣠⡿⠀⣤⡥⣿⣏⡈⠙⣦
⠀⠀⠈⠀⠀⢀⠀⠐⢲⠾⣿⡏⣿⣷⢾⡉⠨⣗⡟⡂⢀⢀⣀⡀⠸⡷⠚⠿⡟⢿⣿⣧⣶⡲⠿⠿⡓⢀⣿⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠐⠀⠉⠉⢛⡋⣀⣨⣟⠉⠈⠿⣊⢸⣿⠋⠉⠉⠉⠉⠡⣀⣀⠹⣾⣀⣀⢽⣿⣀⣤⣤⣤⣾⣷⠟⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⢠⣖⡉⠤⠿⠯⠿⢷⣶⣦⣬⣭⣤⣬⡶⠶⢶⡾⠷⣶⠿⠟⠋⠉⣀⣀⢀⣀⣀⣀⣴⣽⣏⢐⠀⠀⠀⠐⠿⠂
⠀⢐⠀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠯⠼⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⣼⢿⠟⠛⠛⠛⠛⠋⠁⢺⣄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢱⡐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣀⣄⣢⠅⠩⣔⣠⡀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢒⠖⠋⠍⢁⠀⠀⠀⠀⡀⢩⠙⠲⡒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⠧⠶⠚⠳⢡⠎⠁⠈⠱⡈⡞⠓⠶⠼⣶⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⠵⠚⡍⢉⣃⣻⠀⠀⠀⠀⣗⡙⡉⢙⠓⠯⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡈⢸⢀⡆⠱⣼⣘⣜⠳⢬⡥⢞⣱⣁⣧⠞⢰⣀⡧⢁⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⢀⡿⠗⢋⣉⣉⠈⠙⠒⠒⠋⢁⣉⣉⡙⠺⢿⡀⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠽⣤⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣥⡯⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⡠⢀⡀⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠁⢀⡀⢀⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠞⠁⠀⠒⠹⣦⢁⡤⠶⠾⠿⢷⡦⠀⠀⠀⠀⢴⠾⠿⠷⠶⢤⡈⣴⠇⠒⠂⠈⠳⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⠔⠁⠀⢁⣿⢩⣴⣶⣦⣷⣲⣤⠀⠀⠀⠀⡤⣐⣾⣴⣶⣦⡍⣿⡀⠀⠈⠢⡀⠀⠀⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣀⠄⢨⡟⠛⠛⠋⢿⣽⣝⢿⠀⠀⠀⢀⡿⢫⣿⡽⠋⡛⠟⢻⡅⠠⣀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢧⠀⠈⠳⠦⠾⢃⠞⠀⠀⠀⠀⠳⠸⠷⠴⠞⠁⠀⡼⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⡈⠁⠀⢰⣄⠀⠀⠠⡃⡠⠀⠀⠀⠀⢄⢐⠀⠀⠀⣠⡆⠀⠈⢀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⢨⠓⣀⠠⠘⡇⠀⠀⠀⠀⠘⠣⢄⡠⠞⡅⠉⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣈⡠⢐⡶⣦⢀⡆⠀⠀⠀⠀⠀⠀⣾⢵⡂⢌⣁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠑⠮⣴⢃⡏⣡⠀⠀⠀⠀⠈⠻⡘⣦⠵⠊⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡉⠓⠛⢆⠀⠀⠀⠀⠀⠈⠃⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠺⠣⡀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠐⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⢟⡿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣼⣯⣾⣶⣹⣿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠾⠃⠘⠛⠋⠉⢳⡦⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒⣉⣱⡆⠀⠀⠀⠀⠀⠇⣈⣉⡀⠀⢰⡶⠄⠀⠀⠶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠐⠂⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⢰⡆⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣖⠀⠠⠂⠀⠀⡺⠀⠀⠀⠀⠀⠀⡈⠃⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠢⢄⠀⠄⢠⣇⡀⠀⢀⡤
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⣿⠇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢿⣍⣛⢛⣛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣤⠖⠊⠀⠀⠀⠀⠐⠁⠀⠘⢆⡀⠀⠀⠀⣀⠴⣮⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣣⣈⣁⣨⣥⡴⠟⠛⠀⠀⠀⠐⠁⠀⠀⣰⢦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣦⠀⠀⠀⠆⠀⠀⠀⠀⠘⡟⠿⠼⠟⣧⡇⠀⠀⠀⣠⠆⠀⠀⢀⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠣⣜⠹⣆⡀⢀⡀⠀⠀⢀⣤⣦⡤⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠆⠈⢢⠌⠙⠋⠁⠀⠀⣿⡟⠁⢀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣶⡄⠠⣤⣿⠟⠉⠉⠤⠀⠀⠀⢀⣴⢆⡀⠀⣾⡄⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠋⠀⠀⣟⣻⠄⠀⠀⠀⢀⢶⣶⡫⠞⠁⠁⣾⡿⣲⠄⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠂⣀⠁⠀⡘⠶⠏⠀⠀⠳⠶⣷⠃⠈⠀⠀⠀⠀⠐⠻⣏⣻⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠁⠀⠀⠁⣤⠈⠀⠀⡄⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠎⠁⠀⠠⠇⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠁⠀⢀⢠⠀⠄⠀⠂⠀⠐⠀⠀⠀⠧⠀⠃⠀⠀⠀⠀⢠⣤⣄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡤⠤⠴⠶⠖⠒⠶⠲⢤⠀⠀⠀⠀⠀⠀⠠⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⡀⠀⣆⢀⠘⠀⠘⠃⠀⠣⠄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠁⣀⠀⠀⢠⠘⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⡄⠀⢈⣀⠀⢂⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣮⠖⠐⠛⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠷⣾⡷⠆⠈
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⣠⣴⣟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠛⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⢠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣧⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣼⣿⣿⣿⣧⡄
⠀⠀⠀⠀⢹⣹⠿⡏⡏⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⢹⣿⡿⣯⣿
⠀⠀⠀⢀⣿⣿⣤⣿⣷⡀⢸⣿⣿⣷⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣇⢀⣾⣿⣇⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⡿⠀⣿⣿⣿⣿⣿⡅
⠀⠀⢴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣤⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠈⠠⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⣨⣿⡯⠙⣛⣛⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⡿⠋⡴⠋⠉⣹⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠓⣦⠀⠼⠜⠟⢻⣿⡾⢷⣄⢀⣦⠀⠀⠀⠀⠀⠀⢠⡟⣣
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣤⡤⠆⠘⣧⣀⡄⠻⣿⣧⠲⣺⣇⣸⣟⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⡁⠀⠀⠀⠀⠈⣀⡤⢄⣽⢟⡑⢊⣩⣿⠇⣯⡍⠙⠻⠿⠆⡀⠀⠀⠀⠀⡀⡏
⠀⠀⠀⠀⠀⠀⣸⣿⠁⠌⠙⣷⣦⡄⠀⠚⡅⢀⣿⢻⡄⣟⣻⣿⣵⢱⢿⣿⣶⣧⡌⢶⡅⠀⠀⠀⢸⡇⢠
⠀⠀⠀⠀⠀⢰⣿⠇⠀⠘⢟⡁⢸⡟⣶⣶⣾⠿⢻⡟⢣⢸⠇⠙⡇⣼⡋⣿⡿⣿⣄⣠⠿⠇⠀⣠⡿⠀⠈⣆
⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢸⣶⣼⡿⣿⣿⣄⠀⢈⡷⠀⠊⠃⠐⠃⣿⣿⡿⠁⠈⠡⠋⣴⣄⣴⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠃⢻⣿⣿⣷⣼⣷⣴⢂⣇⢀⡀⣿⡿⠃⣀⠀⠁⠀⠛⣿⡿⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⣾⣿⠃⠀⠸⠟⠋⠁⠹⣿⡯⡘⣟⠉⢇⣿⡇⣴⣿⣦⡀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠘⣿⡅⠐⣨⠟⠁⠀⠁⠀⠀⠄⠀⠀⢈⠻⢶⣦⣵⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢢⠀⣿⣶⣦⡄
⠀⠀⠀⠀⠐⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣗⠀⢉⣽⣟⠛⠛⠛⠻⣿⡇⠀⠀⠀⠀⠀⣹⣿⣿⢧
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡀⠀⢈⠀⠀⠀⠀⣨⣿⣿⣿⢶⣶⣿⣟⠿⠛⠂⠀⠀⠻⢆⠀⠀⠀⠀⠀⠻⣿⠾
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⣤⣀⠈⠉⠁⠠⠿⢿⣿⠘⠂⠈⣿⣝⠃⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠈⠣⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⢿⡇⠀⠀⢠⠳⢉⣄⣀⠀⣠⠝⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢸⣿⠀⣿⣿⣄⣄⣀⣀⣤⣤⣦⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠨⠀⠰⢀⡏⢹⡿⣋⣉⠭⠝⡉⠍⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢿⣽⣇⣠⣤⣔⣈
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⢀⣴⠾⠟⠀⢀⣈⣙⡿⣍⠉⠩⢙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢼⣴⡟⠁⠀⠀⠀⠈⠙⠋⠀⠉⠁⣋⣉⣀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠄⠀⠉⣀⣤⣴⣾⡿⠟⠋⠉⠁⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠶⠶⠚⠛⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠏⠀⣘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠙⠡⠿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⣀⣞⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣽⡁
⠀⠀⠀⠀⣀⠀⢧⠀⣤⠀⠀⠀⢰⣽⣆⣼⠀⠴⠀⠀⠀⠀⠀⠃⠀⠀⠉⠈⠀⣻⣛⡄⡌⠀⠀⠀⠀⠀⠈⢷⡀⢀⠈⠉⠁⢹⡙⡄⢀⡔
⠀⠀⠀⠀⣋⣀⠏⢼⣫⠀⡠⠁⣘⣫⣿⣏⢀⡄⠂⠀⠀⡀⣀⣠⣠⠟⠐⠛⠀⣿⠫⢿⠃⣰⡆⢀⡀⣀⡀⠘⢇⣾⠁⡿⠁⣿⢏⣷⠟
⠀⠀⠀⣾⣿⣿⣷⣶⣻⣄⣁⣤⣿⣇⠸⣿⣿⣿⣶⠀⠀⠤⣭⣬⣯⡌⢈⢈⢹⣇⢀⢘⣃⣙⣨⣿⣶⣮⣿⣐⣺⣃⠂⡃⠶⣿⠀⠘
⠀⠀⢠⣿⣿⠿⠛⢉⣺⣏⠉⣽⣿⠻⢧⣻⣿⣿⣿⣦⣄⣀⠀⠒⠄⠁⣽⠉⣿⡻⢿⣷⣳⣶⡞⠓⠒⠀⣥⢸⣿⠟⢒⠀⢼⡿⢦⣄⣥⣄⣀⣄⡀
⠀⠀⣺⠟⢁⣀⣀⣠⣩⣥⣶⣿⣿⣿⡦⣼⣯⣽⣯⣽⣿⠟⠋⠀⠀⣚⣋⣠⣤⣿⣦⣼⢿⣽⣷⣾⣿⣿⠿⠛⠀⠠⢟⣀⣼⣷⣤⡍⢷⣍⠛⠋⠁
⠀⠀⠈⢀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⣿⣿⣿⡏⠀⠐⠚⠿⠟⠛⠛⠛⠛⠺⠿⠾⢿⣿⣿⣿⠇⠀⠴⠶⠾⠟⠛⠛⠛⠷⠶⠶⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠰⠢⠠⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠀⠀⠀⠠⠀⠐⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⢀⣄⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠿⠾⠀⢀⣰⣿⣿⡧⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⠂⠀⠀⠀⠀⠀⠀⡆⣾⣿⡆⠀⣰⠀⠀⠀⢰⣆⢀⣁⣄⣻⣟⣁⣈⠀⣰⡆⠀⠀⠘⡆⠀⣾⡆⠀⡖
⠀⠀⠀⠰⣄⣨⣶⣴⣧⣀⡾⠀⠀⠀⠘⢧⣜⠛⠛⢣⣴⠖⠀⠀⠀⣀⣰⣿⣿⣷⡄⠘⡀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⡛⣡⣤⠀⠀⠀⠙⣞⠻⣿⣾⡁
⠀⠀⠀⠀⠈⠙⣿⣿⢿⡏⠀⠀⠀⠀⢤⠞⠋⠀⠀⠈⠳⣦⠀⠀⠀⠙⠋⠛⠟⠛⠳⠶⠁⠀⠀⠘⠛⠛⢹⣿⣿⣿⣿⡟⠛⠛⠋⠀⠀⠀⡼⠁⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⣰⣤⠀⠀⠀⠀⠀⠀⠀⡀⢠⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⢀⡀⠘⠀⡤⢠⣶⡄⢠⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⡀⢀⠀⣹⣿⣄⡀⠀⠀⠀⠀⠀⠸⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⠰⢿⡿⢄⣀⡤⠀⠀⠘⠋⠘⠦⣷⡼⣿⢧⣼⡴⠃⠀⠀⠀⠀⠀⠾⣿⠆
⠀⠀⠀⠈⠈⣻⠿⣿⣿⠀⠀⠀⠀⠀⠢⢀⣿⣿⣿⠿⣄⡄⠀⠀⠀⠀⠘⣳⣷⡤⠒⢿⣃⡀⠀⠀⠀⠀⠙⠛⣽⢃⣀⡸⣏⠛⠋⠀⠀⠀⠀⡸⠀⠀⠺⡀
⠀⠀⠀⠀⡼⠁⠀⠁⠈⠉⠀⠀⠀⠀⠀⠘⠇⠉⠉⠇⠀⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠘⠁⠈⠉⠁⠈⠃⠀⠀⠀⠀⠚⠁⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠐⠂⠀⠘⠃⠀⠀⠀⠀⠀⠀⠐⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⢴⠆⠀⠘⠃⢐⣤⠀⠀⠀⠀⠀⢾⡇⢠⢄⠠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡆⠀⠀⣶⡀⠀⢹⡄⠀⠀⠀⣤⠀⠀⣦⣴⡄⠀⣤⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣶⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠻⣄⣸⣿⣧⣠⡾⠀⠀⠀⠀⠘⢧⣜⣛⣛⣛⣴⠇⠀⠀⠀⠀⠐⠶⢾⣿⡆⠀⠀⠀⠀⠀⠸⣤⣿⣽⣷⣠⢾⣧⡄⠀⠀⠀⠀⠀⣃⣘⡁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣺⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⢀⣉⡀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠜⠛⠋⠈⠙⠃⠀⠀⠀⠀⠀⠀⠛⠙⠁⠉⠙⠀⠀⠀⠀⠀⠀⠈⠛⠹⠇⠀⠀⠀⠈⠉⢠⣮⣽⣦⠈⠉⠉⠀⠀⠀⠀⠀⡿⠛⠛⠿
⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣟⠁⠀⠀⠀⠀⠀⢀⡔⢠⣤⢰⡄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠿⠀⠀⠀⠀⠀⠀⠛⠃⠸⠇⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠉⠭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠠⠴⠡⠱⠤⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠅⠀⡚⢀⠘⡂⠀⠽⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡄⠴⠤⢿⠄⢼⠧⠴⠄⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣬⡴⠂⠒⠋⠦⠮⠓⠂⠲⣼⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣊⣉⣉⣻⣻⠃⠀⠀⢀⣰⣀⠀⠀⠀⢻⣻⣋⣉⣉⡦⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠊⠉⠀⣿⡧⢧⢈⣉⠓⠈⠉⠉⠐⢋⣉⢠⠇⣿⡃⠈⠉⠊⢣
⠀⠀⠀⠀⠀⠀⠠⢅⠀⠀⠀⠈⠛⢳⡆⠀⠈⠃⠀⠀⠀⠀⠋⠀⠀⣶⡛⠋⠀⠀⠀⢀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠉⣇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣦⣤⡀⠀⠒⠀⠀⢷⣤⡎⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⢀⢿⢳⠃⢀⡁⠀⢰⡤⢻⢇⠠⡀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣶⣓⠡⢾⡀⠀⡀⠀⡞⠙⠦⢑⣳⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣦⡀⠳⡀⠠⠄⠻⣄⣠⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢇⠈⠓⠻⢦⡐⠁⠈⠳⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠓⠤⣀⣀⣈⡳⣄⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⠶⢤⣤⡤⢴⡾⢠⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣀⢀⡠⣌⠉⠋⠒⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⡘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣁⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠈⠑⠛⠛⢻⣄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⢤⣿⣅⣀⡀⠀⢰⠆⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣤⣴⣧⣀⡀
⠀⠀⠀⠀⣠⡄⠀⣧⠀⣴⠀⡀⢀⠀⣿⣼⣀⣾⡀⠶⠀⠀⠀⠀⠀⠀⠁⠀⢠⠘⣀⠀⢸⣯⣹⡄⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀⢀⡀⠄⠀⢠⣯⢹⡀⢠⡞
⠀⠀⠀⠁⢘⣍⣸⠃⢾⣭⠀⣀⠀⢀⣛⣩⣿⣋⢀⣄⠛⠀⠀⣀⢀⣀⣤⣄⠙⠀⠈⠀⢸⡟⠽⣿⠃⣰⡆⠀⣠⢀⣄⠀⠸⢇⣾⠉⡿⢋⢼⡿⡏⣷⠟
⠀⠀⠀⢸⣿⣿⣿⣷⣦⣻⣆⣁⣀⣼⣿⣄⢹⣿⣿⣿⣶⡄⠀⢠⣬⣭⣬⣛⣤⠂⠁⠁⣾⡁⠀⢸⡀⣙⣋⣻⣷⣶⣽⣇⡆⣾⡃⠐⡞⠰⣿⡇⠀⠸
⠀⠀⢠⣿⣿⣿⡿⠛⠋⢽⣯⠙⢉⣿⡿⢿⣎⢿⣿⣿⣿⣧⣄⡀⠀⠠⠤⠝⠉⣸⡟⢻⡟⢿⣿⣾⣷⣶⡞⠿⠭⠭⣉⡍⢿⣿⠟⠲⠣⢠⣾⣧⣤⠘⣄⣀⣀⣀
⠀⠀⢼⣿⠟⠃⠀⠀⢈⢛⣋⣠⣼⣿⣿⣦⢌⣿⣝⣻⣿⣛⣿⣿⡿⠖⠀⠀⠴⠿⠃⣈⣹⣦⣍⣻⣏⣻⣿⣤⣶⣶⣾⣿⠞⠉⢀⡾⠁⢈⣣⣤⣉⡛⣯⡺⠿⠿⠛
⠀⠀⠚⠃⠀⠒⠿⠿⠿⠛⠛⠛⠛⠻⠿⠿⠾⠿⢿⣿⣿⣿⣿⠋⠀⠤⣤⣶⣾⣿⠿⠿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠋⢀⣀⣀⣤⣴⡾⢿⣿⣯⣭⣁⣉⣿⣶⣦⣄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠿⠛⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⢉⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠀⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠃⠀⠀⠀⠉⠉⠁


⣶⣶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿