Country music Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄⠀⠀⠀⠀⠀⠀⠠⡤⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⠟⠀⠀⣿⢦⠀⠐⠓⠾⠁⠀⠀⣀⣤⠴⠖⠛⠉⠉⠁⠀⠀⠀⡀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⣀⠀⠀⠀⠀⠙⠁⠀⠀⢠⡿⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⡀⣤⢦⠺⢥⡘⡌⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⡸⠳⡴⠀⠀⠀⠈⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣀⣤⠀⢳⡿⡘⢮⠆⠒⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠹⠖⠛⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⢀⣠⠄⢾⣧⠘⢺⡀⠈⠃⠁⢀⣠⠴⠚⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⢀⢠⠐⣾⣆⠈⣆⠈⠧⠃⠀⠁⠀⣴⠞⠉⠐⠀⠁⠀⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢠⠤⠰⡻⡌⢧⣣⠸⠜⠂⠈⠀⠀⢀⣀⣤⣾⠁⠀⠀⡀⢀⣀⣥⠶⠟
⠀⠀⠀⠀⠀⠢⣄⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠈⢧⣠⠱⠟⠈⠁⠀⠀⣀⣤⡴⠞⠋⠁⣀⣿⣦⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠓⢦⣄⠀⠀⢀⣠⣴⠶⠛⠉⢀⣠⣤⠶⠛⠋⠁
⠀⠀⠀⠀⣀⣤⠴⠶⠲⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⢹⡶⠞⠋⣁⣤⣤⠴⢾⣿⣍⡀⠀⠀⠀⠀⠺⣯⡀
⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣲⣦⣔⣊⠿⣧⡴⠛⠉⠀⠀⠀⠀⣀⣤⣭⣷⣄⠀⠀⠀⠀⠉⡶⡄
⠀⠀⡟⠀⢀⣠⣤⠀⠀⠀⣀⣠⠴⣟⣩⠵⣚⣿⠶⠚⡿⠁⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠛⠁⠀⡀
⠀⠀⣇⠀⠸⣇⢹⣦⠖⣛⡭⢶⣻⡽⠷⠿⠟⠃⠀⠀⢀⣦⢀⡞⠁⠀⠀⠶⠒⠦⣤⣀⠀⠀⢈⣇⠀⠀⠀⣀⣰⠃
⠀⠀⢹⡄⠀⢹⣞⣿⣿⡷⠞⠋⠁⠀⠀⣀⣤⡤⠤⠶⣿⠞⠈⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡟⠙⣧⠀⠀⠙⠋
⠀⠀⠀⢳⡀⠀⠻⣏⡽⠃⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢹⣄⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⢀⡾⠁⠀⠘⣇
⠀⠀⠀⠈⢷⣄⠀⠁⠀⠀⠀⠀⣠⡾⠁⠀⠀⡴⢦⡄⠀⠙⢷⣄⣀⠀⠉⠉⣓⣲⣶⡾⠿⠒⠓⠲⢦⣿
⠀⠀⠀⠀⠀⠉⠻⠶⣤⡴⠶⠛⠉⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠙⠛⠒⠾⠭⠤⠤⠤⠤⠤⠤⠴⠖⠋

⠀⠀⠀⠀⠀⡀⣀⡀⣤⡀⢠⣀⣀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠉⠉⠉
⠀⣰⠆⠘⢾⠇⠋⠓⠛⠁⠘⠛⠘⠃⠟⢸⠁⠐⣦⠀⠀⠀⠀⠀⠀⢱⠶⠶⠶⠶⡊⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠛⠁⠀⠀⠁⠀⠀⠸⣄
⠀⠙⡶⠶⠶⣶⡶⠾⣟⠀⠀⢘⠿⠷⣶⠶⠶⠾⡟⠀⠀⠀⠀⠀⠀⠘⠃⠂⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠢⢤⠤⠒⠒⠀⠘⠚⢷⡄
⠀⠘⣄⠀⠀⠀⡇⠀⢷⡅⠈⡴⠁⠀⡇⠀⠀⣀⠕⠀⠀⠀⠀⠀⢀⣀⠀⣐⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣐⣁⠀⠤⠤⠶⠶⠤⠄⠹
⠀⠀⠀⠀⠀⠀⠙⠦⣀⣠⣦⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠦⢄⣀⠙⢋⣀⠤⠶⠖⢲⠄⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣄⡀
⠀⠀⠀⠁⢒⢠⣠⣤⢠⠈⡉⢠⡀⡄⢰⠐⡞⡆⠀⠀⠀⠀⡞⢢⣦⢠⣀⣁⢠⣤⣠⣦⢲⡏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⣿⣭⣭⣸⡞
⠀⠀⠀⠃⠋⠈⠃⠙⠘⠈⠀⠈⠀⠁⠈⠀⠁⠁⠀⠀⠀⠀⠳⠘⠞⠀⠟⢛⠘⢟⠛⠊⠘⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠐⠦⢼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⡄⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠸⠈⣊⡁⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠄⠖⠈⠉⠐⠒⠄⠀⠀⠀⠀⠀⢽⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠐⡳⠀⠀⠀⠀⠀⠀⠁⢣⣤⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⣀⠠⣬⣀⡀⠚⠁⠀⠀⢠⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠶⢲⣰⡲⠆⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢠⠀⣄⠀⢀⡄⢠
⠀⠊⠀⠀⠀⣤⣤⣁⣶⡒⠚⠛⠒⠂⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⡆⢤⠄⠄⡀⠀⠀⠀⢸⢸⠀⠀⠀⢈⢠⠃⠀⠀⢧⢹
⠀⠀⡀⢀⣾⣟⣫⣭⣭⣝⣳⣦⡄⠒⠁⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠉⠈⠀⠀⠀⠀⢸⢸⠀⠀⠀⢸⠜⢄⣀⣀⠴⢼
⠀⢀⢦⢸⣿⣿⣤⣤⣧⣤⣿⣿⡇⠀⠀⠀⣠⣴⡇⢸⣦⣄⡀⠀⠀⠀⠘⠘⠙⠡⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠞
⠀⠐⣎⡙⠻⢧⣦⣅⣴⣾⣼⡿⠓⠀⢀⣾⣿⣿⣇⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠾⠿⠖⣤⡀⠀⠈⠐⠀⠐⠉
⠀⢈⡘⠀⠐⡀⠈⠛⠿⠟⠋⠀⠚⠀⠈⣿⣿⡏⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⣎⠫⠴⠒⠒⠲⠨⢋⣆
⠀⠀⠀⠀⠀⠑⢄⠀⠂⠀⠀⠀⡎⠀⠀⡸⠛⠁⠀⠀⠈⠛⢧⠀⠀⠀⠀⢀⣴⠶⠛⡉⠛⢶⣄⠀⢸⡃⠄⠿⠿⠽⡿⠀⠤⢙⠀⠙⠄⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢠⠊⠀⢀⡄⠶⠛⣋⣉⡉⣉⠃⠆⢢⡀⠀⠀⠘⠡⠖⢒⠓⠒⠦⠋⠀⠸⡧⢰⢶⣦⡖⠖⡖⠀⡿⠀⠈⢣⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣼⡁⢸⢿⡿⡷⠹⣽⢏⠀⠈⣧⠀⠀⡅⠸⠿⠼⠽⠷⠇⠀⠸⠀⠙⠿⣆⣨⣥⣀⡴⠟⠁⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢰⢶⣦⣶⡖⡶⢲⠂⣸⡏⠀⠀⢠⡼⢲⣶⡖⠚⢳⣠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠨⡅
⠀⠀⠀⠀⠥⠤⠵⣄⠀⠀⠀⠀⠀⠀⠙⠿⣄⡙⠛⠃⢁⣨⠾⠋⠀⠀⠀⠈⠛⠶⠄⠀⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡂
⠀⠀⠀⠸⡦⢡⡉⠍⠉⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⡀⢸⠃⢀⡇⣀⠃⠀⠀⠀⠀⠀⢠⡀⣖⣶⢸⣦⡗⢲⡶⢤⢄⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠀⠉⠓⠦⡀⠀⠀⠀⠀⣄⣊⣰⣠⡀
⠀⠀⠀⠀⠳⣼⠄⣼⢱⢻⡀⠀⠀⠀⡔⢺⢾⡇⡯⠟⠸⠘⠇⠸⠇⣸⢺⡏⣦⡄⠀⡞⠁⠀⠂⠰⠊⢀⡠⠴⠒⢒⡀⠀⢀⡈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡖⣼⢙⣱⠚⢘⣋⣤⠀⠀⡇⠚⠋⠁⠀⣤⣤⣤⣤⡤⠀⠈⠈⠃⠿⠀⠀⠣⣀⣀⣤⣤⡶⢳⣀⣀⠁⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠈
⡠⢀⠀⠢⠜⠃⠰⠧⡏⣀⡏⠁⠀⠀⠀⣶⢠⡶⢰⡆⢰⡆⡆⢦⡄⣰⡄⡆⠀⠀⠀⠒⠀⠀⢈⣁⣲⡍⡿⠁⠀⠀⠀⠀⠠⠆⠀⠀⢬⠄⠀⠀⢠
⠑⠦⣄⣀⣀⣀⠴⠴⠃⠝⠀⠀⠀⠀⠀⠉⠈⠉⠈⠁⠈⠀⠁⠈⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡄⠤⢀⠤⠄
⣶⣶⡶⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠔⠂⠙⠆⠀⠀⠀⠀⠀⠀⢠⠒⢒⣢⡀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠾⠑⠀⠀⠶⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠦⠻⡄⣿⣇⠀⠀⠀⠀⡌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡌⠀⠀⢀⣀⡀⠋⣀⡀
⠀⠀⠀⠀⡠⠗⠒⠉⠉⠉⠒⠒⠤⡔⠂⠀⠈⡆⠀⠀⠰⠔⣷⢸⣿⡄⠀⠀⠀⢻⠈⣳⡤⠀⣀⡴⠞⠛⠓⢦⡀⠀⢴⡳⣤⠃⠀⠀⠁⠀⣁⡈
⠀⠀⢀⡎⠀⠀⣀⡤⠴⢒⡲⣖⢒⡒⢺⠋⠉⠀⠀⠀⠀⠃⢙⣀⣧⠀⠀⠀⠀⠀⠳⢿⡀⢀⠏⠀⠀⠀⠀⠀⢿⡈⠤⠗⠁⠀⠀⠀⠘⠀⠀⠘
⠀⠀⠘⠦⠐⡟⠁⠀⠀⠠⠤⠌⡄⠸⠀⠀⠀⠀⢰⡆⠀⠀⠘⣧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⡶⢄⡀⠳⢄⡀⣬⠀⠀⠀⠀⠀⢠⢠⣀⢀⡀
⠀⠀⠀⠀⠀⠘⠀⠀⢴⡂⠀⠀⠀⠀⠀⠀⠀⡶⡆⠉⠀⠀⠀⢷⠴⢷⠀⠀⠀⠠⠰⡀⠀⠀⠇⡘⡇⠀⠘⠀⡟⠀⠀⢀⣤⠖⠋⠉⠉⠉⠓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠂⣞⠈⠓⠓⠛⠺⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣟⣹⡇⠀⠀⠢⠀⠈⠀⠀⠐⠀⣄⢠⠌⡜⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠼⠀⠀⠀⠀⠀⠐⢀⣄⠀⠀⢿⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⣟⠂
⠀⠀⠀⠀⠀⡞⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠙⠈⠀⠀⠸⣅⢻⣧⠤⠤⠤⣀⠀⠀⠀⢠⢀⠀⡀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣀⡰⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠒⠛⠛⠈⠒⠀⠀⠀⠀⠀⠀⣠⠒⠉⢳⠎⣿⡀⢀⣤⡀⠑⡄⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠋
⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⡰⠴⠀⢀⠀⠀⠀⣼⠁⠀⠀⢸⡎⢽⡇⠀⠀⠹⡀⢰⠀⠀⠀⠀⢀⣀⡀⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠉⠉⠉⠒⠒⠋⠁⠀⠀⠀⢀⣀⠀⠜⠛⠃⠀⠀⡇⠀⠀⠀⢀⡿⠛⠛⠏⠀⠀⡇⠸⠀⠀⠀⠀⠙⠉⢀⣤⡔⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢤⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⠘⠀⠠⢁⠀⠀⠁⠀⠂⠀⠀⠰⠄⠀⠀⠀⠀⠀⡀⠄⢾⣿⣿⠆⢀⠤⣀⠃
⠀⠀⠀⠀⣢⢴⣄⠀⠀⠙⠲⠬⣑⠢⠤⣤⣀⡀⠀⠀⠀⠀⠳⠀⠀⠀⠀⢧⢦⠗⠉⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢠⢂⡡⠄⠀⠘⠛⠋⠀⠈⠀⡉
⠀⠀⠀⠂⣷⡀⡟⠈⠀⠀⠀⠀⠀⢈⣌⡐⠈⡼⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠇⠀⢀⠤⠀⠀⠀⡴⡄⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢽⡐⢚⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⢅⠀⠀⠀⠈⠋⠁⢀⡀
⠀⠀⠀⠀⣀⠀⠊⢹⠒⠶⣄⠀⠀⠀⠘⠮⠓⢪⠀⠹⡆⠀⢠⡀⠀⠀⠀⠠⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠤
⠀⠀⠀⣸⣁⠀⢀⡸⠀⠀⠈⢀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⡀⠀⢠⡦⠀⢀⠊⠀⢳⡄
⠀⠀⠀⢹⠸⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠈⠑⠀⠞⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⡴⣤⠘⠃⠀⢹⠃⠀⠈⠀⠀⣃⡇
⠀⠀⠀⢸⠀⡰⣧⠀⠀⡀⠁⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠠⠤⠤⠤⠄⠐⠚⠉⢀⣀⣀⠀⠀⠈⠀⢀⡄⠀⠀⠒⠂⠀⠀⠀⠿⠻
⠀⠀⠀⠘⠀⢀⠂⠀⠰⠁⡀⢸⠀⢠⡀⠋⠀⢠⠄⠔⡆⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⡄⠀⡴⢁⠞⠁⠀⠀⠀⠀⢈⣗⢀⠀⠀⠠⠀⡆
⠀⠀⠀⠀⠀⡧⠀⠆⠀⢄⡀⠸⠀⠀⠀⠀⠠⢌⠀⠀⢉⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠞⠈⡷⠀⠀⠀⠃⠀⣼⠀⠀⢦
⠀⠀⠀⢀⢃⠃⠀⠆⠀⠀⠀⢆⠀⠀⠀⠀⠀⠘⠂⠁⠈⠀⠀⠀⢸⡨⠀⠀⠘⢰⡃⠀⠀⠳⣈⠑⠒⢒⠀⠁⠀⢀⠀⢉⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠘⡀⠑⠤⣈⡀⠀⠀⠢⠑⢦⣄⡀⠀⠀⠀⠀⢠⠦⠀⠀⣷⡇⠀⠀⠀⠸⠃⠀⢀⡄⠀⠉⠉⠀⢠⣄⡀⠈⠓⠋⠀⠀⠀⢡⠀⠀⡁⡠⠒⠁
⠀⠀⠀⠀⠰⠲⠤⣀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠲⠄⠀⠈⠁⠀⠀⢣⡥⠄⠀⠠⡡⠂⢀⡄⠀⠀⢠⣶⡔⠀⠀⡙⠀⠀⢀⣤⠀⠀⠸⡆⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠲⠤⠶⠶⠖⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠈⠙⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠈⠃⠀⠀⠀⠣⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡀
⠀⠀⠀⠀⠀⠀⡴⢿⢹⣯⡄⠀⢶⡶⠀⠀⠀⠀⠀⠈⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⢠⠲⣜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢺⡇⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⠀⣤⢠⡄⣠⠀⣄⢠⣤⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠙⠿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡏⠘⠂⡧⢸⡇⣿⢸⡇⣿⣇⣿⠀⣷⠸⣇⣼⠀⣷⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇⣰⠀⣇⢸⠇⣿⢸⡇⣿⠸⣿⠀⣟⢸⡇⢹⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠈⠉⠁⠉⠀⠉⠀⠁⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡮⣵⣦⣄⠀⠀⠀⠀⠤⣤⠄⡤⡤⢀⡠⠄⢰⢦⡤⢤⢰⠆⡄⡄⢠⡄⠀⠀⠀⠀⣠⣬⣉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠂⠞⠊⠸⠆⠘⠈⠇⠸⠚⠆⠃⠇⠸⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠻⢿⣿⠀⠀⣀⡀⣠⣤⣤⣤⣶⣦⣶⣦⣤⣤⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡽⠿⣯⣼⡃
⠀⠀⠀⠀⠀⣴⡄⠀⠀⣾⣋⠀⠁⠈⠀⡙⣷⠀⣿⣷⢺⣛⡟⣖⣲⢲⣒⣖⣖⣲⣻⣛⣾⡿⠠⡄⠀⠀⠀⠀⢠⣟⡁⠈⠀⠁⢈⣳⡄⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⡸⠀⠀⠀⠀⠃⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣷⡆⠀⠀⠀⢻⡧⠇⠛⠚⠓⠸⣸⡇⠀⠀⠠⡇
⠀⠀⠀⠀⠀⢭⠀⠀⠀⠙⠷⣤⡆⢰⣤⡾⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⢦⣴⣷⣦⡴⠟⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡞⣽⣿⣿⣿⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣀
⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢫⣧⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⢹⣿⠁
⠀⠀⣾⣿⣯⣀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⠙⠁⠀⠀⠀⠀⠀⠀⣠⡞⢹⡛⣛⣿⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣿⣷⡀
⠀⢸⣿⣿⡿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⢻⣿⡇
⠀⠀⠿⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡋⠙⣶⣶⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡏⠈⣉⢹⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣼⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠊⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⢶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣿⣿⣿⣿⢛⢻⣿⣿⣿⣇⠀⠀⢀⣤⡀⠀⠀⠀⠠⡄⠙⠦⢪⣼⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⢀⣭⣭⣭⡉⢶⣿⣷⠎⣩⣭⣭⣄⢀⣼⣿⡇⠀⠀⠀⠀⢈⣃⣷⣿⣿⣿⡟⣝⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣭⣭⣭⣭⠸⣛⡻⢨⣭⣭⣭⣵⣿⣿⣿⠇⠀⠀⠀⣠⡜⣿⣿⣿⠿⠅⢮⡈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢠⣶⣮⡻⣮⡝⠛⠈⠳⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⣷⣝⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⡶⣀⡺⣿⣦⡙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣫⣜⢿⣷⣎⠛⠁⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣿⡿⠿⠿⢫⣦⡻⣿⣷⠝⣡⣶⠀⠀⠀⠀⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⣫⣾⠿⡻⢷⣮⢻⠎⣡⣾⣿⣿⠀⠀⣀⡤⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⡣⣿⣿⡇⣿⡇⣾⣿⣿⣿⠇⢀⡞⠁⣠⣾⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⡻⣿⣧⡹⣷⣬⣭⣾⠟⣰⣿⣿⠟⠁⠀⢸⠀⠠⡇⢺⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣌⠻⣮⡻⣿⣶⣭⣭⣷⣾⣿⣿⠁⠀⠀⠀⠘⢦⠀⠃⢸⠀⠀⣠⢇⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣌⠻⠎⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠲⢾⠖⠚⠁⢸⡇⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⠤⠞⠀⠀⠀⢸⡇⠸⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠋⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣿⣿⣷⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠚⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⢿⣿⡏⣹⣍⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⢺⣿⣿⣿⠇⣿⣷⠠⠄⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⣿⡿⠸⠟⠁⠀⠀⠠⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣷⣴⣿⡆⠀⡀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣹⡇⢀⣾⣷⠆⠀⠐⠆⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⣰⣭⣿⣿⣿⡿⠛⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣴⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠐⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣾⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⠀⠀⠀⠁⠀⠀⠘⠃⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⢀⣶⣴⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡿⠿⠛⡋⠉⠉⣿⠛⢿⣿⣿⣿⣿⣇⠀⣤⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠟⣁⡀⠀⠈⣧⡄⠀⢸⣶⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠛⠃⠀⠶⠈⠀⠀⢸⣿⣿⣿⣿⢉⠿⣿⣿⡿⠟⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⡇⠀⠄⢠⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠠⢦⡄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣇⠀⣀⣠⣤⣈⠃⢸⣿⣿⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠹⣿⣿⣿⣆⠀⢠⡤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣰⣿⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣄⠏⠒⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣟⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡟⠠⠄⠈⠀⠠⣝⠻⢿⣿⣿⠿⠋⣠⣿⡏⣹⣿⣿⣿⣿⣏⡀⣀⠀⠀⠀⠀⠀⠀⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠟⠀⠶⠄⠀⠀⠀⠉⠀⠀⠀⠀⢀⣾⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠠⠄⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⣿⣿⣦⣜⠀⠀⠀⡙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠄⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠁
⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⠗⢀⣠⣤⠀⠀⠀⣠⣍⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄
⠀⠀⠀⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣟⣶⡄⢀⡉⠋⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠆⠘⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠿⠛⢻⡿⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠘⠛⠒⠶⠶⠦⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⠤⢤⣀⡀⠀⢀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠉⠛⠛⠓⠶⠶⠦⢤⣤⣄⣼⡏⣇⠸⣇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⠴⠋⠁⠀⣾⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣀⠀⠀⠀⠀⠈⠿⣸⡆⢻⣗⠒⠶⠤⢤⣤⣸⣆⠀⢰⡏⠁⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠛⠛⠒⠒⠀⠀⠀⠸⠣⣉⡀⢸⡄⠀⠀⠀⠀⠈⢻⣧⢸⡇⠀⠀⠀⠀⠀⣿⠀⣀⠹⣧⢤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⣷⠺⡆⠀⠀⠀⠀⠀⠘⣏⣇⢿⡀⠀⠀⠀⠀⠘⠦⡼⠀⢸⡆⣒⠂⠀⠈⢉⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣻⠀⠀⠀⠐⠂⠀⢸⣼⡌⢷⡄⠀⠀⠀⠀⠀⠀⣠⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⣇⠻⣇⠀⠀⠀⠀⢀⣾⣿⣷⠀⠻⣦⣀⠀⠀⣠⠞⠁⠈⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣾⣘⣻⣤⣤⣤⣤⣾⣿⣿⣿⣆⠀⠈⠛⠻⠋⠁⠀⠀⢸⣧⣤⣤⡤⠤⠶⠶⠶
⠀⠭⠭⠭⠭⠿⠷⠾⠶⠶⠶⠶⠿⠿⠷⠶⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⣇⠙⣏⠉⠉⠉⣿⡟⡏⠈⢻⡄⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⣻⡄⠀⠀⡿⣇⢇⠀⠐⣿⠶⣤⣀⣀⡤⠞⣯⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢉⣧⠀⠀⢷⢹⣾⣆⠸⣿⠀⡇⡏⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⠀⢼⣦⠶⠾⣷⠻⣿⣶⠟⠒⠓⠓⠒⢒⣾⣡⢿⡟⢛⣛⣉⣉⣉⣉⣉
⠀⠀⠙⠉⠉⠉⠉⠉⠭⠭⠙⠋⠉⠉⠙⠛⠛⠋⠉⠛⠉⡉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡆⠳⣿⠛⠶⠎⠳⣬⡙⠳⠶⣤⣶⣾⡿⠟⢋⡾⠁⠉⠀⠉⠉⠁⣀⣀
⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠀⠂⠘⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣤⠶⠞⢳⡤⣽⡇⠓⠲⣤⣬⣽⣿⣿⣿⣯⠵⢶⣶⠾⠷⠖⠚⠛⠛⠛⠛⠉⠉
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠶⠶⠶⠒⢲⠖⣿⠟⠁⠀⠀⢸⡷⢶⣷⠀⠀⠘⣄⠀⡃⡇⠀⣧⠴⠋
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠨⣿⠀⠀⠀⠀⠀⣿⣍⣿⣇⠀⠀⢹⠀⡇⡇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⣿⡄⠀⠀⠀⠀⡜⣏⢫⡙⢳⡀⢸⠀⡇⡇⠝⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⠳⡄⠀⠀⠀⡇⢸⢣⡱⢘⡇⢸⠀⡇⡇⣦⣿⢸⡛⢷⣶⡶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣿⡄⠀⠀⠙⢦⣇⣵⡿⠁⠘⣆⡇⠁⢿⣿⡜⢹⡏⣋⣽⡾⠛⡷
⠀⠀⠀⢲⠖⢰⠒⠀⣄⡠⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⡇⠀⠀⠀⠀⢩⡁⠎⠀⠀⠈⠳⣄⢾⣿⡇⡸⢉⣽⡟⢑⣽⡇
⠀⠀⠀⢸⠀⢸⣉⢀⡜⢧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣿⠇⠀⠀⠀⠀⠀⡃⠌⡁⠀⠀⠀⠈⢷⣹⡇⠠⣚⢻⡟⣜⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⡿⡿⠀⠀⠀⠀⠀⠀⢱⡌⢁⡀⠀⠠⠀⠈⢻⠀⠄⠦⣿⠏⢴⣿
⠀⠀⠀⠤⡤⠄⣤⠤⠄⢤⠀⡤⠠⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⡇⠀⠀⠀⠀⡄⠀⠚⠝⠋⣀⣠⠤⠂⠀⠈⣷⠠⣼⢿⠔⡾⢋
⠀⠀⠀⠀⡇⠀⣿⠲⠀⢈⣿⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣇⠀⠀⠀⠀⠳⠖⠒⠊⠉⠁⠀⠀⠀⠀⠀⢸⣠⡇⠸⣴⠇⠘⢦
⠀⠀⠀⠀⠃⠀⠛⠒⠂⠚⠀⠓⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⢈⣦⡀⠸⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⡀⠀⠀⠈⠀⠛⠓⠦⠀⠨⣀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣀⠀⠀⢀⣀⣀⣤⠴⠖⠛⠉⠛⠿⠛⠲⠤⢄⣀⣀⡤⠤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⡜⠙⢄⣀⣠⡴⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡴⠊⠀⠀⢀⠿⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣠⠞⠋⠀⠀⠀⢠⠏⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⠁⠀⠀⠀⠀⠀⣾⠀⠀⢠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠈⡆⠀⠀⠀⢀⣠⣿⠀⢠⠗⣹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠙⠷⠶⠾⠟⠋⢹⣤⠇⠈⣿⣦⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡼⣿⠟⠀⡜⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⣾⠔⢋⡴⠃⢀⠞⠳⣤⡘⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠛⠻⣝⡄⠀⣀⣈⡙⠒⠦⠤⣤⠔⠋⢀⡴⠻⣄⠴⠃⠀⠀⠈⣿⡶⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠖⠠⢼⡞⠋⠁⠀⠉⢷⡄⠀⡘⠇⠚⢱⠃⠀⠁⠀⠀⠀⢠⡞⠉⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⢸⠃⢀⠀⠀⠀⢸⣿⡉⠉⠙⣠⠛⠢⣄⣠⣤⢤⣴⡏⠔⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢩⡰⡻⠁⠀⠀⠀⠉⠉⠉⠉⣿⣀⠀⠉⠁⠀⠀⢸⡇⠔⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡆⠀⠈⠒⠓⣄⢀⠄⠀⠄⠀⠀⠀⡾⠿⢷⣦⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢧⠀⠀⡴⠲⣌⣙⣾⣷⣄⡀⠀⡰⠁⠀⠀⢹⠇⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡯⠐⠀⠡⡚⣾⣿⡿⣱⢋⡟⡶⢧⣀⠀⠀⡼⠀⠀⠀⠀⣨⠙⠄⡐⠠⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠮⣨⠶⠬⣯⠍⠋⠁⢞⡜⢡⠏⣼⡿⡶⣧⣀⡤⠄⠀⠻⣔⣠⣄⣀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⢠⠾⠿⣷⣾⣝⡵⠳⠏⣹⠷⣶⣶⡘⠃⠲⡕⣎⠛⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣧⣀⣀⣠⡔⠃⠀⠀⠀⢈⣽⡖⢘⠈⠸⣾⢃⡞⣹⣳⣦⠬⢿⣦⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣤⣤⣴⠋⠉⠻⢦⣑⣤⡈⠛⠾⣷⡧⣉⠻⢷⣮⡝⣓⢤⡀
⠀⠀⣴⣶⣠⢦⣴⡦⣶⣶⣰⡦⣶⣦⢴⣶⣤⣶⣴⠆⠉⢹⠇⠃⠀⠀⠀⠀⠈⠻⣆⣀⠀⠈⠻⣿⣟⣢⠌⡑⠚⠀⠃
⠀⠀⣗⣠⣿⣸⣿⣇⡇⣿⣿⡇⢸⡃⢸⡿⣇⢘⡏⠀⣶⣴⡆⡆⢰⠰⣗⢰⢰⠒⠂⠉⠉⠉⠉⠛⠙⠛⢾⡿
⠀⠀⠉⠉⠈⠋⠀⠙⠁⠉⠉⠁⠘⠁⠉⠁⠉⠈⠋⠀⠉⠉⠁⠙⠁⠈⠋⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣯⣿⣯⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⣿⣯⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣿⣷⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⢺⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢹⣾⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠛⠳⠦⣤⣀⣀⣴⠏⠀⢀⣴⡿⢸⠀⡇
⠀⠀⠀⠀⠀⠀⣼⡿⢳⠀⠀⠀⠀⠀⠙⢻⣿⣶⣶⣿⣿⡷⢾⠶⡷⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⢰⡿⠁⠘⡄⠀⠀⠀⠀⠀⣰⣿⠿⢫⡞⠁⡇⢸⠀⡇⠀⠀⠀⠈⠉⠳⢦⡀
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⢀⣴⠋⠀⠀⡇⠈⠀⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⠞⠉⠀⠀⠀⢠⡞⠁⠀⠀⠀⣇⣠⣀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠆⢀
⠀⠀⠀⠀⠈⢻⣄⠀⣴⠋⠀⠀⠀⠀⣰⠟⠀⠀⠀⣠⡾⠟⠛⠛⠛⢷⡿⣦⡄⠀⠀⠀⣼⠁⠀⠀⣠⡴⠶⢿⣿⠟⠋⠉⢹⡇⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠙⢿⡟⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⡟⠀⡇⠀⠀⠀⠈⣿⣿⣿⣆⠀⢠⡏⠀⠀⣾⠋⠀⠀⣿⠁⠀⠀⠀⠸⣧⣼⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢠⣿⡆⠀⠀⠀⠸⣧⠀⡇⠀⠀⠀⢀⣿⣻⣿⣿⢀⡾⠀⠀⠀⣿⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡅⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⠏⣿⠀⠀⠀⠀⠙⢷⣦⣤⣤⣴⢾⣱⣿⣿⣿⢸⡇⠀⠀⠀⢹⡀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⡾⠁⡴⠃⠀⠀⠀⠀⠀⠀⡋⠉⣽⣿⣿⣿⣿⣿⡿⠀⢻⡄⠀⠀⠸⣇⠀⠀⠈⣧⠀⠀⠀⠀⠈⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣦⠾⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠅⠀⠻⣿⣿⣿⠿⠛⠁⠀⠀⠹⣆⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⡄⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⠷⣄⠀⢸⣷⡄⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⡟⠀⣿⣆⣸⠇⣿⡇⠀⠀⢘⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢈⡽⠋⠀⠙⠿⢦⣤⣾⡿⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⠻⠗⢀⣤⣾⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠋⠉⢉⡀⠀⣀⡤⠶⠿⠇⠘⠉⠀⠀⠀⠀⠀⣀⣼⣷⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠳⠶⠦⠤⠤⠤⠄⠤⠤⠖⠋⠉⠙⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣠⣄⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣟⢻⣛⣛⣋⣙⣻⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣛⣟⣻⣟⣻⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀
⠀⠀⠀⠠⠤⠠⠀⢈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠉⠙⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣽⠿⠛⠒⠒⢦⣤⣿
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⢻⣿⡄⠐⠂⠀⠀⠀⠙⢿⣿⣿⣅⣀⣀⣀⣀⣀⡈⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠂⠀⠤⠀⠄⠈⠉⠙⠛⡋⠉⣿⣟⣿⡿⢿⣿⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⢸⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⡤⠶⠶⢶⡶⠶⠶⠶⠞⣿⣿⠚⠛⠛⠉⠉⠉⠉⠉⣿⠉⣿⣿⢹⣿⣿⣯⠉⣿⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣸⣿⣿⡛⠀⣿⠰
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣆⣿⣿⣿⣿⣿⡇⢀⣿⣄⡀
⠀⠀⠀⠀⠀⠠⠼⠗⠀⠒⠀⠀⠀⣻⣿⣧⣀⣀⠈⠀⠀⠈⢿⡿⢿⣿⣿⣿⣿⢋⣃⣈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠞⠉⠈⣿⣷⠀⠈⠳⠒⠒⠒⢺⣗⠘⣿⣽⣿⡏⠈⠀⡇
⠀⠀⠀⠀⠉⠈⠉⠉⢩⠀⡏⠀⠀⠀⢹⣿⣆⠀⠀⡄⠀⠀⠀⠻⢶⣿⡿⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⡀⠀⠀⣾⠁⠸⣷⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢲⣦⣤⡟⠀⠀⠀⣠⣾⡿⣧⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢳⡀⠀⠹⡀⠀⣹⠇⠃⠀⠀⠀⠀⠀⣿⠀⠀⠸⢸⡟⠿⠀⠀⢸⣿⠁⢛⡗⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣷⠀⠀⠈⠛⠋⠀⠀⠠⡀⠀⠀⠀⣿⠤⣴⣤⡾⠃⢷⢰⠀⢸⡇⠸⣶⣖⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣿⠀⠀⠙⣿⣦⠛⣿⠂⠀⣧⠷⠿⠴⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠀⠀⢀⣀⣤⣦⣶⣾⠆⠀⣧⠀⣿⡀⠀⠀⣸⣿⣍⢹⡇⠀⢷⢾⢃⡸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⢸⠀⠘⠷⣦⣤⣿⣻⠻⢻⡇⠀⣿⡼⠹⡷⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢸⡗⠀⠀⡇⠴⣟⢠⣠⠟⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⠦⣀⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⢴⣶⣶⣶⣿⣴⣶⣤⡇⠀⠸⣦⣠⣄⣀⡀⣀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣴⣶⣄⠀⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣿⣶⡶⠀⠀⠀⠀⠀⠀⢀⡀⠸⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⠷⠀⠀⠀⠀⠀⠀⠸⣿⣄⡙⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⠇⠀⠀⠀⠀⠠⠀⠀⢻⣿⡀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⢤⡄⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣶⣶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⡄⠀⠀⠀⠀⢹⣆⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⡿⠿⠿⣛⣭⣿⡿⠃⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠠⣾⣿⣶⠃⠀⠀⠀⠀⠃⠀⠈⠛⠿⣿⣿⣾⣿⣿⠿⠟⠉⠀⠀⠀⢠⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠉⠋⠘⠛⠃⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠸⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣶⠂⠀⠀⢠⣶⠄⠀⠀⢀⠀⢀⢄⠀⡀⠀⣀⠀⠀⣀⠀⡀⡀⢀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣭⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⡏⠀⠀⢀⣿⡟⠀⠀⠀⡇⠀⠉⠀⡆⡁⠀⠘⢠⡀⢸⠀⠦⡜⠈⡎⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⣼⣿⠁⠀⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠈⠁⠈⣀⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⢰⣿⠇⠀⠀⢠⣿⠇⠀⠀⣤⡄⠀⢠⣤⠀⠀⢠⡴⠲⣄⠀⢀⣬⡁⠀⠀⣀⣠⢄⠀⠀⠀⠀⠀⢤⣼⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⠃⠀⢀⣿⡟⠀⠀⠀⣾⡟⠀⠀⣸⣿⠃⢀⣿⡟⠀⠀⣿⡇⢠⡟⠀⣾⡿⠀⢀⣾⠟⠁⠸⠃⠀⠀⠀⠀⠀⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡾⣿⡇⠀⠀⣴⣿⠇⠀⢀⣿⡇⠀⣸⣿⠁⢀⡴⣿⣧⠬⠒⢹⣿⠇⠀⢸⣿⠀⠀⢠⡄
⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⢿⣇⠀⠀⢀⡜⠁⠈⠳⠐⠊⠀⠻⣄⡠⠚⠻⠤⠖⠻⠧⠔⣫⠞⣿⡇⠀⠀⣿⡟⠀⠀⠘⠿⠀⠤⠋⠀⠀⠀⠄
⠀⠀⠀⠁⠀⢠⡆⠀⠀⠀⠀⠙⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠟⠁⠀⠀⢹⣧⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠛
⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣶⡦⠔⠛⠛⠻⢉⣁⠀⠀⣈⡷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⣰⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠃⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢨⡷
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣴⠈⠁
⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⢠⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣿⡟⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣴⠆⠀⠀⠀⢸⣿⡇⣰⣿⣿⡿⠋⣀⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠿⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣷⡿⠟⠁⠀⠈⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⡐⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠐⠒⠂⠀⠸⣦⠣⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠡⢦⡆⠀⠀⠁⠀⠘⡆⡇⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠐⠒⠀⠀⢹⡹⡄⠀⠈⢁⠄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡏⢦⠤⠤⠀⢠⣾⢧⠈⠲⠖⠁⣸⣠⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⢸⣿⠀⠣⠄⠠⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢧⠀⠀⡀⢿⢧⡀⠀⢀⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠒⢡⢸⡀⠠⡀⠠⠵⠾⠿⢯⠵⠃⡄⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢸⡅⠀⠀⡤⠧⡀⡀⠀⠀⠀⠰⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣀⢀⡇⠄⠀⠀⠀⠀⠀⢀⣠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠁⠀⠈⠢⡀⠀⠀⠀⣾⡏⢯⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣺⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣿⠇⢻⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢇⠹⡀⠀⠐⠂⠈⠀⠀⠀⡇⠀⠀⢿⣀⠟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢦⣧⡀⠀⠀⠀⢀⣠⠜⠀⠀⠀⢶⣄⠀⠘⠂⠉⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣧⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡷⣿⡷⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⡇⣼⡿⣿⠃⣾⠿⣷⠸⣿⡇⣿⣿⢸⣿⡄⣿⡿⣸⣿⣿⣇⢼⣿⣿⣿⡆⣿⣿⢽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⣿⠀⠛⠀⣿⠀⣿⠀⣿⠀⢸⡇⠀⣿⣧⢸⡇⠛⢸⡇⠛⠀⣿⣀⣿⠇⠀⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⣿⠀⢀⠀⣿⠀⣿⠀⣿⠀⢸⡇⠀⡇⢻⣾⡇⠀⢸⡇⠀⠀⣿⢿⣿⡀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⣿⣄⣿⠆⣿⣀⣿⠀⢿⣆⣼⡇⢠⣧⡘⣿⡇⠀⣼⣧⠀⣠⣿⡄⣿⣧⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣸⡇⠘⠛⠻⠂⠙⠛⠋⠀⠈⠻⠛⠀⠘⠛⠃⠛⠃⠀⠛⠛⠀⠛⠛⠃⠘⠏⠀⠛⠛
⠀⠀⠀⠀⣶⠂⣖⡂⢾⡂⢲⠂⡔⣦⡔⣰⡆⣶⠀⣿⢸⠼⡇⢸⣿⣧⠀⢰⣿⣷⠀⢸⣿⠀⠀⢸⡇⠀⢰⣾⠛⠻⣷⠀⠀⣿⠀⠀⣴⡿⠛⠿⣦
⠀⠀⠀⠀⠃⠀⠳⠆⠒⠃⠘⠀⠃⠘⠃⠋⠓⢻⣦⣿⢸⢸⡇⢸⣿⢿⣆⣿⢻⣿⠀⢸⣿⠀⠀⢸⡇⠀⠘⠻⠷⣶⣦⡀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⠋⠁⢸⣿⠲⡇⢸⣿⠸⣿⡟⢸⣿⠀⠸⣿⣄⣠⣾⠇⠀⢺⣦⣀⣠⣿⠃⠀⣿⠀⠀⢿⣦⣀⣴⡿
⠀⠀⠀⠀⠀⠀⣴⣏⠉⠉⠛⠲⢦⣄⣠⡞⠁⢀⣴⡿⢸⠱⡇⠈⠁⠀⠉⠁⠈⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢠⣿⠉⡀⠀⠀⠀⠀⠉⢻⣿⣾⢟⡿⠿⢻⠿⡗⠒⠶⠦⢤⣀
⠀⠀⠀⠀⢀⡿⠁⠀⠃⠀⠀⠀⢀⣠⠾⠛⢡⠞⠁⣷⢸⢠⡇⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡴⠚⠉⠀⢀⡴⠃⠀⠀⣿⢸⠈⡇⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢻⡄⠀⢀⡴⠋⠀⠀⠀⢠⡾⠁⠀⠀⣠⣿⣾⣶⣧⣤⣄⡀⠀⠀⠀⢠⡇⠀⠀⠀⣀⣀⣤⣤⣴⠶⢾⡇⢰⣄
⠀⠀⠀⠀⠀⠹⣦⣾⠃⠀⠀⠀⢠⡟⠀⠀⠀⣼⠋⠱⢐⠄⠈⠹⣿⣿⣆⠀⠀⣼⠁⠀⣠⠞⠉⠁⡿⠋⠀⠀⢸⡇⢸⠛⢷⡄
⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⢠⣿⡀⠀⠀⠀⣿⠀⢐⠈⠠⠀⠀⣿⣿⣿⡆⢰⠏⠀⠀⣯⠀⠀⠀⡇⠀⠀⠀⠀⢹⡏⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣾⠿⡇⠀⠀⠀⠹⣧⣌⣀⣀⣠⡾⣷⣿⣿⣧⣿⠀⠀⠀⢿⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⡴⠋⣴⠃⠀⠀⠀⠀⠀⢙⠛⣿⣿⣿⣿⣿⣿⡇⠻⣄⠀⠀⢸⡇⠀⠀⢹⡀⠀⠀⠀⠀⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⡴⠟⢀⡼⠁⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⣿⣿⡿⠋⠀⠀⠙⣆⠀⠈⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⣿⡀⠀⠈⡇⠀⠀⠀⠀⣿⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡀⢀⢀⣀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠘⣇⣸⢷⡄⠀⣻⣆⠀⠀⠀⢸⣆⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⣸⠏⠘⣿⣤⡟⢸⣿⠀⠀⢠⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⠀⠀⣠⠟⠀⠀⠛⠷⠶⢾⡟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠶⠯⠙⢋⣠⠾⣷⡄⠀⠀⠀⠀⠀⢸⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⣀⣠⠄⠂⠠⠖⠛⠉⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⠴⠾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠛⠛⠒⠊⠉

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⣿⣿⣿⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠚⣽⠟⠁⠀⠀⢹⣿⣿⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡜⠀⣸⠇⠀⠀⠀⠀⠘⣿⣿⣳⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⣿⠿⢿⠆⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⢾⡏⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⢿⠀⠘⣧⠀⠀⠀⠀⢸⡏⠀⠈⠸⣿⡀⢀⡇⠀⠐⢻⣶⣤⡀⣿⣿⣿⣿⡿⠶⠿⢿⣶⣄⠀⠀⠈⠻⣶⣤
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⣧⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⢸⡇⠀⠀⢸⠀⣦⢻⣼⡿⣿⣿⣅⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠹⣇⠀⠀⠀⠻⣄⠀⣀⣿⠇⠀⠃⠀⠀⠸⠀⣹⡆⢉⡁⠈⠙⢿⣷⣦⣄⡀⠀⠀⠘⣷⣤⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠰⣦⣴⣴⡿⠃⠸⠧⢢⡀⠘⣿⠉⢻⣿⣶⡀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣖⡁⠴⠿⣼⡇⠀⣯⢰⣤⣥⠟⣿⣆⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⣠⢟⡇⠀⢸⠆⠋⡉⠛⠜⣻⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡏⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⡆⠀⠈⢿⣛⣥⡈⢹⡗⠀⢸⡇⣾⡿⢀⣸⡧⣼⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⠀⢸⣿⣶⡧⠼⣇⠀⢸⡿⣠⡷⣿⢀⣴⣿
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠳⢴⣿⠀⢸⣶⡿⠀⠙⣧⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠤⠀⠀⣿⣴⣿⠇⢀⡀⣠⡿⠀⠘⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢁⣀⠀⠀⢹⡈⠙⣷⠈⠉⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣙⢦⣄⣀⡀⠀⠀⣀⣀⣠⣤⠶⠛⠁⠘⠿⣿⣯⣿⣿⡾⠁⠀⠹⠿⠦⠾⠶⠤⣄⣀⣀⣠⣤⡴⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⡀
⠀⠀⠠⠐⠒⠂⡞⠁⠘⡄⠘⢦⡀
⠀⠀⠱⣀⠀⣎⠀⠀⠀⠘⢤⡶⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⢲⠒⢰⠒⠂⢢⣠⠆⠒⡖⠂
⠀⠀⠀⠈⠳⣜⢦⡀⠀⠀⠀⠀⡰⠉⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣉⡁⡰⠳⡄⠀⡇
⠀⠀⠀⠀⠀⠙⢷⣍⠳⠦⣤⡴⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⡀⢀⠀⠀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢲⡚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁⣿⣉⡁⠈⢧⡴⠃⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠉⠁⢀⡜⠳⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠈⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣍⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣲⠋⠁⠀⢧⣿⡆⠀⢢
⠀⠀⠀⠀⠀⠀⠀⡃⣿⠀⠀⠀⢸⣽⠷⡄⠈⠀⠀⢠⡆⣟⢳⣶⡦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⠀⠀⢆⢨⠢⢸⠀⠀⠀⣻⣷⠁⡏⣥⣿⣛⣹
⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡇⠀⠈⠲⡴⠏⠀⢣⡀⡿⢿⠀⠡⣿⡇⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⠀⠀⠀⢀⠡⠀⠀⠙⢷⣿⠀⢉⣼⠇⢵⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⠁⠀⠀⠀⢈⣄⡠⠀⠀⠈⢧⠀⢴⢿⢰⡿⡁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⣄⠠⠤⠔⠒⠀⠀⠘⣤⠟⠘⢞⠁⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠸⢳⣌⡙⠓⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣿⣄⠀⠀⠀⠀⠀⣀⣠⠴⢿⡷⠄⣀⠀⠀⢀⣀⣠⠼⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⣤⠠⡆⡦
⠀⠀⠀⠀⠀⠀⢥⢺⡆⣶⠿
⠀⠀⠀⠀⠀⠀⠰⠾⣧⢿⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢽⣆⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⣿⣼⣷⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢻⣗⣿⣴⣿⣿⣆⠈⠂
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⡽⠚⠷⢻⣿⣿⠀⠀⢀⢠⠊⡷⠶⣶⡰⠲⢦⣄
⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠁⠐⠀⠆⡀⣿⠟⠀⠀⠁⡘⢀⠅⢀⠈⠻⡀⠄⢹
⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠐⠹⣷⠾⠞⠉⠀⠀⠘⠇⠅⠘⠀⡆⠄⠴⣐⠰⢸
⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠊⢁⠀⢉⠀⢀⠩⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢣⠡⡌⠐⠒⠄⢺⠂⠂⣅
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢠⢒⣉⣉⠠⠴⠂⠀⠸⠀⠅⠠⠀⡔⠉⣁⠄⠈
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡘⠂⠦⠄⠐⠀⠀⠡⡀⠀⠑⣄⡀
⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⡆⠀⠀⠀⠀⠀⠜⡲⢤⡀⠉⠓⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣤⣤⣤⣶⣶⣾⣿⠿⠛⠏⠙⢲⣤⣀⠀⠀⠀⠀⠁⠀⢀⣠⡷⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠈⠐⠐⠋⠉⠙⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠴⠤⠦⠤⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⢀⠀⠀⠰⠦⢀⣠⣤⣤⣶⣾⣟⣙⣟⣻⡿⠛⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢷⡄⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠛⣿⠛⠛⠉⠷⢦⡤⠄⣀⣀⠠⠈
⡄⠁⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠘⢀⡀⠀⠀⣤⡄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆⠹⣇
⢣⡄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠿⠇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⡸⠇
⠀⠙⠳⠶⠶⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠈
⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⠀⠀⠘⠇⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⣀⡠⠔⠁⠀⢠⠋⠀⠀⠀⣠⢈⠘⠃⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢧⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢤⣀⣀⣀⣀⠤⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠴⠋⠀⠀⠀⠀⢴⡐⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠈⢻⣏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠶⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⢸⣿⠀⠀⡙⠄⠓⠀⠁⣘⣛⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡄⠛⠋⢠⣄⣀⣘⢋⡡⠤
⠀⠀⠀⠀⢀⡠⠄⡒⠒⠁⠐⠛⠓⠤⠤⢀⣀⣈⡡⠤⠋⠀⠀⠀⠀⠀⠉⠛⠁⠈⠑⢄⠀⠀⠀⠀⠀⠀⣀⡠⣤⡔⠶⠋⠏⠀⠀⣣⡾⠾⠛⠃⠈⠉
⠀⠀⠀⠔⠋⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⡤⠲⠞⠉⠉⢀⣤⣤⡶⠆⠷⠀⠁
⠀⢠⠀⠈⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⣀⡠⠤⠤⠀⠀⠈⢸⣧⣀⣀⡤⠶⠟⠛⠉⠁⢀⠄
⢠⡆⢠⡄⠀⠀⠀⠀⠀⢀⡉⠳⠤⣀⠀⠀⠀⠠⠆⠀⠀⠉⠻⣎⠀⡀⠠⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⡐⠁
⠘⠃⠘⡇⠀⠀⠀⠀⠀⠸⢳⡄⠀⠉⠑⠛⢤⡐⠒⠂⢤⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡾⢧⠀⠀⠀⠀⠂⠼⣖⣀⣈⡣⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢦
⢰⡆⠦⢸⠀⠀⠀⠀⠀⠀⢀⡟⡇⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⡄⠀⣴⡿
⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠆⠉
⠀⠈⣄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠶⠶⠾⠛⠃⠉⠁⢀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠘⢆⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⠆⠁
⠀⠀⠀⠈⠳⣄⠀⠈⠑⠒⢤⣤⠀⠀⣠⣤⠔⠊⢀⡄
⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠤⠄⠀⠂⠉⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠺⠛⠛⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠳⣦⣤⣤⣤⣄
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⢤⠀⡀⠀⠀⣀
⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠉⠈⠙⠆⠀⠀⠀⠀⠢⠄⢀⠺⠭⢭⢌⡓⠐⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠠⣾⠀⠀⢀⠀⢀⠔⠁⠀⠀⡆⢰⠀⠰⠀⠆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⢔⠀⠀⢀⡠⠟⠁⠀⠠⠁⠀⠂⠀⠀⠘⠀⠀⠌⠀⠀⠆⠈⠄
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡱⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⢄⠠⣀⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠐⠙⠒⠐⠤⢄⠀⢀⡠
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠞⢆⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡇⢸⡄⠀⢸⠀⠈⢳⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⡴⢄⡠⡀⣠
⠀⠀⠀⠀⠀⠀⠀⢷⠀⣼⠁⠀⢻⡀⣿⠀⠀⠀⠹⣄⠀⠀⠀⠇⠀⠀⠀⠀⢀⡀⠄⠀⠠⠀⢀⠤⠄⠬⠁⣉⢀⠑⠂⡀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠀⠀⠀⢳⡟⠀⠀⠀⠀⠘⠇⠀⠀⠀⡀⠀⣠⠖⠁⠀⠀⠀⠀⠀⡁⢀⠀⣀⠀⡀⠀⠁⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠸⠇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠢⡉⠃⠀⠀⠀⠁⠈⠊⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠑⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠘⠈⠀⠀⠈

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠰⠀⠀⠀⠀⠉⠁⠖⠀⠐⠒⠒⠒⠒⢺⢧⣤⡄⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢬⢒⣒⣒⣀⠠⠄⡇⠁⠀⠀⠀⠀⠀⢈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠒⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠀⠉⠉⢀⠀⠀⠂⠉⠉⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠀⢐⣲⡲⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⣠⣴⠲⣝⡺⠟⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠿⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⢳⣯⠀⠀⠾⠿⠟⠋⠋⠉⠉⠋⠉⠋⠱
⠀⠀⠀⠀⠀⠸⣥⣄⢀⠂⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⡀⠰⠀⢸⣾⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢸⢽⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠅⠀⠀⠐⢨⡇⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⠀⠀⠀⠀⠀⠒⢒⠀⢒⠀⣸⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠚⠀⠸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠦⡄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡀⠰⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣭⡭⣤⠀⠀⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⠀⠀⣹⣀⣀⣀⣀⣀⣠⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠗⠖⠶⠠⠄⠀⠀⠠⠃⠠⠠⠤⠤⠲⠖⠞⢷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⢠⠟⠙⣷⠀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⣤⠀⠀⠀⣄⣮⠃⠀⠫⣂⡄⠀⠀⢀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢉⡿⠾⠚⣿⠁⠀⠀⠀⢹⠟⠺⢾⣏⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣷⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠀⠀⠀⠘⡀⠀⠀⠀⡌⠀⠀⠀⢹⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⢀⡃⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠸⠀⠀⠀⠀⠀⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⣾⢿⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⢸⡌⣬⣤⠀⢠⣤⡄⣅
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠈⠀⠀⠀⠀⢱⠄⠠⠤⠀⠀⠀⡀⠀⠀⠀⠀⠛⠻⠀⠸⠇⠟⠻⠀⠸⠻⠇⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡀⣀⣠⣀⠀⣀⣠⠇
⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠰⠄⡀⠀⠀⢀⠀⠰⠧⡀⠀⡆⠀⢿⠂⠀⠈⠁⠈⡀⠀⠀⡀⠄⠀⠀⠀⢠⠀⢰⣶⠀⣦⠀⡀⠄
⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠀⠀⢸⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠲⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠼⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠄
⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⡈⠀⠀⠀⣘⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡞⠀⠀⠀⠀⡏
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⡇⠀⢂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠿⠀⠀⠀⠸⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠐⠂⠄⠄⠀⠀⢀⠀⠀⠒⠆⠀⠀⠀⠀⠘⠉⠀⠀⠀⠒⠆⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠠⠀⠀⠀⠒⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠠⠖⠀⠁⠀⡒⠿⠛⣓⡶⠀⠀⠀⡅⢀⣀⠀⠉⠉⠀⣤⡤⢴⡶⠶⠶⠒⠛⣛⠛
⠀⠉⠐⠫⡡⠐⠐⣀⠤⠄⠉⡠⠔⠊⠁⠀⠀⠀⠀⠜⠉⠉⠀⢀
⠀⠀⠀⠀⠐⠾⣗⢀⠠⠒⠁⠀⠀⠀⠊⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⢀⠀⠐⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠀⠀⠠⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⢠⢾⡝⠋⡅⣿⠀⣀⠀⠀⠀⠀⠀⠢
⠀⠚⠀⠀⠀⠐⡀⢀⠀⠈⡀⠀⠀⠀⡙⢯⠉⠉⢿⠀⢻⣤⣾⣿⡄⢐⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⣀⡷
⠀⠀⠀⠀⠀⠀⠸⣍⠀⠠⠞⠀⠀⠸⡈⠄⣣⠀⠈⣧⠀⢿⣿⣿⡇⠈⠀⠀⠴⠀⠀⠀⠀⢄
⠀⠀⠀⠆⠀⠀⠀⢻⣤⠀⢀⠀⠀⠀⠱⡌⢘⢧⠀⠘⣧⠘⣿⠟⠋⠀⡠⠀⠀⠀⠀⠀⠰⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠊⠀⠈⠀⠀⠘⡄⢩⠗⠀⠹⠖⠁⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⣇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢀⠁⠀⠀⢸⣇⠀⠀⠁
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⠘⠁⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠈⣧
⠀⠐⡄⠀⠀⣤⣀⢀⡀⢀⠀⠀⢁⠀⠀⢐⣗⣁⠤⠔⠂⣁⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⠒⠤⠀⢸⡇
⠀⠀⡄⠀⠀⣸⣿⡌⠀⢨⡀⠀⠈⠀⠀⠀⣽⠻⠿⠿⠟⠚⡅⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠓⠀⠀⠐⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠁⠀⠀⠀⠂⠀⠀⠀⠀⠤⢤⣤⡤⠶⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⡀⡈⠢⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣡⣤⠀⠁⢄⠉⢠⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡾⠁⠀⠀⠀⢈⣠⠺⢷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢳⡶⠆⠙⢋⣳⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⣀⣀⠀⠉⣷⠿⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⢿⣭⠙⠇⠻⡄⠀⢺⢽⣻⣄⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣄⠐⠩⢗⡻⣦⢿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣉⣤⣶⣆⠀⠀⠀⡙⣆⠀⠹⣾⠽⣦⣰⣯⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢡⣶⠘⣿⡎⠀⠀⢒⡫⢞⣯⡙⢠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣵⣿⣿⣤⡟⠁⠀⠀⠀⢐⡽⣞⣽⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠨⠵⣪⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⣭⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⠘⣫⢷⣾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠀⠀⠀⠀⠘⠭⢺⣭⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⢀⣤⣶⡒⣐⣦⠀⠀⠀⠀⠀⣀⣴⠿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢵⣺⡿⣳⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠘⠻⠿⠿⠛⠋⠀⠀⣀⣠⣴⡞⠛⣿⡄⠈⢻⣆⠀⠀⠀⠀⠀⠀⠈⢶⡿⣟⡿⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⣾⣿⠉⠉⢿⣧⠀⠘⣿⡄⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⢪⢽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢹⣿⠉⢹⣿⠉⠀⣿⣇⠀⢻⣿⡇⠀⠘⣿⡆⠀⠘⣿⡄⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠱⣚⣯⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣿⡀⢸⣿⡇⠀⢸⣿⠀⠈⣿⣿⠀⠀⢹⣿⣀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠁⠀⣀⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡇⠀⠸⣿⡄⠀⠸⣿⡇⠀⣴⠏⠁⠠⣶⣿⠶⠇⠀⠀⣀⡤⢾⡋⠻⣶⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⢿⣇⠀⠀⢿⣷⠈⣿⢦⣤⣄⣠⠤⣤⠲⣶⡏⠹⣷⠈⢿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⣧⡀⠀⠸⣿⡄⠀⠘⣿⡆⠃⠀⣇⢸⣷⠀⣿⠀⢹⣧⠀⢹⣇⣼⣿⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢷⣄⠀⠘⣿⡄⠀⢻⡇⠀⠀⣿⠀⣿⠀⢹⡇⠀⣿⡄⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣦⡀⠙⢷⣄⠘⢿⡄⠸⡇⠀⠀⣿⠀⣿⡀⠈⣷⠀⠸⣧⣾⢳⣻⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣤⠿⠦⣤⣈⠳⣤⡙⣆⢃⣠⣀⠈⠳⡌⠳⣄⠘⣧⠀⢿⣿⡜⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡇⠀⢰⠇⠀⢨⠁⠉⣿⠀⠀⠙⡇⡤⢛⡶⣌⠓⣌⢳⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢄⠀⢘⡀⠀⣈⢀⡀⠐⠃⠀⢾⡀⣼⠁⠈⠉⠃⠙⢿⣿⣿⣟⡿⢷⣤⣄⣀⣀⣀⣀⣀⣼⡷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣾⣻⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⢿⡿⠻⡿⣿⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣾⣶⣾⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠠⠦⢄⣶⣶⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣠⣾⠀⠀⠀⠀⣚⠒⢰⣿⣿⣿⣿⠇⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡐⠋⠁⠀⠀⠀⠀⠉⠁⣾⣿⣿⣿⡟⢐⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣾⣿⡟
⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠁⣸⣿⣿⠇
⠀⠀⠀⠀⠘⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⢠⣶⡄⠀⠀⠀⡠⢾⣿⠇⠀⠀⠀⠀⣰⣷⣼⣿⣏⠀⠀⢀⣿⣿⡟
⠀⠀⠾⠆⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⣦⠀⠀⢨⣿⡇⠀⠸⣿⡇⠀⠀⣊⣀⣾⣇⠀⠀⠀⠀⠀⠈⣹⣿⡿⣿⠃⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣄⠀⠀⠀⠀⢹⣇⠀⠀⢸⣇⠀⠀⣿⣧⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠁⠀⠀⢠⣿⣿⡟⠀⠀⠀⢀⡀
⠀⠀⣀⢀⡀⠀⠀⠀⢶⡦⠀⠙⢧⡀⠀⠀⠀⢿⡆⠀⠘⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⢀⣿⠇
⢀⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠘⣿⠀⠀⢻⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣾⡟
⠛⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⠘⡇⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣸⡿⠁
⠀⠉⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⢹⡀⠈⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⢠⣿⠃
⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⣷⠀⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣗⠸⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⡇⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⣸⡿
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠯⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣾⣿⣤⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠀⠠⠟⠉⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡽⣿⣄⠀⠀⡀⠀⠘⠛⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠛⠀⠀⣄⠂⣀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣤⣠⠃⡈⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣎⢿⣿⣿⣿⣿⣿⣿⣦⣍⣥⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⡿⠿⠛⠁
⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣼⣶⣧⣴⣧⣶⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⡤⢤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡐⣃⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣇⣛⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⠀⢸⠀⠀⠚⠚⠓⠒⠚⠆⠀⠀⠀⣈⣍⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢿⣮⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⣾⠡⡆⣳⢸⠀⠀⠉⠀⢰⠉⠁⠁⠀⠃⢰⠋⡴⢹⡆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⠘⠳⠖⠃⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠓⠶⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠶⠾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠲⠖⠲⠶⠲⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⠀⠀⠀⠀⠀⡄⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠃⡰⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠇⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⡏⢸⡟⢠⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣴⡿⢠⠄⠀⠀⠀⠀⠁⢿⠇⠀⠀⠀⠀⠀⠀⣿⢰⠇⣼⢀⠃⢀⠂⢠⠁
⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⠈⠀⣠⣴⠟⡠⠂⡠⠀⠀⠀⠀⠀⠃⣼⠆⠀⠀⠀⠀⠀⠀⣿⢸⢠⡇⠄⠀⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠴⡾⢂⡅⢊⠄⠺⣇⠀⠀⠀⠀⠀⠥⢹⠁⠀⠀⠀⠀⠀⠀⣿⡟⣼⡇⠀⠌⢀⠾⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠀⣄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⡤⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⣰⢫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣔⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣟⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⣦⣤⣤⣤⣤⡶⠾⣿⠁⢸
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⣀⡙⠶⠞⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⢸⡇⠀⠀⢸⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣸⡇⠀⢸⡇⠀⠀⢾⠀⠀⣿⠠⠊
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⠇⠀⠠⠾⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠈⢓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⢛⣻⢿⠿⠿⣿⣯⣉⠉⠙⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡏⠀⢀⣀⠀⢠⡴⠖⠀⠀⠈⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡇⠘⣉⣡⢄⢠⠐⠒⠂⠀⠀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣧⠀⠈⠀⣈⣀⣁⠀⠀⠀⠀⣟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢀⣿⠄⣼⠃⠀⠀⢸⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⠘⣿⣴⡏⠀⠀⠀⢸⠏⠙⡖⠒⠶⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠉⢣⠀⠀⣿⠟⠀⠀⠀⠀⡾⠀⣸⠇⠀⠀⠀⠀⠀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠳⣤⣿⠀⠀⠀⠀⢰⡇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⡟⠑⠢⠶⢖⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢸⡇⠀⠀⠀⣸⠇⣸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣷⡀⣶⣼⡓⠒
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠀⣾⡇⠀⠀⢠⡿⠀⡿⠉⠲⡀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣠⡼⠿⠁⠉⠁
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⠃⠀⠀⣼⠃⢸⡇⠀⠀⠱⣄⠀⢠⡤⣿⣦⢶⡞⠉⢙⣤⠀⣶⣦⠿⡶
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⡖⠀⠀⠀⢀⡞⠀⢸⣿⠀⠀⢰⡏⠀⣼⠀⠀⠀⠀⢈⣠⣼⠻⡟⠻⣮⠷⠒⠚⠛⠛⢯⠙⠁
⠀⣠⠟⠛⠓⢦⡀⠀⠀⢀⠞⣿⠁⠀⠀⣀⢸⣇⣀⣼⣿⣀⡀⡿⠀⢠⠇⠀⢀⡤⠖⠹⡟⡟⣧⠙⢦⣸⣶⡶⠖⠶⢦⣸⡆
⣰⠃⠀⠀⠀⠀⣹⣦⡴⠋⢸⡇⠀⠀⢀⣤⡾⠛⠉⣿⠏⢻⡙⠳⣦⣯⣴⣞⣯⣤⣤⣦⠼⢦⣈⣥⡾⠋⠁⠉⠳⣄⠀⡿⠇
⡏⠀⠀⠀⠀⠀⢹⣆⣀⣀⣘⣁⣤⡴⠟⠉⠀⠀⠀⣿⠀⢘⣧⡶⣻⣿⣅⣤⣤⠝⠉⠀⠀⠀⠀⢻⣆⢀⠀⠀⠀⠘⣷⠇
⠙⣄⠀⠀⠀⠀⠀⢿⣏⠀⠉⠉⠀⠀⠀⣀⡤⢤⣀⣿⢞⣫⣿⣾⣿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⢦⡵⠾⡞⠋
⠀⠈⢳⡀⠀⠀⠀⠈⢻⣆⣀⡀⠀⠀⣰⣿⣿⣿⢽⣿⣿⣿⡟⠋⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⡇
⠀⠀⣰⠟⢦⣄⡀⠀⠀⠙⠛⣛⠦⣀⣿⠟⣫⣿⣿⣟⢉⣾⠁⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⢸⡇
⠀⢀⡟⠀⠀⠉⠛⠷⣦⡀⠀⢿⣷⣬⣿⣄⣛⣽⣿⣿⢸⣯⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⡀⡀⢩⡼⠋⠻⠽⢿⣾⣿⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⢧⣙⡏⠀⠀⠀⠀⣿⣇⣿⣼⡿⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⣼⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⣿⠉⠀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠘⡇
⢻⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠟⣿⣿⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢱
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠘⢠⠐⢚⢻⣛⡷⣄⣀⠀⠀⠀⢀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⣻⡟⡓⠂⡄⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⡏⠒⠡⢮⣹⣿⣞⣀⣱⠍⢢⢀⠎⠀⠟⠉⣷⢦⣄⠀⠀⠀⠀⠀⠀⣀⣤⠴⣶⣚⣿⡍⢹⣊⣁⣻⣿⣟⡱⠬⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣟⠀⠀⠀⠀⢀⣽⠈⠉⠁⠉⢡⠂⠀⠀⠀⠀⠁⠠⠏⢱⠆⠀⠀⠀⠸⡁⠛⠀⢿⣷⠠⣾⡛⡃⠉⠈⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡇⠀⠀⠀⣠⡾⠋⠀⠀⠀⢠⣃⣴⠄⢀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣡⡀⠀⣻⣿⠀⣿⣧⢱⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢽⠇⢀⡴⣾⠋⠀⠀⠀⠀⠀⠈⠛⢝⡲⢿⡀⣤⠀⣎⠤⠷⢿⡽⢾⣽⠾⠦⡨⢦⡈⢹⣶⣾⣷⣤⡆⠀⠀⠀⠑⣷⢦⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣏⣼⡀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⢷⡴⠁⠀⠀⢸⠃⠀⡇⠀⠀⢡⡼⠛⠍⣷⣿⠈⠁⠀⠀⠀⠀⢀⣈⣻⢑⢟⡣⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣜⣫⣼⣳⣤⣄⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢻⣿⣿⣸⠾⠷⢕⣶⠶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⢸⡆⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⢀⣠⡾⠟⠛⠉⠉⠉⠉⠙⠻⢷⣦⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣻⠉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⢠⡿⣾⠇⠀⠀⢸⡇⠨⠀⠸⠃⠀⠸⠃⠀⠸⠇⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⢻⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣟⣿⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡗⠛⣿⠚⢻⡗⠚⣿⠂⡟⢷⠆
⠀⠀⢀⣀⠀⡶⡿⠿⣿⣀⡴⢣⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⠤⢄⡀⠀⠀⠀⠀⠀⡆⡷⡇
⠀⠀⡇⣈⠙⣿⠛⠒⢧⠀⢠⠃⢸⡇⢠⣀⣸⣇⣀⣸⣇⣀⣸⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣿⣿⡇⠀⢹⣤⣼⣧⣤⣿⠄⣿⡇
⠀⠀⡇⠀⠀⠈⠉⠙⠋⡀⣾⠀⢸⡇⠈⠉⠉⠉⠉⢹⠋⠉⠉⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⠝⠛⠻⣢⢸⠀⠀⠀⢸⣽⠀⣿⡇
⠀⡜⠁⠀⢀⣤⣀⣀⢀⡇⠸⡀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠀⠀⢀⢧⠀⢣⠀⠀⢸⣻⠀⣿⡇
⡈⠀⠀⠀⠸⠦⣤⣼⡟⠀⣀⢣⣼⣇⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⣼⠏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠁⠀⠀⠱⡀⣸⢿⠀⣿⣇
⡇⠀⠀⠀⢤⣤⣀⡾⠠⣆⣛⢹⠋⠻⡆⠀⠀⠀⣸⢻⠻⣆⠀⣴⠏⠀⠀⠈⠙⠿⠷⣶⣶⣶⣶⠶⠿⠛⢹⠀⠀⣤⠀⢤⣀⡀⠰⠀⠀⣥⠟⠙⣿⠉⠹⣆
⠘⢦⡀⠀⠀⠀⠉⠀⠰⠆⣩⠏⠀⠀⠹⢄⠀⡼⠇⠀⠀⢹⡎⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⣠⡟⢀⠼⠉⡧⠀⠹⢆
⠀⠀⠈⠓⠢⣤⢤⠤⠖⠊⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⣀⣀⣠⡄⠊⠉⠁⠀⠉⠀⠉⠀⠀⠁
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠀⠀⢀⡀⠀⠀⠈⠀⡄⢠⠘⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠔⠀⠀⠀⠀⠠⠀⠀⠄⠂⠁⠀⠈⠁⠀⠀⠀⠀⡆⢂⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇
⡼⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠱⠴⠃⠀⠀⠀⠀⠰⠀⠊⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠁⠳
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠘⠶⣄⡀⠀⠀⠒⠂⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠘⢀⠀⢠
⠀⠀⠀⠀⠀⠉⢠⠆⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠠⠀⠀⠀⠁⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⡐⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠃⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠃
⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠻⠃⠀⠀⠀⠀⠀⢠⡀⠓⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⢀⣄⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠉⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡰⢴⠀⠀⠀⠀⠀⠀⣄⢀⠀⡄⠀⠃
⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠁⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠀⠹⣌⠂
⠀⠀⠀⠀⠀⠮⢈⡙⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡉
⡀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠈
⠄⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢒⡀⠠⠀⠠⠀⠀⠀⠇⢸⠀⠀⠀⠀⠠⣀⠀⠀⠀⠐⠀⠁⠐⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠤⠀⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠉

⢠⠶⡈⠁⠢⡀
⡸⠒⠘⡄⠀⢸⠄⣠⠤⡤
⠉⠲⠠⠧⠴⠋⠈⣩⣿⣜⠚
⡀⠂⢴⡀⠆⢀⠻⣿⣿⣿⣷⣤⡀
⠐⠠⡋⠐⡗⠉⠢⠽⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠉⠊⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢿⣿⣿⣿⣿⣷⣤⡴⠖⠛⠋⠉⠉⠉⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢿⡷⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠙⢾⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠻⣿⣳⣝⢿⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣟⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⣝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣝⣿⠿⡛⠢⠀⠀⠀⠀⠈⠳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⡉⠢⡈⠢⡁⢠⣶⡐⠒⢦⡈⠳⣦⣀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠶⠛⢋⠉⡇⢻⣆⠀⠉⠛⠛⠛⠛⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⣀⣠⣄⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⡶⠉⠀⣈⣤⡴⢇⠀⠹⣷⣀⠀⠾⣷⠄⠀⠀⠉⠻⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⢸⠋⠀⠈⠙⠶⣄⠀⠀⠘⡇⠘⠁⠀⠇⣰⠞⠉⢄⠀⢀⠑⢄⠈⠙⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠶⠶⠤⣄⠘⢧⡀⠀⠹⣆⠀⠀⠘⠁⠀⠑⢄⠀⢄⠁⠤⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⣄⠹⡄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠱⣢⡭⠖⠉⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠞⠀⠸⣇⡼⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠙⢦⡘⢦⡀⠀⠀⠀⠀⣠⠞⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠉⠙⠲⣄⠀⢳⠀⠙⣆⠀⣠⠞⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣷⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢧⡤⠾⢿⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠳⣄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠛⣧⠀⢸⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⠻⢶⣼⣧⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠁⠀⣀⡼⢧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣤⡤⠶⠛⠉
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⣠⣦⣴⡄
⠀⠀⠀⢀⡀⢀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⡯⢘⣹⣿⠀⠀⠰⣷⠐⢒⠤⣤⡀
⠀⠀⡐⠏⢠⣧⣿⣿⣆⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⡀⠀⠀⠀⠀⠀⠈⣿⠇⣽⣿⡅⠀⣴⠆⣾⣿⣿⠉⣧
⠀⣰⣡⠴⠚⣿⣿⣿⣿⣷⣦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⢿⡟⣳⡼⡟⠦⢼⣿⡏⠀⣿
⠀⠙⢿⣦⣿⣿⡟⢿⣿⣿⣿⣿⠄⠈⠀⠐⠫⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢮⣿⡿⠋⡇⠈⠐⢸⢿⠃⠀⣿
⠀⠀⠀⠹⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⡤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⣦⠀⠀⠀⠀⡈⣼⠾⣹⠄⠀⢸⠁⣰⠋⠘⠀⠀⢏
⠀⠀⠀⢀⡹⣿⣮⣿⣿⣿⡏⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡭⠍⠉⠿⠁⡱⢆⠉⢉⡿⠛⠈⠀⠐⣲⣾⣆⣷⣤⣷⣤⣆⣼⡦
⠀⠀⠀⠈⠀⠀⢙⣿⣿⡟⣏⠀⠀⡶⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⡗⠛⢿⣷⣮⡄⣏⡀⣽⡿⣿⣿⠶⡾⡿⣿⣿⠇⢀⣴⣿⣷⡄⡞
⠀⠀⠀⠀⠀⠀⠈⠿⢿⢿⣿⡆⠀⢺⣾⣦⡛⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠈⢿⣿⠃⢿⣷⣶⣶⣿⠏⠀⠀⢰⣿⣿⠖⠋⢻⣟⣹⣿⡻⠗⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⡆⠀⢙⣿⣿⣦⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⡇⠀⠈⢿⣿⣿⡟⠀⠀⠀⣿⡟⡟⣈⣴⣿⣿⣿⣿⣿⠀⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠹⣷⡿⠻⠏⢙⣿⡇⠀⠀⠀⠀⢀⢻⠤⠤⣤⣀⡆⠀⠀⠀⢈⡿⠀⠀⢀⣼⡟⠀⠘⠙⠁⣿⣿⡏⣯⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣾⠇⡀⠈⠁⠀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠐⠀⠀⢻⡟⠁⠀⠀⠀⣾⠴⠄⠠⢿⣿⡇⠀⠠⠀⢰⠈⣿⢱⣾⠆
⠀⠀⠀⡄⠐⢻⢿⡏⠛⡃⣠⡤⢶⣶⠺⢿⣿⣿⢀⣀⣠⣤⡄⢠⣇⠀⠀⠈⡆⠀⠀⠀⠀⣧⠀⠀⠠⠟⣸⡏⣿⣁⣀⣌⣤⣽⣼⣧⣤⣀⡀
⠀⢀⠞⠀⠀⠈⠀⠃⣸⣿⣷⣄⣩⣴⣾⣿⣿⣿⡽⠿⠿⣿⣾⣿⢾⣳⡔⢄⣹⡄⠀⠀⠀⡏⠁⠄⢁⣠⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠐⠒⠓⣦⣴⣶⣾⣿⠋⢏⢧⢀⡹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣤⣤⣤⡷⢊⣠⡞⡿⢧⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⢀⣴⣶⣾⣿⣿⡿⡿⠁⠀⠈⠀⡎⠁⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣼⣿⣶⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣦⣽⣦⣝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠤⢤⠀⠀⠘⠛⠉⠠⢀⣠⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠃⠀⠀⠀⠀⠀⢐⡄⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⢀⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠆⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡅⢰⡅
⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⠻⠊⣾⡥
⠀⠀⠀⠀⠀⠸⠐⠂⣀⠀⠀⠀⢠⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⡿⠆
⠀⠀⠀⠀⠀⠰⠀⠅⢸⡆⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣰⠀⢠⣟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⣷⠀⠀⠀⠠⠐⣎⠡⠐⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠅⠉⠋⢸⣏
⠀⠀⠀⠀⠀⣸⠤⠜⠒⠉⠀⠀⠀⠀⠀⠡⣁⠤⠔⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⢧⠅⣾⠀⠀⢀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠘⡱⠇⢠⡀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡄⡀⠀⣅⠀⠐⠀⠀⠀⡀⠀⠐⢄
⠀⠀⠀⠀⠈⠄⠀⣤⣴⠈⠁⠀⠀⠐⠈⠁⠸⢰⠁⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣀⢆⢠⣈⡁⢠⠈⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣹⠉⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡈⢙⠀⢠⣍⡁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠄⠀⠀⠀⣨⠠⠤⠁⡤⠐⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠟⠧⠄⠀⠠⡇⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠁⠈⡅⠤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠠⠀⠐⠱⠂⠀⠀⠀⠀⠀⠀⠀⡬⣾⡽⡴⠉⢢⣻⠇⠉⣦⠀⠄⠀⠉⠀⡌
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠞⠵⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣹⡇⠻⠤⢊⣍⠀⠀⡾⡐⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠊⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠖⠢⠨⠉⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠾⢸⣄⠄⣥⡴⠂⢲⡀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠰⠠⡀⠀⠁⠀⢀⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠲⠂⢇⣀⢸⠀⢲⡠⠞⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣃⠰⠇⠒⠈⠁⠀⠁⠀⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤⠀⠈⡅⠈⡔⠁⠙⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢄⠀⠀⠀⢀⠐⠀⠀⡆⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠉⠀⠀⣅⠀⠥⣀⣰⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⣀⠈⠀⠀⠁⠀⡃⠄⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⢸⡀⠈⠁⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠐

⡿⠉⠙⡟⢛⠛⠟⠟⠻⣟⠻⠟⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣻⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠿⠟⠉⠀⢠⣶⢶⣾⣟⣏⣻⣻⣻⣿⢷⣶⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢘⣿⠋⣿⣟⣿⣿⢹⢿⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠹⣟⠠⡿⣟⢻⠿⣄⣸⠃⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣿⠆⣾⡟⣿⣿⡁⠁⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢽⣾⣿⡿⣿⣦⠃⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⢨⣭⣿⣿⣭⡅⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣇⣰⣿⡇⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢸⣷⣿⣿⣿⣿⠋⣹⡇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠇⣿⢸⣿⣿⣿⣿⣿⠀⣿⡇⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣴⡎⢁⣀⡿⢸⣿⣿⣽⣾⣿⢀⣿⡇⢸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠣⠝⠛⡿⠾⢷⣾⣿⣻⣾⣿⣽⣿⣿⣿⣈⣽⣧⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⠥⠤⣀⠭⢡⣿⣿⣀⣉⣩⢻⢛⣻⣟⣯⣏⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣙⣿⣿⣵⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠘⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢠⠞⠷⢤⣤⣤⣤⣤⣼⣿⣿⡿⢿⣿⣿⣿⣿⢟⢫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⣒⣚⢛⣛⡛⠛⠃⣿⠉⣰⣿⡿⢟⣯⣾⠙⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠒⠐⠒⠂⠀⠿⠾⠿⠿⠲⠿⠿⠹⠀⠚⠃

⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⡀⠀⠀⠀⠄⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠤⣤⣄
⠀⠀⠀⣀⣴⡇⠀⠀⠀⣦⠉⠙⣿⣿⣿⡶⣶⣀⣀⠀⠠⢀⡿⠇⠀⢀⠀⣀⣉⣉⠉⠉⠉⠉⠉⠉⣉⣀⣀⣈⣱⠀⠀⠀⢰⣿⣿⡆
⠀⠀⢀⣿⣿⡏⠀⠀⢐⣿⡂⠀⢝⣿⣿⣻⣷⢯⠉⠙⠿⢿⠃⣾⣾⣿⠀⠉⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⣛⠉⠋⢻⣿⡿⠇
⠀⠀⠸⣿⣿⣗⠀⠀⠐⣿⠇⠀⠀⠙⠛⠚⠿⠔⠀⠀⠀⠈⠋⠉⣻⠃⠀⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠶⠚⠛⠉⠛⠻⠿⠋
⠀⢀⣀⣿⣿⣗⠁⠀⠨⣿⣅⡀⠠⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠀⠀⠘⣇⠀⠈⠉⠉⠛⢷⠄⠀⢠⠴⠒⠲⣶⠒⠒⠤⡀
⠀⠸⣿⣿⣿⣇⣀⣁⣨⣿⣿⠇⢠⠖⠒⢲⢒⢀⣆⣰⣾⣶⣶⡉⠁⠘⠙⠀⢿⠀⠀⠀⠀⠀⣼⡀⠀⣂⠀⣀⡂⠀⣀⡂⠀⡀
⠀⠀⢻⢸⣿⣿⣿⣿⣿⡏⢿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⠉⠉⠉⠁⠀⠀⢼⡇⠀⠀⠀⠀⣿⣅⡀⢿⣿⣿⣶⣶⣶⣿⣿⠇
⠀⠀⢠⡀⠻⠿⣿⠿⠟⢀⠄⠠⣴⣶⣶⣶⣿⣷⠀⠀⠀⠀⠀⢠⡄⢀⡴⠀⢸⣿⠀⠀⠀⠀⣿⢧⡁⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠙⠲⢦⡥⡴⠖⠋⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠭⣇⣄⠀⠀⠀⣠⡶⠗⠲⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣀⠐⠀⠈⢹⡆⠆⣿⣷⠀⠀⢰⢻⢥⡏⣾⢿⠃⣸⡟⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⢀⣀⡇⡄⠀⠀⠀⠀⠀⣟⠀⠀⣿⠉⠉⢻⣟⠁⡟⠀⠀⣤⠟⢁⠇⢻⡿⠔⠂⠘⣿⣺⢱⣿⡀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠉⠙⠻⠗⡆⠀⠀⠀⠀⠀⠃⠀⢠⣿⣀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠠⠀⣺⢩⣰⣿⡇⠀⢱⣶⣦⣤⣀⣼⣿⡀
⠀⠘⠶⣦⣤⣤⣤⣿⣿⣶⠾⠃⠀⠀⠀⠀⠈⠁⠀⠸⡇⠀⠀⠀⠀⠘⠆⠀⠀⢻⠀⠀⠁⠈⠹⢠⣽⡿⠁⠀⠸⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡏⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⢤⡀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠒⠀⠈⠀⠀⣀⠤⠛⠈⡀⠄⠊⠁
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⣶⣦⠀⠙⢢⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢤⡀
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠺⠿⠟⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡀⠘⠁⠀⠀⠙⠲⠤⢄⠠⠄
⠀⠀⠀⠘⡆⠀⠀⠀⠒⠀⠀⠀⠀⠐⠉⠁⠈⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣀⣥⣴⢂⡆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢐⣤⣾⡙⣟⠝⠋
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠰⣺⣿⢟⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡤⠤⠤⠤⠄⠤⠄⣀⡀⠀⠀⠀⠀⠠⠀⠀⠔⠀⣘⡯⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠓⠦⢤⣀⣠⠆⠀⠈⠉⠒⠤⠀⠀⠣⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠉⠟⠛⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⡜⠀⠀⠀⠀⠴⢤⠀⠠⣴⡴⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠞⠇⢀⣠⣬⣅⠀⠐⠠⣀⠀⠀⠰⠸⠀⢢⡠⠖⠻⣟⠛⠐⡗⣠⣤⡶⠄⠀⠀⢰⢰⠄
⠀⠀⠀⠀⠀⠀⠀⣧⠏⠁⠀⠀⠭⠒⢢⠘⡣⠐⠚⠐⠒⠢⢥⡬⠥⠤⠤⢬⡇⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠠⠐⠂⠀⠂⠀⠀⠡⣀⣀⣀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⡧⣄⣀⣀⡀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠡⡁⠀⠈⠹⠁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠰⣧
⠀⠀⠀⠀⢀⠈⠀⠒⠏⢄⠈⠠⠀⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⡄⢰⢷⠁⡀⠀⠀⠀⠀⠀⢸⡄⣀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠂⠀⠌⠀⠀⠑⠤⣀⣀⣀⣀⡠⡴⠃⠴⠙⠦⢸⡽⠀⠈⠄⠀⠀⠣⠤⢬⣤⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⣀⣀⣠⡀
⠀⠀⠀⢸⣿⣿⡏⣿⣿⡟⠉⠙⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣶⣦⣦⠀⠀⠀⣿⢹⣿⣿⠛⢻⣿⣿⣤⣤⣤⣤⣤⣦⣶⡄
⠀⠀⠀⢸⣿⣿⣇⣿⣿⣷⣤⣤⣿⣿⡋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⢿⣾⣿⣿⡶⢿⣿⡟⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠈⢿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠁⠀⠀⠀⠀⠀⣠⣴⣶⣤⣀⠀⠀⠀⣀⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢰⠛⠛⠀⠀⢼⣿⣿⣷⣿⣿⡃⠀⢈⣿⣿⣿⣷⢶⠶⠶⠶⠶⠶⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⢿⣿⡀⠀⠾⠀⠾⠀⠀⠸⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠁⠀⠀⠉⠉⠀⢠⡀⢀⣄⠀⠀⠀⢠⣼⣧⡆⠀⠤
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢠⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠀⠀⢿⡯⠸⣯⠀⠀⠀⠈⢹⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢨⡁⠀⡅⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⠀⢠⣴⣾⣷⣶⣄⡀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⣴⣾⣷⣦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠸⠿⠿⠿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⢤⣶⣶⠄⠀⢸⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⢾
⠀⠀⠀⠀⠀⠴⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⡀⠀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡖⠃⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠆⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⢸⢰⣶⢰⡆⣶⣦⡇⠀⠀⠀⠜⠿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠠⢤⠀⣤⢠⣄⡀
⠀⠀⠀⠀⠀⠸⠸⠿⢸⡇⡿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⡎⢇⢵⣴⣀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢻⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠸⣸⣿⣿⣾⣾⣷⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠃⠄⠀⢠⠇⢠⡾⠀⠀⢟⢻⠟⡟⢻⠟⡿⢻⠟⡿⢻⡏⣿⢛⠀⠀⠀⢫⣿⡿⠟⠛⠛⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⢰⡦⠀⣄⠀⢰⣿⣿⣿⣿⠀⠀⠀⠈⠓⣤⣤⣤⠶⠶⠶⠒⠛⠋⠀⣾⣿⣷⣶⣤⣄⣀⡀⠀⠀⣴⣿⡏
⠀⠀⠁⣼⠇⢰⠇⠀⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢏⣈⣹⣿⡿⡟⠟⣷⠀⢿⣿⣆⠀⠀⠠⣶
⠀⠀⠘⠋⠀⣸⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠘⠢⡆⠀⠀⠀⠀⠀⠰⠳⡄⠀⠀⠀⠀⣉⡉⠛⠛⠓⠋⠀⠀⠉⠉⠁⠀⡰⠁
⠀⠀⠀⠀⣠⣷⣄⠀⠉⠉⠙⠛⠛⠻⠃⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⢨⣿⣿⣦⡀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⢦⣄⠀⠀⠀⢀⡤⢴⢀⠠⠀⣀⣠⢤⣼⠁⠀⠀⢸⠃⠈⢿⡇
⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⢀⣼⡿⢷⡀⠐⡘⠆⠓⠋⠃⠋⠩⡁⡃⣤⠀⠃⠀⣾⠀⠀⠘⣷⣴⣾⡗
⠀⠀⢰⣿⣿⣿⣿⣷⡆⠀⢠⠿⣗⣲⣄⠀⠀⠀⠠⡿⡿⠿⠿⠥⠗⠗⠃⠀⠀⠀⡏⠀⠀⠀⢠⣾⠏
⠀⠀⢾⣿⡆⣿⣿⣿⡇⠀⢿⢲⣷⣏⣽⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⢸⡇⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠙⠃⠛⠛⠉⠀⠀⠈⠛⠯⠚⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⣸⢀⣴⣿⡿⠃⠀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⡀⣀⣀⣀⣀⣄⡀⢸⣿⣿⡿⣿⣿⣿⡇⠀⠀⢀⣿⣾⣿⡟⠁⠤⠀⠀⢀⡴⠋
⠀⠀⠀⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⠟⠋⠀⠀⠀⠻⠿⠿⠏⠀⠀⠀⠀⠶⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡪⠛⠉⠁⠀⢰⡁⠀⠀⠀⠂⠲⠤⣤⣀⡀⠀⠀⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠐⠁⠀⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⢤⣀⠀⠀⠀⠉⣦⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣌⡁
⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣀⢀⣀⠀⠀⠰
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠄⠒⠖⠊⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠤⠤⠀⠤⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠶⠂⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢠⠼⠦⠺⠛⠖⡀⠉⠄⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢀⣇⣀⡎⡦⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣎
⠀⠀⠀⠀⠘⠂⠀⠀⠈⠃⡰⠃⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢸⡀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡉⢀⠉⠡
⠀⠀⠀⠀⠸⠦⢤⡤⠤⠟⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⢷⠂⠀⠀⠡⠀⠀⠀⠄⠀⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠑⢄⠀⠀⠀⠀⠀⡠⠃⢀⢃⡌⠡⠘⠀⠀⢣⠀⠀⠀⢀⣠⠴⠦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠈⠉⠁⠀⠂⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⠿⠷⠖⣸⣿⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠻⠿⣻⡖⣻⣿⠿⠿⠤⠝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣹⡿⠛⣽⠏⠀⣐⢲⡎⠡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡿⠛⠁⣴⣠⣿⠀⠠⠉⠉⡁⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⣽⠶⠾⠁⠀⢰⡏⢹⡁⠀⠀⢀⣸⢃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣾⣿⣿⣭⣤⣤⣤⣰⣿⠇⠈⠉⠲⡄⠀⢂⣾⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣰⠟⣿⣁⣼⣷⡄⠙⡈⠉⠉⣿⡋⠰⠶⠴⠤⢀⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠃⠘⢳⡝⠃⣸⠃⣠⠁⠀⠀⠹⡇⠀⠀⡀⠀⠸⣇⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠿⢟⠻⠀⣂⣾⢠⡇⠀⠀⠆⢸⣏⠀⠀⢀⡤⢀⣿⠀⠁⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣃⣴⠶⣏⣿⣧⠏⠀⠉⠀⠀⢀⡿⠂⠚⠫⠀⢀⡛⠈⣇⠀⣿⢽⡄
⠀⠀⠀⠀⠀⠠⢶⣿⣯⣯⡿⠋⠠⠤⠭⠹⢿⠦⡅⠤⠶⠂⠈⢿⠆⠩⠄⠀⠘⠻⠀⡋⣸⡿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⢤⣦
⢀⣤⣰⣷⣦⣤⣀⡉⠛⠳⠦⠦⠤⣤⣄⣀⠀⠀⠈⠓⠀⠆⠊⠀⠀⠀⠀⠀⠀⠀⠑⢀⣿⣁⣿⡀⠀⠀⠀⠀⡀⢀⣀⣀⣠⣤⡄⠒⢷⣄⢹⣿⣶⠶⠶⠿⠿⣿⡇
⠋⠻⣿⠿⡆⠹⠽⠿⣿⢶⣶⣶⣦⣤⣀⣀⠉⠓⠆⣀⠄⠐⠀⠀⡀⠀⠀⢀⣀⣀⣠⣤⢼⣯⣹⠅⠆⣿⠻⣆⣿⣻⡭⠿⠿⠧⡑⠾⡟⣸⡶⠉⠙⠃⠙⠁⠙⠉⠁
⠀⠀⢨⣷⢶⣦⣤⢤⣠⠁⠀⢙⣉⡻⢿⡋⠛⡶⣦⣈⡰⣿⣿⣶⡄⢻⡿⢏⣹⣟⣿⣽⣿⡽⣅⣟⣿⡙⠋⠉⠀⠀⠀⠀⠀⠀⣿⠿⠹⣿⠁
⠀⠀⢸⠙⠛⠎⣩⣛⠻⠶⠦⠸⣿⣶⢄⠻⢦⡀⢢⡈⢧⣨⣟⣻⡇⡸⠿⠟⠛⠛⠉⠉⡇⠸⣯⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣾⠃
⠀⠀⢨⡏⠱⠎⠈⠉⠩⠦⣍⡀⣿⣏⠉⠓⠈⠻⣦⣵⣶⠿⠛⣉⠀⠁⠀⠀⠀⠀⠀⢀⠇⠀⠹⣷⡟⠀⣀⣀⣤⣤⣤⣴⣶⣮⡵⠟⠁
⠀⠀⠰⡷⠆⠀⠀⠀⠀⡀⠀⠀⢺⣿⠀⢀⣈⠀⠀⠲⠍⠋⠐⠂⠐⢆⠀⠀⢀⣀⣤⣤⡿⠶⠶⠿⣿⢿⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⢳⢀⣄⠈⠀⠀⠀⠀⡦⠈⠉⡀⢠⣄⠢⠀⠀⣠⣼⣿⣿⡿⠆⠛⠉⠉⠀⠀⠀⠈⠳⡦⠁
⠀⠀⠀⠸⣷⣮⠧⣄⠀⢀⡶⡦⠀⠀⠁⠀⠀⠁⣀⣶⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢄⡄⠰⢿⣄
⠀⠀⠀⠀⠻⣟⣳⠞⠛⣯⢧⠷⡜⠂⣀⣠⣴⡿⠛⠡⠀⢀⡤⢀⣀⣄⡀⠀⠀⠀⠀⠸⢦⡎⡙
⠀⠀⠀⠀⠀⠈⠙⠷⠿⡶⠶⠾⠿⢯⣿⣿⠏⠄⠁⠠⠖⠻⢟⡿⠟⠉⣟⢻⣦⣤⣄⠀⠀⠈⠁⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠀⠀⠀⠀⠀⠈⠻⡻⣮⣍⣯⡙⣿⣿⠛⠳⠶⣤⣀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠀⠀⠀⢙⠊⣉⠛⡃⢻⡹⣿⢶⣧⣿⢻⠷⢦⣄⡈⠛⢥⡴⢀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⢰⡄⢶⣼⡈⢱⡸⣶⣍⣙⡅⢸⣍⣟⠰⣶⣯⣽⢳⣶⣿⣧⢶⣄⡁⠣⠖⡘⢿⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣁⠐⠈⡙⠇⠹⠎⠝⠟⠉⠈⢭⠌⠛⠣⠽⢯⡼⠓⠿⢿⠷⡿⢿⢆⡀⠁⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠓⠶⠄⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢛⡛⢿⣳⡄⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⣷⠄⠀⠀⢀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⣿⡇⠠⠤⢀⡠⠤⣀⠀⠠⣤⣼⠇⡠⠒⠈⠉⡢⡀⠀⠀⢀⠀⢀⣴⡄⢰⣿⠂⢸⠿⠁⠘⢛⣠⣴⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢀⣾⣿⠃⠀⢀⡀⠀⠈⠐⠈⡑⠒⠒⠁⠈⠀⠀⠀⠀⠜⣆⠐⣿⡇⠈⠟⢂⣈⡩⠤⣴⣶⣾⣿⣿⢾⣿⡿⣿⣻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⡿⠁⠀⠀⣼⠉⠓⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⡿⠤⠔⣒⣊⣭⡭⠶⠞⣛⣻⣭⣽⠷⠟⠛⠛⠫⠿⠺⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⠟⠁⠀⣤⣤⡿⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣭⣴⣶⠾⠟⣛⣉⣥⣴⠶⠟⠛⠋⢩⠦⣀⣀⡀⠤⠔⠒⠒⠉
⠀⠀⠀⠀⠀⢀⡴⣵⣿⡏⠀⠀⠀⠈⠁⠀⠀⣤⠀⠀⠀⠀⣽⣿⣿⣿⣿⣟⠭⠕⠐⢺⡟⠋⠉⠀⣀⠠⠤⠀⣒⣸⣉⠠⠤⠐⠒⠊⣉⡀
⠀⠀⠀⠀⡠⢫⣾⠟⣿⣧⠴⠖⠒⠲⡄⠀⠀⣿⡄⠀⠂⠀⠹⢿⡿⠿⠋⠀⠀⠀⠈⣾⡇⠉⣉⣀⠀⠐⠒⠉⣉⠩⠤⠄⠒⢪⣉⡁⠤⠤
⠀⠀⢀⡜⣱⡿⠁⣠⣯⡶⠛⠻⣷⡄⡿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡉⠀⣿⠛⠛⢶⣭⠧⠤⠄⠒⠂⠉⢹⠨⠤⠔⠒⠈
⠀⢀⡞⣼⡟⢀⣾⠟⣿⡇⠀⠀⢸⣿⠃⠀⠀⠐⠀⠀⠀⠀⠀⣀⣥⣐⣀⣀⣨⣾⡿⡡⠤⠄⣿⠂⣉⡁⠤⠤⠒⠒⠈⠉⠙⠋
⠀⢸⣼⡿⠀⡾⠓⠂⣿⢇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠭⠛⠛⢛⣋⠁⠤⠐⢒⣂⣿
⠀⢸⣿⣇⠂⠓⠉⢁⣿⣦⠾⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠥⠀⠒⠊⠉⠀⠀⢰⣷⣶⣶⣶⡿
⠀⠈⠻⢿⣷⡷⠶⠚⣿⠑⠙⢦⣥⣐⣐⣢⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⣀⢀⡤⠄⠐⣿⠈⠉⠀⠈⠉⠙⠋⠉⠁
⠀⠀⢀⣔⣭⣽⠀⣸⠏
⠀⠀⢺⣿⣿⣥⠞⠋
⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣀⣤⣤⣤⣮⣉⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢻⣿⣿⣿⡛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠈⠛⠁⠉⠙⠻⣾⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢀⠀⠀⠀⢀⣠⠀⠀⠙⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⣤⡤⠀⠀⠸⢿⡦⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠸⠇⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠏⠰⣤⣠⠀⢀⣀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠸⠏⠀⠀⠟⠁⠀⢀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠖⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡀⠀⣀⣤⣾⠿⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⡀⠀⢀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠐⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢻⣦⣀⢿⣧⠀⠀⠀⢸⡿⠀⣰⠗⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⠋⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣽⠟⠃⠉⠶⠄⠀⢸⣧⣴⡏⠀⠀⠀⠀⠀⠀⣀⠈⢡⣤⣤⡀⢀⣄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠐⠦⠀⠀⠀⠀⢀⣿⣿⠁⣠⡤⠀⠀⢠⠀⠀⠀⠈⠿⠏⠉⠃⠀⢤⣄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣤⣿⡿⣿⣷⠉⢡⡞⢁⣠⠄⠀⠈⠁⠀⠀⠀⠀⠠⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠻⣿⣶⡿⠋⠀⠀⠀⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⠉⢀⣤⠀⠀⠲⢶⣦⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠛⠛⠃⠀⠶⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠰⠛⠉⠠⣀⠀⠀⢈⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⣀⠀⠀⣀⠀⠈⠁⠀⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⣄⠀⢰⡦⢀⠘⠿
⠉⢄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠴⠀⢸⣷⠀⠀⣿⣿⠀⠀⢠⣾⠉⠀⠼⠋⠀⠈⠁
⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠚⠿⠋⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠂⣀⢀⣀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⡀⠀⡄⠈⠳⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠘⠃⠀⠁⠀⠛⠀⠀⣸⠇⠀⠛⠂⠀⡋⠀⠸⠆⠀⠁
⠀⠀⠀⠀⠀⢀⡀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢛⠓⡐⠛
⠀⠀⠀⠀⢠⠾⠇⠈⠀⠈⣠⣤⣤⠀⠀⢹⣷⡞⠃⢀⡠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡆⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⣠⠾⡉⢴⡶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠁⠀⠐⠏⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠘⢻⣿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⣠⡌⠛⠟⠐⠒⠀⣄
⠀⣤⣤⣤⣤⣤⠀⠀⣀⡸⠃⣶⡞⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡋⠀⠀⠙⠛⢾⣦⣠⣴⡆
⠀⠀⣄⠀⣠⣤⣀⠈⠿⠇⠀⠻⠇⢀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠇⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠈⠋⠙⠋⠉⠀⢿⣆⠀⠀⠀⠈⠀⠀⠁⠀⠘⠁⠰⠆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠐⠲⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⡀⠀⣝⠁⠀⠀⢴⡶⠲⠶⠀⠰⠀⠈⢶⠄⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠛⠀⠀⠀⠘⠃⢠⣄⠀⠀⠘⠂⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⢀⡀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⠀⠀⠀⠀⠀⣼⣯⢁⣠⣴⠂⢿⠃
⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠁⢠⡀⠀⢴⠆⢠⣤⡼⠧⣤⣀⣀⡤⠿⠷⠀⠚⠂⠈⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡌⠁⢀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠠⣶⠈⢠⠄⢀⠀⠴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢀⣴⣦⠶⢄⣀⠀⠀⠀⢦⣴⣧⠀⢠⠈⠁
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠶⠿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠛⢿⠟
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄

⣌⠙⡾⣿⣿⣿⣦⠀⠀⠈⠓⠲⠄⢡⣶⣟⠇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⣴⡿⣛⢻⣿⣮⣿⡿⠀⠀⠘⢆⡴⢟⡐
⠼⣧⢷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠈⠳⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢘⣿⣿⣯⣾⠿⠛⠋⠁⠀⠀⠀⠈⣧⣾⣿
⣚⣭⡿⠟⠁⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠖⠋⠈⠉⠉⠀⠀⢠⣀⠀⠀⣠⠀⠀⠘⢯⣌
⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⡜⠁⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⣯⠀⠀⠀⠀⠈
⠀⢀⣀⣤⣴⣶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣤⠖⠀⠀⢼⣿⠅⠀⠀⠀⠀⠀⣠⣴⣶⣶⡄⠀⠀⠀⣼⡇⠀⠀⢹⣧
⣾⣿⣟⣛⣩⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠰⡟⠓⠊⠉⣇⠀⠀⢸⣿⣧⣿⣿⣼⣿⡆
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣴⣦⣾⡁⠀⠀⠀⠀⣰⣷⡟⠉⠀⠀⠀⠀⠈⠳⠀⢀⣘⣦⠀⠈⠻⢿⣿⣿⠿⠟
⠉⠉⠉⠉⠀⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⠀⠒⠟⢿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣶⣤⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⡾⢛⡯⣉⣻⣦⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⠤⢶⣶⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⢳⣯⡐⢫⣿⣟⢻⢄⡀⠀⠀⠈⢷⠀⠀⠀⠸⡄⠈⢻⣿⣿⣿⣿
⣿⣿⠟⠀⠀⠀⠀⢿⣿⡟⠻⣿⣿⣿⣿⠃⠀⠀⣴⣷⣿⣿⣿⣻⡈⠲⣤⡍⢥⡿⠀⠙⠀⠀⠀⠈⣷⠀⠀⠀⠱⡀⠘⢿⣿⣿⣿
⣿⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⠝⠾⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣼⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠶⣿⡦
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⢀⣴⣾⣿⡆⠀⠀⠀⣰⣦⠶⠋⠁⠀⢠⠞⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⣿⣶⣄⣴⣾⣿⣿⢟⣁⣄⡀⠀⠀⠀⣾⣿⣿⣿⣧⡀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠙⠿⢷
⡿⣟⣽⣝⣿⣿⣯⣄⡅⠉⠀⠀⠀⠈⠻⣿⣯⣽⣻⢿⣦⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣦⡿⢿⣿⡷⡀⠀⠀⠀⠀⢀⣠⣬
⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⡞⢡⡴⠛⣋⢣⢹⡇⠀⢼⣟⣿⣿⣿⣷⠄⠀⠀⠀⠀⠻⣿⣌⢻⣿⣷⡀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⡀⡄⠀⠀⠀⠀⣇⡜⢨⣶⣿⡋⣼⠃⠀⠈⠛⠛⠛⠛⠁⠀⠀⢀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⡀⢿⠿
⠿⣿⣿⣿⡿⢏⠀⠈⠉⡗⡄⠀⠀⠀⠈⠻⢮⣭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠘⠷⢄⡀⠀⠀⠈⠙⠉⠀⠀⠀⠈⠁⠐
⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠘⢻⡅⠀⠀⠀⠙⠲⣄⡀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢻⡗⠒⢲⣟⠀⠀⠀⣧⠀⠀⠀⣀⠀⢠⣽⠿⠃⠈⠒⠲⣤
⣿⣿⣿⣿⡆⠀⠀⠚⠿⠋⠀⠀⠀⠀⠈⢳⣦⣄⠀⠀⠀⢠⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉⠓⢦⣀⣴⣸⡿⠀⠀⢠
⠛⠿⠛⠛⠀⠀⠀⠀⠀⢠⣾⢿⡿⣆⠀⠀⠛⠓⠀⠀⢠⣿⡇⣀⣀⣀⢸⣿⡄⠀⠀⠰⣿⡯⢀⣤⣶⣦⡀⠀⠛⠿⠛⠁
⣢⣄⣠⣤⣤⣀⣀⣀⣀⣿⣃⣉⣠⣈⣲⣄⣀⣀⣀⣀⣸⣿⣷⣿⣿⣿⣼⣿⣇⣀⣀⣀⣁⣠⣿⣿⣟⣿⣿⣆⣀⣀⣀⣀⣀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⡀⠄
⠀⠀⠀⠃⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀
⠀⠠⣦⠴⠒⠀⠤⠄⠀⠀⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠇⢠⠔⠂
⢠⡾⠛⢲⡄⣀⠀⠀⢀⠀⠀⡿⠀⡀⠠⠖⠄⠀⠀⠀⠀⡀⠀⡀⠀⡇⠘⠄⠀⠀⠀⠀⠀⠈⣒⣿⡄⢺⡀⠘⠁
⢸⣧⡀⡄⠉⠻⠃⠀⠒⠂⢀⡀⣢⣵⢤⠀⢀⠀⠀⠀⠘⠓⣾⠋⠇⣿⣠⣎⠀⠀⢀⠀⠼⢣⠿⣏⢁⠸⢃⡄
⢸⡿⠿⠶⠀⠀⢂⣤⣦⡉⠈⣛⣽⡟⢾⣿⡟⠀⣤⡀⣤⠀⢺⡄⢸⣿⣿⣿⠀⠎⠙⠻⠆⠈⠀⢹⡸⡀⣿⣧
⢸⣾⣿⡷⡿⡶⣶⣶⢐⡙⠂⠙⠙⠃⠚⠻⠙⠂⠀⠀⡿⡇⢈⣿⣤⣽⡧⣶⡀⠀⠀⢀⣿⣿⡀⢸⡤⠸⡷⡶⠦
⢸⣿⣿⣧⣦⣼⣿⣿⣿⣧⣵⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⡏⣿⣿⣷⣿⡇⠀⠀⢸⣿⣷⡇⠀⢠⠀⢀⣧⣄
⠿⢿⣿⣿⣿⣿⡉⠛⠟⠃⠁⠀⠀⠀⠙⠀⠀⠀⠀⠸⢿⡿⣿⡷⠸⢧⡽⢸⡁⠀⠀⠘⠛⠿⢿⣶⣿⠀⠈⠉⠉
⠀⠀⠉⠉⠉⢀⣰⠀⢤⡤⠇⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡀⣿⠁⣾⢀⡤⢦⠀⠀⠀⢠⣀⠀⢂⢹⠆⠀⠸⣶⣶
⠀⡴⠐⠀⠀⠀⣟⠀⢸⡃⠀⢠⣴⡆⢽⡾⣄⠀⠀⠀⠀⢸⡇⣟⠃⣸⡇⣿⠀⠀⠀⢘⣿⠀⢸⣆⡇⠀⠀⡏⠛
⠀⣿⣷⡖⠀⠐⠛⠀⠈⠓⠀⢸⣿⣧⠈⠁⠀⠀⠀⠀⠀⠸⠷⠛⠆⠀⠀⠈⠀⠀⠀⠋⠉⠀⠘⢿⣰⡀⣰⣧⣀
⠀⢻⣼⣜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠋⠛⠋
⣶⣾⣿⣿⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶

⠈⣀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠄⠀⢀⣤⢀⠉⠀⠀⠀⠀⠀⠀⠀⠸⣧⣥⣀⣤⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠉⠉⠁
⠷⣾⢠⠆⣠⡶⠶⠶⣤⠀⠀⠂⡤⠀⠀⠀⠀⠀⠀⣢⣤⠀⢀⡀⡠⠄⢀⠉⠈⠉⠛⣮⣤⠀⠀⠀⠀⠀⢀⣠⢾⠷⣾⡰⠆⣠⡶⠶⠶⣤⠠
⠋⠈⠉⢰⢿⠀⢀⠀⠘⡇⢀⣤⣧⠀⠀⠀⠉⠄⢠⠏⠙⠀⢩⡀⠀⠀⢸⣆⠀⠀⠀⠀⢀⣠⠤⠶⠿⠞⠒⠂⠞⠉⠈⠉⢈⣟⠀⢀⠀⠘⡇
⠀⠀⠀⠀⠻⣦⣤⣤⡾⠃⠐⠎⠀⡑⠦⠤⢤⠖⢟⣲⣶⠀⠈⢧⡀⠀⠈⠹⣧⠀⠀⢣⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⡾⠃
⡶⠶⠤⢦⠀⠀⡀⠀⠀⠂⢄⣀⡀⠀⡈⠁⠂⠅⠀⣙⡏⠀⠀⠘⣿⡄⠀⠀⠘⣧⡀⠀⡆⠀⠀⢤⡴⠦⠿⠶⢶⡶⠦⡤⢦⠀⠀⡀⠀⠀⠒
⠛⠲⢦⡀⠀⡴⠃⠀⠀⠀⠫⣄⣈⡻⠻⢄⡀⠀⠀⠈⠀⠀⠄⠀⢸⡽⣆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⡀⠀⠼⠁
⠀⠀⠀⠉⠠⢤⠀⠀⢲⡀⠀⠀⠹⡗⠆⢢⣎⣹⠔⠠⠀⠀⠀⠀⠘⢻⡿⣦⠀⠀⠈⢿⣄⠀⠀⠀⠀⠂⠀⠛⡄⠀⠀⠀⠉⠠⢤⠀⠀⠦
⠀⢠⣤⢤⣠⣠⣤⡀⠀⠑⠀⡀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⠃⠀⠘⠃⠈⣿⡗⠀⠀⠀⠀⠀⠀⡇⠀⢠⡤⣤⣤⣠⣤⡀⠀⠃
⠂⢢⠠⢸⡿⠥⠤⢥⠤⣾⡍⠏⠉⠀⠀⠀⠠⡄⠀⠄⠀⢀⡠⠔⠒⠆⠤⠀⢰⡀⠀⢀⠀⣿⣿⣀⠀⡀⠀⢠⡷⠂⢢⠠⢸⡿⠥⢄⢧⠤⣾
⠦⣤⠒⠀⠓⠖⠨⠛⡓⢿⠁⡃⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡄⠐⠆⠃⠘⠂⠀⠁⠀⠸⠀⠐⠋⠁⠠⠁⠀⠘⡷⠦⣤⠒⠐⠓⠖⠨⠚⡓⠿
⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀⣀⣿⡀⠀⡀⢸⡄⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡧⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀
⠈⠣⡀⠀⣀⡴⡟⠱⠖⠯⠐⠢⣱⠀⠀⠈⡇⠀⠠⣿⠀⠀⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⡈⠁⠘⠣⡀⠀⣀⡔⡟⠱⠒⠯
⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠤⠀⠀⠀⡀⠀⢻⠀⠀⢹⠄⠀⠀⠀⠰⠶⠇⢹⣷⡚⠁⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠
⠈⠳⣄⠀⠀⠂⠀⠒⠈⠀⠀⢶⠀⠀⠀⠀⢸⣄⠀⢸⡇⠀⣾⡦⠀⠈⠀⠈⠈⠂⠀⡠⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠂⠀⠒⠈
⠚⠓⠺⠶⣦⣤⣄⣀⡀⠀⠀⠰⣧⡀⠀⠀⠘⠇⠀⢸⣷⠀⠈⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⡀⠀⠀⠀⠙⠛⠓⠺⠶⣦⣤⣄⣀⡀
⢀⠀⠀⠀⠈⠦⣄⡉⠓⠀⢠⠀⢻⠅⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠢⠤⡈⡀⠀⠀⠀⠒⠒⠂⢁⣀⠀⠀⠀⠰⠀⠀⠀⠈⠦⣄⠉⠓
⠐⠆⣀⡀⢀⠠⠈⠳⡀⠰⠋⠀⠈⣨⢧⡄⠀⠐⠋⠐⣿⣄⠀⠁⢠⢶⣦⣤⣄⡈⠁⠐⠂⢌⠀⠉⠁⠀⠀⠀⠀⠐⢆⣀⡀⠀⠠⠈⠳⠀⠰
⠀⡸⠻⠏⠍⠩⣹⠃⠈⠳⠀⠀⠀⠹⣼⣟⣠⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠏⠍⠉⣹⠃⠈⠣
⠀⣿⣿⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠏⠤⠀⠀⠄⠀⢾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠀⠀⠐⠀⠀⠀⢀⠀⡿⣿⣾⣷⣶⡶
⢰⡿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠚⠁⠃⣠⠂⠀⢀⠃⠀⢠⡀⡃⠀⠀⠀⠀⠔⠀⠀⠀⢼⢰⡿⡿⣿⣿⣿⡇
⠺⠛⠛⠻⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠀⢰⡶⠞⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠛⠛⠻⠛⢛⠅
⣀⣢⠀⡀⠀⣀⣀⣀⠀⠀⠋⡀⢀⠐⠋⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠛⠶⠻⠶⣦⣠⠀⠀⠃⠀⠀⠀⠀⢀⣀⣀⣢⢀⡀⠀⣀⣀⣀
⡭⠿⠾⢁⣾⠋⠉⠉⠻⡄⠀⠀⡏⠈⠀⠀⠤⠀⠀⡾⠿⠀⡔⠒⠈⠁⢰⡀⠀⠀⠀⠙⠛⠀⠀⣀⣤⣠⢰⡚⣽⠭⠻⠮⠡⡾⠋⠉⠉⢻⡌
⠀⠀⠀⠈⣽⡀⠰⠀⣠⡇⢐⡿⠋⢦⡀⠀⠀⣉⣼⢁⣀⠀⠸⡆⠀⠀⠘⢿⡄⠀⠀⡔⠐⠚⠉⢩⡉⠉⠀⠀⠀⠀⠀⠀⠰⣷⡀⠰⠀⣠⠇
⣀⣀⠀⡀⠈⠛⠛⠛⠋⣀⠀⠀⠀⠀⠩⠉⣙⠁⠘⢺⡿⠀⠀⢸⣦⠀⠀⠀⢻⣄⠀⠘⡄⠀⠀⠀⣈⣓⣤⣀⣀⣀⣀⢀⡀⠈⠛⠛⠛⠉⣀
⢯⣉⡉⠙⠀⢠⠆⠀⠀⠀⡴⠒⠢⣄⣦⠀⠀⠀⠐⠲⠂⠀⠀⠀⢻⢧⡀⠀⠀⢻⣆⠀⠃⠀⠀⠙⠋⠉⠉⠉⠙⢯⣉⡉⠙⠀⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢄⢲⠆⠰⣶⢦⡆⡄⠀⠀⠀⠀⠀⠀⠀⢰⠶⡆⣴⢶⡄⡶⢦⢰⡶⠆⣰⢶⡄
⠀⠀⠀⠀⢀⠀⠀⠀⡹⢁⠀⠘⢷⣿⠆⠀⠀⠀⠀⠀⠀⠲⠿⠈⠈⠀⠀⡄⠀⠀⠀⠃⠜⠀⠀⠀⠀⢀⠀⢸⢶⡇⣿⣸⠇⣧⡼⢸⣏⡁⢼⢘⡇⢀
⠀⠀⠀⠀⢀⠨⠃⠃⢛⠈⠐⠁⠊⠘⠃⠀⠀⠀⠀⠤⣀⡀⠀⠀⠠⣤⣴⣷⣤⡴⠂⠀⢀⣀⠠⠄⠀⣾⡀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢀⡧
⠀⠀⢰⣦⠀⠀⠒⠲⠆⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣽⣶⣬⣾⣴⠞⠋⠁⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⡀⠀⠀⢠⠛⠛⠛⠛⠛⠛⠁
⠀⢰⢸⡶⠀⠰⠀⠀⢢⠂⠀⠂⠀⡄⣧⡇⠀⠀⠀⠀⠀⠀⠀⣀⠁⠉⠘⠏⠘⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠘
⠀⠘⢺⡁⠀⠀⣤⣶⣯⣷⣦⡄⠀⠣⡏⠀⠀⠀⠀⢀⣤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓
⠀⠀⠈⠁⠠⠾⢿⣿⣿⣿⣿⠿⠦⠀⠁⡀⠀⠀⠀⠻⠟⠁⠀⠉⠙⠈⠁⠀⠀⠉⠀⠁⠀⠙⠿⠃⢠⣤⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣓⣀⣐⣐⣀⣀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣤⣿⣿⡇⠀⠀⢀⠀⠀⢐⣀⣀⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⢠⣶⡶⣾⢿⢿⣦⣶⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠈⠉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠶⠶⠤⠂
⠀⠀⢠⣶⣿⣍⣠⡿⠘⢶⣯⣠⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠉⠁⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠓⣶⡐⣠⣶⢚⡀⡀
⠀⠀⣸⣿⣿⣿⣯⡄⠘⠻⠛⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡲⣮⣵⣮⡿⢺⡟
⠀⠸⣿⣽⣿⣿⡏⠁⠀⠀⠀⠄⣹⣿⣭⡗⠀⠀⠀⠀⣠⣀⡀⠀⠀⡀⣀⠀⢠⠒⠻⣁⡄⣄⠀⣤⠀⠀⠀⠀⠀⡀⢠⣇⠙⣿⣿⡃⢺⡀
⠀⠀⢹⣷⣿⢿⣿⡄⢻⣿⣡⣿⢿⣷⣿⠀⠀⠀⠀⢀⣻⣾⣀⣿⣿⣸⣏⢠⡿⣷⣾⡟⣿⣿⣷⡷⠀⠀⠀⠀⣸⢻⣿⡿⣿⣿⢿⣿⣿⣿⣿⠁
⠀⠀⠘⠛⢿⣄⣩⡟⢛⣿⠛⣷⣮⠟⠋⠀⠀⠀⠀⠈⠻⠟⠸⢋⣟⡹⢿⣫⣿⡟⣘⣿⠻⠛⠸⠷⠀⠀⠀⠀⠘⠛⠛⣡⣩⣥⣬⣭⠙⠃⠛
⠀⠀⠀⠀⠘⠛⠛⠷⣾⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠤⠄⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠒⠒⠂⠐⠂⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⠁⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣞⡻⢟⠃⠻⢿⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠑⣦⣔⠊
⠀⣄⠀⠠⣿⡟⢀⣿⣿⣿⡇⠙⠿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠒⠒⠒⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠱⣦
⠀⠈⠛⠛⣿⣿⡿⠷⠶⢶⠿⣟⣛⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢫⡶⠁⠀⢀⡀⠀⠘⢮⡑⡦
⠀⠀⠀⠀⢻⡿⡅⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣾⡂⠀⠞⠛⣿⡟⠻⠆⡀⢾⣦⡄⠀⠀⠀⠀⢠⡿⠋⠀⠈⢶⠾⠷⡖⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠈⢷⣿⡄⠶⠆⣾⣶⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠿⣿⣿⣶⡘⣰⣾⣿⡿⠟⢻⣷⡄⠀⠀⠀⢸⣷⡄⠀⠐⠛⢻⡟⠛⠀⠀⢠⣿⡇
⠀⠀⠀⣀⢄⡈⡛⠁⠀⠀⠛⠃⠀⢠⡂⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠉⢻⣧⣾⠛⠁⠀⠀⠘⣿⠿⠂⠀⠀⢨⢁⠀⣀⠀⡀⠀⠀⠀⢀⡀⢀⣈⡅
⠀⠀⠀⣞⣿⣺⣑⣯⠆⢨⠛⡂⢁⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⢷⢠⢿⡄⡇⢠⡏⡷⣿⢸⢸⢿⡇
⠀⠀⠀⠉⠀⠁⠁⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠈⠀⠀⠁⠀⠈⠁
⣿⢿⠿⠿⣿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣻⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣀
⠀⠀⠀⠘⠀⠀⣠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣛⣻⣭⠁⠀⠀⠀⠀⠀⣄⡔⢋⣽⠳⡄⣹⣿⣷⣄
⠀⠀⠀⣀⣰⣴⣷⣮⠔⠀⠀⠀⠀⠀⠀⠀⠒⢺⠛⣡⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣍⢿⢿⢋⣿⡿⠋
⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠟⠋
⠀⠀⠀⠈⠛⠛⠋

⡀
⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢟⣯⡶⢊⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠟⠛⠛⠛⠛⠃
⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣠⠴⠛⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⣠
⠀⠀⣀⡤⠖⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣦⠈⠆
⠀⠛⠉⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢸⣿⣇⠺⢂⣿⣿⠀⡘
⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋
⠄⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠠⣠⡆⠀⠀⢢⠒⢲⣾⣷⣤⣄⣀⠀⠀⢰⣿⠁⢀⠀⣘⣀⠀⠀⠚⠛⠛⠛⠀⠀⢁⠀⠀⠀⣾⣿⡄
⠀⠀⣸⣿⡇⠀⠀⣻⡂⠐⢿⣿⣿⣾⠍⠙⠻⣿⢲⣶⣿⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⣛⣘⠙⣿⡿⠃
⠀⠀⢻⣿⡇⠀⠀⣿⠇⠀⠀⠉⠉⠛⠁⠀⠀⠈⢁⠹⠃⠀⣧⠀⠤⠤⣠⣀⠀⠀⠈⠋⣉⣉⣉⠛⠋
⠀⣴⣾⣿⡇⠀⠀⣽⣷⡄⣈⡀⢠⠤⠄⢠⣴⣶⡀⠀⠠⠤⠘⡆⠀⠀⠀⢸⡇⠀⠊⠁⠀⠛⠀⠉⠁
⠀⠈⡿⣿⣿⣿⣿⣿⠟⠀⠁⠀⠈⠀⠛⠛⠻⠿⠛⠒⠂⠀⠀⣧⠀⠀⠀⢸⡆⠀⣷⣾⣶⣤⣶⣷⡾
⠀⠀⢄⠙⠿⠿⠿⢁⠄⢠⣶⣶⣶⣶⣆⠀⢀⣀⠀⣤⢀⡤⠀⣿⠀⠀⠀⢸⣷⡁⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠙⢲⡴⠚⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠸⣇⠀⢿⡇⠀⠀⢸⡗⣷⣆⣀⠀⣴⠟⠉⠢⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠉⠛⣿⠿⢿⡿⠛⡆⠀⢀⣼⠀⢸⣿⠀⠀⢹⣯⢣⣿⠃⢸⡏⠀⠀⠀⣿⡆
⠀⠀⠐⠒⢾⠯⠀⠀⠀⠀⠘⠀⢀⣿⠀⠸⡏⠀⠁⠀⢸⠀⠀⢰⡿⠀⠀⢸⣛⣹⣧⠀⢸⣥⣄⣀⣠⣿⠁
⠀⠳⠦⣤⣤⣼⣿⡶⠾⠃⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⠘⠆⠀⠸⠇⠀⠀⠘⠣⣿⠟⠀⠰⢿⣿⢿⣿⡿⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⢶⣿⣿⣿⣷⣀⣠⡇⢸⣶⣶⣶⡄⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⣠⣂⣴⣾⣿⡿⠿⠘⠛⠛⠛⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣬⣾⣿⣽⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣩⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣆⣶⣾⣿⣿⡾⠷⠙⠁⠉
⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⠉⠀⠻⢿⣿⣿⣿⣛⠋
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣇⣀⣀⠀⠀⠀⠀⣠⣤⣤⣀⣠⣤⣤⣤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢻⣿⣿⣿⣿⣽⣷⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣈⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠉
⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣏⣀⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠐⠙⠛⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠇
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡏⣀⣠⣀⣈⣻⡿⠿⢿⣿⣿⠟⠿⠛⠉⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠃⠀⠀⣻⣇⠀⠀⠀⢠⣶⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠔⠚⠛⠀⠀⠀⠀⠈⠁⢠⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠊⠀⠀⠸⣤⣤⣤⣤⣤⣶⣿⣷⣤⡰⠆⠆
⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⡿⠛⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡄⠀⠀⠀⠀⠉⠉⢉⣭⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠠⠄⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢛⡭⠁⠀⢈⣷⠴⢦⣤⣀⣀⣀⣾⣁⢀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠻⠁⣾⣁⣤⡶⠛⠁⠀⠀⠀⠈⠉⣿⠋⠉⠉⠁⠀⠀⣶⣄⠀⠀⠀⢿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠉⠀⠀⠀⣀⣀⣸⡏⠁⠀⠙⢷⣀⡾⢀⡾⠁⣸⠏⠀⠀⠀⠀⠀⢰⡇⠙⡇⠀⢠⢹⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠉⠟⠁⠀⠀⢀⡿⠹⣧⠾⣧⠜⣿⡤⠊⠀⠀⣀⣄⣼⠀⠀⠀⠀⢘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠈⠳⢤⣄⣀⣀⣠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⢠⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡇⠀⠀⢀⣀⡀⣀⡀⣀⣀⠀⣀⣀⢀⣀⠀⠀⣀⠀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⢸⣿⢀⡈⠁⢸⣷⠀⢸⣿⢸⡿⠂⠰⣿⣄⡘⠘⠁⣿⡇⠘⠀⠀⣀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⢸⣿⠉⠃⠀⢸⡿⠀⢸⣿⢸⣷⡄⢠⠈⠻⣿⠀⠀⣿⡇⠀⠀⠘⠿⠂⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠛⠃⠀⠀⠛⠛⠀⠚⠛⠀⠙⠋⠈⠁⠚⠉⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⣨⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢛⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⢶⡿⠷⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣴⣶⠄⣠⡄⠀⣤⠀⢠⣄⣤⡄⠀⣿⠃⠀⡶⣦⣀⢀⡴⠀⣰⡆⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⡾⠁⣩⢉⡿⠀⣼⠋⢠⣿⢻⡟⢀⣼⡇⢀⡜⢰⡟⢀⣼⠃⣠⡿⠁⠀⠀⢠⣾⣿⣿⣿⣶⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠘⠷⠴⠋⠸⠷⠞⠿⠶⠿⠃⠺⠷⠊⢿⡴⠋⠀⠿⠶⠊⠿⢶⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⠀⠀⠀⣀⣤⣄⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⣿⠛⠳⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣴⡿⢻⣿⠇⠀⣴⣿⠏⠀⣠⣾⡇⠀⠀⠀⣾⣡⡿⠃⠀⠀⠉⠀⢻⣿⣿⣟⣛⠛⠛⠿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⣾⡟⢀⡾⣿⡟⢀⣼⣿⡟⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢰⡶⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣡⠋⢰⡿⣡⠏⣼⣿⠁⣤⠀⠀⣤⠀⠀⣰⣶⠀⠀⣴⡄⠀⢀⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⣿⣿⠋⢰⣿⠇⣸⡏⠀⣼⠏⠀⡰⢿⡇⠀⣰⡿⠁⢀⣾⠃⠐⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⡏⠀⣼⡟⠀⣿⣀⣼⣿⣀⠞⡵⢺⣿⠾⣿⣇⡠⢿⣇⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠀⠀⣿⡇⠀⠉⠉⠀⠉⠁⠀⠓⠟⠃⠀⠉⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠶⠒⢋⠉⣿⣷⡞⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠶⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠚⢩⣤⣴⣷⣶⣾⡿⠿⢿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⣰⡖⠶⡒⠢⠀⠲⠖⠒⠒⣶⢲⡖⢲⡶⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⢀⣠⢀⣀⣠⣴⣶⠾⠟⠛⠛⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⠤⠤⢤⡥⠤⡥⠤⠥⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢉⣤⣶⣶⣶⣄⠲⣄⢰⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⣿⡿⢻⣿⣿⣿⠄⢹⡆⠉⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡀⣸⡿⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣷⠜⠻⠿⣿⣿⢟⣱⠟⢱⣿⡄⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠘⠿⠟⠛⠁⠃⠀⠀⠀⠙⠛⠁⠀⠀⠉⠰⠟⠉
⠀⠀⠀⠀⠀⠀⠠⠄⡶⠀⠆⠠⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⡄⠀⠀⠀⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠐⠚⠓⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠉⣉⣀⣁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠾⢶⣿⡿⠿⠷⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⢀⡀⣠⣤⣶⣲⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠳⣤⠀⠀⠀⠀⠀⠀⣿⣾⠀⠈⠉⠈⠁⠛⡏⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠀⠀⠈⠃⠀⠀⠀⠀⠀⢹⠇⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⣤⣤⠀⠀⠀⠀⠀⢸⡀⡄⠀⠀⠀⠀⠀⠰⣿⣿⣧⣼⣿⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣿⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡤⠀⠀⠠⣿⣿⣿⣾⣿⠀⠀⠀⠀⠛⠋⠁⠀⠀⢿⣿⡇⠀⠀⠉⢉⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡀⠀⣠⢻⡏⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⢿⣛⢻⣿⣿⠛⣿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⢠⠈⡸⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢴⣤⣤⣴⠄⠀⠀⠈⠋⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡘⠀⣷⣨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⠀⡏⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢧⣽⠟⢶⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣤⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⠀⢀⠿⣀⣷⣿⡿⠁⠀⠀⠀⠀⢠⡶⠛⠉⠀⠀⣾⢿⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣿⣿⣷⣾⣿⣷⣿⣿⣶⣷⣾⣿⣶⣿⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣷⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⠀⠴⠂⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣛⡛⢛⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠲⠄
⠀⠀⠉⠌⠀⠀⠉⠐⣢⢤⣀⣀⠀⠀⠀⠀⠋⠀⣃⡃⣘⡀⠘⠃⠀⠀⠀⢀⣀⣠⢤⣖⠈⠁⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠐⠌⠛⠃⠛⠛⠙⠿⣷⣦⣤⣤⣴⣿⣿⣿⣷⣤⣤⣤⣶⡿⠟⠛⠛⠃⠙⠋⠔
⠀⢀⠀⠠⠤⠤⠤⠤⣬⣶⣦⣴⣮⣴⢼⣿⣿⣿⣟⠉⢙⣿⣿⣿⣿⢴⣬⣶⣥⣶⣮⡤⠤⠤⠤⠤⠀⢀
⠀⠀⠂⢄⡉⡈⠁⠛⠉⠑⠉⠉⠉⠀⢸⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⠀⠈⠉⠉⠑⠉⠙⠃⠉⣈⣁⠀⠂
⠀⠀⠀⠀⠀⠀⠚⠂⠂⠀⠀⠂⠀⠀⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠇⠀⠀⠂⠀⠀⠊⠚⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣫⠅⢹⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢡⣶⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢁⢀⠀⠀⡉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠶⠇⠢⢴⡿⢿⡷⠸⠶⠶⠶⠶⡆
⠀⠀⠀⠀⣀⡴⠚⢉⣄⣤⣄⠀⠄⠀⠀⢠⣤⣀⡈⠙⠦⣄⡀⠀⠀⠀⠀⠀⢸⠉⠀⠊⠍⠗⠃⠀⠈⠃⠈⠀⠀⠨⠭⠉⠀⠉⡇
⠀⠀⠀⡏⠁⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠙⡆⠀⠀⠀⠀⢸⠀⣴⢦⡴⣦⢶⢰⢰⣀⡤⢶⠆⡶⢦⢠⣠⠀⡇
⠀⠀⠀⡇⠀⣀⡀⢀⣀⠀⡀⢀⡀⢀⢀⣀⡀⢀⣀⠀⡀⠀⠀⡇⠀⠀⠀⠀⢸⠀⣿⣠⢇⡿⢺⡜⠸⠙⠇⠹⠀⡏⢡⠈⡇⠀⡇
⠀⠀⠀⡇⢰⡏⠛⣼⢸⡇⢷⢸⡇⡿⢸⡇⡗⣿⢸⡆⢧⡏⠀⡇⠀⠀⠀⠀⢸⠀⠈⡁⠀⢠⢠⡄⠀⠄⡄⢠⣀⠤⠀⠀⠁⠀⡇
⠀⠀⠀⡇⢸⣇⡤⢻⣼⠇⠘⠇⠸⠁⠸⠧⠗⢻⣼⠇⢸⠀⠀⡇⠀⠀⠀⠀⢸⠈⠄⠀⠀⠛⠋⠋⠲⠀⠙⠘⠛⠖⠀⠘⠠⠎⡇
⠀⠀⠀⡇⢀⡉⠁⠀⠀⢰⠄⣠⢠⡄⢰⠠⡄⠀⠀⠀⢈⡀⠀⡇⠀⠀⠀⠀⢸⠀⢰⡆⢰⠀⢤⡀⢲⠂⡆⢆⠆⣰⡆⢰⠀⠀⡇
⠀⠀⠀⡇⠈⠇⠀⣀⢠⣈⣄⠀⣠⣤⣄⠀⢀⢤⢤⠀⠸⠁⠀⡇⠀⠀⠀⠀⢸⠀⠈⠁⠈⠀⠀⠁⢈⣀⣁⡈⠀⠁⠈⠈⠀⠀⡇
⠀⠀⠀⡇⠀⠘⡄⠀⠁⠁⠀⠀⣿⣿⣿⠀⠀⠁⠀⢀⠁⠀⠀⡇⠀⠀⠀⠀⢸⠈⠃⠀⠀⣠⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠋⡇
⠀⠀⠀⡇⠀⢀⣵⣦⡄⠀⠀⢠⣿⣿⣿⠀⠀⣠⣤⣦⡀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⣀⠙⠿⠛⢷⣾⣿⣿⣦⠀⢀⡀⠀⠀⡇
⠀⠀⠀⡇⠀⠸⣿⣿⡿⠀⠀⣸⣿⣿⣿⣀⠀⢿⣿⣿⠇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢻⡈⣧⡀⠀⠘⣿⠃⠉⢛⣥⡏⣸⠂⠀⡇
⠀⠀⠀⡇⠀⠀⢀⠁⠰⠶⠿⠿⣿⡿⠿⠃⠀⠀⠉⢀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠘⢿⡾⠏⠀⠀⣿⠀⠀⠘⠿⣾⠗⠀⠀⡇
⠀⠀⠀⡇⠀⢀⢸⣆⠀⠴⠀⠐⠀⠀⡒⠀⠶⠀⢠⡟⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠤⠤⠤⠠⠤⠄⠀⣿⠀⠠⠤⠤⠄⠤⠤⠀⡇
⠀⠀⠀⡇⠀⢈⢷⣿⣧⡀⠀⢀⣤⣤⡀⠀⢀⣴⣟⣵⢃⠀⠀⡇⠀⠀⠀⠀⢸⠀⢉⣉⣉⠈⠉⠁⠀⣿⠀⠀⠉⠉⢁⣉⡉⠀⡇
⠀⠀⠀⡇⠀⠘⢿⣿⣿⡇⠀⣿⢳⣶⣹⠀⢸⣿⣿⣵⠏⠀⠀⡇⠀⠀⠀⠀⢸⠀⠿⢿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡿⠿⠀⡇
⠀⠀⠀⡇⠀⠈⠳⣿⣿⡇⠀⠘⠓⠒⠋⠀⢸⣿⣿⡷⠃⠀⠀⡇⠀⠀⠀⠀⢸⠠⢷⣾⡿⠇⣠⣶⣿⣦⣿⣶⣄⠸⢿⣷⡾⠆⡇
⠀⠀⠀⡇⠀⠀⠀⠈⠩⢍⠏⠐⡶⡴⠶⠴⠎⡭⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠈⠀⠀⠐⠶⠀⠀⢀⡴⠦⣄⠀⠀⢰⠖⠀⠀⠈⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⣀⣤⡀⠀⠀⣦⡸⠷⣹⠀⠀⢀⣠⣄⠀⠀⠀⡇⠀⠀⠀⠐⠈⠀⠀⣠⡄⠀⠹⢿⣿⣿⣿⡿⠎⠀⢠⣄⠀⠒⠋
⠀⠀⠀⠳⢤⣀⠚⠞⠃⣀⠀⠈⠓⠚⠉⠀⣠⠀⠻⠟⢀⣠⠴⠃⠀⠀⠀⠆⢀⠀⡈⢉⠁⢀⢀⢀⠀⡀⠀⣀⢀⡀⠈⡉⢁⠀⡀⠰
⠀⠀⠀⠀⠀⠉⠓⠦⣄⠈⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠤⠀⠈⠉⠘⣀⠛⣉⠉⡈⠉⠀⠄⠐⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⡶⣶⢶⢶⣷⠾⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠂⠩⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠈⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣶⣀⣯⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣯⠀⢀⣠⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠉⠀⠀⠀⠀⠈⣳
⠀⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⢶⠶⠖⣐⠶⠁⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠘⠷⠒⠖⠲⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⢀⠀⠀⢀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠰⠶⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⠀⠈⠓⢤⠀⠀⠀⠀⠉⠁
⠰⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⠀⠀⠀⠀⠈⠳⡄
⠀⡇⠴⠀⠀⠀⠀⠐⠒⠦⡀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉
⠀⠐⠐⡂⠀⠀⠀⠀⠀⠑⢼⡆⠀⠀⠀⡈⠁⠂⢷⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠘⡈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦
⠀⠀⡄⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠙⠛⡇
⠀⠀⠇⠤⠒⠀⠘⠈⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠽⣆
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠊⠁⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠈⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡀⢀⠠⢀⣴⠆⠀⠀⠀⠀⠯⠸
⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⣤⠴⠶⠋⠁⣀⣦⠀⠀⠂⠀⠡
⠓⢲⠀⠸⢇⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠉⣀⣀⣠⠤⠒⢋⡠
⠒⠋⠀⠀⠀⠁⠀⠀⠀⠠⠆⠃⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠣⠅⠤⠔⠂⠉
⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠌⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣀⠀⠙⣆
⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠘⠧⠄⠀⠀⠀⠈⠁⠀⢹⣄⡀
⢀⣴⠛⢁⣄⠀⣖⡂⡆⡆⣆⣴⢰⣄⡆⣖⡂⣖⡆⠀⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⣴⠶⢏⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠷⢶⡄
⣿⠁⠀⠈⠁⠀⠒⠃⠓⠃⠛⠛⠚⠛⠃⠓⠂⠋⠃⠀⠉⠀⠀⢹⡇⠀⠀⠀⣠⣤⡿⠀⣰⣦⣴⣶⣶⣤⣆⣶⣶⣶⣴⣶⣶⣶⡄⠸⣧⣤⣀
⣿⠀⠉⣈⠀⢉⠁⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⢁⠁⢈⡈⠁⢸⡇⠀⠀⣾⠁⣀⠀⠀⣿⣉⣿⣻⠛⣿⣿⡏⣿⣿⣿⣻⡏⣿⠀⠁⢀⡀⢹
⣿⠀⠀⣂⠀⢐⠀⠨⠀⢠⡉⣉⣉⡉⡠⠀⠀⠀⢐⠀⢐⡂⠀⢸⡇⠀⠀⣿⠀⢈⠀⠀⠙⣛⡉⠉⣤⣤⣤⣤⣬⣡⠈⢉⣀⠛⠀⠀⢈⡅⢸
⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠈⡄⠀⢸⡁⠘⡆⠉⠉⠉⠉⠉⠉⢠⠏⠀⡱⠀⠀⡘⠀⢸
⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠰⣿⡆⠀⠉⠃⠀⠀⠀⠀⠀⠐⠀⠀⠐⠉⠀⢀⡰⠀⠀⢸
⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣄⡔⢸⡇⠀⠀⣿⠀⠀⣿⣿⠄⠀⠀⠀⠰⠤⠤⠤⠤⠤⠀⠀⠂⢸⣿⣿⡆⠀⢸
⣿⠀⠀⠠⢾⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⠿⠀⢸⡇⠀⠀⣿⠀⠀⢈⡀⠀⠀⠀⠀⠶⣤⢠⣤⣤⠴⠂⠀⠀⠈⠛⢋⠀⠀⢸
⣿⠀⠦⣠⣼⣿⣿⣿⡧⠀⠀⢰⣶⠀⠀⠀⠰⠿⢿⢿⣧⠀⠀⢸⡇⠀⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⢸⣿⣿⡄⠀⠀⠀⠀⠀⠉⠀⠀⢸
⣿⠀⠀⠈⢿⠀⠠⠏⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠉⠁⢸⡇⠀⠀⣿⠀⢁⠉⠈⡉⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢉⡀⢉⡁⢸
⣿⠀⠀⠀⠈⠀⠀⣀⢠⡀⢀⢈⠋⣀⢀⡄⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢐⠀⢐⡂⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⠀⢐⡂⢸
⣿⠀⠀⠀⠀⠀⠀⡇⠤⠗⠜⢈⡃⠐⠸⠠⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠀⠀⡀⢸
⣿⠀⠀⠀⠀⡆⣄⠀⠀⠦⠦⡠⠠⠠⢆⠀⠀⠾⣷⣿⡦⠀⠀⢸⡇⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢠⡄⣇⡿⡀⢠⠀⡀⡔⡡⢄⠀⡄⠀⢀⢸⠛⡗⠀⠀⢸⡇⠀⠀⣿⠀⠀⢀⡄⠐⠛⠛⠒⠈⠳⢭⣯⠗⢻⡴⠾⠻⠷⠦⣄⡀⠀⣾
⣿⠀⠀⠸⣇⡟⠁⠀⠀⠀⣀⡴⠦⣄⡀⠀⠀⢸⢸⡟⠁⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⣀⠀⣀⣀⣄⡍⣉⣨⣬⣷⣶⢒⡠⠄⠀⠙⠂⢿
⣿⠀⠀⠀⠈⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣣⡀⠈⢹⠇⠀⠀⠀⢸⡇⠀⠀⣿⠀⠠⠀⠀⠠⣬⡄⠀⠀⠀⣠⡦⠀⠀⠀⠀⣬⡤⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠚⠛⠿⠿⠿⠿⠿⠿⠟⠛⠂⡀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⡀⠀⠀⠀⠀⠀⡎⢸⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⣿⢀⡴⢦⣄⠀⠀⠈⢤⣉⣀⣀⣁⣘⣈⣡⠈⠀⠀⢀⣤⠶⣄⢸⡇⠀⠀⠈⠙⠛⣷⠀⠀⠀⠀⠀⠀⠳⠤⣿⣿⣷⣶⠄⠀⠀⠀⢰⡗⠛⠋
⢿⣌⠁⠀⠙⢄⠀⠀⠀⠙⠿⢿⠿⠿⠟⠁⠀⠀⢀⠜⠁⠀⢉⣼⠇⠀⠀⠀⠀⠀⠿⢴⡄⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⡀⠀⠀⣴⠼⠇
⠀⠙⢷⣄⠠⣀⣃⣀⣀⣀⣀⣾⢿⣇⣀⣀⣀⣀⣋⡠⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⠁
⠀⠀⠀⠙⢧⣌⠁⠀⠀⠈⠛⠉⠉⠉⠛⠀⠀⠀⢉⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠺⠿⢿⣿⣿⣿⠿⠏⣰⠇
⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣀⣖⣀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⢀⣠⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⣀⡀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⡄⠠
⠀⠀⠀⠀⠀⠀⠰⡇⠀⡏⠀⢸⡤⣤⣏⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣄⠘⠀⢠⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠲⠊⠀⠈⠀⡀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠓
⠆⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠠⡀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠔
⠈⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠲⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡆⢀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣈⠀⡄⢀⠊⠉⠁⠀⠀⠀⠈⠁⠐⢄⠀⡁⠀⠀⠀⠀⡀⠀⠀⠰⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡇⠀⠀⠐⠣⣇⡐⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠄⠃⠀⠀⠀⠙⠌⠑⢄⠀⠀⠀⠀⠀⠀⠰⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠁⠀⠀⠸⠳⡀⢁⠀⠀⠀⢀⠀⢐⠐⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣡⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠰⠖⠣⠐⠂⠀⢀⡀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠈⢡⠀⠀⠹⡀⠀⠀⠀⠀⠀⡙⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠀⠀⠘⠀⢃⠀⠀⢱⡄⠠⠔⠾⡆⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠠⠍⢆⠀⠘⠻⠶⠤⣀⣀⡠⠀⣮⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠇⠈⣄⠀⠒⠚⡀⠀⠀⠀⠀⠀⣀⠐⠀⠰⠀⠀⠀⠀⠐⡀⠄⢁⢀⡀⠂⡐⠁⠀⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠀⠐⠀⠠⠘⡐⠅⡠⢀⠀⠡⠙⢉⠉⠁⠀⠀⠀⠖⠀⠀⠔⠀⠀⠀⢗⠛⠋⠈⠝⠎⢈⢁⣶⣦⡄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⠐⡀⠀⡄⠄⢠⠰⡁⠐⠀⠀⢁⠊⡀⠈⢉⠢⢀⡀⠠⠄⠀⠄⢓⠴⡀⢇⠀⠀⠀⢀⣀⣄⡸⠘⠻⠟⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠠⠈⠘⠁⡓⠂⠀⠠⣾⣿⡆⢈⣩⠤⠄⠀⠲⠀⠑⠈⠀⡄⢸⠨⡫⡉⠀⢁⣠⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠂⠐⠀⠘⠀⠇⠐⠀⠀⠙⣋⠉⡀⡀⠀⠀⢀⠀⢀⣠⠀⠀⠀⠁⠌⠀⠀⠀⠬⠢⢰⠀⠶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠓⣤⣀⠤⣦⠦⠚⠉⠁⠀⠠⠂⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠆⠁⠀⠉⠊⠀⠀⠀⠀⠁⡀⠀⣀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⠤⠠⠄⠀⠶⠤⢀⠀⣀⠀⣀⣐⡅⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠓⠂⠀⠦⠤⠤⠤⠞⠀⠀⠉⠰⠂⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⢬⣥⠤⠤⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠁⠀⠄⠄⠂⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠑⠒⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠈⠄⠃⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⢠⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠊⠁⠈⠓⠀⠀⠀⠀⠀⠸⠠⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡼⠀⠆⠀⠰⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⡆⠀⠫⢠⠀⠀⠀⢎⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠐⣦⢦⢦⢀⡴⡀⣤⠍⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠔⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⣆⠐⡀⠂⠀⡞⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢹⡀⣳⠀⣰⠇⠀⠀⠀⢻⣄⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⠤⠄⠀⠀⠈
⠀⠀⠈⠀⡰⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠙⠣⠤⠀⠋⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠐⠲⡀
⠀⠀⠈⠁⠇⢤⠄⠀⠀⢴⡀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠓⠠⠂⠀⠰⠀⠀⠆⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⣴⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⣶⡌⣿⡅⢶⣾⣿⣿⣶⠆⠀⠀⠀⠀⢤⡈⣓⣸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣆⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣥⡾⣫⣾⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠦⠵⠆⠀⠁⠀⠀⠀⠀⢸⣿⣫⣾⡿⣫⡾⡏⢍⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢸⡇⣾⠀⣿⢸⡇⣾⡆⣿⢸⡇⣾⡆⣿⣿⡆⠀⠀⠀⠀⠀⣴⣦⡻⣿⣯⣾⣿⡔⢦⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠘⠇⠻⠁⠟⠘⠇⠻⠃⠟⠘⠃⠻⠃⠿⠛⠃⠀⠀⢀⣴⣜⢦⡙⢿⠆⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢮⡻⢿⣷⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡻⣿⣷⣝⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡆⣶⣶⣤⣄⡀⢀⡰⣿⣷⣝⢮⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⡿⠿⣛⣃⣛⡻⠿⠋⣵⣦⡙⢮⡻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⢝⣩⣾⣿⣿⣿⡿⢛⣤⡻⣌⠻⣿⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢣⣾⡿⠿⢿⡿⢋⡱⣌⢻⣿⣮⠓⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡇⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣾⣿⢴⣿⣶⣔⢿⣿⣮⡳⢍⣵⣿⡎⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⣿⣿⣮⡻⣿⣿⣷⣝⠟⣵⣾⣿⣿⠇⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡸⠟⡛⢿⣮⡻⣿⣿⣷⢹⣿⣿⡟⣸⣿⣿⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣵⣿⣿⢪⣿⣿⣮⣭⣥⣾⡿⢋⢼⣿⣿⠃⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢟⣵⣮⣭⣛⡛⣛⣩⣥⣾⣿⣷⠉⠁⠀⠀⠀⣀⣤⣸⠃⠀⠀⣠⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠿⣿⣿⡇⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⠂⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠙⠛⠁





⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⡁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⡻⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣣⠼⠋
⠀⠀⠀⠀⠀⢣⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡞⣩⢤⠨⢵⡽⣷⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣴⣶⡤⢣⡟⠀⠀⠀⠀⢸⣿⡿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠖⠛⠁⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠳⠿⠷⠶⠋⠀⠀⠀⠀⠀⠀⠙⢿⣾⡿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠐⣦⣤⣤⣴⡆
⠀⠀⠀⠀⠀⢺⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢹⡄
⠀⠀⠀⠀⣤⡟⠙⠙⠋⠉⠙⠛⠛⠙⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠉⠛⡟⠛⣿⠛⠛⠛⠛⠛⠛⢿⠟⠋⠀⠀⠀⠀⠀⠀⣼⣿⣯⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣿⣧⣿⣟
⠀⠀⠀⠀⠀⠀⡇⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡯⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁
⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⣄⣠⣶⣶⣾⢿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠞⠉
⠀⠀⠀⠀⠀⣀⣀⣹⡿⢿⣩⣍⣿⣿⣏⣀⠉⠉⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠺⣻⣿⠇
⠀⠀⠀⠀⢀⠈⠿⠿⣿⣿⣿⣿⣿⣿⠇⠀⣀⡀⠀⠀⠀⠀⢿⣯⣹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⡻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⡙⠿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⣠⢤⢠⡄⡤⢠⡈⡍⠤⣤⠄⣤⢤⠈⡍⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⡿⢸⢸⡇⡗⢸⠛⡇⠀⡗⠀⣿⢺⠀⢱⠇⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠇⠙⠊⠀⠉⠁⠈⢤⡥⠀⠁⠀⠙⠈⠃⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢀⡀⠀⠀⠀⢸⢇⣾⣸⠀⡇⢮⡀⢸⢰⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠘⠘⠘⠈⠒⣡⣂⠋⠘⠘⠚⠀⠀⠀⠀⠀⠀⣿⡆⣠
⠀⠀⠀⠀⠀⠀⢰⡄⢸⣟⣸⡇⢰⡂⢰⡓⠰⣂⠐⢲⢂⣰⢰⢠⠆⢠⣆⠀⡆⠀⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠟⠁⠘⠀⠘⠒⠀⠘⠃⠘⣸⣚⠀⠛⠀⠊⠘⠂⠓⠀⣿⠀⣿⣥⡿
⠀⠀⠀⠀⠀⠀⢸⣧⣼⣿⠀⠀⠀⠀⠀⠀⢀⣠⠴⣖⣛⣛⣳⠶⣤⡀⠀⠀⠀⠀⣿⡀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⢀⡴⢯⣰⣾⣿⣿⣿⣿⣿⣦⣽⢦⡀⠀⠀⠉⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⡚⠛⠂⠠⠤⢤⣞⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⣻⣤⠤⠄⠐⠛⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢰⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠯⠿⠷⢦⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⡆⠰⠆⠀⣶⣦⣦⢰⠀⢰⡆⣦⢰⡄⣦⣶⠀⠰⠀⠸⠒⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⢤⣤⢥⣥⣬⣤⣬⣭⣭⣬⣭⣥⣤⡤⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⡙⢿⣿⣿⣿⣿⡿⠻⣻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠿⠿⠿⠿⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠊⣳⣀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠒⠒⠄⠀⠊⠀⠀⠀⢀⣠⠼⠓⠉⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⡀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠊
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⢨⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢁⡴⠋⠀⠀⣂⠈⠓⠂
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡄⠀⠀⠙⠹⠿⠟⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠀⠏⠀⠀⠀⠀⠈⠙⠓⠺⢤⡤⠴⠄
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⢀⠔⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⣡⣀⣓⠒⢢⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⣴⠿⣿⡿⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⢀⠀⢀⣠⣾⣿⣿⢖⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⢔⣸⣿⠟⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠄⠊⠀⢟⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠠⠀⠀⣠⠈⠉⠓⠲⠤⣀⡀⠀⠀⠈⣆⠀⠁⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⣼⢧⣀⣀⣀⣀⣀⣀⣉⠆⠀⠀⠘⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⠟⠉⠉⠙⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⣀⢸⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⠀⠀⠀⠀⢸⠁⠀⠀⣀⠀⠀⠀⠀⠉⢠⠀⣼⠉⢡⠀⠀⣠⣤⣶⠶⢶⠀⣼⡤⠤⢀⣀⣀⠀⠀⠀⠀⢠⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠃⢨⢀⣴⡶⠶⠿⠦⢄⡀⠀⠙⠲⣄⠀⠀⢘⡁⠉⠀⠘⢶⠋⢁⡀⠿⠀⠀⠀⣭⠂⠚⠛⠛⠋⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠈⠁⠒⠒⠒⠚⠛⢲⠚⣩⠔⠊⠉⠁⠉⠉⠒⠤⣴⠶⠶⠶⠶⠶⢦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⡠⠤⠆⠀⠀⠀⠄⡀⠈⢆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⣏⢹⡏⠋⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⡗⠶⠶⣤⣤⡤⢤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡎⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢢⡁⠀⠀⡁⢸⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠰⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠢⢲⠃⡄⠀⠃⢨⠀⣸⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢹⣀⠜⢠⣾⡜⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⢠⠃⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⡜⢿⠓⢸⡔⠇⠀⠑⡀⠀⠀⠀⢰⠂⠀⠀⡋⠉⣳⣦
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠶⠞⠛⠁⠀⠚⠀⠈⠃⠚⠛⠃⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⡦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠘⡿⠤⣤⠀⠀⠸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⣰⣿⠃⠀⠀⠀⠈⠉⢉⣷⠠⠶⠀⠀⠀⢹⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠛⠆⠀⠀⣠⣶⣿⣿⣿⣇⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉
⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⣼⡧⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢉⡿⠑⠀⠀⠀⢠⣶⣾⣿⣶⣶⡀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠰⠰⣿⣿
⠀⠀⠀⠀⠀⣈⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡘⠀⢀⣶⣾⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢈⢉⣿⣿
⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢨⢀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⡀⡰⠀⣤⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣄⠀⠀⢻⠃⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠠⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠉⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠈⠉⠙⠛⠃⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⠀⣤⣶⣶⡄⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢄⣀⠀⠙⣦
⠀⠀⢀⣴⡿⠉⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠸⣦⠀⠀⠀⠀⠈⠣⠀⢸⡇
⢀⣴⠿⠉⣀⠀⣴⡦⣤⢠⢰⣀⡆⣦⢰⡆⡖⠢⡶⡄⠀⣀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢠⣤⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⣤⣄
⣿⠁⠀⠈⠛⠀⠰⠟⠻⠞⠻⠛⠇⠟⠿⠇⠯⠔⠟⠇⠈⠛⠀⠈⠙⣷⠀⠀⠀⢀⣀⣸⡇⠀⣥⣄⣤⣤⣤⢠⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⣯⣀⣀
⣿⠀⠐⠐⠂⠒⠐⠀⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠐⠒⠂⠐⠒⠂⠀⣿⠀⠀⢰⠏⠉⠈⠐⢸⡇⣋⣷⣿⠻⣿⣿⡟⣿⣿⣿⢾⡟⣿⠃⠐⠈⠉⠙
⣿⠀⠀⠉⠁⠈⠁⠀⠀⢀⡐⠒⠛⠒⠚⡀⠀⡂⠀⠈⠁⠨⠅⠀⠀⣿⠀⠀⢸⡇⠘⠃⠀⠘⠿⠟⠛⢋⣀⣋⣋⣀⣙⢋⡙⠛⠃⠿⠀⠀⠀⡋
⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⠉⠉⠘⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⣿⠀⠀⢸⡇⠀⢃⠀⠀⡔⠉⢢⠘⠛⠛⠛⠛⠋⠛⠀⡔⠉⢢⠀⠀⢀⠏
⣿⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠚⠛⠋⣀⡄⠀⠀⠀⢀⡀⢐⡀⠀⠀⣿⠀⠀⢸⡇⠀⣼⣦⠀⠙⠲⠌⠁⠀⠀⠀⠀⠠⠀⠈⠡⠖⠋⠀⠀⡎
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⢀⠀⣿⠀⠀⢸⡇⠀⢹⣿⣄⠀⢀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⢠⣶⣾⣄
⣿⠀⠀⠀⣠⣶⢄⠀⠀⠀⠀⠒⠀⠈⠁⠀⠀⠀⠀⡀⡐⢻⣷⠁⠀⣿⠀⠀⢸⡇⠀⠘⠛⠋⠀⠀⠀⢠⣈⣉⣉⣉⣉⣁⡀⠀⠀⠘⢿⡿⠏
⣿⠀⡀⠀⢹⣿⣶⣶⣤⠀⠀⠀⣀⣀⠀⠀⠀⢠⣾⣿⣿⡏⠁⠀⠀⣿⠀⠀⢸⡇⠀⠀⠶⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠌⠀⠀⠀⠀⠀⠰⠆
⣿⠀⠉⠹⣿⠟⠛⣿⠟⠀⠀⠀⣿⣿⠀⠀⠀⠈⠋⠈⢹⣿⠤⠄⠀⣿⠀⠀⢸⠁⠤⠠⠄⠤⠀⠀⠀⢀⣴⣷⣾⣿⣿⣧⡄⠀⠀⠀⠤⠄⠠⠤
⣿⠀⠀⠀⠈⠇⠀⠁⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣿⠀⠀⢸⡇⠀⡒⠀⣐⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢐⠂⠀⡂
⣿⠀⠀⠀⠀⠀⠀⡔⢂⢲⡀⡆⢦⠐⡆⢴⠂⢦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⢀⠀⠓⠊⢋⢉⠀⠰⠆⠁⡁⠀⠐⣠⣀⣀⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠄⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠
⣿⠀⠀⠀⠀⣿⢰⠀⠀⠘⠛⠐⢂⠁⠊⠀⠀⠀⠙⢻⣿⡟⠀⠀⠀⣿⠀⠀⢸⡇⠀⠉⠁⠉⢀⣀⣀⠀⠁⠻⢿⡿⠿⣤⠀⢀⣀⣀⠈⠉⠀⠁
⣿⠀⠀⠀⡆⢸⡼⠸⠀⠅⠠⠘⢅⠇⠌⠐⠂⠆⣤⢸⣹⡏⠀⠀⠀⣿⠀⠀⢸⡇⠀⡀⠀⠊⠉⠉⠙⠁⠀⠈⢲⣖⠉⠈⠄⠋⠉⠉⠙⠂⠄
⣿⠀⠀⠀⠧⣾⠀⠀⠀⢀⣤⣶⣟⣳⣦⣄⠀⠀⢿⣸⠋⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⡄⠠⠰⠐⠖⠂⠒⠒⠆⠶⠰⠀⡄⡀
⣿⠀⠀⠀⠀⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣳⣀⠀⠸⠃⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠂⠀⠀⠐⠶⠀⠀⠀⢀⢼⡟⠀⠀⠀⠀⠶⠖⠃⠀⠀⠂
⣿⠀⠀⠀⠀⠀⠀⠉⡉⢛⡛⠛⢛⠛⣛⢛⡋⡉⢁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇⡀⠀⠠⠀⠀⠀⠀⠀⢰⠁⠸⣇⣀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣀
⣿⢠⡼⠻⣦⡀⠀⠀⠠⣤⣤⣤⣤⣥⣭⣤⡤⠀⠀⠀⢠⣴⠟⣦⡀⣿⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠑⢺⣿⣿⣿⣷⡆⠀⠀⠀⠠⣟⠉⠉
⢿⣤⡀⠀⠈⠳⡀⠀⠀⠈⠑⠿⠿⠿⠟⠋⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠀⠀⠀⠀⠀⠘⠷⢶⡁⠀⢠⣤⣶⣶⣾⣿⣿⣿⣿⣅⠀⢌⣴⠶⠟
⠀⠙⢿⣦⡀⢄⣈⣀⣀⣠⣤⣼⣿⣿⣤⣤⣄⣀⣈⣁⡤⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠘⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⣼⠁
⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠋⠉⠉⠙⠃⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠐⠛⠻⠿⠿⣿⣿⠿⠋⣠⠏
⠀⠀⠀⠀⠀⠘⢿⣦⣀⣀⣀⣀⣐⣂⣀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⢀⣠⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⢰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠳⣻⣖⡾⠿⠧⡝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠟⡉⣿⠁⢬⡽⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣲⣿⠟⠀⣼⢻⠋⠈⠀⣰⣸⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⡶⣾⡿⣯⣤⣤⣴⡿⠈⠑⠦⣈⣲⡏
⠀⠀⠀⠀⠀⠘⠉⢀⠞⣹⣣⡟⡇⠠⠂⠀⢿⠁⠉⠙⠂⡟⠉
⠀⠀⠀⠀⠀⠀⠀⢊⣶⠶⠇⢠⣇⡏⠀⠠⢸⡇⠀⢀⠀⣿⠀⠀⣦⡀
⠀⠀⠀⠀⠀⣀⣶⣾⣵⠖⢯⣿⡟⠀⠁⣀⢨⡗⠈⠉⠀⣝⢘⠀⣿⢷
⠀⢀⣄⣀⡙⠻⠿⣋⣁⣉⡀⠈⠋⠣⡍⢁⠀⠋⠀⠁⠈⠉⠀⣴⡏⣟⠀⠀⠀⠀⠀⠀⢀⣀⠠⣤⠠⣶⣶⣶⣽⣿
⠚⢿⡿⠏⠿⠷⣶⣦⣶⣤⣉⣉⠓⠆⣀⢀⡀⠀⠀⢀⣀⣀⣠⣽⣿⣻⢦⣶⣶⣿⣿⠿⠿⢏⡶⡟⣷⠛⠛⠂⠃⠛
⠀⠀⣿⣻⠶⣶⣆⡀⢩⣍⠻⣍⠛⡳⢤⠻⣿⣷⢹⣟⣯⣿⠿⠿⢿⡾⣿⠉⠁⠀⠀⠀⠀⢸⣟⣸⠇
⠀⠀⡗⠬⠚⠒⢫⣍⢸⣿⠓⠌⠳⣌⣪⡿⠷⡋⠈⠉⠀⠀⠀⡸⠈⢷⣿⠀⢀⣀⣀⣠⣤⣜⡽⠋
⠀⠀⠷⠀⠀⠀⠀⠈⠀⣿⡇⠀⠀⠀⠚⠙⣐⣂⠂⣀⣀⣠⠴⠽⡒⠚⠿⠿⠿⠛⠛⠋⠉⠁
⠀⠀⢸⣶⣤⡈⠀⣠⡃⠀⠄⠐⠎⠀⣠⣾⠿⠛⠃⠁⠀⠀⠀⠀⣍⠃
⠀⠀⠀⢿⣷⠵⢶⣧⢧⠖⢀⣠⣴⠟⠉⠁⡀⢀⣀⡀⠀⠀⠙⢦⡈⠃
⠀⠀⠀⠀⠉⠛⠳⠖⠚⠻⣿⠟⠁⠀⠐⠛⢻⣛⣉⣟⣷⣴⣤⣀⠈⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠹⠟⠺⡧⢿⣿⣍⣝⣷⣤⣀⠐⠦⣀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⡩⣴⡀⢦⣶⣟⣻⢸⣿⣫⣿⣿⣷⣼⣿⣶⣌⠘⠤⡺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣤⣁⠙⠁⠓⠋⠁⠀⠒⠉⠑⠛⠛⠙⠛⠛⢿⣷⣤⡈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠛

⠀⠀⠀⠀⡀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡄⠀⠀⠀⠐⡆⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⣩⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠰⢳⡀⠀⠀⢰⠔⠉⣩⡄⠀⠀⠀⣀⣀⡀⡐⠠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢈⠢
⠀⠀⠀⠀⠈⡝⣇⠀⠀⠀⠲⠞⠃⡄⠀⠀⠀⠀⠀⠀⢀⠀⠼⠀⠀⠀⠀⠑⠂⠀⠙⢄
⠀⠀⠀⠀⠀⠩⢼⣄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠰⡭⢿⠉⠑⢈⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠄⠀⢸⠽⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠁⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣦⠷⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡌⣈⠃⠀⠀⠀⡀⠈⡛⢧⠀⠀⠈⠭⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠘⠁⣠⡜⠀⠈⠣⡀⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⠂⠀⠀⠘⢄⡆⠀⠀⠂⠀⠀⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⡧⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠇⠤⠶⠀⢠⡀⡀⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⢄⠠⠇
⠀⠀⠀⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠛⠀⡟⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠲⠤⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁
⠀⠀⠀⢠⡔⠁⡴⠄⠀⠀⠀⣘⡳⢤⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠑⠚⠁⠆⠀⠀⠀⠈⠀⠀⠂⠩⠐⢒⠒⢒⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠒⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡟⡉⠹⢶⣀⣤⣾⠗⠀⢰⣦⣴⣶⣶⠖⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠀⢀⣏⠀⡁
⠀⠀⠀⠀⠀⠀⠠⣄⣠⣽⡿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⣿⠝⠙⠀⠀⠀⠀⠙⠛⣽⣏⠁⠓⠀⠀⠀⠀⠀⠦⠾⣿⣿⣿⣿⣷⣾⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠉⣿⠓⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡭⠛⣹⣿⣄⡀⠀⠀⠀⣀⡠⠦⢙⠓⠀⠀⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠟⣾⣿⠁⠍⠙⠄
⠀⠀⠀⠀⠀⠀⠀⡀⣸⣤⣦⣦⣄⠀⠀⠀⠀⠀⢠⣴⣦⣻⡌⢉⡿⠚⠁⠀⠰⠁⠘⢿⣷⡮⠁⢘⠀⠟⠀⠀⠀⠀⠀⠀⠹⣿⣣⣾⣿⠟⠛⠀⢀⡇
⠀⠀⠀⠀⠀⠀⣿⣳⠾⣷⠐⢿⡟⠃⢀⠀⡈⢴⠟⣫⣿⣿⣿⣾⣿⡆⢶⡟⠀⢀⣤⡄⠈⣶⣾⣿⡿⣷⣾⣿⣷⣦⣴⣷⠶⣹⣿⣿⠏⣀⣤⠜⠋
⠀⠀⠀⠀⢀⣤⣨⡟⡛⢹⠣⡟⢡⣾⣤⣾⣁⣼⣿⡏⢙⡿⠿⣿⠛⢁⡟⠠⣴⡿⣿⡇⠀⣛⣻⣯⣿⣿⣿⣽⣿⣯⢸⠀⠀⣿⣿⣿⣠⣾⠃
⠀⠀⠔⣱⣿⣿⣿⣸⡟⠘⢶⡄⠈⠁⢉⡟⢉⡽⠿⡿⢿⣁⢀⣸⣿⡟⢠⣾⣮⠅⠘⠳⣀⣛⣻⣿⣿⣰⣿⣿⡇⡯⡞⣶⣿⣿⡿⢿⣿⣿
⢀⠊⡾⠉⠀⢈⣿⣿⠋⡶⣀⡀⠀⠀⣸⣟⣿⠀⣸⣷⣾⠉⠈⠙⣧⠁⠀⠈⠉⠀⣐⣈⠰⠿⢿⣿⢿⣿⣿⢸⡟⣿⣇⣿⣿⣿⣿⣆⠹⠏
⠉⠉⠀⠀⠀⣾⣿⣿⠂⠀⠁⡇⠀⠀⢿⣿⣿⣿⡿⠀⠘⡆⠀⠡⡹⠀⠀⠀⠀⠀⢻⡏⠀⠶⣾⣿⣿⣿⣿⣿⣹⡿⢸⡛⣿⢿⣿⣿⠀⡀
⠀⠀⠀⠀⠀⡿⠈⢻⡄⠀⠀⡁⠀⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣲⣾⣮⣽⣿⣿⣿⣿⣷⣾⣷⠏⠀⠸⠁⢀⣷⡆
⠀⠀⠀⠀⢠⡇⣀⠘⡇⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⣶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⣤⣽⣿⡿⠛⢻⣿⣿⡃⠘⠻⠛⣀⠀⠀⢀⣸⣿⠇
⠀⠀⠀⠀⢸⠃⣿⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⡟⠀⣿⠀⠀⢸⣿⠏⣀⠀⠀⠈⣩⠇⣴⣿⡟⠁
⠀⠀⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢈⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⡄⢈⣴⠀⢸⡟⠘⡟⠻⠂⡼⠋⠀⠟⠉
⠀⠀⠀⠀⠸⠀⣿⣧⡀⠀⠀⠠⠀⠀⠀⠀⢷⠀⢼⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⢸⡟⠀⢸⠀⠐⠁⠀⠀⠙⠊⠀⠀⡄⠐
⠀⠀⠀⠀⢸⠀⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⡏⠀⠐⡀⠀⠀⡀⠀⠀⠀⠸⠇⠀⠀⠀⢸⣇⠀⣴⡀⣠⡀⠀⠀⣰⡇⠀⢠⣿⣿
⠀⠀⠀⠀⢸⠀⠛⢀⠇⠀⠀⠀⠀⠀⠀⠀⣿⠿⣾⡇⠀⠀⢷⠀⠀⠇⠀⠀⢀⠞⠀⠀⠀⠀⢸⠃⠀⣿⢻⢿⠇⢀⣾⣿⠟⣠⣿⣿⣿
⠀⠀⠀⠀⡘⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⡁⠀⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⣸⠀⠀⡇⣼⢈⣴⠿⠋⣡⣾⣿⣿⣿⡟
⠀⠀⠀⢰⣄⡀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⢸⡄⠀⡃⠀⠀⡆⢰⢀⠃⠀⠀⣿⣇⠀⡧⢯⣤⣤⣶⡿⢟⣵⣿⠿⣿⠃
⠀⠀⠶⠞⠛⠋⠀⠀⢀⣬⣤⠄⠀⠀⢀⣠⣿⣶⣾⠁⠀⠀⠈⠻⣶⡇⠀⠀⣥⡿⡿⠀⠀⠀⢿⣿⡟⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⠀⠀⠛⢧⣑⣄⠀⠀⠈⠁⠉⠉⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿