Sponge bob Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢛⣴⡾⠛⣋⣙⣹⣿⣿⣤⣴⠾⠛⡓⠻⢶⣤⠀⢆⠀⠀⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⡛⣼⣿⣿⣿⣿⣿⡿⢉⣴⣾⣿⣷⠀⢹⣿⣷⠀⠃⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⢾⣿⣿⣿⣿⡿⣾⠃⢼⣿⣿⣟⣿⠇⢰⣿⣿⠀⠒⠀⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⣹⠦⣖⣟⣟⣿⣿⣿⣆⣬⣿⡿⠛⠃⣤⣾⣿⡿⠀⠷⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣴⢋⡿⣿⢿⡟⠻⣿⣿⣿⣷⣶⠊⠉⠉⠉⠁⠀⠀⢰⣿⣿⣿⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠉⠛⠃⠛⠙⠁⢠⡻⢿⣿⠿⢟⣢⣾⠃⢀⠖⢀⡴⣿⣿⣿⢹⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⣀⠀⢸⣶⣤⣤⣄⣀⣀⣤⣼⣦⣶⣾⣿⣿⠃⠀⠁⠀⠘⣿⠷⣟⠷⢾⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣇⠐⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡿⣀⣄⠀⢀⣼⡹⢧⣷⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠿⠿⠋⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠿⠛⠁⠙⣿⣿⣯⡿⣿⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⣾⣇⠐⢻⣿⣿⣿⣻⡿⢟⢋⣽⠟⠁⢀⣤⣤⠀⠀⢈⣿⣿⡩⢇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠁⢤⣴⠋⠛⠿⠿⠿⠟⠛⠁⠀⠀⣿⣿⡿⣇⣠⣿⣿⡟⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠾⢿⣶⣶⣮⣽⣿⣶⣶⣤⣤⣤⠤⠀⠀⠀⠹⡏⠀⠀⣿⣿⣿⠃⠀⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⣐⣂⣟⡳⠿⠿⢿⣿⣿⢿⡛⢲⣶⣤⣤⣶⣇⣀⡀⣸⣿⣿⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣯⢿⣿⣿⣿⣿⣧⣤⣍⣉⣁⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣇⣼⣇⣸⠉⢻⣿⣿⣿⠻⠛⠃⠉⣿⣿⣿⣷⡶⢶⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⣻⡟⢻⣿⣷⡿⣿⣥⣇⣀⣀⡀⠀⠀⠨⠃⠁⣨⣿⣿⡿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠁⠈⢹⠛⡃⠀⠟⣿⡿⠟⠿⣶⡾⢧⣤⣤⣼⣧⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠑⠀⠈⢹⠁⢤⣄⠁⠇⡔⢻⠋⠇⠛⣟⠉⠘⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣼⠀⠀⠀⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠇⢸⠀⠀⢀⣤⣚⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣗⣌⣀⣠⣟⣉⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠲⠒⠛⠉⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⠀⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡁⡱⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⢦⣀⣰⣄⣀⡤⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠤⣀⣀⣇⣠⡞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠑⡀⠀⠀⠀⠀⠈⣉⡥⠖⠒⠒⠒⠲⢤⣀⠀⢀⣠⠤⠤⠤⠤⣄⡈⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠃⠠⢄⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠀⠀⠀⠀⠀⠀⠉⢢⡀⡊⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠊⢠⠋⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⢹⡀⠀⢀⣀⣀⡀⠀⠀⢱⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡞⠀⠀⠀⠀⠀⣼⣿⣿⣟⠁⠈⣧⠀⡇⣴⣿⣿⡟⠉⢣⠀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣿⢠⡟⣿⣿⣿⣷⣶⣾⠀⢰⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⢄⠸⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠁⡼⠀⠙⠿⣿⣿⠿⠋⢀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠒⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠢⢤⣀⡀⠀⣀⡴⠋⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠙⠓⠒⠶⠒⠚⠉⠀⢠⡀⠀⠀⠀⠉⣏⠁⢀⣀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⢠⠉⠒⠦⠤⠖⠃⠀⠀⠀⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢇⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠘⠦⣽⡒⠶⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⠖⡇⣠⠜⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡤⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⡸⠁⢧⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠀⠈⠻⢶⣒⠤⠤⠤⣀⣄⣀⣀⣀⣀⣠⣀⡤⠤⠤⠄⣲⠞⠁⠀⠀⠣⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⡖⠒⠒⡶⡖⠒⠒⡶⡖⠒⠒⠻⢉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠀⢀⣠⠞⠀⠀⠳⢄⡀⠀⠀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣄⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⢀⡀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⣄⠀⣀⣈⡙⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⡀⠈⡖⣁⡀⠙⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡄⠈⢹⢩⡄⠈⠑⡇⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⣸⣎⠁⠀⣠⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣁⣉⠉⠀⠈⠓⠊⠁⠀⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠉⠓⠒⠲⠒⠒⠋⠁⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⡑⢄⡀⠀⠀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢟⠢⣍⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡄⠀⡏⠒⠬⣍⣒⠒⠤⠤⠤⠤⣤⡤⠤⠤⠤⠖⣒⣋⠥⠂⢳⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠙⡆⠓⠶⢶⠄⠀⠉⢉⣑⠒⢒⡖⠒⠒⠂⠉⠉⡴⠋⢱⣰⠁⢙⡦⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⣀⠀⠀⢸⠆⠉⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠲⢤⣀⡀⠀⠈⢹⠒⠒⠒⣄⠀⠀⠀⠀⠀⢯⡀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢉⡽⠛⠛⠀⠀⠀⠘⠦⠤⣤⠤⠤⠖⠛⢉⠏⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣠⠴⠋⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠾⠿⠿⠿⠿⠷⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠙⠃⠀⠀⠰⢶⠶⠶⠶⠶⠶⠦⣤⣄⣉⠙⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣠⡤⠀⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠻⠶⢦⣈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⠞⢉⠁⠀⠀⠀⠘⠀⠘⠁⣠⠄⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⠟⢁⣴⠇⠈⠀⠀⠀⠀⣀⣀⠀⠀⡠⠀⠁⠀⠙⠠⡖⠀⠀⠐⠃⠀⠀⣠⡀⠠⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣠⡾⢁⣴⠟⣡⡆⠀⠠⠀⠀⠐⣿⣿⠇⠀⠀⢀⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠘⣿⡿⠀⢁⡀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣰⡟⢀⡾⢃⣼⠟⠁⠘⣄⠀⠀⠄⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⢀⠇⠀⠀⠀⠀⢀⡀⠀⢠⡈⢿⡄⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡿⢀⡿⢁⣾⠃⡄⠀⠀⢈⡳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠸⠃⣠⠚⣷⠈⢿⡄⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣿⠃⣼⠇⣼⠇⣼⠃⠀⠀⠀⠑⠢⣄⣀⠀⠀⠀⠀⠀⣀⣠⣶⠂⠀⠀⠀⢀⣾⡆⠀⢀⢹⣇⠸⣇⠘⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡟⢀⡿⢠⡿⢰⡏⠀⠀⠆⠆⠀⠰⣁⣀⣿⡋⠉⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠛⠁⡀⢿⡄⣿⠀⣿⠀⣿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡇⢸⡇⢸⡇⢸⡇⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠆⠀⠀⠀⠰⠆⠀⣿⢸⡇⣿⡆⣿⠀⢹⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠸⣇⢸⣇⢸⣿⢁⠀⠀⠁⠀⠀⠻⢥⣀⣐⣉⡥⠞⠁⠀⡀⠀⠀⠀⠀⣀⠀⢸⡟⢸⡇⣿⠇⣿⠀⣼⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⣷⠀⣿⠀⣿⡘⣿⢲⡇⠀⠀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡞⠉⢦⣾⠇⣾⢀⣿⢀⣿⠀⣿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣿⡆⢹⣇⠸⣧⠹⣦⣷⣶⣦⣤⣤⣀⣻⣿⠋⠀⠀⠂⠀⠀⠀⣀⠀⢼⠀⠀⢸⠏⣼⠇⣼⠇⣼⠇⣸⡿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⣿⡄⢻⡆⠻⣦⡹⠻⢯⣯⣿⣛⢿⣿⣿⣿⣷⡖⣦⣤⣤⣀⣬⣤⣤⣿⢺⣏⣼⠋⣼⠏⣰⠟⢠⣿⠃⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠹⣷⡄⠻⣦⠹⣇⠤⠾⣌⡻⢿⣿⣿⠿⠿⣾⣯⣭⣿⣻⣿⣿⣿⣿⣿⢸⠟⣡⡾⢃⣴⠏⣠⣿⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⢿⣆⠙⢷⣄⠒⢼⣍⡛⠶⡇⣛⡛⠷⠶⠾⠿⣿⢿⣟⣛⣭⡿⠋⠀⡾⠋⣠⡾⢁⣴⡿⠃⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⣷⣄⠙⠷⣤⣉⠻⢶⡇⢹⣙⡛⠛⠒⠒⢻⣼⣋⣩⣴⠶⠀⠀⣴⠞⢋⣰⣾⠏⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡈⠻⢿⣦⣌⣙⠳⣦⣶⣸⣍⡛⠛⠛⠛⢻⠘⣋⣩⣤⡶⠖⢒⣡⣴⡿⠋⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠉⢻⣿⣿⣿⣿⣿⣿⠛⣛⣛⣻⣿⣀⣯⣉⣤⣴⣾⠿⠛⢉⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣿⣟⣛⠙⠛⠻⢿⣿⣽⣿⣿⣿⡿⠛⠋⣉⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⢶⣿⣿⣿⣶⠶⠶⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⣿⣇⣀⠀⠀⣰⡿⠀⠀⠀⠘⢿⣆⢀⣀⠠⠿⠧⢀⣀⠀⢠⡿⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡠⠟⠋⠉⠀⠀⠀⠀⠈⠙⠻⢄⠀⠀⠀⢀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢇
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⣉⡑⢢⡀⢰⡇⠀⠀⠀⡠⢊⣩⣍⡙⢦⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⠆⠃⠸⡇⠀⠀⠀⡇⢸⣿⣿⡷⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢆⡙⠛⢉⡠⠃⠀⢳⠀⠀⠀⠑⢄⡉⢉⣀⠔⠀⠀⠀⠀⢀⣠⣠⣇⡀
⠀⠀⠀⠳⣄⡴⠋⠉⠑⠒⠤⣄⠀⠉⠀⠀⠀⢀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠦⠀⠉⡓⢦
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣴⠊⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠲⠀⠉
⠀⠀⠀⠀⠀⠘⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠉⠃⠀⢶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡶⠶⣤⣤⣤⣤⣄⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⣶⠚⠛⠉⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠉⠉⠉⡏⠉⣯⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣧⠀⢿⣀⣀⣀⣀⣽⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⢀⣀⣀⣀⠀⢠⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡤⠖⠒⠚⠒⢲⠶⠛⠉⠉⠉⠉⣻⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣰⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⢤⣤⣤⣤⣤⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠉⠀⠁
⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠉⠉⠛⠒⠚⠛⠉⠉⠉⠛⠓⠶⠚⢿⡉⠉⠉⠉⣻⢶⠶⠶⢶⡿⣏⠉⠉⠛⠛⣶⠶⠶⠶⠿⠛⠉⠉⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠞⠁⠀⢣⠤⢾⠀⠈⠷⣠⠴⠋⠁
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡞⠀⠈⢧
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⣴⠃⠀⠀⠈⢦⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠹⣄⠀⠀⢀⠜⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢶⠒⣚⣟⢉⠍⠩⠹⡗⢄⠤⡆⠀⠀⠀⢀⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢫⡹⠥⢧⣄⢠⠴⣺⠭⡉⠒⣅⠀⠀⠀⢸⡗⢄⠙⢦⡀⠀⠠⠂⠉⠓⢲⣄⡀
⠀⠀⠀⠀⡠⣤⠄⢄⠀⠀⠀⡇⠀⠀⠈⠀⠀⣿⣼⠃⡀⣿⣺⠇⠀⢸⠀⠀⠀⢸⡇⠈⠢⡀⣹⢀⠁⠀⠀⠀⠀⠀⢳
⠀⠀⢠⡚⠂⠀⠀⠀⢳⠀⠀⡇⠀⠀⠀⠀⠀⠈⢩⡄⠑⢄⣀⣀⡠⠞⠀⠀⠀⢸⠇⠂⠀⠈⡏⢸⠀⠀⠀⠀⠀⠀⡾
⠀⠐⡅⠁⠀⠀⠀⠀⢸⡇⠀⡇⠤⣦⠑⣦⣴⡄⠀⢀⣄⣀⣀⣀⣴⠋⠔⢲⡄⣾⠂⠸⠆⢸⠃⠘⣶⣶⣦⡀⠀⣰⠃
⠀⠀⠘⡆⠀⣠⣴⣿⡟⠀⢸⠃⢤⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠢⣾⠇⣿⠀⠀⠀⣼⣀⣤⠞⠉⠻⢿⡟⠃
⠀⠀⠀⠈⠻⣿⠛⡡⠉⠲⣼⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠀⠀⠀⠀⣿⠁⠢⣀⡏⠁⠀⢂⠀⢀⡞
⠀⠀⠀⠀⠀⠘⡎⠀⠀⠀⠜⠀⠀⠀⠀⢻⣿⡿⠋⠉⠳⠀⠈⠙⠁⠀⠀⠀⢀⡷⣤⠞⠉⠘⡄⠀⠀⠙⡾⠁
⠀⠀⠀⠀⠀⠀⠹⣄⢀⠌⠀⠀⠀⠀⠀⠀⠻⠧⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⣸⠟⠁⢁⠀⠀⠈⢦⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠜⠁⠀⠀⠀⢢⡀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢰⠋⢻⡆⠠⠄⣍⢉⣉⣩⠄⠄⠰⡟⠉⣷⠀⠀⠀⠀⠀⠀⣹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠌⣿⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⡏⠉⢹⣇⢠⣴⢒⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⠛⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠧⠤⠤⠇⠀⣈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠙⠙⠛⢻⣧⣤⣤⣾⡿⠛⠟⠟⠛⠛⠛⠛⢹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠶⠶⡶⣶⠶⠞⠒⠲⠶⠶⠶⠶⢷⠿⡛⢿⡙⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣈⣢⣵⣿⣀⣀⣠⣤⣤⣤⣤⣤⣀⣙⣾⣦⠳⡘⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠓

⣧⣷⠠⠀⠀⠀⣀⣐⡊⠈⠌⠀⠀⠈⢀⠀⠀⠀⠀⢸⡀⠀⣉⡀⠀⡀⢀⠀⠀⠀⢈⡩⠀⢀⡀⠀⠀⠀⠘
⠿⠁⠀⠀⠁⠀⠀⠁⠀⠂⠙⠃⠀⠀⠘⠿⢒⠙⠁⢀⣀⠉⢁⡀⠉⢒⠡⠀⠀⠠⢤⡀⠁⠀⠄⠓⠂⠀⠈
⠀⠀⠀⢀⣷⠒⠂⡀⠀⠀⠒⡄⠀⠀⠀⠀⠒⠐⠀⠈⠁⠀⢈⠅⠸⠡⠤⢤⡄⠀⠀⡸⠀⠀⠰⢀⡀
⠀⠀⠀⠈⣋⡂⠀⠺⡹⣄⡠⠸⠐⣀⢈⠸⠄⠀⠐⢦⠄⠀⡀⢠⠀⠀⠀⣴⣋⠨⣢⣇⢀⣩⡌⣖⡇⣐
⡀⠀⠀⠈⠀⠹⠈⠐⣀⣌⣁⣨⢖⢁⣈⠀⠀⠀⣠⠀⠀⢘⠀⠉⡈⢉⠡⠘⡛⢹⠁⢸⠃⢈⣗⣀⠀⡀
⠁⢸⠀⠀⠀⠂⠀⠀⠿⢿⠛⠟⠷⠗⠗⣧⣤⣀⢀⠀⠀⠌⠻⠭⠙⣩⡋⠀⠸⣿⠀⢸⠀⡼⠀⡼⠐⠄⢄
⠀⡦⢰⠁⠀⠀⠚⠉⠀⠀⠀⡀⠀⠀⠘⠙⠛⠁⠠⣞⢷⠄⢀⣀⢀⡕⢚⣛⠷⣼⡄⢸⠀⡇⢰⠃⠸⠀⢀
⣦⡶⠁⢈⠂⠠⠬⠃⠠⣤⡤⠄⠀⠀⠀⠂⠠⠀⠄⡁⢰⡄⣉⠤⢋⣴⢿⡿⠛⠺⣅⠘⠀⠁⠘⣆⣀⢂
⠘⣃⠑⢜⣛⠷⢚⠰⠉⣇⢰⠾⢛⠁⢀⠀⠀⠀⠀⠐⣠⠞⣡⣴⠛⢁⣾⣀⠀⠀⠈⠳⡄⠀⠀⢻⡿⢺⣿
⠉⠰⠀⠀⠀⠀⠉⢀⠌⠛⠙⣢⠈⢀⢀⡶⢾⡿⠻⣯⣥⠿⣻⣦⣶⣶⣿⣏⣢⠴⢶⣦⡈⠀⠀⠈⢷⣀⠼
⠀⠀⢁⡀⡀⠀⠂⠪⡷⣶⠄⢉⠄⠀⢘⡇⠀⣀⡴⠋⠀⣼⠟⠉⠀⠀⠈⠻⣿⣌⣎⠁⡉⢒⠶⠶⢤⡀
⠀⠣⠁⠀⡁⠀⠀⡄⢁⡙⢠⣤⣂⡤⠊⣠⠞⠉⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢸⣿⣯⢢⡍⠀⠀⡀⢠⣹⣦
⠀⠰⠋⠂⣀⠀⢀⠈⢠⣴⠟⠛⢉⠵⢛⣧⡶⠿⠿⣇⠀⢀⡀⢻⡀⠀⠀⠠⠱⠃⠻⣿⡶⡏⠫⠅⠘⣯⡿
⢄⠒⠒⠒⡈⡅⠜⢦⠘⣷⣤⡤⠀⢀⣿⠋⠀⠀⠀⢈⣻⣾⠏⠸⣇⠐⠊⣀⣴⡆⠀⣸⣷⡾⠾⣡⡾⠋⢀
⣋⡐⢠⠄⠛⠳⠦⢶⡄⠀⠙⠿⣦⣘⣿⢀⠀⠀⠀⣿⡟⢲⠒⠚⣉⠤⡎⠙⢿⣿⠟⠁⡞⠋⠀⠈⠣⠀⡀
⣄⠐⠡⣄⣠⠀⡀⠀⠲⢄⡀⣤⠈⣿⡝⣿⢇⣀⣀⣈⢕⣣⠔⠚⣅⠀⢙⣶⣿⢏⣠⠞⠁⠀⠀⠢⢠⡠⠘
⠉⣲⠸⣁⡀⣹⠁⠄⠠⠼⠁⠔⠈⠙⠿⣿⡑⠮⣍⡙⡍⠀⣳⡤⠊⣹⣿⠿⣣⠏⠂⠐⠂⠀⠀⠀⠀⠙⣿
⠀⠈⡀⠈⡉⢁⠄⠘⡳⡄⠀⢀⠀⠨⡃⠻⢷⣤⣨⡀⠈⢫⠀⠀⢒⣩⠵⠺⠋⠀⡀⠀⢀⠱⠀⠀⠀⠀⢨
⠄⠂⡑⣢⠔⣦⣊⡷⠻⣄⢸⠖⢲⠀⣷⠂⡈⢹⣧⣍⣳⣶⣴⠚⠅⠀⠀⠠⡄⠚⠄⠀⠂⠀⠑⡀⠀⢀⠎
⠂⠼⢗⠥⡑⢧⡬⣇⠐⠉⠋⠀⠀⣦⢽⢉⡖⣰⣈⣿⡄⠀⠤⡀⠁⢰⠀⠀⠘⠄⠀⢀⠀⠈⠀⠀⡠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠶⠤⠔⠒⠛⠛⠓⠶⠤⠔⠂⠉⠙⠓⠶⠐⠂⠙⠛⠒⠶⠶⠒⠉⠉⠓⠶⠤⠴⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⡆⠀⠀⣀⠀⠀⠀⣤⠀⠀⢰⡂⠀⠀⣀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠗⠒⠈⠁⠒⠺⠁⠀⠀⠀⠸⠓⠀⠉⠁⠂⠾⡁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣂⣠⣾⣿⣦⠀⠀⠀⡇⠀⡌⢀⣶⣷⣦⠈⣂⠀⢀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠤⠚⠛⠚⠒⢤⡐⠛⠊⠉⠉⡽⠿⢌⠉⠉⠉⠉⠉⡭⠛⠛⠛⠓⠢⢄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡁⠀⠰⡒⠀⠀⣠⠇⠀⠀⢀⡼⠁⠀⢘⣄⠀⠀⠀⠸⡁⠀⠀⣒⠂⠀⢈⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠂⠀⠈⠢⣄⠉⠒⠓⠈⠁⠀⠀⠀⠊⠀⠉⠀⠒⠊⠁⢀⠔⠁⠀⠐⠉⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⣤⠤⢀⣀⣀⣀⣠⡤⠴⠖⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢈⣿⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠰⢅⣀⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠙⡦⠒⠒⠒⠢⠴⠲⢦⡤⠤⠖⠒⣤⠰⢲⡖⠠⠤⠴⡲⠖⠦⠖⠒⠒⠶⡖⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠘⠦⠎⠈⠢⠐⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡇⠈⣠⣤⣤⣥⡈⠈⢡⣭⣭⣭⠍⠀⠈⣭⣬⣭⠉⠉⣩⣬⣭⣤⡍⠉⡇⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⡄⠀⡇⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠢⣀⠠⠋⠉⠉⠀⠀⠈⠉⠉⠉⠀⠀⠃⠀⡔⠀⠑⢄
⠀⠀⠀⠀⠀⠖⣁⢀⠀⡤⣉⠄⠧⠤⠤⠤⡤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⢤⡤⠤⠤⠼⠀⡒⢁⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠘⠥⠐⣀⠇⠀⠀⠀⠀⠀⠀⠦⢤⣀⣀⡤⠌⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⣀⠼⠇⠀⠀⠀⠀⠈⠀⡀⠃⢌⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢳⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⢀⡞⡭⠷⡀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠘⢭⡗⢡⠃⠀⠀⠀⠀⠀⡰⠱⠆⠈⠉⠉⠢⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠎⡄⠀⠀⠀⠀⠎⢂⠔⠚⠓⠫⡤⠀⢀⠀⠈⠀⠉⠓⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠘⡼⡀⠀⢀⠜⢀⡃⠀⢠⣶⣆⡜⠊⢉⠙⠣⡤⠀⢰⣶⠄⢀⠭⢽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣣⠀⢸⠀⢪⠉⠳⡈⠛⢻⠀⠸⣿⡷⠀⢱⠀⠀⢀⠴⢡⣶⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠓⡇⠀⠶⡓⠤⣈⠒⠙⢄⠀⡠⠤⣠⠃⠀⡠⠃⢀⠀⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠃⠀⠀⢼⣑⣦⠤⢤⠤⠭⢷⠆⢈⠆⡸⡀⠀⠈⡠⠊⠀⠀⠀⠀⢀⡤⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡆⠀⣜⢉⡬⢿⠯⢤⡴⠁⡀⠀⡞⠀⠛⣠⣊⠀⠀⢀⣀⠠⠤⣊⢸⡼⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡑⠬⠝⣒⢒⡒⠁⠀⠘⠋⡰⢁⡔⠊⠁⣶⡯⠭⠒⠂⠉⠁⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣈⣫⢶⣤⣅⣀⡀⠀⠂⠀⡇⠓⢉⡲⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣋⡙⢿⠉⣾⣯⣭⣍⣑⢺⣓⣊⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⡍⢉⠟⠓⠳⠬⢬⣛⣛⢹⣝⣋⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡕⠛⠓⠁⠀⠀⠀⠀⠀⠀⠈⠻⣍⡥⢟⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣤⠴⠖⠲⠤⣤⡤⠶⠒⠲⠤⢤⡤⠴⠒⠶⠤⣤⡤⠖⠒⠦⣄⣀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡄⠀⡀⠀⢰⠀⠀⡀⠀⠀⠀⢀⡀⠀⣶⠀⢀⡀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠠⠁⠀⣹⠦⠚⠂⠾⢅⠀⠀⠀⢀⠷⠄⠛⠠⢾⡀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣀⣀⠑⣄⡔⢁⣀⣀⠀⠀⠀⠘⢆⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠃⢼⠀⠀⠀⢰⢣⣶⡎⠣⢸⢠⢣⣶⣮⢣⠀⠀⠀⠘⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡸⢄⡀⠀⠈⠢⠍⠥⡷⠊⠺⡦⠍⠥⠋⠀⠀⣀⠼⣀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡏⠀⣀⠘⣄⡀⠀⣀⡠⢇⠀⢀⡧⣀⡀⠀⣀⡎⢀⠀⠈⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠳⠈⠳⡀⠀⠉⠉⠀⠀⠈⠀⠈⠀⠀⠈⠉⠁⢀⠞⠁⠴⠃⠀⢨⠇⠀⠀⠀⠀⢠⡄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠰⣸⡸⣾⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠁⠀⠀⠀⠀⠈⠑⢦⠤⣀⣀⣀⡠⢤⠚⠁⠀⠀⡐⠀⢡⠀⠀⣧⡀⠀⠀⠀⠙⡝⠮⡁⠉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢘⠁⢿⣀⣸⠀⠀⠀⠀⠡⠤⠂⠀⣠⠏⠹⡀⠀⠀⠀⠸⣄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣆⠀⠀⠀⠠⠄⠁⠀⣀⠀⠀⣀⣀⣀⠀⠀⢀⠄⠀⠐⠀⠀⠀⠀⡇⠀⣠⠇⠀⠀⠀⢀⡎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢳⠣⢤⠄⠤⣄⣠⠤⢄⣠⠬⠥⣄⡤⢤⣍⣉⣥⡤⢄⣀⡤⠦⢄⡠⠛⢍⢧⣀⠀⠀⣠⠞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠈⠓⠞⠉⡷⣏⠘⠖⠋⠀⠀⢀⣀⣀⣸⠀⠀⠈⠓⠮⠭⠭⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠁⣤⣤⣭⡍⠉⢭⠉⣈⡟⠀⠘⣄⣀⡤⠀⢤⣤⢄⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢳⠀⠉⠉⣻⠙⠛⠛⠛⣿⠛⠓⠛⠛⢻⡛⠛⠛⠉⢹⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠺⢥⠆⡀⢠⡘⡄⠀⠀⠈⠙⡟⢻⠋⠁⠀⠀⠀⠀⠀⠉⢹⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠠⣯⠞⢏⣸⠑⠃⠀⠀⠀⠀⣧⢼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⢽⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⣸⢄⠀⠀⠀⠀⠀⠀⢠⠾⣸⣗⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠙⠀⣡⣾⠀⠀⠀⠀⠀⠀⠘⣦⣄⠈⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠒⠶⢦⣄⡄⠀⠀⠀⢀⡀⣠⡴⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⠃⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣷⣤⠤⠤⣼⡇⠀⠀⠀⢀⡿⠷⠒⠲⢦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢳⡀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣸⠁⠀⠀⣰⢛⣷⣼⡇⢰⠃⠀⠀⣴⢛⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠙⠦⠟⡼⠁⢸⡄⠀⠀⠙⠦⠟⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣤⣀⣀⣤⠞⠁⠀⠀⠹⢦⣀⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣮⣭⣙⣛⣛⣛⣋⣉⣭⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⢿⡏⠁⡜⠁⠀⠀⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣠⡴⠶⣤⡀⠀⠀⠀⢀⣀⣷⣀⣀⣀⡀⠀⠀⠀⣀⣙⠲⠧⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡟⠀⠀⠀⣾⠁
⠀⠀⠀⠀⢠⠞⢛⣧⣶⣿⣷⣠⠴⠚⠋⠁⣿⠀⠀⠈⠉⠉⠙⢻⠁⣈⣉⣿⡛⠓⠒⢲⣄⣀⣀⡀⠀⠀⠀⠀⢠⣇⠀⢸⡏⠀⠀⢠⡟⠀⣠⡤⢤⣤⡀
⠀⠀⠀⠀⢸⡟⠋⠁⣸⣿⡀⠱⣄⣠⣤⠴⣿⠀⠀⠀⠀⠀⠀⢸⣀⣠⣴⣧⠉⢦⡀⣾⠀⠀⠀⠉⠉⠉⠓⠒⢾⠉⠙⠻⢧⣄⡀⣼⠃⣼⣿⣤⣤⡿⠛⢦
⠀⠀⠀⠀⠈⢷⡶⠛⢉⣽⣷⡶⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡨⢡⣿⣿⢣⡀⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣄⠀⠈⠛⠿⣤⡽⣿⣿⡉⠙⠳⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠚⠛⠁⠈⠀⠀⠀⠀⠀⣧⣠⣤⣤⣤⣤⡤⣤⢡⣿⣿⣿⠀⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠲⠦⣄⣼⠁⣿⡛⠛⠶⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠂⠉⠦⠀⠀⠀⣬⡞⣩⡙⣿⡏⠉⠉⢉⣓⣶⡦⠤⣄⣀⡀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⢿⠿⣶⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠢⠴⠃⠀⠀⠀⡯⣷⣬⣴⣿⡇⠀⠀⡇⠀⠀⠈⡆⠀⠈⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠓⠒⠒⠒⠒⠲⠶⠧⠟⢛⣛⣛⡅⠀⠀⠙⠲⠶⠚⠁⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣠⣤⠖⠒⠒⠒⠒⠒⠒⠶⠤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⠊⠉⠳⣌⠳⣄⣤⠤⠴⠶⠒⠒⠲⠦⠤⣄⣀⠀⠀⠀⠀⠈⠉⢙⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⣦⠞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⣀⣀⡴⠟⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠚⠉⢳⣀⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⡤⣴⣿⣿⣿⣿⠟⣫⣴⠿⠋⠉⠉⠉⠙⠘⠛⠒⠒⠒⠲⠲⠴⣏⠁⠀⣰⠲⠶⠦⠤⢤⠤⣀⣀
⠀⠀⣀⣠⡤⠤⠔⠒⠚⠉⠉⠉⠉⠐⣀⡀⠀⢴⣟⣛⣫⣭⣶⣿⣭⣄⡢⠠⠀⡂⢁⠔⠀⠁⠀⠄⠀⠐⠈⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⡐⠀⠍⠉⠙⢒⠢⢤⣀⡀
⣞⠩⠉⠄⠠⠀⠀⠀⠐⠀⠒⠈⠁⠀⠀⠈⠉⠈⠉⠉⠉⠙⠉⠉⠛⠉⠠⠅⠤⣐⣢⡬⢦⣴⣥⠶⠶⠦⠦⣄⢿⣿⣿⣿⣿⣿⣦⣄⢀⢈⡥⠤⣬⠀⠦⠡⠤⠤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⠾⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⣀⡀⢀⠤⠤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡧⠀⢀⠎⠁⠙⠆⠀⠀⠀⠵⠉⠚⠣⡨⠋⢢⡠⠤⡤⠤⢄⡤⠢⣰⠋⠑⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣎⣤⡤⠶⠶⠶⠒⠲⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⡿⠛⠓⠒⠲⠷⠶⠾⢤⣬⣍⣆⣓⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠖⠀⢀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠟⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠶⠆⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠠⣾⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⠇⠀⢀⠈
⠀⠀⠀⢀⠐⠆⠠⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠘⠿⠟⠀⠀⠠⣿⠀⠐⠀⡀⠠
⠀⠀⠀⠀⢀⡀⠒⠀⢸⡆⠀⠘⠃⠀⠀⢸⣿⣆⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠡⠆⠀⠄
⠀⠀⠀⠀⠈⠁⠀⠂⠘⡇⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠻⢦⡀⠀⠀⠀⣤⠾⠋⠉⠉⠉⠛⠷⣄⠀⠀⠀⠀⠀⢸⠇⠐⢂⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣷⠀⠰⣿⣿⠋⠀⠀⣀⣀⣀⠀⠀⠈⢻⡄⢀⡾⠁⠀⢀⣀⣀⡀⠀⠀⠘⢷⣾⡷⠀⠀⣼⣀⡀
⠀⠀⠀⠀⠀⢀⡟⠁⠀⢿⣦⡀⢨⡏⠀⢠⣿⣿⡏⠀⢱⡄⠀⠀⣷⢸⡇⢀⣾⣿⣿⠁⠈⣆⠀⠀⢸⡇⠀⠀⠀⡟⠉⠉⢧
⠀⠀⠀⠀⠀⠀⢷⣘⠦⣼⡟⠁⠘⣧⠀⢻⣿⣿⣿⣿⣿⡇⠀⢠⡟⢸⡇⠸⣿⣿⣿⣿⣿⡿⠀⠀⢸⠇⠀⠀⢼⡧⠔⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⡇⠀⠀⠹⣦⡈⠓⠾⠿⠿⠋⠀⣠⡾⠁⠀⠻⣄⠙⠠⠿⠿⠛⠁⠀⣰⠟⠀⠀⠀⣸⠗⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⠙⠷⠦⣤⡤⠶⠟⠉⠀⠀⠀⠀⡈⠻⠶⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⣿⠀⠀⠐
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⡆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⢠⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠤⣶⠦⠤⠤⠤⣶⡖⠂⠀⠀⠀⠀⠀⠻⠿⠟⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⡇⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⣿⣶⣶⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⣀⡈
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⣷⠀⠀⠀⣾⣶⠀⠀⠀⠀⠀⣿⣿⣿⣉⣙⣿⣿⠀⠀⣀⡀⠀⢀⡀⠀⠀⢠⣏⡈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⡼⠁⡀⢀⡴⢻⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⡙⢓⠀⠻⠋⠀⠈⠁⠀⠀⢸⠋⠙⢲⡄⢀⠙⢧
⠀⠀⠀⠀⠀⠘⣇⣸⣠⠏⠀⠈⢻⡖⣶⣶⠤⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣉⣉⣀⣠⣤⣤⣤⣤⡤⣶⠋⠀⠀⠀⠹⣌⣆⣸⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠘⣇⠀⢸⡀⡀⣏⠀⠀⢹⠀⠘⢏⡉⠞⠀⢸⠁⠀⠀⡇⠀⣸⠉⠁⡟⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⣳⣷⣿⡶⠷⢿⡿⠿⠽⠯⠭⢭⡽⠿⢿⣾⣿⣶⡟⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣁⣀⣀⣀⣠⣤⣼⠇⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣈⣉⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⢠⡌⠷⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⢰⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠘⢁⠔⠐⠏⠐⢦⡀⠀⠀⠀⠘⡌⡀⢒⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠘⡀⠔⠈⢻⠀⣻⠀⠀⠀⠀⡓⡖⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡙⠂⠀⠊⠉⢁⣴⠀⠀⢀⢳⢁⠜⠀⣬⣩⠙⠂⠶⠤⠤⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣶⣶⣿⣏⣁⡴⠀⡔⣥⠣⠊⢁⣀⠀⠻⠄⠛⠲⣤⠀⢨⠚⠉⣉⢱⠀⠀⠀⠀⢰⣀⠠⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠙⢏⣉⣁⡠⠚⠀⣷⢻⢡⠑⠀⠘⠟⠇⢀⣶⣦⠀⠸⠀⠈⡥⠄⡴⢎⢣⠀⠀⠠⣃⠤⢨⣅
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⣷⠤⢁⠒⢆⡀⠉⠁⢴⠁⣠⠞⢤⠀⢁⠤⠛⠄⠀⠈⠀⠀⠀⠒
⢀⠄⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢜⠳⠸⣉⣷⠲⣤⣬⣵⠋⢘⠜⢀⡤⢾⣪⡔
⠘⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⣾⡿⠿⠿⢿⠟⠁⠐⣫⠄⢮⣀⡬⠜
⠀⠀⠈⠉⠉⠛⠒⡖⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠙⠃⣒⣒⠁⡎⢡⠋⡑⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⣍⡈⣻⡖⠲⠦⠰⢤⡼⠤⠀⡼
⠀⠀⠀⠀⠀⣰⠒⡁⠄⠀⠈⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡰⣌⠉⣅⠛⠂⠐⠶⢒⠂⠶⠚⠇
⠀⢠⠀⠐⠒⠻⠀⢈⠃⠀⠀⠀⠀⠁⠀⠰⡆⠀⣀⡶⠒⠒⡛⠉⢡⠾⣄⣀⡟⠙⢛⣖⠘⠐⡿⠉⠀⡀
⠀⠈⢢⣀⠀⠀⠱⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⢀⠀⢀⣡⡴⠋⠀⠀⠹⣕⢤⣿⣿⣿⣞⣆⢠⣿⣿⡇
⠀⠀⠀⠈⠙⠒⠲⠬⠷⠆⠒⢛⠷⠂⠤⢄⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠈⠉⠘⢿⡿⠈⠳⠟⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⢉⣱⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠲⠶⠖⠒⠒⠲⠶⠒⠒⠲⠤⠖⠒⠒⠢⠶⠖⠒⠦⠤⠤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⢀⠝⠛⠲⠤⣀⠀⠄⣀⣠⡤⠴⠶⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡏⠀⡠⢒⡒⡄⢹⡟⢡⢔⡒⡄⠀⢸⡀⠀⠀⣸⠁⠀⠀⢀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢇⠀⠑⢌⡥⢃⡼⠣⡜⢌⡣⠏⠀⣸⠁⠀⠀⢸⠔⠲⣊⠥⠒⠑⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠁⠀⠑⠦⠤⠴⠚⠀⢀⠟⠦⠤⠤⠚⠁⠀⠀⢀⡟⠀⢀⡇⠀⠀⠀⠄⠘⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠀⢀⠄⣲⠂⠲⢲⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⡖⠋⠉⠀⠀⠀⢱⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⢸⠀⠀⠀⠀⠈⢙⡁⠢⠤⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⡶⠡⠀⡸⡆⣀⠤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡐⢠⡉⠩⠔⣛⡁⠀⣀⣴⡐⠒⠦⣤⣤⢤⡤⠤⠄⣠⡤⠤⣄⣀⡞
⠀⠀⠀⠀⠀⠀⠃⠀⠒⠊⠉⣧⠵⠼⠷⠤⠤⠉⠈⢀⠖⢦⠀⠀⠈⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠉⠉⠛⠀⠨⠛⠛⠃⠸⢟⡻⠛⡚⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠛⢛⠟⠛⠓⠒⠚⠓⠒⠲⣀⡀⠘⢒⢳⢏⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣩⣴⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⣊⢬⣶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⠒⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁

⠀⠀⠀⠀⢠⠖⠉⠑⠒⠈⠉⠙⠒⠀⠉⠉⠓⠒⠀⠒⠒⠒⠂⠒⠒⠂⠀⠐⠢⡀
⠀⠀⢀⡤⠋⡀⢀⠀⠀⠈⠀⠱⢀⡀⠀⡆⠀⡤⠀⠀⢠⠀⢰⡄⢀⡀⠠⠀⠀⡇
⠀⣀⠏⠀⠀⠀⠀⠂⠀⠀⠄⠀⡠⠋⠉⠉⠈⠑⢄⡠⠊⠁⠈⠁⠛⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠰⡇⠀⠀⠠⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⣢⣴⠀⠂⠠⣢⡶⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠞⡡⠊
⠀⠹⡄⠀⠀⠀⠀⠘⡄⠀⠀⢘⣄⠀⣀⠀⠙⠋⢠⡂⠐⠽⠗⠀⠀⠠⠀⠀⠰⠁⠀⠀⠀⣠⠂⢾⡪⠧
⠀⠀⢳⡀⢀⢀⠀⠀⠂⠀⠀⠈⠀⣄⠈⠱⠀⠂⠁⠈⠒⠀⠀⠁⢀⡠⠞⠀⢀⡆⠀⠀⠀⢣⡈⠚⠄⡴
⠀⠀⠀⢑⠀⠁⡜⠁⡄⠀⠀⠀⠀⣿⣦⣄⣀⣀⡀⣀⣀⡉⣙⣭⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⢃⠖⠉
⠀⠀⠀⠘⢆⠀⠰⠄⠀⡇⠀⠀⠀⢻⣿⣿⣿⣇⣀⣼⣯⠀⠸⠀⠀⠔⠀⠂⠀⠀⠀⠀⢀⢎⠎
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠁⠀⣀⠀⢸⡛⠻⠿⠿⢿⣿⡟⠀⠀⠀⠀⠁⠀⠀⡞⢂⠦⠤⢃⠎
⠀⠀⠀⠀⢀⠋⠈⠇⠀⠀⠀⡀⠀⠀⢉⡒⣒⠦⠴⠛⠃⠀⠀⠀⠐⠀⠃⢀⣀⣘⠞⠉⠁
⠀⠀⠀⠀⠸⣀⢀⡰⠄⠠⣤⠥⠤⢤⣤⠤⠤⢤⣌⠉⣤⠤⢤⡤⠤⠤⠤⡞
⠀⠀⠀⠀⠀⢸⢸⢢⣤⡄⠤⠀⠀⠀⠈⠁⣀⣁⡼⠺⣄⣁⡀⢀⣀⣀⡠⠇
⠀⠀⠀⠀⠀⠀⠐⣀⠈⠁⠀⠈⠉⠉⠁⠈⠉⠉⠣⠤⠋⠉⠁⠈⠉⠉⢱
⠀⠀⠀⠀⠀⡐⠀⠸⡍⢷⠒⠒⠒⠒⡶⠒⠒⠒⠲⣖⡒⠒⢒⠖⠀⠁⠉
⠀⠀⠀⠀⠀⢣⡄⢓⠈⠀⠙⠒⡖⠈⠀⠀⠀⠀⠀⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣤⠇⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡄⠀⠀⠀⠀⠀⠀⢠⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⡄⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠃⠀⠀⠀⠀⠉⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣂⡉⣦⠢⡀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠊⣡⠤⠄⡊⠉⠀⠑⢘⡘⢄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡐⠂⠈⡁⠀⠠⠌⠌⠁⠠⠁⠇⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⣶⡝⠢⡀⠔⡐⠀⠠⠊⠉⣁⠼⠁⠀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢠⡀⠙⢦⠘⢿⣿⣿⣤⣿⣿⣇⠀⣥⡈⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠒⠒⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡻⠷⠳⡄⣙⠛⢉⣉⣀⡅⠀⣉⡤
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⢀⠉⠡⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠤⠤⣮⠉⠀⡆⠐⡍⠠⣀⣩⡭⢶⣉⣿⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢊⠀⠀⠀⠀⠀⢁⣀⣁⢈⣭⣿⣿⣿⠟⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⡌⠻⢿⣟⣿⠛⠉⣤⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠱⢦⡬⠉⠁⠀⢰⡯⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠙⠟⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣠⣤⣴⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠿⢿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⢾⠄⠘⢗⣴⣿⡇⠀⢠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⣄⣠⠄⠀⢹⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⡧⠀⣸⠿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⠟
⠀⠀⠀⠀⠀⠐⣾⠿⠷⢤⣀⠿⣿⣿⣿⣿⣯⣽⣶⣿⣿⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣼⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣽⣽⣷⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠋⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⠿⠟⠿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣄⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⠀⢰⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠉⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⡁⠠⠂⠀⠀⠙⢤⣀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢊⡡⠖⠒⠓⠲⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠞⡱⠋⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡠⢊⠞⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⣄⣠⠃⠀⣀⡀⢀⡠⠤⠤⢴⣁⡤⠤⠤⣄⠀⠀⠀⠈⠀⠈⠑⠆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⣠⡤⠷⠤⢤⡤⠒⠋⠉⠉⡉⠛⠀⠈⠁⢄⡰⠴⠀⠀⠀⠠⠐⠈⣧⠀⠀⠀⠀⠀⡀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⣞⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠁⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠏⠑⠠⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣶⠄⠀⠀⠀⠛⠦⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠄⠙⡀⠀⠐⠁⠀⠀⠤⠤⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⡠⠀⠀⢀⠆⠀⠀⠀⠈⠀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠂⠈⠲⢄⡀⠀⠀⠁⡄⠃⢹⠀⠀⠀⠀⠀⠁⠒⠈⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⢹⣀⠔⠁
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠀⠀⠄⠈⠢⠀⠐⠆⠒⠋⠀⠀⣈⣀⣀⣀⣀⣠⡤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠈⠛⠲⠦⡀⠁⠊⠀⠀⠀⠀⠀⠆⠀⠈⠄⠀⠀⠀⠀⠀⠉⠀⠈⡄⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⣠⠶⠚⠋⠈⠀⠀⢁⡀⠲⠆⠘⠛⢈⠂⡈⢆⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⢰⠁⠀⠀⠀⠀⠀⡴⠋⠀⠐⠂⠀⠀⠀⠑⢦⠀⢡⠀⠘⢿⣿⣷⣄⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡿
⠀⠸⠀⠀⠀⠑⢠⠌⠀⠤⠌⠁⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢷
⠀⠀⢣⠀⠀⠀⠺⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠙⢇⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠑⢄⡠⠈⡀⠂⠄⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠘⠆⠁⠔⠀⠀⠑⠢⣄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠦⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⢛⣋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢰⠈⠑⠀⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠒⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠐⠀⠀⢀⠝⠒⣈⠓⠤⣀⢠⠀⠀⡈⠠⠄⠐⠂⠀⠢⢀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠉⠒⠠⢈⡉⠠⠀⠀⠀⠀⠀⠈⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣀⣠⠤⠔⢚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⠢⣄⣀⣀⣠⠤⠴⠒⠋⠉⢁⣴⣦⠀⠈⢐⠄⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⣿⠀⠀⢄⠀⠀⠀⠉⠀⠄⠀⠀⠀⢀⣴⡟⠛⣍⡀⠠⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡀⡅⠀⠀⠀⠓⡶⠀⠀⠚⠀⠀⠀⠀⠘⠿⠃⠀⠰⠽⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠉⠤⠊

⠀⠀⠀⠀⠀⠀⣠⡶⠶⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣰⠟⣇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠲⣤⣀⣀⣀⣀
⠀⠀⠀⢀⣰⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠉⠉⠓⠶⠤⠤⠤⢤⣀⡀
⠀⠀⢠⡟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠙⠓⠦⣇⠀⠀⠀⢰⡀⣾⠀⢈⠙⠛⠓⠒⠲⣄
⠀⢠⠟⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⢢⠀⡔⠊⠁⠈⠁⠻⡀⠀⠀⠀⠀⠈⣇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡄⠀⠀⢂⣤⣍⢢⠀⠀⠛⠀⢀⠀⠀⣄⠀⠈⠆⠀⠀⠀⢠⡇
⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣃⠀⠠⡘⠿⠟⠠⠀⠀⢸⠀⡎⢰⣶⡎⠃⠀⠈⡀⠀⠀⠀⢳
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡠⠪⠅⡀⠝⣦⠉⠒⠂⠀⠀⠀⣘⠀⠡⡈⠛⡡⢁⣠⠖⠓⢲⡄⠀⢸⡇
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡁⠀⠠⣥⠀⢦⡀⠀⠀⠀⠀⡰⠉⢄⠀⠀⣀⠴⠋⠀⠀⠀⣸⠧⡀⢸⠃
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⠂⠀⢸⡲⣄⠈⠑⠒⠒⠉⠀⠀⠠⠗⠊⠁⠀⢀⣀⣴⠞⠁⡀⡈⢾⡄
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢇⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠐⠒⠛⠉⠁⢀⣠⡟⠂⢀⠇⣷
⠀⠀⠀⠀⢻⠀⡖⠓⠶⣤⡀⠀⠳⠀⣠⣴⠒⢻⣄⠀⠀⠀⠈⣿⠓⠶⢦⣤⣤⣤⢤⡶⠞⠋⢁⠃⠀⠁⢠⡏
⠀⠀⠀⠀⠸⡇⢃⠀⠀⠀⠙⢦⢀⠀⣇⠊⠀⠈⢉⣧⣀⣀⣀⠿⢤⣀⣸⠀⣗⠀⠀⡇⠀⠀⡘⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢻⠈⡆⢠⡞⢧⣸⢿⠀⠈⣳⠀⢀⣀⣴⣿⣿⣿⠀⢠⣶⣮⠀⠉⠙⠛⠃⠀⢰⠃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢈⡇⠙⠦⠽⣄⠻⣌⣧⠞⢁⡴⠋⠁⠈⢿⣿⣿⣦⣼⣿⣿⡇⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠢⣈⣡⠔⠋⠀⠀⠀⠀⠈⢿⡛⠻⢿⡿⠿⣅⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠈⠙⣆⡴⠋⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡠⠞⠛⠲⠒⠒⠶⣤⣄⣀⣀⣀⡀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⣇⣠⠶⠊⠀⠀⢀⠀⠀⠀⠀⠀⠉⠻⣤⡀⢙⣿⣶⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢀⠤⠂⠋⠈⣀⣉⡐⠒⠀⠤⠀⣙⡋⠀⢹⡦⣤⠞⠳⣭⣽⠿⠿⠷⣤⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠤⢊⣥⣶⠇⠀⠀⠙⠛⠛⠿⠷⠀⣶⣦⣤⣭⠟⠀⢸⡦⠤⠀⣀⡀⠀⠀⠈⠉⢹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠋⢀⣠⠶⠠⠤⣀⣀⡀⠀⠀⠀⠀⠉⢳⡄⠀⣠⠿⠿⣶⣠⣤⣭⣍⣒⠶⠾⠦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠢⠤⠽⣞⣁⣀⡴⠛⢱⡴⢛⣩⠴⠒⣶⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⠾⢉⡧⢤⣀⡿⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⢀⡞⠛⠲⠶⠦⣤⣤⣀⣀⣀⠀⠀⠀⢤⠤⠶⠞⣋⡤⠞⢩⡇⡸⠀⣠⣤⣤
⠀⠀⠀⠀⠀⣰⣶⣶⠀⠀⢻⣦⣀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠴⠚⠉⠀⠀⣜⣠⡃⢰⣿⣥⢿
⠀⠀⣠⣶⣿⣿⠛⠿⠀⣰⠋⡴⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⢀⡼
⠀⠀⣿⣧⡟⢐⡦⡷⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢟⣦⠔⠋
⠀⠀⠈⠉⠀⠀⢆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠔⠃

⠀⢀⡠⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣀⣀⣀⣀
⠀⡎⠑⡎⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠄⠠⠤⢤⣀
⠀⠣⢬⡋⠀⡎⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡰⠦⢠⡆⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠲⠤⢤⡀
⠀⠀⠀⠈⢳⡰⡀⠀⠀⠀⠀⠀⠸⠀⠀⠔⠁⠀⠀⠀⠈⠛⡀⠀⠘⠂⠼⠃⣠⠀⠀⠀⠀⠀⠀⢀⠄⠊⠻
⠀⠀⠀⠀⠀⢳⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⡇⠀⠀⠋⠀⠠⡀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⠀⠢⣄⠀⠈⠀⠀⠄⢆⠀⠀⠀⡀⢀⣀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠶⠋⠀⠀⠀⠀⠀⠀⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⢺⠀⠀⠀⠣⣄⡉⠓⠒⠀⠀⠀⠙⠒⠘⢀⣀⠀⢡⠀⢀⡇⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠⣋⠉⠖⡖⠒⡲⠒⠈⠉⡠⠃⠀⠈⢀⠜⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⡀⠀⠐⠀⣀⢸⣋⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⡜⠉⠀⢁⢀⣁⡠⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⡸⠅⣒⡦⠠⠐⣀⠤⠔⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣔⣁⣀⣡⠔⠊⠀⠀⠀⠀⢠⠂⠀⡖⠁⠀⠀⠷⣶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠑⠲⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⠻⠹⢶⠤⣤⡤⢄⣀⠀⢀⠀⠀⠀⣀⣀⠴⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠶⠦⠉⢥⣴⡉⢳⣑⡉⠀⠉⠉⣉⡀⣟⣁⠤⠒⡊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠄⠀⢄⢀⠀⡠⠉⠉⠁⠐⠲⠶⠀⢹⠀⠶⠛⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⢄⠀⢀⡞⠉⠉⠉⠑⠒⠒⠒⠒⠦⣤⠷⠒⢈⡟⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠴⡯⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠈⠉⠐⠲⠭⣅⣒⢶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠄⠀⡠⠤⠠⠤⠤⠔⠒⠂⠐⠒⠈⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⠉⠁⠀⡀⢀⣄⢀⡀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⡰⠁⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⡠⠋⠁⠀⠈⠑⢤⠖⠉⠀⠀⠉⠢⡀⠀⠀⠀⡃⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⢀⢠⡄⠀⡇⠀⠀⢠⡄⠀⠀⢱⠀⠀⢰⠃⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠒⠢⣄⠀⠀⠀⢇⠀⠈⠂⠀⠀⠀⠼⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⢄⡀⠙⠢⠔⠉⠑⠤⠀⠀⢄⣠⠄⠰⠀⡼⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠮⣬⣉⣉⣁⣀⣀⣤⠴⠒⠉⠂⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢧⠀⠀⠀⠀⠰⠤⠤⠿⠄⠀⠄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡜
⠀⠀⡂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠁⢒⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⢸⠀⠀⠠⠀⠈⠁⣠⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠃⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠀⣀⠀⠠⠠⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⠢⠤⠒⢢⡤⠤⡤⠤⢄⣀⣀⣀⠄⣀⣰⠠⠤⠤⢒⡎⠄⢉⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣠⣄⣀⠀⣈⣀⠔⠢⡄⠂⠀⠀⠀⠀⠀⠀⣀⠀⢠⠊⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠉⠉⠡⠀⠉⠙⠁⠀⠛⠛⠂⠀⠀⠘⠛⠀⣀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃⠀⠒⠒⠲⠒⠀⠤⠆⠲⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠈⠀⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠷⣦⣾⣶⣷⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠿⠛⠀⠀⠀⣾⡛⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠤⠄⠤⠔⠒⠤⠤⠒⠒⠒⠒⠒⠉⠉⢳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⠀⢀⠀⢠⡀⢀⠀⠀⢀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠎⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠜⠋⠉⠈⠉⠲⣄⠔⠉⠉⠈⠉⠢⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⡎⠀⠀⠀⣂⡂⢀⠇⠀⠠⢂⡐⠄⠀⠸⡀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⠧⠤⣀⠐⠍⠅⠈⡆⠀⠐⠬⠡⠂⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢦⣀⠈⠑⠦⣀⡠⠛⢦⣀⠀⠀⡈⢀⡀⠁⡄⢀⡇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣨⠛⠒⠢⠤⠄⠀⠀⠈⣉⡭⠔⠛⠁⠈⠀⢸⠀⠀⠀⠀⠀⡎
⢀⠤⠂⠄⠈⠐⠀⠤⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠉⡏⠉⢱⢲⠂⠉⠋⠀⠀⠠⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄
⢈⢂⢦⠀⠌⠁⠈⠀⠀⠂⠀⠬⣉⠂⠀⠙⡆⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⡁⣀⡠⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⣸⠁⡀
⠡⢀⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠰⡁⠀⠀⠀⠀⠀⢢⠐⠁⠐⠁⡀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠘⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠑⠒⡤⠤⡬⠘⢉⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠉⠙⠫⢉⠝⡒⠲⢖⠒⡲⠤⠤⠴⠒⠲⠴⠗⠒⠒⡪⠙⠒⣁⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠶⠤⠄⢠⣤⣴⠃⠱⣒⣁⡀⠀⣀⣀⡀⠀⠤⠀⣀⡎⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⣀⣀⣀⣀⣀⠁⠀⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠉⠑⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠉⢉⠉⠉⠉⠁⢐⠒⠒⠒⠒⠒⠎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡁⠀⠀⠀⠀⠀⠀⠁⠲⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣶⣼⣦⠀⠀⠀⠀⠀⠀⠀⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡿⠿⣿⠿⠀⠀⠀⣴⡶⣦⣾⣷⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠉⠉⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠖⠋⠉⠉⠙⠲⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡞⠀⡴⠊⠉⠉⠑⢄⠀⢣⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⠀⠈⡆⠈⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡆⠀⢆⡔⠊⠐⢲⠉⠁⠲⡁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠦⣀⠀⠀⠀⠈⡆⠀⠀⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡈⠀⠀⠀⠀⣏⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣸⣆⠀⡏⠀⠀⠰⠋⠉⠉⠉⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⢹⠉⠀⠀⢰⡀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠐⠂⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠓⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⠛⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠎⠩⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⢀⡀⠀⠧⠤⢄
⠀⠀⠀⠀⡠⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠰⣾⣷⠄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⢄
⠀⠀⢀⠞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢤⠀⢸⡇⠀⡤⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⡀
⠀⢀⠎⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠱⡀
⠀⡜⠀⣰⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⠀⣼⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⣆⠀⢣
⠸⠀⢀⣿⣿⡄⠀⠣⡠⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢰⢠⣿⣿⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠜⠀⢠⣿⣿⡄
⡇⠀⣸⣿⣿⣿⡆⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⣾⣿⣿⣧⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢰⣿⣿⣿⡇
⡇⠀⠈⠉⠻⣿⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢰⣹⣿⣿⣿⣿⣆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⢀⣿⠟⠉⠁
⠰⣀⠔⠢⡀⠈⠁⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⣸⣿⣿⣿⣿⣿⣿⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠁⢀⠔⠢⣀
⠀⠀⠀⠀⠈⠦⡀⠀⠀⠈⠑⠢⠤⠄⢀⣀⠀⠤⠤⠒⠙⢄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠑⠒⠤⠤⠀⣀⡀⠠⠤⠔⠊⠁⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣄⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣄⡀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⣀⠠⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠤⣀⡀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠈⠹⢿⣿⠟⠋⠁⢀⡀⠤⠔⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠉⠻⢿⣆⡀⠀⠀⠀⠀⠋⡱⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠙⠋⠐⡢⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠸⠆⠐⠃⠀⣠⠄⠀⣤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠁⠀⠀⠀⠀⠀⠁⢀⠀⠘⠁⠈⠁⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠘⠛⠃⠀⠀⠀⢹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣇
⠀⠀⢀⠀⠔⠂⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⠀⢀⡀⠔⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⡠
⠀⠀⠶⢊⠅⠀⠀⠀⢀⢑⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠦⣄⣀⡈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠃⠒⠉⠉⠉⠀⠀⠈⠁⠂⠈⠀⠂⢄⠀⠀⣀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡀⠁⠁⠀⠀⠀⢀⣀⣤⣾⡟⠂⠀⠀⠀⠀⠀⠀⠛⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⠃⠀⠁⠀⠀⠀⠀⠀⠀⣇⠀⢸⣿⠉⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠄⠀⠀⠀⠀⠀⢨⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⢿⡋⠀⠀⠉⠉⠉⣉⠟⠀⠀⠀⠀⠀⠀⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⣭⣥⡔⠀⣀⣀⡜⠹⣀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⡇⢀⣀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠉⠛⡀⢀⠵⠾⢧⠀⣠⣀⣀⠀⣤⣀⣀⠑⢸⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠓⠲⠶⡬⢥⣀⣀⢀⠀⠀⠉⠉⠁⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢲⠖⠁⠀⠀⠀⢉⡏⠙⠛⠒⢾⠿⠿⠿⠿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠒⠠⠲⠊⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢃⠀⠀⠁⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⠂⠈⠃⠠⡘⢁⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠋⢠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⣉⠘⠀⡰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⢡⠀⠀⠀⠀⠀⠀⡎⠰⠁⠐⠐⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡠⠀⢀⡜⣆⣰⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡐⠁⢀⠊⢇⠳⡈⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠐⠀⠀⠀⠀⢀⡜⠀⢠⠃⡰⢈⠜⡸⠆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡰⠁⠀⡇⢸⠘⣀⠇⠀⢀⠔⠁⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⡠⠃⠀⡔⠁⠀⢰⡉⡞⢀⠇⢀⠴⠃⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⡐⠁⢀⠜⠀⠀⠀⡎⢸⣠⡎⠠⠁⠀⠀⠈⠀⡌
⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⢀⠜⠀⢀⠎⠀⠀⠀⠀⢇⠸⠉⢃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠸⡀⠈⡄⠀⠀⢀⠊⠀⠠⠃⠀⠀⠀⠀⠀⢨⢜⠇⢸⢀
⠀⠀⠀⠀⠀⠀⠣⠀⠈⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣀⡳⠟⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⠒⢈⣁⠴⢺⣍⢦⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠤⠤⠤⠤⠄⠒⠊⠁⠀⠀⠀⠛⠛⠲⣶⢝⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠭⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠐⠒⠶⠚⠁⠀⠲⠒⠈⠐⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣦⡀⠤⠀⠀⠀⠎⠹⠃⠘⠛⢁⡴⣤⠀⠀⢶⡶⠈⢙⡒⠄⢠⣀⠀⠀⠀⠀⠀⠀⡞⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠓⠦⢀⡫⠗⠀⠀⣠⢄⠀⠀⠀⠠⠦⠀⠀⡀⠘⠋⠀⠀⡠⡉⠒⠤⣀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⣔⢂⠈⠉⠲⡖⣌⠉⠀⢴⠶⠀⡴⢦⠈⠛⣀⠤⡀⠀⠉⢠⠖⢲⠌⠓⠶⠤⢤⣀⡀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠃⠈⠁⠀⠀⡀⠀⠀⠉⠒⠤⣄⡀⠉⠁⠀⠀⠓⠚⡁⠀⢀⡈⡙⠉⢠⣶⠆⠀⠀⠈⠙⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⣏⠆⠀⠘⠬⠀⠀⠰⠵⠀⠀⣬⡑⠢⣤⠠⢄⡘⠊⠀⠈⠉⠀⠀⢀⢤⡀⠐⠛⢃⡴⢹
⠀⠀⠀⠀⠀⠀⣀⣠⢤⡄⢀⡤⡄⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠀⣈⣀⠀⠀⠉⠒⠓⠄⡀⠀⠀⣔⠄⠈⠛⠁⣠⠴⢋⡄⣼
⠀⠀⢀⢠⠖⠋⠁⠀⠀⢧⣀⠓⠃⠀⠀⢰⢢⠀⠘⠶⠚⠀⠀⠀⣇⠀⡇⠀⡀⠀⠀⡤⢬⡑⠤⣤⣠⡤⠔⠊⢁⣠⠀⡅⣸
⠀⠀⠏⣯⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⡀⠀⠁⢀⡀⠀⠀⠨⠇⠀⠈⠉⠁⠀⠉⠀⠀⠓⠶⠋⠀⠀⡔⠢⠀⠸⠆⠀⠈⠒⢻⡄⠀⠀⠀⣀⣀⠀⠀⡀
⠀⠀⠀⠈⠓⠶⠶⢤⡀⠀⠀⠀⠀⠀⠛⢄⡀⠘⠚⠀⢀⣀⠀⠀⠀⠀⢰⣓⠀⠀⠀⠛⠃⠀⠀⠀⡇⠰⠳⠀⠈⢁⠐⠂⠘⡟⠉⠉⠉⠉⠉⠙⢳⡀
⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡘⠚⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢠⢶⠀⠀⡀⠀⠣⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⡤⡄⠀⠀⠉⢀⡀⠀⠈⠋⠀⠀⠽⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠴⠞⠃⢤⡀⠀⠘⠞⢠⡀⡄⠀⡀⠔⠉⠀⠀⠀⠀⠀⢀⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠶⠖⠒⠒⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠽⠵⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⡀⢀⣀⣤⣄⣀⣀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⠴⠦⣤⣄⣀⣀⣀⣀⣄⡀
⠀⠀⠀⡾⠋⠉⠉⠉⠉⠁⠀⠀⠙⣯⣉⠉⣉⣼⠋⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠉⠀⠀⢀⣤⠶⠯⣭⡉⠀⠈⢻
⠀⠀⠀⣷⠀⢀⡶⠋⠉⠙⢦⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠹⡆⠀⣾
⠀⠀⠀⢸⡆⠈⠳⢤⣤⡤⠟⠀⡀⠀⠀⠀⡆⠀⠀⣠⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⣠⠘⢦⣀⠀⢀⣰⠇⢸⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⣼⣧⣄⣠⡏⠀⠀⠀⠀⠹⣆⣠⣼⣧⣤⣠⡏⠀⠀⠉⠉⠉⠁⠀⢸⡆
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠉⠻⣦⡀⠀⣠⠞⠋⠁⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⢀⡴⢾⡇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠁⠀⠀⢀⣤⠶⠦⣄⡀⠈⢷⣼⠃⠀⢀⣤⠴⠦⣤⡀⠀⠀⢻⡄⠀⢰⡏⠀⣼⠁
⠀⠀⠀⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⢀⡟⢠⣶⣶⡌⢷⠀⢸⡇⠀⠀⡾⢡⣶⣶⡌⢷⠀⠀⠈⣧⠀⠸⣇⢰⡇
⠀⠀⠀⠀⣸⣧⣤⡀⠀⠘⣇⠀⠀⠀⢷⡘⠿⠟⣣⡟⣠⠼⠷⢤⡀⢷⡘⠿⠿⢃⡾⠀⠀⢰⡇⠀⠀⠈⢻
⠀⠀⠀⠀⣿⠀⠀⠹⣆⠀⠹⣦⠀⠀⠀⠙⠛⠛⠉⢰⡇⠀⠀⠈⡇⠀⠉⠛⠛⠉⠀⠀⣠⠟⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢹⡄⠀⢀⡟⣠⡶⠎⠛⠶⣤⣤⣤⣤⠶⠛⠃⠀⠀⣸⠛⠶⢤⣤⣤⣤⠴⠞⠁⠐⣶⡄⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢿⡴⠟⠁⠋⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠛⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⢀⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠲⠶⣶⣶⠶⠶⢶⡟⠋⠁⠀⠀⠀⢀⣀⡀⠀⠀⣰⠋⢷⡀
⠀⠀⠀⡟⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣿⣿⣀⣀⣸⡇⠀⠀⠀⠀⣴⠋⠉⠉⢳⡄⢹⡄⠀⢻⡄
⠀⠀⠸⣇⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣥⣉⣩⣤⣬⣥⣁⣩⡴⠞⠁⠀⠀⢧⡀⠀⠀⣠⠇⢸⣇⣀⣀⡷
⠀⠀⠀⢸⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢸⣿⡏⣿
⠀⠀⠀⢸⠀⣿⠻⣤⣤⣤⣀⣀⣀⣤⠴⣶⡶⠦⣤⣤⣤⡶⠖⢻⡶⠶⣤⣄⣠⣤⣤⣤⣤⣤⡤⣤⣤⠟⢸⡇⣿
⠀⠀⠀⣾⠀⡿⠀⢻⠀⠀⠉⠉⠉⠀⠀⠈⠙⠶⣤⡴⠛⣷⣴⡏⠙⣦⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⢿
⠀⠀⠀⣿⠀⣧⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡟⠀⢿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⢾⡇⠀⣸⠇⢸⡀
⠀⠀⣰⡃⢀⣾⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⡿⣆⠈⣷
⠀⠀⣿⣷⣸⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢈⣷⣇⣸⢿⡇
⠀⠀⠻⣌⣻⣿⡿⠀⠙⠒⠒⢲⡖⠒⠒⠒⠒⢲⡖⠒⠒⠒⠒⠒⠒⢶⠖⠒⠒⠒⠒⢶⠖⠒⠚⠃⠀⢸⣿⣿⣉⡾⠁
⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠘⠷⢦⣤⣤⡴⠞⠃⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠟⠛⠾⠃⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠶⠋⠷⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⠴⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠳⢦⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⣠⠖⠛⠋⠓⠦⠤⠒⠚⠙⡷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠤⣤⣤⠴⠖⠉⠁⠉⠙⠲⠖⠚⠉⠁⠀⠈⠓⠒⠚⠉⠀⠀⠀⠈⠙⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⢠⠇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣸⠀⠀⠀⠀⣰⠋⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡞⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠀⠈⠧⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⡼⠀⢻⠀⣀⣀⣯⣀⣀⣀⣠⠏⢀⡤⠖⣚⣩⢭⣝⣓⠲⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡀⠀⠀⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠓⠚⠁⣠⠞⣫⠟⠛⠓⠲⣄⠉⢙⡶⠋⣰⠋⠁⠀⠀⠀⠈⠳⡄⠈⠳⣤⠞⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⣧⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⠎⢹⣄⡞⠁⢸⠁⣠⣤⣶⡄⢘⣦⠏⠀⠰⡇⢀⣴⣿⣿⣿⠀⠀⡟⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠁⢰⠇⠀⡟⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⡼⣿⠀⠀⠘⢦⣿⠿⠛⣡⠞⡟⠀⠀⠀⠳⣌⠛⠛⠛⠁⢀⡼⠁⠀⠀⠀⢻⠀⠀⠀⠀⣼⠁⠀⡟⢀⡴⠃⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠀⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⡇⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠈⠓⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠲⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠤⠄⣾⠁⠀⠉⠙⠲⣄⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠈⠑⠤⠀⠀⠀⣿⠀⠀⠀⠀⠐⣇⣀⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠲⠤⣄⣠⣴⠛⢦⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠈⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢠⠖⣦⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⡟⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⣸⠃⢀⡏⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⢀⠠⢤⣀⠀⣀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠞⠁⣏⣠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡀⠀⠀⢀⠊⢁⠔⠉⠀⠀⣨⡀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡤⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠈⡶⠁⠠⠃⠀⠀⡠⠊⠀⢈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⢸⡄⠀⠀⠀⠠⡏⢀⡏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠙⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡼⠀⠀⡼⠀⠀⠀⠀⣠⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⢀⣨⢷⠀⠨⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⢸⠁⠀⠀⢀⡾⠁⠀⠀⢳⡀
⠀⠀⠀⠀⡤⠞⠉⠀⢸⠇⠀⢣⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⡆⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢀⡞⠀⣤⣀⠀⢸⠀⡠⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⢸⡆⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣼⢀⠔⠁⠈⢣⡼⠊⠀⢀⣬⡤⠤⣄⣀⠀⢀⣠⠴⠶⠤⣤⣀⣀⢀⣀⣠⠤⣄⣀⠀⢀⣀⣤⣄⡀⠀⣸⠃⠀⡏⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠸⠃⠀⠀⡠⠊⠀⢀⡴⠁⢠⣀⣀⡤⠬⠉⠉⠀⠀⢶⢦⡤⠤⠭⢭⣥⣄⣀⣀⣉⡭⠍⠁⠀⠀⣍⣛⣉⣙⣋⣻⣄⣐⠋⠉⢱⡤⠋
⠀⠰⠁⠀⠀⠀⠀⡠⠂⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠶⠸⡀⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠙⠻⠀⠀⢀⠁
⠀⠠⠀⠀⠠⠐⠈⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠰⠋⢠⢡⡅⢡⢁⠐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠢⡰⠡⠊⠀⢸⢡⡑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⠟⠻⢿⣿⣮⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡏⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⡷⠔⠒⢖⢲⣞⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⣤⡗⠛⣯⢹⣿⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠛⡇⢰⣿⣾⢻⡅⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⡗⠺⣴⡇⠀⣿⣿⣦⡇⢸⠁⢀⡤⠤⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣹⠶⠶⠶⢶⣒⣋⣹⣄⡹⢧⣀⣿⣿⣦⣏⢻⣷⣿⣿⣷⠐⣷⣏⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⣮⣉⠛⣿⣟⡧⢽⡶⢳⣼⣿⣼⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢙⣿⣶⡏⠻⡧⠶⠞⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣿⡇⣿⡆⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣿⡇⣿⣱⠞
⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠀⢘⣿⡇⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⣠⢋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣴⡟⠀⢸⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣄
⠀⠀⢀⣼⠇⣼⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣐⣳⣇⡀⠸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢳⣜⢧⡀
⠀⢀⣾⠏⢰⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⡋⢙⠿⢿⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣎⢷⡀
⠀⣼⡏⠀⣼⣿⣿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠻⣷⣿⢦⣞⡉⣣⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⣿⣿⣿⣧
⢰⡟⠀⢀⣿⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⣿⣿⠀⣏⣿⣹⠆⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⣿⣿⣿⣿⣿
⡼⢀⣴⠿⡿⣿⣿⡛⠷⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⣿⣿⡆⣿⣡⠏⠀⠀⠀⠀⠀⠀⢠⡾⠷⢛⡿⣹⢻⠿⣟⠻
⡷⠋⠁⠀⢳⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⠸⠦⠐⣿⣿⣿⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣰⡿⡟⠀⠈⠙
⠀⠀⠀⠀⠘⣆⢈⡻⢿⣿⣶⣤⣄⣀⣀⣠⠞⣧⡞⠀⠀⠀⡼⢿⣿⣿⣧⡑⠦⢤⣀⣀⣀⣤⠤⠖⠉⣠⣾⡿⣱⠃
⠀⠀⠀⠀⠀⠘⣞⣿⣷⣍⡛⠿⠿⣿⣿⡟⢤⣿⣖⣀⠤⠚⠀⠀⠙⠿⣿⣿⣷⣶⣤⣤⣤⣴⣶⣷⣿⣿⢟⣴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣝⡛⠛⠁⠀⠀⠀⣷⢬⡏⠉⠙⠲⡄⠀⠀⢠⠴⠛⠛⣻⣿⣿⣿⣿⣿⡿⢟⣫⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣹⡦⣽⡀⢀⣠⣾⣆⢰⠃⠀⠀⠐⠛⣛⣫⣭⣿⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠼⡗⠿⢿⣿⣿⡇⣀⡤⠶⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠢⡇⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⣛⣛⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣿⣿⡏⠁⠀⠉⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣄⠀⢀⣤⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⣡⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣠⣾⣿⣷⣶⣖⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣲⣿⣿⣷⣄
⠀⠰⣿⣯⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⠆
⠀⠀⠈⠻⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿⡄
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⣿⡇⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⣿⣧⣿⣮⡻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢻⣿⣿⣿⣿
⢹⡟⠉⢻⣿⣿⣦⡙⢷⣤⡀⠀⠀⠀⠀⠀⣿⠇⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣤⠾⢋⣴⣿⣿⡟⠉⠻
⠀⠀⠀⠀⠻⣿⣿⣿⣶⣌⡙⠳⠶⣤⣶⡾⠟⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣟⣋⣥⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣭⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣬⣙⠻⠟⣡⣴⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⣤⠄⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠽⠀⠠⠀⠀⠀⠀⠠⠄⠂⠀⠠⠠⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠈⠁⠀⠀⠁⠰⠚⠋⠁⠀⠠⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠠⠂⠈⢁⡀⠀⠀⠠⠄⠀⠀⠐⠂⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠐⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠇
⠀⠀⠀⠀⢀⡤⠀⠀⠁⣤⡌⠁⠀⠀⠀⠁⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠒⠒⠀⠀⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠉⠀⠈⢦⠃⠉⠀⠀⢡⡎⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⢀⠀⣀⠀⠀⠀⠀⠈⠀⠒⠂⠀⠀⠐⠀⠀⠀⠀⢂⠄⠀⠠⣀⡠
⠀⠀⠀⠀⠀⠄⠀⠊⠀⠀⠀⠒⢢⡔⡂⠀⠀⠈⠀⠀⠐⠀⠀⠀⡅⠀⠈⠠⠀⠀⠀⡠⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⡀⠉⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠄⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⡀⡀⠃⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣠⠄⠠⠄⠀⠰⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠔⠈⠀⠄⠀⠀⠂⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠠⠠⠂⠆⠀⢠⠎⠁⠀⠀⠁⠀⠀⠀⢀⠄⠀⠐
⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠠⠄⠢⠀⠤⢄⠀⠀⠀⠀⢀⠀⠘






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠤⠤⠀⠀⣤⡤⠶⠀⠀⢤⡤⠶⠖⠀⠂⠠⠶⠶⠒⠒⠀⠴⠶⠖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠐⠦⡀⠀⠀⡄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠒⠀⠰⣆⡀⠿⠀⢰⡇⠀⠀⠈⡷⠀⠼⠄⣠⡖⠈⠠⠀⠀⠂⠀⢀⠃⠠⠄⠉⢲⡄
⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠁⡴⠉⠀⠀⠀⠀⠀⠑⠄⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠈⠢⡌⢳⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠀⠀⠀⡔⣭⣅⠆⠀⠀⣴⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⣸⠆
⠀⠀⠀⠀⢠⡟⢐⡧⠐⢄⠀⠀⠀⠀⠈⠇⠀⠀⢀⠀⠀⠀⠂⠻⠯⠂⠀⡀⠉⠛⠃⠀⠀⡀⡀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⢁⡀⢈⠷⠆⢘⠀⠀⠀⠀⢀⡄⠀⠀⣄⠀⠀⠀⠠⢀⣀⣤⠊⠉⠂⢀⢀⡔⠋⠁⠀⠙⠂⠀⠀⠀⠅⠀⢈⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠳⠌⣀⠠⠋⠀⠀⠀⠀⠈⣧⠀⠀⠈⠙⠓⠤⢤⠤⠤⠀⠀⠀⠀⠀⠀⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠤⡈⠢⠂⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠀⠹⠀⢀⣀⠀⠀⠚⢳⠖⠀⣤⣤⠀⠀⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠌⠇⠀⡅⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀⠀⢀⠀⢆⠀⠐⠀⠀⠘⠀⠠⣿⣿⣤⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠐⠀⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠳⠤⠾⡉⠻⠆⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⡿⠟⠛⡟⠀⢀⡀⠀⠀⠀⠂⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⢶⠃⠀⣈⠀⠀⠀⠆⠀⠀⠀⠀⠘⠿⢥⣤⡤⠤⠶⠊⠁⡠⠀⠁⠀⠀⠀⠀⠖⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣄⢀⠀⠀⠀⠀⠀⡀⠐⠒⠂⠒⠒⡒⠚⠉⠀⠀⠀⠂⠀⠀⠀⣀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠉⠀⠉⠉⠫⠉⠉⠛⣉⡸⠋⠍⣉⠩⠝⠋⠉⠉⠉⠙⠁⠀⠈⢲⠐⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⠀⣤⣤⣼⠃⠘⣦⣤⣤⠀⢠⣤⣤⣤⠀⠚⠠⡶⠿⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣛⠛⠛⠛⢳⠖⠒⠐⠒⠒⢶⠖⠲⠖⠲⠖⢾⠋⡝⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠉⠁⠀⠀⠀⠀⠀⠈⠑⠀⣶⠴⠖⠉⠀⠥⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠘⠀⠀⠀⠀⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣧⠀⠀⠀⠀⠀⠀⠀⢀⣆⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠉⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠗⠠⠞⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠷⠧⠤⣤⡶⠶⠷⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠷⢧⣤⣤⣶⠶⠷⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣇
⠀⠀⠀⠀⠀⡏⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠀⢀⠀⠉⡏⠙⢶⡀⢀⡔⡇
⠀⠀⠀⠀⠀⠳⡉⠀⠀⠀⠀⠀⠳⠀⠀⠀⢈⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⠀⠰⡏⠀⠀⠻⠀⢸⠇⢈⡽⠃
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣀⣀⠀⢀⣁⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⢋⣀⠀⢀⣉⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢴⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⣷⣟⡿
⠀⠀⠀⠀⠀⠀⠰⠾⠶⠶⢌⠉⣹⠦⠶⢦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⣌⠉⣹⠷⠶⢦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⡇
⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⣟⠳⣤⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠛⣏⠀⠀⠀⠐⠈⢿⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⠀⢰⠞⠀⠘⠿⠀⢸⡇⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢧⣤⣀⣤⠤⡦⣐⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣜⣃⣠⠤⣦⣐⣛⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⡿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⢰⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢢⠇⠀⡸⠁⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠣⠀⢀⠀⠀⠀⠀⠐⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⢠⠀⣥⠆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠸⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠁⠀⠀⡁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢘⠆⠀⢢⡠⠻⠂⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠌⠀⠀⠎⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣉⡐⠙⠊⣀⣀⠔⢂⠸⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡈⠉⠠⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠴⠞⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣀⢠⣮⡳⠉⠀⠦⢼⡷⢤⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠀⣤⠩⠘⠐⢴⡔⡎⠀⠜⠆⣝⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⡈⠁⠀⠀⠁⠀⢙⣀⡀⢀⠌⠀⠓⢄⠀⢀⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠐⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢄⡐⠁⠐⠉⢉⡐⠀⠉⣨⠁⠛⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠂⠂⠀⠀⢀⡀⠀⠀⡼⠛⠐⠀⡇⠰⠐⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠂⠄⠀⠂⠀⠀⠐⣧⠀⠀⠠⢀⡟⠓⠢⠂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡽⠂⠰⢦⣾⠀⠀⠰⡟⢿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠈⠀⠂⢠⣏⠀⢰⡀⠀⡈⠦⢦⡴⠃⣾⡦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡁⠀⠂⠀⠐⠋⡀⠀⣀⡚⠀⢠⠆⣷⠤⣼
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠤⢀⠊⠀⠀⠀⠰⠁⢸⠅⠸⠀⢤⡅
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠸⠀⠐⠀⠀⣬⠒⠐⠙⡷⢊⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⡀⠚⠃⠒⠤⡎⢠⠄⣈⣠⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠓⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⠒⡶⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⢀⡴⡋⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⢬⠍⢩⠍⠉⠀⠀⠂⠀⠆⠀⡀⠆⠉⠓⢦⡀
⠀⠀⠀⢀⡞⡀⠋⠀⠀⠈⠀⠄⠀⠀⠋⠀⠀⠰⠀⠠⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢀⡀⠀⠁⠀⠹⡄
⠀⠀⠀⢸⠃⠁⠀⠈⢀⠀⠀⣀⠀⡀⠀⠁⠀⠀⡀⠀⠀⠰⠆⠀⠐⠀⠸⠆⠀⠄⠀⠀⠠⠀⠁⡀⢻
⠀⠀⠀⢸⡀⠉⠀⠀⠈⠠⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠄⠀⠖⠀⠀⠀⠤⢠⡄⢸
⠀⠀⠀⢸⢳⡀⠀⠀⠐⠗⠀⠀⠀⠂⠀⠀⠠⠀⠴⠀⠀⡠⠆⠀⠀⡀⠀⢀⡀⠀⠀⠂⠀⠀⡀⠀⣾
⠀⠀⢀⣼⡀⡝⢦⣀⠈⠀⠈⠃⠀⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡒⠀⠰⠆⠀⠀⠀⠀⠤⠀⢀⣾⠇
⠀⠀⡏⠈⣧⠀⢀⠈⢹⡗⠒⠶⠶⠶⡒⠒⠟⠉⠉⡁⠐⠀⠀⢨⠉⠙⠓⠲⠤⠤⠤⠤⠴⠚⠁⡞
⠀⠀⢧⠀⠈⠳⣄⠠⠀⠤⠈⠀⠄⠀⠅⢀⡀⠀⢀⠠⡦⠀⠄⢀⡀⠀⠀⠁⠀⠂⡀⠰⠄⣀⡞⢁⣤⣄
⠀⠀⠈⠳⣄⡀⠈⠙⠲⠦⠤⣤⣤⣤⠤⠴⠖⠒⠚⠒⠒⠶⠶⠬⠥⠤⠥⠤⠭⠤⠤⠴⢚⡟⠀⠛⠒⠚
⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠙⠒⠦⢤⣀⠀⠀⠀⢀⣀⡤⠖⠒⠛⠛⠒⠒⠦⠤⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠰⣏⣉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⠿⠿⠷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡾⠀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠙⡁⠀⠈⠉⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣤⣄⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠈⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠁⠀⠀⠀⠈⠀⠂⠱⣸⠃⠻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠽⡀⠀⠀⠿⠢⣄⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠳⣄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⠀⢢⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠈⣦⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⠓⠄⠉⠉⢹⣧⡀⠠⠄⠀⠀⠀⢀⣰⠿⢍⣀⡀⠀⢠⣼⡏⢻⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⠻⢿⣿⣿⠿⠛⢋⠉⠀⢠⡤⠈⣉⣿⣿⣿⡇⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠎⠀⠀⠀⠁⢀⣾⣧⡀⢶⣽⣄⡀⠈⢀⡀⠀⢀⡄⢀⣨⢿⡿⣿⣇⠀⠀⢂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢶⡶⠟⠈⠛⢿⣿⣿⠉⠛⣦⠀⡉⠉⠁⠀⠉⠋⢺⠇⠈⠻⣷⣶⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠹⡄⠀⠠⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⡁⠛⠒⠐⠃⠚⡑⢿⠀⠀⠀⢸⣇⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢐⡆⠀⠀⠀⠀⠀⡿⢦⡀⠀⢇⠀⠀⠠⠀⠀⡇⢸⠀⠀⠀⢸⡇⠦⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠳⡀⢰⠎⡀⠀⠀⠀⠀⢸⡟⠀⠿⡅⠀⠁⠀⠀⠀⣰⣃⠨⡆⠀⠀⠸⣇⠀⠁⡜⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠑⣌⢰⠃⠀⠀⠀⢀⣾⠖⠀⠀⠄⣶⠄⠀⠀⠀⢩⣱⡆⠵⡀⠀⠀⠙⣇⠀⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⠀⠀⠀⠀⠀⢸⣿⠁⠀⠉⣚⠈⣷⡀⠀⠀⠟⠁⡈⢔⣇⠀⠀⠀⠈⢃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⣼⣯⡂⠀⠀⠉⢀⢏⠳⣄⠀⠀⣠⠁⠀⣸⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠤⠢⢷⡘⣠⠞⠋⠀⠀⠻⡇⠀⢀⠠⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠬⢿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠴⠒⠀⠀⠀⣧⠀⠀⣤⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⠖⠀⠘⠀⠀⠀⠀⠀⠀⠰⠻⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠶⠒⠒⠛⠛⠛⠉⠉⠛⠛⠲⠦⡤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⢀⡖⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣀⣀⡀
⠀⠀⠀⠀⠈⡷⢤⣀⡀⠈⠉⠉⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣆
⠀⠀⠀⠀⢀⡇⢀⣄⠉⠉⠒⠲⢤⣀⠀⠀⠀⠈⠙⠒⠤⠤⣀⠀⠀⢀⣠⣀⣠⠤⠤⠤⠒⠒⠒⠒⠉⠋⠉⠁⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠁⣠⡀⠀⢀⠀⢀⠉⠙⠒⠦⢤⣀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠚⠋⠉⢹⡆
⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠙⠃⠀⡦⠀⠀⠈⠙⠲⠤⣄⣠⣤⠤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠴⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠺⠂⠰⠆⠀⠂⠀⠀⠀⠀⠀⠁⠰⠆⠀⡇⠀⠀⠀⠀⠀⠘⠛⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣠⠤⢇⠀⠰⠆⠠⠐⠀⠀⠀⠀⡀⠀⠐⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠄⣠⡀⠰⠷⠀⠀⠔⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⠾⣭⠿
⡴⠊⠁⠀⠀⠀⠑⠤⣀⠀⠀⠛⠃⢀⡄⠀⠀⠀⠀⠀⠐⠂⠀⠀⣇⠀⠰⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠓⠲⢄
⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡶⠀⠀⣠⡈⠀⠀⠀⠣⠃⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠉⠓⠶⠤⠤⠤⠤⢤⣄⣀⠀⠀⠈⠉⠓⠦⣄⣀⠀⠈⠀⠀⠀⠛⠀⢀⡀⠀⠀⠀⠀⠉⠀⢀⣀⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣤⠖⠒⢦⡄⠀⠀⠀⠀⠉⣳⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠈⠁⣀⣠⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠒⠚⣁⣀⣀
⠀⠉⠛⠛⠋⠁⠀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠒⢚⣩⡭⠥⠐⣒⣀⣤⣤⣝⡻⢿⣿⣿⣿⣿⡿⢟⣫⣤⣥⣀⣓⠂⠬⢭⣍⡓⠒⠲⠦⣤⣄⣀
⠀⠀⠀⠀⣴⣿⣿⣏⠀⠀⠀⠘⢿⣧⣀⡀⠘⠿⠿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣾⣿⣿⣿⡿⠿⠿⠃⢀⣀⣼⡿⠃⠀⠀⠀⣹⣿⣿⣦
⠀⠀⠀⠀⠈⠛⠻⠿⣿⣶⣤⣤⣀⣀⣈⡉⠙⠛⠒⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠒⠛⠋⢉⣁⣀⣀⣤⣤⣶⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠳⠀⡜⠀⠀⠀⣰⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⠢⢄⠀⠀⢸⠈⠂⠀⡀⠃⠃⢠⠀⣴⡏⡠⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡁⠂⠠⢁⡐⠻⡶⣄⡀⠘⠢⣁⠀⢰⡎⢲⠃⠔⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠁⠀⢀⡈⠐⠄⢌⠑⢄⡀⠏⠀⠀⠇⠀⢐⠀⢠⡗⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠁⠐⠈⠳⡄⠀⠁⠀⠈⢢⡀⠀⠈⡄⢸⠀⣆⠃⠁⣠⠔⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠑⢀⣀⠀⠀⠀⠫⡁⠁⠉⠑⢂⡤⢬⢸⡀⠀⡠⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠒⠶⠤⠤⣉⠐⣀⠘⡄⠀⡠⠊⠀⢸⡏⡀⠉⢀⢬⠇⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡓⠂⠀⢁⠂⣌⠑⠠⠅⠀⢀⡸⠷⢀⡴⠁⠓⢀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣞⢡⠄⠐⠷⠐⠋⣀⣁⡀⠠⢃⣷⡔⠪⠍⣁⣉⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣴⠨⠄⠚⢈⡀⡀⠰⡞⠘⣋⡤⠄⣲⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣮⡄⠴⣥⣄⣒⣚⠃⢀⢰⣾⢅⠬⠐⠒⠎⢁⣈⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠂⠀⡄⢇⢀⡽⢭⠤⣈⠀⡗⣩⠆⠀⢈⠆⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠩⡄⠵⠶⠞⠁⢆⡀⠒⠮⣽⠐⠒⠀⣈⣀⡅⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⡄⠠⠒⠒⡄⢀⡤⡀⠀⠒⢃⣠⠁⡸⠁⠠⢀⡌⡄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠋⠘⠣⣠⠷⣀⢄⠈⠀⠞⠁⣀⠀⢁⣴⢁⠎⠀⢠⠦⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠑⠢⣌⣠⣀⠃⢀⡤⠤⢤⠚⠀⠝⠁⠀⢈⣤⢡⠁⠠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⢀⡁⢀⡨⠄⣁⣀⠀⢤⡴⠤⢤⠊⡐⠁⠀⢈⡀⠹⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣅⡉⢢⡀⠀⢈⣁⠀⠊⡀⠀⠐⣀⣀⠊⡐⠁⠈⣀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠶⠤⣀⠊⠉⠉⡉⠀⠔⠉⠀⠠⠐⠀⠰⠊⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣦⠀⣈⠃⢀⠔⠓⠒⠤⢈⠴⠊⠀⡁⣀⠀⢄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡁⠓⠒⠄⢀⠰⠶⠨⠄⢂⠔⠋⢁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡉⠥⢄⣀⠀⠀⠀⠀⣠⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⣥⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠤⠤⠴⠖⣖⡒⠶⠒⠲⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⣷
⠀⠀⠀⠀⠀⠠⣤⠴⠶⢚⡋⣉⡉⠛⢁⡀⢘⣋⠀⢰⡮⠀⠛⠀⣤⡀⢶⠄⠙⠓⠦⢤⣀⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⡤⠞⠰⠶⠀⠀⠓⠚⠒⠮⠥⢈⡉⠀⠀⠀⠀⠀⡤⡄⠀⢠⠒⡄⠀⠰⠭⠆⠉⠙⠶⠦⣄
⠀⠀⠀⠀⢸⠃⢰⠒⡄⢠⠤⡀⠀⠀⢠⡚⡆⠀⠈⠻⣉⡹⠄⣈⡀⠶⠀⠉⠀⣖⡀⣤⣠⠔⠒⠂⠉⢹⡆
⠀⠀⠀⠀⢸⡄⠈⠉⠁⠘⠒⠁⣤⢄⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠈⢱⠂⠈⠉⠀⠀⠀⠀⠀⡤⡀⠁⠀⣷
⠀⠀⠀⠀⢸⡇⠀⢠⢤⠀⠀⣀⢌⠁⢀⣀⠀⠛⠁⡤⡀⠀⣠⡀⠀⠸⠀⠐⠝⠀⡴⢆⠀⠈⠒⢁⣀⠀⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠉⠀⠀⠧⠴⠃⠘⠆⠃⠀⠀⠉⠁⠀⠓⠃⢀⣇⠀⢀⡀⠈⠓⠊⠀⠀⣀⠀⠛⢸⡇
⠀⠀⠀⠀⠀⠳⣤⣛⣀⢰⢒⡄⠀⢠⢤⠀⠀⢀⡀⠀⢴⠄⠀⠀⠰⠎⠀⠈⠁⠀⠀⡠⢄⠘⠿⠃⠀⣾⠥⢤⡀⠀⠀⣠⠶⠒⠒⠶⡄
⠀⠀⠀⡴⠊⠉⠀⠁⠘⠮⣍⡀⠀⠳⠔⠁⠀⠣⠜⠀⠀⢀⣀⠀⢠⡇⠀⢀⡞⢲⠀⠓⠊⠀⠠⢄⠀⢸⠀⠸⣄⠀⠀⠓⠶⠖⠒⠚⠁
⠀⠀⠀⠳⢤⣄⣀⣀⣀⠀⠀⠉⠓⠖⢢⡀⠀⠀⣠⡀⠀⠐⠚⠀⣸⠀⠿⠀⠉⠁⠀⠸⠧⠀⠈⠁⢀⣸⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣳⠄⠀⠀⠀⠈⠑⠲⠬⣠⢄⠀⠀⠈⠛⠀⠀⠐⠆⠀⣀⣀⠠⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠦⠤⠔⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠴⠒⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣰⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠹⣆
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡧⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣠⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⠿⢋⠻⣿⣿⣿⣿⠟⣙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⠀⠀⠀⢀⡴⢦⡀
⣿⣿⣿⣿⣦⣭⣴⣾⣿⣿⣶⣬⣥⣶⣿⣿⣷⣦⣭⣼⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠋⠁⠀⠈⠙⠛⠛⠉⠀⠀⠉⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⠀⠀⠀⠀⢠⡾⡟⠛⣻⣿⣿⣴⣶⡄⠀⠀⠀⠀⠀⡈⠉⢙⡲⠠⣄
⠀⠀⠀⠀⠀⠀⢠⣿⢺⣸⠿⡇⠀⠀⠀⢸⠀⡇⢐⣿⡿⠆⢚⡿⠃⠀⠠⠊⠀⠉⠀⠐⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣺⠃⠀⠀⠀⠈⡇⢻⠛⣿⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⠇⡀⣿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⠿⠀⠀⠀⠀⠀⠹⣬⣾⡿⡏⡇⠀⠀⠀⠀⠀⠀⠀⢈⢩⣀⡿⠂⡗⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠠⠙⣿⠻⠀⠀⠀⠀⠀⠀⠀⢹⠙⣿⣿⣆⠀⠀⠀⠀⠀⠒⠀⣣⠘⣿⡏⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣷⡇⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣇⣿⠀⠀⠀⠀⠀⠠⣾⣿⠇⢹⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⡆⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⠋⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣦⣸⠇
⠀⠀⠀⠀⠀⢀⢢⣦⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠘⢻⣘⡍⠇⠀⠀⠀⠀⠀⠀⠀⠈⣆⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣴⡶⠷⠶⠦⣄⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⠏⠀⠀⠀⠀⠈⣧⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣀⣠⠤⠤⢤⣀⠟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⢰⡇⠀⠀⢸⣿⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢽⠿⡇⠀⠀⢸⣿⠟⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⢲⣳⡟⠊⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠶⢰⣯⣀⡀⢀⣀⣀⣀⡀⢀⠀⠀⠀⡀⣄⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣾⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢻⡜⣿⠛⢻⠻⢿⣿⣿⡛⠋⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣦⣸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣿⡟⠳⣟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠈⢧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⢸⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣠⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⢹⣧
⠀⣾⣇⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⢻⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣽⢁⣎⣿
⠀⣿⣿⡈⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣄⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣾⠃⣸⣯⣿
⠀⣿⣿⣷⡌⢿⣧⡵⠶⠀⠀⠀⠀⠀⠀⠀⢀⡠⣣⠴⠊⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠃⣰⣿⣹⡿
⠀⠸⡿⣿⣿⣆⠳⣄⠀⠀⠀⠀⠀⠀⢀⣔⣣⠿⣇⡤⠆⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⢿⠃
⠀⠀⠹⠏⠘⢿⣧⡀⠑⠦⣀⠀⢀⡔⣣⠟⢁⡜⠉⠀⠀⢸⣧⣿⣿⣦⡀⠀⠀⢀⡀⠄⠂⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠉⠉⠙⠓⠊⠁⠀⠀⠀⠀⢸⣿⡟⠝⠛⠉⠀⠉⠁⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣷⣶⣤⣀⠀⠀⠀⠀⢸⣿⡫⣴⣦⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠀⠀⠉⠛⠿⣿⣶⣤⡀⣸⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠷⠀⠀⠀⠀⠀⠉⠻⣿⣷⣿⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⣄⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠿⡿⠷⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠷⠶⠤⣶⣶⣶⣶⡶⠴⠶⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣶⣶⣴⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⡇⣸⡇⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⣸⠀⢧⡀⠀⠀⠀⠀⠀⡇⢹⣷⠀⠀⠀⠀⠀⢠⠏⢸⡆⠀⠀⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿
⠀⣿⡄⠉⣳⡄⠀⠀⠀⢀⡇⢸⣿⠀⠀⠀⠀⣰⡋⠀⣼⡇⠀⠀⣿⣿⣿⡆⠀⣹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡋⠀⣸⣿
⠀⠻⠻⣄⠈⠦⣀⠀⢀⣸⠃⣼⣿⣄⠀⢀⣠⠞⢁⣾⠻⠃⠀⠀⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿
⠀⠀⠀⠙⢷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣭⣤⣶⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣩⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠺⠀⠈⠉⠙⠛⠒⠶⠶⠶⠶⠶⠶⠒⠛⡛⠉⠉⠉⠉⠙⢛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢠⡞⣡⡄⠀⠁⢀⡀⠀⠐⠂⠀⢀⡀⠀⠈⠁⠀⠀⠿⠂⠘⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠉⠁⠀⡈⠙⢦⡀
⠀⠀⠀⠀⢠⡏⡀⠈⠁⠀⠀⠈⠁⠠⠀⠀⠀⠈⢁⠀⠀⠘⠃⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⢀⡄⠀⠀⠁⡀⠀⢷⡀
⠀⠀⠀⠀⢸⠇⠁⠀⠀⠁⢀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠⠆⠀⠀⠐⠀⠰⠷⠀⠀⡀⠀⠀⠀⣀⠀⠋⠀⠈⣇
⠀⠀⠀⠀⣼⠀⠰⠂⠀⠀⠈⠁⡀⠐⠿⠀⠁⠀⠀⣤⠀⠀⠈⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⣀⠀⠁⠀⣿
⠀⠀⠀⠀⣿⣇⠀⠀⠒⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠉⠘⠛⠀⣿
⠀⠀⠀⠀⣿⠙⢦⡀⠀⠀⠀⡉⠀⣀⡀⠀⠁⠀⠀⠀⠉⠀⠘⠃⠀⠀⠄⠋⠀⠀⠀⠄⠀⠀⠰⠄⠀⠀⠈⠀⠀⠀⠆⠀⣰⡇
⠀⠀⠀⣠⢿⡀⠶⠙⢦⣀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠐⢀⣀⣀⣤⣤⣤⣄⣀⡛⠀⠐⠿⠀⠀⠤⠀⠀⠰⠆⠀⢀⡼⡿
⠀⠀⢸⠃⠘⣧⠀⠀⣀⠉⢙⡓⠲⠶⠶⠶⠶⠶⠶⠒⡛⠋⠉⢉⠀⠰⠀⠀⠀⣈⠉⠛⠓⠶⠦⣤⣤⣤⣤⣤⠴⠚⠉⢰⠇
⠀⠀⢸⡀⠀⠘⢧⡀⠀⢀⠈⢁⠀⠒⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⢁⡀⠀⣀⠀⠁⠀⠆⠀⠚⠂⠀⠄⠀⠀⣀⠀⠉⣠⠟
⠀⠀⠈⢳⡄⠀⠀⠙⠶⣬⣀⠈⠁⠀⠀⠁⠀⠈⠀⠘⣃⣀⣀⣆⣈⣁⣀⡀⠀⠲⠂⠀⠆⠀⠀⡤⠀⠐⠀⢁⣠⣾⠁⢰⣋⣉⣳
⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣉⣙⣛⣒⠒⠒⠒⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⢉⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⣉⡵⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠉⠉⠛⠛⠲⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠠⣞⣋⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣶⡶⠲⠶⣶⡶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢠⣾⣿⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣦⠀⠀⢹⣿⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⡟⠀⠀⢀⡠⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠹⣧⠀⠀⢻⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⡿⠁⠀⡠⠊⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠙⢧⡀⠀⢿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡠⠊⣠⣾⡟⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠈⠻⣄⠀⢿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⠋⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⡀⠙⢦⡀⢻⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⣿⣿⣁⣤⣶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠻⣄⠙⢿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡿⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡛⠋⠁⠀⠠⠄⠀⣻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⢻⠟⢀⡠⠄⠊⠀⠀⠰⣽⢇⣿⡇⢾⣻⡯⣿⣿⣿⣿⣿⣯⢶⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣫⠶⠊⠁⠀⠀⠀⠀⠀⢺⣿⣾⣟⣵⣾⣵⡾⣿⣿⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢶⣿⡟⠁⠀⠀⠀⢰⠇⠀⠀⠀⠰⢿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢆⠀⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣽⣿⡿⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠿⣼⠅⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘⣽⣿⠻⣿⣭⣻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣏⣿⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠋⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⣼⣿⠁⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣣⡟⠁⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⣇⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣧⡖⠀⣴⣯⡶⠛⠳⣼⢿⣆⠀⠀⠀⠀⠀⢠⡀⠺⣏⡽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⡆⠸⣇⣿⡀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠀⢻⣝⠻⣤⠶⢛⣿⠏⠀⠀⠀⠀⠀⣀⣴⡿⢯⡿⣿⣾⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠋⠀⠈⠂⠙⠻⠿⠞⠋⡡⠀⠁⠀⠀⠀⠸⣿⡟⣻⣷⣿⣷⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣷⠀⠀⠀⠁⠄⢀⠄⠁⠀⠀⠀⠀⣀⡠⠴⠿⣧⣿⣟⣻⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠛⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡠⣮⣤⠶⠷⠶⣦⡜⢿⣷⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢧⣦⣀⠀⠀⠀⠀⠀⠀⠀⣎⣱⢏⣼⠟⠋⠉⠢⣻⡆⢹⣇⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⢯⡆⠀⢀⠀⠀⠀⢺⠉⣿⣼⠃⠀⠀⠀⠀⢻⣿⠃⣿⣝⣾⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣦⣷⠀⢸⡇⠀⠀⢸⠀⡟⡟⠀⠀⣦⠀⠀⣸⣿⡇⣿⣼⣙⣿⣿⣿⣦⣄⣸⣿⣿⣿⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣻⣿⡄⠘⠃⠀⠀⣼⠀⣿⣯⠘⣿⣿⣿⣟⣻⣼⠃⣿⣎⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣽⣾⣿⣧⡀⢀⣴⣿⠈⣏⡷⠘⠛⣿⡿⠟⣿⢸⡇⣿⣬⡿⣼⣿⣿⣿⣿⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠨⣿⣿⣿⣿⣿⣿⠏⠄⠿⠀⢟⣧⠐⡈⠂⠘⠀⢹⣼⡇⣿⠿⢡⢹⣿⣿⣿⣿⣿⣿⣿⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠻⣿⣟⡘⠋⢰⡆⢚⠀⣸⠿⣤⣤⣄⣠⣀⠼⣿⠃⣉⠀⣫⣯⠹⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠁⠘⣩⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⠛⠉⠉⠃⠛⠋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⢀⡤⢤⣀⣠⡤⠶⠶⠦⣤⣤⠤⠴⠶⠦⣄⣀⣀⣀⣤⣤⣀⠀⠀⢀⣤⢤⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠙⠛⠁⠀⠀⠈⠙⠋⠉⠉⣧
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣩⡕⢆⠀⠂⢀⠖⣀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡤⠤⠤⡀⠀⠀⠀⠣⠌⠥⠂⡠⠀⠘⢄⣛⡡⠁⠀⠀⠀⣠⣀⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⠀⠰⡀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⠆⢧
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠄⠀⠀⠀⠀⠀⠁⠂⠠⠄⡀⢀⣀⣀⣀⡀⡤⠄⠐⠈⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠆⠘⢄⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⡃⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣽⡋⠉⠉⠉⠛⠉⠙⠦⣌⣙⢖⢒⣏⣉⡶⠖⠒⠒⠋⠓⠒⢾⣡⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡇⢀⣐⣒⡒⠒⣒⣒⣒⠲⡎⠙⡆⣥⣤⣤⠤⢤⣤⣤⠤⡞⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠈⠋⠉⠁⠈⠙⠛⠛⠙⢄⡴⠋⠉⠉⠉⠀⠉⠉⠙⢁⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣻⡖⠒⢶⡦⠤⠤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠼⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⢳⣇⠀⠀⠉⢹⠉⡏⠀⠀⠀⠀⢀⡏⣹⠉⠁⠀⣸⡄⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣫⡻⠁⠀⠀⠈⡧⢽⠀⠀⠀⠀⢸⠒⡇⠀⠀⠀⣗⠝⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⡇⠸⡆⠀⠀⠀⢸⠀⡇⠀⢀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⣿⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠿⠿⠂⠀⠀⠀⠈⠛⠋⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡤⠄⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠶⠤⠶⠋⠀⠶⠶⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣆⡀⢤⠄⠀⠀⠶⠭⠖⠐⠟⢃⡤⢤⠀⠀⢴⣺⠉⠓⡒⠄⢀⣀⠀⠀⠀⠀⠀⠀⢰⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠒⢤⣀⡶⠶⠀⠀⢀⣀⡈⠉⠁⢠⣤⠀⠀⠀⠘⠛⠀⠀⣀⡁⠲⢤⣀⠀⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠠⢄⠈⠑⠢⣤⢌⠉⠀⣤⣠⠀⡠⢤⠀⠛⠃⣀⡀⠀⠑⢁⡤⠒⡌⠓⠤⢤⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠫⠃⠈⠋⠀⠀⠀⠈⠈⠑⠒⠤⣀⠀⠉⠉⠀⠀⠻⠔⠃⠀⠀⢈⡓⠚⢁⣤⡦⠀⠀⠈⠙⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡞⡆⠀⠀⠌⠂⠀⠠⢲⠀⠀⢉⡒⠠⣤⠤⢀⡀⠟⠀⠀⠓⠁⠀⠀⡉⡀⠀⠶⠆⢠⠿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⣠⡀⠈⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢈⡁⠀⠈⠁⠲⠷⢄⠀⠀⠀⣠⣄⠀⠓⠃⠀⣠⠖⠁⣰⡇
⠀⠀⠀⢀⡤⠚⠉⠁⠀⢇⠀⠳⠃⠀⠀⢠⢤⠀⠐⠧⠼⠀⠀⠀⣎⠈⢳⠀⠀⠀⠀⢀⣌⡒⢤⣈⣀⣀⡠⠔⠋⡀⡀⢉⣸⡇
⠀⠀⡶⣿⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⡀⠈⠈⠀⠀⠀⠀⠰⡣⠀⠈⠓⠋⠀⠘⠀⠀⠹⢤⠽⠀⠈⢉⠍⠀⠠⣦⠉⠁⠣⠾⡇
⠀⠀⠀⠙⠶⢤⣤⣄⠀⠀⠀⠀⠀⠈⠳⢄⠀⠸⠵⠀⠀⡀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠸⠆⠀⠀⠀⢸⠀⣔⡄⠀⠒⠀⠤⠀⣷⠒⠒⠒⠛⠛⠛⠲⡌
⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠘⠽⠀⠀⡠⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⠵⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠁⠀⢀⣄⠀⠀⠛⠁⠀⠀⠈⢲⠃⠀⢟⠄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣠⣴⢎⣄⡀⠀⠀⠿⠆⡀⢸⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⣀⡤⠖⠚⠁
⠀⠀⠀⠀⠈⠓⠦⠤⣤⣤⣤⡤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣘⣏⡼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠴⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠉⠙⠓⠒⠒⠲⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣍⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠶⣿⠀⣸⠷⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣿⢿⣝⣃⠈⣴⡿⢿⣿⡏⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠃⣸⡆⢸⡆⠛⢻⣏⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣽⡿⣿⣴⣮⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣶⣶⣇⣷⣾⣿⣶⣾⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣿⣿⡹⠟⢳⠛⢿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣿⡟⢻⡇⣸⠛⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢸⠏⣿⣿⠀⢹⠂⢺⣿⠋⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⠃⣿⣿⠞⠙⠙⢾⣿⡇⢻⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⡼⠀⣿⢽⡉⠸⠁⣙⢽⠀⢰⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠀⣿⣿⠀⠀⠀⢸⣿⡇⠘⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠃⠀⣿⡿⡁⠉⠀⠁⢿⡇⠀⢻⣍⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⠀⣻⣧⣄⠀⢀⣠⣽⡇⠀⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⠀⢸⣿⣄⢳⣴⣶⢀⣾⣇⠀⠀⠻⠧⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⢠⣿⡟⠻⣷⡿⠛⢿⣧⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⡦⣦⡄⠀⠀⣾⠋⢻⣿⠉⣻⡿⠋⢿⡀⠀⠀⡄⠐⠆⠀⠀⠀⣴⢆⡄⠀⠀⢈⣿⣄⣠⣿⣷⣀⣼⡏⠀⠀⠀⣦⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⡄⢻⡇⣿⢁⢠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢾⣼⣿⣿⡏⣿⣿⣯⣸⡇⠀⠀⠀⠚⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣸⠃⣿⣾⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡟⣿⣿⡇⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠹⠀⢸⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⡇⠀⢸⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠸⠃⠀⠀⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠄⠀⠀⠸⣿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡄⠀⠀⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⡄⠀⠀⣠⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢹⡇⠀⠀⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⡇⠀⠀⣷⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠁⠀⠀⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠃⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠶⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠔⠈⠁⠢⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡐⠂⠒⠓⠀⠬⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠒⠵⠤⠄⠀⣀⡐⠁⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠒⢁⠶⢀⢀⡠⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠂⠀⠐⠐⠀⢦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⢅⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠊⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠋⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠁⠀⠀⡄⠂⠁
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⡠⠐⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡔⠀⢷⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡘⠀⠀⠈⠕⠄⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌
⠰⠁⠀⠀⠀⠈⢆⠂⡀⠀⡇⠀⠰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠜⠀⢀⠌
⡀⠀⡀⠀⠀⢔⢦⠓⠁⠀⢁⠀⠀⠂⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠊⠤⡤⠀⠀⠀⠀⡃⠀⠀⠀⠀⡠⠂⠀⠠⠂
⠗⠈⠱⠀⠀⠀⠢⡑⢄⠀⠀⠄⠀⢈⡎⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⡠⢀⠔⠁⠀⠀⠉⠐⠂⠀⠀⡠⠊⠀⢀⠔⠁
⠀⠀⠀⠱⡀⠀⠀⠈⠐⠬⠀⠈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⠀⠥⠒⠁⠀⠀⠀⠌⠀⠀⢀⠠⠊⠀⢀⠀⠁
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠠⠄⠊⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣘⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣭⡛⢶⣄⣠⠾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⠶⠋⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⡾⠃⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⢷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⡿⠛⠋⠀⣠⣏⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣱⣾⣯⣭⣭⣤⣴⠟⠉⠀⣠⣤⣶⣿⣯⣭⣭⣭⣭⣛⣶⣿⣿⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⢿⣿⣿⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠁⢠⡞⢹⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⣿⣿⣿⣿⡷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠙⢲⡄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣇⠀⢷⡀⠀⠀⠀⠀⢀⣤⠞⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠈⢓⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⡆⠀⣷⠀⣀⣤⣾⡛⢁⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡧⠀⢸⠀⠈⠉⢉⣽⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡷⠀⢸⠂⢀⣴⣾⣿⠟⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢦⣀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠀⣰⠃⠀⣼⠖⣻⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⠳⢤⣠⠞⠋⠉⡉⠉⠙⠛⠿⠷⢤⠴⠞⠁⢀⣼⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣉⠓⠾⣏⣻⣿⣷⣶⣤⣤⣠⣤⣤⣶⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⠛⠁⣠⡼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠦⠶⠛⠉⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⣤⢄⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠼⠃⠘⣷⡈⠷⠀⠷⡤⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣺⠋⡝⢻⢶⡴⠟⠻⠿⠯⢡⡙⢆⡁⣼⢹⠲⣄⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠔⠢⣽⣆⢿⠁⠛⠀⠸⢡⣄⢁⣈⡜⣂⠖⠀⣼⠸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠏⠠⢖⡠⠌⡳⠾⠧⣦⣘⣂⠓⠎⢘⠋⡳⠤⠠⠶⣿⡄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⡙⠀⠀⠉⣠⠔⠀⣀⠀⠁⢀⡹⢳⣯⢱⠂⠓⢌⠀⠂⠘⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⡄⢀⠚⠃⢘⢄⠲⣭⠀⠀⢹⡇⠠⣋⠀⠀⠀⢈⠙⢀⡶⠉⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠖⠊⡀⠘⠱⢢⡐⠈⠰⠲⠤⣴⡶⠿⠲⣆⠠⢤⠖⠞⠀⠀⢡⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣤⡀⠁⠘⠋⠀⢀⡀⢴⡀⠀⢰⣞⡀⢤⠹⣦⠀⡄⠰⣮⣤⣶⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠠⠀⢰⡖⠀⡿⠏⢀⠠⣌⠳⡖⢿⣿⣶⠑⠁⠐⠸⢠⣿⣼⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣐⢀⠀⡼⠂⠆⠛⢁⡀⠠⣶⡍⢛⢷⡄⠀⣻⣌⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣉⠀⠸⠃⠅⠾⢀⣻⣿⣭⣀⡶⡬⠋⠛⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠯⠽⠧⠞⠓⠶⠋⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⣾⣿⣧⡉⣱⣿⣿⡄⠀⠀⢠⣾⣿⣹⠀⣏⣿⣷⡄⠀⠀⠀⠀⢀⣀⢼⡿⢀⣀⠀⠀⠀⠀⢀⣀⣼⠙⣄⣀
⠀⠀⠀⠀⣿⣿⠿⠇⠿⣿⣿⡇⠀⠀⢨⣷⣿⣿⠀⣿⣿⡿⡇⠀⠀⠀⠀⣿⠉⠁⡄⠉⢻⡆⠀⠀⠀⣾⣿⣿⠸⣾⣿⡇
⠀⠀⠀⠀⣿⢻⣄⡀⣄⡸⢻⡇⠀⠀⢰⡘⢿⡟⠀⢻⡿⢃⡄⠀⠀⠀⠀⣿⢰⣤⣷⣴⢸⡇⠀⠀⠀⠛⢹⣤⠀⣴⠈⠃
⠀⠀⠀⢸⡇⢸⣿⣷⣿⣿⠘⣧⠀⠀⢸⡇⡸⠁⠀⠀⢧⢸⡇⠀⠀⠀⢠⡟⣸⣿⣿⣯⠸⡇⠀⠀⠀⡷⢸⠏⠀⠻⡄⣾
⠀⠀⠀⢸⡁⣿⣿⣿⣿⣿⡇⣽⠀⠀⢘⠀⣵⣦⣀⣴⣾⠀⠋⠀⠀⠀⢸⢳⣿⣿⣿⣿⡆⢿⠀⠀⢸⡇⣾⣶⣤⣶⣇⢹
⠀⠀⠀⠘⠀⡿⣿⡍⣿⡟⠃⠈⠀⠀⠸⠠⢿⣿⠿⣿⡿⠆⠙⠀⠀⠀⠴⢸⣻⣯⢹⣿⡇⠰⠀⠀⢰⠀⢿⣿⢻⣿⠟⠠⡄
⠀⠀⠀⠀⠀⣧⣿⠃⣿⣷⠆⠀⠀⠀⠀⠀⣾⣿⠀⣿⣷⠀⠀⠀⠀⠀⠀⠐⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⠘⣿⣷
⠀⠀⠀⠀⠀⠈⢻⠀⢹⠋⠀⠀⠀⠀⠀⠀⡿⣿⠀⢿⢿⠀⠀⠀⠀⠀⠀⠀⠉⡃⢨⠛⠁⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⣧⡟⠀⢸⣼⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⣆⡇⠈⣇⡆⠀⠀⠀⠀⠀⣼⡟⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⡿⡇⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠿⡇
⠀⠀⠀⠀⠀⢘⠃⠀⠀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠻⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⡄
⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⠃
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣱⢀⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⢠⣅⠀⣀⣀⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⢁⡾⠘⣧⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⢀⣀⣀⣀⡀⡀⣄⢠⣠⣤⣤⣤⣠⣒⣶⣦⣦⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠞⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣶⣤⠉⠁⠀⠀⠀⠀⠙⣽⢽⣾⣮⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣴⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⡶⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⢹⣿⣿⢇⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣼⣿⣿⣿⠇
⣿⣿⣏⠭⠋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣄⣻⣿⢿⣿⣿⣿⢿⣿⣧⣀⡀⡀⡀⠀⠀⠀⣠⡟⠋⠉⣹⣿⣯⠀⢀⣴⡄
⣿⣯⡘⠀⠀⣀⣸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⡀⠀⠘⣴⣿⣿⣷⣿⣿⣿⣶⣾⣿⣶
⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⢿⣿⢣⡀⠊⠀⣻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇
⣠⣤⣤⣤⣤⣤⣼⣿⣿⡿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⢿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠿⡿⠿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⢀
⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣼⣿⣿⣿⣧
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠄⢉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⣠⡤⠶⠶⠶⠶⣖⠲⠶⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⢀⡀⠀⠀⠙⠦⣀⠀⠈⠉⢳⣤⡀⠀⠀⠀⠀⠀⠀⠸⠃⠋⠙⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠑⢤⡀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⣦⣖⠉⠀⠙⣦⣤⠀⠀⠀⠀⠰⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠙⠢⣀⠈⠻⡀⠀⠀⠀⠀⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢠⣲⠀⠀⠀⠀⠈⠢⢄⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢽⡆⠀⠀⠀⣧⠄⣘
⠀⠀⠀⠀⠀⠀⢀⡾⢇⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⣀⠔⠛⠦⡀⠀⠀⠀⠀⠀⠰⠟⠀⠀⡠⠀⢹⡤⠠⢀⡇⠀⠀⡄
⠀⠀⠀⠀⠀⢠⠏⠀⢀⠟⠣⣀⣚⡀⠈⠑⣦⡠⠊⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⣁⡔⠊⣷⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢀⡟⠀⢠⠋⢀⠞⠉⠑⢬⣦⠟⢹⡄⠀⠀⠀⣠⡀⠀⠀⠀⠈⠓⢤⡀⠀⡠⠞⠁⠁⠉⠙⣗⠒⠒⠀⠁
⠀⠀⠀⠰⡿⠁⠀⢸⠀⢸⠀⢀⡴⢪⣟⠢⣼⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠜⠛⢤⡀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢠⠇⠀⠀⠈⢦⣊⠷⠛⠚⠁⣠⠔⠉⠓⢤⡀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠈⠑⠢⣄⠀⠈⡇
⠀⠀⠀⣾⠀⠀⠀⡠⠞⠉⠐⠒⠂⠉⠁⠀⠀⠀⠀⠈⠲⢄⠀⡠⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠦⣷
⠀⠀⢰⠏⢲⣤⠋⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣀⠔⠛⠢⣄⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠛⠁⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⡆
⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⣠⠖⠁⠀⢀⣇
⠀⢀⡇⠀⣦⠀⠀⠀⠀⠀⠈⢑⣤⠖⠉⠀⢀⡀⠀⠀⠀⠀⠰⡗⠀⠀⠀⠀⠀⠀⠈⢳⣤⠊⠁⠀⠀⠀⢸⡟
⠀⢸⠃⠀⠉⠀⠀⠀⠀⣠⠔⠋⢀⡱⢾⣉⣉⣉⡙⠦⡀⠀⣀⣀⡀⠀⠀⠀⢀⡠⠖⠁⠀⠙⠦⣀⠀⠀⢸⠁
⠀⢸⣄⠀⠀⠀⠀⡠⠚⠁⠀⢀⠎⢠⠞⠉⠳⣄⠙⢆⡸⠋⠁⠀⠉⢲⣤⠖⠉⠀⠀⠀⠀⠀⠀⠈⠓⢤⣼
⠀⢸⠈⠳⣄⡴⠋⠀⠀⠀⠀⡎⢠⠇⠀⠀⠀⠀⠑⣾⡀⠀⢀⣠⠔⠋⣧⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⡏
⠀⠸⣆⠴⠋⠳⣄⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⢰⠃⣙⣶⣞⡓⢤⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠈⠑⢄⠀⢸⠀⡆⠀⠀⠀⠀⣀⣴⠚⠋⣼⣟⣿⣆⡁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠑⣾⠀⡇⠀⢀⡤⠚⠁⢰⠀⣶⡜⡚⣋⡤⠉⢺⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⢸⢙⣷⡚⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠀⠙⠢⣄⠀⢀⡴⠊⠁⣰⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠂⠙⠤⠷⠽⠦⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀⣸⠤⠤⠄⣠⠟⠷⡂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣤⣤⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⢹⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠲⠖⠋⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⢶⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⡀⣀⣸⡇⢸⣇⣀⢀⣀⣴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣀⣀⣠⣭⣭⣍⣹⡇⢸⡏⣉⣭⣭⣅⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢹⡇⢸⡏⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄
⠀⠀⠀⠀⠀⢀⡎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠸⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢷
⠀⠀⠀⠀⢀⡟⠀⠀⢄⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⢀⡄⠘⣧⡴⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⣴⠏⠀⠀⠘⡇
⠀⠀⠀⠀⢸⣧⠞⣧⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣸⠓⢦⡇
⠀⠀⠀⠀⠈⠀⠀⠘⣧⡀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⣰⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⠁⠀⠀⠀⣧⣤⡴⠶⠾⠛⠋⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⡀⠀⠀⠀⡞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣥⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣶⣾⣿⣿⣶⣶⣶⣶⣾⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣀⠀⢠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣿⣿⣷⠀⢸⣿⣿⠙⢟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣽⠀⢸⣿⠃⠀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠁⠀⢸⣿⣄⠀⢙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠈⠀⠀⢸⣿⣿⣦⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⢸⣏⠿⣿⣿⣿⢡
⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠉⢿⣿⡆⢠⡀
⠀⢶⠿⣛⣻⣟⣻⡛⠛⠉⠐⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣹⣷⣮⣿⣳⣄⢷⣤⣤⣤⣤⣄⢀⣠⣴⣶⠾⠃⠉⢠⢤⡀
⠀⢾⠿⠛⣹⣿⣫⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⣽⣿⡎⠻⣷⡿⣦⡯⡭⠽⢚⣽⣿⡿⠛⠁⠀⣠⠲⠀⢼⣷
⠀⢺⣶⢿⣿⣏⠉⠙⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣝⣿⠇⢀⢼⣿⣿⣷⢲⣾⣿⠿⠋⣀⠀⡠⠊⠁⠀⠀⢾⣿
⠀⠀⠀⠈⢻⣯⣤⠀⠀⠹⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⡆⢈⣿⣿⢇⣿⠛⢋⣡⣶⣾⣿⣿⣏⠀⠀⠀⢌⣿⣿
⠀⠀⣤⣤⣾⣿⡏⢀⣀⣀⣀⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠙⣧⣿⣿⣷⣤⣝⣿⣶⣿⣧⣸⣿⢿⠟⣿⠟⠻⣶⣄⡲⣷⣿⣿
⠀⠀⠈⠉⠉⠀⠀⠈⢿⣿⡿⠻⢿⠿⣧⡈⠙⠋⠉⠉⠉⠉⠙⠟⠛⠀⠘⣽⣿⣿⡿⣿⣿⣿⡇⣿⣿⣿⣟⣦⡾⠋⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡑⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣷⢯⣿⣿⡇⢿⣿⣋⣿⠁⠀⣠⡶⣻⣿⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⣿⡌⣼⡿⢸⣧⣿⣿⣿⣷⣴⣾⣩⣾⣿⠛⠀⠁⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣠⣄⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⢸⣿⣱⣿⠇⠘⣿⣿⡿⣿⡧⠹⣿⣿⡿⠃⠀⠀⢠⣿⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠚⡇⣼⡏⣧⣿⠀⣄⢀⣿⣿⣟⠻⣾⠇⠘⣷⠀⣤⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⢶⠘⢛⢿⡻⣷⡀⠀⠀⠀⠀⠀⠖⣿⣿⣾⣧⣿⠀⠛⣻⣿⣿⠿⢟⣿⠀⠀⢻⣿⡟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢳⡀⠢⠙⣝⢿⡄⠀⠀⠀⠠⠾⣿⠿⠋⠁⢀⡴⠛⢫⣽⡿⣿⢻⡇⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠣⠀⠙⢌⠃⠙⣦⠀⠀⠘⠇⢸⡆⠀⠀⣀⣴⣾⣿⣿⡷⢻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠈⠂⠀⢨⣧⡀⠐⠆⢸⠄⠀⠀⣻⣽⣿⣿⡖⣿⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠆⠀⠀⠀⠀⠀⠀⡀⢻⣇⠘⠇⢸⡀⠀⠈⣩⣿⣿⡿⡇⢸⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢙⡧⢸⣀⣴⡾⠛⠏⣏⢰⣧⢻⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠃⡿⢿⡋⠀⠀⢠⡿⢸⣿⡟⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣧⡄⢼⡄⠀⠀⠀⠀⠀⠰⠀⡷⠘⢧⢠⣿⢸⡇⢸⣿⣧⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡇⠐⠈⠳⣿⣿⠇⠘⣻⣿⣜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣯⣿⣯⣥⣌⠀⠀⠀⠀⠀⠀⠀⠈⢢⣽⣤⣼⣿⣂⣲⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⣿⡿⠟⣻⣻⡄⠀⠀⠀⠀⠒⠀⠀⠀⣭⠛⣿⡿⣯⣍⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣠⡾⠋⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⡜⢡⡾⠛⠝⠶⠉⠻⣦⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠘⣻⣦⣆⠀⠀⠀⣰⣿⣦⡔⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡇⢆⣰⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⡄⣵⣺⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⡄⠀⠀⠀⠀⠀⠀⢠⢫⣿⣿⣽⣿⣿⣿⣿⣆⡠⡀⠀⢠⣄⣶⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣰⡌⠀⠀⡴⣡⢿⡿⣯⣿⢣⣿⣿⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣾⣿⣴⣿⢿⡽⣻⣴⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢾⡿⢿⡿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⢻⠛⢻⡟⠙⡿⠻⣟⠿⢻⣻⠟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣾⣿⣾⣷⣶⣿⣶⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠛⠋⠉⠉⠛⢯⣉⠉⠉⠛⠛⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢦⣀⠀⠀⠀⠀⠸⡽⠂⠀⠀⠀⠀⠀⠈⠙⢦⣀⡴⠚⠁⠈⠳⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠑⠦⣄⠀⠀⠘⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢰⣋⡗⠀⠀⠀⠀⠀⠈⠙⢦⣄⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣼⣧⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠿⠀⠀⠀⡀⠀⢹⣆⣠⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⣦⣔⠋⠉⣭⠉⠙⠒⢦⡀⠀⢀⡴⠚⠁⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⡤⢿⡅⠀⠈⠉
⠀⠀⠀⠀⠀⣼⠁⠀⢀⡼⣃⠈⣳⢶⡒⠦⣄⠀⣀⣹⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⣸⠶⢉⣀⣼⣷⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⠇⠀⢀⡞⠀⢡⠞⠁⠀⠙⠲⣼⡶⠋⠁⣧⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢀⡴⠋⠁⠀⠀⠀⠀⠹⣏⠉⠉⠉⠉
⠀⠀⠠⣾⡿⠀⠀⢸⡇⠀⣿⠀⠀⠀⣠⠞⣽⡓⢦⣠⠏⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠻⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣽⠁⠀⠀⠀⢧⡠⠜⢧⣤⣎⡥⠞⠁⠉⣠⠟⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠸⡇
⠀⠀⢠⡇⠀⠀⠀⠀⠀⣹⠶⣏⣀⣀⣛⣠⡴⠞⠁⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⣿
⠀⠀⣾⡀⠀⠀⢀⣠⠞⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠳⣾
⠀⢰⡏⠙⣦⣴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣸⠳⠞⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⡿⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣿
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣿⡄
⢸⠃⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡞⠉⠀⠀⠀⠀⠀⠈⡿⠁
⣸⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢙⣦⡖⠚⠋⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠉⠲⣄⠀⠀⠀⠀⢀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⡴⠋⢀⡽⠶⣞⠛⠓⢦⡈⠙⣦⡴⠒⠒⠒⠦⣄⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⢸⡇
⣿⢦⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡼⠁⣠⠏⠀⠀⠈⠳⢤⡀⢳⡴⠋⠀⠀⠀⠀⠀⣈⣷⠚⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠓⣾
⣿⠀⠙⢦⣠⠖⠉⠀⠀⠀⠀⠀⣸⠃⢠⡏⠀⠀⠀⠀⠀⠀⠙⣾⡁⠀⠀⠀⣀⡤⠞⠁⢸⡀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠀⠀⠀⣿
⢻⠀⣠⠞⠙⢦⡀⠀⠀⠀⠀⠀⡟⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠘⢲⣤⠾⠫⣆⡀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢸⡏⠁⠀⠀⠀⠙⠶⣄⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⠋⢽⣿⣷⣦⡙⠞⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⡟⠀⠀⠀⠀⢀⣠⠖⢻⠀⢨⠘⡟⠧⡾⣭⠳⣬⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⠀⡇⠀⠀⣠⠴⠋⠁⠀⢸⠀⠼⡣⠬⠋⢩⡤⡞⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⡟
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣧⡖⠋⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⣷⠈⠙⠲⣄⡀⠀⠀⣀⡴⠚⠁⠀⣼⠃
⠀⠈⠉⠉⠒⠒⠒⠲⠤⠤⠤⠼⣗⠋⣯⣙⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣙⣦⣾⡡⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳⣄⣀⣀⣀⣀⣀⣀⣀⡴⠋⠉⠉⠁⠠⠟⠁⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡽⠃⠈⠣⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡽⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡴⠒⢚⣏⠉⠉⠩⠯⢉⡍⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡼
⠀⠀⠀⢷⡛⠛⠫⠥⢤⡤⣄⠉⢴⡦⢨⣥⠀⠐⠿⠂⠈⠁⠰⠶⠀⠻⠃⠀⠈⠙⣓⡶⢤⣄⣀
⠀⠀⡖⠚⠁⠛⠀⠀⠀⠁⠉⠉⠓⠒⠤⠅⣀⠀⣀⣀⠀⠠⣶⠄⠀⢰⣋⡳⠀⠘⠧⠜⠀⠀⠙⠒⠳⣤
⠀⢸⡇⢠⡞⢲⠀⡴⢢⠀⠀⠀⠰⣏⡣⠀⠀⠘⠥⣤⠵⠤⣄⡀⠟⠀⠀⠀⣿⣃⡠⣖⡶⠒⠙⠉⠉⢸⡇
⠀⠘⡇⠀⠈⠁⠀⠓⠚⠀⡔⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠂⠉⠉⠀⡀⠀⠀⠀⢀⠤⠀⠀⠀⣿
⠀⠀⡇⠀⢀⡤⡀⠀⠀⣀⣈⠁⠀⣀⠀⠙⠃⢀⣄⠀⢀⣀⠀⠀⢸⠀⠀⠯⠂⣠⠦⡀⠀⠙⠚⢀⡀⠀⡏
⠀⠀⡇⠀⠀⠑⠁⠀⠰⣅⡼⠀⠸⠤⠇⠀⠀⠙⠊⠀⠘⠶⠃⢀⡇⠀⠀⡀⠀⠳⠔⠃⠀⠀⠀⠈⠛⢰⡇
⠀⠀⠷⣄⠰⠆⠀⡄⢤⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢫⠞⠀⠘⠋⠀⠀⠀⣀⠀⢺⡹⠀⠀⣼⣃⣀⠀⠀⠀⠀⣠⡤⠤⠤⢤
⢀⠴⠒⠋⠙⠉⢇⡓⠚⠀⠀⢏⡨⠂⠀⢾⣙⠆⠀⠉⠀⠀⠀⢸⠄⠀⠀⡠⢦⠀⠸⣤⠇⠀⢀⡀⠀⢻⠁⢸⡇⠀⠀⠸⣥⣤⣤⣤⠴
⢯⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡠⣄⠀⠀⠀⠁⠀⠀⠀⣎⡕⠀⢸⠀⢤⡀⠣⠖⠁⠀⡤⡀⠀⠫⠑⠀⠸⠀⠀⠙⠲⠤⣀
⠀⠉⠙⠒⠒⠒⠶⢤⣀⠀⠀⠀⠈⠲⠤⣀⠘⠇⠀⠀⠀⠀⠰⡿⠀⠉⢀⣀⠀⠀⠀⠉⠁⠀⣀⡠⠴⠂⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣀⡤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⢦⣀⠀⠀⡇⠀⠀⢀⣁⢠⠔⠲⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢿⣭
⠀⠀⠀⠀⣾⣁⣀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠚⠉
⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡤⠤⠰⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠖⠋⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢃⠃⠀⠀⠀⠀⢀⡤⠴⠖⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠙⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⡆⠀⡀⢀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⢹⡆⠘⠀⠁⠀⠀⢀⡴⠀⡀⠀⠀⢀⠤⠛⠦⣄⣀⠀⠀⠀⠀⠁⠊⠀⠀⢀⡇⠀⠀⠀⢁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠀⠀⠀⠀⠀⠀⢠⡇⠈⢒⣁⣠⠶⠋⠀⠀⠀⠑⡖⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡋⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⡄⠀⣁⠄⠰⠁⠀⠀⢀⠀⡰⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠸⣧⠀⢼⣁⣀⣤⣤⣤⣤⣶⠿⠖⠒⠒⠛⠛⠛⠻⣿⡿⢻⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⢀⣽⠄⣈⡏⠀⠀⠀⢦⣙⣃⠾⡀⠀⠀⠀⠀⠀⠑⠤⠔⡫⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡤⠄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣀⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⡹⢄⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠆⠰⠀⣸⠇
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠳⢤⡀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠈⠑⠂⠴⠊⠁⠀⠉⠒⠒⠒⠚⠁⠀⠀⠀⠀⢀⠁⠠⠈⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠠⠚⠢⠠⢍⠲⣄⠀⠀⢸⡇⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠃⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⠀⡀⢀⠀⠱⣸⠃⠀⠀⢿⠀⠀⠀⠀⠈⠉⠛⢓⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢁⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⢀⡤⠴⢧⡀⠀⠈⠀⢈⡀⠀⠘⡀⢀⡍⠀⠀⠀⡈⠀⠀⠀⠀⠶⢶⠓⠧⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠂⠄⠂⠀⠀⠀⢀⠃
⠀⢸⡧⠦⢴⡇⠀⡆⠐⠂⣵⡀⣀⣴⠏⠀⠀⡶⠈⠃⡀⠀⢀⡤⡦⠈⠀⠠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢸⠆
⠀⢿⣀⡄⢤⠃⠀⡇⠀⠀⠈⠙⠉⡟⠀⠀⠀⢣⡀⠀⠀⠀⠁⠀⢘⠀⠀⠀⢸⠶⡀⠀⠀⠘⠛⠂⠀⠀⠀⢀⣠⡴⠖⠒⠲⣄⠀⠀⠐⠔⠀⡼
⠀⠸⣅⣤⠴⠃⠀⣅⠒⠉⠁⠒⢤⡇⠀⠀⠀⠀⡇⢠⢳⠀⠀⠀⣌⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸⠃
⠀⠀⠉⡇⠀⠀⠀⠸⡀⠐⠀⠀⠀⢱⠀⠀⠀⢰⡇⠘⠋⣼⠖⠋⢻⡀⠀⠀⠐⣍⠙⠲⣄⠀⠀⠀⠀⢸⣀⡶⣄⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⢀⠄⠑⢤⣀⠀⢀⣸⠀⠀⠀⠛⠷⣶⠞⠁⠀⠀⠀⠙⠛⠲⣄⠈⠢⣀⠀⠀⠀⠀⣀⡼⠋⣠⠼⠂⢀⡜⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠉⠉⠙⡍⠲⢄⡤⠦⠀⢸⡷⠶⠶⣤⣤⡴⠶⣦⢬⣷⣄⡈⠳⢖⡲⠟⢁⡤⠞⠙⠢⠴⠛⠛⠛⠒⠊⠙⠛⢿
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢈⡏⠲⢄⡤⠞⠧⢼⣇⣀⡀⠀⠉⠒⠖⠁⠒⢮⠙⠿⢦⡀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⢴⣤⣤⡈⢩⣍⣽⠀⠈⣷⡒⠒⠘⠂⠀⠠⠤⠤⠤⠠⣤⠄⠀⣒⣀⣨⣭⠁⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠈⠉⠛⢆⢠⠛⠛⠛⠀⠀⠿⠿⠶⠶⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⢶⡶⠶⢶⣤⣧⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⡻⠛⠛⠛⠶⠿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠃⣤⠀⢰⠇⠀⠀⠀⠀⢰⡁⢠⣄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠰⠷⠶⠋⠀⠀⠀⠀⠀⠀⢹⠏⢠⣟⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⡶⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⡋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠚⠱⡀⠀⠀⠀⠀⠀⠀⠀⢦⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣷⡀⣨⣿⣆⠀⠀⠀⠀⠀⠈⢷⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣤⣀⣼⣿⣶⣿⣿⡆
⠀⠀⠀⠂⠐⠂⠀⠀⡌⣙⣃⣎⣁⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⠿⠻⠽⠟⠋⠀⢰⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣶⠾⣿⡟⣿⣹⣩⣥⣷⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠉⠉⠉
⠀⠀⠀⠉⠛⠛⠛⠉⠁⠈⠁

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢱⠻⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢻⡁⡈⡼⢡⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⡇⠃⠁⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠬⡞⠓⠵⢅⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠣⡄⠀⠀⠓⠤⠀⡸⡄⡠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠰⢀⠀⠃⠤⠀⡀⠊⠁⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢢⡔⢛⡕⠢⡀⠈⠁⡠⠊⢸⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⢿⣿⡶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢀⠦⠘⢠⡀⠀⡐⠢⢀⡶⣾⠀⠀⠀⠀⠀⣠⣿⣿⡛⠋⠉⠉⠸⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡈⠀⠦⣠⣾⠛⢻⣢⠈⠛⣻⠁⠀⠉⠐⠀⠻⣿⣿⣷⣶⣶⣶⣶⣷⣶⣾⣿
⠀⣠⠴⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠢⣤⣻⠿⣹⠒⣿⡤⣀⡏⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⢦⠴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠻⠤⠴⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠒⣄⠀⠀⠀⢀⡤⠖⠤⠒⠓⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⣨⠇⠀⠀⣾⠀⠀⠀⠒⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⢤⠼⠁⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠉⠉⠙⠦⠤⢤⡀⠀⠀⠈⠣⢤⡀⠀⢀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠓⢆⣠⠖⠉⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⢀⠀⠀⣠⣀⢀⡠
⠀⠀⠀⠀⠀⠀⢇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⠞⠉⠲⠃⠀⠀⠙⠉⠉⠱⡄⠀⠀⠀⠀⠀⠈⠑⠒⠚⠇⠀⠸⣠⠎⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠠⠂⠀⣀⣠⣞⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⡴⠁⡠⠖⢤
⠀⠀⠀⠀⢀⣀⣤⠷⠖⠶⠒⠒⠚⠉⠉⠉⠉⠀⠉⠉⠙⠓⠒⠶⠤⠤⣤⣀⣀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡸⠐⡞⠁⣼⠴⠦⠴⠁
⠀⠀⠀⠐⣏⠀⠀⠀⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⣇⡀⠀⠀⠀⠀⠀⡴⠁⠘⠲⡄⠈
⠀⠀⠀⠀⡏⢉⠑⠒⠠⠄⡀⠀⠀⠉⠑⠤⢄⣀⠀⠀⠀⣀⣀⣀⣀⡠⠤⠤⠤⠐⠐⠒⠀⠀⢿⠀⠀⠀⣠⠎⠀⠀⠉⡰⠃
⠀⠀⠀⠀⡇⠈⢀⡄⠀⠀⠀⡉⠑⠒⠤⣄⡀⠀⠉⠒⠊⠁⠀⠀⠀⠀⣀⣀⠤⠤⠔⠒⠒⠈⢹⠀⢀⡜⠁⠀⢀⠔⠊
⠀⠀⠀⠀⡇⠠⠀⢀⡀⠀⠀⠃⠀⠆⠀⠀⠈⠑⠢⠤⠤⠒⠒⠊⠉⣉⠀⢀⠀⠀⠀⠀⠂⠀⢸⢀⡞⠀⣠⠞⠁
⠀⠀⠀⢀⡇⠀⣀⠈⢁⠈⠀⠀⠀⠀⢀⠀⠀⠘⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⣠⠀⠀⠀⠀⠀⢸⡞⢀⠞⠁⢀⡤⢤⡀
⢀⠔⠊⠉⠑⢤⡀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢠⡄⠀⠀⠀⠚⠀⠈⠀⠀⠀⠀⠀⢸⠃⠙⠒⠂⠠⣍⠉
⢧⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡉⠀⠀⠲⠀⠀⠀⠀⢨⠀⠀⠀⢰⠆⠀⣀⠀⠀⠀⠪⠂⢀⣀⠜⠀⠀⠀⠀⠀⠀⢱
⠀⠉⠒⠲⠄⠰⠦⠤⣄⡀⠀⠉⠑⠢⠤⣀⠈⠀⠀⠈⠀⢠⡀⠀⠀⠀⠁⣀⡠⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⢾⣉⣹⠆⠀⠀⣀⣠⠗⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⡀⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠉⢉⡥⠤⠤⣄
⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠘⠦⡤⠴⠋
⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⢢⣀⢹⣷⡀⣼⠇⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠰⠀⠂⠈⡀⠐⠀⠆⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⡹⣷⣿⣿⣿⣷⣿⣾⣟⣤⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠁⠀⢣⠀⠀⣇⠀⠀⠰⠀⠪⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠀⠀⠀⡸⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠈⠁⠈⠀⠀⠁⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠤⡀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠙⢠⡀⠓⢀⠐⠉⢲⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣾⣿⣿⣿⣿⣿⣿⣿⣆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠂⠈⢀⠦⠀⠰⡄⠁⢹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⢄⠀⠐⠀⠀⠢⠀⢀⠐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡄⠀⠀⡄⠈⠀⠀⠀⠣⢀⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡀⠲⡀⠀⠀⡀⠐⠀⠀⠈⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⠒⠀⠀⠀⠈⠀⡀⠘⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠨⠐⢄⠐⠁⠀⡀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⠄⠀⠀⠠⠀⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠍⠐⠈⠀⢀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉