Shrubbery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠸⢯⡂⢿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠟⣾⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠷⠸⠀⠞⣆⣦⡀⠀⠀⢸⣙⠇⠛⢻⣿⠀⢀⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⢟⣿⠆⢀⠀⠀⠸⢦⢱⠋⢹⢤⣘⠶⣯⠑⡆⠨⠟⡷⢀⣆⡀⢰⠞⡽⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⣶⡄⠀⣼⢳⡀⠘⠻⠀⠀⠏⣰⢫⢶⣬⠆⠇⠀⡾⡆⠈⣿⠛⡷⠼⡶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠄⢿⡇⣧⢹⠀⣾⣦⡙⣆⠀⡆⠀⢐⣥⠈⠈⠈⠀⠂⣴⣅⡀⠑⢋⣜⠀⠰⣾⠂⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⠈⠀⡝⠢⡄⢸⠦⠀⢸⡄⠃⠀⡆⣼⣀⡰⠹⠀⠘⢘⢁⢃⠴⡍⢻⡇⡸⠧⠐⠀⡊⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣗⡂⠈⠀⠀⡘⢲⣞⢳⢶⠀⠸⡖⢋⡽⡁⢠⡄⢸⡿⠀⣤⡀⠇⢀⠊⡰⠗⡦⢮⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢉⣐⡇⣸⠝⡎⠢⠙⠚⢀⣀⢸⣽⠃⢳⡇⣷⢛⣀⡀⠹⡁⢀⡁⠈⡠⠞⢳⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡸⣿⡄⠀⠀⠹⡜⣷⢤⣏⠈⣿⣟⢧⡘⡇⠀⠀⣹⣁⠀⠠⢾⣿⠧⣤⢌⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣵⣯⡁⢺⡷⠆⠹⣏⠐⠉⣓⡰⢦⡴⡍⠡⠀⠾⡏⠸⢠⡶⠌⠁⢘⡷⠀⠞⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠭⠉⠙⣧⠘⠁⠀⢠⣬⣦⡀⠛⠏⠙⡄⣤⡇⠀⣀⠁⠀⠈⠀⠀⠐⣫⢤⡄⠴⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⣃⣀⠳⣄⠂⢀⣿⠇⢳⠀⣇⡀⣿⠁⠇⠔⣹⣠⡆⢰⠐⣶⣯⣤⠿⣧⢠⣮⢠⠆
⠀⠀⠀⠀⢠⡀⢤⡀⠀⠀⠀⠀⡴⠀⠀⠀⠀⡻⢧⡀⢒⠤⠭⡏⠉⢸⠙⢇⠈⠹⣎⠀⠘⠐⢋⡟⡇⠀⢸⢩⡜⠧⡴⠁⠴⢱⠃⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠙⢮⡕⡄⢘⡀⡸⠁⢀⠀⠀⣤⣏⢢⠀⣏⠀⢠⠙⠦⠘⣦⠀⢀⠀⠈⣷⠀⣤⠈⠁⠀⠀⢀⡜⠡⠞⠁⠀⠀⢉⢼⢃⠔⠉⣠
⠀⠀⠀⠀⠀⠀⢦⡱⡈⢾⣥⠁⣀⣿⠒⡔⣿⠙⠓⠆⠸⠂⠘⡳⢄⡆⠉⢧⠘⡄⠐⢸⢎⡟⢹⠖⠀⠔⠹⠠⣤⡤⠍⢠⠀⣿⠆⠊⢠⡆⠼⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠙⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⠀⠘⠁⠰⠊⠗


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀

⠀⠀⠀⢠⡄⢀⡀⣀⠀⢀⣠⣠
⠀⠀⣿⢣⠐⠻⠟⠃⣠⠈⡘⠁
⠐⣋⠃⠀⠈⢡⣀⣰⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠉⠀⢀⣈⡛⢻⢿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⣤⣤⢬⡆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠘⠁⢸
⠀⠀⠀⠀⠈⡀⢸⡀
⠀⠀⠀⠀⠀⠃⢸⠁
⠀⠀⠀⠀⠰⠀⠘

⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡰⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⡄⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢰⠃⠀⠇⢀⡀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠠⠀⠟⠁⠀⠈⠀⠀⠀⠀⠃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠛⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⠀⠘⡆⢠⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⡇⢸⠀⢀⠀⠀⢠⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣿⠠⠀⢾⢻⡀⢸⡀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢿⠓⠤⣼⢰⠀⢸⣧⠸⢀⠌⠀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡏⢸⠀⡸⡜⠀⢠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠃⢸⢀⠃⡇⠀⢸⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⢸⣾⠀⣿⠀⡏⠀⠀⠀⢰
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣅⣬⣏⣀⣹⣠⣇⣀⣀⣀⣈⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢠⣖⠏⢴⡀⠨⠠⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⡁⠘⠠⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠒
⠀⠀⠀⣼⣿⣿⣶⡈⢁⠛⣰⡤⠄⠀⠀⠀⠑⢧⡕⢛⠬⢥⡷⡑⢰⠄⡠⠀⠀⠀⣧⣤⡀⠁⠘⠋⢀⣤⠄
⠀⠀⢀⣿⣿⣿⣤⣧⣄⢻⠌⣿⠿⠀⠀⢀⣀⣺⣿⣾⣷⣿⣿⣯⣾⣵⠤⠀⠀⠀⢊⡁⣀⠀⡀⠨⣭⣠
⠀⠀⠀⠙⠿⠿⠿⠿⠞⠿⠶⠏⠀⠀⠀⠀⠈⠻⠟⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠠⠟⠓⠿⠗⠶⠿⠶⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⢠⡄⠀⣼⣿⣿⣶⠏⠀⠀⠀⠀⠀⢶⣶⣦⡀⡿⠏⠀⠀⠀⠀⠀⠀⠀⠈⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣧
⠀⠀⠀⠀⢲⣄⢹⡆⢿⣿⣨⡥⠤⠶⠆⠀⠀⣀⣀⣈⣉⣽⣀⡤⠀⠀⠀⠀⢀⡀⣠⡯⠀⠇⠀⠀⠀⠀⠀⣤⣤⠀⠀⠨⣿⡀
⠀⠀⠀⢰⡀⠙⣷⢿⣘⣣⣶⣄⣀⠀⠀⠀⣤⡉⠙⠉⣹⣋⣈⠙⠛⠃⠀⠀⠀⠐⠿⡑⠀⠀⠀⠀⠀⠀⠰⣦⢛⡇⠀⢰⠿⢁
⠀⠀⠀⠘⣷⣤⣌⣢⣴⣾⠿⠋⠉⠁⠀⠀⠘⠛⣧⡼⣋⠛⠻⠿⠓⠀⠀⢀⡀⢰⡊⠀⢀⠀⡈⠂⠀⠀⠀⢘⣿⠀⠀⢸⣏⡅
⠀⠀⠀⠀⠜⠓⣈⣭⣍⣀⣀⡀⠀⠀⠀⠀⠴⠟⢿⣦⠛⠻⠶⠄⠀⠀⠀⠈⡙⢿⡥⠀⠈⠄⠙⠀⠀⠀⠀⠠⠗⠃⠀⢼⡯⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠇⠐


⠀⠀⠀⠀⠀⣀⠀⢀⣄⣀⢰⣴⣡⠂⠀⠀⠀⠀⠀⠀⢠⡀⢀⣤⣸⣰⣬⠃⢀⡄⠀⠀⠒⠢⣀⡀⠐⣂⠀⢀⣴⣀⣤⠴
⠀⠀⠀⠀⠘⠟⣀⡄⢹⠚⣿⠫⣿⠉⠀⠀⠀⠀⣤⢠⣸⡆⣼⢻⣿⢿⣿⣾⣡⣤⠄⠀⠀⠀⢬⣿⣷⢟⡙⢻⣿⠿⢅⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠃⢨⠖⠙⠌⣋⠀⠀⠀⠀⣄⡸⣷⣿⣿⡽⣿⣷⣿⣿⣿⡿⠠⠀⠀⠀⠀⢀⡈⢦⠾⡻⠄⣮⣟⣿⣏⡁
⠀⠀⠀⠀⢀⡀⠒⢸⠇⠠⠠⣄⡁⠀⠀⠀⠀⢀⣸⣿⣿⣟⣷⣿⣿⣭⣭⡙⠻⠆⠀⠀⠀⠔⢛⣷⣿⠾⡿⣼⠛⣯⣿⡛⠙⠛⠃
⠀⠀⠀⠀⠀⢀⠸⠿⠒⠀⠁⢀⣀⠀⠀⠀⠚⢉⣾⡻⣿⣶⣿⣿⡿⡏⠉⠉⠀⠀⠀⠀⠀⣠⣿⡿⠛⣾⣷⣷⣿⣿⣎⠛⠂
⠀⠀⠀⠀⠠⣐⠖⠐⠈⠀⠤⠘⠛⠁⠀⠀⠀⠀⠹⠚⢩⠏⣿⡟⠷⠹⡄⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⣼⠉⢿⠏⠛⠿⡧
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢈⡝⣧⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡠⣖⣡⣤⣔⣂⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⠄⠀⠀⠀⢠⣴⡾⠃
⠀⠀⠀⠀⠀⣠⣬⡸⠋⠛⠛⠁⠀⠀⠀⠀⡄⢀⢠⡞⣬⡶⢿⣿⣟⠛⠿⠟⠃⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⣀⣀⣠⣴⡟⠋
⠀⠀⠀⠀⠀⠐⢯⠃⠀⠀⠀⠀⠀⠀⢄⡀⡃⣼⣿⣿⣛⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠾⠟⣻⣟⣿⠋⠀⢠⡞
⠀⠀⠀⠀⢀⣀⣸⡾⣿⠇⠀⠀⠀⠀⠀⠡⣼⣻⡿⢛⠟⠀⠀⢀⣄⣠⣄⠀⠀⠀⠈⠉⠉⠉⡿⠀⠀⠀⣠⠏⣼⠋⠀⠀⣸⡇
⠀⠀⠀⠀⠺⣿⠿⠉⠁⠀⠀⠀⠀⠀⠑⢄⡈⢙⡿⠋⠀⠀⠀⢾⣯⣿⡟⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠠⠏⠀⣿⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢄⡀⢸⠣⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠎⠁⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠋⠛⢳⡠⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠸⢇⡀⠀⣠⢲⡈⠉⠁⠄⣀⢐⡋⠓⢴⡄⠀⠀⠈⡡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢞⢺⠇⠀⠀⠀⢀⠘⡖⠻⢿⡧⠶⠃⠈⠁⡨⢻⣯⠬⢽⣷⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⢀⠴⢊⡀⠀⠘⠂⡴⣶⠖⢀⠀⠀⡇⡂⢷⢖⣶⢿⣿⣷⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠡⣴⠣⠀⡘⠁⣠⠴⢲⣷⣂⠀⠈⠃⠈⠉⠄⠥⢚⣅⢿⠁⣙⢧⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠦⠀⢠⠏⠁⠠⠸⡐⠊⠙⠒⠈⡀⠀⠠⠟⠉⠀⢸⣦⣄⡼⢏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⠄⠈⠦⢁⠀⠆⠑⠀⠇⢀⠀⣹⡏⠶⠢⠀⠀⠘⣇⠛⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣺⠀⢢⠀⠀⠀⠀⢹⠀⠀⢀⠃⠆⠠⠀⠻⣿⠼⡆⠀⠀⢀⠄⢠⡐⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠙⢀⠖⠒⠀⠂⢸⡇⠀⠀⡀⠘⠂⢑⣁⠀⠀⠉⠓⠀⢀⡁⠒⡶⡿⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⠀⢠⢰⠀⠈⡀⢠⡀⠀⢀⢰⣯⠟⠀⠀⣴⡁⠀⠈⢀⢰⢠⡋⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢼⠀⠀⢈⡄⢠⠒⠸⢋⢁⠴⠁⠔⠁⢠⠈⠓⠋⠀⠀⠀⢠⡿⠀⣷⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠸⠀⠄⠈⣯⠈⢀⡴⢻⣞⠘⣿⣴⠾⣾⣏⢵⣈⠝⠀⠀⢈⠂⠀⣿⢸⠀⠎⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⢸⡥⠀⢸⣶⣿⣿⠐⣯⢳⣾⣿⣏⣃⠃⠀⠠⠀⣌⣧⠀⢹⡏⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇⠀⠨⡀⠁⡀⢻⣿⣷⣶⣟⣛⣿⡗⠋⠁⣠⣄⡀⠦⠈⠱⢶⣇⡉⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠃⠀⢀⣠⠼⢷⣿⣥⢄⣉⣻⣿⡿⡷⢢⡶⠛⠊⠁⠀⠀⠀⣠⠏⠀⠀⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⠉⠀⠀⢸⣣⣌⣻⠉⠘⣡⡠⡈⠀⠄⠐⣡⠐⡀⢃⠠⠏⡄⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠠⣄⠀⢀⠈⠻⠿⠿⠁⠀⠈⢇⠀⡀⠀⠀⠛⢉⣷⣌⣳⣾⡯⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠈⢩⡇⠠⢦⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⢷⣉⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠙⠓⠀⠋⠲⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠂⠼⠶⠔⠠⠸⡽⠚⢷⣶⡀
⠀⠀⠐⠆⡘⢁⣋⣤⡀⢀⣀⣀⣱⣮⣷⢮⣷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⢠⣿⡍⠀⣀⡽⡒⣿⣾⣿⣷⣿⣏⣾⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⣸⠗
⠀⠀⠀⣞⣠⣹⣰⣤⡶⢛⣘⣫⡽⢯⣟⣿⣿⣿⣿⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⠟⢒⣁⠘⠗
⠀⠀⠀⢉⡙⠹⣿⣻⣭⣿⣾⣯⣏⡷⢱⣿⢾⣿⣿⠉⠁⠀⠀⠀⢀⣄⠐⠀⠘⠃⡀⠂⠐⠆⠀⠀⠉⠠⠄⢉⡁
⠀⠀⠀⠙⠛⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣀⠀⠀⢀⠾⢧⡘⠙⡃⢀⣿⠆⠠⠰⠖⠒⢀⣰⣦⡀⠘⢀⡀
⠀⠐⠒⠚⠛⠛⠛⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣛⡿⠆⠓⠀⠀⠀⠟⣎⢹⠿⠟⠧⡿⣦⣴⣿⣟⠂⠈⠉⠈⠉⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣾⣿⣦⣤⣈⣤⠀⣰⡂⣰⡦⡀⣠⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣿⣷⣮⣜⣯⣽⠛⢟⣛⣟⣛⠛⣿⡿⢓⣾⣿⣝⠦⢤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣼⣿⡿⣾⣿⡟⠙⠁
⠀⠀⠀⠀⠀⠀⢠⡄⣠⠀⣀⠐⢆⡀⢀⡦⠤⣤⣶⡀⠄⠀⠀⠀⠀⠻⠟⠿⠿⢿⠿⠿⠟⠛⠋⠛⠛⠻⠿⠷⠯⠙⠋
⠀⠀⠀⠀⢴⢀⠾⢏⣬⢎⠉⠁⠢⠉⡁⠀⠀⠀⠠⢘⢂⡀
⠀⠀⠀⣀⡟⣽⣟⡤⣤⠬⣴⣶⣮⡬⠉⢒⢞⡶⠄⡀⠐⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⢯⠠⣿⡿⣿⣿⣿⡿⣿⣿⣷⣼⣿⣠⣷⢶⣀⠄⠉⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⢫⡐
⠀⠀⢸⣭⠷⠿⠗⣺⣿⠋⣶⣿⣿⢻⣿⣿⣿⡿⠷⠿⢡⣗⡋⠁⠀⠀⠀⠀⠀⠀⠀⠎⠙⢧⣟⣹⠧⡁⠀⡸⢥
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣶⣾⣽⣿⣿⣿⣿⣝⣢⢾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣬⣿⣿⣷⣧⣐⠃⡋
⠀⠀⠚⢛⢻⣿⣿⣿⣿⣿⡿⣿⠺⢚⣹⣿⣟⣿⣿⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⡟⠹⡾⢿⣿⡽⠛⠷⡟⠾⡗
⠀⠀⠀⠀⠉⠼⠟⣅⣿⣿⣟⡟⠉⠙⢻⠁⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⣻⣶⣿⣿⣷⡷⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠋⠈⠙⠹⣿⣽⣄⣞⣅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⣷⣼⣿⣿⣿⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡿⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡤⣤⠤⣤⡿⡿⠯⠦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠔⠲⠆⠀⠁⠂
⠀⠀⠀⠀⠀⠀⣐⠀⠲⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⣀⡀⠀⠈⠆⢀
⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠠⣀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠈⠁⠈⠀⠈⠀⠈⠒⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠈⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢈⠁⠁⡰⠂⠀⠀⠀⠘⢦⠀⠀⢐
⠀⠀⠀⠂⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠁⠀⠀⠉⠓⠀⠀⠃⠀⠀⣃
⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠳⢣⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠎⠃⠉⠓⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠰⣄⠆⣌⠀⠇⢈⠀⠎⣾⣅⡀⠀⠀⠀⠀⠀⠀⡠⡤⠄⠑⠀⠀⠀⠀⠀⠀⠩⡄
⠀⠀⠀⠀⠀⠀⠳⢀⡸⠍⢰⡆⠿⢀⡆⠙⣻⠁⠀⠀⠀⠀⠀⢐⡀⠀⡀⠀⡀⠈⢦⡀⠀⠀⠀⢀⡀⢛⡄
⠀⠀⠀⠀⢀⢠⣤⠆⠃⢰⡆⢠⠀⢀⠀⠘⡷⣋⡄⠀⠀⠀⠀⢍⠁⠀⠘⠲⡄⠀⠈⠅⠠⠀⡤⠂⠀⠐
⠀⠀⠀⠀⣌⡳⠁⠀⢹⡌⠃⠛⠀⠏⢠⡄⠚⢵⣚⠁⠀⠀⠀⠀⠳⠀⠀⠀⠳⠀⠀⠏⠀⠰⠃⠁⡀⠝
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠉⠀⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⠀⠠⢦⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣸⣧⢰⣾⣻⡟⢶⣦⡀⠀⠀⠀⢉⠈⠀⢸⣮⣯⠄⠀⠛⠳⠟
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⡄⠐⠈⠑⠀⢄⠀⠂⠠⠓⣼⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠸⠁⠀⢸⣿⠟⠉⠉⠉⠀⣰⣇⠀⢨⠰⡈⠃⣀⡂⣙⠙⡇⢀⠌⣁⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠠⣿⣿⡄⠀⠚⢀⣲⠀⡀⠅⠀⠀⠈⠂⠈⠃⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⠰⡏⠁⠀⠂⠻⠙⠀⠐⠀⠀⠀⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠂⠀⠀⠀⠐⠀⠀⠲⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⢰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢸⣆⡄
⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⢳⢸⣸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠁⠀⠁⠴⠶
⠀⠀⠀⠀⠀⠀⠂⢀⠬⢀⢰⣾⣿⣿⠏⢀⠀⠈⠃⠀⠀⠀⠛⠀⣀⠀⠀⠀⠀⠈⠀⡄⠀⢰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢈⠘⣊⠁⣿⣿⣿⡎⠘⢀⡄⠐⠆⠀⠀⠀⠀⠁⠀⠀⡀⣄⣀⠀⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠇⠀⠀⠀⠀⠀⡆⠘⠛⠗⢤⠀⠀⡄⠉⠀⠀⠘⠿⠿⠗⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠐⠒⠂


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣭⣁⣀⠈⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠶⠶⢲⡈⠉⠀⠀⠚⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠈⠀⠀⠊⢀⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠘⠃⠀⠀⠀⠀⠀⠴⡼⡄⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠐⡀⣆⡀⡀⠀⣀⣰⠄⢀⢠⣜⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⡇⠀⡁⢁⡄⢀⣽⡖⣡⠐⣣⣀⡩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠻⣷⣾⠿⣋⣙⣯⣤⣬⣅⣹⣶⡫⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣶⢟⣹⡶⣤⣤⡀⠉⠳⠿⠿⢿⣽⣤⣭⠜⣫⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣏⡽⠿⢛⣁⢪⠷⢻⢿⣿⣟⣆⠀⠀⠀⢸⡏⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠠⠈⠋⠀⠈⠛⢙⣷⣺⣿⣿⣿⣿⣿⣿⣿⠶⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⠿⠃⠀⠐⠀⠀⢀⣰⣿⡁⠉⠉⡤⢭⡿⣶⠋⠛⠀⠈⠻⢻⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠀⠀⠀⠀⠀⠀⠢⡈⠋⠀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⢸⢿⣟⣻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣄⠀⠀⠀⠀⡀⠀⣠⣤⣶⡃⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⢻⠲⣥⣸⢷⡈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠛⠛⠛⠛⠉⠛⠋⠛⠛⠛⠉⠉⠓⠒⠂⠢⠓⢶⣀⡀⠀⡀⠀⠀⠀⣠⠖⠾⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠂⠉⠑⠒⠊


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢹⣆⣿⡀⣶⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡙⢀⣦⣸⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣽⣿⡇⢸⣿⣇⣤⣤⠃⣤⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢼⣿⣿⣿⣿⡿⣧⣆⠀⢰⠂
⠀⠀⠀⠀⠀⠐⢄⡀⢰⡗⣷⡄⣸⣿⣟⢠⣿⣿⣶⣿⣶⠟⣡⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣨⣿⣿⣿⣿⣿⡇⡸⢲⣾⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣾⣷⡟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣶⣿⣿⣿⣿⣿⣴⣿⣿⣿⢠⠇
⠀⠀⠀⠀⠀⠐⠛⣦⣌⢛⣾⠹⣿⢻⣿⣿⣿⣿⣿⣿⡟⢂⣠⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⢽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸
⠀⠀⠀⠀⠀⠀⠀⠈⢈⡓⣋⡁⢹⢲⣿⣿⣿⠿⣽⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠇⠘⡴⡿⢿⣿⡗⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⠿⣿⣿⢿⣿⣿⡿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣼⣶⣆⣰⣿⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣿⡥⣶⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠷⣯⣶⢼⣯⡄⠁⢈⣤⣀⣄⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣌⣉⣅⣿⣷⣾⣿⣟⠃⣻⣱⣿⡟⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣾⣿⣉⣿⣿⣭⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠾⣾⣫⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠙⠛⠻⠿⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢙⠶⣀⡀⠀⠀⢦⣼⡇⠀⢀⡻⠃
⠀⠀⠀⠀⠀⢀⡀⠀⠷⣼⠁⢠⣤⠆⠰⢒⡶⠶⣽⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠉⠃⢾⡇⠠⠄⢻⣇⣰⠿⡿⣀⣭⣶⡟⣦⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⣀⣶
⠀⠀⠀⠀⠀⠀⠀⢴⣤⣤⠆⠈⡜⠛⠉⢼⣷⣌⣱⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣲⣤⣿⣿⣿⣿⣧⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣸⡑⢞⡑⠀⣿⢿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⢟⣿⣿⣿⣿⣿⣿⣿⣴⡲⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡇⠈⣭⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣿⠶⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠠⣠⡀
⠀⠀⠂⠀⠀⠀⡀⣐⠀⠄⠀⠀⢀⠤⠊⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡀⡀⣤⠀⠀⠀⠀⡴⠋⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠂⠀⠀⠁⠀⠀⠀⢠⠄⠀⠀⠳⡄⠀⡀⠐⠲⠧⠯⠀⣀⠀⠰⠀⠀⠀⡖⠀⠈
⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠃⠀⠀⡼⡀⠒⠀⠢⡀⠀⠃⠀⢀⠀⠀⠐⠚⡤⠠⠀⢠⣀⠃⡀
⠀⠀⠂⠄⠀⠀⢁⠃⠀⠀⠄⡘⠀⠀⠘⢰⠀⠠⠄⢠⠀⠈⠒⠄⠉⠀⠀⠀⠂⠒⡠⠐⠂⠀⠈⠟⠃⠀⠃
⠀⡖⠀⠀⠀⠀⡆⠀⠁⠀⡰⠀⠀⠀⡀⣈⠜⠘⠀⠀⠫⠶⡠⠄⠀⠀⠀⠉⠀⠂⠠⠐⠀⠐⠛⢇⡴
⠀⢀⠀⠀⠀⠀⠀⠠⢠⠄⠀⢤⠠⡀⠈⢻⠀⠂⢀⡠⠰⢤⠄⠈⠀⠘⠂⠄⠁⠤⡠⠀⠐⠀⣠⣘⢀⡖
⠀⢀⠀⠀⠀⠀⠀⠈⠀⠌⠈⡈⠐⠀⠀⠰⠀⠒⡄⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠐⠀⠀⠸⠳⡀⢰⠁⠴⠀⠀⡀⠀⢨⢂⠀⠀⢀⠈⠀⠰⡜⢆⠀⠤⠀⠀⡀
⠀⠀⠀⠠⣄⠀⠀⢠⣂⠌⠀⠀⠛⠲⣄⠑⠇⠛⠋⢲⡄⠈⠀⡐⡋⠀⠀⢀⠀⠑⠾⢋⢟⠩⠹⠷⢤⡀⡀
⠀⠀⡄⣼⣐⡃⢳⠩⠉⠊⠁⠀⠠⠄⢙⡁⠙⢖⣀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠄⠀⠎⠀⡀⠉⠁⠠⢸⠃
⠠⢵⠧⠀⠀⠈⠉⠀⡀⡀⠔⠂⠀⠀⠚⠃⠾⠅⠈⠀⠀⠀⠨⠀⠀⠀⠀⡀⠀⣄⠔⣈⡠⣤⠤⢀⡀⠘⡇
⠀⠘⠈⠀⠐⠀⠀⠁⠁⠀⠀⠀⠀⢴⠄⠀⠀⠠⠀⠀⠘⠀⠀⠀⠄⠀⠀⠉⠢⠌⠂⠄⠅⠀⠐⠈⠑⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠐⢱⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⠭⣄⠀⠀⠀⣼⣿⠀⡿⠦⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠄⠉⠆⠁⠰⠶⠫⢑⣿⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡆⠄⠀⠀⠀⠀⠀⢀⣀⠂⠀⡠⠞⠀⠂⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠊⠰⠶⢶⠀⠀⠀⠉⡁⠉⠀⠀⢀⣤⠀⠀⣧⡀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠔⠁⠀⠀⠀⠈⠃⠀⠀⠀⠹⠁⠀⠀⢶⣤⠇⠀⠽⣿⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠀⠸⠙⠀⠀⠀⠀⠀⠐⢀⣤⣥⣿⣦⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠈⠀⠰⠀⠂⠀⠀⠀⠤⠰⠏⠑⣤⠊⠿⠂⢀⡛⠛⢻⡧⠚⠀⡩⠆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀⡏⠀⠀⣤⡀⠸⠃⠀⡀⠐⢿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠁⣰⣆⠀⠈⢻⣧⠀⠀⠀⠀⢁⡀⢀⣀⠀⠀⠀⢡⣷⣀⣼⠿⠋⠀⡀⠂⠁⠀⠀⢀⠈⠈⠛⠀⠀⢠⣿⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⡖⠒⠠⠷⡶⠦⠀⢀⡤⢻⠋⠆⠐⠐⠁⠙⠁⠄⢻⠐⡁⠆⢻⣖⠂⠀⠀⠀⠀⢀⠠⠀⠢⠌⢳⢆⠑
⠀⠀⠀⠀⣿⣧⠀⠀⠫⠟⠓⣄⠀⠀⠄⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢨⠎⠙⢋⡽⠿⡄⠠⠀⠀⠠⣨⠜⠁⠀⠀⢀⠋⠀⡐
⠀⢂⣀⣀⣈⣻⡀⢀⢀⡀⠀⠀⠀⠀⠀⢰⣤⡠⠀⠀⠌⠀⠀⠀⠀⣠⡆⢀⠀⠀⠀⠂⠄⠀⠀⠀⠄⠀⠀⠁
⠃⠀⠀⠀⠍⠁⠄⠙⠦⣅⣀⣀⠀⢀⣀⡘⢿⡇⠀⠀⠀⠂⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠠⠂⢉⡂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠀⠀⠉⣹⣿⣿⠋⠛⠀⠀⠀⠹⣁⡄⣠⡇⠀⠀⠐⡞⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣦⣨⡀⠀⡠⢶⡶⠀⠙⢷⡏⡅⠀⡰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠉⠙⡄⢼⡿⠀⠀⣀⣈⡁⠳⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⠀⠻⠇⠀⠀⠉⠈⠘⠆⢠⠄⠀⠀⣴⡀⠠⠀⠀⠀⠐⡦⣴⡯
⠀⠀⠀⠀⠀⠶⠰⣆⣀⣤⣋⠑⢄⡀⠀⣞⡷⠀⢀⠀⠈⠀⠀⢐⠴⣤⣸⠁⠐⠀⠀⢴⠂⠀⠙⣷⠚⢠⣀⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠀⠀⠐⠎⣵⡀⡬⠠⠀⠀⠠⠀⠀⠀⠛⠂⣼⡔⠒⢺⣿⡡⠾⠄⣀⡨⢻⠅⣂⠠⢖⡼⠿⣾⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠔⢰⡆⣑⠴⠀⠀⠀⠀⠈⠀⠀⠈⠈⠠⠀⠀⡀⢻⠆⡠⠈⠀⠚⢿⠂⠀⠀⠀⠁⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠄⡎⠀⠀⠈⠀⡀⠀⠀⠀⠀⣠⡆⠐⠄⢀⡀⠘⠖⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠗⡟⠆⠀⡉⣉⠀⠀⠀⠠⠀⠀⠐⢢⡔⠻⣆⠉⠁⢹⡇⠀⠀⣿⢿⣶⣷⣄⠲⠶⡃⠀⠀⠀⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠃⠀⠙⠂⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠳⡀⢸⠀⠀⢸⠋⢸⡿⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⠊⠘⠳⣾⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⠖⠈⠀⠀⠀⠖⡚⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣳⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⠖⣲⣶⣫⣷⣿⣧⣀⣒⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⠈⠉⠈⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⣸⡉⠀⣠⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠠⠀⢠⠄⢢⠀⠀⣼⣫⡾⠋⠉⢉⡜⠫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠹⠗⠾⠀⠀⠘⢹⣁⡑⠀⠘⠳⠒⠁⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣄⣿⣿⣇⢘⠱⠟⣆⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠂⠀⢠⡴⢀⣿⡈⢻⣏⡆⠀⠀⠀⠀⠸⣉
⠀⠀⠀⠀⠀⠈⢿⡿⣏⣯⡛⣿⣏⣤⣿⣦⣷⠀⣠⡞⠛⠊⠄⠀⠉⠠⡀⠀⠀⠀⠀⣷⣾⡟⠘⡀⠩⠁⠠⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡙⠋⠙⠀⠀⠈⠉⡙⠙⠿⠀⣿⣣⠀⢀⠀⠀⠀⠀⠈⣤⠀⠀⠸⣿⢿⠦⠊⠉⠙⢿⣶⣦⡀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡆⠃⠒⠂⠦⢒⢬⣑⢄⡢⣀⡀⣿⠋⣁⣽⡧⠤⠄⠀⠀⠀⢀⣤⡀⡷⠂⠀⠀⠀⠀⠈⠙⣿⣿⢀⡞
⠀⠀⠀⢀⣠⣿⠧⠭⢴⠶⠯⠷⣮⣿⣿⣿⣿⣿⣹⣿⣿⣿⣷⣄⣀⣀⠉⠀⠻⠵⢾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⠞
⠀⠀⠀⠈⠁⠀⢠⣴⠍⠀⠀⣂⠀⢙⣩⣿⣯⡿⠿⢇⡁⠢⠉⠙⢿⣧⣄⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢠⡞⠓⣨⠖⣲⡩⢒⣣⣽⣿⣿⠷⣸⠆⠙⠢⣀⡀⠀⠙⢦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⡓⠚⣁⠒⣩⣾⣿⣿⠛⠀⢸⡄⠀⠀⠈⢿⠓⠂⣄⡙⠀⠀⠀⢠⣠⠄⠀⠠⠊⣀⣘⣿⣯⣿⣍⣻⣶⣶⣶⣾⣷
⠀⠀⠀⠀⣠⣤⣿⣟⠤⣋⡴⠈⣰⣿⣿⣿⣿⠀⠀⡇⢂⠀⠀⠘⣇⠀⠀⢉⠓⠦⢠⡞⠉⢀⣄⣤⣦⣧⡸⣿⡿⠛⣩⣭⣤⣤⠤⣤⡀
⠀⠀⣠⣾⣿⡿⣿⣟⡰⠊⠐⠡⣾⣿⣿⣿⣟⠀⠀⠸⡄⠡⡀⠀⢿⢀⣀⣞⣠⣦⣿⣏⣚⣦⣼⣫⣿⣿⡟⠳⡾⣿⣿⣿⣿⣯⢍⣛⣻⡄
⠀⢰⡿⠿⠟⠛⠉⠿⣇⠈⡀⣵⣿⣿⠟⠋⠈⠑⢦⡀⠑⡄⠱⡄⢸⣟⣿⡏⡿⢧⣾⣿⣿⣿⠛⠛⠿⠿⠃⠈⢕⣃⢇⣿⢻⣿⣝⠪⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣾⣀⣿⡿⠋⠀⠀⠀⠀⠀⠙⢦⡈⢦⡸⣌⣿⣧⣿⡔⠉⣹⡿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⠘⠛⠳⠿⠽⣿⣮⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣷⣿⠻⣯⢈⣧⠞⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⣤⣤⣶⣤⣤⣿⣿⣿⣶⣿⡿⣧⣤⣀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠻⠿⠛⠛⠿⡿⠻⠿⠿⠿⣿⢿⡿⢿⡿⠿⠿⠿⡞⠒⠲⠛⠟⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠳⣄⠀⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣸⠀⢳⡷⢫⠞⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⣄⣼⣀⡼⠿⠤⠴⠃
⠀⠀⠀⠀⠀⢀⣤⣄⢀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁
⠀⠀⠀⠀⠀⢾⠀⠈⣿⣇⡀⡼⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠈⠳⠿⣇⢹⠏⠁⠀⠀⠀⠀⠀⠀⡟⠈⢧⠀⠀⠀⣼⠁⠀⠀⠀⢀⡴⣦
⠀⠀⠀⢠⠞⠉⢹⣦⡬⠿⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣧⠀⢠⡇⠀⢀⡠⠞⠁⣰⠃
⠀⠀⠀⠈⠳⠶⠚⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣷⠀⠀⠸⡆⣸⠀⡴⠋⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠘⡆⠀⠀⣷⣯⠞⠀⠀⢀⡴⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠙⣄⠀⠀⠀⠙⢦⡀⢸⣃⣀⡤⠖⠋⢀⡴⢋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⢦⡘⣆⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⣠⠏⠀⣼⠁⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⡆⠀⢹⡀⠀⠹⣼⣆⠀⠀⠀⠀⡏⠀⠀⢀⡼⠁⠀⢰⠃⠀⠀⠀⣯⣠⣞⡀
⠀⠀⠀⠀⢠⠞⠳⣄⠑⢿⠁⠀⠀⠳⡀⠀⠈⢿⡄⠀⠀⠀⡇⠀⣠⠏⠀⠀⢠⠏⠀⠀⠀⣰⣋⣿⣍⣩⠇
⠀⠀⠀⠀⠈⠳⢼⣛⢒⣾⠧⣄⣀⠀⠙⠦⣄⡈⢳⠀⠀⢸⡇⡴⠃⠀⠀⣠⠏⢀⣠⠖⠋⠙⢧⣶⠯⡅
⠀⠀⠀⠀⠀⢰⡙⣻⠏⠀⠀⠀⠉⠛⠦⣄⠀⠉⠉⣇⠀⢸⡿⠁⠀⢀⡴⢃⡴⣫⠴⢺⠇⠀⠈⠳⠶⠋
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢶⠒⠦⣄⡈⠳⡄⠀⢸⡄⢸⣧⡤⠖⠋⣰⣫⠞⠁⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠉⠳⢼⣆⠀⢧⢸⡇⠀⠀⡴⣳⠃⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠂⠈⠀⠀⠀⠀⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠘⣯⠙⢷⣄
⠀⠀⠀⠀⣿⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣠⡞⠁⣾⠁⠀⠀⢀⡾⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠉⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⣴⠏⠀⠀⣿⠀⠀⠀⣼⠃⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⣷⠀⠀⣼⠃⠀⠀⢸⠇⠀⠀⠀⣿⠀⠀⠀⢻⡄⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣿⠀⢰⡏⠀⠀⢠⡟⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⡾⠃⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣾⠁⠀⢀⡿⢡⡶⣦⠀⠀⢿⡀⠀⠀⢸⡇⠀⠀⣸⣇⣠⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣠⡟⢁⡿⠁⠹⣇⠀⠸⣇⠀⠀⢸⡇⣠⡾⢋⣉⣁⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⣄⡀⠀⠀⠘⣿⣴⠏⠀⢸⡇⠀⠀⢹⡆⠀⠹⣆⠀⣾⣷⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠷⣄⠀⢻⡄⠀⠀⢸⡇⠀⠀⠈⣷⠀⠀⠙⣶⠟⠙⠳⢦⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠈⢷⣜⣧⠀⠀⢸⡇⠀⠀⠀⢻⡄⠀⣴⠏⠀⠀⠀⣀⣀⠉⠉⠉⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠹⣿⡀⠀⠀⢻⡄⠀⠀⢸⣇⣼⣧⡶⠞⠛⠛⠉⠉⠙⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢿⡇⠀⠀⠈⢿⡄⠀⣸⣿⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠹⣦⡿⠁⠀⠉⠙⠛⠛⠓⠚⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠹⡀
⠀⠀⠀⢾⠓⠦⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢷⠀⠀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢆⠀⠈⠳⡀⠀⢀⡎⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡼⠀⡜⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢳⠀⠀⢀⡴⠒⠉⣹⠃
⠀⠀⠀⠀⠈⠳⣄⡀⢳⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⢹⣸⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⡰⠋⠀⢀⡴⠁
⠀⠀⢠⡤⠖⠒⠲⠭⢟⣦⣿⠀⣸⠁⡠⢦⠀⠀⠀⠀⠀⢇⠀⠑⢆⢸⡇⣠⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢳⠀⢸⣰⠧⠴⠚⠁
⠀⠀⠀⠉⠓⠦⠤⠤⠤⠬⢿⡰⠃⡼⠁⢸⠀⠀⠀⠀⠀⠈⢦⡀⠈⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⢱⡀⠘⣆⣾⠓⠚⠉⠉⠙⠒⣢⠄
⠀⠀⠀⠀⠀⢞⡉⠉⠙⠒⢬⣇⢸⠁⢀⡞⠀⠀⠀⠀⠀⠀⣀⡈⠓⠺⡇⣠⠖⢻⡆⠀⠀⠀⠀⢸⡀⠀⣇⢀⠞⣀⣉⣓⣒⡒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠶⠺⣟⡠⠊⠀⠀⠀⠀⠀⠀⠀⡇⠙⢆⠀⡷⠁⠀⡼⠀⠀⠀⠀⠀⠀⢣⠀⢸⣾⣉⣀⣀⣀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣦⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⢄⡀⡠⠚⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠁⠀⢀⡀⢀⡉⢀⠤⠔⠢⠀⠸⠤⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡄⣄⠀⠀⠀⠀⠉⠒⡼⣬⠒⢝⢈⡇⠀⢠⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠗⠁⡘⡀⠀⠀⠾⠊⠀⠉⢡⡁⠀⠀⠟⠀⠀⠠⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠫⣉⡢⠰⠃⢰⢉⢥⢱⠀⠀⡇⡆⠀⠀⠀⠐⠓⠃⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⢲⠢⡀⠀⠀⠀⠸⣀⣥⢴⠓⠄⠈⠱⠨⠝⣁⣀⠔⡲⠆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠠⢅⠃⠀⣴⢣⢸⠋⠘⢾⠀⡀⠀⠀⠀⠀⣞⡶⢅⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠓⠂⠁⢐⠲⠊⠸⠀⡆⠀⢈⠀⠃⡀⠤⡤⠀⠀⠈⠪⠄⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠂⠙⠭⠾⠄⢣⠀⡆⢰⠀⡈⠀⠀⠁⢉⠔⡑⢠⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡄⢔⣢⡘⡄⢣⠠⠀⡆⡇⢸⠀⢠⠂⡜⠀⢇⢇⢔⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡠⣻⣑⡥⠂⠱⠀⢳⠀⢣⠁⢸⢠⠃⡜⡀⡄⠌⠈⠁⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⠰⠃⠀⠀⢇⠘⠆⢸⠀⢰⠃⡸⠀⠲⣛⠅⠀⡔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢠⣅⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊⠇⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢄⢄⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠿⠛⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠟⠛⠻⠿⣿⣷⣶⣶⣦⣼⡇⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠇⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠏⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠉⠁⠀⢀⣴⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠟⠉⠀⠻⠋
⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠈⠻⣿⣿⣦⣀⣠⣴⣾⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣀⣠⣾⣿⡿⠋⣠⠽⠻⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣦⣀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠁
⣶⣶⡶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢃⣤⡀
⠀⠀⠀⠀⠀⢸⢰⠞⠁⠁⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠈⣣⣼⡉⣠⠄⠄⠀⣀⠀⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢸⡤
⠀⠀⠀⠘⠦⠀⠿⠂⠘⠃⠀⠀⠀⢆⠰⠀⠀⢀⢰⡆⠀⠀⣩⣷⠀⠀⠀⠀⣤⡀⣄⢃⣨⡶⠗⠀⠉⠁⠀⢀⠈⠳⠄⢀⠀⣀⠀⠀⠠⢀⠀⠘⠟⠁
⠀⠀⠄⡀⠠⡿⠤⠤⠔⠂⠀⢶⠄⠈⢶⡀⠐⠁⡘⠀⠀⠀⠉⢹⠀⠀⠀⠀⠈⠛⣤⣏⡏⠒⣧⠔⠀⠀⠀⠀⠁⠤⢮⢠⣤⡄⠀⠈⠦⠐⢂⡴⠆
⣀⠀⠑⠼⣶⠆⠀⣀⡰⠀⠀⠀⠀⡀⠘⣧⡔⠀⠀⠀⠀⠀⠘⠝⡇⠴⠀⠀⠀⠀⠀⢸⣽⠻⠃⣤⠀⠀⠀⠙⢦⡀⠈⣥⡅⠀⠀⠐⠶⠂⠾⠆⠀⢀⡀
⠀⠀⢠⣤⠅⠀⢀⡴⠀⠀⠀⠀⠠⡈⣤⡼⠀⠐⠒⢰⠇⠀⢀⢠⣧⠤⡄⠀⠀⢰⡟⠂⢸⠀⣀⡰⠆⠀⠀⠀⠀⠐⠄⠘⡁⠀⠀⡀⢠⡀⢀⠀⠀⠘⠊
⠀⠀⢰⠉⢁⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⣸⣀⣁⠠⠂⠀⠀⠘⠈⡁⠀⠀⠀⠀⠀⠘⠟⣛⣯⡌⠁⠀⠀⡶⠀⠀⠀⠈⣿⠀⠀⠀⠙⠛⣁⢨⠦⡤⢀⠬
⠀⠀⠀⠀⠻⠀⣀⠀⠀⠀⠁⠀⢢⠀⠀⠉⠀⠀⠤⢺⠃⠀⠀⠻⠟⠀⠃⠀⢀⠀⠀⣀⠈⢃⠀⡠⢪⡞⠁⠀⠀⠀⠀⠘⠀⠀⠠⣠⠀⠻⠂⣤⠀⠾⠆
⠀⠀⠃⣀⠀⠀⠀⠑⢄⠀⠈⣦⠀⠁⢀⡄⣃⠠⢀⠂⠀⠀⠸⠽⣷⡰⠀⠀⠈⠙⠦⠬⠽⢶⣔⡤⠊⠀⠀⢠⠎⡆⠀⠰⠀⠀⢠⠼⠦⠀⠀⠉⣀⡀
⠀⠀⠀⡌⠀⠂⠀⠀⠀⢢⠀⠈⠳⣇⣸⠁⠉⢀⠁⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠁⢃⡅⣀⠀⠀⠀⠈⠚⠁⡤⣄⢠⠉⠋
⠀⠀⠀⠆⠀⠩⡀⠀⠀⠀⡆⠀⠀⠈⠏⠁⠀⠁⠀⠀⠀⠀⠑⠊⠋⠀⠀⠀⠀⡤⠄⠀⠀⠘⠀⠀⠈⢇⠀⡆⢸⠃⡋⢀⠀⠀⠀⠐⣀⣿⠁⠀⡤⢌⡆
⠀⠀⠀⠘⡀⠀⢧⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠐⠀⡀⠀⠀⢰⠀⠀⠀⡀⠀⠲⣆⢠⠀⠉⠂⠀⠀⠀⠠⠈⠀⢹⠁⡤⡑
⠀⠀⠀⠀⠀⠦⠘⠦⠀⢀⠃⠀⠀⠀⡆⠀⠀⠀⢈⣋⠀⠀⠀⠀⠀⠈⠄⢁⢰⠀⠀⠀⠀⠈⠀⠀⠈⠙⠁⠀⡹⠊⢀⠀⠁⢠⠞⡇⠀⠀⠀⠌⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠁⠀⢀⠀⠀⠐⠀⢀⡀⠉⠉⠰⢄⠀⠰⡄⣄⠈⢠⡌⠀⢸⠇⠀⠠⠀⠀⠀⠑⢵⣀⢻⠀⢂⠀⠠⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢑⠀⠀⠀⠈⠳⠀⠀⠑⢬⡃⠀⠀⠫⡁⡀⢣⡀⠂⠃⠀⠀⠀⠀⠰⣄⠀⠙⢢⡦⠂⠀⡡⠀⢠⠊⠇
⠀⠀⠀⠀⠀⡀⠰⣆⠀⢀⠀⠀⠘⢆⣴⡄⠀⠳⠇⠀⠀⠀⠀⠀⢀⡀⠀⠳⣘⢁⣅⡀⠐⡦⠀⠀⠰⡈⢆⢂⠀⠡⡀⣸⠃⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠐⡀⢈⣆⠈⠀⠀⠰⠻⢀⡀⢠⠶⢀⠀⠀⠀⠀⡀⠀⠆⠐⠦⢜⡆⣑⣀⠄⠀⠀⠀⠀⠈⠒⠶⣄⠀⠡⠀⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠋⠀⠈⢆⠱⣅⠀⠀⡸⠁⠀⠀⠄⠠⠘⡗⠁⠀⠀⠀⠀⢀⠀⠀⢀⡀⠈⠀⠢⣇⠀⠋⢀⡶
⠀⠀⠀⠀⠀⠀⠃⠈⡒⢷⠀⠀⠾⠀⠀⠀⠦⠀⠑⢾⠇⠈⢀⡀⠀⠀⢆⢀⠁⠀⠰⣠⠁⠠⠀⠉⠀⠀⠈⠫⣆⡃⠀⠘⡀⢀⣨⠌
⠀⠀⠀⠀⠀⠀⣤⠀⡀⠹⡇⣀⠆⠀⠀⠀⠈⢌⠄⢸⡆⠀⠘⠁⠀⠀⢀⠑⣤⡔⡐⢡⡎⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠀⡟⠉⠁⠀⣤
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡟⠡⢂⠏⠀⠀⠀⠀⠙⢾⡇⡴⠰⡄⠀⠇⠈⠃⢸⢪⡴⠊⠁⢀⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⡧
⠀⠀⠀⠀⠀⠀⠀⣤⠈⡘⢿⠔⣃⠀⠀⠀⢂⠀⠀⢸⡟⢁⡠⠁⠀⠛⠷⣷⠀⡼⠀⠀⡄⠘⠀⠀⠀⠀⢊⡁⠀⠀⠀⠀⠀⠀⠐⠠⠀⢱⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⡇⠀⠁⠀⠀⠀⠈⠢⡀⢄⣧⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢰⠀⡠⠁⠀⠠⠀⡤⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠘⢢⡀
⠀⠀⠀⠀⠀⠈⠣⡀⠀⣀⡅⢐⠂⠀⠀⠀⠀⠄⢈⡀⡟⠠⠐⠹⠁⠀⠀⢰⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⢈⠁⠀⠀⠐⠃⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠓⠻⠃⠍⣀⠀⠀⠀⠀⠀⠀⠈⢟⠐⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠃⠀⠀⠀⡤⡄⡠⠀⠨⠀⠀⠀⠤⠀⠀⠀⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢇⢰⣿⣠⠍⠀⠀⠠⢀⠤⠀⠀⡏⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠐⠼⠧⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⡠⢀⢍⠜⠀⠀⠀⠀⠀⠓⠀⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠶⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡇⠀⠀⠀⣿⣿⣿⡆
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢿⣿⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣀⣉⣀⡀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠟⠋⠀⢀⣀⣀⣀⡀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⢀⣤⣤⣴⣶⣶⣶⣾⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠠⣿⣿⣿⡇⠀⢠⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡆⠀⠀⣷⣿⣿⡃⠀⢸⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠇⠀⠀⣿⣿⣿⠇⠀⠀⣿⣿⣿⠇
⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⣼⣦⡁⡠⠀⠀⠀⠀⢠⠀⣷⣷⣥⠀⠀⠠⢠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⢻⣅⠆⠀⠀⠈⡈⣟⣷⣿⠏⢠⢸⣾⣿⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣻⣿⣏⣿⡰⠁⠀⡆⣷⢻⡿⣿⠎⠈⣼⡿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢺⣿⣿⣿⣾⣷⠁⢀⢰⠿⣿⣟⣯⠼⣸⣿⢫⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢾⡿⣿⣿⢷⣷⢣⠛⣾⣷⣿⣿⡷⡀⣧⡿⣟⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣿⣿⣿⣷⠋⡆⢻⣿⣿⡎⣤⣿⣹⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⢷⠀⠘⣿⣿⣿⣿⠻⣸⣿⣯⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⣏⠆⠀⠀⢿⣹⣯⡝⢰⣷⣽⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⢹⣏⠀⠈⢺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢣⠀⠀⠀⢸⣿⠀⠀⠀⣿⠇⠀⡔⡻⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⢸⠻⣿⢧⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⢻⡷⠚⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠀⠀⣸⠀⠘⣆⣇⠀⢸⣿⠀⠀⠀⢹⠀⠘⣾⠃⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡏⢻⣇⠀⣿⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⢸⠀⣸⡿⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠈⣿⡄⣿⠀⠀⠀⠹⣧⣾⡇⠀⠀⠀⢸⢀⣿⠇⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡞⠀⠀⢸⣷⣿⠀⠀⠀⠀⠹⣿⠀⢠⡄⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⢻⣿⠀⠀⠀⣄⡆⣿⠀⣸⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⢴⡏⠀⠀⢠⣿⠀⣿⠀⣿⡄⢷⢸⡇⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡟⣸⠇⢰⠀⣸⠛⢀⡟⠀⣾⡇⢸⣿⡇⣾⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠃⣿⢀⡏⢀⡇⣼⢾⣿⢸⡸⡇⣿⣿⣇⡟⣸⠀⢀⣴⠃⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⢠⢸⣷⣼⢰⡇⢾⠇⢸⣇⣿⡾⣿⣸⠁⣷⣿⣿⣿⣧⢟⣴⣼⢟⠀⣠⠎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣆⣸⢸⣿⣿⣿⣾⡻⣸⢠⢸⡿⣿⣷⣿⡿⣠⣿⣿⣿⢇⡾⣾⣿⣿⣿⣿⡟⢨⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠿⠿⠿⠿⠿⠿⣿⣿⣼⠛⣿⣿⢹⣿⠻⢿⣿⠿⡟⢸⡇⡿⣿⣿⣿⣼⢇⣾⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢷⠶⠟⠛⠁⠀⠘⡄⣤⣀⣄⠠⢾⠿⠿⠿⠿⠿⠟⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⠄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡤⠞⠪⢊⠛⠒⣂⠄⡆
⠀⠀⠀⠀⠀⠀⠈⠲⣴⡧⠤⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠙⠌⣀⢸⣷⡬⠼⠃⠀⠀⠀⠂⢾⣙⢠⡏⢸⢸⠇⠘
⠀⠀⠀⠀⠄⠀⢀⡀⢻⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠥⣢⡈⠛⡩⢁⠀⢀⠀⠀⠀⠀⠢⠬⠿⢹⠼⠬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⣀⢠⣤⡀⠉⢱⠛⠋⠅⠭⠅⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣔⡀⡙⠛⢙⠢⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⡙⢷⡀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠺⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠋⠛⠂⠀⠀⠀⠀⠠⠀⠀⠄⠑⠠⢌⡞⢁⡄⠁⠀⡀
⠀⠀⠀⠀⠀⠠⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⡀⢀⡀⠀⠀⠀⠀⠀⠒⢤⣀⢀⢰⠉⡠⢁⣤⠘⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣠⣰⠲⠆⠬⢶⡾⣿⠀⠀⠀⠀⠀⠀⢀⡐⠉⠑⣯⣦⡷⠃⠄⠁⠁
⠀⠀⠀⠨⢄⠶⢐⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⣠⠤⠲⢌⣳⣶⢞⣻⣿⣝⠄⠀⠀⠀⠠⠐⢄⠀⣶⡼⣿⢿⠓
⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣈⡺⢿⠋⠤⡟⡀⠿⠀⠀⠀⠀⠀⠀⠐⠡⠈⡡⠼⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠄⠋⡬⠹⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣴⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧
⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆
⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⣶⢶⣦⣤⣾⣷⣶⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡶⣤⡀⠀⠀⢀⣴⣯⣤⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣾⣋⣰⣾⣿⢷⣴⣏⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⣿⠀⢠⡾⢻⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⣿⢐⣿⣿⡿⣿⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⣠⠄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⢷⡁⢌⢂⢰⡜⣣⢉⡼⣈⣟⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⢙⡇⣘⡁⢉⡌⢻⣸⡤⠞⢶⣘⡥⢠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠏⢬⠡⢄⡶⢤⣽⡉⠞⢃⣉⣩⣙⡒⣚⢠⣈⠏⣷⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡚⢱⡥⣴⣢⡵⡫⠚⣡⠑⣼⠳⢈⡡⢈⠉⣗⢪⠁⠨⠣⠀⠙⢳⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⢩⡝⠒⠃⢺⡭⣥⠃⠉⢠⠝⢂⣤⠛⠅⣈⡦⢣⠀⠈⢓⠀⠖⣇⡀⢉⣹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠛⠀⣀⣠⣾⠰⣿⠇⡰⠙⠀⠈⠸⠀⠄⡀⠐⡧⢻⠐⢸⠄⢀⢝⠁⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣦⡀⢈⣍⣾⡟⠠⣽⠘⠷⠀⠀⠀⠀⠀⠀⠀⠰⣄⠺⡆⡴⡂⠀⢨⠃⠀⠐⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⡤⠹⡿⣶⠋⣰⡿⠁⠠⠶⣣⠄⠀⠀⡀⠀⡐⠀⠄⢸⡁⠄⠇⣸⡌⠁⡠⡟⠀⠀⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⣸⠃⢸⡄⠀⠀⠖⠷⠀⠀⠀⠁⠀⠀⠀⠀⠼⡀⢠⠀⠁⠒⠀⠁⡳⠄⠀⢘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠀⠀⠀⠸⡆⠆⠾⡁⠀⣀⢧⠻⣄⡀⠀⠂⠀⠀⠀⠀⡦⠈⠈⠀⢚⡃⠀⠚⡻⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠗⠀⠀⠀⠀⡞⠈⠀⠚⡁⠀⡁⢪⣐⡈⢦⠀⡤⠀⠀⠀⢰⡄⠀⠀⠠⡼⠈⠀⢘⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠄⠀⠀⠀⠀⢋⡐⠀⠀⠀⢀⡇⠀⠁⢀⠀⣬⠐⠂⡀⠀⢹⠅⠀⠀⡆⢠⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⡀⠠⠘⠂⠀⠈⠃⠂⠐⠁⠈⠀⠠⠀⢀⠁⠀⠀⠀⢸⣧⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡏⡀⢁⠆⡰⢀⣀⠐⠄⠀⠀⠀⡄⠀⠀⠀⠘⣿⠀⣆⢠⣦⡇⢀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠉⠃⠀⠀⡐⢠⣾⣿⠀⠀⠀⢀⠆⠀⠀⡆⢸⠀⠻⡆⠈⢼⣿⠁⢈⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢉⡆⢀⠀⡠⠀⠀⡐⠀⠀⠁⠺⠁⡐⠀⠀⡀⡌⠀⡀⠀⣧⠈⠄⠀⠦⢄⠈⡿⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⢃⠰⢚⠀⠀⠀⠃⠀⣰⠀⠀⠀⠀⠺⠀⡠⠈⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠁⠂⠂⠂⠈⠀⠀⠀⠐⠂⠀⠸⠅⡀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠌⢁⠞⣼⠀⢠⠇⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⡄⠐⠐⠀⠀⠀⡠⠄⣀⡀⠂⠀⠀⢀⠄⠀⠉⠦⠐⠠⢠⠀⠀⠀⡠⠊⢀⡜⡄⠞⢀⠀⠰⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⡑⠀⠀⠀⠸⠠⠤⠌⠀⠁⢥⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠔⠤⣧⠐⠄⠀⢠⡞⢇⠀⠇⢸⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⡀⢀⠦⠼⣥⠘⡀⣁⠤⠖⠒⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢰⠀⢀⠂⢀⠔⠂⢀⠀⢀⠀⠀⠀⠠⠀⠄⠀⡀⠠⣄⣀⣠⠆⠀⠀⠀⠀⢨⠁⠈⢙⠐⡦⢤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠡⠘⠀⠘⠂⠀⠉⡐⠁⠁⠀⠀⠀⠀⠀⢠⡀⡘⠁⣠⠆⠞⠁⠄⠀⠀⡀⠀⠈⣩⡄⠦⠠⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠇⠀⠀⠀⣰⢖⠆⠉⠈⠀⠀⠄⠐⠁⠑⠂⠀⠀⠐⠀⠀⠀⠀⠑⠄⠃⠡⠠⠂⠀⠀⢀⠀⠡⣯⠆⠀⠀⠈⡀⠀⠇⠀⠀⠀⠀⠈⢊⠂⡰⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠐⠋⠀⠢⢀⡀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠄⠀⠐⠀⠀⠀⠾⠀⠀⢈⡘⠁⠀⣄⠀⠀⠑⢸⡀⠀⠀⠀⢰⠈⠐⠋⠀⠀⠐⠠⢄⣮⡤⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠄⠀⠀⠠⠀⠀⣄⡀⠀⠠⠆⠀⠀⠠⠐⠀⠘⠁⠀⠀⠀⠀⠂⢼⡁⠘⠠⠄⠀⠠⠤⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⣠⠊⠉⠒⠉⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡁⢘⣆⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⢀⣠⡤⣤⡀
⠀⠀⠀⢀⡴⠊⠉⢠⡰⢏⠃⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣘⣁⠙⣉⣏⠀⠀⠀⠀⠀⠀⠀⣀⣽⣷⣾⣿⢶⣤⠁
⠀⠀⠀⢺⢀⡷⠚⠃⠀⡜⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣍⢤⣩⣀⣯⠀⠀⠀⠀⠀⠀⢸⠟⠈⢲⡷⠊⠀⠘⠃
⠀⠀⠀⢸⠻⢥⣤⠤⠊⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⢲⠓⠂⠚⠀⠀⠀⠀⠀⠀⠼⠥⣌⣡⣨⢽⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚

⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⠀⠀⡄⡀⠀⢰⣀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢀⣠⡴
⠀⠀⢀⢤⠀⡊⠀⢈⡀⡏⣷⠀⠀⠀⠀⠀⠀⢠⡀⠀⡰⠟⢠⠖⠁⠀⠀⢈⠙⣶⠂⣿⡃⢀⣞⣥⠾⠤⠀⠀⠀⠀⢹⣧⠀⢀⢔⡿⠉
⠀⠀⢸⣸⣦⣰⠀⢸⣾⢟⠟⠀⠀⠀⠀⣀⣈⢳⣿⣠⢶⣟⣿⣀⠀⠀⠀⠋⠉⠙⠫⡹⡴⠟⠛⠻⢯⠀⠀⠀⠀⠀⠀⣯⣇⢎⡞
⠀⠀⠈⠳⠥⡟⠀⢰⠏⠁⠀⠀⠀⠀⠀⠈⢎⠳⡽⢡⢻⡟⣥⠴⠀⠀⠀⠀⠀⠀⠀⢧⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⣿⣼⡀
⠀⠀⠀⠀⠀⠱⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣇⣬⣬⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣇⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣆⣸⣿⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⠤⡄
⠀⠀⠠⠶⢤⡄⡾⢁⣤⡆⠠⠀⠀⠀⠀⠀⣴⣸⣿⣷⢟⣾⣶⡁⠀⠀⠀⠀⠀⢀⠮⠭⠥⠬⠭⢷⠀⠀⠀⢀⡴⠅⣤⢤⠒⠶⠻⣄⣄
⠀⠀⠀⠑⠂⠉⣧⠟⠭⠔⠀⠀⠀⠀⠀⠀⣿⣿⣾⡏⣼⣿⣹⣃⠀⠀⠀⠠⣦⠞⠀⠀⠀⢀⠀⢈⢣⣄⠀⢨⠧⡶⠿⢀⡀⢐⠶⠀⠘⢶⡄
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⡟⣾⡛⣿⢗⡿⡏⠁⠀⠀⠘⠓⠚⠙⢦⡜⠉⠑⠊⠀⠀⠀⠀⢱⠃⣠⠋⠉⠙⠋⠙⣦⠀⢣
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠟⠚⠃⠛⠂⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⡤⠢⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢟⣻⠒⢤⠀⡴⢫⠝⠋⠉⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⣀⣀⣃⢀⣀⡸⠊⠉⢿⠀⠀⠀⠀⠀⠠⡀⠀⡆⢀⡠⠔⠂⠀⠀⠀⠀⣀⠤⡤⡭⣿⣿⣧⡀⣲⢦⡀⠀⠀⠀⢀⠞⠁⠀⠀⠙⡄
⠀⠘⠢⡤⠈⣿⢉⡷⠠⢤⠚⠀⠀⠀⢀⣀⣀⡈⢦⣷⢞⣡⡤⠤⠀⠀⢠⣮⢴⠎⣰⠇⠈⠘⡆⢷⠈⠉⠁⠀⠀⠀⠸⠀⣄⠀⠀⢀⢱
⠀⠀⠘⠤⠚⢈⡉⡧⣸⠞⠀⠀⠀⠀⠉⠀⠀⠉⠻⣷⠋⠁⠀⠀⠀⠀⠈⠀⠈⡼⠀⠀⡇⡆⠙⣾⠀⠀⠀⠀⠀⠀⠘⠚⢻⠒⢲⠛⠋
⠀⠀⠀⠀⠑⠊⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠶⠠⠧⢄⠀⡅⢏⠶⠳⣶⣦
⠀⠀⠠⢄⠐⢂⠚⢣⡀⠀⠀⠀⡘⣴⣻⡭⣛⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⢀⣼⡎⠉⠁⣝⡆⢿⣯⣿⣿⣷⣷⠃⢟⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⣶⡇
⠀⠀⠀⡸⢋⢛⡆⡌⣥⡾⠏⠿⣛⣿⣫⡿⣿⣿⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣾⠶⠔⠁⠴⡄
⠀⠀⠀⠙⠻⢿⣿⠿⠗⣲⣫⡿⣛⢳⡍⢱⣯⣽⣷⣿⠒⠋⠉⠀⠀⠀⡀⠠⠄⠰⠆⠀⠀⠀⢤⠀⠀⠘⠋⡉⠐⠛⠉
⠀⠀⠀⠰⠷⣖⣾⣸⣿⣿⣿⣿⣿⣿⣶⣿⣾⣾⣿⡿⠀⠀⠀⠀⠀⣰⣏⡰⠂⢆⠈⢰⡤⠈⡀⣄⣠⡄⠀⣨⡀⠈⠖
⠀⢀⣄⡤⠴⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣇⡐⡂⠀⠀⠊⣴⡈⢳⣴⣾⣦⡻⣇⢀⣠⣴⣤⠀⠚⠋⠛⠂⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠛⠋⠋⠙⠒⠁⠀⠀⠀⠰⣤⣴⣿⢶⣭⣤⣄⢉⡙⠚⠉⠛⣦⠀⣠⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⣷⣮⣛⢻⣟⢿⡿⣷⡾⣧⣶⠷⢴⣿⣵⣐⣿⡧⢇⡀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢻⣿⣿⣾⣿⣧⣩⣶⣾⣶⣦⣔⡛⣡⣾⣟⣻⣧⣭⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣛⡿⣿⠤
⠀⠀⠀⠀⢀⠄⠀⣷⠴⣆⠴⠄⡈⠲⣄⠘⠉⠹⠻⠓⣔⡃⠀⠀⠀⠀⠈⠉⠉⠋⠙⠋⠉⠉⠀⠁⠀⠀⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣝⣥⣍⡓⠒⠋⡄⠀⢀⡈⠤⢄⡀⡀⠀⠊⠑⠐⣂⡄
⠀⠀⠀⢰⠎⢾⣧⣾⣵⣖⣴⣿⣿⣶⠂⢀⡌⢡⡟⠀⠀⠈⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠠⡼⣄⣿⣯⠻⣿⡷⠿⢛⣿⣿⣿⣿⣷⣾⣾⣛⡴⡁⡀⣾⡄⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⢄⣳⣮⢶⠀⠀⢦
⠀⠀⣸⣷⣛⣙⣋⣭⣿⡇⠻⠿⣿⣏⣿⣿⣿⣿⡛⠛⣛⣰⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠑⣼⣥⣟⢣⡀⢠⠍⣲
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⡷⡿⠿⣿⣿⣷⣮⣴⣻⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣶⡮⣿⣿⣯⣦⣍⢈⡁⢀
⠀⠀⠉⢉⢹⢿⣟⣻⣿⣯⣿⣷⣞⣛⣡⣿⡿⣭⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⣁⣻⠻⣿⠷⣛⢛⢻⡓⠯⠏
⠀⠀⠀⠀⠀⠰⠟⢥⡾⣝⣿⡽⡉⡁⠋⡏⠰⡙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⢿⣿⡯⣿⣾⣿⣯⣿⡿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠻⣥⣧⣰⣇⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⣶⣿⣿⣿⡻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⢿⣿⣿⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠤⠤⠶⡶⠿⠿⠶⠦⠄

⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⢀⡴⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⢦⡀⣾⣿⠿⠏⠀⠀⠀⠀⠀⠻⠿⠦⡘⠋⠀⠀⠀⠀⠀⠀⡤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠈⢽⡆
⠀⠀⠀⡀⠳⣌⣷⠹⡛⡚⠛⠉⠁⠀⠀⠶⢶⠶⣾⠷⠶⢤⡄⠀⠀⠒⣲⠗⠀⠁⠀⠀⠀⠀⣘⡻⡄⠀⢹⡷
⠀⠀⠀⢿⣀⡙⢏⣁⣾⡿⠷⠖⠀⠀⠻⣦⣄⣴⠳⢶⣦⡤⠀⠀⠀⠀⣤⠃⠄⠀⠠⠀⠀⠀⠉⢦⠀⠀⣼⡀⠂
⠀⠀⠀⠈⠿⠉⣛⡋⠉⠀⠀⠀⠀⠀⡠⠖⣿⡘⠷⣦⡀⠀⠀⠀⠘⢲⣟⠀⠘⠀⠃⠀⠀⠀⠀⠭⠆⠀⣺⡟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠰⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⣤⡄⠀⣦⢢⣴⣷⣦⠀⠀⠀⠀⠀⠀⣦⢀⡶⣴⣾⣾⣀⠔⠀⠀⠈⠑⢤⣄⣨⣄⣀⣾⣤⠖⠃
⠀⠀⠀⠀⠈⠐⠗⠸⣹⠟⠺⠂⠀⠀⠀⠀⢷⣷⣿⣸⣷⣟⣽⣿⣷⡞⠃⠀⠀⠀⠙⢿⣋⣦⡄⡛⣯⣵⡶⠂
⠀⠀⠀⠀⠈⢤⠰⡜⠅⢀⠘⠂⠀⠀⠀⠛⣾⣿⣿⢿⣿⣿⣟⣛⢿⣍⠀⠀⠀⡠⢶⣴⣯⣶⣠⠿⣟⣿⡷⠶⠤
⠀⠀⠀⠀⠁⠐⣴⠀⠀⠂⢉⠀⠀⠀⠰⢋⣽⣿⣿⣿⣿⣿⡟⠛⠒⠀⠀⠀⠀⢀⣾⡿⢯⣮⣼⣶⣿⡝⠲
⠀⠀⠀⠀⢀⡖⠀⠀⠀⠄⠻⠃⠀⠀⠀⠈⠽⠚⡹⢻⣟⠷⢱⠀⠀⠀⠀⠀⠐⠛⠋⠀⢀⡟⢻⡏⠛⠿⠆
⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠠⢛⡷⣿⣶⠀⠀⠀⠀⠀⠀⠀⡀⢰⣧⣿⣶⣷⣮⣤⠄⠀⠀⠀⠀⢴⣶⣶⡿⠇⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠰⡿⠞⠀⠈⠁⠀⠀⠀⠀⡆⢸⣾⣴⢿⡿⠿⠛⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⠁⢀⡄
⠀⠀⠀⠀⠀⠘⣡⣶⡄⠀⠀⠀⠈⢂⣸⣿⡿⢿⠟⠀⠀⠀⢀⠀⠀⠀⠀⠒⠛⠛⣿⠋⠉⠁⡼⢻⠟⠀⠀⣾⠃
⠀⠀⠀⠠⣾⣿⠓⠋⠀⠀⠀⠀⠐⢄⠙⢻⡷⠆⠀⠀⢰⣿⢿⡧⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⠁⣼⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠘⠋
⣀⣀⡀⣀⡀⡀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⡀⢀⡀⠀⢀⡀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⢖⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢿⠸⣠⠇⠀⠀⠸⣆⠈⣩⡆⠀⠀⠀⠀⢀⠄⠀⠀⠀⣿⠀⢛⡛⠁⠀⠀⠀⠀⠀⠀⢀⡤⠘⢁⡀
⠀⠀⢈⠐⢋⡶⠀⠀⠀⠈⢈⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡈⠚⡏⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⠴⠛⠁
⠀⠀⠸⣦⡈⢠⢴⡆⠛⣩⠃⣞⣴⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠇⠀⠀⠀⠀⠁⠀⠀⠸⣷⡄⣰⡦
⠀⠀⠰⣄⠙⣠⠶⠀⢤⣘⠧⢁⣴⠇⠀⠀⠐⠀⠀⠀⠀⣄⡻⠄⣀⡶⠀⠀⠁⠀⠀⠀⠀⣤⣽⣡⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠚⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡶⢀⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠆⠀⠀⠀⡈⠗⠾⠇
⠀⠀⠰⡆⢚⡋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠰⠈⠛⠋⠀⠀⠀⠀⠀⠊⠸⣀⠁⢋⣠⠄⠀⠀⣻⢇⢴⣦
⠀⠀⢀⠐⢋⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣠⡄⠀⠀⠀⠀⠀⢀⠀⠈⠁⠋⢡⠆⠀⢀⡹⠀⢰⠇
⠀⠀⠘⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⡾⠍⡉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣗⡏⢠⡶⠘⣛⠁⢉⡙⠁
⠀⠀⠰⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣈⣹⣏⣤⠀⠙⠳⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠂⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠀⠀⠀⣿⣿⠋⣿⣆⡹⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⢸⡄⠀⠀⠟⠁⠀⣽⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢸⣿⣿⣿⡆⢸⡇⢀⡆⠀⣠⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⠀⠀⢻⣿⣿⣟⢀⣬⣱⣶⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⣀⡀⠈⣿⣿⡿⠸⠏⠁⣤⠛⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣿⣿⣇⡀⢿⣿⣿⣄⣠⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣾⣿⣿⣹⡟⣋⣠⣶⡿⠻⠋⣹⣿⣿⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣋⡻⠿⣹⡧⠀⠶⠖⠉⠀⢀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣇⠙⣿⣷⣬⣇⠀⡀⢢⡀⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠈⣿⠟⠉⠉⠙⣄⠰⢶⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⠿⠶⢷⣆⣨⣧⣼⣿⣿⡿⠿⠿⠛⠛
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⣸⠇⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠘⠋⠉⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⠀⢸⡅⢰⣿⠄
⠀⠓⣤⡄⣿⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠸⣿⡟⠁⣀⡴⠀⣠⡞
⠀⠀⣿⠁⠙⣯⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣴⣾⣶⠚⠉⠠⢞⠛
⠀⠀⠀⠰⠃⠀⠀⠀⢀⡀⠐⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡌⠻⣿⣿⣿⣁⠤⣠⣾⡵⠊
⠀⠀⠀⠀⠀⠀⢤⣴⣀⡷⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠙⣿⡄⠘⣿⣿⣿⡿⠟⠋⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⡟⠁⠀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣧⡸⣇⠀⣾⠉⠁⠀⡀⢀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⣠⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣶⠏⣠⡄⠟⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠀⠛⠀⠀⠀⢀⡀⠀⠘⣿⣿⡟⣿⣿⣟⠰⣿⣀⣠⣴⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣴⡎⡹⣶⣄⢿⡟⠀⠈⢻⠋⢁⣴⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣷⣠⡆⠉⠘⣧⠘⣿⣿⠁⢠⠀⠀⣠⣟⣱⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⢸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣣⣄⠀⢠⣄⠸⣿⡄⠸⡆⠀⣹⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢿⣏⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⡟⡋⠉⠙⠁⠈⢿⣧⢿⣷⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⢰⣦⣴⣄⠀⠉⠠⣿⣧⣿⠇⠀⠀⢀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⣾⣀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⡌⢻⣿⣿⣷⣤⣀⠙⣿⠇⢀⡄⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣼⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡃⣼⠏⠻⣿⣿⠱⠀⢾⣠⡎⢡⡾⠃⠀⠀⠀⠀⠀⢦⣄⠀⢀⡁⠀⠙⡏⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠑⠀⠀⠀⠙⠟⠀⠗⠀⢿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄⠀⠀⢶⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣦⡀⠀⣾⠀⠀⢴⣧⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⣄⣸⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣴⡟⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠿⣿⣿⡅⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠙⠟⠀⠀⠀⡀⢻⡷⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡟⢻⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠐⡇⠀⣾⡇⢸⣿⡀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠘⣟⣧⡴⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣄⡀⠀⠀⠉⠻⢼⡆⠻⡇⠈⣿⠁⠀⠀⠀⣴⠀⠀⠈⠁⠀⢠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣈⠳⣎⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠄⠃⢰⣧⠀⠆⣠⣴⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣮⣿⣦⡄⠀⣦⠀⠀⠀⢀⣴⣷⡆⠘⣿⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠙⢿⣿⣿⡇⠀⡷⢀⡄⢠⡾⠋⢹⣿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠙⢿⣧⣤⣥⢀⣴⠟⢀⣶⣾⣿⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠉⢿⡇⠈⢡⡄⢸⣿⠀⣈⢠⣶⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠈⡇⢀⣾⡇⢸⣿⣦⣈⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⣿⠈⢿⡇⠀⡻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣷⣄⠀⣿⡆⠘⠃⠀⢃⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⢿⣿⣿⠿⢇⣿⠀⢀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⡆⠈⠛⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠛⣿⡄⢰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣼⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⡾⢹⡟⠆
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠹⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠁⠀⠀⣰⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠟⠀⠀⢀⡴⠋⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⠋⠀⠀⠁⠀⠀⠀⢠⣿⣷⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢋⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⣥⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢞⣫⣥⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⡴⠀⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣬⣭⡷⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣠⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠛⢁⡀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⢠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢈⠛⠦⡄⠀⠀⣿⠀⠀⠀⠀⠀⠖⠋⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⠃⠙⣿⣆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠤⠶⠋⢸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠴⠞⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⠖⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣠⡴⠀⣿
⠀⠀⠀⠀⠀⣿⠀⢀⠴⠚⡁⠀⠀⠀⠀⠀⣀⣤⠀⡉⠻⢦⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡆⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣴⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⣠⠀⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⢁⡤⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⣠⠀⣿
⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⣿⠀⠀⠀⠀⠐⠛⢁⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠚⠋⣁⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠛⢁⢀⣿
⠀⠁⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠖⠋⢀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⠚⠁⣾⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠖⠋⣸⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠛⠛⠛⠟⠛⠛⠿⠛⠛⠛⠀⠀⠀⠀⠙⠛⠟⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠈⠛⠛⠛⠛⠛⠟⠻⠟⠛⠛
⠀⠀⠀⠀⠀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣲⣦⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠓⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠉⠐⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⡀⠦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⢀⡀⢷⡠⠘⢁⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠐⣁⡰⠊⣁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠪⡀⠀⠀⢀⠀⣀⠀⠀⠃⠀⡂⠰⠃⠄⢀⠀⠀⠀⠈⡇⠀⠀⠰⠁⢠⠖⡏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠑⣰⡤⠀⠀⢀⠀⢁⠴⣦⠀⠀⠁⢶⢈⠂⠈⠂⠀⠀⠀⡇⠀⠀⠀⢷⣧⣤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠄⠀⠃⠀⠁⠀⠈⠠⠈⢉⠀⡀⠸⠇⠀⠀⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠐⡂⢐
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢧⡄⠠⠤⣄⣄⡀⠀⠀⠀⣄⠀⢀⠁⢺⠁⠀⡸⢂⡐⠒⡀⢀⡒⠂⠐⠃⠘⠀⢈⡆⠀⢸⠗⠠⠂⠀⠀⢇⠈⠈⠀⢀
⠀⠀⢀⡀⠀⠀⠀⠀⢠⢀⠳⠀⠀⠀⠀⠉⠛⢲⡀⠀⢁⠀⢚⣷⣿⠀⢀⠅⢀⡤⠈⠁⣰⡄⠀⠀⠸⣠⣄⡸⠗⠈⣡⡴⢷⡞⠀⠀⣰
⠀⠀⠉⠀⠀⠀⠀⠀⠈⠣⣉⣶⠀⠀⡁⠑⠀⠀⠙⠢⣿⢢⠈⠙⣿⠀⣾⠀⢘⣥⡜⠁⣼⠉⢢⣄⠀⣹⠟⢀⣠⣾⡿⠤⠀⢹⡄⠀⢿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⠄⡙⠃⠀⠉⠒⡀⠀⠂⠀⠹⡜⣷⣶⡏⢀⠂⠘⠃⣼⡁⢠⡇⠀⣾⣿⡾⢋⡄⠋⠉⠁⠀⠀⢀⠀⠑⠛⠃⢬⡠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠺⠀⠀⣆⢀⠒⠀⠉⠰⡀⠘⢄⠹⣹⣯⡇⣀⡀⠘⠃⣨⢀⣾⡿⠊⠀⠘⠓⠛⠱⠂⠈⠑⡄⠀⠀⠀⠀⠀⠀⠂⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠋⣿⣿⠈⠖⠂⠛⣆⡈⠁⠈⠉⠻⢭⣿⡿⣾⣶⣼⠋⠁⠀⠀⠀⠀⣸⡟⠂⣠⡥⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⢀⢀⣏⡿⠇⠊⠐⠒⠋⠿⠀⠀⢀⠀⠈⢨⣄⣁⣠⠉⠀⠀⠠⠀⢠⣶⣿⠿⠂⡉⠴⠶⠛⢀⠀⠀⢐⠀⠀⠈⠉⢣
⠀⠀⠀⠀⣰⡙⣏⢓⠒⠳⠄⡊⣶⠟⣀⣠⣀⡀⠀⠀⠀⠀⠢⣬⠀⢤⣀⢉⣿⠇⠀⡀⠐⠀⢠⣯⡉⠁⠠⡴⢿⣿⠶⠛⢋⣉⣙⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠒⣫⣿⠲⣤⡨⢻⢿⣿⣿⠀⢻⣶⣄⠀⠀⠀⠱⣦⣌⡽⠿⢿⣦⡎⠁⠇⣠⣾⠋⣉⣳⣦⣌⡋⠤⣀⣤⡜⠛⠂⣄⡀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠺⠇⢸⣄⠙⢿⡆⠘⣷⣿⢧⡀⠀⠀⠹⣿⣇⠀⠀⣸⣿⠟⠂⠉⠀⠀⠀⠈⠉⠙⠻⠦⣌⠑⣤⣔⣺⢤⣥⣤⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢖⣰⡦⠀⢉⠁⠀⠹⣆⠹⢿⢜⣿⣆⠀⠀⢹⡿⠀⣠⣿⣃⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣾⣉⣽⣾⣷⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠧⠧⣈⢷⣄⠀⡈⠄⠈⢧⡙⢻⣆⠀⡾⠁⣼⣿⡿⠿⠿⢯⣍⣽⠿⠷⠶⣦⣤⣀⡀⠀⠂⠀⠀⠀⠙⠎⠉⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣀⠀⠻⣷⣿⣾⣴⣼⣿⣧⢿⣷⢁⣼⣯⣭⣀⡀⠀⠀⠈⠙⠿⣦⣰⣿⣿⣿⣿⠿⠓⣀⡀⡀⠀⢠⡄⠤⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠦⣹⠿⣷⣤⣈⣿⠟⠉⠀⢉⣻⣿⡿⠿⣿⣿⣿⣿⡿⣷⣦⣀⠀⠀⠈⠛⢷⡍⠻⢷⣎⡰⠿⠿⠇⠀⠀⠻⠛⠈⠉⠙⣿
⠀⠀⠀⠀⠀⡠⠀⠈⠂⠄⠩⢀⣍⣠⣛⣶⣿⠁⠀⣠⣾⣿⠞⠉⠀⠀⠀⠻⢿⣿⡴⣟⣯⣽⣷⣦⣀⠀⠀⠙⠄⠀⠉⢶⣄⣀⡄⠀⠀⢀⣠⣿⠇⠈
⣧⠀⠀⢏⣼⠁⠀⣠⠔⠒⠈⢁⠙⠦⢺⣿⠇⠀⣰⣿⡿⠋⠀⠀⣀⣠⣴⣶⣾⡿⠟⣩⣿⢫⣿⣿⣿⣿⣶⣤⣹⣆⠀⠀⢹⣅⣠⣠⡔⠉⠁
⣏⠀⠀⠘⠇⡠⠎⠀⠀⠀⠀⠀⠀⠘⠻⣿⣤⣾⣿⠟⢁⣶⣴⣾⠋⣿⣿⣿⠟⣠⣞⢿⣇⣽⣿⡿⢛⣿⠏⣿⡿⠛⠣⠀⠀⠷⠟⠋
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⢿⠿⣿⠿⢿⠿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠠⠀⡟⠀⠀⠂⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡐⠀⣠⠀⠠⣄⡀⠰⣷⠆⢀⠄⢰⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⢠⠄⠄⠊⠱⠀⠀⠀⠀⠘⠁⠀⠀⠘⠀⠀⠠⡈⠟⠈⣀⣠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠐⠆⠁⠉⠁⢲⢗⣖⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⣠⠟⠛⠷⠀⢨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠾⢯⠔⠠⠵⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠚⠇⠀⠀⠩⠄⠀⠘⠀⠀⢠⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠂⠀⠤⠀⠀⠈⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠈⠁⠈⠸⠀⡀⠀⠀⠀⠀⠜⣷⠎⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡰⡍⠶⠀⠀⠀⠀⠀⢠⣤⣴⠶⣶⡄⢀⣀⣀⡄⡶⢀⢲⣾⣿⣶⠉⣩⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠰⡇⠰⢀⠄⠂⠀⠀⢰⣿⣫⡟⣴⠸⠗⠿⠿⠿⢿⣷⣿⠹⣿⣿⣁⡶⠠⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⢇⠀⢧⢠⡀⠀⠛⠀⠀⠀⠙⣾⡋⠉⢻⡄⠀⠀⠀⠀⠀⠠⠷⠖⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣶⡃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⣠⣌⠲⠔⠈⠿⠁⠀⠀⢀⡀⠰⢷⡸⠟⠀⠀⠀⠘⠀⢸⡆⢀⣀⣀⣤⣤⠄⣀⠀⠰⠇⠀⠀⠀⠀⠀⠀⢀⣶⣾⣾⢜⠏⠁⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠈⠁⡙⠦⢠⠄⠀⠀⠀⢀⠀⠙⢅⠀⡄⢀⠀⠀⠀⣨⣷⣿⣿⣿⣷⡇⢾⢁⡄⠀⠀⠀⡀⢀⠀⢀⣠⣿⣴⣿⡿⠏⠀⠀⠀⣠⣴⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠠⠀⡄⢘⣛⣿⣷⣘⠀⢈⣾⣿⣿⣿⣿⣿⠛⣷⠀⢸⣧⣦⡛⢿⣷⣽⡁⣾⠿⣙⢿⣭⣄⠀⣠⠘⣀⣉⣣⢀⡙⢤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠈⣧⠉⠀⠙⢦⠶⣄⢰⣿⡟⣿⠿⠝⣷⣯⣿⡟⠘⢣⡄⢹⡄⢹⡦⣾⠀⢨⡇⣾⣻⡿⠿⣫⣶⣿⡿⣿⣶⣶⡍⢳⣬⠿⠍⢠⠔
⠀⠀⠀⠀⠀⢠⡈⠉⠀⠁⠀⠀⠛⢃⣠⡽⠺⢿⣫⡟⠀⠸⣿⣋⠻⣷⡀⠘⣿⢸⣇⠈⣷⣿⣆⡾⠃⣼⢃⣶⠿⣿⡟⣙⠃⠘⠶⡉⠙⠣⠠⠖⠀⠁
⠀⠀⠀⠀⠀⠈⢀⣠⠀⠀⠀⠀⠸⢿⣿⣿⣿⣟⠻⣄⠀⠈⠿⣿⠂⠹⣧⠀⢻⣿⠿⠁⣿⣹⢿⣧⣾⡽⠛⠁⠈⢻⣷⠀⠘⣟⠇⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠈⢡⠄⠀⠀⠀⠀⠘⠉⠙⢡⣤⣶⣈⠳⣄⠀⠀⠀⠀⢻⡇⢾⣿⣧⣾⣿⠻⢨⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠉⡵⢤⡀⠀⠀⠀⠠⣵⡆⡅⠎⡿⠓⠌⠻⢧⡀⠑⢾⣿⡜⣿⡿⣿⣯⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠰⠄⡿⠙⠧⠐⠆⠀⠀⠀⠀⠙⢿⡄⢻⣧⢿⣇⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠜⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⣼⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⢀⢀⣄⢠⡶⡶⠒⠀⠐⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣀⣤⣤⣤⣤⣴⣟⣻⣿⣿⣿⣿⣿⡿⠿⡿⠿⡟⠛⢻⠳⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠿⠿⠟⠛⠉⢹⣿⠿⢛⠋⠙⢿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠶⠇⠀⠀⠀⠀⢀⡤⡄⠀⠀⢀⡔⡻⠀⠀⠀⠈⠧⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡄⢠⠎⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠣⡀⢹⡜⣠⠎⠀⢀⡠⠴⣲⠆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢣⡈⠢⡀⠀⡎⢹⡀⠀⠀⠀⠈⠋⠉⠁⠀⠘⠳⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠼⠀⠀⠀⠀⠀⠈⠉⠋⠀⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠤⣄⣀⡀⠀⠙⠁⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡹⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠖⠛⠀⠀⠀⠀⠀⢠⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠇⠀⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⡴⢻⠆⠀⠀⠀⠀⠛⢫⣖⣉⡠⠞⠁⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠁⠀⠀⡼⢡⠏⠀⠀⠀⠀⠀⢠⡤⢄⣀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠂⢠⣀⡀⠀⠀⢳⣸⠀⢰⡲⣄⠀⠀⠀⠀⢸⠀⢸⠀⠀⡼⢀⠎⠀⠀⣠⣄⠀⠀⠀⠱⣄⠈⠙⠢⣄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠳⣍⠑⢦⡀⠁⠀⠀⠙⢌⠳⡀⠀⠀⡎⠀⢸⠀⡼⠁⡞⠀⢀⡜⣡⠋⠀⠀⠀⠀⠀⠉⠉⠉⠛⠃⢀⡼
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣈⣙⠶⣿⠀⠀⠀⠀⠈⢧⡘⢆⠀⡇⠀⢀⡼⠁⢸⠁⣠⠋⡴⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠰⢏⣁⣠⠴⠋⠀⠀⠀⠀⠀⠀⢳⡈⢣⡇⠀⠘⠁⢀⢇⡼⢁⡜⢁⡤⢒⠄⠀⠀⡴⢋⠇⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣍⠒⠦⣳⠀⠁⠀⠀⠀⣼⠏⢀⣾⠖⣡⠔⠁⠀⠀⢰⢁⡼⢀⣠⡤⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⡤⠴⣄⠀⠀⠀⠀⠀⠙⠢⡈⠃⠀⠀⠀⠀⠀⠀⠚⢁⠞⠁⠀⠀⠀⠀⠀⠉⠴⡭⠤⠖⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⡤⠴⠞⣆⠀⠀⠀⢠⠎⠀⠀⠀⠀⣀⣀⡀⢀⣀⡴⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣯⣄⣀⣤⡤⠞⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠻⣿⣧⡀⠀⠀⠀⠀⢀⣾⡿⢱⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⣿⣷⡀⠀⠀⠀⣾⣿⢃⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣌⢿⣇⠀⠀⢰⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠈⠻⣿⣦⢿⡄⠀⢸⣿⠇⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣮⣭⣛⠻⠿⣿⣷⣦⡀⠀⠙⠿⣧⠀⠘⣿⢸⣿⡏⠀⠀⠀⠀⣠⣴⡿⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣦⣍⡛⢿⣦⡀⠀⠘⣷⡀⡿⣾⠟⠀⠀⠀⣠⣾⡿⢋⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣷⣮⣿⣦⡀⠘⣧⣼⠋⠀⠀⠀⣴⣿⠟⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠓⢾⡏⠀⠀⠀⣼⣿⠏⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣝⡻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⣿⢏⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⡻⢿⣿⣦⡀⠀⠀⠀⢸⡇⠀⢸⣏⣾⡿⠋⠀⠀⠀⢀⣀⣤⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⣿⠀⣬⡿⠋⠀⠀⢀⣠⣶⡿⢛⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣙⢿⡄⠀⠀⢻⡾⠋⠀⠀⠀⣴⣿⡿⢋⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠉⠛⠿⣦⣿⡄⠀⢸⡇⠀⠀⢠⣾⣿⢋⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣙⠿⣿⣦⣄⠀⠀⠀⠀⠉⠛⢦⣸⡇⠀⢀⣿⡟⣡⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⡛⢿⣷⣦⠀⠀⠀⠀⠀⢹⡇⠀⣸⢟⣼⣿⠟⠋⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⢸⡇⢠⣿⡾⠟⠁⣀⣴⣾⢟⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡻⣿⡀⠀⠀⢸⣷⠟⠁⠀⣠⣾⡿⢋⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⢦⣄⡀⠀⠈⠛⠿⣷⣜⢷⡀⠀⢸⡇⠀⢀⣾⣿⠟⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡝⢿⣶⣄⠀⠀⠈⠙⠻⢧⡀⢸⡇⢀⣾⡿⣡⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡹⣿⣷⡄⠀⠀⠀⠀⠙⣿⠁⣸⡟⣴⣿⡿⠋⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡌⢿⣿⡄⠀⠀⠀⠀⣿⢀⣿⣾⠟⠋⢀⣤⣶⣾⠿⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣎⢻⣿⡄⠀⠀⢠⣿⠞⠋⠁⣠⣶⣿⠿⣋⣵⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢻⡇⠀⠀⢸⡏⠀⢀⣼⣿⠟⣡⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⠀⠀⣿⠀⢀⣾⢟⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⢠⡏⢀⣾⣣⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣡⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣄⣀
⢀⣾⣷⣀⢠⣶⠖⡀⠀⠀⠀⠀⠀⣬⣣⣒⣻⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⢀⠰⠞⠁⢀⠀⠀⠀⠀⠀⠀⣿⣭⣧⠼⠿⢟⠃
⢹⢿⡿⣿⣵⣥⡩⠒⠀⠀⠀⠀⢓⣑⣢⣶⠗⠆⠀⠀⠀⠀⠶⠀⣀⠈⡲⢤⡆⠒⡀⠀⡤⠆⠀⠀⢠⣶⣿⡿⣿⣶⣷⣿⣿⣄
⠠⠉⢲⣿⣿⢬⡟⠛⠃⠀⠀⠀⣷⣾⣶⣶⣾⠆⠀⠀⠀⠀⠀⠀⠖⣠⣄⣁⣴⠖⠒⢤⣀⠀⠀⠀⠸⠟⢠⣾⣿⣿⡿⠉⠛⠁
⠀⢂⡾⠜⣿⣷⡽⠲⠢⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿
⠀⠸⠁⢈⡿⠹⡗⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟
⠀⠀⢀⣶⠅⢺⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⣀⣤⣴⣴⣦⣤
⠀⠀⠚⣯⠀⣿⠇⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣸⣾⠟⠘⠁⠀⠀⠀⠀⠀⠀⠀⣦⡀⣦⢀⣴⠟⠀⠀⠀⠀⠀⣠⢿⣿⣿⣷⣽⣖
⠀⠀⠀⢀⣸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⣇⣿⣿⣿⣥⣾⠃⠀⠀⠀⠀⠞⠋⣿⢻⡉⠙
⠀⠀⠀⠀⠱⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣼⣿⣿⡧⢾⣒⠀⠀⠀⠀⠀⠀⠀⣿⡄⠁
⠀⠀⠀⠀⠀⠃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⣽⣿⣿⣱⣆⠈⠁⠀⠀⠀⠀⠠⠶⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣿⠀⠀⡌⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣀⡀⠈⡤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⢧⡌⣠⠈⠉⠉⠻⣦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡴⢶⡀⠠⣀⠀⠘⣷⡀⠀⠀⣤⠀⠀⠀⠰⠀⠰⡿⠁⠀⠀⠀⠀⢀⠀⠤⣤⠶⠶⠦⣤⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣤⡙⢦⣌⠑⠀⠈⢷⡀⠀⠏⠀⠀⠀⠀⠖⠰⠁⠀⠀⠀⢀⡱⠂⠉⠀⠀⠀⠀⢰⡏⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠈⠀⠀⠀⠀⠙⠷⣄⠈⠸⡇⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⣡⠖⠁⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢀⣄⣀⠀⠀⠁⠀⠘⠳⣆⣹⠆⠁⠀⠀⠆⠀⠀⠄⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⣠⡤⠄⠀⠀⢀⠈⠐⠀⠀⠀⠰⠙⢿⡆⠀⠀⠘⢀⡆⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣠⠴⠋⠉⡀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠰⣾⡄⠀⠘⠀⢶⡟⠁⠀⠖⠛⠛⢣⠦⣄⠀⠀⢸⡇⠀⠀⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⠐⠁⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠙⣦⡠⠀⢿⠃⠀⠇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠡⡈⠀⠀⣿⠁⠀⢀⠀⠀⠈⠁⠀⠙⣿
⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠟⠁⡴⣀⡁⡀⠀⡟⠀⠀⠀⠀⡰⠚⢉⣶⣄⠀⠀⡀⢸⡆⢀⡄⠀⠀⠀⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠆⠀⠈⠀⠛⠇⠁⠘⠃⠀⠀⢀⡜⢀⠔⠛⢇⠈⢡⢠⣿⡏⢰⡿⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃
⠀⡴⠂⠀⠀⠀⠀⠈⠃⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣦⠀⠀⠀⠐⣿⠖⢠⡆⠀⠀⠀⠄⢀⠂⠀⠀⠸⡆⠈⠀⢩⠠⠟⠀⠀⠀⠀⠀⠀⠐⢊⠊
⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⡑⣀⠀⠀⠀⡞⠀⠀⢠⠀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⣹⠆⢀⠆⠀⣀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠌⢧⡀⠀⡇⠀⠀⠈⡄⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠠⠀⠀⠀⢀⠀⠠⡇⠀⢰⡿⢠⣏⠐⠉⣀⡴⢁⡐⢂⣀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⣄⠃⠀⠀⣾⡇⠀⠀⡰⠁⠀⠘⠟⠀⠀⢀⡀⠀⠀⡔⢁⣤⣶⣾⠂⣸⠃⠺⠃⣤⠊⠉⢀⠈⠛⢊⡀⠈⠻⠿
⠀⠀⠀⢠⡤⠤⠴⠶⠤⠀⠀⠀⠀⠀⢡⣼⠷⠀⣦⢸⠁⢀⠎⠠⠁⠀⠀⣀⡀⣦⠊⠀⣀⡐⠀⠎⠀⠘⣿⠀⡟⢠⠀⡾⠁⣤⠀⠈⠀⠴⢫⡅⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⡁⠀⠀⢻⣄⠀⣵⣿⠀⠀⡠⠂⠀⠀⠀⠻⡿⠉⠁⠶⣝⠓⠆⣠⠀⠀⣽⠦⠀⠀⣬⠁⠈⣡⡄⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢿⡀⣿⣟⡄⢀⠇⠀⠀⠀⠈⣁⡀⠀⠀⠀⢀⠛⡾⠁⡰⢾⡿⣿⣶⡿⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠘⢣⣿⣿⠁⠘⠀⢈⠄⠀⠀⢻⠁⠀⣀⠖⠁⢠⢁⡼⠃⠘⠀⣿⡿⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⢦⡀⣄⠸⣿⡟⢐⡆⢠⠌⠀⠀⡄⢉⣀⠀⠁⠀⠀⠌⠀⠁⠀⢀⠀⢻⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⣤⡶⠶⠻⣶⣶⣲⡄⠀⠙⢦⠈⢻⠀⢹⡇⡸⠃⠀⠀⣠⠊⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢠⠉⠀⠀⠀⠁⠀⠉⠐⣌⠐⠌⣣⡈⢳⣸⡄⢇⠀⠀⢀⣠⣄⡀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢹⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠡⡀⠙⣧⠘⣿⣧⠘⢀⠺⠛⠁⠈⠋⠐⠇⠠⠂⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣆
⠀⠀⠘⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠙⢆⠘⠇⢹⡏⠀⠀⠀⠀⠀⠀⠀⠲⠾⡇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⣠⣤⡁⠀⠀⠀⠀⠀⠀⠀⢢⡘⢄⠀⠀⠀⠀⠀⠀⢸⡆⠀⡷⠀⠀⠘⠇⠀⢀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠳⠆⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⢰⡇⠀⠞⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢐⠀⣀⠇⠠⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⢾⡄⣿⡆⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⢎⠀⠀⠘⠀⡀⣷⡿⠁⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢠⣆⣠⡟⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⢸⡟⠀⠀⠀⠀⣂⠩⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠘⡎⢡⠶⡤⣠⠞⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⣦⠀⠀⢀⣿⢷⡤⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⡀⠠⠀⠀⢸⠟⣨⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⠗⠀⣠⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⢠⣤⠀⡰⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣂⠀⠀⠀⠘⠗⠂⠀⠘⢋⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⠀⠀⠀⣀⠆⠀⠷⣾⠂⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡸⡃⢠⡤⣤⠉⡶⠂⣰⣦⠚⣋⠉⠉⠉⠛⠳⢶⡶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠶⠟⠃⠈⠉⠀⠉⠙⠛⠉⠁⠈⠙⠙⠻⠿⣦⡠⡼⢶⠶⠾⡟⠛⠁⠉⠁⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⢒⠰⠁⠀⡐⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠦⢠⡦⢁⠀⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠁⠈⠀⠂⠙⠃⠀⡄⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆⢀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠙⡟⠄⠈⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣈⠈⣷⡀⠀⠀⠀⢀⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠀⡀⠀⠃⠀⠀⡖⠀⠀⡀⠀⠀⠀⠀⠀⣀⡤⠀⠈⠀⠐⠀⠀⠟⠱⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⣦⣠⣶⡅⣤⢰⣧⡖⠃⢷⣿⡆⡄⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣧⣈⣆⣿⠻⢿⠙⢧⠙⡿⡈⢛⠆⠨⣭⠶⢿⢈⡥⢙⣶⡦⢦⠀⠀⣈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⣶⣯⣿⠿⠅⠘⠛⠇⠀⢈⣿⢷⣾⣠⣆⣉⠃⠋⡍⣶⡈⢀⡃⡈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣲⣤⠛⣽⣃⠙⣄⠀⠀⠀⠀⡤⢾⠉⡆⠉⠟⠿⡿⣊⡀⠧⠈⠿⢂⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠂⢲⡌⠋⠛⠙⠀⠈⠁⠄⠀⡀⠈⠀⡀⠃⠘⠀⠀⠀⠈⠀⡁⠀⠀⠀⡐⠙⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢲⠀⠈⠳⠄⠀⢠⠀⠀⠀⢤⡔⠛⢿⠁⢹⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠨⢁⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠀⠺⢆⠀⠀⠁⠈⣻⡏⠰⡆⠁⢸⠀⡇⠘⠸⠃⡀⠀⠀⡆⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣆⠀⠀⠑⢄⡑⢆⠀⠀⠀⢸⡀⢳⠀⢸⠀⡇⡆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠹⣄⠑⠀⠘⢦⡇⣼⡀⡼⡄⠁⡄⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⡐⢾⡏⣷⡇⣿⡆⢸⠸⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⡀⢳⣼⡇⣸⣇⣹⣧⣾⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢤⣤⣴⣯⣿⣿⣿⣇⣿⣿⣸⣿⣿⣿⣿⣶⣦⣤⣤⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⠟⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⣭⡽⢿⣿⣿⣿⠓⠂


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

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢶⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⢀⡶⠈⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⢸⣦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠚⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠾⠷⠀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠠⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣞⡷⠟⢿⣶⡀⠀⠀⢈⣇⡀⢠⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡜⡋⠀⠀⠀⠈⢷⣦⠀⠈⠻⠄⣸⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣖⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠃⠀⣀⣶⠖⠀⠙⠀⠀⠂⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠆⠺⠉⠀⠀⠀⠀⠀⠀⠀⠈⢽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⡤⣾⣷⢤⡶⠾⣷⢿⢾⣷⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄⣠⣆⡴⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⡀⠀⠀⡠⠔⠒⠒⠒⠢⢤⡀⠀⠀⠀⢹⠉⢃⠒⠦⣀⠀⠀⠀⠀⢠⡧⣀⡀
⠙⠦⡍⠐⠂⠶⠄⣌⣂⡐⠌⢢⠀⠀⡞⢀⠀⡆⠀⠈⠳⡀⠀⡰⠁⣄⠄⡈⢂
⠀⠀⠈⢦⡀⠀⠀⠄⠐⠙⡛⢮⣇⠀⢣⠀⠀⠹⣆⡠⠀⢧⠀⠃⠐⢧⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠓⠤⠤⠬⠤⠒⠉⠈⠙⠲⢕⣦⣘⠛⢦⡀⠇⠀⠡⣀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⢒⠀⢄⣤⠞⠓⢬⣍⣻⡄⠀⠀⠈⠂⠤⠻⣄⠁
⠀⠀⠀⠀⠀⠀⢀⠜⢀⢀⣈⠖⠒⠋⠉⡸⠀⠀⠀⠀⠈⠉⠓⠒⠦⢄⣀⡀⠈⣧⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠠⢞⠀⠀⠂⢀⡴⠁⠀⠀⡀⠔⠊⠉⠁⣒⢺⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠓⠦⣤
⠀⠀⠀⠀⠀⠀⠈⢄⠐⢀⡠⠤⠔⠉⠀⠀⢀⡎⠀⠀⠀⢒⠴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⡸⠁⠤⠤⠛⠋⢘⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡄⠠⣄⠀⢦⠄⡤⠠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠊⠑⠀⠀⠀⠈⠀⠀⠁⠀⠐⢘⠀⠤⢂⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠶⢦⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⢵⣇⠄⡢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠂⠀⠘⠄⠀⢀⠀⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⣁⢀⢀⠈⠀⠀⠀⠀⢈⣛⡀⠀⠀⠀⣀⢀⣢⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢁⠨⡄⢄⡄⠀⠀⢠⣟⣟⡬⠿⠾⠾⢿⣧⡖⣿⣿⣠⠠⠀⠐
⠀⠀⠀⠀⠀⠃⡘⣴⠄⠈⠀⠀⣈⢾⡍⠹⠀⡀⢀⠀⠀⠛⠂⠀⠉⠿⡀⠀⠈⠀⠀⠀⢀⣀⢻⡼⠃⢀⠀⠀⠘
⠀⠀⠀⠀⠒⠎⢤⢉⠀⠀⠐⠀⠹⡊⢁⠀⠀⠀⢸⣴⣶⣾⣿⢣⢆⠀⠁⠀⠀⠀⠀⣴⣻⣿⡅⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠠⢐⣻⣾⣘⠀⣴⣿⣿⠿⣟⢻⠀⣸⣤⡒⣾⣼⣠⡿⣙⣯⡅⠀⡄⢂⣙⡅⡕⠤
⠀⠀⠀⠀⠠⠄⠸⠂⢀⡙⠛⣆⣿⡿⡟⢩⣿⢿⡇⠈⣶⢻⠘⣷⣇⢀⡇⣫⢛⣫⣾⢿⡿⣟⠶⣬⠶⡓⠠⠂
⠀⠀⠀⠀⠂⣀⠀⠀⠀⣼⣿⣷⣾⢯⡀⠀⢿⡎⢻⡆⢹⣾⠆⣼⣻⣿⣴⡷⠋⠸⣷⠘⢰⠮⠂⠐⠈
⠀⠀⠀⠀⠈⡡⠀⠀⠀⠀⠉⠉⡤⢶⣙⢦⣀⠁⡈⢿⢸⣿⣶⣿⢃⡝⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠋⠂⠀⢀⡘⡿⣶⢘⠋⠀⠉⠳⣬⢻⣧⣿⣹⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⠓⠀⠀⠀⠀⠀⠀⠈⢧⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⡠⠤⠟⠃⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡷⠿⠿⣿⣿⠶⠿⣿⠿⠿⠋⠙⠉⠀⠈⠉⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡀⠀⠀⠀⠀⣠⡾⢛⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⣿⡇⠀⠀⣠⠞⠉⣠⠟⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢸⣿⡇⣠⠞⠁⣠⣾⣿⣿⣿⠿⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢸⣿⡿⠃⢀⣴⠟⠛⠉⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣶⣦⠀⠀⠀⣼⠟⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⣿⠀⢀⣾⠋⠀⣰⠟⣀⣠⣤⣴⣦⡄⠀⠀⣴⠏
⠀⠀⢸⡏⠉⠉⠛⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⣇⣾⠃⠀⣼⣿⣿⠿⠟⠛⠋⠁⠀⢀⣼⠋
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⣦⠈⠙⠳⣦⡀⠀⠀⠀⢸⣇⠀⠀⠀⢿⣿⠃⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⢸⡇⠀⠀⢺⣟⠷⣾⣿⠀⠀⠀⣈⠻⣦⡀⠀⠀⢻⡄⠀⠀⣼⠇⠀⣼⠏⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠸⡇⠀⠀⠀⠙⢷⣌⠻⣦⡀⢸⣿⡄⠘⣷⡀⠀⠀⠻⣦⣰⡟⠀⣰⠏⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⣿⡀⢀⣤⣤⣤⣽⣷⣌⠻⣾⣿⡇⠀⠸⣧⠀⠀⠀⠈⣿⠁⢠⣟⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠘⣧⠈⠙⠛⠛⠛⠛⠻⣦⡙⢿⡀⠀⠀⣿⠀⠀⠀⢸⡇⢀⡿⠉⠉⠁
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⢻⣌⢷⡄⢰⡟⠀⠀⠀⣿⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⡀⠀⠀⣹⣦⢻⣟⠀⠀⠀⢸⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠙⢷⡻⣆⠀⠀⣾⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⣆⢀⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣷⣿⣾⣧⣼⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⣷⣄
⠀⠀⢀⣴⣿⣿⣿⣿⠿⣟⠻⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⢋⣾⢟⣼⣿⣿⣿⣿⣧⡀
⠀⢀⣾⣿⣿⣿⣿⣿⣷⣌⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠾⠛⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠟⠛⠉⠉⠀⠀⣤⣤⣤⣬⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠐⡿⠛⢻⣧⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣀⣀⣀⡀⠀⠀⢸⡇⠀⢸⡿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⢀⣠⡾⠁⠀⠀⢸⡟⠛⢻⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟⠛⢻⡇⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠐⠶⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⣤⡤⢤⣤⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⠶⣿⠀⠀⠀⢸⠇⠀⣸⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡀⢀⣿⠀⠀⠀⠀⣧⣀⣠⣧⠀⠀⠀⢸⣧⣀⣸⡇⠀⠀⢸⣇⣀⣀⡇⠀⠀⠀⠀⣿⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠛⠛⠛⣿⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠱⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⢸⠉⢢⠎⢇⠀⠀⠀⠀⠀⢀⠜⡇⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠈⣧⡀⠠⢣⡀⠀⠀⠀⢀⡟⠘⢋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢳⡀⢸⠉⠃⠀⡇⠀⠀⠀⡇⠰⠊⡏⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣤⢄⠀⠀⠀⠀⡇⠈⢇⠈⣆⠀⣰⡃⠀⠀⢠⠷⣀⢾⡠⢴⠃⢈⡽⠀⠀⠀⠀⣠⠒⣆
⠀⠀⠀⠀⣀⠀⠀⠀⢸⠃⠲⠀⢳⢄⠀⠀⢹⠀⠘⣆⡇⠱⠇⢳⠀⠀⡏⠀⣁⡼⠁⠒⡞⠋⠀⠀⠀⢀⣴⠃⠈⡸
⠀⠀⠀⠀⢏⢢⡀⠀⠈⠣⡀⠀⠇⠈⡆⠀⠘⡀⠀⠘⣧⡀⠀⣼⠁⠀⣹⢰⠁⢸⠐⡏⠀⠀⣀⣴⢰⠏⠸⠖⡎
⠀⠀⠀⠀⠈⢦⠱⣄⠀⠀⢸⠉⠛⠀⡏⠙⡄⡇⠀⠀⢸⡉⢶⠀⡇⠀⢧⡼⣂⣠⡞⠀⢀⡔⡵⢣⠼⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠳⡈⠢⡀⠈⠱⣄⣀⠃⠀⢃⢸⠀⠀⠀⡷⡀⠀⢇⠀⢸⠀⠉⣸⠃⣠⢊⡞⣠⡇⠈⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡀⠳⣄⠙⠀⡏⠙⡆⠀⠀⢇⠘⠃⣸⢀⠎⢆⠔⣧⡾⠁⡞⡼⠩⠗⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡈⡟⠂⠧⠀⡧⡄⠀⢸⠑⠔⠉⣿⠀⠈⣰⠟⠀⡼⠚⣃⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢾⣦⠄⣰⡇⢳⡀⠸⡀⠀⢰⠟⢧⠜⡽⢠⠶⠁⠈⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠢⣄⠀⠙⢦⠙⣦⡀⠁⠘⢸⠀⠑⣤⣺⡀⢀⡴⡁⡇⠈⡺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠫⣄⣤⠬⢏⠙⣦⠵⣼⣄⡙⠃⢸⡆⠀⣿⡄⠘⠊⣰⢃⠗⠊⠀⣀⡠⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢤⡤⠚⠂⠘⡷⡝⣏⠳⣹⠀⣧⠈⢲⠒⢡⠏⣠⢔⡫⠕⠚⠉⠉⠓⠒⠤⣑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢔⣒⣛⣮⣮⣦⠹⣧⢹⠀⡇⢀⡾⣫⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠁⢀⣈⣉⠉⠻⣧⠹⣿⢸⢇⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣠⠤⠒⠋⠉⠁⠀⠀⠉⠙⠚⢧⣿⣾⣿⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⢏⡴⠋⠀⠀⠀⠀⠀⠀⠀⢰⠉⠈⠉⠒⣿⣿⣷⠚⠁⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⣚⠟⢹⣿⣟⢯⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⢀⢞⣿⡟⢆⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⢀⠀⠀⠀⢲⣤⡄⠀⠀⢀⠀⠀⡸⣆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⣿⣶⠘⣧⣿⡟⠀⠀⠈⠿⣿⣄⢐⣾⡷⢳⣽⡍⠀⠀⠀⠀⠀⢻⣖⠀⠀⣤⣶⠧⠀⠀⠀⢀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⡤⣤⣠⡿⣌⢡⡄⢶⣷⣤⢨⣉⡱⣎⣠⡔⠊⠀⠀⠀⠀⠻⣤⣀⠘⣿⡦⠴⠛⣧⣴⠀⠀⠙⣾⣇⠈⣯⣵⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣴⡓⢿⡀⠘⡯⣞⠛⢿⠃⠠⣍⣡⣔⠛⣵⠋⠸⣿⡍⠀⠀⣰⡦⡿⠶⣏⢠⡟⢀⠀⠀⠸⠻⠄⢠⣄⡄⢉⣌⣰⡞⠟⠃⢰⣠⣆⡤
⠀⠀⠀⠀⠀⠀⡼⠟⠋⠀⢉⣭⡿⡿⢟⢧⣈⣯⣟⣯⠃⠀⠙⢻⡄⢀⠙⠠⣄⣤⠀⣀⣼⣄⡎⣻⠹⡿⠶⠂⠀⢀⡰⠀⠽⠻⡟⢣⠶⣀⢀⣤⣊⠃⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢠⣄⣰⠀⠀⠀⠀⠀⡿⡿⠙⣷⢼⡟⠀⠀⠀⠀⢻⣜⣿⣤⡽⢿⠆⡁⢀⠈⠁⢿⡘⣶⡂⣀⡴⣮⡛⢃⣀⣺⣡⡴⠞⣉⠁⠀⠨⠗⠢⣴⣧⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣽⠿⡃⢦⣾⣧⠄⠀⢀⠙⣲⣆⢺⣴⣧⢀⡄⠹⣿⢿⣟⢪⡴⣷⠿⣄⠀⡀⢹⡝⠁⣼⣟⣋⡉⢚⡿⠋⠀⢙⡘⠿⢾⡀⠀⢸⣷⠃⠉⠟⠷
⠀⠀⠀⠀⠀⠀⡼⠟⠋⢉⣿⢶⣿⡁⠀⠒⠻⠟⡿⠛⢿⡁⠀⢠⣿⣶⣿⠉⣽⢦⡶⣤⣤⠀⠀⠽⣾⢀⣔⠉⣀⠿⢳⢎⣴⠃⠀⢿⡿⠁⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠻⠃⠈⠙⣦⡷⣏⠀⢠⠄⠈⣷⠀⠀⠀⠀⠹⣦⡆⠈⠞⢳⢾⡇⠀⢀⡟⠋⠈⠽⣋⣠⢸⠋⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣾⢷⣄⣀⣬⣷⡀⣹⣿⣶⠀⢿⡄⠀⠀⡽⡏⢻⡇⢀⠴⢶⡍⢉⡝⢺⡇⠀⢠⣴⣍⣇⢸⠀⠀⠀⠀⢀⢠⣤⠄
⠀⣀⣶⣼⣦⢤⣤⣄⡤⢿⣿⡿⠟⠋⠀⠈⠻⢶⡶⠿⠶⢾⣷⣦⣤⣅⣄⣼⡇⣸⠻⠎⢀⣻⡛⠀⣷⢢⣴⠚⠟⠙⣿⠀⠀⣳⢆⢸⠟⠁⢀⣦⡞⠀⢠⡀⣴⣀⡀
⠘⠉⠋⣸⠗⠋⢀⣹⠳⠈⠸⠆⠀⠀⠀⠀⢻⡻⠀⢀⢀⣤⣤⡋⠉⠉⠉⠛⢿⣷⡄⢤⡬⠉⣥⣠⣟⠁⠉⣉⣢⠀⡏⠰⣾⣈⣋⡇⠀⣀⣼⢷⠶⢖⣉⡛⠉⠈⠁
⢀⣀⡞⣋⣓⠀⠈⠏⠃⠰⣆⣀⡀⢲⡤⣶⣫⡝⢳⣿⠀⡴⣿⠏⠀⠀⣄⣲⠺⣉⣿⣎⣹⠏⣙⠈⣧⢼⡔⣊⢉⡾⢡⣸⡏⣙⣫⣷⡋⠀⠛⠻⠦⠈⢿⡦⠄
⣘⣽⠻⠁⣯⠀⠀⠀⢀⣏⣹⣻⣥⣿⠾⠧⣿⣛⣹⣏⣀⡀⠘⠂⠀⠀⠚⣫⡾⢹⠇⢻⣇⠰⣿⢷⡇⣰⣽⡛⢻⣇⣹⡿⠛⣉⣡⣸⣷⢀⣠⣦⣶⡀⠀⠛
⠉⡎⠃⠀⠀⠀⠀⠀⢶⣾⣣⡝⠁⣞⡆⠀⠀⣉⢹⡭⠛⠛⠻⠶⢦⣴⣿⣤⠈⣏⣻⣾⢻⣧⢀⣾⣥⡿⢟⡏⢹⡟⠻⢞⣰⡜⢻⣽⠖⢺⣿⢩⢧⣇⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠘⠁⠾⡿⠀⠙⠇⠀⠈⡽⠟⠃⠀⠀⢠⣠⡄⠈⢛⣿⣶⠋⠓⠀⠀⢻⣿⠋⣷⡤⠘⣿⣿⠘⢶⣸⣻⣶⠻⡄⢐⣤⠖⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣝⢫⣽⣍⠛⣦⡀⠀⠀⢰⣿⣆⠘⠿⠀⢠⡿⠤⠚⣹⡦⠈⢿⡉⠉⢩⢾⠃⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣯⠐⢻⡏⠀⠈⠻⣦⣀⡿⠀⣿⣄⣀⣀⣿⣁⣰⡧⠄⢹⢢⣼⣧⣗⢀⣼⣤⠤⠴⣚⣟⠻⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⣉⣿⣿⣽⣫⡴⠶⠂⡉⢸⣯⢀⡟⠀⠀⡀⠀⠋⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⣰⠄⠻⣷⣄⣼⣿⣿⡇⢡⡈⢯⣥⡄⠙⠛⠛⢻⣾⠖⣰⡮⠷⠍⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣼⣿⣱⣦⣿⣿⣿⣿⣿⡇⠺⣟⡄⡿⠀⠲⣿⠋⣸⣿⣉⠀⣻⣆⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣤⣸⣿⡎⢸⣿⣿⣿⡇⠈⠉⢙⠇⠀⢸⣠⡾⣅⠀⠞⣗⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣹⣾⣿⣿⣿⣿⣶⣶⣾⠶⣤⣾⠻⣟⠟⠃⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡝⠀⢹⣿⣿⣿⣿⡏⢠⢷⡂⠸⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⣿⣿⡇⠀⢫⡟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢄⣰⣿⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⡆⠀⠀⣠⠤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⠞⠁⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⣄⠀⠀⠀⠀⠀⠰⣶⠦⡘⢆⣠⠃⣼⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄⢀⡤⠒⠛⡇⠈⠒⠼⠾⣯⠞⣁⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⣠⠃⡟⠀⠀⢀⡇⠀⠀⣠⠞⠳⢏⡁⠀⠀⠀⠀⠈⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⣀⠙⣄⣇⠀⣠⠞⠀⡠⠚⠁⢀⣀⣀⣉⡒⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⣦⠸⡟⠉⠀⣠⣾⣖⠒⠺⣏⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣈⠉⠉⠳⣇⣠⠞⠁⡏⠀⠈⢳⠈⠑⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⢰⠋⢣⠀⢀⡟⠁⠀⠀⢣⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⡄⠀⠀⠀⠘⢆⣸⢠⣯⠖⠋⠉⣹⠂⠈⠑⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣼⠀⣠⠞⡇⠀⢻⡿⢇⣀⠠⠔⢁⡤⠤⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠦⣌⠑⢾⢸⡇⠀⢰⢀⡏⠀⠀⡞⢦⢠⠏⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⠀⢈⡹⠮⣿⣇⠀⡘⢸⠀⢀⣤⠳⣼⡾⠤⠤⣔⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠒⢾⣿⡶⠃⣿⠀⡏⠈⢧⠈⢇⣠⠋⠁⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠻⠾⣿⣧⡀⢿⠀⡇⠀⢸⣸⠏⠙⠢⠤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢨⠏⠉⢻⠀⠸⡄⣼⡟⢀⠔⠊⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠔⢚⣁⣀⡀⠈⣇⠀⠘⣿⡵⠃⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⣳⠼⣦⠞⠉⠓⠢⠤⠄⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠶⠒⠊⣡⣦⠈⢦⡀⠀⠀⣰⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠈⢆⠀⠑⢄⠀⣇⠀⢘⢀⡤⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠲⢤⡳⣀⣸⢀⣖⣚⡷⢮⡲⣼⣏⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢄⣀⣀⣀⡠⠟⠪⣿⠼⠗⠛⠒⠒⠛⠛⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣤⠴⢚⣧⡀⠀⠀⡠⠚⠛⠓⠒⡶⠋⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠃⠀⡞⠀⠙⣆⠀⡇⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠧⡀⠀⡼⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⡇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⠃⠀⠰
⠀⠀⠀⠀⠀⢠⠀⣠⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢺⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡴⠊⠁
⠀⠀⠀⠀⣰⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣤⡿⠏
⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠨⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⢡⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠰⣀⣿⠿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣯⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⢷⣦⣄⡁
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣧
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⣶⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠛⢿⣿⣿⣦⣤⣾⣿⣿⠟⠋⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⣿⡿⠟⠁⠀⢰⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⢠⡄⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⡀⣀⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⣠⣶⠋⠀⠀⢀⣴⡤⣤⠘⠿⢿⡧⢘⣟⡃⠀⣀⠀⠀⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠈⣛⣃⣈⢁⠀⠀⠀⢘⣻⣿⣾⠟⠀⠀⠛⠴
⠀⠀⠀⠀⠀⠀⠀⠾⠀⢈⠉⠉⠙⠃⢴⣶⣦⠀⠀⠿⣿⡿⢸⣿⣷⠀⠉⠉⠉⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣾⢻⣿⠀⠀⠀⠀⠀⢸⡏⣿⡀⠀⠀⠀⠀⠀⠀⢹⡿⣿
⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⢠⡏⠘⡟⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⣾⠁⢿⡀
⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠙⠀⠈⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢀⡀⠀⣀⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢠⣄⠀⠀⣿⣷⠾⠋⠁⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠻⣆⣸⣿⠃⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⣿⣇⣠⡶⠀⠀⢸⣿⠁
⣤⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣧⡀⢀⣿⣿⠟⠁⠀⠀⢀⣿⡏
⢿⣯⠉⠉⠉⠛⠛⠿⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠘⣷⣼⣿⣿⠀⠀⠀⢠⣿⡟
⠸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⢿⣷⠀⠀⠈⣿⣿⡏⠀⠀⣠⣿⠟
⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠙⢿⣷⣄⠀⠀⠈⢿⣧⡀⢰⣿⣿⡇⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⣀⢸⣧⠀⠀⠉⢿⣷⡄⠀⠀⠙⢿⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⢿
⠀⠀⠘⢿⣆⠀⠀⠀⠀⠈⠻⣿⣿⡀⠀⠀⠀⠙⢿⣦⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠁⠀⠀⢸
⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢰⡌⢻⣷⡀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠈⢻⣷⡄⠀⢀⣀⣤⣤⣤⣿⣿⣦⡈⣿⠀⢻⣷⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠉⠁⠀⠀⠀⠈⠻⣿⣿⡄⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣿⣿⣿⡏⠀⠀⠀⣴⡿⠟⠀⢾⡄⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⡀⠀⠀⠀⠈⠻⣷⣿⣿⣿⡇⠀⢠⣾⠟⠁⠀⠀⢸⣧⢀⣤⣾⠟⠛⠻⠛⠛⠓⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣦⣤⣴⣿⣿⣿⣿⡇⢰⣿⠋⠀⠀⠀⠀⢀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⣠⣾⣿⣿⡶⠶⠶⠶⠶⠖⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣦⣤⣶⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⢀⣾⡿⠛⠉⠉⠉⠉⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⢿⣶⣦⣄
⠀⢸⣿⠀⠠⣄⠀⢰⣄⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⢸⣿⠀⠀⠘⢷⡄⠙⣧⡀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠈⢿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣀⣤⣤⣴⣿⠟
⠀⠀⠀⠉⠙⠛⠛⠛⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⣶⠀⣠⡶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢰⠟⠁⡾⠋⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⠀⠐⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠁⠀⠀⠀⠀⠙⡷
⠀⠀⠀⠀⠀⠀⠰⣈⡾⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠈⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡤⣻⣔⣇⣔⢢⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣦⡴⠞⠃⠀⠀⠀⠀⠀⠀⠘⣺⡁
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠵⣪⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠽⠝⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢰⢧⠨⠷⠜⠁⠀⠀⠀⠀⢀⠠⠤⠰⠤⠤⣄⠀⠀⠀⠀⠹⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠄⣨⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⣄⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠶⠤⣴⡶⠾⣿⡇
⠀⠀⠀⠀⠀⠻⠥⣞⣲⡴⢼⣽⣟⡙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⣽⡇
⠀⠀⠀⠀⠀⠀⠐⠟⢻⣛⣷⣶⠶⣭⡧⢷⠮⡥⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣀⣀⣠⣤⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠯⣿⣿⠿⠿⠛⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠀⢀⠜⣽⠋⠁⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠜⠁⠠⠒⠉⠉⠁⠒⠤⠀⢀⣀⣤⡶⠏⠀⠀⠀⠒⡲⠖⠐⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢀⢀⡴⠅⠀⠀⠠⢤⣤⣶⣶⢿⢿⠭⠭⠓⠒⣚⠡⠄⠊⠁⠀⠀⠁⠀⠄⠀⠀⠀⢠⣤⣦⡾
⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠀⠀⢀⠔⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢝⣿⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⡴⠒⢒⣲⡖⠉⢉⣈⠉⠉⠋⠀⠀⡄⠐⠀⠆⠀⠀⡍
⠀⠀⠀⠀⠀⡸⣋⠄⠀⠀⠁⠀⠀⠀⠀⠀⠁⢐⠀⠀⠠⢀⡂⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠀⠀⠀⠘⠀⠀⢀⠄⡉⢆⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠁⠔⠁⠠⠁⠀⢀⡀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢾⣦⡀⣀⡜⠊⠅⢰⠂⠰⠀⠀⠀⠀⠚⠋⠁⠀⡀⠠⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣦⣿⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⢀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⢂⡀⢬⣿⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡞⠀⠀⢠⢃⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡁⢠⠊⠁⠀⠀⢈⠡⠴⢒⠂⠒⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡾⠉⡿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⢛⣶⣧⡀⠂⢀⠀⢀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠓⣄⢸⣶⢸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢉⡿⠿⡇⠄⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠞⠀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡞⠄⠀⢀⣶⠲⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⢈⢃⠐⠛⡹⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠚⠤⣤⠀⠘⡃⠊⠁⢀⠀⢰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠀⠀⢨⠁⠀⠘⠀⠀⠳⣧⡐⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣼⠆⡄⠲⠆⠺⠛⣿⠃⠰⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⣴⡄⠀⠀⠀⠄⠈⠀⠐⣠⠀⣴⠎⠃⠠⠈⠛⠁⢤⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡖⠨⢧⠆⠀⡘⡖⠁⠀⠒⠋⠸⢏⣐⢺⡄⠀⠀⠁⠀⠀⠄⢫⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡆⠀⠋⠑⠀⠈⢀⢀⠒⢀⠀⠀⠀⣀⠀⠋⠈⠛⠑⠀⠀⠐⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠁⠢⢧⣀⠀⣀⣘⣾⡀⠀⠀⡐⠀⢁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡟⠏⠉⣀⣄⠱⣦⡏⠀⣨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠛⣄⣿⠇⠠⢈⠓⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠂⣤⠀⠈⢳⡀⠀⠁⠀⠂⣀⢸⠆⠀⠀⡀⠳⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠋⠀⠐⠋⣥⠤⠀⠀⢈⠈⠛⠢⠴⠰⣿⠱⢎⡠⣟⡃⠠⣶⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡙⡗⠒⢄⠀⠀⠀⠀⡀⠀⠀⢘⡠⠄⠈⠹⠁⠀⠀⠠⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡆⡀⣈⠀⠀⠁⠀⠀⠜⠲⡀⢸⠇⠀⡿⣶⣷⡰⠶⠀⠀⠀⠀⠘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢈⣄⠠⠵⣼⠀⠘⢠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠊⠀⠀⠲⠻⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠛⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠛⠟⠛⠛⠛⠒⠂⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠙⡏⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣷⡆⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⢸⠇⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⣿⢡⡟⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⣾⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡏⣸⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⢸⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋⠀⡿⢸⠇⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡌⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠸⡾⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣴⣿⣿⡛⠁⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡄⠀⠀⢀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⢸⣧⠴⠚⠉⢿⣿⣦⣍⠉⠛⠿⣿⡿⠿⠛⠉⠀⢀⠀⠀⠀⠀⢀⠀⠠⠍⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣿⡇⠀⢠⠎⠻⣿⣷⣦⠀⠙⠻⠿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠚⢆⠀⠀⠀⠁⢀
⠀⠀⠀⣀⠀⠈⠻⢦⠇⠀⠀⠈⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠹⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠹⣿⣦⠀⢸⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠥
⠀⠀⠀⠀⠙⠛⠷⠾⣾⠉⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢒⡂⠀⠀⠀⠔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⣼⡿⠏⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠠⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⣀⢂⢻⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠖⠉⢈⡇⠀⠀⠀⠀⠀⠐⠀⢍⢻⡋⠕⠩⠀⠀⠀⠀⠀⠘⣷⣄⢸⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⡀⠀⡟⠀⣠⠞⠀⠀⠀⠀⠀⠀⡀⠈⡀⢻⠃⠁⠒⠀⠀⠀⠀⠀⠀⠈⢻⡜⡇⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇⢠⣥⠞⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡈⢺⠓⡢⠑⡆⠀⠀⠀⠀⢠⣄⠀⠙⣷⠎
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢧⢠⣇⠞⣡⠤⠤⠶⣶⠀⠀⠀⠀⠠⠒⠂⠈⢺⠃⢀⠨⠠⠀⠀⠀⠀⠀⠻⣇⠀⢹⠀⢠⣾⠃
⠀⠀⠀⠀⠀⢸⠙⢦⡀⠈⣿⣷⣎⣁⣀⡤⠞⠁⠀⠀⠀⠀⠠⠠⠀⠘⢺⠓⠂⠀⠤⡄⠀⠀⠀⠀⠀⠈⢦⣸⠀⡾⠃
⠀⠀⠀⠀⠀⢸⡀⠀⢳⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠀⠂⢻⠋⠐⠀⠀⡁⠀⠀⠀⠀⣦⡀⠀⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠳⣄⣾⡥⠖⠉⠉⢉⡿⠂⠀⠀⠀⠀⠀⠀⠅⠦⠀⠈⢻⠃⠁⠀⠀⠁⠀⠀⠀⠀⠙⢷⡀⢸⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠁⢾⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢳⣜⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢺⠖⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣮⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠉⠘⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣷⠀⠘⡄⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⣀⠤⠁⠄⣀⠀⠐⠂⢳⣼⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⢸⣿⠆⣤⠀⡀⣀⡀⢠⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠈⠱⠀⠀⠀⠁⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⡏⠀⠀⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠡⠋⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣶⣶⣄
⠀⠀⠀⠀⠀⣠⣤⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣟⣽⣿⣿⣿⣿⣿⣿⣿⣏⣂⣀
⠀⠀⠀⠄⠾⠹⠿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠧⢛⣓⣉⣀⠁⠓⠂⠀⠀⠀⠀⠀⠀⠚⠃⣡⣈⣘⡟⢹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠙⠋⠙⠋⠛⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣄⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠈⠐⠢⠀⠀⠀⠂⠀⠀⣴⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⡀⢰⠞⣀⡬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⡆⠘⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡔⣿⣤⣤⠟⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡰⢄⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣟⣶⠂⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠢⠀⠀⠂⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢄⡜⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢺⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣦⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠤⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡱⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣻⣿⣿⣿⣿⣿⢿⣿⣿⣒⢀⡀
⠀⠀⠀⠀⣠⡾⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⠻⠊⠓⢤⣄⡀⠀⠀⠀⠀⠒⠒⢉⣉⣃⣿⡟⣿⣿⣿⣿⣿⣿⣿⣟⢷⣾⡷⣶⣄
⠀⠀⠀⠀⠉⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠈⠛⠲⠍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠁⠀⠁⠉⠛⠛⠛⠻⠛⠛⠓⠛⠛⠓⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡂⠀⠀⠀⠂⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠢⣀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢃⡰⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠀⠈⠓⢤⡀⢀⠊⠀⠀⠀⢀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡾⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣺⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⡿⡿⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣟⢛⡓⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠁⠀⠀⠈⠉⠁

⠀⠀⠀⢀⣤⣤⣀⣶⣿⣶⡄⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣶⣤
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣿⣿⠇
⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣙⠟⢋⣠⠄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠈⠳⠋⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠙⠛⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢸⣷⣶⠆⠀⠀⠀⢀⡀⢠⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠛⠀⠁⠸⠇⠀⠀⠈⠉⠀⣿⡛⠛⠛⠁
⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⡟⠀⢀⡀⠀⠀⣠⣾⡄⠀⠀⠀⠀⢀⣀⡀⣠⣴⣤⠀⠀⠑⢶⠴⠊⠀⠀⠀⠀⠰⣼⣿⣧⡄
⠀⠀⠀⠀⠈⠛⢻⣏⠉⠁⠀⠀⠀⢿⣿⠂⠈⢉⣡⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠰⣤⡀⠰⠛⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣷⣤⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣶⣸⣿⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⡿⡿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⠙⠛⠿⠛⠓⠀⠀⣤⣶⣄⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠈⠛⠿⠟⠃⠀⠻⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣤⣼⣿⠿⣻⣦⣤⠀⠀⠀⠀⠀⣆⢀⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣠⣰⣾⣧⣿⣇⣄⠀⠀⢀⣦
⠀⠀⢠⣼⣷⢿⣿⣿⣷⣿⢿⣷⠀⠀⣈⠛⠛⢨⣦⠀⠀⠈⠻⠿⠿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠙⠋⠉⠙⠋⠀⠀⠀⣾⣿⣆
⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣝⣿⠀⠀⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣠⣶⣶⣷⣶⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠈⠳⢾⣿⡇⠈⣻⣿⣝⡇⠀⠀⠀⢀⣴⡶⢤⡀⠀⠀⠀⠲⣼⣿⣿⠖⠀⠀⣠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠾⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠉⠁⠘⠋⠉⠀⠀⠀⡠⢶⢿⣿⣿⣯⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠿⠻⠟⢻⡟⠿⠻⠄⠀⠀⢼⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⣀⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⡇⠰⣿⡆⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣀⠀⠀⠀⠀⣾⠀⡄⠻⠟⠀⠀⢈⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⢠⣭⡀⢠⣤⣤⡀⠀⠀⢼⣿⣿⡷⠀⠀⠀⢿⣽⣿⣿⣿⣿⣿⡿⠃⠀⠘⠶⠥⠞⢛⡤⠀⠀⠀⠛⠛⠛⢿⣿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣸⣹⠇⠀⠀⠀⠀⠀⢀⣴⡧⠁⠸⣿⣎⠈⣿⡟⣧⠘⣷⡿⣶⣞⠀⠁⡚⣸⢻⣿⣿⣿⣿⡟
⠀⠀⠀⢀⠀⣠⣤⣤⠹⣿⣼⣿⣦⣰⣾⣶⣿⠂⠀⠀⠀⢻⣿⣷⠘⠏⣿⡎⣿⡇⠈⠛⢅⣿⡇⡿⣿⢿⣿⣿⡿⢦⢀⡀⠀⡀⣨
⠀⢀⣠⣾⢼⣿⣿⣿⠑⠜⢿⣿⣻⡙⢻⣿⠎⠂⠀⠀⠀⢸⠘⣿⣧⣤⢻⡷⣿⠂⠀⠀⢠⣿⢫⢷⣿⣿⣿⣿⠁⠀⢻⣷⡿⣫⠟
⣀⢀⢙⣽⣼⣿⣿⣿⡧⢀⣜⣿⡯⢿⣧⡈⠲⣤⣿⣆⠀⠘⣇⠘⢿⣿⢸⣟⣿⠀⠀⢀⠟⣿⣾⣺⡏⣿⣿⡏⠀⢼⠟⢉⠿⣷⣀
⢻⠟⣛⣩⣿⡿⣿⣿⢿⠀⢿⡾⣿⣌⣿⣷⣄⠈⠛⢿⣆⠀⢻⣤⡈⣿⣿⡇⣿⡇⠀⡼⠀⣿⣿⡟⣸⣿⠟⣒⢷⣇⡲⠁⠀⠀⠑
⣴⢺⠟⠉⠀⣿⢿⣸⡌⠃⠀⠀⠈⠙⣏⣿⣿⣷⡄⠀⠉⢳⡈⣿⣧⡈⣿⡇⣿⡇⣰⠃⢰⣿⡿⣱⣿⣿⣿⣾⣽⣿⣯⣐⣠⣀
⠈⠪⠀⢀⠀⣿⡘⣯⢧⠁⠋⣀⠠⡑⡜⣞⣿⣿⣿⡀⠀⠀⠁⠘⣿⣷⣿⣇⣿⣇⡟⠀⣸⡿⢀⣿⢷⣿⣿⣿⢋⣰⠄⣀⠉⠻⣆
⠀⠀⠀⡜⠀⢸⣷⣿⡏⣧⢰⠸⡌⢧⢱⠘⣼⣿⣿⡇⡄⠀⠀⠀⠘⢿⣿⡿⠹⣿⡇⠀⣽⢣⣿⡟⣹⣿⣿⢏⣾⢇⣾⣿⠀⠀⡼
⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⢘⡀⢫⠉⡌⢧⢹⣞⣿⣧⣿⡒⢠⣶⣶⣤⣿⣿⣿⢿⠇⠀⡟⡼⢏⡸⣿⣿⣏⣼⣏⠌⣿⣿⡀⡰⠁
⠀⠀⠀⠀⠀⠐⠋⣵⣿⣿⣇⢹⡈⡧⠼⡽⣆⢽⡞⣿⣿⣿⣿⡛⠯⠟⢛⣛⡛⠛⠃⠀⢬⣣⣼⣿⣿⣿⣿⡟⡜⠀⡿⠫⢠⠇
⠀⠀⢀⣴⠅⠀⡼⡿⣿⣿⣿⡂⠳⢘⡥⢪⠹⣊⣿⢻⣿⣻⣿⣧⠀⠀⠀⠨⣻⣿⠙⣳⡶⢿⣿⠿⢿⣿⢋⠎⠀⠀⣠⠀⡘
⠀⢰⣯⣿⢀⡾⠀⢻⡍⠟⣿⣷⡈⠄⢻⠄⠣⢰⡸⡿⣿⣟⢿⣿⡆⠀⠀⢈⣿⣿⡀⢺⡏⣾⣿⣷⣷⣵⡁⠀⣠⣾⢯⠀⡇
⠀⢸⣿⡏⣗⡇⠀⠈⣟⡜⠸⣿⣷⢩⠄⣧⠘⡭⢆⢿⢻⣿⣸⣿⣿⡀⠀⠀⣾⣿⡐⡸⣡⣿⣿⡿⠃⠈⢓⣻⣿⣿⣧⢻⠁
⠀⢸⣿⣷⣿⡇⠀⠀⠸⣷⠐⢹⣿⡎⠥⠘⡥⢻⠵⣊⢿⣿⣿⣿⣿⡇⠀⠀⢾⣿⣷⣃⣿⢿⠟⠁⠀⢠⣿⣿⣿⣏⢾⣿⠃
⠀⠐⣿⣿⣿⡇⠀⠀⠀⢹⣷⡀⢿⣷⠩⡏⢷⠈⢧⠵⡊⢿⣿⣿⣿⣿⠀⠀⡬⡿⢛⣫⠔⠁⠀⠀⢀⣾⣿⣿⣿⣟⣾⡏
⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⢻⣧⠸⣿⣇⠽⠄⢏⠉⡧⢒⡨⣿⣿⣿⣿⡇⠀⠈⣱⣿⠇⠀⠀⠀⠀⠜⡟⣱⡿⠭⡎⣼⣧⣴⠃
⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠈⢿⣵⡽⣿⣆⢯⠽⡇⢹⡄⢗⠹⣿⣿⣿⣷⠀⢀⣿⣿⠀⠀⠀⢀⠆⠀⢠⡏⠀⠀⣰⣿⣿⣿⣶⠞
⠀⠀⠀⣿⣿⢹⠀⠀⠀⠀⠀⠀⢻⣾⡝⣷⡌⢧⠸⡀⢧⡘⡏⣫⣿⣿⣿⣇⣰⣿⡇⠀⠀⠀⠂⠀⢔⠎⠀⠀⣴⡟⠁⢈⠞⠁
⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡭⢧⢻⠈⣇⠹⡺⣿⣿⣿⣿⣼⣿⡇⠀⠀⣰⣴⣿⣿⡣⢀⣼⣿⢇⡴⠃
⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣽⣂⢣⣸⡎⢣⣿⣿⣿⣿⣿⣿⠇⠀⣬⣿⣿⣿⣷⣷⣿⣿⣿⡿⠁
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣿⣮⡇⢽⣸⢽⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣝⣧⢻⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⠋⡴⠁
⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠙⢹⠁⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛
⠀⠀⠀⠀⠀⠀⢀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠴⣦⢴⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠂⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠋⠄⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠂⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠋⠉⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⣠⣶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣛⣟⣛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠉⠛⠋⠙⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⣿⡶⠿⠿⠿⠿⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢼⡇⠀⢸⣿⠀⣶⠀⠀⠀⠀⢠⣶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⢸⣿⢀⣿⠀⠀⠀⠀⢀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠋⠀⠀⠀⠀⣿⡟⠛⠿⠛⠻⢿⡟⠀⠀⣿⡆⠀⠀⠀⠀⢹⡇⠀⠀⠻⠿⣿⠀⠀⠀⠀⠘⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⡁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠰⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⠀⠀⣿⡇⠀⠀⠀⠀⢸⣧⠀⠀⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⢸⣏⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣤⣤⣼⣧⣤⣤⣤⣤⣼⣿⣤⣤⣿⣧⣤⣤⣤⣤⣼⣿⣤⣤⣿⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣿⣤⣴⣿⣤⣴⣿⣤⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢿⣆⠀⢸⣆⠘⠋⣀⠀⠀⠀⣷⡆⢀⠀⢠⣄⠀⠰⠀⠀⠀⢀⠘⠇⠀⠀⠀⢠⣄⠁⣀⠀⠀⠠⣤⣁⣼⠂⠀⠀⢀⠛⢀⠂
⠀⠀⠈⠻⠆⠈⡛⠀⠾⠋⠀⠀⠀⠈⠁⡿⠁⠀⠁⠲⠀⠀⠀⢀⡘⢧⡶⠂⠀⠀⠀⣉⠾⠋⠀⠀⠀⣬⡙⠁⣀⠀⠀⠈⣈⠺⠈
⠀⠀⢶⣦⡀⣰⠆⢀⣴⡶⠀⠀⠀⠀⠃⠀⠀⠀⠰⡀⢀⡀⠀⠈⣿⣆⣴⡇⠀⠀⠈⢻⣧⡶⠀⠀⠀⠉⠛⣿⡟⠀⠀⠀⠉⠲
⠀⠀⠀⠉⠀⡿⠀⠈⠁⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⡹⠈⠁⠀⠀⠈⠉⠋⠀⠀⠀⠸⣇⣡⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢈⡙⡔⠗
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⠰⣶⡄⢠⡄⠀⠰⢾⣶⢄⢿⠄⠀⠀⠸⣶⣾⣯⡔⠀⠀⢀⡀⠀⡄⣧⡀⠀⢰⣿⠀⠀⡀⠀⠀⢠⡄⠀⠀⡀
⠀⠀⢈⡄⠈⠀⠃⣀⠀⠀⢠⣌⠃⢸⠇⢀⡀⠀⠺⠃⠙⢇⣴⡆⠀⠀⠁⠀⠀⠀⠰⣌⢰⣧⡿⠆⠀⢠⣜⣡⠀⠀⠙⠳⠀⠘⠃⠀⢚⡁
⠀⠀⢀⠀⡄⠀⠀⣨⠀⢰⣬⡛⠀⡆⢰⣿⠃⠀⠀⠀⠶⢌⣾⠀⠀⠀⣠⠀⠀⠀⢳⣶⡧⠍⠀⠀⠀⢦⡟⢋⠀⠀⢠⣤⣦⣶⣤⠛⠉⠁
⠀⠀⠉⠀⠀⠐⠀⠀⠀⠘⠿⣷⠀⠄⠈⣁⣀⠀⠀⠀⠀⠀⠁⠀⠐⢶⣿⣶⠆⠀⢸⠃⠀⠀⠀⠀⠠⣤⣷⣿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠐⠛⠛⠛⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⣀
⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⢀⠀⠀⠀⠄⢁⠀⠀⠀⠀⠀⠀⣬⣿⣼⡿⣃⡀
⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣦⣸⣋⣀⠀⠀⠀⢢⠀⢸⠃⣠⠏⠀⠀⠀⠀⠉⢣⡶⠀⠀⠀⠀⠙⣿⣭⣾⡿⢃
⠀⠀⢶⣦⣤⡈⢻⢠⣶⣿⠇⠀⠀⢀⣬⡉⡟⣻⡟⠀⠀⠀⢸⡆⡴⠞⢃⡄⠀⠀⠀⠠⠀⣄⣇⠀⠀⠀⠀⠀⢉⣭⣭⣶⡿⠃
⠀⠀⠀⠙⠻⠿⠾⠟⠛⣁⡄⠀⠀⢈⣛⢻⡟⠻⠛⠀⠀⢸⡄⠙⠂⣠⡞⠀⠀⠀⠀⠀⠀⠀⢹⣠⠄⠀⠀⠀⠈⣭⣍⣧⣶⡷
⠀⠀⠻⣿⣶⣄⢀⣴⣿⡿⠁⠀⠀⠻⠿⢿⠿⢿⡿⠀⠐⣄⢿⣄⠋⠁⣴⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣹⣛⣋⣡⣤⡀
⠀⠀⣀⣈⣙⠛⢻⠉⣁⣠⣤⡄⠀⣾⣷⣾⣥⣶⣶⡄⠀⠸⣆⠈⡤⠞⣡⠎⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⣙⣛⣛⣩⣭⡀
⠀⠀⠙⠿⠿⠷⠾⠾⠿⠟⠋⠀⠀⠉⠉⠁⡏⠙⠋⠀⠀⠀⠈⠓⣀⡴⠋⠀⠀⠀⠀⠀⠀⣀⠸⠛⠀⠀⠀⠀⠈⣛⡛⣟⣻⣭
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠀⠀⠀⠀⠀⠈⠻⠟⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⡆⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⠀⣇⣿⣰⠏⠀⠀⠀⠀⠀⡀⠀⠠⢎⢞⡇⠀⠀⠀⠀⢸⢀⠞⠉⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⣧⢿⣿⣫⡶⠟⠁⠀⠀⠀⢝⢯⣢⡿⠚⣤⡄⠀⢸⠃⢠⢃⡰⠇⠀⠀⠀⢠⡙⢿⢃⣴⡗⠀⠀⢀⡀⠀⣀⠀⠀⢀
⠀⠀⢀⢳⣼⣿⣯⣴⣾⣛⡁⠀⠀⣤⡤⢅⣸⡫⠍⣊⠀⠀⠘⢄⡞⠉⢀⡀⠀⠀⠀⠸⣿⣦⠿⠟⣁⠀⠀⠀⠁⠂⣬⡄⠀⠉
⠀⠀⣈⢷⣝⢿⣛⣿⣯⠵⠂⠀⢀⣈⡊⠽⡿⢒⠭⠋⠀⣀⠀⢨⠃⡠⠊⠁⠀⠀⠸⣦⣌⢹⣶⣿⠏⠀⠀⠐⠆⠀⣈⡀⠀⠞
⠀⠀⣌⡳⣝⠢⠥⢶⣞⣛⡁⠀⠙⣕⠮⢵⡖⡭⢽⡿⠀⠙⣄⢸⠉⠀⠀⠀⠀⠀⢠⣙⠻⢟⣩⣶⡏⠀⠀⢠⡀⠀⠙⠃⢀⡄
⠀⠐⢮⣝⡾⣝⣛⣻⣭⡥⠄⠀⢶⢖⡋⢭⡭⢛⣃⣤⠠⣦⠀⢹⣀⡼⠋⠀⠀⠀⢈⠿⣷⡞⣛⣭⣴⠀⠀⠀⠀⠀⠲⠗⠁
⠀⠀⠀⠉⠛⠺⠵⠶⠟⠛⠁⠀⠈⠑⠎⠹⠋⠍⠚⠁⠀⠈⠢⣼⠁⠀⠀⠀⠀⠀⠘⢿⣶⣼⠛⠛⠁⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢓⣄⡀⠀⠀⠀⠀⢀⣔⠀⡀⠀⠀⠀⡐⠁⣼⢡⣯⠤⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⣷⠀⣟⠀⢁⠀⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠹⣦⠄⠠⠾⡿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢲⠃⠁⠀⠁⠀⢸⡄⠙⣴⠋⠉⠁⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠷⣤⡙⠖⠂⠈⠀⠀⢙⠁⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⡿⠷⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠗⠀⠀⠀⠀⠀⠐
⡐⠒⠲⠄⣀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⡰⠊⠀⠀⠀⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠳⠊⠀⠀⠀⠀⠀⠀⠀⠙⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⡄⣠⠜⠀⠀⠰⠀⠀⠀⢠⣿⠆⢀⠈⠀⠀⠀⠈⢦⡑⠙⢁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣄⣠⡄⠀⠀⢃⢀⠀⣧⡍⠀⠀⠀⠀⠀⣀⣾⣿⣿⠆⠀⠀⠀⠀⠀⡈⠄⢿⣧⠴⢊⠀⠀⠀⠀⠀⠀⢹⡔⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠤⠀⠬⠹⡄⠀⠀⠀⣾⢆⠋⠀⠀⠀⠀⠀⠀⠈⡻⠛⠁⠀⠀⠀⠀⠀⠀⢛⣄⣞⠠⢀⡀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠊⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠉
⠀⠀⠀⠀⠐⣷⠀⢂⡀⢀⠉⠀⠀⡋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠹⠈⢻⡇⢈⡇⠀⢠⠁⢀⡀⠀⠀⢀⣀⡤⠀⡰⠀⠀⡠⢾⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣿⣟⡴⡾⠿⡏⠀⠔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡸⢁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⢀⠀⠈⠄⠀⠀⢀⡤⠂
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠛⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠷⣬⠀⡄⡰⠋⢀⠀⠁
⠀⠙⢛⢷⡶⠂⠀⢀⠀⠀⠀⠀⠀⡏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣶⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢄⠠⠀⢂⠙⠛⠂⠂
⠀⠀⠀⠉⠋⠐⠂⢀⡻⢦⡀⠀⠀⠄⠐⣾⡋⢻⡄⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⣀⣠⠀⠉⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡀⠙⡆⠀⠙⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣁⣈⣠⣉⡛⠍⠉⡋⠉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠇⠸⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡉⠳⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⢀⣀