Water tap Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠛⠲⠦⠤⠀⣀⣤⡎⠉⠉⠉⠉⠉⠉⠉⢳⡄⣀⣠⡤⠶⠶⠲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢟⣋⣭⠤⠤⠼⢿⡇⣤⣤⣤⣀⣀⣀⣀⠸⡇⠀⣀⣰⠶⢶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠓⠚⠛⣿⣿⠿⡿⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⠀⠁
⠀⠀⠀⠀⠀⡴⢃⠎⠀⠀⢀⠞⠀⠐⠁⠔⠁⠐⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠈⠀⠁⠟⠀⠀⠐⠀⡀
⠀⠀⠀⢠⠊⡔⠁⠀⠀⡀⠁⠀⠂⠀⠊⠀⠀⡠⠂⠀⠚⠄⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠀⠀⠀⠐⠈⠙⠉⢹
⠀⠀⠀⣡⠊⠀⠀⢠⠎⠀⠀⠀⠐⠁⠀⠀⠔⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⠄⡄⠀⠀⠀⠀⣿
⠀⠀⡔⠁⠀⠁⡐⠁⠠⠂⢠⠂⠀⠂⡠⠂⡀⠀⡔⠁⣰⠁⠀⠀⠀⠀⠀⠀⣴⣧⣄⣿⡇⣁⡀⠀⠀⠀⣀⡀
⠀⠜⢀⠂⢀⠈⠀⡀⠁⡰⠃⠀⠀⡔⠁⠐⢁⠊⣠⠊⣠⠀⠀⠀⠀⠀⣠⠚⠻⢭⣋⣙⡈⠭⠁⠠⠍⠛⠋⠀⣿⣀
⠀⠀⠁⠠⠂⢀⠎⢀⡜⢁⠄⢀⠎⠠⠂⡰⠁⡴⢁⠌⢘⠀⠀⠀⠀⠀⣿⣿⣯⣄⣀⡉⠛⠃⠀⠤⠴⠶⠦⠭⠖⠛⡇
⠀⠀⠀⠀⡠⠃⢀⠞⢀⠈⣠⠂⠐⠁⠌⠀⠜⠰⠁⠂⢸⠀⠀⠀⠀⠀⠙⢻⣿⣿⣟⣛⣛⣀⣀⣀⣀⣀⣀⣀⣤⡶⠃
⠀⠌⠀⡔⠁⢠⠋⡠⠃⣰⠃⢬⣠⣤⣤⣬⣤⡴⡳⠒⣻⣆⡀⠀⠀⢀⣠⠾⣗⡿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠘⢦⡀
⠀⢀⠎⠀⡠⠃⡰⢁⣼⠋⠀⠀⠀⠀⠀⠀⠊⣴⠁⣴⠉⠈⠉⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⡀
⢀⠃⠀⡜⢁⡜⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⢀⠎⢀⠞⠀⠊⣿⢀⡀⡀⢀⡄⡀⠀⠀⡂⡇⠸⢣⣤⣤⣠⣤⣤⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢠⠊⢀⠀⡠⠁⡰⣿⣼⣿⣿⣿⣿⣿⣿⣾⡇⢃⠀⣿⣿⣿⡿⠿⠿⠻⢿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣿⣿⣞⣡⣀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠁⠀⢁⡼⠀⡐⠀⡸⣿⡿⠛⠻⠻⠹⠿⠟⢿⡘⡄⠙⠛⠈⣀⣤⣤⣤⣄⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠿⠿⠿⣿⣿⣿⣯⡖⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠘⠀⡜⢀⡜⠀⠈⠛⣿⣶⣶⡶⣶⣶⡞⣿⣷⣀⣴⠟⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠚⠛⠒⢦⣌⠘⠻⣟⣭⣴⡀⠀⠀⠀⠀⠀⢿⡀
⠀⠈⠀⡜⢀⠎⠀⡠⠁⡘⠛⣿⢟⣼⣟⣟⣼⡿⣱⠃⣠⠂⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣤⣤⣤⡤⠾⠃⠀⠀⠀⠀⠈⠻⣆⠈⣿⣿⡯⠀⠀⠀⠀⠀⠘⣧
⠈⠀⠜⢀⠎⠀⡰⠁⡔⠀⡜⠁⡾⢋⣿⢞⡟⣴⣿⣟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠨⣻⣿⡥⠀⠀⠀⠀⠀⢹
⠀⠈⠀⠎⠀⡼⠁⡼⠀⠜⠀⡔⠀⠜⢉⠞⡼⣳⣿⡟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⣿⣏⠕⠀⠀⠀⠀⠈
⠀⠀⡎⠀⡰⠁⡜⢀⡎⠀⡼⠀⠈⠀⠈⡼⣵⢟⡟⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻⣿⠗⣫⠄
⠀⠜⠀⣰⠁⡜⠀⠈⠀⠸⠁⠘⠀⠀⡜⠁⡞⠈⣼⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢾⣿⣟⡅⣾
⠠⠀⢠⠃⡸⠁⠄⠀⠰⠁⠐⠀⠀⠰⠁⠜⠀⡼⠉⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣿⣥⣻⣏⣀⣀⣤⡾
⠀⢠⢃⡔⠀⡄⠀⢠⠁⠀⠀⠄⢠⠃⡰⠀⡸⠁⢠⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠊⡸⠁⡔⠀⢀⠇⠠⠁⡘⠀⠇⡰⠁⣰⠁⢠⠃⡰⣿
⡄⠰⠁⠀⠀⢀⡎⠀⠀⠀⠀⡞⠰⠁⢠⠇⢀⠃⣸⠃⡏
⠰⠂⡰⠀⠀⡜⠀⠄⢀⠂⠘⢠⠃⠀⡎⠀⠌⢠⠃⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣛⡻⣯⡉⠉⠉⠁⠀⣀⡈⣁⡀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣋⣡⣿⣯⣿⣿⣿⣿⡿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢹⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣽⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢿⣏⢉⢹⣏⠙⣿⣆⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⣿⡿⣿⢿⣾⣿⡿⣰⣞⣿⣆⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣤⣤⣤⣀⣀⣀⣹⣿⠁⠀⠀⢉⣿⣧⣤⡿⠅⢘⣿⡆⠀⠸⣿⣷⣶⣚⡿⣷⢶⠾⣿⢿⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⣿⡇⠀⠀⣹⣿⡟⠙⠉⠈⠈⠀⠉⠀⠘⠈⢻
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⣀⠀⡀⠀⢀⠀⠀⠀⢀⢀⠀⠄⠀⢀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣔⣽⠿⠶⠷⠶⢮⣧⣴⡶⠶⠶⠶⠶⠶⣬⣅⡐⣴⣿⠇⠀⠀⣿⣿⢿⣾⣷⣶⣥⣿⣼⡽⣶⣿⣾⠁
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣄⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⢸⣟⣀⣠⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠘⣧
⠀⠀⠀⠀⠀⠀⢠⣿⠂⠈⢿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣷⣴⣆⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠙⡿⣿⠉⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣷⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢠⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠉⠙⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠛⠁⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⢀⣀⣤⣄⠀⠀⣀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠓⠒⠖⠀⠉⠉⠀⣿⣯⣙⣿⣿⡆
⠀⠀⠀⠀⠀⢀⡴⠊⢁⣴⣾⣿⣿⣿⣿⣧⣤⣭⣴⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣤⣤⣴⣶⣶⣀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡰⠃⢀⣾⣿⡿⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢰⠃⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉⠉⠁
⠀⠀⠀⣾⠀⣾⣿⠃
⠀⠀⠀⠈⠈⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣤⣤⣄⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠛⣛⡛⠛⠛⠛⣛⠋⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠛⠉⢹⡿⠛⣿⠉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣟⣛⣻⣷⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡉⠻⡍⠋⠉⠙⠉⠉⠙⢷⡴⢶⡶⠶⠶⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠈⢻⡆⢹⡀⠀⠀⠀⠀⠀⠈⣷⠈⡇⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⡟⣸⠀⠀⠀⠀⠀⠀⣰⡟⣰⡇⠀⠀⢀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡿⠿⣶⣧⣤⣤⣤⣤⣤⡾⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢻⣄⠀⠀⠀⢀⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠢⢽⣛⣛⣛⣯⠵⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠦⡴⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⣦⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠀⢸⠀⠀⠀⣿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⢸⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣿⠀⢸⠀⢀⡀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⡇⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠘⠁⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣿⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⡇⡇⠀⠀⣿⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⢀⡇⠁⠀⠀⢿⠀⠛⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⠀⣿⠈⠁⠀⡆⠀⣼⠀⠀⣉⡀
⠀⠄⠀⠀⢀⣀⣀⠀⠀⢠⡾⠛⠶⠀⣿⠀⠀⠘⠃⠀⢹⡄⠘⠋⠃⣀⠀⠀⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠓⠀⣠⠄⠀⠀⣀⠀⣀⠀⠋⠀⠒⠆⠈⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠙⠂⠀⠸⠉⠀⠈⠁⠘⢤⠀⠀⠀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡴⢿⣄⠀⢰⡦⠀⣶⣀⣠⡿⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣤⠤⠤⣠⣤⣤⣄⣀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠀⠀⠀⠉⠉⢒⠚⠿⣹⠀⠀⠀⠀⢀⠏⠛⠓⠒⠉⠉⠀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⠀⠀⠀⣀⡠⠤⣼⣠⣤⠃⡆⠀⠀⠀⣸⠸⣥⣀⡤⠤⢄⡀⠀⠀⠐⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠶⠒⠚⠉⠀⠀⠘⣆⢁⣀⣀⣀⡇⡼⠁⠀⠈⠙⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣏⣉⣉⣉⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢥⣴⠥⠤⠤⠤⠬⣧⠸⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⢞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣄⣀⣤⣤⡏⢁
⠀⠀⠀⠀⠀⠀⣠⠤⠖⢚⣉⡉⠭⠤⠄⠐⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡴⠋⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⢀⡄⢸
⠀⠀⢀⡞⢠⠊⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⣾⣿⣶⡇⢸⣿⡏⣿⡷⣿
⠀⠀⡼⢠⠇⠀⠀⠀⢸⠀⢠⠖⠋⠉⠉⠉⠙⠓⠲⠦⢤⣄⣀⣀⣀⣀⣀⣒⣬⠥⠖⠚⠉⠉⠀⠉⢇⡸⣹⣇⣿⣏⣿
⠀⢠⡇⡾⠀⠀⠀⠀⡜⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠬⠭⠭⠭⠽
⢰⠾⠡⡇⣀⡀⠀⢀⣇⡸⡇
⢸⠀⠀⣥⠀⣒⣒⡒⢦⣬⡇
⠀⠉⠒⠓⠾⠿⠿⠟⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸
⣀⢀⡀⠀⠀⠀⠀⠀⠙⡁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣶⣀⠀⣀⣤⠾⠛⠀⢀⣀⠀⣠⡀⢠⣄⡀⢀⠀⠀⠀⢀⣠⣤⢤⣠⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⠘⠉⠉⡁⠀⠀⠀⡜⣦⡼⡿⢷⢿⡿⠆⠘⡾⡶⣡⢿⢷⡇⣾⠇⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣡⡶⠶⣦⣴⡙⣦⣄⠀⠈⠈⠀⠀⠈⢀⡀⠀⣀⠀⢠⣀⡀⢨⡆⠀⣀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⠣⠂⢀⣘⠛⠈⠉⠀⠀⠀⠀⠀⠀⡛⣤⡼⡟⣷⢿⡿⠀⡞⢸⣳⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠄⣾⠁⢳⣤⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠉⠈⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢠⣶⢾⣾⢿⣤⠀⡄⠀⢀⣤⣴⣿⠟⠷⢦⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢦⣿⠘⣿⣯⣙⣲⡇⢚⣫⣴⠟⠃⠀⠀⠰⠆⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣌⠫⣳⣼⣿⣭⣭⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣷⣿⣦⣬⣽⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠃⠀⡸⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣀⣼⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠢⣄⣠⠖⠓⠢⣀⣠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡴⠚⠓⢄⢀⡴⠛⠳⢤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠚⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠽⠙⠯⣅⠀⠀⠀⠀⠀⢀⡤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠚⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⠈⠓⠦⠤⠴⠊⠀⠀⠀⠀⠀⠘⠦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠙⣞⠉⠉⠉⠉⠉⠑⠢⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢺⠁⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠁⠀⠘⣆⠀⠀⠀⣠⠇⠀⠀⠀⠀⣠⠦⢄⣀⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠙⠒⠛⠉⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠀⠀⠀⠀⠄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡠⢴⠿⠋⠀⠀⠀⡈⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠖⠋⢰⠃⠀⠀⢀⡠⠚⠳⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡮⠂⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠙⠻⢤⣠⡶⠶⠶⡶⢶⣤⣴⠞⠁⠈⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣠⡤⠖⠚⠚⢷⠀⠀⠀⢸⡏⠉⠙⠳⢦⣄⣤⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣼⠟⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⣀⣀⡀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠈⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠿⣿⣻⣯⠀⠀⠀⠀⣀⣾⣿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠀⣠⣸⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠷⣤⣄⣀⣀⡀⠀⣀⣀⣠⣤⡼⠿⠃⠈⢉⠉⠉⠉⠉⠉⢰
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⠴⠶⠞⠉⢀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠹⠀⢸⡆
⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⡇
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠛⠛⠉⠉⠛⠋⠁
⠀⠀⢸⡙⠿⠤⣤⣤⣤⣤⣧⣭⡿⣆⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠈⠛⠷⣤⣤⣀⣀⣀⣀⣤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡏⠨⡉⠁
⠀⠀⠀⠀⠀⠀⣼⠇⠀⣇⣆⠣
⠀⠀⠀⠀⠀⣼⡇⠀⡆⢸⡌⠛
⠀⠀⠀⠀⠀⣿⣶⠘⠃⢨⡇
⠀⠀⠀⠀⠀⢿⣟⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⢀⣀⡀⠀⢀⡠⠤⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢤⣀⣀⣠⢤⢤⠈⠀⣀⣾⢈⣍⠁⣀⡀⠀⠀⠀⢈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠍⠑⠓⠃⠛⠑⣜⣛⡀⠀⠁⠛⠓⠻⠭⠭⠏⡛⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐⠀⢀⣀⡛⣛⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠁⠨⡉⠉⠍⠭⣛⡻⠇⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠄⠀⠉⠀⠀⠅⠀⡐⠄⠀⢱⠈⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⢀⣀⠀⠀⠀⠀⠀⠄⠀⠄⡂⠀⡾⠁⠂⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡤⢚⠉⠀⢀⢨⡀⠀⢀⠀⠀⠀⠀⠀⡇⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠀⡐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠎⠀⠀⢐⡨⠌⠈⠀⠀⠀⠀⡈⠐⠀⠀⣗⠪⠀⠁⠀⠀⠤⠤⠤⠀⠀⠀⠀⠰⠊⡀⠢⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡴⠁⠀⠀⠔⠁⠀⠀⢠⠀⠀⠠⠀⠢⠁⠀⠀⠧⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⢤⣤⣶⣶⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠄⠀⠠⡀⠀⠀⠀⠀⢆⠁⡂⡀⠠⠀⠐⡃⣤⢤⠠⠄⠤⠤⠤⠄⡤⢠⠠⢤⠤⠴⠂⢾⠀⡇⠰⠶⠶⠶⠦⢸
⠀⠀⠀⠀⢀⠀⠀⠈⡄⣰⡀⣀⢀⡔⢀⡘⡀⠀⠀⠀⠈⠐⠨⠀⠀⠠⠈⢐⠔⠕⡡⡪⡨⡪⢋⡪⠢⢂⢂⢀⡂⠠⡀⠈⠀⡇⣘⣛⣻⣿⠗⢘⠅
⠀⠀⠀⠀⠀⡀⠀⠀⡇⢻⡇⣿⠈⡇⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠂⠀⠁⠀⢄⠁⠰⢀⣹⣾⣭⡭⠁⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣅⢈⣁⣛⣀⣓⠘⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⣐⡲⠶⢒⣂⠼⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠕⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣊⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡫
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡟⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢆⡐⠠⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠻⠷⣶⣶⣴⡶⠿⠋⠀⠀⠀⠈⠙⠿⣶⣶⣶⡶⠾⠟⠛⠛⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀⣠⣤⣤⣴⣶⣦⣤⣄⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣤⣄⣀⣀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⠻⣿⠿⠿⠿⢿⣿⠋⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⠿⠿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣽⣿⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⣶⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⣤⣤⣴⣶⣶⣶⡶⠶⠶⠾⠿⠿⢿⣿⣦⣄⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠶⣶⣦⣤⣀⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⣿⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠷⠶⠾⡿⠛⠉⠁⠀⠈⠉⠙⠛⠛⠿⠷⠾⠿⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣀⣀⣤⣤⣴⡶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⠋⠉⠉⠛⠳⢶⠶⠛⠛⠛⠓⠒⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠒⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⣤⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡁
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣤⠤⠲⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⢠⡞⢻⠇⠀⠀⠈⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣷⡇⢀⠀⠀⣴⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⠓⠛⠋
⣿⠀⣸⠀⠀⠀⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠹⠃⠘⢀⣾⠁⠀⠀⠙⠶⠶⠶⣄⣀⣀⡴⠋⠀⠀⠀⠀⢠⣤⣄
⠙⠶⠋⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢀⣤⠤⠶⠦⠶⠞⠋⢹⡄⠀⡀⠀⣼⠃⠀⠀⢀⠀⠀⠀⠀⠈⠉⢁⡀⠀⠀⠀⠀⠀⢸⡄⢸
⠀⠀⠀⠀⠀⠀⡴⣶⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⢰⠁⢰⠇⠀⠀⠀⠸⡿⢦⡀⠀⠀⠀⠈⡟⠳⣦⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⠀⠀⠀⠀⠀⣇⢀⡵⠀⠀⠀⠀⠻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣴⣧⣤⣼⣿⠂
⣿⣿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⢻⣆⣀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⣰⡟⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⢸⡏⢹⣧⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢺⢛⣻⣟⡛⣿⠛⠀⢸⣿⣿⣥⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀
⠀⠀⠀⠀⠀⢻⡆⠀⠀⣸⢋⠴⠢⡙⣿⠀⠀⠀⠉⠉⠉⠉⠉⢹⠀⠀⡀⠀⠀⠀⢀⠀⢸⡏⠉⠹⣧
⠀⠀⠀⠀⠀⠈⢿⣄⠀⢹⡈⠦⠤⢃⣿⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⡇⠀⣿⠀⢸⠀⢸⡇⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠻⠷⠿⠟⠷⠾⠛⠛⠛⠛⠛⠛⠛⠻⣿⠉⠉⠀⢀⡇⠀⡏⠀⣸⠀⢸⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠾⠶⠾⠷⠶⠷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠡⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠛⢿⣿⣶⣾⣿⠟⠉⠉⠛⣿⣷⣶⣿⡿⠛⠛⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢀⣨⣭⣭⣅⠀⠀⠀⠀⣨⣭⣭⣥⡀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣴⣿⠟⠛⠻⣿⣦⡄⢀⣴⣿⠟⠛⠿⣿⣶⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣶⡿⣿⣧⣼⣿⣿⣷⣄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣀⣀⣀⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠏⠙⢿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠙⣿⣷⣤⣤⣤⣤⣤⣤⣤⣾⣿⠋⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⣿⠋⠉⠻⣿⣷⣄⣀⣀⣀⣀⣠⣶⣿⠟⠉⠉⠉⠉⠉⠉⠋⢻⣿⣦⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⢰⣿⣏⣀⣀⣀⣀⣘⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠘⢿⣤⡀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣐⣬⣲⣾⣿⡿⣶⢶⠷⠖⠒⠒⠒⢺⢶⣶⣶⣶⣶⣶⣶⣶⠶⠛⢉⣙⣋⣈⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠙⠛⢿⡿⡟⢀⡀⠀⠀⠀⢸⣮⣿⣿⣿⣿⣿⡿⣿⡴⠛⠉⠉⠉⠉⠙⠢⡄⡝⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⡁⠀⠀⢶⢾⣿⣿⣿⡿⢿⣿⠋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠎⠁⠀⠀⢀⣬⠀⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠦⣄⠘⢿⣴⢿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠛⢅⠀⢙⣺⠢⠈⣻⣿⣽⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣀⠀⠀⠑⢿⣿⣀⢄⠈⠳⣿⣿⣷⣥⡀⠀⠀⠀⠀⠀⠀⠞⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠁⠀⠀⠀⠈⣿⣿⣧⡀⣹⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⡸⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠭⠭⠭⠠⠤⢄⢤⠤⠄⡤⠀⢽⢿⡿⠿⢯⣭⠭⢭⠍⢭⠹⠭⠩⠶⠄⣧⣷⣥
⠀⠀⠀⠀⢀⣤⡖⢉⡀⠠⢶⣀⡠⡀⠀⡠⢈⣠⠴⠋⡄⠀⣸⠾⡉⢢⠀⠈⢷⡄⢡⠀⡄⠀⢀⡔⠶⠀⠈⠙⠳⢄
⠀⠀⣠⡶⠋⠯⠙⠯⢹⣾⠋⠙⠡⠃⡐⢻⡟⠁⠀⠀⠄⣼⢻⠀⡈⠀⢳⠦⠀⢻⡘⣿⡇⠀⠈⠻⣶⡶⣾⣷⣤⣤⣁⠄
⠀⡴⠻⠇⠀⠀⠀⡼⢿⠿⠇⠀⠀⡼⢟⡟⠀⠀⠠⡞⣿⠷⢾⠚⠁⠀⠀⡄⠀⠘⡇⣿⣿⠀⠀⠀⢙⣿⣿⡿⢿⣟⠛⠿⣦
⠰⢁⡀⠠⢲⠄⠀⠀⠀⠀⠀⠀⣼⣶⡟⣀⣀⣀⠀⡸⠉⠆⢸⣀⠀⠀⠀⡇⠀⠀⡇⢿⣿⠀⠀⠀⢘⣿⣟⢠⣽⡿⠷⣦⡘
⡆⠈⣹⣾⡯⠄⡰⠀⠀⠀⠀⢰⣿⣿⠃⣽⠃⢈⣷⠃⠀⠀⣸⣿⠀⠀⢠⠁⠀⢰⡅⢸⣿⡂⠀⠀⢸⣟⢧⣽⢫⣾⣿⣌⣳
⠇⠀⣤⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⡟⢠⡿⠀⠉⡾⠀⠀⡤⢽⣿⠀⢀⡎⠀⢀⡿⠁⢸⣿⡇⠀⠃⣾⣿⣣⣿⠞⢿⣿⣿⣷
⢸⡄⠋⠙⠋⠀⠀⠀⠀⠀⠀⣿⣯⡇⠚⠃⠘⣹⣦⠴⠞⠀⠸⠛⢢⡎⠈⢐⡿⠁⠀⣸⣿⣷⣾⣶⣿⣯⣷⡻⣷⣿⣤⣿⡟
⠀⠹⡀⣰⢀⠀⠀⠀⠘⠀⢀⣿⣿⠁⡤⠞⢁⡬⢙⡓⠃⠀⢸⣤⢂⠀⣰⠟⢁⣠⣌⣽⣿⣿⣿⣿⣿⣿⣿⣯⣠⣌⠉⢛⡵
⠀⠀⠹⣧⡤⢀⠢⣀⣠⣤⣾⣻⠏⠀⢡⠄⠀⡷⠦⢜⣠⣴⣻⣧⡽⠚⣁⣤⣶⡿⠿⣿⣟⡋⣽⡟⢿⣵⡿⢟⠛⠁⢀⠝
⠀⠀⠀⠈⠻⢿⣿⡏⢠⣞⣋⣥⣴⠞⢀⣀⣤⣴⠶⣿⣿⠾⢛⣩⣴⣾⣯⣿⣿⣿⣿⣿⣿⠿⢿⣿⣾⣿⣛⣩⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠿⢿⡿⠿⠿⠿⡿⣿⠟⠻⣍⡉⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢿⣿⣟⣛⣛⡷⢿⣷⣶⣶⣶⣶⡲⡶⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠛⠛⠛⢻⠿⣿⣿⣿⠏⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢨⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠇⠀⠀⠀⢰⠐⣦⣿⣿⣧⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠶⠶⢶⣶⣾⣿⣿⣿⣿⣧⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣤⣀⠂⠸⣿⣿⣿⣛⡟⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⣡⣤⠀⠻⣿⣿⡿⠁⢠⢿⣿⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠉⠉⠱⠀⠱⠞⠀⠆⢹⡟⠐⠆⠹⠼⢫⣿⣆⠙⠻⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⠿⠿⢯⡯⠉⠇

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


⣿⠿⠿⠿⠿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣿⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⢏⠇⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠡⠄⠐⠒⣒⣒⣒⣒⣒⡒⠂⠀⠤⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣅⢀⢚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠠⢂⠭⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡆
⠀⠀⠀⠀⠀⢀⢁⠂⠀⠏⠭⠀⡀⠀⠀⠀⠠⠤⠀⠠⠤⠀⠀⠐⠀⡂⠨⠍⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠌⠈⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁
⠀⠀⠀⠀⢀⢀⠁⠀⠉⠀⠂⠀⠂⠉⠡⠤⠀⠀⠀⠀⠀⠠⠤⠉⠁⠂⠐⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠄⢠
⠀⠀⠀⠀⡄⠁⠀⡁⠔⢢⠀⠀⠠⠒⠀⠀⢀⠤⠀⠀⠀⡀⠀⠀⠀⡠⠄⠀⠀⠦⡁⠀⠀⠀⠀⡈⠈⠘
⠀⠀⠀⢀⠘⠀⢠⠁⠀⠀⢄⠔⠁⠀⢃⡠⠀⠀⢃⢀⠎⠈⠄⠀⠔⠁⠘⣀⠎⠀⢡⠀⠀⠀⠀⠯⠀⣚
⠀⠀⠀⠘⢜⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⢰⠠⠀⠩⠀⠐⠒⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⠒⠀⠀⠁⠄⢠⠀⠀⠰⠠⢠⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡋⠉⠹
⠀⠀⠀⠀⠀⢒⠀⠀⠤⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⢐⡀⠜⠊⡴⠃
⠀⠀⠀⠀⠀⠠⠀⠈⠁⠒⠀⠀⠀⠀⠠⠤⠤⠀⠭⠥⠤⠤⠄⠀⠀⠀⠀⠒⠀⠉⠀⢸⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠑⠂⠄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠉⠉⠓⠲⠦⢤⣤⣤⣀⣰⡋⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣤⠤⠴⠒⠋⠉⠁⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⢀⣀⣤⠴⠖⠚⠋⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⢀⡷⠃⠈⠉⠙⠛⠲⠦⢤⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡶⢶⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠷⠾⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠋⠉⠉⠉⠉⠉⠉⠻⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⣹⣉⣋⡏⢹⠛⡟⢻⠛⡟⢻⠛⡏⢻⢙⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠋⠉⠉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡴⠞⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢠⡿⠁⠀⠀⠀⠘⣷⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⣼⠃⠀⠀⠀⠀⢰⠏⠀⢈⡿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡖⠲⠶⠤⢤⣤⣀⣀
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⢸⡇⠀⠀⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠈⢿⡀⠀⠀⠀⠀⢻⡤⠖⠛⠛⠛⠒⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⢷⣄⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠲⠶⠦⠴⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⠲⠤⣤⣄⣀⣀⣀⣤⡤⠶⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣤⣤⣤⣤⡴⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⣼⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢻⡆⠀⠀⠈⠻⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠈⠿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⠀⠀⠀⣠⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡇⠀⠀⢻⡏⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠞⠛⠋⠀⠀⠀⠘⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣠⡴⠞⠛⠋⠉⠀⠀⠀⠀⠀⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⢠⡞⠁⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠏⠀⢀⡴⠋⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⡀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⣀⡠⠶⠶⣈⡉⠻⠿⠶⢶⣤⡀⠀⢀⣿⠀⠀⣾⠋⢠⡾⠋⠀⠀⣀⡴⠶⠛⠛⠉⠁⠀⠀⠀⠉⠻⣦⣠⠾⠃⠀⠀⣀
⠀⠀⠀⠀⣤⠟⠉⣡⠖⠂⠈⠁⠀⠀⠀⠀⠉⠻⣦⣸⡟⢀⡿⢁⡴⠋⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠿⣆
⠀⠀⢠⡾⠁⢠⠞⠁⠀⠀⡀⠛⢳⠄⠀⣴⠆⠀⠙⣿⣧⣞⣧⠛⢀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣼
⠀⢠⡎⠀⣴⠃⠀⠀⠀⠀⠉⠒⠁⠀⠀⠓⠜⠀⠀⣿⣿⡿⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣹⡆⠀⠀⠀⢠⡾⢳⣄⠈⠁
⠀⣾⠁⣴⠉⣠⣄⠀⠀⠀⢀⣠⠤⣤⣤⣤⣄⣀⣀⣿⣿⣥⣟⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠇⢀⡌⠀⣉⣸⠇⠀⠰⠉⣀⣶⠶⣽⢿⡟⠉⠉⣹⠋⠉⠉⣹⠿⠛⠙⠲⢶⣶⡦⢤⣄
⣧⠀⢸⡀⠀⠀⠀⢠⡘⠆⢠⡟⠁⣼⠁⠀⠃⠀⣠⠋⠀⢠⡾⠉⠀⢀⡤⠚⠃⠈⡇⠀⠉⢿⡄
⣿⠀⠸⠁⠀⠀⠀⢸⡿⠀⡿⠀⢰⠀⠀⢠⡆⢀⠛⠀⢠⡏⠁⢀⡶⠁⠀⢀⠀⢠⡇⠀⠀⠸⣿
⣿⠀⢰⠀⠀⠀⠀⣿⡇⠀⠇⠀⢸⠀⠀⠘⢧⡜⠀⠀⡏⠀⣠⠋⠀⠀⠐⠈⠀⠛⠀⠀⠀⠀⢸⡆
⣿⠀⢸⡇⢈⣑⠄⢹⡇⠀⣆⠀⢸⠀⠀⠀⡸⠃⠀⡆⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠹⣆⠈⢀⠈⠁⠀⠈⢿⣄⢋⡄⠈⣀⠀⢸⡇⠀⠀⠇⠐⠃⠀⠙⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢻⡄⠸⣀⠀⠀⠀⠀⠛⠛⠿⢤⠾⣶⣾⣀⣀⣀⣼⡆⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠈⢳⡄⠙⡀⠠⡎⣡⠀⠀⠀⢀⡤⡀⠀⢸⣿⠋⠙⢷⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠻⣦⣈⡆⠀⠁⠀⠀⠀⠸⠥⠛⢀⣾⠇⠀⠀⢸⡇⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠻⢾⣷⣦⣀⠀⠀⠀⣀⣰⠾⠃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢰⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⠶⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠙⠛⠻⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠻⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠾⠟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠙⢷⣤⡀⠀⠀⠀⢀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⡀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠀⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡴⠶⣷⡤⢤⣼⣆⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⣲⡸⠏⠀⢠⣸⣧⡄⠒⢻⣷⡆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠛⢋⣵⣾⣷⡐⣧⠀⠈⠶⢿⣷⣚⣩⠟⠂⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⣿⡇⠀⠐⠿⣿⣿⣾⢄⠀⠀⣾⣿⣉⡽⢧⣤⣶⣤⠀⠉⠓⠲⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠸⣿⣿⣿⣿⣾⣇⠀⠘⢻⣿⣿⣮⢆⠀⠈⣿⠟⠿⣷⣿⣭⣷⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⢿⣿⣿⣿⣿⣆⠀⠘⢿⣿⣿⣦⠃⠀⠹⠀⠀⠀⠀⠀⠉⠛⠿⣟⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣷⡰⣸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠻⣿⣿⣷⡽⣷⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⡄⠀⠀⣻⣿⣿⣿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣅⠀⠈⢱⣿⣿⣷⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣆⡀⠀⣩⡿⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⣚⣭⠾⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢠⡀

⠀⠀⠀⠀⠁⠀⠁⠳⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠛⠛⠛⢻⣿⡟⠛⠛⠛⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣧⣤⣤⡄
⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⠛⡙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃





⣶⡶⢲⡶⣶⣶⢶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠈⠉⠉⠉⠉⣿⡏⠀⠀⢹⣿⠉⠉⠉⠉⠀⠀⠀⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣶⡶⠶⠶⠶⢿⣷⣤⣤⣾⡿⠶⠶⠶⢶⣦⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⣿⠉⠉⣿⡇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣤⣴⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣤⣤⣤⣤⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠁⠈⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⣀⣀⣀⣸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡄
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢻
⠀⠀⣸⠙⢦⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⡇⢰
⠀⠀⣿⠀⠀⠉⠓⠶⠖⠋⠁⠀⠀⠀⠀⣸⡇⠸⠸⠁⠀⠀⠀⡠⠠⠔⠐⠤⠐⢄
⠀⠀⢹⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠱
⡀⣄⠈⠳⣤⣀⠀⠀⣸⠇⠀⠘⢶⡛⠁⠀⠀⠀⠀⠀⠀⠈⢒⠀⠀⠄⢂⠀⠀⠀⠐⢀⠄
⠳⡈⠑⠀⠈⠉⠉⠉⢹⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠙⠀⠘⠆⠉⡠⡀⠤⠂⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠒⠛⠓⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠲⠶⠶⠶⡆⢠⠶⡶⠶⠒⠒⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣠⠀⠀⢊⠄⠠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢟⠋⠀⠀⠀⡇⠆⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢤⣤⠤⠤⠖⠚⠉⢷⡄⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡌⠈⢆⠀⠀⠀⠰⠦⠔⠂⠀⠀⠀⠀⠀⠀⢸⡗⠢⠤⠤⠒⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⠦⣌⡻⣦⡀⠀⠀⠀⠈⠳⠶⠤⣤⠄⠀⠀⠀⠀⠈⢤⠠⠊⠀⠈⢐⠆⠠⠀⣀⣀⣀⣀⣠⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣤⠐⠁⠀⣀⠔⠁⣠⣞⣁⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠬⠓⠓⠤⣀⣀⣀⣀⣠⢤⡀⠀⠀⠐⠳⠤⡀⠈⠁⡩⠀⠀⣰⠏⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠙⠒⠉⠉⠙⠢⠤⠴⠒⠛⠧⢄⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠁⠒⠒⠒⠒⢠⠊⠉⠑⡄⠠⠤⠤⠄⠀⢐⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⢀⣄⣠⣤⣼⡰⢯⣺⣤⣠⣀⠤⠄⠀⢸⡅⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⣿⠀⠈⠉⠉⠙⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠙⡔⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣅⣠⣠⣧⡬⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢤⣼⣧⠦⠶⠿⠷⢾⡿⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡱⠉⠀⠀⠁⠀⠀⠀⠺⣧⠀⠀⠀⠀⡖⠺⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡠⠤⠔⠒⠒⠂⠈⣿⡽⠯⠒⠁⡠⠒⠂⠀⠀⠈⠐⠩⢜⠟⠖⠖⡞⢷⠀⣧⣰⠀⠀⠀⣀⠀⡀⠤⠠⢼
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⢀⢸⡗⣿⢹⠀⠁⠚⠛⠛⠓⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⡄⠐⠀⡀⠀⢀⠀⠀⠰⡂⣰⠆⠀⠀⢻⠀⠀⡟⢸⣿⣿⣾⠀⠆⠀⢀⣠⠄⠀⠤⢠
⠀⠀⠀⠀⠀⠀⢀⢀⡦⠞⠓⠛⠛⠮⣀⠀⠀⠈⠀⠁⠀⡐⣤⡶⠚⠓⠛⢧⢺⣿⡿⡇⠠⠈⠠⠄⠀⠐⠒⠒⢒
⠀⢰⠀⠀⢀⠀⢨⠏⠀⠀⠀⠀⠀⠀⠈⠛⠦⢶⣰⣶⠼⠟⠁⠀⠀⠀⠀⠀⠙⢿⣽⠃⣂⠉⠀⠀⠀⠀⠀⠀⣼
⠀⢰⠀⠀⢠⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣖⠖⠴⠒⢚⣃⣀⣤⣼⠋
⢸⢸⠀⠀⢈⣈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⠙⡏⣹
⡇⣙⠒⠀⠈⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠄⡅
⠱⠭⣀⣀⣐⠭⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⠉

⠀⠀⠠⢓⣄
⠀⠠⡁⠀⡌⠢⡀
⢠⡷⠁⠀⡀⢔⡷⡀
⠰⠆⠀⢠⣤⣼⣟⠇
⠘⢤⢀⣉⣙⣉⠍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠉⠉⠙⠓⠶⠖⠛⠋⠛⠓⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠒⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢶⣄
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⣠⣤⡄⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⡟⠋⠉⠛⢛⣦⣤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡤⠞
⣼⠁⣸⠀⠀⠀⠀⠙⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢿⡇⠰⠀⣰⠏⠀⠸⣄⣀⣀⡀⠀⠀⠀⣸⠃
⢷⣀⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡼⢿⡀⠈⠀⠀⣰⠏⠀⠀⠀⠀⠉⠉⠙⠲⠖⠛⠁⠀⠀⠀⠀⢸⡟⢳
⠀⠉⠀⠀⠀⠀⣠⡄⠈⠳⠦⣤⡴⠞⠋⠉⠉⠉⠁⠀⠸⡇⢀⠆⢠⡏⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⣶⣦⣀⠀⠀⠀⠈⢷⣼
⠀⠀⠀⠀⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⡾⠀⠀⠀⠀⢸⡏⠹⡄⠀⠀⠀⢸⡄⠉⡇
⠀⠀⠀⠀⠀⠸⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⡇⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣩⣇⣀⣸⣷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠉⠉⠓⠲⡶⠾⢟⢻⠉⠉⠀⠀⠉⢹⢛⠿⠶⠶⠒⠊⠉⠉⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠡⠀⠀⠀⠀⠀⢀⣀⡇⠀⣀⠞⡄⠀⠀⠀⠀⡞⢸⡀⠀⣀⡀⠀⠀⠀⠀⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣐⣒⣒⣩⠥⠖⠛⠋⢻⡀⣇⠀⠀⠀⢠⠃⣸⠋⠙⠳⠮⢍⣒⣒⣂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢷⣼⣤⣤⣦⣞⣴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⡷⠶⠶⠶⠶⢷⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠶⣾⠒⠒⠒⠒⠒⠺⣷⠸⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡟⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⡷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⢀⡖⢛⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠒⠒⣚⣛⠩⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⡇⢸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⡤⠞⢋⣡⠤⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢸⠀⠀⡆⡇
⠀⠀⠀⠀⡴⠋⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡇⢸⢸⢸⢠⡆⡇⣿
⠀⠀⠀⡼⢁⡜⠁⠀⠀⠀⡠⠂⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢛⣛⣿⣿⣿⡇⢸⢸⢸⢸⣿⡇⣿
⠀⠀⢸⠃⡼⠀⠀⠀⠀⢸⠀⢀⡴⠋⠉⠉⠉⠉⠉⠛⠛⠲⠶⢤⣤⣀⣀⣤⣤⣄⣒⣨⣭⠴⠖⠛⠉⠁⠀⠀⠈⣧⣸⢸⣿⣸⣿⣧⣿
⠀⠀⡿⢰⠇⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣭⣉⣉⣩⡽
⢀⣶⣇⣼⠀⠀⠀⠀⠀⣿⢀⣏
⢸⠅⡀⠈⠩⠭⠭⠭⠭⠭⠭⣾
⠘⠢⢴⣋⣩⡿⠿⢿⣯⣭⣿⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⣀⣠⣀⡀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⢻⣿⣿⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣛⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠘⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣤⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣉⣹⣇⠀⣹⣋⣉⣉⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⢙⡇⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⢤⡀⠀⠀⠀⠀⢸⡧⠶⠶⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡟⠛⠛⠛⢻⠏⠀⠀⠀⠀⠈⢻⡛⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣤⠟⠒⠒⠒⠛⢧⣀⠀⠀⢀⣠⠞⠓⠒⢲⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⢀⣇⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⢸⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣹⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢤⠀⠀⠀⣼⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠸⣆⡤⣤⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠁⠀⣼⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠉⣹⠆⠀⢹⡍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡤⠖⠚⠋⠁⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⡤⠴⠶⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣰⠋⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡼⠁⣠⠖⠉⠀⠀⢀⣀⣠⣤⢤⣤⡀⠀⠈⡷
⠀⠀⠀⠀⣠⠴⢚⣫⠭⠛⠛⠛⠶⣤⡀⢸⠇⢠⠞⣠⠞⠁⢀⡠⠖⠋⠉⠁⠀⠀⠀⠀⠙⠶⠞⠁⠀⢠⣄
⠀⠀⣠⠞⢁⠔⠉⠀⡠⢤⠀⠀⣀⠈⢳⣾⢠⢏⡴⠁⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⣰⠃⢠⠋⠀⠀⠀⠳⠞⠀⠘⠭⠆⠈⣿⣿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣻⡄⠀⠀⢠⡶⣤⠉
⢠⡇⢠⢃⡤⡀⠀⠀⣠⠤⢦⣤⣤⣤⣤⣿⣧⣞⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠋
⣼⠀⡞⠈⠲⠋⢠⢊⢔⡾⢫⠟⡟⠀⢀⡟⠀⢠⠞⠉⠉⣩⠿⣷⠒⢦⡀
⡏⠀⡇⠀⠀⢀⣷⢃⡞⠀⡏⠀⣇⠀⡞⠀⣰⠋⢀⡴⠋⠀⠀⡈⠀⠀⢹⡀
⡇⠀⡆⢀⡀⢸⡏⢸⠁⢀⠁⠀⠹⡼⠁⢰⠃⢠⠎⠀⠀⡞⠒⠃⠀⠀⠘⡇
⢷⠀⡇⢯⡵⠘⣷⠘⡆⠀⡄⠀⢰⠃⠀⡇⣰⢻⣀⠀⠀⡇⠀⠀⠀⠀⠀⣷
⠸⡄⢸⡀⠀⠀⠙⢦⣳⣀⢳⣀⡏⠀⢰⣅⠇⠀⠉⡇⢰⠁⠀⠀⠀⠀⠀⢿
⠀⠹⡄⢣⠀⣰⢲⡄⠀⠉⣉⠉⠛⣶⠞⢿⡄⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠙⢦⡳⡌⠉⠀⠀⠘⠥⠃⣰⠏⠀⠀⢷⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⠾⢶⣄⣀⣀⣤⠶⠋⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣄⡀⠀⠀⣠⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⢸⣇⣠⣤⡘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⠀⣿⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣀⣤⣤⡶⠟⠋⠀⠀⠹⣦⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡞⠃⠀⠀⣀⣠⡴⠛⠛⠉⠉⠉⠉⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣤⠋⠀⢀⣤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣼⠇⢀⡼⠃⢀⡶⠋⠀⠀⣠⣤⠴⠶⠶⠶⠶⠶⣄⠀⣸⡿
⠀⠀⠀⠀⣠⡶⣿⣿⠟⠛⠋⠉⠙⠛⢷⣄⢰⡟⢠⡾⢁⡴⠋⢀⣤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⣶⣄
⠀⠀⣠⡾⢩⡾⠋⠀⢀⣴⣦⡀⢀⣤⡀⢹⣾⣇⢿⣴⠏⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸
⠀⢰⡟⣱⠏⠀⠀⠀⠈⠛⠋⠀⠈⠿⠇⠀⣿⣿⡟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣷⠀⠀⠀⢠⡶⣦⠈⠉
⢠⣿⢙⠟⣠⣄⠀⠀⢀⡠⢤⣀⣠⣤⣤⣤⣿⣿⣶⡋⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠋
⣸⣏⣿⠀⠻⠿⠃⡰⢋⣰⡾⢋⠻⡟⠁⠀⣼⠃⠀⣠⠟⠋⠉⢩⡶⣶⠶⣤⡀
⣿⢸⡇⠀⠀⠀⣠⡟⢀⠛⢀⡌⠀⡇⠀⣰⠁⢀⡾⠁⢀⡠⠛⠁⠀⣿⠀⠀⢻⡄
⣿⢸⡇⠀⠀⠀⣿⠃⢸⠀⠸⠇⠀⢁⣤⠉⢀⡜⠁⣰⠎⠀⢠⡴⢤⡟⠀⠀⠘⣇
⣿⢈⣡⣶⣷⡄⣿⡀⢸⠀⠀⠀⠀⢈⡏⠀⡈⠁⢰⣟⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀
⢹⣇⣿⠀⠋⠀⠸⣧⡘⣀⠐⡆⠀⡜⠁⠀⡇⠰⠀⠛⢶⡀⣠⠃⠀⠀⠀⠀⠀⢸⡇
⠈⢿⣌⣧⠀⠀⢀⡈⠻⠿⠦⠼⣶⣧⣀⣠⣿⡄⠀⠀⠘⢧⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⢿⣾⣇⠀⢿⡟⠀⠀⠀⣶⡄⠀⣿⠏⠉⢳⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠻⣿⣷⣀⠀⠀⠀⠘⠛⢁⣼⠋⠀⠀⠘⡇⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠻⠷⢦⣤⡴⠾⠋⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣤⣤⣤⣤⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠈⠁⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠁⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⡆⠀⠀⠀⠸⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡇⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⡇⠀⠀⠀⢀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠇⠀⢀⠀⢸⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠿⠾⠿⠿⠁⠈⠻⠃⠀⠀⠦⠀⢸⠀⠀⢀⠀⠀⢹⡿⠶⠾⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠾⠟⠁
⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣤⡶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠙⢿⣤⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⣀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣄⣀⣿⣶⣦⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁⠈⡟⣿⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠾⣿⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⢿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠴⠃⢰⣦⢶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣀⠰⠊⢀⣤⣶⣾⣿⣆⠀⠰⢂⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠀⠈⠁⣀⣀⡀⢸⢿⣯⣿⣿⡇
⠀⠀⠀⠀⢠⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⠃⢀⣾⣿⠏⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠿⡿⠿⠿⠿⠿⠇
⠀⠀⠀⡾⠀⣾⣿⠃
⠀⠀⠀⠃⠸⠿⠇


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⢻⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡇⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⡇⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣸⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢹⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠿⠃⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣄⣼⣷⡆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⢸⣿⣿⡆⣤⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠛⣿⠀⠀⢹⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢸⣿⣿⡇⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⣶⣤⣤⣿⠀⠀⢸⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡶⠶⢶⡷⠿⠿⠿⠿⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⡄⠀⠀⣴⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢧⠴⢦⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣀⣠⠼⠁⠀⢹⣀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⠞⠉⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⠞⠁⠀⣠⠴⠚⠉⠁⠀⠀⠀⠈⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡰⠃⣀⠔⠋⠀⠀⢀⣀⣀⣀⣀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⡫⠝⠛⠳⠦⣄⠀⡿⢀⡼⢁⠞⠁⢀⡤⠒⠋⠉⠁⠀⠀⠈⠳⠴⠋⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠞⠁⢠⠤⡀⢀⣄⠘⣷⣇⣞⡴⢃⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠁⠀⠀⠘⠚⠀⠘⠶⠀⢸⣿⢏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠀⠀⠀⣖⣦⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡇⢰⢡⠒⡄⢀⡤⢒⣯⣵⣶⠶⢾⡿⠿⢶⣤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠉⢀⣮⢢⠏⣰⠁⡇⠀⡜⠀⣰⠋⢀⡠⠚⠉⠏⠉⢷
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣼⠇⡎⠀⠇⠀⢇⡸⠁⡰⠁⡠⠋⠀⡤⣠⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⣖⡆⢻⡀⡇⠀⡄⠀⢸⠃⢰⠃⡼⡅⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⡆⢱⠈⠀⠈⢧⣸⡄⢣⣀⡎⠀⢈⡸⠀⠉⡆⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢇⠀⡴⣄⠉⠉⣉⠙⠓⣶⠺⣇⠀⠀⠘⠊⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡳⡈⠁⠀⠀⠳⠃⣸⠃⠀⠸⡆⠀⠀⢰⡆⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠤⠤⠶⠚⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣤⣄⣀⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⢀⣤⣤⣄⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠛⣛⡛⠛⠛⠛⡛⠋⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠛⠉⢹⡿⠛⣿⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣟⣛⣻⣷⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⡉⠻⡍⠉⠉⠋⠉⠉⠙⢶⡴⢶⡶⠶⠶⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠈⢻⡆⢹⡀⠀⠀⠀⠀⠀⠈⣿⠈⡇⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡀⣰⡟⣸⠀⠀⠀⠀⠀⠀⣰⡟⣰⡃⠀⠀⢀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡿⠿⣶⣧⣤⣤⣤⣤⣤⡾⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢻⣄⠀⠀⠀⢀⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠢⢭⣛⣛⣛⣫⠵⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠦⠴⡶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⠀⠀⠀⠀⣦⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⢸⠀⠀⠀⣿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⢸⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣿⠀⢸⠀⢀⡀⢸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⡇⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠘⠂⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣿⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⠀⡇⡇⠀⠀⣿⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣿⢠⡇⠁⠀⠀⣿⠀⠛⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⠀⣿⠈⠀⠀⡆⠀⣾⠀⠀⣉⡀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⡼⠛⠶⠀⣿⠀⠀⠘⠃⠀⢻⡄⠘⠋⠃⣀⠀⠀⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠓⠀⣠⠄⠀⠀⣀⠀⣀⠀⠋⠀⠒⠆⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠙⠂⠀⠸⠉⠀⠈⠁⠘⢤⠀⠀⠀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡴⢿⣄⠀⢠⡦⠀⢶⣀⣠⡿⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠤⠶⠶⢦⡄⠄⣠⣄⣤⣤⣀⢀⣀⣀⣤⣴⣷⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⣿⡿⠛⠋⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠀⠀⠤⠄⠤⠤⠤⠤⠤⠀⠀⠀⠀⠬⣿⣿⣿⣥⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⢀⣁
⠀⠀⠀⠀⠀⠁⠶⠷⠤⠴⠶⠤⠭⢯⠶⠶⠶⠶⠶⠶⠶⢶⡶⣶⣿⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠷⠶⠖⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠒⠒⠒⠒⠲⠿⠛⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⣿⡿⠷⠶⠶⠖⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣈⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⢀⡴⠖⠶⣄⠀⢀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⡶⠦⣤⡀⠀⠀⠀⠀⣼⠁⠀⠉⠉⠉⢻⠁⠀⠀⢸⡏⠉⠉⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣦⠀⠀⠀⠘⢦⠤⠴⠶⠒⢻⠀⠀⠀⢸⠓⠲⠶⠦⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣤⣤⣼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⣧⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⢤⣤⣤⡼⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠞⠁



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣄⣠⡤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⣧⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⢦⡀
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⣹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⢀⣀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡶⠒⠓⠖⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠋
⣰⠋⣿⠀⠀⠀⠙⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢹⡇⡔⢀⡼⠁⠘⣆⣀⣀⡀⠀⠀⣸⠋⠉
⠹⣤⠏⠀⠀⠀⠀⢺⡀⠀⠀⠀⣀⣠⣄⣀⡤⠟⡇⠀⠀⠀⡾⠁⠀⠀⠀⠉⠉⠛⠒⠛⠁⠀⠀⠀⠀⡏⠳
⠀⠀⠀⠀⠀⣠⡶⠀⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⣿⢠⠃⣸⠃⠀⠀⢸⡶⣄⠀⠀⠀⢸⠷⢤⠀⠀⠀⠙⠞
⠀⠀⠀⠀⠀⣇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠸⣇⣸⠂⠀⠀⠘⢧⣤⠇
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⣼⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣻⣀⣸⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⠀⠀⠀⢠⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠸⣇⣀⣄⠘⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⠀⠀⢿⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠋⠀⠀⠸⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠉⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⠎⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣼⠀⠀⣴⠃⢀⡴⠋⠀⠀⢀⣠⣤⠴⠶⠶⠶⢦⣄⠀⢀⡿
⠀⠀⠀⠀⣠⠴⠚⣩⠵⠚⠋⠉⠉⠛⢶⡄⢀⡏⢀⡼⢁⡴⠋⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠠⣦⣄
⠀⠀⢀⠞⢁⡴⠋⠀⠀⡴⣦⠀⠀⣠⡀⠹⣾⣇⡾⣡⠎⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸
⠀⢠⠏⢀⠞⠀⠀⠀⠘⠷⠟⠀⠸⣭⠇⠀⢿⣿⡟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠄⠀⠀⢀⡴⢦⡈⠉
⢀⡟⢀⡎⣠⣀⠀⠀⠀⣀⡤⠤⢤⣤⣀⣀⣸⣟⣴⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠛⠁
⢸⠃⣸⠀⠣⡾⠃⣠⢊⠠⡶⢛⡟⣻⠉⠁⣸⠋⠈⣩⠝⠛⠛⢛⣶⣶⠦⣤⡀
⣾⠀⡇⠀⠀⠀⢰⣱⢃⡞⠀⡞⠀⣏⠀⢰⠃⠀⡴⠃⠀⣠⠞⠉⠀⣻⠀⠀⢻⡄
⡇⠀⡇⠀⠀⠀⣿⠇⠸⠀⢰⠁⠀⢹⢀⠏⠀⡼⠁⢠⠞⠁⢀⡤⢤⡇⠀⠀⠀⣧
⣷⠀⡇⡰⢲⡄⣿⡀⢠⠀⢸⠀⠀⠈⡟⠀⢰⠁⣰⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⢻
⢹⡄⢿⠈⠛⠁⠸⣇⠸⡄⠈⡆⠀⣸⠁⠀⡆⢰⠃⠳⢦⡀⢸⠃⠀⠀⠀⠀⠀⢸⡇
⠈⣷⡸⣇⠀⠀⠀⠘⠷⠿⢤⣽⣦⣏⣀⣀⣧⡏⠀⠀⠘⣇⡟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⢷⣿⣆⠠⣏⣷⠀⠀⢀⣤⡄⠈⣿⠏⠙⢷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠘⠞⠃⣸⠏⠀⠀⠸⡇⠀⠀⠀⣔⡆⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠈⠛⠿⢶⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⣇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣀⣀⣀⣀⣠⡴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠞⠛⠛⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠉⣿⢻⠒⠒⠒⠒⠛⠉⣿⠁⠀⠀⠀⣼⣿⡏⣿⠓⠲⠦⠤⠶⠒⣿⠉⠉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣴⣿⣿⠟⢛⠻⠷⣶⣤⣿⣀⡄⠀⣈⣱⣿⣿⣿⣷⣶⣶⣿⣶⣶⣿⣠⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠛⢽⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⣸⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣠⣰⣤⣼⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⡙⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣇⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠦⣭⣶⣿⡿⠯⣭⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⠀⣿⣿⣇⠀⠀⣸⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠓⠒⠒⠒⠂⠀⠐⠾⣿⣿⣿⣯⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠍⠉⠉⠉⠉⠙⢋⢻⣿⣿⣿⡟⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠱⢄⡀⠀⠀⠀⠀⠀⠀⣰⠶⠆
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⠓⠶⣤⣤⡤⢾⣿⠀⢠⢴⣴⡤
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⠤⡄⠀⡀⡄⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⠀⣿⢸⡇⡇
⠀⠀⢠⡾⠁⠀⠀⠀⣠⣴⣾⣿⣿⣷⣿⣿⣿⣄⣇⣧⡀⢀⢰⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⠀⣿⢸⡇⣇
⠀⢠⠏⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢾⡷⣿
⢀⡟⠀⠀⠀⢠⣿⣿⡿⣿⠯⠁⠀⠉⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠹⣿⠛⡏⠛⠙⠋
⣸⠇⠀⠀⢃⣿⣿⣿⣱⠃⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃
⣿⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉
⣏⡄⠀⠀⢷⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠿⢷⣶⣤⣤⣤⣶⠿⠋⠁⠀⠀⠈⠛⢿⣶⣤⣤⣴⣶⡾⠿⠛⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⠿⠟⠛⠛⠉⠉⠉⠉⠛⣷⣦⣤⣤⣤⣤⣴⡿⠛⠉⠉⠉⠉⠛⠛⠻⠿⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠉⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣤⣤⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡿⠛⠉⠉⠉⠉⠉⠙⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡛⠛⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠻⠿⠿⠿⠶⠶⠶⣶⣶⣶⣶⣶⣶⡶⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠶⠾⠿⢿⣿⣦⣄⣀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣶⣦⣤⣀⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣤⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠿⢷⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣸⣿⣴⡶⠿⠿⠿⠿⢶⣶⣤⣤⣄⣀⣀⣀⣤⣤⣤⣶⣶⠾⠿⠿⠟⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣤⣤⣴⣶⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠒⠒⢶⡯⣀⠀⠈⢳⠖⠒⠚⠚⠛⠓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⠤⠤⠤⠴⠾⣿⣁⣆⣄⣼⠿⠾⠴⠦⠦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣬⣭⣥⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠋⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⣯⣤⣠⣀⣀⣠⣧⡀⠀⢀⡴⠻⣍⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠉⡉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠙⠛⠳⡄⠈⢧⠀⢻⡒⡒⠒⠒⠒⠒⠒⠒⠻⡄⠈⢳⡖⣲⢒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣜⡡⠀⠀⠀⠀⠀⢈⠀⠠⠖⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡄⠀⣯⡴⢂⡈⢠⠄⠀⠀⠀⢹⡀⠈⡷⢡⠆⠈⢄⠄
⠀⠀⠀⠀⠀⠀⠀⢸⢋⡤⠀⠀⠀⠀⢡⣊⣰⠂⢀⡄⠉⠀⠠⠀⢁⡀⠀⠀⠀⢀⡟⠀⢸⠃⠀⣯⠔⣩⠞⣁⠀⠂⡀⠀⢸⡇⠀⡿⢁⠜⡡⣉⠐⢃
⠀⠀⠀⠀⠀⠀⠀⣼⢉⡄⠊⠀⠀⣰⠟⠉⠉⠓⠾⣤⡏⢰⠂⢠⣀⣤⠖⠛⢻⡉⠀⢀⡞⠀⣸⠷⠾⠤⠾⠧⠶⠤⠤⠶⣾⡀⢀⡟⠓⠚⠒⠛⠛⠒⠛
⠀⠀⠀⠀⠀⠀⣠⣿⣉⣴⠀⠘⠁⣏⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠀⠙⠶⠯⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠉⠉
⠀⠀⠀⠀⠀⠘⣷⣢⢈⠉⡉⠉⠉⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠙⠻⣿⣿⣿⡿⠋⠀⠀⠉⢿⣿⣿⣿⠿⠋⠉⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠀⠀⢀⠰⠶⣶⣄⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠈⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢹⣷⡄⢠⣾⣿⠟⠉⠑⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣼⠟⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣀⣀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠋⠀⠌⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⢾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠉⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢰⣿⡿⠻⠻⢿⣷⡄⠀⠀⠀⠀⠀⢀⣠⢎⠻⠿⠿⠿⠿⠿⠟⠿⠿⣿⣷⡀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⢸⣿⡇⠀⠀⠈⠁⠀⠄⠀⠀⠐⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢓⣀⡀⠀⠀⣀⡚⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣭⣽⣷⣶⣶⣾⢹⣿⣿⣶⣶⣶⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠈⣻⣛⠃⠀⠀⠀⠉⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⣿⣿⡶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣷⣤⡄⣀⡀⣀⣠⡿⣿⣿⣿⣿⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣯⠏⣿⣽⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢰⣿⢿⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠁⠛⠙⠺⣿⠿⠇⠋⠁⠀⠉⠉⠛⠛⠛⠛⠉⠁⠉⢳⡝⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⢫⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣴⠶⢶⣦⣤⣶⣿⣿⡿⣷⡶⠾⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣤⡶⢶⣦⣴⣶⣶⣶⣤⣄⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⣿⣉⣹⣧⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣙⣻⣿⣷⣤⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣏⡀⠻⡎⠙⠛⠛⠉⠁⠈⠙⢿⣶⡶⣶⠶⠶⠶⠶⠶⠶⠶⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠟⠋⠁⠀⠙⣷⡆⠹⡄⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠸⣷⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⣤⣦⣾⢃⡾⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⣿⣤⣤⣤⣤⣴⣶⢶⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⢼⣏⠛⠿⠷⠶⠶⠶⠶⠶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⣿⠉⣿⣄⣀⣀⣀⣀⣸⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⠛⠦⣍⣛⣛⣛⣉⡭⠞⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢰⡆⠀⠀⠀⠀⠀⢀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⡇⠀⢰⠀⠀⠀⢸⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⣏⠀⢸⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⣿⠀⢸⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⣸⠀⠀⣀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢹⠀⠀⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⠀⠀⡇⠀⣿⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡇⠀⡀⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇⢸⠇⡇⠀⠀⢸⣿⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⢸⡇⢸⠇⠃⠀⠀⠀⣿⠀⠛⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⡇⠸⠀⠀⣤⠀⠀⣿⠀⠀⠰⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣲⣤⣄⡀⢸⡇⠀⠀⠀⡇⠀⠀⣿⠀⢠⡶⣶⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠰⠶⠶⠄⠀⢀⣾⡏⠉⠉⠁⠘⠃⠀⠀⠀⠁⠀⢀⡿⠀⠈⠁⠀⣶⣦⠀⠀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠁⠀⣴⠒⠂⠀⢀⣤⠀⢤⣄⠉⡀⠈⠉⠓⠀⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠛⠀⠀⠿⠀⠀⠀⠈⠀⠹⠦⠀⠀⠀⠈⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣴⣿⣇⠀⠀⢰⡦⠀⢸⣆⣀⣴⣿⣦⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠻⠾⠟⠁⠀⠀⠉⠉⠉⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠙⠿⠟⠙⡟⠻⣟⠻⢹⣻⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣁⣀⣀⠀⠉⠀⠀⢀⡀⣴⠋⠉⠉⠉⣳⡄⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣽⣟⣻⣻⡻⣛⣚⣶⠟⠧⣤⣤⠄⠉⣁⣀⣀⣀⣀⣀⣀⡀⡈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠙⠛⠻⢿⣿⣆⠀⠙⠃⠀⣠⣷⣿⣶⣭⣭⣝⣛⣉⣉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⠋⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠾⠿⠿⢿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠧⠤⠤⣤⣼⢧⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣼⣧⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣒⣻⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠿⠿⢿⣟⠛⣻⣟⣛⣧⣄⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡋⢙⠙⠋⠉⠉⠉⠉⠉⠉⠀⢨
⠀⠀⢠⠠⠤⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠀⠀⣀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠠⠤⠄
⠀⠀⠐⠐⠲⠛⠚⠇⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⠷⣦⣀⡀⠀⠠⣀⡀⠀⠰⢀⠃⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣡⢡⣆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠸⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⢠⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠒⣦⣰⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠸⢀⣀⢠⣄⡇⡇⠀⠀⠀⢀⡀⣢⢼⣮⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣼⡿⡅⢻⡀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⢸⣿⣿⣿⣿⣇⣿⣴⣤⣴⣶⣶⣷⣬⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣖⡂
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠻⣿⣷⣦⡀⠀⢠⣀⡀⠀⠀⠀⣰⡽⠛⠁⠈⠹⣿⣿⣽⣶⣆⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢧⣾⠧⠤⠤⠶⠛⢳
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡬⠿⠷⢒⣒⡓⠠⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡯⣤⣴⣶⣞⣛⣛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⢀⣀⣀⣀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠸⣿⣿⠟⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠆⠀⠀⠀⠀⢙⣿⣿⡀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡀
⠀⠀⠘⡀⠀⠀⠀⠀⢨⣿⣿⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⡆⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⡀⠆⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠙⠉⠉⠉⠁⡉⠉⠋⠉⣿⣿⡏⠉⠉⠉⠁
⠀⠀⢁⡀⠀⠀⠀⠀⠘⣿⣿⡁⠀⠀⠀⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣿⣿⡗
⠀⠀⣄⠁⠀⠀⠀⠀⠀⠻⣿⣿⣶⣷⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡄⠀⠀⣿⣿⣷⢴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠁⠀⠀⢿⣿⠏⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀⠀⠀⠀⡾⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠈⣧⢀⣤⡀⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⠉⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⡄⠀⢺⡟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠀⠀⠀⣷⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡾⠁⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠇⠀⣠⠏⠀⣠⠞⠁⠀⠀⣀⣠⡤⠴⠶⠶⠶⣄⡀⠀⣸⠇
⠀⠀⠀⠀⣀⡴⠞⣻⡽⠿⠛⠛⠛⠛⢦⣄⠀⣿⠀⣴⠋⣠⠞⠁⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠈⠻⠞⠁⠀⠀⢤⣄
⠀⠀⠀⡜⠋⡰⠟⠁⠀⣠⣤⡀⠀⣀⡀⠹⣶⡏⣼⢃⡞⠁⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉
⠀⢠⡾⢠⡞⠀⠀⠀⠘⠷⠞⠁⠐⣯⡷⠀⢻⣿⣷⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⡆⠀⠀⠀⣠⢤⡄⠉
⢀⡾⢁⡿⢁⣀⠀⠀⠀⢀⣠⡤⢤⣀⣀⣀⣸⣿⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⠒⠋
⢸⡇⣾⠁⢿⣽⠇⢠⠞⡉⣴⠞⡿⢻⠋⠉⢹⠏⠉⢉⡹⠛⠛⠒⣲⣦⣤⣄⡀
⣾⠀⡏⠀⠀⠀⢠⣧⢎⡾⠁⡼⠁⢸⠀⢠⡏⠀⣠⠟⠀⢀⡴⠚⠉⢸⠀⠀⠹⣆
⣿⠀⡇⠀⠀⠀⣾⡇⢸⠁⢠⡇⠀⢸⡀⡞⠀⣰⠃⢀⡴⠋⠀⣠⣄⣸⠀⠀⠀⢿
⣿⠀⡇⣠⢤⡀⣿⡇⢸⠀⠘⡀⠀⠈⣿⠀⢠⡇⢀⣾⠀⠀⠀⡇⠀⠁⠀⠀⠀⢸⡇
⢹⡄⣷⠙⠚⠁⠸⣇⠸⡆⠀⡇⠀⢰⠇⠀⣸⢀⡏⠹⢤⡀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠘⣷⠸⣇⠀⠀⠀⠙⠷⣿⣄⣹⣤⡟⠀⠀⣿⡼⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠘⣧⡹⣆⠀⣞⣲⠀⠀⠀⣤⡉⠉⣹⡟⠛⢷⡀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢷⣝⣦⡉⠁⠀⠀⠘⠷⠋⢠⡿⠀⠀⠈⣇⠀⠀⠀⢠⢦⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠉⠻⢿⣦⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⣿⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⡀⠀⠀⠀⢀⣀⡾⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⡀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⡤⠤⠔⠒⠒⢢⠀⠀⠀⠀⡔⠒⠒⠢⠤⢤⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⠂⣶⠒⠒⠖⠒⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠛⠤⠤⠒⢖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠔⠁⠀⠀⠀⠀⠈⠑⠢⠄⣀⣀⣠⠄⢤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢘⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⠴⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡰⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢼⡀⣰⠤⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠉⠑⠒⠒⠂⠐⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠠⠤⡤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⢼⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢆⠀⠀⡔⠐⡄⠀⡸⠀⠀⢰⠀⠈⠉⠁⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢦⡤⡗⠒⠁⠀⡇⠀⠀⢸⠀⠀⠀⡰⢋⠷⠴⠃
⠀⠀⠀⠀⠀⠀⡠⡀⢰⠢⣱⡀⠀⢢⠜⠉⢲⣇⠔⠁⠈⠳⡀⡰⢁⠏⡤⠒⠠⡀
⠀⠀⠀⠀⠀⠈⠢⠊⠈⢣⡈⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠳⠁⠮⠊⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⢤⣀⡀⠀⠀⣀⣀⡤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠉⠉⠙⢳⡄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⢶⣄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣟
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⣠⡴⣶⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣏⡿⠉⠀⠈⠉⣽⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⡴⠛⠁
⢰⠏⠀⡟⠀⠀⠀⠀⠉⠻⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢻⡇⢰⠃⢀⡾⠁⠀⠹⣦⣀⣀⣠⠀⠀⠀⢀⣼⠃
⢸⣄⣰⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⡾⢿⠀⠈⠀⠀⢀⣾⠁⠀⠀⠀⠀⠉⠉⠙⠳⠶⠖⠋⠁⠀⠀⠀⠀⠀⣿⠛⢦
⠀⠉⠉⠀⠀⠀⠀⢀⣀⠈⠻⢦⣄⣀⣤⡾⠛⠛⠋⠉⠉⠉⠀⢸⡇⠀⡔⠀⣼⠃⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⢻⣄⣼
⠀⠀⠀⠀⠀⠀⢰⡟⣯⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠁⢰⠇⠀⠀⠀⠀⢹⡉⢳⡄⠀⠀⠀⠀⣿⠉⠻⣆⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⣠⠇⠀⠀⠀⠀⠙⠷⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠔⢸⠇⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡟⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣼⣧⣤⣼⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠛⠒⠦⢤⣄⣀⣀⡀⣰⠃⠀⠀⠀⠀⠀⠘⣦⣀⣀⣀⣤⠤⠖⠛⠉⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⢀⣀⣤⠴⠖⠚⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠙⠓⠲⠤⣤⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⠓⡦⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠶⠶⠶⠶⠶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⢾⢿⠥⡤⡤⣤⣤⣤⣤⣤⣽⡶⡦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠛⠚⠒⠶⠶⠶⠶⠶⠷⠾⠶⠶⠷⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⡶⠒⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣰⠏⠀⠀⠀⠈⢳⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⣿⠀⠀⠀⠀⢠⡏⠀⢠⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠛⠒⠲⠶⠤⢤⣄⣀⡀
⢸⡇⠀⠀⠀⠀⣼⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠸⡇⠀⠀⠀⠀⢿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⣿⠀⠀⠀⠀⢸⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⢹⡄⠀⠀⠀⠀⢧⣀⣀⣷⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢻⣄⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⠤⣤⣄⣀⣀⣀⣠⣤⠤⠶⠖⠚⠛⠛⠛⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠓⠦⣤⣀⣀⣀⣀⣀⣀⣤⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣤⣤⣤⣤⡴⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢠⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⣿⡇⠀⢸⣿⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠀⠈⠉⠁⠀⣿⡇⠀⢸⣿⠀⠈⠉⠁⠀⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⡇⠀⢸⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡇⠀⢸⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠀⢀⣀⡀⠀⣿⡇⠀⢸⣿⠀⢀⣀⡀⠀⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⣿⡇⠀⢸⣿⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⠶⠞⠓⠶⠶⠟⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⢀⡞⠁
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⢰⡇⣀⣀⣤⣤⣄⣀⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠦⠶⠶⠖⠛⠉
⠀⠀⢸⣏⠉⠀⠀⠀⠀⠈⢉⣿
⠀⠀⠀⠉⠙⠛⠒⠒⠚⠛⠋⠁
⠀⠀⠀⠀⠀⣠⠞⠙⢧⡀
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠻⣄
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠘⣦
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠙⠶⢤⣀⣀⣀⣀⣠⡤⠞⠁
⣶⣶⡶⠶⠶⠾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢄⡀⠀⠀⠀⡾⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠸⣇⣀⣀⡈⠳⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠙⠉⢈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠀⠀⢶⡶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠟⠀⠀⠈⢧⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣴⠟⠁⠀⠀⣀⣤⠴⠒⠛⠉⠉⠉⠉⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⡞⠁⠀⣠⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠋⠀⣠⠞⠁⠀⠀⢀⣀⣀⠤⠶⠶⢦⣄⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣠⠤⠛⠃⠤⠍⠛⠛⠻⢶⣄⠀⢸⡇⢀⡼⠃⣰⠟⠁⢀⣠⠴⠛⠉⠉⠀⠀⠀⠀⠀⠉⠳⠴⠋⠀⠀⢠⣄⡀
⠀⠀⠀⡴⠋⢁⡔⠉⠁⢠⣤⡀⠀⠀⡀⠙⢷⣼⠃⣾⢡⠞⠁⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⢳
⠀⢀⡾⠁⡰⠋⠀⠀⠀⠂⣠⠃⠀⣾⢉⠀⠸⣿⣿⡿⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄⠀⠀⠀⢀⣤⡌⠛⠞
⠀⡼⠁⡸⠃⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⡟⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠙⠶⠟
⠸⠇⢀⠃⠘⣁⡆⠀⡤⠚⣡⣬⢭⢿⡿⠛⠛⡿⠛⠛⢛⡷⠾⠲⢤⣤⣤⡄⣀
⡆⠀⣨⠀⠀⠉⠀⡸⠄⢠⠋⢠⠎⠀⠁⠀⠸⠃⠀⣰⠏⠁⢀⡤⠖⠉⢹⠀⠉⢷⡄
⣷⠀⠛⠀⠀⠀⢠⡿⠀⡇⠀⡆⠀⠀⡆⢠⠀⠀⣴⠁⢀⡴⠃⠀⢀⡀⢸⠀⠀⠀⣿
⡿⠀⣶⠀⣀⠀⢸⡇⠀⠁⠀⡇⠀⠀⢳⡞⠀⠸⠁⢠⡎⠀⠀⠸⠀⠘⠁⠀⠀⠀⢸⡆
⢇⠀⠘⠀⠤⠁⠸⣧⠀⡇⠀⠇⠀⠀⡜⠁⠀⡇⢠⠛⢇⡀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⡇⠀⡆⠀⠀⠀⠻⣦⣴⣆⢐⣆⣠⠃⠀⠀⣧⠈⠀⠀⠹⠀⠘⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣆⠰⡆⠀⡠⢆⠀⠈⠉⠉⠙⠛⠰⣶⠾⢿⡄⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⣦⡘⣀⠁⠛⠀⠀⠀⢟⠰⠀⣸⡏⠀⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠈⠻⢷⣶⣄⡀⠀⠀⢀⣀⡼⠋⠀⠀⠀⠘⡆⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠓⠋⠉⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⠶⠶⠶⠶⠶⠶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠻⠿⠏⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⢠⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⠀⣀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠙⢷⡀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠙⢷⣤⣤⣤⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣶⣦⣤⣶⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢀⣿⠁⢀⡴⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣦⡀⠈⣿
⠀⠀⠀⠀⠀⢸⡇⢀⣾⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⣷⡀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠸⣇⣸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⠁