Light year Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡉⠉⠉⠁⠲⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⠤⠚⠛⠋⠑⠛⠂⠠⣀⠈⠙⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⡤⠊⠁⠈⠓⣄⠤⠐⠊⢋⠐⠙⠶⠀⠀⠀⠀⠒⢂⠸⡇⠐⠒⠠⠄⣈⠷⠒⢤⣀⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠐⠋⠁⣀⡠⠆⠛⠖⢤⡔⠀⢸⢣⡴⠖⠾⡇⢰⠀⠀⠀⠀⠸⠓⣦⡀⢏⠙⡆
⠀⠀⠀⢀⠏⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠰⠈⠒⢪⠁⠈⠢⠅⠂⠀⠂⣼⠁⠁⢀⡀⠚⠆⢘⡇⢸⡃⣾
⠀⠀⠀⣌⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢰⡆⠀⠀⠒⠀⠐⠀⣠⠂⠀⢠⢰⠀⠀⠀⠈⠄⠀⠙⡞⡿⠃⢙⡓⢦⣀
⠀⢀⡼⠃⡠⢴⡊⠀⠀⡀⠄⠀⢀⠀⢺⠀⠀⠀⠩⠤⠄⠉⠁⠀⠀⢸⠀⠀⠀⠀⡠⠛⠒⠀⡾⠁⡀⠈⡇⠀⠈⠳⣄⡀
⠀⣾⠁⢀⠓⠀⠙⣆⠀⠀⠀⠔⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠛⠀⢠⠁⠀⣠⠞⠴⠁⠀⠀⡇⠀⠀⠀⠀⣹⣄
⠀⣿⣴⠫⡉⢳⡄⠘⡀⠀⠀⢄⠀⠀⠘⢧⡀⠀⠀⠃⠀⠀⠀⣀⣴⠋⠄⠀⠘⢃⣤⢞⡡⠀⠀⡠⠂⠀⡟⠒⠒⠒⠈⠁⠈⠳⣄
⠀⠸⣧⠀⢱⡔⠛⢤⣥⡀⠀⠀⠉⠒⠀⢀⡉⠴⠶⠶⠶⠄⠩⠈⣀⡀⣤⠴⠛⠁⠰⠀⠀⠀⠊⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⡸⠋
⠀⠀⠹⣆⣸⣄⡀⠀⠈⠛⢶⠶⠤⣤⣤⣶⣀⣤⣤⣤⣤⠴⠶⠾⠉⠁⠀⠀⠀⠀⠀⠁⠈⢀⠤⢤⠀⣸⢧⣀⣤⠤⠀⣀⢪⡑⢸
⠀⠀⢠⡿⠿⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⡠⠁⡀⠈⠁⢂⠀⢀⣟⡘⠀⠀⠒⠂⠈⠁⣠⡟
⠀⣴⠋⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⢀⣠⡤⢶⡐⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⡘⢀⠾⢿⡇⢀⠠⠀⠀⠀⢠⡟
⠀⣯⣤⠒⠒⡶⠀⠠⠌⣿⣿⠳⣔⡀⠀⠀⠀⣼⠀⢨⠉⠉⢉⡷⢤⠠⠀⠀⠀⠀⡀⠙⠒⢀⣠⠎⠠⣿⠉⠀⠀⠀⠀⢠⠏
⣼⠋⠀⠀⢸⡇⠀⠀⠀⠘⡏⠀⠈⠑⠠⣀⣠⢻⡀⢠⡄⠀⠀⢡⣀⡄⠃⠀⣀⠀⠁⠘⠛⠉⢉⡴⠃⣿⠀⠀⠀⠀⣰⠃
⢇⠀⣄⡀⢸⠃⠀⠀⠀⠀⠛⠀⢀⣀⠠⢬⡏⠀⣧⠀⠁⠀⠀⣴⣩⠇⠐⠈⠀⠀⢀⣠⣶⡔⠋⢀⡤⠛⠂⠀⠀⠘⢣
⠘⣶⠀⠳⠌⠀⠀⢀⣤⠶⠚⠛⠋⠀⠀⠀⡃⠀⠋⠀⢈⣠⢠⡟⣠⣴⠶⠆⠀⠀⠀⠡⣿⡇⢀⠏⠀⠀⠠⠀⠀⠀⠠⡇
⠀⣿⠈⠀⠀⢀⠞⠁⠀⠀⠈⠠⡠⠀⠀⠀⠐⢄⣀⠴⣊⣥⣶⣿⡟⠋⠁⠀⠀⠀⠀⢲⣿⡁⠀⢲⡉⠄⠀⣀⡤⠤⣀⡽
⠀⢸⡆⠀⠀⡆⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⣠⠞⠁⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠛⢋⠱⠃⠀⠈⠳⣤⡄⠴⠖⠛
⠀⠀⠛⢶⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠈⢉⠁⠀⠀⠀⠀⠀⠀⠐⡒⠀⠀⢁⠠⢼⠃
⠀⠀⠀⠀⠑⢧⡀⠀⠀⠈⠒⠀⣠⡴⢋⡟⠈⠒⣄⠈⠰⠄⠀⡄⠀⠀⠈⠁⠀⠀⠀⢤⡞
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣠⡴⠋⠀⣸⠃⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡏⠁⠈⢻⠀⠀⠀⠀⠀⢀⡤⢼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠋⢂⠀⠀⡆⠀⠀⠀⢰⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠘⠀⠘⢳⠄⢣⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⣀⣀⣀⣀⡤⠃⠀⡇⢸⠄⠘⣤⢋⡠⢇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣌⠋⠀⠈⠉⠀⠀⠀⠷⣾⠀⠀⡼⠋⠀⠈⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡉⠤⠀⢀⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠐⠂⠀⠀⠀⡤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⡠⠔⠃⠀⢸⠀⠀⠀⠀⠀⣀⡠⠤⠀⠠⠤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠦⣀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠉⠀⠀⠀⣀⠠⠤⠀⣠⡴⠤⠤⠿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡠⠂⠉⠀⠀⠠⠋⠡⠐⠂⠀⠀⠐⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣨⠁⠀⠀⠀⣠⠟⠡⠂⠀⠀⠀⠀⠀⠀⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡈⠻⠂⠀⠠⠤⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣬⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⡎⠁⠉⠀⡀⠀⠀⠀⣀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⡀⠀⠀⠀⠀⣀⡴⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠛⠒⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣶⡶⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠈⠻⣦⡀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠹⣦
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘
⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠤⠤⢤⣤⣤⣤⣤⣤⠤⠤⠶⠦⣤⣀⠀⠀⠙⣧⠀⢀⡜⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣿⣧⡀⠀⠘⣷⡯⠶⠖⠚⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠶⣦⣈⢷⡀
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢶⣄⣀⠀⠀⠠⡀⠤⢞⡫⠵⠒⠦⣈⣿⡿⣧⠀⠀⢹⡆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠳⢦⣄⠀⠙⢿⣷
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⢸⠇⠀⠀⠉⣿⣿⡄⠀⢰⠁⠊⣷⢷⠀⠘⡟⠃⢹⡄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠈⣿
⠀⣼⠁⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠈⠓⢾⠀⢆⠀⠈⠈⣁⡟⠀⠈⡀⠀⠀⠁⠀⣠⠇⠀⠈⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏
⠀⡿⠀⠀⠀⢀⡤⠚⢱⠏⠀⠀⣀⣤⠶⠚⣿⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⠈⢻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡾⢁
⢸⡇⢀⣤⡾⠋⠀⠀⣿⢀⡴⠋⡿⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠤⠶⠒⠒⠶⢦⣄⠀⠀⠀⠀⣠⠏⣠⠟⢁⡞
⣸⡷⠋⡰⠁⠀⠀⢠⣇⡾⠁⢸⠃⠀⠀⢸⠸⡄⠀⠀⠀⠀⢧⣀⣀⣀⡀⠇⠀⢀⡀⠀⡀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠞⣡⡾⠋⢀⡞
⢹⡇⢀⠇⠀⠀⢀⡞⢸⠇⠀⠸⠀⠀⢀⣼⡤⣇⠠⠛⠁⢀⡀⠀⠀⠀⣀⣠⠴⣺⠃⠈⠉⠃⠀⠀⠀⠀⣿⣧⣀⡀⠀⠀⠀⠀⠀⣠⠞⣡⡾⠋⠀⣰⠋⠀⣰
⠸⡇⢸⠀⠀⢠⠟⠀⢹⡄⠀⠈⠄⢠⢞⡜⠁⢻⠀⠀⠀⠈⣷⣀⠀⠀⠀⣀⢴⠅⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⠈⠉⠳⠶⣤⡴⢊⣴⠞⠁⠀⢠⠞⠁⠀⣴⠋
⠀⣿⢸⡀⠀⣏⠀⠀⠈⠻⣄⡀⢠⢏⡞⠀⠀⢸⡇⠀⠀⠀⠈⠓⠪⠭⠭⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣠⡴⠶⠶⠾⠿⣯⣀⠀⠀⡴⠋⠀⢀⡼⠁
⠀⢹⡄⠳⣄⠈⢀⣀⣀⣠⣬⣽⢏⡾⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⢋⡥⠖⠚⠛⠛⠒⠀⠙⢷⡟⠁⠀⣠⠞
⠒⠚⣷⠚⠛⠋⠉⠉⠉⠀⢀⡞⣼⠁⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⡠⠋⠀⠀⢀⣤⣤⣤⣄⣀⡼⠁⢀⠔⠁
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣼⢹⠇⠀⠀⠀⠀⣰⠏⠙⣦⡀⠀⢰⣀⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡟⠀⠁⠀⠀⣴⠋⠁⠀⠀⠈⠻⣦⠈⢹⠀⠀⠀⠀⣀⣤
⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣯⡿⠀⠀⠀⠀⣰⠏⢀⡞⠈⠛⢦⣄⣀⠉⠀⠀⠀⠀⣀⣠⡴⠟⠁⢸⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡷⣬⣤⡴⠖⠛⠉⠁
⠀⠀⠀⠀⠹⣆⠀⠀⠀⢸⣿⠃⠀⠀⠀⢰⠏⠀⡜⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠀⣠⣴⡾⢻⠀⢀⡤⠖⠻⣇⠀⠀⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⠉⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⡴⢠⢀⠀⠐⠉⣐⠀⠀⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠋⠑⠪⠀⠐⠂⠋⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⣉⡀⠲⣦⠄⠀⠀⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠣⢄⣁⣀⣀⡶⠤⠃⠑⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⠀⢷⢤⣈⠢⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠞⣀⠤⡼⠉⡷⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠉⠙⣇⢈⡀⠀⠑⠢⢭⢛⣒⠭⠄⠀⠀⡀⠀⠠⠦⢯⣒⠻⠭⠔⠊⠀⢠⠅⣸⠃⠙⡤⣀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡄⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠰⠀⠈⢆
⠀⠀⠀⠀⢀⡴⠊⠣⡀⠀⢱⠀⢨⠙⡀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⢊⠁⢠⠃⠀⣠⠞⠢⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠈⠢⡀⠣⠀⡀⢡⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡀⠤⠔⠁⠀⠀⠀⠀⠀⠀⢀⠎⡘⢀⠆⡤⠊⠁⠀⠀⠈⢦⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⠟⠙⠓⡄⠱⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠄⠋⡠⠓⠚⣏⠀⠀⠀⠀⠀⠀⠀⢙
⠀⢠⠞⠲⢤⠤⠤⣀⡠⠔⠁⠀⠀⠀⠘⡆⠀⠀⠈⠑⠲⠀⠤⠰⠊⠉⠲⠠⠄⠐⠒⠉⠁⠀⠀⡞⠀⠀⠀⠈⠢⣄⡀⣀⣀⣀⡠⢏
⠀⡸⠤⠒⠲⣄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⣀⣀⣈⡆
⠫⣀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠳⠒⣶⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⢿⠑⠲⠃⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠈⠑
⠀⠙⢌⠉⠁⠒⠒⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⠠⠤⠤⠄⠠⠤⠤⠤⢀⠒⢒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠠⠤⠤⠐⣲⠋
⠀⠀⠈⢣⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⣈⠛⡟⠁⠘⠒⠒⠒⠶⠏⠉⡀⢺⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠑⠄⣤⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢮⡉⠒⠫⠄⠶⣆⠼⠓⠊⣩⠴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠘⡆⠘⠒⠤⡀⠀⠀⠀⠀⠀⢸⠀⠀⢹⢆⡀⠀⠀⠀⠀⣠⢾⠁⠀⠈⡆⠀⠀⠀⠀⠀⣀⠤⠜⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⢱⠀⢠⠤⡈⢢⡤⢤⠀⠀⠸⠀⠀⢸⠀⠱⡄⠀⢀⡜⠁⢸⠀⠀⠀⡇⠀⢀⣀⣠⠎⠀⣀⠆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⡉⠙⢚⡵⠋⠀⠀⠀⠀⠀⢸⠀⠀⢘⠒⠚⠃⠀⢸⠀⠀⠀⠃⠀⠘⠦⣥⡾⠜⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠤⢸⠢⠄⣸⠀⠀⡟⢀⠼⡦⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠃⠀⢸⠀⠀⢻⠀⠀⠸⠁⠀⡆⠀⠙⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢀⠘⠀⠀⠀⡀⠀⡇⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢼⠖⠁⠠⠀⠀⡇⠈⠲⡷⠞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠰⠀⠀⡇⠀⠀⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⣅⠀⡅⠀⠀⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠒⠺⠒⠒⠚⢫⡜⠓⠒⠒⢺⠒⠒⠒⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠂⠀⠺⠀⠀⢲⣤⢧⣠⡖⠂⠘⠤⠔⠲⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⡀⠀⢀⡄⠀⡬⢀⣀⡀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠁⠀⠀⠈⠉⠲⣷⢰⡟⠁⠀⠀⠀⠉⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣒⠂⠤⠤⠔⢒⡡⠏⠈⠭⡒⠠⠤⠤⠤⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠄⠀⠀⠀⠀⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡀⢊⣁⠐⢀⣉⠢⡁⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠡⠀⠿⠆⠿⠏⠰⠑⡀⠀⠀⢰
⠀⠀⢀⢒⠄⠤⡤⠤⠄⠀⢤⠀⢴⠊⢢⡠⡅⡀⠀⠀⠀⠀⠀⠀⡀⣤⣠⠒⡶⠄⠤⠄⠤⠤⠄⡤⠄⢄⢂
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁⡜⣆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠨⣀⠇⡆⠀⠀⠀⠀⠈⠀⠀⠋⠈
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⣇⠀⠘⡐⡃⠈⣄⠀⠀⠀⠀⢀⢀⡜⠀⢒⡘⠀⢀⡋⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠐⠄⠑⠢⠀⠀⠀⠀⢀⡀⢂⠀⠀⠀⠉⠀⠒⠀⠀⠀⠐⠀⢂⠈⠀⠀⢀⠀⡁⠀⠀⠀⢀⠠⠂⠉⠜
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠎⠃⠀⠡⡀⠀⠀⠀⠀⠑⠠⠀⠁⠠⠀⠀⠀⡠⠁⠠⠉⢄⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⢢⠬⢗⠂⠤⡀⡀⠤⢀⡀⠠⠤⢒⠮⢤⠂⠁⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⢀⠊⠂⢄⢣⡀⠀⡀⠄⠠⡀⠀⣠⢃⠔⠊⢂⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⢠⠃⡀⠑⠀⠤⠌⢡⠀⠀⠈⢳⠀⣀⣀⣀⡈⠰⠋⠀⠀⢠⠉⠤⠄⠐⠁⠀⢃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡈⠠⣀⠀⢀⠠⠊⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠢⡀⠔⠂⢀⡠⠉⠡⣀⠄⠒⠄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠈⢁⠀⠀⠉⠀⠀⠓⢁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠁⠆⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠆⠙⠃⠀⠀⠀⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣊⠌⠁⣀⠐⠂⡀⠀⠀⡀⠂⠈⣁⠁⢌⡀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢡⠴⠃⠀⠀⠇⢤⠁⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠀⠀⠀⠁⠥⠂⠀⠀⠀⠀⠢⠅⠀⠀⠀⠀⠨⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⢠⣿⡟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢀⡟⢉⣵⡟⠻⠉⢛⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⣤⣤⣤⡌⠀⣋⣀⠈⠁⠀⠀⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣤⣶⣾⣿⠿⠟⠋⠉⠁⢰⡇⠀⠈⠁⠀⠀⠀⠀⣾⡯⠤⠄⠙⠛⣿⣿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢻⣿⣿⣿⣋⣤⣴⣒⠛⣀⢀⡌⠁⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⣀⣀⣀⣹⣿⢸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣧⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣼⣿⣭⣾⣿⣿⣿⣿⣿⣥⣾⣿⣷⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣟⣩⣾⣿⣿⣿⢟⣉⣿⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣹⣿⣿⣿⣿⣿⠿⣿⣝⣛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣾⡿⢿⣿⣿⣿⢻⡜⠋⠉⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣽⣿⡿⣷⡈⢻⡟⠛⠛⠻⠿⠛⠛⠛⠛⠛⢧⡴⠻⠏⡱⣾⢿⣹⣿⠀⠀⢀⣤⣶⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠃⠀⠀⠈⠻⣿⣷⡘⣮⣻⣆⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠰⠛⡏⣱⠏⠀⠀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠠⡿⣿⣯⠈⠻⡟⣧⠀⠀⢾⠀⠠⣿⠂⣴⠁⠀⠀⠀⠉⠁⠀⢹⣧⠀⠀⠀⠀⢹⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⣶⡶⢶⠖⠠⠀⢹⣿⠀⠀⠙⢿⣧⡀⠈⠁⠀⠟⠰⠿⠦⠀⠀⠀⠀⠀⢀⣴⠟⠶⠶⣦⣴⣾⣟⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢁⡄⢠⡿⠀⠈⢸⠟⠀⠀⠀⠀⠙⠿⢿⣶⣶⣤⣤⣤⣤⣤⣤⣤⠤⠘⠛⠁⠀⠀⠀⠀⠀⠻⣿⣿⠏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⣷⡿⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⣃⠛⣀⠀⠀⣸⡇⡀⠀⠀⠀⠀⣠⣾⡿⠛⢁⠈⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣻⣷⣶⣦⣄⣰⣿⣶⠶⢤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⣠⣀⣼⡋⠀⠈⠀⣀⣠⡾⠏⠉⠀⡰⠋⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠋⠁⠀⠀⠀⣬⠿⣦⡈⢻⣿⣿⣷⣶⠶⠟⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠃⢢⠄⠶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡰⠚⠛⠋⠙⠀⠀⠉⡿⣦⡉⠛⠻⠷⠖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⢠⠞⢠⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠤⠴⠶⠶⠾⠗⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠒⠂⠂⠀⠀⠒⠒⠀⠀⠸⣶⡾⣿⡿⠟⠛⢯⣔⠁⠈⠉⠀⠀⠀⣴⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡟⠀⣿⠁⠀⠀⠂⠈⠳⣦⡀⠀⠀⠀⣰⠟⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡏⣀⢀⡨⠀⠀⠀⠀⠀⠀⢿⣷⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠛⡧⠀⠀⠀⠀⠀⠀⢸⣯⣴⣿⣿⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⣿⣀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠹⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⡤⠀⠀⠀⡾⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠏⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢠⣾⡟⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⣿⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡀⢀⡖⠁⠀⠐⠒⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠄⠀⠂⠈⠁⠀⠀⠀⠀⢐⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡀⠀⢠⣿⠗⠀⢀⡤⠀⠈⠁⠀⠀⠐⡷
⠀⠠⣄⣤⣤⣤⣄⣀⣀⣀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⡿⠏⠀⠀⠀⢈⣏⠀⠀⠀⠀⠘⣧⠀⢾⣝⠀⠀⢰⠀⢀⣀⠠⠤⣤⣤⣧
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⢳⣿⣷⣶⡶⠶⠚⠛⠛⠓⠒⠶⢤⣤⣿⠀⣼⠋⠀⠀⠘⠛⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡷⠖⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡴⣦⣴⡎⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡤⠶⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢛⣠⢿⠯⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣀⣀⣀⡘⠑⠊⠉⠂⠀⠈⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⣤⣶⣶⡿⠟⠛⠉⢩⡇⠀⠉⠁⠀⠀⠀⣿⡏⠉⠙⠛⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⣿⣿⣫⣤⣶⣒⣂⣀⡌⠁⠀⠀⠀⠀⠀⣰⣿⣆⣀⣀⣀⣹⣇⣹⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⢿⣿⣿⣿⣿⣿⠿⣷⡀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠴⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣛⣻⣯⣴⣿⣿⡿⣿⠦⠿⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣿⣿⣿⣿⣿⡉⢷⣾⣮⣭⣽⣿⣿⣿⣿⣿⡟⣩⣿⠏⣹⣿⢿⡧⠘⠀⠀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠏⠉⠙⠿⣿⣯⠻⣻⣦⠙⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠘⡽⡿⢫⠇⠀⢠⣾⣿⣧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣽⣿⣇⠙⢿⢧⠀⠀⣔⠀⢰⡆⣠⠂⠀⠀⠐⠒⠐⠱⣏⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣶⠶⠶⠠⠀⢸⣿⠀⠈⠻⣷⣀⠈⠀⠘⠃⠿⠧⠀⠀⠀⠀⢀⣤⠟⠶⠶⣤⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣠⢀⡼⠁⠈⢹⠋⠀⠀⠀⠈⠛⢻⣶⣶⣦⣤⠤⠤⠤⠤⠔⠛⠁⠀⠀⠀⠀⠘⢿⡿⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡿⡼⠃⠀⠀⣏⠀⠀⠀⠀⠀⢀⣾⣿⠛⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡔⠂⠀⡼⠃⠀⠀⠀⢀⣴⠿⠋⢀⠆⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⠉⠓⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠾⠛⠉⠋⢛⣧⣄⠰⣶⣾⣿⣤⣤⡴⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣠⠴⠒⠒⠊⠁⠛⣧⣌⠻⠿⣿⡵⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⢠⠞⢰⣿⣿⣿⣿⠿⡿⢿⣿⠿⠿⠿⢿⣿⣧⠴⠶⠶⠒⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠉⠁⠀⠀⣻⠟⣿⠟⠉⠙⠾⣅⠀⠀⠀⠀⠐⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⠏⠠⠏⠀⠀⠀⠀⠈⣷⡄⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣷⣴⠶⡆⠀⠀⠀⠀⠀⢹⣇⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⡇⠀⠀⠀⠀⠀⡜⠉⠙⢿⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠃⠀⠀⠘⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣠⠄⠀⠀⡼⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⢲⡇⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⣾⡟⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠙⣶⠿⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢠⠄⢼⠉⠀⠉⠙⠓⠒⠒⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠒⠀⠀⠀⡀⠀⣀⡀⢠⣧⠀⠀⠀⢰⡆⠀⠀⠀⢠⡄⠀⣾⡏⠀⠰⠂⠀⠀⠀⠀⠀⡇
⠀⠉⢲⣿⣿⣷⣶⡶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣉⣀⣤⣤⠼⠦⣀⣀⡀⢀⡇⠈⣿⠆⠀⠸⣤⠒⠂⠉⠹⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⠀⠠⠀⠀⠀⠀⠈⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⣠⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠝⠉⢀⣀⠀⠤⠤⠤⠤⠤⢀⡀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠔⠀⠀⠀⣿⡉⠁⠀⢀⣀⣀⣠⣤⡉⠳⡀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠠⠁⠀⠀⠀⠀⡈⠃⢴⡆⡈⠉⢉⣉⡈⣿⠀⢸⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡀⠁⠀⠀⠀⠀⣔⠉⠢⡶⠀⢆⠀⠀⣘⠃⢈⢣⠊⠆⠀⠀⠀⠀⠘⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠰⠀⠀⠀⠀⠀⢠⠇⡀⠀⠁⠄⠄⠈⠉⠀⠀⠸⠠⢀⠆⠀⠀⠀⠀⠀⢡⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣄⠀⠀⠀⠀⢠⠃⠀⠠⠀⠀⠀⡄⠰⠀⠀⠀⠀⡆⡁⠀⠀⠀⠀⠀⠀⠈⡄⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠀⠬⣄⠀⠀⠀⢸⠀⠀⠀⠉⠒⠈⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⠤⣀⠃⢰⠀⠐⠂⠠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠓⢢⠀⠀⠀⠀⡠⠒⡟⢨⣇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⢀⡾⠁⠔⣡⢊⣅⢀⠁⠈⠁⠀⣀⣤⡜⣷⣄⡀⠀⠀⠀⠀⢀⣠⠞⠀⠀⡄⠨⠄⢀⣀⣀⢣⠖⠁⠎⠉⠛⠶⡄⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠣⠈⠘⠦⢀⣤⠊⠁⡠⠖⠳⢈⣉⡛⠓⠒⢚⣋⣁⠠⠤⠀⣳⠖⢋⡩⠍⠸⣇⣠⡤⠛⠴⡋⢀⡇⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡾⠀⠀⠀⢂⠀⠀⡱⠂⠀⠀⠤⠌⣉⡁⠒⠒⠒⠒⠐⣐⣒⣒⠒⠒⠒⠂⠈⠉⢥⡤⠔⠂⢉⣀⠤⠘⠇⠀⡦⡈⢧⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⠁⠀⠠⠀⠄⠀⡠⢀⠋⢀⠐⠒⠒⠀⠒⠒⠒⠆⠀⠀⢀⠔⠉⠀⡠⠖⠉⣀⣠⣤⣵⣚⠤⢁⡞⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠘⡇⠀⠃⡄⠀⠄⢣⠀⠠⠀⠀⠀⢈⡰⠁⠀⢀⡀⠀⢀⡀⢀⠀⠈⠀⠀⠜⠁⠀⡠⠊⣠⡴⠛⠉⠀⠀⠈⠉⠳⠞⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠑⡤⠄⠒⠀⠉⠀⠀⢀⠋⠀⠀⠀⡅⠀⠁⠀⠀⠀⠀⡠⠊⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠀⣠⡁⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⡠⠁⠀⠀⠀⠀⣀⠜⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠙⠶⣤⣄⣀⣀⣀⠀⠈⠉⠁⠀⠀⠀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⣀⠀⠀⢀⣄⠀⢀⢀⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠊⠉⠉⠉⠁⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⡔⠈⠁⠀⠠⡞⠒⠤⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢾⠦⣭⠼⠁⡄⣠⠰⠇⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠆⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠚⠁⠘⢤⣤⠄⢀⠁⢀⡤⠔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⢄⣈⣀⢀⣀⣦⡤⠜⠀⠓⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡏⠹⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⢉⡼⠁⢀⣀⡞⠛⣦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠸⣧⠀⠇⠈⠑⠢⣍⡒⢤⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⣀⠠⠤⣤⣤⡤⠔⣉⠤⠚⠁⡸⠁⣰⠅⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⠀⠀⢹⡆⠸⠀⠀⠀⠀⠉⠒⠠⠶⣚⡓⠀⠀⠀⠀⠀⠀⠉⢛⡓⠶⠄⠒⠊⠁⠀⠀⢠⠃⢀⡿⠀⠀⠟⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⡇⠀⠀⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡸⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⡀⠀⠰⠀⠀⡇⢣⠀⠀⡀⠀⠀⠀⠀⠠⠀⢻⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣉⠀⢠⠃⠀⢀⡴⠛⠦⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⢳⡀⢠⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⢀⡀⢀⠤⠞⠁⠀⠂⠀⠀⠀⠀⠀⠀⡼⠁⠇⢀⠆⣠⠔⠉⠀⠀⠀⠈⢦⡀
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠟⠾⢄⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠼⠁⡸⣤⢾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⢀⣧⣀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢣⡀⠈⠑⠒⠢⣄⣀⡀⠀⠀⣀⡨⠧⣀⠀⠀⠀⣀⣀⡤⠴⠒⠉⠀⢠⠋⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⢠⠏⠀⠉⠛⠓⠚⢲⠤⠚⠁⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠈⠳⠤⡤⠤⠤⠤⠄⠛⠦
⣀⡼⠗⠊⠉⠙⢦⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡤⠤⢤⢤⣸⡀
⠣⣄⡀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠻⡯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠍⢽⡏⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠈⢙
⠀⠙⢆⠉⠉⠑⠒⠒⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣠⠤⠤⠤⠤⠄⢠⠤⣤⣤⠤⠤⠴⠒⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⣀⡠⣤⠄⠒⡶⠋
⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠋⠵⠶⣖⣒⣒⣢⣤⣤⣤⣤⣴⣛⡓⠩⠭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠉⠁⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠙⣄⠀⠀⣀⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠒⢤⣛⣠⠤⢀⣀⡀⠠⣤⣃⣤⠤⢒⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠈⠓⠾⡉⠉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠑⣄⠈⠁⠚⠊⠛⠧⠚⠂⠉⣀⠖⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⣲⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠘⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠓⣄⠀⠀⠀⠀⠀⣠⠜⢫⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⠤⣀⠙⢦⠤⢤⡀⠀⠀⠇⠀⠀⢸⠀⠈⢣⡀⠀⠀⡰⠁⠀⢿⠀⠀⠀⢸⠀⠀⣀⣀⣀⡔⠁⠀⣀⠆⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣸⠃⠙⠧⢚⡴⠋⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⢱⠖⠺⠇⠀⠀⢸⠀⠀⠀⠸⠀⠀⠙⢤⣙⣠⣯⠽⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠉⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⢰⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠉⠛⠠⠆⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⡄⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡔⠋⢸⠉⠑⢤⡇⠀⠀⢸⣀⠖⠛⠛⠒⢤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠁⠀⢸⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⡇⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡀⠇⠀⠀⠘⢀⠀⠀⡇⠀⣠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢦⣼⡤⠚⠁⢀⠀⠀⢸⠀⠑⢤⣧⠴⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⢸⠀⠀⠀⢸⣦⠀⡼⠀⠀⠀⣃⠀⠀⠀⢘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠉⢹⠉⠉⠉⠉⢱⡆⠋⠉⠉⠉⢻⠉⠉⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠂⠀⠺⠂⠀⠒⢲⣸⠇⣀⡴⠒⠂⠚⠦⠴⠒⢲⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠤⠔⠚⠛⠓⠲⠤⣸⡧⠀⣿⠖⠛⠛⠃⠙⠓⠦⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⢀⣠⠜⡷⠀⡿⣄⡀⠀⠀⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢍⣉⣉⣛⣋⡉⠴⠞⠁⠀⠘⠢⠍⢂⣘⣓⣓⠺⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡴⣁⡀⢀⠱⡄⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠁⠜⠁⠤⠐⡳⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⠁⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢧⠀⢀⠀⢀⠠⢆⠀⠀⠉⠀⢀⠀⠀⠀⠑⠤⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡞⢰⠈⡆⠘⡀⠻⡀⠀⠀⠀⠀⠐⠉⠉⡇⠂⡠⠀⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠰⡄⠀⡇⢸⡀⠈⠢⣌⠢⢌⡢⠅⠀⣀⣨⠞⢋⡠⢞⡠⠊⢀⢯⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣲⢇⣘⣇⠀⢀⠀⠉⢢⠈⠉⠀⠀⡠⠛⠑⠀⠁⠀⢠⠏⡈⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠸⠄⠄⣤⢾⠁⠀⠀⠘⣦⠘⠀⠀⢎⠀⠀⠀⡈⠀⠀⠀⠀⠀⡠⡏⠀⡇⡠⠊⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠂⠀⠁⢀⠷⡀⠀⢆⠈⠓⢥⣈⠀⠈⡇⠈⠁⠀⠀⢀⡠⠚⢰⠃⠒⠙⢧⣀⠀⠀⠀⡼⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢌⡁⠀⡸⠠⢤⠑⣦⢄⣈⠉⠉⠑⠒⠒⠒⠊⠉⠀⣠⠇⠀⠀⠀⡠⠜⠻⠍⡉⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⡄⡧⡀⠀⠉⠉⠓⠒⠒⠒⠒⣾⠋⠁⠀⠀⡔⠈⠉⠒⠄⣀⠈⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠥⡔⠙⠢⠕⠂⠀⠠⠄⠀⢀⡶⢿⠂⠒⠀⠁⠑⠤⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢄⡀⠀⣀⠔⠋⠀⠱⣌⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠈⠙⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡀⠀⡸⠀⠀⠀⠈⠣⡀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠈⢳⡇⠀⠀⠀⠀⠀⠙⣆⡔⢁⡨⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢈⠇⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣧⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠄⠆⠀⢄⣸⠀⠀⠀⢃⠀⢄⡀⠀⠄⠐⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⠀⢀⠰⡄⠀⠀⠀⠀⢆⣀⠗⠒⠙⠫⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⠀⣠⡹⠁⠀⠀⠀⠘⢄⠠⢄⠀⢀⠔⠈⠈⣃⠀⠀⠀⢄⡄⡄⠄⢀⡄⡰⠢⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠻⠷⠶⠟⠋⠀⠀⠀⠈⠀⠁⠀⠁⠀⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠛⠛⠛⠛⠓⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⡖⠲⢦⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠙⢦⡀⠈⢳⡀
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠈⠙⠲⡄⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠹⣄⠀⠹
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⠒⠢⠤⠤⠴⠖⠒⣒⣦⣄⠀⠙⣆⠠⠊⣀⣀⣀⣀⣤⣤⣄⣀⡀⠘⣆
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⠀⠀⠀⡀⣠⣴⡚⢋⡹⣿⣇⠀⠸⡏⠉⠉⠀⠀⠀⠰⠦⠤⣄⡉⠓⢾⣆
⠀⣼⠀⠀⠀⠀⠀⢀⣠⣤⣀⢸⡇⠈⠉⣿⢧⠁⡜⠁⡶⠆⠘⠛⠸⡄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⣿
⢠⡇⠀⠀⢀⡠⣴⠋⠀⠀⣀⣹⠇⠢⠀⠠⠞⠀⠀⠀⠀⡀⠔⠀⠀⠳⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠏
⢸⠁⣠⡴⠋⢀⡇⡠⢲⠏⠁⣸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠤⠤⠤⢤⡀⠀⠀⢀⡜⣠⠏⡼
⣼⠋⠑⠀⠀⣸⣼⠁⠘⠀⠀⡏⡆⢀⡀⠀⠤⠤⠤⠀⠀⣤⠀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢀⡰⣫⠞⢁⡜⢁
⢸⠀⠁⠀⡰⠃⡇⠀⠀⠀⣴⡟⢱⠈⠀⢰⡄⠀⠐⠒⣩⠃⠀⠀⠀⠀⠀⡟⠗⠲⢤⣀⠀⢔⣩⠞⠁⡠⠋⢀⠞
⠸⡇⡄⠰⠁⠀⠙⢄⣀⣾⡞⠀⢸⡀⠀⠀⠙⠒⠭⠉⠁⠀⠀⠀⠀⠀⢀⡇⣀⡤⠶⠾⠷⣏⡀⢀⠞⠁⣠⠏
⣀⣧⣘⣤⠤⠤⠶⠖⣿⡟⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠕⠊⠉⠉⠁⠀⢹⠇⠀⠔⠁
⠀⠸⡆⠀⠀⠀⠀⣸⣿⠁⠀⠀⢠⠛⣦⠀⠀⡀⢀⠀⠀⠀⠀⠀⢀⣾⠏⠈⠀⣠⠞⠉⠉⠓⣯⠐⡆⠀⠀⢀⣠
⠀⠀⠹⡄⠀⠀⠀⣿⡇⠀⠀⢠⠏⡰⠉⠙⠦⣄⣁⣀⣀⣠⠤⠞⢉⣸⠀⠀⢀⡏⠀⠀⠀⠀⢸⡷⠤⠖⠚⠉⠁
⠀⠀⠀⠙⣄⠀⢰⣿⠀⠀⢀⡏⢠⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⡾⠋⢹⡴⠊⠁⡙⢄⣀⣀⡤⠞⣀⣠⡤⠤⢤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⣖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠈⠳⣄⠀⠙⣦
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠘⢦⠀⠈⢷⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠥⠤⢄⣀⣠⡤⠤⠤⠤⣤⣀⠀⠘⢦⠀⡠⠊⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⢷⡀⠈⢳
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠻⣿⣧⠀⠘⣷⠗⠚⠋⠉⣉⣉⣉⣉⣉⣉⠛⠲⢤⣷⡀⢰
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠲⢦⣤⡘⠒⡩⠃⣩⡉⠲⡿⠻⡆⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢻⣧⢸
⠀⠀⣼⠀⠀⠀⠀⠀⣠⠴⠋⠉⠓⢤⡇⢄⠀⠚⢋⡇⠀⠀⠀⠉⠀⢀⠇⠀⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠿⡟
⠀⢀⡇⠀⠀⣠⠔⢩⡏⠀⣀⣤⠖⢺⡇⠀⠉⠈⠉⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⢳⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⡞⣸⠁
⠀⢸⣇⡴⡚⠁⠀⣸⢠⠏⡸⠁⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢻⡇⠐⠛⠉⠙⠓⠦⠀⠀⢠⢞⡴⠋⣰⠃⣰
⡴⢺⡇⠠⠀⠀⢠⢿⡏⠀⠁⠀⠀⣷⣠⠀⠤⠀⠈⠒⠒⠂⢁⣠⡶⠐⠲⠄⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⣀⢔⣵⠟⢁⡼⠁⣴⠃
⠀⢸⡇⡇⠀⢠⠏⠸⡇⠀⠀⢀⢞⠟⢸⡀⠀⠀⢳⡀⠈⠉⢁⡴⠁⠀⠀⠀⠀⠀⢸⠋⠉⠓⠶⢤⡠⣊⡴⠋⠀⣠⠋⠀⡼⠃
⠀⠀⣧⢣⠀⠇⠀⠀⠙⢦⣀⣮⠏⠀⠘⡇⠀⠀⠀⠉⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⡼⢀⡤⠖⣒⣚⠛⠧⣄⢀⠜⠁⢀⡞⠁
⢀⣀⣹⣤⣵⠤⠴⠶⠖⢒⣯⡟⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡩⠚⠉⠀⠀⠀⠀⢈⡇⠀⡠⠋
⠀⠀⠈⣧⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢀⡞⢳⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⡴⡿⠀⠀⠀⣰⠚⠉⠉⠛⢯⠐⢲⠀⠀⠀⢀⣠⠶
⠀⠀⠀⠘⣆⠀⠀⠀⢠⣿⠇⠀⠀⢀⡞⢀⠎⠙⠲⣤⣁⣁⣀⣀⣀⣤⠴⠋⣠⡇⠀⠀⢰⡇⠀⠀⠀⠀⠈⡷⢬⡤⠖⠛⠉
⠀⠀⠀⠀⠘⢧⠀⠀⣸⡿⠀⠀⠀⡾⠀⡞⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⣴⡿⢻⣇⡴⠊⢙⢣⣀⠀⠀⣀⡼⠃⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠳⣠⠻⡇⠀⠀⢰⡇⠈⠳⣤⡀⠀⠀⠀⣀⣤⠖⢋⠕⠋⣠⠞⠁⠀⠀⠈⠀⣨⠟⣋⡥⠞⠋⠉⠁⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⣿⢦⡇⠀⠀⢸⠀⠀⠀⠀⠙⠷⠚⠋⢉⡠⠚⠁⢀⡞⠁⠀⠀⠀⠀⢀⡾⢡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⢿⢰⢿⡆⠀⠘⢆⠀⠀⠀⣀⣀⠤⠒⠉⠀⠀⢠⠏⠀⠀⠀⠀⠀⣰⠋⣰⠋⠀⠠⣠⢠⠠⠀⣀⢠⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠳⡄⠠⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡰⠁⢰⠃⠀⠀⠀⠁⠈⠀⠈⠀⠈⠁⠀⠀⠁

⠀⠀⠀⠀⣶⣶⠀⣦⣶⠶⣶⣶⡆⣴⣶⣦⣶⡶⣶⡦⢰⣶⢰⣶⣖⣶⣶⣶⣶⣶⣶⣶⣦⣶⠂⣶⣶⡆
⠀⠀⠀⠀⠉⢉⠀⣏⠻⡶⠿⠵⠇⢹⢿⠹⠿⠿⢵⡷⠈⠀⠀⠉⠉⠿⠿⠿⠿⠯⠿⠼⠿⠿⡇⠿⢾⠇⡀⠄
⠀⠀⢀⡤⠶⢺⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⡀⠀⠀⠀⠀⠀⠠⢀⢢⡀
⠀⠀⡏⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⢿⣿⡟⠉⠀⢀⣀⣤⣤⡀⢄⠠⠱⡑⡄
⠀⠀⠉⠒⠂⠈⠙⡍⣻⡟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣭⣿⣿⣷⠏⢀⣤⡾⣹⣿⣾⣿⣿⡆⢧⠃⠇⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣻⣿⣟⠻⣿⣫⣼⣿⣿⣿⡟⡏⣾⣿⣿⣿⢸⠘⠸⠐⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣦⣀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢮⣝⠛⡁⠇⠀⠀⣿⣿⣿⣿⡇⡄⡄⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⣱⣾⣿⢻⡀⠀⠀⠀⢀⣴⣾⣇⠈⢿⣿⣿⣿⣶⡞⠛⣻⣙⡧⢀⠀⠈⠻⣦⡑⠄⠀⣿⣿⣿⣿⣇⢁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣬⣵⣥⣤⣽⠿⠃⠙⠳⣬⡙⢿⣦⠘⢿⣿⣿⠟⠻⠟⢩⠞⣰⡿⠃⣀⠀⠈⠻⣦⡁⣿⣿⣿⣿⣿⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣟⣋⣀⣀⡀⠀⣀⣬⣿⣮⢿⣷⠈⠻⣿⠀⢀⣠⢋⣼⠏⣠⡾⠋⣡⠀⠀⠹⣷⡈⢿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣠⡿⡛⠉⣈⣉⣻⣟⣮⣷⡄⢸⣿⡿⣣⢟⡵⢞⣡⠶⢛⣉⣅⠀⠀⠻⠓⠈⡏⠉
⠀⠀⠀⠀⠀⣠⢰⡀⠀⠀⠀⠀⣀⣴⠟⢁⣠⡴⠞⢻⡟⣿⣿⣿⠏⠀⢠⣿⣿⣷⣯⣞⡭⠶⠚⠋⠉⠸⠀⠀⠘⠀⠁⠸
⠀⠀⠀⠀⠀⠹⢿⣷⣄⣀⣀⣈⣩⣵⣞⣫⣁⠀⠀⣾⣷⣼⡟⠁⠐⠓⢸⣿⣿⣯⣄⣤⠄⠀⠀⠀⠀⢐⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢽⡿⠛⠛⢉⡠⡤⢟⡟⡻⢿⣶⣿⣿⣿⣷⣶⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⣤⣤⡌⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠝⠐⠛⣯⠀⠀⠀⢙⣿⠿⢻⡿⠿⣾⣿⣿⡇⠈⠻⣿⡟⠛⠻⠿⣻⠟⠀⢹⣿⠀⣾⠁⣞⣿⣷⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠋⡡⣴⠏⠀⣰⣿⣿⣿⣁⣀⡀⠹⣿⣾⣿⡿⢏⠀⢀⣼⠇⠰⠇⢰⣸⣥⣽⡋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⠒⢈⡠⠞⠁⠀⣰⡿⠿⣛⣭⡿⡮⢏⣾⠿⠋⠉⣀⣸⣥⣾⣿⣀⠀⠀⢹⣿⣿⠭⡊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠄⠀⠀⠀⠁⠀⠀⠀⣴⣶⣶⡿⠋⠁⣟⡻⠋⠀⠀⡰⠾⠋⠁⠀⠙⣿⠋⠀⣰⡿⠟⠑⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠻⡀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣖⣫⡽⠆⣀⠀⡟⠁⠀⢀⣬⣤⣀⡀⣠⢴⣿⣿⣤⠾⠫⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠈⠠⡀⠀⢀⠔⠊⠉⠝⢭⡶⢟⣲⣟⡥⢞⣷⣤⣼⠋⢻⣠⣽⣿⣇⢀⣿⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⠈⠓⠶⢤⣤⠆⠀⠀⠈⠻⣵⢞⣷⣫⣿⡗⣿⡷⠛⠿⣿⣿⣿⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢯⢶⣿⣾⣧⠏⠀⠀⠀⠀⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⣞⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠽⠛⠇

⠀⠀⠀⠀⢲⣦⣤⢠⣤⣤⣦⣤⡤⣶⢠⣤⣴⣤⣦⡶⣤⣤⢠⣤⡄⠤⣤⡄⣶⣤⣶⣴⢢⣤⣤⢴⣠⣴⠢⣶⣤⣦
⠀⠀⠀⠀⠘⠛⠛⢸⡿⢿⣤⣿⡇⣿⠘⢿⡿⣿⣿⣷⢫⣷⠈⠋⠁⠘⠛⠃⣿⣿⣿⣿⣞⣻⣏⢸⣿⣿⡆⣿⣼⣧⠀⢀⡀
⠀⠀⠀⠀⣀⣀⣾⣈⣉⡈⠉⠁⠁⠁⠀⠉⠉⠁⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠉⠈⠈⠈⠉⠁⠉⣈⣥⠎⠀⠀⠀⠀⠀⠀⡐⠠⢄
⠀⠀⣰⠟⠉⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡧⠐⠀⠀⠀⠀⠄⡀⠀⡁⢢⠳⡄
⠀⠀⠻⣄⣀⡀⠼⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⣿⣷⡝⣿⠋⠀⢀⣠⣴⢖⣻⣷⣦⡑⡌⢦⢣⠸
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⡏⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢶⣿⣷⣾⣿⣷⣿⢃⣠⣾⡿⣵⣿⡿⣽⣿⣿⣧⢸⠘⠈⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣮⣿⣿⣉⣛⣾⢥⣾⣿⡿⣿⢿⠹⢡⣿⣿⣿⣿⡄⡇⡅⢃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣾⣶⣄⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠙⠶⣭⡛⢥⠛⠀⠀⢸⣿⣿⣿⣿⣇⢠⢰
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⢱⢺⣿⣏⣓⠀⠀⠀⠀⢀⣤⣾⣿⡀⠸⣿⣿⣿⣿⣶⡞⠛⢛⣯⣹⠆⣀⠀⠈⠙⢷⣌⠢⠀⢸⣿⣿⣿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣬⣭⣎⣀⣈⣿⣿⠂⠛⠷⣬⡙⢿⣷⡄⠹⣿⣿⣿⠿⠿⠿⠛⣳⠋⣴⡿⠃⢀⠀⠀⠙⣷⡌⢺⣿⣿⣿⣿⣿⣆⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠉⠄⠀⠀⠀⣈⣻⣦⡹⣿⣆⠘⢿⣿⠀⠀⢀⡰⢃⣾⠟⣠⣶⠟⢃⠀⠀⠈⢿⣆⠹⣿⣿⣿⣿⣿⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⢙⣷⠶⠛⠛⠛⠿⣷⠧⡙⣄⠀⠉⣷⣶⡿⣡⠟⣡⡾⢋⣡⡴⠟⢃⠀⠀⠘⣿⡇⠸⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⣠⣶⠏⠉⣒⣴⣾⣿⣿⣿⣶⣿⡿⠁⠀⣿⣿⣼⣧⣞⡥⢞⣫⣥⠶⠞⠛⡀⠀⠀⡄⠀⠄⢡⠀⠀⠂
⠀⠀⠀⠀⠀⠰⣿⢻⡄⠀⠀⠀⠀⠴⠿⢋⣡⡶⠞⠉⠁⢰⣯⠸⣿⡿⠛⣁⣄⠐⣿⣿⣿⠟⠛⠚⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣴⣶⠶⠾⠿⣶⣿⣦⣄⣀⣼⣿⣿⣿⣀⠀⠀⠁⣼⣿⣿⣿⣷⣶⣮⣤⣄⣀⣀⡀⢠⠆⠀⠀⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠟⢉⣁⢁⡤⢲⣛⡩⠋⠝⠻⣿⣿⣿⣿⣿⣿⣿⢦⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣶⣶⠀⣤⠅⣀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠫⠁⠉⢹⣦⠀⠀⠀⣈⣿⠿⢋⣿⠟⠛⣿⣿⣿⡇⠀⠘⢻⣿⡋⠉⢛⣛⣻⠟⠀⠀⣿⠇⢠⡿⠀⣏⡿⠿⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢉⡠⢴⡟⠁⠀⣼⣿⣿⣷⣇⣀⣀⠀⢿⣿⣿⣭⠿⢧⡀⠀⣰⡿⠀⠸⠃⣴⣸⣧⣽⡋⢕⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠐⠒⠈⣁⠔⠋⠀⢀⣾⡿⠿⣛⣭⡿⢶⠿⣐⡯⠟⠉⠁⣀⣰⣧⣾⣿⣇⠀⠀⠀⣻⣿⣿⡯⢂⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣀⠀⠤⠐⠂⠁⠀⠀⠀⢠⣮⣥⣴⡿⠛⠁⣟⢿⡿⠋⠀⠀⢰⡾⠛⠁⠀⠙⢿⠟⠁⠀⣰⣿⠟⠉⢪⡥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠾⢛⣫⡀⠀⠀⣿⠋⠀⠀⢀⣘⣀⠠⠀⠀⣠⣴⣿⡇⣠⡾⢟⣥⣴⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠑⢄⠀⠀⠀⠀⠀⠴⠚⢻⠟⣋⣽⡯⣥⠶⢛⣰⣇⡀⢀⡴⠿⡟⠙⣻⣶⡏⠁⢹⣿⣿⠋⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠑⢦⣄⣊⠀⠀⡀⠀⠈⠙⢵⡾⣛⣿⣯⡴⣿⣿⣽⣷⣤⣽⣿⣿⣿⣷⡶⢫⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠀⠈⠉⠛⡻⠁⠀⠀⠀⠀⠘⢯⡶⣛⣾⣻⣷⣸⠟⠁⠀⠉⠛⠿⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⢿⡟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⣯⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠞⠉⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠉⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠞⠁⠀⡀⠆⠀⠀⠀⠒⠄⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣹⠋⠀⠀⠀⠀⡘⢀⡶⢤⠀⠀⣠⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠃⠀⠈⠃⠀⠛⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⠀⢃⡘⠀⠀⠀⠁⠬⠁⠀⠀⡀⠀⡀⢀⡀⠀⠀⠂⠱⣵⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠚⠈⠀⠈⣿⡇⠀⣿⡄⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢰⠀⠹⠀⠀⢣⢰⣿⠘⣿⡯⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠑⠀⠀⢀⠀⠀⢡⢹⡇⡀⢰⠑⢄⠀⠀⠀⠀⠑⠠⠤⠥⠔⠁⠀⢀⠀⠸⡈⢸⡿⢰⣿⡷⠂⢀⠃⠘⠂
⠀⠀⠀⠀⡰⠗⠈⠀⣀⡤⢤⡀⠠⠀⠀⠀⠀⣬⣸⠁⠃⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢁⡿⠓⠢⠤⠤⣀⠀⠀⠀⠐⠑
⠀⠀⠀⢀⢀⠴⢚⣉⠔⠀⠳⠑⡀⠀⣢⠒⠁⠀⢸⡀⠸⡀⠀⠀⠀⠀⠈⠅⠒⠢⠤⠀⡐⠊⠉⠀⠄⢀⠎⠀⠀⠀⠀⠀⠈⠁⠒⠀⢀⡀⠂
⠀⠀⣠⠞⢁⡔⠁⠈⣆⠀⠀⠑⢾⠢⡆⠀⠀⠀⠀⢇⠀⠉⠦⡀⠀⠀⠀⠐⠄⠉⠂⠠⢀⠀⡄⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⡀
⢠⠞⣡⠊⠀⢣⠀⠀⠘⣆⠀⠀⠀⢣⠈⢦⠀⠀⠀⠀⠁⢶⣀⠀⠓⠢⢄⠀⠤⠄⣀⡠⠤⢶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⠘⠱
⢇⠀⠀⢦⠀⠀⢳⡀⠀⠈⢦⠀⠀⠀⠇⡘⠀⠀⠀⠀⠀⢸⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢄
⠈⠢⡀⠀⠣⡀⠀⠹⣄⠀⠀⢣⡤⠴⡃⠃⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⡛⠛⠛⠛⠩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠐⢄⠀⠑⣄⣀⡼⠒⠚⠓⠀⠊⠀⠀⠀⠀⡰⠁⠀⠀⠀⠐⢄⠀⠀⠠⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡔⠉⠉⠀⠣⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠗⠁⠱⡆⠀⠀⠀⢱⠆⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⢀⠀⠀⠀⢂⠇⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡠⠔⠁⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠉⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠤⠤⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⢉⡠⠒⠉⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢀⡴⢟⡃⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡞⢀⡈⠁⠢⣄⢠⣤⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠈⠑⠂⢤⣌⣳⠄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠒⠠⡤⣖⡷⠈⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠂⠒⠤⠍⠀⣀⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁⠀⢀⣉⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠂⢀⠐⡀⠡⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⠀⠋⢭⠭⠛⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠐⠂⠁⢀⡋⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠂⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣀⠀⠈⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⡎⠀⠇⠀⠠⠀⠀⠀⠐⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⠀⠀⠀⢀⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠑⠄⠀⣅⠐⠂⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⢄⠠⠴⢎⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠊⠔⠀⠀⠀⠀⠀⠀⡦⠀⡀⠀⠀⠀⠐⠀⢀⢠⡄⠀⢀⡈⠈⠰⣄⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢁⡀⡀⠀⠀⠀⡀⠀⠬⠽⠍⣃⠻⠅⠄⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢛⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⠁⠀⠀⠀⢀⠄⠂⢀⢀⡀⣼⡄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡜⠰⡀⠀⠈⠀⠂⣈⠈⠁⠀⡀⢀⡀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠠⠀⢀⣴⠛⠳⠂⠉⢨⠁⡆⠈⠄⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢰⡅⣸⠀⠋⠠⠀⠀⣠⠁⠀⠀⠀⠡⠂⠁⠊⢃⠴⠀⠀⠀⢀⠔⠁⠀⢀⣾⡇⠀⡇⠀⠀⠀⠢⠑⠤⣈⣠⡀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⡿⠀⠉⠀⠸⡄⠀⠁⠀⠈⠒⠠⢤⠤⣀⠀⠀⠀⢀⣀⡀⠔⠁⠀⠀⠀⢸⣿⡇⠀⠡⡄⠀⠀⢀⡀⠀⠀⣠⡅
⠀⠀⠀⠀⢸⡇⠂⠀⠀⢄⠹⣤⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⡠⠆⠐⠊⠛⠛⠉⠉
⠀⠀⠀⠀⠸⣇⠊⠀⠀⠀⢀⡌⠈⠁⠙⣿⣷⣶⣄⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣩⢋⠟⠉
⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⣄⣀⠈⠂⠄⣀⠀⠀⢈⡡⣻⠋
⠀⠀⠀⠀⠀⢰⡄⠀⢀⠎⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣴⡿⠃⠔⠁
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⢢⠤⠄⠀⢧⡠⠀⣈⠉⠉⠙⠛⠉⠉⣉⠉⠀⠼
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠻⠞⠋⣼⠀⣮⠑⣌⠉⠒⠒⠀⢈⡥⠓⠈⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⢱⡀⢢⡀⢈⣾⠇⠀⢸⡆⠈⠳⢄⣀⣰⠃⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠠⠎⠀⠀⠈⣧⠀⠀⠀⠈⠙⣇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠖⠘⣆⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠆⠀⠀⠀⣻⢄⡄⠀⠀⢀⡠⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢤⡀⠠⢛⡘⡄⠀⠀⡄⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠁⠴⡄⠘⡄⡠⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢶⠀⢸⠁⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⡆⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠐⠢⠄⠀⠀⠀⠀⠈⡇⠀⠆⠀⠀⠀⡠⠄⠂⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠦⠤⠤⣀⠀⠀⠐⢁⣰⡇⠀⣶⠀⠀⠈⢀⡠⠔⠒⠲⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠘⠂⣀⠈⣘⡇⠀⢘⠇⠁⠰⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠙⠢⠄⠀⠀⣀⠀⣦⠔⠋⠁⠀⠀⠛⢯⡵⢀⠀⠀⠐⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⣣⡤⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄⣇⠐⠒⠒⠂⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⣠⣶⠿⠛⠋⢉⣉⣛⡻⢿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢀⣾⠟⠁⠀⢀⣰⣿⠟⢭⠉⡛⢻⠳⡝⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⢀⣿⠃⠀⠀⠀⢸⣿⡇⠈⠁⠐⠇⢹⡆⠘⢎⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⢸⣟⠀⠀⠀⠀⣼⣿⠀⠠⡀⢀⡀⢸⠃⠀⠘⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣶⣾⣍⣑⣦⣀⣠⣿⡇⠀⠀⢀⡀⠀⣼⠀⠀⣠⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣿⣽⣯⡉⠙⠻⢿⣿⣷⣦⣤⣬⣅⣴⣟⣛⠛⢛⢮⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡷⢌⠙⣿⣦⡀⠀⠙⡍⠉⣉⡉⢙⠛⣟⠋⠻⠛⢿⠟⠒⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡃⠈⣧⠘⡏⠻⣦⡀⠀⠀⡇⢹⣏⣷⡟⣧⣸⣧⣹⠀⡴⡜⣧⡘⣿⣷⢦⣤⣀⡀⠀⢸⡇
⠀⠀⠀⢸⡻⣆⢸⠀⡇⠀⠙⢿⣤⣀⣈⡁⠘⠋⠳⠃⠈⡏⠉⠘⣄⠟⡏⡿⢷⡿⠦⠼⢎⣻⣛⣿⡇
⠀⠀⠀⢸⠖⣿⣾⠜⠁⠀⠀⠀⢀⣭⡿⠛⣻⡷⠶⠶⠶⠿⢦⣤⣴⣞⣽⠛⡏⢹⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡟⣿⠀⠀⠀⣠⣴⠞⠋⢁⣤⠞⠋⢀⣀⣀⡀⠀⠀⢸⣷⡏⠈⠙⠛⠃⣩⣇⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣿⣿⣦⠶⠛⠉⣠⡴⢞⣯⣶⣾⣿⣿⣿⣿⣿⣿⠓⣦⣿⠛⢶⣞⠩⠟⠛⢾⣇⣄⣀⣸⡇
⠀⠀⠀⢸⠧⡈⠻⣶⠶⣛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡾⠛⣻⠿⠶⠶⣶⠦⣄⣻⠀⠀⢸⡇
⠀⠀⠀⢸⡀⠀⣰⠋⢻⢿⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢽⡳⢯⣄⢰⠋⣀⡴⠛⠁⠀⠀⢸⡇
⠀⠀⠀⢸⠉⠉⢻⡄⠸⣄⣿⣿⠲⢶⣤⣈⠉⠉⠉⠉⠉⢠⡿⠀⣧⢀⣹⡶⠞⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠻⣶⢤⣼⠏⠀⢸⠀⢹⣧⠀⠀⢀⣴⠏⢿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⠉⠀⠀⠸⠀⣼⠁⣀⣴⠟⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⠓⠲⠶⠶⠶⠿⠶⠶⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⠉⣭⠕⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠀⠀⠂⠀⢹⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⣄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠜⡳⣆⡤⠤⠤⡆⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠙⢮⡀⢥⡀⠀⠈⠈⣹⢄⣀⠀⠀⢀⠤⠋⠸⠀⠒⠒⢲⡞⣩⠎⢉⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⠙⠊⠙⡏⠉⠶⠷⠶⠟⢻⠟⠛⠒⣒⡛⣉⣉⣉⣙⣡⠝⠁⠉⣢⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠅⠀⠇⠀⠩⡆⣦⠄⠀⠇⠀⠀⠀⠉⣩⠣⠀⠤⠤⠤⠠⠤⠀⠀⠀⠁⢀⠠⡶⠟⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡄⢠⠀⢠⠀⠼⣆⢹⠀⠀⠄⠀⠐⠀⠠⠃⠀⡤⠐⠀⡀⠀⠀⠀⠀⠀⡠⢋⠞⠁⢀⡶⠉⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣅⢈⡳⢄⠣⣘⠦⡀⠈⠈⠂⠀⠀⢀⠉⠀⠀⠀⠀⢄⠀⣀⠀⠀⠀⠀⣠⠞⠀⡘⠀⠀⡾⠀⠀⠀⠨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠁⠀⠀⠉⣹⡤⠋⢁⠶⠠⠤⠐⠚⠤⣀⣀⣀⣀⢀⣀⢤⣤⠤⠖⠋⠁⠀⠀⡇⠀⢸⠀⠀⠀⣠⠎⡄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠆⣈⠘⠣⡴⠊⢸⠃⣠⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢣⡀⠀⠙⢄⠀⠀⠀⠀⠀⢃⠀⣶⣀⡤⠚⠁⠀⠀⠲⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⣀⣉⢒⣓⡄⠈⣴⠃⡠⢤⡀⠀⠠⠤⠤⠄⢀⣀⡀⠀⠙⢦⡀⠀⠑⠦⡀⠀⠀⢀⠟⠁⠙⢆⡀⠀⠈⠐⠢⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠀⠀⠀⠀⠀⠱⠀⠈⠲⣇⣨⣅⡀⠀⣀⣈⠉⠉⠉⠙⠛⠒⢤⡉⠢⣄⠀⠈⠓⢤⡎⠀⠀⠀⢀⡉⠶⠏⠈⠉⣹⡏⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡙⠀⠀⠔⢳⠤⢤⣤⡷⠤⠤⠤⢀⣉⣉⣉⣉⡉⠉⠀⠀⠙⢢⡈⠑⢤⣧⠖⠀⢀⡤⠒⠉⠁⠠⢀⠀⠀⠈⢦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡴⠂⠀⠀⣏⠻⢔⡒⠒⠀⠤⠤⠤⠤⠤⠤⠤⢤⣠⡼⠨⣖⣊⢤⠤⠔⢫⡄⠀⡀⠀⠀⠀⠈⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡘⠳⢤⣁⠈⠛⠃⠐⠒⠀⠀⠀⢙⣡⠴⠾⣿⡏⠀⠀⡂⠀⣠⣧⣀⣀⠄⠀⠴⠶⠆⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣀⠃⠀⠀⠙⢮⡀⠐⠀⠒⠂⢀⠬⠋⠁⠀⠀⢹⡷⣀⠄⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠙⣆⠀⠀⢠⡋⠀⠀⠀⠁⠀⠈⣤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⠒⠊⠙⡀⠀⠀⠀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠁⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠢⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢡⡄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠻⡠⢀⠜⢃⠀⠀⠀⠀⠀⠀⠘⡂⢀⠆⠀⠄⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⡠⠂⠈⠳⢊⡌⠀⠀⠀⠀⠀⠀⠀⠹⠆⡀⠀⢀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠙⠄⡀⣠⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠦⠤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡤⠤⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡄⣀⠈⠑⠤⣀⡠⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠊⠁⠀⣁⠀⣤⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣨⡟⠢⢄⡨⠃⠈⠟⢋⡇⠀⠀⠀⠀⠀⠀⢠⠸⣄⠴⠘⠃⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊⠁⠀⠀⠘⢣⡄⢠⡔⢺⠀⠀⠀⠀⠀⠀⠀⠀⢳⠇⠀⠀⠀⠀⡠⠀⠂⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠑⢀⠀⠀⠀⠀⠀⠈⠀⠀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡐⠠⠂⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠄⢀⣀⣀⠱⠄⠀⠀⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠉⠀⠍⠈⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠱⠆⡿⠄⣠⠂⡀⠀⠀⢘⣋⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠈⠐⠂⠀⠀⠀⠀⣔⡖⠒⡃⠀⠠⠄⠄⠀⠀⠈⡹⠄⢂⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⢤⢀⣀⡀⠀⠀⠀⠀⠜⢏⠴⠓⠃⠀⢀⣀⣰⠜⠁⢆⣥⢦⠈⢠⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣦⣀⠓⠓⠠⠒⠒⠚⠡⠀⡐⢼⠁⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⡻⠀⠀⠀⠐⠂⡀⠀⡜⠀⠘⢤⢤⠀⠀⠐⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡹⢂⠈⡇⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢄⠀⠃⠀⣷⣿⣿⣿⣶⣤⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠛⠛⠛⠛⠋⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠘⠂⡀⠀⢀⠀⠈⠈⠣⡀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠰⠂⠁⠀⠀⠀⠀⠐⢄⢀⠀⡈⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠖⠁⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⣄⣀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⢤⠠⠤⠁⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠀⠤⠐⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠀⠀⠂⠀⠏⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⡄⠀⢀⠤⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠜⢩⠳⠖⢒⡒⣇⠀⠀⠀⠀⠀⠀⡸⢇⠀⠀⠀⠀⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠋⠀⠙⢄⡐⣦⣀⣄⡀⠼⠳⣤⣄⣀⣤⠊⢀⣏⣈⣉⣉⣽⠡⣼⢁⡼⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢸⠀⢀⠀⠀⠀⠀⡗⠐⠘⠋⠉⢉⡹⠉⠉⠉⠀⠁⠀⠀⠄⠠⠖⠁⠀⢨⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠐⠀⠘⠀⠀⡟⢸⠒⠄⠁⠀⠀⡀⠀⡰⠀⠀⠒⠒⠂⠐⠃⠀⠀⠀⢀⡄⡺⠋⠉⣱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⢷⡀⢂⠀⣆⠐⠳⠌⡀⠀⠐⠀⠬⠤⠐⠁⢀⠊⠉⠑⠀⠀⠀⠀⠀⡠⠋⡼⠁⢀⡾⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠒⠢⠔⠙⠢⢤⡟⢳⠤⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠐⠀⠐⠀⠀⣀⡤⠞⠀⢠⠀⠀⣼⠁⠀⠀⢀⠟⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⣀⠀⢀⡤⣿⠁⣠⠋⠁⠋⠈⠁⠙⠢⠴⠤⠶⡄⠐⠒⢟⠋⠁⠀⠀⠀⠸⠀⢀⡋⠀⢀⡴⠋⠒⢀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠗⠋⠐⠢⢄⣸⡁⠀⠇⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠓⢄⠀⠀⠀⠀⢲⡼⠳⢖⠉⠀⠀⠄⣈⠁⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄⠒⠒⠂⠒⠺⡀⠘⢇⡰⢉⠇⠀⠀⠍⠩⠥⠴⠶⠦⣤⣀⠙⠦⡀⠀⠑⠢⣀⢀⠞⠀⠀⠈⠲⢄⣠⠄⠤⠤⣤⠜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠁⠄⠀⢀⢱⣀⠀⠙⢾⡋⣁⠀⠒⠒⠒⠒⠒⠂⠀⠀⠙⠦⡈⠲⣄⣀⢄⡙⠀⠀⣀⡤⠶⠌⠉⠈⠉⠐⢏⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣠⠀⣠⠉⠉⣻⢿⣍⢉⣉⠁⠐⠛⠓⠒⠂⠀⠐⠀⠂⣻⢢⣀⠝⠋⠀⣠⡞⠁⠀⠀⠀⠀⠂⠄⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢹⡦⣁⠒⠠⠤⠬⠭⠍⠉⠉⠭⠭⠍⣛⣥⣾⡗⠊⠉⠉⠁⢘⠀⠐⠀⠀⣀⣀⣀⡡⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠻⠀⠈⠛⣄⠂⠠⠀⠤⠄⠀⢠⠖⠏⠁⠀⢟⣇⠀⡐⠀⡴⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠳⣄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡐⣁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡜⠢⠤⠜⠣⠀⠀⠀⠀⠀⠀⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠂⢠⠁⠀⠀⠀⠀⢃⠀⠀⠀⠠⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣂⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⡄⠀⡐⠇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠄⠉⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⠀⠲⡔⡀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⢀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠔⠊⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⢸⠄⠳⢄⠘⣀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠃⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣥⠠⠴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⢀⡀⠉⠢⣄⡀⢀⡀⢰⡄⠀⠀⠀⠀⠀⠀⢰⣆⠔⠊⠁⢈⣀⢠⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡝⠑⠢⡄⠉⠈⠙⢋⡕⠀⠀⠀⠀⠀⠀⢦⠹⡤⠖⠉⠁⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠁⠀⠀⠀⠣⡄⢠⡔⢺⡄⠀⠀⠀⠀⠀⠀⠈⢳⠃⠀⠀⠀⢀⠄⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠄⠀⠀⠀⠀⠈⡁⠀⣚⠅⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣂⠴⠀⣀⢀⡀⠀⠄⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣒⠀⠤⠤⠌⠒⣐⢂⠩⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠄⠀⠀⠄

⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠖⠒⠒⠲⠶⠦⣤⣀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠉⢀⣤⣄⠐⠒⠒⠒⠂⢤⡀⠉⠙⠲⣄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⠀⠀⠸⣇⠀⠀⢠⠤⢤⡶⣦⡈⢢⠀⠀⠈⠻⣦
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠄⠀⠀⠀⠀⡰⠀⢘⠃⡀⠀⠒⣶⠘⡇⠨⠅⠀⠀⠀⠘⣷⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡈⠀⠀⠀⠀⣸⠀⠈⠉⡀⠀⠠⠔⠂⠠⡎⠀⠀⠀⠀⠀⠀⠘⠹⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠁⠀⠀⠀⣰⠃⠈⠀⠀⠀⡀⠠⠀⠀⠀⣤⠐⠀⠀⠀⠀⠀⠀⠇⢻
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠨⢤⠀⠀⠀⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⠘⡇
⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⡉⢄⠐⢀⡆⠰⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠐⢢⠀⠀⠀⠀⠔⢺⢠⣇
⠀⡇⠀⠀⠀⠀⢀⡞⢁⠊⠔⡨⡀⡁⠈⠁⢀⡠⠤⢹⠦⣀⠀⠀⠀⠀⣀⠴⠁⠀⡤⠨⣄⣀⣀⣜⠔⠉⢲⠈⠙⢶⡄
⠀⡇⠀⠀⠀⢠⡟⠀⢀⠀⠈⢀⠀⠓⠠⠴⢉⣠⡔⠉⠀⠤⠍⠉⠉⠩⠥⠄⠒⢂⣽⠋⠩⠔⠀⡺⠤⢦⡉⠒⠅⢸⠇
⠀⡇⠀⠀⠀⣼⠁⠀⠀⠠⠀⢠⠃⠀⠀⠒⠂⠀⢀⡉⠉⡉⠀⠀⠉⠉⠉⠉⠉⠀⠀⡰⠒⠈⣀⠤⠐⠊⢹⣀⠃⠈⡧
⠀⡇⠀⠀⠀⣿⠀⡄⠀⢀⢠⠃⠀⠀⠁⠁⠠⢋⠌⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠔⠈⠀⡠⠊⣡⡴⠖⠒⠚⠷⣍⡼⠃
⠀⡇⠀⠀⠀⢿⠀⠀⠃⠈⠀⠱⢄⣁⠡⠀⠒⠁⠀⠠⠂⠀⠀⠂⠀⠂⠀⠀⠀⠀⡠⠊⣠⠞⠁⠀⠀⠀⠀⠀⠈⠁
⠀⡇⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⡠⠊⣠⠞⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠙⠦⣄⣀⣀⠀⠀⠈⠑⠂⠁⠀⠀⢀⡀⢈⣠⠞⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⡀⢀⠀⠀⣠⡄⠀⠀⣀⣀⢀⠀⠀⠀⡀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠤⠐⠒⠒⠒⠒⠂⠤⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡈⡰⠉⠒⠤⠤⠒⠑⢆⠸⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠠⠧⠐⢻⣷⡆⢰⣶⡟⠂⡼⡄⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⡆⢸⠀⠉⠋⠃⠘⠙⠉⠀⠇⠸⠀⠀⠀⠀⠸
⠀⠀⠀⢐⠉⡦⠠⠤⡄⠤⠠⡄⠀⠤⠤⠠⠰⡟⠉⢳⡄⢴⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣦⢠⡜⠓⡶⠆⠀⡤⠄⠠⢠⠤⠤⢠⠤⠤⢴⠘⡂
⠀⠀⠀⠈⠉⠓⢀⠀⠈⠢⡀⠈⠢⡀⠈⠂⣸⢣⠄⠊⠁⡌⢠⠁⠀⠀⠆⠀⠀⠰⠀⠀⠈⡄⢉⠙⡣⢤⡇⣇⠈⠀⢀⠔⠁⢀⠔⠁⠀⡀⢛⠈⠁
⠀⠀⠀⠀⠀⠶⠤⠶⠤⠤⠴⠦⠤⠀⠦⡔⠉⠈⣷⣂⡘⠁⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⣃⢙⣶⠁⠉⢢⠴⠁⠠⠴⠤⠤⠤⠶⠤⢾⠀⠆
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀⠀⠰⠦⠭⢒⣂⠷⠤⠄⠀⠀⠀⠀⠤⠤⠴⠃⢒⡨⢵⠂⠀⢀⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⡀
⠀⠀⠀⠐⡤⠂⠙⠢⣄⠀⠀⠀⠀⠀⢰⠀⠱⡀⠀⠁⠀⠀⠀⠀⠉⢋⠉⠀⠂⠒⠒⠀⢉⡉⠀⠀⠀⠀⢀⠎⢈⠀⠀⠀⠀⠀⠀⡠⠔⠉⠉⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢠⠊⠇⠀⠑⢄⠀⠀⠀⠀⠂⠀⠈⠦⢀⡀⠴⠃⢐⠀⠀⠀⠀⠀⣠⠊⠀⡸⠱⡀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠃⠀⢈⠦⣀⠈⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣀⣀⠔⠁⣀⠴⡁⠀⠹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠀⠀⠁⠀⠈⣜⠓⠛⢍⠘⠛⠲⠰⠤⠞⠳⠤⠄⠖⠛⠃⡩⠛⠚⣋⠁⠀⠈⠄⠀⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡃⠀⠀⠀⠀⡘⠉⠓⠤⡈⢣⡀⠀⠀⡠⠖⠢⢄⠀⠀⢀⡔⢁⠤⠚⠉⢂⠀⠀⠀⠀⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠑⢄⠀⠀⢠⠙⡄⠀⠀⠈⠙⣧⠉⠈⠀⠀⠀⠀⠁⠉⣼⠋⠁⠀⠀⢠⠋⡄⠀⢀⡠⠊⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⢀⠀⠈⠉⠁⢀⡇⠀⠀⠀⠀⢸⡁⠒⠒⠒⠒⠒⠂⢉⡧⠀⠀⠀⠀⢸⡀⠈⠉⠁⠀⡠⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠈⠉⠘⡀⠀⠀⠀⠀⠆⠈⠒⠄⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀⢈⠁⠉⠈⠉⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠉⠢⡀⠀⠔⠒⢀⠀⡰⠁⠈⠆⠀⠤⠒⠲⡀⢀⠔⠉⠀⠀⠀⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠁⢰⠀⠀⠀⠋⠡⠀⠀⠘⠛⠁⠀⠀⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡜⠀⠃⠀⠀⠀⠀⡘⠀⠀⢀⡀⠀⠀⠀⠘⡀⢣⣤⡄⠀⠀⠀⠀⠀⠀⠀⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣀⠀⠀⠀⠀⠀⠈⠀⠀⡛⠀⠀⠀⢀⠈⡁⠀⠀⢈⠁⠀⠀⠀⠀⢙⠀⡆⠁⠀⠀⠀⠀⢀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠐⣁⡜⠉⠉⠉⠐⠺⠀⡇⠀⠀⢘⠀⠓⠀⠉⠁⠉⢣⣈⠂⠤⠤⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠀⠀⠈⠉⠲⠀⣰⡇⠀⠀⢸⢆⠀⠒⠉⠉⠀⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⠀⠀⠀⠀⠤⠤⠴⢋⠌⠀⠀⠀⠀⠡⡘⠦⠀⠀⠀⣀⣀⡀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⠤⠄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠤⠤⠤⠠⠀⠒




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠐⠀⠀⠂

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⢉⣉⣍⣉⡛⠿⣟⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⢠⣾⡟⠁⠀⠀⠀⣠⣿⡿⢛⣍⠙⠛⠓⢟⢮⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢠⣿⠏⠀⠀⠀⠀⢸⣿⡿⠁⠰⢊⠠⣮⠑⣿⠀⠙⣎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⣿⡏⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠁⠀⣿⠀⠀⠘⡆⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⢀⣿⣅⡀⠀⠀⠀⢀⣿⣿⠀⠀⠑⠆⣀⠴⠀⣿⠀⠀⠀⢹⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣷⣿⣧⣀⣙⣶⣄⣀⣸⣿⡇⠀⠀⠀⢀⡀⠀⢠⡇⠀⠀⣠⣼⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡿⣇⣿⣋⠉⠙⠻⢿⣿⣿⠷⢤⣤⣀⣈⣋⣠⡾⠿⢻⠟⠻⡲⣹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⣉⠛⢿⣷⣄⠀⠀⠙⢿⡛⠛⠓⠓⠾⠿⠿⣿⡿⠿⣶⣶⣧⣟⣿⡭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠙⢧⠀⢻⡿⣷⣄⠀⠀⠑⠀⢰⠒⣆⡔⢆⢨⣧⡤⢠⣤⠤⣯⠀⠀⠘⣿⠓⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠈⣇⠀⣧⠈⢻⣷⡄⠀⠀⠸⣄⡽⢧⣸⣿⡈⡿⢴⣿⣶⡿⢠⠟⢧⢹⣧⣀⣻⢿⡟⠻⣶⢦⣤⣀⡀⣸⡇
⠀⠀⠀⠀⢸⡛⢷⡀⣿⠀⣿⠀⠀⠙⢿⣦⣤⣀⣈⣀⠈⠉⠈⠛⠁⠀⢹⠀⠀⠘⣦⡼⢸⡏⡟⠳⣾⠷⠶⠾⢦⣼⣯⣹⣿⡇
⠀⠀⠀⠀⢸⡧⢺⣷⣏⡼⠃⠀⠀⠀⠀⠀⣉⣽⡿⠟⢿⣷⣶⣶⣶⣶⡾⣦⣤⣤⣤⣴⢛⡿⢹⡟⠛⣷⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡶⣿⡋⠉⠀⠀⠀⠀⣠⣴⠾⠛⠉⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠛⢦⣿⡾⠙⢻⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣷⢻⣧⠀⣀⣤⡶⠟⠋⠀⣠⣴⠞⣋⣡⣤⣤⣶⣶⣶⣶⣤⣤⣀⠸⣿⣿⣄⣀⣠⡤⠤⣴⣞⣳⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡿⢿⣿⣟⠋⠁⣀⣠⡶⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣷⣿⣀⣈⡿⠤⠐⠋⠁⠈⠻⣷⡶⠶⠶⣾⡇
⠀⠀⠀⠀⢸⠯⣐⠍⢻⣶⠟⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠟⠉⢩⡿⠷⠚⠛⣛⡒⠲⣄⣹⠇⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡁⠀⠀⣼⠛⢻⣿⣿⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⠶⣿⣄⠀⢠⠊⠔⣠⣴⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠗⠒⠾⣇⠀⢸⡀⢹⣿⣦⣤⣤⣈⡉⠙⠛⠛⠛⠛⠛⠛⠋⢹⡯⠘⣧⠀⠙⣷⣈⣵⠞⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠂⠀⠀⠘⣦⣀⠙⠚⣽⡟⠀⠀⡟⠛⢶⣄⠀⠀⠀⠀⢀⣴⣿⣇⣀⣿⣴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢻⣛⣺⡿⠁⠀⠀⡇⠀⢸⡟⠆⠀⠀⣠⡾⠋⠈⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠇⠀⣿⡃⣀⣴⡿⠋⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇
⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⠶⠿⠃

⠀⢀⠄⡀⠀⠀⡀⠀⢀⡀⣀⣀⢀⠀⠀⠠⠀⠄⢤⠄⠂⠀⣀⠄⡠⠔⠚⠛⠒⠄⠀⠀⠀⠀⠐⠤⠀⠄⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀
⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠊⠀⠨⠀⠀⠀⢀⠀⠐⣀⠈⢂⠐⡆⢀⠒⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠤⠀⣠⠾⢹⠃⢴⠀⠀⠠⢲⠀⠀⠀⠀⠀⠈⡀⢡⠈⡆⠇⠀⠀⠀⠀⠀⠀⠀⠰⡀⠁⠘⢶⡒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠀⠀⠁⠀⠀⠀⡄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡄⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠂⡀⠀⠀⢀⠀⠁⠀⠀⠀⠘⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡜⣇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠱⣄⠀⠀⠀⠀⠐⠠⢤⠤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡅⢧⠀⠀⠀⠀⠀⠒⠈⠄⠐⠀⠀⠀⠀⠈⢸⠀⠀⠀⠈⠉⠓⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠑⡆⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠈⠉⠙⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠂⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠈⠉⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⡆⠀⠀⠀⠚⠄⠈⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡸⠃⠀⠀⠀⠀⡘⢀⡴⢄⠀⠀⢐⡄⠀⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠂⢡⠀⠀⠀⠀⠀⠃⠈⠉⠂⠀⠶⠛⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⢆⠆⠀⠀⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⡂⠀⠀⠠⠘⢼⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠆⠪⡀⢹⣿⠂⠘⣧⠀⠀⠀⠀⠀⢂⠀⠀⠁⠀⠉⠀⡇⠑⡄⠀⠘⡈⣽⡏⢿⣶⡄⠀⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠊⠈⠀⠘⠄⠀⠀⠀⠀⠈⠀⣿⠆⠀⠎⢣⡀⠀⠀⠀⠀⠠⢀⣀⣀⣠⠈⠀⠀⠀⢀⠆⠇⣿⡇⣸⣿⡤⠀⠀⠀⠲⡀
⠀⠀⠀⠀⢀⣾⠑⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⡃⣿⠘⠆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⡠⠀⠘⢰⡿⢤⣉⠉⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠎⣀⡤⠖⢊⠍⠡⠑⡄⠁⠠⣀⠄⠊⠉⡇⠀⢣⠀⠀⠀⠀⠈⠓⠢⠤⣀⣀⡀⠠⡤⠔⠊⠀⠀⢠⠋⠀⠀⠀⠀⠉⠓⠢⠄⡀⠀⠀⡄
⠀⠀⠀⡸⠚⢡⠖⠉⣇⠀⠀⠱⣐⣤⣨⠁⠀⠀⠀⠸⠀⠈⢢⡀⠀⠄⠀⠀⢁⠀⠶⠄⠀⠀⠀⠀⠀⠈⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢠
⠀⡠⠊⡠⠊⢇⠀⠀⠘⣆⠀⠀⠀⢳⡙⢦⡀⠀⠀⠀⠑⢄⣀⠈⠐⣤⣀⠀⠀⠀⡀⠀⠉⢀⣂⡨⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢆
⡞⠐⠘⡄⠀⠈⢧⠀⠀⠘⣆⠀⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀⢻⣶⣦⣤⣤⣽⣥⣤⣭⣤⣭⡩⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠒⠀⢀⠈
⠰⡀⠀⠘⢆⠀⠈⢳⡀⠀⠈⢣⠀⢀⣨⢒⠅⠀⠀⠀⠀⡀⠚⡀⠙⠻⠿⣿⣿⣿⡿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠣⠀⠈⢣⡀⠀⠙⣄⣠⢤⡋⢉⠕⠁⠀⠀⠀⢠⠊⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠑⠄⣠⠕⠒⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠵⢄⣀⡌⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠴⢅⠀⠀⠀⠈⢄⡀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠐⠁⠀⠘⠇⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠢⠤⠄⠈⡴⠁⠀⠀⠀⠀⢱⡆⠀⠀⠀⢠⠜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠤⠒⣒⡲⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⣁⣤⠊⠁⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⡾⠋⡅⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠞⢀⡄⠀⠁⢶⣀⠤⠆⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠉⠒⠲⣤⢍⡆⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⠑⠂⣶⢽⣻⠂⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠐⠚⠢⠌⠀⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢩⡉⠉⠁⠒⠠⣀
⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⠀⣠⠴⣆⡉⠉⠁⠉⢁⠐⢤⠀⡉⠐⠢⢄⣀
⠀⠀⠀⠀⣠⠊⠀⠀⡠⠗⠈⢀⠠⣆⣀⣉⠀⣤⣀⣀⣰⠘⡀⠀⠀⠁⢺⣁⠙⡶⢦
⠀⠀⠀⡰⠁⠀⠀⠀⣀⠔⠊⠀⠀⠀⠨⢕⠀⠃⡛⠀⠈⢄⡗⠀⠀⠀⠤⠈⣇⢸⢆⡇
⠀⠀⢠⠁⠀⠀⠴⠊⠀⠀⠀⠀⡴⠀⠀⠂⠀⠀⢀⠄⠀⠀⡅⠀⠈⠑⠀⠘⠯⡾⠃⢓⠢⣄
⠀⢠⠏⣠⠶⡁⠀⠀⠀⠀⠀⠐⡇⠀⠀⠁⠀⠈⠁⠀⠀⠅⢀⠀⠀⡐⠁⠀⡾⠁⠄⠸⠀⠈⠑⢦⡀
⠀⡇⣠⠍⣄⠘⡆⠀⠀⡂⠀⠀⣇⠀⠀⠀⡀⠀⠀⠀⢀⡤⠈⢀⡔⠀⣠⠞⠐⠀⡀⠐⣆⣀⣀⠠⠟⢦⡀
⠀⢻⠋⠀⣈⣦⠐⠀⠀⠐⠠⡀⠈⠢⢄⣀⣀⣀⠠⠐⠓⠈⢀⡰⠔⠋⠑⠁⠀⠌⠀⢠⠁⠀⠀⠀⠀⠀⡗
⠀⠈⢧⢨⣅⠀⠉⠳⢦⠤⣄⣀⣠⣉⣀⣀⣀⣠⡤⠴⠒⠊⠁⠀⠀⠀⠀⠂⠀⣄⠀⣸⣀⢀⡀⠀⠀⡚⠁
⠀⠀⣸⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⡠⠀⠀⠈⠀⠀⢠⣇⠋⠀⠐⠂⠉⢀⡼
⠀⡞⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⢠⠖⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠚⣿⡀⠄⠀⠀⢀⡼⠁
⢠⡗⠊⠉⡟⠀⠐⠺⣿⠈⠳⡄⠀⠀⣾⠀⠇⠀⠀⠟⠂⠀⠀⠀⠀⠄⣈⡁⠴⠃⡜⡇⠀⠀⠀⢀⡞
⡏⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠑⣾⠉⡆⠸⠀⠀⣘⢾⡃⠀⠐⠀⠀⢀⣀⠠⠋⣀⣧⠀⠀⢠⡎
⢰⡜⠙⡄⠀⠀⢀⡠⠴⠶⠊⠁⠀⠛⠀⠓⠀⢂⣀⡼⣉⣤⠤⠀⠀⠈⢹⣯⠀⡞⠁⠀⠀⠀⠀⢨
⠀⡇⠁⠀⢀⠞⠁⠀⠀⡁⡀⠀⠀⠐⢤⣠⢔⣩⣴⣿⠟⠋⠀⠀⠀⠀⣾⣏⠀⢲⡡⠀⢀⡠⠀⣈⠧
⠀⢻⣀⢀⡄⠀⠀⠀⠁⠀⠀⠀⠀⡠⠞⠁⠉⠛⠛⠓⠒⠒⠒⠒⠛⠋⠁⣊⠀⠀⠓⠤⠐⠒⠉
⠀⠀⠉⢯⣅⠀⠀⠀⢄⠀⠀⣠⢾⡅⢄⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠙⠦⣀⠀⠀⣠⠞⠁⡾⠀⠀⠑⢄⠉⠀⠉⠀⠀⠀⠐⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢰⡇⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣘⠁⠈⠇⠀⠀⠀⠀⣠⠤⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⢀⡀⢸⠀⠀⠀⡘⠁⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⠀⠈⢸⠀⡆⠠⠐⡇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠶⠒⠒⠚⠁⠀⢠⡸⠀⢘⡷⠊⠑⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢖⠂⠀⠀⠀⠀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠚⠁⠀⡇⠀⠀⢀⡠⠄⠒⠂⠐⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠢⠐⠁⠀⠀⠀⠀⠀⣀⣀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠁⠁⠴⠋⠉⠉⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⠃⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣠⡘⠃⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠁⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠃⠀⠀⠀⠀⢀⡤⠞⠁

⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⣀⠤⠀⠀⢀⠀⣠⠔⠒⠒⠶⢄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⣀⡀
⠀⠘⢄⠁⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠊⠁⠈⠀⠀⠀⠀⠀⠀⡀⠈⢢⠠⡤⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡠⠁
⠀⠀⠀⠈⠀⠀⠔⠂⠀⠀⠀⠀⠐⠄⡀⢀⣠⡖⣶⠄⡘⠁⠀⡠⢦⠀⠁⠀⠈⠀⠐⡋⠢⠀⡇⠳⠈⠀⠀⠀⠀⠁⠀⠀⣄⠈⠀⠲⣖⠆⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠐⠈⠀⠁⢀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠁⠁⠀⠀⠀⠀⢠⠀⠆⠀⠘⡄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⠈⠀⠒⠒⠈⠀⠀⠀⠀⠀⠀⢠⠋⠹⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠐⢠⡏⠀⠀⠈⠒⠦⠤⠤⠖⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠀⠀⠀⠀⠀⠰⢠⠊⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠉⠉⠂⠐⠒⠢⠤⠤⠤⠖⠂⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⠠⠖⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⡛⠻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⠃⠛⠀⠙⠻⠿⠟⢿⣦⡀
⠀⠀⠀⠀⣴⣤⣀⢰⠰⠀⠐⠂⠀⠀⣀⣼⡿⢿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡙⠛⠀⠀⠀⠀⠐⠀⠴⢹⣿⠁⠙⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣦⣄⠈⠐⠾⣿⣿⠣⠄⡬⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡏⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈
⠀⠀⠀⣿⠉⣭⣉⣉⡙⠣⠅⠘⣶⣤⣿⣀⣀⣤⡀⠿⠆⢀⣴⣶⠶⠶⣶⣦⢤⣿⡡⣤⠲⣶⡆⠀⠐⠀⠾⠗⠀⠀⠀⣦⡀
⠀⠀⠀⣿⡶⠞⢻⡯⠀⠀⠀⢠⣄⣹⣿⣿⣯⣀⡇⡀⠀⠀⡟⠁⠀⠄⠠⢃⡾⠛⠗⠚⠀⠀⡠⠀⠀⠀⠀⠁⢀⣠⣾⣿⡁
⠀⠀⠀⠘⣿⣶⣦⡀⣠⠀⣴⠃⠙⠉⠈⠉⠙⠻⣋⡅⠀⢠⡷⠢⠀⠀⠪⠽⣿⢄⢂⠀⠥⠀⠘⠻⣿⣿⣿⣿⣿⠛⣿⣿⣧
⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠙⠀⣄⡀⠀⠀⠀⠀⣹⣷⣤⣯⣴⠁⠀⠀⠀⣀⠼⠟⠀⠀⣀⡠⠘⢰⡉⠉⠉⠉⠁⠀⠈⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠩⠛⠷⠶⠶⢺⣿⣧⣀⠀⢩⠀⠒⠬⠀⠤⢀⠀⢀⡠⠈⠀⠀⠀⠀⠆⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢿⡏⠥⠢⠙⣿⡟⢴⠆⣤⠀⠀⣸⡿⠏⠈⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⢸⣇⠘⡈⠳⢸⡇⠀⠀⠀⠀⠂⣸⡇⠀⠘⢤⡀⢠⢎⡀⡉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢸⣿⣶⣥⡁⣿⡇⠢⠐⠂⢠⣿⣿⣿⣶⠇⠀⢀⠀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣯⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠙⠿⢿⣷⠘⣷⡄⠀⢰⣋⢉⣿⠿⣧⣤⠁⠀⢾⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⢧⣾⡁⡘⢡⡟⠻⠁⠀⠀⣹⠀⠀⢐⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣦
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢁⠀⠀⠀⠨⢻⡿⠄⢶⠎⢀⣄⠐⡄⠄⢶⠈⠁⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡶⣶
⠀⡰⠿⠛⠛⠛⣳⡄⠀⠀⠀⠀⠀⠀⢩⡟⠋⠀⠀⠀⠃⠘⢿⢀⠰⠦⠹⣿⡆⢐⣷⢸⡚⠒⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⣷
⠀⡟⢂⣈⣉⣉⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⣞⠙⠋⠁⠀⣿⣿⠀⢻⣷⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⢿
⠀⠻⣿⣿⣭⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⣿⡇⢠⣤⠀⠻⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠒⠒⠲⢦⣤⡶⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠲⢴⠟⠁⣀⠤⠤⠤⢀⡀⠀⠄⠀⠀⠤⣄⠀⠻⠖⠚⠓⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠄⠈⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⡤⠶⠋⣀⡁⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⡠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢸⣦⣄⣀
⠀⠀⠀⠀⣠⠟⢁⠄⠀⠈⣧⠋⠀⠀⣿⣁⣿⠀⠀⠀⠀⠀⠀⠉⠲⠇⠀⠀⠀⠀⠀⠀⣶⢦⡀⠀⢰⠳⣻⠃⠀⠀⠉⠳⣄
⢀⣶⣄⢰⠏⢠⠃⠀⣀⣀⠀⠀⠀⢀⣉⣀⣁⣄⠀⠀⣤⠤⠤⠤⢤⢀⡴⠶⠤⠤⣤⣀⣈⡉⠁⠀⠘⠛⠃⠀⠀⠐⠄⠀⠘⣆
⠙⠳⠬⣿⡤⠞⠊⠉⠉⠉⠉⠳⡄⣼⠀⠀⠀⠸⣄⣠⠇⠀⠀⠀⠘⡏⢄⠀⠀⠀⠀⠀⠀⠉⠉⠛⣶⠺⠉⠉⠉⠙⠛⠒⢲⢿
⠀⠀⣰⡏⠀⠀⠀⣠⡀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠦⢬⣉⣑⡶⠀⠀⠀⠀⢠⡇⡄⠀⠀⠀⠀⠀⠀⡜⣸
⠀⢰⡏⢹⠀⠀⠀⠓⠋⠀⠀⣴⣃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡤⠚⠁⠀⠀⠀⣀⣤⠾⢥⣁⠒⢲⠄⠀⠀⠀⡇⠻⣄
⠀⣿⠀⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠙⠀⠀⠀⠀⠀⠚⠻⠦⢤⣤⡾⠋⠁⠀⢀⣤⢶⠃⠀⢹
⠀⣇⠀⠃⠸⡄⠀⠀⢰⡦⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠁⠀⠀⠀⠀⠈⠉⡇⠀⢸
⠀⢻⡄⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠐⣭⠢⣀⠀⠀⠀⠀⢀⢄⡾⠓⠦⣤⣈⣀⠐⠒⠤⢄⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⢠⡾
⠀⠀⠹⢷⡀⠈⣆⣀⣀⡠⠤⢒⣩⢞⣤⡙⠦⠭⠥⠤⠵⠒⣩⡞⢷⡆⠀⠀⠉⠉⠙⠒⠶⠚⢯⣀⣓⣒⣒⣀⣀⣒⡶⠾⣷⠋
⠀⠀⠀⢸⡅⠀⠹⠒⠒⠒⠊⠉⠀⠀⠙⠛⠀⠀⣶⡆⠀⠈⢉⠳⠊⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⢠⣩⠀⠀⢶⡿
⠀⠀⠀⠈⢧⣠⣖⣳⠢⠀⣀⠀⠀⠤⣽⣏⣿⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠸⠷⣾⠀⢀⣀⠀⢀⠠⠚⠟⠁⢀⡼⠃
⠀⠀⠀⠀⠀⠙⠻⠧⣤⣀⣠⣤⣄⠀⠈⠢⠄⣀⠀⠀⠀⠀⠠⠦⣀⠀⠀⠀⠀⠀⠀⣀⠩⠀⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⣀⣤⠾⠓⠲⠖⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣠⡤⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣴⠋⠁⢠⣾⢟⠚⣻⢟⢦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠃⠀⠀⣿⠃⠁⠈⢸⠀⢩⢷⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣳⣄⣰⣟⠀⠀⡈⢸⣀⣠⣾⠂⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣦⡈⠻⡿⠷⠶⠶⣯⠯⢭⣿⣶⣄⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢳⢸⡛⣦⡀⠀⣱⣆⣞⣦⣦⡇⡤⣽⣙⣶⠦⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⠃⠈⠓⣲⡶⣬⣬⣤⣤⣀⣑⣽⢯⠿⡅⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⢀⣠⠴⢚⣡⢖⣉⣀⣀⣀⡈⣿⣏⢙⣛⣹⣆⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣹⠿⣼⡷⢬⣌⢻⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣵⠋⡿⣿⣛⠻⠿⢿⣿⣿⠿⡿⡗⢧⡐⣩⠖⠋⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⢳⣝⣽⠇⠹⢳⣄⠀⢀⡾⣧⣾⠚⠉⠀⠀⠀⢸⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣂⣀⣹⣁⣀⣀⣸⣤⣶⣋⣀⣸⣆⣀⣀⣀⣀⣀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡉⠉⡐⠮⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠆⠀⣠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⣠⠀⠂⠀⠀⠀⣾⢦⣀⠀⠀⠘⠡⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡦⠤⠤⠺⠡⠤⣌⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⣤⠒⠁⢃⣴⣮⣤⠤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⡈⠁⠀⠀⡏⠁⠘⠀⠁⠅⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⠀⠀⠀⠀⠀⡤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠙⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣯⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⣤⣄⣀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣶⣄
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢀⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣦
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢈⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢸⣿⣿⣟⣻⣿⣿⣽⣿⣿⣿⡍⠀⠀⢸⣿⣿⢳⣾⣿⣿⣿⡿⠷⠶⣶⣮⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠻⣿⣿⣿⣿⣿⣿⣏⡀⠭⠀⠘⣿⠿⠿⢿⠛⢿⣿⠿⠿⠿⡿⠛⢻⣛⠻⠯⠍
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⡇⠁⠀⠀⢀⠠⡀⠀⣰⠋⣿⡇⠀⢘⣞⠙⡈⠁
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠀⠘⠻⠿⠻⡟⠁⠀⠀⢀⠄⠀⠠⢀⡌⠀⠿⢧⠀⠁⠢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣤⡒⠀⢀⡖⠆⠶⡀⠁⠀⠐⢈⠠⠞⠋⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⡛⣢⢼⣷⠀⢀⠀⠰⡁⠀⡼⠀⠸⠿⢂⠄⠀⠀⢰⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡿⡯⠝⠊⠙⡀⠀⠉⠣⣌⠚⠿⠆⠈⠄⠀⠀⠐⠁⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠊⠁⠀⠀⠀⠀⠐⡀⢀⣀⣬⣿⣄⣀⡀⣀⣠⣤⣴⣶⣾⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠡⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠟⠃⠀⠉⠛⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⢙⣿⣿⣷⣿⣿⡟⠀⢀⡀⠀⢤⣶⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠀⠀⠀⠀⢡⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶
⠀⣠⠾⠿⠟⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢶⣿
⠀⡟⣀⣈⣉⣉⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠶⠿
⠀⠙⢿⣿⣐⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣷
⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⠈⠁⠢⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡀⡠⡐⠄⠀⠀⠄⡀⠀⠈⠢⡀⠀⠁⠀⠀⡌⠀⢂⠂⠀⠔⠤⠑⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠊⡀⣠⠐⠉⠈⡑
⠀⢀⠐⠀⠒⠄⡀⠀⡐⢐⠐⠄⠀⠀⠰⠀⠑⠐⠁⠀⠀⠀⠀⠠⠀⠀⠐⠀⠠⠀⠀⢠⠀⠀⠀⡈⠀⠁⠈⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⢀⠔⠠⠀⠠
⠀⣃⡤⣀⣀⠀⢌⠢⡀⠀⠀⠸⢀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠸⠀⡀⠀⠘⠂⡀⠀⠃⢄⠀⠀⠀⠀⡀⠀⠢⣀⠈⠈⠐⣀⣂⠊⠀⠀⠐
⡌⠀⠀⠀⢠⠄⠐⠠⡈⢠⠁⠀⢀⢹⡐⠀⢀⠖⠦⣄⡀⠈⠢⡐⠀⠀⠀⡖⠓⠇⠀⠀⠂⣅⠒⠀⢠⢤⡄⢀⣀⠀⠀⠠⠸⣌⣀⡠⠋⠹⡆⠀⠀⠀⢂⠠⠊
⠇⠁⠀⠈⢠⠀⠀⠀⡴⠛⢄⡀⣀⠜⠉⠀⢁⠔⠀⠀⠙⣄⠀⠈⠂⠄⣰⠇⠠⡈⠒⠐⠊⠀⠑⠊⡡⠀⡇⡏⠈⠢⠄⠤⠊⠀⠀⡠⠊⠀⢷⠨⠄⠂⠁
⠈⠦⡀⠀⠀⢀⠀⠀⣷⠀⠂⠀⠀⠀⢀⣒⣁⣀⣀⣤⣤⣾⠀⠀⠀⠀⡼⠀⠀⠈⠁⠒⠒⠒⠂⠉⠀⢰⡇⣧⠀⠑⠀⠀⠀⣂⣁⣠⣤⠤⠾
⠀⠀⠈⠀⠐⠂⠀⠀⢿⣠⣤⣤⣶⣾⠉⢉⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⣷⣦⣤⣤⣤⡜⠉⠉⠉⠉⠛⠛⠁⢻⠀⢀⣀⣀⣼⠉⠁⣀⣄⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⢠⠟⠀⠀⠀⠰⠿⠿⠿⠿⠿⠷⠶⠶⠿⡤⠶⣄⠀⢸⣿⣿⣿⣿⣿⠾⠿⠛⠛⣏⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣿⣦⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠂⢸⠛⠉⠉⠁⠀⠀⠀⠀⣀⣸⡖⢲⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠙⣷⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⡄⢰⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡿⠙⡆⠀⠘⣇⣀⣤⣤⣶⣶⣿⡿⠿⠛⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠈⢀⣤⣿⠿⠟⠛⠋⣿⠛⠛⠓⡆⠀⠀⢀⣀⡇⡼⠛⠛⠛⠛⣻⠉⠀⠀⠀⠀⠀⠀⢃⡖⠲⣿⣿⣿⡿⠿⣏⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣀⣀⣽⣤⣴⣾⣶⣿⣿⣿⣿⢇⣇⣀⣀⣀⣀⣛⣒⣒⣒⠒⢲⡄⠀⠘⠀⣀⡏⠁⠀⠀⠀⠻⢒⣀⣩⣥⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢛⣽⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⠉⢻⣤⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠋⠉⠉⠀⠀⠀⢀⣠⠶⠋⠁⠀⣏⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣹⡇⠀⠀⠉⠀⢸⣿⠿⠿⠛⠛⢉⣉⣤⡤⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣤⣤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣤⣤⠶⠖⠛⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⢈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠣⠤⡡⡀⠑⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠫⠀⠀⠀⠈⠻⠾⡕⢢⠀⠀⠀⠀⠀⠚⣶⠖⠂⢀⣴⢶⡄⠀⠀⠀⠀⠈⠢⡀⠑⢠⢢⠈⢿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⡠⣶⡏⠀⠀⠀⠀⣀⡠⢛⠵⠋⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⣦⣁⣴⡟⠀⠠⡀
⠀⠀⠀⠀⠀⠸⣀⣓⠳⣐⣲⡪⠭⠓⡸⠁⠀⠀⠀⣠⣴⠶⣄⠀⣿⠀⠘⣿⠀⣸⠃⠀⠀⠀⠀⢀⡀⠀⠻⣿⡇⠀⠄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠊⠀⠀⠀⠀⣴⡟⠁⠀⣸⠀⠛⠀⠀⠙⠓⠋⣀⡀⠀⠀⢀⣾⣃⣀⣀⡀⠉⠂⠈⠘⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡿⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣀⢀⣤⡀⠀⢠⣿⠃⠀⢠⠎⠀⡶⠂⠀⡀⣠⣤⠀⠀⢰⠶⠀⢸⡇⠀⠀⢠⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⡟⢸⡇⠀⢸⡿⢀⡴⠃⠀⢸⡏⠀⢸⣿⠃⣿⠀⠀⣾⠃⠀⢸⡇⠀⠀⣾⣃⡼⢹⣧⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⣿⠀⠸⣇⡤⢿⡷⠋⠀⠀⣠⠼⣧⣠⣾⡏⠀⢿⣀⡼⢿⣄⡴⠻⣧⠀⠀⢸⣋⡴⢻⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠀⣾⣧⡤⠖⠋⠁⠀⠈⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⢻⡀⣠⠟⠁⠀⣿⠇⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⢿⠱⣄⠀⢀⣶⣶⠀⠀⣤⡄⢠⠐⣶⡶⣦⡀⠀⠀⣽⠋⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⡤⢬⡓⠛⠀⢸⡏⣿⠀⢰⣿⣧⣸⠀⣿⠃⢹⡇⠀⢸⠃⠀⠀⢠⡿⢡⣴⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⣿⠀⠀⣿⠃⣿⣇⢸⡟⣿⣿⠀⣿⠀⣾⠃⠀⠸⣦⣠⡴⠋⢰⡿⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣰⠃⠀⠐⢿⠏⢿⡇⠸⠇⠙⠟⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢠⣦⠄⠀⠀⠀⣾⠇⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⠀⢀⡾⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⢠⣶⡦⠀⣼⠇⣠⣾⡆⠀⣴⢶⣄⢀⣴⣤⢾⡆⠀⢀⣴⢿⣿⡴⠋⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣰⠟⣷⡤⣿⠛⠁⢀⣿⡴⢋⣿⡷⢺⣟⢸⡏⢹⣿⠇⢸⡇⠀⣾⠃⡼⣿⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣯⣾⠏⠀⠻⠦⠶⠋⣠⠖⠋⣿⠃⠀⠻⠾⠀⠸⡿⠀⠘⠷⠞⠿⠾⠃⢹⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⠉⠀⠀⠀⠀⢀⡾⠁⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣾⠃⠀⠀⠀⠀⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⣀⣠⠴⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡟⠉⣠⡴⠚⠀⣈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠛⣧⣠⡴⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠲⢾⣙⡏⢀⣀⣰⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠉⠳⢤⣼⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣾⠁⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢻⡄⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⣭⣭⣭⣻⣦⣄⠀⠀⠀⣴⣿⠀⠀⠀⠉⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣿⣿⣿⣿⣿⡋⢿⣦⡀⠀⣿⡞⢧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣀⣿⣿⡇⢾⠛⣧⣼⣿⣷⢾⡛⠻⡄⠙⠲⠤⢴⣿⣾⠻⣳⡆
⠀⢠⡟⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣖⡯⢽⣿⡇⠁⠘⠃⣿⠒⠨⣿⣌⢷⡀⠈⠢⢤⣤⣞⣿⣽⣿⡿⠃
⠀⠘⣇⣿⡲⠯⢉⣽⠛⠓⡶⠦⣶⡟⠻⣿⣁⡀⠚⠈⠳⠤⣼⣷⡿⠖⣫⠟⢿⡜⡇⠀⢀⡿⢋⣩⣴⣿⡟⠁
⠀⠀⠘⣿⣿⠒⠦⣄⡈⣸⡷⠋⠉⢺⣦⡘⣶⠭⠩⢍⡉⠉⠭⣕⢚⣽⣧⣰⣉⡇⣿⣰⠿⠛⠉⠀⠛⠋
⠀⠀⠀⠈⠁⠀⠀⢀⣿⣿⡇⠀⠀⠀⠹⣷⡈⠀⣀⢸⠻⡻⢾⣿⣿⣿⡷⠃⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢻⣳⡶⠤⠤⣤⡼⢷⣾⡞⣳⡕⠪⢜⡻⣿⠟⠁⢀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⢿⡄⣀⣿⣉⡀⢠⡞⣿⣷⣀⠹⠿⠶⣥⡤⠤⠬⠵⠶⣞⣽⠟⠁
⠀⠀⠀⠀⠀⢀⣠⣷⣿⣟⡻⢹⡟⠀⢸⣿⡮⢉⠉⢛⣩⣽⣿⣦⠴⠞⠋
⠀⠀⠀⣠⡾⡿⢧⣿⢿⣿⢠⠞⠀⠀⡼⠧⣽⣶⠿⠛⠁
⠀⠀⢸⡛⣇⣧⣸⡿⡜⢟⣾⡄⢀⣼⠛⠋⠉
⠀⠀⠈⠓⠞⠛⠉⠳⠼⠋⠁⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠟⠃⠀⠀⡟⠋⢸⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⠆⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⠀⠀⢀⡶⡴⡿
⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠟⠉⠛⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣠⣄⣀⣀⡀⠀⠀⠈⠓⠛⠀⠀⠸⠷⠾⠁
⢴⣞⠛⢦⠀⠀⢀⣠⠤⠶⠒⠒⠦⢤⡀⠀⡖⠚⠛⠛⠛⡇⠀⠀⡏⠉⠉⠀⠀⢹⡴⠛⠀⠀⠈⠉⠉⠛⠓⠲⠦⠤⣤⣀⣠⡴⠦⠤⠤⣤⣤⣤⣀
⠀⠀⠙⢋⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢹⣀⡇⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠘⣇⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠃
⠀⠀⠀⢸⡀⠀⠀⠀⣤⢦⡄⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠒⠦⣤⡠⠟⠀⠀⠀⠀⠀⢰⡇⣼⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢧⠀⠀⠀⠘⠋⠁⠀⠀⣠⣟⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡤⠖⠉⠀⠀⠀⠀⠀⣠⡴⠿⢧⣈⡉⠓⣲⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⠁⠀⠀⠀⠀⠀⠰⠿⠭⣤⣄⣀⣤⠟⠋⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡇⠀⠀⠀⠀⠈⠛⠛⢳
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠙⠃⠀⠀⠀⠀⢰⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⡘⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⠔⣱⠳⣌⠒⠤⣀⣀⣀⠠⠔⣪⠵⣋⡈⡉⠛⠶⠠⣄⣀⣈⣉⠛⢂⣠⡉⠀⣉⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠛⠃⠀⠀⢷⡤⠤⠤⠴⠒⣋⡥⠞⢹⡳⣈⠙⠒⠲⠶⠒⠚⢋⣥⣾⠙⢻⠇⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠧⠤⠭⠭⢭⣭⣭⣭⡭⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠉⠁⠀⠀⠀⠙⠛⠃⠀⢲⣶⡆⠀⠀⠀⣈⠓⠋⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢀⡴⢒⡆⠀⠀⠀⠀⠀⠀⠀⣻⡍⢿⡃⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣮⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢾⡋⠛⠲⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠙⢦⡀⠈⢳⡄
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠻⣄⠀⠹⡄
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠒⠒⠒⠒⠒⠒⣒⣶⣦⠀⠈⢧⣀⢊⣀⣀⣠⣤⡤⠤⢤⣤⣀⣀⠹⣆⠀⠹
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣀⠀⠀⢀⣀⣠⢶⡛⢉⡙⣿⣧⠀⠘⣏⠉⠀⠀⠀⠒⠒⠒⠲⠦⣄⡉⠓⣾⡆⢰
⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⡤⣄⡀⢸⠂⠈⢹⣿⢆⠀⠎⠀⠶⠂⠈⡟⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠸⣿⣼
⠀⠀⡏⠀⠀⠀⣀⢴⡞⠁⠀⢀⣈⣿⠐⠤⠀⠤⠊⠀⠀⠀⢀⣀⠔⠁⠀⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣸⢋⡇
⠀⢸⡇⢀⡤⠊⠁⡼⢀⡔⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠀⣠⠤⠤⢤⣀⠀⠀⠀⢠⠎⡴⢋⡞⢀
⢀⣼⠟⠡⠀⠀⢠⣧⡏⠐⠃⠀⢸⠛⠀⢀⠀⠀⠤⡀⠀⠀⠀⣀⢀⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠁⢀⠴⣡⠞⢁⠞⢀⡞
⠋⢸⡇⡄⠀⢀⠞⢼⠀⠀⠀⢀⢼⠟⡆⠉⠀⢤⠀⠀⠀⠐⢪⠏⠀⠈⠀⠀⠀⢸⢳⠤⣄⣀⠀⠀⢔⣡⠞⠁⡰⠋⢠⠞
⠀⠘⡇⡇⠀⡏⠀⠘⢦⡀⢠⢯⠏⠀⣷⠀⠀⠈⠲⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⡟⠀⣀⣤⠭⢿⣶⡋⠀⢀⠞⠁⣠⠏
⠀⠀⢷⠘⣄⣀⣀⣤⣤⢽⣿⠏⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢋⠕⠒⠉⠐⠂⠙⢶⠁⠀⡴⠁
⠉⠉⠹⡏⠉⠁⠀⠀⠀⣾⡟⠀⠀⠀⢠⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠁⠀⣠⠖⠒⠲⢴⡃⢤⠈⠀⠀⠀⢀⣠
⠀⠀⠀⢹⡄⠀⠀⠀⢸⣿⠁⠀⠀⣠⠃⡰⠛⢦⣈⠂⠂⠀⠀⠀⣀⡤⠞⢱⠃⠀⠀⢸⠁⠀⠀⠀⠈⢳⣄⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠹⡄⠀⠀⣿⡇⠀⠀⢠⠇⢰⠁⠀⠀⠈⠉⠛⠛⠋⠉⢁⣤⡶⢻⢀⡤⠒⡻⣄⠀⠀⠀⣠⠟⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠙⢆⡰⢿⠃⠀⠀⡾⠀⠳⣄⡀⠀⠀⠀⠀⣀⡴⢚⡩⠊⣠⠞⠉⠀⠀⠑⠈⣱⠖⣋⡥⠖⠛⠉⠉⠉⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠈⡷⣼⡄⠀⠀⡇⠀⠀⠀⠙⠶⠖⠚⠋⣡⠔⠁⢀⡼⠁⠀⠀⠀⠀⣠⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡇⣼⣷⠀⠀⢣⡀⠀⠀⠀⣀⡠⠔⠋⠀⠀⢠⠏⠀⠀⠀⠀⠀⡴⠃⡜⠁⠀⢄⣀⠀⠠⢀⢠⢤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⠘⢦⠀⠴⠚⠛⠉⠉⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡜⠁⡜⠀⠀⠀⠈⠈⠀⠈⠀⠈⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠲⠤⠞⠋⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠙⠺⠃⡀⠐⠒⠀⠀⠄⠀⠀⠀⠀⠒⠄⠈⠛⠉⠉⠉⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠈⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⢴⣦⠄⠀⣤⠜⡇⠀⠀⠀⠀⠀⠶⣙⡆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣑⣤⠘⠟⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡞⢁⠎⠀⠀⠘⠁⠀⠀⠾⠒⠃⠀⠀⠀⠀⢀⣀⣀⠁⣀⣀⣀⠀⠀⠈⠿⠗⠀⠸⠭⠞⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠰⠞⣓⣾⢀⡤⠴⠒⠒⠒⠦⡀⢰⠛⠛⠉⢻⠀⣸⠉⠁⠀⠈⣶⠃⠀⠈⠉⠉⠐⠒⠲⠤⣤⡴⠖⠶⠤⠤⠦⠤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⣀⠀⠀⠀⢹⢸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⢄⣒⠀⠠⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢣⠀⠀⠘⠟⠀⠀⢀⡞⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡠⠙⠉⠀⠀⠀⣀⡴⢇⡁⠀⢠⠀⠀⠀⢸⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠁⡘⢇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠐⠾⠥⢤⣤⡼⠛⠁⠀⢀⡤⡞⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠸⡄⠀⠀⣶⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠁⠀⠀⠀⠈⠉⢹⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣧⠀⠀⠀⠀⠀⢀⠀⣯⡀⢄⡀⠀⠀⠀⢄⡼⠛⠲⠤⣤⣈⣀⠂⠀⠤⣀⠃⡄⠀⠀⠀⠀⠀⠀⢸⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠘⣤⠤⠀⠀⣂⡥⠚⣶⣉⠓⠢⠤⠒⠚⣩⣎⢙⠇⠀⠀⠀⠈⠉⠓⠋⠹⠤⠬⠭⠭⠭⣥⠴⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢉⡉⠉⠉⠀⠀⠀⢨⣉⣀⠘⠿⠀⢀⣠⡌⠉⠀⠀⠀⠀⠀⢰⠦⡄⠀⠀⠀⠀⠀⢰⣦⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣥⡏⠀⠀⠀⠀⠒⢾⡷⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠹⡇⠀⠦⠀⠀⠀⠈⠁⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠖⠻⣆⠀⠈⠐⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⣠⡴⢦⣄⣀⣀⣀⣀⣠⡤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⢀⠈⢎⠦⠀⠀⠀⠀⠀⠀⠈⢫⡱⠀⠀⠀⠀⠀⢾⠐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠠⠔⠢⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⢕⠔⠋
⠀⠀⠀⣀⣠⠤⠤⢤⣄⡀⠀⠤⠒⠒⠒⡖⢠⠖⠒⠒⠒⡆⠠⠤⠤⠄⣀⣀⣀⣀⣀⡀⠐⠋⠓⠁
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠹⡆⣿⠀⠀⠀⠹⠼⠀⠀⠀⠀⣧⣄⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⡖⠒⠶⠤⠤⣄⣀
⠀⠀⠈⡄⠀⢖⠂⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠧⢤⣀⠀⠀⠀⠀⢀⣼⢰⠃⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⠓⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⡶⠉⠀⠀⠀⡴⠃⢸⡼⠦⠤⣄⡀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⢰⢃⡤⠊⠀⠀⠀⣠⠊⠀⠀⠀⠉⣉⠶⠖⠋⠀⢀⡠⠞⠁
⠀⠀⠀⠀⢻⠀⠀⣠⠤⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣾⢺⠀⠀⠀⠀⠘⠓⠒⢲⠆⠔⡏⠀⠀⠀⣠⣔⣋⣀⡀
⠀⠀⠀⠀⠈⡇⠀⠘⠖⠃⠀⠀⢀⣼⠧⠤⠤⢤⡶⠋⢸⡸⠤⢄⣀⣀⠀⠀⠀⢸⢰⢠⠃⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⢻⣀⣠⡤⠴⢒⡫⠝⠉⠀⠀⠉⠁⠀⠀⠸⠥⢄⣀⣀⣈⠉⠛⣲⠏⣸⠜⠙⠒⠒⠲⠦⠤⢄⡜
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠁⠠⠸⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⠀⠉⠉⠉⠐⠒⠢⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣨⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠔⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⣍⢻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠄⠀⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠁⠁⠀⠉⠉⠛⣹⡿⢆
⠀⠀⠀⣼⣿⣶⣬⡈⢀⠈⢀⣤⣴⡾⠛⠹⠉⠛⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠧⡍⠀⠀⡀⠀⠤⠈⠁⣿⡀⠀⠃
⠀⠀⢰⡿⠿⠛⠛⠻⣟⡀⢠⣙⣻⡏⠁⢋⠠⣧⠀⠀⣀⣠⣀⣀⣀⠀⣿⢘⣠⣄⡐⡀⡰⠀⣤⡄⠀⠀⢀⠀⠁
⠀⠀⢸⣧⡼⢿⣿⠑⠀⠀⣈⠹⣿⣷⣿⠋⡇⠈⠀⢹⠟⠉⣉⢙⠏⡼⢿⡭⠇⠉⠁⠀⠀⠀⠈⠀⠀⣠⣿⡇⠈
⠀⠀⠀⢿⣦⣤⡝⣠⠀⣴⠋⠋⠋⠛⠛⠻⢛⡃⠀⣸⡶⠀⠀⠤⣺⣧⡀⠀⢀⠄⠘⠶⣶⣶⣿⣶⡿⣿⣿⣇
⠀⠀⠀⠀⠙⢿⡇⠀⠀⠙⢠⣀⠀⠀⠀⠀⣹⣧⣴⣧⡆⠀⠀⠀⣀⠽⠇⠀⢀⣀⠜⢲⠉⠉⠉⠉⠀⠈⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠶⠶⣻⣿⢧⣀⣠⣄⠁⠨⠀⠄⢀⠀⡀⠄⠀⠀⠀⠀⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢻⡏⢒⣒⠙⣿⠑⠇⠰⠀⠀⢼⠟⠁⡁⠀⠀⢀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧⡉⠄⢁⣿⢀⢀⡀⠀⣡⣾⣄⢀⠙⠇⠰⢳⣤⠄⠀⠀⠀⠀⠀⠀⠀⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠰⢿⣿⣷⡜⣿⡈⠀⢀⡴⠿⣿⣿⡋⠀⠐⣢⣾⡿⠖⠀⠀⠀⠀⠀⠀⠀⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠉⠿⢷⢘⡿⠠⢐⡳⣶⠋⠉⠻⡃⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡲⣿⣗⢰⡜⠇⡀⠠⠀⠨⡅⠒⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭
⠀⡰⠾⠿⠟⢲⡄⠀⠀⠀⠀⠀⠸⣷⠚⠀⠀⢰⠂⠻⡂⡘⣥⢸⣿⡀⢴⡆⡇⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣶
⠰⠓⣂⣉⣩⣍⣩⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢠⣴⡋⠋⠁⠀⣿⣯⠘⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿
⠀⠻⣿⣧⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠿⠀⠶⠀⠻⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⠒⠒⠲⢤⣤⠶⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠶⠞⠁⡀⠤⠤⠤⢄⡀⠠⠄⠀⠠⠤⣄⠈⠓⠚⠛⠓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠠⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣀⡤⠶⠚⣁⣌⡀⠀⢀⣠⢿⠀⠀⠀⠀⠀⢀⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⡘⣧⣤⣄⡀
⠀⠀⠀⠀⡴⠋⡠⠂⠀⠸⠞⠁⠀⢸⡭⣼⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠰⣖⣦⠀⠀⡟⣺⠇⠀⠀⠀⠙⢦
⣀⣷⢄⣼⠁⠘⣀⣀⣤⣄⣀⠀⠀⡬⠤⠤⢤⡄⠀⡴⠒⠒⠒⢲⣠⡞⠒⠒⠲⠤⠤⣄⣀⣀⠀⢉⣉⣀⣀⣈⢢⠀⠈⣧
⠈⠑⠚⣿⠖⠋⠁⠀⠀⠀⠈⢱⢸⠁⠀⠀⠈⠣⠴⠃⠀⠀⠀⠘⡇⠦⣀⣀⡀⠀⠀⠀⠀⠈⢹⠋⠃⠀⠀⠈⠉⠉⢹⢻
⠀⠀⡼⡇⠀⠀⢠⣶⡄⠀⠀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠒⣤⠼⠃⠀⠀⠀⠀⡿⢸⡀⠀⠀⠀⠀⠀⡞⣼
⠀⣸⠃⢸⡀⠀⠀⠉⠀⠀⠰⠿⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠊⠁⠀⠀⠀⣠⠴⠛⠑⠢⣤⡭⠃⠀⠀⢀⡇⠙⢦
⠀⡟⠀⡆⢧⠀⠀⠀⣀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠉⠉⠛⠶⠟⠁⠀⠀⠠⠶⠭⡄⠀⢸
⠀⣧⠀⠁⠘⡄⠀⠀⠛⠃⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⣠⣟⠐⠤⠄⢀⣀⡀⠀⠀⠀⡘⢀⠃⠀⠀⠀⠀⠀⠀⡇⠀⣸
⠀⠘⣧⣀⠐⢳⠀⠀⠀⠀⢀⡠⢔⡜⢦⣑⠤⠄⠀⠠⣐⡬⣪⣌⡉⠓⠲⠦⠤⣍⣉⣐⣶⠇⢸⣀⣀⣀⣀⣀⣀⣸⣇⣼⠋
⠀⠀⠈⢻⠂⠈⣷⣒⣒⣨⠥⠖⠋⠻⣧⡌⠉⣉⡉⠉⠡⠾⣇⡹⠃⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠒⠲⠞⠋⣉⣿⠁
⠀⠀⠀⢸⡄⢀⡰⣄⠀⠀⠀⠀⠀⡰⣦⢤⠄⠙⠋⠀⢠⣴⠎⠀⠀⠀⠀⠀⠀⢸⣓⡆⠀⠀⠀⠀⠀⢘⣿⠆⠀⢸⡟
⠀⠀⠀⠀⠙⢾⣶⡃⠈⠁⠂⠀⠉⠙⢟⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠘⢇⠠⠒⠒⠒⠈⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢧⡀⠀⠈⠁⠐⠒⠒⠈⠉⠀⠑⠒⠀⠀⠐⠒⠒⠈⠀⣠⣤⣤⣤⣤⡤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣤⣤⣠⣤⡤⠶⠦⣤⣀⣀⣀⣀⣤⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠖⢦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡈⠀⠈⣀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡻⠿⢷⣤⣴⠿⠿⣿⣇⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⣷⣿⣟⢰⣵⡀⣀⣙⠀⢹⠂⠀⣠⣥⡜⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢉⡵⢨⠞⠉⠭⢢⠅⠽⠦⢴⣢⠉⠙⣇⠠⡀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢃⢸⡃⠀⠀⢹⡷⠒⠀⣿⠁⠀⠀⣏⠘⠀⠀⠀⢀⣠⡄⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡎⠹⡦⢼⣫⣇⣤⣎⣽⣾⣽⡏⣾⠉⠉⠿⠶⠾⠃⠁⣰⠘⠧⢽⠷⠴⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⡷⢰⠁⢸⣭⣀⣀⣀⣀⣿⠀⢹⣿⡇⡤⡴⢀⠀⠀⠀⣿⣞⣀⣼⣤⣤⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⠀⢸⠛⣯⠉⠉⠉⠹⠿⠿⡍⢙⣭⣖⣊⣒⣂⢀⠀⣔⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠼⡇⢻⣯⣿⠀⠀⠀⠀⠀⠀⠑⠼⣻⣿⠿⢿⡿⠙⠄⠀⠀⢀⡤⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠁⠈⢀⡀⠀⢠⣶⡿⡓⠂⠐⢚⠳⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⡀⠀⠀⠀⠰⠋⠃⠀⠀⠋⠉⠀⠈⢿⡰⣷⠄⠠⣾⢂⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⢟⡿⠋⠛⠛⢻⣿⣆⠀⢀⢀⡄⠀⠀⠀⠀⣠⠀⠀⠀⠳⣿⠀⡇⢸⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣔⣆⠈⠸⣍⣹⣷⣌⠉⡐⠀⠀⠀⠀⣄⡀⠀⠀⠀⠻⠄⠧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠛⠋⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠲⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠡⡈⢄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠁⠀⠀⠀⠁⢀⣉⠒⠄⠈⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠤⡚⠍⢙⠓⠈⠀⠀⠀⢀⠀⠀⠀⡀⠀⠄⠀⠀⠤⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠒⠶⣶⠀⠀⡌⠰⣶⠄⠐⠀⡄⠀⡄⠞⠒⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠈⢈⡇⠀⠐⠄⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡜
⠀⠀⠀⠐⠀⠀⢀⠄⠀⢄⢀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⢀⡠⠊⠀⠠⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌
⠀⢀⠔⡣⠁⠀⠀⠁⠀⠀⠀⠀⡠⠐⠘⠀⠀⠀⠀⣈⠀⣀⠠⠘⠉⠁⠠⠀⠀⠀⠰⡤⡀⠀⡀⠔⠀⠀⢀⠂⠀⢀
⠀⠁⠀⠁⡀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠀⠀⠊⠀⠘⠇⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⢀⠀⡐⠁⢀⠐
⠀⠀⠀⢀⠐⠀⠀⢄⠀⠄⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡡⠐⠈⠔⠀⠀⠈⢂⠁⠁
⠀⠀⠀⠀⡠⠀⠀⣠⠏⠀⡀⠁⠀⠀⡀⠱⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡠⠐
⠀⠠⣀⠀⠧⠀⠁⡀⠀⡐⠀⠀⠀⠐⠀⠀⠀⠑⠢⠀⠀⠀⠀⢂⡤⠐⠈⠀⡄⢀⠠⠰⢆⠀⠀⠀⠀⣐⠀⠌
⠀⠂⠀⠀⠀⢆⢠⠀⠐⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⢀⠠⢂⠜⠀⠀⠀⡠⠊⠀⠀⠠⢀⠁⠀⠰⠊⠁
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠂⠁⢀⠄⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠸⠹⢄⠀⠀⠀⠀⢂⠀⠀⠈⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠢⣢⢁⠢⢀⢀⡀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡤⠖⠒⠋⠉⠉⠉⠉⠉⠙⠒⢲⣤⣄⡀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠙⢦⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⢧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣇⣧⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⢻⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢠⠎⠳⣄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣶⣄⡀⠈⢣⠀⣿⠀⠀⠘⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠶⠶⣶⣶⠶⠀⠀⠛⠟⢛⡿⢷⡶⢤⡀⠀⠁⠀⠈⡇⢸⠀⠀⠀⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⢰⠻⣽⡟⢳⢹⠀⠀⠀⢾⣙⣛⣁⣠⠼⠀⠀⠀⠀⢸⡘⡆⠀⠀⣻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠘⠲⠶⠖⠊⢸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⡇⢷⠀⢀⡟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⣸⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⢦⠊⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠰⡿⠀⢀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⡆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇⠀⠀⠀⠀⠉⠓⠚⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠈⠷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠀⢶⣋⠉⠉⣉⣩⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠒⠶⠤⣄⣉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣉⡤⣧⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡗⠦⢤⣀⠈⠙⠲⢄⡉⠳⢦⡀
⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠁⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢳⡀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠻⣄
⠀⠀⠀⠀⣼⠃⡴⠃⠀⢀⡔⠉⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠳⢄⡀⠀⢸⠄⠀⠀⠀⢻⡀⢹⡆
⠀⠀⠀⢸⠇⣸⠁⠀⠀⣼⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠹⡄⠸⡄⠀⠀⠀⢀⡇⢠⡇
⠀⠀⠀⢸⡆⢻⠀⠀⠀⢹⡀⠀⡴⠃⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⣆⠀⢀⡼⠀⣼⠁
⠀⠀⠀⠀⢳⡈⢧⡀⢠⠏⠈⠓⠷⣄⡀⠀⠙⠲⢤⣀⣀⣀⠀⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⡰⢋⡠⠊⢠⡾⠁
⠀⠀⠀⠀⠀⠙⢦⡙⠿⣄⠀⠀⠀⠀⠉⠓⠢⢄⡀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣠⣾⠖⢋⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣙⠒⠦⢤⣀⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣤⠤⠖⢋⣁⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣍⣉⣛⠓⠛⠲⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⣋⣉⣩⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠁

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠉⠉⠉⠉⡉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⠈⠀⢰⠒⠆⠉⠁⠈⢉⣙⠲⢄⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠊⠀⠀⠀⢈⠣⢠⠄⡙⠉⣛⡙⣷⠈⡆⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠁⠀⠀⠀⢠⠊⠠⡶⠀⠀⠀⢸⠃⢸⠄⠱⠀⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠂⠀⠀⠀⢀⡞⠠⠀⠐⠂⠀⠀⠀⠀⢙⢠⠜⠀⠀⠀⠀⠀⡎⣧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⠰⢆⠀⠀⠀⡾⠀⠈⠠⣀⠴⠂⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⢸⡆⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⣠⠴⢛⠀⠈⡉⢠⠀⠀⣷⠀⠄⠀⠀⠀⠀⠀⠀⠀⣰⠣⢄⠀⠀⠀⠀⣀⢼⢈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⢀⡞⢡⢂⠔⡃⠐⠑⠂⠀⠀⣈⢳⣄⠀⠀⠀⠀⠀⢀⡼⠁⢀⡀⡇⠀⠀⡰⡡⠚⢬⠛⢦⣄⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢠⠏⠀⠁⠀⠊⠈⠲⠄⣠⠚⢁⡠⠚⠄⣉⡒⠒⠒⣚⠉⠠⠤⢘⡶⢚⡩⠍⢽⣀⣤⠚⠤⠂⢸⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⡞⠀⠀⠀⠄⠀⡐⠀⠀⠀⠀⠩⢁⡁⠀⠂⠀⠤⠤⠔⠒⠒⠂⠉⢀⠤⠐⠀⡠⠤⠊⢳⢀⢆⠘⡆⠀⠀⠀⡇
⠀⡇⠀⠀⠀⡇⢀⠀⠀⠀⡐⠀⠀⠀⠂⢀⠐⠜⠁⠄⠉⠉⠉⠉⣉⠑⠀⢀⠔⠁⢀⠔⢉⣠⠴⠶⠾⢭⡆⡼⠁⠀⠀⠀⡇
⠀⡇⠀⠀⠀⣇⠀⠘⠠⠁⠐⢄⡉⠀⠀⠤⠊⠀⢠⠖⠀⠐⠂⠂⠀⠀⠀⠁⢀⠔⢁⡴⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠘⠳⢤⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡇⠀⠀⢀⠂⠀⠀⠀⠀⠐⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠳⣄⣀⣀⡀⠀⠈⠐⠂⠁⠀⠀⣀⡐⣈⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠴⠐⠂⠀⠰⠂⠄⠂⠒⠀⠠⠤⠀⠐⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⡗⠻⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⢀⠄⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢯⣿⣿⣿⠳⠞⠀⠂⢸⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠙⠀⠀⠗⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢰⣿⣿⣿⣴⣤⣤⣤⣼⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣸⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠛⡻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡆⠘⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠚⠀⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣽⣿⣿⣴⣶⣶⣶⣿⣿⣿⣷⣶⡾⢰⣿⣿⣯⣿⠿⣿⣿
⠀⠀⠀⠐⠁⠀⠘⢦⡄⢀⠀⢀⡠⠤⠀⡀⠀⡀⠊⠐⠋⠉⠀⠀⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠸⣿⣿⡟⠃⠰⡝⠿
⠀⠀⠀⠀⠄⠀⠒⠀⢉⣿⣶⣿⡄⠬⠭⡬⣿⡀⢡⠀⠀⡀⠀⠔⠀⠀⢰⣿⣿⣿⠋⢈⣿⣿⣧⣿⣿⠻⠛⠛⠛⠋⠛⢿⣷⣦⣀⠀⢹⣿⣿⣦⣤⣤⣤
⠀⠀⠀⠘⠀⠂⠀⠀⣾⠈⢰⣏⣀⡀⠁⠀⠘⠁⠀⠁⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣷⣶⣶⣶⣶⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⢯⣿⣿⣿⣿⣿⠿⠟⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣵⢛⣹⣿⣿⣿⠏⠀⢹⣿⣯⣥⡾⠁⠀⠀⢻⣿⣿⣿⢱⣄⡰⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⠀⢀⣀⢀⠀⠀⠀⠛⠚⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣀⠀⠈⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢓⢢⡀⠀⠀⠀⠀⠀⠀⠐⡾⢣⠀⠀⠀⠀⠀⢠⣆⠄⡢⠋⠁
⠀⠀⠀⠀⠀⠀⠃⢐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⣀⣈⣁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣂⢀⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣤⠤⣤⢀⣀⣀⣀⣀⣀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣌⠔⠁
⠀⠀⠠⠖⠛⠉⠉⠉⠙⠲⣄⠀⡇⠀⠀⠀⣇⣿⠀⠀⠀⠀⣿⠈⡍⠉⠉⠉⠙⠒⠒⠒⠒⢦⢀⣀⣀⣀
⠀⠀⠐⡀⠀⣀⣀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡅⠀⠈⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⢧⠀⠘⠊⠀⠀⠀⣼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⢉⣙⣲⠆⠀⠀⠀⢀⠜⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠉⠉⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⠜⠁⠀⠀⠀⡴⠋⠀⠰⢭⣉⣓⠲⣦⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢰⣧⡔⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⣠⠴⠋
⠀⠀⠀⠀⠘⡆⠀⠠⡖⢲⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠟⡃⡇⠀⠀⠀⠀⠉⠉⠉⡹⢰⠋⡇⠀⠀⠀⠴⠾⠥⠤⣄
⠀⠀⠀⠀⠀⢻⠀⠀⠉⠉⠀⠀⣀⣤⡾⠓⠶⠶⣒⠟⠋⠀⡷⠓⠦⠤⢤⣀⣀⠀⠀⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⣦⠤⠤⠶⢚⡫⠕⢊⠀⠀⠈⠁⠀⠀⠀⠘⠣⠤⠤⠤⢀⣀⣉⣉⠟⢁⡷⠋⠉⠉⠙⠛⠒⠲⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⡐⢻⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠐⠒⠢⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡭⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠲⠊⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⢜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁