Bunga Emojis & Symbols

⠀⠀⡀⠠⠐⠘⢶⣆
⠀⡘⠃⢀⣤⣀⡸⠃⠀⡀
⠐⠖⠚⠉⠀⠘⡇⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠈⠄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⣖⠄
⠀⠀⠀⠀⠀⣈⣦⠄⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⣨⠞⠋⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣶⣀⠷⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣼⡁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢴⣇⣐⢛⣧⠀⠀⢠⡟⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣥⣲⣦⣄⣤⡾⠋⠀⠀⠀⠀⠀⠀⣜⠈⠀⠉⠛⠷⠦⠖⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠐⠂⠀⢐⣶⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣬⠉⠉⠁⠀⠀⠀⠄⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣦⠤⢀⠀⢀⣜⣁⢤⡀⣰⡆⠀⠀⠀⢀⣄⡤⠂⠘⣿⠛⡈⠦⠀⠀⠀⠀⠐⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠃⠀⠀⠈⠉⠁⠀⠀⡛⢁⠇⠀⠀⣠⡟⠉⠀⠀⠀⠈⠳⣤⠚⠹⡆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠠⡴⠖⠘⣆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣻⡶⠁⠀⠀⠰⠀⠀⠈⣧⠀⠀⠀⡀⠀⠀⢀⡾⠋
⢰⣏⣀⣀⣼⣧⠔⠛⢁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣴⣥⡰⠞⠋
⡇⡉⠉⠈⠁⠁⠀⠀⠸⡴⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠈⢧⡔⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠱⣈⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠶⠄⠰⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠋⠁
⠀⠻⣆⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢠⣆⣰⠦⠀⡠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠙⢦⣄⣄⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠛⣾⠛⠦⠾⠴⠆⣤⣼⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⢸⠃⠀⠀⠀⠀⠀⡆⠐⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⡔⢙⣏⠉⣠⣼⠦⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⢈⣠⠀⠀⠀⠘⠀⠐⠀⠀⠀⢰⣿⠉⠉⠁⠀⠀⠀⠈⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⡌⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣇⣬⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣆⠀⢀⡴⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⢹⣷⠞⠁⠀⠀⠀⠀⠀⠄⠀⠀⣤⡾⠛⢧⣙⠐⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⢀⣾⠋⠀⠀⠀⠈⠉⢹⣌⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡘⠀⡾⠁⠀⠀⠀⠀⠀⢠⠏⢈⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⢀⡴⢁⠴⠉
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⢻⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣇⢳⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣎⣏⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠖⠒⠦⣄⣀⣀⡀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣀⡴⠋⠙⠒⢺⣹⠛⠒⠊⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⡎⡏⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡜⡼⠁⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⡀⠀⠀⢠⠸⡄⡄⠀⠀⡟⣠⢊⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠁⠁⠀⢀⠼⢋⠕⢁⣩⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡽
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⡀⠀⢀⠜⢁⠔⣁⡠⠤⠤⠤⠤⠤⠶⠶⠶⠶⠯⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⠙⠦⣯⣀⣾⠋⠁⢀⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⣈⠑⢦⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠐⢰⢹⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠲⢤⡤⠔⠒⠚⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣀⣀⣀⡤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⣀⣀⡤⣤⣀⠀⠀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠚⠉⠉⠉⠙⡋⠉⠓⠚⠓⠦⣀⠀⠈⢧⢸⡈⠉⠉⠁⠀⠀⠀⠀⣀⡤⣶⠦⠖⠚⠉⢉⠉⠛⠚⠓⠒⠒⡒⢲⠄
⠀⠠⣶⣶⣒⣒⠉⠰⢤⡀⠀⠈⠳⡀⠀⠀⠙⣆⠀⠀⠳⡀⠈⢳⡀⠘⡇⢳⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⡤⠀⠀⣐⣡⡤⠤⠐⠂⠈⢁⡴⠃
⠀⠀⠀⠙⢦⡀⠀⠭⠝⠋⠓⠒⠒⡾⠦⠤⣄⣘⣆⠀⠀⠹⡄⠀⢳⠀⢹⠸⡆⠀⠀⡴⠋⡠⠂⠀⣠⣫⠴⠒⠋⠙⠒⠠⠄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠒⠒⠉⠀⠀⠀⢀⡠⠋⠙⠒⠤⣽⠀⠈⡇⠈⡇⡇⢀⡜⠁⠀⢀⡤⠚⠫⢄⡀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠠⠄⠒⠚⠁⠀⠀⠀⢀⡠⠊⠉⠢⡹⡀⣇⡇⡼⠀⡠⠚⠁⠀⠀⠀⠀⠈⠉⠀⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⠀⠀⠀⢀⣀⠤⠔⠊⠉⠀⠀⠀⡠⠟⢿⠿⣿⡡⠋⠓⠤⢀⡀⢀⠀⠀⠀⠀⢠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣶⡄⠀⠀⠀⢀⣀⡤⠔⠋⠀⠀⠈⡇⡿⠥⣄⣀⠀⠀⠀⠀⣈⣩⠥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠀⠈⠉⠙⠓⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢗⣠⡴⠂⠀⠀⠰⢠⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⠀⠐⠀⠠⡀⣀⡀⢀⡼⠟⠋⠀⡀⠀⢲⣦⡀⠓⠬⠁
⠀⠀⠀⠀⠀⣀⡀⢤⠄⡹⣇⠀⠀⠀⣰⣿⣿⣿⣏⠀⠀⠀⠀⠀⠤⠬⢈⠉⠔⠀⡄
⠀⠀⠀⠀⠀⠈⠐⡗⡈⠻⣻⠷⠖⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠄⠋⠰⠀⠛⠰⠻⠈⠀⠀⢘⠿⣿⡿⠉⠀⠉⠒⠄⠀⠀⠀⠀⣄⣤⡀⣸⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⠃⠀⠀⠀⠀⠈⡆⠀⣸⣿⣿⣿⣿⡉⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⡀⠀⠀⠀⠀⠠⠀⠛⠁⠙⢻⣿⣿⣿⠟⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⠋⠀⠀⣄⢸⢏⢤⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⣱⡏⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⢼⣿⣿⣿⣾⠤⠄⠑⢤⣾⠃⣦⠀⢀⢪⣠⠈⡋⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢿⣿⣿⣿⡁⠀⠀⠀⡇⠀⠘⠀⠀⠈⠁⡞⠙⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠼⠏⠍⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣴⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠘⠀⠀⠀⠀⠈⠉⢁⣶⡆⠀⠀⠉⠐⠖⠈⠉⢛⣿⠦⣥⣈⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣠⡠⠀⣠⠀⠀⠀⠀⠀⠈⠉⠻⠄⠀⠀⠀⠀⠈⣿⣿⣿⣶⠄⢀⣀⡀⠠⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⣴⠳⠔⠚⣡⣤⣌⣼⣷⠀⠀⠀⠀⢀⣰⣿⠆⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣼⣏⢩⣷⣾⣿⣿⣿⠿⠣⣄⣀⣀⡴⣶⣶⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠟⣯⠁⠀⣀⢺⣿⠟⠘⠋⠁⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠀⠙⣄⢀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣶⠀⣀⣄⡤⠀⡀⠠⣇⠀⢸⣿⢿⣿⣿⡿⢀⡠⠾⠒⠀⠀⠰⣽⣦⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠚⠛⠁⠀⠀⠀⠉⠎⢵⡉⠀⠀⠀⠀⠀⠀⢾⣿⡿⠟⠓⠢⠤
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠊⢇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⣶⣶⣾⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣤⢱⡍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠙⠟⡿⣲⣶⡄⢀⠀⠀⠀⠈⢶⣶⣿⣶⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡾⣿⢉⣰⣿⢟⡛⠀⠀⠒⠢⣝⣶⣾⡆⠀⣠⣄⢘⣉⡀⠀⠀⠀⠀⠀⠀⣼⣫⣿⠿⣄⣀
⠀⠀⠀⠀⠀⠘⣭⡍⠓⠢⢍⡩⡌⣀⣬⣓⡙⣦⣀⡀⠀⠘⠻⠿⣷⢸⣿⣄⠉⠀⢍⠳⣶⣄⣠⣴⠊⠉⠉⠉⠀⠠⣍⠛⠓
⠀⠀⠀⠀⠀⠠⠋⠀⠀⠉⠢⡙⢮⡿⠛⠉⠀⠘⡏⠙⠣⠀⠀⠀⠿⢸⠋⠻⣧⡀⠀⠻⣾⣿⡽⠿⠷⠄⠀⣀⡀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢀⣀⣀⡁⠤⢼⡿⣛⣤⣼⣿⣤⣤⢼⣿⣦⠄⣰⠋⠀⠀⠀⠀⠑⠺⣽⣣
⠀⠀⠀⠀⢀⣀⠀⠀⢀⣤⣀⣀⣴⣧⣤⡿⢳⡿⠁⢀⣤⡶⠟⠛⠫⠯⠩⡤⣄⡈⠉⣹⣯⣃⠐⠂⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠐⠋⠉⠀⠀⠀⠀⠂⠤⢬⣙⣿⣿⡇⡿⠁⢀⡜⢰⢃⡠⠐⢛⣍⠉⠛⠛⠙⢷⣿⣿⣛⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠻⣄⠀⢸⣧⣤⠂⠀⠈⢲⣢⣄⣪⡁⢀⠟⠈⠉⠁⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡾⣷⣼⣿⣿⠇⣠⢶⠏⣿⠈⣿⣿⠿⡶⠄⠀⢀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢅⠜⠛⠁⠀⠀⠈⣩⣿⣾⣿⣿⠀⢹⣄⣸⣿⡿⠛⠀⠀⠊⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠁⠀⠀⠀⢀⡤⠒⠉⠙⠛⠛⡫⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡿⠁⠈⢿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⠀⢀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⣿⣿⣻⣿⣿⣄⣾⣿⣿⡇⡀⠀⠀⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣷⣶⣦⡸⠿⠫⢿⣿⣿⢿⣿⣿⣯⡿⢿⠿⣙⠃⠀⣤⣍⡀⠀⣾⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⢻⣯⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⡍⠃⠀⠻⣿⣷⡶⣪⡻⢟⣿⡿⢿⣷⣦⠄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⡿⠙⢿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣮⠁⠀⣠⡀
⠀⠀⠀⠀⠀⠈⠀⠛⠛⠳⢿⣿⣵⣿⣿⡿⠁⠀⠀⢹⠃⠀⣰⣿⣿⣿⠿⢻⣿⠟⠁⢦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡿⠺⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⣰⡀⠀⣀⣤⣤⣶⣿⡆⠀⣀⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⢰⣿⣗⢰⣿⣿⣿⣿⢿⣷⣿⣿⣷⣾⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠘⢡⠀⠸⣮⣭⣥⢛⣛⠛⢿⣿⣿⣷⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠿⠿⠹⣿⣿⡿⣿⣿⣿⣗⣟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⢹⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⠀⠹⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠓⢄⣰⠊⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⢸⠇⠀⠀⠀⡰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠐⢼⣤⣆⡠⠖⠓⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠩⡷⣤⢏⠒⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⣠⠃⠈⠀⠹⠒⠤⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠀⠈⠉⠁⡨⠋⢹⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠑⠀⣰⠁⠀⡀⢧⠀⠀⡜⡟⠲⡄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⣧⠀⡈⡐⠀⠑⠊⣀⣇⢀⡞⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠈⠈⠙⣆⠀⡁⠀⠰⣉⠀⢈⡿⢽⠊⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠙⢧⣇⠀⠀⠀⢉⣟⠀⢨⠓⠒⢒⣃⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠘⠛⢄⡀⠀⢸⡘⠖⠁⡠⠊⠁⠀⠉⠲⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡇⣿⣄⠾⠟⠁⠀⠀⠀⢀⣟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣇⢙⣧⣶⠖⡀⠠⣤⠄⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠈⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆⠀⠀⠀⠀⠀⢀⠀⡈⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠛⡀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠤⣤⡁⠠⠊⠀⠀⠀⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦⣀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠓⠀⢢⢀⢐⠠⠀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠐⠂⢠⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡤⠈⢕⣣⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠈⠲⣄⠀⢀⡠⠀⠐⠀⢀⡀⠀⣠⣤⠵⣧⡔⠋⠉⢉⡓⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠈⠊⠁⢹⣿⣶⡗⠠⡀⠀⠀⠀⠐⠏⡀⢲⠀⠀⠁⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢩⡀⢀⣾⣿⠿⠁⠀⠈⠒⣄⠀⠠⠔⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠃⠀⠀⠀⠀⠘⡧⠈⠈⠀⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠛⠙⠀⣤⣞⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠐⠀⠀⠀⠒⠉⣀⣀⣠⠞⠁⡉⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣮⠇⢀⠈⢠⠀⢠⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠆⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠈⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⢆⠀⠀⠀⢦⠀⠠⠀⠀⠀⠀⣄⠀⠈⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢃⠐⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠉⢷⡛⣷⣦⠀⠀⠀⠀⠊⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠰⠀⠋⠀⠀⠀⡰⠻⢿⣿⠛⠉⠉⢀⠀⢀⡠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⡘⢠⠚⠂⠠⠀⣰⡾⠇⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⢀⠹⠆⠘⠁⠘⢆⠀⠀⢠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠣⡀⠀⠠⠀⠀⡌⠄⠀⠀⡷⠀⢀⣑⣶⠻⣦⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠤⢄⠀⢙⣄⣶⣠⠈⠀⠀⡠⠎⠀⠀⠈⠉⠙⣿⡅⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠀⠄⠄⠀⠙⣿⡋⠅⣽⡧⠒⠉⠐⠂⠠⢶⠀⠀⠐⠈⠇⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠘⠂⠀⠳⢐⣻⠤⠤⠀⠐⢿⣿⣾⠟⢿⡀⠂⠀⠀⠀⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⠈⠁⡌⢽⡀⢀⡠⠀⠀⡟⠈⢀⠀⠙⢄⠐⠂⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢠⠴⠾⡃⡠⠂⡆⠀⠸⠀⠦⠀⠈⢃⡀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠂⠀⠉⢀⡞⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠏⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠀⠀⠀⠀⢀⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⢿⣭⣷⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⢀⣀⣠⣴⠯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣫⡵⠒⠉⢉⣭⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠿⠿⠉⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⡄⠀⠀⠀⣠⠟⢋⣠⣴⣶⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡿⠃⠀⠀⣼⣵⡾⠟⠛⠉⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡅⠀⠀⠀⣼⡟⠉⢀⣀⣤⣼⣿⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣼⠏⣠⡶⠛⠉⠁⠀⠀⠀⠈⢹⣿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣟⡴⢋⣠⣴⡶⠶⢶⣤⣀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⢰⣿⣿⣿⣡⣿⠟⠁⠀⢀⡀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣶⣶⣶⡾⠃⠀⠀⣠⠞⠉⠁⣿⣶⠀⠀⠈⠉⠳⢦⣹⣏⣿⣿⠃⠀⠀⢰⡟⠻⡆⢸⡆
⠀⠀⠀⠀⠀⠀⣾⠃⢠⡶⢦⢸⡆⠀⠀⠀⢀⡾⠁⠀⣤⣤⣌⠁⠀⠀⠀⢀⣠⠀⠙⣿⣿⡟⠀⠀⠀⣨⣷⣬⣥⠞
⠀⠀⠀⢰⣶⣶⡇⠀⠸⢧⣤⠾⠁⠀⠀⣠⣾⠃⠀⠀⢈⣿⣿⣧⣾⣿⣿⣿⣿⠀⠀⠈⢿⡇⠀⠀⠼⠛⠋⠉
⠀⠀⠀⠈⠉⠀⠻⣄⠀⠀⠀⠀⠀⣀⡴⠋⢸⡄⠀⠀⣾⣿⠟⡻⣿⣿⣿⣿⠏⠀⠀⠀⢸⡇⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⢻⣯⣄⠀⠀⢷⡀⠀⠻⣿⡶⢇⣿⡿⠿⠿⣿⣦⠀⠀⢸⣇⡴⠟⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣛⠋⠀⠀⠈⠻⣶⡶⠶⠚⠋⠁⣀⣀⡀⠈⣿⡇⠀⣾⣋⡀⠀⠀⣀⣤⡘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⢳⣄⠀⠀⠀⢸⣷⠀⠀⠀⠐⣿⡉⠃⣠⡿⢁⣼⠟⢽⣿⠀⢸⣿⣻⣧⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⠀⠞⠁⠀⠀⠀⠀⠈⠉⠉⢁⣠⡾⠃⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⢸⣅⣼⣿⡿⢦⣄⣀⣀⠀⣀⣀⣠⣤⠶⢛⣡⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇
⠀⠀⠀⣶⣶⣶⣶⣴⣿⣿⣧⡀⠀⠈⠉⢹⣿⡇⠀⠈⠉⠉⠙⠛⠿⠥⣴⠶⢿⣷⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠹⣿⣿⣿⣿⢏⠙⣿⣷⠀⠀⠀⣼⠋⣷⡀⣾⠛⢷⡀⠀⠀⠀⠸⣦⡈⠛⠳⢀⡼⠃
⠀⠀⠀⢠⣾⡿⠿⠿⣮⣛⣛⣁⣤⣴⠞⠁⢀⣿⠿⣾⣥⠟⠀⠀⠀⠀⠀⠈⠛⢿⣟⡉⢀⣠⣀
⠀⠀⠀⣿⡏⠀⣠⣤⡀⠀⠀⠀⣿⡁⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣧
⠀⠀⠀⠙⢧⣀⣁⡼⠃⠀⠀⠀⠙⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠈⡦⠐⠐⠀⠊⠀⠀⠀⢵⠀⡀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠔⠈⠀⠑⠊⠀⠀⠀⠀⠀⢂⠀⠀⢀⠠⠀⣰⠃⠠⠄⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠸⡆⠀⠁⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠣⣤⠀⠀⠀⠀⣄⠄⡤⡄⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠠⠊⠀⠀⠀⢀⡀⠈⢢⣯⢠⢀⠘⡄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠑⠁⠀⠹⠽⢍⡂⢴⣙⣳⣼⣼⡌⡇⣾⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢄
⠀⠀⠀⠀⠱⠠⢀⣀⡔⠀⠠⣄⣤⣴⡵⠽⠶⣬⣉⠛⠓⠺⡁⠛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⠠⠆⠀⠀⠀⠴⠂⠀⠀⠊⠉⠽⠿⣿⢿⣿⣿⣿⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⡄⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠈⣠⠿⢋⣼⡃⠻⣿⠧⠐⠒⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉
⠀⠀⠁⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠛⢿⠇⠈⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠁⠆⠀⠀⠀⡀⠀⠀⢀⡴⢀⣌⠔⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢕⢄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⠠
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⡟⢠⠊⠀⠀⢠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠉⠡⡠⠂⠉⠐⠂⠀⠄⠀⠀⠀⠀⠈⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠁⠈⠁⠸⠀⠀⢀⡇⠀⠀⠀⠹⠀⠀⠀⠀⢀⠳⠀⠀⠀⠀⢀⢾⠙⢦⢀⣀⡀⠀⠀⠀⣐⢀⣀⡴⢔⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠐⠄⠖⠢⠀⣇⠀⠀⠀⠀⠀⣶⣿⣷⠂⠃⠘⣇⠀⠀⠈⠉⢒⠒⠛⠉⢭⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠃⠀⠀⠀⠀⡀⢜⡿⠉⠀⠈⡄⣷⠀⠁⢳⣄⠀⠓⠄⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠼⠓⠲⠤⠤⣶⠋⢰⠒⠀⠀⠁⠋⠐⠂⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⡇⠀⠀⢠⠀⠀⠀⠀⠣⡳⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠂⢀⡼⠋⠀⠀⣇⠀⠀⠈⠁⠠⠀⠀⠀⠈⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⠋⠇⠀⠀⠀⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈⠢⣀⠀⠀⠀⠀⠀⢄⡸⠇⢠⡴⢂⡠⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠛⢌⠀⠀⠀⠐⠶⣍⡀⠀⣼⠇⠈⠀⠀⠀⠀⠀⢀⡴⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢢⡑⠐⠦⢠⠀⠉⠑⠀⢳⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡌⠆⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢁⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠖⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣈⣲⢾⡟⠌⠀⠀⠀⠀⠈⠈⡆⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠃⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⢻⡄⠀⠀⠀⠀⠀⢈⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠾⢹⠀⡄
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠄⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢧⠀⠀⠀⠀⠈⣿
⠀⠁⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣇⠀⠀⠸⠀⣿
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⢠⠀⣿
⠀⠀⡀⡀⠀⢀⡄⢀⠀⠀⠠⠁⠠⠄⠀⠀⣀⡴⠤⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣆⠈⡇⣻
⠀⡐⠱⠀⠠⡟⠀⠂⠀⡐⠁⢠⡶⠀⠀⡐⠍⠀⠔⠃⠀⠀⢈⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠨⣿⣆⡇⢻
⡐⠀⠁⠀⠳⠀⠀⠀⠔⠁⠀⠉⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⣠⣠⢤⣵⣮⣦⠿⢧⣜⣳⣧⣲⡄⢠⣤⣓⣼⣧⡶⠂⢀⣤⡮
⠀⠀⠀⠀⠀⢀⣠⣭⣥⣤⣬⡉⠻⣿⣎⡟⢻⣿⣇⢈⣿⣿⣿⣷⣾⠃⠂⠨⡟⣗⣶⣷⠿⢟⣁⣐⣈⣉⣁
⠀⠀⣀⣀⢰⣦⡉⣿⡻⢛⣿⣿⣷⣤⣿⣿⣾⣿⣿⡧⢿⣿⡟⡿⣿⣧⣶⣶⣾⣿⣿⣿⣿⣾⡿⢿⡿⠟⠒
⢀⡤⢜⡳⣥⣣⣏⢃⣧⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡀⣰⠟⠛⢿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣾⣃⡺⣃⣀
⠉⠙⠛⣉⣿⠻⡿⠟⠓⣽⣯⣍⣀⡈⠀⠠⢾⣿⣿⣿⠁⠀⠠⠟⠀⣰⣿⣿⣿⠏⠁⠀⠀⠘⢿⣿⣿⣿⡯⡉⠁
⠀⠀⠸⠷⢚⣶⣵⣠⣾⣿⡧⠀⠈⠙⠀⠀⢘⣿⣿⣯⣶⡁⠀⢀⢀⣾⣿⣿⣧⡀⠀⠘⠓⠲⢼⣿⣿⠟⠉⠉
⠀⠀⠀⠀⠀⢁⣸⣿⣿⣿⣿⣿⢢⣦⣴⣾⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣠⣤⣤⣰⣿⣿⡀
⠀⠀⠀⠀⠤⢾⣿⣷⣨⣿⣿⣿⢻⣿⣿⣿⡿⠟⠀⠉⠻⠿⠟⠿⠿⠛⠁⠙⠿⠟⢻⣿⣿⣿⣿⡟⠻⢶⣆
⠀⠀⠀⠠⣺⢝⢟⣿⣿⡿⠟⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣶⣔⠻⢷⠄
⠀⠀⠀⠊⢡⠏⡎⣿⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⡐⡀
⠀⠀⠀⢀⠏⢸⠁⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⢱
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣎⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠈⠉⠉⠀⠀⢀⣀⡀⡄⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠸⠿⠿⣧⣶⣿⠿⡇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⠶⡾⠾⣇⠀⠀⠀⠀⠀⠀⢀⣀⣄⢹⠀⢀⣤⣇⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢾⣷⣶⣶⣆⣴⣿⣿⡟⢸⠀⠈⢻⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⠁⣿⠛⢛⣉⣀⢸⣴⣿⢿⠀⣠⣼⠁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣷⣾⡀⠹⠿⠿⢿⣦⡄⢸⡾⠟⣿⣾⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⢸⡇⣠⣶⡖⣸⠘⢿⣾⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠟⠛⠋⠀⠿⠀⠀⠿⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⣄⠀⠀⢀⡤⠶⠶⠖⠲⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⢘⣦⠤⠞⢁⣀⠀⠀⠀⠒⠒⠦⠍⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⢻⡟⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⡄⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⡀⠀⠀⠀⡀⣇⣠⡥⣤⠤⢴⡟⢛⡻⢤⣌⡟⠒⠀⠀⡀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠺⠟⠃⠀⠍⠓⣦⣤⣶⠟⠁⣀⣿⣶⣿⣿⣆⠈⠀⠈⠳⡄⢀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡉⢙⡇⢀⣾⣿⡿⠟⠁⡈⢽⡆⡖⠎⠀⢹⣤⣤⣶⡿⠷⢦⣄
⠀⠀⠀⠀⠀⢰⠁⠀⡆⠀⠀⠀⠀⠀⠓⢸⣇⠸⣿⣿⠃⡴⠋⠈⡿⣀⡇⢆⡃⣸⠿⠛⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⣾⠀⢠⡇⠀⠀⠀⠀⠀⢘⣺⠀⠀⠙⢿⣶⣃⡠⠞⣡⠏⠴⣺⠜⠡⠃⠀⠀⠀⠀⠀⠸⡿⢧
⠀⠀⠀⠀⠀⠘⣦⣿⣐⣀⠤⠤⠤⣄⠄⠈⢿⡧⠨⠓⠒⠛⠒⣭⠀⢀⢞⡅⠁⠀⠉⠀⠀⠀⢠⡖⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡏⠻⠆⠀⠀⠈⠀⠄⠠⢝⡲⢦⣭⣤⣬⣥⡾⠃⠀⠀⠀⠀⠀⠀⠠⣶⠟⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⡤⠂⠀⠀⠀⠛⠒⠉⠥⠲⠞⣽⠃⠀⠀⠀⣠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣯⣾⠋⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠳⠤⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣷⡄⣀⠀⠀⠀⠀⠉⠈⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣒⣤⣶⣤⣀⠀⣀⣤⠞⠉⠛⠷⢤⣼⣧⣄⠀⢀⡴⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠉⢻⣀⢸⡇⠀⠀⠀⣀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣤⣶⣖⠶⢤⡀⠀⠀⠸⡿⢷⡀⠀⠀⣰⡋⠀⣀⠀⠀⠀⢨⡏⢸⡇⠀⢀⣼⣿⣿⣿⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣾⠟⠙⠟⠀⠀⠹⡆⠀⠀⠀⠀⢻⡖⠰⠃⣰⡆⠀⡇⠀⢀⡼⣡⠟⠀⠀⣿⣿⣿⡿⢶⣿⣿⠆⠀⠀⠀⢠⣤⣴⣿⡟⠉
⠀⠀⠀⠀⠀⢿⠀⡀⠀⠴⢶⣦⣽⣴⢟⠓⣦⠘⡇⢀⠤⣿⣷⣾⣥⣴⣿⡚⠁⣶⣦⠀⢸⣿⡞⣳⣿⣿⠟⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠈⢿⣿⠻⠶⠏⣰⣷⣿⠿⠭⠵⠶⠶⢤⣭⣙⡻⢿⣅⣀⣴⠧⠾⢿⣿⡯⢴⣶⣶⣶⣿⣿⠻⣟⣁⠀⠘⠷⣿
⠀⠀⠀⠀⠀⢀⣤⢾⣟⣫⡛⠛⢶⣿⣄⢀⣼⠟⠋⠀⠀⠀⢀⣠⣀⣄⠈⠻⣿⣷⠙⣧⣀⣴⠞⣉⠀⢀⣤⠶⠶⣄⠙⠉⠃⣠⢌⡟⠛⠛⠁
⠀⠀⠀⠀⣴⣫⣷⡿⠛⠋⠀⠀⢀⡽⠿⢾⠋⢠⣤⣀⠀⣾⣿⣿⣿⣿⣽⣷⣮⣅⠀⠈⣿⣿⠀⠈⠛⠹⣇⣘⡆⠘⡆⠀⠀⠙⠛⢁⣴⠆
⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠰⣄⡘⠤⣼⣦⠀⠀⠈⢿⡶⢻⣿⠟⠻⠋⠉⢀⠀⠈⠑⡀⢹⣿⣦⡀⠀⠀⠉⠉⠁⢀⡿⠉⠀⠰⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠙⠀⢀⣠⣾⠁⠀⠁⢰⣄⠀⣴⣿⠀⣀⣀⡀⣼⣿⢿⣿⣶⣦⣤⣤⣶⠟⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠙⢓⣮⡉⠀⢻⡀⠀⠀⠸⣿⣷⣿⣿⣿⡿⠋⢱⣿⡟⢮⣿⣿⢦⣬⣉⣀⣠⣤⡶⢿⡇⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣷⣦⣾⣿⣅⣀⣈⣧⡘⢷⣶⣿⣿⣿⣻⠟⢁⡴⢋⡟⠀⠈⢷⡙⢷⣤⣉⡉⠉⠀⣀⣀⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⡴⠚⠉⠀⠀⠀⠉⠙⠻⠦⣄⣉⣉⣉⣬⠶⣋⣤⡏⢀⠀⠀⢸⡇⠀⠈⠉⢻⣟⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⠁⠀⣠⠶⠶⣄⠀⠀⠀⠀⠀⠈⠙⢦⠄⠰⣇⠈⢃⣼⡇⢠⣿⣡⣤⣤⡀⠀⠻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣆⠀⠻⣤⠇⢸⣶⠟⠛⠓⠀⠀⠀⢨⣧⠀⠈⠉⢉⣼⠁⠻⠛⠁⠀⠈⣿⠀⠀⠈⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠳⠤⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠈⠻⠆⠀⠀⢀⣀⡤⠟⠀⠀⠀⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄⠀⢤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡜⠃⠈⠓⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠈⠉⠠⠀⠄⢠⡄⠀⠒⠂⠀⠀⠀⡘⠗⢤⣀⣰⣿⣿⠁⣸⡆
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢰⣶⠀⢠⠆⠀⠀⠈⠀⢠⠄⠀⠈⠠⠲⠄⢻⣠⣿⣿⠙⠁⢠⠛⠀⠀⣤⡄⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣈⣿⡧⠂⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⣸⣷⡿⠁⠀⠀⠁⠀⠀⠈⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⠈⠉⠁⣀⡀⠊⢠⡄⠀⠀⠀⠀⠀⠀⡠⢽⡿⠻⠷⣻⠇⠐⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⢀⣄⣿⣤⡄⣌⢁⣴⠉⠀⠀⠀⠃⠀⣼⠶⠴⠶⠃⠀⠰⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀⠐⠋⠠⣿⡿⢠⡞⠋⠁⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⢹⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢻⠧⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡸⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣘⣁⣤⠀⢭⠓⣌⡓⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠀⠀⠀⠀⠀⠀⠖⠐⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⡉⠉⠆
⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢃⣀⠂
⠀⠀⠰⠀⢀⠾⠛⠀⠴⢂⠀⢀⢀⠀⠀⠀⠀⠁⠀⡀⢀⠴⠒⠒⠢⣤⡀⣀⣠⣠⡶⠀⠀⡀⠀⠾⠟
⠀⢠⠃⠀⠀⠀⠀⡀⠀⠨⠀⠀⠈⠀⠀⠀⠀⠦⠀⣴⣯⣤⣾⡶⠶⠦⡾⠛⠣⡼⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⠀⡃
⠀⠀⠐⠀⠀⠀⠌⠀⠀⠀⢄⠐⠀⠀⠀⠀⠀⠀⠴⠟⢛⡉⠉⠁⢠⣴⠞⠛⠉⠀⠀⠈
⠀⠐⣾⠀⠤⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠉⠚⠛⠃⠉⣳⠶⣨⡁⠠⠔⠋⠀⠀⠀⠀⠀⠀⠆
⠀⢀⣼⣁⣄⡀⠀⠀⠈⣁⣄⣀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠁⢀⣥⠙⣷⠠⠄⣀⠀⠀⡀⠀⠂⠈⠉⢢⠀⠑⠂
⠐⠊⠀⠀⠀⠀⢀⣤⣉⣂⣀⡈⠉⠱⢦⡄⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⣠⠍⠂⠀⠀⠀⠀⠀⠈⠙⠟⠀⠠⠄⠀⠀⠻⡶⠋
⠀⠀⠀⠀⢀⡶⢺⠿⣿⠿⠟⠛⣿⣷⣤⣌⣄⠀⠀⠀⠀⡠⠺⠇⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠁⠐⠀⠤⠀⢀
⠛⠀⠀⠀⠿⢣⣴⣀⣠⣤⡴⣤⣈⣠⣤⣭⠻⠷⢄⢀⠜⠁⠀⢈⣀⡄⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠁⣠⡀⠀⠀⣀⣉⣉⣉⣠⣄⣀⣀⡀⠀⠀⠀⠠⠴⢁⡀⠀⠉⠁⠉⢠⣄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠉⠙⠠⢀⠀⠀⠈⠉⢩⣿⣿⡉⠉⢣⡄⠀⠀⠀⢬⠙⠳⠤⠀⠁⠉⠛⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠘⠓⠀⠄⠀⢻⡿⠉⠰⡾⠁⠀⠀⠀⠲⠖⢀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⢀⠀⠀⠀⠀⢀⡁⢾⣿⠀⡾⠀⠀⠀⠀⠀⢄⠀⠀⠂
⠀⠀⠁⠈⠀⠀⠠⠈⠁⠀⠀⣏⣀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⢤⠘⣿⠈⠢⡀⠀⡀⠀⢀
⠀⠢⠀⠀⠀⠃⠠⢸⡇⠀⠀⠀⠙⠂⠀⠜⠛⠁⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠟⠀⠑⠃⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⡀
⣿⣿⣿⣿⠿⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣬⣥⣤⣯⣤⣾⣤⣼⣦⣥⣾⣯⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣃⡾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⠞⠋⠀⢄⡴⠚⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣔⡄⢻⣾⣦⠰⠚⠃⠚⠁⠀⢠⡖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⢞⣁⡀⠀⠀⢀⡠⠤⢾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⢿⡅⢈⡿⠀⠀⣤⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠟⠀⠈⠀⠀⣠⡖⣳⣿⠟⠻⡾⠿⠟⢛⡲⠦⣈⡧⠋⠀⠀⢠⠿⣦⡤⡠⠃
⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡀⠀⢰⡟⣼⣿⠀⢀⣴⢰⡞⣠⡉⡏⠀⠀⡛⠀⠀⢠⣿⣷⣶⡏⡱⣠⣶⠶⠚⢤⡟⠁
⠀⣠⢞⣛⣿⣿⣿⡿⠶⢮⣿⣦⣼⣯⣛⣿⠀⣾⢷⣾⣧⠈⠻⡄⠀⢸⢃⣶⣶⣿⣿⣿⠟⡐⠀⢾⣟⠀⠀⠀⠈⢣⡀
⢰⡯⣻⢋⡈⠀⠁⠀⠀⣀⡤⠭⣿⣿⣿⣿⣽⣿⣿⣿⣿⣄⠑⣌⠙⢿⣼⣿⣿⡿⠿⠏⠐⣀⣠⠏⣿⠄⠀⠁⠀⢸⡇
⠛⠓⠛⠉⠉⠁⠀⠀⣠⡍⢀⣾⡿⠻⡍⣿⣿⣿⣿⡿⣿⣿⣇⠘⡆⡀⠹⠟⠉⠀⢠⠶⢂⠅⠊⠀⣿⡀⠀⠀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠟⠀⠀⠁⠸⣯⣽⣿⣿⣿⣿⣿⡆⢿⣅⢀⣴⡦⠔⣃⡖⠀⠀⠀⡴⠋⠉⠉⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋⠀⢀⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡵⠞⠋⠉⠁⢀⣴⠋⠀⠀⠀⠀⠒⠀⢸⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠊⠀⠀⠀⠀⢨⠟⠻⢿⠿⣿⣿⣿⣿⡃⠀⠀⠀⣀⣴⠿⠋⠑⠂⠂⠀⠈⠀⢀⣼⢛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠶⠈⢀⠀⠀⠉⠻⡀⠘⢿⣙⠀⠀⠀⠀⠀⠀⣀⣴⠟⢫⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⣄⠀⠊⠀⠀⠠⠀⠱⢅⠀⢙⠷⢤⣤⠶⢚⣿⠙⣄⣿⣾⠑⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⣄⠒⠒⠀⠀⠀⣤⡄⠔⠋⠀⢰⠏⠀⣼⣯⣴⣿⣿⡟⠀⢠⡏⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡶⠿⣟⣛⣛⡻⠛⠶⢦⣄⢀⣿⣿⣿⣿⠈⠙⢳⢶⡛⠁⠀⡄⡃⠀⠀⡼⠞⠀⣿⣿⣿⣿⣿⠀⠀⠞⢠⣶⣟⡫⢽⡻⠿⢿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠉⠛⠳⢶⣶⣜⣿⣿⣿⣿⠀⢢⡖⠀⠛⡴⠀⠀⡆⠁⠀⢰⠟⠀⠀⢸⣿⣿⣟⣡⡤⠀⠴⣿⣾⣿⠾⣗⠒⠦⡄⢤⣤⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢢⣀⠀⠀⠀⠈⠛⡿⠏⢻⣿⣰⠟⠀⠀⠰⠕⠀⢈⠇⠁⠸⣷⠀⠀⠀⣸⠿⠇⣉⠁⠀⠀⠀⠳⣤⣀⣘⣉⡁⠀⠈⠂⠉⠑⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⠀⣠⠴⣶⢿⠟⢤⠀⠀⠀⠀⡌⠀⡼⡐⠰⣋⠀⠀⣴⠾⢿⣾⣷⣀⠀⠀⠀⠓⢄⠀⠉⠉⠉⠉⠒⠠⠴⢶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣾⠏⠀⠀⠈⢣⡀⠀⠀⢹⠸⢣⡄⡵⢁⣰⠏⠁⠀⣿⡏⢋⣿⣷⣄⡐⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢐⣿⡟⠀⠀⠁⠀⠙⣃⠀⠐⣿⢇⡫⠀⣠⠟⠀⠀⠀⠀⢻⣧⣜⣵⣫⡿⣧⣀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⢩⡿⠀⠀⠀⠀⠀⠀⠹⡆⢸⢏⡞⢷⡶⠃⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣽⣾⣿⣯⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⠇⢠⠄⠀⠀⠀⠀⢸⣣⡟⡾⣧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⣰⡇⠀⠀⠀⠀⠀⣠⠘⣼⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢠⡟⢰⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢻⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠛⢊⠙⡆⣿⡈⠷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⢶⠦⣤⣚⠃⠤⡶⢦⢴⡆⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⢈⣷⣶⣬⢵⣆⠐⢋⡞⢁⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣀⣀⢤⠠⠮⣵⢶⠋⢴⣋⣀⣀⡐⠒⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢶⠏⠋⠳⠄⠘⠧⢀⣀⡤⠜⠋⢻⡙⠛⢶⠾⣟⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠆⠀⠀⠀⠀⠀⠶⠤⠤⡄⠊⢱⡦⠚⠉⢤⣀⢠⣀⣁⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⢂⠀⠀⠀⠀⠀⣿⠀⣌⠁⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢻⠇⠈⠀⢰⠃⠀⣠⠂⠀⣿⠀⠀⠁⠙⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⡁⣾⢱⡟⠁⠀⠀⣀⡀⢀⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⢻⠙⡟⣿⠁⠀⢠⡬⠴⢦⣼⠿⢶⣤⡱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⡳⠖⣿⠀⠀⠀⠺⢦⣬⣟⠆⠐⠠⣉⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠊⢧⢀⡞⠁⣾⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣌⢻⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠋⠐⠚⠿⣇⣾⣯⠆⠀⢀⣀⠀⣠⣀⡀⠰⠂⣲⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢹⢸⠉⠒⢾⣯⣡⣿⣭⣴⣾⠿⠛⢉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⣤⠁⢂⠀⠀⠀⣸⠀⠀⠈⠋⠁⠠⠽⠷⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠶⣇⡂⠀⢀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠈⢾⣇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠉⠉⠛⢿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣀⣤⣤⣤⣾⣿⣷⣤⣤⡼⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⡟⠁⠀⢀⣭⣶⣿⣿⣿⣿⠛⢹⣿⡿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠋⢉⠛⣯⡀⠀⠀⠀⠙⠿⣷⠞⠉⠉⠀⠘⠻⠿⠋⣿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡀⠺⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠟⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠒⣤⣶⣶⠖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣙⢋⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠛⠙⢿⣭⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣩⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢻⣿⣿⣿⠟⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢹⣿⣿⣿⡆⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⢺⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣡⣤⣼⣿⣶⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢤⣤⡶⠯⠷⠆⠈⠁
⠀⠀⠀⠀⠀⣠⡴⢞⣫⡥⠀⠀⣀⣀⡈⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⢀⠏⣤⡤⠤⣵⠄
⠀⠀⠀⣠⢾⣿⠞⢉⡿⠗⠋⢉⣽⣋⣀⣀⣀⣀⠈⠲⣄⠀⠀⠀⠀⣎⣀⣬⣽⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠁⠀⢀⣴⠯⠭⣄⣀⠈⠳⡀⠀⢰⠀⢉⡻⠂⢀⣠⠴⠒⠉⠁⠀⠀⣀⡀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢯⣍⡀⠙⡄⠘⣠⠎⣠⠖⠉⣀⣀⡐⠿⣖⠢⢄⣙⣍⠓⢦⣽⡷⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⣌⡓⢌⣾⣣⠞⣁⣤⢭⣿⣬⠉⠉⠻⠆⠀⠈⠛⠀⠀⠈⠇⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⡄⢀⣠⡶⢂⣀⣿⣶⣇⣨⣟⢿⠛⢒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣾⣠⠋⣧⠎⠶⠚⠉⢰⠉⢹⢨⠀⢿⠳⣄⢸⡇⢰⡆⢈⡓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣴⣼⠈⠟⠀⠋⠀⠀⠀⠀⠈⣹⠅⣾⠓⠋⠀⠘⠟⢻⡞⣿⢸⡇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣿⠀⠀⠀⠀⠀⠈⠀⢽⡜⢷⣿⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡿⣷⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠤⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⠴⠻⡄⠀⠀⣀⢀⡾⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄⢹⡀⠀⠀⠀⣀⠙⣆⢰⣿⡎⣧⠊⠔⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢦⣣⠀⢷⠒⠚⠋⠁⠀⠈⢷⣇⠁⠹⠸⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⠀⣸⠦⠀⠀⠀⠀⢀⡤⠬⠿⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠁

⣏⠉⣹⣋⣛⣛⣛⣛⣏⣛⣛⣛⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡅⢿⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣫⣭⡁⠀⠀⠻⡆⠘⢷⣞⢤⡤⣶⣀⠀⠀⠀⣀⣤⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢠⣤⣤⢾⣿⣿⠿⣿⣿⡿⠀⠐⠀⠀⠀⠀⠀⠙⠷⠄⠀⠈⠳⠶⠾⠿⠛⠻⢶⣄⣤⠚⠉⠻⢆⡀
⠀⠀⠀⠁⢈⣀⣉⠃⢴⣿⡿⠗⠀⠀⠀⣠⣶⣾⣿⡔⢤⡀⠀⠀⠲⠦⣤⢀⠠⠞⠛⢻⠈⠀⠀⠀⡀⠉⠓⠉⠉⠑⠢
⠀⠀⠀⠀⠈⠋⠉⠢⠈⠉⠣⣤⣄⣴⣾⣿⣿⠿⣿⣧⣠⣅⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⢻⣿⠙⠃⠎⠀⠟⣿⡿⢿⠀⠀⠀⠀⢀⣤⣾⡟⠀⠀⠀⠀⣾⣿⡆⠀⠀⠤
⠀⠀⢰⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢀⢠⠞⠉⣤⣈⣤⡀⠀⠀⠀⠉⠻⣿⣤⣄⠀⢸⣿⣿⣷⠞⠁⠉
⠀⠀⠸⢿⠛⠓⣿⣶⣄⣤⡀⢀⢠⣿⡄⢀⠀⠈⠀⠒⢼⣿⣿⠿⠟⠆⠀⠀⠀⠀⠈⠙⠀⠀⣾⣿⣿⣿⣧
⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣾⣿⣧⣿⣷⠀⠀⢀⣤⠈⠙⠓⠶⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣠⣄⠀⣀
⠀⠀⠈⠓⠻⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣇⣀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠙⠛⠛⠛⠛⠻⠿⠿⢧⣼⣿⡀⠀⠀⣤⣠⣿⡿⠻⠿⢿⣿⣿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡐⢦⡀⠀⣸⡇⢀⣤⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⢿⣿⣿⣄⣿⣷⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣾⣿⣾⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢻⣿⣿⣿⣿⣿⣍⠉⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢠⣾⠃⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⣾⣿⠟⠿⠁⢻⣿⡄⠀⠀⠉
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣿⣷⣿⣷⣿⣟⠻⢿⣷⡄⠀⠀⠀⠀⣸⠏⠀⢀⣼⣿⡗⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠁⠀⠀⢀⣠⣴⡿⢿⣿⣿⣟⠙⠛⢷⡄⠈⠁⠀⠀⠀⠀⠟⠀⢠⡾⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡿⠉⠀⢠⡿⣿⣿⣿⣆⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈
⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⡇⠀⢻⡝⢿⡄⠀⠸⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠻⣎⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣿⣿⠀⣿⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣾⣿⣿⣾⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠻⠿⠿⠟⠛⠛⠃
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠾⠁⠀⠀⠈⠉⠋⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣁⡴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⠿⣛⡒⠁⡰⢾⣿⣦⡗⣦⠀⢸⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢋⣵⣾⣿⠁⢀⣷⣾⣿⣛⣿⢸⡷⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠉⣿⡏⠀⢿⣽⣿⣿⣿⠏⣼⢧⡈⢸⡃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠀⠿⢷⡝⠀⢛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⠶⠶⢤⡶⠶⡲⣦⠀⠀⠁⢀⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⢰⠻⡄⠀⠀⢿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⢀⠀⣈⡶⠇⠀⣠⡜⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⠋⠀⠀⢀⡤⠶⠷⠋⠀⠀⡞⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⡶⠳⠚⠋⠀⠀⢀⠴⢢⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⠀⣧⡄⠀⠀⠀⠀⡞⢡⣤⢠⣶⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⠀⠉⠙⢶⠀⠺⣧⣀⠀⠀⠀⢨⠇⢸⣿⢸⡿⢋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⢿⣫⣄⣶⣧⠘⠳⠶⡥⠟⠀⠀⠀⠀⣠⣤⣀⣤⠶⠋⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣙⠹⠿⠿⠁⠀⠀⣴⢒⣒⣚⡋⡹⠋⠊⠀⠀⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⠳⣆⡀⠀⠀⠙⠧⣄⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⠶⠶⣤⡌⢱⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⢦⡝⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠁⣮⠃⠀⠀⠀⠀⢀⣴⡿⢛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢤⡞⠻⣧⠀⠀⠀⠀⠀⠀⠐⢿⣄⠀⣾⡁⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⡀⠼⣇⠀⠀⠀⠀⡀⠀⠀⠙⠷⢌⡛⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⡙⣇⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠐⡀⠈⢳⡄⠀⠀⢸⠃⠀⠀⠈⠀⡟⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀⣶⠿⢆⠀⠀⠀⠀⠀⠀⠰⡿⣥⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠙⣏⣁⠀⠈⢣⠀⠀⠀⠀⢀⣤⣹⠌⢷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢄⠀⠄⣸⠀⠀⣨⠒⣧⠤⣤⠜⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⣼⠁⠀⠀⣸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⣤⣄⣴⣾⣧⣀⣀⣤⣾⣿⡟⣒⣠⣟⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠥⠶⠏⠉⠛⠯⠿⡟⠻⠛⠻⠉⠁⠛⢻⠛⢩⠴⠶⠴⠖⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣤⣦⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣄⠀⠹⣿⣿⣇⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣐⣺⣿⣿⢀⣿⡿⢂⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣅⣘⠿⣿⣷⣼⣿⣿⣾⣏⣴⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⣠⣶⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣯⣾⡿⠛⣵⣿⡟⠀⣿⣿⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⢀⣀⡀⢀⢱⡇⣰⣴⣶⠦⠀⠀⢠⠟⢁⣾⡿⠛⣡⣾⣿⡿⠀⠀⣿⣿⠈⠘⢻⣿⣿⡄
⠀⠀⠠⢄⣛⣿⣿⣿⣆⣿⣿⣿⠁⠀⠀⢀⠀⠀⠸⠉⠠⣾⣿⣿⡿⠁⠀⠠⣿⣿⠀⠀⠀⣿⡿
⠀⠀⠀⠀⢈⣹⣾⣿⣿⣿⣿⡗⠀⣠⣿⣿⣿⣷⠄⠀⠀⠉⠉⣿⠃⠀⠀⠚⣿⣿⠀⠀⠀⠉
⠀⣠⣤⣴⣾⣿⣻⣿⣿⣿⣿⢇⣼⡿⠟⠉⠉⠉⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠁
⠀⠈⠉⣉⣭⣭⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⡿⠇⠀⠀⢰⡟
⠀⠀⠺⠟⢋⣻⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣷⣧⡀⠀⢀⣿⠁
⠀⠀⢀⣴⠿⠻⢫⣿⣿⣿⣿⠈⣿⠿⣿⣦⡉⠻⠻⡀⣼⡇
⠀⢀⡾⠁⢀⣴⡿⣹⣿⢻⣿⣇⠘⣇⠘⣿⡏⠀⠀⢰⡿
⠀⠈⠀⠀⢸⡿⠱⣿⡿⠈⣿⣿⠄⠘⣆⠉⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠀⠀⢹⡄⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⣾⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣴⣟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣯⣉

⠀⣤⡤⡆⢀⣀⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⠤⡀⠀⢰⠤⣀⡀⠰⣒⠆⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠈⢡⠊⠁⠀⠀⠀⠋⠳⡀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠘⡠⣍⠀⠀⠀⣼⠭⠴⡫⠦⢅⡀⢀⠀⢿⣾⡷⠀⠀⠆⡢⠀⠀⠁⠸⠍⢸
⠀⠀⣃⣀⣀⡀⢀⡀⣀⢀⡇⠄⠀⠛⢿⠛⠀⠀⠀⢀⠴⣾⠘⡿⠀⡀⢠⠋⠉⣏⠤⣠⣤⠾⠄⠀⠈⠙⠃⠀⠀⢀⡹⢄⣀⡠⢄
⠀⠀⣷⢦⣒⣤⠲⣤⠦⡾⣧⠀⠀⠀⠄⠀⠂⡠⢊⡷⠶⠰⢻⡇⠀⠇⢣⡼⠛⢇⡀⣠⡄⡶⣃⢂⠀⠀⠈⢀⠎⠃⠀⠀⠀⠈⢎
⠀⡄⣏⠙⠛⠒⠉⠉⠉⣁⡽⡠⢀⠀⢀⢴⡋⣲⠙⢠⡝⣠⢿⠁⠀⠈⠀⠑⢲⣾⣏⡾⣽⠣⣝⡈⠀⢀⡀⢨⣀⣠⣤⣤⠤⠤⢼
⠀⠈⠈⣉⣉⠉⠉⠁⠁⠀⠊⠁⠨⢐⠃⠺⣋⢀⠘⡱⡄⢤⡟⠀⠀⣀⠀⠀⠀⠙⣬⢓⠯⡽⣾⣇⠀⢨⣸⠌⡄⢀⣀⡤⣀⣀⣸
⠀⢠⠊⠁⠀⣙⠊⠑⡒⠊⠑⠂⡐⡈⡄⠈⢇⠿⠁⢕⠴⢾⠇⠀⢀⣀⡱⠀⠀⠀⠀⠻⢶⣋⢷⣿⠀⠀⠀⠀⢹⢡⣣⠘⣁⡀⡆
⢰⠁⢠⣿⡤⢏⡟⠟⠿⠻⠹⢿⡇⢣⠈⠢⣀⠀⠉⠚⠛⡾⠀⠀⣈⣩⠃⠀⢶⣾⡷⠀⠀⠛⢿⣼⡇⣏⡝⠀⢸⡔⠇⡀⢑⡁⡇⢀⣀
⠈⠂⢠⡇⢀⣀⠤⢤⢤⠀⠠⠾⡁⢌⠄⠀⠀⠈⠉⠭⠭⠒⠁⠀⡹⠃⠀⠀⢀⣀⣁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠘⠓⠵⠧⠤⠔⠁⢫⠴
⠀⢣⣈⣸⠏⠀⠀⣐⣀⣹⠶⠾⠥⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠁⠀⡰⠋⠁⠀⠈⢳⠀⠀⠀⣠⣠⢤⡴⠂⠀⠀⠀⠀⠠⠂⣶⣦⠂
⠀⠀⠈⡠⠶⣚⣉⣀⠠⠤⠤⠔⣒⣒⣒⣒⣒⣒⠛⠒⠢⣄⠀⠀⠀⠀⣇⠼⠣⠞⠚⠉⡇⠀⠈⠐⠇⠘⢁⣠⠤⠒⠒⠒⠦⢄⡀⠉
⠀⡔⡠⢓⣩⣜⡲⠶⠮⠭⠿⠛⠐⠚⠛⠁⠰⠿⠤⠐⢤⠎⠀⠀⠀⠀⠏⠀⡖⡄⡏⡆⢃⠀⠀⠀⡠⠞⠁⠀⠀⠀⠄⠠⠀⠀⠉⢦
⠀⠘⢇⣠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⠀⠀⠀⠀⢸⠀⡇⠇⠇⢰⢸⠀⠀⡜⠁⠀⠁⣠⠔⠒⡢⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠸⡘⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠀⢒⠨⠔⠁⠀⠀⠀⠀⠀⢇⢰⣠⣸⡸⠼⠀⡌⠀⠀⠀⠰⠥⠴⠊⠁⠀⠀⢀⡰⣹⠃
⠀⢰⣆⡀⠈⠉⠉⠉⠁⠈⢉⠤⡀⡔⢆⢀⠈⠀⠀⠀⡴⠒⠢⡀⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⣇⠀⠀⠀⠀⠀⠠⠀⠀⣠⠚⢉⠔⠁
⠀⠉⠠⠟⡦⠀⡀⣀⣐⠓⣘⡞⡟⡾⡌⢇⠃⠀⠀⠀⡄⢸⠀⠸⡀⠀⣠⠄⡆⠀⡇⠇⠀⠀⠈⠲⣤⡒⠲⠤⢚⣉⣩⠤⠚⢡⢤⡤⣤
⠀⠀⠀⡠⡄⠺⡙⡄⢇⢣⢫⡇⢛⣃⠸⡌⣿⣀⠀⠀⢱⠀⡱⠀⢣⠀⠈⠚⠁⠀⢹⡼⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠁⠘⠁⠉
⠀⠀⠀⡵⢾⣾⠹⣌⢎⢢⢣⠻⢸⢯⢦⡏⠁⠈⡄⠀⠀⢇⠑⢄⠘⡄⢀⡔⢲⠀⠀⠀⠀⠀⢏⡩⠃⠀⢸⡷⡠⠊⠉⠉⠉⠬⣙⠲⡀
⠀⠀⠀⢈⢦⣉⠢⣯⠣⡳⡱⢽⣜⡧⠕⠃⠀⠀⣷⠀⠀⠸⡀⢇⡀⢃⠀⠉⠋⠀⠀⣀⡀⠀⠀⠀⠀⡀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠁⢇
⠀⠀⠀⠀⠑⡽⠛⠙⠷⠼⠚⠉⠁⠀⠀⠀⠀⠀⠹⣇⠀⠀⠇⢰⠃⡽⠀⠀⠀⢠⠊⠀⠈⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠑⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠘⠦⡔⠃⠀⠀⠀⠀⠉⠒⠒⠒⠒⠂⠒⠒⠒⠒⢦⣈⠑⢂⡀⠀⣠⠴⠃
⠀⠐⢏⡹⠂⠀⠈⢪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⢷⠀⠀⠀⢀⣄⠀⣠⣄⣠⠴⠤⠤⢄⣀⡠⢄⣈⡩⣍⠉⠉⠁⡀
⠀⠀⠈⠁⠀⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⣀⣤⠖⡋⡅⣻⠀⠀⠀⠀⠀⠀⢲⠡⠦⣍⡥⢤⠀⣂⡄⢐⢠⢢⢠⢀⡄⣆⠀⠻⡀
⠀⠀⠀⠀⠀⠧⠜⠁⠀⠀⠙⢦⡶⠚⡙⡈⣀⣤⠷⠛⠁⠀⠀⠀⠀⠀⠀⢺⡀⠧⠋⠛⠘⠆⠙⠦⠘⠈⠛⠀⠋⠁⠘⢃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⠲⠋⠉⠒⠊⠑⠶⠉⠉⠊⠉⠉⠒⠁⠀⠀⠈

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⣵⣿⣷⠡⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⠇⠘⠀⠀⠀⠊⠩⠉⠂⠀⠀⢰⡏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣄⣀⠀⣿⠔⣦⣠⡞⢂⡶⢲⡖⠀⡴⠆⣼⡕⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⠀⠛⢨⡟⠸⡇⠘⠓⢹⡧⠚⠧⠔⠛⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡀⠀⠀⠀⠀⢠⡖⢂⠀⠀⠀⠀⠀⠀⠁⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠁⠀⠐⠀⣿⢁⡁⢀⣤⠀⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠲⠐⡏⢠⡿⡠⣿⢸⠃⡠⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⠈⠛⠁⠀⠛⠁⠀⢙⣁⡈⠁⠀⣆⡼⠃⣰⣿⣿⡿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⠟⠋⠐⠀⠀⠐⠀⢠⣿⠠⠀⠀⠀⠀⠀⠈⢹⡏⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡅⣶⡎⣿⢸⡇⢀⡾⢰⡆⠀⠀⣀⣤⣷⣯⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠀⠉⠀⣿⠘⣇⠜⡛⢸⡇⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠤⠞⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⣦⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⡛⢦⣷⡀⠀⣠⠶⠚⠋⠉⢉⣹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠉⠙⢳⣿⣧⠞⢁⣴⠶⠦⠤⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣞⡥⠖⠛⢳⠴⠚⠋⠉⢉⣿⣿⡿⠯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⢻⠹⡄⣀⠙⠳⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⠃⢷⢸⡇⠛⠉⢷⠀⣹⣆⠀⠀⠀⠀⠐⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⡏⠀⢸⡿⠀⠀⠀⠈⠟⠉⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⠃⠀⠀⠀⣶⡴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⣿⠀⠀⠀⢰⣿⠰⢧⡀⣴⡆⣠⢤⡄⢀⡴⠂⣿⣮⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⠘⣷⣴⣸⠿⣏⡠⣟⡼⣇⣼⣇⡠⢿⠇⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⢶⡇⠀⠀⠀⠀⠙⠈⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢨⡇⠀⠀⠀⠀⢀⡔⣄⠀⠀⢀⡴⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠺⡇⠀⠙⣧⠀⠸⡇⣽⢀⠀⣸⢃⡴⠃⢀⡀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣇⠀⠀⢹⡇⠀⣹⢏⣼⠀⣿⠭⣤⢠⣿⠡⠏⣼⣅⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠒⢿⠀⠀⠘⣧⡴⠃⠀⣯⠜⣡⣢⠟⠘⢧⠠⠊⠀⣼⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⡆⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠒⠛⠉⠛⠒
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⢶⣄⡀⠀⣀⣤⠾⠷⣤⣀⡀⣀⣠⡶⣄⡀⠀⣀⣠⠶⠳⣤⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⢠⣼⣦⣠⣾⣥⡄⠀⠀⠀⠀⢀⣭⣿⣦⣴⣶⣂⠀⠀⣈⣿⣧⣾⣯⡄⠀⢤⣶⣿⡆⣠⣴⣤⡀
⠀⠀⠀⢀⣼⣿⠛⣿⡿⠗⠂⢀⣦⣄⣾⣾⠉⡟⠉⣿⢹⠀⠈⢩⡿⢻⣿⠏⠋⠀⠿⣿⠁⡆⢿⡍⠻
⠀⠀⠀⠀⢰⠃⠀⠈⠛⠀⠀⠛⣟⠙⡏⠃⣼⠁⠀⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⡇⠀⠛
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠐⣦⣼⣀⡤⠀⠀⡼⣿⣷⣴⣿⣿⠂⠀⢐⣶⣿⣷⣴⣿⣏⠀⠀⢀⣠⣤⣾⣿⣯
⠀⠀⢀⣰⣦⡿⠿⢍⣿⡿⢿⣗⠀⣾⢹⡏⢩⠉⠙⠃⠀⠈⢹⡟⣹⠻⣿⠿⠁⠀⠽⢿⠛⢋⠙⠣
⠀⠀⠠⠟⣿⠙⢦⠏⠀⡟⠀⠈⠀⠈⠀⠁⠘⡆⠀⠀⠀⠀⠈⢁⡇⠀⠉⠀⠀⠀⠀⠈⠀⠘⡄
⠀⠀⠀⠀⠈⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣷⣫⠟⠉⠛⢦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠛⢁⣤⣤⡀⠀⠀⠀⢀⡀⣠⠴⠛⠁⡌⠉⢁⡀⠀⠀⠈⠑⢲⠜⠁⣤⠔
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠟⠉⠀⠙⢶⡄⠄⡉⣟⠡⠀⠊⢀⣄⠀⣸⣷⠀⠀⢀⣴⠇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⠀⠀⠀⠀⠉⢶⣄⡤⠀⣠⠄⢈⣿⣀⣿⣿⡖⠊⠀⠁⠀⠠⢇⣼⣿
⠀⠀⠀⢠⣦⣀⡀⢈⡴⠁⠀⠀⠀⠀⠀⢈⣿⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⠄⠀⢀⢡⡶⢋⢉
⠀⠀⠀⠀⠈⠙⠻⣮⣼⠷⢤⣀⠀⠀⣠⣾⠗⠀⣀⠈⠀⢨⣿⣿⣿⣿⣿⣿⣶⣿⢠⣶⣤⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠲⣬⡁⠀⠀⠉⠷⢶⣿⣃⡀⣀⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⢀⣴⠄⠈⠙⢶⡀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣉⣀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠛⠋⠲⠦⣀⡀⠉⠲⢦⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠈⠛⠉⠀⠀⠀⣠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠷⣶⣤⣽⣿⣿⣿⣿⡿⠿⠟⠿⠛⠋⠀⢀⡄⢀⡀⠀⠀⣠⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢁⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠴⠿⠟⠉⠀⠀⠈⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡰⠲⠀⢰⠋⠁⠀⢠⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⡇⠀⠀⢸⠆⠀⢀⠇⡆⠀⣼⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⡆⢱⠀⡀⢸⠀⠀⡜⠀⡇⡸⢈⡜⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠙⠁⠈⠉⠀⠁⠀⠁⠃⠸⠁⠀⠀⠀⠀⡼⣡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠁⣠⠞⢁⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡡⠖⢻⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣀⣀⡀⠀⠐⣺⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⣀⠀⠀⠀⠘⠦⠤⠊⣀⡤⠒⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⢃⣋⣑⣦⣽⣠⡴⠶⠲⠻⠒⠲⠀⠀⠀⠀⠀⡴⠋⠉⡉⢢⠀⠀⠀⢖⠉⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠛⠀⣯⡽⣶⠧⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠀⠀⠀⠸⠄⡇⠀⠀⠀⢠⠖⠀⡜⠁⡨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⢠⢎⡟⠓⠃⠀⠀⠙⢦⡀⠀⠀⢀⡄⠊⠀⠤⠤⣄⢀⡠⠀⠉⠉⢢⠀⠘⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡞⠀⢀⣀⡀⠀⠀⠀⠑⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢳⠀⢏⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠺⡄⠀⠀⠙⢦⡤⠒⠒⢤⡀⠀⠀⠀⠀⡇⠀⠠⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠈⠲⠤⠤⠞⠁⠀⠀⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠤⣀⣀⠀⠀⣀⡠⠤⢄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠤⢄⣈⠉⠉⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡞⠉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⣿⠀⡶⣦⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣇⠀⣿⠳⠇⠹⣷⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣸⣣⠖⠛⠙⣳⣏⠀⣠⣦⢰⡏⢻⣧⠀⢸⣿⣄⡟⠀⠀⠀⠙⣷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠁⠀⠀⡴⠁⢹⣧⣿⡿⢘⣷⣼⠹⣧⣸⠃⠀⠀⠠⠀⢴⣦⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⡞⠁⠀⠀⣿⡹⣇⡼⠃⠀⠀⠈⠁⠀⠀⣡⣶⣶⣶⣿⣿⣦⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣿⠇⠀⠀⡀⠐⠀⠈⠀⠀⠀⢁⣤⣶⣿⣿⣿⣿⣟⡛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⡿⢀⣂⡀⠀⠀⠀⠀⢀⠄⠀⠸⢋⣉⣉⠙⣿⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣠⡿⣱⠟⢠⡇⠀⠀⠀⢠⡟⠀⠀⣰⡟⠁⢸⠇⣿⠀⠘⣿⣿⣶⣾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠁⢰⣿⡴⠋⠀⠀⠀⢀⡞⠀⠀⢰⡿⠀⢠⠟⠀⣿⡄⠸⠛⡿⠿⣿⡝⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⡏⠀⠀⠀⠀⢀⡞⠀⠀⢀⣿⠃⣰⠏⠀⠀⢿⡇⢠⡞⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡞⠀⠆⠀⢸⣯⡾⠁⠀⠀⠀⠰⠶⠊⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⡞⠀⣴⠆⠀⣾⣫⠤⢤⡀⣴⣿⡟⣺⡟⠁⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⡞⠀⢸⡿⢀⣼⡿⠁⠀⣸⣿⡟⢉⡴⠋⠙⠓⢦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡞⠀⠀⠘⠷⠊⢰⣇⡴⢛⣿⠛⠓⠋⠀⠀⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠎⠀⠀⠀⠀⠀⠀⢠⣏⣴⠿⠃⠀⠀⠀⠀⣰⠋⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣾⣿⣿⣿⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣷⣿⣯⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⣍⡁
⠀⠀⠀⠀⠀⠉⠉⣛⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣾⠿⢛⡽⣿⣿⣿⣿⠻⣿⣦
⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⡻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣴⠋⣸⣿⠏⢿⣿⡄⠀⠙⠇
⠀⠀⠀⠀⠀⠟⠁⠀⣿⣿⠹⣿⣏⠻⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⠟⠁⠀⢘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠛⠦⠘⢦⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⣴⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣠⣿⣿⣿⣿⡿⠛⠛⢩⡤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣓⡙⠃⣼⣿⠟⠋⠙⢿⣧⠀⠀⠘⢁⣭⠄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣍⠁⢠⡬⠤⠄⢀⣶⡆⢁⣶⠋⢷⢰⣆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣟⠀⢸⣇⠀⠀⢸⡿⣷⢸⣿⠀⠀⠈⣿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⣷⡘⣿⠶⠂⢸⡇⢹⡞⣿⡀⠀⡄⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⠃⠿⠶⠚⣨⡟⠉⡃⠘⠓⠚⠁⠈⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⡀⠀⣰⡟⠀⡰⠁⠀⠀⠀⠀⠀⣴⡦⠀⢀⡠⠄⠒⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢠⣶⠀⣛⠁⢀⣿⠥⡪⠶⣦⠀⣰⣟⡽⢀⢿⡧⠚⠁⠀⠀⠀⠀⠀⠘⠃
⠀⠀⢠⡄⠀⠀⠀⢀⠴⠋⠸⣟⡿⠒⣿⣀⢾⣯⠊⢀⣠⡿⠊⠙⠧⠒⡡⢻⡇
⠀⠀⠘⠧⠤⠤⠒⠁⠀⠀⠀⠉⠀⠀⠈⠁⠘⠃⠰⣥⠟⠁⠀⠀⠀⠀⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡠⢀⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣧⡅⠢⡀⠐⣿⣦⡀⠀⠠⢊⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⣧⠬⠢⡙⣿⡰⠠⢁⣾⠛⢁⢄⣤⡶⠦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⠿⡷⣶⣤⣐⠺⣗⡑⣘⣧⡇⣽⣭⣯⣴⠟⠛⢉⣁⠠⣄⢤⡨⣤⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣈⠍⣉⠁⡛⠻⠿⣵⠢⡘⣯⣅⠟⡵⢋⣰⣦⡙⠧⠙⠳⠙⠃⠙⠈⠑⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣵⢟⡾⣻⠇⡾⢃⡾⣱⡾⡄⠨⣙⢺⣼⣿⠏⠔⢃⣨⣍⣭⣭⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⢠⣂⣥⡦⣶⡶⠖⠐⣾⣡⠛⡏⢙⡭⠥⠬⣍⢩⡉⠛⠫⢛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢛⠝⠃⢡⣠⢞⣩⠿⣀⣸⢈⡿⠫⡐⢦⣦⣼⣳⡗⢰⡄⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡄⠿⢈⣧⣾⢃⡈⠀⡇⡁⢨⡌⢦⡄⠩⠙⠋⠇⠘⢱⣷⡲⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣴⣆⠻⠀⠘⠇⡇⢬⡏⠀⠁⠁⠐⣯⡈⡼⡂⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠸⠉⠀⠀⠀⠀⠡⡸⠍⢀⡄⣀⠠⠞⠀⠘⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠦⠘⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠦⣄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣶⣶⣶⣤⣀⡀⠀⠀⡇⠀⠀⡏⠀⠀⣀⡀
⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣠⠇⠀⣘⣠⠖⠋⢸⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣇⠀⠈⠉⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠻⠿⠿⣧⣼⣶⡶⠶⠶⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿⣿⣿⡇⠀⠀⢀⣠⣴⠶⣶⣶⡀⠀⠀⠀⠀⠀⡠⠖⠻⢷⣦⣸⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡾⠛⣡⣴⣶⣦⣍⠓⠀⠀⠀⠀⢀⣴⣿⣷⣆⠙⣿⣿⡇⠀⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⣿⣭⣭⣿⡿⠁⣼⣿⣟⠉⠙⣿⡇⠀⠀⠀⠀⢸⣿⣁⡹⢻⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡀⠀⢻⡛⢿⣦⠆⣠⠃⠀⠀⠀⠀⠘⠘⠛⠁⠊⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⣿⣧⠀⣿⣿⣿⣿⣿⡇⠀⠐⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢦⣤⣀⡀⠀⠀⢀⣀⣤⣶⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣟⢉⣉⣽⣿⣿⢿⣿⣿⡇⠈⣿⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣮⣝⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⠀⢸⣿⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⡀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⡆⠠⡀⠍⣽⡿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢰⣼⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣤⣭⣤⣿⢀⠂⣱⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠸⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⢿⣿⣿⣿⣿⣿⣿⣶⣿⢿⡙⢿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿
⠀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⢸⣿⣿⣿⣿⣿⣿⠇⠂⠈⢷⡄⣿⣿⣿⣿⣿⣧⠀⠀⢸⡏
⠀⠠⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣼⣿⣹⣿⣿⣿⣿⠠⠁⠡⡸⣿⣿⣿⣿⣿⣿⣿⡇⢀⡿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠸⣿⣯⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⠠⠄⠪⢀⣿⣿⣿⢻⣿⣿⣿⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⠐⣔⢐⣿⢻⣿⣿⣾⣿⣿⣿⣿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣷⣽⣿⣿⣷⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣂⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠆⠀⠀⠀⠀⠀⠀⢀⣀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠟⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣮⡽⠛⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣰⠁⠀⠀⠀⢷⣄⢀⣠⠞⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠈⣧⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢀⠇⠀⠀⠀⠀⡟⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢘⡆⠀⢀⠃⡴⠀⠀⠀⠀⠠⢦⠀⠀⠀⠈⠓⠤⣤⡤⢶⠁⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠲⠚⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢀⠈⠄
⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⢠⡶⠀⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⣇⢘⠁⠀⠀⠎⠱⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠘⠀⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⣿⠁⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠀⠀⠀⢀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠓⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠃⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠐⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠐⡄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠘⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡐
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⢿⢿⣿⣿⣿⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⢃⣾⣿⡿⢹⣿⣻⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⢸⣿⣿⣤⠇⠀⣼⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⢰⠃⣼⡟⣼⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠁⣼⣿⠝⠛⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣶⣾⣷⡏⠠⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⣰⣯⢻⠏⠁⠀⠀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⡀⠀⣠⡾⣥⢟⣯⡿⠛⠁⠻⠃⠀⠃⡴⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⣀⢀⣚⣵⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣈⣽⢿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣻⠛⢲⣾⡿⣷⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠶⠾⢶⣿⣿⠾⠋⣠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣠⡾⠛⠉⠀⠋⣽⣿⣿⣿⣿⣿⣛⡛⠋⢋⣁⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣾⣿⣯⠽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⠀⢠⣔⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⡸⢀⠔⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠠⣰⡀⠈⣵⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⡇⠀⢰⡍⠲⡅⠀⡄⠀⣀⠔⢀⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠚⠃⠀⠀⠀⠁⡵⠛⠴⢿⣿⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣴⠛⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠤⠐⢺⣶⣿⣿⡗⠉⠉⠻⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⠀⠀⢰⣶⣾⣿⡛⠉⣠⣶⣶⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⡀⠘⢻⣿⢿⠇⠸⣿⡿⢧⣬⣻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠘⡇⡇⠀⢸⢿⠆⠀⠀⠙⢷⣼⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⡿⠿⠿⠿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀
⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⣼⣿⠁⠀⠀⠀⠀⢀⡴⠒⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠇⠀⠀⠀⠀⢻⣿⡀
⢰⣿⠇⠀⠀⠀⠀⠀⣾⡀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣤⣄⡀⠀⠀⠀⠈⣿⣇
⣾⣿⠀⠀⠀⠀⠀⠀⢻⣿⣶⠒⣇⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⠉⠛⠿⠀⠀⣀⡀⢹⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⢠⣾⠿⠿⣷⡄⣠⣶⣿⠿⠿⢿⣶⣄⢀⣤⣾⡿⠿⠿⣿⣿⣇
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠈⢻⣿⠟⠁⠀⠀⠀⠀⠙⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠻⣿⣏⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣿⠏⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠙⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣷⣶⣶⣶⣶⣾⣿⠿⠿⠛⠋⠁
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡎⠀⠀⣠⠞⣁⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄⠸⠀⠜⠀⣠⠞⠁⠒⢂⣠⠴⠚⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⡴⠚⠉⠙⠢⡈⣁⠤⠖⠋⠁⠀⠠⡤⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢸⠁⠀⠀⠀⠀⢹⠠⠤⠤⠤⠤⠤⠤⠤⠀⣰⡟⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⠣⣀⠀⢀⡠⠋⠒⠆⠙⢻⠗⠶⢤⣄⢀⣿⣤⠶⠟⠯⠻⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⡠⠊⢀⡌⢩⠉⢦⠈⠣⡄⠀⢈⣡⡴⡾⢟⣿⣿⣶⣚⠟⠟⢗⢶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠊⠀⠀⡜⠀⢸⠀⠈⢇⠀⢀⣴⢻⠹⠈⣱⢿⠋⢳⣿⡙⠻⡶⣌⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⡀⠀⡸⠁⠀⢘⣀⠀⠈⢠⠿⠸⠈⠀⢰⣯⠃⠀⠀⣷⢳⡀⠀⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⡤⠴⠋⣉⡉⡉⢦⡀⠠⢤⡖⠀⢿⠓⠀⠀⠀⢸⡞⣇⠀⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣀⣺⢷⡫⡧⠞⠃⠀⠀⠀⠀⠈⠀⢠⣀⠄⠈⣏⣹⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⢖⡚⡰⠁⠳⠳⢄⣀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣥⡬⠴⠺⢽⡦⣄⡈⠙⠚⠯⠝⠒⠒⠒⠒⠒⠒⣇⣠⡗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠓⠋⠉⠛⠳⣞⠉⠉⠭⠭⠭⢹⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠭⠭⢁⣈⡭⠭⠤⠞⠠⠠⣤⣬⠍⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡀⠔⠊⠩⠀⠐⠚⠒⠂⠈⠁⠢⢄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣴⣪⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣿⢤⡀⠀⠀⠀⠄⠄⠈⠀⠀⢀⠠⣦⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⠟⠉⣿⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣩⣿⣿⢿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡟⠁⠈⠏⡀
⠀⠀⠀⠀⠀⠓⠂⠐⠾⡟⣶⣶⣶⣶⣶⣶⣶⡆⠂⠀⠀⠀⠀⠀⠀⠀⢳⣶⢶⡗⡟⠂⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢳⣨⣷⢽⢿⣟⣿⣓⡂⠀⠀⠀⠀⠀⠀⠀⢩⣏⡹⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢯⣱⣀⣟⣛⣒⣒⣒⣒⣀⣀⣄⣀⣐⣒⣾⡿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣻⣷⡆⢸⡄⠀⠀⠀⠀⢀⡠⣄⣬⣿⠿⣥⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠪⢝⠺⠯⣷⣀⣀⣀⣀⠴⠖⡋⠅⠊⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠈⠁⠒⠂⢺⠔⠒⠊⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣦⡀⢀⣴⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠻⠿⠿⣷⣬⣿⣾⣷⣶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠶⣤⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣻⣿⣿⣿⣿⠏⣿⣿⣿⣿⡿⣿⣷⣌⠛⢿⣦⣀⣀⡀⠀⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⣾⢩⡾⢋⣿⣉⣸⣿⠇⢰⣿⣿⣿⣿⣧⡈⠙⠻⣆⠀⠙⢿⣍⡙⠻⣶⣤⣼⣯⣶⠶⠺⠲⢤
⠀⠀⠀⠀⢲⣴⣿⣿⣿⣟⣁⣤⣼⣧⣄⣸⣿⡟⠉⣿⣿⣷⠀⠀⣠⠶⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⡛⠓⠦⡀
⠀⣠⠖⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⢿⡇⠀⠀⠙⣿⡆⠐⠋⠀⠀⢀⣤⣶⣿⣿⣿⣿⣹⣿⣽⣷⣤⡀
⠀⠀⣴⡾⣻⣿⣿⣿⣿⣿⣿⠿⣿⣦⡈⠀⠘⠃⠀⠠⠀⠈⠃⠀⠀⣠⣴⠿⣫⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣆
⠀⣼⠏⡼⢻⣿⣿⣿⣿⣿⣿⣷⣄⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠟⠛⣿⣿⣿⣿⡇⠸⣿⠈⠻⠀⠉
⠀⠇⠀⠀⣸⡏⣼⡟⢸⣿⡇⠙⢿⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⣿⡇⠀⠸
⠀⠀⠀⠀⣿⠁⠹⠀⠀⢿⡇⠀⠀⠉⠣⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠿⠁
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠨⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣇⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⢀⣷⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠧⠿⠛⠾⠿⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣠⣀⠀⠐⠋⣀⣀⣀⣀⣀⣠⣤⣤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣾⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋⠉⠉⠉⠉⠻⣿⣣⢶⣦⣀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⢀⣀⡀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠀⠀⠀⢀⠉⠀⠟⡛⣿⣿⣿⣿⣿⣿⣄⠀⠈⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠶⠦⣀⣴⣿⣿⣯⠉⢻⣿⣿⣷⣤⣤⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⢀⠀⠁⠀⠐⢹⣿⣿⣿⣿⣿⣧⠀⣿⣷⡌⠉⠉⠉⢿⣯⣙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣻⣿⣷⠀⠀⠀⠀⠉⠛⠛⠿⢿⡟⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⠀⠈⢿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⡀⢀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⡟⢳⣶⣶⠋⠉⠉⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠙⠉⠁⠀⠀⠈⠁⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣿⣿⣿⢿⣤⣤⣾⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣇⣀⠠⢤⠿⡿⠿⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠟⠛⠛⢻⣿⣿⣿⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⡀⠀⠄⠀⠀⠀⠀⠀⢾⣷⣤⣀⡀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣿⣿⣛⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠈⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢱⣮⣻⡞⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⠟⠉⡤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⢤⠒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡛⠲⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠆⠊⠅⠀⠀⣇⠀⠀⠄⠀⠀⠀⠖⠀⠙⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⢌⠀⠈⠄⠀⠈⡀⠴⠁⠀⠀⠀⣠⠀⠁⠀⡔⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⢲⠇⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⡚⠠⠂⣀⡠⠀⠹⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢰⠀⠀⡀⢀⠲⠄⣀⣀⣠⡊⠀⠀⠀⠀⠘⡀⠀⠀⠀⡠⠀⡈⠀⠀⠈⠁⠀⠀⠀⠀⡘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠈⠺⡷⠶⠄⢠⣭⣁⠀⠀⠀⠀⠀⠱⢶⠶⠦⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠀⡤⠌⠐⠠⣠⡇⠀⠀⠀⠀⠙⣆⠀⠀⠀⢀⠐⢀⠀⠀⡀⠁⢠⠾⠶⡂⠐⠂⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠐⠋⠫⡀⢄⠀⠀⠀⠘⣄⠀⠀⣾⠀⠁⠀⠈⠀⡠⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⡀⠀⠀⠈⣦⠈⢠⠰⠀⢀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢸⡦⠆⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⢀⡀⠀⠀⠈⠠⠀⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠰⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⠧⠤⠄⠒⠂⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠒⣤⣄⠀⢀⡤⣶⠊⡵⢣⠇⠠⠤⠤⠤⠤⠤⠤⠄⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠒⠻⣅⢰⠁⣟⠀⡌⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⣤⠐⠒⠂⡵⠒⣲⠷⢄⠒⠺⡇⠸⠁⣾⣴⠒⠒⠖⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠦⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣈⣁⣐⠙⣄⠐⠇⢣⠮⠄⢈⣀⣠⡔⠋⠁⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⢀⡴⡞⠁⠜⠀⠐⠋⠙⣳⣾⣥⣤⣖⠉⠃⠸⠉⠷⢤⠀⠀⠀⣀⠀⣀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠠⠯⢴⠖⠢⠒⠉⠉⣩⠟⣡⠊⢢⡀⠙⠉⢳⢖⠒⠒⠒⠓⠀⠀⠘⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐⠂⢀⡔⢁⠞⠀⠧⠐⢙⡙⢆⠘⠀⢳⠀⠀⡀⣠⠄⠀⠀⠀⠠⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠎⣠⠋⠐⠀⡇⠘⠉⠇⠈⠑⠦⡈⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⢸⠈⠀⣠⠃⢠⠃⠀⠀⠀⢡⠐⡾⠀⣀⣀⡀⠈⠃⠀⠀⠀⠀⠀⠈⠶⠁⠀⣀⠀⠈⠑⠢⠤⠤⠤⠤⠒⠏
⠀⠀⠀⠀⠀⠀⢸⠀⢠⠋⢁⠇⠀⠆⠀⠀⢨⠞⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠐⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⣄⢇⣀⡼⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢯⡹⣁⠗⠒⠒⣲⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢨⠃⠈⠀⣀⡈⠉⢉⠉⠉⣀⣀⣁⠀⡤⣄⠞⡇⣠⡉⠁⢀⠈⢁⣀⠁⠰⠯⠟⢄⠉⣼⠾⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢆⣸⡤⠒⠒⠤⣀⠀⠄⠀⠤⠤⠀⠠⠀⢘⣮⣶⢡⠓⠋⠠⠀⠀⢀⡴⡖⢦⡐⠢⢌⣾⢁⡭⠝⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣏⠳⡞⠶⠌⠢⣀⠤⠤⠤⠄⠀⠄⠈⠁⠉⠹⡀⠄⢠⠔⣋⣅⢠⡇⢄⠙⡆⢠⢹⢃⠞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠜⢹⠑⢹⣉⠑⠢⡈⢑⣒⠒⡶⠀⠤⠄⠫⠝⠢⣵⡰⢃⠾⡷⡅⠀⣱⡈⠁⠸⣜⣿⡟⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⢻⠢⢸⠨⠻⡅⠈⠢⣴⣊⠠⣀⠠⢀⣀⣀⣀⡼⢇⡏⣰⣈⣁⠐⠃⠉⠢⠈⡲⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡉⢸⡤⠸⣦⡀⠟⠫⣤⠤⠈⢉⡼⠁⢙⡢⡀⢌⢣⣿⢋⡤⡠⠚⣡⢀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣑⠆⠑⢌⡒⠒⠲⠶⣚⣩⠭⢉⠕⣒⣛⣮⣽⣿⠞⣰⣃⣚⢴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⡧⠤⠬⠤⠥⠜⠙⠯⠤⠼⠎⠤⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣾⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠀⠉⣙⣻⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣴⣧⣾⣷⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡹⢿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡩⠿⣿⣿⣄⠀⠀⣠⣾⣿⣟⠻⠿⠟⢛⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠑⣞⣿⣿⣦⣴⣿⡿⠯⠝⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣻⣷⡶⣶⣶⣾⣿⣟⢿⡷⡶⣖⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⡿⣿⢿⣟⡿⣿⣿⢒⣿⣿⣟⣽⣿⣿⣿⣿⣯⣿⡷⣿⡉⠛⠟⠚⠓⠁⠙⠈⠎⢿⠛⡏⢻⢶⣄
⠀⠀⠀⣀⣴⣿⢿⣿⡿⢫⢞⠞⡡⠋⠊⠐⠋⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠙⡷
⠀⢀⣼⣿⣿⢫⡾⠋⠐⠁⠈⠈⠀⠀⠀⢀⣾⣿⣿⣿⡿⢱⠏⢻⣿⠻⠟⢻⣿⣿⣿⣿⣆⡀
⢰⣿⡟⣹⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠙⠀⠀⠀⣸⣿⠀⠀⠠⠘⢸⠘⢿⣿⣿⣦
⠨⡟⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠀⠘⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡝⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠁⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⡿⣄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠈⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣚⣩⣵⣶⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠋⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣊⣥⣶⡿⠿⡿⠟⣛⣉⣭⣤⣴⣶⣶⣶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠉⠀⣰⣿⣿⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠴⠞⠛⠉⠁⠈
⠀⠀⠀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢀⡀⠀⢀⡀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠽⣾⠗⠒⠛⣗⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⣰⣷⣾⣯⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⡀⣰⠛⢉⣸⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣾⡿⡇⠀⣨⣿⣿⣿⣿⣿⣾⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠻⠿⣤⣾⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢤⡌⠛⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⢘⣯⢶⣿⣏⣤⣼⣿⣿⣻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡘⣷⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠺⣿⣿⣿⣿⣿⡿⣳⣿⣟⣀⣤⠠⠔⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣹⣿⣦⣸⣇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠟⢋⣼⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣿⡷⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡇⡇⡀⠀⣸⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⣻⠇⠀⡏⠀⠀⢀⠀⢀⡿⠃⠀⠀⠀⠀⣀⡀⢻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢹⠀⠀⡇⠀⠀⠈⠀⠜⠀⠀⠀⣠⣴⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡇⢀⡀⠀⣬⣾⡧⡶⠟⠋⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⠛⣷⠶⣾⡠⢰⡿⢧⠤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢦⣤⣄⡀⠀⠀⠀⢠⠀⠀⣸⣧⣴⣿⣷⡀⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣴⣶⣦⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⣦⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢨⠛⠻⣿⣿⢿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⣧⠀⣼⣯⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⢀⡏⠀⣀⠀⠀⠀⠀⠀⠈⣿⡝⣿⣿⡿⠃⠀⠀⠀⠀⢰⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡼⠁⠀⠉⠀⠀⠀⠀⠀⠐⠈⣃⢹⣿⡷⠛⢩⣴⣶⣿⠎⠹⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣟⠀⠀⠘⠉⠙⣿⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠊⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠃⠀⠀⠀⠀⠀⠀⣀⣿⣿⠋⠙⠫⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⡀⢠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣿⣿⣿⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠐⠛⠓⠂⠀⠉⠁⣰⣿⠟⠁⠈⠻⣿⣦⣤⣤⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠈⢻⣧⣾⡿⢿⣴⣶⣶⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣀⣄⠺⣧⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⠻⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣶⣦⠐⣶⣶⡶⢰⣶⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠉⠁⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣶⣦⣀⢀⠀⠀⡀⠀⢀⠀⠀⣠⣾⣿⡏⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⢿⣿⣿⡟⢁⡤⣄⣦⣁⢨⣷⢠⣾⣿⣿⠅⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠉⠀⠛⠛⠋⢠⣿⣵⣶⣯⢽⣷⣿⣾⣻⣿⠟⠀⠀⠀⢘⠂⢈⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⠟⣻⢇⣠⣂⠀⠀⠈⠀⠐⠅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢠⡴⣿⣿⣿⣿⣷⣶⣿⣿⣿⣟⣿⠟⣡⣾⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣈⣀⣉⣉⣻⣿⣿⣿⣿⣾⣿⢟⣀⡀⡠⣄⣤⡤⠄⢀⣀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⢿⣿⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⡿⡯⠊⣿⢶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠃⠁⣀⡾⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⡨⢿⣯⡙⢿⣿⣯⢿⣿⣆⠀⠢⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀⢀⣼⡿⢈⣼⣿⢿⡷⠙⢰⣿⡇⢿⣻⣿⣷⣾⣧⣀⠻⣿⣿⡟⣿⣅
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⢀⣾⠟⠀⣾⠏⠟⠏⠁⠀⢸⣿⠇⠀⠻⡟⣿⣿⣿⢯⡀⠉⠹⠻⠹⢿⣦
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣸⠃⠀⠈⣿⠊⠀⠀⠀⠀⢸⣿⠀⠀⠀⠁⠊⣷⣯⣟⠆⠀⠀⠀⠀⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⡽⠀⠀⠀⠀⠀⠉⢹⣾⡇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡠⠠⠤⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠚⠉⠉⠉⠉⠉⠉
⠀⢀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠤⠁⠠⡄⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠘⠻⣿⣧⣠⣤⣤⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⣉⠀⠉⡁⠀⠀⠀⠀⠀⠀⣿⡏⣽⣟⠈⣻⡇⠉⠀⠀⠀⠀⣠⣤⣴⣤⡀⠀⣾⣿⣿⠥⠄⠐⠀⠉⠳⠀⢀⡠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⠿⠛⠛⠁⠀⠀⠀⠀⢠⣟⢈⣿⠏⢻⣼⣿⣿⡿⢤⣀⣀⠀⡀⠀⠘⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⠟⢀⣤⣿⣿⣿⠁⠀⠀⠉⠀⠈⠛⠶⠂⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⣿⣿⣧⢸⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠟⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠈⠀⢰⠇⢻⢸⠀⣀⣀⣤⣶⣤⣴⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢉⣿⣿⣿⠇⢾⣿⡇⠀⠓⢤⣀⢀⣀⣀⣤⣄⠀⠀⠀⠀⠸⠀⢸⣾⣿⣏⣹⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠈⢉⡁⠠⠏⠱⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠇⠀⣾⣿⣆
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠛⠛⠋⠀⠘⡀⢸⣿⠀⢀⡀⠀⠀⠀⣀⠀⠞⠀⠀⠀⠀⠀⠂⢼⣿⣿⣿
⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⡘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢻⣄⠀⢀⣀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡆⠀⠀⠘⠟⠀⠘⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠃⠀⠀⠀⡋⠒⠂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇
⣀⢀⠀⠀⡀⠂⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣀⣈⣳⣄⣄⠀⢀⣀⣀⣀⣠⣃⠀⣾⠀⣀⣀

⠀⠀⠀⠀⠀⡀⣀⡀⠜⠛⠶⣄⡟⠡⠄⣀
⠀⠀⠀⠀⢀⠁⠈⠻⣿⡀⠀⠙⣧⠀⠀⠉⠲⣄
⠀⠀⠀⠴⢾⣷⡾⠋⠛⢷⣄⣀⣿⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢸⡆⠀⣻⡇⠀⠀⠀⠙⠻⣿⣇⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⣿⡇⠀⣿⠁⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⢸⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⣷⡀
⠀⠀⢼⡆⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠘⢿⡄
⠀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠈⣤⠘⣿⡄
⠀⠀⠈⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢹⣆⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⢿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⣿⣌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠘⣿⣿⡀⠀⡀⠀⠀⠸⣷⡀⠀⠀⠀⢠⡀⠀⠀⣿⣇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿
⠀⠀⠀⠀⠀⠘⢿⣷⠀⢣⡀⠀⠀⢹⣷⡀⠀⠀⢻⣇⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣷⡌⢻⣦⡀⣆⣹⣿⣤⠀⢸⣿⣀⣼⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣇⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠄⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡄⠀⠀⠀⢀⣾⠋⠀⠀⢀⠃⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⠀⢠⡿⠁⠀⠀⠰⠉⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠀⢰⡟⠁⠀⠀⡼⠃⠀⠀⠀⢀⣿⠟
⠀⠀⠀⢀⣠⣴⡾⣿⣿⡿⠿⠟⠻⠷⢦⣤⡀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⢠⡿⠁⠀⢀⡾⠁⠀⠀⠀⣠⣿⠏
⠀⠀⣰⣿⠋⠁⣼⠟⠁⠀⠀⠀⣀⣀⣀⣈⣙⣦⡀⠀⠀⠀⠀⢸⡇⢸⣧⣿⠃⠀⢀⠛⠀⠀⠀⠀⣴⣿⠋
⠀⢰⡟⠁⢀⣼⠁⠀⠀⠀⣠⣾⡟⠋⠉⠉⠉⠛⢿⣷⡀⠀⠀⢨⣇⢸⣿⡏⠀⢠⡏⠀⠀⠀⢀⣼⡟⠁
⠀⣼⠇⠀⣼⠃⠀⠀⢀⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈⢿⣦⡀⠈⣿⢸⣿⠃⢠⡞⠁⠀⠀⢠⣾⠟
⢈⡏⠀⢀⠋⠀⠀⢀⣾⣟⠛⠿⢿⣿⣿⣿⣦⠀⠀⠀⠀⢹⣷⡐⣿⢸⣿⠀⣿⠁⠀⠀⣠⣿⠋
⣾⠃⠀⢺⠀⠀⢀⣿⠛⠿⣿⣦⣄⠈⠛⣿⣿⣷⡀⠀⠀⠀⢻⣿⡇⢸⡇⣾⠏⠀⠀⣼⣿⠏
⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⠙⠻⣷⣄⠈⠻⣿⣿⡄⠀⠀⠀⣿⡇⢸⣿⣿⠀⠀⣼⣿⠃
⣿⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠘⢿⣿⡀⠀⠀⢹⣇⢸⣿⡇⠀⣸⣿⠃
⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡈⢿⣿⠀⠀⠀⣿⢸⣿⠃⢰⣿⠇
⣿⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⢿⣧⠀⠀⣿⢸⣿⢀⣿⠏
⢹⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠘⣿⡄⠀⣿⣾⡇⣼⡿
⢸⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣇⠀⢹⣿⣿⣿⠁
⠀⢿⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢿⡄⢸⣿⣿⡇
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣸⡁⠈⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⠠⣿⡏
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠀⣿⠃
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠁

⠀⠀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⢠⡾⠕⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⢸
⢸⡷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢧⡀⢸
⢸⡇⠀⠀⠉⠉⠋⢙⡋⢻⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋
⢸⡇⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀
⢸⡇⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠋⠉⠉⠉⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣶⣦⣄
⢸⡇⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠻⢿⣷⡀
⢸⡃⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣄⡀⠀⠀⠀⠹⣧
⢸⠆⡀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠸⡆
⣸⠀⠀⠁⠐⠛⠛⢚⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⢹⠃⢄⡀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣿⠀⠀⠀⠀⠉⠉⢨⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⣿⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡼
⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⣤⣿⡿⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⣋⣿⣿⠀⠀⠀⠀⠀⠀⢠⡇
⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠴⠊⠉⠀⠈⠑⠦⠀⢳⡀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣠⠏⠀⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⢀⡞
⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢀⣤⣶⣶⠖⠂⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏
⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠈⠁⣼⣿⣿⠀⠀⠀⠀⠀⠀⠙⠲⠤⢄⣀⣀⠤⠴⠚⠁⠀⠀⠀⠙⠒⠤⣄⣀⣀⣀⠤⠖⠋
⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⡏⠀⢻⡄
⡿⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⣼⠃⠀⠀⠻⣄
⡷⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠈⠛⠒⠦⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠔⠚⠁
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠈⠈⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⢸⡇
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣿⣷⣶⣦⣤⣤⣶⣷⣶⣤⣤⣤⡴⠒⠋⠙⠛⠒⠒⠛⠉
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⢿⣍⠀⠀⠀⠀⠈⠉⠳⣦⡀
⡷⢀⡀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢀⣠⣤⠤⠿⠶⠶⢤⣤
⡇⠀⠈⠉⠀⠐⠒⢘⡇⢸⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁
⡏⠒⠤⣀⣀⡀⠀⢨⡇⢸⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⡇⠀⠀⠀⠀⠀⠀⢨⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⣠⠞⠁
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⡼⠃
⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸
⢳⡀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠙⢦⣄⣀⠀⠀⢸⡇⢸

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⢀⡠⠂⠈⠉⠐⢢⡀⠀⠀⠀⠀⠀⠠⠔⠈⠉⠁⠢⠄⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠒⢄⠀⠀⠀⠀⠀⠀⠄⠂⠉⠉⠐⢤⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠒⡤⡀
⣯⣿⣿⣗⢞⣿⣿⣯⠂⠀⠀⠀⠀⠩⣉⡓⠀⢈⣉⠜⡀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠔⠄⢣⠀⠀⠀⠀⡈⠀⡠⠀⡀⣠⠆⣑⠀⠀⠀⠀⢠⠁⣀⡀⠀⢀⢁⠈
⠉⠙⠋⠃⠘⠉⠛⢩⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠃⠀⠀⠀⠀⡄⠀⠀⠐⠩⠂⠀⡘⠀⠀⠀⠀⢇⠀⠀⠀⠛⠀⠉⢀⠄⠀⠀⠀⢨⠀⠀⠐⠹
⠀⠢⢀⡀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⡠⠜⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⡀⠖⠁⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⡠⠔⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠠⡀
⠐⠀⡂⠀⠀⢐⡁⠱⠀⠀⠀⠀⠀⠁⣀⡀⠀⢀⣀⠘⠀⠀⠀⠀⠀⠎⢠⡄⠀⠀⢠⠄⢂⠀⠀⠀⠀⠐⢀⢂⠀⠀⣀⠂⠑⠀⠀⠀⠀⢠⠁⡠⠀⠀⠀⢄⠈
⢃⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⢈⠐⠋⠀⠀⠂⠙⠂⠇⠀⠀⠀⠀⡀⠀⠀⠄⢢⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠦⡭⠄⠀⠈⠀⠀⠀⠀⢠⠀⠀⠠⠴⠆
⠈⠢⡀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠑⢄⠀⠈⠁⢀⠔⠁⠀⠀⠀⠀⠈⠦⡀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⡀⠜


⢀⢤⣀⡀⠀⣀⣠⢄⠀⠀⠀⠀⠀⠀⡠⠄⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠠⠄⢄
⠸⠋⠥⠒⠒⠦⡍⢫⠀⠀⠀⠀⠠⠊⡤⠀⠀⠀⢤⠑⠀⠀⠀⠀⠀⡜⢀⠀⠀⠀⢀⠈⠆⠀⠀⠀⠀⠐⠁⢀⠀⠀⢀⠀⠣⠀⠀⠀⠀⢠⠊⣀⠀⠀⢈⢤⠸
⠇⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⡀⠂⠀⠆⠀⠀⠀⠀⠟⠂⠠⣄⣠⠀⠘⠿⠀⠀⠀⠀⠀⠀⠁⠠⠤⠈⠁⠠⠀⠀⠀⠀⢐⠀⠀⠰⠶⡆
⠘⢄⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠱⡀⠀⠈⠀⠀⡠⠃⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⠔
⠀⠀⠉⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁

⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⡀
⠀⠊⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⢀⢈⣁⠀⠀⢀⣈⠡⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢀⠑⡄⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠡
⡄⠀⠀⢀⣠⡈⠂⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⡄⠈⠀⠆⠀⠀⠀⠀⠀⠁⢀⡀⢀⠀⠁⢸⠀⠀⠀⠀⠀⠐⠂⣀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠛⢀⣀⡀⠒
⠐⡄⠀⠀⠁⠀⢀⠜⠀⠀⠀⠀⠐⢄⠀⠈⠉⠁⠀⡰⠀⠀⠀⠀⠀⠣⡀⠀⠈⠈⠀⢀⠆⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠘⢄⠀⠈⠁⠁⠀⡰
⠀⠈⠑⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠊

⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⢀⠎⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠑⡀⠀⠀⠀⠀⠠⠚⡀⠀⠀⠠⠑⢄⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⢢
⡆⠀⠃⣀⣀⡘⠃⠈⠀⠀⠀⠀⠈⠀⠒⠂⠀⠐⠒⠀⡄⠀⠀⠀⠀⠁⠐⠂⣠⠀⠒⠂⢰⠀⠀⠀⠀⠀⠀⠝⢀⠀⠠⠄⠠⠀⠀⠀⠀⠘⠠⠒⠒⠀⠒⠲⡄
⠠⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠐⡄⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⢂⠀⠀⠈⠁⠀⢀⠎⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣴
⣀⣈⣢⣤⣤⣔⣊⣀⣀⣀⣀⣀⣀⣈⣐⣤⣤⣤⣂⣁⣀⣀⣀⣀⣀⣀⣑⣠⣤⣤⣐⣁⣀⣀⣀⣀⣀⣀⣈⣢⣤⣤⣔⣈⣀⣀⣀⣀⣀⣀⣈⣛⣦⣤⣔⣛⣁
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⠀⠀⠀⡟⣆⠀⢀⣀⡀⠀⠀⠀⠀⣠⠞⡽⠙⣆⣩⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⢀⣀⡤⠇⠈⢉⡵⠋⠀⢀⣄⠀⠰⠯⠖⠛⠉⢹⡄⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠉⠙⡇⠀⠈⠉⠉⣇⡜⠓⠿⣦⠀⠈⠁⠀⣀⣠⣤⣄⣀⠀⠳⠀⡴⠋⣡⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣼⠃⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⡀⠀⠸⠋⠀⠀⣈⣉⡛⠶⣄⣠⣾⡿⠋⠁⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣠⡞⠁⠀⠀⠀⢀⣴⡿⢿⡆⢀⣶⡿⠛⣷⣶⠀⢀⣾⡿⠛⣿⠀⢸⣿⡿⢧⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡞⠉⢠⡶⢶⣄⠀⣸⣿⣧⠞⢁⣿⡟⠀⢰⣿⡏⠀⣼⣿⠡⣴⠏⠀⣿⡿⠁⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⣧⠀⡟⠀⠈⣿⡶⢻⣿⠀⠀⣼⣿⠀⢀⣾⣿⠁⠀⣿⣿⠀⠀⠀⣼⣿⠇⣼⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠻⣿⣆⡇⢀⡼⢻⡇⠈⠻⢦⠾⠃⠻⠶⠋⠘⣿⣀⡴⠋⠿⣦⣤⠞⠉⣿⣼⠃⣸⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⠙⢿⡷⠘⠷⢟⣁⣠⣤⣤⣤⣤⣤⣄⣀⣀⠈⠉⠀⠀⣀⠀⠀⠀⠀⣬⡁⠀⢿⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡄⠀⢀⣴⡾⠟⠋⣉⣥⣴⣶⣦⣤⣬⠉⠉⠛⠳⠶⣤⣌⣙⡛⠒⠒⠛⢠⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠘⠋⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⣴⣿⠿⣦⠀⠀⣬⡍⠙⠛⠛⠛⠛⠁⠀⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⢸⡟⣦⠀⠀⢰⣿⠆⠀⣸⣿⠃⢀⡿⠀⠀⠛⠃⠀⣀⣀⠀⠀⣠⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢸⣿⡄⠀⠀⠙⢾⣦⣀⣠⣤⠀⠀⣿⣿⡴⠞⠁⠀⠀⠀⣰⣿⡟⠛⣷⢰⣿⠏⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣧⠀⠀⠀⢸⡇⢀⣿⡟⠀⠀⣿⣿⢠⡾⠛⣷⣄⣴⣿⣿⡤⠞⠁⣸⣿⡆⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠀⠀⢻⣿⡄⠀⠀⢸⠃⢸⣿⡇⠀⢠⢿⣿⡿⢀⣴⣿⠋⠸⣿⡇⠀⠀⣰⠏⠹⣿⣄⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⣀⡟⠀⠀⢻⣷⣠⠟⠈⠿⠇⢾⣼⠟⠀⠀⠙⠷⡤⠾⠃⢀⡴⠛⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡶⡄⠀⠀⠀⠰⢿⠿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢐⢻⠏⢁⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠉⢻⣿⡔⡢⠄⢰⡸⢰⣏⣾⠇⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⠋⠀⠀⢻⡁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⠞⠋⢸⢃⡌⠈⠳⣾⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⣠⡿⠁⢸⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠙⣦⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢀⣰⣿⠇⠀⣼⣿⠇
⠀⠀⠀⠀⠀⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣤⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠆⡀⠀⠸⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠃⠀⡏⠀⠀⣰⠎⠁⣸⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⡀⠀⢰⠇⡆⠀⠀⠀⢰⠠⠀⣿⠏⠀⠠⡇⠀⡈⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠸⠀⠈⣶⠃⠀⠀⠀⢸⡴⠈⠃⡄⢹⣤⢤⠔⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠈⢠⢰⡄⠀⢨⠇⣴⡷⠀⠸⢳⠇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢰⣄⠂⠘⡝⣶⡿⢰⡿⣇⣰⡇⣸⣴⠏⣠⡴⠖⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠙⢰⠁⠀⢰⢀⣿⢥⢻⡿⢠⡿⢋⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⡀⠈⣤⣤⡆⣾⣿⣆⣼⢃⢟⣵⣯⣾⣿⡶⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠈⠀⠳⢛⣽⡿⡼⠿⢻⡿⣾⣿⢟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠄⠀⠄⠀⠄

⠀⠀⠀⠀⠀⢤⡠⠄⠀⠀⠀⠀⣀⡤⢠⠀⣤⢤⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠄
⠀⠀⠀⠀⠇⢼⠁⢨⠀⠀⠀⠀⠀⠈⠸⡀⠁⢸⠀⠀⠀⢴⠀⠉⣴⠛⡇⠀⠀⠀⣿⠳⢧⡴⢀⣄⣀⡀
⠀⠀⠀⠀⡄⢸⠄⠰⠀⠀⠀⠀⢂⠀⠘⡇⠀⡜⠀⠀⠀⢰⠀⠀⠁⠀⡅⠀⠀⠐⠇⠀⠠⠀⢀⡴⠁
⠀⠀⠀⠀⠙⠾⣧⠾⠀⠀⠀⠀⠈⠓⠴⠷⠐⠁⠀⠀⠀⠘⠆⣠⣂⠴⠃⠀⠀⠀⠀⠐⠷⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣾⣿⠏⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢸⡿⠋⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⡿⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢾⣶⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣧⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⣺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⡿⣏⢿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣹⡝⣿⣏⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡛⣿⣿⣶⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢹⣿⡹⠿⣆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣬⣽⣿⡽⠽⠿⠿⠿⠾⠿⠷⠤⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣽⣷⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡃⠂⠀⠀⠉⠀⠉⠀⠀⠁⡀⠀⠈⣀⣽⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢁⣰⡿⠟⠋⠁⠀⠀⠀⠄⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠤⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠋⠉⠀⠈⠉⠙⠻⣿⣷⣄⡀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⠀⠀⠀⠀⠀⢠⠖⡚⠒⠒⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⢨⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡴⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡠⠖⠀⠀⠀⠀⠀⢐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣦⡀⠀⠂⠞⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣶⠦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣅⢱⡄⠁⠀⠀⠀⠀⠀⠀⠀⣦⡲⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣿⢧⣂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠆⣸⣢⠰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣨⠟⢻⠛⠓⠛⠽⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣉⣀⣙⠳⣶⣾⣷⣶⠒⢶⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠉⠁⠛⠛⠛⠒⠈⠈⠈
⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⠤⠤⠀⠄⠠⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠲⡆⢠⠖⠢⠤⠠⡄⢀⡄⠐⠰⡦⠂⠀⢰⠦⣴⡂⠴⢠⡤⠀⠀⠄⡴⠐⣤⡄⠀⢠⡶⠀⠀⡄⠀⠀⠠⠀⡠⠄⠀⠀⠀⢀
⠀⠄⠃⣀⠑⢆⣄⣀⠉⠀⠙⠀⠚⠋⠀⠀⠀⣤⡼⠁⠀⢀⠀⠃⠀⠀⢄⠂⢀⠭⠤⠐⠓⠈⠋⠉⠓⠐⠄⢀⠁⠀⠀⢐⠔⠁⠀⡀
⠀⠀⠄⠀⠀⠾⠋⠉⡿⠐⠂⠀⠰⡌⠉⢀⠀⡉⠥⣤⡀⠀⠂⠐⠃⠀⢈⠴⠉⠀⡀⠄⠤⢒⠲⢄⠀⠀⠂⠀⠑⠀⠄⢁⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠁⠀⠉⢉⣹⡁⠀⠈⠀⢠⣃⠀⠀⠀⡘⠀⠀⣮⠀⠀⠩⡈⠀⠀⠀⠑⠂⠐⠀⢀⠀⠛⠵⠈⠉⠉
⠐⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⡎⡎⣠⠔⠒⠲⠘⠚⠃⠀⢐⡁⠀⠀⠀⠁⠀⠀⠀⠈⡀⠀⠀⠀⢆⡀⠘⠂⡠
⢀⠃⠀⠀⠀⠤⠀⠀⠈⠀⠀⣠⠀⠠⡞⡾⠅⣶⠶⡚⡃⠀⡀⠀⠀⠜⠒⠀⠀⢆⠁⠀⠀⠀⠀⠁⠂⡀⠂⠘⠛⣀⣄⠿⠓⠀⠀⢁⢢
⠸⡄⠀⠀⠀⡱⠒⠋⠐⠇⠀⠈⠴⠒⠀⠴⠦⠒⠆⡀⡀⠤⣄⠀⡇⠀⠀⠀⠀⠈⡆⠈⠉⠀⠀⠀⠈⠀⠀⠂⠀⢉⡻⢷⣆⠀⠀⠀⠟
⢀⡇⠀⠀⠻⡄⠛⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠀⠀⠉⠐⠚⠛⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⠀⢠⡄⢀⡃⠐⠒⠀⢀⠀⡀⠨
⠀⢣⡔⣀⠐⡆⠀⠀⠀⢠⠀⡆⢠⢘⠀⠀⣾⣿⡙⠁⠢⡤⡀⣀⢀⡆⠤⠤⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢀⠀⠈⢇⠀⣈
⠀⠉⠀⠀⠀⠁⠀⠀⠠⠈⠀⠘⠀⠀⡵⠔⠅⠙⡄⠶⠈⠀⠈⠳⡌⣣⠸⣀⡀⠀⠀⠀⠘⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠘
⠀⠀⠋⠀⠀⠀⠆⠀⠴⠂⠀⢀⠀⠀⠀⠒⠀⠘⠀⠙⠁⠀⢂⠏⠉⠉⢠⠴⢈⠀⠉⠁⠐⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⡆⠀⠁
⠀⠀⠀⠆⠌⢹⣐⣤⡀⠀⠁⠀⠂⠀⢀⠠⠐⠀⠀⢠⠀⠀⠷⠀⠀⠀⠀⠀⠈⡀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠉⠈
⠀⠀⠀⠀⠐⠒⠒⢍⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠐⢐⠂⠁⠀⢀⡈⠀⠂⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠡⠈⠂⣤⠀⠀⠀⠀⠀⠀⠀⢐⣂⣀⡐⢀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠄⠀⠀⠀⢀⣁⡈⠈⠀⠀⠠⠰⠹⠄⠘⠛⢰⠲⠀⠀⠀⠰
⠀⠀⠀⠀⢀⠀⠀⠉⡀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠁⠉⢀⡳⠀⢈⡔⠂⡄⠐⠀⠐⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠂⠀⡀⠀⠀⠀⡂
⠀⡔⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠂⠀⠉⠁⢀⠀⠀⠀⠈⢭⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡄⠀⠀⠀⠀⡤
⠀⠤⢐⣚⠍⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠰⣶⠀⠺⠀⠀⡄⠀⠀⠀⠁⠐⢀⡀⠀⠤
⠀⢠⡄⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠀⡂⠈⠁⠀⠠
⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢶⣄⠀⠀⠀⡀⠀⠀⠒⠀⡔⠀⡀⠋⠐⢀⣄⡄⠁⠄⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣸⡤⣀⣀⣀⠄⠀⠀⠀⠀⠈⠀⠄⠀⠀⢁⠀⠙⠂⠈⠀⠠⠋⠀⠠⠈⠁⠀⢉⣠⠀⠀⠉⢁⡂⠀⠀⠀⠘
⠀⡃⠀⠀⠀⠀⠈⡉⡧⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⣸⣮⠀⠀⠀⠀⠀⠀⠠⠀⢠
⠀⠦⠀⠄⠒⠀⢈⠁⠁⠀⠀⢀⡀⡀⠀⠀⠠⠆⡴⠀⠁⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣂⠀⣤⣼⠀⠀⠀⠃⠀⠀⠀⣤⣤⠼
⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡴⠷⠖⠃⢸⣤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣥⣤⣦⠄⠀⡀⠀⠀⠀⠀⠺⣄
⠀⠀⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠭⡀⠀⠀⠀⠖⠁⠐⠀⠙⡴⠱⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠘⠃⠀⠀⡀⠀⢠⡧⠄
⠀⠶⠶⠴⠾⠁⠀⠰⠦⠶⠶⠆⠀⠈⠒⠖⠊⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠞⠻⠖⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⡀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⡀⠀⢂⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠠⣥⡀⣤⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡤⣠⡥⠀⠀⠀⡘⣭⠟⠛⠻⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣤⡤
⠀⠀⠁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣴⢃⡐⣶⢂⠚⡆⠀⠀⠀⠀⠄⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠂⠠⠠
⠀⠉⠉⠉⠈⠉⠉⠃⠀⠀⠀⠤⠤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠴⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢡⠀⠉⠀⠀⣰⡆⠐⠂⠀⠂⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⣤⠀⢠⠄⠀⠀⠀⠀⢥⢠⣠⠁
⠀⠀⠀⢠⣠⠄⠀⠀⠘⢇⠀⡀⠀⠀⠀⠛⠀⠀⠀⠤⠄⠠⠀⠀⠀⠄⠀⠒⠒⠀⠀⠀⠀⠀⠀⠠⠀⠠⡄⠀⠀⣜⠁⠤⠄⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠄⠀⠤⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡈⠀⠠⠀⠀⠁⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠰⣶⠆⢶⡶⠀⠀⠀⠰⠶⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠠⠶⠶⠋⠀⠀⠀⠀⠀⠒⠢⠀⠄⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠸⠥⠀⠀⠬⠀⠀⠀⠸⠤⠀⠀⠤⠀⠀⠀⡡⠀⠀⠀⠀⡁
⠀⠀⠀⠄⠀⠤⠀⠀⠀⠀⢰⡆⠀⣆⠀⠀⠀⠻⣿⠟⠻⣿⠿⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⢤⠀⢠
⠀⠀⠀⠂⠆⠐⠀⠀⠀⠀⠈⠀⠆⠁⠀⠀⠀⠀⠀⠀⠇⢀⠐⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠲⠶⠖⠃
⠀⠠
⠀⠰⢆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⣠⣶⣾⣶⣦⡀⠀⠀⢡⠂⠀⠀⢂
⠀⠀⣴⣀⢀⣠⣦⠁⠀⠀⠀⠀⠀⡀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠰⠎⠅⠀⠀⠀⠀⡤⠉⠁⡄⠀⠀⠈⠀⢃⠀⠐⠃⠁
⠀⠀⠙⠭⠀⠴⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣷⡶⠂⠀⠀⠢⡓⠀⠚⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⢀⠖⡟⣏⢻⡭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠁⢀⣠⠔⠈⢨⠟⠁⢠⡄⠀⠯⠚⠃⠹⡅⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⣹⠀⠀⠀⢹⡌⠙⠓⠀⠀⠀⣠⠴⠶⠤⣄⡁⠰⢋⣴⡶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡴⠃⠀⠀⢀⣬⣤⡀⢀⣴⣶⣤⡁⠀⣴⡶⣦⠙⣳⣿⣏⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠋⣠⢤⣄⠀⣾⣯⠜⢡⡿⠁⢰⣿⠁⣸⡟⢠⠞⢠⣿⠇⣨⣭⡉
⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⢠⡇⠀⣻⡟⢿⡇⢀⣾⡇⣠⢾⡏⠀⣿⡇⠀⢀⣾⡿⣰⢃⣿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠻⣿⡇⣞⣹⠇⠈⠛⠋⠀⠉⠁⠈⠳⠞⠁⠙⠒⠋⠈⡿⠃⣼⡇⣴
⠀⠀⠀⠀⠀⠀⠀⠈⣠⡀⠈⢁⣬⡷⠞⣛⣻⣭⣭⣛⠛⠲⠶⢤⣄⣓⠶⠤⠼⠟⡀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠁⣀⠸⠋⠁⠀⠀⠀⣰⡾⢳⡄⢀⣭⡙⠓⠒⠚⠃⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡶⢻⣦⠀⠀⢯⣧⠀⠘⠿⠀⢰⣿⢁⡼⠁⠀⠉⢀⣤⣤⡀⣴⣿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡆⠀⠀⢹⠓⣺⡿⠀⢸⣿⢋⡤⣦⡀⣰⣿⣃⡼⠓⣿⡇⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⢻⣷⠀⠀⣸⠀⣿⡇⠀⡼⣿⡞⢠⣼⡏⢹⣿⠁⠀⡼⠛⣷⡀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠏⠀⠙⢷⠴⠁⠙⠃⠷⠟⠀⠈⠛⠶⠚⠁⣴⣛⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠁⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡬⠿⢿⣿⣶⣦⡀⠛⣸⡇⢀⠖⣁⠀⢈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⠿⣷⠀⣼⣣⠏⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣭⣭⣶⣦⣬⣵⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣡⣤⣜⣿⣿⣾⣶⡭⢙⣷⣶⡶⠦⣝⣣⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠿⢿⣿⣿⣯⣾⣟⡟⢩⣿⣿⣦⡘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠸⣿⠋⣿⢛⣿⣿⢸⠈⠉⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢻⠋⡰⠈⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣤⣏⠀⠀⠀⠀⢀⠀⣀⡀⡀
⠀⠀⠀⠀⣠⣤⡤⣤⣤⣤⣤⣤⡉⣭⣭⣽⡿⠿⠩⠈⣿⠤⢬⣕⣛⠚⢻⠉⠉⠩⠁
⠀⠀⢠⣤⡴⠦⣴⣿⣿⣿⣽⠻⠷⠛⠉⠁⠀⠀⠀⢀⣹⣧⠀⠉⠙⠻⢛⣛⣛⠓⢲⣖⣀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠠⢶⡶⢶⣶⣦⣭⣙⢂⣀⡀⡀⠀⠀⠀⠀⠈⠉⠳⣄⠐⠀⠀⠙⠻⢿⣷⠍⠉⡉⠈⠉⠉⠛⠛
⠀⠀⠀⠀⣤⣤⣶⣿⣶⣬⣭⣾⣶⣿⣿⣿⣧⣈⠓⠒⠓⠈⠀⠈⠳⠄⠀⠀⠀⠴⠾⠒⠿⠿⠶⠆⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⠒⠶⠶⣾⣯⣤⣀⡈⠛⠋⠀⠲⠾⠿⠿⠿⠻⠒⠒⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⣿⣿⣦⣀⣈⡧⢳⣟⠓⢧⠆⠉⣾⠻⣷⣿⣿⣿⣷⣽⣯⣯⠉⠀⠸⠏⠰⠀⠻⠈⠛⠈⠋⢿⣶⠼⠃⠀⡟⠀⢸
⣿⣿⣿⣿⣿⣶⠮⢍⡀⠈⠙⠆⠸⠛⠻⣚⣻⣿⣟⣝⡶⢿⣳⠉⠁⣯⣤⣀⠒⠀⠀⠀⠀⠈⡏⠀⠘⠠⡄⠔⢋
⣿⣿⠟⠛⣳⢾⣿⢸⢟⠖⠂⠀⠁⢸⡟⠯⠉⠛⠉⠉⠛⠃⠀⠰⠏⠛⡿⡻⡡⢀⠂⠄⠀⠢⠠⠀⢁⣠⡷⠖⠛
⣿⣿⣿⣿⣧⣼⡿⣛⣋⣴⠶⢀⣘⡓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡞⠀⠋⠁⠰⠆⣠⠀⠑⢰⡄⠠⠀⠸⠁⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠟⠘⠁⠀⠙⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡅⣿⢸⠃⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣴⡶⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⣶⠞⡿⣵⣿⢿⡇⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣷⠀⠀⠀⠈⣅⡀⠀⠀⠀⠄⠈⠁⢄⠒⠋⠸⡆⠉⡟⠁⢀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢀⣄⢤⠋⠁⠃⠀⠀⠀⠀⠀⡽⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡴⣢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠴⠠⠄⠀⠀⣀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣾⠁⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠈⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣰⣿⣅⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠏⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⡟⠃⣄⡀⠀⠀⠀⡶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠿⠶⠀⣷⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⠏⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⢉⣶⣴⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢤⣼⣿⣭⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⣨⠚⢻⣣⣾⠿⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⡠⠬⠍⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢰⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠙⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⣴⣀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠳⣤⠀⡀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡘⠷⣧⣴⡂⣀⠻⡇⠀⠀⠀⠀⠘⠠⡀⠀⠘⠶⢦⣴⣿⡧⠔⠁⠀⠀⢳⣸⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠻⣥⣈⣻⣿⣿⡾⠀⢠⠤⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣗⠀⠀⠀⠀⢹⣿⣃⡠⠉⠙⠋
⠀⠀⠀⠀⠀⢠⢁⡤⠴⠆⠶⠶⠿⣿⠿⣿⣧⡠⣷⠀⢀⠀⠀⠁⠀⣠⣤⠶⠋⠀⠀⠛⢆⡀⠀⣤⣾⣿⢻⣍⢛⠠⢄
⠀⠀⠀⠀⠀⠈⠈⠒⠤⠀⢀⣤⠤⠾⣄⠀⠉⠧⢿⣄⡽⠒⠀⠂⠀⠑⢆⠀⠀⠀⠀⠀⠈⠁⠀⠘⠿⠿⠏⠉⠙⠷⠬⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣟⢠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡄⡄
⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢣⠈⣄⠀⠀⠀⡞⠀⡄
⠀⠀⠀⠀⠁⢀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣼⡀
⠀⠀⣀⠀⠀⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⢨⣀⣴⣿⠷⣠⠀⣠⠔
⠀⠈⠀⠀⣀⠀⠀⢧⠀⠀⠀⠀⠐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⢀⣄⠤⣙⣿⣿⣿⣷⣶⡈⠀⠀⠂
⠀⢀⡠⠜⠁⠀⠀⠼⡖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡇⣆⡏⠀⡀⠀⠀⠀⠐⠂⠀⠉⠿⡿⠟⠿⠿⣿⡂
⠀⠸⠀⠀⣄⠍⠀⠀⠉⠀⡀⠀⠀⠲⠄⠀⠀⠀⢀⡃⢀⠹⣿⣠⣨⣾⡶⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠁⠀⠀⢀⠀⢁⠉⠚⠉⠀⠀⠀⠀⠀⠰⢄⡪⣤⣰⢳⣿⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⠈⣑⢿⡻⡘⣿⣗⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡇⠀⢸⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⣿⠇⢇⠘⢻⣃⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⡀
⠀⠀⠀⠀⣤⡀⠆⠸⠀⢐⡤⠂⢐⠀⠀⠀⠀⠀⠠⠄⠉⠙⢳⠄⢧⡘⡵⢊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⣸⣿⣰⠁⡠
⠀⠀⠂⠀⠨⣍⠳⡟⢤⣠⣦⠄⠚⠚⠀⠘⠁⠀⠀⠀⠄⠚⣉⡥⠄⢣⣘⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⣿⣇⠎
⠀⠀⠀⠀⢢⣝⣦⣶⠈⣿⣡⣴⣷⡶⠂⢀⠀⡀⠀⠀⠀⠈⠐⠚⠿⠶⣛⠅⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢈⣻⣷⣿⠃
⠠⠀⠀⠀⠀⢉⡽⠿⠿⣿⡿⠑⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠬⢝⣿⡏
⠀⠀⠀⠀⠀⠨⣀⠀⠠⡿⠛⣦⣤⣴⣶⣍⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠴⠾⢿⡦⠂
⠀⠀⠀⠀⠀⠀⣦⠀⠀⣏⠉⣡⠋⠯⠙⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣥⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡤⠒⠉⠉⠉⠒⢄⠀⠀⠀⡠⠐⠀⠀⠀⠒⢄⠀⠀⠀⢀⠤⠒⠒⠒⠢⣄⠀⠀⠀⣠⠒⠉⠉⠉⠓⢤⡀
⡌⠀⣀⠀⠀⢠⡄⠀⠇⠀⠊⠀⠀⡀⢀⠀⠀⠀⢣⠀⢠⠃⣀⠀⠀⠀⣤⠈⢦⠀⢰⠁⠀⠀⠀⠀⢀⡀⢳
⡇⢠⠁⠀⠀⠀⢠⠀⡄⢸⠀⣀⠀⠃⠈⠀⠰⡆⢸⠀⠀⠀⣉⣀⣀⣀⣠⣄⢸⠀⢸⠀⣆⢠⠄⠺⠂⡇⢀
⠐⡄⠑⠂⠠⠒⠁⡰⠁⠀⢢⠀⠈⠒⠓⠊⠉⢀⠎⠀⠘⢄⠙⢾⣚⡦⠟⢁⡜⠀⠈⢦⡈⠒⠤⠔⠊⢀⠜
⠀⠀⠁⠒⠒⠒⠉⠀⠀⠀⠀⠈⠒⠀⠀⠀⠒⠁⠀⠀⠀⠀⠑⠒⠠⠀⠒⠉⠀⠀⠀⠀⠉⠐⠒⠒⠉⠁
⠀⢀⡠⠐⠒⠢⢤⡀⠀⠀⠀⠀⡠⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⠤⠐⠒⠤⡀
⠠⠃⠀⠀⠀⠀⠀⠘⢆⠀⢠⠊⠀⠀⠀⠀⠀⠙⣆⠀⢀⠊⠀⠀⠀⡀⠀⠙⢆⠀⢀⠜⠁⠀⠀⠀⠀⠈⢦
⡇⡀⠀⠉⠀⠁⠀⢰⢸⠀⡇⠀⠓⠀⠀⠈⠁⠀⢸⠀⡌⠀⠀⠀⢀⣀⣤⠀⠘⠀⠸⠀⢠⡄⠀⠀⣤⠀⢸
⢃⠣⡀⠀⠀⠀⢀⢜⡜⠀⢇⠐⣦⠤⠭⢉⠟⢀⡞⠀⠰⡀⠔⠯⠀⠀⠈⠁⡰⠀⠸⡀⠀⠐⠂⠂⠀⢀⡜
⠀⠑⠨⠅⠀⠬⠕⠊⠀⠀⠈⠓⠤⣉⣉⡡⠔⠊⠀⠀⠀⠑⠢⢄⣀⣀⠤⠒⠁⠀⠀⠈⠢⠤⠤⠤⠔⠋
⠀⠀⣀⠠⠤⢄⣀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⠀⠀⠀⠀⠀⣀⠠⠤⢤⣀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀
⢠⠎⠁⠀⠀⠀⠀⠑⣄⠀⠀⡴⠉⠀⠀⠀⠀⠑⡄⠀⢀⠎⠀⠀⠀⠀⠈⠳⡀⠀⠀⡔⠉⠀⠀⠀⠀⠈⠳
⡇⠀⠰⠆⠀⠿⠀⠀⢸⠀⢸⠀⠠⠤⠐⠠⠤⠀⢸⠀⡌⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⢀
⢇⠀⠐⠒⠒⠲⡶⠂⡸⠀⢸⠀⠀⠀⢴⡄⠀⠀⡜⠀⢰⡀⠀⠀⣀⣀⠀⠀⡎⠀⠸⡀⠐⡖⡞⠉⠉⠁
⠀⠑⠤⣀⣀⣀⡠⠖⠁⠀⠀⠑⢄⣀⣀⣀⡠⠚⠀⠀⠀⠑⠤⣈⣀⣀⠤⠊⠀⠀⠀⠙⠦⣌⣁⣀⣠⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣸⡧⢠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣤⡄⡀⠀⠛⠀⣶⠇⠀⡀⠀⠀⢹⠗⠁⠈⡀⠀⠁⠻⣁⡀⠀⠢⠄⠐⢃⡄⠀⠀⠄⠀⡉⠬⠵
⠀⠀⣴⣿⠁⠀⠈⠀⠀⣴⠦⠾⠖⠀⠀⠀⠀⡰⠋⠐⣠⡟⠁⢠⣬⠀⠀⠀⠀⠦⠘⠁⠀⢙⣏⠀⠠⠀⡀⠀⣀⣀⣙⣁⠀⠓⠀⠀⠈⠀⠀⠁⠀⠖⠁
⠀⣸⣿⣿⠀⠀⠀⠀⠀⠰⣴⣁⡴⢲⣄⡀⢰⢃⣈⢠⣿⠁⠀⠀⠗⢀⠐⢺⣷⣰⠘⠛⠀⠛⣫⠀⠲⠀⠀⠀⠀⠀⣜⠉⠀⠀⠢⠄⠀⣀⠀⠀⠨
⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠹⣿⡷⠤⠘⠁⠘⡄⣠⠘⣿⡀⠀⠀⠈⠀⠀⠐⣷⠃⠀⠀⠀⠈⠉⣰⡤⣁⢆⣀⠠⣮⠉⠁⠀⠀⠠⡀⠀⠁⠀⣀⠀⢂⡀
⠀⠀⠙⢿⣿⣿⣦⣤⣤⡤⠀⠉⠀⠀⠀⠀⠀⠙⢦⡐⠈⠷⣄⠀⠀⣀⡀⣦⡀⣦⠀⠠⠀⠀⠀⠉⠀⠻⠀⠛⠀⠀⠀⠀⠀⣀⠦⠀⠸⡀⣠⠀⠒⠀⢠⢃⡞
⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠄⠂⠈⠀⠁⠈⠠⠐⠈⠉⠛⠉⠑⢶⡼⠛⠉⡉⠛⠀⠁⠀⡀⠳⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠐⠃⠀⠀⠄⠀⡀
⠀⠘⠇⡀⠀⢀⡀⠀⡄⠀⠁⡂⠀⢰⡟⠛⣧⠀⢀⡀⠁⠀⢈⣛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡤⠁⠂⠐⠁⠋⣗⢀
⠀⠀⣿⠃⠀⠠⠍⠀⠀⠇⠀⠙⠳⠨⢷⢾⢯⠤⠋⠁⠀⠀⢉⣹⡄⠀⠀⠀⠀⠀⠀⠀⢰⣄⣠⣀⣨⣦⠈⠒⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀⠴⠆⡄⠀⠀⢊
⠀⠐⠂⢀⣤⣤⡦⡤⠀⠠⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⠷⣄⠀⠀⠀⠀⠀⠈⡐⠻⣿⣿⠿⠋⠀⠀⠀⠀⠀⡀⠀⢁⣅⣄⣤⡀⠀⠠⠐⠀⠀⢀⠠
⠀⠀⣴⣿⣿⣿⢋⠀⠀⠜⠉⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢹⠖⣶⢾⡄⠐⣿⣦⣤⣤⣤⣾⣿⠀⠀⠀⠀⢃⠐⢂⠸⡿⠛⠁⠀⠀⠃⠀⠘⠘
⠀⠀⣿⣿⣿⡇⢄⠉⢠⡆⠀⣸⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠴⠴⠎⠀⠈⠀⠀⠀⠙⢿⣿⢸⣿⠿⠃⠀⣀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⡀⣠⠀⣀⠲⠔
⠀⠀⢻⣿⣿⣾⣁⠁⠀⡶⠈⣽⣿⣿⡟⠙⣷⡀⡀⠀⠰⠀⠀⠀⠠⣤⠂⠀⢀⣀⣀⡀⠀⠀⠈⠀⠀⢠⡦⠀⣀⠈⣠⡤⢖⠀⠒⠀⡊⢆⣤⠁⣀⢀⣈⠴
⠀⠀⠀⠉⠻⠿⠿⠆⠀⠠⠾⠿⠟⠋⠀⠀⠙⢿⣿⣷⣄⠑⠶⠀⠀⠁⠀⣰⣾⣿⠛⠀⠀⠀⠀⠀⠀⢲⢀⣤⠉⣀⠀⢰⣠⠀⠉⠀⣄⠄⠸⣀⠉⠀⠁
⠀⠀⠀⢀⣤⣶⣿⡿⠗⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⡿⠿⠀⠀⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣤⡈⣙⠀⣿⣆⣔⠠⣀⣀⡀⠀⣢⣠⣿
⠀⠀⢀⣿⣿⣿⡟⠁⣀⠀⣶⣤⠀⠀⠀⠀⠃⠿⠂⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠿⠃⣃⡀⠈⠛⢿⣿⠄⠀⠀⣿⡿⠛⠁⠀⣾⣷⣴⣶
⠀⠀⢨⣹⣿⣿⡷⠀⠛⠀⢁⡤⠀⠀⢤⠀⠀⠀⠀⠀⠀⠶⢾⣿⣷⣶⣄⠀⠘⠛⠛⠂⠀⠀⠀⠀⠀⣰⠆⠛⠀⠀⠀⠀⠉⠀⠐⠀⠉⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⣘⣿⣿⣿⣷⠐⠃⢠⠄⠀⠘⠛⠈⠁⠰⠆⡀⢠⠀⠀⠀⢹⣿⣿⣽⣧⠀⠀⠀⢀⣀⣤⣄⣀⠀⠠⡦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⢿⣿⣿⣿⣷⡤⠀⠀⠀⡄⠀⠸⠃⠀⠀⠈⠈⢀⣴⢶⡄⣿⣿⡷⣿⠀⣠⣾⣿⣿⣭⠞⠣⠈⠄⠀⠄⠀⠓⠚⠋⢀⡆⠀⠀⡀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⢇⡏⢀⣠⣤⣤⣤⡀⠀⠈⠁⣵⣷⣿⣿⣿⠏⢠⣿⡿⢿⣷⡟⠀⣠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠁⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠐⠻⠛⠛⠁⠀⢸⣿⣧⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⠐⣆
⠀⢀⡀⠀⠀⠐⠶⠆⠀⠀⠀⡀⢺⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⡈⢿⣿⣿⣿⣄⠀⠀⢠⣄⠀⠀⠀⠀⠀⢐⢀⣷⡇⠀⠀⠈⠇⠀⠀⠀⣿⠀⣸
⠀⠨⠄⢀⡀⠀⠀⠀⠠⡤⡀⠄⠈⢻⣿⣿⣿⣿⡿⢋⡤⠶⠤⠀⠀⢹⣷⢀⡀⠛⠓⠻⠿⢿⠷⠄⢸⣿⣷⣦⣼⡶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣴⠟⢀⣟
⠀⠀⠠⡌⠠⠀⠀⠀⠰⠀⠄⠀⠀⠀⠈⠁⠉⠈⠀⣾⢴⠉⠀⠀⠀⠈⠻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣾⣿⣿⠿⠀⠀⠀⣄⡉⠉⢉⣁⣴⣯⠟
⠀⠀⠀⠀⠁⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠶⠤⢤⣤⣀⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⡇⠪⡍⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢀⠭⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡞⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠃⡼⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠁⠘⠧⣀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⡤⠶⠖⠛⠛⠛⠉⠉⢹⠇⠀⠀⠀⠀⠀⠀⠈⡦⣤⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⣄⢀⡤⠶⠶⣄⡴⠚⠛⠲⠦⠴⠖⠋⠛⠲⣄⠀⠙⠳⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠙⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⣀⣤⣤⡤⠶⠚⠉⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠚⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣶⡆⢀⡿⠛⣷⣆⢰⡞⠛⠒⠒⣰⠾⣿⣆⠀⢀⣴⡞⠋⠉⠙⠆⣿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣧⡞⠀⠀⣼⣿⢿⣇⠀⠀⢀⡏⠀⠘⣿⣆⣼⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⣴⠿⠃⢸⣿⢀⣀⢸⡟⠛⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡋⠻⣧⡀⠀⠸⣿⡉⠀⢸⡇⠀⠀⢸⣿⠘⣿⣇⠀⠀⠀⡆⢻⣿⠒⠚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠒⠋⠀⠀⠀⢿⡷⣶⡊⠇⠀⠀⠸⠟⠀⠈⠙⠓⠶⠚⢁⠸⠟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣨⡅⣿⡅⠀⣀⣀⡀⢀⣤⠖⠐⢤⢠⡾⠉⠙
⠀⠀⠀⠀⠀⠀⠠⠞⡜⠹⣷⡀⠀⢠⠏⣿⡇⣿⣇⡾⠉⢹⣷⣾⡏⠀⠀⣰⢿⣧⡤⠶⣶⣄
⠀⠀⠘⢦⡀⠈⡐⠠⢅⡀⢻⣧⢀⡞⠀⣿⡇⢹⣿⣡⠔⣺⡟⢻⣷⠴⠚⡁⠀⢀⡞⠉⣽⠏⠉
⠀⠀⠀⢠⠎⢀⠀⢰⣀⠤⠓⠻⠟⢦⣀⠘⠧⠺⠟⠓⠚⠁⠀⠀⠙⠲⠖⠁⣀⣼⠲⠞⠋⠀⣀⣀
⠀⠀⠀⠯⠞⠀⠡⣀⡉⠉⠉⠉⠛⠉⠉⠛⠲⠦⠤⣤⣤⣤⣤⣤⡤⠶⠶⠛⠉⠉⠙⠋⠉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢶⣄⠀⠀⠄⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣥⣤⣤⣤⣋⣶⢀⠀⠀⢠⢴⣟⠿⠿⢿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⡽⠟⠋⠉⡁⠺⣀⣀⣠⣂⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢰⠯⠿⠋⠈⢁⡴⠋⠀⠀⣀⠘⣷⠈⣷⡄⠻⢟⠟⣤⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⡐⡘⠲⣿⣷⠀⠈⠰⢼⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠑⣿⠀⢹⣿⡆⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠘⣿⡇
⠛⠛⠛⠛⠛⠛⠛⠿⠟⡏⠀⣠⣿⠿⠋⡙⠂⠿⣿⣤⣽⠉⣿⡇⠀⠙⠛⠻⠛⠻⠿⠿⠿⢿⣿⡟⠻⠛⠻⠿⠿⠯⠟⠛⠛⠛⠚⠛⠛⠻⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠉⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠋⡀⠥⠠⠄⠀⢀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠒⠶⠦⣠⣄⡋⠁⠁
⠁⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⠤⠤⢶⡤⢄⡈⠛⠓⠀⠀⠐⠒⠲⠶⠆⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢴⡆⠀⠀⡀
⠀⠀⠀⠀⢄
⠀⠀⠈⠁⢈⡤⣬⠤⠤⠴⠀⠦

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠐⣶⣤⡄⠀⠀⣀⢰⡶⣾⣶⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⢀⣆⡀
⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⡀⢿⣼⢟⣿⣛⡆⠀⣤⢹⣼⣿⣿⡩⠄⣠⣴⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⡿⡃⠀⠀⠐⢿⣷⡄
⠀⠀⠀⠀⠀⠲⣿⠂⠀⠀⠀⠀⠻⣾⣫⣾⠿⢦⠀⢰⣸⣿⣿⣽⣿⡗⠀⣿⣿⣿⣿⣿⣷⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣯⣴⡶⠂⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⢯⠷⠀⠀⠀⠉⠙⠿⠟⠃⠀⠀⠻⢿⣿⣧⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠙⣿⡓⠀⠀⠀⠠⣾⣿⡇
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡡⠄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠹⢿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⢠⣿⠂⠀⠀⠀⠀⢀⡴⡛⠈⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⡀⣄⣀⠀⠀⢠⣄⠀⠀⠀⠀⣀
⠀⠀⠸⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣿⡟⢁⣴⡿⠀⠀⢀⠎⡀⠁⠀⡀⠄⠀⢸⣿⡆⠀⠉⠀⠠⣉⣻⡥⢆⡀⠘⣿⣷⠀⣠⣾⣿⠀⠀⠀⢀
⠀⠀⢻⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⢬⣷⡿⣋⣤⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⢐⠲⠶⣽⠋⠩⠀⠀⠈⠛⠃⣿⣿⠟
⠀⠀⠻⣿⣿⣿⡗⠀⣤⣤⠀⣼⣷⠀⣠⣤⠸⠿⡶⠦⣿⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠀⠀⠠⠭⢭⣯⠴⠞⣋⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠁
⠀⠀⠈⢿⣿⠆⠀⠀⡻⣿⣷⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠘⠀⠀⡀⠀⠀⢠⠀⠐⣻⡭⠀⠠⣤⣀⡒⣶⣚⣯⠗
⠀⠀⢠⣀⠀⠀⠀⠘⠿⠿⣿⣿⣿⡷⠿⠷⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠐⢢⡤⠙⠀⠄⠀⠀⠀⢻⡯⠀⠲⠦⣤⣄⣋⣡⠴⠚
⠀⠀⠸⣿⣿⣦⠀⠀⠀⠰⠿⠛⠻⠿⠀⣴⣄⢠⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠂⠐⠠⠀⠀⠀⠁⠀⠑⠶⢦⣄⣉⣴⠾⠋⠀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⢰⠀⠀⠀⣬⣽⠿⡇⠀⠀⠀⠀⠀⠀⣾⡆⠾⠡⡤⠆⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠁⠀⠀⠀⠛⠏
⠀⠀⠀⠀⠈⠉⠁⠀⢠⡀⣴⠀⢁⣀⣠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣦⡘⠳⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡀⠀⢰⣴⡀⠀⣄⠀⠀⣶⡧
⠀⠀⠀⠀⠀⣀⠸⣆⢸⠇⣯⣴⣿⡉⠁⠀⠀⢀⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠛⠀⢼⣯⠄⠈⠉⠀⠀⠿⢀⡀⠈⠁⠀⢠⡐⣴⢃
⠀⠀⠀⠀⢦⡙⢦⠻⣼⣿⠯⠄⠀⢀⢠⣶⠶⠘⣿⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡙⠶⣋⣤⠄⠀⠀⠲⣝⣗⣫⣔
⠀⠀⠀⠳⣮⡻⣦⣍⣛⡛⠁⠀⠠⢜⠛⠁⣀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⡇⠀⢠⣛⠯⢈⠥⠶⡂⠀⣈⡻⢮⡭⢟⡋
⠀⠀⠐⠲⣞⣿⡓⢦⡄⠀⠀⠀⠀⠀⣶⡿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡿⠇⠀⠀⢭⣍⡀⢚⡋⠁⠀⠠⣭⣹⣛⡭
⠀⠀⠀⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠱⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣤⣭⣥⣦⣭⣷⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠀⣰⠿⠋⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠙⠿⣆⠀⠀⠀⠀⠀⠙⣧
⠀⣸⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠛⠛⠷⢦⣄⠈⠀⠀⠀⠀⠀⠀⠹⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⣀⡀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢻
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣷⣄⠀⠀⠀⠀⠀⣯⠀⠀⢿⣶⣾⣿⣿⣿⣿⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠈⠻⣿⣿⣿⠟⠃⠀⣰⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⢀⣠⡾⠋
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣿⣛⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣼⠋⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠛⣿⡆⠀⠐⣿⠀⠀⠀⠀⠛⠛⢷⣄⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⢸⣧⣀⣄⣠⣤⣤⡴⠟⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⠇⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⣶⣶⣦⣤⣤⣴⣶⣶⠶⠛⠛⠉⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠤⠶⠚⠃⣀⣀⣀⡀⠀⠀⠀⠀⢀⣴⠾⠿⢷⣄⠘⠳⠶⠤⠤⣤⣀⣀⣀⡀
⣤⡤⠤⠖⠒⠒⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠉⠉⠁⠀⠀⠀⠈⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠒⠶⠤⠤⣤
⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡀⠄⠀⠀⠂⢴⠁⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢾⡿⠀⠀⠀⢰⠘⠛⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢀⡔⠀⠈⢆⡀⠀⠀⠀⠀⢀⠞⠤⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣿⠛⢄⠀⠀⠉⠒⠀⠐⠊⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢣⠀⠀⠀⠉⠓⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠳⠀⠀⠆⠤⠤⠐⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⣀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣸⡇