Vessel Emojis & Symbols

⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉
⣛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⣤⣴⣾⣿⣷⣤⣤⣤⣤⣤⡶⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣤⣤⣾⣿⠇⣀⠀⣀⠀⠀⠀⡀⢶⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⠛⠉⣛⠉⠉⠉⠉⠙⠛⠻⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣀⢴⣀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣁⣀⣀⢀⡘⣿⣿⣿⣦⣀⣀⣀⣀⣴⣥⣤⣈⣤⣴⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⠉⢉⣻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⡤⠖⠉⠉⣿⡿
⠀⠀⠀⠀⠀⠀⠸⡇⢻⣿⠳⣄⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠄⠸⠀⢻⣆⠈⢃⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣼⣯⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠘⠀⢠⠀⠈⢿⡄⠈⠀⣱⣮⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣴⣶⣶⣀⣤⣀⢀⣀⣠⣌⣹⣿⣿⣆
⠀⠀⠀⠀⠀⠆⠀⢾⠀⠀⠘⢷⡀⢠⡿⢏⠳⣄⠀⠀⠀⢠⣿⡿⢿⡿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣾⠀⠀⣼⠁⣼⣿⣿⣿⣿⣦⡪⣷⢈⠳⣄⠀⢆⡰⠀⣼⣿⣿⣿⠀⣿⣷⠀⠈⠛⠻⣿⠻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣀⣼⡟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣦⣌⠷⣤⠁⣂⣿⣿⣿⣿⣿⣿⣿⣀⣄⣀⡀⠀⠀⠺⢍⣿⣿⣿⣿⣿⣷⡀⠀⢁
⠀⢠⣿⠏⠀⠀⢀⣾⡿⠿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡿⣴⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⠋⠉⢻⡏⠉⠛⠓⠦⣬⣭⣟⣿⣿⣿⣧⡀⢸⣷⡀
⠀⣼⡏⠀⠀⠀⠈⢻⠀⡾⠋⠁⠀⠀⢻⡟⢻⣿⡿⢠⣿⣿⣿⣿⠿⠟⢹⣿⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣷⣼⣿⣿⡀
⠀⠻⠀⠘⠃⠰⡶⢾⣶⣶⣶⣶⣶⣶⣶⣿⣾⣶⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⡶⣾⣿⡿⡷⡶⠶⠶⠶⠶⠶⠶⠶⡶⠾⠿⠿⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠛⠉⠉⠉⢸⣿⣿⠀⠀⠀⠀⢀⡝⠂⢠⠏⠉⢶⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠻⠦
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠆⠀⠀⠙⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣀⣀⣀⣀⣀⣀
⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⢀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡏⠉⠉⠈⣭⠉
⣧⣴⣧⣤⣤⣤⣤⣿⣦⣤⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⡿⠿⣿⡿⠶⠶⠶⠶⠶⠶⠶⠶⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣌⣿⣧
⢥⠀⠀⠀⠀⠀⠀⣶⠐⢦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⣠⠶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢘⣿⣿⡏
⠀⠃⠀⠀⠀⠀⠀⠹⣷⣦⣾⢶⣤⠀⣀⣶⣄⣴⣟⣿⣿⣋⣴⣯⣤⣤⣤⣤⣴⣶⣶⣶⣶⣷⣶⣤⣤⣄⣀⣄⣿⣶⣤⣤⢻⣤⣿⣿⣿⠁
⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢿⣿⣿⠿⠿⠋⣿⣿⠿⣿⣿⡿⠋⢻⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⣿⣿⠀⠀⠐⠀⠀⢸⡏⢫⢧⡀⠀⠀⠉⠁⠀⠀⠈⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣶⠀⣿⣿⣀⠀⠀⠀⠀⢸⡇⠸⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⣠⣔⠶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣤⡀⣿⣀⣾⣇⠀⡇⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣶⣶⣤⣄⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡈⠉⠉⠙⠋⠉⠉⠉⠑⠶⠦⣤⡀
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠉⠙⡻⠟⠛⠛⣉⣀⣀⣀⡈⠉⠉⠛⠋⠛⠛⠛⠛⣻⣿⣿⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠛⢿⣿⡉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢡⣴⣾⡿⠟⠛⠙⠛⠻⠷⣶⣶⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠂⠀⠀⠂⣿⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⡏⢠⠀⠰⣤⣤⣍⣮⣤⡆⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠐⠀⠀⢀⣄⣥⣸⠀⠀⠘⢻⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠲⣾⠗⠉⠙⠻⠻⠛⠻⢗⣿⣿⡗⠒⠲⠲⠖⣢⣴⡦⢠⣌⣩⣽⣋⠋⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣏⠀⠀⠰⣺⠷⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⢿⠋⠉⠁⠑⠚⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠸⡄⢿⠀⠀⠀⠨⠉⢓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠘⣿⠃⠀⠀⠀⠄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠃⠉⠆⠰⢹⣇⠀⠀⠀⠀⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠤⣶⣿⡿⣷⠀⠁⠀⠀⠀⢸⢻⣆⠀⠀⠀⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⠀⠐⠆⠀⠁⢸⠀⠘⢧⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣿⣿⡆⠀⠀⠀⠀⣼⠀⡀⠈⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡼⢃⠐⠂⡀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⣀⡀⠀⠈⢀⣁⠀⠀⠀⠀⠀⠀⠈⠠⠊⠀⠀⠀⠀⠀⠀⠸⠀⠰⣿⣿⡟⢠⡫⢁⠀⡞⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⣯⣿⣿⣿⣿⣯⠙⢻⡀⠀⠀⠘⠀⠀⠀⠂⡀⠀⠂⠀⠀⠀⢠⠀⢠⡀⠀⠀⠀⣶⡷⣾⣶⣿⣷⣿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⣾⣤⣵⣮⣤⣧⣽⣗⣰⣧⣄⣄⣀⡀⠀⠀⢀⣵⣆⣔⠐⠒⠐⠁⠀⠘⠧⣄⡀⣸⡯⣛⣿⣿⡿⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣉⢙⠚⢳⣦⠈⠘⠉⠃⠟⠚⠓⠒⠐⠓⠀⠀⡉⠉⠠⠁⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⢻⣿⡎⢹⣿⠈⡽⠉⠉⠙⠛⠻⢿⠿⣏⡉⠁⠁⠘⠀⠂⠀⠖⠆⠀⠚⠂⠀⢉⠁⠄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⣛⢷⡄⠾⠄⢰⠄⢠⣄⠻⢿⣿⣷⠶⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠉⢽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣬⣽⣷⣶⣶⣯⣿⣷⡀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠄⠀⠀⢠⣤⡀⠀⠀⠀⢾⠆⢀⠀⠉⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⣿⣧⣿⣿⡉⣿⣿⣿⣶⣶⣶⣦⣤⣤⣟⣡⣤⣤⣤⣼⣿⠥⠄⠐⠀⠀⠀⠀⠀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠡⢴⣾⣷⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢯⡇⠒⠂⠀⠀⠀⢀⠀⠄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣶⢀⣿⢩⣽⣟⢿⡆⣹⡿⣿⡿⣿⡩⢽⣯⠭⠭⠄⠀⠖⠀⠒⠠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠓⠚⠛⢻⣿⠁⠻⣯⡍⠀⠉⠰⣲⣿⡋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡟⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣬⣤⣴⣧⣤⣄⣀⣤⣤⣄⣀⣀⡀⣀⠔⢸⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣓⣲⣶⣶⣶⣶⣶⡶⠶⠦⠤⠴⢦⡥⠤⠤⠼⢧⣤⣬⣴⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣾⣛⣛⣛⣛⣻⣟⣛⣛⣟⣡⣾⣿⣿⣛⣛⡋⠉⣿⠛⠛⠻⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠲⠶⢶⣶⣶⣶⣶⣶⢾⢧⣭⡵⣿⣭⣍⣍⣉⣉⣉⣁⣀⢿⣀⣀⣀⣀⣈⣻⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⣿⣿⣿⣷⣶⣷⠀⠀⠶⣶⣶⣾⣮⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠻⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠛⠿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢹⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⠁⠀⠀⠀⢀⣤⢖⡋⣡⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠇⠀⢀⣠⢞⣭⣾⢏⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡟⠀⠀⢀⣭⣭⣿⣿⣿⣿⣿⢸⣿⣿⠏⢀⡴⣫⣵⣿⡿⢣⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢽⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⢃⡴⣫⣾⣿⣿⡿⢡⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡝⠀⠀⠾⢿⣿⣿⣿⣿⣿⡿⢡⣟⡵⢋⣚⣩⠥⠴⠖⠀⠈⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣽⠅⢀⣾⣿⣿⣿⣿⣿⣿⡟⣡⠿⣟⣯⣿⡶⠿⡛⡿⠀⣆⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⡴⠟⠛⠉⠁⣿⣇⡠⢖⣯⣷⣿⣟⣫⣵⣾⡿⢻⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣾⠇⠀⠀⠀⠀⠠⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⣒⣋⣛⣛⣛⣛⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣰⣶⣀⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⠁⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣯⣯⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡼⠁⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠎⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠁⠴⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛⢛⣋⣉⣀⣀⣀⣀⡀⠀⠈⠙⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⠿⠿⠿⠿⠿⠿⠿⠭⠍⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣄⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠐⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣶⣶⣶⣼⣭⣥⣀⡠⠀⠀⠁⠀⠒⠛⠋⠉⠈⠈⠉⠉⠀⠀⠀⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣶⣦⠈⠀⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠀⣠⣿⣿⡁⠀⠀⢀⣀⣰⠾⠟⠉⠀⠀⠀⠀⢀⣼⡤⡄⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠿⠦⣴⣷⣿⣿⣿⣿⣿⣦⣿⣿⡟⣠⣤⡤⠾⠛⠩⠰⠤⠴⠤⠤⠶⣤⣤⣴⣉⣉⣀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣴⣿⣠⡟⣿⠏⠛⠉⠉⠉⠉⠉⠉⢭⡥⠿⠉⠀⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠻⠋⠉⠉⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⣳⣿⠞⠁⠀⠀⠀⠀⠀⣀⣰⣶⣿⠀⠀⠀⠀⢲⡴⢶⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠿⠟⣋⣸⣿⢿⣿⣶⣤⡤⣶⡾⣾⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⠦⠴⠷⠏⠀⠀⠄⠀⢰⡄⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠚⠟⠭⢄⠚⠉⣀⠀⢀⣏⣰⣚⣡⣶⣴⣦⣦⣤⣴⣤⣀⢀⡀⣼⣀⣀⣀⣀⡀⢀⣤⣤⣤⣬⣼⣏⣩⣩⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣉⣉⣛⣛⣫⣭⣿⠿⠿⢿⠿⣟⣻⣯⣭⠭⢭⠿⠛⠉⠉⠋⣉⣉⠉⠡⠋⠉⠙⢡⢶⡮⣿⣿⣿⣿⣳⣶⣶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢸⡷⠰⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⢹⣿⡃⠒⠲⠶⠼⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣦⡀⠀⢀⣷⣀⣤⣤⣴⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣶⣶⣶⣶⣴⣶⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠠⠄⠁⢠⣤⣬⣉⡐⠂⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢉⣠⣵⣶⣭⣿⣿⠁⠀⠀⠄⠀⠤⠄⠈⠉⠷⠆⠈⠉⠑⠂
⠀⠀⠈⠉⣀⣠⣤⣤⣶⣶⣿⣿⡿⢿⣿⣶⣶⣶⣷⣶⣿⣿⠛⣿⣿⣿⣟⢟⣿⣭⣭⣥⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣷⣄⠀⠀⠒⠛⠛⠛⠛⠒⠂
⠀⠀⢠⣬⣭⣤⣀⣀⣈⠻⣿⣶⣶⣶⣶⣾⡟⣻⣿⣿⠿⠿⠶⠿⣿⣯⣤⣬⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⣿⣿⣿⣿⣯⣥⣤⣤⣤⡤⠀⠓⠒⠒
⠈⠛⠚⠛⠛⠻⠿⠿⠿⠿⠿⣏⠉⠉⠉⠑⠚⠛⠛⢻⣿⣿⣿⠛⠋⣩⣿⣿⣿⣿⠶⠶⠶⠎⠉⠉⢉⣙⣿⣙⣟⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠈⠛⠲⠶⠶⠖⠀⢀⣀⣈⡙⠛⠛⠛⠛⠁⠀⠀⠹⠿⠿⠖⠂⠓⢻⣿⣿⠁⠀⠀⠤⠤⠤⣤⣤⣤⡖⠲⠖⠖⠚⠛⠛⠂⢀⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠖⠀⣀⣀⣀⣀⣈⡉⠉⠉⣿⣿⡉⠀⠀⢀⣀⣀⣀⠀⠤⠴⠶⠚⠛⢉⣀⣀⣀⣀⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠶⠾⠛⡆⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⢀⠀⠀⠀⠀⣀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠖⠒⠁⢠⣾⡤⠽⠖⠀⠉⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⣿⡁⠀⠀⠀⢠⣾⡍⠀⠀⠀⢰⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⢀⣄⣼⣶⣿⣿⡷⠀⠀⠀⠀⣇⠠⠀⢀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡿⠟⠊⣿⣍⣅⣤⣴⡶⠎⣿⠀⠈⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢤⡯⠔⠂⠁⠝⡿⣯⠉⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢿⠂⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡟⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣸⣧⢧⠀⠀⠀⠈⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢺⣿⡇⣠⣄⣬⢰⣸⣿⣿⣷⡿⠟⠛⣿⢸⣤⣤⣀⣠⣀⡈⢠⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣿⣯⣿⣾⣿⣿⣯⠀⠀⠀⠀⢿⡀⢛⣛⣋⣛⠛⢿⡛⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⡿⠻⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠼⣿⠿⣿⣏⣿⣛⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⢀⣇⣷⣿⣿⣿⢿⣿⣿⣿⣧⢬⠃⣈⣿⣷⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣮⡟
⠀⠀⠀⠀⠀⣠⡄⠀⢰⣿⣦⡾⠾⠿⠿⠿⠿⡾⠿⢿⣿⣿⣦⣴⠋⠋⣿⣤⣶⣿⣿⡯⠋⠀⠀⠀⠀⠀⠠⠴⢮⣝⣿⠁
⠀⠀⠀⠀⢸⣟⣥⣖⣿⡆⠈⠀⠀⠀⠀⣀⣁⢃⣀⠒⢿⡝⢉⣭⣴⣾⣿⣿⣿⣿⣿⡠⠀⠀⠀⠠⠀⠀⢤⠲⠀⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣿⣡⣶⡀⠀⢰⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⡿⣛⣉⡙⠻⠿⢿⣿⣄⠀⠀⠀⠀⠀⣄⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠓⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠸⠛⢋⣿⣇⣤⣄⣿⣿⣱⣤⣐⣆⣄⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣶⣿⣶⣭⣍⣭⣽⣤⣬⠉⣤⣤⣤⣴⣿⢿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣙⣿⣿⣿⣿⣥⣀⣀⣀⣐⣶⣾⠋⠿⣿⣿⠟⠱⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⢈⣥⣷⣶⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠻⠿⠿⢿⣿⣶⣶⡾⠿⠿⠛⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠤⠴⠂⠀⠀⠀⠀⠀⠿⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢸⠇⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⢠⡄⠀⢳⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢰⡀⠀⠀⢀⠉⠉⠉⠉⠁⠀⠁⠀⠈⠁⠁⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣄⡄⠀⢠⠀⠀⠀⠀⠨⠿⠟⠠⠄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⡗⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⢘⡗⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢤⡤⡄⡤⠀⠊⠀⠀⠀⠀⣀⣀⠀⠀⠀⢴⠂⠈⠁
⠀⠒⠼⢢⣀⣀⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠰⣏⠀⣠⠀⠀⠀⠀⠀⠀⢀⢠⣀⢀⢸⡇⣪⡏⠀⠀⣀⣀⣠⡤⣠⡴⡦⠀⠀⠀⠣
⠀⠀⠀⠸⣯⣽⣏⣙⣛⠛⠓⠛⢸⢻⢿⢻⠿⠾⠿⠼⠷⠤⠤⠾⠿⠷⠶⠾⢿⡿⣞⣛⣟⣛⡿⠿⠿⠯⠿⡟⠻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣶⣶⣶⣶⣾⣼⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣯⣧⣦⣾⣶⣶⣶⣶⡶⠖⠛⢉⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣭⠉⠩⣩⣉⠛⣛⣋⡉⣟⣛⡛⣛⡛⠛⢻⣛⣛⣛⡛⠋⣛⠓⢛⣚⠀⠚⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠈⠙⠛⠉⠀⠉⠛⠁⠐⠀⠀⠉⠈⠁⠈⠁⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠞⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⣼⠃⡇⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡋⠙⠷⠠⠀⠀⠐⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⡀⢀⢸⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠤⢬⣿⡀⠀⡧⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣸⠂⠈⠉⠛⢶⠿⢤⣑⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡄⠀⠀⢀⡤⠀⠀⢀⢿⡏⠀⠀⠀⠀⠈⣇⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣘⡂⠘⠀⠦⣽⠇⢀⣴⣾⣿⣁⣀⣀⢀⡀⠀⢹⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠉⠙⠛⠻⠿⣿⣿⣿⣾⣿⣿⡏⠉⠙⠛⠿⠤⣀⣿⠚⡇⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⢻⠃⠀⠀⠀⠀⠀⠀⠈⠙⡟⠲⠦⢄⣱⡀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠇⠀⠀⠄⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣣⠠⢂⢀⣄⣠⣀⣤⢄⣴⣿⠋⠀⣥⢀⡄⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⢀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣉⢐⣱⠷⣿⢿⣿⣿⣿⣿⣿⣿⣡⣤⣤⣤⣤⣀⡀⠀⠀⠀⣠⣿⠇⣀⡽⠛⠦⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡛⠛⠿⣿⣿⣿⣧⣽⣿⠟⠽⢻⡿⣿⣿⣿⣿⣯⣅⣀⣈⣷⣿⣿⣴⣯⣤⣀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⡿⠤⣌⡙⠛⠛⠀⠀⢹⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⣴⣞⣛⢿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠏⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⡜⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⢸⡛⠹⢿⣾⣿⣿⣿⣿⣿⣿⢋⣥⠶⠦⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠰⣻⣭⣴⣶⣷⣾⣿⣿⣿⣿⣿⣿⣩⣾⣿⠄⠀⠀⠛⠿⡻⡛⠛⢛⣇⠘⠛⠀⠀⢀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠈⠳⢦⣬⣿⡿⠛⠟⢛⣻⡿⠿⠿⢿⡿⢭⣍⣛⠧⣀⠀⠀⢀⣐⣛⢦⣘⠿⣿⣦⣴⣦⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠀⠈⠉⠴⣶⣿⣿⣿⣷⣦⡌⠛⢷⣬⡀⠐⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⡶⠶⢟⣉⣙⣿⣿⣿⣿⣿⡧⢀⣌⠻⣄⡀⠢⢭⣯⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠋⠙⠿⣿⣿⣟⠹⠇⢀⣿⣦⣀⣙⠛⠲⠶⠾⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠹⠿⠷⣤⡐⠈⠙⠻⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⣤⠦⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠒⠢⣤⡄⠀⢰⡆⢰⣄⣠⣾⠟⢀⣄⡀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠈⣷⠀⠀⠀⠀⠀⣬⠀⠀⢻⣿⢞⣫⣿⣿⣶⣿⣿⢃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣠⡤⠞⠉⠀⠀⠀⠀⠸⡄⠀⠀⠀⢐⣿⠶⠖⠬⢒⣿⣿⣿⣿⣿⣿⣯⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⣅⣀⣀⣀⣀⣀⣀⣤⣬⡷⠶⠚⠛⠉⠀⢀⣄⠔⠉⣿⡿⣿⣿⣿⣿⣿⢿⣾⣿⡇⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣬⣤⣭⣍⣉⣈⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣤⣀⡄⠀⠈⠙⠛⠋⠛⠈⠉⣛⣧⣄⣼⣿⣶⡆
⠀⠀⠀⠀⠀⠈⠀⠘⠒⡚⠉⣛⢿⠛⠛⣿⣿⣿⡿⠿⢭⣭⣷⣦⣶⣶⣶⣶⣦⣀⣈⣭⣵⣼⣿⣿⣶⣼⣧⣶⣿⣇⣴⣿⣶⣌⢻⣿⣿⡿⠟
⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⣿⣿⣿⠿⠿⢟⣛⣉⣤⣶⣶⣿⣿⣿⠟⢁⣀⠀⠶⣿⣯⡉⠉⠀⣉⣟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢦⣷⣶⡾⡿⠿⠿⠿⠷⠿⠿⠟⠉⠀⠀⠛⠿⣿⣿⠆⠀⠈⠀⠀⢹⣿⣿⣤⣄⠈⠉⠙⣻⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣀⣤⣄⣐⠾⣿⢿⣿⣿⣿⠿⠖⠤⠄⠀⠀⠄⠘⠻⠟⠛⠛⠛⠀⠀⠀⠀⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠻⠿⠿⠿⠟⠛⠂⠘⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠢⢈⡀⠀⠀⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠠⡀⠀⠀⡦⣀⠀⠨⢑⢶⠒⠊⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⡜⠀⠀⠀⠁⠺⠈⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⣉⣀⣀⡓⠒⢀⡤⡀⢠⠁⠀⠀⠀⠀⣦⠐⠦⡀⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⢀⣀⣀⣀⠀⠀⡈⢑⣮⡚⣄⠀⠀⠀⠀⡟⠀⠀⡜⠂⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⡐⠉⠉⠉⠁⣀⠀⢀⠀⣀⠀⠀⠉⠹⢓⠋⣪⣓⢄⠀⢀⠀⠀⠀⠃
⠀⠀⠉⡉⠉⠁⠐⠚⠒⠀⠤⠄⢀⣀⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡷⡀⠑⢮⡙⠏⠀⠈⠀⠀⢰
⠀⠀⠀⠈⠑⢄⡠⠤⠤⠤⠤⠤⠄⠀⢀⣉⡉⠁⠒⠶⠶⢀⡀⠀⠀⠠⢠⠀⠜⢦⡈⠙⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠤⢄⣉⠑⠂⠬⢔⣈⠀⠝⢦⡀⠑⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠄⢀⡉⠀⠒⠠⠌⣉⠓⠠⢭⡢⡀⠑⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢀⡀⠠⠀⠀⠠⠦⠀⠀⠠⠀⠉⠁⠐⠂⠤⠭⣑⠂⠬⢙⠲⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠨⠉⢐⡊⠏⡛⠶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠅⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠈⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣤⣤⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠈⡄⣗⡿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⣠⠄⠓⡛⣩⠏⠉⠈⠀⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠉⠒⠧⠤⣤⡲⠶⠒⠛⣛⣉⣁⠠⠫⠣⠊⠁⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⢠⡤⢤⠤⡁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣀⡀⠀⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡀⠀⠧⠄⠐⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⣤⡤⠶⢶⠒⢳⣀⡹⠛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣉⣥⣴⣶⠿⡟⣿⢇⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠁⠀⠈⠀⠀⢀⠁⠻⠀⠲⠾⠿⣿⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣴⣶⣾⣛⢉⣩⠀⠀⠀⠀⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣸⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠟⠛⠛⠻⠛⠿⢿⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⡆⣀⣀⣀⣀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⣿⢀⡄⠈⠁⣶⣖⠉⠛⠿⠦⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢾⣿⠈⠁⣶⣦⠻⠿⠷⣄⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢡⡈⣷⠀⠀⢸⣿⣦⢀⣙⣿⣷⡀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⠵⠿⡷⣤⢼⣟⡛⠛⢰⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣷⣽⣿⣿⢛⣉⠀⠀⠁⡄⢸⣿⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⡿⠿⢻⢿⣿⣧⠀⡀⠲⠀⠈⠉⠡⠓⣓⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠉⠛⠂⠠⢖⣶⠷⠞⣿⣿⡟⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⡟⠻⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠹⢿⣷⡀⣀⣀⣤⣤⣿⠶⠶⢠⡄⠀⢀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣤⠀⠛⣿⣿⠋⠀⠀⠁⠀⠀⢀⣿⡃⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠂⣀⣉⡁⠀⠀⠀⠀⡀⠀⠈⢿⡖⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⣀⣡⣍⣿⣾⣷⣺⣿⣿⣿⣛⣳⠈⠁⢡⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⡟⠙⠫⣯⠙⠙⠈⠻⠟⠀⠀⠋⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⠀⠀⢘⣿⡆⠀⠀⠀⠀⠀⡼⠻⠞⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣇⠀⠀⠀⡀⠁⠀⠀⢸⣧⢷⡆⠀⠀⣾⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡄⢀⣁⡷⡶⠀⢚⠛⢻⣎⣿⡄⠠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠁⠉⠛⠳⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠿⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⢠⣀⣤⡤⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢴⡖⠈⠃⠛
⠀⠀⠀⠀⠀⠀⣦⣠⣴⡾⠵⢿⡄⠀⡀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠀⠀⢀⠟⠉⠘⠒⣴⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣄⠀⠀⠀⣀⣀⣠⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⡄⣀⠤⢺⣿⡌⠣
⠀⠀⠀⠀⠀⣻⢀⣀⠴⣶⣟⣛⣋⣛⣋⡴⠚⢻⣿⡇⠠⡄⢀⣈⡗⠂⠀⠀⠀⠀⠀⢹⡿⠻⣻⣿⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠠⣿⣟⣫⣄⣱⣼⠟⠛⠭⠃⠄⢦⢤⣦⣶⠶⠟⠛⠁⠀⠀⠀⣀⡀⠀⠀⠞⠴⢄⠀⠉⢢⡀⠀⡀⢰⣆⠀⠈⣦⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠃⣿⣸⣟⣿⣆⣀⣀⣤⣤⣴⡿⠋⢿⣧⠠⠀⠀⠈⢳⣤⣾⣷⠷⠿⠊⠉⠄⠀⣿⣿⣀⡠⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠁⠀⠀⣺⣿⣠⠀⠉⠳⢼⣿⣻⡇⠀⠀⢀⣀⡀⡸⠛⣛⣻⡿⡶⠖⠛⠉⠉
⠀⠀⢲⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢼⣿⣷⣶⣶⣾⠿⡶⠦⠜⣿⣗⣞⣛⣛⣿⣿⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⠏⠂⠒⠃
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡀⠀⣠⣐⣷⡀
⠀⠀⣒⣛⣓⣚⢒⣾⣿⣿⢿⡟⢿⣛⣿⡽⢋⣉⣠⣴⣠⣉⣉⡩⣄⠩⠻⠿⠿⠷⠉⠉⠿⠉⠍⠋⢍⠛⠁⠀⠈⠉⠉⠉⠃⠘⠋⠙⠉⠙⠛⠉⠉⠁
⠀⠀⠀⠀⠉⢍⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣶⡖⠂⠘⡓⣤⣤⣀⡄⠀⢀⣤⣴⣶⣦⣧⣤⣬⣥⣌⣀⡀
⠀⠀⠀⠀⠀⠘⠷⠶⠶⠀⠐⠓⠤⠬⣬⠈⣙⣉⣩⣽⣿⣿⣿⡿⢿⣧⣽⢿⡿⣿⣿⣿⣿⣿⣤⣿⣷⣼⣬⣿⣯⣹⣷⡶⠶⣤⠴⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠚⠛⠾⢕⣯⣼⣦⢮⣶⣤⣾⣿⠲⢿⢦⡉⣉⠩⡉⠈⠉⠉⠻⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⢀⡇⠀⠀⠀⠈⣿⢰⣦⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡀⠀⠀⠀⢤⡀⠸⠟⡀⠀⣸⠀⡅⠀⠠⠬⠠⣿⢸⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠄⠀⠀⠳⠿⣿⡔⡧⠀⠀⠀⠀⣿⢺⣿⣿⠍⠉⠈⠋⢸⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣇⣀⣀⣀⣀⣵⣤⠀⠉⠯⠽⠽⢯⣵⣤⣤⣤⣿⡗⣛⣿⡆⠄⢀⠀⢸⣴⡆⢸⣟⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠽⠿⠿⠟⠛⠗⠛⠛⠓⠒⠲⠿⠛⠛⠿⠿⠟⢻⣿⣿⣿⡓⣒⠀⢼⣿⡇⢸⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣾⣯⣿⣁⡂⣿⣇⡁⣿⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⢀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣥⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⢂⣀⣀⣀⣀⣠⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣤⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠾⠿⠿⡿⠿⠿⠿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣴⣦⣤⣦⣴⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠛⠉⠛⠓⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⣶⣼⠿⠛⠂⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⣼⡿⠟⠃⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⢰⣦⣽⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠆⠀⠀⠀⠀⠑⣦⣿⡈⠙⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠠⣄⡀⠀⠀⠀⡤⠀⠀⠀⢸⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⡆⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁⢀⣀⢀⢀⡀⠰⠒⢾⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⡇⢄⠹⣷⣄⠀⠀⠀⠀⠀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⠏⠀⠠⣜⣾⣿⣿⣿⣷⠘⠻⢿⣿⣿⣿⡇⠈⢧⠹⣿⣷⡄⢀⣀⣠⣜⣻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⣿⣹⣿⣿⣿⣷⣦⡥⠄⠘⣧⠛⠛⢻⣨⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠰⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⠁⠘⣿⣿⣿⣿⡿⢶⣄⢸⣧⡠⠊⣹⣿⣿⡿⢃
⠀⠀⠀⠀⠀⠀⠘⡇⠀⣰⣦⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣆⣹⣿⠿⢿⡇⠀⣹⣿⣿⣤⣾⣿⣿⠟⢁⡟
⠀⠀⠀⠀⠀⠀⠀⢻⡀⣽⣟⣿⣵⣯⣿⣿⣯⣿⠏⣿⠏⠈⠻⠃⠛⣷⣾⣤⣼⣷⣿⣿⣿⡿⠛⠛⠉⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢨⣿⣿⣿⣼⣿⣿⣿⣿⣷⣿⣶⣶⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣏⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⢟⣿⣿⣿⣿⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡭⠭⠯⠥⠥⠭⠤⠼⠾⠛⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡆⠀⠀⠀⠀⠀⢀⣠⣤⣾⡟⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡦⡿⠳⣖⡒⠊⠭⠽⠚⠉⢉⠉⡇⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡃⣿⣻⣿⣿⣲⢄⡀⠀⠀⢸⢀⡇⠀⡘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡤⠤⣤⠀⠈⠻⡟⡟⠛⠉⡛⢯⣷⣾⠓⠒⠞⠒⠓⠒⠛⠚⡻⣷⣦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡀⠀⣸⠀⠉⠺⢧⡧⠤⠤⡧⢀⣈⣹⣆⣀⣇⣀⣀⣇⣀⣀⡇⢠⠀⠀⢈⠰
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠩⠉⠉⡉⠉⠉⢱⢀⡇⡶⢤⣷⠀⠀⠅⠀⠀⡄⠀⠀⡀⠀⠀⡏⢺⠀⠉⢻⢾⠩⢿⡇⠀⠀⢤⢀
⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠉⠉⠙⠷⣤⣼⣘⡃⠘⢾⣿⠂⠂⠚⠒⠒⠛⠒⠚⠓⠒⠒⡷⢼⠤⠤⢼⣸⠀⠀⢹⡆⠀⣼⠈⣇⣀
⠀⠀⠀⢀⣠⠞⣫⡴⠒⡛⠛⠒⠒⠲⠶⠤⠭⣭⣙⣛⠛⠶⠦⢦⣤⣀⣄⣀⣀⣇⣀⠈⢱⢸⠀⠀⢸⢹⠂⠐⠚⠧⡀⢸⠙⣯⢸⠀⡀
⠀⠀⢀⠊⣡⠞⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠤⢭⣉⣛⡛⠻⠶⠾⣾⣁⡉⢹⢺⡀⣀⣰⡀⢸⢸⠢⣿⢸⠉⢩⣅⠩⠇
⠀⠀⢼⠊⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠾⢷⣸⣀⠁⠀⢸⠙⢾⢸⢀⣿⢸⠀⢈⣏⢑⡆
⠀⠀⠈⢧⡀⠀⠀⣀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢐⡣⠖⢛⣲⣤⢸⠈⣿⢸⠉⠉⣏⢈⡇⡄
⠀⠀⠀⠀⠳⣄⠀⠹⠇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⣅⣆⣐⣭⠰⢠⣙⡳⢾⣀⠉⠧⢠⣧⡇
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠾⣯⣿⣲⡬⢝⠓⠴⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠦⣷⣯⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢩⡏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣟⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠷⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⠁⢸⡎⡷⣄⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷
⠀⠀⠀⠀⠀⢀⡀⢸⣭⣩⣍⣉⣉⣛⣛⣛⣛⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠈⠒⣦⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⡍⢉⠉⣉⢙⠉⠉⠉⡉⣩⣉⣉⣹⣀⣀⣈⡛⡁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⠀⠀⠀⠀⠀⢀⣀⣵⠀⠁⡃⠘⠇⡏⢹⠉⣽⢹⠋⢙⡝⢩⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠸⢦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢹⢀⡄⢼⠚⡗⡇⠘⠃⡟⢺⣓⣿⣼⡷⠯⠤⠾⠶⠖⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡆
⠀⠀⠀⠀⠀⢠⣤⣿⣿⡀⡀⢀⢸⣘⠀⡇⢾⠘⠃⠃⠘⡋⡏⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠆⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣿⠉⡷⠓⣚⣚⣺⣬⡤⠥⢼⣖⣒⣟⣯⠭⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⠂⠀⠀⠀⢠⣟⣌⣼⡃
⠀⠀⠀⠀⠠⢴⠛⣛⣛⣏⣭⡽⠴⠖⠓⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡾⣠⠏
⠀⠀⠀⢸⡆⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠄⣾
⠀⠀⠀⠀⠈⠳⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡤⠀⠠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠈⠀⠀⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠤⠄⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢡⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⠄⠀⠀⣀⣠⣠⣤⡶⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣴⣤⣤⣄⣤⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠉⠉⠭⠭⠩⠭⠍⠍⣉⠉⣉⠐⣯⣮⣉⣙⣿⣾⠆⢉⠻⣎⠓⡻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠊⠉⣉⣉⣉⣩⣥⣶⣤⠌⠙⠿⠛⠛⠿⠒⠈⠀⠈⠉⠉
⠀⠀⠀⠑⠒⠒⠒⠀⠀⠀⠸⠍⢀⣀⣈⡉⠉⠉⠁⠉⠙⠉⠀⠉⠀⠀⠐⠒⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠳⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠿⠷⠾⠿⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⠒⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠐⣿⣿⣛⣿⣿⢂⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠤⠾⠦⠤⠤⠤⠤⠤⢴⡇⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⡇⠰⣿⡆⢴⣷⠀⣾⡷⠰⡇⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀
⠀⠀⠀⣠⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⡇⣾⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⣿⢉⣉⣉⣉⣉⣉⣉⣇⣀⣀⣀⡀
⠀⣿⣛⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣿⣛⣛⣛⣛⣛⣛⣛⣿⣛⣛⣛⣛⣛⣻⣧⠿⠋⠉⠉⠉⠉⢉⣩⣉⠉⢉⡿⠁
⠀⢹⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⢧⡿⠀⡾⠁
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠃
⠀⠀⠀⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠹⠒⠉⠉⠑⠔⠒⡲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠒⠒⠒⠲⢄⡀⠀⢀⡠⢘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡞⠉⠉⠉⠓⣆⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⡤⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢼⣤⢀⣀⠀⠀⣗⣒⡄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣛⣻⠷⣾⣛⣛⣭⣿⣷⡾⡧⣤⣴⢾⣛⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⢘⡇⠉⠉⠛⠻⠿⣿⠿⠛⠉⠁⣿⠻⠷⢿⠍⠛⠋⣉⣸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣶⣾⠿⠿⠛⢻⡇⠷⢀⡀⢠⠄⢸⠀⡀⠀⠀⣹⣤⣤⣼⣶⠟⣛⡥⠖⠛⡇⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣽⣿⣷⢶⣿⣷⣾⣷⣷⣌⣁⣼⡦⠶⢚⣯⠿⠁⣁⡤⠞⠋⠁⢀⠰⠆⡿⢹⡽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣮⣯⠐⡆⡭⢙⡛⣿⠉⣻⠾⠗⣏⣡⡷⠞⠋⠁⢀⠄⠠⠅⠈⣀⣴⠗⣫⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣧⢼⠿⡟⠷⣷⣬⡄⣿⣁⣴⣶⠞⠛⢉⠀⡆⣂⠀⠈⢁⣠⣶⡿⢋⡵⣊⠁⣘⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣤⠴⡞⠛⡇⣿⠴⠛⣧⣌⣠⠋⡛⡟⣿⠁⢸⠀⠘⠘⠀⢏⣸⠴⣚⡽⠛⣡⠞⡉⠂⢐⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⣉⠑⣢⠴⠛⢳⡿⠔⠊⣀⠤⠈⣙⠷⣾⢻⣄⣸⡇⢀⡤⠖⣫⠴⠚⣁⡴⠛⠑⡠⢊⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⡁⠂⣠⠴⠋⣁⠤⠂⢁⠠⠒⢉⠠⠐⡉⠄⣂⠽⣸⡏⠝⣛⡥⠖⠋⢀⡤⠚⡁⠀⠀⢊⡴⠋⡠⠃
⠀⠀⠀⠀⢤⢀⠀⣀⡴⠚⢁⠁⠂⣤⠴⠋⡡⠔⠈⣀⠄⠊⡡⠔⠊⠠⠀⢀⣔⣚⣧⠴⠟⠛⠉⠁⣀⡤⠞⢉⠀⢀⠔⢁⡴⠿⠖⠋
⠀⠀⠀⠀⠘⣧⣞⣁⣈⣒⣢⣔⣋⣀⣔⣈⣀⣤⣊⣠⣴⣥⡤⠴⠶⠖⠚⠋⠉⠁⠀⠀⢀⣠⠴⠚⠉⠰⠀⡠⢀⣤⠞⡛⠠
⠀⠀⠀⠀⠀⠙⢢⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉⠀⠒⠀⠀⡠⢊⣠⢟⡹⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⡠⠐⢁⡴⠿⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠉⠉⠀⠀⡔⠉⢻⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣠⣴⠏⢔⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠈⢧⣶⣾⠎⠀⠀⠀⠀⠀⠐⠈⠠⠔⣲⡞⠑⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡶⣼⣿⡷⠶⠬⣄⣀⡠⣴⣬⣴⢊⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⡿⠿⡒⠾⠛⠙⠋⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣈⣶⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠇⠀⢏⡉⠛⠂⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠑⢄⠀⠀⣸⠀⠀⠈⢳⣄⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡳⠀⠀⠀⠑⢀⡟⠀⠀⠀⣸⠛⠣⡀⠀⡿⠀⠒⡶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡀⠀⣴⠛⠡⢤⠐⡄⠀⠀⠈⠓⡀⢀⡴⠣⠀⠀⠈⠲⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣽⠁⢄⠀⠈⠙⢃⢠⣤⣴⣟⠋⠶⠖⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣾⠀⠀⠙⠢⡀⠀⢩⣯⠻⣿⣿⣶⡆⠠⢑⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣿⢠⠀⠀⠀⠈⠱⣾⢀⠷⠈⠻⣿⡧⠀⠀⢹⡦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠐⢤⢆⡜⢤⡀⠀⠀⠀⠀⣬⣿⢸⡆⠀⠀⠑⢄⠀⣾⠁⠀⠐⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣀⣀⠀⠂⣿⠃⣼⡁⡀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠛⢿⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠢⢄⡀⢰⡿⠀⠓⢈⣡⣗⣤⣿⢏⢬⡀⠀⢀⡀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⢤⣀⣤⠀⢭⡼⠾⠑⠍⢉⢜⣷⠒⡄⣠⡄⠀⠀⠀⠀⠉⠢⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣄⡙⢷⣤⣿⡿⣟⡑⢶⡶⢾⣭⣀⠁⢡⠇⢢⡄⣰⠄⠀⡄⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢡⠀⠈⠙⠿⢾⣿⣄⠀⠉⠳⠶⣄⣻⡟⠈⠉⢢⡄⠁⠉⣿⠀⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⠆⠙⣯⠀⠀⠀⠀⠀⠉⠳⠢⢄⣿⠀⠈⠐⣜⠃⠉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠀⣼⣷⣠⠀⠀⠀⠈⡎⣿⢀⡖⠁⠀⠀⠀⠀⠀⠀⠉⢲⢶⣀⠘⢗⠢⢽⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠸⠎⣰⣻⣿⠹⢆⡆⢠⡞⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⣿⣁⠀⠈⠒⠠⣀⠀⢀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠨⢻⣿⣽⣏⡋⣶⢿⡟⡡⣿⣿⡇⠀⠘⡆⠈⡀⠀⠀⢀⠀⠠⣴⢀⡝⣿⢿⣆⡄⣳⡀⠀⠉⠛⢅⡀
⠀⠀⠀⠀⠀⠃⠐⠒⠒⠻⡿⣿⡿⢝⣿⡿⠁⣸⣿⣿⣇⣿⡀⣇⢸⣿⢠⠆⡈⠀⠀⣿⣸⠀⣾⣿⡟⠃⡧⢠⢀⣦⠀⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⢀⢀⣀⢳⡾⢀⣓⣈⣭⠥⣽⣯⣟⣻⢻⡏⠉⢱⠈⠋⠈⣀⣋⣠⣼⣽⣧⣼⣯⣭⣡⣤⡅⠐⣻⢱⠀⡸⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡿⢿⢿⣿⣿⣽⣿⣄⣀⣠⣌⡛⡈⣝⡤⢶⣶⣿⠿⢛⣩⣭⣤⡭⠽⢿⡿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠢⠰⣴⡿⠁
⠀⠀⠀⠀⠀⣸⠇⠰⣚⠞⠈⠙⢹⣿⣿⣿⣯⡤⡾⢿⡖⣋⠣⠞⠛⠙⠁⠠⠤⠤⠤⠤⣤⣷⣿⣾⠇⣿⣿⡄⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⢿⠀⢒⠃⠈⢥⣀⠒⠠⠽⠛⣽⣯⣿⣿⢿⠿⠂⠀⠀⠀⠀⠒⣀⣀⣀⣀⣒⣻⣿⢏⣾⡉⡽⠓⠀⠀⠂
⠀⠀⠀⠀⠀⢸⡄⠀⠉⣀⠒⠢⠄⠤⠄⢨⢏⣉⢺⠙⣦⣀⠈⠀⠀⠀⠀⠁⠤⠤⣤⣭⣿⡿⣵⡟⢣⠋
⠀⠀⠀⠀⠀⡸⣿⡍⢐⡀⠤⢍⣁⠐⠂⣚⢀⠈⣩⡾⢷⡤⠄⠒⣂⠀⠤⠐⢒⣠⣶⣾⢟⣾⢇⡘⠁
⠀⠀⠀⠀⠀⠷⠞⡛⠘⣿⣷⣒⣲⣒⣀⠩⣇⣀⡴⠾⠛⠓⠛⢟⣣⣴⣶⣭⠴⢶⣿⣟⣾⢁⣮⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠉⠉⠙⠁⠈⠉⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠂⠀⠙⠻⠿⠷⠾⠖⠋⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡇⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠒⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⢄⢠⠄⠀⠀⢸⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠀⠤⢠⠂⠀⠁⡬⠁⠀⢨⡀⢣⠀⠀⠈⠀⢎⠳⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣷⣶⣧⢰⣿⡄⠀⢀⠇⠘⡇⠀⠀⠀⠘⡆⠈⢊⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣂⢀⣼⡆⠀⠀⠀⠀⠀⠀⠈⣢⣀⡇⠀⠀⠀⠀⢻⡀⠘⢷⡀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⠍⠐⠶⣖⣂⣂⠧⠀⠀⢳⡄⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⠁⡆⠀⠈⢿⡄⠀⠀⠹⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⡟⠀⠀⠀⠀⢀⠄⢠⡾⣿⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣍⠿⠿⣯⡀⠒⠛⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢘⣀⡴⣿⠇⣀⣤⡬⢤⠀⠤⠽⢷⡟⠐⣌⠢⠀⣀⣀⡀⢨⡇⡰⠃⠈⠉⢉⣉⠿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢘⣍⣀⣀⣀⣿⠉⠀⠸⠇⢸⠀⠀⠀⢠⠁⠤⢶⡞⣯⢿⣇⣀⣼⣼⣤⣴⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡧⠘⢛⢙⠛⠛⠟⠛⠲⠾⠶⢶⠖⣛⣒⣚⣻⡿⠛⠭⠿⠻⠛⣛⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⡬⠤⣤⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢰⣶⣿⣿⡿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠁⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣀⡀⠠⡯⠣⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢢⠀⠀⠀⢸⠀⠀⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⣏⣩⣖⢦⣤⣄⣀⣀⠀⢈⡇⠀⠀⠁⡀⢀⣆⣩⣤⡶⠃
⠀⠀⠀⢀⣀⣊⣛⣿⣷⣴⣶⣶⣦⣼⣿⣿⣿⣿⣓⡻⠶⠾⠶⠾⢒⡚⢳⣿⣿⣭⣉⣙⠝⢁
⠀⠒⠀⠀⠿⡉⠹⠿⠶⠟⡉⠽⢯⣭⠋⡐⠿⠿⠧⠽⠿⠟⢀⣽⣿⡋⠙⣛⡂⠘⠛⠯⠐⠛⠀⠀⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠀⠖⠐⠛⠛⠧⠄⠀⠛⠂⠰⠦⠉⠉⠡⠄⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⢃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠒⠈⠁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⣤⠤⠞⠓⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠘⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⠀⠠⢀⡀⣀⣠⣵⠶⠗⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠞⠒⢻⡏⠁⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡏⠁⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠃⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡇⠀⠀⠀⠀⠀⣸⡇⣤⣀⣠⠤⠒⣺⠈⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣀⣤⠤⠴⠒⣿⠉⠁⠀⠀⠀⠀⡈⠠⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠉⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣧⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠃⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠄⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠆⠐⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢡⡶⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡴⢀⣴⡟⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣬⣴⢖⣋⢁⠀⣱⠋⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⣸⡂⣤⣤⠤⠒⣿⡩⠐⠉⢀⣀⣸⢠⡋⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⢠⡴⠓⠋⣿⠀⠀⠠⠒⢁⣤⣶⣾⣿⣿⣿⣾⣿⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⢀⣁⠼⠒⢈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣩⣤⣴⣾⣿⣿⣿⣿⠿⠋⠻⡿⣿⣿⣿⣟⡁⣀⣀⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡤⠠⠝⠻⠿⠿⠛⠛⣛⣋⡉⠷⢛⣿⣶⡓⣿⣻⣯⡍⠻⣿⣿⣿⣿⠿⠷⣶⣤⣿⣿⣶⣛⠋
⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⠐⠶⠚⠃⣲⣖⢚⣳⣶⣿⣢⣾⣿⣟⣃⣠⣾⣿⠿⢿⣿⡿⠿⢋⣤⠘⠃⡙⠳⠾⠿⠿⣿⣿⣾⣿⣦⣭⣿⣟⣻⠿⠿⠋⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣤⣄⠸⠧⠤⠾⠟⠛⠉⢻⣿⣿⠿⠷⠖⠒⢻⣿⣿⠿⠿⠿⢃⡄⠐⣺⣿⡿⠂⠀⣝⡛⠷⣲⠂⠀⠈⣛⣋⣩⣍⣉⠛⠛⠛⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠓⢀⠲⠿⠦⠤⠄⠈⠛⠋⣀⣤⣤⣤⣉⠁⠀⠰⢿⣫⠄⠀⠀⠘⠿⣷⣯⣭⠖⠛⠙⠻⠿⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣴⡤⠄⣀⡀⠀⢇⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢄⠈⠴⣿⠖⠂⠈⠉⠑⠊⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⣿⡃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠸⠟⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⢿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢋⡁⠀⠀⠀⠀⠀⢠⡴⠒⠀⠠⡿⠿⠿⠿⠿⣿⣿⡟⠉⠀⢀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡠⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⢢⡀⠀⠀⠀⣿⣿⣇⠘⠷⡼⠋⢻⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⣁⣀⣀⣠⣀⣘⣶⡄⠀⠀⣿⡿⣟⡦⣸⡧⡶⢸⡿⠛⣋⣉⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡴⠾⢿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⣱⣶⣿⣿⣯⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠜⢧⡤⠐⠞⠋⠉⠉⠉⠁⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⡿⢻⣿⣿⡎⣻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠁⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⣧⠘⠛⠛⠛⠛⠛⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠀⠀⠶⠀⣀⣀⡀⠀⣠⣄⣀⣀⣀⡀⠀⣸⣆⡀⠀⠙⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣴⠖⠚⢙⠿⣿⡇⠀⣸⡟⣿⣿⣿⠿⠿⠿⠿⠧⣤⣀⣵⡀⠀⠀⠀⠘⠛⢿⣿⣿⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡿⠃⠀⠀⠐⠚⠛⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠁⠀⠀⠀⠀⠀⠀⠹⣿⣧⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠂⠀⠀⠀⣤⠄⠀⠀⠀⢹⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⣀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠉⣀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠻⣎⡄⠀⠀⢱
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠹⣆⠀⢀⣠⣶⣾⣋⠁⣸⡇⠀⣿⣿⣿⣿⣿⠟⠛⢛⣷⣦⣶⣿⣄⠀⢀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⣣⡀⢀⡙⣿⣾⣿⣿⣿⡿⡿⠿⠧⠴⠿⠿⠿⠷⠶⠶⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⣻⠇
⠀⣀⡤⠶⠚⠛⠉⠉⠙⢦⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⣀⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠛⠂
⠉⢹⡇⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⢀⠔⡡⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠛
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⡀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣿⣿⣷⣄⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠂
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢠⣶⣟⢻⠟⠻⣿⣿⣇⣬⡃⠀⢿⣶⣤⡀⠀⠀⠀⢠⣤⣾⣏
⠀⠀⠀⠀⠈⢷⣄⢠⣇⣴⣿⡿⢫⢻⣶⡿⠛⠋⢹⣿⡰⢆⣬⠛⢿⣿⣶⣄⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⣉⡶⠚⠻⣯⡀⠀⣤⣸⣿⡇⠀⠈⠙⠢⣬⡛⢿⣿⣦⣿⡇⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡠⢞⡷⠞⠁⠀⠀⠀⠈⢿⣀⣸⣿⣼⡇⠀⠀⠀⠀⠈⠙⠶⣌⡻⢿⣧⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠻⣴⡟⠀⠀⠀⠀⠀⠀⠀⠰⣆⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣝⢿⣿⢭⡟⠀⠈⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠸⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡛⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣦⣀⡀⠀⠀⠀⠀⠘⠂⠉⠉⡆⠀⠀⠀⠀⠀⠀⢠⡀⢠⡀⠀⠸⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⣿⣿⣼⣦⠀⠀⠀⠀⠀⢰⠱⡀⠀⠀⠀⠀⣾⣶⣿⣾⣧⣴⣦⡄⢹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠛⣻⣿⣿⣷⣄⠀⠀⡆⠸⣄⣿⠀⣠⣄⣰⣿⡿⣿⣿⡍⢻⣿⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢫⣽⣿⣿⣟⣿⡄⣿⠀⣿⣿⣆⣿⣿⣿⣿⣿⣦⠙⠃⠈⠋⠈⠻⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⢿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⡇⢸⣿⣿⣿⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡇⢸⡿⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⢄⠖⠉⠳⠄⠀⠀⠙⠀⠀⣦⠴⢶⣦⠶⣑⠟⢙⣇⣴⣤⣄⣠⣺⣷⣂⢄
⠀⠀⠀⠀⠐⠛⠚⠛⠭⠯⢍⣴⣶⣾⣯⣵⣿⣷⣷⢾⣖⣲⣶⣾⣿⡷⣶⣤⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⡃⢰⡗⣰⣦⣄⣀⣴⡄
⠀⠀⠀⢀⢀⣄⣤⣴⡆⠄⠴⣿⣍⣿⣿⣿⣿⠾⡶⢾⣿⣭⣿⢿⣿⣿⣞⣩⣾⡿⠴⠧⢿⣿⣿⣿⣿⣷⣦⣽⣿⣿⡷⣿⣿⣿⠿⠿⠃
⠀⠂⠰⠗⠶⣾⠛⣛⠿⡿⢷⣶⣿⣿⡟⢻⡟⢺⣿⣾⣿⣩⠇⠀⠀⣠⣿⣿⣷⠁⠀⠀⠀⢀⣼⣿⣟⣿⣻⣿⣟⡿⡟⢹⡂⠀⠀⠄⠀⡀
⠐⠂⠲⣦⣨⣨⣥⣼⡚⠻⢿⣿⣟⣻⣿⣽⣿⣿⣿⣽⣿⠟⣲⡿⠿⠿⢿⣿⣿⡶⠶⡶⢶⠽⢿⣿⠉⢉⠉⠉⣻⣿⣿⣿⣿⣿⣯⠷⠀⠻
⠀⠀⣠⣟⣻⣿⣏⣩⣹⣿⣟⣻⣏⢻⢿⣾⣿⣷⣿⠿⠋⣵⣿⣀⢀⡀⣼⢟⡉⠓⡠⠀⠀⠀⠠⣿⡤⢤⣤⣶⣿⣿⣿⢻⣍⠉⠃⢿⡈
⠀⠀⠀⠀⠀⣉⣩⣟⣛⣻⣿⣿⣯⣶⣭⣿⠟⠉⠀⢀⣼⣿⠏⠉⠙⠉⣳⣯⠀⠀⠃⠀⠀⠐⣶⣿⠇⠀⠀⠀⣹⣿⣿⣶⣾⣿⣶⣴⣄⡀
⠀⠀⢐⡿⠻⣿⣾⣿⣿⣿⣿⣾⣿⠿⢋⡤⢀⡴⢁⣾⣿⣿⠶⠦⣤⣶⣿⣿⡠⠰⢶⡶⣶⣱⣿⣿⣧⣀⣄⣶⣿⡏⢹⣿⣿⣿⣿⣿⣷⣦
⠈⠀⠀⣯⠖⠷⢶⣿⣿⣿⠿⠋⢡⣶⠟⣠⡟⣠⣿⣿⡿⠁⠀⠀⠀⠀⢈⣿⡏⠀⠁⠀⠀⠀⠈⢹⣿⡙⡛⠛⠻⡇⠈⣿⣿⣿⣿⣿⣿⡗⠂
⠀⢈⢉⣿⣭⣿⣶⣿⣯⣥⣔⡚⡋⠽⠾⢿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡯⡆⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⣷⠀⠘⢿⣿⣿⣻⣿⠷⡦⠁
⠀⠈⠀⠉⣟⣿⣣⣿⣵⣿⣿⣽⣷⣲⣶⣿⣿⣿⣿⣿⣳⣶⣤⣤⡀⢀⣿⠿⣷⣿⣷⣶⣤⣶⣶⣿⢻⣶⠒⢦⣕⣿⣇⣀⢌⣿⡡⠘⢧⣀
⢤⣼⣤⣥⣭⣭⣭⣿⣿⣿⣿⣿⣿⣭⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣤⣤⣤⣤⣦
⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣟⣿⣿⣿⣟⣿⡏⠉⠁
⠀⠀⠀⠘⠛⠛⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣭⣿⣿⣿⣏⣾⣿⣿⢛⣤⣴⣋⣹⠾⠛⠿⠮⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⠺⠛⠳⠛⠛⠻⠟⠻⠟⠿⠿⠿⠎⠹⠤⠌⠽⠉⠛⠉⠛⠉⠁⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣀⡤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠒⢫⠁⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⣀⠀⠁⠲⣄⣀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠐⡉⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠦⣐⢿⠋⠁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⣿⡧⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⡀⠀⠀⠠⢷⠀⠀⠒⠚⠉⠉⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⠙⠢⣀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢠⠤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠲⢜⣿⢀⣀⣤⡀⠀⠀⠸⡆⠀⠈⠲⣄⢻⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡠⠾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣫⣿⣿⣷⡄⣄⣤⡗⡀⡤⠀⣎⠘⣇⠀⠀⠀⠀⠀⠀⢹⡀⠀⢐⡀⣠⣬⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⣿⣿⣿⡓⢙⡧⠻⢛⠓⣖⠃⡄⠛⣤⠀⠀⠀⠀⣠⡬⣷⠾⠛⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⣤⣅⣉⣉⣀⣁⣰⣾⣂⣵⣾⣥⣤⣾⣥⣶⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡁⠀⠁⠀⠀⠐⠉⣿⣿⣿⢿⣿⣿⡿⣿⠿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡦⣾⣿⣿⠿⠿⠿⠿⢟⣂⣐⣢⣶⢿⡿⣿⠿⠶⢾⠷⠞⠛⠛⠛⡙⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠿⢯⢯⣬⣤⣢⠥⠽⢭⣑⢲⣚⠾⢿⡧⠽⢿⣯⠽⢭⡿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠶⠶⠮⠉⠁⠀⠀⠚⠉⠉⠑⠒⠊⠀⠙⠛⠒⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣼⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠒⡇⠀⠀⣄⣀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠠⣤⣀⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣼⣄⣰⣇⡀⣀⠀⠀⣸⢻⠋⠉⢨⡅⠀⢀⡄⠀⠀⠀⠉⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⣜⡏⡀⠀⠀⠠⠃⢸⠀⠀⠠⠀⠀⠀⠄⠀⢀⠀⠀⡏⢠⡀⢀⣀⣀⣀⣠⣤⠴⠛⠉
⠀⠀⠀⠀⠀⢀⣀⣈⣳⡓⠀⣐⣛⣀⣸⣐⣄⣨⣤⣶⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠃⠀⠀⠀⠁
⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⠽⠙⠯⢽⣭⣯⣽⣶⣿⣿⣶⣷⣾⠶⠷⠾⠾⠿⠿⢿⡿⣴⡶⣆
⠀⠀⠀⠀⠩⠉⠉⠉⠉⠉⢋⠉⠁⠀⠀⠀⠈⠛⢫⣭⠍⠀⡨⠀⢋⠀⠴⠿⠧⠶⣿⡿⢿⣿⣿⡿⣤⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠂⠀⡀⠀⠀⠤⠤⠈⠀⠀⠑⠂⡈⠀⠀⠒⣒⠈⠉⢆⣀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⣴⡖⢤⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣦⡀⠀⠀⠀⢸⡆⠀⠀⠸⣦⣄⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡷⠘⣏⠑⢄⡀⢸⡇⠀⠀⠀⣿⡿⠁⠢⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⠀⠘⡀⠀⠙⢾⣧⠀⠀⠀⡏⠁⠀⠀⠈⢂⣄⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡏⠀⠀⢀⠄⠀⠀⠀⠀⠀⢉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡆⠀⢸⠀⠀⠀⠀⠀⠀⠋⢹⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢼⡇⢀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣾⢷⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⡿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠃⠀⠀⠀⠀⠀⠁⢈⣷⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢻⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠔⡛⠠⠁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⢿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⠀⢣⠀⠀⠀⠀⠀⠀⠈⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⠟⣋⠴⣶⠶⠦⠄⠀⠀⠀⠀⠀⠾⢶⡁⠀⠀⠀⠐⠂⢀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⣟⣀⠠⠘⣁⡀⣀⣀⣀⠤⣈⣿⣿⡿⢿⣿⠀⠒⠒⠛⠀⠀⠀⠀⠿⠿⠿⠶⢀⣠⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠐⠛⠐⠊⠤⠤⠤⠄⠀⠀⠀⠀⠉⣻⣻⡿⣾⣿⡆⠀⠀⠀⠀⠀⢠⡤⣟⣭⣴⣾⣿⣿⣿⣿⣿⣿⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⡃⠀⣸⣿⠏⢀⣀⣤⣶⣾⣿⡿⢿⣿⠿⠛⠃⠀⠈⠙⠃⡠⠎
⣀⣀⣀⣀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣼⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣬⣭⣶⡿⠛⠀⣴⡆⠀⣺⣿⠂⢀⣄
⣿⣿⣿⣿⣿⣖⠀⠑⠪⠄⡀⢀⣤⣀⠀⠛⢿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠿⣟⣻⣿⣭⠉⠁⠉⠉⣴⣶⣾⣿⣿⡇⢸⣿⡿⠗⢸⣿⡷⣄⣀⡀⠀⢀⡠⠀⡀
⠛⠛⠛⠳⠆⡀⠀⠀⠀⢰⣬⣀⠉⠙⠛⢶⣶⣭⣭⣭⣭⣭⣿⣿⣭⣤⣼⣿⣿⣿⣿⣷⣦⣿⢿⣿⣿⣿⣿⣿⡟⠘⢿⠀⠀⢾⣿⣿⣏⠻⢿⣿⣷⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣤⣄⠈⠉⠻⠿⠟⠻⣯⣝⣛⡛⠛⠋⠉⠀⠀⠈⠉⠙⠷⠀⠉⠉⠉⠀⠀⠀⠀⠀⠆⠸⣿⣿⣛⠂⠀⢨⣝⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⣄⡀⠀⠙⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⢀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⡠⠖⠲⣿⠒⠐⠂⠀⠀⠀⠡⡰⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣹⡏⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣄⣀⡀⠀⠀⠂⠒⠛⣿⠒⠂⠀⠂⠀⠀⠀⠀⠠⠄⠴⣾⡦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠐⣿⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠙⡏⢀⠀⠀⠀⠀⠀⠀⠀⣻⠈⠙⠉⠉⢹⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠚⠁
⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⡿⠉⠀⠄
⠠⣤⠄⠈⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡠⠤⠤⠤⠴⠶⠤⠤⠤
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣯⣿⣿⣿⣿⣵⣦⣤⣤⣤⣄⣀⣈⣈⣀⣠⣤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⣿⠏⢩⠝⣋⡥
⣿⣯⣛⡛⠿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣮⣷⣦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠓⠒⣺⣟⡐⠒⠤⢸⠀⠀⠀⠀⠀⣀⣠⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣄⣀⣼⣤⣴⣶⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠲⠤⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢟⣛⠿⣷⡄⠀⠀⠀⠀⠀⠠⢄⡀⠠⠤
⠀⠀⠀⠁⣀⣈⣉⣽⣶⣶⣶⣿⣭⣽⣯⣭⣿⡿⠿⣿⢿⠿⣿⣛⣛⣫⣥⣤⣴⣶⣿⣿⣿⣿⣖⣦⠀⠀⠠⠤⠤⠤⠤⠄
⠀⢀⣀⣭⣍⣉⣉⡻⣯⣥⣶⣾⣿⢟⣿⣿⡿⠧⠾⡿⣏⣠⣭⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣭⣥⣤⠤⠐⠒⠒
⠈⠉⣉⡉⠛⠛⠛⠛⠻⢌⣉⣉⣐⣋⠉⠻⣿⣿⡛⠉⣴⣿⣿⡯⠛⠓⠊⠀⠉⠩⠭⠭⠭⠽⣿⣿
⠀⠀⠈⠉⠉⠉⠁⠀⠲⠦⢬⣍⣉⣁⡀⠀⠉⠉⠉⠥⠬⢽⣿⠧⠀⠀⠛⠓⠒⠚⢊⣉⣩⡭⠉⡉⠀⠐⠚⠛⠓⠒⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠒⠒⠂⠀⠘⠿⠃⠀⠀⠀⠑⠒⠂⠨⠁⠀⠀⠉⠙⠒⠲⠶⠟⠋

⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉
⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⣈⣿⣇⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⢛⢛⣿⡟⠛⠛⠛⠛⠉⠉⢙⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⢿⣿⣿⣷⣶⣶⣷⣶⣤⣾⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣼⡿⠿⠛⣛⠛⠛⠛⠛⠿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣿⠂⠀⠀⠀⢀⢠⡀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣀⣀⣀⣀⣿⣿⣿⢦⣤⡄⠤⣬⠤⠤⠤⠤⠴⢦⣤
⠀⠀⠀⠀⠀⠀⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠉⠉⢉⡉⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⡸⢿⣦⡀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠚⠋⠀⣽⡿
⠀⠀⠀⠀⠀⢠⢡⠘⣿⠘⢦⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢡⡤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢘⠀⠸⣧⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣆⡀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣇
⠀⠀⠀⠀⢀⠀⢸⠀⠀⢹⣇⠀⣰⡟⢦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣿⣶⣍⣷⣶⣿⣿⣿⡄
⠀⠀⠀⢀⡄⠀⢨⠄⣴⣶⣿⣶⣿⠸⣦⡐⢤⡀⠀⠌⡍⢠⣿⣿⣿⠀⣿⡏⠉⠻⢿⣿⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢀⣾⠓⠁⢨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⣈⡴⣹⣿⣿⣿⣶⣿⣧⣀⣀⡀⠈⠁⠮⣟⣿⣿⣿⣿⣷⡀⠀⣀
⠀⢰⣿⠃⠀⠀⣼⡿⢟⣿⡿⠻⣿⣿⣿⣿⣿⠿⣴⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⢹⣿⠙⠒⠒⠮⣭⣽⣻⣿⣿⣷⡀⢹⣦
⠀⣾⠇⣀⠀⠈⢹⠠⠞⠋⠀⠀⠘⣯⢻⠿⠟⣠⣿⣿⣿⡿⢛⢹⣿⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣷⣾⣿⣧⡀
⠀⠋⠀⠉⠀⠿⢻⣿⣾⣿⣿⣿⣷⢿⣿⣾⠿⠿⠿⠿⠿⡿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠻⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠋⠉⠁⠀⠀⢠⣿⣿⠀⠀⠀⢀⡔⠀⢢⠁⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⠀⠀⡄⠁⠀⠀⠀⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⠦⠶⠦⠶
⣆⣠⣀⣀⣀⣀⣸⣁⣀⣴⣴⣶⣶⣶⣾⣿⣶⣴⣶⣴⣶⣶⣄⣀⣀⣠⣄⣀⣌⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢻⣿⡀⠀⠀⠙⠁
⢛⠉⠉⠉⠉⠉⢹⠛⡉⠉⠉⠉⠉⠈⠁⢹⣿⣏⠀⢠⣜⣍⠀⠀⠀⠀⠀⠀⠀⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡃
⠈⠄⠀⠀⠀⠀⠘⣧⣽⡴⣤⡄⠀⣠⡀⣠⣿⣿⣾⣃⣽⣏⣤⣤⣤⣤⣤⣤⣤⣮⣥⣤⣀⣀⣠⣴⣂⣤⣄⣼⣇⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⣿⣿⡿⠿⠛⢻⣿⠿⣿⣿⠟⠛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠋⠉⠀⠀⠀⠀⠘⣿⡄⠀⠀⣿⣿⠀⠀⠈⠀⠀⣿⢻⠏⡀⠀⠀⠉⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣶⡆⣿⣿⣀⠀⢀⡀⢀⣿⠸⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⠀⠀⣰⣮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣧⣾⣿⣄⣦⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡉⠉⠉⠙⠛⠉⠉⠙⠲⠤⣤⣀
⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠙⡟⠛⠛⣋⣠⣤⣤⣤⡈⠉⠉⠉⠉⠙⣛⣻⣿⣿⣟⣙⣛⣛⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠹⢿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣾⡿⠛⠉⠉⠉⠙⠛⠛⠿⠶⠾⠟⠛⠛⠛⠛⠛⠉⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠀⡀⡄⠠⠒⠚⠀⠠⠀⠠⠄⠐⠢⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⢉⡅⠀⠘⢉⢈⣁⣀⣐⠐⣠⡄⠀⢀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⡆⠸⠀⠀⡀⠂⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⠤⠀⠀⠀⠀⠰⠇⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⡆⢸⠀⢃⠀⠀⠈⠈⠁⠈⠈⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢸⠀⠀⡇⠀⠇⠀⡇⢸⠀⢸
⠀⠀⠀⠑⣖⠠⠤⠔⠒⠊⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠔⠊⢡⠀⠉⠱⣀⣸⠀⠀⡇⢀⡀⠀⣀⢸⣀⣈⣀
⠀⠀⠀⠀⠈⠻⡐⠢⠄⣀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠨⠄⢂⣸⣉⣥⣸⠤⠠⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣸⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠉⡉⠉⠉⠑⠒⠒⠒⠒⠛⠚⠒⠛⠛⠛⠒⠚⠛⠛⠛⠉⢉⣉⣉⣉⣉⣉⠀⠠⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠇⣀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢤⣤⠶⢒⣊⣩⠵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠛⢶⣄⢐⣠⣤⣄⡤⠦⠴⠶⠖⠚⣻⣛⡉⡉⠩⠔⠒⠈⠊⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⠚⠒⠂⠎⠖⠲⠔⠒⠓⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⢾⠗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠿⣿⢤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⢻⡆⠠⠈
⠀⠀⠀⠀⠀⠀⠙⢗⠒⠒⠶⠼⣧⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠁⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠉⠁⣿⡿
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣿⣴⣿⣛⣻⣿⡿⣿⡾⣦⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡵⢌⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠲⠤⠶⣼⠇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡀
⠀⠀⠀⠀⠀⠰⠧⠐⠒⠲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⢐⣃⣹⣿⣠⡤⠬⣽⡿⠶⠖⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⢀⣿⣄⣠⣴⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣻⡷⣧⣙⠤⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠾⢿⣛⣿⣿⣿⣿⣍⡉⣴⣜⣯⡾⠞⠓⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⠀⢻⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⠛⠻⣿⣍⢙⡿⢿⣿⡇⢠⣿⡿⣼⢀
⠀⠀⠀⠀⠀⠀⣨⠿⣿⣿⣿⣯⣮⡀⠛⢛⣤⢀⠈⠛⠲⢿⡟⠓⢿⣇⠳⣄⡀
⠀⠀⠀⠀⢠⣶⣿⠆⠠⠀⠘⠉⠉⠉⠒⠀⠀⠈⠠⠂⠀⠠⠄⠀⢘⠻⠿⢮⣉⠁⢤⣴⣶⣤⡤
⠀⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣤⣽⣄⣈⠙⠳⠦⠀⠀⢀⣠⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠋⠉⠐⠀⠈⠙⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣸⣯⣝⣿⣭⣉⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡟⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠋⠉⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠚⠈⠀⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⣀⣄⠀⠀⢄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⡴⣿⢻⣏⢙⣁⠀⠈⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠵⠓⠛⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡠⠀⣸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠈⣤⡀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣀⣴⣺⡥⢿⣤⣉⣰⣄⣠⣨⣦⣼⣅⣀⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡴⠞⣛⣩⡤⠷⠞⢻⠚⠛⠁⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢿⠚⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣃⣢⠘⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡄⣘⡿⣿⣿⣿⣿⣯⣝⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠞⠁⣹⣁⡟⣻⣔⣻⣿⣿⣿⣷⣮⣟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⣦⣤⢿⣻⣮⣷⣿⣿⣿⣿⣿⣿⣿⡏⠈
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠛⠉⠉⠙⢿⡿⠋⠄
⠀⡂⠀⠀⠀⠀⢤⠤⣤⣤⠤⠶⠦⢤⣤⣬⣿⢿⠿⢁⣤⡀⠀⢀⢢⣼⡇⠀⡄⠖⠠⣤⠄⠀⠀⠀⠠⠶⠦⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠡⢶⣾⢂⣶⢶⣦⣤⡤⠀⠐⢺⣽⡿⠈⣽⣾⣿⣇⣀⠻⢿⣿⣃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢶⣶⡬⢙⣠⣴⠚⠿⠃⠀⠈⣛⣯⡌⠻⣿⣦⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⠷⠐⠀⠀⠀⠀⠀⢀⣀⢼⠷⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⢀⡀⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣙⠶⠟⠊⠉⠀⠀⠀⠀⣀⣧⡄⣰⡼⢤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⢀⣶⣤⠤⠔⠚⠉⠁⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠛⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠐⠈⠉⠀⠀⠀⠠⣶⠀⢸⠀⢀⣀⣠⣤⠤⢤⠘⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⡆⠶⠒⠂⠀⠀⠀⠀⢀⠀⠀⣰⣿⠀⠾⠛⠉⠉⠀⠀⠀⠀⣤⠀⠹⢦⡀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⢀⣆⡠⢾⡶⠛⠛⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⡀⠈⠛⠻⠛⠃⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣰⠭⠀⠒⢈⣽⠷⠶⠛⠀⠀⠀⠀⠀⢀⣀⣄⣤⣷⠿⠷⠆⢀⣀⡀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠦⠶⢒⡃⠈⠀⠀⠀⢿⠀⢀⣠⠂⣀⠠⠖⠚⢻⡉⢻⣧⣤⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠸⡆⠀⢧⡾⠁⠀⠀⠀⣨⣷⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣧⠀⣈⣥⣴⣶⣷⣿⣿⣿⣛⡹⠿⢿⣿⣿⣷⣾⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠯⠼⢿⣶⣶⣿⣿⠭⠍⣉⣨⣽⣿⣿⣿⣿⣿⣿⣿⠟⣯⣷⣶⣶⣤⡀⢹⣿⣿⣿⣷⠆
⠀⠀⠐⢿⣿⣦⣤⣀⠀⠈⢿⣷⠇⣰⣶⠶⣾⣿⡿⢿⡿⣭⣭⣭⣛⠛⠛⠛⣙⣧⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯
⠀⠀⠀⠐⠋⠉⠙⠛⠿⠷⣶⣾⠟⡋⠙⠋⠻⣍⡁⣤⣠⠤⠀⣤⣴⣶⣤⣾⠿⣿⣿⣿⣿⣿⣿⠏⠘⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡆⠈⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣤⡤⠼⠗⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⢀⠀⠀⣀⢀⣀⣼⠦⠻⠚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠴⠖⠒⠛⡟⠁⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣼⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡍⣀⡀⠀⠀⠶⢺⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⣀⣠⣤⠶⠖⣶⠏⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠉⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢹⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢷⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠘⠀⠂⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠁⠀⢀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⡠⢀⣴⠿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠤⣂⣠⡾⠋⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡄⠀⠀⠀⠀⢀⣰⣤⡶⢞⡁⡀⢈⡟⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣃⣤⣤⠴⠆⢻⡏⠄⠋⢀⣀⣠⣄⣼⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⢢⡤⠟⠞⢹⡃⠀⡠⠔⠈⣠⣴⣶⣿⣿⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⣀⠸⠗⢈⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣨⣥⣴⣾⣿⣿⣿⣿⡿⠟⠙⣿⢿⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡭⠛⠟⠛⠛⠛⢛⣛⣉⠻⠞⣻⣗⡜⢼⣟⣿⣍⠛⢿⣶⣾⣿⡛⠿⢿⣤⣴⣬⣶⣶⣋⠁
⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⠀⠶⠖⠋⢲⣶⠚⣳⣶⢿⣦⡾⢿⣿⣋⣀⣴⣿⡿⠿⣿⡿⠿⢛⣡⡘⠋⢘⠛⠶⠿⠿⢿⣿⣶⣿⣷⣬⣽⣿⣿⣿⡿⠟⠁⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠥⠤⠶⠾⠛⠋⠹⣿⣿⣿⠿⠂⠒⠻⣭⣿⠿⠿⠿⢓⡠⠀⢾⣿⣿⠇⠀⢨⡛⠻⢶⣶⠀⠀⠛⢛⣉⣩⣍⡙⠛⠛⠃⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⢀⣙⠫⠥⠤⠄⠈⠉⠋⢡⣤⣤⣤⣉⡁⠀⠐⢛⣫⡵⠀⠀⠈⠻⣷⣾⣯⡭⠉⠉⠛⠿⣿⡿⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠖⠂

⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⣀⣀⣀⣠⡀⠀⠀⡗⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⠉⣇⣀⣀⣤⣴⣶⣿⠇
⠀⠀⠠⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣯⡀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⢈⣀⣉⣭⣶⣶⢶⣿⣽⣿⣽⣿⢿⣿⣿⣿⣿⣿⣭⣥⣴⣾⣿⣿⣿⣶⣄⠁⠀⠒⠒⠂
⢠⣤⣶⣦⣤⣬⣿⠾⠿⠿⣿⣿⣿⣿⣿⡿⣷⣶⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡶⠒⠒⠉⠉⠁
⠀⠐⠲⠦⠤⠀⣈⣑⣒⠒⠒⠀⠙⠿⠷⣂⣻⣿⡏⠈⠠⠤⠤⠭⠭⠿⡟⠛⠃⠠⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠐⠒⠒⠀⠀⠿⠇⠀⠀⠒⠂⠬⠍⠉⠁⠒⠒⠶⠶⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠚⠷⠈⠛⠀⢲⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠙⡷⢄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠷⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡓⠲⠦⣤⣇⣀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠴⢦⢤⠀⠀⠀⠀⠈⠉⠙⠛⢆⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠀⠉⣟⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⣼⣦⡠⠀⠀⣀⠀⠀⢴⡀⠀⢀⠀⠀⢸⠈⠉⠒⠻⢦⣈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⠦⠤⣤⣀⣀⣿⣿⡇⠈⠀⠀⣼⠀⠀⠀⠀⠀⠀⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢳⡀⠀⠀⠀⠉⠉⠙⠒⠒⢦⣼⠂⠐⣄⣀⣠⠀⢀⡆⣠⢸
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠐⠒⠚⠿⠿⣤⣀⣁⣛⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢶⣟⣳⡶⠤⣤⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⠀⠀⠈⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣧⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠃⠀⠀⠛⠀⣴⡖⣤⢠⣼⡏⠀⠒⠂⣶⡶⣶⣶⣿⠒⠚⠿⠀⣼⣰⢿⡆⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⣰⢨⣽⣏⠙⠒⠒⠒⠿⠧⠿⢬⣿⡙⠛⠒⠒⠻⠷⠾⠿⠿⣤⣤⣄⣀⣿⣃⡈⡇⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⡏⠀⠀⠀⠀⢱⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣿⣹⡇⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣿⣸⠇⠀⠀⢀⣠⣼⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣀⡾⠵⠚⢻⣿⠉⢿⡏⠃⠀⣰⢀⣀⠆⣀⢼⡇⠀⢀⠄⢀⣠⡄⡀⣠⠂⣀⡐⠀⣠⣾⣹⣿⣿⣷⣶⣿⣯⣰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⢶⣾⢿⡦⣾⣟⣴⣄⣩⣿⡇⠰⣿⠆⣠⡼⠋⣾⣿⠁⠀⢹⣏⣼⣿⣶⣾⣿⡿⢶⣞⠉⠀⠀⢹⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣼⣿⣺⣗⣿⣟⡹⣿⣿⣿⣇⡀⣿⠞⣿⡇⢠⣿⣿⣶⣶⣿⣿⣿⠣⡿⡿⡿⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣼⣷⣼⣿⣿⣿⣿⣿⠿⠿⠻⣴⣾⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣾⣿⣿⣿⣛⣿⡟⢻⣿⠋⢻⣿⠛⢻⣿⡟⠻⣿⣏⡉⣿⣿⣼⠿⠿⢶⣾⣿⣿⣏⣼⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠉⠻⠛⠿⠿⡿⠿⢿⣿⡿⣿⣿⠿⣿⣯⠿⣭⣭⠿⣶⣤⡤⢤⢶⢾⡟⠻⣿⣿⠿⠿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂⠁⠐⠂⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⡗⠀⠀⠀⠀⠀⠀⣀⡀⠼⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢀⡀⠋⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⠶⠛⠊⠉⠀⠀⠀⠀⢀⣧⣄⣲⡬⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⢀⣶⣬⠄⠒⠘⠉⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⣠⡲⠟⠛⠛⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠔⠂⠈⠁⠀⠀⠀⠠⣷⠀⢨⢀⣀⣀⠤⠤⠤⢦⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⠦⠖⠒⠂⠀⠀⠀⠀⢀⠀⠀⣸⡿⠀⠚⠋⠉⠁⠀⠀⠀⠈⢆⡀⠸⢷⡀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠆⢠⣇⠤⢶⡞⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⡀⠀⠉⠛⠛⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠍⢂⠂⢉⡴⠷⠖⠋⠄⢀⠀⠀⠀⣀⣠⣄⡤⠷⠿⠿⣇⣀⣀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠶⠖⢂⠍⠁⠀⠀⠀⢻⠀⠠⢰⢂⡠⠐⠒⠋⢹⡄⢛⣷⣴⣶⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⠀⠈⠀⠀⠀⠀⠀⠸⡆⠀⢷⡛⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣆⠀⡀⢀⡀⠀⣀⣀⣷⢀⣨⣵⣾⣿⣿⣿⣿⣿⣛⣹⠛⠿⣿⠿⣷⣷⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣳⠾⠿⠶⠶⠿⠿⢏⣉⣡⣤⣽⣿⣿⣿⣿⣿⣿⣿⠛⣿⣾⣶⣷⣦⡀⢹⣿⣿⣿⣷⠆
⠀⠀⠘⠿⣿⣶⣦⣄⣀⠈⠻⠿⢏⣠⣞⡻⣿⣿⡿⠿⠿⠯⠮⣭⡭⠛⠛⠉⣩⣷⣾⣿⣿⣿⣿⣿⢸⡿⠿⢿⡷
⠀⠀⠀⠐⠉⠉⠉⠉⠻⠿⠿⠿⢟⠍⠉⠁⠹⣄⠀⠤⠤⠆⠀⠤⠶⡷⢶⠿⠿⣿⣿⣻⣿⢿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠙⠁

⠀⡀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⠈⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠰⠤⡤⠤⢤⣀⣀⣀⣉⣃⠀⠀⠀⠀⠐⠂⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠤⠀⠀⢘⠁⠀⠀⠙⠲⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠘⠛⠷⠾⡖⠒⠖⠂⠀⠀⠾⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠤⠐⠢⠴⡤⠄⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠛⠓⠲⠶⠶⠷⠤⢤⣤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⣀⣀⡔⠀⡄⠀⣀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣤⣄⠀⠀⠖⠚⠛⠙⠋⠉⠉⠀⠙⠀⣿⠁⠀⠉⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣀⢠⡐⣫⠦⠴⠿⠷⣤⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠐⠷⣾⣶⣼⣟⣉⡉⠀⠀⠀⢀⣧⣀⡀⣤⣤⣿⣦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢄⠀⠀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠉⠉⠛⠻⠶⠾⢿⣯⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠦⣀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣟⣀⠀⠀⢀⣤⣤⣅⣈⣁⣰⣆⣙⣈⡓⠮⠤⠐⠀⠹⡆⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠴⠦⣤⣶⣀⣠⡄⠛⢋⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠥⠅⠀⠀⠀⠀⠀⠱⠄⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠐⢀⠀⠉⠉⠉⠓⠲⠶⠶⠤⣤⣤⣄⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠚⠒⠿⡀⠂⠤⣀⡀⠘⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠗⠁⠀⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⢃⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡔⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠲⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠀⠀⠀⢨⠀⠀⠀⡀⠀⣈⠇⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠹⠀⣧⠀⠀⣤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢰⡏⠀⠀⠀⡟⠀⠀⠀⠀⢀⡜⠁⢀⡽⠆⢈⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡿⠊⡠⠂⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⠇⠀⠀⡸⠁⠀⠀⠀⠀⠙⠂⣀⠀⣤⠀⢸⠇⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⢺⡄⢀⠀⠀⠀⠀⠊⠀⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠀⠼⠀⠀⠠⠁⠀⢀⡠⠄⢰⡷⢉⢹⣶⠀⠀⡌⢀⢰⠆⢀⣰⠶⠶⠛⠀⠀⠀⠀⠀⠇⠀⠀⠠⠄⠀⠔⠀⢀⠖⠉
⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⡎⣿⡀⠀⠈⡟⠸⡾⠁⢀⡜⣁⡴⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⣰⠆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡴⠐⠉⠀⢺⡇⢿⡇⠀⠀⣧⣐⣁⡴⠛⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠞⣡⢾⣀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⠘⠃⠀⢀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⢰⠅⡀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡀⣸⡇⠀⠃⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⣿⣄⡀⣈⣓⣲⣤⣀⡀⠀⣄⣉⣁⣬⡷⠁⣀⣷⣆⡄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣿⣿⣍⢉⣿⣿⣿⣿⣿⡛⣂⣿⣌⣩⣿⣴⠟⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢻⣻⣟⡻⣟⣿⠛⣻⣻⣟⠛⡟⣯⡉⣹⣽⣅⠀⠀⠀⡁⠈⠋⣠⣾⡏⣿⣾⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠐⠿⣿⠇⢿⡿⠯⠸⠿⠿⠀⠿⠿⠃⢀⣀⣤⣴⣶⠟⠫⣽⡇⡌⠙⢳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠒⠒⠒⠒⣖⢲⣶⢒⣖⣒⣒⣲⣒⣒⠖⠒⠋⠉⠉⠥⠀⠂⠠⡀⣼⣷⣆⣠⠍⠻⠧⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠋⠉⠛⠛⠛⠛⡛⠛⠉⠈⠉⠁⡀⢠⡀⠀⠀⠀⡀⠀⠀⠀⠘⠻⠿⠛⢁⡀⠰⠦⠓⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠠⠄⠀⠀⢀⡀⠒⣀⣀⠈⠁⠀⠀⠀⠈⠀⠑⠚⠛⠁⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⣒⣛⣭⣭⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⢸⡟⠋⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⣁⣀⣸⣇⣸⡇⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⠿⠖⠚⣿⣿⠁⢀⣀⣠⣤⣴⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⣼⡿⣟⣛⣉⣩⣤⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠾⠷⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣀⣼⡏⠀⣿⣉⣉⣭⡥⣤⣤⢶⣶⡶⡶⣶⣶⣲⣲⣖⣖⣖⣶⣶⣶⣶⢦⣤⣬⣍⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⠶⠖⢛⢛⡉⡍⣽⠓⠂⣿⠧⠿⠾⠶⠛⠛⢛⣛⣋⣉⣉⣉⣉⣭⣭⣭⣭⣭⣉⣉⣉⣙⣛⣛⣛⣠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠆⠐⠀⠃⣘⣁⣉⣤⠤⠴⣿⠀⠂⣿⠶⠶⠚⠛⠛⠛⢉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣻⡇
⠀⠀⠀⠀⠀⢠⣖⣚⣓⣚⣛⣭⣭⣭⣥⣶⣶⣾⢿⡿⠘⠀⣿⡖⣶⢻⡏⢻⡉⣿⢉⡏⢹⠀⡿⢸⡇⣿⢸⠀⡏⢸⠉⡏⣿⣹⣹⣿⣥⣤⣤⣄
⠀⠀⠀⠀⣀⣼⣟⣛⣛⣛⣫⣭⠭⠭⠭⠴⠒⠒⠚⠁⡀⠁⣿⣇⣿⣼⣧⠼⠶⠿⠚⠓⠛⠛⠛⢛⣛⣛⣻⣿⣿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⢹⢷⣄
⠀⢠⡶⠾⠟⠠⠄⠠⠄⠤⠠⠆⠰⠀⠲⠀⠂⣀⣋⣀⣡⣤⣿⣀⣀⣀⣀⣠⣤⣤⠶⠶⠖⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢤⠴⠶⣾⣽⠟
⠀⠀⠓⢲⡶⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⠉⠁⠀⡀⢀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠖⠚⠛⠉⣉⣁⢀⣀⣀⣠⣼⣿⠋
⠀⠀⠀⢸⣀⣐⣐⡂⠂⠐⠀⠂⠒⠐⠀⠃⠚⠈⢁⣉⣀⣁⣀⣀⣤⣤⠤⠤⠶⠖⠒⠛⠛⣉⣉⣁⣤⣤⠤⠴⠶⠒⠒⢻⣿⣿⠏⠉⠁⠀⣾⠃
⠀⠀⣀⠀⣿⠚⠿⠿⠯⠭⠭⠽⠯⣭⣭⣭⣭⣭⡭⠭⠭⠥⠤⠶⠶⠶⠖⠒⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢷⡤⠻⣁⣀⡄⠀⢰⡏
⠐⠛⠛⠻⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⣾⠁
⠤⠤⠤⢤⣀⣷⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠀⣀⣀⣀
⣠⠴⠚⠑⠫⣟⠛⠉⠀⢉⡿⣯⣍⣙⣛⣛⣲⠶⠶⣶⡦⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⣾⣯⣭⡛⠁⠀⠈
⠀⠀⠀⠀⠀⠈⠙⠲⠤⠾⠀⠀⠉⠳⢭⣉⣁⣀⡼⠉⠉⠛⠳⠶⣇⣀⡉⠓⢦⣄⣀⡿⠉⠙⢯⣍⠉⠉⢿⠙⠻⣭⣉⠀⣶⣯⣍⠓⢿⡄⠈⠙⠶⠦⠴
⡀⠀⣠⠷⠦⢤⣀⣀⡀⠀⠀⠀⠀⢀⣤⣌⣉⠉⠀⠀⠀⠀⠀⠀⣤⣤⣉⡉⠉⠉⠉⠀⣤⣀⡀⠈⠙⠛⠋⠀⠀⣀⡉⠳⠦⠴⠟⠀⠀⣟⠛⠲⢤⡀
⠉⠉⠁⠀⠀⠀⢀⣀⣉⣉⣉⠉⠛⠋⠁⠀⠉⠙⠓⠦⠤⣤⡤⠞⠁⠀⠉⠙⠓⠶⠤⠤⠃⠈⠉⠛⠲⢤⣄⣀⣴⠏⠉⠓⠲⠤⣤⡤⠶⠋⠀⠀⠀⠙⢦
⠀⠀⣀⣠⣴⠞⠋⠁⠀⠀⠉⠉⠓⠢⢤⣀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠉⠙⠒⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠛⠒⠲⠤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢀⣤⣤⡤⠀⠀⣀⡠⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠛⢉⣭⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⡤⠆⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠐⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢭⡥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⢳⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠁⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠛⠛⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠛⠁
⠀⠀⠀⠤⠎⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡡⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠋⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠫⡵⠍⠙⠋⣡⣾⡿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠻⠃
⠀⠀⠀⠀⠀⣀⣴⣿⡏⠁⠀⠀⢠⣼⣿⣿⡿⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣟⡉
⠀⠀⠀⣠⣾⣿⠟⠁⠉⠁⠀⠀⠠⠴⢿⣿⣷⣶⣶⣾⣿⡿⠿⠛⠛⠉⠉⠀⠁
⢀⣴⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁
⣿⣿⠛⠉⠀⠀⠀⠤⠄
⣿⠿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢀⡖⠈⠁⠠⠔⢋⠺⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠻⣕⠢⢄⡀⢸⠖⠘⡟⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠈⠑⢦⡈⣿⠀⣀⠁⠀⠀⠀⠀⠀⣤⠐⠖⠀⠀⢰⠏⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠉⠣⣀⣽⠛⣄⠠⢀⠀⢸⣇⠠⣴⠁⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄⠀⠀⢀⠞⠁⠀⢀⠀⠀⠀⠀⠀⢈⡟⠀⠈⠑⢦⡀⣿⠉⠄⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣶⣗⠒⠒⢰⡅⢀⡀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠈⠻⣌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⢸⡏⠙⢦⣾⠀⠀⠉⢳⣴⣋⣀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢸⡷⠀⠀⡏⠓⢦⣀⣿⡟⢦⣈⠉⠒⢤⣀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣸⡗⡀⢠⠀⠀⠈⡟⣿⠇⠀⠘⠷⢤⡀⠈⢳⣤⡰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢦⣼⡃⠙⢦⡰⠄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢏⡛⠲⢦⣄⣼⠃⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⠀⠙⠦⣀⠹⣄⢸⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⠲⣄⡼⢣⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢳⢾⣞⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣠⠞⠠⠀⠀⡐⠁⠀⠀⣠⣏⣀⣀⡀⡠⠃⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢹⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣖⠲⠦⢼⣅⣀⠀⠔⢹⡏⠫⣍⠉⠛⠶⢤⣀⣴⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⠈⠙⠲⣤⣀⠉⠻⢶⣿⣾⠀⠈⠻⠲⣄⠀⡝⢻⣦⡀⢀⢣⠀⠀⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢸⠀⠀⠀⠈⣉⠛⢶⣿⣿⡟⠀⠀⠀⠀⠈⠻⠷⣾⡆⠈⠻⡀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⠇⠀⠀⠀⢻⢀⣾⡿⠟⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣄⠈⢠⡎⠀⢸⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡘⠀⠀⣸⠃⠀⠀⠀⢀⣾⣿⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣻⢦⣵⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⠌⠀⠀⡟⠈⠀⠀⠀⣾⣛⡺⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠳⠾⣿⡀⠀⠀⠀⠀⠀⢀⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠠⠀⢸⡇⠂⠀⠀⡼⣽⢯⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⠈⠑⠦⣀⠀⠀⣠⠟⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⠲⢤⡿⠀⠀⢀⣼⣱⣏⠏⠀⣸⢃⠁⠀⠀⠀⠀⢀⠂⠀⠀⡀⢿⡾⠀⠀⠀⠀⠀⠀⠀⠙⠿⢇⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠄⠃⣼⢣⠟⡞⠀⣰⢏⠳⠀⠰⠂⠀⢀⣎⣀⣀⣐⣐⣿⠳⠃⠀⠆⠀⠀⡀⠀⠀⠀⠀⠙⠒⢄⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡞⣁⠀⣀⣼⣯⣯⣼⣥⡴⠏⣀⣠⠴⡟⠚⠙⠍⣿⣿⠉⣉⣽⣟⣛⣷⣟⣒⢲⣶⣤⣄⡀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠾⢽⣿⡯⢍⣉⣠⢇⡾⢰⢁⣾⡷⠊⠉⢙⣳⣦⣤⣞⣛⣯⣽⡟⠛⠛⡛⠓⠛⠾⢯⣿⢿⡄⠈⠙⢦⣼⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠐⠮⠽⣛⣾⢿⠿⡷⡶⢿⣿⣗⣛⠿⢽⡛⣯⣁⠀⠈⠙⠞⠋⣩⣭⣭⣭⣉⣓⢞⣵⡿⢿⡆⠀⢈⠆⣫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢑⠂⠬⢉⣉⣉⣭⢉⣭⢁⡷⠠⠟⠚⠋⣡⡤⠶⠐⢒⡻⢭⣁⣀⣀⣈⣉⣋⣾⡯⠱⡎⢁⣠⠾⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⡀⡉⠐⠒⠶⠦⠄⢠⣀⢴⠆⡐⠛⠋⣉⠀⠄⠀⠀⠨⢛⣋⠠⠤⣤⣭⣿⣾⠷⣤⠋
⠀⠀⠀⠀⠀⠀⣠⣤⠤⠚⠚⠛⢷⣄⣉⣱⣶⣶⣶⠦⠤⣲⣶⣂⣙⣁⣀⣠⣤⣖⡚⢛⣋⣛⣛⠟⠿⠿⠿⣿⠶⠗⢒⣋⣀⣀⠄
⠀⠀⠀⠀⠀⠉⠓⠈⠒⠂⠀⠀⠡⠟⠛⠋⠉⠓⢂⣠⣀⣬⡟⠛⠉⠁⠀⠉⣭⠽⠿⠯⠤⠀⠀⢈⡉⠤⠤⠤⠤⢉⣉⠀⠀⠠⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⣴⠆⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⣾⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢲⡯⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠋⠉⠀⠂⡀⠉⠀⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠠⠄⢀⣔⡏⠀⢰⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢿⣇⣀⢸⡇⢰⡶⣄⣀⠐⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠈⠙⡛⣸⠃⠀⠉⠙⠻⡾⠧⣤⣛⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⣤⠄⠀⠀⢨⣵⡏⠀⠀⠀⠀⠀⢹⡄⠀⠈⢿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠚⠂⠲⠀⡜⣨⡿⠀⣀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠛⠛⠿⠿⣿⣿⣾⣶⣿⣥⣶⣿⣿⡛⠛⠻⠿⣿⣆⡉⢰⡦⢿⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢩⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠯⠿⣿⠃⠀⠀⠀⠀⠀⠉⠙⠳⢾⡧⣤⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠚⣇⠀⠀⠀⠀⠀⠀⡠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⣠⣾⠟⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⠈⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣰⣃⢋⢌⣼⣦⣗⣴⣷⣧⣾⣿⠋⠀⠐⠇⠴⠃⠀⠀⠀⠀⠀⢰⣽⠃⠀⣀⣀⠐⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣬⣅⣟⣻⣟⣿⡿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣤⡀⠀⡀⣀⢀⣼⡿⢀⣴⠟⠉⠓⢢⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣉⡉⠛⢻⡿⣿⣿⣷⣮⣿⠋⠰⢟⡿⠿⡿⣿⡿⣿⣷⣦⣤⣤⣽⣿⣿⣷⣿⣧⣦⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⠷⢤⢄⣉⠛⠃⠀⠀⢈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⠆
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣠⣞⣛⢻⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⣀⣸⠃⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡅⡟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣭⡤⣄⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠈⢂⠀⠀⠀⢴⢞⣛⣩⣥⣶⣤⣿⣿⣿⣿⣿⡿⣿⢟⣩⣾⣏⠀⠀⠉⠿⢿⢿⡿⠿⠿⢿⡅⠾⢿⠀⠀⠂⠀⢀⣤⡞
⠀⠀⠀⠀⠀⠈⠳⣤⣀⣐⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣟⣛⠛⠿⣿⡅⠀⠀⠀⠀⢠⠷⣍⠢⣶⣿⣧⣀⢤⣀⣀⣰⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠐⠓⠶⢚⣋⣩⣭⣭⣭⣏⣉⡛⠿⣦⣝⠂⠀⢐⣕⣾⣶⣮⣷⣮⣽⣿⣿⣿⣿⣿⣟⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⣁⣐⣨⣽⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢷⣄⠀⠉⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣭⣭⣤⣶⣾⣿⣿⣿⣿⢿⡏⠁⢾⣆⠙⠶⣤⣈⣛⠿⠿⠿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢈⠙⢿⣿⣧⡍⠙⠀⠶⢿⣷⣴⣤⣉⣉⣛⡛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠻⠶⠦⠉⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠲⢄⣠⠤⢄⣀⣀⣠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠤⠤⢌⡀⠀⠀⢁⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡖⠀⠐⠲⣼⠖⠊⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⡀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢨⣄⣀⡀⢀⡷⣆⠀⠀⢱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢾⣯⣿⣿⣿⣿⣽⡿⣿⣿⣶⣶⣯⣽⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣠⣤⣤⣤⣇⡀⠀⠈⠉⢋⠉⠀⠀⣏⠉⢹⣏⣥⡴⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣻⣶⣤⣴⣧⣼⣽⣌⢂⣸⣤⠤⣶⠿⢛⣉⡽⠒⠋⡁⠼⡷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⣿⣇⣃⠩⢙⢻⡏⢻⠿⢲⣩⡷⠞⠋⢁⡄⠰⠀⣁⡴⢟⠽⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣷⣷⠚⣻⠛⠿⣶⣼⣧⡴⠞⠋⠁⠀⡦⡆⢀⣥⣶⠟⣫⠞⠅⣠⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠷⢉⣡⢽⣾⡉⠜⠓⡲⢤⣎⣿⡀⢸⠀⠁⣠⢶⣫⠕⣋⡴⠋⠠⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢁⣨⠖⢋⠡⠒⠉⠄⢂⠡⠐⠈⢈⣟⡟⠻⣒⡭⠖⢉⡤⠚⠁⠀⣀⠔⣫⠂
⠀⠀⠀⢠⡠⢀⡴⠚⠉⣐⣤⠜⠋⠄⠂⡁⠐⡈⠔⠈⠀⢀⣄⣺⠷⠞⠛⠉⢁⡤⠞⠉⢀⠀⣠⠾⠓⠊
⠀⠀⠀⠈⢷⠥⠤⠬⠴⠯⠤⠤⠤⠴⠦⠴⠶⠒⠚⠛⠉⠉⠀⠀⣀⡠⠔⡊⠁⠀⢀⢄⣵⡚⠍⠂
⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠚⠉⠁⠀⠀⠀⠀⢊⣴⠋⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠫⣍⠉⠙⠋⠉⠉⡹⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣄⡀⠳⣶⡗⠀⠀⠀⠀⠀⢈⠀⣰⡞⢙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⣿⣉⣑⣦⣴⣾⠶⠯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡖⠶⠔⠂⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠉⠉⠉⠑⣀⣘⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣓⣼⣔⣶⣒⣤⡇⡃⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢣⠀⠀⠀⠀⣼⡧⠤⢶⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠷⠶⣐⣾⠤⢤⡤⠤⣄⡇⠀⠀⠈⠯⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡲⠤⣼⠀⠀⠈⠫⠉⠉⠉⢭⣽⠷⠶⠶⣶⣤⣙⣦⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠞⠒⠋⠑⠒⡇⠀⠀⠀⠈⢆⠀⠀⠈⠻⡲⢄⣣⠀⠀⢈⣑⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱⠠⢼⣇⣾⣻⣟⣥⡲⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡼⠀⣀⣀⣀⠀⡇⣠⢏⣘⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢸⢃⣠⡴⢒⠾⡟⢻⣿⠿⣽⣽⠗⣋⢭⣿⣌⡝⣻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡾⣛⡛⡓⡚⣶⣷⣾⣇⣀⣾⣿⣿⣿⣿⣾⣷⣷⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣵⣓⣐⣐⣸⡿⢿⠿⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠄⠠⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣂⣐⡿⢿⣿⣿⣿⣷⣾⣿⣿⡿⠿⠿⠟⠋⠉⣭⣩⢉⣁⢻⡑⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠭⠭⠥⠷⠒⣦⡀⠙⠛⠓⠠⠤⠍⠀⠐⠂⠀⠴⠚⠃⠼⠃⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠉⠁⠀⠒⠒⠒⠂⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣶⡾⠛⣿⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢻⣿⣾⣮⡠⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡿⠟⢿⡀⠀⠀⠀⠈⣿⣧⡿⠿⠛⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠉⠁⠀⠠⠘⣧⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢟⠲⠶⠾⢿⣦⣄⣄⣀⡀⠐⡖⠶⠤⢴⣤⣷⣀⠈⢷
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠀⠀⠀⠀⠀⠉⠉⠛⠳⠷⠦⢤
⠀⠀⠀⢀⣠⣴⡾⣷⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣸⣷⢤⡀⠀⠀⠀⡘⠀⢀⣀⣠⣄⣀⠀⠀⠀⠞⠀⠀⠐⠀⠶⢲⡀⣶⠆⠀⠀⠀⠐
⠀⢛⠶⢤⣄⣀⠀⠙⢧⡜⠂⠀⠀⣜⣁⠀⠀⠀⣽⢿⣏⣤⠀⠀⠀⠀⠿⠙⠛⠛⠚⠷⠿⠶⠤⢤⣤⣥⣤⣤⡀
⠀⠈⠓⠂⠼⠿⠓⠲⢾⣧⡀⠀⡀⠉⢏⠉⠛⠛⠛⠿⠿⢷⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣙⡳⢷⣤⣀⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠉⠉⠒⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣠⣴⡶⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣠⣬⡿⢏⠉⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣿⣠⣼⣼⡾⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢺⡟⣿⣻⣯⣤⣴⢾⢿⡿⠋⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⠍⠺⢿⣿⣿⣿⣿⣥⢴⣶⣺⣿⣿⣿⣧⣀⠐⠚⠀⠀⡀⢀⣼⣇⣽⣿⣿⣯⣶⣶⠏⠀⠀⠀⠀⠤⠎⠀⠤⠤⠤⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣭⣷⣾⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠀⠀⠀⠀⡤⣤⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠻⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡜⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢾⠆⢗⣷⣿⡇⡄⠀⠠⠴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡈⣷⠀⡸⡿⣼⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢂⣴⣼⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠘⠀⠀⣧⣸⣿⣤⠄⢀⣀
⠀⠀⠀⠀⠀⢡⡈⢉⠈⠈⡸⠀⠈⠀⠀⠀⠀⠀⠀⠢⢾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣅⡺⢿⣿⣁⠴⠃⡆⠻⣿⣾⣿⠏
⠀⠀⠀⠀⠀⣼⣷⣶⣤⣄⠀⠀⠀⠀⠀⣧⣴⣿⡇⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⢳⣦⣆⣀⠈⠬⠿⢿⡿⣴⣿⣿⣿⣯⣽⠿⡷⠆⡄⠀⠀⠀⣿⣿⣿⡿⣿⢫⣭⣿⡍⠻⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣾⢿⣿⢉⢿⡶⢆⢸⣿⣼⣿⣿⡏⠙⣿⣿⣾⡐⢦⣠⠀⠀⣿⠀⡿⢑⣧⠘⢫⣷⣶⣾⣿⡿⠿⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣬⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣷⣿⣀⣶⣜⣿⣇⢸⣿⣴⣿⣿⣿⢁⣴⣤
⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣦⣵⢁⠨⣿⣿⣿⣿⣿⡿⠋⠘⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⣥⣤⡀
⠀⠀⠀⠀⠀⣠⣤⣉⣿⣟⠋⠉⢉⣛⣝⢿⣿⣿⠟⠛⣃⣤⣴⣦⣴⣬⣟⣿⣿⠿⢷⣾⣿⣿⡿⠿⠟⡛⠿⠉⠈⢙⣛⣿⠿⠭
⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠂⠀⢫⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣮⠥⠼⠿⠟⠛⠉⠀⠠⠄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠚⠉⠛⣛⡛⠠⣬⠉⠉⠉⠛⠉⠛⠛⠛⠛⠛⠻⠇⠐⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠽⠯⠤⠔⠒⢦⡀
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢠⠇⣀⣠⣤⡤⠤⠤⠤⠤⣀⡇⠀⠀⠀⠀⢴⣤⣄
⠀⠀⢲⡀⠀⠀⢇⢣⠀⠀⢠⡾⠯⠤⠖⠚⠓⠒⠒⠚⠋⠉⠑⡄⠀⠀⠀⢸⠚⠿⣦⣤⣄⡀
⠀⠀⢸⡻⡄⠀⢸⠀⢣⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋⠉⠉⠉⠉⠉⠙⣆
⠀⠀⢸⡇⠘⡄⠈⡇⠀⢣⡀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⠀⠀⠘⣄⡇⠀⠀⢳⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡸⠀⠀⠀⠘⠃⠀⠀⠀⢳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⣄⡤⢀⣀⡀⣰⠁
⠀⠀⠧⠤⠤⣀⣀⠀⣀⣀⠀⠀⢳⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡿⡇⠀⠀⠈⠁⠀⣀⣠⣤⠶
⠀⠀⣀⣲⠒⠛⠲⠭⢥⣈⣟⠓⠢⢿⠉⡇⡏⠉⠙⠒⠒⠒⣤⠼⠤⠤⠴⠃⠓⠒⠒⠚⣉⠟⠉⠁
⠀⠈⠳⡄⠀⠀⠀⠀⠀⠉⠈⠉⠉⠒⠒⠃⡇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢠⠖⠉
⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡶⢲⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠉⠁⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠴⠂⢠⡤⢐⡺⡭⣭⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠸⠓⠲⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠⣤⣤⢶⣶⢄⠀⠀⠀⣤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⡾⠛⣿⣏⠳⣾⡥⠤⠾⠛⠓⣿⡶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⠃⢀⣠⠿⠒⠚⠉⠉⢻⠏⠀⠀⠀⠀⠀⠀⠀⣰⣦⡤⢶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡉⠀⡀⠛⡾⠋⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⣀⠀⠀⠀⣿⣿⠁⠀⢸⡇
⠀⠀⠀⡀⠀⠀⠀⠀⣾⣏⡉⣉⣤⡟⠀⢠⣦⠴⠶⢳⣶⣶⣜⣩⣭⣭⣿⣿⣶⣤⣹⣿⡄⠀⣼⡀
⠀⠀⠀⠈⠲⢤⡀⠀⢿⣿⣾⣿⠿⢇⣴⠯⠤⠴⠾⠛⠛⢿⣾⣿⠿⠟⠛⠛⠻⠿⣿⣿⡇⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠙⠢⣌⠻⡏⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⢧⣠⣦⣶⣦⣤⣀⡀⠀⣿⣷⣶⣦⣄⠀⠀⠁⣿⣿⣿⣶⣿⣿⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣽⣁⣀⣄⡀⣿⡿⣦⡉⠀⠈⢙⣿⠷⣦⡀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⢿⣿⣿⣿⣿⣧⣬⡙⠦⡄⠀⣿⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣯⢷⡿⢟⡛⠙⣿⣷⣯⣟⣿⢻⠶⠿⡷⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⣍⣻⣶⣿⣿⣿⣌⡿⢉⣿⡟⣷⣶⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢬⡘⢪⣿⡏⢉⠛⠻⡟⢻⣿⡿⢿⣿⣿⡿⢻⣿⠿⠟⢻⢿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⠈⠉⠁⠀⠀⠐⠃⠀⠉⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⡿⠟⠃⢰⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡛⠿⠚⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣿⠋⢹⣷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⠶⠦⣾⣤⣬⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠐⠶⢿⡀⠀⠀⠀⠀⠉⠁⠁⠉⠈⠙⠉⠛
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠈⠆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣀⣤⣴⣾⣷⣿⣿⣿⣯⣭⣧⡀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⠯⣥⣬⣿⣿⣛⣿⣟⣛⣿⣀⣀⡀⠀⠀⠂⠄⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⢆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠒⠶⠶⢶⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡚⢀⡀⢀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⡠⢔⡲⠚⣿⣿⠁⣉⣀⣈⣁⣿⣧⣤⠤⠤⠄⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠶⠿⠶⠒⠛⠛⢻⣿⠋⠉⠉⢀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⣿⣷⣲⣿⣿⣿⢦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⡦⣉⠲⢆⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡌⣿⡿⠿⢟⣛⣛⣻⣿⣌⠛⠋⢑⣤⠻⣯⣴⣾⠷⠶⠐⠖⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣋⣤⣶⣾⣿⣿⣿⣿⣿⣿⠉⠻⣦⣻⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣽⣿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⡏⠙⠿⣿⣧⡄⢛⢹⢿⣿⣿⡏⠀⢰⣿⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣖⣋⠀⠛⠻⢇⡈⠀⠀⠙⠿⢦⣶⣿⡿⠵⣾⣿⣆⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣛⣣⠀⠉⠉⠙⣿⠿⠿⠿⢶⣄⡀⠉⠛⠐⠃⣀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣦⣍⡛⠶⠦⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠉⠈⠀⠋⠓⠀⠀⢤⣉⠛⠛⢿⣦⣀⠀⠳⠿⠿⠿⠿⠗⠂
⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⣶⣦⣬⣤⣀⡀⠉⠛⠻⠶⠀⠀⠀⢠⣠⣶⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡿⠿⠟⠛⠛⠓⠢⠀⠉⠛⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠠⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠠⠒⠈⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣀⢴⡤⠴⠓⠀⠀⠀⠀⢸⠀⠀⣀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠤⠐⠛⠉⠀⠀⠀⢀⡀⡀⠀⣈⣺⠼⠓⠚⠉⠙⣦⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠀⠀⠀⠀⠀⠀⢀⡰⠍⠋⠁⠀⢈⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠉⠀⠀⠀⠀⠀⠀⢺⡇⠀⢈⣤⣤⣶⠶⠓⠒⠚⡂⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠿⠑⠛⠉⠁⠀⠀⠀⠀⠠⡄⣀⣠⣿⠇⠀⠋⠁⠀⠀⠀⠀⠀⠀⢰⣄⠀⠛⢧⣀⣀⣀⡀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣇⡯⠴⠾⣟⡋⠉⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠈⠉⠋⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡬⠉⢒⠈⠁⣥⠟⠷⠛⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⠾⡾⠿⢿⣀⣀⣀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠲⠶⠖⢒⡫⠈⠀⠀⠀⢸⡆⠀⡀⡴⢀⡄⠴⠒⠋⢹⡅⠹⣿⣤⣶⣾⣿⣿⣿⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠻⠈⠀⠀⢤⠀⠘⠀⠀⠀⠀⠀⠀⣷⠀⠀⡴⠛⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣫⣠⢴⣶⣶⣿⣿⣿⡿⢻⠿⠿⣿⣿⣿⣵⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣯⣼⣯⣤⣥⣾⣷⣖⡚⠻⢉⣑⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣭⣤⣤⣬⡁⠈⣿⣿⣿⣿⣦⡄
⠀⠀⠀⣶⣶⣤⣀⡀⠀⠀⠙⣶⣶⠒⢀⡤⣤⣶⣶⣶⣿⣿⣟⣛⣛⣛⠻⠿⠿⠟⠻⣂⣽⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣏
⠀⠀⠀⠈⠽⠟⠛⠿⢷⣶⣤⣬⣭⣶⠿⠿⠖⢸⡋⠋⠀⡉⣈⡉⠉⢉⣩⣄⣀⣴⣿⣿⣿⡿⣿⣿⣿⣿⠃⠟⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠁⠀⠀⠀⠓⠂⠈⠉⠁⠀⠈⠉⠉⠉⠉⠉⠈⠻⠛⠿⠛⢫⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢰⡎⠹⠶⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠛⠉⠉⠀⠀⠶⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⣀⣀⠀⠀⠀⣀⡠⣿⠆⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⣿⠍⠉⠀⣀⣪⡭⠐⠖⠛⠋⠹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠐⠋⠉⠹⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣦⣤⣤⣀⠀⠀⠀⠀⣂⡀⢤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⡶⢶⣄⢘⡿⠋⢉⣁⣿⣷⣟⣳⣤⣀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⣻⠟⠁⣀⣾⣷⣤⣬⣿⡟⠉⠉⠉⠁⠀⠀⠘⠻⠋⠀⡃⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⢻⣿⠁⢀⣀⢤⠞⠚⠋⠉⠁⠀⠈⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣯⡴⠶⢺⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⡁⠀⠀⠺⢗⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣄⢀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠟⡶⢞⠃⣠⡴⠃⠀⢸⣀⣀⣤⣤⣤⣤⣤⡀⢿⠿⠛⡿⠿⣿⣷⣦⣤⠀⠘⣿⣻⡇⠀⠀⢼⡇
⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⢸⣿⣯⣿⣴⣷⣟⣿⠁⠀⣠⡿⠟⠉⠙⣯⣿⣿⣿⡛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇⠀⠀⢿⡧
⠀⠀⠀⠀⠀⠈⠳⢤⣄⠀⠘⣿⣿⣽⣿⡶⠿⠿⣤⣼⠥⠶⠖⠒⠛⠛⠛⠛⠛⣿⣿⣿⡿⠛⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡈⠻⣿⠏⠀⠀⢠⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⣃⠀⠀⢸⠀⠀⣀⠀⣀⣄⠀⠀⠀⠀⠀⢸⣿⣇⣤⣀⡀⠀⠀⠀⠀⠆⢰⣿⣿⣿⣄⣤⣼⣿⣷⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⡈⢿⣶⡿⠿⠿⠿⠿⢶⣶⣄⡀⢸⡿⠿⠿⢿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣷⣾⣄⡀⣤⣤⡀⢐⣿⡟⢿⣦⡁⠀⠀⠀⢘⣿⡟⢿⣶⣄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣧⣀⡙⠻⣦⣀⠀⠀⣿⡇⠀⢻⣻⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣞⣋⣵⡿⣿⢟⡿⣿⣽⣟⣛⢿⡶⣶⣯⣶⣄⣿⣷⣤⣤⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠿⣿⡹⣿⠝⣳⣌⠀⢸⣿⣯⢿⡿⢶⣿⡤⣟⣉⣁⣛⣛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣶⡤⣽⣿⣿⣿⣿⣧⣷⣘⣟⠇⣸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣨⠐⠲⣜⣿⣾⠍⡓⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⡿⣿⠛⢿⣿⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠦⢶⠓⠒⠉⠉⠉⠄⠙⠀⠂⠒⠅⠀⠊⠉⠳⠌⠛⠛⠻⠗⠐⠚⢉⣃⠤⠄⠉⡒⠳⡯⠛⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠐⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣆⣠⣼⠁⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠨⠀⠜⣼⣿⠚⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢀⣾⠏⣿⡄⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠄⠠⠋⢀⣾⣿⠀⡇⣧⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠈⠀⢀⣾⣿⡏⠀⡇⢻⡀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠶⣀⠀⢀⢟⣿⠿⠇⠠⡇⠸⣗⠀⠀⠀⠀⠐⠀⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣤⣤⣤⣀⡇⣈⣻⡀⠀⢀⡀⠀⠀⣟⠒⠲⠶⠂
⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣶⡶⢒
⠀⠀⠀⠀⠈⠩⠵⠬⠉⣉⣩⠔⠶⣆⣠⠴⣄⡄⠀⣈⣭⣭⡿⢋⣀⣀⣈⣭⠉⣏⣁⠛⠁⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠀⠈⣑⣋⣩⠴⠦⠬⠤⠤⠈⠛⠋⠀⠀⠙⠲⠆⠀⠁

⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⠔⠒⠋⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠉⠀⠸⡄
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠐⠢⣄⠀⠀⠀⢠⣧⡄⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠈⠋⠙⠢⣀⢾⡿⠓⠀⠀⢹⡅⠀⠀⠀⠀⠀⢴⣆⣠⠤⠒⠛⠉⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢧⡀⠀⠀⠸⣧⠀⠤⠶⠖⠚⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⡌⠲⢄⠀⢸⡆⠀⠀⠀⠀⡄⢸⡆⠀⠀⠀⠀⠀⠀⡤⡴⠊⠁
⠀⠀⠀⠀⠐⠬⣿⣀⣠⣤⠀⠀⠀⣧⠀⠈⠳⡄⢷⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⠀⢀⢼
⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷⢰⣤⣾⣄⣤⢀⡇⢸⡆⠀⠀⠀⠀⠀⢸⡄⢀⣊⣡⢴⡵⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠁⢽⢏⣫⣉⣾⠑⣆⢱⡆⣀⠀⢀⡤⠖⣿⣛⣫⣵⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣶⡲⠶⠤⠼⢿⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣀⢀⠀⣠⣭⣸⣿⣟⣛⣿⣻⣿⣿⣭⣿⣏
⠀⠀⠀⠀⠀⠉⢋⣿⣿⡿⠍⢉⡩⢑⣶⢾⣺⣯⣽⣯⡻⣭⡽⠯⠷⣤⡠⠐⠲⠋
⠀⠀⠀⠀⠉⠛⠋⢉⣉⣽⡿⠟⠋⢁⢹⠖⠾⣒⣩⠟⡩⠭⠯⠭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒

⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢀⣠⣇⡀⢤⣤⣀⣀⣤⣤⣴⣿⣆⣰⡆⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠈⠙⢗⠢⢤⣀⠀⠀⠀⠀⠀⠀⠈⣟⢻⣺⡟⣿⠇⣻⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⡿⣿⣿⠿⣷⣾⡿⢦⣤⣶⣶⣦⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠙⠒⠤⣀⡀⠀⠀⠙⢿⣿⡟⠋⠘⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠓⠦⢄⣈⣿⠁⠀⠀⠀⣀⣴⣤⣤⣄⣦⠀⣾⣿⣶⣶⣿⣿⣿⣿⣿⠿⣿⣿⡃⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠠⢤⣀⡀⠀⠀⠈⣿⠲⠤⣄⡀⢸⣽⣷⣾⣭⠛⢴⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠿⠿⠟⠛⠛⠛⠻⠷⠶⠤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠙⠿⣖⠤⣿⡁⠀⠈⠉⠓⢻⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠳⣿⠀⠉⠑⢶⡤⢾⣿⡟⠿⡄⠀⠂
⠀⠀⠀⠀⠀⢶⣀⣠⣤⣄⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣿⢷⡄⠀⠈⠳⡄⠈⠻⡗⠦⣤⣀⡀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⣿⠀⢻⡄⠀⠀⠱⡀⠀⠹⡄⠈⢧⠙⣄⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⠀⠀⢿⡀⠀⠀⣧⠀⠀⣷⠀⠈⣇⠸⣆⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⡿⠻⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⡟⠀⠀⣿⠀⠀⣿⠀⢹⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣈⣘⡁⡖⠀⠀⠀⢀⠂⠠⠀⠀⠀⠀⣿⡀⠀⣾⠀⠀⣸⠃⠀⢰⡇⠀⢰⡇⠀⡸⠀⠀⠀⠀⠀⢀⣴⠎
⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⡀⠄⡎⣀⠡⠰⡖⠂⠀⣿⡇⡸⠃⡀⣴⡏⢸⡏⣡⡰⢁⡌⠀⣿⠁⠀⠀⠀⣠⡶⢋
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣥⣀⡆⢃⠀⠀⣿⡿⠃⠀⢀⣿⠇⢸⡇⢹⣇⠺⢡⠜⣡⣤⣶⣶⣿⡫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣿⣻⣿⣷⠂⠁⣿⡇⠀⢀⣼⣬⣤⣾⣧⣶⣿⣶⢿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣷⣻⣧⠀⣿⡇⠀⠻⣿⣻⣿⣿⣿⣷⣿⣽⣷⣷⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠆⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠸⠿⣿⣷⣿⣿⡻⠿⠷⠷⠿⠻⠿⢛⣻⡿⠿⣿⣿⣿⣿⣿⠏⠻⠟⠁⠠⠄⠀⠂⠒⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠛⠋⠈⠈⠛⠉⠈⠛⠀⠀⠀⠠⠋⠄⠒⠠⠤⠒⠀⠐⠐⠦⠀⠤⠂⠀⠀⠀⠀⠀⠀⠠⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡷⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠉⠀⠘⠻⠓⠒⠂⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠀⠀⡔⠁⠀⠀⠀⠀⢀⠀⢠⣄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠞⠀⢀⣤⣶⡷⢶⣿⣿⣿⠛⠻⢿⣦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡠⠃⢠⣴⠿⠥⠤⠄⠞⠻⠟⠋⠀⠀⠒⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠁⢀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⢀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡏⢠⡾⠁⠀⡄⢠⣀⣀⣀⡀⢀⡀⣀⡀⢧⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⡿⠁⢠⣧⣴⠟⠛⠛⣿⣿⣿⣿⠟⠻⡟⠿⢿⣯⣸⣶⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣷⡟⠀⠀⣼⡿⠤⠴⠦⠴⠿⠟⠛⠛⠃⠘⠛⠚⠛⢿⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⢱⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇⢰⡏⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢋⠛⣷⣦⣤⠤
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡘⢃⠈⡿⠀⠀⠀⠀⣸⣀⣤⣤⣤⣤⣴⣶⣶⣶⣾⣶⠶⣤⣀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠁⠀⠀⠀⠀⡿⠛⠉⠉⠋⢉⣽⣿⣿⣿⣿⣀⡀⢛⣛⠻⣷⣤⡀⠰
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠁⢸⡏⠀⠀⠀⠀⠀⡆⠀⠲⠤⠖⠛⠛⠛⠛⠛⠛⠋⠉⡹⠛⢛⣛⠉⢀⠀⢠⣦⡀
⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⠃⣾⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⣿⣷⣦⡾⠷⠦
⠀⠀⠈⠻⣀⠀⠀⠀⠀⢰⣼⣿⣧⣄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠁⠀⠀⠉⠀⠌⢠⠆
⠀⠀⠀⢀⣯⠀⠀⠀⠀⣸⣯⡉⢻⣿⣧⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡈⠀⠀⠃
⠀⠀⡠⠊⠙⣧⠀⠀⢀⡟⠁⠉⠂⠙⢮⡙⢷⡄⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠁⣄
⠀⢠⠀⠀⠀⠸⣇⠀⢸⠇⠀⠀⠀⠀⠈⠻⢆⠹⣮⡟⠙⢻⣿⣶⣶⣦⣤⣀⣀⠀⠀⠁⠀⠀⠀⠛⠷⠶⠦⡨⢶⣄
⠀⢈⠀⠀⠀⠀⠸⣆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠉⢴⣿⣿⣿⣿⣿⣛⠻⣦⣀⠀⠀⠀⢸⠗⣴⣤⣤⣄⣉⣡⡴⢦
⠀⠘⣄⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣾⣿⢿⣿⣿⣆⠉⢻⣾⣿⡗⠶⣄⠀⠀⠃⠀⠀⠀⠀⠉
⠀⠀⠘⣇⠀⢀⠎⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⠛⣿⡟⢻⣿⡆⢰⣄⠙⣿⣄⠀⠈⠀⠀⠀⢰⠁
⠀⠀⠀⠹⣠⣿⢠⡟⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣆⡀⠀⠀⣿⡇⠈⣿⡏⠀⢿⣦⡙⣉⣧⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠏⠈⠿⣀⣾⣿⣇⠀⠀⠀⠀⣀⣴⣿⣶⣦⣼⣁⠀⢰⣿⣷⠀⢸⣷⡀⢠⣼⠟⢹⣿⠷⣠⣆⠀⢸⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠀⠀⢰⣿⣿⡟⠠⠛⠛⠿⣷⣿⣿⣷⣀⣼⣿⣏⣸⣿⠀⢀⣿⡄⠘⣿⣧⡀⣝⡳⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⢸⡿⡿⣷⣶⣶⣤⣄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣀⣯⠙⢈⡙⠳⢄⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⣿⣾⣿⣷⣟⣠⠀⠀⠈⠉⠛⠻⣿⢗⣦⡆⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⡟⢨⠁⠀⢠⣤⣄⠀⢀⡀⠈⠙⠻⢿⣷⣦⣌⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢛⣿⡿⢀⠀⠀⠈⠉⠋⠀⢀⡼⠿⣦⣀⡄⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⡿⠛⢹⡿⠋⠰⣀⣠⣼⣧⡤⠯⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⢉⣿⣿⠀⠀⠀⢀⠄⠀⡸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠉⠁⠸⢿⣟⢃⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠛⢀⣀⠀⢀⣠⣤⠤⣀⣀⣀⣀⣀⣀⣴⣿⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣹⣿⣿⣿⡆⠀⢀⣰⠟⠙⠿⠿⢿⣿⣷⣿⡿⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣾⣿⣿⣿⠧⠔⢃⣽⣶⣶⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣿⣿⣿⣧⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢺⣷⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠒⠂⠉⠠⣀⡿⠿⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠁⠀⠠⠠⠀⠂⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢠⠨⠂⠀⠐⠀⣌⠐⡼⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⠋⠀⠀⠀⠀⠀⠐⠈⠀⡤⣦⣄⡀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⡒⠬⢑⠘⠁⠹⣿⣿⣟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣦⡀⢡⡈⠁⠀⠀⢠⠀⢀⠀⠙⢿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠀⢎⠉⠡⡀⢱⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠳⣄⠀⢑⢀⠉⢣⣈⡳⡀⢸⡶⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⢧⡀⠙⢇⡈⠉⣠⠌⠳⣸⠒⢸⡀⠀⠤⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠑⢄⠀⠉⠦⡀⠰⢶⠊⠣⡀⢑⢆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠙⢷⡀⠁⡀⠈⠻⣦⣀⣡⡤⠞⠀⠁⢕⢄⠀⠀⠈⠆⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣦⡈⠢⡀⠈⠉⠁⠀⠀⢀⠀⠀⢉⡳⢄⣀⠰⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠑⢢⠀⠀⠈⠻⣦⡈⠢⣀⠀⠀⠀⠈⠁⠀⣀⢁⣀⣦⠀⢸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⠐⠆⠀⠈⠀⠀⠀⠀⠈⠻⣦⣀⠉⠁⠲⣄⠀⠀⠈⠉⠁⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣷⣤⡐⠀⡙⠢⢈⠐⠚⠀⠀⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⢀⢄⡂⢥⣶⣤⡤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠉⠻⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠈⠀⠀⢠⣊⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠀⢀⢰⡇⠀⠈⠈⠑⠦⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣠⣿⣿⣇⠒⢶⢤⣄⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠛⢻⠿⡟⠀⢸⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡄⠀⠀⠀⠀⣸⣶⣷⠰⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⠀⣿⣿⣿⡀⢦⠉⠉⠁⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⣷⣷⣿⣀⣀⡀⢀⢠⣿⠿⢾⡇⢘⡆⠀⣀⣠⡴⠒⠋⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠓⠓⣒⣂⣿⠛⣛⣋⣧⣼⢧⣤⢸⣟⣀⣤⣷⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣔⣾⣛⣛⡀
⠀⠀⠀⠠⡤⠤⠤⢄⣿⢿⣿⣿⠿⣿⣿⠿⣿⣿⡟⣿⡟⢻⣯⣍⣿⣫⣿⠀⠠⠖⢒⡶⠆⢕⠛⠿⠛⠿⠯
⠀⣀⣝⢀⣐⣦⣭⣑⠒⠦⢽⣁⠴⢛⣁⡴⠿⢃⣉⣩⣤⣤⣿⣿⣿⣭⠥⠤⣼⣷⣬⣷⡄⠨⠭⠉⠛
⠀⠀⠀⠀⠀⠀⠤⠬⠽⠛⠛⠉⠍⠶⠤⢨⣍⠉⠉⣩⣤⠴⢾⣟⣩⡵⠖⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠊⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡰⣆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣂⡷⠀⢄⣀⣀⣀⠴⠉⣀⣤⣷⠞⠉⡫⣻⣧⣦⡀⠀⠀⠀⣀⣀⣀⠀⢴
⠀⠀⠀⠀⠀⡤⠤⠒⡢⠞⡁⠤⠸⡤⡗⡤⠀⠀⠚⠁⠁⢰⡿⢱⠁⡄⠀⠞⠉⠉⠉⠁⠀⠀⡁⢀⠁⡁⠀⠈
⠀⠀⠀⠀⠀⠀⡤⠞⡠⣋⡅⠶⠹⡴⡿⡄⠀⡠⠀⠀⠀⣗⣷⣸⣀⣄⣠⡈⢄⠀⠀⠀⠀⢸⠃⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⡀⢐⠋⠀⠉⢉⣁⣼⣽⣿⠟⣻⢶⣶⣤⣀⠈⢮⣏⣨⣬⣭⢯⠼⠷⡤⣤⣄⣈⡀⠀⠉⠁⠈⣿⡆⠀⠀⠀⠀⠀⣠⣴
⠀⢀⢀⠔⠊⠀⠀⢀⣴⠚⠟⢋⠿⢺⠁⡞⣵⠿⠟⠋⢛⡵⣾⠿⣿⠛⡇⡾⠀⢠⣾⠛⣙⣭⣿⢷⣦⠠⠃⣠⡖⠀⠀⢐⡲⣞⡽⠃
⠈⢦⠣⠄⠀⣀⣰⣿⡇⢠⠄⠉⠀⠁⠀⠉⠉⠂⢀⡴⣿⢱⠏⡈⠛⠞⠸⡗⣴⠏⢳⠆⢫⠉⠀⠘⠠⠀⠐⡙⠿⠀⠰⡡⠔⢠⠁
⠀⠈⠳⡐⠀⠸⣿⡥⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⡇⢺⠀⡇⠀⠀⠀⠀⠀⠀⠆⠀⠄⠡⡄⡀⠡⠀⡰⣃⢐⣷⠈⠀⢠⠃
⠀⠀⠀⡌⢌⢸⡟⣇⢷⡀⠄⠘⠀⠀⢀⠀⠀⠸⣾⢼⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣄⠴⣎⣠⡟⠻⢷⡀⣖⡶⡄
⠀⠀⠀⠐⡀⠢⡱⣿⣦⡳⣌⣦⣴⡦⣌⡀⠀⠀⣿⣶⣷⢸⡀⠀⠀⠀⠀⠀⢠⠀⢀⠀⣤⠖⡹⠚⢊⡼⡏⣿⡀⠿⣧⠋⠙⠇
⠀⠀⠀⠀⢠⣀⡑⣌⠻⣿⠃⣾⠃⡇⠘⣿⡖⠤⣽⢻⡸⣮⡷⢴⣶⣿⡟⢺⣤⣇⠀⢧⠈⠁⠀⠀⢸⣿⡇⣿⣷⣾⣿⡶⢾⣿⠟
⠀⠀⠀⠀⡮⠍⣟⣻⢫⠏⢿⡟⢖⣗⡶⣿⢧⣤⠘⢮⢿⡿⠁⡚⣯⣿⡇⢸⣿⡏⢹⣾⣷⣄⡀⢀⣿⠄⠠⠴⠆⠲⢿⣷⠿⠋
⠀⠀⠀⠀⠀⠁⠂⠀⢩⣭⣉⣉⣂⡚⠘⠃⠫⠌⠆⠈⠣⣽⣶⣻⣿⢹⣷⠀⣟⣇⣀⣘⣈⣿⡿⢶⣴⠧⠤⠥⠼⠾⣿⡁
⠀⠀⠀⠀⠀⠀⣠⡠⣍⣿⣿⣿⣿⣿⣿⣶⢠⣆⡖⡂⢲⠒⡟⢻⠛⡞⡟⢲⡟⢻⠰⠶⡆⠶⣶⠰⢶⡀⠶⣶⣾⣶⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⢻⡤⡄⠀⣀⣀⠀⠀⣀⣤⠀⣀⣀⠀⢀⣀⡀⢀⣀⣄⠀⣐⣄⢐⣿⣭⡏⡍⠀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⡤⡤⣤⣜⣛⣻⣿⣿⡿⠿⠷⠤⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠉⣀⣈⣉⣁⣀⣁⢀⢀⠀⠲⠶⠿⣿⠿⣿⠛⠙⠉⢯⠉⠛
⢘⡁⠀⠊⠎⠘⠐⠁⢈⡴⠠⡛⡛⠛⠿⣿⡿⠟⠶⠶⠶⣶⣶⡶⠶⠶⣶⠶⡶⢶⣶⣶⡶⢶⠶⠶⠶⣶⣿⡿⠿⠊⠁⢀⡄⠀⠄⠀⠎
⠈⠥⠀⠀⠀⠤⠤⠄⠈⠀⠀⠙⠀⠀⠀⠀⠁⠀⠈⣁⠢⢍⠉⠀⠀⠀⠐⠉⠀⠂⠀⠉⠁⠈⠁⠀⠠⠄⠒⠁⡀⢀⡀⠡⠤⠒⠁⠀⠜
⠀⠙⠛⠊⠉⠒⠒⠒⠒⠒⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠠⠤⠬⠭⠥⠤⠈⠥⠤⠀⠀⠀⠀⠂⠠⠀⠀⠤⠄⠀⠀⠠⠤⠤⠬⠭⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠴⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⠟⠻⠦⠀⠠⠏⠀⢠⠀⠀⠀⠐⠂⠋⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢰⠀⠉⠀⠚⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⡠⠀⠀⢀⣠⠂⠀⢀⠄⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢒⣋⠀⠀⣻⠻⢷⣷⣶⠚⠠⣮⡀⠠⣄⣤⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠙⣯⣻⡿⠤⣀⠈⠻⠀⠀⠀⠀⠀⠠⠙⠻⢷⡚⠿⠉⠂⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⢀⣾⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⡀⠈⢣⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣞⢻⣿⣿⣦⡾⣿⢁⡾⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠰⠄⠴⢄⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡛⣷⣯⣿⣿⣿⣿⣶⡞⠀⠀⠉⠈⣹⡇⣏⡁⠀⣀⣰⠋⢠⡄⢠⠄⠀⠀⠀⣸⠀⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⠛⢿⣿⣿⣿⢿⣴⣶⣶⣦⣿⣠⣿⣗⣾⣿⣿⣶⣾⣷⣿⢧⣄⢀⠀⣒⣛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣇⡒⠠⣬⡛⠁⠈⠛⠛⠻⠟⠉⠋⢉⣿⣿⣿⣹⣯⡉⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠩⠛⠋⠿⠊⠡⠍⠛⣿⠦⣤⣤⣀⣀⣀⣎⣀⣀⣀⣀⣀⣼⣨⣽⣾⣿⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠊⠚⠋⠹⠏⠉⠉⢩⡉⠉⠉⠉⢁⣉⠼⠳⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠅⠀⠙⠁⠀⢄⠁


⣀⠀⣀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡤⠞⣻⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣥⠤⠴⠶⠒⣲⠶⠤⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢡⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡽⠁⢠⠃⠀⡠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡜⠀⠀⡎⠠⢾⡶⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⡼⠀⠀⠀⠇⠠⠤⠤⣤⣤⣤⣤⣬⡿⠿⠷⢷⣶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⣝⠇⢰⠃⠀⡜⠉⠉⠓⠲⠤⠤⠒⠚⠉⢹⢇⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡤⠊⠐⠲⢄⠪⡏⠀⡆⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠇⢀⣀⣀⡀⠸⡄
⠀⠠⢤⡔⢁⠀⠀⠀⠀⠀⠙⣄⢸⠀⠀⡇⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣱⠏⠀⠉⠉⠙⠛⠒⠶⠤⣤⣀
⠀⠀⠀⠈⠓⢭⡁⠀⠀⠀⢀⠈⢿⠀⠀⡇⢀⠤⠶⠲⠤⣄⡀⠀⠀⠀⠸⣠⠏⠀⠀⣀⣀⣀⣀⣀⣀⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠈⠉⠐⠂⠰⠥⠤⠤⠤⠤⠤⠭⠷⠶⠤⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠂⠀⠀⠀⠀⠀⠙⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠴⢤⠈⣇⠀⠀⠀⠀⠀⢀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣦⡧⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢰⢰⢸⣀⣿⣤⣤⣤⣬⠥⠤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⡿⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣤⠤⠶⠶⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠤⠤⠠⠤⠤⠔⠒⠒⠋⠉⠩⡥⠤⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠈⠉
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠌⠛⠛⠉⢳⠀⠀⠀⡇⠀⠀⠀⠀⣀⣠⢤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠤⠓⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠒⠊⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⢀⣀⣂⠀⠀⣴⣶⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣠⣤⣶⣶⠟⠛⢻⡏⠉⢩⣄⣠⡤⠄⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⢛⢀⣸⣤⣬⣼⡿⡿⢿⢿⡁⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠶⠚⠛⡫⠟⠛⠋⠁⠰⠁⣼⡄⡑⡀⢀⣠⣤⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠃⠀⠘⠟⠛⣛⢛⣿⠾⠷⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣠⣤⣶⣶⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠘⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣛⡃⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠲⣿⠿⠿⢿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⠀⠀⡀⠀⠘⠀⠀⠉⠉⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠩⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⡀⠀⠀⠀⢀⡇⠀⠀⠀⣄⡞⢀⣤⣄⣀⣀⣀⡐⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⢀⣾⡇⠀⡀⠀⠙⠓⢲⣶⡤⠬⠝⠻⣿⣿⣆⠈⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣧⠃⠀⡇⠀⢈⣯⣿⡇⢰⣇⢀⠀⠀⠺⣿⣿⣦⡀⠀⠀⠀⠉⠉⣡⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢸⢻⣇⠀⠃⠀⠌⣿⣿⣇⠀⠀⠘⣿⣿⣇⠛⠛⠻⠿⢦⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⢺⡈⠸⣿⡄⢀⠀⠀⣿⣿⣿⢠⠀⠀⢹⣿⣿⣆⠀⠀⡠⣨⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢑⠂⠸⠷⡀⢻⣷⡘⡀⠀⣿⣿⣿⣿⣖⠒⠒⢻⣿⣿⠗⣡⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡄⠛⠛⠿⠷⣦⠶⠿⢟⣋⡉⠙⠀⢈⣿⡿⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡸⣷⣖⣚⣛⣶⣿⠿⠟⠋⠁⡀⠄⠐⠉⣀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⣴⡞⠁⠀⠀⠀⠀⠹⠀⠾⢿⡧⠀⠔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠿⠿⠿⠛⠋⣙⠿⢿⣿⣿⣂⠀⢤⠈⠛⠀⠁⡀⠀⠀⠐⠉⣉⣉⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠱⠚⠛⠛⠁⠻⠷⠆⠀⢠⣤⢶⣶⣶⠖⡒⢲⣿⣿⣿⠿⣿⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠟⠁⠈⠀⠛⠛⠑⠂⠊⠁