Subway Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⡠⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⠀⠈⠉⠑⠒⠤⡀
⠀⠀⣀⡈⠂⢀⡆⡀⣠⠇⢀⣀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠈⠉⠉⠁⡤⠄⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣀⠉⠑⠄⡃⣀⡀⠂⠀⠄⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠀⠀⢀⠀⠀⠀⡠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢰⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠄⣀⡠⠒⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⠁⠀⠀⠂⡠⠴⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠂⠀⠀⠠⠀⡔⠁⠀⠀⠀⣰⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠈⠻⣤⠈⢧⡉⠀⢀⠀⠀⣰⠀⠀⠀⢀⡾⢁⡴⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠂⢁⠀⠀⢀⣀⠀⠈⢷⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⡾⢀⠏⠀⠀⠀⠀⠀⠀⠓⢄⣀⢐⣀
⠀⠀⢀⡀⠀⠀⠀⠠⠐⠀⠈⠀⠀⠀⣀⣠⡷⣾⣿⣿⠿⠿⣿⣿⣷⣾⣷⣯⡀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⢀
⠀⢀⡈⠉⠙⠠⡀⠀⠀⠀⠀⢀⣰⡾⠋⣡⡾⠟⢁⣴⣾⢿⡯⠟⠁⣠⣼⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⢷⣦⡀⠈⢢⡀⠀⣠⣿⠋⠀⣾⠟⠀⣴⡟⠿⢲⣿⣿⣶⣾⣿⣿⣿⢿⣿⣻⡗⡄⠀⠀⠀⣀⠉⠓⠢
⠀⠀⠀⠀⢹⡏⠄⠀⠈⠉⣿⣧⢠⣰⣏⠠⢼⣾⣿⢶⡟⠀⠲⠘⠛⢿⠷⢿⣿⣿⣿⣿⢸⠀⠠⠊
⠀⠀⠀⢄⠈⢹⢸⠀⢀⡹⠏⠉⠀⠀⠀⠘⢚⣿⣋⢽⡇⠀⢚⢠⠄⠊⣿⣿⣿⣿⣿⡿⣼⢠⠁
⠀⠀⠐⠦⣈⢻⣾⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣡⣵⣿⣿⣞⣀⣤⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣾⣿⡿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⢿⣿⣿⡿⢿⣮⡻⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡛⠩⣴⡾⠟⣩⡾⢃⣬⢛⠿⣿⠷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠙⠓⠮⣤⡻⠋⠠⠛⠁⠾⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⡴⠀⠒⠶⣶⠶⣶⠶⠲⣶⡶⠶⠿⡿⠂⠀⡠⠐
⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⢄⠀⠈⠀⣤⣄⣄⣀⣤⣤⣤⣤⣤⣤⣤⣦⣤⠂⠁⠔⠁
⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠘⣦⠀⠀⠑⠂⣈⢉⣀⣀⡀⣀⣐⣒⡀⠐⡡⠂⠀⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⢀⣀⡀⠀⠀⠀⣀⣭⣧⡀⠀⢩⣭⣭⣭⣭⣽⠵⢶⣾⠥⠊⠀⠀⠘⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⡄⣤⠤⢤⣬⣍⣶⣶⣿⣷⣶⣽⠒⠂⡀⡀⠀⢶⡀⠠⠀⠀⣶⣄⠤⡀⠀⢀⢄⠀⠀⡇
⠀⠀⠀⣶⡶⠐⠓⠛⠉⠉⠉⠁⠁⡀⢰⣊⠭⣧⠖⣿⣻⣯⣿⣿⣧⠀⣴⡐⢨⡘⠞⣇⢳⡧⣄⣛⣼⡘⢷⠀⠘⡌⣇⠀⠁
⠀⠀⠈⡾⠀⢀⡶⣢⣶⢖⡂⠀⠸⣹⣇⢗⣰⣿⣿⣿⣿⢿⣷⠋⠀⣀⡾⢃⠀⢉⡾⠁⢄⡙⣆⣏⡿⠁⠰⢱⠔⡙⠙⡄
⠀⠀⢐⣟⠀⠸⠛⠉⠔⣩⠃⠀⠄⣹⣿⠸⠾⣻⢉⣷⢻⠟⢡⡆⠀⠙⠃⢀⠔⢣⡿⢀⡉⠪⢽⡅⠅⢬⠀⠐⡇⠀⠀⣇
⠀⠀⢨⣿⡟⡟⠓⠛⠛⠚⠂⢠⠶⣿⠈⠆⢠⢽⢏⡽⠋⠐⠋⠁⠀⠛⢀⣣⠤⠿⠷⢤⣤⢾⣏⠘⠤⣧⣤⡾⣱⣤⣶⡯⣄
⠀⠀⠘⡯⠉⣁⡀⠀⠀⢀⠀⠈⡛⣋⣴⠀⢛⣴⠞⠁⠀⠀⠀⢀⠒⠭⠈⣷⠒⠒⠚⣺⠖⢓⠛⠀⠐⣻⣿⣧⣿⣿⣿⣧⡀
⠀⠀⠀⣿⠀⠀⢀⣤⢤⣤⠀⢰⠀⣿⠘⣠⠞⢁⣠⣶⠀⠀⠀⠀⠀⠀⠀⠸⠉⢙⡇⢹⣿⣻⢀⠀⠀⠫⡹⣇⠉⠉⠉⠉⠁
⠠⠐⠈⣿⣤⣍⣘⣳⣾⣃⣀⣂⣂⣿⡾⠋⠐⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⢨⣮⠹⡏⠉⠉⠉⠉⠀⠹⠼⠷⠞
⠀⠐⠉⠙⣽⠟⠛⠉⠀⠉⡻⣋⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢘⡿⣐⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⢸⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢸⣿⠁⢹⠉⢹⣿⠉⠉⠉⢹⣿⣿⠉⢩⠉⢹⣿⠉⠉⠉⢹⣿⣿⠁⠉⠉⣻⣿⠉⠉⠉⢹⣿⣿⠉⠉⠉⣿⣿⡏⠉⢻⣿⣿⡆
⠀⠀⠀⠀⢸⣿⠀⢸⠀⢸⣿⡀⠀⠀⢸⣿⣿⠀⢸⠀⢸⣿⠀⠀⠀⢸⣿⣿⠀⢈⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢻⣿⣷
⠀⠀⠀⠀⢸⣿⣦⣾⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⣾⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⣿⣿⣷⣄⣀⣠⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠘⠛⠛⢿⠟⠿⠿⠻⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠛⠿⠟⢻⡟⠛⠛











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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⢀⣠⣤⣴⣶⣢⡤⠶⠶⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⣈⠀⠤⢤⠄⠴⢿⣿⡿⡿⠋⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣯⣶⣿⣿⣿⣿⣿⣿⣿⣟⡞⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡼⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢏⣾⣿⣿⣿⣿⣿⣿⣿⡿⣽⣹⡇⠀⠀⣾⣿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠟⠟⠛⠛⠛⠉⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣇⣾⣿⣿⣿⠿⠟⠛⠉⣡⣴⢧⣿⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⡶⠾⢿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⣶⡶⠃⠀⢀⣠⡴⠚⢁⣾⡘⡌⠀⠀⢰⠇⢀⣴⣶⣾⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠁⣀⡀⢀⠼⠀⠀⠉
⠀⠀⠀⠀⠀⢠⠢⠈⢀⣼⣟⣁⣠⠴⠞⠋⠁⠀⣠⠎⠙⠋⡶⠀⢠⠋⢠⣿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠿⠛⠁
⠀⠀⠀⠀⠀⢸⡆⠀⠀⡟⠁⠀⠀⠀⠀⠀⣠⣾⠡⠷⣀⠀⠀⠐⠁⢠⡟⠁⣀⣀⣤⣤⣶⣾⡟⠀⠀⠀⠀⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠘⡗⢀⡀⠀⠀⠀⣀⣤⠶⠯⠝⠛⠂⠀⠀⣀⣠⡤⠶⠋⢀⣿⣿⣿⢿⣿⡿⠁⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⡟⠤⣉⣉⣉⣁⣀⣀⣀⡠⠤⠔⠒⠚⠉⠉⠀⢀⣘⠤⠚⣻⠿⠛⢉⣡⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⢲⣤⣤⣤⣤⢀⣀⣠⣤⣄⣠⣤⣴⣶⣶⣿⠟⠋⠀⢀⣠⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣋⣤⡶⠟⠋⠁
⠀⠀⣀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠁
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠄⠐

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⣾⣿⠉⢱⠉⣿⣿⠉⠉⠉⢽⣿⡈⢁⠈⢹⣿⡏⠉⠉⢹⣿⡏⠉⠌⠁⣾⡯⠉⠉⠉⣿⣿⠉⠈⠉⢸⡇⠉⠓⠄
⠀⠀⠀⠀⣿⣿⠀⢸⠀⣿⣿⡀⠀⡀⣸⣿⠀⠀⠀⢸⣿⡇⠀⢀⣸⣿⡇⠀⠀⠀⣿⣇⢀⡀⣀⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣽⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣧⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠛⠛⠛⠛⠺⠗⠚⠛⠛⠸⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠘⠛⠛⠘⠿⠙⠛⠛⠛⠓










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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣤⠄⠤⠴⠤⠴⠒⠒⠒⠢⢀⡀⡀⡀⣀⣀⣀⣺⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠉⠉⢩⠉⠁⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣁⠀⠤⠐⠀⠒⠒⡢⠤⠄⠥⠤⠀⢀⣈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠈⠉⣭⣉⠓⠒⠒⠒⠢⠤⠤⠤⠽⢃⣤⣔⣃⠉⠙⠲⡖⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠄⠪⠀⠤⠀⡶⢓⢤⢲⡶⣶⡴⡹⢷⠀⡠⠀⠤⢀⠀⠈⠡⠄⠐⠆⠚⠧⠘⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢁⡐⠂⢡⡼⡶⢀⠁⡀⠘⠟⣘⣄⠐⠀⠘⠡⡅⠀⡏⠀⡔⠾⣟⠖⠧⠀⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣺⠘⣰⢠⠇⠛⠛⡄⠀⠁⠒⠀⠆⠀⠃⢠⡞⠧⢿⣈⡃⢀⡀⣠
⠀⠀⠀⠀⣍⠀⠀⠄⠐⠒⠂⠤⠀⣄⣀⣀⣘⠛⠤⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠉⠉⠀⢘⣻⡤⡄
⠀⠀⠀⠀⢯⡆⢂⠘⠀⠒⠠⠄⢀⠀⠀⠉⠉⠛⠒⠲⠤⠤⠁⠀⠀⠀⠀⠄⠀⠀⠂⢆⠙⠙⠀⠐⣲⣾⣿⣿⡤⠤⠀⣀⣈⣁⠈⠁⠒⠒
⠀⠀⠀⠤⠼⢀⡬⡦⢔⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⡀⠀⠈⠉⠐⠒⠀⠤⠀⡀⣸⣉⣩⣄⣻⣍⣭⣭⣉⣉⣉⣁⢠⣤⣄⣉⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠐⠀⠄⠀⢀⠀⠀⠀⠉⠉⠘⠛⠒⠶⠶⢶⡤⣌⡀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠭⠭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⢒⠏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣤⠤⠼⠛⠋⠉⢀⡤⠞⠱⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣶⣤⠤⠴⠒⠋⠙⠁⠁⠀⠂⢀⠀⠀⢠⠔⠁⠀⡼⠁⠸
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⠤⠄⠒⣊⠩⠅⠒⠈⠀⠀⠀⠀⠀⠐⡀⢀⠄⣀⠜⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠘⠋⠁⠉⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠢⠀⣠⠞⠁⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠐⠂⢤⠀⠀⣄⠂⡀⡆⠸⠊⡆⠈⣴⠞⠡⠀⠀⠀⢀⢞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⣴⢃⠁⠘⠀⡡⠚⡡⠀⠀⠀⠀⢀⠎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣠⡄⠀⡇⠂⢠⠸⢈⣤⡤⠊⠀⠈⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠉⠉⢉⣀⣾⡇⠀⠀⣶⡿⠋⢀⠔⠁⠀⠀⠀⠀⢀⠎⡜
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠳⢤⣄⣀⡀⣡⡀⠧⢐⡼⠋⢀⡔⠅⡀⠀⠀⠀⠀⢀⡎⡘
⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠈⠁⠈⠁⢀⡴⠋⢀⠴⠁⢀⠀⠀⠀⠀⠀⢀⡞⠰⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠏⠀⠀⠁⠀⠀⠀⠀⢀⠞⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⡠⠊⠀⠀⠊⠀⠀⠀⠀⠀⢀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠎⠀⠀⠔⠁⠀⠀⠀⠀⠀⢀⠎⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠎⢀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢄⠀⠀⠀⡄⠀⠐⢂⠀⠄⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠂⠒⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠂⢉
⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠀⠤⠐⢂⠉⠀⠤⠄⠒⠈⠉
⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠶⠖⠒⠶⣶⣦⣤⣤⣖⣈⠉⠀⣤⠀⠀⣈⣐⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡠⠔⣊⣥⠴⠚⣉⢩⣴⠲⣍⠉⠙⢿⣿⣦⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣶⠉⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠂⠁⣈⠩⠅⠂⠘⠁⠀⢰⠉⣄⠈⢳⣄⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠴⠶⠒
⠀⠀⠀⠀⠀⣧⠐⠀⠀⠀⠀⠀⡠⠰⣾⡿⠿⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣷⡄⠙⢷⣄⠙⣿⣿⣿⣄⠀⠀⠀⠀⠈⢿⣿⣿⣯⡻⣿⣆
⠒⠀⠀⠀⠀⡗⠒⠒⠒⠒⣶⠥⠖⠨⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣦⡈⠻⣷⡜⢿⣿⣿⣧⡀⠀⠀⠀⠀⠻⣿⣿⣷⡌⢿⡀⠠⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⢠⣤⠈⣿⣿⣿⣆⠘⢿⣎⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⣿⣿⣿⣆⢇
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⢹⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄
⠘⡀⠀⠀⠀⡟⠀⠁⠰⣆⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠘⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣷
⠀⠆⠀⠀⠀⡗⠀⠀⠀⠘⢧⡀⠙⠻⣗⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⡆
⠀⡉⠀⠈⠀⡗⠀⠀⠀⠀⠀⠻⣄⠀⠈⠛⢮⣓⢦⣀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⢨⢍⡙⠛⠛⠻⠆⠠⠿⠿⠿⠿⠷⠄⠠⠀⠀⠂⢉⡉⠤⢧
⠀⠄⠀⠠⠄⡇⠀⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⠙⠳⣬⡛⢦⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⢀⡠⢸⠓⠂
⣾⡭⢤⠬⠤⠇⠀⠀⠀⠀⠀⠀⠀⠈⢊⢂⠀⠀⠀⠈⠛⢶⣌⠛⢦⣄⠐⡇⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡑⡄⠀⠀⠀⠀⠙⠻⣦⣈⠙⣧⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⢢⠀⠀⠀⠀⠀⠈⠛⢷⣬⡚⠗⡤⣀⢸⣗⡶⣒⠖⢒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠖⠶⠲⠶⠶⠲⠖⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠑⡄⠀⠀⠀⠀⠀⠀⠙⠻⣶⣼⣦⣉⠛⠛⠿⠟⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠻⠟⠛⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠢⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣯⣙⠲⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣑⠘⠠⠤⠄⠀⠀⠀⠀⠀⠤⠄⠂⣴⣤⣉⠒⠤⢀⡀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡛⢟⠛⠶⣶⣶⣶⣶⣶⣶⣶⣿⣿⢟⠛⠿⣿⣶⣤⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣅⠢⡈⠙⠶⡐⠀⠀⠐⠂⠘⠒⠭⠒⠄⡉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡑⢄⡈⠑⠆⡀⠀⠀⠀⠀⠈⠓⠂⢅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠂⢄⠈⠲⢦⠀⠀⠂⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠤⠤⠤⠤⠤⠤⠘⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠘⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠘⠠⠤⠤⠤⠤⠤
⣶⣶⣶⣶⣶⡆⢸⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣶⡶⠶⠶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⣶⣶⣶⣶
⣿⠁⠀⠀⢹⡇⢸⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠁⠀⠀⢹
⣿⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⢸
⣿⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⢸
⣿⠀⠀⠀⢸⡇⢸⠰⠆⠀⠠⠆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⢸
⣿⣦⣀⣀⣼⡇⢸⠄⠀⠰⠦⠰⠆⠀⠄⠀⠀⠀⠀⠠⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⣼⠀⣿⣄⣀⣠⣾
⣿⠉⣿⣿⣿⡇⢸⠀⢰⣶⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡏⣹
⣿⣿⣿⣿⣿⡇⢸⠦⢸⣿⠉⠉⢻⣿⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⢾⠀⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠁⢸⠀⠈⠉⠀⠀⠈⠹⠇⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠤⠤⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⡠⠤⠤⠤⠤⠤⠀⢰⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠋⣝⣇
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⢠⡄⠀⡄⠄
⠀⠀⠀⠀⣤⣤⠯⠤⠵⠤⠀⠀⠀⠐⠛⠛⠛⠳⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠾⠸⠧⠰⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠤⠶⠒⠒⠚⠶⠶⠄⠀⡴⠀⠀⠀⠀⢰⠀⠀⢰⣶⣿⡄⣄⡼⢴⠀⠀⠀⠀⠀⠀⠁⠐⢷⡾⠇⠂⠀⠛⠒⠚⡃⠀⢤⡤⠤⡤⠤⠠⣤⣤⣤⠍⡋⠁
⠀⠀⠀⠓⠂⠓⠒⠒⠒⠃⠀⠰⠃⠀⠀⠀⠀⢸⢂⡄⣸⡛⣿⠃⠛⠿⠬⠂⠀⣀⢀⠀⠀⠀⠀⡱⣣⡜⡇⢰⠚⡞⠞⢱⢠⣾⠿⠿⠛⢛⠃⠀⠀⠀⠓⠓⢠
⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠰⣯⢹⣿⠀⠀⠠⠐⡒⣖⢒⠢⡆⢴⠬⡇⣿⡇⠛⠀⠇⢹⡇⡟⠿⢾⠘⠋⠂⠀⣒⢐⠀⠀⠀⢀⡀⢠⡞
⠀⠀⠀⡇⢀⡿⢀⣂⣤⣤⢀⣼⣸⣤⡔⠚⢁⣘⡀⢻⡸⣿⠀⠀⠀⠘⡏⣻⠛⠟⠟⠻⠛⡃⠻⣇⡠⠀⠴⠤⠶⠗⠚⡛⠃⠀⠀⠀⣷⣼⣆⣶⢲⢲⣖⣶⠂
⠀⣤⣼⣿⣷⢾⣿⠿⠟⡄⡄⠔⠞⠛⠛⠗⠒⡝⢻⡿⠄⠨⢀⣀⣚⣻⣩⠉⠈⠁⠹⠈⠁⠇⠀⢀⠋⠓⠒⠒⠒⠘⠛⡥⢖⢠⣀⣺⡅⠈⠀⠩⠰⣤⠦⠶⠂
⠀⠧⠃⠽⠷⠶⠶⢲⡖⠶⠲⠂⠒⠒⡂⠀⠊⠛⢃⣠⣆⣘⡇⠀⠀⣛⡓⡚⣁⠀⠀⢀⠀⠠⡤⠀⠅⠀⠀⠀⠘⠒⠒⠒⠘⠀⠀⣀⣀⠠⠤⢶⠦⠤⠐⠐
⠀⠉⠈⠈⠉⠉⠁⠀⠁⠁⠬⠥⠤⢤⣍⣺⠐⠀⣻⠀⠀⠀⡄⠀⠀⡡⡗⠄⢟⠸⡏⡸⠄⣀⠐⠒⡆⠀⠐⠠⠀⠄⠄⠄⠠⡟⠛⠿⡗⠖⠒⣥⣤⣤⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠠⠭⠈⢀⠉⡀⠀⡀⠐⠂⠀⠂⠋⢲⣾⠬⠁⠀⠀⠀⠙⡋⡷⠀⠠⢠⠦⣆⣆⠀⠰⡗⠀⠂⡀⠀⠠⠶⣶⠶⠶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠⠇⠀⠂⠹⢶⠛⢋⠀⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠠⡄⠀⠐⠊⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡆⠀⠀⠀⠀⠀⠀⢤⣤⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⢀⡎⠀⠀⠈⠛⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠒⠦⠔⠒⠉⠁⠀⢈⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠼⠆⠀⠀⠀⠀⡜⣡⡀⠀⠀⠘⢦⣤⣤⠤⠤⠤⠤⣀⠀⢀⣀⣀⣀⣀⠔⠁⠀⠀⠀⠀⠤⠶⢤⠤⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠢⢀⡀⡀⠀⠀⠀⢸⣎⣠⡷⠀⠀⠀⠐⢇⠹⠖⢒⠒⠒⠲⠟⠷⡄⢀⠤⣤⢤⠀⡄⠀⣀⣸⣀⡀⠀⠀⠀⠀⠀⠓⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠀⠈⠃⠺⣁⠀⠀⠀⢰⢸⢠⠘⠛⡃⠀⠃⠇⢰⠀⣿⡶⠝⠛⠊⢠⡭⠤⠄⠐⠞⢷⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣴⠖⠈⠉⠹⠉⠉⠹⣗⠛⠘⠂⣶⠼⢴⣇⠗⠒⠒⢦⣼⡀⣏⡏⡍⡇⢸⠑⠉⠉⠑⠒⠒⠁
⠀⠀⠀⠀⠀⠀⢠⣊⣉⣉⡉⡯⠤⠤⠀⠶⠒⠒⠒⠒⠒⠒⠒⠒⢺⠋⠓⡟⢉⡑⣒⡒⢒⠒⡎⡠⢤⢸⢃⠀⣗⣇⣸⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠛⠓⠒⠒⠒⢲⢸⢳⢘⠉⡇⣎⠣⠀⣇⣁⣛⣇⣸⡧⣧⣇⣯⠅⡇⢧⡸⢸⢩⡥⠁⠀⠀⠀⠀⡷⠒⢦⡀
⠀⠀⠀⠀⡐⠉⠉⢺⠉⡤⣔⢲⠶⡖⢲⣺⢨⢩⠠⠭⡅⡼⠳⡄⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆⡇⠀⠀⢸⠴⢄⡀⠀⢀⣀⡀⢱⠀⡌⢳
⠀⠀⠀⠀⢱⠀⠀⠘⡀⡇⠸⢸⠀⡇⠈⣷⢨⣸⢠⠠⠇⠧⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⣀⣤⣚⡳⠲⣌⠀⣭⠤⠤⠭⣴⠁⢸
⠀⠀⠀⡔⠁⠀⠀⠀⣇⢓⣚⡀⠓⠃⠀⣿⢰⠒⢰⣒⢰⠒⡆⢰⢒⡒⢒⠒⣒⠒⣒⠒⢒⢚⡟⠀⠀⠀⠙⢤⠀⢭⡇⣞⡲⣎⢿⠀⢸
⠀⠀⠀⠳⠤⢄⠀⠀⢸⠘⡄⣥⣏⣉⡆⣿⠸⠤⠀⠚⠈⣒⣃⢸⢩⡹⡏⡧⣇⣿⣉⠇⢘⢸⢇⠀⠀⠀⠀⠘⡄⢠⢓⡨⠝⠓⠾⢄⣸⡀
⠀⠀⠀⠀⠀⠀⠳⣤⠼⡇⠧⠼⠹⠤⠇⡇⡶⣋⡉⠥⠭⠤⠜⠘⠠⢤⡼⢢⡠⢢⡠⢦⣸⢾⠶⢷⢦⠶⠚⠯⢔⡋⢁⣀⣀⣀⡀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢃⠀⡶⢲⡄⠀⡇⠇⡖⠒⡦⡖⠲⠄⡇⠒⠊⠙⠊⠉⠈⠙⠂⠟⠚⠀⠘⣇⠀⠀⠀⠀⣿⠤⠤⠤⠤⠤⠤⠭⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠀⢰⢸⡇⠀⠃⠂⠙⠒⠃⡇⢸⠀⡇⡠⣠⠊⠉⢦⡤⡤⡤⡤⡄⠀⠀⢮⣀⢀⠴⡆⢹⣒⣒⣒⣒⣒⣒⣒⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⣘⡼⠧⠤⠆⠄⠀⠀⠀⠁⠈⠀⠛⠀⠀⠀⠀⠸⠇⠇⠄⠂⠡⠀⠦⠠⠘⠀⠀⠃⠘⠃⠤⠤⠤⠤⠤⠠⠜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢘⣿⠀⠀⣠⣿⣤⣤⣤⡄⠀⠀⠀⣼⡇⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣸⠇⣀⠀⢹⡏⠀⠀⠉⠁⠀⠀⠀⣿⡇⠀⣠⠀⠀⣿⡶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠐⠋⢠⡟⢀⣿⠀⢰⡟⠀⠀⢻⣇⠀⣿⡇⠀⣿⠀⠀⣿⠀⢀⣴⠞⢛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢠⡶⣾⠃⣼⠇⠀⠹⣧⣤⡴⠟⣿⠀⢽⡇⠀⣿⡄⠀⣿⣄⣿⠛⠛⠛⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢠⡾⠁⠋⢰⡟⠀⠀⢀⣨⡅⠀⠀⣿⠀⢸⡇⠀⢙⣁⣠⣬⡼⣿⣄⣀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣀⣴⠟⠀⠀⠀⣾⢁⣠⡶⠟⠉⠀⣠⡾⠃⠀⢸⣷⠞⠛⠉⠉⠁⠀⠈⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠁⠀⠀⠀⠀⠛⠛⠉⠸⢷⠶⠞⠋⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠑
⠀⠀⠀⠀⠐⢶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠊⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣠⠄⡀⠀⡾⢹⣿⣿⢻⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠊⠁⠀⠇⠘⣟⣾⣻⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠓⠒⠀⠀⠀⠀⠀⣟⣿⣻⡗⠀⠀⠀⢛⠀⠛⠛⡟⢿⣻⡗⢺⠆⣷⠓⡇
⡟⡗⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢙⠀⠁⢈⡇⠉⢘⡃⢸⠀⡋⠀⡇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡏⠬⢡⠄⠀⣿⣿⣿⡇⠀⠀⠀⢨⠀⡴⢄⠀⢸⠀⠅⢸⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⣤⡆⠀⢲⣶⠂⠀⠀⠀⠀⣟⣿⣻⡇⠀⠀⠀⢸⠀⣿⢋⣃⣻⡇⠆⢰⠀⠀⠀⡆
⠀⠠⠄⠤⠀⠀⠶⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣲⣶⣾⡇⣶⠰⠶⠶⠀⠀⠀⠀⣯⣿⣯⡇⠀⠀⠀⢐⢀⢶⣿⣿⡐⠳⢂⢰⠀⠂⠀⡇
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣼⣿⣿⡧⣿⡆⠀⠀⠀⠀⠆⠀⣿⣿⣿⡇⠀⠀⠀⢸⣸⡞⠓⢹⡇⠅⢸⢻⠀⣁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣈⣽⣛⡇⢿⡗⡆⠀⠀⠀⠁⠀⣿⣿⣿⡇⠀⠀⠀⢨⣸⣇⠤⣀⠁⠂⠨⢸⠀⠄⠀⡇
⠀⠀⠀⠀⠀⢀⣠⣤⢴⣲⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⡛⢙⣏⡇⢼⣿⣙⡆⠀⠀⠄⠀⣯⠿⣽⡇⠀⠀⠀⠸⠸⠽⠀⠈⠂⢰⠎⠸⠀⠤⠀⠇
⢠⢠⡖⢲⡅⠘⠛⠉⠀⠂⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠿⣿⡿⠿⠃⢾⡟⢻⢸⣆⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⢀⠸⠀⠀⢰⣥
⡇⠐⠃⠉⠁⠐⢶⣶⣴⣤⣤⣤⠀⠀⢠⠴⠂⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠀⠀⠘⠘⣿⠄⠸⡏⣦⠀⠈⣿⣿⣿⡇
⠈⢀⠀⠀⠀⠀⠀⠉⢿⣛⠩⠇⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡄⢡⣧⠸⡇⣿⠂⠐⣿⣿⣿⡇⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⣀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⣀⠀⠀⢰⠂⢀⣠⣴⢶⣿⣭⣿⠀⠀⠀⠠⠘⣼⢆⠃⢿⠀⠘⣷⣟⡾⡧⠀⢸⡇⠀⢠⣿⣿⡷⣿⣿⣾⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠠⠀⠓⠲⠤⠀⠀⠀⠈⠁⠀⠀⠀⠹⢭⢭⠽⢭⡟⣭⡍⣯⠀⠀⠀⢀⠀⢹⢹⡇⢸⠀⠐⣿⣿⣷⡇⠀⢸⡇⠸⠉⡇⣿⡇⠿⣿⣿⣿⠀⠀⠀⢸
⡆⠀⠃⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⣉⣉⣉⣿⣏⡇⠀⠀⠀⠀⡆⠈⠸⠇⣜⠀⠰⣿⣿⣿⡇⠀⢸⡇⠀⠀⣫⣿⡇⢸⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠚⠛⠛⠛⠟⠛⠳⡇⠀⠀⠀⠀⢁⠀⠀⠀⣿⠀⠐⣯⢿⣽⡇⠀⢸⣇⠀⠀⠑⣿⡇⠞⢻⢾⣿⠀⠀⠀⢸
⠀⠀⢀⡀⠔⠊⠀⠀⠀⠀⠰⠤⠀⠀⣀⣌⢔⡚⢂⡘⣂⣒⣐⣀⣓⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⣿⠂⠰⣿⠶⡛⡇⠀⢸⡏⠂⠀⠀⣿⡇⠀⠄⢸⣿⠀⠀⠀⢸
⠀⡠⠋⠀⠀⠀⢀⠀⠀⣀⠵⠖⠛⠁⠀⠀⠀⠀⠀⡤⢤⠤⠤⢤⡤⠤⢴⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠀⢠⣿⣶⣻⡇⠀⢸⡇⠀⠀⠀⣿⡧⡁⠀⢸⣿⠀⠀⠀⢸
⠳⡱⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢁⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⣟⣷⡛⡇⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠙⠘⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⣲⣶⣶⣶⣶⣾⣧⣶⠀⠀⠀⡂⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸

⠀⢠⡄⠀⣧⣤⢦⡈⠲⠀⠀⠀⢠⣀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠚⠀⠀⡇⠀⡠
⠀⢸⡿⠀⠋⠈⠐⠛⠁⠀⠀⡆⠸⠛⠒⠄⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠰⠃⠀⣭⡏⠀⠀⢠⡴⠛⠀⢀
⠀⠈⠃⠀⠀⢹⠀⠀⠀⢘⡓⠂⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠱⡂⣃⡀⠀⠴⠈⠀⣠⠔⠁
⠤⠤⡃⠀⣀⣠⣀⠀⠀⢸⡇⠀⠸⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠊⠁⠛⠂⠁⠀⠀⠊⣀
⠐⡀⠀⠈⠙⠠⣼⠁⢠⢸⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⣠⣤⡎⢙⣄⣀
⠀⡃⠀⠀⠀⠀⠀⠀⠺⠄⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠄⡄⠀⠝⠓⠈⠋⠁
⠤⠧⠀⠀⠰⠄⠀⠠⣠⢀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡀⠒⠂⠁⡠⢊⣀⣠⠤⢴
⠒⠀⠠⠤⠀⠀⠠⢤⣤⣄⣀⣀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⣠⠀⠀⠒⠚⢯⢥⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⣏⠈⠇⠋⠉⡟⠋⠐⡈⣹⣛⡆⡃⠈⠀⠀⢀⣀⣀⡉⠀⣨⡇⠀⢀⣀⠀⢰
⠀⠀⠀⠀⠀⠀⠘⣧⠀⡄⣤⣠⡧⠀⠴⠀⣹⡽⠗⠛⠛⠛⣾⡏⣰⠉⢹⠃⠉⠉⠉⠉⠉⠉⠛⢄⡀
⠀⠀⠀⠀⠀⡀⣀⠛⢲⠉⠁⠀⡁⠀⡠⠁⠁⠀⠀⠀⠀⠀⢯⣠⠉⠃⠾⠄⠀⠀⠀⠀⠀⠀⠀⠈⠧⠉⠩
⠀⡴⢾⣿⣆⠈⠁⠀⠀⡀⠀⡠⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣠⡀⣄⣀⡠⠀⠤⠖⡪⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⣠⢤⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢠
⠄⠂⠐⠂⠀⣀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠃⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠡
⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⢼⠀⠀⠀⠀⠀⠀⠀⠰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⣐⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡒⡇⠚⣴⣶⠁⠀⠉⠉⠉⢘⣯⣽⠀⠉⠉⠉⠃⢀⢀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠇⠐⣾⣿⡇⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠂⠉⠀⢠⢄⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⡂⠀⠀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⢠⠉⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠂⠀⠀⢺⠀⠀⠈⠀⠘⠀⠀⢨⠀⠀⠀⠒⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠁⠈⠐⡄⡅⣇⣴
⠀⠀⠀⠀⠀⠀⠐⠘⠂⢀⣀⠀⣆⣀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠇⠋⠽⠁
⠀⠀⠀⠀⠀⠀⣦⣄⣤⡄⢠⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠈⢀⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⢀⡠⠀⢠⣦⢀⠉⡉⠿⠝⠀⠀⠀⠁⡠⠠⡴⣀⣠⢈⢩⡀⢳⠎⠶⠙⠀⠀⢛⣖⠐⢂⠲⠮⠏⠋⠏⠓⣸⠀⠰⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⡖⣀⣀⠀⣾⣁⠀⢀⣽⡧⢤⡞⠁⠀⠀⠁⠉⠙⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠴⠀⠀⠀⡠⠂⠘⠀⠗⢆
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋⠁⠐⠒⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠦⣄⠔⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⠤⠔⠒⠒⡤⠒⠒⠂⠀⠀⠈⠀⠀⠀⠈⡆⡀
⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⡀⣀⠀⠀⠐⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠁⡈⠃⠀⠀⠀⢀⠤⣀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠨⣀⣀⡀⠀⠀⠰⡇⣸⡄⠀⠀⠀⡏⠳⠠⠠⠤⠬⠿⢯⠉⣉⣁⢄⢠⡀⠀⣀⣇⡀⠈⠀⠀⠀⠜⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠀⠓⠻⡄⠀⠀⣸⣸⣀⣘⢋⡁⠛⠟⢠⢸⣷⠎⠛⠉⢴⠅⣄⣒⡚⢷⠀⣀⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠄⠐⠀⠒⠟⠉⠁⠙⢀⣈⢹⣍⣉⣡⣿⣒⣾⡜⠉⣑⠶⠾⣸⠼⢯⡇⢈⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⢰⠗⠶⢠⣼⣃⣉⣉⡏⣉⡉⡥⡄⣠⡀⢈⢫⣬⠁⢠⣤⢶⢠⠌⡇⡎⡇⠨⠤⡷⠷⠒⠒⢲⡀
⠀⠀⠀⢀⠤⠾⢤⠮⢤⠤⣤⡤⢤⡅⢣⡃⣳⡂⣳⣃⢸⠒⠚⠛⠚⠙⠉⢺⣅⡇⠉⠁⣖⡋⡇⠀⠀⠀⠘⡁⢹⢇
⠀⠀⠀⠸⡄⠀⢸⢸⠉⡇⡇⡃⢸⣿⡇⣿⣁⡇⣇⣸⢸⠀⠀⠀⠀⠀⠀⠀⢫⡇⢀⣠⠳⠥⣗⠒⣖⣀⣒⣃⡆⢸⠂
⠀⠀⢀⠔⠀⠀⠈⡖⢃⡇⠓⠊⠀⣧⡜⠃⡄⠀⠲⠄⠸⠒⠒⠒⣒⢒⡒⠒⡞⡇⠉⠉⠉⢦⡈⢱⡇⣒⢶⣺⠇⢸
⠀⠀⠘⠢⠤⡀⠀⢣⢩⢨⣾⣉⡆⡇⠠⠆⠐⠈⢒⡀⠶⡌⢃⡰⡌⠹⠠⠀⠠⠇⠀⠀⠀⢀⡧⢠⣓⠩⠛⠒⠦⢼⡀
⠀⠀⠀⠀⠀⠙⢶⠚⡘⠒⠙⠒⠃⣇⠨⣄⡘⠐⠒⠂⣀⠒⣄⣑⣄⣲⣖⣜⣺⠃⢻⡒⠊⠙⠣⣍⠤⠤⠤⠤⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠸⠉⡇⠀⡏⠸⣁⣹⡏⢹⠀⠁⠉⢀⠤⡀⠀⠈⠈⠉⠀⠈⡆⠀⠀⣀⢾⣓⣒⣒⣒⡒⢒⣹⡇
⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⣇⡇⢀⣅⠃⠀⠀⠇⠘⠠⠆⠙⠃⠀⢻⣿⢹⢹⢹⣀⣀⣙⡖⠊⠉⠸⣖⣒⣒⣒⣒⣒⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⣿⠀⠀⣸⣯⣤⣤⡀⠀⠀⢀⣷⠀⠀⠀⠀⣿⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢠⡟⣠⠀⣿⠃⢀⡉⠁⢀⠀⢸⣿⠀⣠⠀⢰⡿⠶⠶⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠉⢠⡟⢰⡏⠀⣿⠁⠀⣻⣇⠈⣿⠀⣿⠀⢸⣇⢠⣴⣟⣭⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⡾⢿⠃⡿⠁⠀⠻⠷⠛⠉⣿⠀⣿⠀⢻⠇⠈⠿⣾⡁⠉⠀⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡞⠁⠀⣸⠇⢀⣠⠶⠃⠀⣰⠏⠀⣿⣠⡴⠶⠞⠛⠙⠷⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠞⠋⠀⠀⠀⠿⠶⠋⢷⣤⡴⠞⠁⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠉⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡁⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠘⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⢠⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢛⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣧⣤⠀⠀⠀⠀⣠⣿⣿⣿⣧⠀⠀⠀⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣿⣿⣁⠀⠀⠀⠐⠟⢻⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⠀⠀⠀⠀⠶⠰⠆⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠀⠀⠀⠠⠶⠿⠿⠿⠿⠆⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⠀⣶⠀⣤⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⡿⠁⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⡆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢠⣦⡆⣤⣴⣴⣶⠰⡆⠀⠀⠀⠀⠀⠰⡆⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠁⠘⠋⠰⠆⠦⠀⠀⠴⠳⠧⠀⠀⠰⠢⠄⠀⠀⠉⠉⢀⡁⠀⠈⠉⠀⢠⡄⠀⠀⠀⠀⠀⢀⣀⠄⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⣀⣀⠀⢀⡀⢀⡀⢀⡀⠀⡀⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠁⠈⠀⠈⠉⠀⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠋⠉⢁⡀⠀⠀⠈⠙⠉⠀⠀⠀⠀⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠆⠀⠀⠰⠆⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠁⠀⠀⠛⠁⠙⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢀⠀⠀⠘⢋⣍⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⡄⣤⣤⢀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢻⣿⣿⣄⢀⣌⣤⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠋⠙⠉⠋⠉⠛⠁⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⠀⣿⣿⣿⡼⠿⡏⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⢁⣽⣿⡇⠀⠁⠁⠈⠀⠁⠀⣤⣤⡤⢤⠄⠀⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠉⠀⠀⠰⠟⠙⠁⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡋⠛⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⡀⣀⠀⠀⠠⠟⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢀⣾⠿⠃⠀⠀⠀⢡⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠛⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⡠⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⣄⡠⠄⢼⠀⠀⠀⠉⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠈⠁⢈⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠔⠒⠋⠀⠀⠀⢀⡢⠒⡄⠀⠀⠈⣲⠲⣒⠒⠒⠒⠒⣤⡄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠂⠉⠑⠊⠁⠈⢙⣆⡀
⠀⠀⠀⠀⠀⠀⠑⠒⠲⣀⢀⠀⠈⣇⣺⠋⠀⠀⠀⠈⡆⠃⣤⡄⠀⡍⡩⢉⢁⣔⡙⢯⣇⠜⡠⠀⠒⠒⣢⣀⠀⠀⠀⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⡠⠤⠠⡶⠷⠦⣄⠰⢠⡄⣁⢸⢰⡟⡍⣀⣀⡀⡏⠡⢦⠤⡄⢹⠤⠄⠦⠤⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢰⢉⣉⣉⣩⣉⡀⠠⠤⠥⠤⠤⢽⠦⠤⡴⠻⠭⠭⠯⠤⢤⠂⣉⠓⡾⠀⡅⡇⢸
⠀⠀⠀⠀⠀⠀⡏⠉⢉⠱⠯⠤⠤⠀⠅⡤⠄⠐⢲⢠⠢⠀⠘⠠⢶⡀⢸⣆⣋⠂⣒⢸⢸⢈⠀⡗⡃⠋⠉⠉⠉⠉⡅⠀⡀
⠀⠀⠀⠀⠔⠒⠓⡞⢃⣰⠶⣤⡶⢶⠾⣙⣂⢸⢚⢈⠿⡄⡌⠉⠉⠉⠉⠀⠉⠉⢧⢸⠀⠁⠀⣏⡅⡆⠀⠀⠀⠀⠇⠀⠛⡄
⠀⠀⠀⠀⠆⠀⠀⠇⢰⠈⠀⡀⡇⠘⣀⢇⡨⣀⢸⢸⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⣀⣔⡳⠤⣍⠀⣉⣉⣉⣁⡔⠀⡏
⠀⠀⠀⠔⠁⠀⠀⢸⠘⣒⡂⠓⠃⠀⣿⠔⠒⢰⠂⠔⢲⠀⡖⡐⢒⠒⣒⢒⣒⠒⠲⢻⠂⠀⠀⠘⢤⠀⢡⡇⣒⡲⡲⠆⠀⡇
⠀⠀⠀⠣⠤⣄⠀⠈⡄⣧⢩⣎⣉⡆⡿⠣⠄⠘⠂⢐⣊⡀⢿⣩⢇⠡⣇⣽⡨⠀⡀⡾⡄⠀⠀⠀⠀⡆⢠⢓⡨⠝⠒⠦⢄⣇
⠀⠀⠀⠀⠀⠈⠢⡄⢣⠹⠴⠸⠤⠇⡄⡾⡉⠩⠃⠧⠔⠀⢠⠢⡜⢲⡄⢢⡔⢆⡷⡓⠚⡖⠶⠛⠻⢤⡉⡀⣀⣀⡀⣀⣀⣀⡙
⠀⠀⠀⠀⠀⠀⠀⠇⠘⡄⠸⠙⡆⠀⡇⠀⡏⢉⣶⠒⡒⢸⠈⠊⠈⣉⠈⠁⠈⠹⠋⠃⠀⢻⡀⠀⠀⠀⣿⠂⠲⠶⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠸⠀⡇⠀⠁⠇⠉⠉⢸⠀⡇⢸⡀⠠⠊⠀⢳⡒⠒⠖⠖⠄⠀⠐⠢⡄⠖⡏⢸⠭⠭⠭⠭⠭⠨⠥⠅⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠤⠗⠑⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠋⠉⠀⠉⠀⠀⠁⠀⠉⠉⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢷⡄⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡶⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣸⠇⠀⠰⣿⠛⠛⠿⠆⠀⠀⠀⣿⠀⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢰⠟⢰⡇⢰⡏⠀⣴⠀⠀⣤⡄⠀⣿⠀⢰⡇⠀⢸⡏⠉⢉⣤⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡄⣿⢀⣾⠀⢸⣧⡀⣠⡼⣷⠀⣿⠀⢸⣇⠀⢸⡇⣰⠿⠷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡾⠹⠇⣸⠇⠀⠀⠙⡛⠉⠀⣿⠀⣿⠀⠈⠟⠀⣘⣃⣿⡀⠀⠀⣀⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠟⠁⠀⢠⡟⢀⣠⡴⠛⠁⢀⣴⠏⠀⣿⣤⠶⠛⠛⠋⠁⠘⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠘⠿⠛⠁⢷⣤⠶⠛⠁⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠠⣀⠂⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⣀⡀⠄⠀⠒⠲⠄⠂⠚⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⢨⠀⠀⠀⠀⠐⡀⠀⠀⠸⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⡀⢀⣀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠨⣀⣀⠀⠀⠀⢰⡆⣨⠄⠀⠀⢸⠋⠳⠀⠀⠀⠈⠻⠯⠉⠁⡠⠄⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠂⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠃⠫⡄⠀⠀⣀⣀⡂⡋⣃⠈⠛⠚⡄⣸⡖⠙⠋⠁⠮⠀⣐⣒⠛⡆⢀⣀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠄⠀⠀⢐⠏⠁⠀⠁⠀⠈⢻⣌⣀⣠⣗⡓⠧⠊⠉⡀⠒⠦⡠⠜⢠⠀⡏⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠰⠓⠂⣠⣞⣉⣁⣈⡏⣈⠀⠤⡄⣠⠀⢨⠀⡌⡃⡤⢠⠀⠠⠌⠀⡎⡆⡥⠄⠖⠂⠓⠒⣆⣀⡀
⠀⠀⠀⢀⠄⠲⠤⠎⠤⠤⢠⠤⠤⠆⠲⠀⣒⡃⣓⣀⠘⠀⠁⠓⠉⠈⠑⢻⡀⠀⠁⠁⣒⡁⠀⠀⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠘⡀⠀⠸⢸⠈⡆⡀⡇⢸⠠⡁⣇⣀⠆⣇⡘⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⣀⡀⠢⠬⡁⠀⣂⢀⠈⣀⠁⡗
⠀⠀⢀⠀⠀⠀⠀⡀⠒⡃⠓⠃⢸⣧⡆⡆⠖⢰⢲⠀⡗⡒⢒⠒⣒⢒⡒⢲⢺⠎⠀⠈⠙⢄⠈⢽⢰⡲⣖⢾⠀⡇
⠀⠀⠈⠢⠤⡀⠀⢃⢣⢸⢬⢨⠀⠏⠣⢃⡒⣘⠊⡀⠫⠼⢁⠃⡠⠤⠅⠘⠸⢥⠀⠀⠀⣐⠆⣜⠀⠄⠓⠚⠤⢅⡀
⠀⠀⠀⠀⠀⠉⠖⠘⡘⠒⣘⠒⠀⢀⠣⡀⡂⠑⠀⠁⢠⢲⣎⡳⣄⡦⣳⢸⣛⠈⣟⠚⠉⠛⠪⡠⠤⠤⠤⠤⠤⠠⠘
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠈⠀⠀⡆⠨⠀⠍⠁⠀⠀⠀⠀⡀⢤⠀⡀⠀⡇⠀⠀⠘⠄⠀⢀⡀⢯⠁⠀⣐⣒⣂⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣄⠀⣀⣀⠀⠀⠀⠂⠀⠰⠆⠙⠀⠀⢫⣏⠉⠹⢁⢀⣀⠑⠂⠁⠀⠲⣀⣀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⣤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠈⣿⠀⢀⣼⣧⣤⣤⡀⠀⠀⢸⡇⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⠇⣤⠈⡿⠀⣀⠀⠀⣀⠀⢸⡇⠀⣤⠀⢸⡷⠶⠖⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠉⢰⡇⣸⠇⢰⡏⠀⢀⣿⡆⢸⡇⠀⣿⠀⢸⡇⣠⣾⣭⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⡟⠿⢠⡟⠀⠈⠛⠛⠋⢸⡇⢸⡇⠀⠿⠀⠘⠃⣿⠀⠀⠀⣀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣰⠏⠀⠀⣾⠁⣀⡴⠞⠃⢀⡼⠃⢸⣧⡴⠶⠟⠛⠉⠙⠷⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠖⠛⠁⠀⠀⠀⠻⠚⠉⢷⣤⠶⠋⠀⠀⠘⠋

⣿⣿⣿⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣛⣿⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡽⣁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠈⡇⠀⠅⠀⠀⠀⠀⠾⡇⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⡒⠀⢠⠄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⠃⠀⣟⢹⠉⠉⠁⢳⡆⠀⠁⠀⢀⠀⠐⢶⢲⣀⢠⣠⠤⡴⠤⠀⢁⣀⣀⢠⡞
⣀⣤⡀⢠⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⢱⠛⡶⣿⣿⣿⠶⠄⠀⢨⡇⠀⠀⠀⠬⠀⡄⠀⣨⠄⠀⠁⠈⠀⠀⠀⠀⠀⠸⠉⠉
⠈⢷⠔⢸⠉⡆⠀⢴⠀⢶⡅⠀⠀⠀⠘⠀⣿⣿⡟⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⣀⣀⣀⣀
⢘⠙⠁⢸⠀⡇⠀⠸⢀⠋⢑⠀⠈⣧⣄⠠⣿⠀⡇⢸⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢹⡁⢠⢿
⠀⠈⡀⣸⠀⠇⠤⢀⠸⠇⠀⠀⠘⣿⠌⠀⢄⠀⣇⢸⠀⠀⠀⠠⣿⠀⢢⣀⠀⠀⠀⠠⠀⢸⡆⢰⠸⠿⠷⠾
⣼⣭⣵⡞⣧⣆⣗⣢⠀⠀⢰⣧⡀⡿⡶⠞⠦⠠⣌⣸⠂⢀⣣⡼⣿⠁⢩⠘⠀⠀⠀⠀⠀⢘⢤⢘⣛⠃⠀⠐⠀⠀⠀⠀⡀
⠭⠀⠤⠒⣘⢛⠛⠻⠀⠀⣄⢾⢦⠄⠆⠀⠀⠈⡄⣘⡂⠀⠀⠀⢘⠟⣿⠢⣤⠀⣓⣢⠔⠉⠀⢨⣀⢀⡀⠀⠀⢰⠀⡇⡇
⣿⣼⣿⡇⣿⢸⣿⣷⣴⣶⣼⣿⣿⣷⡇⡇⢀⣿⣝⣿⡃⣂⡀⣔⣛⣃⡻⠒⡶⠀⣄⣼⠿⢠⣶⣆⠼⣬⡏⣀⠀⢸⠀⡇⡇
⣯⡜⣩⣥⣭⣿⠿⠿⠿⣿⠭⣽⠿⠿⡿⠿⠿⣿⠿⣛⢟⠿⠿⢯⣿⠿⠿⣿⡟⢆⣴⣶⣮⣷⣶⣽⣿⠛⠛⢸⢏⡸⠒⣧⣷
⠀⣠⡁⠁⠁⠁⡠⢄⡤⠷⠶⠞⠛⠛⣴⣦⣆⣴⣴⣭⠈⠀⠉⠉⠙⠛⠛⠛⠉⠈⠉⠉⠉⠉⠉⠉⠙⠉⣿⣥⠿⠿⠆⠣⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠒⠀⠉⡉⠉⠉⢉⠉⢀⠐⠀⡀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⡆⠀⠀⠀⠀⠀⠂
⠀⠆⡄⠀⡀⡀⠀⠼⣀⢀⢠⠤⠅⠀⠤⠀⠆⠀⠠⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⡇⡏⡉⠉⡉⡉⢉⠉⡉⣉⢙⣄
⠈⡁⡀⠠⣄⠈⠀⠀⠤⠤⣸⠀⡀⣀⣀⣰⣀⣰⡀⡆⣠⡀⣀⣀⣀⣩⣀⣀⣀⣰⡀⢀⣀⡇⡀⠀⠂⠀⢀⣿
⢀⠁⠀⢀⠈⠀⠀⠴⣠⡠⢝⢠⠀⠄⢤⠀⠄⠀⠄⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠤⢄⠀⠀⠀⡀⠐
⠀⠁⠀⠀⠂⡖⢰⡄⠀⠐⢸⠈⠀⠆⠼⠀⠀⠀⠀⣀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢀⠃⠚⠓⠀⠀⠘⠀⠤⠄⡇⠄
⠀⠅⠀⠀⠂⠐⠐⠀⠀⠚⢸⠚⠀⡀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠒⠀⢰⠶⣦⢸⠀⠁⠉⠤⠀⢠⠊⠈⡃⡇
⠀⠀⠈⠀⢸⠎⠀⠀⠀⢈⢸⠀⡇⠃⠐⠀⠢⠤⠄⡄⠂⠒⠂⠀⠀⠊⠘⠒⠚⡿⠀⠈⣈⠀⡈⡁⢀⠀⢀⡇
⠀⠀⠀⢈⣉⡈⠉⡀⠀⢀⠀⡀⠀⠊⠉⠀⡇⠉⡽⠁⡆⠀⠂⠀⠉⠉⠂⠉⢢⡟⠀⠄⠜⠀⠄⠆⠠⣀⠜⡇
⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠄⠀⠀⡄⠀⣠⠀⣩⡅⠁⠀⠀⣀⠀⠈⠁⡇⠐⠀⠀⠀⠀⠁⠀⠀⠱⡇
⠀⢀⠡⠀⠀⠄⠀⠠⠄⠀⠠⠤⡄⠀⠀⠀⠁⠀⠚⡀⣅⣀⣀⣠⣤⠜⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠢⠈⠀⠀⠀⡀⠀⠀⡄⠠⠀⠀⣾⠒⡖⠢⡀⢀⣀⡀⠀⠄⢶⣂⢴⠂⣡⡀⠀⣀⠀⠀⠀⠀⠀⠀⢲⠠⡀⡀
⠀⠤⠀⣠⠊⠉⠁⠆⠙⠒⢰⠒⠚⠁⠀⢈⡵⠉⣶⠉⡲⣈⣉⢸⠀⠜⠰⠼⡄⠘⠀⠀⠀⠀⠠⠀⢸⣠⠜⠙⠏
⠒⠄⠀⠚⠄⠀⢠⡄⠀⠀⡼⠀⡄⠜⡇⢰⠐⠀⠀⠀⢀⠁⢐⠈⠙⢇⡆⠀⠠⡠⡘⠉⠟⠀⣷⣆⡸⢫⠀⠀⣦
⠀⠱⠒⠠⠉⠀⠀⠀⠀⠀⠈⠂⠉⠀⠀⠚⠑⠀⠁⠂⠁⡑⠀⠄⠴⢁⠔⠂⠒⠀⠠⠀⢢⠅⣸⠃⠀⠀⠂⢸⠓