Cold season Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠈⠙⠲⣄⢠⠴⠚⠉⠉⠉⠉⠉⠉⠓⢄
⠀⠀⠀⠀⢀⡴⠖⠒⠒⠺⠦⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣀⡀
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠈⠉⠙⣆
⠀⠀⠀⠘⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣻⠛⠛⠻⣴⣏
⠀⠈⠧⣄⣀⣀⣀⣠⠤⠖⠋⠙⠲⠤⠤⢶⣾⠁⠛⢶⢦⣤⣤⣤⢤⡾⡽⡵⢚⡃⠀⢀⢏⣼⠇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣻⣶⣞⢃⣑⣛⢈⣛⡃⠘⣿⣏⢹⣿⡉⣬⠭⠭⣅⢭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣾⠋⡎⠀⠈⣿⠞⣽⢳⠙⣺⠋⠀⠙⡜⢶⡄⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠳⠤⠤⢟⡴⠛⠙⠲⡝⠦⢤⠼⣷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠞⢉⢟⣤⢧⣀⣀⡜⡵⣜⣟⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠋⣎⠺⠤⠟⢧⡬⠇⢘⡎⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠟⠞⠀⠀⠀⠀⠀⠀⠘⠛⠾⠃

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⣀⡇⡠⠆⠀⠘⠏⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⠔⡟⠲⠄⠀⠀⠀⠠⠊⠛⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠐⠁⠀⠀⠠
⠀⠀⠀⠀⠛⠀⠀⠀⠐⡀⠀⠀⠀⠤⠤⠤⠤⠤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠁⠀⠀⠀⠀⠀⢠⡤⠆⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⡃⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠘⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠓⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⢄⠀⠀⠈⠀⠒⠀⠁⠀⠀⢸⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢠
⠀⢀⠔⣴⣷⣇⡡⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠄⠠⠈⠀⠀⠀⢀⡄⢠⠀⠀⠀⠀⢂⡜⠹⡁⠄⠀⠀⢠⠃⠀⠈⠁⢠⠄⠉
⠀⠀⠊⡿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢨⠐⠀⡥⠂⠀⠀⠀⠀⠀⠀⠂⢠⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣽⡯⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤
⠀⣸⣤⢿⠏⠱⣴⣷⣤⢬⣤⡄⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⣀⡀⠀⠀⢠⡇⠀⣼⣶⣫⡷⠤⢤⡄⣀⣀⣼⠕⣤⣰⢄⣿⠀⡆
⠀⠴⣛⠨⠟⠲⣿⣿⡿⢏⠙⢙⢫⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠚⠃⣼⢄⣜⠷⡤⢝⡇⣳⡷⣔⠚⣿⣿⡟⠁⠮⠽⡏⣋⢿⣙⣿⡀
⠀⣶⢹⣄⠀⣤⢣⠽⣶⣺⣄⠴⡏⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠸⡼⠅⢷⠂⢩⡃⣘⣱⠚⣄⣹⣷⡀⢖⠈⠣⢼⣩⣲⣧⣉⡇
⠀⠫⠀⣼⠛⡇⣟⠁⣽⠷⣷⡴⠁⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣭⢽⢿⣧⠀⠀⠀⠀⠱⠾⣼⢣⡞⢻⠌⣯⠑⣌⠉⠻⠗⢨⡈⣧⢰⡆⣼⠌⣿⡀
⠘⠀⠰⢟⡓⢠⡞⢑⡋⢂⠨⢷⣴⠻⠍⠙⡙⢷⡀⠀⣀⣀⢀⣀⣰⡓⠒⠓⠒⠚⠛⠢⢤⣶⣶⣶⣭⣟⠤⢧⣨⠗⢌⣣⡌⠹⠟⡧⠈⢃⠴⡀⡹⢟⠙⠢⠅
⠀⠀⢀⡤⠀⡄⠉⠛⠐⣀⡐⠌⣻⢰⣶⣷⡶⠀⢹⣿⣿⣿⣿⠿⠟⣿⣶⣶⠶⢶⣷⣶⣿⣿⣿⣯⡴⢧⠀⣄⠙⠐⣤⣈⠳⣿⡦⠯⠔⠮⠈⠐⠓⠩⠠⠓⠠
⠀⠀⠉⠁⠀⠙⣛⠉⡽⣁⡟⠢⣼⢬⡿⠿⡇⢀⣸⡷⣿⠿⣗⠂⠀⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⡫⠤⠿⠤⠿⠶⠰⠘⠤⠁⠛
⠀⠀⠀⠀⠀⠀⠀⢚⣤⠋⢤⢳⡤⡈⠉⠉⠉⠀⠘⠋⠙⠛⠋⠀⠉⠉⠉⠉⠙⢾⠧
⠀⠀⠀⠀⠀⠀⠈⠓⠈⠒⠀⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢠⣤⠀⠀⠀⠀⢠⢠⠄⠀⠀⠀⠀⠀⠀⢠⡄⢀⣠⠀⢀⢠⠀⣠
⠀⠀⠀⠀⠀⠀⡀⠂⠀⠙⣇⢀⠀⢸⣟⠤⠆⢀⢰⢸⠁⠘⠀⢀⠀⠀⠐⡄⢸⡇⢸⠑⡀⠊⢸⠀⡇⠨
⠀⠀⠀⠀⠀⠀⠀⠈⡆⣹⢹⡔⠀⠈⣧⡄⠀⠉⠀⡈⠀⠀⣰⠃⠀⠀⠀⠡⣸⠿⢋⠈⠀⠀⢼⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⠈⡇⠀⠀⣿⡇⠀⡀⠀⠧⠶⠚⣁⠀⠀⠀⠀⠀⢸⣇⠂⠀⡀⠀⢘⣗⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⣿⡑⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠰⡏⢃⠀⠀⠀⠀⠩⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣗⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣷⠋⠉⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣧⣾⠻⢿⣆⠀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠇⠀⠀⠀⢀⣤⡶⠛⠻⣿⣿⣿⣿⣿⠙⣤⡀⠁⠀⣇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣸⣿⡏⠀⣁⣤⠾⠛⠁⠀⠀⠀⠀⠙⠻⣿⣿⡠⣿⣿⣶⣄⣿⡈⢢⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠈⢹⣿⣇⡟⠉⠀⣊⣀⣀⣔⢀⠄⠀⢶⡄⡌⣿⡅⣿⣿⣿⣿⣿⣧⣈⠛⠛⢋
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⢈⣠⠖⢛⣿⡉⡇⢀⣴⠋⠠⠈⢡⠀⠀⠀⠈⠃⣏⣿⢾⠙⠻⣿⣿⣿⣙⣩⣶⠞⡫
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⡀⠀⠋⣯⣥⣰⡏⠀⠛⠀⠀⢸⠀⠀⠀⠀⠀⢹⣿⡄⠀⣴⣿⣿⣿⢋⣷⣿⡇⠇
⠀⠀⠀⠀⠀⠀⠛⠩⡆⠀⡀⣹⠾⣄⣿⡇⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⢀⣾⣿⣿⣿⣿⠈⡿⡇⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠄⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⣿⣿⣿⡟⣿⢀⡇⢧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣠⣾⣿⡠⣿⣿⣿⣿⣿⠘⡇⣿⢸⡇
⠀⠀⣀⢀⡠⣤⣸⣦⡆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠷⢩⣿⣿⣿⣿⠀⠇⣿⣻⣇
⠀⢰⣿⣷⡶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣞⠀⠀⠀⠀⠀⡀⠀⣠⣿⣿⣿⣿⣿⠈⣺⣿⣿⡇⡿⢼⡄⣿⢸⣿
⠀⢸⣿⣿⣳⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣗⠹⠀⠀⠀⠀⠈⠁⠾⠿⡿⠿⠿⠿⣿⡤⠻⠿⣿⠟⣷⣸⠷⠿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢫⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠀⠀⠛⠛⠀⠀⠀⢠⡟⠃⠀⠀⢠⡇
⠀⠀⠀⡀⢀⡀⠀⣀⣀⣀⣀⣀⣠⠤⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⣙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡶
⠀⠀⢀⠀⠀⠀⠀⠌⡁⠀⠀⠀⠋⢱⣖⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢬⡅⣡⠄⠀⢀⢇
⠀⠀⢘⠂⠀⠀⣈⠃⠼⠀⠀⠈⢙⠃⠩⠀⠀⢄⡂⠀⠀⠀⢰⠀⢀⠀⠆⠂⠀⠸⠀⠈⣡⢔⠉⠖⠀⠐⠤
⢒⠀⠁⡠⢠⣄⡌⣆⠈⢈⢈⣉⠉⠈⠓⠀⢰⠇⣰⠀⡄⢀⡌⠀⣞⠤⡠⠯⠄⠩⠄⢡⠄⠈⠈⠙⡢⠅⠒
⠁⣤⠐⠀⠩⡷⣆⡙⠈⡡⠆⠀⠦⠙⠃⢴⡬⠓⠔⣂⢹⡷⠵⠹⣏⡒⢠⣈⣩⢕⢥⣀⡰⠶⠈⠉⣉⠌⠒
⢝⣵⡂⢑⠽⡤⠰⠄⡤⠐⠖⠘⢱⡤⠰⡬⠷⠅⡈⢃⣯⡞⠂⡡⡝⠑⢄⠐⡀⠷⡻⣯⣀⣀⠐⠲⠋⠞⢈
⡥⢦⠐⣢⣞⠊⠰⠀⠶⠟⡤⠞⠁⡀⠀⣤⣀⡥⠂⢁⣯⠛⠁⠀⠉⠙⠦⠲⠐⠚⠂⡀⢈⡀⣠⣤⠘⠛⡶
⠺⠩⢁⣱⠛⢫⠄⠀⢻⡇⠀⢀⣀⡙⠃⠀⢀⣉⢧⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⠉⠀⡥⠤⠷⢤⠿
⠀⠀⠀⠈⠛⠒⠯⠰⠃⠉⠁⠀⠉⠘⢢⣤⡤⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠃⠒⠃⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠻⣶⡂⠚⡘⣲⠢⢤⡐⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣒⣴⣶⣖⣆⢄⣀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠂⠀⠄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⢈⠛⡇⢠⡆⠈⠉⣛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠲⢦⡵⠈⠑⡎⠙⠾⠯⠎⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⣸⠁⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠐
⠀⠐⠀⠀⢕⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⠦⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠔⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⢀⠠⢔⠀⢠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⠤⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠲⠶⠦⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣇⣠⣡⠄⠠⠱⠀⠀⠠⠀⠐⠲⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠑⡠⠈⡄⡌⠀⠀⠑⢄⠀⠘⢿⣍⣙⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠱⣀⢌⠀⠀⠀⠘⢏⢁⡠⠷⠐⢉⡡⢔⠢⣉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⠀⠀⠐⠉⠌⠀⢀⠤⠒⠉⣉⡠⠔⠊⠁⠀⠀⠈⠲⠵⡢⣈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠎⠀⢀⡀⡠⠊⠀⠀⠈⡛⣁⡉⡇⠀⡭⠭⡅⠀⠀⠀⢈⠁⠀⠏⠉
⠀⠀⠀⠀⠀⠀⡔⠉⡉⠆⠐⠒⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠀⠒⠀⠷⠦⢇⣇⡠⠄⠀⠧⠀⠐⠐⠐⠰⠀⢸
⠀⠀⠀⠀⠂⠀⠱⠊⢀⡠⠐⠂⠀⠀⠒⠨⢢⡀⠀⠰⠀⠀⠀⡎⠀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠃⠒⠒⠒⠒⠒⠚⠒
⠀⠀⠀⠀⠀⠀⠁⡔⠁⠀⡠⠄⠒⢂⡒⠠⢄⠙⡄⠀⠀⢀⠄⣊⠁⠀⠀⠨⠁⢢⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢀⠀⢠⡞⠂⠂⠙⠛⠀⠐⠊⡓⡄⠀⢠⠞⡨⠔⣂⡀⠉⠁⠀⣀⡺⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢤⠀⠞⠀⠀⢹⠆⠀⠀⢽⡆⠀⡄⠀⣎⢊⠔⣡⡄⣐⠀⢀⣰⡂⠀⢽
⠀⠀⠀⠀⠀⠀⠈⢧⠰⡀⠀⠀⠠⠤⠄⠀⠀⢠⠀⠀⣇⠂⠜⠠⢁⡄⠀⠀⠀⠈⠉⢐⠀⠀⠀⡠⠚⠁⠉⠑⢦
⠀⠀⠀⠀⠀⢀⣀⠀⡱⢄⣦⣄⣀⣀⡀⠠⠐⠁⠀⠀⢫⡈⠀⠸⠈⠃⠀⠀⠺⠏⠀⠘⠀⢀⣔⣁⠀⠀⠀⠀⢀⡱⢄
⠀⠀⠀⠀⠿⠤⠤⢠⠍⢳⣤⣀⢠⡼⠀⠀⠀⠀⠄⠀⠈⡅⠀⠀⠀⠀⠭⠅⠀⠀⢀⠇⡰⠃⠐⠀⠈⡍⠐⠠⣸⠣⠔
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠠⣸⣰⡟⡤⡀⠀⠀⠀⠀⠀⠐⣄⢸⡐⠲⠤⠐⡶⢊⣁⢘⡇⠀⢨⡻⢃⡠⠀⠀⡏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢨⠀⠈⠦⢠⣠⢠⠾⠗⠁⠀⠀⠀⠀⠀⡘⢠⠋⠉⠁⠐⠊⠱⣈⣧⡀⡜⠒⠖⡈⠁⠐⠒⠚⡄⠀⠀⡒⠐⢀⡎
⠀⠀⠀⢠⡖⠠⠒⢌⠃⠀⢀⡞⢸⠸⢄⠀⠀⠀⠀⠀⠀⣧⡇⠠⠀⠉⠚⡆⡦⠬⠿⡖⠉⠐⠒⠒⢒⠞⡞⢲⠑⡤⠒⠓⠛⠈
⠀⠀⠀⠣⠧⠄⠀⠠⠚⠀⠉⠑⢄⠀⣀⡧⡀⠀⠀⠀⠀⠀⢰⠀⠈⠉⠙⢁⡇⠀⢸⠀⠀⠀⠈⢀⠺⢦⡇⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠔⠁⠀⠀⠀⠀⠀⠀⢩⠉⢩⡉⢉⠀⠀⠸⡀⠀⠀⠁⠀⠉⢉⠷⢶⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣽⣋⢹⡀⠀⠀⠑⢄⡀⠀⠀⠀⠈⠉⣉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⠠⠆⣉⡉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⡁⠔⠂⠁⠀⠀⢀⠈⠀⠁⠲⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠡⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⡸⠄⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⢀⠀⠀⢨⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠺⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠖⠀⠀⠉⠀⠀⠀⠀⠉⠀⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⡐⠀⠀⠀⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢦
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠠⠊⠀⠀⠎⢠⣽⣿⡄⠀⠀⠀⠀⠀⣪⢴⣌⠢⠀⠀⠠⠀⠘⠐⢄⡀
⠀⢀⠔⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⡆⠀⠀⠡⠰⠆⠀⠐
⠀⠈⠀⠀⠀⠀⡀⠈⢁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢂
⠀⠈⠂⠀⠀⠀⠀⠀⠘⠀⢄⠀⠀⠀⠀⡌⠀⠐⠠⠁⠀⠀⠁⠄⠀⡄⠀⠀⠀⠀⠀⡌⠰⠀⠱⢄⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡁⠇⠀⠀⠀⠀⠔⠀⠀⠇⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠂
⠀⠀⠀⠀⠠⡄⣁⠰⠆⠀⠀⠀⠀⠀⠀⠁⠂⠀⡀⠀⠀⠀⠀⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⠘⠲⡤⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠣⠀⠙⠄⠀⠈⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠄⠉⠀⠡⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠀⢠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠂⠀⠴⠀⠈⠈⠀⠀⢸
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠂⠀⣀⣤⠤⠀⠀⠁⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠀⢠⠃
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⠐⠒⠈⠀⠀⠟
⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠠⠀⠉⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠠⢀⠀⣠⠄⣰⢮⠄⣤⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠐⠂⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⢀⠤⠈⠙⠅⠦⠂⠰⠚⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠄⠰⠀⠀⠀⠄⠄⢀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠂⠠⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠘⠀⠀⠀⠀⠀⢀⠉⠐⠦⡀⠀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⡇⠀⠀⠐⠀⠀⠈⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠐⠂⠁⠀⠖⡑⠆⠠⠄⡀⠰⠀⡀⠀⠑⠤⠀⠄⠠⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡐⠁⠀⢀⠀⠠⠊⠀⠀⠈⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠂⢑⢇⣃⠸⠭⠸⠀⠀⠀⠱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠎⠁⢈⠢⠀⢠⠀⠀⠀⣄⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡄⠀⠀⠀⠑⠀⠀⠀⠤⠠⢀⡀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠌⠀⡠⠲⠄⡈⠂⠀⠉⠀⣀⣼⠁⠀⠑⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣗⠤⠀⠀⠀⠩⠄⢸⠀⠀⠀⢁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸⠀⠀⢸⠀⠀⠀⠀⢀⢠⡎⠀⠀⠀⢨⡀⣁⠀⠀⡠⠂⠒⠐⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⢠⠀⡈⠂⠄⠄⠹⠀⠆⢀⠀⠀⠀⡼⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠑⠃⠀⡖⠢⠄⠀⠒⠈⠁⠀⠀⢀⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠡⢀⡀⠀⡅⠀⠀⠀⠀⠀⠀⣀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠁⠀⠈⠈⢣⠐⠃⣀⠌⠁⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠑⠀⠂⢄⠀⠀⠀⠀⠣⣀⣀⠀⢀⣈⣋⡁⠤⠠⡎⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠢⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠣⡀⠀⡆⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⡦⠷⣄⠀⠤⣴⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢠⡅⠀⠦⠂⢀⠠⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⠀⢀⡀⠄⠤⠤⠀⠐⠂⠀⠉

⠀⢀⠆⠉⠀⠒⣄
⠀⠎⠀⠀⠀⠀⢀⣰⣆⢄⡀
⠀⠀⠐⠂⠚⠃⡐⠙⠃⠒⠭
⠀⠀⠀⠀⠐⠐⠋⠠⠀⠐⣐
⠀⠀⠀⡀⠀⡀⠁⠀⠈⠁
⠀⠀⠀⡤⢤⠬⠀⠀⠀⢀⠴⡄
⠀⠀⡤⠀⠀⠄⠀⠈⠉⠉⠀⠲⣄
⠀⢠⣁⠼⠂⠃⠐⠂⠀⠁⠈⡀⠘⡆⢰⡀⢀⠀⢂
⠀⣼⠁⢠⠄⠀⠀⠀⠈⣆⠀⠁⠀⠛⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀
⠀⡇⠀⠀⡀⠀⠀⠀⠀⠨⠀⢀⠼⠆⠀⣠⠎⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⡃⡀⠀⠀⠀⢸⠃⠀⠈
⠐⠂⠀⠐⡁⠀⠀⠀⡠⠐⠛⠁⠈⠒⠸⠃⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠂⠸⠆⠀⠀⠀⠓⠦
⢠⠀⢀⠀⠑⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⡠
⠸⠀⠀⢀⡀⠀⠢⠀⠀⠀⠀⠠⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡆⠀⠀⠰⠤⡤⠀⣠⣤⠠⠒
⠐⠷⠟⠉⠀⠀⠀⠀⠒⠆⠀⠀⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠄⠀⠀⠠⢅⡂⡀⠀⠀⣀⡴⢣
⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡄⠀⠀⠀⢠⠿⠙⠃⢉⠓⡍⠀⠐⣄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢂⣀⣰⣵⢧⠾⣤⢍⡷⣈⣄⠀⡸
⠀⢸⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⣬⠃⠙⠺⠂⠃⠘⢱⡿⠙⠋
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣉⣺⡤⢀⡀⠠⢾⡆⠘⡃⢣
⠀⠀⠈⠑⢤⠄⠀⢀⣀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠃⠖⠻⠊⡃⠈⡚⣛⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣿⢻⠛⠂⠀⠓⠓⠈⠟⠛⡁⢭
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣝⣸⠛⠛⢛⣓⣻⡠⠾⠋⣃⠈
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⢿⣻⣇⣨⠁⢸⠄⢾⣸⠙⠊
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⣿⢛⠉⣇
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣶⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣻⠀⣡⡇
⠀⠀⠀⠀⠘⣄⠀⠀⢀⣈⢧⣺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢿⣉⠀⠜
⠀⠀⠀⠀⢠⡀⠀⠀⠉⠁⠘⠋⠁⠀⢌⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠯⠴⠟⠁⠀⠰
⣀⣀⣀⣀⣤⣈⣈⣡⣤⣤⣤⣀⣀⣀⣸⣏⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣁⣤⣴⣒⣤⣤⣚⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠁⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠐⣩⡞⠁⠀⠀⠀⠀⣀⠄⡖⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⢠⠔⣁⠤⣀⡀
⠀⣠⢀⣤⠀⡀⠀⠀⠀⢀⡴⠏⡀⠀⠀⠘⠀⠀⠀⠁⠀⣀⣠⡞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣇⠀⠀⢀⣽⣄⠶⠾⣿⣆⡈⢀
⣼⣟⡡⠞⡑⣷⠀⢀⣀⠠⠶⢂⠙⠄⠀⠈⠹⡇⠀⠀⠉⠀⠘⠃⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⡄⠀⠀⢸⢻⡄⠀⣾⡿⡻⢶⡖⠉⠘⣯⠛⢡⣿
⣿⡡⢶⠰⣏⢻⣿⣿⣥⠐⠀⡾⠑⠒⡄⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡀⢀⠞⠿⣁⠈⡧⠜⣇⠒⢷⣾⢧⡘⠲⣤⣹⣷
⣿⡤⠚⡞⢧⡘⣿⣟⠠⢆⡠⠖⠤⣆⠘⣄⣄⡀⡀⢀⡄⠀⢀⣿⡀⠀⢀⡀⣀⣀⣴⣄⣴⢟⠟⢰⣦⠖⡧⣸⠂⡤⠺⣏⠓⣞⢻⣄⢙⠀⠈⢿⣿
⣠⡔⠹⡧⣿⠛⣉⣠⡆⢀⣴⣤⢰⡌⠱⣮⣿⣿⣿⣾⣷⡿⠔⣿⢬⣿⣿⣿⡟⢻⣿⣿⣟⣱⠟⠦⠷⢒⠳⠾⠁⠀⢤⡌⢢⣈⣿⣿⠉⠻⣦⣀⣿
⡹⢧⣀⣷⣼⠟⠋⡀⠙⣟⠁⠘⣺⡷⣄⠈⣻⣿⣿⣿⣿⠟⢂⡝⠀⢿⣿⣿⡠⠘⣿⡿⠋⣀⣷⢤⣄⣹⡆⣸⣉⣠⠜⢷⣎⠉⢿⡛⠓⣀⠀⠈⢻
⠀⣴⡟⣿⣷⠖⠈⢁⡟⠉⣤⠐⠁⠁⠈⠻⢶⣿⣿⢺⣿⠭⠉⢧⣸⠎⣿⡭⠁⠊⢹⠗⠈⠀⣠⣤⣈⠻⣿⡇⠀⢠⠀⠀⢏⠑⠲⣧⠀⠈⠂⢀⣀
⣾⣁⣽⣿⠇⠐⠒⣏⣀⡴⠁⠠⡀⠘⢶⡀⣀⢹⠿⣯⠀⠀⠙⢸⠀⠀⠠⡖⠁⠲⣊⠐⣀⣼⠀⣰⣄⣙⣻⣿⠔⢻⣆⠀⣸⠳⣤⣈⢻⣀⡆⠀⢻
⠀⢈⡟⠁⠀⢀⣠⠜⠋⠁⠀⠀⠙⣆⢨⠗⠛⠒⠂⠙⠂⠒⠉⠛⠓⠀⠀⠈⠀⠀⠈⠀⠀⠈⠈⠀⠀⠛⣁⠆⠀⢈⠙⠸⠁⠀⠀⠈⠛⣯⡁⢀⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠀⠀⠀⠘⠛⠇⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠠⠟⠲⣄⡀⠀⢤⣸⣄⠀⢹⠛⠻




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⢀⠔⢀⠀⠀⢈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠈⠀⠀⣀⣠⠴⠋⠀⠐⠐⠆⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⠁⠂⠀⠀⢀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡄⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠐⠁⠀⠀⢀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠈⠀⠈⠒⠤⢀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠁⠂⠀⠀⠄⠀⢀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠲⠀⠀⠀⡠⢄⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⠠⠄⠁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⢠⠄⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠐⡠⠄⠂⠈⠈⠀⠠⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢌⣃⠀⢀⡠⠗⢀⢒⢂⠂⠀⠠⠄⠀⢈⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⡀⠀⠁⠘⠛⠚⠈⠉⠉⣉⣉⣁⣾⣄⣇⠘⣠⠁
⠀⠀⠀⠀⠀⠄⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⠤⠤⠤⠭⢾⢒⣤⣤⣄⣀⣀⢀⡀⠄⡄⡀⠉⠁⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡁⠍⡁⠉⠉⠙⢿⣤⡌⠀⡇
⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠨⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠆⠆⠖⠶⠀⠔⠂⣠⠚⣀⠐⠀⠀⠀⠀⢸⠃⠀⠰⠇
⠀⠀⠀⠀⠊⠀⠐⠂⠒⠤⢄⡀⢠⢄⡀⠀⠁⠠⠀⠠⠔⠒⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠄⣠⣾⠕⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠡⡀⠤⣤⡀⢀⡀⠀⠀⠀⠀⡜⢦⣯⠖⠃⠤⢥⣮⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠠⢫⣄⣢⡇⠀⠀⠂⠨⣯⣹⣆⡐⠀⠀⠀⠀⠀⠂⠀⠄⠁⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠙⠃⠶⣤⣳⣽⣿⠯⣼⣦⢀⡀⠀⠀⠀⠈⠀⠀⡰⠤⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠛⠿⠟⠨⠙⠪⠽⣤⠠⠀⣰⠀⠀⢈⡀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠉⠂⠼⠌⢠⣾⣗⣠⡮⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠈⠀⠠⣗⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠶⠐

⠀⠀⠀⢰⡶⢶⣶⡾⡂⠀⠀⠀⠀⢸⢉⡧⢼⠥⢼⠀⠀⠀⠀⠮⠷⠯⢷⠯⡆⠀⠀⠀⠀⠀⡹⠭⠿
⠀⠀⠀⢸⢱⣸⠉⠑⠁⠀⠀⠀⠀⣖⢉⡇⢘⣩⢹⠀⠀⠀⠀⠘⢊⡇⢦⡌⡀⠀⠀⠀⠀⢸⢰⠃⣢⢱
⠀⠀⠀⢸⣺⣹⠀⡋⣱⠀⠀⠀⠀⠧⠿⠟⠵⠤⠼⠀⠀⠀⠀⠀⠀⠻⠘⠄⠾⠀⠀⠀⠀⠸⠤⠥⠭⠴

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⢀⢴⢫⣭⡻⣄⠀⠀⠀⠀⢰⡟⠉⡉⠻⣦⠀⠀⠀⢀⡔⢠⡀⡣⡤⠃⠀⠀⠀⠀⡈⢴⠆⢶⠆⡇
⠀⠀⠀⠈⠻⠴⠁⡴⠋⠀⠀⠀⠀⢹⣇⠀⢁⠄⢶⠀⠀⠀⠘⢦⠐⠰⠇⡰⠛⠀⠀⠀⠠⢧⠀⠺⢧⠠⡆
⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠙⠛⠘⠃⠊⠀⠀⠀⠀⠀⠓⠂⠒⠁⠀⠀⠀⠀⠀⠈⠙⠒⠘⠃⠃

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣄⢠⢄⢀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢸⡉⡉⣭⢉⡟⠀⠀⠀⠀⣨⠏⡶⢠⠘⢅⠀⠀⠀⠀⢸⠁⢄⡀⢹⠁⠀⠀⠀⠀⠟⣿⢿⠭⠽⡄
⠀⠀⠀⢸⡀⠖⠘⣀⣿⠀⠀⠀⠀⠈⣇⣁⢙⣠⡅⠀⠀⠀⠀⠸⢦⣈⡰⠒⡄⠀⠀⠀⠀⡀⠫⢠⡇⠋⡅
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁⠈⠘⠃⠀⠀⠀⠀⠈⠉⠁⠈⠉

⠀⠀⠀⢠⢶⣶⣶⣶⣦⠀⠀⠀⠀⠀⡠⡴⢲⠤⡀⠀⠀⠀⠀⢠⣖⣚⣳⡢⡀⠀⠀⠀⠀⣠⡲⠶⣲⣦
⠀⠀⠀⢰⡏⡿⠐⡄⣷⠀⠀⠀⠀⠼⠠⠇⡼⠆⠵⠀⠀⠀⠀⡇⢼⢸⢇⡇⠑⠀⠀⠀⠀⣿⢰⣧⠘⠏⠇
⠀⠀⠀⢸⣣⣬⣘⣣⣟⠀⠀⠀⠀⠀⠀⣀⠿⡃⣱⠀⠀⠀⠀⠘⠾⣽⠸⠡⡅⠀⠀⠀⠀⠻⣂⡀⣟⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠛⠋⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣼⣦⡀⠀⣠⣄⢤⠀⣔⣦⣀⡠⠀⠠⠀⠁⠀⣠⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢒⠀⠀⠀⠀⠀⠀⠀⠐⣺⡘⣿⣿⣶⡟⠉⠈⠀⠁⠈⢻⣇⠀⠄⣠⠀⠘⢣⡀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢻⠑⠶⠆⠀⠀⠀⠀⠀⠀⣠⠁⠛⠹⠋⠙⢧⣐⣘⡀⠀⣀⣉⡉⣐⣴⣧⠀⢀⣸⣿⠟⢁⣺
⠀⠀⠀⠀⠀⠀⠈⣹⠆⣰⣦⠀⠀⠀⠁⠀⡄⠙⠿⠅⢿⠇⠞⣉⠈⠉⠉⠞⠻⣷⣾⣿⣾⢿⣤⣿⡿⠃⠀⢸⣿
⠀⠀⠀⠀⠂⠀⠻⡟⡀⣠⠛⠀⠀⠀⡼⠗⠀⠠⠤⡥⠀⣻⣿⢯⣰⢻⡄⣿⣦⣈⣭⣏⣿⣿⣿⡿⠀⠀⣠⣼⣿
⠀⠀⠀⠀⠖⣠⢼⡃⣸⣿⣢⣬⣤⢤⣠⣄⣀⡄⠀⢁⣮⠟⢡⣠⡌⠈⠀⠀⢽⣿⣿⢛⡉⣽⠛⠁⡀⠀⢙⣛⣿
⠀⠀⣼⠀⢢⣿⣿⢁⣈⣹⡟⠋⠀⠀⠛⠁⡈⣲⡎⠀⢁⣴⣿⠋⠀⠀⢸⣾⣮⠙⣿⣿⣿⣿⣶⣾⣷⣶⣿⡷⠏
⠀⠫⣟⠀⠛⣹⢟⣹⣿⣾⣷⣸⣾⠃⣤⣼⡃⢈⣿⣿⣿⠛⡛⣴⡆⣾⣼⣿⡟⠳⣿⣿⣾⠿⣿⣥⣾⠋⠁⣀⣸
⠀⣿⣟⠔⢛⣿⣸⣿⣿⣿⠟⣉⣷⠈⠛⡉⡷⠊⢻⣿⣿⣿⣿⡏⠀⠀⣹⣿⡇⠠⠙⣿⣿⢳⣿⣁⣽⣧⣼⣽⣿
⠀⣿⠯⣾⣿⣿⣿⣿⣿⣧⣾⣿⡇⠀⢀⣿⣿⣦⣼⣿⣿⣛⣿⡵⣾⣶⣟⡟⠀⣰⠆⣿⣿⣾⣿⣿⣿⣿⣿⠿⠟
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣦⣾⣿⣿⣿⣿⣻⣭⣴⡾⣿
⠀⣿⣿⣿⣿⡿⣿⣿⣏⡄⣰⣷⣧⣸⣯⣿⣻⢛⠻⣿⣟⣿⡿⠉⢻⣿⣿⣿⣿⣿⠷⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⣿⣿⣿⣿⣴⣿⣿⣿⣧⠈⣽⣿⢃⣾⣷⣌⣿⢦⣿⣿⣿⠃⠀⢺⣿⣿⣶⣿⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⢈⢹⣷⣶⠏⢹⣯⣿⣸⣿⣿⣿⠄⢠⣴⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠠⣿⣿⣿⣿⣿⣿⣿⡟⠁⣮⣿⡏⠁⢰⣾⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣾⣿⣿⡟⠈⣩⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠲⢾⣿⣦⣀⢈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣌⠙⠿⣿⣷⡤⠝⠛⠉⠁⠀⠠⠀⠁⠊⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠲⢿⣷⣦⣈⠛⠿⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢉⡙⢿⣿⠶⠄⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣀⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⡜⠅⣤⣤⡄⢀⣶⣶⠂⣰⣶⡖⠀⣶⣶⡖⠀⣰⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡌⠡⠽⠿⠏⠠⠾⠿⠁⠴⠿⠏⠀⠼⠿⠏⠀⠼⠿⠏⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⣀⣀⡀⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠂


⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⢘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡆
⠀⠞⡞⢻⡇⠰⣾⣷⢖⡶⡖⣀⣤⣤⡌⢓⣂⣄⢘⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⠯⢿⠓⠒⣦⣠⣤⡔⢂⣤⣼⣰⣇⢰⡆
⠀⣛⣥⠘⠉⢛⠿⡟⢙⡄⠁⡩⢨⣗⢩⡍⢹⡟⢊⣩⣬⠇⣀⠀⠀⢀⣤⠀⠀⣀⣀⣀⠾⢠⡮⢳⠈⣼⠨⣯⣳⡍⢿⣿⠯⠀⠛⡚⢇⠤⢳⠼⣧
⠀⡯⠘⢶⣸⢓⡖⢹⣅⣷⠚⡳⢘⣵⠈⣓⡭⠶⣤⠒⣶⡂⢿⣿⢻⡏⠛⢿⣿⣯⣿⡿⣺⣙⢈⢫⠀⣶⡠⢿⢧⠱⠶⣿⣆⠩⢠⡈⢻⠒⠸⢱⡼
⠀⠈⢀⣯⡜⠸⣆⡠⠿⣠⠋⣡⡬⡀⢛⡿⢖⡱⢉⣞⠉⡍⠺⣻⡤⠁⠡⠈⢿⢁⡹⡂⡩⠌⢹⡏⣹⠁⢩⡘⢄⠱⠦⣬⡁⠲⡆⠓⠘⣥⡋⡜⠳
⠀⠀⠀⠙⠀⠺⠤⡘⠀⡀⠀⠉⠐⠉⠛⢡⣄⢱⣏⠀⢢⣸⠓⠈⠁⠐⠒⠀⠈⠀⠀⠈⠁⠉⢚⡙⢉⠑⠏⠉⠒⢇⣠⡁⠉⠠⠆⠨⠂⡌⠔⢠⡉
⠀⠀⠀⠃⠐⠁⠄⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⢈⠧⠀⠘⡟⠠⠩⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣭⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢉⣀⣀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠎⡙⠋⢁⡁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢻⡦⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣆⠰⠤⢀⠸⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣉⠁⠛⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢰⣶⣦⣄⢄⣀
⠀⠀⠀⠀⠴⠂⠀⡶⢴⠏⢠⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⢀⠄⡀⣰⣿⡟⠛⠙⢯⣸
⠀⠀⠀⠐⠀⢠⢠⣠⡀⣲⣦⣤⡄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠉⠉⠁⠘⠏⣁⣀⣠⣤⣿
⠀⠀⠀⡀⢣⣾⡟⡻⠋⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⡤⠀⠐⠂⠠⣴⠿⠛⠉⠉⠉
⠀⢀⠰⠶⣿⣿⠿⠁⢠⣷⢤⣼⣒⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠂⠚⠷⠟⠃⠢⣶⣤⣤
⠀⠰⠶⠴⠿⢁⠤⠋⢸⣷⣄⣀⢈⣿⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⡆⠀⢀⣤⣤⣤⣶⡂⢀
⠀⠀⠠⠶⠂⠀⠀⠀⠈⠁⠙⠿⢩⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⠶⠚⠉⡭⠞⠀⠄⠈⠁⠙⢫
⠀⠠⠂⠀⢰⣖⣁⣤⣤⡴⣴⣄⠀⠑⠌⣐⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠋⠀⠦⠀⠀⢶⡾⠇⠀⠀⠉⠀⠀⡀⢴⣧⣀⣖⡀⠀⠛⠂⠚⠁⣈⠿⣀
⠀⠊⠴⢺⠟⠋⠙⠋⠉⠉⠛⠫⡤⠄⠀⣤⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢴⡶⠒⠂⠀⠠⠔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠡⠂⠠⠜⡶⣿⠀⠙
⠀⠀⠀⠀⠒⡶⠒⢰⠈⠛⣷⠤⣀⢨⣧⡀⠈⠉⠂⠀⠀⠀⠀⠀⠀⢶⠉⠉⢛⣟⠁⢸⠃⠀⠐⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠐⠂⠐⢠⡴⣷⣶⡶⠀⣈⠀⠋⠀⣤
⠀⠨⠀⠀⢠⠀⠀⠉⠛⠁⠉⠢⠈⠀⠉⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠙⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⠋⠩⢉⢋⠴⠿⡿⠀⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠄⢀⠠⡵⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣠⠴⠇⠀⠀⠀⢟⠎⠙⢆⣀⠔⠒⠒⠒⠲⢮⣀⢀⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢈⡲⣄⠀⠀⠀⢉⡹⢇⠀⠀⠠⠤⠤⠀⠤⠋⠀⠀⢀⠠⢀⠶⠒⠠⠔⣉⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠞⠁⠀⣈⠧⢤⡀⠚⢓⡶⠋⠀⠤⠪⠅⠐⠀⢶⡀⢀⡄⠀⠀⠀⠘⡀⠀⠰⣈⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠈⠀⠀⠀⠙⣯⡤⣶⠉⠀⠀⠤⢤⣄⣠⠀⠀⢠⡙⣺⢦⣀⣀⡠⢼⡂⠀⠠⠈⠳⢤⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢘⣯⠶⢃⣀⣀⢀⠂⠀⡠⠀⠊⠁⠐⠀⠤⠈⠄⢠⠄⠀⠀⠽⠿⡤⠤⠆⢶⠣⠴⠄⠨⠙⠷⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⡀⠂⠀⢀⣵⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠦
⠀⠀⠀⠀⠈⢁⠀⠀⠈⢇⠀⠀⠀⠀⠄⠐⠐⠇⢀⡈⠃⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠀⠀⠀⣿⠸⢀⢀⠆
⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠳⠂⠐⠒⠋⠉⠉⠀⠀⠁⠀⢀⠭⠐⠠⣄⠀⠀⠀⠀⡰⠆⠗⣇⠀⡀⡀⠀⠩⢅
⠀⠀⠀⡐⠀⢀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⢄⠨⣀⢘⠀⠀⡰⠃⠀⠀⠉⠂⠀⢄⠀⠀⠀⠡
⠀⠀⠀⠃⠐⠈⠰⠚⠂⡀⠀⣀⠀⠀⠀⠀⠀⠈⡅⠢⠎⢰⠤⠔⠂⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣀⣸⣀⣠⠴⠒⠊⠁⠀⠀⡀⠀⠰⠄⡀⠀⠐⣤⠀⠀⠺⠀⡀⠀⠀⠂
⠀⠀⢐⡒⠀⠀⠠⠤⠨⠓⠈⠁⠉⠀⠀⠀⠟⠦⠓⠂⠉⠀⠑⠊⠈⠀⠀⠀⠀⠀⠀⠒⠒⠒⠠⠸⠱⠈⠑⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂
⠀⠀⠀⠀⠀⠀⢤⡴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣥⠆
⠀⠀⠀⠀⠀⢴⣀⡠⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣴⠶⠾⢋⡀
⠀⠀⠀⠀⢠⣀⣉⣴⣄⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⢠⣌⣩⣿⣦⢼⠛⠃
⠀⠀⠀⢀⣀⠉⠈⣠⣏⢁⣀⣤⠀⢀⡀⠀⠀⢀⡄⠈⠁⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⣡⣤⣬⣡⡼⠿⣶⢶⠗⠀⠀⠀⣠
⠀⠀⠀⠀⠹⠶⠚⣏⠉⠋⠉⢀⡀⠸⠁⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡄⢠⠎⠀⠀⠀⢠⠆⠂⢶⣎⡽⠷⢶⣭⣿⢿⣦⣤⣶⠾⠢⠃⠀⠇
⠀⣠⠀⣤⣀⣤⡾⠿⢦⡾⠚⠛⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣧⣀⠀⡀⢀⠄⠀⠠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣭⣿⠶⣻⣧⣤⣾⣿⣤⣤⡤
⠀⠉⢠⣀⠉⠁⣠⣾⣶⣄⡀⢠⣤⣴⠈⠏⠐⠀⠸⠀⠀⠁⠀⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⢛⣗⢛⣶⣶⣶⣧⣌⣥⣦
⠀⠀⠈⠙⠿⢛⠋⢁⣤⡟⠻⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠿⣏⣙⣋⣿⣶⣿⣏⡉⠉⢉⡀
⠀⡠⢿⡿⣶⣯⣶⠿⢿⣧⣤⣼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⢶⣾⣏⠙⣁⣁⣴⣿⡟⠛⠻⠻⠋
⠀⣄⣀⡀⣀⡤⠀⣀⣼⣥⣀⠁⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠗⠷⠶⠛⠁
⢠⣞⣉⣛⣷⡤⡞⠋⢹⡟⠻⠋⠾⢞⡀
⠀⣹⠫⢠⣄⡄⠀⣤⢻⣧⣤⣀⡛⠟⠁
⠀⠀⠀⠀⠸⠟⠙⠃⠈⠉⠛⠋⠁

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⡤⠞⠉⢀⡤⠒⠂⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣠⠋⠀⠀⢀⡎⠀⠀⣠⠖⠉⠀⠀⠑⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠞⠀⠀⡼⠁⠀⠀⠀⡜⠀⢀⠞⠁⢀⡴⠒⠒⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⡌⠀⠀⡼⠁⠀⠀⠀⡼⠁⢀⠎⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢢⠀⢱
⠀⠀⠀⠀⠀⠀⡀⣰⠁⠀⠀⠀⡰⠁⡀⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸
⠀⠀⠀⠀⠀⢠⢁⠇⠀⠀⠀⡴⠁⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⡄
⠀⠀⠀⠀⣰⠃⡜⠀⠀⢀⡜⠀⠀⠀⢻⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⠈⢦⡀
⠀⠀⠀⣰⠃⠀⠁⢀⡴⠋⠀⠀⠀⢀⠏⢸⠀⠀⠀⢸⢀⡤⠄⠀⠀⠀⠀⠒⠀⠡⠀⠈
⠀⠀⢠⠇⠀⠀⡴⠋⠀⠀⣀⠤⠖⣉⠴⠋⠀⠀⡠⠋⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⡾⠀⢠⠊⢀⠀⢠⠊⠀⠠⠊⠀⢀⣠⠔⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡇⢰⠃⠀⢸⠀⠀⠀⠀⢁⡠⠖⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⡇⢸⠀⠀⠘⡆⠀⠀⣠⠋⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⡇⠈⢆⠀⠀⠹⡄⠀⠇⢀⠔⠋⠀⠀⠀⠀⠀⣸
⠀⠀⢳⠀⠈⢆⠀⠀⠹⡄⢰⠋⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠙⠳⣆
⠀⠀⠈⡇⠀⠘⡆⠀⠀⢱⣸⠀⠀⠀⢀⡴⠋⠀⠢⣄⠠⠤⠤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⢀⠇⠀⣸⠁⠀⡀⠀⡏⢇⠀⣰⠋⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⡰⠋⠀⡴⠁⢀⡰⠃⠀⣸⠘⣦⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠞⠀⣠⠞⣠⠖⠉⠀⠀⢀⠇⠀⠋⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡽⠛⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠒⡿⠒⠂
⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠖⠁⠴⡏⠀⠀⠀⠀⢀⠀⠔⠠⠏⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⢸⣧⠀⡴⢏⣤⠒⢦⠄
⠀⣴⢠⣿⡿⢀⡀⠀⠀⠀⣠⡶⠂⣀⠀⠀⠀⢁⣀⠀⡐⠀⠀⣠⢤⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣸⣷⡄⢿⠛⢿⣣⣀⣀⡄⢀⡀
⣾⣿⣿⣿⣇⣾⠁⡀⢀⢠⠠⠶⢂⠈⠀⠀⠀⠁⢸⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⡀⠀⠀⠸⢻⡄⠀⢸⣿⠟⠷⣦⠒⠀⠈⣯⠉⢉⣸⡇
⢺⣿⠛⢨⣿⣿⣼⣷⣟⣠⠰⠀⡼⠁⠲⡴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⡀⢀⠞⠿⣁⠀⢙⡀⠚⡀⠲⣧⠔⢦⡘⢶⣤⡙⢻⣴
⢸⢿⣃⣤⢹⣿⣿⣿⠟⣡⡄⠀⡤⢀⡠⠀⢲⣶⣴⡄⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡬⢓⠇⢠⣠⡼⠆⠙⡧⣎⣀⠚⠙⢢⣻⠆⠀⠑⠂⠘⠿⣿⣿
⠠⡾⠋⢃⢸⣿⠟⠋⢁⠇⠈⣀⠀⠀⠀⠓⡀⣻⣿⣿⣿⣷⣶⣼⣴⣶⣠⣄⢀⣠⣴⣶⣼⣷⣶⣾⡶⠣⠤⣘⣇⡠⢢⣈⡶⠉⢀⡄⠀⠀⢻⡃⠀⠀⠠⣄⠀⢈⣿
⢀⣆⠀⠋⢘⣥⡴⠚⠛⠠⠖⠃⠀⠀⣀⠀⠉⢺⣿⢿⣿⢻⣟⣿⣻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡿⠂⢀⡀⠈⠡⣴⠀⢹⡴⠞⢉⡴⣦⠜⢶⡤⠀⠀⠀⠘⠛⠿⣿
⠸⠧⠆⢁⡞⠋⠀⠰⠂⡴⠦⠀⠀⡾⣯⠉⠢⣄⡛⣏⠍⣋⣽⣥⡿⠟⢁⡀⠀⠀⠀⠀⠈⠛⣿⡀⠄⠈⠉⠻⢷⣎⢢⡼⠷⠒⠉⠀⠘⠦⢄⡙⠀⠀⠐⣆⠀⠀⢈
⠀⠀⠀⠈⡽⠋⡀⣀⡔⠀⢀⠌⠛⢇⠘⡶⠀⠈⠉⠉⠉⠉⠏⢀⠤⢾⣧⣽⣷⣤⣀⣀⣠⣤⠌⡀⠀⠐⠂⡐⠦⣽⣿⣯⠔⡠⣆⠀⠀⢦⡄⠈⠛⣤⠀⠈⠁⠢⣌
⠀⠀⢀⡼⠓⠀⠁⠰⢤⡤⠟⠀⠀⢀⡓⠙⡇⢠⣄⢨⠀⠀⠀⠙⠺⠿⠛⠒⠓⠚⠛⠛⠚⠡⠀⠤⠐⠃⠠⠟⢦⣤⡹⠟⠊⠁⡼⡀⢠⠿⠟⠀⢠⢈⣦⣾⠀⠀⢻
⠀⠠⠞⠡⠀⣀⣤⠖⠾⡄⠀⠀⠀⠈⢳⣠⠝⢦⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀⡀⠙⠈⢢⠀⢄⠀⠻⣆⡀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠃⠐⠊⠉⠂⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣤⠄⠞⠉⠣⠠⡀⠀⢦⡨⠦⠀⢨⣿⢯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠰
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣽⣭⣿⣭⣯⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣶⣾⣿⣿⣶⣾⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠞⠛⠛⠛⠛⠶⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⢀⣀⣴⠟⠋⠉⠻⠋⠀⠀⠈⢻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠙⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠻⡶⠛⠛⠛⠷⣦⣰⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠷⣦⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣽⣿⢭⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢤⡆⠀⠀⠀⠀⠀⠀⠀⠈⠾⠽⠶⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣺⣗⢺⠂⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣻⡟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⠀⠀⠀⢾⡷⣽⠆⠀⠀⠀⠀⣴⡖⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠸⣗⡿⣗⡟⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢲⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠙⠀⠀⠀⠈⠩⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣺⢿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣰⢷⡔⢮⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠃⡼⠃⠀⠉⠈⠻⣿⣿⣿⣦⣀⠀⢀⣤⠾⠫⠞⠉⠁⣙⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠞⠀⠈⠀⠀⠀⠀⠀⠀⠙⠏⢿⡙⢿⡿⣟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠙⠳⠦⣀
⠀⠀⠀⠀⠐⠁⠀⢠⣇⣸⣧⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⠀⠀⣾⠀⣀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢀⡠⠴⣚⣫⡭⠥⠶⠶⢒⣲⣶⡶⠶⠶⠶⠦⠤⣤⣀⡀⠈⠉⠙⠛⠻⠿⢷⣿⣄⣀⣼⣿⣼⡇⠀⠀⣸⡄⣾⡆⢀⣀⠤⠂
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠠⢄⣀⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠑⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⢺⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠐⠁⠐⠁⠠⠃⠀⠿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠖⡉⣀⡏⠀⣄⠀⠀⠀⠀⠐⢆⠠⠈⠁⠀⠈⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠓⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⢀⠊⠠⠀⠲⠄⣹⡈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠴⠶⠣⠛⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠈⠀⠠⡄⡀⠀⠁⢄⠙⡜⠋⠤⠀⠈⠑⢀⠀⠀⡀⠀⠀⠈⠻⠖⠒⠐⠂⠀⠀⠰⡀⡀⡀⠃
⠀⠀⠀⠀⠀⢀⠸⠈⣘⠄⠈⠀⠃⠀⠂⠠⣥⡌⠀⠌⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠦⣥⣇⢰⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡌⢦⠀⣲⠁⠀⣀⠁⠘⠂⢈⠑⢲⡀⠂⢁⢀⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠉⠈⠀⢤⠙⠀⠨⣐⡀⠄⡠⢀⡀⠀⢠⡀⠈⢙⡀⠘
⠀⠀⠀⠀⠀⠠⡈⢱⠁⣐⠍⠈⠀⠀⠠⠀⠉⠀⠒⠺⢧⡂⠼⠀⣀⡄⠁⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢌⠧⡤⢀⠊⠀⠀⠀⠢⠀⠀⠀⠂⠘⠲⠬⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠉⠂⠦⣔⠂⠈⠀⠠⠁⠀⢀⠀⠀⠀⢄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠀⠉⠁⠙⠪⠁⠋⠠⢈⣀⡰⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⣀⠀⠀⢀⠀⡀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠺⣼⡇⠠⠀⠀⠸⣿⡷⠘⡀⠀⠀⢀⠀⣧⠟⢀⡆⠀⠀⠀⠀⠀⢠⠘⠀⢸⡇⠀⣸⢉⡇⢀⠸⠀⡇⠴⡟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⠀⢂⡈⣷⠀⠖⠁⠀⣿⡇⠋⠁⢀⣦⠸⠀⣇⠄⠂⠀⠀⣠⠀⠀⠀⠀⢻⠀⢸⡇⣄⡏⢈⠥⠀⠣⠠⡇⢀⡅⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣧⢸⡶⠃⠀⠀⣿⣦⠀⢠⠈⠀⠀⢀⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⣸⠿⠏⢠⠂⢀⠀⠠⢤⡧⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡁⠈⣧⠀⠀⠀⣿⣿⡇⡈⠀⠀⠀⢸⣀⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡶⢰⠀⠀⠄⠀⠀⠀⣿⠦⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣸⡀⠀⠀⣿⣿⠄⡠⠖⠀⠀⠈⠁⠀⠀⠓⠦⠀⠀⠀⠀⠀⠀⠀⠘⣷⢦⠀⠀⠒⠀⠀⠀⢿⠶⠀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⡟⠈⡄⠀⠀⠀⠀⠂⠈⢲⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⣿⠶⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⣰⠔⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣿⣿⡿⢆⣴⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⡀⣿⢠⣶⣷⣶⣄⡀⠀⢰⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢱⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⡧⠇⠘⠛⠿⠷⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠏⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⡁⢸⣦⣄⠀⠀⠐⢾⡄⣠⠴⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡀⠸⣿⣿⡏⠀⠘⠁⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠇⣸⣿⣿⣷⣤⡀⢸⡇⡏⢤⣠⣿⣴⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⠀⠷⢾⣿⣿⡇⣤⣴⠞⠋⢡⠔⢸⠀⠀⢀⠂⠀⠀⡇⡇⡄⡉⠻⣿⡟⠃⣿⣿⣿⣿⣿⣾⣇⡇⠀⢿⣶⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡚⠀⠁⢀⣿⣿⣧⣿⠀⠀⠀⢦⡴⢤⣤⣶⣅⡰⠃⠀⠡⠃⣧⢸⣄⣿⡷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠡⠊⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠆⠈⣁⣴⠞⠋⣿⣿⠀⣼⠀⢀⣴⠟⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠇⢸⡇⣿⡟⣧⠈⠻⣿⣿⣿⣿⣯⢛⣉⣴⣾⠛⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⡴⠟⠉⠀⠀⠟⣿⠟⠀⢈⣴⡏⠁⠳⢎⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠉⠀⠀⣬⣿⣿⢸⣿⢹⣯⣦⣿⡇⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⢟⠁⠀⠀⢦⡀⢠⠀⢸⣿⡟⢾⠋⡇⠀⠀⠀⠀⠀⠃⡾⢰⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃⣠⣾⣿⣿⣿⢿⡗⢸⣿⣸⠛⡇⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⣿⠀⠠⠄⢼⠷⠛⢦⣸⣿⠃⠈⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⢰⣿⣿⣿⣿⣿⢸⣇⠘⡟⢿⠀⢳⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⢰⠀⠀⠈⢹⣿⡏⢀⠀⠀⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⣧⢸⣿⣿⣿⣿⣿⢸⣏⢰⣿⠸⡀⠘⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⠈⠀⠀⠀⢸⣿⠇⠠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣾⣿⡍⠈⣿⣿⣿⣿⣿⢸⣿⢸⣾⢠⣷⢈⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢸⠀⠀⣠⣾⣿⣿⣧⡓⡿⣯⣿⣿⣿⢸⡏⠀⢻⢸⣮⢀⡇⡇
⠀⠀⢀⡀⠀⣠⠤⣴⣀⣿⣶⣾⠀⠀⠀⠘⠀⠀⠀⢸⣿⣿⡅⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠰⠀⢀⣴⣿⣿⣿⣿⡷⠟⢰⣿⣿⣿⣿⢸⡇⢀⠹⢸⣿⢸⡇⡅
⠀⢠⣼⣿⣿⣽⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠇⠀⢸⣾⣷⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⠃⣾⣿⣿⣿⡇⣿⣇⣼⡀⢸⡟⢸⡏⡇
⠀⠸⣿⣿⣿⣿⢋⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⢷⡇⠀⠀⠀⠀⠀⠀⡿⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣇⢿⡁⣸⣧⣸⣇⣸⡇⠃
⠀⠀⣿⣿⡿⠏⢿⡿⠿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢿⣿⢯⡈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠛⣛⢻⢛⡟⠛⠛⠛⣿⣷⡊⡘⠛⡿⠻⠛⢸⣯⣾⠻⠛⠟⠟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣇⠀⠀⠀⠻⠛⠃⠁⠀⠅⢰⠀⣾⠛⢳⢠⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⡈⠀⠛⠀⠈⠈⠀⠀⢸⣿
⠀⠀⠂⠠⢤⢤⢰⠆⠄⠀⠶⠶⠶⠶⠦⠶⠲⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠈⠩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠆⣀⡀
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⢤⢀⢬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡸⠄⡀
⠀⣠⡾⠟⠁⠀⠀⢀⠀⠐⣊⣠⢤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⠀⡾⠃⠠⣄⠒⠆
⠠⠿⠿⠿⠄⠀⠀⠀⠀⡀⠈⣤⠀⢀⠰⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠛⠂⣮⠅⣈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⢨⠀⡠⠀⠺⠇⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠵⠂⠨⡡
⡀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠉⠙⠒⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⢠⣅⣋⣭⡟⠒
⠈⠀⠀⠀⠀⠀⠀⢐⡤⠾⠀⠼⠀⢳⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠄⠿⢶⣶⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠛⠦⣄⠀⠀⣀⡤⠖⠛⠛⠋⠉⠛⠛⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣇⠀⠀⠀⠀⠀⠀⠈⢳⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡤⠤⢤⣄⡀
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣶⢤⣤⣴⣶⡞⢛⡷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⠀⠀⠀⠀⠀⣠⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡏⠁⢾⡄⠀⠀⢹⡿⢦⡄
⠀⠀⠘⠳⠤⢤⣤⣤⠤⠴⠖⠛⠉⠀⠈⠙⠓⠒⠚⣿⢷⡀⠈⠙⢿⢳⡶⢶⣶⣶⢾⡛⠾⣱⠏⢩⣅⠀⢀⡼⣣⠾⠇⣠⢟⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⣙⣛⣛⣛⠁⣙⣛⡃⢘⣛⡋⠀⣛⣿⡉⢨⣭⣍⢠⣭⣭⣭⣥⠨⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠋⢰⡒⢫⡞⠁⠀⢹⣯⡼⣡⠿⡜⠦⣽⠞⠁⠈⢧⠻⣤⡄⠈⠳⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣾⣇⠀⠀⢘⡷⣠⡽⠼⣧⣄⢿⡀⠀⠀⣼⣥⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣨⣭⣭⡍⢸⡃⠀⠀⠀⣸⢊⢩⣽⣛⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⡼⣧⠳⣤⣤⠼⢡⠟⢦⢳⣘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣒⠋⢾⡉⠳⠦⠟⢿⣤⠼⠃⠈⡷⠉⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠘⠷⢷⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⠛⢿⣿⡿⠀⢸⣿⡿⠿⢿⣿⣿⠀⢸⣿⡿⠿⢿⣿⣿⠀⢸⣿⡿⠿⠿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠀⢸⣿⠀⣶⠀⣿⣟⠀⢸⣿⣥⡆⢸⣿⣿⠀⢸⣿⣀⣶⠀⣿⣿⠀⢸⣿⣀⣶⠀⣿⣿⠀⢸⣿⡿⢀⣿⣿⣿
⠀⠀⠀⣹⣿⣿⣿⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⠒⣿⠒⣿⣿⠀⢸⣿⣿⠗⢺⣿⣿⠀⢸⣿⣿⠛⢲⣿⣿⠀⢸⣿⣿⣿⠒⣿⣿⠀⢸⣿⠓⣾⠛⣿⣿
⠀⠀⠀⣽⣿⣿⣿⣠⣶⡇⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⠀⠿⠀⣿⣯⠀⢸⣿⣿⡇⢸⣿⣿⠀⢸⣿⠋⠰⠿⣿⣿⠀⢸⣿⠉⠿⠀⣾⣿⠀⢸⣿⣀⣉⠀⣹⣿
⠀⠀⠀⢾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣷⣶⣾⣿⣿⠀⢸⣿⣿⣷⣾⣿⣿⠀⢸⣿⣶⣶⣶⣿⣿⠀⢸⣿⣷⣶⣾⣿⣿⠀⢸⣿⣿⣿⣶⣿⣿
⠀⠀⠀⢾⣿⣿⣿⣿⣿⡷⠶⢾⣿⣿⣿⣿⣿⠀⠈⠛⠛⠛⠛⠛⠋⠀⠘⠛⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛
⠀⠀⠀⢺⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⠀⢰⣶⣶⣶⣶⣶⡦⠀⢰⣶⣶⣶⣶⣶⣦⠀⢰⣶⣶⣶⣶⣶⣦⠀⢰⣶⣶⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⣦
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⠉⣉⣉⣿⣟⠀⢸⣿⣿⠋⣹⣿⣿⠀⢸⣿⠉⣉⠉⣿⣿⠀⢸⣿⠏⣉⠙⣿⣿⠀⢸⣿⠏⣉⠙⣿⣿
⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⡀⠛⢻⣿⣟⠀⢸⣿⣏⡠⣿⣿⣿⠀⢸⣿⣿⣏⣠⣿⣿⠀⢸⣿⣀⣿⣀⣿⣿⠀⢸⣿⡀⣿⡀⣿⣿
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣯⠀⢸⣿⠀⣿⠀⣿⣿⠀⢸⣿⣿⠁⣽⣿⣿⠀⢸⣿⠁⣿⠀⣹⣿⠀⢸⣿⣷⡄⢠⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣄⣉⣠⣿⣯⠀⢸⣿⣄⣉⣠⣿⣿⠀⢸⣿⣇⣰⣿⣿⣿⠀⢸⣿⣄⣙⣀⣿⣿⠀⢸⣿⣟⢀⣾⣿⣿
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡷⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠿⠿⠷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣄⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣠⣴⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠉⠙⠻⢷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⣷⢀⣀⣤⣶⠛⠁⠀⣸⡇
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⡿⠛⠉⠉⠉⠁⠀⣰⡿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣴⠿⠟⠛⠛⠃⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⠶⣦⣀⠀⣠⣾⣿⠿⠛⠛⠛⠿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣷⣦⣤⣤⣤⣤⣀⣰⡟⠁⠀⠀⠀⠀⠹⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢶⡾⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣦⣤⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣤⣤⣴⡶⠟⠋⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠁⠀⣀⣀⣰⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠈⠉⣹⡟⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠛⣿⠏⠻⡄⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣿⠛⠿⢶⣶⡶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⡷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠾⠛⠛⠛⠛⠛⠛⠁⠈⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⣀⣴⠾⠋⠀⣰⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⢀⣠⣤⠶⠞⠛⠛⠋⠉⠉⠉⢹⣷⠾⠋⠁⠀⠀⣴⡟⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⡀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠾⠛⠻⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠈⢻⣄
⠀⠀⠀⠀⢰⣟⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠈⠙⠻⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣤⡶⠟⠛⠛⠷⣦⡀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢻⡆
⠀⠀⢀⣼⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢀⣾⠃⠀⢀⢀⠀⠀⠈⢻⣆⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢿⡀
⠀⢠⡾⠃⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠛⠛⠃⠀⠀⠈⠛⠛⠛⠛⣿⠇⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⣇
⣰⣟⡁⠀⠀⢀⣹⣧⡀⠀⠀⠀⠀⠀⣼⣃⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣿
⠉⠙⣿⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡇⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⠀⠀⢸⣇⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⣿⣄
⠀⠀⣿⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠁⠀⠀⢈⣽
⠀⠀⢸⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣤⡄⠀⠀⢀⣤⣤⣤⣼⡏⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢠⡾⠃
⠀⠀⠈⣿⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⠀⠀⠈⢿⡉⠉⠉⠀⠀⠀⢀⣼⠏⠉⠉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁
⠀⠀⠀⠸⣧⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠛⢶⣤⣤⣤⡶⠟⠁⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣼⠿⢦⣄⡀
⠀⠀⠀⠀⠹⣧⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣽⠏
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⣦⣤⣤⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⣼⠏⠀⠀⢀⣠⡶⢿⣇⣀⣀⣀⣤⣤⣤⡶⠾⠛⠋⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠾⠏⠀⣤⡾⠛⠁⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⡀⢠⣤⣤⣤⣤⣤⡶⠶⠶⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠦⠀⠀⠀⠠⠄⠀⠀⠀⡠⣤⡄⠀⠀⠀⡠⡶⡄⠀⠀⠀⢀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠰⡐⠀⠐⠀⠀⠀⠀⠀⠀⠂⠚⠍⠀⠀⢴⠟⠐⣷⠄⠀⢰⣿⡯⠿⠁⠀⠀⠘⢒⠴⣶⠀⠀⠸⠟⠛⠓
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⣾⣿⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢷⠐⣆⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠐⡆⠀⠸⣿⣿⡟⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠺⠦⠟⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠒⠀⠀⠙⠀⠐⠺⠓⠂

⠀⠀⢴⣀⠀⣐⠆⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣤⢠⣦⠀⠀⢸⣶
⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠉
⠀⠀⠀⣄⣀⣠⠀⢀⣠⣤⣀⡀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣠⣶⣴⡄
⠀⠀⠈⠙⠿⠋⠀⠈⠻⠿⡿⠿⠈⠱⠆⠶⠀⠀⡈⢶⢘⡀⣴⠀⠻⠿⠇⠀⠀⠀⠀⠀⢀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⢸⣿⣧⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣽⣿⣇⠀⠀⠀⣰⣿⣷⣶⣼⣿⣿⣤⣤⣤⣶⣶⣆⠀⠀⠀⢀⣿⣿⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⣿⣆⡀⠀⣿⣿⠋⠛⢿⣿⣿⠟⠛⠛⢻⣿⣿⠀⢀⣠⣾⣿⣿⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠺⡿⠿⠿⠟⠛⠻⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣾⣿⡿⠟⠋⠉⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣶⣤⣿⣿⣀⣠⣴⣾⣿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠙⠻⣿⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠛⠁⣿⣿⡇⠈⠙⠻⢿⣿⣿⣿⣇⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⡄⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠁⠀⢸⣿⣷⣶⣶⣿⣿⣿⣶⣦⣤⣰⣿⡏⠀⠈⢿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⣿⣿⠃⠀⠀⠀⠙⠛⠛⠛⢻⣿⡟⠙⠛⠿⣿⣿⠇⠀⠀⠈⣿⣿⡍⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠓⢓⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠈⠀⠠⠀⣶⡶⠀⠀⠀⠠⠀⠀⠀⠀⠐⠖⠓⠶⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣭⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠚⠓⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⠛⠙⠚⠓⠓⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⢠⠖⠀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠚⠐⠳⠖⠤⠂
⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠌⣠⠖⠈⠈⣧⣽⠋⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⠧⠢⠔⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠀⠈⠐⠉⠈⠒⠚⠀⠙⢆⢀⡠⢀⢀⠀⢠⡄⠤⠒⢲⣴⣧⣶⡜⢚⣒⠘⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠐⡐⠒⠊⠉⠁⢡⣹⣷⢰⠀⣰⣶⡆⠀⡄⣯⡴⣄⢅⠠⡌⡛⣿⣏⣴⠀⠌⠁⢉⡁⡀⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣌⠄⠈⠉⢅⣐⣋⠏⡁⢹⠀⢀⡇⠀⣠⠤⠼⠂⠂⡁⠀⠈⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠋⠉⠁⠉⠐⠄⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⡀⠀⡄⠠⣮⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢳⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠻⠂⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣽
⠀⠀⠀⠀⠀⠀⢘⡼⠈⠵⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⡏⠘⡇
⠀⠀⠀⠁⠀⣠⠟⠁⠲⠇⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⣇⠀⡄
⠀⠀⠀⠀⠀⠅⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⠊⡏⠀⣥
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠃⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⢈⢻⣼⠀⠀⢠⡞⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠈⣬⣿⣄⣻⡆⠀⡾⢀⣠⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠀⠈⠁⢠⠌⣿⡇⠀⢻⠟⠀⠊⢶⠁⠀⠢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠠⠄⠂⣀⠀⣀⣠⠿⡇⣀⠘⣤⡄⡤⠚⠀⠀⠀⠈⢸⠀⠀⠀⠢⡀⠀⣀
⠀⠀⠀⠠⠠⢀⠀⠀⠒⠄⠀⢀⡀⠀⠀⢀⢠⠀⡄⣿⠀⡇⠈⢩⠼⠀⡇⠀⠀⠀⠀⠂⡸⠀⠑⠀⠀⠈⠂⠀⡑⠀⠀⠐⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠔⠃⠂⠀⠀⠀⢸⡐⠂⡛⣦⣇⡀⢙⡿⠓⠛⢠⡆⠀⠀⢀⡃⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⡀⡀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠀⠀⣿⡁⠠⢀⣿⣏⠀⣼⣇⠀⢂⣏⣿⡀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠀⠀⠈⠛⠛⠿⢷⣶⣮⡍⣖⣲⡆⣶⣤⣒⣾⡥⢠⣸⣿⣮⣦⣿⣯⣉⠭⢤⡟⣣⠄⣴⠀⣠⢠⡐⣤⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⣤⣥⢬⠀⠀⡇⢸⡿⢹⡁⠀⠀⡇⢹⠀⠀⠀⠀⢠⠉⠉⠋⠉⠉⠙⠷⢾⣧⣰⣢⡐⣠⢄
⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠉⠉⠋⠉⠘⠛⠀⠉⠉⠉⠁⠓⠛⠻⠾⠷⠶⡤⠆⠀⢄⡀⢀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀
⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠐⠪⢟⠄⠀⣠⡏⢹⡄⠀⢀⣶⡞⣿⠃⠀⠠⢤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠛⠃⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣤
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣀⠀⠀⣤⣤⡄⠀⠀⠀⠀⢀⠤⢾⠤⣄⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠤⠀⠀⠹⣿⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠄⠠⠝⠁⠀⣤⣤⣀⣀
⠀⠀⠀⠀⠄⠀⠀⠐⢀⠀⠀⢻⠸⡇⠀⠸⠿⢿⠃⠀⠀⢸⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠁⠀⠀⢒⢀⠀⡙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠤⠉
⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠋⠈⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⠘⡛⠓⡀
⠀⠀⣀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠚⠿⠿⠻⠥⠿⠷
⠀⠀⠻⠿⠃⠀⠻⠿⣿⠷⠀⠡⠆⢤⠁⠀⡈⢤⣃⢠⠄⠀⢿⣿⠆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣾⣿⡿⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⢰⣿⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⠀⠸⣿⣷⣄⠀⠈⣿⣿⠀⠀⣠⣾⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⡀⠀⠈⠻⣿⣷⣄⣿⣿⣠⣾⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⢿⣿⣦⡀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⢀⣴⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠙⢿⣿⣦⡀⠀⠈⣿⣿⠁⠀⢀⣴⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣶⣦⡀⠀⠙⢿⣿⣧⡀⠀⠀⠙⢿⣿⣦⡀⣿⣿⢀⣴⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⣿⣿⣤⡀⠀⠙⢻⣿⣦⣀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⡿⣿⣿⢿⣿⣦⡀⠀⠈⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠛⠋⠀⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⡿⠋⠀⣿⣿⠀⠙⢿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⢀⣴⣿⡿⠋⠀⠀⣠⣿⣿⣄⠀⠀⠙⢿⣿⣦⠀⢸⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣴⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠙⢿⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⠀⠀⣠⣾⣿⠟⠉⣿⣿⠉⢻⣿⣷⣄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢻⣿⣿⠀⠸⣿⠟⠁⠀⢀⣿⣿⡀⠀⠈⠻⣿⠆⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠸⢿⠟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⣿⣿⠻⣿⣿⠄⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⠀⠈⠁⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣾⣿⣿⡿⠟⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣴⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣎⣹⣿⡽⠛⣷⣤⣗⢘⣋⣩⣉⣍⢩⣽⢦⡤⡾⡟⣶⢂⡤⣒⢐⡤⣶⠶⣗⡴⠶⡤⣴⢴⣤⠶⠴⢶⢶⡶⠶⠶⠲⢶⣒⣲⣒⢲
⣟⣿⣿⣳⣴⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣙⣿⣟⣹⣿⣾⣥⣿⣿⣿⣚⣃⣘⣛⣓⣆⣹⣟⢪⣫⣿⡝⢛⣿⣽⢿⣫⣡⠀⣜⣻
⡏⣿⣯⣽⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⡿⣷⣿⡯⣭⠿⡿⢿⠿⠟⠙⠘⠉⢉⠉⢡⢤⢀⣌⣁⣁⣶⣿⣿⣿⣶⣿⣬⣯⣞⣿⣼
⣟⣻⣟⣻⣿⢿⡽⡯⣭⠿⣉⠿⣏⣙⣘⣃⣁⢠⡉⣄⣠⡀⡠⡖⡚⠤⣾⢽⣭⢿⣿⡿⡿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾
⣇⣾⣿⣿⣿⣿⣷⡷⡶⣶⠻⣿⣴⣾⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣲⣾⣛⡾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣯⣽⣿⡿⣯⣿⡟⣿⣮⣏⣿⣷⣿⣾⣿⣷⢿⣿⠻⣽⣿⣿⣿⢻⡛⠛⢋⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⡿⣾⣿⣗⣿⢿⡿⣿⣿⣽⣶⣿⣿⣯⡿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣾⡿⣿⡿⠻⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡿⣭⡍⠠⢍⢉⠡⡥⡨⢄⣶⠂⣄⣼⣿⣿⣷⣭⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢼⣿⡵⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⠿⢥⢿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⢭⡾⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢹⣿⡿⡿⠿⠿⠟⠻⠛⠿⢿⣿⣷⣯⣼⣿⣿⣿⣿⣝
⣿⣿⣿⣿⣿⣿⣿⡿⢿⠓⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠃⠀⠉⠁⠀⠀⠀⠀⠀⣠⣿⣆⠻⢿⣟⣥⣾⣯⣍⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⡸⣿⣿⣿⣿⡟⢿⣿
⢿⣿⣿⣻⣛⣿⡿⠛⢻⠿⠿⠿⠿⠯⠟⠿⣿⢿⣟⢽⣋⣱⢿⣃⣤⣄⣤⣤⣶⣤⢤⣤⣤⣴⣟⢟⣿⣟⣿⢧⣼⣿⣗⢿⢍⢷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⡿⣿⡼⢿⣿⣿⣿⣿⣿⣿⣘⣚⣿⣿⣿⣉⣿⣿⣿⢸⣿⡿⠛⣸⠟⡋⢙
⣿⣿⣿⠻⠟⢻⣿⠈⡛⠉⠋⠉⠉⠁⠉⠁⠉⠉⠁⠁⠙⠘⠃⠛⠁⠉⠿⠿⡯⠝⠛⡛⣧⡟⣿⢽⣿⣿⡿⣋⣽⣶⣷⣾⣿⣿⣿
⣷⠿⢁⣗⣠⣾⠏⠁⠁⠀⣸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣀⠘⠆⠛⠓⠛⠛⠻⠛⣿⣧⣿⢙⡻⣿⣻⣏⡛⢛
⡏⢀⣙⡟⠁⠀⢠⣔⠀⢠⣺⣿⠶⠀⠀⠘⠃⠀⠀⠀⠀⠈⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠉⠻⢄⡉⠛⠘⠦
⡧⢀⠀⠋⠀⠀⣻⣧⠄⠀⢟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⣷⠀⠀⢀⡄⢠⠉⠀⠀⠀⠀⠀⠀⠁⠂
⣡⠆⢘⠁⢀⢠⣿⣿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠐⣿⣿⣦⢟⢄⣷⡤⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⣉⣽⡧⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣯⣿⣾⢿⡁⠀⠀⠀⢛⠀⠀⠀⡀
⡅⠀⢁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⢧⡌⠛⠀⠁⠢⠀⠀⡅⠀⠀⣸⣧⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⠀⠀⣀⠁⠰⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢀⣼⣻⣿⠅
⠁⠀⠂⠀⢀⡄⠀⠠⠏⠀⠀⠀⠀⠠⠆⠰⠉⠀⠀⠀⢀⡀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣹⣿⣻⠄
⠀⠀⠀⠀⠠⠂⢤⡔⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠆⠀⠀⠀⠀⡖⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⠿⣄
⡄⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⡈⡄⠠⢀⡈⠀⠀⠀⠈⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⢀⡈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢶⠀⠙⠀⠀⠉⠀⠀⠀⠀⠠⠀⠰⠀⠀⡄⢠⠀⠀⡄⢀
⢃⠀⠀⠀⢀⣠⠀⢡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⠂
⠀⠀⣤⠀⠀⣰⡄⠀⠠⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠢⢔⠄⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡀⠀⠀⣐⠜⢁⡀⠂⠄⠁⢂⠠⠀⠀⠀⠀⣸⡇⠀⠒⠀⠀⠨⠸⠃⠂⠀⠂⠄⠑⢠⠀⢠⡇⠨⢁⡂⠄⠀⠉
⠀⠀⠀⠀⠁⠘⠀⠃⠀⣀⣠⣤⣱⠆⠀⠠⠴⠬⠤⠦⡄⠐⡍⠔⠀⠈⠈⡠⠀⡀⣐⡆⠠⠇⠸⠀⠠⡤⣷
⢀⣼⡀⠀⠠⠅⠥⢠⠾⠿⠿⠏⡈⢣⠤⠄⠰⠆⠰⠆⠰⠰⡇⣿⠆⢾⡇⢰⠕⢈⣌⠛⢶⢏⡷⠷⠀⠃⠹⠆⢀⣀
⢰⣿⡣⠀⠀⠂⡆⠀⢠⠀⣄⠀⠄⠀⢰⡆⢀⢀⣀⠀⢴⠄⡇⠀⠶⡂⠀⠀⢠⡌⠉⣤⠠⣶⣶⡄⠃⣀⠃⡖⠉⠙⠂
⢰⣿⡃⢸⡇⣥⡅⢠⢠⠀⡄⢠⢰⠀⠀⠀⢀⠀⣀⠐⠀⢠⡇⠀⡟⢧⠀⠂⣸⣇⢀⣿⣀⣭⠭⡇⠀⣿⠀⡇⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠛⠉⠙⢦⠀⠙⢶⠦⣄⡀
⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⣆⠀⠙⠲⣄
⢣⠀⠀⠀⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠓⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⡆⠀⠀⠈⢳⡀
⢻⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⠀⠀⠘⣆⠀⢹⡀⠀⠀⠀⢻⡀
⢸⠀⠀⢀⢠⢶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⣽⡀⠀⢧⠀⠀⠀⠀⣇
⢸⡀⠀⠨⢸⠰⡏⠅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡷⢤⣀⠀⣿
⢸⡇⠀⠨⢸⠀⡇⡃⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠒⠒⠒⠲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⠈⠳⣇
⢸⡇⠀⠶⠺⡄⡗⠶⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠒⢦⣀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣄⣀⣀⣰⡒⠢⢼⣀⠤⣼⠴⢦⠀⢸⡆
⠈⡇⠀⠀⠥⡇⡇⠅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡇⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠄⠀⠁⠀⠈⠁⠀⠀⠀⠛⠉⡿
⠀⡇⠀⠀⠄⡇⡇⠁⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢷⣀⡀⠀⢸⢸⡆⠀⠀⠀⠀⠀⠀⠛⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆
⠀⡇⠀⠚⢋⡇⣇⣉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⣿⣁⣤⠏⠘⠃⠀⠀⠀⠀⠀⠀⠰⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧
⠀⢿⠀⠀⠄⣇⢿⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⡀⠀⠀⠘⣇⠠⣄⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⢸⠀⠀⠀⣿⢸⠀⡰⠄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡞⣇⡇⡇⢠⠶⢮⡳⠀⠀⠀⠀⣼⣯⠏⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⢸⠀⠘⢋⢹⢸⢨⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⠳⠻⠇⠁⠀⠀⠈⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢻⠀⢀⡀⠀⣄⠀⢸⠻⣅
⠀⢸⡆⠀⢐⢸⣸⠐⠀⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣜⣋⠛⠦⠟⠀⠀⠀⣀⣤⠴⠶⠶⠦⣄⠀⠀⠀⠈⠓⠋⠣⠤⠏⢹⠏⠀⡻⣄
⠀⠸⡇⢠⣴⢸⣾⠐⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣀⠀⠀⠀⠈⠳⣀⣠⠴⠖⢻⡁⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡇⣸
⠀⠀⡇⠀⢀⢺⣿⠀⡂⠀⠸⡇⠀⠀⠀⣀⡤⠖⠛⠋⠉⠁⠀⠀⠀⠀⠙⠲⢖⡶⠒⣲⠖⠲⢤⡀⣽⠀⠀⠀⠐⠛⣿⡟⠀⠀⠀⠀⠀⢀⡴⠁⠀⢠⡟⢀⡟
⠀⠀⡇⠀⠀⠈⣿⡆⠂⠰⠰⡇⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠙⠲⣄⠀⠙⠳⣄⡀⠀⠀⠀⣿⠇⠀⠀⠀⢀⡴⠋⠀⠀⢠⡟⠀⡼⠁
⠀⠀⣿⠀⣤⠄⣿⡗⠚⠁⠀⣿⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⡿⠀⠀⠀⠀⠉⠓⠒⠚⠁⠀⠀⣀⡴⠋⠀⠀⠀⣠⠏⢀⡾⠁
⠀⠀⣿⠀⠀⠀⡿⣇⡀⠀⠀⢹⠀⠀⠈⠣⣤⣀⡀⠀⠀⠀⠀⠀⣴⡆⠀⣾⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠸⠃⣠⠏
⠀⠀⢸⠀⠀⣰⠃⣀⣽⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧⢀⣼⣦⢠⣤⠇⢧⡿⣸⠀⠀⠀⢀⡞⠻⠦⠤⠤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⢸⠀⠀⠘⠿⠶⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⢸⠁⢺⢸⣿⠀⠘⠑⠟⠀⠀⠀⠈⢳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢦⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠘⡇⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⡴⢦⠀⠀⢸⠀⢣⠀⠀⡏⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢹⠀⠀⡜⠀⡇⠀⠀⡴⢦
⠀⠀⠀⠀⠀⡇⠈⢇⠀⢸⠀⠸⡀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⠇⠀⡇⠀⡸⠀⢸
⠀⢀⡀⠀⠀⢹⠀⠘⡄⠸⡀⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⢠⠇⢠⠃⠀⡏⠀⠀⢀⡀
⠀⢧⠈⢢⡀⠈⡆⠀⢳⠀⡇⠀⢳⢰⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡆⡎⠀⢸⠀⡞⠀⢰⠁⢀⡔⠁⡼
⠀⠈⢆⠀⠳⡀⢱⠀⠈⡆⢷⠀⠸⣼⢀⠀⡇⠀⠀⠀⢀⡔⠋⡇⢸⠙⢢⡀⠀⠀⠀⢸⠀⠀⣧⠇⠀⡞⢰⠁⠀⡎⢀⠞⠀⡰⠁
⠀⠀⠈⢦⠀⠱⡜⡆⠀⠘⠋⠀⠀⠀⠀⠀⢣⠀⠀⢠⠎⠀⡜⠀⠀⢣⠀⠱⡄⠀⠀⡜⠀⠀⠀⠀⠀⠙⠁⠀⢰⢣⠎⠀⡴⠁
⠀⠀⠀⠈⢣⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡠⠋⠀⡸⠁⠀⠀⠈⢇⠀⠙⢄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡜⠁
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⡬⠤⢤⠄⠀⠀⠀⠀⠗⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⡶⠤⢤⠄⠀⠀⠀⠀⠕⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠉⠙⠛⠉⠆⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠜⢡⢄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢱⢄⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀
⠀⠀⡇⢈⣸⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠇⢈⣘⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⡆
⠀⠀⢻⢻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠉⢀⡀⠀⠀⠀⠀⣽⣿⣷⡁⠀⠀⠀⠀⢻⣻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠉⢀⡀⠀⠀⠀⠀⠵⣿⣷⡁
⠀⠀⠘⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣼⠄⠈⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣼⠆⠈⠀⠀⠀⠀⠀⢿⣿⣿⣷
⠀⠀⠀⠈⠁⠀⠀⣠⣤⠀⠀⠀⠀⢸⣰⡶⠟⣉⡁⠀⠀⠀⠀⠀⠩⣹⣿⣿⢧⠀⠀⠀⠀⠉⠁⠀⠀⣀⣤⠀⠀⠀⠀⢸⣰⡾⠛⣉⡁⠀⠀⠀⠀⠀⠩⣙⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⢠⠜⡀⠀⠀⠀⠈⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⡀⠀⠀⠀⠊⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠹⣄⡔⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣧⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣰⡄
⠀⡀⠀⠀⠀⠀⢸⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⢐⡢⣽⣛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣸⡢⣽⣟⠂⠀⠀⠀⠀⠀⢀
⢦⡇⢀⠀⠀⠀⠈⣄⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡎⠀⠀⠀⠀⠀⠀⠀⣠⣸⢧⡇⢀⠀⠀⠀⠈⣄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡎⠀⠀⠀⠀⠀⠀⠀⣠
⠿⠿⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠿⠿⠿⢩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠄⢢⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⡇⡄⠀⠀⠀⠀⠀⠀⢀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⣸⢛⠠⠇⠀⠀⠀⠀⠀⠀⡆⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⣹⢏⠠⠇⠀⠀⠀⠀⠀⠀⡆⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⡴⠤⢤⡄⠀⠀⠀⠀⠗⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣾⣿⣿⡦⠤⢤⡄⠀⠀⠀⠀⠗⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠈⠉⠙⠛⠉⠆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠉⠙⠛⠉⠄⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⡜⢡⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⢄⠀⠀⠀⠀⠀⠨⡀⠀⠀⡀
⠀⠠⠇⠈⣸⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠇⢈⣸⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⡆
⠀⠀⢻⢻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠉⢀⡀⠀⠀⠀⠀⡵⣿⣷⡃⠀⠀⠀⠀⢻⣻⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠉⢀⡀⠀⠀⠀⠀⠽⣿⣷⡀
⠀⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⣼⠆⠈⠀⠀⠀⠀⠀⣽⣿⣿⣷⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣼⠆⠈⠀⠀⠀⠀⠀⢽⣿⣿⣷⡀
⠀⠀⠀⠈⠁⠀⠀⣠⣤⠀⠀⠀⠀⢸⣰⠶⠗⣊⡁⠀⠀⠀⠀⠀⠙⣻⣿⣿⢇⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⠀⠀⠀⠀⢸⣰⠶⠗⣈⡁⠀⠀⠀⠀⠀⠙⣛⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠡⠜⡀⠀⠀⠀⠈⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢡⠌⣀⠀⠀⠀⠊⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠿⠟
⠀⠀⠀⠀⠀⠀⠸⣌⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⡔⡃
⠀⠀⠀⠀⠀⠀⣠⣧⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⡌
⠀⡀⠀⠀⠀⠀⢸⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⢈⡢⣽⣛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⢈⡢⣽⣛⠇⠀⠀⠀⠀⠀⢀
⢦⠇⢀⠀⠀⠀⠈⣄⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠊⠀⠀⠀⠀⠀⠀⠀⣠⣸⢧⠇⢀⠀⠀⠀⠈⣄⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠎⠀⠀⠀⠀⠀⠀⠀⣠
⠿⠿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠿⠿⠿⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⡇⡀⠀⠀⠀⠀⠀⠀⢀⠔⢢⠀⠀⠀⠀⠀⠨⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⡇⡄⠀⠀⠀⠀⠀⠀⢀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⣹⢚⠠⠇⠀⠀⠀⠀⠀⠀⡄⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⣹⢿⢠⠇⠀⠀⠀⠀⠀⠀⡆⠀⡘

⠀⠀⠀⣤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⢉⠀⣄⡷⠦
⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣇⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠹⣽⠺⠂⠀⠀⠀⠀⢤
⣿⢰⣤⣠⡝⠛⠛⠀⠀⣴⢠⣰⣶⠄⡀⠈⠠⢧⠘⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣄⣿⣿⣿⠀⠀⠤⠾⡟⠋⠉⠀⠀⠀⠀⠑⠰⠀⢈⡟⢿⣯⣀⡀⠂⠁⠠⣄⣠⣤⠤⠀⠐⣤⣀⣁⠐⠄⠀⢰
⣿⣿⣛⠀⣃⢴⡆⠆⠘⠈⢓⠒⠀⠀⠳⡀⠠⢄⡀⠀⠀⠐⠈⠉⠥⢤⠀⠀⠀⠀⠀⠑⣿⣶⣦⡙⠛⢿⣗⡀⠘
⠙⠉⢳⣾⣻⠛⡛⢀⣃⢙⠉⣅⣀⠀⠚⠃⠈⠛⠻⢧⣦⣲⣤⡀⠀⠀⢀⠀⢰⢦⡀⠀⠀⠙⡍⠛⠛⢸⣿⣧⠀⠀⢰
⠀⠀⢸⡿⣷⠶⠗⣿⣿⣿⣛⡍⠋⠁⠀⡀⠀⠀⠀⡀⠀⠁⢙⡗⢶⠆⠈⠐⠻⣞⣀⣀⠀⠀⢋⠑⠂⠸⣿⣿⣿⣷⣾
⣀⣦⡮⣴⣆⣠⣅⣿⣹⢹⠏⠁⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⢡⣤⣬⡛⢷⣂⠌⠙⠛⠂⢸⠀⠹⣆⡸⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣿⡏⡏⡄⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠓⠉⢻⠂⣠⢠⠸⠇⠀⣎⣷⣼⡿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠛⠛⠻⠿⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⢤⣼⡿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣠⣴⠞⠋⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣿
⠀⠀⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡟
⠀⠀⠹⣷⣁⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠀⢈⣴⡟
⠀⠀⠀⠙⢿⣦⣁⡂⠀⠀⡀⠄⠀⢀⣀⣠⡾⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣉⡀⠂⠥⣑⢂⣡⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠻⠿⢶⣶⣶⠶⠿⠛⠯⣅⣂⢐⠠⠀⠄⠀⠀⠀⡀⡀⠰⠐⢜⣿⣯⣐⡀⡀⠀⠀⠀⠀⠀⢀⢀⢠⣼⠟⠁⠉⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠶⣷⣷⣷⠶⠶⠟⠛⠉⠀⠉⠛⠷⢾⣦⣵⣤⣬⣬⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠂⢀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠄⠀⠀⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⡀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠄⢠⠠⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠐⢀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡀⡀⠂⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⠂⠁⢁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⠐⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠃⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⡀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠀⢁⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠁⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠅⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠠⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠲⣢⣾⣧⡲⠃⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣷⣴⠂⠀⠀⠀⠀⠀⣴⣿⠁
⠀⠲⠾⣿⣿⣿⡿⠶⠂⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠒⠢⡀⠀⠀⠀⢀⠈⠉⠿⠿⢟⠉⠀⠀⠀⠠⠀⠹⠿⣄
⠀⠀⠼⠊⢻⡏⠳⠆⠀⠀⠀⠈⠿⣿⣷⣤⣀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠁⡱⠀⠀⠀⠀⠀⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠠⣄⣿⣠⠄⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠄⣲⣶⠂⢄
⠀⠀⡀⠆⣿⣿⣿⠒⠀⠀⠀⠀⠠⠘⣿⡄⠀⠀⠀⠀⠀⡔⠀⠐⠤⢄⠀⠀⠀⠀⠀⣠⣿⣆⠀⢿⠗⠀⠀⢐⠁⢰⣿⣿⣧⠀⢁
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠂⠀⠀⠀⠘⠓⠂⠀⠀⠎⠀⠀⠀⠀⠀⠓⢢⠀⠀⢰⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠉⠉⠙⠉
⠀⠈⡄⡀⡄⡀⡄⠀⠀⠀⠀⢀⠀⢠⢀⢠⠁⠀⠀⠀⠈⢁⠀⢀⡀⠀⣀⠁⠀⠀⠈⠮⣿⠿⠃⠀⠀⠀⠀⠀⠀⠠⣤⠆
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢈⣀⠀⠀⠀⠀⠀⠈⠘⠈⠀⠃⠁
⠀⠀⠀⠐⣦⣿⣴⠂⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⡀⠐⠂⠒⠄⣀
⠀⠀⠀⠃⠻⠿⢿⡉⠀⠀⠀⠀⠐⠚⠿⢆⡀⠀⠀⠀⢀⠌⠁⠈⠂⠠⡀⠀⠀⠀⠀⢀⣿⣏⡄⠀⠀⠀⡠⠁⠀⠑⠒⢄⠀⠀⠓
⠀⢈⠀⠀⠀⠀⠀⠁⠀⠀⠀⡁⠀⠀⠀⠈⠩⠁⠀⠀⢇⡀⠀⠀⠀⠀⠉⡱⠀⠀⠀⠀⢀⠟⠁⠀⠀⠘⣀⠀⠀⠀⠀⠈⢈⠆⠒
⠀⠀⠈⠃⠘⠃⠀⠀⠀⠀⠀⠀⠘⠀⠛⠀⠀⠀⠀⠀⠀⠀⢻⠅⠹⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣘⣷⣿⣾⣁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢠⣄⣈⣿⣇⣠⣄⠀⠀⣠⠤⠤⣤⣠⠤⠤⣤
⠀⢀⠀⠁⠙⠻⠿⡌⠀⠀⠀⡠⠀⠈⠛⢦⣀⡀⠀⠀⡠⠊⠀⠀⠁⠐⣄⡀⠀⠀⠘⢹⣓⣬⣞⡋⠋⠀⠀⠒⣚⣛⡒⠖⣚⣓⡒
⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⠈⠀⠀⠀⠣⠀⢀⠀⠀⡀⢀⠜⠀⠀⠸⠿⠫⣾⡜⠻⠿⠀⠀⢩⠥⠤⢭⣭⠥⠦⢭
⠀⠀⠰⠀⠂⠰⠀⠀⠀⠀⠀⠀⠆⠐⠀⠆⠀⠀⠀⠀⠀⢠⡆⠠⠄⢰⡄⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⣰⡆⠀⣴⠂⢀⣶⠀⠀⠀⠀⣤⠀⢼⣿⡯⠀⠀⠀⠀⠀⠀⢘⣶⣷⡃
⠀⣶⣶⣶⡦⠤⠄⠁⠀⠀⠘⠛⣓⠚⢛⡓⠛⢛⠂⠀⠀⠀⣿⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠈⠀⠃⠁⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣾⣇⣠⣿⣀⣴⣿⡀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣾⣴⣂
⠀⠀⢀⣙⣷⠾⢶⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⠿⠻⠍
⠀⠀⠈⢩⠿⢳⠛⢯⡁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡞⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⡾⢷⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠂⠦⢀⡠⢀⠀⠀⠀⠀⠀⢠⠾⢳⡛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠈⠀⠓⠐⠒⠀⠁⠀⠈⠒⣄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠫⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠌⠃⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠐⠂⠠⠤⠤⠄⠒⠈⠀⠀⠀⠀⠐⡀
⠀⠀⢀⣸⣶⢳⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣢⡼⣦⣆
⠀⠀⠀⠘⠉⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⢳⠛⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣀⠊⡑⡛⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠄⠈⡀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⢀⠴⠊⠀⠀⠀⠠⢀⠀⠀⠑⠠⡀⠀⣀⠀⠄⠠⠄⠀⣀⠀⠀⠀⠀⠀⢀⡠⠚⠁⣀⠄⠀⠄⠁⠦⣄⡀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠒⠁⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄

⠀⣠⣤⣤⣤⣤⣤⣄⣠⣀⣀⣠⣀⣄⣤⣀⣤⣄⣤⣠⣀⣠⣄⣀⣠⣤⣤⣤⣀⣠⣀⣠⣄⣄⣄⣀⣄⣄⣀⣀⣤⣀⡀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡧
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧
⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣷⢻⣿⣿⣸⢏⣾⡇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⢫⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡈⣿⣿⣿⣿⣿⣿⣿⡇⣿⢃⣾⣿⣿⣏
⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠇⢿⣿⣿⣿⣿⣿⣿⠇⠃⣾⣿⣿⣿⡗
⠀⢼⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⡇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡇
⠀⢻⣿⣿⣿⣿⡿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇
⠀⢾⣿⣿⣿⡏⣿⣿⣿⡇⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣧⣿⣿⣿⡇⠈⣿⢟⣤⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⡿⠹⠿⠟⠛⠀⣡⣾⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡧
⠀⠙⠻⠿⠿⠿⠾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠿⠿⠿⠃⠘⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠏⠙⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠰⠀⠀⠐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡶⠀⠀⠀⠀⠀⠉⡙⠐⠋⠀⠀⠀⠀⠠⠈⢄⡜⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠐⢛⠘⠟⣾⠀⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⠻⡉⠀⠀⢀⠔⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠋⢣⠀⠠⠎⠔⠂⡠⠆⠁⠄⠀⠀⠀⠀⠀⣁⣩⡁
⠀⠀⠀⠀⣠⣀⣠⠀⣤⠤⣤⠄⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠛⠚⠒⢥⣤⣠⣀⡀
⠀⠀⠀⠀⡮⠤⢬⡦⠶⠢⠤⠤⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⢣⣤⠠⣤⡀
⠀⠀⠀⠠⠴⠤⠴⡖⠰⠴⠄⠲⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⣈⣉⢁⡉⠑⢢⡐⠀⠈
⠀⠀⠀⠐⠒⠒⠶⠦⣄⢤⡠⢴⡔⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⡀⠁⠉⢐⡇
⠀⠀⠀⠈⢐⡇⠂⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠈⠃⠀⠀⢐⠂
⠀⠀⠀⠀⢈⡁⠀⠀⠠⠜⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣿⣿⣿⣿⣿⣿⢄⣄⡀⠀⠀⠈⠣⣀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⡷⢾⣿⣟⢋⠉⠁⠀⠀⠀⠀⠙⣿⣷⡖⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⣿⡷⠛⢿⣦⢿⠛⠷⠶⢦⡀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢇⠣⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣽⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠂⠀⠀⠰⢶⣾⣿⠯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣀⢀⣀⠀⠀⢈⣭⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢻⠏⠁⠺⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄
⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢰⣰⡆⣶⡆⢲⠒⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇⡿⣿⢸⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣆⡆⣶⡂⣾⣻⠸⣾⠃⡟⡇⣶⣶⢰⠶⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠳⡄⢹⡁⢻⡇⢸⣅⣿⢻⠀⢿⠀⢧⠇⣿⡟⣿⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡠⠖⠈⠀⠠

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠟⣋⣥⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⡟⣿⡿⣹⡇
⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣇⣟⣼⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋⣾⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⠸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠏⣼⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⣿⣿⣿⣿⣿⣿⣿⡇⠛⢸⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢛⣾⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⡇⠘⣿⡿⢋⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣇⠀⠟⣴⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣅⣤⣤⣤⣤⠀⣾⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⡇⠀⣿⠿⠿⠟⠛⠛⠁
⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠄⠂⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠸⠀⠀⠀⢠⠎⠀⢀⠀⠂⠍⠀⠀⠠⠀⠘⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣈⡀⠀⠀⠠⠄⠀⠀⠀⢡
⠀⡠⠆⡀⠀⡠⠁⠀⠔⠉⠢⠌⠀⠀⠀⠀⢠⣤⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠄
⠀⡀⠀⠁⢀⠁⠀⡌⢀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡘
⠀⠈⠂⠂⢅⠀⠀⠇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠂⣤⠀⠀⢈⠙⠀⠀⠀⠀⡀⠆⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠉⠀⠢⠀⠀⠀⠀⠀⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡄⡠⠄⠊⣀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡲⠀⠁⠀⣤⠀⠈⠋⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠓⠄⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠤⡀⠀⡀⢀⠀⠈⠁⠀⠀⠁⠀⢀⠀⡆⠀⠈⠈⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠓⢄⠀⠀⠀⠀⠀⠀⠑⠔⠀⠀⠀⠠⠀⠀⠈⠢
⠀⠀⠀⣄⠈⠀⠁⢂⠀⠀⠀⢀⡄⠠⠀⠐⠈⠰⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠁⠀⠀⠀⠠⡀⠑⠰⠊⠀⡆⠀⠀⠀⢀⠄⠀⢤⠆⠀⠀⣠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠐⠄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠂⠀⠈⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡠⠄⠂⠀⠀⠐⠠⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠒⠀⠀⠁⠐⠀⠀⢀⣀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⠀⠡⢀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠔⠈⠀⠠⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⡀⠀⠀⠀⢀⠠⠀⠊
⣤⣄⣤⣤⣤⣤⣄⣤⣠⣤⣤⣤⣤⣤⣤⣤⣌⣀⣀⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣠⣤⣠⣤⣤⣤⣤⣤⣠⣄⣠⣄
⣿⣛⣛⣟⣻⣯⣛⣻⣛⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣽⣿⣯⣽⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠔⠊⠹⠚⠁⠀⢎⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠟⠉⠀⢰⣷⣄
⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⡴⢊⡩⢭⡑⢦⠀⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣠⣶⣿⣿⣷⣦⡀⠙⣿⣇
⠀⠀⠀⠀⠀⠀⠘⠘⠀⢸⢠⠁⢾⣗⠈⡄⡇⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⣿⣿⣿⢺⣿⣿⣷⠀⢹⣿
⠀⠀⠀⠀⠀⠀⢰⠦⢄⡘⢄⠣⢝⡫⠜⣠⢃⣤⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⢻⣿⣿⣼⣿⣿⠏⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠸⠤⡘⢅⡀⠑⠒⠒⠊⠀⠘⣀⡨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣧⡀⠉⠛⠛⠋⠁⠀⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⣑⠒⠒⣊⡣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣶⣶⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠙⢷⣄⠀⠀⠀⠀⢠⡾⠋⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠹⠷⠶⠷⠶⠟⠁⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠰⣦⣤⣤⠖⠀⠀⠀⠀⢶⣤⣤⡶⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠈⠀⠀⠐⢿⡷⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠰⣦⣴⠟⠳⢤⡶⠆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣤⣼⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⣶⣶⡶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠛⠻⠶⣤⣀⡀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⠾⠛⠛⠛⠛⠛⠻⠶⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠛⠁⠀⠀⠀⠀⠀⣶⠶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠀⠀⠀⠈⠉⠛⢷⣦⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⣤⡶⠶⢶⣤⡀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠁⠀⠀⠀⠈⢻⣦⣴⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠻⢶⣤⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠸⣧
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠈⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⢻⣟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⣿
⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠈⠙⠷⣶⣤⣀⡀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠾⠷⠶⠶⠶⣶⡄⠀⠀⠀⠀⠀⣶⡶⠶⠶⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⣧⠀⠀⠀⠀⠀⣿⠆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠙⠷⣶⣤⣴⠾⠋⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠈⠙⠛⣷⠀⠀⠀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⠶⠶⠶⠶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣦⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠟⠛⠉
⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⠶⣦⣤⣴⡶⠿⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢀⣠⣤⣴⣶⠶⣶⣤⣤⣀⣠⣴⠶⠿⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⣽⡟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢀⣾⠏⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠶⢶⣼⣇
⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢿⣦
⠹⣧⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠙⢷⣄⡀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠉⠛⠻⠿⠿⠛⠋⠻⢶⣤⣄⣀⣀⣀⣤⣴⠾⢻⣧⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢭⣉⡍⣩⠁⡀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣸⠀⠀⢹⡟⠁⠀⣿⡤⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣠⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠙⢦⡀⢸⡇⢀⡴⠋⠉⠉⣀⠀⠀⠙⠛⠷⠶⠶⠶⠶⠿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠻⠶⠶⠶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣀⣀⣙⣶⣷⣏⣀⣀⣠⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠟⠛⠛⢛⣿⣿⡿⠟⠛⠻⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⡴⢛⡟⢦⡀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⢀⡴⠋⢸⡇⠙⢦⡀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⠋⠀⢸⡇⠀⠙⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⢿⠀⠀⢸⣇⠀⠀⡿⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⣠⠾⡷⣄⠀⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶⠻⠏⠳⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠈⢻⡷⠃⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⠻⣄⢸⡇⣠⠞⠛⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⠤⠬⣿⣿⠧⠤⠴⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣠⠞⢹⡏⠳⣄⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣼⣧⡀⢸⠛
⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠠⠀⠀⠀⠘⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠴⠆⠀⠀⢼⣇⠀⠐⠒⢄⡀⠀⠀⠀⠀⠶⠀⠀⠀⣀⠀⠀⠀⠀⠀⡐⡁⣒⠪⢂⠀⠊⠉⢂⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣌⠌⠡⣅⠈⠒⠠⠬⢁⡒⡄⠀⠀⠀⠀⡰⡿⠀⠀⠛⠀⠀⠇⡅⠛⢁⢀⠀⠑⠒⠠⡁⠢⠀⢰⢷⠀⠣⠉⢐⢄
⠀⠀⠀⠀⢸⠀⠘⠃⢸⠀⢀⣀⢀⣤⣁⣶⠀⠀⡤⠴⢸⠤⠷⢤⡀⠐⡍⠥⠃⠀⠘⢜⣈⠆⢈⠀⣲⡅⢠⠏⠈⠧⢀⠠⡠⣿
⠀⢠⡆⠀⠘⢘⡃⣘⢘⣴⡿⣿⣿⡿⠈⢿⣀⣀⡇⢠⣆⢀⣦⠀⣦⣠⡇⡼⣵⢠⢿⡆⢠⣊⠕⢉⠙⠗⣴⣶⢳⣶⡕⠈⢎⠪⡆⠀⢀
⢐⢕⣿⠄⠀⢠⡄⡤⠸⠁⡀⠀⡀⠀⢘⠀⠁⣈⡀⠀⠀⠀⠀⠀⣠⡀⡇⠉⢉⡤⡍⠁⠈⠀⡀⠻⠃⡀⠹⣈⣉⣸⠰⠄⠀⠤⢠⡐⢛⣳⡄
⠀⡺⣷⡁⢴⡠⠄⠷⠀⠀⠛⠐⠋⠀⣈⠀⡆⠛⠃⡔⠂⠃⠒⡄⠉⠁⡇⠀⢸⣁⡇⠀⡇⢸⣿⠀⢸⣿⢀⠿⠿⢿⠀⠠⣶⠀⣈⠀⣶⡄⡄
⠨⢚⠣⡂⢽⡇⣶⣺⠀⡆⠷⠰⠇⢸⣉⡇⠁⠀⢘⠠⠂⡅⠄⢠⠀⢰⡧⢀⣞⣒⣣⡀⡇⠼⠻⠆⠼⡻⠄⣿⣭⢿⠀⠀⠛⠀⣿⠀⡭⡄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡈⣁⠀⡅
⠀⠀⠀⠀⠀⣈⠉⠈⠋⠤⠄
⠀⠀⠀⠀⠀⣴⣤⡆⡀⣀⣀
⠀⠀⠀⢀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⢒⡀
⠀⠀⠀⠈⠉⡁⠀⢠⣤⡰⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣋⣁⣀
⠀⠀⠀⠀⠚⠁⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣫⢀⣠⣭
⠀⠀⠠⠄⣀⡤⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⠁⢀⡉
⠀⠀⠀⠀⠞⠁⠐⣄⠀⠲⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠀⣈
⠀⠘⠦⠀⢄⠀⠀⡈⢃⣀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣀⠔⠛⠐⠏
⠀⠀⠀⠀⠛⠀⠈⢄⠀⠌⠝⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠶⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠚⠴⠁⠴⢤⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣶⣦⣄⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢻⣿⣿⡳⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣀⠀⠀⣼⡇⢀
⠀⠀⠀⠀⠀⢰⡄⠀⠀⢀⣴⣿⣿⣿⡛⠛⢿⣿⣲⣄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣸⡄⡀
⠀⠀⠀⠀⣦⣼⣇⣰⢴⣿⣿⢻⣻⣻⣷⣦⣀⡀⣄⣽⣷⣆⣾⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠾⣿⣯⣛⡛⠛⠻⠿⠏⠻⣿⣿⣿⣧⣧
⠀⣀⣀⣀⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠈⠙⠛⠿⠿⣿⣟⣺⣿⣿⣷⣤⢀⡀⠀⠀⠐⣚⣛⣿⣿⣿⣿⣿⣿⣦⣤⣉⣉⣉⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢶⣿⣿⣦⡀
⠀⠀⠀⢀⠀⠀⢀⣴⣀⡀⠀⣀⣤⣾⣫⣾⣿⣿⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣴⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣄⣤⡀
⠀⠠⠴⢾⣷⢶⠿⠿⢿⣿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⣤⣶⣾⣷⣄⣀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠼⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠙⠋⠉⠉⠀⠀⠀⠐⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⣠⣶⣯⣴⣮⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⠾⣦⡞⠀⠈⠋⠑⠄⠀⠀⠀⠀⠀⢀⠴⠞⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢀
⠀⠴⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠷⠄⠀⠀⠐⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠠⣾⠀⠀⣠⠂
⠀⠀⠛⠀⠀⠊⠁⠀⠈⠛⠒⠀⢢⡄⠀⠀⢀⣤⣀⣤⣴⣿⣄⣠⣾⣤⣤⣤⣶⣦⣀⠀⠀⠀⠀⠠

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠘⠉⠙⠢⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠠⠤⠤⠤⠤⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿